LMFDB - Embedded newform 21.30.e.a.4.6

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			4.6
Character	$\chi$	$=$	21.4
Dual form			21.30.e.a.16.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10085.3 - 17468.3i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(6.50070e7 - 1.12595e8i) q^{4} +(4.83495e9 + 8.37438e9i) q^{5} -9.64758e10 q^{6} +(-7.77849e11 + 1.61705e12i) q^{7} -1.34515e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(-10085.3 - 17468.3i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(6.50070e7 - 1.12595e8i) q^{4} +(4.83495e9 + 8.37438e9i) q^{5} -9.64758e10 q^{6} +(-7.77849e11 + 1.61705e12i) q^{7} -1.34515e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(9.75244e13 - 1.68917e14i) q^{10} +(6.62931e14 - 1.14823e15i) q^{11} +(-3.10926e14 - 5.38540e14i) q^{12} -2.72703e15 q^{13} +(3.60921e16 - 2.72081e15i) q^{14} +4.62509e16 q^{15} +(1.00763e17 + 1.74527e17i) q^{16} +(-2.12312e17 + 3.67735e17i) q^{17} +(-2.30720e17 + 3.99619e17i) q^{18} +(3.18927e18 + 5.52398e18i) q^{19} +1.25722e18 q^{20} +(4.83790e18 + 7.08914e18i) q^{21} -2.67436e19 q^{22} +(-3.01649e19 - 5.22471e19i) q^{23} +(-3.21691e19 + 5.57186e19i) q^{24} +(4.63787e19 - 8.03303e19i) q^{25} +(2.75031e19 + 4.76367e19i) q^{26} -1.09419e20 q^{27} +(1.31507e20 + 1.92702e20i) q^{28} -5.79588e20 q^{29} +(-4.66456e20 - 8.07925e20i) q^{30} +(9.42484e20 - 1.63243e21i) q^{31} +(-1.57841e21 + 2.73388e21i) q^{32} +(-3.17078e21 - 5.49195e21i) q^{33} +8.56496e21 q^{34} +(-1.73027e22 + 1.30437e21i) q^{35} -2.97430e21 q^{36} +(1.46036e22 + 2.52941e22i) q^{37} +(6.43298e22 - 1.11423e23i) q^{38} +(-6.52166e21 + 1.12958e22i) q^{39} +(-6.50375e22 - 1.12648e23i) q^{40} +2.29250e23 q^{41} +(7.50436e22 - 1.56006e23i) q^{42} +1.35079e22 q^{43} +(-8.61903e22 - 1.49286e23i) q^{44} +(1.10608e23 - 1.91579e23i) q^{45} +(-6.08446e23 + 1.05386e24i) q^{46} +(-2.79171e23 - 4.83539e23i) q^{47} +9.63893e23 q^{48} +(-2.00981e24 - 2.51564e24i) q^{49} -1.87098e24 q^{50} +(1.01548e24 + 1.75886e24i) q^{51} +(-1.77276e23 + 3.07051e23i) q^{52} +(2.64429e24 - 4.58005e24i) q^{53} +(1.10353e24 + 1.91137e24i) q^{54} +1.28210e25 q^{55} +(1.04633e25 - 2.17518e25i) q^{56} +3.05084e25 q^{57} +(5.84535e24 + 1.01244e25i) q^{58} +(-4.39572e23 + 7.61361e23i) q^{59} +(3.00663e24 - 5.20763e24i) q^{60} +(-9.75690e24 - 1.68995e25i) q^{61} -3.80211e25 q^{62} +(4.09342e25 - 3.08584e24i) q^{63} +1.71869e26 q^{64} +(-1.31851e25 - 2.28372e25i) q^{65} +(-6.39568e25 + 1.10776e26i) q^{66} +(6.20696e25 - 1.07508e26i) q^{67} +(2.76035e25 + 4.78107e25i) q^{68} -2.88555e26 q^{69} +(1.97289e26 + 2.89094e26i) q^{70} +3.63928e26 q^{71} +(1.53864e26 + 2.66500e26i) q^{72} +(9.53533e26 - 1.65157e27i) q^{73} +(2.94564e26 - 5.10200e26i) q^{74} +(-2.21828e26 - 3.84217e26i) q^{75} +8.29299e26 q^{76} +(1.34109e27 + 1.96514e27i) q^{77} +2.63093e26 q^{78} +(-2.58725e27 - 4.48125e27i) q^{79} +(-9.74369e26 + 1.68766e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-2.31207e27 - 4.00461e27i) q^{82} +6.18532e27 q^{83} +(1.11270e27 - 8.38813e25i) q^{84} -4.10607e27 q^{85} +(-1.36232e26 - 2.35960e26i) q^{86} +(-1.38608e27 + 2.40075e27i) q^{87} +(-8.91744e27 + 1.54455e28i) q^{88} +(-8.94711e27 - 1.54969e28i) q^{89} -4.46209e27 q^{90} +(2.12122e27 - 4.40976e27i) q^{91} -7.84370e27 q^{92} +(-4.50787e27 - 7.80787e27i) q^{93} +(-5.63108e27 + 9.75331e27i) q^{94} +(-3.08399e28 + 5.34164e28i) q^{95} +(7.54948e27 + 1.30761e28i) q^{96} -4.02847e28 q^{97} +(-2.36745e28 + 6.04792e28i) q^{98} -3.03315e28 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 $

$2$	−10085.3	−	17468.3i	−0.435267	−	0.753905i	0.562050	−	0.827103i	$-0.310013\pi$
$2$	−10085.3	−	17468.3i	−0.435267	−	0.753905i	−0.997317	+	0.0731982i	$0.976679\pi$
$3$	2.39148e6	−	4.14217e6i	0.288675	−	0.500000i
$3$	2.39148e6	−	4.14217e6i	0.288675	−	0.500000i
$4$	6.50070e7	−	1.12595e8i	0.121085	−	0.209725i
$5$	4.83495e9	+	8.37438e9i	0.354264	+	0.613603i	0.986992	−	0.160771i	$-0.0513981\pi$
$5$	4.83495e9	+	8.37438e9i	0.354264	+	0.613603i	−0.632728	+	0.774374i	$0.718065\pi$
$6$	−9.64758e10			−0.502603
$7$	−7.77849e11	+	1.61705e12i	−0.433484	+	0.901161i
$7$	−7.77849e11	+	1.61705e12i	−0.433484	+	0.901161i
$8$	−1.34515e13			−1.08135
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	9.75244e13	−	1.68917e14i	0.308399	−	0.534163i
$11$	6.62931e14	−	1.14823e15i	0.526350	−	0.911664i	−0.473179	−	0.880966i	$-0.656894\pi$
$11$	6.62931e14	−	1.14823e15i	0.526350	−	0.911664i	0.999529	−	0.0306981i	$-0.00977303\pi$
$12$	−3.10926e14	−	5.38540e14i	−0.0699084	−	0.121085i
$13$	−2.72703e15			−0.192093			−0.0960466	−	0.995377i	$-0.530620\pi$
$13$	−2.72703e15			−0.192093			−0.0960466	+	0.995377i	$0.530620\pi$
$14$	3.60921e16	−	2.72081e15i	0.868071	−	0.0654398i
$15$	4.62509e16			0.409069
$16$	1.00763e17	+	1.74527e17i	0.349592	+	0.605511i
$17$	−2.12312e17	+	3.67735e17i	−0.305819	+	0.529695i	−0.977443	−	0.211197i	$-0.932264\pi$
$17$	−2.12312e17	+	3.67735e17i	−0.305819	+	0.529695i	0.671624	+	0.740892i	$0.265597\pi$
$18$	−2.30720e17	+	3.99619e17i	−0.145089	+	0.251302i
$19$	3.18927e18	+	5.52398e18i	0.915723	+	1.58608i	0.805839	+	0.592135i	$0.201715\pi$
$19$	3.18927e18	+	5.52398e18i	0.915723	+	1.58608i	0.109884	+	0.993944i	$0.464952\pi$
$20$	1.25722e18			0.171584
$21$	4.83790e18	+	7.08914e18i	0.325444	+	0.476885i
$22$	−2.67436e19			−0.916411
$23$	−3.01649e19	−	5.22471e19i	−0.542560	−	0.939741i	−0.998756	−	0.0498619i	$-0.984122\pi$
$23$	−3.01649e19	−	5.22471e19i	−0.542560	−	0.939741i	0.456196	−	0.889879i	$-0.349211\pi$
$24$	−3.21691e19	+	5.57186e19i	−0.312159	+	0.540676i
$25$	4.63787e19	−	8.03303e19i	0.248994	−	0.431270i
$26$	2.75031e19	+	4.76367e19i	0.0836118	+	0.144820i
$27$	−1.09419e20			−0.192450
$28$	1.31507e20	+	1.92702e20i	0.136508	+	0.200030i
$29$	−5.79588e20			−0.361700			−0.180850	−	0.983511i	$-0.557885\pi$
$29$	−5.79588e20			−0.361700			−0.180850	+	0.983511i	$0.557885\pi$
$30$	−4.66456e20	−	8.07925e20i	−0.178054	−	0.308399i
$31$	9.42484e20	−	1.63243e21i	0.223630	−	0.387338i	−0.732278	−	0.681006i	$-0.761543\pi$
$31$	9.42484e20	−	1.63243e21i	0.223630	−	0.387338i	0.955907	+	0.293668i	$0.0948760\pi$
$32$	−1.57841e21	+	2.73388e21i	−0.236344	+	0.409360i
$33$	−3.17078e21	−	5.49195e21i	−0.303888	−	0.526350i
$34$	8.56496e21			0.532452
$35$	−1.73027e22	+	1.30437e21i	−0.706524	+	0.0532615i
$36$	−2.97430e21			−0.0807233
$37$	1.46036e22	+	2.52941e22i	0.266400	+	0.461418i	0.967929	−	0.251222i	$-0.0808325\pi$
$37$	1.46036e22	+	2.52941e22i	0.266400	+	0.461418i	−0.701529	+	0.712640i	$0.747499\pi$
$38$	6.43298e22	−	1.11423e23i	0.797168	−	1.38074i
$39$	−6.52166e21	+	1.12958e22i	−0.0554525	+	0.0960466i
$40$	−6.50375e22	−	1.12648e23i	−0.383084	−	0.663521i
$41$	2.29250e23			0.943938			0.471969	−	0.881615i	$-0.343544\pi$
$41$	2.29250e23			0.943938			0.471969	+	0.881615i	$0.343544\pi$
$42$	7.50436e22	−	1.56006e23i	0.217871	−	0.452926i
$43$	1.35079e22			0.0278801			0.0139401	−	0.999903i	$-0.495563\pi$
$43$	1.35079e22			0.0278801			0.0139401	+	0.999903i	$0.495563\pi$
$44$	−8.61903e22	−	1.49286e23i	−0.127466	−	0.220778i
$45$	1.10608e23	−	1.91579e23i	0.118088	−	0.204534i
$46$	−6.08446e23	+	1.05386e24i	−0.472317	+	0.818077i
$47$	−2.79171e23	−	4.83539e23i	−0.158654	−	0.274797i	0.775729	−	0.631066i	$-0.217382\pi$
$47$	−2.79171e23	−	4.83539e23i	−0.158654	−	0.274797i	−0.934384	+	0.356268i	$0.884049\pi$
$48$	9.63893e23			0.403674
$49$	−2.00981e24	−	2.51564e24i	−0.624183	−	0.781279i
$50$	−1.87098e24			−0.433515
$51$	1.01548e24	+	1.75886e24i	0.176565	+	0.305819i
$52$	−1.77276e23	+	3.07051e23i	−0.0232596	+	0.0402868i
$53$	2.64429e24	−	4.58005e24i	0.263214	−	0.455900i	−0.703880	−	0.710319i	$-0.748551\pi$
$53$	2.64429e24	−	4.58005e24i	0.263214	−	0.455900i	0.967094	+	0.254419i	$0.0818841\pi$
$54$	1.10353e24	+	1.91137e24i	0.0837672	+	0.145089i
$55$	1.28210e25			0.745867
$56$	1.04633e25	−	2.17518e25i	0.468749	−	0.974472i
$57$	3.05084e25			1.05739
$58$	5.84535e24	+	1.01244e25i	0.157436	+	0.272687i
$59$	−4.39572e23	+	7.61361e23i	−0.00924008	+	0.0160043i	−0.870608	−	0.491977i	$-0.836275\pi$
$59$	−4.39572e23	+	7.61361e23i	−0.00924008	+	0.0160043i	0.861368	+	0.507981i	$0.169608\pi$
$60$	3.00663e24	−	5.20763e24i	0.0495321	−	0.0857921i
$61$	−9.75690e24	−	1.68995e25i	−0.126482	−	0.219074i	0.795829	−	0.605521i	$-0.207035\pi$
$61$	−9.75690e24	−	1.68995e25i	−0.126482	−	0.219074i	−0.922311	+	0.386448i	$0.873702\pi$
$62$	−3.80211e25			−0.389355
$63$	4.09342e25	−	3.08584e24i	0.332390	−	0.0250573i
$64$	1.71869e26			1.11068
$65$	−1.31851e25	−	2.28372e25i	−0.0680517	−	0.117869i
$66$	−6.39568e25	+	1.10776e26i	−0.264545	+	0.458205i
$67$	6.20696e25	−	1.07508e26i	0.206440	−	0.357565i	−0.744150	−	0.668012i	$-0.767145\pi$
$67$	6.20696e25	−	1.07508e26i	0.206440	−	0.357565i	0.950591	+	0.310447i	$0.100479\pi$
$68$	2.76035e25	+	4.78107e25i	0.0740602	+	0.128276i
$69$	−2.88555e26			−0.626494
$70$	1.97289e26	+	2.89094e26i	0.347681	+	0.509469i
$71$	3.63928e26			0.522119			0.261060	−	0.965323i	$-0.415928\pi$
$71$	3.63928e26			0.522119			0.261060	+	0.965323i	$0.415928\pi$
$72$	1.53864e26	+	2.66500e26i	0.180225	+	0.312159i
$73$	9.53533e26	−	1.65157e27i	0.914438	−	1.58385i	0.106715	−	0.994290i	$-0.465967\pi$
$73$	9.53533e26	−	1.65157e27i	0.914438	−	1.58385i	0.807723	−	0.589563i	$-0.200700\pi$
$74$	2.94564e26	−	5.10200e26i	0.231910	−	0.401680i
$75$	−2.21828e26	−	3.84217e26i	−0.143757	−	0.248994i
$76$	8.29299e26			0.443521
$77$	1.34109e27	+	1.96514e27i	0.593392	+	0.869518i
$78$	2.63093e26			0.0965466
$79$	−2.58725e27	−	4.48125e27i	−0.789306	−	1.36712i	−0.926393	−	0.376559i	$-0.877107\pi$
$79$	−2.58725e27	−	4.48125e27i	−0.789306	−	1.36712i	0.137087	−	0.990559i	$-0.456226\pi$
$80$	−9.74369e26	+	1.68766e27i	−0.247696	+	0.429022i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	−2.31207e27	−	4.00461e27i	−0.410865	−	0.711639i
$83$	6.18532e27			0.921997			0.460999	−	0.887401i	$-0.347491\pi$
$83$	6.18532e27			0.921997			0.460999	+	0.887401i	$0.347491\pi$
$84$	1.11270e27	−	8.38813e25i	0.139421	−	0.0105103i
$85$	−4.10607e27			−0.433363
$86$	−1.36232e26	−	2.35960e26i	−0.0121353	−	0.0210190i
$87$	−1.38608e27	+	2.40075e27i	−0.104414	+	0.180850i
$88$	−8.91744e27	+	1.54455e28i	−0.569169	+	0.985830i
$89$	−8.94711e27	−	1.54969e28i	−0.484761	−	0.839631i	0.515086	−	0.857139i	$-0.327760\pi$
$89$	−8.94711e27	−	1.54969e28i	−0.484761	−	0.839631i	−0.999847	+	0.0175078i	$0.994427\pi$
$90$	−4.46209e27			−0.205599
$91$	2.12122e27	−	4.40976e27i	0.0832694	−	0.173107i
$92$	−7.84370e27			−0.262783
$93$	−4.50787e27	−	7.80787e27i	−0.129113	−	0.223630i
$94$	−5.63108e27	+	9.75331e27i	−0.138114	+	0.239220i
$95$	−3.08399e28	+	5.34164e28i	−0.648816	+	1.12378i
$96$	7.54948e27	+	1.30761e28i	0.136453	+	0.236344i
$97$	−4.02847e28			−0.626542			−0.313271	−	0.949664i	$-0.601425\pi$
$97$	−4.02847e28			−0.626542			−0.313271	+	0.949664i	$0.601425\pi$
$98$	−2.36745e28	+	6.04792e28i	−0.317324	+	0.810639i
$99$	−3.03315e28			−0.350900
$100$	−6.02988e27	−	1.04441e28i	−0.0602988	−	0.104441i
$101$	1.09569e28	−	1.89779e28i	0.0948481	−	0.164282i	−0.814697	−	0.579887i	$-0.803097\pi$
$101$	1.09569e28	−	1.89779e28i	0.0948481	−	0.164282i	0.909545	+	0.415605i	$0.136430\pi$
$102$	2.04830e28	−	3.54775e28i	0.153706	−	0.266226i
$103$	8.81406e27	+	1.52664e28i	0.0574165	+	0.0994482i	0.893305	−	0.449451i	$-0.148380\pi$
$103$	8.81406e27	+	1.52664e28i	0.0574165	+	0.0994482i	−0.835889	+	0.548899i	$0.815047\pi$
$104$	3.66828e28			0.207720
$105$	−3.59762e28	+	7.47900e28i	−0.177325	+	0.368637i
$106$	−1.06674e29			−0.458274
$107$	−2.10019e29	−	3.63764e29i	−0.787398	−	1.36381i	−0.927556	−	0.373684i	$-0.878094\pi$
$107$	−2.10019e29	−	3.63764e29i	−0.787398	−	1.36381i	0.140158	−	0.990129i	$-0.455239\pi$
$108$	−7.11300e27	+	1.23201e28i	−0.0233028	+	0.0403616i
$109$	4.61286e28	−	7.98972e28i	0.132217	−	0.229006i	−0.792314	−	0.610113i	$-0.791124\pi$
$109$	4.61286e28	−	7.98972e28i	0.132217	−	0.229006i	0.924531	+	0.381107i	$0.124457\pi$
$110$	−1.29304e29	−	2.23961e29i	−0.324652	−	0.562313i
$111$	1.39697e29			0.307612
$112$	−3.60597e29	+	2.71837e28i	−0.697206	+	0.0525591i
$113$	6.60688e27			0.0112295			0.00561473	−	0.999984i	$-0.498213\pi$
$113$	6.60688e27			0.0112295			0.00561473	+	0.999984i	$0.498213\pi$
$114$	−3.07687e29	−	5.32930e29i	−0.460245	−	0.797168i
$115$	2.91691e29	−	5.05224e29i	0.384419	−	0.665833i
$116$	−3.76773e28	+	6.52590e28i	−0.0437964	+	0.0758576i
$117$	3.11929e28	+	5.40277e28i	0.0320155	+	0.0554525i
$118$	1.77329e28			0.0160876
$119$	−4.29500e29	−	6.29361e29i	−0.344772	−	0.505207i
$120$	−6.22145e29			−0.442347
$121$	−8.58001e28	−	1.48610e29i	−0.0540879	−	0.0936830i
$122$	−1.96804e29	+	3.40874e29i	−0.110107	+	0.190711i
$123$	5.48248e29	−	9.49593e29i	0.272491	−	0.471969i
$124$	−1.22536e29	−	2.12239e29i	−0.0541564	−	0.0938016i
$125$	2.69812e30			1.06137
$126$	−4.66740e29	−	6.83930e29i	−0.163569	−	0.239684i
$127$	−2.03335e30			−0.635415			−0.317707	−	0.948189i	$-0.602913\pi$
$127$	−2.03335e30			−0.635415			−0.317707	+	0.948189i	$0.602913\pi$
$128$	−8.85954e29	−	1.53452e30i	−0.247096	−	0.427984i
$129$	3.23039e28	−	5.59520e28i	0.00804830	−	0.0139401i
$130$	−2.65952e29	+	4.60643e29i	−0.0592414	+	0.102609i
$131$	−4.44816e30	−	7.70444e30i	−0.886639	−	1.53570i	−0.843824	−	0.536621i	$-0.819701\pi$
$131$	−4.44816e30	−	7.70444e30i	−0.886639	−	1.53570i	−0.0428154	−	0.999083i	$-0.513633\pi$
$132$	−8.24491e29			−0.147185
$133$	−1.14133e31	+	8.60398e29i	−1.82626	+	0.137674i
$134$	−2.50397e30			−0.359427
$135$	−5.29036e29	−	9.16317e29i	−0.0681782	−	0.118088i
$136$	2.85592e30	−	4.94660e30i	0.330698	−	0.572786i
$137$	−6.29805e30	+	1.09085e31i	−0.655779	+	1.13584i	0.325918	+	0.945398i	$0.394327\pi$
$137$	−6.29805e30	+	1.09085e31i	−0.655779	+	1.13584i	−0.981698	+	0.190445i	$0.939007\pi$
$138$	2.91018e30	+	5.04058e30i	0.272692	+	0.472317i
$139$	−1.17230e31			−0.989289			−0.494644	−	0.869095i	$-0.664702\pi$
$139$	−1.17230e31			−0.989289			−0.494644	+	0.869095i	$0.664702\pi$
$140$	−9.77929e29	+	2.03299e30i	−0.0743791	+	0.154625i
$141$	−2.67053e30			−0.183198
$142$	−3.67034e30	−	6.35722e30i	−0.227261	−	0.393628i
$143$	−1.80783e30	+	3.13126e30i	−0.101108	+	0.175124i
$144$	2.30513e30	−	3.99261e30i	0.116531	−	0.201837i
$145$	−2.80228e30	−	4.85369e30i	−0.128137	−	0.221940i
$146$	−3.84668e31			−1.59210
$147$	−1.52267e31	+	2.30885e30i	−0.570825	+	0.0865556i
$148$	3.79734e30			0.129028
$149$	−2.25223e31	−	3.90097e31i	−0.694083	−	1.20219i	−0.970489	−	0.241146i	$-0.922477\pi$
$149$	−2.25223e31	−	3.90097e31i	−0.694083	−	1.20219i	0.276406	−	0.961041i	$-0.410857\pi$
$150$	−4.47442e30	+	7.74993e30i	−0.125145	+	0.216758i
$151$	1.32827e31	−	2.30063e31i	0.337381	−	0.584361i	−0.646558	−	0.762865i	$-0.723792\pi$
$151$	1.32827e31	−	2.30063e31i	0.337381	−	0.584361i	0.983939	+	0.178504i	$0.0571257\pi$
$152$	−4.29006e31	−	7.43060e31i	−0.990219	−	1.71511i
$153$	9.71403e30			0.203880
$154$	2.08024e31	−	4.32457e31i	0.397250	−	0.825834i
$155$	1.82275e31			0.316896
$156$	8.47907e29	+	1.46862e30i	0.0134289	+	0.0232596i
$157$	−5.68471e31	+	9.84621e31i	−0.820661	+	1.42143i	0.0845301	+	0.996421i	$0.473061\pi$
$157$	−5.68471e31	+	9.84621e31i	−0.820661	+	1.42143i	−0.905191	+	0.425005i	$0.860272\pi$
$158$	−5.21866e31	+	9.03898e31i	−0.687118	+	1.19012i
$159$	−1.26476e31	−	2.19062e31i	−0.151967	−	0.263214i
$160$	−3.05261e31			−0.334913
$161$	1.07950e32	−	8.13784e30i	1.08205	−	0.0815706i
$162$	1.05563e31			0.0967260
$163$	1.12894e32	+	1.95538e32i	0.946127	+	1.63874i	0.753478	+	0.657473i	$0.228375\pi$
$163$	1.12894e32	+	1.95538e32i	0.946127	+	1.63874i	0.192649	+	0.981268i	$0.438292\pi$
$164$	1.49028e31	−	2.58125e31i	0.114297	−	0.197968i
$165$	3.06611e31	−	5.31066e31i	0.215313	−	0.372934i
$166$	−6.23811e31	−	1.08047e32i	−0.401315	−	0.695098i
$167$	2.15599e32			1.27133			0.635664	−	0.771966i	$-0.280726\pi$
$167$	2.15599e32			1.27133			0.635664	+	0.771966i	$0.280726\pi$
$168$	−6.50771e31	−	9.53598e31i	−0.351920	−	0.515680i
$169$	−1.94101e32			−0.963100
$170$	4.14112e31	+	7.17262e31i	0.188629	+	0.326715i
$171$	7.29603e31	−	1.26371e32i	0.305241	−	0.528693i
$172$	8.78107e29	−	1.52093e30i	0.00337587	−	0.00584717i
$173$	−3.14198e30	−	5.44207e30i	−0.0111054	−	0.0192351i	0.860419	−	0.509587i	$-0.170202\pi$
$173$	−3.14198e30	−	5.44207e30i	−0.0111054	−	0.0192351i	−0.871525	+	0.490352i	$0.836868\pi$
$174$	5.59162e31			0.181792
$175$	9.38227e31	+	1.37482e32i	0.280709	+	0.411332i
$176$	2.67196e32			0.736030
$177$	2.10246e30	+	3.64156e30i	0.00533476	+	0.00924008i
$178$	−1.80470e32	+	3.12582e32i	−0.422001	+	0.730928i
$179$	3.21616e32	−	5.57056e32i	0.693377	−	1.20096i	−0.277348	−	0.960769i	$-0.589456\pi$
$179$	3.21616e32	−	5.57056e32i	0.693377	−	1.20096i	0.970725	−	0.240194i	$-0.0772110\pi$
$180$	−1.43806e31	−	2.49079e31i	−0.0285974	−	0.0495321i
$181$	9.04245e32			1.65938			0.829692	−	0.558221i	$-0.188516\pi$
$181$	9.04245e32			1.65938			0.829692	+	0.558221i	$0.188516\pi$
$182$	−9.84243e31	+	7.41975e30i	−0.166751	+	0.0125705i
$183$	−9.33339e31			−0.146049
$184$	4.05763e32	+	7.02803e32i	0.586698	+	1.01619i
$185$	−1.41215e32	+	2.44592e32i	−0.188752	+	0.326928i
$186$	−9.09269e31	+	1.57490e32i	−0.112397	+	0.194677i
$187$	2.81496e32	+	4.87566e32i	0.321936	+	0.557609i
$188$	−7.25923e31			−0.0768426
$189$	8.51114e31	−	1.76936e32i	0.0834241	−	0.173429i
$190$	1.24413e33			1.12963
$191$	−1.74327e32	−	3.01943e32i	−0.146683	−	0.254063i	0.783317	−	0.621623i	$-0.213526\pi$
$191$	−1.74327e32	−	3.01943e32i	−0.146683	−	0.254063i	−0.930000	+	0.367561i	$0.880193\pi$
$192$	4.11021e32	−	7.11910e32i	0.320624	−	0.555338i
$193$	−8.93196e32	+	1.54706e33i	−0.646198	+	1.11925i	0.337825	+	0.941209i	$0.390309\pi$
$193$	−8.93196e32	+	1.54706e33i	−0.646198	+	1.11925i	−0.984023	+	0.178039i	$0.943025\pi$
$194$	4.06286e32	+	7.03707e32i	0.272713	+	0.472353i
$195$	−1.26128e32			−0.0785793
$196$	−4.13901e32	+	6.27608e31i	−0.239433	+	0.0363058i
$197$	−1.08836e33			−0.584805			−0.292403	−	0.956295i	$-0.594455\pi$
$197$	−1.08836e33			−0.584805			−0.292403	+	0.956295i	$0.594455\pi$
$198$	3.05903e32	+	5.29840e32i	0.152735	+	0.264545i
$199$	−3.50396e32	+	6.06904e32i	−0.162626	+	0.281676i	−0.935810	−	0.352506i	$-0.885330\pi$
$199$	−3.50396e32	+	6.06904e32i	−0.162626	+	0.281676i	0.773184	+	0.634182i	$0.218663\pi$
$200$	−6.23865e32	+	1.08057e33i	−0.269250	+	0.466355i
$201$	−2.96877e32	−	5.14206e32i	−0.119188	−	0.206440i
$202$	−4.42017e32			−0.165137
$203$	4.50832e32	−	9.37224e32i	0.156791	−	0.325950i
$204$	2.64053e32			0.0855174
$205$	1.10841e33	+	1.91983e33i	0.334403	+	0.579203i
$206$	1.77786e32	−	3.07934e32i	0.0499830	−	0.0865731i
$207$	−6.90075e32	+	1.19525e33i	−0.180853	+	0.313247i
$208$	−2.74784e32	−	4.75940e32i	−0.0671542	−	0.116315i
$209$	8.45707e33			1.92796
$210$	1.66929e33	−	1.25840e32i	0.355101	−	0.0267694i
$211$	1.25182e33			0.248569			0.124285	−	0.992247i	$-0.460336\pi$
$211$	1.25182e33			0.248569			0.124285	+	0.992247i	$0.460336\pi$
$212$	−3.43795e32	−	5.95470e32i	−0.0637425	−	0.110405i
$213$	8.70328e32	−	1.50745e33i	0.150723	−	0.261060i
$214$	−4.23623e33	+	7.33737e33i	−0.685457	+	1.18725i
$215$	6.53100e31	+	1.13120e32i	0.00987693	+	0.0171074i
$216$	1.47185e33			0.208106
$217$	1.90662e33	+	2.79383e33i	0.252114	+	0.369431i
$218$	−1.86089e33			−0.230198
$219$	−4.56072e33	−	7.89939e33i	−0.527951	−	0.914438i
$220$	8.33452e32	−	1.44358e33i	0.0903133	−	0.156427i
$221$	5.78982e32	−	1.00283e33i	0.0587458	−	0.101751i
$222$	−1.40889e33	−	2.44027e33i	−0.133893	−	0.231910i
$223$	−9.99968e32			−0.0890360			−0.0445180	−	0.999009i	$-0.514175\pi$
$223$	−9.99968e32			−0.0890360			−0.0445180	+	0.999009i	$0.514175\pi$
$224$	−3.19307e33	−	4.67891e33i	−0.266448	−	0.390435i
$225$	−2.12199e33			−0.165996
$226$	−6.66327e31	−	1.15411e32i	−0.00488782	−	0.00846595i
$227$	5.39637e33	−	9.34679e33i	0.371302	−	0.643113i	−0.618464	−	0.785813i	$-0.712245\pi$
$227$	5.39637e33	−	9.34679e33i	0.371302	−	0.643113i	0.989766	+	0.142699i	$0.0455782\pi$
$228$	1.98326e33	−	3.43510e33i	0.128034	−	0.221761i
$229$	−3.26881e33	−	5.66174e33i	−0.198050	−	0.343033i	0.749846	−	0.661612i	$-0.230128\pi$
$229$	−3.26881e33	−	5.66174e33i	−0.198050	−	0.343033i	−0.947896	+	0.318580i	$0.896794\pi$
$230$	−1.17672e34			−0.669300
$231$	1.13472e34	−	8.55409e32i	0.606057	−	0.0456878i
$232$	7.79635e33			0.391125
$233$	−1.83456e34	−	3.17756e34i	−0.864713	−	1.49773i	−0.867331	−	0.497731i	$-0.834167\pi$
$233$	−1.83456e34	−	3.17756e34i	−0.864713	−	1.49773i	0.00261813	−	0.999997i	$-0.499167\pi$
$234$	6.29182e32	−	1.08978e33i	0.0278706	−	0.0482733i
$235$	2.69956e33	−	4.67577e33i	0.112411	−	0.194702i
$236$	5.71505e31	+	9.89875e31i	0.00223767	+	0.00387576i
$237$	−2.47495e34			−0.911412
$238$	−6.66224e33	+	1.38500e34i	−0.230810	+	0.479825i
$239$	−1.51956e34			−0.495392			−0.247696	−	0.968838i	$-0.579673\pi$
$239$	−1.51956e34			−0.495392			−0.247696	+	0.968838i	$0.579673\pi$
$240$	4.66038e33	+	8.07201e33i	0.143007	+	0.247696i
$241$	−1.47827e34	+	2.56044e34i	−0.427078	+	0.739721i	−0.996612	−	0.0822468i	$-0.973790\pi$
$241$	−1.47827e34	+	2.56044e34i	−0.427078	+	0.739721i	0.569534	+	0.821968i	$0.307124\pi$
$242$	−1.73065e33	+	2.99757e33i	−0.0470854	+	0.0815543i
$243$	1.25158e33	+	2.16780e33i	0.0320750	+	0.0555556i
$244$	−2.53707e33			−0.0612604
$245$	1.13496e34	−	2.89939e34i	0.258270	−	0.659779i
$246$	−2.21171e34			−0.474426
$247$	−8.69725e33	−	1.50641e34i	−0.175904	−	0.304675i
$248$	−1.26779e34	+	2.19587e34i	−0.241822	+	0.418849i
$249$	1.47921e34	−	2.56207e34i	0.266158	−	0.460999i
$250$	−2.72114e34	−	4.71316e34i	−0.461978	−	0.800169i
$251$	−5.19797e34			−0.832846			−0.416423	−	0.909171i	$-0.636716\pi$
$251$	−5.19797e34			−0.832846			−0.416423	+	0.909171i	$0.636716\pi$
$252$	2.31356e33	−	4.80960e33i	0.0349923	−	0.0727447i
$253$	−7.99889e34			−1.14230
$254$	2.05070e34	+	3.55192e34i	0.276575	+	0.479042i
$255$	−9.81961e33	+	1.70081e34i	−0.125101	+	0.216682i
$256$	2.82653e34	−	4.89570e34i	0.340232	−	0.589298i
$257$	−8.66419e32	−	1.50068e33i	−0.00985593	−	0.0170710i	0.861055	−	0.508511i	$-0.169804\pi$
$257$	−8.66419e32	−	1.50068e33i	−0.00985593	−	0.0170710i	−0.870911	+	0.491440i	$0.836471\pi$
$258$	−1.30319e33			−0.0140127
$259$	−5.22613e34	+	3.93973e33i	−0.531292	+	0.0400516i
$260$	−3.42849e33			−0.0329601
$261$	6.62956e33	+	1.14827e34i	0.0602833	+	0.104414i
$262$	−8.97225e34	+	1.55404e35i	−0.771850	+	1.33688i
$263$	−3.57459e34	+	6.19137e34i	−0.290983	+	0.503998i	−0.974043	−	0.226365i	$-0.927316\pi$
$263$	−3.57459e34	+	6.19137e34i	−0.290983	+	0.503998i	0.683059	+	0.730363i	$0.260649\pi$
$264$	4.26518e34	+	7.38751e34i	0.328610	+	0.569169i
$265$	5.11401e34			0.372989
$266$	1.30137e35	+	1.90694e35i	0.898706	+	1.31690i
$267$	−8.55875e34			−0.559754
$268$	−8.06992e33	−	1.39775e34i	−0.0499936	−	0.0865915i
$269$	1.20236e35	−	2.08256e35i	0.705713	−	1.22233i	−0.260720	−	0.965414i	$-0.583960\pi$
$269$	1.20236e35	−	2.08256e35i	0.705713	−	1.22233i	0.966434	−	0.256917i	$-0.0827066\pi$
$270$	−1.06710e34	+	1.84827e34i	−0.0593514	+	0.102800i
$271$	−1.15124e35	−	1.99401e35i	−0.606894	−	1.05117i	−0.991749	−	0.128194i	$-0.959082\pi$
$271$	−1.15124e35	−	1.99401e35i	−0.606894	−	1.05117i	0.384855	−	0.922977i	$-0.374251\pi$
$272$	−8.55727e34			−0.427648
$273$	−1.31931e34	−	1.93323e34i	−0.0625156	−	0.0916063i
$274$	2.54072e35			1.14176
$275$	−6.14918e34	−	1.06507e35i	−0.262116	−	0.453998i
$276$	−1.87581e34	+	3.24900e34i	−0.0758590	+	0.131392i
$277$	2.26965e35	−	3.93115e35i	0.870968	−	1.50856i	0.00997152	−	0.999950i	$-0.496826\pi$
$277$	2.26965e35	−	3.93115e35i	0.870968	−	1.50856i	0.860997	−	0.508611i	$-0.169841\pi$
$278$	1.18230e35	+	2.04781e35i	0.430605	+	0.745830i
$279$	−4.31220e34			−0.149087
$280$	2.32747e35	−	1.75457e34i	0.764000	−	0.0575944i
$281$	5.70551e35			1.77850			0.889249	−	0.457424i	$-0.151228\pi$
$281$	5.70551e35			1.77850			0.889249	+	0.457424i	$0.151228\pi$
$282$	2.69333e34	+	4.66498e34i	0.0797401	+	0.138114i
$283$	1.76821e35	−	3.06263e35i	0.497314	−	0.861373i	−0.502681	−	0.864472i	$-0.667653\pi$
$283$	1.76821e35	−	3.06263e35i	0.497314	−	0.861373i	0.999995	+	0.00309897i	$0.000986435\pi$
$284$	2.36579e34	−	4.09766e34i	0.0632208	−	0.109502i
$285$	1.47507e35	+	2.55489e35i	0.374594	+	0.648816i
$286$	7.29306e34			0.176036
$287$	−1.78322e35	+	3.70709e35i	−0.409182	+	0.850640i
$288$	7.22178e34			0.157563
$289$	1.50832e35	+	2.61248e35i	0.312949	+	0.542044i
$290$	−5.65240e34	+	9.79024e34i	−0.111548	+	0.193207i
$291$	−9.63403e34	+	1.66866e35i	−0.180867	+	0.313271i
$292$	−1.23973e35	−	2.14727e35i	−0.221449	−	0.383561i
$293$	8.42269e35			1.43176			0.715880	−	0.698223i	$-0.246026\pi$
$293$	8.42269e35			1.43176			0.715880	+	0.698223i	$0.246026\pi$
$294$	1.93898e35	+	2.42699e35i	0.313716	+	0.392673i
$295$	−8.50124e33			−0.0130937
$296$	−1.96440e35	−	3.40245e35i	−0.288072	−	0.498955i
$297$	−7.25372e34	+	1.25638e35i	−0.101296	+	0.175450i
$298$	−4.54290e35	+	7.86853e35i	−0.604223	+	1.04654i
$299$	8.22606e34	+	1.42479e35i	0.104222	+	0.180518i
$300$	−5.76815e34			−0.0696271
$301$	−1.05071e34	+	2.18430e34i	−0.0120856	+	0.0251245i
$302$	−5.35842e35			−0.587403
$303$	−5.24066e34	−	9.07709e34i	−0.0547606	−	0.0948481i
$304$	−6.42721e35	+	1.11323e36i	−0.640259	+	1.10896i
$305$	9.43483e34	−	1.63416e35i	0.0896162	−	0.155220i
$306$	−9.79694e34	−	1.69688e35i	−0.0887421	−	0.153706i
$307$	1.52530e36			1.31780			0.658899	−	0.752231i	$-0.271022\pi$
$307$	1.52530e36			1.31780			0.658899	+	0.752231i	$0.271022\pi$
$308$	3.08446e35	−	2.32523e34i	0.254211	−	0.0191638i
$309$	8.43148e34			0.0662988
$310$	−1.83830e35	−	3.18404e35i	−0.137934	−	0.238909i
$311$	−6.13502e35	+	1.06262e36i	−0.439329	+	0.760940i	−0.997638	−	0.0686928i	$-0.978117\pi$
$311$	−6.13502e35	+	1.06262e36i	−0.439329	+	0.760940i	0.558309	+	0.829633i	$0.311450\pi$
$312$	8.77263e34	−	1.51946e35i	0.0599637	−	0.103860i
$313$	−9.35025e34	−	1.61951e35i	−0.0610141	−	0.105680i	0.833905	−	0.551908i	$-0.186100\pi$
$313$	−9.35025e34	−	1.61951e35i	−0.0610141	−	0.105680i	−0.894919	+	0.446229i	$0.852767\pi$
$314$	2.29329e36			1.42883
$315$	2.23757e35	+	3.27879e35i	0.133129	+	0.195079i
$316$	−6.72757e35			−0.382292
$317$	−1.14800e36	−	1.98840e36i	−0.623136	−	1.07930i	−0.988898	−	0.148595i	$-0.952525\pi$
$317$	−1.14800e36	−	1.98840e36i	−0.623136	−	1.07930i	0.365762	−	0.930708i	$-0.380808\pi$
$318$	−2.55110e35	+	4.41864e35i	−0.132292	+	0.229137i
$319$	−3.84227e35	+	6.65501e35i	−0.190381	+	0.329749i
$320$	8.30977e35	+	1.43929e36i	0.393472	+	0.681514i
$321$	−2.00903e36			−0.909209
$322$	−1.23087e36	−	1.80363e36i	−0.532477	−	0.780257i
$323$	−2.70848e36			−1.12018
$324$	3.40212e34	+	5.89265e34i	0.0134539	+	0.0233028i
$325$	−1.26476e35	+	2.19063e35i	−0.0478300	+	0.0828440i
$326$	2.27715e36	−	3.94413e36i	0.823636	−	1.42658i
$327$	−2.20632e35	−	3.82146e35i	−0.0763354	−	0.132217i
$328$	−3.08376e36			−1.02073
$329$	9.99060e35	−	7.53145e34i	0.316411	−	0.0238527i
$330$	−1.23691e36			−0.374875
$331$	2.22730e35	+	3.85780e35i	0.0646060	+	0.111901i	0.896519	−	0.443005i	$-0.146088\pi$
$331$	2.22730e35	+	3.85780e35i	0.0646060	+	0.111901i	−0.831913	+	0.554906i	$0.812754\pi$
$332$	4.02089e35	−	6.96438e35i	0.111640	−	0.193366i
$333$	3.34083e35	−	5.78649e35i	0.0888000	−	0.153806i
$334$	−2.17439e36	−	3.76615e36i	−0.553367	−	0.958460i
$335$	1.20041e36			0.292538
$336$	−7.49763e35	+	1.55866e36i	−0.174986	+	0.363775i
$337$	−7.75832e36			−1.73434			−0.867170	−	0.498012i	$-0.834063\pi$
$337$	−7.75832e36			−1.73434			−0.867170	+	0.498012i	$0.834063\pi$
$338$	1.95758e36	+	3.39063e36i	0.419206	+	0.726086i
$339$	1.58003e34	−	2.73668e34i	0.00324167	−	0.00561473i
$340$	−2.66923e35	+	4.62325e35i	−0.0524738	+	0.0908872i
$341$	−1.24960e36	−	2.16438e36i	−0.235415	−	0.407751i
$342$	−2.94332e36			−0.531446
$343$	5.63125e36	−	1.29318e36i	0.974631	−	0.223817i
$344$	−1.81702e35			−0.0301482
$345$	−1.39515e36	−	2.41647e36i	−0.221944	−	0.384419i
$346$	−6.33759e34	+	1.09770e35i	−0.00966764	+	0.0167448i
$347$	1.66682e36	−	2.88702e36i	0.243844	−	0.422350i	−0.717962	−	0.696082i	$-0.754925\pi$
$347$	1.66682e36	−	2.88702e36i	0.243844	−	0.422350i	0.961806	+	0.273732i	$0.0882581\pi$
$348$	1.80209e35	+	3.12132e35i	0.0252859	+	0.0437964i
$349$	1.03862e37			1.39794			0.698968	−	0.715153i	$-0.253643\pi$
$349$	1.03862e37			1.39794			0.698968	+	0.715153i	$0.253643\pi$
$350$	1.45534e36	−	3.02548e36i	0.187922	−	0.390667i
$351$	2.98389e35			0.0369683
$352$	2.09275e36	+	3.62475e36i	0.248799	+	0.430933i
$353$	5.15377e36	−	8.92660e36i	0.588020	−	1.01848i	−0.406471	−	0.913663i	$-0.633241\pi$
$353$	5.15377e36	−	8.92660e36i	0.588020	−	1.01848i	0.994492	−	0.104817i	$-0.0334257\pi$
$354$	4.24080e34	−	7.34529e34i	0.00464409	−	0.00804381i
$355$	1.75958e36	+	3.04767e36i	0.184968	+	0.320374i
$356$	−2.32650e36			−0.234789
$357$	−3.63407e36	+	2.73955e35i	−0.352131	+	0.0265455i
$358$	−1.29744e37			−1.20722
$359$	−2.59029e36	−	4.48652e36i	−0.231462	−	0.400904i	0.726777	−	0.686874i	$-0.241018\pi$
$359$	−2.59029e36	−	4.48652e36i	−0.231462	−	0.400904i	−0.958239	+	0.285970i	$0.907684\pi$
$360$	−1.48785e36	+	2.57703e36i	−0.127695	+	0.221174i
$361$	−1.42780e37	+	2.47302e37i	−1.17710	+	2.03879i
$362$	−9.11963e36	−	1.57957e37i	−0.722275	−	1.25102i
$363$	−8.20759e35			−0.0624553
$364$	−3.58624e35	−	5.25504e35i	−0.0262222	−	0.0384243i
$365$	1.84411e37			1.29581
$366$	9.41305e35	+	1.63039e36i	0.0635704	+	0.110107i
$367$	−7.84727e36	+	1.35919e37i	−0.509402	+	0.882310i	0.490539	+	0.871419i	$0.336800\pi$
$367$	−7.84727e36	+	1.35919e37i	−0.509402	+	0.882310i	−0.999941	+	0.0108906i	$0.996533\pi$
$368$	6.07900e36	−	1.05291e37i	0.379349	−	0.657052i
$369$	−2.62225e36	−	4.54187e36i	−0.157323	−	0.272491i
$370$	5.69682e36			0.328630
$371$	5.34931e36	+	7.83854e36i	0.296740	+	0.434824i
$372$	−1.17217e36			−0.0625344
$373$	−2.25936e36	−	3.91333e36i	−0.115933	−	0.200802i	0.802219	−	0.597030i	$-0.203653\pi$
$373$	−2.25936e36	−	3.91333e36i	−0.115933	−	0.200802i	−0.918152	+	0.396227i	$0.870319\pi$
$374$	5.67797e36	−	9.83454e36i	0.280256	−	0.485418i
$375$	6.45250e36	−	1.11761e37i	0.306390	−	0.530683i
$376$	3.75528e36	+	6.50434e36i	0.171561	+	0.297152i
$377$	1.58056e36			0.0694801
$378$	−3.94916e36	+	2.97709e35i	−0.167060	+	0.0125939i
$379$	−2.62656e37			−1.06935			−0.534674	−	0.845059i	$-0.679565\pi$
$379$	−2.62656e37			−1.06935			−0.534674	+	0.845059i	$0.679565\pi$
$380$	4.00962e36	+	6.94487e36i	0.157124	+	0.272146i
$381$	−4.86272e36	+	8.42247e36i	−0.183429	+	0.317707i
$382$	−3.51629e36	+	6.09039e36i	−0.127693	+	0.221170i
$383$	1.02321e37	+	1.77225e37i	0.357752	+	0.619644i	0.987585	−	0.157086i	$-0.0502100\pi$
$383$	1.02321e37	+	1.77225e37i	0.357752	+	0.619644i	−0.629833	+	0.776731i	$0.716877\pi$
$384$	−8.47498e36			−0.285322
$385$	−9.97276e36	+	2.07322e37i	−0.323322	+	0.672146i
$386$	3.60328e37			1.12508
$387$	−1.54509e35	−	2.67617e35i	−0.00464669	−	0.00804830i
$388$	−2.61879e36	+	4.53588e36i	−0.0758649	+	0.131402i
$389$	2.18404e37	−	3.78287e37i	0.609525	−	1.05573i	−0.381793	−	0.924248i	$-0.624693\pi$
$389$	2.18404e37	−	3.78287e37i	0.609525	−	1.05573i	0.991319	−	0.131481i	$-0.0419732\pi$
$390$	1.27204e36	+	2.20324e36i	0.0342030	+	0.0592414i
$391$	2.56174e37			0.663701
$392$	2.70350e37	+	3.38393e37i	0.674961	+	0.844837i
$393$	−4.25508e37			−1.02380
$394$	1.09765e37	+	1.90118e37i	0.254546	+	0.440887i
$395$	2.50184e37	−	4.33332e37i	0.559245	−	0.968641i
$396$	−1.97176e36	+	3.41518e36i	−0.0424887	+	0.0735925i
$397$	1.87941e37	+	3.25523e37i	0.390444	+	0.676268i	0.992508	−	0.122179i	$-0.0389883\pi$
$397$	1.87941e37	+	3.25523e37i	0.390444	+	0.676268i	−0.602065	+	0.798447i	$0.705655\pi$
$398$	1.41355e37			0.283143
$399$	−2.37309e37	+	4.93336e37i	−0.458360	+	0.952875i
$400$	1.86930e37			0.348185
$401$	2.19287e37	+	3.79816e37i	0.393930	+	0.682306i	0.992964	−	0.118417i	$-0.0377820\pi$
$401$	2.19287e37	+	3.79816e37i	0.393930	+	0.682306i	−0.599034	+	0.800723i	$0.704449\pi$
$402$	−5.98822e36	+	1.03719e37i	−0.103758	+	0.179713i
$403$	−2.57019e36	+	4.45169e36i	−0.0429577	+	0.0744050i
$404$	−1.42455e36	−	2.46740e36i	−0.0229694	−	0.0397841i
$405$	−5.06072e36			−0.0787254
$406$	−2.09185e37	+	1.57695e36i	−0.313981	+	0.0236696i
$407$	3.87246e37			0.560878
$408$	−1.36598e37	−	2.36594e37i	−0.190929	−	0.330698i
$409$	5.00829e37	−	8.67461e37i	0.675618	−	1.17021i	−0.300670	−	0.953728i	$-0.597210\pi$
$409$	5.00829e37	−	8.67461e37i	0.675618	−	1.17021i	0.976288	−	0.216477i	$-0.0694565\pi$
$410$	2.23575e37	−	3.87242e37i	0.291109	−	0.504216i
$411$	3.01234e37	+	5.21752e37i	0.378614	+	0.655779i
$412$	2.29190e36			0.0278091
$413$	−8.89240e35	−	1.30303e36i	−0.0104170	−	0.0152644i
$414$	2.78386e37			0.314878
$415$	2.99057e37	+	5.17982e37i	0.326631	+	0.565741i
$416$	4.30437e36	−	7.45539e36i	0.0454001	−	0.0786352i
$417$	−2.80353e37	+	4.85586e37i	−0.285583	+	0.494644i
$418$	−8.52924e37	−	1.47731e38i	−0.839179	−	1.45350i
$419$	1.70896e38			1.62416			0.812080	−	0.583546i	$-0.198335\pi$
$419$	1.70896e38			1.62416			0.812080	+	0.583546i	$0.198335\pi$
$420$	6.08231e36	+	8.91263e36i	0.0558411	+	0.0818259i
$421$	−5.60586e37			−0.497224			−0.248612	−	0.968603i	$-0.579974\pi$
$421$	−5.60586e37			−0.497224			−0.248612	+	0.968603i	$0.579974\pi$
$422$	−1.26251e37	−	2.18673e37i	−0.108194	−	0.187397i
$423$	−6.38654e36	+	1.10618e37i	−0.0528848	+	0.0915991i
$424$	−3.55698e37	+	6.16086e37i	−0.284627	+	0.492988i
$425$	1.96935e37	+	3.41102e37i	0.152294	+	0.263781i
$426$	−3.51103e37			−0.262419
$427$	3.49167e37	−	2.63221e36i	0.252249	−	0.0190158i
$428$	−5.46109e37			−0.381368
$429$	8.64682e36	+	1.49767e37i	0.0583748	+	0.101108i
$430$	1.31735e36	−	2.28171e36i	0.00859821	−	0.0148925i
$431$	8.45164e37	−	1.46387e38i	0.533360	−	0.923807i	−0.465881	−	0.884848i	$-0.654262\pi$
$431$	8.45164e37	−	1.46387e38i	0.533360	−	0.923807i	0.999241	−	0.0389594i	$-0.0124043\pi$
$432$	−1.10254e37	−	1.90965e37i	−0.0672790	−	0.116531i
$433$	−3.30261e38			−1.94887			−0.974435	−	0.224669i	$-0.927870\pi$
$433$	−3.30261e38			−1.94887			−0.974435	+	0.224669i	$0.927870\pi$
$434$	2.95747e37	−	6.14821e37i	0.168779	−	0.350871i
$435$	−2.68065e37			−0.147960
$436$	−5.99737e36	−	1.03877e37i	−0.0320189	−	0.0554584i
$437$	1.92408e38	−	3.33260e38i	0.993669	−	1.72109i
$438$	−9.19928e37	+	1.59336e38i	−0.459599	+	0.796049i
$439$	−1.52216e38	−	2.63645e38i	−0.735739	−	1.27434i	−0.954398	−	0.298536i	$-0.903502\pi$
$439$	−1.52216e38	−	2.63645e38i	−0.735739	−	1.27434i	0.218659	−	0.975801i	$-0.429832\pi$
$440$	−1.72462e38			−0.806545
$441$	−2.68506e37	+	6.85930e37i	−0.121505	+	0.310399i
$442$	−2.33569e37			−0.102280
$443$	2.27150e38	+	3.93435e38i	0.962627	+	1.66732i	0.715860	+	0.698243i	$0.246035\pi$
$443$	2.27150e38	+	3.93435e38i	0.962627	+	1.66732i	0.246766	+	0.969075i	$0.420632\pi$
$444$	9.08127e36	−	1.57292e37i	0.0372472	−	0.0645140i
$445$	8.65177e37	−	1.49853e38i	0.343467	−	0.594902i
$446$	1.00850e37	+	1.74678e37i	0.0387544	+	0.0671247i
$447$	−2.15447e38			−0.801458
$448$	−1.33688e38	+	2.77921e38i	−0.481460	+	1.00090i
$449$	−4.52511e38			−1.57782			−0.788909	−	0.614510i	$-0.789354\pi$
$449$	−4.52511e38			−1.57782			−0.788909	+	0.614510i	$0.789354\pi$
$450$	2.14010e37	+	3.70677e37i	0.0722526	+	0.125145i
$451$	1.51977e38	−	2.63232e38i	0.496841	−	0.860554i
$452$	4.29493e35	−	7.43905e35i	0.00135972	−	0.00235510i
$453$	−6.35307e37	−	1.10038e38i	−0.194787	−	0.337381i
$454$	−2.17697e38			−0.646462
$455$	4.71850e37	−	3.55705e36i	0.135718	−	0.0102312i
$456$	−4.10384e38			−1.14341
$457$	1.65008e37	+	2.85803e37i	0.0445370	+	0.0771403i	0.887435	−	0.460934i	$-0.152485\pi$
$457$	1.65008e37	+	2.85803e37i	0.0445370	+	0.0771403i	−0.842898	+	0.538074i	$0.819152\pi$
$458$	−6.59341e37	+	1.14201e38i	−0.172409	+	0.298622i
$459$	2.32310e37	−	4.02372e37i	0.0588550	−	0.101940i
$460$	−3.79239e37	−	6.56862e37i	−0.0930947	−	0.161245i
$461$	3.57971e38			0.851499			0.425750	−	0.904841i	$-0.360010\pi$
$461$	3.57971e38			0.851499			0.425750	+	0.904841i	$0.360010\pi$
$462$	−1.29383e38	−	1.89589e38i	−0.298241	−	0.437023i
$463$	−3.87672e38			−0.866044			−0.433022	−	0.901383i	$-0.642553\pi$
$463$	−3.87672e38			−0.866044			−0.433022	+	0.901383i	$0.642553\pi$
$464$	−5.84011e37	−	1.01154e38i	−0.126447	−	0.219013i
$465$	4.35907e37	−	7.55013e37i	0.0914800	−	0.158448i
$466$	−3.70044e38	+	6.40936e38i	−0.752763	+	1.30382i
$467$	−2.21660e38	−	3.83926e38i	−0.437112	−	0.757099i	0.560354	−	0.828253i	$-0.310665\pi$
$467$	−2.21660e38	−	3.83926e38i	−0.437112	−	0.757099i	−0.997465	+	0.0711539i	$0.977332\pi$
$468$	8.11102e36			0.0155064
$469$	1.25565e38	+	1.83995e38i	0.232735	+	0.341035i
$470$	−1.08904e38			−0.195715
$471$	2.71898e38	+	4.70941e38i	0.473809	+	0.820661i
$472$	5.91291e36	−	1.02415e37i	0.00999177	−	0.0173063i
$473$	8.95480e36	−	1.55102e37i	0.0146747	−	0.0254173i
$474$	2.49607e38	+	4.32332e38i	0.396708	+	0.687118i
$475$	5.91657e38			0.912038
$476$	−9.87837e37	+	7.44684e36i	−0.147701	+	0.0111345i
$477$	−1.20986e38			−0.175476
$478$	1.53253e38	+	2.65442e38i	0.215628	+	0.373479i
$479$	5.53473e38	−	9.58643e38i	0.755495	−	1.30855i	−0.189634	−	0.981855i	$-0.560730\pi$
$479$	5.53473e38	−	9.58643e38i	0.755495	−	1.30855i	0.945128	−	0.326700i	$-0.105937\pi$
$480$	−7.30027e37	+	1.26444e38i	−0.0966810	+	0.167456i
$481$	−3.98244e37	−	6.89779e37i	−0.0511736	−	0.0886353i
$482$	5.96356e38			0.743572
$483$	2.24452e38	−	4.66609e38i	0.271575	−	0.564572i
$484$	−2.23104e37			−0.0261969
$485$	−1.94775e38	−	3.37360e38i	−0.221961	−	0.384449i
$486$	2.52452e37	−	4.37260e37i	0.0279224	−	0.0483630i
$487$	5.98460e38	−	1.03656e39i	0.642489	−	1.11282i	−0.342387	−	0.939559i	$-0.611235\pi$
$487$	5.98460e38	−	1.03656e39i	0.642489	−	1.11282i	0.984875	−	0.173264i	$-0.0554314\pi$
$488$	1.31245e38	+	2.27324e38i	0.136772	+	0.236896i
$489$	1.07993e39			1.09249
$490$	−6.20941e38	+	9.41547e37i	−0.609827	+	0.0924695i
$491$	6.48545e38			0.618385			0.309192	−	0.951000i	$-0.399941\pi$
$491$	6.48545e38			0.618385			0.309192	+	0.951000i	$0.399941\pi$
$492$	−7.12798e37	−	1.23460e38i	−0.0659892	−	0.114297i
$493$	1.23053e38	−	2.13135e38i	0.110615	−	0.191591i
$494$	−1.75430e38	+	3.03853e38i	−0.153131	+	0.265230i
$495$	−1.46651e38	−	2.54007e38i	−0.124311	−	0.215313i
$496$	3.79870e38			0.312717
$497$	−2.83081e38	+	5.88491e38i	−0.226330	+	0.470513i
$498$	−5.96734e38			−0.463399
$499$	3.86491e38	+	6.69422e38i	0.291529	+	0.504943i	0.974171	−	0.225810i	$-0.0725028\pi$
$499$	3.86491e38	+	6.69422e38i	0.291529	+	0.504943i	−0.682643	+	0.730752i	$0.739169\pi$
$500$	1.75396e38	−	3.03795e38i	0.128516	−	0.222595i
$501$	5.15601e38	−	8.93047e38i	0.367001	−	0.635664i
$502$	5.24233e38	+	9.07999e38i	0.362511	+	0.627887i
$503$	1.58192e39			1.06279			0.531397	−	0.847123i	$-0.321667\pi$
$503$	1.58192e39			1.06279			0.531397	+	0.847123i	$0.321667\pi$
$504$	−5.50628e38	+	4.15092e37i	−0.359431	+	0.0270958i
$505$	2.11905e38			0.134405
$506$	8.06715e38	+	1.39727e39i	0.497208	+	0.861189i
$507$	−4.64191e38	+	8.04002e38i	−0.278023	+	0.481550i
$508$	−1.32182e38	+	2.28945e38i	−0.0769392	+	0.133263i
$509$	−1.13515e38	−	1.96614e38i	−0.0642165	−	0.111226i	0.832130	−	0.554581i	$-0.187121\pi$
$509$	−1.13515e38	−	1.96614e38i	−0.0642165	−	0.111226i	−0.896346	+	0.443355i	$0.853788\pi$
$510$	3.96137e38			0.217810
$511$	1.92897e39	+	2.82658e39i	1.03091	+	1.51063i
$512$	−2.09155e39			−1.08656
$513$	−3.48967e38	−	6.04428e38i	−0.176231	−	0.305241i
$514$	−1.74763e37	+	3.02698e37i	−0.00857993	+	0.0148609i
$515$	−8.52312e37	+	1.47625e38i	−0.0406812	+	0.0704619i
$516$	−4.19996e36	−	7.27454e36i	−0.00194906	−	0.00337587i
$517$	−7.40285e38			−0.334030
$518$	5.95894e38	+	8.73184e38i	0.261449	+	0.383111i
$519$	−3.00560e37			−0.0128234
$520$	1.77359e38	+	3.07196e38i	0.0735878	+	0.127458i
$521$	1.20549e38	−	2.08797e38i	0.0486425	−	0.0842513i	−0.840679	−	0.541534i	$-0.817844\pi$
$521$	1.20549e38	−	2.08797e38i	0.0486425	−	0.0842513i	0.889322	+	0.457282i	$0.151177\pi$
$522$	1.33723e38	−	2.31615e38i	0.0524787	−	0.0908958i
$523$	−1.17908e38	−	2.04223e38i	−0.0450058	−	0.0779524i	0.842645	−	0.538470i	$-0.180997\pi$
$523$	−1.17908e38	−	2.04223e38i	−0.0450058	−	0.0779524i	−0.887651	+	0.460517i	$0.847664\pi$
$524$	−1.15665e39			−0.429434
$525$	7.93848e38	−	5.98445e37i	0.286700	−	0.0216130i
$526$	1.44204e39			0.506622
$527$	4.00201e38	+	6.93169e38i	0.136781	+	0.236911i
$528$	6.38994e38	−	1.10677e39i	0.212474	−	0.368015i
$529$	−2.74307e38	+	4.75114e38i	−0.0887422	+	0.153706i
$530$	−5.15765e38	−	8.93332e38i	−0.162350	−	0.281198i
$531$	2.01120e37			0.00616005
$532$	−6.45069e38	+	1.34102e39i	−0.192259	+	0.399684i
$533$	−6.25172e38			−0.181324
$534$	8.63180e38	+	1.49507e39i	0.243643	+	0.422001i
$535$	2.03087e39	−	3.51756e39i	0.557894	−	0.966300i
$536$	−8.34931e38	+	1.44614e39i	−0.223235	+	0.386654i
$537$	−1.53828e39	−	2.66438e39i	−0.400321	−	0.693377i
$538$	−4.85051e39			−1.22870
$539$	−4.22090e39	+	6.40025e38i	−1.04080	+	0.157819i
$540$	−1.37564e38			−0.0330214
$541$	1.45754e39	+	2.52454e39i	0.340613	+	0.589959i	0.984547	−	0.175122i	$-0.0560321\pi$
$541$	1.45754e39	+	2.52454e39i	0.340613	+	0.589959i	−0.643934	+	0.765081i	$0.722699\pi$
$542$	−2.32214e39	+	4.02206e39i	−0.528322	+	0.915081i
$543$	2.16249e39	−	3.74554e39i	0.479023	−	0.829692i
$544$	−6.70230e38	−	1.16087e39i	−0.144557	−	0.250380i
$545$	8.92119e38			0.187359
$546$	−2.04646e38	+	4.25435e38i	−0.0418515	+	0.0870041i
$547$	−1.99642e39			−0.397590			−0.198795	−	0.980041i	$-0.563703\pi$
$547$	−1.99642e39			−0.397590			−0.198795	+	0.980041i	$0.563703\pi$
$548$	8.18834e38	+	1.41826e39i	0.158810	+	0.275067i
$549$	−2.23207e38	+	3.86605e38i	−0.0421607	+	0.0730245i
$550$	−1.24033e39	+	2.14832e39i	−0.228181	+	0.395221i
$551$	−1.84846e39	−	3.20163e39i	−0.331217	−	0.573685i
$552$	3.88151e39			0.677460
$553$	9.25889e39	−	6.97985e38i	1.57414	−	0.118667i
$554$	−9.15608e39			−1.51642
$555$	6.75428e38	+	1.16988e39i	0.108976	+	0.188752i
$556$	−7.62075e38	+	1.31995e39i	−0.119788	+	0.207479i
$557$	3.98777e39	−	6.90701e39i	0.610702	−	1.05777i	−0.380420	−	0.924814i	$-0.624221\pi$
$557$	3.98777e39	−	6.90701e39i	0.610702	−	1.05777i	0.991122	−	0.132953i	$-0.0424460\pi$
$558$	4.34901e38	+	7.53270e38i	0.0648925	+	0.112397i
$559$	−3.68365e37			−0.00535558
$560$	−1.97112e39	−	2.88835e39i	−0.279245	−	0.409188i
$561$	2.69278e39			0.371739
$562$	−5.75421e39	−	9.96658e39i	−0.774121	−	1.34082i
$563$	−2.19088e39	+	3.79471e39i	−0.287241	+	0.497516i	−0.973150	−	0.230171i	$-0.926071\pi$
$563$	−2.19088e39	+	3.79471e39i	−0.287241	+	0.497516i	0.685909	+	0.727687i	$0.259405\pi$
$564$	−1.73603e38	+	3.00690e38i	−0.0221825	+	0.0384213i
$565$	3.19440e37	+	5.53286e37i	0.00397820	+	0.00689044i
$566$	−7.13320e39			−0.865858
$567$	−5.29358e38	−	7.75686e38i	−0.0626318	−	0.0917766i
$568$	−4.89539e39			−0.564594
$569$	−4.07159e39	−	7.05220e39i	−0.457758	−	0.792861i	0.541084	−	0.840969i	$-0.318014\pi$
$569$	−4.07159e39	−	7.05220e39i	−0.457758	−	0.792861i	−0.998842	+	0.0481080i	$0.984681\pi$
$570$	2.97531e39	−	5.15339e39i	0.326097	−	0.564816i
$571$	6.14211e39	−	1.06384e40i	0.656287	−	1.13672i	−0.325282	−	0.945617i	$-0.605459\pi$
$571$	6.14211e39	−	1.06384e40i	0.656287	−	1.13672i	0.981569	−	0.191106i	$-0.0612074\pi$
$572$	2.35044e38	+	4.07108e38i	0.0244854	+	0.0424099i
$573$	−1.66760e39			−0.169375
$574$	8.27411e39	−	6.23746e38i	0.819405	−	0.0617711i
$575$	−5.59603e39			−0.540376
$576$	−1.96590e39	−	3.40504e39i	−0.185113	−	0.320624i
$577$	5.50094e39	−	9.52790e39i	0.505112	−	0.874879i	−0.494871	−	0.868967i	$-0.664785\pi$
$577$	5.50094e39	−	9.52790e39i	0.505112	−	0.874879i	0.999983	−	0.00591249i	$-0.00188201\pi$
$578$	3.04238e39	−	5.26955e39i	0.272433	−	0.471868i
$579$	4.27213e39	+	7.39954e39i	0.373083	+	0.646198i
$580$	−7.28672e38			−0.0620620
$581$	−4.81124e39	+	1.00020e40i	−0.399672	+	0.830868i
$582$	3.88650e39			0.314902
$583$	−3.50596e39	−	6.07251e39i	−0.277085	−	0.479926i
$584$	−1.28265e40	+	2.22161e40i	−0.988829	+	1.71270i
$585$	−3.01632e38	+	5.22442e38i	−0.0226839	+	0.0392897i
$586$	−8.49457e39	−	1.47130e40i	−0.623198	−	1.07941i
$587$	−2.74448e39			−0.196430			−0.0982150	−	0.995165i	$-0.531313\pi$
$587$	−2.74448e39			−0.196430			−0.0982150	+	0.995165i	$0.531313\pi$
$588$	−7.29873e38	+	1.86454e39i	−0.0509655	+	0.130197i
$589$	1.20234e40			0.819132
$590$	8.57379e37	+	1.48502e38i	0.00569926	+	0.00987141i
$591$	−2.60279e39	+	4.50816e39i	−0.168819	+	0.292403i
$592$	−2.94300e39	+	5.09743e39i	−0.186263	+	0.322616i
$593$	1.47202e40	+	2.54962e40i	0.909120	+	1.57464i	0.815289	+	0.579054i	$0.196578\pi$
$593$	1.47202e40	+	2.54962e40i	0.909120	+	1.57464i	0.0938314	+	0.995588i	$0.470089\pi$
$594$	2.92625e39			0.176363
$595$	3.19390e39	−	6.63973e39i	0.187856	−	0.390530i
$596$	−5.85642e39			−0.336172
$597$	1.67593e39	+	2.90280e39i	0.0938921	+	0.162626i
$598$	1.65925e39	−	2.87391e39i	0.0907288	−	0.157147i
$599$	−1.44927e40	+	2.51022e40i	−0.773502	+	1.33975i	0.162130	+	0.986769i	$0.448163\pi$
$599$	−1.44927e40	+	2.51022e40i	−0.773502	+	1.33975i	−0.935632	+	0.352976i	$0.885170\pi$
$600$	2.98393e39	+	5.16831e39i	0.155452	+	0.269250i
$601$	2.11426e40			1.07518			0.537588	−	0.843208i	$-0.319336\pi$
$601$	2.11426e40			1.07518			0.537588	+	0.843208i	$0.319336\pi$
$602$	4.87528e38	−	3.67524e37i	0.0242020	−	0.00182447i
$603$	−2.83991e39			−0.137627
$604$	−1.72694e39	−	2.99114e39i	−0.0817035	−	0.141515i
$605$	8.29679e38	−	1.43705e39i	0.0383228	−	0.0663770i
$606$	−1.05708e39	+	1.83091e39i	−0.0476710	+	0.0825685i
$607$	−5.38375e39	−	9.32493e39i	−0.237055	−	0.410591i	0.722813	−	0.691044i	$-0.242849\pi$
$607$	−5.38375e39	−	9.32493e39i	−0.237055	−	0.410591i	−0.959868	+	0.280453i	$0.909515\pi$
$608$	−2.01359e40			−0.865703
$609$	−2.80399e39	−	4.10878e39i	−0.117713	−	0.172489i
$610$	−3.80614e39			−0.156028
$611$	7.61309e38	+	1.31863e39i	0.0304764	+	0.0527867i
$612$	6.31480e38	−	1.09375e39i	0.0246867	−	0.0427587i
$613$	−2.34291e40	+	4.05803e40i	−0.894496	+	1.54931i	−0.0600683	+	0.998194i	$0.519132\pi$
$613$	−2.34291e40	+	4.05803e40i	−0.894496	+	1.54931i	−0.834427	+	0.551118i	$0.814201\pi$
$614$	−1.53832e40	−	2.66445e40i	−0.573594	−	0.993494i
$615$	1.06030e40			0.386136
$616$	−1.80397e40	−	2.64342e40i	−0.641665	−	0.940255i
$617$	2.25658e40			0.784000			0.392000	−	0.919965i	$-0.371783\pi$
$617$	2.25658e40			0.784000			0.392000	+	0.919965i	$0.371783\pi$
$618$	−8.50344e38	−	1.47284e39i	−0.0288577	−	0.0499830i
$619$	−2.82208e39	+	4.88798e39i	−0.0935523	+	0.162037i	−0.909003	−	0.416789i	$-0.863156\pi$
$619$	−2.82208e39	+	4.88798e39i	−0.0935523	+	0.162037i	0.815451	+	0.578826i	$0.196489\pi$
$620$	1.18491e39	−	2.05233e39i	0.0383713	−	0.0664611i
$621$	3.30061e39	+	5.71682e39i	0.104416	+	0.180853i
$622$	2.47495e40			0.764902
$623$	3.20187e40	−	2.41374e39i	0.966779	−	0.0728810i
$624$	−2.62857e39			−0.0775430
$625$	4.40655e39	+	7.63237e39i	0.127010	+	0.219988i
$626$	−1.88601e39	+	3.26667e39i	−0.0531149	+	0.0919977i
$627$	2.02249e40	−	3.50306e40i	0.556555	−	0.963981i
$628$	7.39092e39	+	1.28015e40i	0.198739	+	0.344227i
$629$	−1.24020e40			−0.325881
$630$	3.47083e39	−	7.21543e39i	0.0891241	−	0.185278i
$631$	7.07002e40			1.77417			0.887085	−	0.461607i	$-0.152727\pi$
$631$	7.07002e40			1.77417			0.887085	+	0.461607i	$0.152727\pi$
$632$	3.48024e40	+	6.02796e40i	0.853517	+	1.47833i
$633$	2.99371e39	−	5.18526e39i	0.0717557	−	0.124285i
$634$	−2.31560e40	+	4.01073e40i	−0.542462	+	0.939571i
$635$	−9.83113e39	−	1.70280e40i	−0.225105	−	0.389893i
$636$	−3.28872e39			−0.0736035
$637$	5.48082e39	+	6.86024e39i	0.119901	+	0.150078i
$638$	1.55003e40			0.331466
$639$	−4.16275e39	−	7.21010e39i	−0.0870198	−	0.150723i
$640$	8.56709e39	−	1.48386e40i	0.175075	−	0.303238i
$641$	7.67771e39	−	1.32982e40i	0.153388	−	0.265675i	−0.779083	−	0.626921i	$-0.784315\pi$
$641$	7.67771e39	−	1.32982e40i	0.153388	−	0.265675i	0.932471	+	0.361246i	$0.117648\pi$
$642$	2.02618e40	+	3.50944e40i	0.395749	+	0.685457i
$643$	1.06566e40			0.203499			0.101749	−	0.994810i	$-0.467556\pi$
$643$	1.06566e40			0.203499			0.101749	+	0.994810i	$0.467556\pi$
$644$	6.10121e39	−	1.26837e40i	0.113912	−	0.236810i
$645$	6.24752e38			0.0114049
$646$	2.73160e40	+	4.73126e40i	0.487579	+	0.844512i
$647$	−7.04610e39	+	1.22042e40i	−0.122981	+	0.213009i	−0.920942	−	0.389700i	$-0.872579\pi$
$647$	−7.04610e39	+	1.22042e40i	−0.122981	+	0.213009i	0.797961	+	0.602709i	$0.205912\pi$
$648$	3.51991e39	−	6.09667e39i	0.0600751	−	0.104053i
$649$	5.82812e38	+	1.00946e39i	0.00972702	+	0.0168477i
$650$	5.10223e39			0.0832753
$651$	1.61322e40	−	1.21613e39i	0.257495	−	0.0194113i
$652$	2.93555e40			0.458247
$653$	−5.87301e40	−	1.01723e41i	−0.896642	−	1.55303i	−0.831759	−	0.555137i	$-0.812666\pi$
$653$	−5.87301e40	−	1.01723e41i	−0.896642	−	1.55303i	−0.0648838	−	0.997893i	$-0.520668\pi$
$654$	−4.45030e39	+	7.70814e39i	−0.0664526	+	0.115099i
$655$	4.30133e40	−	7.45012e40i	0.628209	−	1.08809i
$656$	2.30999e40	+	4.00102e40i	0.329993	+	0.571565i
$657$	−4.36275e40			−0.609625
$658$	−1.13915e40	−	1.66923e40i	−0.155706	−	0.228161i
$659$	5.64684e40			0.755035			0.377517	−	0.926002i	$-0.376778\pi$
$659$	5.64684e40			0.755035			0.377517	+	0.926002i	$0.376778\pi$
$660$	−3.98637e39	−	6.90460e39i	−0.0521424	−	0.0903133i
$661$	−6.91891e40	+	1.19839e41i	−0.885353	+	1.53348i	−0.0400439	+	0.999198i	$0.512750\pi$
$661$	−6.91891e40	+	1.19839e41i	−0.885353	+	1.53348i	−0.845309	+	0.534278i	$0.820584\pi$
$662$	4.49262e39	−	7.78144e39i	0.0562417	−	0.0974135i
$663$	−2.76925e39	−	4.79648e39i	−0.0339169	−	0.0587458i
$664$	−8.32020e40			−0.997003
$665$	−6.23882e40	−	9.14196e40i	−0.731457	−	1.07183i
$666$	−1.34774e40			−0.154607
$667$	1.74832e40	+	3.02818e40i	0.196244	+	0.339904i
$668$	1.40154e40	−	2.42754e40i	0.153939	−	0.266630i
$669$	−2.39141e39	+	4.14204e39i	−0.0257025	+	0.0445180i
$670$	−1.21066e40	−	2.09692e40i	−0.127332	−	0.220545i
$671$	−2.58726e40			−0.266295
$672$	−2.70170e40	+	2.03669e39i	−0.272134	+	0.0205149i
$673$	−1.59005e40			−0.156744			−0.0783722	−	0.996924i	$-0.524972\pi$
$673$	−1.59005e40			−0.156744			−0.0783722	+	0.996924i	$0.524972\pi$
$674$	7.82454e40	+	1.35525e41i	0.754901	+	1.30753i
$675$	−5.07471e39	+	8.78966e39i	−0.0479189	+	0.0829980i
$676$	−1.26179e40	+	2.18549e40i	−0.116617	+	0.201986i
$677$	5.09244e40	+	8.82036e40i	0.460670	+	0.797904i	0.998994	−	0.0448339i	$-0.0142759\pi$
$677$	5.09244e40	+	8.82036e40i	0.460670	+	0.797904i	−0.538325	+	0.842738i	$0.680943\pi$
$678$	−6.37404e38			−0.00564397
$679$	3.13354e40	−	6.51425e40i	0.271596	−	0.564616i
$680$	5.52330e40			0.468618
$681$	−2.58107e40	−	4.47054e40i	−0.214371	−	0.371302i
$682$	−2.52054e40	+	4.36570e40i	−0.204937	+	0.354961i
$683$	7.06312e40	−	1.22337e41i	0.562207	−	0.973771i	−0.435096	−	0.900384i	$-0.643286\pi$
$683$	7.06312e40	−	1.22337e41i	0.562207	−	0.973771i	0.997304	−	0.0733874i	$-0.0233810\pi$
$684$	−9.48586e39	−	1.64300e40i	−0.0739202	−	0.128034i
$685$	−1.21803e41			−0.929276
$686$	−7.93828e40	−	8.53265e40i	−0.592962	−	0.637359i
$687$	−3.12692e40			−0.228688
$688$	1.36110e39	+	2.35749e39i	0.00974667	+	0.0168817i
$689$	−7.21107e39	+	1.24899e40i	−0.0505616	+	0.0875753i
$690$	−2.81412e40	+	4.87419e40i	−0.193210	+	0.334650i
$691$	−8.31807e40	−	1.44073e41i	−0.559231	−	0.968616i	−0.997561	−	0.0698020i	$-0.977763\pi$
$691$	−8.31807e40	−	1.44073e41i	−0.559231	−	0.968616i	0.438330	−	0.898814i	$-0.355570\pi$
$692$	−8.17002e38			−0.00537879
$693$	2.35933e40	−	4.90476e40i	0.152110	−	0.316217i
$694$	−6.72420e40			−0.424549
$695$	−5.66800e40	−	9.81727e40i	−0.350470	−	0.607031i
$696$	1.86449e40	−	3.22938e40i	0.112908	−	0.195562i
$697$	−4.86725e40	+	8.43032e40i	−0.288674	+	0.499999i
$698$	−1.04748e41	−	1.81429e41i	−0.608476	−	1.05391i
$699$	−1.75493e41			−0.998485
$700$	2.15789e40	−	1.62673e39i	0.120256	−	0.00906557i
$701$	−1.26673e41			−0.691469			−0.345735	−	0.938332i	$-0.612370\pi$
$701$	−1.26673e41			−0.691469			−0.345735	+	0.938332i	$0.612370\pi$
$702$	−3.00936e39	−	5.21236e39i	−0.0160911	−	0.0278706i
$703$	−9.31495e40	+	1.61340e41i	−0.487897	+	0.845063i
$704$	1.13937e41	−	1.97345e41i	0.584603	−	1.01256i
$705$	−1.29119e40	−	2.23641e40i	−0.0649005	−	0.112411i
$706$	−2.07910e41			−1.02378
$707$	2.21655e40	+	3.24799e40i	0.106929	+	0.156687i
$708$	5.46698e38			0.00258384
$709$	−2.81992e40	−	4.88425e40i	−0.130577	−	0.226166i	0.793322	−	0.608802i	$-0.208350\pi$
$709$	−2.81992e40	−	4.88425e40i	−0.130577	−	0.226166i	−0.923899	+	0.382636i	$0.875016\pi$
$710$	3.54919e40	−	6.14737e40i	0.161021	−	0.278897i
$711$	−5.91879e40	+	1.02517e41i	−0.263102	+	0.455706i
$712$	1.20352e41	+	2.08456e41i	0.524197	+	0.907936i
$713$	−1.13720e41			−0.485330
$714$	4.14364e40	+	6.07182e40i	0.173284	+	0.253919i
$715$	−3.49632e40			−0.143276
$716$	−4.18146e40	−	7.24250e40i	−0.167915	−	0.290837i
$717$	−3.63401e40	+	6.29430e40i	−0.143007	+	0.247696i
$718$	−5.22480e40	+	9.04962e40i	−0.201496	+	0.349001i
$719$	7.91246e40	+	1.37048e41i	0.299049	+	0.517968i	0.975919	−	0.218135i	$-0.0699972\pi$
$719$	7.91246e40	+	1.37048e41i	0.299049	+	0.517968i	−0.676869	+	0.736103i	$0.736664\pi$
$720$	4.45809e40			0.165131
$721$	−3.15426e40	+	2.37785e39i	−0.114508	+	0.00863222i
$722$	5.75994e41			2.04941
$723$	7.07053e40	+	1.22465e41i	0.246574	+	0.427078i
$724$	5.87823e40	−	1.01814e41i	0.200926	−	0.348015i
$725$	−2.68806e40	+	4.65585e40i	−0.0900611	+	0.155990i
$726$	8.27764e39	+	1.43373e40i	0.0271848	+	0.0470854i
$727$	−2.35039e41			−0.756644			−0.378322	−	0.925674i	$-0.623499\pi$
$727$	−2.35039e41			−0.756644			−0.378322	+	0.925674i	$0.623499\pi$
$728$	−2.85336e40	+	5.93180e40i	−0.0900435	+	0.187189i
$729$	1.19725e40			0.0370370
$730$	−1.85985e41	−	3.22136e41i	−0.564023	−	0.976917i
$731$	−2.86789e39	+	4.96732e39i	−0.00852629	+	0.0147680i
$732$	−6.06736e39	+	1.05090e40i	−0.0176843	+	0.0306302i
$733$	2.98030e41	+	5.16202e41i	0.851631	+	1.47507i	0.879735	+	0.475464i	$0.157720\pi$
$733$	2.98030e41	+	5.16202e41i	0.851631	+	1.47507i	−0.0281039	+	0.999605i	$0.508947\pi$
$734$	3.16570e41			0.886904
$735$	−9.29554e40	−	1.16351e41i	−0.255334	−	0.319597i
$736$	1.90450e41			0.512923
$737$	−8.22957e40	−	1.42540e41i	−0.217320	−	0.376408i
$738$	−5.28926e40	+	9.16127e40i	−0.136955	+	0.237213i
$739$	1.50411e41	−	2.60519e41i	0.381887	−	0.661448i	−0.609445	−	0.792828i	$-0.708608\pi$
$739$	1.50411e41	−	2.60519e41i	0.381887	−	0.661448i	0.991332	+	0.131381i	$0.0419410\pi$
$740$	1.83599e40	+	3.18004e40i	0.0457100	+	0.0791721i
$741$	−8.31973e40			−0.203117
$742$	8.29765e40	−	1.72498e41i	0.198655	−	0.412978i
$743$	4.50525e41			1.05774			0.528872	−	0.848702i	$-0.322615\pi$
$743$	4.50525e41			1.05774			0.528872	+	0.848702i	$0.322615\pi$
$744$	6.06378e40	+	1.05028e41i	0.139616	+	0.241822i
$745$	2.17788e41	−	3.77220e41i	0.491777	−	0.851783i
$746$	−4.55730e40	+	7.89347e40i	−0.100924	+	0.174805i
$747$	−7.07501e40	−	1.22543e41i	−0.153666	−	0.266158i
$748$	7.31969e40			0.155926
$749$	7.51588e41	−	5.66587e40i	1.57034	−	0.118381i
$750$	−2.60303e41			−0.533446
$751$	4.20248e41	+	7.27891e41i	0.844747	+	1.46314i	0.885841	+	0.463990i	$0.153583\pi$
$751$	4.20248e41	+	7.27891e41i	0.844747	+	1.46314i	−0.0410935	+	0.999155i	$0.513084\pi$
$752$	5.62603e40	−	9.74456e40i	0.110928	−	0.192134i
$753$	−1.24309e41	+	2.15309e41i	−0.240422	+	0.416423i
$754$	−1.59405e40	−	2.76097e40i	−0.0302424	−	0.0523814i
$755$	2.56885e41			0.478088
$756$	−1.43894e40	−	2.10852e40i	−0.0262709	−	0.0384957i
$757$	−6.62108e41			−1.18587			−0.592937	−	0.805249i	$-0.702032\pi$
$757$	−6.62108e41			−1.18587			−0.592937	+	0.805249i	$0.702032\pi$
$758$	2.64898e41	+	4.58816e41i	0.465452	+	0.806186i
$759$	−1.91292e41	+	3.31328e41i	−0.329755	+	0.571152i
$760$	4.14845e41	−	7.18532e41i	0.701598	−	1.21520i
$761$	−2.55461e41	−	4.42471e41i	−0.423884	−	0.734189i	0.572431	−	0.819953i	$-0.306000\pi$
$761$	−2.55461e41	−	4.42471e41i	−0.423884	−	0.734189i	−0.996315	+	0.0857638i	$0.972667\pi$
$762$	1.96169e41			0.319362
$763$	9.33168e40	+	1.36740e41i	0.149057	+	0.218419i
$764$	−4.53298e40			−0.0710444
$765$	4.69669e40	+	8.13490e40i	0.0722272	+	0.125101i
$766$	2.06388e41	−	3.57475e41i	0.311435	−	0.539422i
$767$	1.19873e39	−	2.07626e39i	0.00177496	−	0.00307431i
$768$	−1.35192e41	−	2.34160e41i	−0.196433	−	0.340232i
$769$	−2.57672e41			−0.367396			−0.183698	−	0.982983i	$-0.558807\pi$
$769$	−2.57672e41			−0.367396			−0.183698	+	0.982983i	$0.558807\pi$
$770$	4.62735e41	−	3.48834e40i	0.647466	−	0.0488094i
$771$	−8.28811e39			−0.0113806
$772$	1.16128e41	+	2.01139e41i	0.156490	+	0.271048i
$773$	−5.32849e41	+	9.22922e41i	−0.704696	+	1.22057i	0.262105	+	0.965039i	$0.415583\pi$
$773$	−5.32849e41	+	9.22922e41i	−0.704696	+	1.22057i	−0.966801	+	0.255530i	$0.917750\pi$
$774$	−3.11655e39	+	5.39802e39i	−0.00404510	+	0.00700633i
$775$	−8.74224e40	−	1.51420e41i	−0.111365	−	0.192890i
$776$	5.41892e41			0.677513
$777$	−1.08663e41	+	2.25897e41i	−0.133345	+	0.277208i
$778$	−8.81073e41			−1.06123
$779$	7.31140e41	+	1.26637e42i	0.864385	+	1.49716i
$780$	−8.19918e39	+	1.42014e40i	−0.00951478	+	0.0164801i
$781$	2.41259e41	−	4.17873e41i	0.274817	−	0.475997i
$782$	−2.58361e41	−	4.47494e41i	−0.288887	−	0.500367i
$783$	6.34180e40			0.0696092
$784$	2.36532e41	−	6.04249e41i	0.254864	−	0.651078i
$785$	−1.09941e42			−1.16292
$786$	4.29140e41	+	7.43292e41i	0.445628	+	0.771850i
$787$	−8.14592e41	+	1.41092e42i	−0.830437	+	1.43836i	0.0672553	+	0.997736i	$0.478576\pi$
$787$	−8.14592e41	+	1.41092e42i	−0.830437	+	1.43836i	−0.897692	+	0.440623i	$0.854758\pi$
$788$	−7.07508e40	+	1.22544e41i	−0.0708111	+	0.122648i
$789$	1.70972e41	+	2.96131e41i	0.167999	+	0.290983i
$790$	−1.00928e42			−0.973685
$791$	−5.13915e39	+	1.06837e40i	−0.00486780	+	0.0101196i
$792$	4.08005e41			0.379446
$793$	2.66074e40	+	4.60854e40i	0.0242964	+	0.0420825i
$794$	3.79089e41	−	6.56602e41i	0.339894	−	0.588715i
$795$	1.22301e41	−	2.11831e41i	0.107673	−	0.186495i
$796$	4.55564e40	+	7.89060e40i	0.0393831	+	0.0682135i
$797$	−8.82010e41			−0.748734			−0.374367	−	0.927281i	$-0.622140\pi$
$797$	−8.82010e41			−0.748734			−0.374367	+	0.927281i	$0.622140\pi$
$798$	1.10111e42	−	8.30076e40i	0.917886	−	0.0691952i
$799$	2.37085e41			0.194078
$800$	1.46409e41	+	2.53588e41i	0.117696	+	0.203856i
$801$	−2.04681e41	+	3.54518e41i	−0.161587	+	0.279877i
$802$	4.42316e41	−	7.66115e41i	0.342929	−	0.593971i
$803$	−1.26425e42	−	2.18975e42i	−0.962628	−	1.66732i
$804$	−7.71963e40			−0.0577277
$805$	5.90082e41	+	8.64668e41i	0.433383	+	0.635052i
$806$	1.03685e41			0.0747924
$807$	−5.75087e41	−	9.96080e41i	−0.407444	−	0.705713i
$808$	−1.47387e41	+	2.55282e41i	−0.102564	+	0.177646i
$809$	2.25833e41	−	3.91155e41i	0.154360	−	0.267359i	−0.778466	−	0.627687i	$-0.784002\pi$
$809$	2.25833e41	−	3.91155e41i	0.154360	−	0.267359i	0.932826	+	0.360328i	$0.117335\pi$
$810$	5.10391e40	+	8.84024e40i	0.0342666	+	0.0593514i
$811$	1.75473e42			1.15720			0.578599	−	0.815612i	$-0.303600\pi$
$811$	1.75473e42			1.15720			0.578599	+	0.815612i	$0.303600\pi$
$812$	−7.62199e40	−	1.11688e41i	−0.0493749	−	0.0723507i
$813$	−1.10127e42			−0.700781
$814$	−3.90551e41	−	6.76455e41i	−0.244132	−	0.422849i
$815$	−1.09167e42	+	1.89083e42i	−0.670358	+	1.16109i
$816$	−2.04646e41	+	3.54457e41i	−0.123451	+	0.213824i
$817$	4.30803e40	+	7.46173e40i	0.0255305	+	0.0442201i
$818$	−2.02041e42			−1.17630
$819$	−1.11629e41	+	8.41518e39i	−0.0638499	+	0.00481334i
$820$	2.88218e41			0.161965
$821$	6.17152e41	+	1.06894e42i	0.340735	+	0.590170i	0.984569	−	0.174995i	$-0.0559909\pi$
$821$	6.17152e41	+	1.06894e42i	0.340735	+	0.590170i	−0.643835	+	0.765165i	$0.722658\pi$
$822$	6.07609e41	−	1.05241e42i	0.329597	−	0.570878i
$823$	3.12853e41	−	5.41878e41i	0.166741	−	0.288805i	−0.770531	−	0.637403i	$-0.780009\pi$
$823$	3.12853e41	−	5.41878e41i	0.166741	−	0.288805i	0.937272	+	0.348598i	$0.113342\pi$
$824$	−1.18563e41	−	2.05357e41i	−0.0620874	−	0.107538i
$825$	−5.88227e41			−0.302665
$826$	−1.37935e40	+	2.86751e40i	−0.00697373	+	0.0144975i
$827$	−3.14620e42			−1.56299			−0.781496	−	0.623910i	$-0.785543\pi$
$827$	−3.14620e42			−1.56299			−0.781496	+	0.623910i	$0.785543\pi$
$828$	8.97194e40	+	1.55399e41i	0.0437972	+	0.0758590i
$829$	−1.99771e41	+	3.46013e41i	−0.0958276	+	0.165978i	−0.909954	−	0.414710i	$-0.863883\pi$
$829$	−1.99771e41	+	3.46013e41i	−0.0958276	+	0.165978i	0.814126	+	0.580688i	$0.197216\pi$
$830$	6.03219e41	−	1.04481e42i	0.284343	−	0.492497i
$831$	−1.08557e42	−	1.88026e42i	−0.502854	−	0.870968i
$832$	−4.68692e41			−0.213353
$833$	1.35180e42	−	2.04976e41i	0.604726	−	0.0916960i
$834$	1.13098e42			0.497220
$835$	1.04241e42	+	1.80551e42i	0.450386	+	0.780091i
$836$	5.49768e41	−	9.52227e41i	0.233447	−	0.404342i
$837$	−1.03126e41	+	1.78619e41i	−0.0430376	+	0.0745433i
$838$	−1.72355e42	−	2.98527e42i	−0.706944	−	1.22446i
$839$	−2.22397e42			−0.896561			−0.448281	−	0.893893i	$-0.647964\pi$
$839$	−2.22397e42			−0.896561			−0.448281	+	0.893893i	$0.647964\pi$
$840$	4.83935e41	−	1.00604e42i	0.191751	−	0.398626i
$841$	−2.23176e42			−0.869173
$842$	5.65371e41	+	9.79251e41i	0.216425	+	0.374859i
$843$	1.36446e42	−	2.36332e42i	0.513408	−	0.889249i
$844$	8.13772e40	−	1.40949e41i	0.0300980	−	0.0521312i
$845$	−9.38471e41	−	1.62548e42i	−0.341192	−	0.590962i
$846$	2.57642e41			0.0920760
$847$	3.07050e41	−	2.31471e40i	0.107870	−	0.00813179i
$848$	1.06579e42			0.368070
$849$	−8.45729e41	−	1.46485e42i	−0.287124	−	0.497314i
$850$	3.97232e41	−	6.88026e41i	0.132577	−	0.229631i
$851$	8.81029e41	−	1.52599e42i	0.289076	−	0.500694i
$852$	−1.13155e41	−	1.95990e41i	−0.0365005	−	0.0632208i
$853$	2.01817e42			0.640025			0.320013	−	0.947413i	$-0.396313\pi$
$853$	2.01817e42			0.640025			0.320013	+	0.947413i	$0.396313\pi$
$854$	−3.98127e41	−	5.83390e41i	−0.124132	−	0.181895i
$855$	1.41104e42			0.432544
$856$	2.82508e42	+	4.89318e42i	0.851454	+	1.47476i
$857$	1.71035e42	−	2.96242e42i	0.506832	−	0.877859i	−0.493136	−	0.869952i	$-0.664150\pi$
$857$	1.71035e42	−	2.96242e42i	0.506832	−	0.877859i	0.999969	−	0.00790735i	$-0.00251702\pi$
$858$	1.74412e41	−	3.02091e41i	0.0508173	−	0.0880181i
$859$	−6.97176e41	−	1.20754e42i	−0.199729	−	0.345941i	0.748711	−	0.662896i	$-0.230673\pi$
$859$	−6.97176e41	−	1.20754e42i	−0.199729	−	0.345941i	−0.948441	+	0.316955i	$0.897340\pi$
$860$	1.69824e40			0.00478379
$861$	1.10909e42	+	1.62518e42i	0.307199	+	0.450150i
$862$	−3.40951e42			−0.928617
$863$	5.19395e41	+	8.99618e41i	0.139104	+	0.240936i	0.927158	−	0.374671i	$-0.122244\pi$
$863$	5.19395e41	+	8.99618e41i	0.139104	+	0.240936i	−0.788053	+	0.615607i	$0.788911\pi$
$864$	1.72708e41	−	2.99139e41i	0.0454844	−	0.0787813i
$865$	3.03826e40	−	5.26243e40i	0.00786850	−	0.0136286i
$866$	3.33080e42	+	5.76911e42i	0.848279	+	1.46926i
$867$	1.44285e42			0.361362
$868$	4.38516e41	−	3.30576e40i	0.108006	−	0.00814209i
$869$	−6.86067e42			−1.66180
$870$	2.70352e41	+	4.68264e41i	0.0644023	+	0.111548i
$871$	−1.69266e41	+	2.93177e41i	−0.0396558	+	0.0686858i
$872$	−6.20501e41	+	1.07474e42i	−0.142973	+	0.247636i
$873$	4.60793e41	+	7.98117e41i	0.104424	+	0.180867i
$874$	−7.76200e42			−1.73005
$875$	−2.09873e42	+	4.36299e42i	−0.460086	+	0.956462i
$876$	−1.18591e42			−0.255708
$877$	3.01528e42	+	5.22262e42i	0.639490	+	1.10763i	0.985545	+	0.169415i	$0.0541879\pi$
$877$	3.01528e42	+	5.22262e42i	0.639490	+	1.10763i	−0.346054	+	0.938214i	$0.612479\pi$
$878$	−3.07030e42	+	5.31791e42i	−0.640486	+	1.10935i
$879$	2.01427e42	−	3.48882e42i	0.413313	−	0.715880i
$880$	1.29188e42	+	2.23760e42i	0.260749	+	0.451631i
$881$	−8.50918e42			−1.68942			−0.844708	−	0.535227i	$-0.820226\pi$
$881$	−8.50918e42			−1.68942			−0.844708	+	0.535227i	$0.820226\pi$
$882$	1.46900e42	−	2.22749e41i	0.286899	−	0.0435031i
$883$	4.21449e42			0.809683			0.404842	−	0.914387i	$-0.367327\pi$
$883$	4.21449e42			0.809683			0.404842	+	0.914387i	$0.367327\pi$
$884$	−7.52757e40	−	1.30381e41i	−0.0142265	−	0.0246410i
$885$	−2.03306e40	+	3.52136e40i	−0.00377983	+	0.00654686i
$886$	4.58177e42	−	7.93585e42i	0.838000	−	1.45146i
$887$	−1.27739e41	−	2.21250e41i	−0.0229842	−	0.0398099i	0.854305	−	0.519773i	$-0.173983\pi$
$887$	−1.27739e41	−	2.21250e41i	−0.0229842	−	0.0398099i	−0.877289	+	0.479963i	$0.840650\pi$
$888$	−1.87914e42			−0.332637
$889$	1.58164e42	−	3.28803e42i	0.275442	−	0.572611i
$890$	−3.49025e42			−0.598000
$891$	3.46943e41	+	6.00923e41i	0.0584833	+	0.101296i
$892$	−6.50049e40	+	1.12592e41i	−0.0107809	+	0.0186731i
$893$	1.78071e42	−	3.08427e42i	0.290567	−	0.503276i
$894$	2.17285e42	+	3.76349e42i	0.348848	+	0.604223i
$895$	6.22000e42			0.982554
$896$	3.17053e42	−	2.39011e41i	0.492795	−	0.0371495i
$897$	7.86899e41			0.120345
$898$	4.56373e42	+	7.90461e42i	0.686773	+	1.18953i
$899$	−5.46253e41	+	9.46138e41i	−0.0808869	+	0.140100i
$900$	−1.37944e41	+	2.38927e41i	−0.0200996	+	0.0348135i
$901$	1.12283e42	+	1.94480e42i	0.160992	+	0.278846i
$902$	−6.13096e42			−0.865035
$903$	6.53498e40	+	9.57593e40i	0.00907344	+	0.0132956i
$904$	−8.88727e40			−0.0121430
$905$	4.37198e42	+	7.57250e42i	0.587860	+	1.01820i
$906$	−1.28146e42	+	2.21955e42i	−0.169569	+	0.293702i
$907$	1.13502e42	−	1.96591e42i	0.147808	−	0.256011i	−0.782609	−	0.622513i	$-0.786112\pi$
$907$	1.13502e42	−	1.96591e42i	0.147808	−	0.256011i	0.930417	+	0.366503i	$0.119445\pi$
$908$	−7.01604e41	−	1.21521e42i	−0.0899181	−	0.155743i
$909$	−5.01318e41			−0.0632321
$910$	−5.38013e41	−	7.88369e41i	−0.0667871	−	0.0978654i
$911$	4.00042e42			0.488753			0.244377	−	0.969680i	$-0.421417\pi$
$911$	4.00042e42			0.488753			0.244377	+	0.969680i	$0.421417\pi$
$912$	3.07412e42	+	5.32452e42i	0.369654	+	0.640259i
$913$	4.10044e42	−	7.10217e42i	0.485293	−	0.840552i
$914$	3.32833e41	−	5.76484e41i	0.0387710	−	0.0671533i
$915$	−4.51265e41	−	7.81614e41i	−0.0517399	−	0.0896162i
$916$	−8.49981e41			−0.0959235
$917$	1.59185e43	−	1.20002e42i	1.76826	−	0.133301i
$918$	−9.37169e41			−0.102471
$919$	2.47718e42	+	4.29060e42i	0.266614	+	0.461789i	0.967985	−	0.251007i	$-0.0807619\pi$
$919$	2.47718e42	+	4.29060e42i	0.266614	+	0.461789i	−0.701371	+	0.712796i	$0.747429\pi$
$920$	−3.92369e42	+	6.79604e42i	−0.415692	+	0.720000i
$921$	3.64773e42	−	6.31806e42i	0.380416	−	0.658899i
$922$	−3.61026e42	−	6.25316e42i	−0.370630	−	0.641949i
$923$	−9.92444e41			−0.100295
$924$	6.41329e41	−	1.33324e42i	0.0638024	−	0.132637i
$925$	2.70918e42			0.265328
$926$	3.90981e42	+	6.77198e42i	0.376961	+	0.652915i
$927$	2.01638e41	−	3.49246e41i	0.0191388	−	0.0331494i
$928$	9.14827e41	−	1.58453e42i	0.0854856	−	0.148065i
$929$	−3.93431e42	−	6.81443e42i	−0.361944	−	0.626905i	0.626337	−	0.779553i	$-0.284553\pi$
$929$	−3.93431e42	−	6.81443e42i	−0.361944	−	0.626905i	−0.988281	+	0.152647i	$0.951220\pi$
$930$	−1.75851e42			−0.159273
$931$	7.48654e42	−	1.91252e43i	0.667591	−	1.70544i
$932$	−4.77038e42			−0.418815
$933$	2.93436e42	+	5.08246e42i	0.253647	+	0.439329i
$934$	−4.47103e42	+	7.74406e42i	−0.380521	+	0.659081i
$935$	−2.72204e42	+	4.71471e42i	−0.228101	+	0.395082i
$936$	−4.19592e41	−	7.26755e41i	−0.0346200	−	0.0599637i
$937$	−7.11318e42			−0.577882			−0.288941	−	0.957347i	$-0.593303\pi$
$937$	−7.11318e42			−0.577882			−0.288941	+	0.957347i	$0.593303\pi$
$938$	1.94771e42	−	4.04906e42i	0.155806	−	0.323901i
$939$	−8.94439e41			−0.0704531
$940$	−3.50980e41	−	6.07916e41i	−0.0272226	−	0.0471509i
$941$	1.58377e42	−	2.74318e42i	0.120961	−	0.209510i	−0.799186	−	0.601084i	$-0.794736\pi$
$941$	1.58377e42	−	2.74318e42i	0.120961	−	0.209510i	0.920147	+	0.391574i	$0.128069\pi$
$942$	5.48437e42	−	9.49921e42i	0.412467	−	0.714413i
$943$	−6.91529e42	−	1.19776e43i	−0.512143	−	0.887057i
$944$	−1.77170e41			−0.0129210
$945$	1.89324e42	−	1.42723e41i	0.135971	−	0.0102502i
$946$	−3.61249e41			−0.0255497
$947$	5.96948e42	+	1.03394e43i	0.415778	+	0.720149i	0.995510	−	0.0946585i	$-0.0301759\pi$
$947$	5.96948e42	+	1.03394e43i	0.415778	+	0.720149i	−0.579732	+	0.814808i	$0.696843\pi$
$948$	−1.60889e42	+	2.78667e42i	−0.110358	+	0.191146i
$949$	−2.60032e42	+	4.50388e42i	−0.175657	+	0.304247i
$950$	−5.96707e42	−	1.03353e43i	−0.396980	−	0.687590i
$951$	−1.09817e43			−0.719536
$952$	5.77743e42	+	8.46588e42i	0.372820	+	0.546306i
$953$	2.92410e43			1.85842			0.929211	−	0.369548i	$-0.120488\pi$
$953$	2.92410e43			1.85842			0.929211	+	0.369548i	$0.120488\pi$
$954$	1.22018e42	+	2.11342e42i	0.0763790	+	0.132292i
$955$	1.68572e42	−	2.91976e42i	0.103929	−	0.180010i
$956$	−9.87823e41	+	1.71096e42i	−0.0599846	+	0.103896i
$957$	1.83775e42	+	3.18307e42i	0.109916	+	0.190381i
$958$	−2.23279e43			−1.31537
$959$	−1.27407e43	−	1.86695e43i	−0.739307	−	1.08333i
$960$	7.94907e42			0.454343
$961$	7.10439e42	+	1.23052e43i	0.399979	+	0.692785i
$962$	−8.03287e41	+	1.39133e42i	−0.0445484	+	0.0771601i
$963$	−4.80457e42	+	8.32175e42i	−0.262466	+	0.454604i
$964$	1.92196e42	+	3.32893e42i	0.103425	+	0.179138i
$965$	−1.72742e43			−0.915699
$966$	−1.04146e43	+	7.85104e41i	−0.543841	+	0.0409977i
$967$	−1.19918e43			−0.616880			−0.308440	−	0.951244i	$-0.599807\pi$
$967$	−1.19918e43			−0.616880			−0.308440	+	0.951244i	$0.599807\pi$
$968$	1.15414e42	+	1.99903e42i	0.0584880	+	0.101304i
$969$	−6.47729e42	+	1.12190e43i	−0.323369	+	0.560092i
$970$	−3.92874e42	+	6.80478e42i	−0.193225	+	0.334676i
$971$	6.23631e42	+	1.08016e43i	0.302168	+	0.523371i	0.976627	−	0.214942i	$-0.0689562\pi$
$971$	6.23631e42	+	1.08016e43i	0.302168	+	0.523371i	−0.674459	+	0.738313i	$0.735623\pi$
$972$	3.25445e41			0.0155352
$973$	9.11870e42	−	1.89567e43i	0.428841	−	0.891509i
$974$	−2.41427e43			−1.11862
$975$	6.04932e41	+	1.04777e42i	0.0276147	+	0.0478300i
$976$	1.96627e42	−	3.40568e42i	0.0884343	−	0.153173i
$977$	1.80431e43	−	3.12515e43i	0.799539	−	1.38484i	−0.120377	−	0.992728i	$-0.538410\pi$
$977$	1.80431e43	−	3.12515e43i	0.799539	−	1.38484i	0.919917	−	0.392114i	$-0.128256\pi$
$978$	−1.08915e43	−	1.88647e43i	−0.475527	−	0.823636i
$979$	−2.37253e43			−1.02062
$980$	−2.52678e42	−	3.16272e42i	−0.107100	−	0.134055i
$981$	−2.11055e42			−0.0881445
$982$	−6.54081e42	−	1.13290e43i	−0.269163	−	0.466203i
$983$	−1.15592e43	+	2.00210e43i	−0.468706	+	0.811822i	−0.999360	−	0.0357662i	$-0.988613\pi$
$983$	−1.15592e43	+	2.00210e43i	−0.468706	+	0.811822i	0.530655	+	0.847588i	$0.321946\pi$
$984$	−7.37477e42	+	1.27735e43i	−0.294659	+	0.510364i
$985$	−5.26216e42	−	9.11432e42i	−0.207175	−	0.358838i
$986$	−4.96415e42			−0.192588
$987$	2.07727e42	−	4.31839e42i	0.0794135	−	0.165091i
$988$	−2.26153e42			−0.0851974
$989$	−4.07464e41	−	7.05748e41i	−0.0151266	−	0.0262001i
$990$	−2.95806e42	+	5.12350e42i	−0.108217	+	0.187438i
$991$	4.60053e42	−	7.96836e42i	0.165859	−	0.287277i	−0.771101	−	0.636713i	$-0.780294\pi$
$991$	4.60053e42	−	7.96836e42i	0.165859	−	0.287277i	0.936960	+	0.349436i	$0.113627\pi$
$992$	2.97525e42	+	5.15328e42i	0.105707	+	0.183090i
$993$	2.13062e42			0.0746005
$994$	1.31349e43	−	9.90180e41i	0.453237	−	0.0341674i
$995$	−6.77659e42			−0.230450
$996$	−1.92318e42	−	3.33104e42i	−0.0644554	−	0.111640i
$997$	−2.21379e43	+	3.83440e43i	−0.731235	+	1.26654i	0.225121	+	0.974331i	$0.427722\pi$
$997$	−2.21379e43	+	3.83440e43i	−0.731235	+	1.26654i	−0.956356	+	0.292205i	$0.905611\pi$
$998$	7.79579e42	−	1.35027e43i	0.253786	−	0.439570i
$999$	−1.59791e42	−	2.76766e42i	−0.0512687	−	0.0888000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.a.4.6	✓	38
7.2	even	3	inner	21.30.e.a.16.6	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.a.4.6	✓	38	1.1	even	1	trivial
21.30.e.a.16.6	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)

\(f(q)\)	\(=\)	\(q+(-10085.3 - 17468.3i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(6.50070e7 - 1.12595e8i) q^{4} +(4.83495e9 + 8.37438e9i) q^{5} -9.64758e10 q^{6} +(-7.77849e11 + 1.61705e12i) q^{7} -1.34515e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(-10085.3 - 17468.3i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(6.50070e7 - 1.12595e8i) q^{4} +(4.83495e9 + 8.37438e9i) q^{5} -9.64758e10 q^{6} +(-7.77849e11 + 1.61705e12i) q^{7} -1.34515e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(9.75244e13 - 1.68917e14i) q^{10} +(6.62931e14 - 1.14823e15i) q^{11} +(-3.10926e14 - 5.38540e14i) q^{12} -2.72703e15 q^{13} +(3.60921e16 - 2.72081e15i) q^{14} +4.62509e16 q^{15} +(1.00763e17 + 1.74527e17i) q^{16} +(-2.12312e17 + 3.67735e17i) q^{17} +(-2.30720e17 + 3.99619e17i) q^{18} +(3.18927e18 + 5.52398e18i) q^{19} +1.25722e18 q^{20} +(4.83790e18 + 7.08914e18i) q^{21} -2.67436e19 q^{22} +(-3.01649e19 - 5.22471e19i) q^{23} +(-3.21691e19 + 5.57186e19i) q^{24} +(4.63787e19 - 8.03303e19i) q^{25} +(2.75031e19 + 4.76367e19i) q^{26} -1.09419e20 q^{27} +(1.31507e20 + 1.92702e20i) q^{28} -5.79588e20 q^{29} +(-4.66456e20 - 8.07925e20i) q^{30} +(9.42484e20 - 1.63243e21i) q^{31} +(-1.57841e21 + 2.73388e21i) q^{32} +(-3.17078e21 - 5.49195e21i) q^{33} +8.56496e21 q^{34} +(-1.73027e22 + 1.30437e21i) q^{35} -2.97430e21 q^{36} +(1.46036e22 + 2.52941e22i) q^{37} +(6.43298e22 - 1.11423e23i) q^{38} +(-6.52166e21 + 1.12958e22i) q^{39} +(-6.50375e22 - 1.12648e23i) q^{40} +2.29250e23 q^{41} +(7.50436e22 - 1.56006e23i) q^{42} +1.35079e22 q^{43} +(-8.61903e22 - 1.49286e23i) q^{44} +(1.10608e23 - 1.91579e23i) q^{45} +(-6.08446e23 + 1.05386e24i) q^{46} +(-2.79171e23 - 4.83539e23i) q^{47} +9.63893e23 q^{48} +(-2.00981e24 - 2.51564e24i) q^{49} -1.87098e24 q^{50} +(1.01548e24 + 1.75886e24i) q^{51} +(-1.77276e23 + 3.07051e23i) q^{52} +(2.64429e24 - 4.58005e24i) q^{53} +(1.10353e24 + 1.91137e24i) q^{54} +1.28210e25 q^{55} +(1.04633e25 - 2.17518e25i) q^{56} +3.05084e25 q^{57} +(5.84535e24 + 1.01244e25i) q^{58} +(-4.39572e23 + 7.61361e23i) q^{59} +(3.00663e24 - 5.20763e24i) q^{60} +(-9.75690e24 - 1.68995e25i) q^{61} -3.80211e25 q^{62} +(4.09342e25 - 3.08584e24i) q^{63} +1.71869e26 q^{64} +(-1.31851e25 - 2.28372e25i) q^{65} +(-6.39568e25 + 1.10776e26i) q^{66} +(6.20696e25 - 1.07508e26i) q^{67} +(2.76035e25 + 4.78107e25i) q^{68} -2.88555e26 q^{69} +(1.97289e26 + 2.89094e26i) q^{70} +3.63928e26 q^{71} +(1.53864e26 + 2.66500e26i) q^{72} +(9.53533e26 - 1.65157e27i) q^{73} +(2.94564e26 - 5.10200e26i) q^{74} +(-2.21828e26 - 3.84217e26i) q^{75} +8.29299e26 q^{76} +(1.34109e27 + 1.96514e27i) q^{77} +2.63093e26 q^{78} +(-2.58725e27 - 4.48125e27i) q^{79} +(-9.74369e26 + 1.68766e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-2.31207e27 - 4.00461e27i) q^{82} +6.18532e27 q^{83} +(1.11270e27 - 8.38813e25i) q^{84} -4.10607e27 q^{85} +(-1.36232e26 - 2.35960e26i) q^{86} +(-1.38608e27 + 2.40075e27i) q^{87} +(-8.91744e27 + 1.54455e28i) q^{88} +(-8.94711e27 - 1.54969e28i) q^{89} -4.46209e27 q^{90} +(2.12122e27 - 4.40976e27i) q^{91} -7.84370e27 q^{92} +(-4.50787e27 - 7.80787e27i) q^{93} +(-5.63108e27 + 9.75331e27i) q^{94} +(-3.08399e28 + 5.34164e28i) q^{95} +(7.54948e27 + 1.30761e28i) q^{96} -4.02847e28 q^{97} +(-2.36745e28 + 6.04792e28i) q^{98} -3.03315e28 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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