LMFDB - Embedded newform 21.30.e.a.4.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(4,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 30, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$111.883889004$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	21.4
Dual form			21.30.e.a.16.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4961.84 + 8594.16i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.19196e8 - 3.79658e8i) q^{4} +(8.80219e9 + 1.52458e10i) q^{5} +4.74646e10 q^{6} +(1.78765e12 + 1.55597e11i) q^{7} +9.67819e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(4961.84 + 8594.16i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.19196e8 - 3.79658e8i) q^{4} +(8.80219e9 + 1.52458e10i) q^{5} +4.74646e10 q^{6} +(1.78765e12 + 1.55597e11i) q^{7} +9.67819e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-8.73501e13 + 1.51295e14i) q^{10} +(4.30270e13 - 7.45250e13i) q^{11} +(-1.04841e15 - 1.81589e15i) q^{12} -1.12750e15 q^{13} +(7.53281e15 + 1.61354e16i) q^{14} +8.42012e16 q^{15} +(-6.96582e16 - 1.20652e17i) q^{16} +(5.70294e17 - 9.87779e17i) q^{17} +(1.13511e17 - 1.96607e17i) q^{18} +(1.03223e17 + 1.78787e17i) q^{19} +7.71761e18 q^{20} +(4.91965e18 - 7.03265e18i) q^{21} +8.53972e17 q^{22} +(-4.53763e19 - 7.85940e19i) q^{23} +(2.31452e19 - 4.00887e19i) q^{24} +(-6.18247e19 + 1.07084e20i) q^{25} +(-5.59447e18 - 9.68991e18i) q^{26} -1.09419e20 q^{27} +(4.50919e20 - 6.44590e20i) q^{28} +4.27468e20 q^{29} +(4.17793e20 + 7.23638e20i) q^{30} +(4.07640e20 - 7.06054e20i) q^{31} +(3.28924e21 - 5.69712e21i) q^{32} +(-2.05797e20 - 3.56451e20i) q^{33} +1.13188e22 q^{34} +(1.33630e22 + 2.86238e22i) q^{35} -1.00290e22 q^{36} +(2.88968e22 + 5.00508e22i) q^{37} +(-1.02435e21 + 1.77423e21i) q^{38} +(-2.69640e21 + 4.67030e21i) q^{39} +(8.51892e22 + 1.47552e23i) q^{40} +3.13765e23 q^{41} +(8.48502e22 + 7.38537e21i) q^{42} -7.56573e23 q^{43} +(-1.88627e22 - 3.26711e22i) q^{44} +(2.01366e23 - 3.48776e23i) q^{45} +(4.50300e23 - 7.79942e23i) q^{46} +(-4.66853e23 - 8.08613e23i) q^{47} -6.66346e23 q^{48} +(3.17148e24 + 5.56307e23i) q^{49} -1.22706e24 q^{50} +(-2.72770e24 - 4.72451e24i) q^{51} +(-2.47143e23 + 4.28064e23i) q^{52} +(-1.86070e24 + 3.22282e24i) q^{53} +(-5.42919e23 - 9.40364e23i) q^{54} +1.51493e24 q^{55} +(1.73012e25 + 1.50590e24i) q^{56} +9.87423e23 q^{57} +(2.12103e24 + 3.67373e24i) q^{58} +(-2.76717e25 + 4.79289e25i) q^{59} +(1.84565e25 - 3.19677e25i) q^{60} +(-7.48221e24 - 1.29596e25i) q^{61} +8.09058e24 q^{62} +(-1.73652e25 - 3.71965e25i) q^{63} -9.51231e24 q^{64} +(-9.92446e24 - 1.71897e25i) q^{65} +(2.04226e24 - 3.53730e24i) q^{66} +(2.29683e26 - 3.97823e26i) q^{67} +(-2.50012e26 - 4.33034e26i) q^{68} -4.34067e26 q^{69} +(-1.79692e26 + 2.56871e26i) q^{70} -3.11609e26 q^{71} +(-1.10703e26 - 1.91743e26i) q^{72} +(6.04788e26 - 1.04752e27i) q^{73} +(-2.86763e26 + 4.96688e26i) q^{74} +(2.95706e26 + 5.12177e26i) q^{75} +9.05040e25 q^{76} +(8.85131e25 - 1.26530e26i) q^{77} -5.35164e25 q^{78} +(2.54329e27 + 4.40511e27i) q^{79} +(1.22629e27 - 2.12399e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(1.55685e27 + 2.69655e27i) q^{82} -5.91753e27 q^{83} +(-1.59164e27 - 3.40931e27i) q^{84} +2.00793e28 q^{85} +(-3.75399e27 - 6.50211e27i) q^{86} +(1.02228e27 - 1.77065e27i) q^{87} +(4.16424e26 - 7.21267e26i) q^{88} +(6.37262e27 + 1.10377e28i) q^{89} +3.99658e27 q^{90} +(-2.01557e27 - 1.75436e26i) q^{91} -3.97852e28 q^{92} +(-1.94973e27 - 3.37703e27i) q^{93} +(4.63290e27 - 8.02442e27i) q^{94} +(-1.81717e27 + 3.14744e27i) q^{95} +(-1.57323e28 - 2.72492e28i) q^{96} +1.53877e28 q^{97} +(1.09554e28 + 3.00165e28i) q^{98} -1.96864e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9}+O(q^{10}) $ 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9	$ 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9} - 226333527764279 q^{10} + 968182184010316 q^{11} + 26\!\cdots\!77 q^{12}+ \cdots - 44\!\cdots\!52 q^{99}+O(q^{100}) $ 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9 - 226333527764279 * q^10 + 968182184010316 * q^11 + 26060407088843277 * q^12 + 30248752986495458 * q^13 + 188292059868669736 * q^14 - 20103696649657764 * q^15 - 1414287713687569841 * q^16 + 102438111755912556 * q^17 + 572491731185399025 * q^18 - 6872193027481150651 * q^19 + 16866263496288505610 * q^20 - 5139459612060640272 * q^21 + 84243517982597870158 * q^22 + 182508386582843064516 * q^23 - 128758913948422543095 * q^24 - 382162743635168213111 * q^25 + 273922968110752759988 * q^26 - 4157921586997469649942 * q^27 + 446171481016036543439 * q^28 + 281390518253865391744 * q^29 + 1082546246957185764351 * q^30 - 4929614086953636263583 * q^31 + 8866445878410226322935 * q^32 - 4630785372473637108204 * q^33 + 50361339344572132704984 * q^34 - 81794408570709523734766 * q^35 + 249292238466635279498826 * q^36 + 89823590712918979606269 * q^37 - 71913737995612310138956 * q^38 + 72339423911532597127401 * q^39 + 239411588777146294644135 * q^40 - 87942011922863277796324 * q^41 + 42507596433452096284317 * q^42 - 998334377830130582257058 * q^43 - 273085832669135222196817 * q^44 - 48077678930358472910658 * q^45 + 1477208812031594497944852 * q^46 + 663752760815551395364602 * q^47 - 13528988583297044469675858 * q^48 + 12702719376591835722353537 * q^49 - 18072517907683707274881248 * q^50 - 489958312947065322058764 * q^51 + 31739881554208954447778464 * q^52 - 7756933906079396951027112 * q^53 - 2738210203016096789205225 * q^54 + 104982116314469285161107056 * q^55 + 43372930131234039576619953 * q^56 - 65738972424916983296125638 * q^57 + 102453432804996437331910603 * q^58 + 114603050264779854082124610 * q^59 + 40335407724289768694478045 * q^60 - 139825411428909464532671986 * q^61 + 1134093332259905081074973442 * q^62 + 1666599266299329474494571 * q^63 - 148837669255394086765278622 * q^64 + 640556086591054006830698254 * q^65 + 201467067480854076215869551 * q^66 - 56315776880006609951132917 * q^67 - 697317633686048315259709452 * q^68 + 1745863910531508618890056008 * q^69 + 433002366057136467231968657 * q^70 - 1824065145665995608812965764 * q^71 + 615849893888972622524549055 * q^72 + 1789614217588580556564713367 * q^73 - 4257059926604086801593103848 * q^74 + 1827872555761956873095306559 * q^75 + 15166984931487860090924899312 * q^76 + 6892418991139201958931374756 * q^77 + 2620330129723438035374088744 * q^78 + 3126227451212705816416145239 * q^79 + 469705326396281168184173015 * q^80 - 9943605027519850207056718899 * q^81 - 15954412288094954111486068024 * q^82 + 12686840070702737045002032792 * q^83 - 10284086370388485211004655396 * q^84 + 280144859318398185224279400 * q^85 + 14385045580944496750492040974 * q^86 + 672941062851086149442203968 * q^87 - 20844393366380736578332102317 * q^88 - 26279447891842894095818723312 * q^89 + 10355570280525127676264276238 * q^90 - 22701798036712589137512005879 * q^91 - 374697938227250791106256400776 * q^92 + 23578191359862546685993317927 * q^93 + 73717519436348854656628916898 * q^94 - 56410666407609081482857118294 * q^95 - 42407935776613881785582094015 * q^96 + 235542920591717835435096218928 * q^97 - 293433749500426066164790446415 * q^98 - 44297805764389719211578755352 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4961.84	+	8594.16i	0.214145	+	0.370910i	0.953008	−	0.302946i	$-0.0979702\pi$
$2$	4961.84	+	8594.16i	0.214145	+	0.370910i	−0.738863	+	0.673856i	$0.764637\pi$
$3$	2.39148e6	−	4.14217e6i	0.288675	−	0.500000i
$3$	2.39148e6	−	4.14217e6i	0.288675	−	0.500000i
$4$	2.19196e8	−	3.79658e8i	0.408284	−	0.707168i
$5$	8.80219e9	+	1.52458e10i	0.644949	+	1.11708i	0.984313	+	0.176430i	$0.0564548\pi$
$5$	8.80219e9	+	1.52458e10i	0.644949	+	1.11708i	−0.339364	+	0.940655i	$0.610212\pi$
$6$	4.74646e10			0.247273
$7$	1.78765e12	+	1.55597e11i	0.996233	+	0.0867122i
$7$	1.78765e12	+	1.55597e11i	0.996233	+	0.0867122i
$8$	9.67819e12			0.778017
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	−8.73501e13	+	1.51295e14i	−0.276225	+	0.478436i
$11$	4.30270e13	−	7.45250e13i	0.0341623	−	0.0591709i	−0.848439	−	0.529294i	$-0.822457\pi$
$11$	4.30270e13	−	7.45250e13i	0.0341623	−	0.0591709i	0.882601	+	0.470123i	$0.155790\pi$
$12$	−1.04841e15	−	1.81589e15i	−0.235723	−	0.408284i
$13$	−1.12750e15			−0.0794214			−0.0397107	−	0.999211i	$-0.512644\pi$
$13$	−1.12750e15			−0.0794214			−0.0397107	+	0.999211i	$0.512644\pi$
$14$	7.53281e15	+	1.61354e16i	0.181176	+	0.388082i
$15$	8.42012e16			0.744723
$16$	−6.96582e16	−	1.20652e17i	−0.241675	−	0.418594i
$17$	5.70294e17	−	9.87779e17i	0.821466	−	1.42282i	−0.0831243	−	0.996539i	$-0.526490\pi$
$17$	5.70294e17	−	9.87779e17i	0.821466	−	1.42282i	0.904590	−	0.426282i	$-0.140177\pi$
$18$	1.13511e17	−	1.96607e17i	0.0713816	−	0.123637i
$19$	1.03223e17	+	1.78787e17i	0.0296380	+	0.0513345i	0.880464	−	0.474113i	$-0.157231\pi$
$19$	1.03223e17	+	1.78787e17i	0.0296380	+	0.0513345i	−0.850826	+	0.525448i	$0.823898\pi$
$20$	7.71761e18			1.05329
$21$	4.91965e18	−	7.03265e18i	0.330944	−	0.473085i
$22$	8.53972e17			0.0292627
$23$	−4.53763e19	−	7.85940e19i	−0.816160	−	1.41363i	−0.908492	−	0.417903i	$-0.862765\pi$
$23$	−4.53763e19	−	7.85940e19i	−0.816160	−	1.41363i	0.0923316	−	0.995728i	$-0.470568\pi$
$24$	2.31452e19	−	4.00887e19i	0.224594	−	0.389009i
$25$	−6.18247e19	+	1.07084e20i	−0.331919	+	0.574901i
$26$	−5.59447e18	−	9.68991e18i	−0.0170077	−	0.0294582i
$27$	−1.09419e20			−0.192450
$28$	4.50919e20	−	6.44590e20i	0.468066	−	0.669102i
$29$	4.27468e20			0.266767			0.133384	−	0.991064i	$-0.457416\pi$
$29$	4.27468e20			0.266767			0.133384	+	0.991064i	$0.457416\pi$
$30$	4.17793e20	+	7.23638e20i	0.159479	+	0.276225i
$31$	4.07640e20	−	7.06054e20i	0.0967237	−	0.167530i	−0.813603	−	0.581421i	$-0.802497\pi$
$31$	4.07640e20	−	7.06054e20i	0.0967237	−	0.167530i	0.910327	+	0.413890i	$0.135830\pi$
$32$	3.28924e21	−	5.69712e21i	0.492516	−	0.853063i
$33$	−2.05797e20	−	3.56451e20i	−0.0197236	−	0.0341623i
$34$	1.13188e22			0.703651
$35$	1.33630e22	+	2.86238e22i	0.545655	+	1.16880i
$36$	−1.00290e22			−0.272189
$37$	2.88968e22	+	5.00508e22i	0.527139	+	0.913032i	0.999500	+	0.0316265i	$0.0100687\pi$
$37$	2.88968e22	+	5.00508e22i	0.527139	+	0.913032i	−0.472361	+	0.881405i	$0.656598\pi$
$38$	−1.02435e21	+	1.77423e21i	−0.0126936	+	0.0219860i
$39$	−2.69640e21	+	4.67030e21i	−0.0229270	+	0.0397107i
$40$	8.51892e22	+	1.47552e23i	0.501782	+	0.869112i
$41$	3.13765e23			1.29193			0.645964	−	0.763368i	$-0.276455\pi$
$41$	3.13765e23			1.29193			0.645964	+	0.763368i	$0.276455\pi$
$42$	8.48502e22	+	7.38537e21i	0.246342	+	0.0214416i
$43$	−7.56573e23			−1.56156			−0.780779	−	0.624807i	$-0.785178\pi$
$43$	−7.56573e23			−1.56156			−0.780779	+	0.624807i	$0.785178\pi$
$44$	−1.88627e22	−	3.26711e22i	−0.0278958	−	0.0483170i
$45$	2.01366e23	−	3.48776e23i	0.214983	−	0.372362i
$46$	4.50300e23	−	7.79942e23i	0.349553	−	0.605444i
$47$	−4.66853e23	−	8.08613e23i	−0.265315	−	0.459538i	0.702331	−	0.711850i	$-0.252143\pi$
$47$	−4.66853e23	−	8.08613e23i	−0.265315	−	0.459538i	−0.967646	+	0.252312i	$0.918809\pi$
$48$	−6.66346e23			−0.279063
$49$	3.17148e24	+	5.56307e23i	0.984962	+	0.172771i
$50$	−1.22706e24			−0.284315
$51$	−2.72770e24	−	4.72451e24i	−0.474274	−	0.821466i
$52$	−2.47143e23	+	4.28064e23i	−0.0324265	+	0.0561643i
$53$	−1.86070e24	+	3.22282e24i	−0.185215	+	0.320802i	−0.943649	−	0.330948i	$-0.892631\pi$
$53$	−1.86070e24	+	3.22282e24i	−0.185215	+	0.320802i	0.758434	+	0.651750i	$0.225965\pi$
$54$	−5.42919e23	−	9.40364e23i	−0.0412122	−	0.0713816i
$55$	1.51493e24			0.0881318
$56$	1.73012e25	+	1.50590e24i	0.775087	+	0.0674636i
$57$	9.87423e23			0.0342230
$58$	2.12103e24	+	3.67373e24i	0.0571269	+	0.0989466i
$59$	−2.76717e25	+	4.79289e25i	−0.581678	+	1.00750i	0.413603	+	0.910457i	$0.364270\pi$
$59$	−2.76717e25	+	4.79289e25i	−0.581678	+	1.00750i	−0.995281	+	0.0970378i	$0.969063\pi$
$60$	1.84565e25	−	3.19677e25i	0.304059	−	0.526645i
$61$	−7.48221e24	−	1.29596e25i	−0.0969946	−	0.168000i	0.813445	−	0.581642i	$-0.197590\pi$
$61$	−7.48221e24	−	1.29596e25i	−0.0969946	−	0.168000i	−0.910439	+	0.413643i	$0.864256\pi$
$62$	8.09058e24			0.0828515
$63$	−1.73652e25	−	3.71965e25i	−0.141007	−	0.302040i
$64$	−9.51231e24			−0.0614718
$65$	−9.92446e24	−	1.71897e25i	−0.0512228	−	0.0887205i
$66$	2.04226e24	−	3.53730e24i	0.00844742	−	0.0146314i
$67$	2.29683e26	−	3.97823e26i	0.763914	−	1.32314i	−0.176905	−	0.984228i	$-0.556608\pi$
$67$	2.29683e26	−	3.97823e26i	0.763914	−	1.32314i	0.940819	−	0.338910i	$-0.110058\pi$
$68$	−2.50012e26	−	4.33034e26i	−0.670783	−	1.16183i
$69$	−4.34067e26			−0.942421
$70$	−1.79692e26	+	2.56871e26i	−0.316671	+	0.452682i
$71$	−3.11609e26			−0.447058			−0.223529	−	0.974697i	$-0.571758\pi$
$71$	−3.11609e26			−0.447058			−0.223529	+	0.974697i	$0.571758\pi$
$72$	−1.10703e26	−	1.91743e26i	−0.129670	−	0.224594i
$73$	6.04788e26	−	1.04752e27i	0.579992	−	1.00458i	−0.415488	−	0.909599i	$-0.636389\pi$
$73$	6.04788e26	−	1.04752e27i	0.579992	−	1.00458i	0.995480	−	0.0949765i	$-0.0302776\pi$
$74$	−2.86763e26	+	4.96688e26i	−0.225768	+	0.391042i
$75$	2.95706e26	+	5.12177e26i	0.191634	+	0.331919i
$76$	9.05040e25			0.0484028
$77$	8.85131e25	−	1.26530e26i	0.0391645	−	0.0559857i
$78$	−5.35164e25			−0.0196388
$79$	2.54329e27	+	4.40511e27i	0.775896	+	1.34389i	0.934289	+	0.356515i	$0.116035\pi$
$79$	2.54329e27	+	4.40511e27i	0.775896	+	1.34389i	−0.158393	+	0.987376i	$0.550631\pi$
$80$	1.22629e27	−	2.12399e27i	0.311737	−	0.539944i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	1.55685e27	+	2.69655e27i	0.276660	+	0.479189i
$83$	−5.91753e27			−0.882080			−0.441040	−	0.897487i	$-0.645390\pi$
$83$	−5.91753e27			−0.882080			−0.441040	+	0.897487i	$0.645390\pi$
$84$	−1.59164e27	−	3.40931e27i	−0.199432	−	0.427186i
$85$	2.00793e28			2.11922
$86$	−3.75399e27	−	6.50211e27i	−0.334400	−	0.579198i
$87$	1.02228e27	−	1.77065e27i	0.0770091	−	0.133384i
$88$	4.16424e26	−	7.21267e26i	0.0265789	−	0.0460360i
$89$	6.37262e27	+	1.10377e28i	0.345273	+	0.598031i	0.985403	−	0.170235i	$-0.0544528\pi$
$89$	6.37262e27	+	1.10377e28i	0.345273	+	0.598031i	−0.640130	+	0.768267i	$0.721120\pi$
$90$	3.99658e27			0.184150
$91$	−2.01557e27	−	1.75436e26i	−0.0791223	−	0.00688681i
$92$	−3.97852e28			−1.33290
$93$	−1.94973e27	−	3.37703e27i	−0.0558434	−	0.0967237i
$94$	4.63290e27	−	8.02442e27i	0.113632	−	0.196816i
$95$	−1.81717e27	+	3.14744e27i	−0.0382300	+	0.0662163i
$96$	−1.57323e28	−	2.72492e28i	−0.284354	−	0.492516i
$97$	1.53877e28			0.239323			0.119661	−	0.992815i	$-0.461819\pi$
$97$	1.53877e28			0.239323			0.119661	+	0.992815i	$0.461819\pi$
$98$	1.09554e28	+	3.00165e28i	0.146842	+	0.402330i
$99$	−1.96864e27			−0.0227749
$100$	2.71034e28	+	4.69445e28i	0.271034	+	0.469445i
$101$	−1.04442e28	+	1.80898e28i	−0.0904095	+	0.156594i	−0.907684	−	0.419655i	$-0.862151\pi$
$101$	−1.04442e28	+	1.80898e28i	−0.0904095	+	0.156594i	0.817274	+	0.576249i	$0.195484\pi$
$102$	2.70688e28	−	4.68846e28i	0.203127	−	0.351826i
$103$	−6.74834e28	−	1.16885e29i	−0.439599	−	0.761408i	0.558059	−	0.829801i	$-0.311546\pi$
$103$	−6.74834e28	−	1.16885e29i	−0.439599	−	0.761408i	−0.997658	+	0.0683927i	$0.978213\pi$
$104$	−1.09122e28			−0.0617913
$105$	1.50522e29	+	1.31015e28i	0.741918	+	0.0645766i
$106$	−3.69299e28			−0.158651
$107$	1.76483e29	+	3.05678e29i	0.661667	+	1.14604i	0.980178	+	0.198121i	$0.0634839\pi$
$107$	1.76483e29	+	3.05678e29i	0.661667	+	1.14604i	−0.318511	+	0.947919i	$0.603183\pi$
$108$	−2.39842e28	+	4.15418e28i	−0.0785743	+	0.136095i
$109$	1.62626e29	−	2.81677e29i	0.466129	−	0.807360i	−0.533122	−	0.846038i	$-0.678981\pi$
$109$	1.62626e29	−	2.81677e29i	0.466129	−	0.807360i	0.999252	+	0.0386785i	$0.0123148\pi$
$110$	7.51682e27	+	1.30195e28i	0.0188730	+	0.0326890i
$111$	2.76425e29			0.608688
$112$	−1.05751e29	−	2.26521e29i	−0.204468	−	0.437974i
$113$	1.81690e29			0.308811			0.154405	−	0.988008i	$-0.450654\pi$
$113$	1.81690e29			0.308811			0.154405	+	0.988008i	$0.450654\pi$
$114$	4.89943e27	+	8.48607e27i	0.00732868	+	0.0126936i
$115$	7.98821e29	−	1.38360e30i	1.05276	−	1.82344i
$116$	9.36992e28	−	1.62292e29i	0.108917	−	0.188649i
$117$	1.28968e28	+	2.23379e28i	0.0132369	+	0.0229270i
$118$	−5.49211e29			−0.498253
$119$	1.17318e30	−	1.67707e30i	0.941748	−	1.34623i
$120$	8.14915e29			0.579408
$121$	7.89452e29	+	1.36737e30i	0.497666	+	0.861983i
$122$	7.42511e28	−	1.28607e29i	0.0415418	−	0.0719525i
$123$	7.50364e29	−	1.29967e30i	0.372948	−	0.645964i
$124$	−1.78706e29	−	3.09528e29i	−0.0789814	−	0.136800i
$125$	1.10230e30			0.433615
$126$	2.33509e29	−	3.33802e29i	0.0818336	−	0.116981i
$127$	−5.03040e29			−0.157199			−0.0785993	−	0.996906i	$-0.525045\pi$
$127$	−5.03040e29			−0.157199			−0.0785993	+	0.996906i	$0.525045\pi$
$128$	−1.81309e30	−	3.14037e30i	−0.505680	−	0.875863i
$129$	−1.80933e30	+	3.13386e30i	−0.450783	+	0.780779i
$130$	9.84871e28	−	1.70585e29i	0.0219382	−	0.0379981i
$131$	−1.35293e30	−	2.34334e30i	−0.269676	−	0.467092i	0.699102	−	0.715022i	$-0.253583\pi$
$131$	−1.35293e30	−	2.34334e30i	−0.269676	−	0.467092i	−0.968778	+	0.247930i	$0.920250\pi$
$132$	−1.80439e29			−0.0322113
$133$	1.56708e29	+	3.35670e29i	0.0250750	+	0.0537111i
$134$	4.55860e30			0.654353
$135$	−9.63126e29	−	1.66818e30i	−0.124121	−	0.214983i
$136$	5.51942e30	−	9.55991e30i	0.639115	−	1.10698i
$137$	7.43480e30	−	1.28774e31i	0.774142	−	1.34085i	−0.161133	−	0.986933i	$-0.551515\pi$
$137$	7.43480e30	−	1.28774e31i	0.774142	−	1.34085i	0.935275	−	0.353921i	$-0.115152\pi$
$138$	−2.15377e30	−	3.73044e30i	−0.201815	−	0.349553i
$139$	2.34484e31			1.97879			0.989394	−	0.145257i	$-0.0464009\pi$
$139$	2.34484e31			1.97879			0.989394	+	0.145257i	$0.0464009\pi$
$140$	1.37964e31	+	1.20084e30i	1.04932	+	0.0913331i
$141$	−4.46589e30			−0.306359
$142$	−1.54615e30	−	2.67802e30i	−0.0957353	−	0.165818i
$143$	−4.85129e28	+	8.40268e28i	−0.00271322	+	0.00469943i
$144$	−1.59356e30	+	2.76012e30i	−0.0805585	+	0.139531i
$145$	3.76265e30	+	6.51711e30i	0.172051	+	0.298002i
$146$	1.20034e31			0.496809
$147$	9.88888e30	−	1.18064e31i	0.370720	−	0.442606i
$148$	2.53363e31			0.860890
$149$	8.51530e30	+	1.47489e31i	0.262421	+	0.454527i	0.966885	−	0.255213i	$-0.0821457\pi$
$149$	8.51530e30	+	1.47489e31i	0.262421	+	0.454527i	−0.704464	+	0.709740i	$0.748812\pi$
$150$	−2.93449e30	+	5.08268e30i	−0.0820747	+	0.142158i
$151$	−1.04959e31	+	1.81794e31i	−0.266596	+	0.461758i	−0.967981	−	0.251025i	$-0.919232\pi$
$151$	−1.04959e31	+	1.81794e31i	−0.266596	+	0.461758i	0.701384	+	0.712783i	$0.252566\pi$
$152$	9.99010e29	+	1.73034e30i	0.0230589	+	0.0399391i
$153$	−2.60930e31			−0.547644
$154$	1.52660e30	+	1.32876e29i	0.0291525	+	0.00253744i
$155$	1.43525e31			0.249527
$156$	1.18208e30	+	2.04742e30i	0.0187214	+	0.0324265i
$157$	1.62809e31	−	2.81994e31i	0.235036	−	0.407094i	−0.724247	−	0.689540i	$-0.757813\pi$
$157$	1.62809e31	−	2.81994e31i	0.235036	−	0.407094i	0.959283	+	0.282446i	$0.0911459\pi$
$158$	−2.52388e31	+	4.37149e31i	−0.332308	+	0.575575i
$159$	8.89966e30	+	1.54147e31i	0.106934	+	0.185215i
$160$	1.15810e32			1.27059
$161$	−6.88880e31	−	1.47559e32i	−0.690507	−	1.47908i
$162$	−5.19353e30			−0.0475878
$163$	−4.87514e31	−	8.44399e31i	−0.408570	−	0.707664i	0.586160	−	0.810196i	$-0.300639\pi$
$163$	−4.87514e31	−	8.44399e31i	−0.408570	−	0.707664i	−0.994730	+	0.102531i	$0.967306\pi$
$164$	6.87760e31	−	1.19123e32i	0.527474	−	0.913611i
$165$	3.62292e30	−	6.27509e30i	0.0254415	−	0.0440659i
$166$	−2.93618e31	−	5.08562e31i	−0.188893	−	0.327172i
$167$	−2.60330e31			−0.153509			−0.0767547	−	0.997050i	$-0.524456\pi$
$167$	−2.60330e31			−0.153509			−0.0767547	+	0.997050i	$0.524456\pi$
$168$	4.76133e31	−	6.80633e31i	0.257480	−	0.368068i
$169$	−2.00267e32			−0.993692
$170$	9.96305e31	+	1.72565e32i	0.453819	+	0.786038i
$171$	2.36141e30	−	4.09008e30i	0.00987932	−	0.0171115i
$172$	−1.65838e32	+	2.87239e32i	−0.637559	+	1.10429i
$173$	−1.59640e32	−	2.76504e32i	−0.564251	−	0.977312i	−0.997119	−	0.0758544i	$-0.975832\pi$
$173$	−1.59640e32	−	2.76504e32i	−0.564251	−	0.977312i	0.432868	−	0.901457i	$-0.357502\pi$
$174$	2.02896e31			0.0659644
$175$	−1.27183e32	+	1.81808e32i	−0.380520	+	0.543954i
$176$	−1.19887e31			−0.0330248
$177$	1.32353e32	+	2.29242e32i	0.335832	+	0.581678i
$178$	−6.32399e31	+	1.09535e32i	−0.147877	+	0.256131i
$179$	−4.21312e32	+	7.29734e32i	−0.908312	+	1.57324i	−0.0919024	+	0.995768i	$0.529295\pi$
$179$	−4.21312e32	+	7.29734e32i	−0.908312	+	1.57324i	−0.816409	+	0.577474i	$0.804039\pi$
$180$	−8.82771e31	−	1.52900e32i	−0.175548	−	0.304059i
$181$	9.84022e32			1.80578			0.902892	−	0.429868i	$-0.141440\pi$
$181$	9.84022e32			1.80578			0.902892	+	0.429868i	$0.141440\pi$
$182$	−8.49324e30	−	1.81927e31i	−0.0143892	−	0.0308220i
$183$	−7.15744e31			−0.112000
$184$	−4.39160e32	−	7.60648e32i	−0.634987	−	1.09983i
$185$	−5.08711e32	+	8.81113e32i	−0.679956	+	1.17772i
$186$	1.93485e31	−	3.35126e31i	0.0239172	−	0.0414258i
$187$	−4.90761e31	−	8.50023e31i	−0.0561264	−	0.0972137i
$188$	−4.09329e32			−0.433295
$189$	−1.95603e32	−	1.70253e31i	−0.191725	−	0.0166878i
$190$	−3.60661e31			−0.0327470
$191$	3.27374e32	+	5.67028e32i	0.275461	+	0.477113i	0.970251	−	0.242100i	$-0.0778361\pi$
$191$	3.27374e32	+	5.67028e32i	0.275461	+	0.477113i	−0.694790	+	0.719212i	$0.744503\pi$
$192$	−2.27485e31	+	3.94016e31i	−0.0177454	+	0.0307359i
$193$	−9.45113e32	+	1.63698e33i	−0.683758	+	1.18430i	0.290067	+	0.957006i	$0.406322\pi$
$193$	−9.45113e32	+	1.63698e33i	−0.683758	+	1.18430i	−0.973825	+	0.227298i	$0.927011\pi$
$194$	7.63514e31	+	1.32244e32i	0.0512498	+	0.0887672i
$195$	−9.49368e31			−0.0591470
$196$	9.06382e32	−	1.08214e33i	0.524322	−	0.625994i
$197$	−2.90069e33			−1.55862			−0.779311	−	0.626637i	$-0.784431\pi$
$197$	−2.90069e33			−1.55862			−0.779311	+	0.626637i	$0.784431\pi$
$198$	−9.76807e30	−	1.69188e31i	−0.00487712	−	0.00844742i
$199$	−9.82040e32	+	1.70094e33i	−0.455784	+	0.789442i	−0.998733	−	0.0503242i	$-0.983975\pi$
$199$	−9.82040e32	+	1.70094e33i	−0.455784	+	0.789442i	0.542948	+	0.839766i	$0.317308\pi$
$200$	−5.98351e32	+	1.03638e33i	−0.258239	+	0.447283i
$201$	−1.09857e33	−	1.90277e33i	−0.441046	−	0.763914i
$202$	−2.07289e32			−0.0774430
$203$	7.64163e32	+	6.65128e31i	0.265762	+	0.0231320i
$204$	−2.39160e33			−0.774553
$205$	2.76182e33	+	4.78361e33i	0.833228	+	1.44319i
$206$	6.69683e32	−	1.15993e33i	0.188276	−	0.326103i
$207$	−1.03806e33	+	1.79798e33i	−0.272053	+	0.471210i
$208$	7.85396e31	+	1.36035e32i	0.0191942	+	0.0332453i
$209$	1.77655e31			0.00405001
$210$	6.34271e32	+	1.35862e33i	0.134926	+	0.289013i
$211$	6.72566e33			1.33549			0.667743	−	0.744392i	$-0.267260\pi$
$211$	6.72566e33			1.33549			0.667743	+	0.744392i	$0.267260\pi$
$212$	8.15714e32	+	1.41286e33i	0.151240	+	0.261956i
$213$	−7.45209e32	+	1.29074e33i	−0.129055	+	0.223529i
$214$	−1.75136e33	+	3.03345e33i	−0.283385	+	0.490837i
$215$	−6.65950e33	−	1.15346e34i	−1.00713	−	1.74439i
$216$	−1.05898e33			−0.149730
$217$	8.38579e32	−	1.19875e33i	0.110886	−	0.158512i
$218$	3.22770e33			0.399277
$219$	−2.89268e33	−	5.01027e33i	−0.334858	−	0.579992i
$220$	3.32066e32	−	5.75154e32i	0.0359828	−	0.0623240i
$221$	−6.43006e32	+	1.11372e33i	−0.0652420	+	0.113002i
$222$	1.37158e33	+	2.37564e33i	0.130347	+	0.225768i
$223$	−4.63097e33			−0.412336			−0.206168	−	0.978517i	$-0.566099\pi$
$223$	−4.63097e33			−0.412336			−0.206168	+	0.978517i	$0.566099\pi$
$224$	6.76646e33	−	9.67267e33i	0.564632	−	0.807142i
$225$	2.82870e33			0.221279
$226$	9.01514e32	+	1.56147e33i	0.0661302	+	0.114541i
$227$	−8.02205e32	+	1.38946e33i	−0.0551964	+	0.0956030i	−0.892303	−	0.451436i	$-0.850912\pi$
$227$	−8.02205e32	+	1.38946e33i	−0.0551964	+	0.0956030i	0.837107	+	0.547039i	$0.184245\pi$
$228$	2.16439e32	−	3.74883e32i	0.0139727	−	0.0242014i
$229$	−1.20826e34	−	2.09277e34i	−0.732058	−	1.26796i	−0.956002	−	0.293360i	$-0.905227\pi$
$229$	−1.20826e34	−	2.09277e34i	−0.732058	−	1.26796i	0.223944	−	0.974602i	$-0.428107\pi$
$230$	1.58545e34			0.901776
$231$	−3.12430e32	−	6.69231e32i	−0.0166870	−	0.0357439i
$232$	4.13712e33			0.207550
$233$	−1.17960e34	−	2.04313e34i	−0.555999	−	0.963018i	−0.997825	−	0.0659176i	$-0.979003\pi$
$233$	−1.17960e34	−	2.04313e34i	−0.555999	−	0.963018i	0.441826	−	0.897101i	$-0.354331\pi$
$234$	−1.27984e32	+	2.21674e32i	−0.00566923	+	0.00981940i
$235$	8.21865e33	−	1.42351e34i	0.342229	−	0.592758i
$236$	1.21311e34	+	2.10116e34i	0.474979	+	0.822688i
$237$	2.43290e34			0.895928
$238$	2.02341e34	+	1.76118e33i	0.701001	+	0.0610151i
$239$	4.37820e34			1.42734			0.713668	−	0.700484i	$-0.247033\pi$
$239$	4.37820e34			1.42734			0.713668	+	0.700484i	$0.247033\pi$
$240$	−5.86530e33	−	1.01590e34i	−0.179981	−	0.311737i
$241$	1.80926e34	−	3.13373e34i	0.522702	−	0.905347i	−0.476949	−	0.878931i	$-0.658257\pi$
$241$	1.80926e34	−	3.13373e34i	0.522702	−	0.905347i	0.999651	−	0.0264158i	$-0.00840939\pi$
$242$	−7.83427e33	+	1.35693e34i	−0.213145	+	0.369178i
$243$	1.25158e33	+	2.16780e33i	0.0320750	+	0.0555556i
$244$	−6.56028e33			−0.158405
$245$	1.94346e34	+	5.32486e34i	0.442250	+	1.21171i
$246$	1.48927e34			0.319459
$247$	−1.16384e32	−	2.01582e32i	−0.00235389	−	0.00407706i
$248$	3.94522e33	−	6.83332e33i	0.0752527	−	0.130341i
$249$	−1.41517e34	+	2.45114e34i	−0.254635	+	0.441040i
$250$	5.46943e33	+	9.47333e33i	0.0928564	+	0.160832i
$251$	−4.05835e34			−0.650250			−0.325125	−	0.945671i	$-0.605406\pi$
$251$	−4.05835e34			−0.650250			−0.325125	+	0.945671i	$0.605406\pi$
$252$	−1.79283e34	−	1.56048e33i	−0.271164	−	0.0236021i
$253$	−7.80962e33			−0.111528
$254$	−2.49600e33	−	4.32321e33i	−0.0336633	−	0.0583065i
$255$	4.80194e34	−	8.31721e34i	0.611765	−	1.05961i
$256$	1.54391e34	−	2.67413e34i	0.185842	−	0.321887i
$257$	−4.04677e34	−	7.00922e34i	−0.460340	−	0.797332i	0.538638	−	0.842537i	$-0.318939\pi$
$257$	−4.04677e34	−	7.00922e34i	−0.460340	−	0.797332i	−0.998978	+	0.0452052i	$0.985606\pi$
$258$	−3.59105e34			−0.386132
$259$	4.38697e34	+	9.39696e34i	0.445983	+	0.955302i
$260$	−8.70160e33			−0.0836538
$261$	−4.88955e33	−	8.46894e33i	−0.0444612	−	0.0770091i
$262$	1.34260e34	−	2.32546e34i	0.115499	−	0.200051i
$263$	3.80700e34	−	6.59392e34i	0.309902	−	0.536767i	−0.668438	−	0.743767i	$-0.733037\pi$
$263$	3.80700e34	−	6.59392e34i	0.309902	−	0.536767i	0.978341	+	0.207001i	$0.0663703\pi$
$264$	−1.99174e33	−	3.44980e33i	−0.0153453	−	0.0265789i
$265$	−6.55128e34			−0.477817
$266$	−2.10724e33	+	3.01231e33i	−0.0145523	+	0.0208025i
$267$	6.09601e34			0.398687
$268$	−1.00691e35	−	1.74402e35i	−0.623788	−	1.08043i
$269$	−6.95939e34	+	1.20540e35i	−0.408473	+	0.707496i	−0.994719	−	0.102637i	$-0.967272\pi$
$269$	−6.95939e34	+	1.20540e35i	−0.408473	+	0.707496i	0.586246	+	0.810133i	$0.300605\pi$
$270$	9.55776e33	−	1.65545e34i	0.0531596	−	0.0920751i
$271$	6.99120e34	+	1.21091e35i	0.368550	+	0.638348i	0.989339	−	0.145630i	$-0.0465209\pi$
$271$	6.99120e34	+	1.21091e35i	0.368550	+	0.638348i	−0.620789	+	0.783978i	$0.713188\pi$
$272$	−1.58903e35			−0.794113
$273$	−5.54690e33	+	7.92931e33i	−0.0262840	+	0.0375731i
$274$	1.47561e35			0.663115
$275$	5.32027e33	+	9.21497e33i	0.0226782	+	0.0392799i
$276$	−9.51456e34	+	1.64797e35i	−0.384775	+	0.666450i
$277$	1.03994e34	−	1.80122e34i	0.0399071	−	0.0691211i	−0.845382	−	0.534162i	$-0.820627\pi$
$277$	1.03994e34	−	1.80122e34i	0.0399071	−	0.0691211i	0.885289	+	0.465041i	$0.153960\pi$
$278$	1.16347e35	+	2.01520e35i	0.423747	+	0.733952i
$279$	−1.86510e34			−0.0644824
$280$	1.29330e35	+	2.77027e35i	0.424529	+	0.909349i
$281$	−2.21204e35			−0.689527			−0.344764	−	0.938690i	$-0.612041\pi$
$281$	−2.21204e35			−0.689527			−0.344764	+	0.938690i	$0.612041\pi$
$282$	−2.21590e34	−	3.83805e34i	−0.0656052	−	0.113632i
$283$	−2.10413e35	+	3.64447e35i	−0.591793	+	1.02502i	0.402198	+	0.915553i	$0.368246\pi$
$283$	−2.10413e35	+	3.64447e35i	−0.591793	+	1.02502i	−0.993991	+	0.109463i	$0.965087\pi$
$284$	−6.83034e34	+	1.18305e35i	−0.182527	+	0.316146i
$285$	8.69148e33	+	1.50541e34i	0.0220721	+	0.0382300i
$286$	−9.62853e32			−0.00232409
$287$	5.60902e35	+	4.88210e34i	1.28706	+	0.112026i
$288$	−1.50494e35			−0.328344
$289$	−4.09487e35	−	7.09252e35i	−0.849613	−	1.47157i
$290$	−3.73394e34	+	6.46737e34i	−0.0736878	+	0.127631i
$291$	3.67995e34	−	6.37386e34i	0.0690865	−	0.119661i
$292$	−2.65134e35	−	4.59226e35i	−0.473603	−	0.820304i
$293$	−3.14411e34			−0.0534463			−0.0267232	−	0.999643i	$-0.508507\pi$
$293$	−3.14411e34			−0.0534463			−0.0267232	+	0.999643i	$0.508507\pi$
$294$	1.50533e35	+	2.64049e34i	0.243555	+	0.0427217i
$295$	−9.74287e35			−1.50061
$296$	2.79669e35	+	4.84401e35i	0.410124	+	0.710355i
$297$	−4.70797e33	+	8.15445e33i	−0.00657454	+	0.0113874i
$298$	−8.45031e34	+	1.46364e35i	−0.112392	+	0.194669i
$299$	5.11617e34	+	8.86147e34i	0.0648206	+	0.112273i
$300$	2.59270e35			0.312964
$301$	−1.35249e36	−	1.17721e35i	−1.55568	−	0.135406i
$302$	−2.08316e35			−0.228361
$303$	4.99542e34	+	8.65231e34i	0.0521980	+	0.0904095i
$304$	1.43806e34	−	2.49080e34i	0.0143255	−	0.0248126i
$305$	1.31720e35	−	2.28145e35i	0.125113	−	0.216702i
$306$	−1.29469e35	−	2.24247e35i	−0.117275	−	0.203127i
$307$	−1.07546e36			−0.929152			−0.464576	−	0.885533i	$-0.653793\pi$
$307$	−1.07546e36			−0.929152			−0.464576	+	0.885533i	$0.653793\pi$
$308$	−2.86363e34	−	6.13395e34i	−0.0236011	−	0.0505539i
$309$	−6.45542e35			−0.507606
$310$	7.12148e34	+	1.23348e35i	0.0534350	+	0.0925522i
$311$	−9.68236e35	+	1.67703e36i	−0.693355	+	1.20093i	0.277377	+	0.960761i	$0.410535\pi$
$311$	−9.68236e35	+	1.67703e36i	−0.693355	+	1.20093i	−0.970732	+	0.240165i	$0.922798\pi$
$312$	−2.60962e34	+	4.52000e34i	−0.0178376	+	0.0308956i
$313$	8.53910e35	+	1.47901e36i	0.557210	+	0.965116i	0.997728	+	0.0673724i	$0.0214616\pi$
$313$	8.53910e35	+	1.47901e36i	0.557210	+	0.965116i	−0.440518	+	0.897744i	$0.645205\pi$
$314$	3.23133e35			0.201327
$315$	4.14240e35	−	5.92157e35i	0.246462	−	0.352317i
$316$	2.22992e36			1.26714
$317$	1.05643e36	+	1.82978e36i	0.573429	+	0.993209i	0.996210	+	0.0869768i	$0.0277206\pi$
$317$	1.05643e36	+	1.82978e36i	0.573429	+	0.993209i	−0.422781	+	0.906232i	$0.638946\pi$
$318$	−8.83174e34	+	1.52970e35i	−0.0457987	+	0.0793256i
$319$	1.83927e34	−	3.18570e34i	0.00911339	−	0.0157848i
$320$	−8.37291e34	−	1.45023e35i	−0.0396462	−	0.0686693i
$321$	1.68823e36			0.764027
$322$	9.26335e35	−	1.32420e36i	0.400736	−	0.572853i
$323$	2.35469e35			0.0973863
$324$	1.14716e35	+	1.98693e35i	0.0453649	+	0.0785743i
$325$	6.97073e34	−	1.20737e35i	0.0263615	−	0.0456594i
$326$	4.83793e35	−	8.37954e35i	0.174986	−	0.303085i
$327$	−7.77836e35	−	1.34725e36i	−0.269120	−	0.466129i
$328$	3.03668e36			1.00514
$329$	−7.08752e35	−	1.51816e36i	−0.224468	−	0.480814i
$330$	7.19055e34			0.0217926
$331$	−1.54246e36	−	2.67162e36i	−0.447412	−	0.774940i	0.550805	−	0.834634i	$-0.314321\pi$
$331$	−1.54246e36	−	2.67162e36i	−0.447412	−	0.774940i	−0.998217	+	0.0596939i	$0.980988\pi$
$332$	−1.29710e36	+	2.24664e36i	−0.360139	+	0.623779i
$333$	6.61067e35	−	1.14500e36i	0.175713	−	0.304344i
$334$	−1.29171e35	−	2.23731e35i	−0.0328732	−	0.0569381i
$335$	8.08686e36			1.97074
$336$	−1.19119e36	−	1.03682e35i	−0.278012	−	0.0241981i
$337$	−1.06211e36			−0.237430			−0.118715	−	0.992928i	$-0.537878\pi$
$337$	−1.06211e36			−0.237430			−0.118715	+	0.992928i	$0.537878\pi$
$338$	−9.93692e35	−	1.72113e36i	−0.212794	−	0.368570i
$339$	4.34508e35	−	7.52589e35i	0.0891460	−	0.154405i
$340$	4.40131e36	−	7.62329e36i	0.865242	−	1.49864i
$341$	−3.50791e34	−	6.07588e34i	−0.00660861	−	0.0114464i
$342$	4.68677e34			0.00846243
$343$	5.58295e36	+	1.48796e36i	0.966271	+	0.257529i
$344$	−7.32226e36			−1.21492
$345$	−3.82074e36	−	6.61771e36i	−0.607813	−	1.05276i
$346$	1.58421e36	−	2.74394e36i	0.241663	−	0.418573i
$347$	−3.49435e36	+	6.05239e36i	−0.511198	+	0.885420i	0.488718	+	0.872442i	$0.337465\pi$
$347$	−3.49435e36	+	6.05239e36i	−0.511198	+	0.885420i	−0.999916	+	0.0129786i	$0.995869\pi$
$348$	−4.48160e35	−	7.76236e35i	−0.0628831	−	0.108917i
$349$	7.58978e36			1.02155			0.510776	−	0.859714i	$-0.329358\pi$
$349$	7.58978e36			1.02155			0.510776	+	0.859714i	$0.329358\pi$
$350$	−2.19355e36	−	1.90927e35i	−0.283244	−	0.0246536i
$351$	1.23370e35			0.0152847
$352$	−2.83052e35	−	4.90260e35i	−0.0336510	−	0.0582852i
$353$	−2.71171e36	+	4.69682e36i	−0.309393	+	0.535884i	−0.978230	−	0.207525i	$-0.933459\pi$
$353$	−2.71171e36	+	4.69682e36i	−0.309393	+	0.535884i	0.668837	+	0.743409i	$0.266792\pi$
$354$	−1.31343e36	+	2.27493e36i	−0.143833	+	0.249127i
$355$	−2.74284e36	−	4.75074e36i	−0.288330	−	0.499402i
$356$	5.58741e36			0.563878
$357$	−4.14105e36	−	8.87020e36i	−0.401256	−	0.859497i
$358$	−8.36193e36			−0.778041
$359$	2.78243e36	+	4.81930e36i	0.248630	+	0.430640i	0.963146	−	0.268979i	$-0.0866862\pi$
$359$	2.78243e36	+	4.81930e36i	0.248630	+	0.430640i	−0.714516	+	0.699619i	$0.753353\pi$
$360$	1.94886e36	−	3.37552e36i	0.167261	−	0.289704i
$361$	6.04360e36	−	1.04678e37i	0.498243	−	0.862983i
$362$	4.88256e36	+	8.45684e36i	0.386699	+	0.669783i
$363$	7.55185e36			0.574655
$364$	−5.08411e35	+	7.26775e35i	−0.0371745	+	0.0531410i
$365$	2.12938e37			1.49626
$366$	−3.55141e35	−	6.15122e35i	−0.0239842	−	0.0415418i
$367$	−7.35508e36	+	1.27394e37i	−0.477452	+	0.826971i	−0.999666	−	0.0258436i	$-0.991773\pi$
$367$	−7.35508e36	+	1.27394e37i	−0.477452	+	0.826971i	0.522214	+	0.852814i	$0.325106\pi$
$368$	−6.32166e36	+	1.09494e37i	−0.394492	+	0.683280i
$369$	−3.58897e36	−	6.21628e36i	−0.215321	−	0.372948i
$370$	−1.00966e37			−0.582436
$371$	−3.82774e36	+	5.47176e36i	−0.212335	+	0.303533i
$372$	−1.70949e36			−0.0911999
$373$	2.12453e36	+	3.67979e36i	0.109015	+	0.188819i	0.915371	−	0.402611i	$-0.131897\pi$
$373$	2.12453e36	+	3.67979e36i	0.109015	+	0.188819i	−0.806357	+	0.591429i	$0.798564\pi$
$374$	4.87016e35	−	8.43536e35i	0.0240383	−	0.0416356i
$375$	2.63613e36	−	4.56591e36i	0.125174	−	0.216807i
$376$	−4.51829e36	−	7.82591e36i	−0.206419	−	0.357529i
$377$	−4.81970e35			−0.0211870
$378$	−8.24232e35	−	1.76552e36i	−0.0348673	−	0.0746864i
$379$	1.52118e37			0.619314			0.309657	−	0.950848i	$-0.399786\pi$
$379$	1.52118e37			0.619314			0.309657	+	0.950848i	$0.399786\pi$
$380$	7.96633e35	+	1.37981e36i	0.0312174	+	0.0540701i
$381$	−1.20301e36	+	2.08368e36i	−0.0453793	+	0.0785993i
$382$	−3.24875e36	+	5.62701e36i	−0.117977	+	0.204342i
$383$	1.94492e37	+	3.36871e37i	0.680018	+	1.17783i	0.974975	+	0.222315i	$0.0713613\pi$
$383$	1.94492e37	+	3.36871e37i	0.680018	+	1.17783i	−0.294957	+	0.955510i	$0.595305\pi$
$384$	−1.73439e37			−0.583909
$385$	2.70816e36	+	2.35718e35i	0.0877999	+	0.00764210i
$386$	−1.87580e37			−0.585693
$387$	8.65398e36	+	1.49891e37i	0.260260	+	0.450783i
$388$	3.37292e36	−	5.84207e36i	0.0977116	−	0.169242i
$389$	−6.66020e36	+	1.15358e37i	−0.185874	+	0.321943i	−0.943871	−	0.330315i	$-0.892845\pi$
$389$	−6.66020e36	+	1.15358e37i	−0.185874	+	0.321943i	0.757997	+	0.652258i	$0.226178\pi$
$390$	−4.71061e35	−	8.15901e35i	−0.0126660	−	0.0219382i
$391$	−1.03511e38			−2.68179
$392$	3.06942e37	+	5.38404e36i	0.766318	+	0.134419i
$393$	−1.29420e37			−0.311395
$394$	−1.43928e37	−	2.49290e37i	−0.333771	−	0.578109i
$395$	−4.47731e37	+	7.75493e37i	−1.00083	+	1.73348i
$396$	−4.31518e35	+	7.47410e35i	−0.00929861	+	0.0161057i
$397$	1.54640e37	+	2.67845e37i	0.321262	+	0.556443i	0.980749	−	0.195274i	$-0.0625595\pi$
$397$	1.54640e37	+	2.67845e37i	0.321262	+	0.556443i	−0.659486	+	0.751717i	$0.729226\pi$
$398$	−1.94909e37			−0.390416
$399$	1.76517e36	+	1.53640e35i	0.0340941	+	0.00296755i
$400$	1.72264e37			0.320867
$401$	1.10614e37	+	1.91590e37i	0.198709	+	0.344175i	0.948110	−	0.317942i	$-0.102992\pi$
$401$	1.10614e37	+	1.91590e37i	0.198709	+	0.344175i	−0.749401	+	0.662117i	$0.769658\pi$
$402$	1.09018e37	−	1.88825e37i	0.188896	−	0.327177i
$403$	−4.59614e35	+	7.96075e35i	−0.00768193	+	0.0133055i
$404$	4.57864e36	+	7.93043e36i	0.0738255	+	0.127870i
$405$	−9.21321e36			−0.143322
$406$	3.22003e36	+	6.89737e36i	0.0483318	+	0.103528i
$407$	4.97338e36			0.0720332
$408$	−2.63992e37	−	4.57248e37i	−0.368993	−	0.639115i
$409$	4.48360e37	−	7.76583e37i	0.604838	−	1.04761i	−0.387239	−	0.921979i	$-0.626571\pi$
$409$	4.48360e37	−	7.76583e37i	0.604838	−	1.04761i	0.992077	−	0.125631i	$-0.0400955\pi$
$410$	−2.74074e37	+	4.74710e37i	−0.356863	+	0.618105i
$411$	−3.55604e37	−	6.15924e37i	−0.446951	−	0.774142i
$412$	−5.91683e37			−0.717925
$413$	−5.69250e37	+	8.13744e37i	−0.666849	+	0.953262i
$414$	−2.06028e37			−0.233035
$415$	−5.20872e37	−	9.02176e37i	−0.568897	−	0.985358i
$416$	−3.70861e36	+	6.42350e36i	−0.0391163	+	0.0677514i
$417$	5.60766e37	−	9.71275e37i	0.571227	−	0.989394i
$418$	8.81494e34	+	1.52679e35i	0.000867288	+	0.00150219i
$419$	−6.21674e37			−0.590825			−0.295413	−	0.955370i	$-0.595457\pi$
$419$	−6.21674e37			−0.590825			−0.295413	+	0.955370i	$0.595457\pi$
$420$	3.79679e37	−	5.42752e37i	0.348580	−	0.498296i
$421$	1.94042e38			1.72110			0.860548	−	0.509369i	$-0.170121\pi$
$421$	1.94042e38			1.72110			0.860548	+	0.509369i	$0.170121\pi$
$422$	3.33717e37	+	5.78014e37i	0.285988	+	0.495345i
$423$	−1.06801e37	+	1.84985e37i	−0.0884382	+	0.153179i
$424$	−1.80082e37	+	3.11911e37i	−0.144100	+	0.249589i
$425$	7.05166e37	+	1.22138e38i	0.545320	+	0.944523i
$426$	−1.47904e37			−0.110546
$427$	−1.13591e37	−	2.43314e37i	−0.0820616	−	0.175777i
$428$	1.54738e38			1.08059
$429$	2.32036e35	+	4.01898e35i	0.00156648	+	0.00271322i
$430$	6.60867e37	−	1.14466e38i	0.431342	−	0.747106i
$431$	−6.78893e37	+	1.17588e38i	−0.428431	+	0.742065i	−0.996734	−	0.0807549i	$-0.974267\pi$
$431$	−6.78893e37	+	1.17588e38i	−0.428431	+	0.742065i	0.568303	+	0.822819i	$0.307600\pi$
$432$	7.62193e36	+	1.32016e37i	0.0465105	+	0.0805585i
$433$	1.07117e38			0.632099			0.316050	−	0.948743i	$-0.397643\pi$
$433$	1.07117e38			0.632099			0.316050	+	0.948743i	$0.397643\pi$
$434$	1.44631e37	+	1.25887e36i	0.0825394	+	0.00718424i
$435$	3.59933e37			0.198668
$436$	−7.12940e37	−	1.23485e38i	−0.380626	−	0.659264i
$437$	9.36774e36	−	1.62254e37i	0.0483787	−	0.0837943i
$438$	2.87061e37	−	4.97204e37i	0.143416	−	0.248405i
$439$	−8.48546e37	−	1.46972e38i	−0.410147	−	0.710396i	0.584758	−	0.811208i	$-0.301189\pi$
$439$	−8.48546e37	−	1.46972e38i	−0.410147	−	0.710396i	−0.994906	+	0.100812i	$0.967856\pi$
$440$	1.46618e37			0.0685681
$441$	−2.52552e37	−	6.91963e37i	−0.114286	−	0.313129i
$442$	−1.27620e37			−0.0558850
$443$	1.38264e38	+	2.39480e38i	0.585942	+	1.01488i	0.994757	+	0.102264i	$0.0326085\pi$
$443$	1.38264e38	+	2.39480e38i	0.585942	+	1.01488i	−0.408816	+	0.912617i	$0.634058\pi$
$444$	6.05913e37	−	1.04947e38i	0.248517	−	0.430445i
$445$	−1.12186e38	+	1.94312e38i	−0.445368	+	0.771399i
$446$	−2.29781e37	−	3.97993e37i	−0.0882997	−	0.152940i
$447$	8.14568e37			0.303018
$448$	−1.70047e37	−	1.48009e36i	−0.0612403	−	0.00533036i
$449$	2.45108e38			0.854643			0.427321	−	0.904100i	$-0.359457\pi$
$449$	2.45108e38			0.854643			0.427321	+	0.904100i	$0.359457\pi$
$450$	1.40356e37	+	2.43103e37i	0.0473858	+	0.0820747i
$451$	1.35004e37	−	2.33833e37i	0.0441353	−	0.0764445i
$452$	3.98256e37	−	6.89799e37i	0.126082	−	0.218381i
$453$	5.02015e37	+	8.69516e37i	0.153919	+	0.266596i
$454$	−1.59217e37			−0.0472801
$455$	−1.50668e37	−	3.22733e37i	−0.0433367	−	0.0928279i
$456$	9.55647e36			0.0266261
$457$	−6.69730e37	−	1.16001e38i	−0.180765	−	0.313095i	0.761376	−	0.648310i	$-0.224524\pi$
$457$	−6.69730e37	−	1.16001e38i	−0.180765	−	0.313095i	−0.942141	+	0.335216i	$0.891191\pi$
$458$	1.19904e38	−	2.07679e38i	0.313533	−	0.543055i
$459$	−6.24010e37	+	1.08082e38i	−0.158091	+	0.273822i
$460$	−3.50196e38	−	6.06558e38i	−0.859653	−	1.48896i
$461$	2.90176e38			0.690236			0.345118	−	0.938559i	$-0.387839\pi$
$461$	2.90176e38			0.690236			0.345118	+	0.938559i	$0.387839\pi$
$462$	4.20124e36	−	6.00569e36i	0.00968432	−	0.0138438i
$463$	−9.94687e37			−0.222209			−0.111105	−	0.993809i	$-0.535439\pi$
$463$	−9.94687e37			−0.222209			−0.111105	+	0.993809i	$0.535439\pi$
$464$	−2.97766e37	−	5.15747e37i	−0.0644711	−	0.111667i
$465$	3.43238e37	−	5.94506e37i	0.0720323	−	0.124764i
$466$	1.17060e38	−	2.02753e38i	0.238129	−	0.412451i
$467$	3.69078e38	+	6.39262e38i	0.727819	+	1.26062i	0.957803	+	0.287425i	$0.0927992\pi$
$467$	3.69078e38	+	6.39262e38i	0.727819	+	1.26062i	−0.229984	+	0.973194i	$0.573867\pi$
$468$	1.13077e37			0.0216177
$469$	4.72493e38	−	6.75430e38i	0.875769	−	1.25191i
$470$	1.63119e38			0.293146
$471$	−7.78711e37	−	1.34877e38i	−0.135698	−	0.235036i
$472$	−2.67812e38	+	4.63865e38i	−0.452555	+	0.783849i
$473$	−3.25531e37	+	5.63836e37i	−0.0533465	+	0.0923988i
$474$	1.20717e38	+	2.09087e38i	0.191858	+	0.332308i
$475$	−2.55269e37			−0.0393496
$476$	−3.79556e38	−	8.13014e38i	−0.567511	−	1.21562i
$477$	8.51336e37			0.123477
$478$	2.17239e38	+	3.76269e38i	0.305657	+	0.529413i
$479$	−6.18273e38	+	1.07088e39i	−0.843947	+	1.46176i	0.0425847	+	0.999093i	$0.486441\pi$
$479$	−6.18273e38	+	1.07088e39i	−0.843947	+	1.46176i	−0.886532	+	0.462667i	$0.846893\pi$
$480$	2.76957e38	−	4.79704e38i	0.366788	−	0.635295i
$481$	−3.25812e37	−	5.64322e37i	−0.0418661	−	0.0725143i
$482$	3.59091e38			0.447736
$483$	−7.75960e38	−	6.75396e37i	−0.938871	−	0.0817194i
$484$	6.92178e38			0.812756
$485$	1.35446e38	+	2.34599e38i	0.154351	+	0.267344i
$486$	−1.24203e37	+	2.15125e37i	−0.0137374	+	0.0237939i
$487$	−7.52346e38	+	1.30310e39i	−0.807696	+	1.39897i	0.106760	+	0.994285i	$0.465952\pi$
$487$	−7.52346e38	+	1.30310e39i	−0.807696	+	1.39897i	−0.914456	+	0.404685i	$0.867381\pi$
$488$	−7.24143e37	−	1.25425e38i	−0.0754635	−	0.130707i
$489$	−4.66353e38			−0.471776
$490$	−3.61196e38	+	4.31236e38i	−0.354731	+	0.423518i
$491$	−3.47246e38			−0.331097			−0.165549	−	0.986202i	$-0.552939\pi$
$491$	−3.47246e38			−0.331097			−0.165549	+	0.986202i	$0.552939\pi$
$492$	−3.28953e38	−	5.69764e38i	−0.304537	−	0.527474i
$493$	2.43783e38	−	4.22244e38i	0.219140	−	0.379562i
$494$	1.15495e36	−	2.00044e36i	0.00100815	−	0.00174616i
$495$	−1.73283e37	−	3.00136e37i	−0.0146886	−	0.0254415i
$496$	−1.13582e38			−0.0935029
$497$	−5.57049e38	−	4.84855e37i	−0.445375	−	0.0387654i
$498$	−2.80873e38			−0.218115
$499$	8.16832e38	+	1.41479e39i	0.616133	+	1.06717i	0.990185	+	0.139766i	$0.0446350\pi$
$499$	8.16832e38	+	1.41479e39i	0.616133	+	1.06717i	−0.374051	+	0.927408i	$0.622032\pi$
$500$	2.41619e38	−	4.18497e38i	0.177038	−	0.306639i
$501$	−6.22574e37	+	1.07833e38i	−0.0443143	+	0.0767547i
$502$	−2.01369e38	−	3.48781e38i	−0.139248	−	0.241184i
$503$	−1.76699e39			−1.18713			−0.593567	−	0.804785i	$-0.702281\pi$
$503$	−1.76699e39			−1.18713			−0.593567	+	0.804785i	$0.702281\pi$
$504$	−1.68064e38	−	3.59995e38i	−0.109706	−	0.234992i
$505$	−3.67726e38			−0.233238
$506$	−3.87501e37	−	6.71171e37i	−0.0238831	−	0.0413667i
$507$	−4.78935e38	+	8.29540e38i	−0.286854	+	0.496846i
$508$	−1.10264e38	+	1.90983e38i	−0.0641817	+	0.111166i
$509$	1.50290e37	+	2.60311e37i	0.00850204	+	0.0147260i	0.870245	−	0.492619i	$-0.163960\pi$
$509$	1.50290e37	+	2.60311e37i	0.00850204	+	0.0147260i	−0.861743	+	0.507345i	$0.830627\pi$
$510$	9.53059e38			0.524025
$511$	1.24414e39	−	1.77850e39i	0.664916	−	0.950499i
$512$	−1.64037e39			−0.852171
$513$	−1.12945e37	−	1.95627e37i	−0.00570383	−	0.00987932i
$514$	4.01589e38	−	6.95572e38i	0.197159	−	0.341489i
$515$	1.18800e39	−	2.05768e39i	0.567039	−	0.982140i
$516$	7.93196e38	+	1.37386e39i	0.368095	+	0.637559i
$517$	−8.03492e37			−0.0362550
$518$	−5.89915e38	+	8.43285e38i	−0.258826	+	0.369992i
$519$	−1.52710e39			−0.651541
$520$	−9.60508e37	−	1.66365e38i	−0.0398522	−	0.0690261i
$521$	−1.95910e39	+	3.39326e39i	−0.790513	+	1.36921i	0.135137	+	0.990827i	$0.456853\pi$
$521$	−1.95910e39	+	3.39326e39i	−0.790513	+	1.36921i	−0.925650	+	0.378382i	$0.876481\pi$
$522$	4.85223e37	−	8.40431e37i	0.0190423	−	0.0329822i
$523$	2.05427e39	+	3.55810e39i	0.784120	+	1.35814i	0.929523	+	0.368763i	$0.120219\pi$
$523$	2.05427e39	+	3.55810e39i	0.784120	+	1.35814i	−0.145403	+	0.989372i	$0.546448\pi$
$524$	−1.18623e39			−0.440417
$525$	4.48925e38	+	9.61605e38i	0.162130	+	0.347286i
$526$	7.55589e38			0.265456
$527$	−4.64950e38	−	8.05317e38i	−0.158910	−	0.275241i
$528$	−2.86709e37	+	4.96594e37i	−0.00953343	+	0.0165124i
$529$	−2.57249e39	+	4.45568e39i	−0.832235	+	1.44147i
$530$	−3.25064e38	−	5.63028e38i	−0.102322	−	0.177227i
$531$	1.26608e39			0.387785
$532$	1.61790e38	+	1.40822e37i	0.0482205	+	0.00419712i
$533$	−3.53770e38			−0.102607
$534$	3.02474e38	+	5.23901e38i	0.0853769	+	0.147877i
$535$	−3.10688e39	+	5.38127e39i	−0.853483	+	1.47828i
$536$	2.22292e39	−	3.85021e39i	0.594339	−	1.02942i
$537$	2.01512e39	+	3.49029e39i	0.524414	+	0.908312i
$538$	−1.38126e39			−0.349889
$539$	1.77918e38	−	2.12419e38i	0.0438716	−	0.0523788i
$540$	−8.44453e38			−0.202706
$541$	−4.04215e39	−	7.00121e39i	−0.944609	−	1.63611i	−0.756533	−	0.653956i	$-0.773108\pi$
$541$	−4.04215e39	−	7.00121e39i	−0.944609	−	1.63611i	−0.188076	−	0.982154i	$-0.560225\pi$
$542$	−6.93784e38	+	1.20167e39i	−0.157846	+	0.273398i
$543$	2.35327e39	−	4.07599e39i	0.521285	−	0.902892i
$544$	−3.75166e39	−	6.49807e39i	−0.809170	−	1.40152i
$545$	5.72587e39			1.20252
$546$	−9.56685e37	−	8.32699e36i	−0.0195648	−	0.00170292i
$547$	8.98078e39			1.78854			0.894269	−	0.447530i	$-0.147696\pi$
$547$	8.98078e39			1.78854			0.894269	+	0.447530i	$0.147696\pi$
$548$	−3.25935e39	−	5.64536e39i	−0.632140	−	1.09490i
$549$	−1.71169e38	+	2.96474e38i	−0.0323315	+	0.0559999i
$550$	−5.27966e37	+	9.14464e37i	−0.00971286	+	0.0168232i
$551$	4.41244e37	+	7.64258e37i	0.00790644	+	0.0136944i
$552$	−4.20098e39			−0.733220
$553$	3.86110e39	+	8.27053e39i	0.656442	+	1.40611i
$554$	2.06400e38			0.0341836
$555$	2.43315e39	+	4.21434e39i	0.392573	+	0.679956i
$556$	5.13980e39	−	8.90239e39i	0.807907	−	1.39934i
$557$	5.88584e39	−	1.01946e40i	0.901380	−	1.56124i	0.0756766	−	0.997132i	$-0.475888\pi$
$557$	5.88584e39	−	1.01946e40i	0.901380	−	1.56124i	0.825704	−	0.564104i	$-0.190778\pi$
$558$	−9.25433e37	−	1.60290e38i	−0.0138086	−	0.0239172i
$559$	8.53036e38			0.124021
$560$	2.52266e39	−	3.60615e39i	0.357382	−	0.510879i
$561$	−4.69459e38			−0.0648091
$562$	−1.09758e39	−	1.90106e39i	−0.147659	−	0.255752i
$563$	5.00584e39	−	8.67037e39i	0.656304	−	1.13675i	−0.325261	−	0.945624i	$-0.605452\pi$
$563$	5.00584e39	−	8.67037e39i	0.656304	−	1.13675i	0.981565	−	0.191128i	$-0.0612145\pi$
$564$	−9.78904e38	+	1.69551e39i	−0.125081	+	0.216647i
$565$	1.59926e39	+	2.77001e39i	0.199167	+	0.344968i
$566$	−4.17615e39			−0.506918
$567$	−5.38303e38	+	7.69505e38i	−0.0636902	+	0.0910453i
$568$	−3.01581e39			−0.347819
$569$	9.98254e38	+	1.72903e39i	0.112231	+	0.194390i	0.916670	−	0.399646i	$-0.130867\pi$
$569$	9.98254e38	+	1.72903e39i	0.112231	+	0.194390i	−0.804438	+	0.594036i	$0.797534\pi$
$570$	−8.62515e37	+	1.49392e38i	−0.00945325	+	0.0163735i
$571$	−5.82655e39	+	1.00919e40i	−0.622570	+	1.07832i	0.366436	+	0.930443i	$0.380578\pi$
$571$	−5.82655e39	+	1.00919e40i	−0.622570	+	1.07832i	−0.989005	+	0.147879i	$0.952755\pi$
$572$	2.12677e37	+	3.68367e37i	0.00221553	+	0.00383741i
$573$	3.13164e39			0.318075
$574$	2.36353e39	+	5.06272e39i	0.234066	+	0.501374i
$575$	1.12215e40			1.08360
$576$	1.08806e38	+	1.88457e38i	0.0102453	+	0.0177454i
$577$	−7.79518e38	+	1.35016e39i	−0.0715775	+	0.123976i	−0.899593	−	0.436730i	$-0.856137\pi$
$577$	−7.79518e38	+	1.35016e39i	−0.0715775	+	0.123976i	0.828015	+	0.560705i	$0.189470\pi$
$578$	4.06362e39	−	7.03839e39i	0.363881	−	0.630260i
$579$	4.52044e39	+	7.82964e39i	0.394768	+	0.683758i
$580$	3.29903e39			0.280983
$581$	−1.05785e40	−	9.20751e38i	−0.878757	−	0.0764871i
$582$	7.30373e38			0.0591781
$583$	1.60121e38	+	2.77337e38i	0.0126547	+	0.0219186i
$584$	5.85326e39	−	1.01381e40i	0.451244	−	0.781577i
$585$	−2.27040e38	+	3.93244e38i	−0.0170743	+	0.0295735i
$586$	−1.56006e38	−	2.70210e38i	−0.0114453	−	0.0198238i
$587$	−1.55233e39			−0.111104			−0.0555521	−	0.998456i	$-0.517692\pi$
$587$	−1.55233e39			−0.111104			−0.0555521	+	0.998456i	$0.517692\pi$
$588$	−2.31481e39	−	6.34231e39i	−0.161638	−	0.442870i
$589$	1.68311e38			0.0114668
$590$	−4.83426e39	−	8.37318e39i	−0.321348	−	0.556591i
$591$	−6.93696e39	+	1.20152e40i	−0.449936	+	0.779311i
$592$	4.02580e39	−	6.97290e39i	0.254793	−	0.441315i
$593$	−1.42165e40	−	2.46238e40i	−0.878013	−	1.52076i	−0.853518	−	0.521064i	$-0.825535\pi$
$593$	−1.42165e40	−	2.46238e40i	−0.878013	−	1.52076i	−0.0244955	−	0.999700i	$-0.507798\pi$
$594$	−9.34408e37			−0.00563162
$595$	3.58949e40	+	3.12429e39i	2.11123	+	0.183762i
$596$	7.46607e39			0.428569
$597$	4.69707e39	+	8.13556e39i	0.263147	+	0.455784i
$598$	−5.07713e38	+	8.79384e38i	−0.0277620	+	0.0480852i
$599$	−4.50252e39	+	7.79860e39i	−0.240307	+	0.416224i	−0.960802	−	0.277236i	$-0.910582\pi$
$599$	−4.50252e39	+	7.79860e39i	−0.240307	+	0.416224i	0.720495	+	0.693461i	$0.243915\pi$
$600$	2.86190e39	+	4.95695e39i	0.149094	+	0.258239i
$601$	−3.00816e40			−1.52975			−0.764876	−	0.644177i	$-0.777200\pi$
$601$	−3.00816e40			−1.52975			−0.764876	+	0.644177i	$0.777200\pi$
$602$	−5.69912e39	−	1.22076e40i	−0.282917	−	0.606012i
$603$	−1.05088e40			−0.509276
$604$	4.60131e39	+	7.96971e39i	0.217694	+	0.377057i
$605$	−1.38978e40	+	2.40717e40i	−0.641938	+	1.11187i
$606$	−4.95729e38	+	8.58628e38i	−0.0223559	+	0.0387215i
$607$	−1.51763e40	−	2.62861e40i	−0.668236	−	1.15742i	−0.978397	−	0.206734i	$-0.933717\pi$
$607$	−1.51763e40	−	2.62861e40i	−0.668236	−	1.15742i	0.310162	−	0.950684i	$-0.399617\pi$
$608$	1.35810e39			0.0583887
$609$	2.10299e39	−	3.00623e39i	0.0882850	−	0.126204i
$610$	2.61429e39			0.107169
$611$	5.26376e38	+	9.11711e38i	0.0210717	+	0.0364972i
$612$	−5.71948e39	+	9.90642e39i	−0.223594	+	0.387277i
$613$	−2.35782e40	+	4.08386e40i	−0.900189	+	1.55917i	−0.0729414	+	0.997336i	$0.523239\pi$
$613$	−2.35782e40	+	4.08386e40i	−0.900189	+	1.55917i	−0.827248	+	0.561837i	$0.810095\pi$
$614$	−5.33625e39	−	9.24265e39i	−0.198973	−	0.344632i
$615$	2.64194e40			0.962129
$616$	8.56647e38	−	1.22458e39i	0.0304706	−	0.0435578i
$617$	−3.98398e40			−1.38415			−0.692073	−	0.721827i	$-0.743302\pi$
$617$	−3.98398e40			−1.38415			−0.692073	+	0.721827i	$0.743302\pi$
$618$	−3.20307e39	−	5.54789e39i	−0.108701	−	0.188276i
$619$	−1.39751e40	+	2.42055e40i	−0.463276	+	0.802417i	−0.999122	−	0.0418985i	$-0.986659\pi$
$619$	−1.39751e40	+	2.42055e40i	−0.463276	+	0.802417i	0.535846	+	0.844316i	$0.319993\pi$
$620$	3.14601e39	−	5.44905e39i	0.101878	−	0.176458i
$621$	4.96503e39	+	8.59968e39i	0.157070	+	0.272053i
$622$	−1.92169e40			−0.593914
$623$	9.67459e39	+	2.07231e40i	0.292116	+	0.625718i
$624$	7.51305e38			0.0221636
$625$	2.12184e40	+	3.67513e40i	0.611579	+	1.05929i
$626$	−8.47392e39	+	1.46773e40i	−0.238647	+	0.413349i
$627$	4.24859e37	−	7.35877e37i	0.00116914	−	0.00202500i
$628$	−7.13742e39	−	1.23624e40i	−0.191923	−	0.332420i
$629$	6.59188e40			1.73211
$630$	7.14449e39	+	6.21856e38i	0.183456	+	0.0159681i
$631$	2.37333e39			0.0595570			0.0297785	−	0.999557i	$-0.490520\pi$
$631$	2.37333e39			0.0595570			0.0297785	+	0.999557i	$0.490520\pi$
$632$	2.46145e40	+	4.26335e40i	0.603661	+	1.04557i
$633$	1.60843e40	−	2.78589e40i	0.385522	−	0.667743i
$634$	−1.04836e40	+	1.81582e40i	−0.245594	+	0.425381i
$635$	−4.42785e39	−	7.66927e39i	−0.101385	−	0.175604i
$636$	7.80307e39			0.174637
$637$	−3.57585e39	−	6.27236e38i	−0.0782271	−	0.0137217i
$638$	3.65046e38			0.00780634
$639$	3.56431e39	+	6.17357e39i	0.0745097	+	0.129055i
$640$	3.19184e40	−	5.52842e40i	0.652276	−	1.12977i
$641$	−1.81208e40	+	3.13862e40i	−0.362023	+	0.627043i	−0.988294	−	0.152563i	$-0.951247\pi$
$641$	−1.81208e40	+	3.13862e40i	−0.362023	+	0.627043i	0.626270	+	0.779606i	$0.284581\pi$
$642$	8.37672e39	+	1.45089e40i	0.163612	+	0.283385i
$643$	−4.59923e40			−0.878267			−0.439133	−	0.898422i	$-0.644714\pi$
$643$	−4.59923e40			−0.878267			−0.439133	+	0.898422i	$0.644714\pi$
$644$	−7.11220e40	−	6.19046e39i	−1.32788	−	0.115579i
$645$	−6.37043e40			−1.16293
$646$	1.16836e39	+	2.02366e39i	0.0208548	+	0.0361216i
$647$	2.38071e39	−	4.12352e39i	0.0415523	−	0.0719707i	−0.844501	−	0.535554i	$-0.820103\pi$
$647$	2.38071e39	−	4.12352e39i	0.0415523	−	0.0719707i	0.886054	+	0.463583i	$0.153436\pi$
$648$	−2.53253e39	+	4.38647e39i	−0.0432232	+	0.0748648i
$649$	2.38126e39	+	4.12447e39i	0.0397429	+	0.0688367i
$650$	1.38351e39			0.0225807
$651$	−2.95998e39	−	6.34033e39i	−0.0472460	−	0.101202i
$652$	−4.27444e40			−0.667251
$653$	−3.48284e39	−	6.03246e39i	−0.0531732	−	0.0920986i	0.838214	−	0.545342i	$-0.183600\pi$
$653$	−3.48284e39	−	6.03246e39i	−0.0531732	−	0.0920986i	−0.891387	+	0.453243i	$0.850267\pi$
$654$	7.71900e39	−	1.33697e40i	0.115261	−	0.199638i
$655$	2.38175e40	−	4.12531e40i	0.347854	−	0.602501i
$656$	−2.18563e40	−	3.78562e40i	−0.312227	−	0.540794i
$657$	−2.76712e40			−0.386661
$658$	9.53058e39	−	1.36240e40i	0.130270	−	0.186221i
$659$	−5.74750e40			−0.768494			−0.384247	−	0.923230i	$-0.625539\pi$
$659$	−5.74750e40			−0.768494			−0.384247	+	0.923230i	$0.625539\pi$
$660$	−1.58826e39	−	2.75095e39i	−0.0207747	−	0.0359828i
$661$	4.08167e40	−	7.06967e40i	0.522297	−	0.904644i	−0.477367	−	0.878704i	$-0.658409\pi$
$661$	4.08167e40	−	7.06967e40i	0.522297	−	0.904644i	0.999663	−	0.0259401i	$-0.00825791\pi$
$662$	1.53069e40	−	2.65123e40i	0.191622	−	0.331899i
$663$	3.07548e39	+	5.32689e39i	0.0376675	+	0.0652420i
$664$	−5.72710e40			−0.686274
$665$	−3.73820e39	+	5.34377e39i	−0.0438277	+	0.0626518i
$666$	1.31204e40			0.150512
$667$	−1.93969e40	−	3.35964e40i	−0.217725	−	0.377110i
$668$	−5.70632e39	+	9.88363e39i	−0.0626754	+	0.108557i
$669$	−1.10749e40	+	1.91823e40i	−0.119031	+	0.206168i
$670$	4.01257e40	+	6.94997e40i	0.422025	+	0.730968i
$671$	−1.28775e39			−0.0132542
$672$	−2.38840e40	−	5.11599e40i	−0.240576	−	0.515318i
$673$	8.15082e40			0.803494			0.401747	−	0.915751i	$-0.368403\pi$
$673$	8.15082e40			0.803494			0.401747	+	0.915751i	$0.368403\pi$
$674$	−5.27002e39	−	9.12795e39i	−0.0508445	−	0.0880653i
$675$	6.76480e39	−	1.17170e40i	0.0638778	−	0.110640i
$676$	−4.38976e40	+	7.60330e40i	−0.405709	+	0.702708i
$677$	8.17501e39	+	1.41595e40i	0.0739524	+	0.128089i	0.900630	−	0.434586i	$-0.143105\pi$
$677$	8.17501e39	+	1.41595e40i	0.0739524	+	0.128089i	−0.826678	+	0.562676i	$0.809772\pi$
$678$	8.62383e39			0.0763606
$679$	2.75079e40	+	2.39429e39i	0.238421	+	0.0207522i
$680$	1.94332e41			1.64879
$681$	3.83692e39	+	6.64575e39i	0.0318677	+	0.0551964i
$682$	3.48114e38	−	6.02951e38i	0.00283040	−	0.00490239i
$683$	1.22944e41	−	2.12946e41i	0.978608	−	1.69500i	0.311133	−	0.950366i	$-0.399292\pi$
$683$	1.22944e41	−	2.12946e41i	0.978608	−	1.69500i	0.667475	−	0.744632i	$-0.267375\pi$
$684$	−1.03522e39	−	1.79305e39i	−0.00806714	−	0.0139727i
$685$	2.61770e41			1.99713
$686$	1.49140e40	+	5.53637e40i	0.111402	+	0.413548i
$687$	−1.15581e41			−0.845308
$688$	5.27015e40	+	9.12817e40i	0.377390	+	0.653659i
$689$	2.09794e39	−	3.63373e39i	0.0147100	−	0.0254785i
$690$	3.79158e40	−	6.56720e40i	0.260320	−	0.450888i
$691$	3.63273e40	+	6.29208e40i	0.244232	+	0.423022i	0.961915	−	0.273348i	$-0.0881310\pi$
$691$	3.63273e40	+	6.29208e40i	0.244232	+	0.423022i	−0.717684	+	0.696369i	$0.754798\pi$
$692$	−1.39969e41			−0.921499
$693$	−3.51924e39	−	3.06315e38i	−0.0226891	−	0.00197486i
$694$	−6.93536e40			−0.437881
$695$	2.06397e41	+	3.57491e41i	1.27622	+	2.21047i
$696$	9.89385e39	−	1.71366e40i	0.0599144	−	0.103775i
$697$	1.78938e41	−	3.09930e41i	1.06128	−	1.83818i
$698$	3.76593e40	+	6.52277e40i	0.218760	+	0.378904i
$699$	−1.12840e41			−0.642012
$700$	4.11470e40	+	8.81376e40i	0.229307	+	0.491179i
$701$	−6.69409e40			−0.365410			−0.182705	−	0.983168i	$-0.558485\pi$
$701$	−6.69409e40			−0.365410			−0.182705	+	0.983168i	$0.558485\pi$
$702$	6.12141e38	+	1.06026e39i	0.00327313	+	0.00566923i
$703$	−5.96563e39	+	1.03328e40i	−0.0312467	+	0.0541208i
$704$	−4.09286e38	+	7.08904e38i	−0.00210002	+	0.00363734i
$705$	−3.93096e40	−	6.80862e40i	−0.197586	−	0.342229i
$706$	−5.38203e40			−0.265019
$707$	−2.14853e40	+	3.07132e40i	−0.103648	+	0.148164i
$708$	1.16045e41			0.548459
$709$	−1.88606e41	−	3.26676e41i	−0.873345	−	1.51268i	−0.858516	−	0.512787i	$-0.828613\pi$
$709$	−1.88606e41	−	3.26676e41i	−0.873345	−	1.51268i	−0.0148290	−	0.999890i	$-0.504720\pi$
$710$	2.72191e40	−	4.71448e40i	0.123489	−	0.213889i
$711$	5.81824e40	−	1.00775e41i	0.258632	−	0.447964i
$712$	6.16755e40	+	1.06825e41i	0.268629	+	0.465279i
$713$	−7.39888e40			−0.315768
$714$	5.56847e40	−	7.96014e40i	0.232869	−	0.332887i
$715$	−1.70808e39			−0.00699955
$716$	1.84700e41	+	3.19909e41i	0.741698	+	1.28466i
$717$	1.04704e41	−	1.81353e41i	0.412036	−	0.713668i
$718$	−2.76119e40	+	4.78252e40i	−0.106486	+	0.184439i
$719$	−1.03410e41	−	1.79112e41i	−0.390836	−	0.676947i	0.601724	−	0.798704i	$-0.294481\pi$
$719$	−1.03410e41	−	1.79112e41i	−0.390836	−	0.676947i	−0.992560	+	0.121756i	$0.961147\pi$
$720$	−5.61071e40			−0.207825
$721$	−1.02450e41	−	2.19449e41i	−0.371920	−	0.796659i
$722$	1.19950e41			0.426785
$723$	−8.65365e40	−	1.49886e41i	−0.301782	−	0.522702i
$724$	2.15694e41	−	3.73592e41i	0.737272	−	1.27699i
$725$	−2.64281e40	+	4.57748e40i	−0.0885451	+	0.153365i
$726$	3.74711e40	+	6.49018e40i	0.123059	+	0.213145i
$727$	−4.15927e41			−1.33896			−0.669481	−	0.742829i	$-0.733483\pi$
$727$	−4.15927e41			−1.33896			−0.669481	+	0.742829i	$0.733483\pi$
$728$	−1.95071e40	−	1.69790e39i	−0.0615585	−	0.00535806i
$729$	1.19725e40			0.0370370
$730$	1.05657e41	+	1.83003e41i	0.320417	+	0.554978i
$731$	−4.31469e41	+	7.47327e41i	−1.28277	+	2.22182i
$732$	−1.56888e40	+	2.71738e40i	−0.0457277	+	0.0792027i
$733$	−2.28832e41	−	3.96349e41i	−0.653897	−	1.13258i	−0.982169	−	0.187999i	$-0.939800\pi$
$733$	−2.28832e41	−	3.96349e41i	−0.653897	−	1.13258i	0.328273	−	0.944583i	$-0.393534\pi$
$734$	−1.45979e41			−0.408975
$735$	2.67043e41	+	4.68417e40i	0.733524	+	0.128667i
$736$	−5.97013e41			−1.60789
$737$	−1.97652e40	−	3.42343e40i	−0.0521941	−	0.0904029i
$738$	3.56158e40	−	6.16883e40i	0.0922200	−	0.159730i
$739$	1.56682e41	−	2.71382e41i	0.397810	−	0.689027i	−0.595646	−	0.803247i	$-0.703104\pi$
$739$	1.56682e41	−	2.71382e41i	0.397810	−	0.689027i	0.993455	+	0.114220i	$0.0364370\pi$
$740$	2.23014e41	+	3.86272e41i	0.555230	+	0.961687i
$741$	−1.11332e39			−0.00271804
$742$	−6.60178e40	−	5.74619e39i	−0.158054	−	0.0137570i
$743$	2.16911e41			0.509265			0.254633	−	0.967038i	$-0.418045\pi$
$743$	2.16911e41			0.509265			0.254633	+	0.967038i	$0.418045\pi$
$744$	−1.88699e40	−	3.26836e40i	−0.0434472	−	0.0752527i
$745$	−1.49906e41	+	2.59646e41i	−0.338497	+	0.586294i
$746$	−2.10831e40	+	3.65171e40i	−0.0466898	+	0.0808692i
$747$	6.76870e40	+	1.17237e41i	0.147013	+	0.254635i
$748$	−4.30291e40			−0.0916620
$749$	2.67928e41	+	5.73906e41i	0.559799	+	1.19910i
$750$	5.23202e40			0.107221
$751$	1.91080e41	+	3.30961e41i	0.384094	+	0.665269i	0.991643	−	0.129012i	$-0.0411807\pi$
$751$	1.91080e41	+	3.30961e41i	0.384094	+	0.665269i	−0.607549	+	0.794282i	$0.707847\pi$
$752$	−6.50403e40	+	1.12653e41i	−0.128240	+	0.222118i
$753$	−9.70547e40	+	1.68104e41i	−0.187711	+	0.325125i
$754$	−2.39146e39	−	4.14212e39i	−0.00453710	−	0.00785848i
$755$	−3.69547e41			−0.687764
$756$	−4.93391e40	+	7.05304e40i	−0.0900794	+	0.128769i
$757$	−5.08036e41			−0.909923			−0.454962	−	0.890511i	$-0.650347\pi$
$757$	−5.08036e41			−0.909923			−0.454962	+	0.890511i	$0.650347\pi$
$758$	7.54783e40	+	1.30732e41i	0.132623	+	0.229710i
$759$	−1.86766e40	+	3.23488e40i	−0.0321953	+	0.0557638i
$760$	−1.75869e40	+	3.04615e40i	−0.0297436	+	0.0515174i
$761$	−4.73595e41	−	8.20291e41i	−0.785832	−	1.36110i	−0.928501	−	0.371331i	$-0.878902\pi$
$761$	−4.73595e41	−	8.20291e41i	−0.785832	−	1.36110i	0.142668	−	0.989771i	$-0.454432\pi$
$762$	−2.38766e40			−0.0388710
$763$	3.34547e41	−	4.78236e41i	0.534381	−	0.763899i
$764$	2.87036e41			0.449865
$765$	−2.29676e41	−	3.97810e41i	−0.353203	−	0.611765i
$766$	−1.93008e41	+	3.34300e41i	−0.291245	+	0.504451i
$767$	3.11999e40	−	5.40398e40i	0.0461977	−	0.0800167i
$768$	−7.38448e40	−	1.27903e41i	−0.107296	−	0.185842i
$769$	6.07203e41			0.865769			0.432884	−	0.901449i	$-0.357496\pi$
$769$	6.07203e41			0.865769			0.432884	+	0.901449i	$0.357496\pi$
$770$	1.14117e40	+	2.44440e40i	0.0159674	+	0.0342023i
$771$	−3.87112e41			−0.531555
$772$	4.14329e41	+	7.17640e41i	0.558335	+	0.967065i
$773$	−1.74183e41	+	3.01694e41i	−0.230358	+	0.398992i	−0.957913	−	0.287057i	$-0.907323\pi$
$773$	−1.74183e41	+	3.01694e41i	−0.230358	+	0.398992i	0.727555	+	0.686049i	$0.240656\pi$
$774$	−8.58793e40	+	1.48747e41i	−0.111467	+	0.193066i
$775$	5.04045e40	+	8.73032e40i	0.0642088	+	0.111213i
$776$	1.48925e41			0.186197
$777$	4.94152e41	+	4.30110e40i	0.606395	+	0.0527807i
$778$	−1.32187e41			−0.159216
$779$	3.23877e40	+	5.60971e40i	0.0382901	+	0.0663205i
$780$	−2.08097e40	+	3.60435e40i	−0.0241488	+	0.0418269i
$781$	−1.34076e40	+	2.32227e40i	−0.0152725	+	0.0264528i
$782$	−5.13607e41	−	8.89593e41i	−0.574292	−	0.994703i
$783$	−4.67731e40			−0.0513394
$784$	−1.53801e41	−	4.21396e41i	−0.165720	−	0.454054i
$785$	5.73231e41			0.606345
$786$	−6.42164e40	−	1.11226e41i	−0.0666835	−	0.115499i
$787$	−6.62978e41	+	1.14831e42i	−0.675873	+	1.17065i	0.300339	+	0.953832i	$0.402900\pi$
$787$	−6.62978e41	+	1.14831e42i	−0.675873	+	1.17065i	−0.976213	+	0.216815i	$0.930433\pi$
$788$	−6.35819e41	+	1.10127e42i	−0.636361	+	1.10221i
$789$	−1.82088e41	−	3.15385e41i	−0.178922	−	0.309902i
$790$	−8.88627e41			−0.857288
$791$	3.24797e41	+	2.82704e40i	0.307648	+	0.0267777i
$792$	−1.90529e40			−0.0177192
$793$	8.43619e39	+	1.46119e40i	0.00770345	+	0.0133428i
$794$	−1.53460e41	+	2.65800e41i	−0.137593	+	0.238319i
$795$	−1.56673e41	+	2.71366e41i	−0.137934	+	0.238908i
$796$	4.30518e41	+	7.45679e41i	0.372179	+	0.644633i
$797$	−4.58624e39			−0.00389324			−0.00194662	−	0.999998i	$-0.500620\pi$
$797$	−4.58624e39			−0.00389324			−0.00194662	+	0.999998i	$0.500620\pi$
$798$	7.43807e39	+	1.59325e40i	0.00620038	+	0.0132813i
$799$	−1.06497e42			−0.871788
$800$	4.06712e41	+	7.04446e41i	0.326951	+	0.566295i
$801$	1.45785e41	−	2.52507e41i	0.115091	−	0.199344i
$802$	−1.09770e41	+	1.90127e41i	−0.0851051	+	0.147406i
$803$	−5.20445e40	−	9.01436e40i	−0.0396277	−	0.0686372i
$804$	−9.63205e41			−0.720288
$805$	1.64330e42	−	2.34910e42i	1.20691	−	1.72528i
$806$	−9.12213e39			−0.00658018
$807$	3.32866e41	+	5.76540e41i	0.235832	+	0.408473i
$808$	−1.01081e41	+	1.75077e41i	−0.0703402	+	0.121833i
$809$	2.01974e41	−	3.49829e41i	0.138052	−	0.239112i	−0.788707	−	0.614769i	$-0.789249\pi$
$809$	2.01974e41	−	3.49829e41i	0.138052	−	0.239112i	0.926759	+	0.375656i	$0.122583\pi$
$810$	−4.57145e40	−	7.91798e40i	−0.0306917	−	0.0531596i
$811$	7.67013e41			0.505825			0.252912	−	0.967489i	$-0.418612\pi$
$811$	7.67013e41			0.505825			0.252912	+	0.967489i	$0.418612\pi$
$812$	1.92754e41	−	2.75542e41i	0.124865	−	0.178494i
$813$	6.68774e41			0.425565
$814$	2.46771e40	+	4.27420e40i	0.0154255	+	0.0267178i
$815$	8.58238e41	−	1.48651e42i	0.527014	−	0.912815i
$816$	−3.80013e41	+	6.58202e41i	−0.229241	+	0.397056i
$817$	−7.80956e40	−	1.35266e41i	−0.0462814	−	0.0801618i
$818$	8.89877e41			0.518092
$819$	1.95792e40	+	4.19390e40i	0.0111990	+	0.0239884i
$820$	2.42152e42			1.36077
$821$	−6.84785e41	−	1.18608e42i	−0.378075	−	0.654845i	0.612707	−	0.790310i	$-0.290081\pi$
$821$	−6.84785e41	−	1.18608e42i	−0.378075	−	0.654845i	−0.990782	+	0.135465i	$0.956747\pi$
$822$	3.52890e41	−	6.11223e41i	0.191425	−	0.331557i
$823$	1.18208e42	−	2.04742e42i	0.630012	−	1.09121i	−0.357537	−	0.933899i	$-0.616383\pi$
$823$	1.18208e42	−	2.04742e42i	0.630012	−	1.09121i	0.987549	−	0.157314i	$-0.0502833\pi$
$824$	−6.53117e41	−	1.13123e42i	−0.342016	−	0.592389i
$825$	5.08933e40			0.0261866
$826$	−9.81797e41	−	8.54557e40i	−0.496376	−	0.0432046i
$827$	3.08674e41			0.153345			0.0766726	−	0.997056i	$-0.475570\pi$
$827$	3.08674e41			0.153345			0.0766726	+	0.997056i	$0.475570\pi$
$828$	4.55078e41	+	7.88219e41i	0.222150	+	0.384775i
$829$	−6.61322e41	+	1.14544e42i	−0.317228	+	0.549456i	−0.979909	−	0.199447i	$-0.936085\pi$
$829$	−6.61322e41	+	1.14544e42i	−0.317228	+	0.549456i	0.662680	+	0.748902i	$0.269419\pi$
$830$	5.16896e41	−	8.95291e41i	0.243653	−	0.422019i
$831$	−4.97398e40	−	8.61519e40i	−0.0230404	−	0.0399071i
$832$	1.07251e40			0.00488218
$833$	2.35819e42	−	2.81547e42i	1.05494	−	1.25950i
$834$	1.11297e42			0.489301
$835$	−2.29147e41	−	3.96894e41i	−0.0990057	−	0.171483i
$836$	3.89412e39	−	6.74481e39i	0.00165355	−	0.00286404i
$837$	−4.46036e40	+	7.72557e40i	−0.0186145	+	0.0322412i
$838$	−3.08465e41	−	5.34276e41i	−0.126522	−	0.219143i
$839$	−1.16518e42			−0.469727			−0.234863	−	0.972028i	$-0.575464\pi$
$839$	−1.16518e42			−0.469727			−0.234863	+	0.972028i	$0.575464\pi$
$840$	1.45678e42	+	1.26798e41i	0.577225	+	0.0502417i
$841$	−2.38496e42			−0.928835
$842$	9.62805e41	+	1.66763e42i	0.368564	+	0.638371i
$843$	−5.29006e41	+	9.16265e41i	−0.199049	+	0.344764i
$844$	1.47424e42	−	2.55345e42i	0.545258	−	0.944414i
$845$	−1.76279e42	−	3.05324e42i	−0.640881	−	1.11004i
$846$	−2.11972e41			−0.0757544
$847$	1.19851e42	+	2.56722e42i	0.421047	+	0.901890i
$848$	5.18452e41			0.179048
$849$	1.00640e42	+	1.74314e42i	0.341672	+	0.591793i
$850$	−6.99784e41	+	1.21206e42i	−0.233555	+	0.404529i
$851$	2.62246e42	−	4.54224e42i	0.860460	−	1.49036i
$852$	3.26693e41	+	5.65849e41i	0.105382	+	0.182527i
$853$	−4.18452e41			−0.132704			−0.0663521	−	0.997796i	$-0.521136\pi$
$853$	−4.18452e41			−0.132704			−0.0663521	+	0.997796i	$0.521136\pi$
$854$	1.52746e41	−	2.18351e41i	0.0476245	−	0.0680793i
$855$	8.31422e40			0.0254866
$856$	1.70804e42	+	2.95841e42i	0.514788	+	0.891639i
$857$	−2.93332e42	+	5.08067e42i	−0.869237	+	1.50556i	−0.00645914	+	0.999979i	$0.502056\pi$
$857$	−2.93332e42	+	5.08067e42i	−0.869237	+	1.50556i	−0.862778	+	0.505583i	$0.831277\pi$
$858$	−2.30265e39	+	3.98830e39i	−0.000670906	+	0.00116204i
$859$	3.14906e42	+	5.45434e42i	0.902154	+	1.56258i	0.824693	+	0.565581i	$0.191348\pi$
$859$	3.14906e42	+	5.45434e42i	0.902154	+	1.56258i	0.0774616	+	0.996995i	$0.475318\pi$
$860$	−5.83894e42			−1.64477
$861$	1.54361e42	−	2.20660e42i	0.427556	−	0.611192i
$862$	−1.34742e42			−0.366985
$863$	−1.80154e42	−	3.12036e42i	−0.482489	−	0.835696i	0.517308	−	0.855799i	$-0.326934\pi$
$863$	−1.80154e42	−	3.12036e42i	−0.482489	−	0.835696i	−0.999798	+	0.0201028i	$0.993601\pi$
$864$	−3.59905e41	+	6.23373e41i	−0.0947847	+	0.164172i
$865$	2.81036e42	−	4.86768e42i	0.727827	−	1.26063i
$866$	5.31499e41	+	9.20583e41i	0.135361	+	0.234452i
$867$	−3.91713e42			−0.981049
$868$	−2.71302e41	−	5.81134e41i	−0.0668217	−	0.143133i
$869$	4.37721e41			0.106026
$870$	1.78593e41	+	3.09332e41i	0.0425437	+	0.0736878i
$871$	−2.58968e41	+	4.48545e41i	−0.0606711	+	0.105086i
$872$	1.57393e42	−	2.72612e42i	0.362657	−	0.628140i
$873$	−1.76011e41	−	3.04860e41i	−0.0398871	−	0.0690865i
$874$	1.85925e41			0.0414402
$875$	1.97053e42	+	1.71515e41i	0.431982	+	0.0375997i
$876$	−2.53626e42			−0.546869
$877$	3.33124e42	+	5.76987e42i	0.706499	+	1.22369i	0.966148	+	0.257988i	$0.0830597\pi$
$877$	3.33124e42	+	5.76987e42i	0.706499	+	1.22369i	−0.259649	+	0.965703i	$0.583607\pi$
$878$	8.42070e41	−	1.45851e42i	0.175662	−	0.304255i
$879$	−7.51910e40	+	1.30235e41i	−0.0154286	+	0.0267232i
$880$	−1.05527e41	−	1.82778e41i	−0.0212993	−	0.0368915i
$881$	−8.51444e42			−1.69046			−0.845231	−	0.534400i	$-0.820537\pi$
$881$	−8.51444e42			−1.69046			−0.845231	+	0.534400i	$0.820537\pi$
$882$	4.69372e41	−	5.60388e41i	0.0916690	−	0.109445i
$883$	3.13840e42			0.602946			0.301473	−	0.953475i	$-0.402522\pi$
$883$	3.13840e42			0.602946			0.301473	+	0.953475i	$0.402522\pi$
$884$	2.81889e41	+	4.88245e41i	0.0532745	+	0.0922742i
$885$	−2.32999e42	+	4.03567e42i	−0.433189	+	0.750305i
$886$	−1.37208e42	+	2.37652e42i	−0.250953	+	0.434663i
$887$	−6.27180e41	−	1.08631e42i	−0.112850	−	0.195461i	0.804069	−	0.594537i	$-0.202664\pi$
$887$	−6.27180e41	−	1.08631e42i	−0.112850	−	0.195461i	−0.916918	+	0.399075i	$0.869331\pi$
$888$	2.67530e42			0.473570
$889$	−8.99260e41	−	7.82717e40i	−0.156607	−	0.0136310i
$890$	−2.22660e42			−0.381493
$891$	2.25181e40	+	3.90025e40i	0.00379581	+	0.00657454i
$892$	−1.01509e42	+	1.75819e42i	−0.168350	+	0.291591i
$893$	9.63798e40	−	1.66935e41i	0.0157268	−	0.0272396i
$894$	4.04176e41	+	7.00053e41i	0.0648897	+	0.112392i
$895$	−1.48339e43			−2.34326
$896$	−2.75254e42	−	5.89600e42i	−0.427827	−	0.916413i
$897$	4.89410e41			0.0748484
$898$	1.21618e42	+	2.10649e42i	0.183017	+	0.316996i
$899$	1.74253e41	−	3.01815e41i	0.0258027	−	0.0446916i
$900$	6.20040e41	−	1.07394e42i	0.0903448	−	0.156482i
$901$	2.12229e42	+	3.67592e42i	0.304295	+	0.527055i
$902$	2.67947e41			0.0378054
$903$	−3.72207e42	+	5.32071e42i	−0.516788	+	0.738750i
$904$	1.75843e42			0.240260
$905$	8.66155e42	+	1.50022e43i	1.16464	+	2.01721i
$906$	−4.98184e41	+	8.62880e41i	−0.0659221	+	0.114180i
$907$	1.90879e42	−	3.30611e42i	0.248572	−	0.430539i	−0.714558	−	0.699576i	$-0.753372\pi$
$907$	1.90879e42	−	3.30611e42i	0.248572	−	0.430539i	0.963130	+	0.269037i	$0.0867055\pi$
$908$	3.51680e41	+	6.09128e41i	0.0450716	+	0.0780663i
$909$	4.77858e41			0.0602730
$910$	2.02603e41	−	2.89622e41i	0.0251505	−	0.0359526i
$911$	−2.39559e42			−0.292682			−0.146341	−	0.989234i	$-0.546750\pi$
$911$	−2.39559e42			−0.292682			−0.146341	+	0.989234i	$0.546750\pi$
$912$	−6.87821e40	−	1.19134e41i	−0.00827085	−	0.0143255i
$913$	−2.54613e41	+	4.41003e41i	−0.0301339	+	0.0521934i
$914$	6.64619e41	−	1.15115e42i	0.0774199	−	0.134095i
$915$	−6.30011e41	−	1.09121e42i	−0.0722341	−	0.125113i
$916$	−1.05938e43			−1.19555
$917$	−2.05395e42	−	4.39959e42i	−0.228157	−	0.488717i
$918$	−1.23850e42			−0.135418
$919$	5.13270e42	+	8.89010e42i	0.552422	+	0.956824i	0.998099	+	0.0616297i	$0.0196298\pi$
$919$	5.13270e42	+	8.89010e42i	0.552422	+	0.956824i	−0.445677	+	0.895194i	$0.647037\pi$
$920$	7.73114e42	−	1.33907e43i	0.819069	−	1.41867i
$921$	−2.57194e42	+	4.45473e42i	−0.268223	+	0.464576i
$922$	1.43980e42	+	2.49382e42i	0.147810	+	0.256015i
$923$	3.51339e41			0.0355060
$924$	−3.22562e41	−	2.80758e40i	−0.0320900	−	0.00279312i
$925$	−7.14616e42			−0.699870
$926$	−4.93548e41	−	8.54850e41i	−0.0475850	−	0.0824196i
$927$	−1.54380e42	+	2.67395e42i	−0.146533	+	0.253803i
$928$	1.40604e42	−	2.43534e42i	0.131387	−	0.227569i
$929$	−2.59361e42	−	4.49226e42i	−0.238603	−	0.413273i	0.721710	−	0.692195i	$-0.243356\pi$
$929$	−2.59361e42	−	4.49226e42i	−0.238603	−	0.413273i	−0.960314	+	0.278922i	$0.910023\pi$
$930$	6.81237e41			0.0617014
$931$	2.27909e41	+	6.24444e41i	0.0203232	+	0.0556831i
$932$	−1.03425e43			−0.908022
$933$	4.63105e42	+	8.02121e42i	0.400309	+	0.693355i
$934$	−3.66261e42	+	6.34383e42i	−0.311717	+	0.539910i
$935$	8.63954e41	−	1.49641e42i	0.0723973	−	0.125396i
$936$	1.24818e41	+	2.16190e41i	0.0102985	+	0.0178376i
$937$	1.23213e42			0.100099			0.0500497	−	0.998747i	$-0.484062\pi$
$937$	1.23213e42			0.100099			0.0500497	+	0.998747i	$0.484062\pi$
$938$	8.14919e42	+	7.09306e41i	0.651889	+	0.0567404i
$939$	8.16845e42			0.643411
$940$	−3.60299e42	−	6.24056e42i	−0.279453	−	0.484027i
$941$	−8.74773e42	+	1.51515e43i	−0.668107	+	1.15719i	0.310326	+	0.950630i	$0.399562\pi$
$941$	−8.74773e42	+	1.51515e43i	−0.668107	+	1.15719i	−0.978433	+	0.206564i	$0.933772\pi$
$942$	7.72768e41	−	1.33847e42i	0.0581181	−	0.100663i
$943$	−1.42375e43	−	2.46601e43i	−1.05442	−	1.82631i
$944$	7.71025e42			0.562309
$945$	−1.46217e42	−	3.13199e42i	−0.105011	−	0.224936i
$946$	−6.46093e41			−0.0456955
$947$	7.75853e41	+	1.34382e42i	0.0540387	+	0.0935977i	0.891779	−	0.452471i	$-0.149457\pi$
$947$	7.75853e41	+	1.34382e42i	0.0540387	+	0.0935977i	−0.837741	+	0.546068i	$0.816124\pi$
$948$	5.33281e42	−	9.23670e42i	0.365793	−	0.633572i
$949$	−6.81898e41	+	1.18108e42i	−0.0460638	+	0.0797848i
$950$	−1.26660e41	−	2.19382e41i	−0.00842652	−	0.0145952i
$951$	1.01057e43			0.662139
$952$	1.13543e43	−	1.62310e43i	0.732696	−	1.04739i
$953$	8.82976e42			0.561180			0.280590	−	0.959828i	$-0.409470\pi$
$953$	8.82976e42			0.561180			0.280590	+	0.959828i	$0.409470\pi$
$954$	4.22419e41	+	7.31652e41i	0.0264419	+	0.0457987i
$955$	−5.76321e42	+	9.98218e42i	−0.355317	+	0.615427i
$956$	9.59683e42	−	1.66222e43i	0.582758	−	1.00937i
$957$	−8.79716e40	−	1.52371e41i	−0.00526162	−	0.00911339i
$958$	−1.22711e43			−0.722908
$959$	1.52945e43	−	2.18635e43i	0.887495	−	1.26868i
$960$	−8.00947e41			−0.0457795
$961$	8.54860e42	+	1.48066e43i	0.481289	+	0.833617i
$962$	3.23325e41	−	5.60015e41i	0.0179308	−	0.0310571i
$963$	4.03737e42	−	6.99294e42i	0.220556	−	0.382013i
$964$	−7.93165e42	−	1.37380e43i	−0.426822	−	0.739277i
$965$	−3.32762e43			−1.76396
$966$	−3.26974e42	−	7.00384e42i	−0.170744	−	0.365736i
$967$	1.65732e43			0.852553			0.426277	−	0.904593i	$-0.359825\pi$
$967$	1.65732e43			0.852553			0.426277	+	0.904593i	$0.359825\pi$
$968$	7.64047e42	+	1.32337e43i	0.387193	+	0.670638i
$969$	5.63122e41	−	9.75355e41i	0.0281130	−	0.0486932i
$970$	−1.34412e42	+	2.32808e42i	−0.0661070	+	0.114501i
$971$	1.58960e43	+	2.75327e43i	0.770210	+	1.33404i	0.937447	+	0.348127i	$0.113182\pi$
$971$	1.58960e43	+	2.75327e43i	0.770210	+	1.33404i	−0.167237	+	0.985917i	$0.553484\pi$
$972$	1.09736e42			0.0523829
$973$	4.19176e43	+	3.64851e42i	1.97133	+	0.171585i
$974$	−1.49321e43			−0.691856
$975$	−3.33408e41	−	5.77480e41i	−0.0152198	−	0.0263615i
$976$	−1.04240e42	+	1.80548e42i	−0.0468824	+	0.0812027i
$977$	−1.28431e43	+	2.22449e43i	−0.569112	+	0.985731i	0.427542	+	0.903996i	$0.359380\pi$
$977$	−1.28431e43	+	2.22449e43i	−0.569112	+	0.985731i	−0.996654	+	0.0817358i	$0.973954\pi$
$978$	−2.31397e42	−	4.00791e42i	−0.101028	−	0.174986i
$979$	1.09678e42			0.0471814
$980$	2.44763e43	+	4.29336e42i	1.03745	+	0.181978i
$981$	−7.44073e42			−0.310753
$982$	−1.72298e42	−	2.98429e42i	−0.0709028	−	0.122807i
$983$	5.95889e42	−	1.03211e43i	0.241624	−	0.418504i	−0.719553	−	0.694437i	$-0.755653\pi$
$983$	5.95889e42	−	1.03211e43i	0.241624	−	0.418504i	0.961177	+	0.275933i	$0.0889867\pi$
$984$	7.26217e42	−	1.25784e43i	0.290160	−	0.502572i
$985$	−2.55324e43	−	4.42234e43i	−1.00523	−	1.74111i
$986$	4.83844e42			0.187711
$987$	−7.98345e42	−	6.94880e41i	−0.305205	−	0.0265651i
$988$	−1.02043e41			−0.00384422
$989$	3.43305e43	+	5.94621e43i	1.27448	+	2.20747i
$990$	1.71961e41	−	2.97845e41i	0.00629099	−	0.0108963i
$991$	8.80558e42	−	1.52517e43i	0.317461	−	0.549858i	−0.662497	−	0.749065i	$-0.730503\pi$
$991$	8.80558e42	−	1.52517e43i	0.317461	−	0.549858i	0.979957	+	0.199207i	$0.0638365\pi$
$992$	−2.68165e42	−	4.64475e42i	−0.0952759	−	0.165023i
$993$	−1.47551e43			−0.516627
$994$	−2.34729e42	−	5.02794e42i	−0.0809962	−	0.173495i
$995$	−3.45764e43			−1.17583
$996$	6.20397e42	+	1.07456e43i	0.207926	+	0.360139i
$997$	1.91103e43	−	3.31001e43i	0.631232	−	1.09333i	−0.356069	−	0.934460i	$-0.615883\pi$
$997$	1.91103e43	−	3.31001e43i	0.631232	−	1.09333i	0.987300	−	0.158865i	$-0.0507836\pi$
$998$	−8.10597e42	+	1.40400e43i	−0.263884	+	0.457060i
$999$	−3.16186e42	−	5.47651e42i	−0.101448	−	0.175713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.a.4.12	✓	38
7.2	even	3	inner	21.30.e.a.16.12	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.a.4.12	✓	38	1.1	even	1	trivial
21.30.e.a.16.12	yes	38	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4961.84 + 8594.16i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.19196e8 - 3.79658e8i) q^{4} +(8.80219e9 + 1.52458e10i) q^{5} +4.74646e10 q^{6} +(1.78765e12 + 1.55597e11i) q^{7} +9.67819e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(4961.84 + 8594.16i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.19196e8 - 3.79658e8i) q^{4} +(8.80219e9 + 1.52458e10i) q^{5} +4.74646e10 q^{6} +(1.78765e12 + 1.55597e11i) q^{7} +9.67819e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-8.73501e13 + 1.51295e14i) q^{10} +(4.30270e13 - 7.45250e13i) q^{11} +(-1.04841e15 - 1.81589e15i) q^{12} -1.12750e15 q^{13} +(7.53281e15 + 1.61354e16i) q^{14} +8.42012e16 q^{15} +(-6.96582e16 - 1.20652e17i) q^{16} +(5.70294e17 - 9.87779e17i) q^{17} +(1.13511e17 - 1.96607e17i) q^{18} +(1.03223e17 + 1.78787e17i) q^{19} +7.71761e18 q^{20} +(4.91965e18 - 7.03265e18i) q^{21} +8.53972e17 q^{22} +(-4.53763e19 - 7.85940e19i) q^{23} +(2.31452e19 - 4.00887e19i) q^{24} +(-6.18247e19 + 1.07084e20i) q^{25} +(-5.59447e18 - 9.68991e18i) q^{26} -1.09419e20 q^{27} +(4.50919e20 - 6.44590e20i) q^{28} +4.27468e20 q^{29} +(4.17793e20 + 7.23638e20i) q^{30} +(4.07640e20 - 7.06054e20i) q^{31} +(3.28924e21 - 5.69712e21i) q^{32} +(-2.05797e20 - 3.56451e20i) q^{33} +1.13188e22 q^{34} +(1.33630e22 + 2.86238e22i) q^{35} -1.00290e22 q^{36} +(2.88968e22 + 5.00508e22i) q^{37} +(-1.02435e21 + 1.77423e21i) q^{38} +(-2.69640e21 + 4.67030e21i) q^{39} +(8.51892e22 + 1.47552e23i) q^{40} +3.13765e23 q^{41} +(8.48502e22 + 7.38537e21i) q^{42} -7.56573e23 q^{43} +(-1.88627e22 - 3.26711e22i) q^{44} +(2.01366e23 - 3.48776e23i) q^{45} +(4.50300e23 - 7.79942e23i) q^{46} +(-4.66853e23 - 8.08613e23i) q^{47} -6.66346e23 q^{48} +(3.17148e24 + 5.56307e23i) q^{49} -1.22706e24 q^{50} +(-2.72770e24 - 4.72451e24i) q^{51} +(-2.47143e23 + 4.28064e23i) q^{52} +(-1.86070e24 + 3.22282e24i) q^{53} +(-5.42919e23 - 9.40364e23i) q^{54} +1.51493e24 q^{55} +(1.73012e25 + 1.50590e24i) q^{56} +9.87423e23 q^{57} +(2.12103e24 + 3.67373e24i) q^{58} +(-2.76717e25 + 4.79289e25i) q^{59} +(1.84565e25 - 3.19677e25i) q^{60} +(-7.48221e24 - 1.29596e25i) q^{61} +8.09058e24 q^{62} +(-1.73652e25 - 3.71965e25i) q^{63} -9.51231e24 q^{64} +(-9.92446e24 - 1.71897e25i) q^{65} +(2.04226e24 - 3.53730e24i) q^{66} +(2.29683e26 - 3.97823e26i) q^{67} +(-2.50012e26 - 4.33034e26i) q^{68} -4.34067e26 q^{69} +(-1.79692e26 + 2.56871e26i) q^{70} -3.11609e26 q^{71} +(-1.10703e26 - 1.91743e26i) q^{72} +(6.04788e26 - 1.04752e27i) q^{73} +(-2.86763e26 + 4.96688e26i) q^{74} +(2.95706e26 + 5.12177e26i) q^{75} +9.05040e25 q^{76} +(8.85131e25 - 1.26530e26i) q^{77} -5.35164e25 q^{78} +(2.54329e27 + 4.40511e27i) q^{79} +(1.22629e27 - 2.12399e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(1.55685e27 + 2.69655e27i) q^{82} -5.91753e27 q^{83} +(-1.59164e27 - 3.40931e27i) q^{84} +2.00793e28 q^{85} +(-3.75399e27 - 6.50211e27i) q^{86} +(1.02228e27 - 1.77065e27i) q^{87} +(4.16424e26 - 7.21267e26i) q^{88} +(6.37262e27 + 1.10377e28i) q^{89} +3.99658e27 q^{90} +(-2.01557e27 - 1.75436e26i) q^{91} -3.97852e28 q^{92} +(-1.94973e27 - 3.37703e27i) q^{93} +(4.63290e27 - 8.02442e27i) q^{94} +(-1.81717e27 + 3.14744e27i) q^{95} +(-1.57323e28 - 2.72492e28i) q^{96} +1.53877e28 q^{97} +(1.09554e28 + 3.00165e28i) q^{98} -1.96864e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9}+O(q^{10}) \) 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9	\( 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9} - 226333527764279 q^{10} + 968182184010316 q^{11} + 26\!\cdots\!77 q^{12}+ \cdots - 44\!\cdots\!52 q^{99}+O(q^{100}) \) 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9 - 226333527764279 * q^10 + 968182184010316 * q^11 + 26060407088843277 * q^12 + 30248752986495458 * q^13 + 188292059868669736 * q^14 - 20103696649657764 * q^15 - 1414287713687569841 * q^16 + 102438111755912556 * q^17 + 572491731185399025 * q^18 - 6872193027481150651 * q^19 + 16866263496288505610 * q^20 - 5139459612060640272 * q^21 + 84243517982597870158 * q^22 + 182508386582843064516 * q^23 - 128758913948422543095 * q^24 - 382162743635168213111 * q^25 + 273922968110752759988 * q^26 - 4157921586997469649942 * q^27 + 446171481016036543439 * q^28 + 281390518253865391744 * q^29 + 1082546246957185764351 * q^30 - 4929614086953636263583 * q^31 + 8866445878410226322935 * q^32 - 4630785372473637108204 * q^33 + 50361339344572132704984 * q^34 - 81794408570709523734766 * q^35 + 249292238466635279498826 * q^36 + 89823590712918979606269 * q^37 - 71913737995612310138956 * q^38 + 72339423911532597127401 * q^39 + 239411588777146294644135 * q^40 - 87942011922863277796324 * q^41 + 42507596433452096284317 * q^42 - 998334377830130582257058 * q^43 - 273085832669135222196817 * q^44 - 48077678930358472910658 * q^45 + 1477208812031594497944852 * q^46 + 663752760815551395364602 * q^47 - 13528988583297044469675858 * q^48 + 12702719376591835722353537 * q^49 - 18072517907683707274881248 * q^50 - 489958312947065322058764 * q^51 + 31739881554208954447778464 * q^52 - 7756933906079396951027112 * q^53 - 2738210203016096789205225 * q^54 + 104982116314469285161107056 * q^55 + 43372930131234039576619953 * q^56 - 65738972424916983296125638 * q^57 + 102453432804996437331910603 * q^58 + 114603050264779854082124610 * q^59 + 40335407724289768694478045 * q^60 - 139825411428909464532671986 * q^61 + 1134093332259905081074973442 * q^62 + 1666599266299329474494571 * q^63 - 148837669255394086765278622 * q^64 + 640556086591054006830698254 * q^65 + 201467067480854076215869551 * q^66 - 56315776880006609951132917 * q^67 - 697317633686048315259709452 * q^68 + 1745863910531508618890056008 * q^69 + 433002366057136467231968657 * q^70 - 1824065145665995608812965764 * q^71 + 615849893888972622524549055 * q^72 + 1789614217588580556564713367 * q^73 - 4257059926604086801593103848 * q^74 + 1827872555761956873095306559 * q^75 + 15166984931487860090924899312 * q^76 + 6892418991139201958931374756 * q^77 + 2620330129723438035374088744 * q^78 + 3126227451212705816416145239 * q^79 + 469705326396281168184173015 * q^80 - 9943605027519850207056718899 * q^81 - 15954412288094954111486068024 * q^82 + 12686840070702737045002032792 * q^83 - 10284086370388485211004655396 * q^84 + 280144859318398185224279400 * q^85 + 14385045580944496750492040974 * q^86 + 672941062851086149442203968 * q^87 - 20844393366380736578332102317 * q^88 - 26279447891842894095818723312 * q^89 + 10355570280525127676264276238 * q^90 - 22701798036712589137512005879 * q^91 - 374697938227250791106256400776 * q^92 + 23578191359862546685993317927 * q^93 + 73717519436348854656628916898 * q^94 - 56410666407609081482857118294 * q^95 - 42407935776613881785582094015 * q^96 + 235542920591717835435096218928 * q^97 - 293433749500426066164790446415 * q^98 - 44297805764389719211578755352 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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