LMFDB - Embedded newform 21.30.e.a.4.9

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			4.9
Character	$\chi$	$=$	21.4
Dual form			21.30.e.a.16.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-803.934 - 1392.45i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.67143e8 - 4.62705e8i) q^{4} +(-1.04266e10 - 1.80594e10i) q^{5} -7.69038e9 q^{6} +(-3.52235e11 - 1.75950e12i) q^{7} -1.72228e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(-803.934 - 1392.45i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.67143e8 - 4.62705e8i) q^{4} +(-1.04266e10 - 1.80594e10i) q^{5} -7.69038e9 q^{6} +(-3.52235e11 - 1.75950e12i) q^{7} -1.72228e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-1.67646e13 + 2.90371e13i) q^{10} +(-3.05162e14 + 5.28556e14i) q^{11} +(-1.27774e15 - 2.21310e15i) q^{12} +9.53587e15 q^{13} +(-2.16685e15 + 1.90499e15i) q^{14} -9.97400e16 q^{15} +(-1.42037e17 - 2.46015e17i) q^{16} +(-2.54568e17 + 4.40924e17i) q^{17} +(-1.83914e16 + 3.18549e16i) q^{18} +(1.10068e18 + 1.90643e18i) q^{19} -1.11415e19 q^{20} +(-8.13051e18 - 2.74879e18i) q^{21} +9.81319e17 q^{22} +(-2.69706e19 - 4.67144e19i) q^{23} +(-4.11880e18 + 7.13397e18i) q^{24} +(-1.24295e20 + 2.15285e20i) q^{25} +(-7.66621e18 - 1.32783e19i) q^{26} -1.09419e20 q^{27} +(-9.08226e20 - 3.07056e20i) q^{28} -1.65041e21 q^{29} +(8.01844e19 + 1.38883e20i) q^{30} +(-1.55382e21 + 2.69129e21i) q^{31} +(-6.90696e20 + 1.19632e21i) q^{32} +(1.45958e21 + 2.52807e21i) q^{33} +8.18622e20 q^{34} +(-2.81028e22 + 2.47067e22i) q^{35} -1.22227e22 q^{36} +(3.28745e22 + 5.69403e22i) q^{37} +(1.76975e21 - 3.06529e21i) q^{38} +(2.28049e22 - 3.94992e22i) q^{39} +(1.79575e22 + 3.11032e22i) q^{40} +2.39899e23 q^{41} +(2.70882e21 + 1.35312e22i) q^{42} -2.07201e23 q^{43} +(1.63044e23 + 2.82400e23i) q^{44} +(-2.38527e23 + 4.13140e23i) q^{45} +(-4.33651e22 + 7.51105e22i) q^{46} +(-1.41206e24 - 2.44577e24i) q^{47} -1.35871e24 q^{48} +(-2.97177e24 + 1.23952e24i) q^{49} +3.99700e23 q^{50} +(1.21759e24 + 2.10893e24i) q^{51} +(2.54744e24 - 4.41229e24i) q^{52} +(-2.46572e24 + 4.27076e24i) q^{53} +(8.79656e22 + 1.52361e23i) q^{54} +1.27272e25 q^{55} +(6.06647e23 + 3.03035e24i) q^{56} +1.05290e25 q^{57} +(1.32682e24 + 2.29812e24i) q^{58} +(2.68601e25 - 4.65231e25i) q^{59} +(-2.66448e25 + 4.61502e25i) q^{60} +(3.45724e25 + 5.98811e25i) q^{61} +4.99667e24 q^{62} +(-3.08300e25 + 2.71043e25i) q^{63} -1.50290e26 q^{64} +(-9.94265e25 - 1.72212e26i) q^{65} +(2.34681e24 - 4.06479e24i) q^{66} +(1.57843e26 - 2.73393e26i) q^{67} +(1.36012e26 + 2.35579e26i) q^{68} -2.57999e26 q^{69} +(5.69958e25 + 1.92693e25i) q^{70} -5.45935e26 q^{71} +(1.97001e25 + 3.41216e25i) q^{72} +(8.35972e26 - 1.44795e27i) q^{73} +(5.28579e25 - 9.15525e25i) q^{74} +(5.94499e26 + 1.02970e27i) q^{75} +1.17616e27 q^{76} +(1.03748e27 + 3.50756e26i) q^{77} -7.33344e25 q^{78} +(-3.38279e26 - 5.85917e26i) q^{79} +(-2.96191e27 + 5.13018e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-1.92863e26 - 3.34048e26i) q^{82} -6.90164e27 q^{83} +(-3.44389e27 + 3.02771e27i) q^{84} +1.06171e28 q^{85} +(1.66576e26 + 2.88518e26i) q^{86} +(-3.94693e27 + 6.83629e27i) q^{87} +(5.25573e26 - 9.10320e26i) q^{88} +(1.83967e27 + 3.18640e27i) q^{89} +7.67039e26 q^{90} +(-3.35887e27 - 1.67783e28i) q^{91} -2.88200e28 q^{92} +(7.43187e27 + 1.28724e28i) q^{93} +(-2.27041e27 + 3.93247e27i) q^{94} +(2.29527e28 - 3.97552e28i) q^{95} +(3.30358e27 + 5.72197e27i) q^{96} +4.48488e28 q^{97} +(4.11507e27 + 3.14156e27i) q^{98} +1.39622e28 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 $

$2$	−803.934	−	1392.45i	−0.0346965	−	0.0600960i	0.848156	−	0.529747i	$-0.177713\pi$
$2$	−803.934	−	1392.45i	−0.0346965	−	0.0600960i	−0.882852	+	0.469651i	$0.844380\pi$
$3$	2.39148e6	−	4.14217e6i	0.288675	−	0.500000i
$3$	2.39148e6	−	4.14217e6i	0.288675	−	0.500000i
$4$	2.67143e8	−	4.62705e8i	0.497592	−	0.861855i
$5$	−1.04266e10	−	1.80594e10i	−0.763971	−	1.32324i	−0.940789	−	0.338993i	$-0.889914\pi$
$5$	−1.04266e10	−	1.80594e10i	−0.763971	−	1.32324i	0.176818	−	0.984244i	$-0.443420\pi$
$6$	−7.69038e9			−0.0400640
$7$	−3.52235e11	−	1.75950e12i	−0.196296	−	0.980545i
$7$	−3.52235e11	−	1.75950e12i	−0.196296	−	0.980545i
$8$	−1.72228e12			−0.138452
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	−1.67646e13	+	2.90371e13i	−0.0530142	+	0.0918233i
$11$	−3.05162e14	+	5.28556e14i	−0.242290	+	0.419659i	−0.961366	−	0.275272i	$-0.911232\pi$
$11$	−3.05162e14	+	5.28556e14i	−0.242290	+	0.419659i	0.719076	+	0.694932i	$0.244565\pi$
$12$	−1.27774e15	−	2.21310e15i	−0.287285	−	0.497592i
$13$	9.53587e15			0.671710			0.335855	−	0.941914i	$-0.390975\pi$
$13$	9.53587e15			0.671710			0.335855	+	0.941914i	$0.390975\pi$
$14$	−2.16685e15	+	1.90499e15i	−0.0521161	+	0.0458180i
$15$	−9.97400e16			−0.882158
$16$	−1.42037e17	−	2.46015e17i	−0.492789	−	0.853535i
$17$	−2.54568e17	+	4.40924e17i	−0.366685	+	0.635118i	−0.989045	−	0.147614i	$-0.952841\pi$
$17$	−2.54568e17	+	4.40924e17i	−0.366685	+	0.635118i	0.622360	+	0.782731i	$0.286174\pi$
$18$	−1.83914e16	+	3.18549e16i	−0.0115655	+	0.0200320i
$19$	1.10068e18	+	1.90643e18i	0.316034	+	0.547387i	0.979657	−	0.200680i	$-0.0643153\pi$
$19$	1.10068e18	+	1.90643e18i	0.316034	+	0.547387i	−0.663623	+	0.748067i	$0.730982\pi$
$20$	−1.11415e19			−1.52058
$21$	−8.13051e18	−	2.74879e18i	−0.546938	−	0.184911i
$22$	9.81319e17			0.0336265
$23$	−2.69706e19	−	4.67144e19i	−0.485106	−	0.840228i	0.514748	−	0.857342i	$-0.327886\pi$
$23$	−2.69706e19	−	4.67144e19i	−0.485106	−	0.840228i	−0.999854	+	0.0171138i	$0.994552\pi$
$24$	−4.11880e18	+	7.13397e18i	−0.0399676	+	0.0692259i
$25$	−1.24295e20	+	2.15285e20i	−0.667303	+	1.15580i
$26$	−7.66621e18	−	1.32783e19i	−0.0233060	−	0.0403671i
$27$	−1.09419e20			−0.192450
$28$	−9.08226e20	−	3.07056e20i	−0.942763	−	0.318733i
$29$	−1.65041e21			−1.02996			−0.514981	−	0.857202i	$-0.672201\pi$
$29$	−1.65041e21			−1.02996			−0.514981	+	0.857202i	$0.672201\pi$
$30$	8.01844e19	+	1.38883e20i	0.0306078	+	0.0530142i
$31$	−1.55382e21	+	2.69129e21i	−0.368686	+	0.638582i	−0.989360	−	0.145486i	$-0.953525\pi$
$31$	−1.55382e21	+	2.69129e21i	−0.368686	+	0.638582i	0.620675	+	0.784068i	$0.286859\pi$
$32$	−6.90696e20	+	1.19632e21i	−0.103422	+	0.179132i
$33$	1.45958e21	+	2.52807e21i	0.139886	+	0.242290i
$34$	8.18622e20			0.0508908
$35$	−2.81028e22	+	2.47067e22i	−1.14753	+	1.00885i
$36$	−1.22227e22			−0.331728
$37$	3.28745e22	+	5.69403e22i	0.599701	+	1.03871i	0.992865	+	0.119244i	$0.0380470\pi$
$37$	3.28745e22	+	5.69403e22i	0.599701	+	1.03871i	−0.393164	+	0.919468i	$0.628620\pi$
$38$	1.76975e21	−	3.06529e21i	0.0219305	−	0.0379848i
$39$	2.28049e22	−	3.94992e22i	0.193906	−	0.335855i
$40$	1.79575e22	+	3.11032e22i	0.105773	+	0.183204i
$41$	2.39899e23			0.987784			0.493892	−	0.869523i	$-0.335574\pi$
$41$	2.39899e23			0.987784			0.493892	+	0.869523i	$0.335574\pi$
$42$	2.70882e21	+	1.35312e22i	0.00786441	+	0.0392846i
$43$	−2.07201e23			−0.427661			−0.213830	−	0.976871i	$-0.568594\pi$
$43$	−2.07201e23			−0.427661			−0.213830	+	0.976871i	$0.568594\pi$
$44$	1.63044e23	+	2.82400e23i	0.241124	+	0.417639i
$45$	−2.38527e23	+	4.13140e23i	−0.254657	+	0.441079i
$46$	−4.33651e22	+	7.51105e22i	−0.0336629	+	0.0583059i
$47$	−1.41206e24	−	2.44577e24i	−0.802483	−	1.38994i	−0.917977	−	0.396633i	$-0.870179\pi$
$47$	−1.41206e24	−	2.44577e24i	−0.802483	−	1.38994i	0.115495	−	0.993308i	$-0.463155\pi$
$48$	−1.35871e24			−0.569023
$49$	−2.97177e24	+	1.23952e24i	−0.922936	+	0.384954i
$50$	3.99700e23			0.0926123
$51$	1.21759e24	+	2.10893e24i	0.211706	+	0.366685i
$52$	2.54744e24	−	4.41229e24i	0.334238	−	0.578916i
$53$	−2.46572e24	+	4.27076e24i	−0.245439	+	0.425114i	−0.962255	−	0.272149i	$-0.912266\pi$
$53$	−2.46572e24	+	4.27076e24i	−0.245439	+	0.425114i	0.716816	+	0.697263i	$0.245599\pi$
$54$	8.79656e22	+	1.52361e23i	0.00667734	+	0.0115655i
$55$	1.27272e25			0.740411
$56$	6.06647e23	+	3.03035e24i	0.0271775	+	0.135758i
$57$	1.05290e25			0.364925
$58$	1.32682e24	+	2.29812e24i	0.0357360	+	0.0618966i
$59$	2.68601e25	−	4.65231e25i	0.564616	−	0.977944i	−0.432469	−	0.901649i	$-0.642357\pi$
$59$	2.68601e25	−	4.65231e25i	0.564616	−	0.977944i	0.997085	−	0.0762953i	$-0.0243092\pi$
$60$	−2.66448e25	+	4.61502e25i	−0.438955	+	0.760292i
$61$	3.45724e25	+	5.98811e25i	0.448174	+	0.776260i	0.998267	−	0.0588430i	$-0.0187411\pi$
$61$	3.45724e25	+	5.98811e25i	0.448174	+	0.776260i	−0.550093	+	0.835103i	$0.685408\pi$
$62$	4.99667e24			0.0511683
$63$	−3.08300e25	+	2.71043e25i	−0.250343	+	0.220090i
$64$	−1.50290e26			−0.971224
$65$	−9.94265e25	−	1.72212e26i	−0.513167	−	0.888831i
$66$	2.34681e24	−	4.06479e24i	0.00970713	−	0.0168132i
$67$	1.57843e26	−	2.73393e26i	0.524979	−	0.909290i	−0.474598	−	0.880203i	$-0.657407\pi$
$67$	1.57843e26	−	2.73393e26i	0.524979	−	0.909290i	0.999577	−	0.0290871i	$-0.00926003\pi$
$68$	1.36012e26	+	2.35579e26i	0.364920	+	0.632059i
$69$	−2.57999e26			−0.560152
$70$	5.69958e25	+	1.92693e25i	0.100443	+	0.0339582i
$71$	−5.45935e26			−0.783240			−0.391620	−	0.920127i	$-0.628085\pi$
$71$	−5.45935e26			−0.783240			−0.391620	+	0.920127i	$0.628085\pi$
$72$	1.97001e25	+	3.41216e25i	0.0230753	+	0.0399676i
$73$	8.35972e26	−	1.44795e27i	0.801697	−	1.38858i	−0.116802	−	0.993155i	$-0.537264\pi$
$73$	8.35972e26	−	1.44795e27i	0.801697	−	1.38858i	0.918499	−	0.395424i	$-0.129402\pi$
$74$	5.28579e25	−	9.15525e25i	0.0416150	−	0.0720793i
$75$	5.94499e26	+	1.02970e27i	0.385268	+	0.667303i
$76$	1.17616e27			0.629024
$77$	1.03748e27	+	3.50756e26i	0.459055	+	0.155199i
$78$	−7.33344e25			−0.0269114
$79$	−3.38279e26	−	5.85917e26i	−0.103201	−	0.178749i	0.809801	−	0.586705i	$-0.199575\pi$
$79$	−3.38279e26	−	5.85917e26i	−0.103201	−	0.178749i	−0.913002	+	0.407956i	$0.866242\pi$
$80$	−2.96191e27	+	5.13018e27i	−0.752952	+	1.30415i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	−1.92863e26	−	3.34048e26i	−0.0342726	−	0.0593619i
$83$	−6.90164e27			−1.02877			−0.514387	−	0.857558i	$-0.671981\pi$
$83$	−6.90164e27			−1.02877			−0.514387	+	0.857558i	$0.671981\pi$
$84$	−3.44389e27	+	3.02771e27i	−0.431519	+	0.379371i
$85$	1.06171e28			1.12055
$86$	1.66576e26	+	2.88518e26i	0.0148383	+	0.0257007i
$87$	−3.94693e27	+	6.83629e27i	−0.297324	+	0.514981i
$88$	5.25573e26	−	9.10320e26i	0.0335455	−	0.0581026i
$89$	1.83967e27	+	3.18640e27i	0.0996745	+	0.172641i	0.911550	−	0.411189i	$-0.134887\pi$
$89$	1.83967e27	+	3.18640e27i	0.0996745	+	0.172641i	−0.811875	+	0.583831i	$0.801553\pi$
$90$	7.67039e26			0.0353428
$91$	−3.35887e27	−	1.67783e28i	−0.131854	−	0.658641i
$92$	−2.88200e28			−0.965540
$93$	7.43187e27	+	1.28724e28i	0.212861	+	0.368686i
$94$	−2.27041e27	+	3.93247e27i	−0.0556866	+	0.0964521i
$95$	2.29527e28	−	3.97552e28i	0.482882	−	0.836376i
$96$	3.30358e27	+	5.72197e27i	0.0597107	+	0.103422i
$97$	4.48488e28			0.697527			0.348763	−	0.937211i	$-0.386602\pi$
$97$	4.48488e28			0.697527			0.348763	+	0.937211i	$0.386602\pi$
$98$	4.11507e27	+	3.14156e27i	0.0551568	+	0.0421082i
$99$	1.39622e28			0.161527
$100$	6.64090e28	+	1.15024e29i	0.664090	+	1.15024i
$101$	9.79033e28	−	1.69574e29i	0.847496	−	1.46791i	−0.0359405	−	0.999354i	$-0.511443\pi$
$101$	9.79033e28	−	1.69574e29i	0.847496	−	1.46791i	0.883436	−	0.468552i	$-0.155224\pi$
$102$	1.95772e27	−	3.39087e27i	0.0146909	−	0.0254454i
$103$	3.70385e28	+	6.41526e28i	0.241276	+	0.417902i	0.961078	−	0.276277i	$-0.0891008\pi$
$103$	3.70385e28	+	6.41526e28i	0.241276	+	0.417902i	−0.719802	+	0.694179i	$0.755767\pi$
$104$	−1.64234e28			−0.0929994
$105$	3.51320e28	+	1.75492e29i	0.173164	+	0.864995i
$106$	7.92912e27			0.0340635
$107$	−2.81995e28	−	4.88429e28i	−0.105725	−	0.183120i	0.808309	−	0.588758i	$-0.200383\pi$
$107$	−2.81995e28	−	4.88429e28i	−0.105725	−	0.183120i	−0.914034	+	0.405638i	$0.867050\pi$
$108$	−2.92305e28	+	5.06287e28i	−0.0957617	+	0.165864i
$109$	−2.14845e29	+	3.72122e29i	−0.615801	+	1.06660i	0.374442	+	0.927250i	$0.377834\pi$
$109$	−2.14845e29	+	3.72122e29i	−0.615801	+	1.06660i	−0.990243	+	0.139348i	$0.955499\pi$
$110$	−1.02318e28	−	1.77220e28i	−0.0256897	−	0.0444958i
$111$	3.14476e29			0.692475
$112$	−3.82832e29	+	3.36568e29i	−0.740197	+	0.650747i
$113$	−9.46613e28			−0.160892			−0.0804461	−	0.996759i	$-0.525634\pi$
$113$	−9.46613e28			−0.160892			−0.0804461	+	0.996759i	$0.525634\pi$
$114$	−8.46465e27	−	1.46612e28i	−0.0126616	−	0.0219305i
$115$	−5.62422e29	+	9.74143e29i	−0.741214	+	1.28382i
$116$	−4.40896e29	+	7.63653e29i	−0.512501	+	0.887678i
$117$	−1.09075e29	−	1.88924e29i	−0.111952	−	0.193906i
$118$	−8.63749e28			−0.0783608
$119$	8.65473e29	+	2.92602e29i	0.694740	+	0.234880i
$120$	1.71780e29			0.122136
$121$	6.06907e29	+	1.05119e30i	0.382591	+	0.662667i
$122$	5.55878e28	−	9.62809e28i	0.0311001	−	0.0538670i
$123$	5.73714e29	−	9.93701e29i	0.285149	−	0.493892i
$124$	8.30184e29	+	1.43792e30i	0.366910	+	0.635507i
$125$	1.29968e30			0.511260
$126$	6.25267e28	+	2.11393e28i	0.0219125	+	0.00740827i
$127$	4.59658e30			1.43642			0.718208	−	0.695828i	$-0.244962\pi$
$127$	4.59658e30			1.43642			0.718208	+	0.695828i	$0.244962\pi$
$128$	4.91638e29	+	8.51541e29i	0.137120	+	0.237499i
$129$	−4.95518e29	+	8.58263e29i	−0.123455	+	0.213830i
$130$	−1.59865e29	+	2.76894e29i	−0.0356101	+	0.0616786i
$131$	3.99541e30	+	6.92025e30i	0.796393	+	1.37939i	0.921951	+	0.387307i	$0.126595\pi$
$131$	3.99541e30	+	6.92025e30i	0.796393	+	1.37939i	−0.125558	+	0.992086i	$0.540072\pi$
$132$	1.55966e30			0.278426
$133$	2.96667e30	−	2.60816e30i	0.474701	−	0.417335i
$134$	−5.07582e29			−0.0728596
$135$	1.14087e30	+	1.97604e30i	0.147026	+	0.254657i
$136$	4.38436e29	−	7.59393e29i	0.0507682	−	0.0879331i
$137$	−4.01247e30	+	6.94981e30i	−0.417796	+	0.723643i	−0.995717	−	0.0924489i	$-0.970531\pi$
$137$	−4.01247e30	+	6.94981e30i	−0.417796	+	0.723643i	0.577922	+	0.816092i	$0.303864\pi$
$138$	2.07414e29	+	3.59251e29i	0.0194353	+	0.0336629i
$139$	−1.79174e31			−1.51203			−0.756014	−	0.654556i	$-0.772856\pi$
$139$	−1.79174e31			−1.51203			−0.756014	+	0.654556i	$0.772856\pi$
$140$	3.92445e30	+	1.96035e31i	0.298485	+	1.49100i
$141$	−1.35077e31			−0.926627
$142$	4.38895e29	+	7.60189e29i	0.0271756	+	0.0470696i
$143$	−2.90998e30	+	5.04024e30i	−0.162749	+	0.281889i
$144$	−3.24934e30	+	5.62803e30i	−0.164263	+	0.284512i
$145$	1.72081e31	+	2.98054e31i	0.786861	+	1.36288i
$146$	−2.68826e30			−0.111264
$147$	−1.97265e30	+	1.52739e31i	−0.0739516	+	0.572595i
$148$	3.51288e31			1.19363
$149$	2.22543e31	+	3.85456e31i	0.685825	+	1.18788i	0.973177	+	0.230058i	$0.0738917\pi$
$149$	2.22543e31	+	3.85456e31i	0.685825	+	1.18788i	−0.287352	+	0.957825i	$0.592775\pi$
$150$	9.55875e29	−	1.65562e30i	0.0267349	−	0.0463061i
$151$	2.58050e31	−	4.46956e31i	0.655449	−	1.13527i	−0.326332	−	0.945255i	$-0.605813\pi$
$151$	2.58050e31	−	4.46956e31i	0.655449	−	1.13527i	0.981781	−	0.190015i	$-0.0608538\pi$
$152$	−1.89568e30	−	3.28341e30i	−0.0437555	−	0.0757867i
$153$	1.16474e31			0.244457
$154$	−3.45655e29	−	1.72663e30i	−0.00660074	−	0.0329723i
$155$	6.48041e31			1.12666
$156$	−1.21843e31	−	2.11039e31i	−0.192972	−	0.334238i
$157$	−5.15814e31	+	8.93417e31i	−0.744644	+	1.28976i	0.205717	+	0.978611i	$0.434047\pi$
$157$	−5.15814e31	+	8.93417e31i	−0.744644	+	1.28976i	−0.950361	+	0.311149i	$0.899286\pi$
$158$	−5.43908e29	+	9.42077e29i	−0.00716140	+	0.0124039i
$159$	1.17935e31	+	2.04269e31i	0.141705	+	0.245439i
$160$	2.88064e31			0.316045
$161$	−7.26939e31	+	6.39091e31i	−0.728657	+	0.640601i
$162$	8.41474e29			0.00771033
$163$	−6.04835e31	−	1.04761e32i	−0.506894	−	0.877965i	−0.999968	−	0.00797837i	$-0.997460\pi$
$163$	−6.04835e31	−	1.04761e32i	−0.506894	−	0.877965i	0.493075	−	0.869987i	$-0.335873\pi$
$164$	6.40872e31	−	1.11002e32i	0.491514	−	0.851326i
$165$	3.04368e31	−	5.27182e31i	0.213738	−	0.370206i
$166$	5.54846e30	+	9.61022e30i	0.0356948	+	0.0618253i
$167$	−2.19520e32			−1.29445			−0.647226	−	0.762299i	$-0.724071\pi$
$167$	−2.19520e32			−1.29445			−0.647226	+	0.762299i	$0.724071\pi$
$168$	1.40030e31	+	4.73419e30i	0.0757245	+	0.0256012i
$169$	−1.10605e32			−0.548806
$170$	−8.53542e30	−	1.47838e31i	−0.0388791	−	0.0673405i
$171$	2.51800e31	−	4.36131e31i	0.105345	−	0.182462i
$172$	−5.53523e31	+	9.58730e31i	−0.212801	+	0.368582i
$173$	−5.34842e31	−	9.26374e31i	−0.189041	−	0.327429i	0.755889	−	0.654699i	$-0.227205\pi$
$173$	−5.34842e31	−	9.26374e31i	−0.189041	−	0.327429i	−0.944931	+	0.327270i	$0.893871\pi$
$174$	1.26923e31			0.0412644
$175$	4.22575e32	+	1.42866e32i	1.26431	+	0.427441i
$176$	1.73377e32			0.477592
$177$	−1.28471e32	−	2.22518e32i	−0.325981	−	0.564616i
$178$	2.95794e30	−	5.12330e30i	0.00691671	−	0.0119801i
$179$	1.93904e32	−	3.35851e32i	0.418039	−	0.724065i	−0.577703	−	0.816247i	$-0.696051\pi$
$179$	1.93904e32	−	3.35851e32i	0.418039	−	0.724065i	0.995742	+	0.0921819i	$0.0293841\pi$
$180$	1.27441e32	+	2.20735e32i	0.253431	+	0.438955i
$181$	−1.00766e33			−1.84915			−0.924576	−	0.380997i	$-0.875581\pi$
$181$	−1.00766e33			−1.84915			−0.924576	+	0.380997i	$0.875581\pi$
$182$	−2.06628e31	+	1.81658e31i	−0.0350069	+	0.0307764i
$183$	3.30717e32			0.517507
$184$	4.64508e31	+	8.04552e31i	0.0671637	+	0.116331i
$185$	6.85538e32	−	1.18739e33i	0.916308	−	1.58709i
$186$	1.19495e31	−	2.06971e31i	0.0147710	−	0.0255842i
$187$	−1.55369e32	−	2.69106e32i	−0.177689	−	0.307766i
$188$	−1.50889e33			−1.59724
$189$	3.85412e31	+	1.92523e32i	0.0377772	+	0.188706i
$190$	−7.38097e31			−0.0670172
$191$	−9.55620e32	−	1.65518e33i	−0.804084	−	1.39271i	−0.916908	−	0.399099i	$-0.869323\pi$
$191$	−9.55620e32	−	1.65518e33i	−0.804084	−	1.39271i	0.112824	−	0.993615i	$-0.464011\pi$
$192$	−3.59415e32	+	6.22525e32i	−0.280368	+	0.485612i
$193$	1.17098e33	−	2.02820e33i	0.847166	−	1.46733i	−0.0365616	−	0.999331i	$-0.511641\pi$
$193$	1.17098e33	−	2.02820e33i	0.847166	−	1.46733i	0.883727	−	0.468002i	$-0.155026\pi$
$194$	−3.60555e31	−	6.24499e31i	−0.0242017	−	0.0419186i
$195$	−9.51108e32			−0.592554
$196$	−2.20356e32	+	1.70618e33i	−0.127471	+	0.986987i
$197$	−3.34318e32			−0.179639			−0.0898193	−	0.995958i	$-0.528629\pi$
$197$	−3.34318e32			−0.179639			−0.0898193	+	0.995958i	$0.528629\pi$
$198$	−1.12247e31	−	1.94418e31i	−0.00560441	−	0.00970713i
$199$	1.14712e33	−	1.98687e33i	0.532401	−	0.922146i	−0.466883	−	0.884319i	$-0.654623\pi$
$199$	1.14712e33	−	1.98687e33i	0.532401	−	0.922146i	0.999284	−	0.0378269i	$-0.0120435\pi$
$200$	2.14070e32	−	3.70781e32i	0.0923893	−	0.160023i
$201$	−7.54960e32	−	1.30763e33i	−0.303097	−	0.524979i
$202$	−3.14831e32			−0.117620
$203$	5.81333e32	+	2.90390e33i	0.202177	+	1.00992i
$204$	1.30108e33			0.421373
$205$	−2.50132e33	−	4.33242e33i	−0.754638	−	1.30707i
$206$	5.95530e31	−	1.03149e32i	0.0167428	−	0.0289994i
$207$	−6.17000e32	+	1.06868e33i	−0.161702	+	0.280076i
$208$	−1.35444e33	−	2.34596e33i	−0.331011	−	0.573328i
$209$	−1.34354e33			−0.306288
$210$	2.16121e32	−	1.90004e32i	0.0459746	−	0.0404187i
$211$	4.82613e33			0.958305			0.479152	−	0.877732i	$-0.340944\pi$
$211$	4.82613e33			0.958305			0.479152	+	0.877732i	$0.340944\pi$
$212$	1.31740e33	+	2.28181e33i	0.244258	+	0.423067i
$213$	−1.30559e33	+	2.26136e33i	−0.226102	+	0.391620i
$214$	−4.53410e31	+	7.85329e31i	−0.00733654	+	0.0127073i
$215$	2.16040e33	+	3.74192e33i	0.326721	+	0.565897i
$216$	1.88450e32			0.0266450
$217$	5.28264e33	+	1.78597e33i	0.698530	+	0.236162i
$218$	6.90883e32			0.0854645
$219$	−3.99843e33	−	6.92548e33i	−0.462860	−	0.801697i
$220$	3.39997e33	−	5.88893e33i	0.368423	−	0.638127i
$221$	−2.42752e33	+	4.20459e33i	−0.246306	+	0.426615i
$222$	−2.52818e32	−	4.37893e32i	−0.0240264	−	0.0416150i
$223$	−1.23240e34			−1.09731			−0.548657	−	0.836048i	$-0.684861\pi$
$223$	−1.23240e34			−1.09731			−0.548657	+	0.836048i	$0.684861\pi$
$224$	2.34821e33	+	7.93893e32i	0.195948	+	0.0662469i
$225$	5.68694e33			0.444869
$226$	7.61014e31	+	1.31811e32i	0.00558239	+	0.00966898i
$227$	−4.99046e33	+	8.64373e33i	−0.343373	+	0.594739i	−0.985057	−	0.172230i	$-0.944903\pi$
$227$	−4.99046e33	+	8.64373e33i	−0.343373	+	0.594739i	0.641684	+	0.766969i	$0.278236\pi$
$228$	2.81276e33	−	4.87184e33i	0.181584	−	0.314512i
$229$	7.71265e33	+	1.33587e34i	0.467293	+	0.809375i	0.999302	−	0.0373640i	$-0.0118961\pi$
$229$	7.71265e33	+	1.33587e34i	0.467293	+	0.809375i	−0.532009	+	0.846739i	$0.678563\pi$
$230$	1.80860e33			0.102870
$231$	3.93401e33	−	3.45860e33i	0.210117	−	0.184726i
$232$	2.84247e33			0.142600
$233$	6.55551e33	+	1.13545e34i	0.308991	+	0.535188i	0.978142	−	0.207938i	$-0.0666753\pi$
$233$	6.55551e33	+	1.13545e34i	0.308991	+	0.535188i	−0.669151	+	0.743127i	$0.733342\pi$
$234$	−1.75378e32	+	3.03764e32i	−0.00776865	+	0.0134557i
$235$	−2.94460e34	+	5.10020e34i	−1.22615	+	2.12375i
$236$	−1.43510e34	−	2.48566e34i	−0.561897	−	0.973235i
$237$	−3.23596e33			−0.119166
$238$	−2.88348e32	−	1.44036e33i	−0.00998965	−	0.0499007i
$239$	1.77610e34			0.579025			0.289513	−	0.957174i	$-0.406507\pi$
$239$	1.77610e34			0.579025			0.289513	+	0.957174i	$0.406507\pi$
$240$	1.41667e34	+	2.45375e34i	0.434717	+	0.752952i
$241$	−1.43862e34	+	2.49177e34i	−0.415623	+	0.719880i	−0.995494	−	0.0948284i	$-0.969770\pi$
$241$	−1.43862e34	+	2.49177e34i	−0.415623	+	0.719880i	0.579871	+	0.814709i	$0.303103\pi$
$242$	9.75826e32	−	1.69018e33i	0.0265491	−	0.0459844i
$243$	1.25158e33	+	2.16780e33i	0.0320750	+	0.0555556i
$244$	3.69431e34			0.892032
$245$	5.33702e34	+	4.07443e34i	1.21448	+	0.927169i
$246$	−1.84491e33			−0.0395746
$247$	1.04959e34	+	1.81795e34i	0.212283	+	0.367685i
$248$	2.67611e33	−	4.63516e33i	0.0510451	−	0.0884128i
$249$	−1.65052e34	+	2.85878e34i	−0.296982	+	0.514387i
$250$	−1.04486e33	−	1.80975e33i	−0.0177389	−	0.0307247i
$251$	2.68489e34			0.430187			0.215094	−	0.976593i	$-0.430994\pi$
$251$	2.68489e34			0.430187			0.215094	+	0.976593i	$0.430994\pi$
$252$	4.30528e33	+	2.15059e34i	0.0651169	+	0.325274i
$253$	3.29216e34			0.470146
$254$	−3.69534e33	−	6.40052e33i	−0.0498386	−	0.0863230i
$255$	2.53906e34	−	4.39778e34i	0.323474	−	0.560274i
$256$	−3.95526e34	+	6.85070e34i	−0.476097	+	0.824624i
$257$	−8.28648e34	−	1.43526e35i	−0.942627	−	1.63268i	−0.760434	−	0.649415i	$-0.775014\pi$
$257$	−8.28648e34	−	1.43526e35i	−0.942627	−	1.63268i	−0.182193	−	0.983263i	$-0.558319\pi$
$258$	1.59346e33			0.0171338
$259$	8.86069e34	−	7.78991e34i	0.900785	−	0.791928i
$260$	−1.06244e35			−1.02139
$261$	1.88781e34	+	3.26978e34i	0.171660	+	0.297324i
$262$	6.42409e33	−	1.11268e34i	0.0552640	−	0.0957201i
$263$	−6.50498e34	+	1.12670e35i	−0.529526	+	0.917167i	0.469880	+	0.882730i	$0.344297\pi$
$263$	−6.50498e34	+	1.12670e35i	−0.529526	+	0.917167i	−0.999407	+	0.0344367i	$0.989036\pi$
$264$	−2.51380e33	−	4.35403e33i	−0.0193675	−	0.0335455i
$265$	1.02836e35			0.750035
$266$	−6.01675e33	−	2.03416e33i	−0.0415507	−	0.0140476i
$267$	1.75981e34			0.115094
$268$	−8.43334e34	−	1.46070e35i	−0.522451	−	0.904911i
$269$	−5.90178e34	+	1.02222e35i	−0.346398	+	0.599979i	−0.985607	−	0.169054i	$-0.945929\pi$
$269$	−5.90178e34	+	1.02222e35i	−0.346398	+	0.599979i	0.639209	+	0.769033i	$0.279262\pi$
$270$	1.83436e33	−	3.17721e33i	0.0102026	−	0.0176714i
$271$	−2.78364e34	−	4.82141e34i	−0.146743	−	0.254167i	0.783279	−	0.621671i	$-0.213546\pi$
$271$	−2.78364e34	−	4.82141e34i	−0.146743	−	0.254167i	−0.930022	+	0.367504i	$0.880212\pi$
$272$	1.44632e35			0.722793
$273$	−7.75315e34	−	2.62121e34i	−0.367384	−	0.124206i
$274$	1.29030e34			0.0579841
$275$	−7.58601e34	−	1.31394e35i	−0.323362	−	0.560080i
$276$	−6.89225e34	+	1.19377e35i	−0.278727	+	0.482770i
$277$	9.35607e34	−	1.62052e35i	0.359035	−	0.621867i	−0.628765	−	0.777595i	$-0.716439\pi$
$277$	9.35607e34	−	1.62052e35i	0.359035	−	0.621867i	0.987800	+	0.155729i	$0.0497726\pi$
$278$	1.44044e34	+	2.49491e34i	0.0524620	+	0.0908669i
$279$	7.10928e34			0.245790
$280$	4.84009e34	−	4.25518e34i	0.158877	−	0.139678i
$281$	3.72075e34			0.115981			0.0579907	−	0.998317i	$-0.481531\pi$
$281$	3.72075e34			0.115981			0.0579907	+	0.998317i	$0.481531\pi$
$282$	1.08593e34	+	1.88089e34i	0.0321507	+	0.0556866i
$283$	−6.91495e34	+	1.19770e35i	−0.194485	+	0.336858i	−0.946732	−	0.322024i	$-0.895637\pi$
$283$	−6.91495e34	+	1.19770e35i	−0.194485	+	0.336858i	0.752247	+	0.658882i	$0.228970\pi$
$284$	−1.45843e35	+	2.52607e35i	−0.389734	+	0.675039i
$285$	−1.09782e35	−	1.90148e35i	−0.278792	−	0.482882i
$286$	9.35773e33			0.0225872
$287$	−8.45008e34	−	4.22101e35i	−0.193898	−	0.968566i
$288$	3.16018e34			0.0689479
$289$	1.11375e35	+	1.92907e35i	0.231084	+	0.400249i
$290$	2.76684e34	−	4.79231e34i	0.0546026	−	0.0945745i
$291$	1.07255e35	−	1.85772e35i	0.201359	−	0.348763i
$292$	−4.46648e35	−	7.73617e35i	−0.797836	−	1.38189i
$293$	−3.25146e35			−0.552711			−0.276355	−	0.961056i	$-0.589127\pi$
$293$	−3.25146e35			−0.552711			−0.276355	+	0.961056i	$0.589127\pi$
$294$	2.28540e34	−	9.53234e33i	0.0369765	−	0.0154228i
$295$	−1.12024e36			−1.72540
$296$	−5.66191e34	−	9.80671e34i	−0.0830296	−	0.143811i
$297$	3.33905e34	−	5.78340e34i	0.0466288	−	0.0807635i
$298$	3.57820e34	−	6.19762e34i	0.0475914	−	0.0824307i
$299$	−2.57188e35	−	4.45462e35i	−0.325850	−	0.564389i
$300$	6.35264e35			0.766825
$301$	7.29836e34	+	3.64570e35i	0.0839481	+	0.419341i
$302$	−8.29821e34			−0.0909670
$303$	−4.68269e35	−	8.11065e35i	−0.489302	−	0.847496i
$304$	3.12674e35	−	5.41567e35i	0.311476	−	0.539492i
$305$	7.20944e35	−	1.24871e36i	0.684784	−	1.18608i
$306$	−9.36372e33	−	1.62184e34i	−0.00848179	−	0.0146909i
$307$	7.61645e35			0.658031			0.329015	−	0.944325i	$-0.393283\pi$
$307$	7.61645e35			0.658031			0.329015	+	0.944325i	$0.393283\pi$
$308$	4.39452e35	−	3.86346e35i	0.362182	−	0.318413i
$309$	3.54308e35			0.278601
$310$	−5.20982e34	−	9.02367e34i	−0.0390911	−	0.0677078i
$311$	−5.88771e35	+	1.01978e36i	−0.421620	+	0.730267i	−0.996098	−	0.0882529i	$-0.971872\pi$
$311$	−5.88771e35	+	1.01978e36i	−0.421620	+	0.730267i	0.574478	+	0.818520i	$0.305205\pi$
$312$	−3.92763e34	+	6.80286e34i	−0.0268466	+	0.0464997i
$313$	1.26174e36	+	2.18540e36i	0.823337	+	1.42606i	0.903184	+	0.429254i	$0.141224\pi$
$313$	1.26174e36	+	2.18540e36i	0.823337	+	1.42606i	−0.0798467	+	0.996807i	$0.525443\pi$
$314$	1.65872e35			0.103346
$315$	8.10938e35	+	2.74165e35i	0.482486	+	0.163121i
$316$	−3.61476e35			−0.205407
$317$	−1.11780e36	−	1.93609e36i	−0.606745	−	1.05091i	−0.991773	−	0.128009i	$-0.959141\pi$
$317$	−1.11780e36	−	1.93609e36i	−0.606745	−	1.05091i	0.385028	−	0.922905i	$-0.374192\pi$
$318$	1.89624e34	−	3.28438e34i	0.00983329	−	0.0170318i
$319$	5.03642e35	−	8.72334e35i	0.249550	−	0.432233i
$320$	1.56701e36	+	2.71413e36i	0.741987	+	1.28516i
$321$	−2.69754e35			−0.122080
$322$	1.47432e35	+	4.98442e34i	0.0637794	+	0.0215628i
$323$	−1.12079e36			−0.463540
$324$	1.39809e35	+	2.42156e35i	0.0552880	+	0.0957617i
$325$	−1.18526e36	+	2.05293e36i	−0.448234	+	0.776364i
$326$	−9.72495e34	+	1.68441e35i	−0.0351748	+	0.0609246i
$327$	1.02760e36	+	1.77985e36i	0.355533	+	0.615801i
$328$	−4.13172e35			−0.136760
$329$	−3.80595e36	+	3.34601e36i	−1.20537	+	1.05971i
$330$	−9.78768e34			−0.0296639
$331$	1.31854e35	+	2.28377e35i	0.0382460	+	0.0662440i	0.884515	−	0.466512i	$-0.154490\pi$
$331$	1.31854e35	+	2.28377e35i	0.0382460	+	0.0662440i	−0.846269	+	0.532756i	$0.821156\pi$
$332$	−1.84372e36	+	3.19343e36i	−0.511910	+	0.886655i
$333$	7.52064e35	−	1.30261e36i	0.199900	−	0.346237i
$334$	1.76480e35	+	3.05672e35i	0.0449129	+	0.0777914i
$335$	−6.58307e36			−1.60427
$336$	4.78587e35	+	2.39065e36i	0.111697	+	0.557953i
$337$	4.91035e36			1.09769			0.548844	−	0.835925i	$-0.315068\pi$
$337$	4.91035e36			1.09769			0.548844	+	0.835925i	$0.315068\pi$
$338$	8.89194e34	+	1.54013e35i	0.0190416	+	0.0329811i
$339$	−2.26381e35	+	3.92103e35i	−0.0464456	+	0.0804461i
$340$	2.83628e36	−	4.91257e36i	0.557576	−	0.965750i
$341$	−9.48333e35	−	1.64256e36i	−0.178658	−	0.309445i
$342$	−8.09723e34			−0.0146204
$343$	3.22769e36	+	4.79222e36i	0.558633	+	0.829415i
$344$	3.56858e35			0.0592104
$345$	2.69005e36	+	4.65929e36i	0.427940	+	0.741214i
$346$	−8.59955e34	+	1.48949e35i	−0.0131181	+	0.0227213i
$347$	4.53896e36	−	7.86172e36i	0.664017	−	1.15011i	−0.315533	−	0.948914i	$-0.602183\pi$
$347$	4.53896e36	−	7.86172e36i	0.664017	−	1.15011i	0.979551	−	0.201197i	$-0.0644833\pi$
$348$	2.10879e36	+	3.65253e36i	0.295893	+	0.512501i
$349$	9.70918e36			1.30681			0.653407	−	0.757007i	$-0.273339\pi$
$349$	9.70918e36			1.30681			0.653407	+	0.757007i	$0.273339\pi$
$350$	−1.40788e35	−	7.03271e35i	−0.0181794	−	0.0908105i
$351$	−1.04341e36			−0.129271
$352$	−4.21548e35	−	7.30143e35i	−0.0501163	−	0.0868039i
$353$	8.01170e35	−	1.38767e36i	0.0914095	−	0.158326i	−0.816695	−	0.577070i	$-0.804196\pi$
$353$	8.01170e35	−	1.38767e36i	0.0914095	−	0.158326i	0.908104	+	0.418744i	$0.137529\pi$
$354$	−2.06564e35	+	3.57780e35i	−0.0226208	+	0.0391804i
$355$	5.69223e36	+	9.85924e36i	0.598372	+	1.03641i
$356$	1.96582e36			0.198389
$357$	3.28177e36	−	2.88518e36i	0.317994	−	0.279566i
$358$	−6.23543e35			−0.0580179
$359$	6.31004e35	+	1.09293e36i	0.0563849	+	0.0976615i	0.892840	−	0.450374i	$-0.148709\pi$
$359$	6.31004e35	+	1.09293e36i	0.0563849	+	0.0976615i	−0.836455	+	0.548035i	$0.815376\pi$
$360$	4.10809e35	−	7.11542e35i	0.0352577	−	0.0610681i
$361$	3.64192e36	−	6.30799e36i	0.300245	−	0.520040i
$362$	8.10088e35	+	1.40311e36i	0.0641591	+	0.111127i
$363$	5.80564e36			0.441778
$364$	−8.66072e36	−	2.92805e36i	−0.633263	−	0.214096i
$365$	−3.48653e37			−2.44989
$366$	−2.65875e35	−	4.60509e35i	−0.0179557	−	0.0311001i
$367$	−9.44348e36	+	1.63566e37i	−0.613019	+	1.06178i	0.377709	+	0.925924i	$0.376712\pi$
$367$	−9.44348e36	+	1.63566e37i	−0.613019	+	1.06178i	−0.990729	+	0.135856i	$0.956622\pi$
$368$	−7.66162e36	+	1.32703e37i	−0.478109	+	0.828109i
$369$	−2.74406e36	−	4.75284e36i	−0.164631	−	0.285149i
$370$	−2.20451e36			−0.127171
$371$	8.38291e36	+	2.83413e36i	0.465022	+	0.157216i
$372$	7.94148e36			0.423671
$373$	−1.69880e36	−	2.94241e36i	−0.0871694	−	0.150982i	0.819144	−	0.573588i	$-0.194449\pi$
$373$	−1.69880e36	−	2.94241e36i	−0.0871694	−	0.150982i	−0.906314	+	0.422606i	$0.861115\pi$
$374$	−2.49812e35	+	4.32687e35i	−0.0123303	+	0.0213568i
$375$	3.10817e36	−	5.38350e36i	0.147588	−	0.255630i
$376$	2.43197e36	+	4.21229e36i	0.111105	+	0.192440i
$377$	−1.57381e37			−0.691835
$378$	2.37094e35	−	2.08442e35i	0.0100297	−	0.00881769i
$379$	1.25112e35			0.00509366			0.00254683	−	0.999997i	$-0.499189\pi$
$379$	1.25112e35			0.00509366			0.00254683	+	0.999997i	$0.499189\pi$
$380$	−1.22633e37	−	2.12406e37i	−0.480556	−	0.832348i
$381$	1.09926e37	−	1.90398e37i	0.414658	−	0.718208i
$382$	−1.53651e36	+	2.66131e36i	−0.0557978	+	0.0966445i
$383$	−1.28399e37	−	2.22394e37i	−0.448931	−	0.777572i	0.549385	−	0.835569i	$-0.314862\pi$
$383$	−1.28399e37	−	2.22394e37i	−0.448931	−	0.777572i	−0.998317	+	0.0579971i	$0.981529\pi$
$384$	4.70298e36			0.158332
$385$	−4.48296e36	−	2.23935e37i	−0.145340	−	0.726007i
$386$	−3.76556e36			−0.117575
$387$	2.37005e36	+	4.10504e36i	0.0712768	+	0.123455i
$388$	1.19810e37	−	2.07518e37i	0.347084	−	0.601167i
$389$	−1.77913e37	+	3.08154e37i	−0.496522	+	0.860002i	−0.999992	−	0.00401126i	$-0.998723\pi$
$389$	−1.77913e37	+	3.08154e37i	−0.496522	+	0.860002i	0.503470	+	0.864013i	$0.332057\pi$
$390$	7.64628e35	+	1.32437e36i	0.0205595	+	0.0356101i
$391$	2.74633e37			0.711525
$392$	5.11821e36	−	2.13479e36i	0.127782	−	0.0532975i
$393$	3.82198e37			0.919595
$394$	2.68770e35	+	4.65523e35i	0.00623282	+	0.0107956i
$395$	−7.05419e36	+	1.22182e37i	−0.157685	+	0.273118i
$396$	3.72991e36	−	6.46040e36i	0.0803746	−	0.139213i
$397$	−3.65155e37	−	6.32467e37i	−0.758604	−	1.31394i	−0.943563	−	0.331194i	$-0.892549\pi$
$397$	−3.65155e37	−	6.32467e37i	−0.758604	−	1.31394i	0.184959	−	0.982746i	$-0.440785\pi$
$398$	−3.68883e36			−0.0738898
$399$	−3.70870e36	−	1.85258e37i	−0.0716333	−	0.357825i
$400$	7.06177e37			1.31536
$401$	−2.36433e37	−	4.09514e37i	−0.424732	−	0.735657i	0.571664	−	0.820488i	$-0.306298\pi$
$401$	−2.36433e37	−	4.09514e37i	−0.424732	−	0.735657i	−0.996395	+	0.0848311i	$0.972965\pi$
$402$	−1.21388e36	+	2.10249e36i	−0.0210328	+	0.0364298i
$403$	−1.48170e37	+	2.56638e37i	−0.247650	+	0.428942i
$404$	−5.23083e37	−	9.06007e37i	−0.843415	−	1.46084i
$405$	1.09135e37			0.169771
$406$	3.57619e36	−	3.14402e36i	0.0536776	−	0.0471908i
$407$	−4.01282e37			−0.581207
$408$	−2.09703e36	−	3.63215e36i	−0.0293110	−	0.0507682i
$409$	4.47379e37	−	7.74884e37i	0.603515	−	1.04532i	−0.388770	−	0.921335i	$-0.627100\pi$
$409$	4.47379e37	−	7.74884e37i	0.603515	−	1.04532i	0.992284	−	0.123983i	$-0.0395669\pi$
$410$	−4.02179e36	+	6.96595e36i	−0.0523665	+	0.0907015i
$411$	1.91915e37	+	3.32407e37i	0.241214	+	0.417796i
$412$	3.95783e37			0.480228
$413$	−9.13183e37	−	3.08732e37i	−1.06975	−	0.361665i
$414$	1.98411e36			0.0224419
$415$	7.19606e37	+	1.24639e38i	0.785954	+	1.36131i
$416$	−6.58639e36	+	1.14080e37i	−0.0694695	+	0.120325i
$417$	−4.28491e37	+	7.42169e37i	−0.436485	+	0.756014i
$418$	1.08012e36	+	1.87082e36i	0.0106271	+	0.0184067i
$419$	−1.26959e38			−1.20659			−0.603294	−	0.797519i	$-0.706145\pi$
$419$	−1.26959e38			−1.20659			−0.603294	+	0.797519i	$0.706145\pi$
$420$	9.05865e37	+	3.06258e37i	0.831666	+	0.281173i
$421$	−1.19629e38			−1.06108			−0.530539	−	0.847661i	$-0.678010\pi$
$421$	−1.19629e38			−1.06108			−0.530539	+	0.847661i	$0.678010\pi$
$422$	−3.87989e36	−	6.72017e36i	−0.0332498	−	0.0575903i
$423$	−3.23035e37	+	5.59513e37i	−0.267494	+	0.463314i
$424$	4.24666e36	−	7.35543e36i	0.0339815	−	0.0588577i
$425$	−6.32829e37	−	1.09609e38i	−0.489381	−	0.847632i
$426$	4.19844e36			0.0313797
$427$	9.31832e37	−	8.19223e37i	0.673183	−	0.591831i
$428$	−3.01331e37			−0.210431
$429$	1.39184e37	+	2.41073e37i	0.0939631	+	0.162749i
$430$	3.47364e36	−	6.01651e36i	0.0226721	−	0.0392692i
$431$	−1.29045e38	+	2.23513e38i	−0.814369	+	1.41053i	0.0954112	+	0.995438i	$0.469583\pi$
$431$	−1.29045e38	+	2.23513e38i	−0.814369	+	1.41053i	−0.909780	+	0.415090i	$0.863750\pi$
$432$	1.55415e37	+	2.69187e37i	0.0948372	+	0.164263i
$433$	7.41144e37			0.437349			0.218675	−	0.975798i	$-0.429827\pi$
$433$	7.41144e37			0.437349			0.218675	+	0.975798i	$0.429827\pi$
$434$	−1.76000e36	−	8.79164e36i	−0.0100441	−	0.0501728i
$435$	1.64612e38			0.908589
$436$	1.14788e38	+	1.98819e38i	0.612836	+	1.06146i
$437$	5.93719e37	−	1.02835e38i	0.306620	−	0.531081i
$438$	−6.42894e36	+	1.11353e37i	−0.0321192	+	0.0556321i
$439$	1.15352e38	+	1.99795e38i	0.557557	+	0.965717i	0.997700	+	0.0677891i	$0.0215945\pi$
$439$	1.15352e38	+	1.99795e38i	0.557557	+	0.965717i	−0.440143	+	0.897928i	$0.645072\pi$
$440$	−2.19197e37			−0.102511
$441$	5.85494e37	+	4.46982e37i	0.264949	+	0.202270i
$442$	7.80627e36			0.0341838
$443$	2.41072e37	+	4.17549e37i	0.102163	+	0.176951i	0.912575	−	0.408908i	$-0.134090\pi$
$443$	2.41072e37	+	4.17549e37i	0.102163	+	0.176951i	−0.810413	+	0.585859i	$0.800757\pi$
$444$	8.40099e37	−	1.45509e38i	0.344570	−	0.596813i
$445$	3.83629e37	−	6.64464e37i	0.152297	−	0.263786i
$446$	9.90767e36	+	1.71606e37i	0.0380729	+	0.0659442i
$447$	2.12883e38			0.791922
$448$	5.29373e37	+	2.64434e38i	0.190647	+	0.952328i
$449$	1.73086e38			0.603516			0.301758	−	0.953385i	$-0.402426\pi$
$449$	1.73086e38			0.603516			0.301758	+	0.953385i	$0.402426\pi$
$450$	−4.57192e36	−	7.91880e36i	−0.0154354	−	0.0267349i
$451$	−7.32079e37	+	1.26800e38i	−0.239331	+	0.414533i
$452$	−2.52881e37	+	4.38002e37i	−0.0800587	+	0.138666i
$453$	−1.23425e38	−	2.13778e38i	−0.378423	−	0.655449i
$454$	1.60480e37			0.0476553
$455$	−2.67985e38	+	2.35600e38i	−0.770806	+	0.677657i
$456$	−1.81339e37			−0.0505244
$457$	−2.11833e38	−	3.66906e38i	−0.571753	−	0.990306i	−0.996386	−	0.0849403i	$-0.972930\pi$
$457$	−2.11833e38	−	3.66906e38i	−0.571753	−	0.990306i	0.424633	−	0.905366i	$-0.360403\pi$
$458$	1.24009e37	−	2.14790e37i	0.0324268	−	0.0561649i
$459$	2.78545e37	−	4.82454e37i	0.0705686	−	0.122228i
$460$	3.00494e38	+	5.20471e38i	0.737644	+	1.27764i
$461$	−6.89778e38			−1.64076			−0.820382	−	0.571816i	$-0.806239\pi$
$461$	−6.89778e38			−1.64076			−0.820382	+	0.571816i	$0.806239\pi$
$462$	−7.97863e36	−	2.69745e36i	−0.0183916	−	0.00621790i
$463$	9.89949e37			0.221151			0.110575	−	0.993868i	$-0.464731\pi$
$463$	9.89949e37			0.221151			0.110575	+	0.993868i	$0.464731\pi$
$464$	2.34419e38	+	4.06025e38i	0.507553	+	0.879108i
$465$	1.54978e38	−	2.68430e38i	0.325239	−	0.563330i
$466$	1.05404e37	−	1.82565e37i	0.0214418	−	0.0371383i
$467$	1.25506e38	+	2.17382e38i	0.247496	+	0.428676i	0.962830	−	0.270106i	$-0.0870589\pi$
$467$	1.25506e38	+	2.17382e38i	0.247496	+	0.428676i	−0.715334	+	0.698782i	$0.753726\pi$
$468$	−1.16554e38			−0.222825
$469$	−5.36632e38	−	1.81427e38i	−0.994650	−	0.336275i
$470$	9.46906e37			0.170172
$471$	2.46712e38	+	4.27319e38i	0.429920	+	0.744644i
$472$	−4.62605e37	+	8.01256e37i	−0.0781721	+	0.135398i
$473$	6.32299e37	−	1.09517e38i	0.103618	−	0.179472i
$474$	2.60150e36	+	4.50592e36i	0.00413463	+	0.00716140i
$475$	−5.47236e38			−0.843562
$476$	3.66593e38	−	3.22292e38i	0.548130	−	0.481891i
$477$	1.12816e38			0.163626
$478$	−1.42786e37	−	2.47313e37i	−0.0200901	−	0.0347971i
$479$	−9.88087e37	+	1.71142e38i	−0.134875	+	0.233610i	−0.925550	−	0.378627i	$-0.876396\pi$
$479$	−9.88087e37	+	1.71142e38i	−0.134875	+	0.233610i	0.790675	+	0.612236i	$0.209730\pi$
$480$	6.88901e37	−	1.19321e38i	0.0912344	−	0.158023i
$481$	3.13487e38	+	5.42976e38i	0.402825	+	0.697713i
$482$	4.62623e37			0.0576826
$483$	9.08763e37	+	4.53949e38i	0.109956	+	0.549254i
$484$	6.48524e38			0.761497
$485$	−4.67620e38	−	8.09941e38i	−0.532890	−	0.922993i
$486$	2.01237e36	−	3.48553e36i	0.00222578	−	0.00385516i
$487$	9.04548e38	−	1.56672e39i	0.971095	−	1.68199i	0.278834	−	0.960339i	$-0.410052\pi$
$487$	9.04548e38	−	1.56672e39i	0.971095	−	1.68199i	0.692261	−	0.721647i	$-0.256615\pi$
$488$	−5.95432e37	−	1.03132e38i	−0.0620505	−	0.107475i
$489$	−5.78582e38			−0.585310
$490$	1.38285e37	−	1.07071e38i	0.0135810	−	0.105155i
$491$	−2.04807e38			−0.195283			−0.0976414	−	0.995222i	$-0.531130\pi$
$491$	−2.04807e38			−0.195283			−0.0976414	+	0.995222i	$0.531130\pi$
$492$	−3.06527e38	−	5.30920e38i	−0.283775	−	0.491514i
$493$	4.20141e38	−	7.27706e38i	0.377672	−	0.654147i
$494$	1.68761e37	−	2.92302e37i	0.0147310	−	0.0255148i
$495$	−1.45579e38	−	2.52149e38i	−0.123402	−	0.213738i
$496$	8.82797e38			0.726736
$497$	1.92298e38	+	9.60571e38i	0.153747	+	0.768001i
$498$	5.30763e37			0.0412169
$499$	1.43338e37	+	2.48268e37i	0.0108119	+	0.0187268i	0.871381	−	0.490607i	$-0.163225\pi$
$499$	1.43338e37	+	2.48268e37i	0.0108119	+	0.0187268i	−0.860569	+	0.509334i	$0.829892\pi$
$500$	3.47200e38	−	6.01369e38i	0.254399	−	0.440632i
$501$	−5.24979e38	+	9.09291e38i	−0.373676	+	0.647226i
$502$	−2.15847e37	−	3.73859e37i	−0.0149260	−	0.0258526i
$503$	−1.87342e39			−1.25863			−0.629316	−	0.777150i	$-0.716665\pi$
$503$	−1.87342e39			−1.25863			−0.629316	+	0.777150i	$0.716665\pi$
$504$	5.30978e37	−	4.66811e37i	0.0346604	−	0.0304718i
$505$	−4.08319e39			−2.58985
$506$	−2.64667e37	−	4.58417e37i	−0.0163124	−	0.0282539i
$507$	−2.64511e38	+	4.58146e38i	−0.158427	+	0.274403i
$508$	1.22794e39	−	2.12686e39i	0.714750	−	1.23798i
$509$	−1.15124e39	−	1.99400e39i	−0.651263	−	1.12802i	−0.982817	−	0.184585i	$-0.940906\pi$
$509$	−1.15124e39	−	1.99400e39i	−0.651263	−	1.12802i	0.331553	−	0.943437i	$-0.392427\pi$
$510$	−8.16493e37			−0.0448937
$511$	−2.84212e39	−	9.60874e38i	−1.51893	−	0.513527i
$512$	6.55082e38			0.340315
$513$	−1.20435e38	−	2.08600e38i	−0.0608208	−	0.105345i
$514$	−1.33236e38	+	2.30771e38i	−0.0654117	+	0.113296i
$515$	7.72370e38	−	1.33778e39i	0.368655	−	0.638530i
$516$	2.64748e38	+	4.58558e38i	0.122861	+	0.212801i
$517$	1.72363e39			0.777735
$518$	−1.79705e38	−	6.07553e37i	−0.0788458	−	0.0266565i
$519$	−5.11627e38			−0.218286
$520$	1.71240e38	+	2.96596e38i	0.0710488	+	0.123060i
$521$	−1.04234e39	+	1.80538e39i	−0.420592	+	0.728486i	−0.995997	−	0.0893818i	$-0.971511\pi$
$521$	−1.04234e39	+	1.80538e39i	−0.420592	+	0.728486i	0.575406	+	0.817868i	$0.304844\pi$
$522$	3.03534e37	−	5.25736e37i	0.0119120	−	0.0206322i
$523$	1.73067e39	+	2.99760e39i	0.660601	+	1.14419i	0.980458	+	0.196728i	$0.0630316\pi$
$523$	1.73067e39	+	2.99760e39i	0.660601	+	1.14419i	−0.319858	+	0.947466i	$0.603635\pi$
$524$	4.26938e39			1.58512
$525$	1.60236e39	−	1.40872e39i	0.578694	−	0.508761i
$526$	2.09183e38			0.0734908
$527$	−7.91104e38	−	1.37023e39i	−0.270383	−	0.468317i
$528$	4.14627e38	−	7.18156e38i	0.137869	−	0.238796i
$529$	9.07063e37	−	1.57108e38i	0.0293447	−	0.0508266i
$530$	−8.26736e37	−	1.43195e38i	−0.0260236	−	0.0450741i
$531$	−1.22895e39			−0.376411
$532$	−4.14283e38	−	2.06944e39i	−0.123475	−	0.616787i
$533$	2.28764e39			0.663504
$534$	−1.41477e37	−	2.45046e37i	−0.00399336	−	0.00691671i
$535$	−5.88048e38	+	1.01853e39i	−0.161541	+	0.279797i
$536$	−2.71850e38	+	4.70858e38i	−0.0726842	+	0.125893i
$537$	−9.27435e38	−	1.60636e39i	−0.241355	−	0.418039i
$538$	1.89786e38			0.0480751
$539$	2.51716e38	−	1.94900e39i	0.0620690	−	0.480589i
$540$	1.21910e39			0.292637
$541$	1.69025e39	+	2.92760e39i	0.394994	+	0.684149i	0.993100	−	0.117267i	$-0.0374134\pi$
$541$	1.69025e39	+	2.92760e39i	0.394994	+	0.684149i	−0.598107	+	0.801417i	$0.704080\pi$
$542$	−4.47572e37	+	7.75218e37i	−0.0101830	+	0.0176374i
$543$	−2.40979e39	+	4.17388e39i	−0.533804	+	0.924576i
$544$	−3.51658e38	−	6.09089e38i	−0.0758466	−	0.131370i
$545$	8.96038e39			1.88182
$546$	2.58310e37	+	1.29032e38i	0.00528260	+	0.0263878i
$547$	−9.93510e39			−1.97859			−0.989295	−	0.145928i	$-0.953383\pi$
$547$	−9.93510e39			−1.97859			−0.989295	+	0.145928i	$0.953383\pi$
$548$	2.14381e39	+	3.71318e39i	0.415784	+	0.720159i
$549$	7.90905e38	−	1.36989e39i	0.149391	−	0.258753i
$550$	−1.21973e38	+	2.11263e38i	−0.0224391	+	0.0388656i
$551$	−1.81657e39	−	3.14640e39i	−0.325503	−	0.563788i
$552$	4.44346e38			0.0775540
$553$	−9.11766e38	+	8.01583e38i	−0.155013	+	0.136281i
$554$	−3.00866e38			−0.0498290
$555$	−3.27891e39	−	5.67923e39i	−0.529031	−	0.916308i
$556$	−4.78650e39	+	8.29046e39i	−0.752373	+	1.30315i
$557$	−2.91637e39	+	5.05129e39i	−0.446623	+	0.773575i	−0.998164	−	0.0605737i	$-0.980707\pi$
$557$	−2.91637e39	+	5.05129e39i	−0.446623	+	0.773575i	0.551540	+	0.834148i	$0.314040\pi$
$558$	−5.71539e37	−	9.89935e37i	−0.00852806	−	0.0147710i
$559$	−1.97584e39			−0.287264
$560$	1.00698e40	+	3.40445e39i	1.42658	+	0.482304i
$561$	−1.48625e39			−0.205177
$562$	−2.99123e37	−	5.18097e37i	−0.00402415	−	0.00697003i
$563$	9.41996e38	−	1.63158e39i	0.123503	−	0.213913i	−0.797644	−	0.603129i	$-0.793921\pi$
$563$	9.41996e38	−	1.63158e39i	0.123503	−	0.213913i	0.921147	+	0.389215i	$0.127254\pi$
$564$	−3.60849e39	+	6.25009e39i	−0.461082	+	0.798618i
$565$	9.86994e38	+	1.70952e39i	0.122917	+	0.212898i
$566$	2.22366e38			0.0269917
$567$	8.89633e38	+	3.00770e38i	0.105258	+	0.0355861i
$568$	9.40251e38			0.108441
$569$	7.74710e39	+	1.34184e40i	0.870986	+	1.50859i	0.860978	+	0.508643i	$0.169853\pi$
$569$	7.74710e39	+	1.34184e40i	0.870986	+	1.50859i	0.0100089	+	0.999950i	$0.496814\pi$
$570$	−1.76515e38	+	3.05732e38i	−0.0193462	+	0.0335086i
$571$	3.48745e39	−	6.04044e39i	0.372636	−	0.645424i	−0.617335	−	0.786701i	$-0.711787\pi$
$571$	3.48745e39	−	6.04044e39i	0.372636	−	0.645424i	0.989970	+	0.141277i	$0.0451208\pi$
$572$	1.55476e39	+	2.69293e39i	0.161965	+	0.280532i
$573$	−9.14140e39			−0.928476
$574$	−5.19824e38	+	4.57005e38i	−0.0514794	+	0.0452583i
$575$	1.34092e40			1.29485
$576$	1.71907e39	+	2.97752e39i	0.161871	+	0.280368i
$577$	−4.66099e39	+	8.07307e39i	−0.427985	+	0.741292i	−0.996694	−	0.0812467i	$-0.974110\pi$
$577$	−4.66099e39	+	8.07307e39i	−0.427985	+	0.741292i	0.568709	+	0.822539i	$0.307443\pi$
$578$	1.79076e38	−	3.10169e38i	0.0160356	−	0.0277744i
$579$	−5.60076e39	−	9.70080e39i	−0.489111	−	0.847166i
$580$	1.83881e40			1.56614
$581$	2.43100e39	+	1.21434e40i	0.201944	+	1.00876i
$582$	−3.44904e38			−0.0279457
$583$	−1.50489e39	−	2.60655e39i	−0.118935	−	0.206002i
$584$	−1.43978e39	+	2.49376e39i	−0.110996	+	0.192251i
$585$	−2.27456e39	+	3.93965e39i	−0.171056	+	0.296277i
$586$	2.61396e38	+	4.52751e38i	0.0191771	+	0.0332157i
$587$	−3.42951e39			−0.245459			−0.122730	−	0.992440i	$-0.539165\pi$
$587$	−3.42951e39			−0.245459			−0.122730	+	0.992440i	$0.539165\pi$
$588$	6.54031e39	+	4.99305e39i	0.456696	+	0.348654i
$589$	−6.84103e39			−0.466069
$590$	9.00595e38	+	1.55988e39i	0.0598654	+	0.103690i
$591$	−7.99517e38	+	1.38480e39i	−0.0518572	+	0.0898193i
$592$	9.33877e39	−	1.61752e40i	0.591051	−	1.02373i
$593$	−4.62397e39	−	8.00896e39i	−0.285576	−	0.494633i	0.687172	−	0.726494i	$-0.258852\pi$
$593$	−4.62397e39	−	8.00896e39i	−0.285576	−	0.494633i	−0.972749	+	0.231862i	$0.925518\pi$
$594$	−1.07375e38			−0.00647142
$595$	−3.73971e39	−	1.86807e40i	−0.219959	−	1.09875i
$596$	2.37803e40			1.36504
$597$	−5.48664e39	−	9.50313e39i	−0.307382	−	0.532401i
$598$	−4.13524e38	+	7.16244e38i	−0.0226117	+	0.0391646i
$599$	−1.34745e40	+	2.33385e40i	−0.719155	+	1.24561i	0.242180	+	0.970231i	$0.422138\pi$
$599$	−1.34745e40	+	2.33385e40i	−0.719155	+	1.24561i	−0.961335	+	0.275382i	$0.911196\pi$
$600$	−1.02389e39	−	1.77343e39i	−0.0533410	−	0.0923893i
$601$	−2.14779e40			−1.09223			−0.546113	−	0.837711i	$-0.683893\pi$
$601$	−2.14779e40			−1.09223			−0.546113	+	0.837711i	$0.683893\pi$
$602$	4.48973e38	−	3.94716e38i	0.0222880	−	0.0195946i
$603$	−7.22190e39			−0.349986
$604$	−1.37873e40	−	2.38802e40i	−0.652292	−	1.12980i
$605$	1.26559e40	−	2.19207e40i	0.584576	−	1.01252i
$606$	−7.52914e38	+	1.30408e39i	−0.0339541	+	0.0588102i
$607$	5.41491e39	+	9.37889e39i	0.238427	+	0.412967i	0.960263	−	0.279097i	$-0.0900350\pi$
$607$	5.41491e39	+	9.37889e39i	0.238427	+	0.412967i	−0.721836	+	0.692064i	$0.756702\pi$
$608$	−3.04094e39			−0.130739
$609$	1.34187e40	+	4.53664e39i	0.563325	+	0.190451i
$610$	−2.31836e39			−0.0950383
$611$	−1.34653e40	−	2.33225e40i	−0.539035	−	0.933637i
$612$	3.11151e39	−	5.38930e39i	0.121640	−	0.210686i
$613$	−7.82090e39	+	1.35462e40i	−0.298593	+	0.517179i	−0.975814	−	0.218601i	$-0.929851\pi$
$613$	−7.82090e39	+	1.35462e40i	−0.298593	+	0.517179i	0.677221	+	0.735780i	$0.263184\pi$
$614$	−6.12312e38	−	1.06056e39i	−0.0228314	−	0.0395451i
$615$	−2.39275e40			−0.871381
$616$	−1.78683e39	−	6.04099e38i	−0.0635570	−	0.0214876i
$617$	3.13844e40			1.09038			0.545191	−	0.838312i	$-0.316457\pi$
$617$	3.13844e40			1.09038			0.545191	+	0.838312i	$0.316457\pi$
$618$	−2.84840e38	−	4.93358e38i	−0.00966648	−	0.0167428i
$619$	1.19101e39	−	2.06289e39i	0.0394821	−	0.0683851i	−0.845609	−	0.533803i	$-0.820763\pi$
$619$	1.19101e39	−	2.06289e39i	0.0394821	−	0.0683851i	0.885091	+	0.465418i	$0.154096\pi$
$620$	1.73120e40	−	2.99852e40i	0.560617	−	0.971018i
$621$	2.95109e39	+	5.11144e39i	0.0933587	+	0.161702i
$622$	1.89333e39			0.0585149
$623$	4.95846e39	−	4.35925e39i	0.149717	−	0.131624i
$624$	−1.29565e40			−0.382218
$625$	9.60051e39	+	1.66286e40i	0.276716	+	0.479286i
$626$	2.02871e39	−	3.51383e39i	0.0571338	−	0.0989586i
$627$	−3.21306e39	+	5.56518e39i	−0.0884178	+	0.153144i
$628$	2.75592e40	+	4.77340e40i	0.741058	+	1.28355i
$629$	−3.34751e40			−0.879606
$630$	−2.70178e38	−	1.34960e39i	−0.00693765	−	0.0346552i
$631$	−5.01433e40			−1.25831			−0.629155	−	0.777280i	$-0.716599\pi$
$631$	−5.01433e40			−1.25831			−0.629155	+	0.777280i	$0.716599\pi$
$632$	5.82611e38	+	1.00911e39i	0.0142883	+	0.0247481i
$633$	1.15416e40	−	1.99907e40i	0.276639	−	0.479152i
$634$	−1.79728e39	+	3.11298e39i	−0.0421038	+	0.0729260i
$635$	−4.79266e40	−	8.30113e40i	−1.09738	−	1.90072i
$636$	1.26022e40			0.282044
$637$	−2.83384e40	+	1.18199e40i	−0.619945	+	0.258577i
$638$	−1.61958e39			−0.0346340
$639$	6.24462e39	+	1.08160e40i	0.130540	+	0.226102i
$640$	1.02522e40	−	1.77573e40i	0.209511	−	0.362884i
$641$	3.76959e40	−	6.52911e40i	0.753099	−	1.30441i	−0.193215	−	0.981157i	$-0.561891\pi$
$641$	3.76959e40	−	6.52911e40i	0.753099	−	1.30441i	0.946314	−	0.323249i	$-0.104775\pi$
$642$	2.16864e38	+	3.75620e38i	0.00423575	+	0.00733654i
$643$	−6.18533e40			−1.18115			−0.590574	−	0.806984i	$-0.701098\pi$
$643$	−6.18533e40			−1.18115			−0.590574	+	0.806984i	$0.701098\pi$
$644$	1.01514e40	+	5.07087e40i	0.189532	+	0.946755i
$645$	2.06662e40			0.377264
$646$	9.01040e38	+	1.56065e39i	0.0160832	+	0.0278569i
$647$	−3.73030e40	+	6.46107e40i	−0.651076	+	1.12770i	0.331786	+	0.943355i	$0.392349\pi$
$647$	−3.73030e40	+	6.46107e40i	−0.651076	+	1.12770i	−0.982862	+	0.184342i	$0.940985\pi$
$648$	4.50675e38	−	7.80592e38i	0.00769176	−	0.0133225i
$649$	1.63934e40	+	2.83941e40i	0.273602	+	0.473893i
$650$	3.81148e39			0.0622086
$651$	2.00312e40	−	1.76105e40i	0.319729	−	0.281091i
$652$	−6.46310e40			−1.00891
$653$	1.12493e40	+	1.94844e40i	0.171745	+	0.297471i	0.939030	−	0.343835i	$-0.111726\pi$
$653$	1.12493e40	+	1.94844e40i	0.171745	+	0.297471i	−0.767285	+	0.641306i	$0.778393\pi$
$654$	1.65224e39	−	2.86176e39i	0.0246715	−	0.0427322i
$655$	8.33169e40	−	1.44309e41i	1.21684	−	2.10763i
$656$	−3.40744e40	−	5.90186e40i	−0.486768	−	0.843108i
$657$	−3.82487e40			−0.534465
$658$	7.71889e39	+	2.60963e39i	0.105507	+	0.0356701i
$659$	1.24818e41			1.66893			0.834464	−	0.551063i	$-0.185778\pi$
$659$	1.24818e41			1.66893			0.834464	+	0.551063i	$0.185778\pi$
$660$	−1.62620e40	−	2.81666e40i	−0.212709	−	0.368423i
$661$	5.82147e40	−	1.00831e41i	0.744923	−	1.29024i	−0.205308	−	0.978697i	$-0.565820\pi$
$661$	5.82147e40	−	1.00831e41i	0.744923	−	1.29024i	0.950231	−	0.311547i	$-0.100847\pi$
$662$	2.12003e38	−	3.67200e38i	0.00265400	−	0.00459687i
$663$	1.16108e40	+	2.01104e40i	0.142205	+	0.246306i
$664$	1.18865e40			0.142436
$665$	−7.80339e40	−	2.63820e40i	−0.914891	−	0.309310i
$666$	−2.41844e39			−0.0277433
$667$	4.45125e40	+	7.70980e40i	0.499641	+	0.865403i
$668$	−5.86432e40	+	1.01573e41i	−0.644109	+	1.11563i
$669$	−2.94726e40	+	5.10481e40i	−0.316767	+	0.548657i
$670$	5.29235e39	+	9.16662e39i	0.0556626	+	0.0964105i
$671$	−4.22007e40			−0.434353
$672$	8.90416e39	−	7.82812e39i	0.0896888	−	0.0788503i
$673$	3.09389e40			0.304990			0.152495	−	0.988304i	$-0.451269\pi$
$673$	3.09389e40			0.304990			0.152495	+	0.988304i	$0.451269\pi$
$674$	−3.94759e39	−	6.83743e39i	−0.0380859	−	0.0659667i
$675$	1.36002e40	−	2.35563e40i	0.128423	−	0.222434i
$676$	−2.95474e40	+	5.11776e40i	−0.273082	+	0.472991i
$677$	7.58751e40	+	1.31419e41i	0.686378	+	1.18884i	0.973002	+	0.230798i	$0.0741337\pi$
$677$	7.58751e40	+	1.31419e41i	0.686378	+	1.18884i	−0.286624	+	0.958043i	$0.592533\pi$
$678$	7.27981e38			0.00644599
$679$	−1.57973e40	−	7.89114e40i	−0.136922	−	0.683956i
$680$	−1.82856e40			−0.155142
$681$	2.38692e40	+	4.13427e40i	0.198246	+	0.343373i
$682$	−1.52479e39	+	2.64102e39i	−0.0123976	+	0.0214733i
$683$	−9.17025e40	+	1.58833e41i	−0.729929	+	1.26427i	0.226983	+	0.973899i	$0.427114\pi$
$683$	−9.17025e40	+	1.58833e41i	−0.729929	+	1.26427i	−0.956913	+	0.290376i	$0.906220\pi$
$684$	−1.34533e40	−	2.33018e40i	−0.104837	−	0.181584i
$685$	1.67345e41			1.27673
$686$	4.07810e39	−	8.34703e39i	0.0304620	−	0.0623494i
$687$	7.37787e40			0.539583
$688$	2.94301e40	+	5.09745e40i	0.210746	+	0.365023i
$689$	−2.35128e40	+	4.07254e40i	−0.164864	+	0.285553i
$690$	4.32524e39	−	7.49153e39i	0.0296960	−	0.0514350i
$691$	5.04521e40	+	8.73856e40i	0.339193	+	0.587500i	0.984281	−	0.176608i	$-0.0565126\pi$
$691$	5.04521e40	+	8.73856e40i	0.339193	+	0.587500i	−0.645088	+	0.764108i	$0.723179\pi$
$692$	−5.71517e40			−0.376262
$693$	−4.91800e39	−	2.45666e40i	−0.0317071	−	0.158384i
$694$	−1.45961e40			−0.0921562
$695$	1.86817e41	+	3.23576e41i	1.15515	+	2.00077i
$696$	6.79771e39	−	1.17740e40i	0.0411651	−	0.0713000i
$697$	−6.10704e40	+	1.05777e41i	−0.362206	+	0.627359i
$698$	−7.80554e39	−	1.35196e40i	−0.0453418	−	0.0785344i
$699$	6.27096e40			0.356792
$700$	1.78993e41	−	1.57362e41i	0.997501	−	0.876957i
$701$	−3.35866e41			−1.83339			−0.916694	−	0.399590i	$-0.869153\pi$
$701$	−3.35866e41			−1.83339			−0.916694	+	0.399590i	$0.869153\pi$
$702$	8.38828e38	+	1.45289e39i	0.00448523	+	0.00776865i
$703$	−7.23687e40	+	1.25346e41i	−0.379052	+	0.656537i
$704$	4.58626e40	−	7.94364e40i	0.235318	−	0.407583i
$705$	1.40839e41	+	2.43941e41i	0.707916	+	1.22615i
$706$	−2.57635e39			−0.0126863
$707$	−3.32849e41	−	1.12531e41i	−1.60571	−	0.542863i
$708$	−1.37280e41			−0.648823
$709$	6.27268e40	+	1.08646e41i	0.290458	+	0.503088i	0.973918	−	0.226900i	$-0.0728591\pi$
$709$	6.27268e40	+	1.08646e41i	0.290458	+	0.503088i	−0.683460	+	0.729988i	$0.739526\pi$
$710$	9.15235e39	−	1.58523e40i	0.0415228	−	0.0719196i
$711$	−7.73874e39	+	1.34039e40i	−0.0344002	+	0.0595829i
$712$	−3.16842e39	−	5.48786e39i	−0.0138001	−	0.0239025i
$713$	1.67630e41			0.715406
$714$	−6.65581e39	−	2.25022e39i	−0.0278341	−	0.00941025i
$715$	1.21365e41			0.497342
$716$	−1.03600e41	−	1.79440e41i	−0.416026	−	0.720578i
$717$	4.24751e40	−	7.35690e40i	0.167150	−	0.289513i
$718$	1.01457e39	−	1.75729e39i	0.00391271	−	0.00677702i
$719$	−2.14887e41	−	3.72195e41i	−0.812159	−	1.40670i	−0.911350	−	0.411632i	$-0.864959\pi$
$719$	−2.14887e41	−	3.72195e41i	−0.812159	−	1.40670i	0.0991908	−	0.995068i	$-0.468375\pi$
$720$	1.35518e41			0.501968
$721$	9.98301e40	−	8.77660e40i	0.362410	−	0.318614i
$722$	−1.17114e40			−0.0416698
$723$	6.88088e40	+	1.19180e41i	0.239960	+	0.415623i
$724$	−2.69188e41	+	4.66247e41i	−0.920124	+	1.59370i
$725$	2.05138e41	−	3.55309e41i	0.687297	−	1.19043i
$726$	−4.66735e39	−	8.08408e39i	−0.0153281	−	0.0265491i
$727$	−9.78183e40			−0.314899			−0.157450	−	0.987527i	$-0.550327\pi$
$727$	−9.78183e40			−0.314899			−0.157450	+	0.987527i	$0.550327\pi$
$728$	5.78491e39	+	2.88970e40i	0.0182554	+	0.0911900i
$729$	1.19725e40			0.0370370
$730$	2.80294e40	+	4.85483e40i	0.0850026	+	0.147229i
$731$	5.27467e40	−	9.13599e40i	0.156817	−	0.271615i
$732$	8.83488e40	−	1.53025e41i	0.257507	−	0.446016i
$733$	−2.28485e40	−	3.95748e40i	−0.0652906	−	0.113087i	0.831532	−	0.555476i	$-0.187464\pi$
$733$	−2.28485e40	−	3.95748e40i	−0.0652906	−	0.113087i	−0.896823	+	0.442390i	$0.854131\pi$
$734$	3.03677e40			0.0850784
$735$	2.96404e41	−	1.23629e41i	0.814175	−	0.339590i
$736$	7.45139e40			0.200682
$737$	9.63355e40	+	1.66858e41i	0.254395	+	0.440624i
$738$	−4.41208e39	+	7.64194e39i	−0.0114242	+	0.0197873i
$739$	−1.03523e41	+	1.79307e41i	−0.262841	+	0.455253i	−0.966996	−	0.254793i	$-0.917993\pi$
$739$	−1.03523e41	+	1.79307e41i	−0.262841	+	0.455253i	0.704155	+	0.710046i	$0.251326\pi$
$740$	−3.66273e41	−	6.34403e41i	−0.911895	−	1.57945i
$741$	1.00404e41			0.245123
$742$	−2.79292e39	−	1.39513e40i	−0.00668653	−	0.0334008i
$743$	2.07044e41			0.486098			0.243049	−	0.970014i	$-0.421852\pi$
$743$	2.07044e41			0.486098			0.243049	+	0.970014i	$0.421852\pi$
$744$	−1.27997e40	−	2.21698e40i	−0.0294709	−	0.0510451i
$745$	4.64073e41	−	8.03797e41i	1.04790	−	1.81502i
$746$	−2.73144e39	+	4.73100e39i	−0.00604894	+	0.0104771i
$747$	7.89437e40	+	1.36735e41i	0.171462	+	0.296982i
$748$	−1.66022e41			−0.353666
$749$	−7.60062e40	+	6.68211e40i	−0.158804	+	0.139613i
$750$	−9.99504e39			−0.0204831
$751$	8.46860e40	+	1.46680e41i	0.170229	+	0.294844i	0.938500	−	0.345280i	$-0.112216\pi$
$751$	8.46860e40	+	1.46680e41i	0.170229	+	0.294844i	−0.768271	+	0.640125i	$0.778883\pi$
$752$	−4.01130e41	+	6.94777e41i	−0.790908	+	1.36989i
$753$	6.42087e40	−	1.11213e41i	0.124184	−	0.215094i
$754$	1.26524e40	+	2.19146e40i	0.0240042	+	0.0415766i
$755$	−1.07623e42			−2.00298
$756$	9.93772e40	+	3.35978e40i	0.181435	+	0.0613402i
$757$	1.48687e41			0.266307			0.133153	−	0.991095i	$-0.457490\pi$
$757$	1.48687e41			0.266307			0.133153	+	0.991095i	$0.457490\pi$
$758$	−1.00582e38	−	1.74213e38i	−0.000176732	−	0.000306109i
$759$	7.87314e40	−	1.36367e41i	0.135719	−	0.235073i
$760$	−3.95309e40	+	6.84694e40i	−0.0668558	+	0.115798i
$761$	−1.94098e41	−	3.36187e41i	−0.322065	−	0.557832i	0.658849	−	0.752275i	$-0.271044\pi$
$761$	−1.94098e41	−	3.36187e41i	−0.322065	−	0.557832i	−0.980914	+	0.194443i	$0.937710\pi$
$762$	−3.53494e40			−0.0575486
$763$	7.30424e41	+	2.46944e41i	1.16673	+	0.394451i
$764$	−1.02115e42			−1.60042
$765$	−1.21442e41	−	2.10344e41i	−0.186758	−	0.323474i
$766$	−2.06449e40	+	3.57580e40i	−0.0311527	+	0.0539580i
$767$	2.56134e41	−	4.43638e41i	0.379258	−	0.656895i
$768$	1.89179e41	+	3.27667e41i	0.274875	+	0.476097i
$769$	−1.09835e42			−1.56606			−0.783028	−	0.621986i	$-0.786326\pi$
$769$	−1.09835e42			−1.56606			−0.783028	+	0.621986i	$0.786326\pi$
$770$	−2.75778e40	+	2.42452e40i	−0.0385873	+	0.0339242i
$771$	−7.92680e41			−1.08845
$772$	−6.25638e41	−	1.08364e42i	−0.843086	−	1.46027i
$773$	−7.75935e40	+	1.34396e41i	−0.102618	+	0.177739i	−0.912762	−	0.408491i	$-0.866055\pi$
$773$	−7.75935e40	+	1.34396e41i	−0.102618	+	0.177739i	0.810145	+	0.586230i	$0.199389\pi$
$774$	3.81072e39	−	6.60037e39i	0.00494611	−	0.00856691i
$775$	−3.86264e41	−	6.69029e41i	−0.492050	−	0.852256i
$776$	−7.72421e40			−0.0965738
$777$	−1.10769e41	−	5.53320e41i	−0.135930	−	0.679002i
$778$	5.72121e40			0.0689103
$779$	2.64052e41	+	4.57351e41i	0.312173	+	0.540700i
$780$	−2.54082e41	+	4.40082e41i	−0.294850	+	0.510696i
$781$	1.66598e41	−	2.88557e41i	0.189771	−	0.328694i
$782$	−2.20787e40	−	3.82414e40i	−0.0246874	−	0.0427598i
$783$	1.80586e41			0.198216
$784$	7.27039e41	+	5.55041e41i	0.783384	+	0.598057i
$785$	2.15127e42			2.27554
$786$	−3.07262e40	−	5.32194e40i	−0.0319067	−	0.0552640i
$787$	5.83726e41	−	1.01104e42i	0.595080	−	1.03071i	−0.398455	−	0.917188i	$-0.630454\pi$
$787$	5.83726e41	−	1.01104e42i	0.595080	−	1.03071i	0.993536	−	0.113522i	$-0.0362131\pi$
$788$	−8.93107e40	+	1.54691e41i	−0.0893868	+	0.154822i
$789$	3.11131e41	+	5.38895e41i	0.305722	+	0.529526i
$790$	2.26844e40			0.0218844
$791$	3.33431e40	+	1.66556e41i	0.0315825	+	0.157762i
$792$	−2.40469e40			−0.0223637
$793$	3.29678e41	+	5.71019e41i	0.301043	+	0.521422i
$794$	−5.87121e40	+	1.01692e41i	−0.0526417	+	0.0911781i
$795$	2.45931e41	−	4.25966e41i	0.216516	−	0.375017i
$796$	−6.12889e41	−	1.06156e42i	−0.529837	−	0.917705i
$797$	−5.27294e41			−0.447617			−0.223809	−	0.974633i	$-0.571849\pi$
$797$	−5.27294e41			−0.447617			−0.223809	+	0.974633i	$0.571849\pi$
$798$	−2.28148e40	+	2.00577e40i	−0.0190184	+	0.0167201i
$799$	1.43786e42			1.17703
$800$	−1.71700e41	−	2.97393e41i	−0.138028	−	0.239071i
$801$	4.20857e40	−	7.28945e40i	0.0332248	−	0.0575471i
$802$	−3.80153e40	+	6.58444e40i	−0.0294734	+	0.0510494i
$803$	5.10213e41	+	8.83715e41i	0.388487	+	0.672879i
$804$	−8.06728e41			−0.603274
$805$	1.91211e42	+	6.46453e41i	1.40434	+	0.474784i
$806$	4.76476e40			0.0343703
$807$	2.82281e41	+	4.88924e41i	0.199993	+	0.346398i
$808$	−1.68617e41	+	2.92053e41i	−0.117337	+	0.203234i
$809$	1.29688e42	−	2.24627e42i	0.886436	−	1.53535i	0.0423765	−	0.999102i	$-0.486507\pi$
$809$	1.29688e42	−	2.24627e42i	0.886436	−	1.53535i	0.844059	−	0.536250i	$-0.180160\pi$
$810$	−8.77369e39	−	1.51965e40i	−0.00589047	−	0.0102026i
$811$	−1.36729e42			−0.901689			−0.450844	−	0.892603i	$-0.648877\pi$
$811$	−1.36729e42			−0.901689			−0.450844	+	0.892603i	$0.648877\pi$
$812$	1.49895e42	+	5.06769e41i	0.971010	+	0.328283i
$813$	−2.66281e41			−0.169445
$814$	3.22604e40	+	5.58767e40i	0.0201658	+	0.0349282i
$815$	−1.26127e42	+	2.18459e42i	−0.774504	+	1.34148i
$816$	3.45884e41	−	5.99089e41i	0.208653	−	0.361397i
$817$	−2.28062e41	−	3.95015e41i	−0.135155	−	0.234096i
$818$	−1.43865e41			−0.0837593
$819$	−2.93991e41	+	2.58463e41i	−0.168158	+	0.147837i
$820$	−2.67284e42			−1.50201
$821$	1.01446e42	+	1.75710e42i	0.560092	+	0.970107i	0.997488	+	0.0708381i	$0.0225674\pi$
$821$	1.01446e42	+	1.75710e42i	0.560092	+	0.970107i	−0.437396	+	0.899269i	$0.644099\pi$
$822$	3.08574e40	−	5.34466e40i	0.0167386	−	0.0289921i
$823$	−1.73274e42	+	3.00119e42i	−0.923497	+	1.59954i	−0.129535	+	0.991575i	$0.541349\pi$
$823$	−1.73274e42	+	3.00119e42i	−0.923497	+	1.59954i	−0.793961	+	0.607968i	$0.791985\pi$
$824$	−6.37906e40	−	1.10489e41i	−0.0334050	−	0.0578592i
$825$	−7.25673e41			−0.373387
$826$	3.04243e40	+	1.51977e41i	0.0153819	+	0.0768362i
$827$	−1.45788e42			−0.724253			−0.362127	−	0.932129i	$-0.617949\pi$
$827$	−1.45788e42			−0.724253			−0.362127	+	0.932129i	$0.617949\pi$
$828$	3.29654e41	+	5.70978e41i	0.160923	+	0.278727i
$829$	−1.48055e42	+	2.56440e42i	−0.710205	+	1.23011i	0.254575	+	0.967053i	$0.418064\pi$
$829$	−1.48055e42	+	2.56440e42i	−0.710205	+	1.23011i	−0.964780	+	0.263058i	$0.915269\pi$
$830$	1.15703e41	−	2.00404e41i	0.0545397	−	0.0944655i
$831$	−4.47498e41	−	7.75089e41i	−0.207289	−	0.359035i
$832$	−1.43314e42			−0.652380
$833$	2.09983e41	−	1.62586e42i	0.0939360	−	0.727330i
$834$	1.37791e41			0.0605779
$835$	2.28885e42	+	3.96440e42i	0.988923	+	1.71286i
$836$	−3.58918e41	+	6.21664e41i	−0.152407	+	0.263976i
$837$	1.70017e41	−	2.94479e41i	0.0709536	−	0.122895i
$838$	1.02066e41	+	1.76784e41i	0.0418643	+	0.0725111i
$839$	2.99131e42			1.20591			0.602953	−	0.797777i	$-0.293991\pi$
$839$	2.99131e42			1.20591			0.602953	+	0.797777i	$0.293991\pi$
$840$	−6.05070e40	−	3.02247e41i	−0.0239749	−	0.119760i
$841$	1.56171e41			0.0608217
$842$	9.61740e40	+	1.66578e41i	0.0368156	+	0.0637665i
$843$	8.89811e40	−	1.54120e41i	0.0334810	−	0.0579907i
$844$	1.28927e42	−	2.23308e42i	0.476845	−	0.825920i
$845$	1.15324e42	+	1.99746e42i	0.419272	+	0.726200i
$846$	1.03880e41			0.0371244
$847$	1.63580e42	−	1.43812e42i	0.574673	−	0.505226i
$848$	1.40089e42			0.483799
$849$	3.30740e41	+	5.72858e41i	0.112286	+	0.194485i
$850$	−1.01751e41	+	1.76237e41i	−0.0339596	+	0.0588197i
$851$	1.77329e42	−	3.07143e42i	0.581836	−	1.00777i
$852$	6.97560e41	+	1.20821e42i	0.225013	+	0.389734i
$853$	−2.60521e42			−0.826193			−0.413097	−	0.910687i	$-0.635553\pi$
$853$	−2.60521e42			−0.826193			−0.413097	+	0.910687i	$0.635553\pi$
$854$	−1.88986e41	−	6.38931e40i	−0.0589238	−	0.0199212i
$855$	−1.05017e42			−0.321921
$856$	4.85673e40	+	8.41210e40i	0.0146377	+	0.0253533i
$857$	−2.78390e41	+	4.82185e41i	−0.0824956	+	0.142887i	−0.904321	−	0.426852i	$-0.859622\pi$
$857$	−2.78390e41	+	4.82185e41i	−0.0824956	+	0.142887i	0.821826	+	0.569739i	$0.192956\pi$
$858$	2.23789e40	−	3.87613e40i	0.00652037	−	0.0112936i
$859$	−6.76889e41	−	1.17241e42i	−0.193917	−	0.335874i	0.752628	−	0.658446i	$-0.228786\pi$
$859$	−6.76889e41	−	1.17241e42i	−0.193917	−	0.335874i	−0.946545	+	0.322572i	$0.895453\pi$
$860$	2.30854e42			0.650294
$861$	−1.95050e42	−	6.59432e41i	−0.540257	−	0.182652i
$862$	4.14975e41			0.113023
$863$	2.48314e42	+	4.30092e42i	0.665035	+	1.15187i	0.979276	+	0.202531i	$0.0649167\pi$
$863$	2.48314e42	+	4.30092e42i	0.665035	+	1.15187i	−0.314241	+	0.949343i	$0.601750\pi$
$864$	7.55753e40	−	1.30900e41i	0.0199036	−	0.0344740i
$865$	−1.11531e42	+	1.93178e42i	−0.288844	+	0.500293i
$866$	−5.95831e40	−	1.03201e41i	−0.0151745	−	0.0262830i
$867$	1.06541e42			0.266832
$868$	2.23760e42	−	1.96719e42i	0.551120	−	0.484519i
$869$	4.12920e41			0.100018
$870$	−1.32337e41	−	2.29215e41i	−0.0315248	−	0.0546026i
$871$	1.50517e42	−	2.60704e42i	0.352633	−	0.610779i
$872$	3.70022e41	−	6.40897e41i	0.0852587	−	0.147672i
$873$	−5.12999e41	−	8.88540e41i	−0.116254	−	0.201359i
$874$	−1.90924e41			−0.0425545
$875$	−4.57794e41	−	2.28679e42i	−0.100358	−	0.501313i
$876$	−4.27260e42			−0.921262
$877$	4.07817e41	+	7.06360e41i	0.0864910	+	0.149807i	0.906026	−	0.423223i	$-0.139101\pi$
$877$	4.07817e41	+	7.06360e41i	0.0864910	+	0.149807i	−0.819535	+	0.573030i	$0.805768\pi$
$878$	1.85471e41	−	3.21244e41i	0.0386905	−	0.0670139i
$879$	−7.77581e41	+	1.34681e42i	−0.159554	+	0.276355i
$880$	−1.80773e42	−	3.13107e42i	−0.364866	−	0.631967i
$881$	−2.79098e42			−0.554124			−0.277062	−	0.960852i	$-0.589361\pi$
$881$	−2.79098e42			−0.554124			−0.277062	+	0.960852i	$0.589361\pi$
$882$	1.51704e40	−	1.17462e41i	0.00296280	−	0.0229404i
$883$	−9.16941e41			−0.176162			−0.0880808	−	0.996113i	$-0.528073\pi$
$883$	−9.16941e41			−0.176162			−0.0880808	+	0.996113i	$0.528073\pi$
$884$	1.29699e42	+	2.24645e42i	0.245120	+	0.424560i
$885$	−2.67903e42	+	4.64021e42i	−0.498081	+	0.862701i
$886$	3.87612e40	−	6.71363e40i	0.00708938	−	0.0122792i
$887$	−4.64516e42	−	8.04565e42i	−0.835811	−	1.44767i	−0.893368	−	0.449325i	$-0.851664\pi$
$887$	−4.64516e42	−	8.04565e42i	−0.835811	−	1.44767i	0.0575571	−	0.998342i	$-0.481669\pi$
$888$	−5.41614e41			−0.0958743
$889$	−1.61908e42	−	8.08767e42i	−0.281963	−	1.40847i
$890$	−1.23365e41			−0.0211367
$891$	−1.59706e41	−	2.76618e41i	−0.0269212	−	0.0466288i
$892$	−3.29227e42	+	5.70237e42i	−0.546015	+	0.945726i
$893$	3.10846e42	−	5.38401e42i	0.507224	−	0.878537i
$894$	−1.71144e41	−	2.96430e41i	−0.0274769	−	0.0475914i
$895$	−8.08701e42			−1.27748
$896$	1.32511e42	−	1.16498e42i	0.205962	−	0.181072i
$897$	−2.46024e42			−0.376259
$898$	−1.39149e41	−	2.41014e41i	−0.0209399	−	0.0362689i
$899$	2.56444e42	−	4.44174e42i	0.379732	−	0.657715i
$900$	1.51922e42	−	2.63137e42i	0.221363	−	0.383413i
$901$	−1.25539e42	−	2.17439e42i	−0.179998	−	0.311766i
$902$	2.35417e41			0.0332157
$903$	1.68465e42	+	5.69553e41i	0.233904	+	0.0790791i
$904$	1.63033e41			0.0222758
$905$	1.05064e43	+	1.81976e43i	1.41270	+	2.44687i
$906$	−1.98451e41	+	3.43726e41i	−0.0262599	+	0.0454835i
$907$	6.00136e42	−	1.03947e43i	0.781527	−	1.35364i	−0.149525	−	0.988758i	$-0.547775\pi$
$907$	6.00136e42	−	1.03947e43i	0.781527	−	1.35364i	0.931052	−	0.364886i	$-0.118892\pi$
$908$	2.66633e42	+	4.61822e42i	0.341719	+	0.591875i
$909$	−4.47943e42			−0.564997
$910$	5.43504e41	+	1.83750e41i	0.0674687	+	0.0228101i
$911$	−1.13716e43			−1.38933			−0.694664	−	0.719334i	$-0.744447\pi$
$911$	−1.13716e43			−1.38933			−0.694664	+	0.719334i	$0.744447\pi$
$912$	−1.49551e42	−	2.59030e42i	−0.179831	−	0.311476i
$913$	2.10612e42	−	3.64790e42i	0.249262	−	0.431735i
$914$	−3.40599e41	+	5.89935e41i	−0.0396756	+	0.0687202i
$915$	−3.44825e42	−	5.97255e42i	−0.395360	−	0.684784i
$916$	8.24151e42			0.930085
$917$	1.07688e43	−	9.46747e42i	1.19623	−	1.05167i
$918$	−8.95727e40			−0.00979393
$919$	9.49618e41	+	1.64479e42i	0.102205	+	0.177025i	0.912593	−	0.408869i	$-0.134077\pi$
$919$	9.49618e41	+	1.64479e42i	0.102205	+	0.177025i	−0.810388	+	0.585894i	$0.800743\pi$
$920$	9.68646e41	−	1.67774e42i	0.102622	−	0.177747i
$921$	1.82146e42	−	3.15487e42i	0.189957	−	0.329015i
$922$	5.54536e41	+	9.60485e41i	0.0569287	+	0.0986034i
$923$	−5.20596e42			−0.526110
$924$	−5.49369e41	−	2.74423e42i	−0.0546538	−	0.273009i
$925$	−1.63445e43			−1.60073
$926$	−7.95853e40	−	1.37846e41i	−0.00767315	−	0.0132903i
$927$	8.47322e41	−	1.46761e42i	0.0804253	−	0.139301i
$928$	1.13993e42	−	1.97442e42i	0.106521	−	0.184499i
$929$	3.86997e42	+	6.70298e42i	0.356024	+	0.616652i	0.987293	−	0.158912i	$-0.0507988\pi$
$929$	3.86997e42	+	6.70298e42i	0.356024	+	0.616652i	−0.631269	+	0.775564i	$0.717465\pi$
$930$	−4.98368e41			−0.0451385
$931$	−5.63402e42	−	4.30117e42i	−0.502398	−	0.383545i
$932$	7.00503e42			0.615006
$933$	2.81607e42	+	4.87758e42i	0.243422	+	0.421620i
$934$	2.01796e41	−	3.49522e41i	0.0171745	−	0.0297471i
$935$	−3.23993e42	+	5.61172e42i	−0.271498	+	0.470248i
$936$	1.87857e41	+	3.25379e41i	0.0154999	+	0.0268466i
$937$	−1.78618e43			−1.45111			−0.725554	−	0.688165i	$-0.758417\pi$
$937$	−1.78618e43			−1.45111			−0.725554	+	0.688165i	$0.758417\pi$
$938$	1.78788e41	+	8.93090e41i	0.0143021	+	0.0714421i
$939$	1.20697e43			0.950708
$940$	1.57326e43	+	2.72496e43i	1.22024	+	2.11352i
$941$	1.07148e42	−	1.85585e42i	0.0818340	−	0.141741i	−0.822204	−	0.569193i	$-0.807256\pi$
$941$	1.07148e42	−	1.85585e42i	0.0818340	−	0.141741i	0.904038	+	0.427453i	$0.140589\pi$
$942$	3.96681e41	−	6.87071e41i	0.0298334	−	0.0516730i
$943$	−6.47020e42	−	1.12067e43i	−0.479180	−	0.829963i
$944$	−1.52605e43			−1.11295
$945$	3.07498e42	−	2.70338e42i	0.220842	−	0.194154i
$946$	−2.03330e41			−0.0143807
$947$	−4.41531e42	−	7.64754e42i	−0.307529	−	0.532656i	0.670292	−	0.742097i	$-0.266169\pi$
$947$	−4.41531e42	−	7.64754e42i	−0.307529	−	0.532656i	−0.977821	+	0.209441i	$0.932835\pi$
$948$	−8.64463e41	+	1.49729e42i	−0.0592960	+	0.102704i
$949$	7.97172e42	−	1.38074e43i	0.538508	−	0.932722i
$950$	4.39941e41	+	7.62001e41i	0.0292686	+	0.0506948i
$951$	−1.06928e43			−0.700609
$952$	−1.49058e42	−	5.03942e41i	−0.0961880	−	0.0325196i
$953$	7.96609e42			0.506289			0.253144	−	0.967429i	$-0.418535\pi$
$953$	7.96609e42			0.506289			0.253144	+	0.967429i	$0.418535\pi$
$954$	−9.06964e40	−	1.57091e41i	−0.00567726	−	0.00983329i
$955$	−1.99277e43	+	3.45158e43i	−1.22859	+	2.12799i
$956$	4.74472e42	−	8.21809e42i	0.288118	−	0.499036i
$957$	−2.40891e42	−	4.17235e42i	−0.144078	−	0.249550i
$958$	3.17742e41			0.0187187
$959$	1.36415e43	+	4.61197e42i	0.791576	+	0.267619i
$960$	1.49899e43			0.856772
$961$	4.05223e42	+	7.01867e42i	0.228142	+	0.395154i
$962$	5.04046e41	−	8.73033e41i	0.0279532	−	0.0484163i
$963$	−6.45113e41	+	1.11737e42i	−0.0352415	+	0.0610401i
$964$	7.68635e42	+	1.33132e43i	0.413622	+	0.716414i
$965$	−4.88372e43			−2.58884
$966$	5.59044e41	−	4.91486e41i	0.0291929	−	0.0256651i
$967$	3.01060e43			1.54871			0.774353	−	0.632753i	$-0.218075\pi$
$967$	3.01060e43			1.54871			0.774353	+	0.632753i	$0.218075\pi$
$968$	−1.04526e42	−	1.81045e42i	−0.0529703	−	0.0917473i
$969$	−2.68035e42	+	4.64250e42i	−0.133813	+	0.231770i
$970$	−7.51871e41	+	1.30228e42i	−0.0369788	+	0.0640492i
$971$	2.53096e42	+	4.38375e42i	0.122633	+	0.212406i	0.920805	−	0.390023i	$-0.127533\pi$
$971$	2.53096e42	+	4.38375e42i	0.122633	+	0.212406i	−0.798172	+	0.602429i	$0.794200\pi$
$972$	1.33740e42			0.0638411
$973$	6.31113e42	+	3.15256e43i	0.296805	+	1.48261i
$974$	−2.90879e42			−0.134774
$975$	5.66906e42	+	9.81910e42i	0.258788	+	0.448234i
$976$	9.82109e42	−	1.70106e43i	0.441710	−	0.765064i
$977$	−1.95953e41	+	3.39400e41i	−0.00868321	+	0.0150398i	−0.870334	−	0.492461i	$-0.836097\pi$
$977$	−1.95953e41	+	3.39400e41i	−0.00868321	+	0.0150398i	0.861651	+	0.507501i	$0.169431\pi$
$978$	4.65141e41	+	8.05648e41i	0.0203082	+	0.0351748i
$979$	−2.24558e42			−0.0966007
$980$	3.31101e43	−	1.38101e43i	1.40340	−	0.585355i
$981$	9.82991e42			0.410534
$982$	1.64652e41	+	2.85185e41i	0.00677562	+	0.0117357i
$983$	−7.02831e42	+	1.21734e43i	−0.284987	+	0.493612i	−0.972606	−	0.232460i	$-0.925323\pi$
$983$	−7.02831e42	+	1.21734e43i	−0.284987	+	0.493612i	0.687619	+	0.726072i	$0.258656\pi$
$984$	−9.88094e41	+	1.71143e42i	−0.0394793	+	0.0683802i
$985$	3.48579e42	+	6.03757e42i	0.137239	+	0.237704i
$986$	−1.35106e42			−0.0524155
$987$	4.75790e42	+	2.37668e43i	0.181893	+	0.908599i
$988$	1.12157e43			0.422522
$989$	5.58833e42	+	9.67928e42i	0.207461	+	0.359333i
$990$	−2.34071e41	+	4.05423e41i	−0.00856322	+	0.0148319i
$991$	2.46967e43	−	4.27759e43i	0.890370	−	1.54217i	0.0509380	−	0.998702i	$-0.483779\pi$
$991$	2.46967e43	−	4.27759e43i	0.890370	−	1.54217i	0.839432	−	0.543465i	$-0.182888\pi$
$992$	−2.14644e42	−	3.71774e42i	−0.0762603	−	0.132087i
$993$	1.26130e42			0.0441627
$994$	1.18296e42	−	1.04000e42i	0.0408194	−	0.0358865i
$995$	−4.78421e43			−1.62696
$996$	8.81848e42	+	1.52741e43i	0.295552	+	0.511910i
$997$	−5.52581e42	+	9.57099e42i	−0.182523	+	0.316138i	−0.942739	−	0.333532i	$-0.891760\pi$
$997$	−5.52581e42	+	9.57099e42i	−0.182523	+	0.316138i	0.760216	+	0.649670i	$0.225093\pi$
$998$	2.30468e40	−	3.99182e40i	0.000750270	−	0.00129951i
$999$	−3.59710e42	−	6.23036e42i	−0.115412	−	0.199900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.a.4.9	✓	38
7.2	even	3	inner	21.30.e.a.16.9	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.a.4.9	✓	38	1.1	even	1	trivial
21.30.e.a.16.9	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)

\(f(q)\)	\(=\)	\(q+(-803.934 - 1392.45i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.67143e8 - 4.62705e8i) q^{4} +(-1.04266e10 - 1.80594e10i) q^{5} -7.69038e9 q^{6} +(-3.52235e11 - 1.75950e12i) q^{7} -1.72228e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(-803.934 - 1392.45i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(2.67143e8 - 4.62705e8i) q^{4} +(-1.04266e10 - 1.80594e10i) q^{5} -7.69038e9 q^{6} +(-3.52235e11 - 1.75950e12i) q^{7} -1.72228e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-1.67646e13 + 2.90371e13i) q^{10} +(-3.05162e14 + 5.28556e14i) q^{11} +(-1.27774e15 - 2.21310e15i) q^{12} +9.53587e15 q^{13} +(-2.16685e15 + 1.90499e15i) q^{14} -9.97400e16 q^{15} +(-1.42037e17 - 2.46015e17i) q^{16} +(-2.54568e17 + 4.40924e17i) q^{17} +(-1.83914e16 + 3.18549e16i) q^{18} +(1.10068e18 + 1.90643e18i) q^{19} -1.11415e19 q^{20} +(-8.13051e18 - 2.74879e18i) q^{21} +9.81319e17 q^{22} +(-2.69706e19 - 4.67144e19i) q^{23} +(-4.11880e18 + 7.13397e18i) q^{24} +(-1.24295e20 + 2.15285e20i) q^{25} +(-7.66621e18 - 1.32783e19i) q^{26} -1.09419e20 q^{27} +(-9.08226e20 - 3.07056e20i) q^{28} -1.65041e21 q^{29} +(8.01844e19 + 1.38883e20i) q^{30} +(-1.55382e21 + 2.69129e21i) q^{31} +(-6.90696e20 + 1.19632e21i) q^{32} +(1.45958e21 + 2.52807e21i) q^{33} +8.18622e20 q^{34} +(-2.81028e22 + 2.47067e22i) q^{35} -1.22227e22 q^{36} +(3.28745e22 + 5.69403e22i) q^{37} +(1.76975e21 - 3.06529e21i) q^{38} +(2.28049e22 - 3.94992e22i) q^{39} +(1.79575e22 + 3.11032e22i) q^{40} +2.39899e23 q^{41} +(2.70882e21 + 1.35312e22i) q^{42} -2.07201e23 q^{43} +(1.63044e23 + 2.82400e23i) q^{44} +(-2.38527e23 + 4.13140e23i) q^{45} +(-4.33651e22 + 7.51105e22i) q^{46} +(-1.41206e24 - 2.44577e24i) q^{47} -1.35871e24 q^{48} +(-2.97177e24 + 1.23952e24i) q^{49} +3.99700e23 q^{50} +(1.21759e24 + 2.10893e24i) q^{51} +(2.54744e24 - 4.41229e24i) q^{52} +(-2.46572e24 + 4.27076e24i) q^{53} +(8.79656e22 + 1.52361e23i) q^{54} +1.27272e25 q^{55} +(6.06647e23 + 3.03035e24i) q^{56} +1.05290e25 q^{57} +(1.32682e24 + 2.29812e24i) q^{58} +(2.68601e25 - 4.65231e25i) q^{59} +(-2.66448e25 + 4.61502e25i) q^{60} +(3.45724e25 + 5.98811e25i) q^{61} +4.99667e24 q^{62} +(-3.08300e25 + 2.71043e25i) q^{63} -1.50290e26 q^{64} +(-9.94265e25 - 1.72212e26i) q^{65} +(2.34681e24 - 4.06479e24i) q^{66} +(1.57843e26 - 2.73393e26i) q^{67} +(1.36012e26 + 2.35579e26i) q^{68} -2.57999e26 q^{69} +(5.69958e25 + 1.92693e25i) q^{70} -5.45935e26 q^{71} +(1.97001e25 + 3.41216e25i) q^{72} +(8.35972e26 - 1.44795e27i) q^{73} +(5.28579e25 - 9.15525e25i) q^{74} +(5.94499e26 + 1.02970e27i) q^{75} +1.17616e27 q^{76} +(1.03748e27 + 3.50756e26i) q^{77} -7.33344e25 q^{78} +(-3.38279e26 - 5.85917e26i) q^{79} +(-2.96191e27 + 5.13018e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-1.92863e26 - 3.34048e26i) q^{82} -6.90164e27 q^{83} +(-3.44389e27 + 3.02771e27i) q^{84} +1.06171e28 q^{85} +(1.66576e26 + 2.88518e26i) q^{86} +(-3.94693e27 + 6.83629e27i) q^{87} +(5.25573e26 - 9.10320e26i) q^{88} +(1.83967e27 + 3.18640e27i) q^{89} +7.67039e26 q^{90} +(-3.35887e27 - 1.67783e28i) q^{91} -2.88200e28 q^{92} +(7.43187e27 + 1.28724e28i) q^{93} +(-2.27041e27 + 3.93247e27i) q^{94} +(2.29527e28 - 3.97552e28i) q^{95} +(3.30358e27 + 5.72197e27i) q^{96} +4.48488e28 q^{97} +(4.11507e27 + 3.14156e27i) q^{98} +1.39622e28 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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