LMFDB - Embedded newform 7.26.c.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,26,Mod(2,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("7.2");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	7.c (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:	$27.7197745967$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.2
Character	$\chi$	$=$	7.4
Dual form			7.26.c.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5310.35 - 9197.79i) q^{2} +(-231399. + 400795. i) q^{3} +(-3.96223e7 + 6.86279e7i) q^{4} +(3.63378e8 + 6.29389e8i) q^{5} +4.91524e9 q^{6} +(6.81365e9 + 3.59811e10i) q^{7} +4.85262e11 q^{8} +(3.16553e11 + 5.48286e11i) q^{9} +O(q^{10})$	\(q+(-5310.35 - 9197.79i) q^{2} +(-231399. + 400795. i) q^{3} +(-3.96223e7 + 6.86279e7i) q^{4} +(3.63378e8 + 6.29389e8i) q^{5} +4.91524e9 q^{6} +(6.81365e9 + 3.59811e10i) q^{7} +4.85262e11 q^{8} +(3.16553e11 + 5.48286e11i) q^{9} +(3.85933e12 - 6.68455e12i) q^{10} +(-9.45154e12 + 1.63705e13i) q^{11} +(-1.83371e13 - 3.17609e13i) q^{12} -1.00107e14 q^{13} +(2.94764e14 - 2.53743e14i) q^{14} -3.36342e14 q^{15} +(-1.24740e15 - 2.16057e15i) q^{16} +(2.41453e14 - 4.18208e14i) q^{17} +(3.36201e15 - 5.82318e15i) q^{18} +(-1.70555e15 - 2.95410e15i) q^{19} -5.75915e16 q^{20} +(-1.59977e16 - 5.59513e15i) q^{21} +2.00764e17 q^{22} +(4.05802e16 + 7.02869e16i) q^{23} +(-1.12289e17 + 1.94491e17i) q^{24} +(-1.15076e17 + 1.99317e17i) q^{25} +(5.31602e17 + 9.20761e17i) q^{26} -6.85124e17 q^{27} +(-2.73928e18 - 9.58050e17i) q^{28} +1.97993e17 q^{29} +(1.78609e18 + 3.09360e18i) q^{30} +(3.16780e18 - 5.48679e18i) q^{31} +(-5.10694e18 + 8.84549e18i) q^{32} +(-4.37416e18 - 7.57626e18i) q^{33} -5.12879e18 q^{34} +(-2.01702e19 + 1.73632e19i) q^{35} -5.01703e19 q^{36} +(2.17498e19 + 3.76718e19i) q^{37} +(-1.81141e19 + 3.13745e19i) q^{38} +(2.31646e19 - 4.01223e19i) q^{39} +(1.76333e20 + 3.05419e20i) q^{40} +3.51736e19 q^{41} +(3.34907e19 + 1.76856e20i) q^{42} +1.02055e20 q^{43} +(-7.48984e20 - 1.29728e21i) q^{44} +(-2.30057e20 + 3.98470e20i) q^{45} +(4.30990e20 - 7.46496e20i) q^{46} +(-3.11095e20 - 5.38832e20i) q^{47} +1.15459e21 q^{48} +(-1.24822e21 + 4.90326e20i) q^{49} +2.44437e21 q^{50} +(1.11744e20 + 1.93546e20i) q^{51} +(3.96647e21 - 6.87012e21i) q^{52} +(1.37591e20 - 2.38315e20i) q^{53} +(3.63825e21 + 6.30163e21i) q^{54} -1.37379e22 q^{55} +(3.30641e21 + 1.74603e22i) q^{56} +1.57865e21 q^{57} +(-1.05141e21 - 1.82110e21i) q^{58} +(7.26563e21 - 1.25844e22i) q^{59} +(1.33266e22 - 2.30824e22i) q^{60} +(1.03013e22 + 1.78423e22i) q^{61} -6.72885e22 q^{62} +(-1.75711e22 + 1.51258e22i) q^{63} +2.47667e22 q^{64} +(-3.63766e22 - 6.30062e22i) q^{65} +(-4.64566e22 + 8.04651e22i) q^{66} +(1.90339e21 - 3.29678e21i) q^{67} +(1.91338e22 + 3.31408e22i) q^{68} -3.75609e22 q^{69} +(2.66814e23 + 9.33168e22i) q^{70} -1.80688e23 q^{71} +(1.53611e23 + 2.66062e23i) q^{72} +(-2.11158e22 + 3.65736e22i) q^{73} +(2.30998e23 - 4.00100e23i) q^{74} +(-5.32568e22 - 9.22435e22i) q^{75} +2.70311e23 q^{76} +(-6.53431e23 - 2.28534e23i) q^{77} -4.92049e23 q^{78} +(1.31966e23 + 2.28571e23i) q^{79} +(9.06558e23 - 1.57020e24i) q^{80} +(-1.09675e23 + 1.89962e23i) q^{81} +(-1.86784e23 - 3.23519e23i) q^{82} +5.25223e23 q^{83} +(1.01785e24 - 8.76199e23i) q^{84} +3.50954e23 q^{85} +(-5.41949e23 - 9.38683e23i) q^{86} +(-4.58154e22 + 7.93546e22i) q^{87} +(-4.58647e24 + 7.94400e24i) q^{88} +(1.03378e24 + 1.79056e24i) q^{89} +4.88673e24 q^{90} +(-6.82093e23 - 3.60196e24i) q^{91} -6.43153e24 q^{92} +(1.46605e24 + 2.53928e24i) q^{93} +(-3.30404e24 + 5.72276e24i) q^{94} +(1.23952e24 - 2.14691e24i) q^{95} +(-2.36349e24 - 4.09368e24i) q^{96} +6.63668e24 q^{97} +(1.11384e25 + 8.87703e24i) q^{98} -1.19677e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4050 q^{2} + 531440 q^{3} - 286295596 q^{4} + 288173088 q^{5} - 13063290884 q^{6} - 55218840880 q^{7} + 274366746720 q^{8} - 5146896583216 q^{9}+O(q^{10}) $ 32 * q - 4050 * q^2 + 531440 * q^3 - 286295596 * q^4 + 288173088 * q^5 - 13063290884 * q^6 - 55218840880 * q^7 + 274366746720 * q^8 - 5146896583216 * q^9	$ 32 q - 4050 q^{2} + 531440 q^{3} - 286295596 q^{4} + 288173088 q^{5} - 13063290884 q^{6} - 55218840880 q^{7} + 274366746720 q^{8} - 5146896583216 q^{9} - 918803280822 q^{10} + 253661467680 q^{11} + 59498382182260 q^{12} + 136259290951840 q^{13} + 669930284417310 q^{14} - 28\!\cdots\!16 q^{15}+ \cdots + 42\!\cdots\!56 q^{99}+O(q^{100}) $ 32 * q - 4050 * q^2 + 531440 * q^3 - 286295596 * q^4 + 288173088 * q^5 - 13063290884 * q^6 - 55218840880 * q^7 + 274366746720 * q^8 - 5146896583216 * q^9 - 918803280822 * q^10 + 253661467680 * q^11 + 59498382182260 * q^12 + 136259290951840 * q^13 + 669930284417310 * q^14 - 2808664429278016 * q^15 - 5327562569765872 * q^16 + 5022112861130400 * q^17 + 1957025270033980 * q^18 + 10588631642557696 * q^19 + 24731206489166184 * q^20 + 8085415409820784 * q^21 - 189302943512898660 * q^22 + 20610047702550960 * q^23 + 573793671932159616 * q^24 - 958211520923613472 * q^25 + 2724774668939531124 * q^26 - 2206109587432690240 * q^27 + 9458322343110556580 * q^28 - 8689264986101232672 * q^29 - 2619504629356224458 * q^30 + 10841379318391039264 * q^31 + 6763645131553838880 * q^32 - 11546953084647657040 * q^33 + 13082632789597647612 * q^34 - 65806476706321130304 * q^35 + 282452039645146513456 * q^36 + 29321738000603330320 * q^37 - 70525127026788123690 * q^38 + 25840220465930531024 * q^39 - 85110519871079993136 * q^40 - 330540029228046240288 * q^41 + 315672536170051901120 * q^42 + 431015165468582915200 * q^43 - 879888416642398340460 * q^44 + 485170985786336771600 * q^45 + 1667203425207259516686 * q^46 + 2014371898465936816800 * q^47 - 11662563919658426657120 * q^48 + 1488998457641379674528 * q^49 - 1672792512944596205616 * q^50 - 7525441297042267778496 * q^51 + 6992249387859106251160 * q^52 + 8918984691607286334960 * q^53 + 34981309708344282421726 * q^54 - 65886425153156913843552 * q^55 - 6796685514980676446208 * q^56 + 56688134325496104699680 * q^57 - 26386021221286483940940 * q^58 - 10935316261765587024144 * q^59 + 139984946157807148568716 * q^60 - 17484129051186787701488 * q^61 - 262788504919801688816100 * q^62 - 63958098944828837939120 * q^63 + 331619102526249229604096 * q^64 - 60109967964600925224336 * q^65 + 61498292814044614748374 * q^66 + 218997561331718103994960 * q^67 + 482184105822238591781100 * q^68 - 815717958910888805206848 * q^69 + 590837748017767784846550 * q^70 - 556118852555986042838976 * q^71 - 332574755512105623952800 * q^72 + 181923789786333620742640 * q^73 - 788377165482644151934950 * q^74 - 66014699727433523602592 * q^75 + 1262772869625204941438344 * q^76 - 101350576550797077490560 * q^77 + 311390952582194080319080 * q^78 + 438039985868556642949360 * q^79 - 1229118480867135510718416 * q^80 - 738103636463171961601504 * q^81 - 4913051673767471255932260 * q^82 + 4355401847600512595234880 * q^83 - 4660353883629012393074068 * q^84 - 505677682638035696807712 * q^85 + 5848093469680723949747688 * q^86 - 2195492958449506107537040 * q^87 - 10064215655338142337197760 * q^88 + 449697822243925695740496 * q^89 + 41750741714541116033274904 * q^90 + 4132471530877362173570272 * q^91 - 18512115732486299505457080 * q^92 - 2539354660954665131215920 * q^93 - 1689612490320614160295890 * q^94 - 2244103526711501036678160 * q^95 - 3851732620967552391601888 * q^96 - 17074074602311685528685920 * q^97 + 12285904054220374515545790 * q^98 + 4273620815399973239951456 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5310.35	−	9197.79i	−0.916744	−	1.58785i	−0.804328	−	0.594185i	$-0.797475\pi$
$2$	−5310.35	−	9197.79i	−0.916744	−	1.58785i	−0.112415	−	0.993661i	$-0.535859\pi$
$3$	−231399.	+	400795.i	−0.251389	+	0.435418i	−0.963908	−	0.266234i	$-0.914221\pi$
$3$	−231399.	+	400795.i	−0.251389	+	0.435418i	0.712520	+	0.701652i	$0.247554\pi$
$4$	−3.96223e7	+	6.86279e7i	−1.18084	+	2.04527i
$5$	3.63378e8	+	6.29389e8i	0.665631	+	1.15291i	0.979114	+	0.203313i	$0.0651709\pi$
$5$	3.63378e8	+	6.29389e8i	0.665631	+	1.15291i	−0.313483	+	0.949594i	$0.601496\pi$
$6$	4.91524e9			0.921837
$7$	6.81365e9	+	3.59811e10i	0.186061	+	0.982538i
$7$	6.81365e9	+	3.59811e10i	0.186061	+	0.982538i
$8$	4.85262e11			2.49661
$9$	3.16553e11	+	5.48286e11i	0.373607	+	0.647107i
$10$	3.85933e12	−	6.68455e12i	1.22043	−	2.11384i
$11$	−9.45154e12	+	1.63705e13i	−0.908017	+	1.57273i	−0.0912016	+	0.995832i	$0.529071\pi$
$11$	−9.45154e12	+	1.63705e13i	−0.908017	+	1.57273i	−0.816815	+	0.576899i	$0.804263\pi$
$12$	−1.83371e13	−	3.17609e13i	−0.593699	−	1.02832i
$13$	−1.00107e14			−1.19171			−0.595857	−	0.803091i	$-0.703187\pi$
$13$	−1.00107e14			−1.19171			−0.595857	+	0.803091i	$0.703187\pi$
$14$	2.94764e14	−	2.53743e14i	1.38955	−	1.19617i
$15$	−3.36342e14			−0.669329
$16$	−1.24740e15	−	2.16057e15i	−1.10792	−	1.91897i
$17$	2.41453e14	−	4.18208e14i	0.100513	−	0.174093i	−0.811383	−	0.584514i	$-0.801285\pi$
$17$	2.41453e14	−	4.18208e14i	0.100513	−	0.174093i	0.911896	+	0.410421i	$0.134618\pi$
$18$	3.36201e15	−	5.82318e15i	0.685004	−	1.18646i
$19$	−1.70555e15	−	2.95410e15i	−0.176784	−	0.306199i	0.763993	−	0.645225i	$-0.223236\pi$
$19$	−1.70555e15	−	2.95410e15i	−0.176784	−	0.306199i	−0.940777	+	0.339025i	$0.889903\pi$
$20$	−5.75915e16			−3.14401
$21$	−1.59977e16	−	5.59513e15i	−0.474589	−	0.165985i
$22$	2.00764e17			3.32967
$23$	4.05802e16	+	7.02869e16i	0.386114	+	0.668770i	0.991923	−	0.126841i	$-0.0404836\pi$
$23$	4.05802e16	+	7.02869e16i	0.386114	+	0.668770i	−0.605809	+	0.795610i	$0.707150\pi$
$24$	−1.12289e17	+	1.94491e17i	−0.627621	+	1.08707i
$25$	−1.15076e17	+	1.99317e17i	−0.386130	+	0.668796i
$26$	5.31602e17	+	9.20761e17i	1.09250	+	1.89226i
$27$	−6.85124e17			−0.878461
$28$	−2.73928e18	−	9.58050e17i	−2.22926	−	0.779674i
$29$	1.97993e17			0.103914			0.0519571	−	0.998649i	$-0.483454\pi$
$29$	1.97993e17			0.103914			0.0519571	+	0.998649i	$0.483454\pi$
$30$	1.78609e18	+	3.09360e18i	0.613603	+	1.06279i
$31$	3.16780e18	−	5.48679e18i	0.722332	−	1.25112i	−0.237731	−	0.971331i	$-0.576404\pi$
$31$	3.16780e18	−	5.48679e18i	0.722332	−	1.25112i	0.960063	−	0.279785i	$-0.0902631\pi$
$32$	−5.10694e18	+	8.84549e18i	−0.783044	+	1.35627i
$33$	−4.37416e18	−	7.57626e18i	−0.456531	−	0.790735i
$34$	−5.12879e18			−0.368577
$35$	−2.01702e19	+	1.73632e19i	−1.00893	+	0.868519i
$36$	−5.01703e19			−1.76468
$37$	2.17498e19	+	3.76718e19i	0.543168	+	0.940794i	0.998720	+	0.0505850i	$0.0161086\pi$
$37$	2.17498e19	+	3.76718e19i	0.543168	+	0.940794i	−0.455552	+	0.890209i	$0.650558\pi$
$38$	−1.81141e19	+	3.13745e19i	−0.324132	+	0.561413i
$39$	2.31646e19	−	4.01223e19i	0.299584	−	0.518894i
$40$	1.76333e20	+	3.05419e20i	1.66182	+	2.87836i
$41$	3.51736e19			0.243455			0.121727	−	0.992564i	$-0.461157\pi$
$41$	3.51736e19			0.243455			0.121727	+	0.992564i	$0.461157\pi$
$42$	3.34907e19	+	1.76856e20i	0.171518	+	0.905740i
$43$	1.02055e20			0.389475			0.194738	−	0.980855i	$-0.437614\pi$
$43$	1.02055e20			0.389475			0.194738	+	0.980855i	$0.437614\pi$
$44$	−7.48984e20	−	1.29728e21i	−2.14444	−	3.71428i
$45$	−2.30057e20	+	3.98470e20i	−0.497369	+	0.861469i
$46$	4.30990e20	−	7.46496e20i	0.707936	−	1.22618i
$47$	−3.11095e20	−	5.38832e20i	−0.390543	−	0.676441i	0.601978	−	0.798513i	$-0.294379\pi$
$47$	−3.11095e20	−	5.38832e20i	−0.390543	−	0.676441i	−0.992521	+	0.122072i	$0.961046\pi$
$48$	1.15459e21			1.11407
$49$	−1.24822e21	+	4.90326e20i	−0.930763	+	0.365623i
$50$	2.44437e21			1.41593
$51$	1.11744e20	+	1.93546e20i	0.0505355	+	0.0875300i
$52$	3.96647e21	−	6.87012e21i	1.40722	−	2.43738i
$53$	1.37591e20	−	2.38315e20i	0.0384718	−	0.0666351i	−0.846148	−	0.532947i	$-0.821084\pi$
$53$	1.37591e20	−	2.38315e20i	0.0384718	−	0.0666351i	0.884620	+	0.466312i	$0.154418\pi$
$54$	3.63825e21	+	6.30163e21i	0.805323	+	1.39486i
$55$	−1.37379e22			−2.41762
$56$	3.30641e21	+	1.74603e22i	0.464522	+	2.45302i
$57$	1.57865e21			0.177767
$58$	−1.05141e21	−	1.82110e21i	−0.0952626	−	0.165000i
$59$	7.26563e21	−	1.25844e22i	0.531647	−	0.920839i	−0.467671	−	0.883903i	$-0.654907\pi$
$59$	7.26563e21	−	1.25844e22i	0.531647	−	0.920839i	0.999318	−	0.0369367i	$-0.0117600\pi$
$60$	1.33266e22	−	2.30824e22i	0.790369	−	1.36896i
$61$	1.03013e22	+	1.78423e22i	0.496899	+	0.860654i	0.999994	−	0.00357750i	$-0.00113876\pi$
$61$	1.03013e22	+	1.78423e22i	0.496899	+	0.860654i	−0.503095	+	0.864231i	$0.667805\pi$
$62$	−6.72885e22			−2.64877
$63$	−1.75711e22	+	1.51258e22i	−0.566293	+	0.487484i
$64$	2.47667e22			0.655570
$65$	−3.63766e22	−	6.30062e22i	−0.793241	−	1.37393i
$66$	−4.64566e22	+	8.04651e22i	−0.837043	+	1.44980i
$67$	1.90339e21	−	3.29678e21i	0.0284180	−	0.0492215i	−0.851467	−	0.524409i	$-0.824286\pi$
$67$	1.90339e21	−	3.29678e21i	0.0284180	−	0.0492215i	0.879885	+	0.475187i	$0.157620\pi$
$68$	1.91338e22	+	3.31408e22i	0.237378	+	0.411151i
$69$	−3.75609e22			−0.388260
$70$	2.66814e23	+	9.33168e22i	2.30400	+	0.805813i
$71$	−1.80688e23			−1.30677			−0.653386	−	0.757025i	$-0.726652\pi$
$71$	−1.80688e23			−1.30677			−0.653386	+	0.757025i	$0.726652\pi$
$72$	1.53611e23	+	2.66062e23i	0.932753	+	1.61558i
$73$	−2.11158e22	+	3.65736e22i	−0.107912	+	0.186910i	−0.914924	−	0.403625i	$-0.867750\pi$
$73$	−2.11158e22	+	3.65736e22i	−0.107912	+	0.186910i	0.807012	+	0.590535i	$0.201083\pi$
$74$	2.30998e23	−	4.00100e23i	0.995891	−	1.72493i
$75$	−5.32568e22	−	9.22435e22i	−0.194137	−	0.336256i
$76$	2.70311e23			0.835014
$77$	−6.53431e23	−	2.28534e23i	−1.71422	−	0.599538i
$78$	−4.92049e23			−1.09856
$79$	1.31966e23	+	2.28571e23i	0.251260	+	0.435194i	0.963873	−	0.266363i	$-0.0858219\pi$
$79$	1.31966e23	+	2.28571e23i	0.251260	+	0.435194i	−0.712613	+	0.701557i	$0.752489\pi$
$80$	9.06558e23	−	1.57020e24i	1.47493	−	2.55465i
$81$	−1.09675e23	+	1.89962e23i	−0.152772	+	0.264609i
$82$	−1.86784e23	−	3.23519e23i	−0.223186	−	0.386569i
$83$	5.25223e23			0.539346			0.269673	−	0.962952i	$-0.413084\pi$
$83$	5.25223e23			0.539346			0.269673	+	0.962952i	$0.413084\pi$
$84$	1.01785e24	−	8.76199e23i	0.899896	−	0.774661i
$85$	3.50954e23			0.267617
$86$	−5.41949e23	−	9.38683e23i	−0.357049	−	0.618427i
$87$	−4.58154e22	+	7.93546e22i	−0.0261229	+	0.0452461i
$88$	−4.58647e24	+	7.94400e24i	−2.26697	+	3.92650i
$89$	1.03378e24	+	1.79056e24i	0.443663	+	0.768448i	0.997958	−	0.0638730i	$-0.0203453\pi$
$89$	1.03378e24	+	1.79056e24i	0.443663	+	0.768448i	−0.554295	+	0.832321i	$0.687012\pi$
$90$	4.88673e24			1.82384
$91$	−6.82093e23	−	3.60196e24i	−0.221731	−	1.17090i
$92$	−6.43153e24			−1.82375
$93$	1.46605e24	+	2.53928e24i	0.363173	+	0.629033i
$94$	−3.30404e24	+	5.72276e24i	−0.716056	+	1.24025i
$95$	1.23952e24	−	2.14691e24i	0.235346	−	0.407632i
$96$	−2.36349e24	−	4.09368e24i	−0.393697	−	0.681904i
$97$	6.63668e24			0.971190			0.485595	−	0.874184i	$-0.338603\pi$
$97$	6.63668e24			0.971190			0.485595	+	0.874184i	$0.338603\pi$
$98$	1.11384e25	+	8.87703e24i	1.43382	+	1.14273i
$99$	−1.19677e25			−1.35697
$100$	−9.11913e24	−	1.57948e25i	−0.911913	−	1.57948i
$101$	1.05280e25	−	1.82350e25i	0.929668	−	1.61023i	0.145791	−	0.989315i	$-0.453427\pi$
$101$	1.05280e25	−	1.82350e25i	0.929668	−	1.61023i	0.783877	−	0.620917i	$-0.213239\pi$
$102$	1.18680e24	−	2.05559e24i	0.0926562	−	0.160485i
$103$	1.16616e25	+	2.01984e25i	0.805918	+	1.39589i	0.915669	+	0.401932i	$0.131661\pi$
$103$	1.16616e25	+	2.01984e25i	0.805918	+	1.39589i	−0.109751	+	0.993959i	$0.535005\pi$
$104$	−4.85780e25			−2.97525
$105$	−2.29171e24	−	1.21020e25i	−0.124536	−	0.657642i
$106$	−2.92263e24			−0.141075
$107$	6.59745e24	+	1.14271e25i	0.283191	+	0.490501i	0.972169	−	0.234281i	$-0.0752737\pi$
$107$	6.59745e24	+	1.14271e25i	0.283191	+	0.490501i	−0.688978	+	0.724782i	$0.741940\pi$
$108$	2.71462e25	−	4.70186e25i	1.03732	−	1.79669i
$109$	1.38212e25	−	2.39390e25i	0.470667	−	0.815219i	−0.528770	−	0.848765i	$-0.677347\pi$
$109$	1.38212e25	−	2.39390e25i	0.470667	−	0.815219i	0.999437	+	0.0335462i	$0.0106801\pi$
$110$	7.29531e25	+	1.26359e26i	2.21634	+	3.83881i
$111$	−2.01316e25			−0.546185
$112$	6.92403e25	−	5.96043e25i	1.67932	−	1.44562i
$113$	2.44510e25			0.530660			0.265330	−	0.964158i	$-0.414519\pi$
$113$	2.44510e25			0.530660			0.265330	+	0.964158i	$0.414519\pi$
$114$	−8.38317e24	−	1.45201e25i	−0.162966	−	0.282266i
$115$	−2.94919e25	+	5.10815e25i	−0.514020	+	0.890308i
$116$	−7.84494e24	+	1.35878e25i	−0.122706	+	0.212533i
$117$	−3.16891e25	−	5.48872e25i	−0.445233	−	0.771166i
$118$	−1.54332e26			−1.94954
$119$	1.66928e25	+	5.83822e24i	0.189754	+	0.0663656i
$120$	−1.63214e26			−1.67106
$121$	−1.24490e26	−	2.15622e26i	−1.14899	−	1.99011i
$122$	1.09407e26	−	1.89498e26i	0.911057	−	1.57800i
$123$	−8.13914e24	+	1.40974e25i	−0.0612019	+	0.106005i
$124$	2.51031e26	+	4.34799e26i	1.70591	+	2.95473i
$125$	4.93264e25			0.303183
$126$	2.32432e26	+	8.12920e25i	1.29320	+	0.452289i
$127$	−3.51334e26			−1.77082			−0.885408	−	0.464815i	$-0.846121\pi$
$127$	−3.51334e26			−1.77082			−0.885408	+	0.464815i	$0.846121\pi$
$128$	3.98407e25	+	6.90061e25i	0.182055	+	0.315328i
$129$	−2.36155e25	+	4.09033e25i	−0.0979098	+	0.169585i
$130$	−3.86345e26	+	6.69169e26i	−1.45440	+	2.51909i
$131$	−1.32756e26	−	2.29941e26i	−0.454113	−	0.786547i	0.544524	−	0.838745i	$-0.316710\pi$
$131$	−1.32756e26	−	2.29941e26i	−0.454113	−	0.786547i	−0.998637	+	0.0521986i	$0.983377\pi$
$132$	6.93257e26			2.15635
$133$	9.46707e25	−	8.14957e25i	0.267960	−	0.230669i
$134$	−4.04307e25			−0.104208
$135$	−2.48959e26	−	4.31210e26i	−0.584731	−	1.01278i
$136$	1.17168e26	−	2.02940e26i	0.250941	−	0.434643i
$137$	−4.22694e26	+	7.32127e26i	−0.826073	+	1.43080i	0.0750229	+	0.997182i	$0.476097\pi$
$137$	−4.22694e26	+	7.32127e26i	−0.826073	+	1.43080i	−0.901096	+	0.433619i	$0.857236\pi$
$138$	1.99461e26	+	3.45477e26i	0.355934	+	0.616497i
$139$	−2.58974e26			−0.422251			−0.211126	−	0.977459i	$-0.567713\pi$
$139$	−2.58974e26			−0.422251			−0.211126	+	0.977459i	$0.567713\pi$
$140$	−3.92409e26	−	2.07221e27i	−0.584976	−	3.08911i
$141$	2.87948e26			0.392713
$142$	9.59516e26	+	1.66193e27i	1.19797	+	2.07495i
$143$	9.46164e26	−	1.63880e27i	1.08210	−	1.87425i
$144$	7.89739e26	−	1.36787e27i	0.827851	−	1.43388i
$145$	7.19463e25	+	1.24615e26i	0.0691685	+	0.119803i
$146$	4.48528e26			0.395712
$147$	9.23160e25	−	6.13740e26i	0.0747843	−	0.497185i
$148$	−3.44711e27			−2.56557
$149$	−6.51322e26	−	1.12812e27i	−0.445623	−	0.771842i	0.552472	−	0.833531i	$-0.313684\pi$
$149$	−6.51322e26	−	1.12812e27i	−0.445623	−	0.771842i	−0.998095	+	0.0616895i	$0.980351\pi$
$150$	−5.65624e26	+	9.79690e26i	−0.355948	+	0.616521i
$151$	8.06124e25	−	1.39625e26i	0.0466864	−	0.0808632i	−0.841738	−	0.539886i	$-0.818467\pi$
$151$	8.06124e25	−	1.39625e26i	0.0466864	−	0.0808632i	0.888424	+	0.459023i	$0.151801\pi$
$152$	−8.27637e26	−	1.43351e27i	−0.441362	−	0.764462i
$153$	3.05730e26			0.150209
$154$	1.36793e27	+	7.22371e27i	0.619522	+	3.27153i
$155$	4.60444e27			1.92323
$156$	1.83567e27	+	3.17948e27i	0.707519	+	1.22546i
$157$	−1.57408e27	+	2.72639e27i	−0.560120	+	0.970157i	0.437365	+	0.899284i	$0.355912\pi$
$157$	−1.57408e27	+	2.72639e27i	−0.560120	+	0.970157i	−0.997485	+	0.0708727i	$0.977422\pi$
$158$	1.40157e27	−	2.42759e27i	0.460681	−	0.797923i
$159$	6.36770e25	+	1.10292e26i	0.0193428	+	0.0335027i
$160$	−7.42300e27			−2.08487
$161$	−2.25251e27	+	1.93903e27i	−0.585251	+	0.503804i
$162$	2.32964e27			0.560211
$163$	−8.53197e26	−	1.47778e27i	−0.189978	−	0.329052i	0.755264	−	0.655420i	$-0.227508\pi$
$163$	−8.53197e26	−	1.47778e27i	−0.189978	−	0.329052i	−0.945243	+	0.326368i	$0.894175\pi$
$164$	−1.39366e27	+	2.41389e27i	−0.287481	+	0.497931i
$165$	3.17895e27	−	5.50609e27i	0.607762	−	1.05268i
$166$	−2.78912e27	−	4.83089e27i	−0.494442	−	0.856399i
$167$	−2.82156e27			−0.464017			−0.232009	−	0.972714i	$-0.574530\pi$
$167$	−2.82156e27			−0.464017			−0.232009	+	0.972714i	$0.574530\pi$
$168$	−7.76309e27	−	2.71510e27i	−1.18486	−	0.414400i
$169$	2.96497e27			0.420180
$170$	−1.86369e27	−	3.22800e27i	−0.245336	−	0.424935i
$171$	1.07979e27	−	1.87026e27i	0.132096	−	0.228797i
$172$	−4.04367e27	+	7.00384e27i	−0.459907	+	0.796582i
$173$	3.02255e27	+	5.23520e27i	0.319740	+	0.553806i	0.980434	−	0.196850i	$-0.0630712\pi$
$173$	3.02255e27	+	5.23520e27i	0.319740	+	0.553806i	−0.660694	+	0.750655i	$0.729738\pi$
$174$	9.73183e26			0.0957919
$175$	−7.95573e27	−	2.78248e27i	−0.728961	−	0.254951i
$176$	4.71595e28			4.02403
$177$	3.36252e27	+	5.82406e27i	0.267300	+	0.462978i
$178$	1.09795e28	−	1.90170e28i	0.813451	−	1.40894i
$179$	−2.16190e27	+	3.74452e27i	−0.149339	+	0.258663i	−0.930983	−	0.365062i	$-0.881048\pi$
$179$	−2.16190e27	+	3.74452e27i	−0.149339	+	0.258663i	0.781644	+	0.623724i	$0.214381\pi$
$180$	−1.82308e28	−	3.15766e28i	−1.17462	−	2.03451i
$181$	4.82985e27			0.290370			0.145185	−	0.989405i	$-0.453622\pi$
$181$	4.82985e27			0.290370			0.145185	+	0.989405i	$0.453622\pi$
$182$	−2.95079e28	+	2.54014e28i	−1.65595	+	1.42549i
$183$	−9.53482e27			−0.499659
$184$	1.96920e28	+	3.41076e28i	0.963978	+	1.66966i
$185$	−1.58068e28	+	2.73782e28i	−0.723099	+	1.25244i
$186$	1.55705e28	−	2.69689e28i	0.665872	−	1.15332i
$187$	4.56420e27	+	7.90542e27i	0.182534	+	0.316159i
$188$	4.93052e28			1.84467
$189$	−4.66820e27	−	2.46516e28i	−0.163447	−	0.863121i
$190$	−2.63291e28			−0.863009
$191$	−1.97365e28	−	3.41845e28i	−0.605832	−	1.04933i	−0.991919	−	0.126869i	$-0.959507\pi$
$191$	−1.97365e28	−	3.41845e28i	−0.605832	−	1.04933i	0.386088	−	0.922462i	$-0.373826\pi$
$192$	−5.73100e27	+	9.92638e27i	−0.164803	+	0.285447i
$193$	−9.14300e27	+	1.58361e28i	−0.246390	+	0.426759i	−0.962521	−	0.271206i	$-0.912578\pi$
$193$	−9.14300e27	+	1.58361e28i	−0.246390	+	0.426759i	0.716132	+	0.697965i	$0.245911\pi$
$194$	−3.52431e28	−	6.10428e28i	−0.890332	−	1.54210i
$195$	3.36701e28			0.797648
$196$	1.58072e28	−	1.05090e29i	0.351281	−	2.33540i
$197$	7.98007e27			0.166410			0.0832049	−	0.996532i	$-0.473484\pi$
$197$	7.98007e27			0.166410			0.0832049	+	0.996532i	$0.473484\pi$
$198$	6.35524e28	+	1.10076e29i	1.24399	+	2.15465i
$199$	−4.06813e28	+	7.04621e28i	−0.747707	+	1.29507i	0.201212	+	0.979548i	$0.435512\pi$
$199$	−4.06813e28	+	7.04621e28i	−0.747707	+	1.29507i	−0.948919	+	0.315519i	$0.897821\pi$
$200$	−5.58418e28	+	9.67208e28i	−0.964016	+	1.66973i
$201$	8.80888e26	+	1.52574e27i	0.0142880	+	0.0247475i
$202$	−2.23629e29			−3.40907
$203$	1.34906e27	+	7.12401e27i	0.0193343	+	0.102100i
$204$	−1.77102e28			−0.238697
$205$	1.27813e28	+	2.21379e28i	0.162051	+	0.280681i
$206$	1.23854e29	−	2.14521e29i	1.47764	−	2.55935i
$207$	−2.56916e28	+	4.44991e28i	−0.288510	+	0.499714i
$208$	1.24874e29	+	2.16287e29i	1.32032	+	2.28686i
$209$	6.44802e28			0.642093
$210$	−9.91414e28	+	8.53443e28i	−0.930066	+	0.800632i
$211$	1.91959e29			1.69698			0.848491	−	0.529210i	$-0.177512\pi$
$211$	1.91959e29			1.69698			0.848491	+	0.529210i	$0.177512\pi$
$212$	1.09034e28	+	1.88852e28i	0.0908579	+	0.157371i
$213$	4.18110e28	−	7.24189e28i	0.328508	−	0.568993i
$214$	7.00695e28	−	1.21364e29i	0.519227	−	0.899327i
$215$	3.70847e28	+	6.42325e28i	0.259247	+	0.449029i
$216$	−3.32465e29			−2.19318
$217$	2.19005e29	+	7.65960e28i	1.36367	+	0.476935i
$218$	−2.93581e29			−1.72592
$219$	−9.77234e27	−	1.69262e28i	−0.0542559	−	0.0939740i
$220$	5.44329e29	−	9.42805e29i	2.85481	−	4.94468i
$221$	−2.41711e28	+	4.18655e28i	−0.119782	+	0.207469i
$222$	1.06906e29	+	1.85166e29i	0.500712	+	0.867259i
$223$	−3.51435e29			−1.55609			−0.778045	−	0.628209i	$-0.783788\pi$
$223$	−3.51435e29			−1.55609			−0.778045	+	0.628209i	$0.783788\pi$
$224$	−3.53068e29	−	1.23484e29i	−1.47828	−	0.517022i
$225$	−1.45710e29			−0.577043
$226$	−1.29843e29	−	2.24895e29i	−0.486479	−	0.842607i
$227$	−8.19444e28	+	1.41932e29i	−0.290533	+	0.503219i	−0.973936	−	0.226823i	$-0.927166\pi$
$227$	−8.19444e28	+	1.41932e29i	−0.290533	+	0.503219i	0.683403	+	0.730042i	$0.260499\pi$
$228$	−6.25498e28	+	1.08339e29i	−0.209913	+	0.363581i
$229$	1.25755e29	+	2.17814e29i	0.399559	+	0.692057i	0.993672	−	0.112325i	$-0.0358298\pi$
$229$	1.25755e29	+	2.17814e29i	0.399559	+	0.692057i	−0.594112	+	0.804382i	$0.702496\pi$
$230$	6.26449e29			1.88490
$231$	2.42799e29	−	2.09009e29i	0.691985	−	0.595684i
$232$	9.60784e28			0.259433
$233$	−3.04351e26	−	5.27152e26i	−0.000778801	−	0.00134892i	0.865636	−	0.500674i	$-0.166915\pi$
$233$	−3.04351e26	−	5.27152e26i	−0.000778801	−	0.00134892i	−0.866415	+	0.499325i	$0.833581\pi$
$234$	−3.36560e29	+	5.82940e29i	−0.816328	+	1.41392i
$235$	2.26090e29	−	3.91599e29i	0.519915	−	0.900520i
$236$	5.75763e29	+	9.97250e29i	1.25558	+	2.17472i
$237$	−1.22147e29			−0.252656
$238$	−3.49458e28	−	1.84540e29i	−0.0685777	−	0.362141i
$239$	4.63291e28			0.0862741			0.0431371	−	0.999069i	$-0.486265\pi$
$239$	4.63291e28			0.0862741			0.0431371	+	0.999069i	$0.486265\pi$
$240$	4.19554e29	+	7.26688e29i	0.741561	+	1.28442i
$241$	1.71208e29	−	2.96542e29i	0.287284	−	0.497591i	−0.685876	−	0.727718i	$-0.740581\pi$
$241$	1.71208e29	−	2.96542e29i	0.287284	−	0.497591i	0.973161	+	0.230127i	$0.0739142\pi$
$242$	−1.32217e30	+	2.29006e30i	−2.10666	+	3.64884i
$243$	−3.41006e29	−	5.90640e29i	−0.516041	−	0.893809i
$244$	−1.63264e30			−2.34703
$245$	−7.62181e29	−	6.07441e29i	−1.04107	−	0.829713i
$246$	1.72887e29			0.224426
$247$	1.70737e29	+	2.95725e29i	0.210676	+	0.364902i
$248$	1.53721e30	−	2.66253e30i	1.80338	−	3.12355i
$249$	−1.21536e29	+	2.10507e29i	−0.135586	+	0.234841i
$250$	−2.61940e29	−	4.53694e29i	−0.277941	−	0.481407i
$251$	2.89774e29			0.292509			0.146254	−	0.989247i	$-0.453278\pi$
$251$	2.89774e29			0.292509			0.146254	+	0.989247i	$0.453278\pi$
$252$	−3.41843e29	−	1.80518e30i	−0.328337	−	1.73386i
$253$	−1.53418e30			−1.40239
$254$	1.86570e30	+	3.23149e30i	1.62338	+	2.81178i
$255$	−8.12105e28	+	1.40661e29i	−0.0672760	+	0.116525i
$256$	8.38653e29	−	1.45259e30i	0.661580	−	1.14589i
$257$	−6.80425e29	−	1.17853e30i	−0.511230	−	0.885476i	−0.999915	−	0.0130157i	$-0.995857\pi$
$257$	−6.80425e29	−	1.17853e30i	−0.511230	−	0.885476i	0.488686	−	0.872460i	$-0.337476\pi$
$258$	5.01626e29			0.359033
$259$	−1.20728e30	+	1.03927e30i	−0.823304	+	0.708728i
$260$	5.76531e30			3.74676
$261$	6.26753e28	+	1.08557e29i	0.0388231	+	0.0672435i
$262$	−1.40996e30	+	2.44213e30i	−0.832610	+	1.44212i
$263$	8.49347e29	−	1.47111e30i	0.478232	−	0.828322i	−0.521457	−	0.853278i	$-0.674611\pi$
$263$	8.49347e29	−	1.47111e30i	0.478232	−	0.828322i	0.999689	+	0.0249559i	$0.00794454\pi$
$264$	−2.12261e30	−	3.67647e30i	−1.13978	−	1.97416i
$265$	1.99991e29			0.102432
$266$	−1.25231e30	−	4.37991e29i	−0.611918	−	0.214015i
$267$	−9.56865e29			−0.446128
$268$	1.50834e29	+	2.61252e29i	0.0671141	+	0.116245i
$269$	−1.80576e29	+	3.12767e29i	−0.0766932	+	0.132837i	−0.901821	−	0.432109i	$-0.857770\pi$
$269$	−1.80576e29	+	3.12767e29i	−0.0766932	+	0.132837i	0.825128	+	0.564946i	$0.191103\pi$
$270$	−2.64412e30	+	4.57975e30i	−1.07210	+	1.85693i
$271$	1.18166e30	+	2.04669e30i	0.457484	+	0.792386i	0.998827	−	0.0484160i	$-0.0154173\pi$
$271$	1.18166e30	+	2.04669e30i	0.457484	+	0.792386i	−0.541343	+	0.840802i	$0.682084\pi$
$272$	−1.20476e30			−0.445438
$273$	1.60148e30	+	5.60110e29i	0.565574	+	0.197807i
$274$	8.97860e30			3.02919
$275$	−2.17528e30	−	3.76770e30i	−0.701225	−	1.21456i
$276$	1.48825e30	−	2.57772e30i	0.458471	−	0.794096i
$277$	2.01943e30	−	3.49775e30i	0.594609	−	1.02989i	−0.398993	−	0.916954i	$-0.630640\pi$
$277$	2.01943e30	−	3.49775e30i	0.594609	−	1.02989i	0.993602	−	0.112939i	$-0.0360264\pi$
$278$	1.37524e30	+	2.38199e30i	0.387096	+	0.670470i
$279$	4.01111e30			1.07947
$280$	−9.78783e30	+	8.42570e30i	−2.51890	+	2.16836i
$281$	−3.53953e30			−0.871197			−0.435599	−	0.900141i	$-0.643463\pi$
$281$	−3.53953e30			−0.871197			−0.435599	+	0.900141i	$0.643463\pi$
$282$	−1.52910e30	−	2.64849e30i	−0.360017	−	0.623568i
$283$	−1.35492e30	+	2.34680e30i	−0.305200	+	0.528622i	−0.977306	−	0.211833i	$-0.932057\pi$
$283$	−1.35492e30	+	2.34680e30i	−0.305200	+	0.528622i	0.672106	+	0.740455i	$0.265390\pi$
$284$	7.15928e30	−	1.24002e31i	1.54309	−	2.67270i
$285$	5.73647e29	+	9.93585e29i	0.118327	+	0.204948i
$286$	−2.00978e31			−3.96802
$287$	2.39661e29	+	1.26559e30i	0.0452974	+	0.239204i
$288$	−6.46648e30			−1.17020
$289$	2.76871e30	+	4.79556e30i	0.479794	+	0.831028i
$290$	7.64119e29	−	1.32349e30i	0.126820	−	0.219658i
$291$	−1.53572e30	+	2.65995e30i	−0.244146	+	0.422874i
$292$	−1.67331e30	−	2.89826e30i	−0.254854	−	0.441420i
$293$	9.51374e30			1.38837			0.694186	−	0.719796i	$-0.255764\pi$
$293$	9.51374e30			1.38837			0.694186	+	0.719796i	$0.255764\pi$
$294$	−6.13528e30	+	2.41007e30i	−0.858011	+	0.337045i
$295$	1.05607e31			1.41552
$296$	1.05544e31	+	1.82807e31i	1.35608	+	2.34880i
$297$	6.47548e30	−	1.12159e31i	0.797657	−	1.38158i
$298$	−6.91749e30	+	1.19815e31i	−0.817044	+	1.41516i
$299$	−4.06235e30	−	7.03620e30i	−0.460138	−	0.796982i
$300$	8.44063e30			0.916979
$301$	6.95369e29	+	3.67207e30i	0.0724660	+	0.382674i
$302$	−1.71232e30			−0.171198
$303$	4.87233e30	+	8.43913e30i	0.467416	+	0.809589i
$304$	−4.25501e30	+	7.36990e30i	−0.391725	+	0.678487i
$305$	−7.48651e30	+	1.29670e31i	−0.661502	+	1.14576i
$306$	−1.62353e30	−	2.81204e30i	−0.137703	−	0.238509i
$307$	−7.32766e30			−0.596672			−0.298336	−	0.954461i	$-0.596432\pi$
$307$	−7.32766e30			−0.596672			−0.298336	+	0.954461i	$0.596432\pi$
$308$	4.15742e31	−	3.57885e31i	3.25043	−	2.79808i
$309$	−1.07939e31			−0.810396
$310$	−2.44512e31	−	4.23507e31i	−1.76311	−	3.05379i
$311$	−9.35701e30	+	1.62068e31i	−0.648085	+	1.12252i	0.335495	+	0.942042i	$0.391097\pi$
$311$	−9.35701e30	+	1.62068e31i	−0.648085	+	1.12252i	−0.983580	+	0.180474i	$0.942237\pi$
$312$	1.12409e31	−	1.94698e31i	0.747944	−	1.29548i
$313$	−7.57981e29	−	1.31286e30i	−0.0484567	−	0.0839295i	0.840780	−	0.541377i	$-0.182097\pi$
$313$	−7.57981e29	−	1.31286e30i	−0.0484567	−	0.0839295i	−0.889236	+	0.457448i	$0.848764\pi$
$314$	3.34356e31			2.05395
$315$	−1.59049e31	−	5.56267e30i	−0.938967	−	0.328399i
$316$	−2.09152e31			−1.18679
$317$	−6.80709e29	−	1.17902e30i	−0.0371296	−	0.0643104i	0.846863	−	0.531810i	$-0.178488\pi$
$317$	−6.80709e29	−	1.17902e30i	−0.0371296	−	0.0643104i	−0.883993	+	0.467500i	$0.845155\pi$
$318$	6.76294e29	−	1.17138e30i	0.0354647	−	0.0614267i
$319$	−1.87134e30	+	3.24125e30i	−0.0943558	+	0.163429i
$320$	8.99969e30	+	1.55879e31i	0.436368	+	0.755811i
$321$	−6.10658e30			−0.284764
$322$	2.97964e31	+	1.04211e31i	1.33649	+	0.467430i
$323$	−1.64724e30			−0.0710762
$324$	−8.69113e30	−	1.50535e31i	−0.360798	−	0.624920i
$325$	1.15199e31	−	1.99530e31i	0.460156	−	0.797013i
$326$	−9.06154e30	+	1.56951e31i	−0.348323	+	0.603313i
$327$	6.39641e30	+	1.10789e31i	0.236641	+	0.409874i
$328$	1.70684e31			0.607813
$329$	1.72681e31	−	1.48649e31i	0.591964	−	0.509583i
$330$	−6.75252e31			−2.22865
$331$	7.07582e30	+	1.22557e31i	0.224867	+	0.389482i	0.956280	−	0.292454i	$-0.0944717\pi$
$331$	7.07582e30	+	1.22557e31i	0.224867	+	0.389482i	−0.731412	+	0.681936i	$0.761138\pi$
$332$	−2.08106e31	+	3.60449e31i	−0.636880	+	1.10311i
$333$	−1.37699e31	+	2.38502e31i	−0.405863	+	0.702975i
$334$	1.49835e31	+	2.59522e31i	0.425385	+	0.736788i
$335$	2.76661e30			0.0756637
$336$	7.86699e30	+	4.15436e31i	0.207285	+	1.09462i
$337$	−3.73362e31			−0.947886			−0.473943	−	0.880556i	$-0.657170\pi$
$337$	−3.73362e31			−0.947886			−0.473943	+	0.880556i	$0.657170\pi$
$338$	−1.57450e31	−	2.72711e31i	−0.385198	−	0.667182i
$339$	−5.65795e30	+	9.79985e30i	−0.133402	+	0.231059i
$340$	−1.39056e31	+	2.40853e31i	−0.316012	+	0.547350i
$341$	5.98812e31	+	1.03717e32i	1.31178	+	2.27207i
$342$	−2.29363e31			−0.484392
$343$	−2.61474e31	−	4.15714e31i	−0.532417	−	0.846482i
$344$	4.95235e31			0.972369
$345$	−1.36488e31	−	2.36404e31i	−0.258438	−	0.447627i
$346$	3.21015e31	−	5.56015e31i	0.586239	−	1.01540i
$347$	3.99893e31	−	6.92635e31i	0.704410	−	1.22007i	−0.262494	−	0.964934i	$-0.584545\pi$
$347$	3.99893e31	−	6.92635e31i	0.704410	−	1.22007i	0.966904	−	0.255140i	$-0.0821216\pi$
$348$	−3.63063e30	−	6.28843e30i	−0.0616937	−	0.106857i
$349$	1.46039e31			0.239415			0.119707	−	0.992809i	$-0.461804\pi$
$349$	1.46039e31			0.239415			0.119707	+	0.992809i	$0.461804\pi$
$350$	1.66551e31	+	8.79511e31i	0.263448	+	1.39120i
$351$	6.85856e31			1.04687
$352$	−9.65370e31	−	1.67207e32i	−1.42204	−	2.46304i
$353$	−1.07814e31	+	1.86739e31i	−0.153282	+	0.265492i	−0.932432	−	0.361345i	$-0.882318\pi$
$353$	−1.07814e31	+	1.86739e31i	−0.153282	+	0.265492i	0.779150	+	0.626837i	$0.215651\pi$
$354$	3.57123e31	−	6.18556e31i	0.490092	−	0.848864i
$355$	−6.56580e31	−	1.13723e32i	−0.869828	−	1.50659i
$356$	−1.63843e32			−2.09558
$357$	−6.20262e30	+	5.33943e30i	−0.0765989	+	0.0659390i
$358$	4.59218e31			0.547622
$359$	−3.59319e31	−	6.22358e31i	−0.413808	−	0.716737i	0.581494	−	0.813550i	$-0.302468\pi$
$359$	−3.59319e31	−	6.22358e31i	−0.413808	−	0.716737i	−0.995303	+	0.0968137i	$0.969135\pi$
$360$	−1.11638e32	+	1.93362e32i	−1.24174	+	2.15075i
$361$	4.07205e31	−	7.05299e31i	0.437495	−	0.757763i
$362$	−2.56482e31	−	4.44239e31i	−0.266195	−	0.461063i
$363$	1.15227e32			1.15537
$364$	2.74221e32	+	9.59073e31i	2.65664	+	0.929147i
$365$	−3.06920e31			−0.287319
$366$	5.06332e31	+	8.76993e31i	0.458059	+	0.793382i
$367$	−9.01339e31	+	1.56117e32i	−0.788066	+	1.36497i	0.139084	+	0.990281i	$0.455584\pi$
$367$	−9.01339e31	+	1.56117e32i	−0.788066	+	1.36497i	−0.927150	+	0.374690i	$0.877749\pi$
$368$	1.01240e32	−	1.75352e32i	0.855565	−	1.48188i
$369$	1.11343e31	+	1.92852e31i	0.0909565	+	0.157541i
$370$	3.35759e32			2.65158
$371$	9.51235e30	+	3.32690e30i	0.0726297	+	0.0254019i
$372$	−2.32354e32			−1.71539
$373$	1.15456e32	+	1.99975e32i	0.824242	+	1.42763i	0.902498	+	0.430695i	$0.141732\pi$
$373$	1.15456e32	+	1.99975e32i	0.824242	+	1.42763i	−0.0782559	+	0.996933i	$0.524935\pi$
$374$	4.84749e31	−	8.39611e31i	0.334674	−	0.579673i
$375$	−1.14141e31	+	1.97698e31i	−0.0762167	+	0.132011i
$376$	−1.50962e32	−	2.61474e32i	−0.975035	−	1.68881i
$377$	−1.98204e31			−0.123836
$378$	−2.01950e32	+	1.73845e32i	−1.22067	+	1.05079i
$379$	2.72543e31			0.159384			0.0796920	−	0.996820i	$-0.474606\pi$
$379$	2.72543e31			0.159384			0.0796920	+	0.996820i	$0.474606\pi$
$380$	9.82251e31	+	1.70131e32i	0.555812	+	0.962694i
$381$	8.12983e31	−	1.40813e32i	0.445163	−	0.771046i
$382$	−2.09615e32	+	3.63064e32i	−1.11078	+	1.92394i
$383$	−1.75804e32	−	3.04501e32i	−0.901662	−	1.56172i	−0.825336	−	0.564642i	$-0.809014\pi$
$383$	−1.75804e32	−	3.04501e32i	−0.901662	−	1.56172i	−0.0763261	−	0.997083i	$-0.524319\pi$
$384$	−3.68764e31			−0.183066
$385$	−9.36055e31	−	4.94306e32i	−0.449824	−	2.37540i
$386$	1.94210e32			0.903505
$387$	3.23059e31	+	5.59555e31i	0.145511	+	0.252032i
$388$	−2.62961e32	+	4.55461e32i	−1.14682	+	1.98635i
$389$	−1.60177e32	+	2.77434e32i	−0.676440	+	1.17163i	0.299606	+	0.954063i	$0.403145\pi$
$389$	−1.60177e32	+	2.77434e32i	−0.676440	+	1.17163i	−0.976046	+	0.217565i	$0.930189\pi$
$390$	−1.78800e32	−	3.09690e32i	−0.731239	−	1.26654i
$391$	3.91928e31			0.155237
$392$	−6.05712e32	+	2.37937e32i	−2.32375	+	0.912820i
$393$	1.22879e32			0.456636
$394$	−4.23769e31	−	7.33990e31i	−0.152555	−	0.264233i
$395$	−9.59069e31	+	1.66116e32i	−0.334492	+	0.579358i
$396$	4.74186e32	−	8.21315e32i	1.60236	−	2.77536i
$397$	−5.84329e31	−	1.01209e32i	−0.191327	−	0.331388i	0.754363	−	0.656457i	$-0.227946\pi$
$397$	−5.84329e31	−	1.01209e32i	−0.191327	−	0.331388i	−0.945690	+	0.325069i	$0.894612\pi$
$398$	8.64127e32			2.74182
$399$	1.07564e31	+	5.68016e31i	0.0330754	+	0.174662i
$400$	5.74183e32			1.71120
$401$	−1.75650e32	−	3.04235e32i	−0.507393	−	0.878830i	−0.999963	−	0.00855752i	$-0.997276\pi$
$401$	−1.75650e32	−	3.04235e32i	−0.507393	−	0.878830i	0.492571	−	0.870272i	$-0.336057\pi$
$402$	9.35564e30	−	1.62044e31i	0.0261968	−	0.0453741i
$403$	−3.17119e32	+	5.49265e32i	−0.860813	+	1.49097i
$404$	8.34286e32	+	1.44503e33i	2.19557	+	3.80284i
$405$	−1.59413e32			−0.406759
$406$	5.83612e31	−	5.02393e31i	0.144394	−	0.124299i
$407$	−8.22277e32			−1.97282
$408$	5.42250e31	+	9.39205e31i	0.126168	+	0.218529i
$409$	8.97547e31	−	1.55460e32i	0.202542	−	0.350814i	−0.746805	−	0.665044i	$-0.768413\pi$
$409$	8.97547e31	−	1.55460e32i	0.202542	−	0.350814i	0.949347	+	0.314230i	$0.101746\pi$
$410$	1.35746e32	−	2.35120e32i	0.297119	−	0.514625i
$411$	−1.95622e32	−	3.38827e32i	−0.415331	−	0.719375i
$412$	−1.84823e33			−3.80663
$413$	5.02308e32	+	1.75680e32i	1.00368	+	0.351031i
$414$	5.45724e32			1.05796
$415$	1.90854e32	+	3.30570e32i	0.359006	+	0.621816i
$416$	5.11240e32	−	8.85493e32i	0.933164	−	1.61629i
$417$	5.99263e31	−	1.03795e32i	0.106149	−	0.183856i
$418$	−3.42412e32	−	5.93075e32i	−0.588634	−	1.01954i
$419$	7.83929e32			1.30798			0.653991	−	0.756503i	$-0.273094\pi$
$419$	7.83929e32			1.30798			0.653991	+	0.756503i	$0.273094\pi$
$420$	9.21335e32	+	3.22232e32i	1.49211	+	0.521858i
$421$	5.64321e32			0.887156			0.443578	−	0.896236i	$-0.353709\pi$
$421$	5.64321e32			0.887156			0.443578	+	0.896236i	$0.353709\pi$
$422$	−1.01937e33	−	1.76560e33i	−1.55570	−	2.69455i
$423$	1.96956e32	−	3.41138e32i	0.291820	−	0.505446i
$424$	6.67678e31	−	1.15645e32i	0.0960493	−	0.166362i
$425$	5.55706e31	+	9.62511e31i	0.0776218	+	0.134445i
$426$	−8.88124e32			−1.20463
$427$	−5.71798e32	+	4.92223e32i	−0.753172	+	0.648356i
$428$	−1.04563e33			−1.33761
$429$	4.37883e32	+	7.58436e32i	0.544054	+	0.942329i
$430$	3.93865e32	−	6.82194e32i	0.475326	−	0.823288i
$431$	−8.60085e31	+	1.48971e32i	−0.100827	+	0.174637i	−0.912025	−	0.410134i	$-0.865482\pi$
$431$	−8.60085e31	+	1.48971e32i	−0.100827	+	0.174637i	0.811199	+	0.584770i	$0.198815\pi$
$432$	8.54626e32	+	1.48026e33i	0.973261	+	1.68574i
$433$	1.53446e33			1.69769			0.848844	−	0.528643i	$-0.177299\pi$
$433$	1.53446e33			1.69769			0.848844	+	0.528643i	$0.177299\pi$
$434$	−4.58480e32	−	2.42112e33i	−0.492832	−	2.60252i
$435$	−6.65932e31			−0.0695528
$436$	1.09525e33	+	1.89703e33i	1.11156	+	1.92528i
$437$	1.38423e32	−	2.39755e32i	0.136518	−	0.236456i
$438$	−1.03789e32	+	1.79768e32i	−0.0994775	+	0.172300i
$439$	4.66619e32	+	8.08208e32i	0.434666	+	0.752864i	0.997268	−	0.0738639i	$-0.0235330\pi$
$439$	4.66619e32	+	8.08208e32i	0.434666	+	0.752864i	−0.562602	+	0.826728i	$0.690200\pi$
$440$	−6.66649e33			−6.03586
$441$	−6.63966e32	−	5.29166e32i	−0.584337	−	0.465703i
$442$	5.13427e32			0.439238
$443$	−6.21859e31	−	1.07709e32i	−0.0517185	−	0.0895790i	0.839007	−	0.544120i	$-0.183137\pi$
$443$	−6.21859e31	−	1.07709e32i	−0.0517185	−	0.0895790i	−0.890726	+	0.454541i	$0.849803\pi$
$444$	7.97659e32	−	1.38159e33i	0.644956	−	1.11710i
$445$	−7.51307e32	+	1.30130e33i	−0.590632	+	1.02301i
$446$	1.86624e33	+	3.23243e33i	1.42654	+	2.47083i
$447$	6.02862e32			0.448099
$448$	1.68752e32	+	8.91135e32i	0.121976	+	0.644122i
$449$	−7.18416e32			−0.505006			−0.252503	−	0.967596i	$-0.581254\pi$
$449$	−7.18416e32			−0.505006			−0.252503	+	0.967596i	$0.581254\pi$
$450$	7.73771e32	+	1.34021e33i	0.529001	+	0.916256i
$451$	−3.32445e32	+	5.75811e32i	−0.221061	+	0.382889i
$452$	−9.68806e32	+	1.67802e33i	−0.626623	+	1.08534i
$453$	3.73073e31	+	6.46181e31i	0.0234729	+	0.0406562i
$454$	1.74061e33			1.06538
$455$	2.01918e33	−	1.73817e33i	1.20235	−	1.03503i
$456$	7.66058e32			0.443814
$457$	4.30979e32	+	7.46478e32i	0.242943	+	0.420789i	0.961551	−	0.274626i	$-0.0885540\pi$
$457$	4.30979e32	+	7.46478e32i	0.242943	+	0.420789i	−0.718609	+	0.695415i	$0.755221\pi$
$458$	1.33560e33	−	2.31333e33i	0.732587	−	1.26888i
$459$	−1.65425e32	+	2.86525e32i	−0.0882963	+	0.152934i
$460$	−2.33708e33	−	4.04793e33i	−1.21395	−	2.10262i
$461$	3.61625e33			1.82809			0.914043	−	0.405618i	$-0.132944\pi$
$461$	3.61625e33			1.82809			0.914043	+	0.405618i	$0.132944\pi$
$462$	−3.21177e33	−	1.12330e33i	−1.58023	−	0.552676i
$463$	−3.51337e33			−1.68252			−0.841262	−	0.540627i	$-0.818187\pi$
$463$	−3.51337e33			−1.68252			−0.841262	+	0.540627i	$0.818187\pi$
$464$	−2.46977e32	−	4.27777e32i	−0.115128	−	0.199408i
$465$	−1.06546e33	+	1.84544e33i	−0.483478	+	0.837408i
$466$	−3.23242e30	+	5.59872e30i	−0.00142792	+	0.00247323i
$467$	−1.43243e33	−	2.48105e33i	−0.616047	−	1.06702i	−0.990200	−	0.139657i	$-0.955400\pi$
$467$	−1.43243e33	−	2.48105e33i	−0.616047	−	1.06702i	0.374153	−	0.927367i	$-0.377933\pi$
$468$	5.02239e33			2.10299
$469$	1.31591e32	+	4.60232e31i	0.0536494	+	0.0187636i
$470$	−4.80246e33			−1.90652
$471$	−7.28482e32	−	1.26177e33i	−0.281616	−	0.487773i
$472$	3.52573e33	−	6.10675e33i	1.32732	−	2.29898i
$473$	−9.64580e32	+	1.67070e33i	−0.353650	+	0.612540i
$474$	6.48643e32	+	1.12348e33i	0.231620	+	0.401178i
$475$	7.85068e32			0.273047
$476$	−1.06207e33	+	9.14267e32i	−0.359805	+	0.309732i
$477$	1.74220e32			0.0574934
$478$	−2.46024e32	−	4.26126e32i	−0.0790912	−	0.136990i
$479$	1.35661e32	−	2.34972e32i	0.0424875	−	0.0735905i	−0.844000	−	0.536344i	$-0.819805\pi$
$479$	1.35661e32	−	2.34972e32i	0.0424875	−	0.0735905i	0.886487	+	0.462753i	$0.153138\pi$
$480$	1.71768e33	−	2.97510e33i	0.524114	−	0.907793i
$481$	−2.17730e33	−	3.77120e33i	−0.647300	−	1.12116i
$482$	−3.63670e33			−1.05346
$483$	−2.55927e32	−	1.35148e33i	−0.0722398	−	0.381480i
$484$	1.97303e34			5.42708
$485$	2.41162e33	+	4.17705e33i	0.646454	+	1.11969i
$486$	−3.62172e33	+	6.27301e33i	−0.946154	+	1.63879i
$487$	−1.65031e33	+	2.85842e33i	−0.420197	+	0.727803i	−0.995958	−	0.0898147i	$-0.971373\pi$
$487$	−1.65031e33	+	2.85842e33i	−0.420197	+	0.727803i	0.575761	+	0.817618i	$0.304706\pi$
$488$	4.99881e33	+	8.65820e33i	1.24056	+	2.14872i
$489$	7.89717e32			0.191034
$490$	−1.53967e33	+	1.02361e34i	−0.363058	+	2.41370i
$491$	−3.51808e33			−0.808698			−0.404349	−	0.914605i	$-0.632502\pi$
$491$	−3.51808e33			−0.808698			−0.404349	+	0.914605i	$0.632502\pi$
$492$	−6.44983e32	−	1.11714e33i	−0.144539	−	0.250349i
$493$	4.78059e31	−	8.28023e31i	0.0104447	−	0.0180907i
$494$	1.81334e33	−	3.14080e33i	0.386272	−	0.669043i
$495$	−4.34878e33	−	7.53232e33i	−0.903239	−	1.56446i
$496$	−1.58061e34			−3.20113
$497$	−1.23115e33	−	6.50136e33i	−0.243139	−	1.28395i
$498$	2.58160e33			0.497189
$499$	−1.47939e33	−	2.56237e33i	−0.277859	−	0.481266i	0.692993	−	0.720944i	$-0.256291\pi$
$499$	−1.47939e33	−	2.56237e33i	−0.277859	−	0.481266i	−0.970852	+	0.239678i	$0.922958\pi$
$500$	−1.95443e33	+	3.38517e33i	−0.358009	+	0.620090i
$501$	6.52908e32	−	1.13087e33i	0.116649	−	0.202042i
$502$	−1.53880e33	−	2.66528e33i	−0.268155	−	0.464459i
$503$	−9.10543e33			−1.54775			−0.773874	−	0.633339i	$-0.781684\pi$
$503$	−9.10543e33			−1.54775			−0.773874	+	0.633339i	$0.781684\pi$
$504$	−8.52657e33	+	7.33996e33i	−1.41382	+	1.21706i
$505$	1.53025e34			2.47526
$506$	8.14703e33	+	1.41111e34i	1.28564	+	2.22679i
$507$	−6.86091e32	+	1.18834e33i	−0.105629	+	0.182954i
$508$	1.39207e34	−	2.41113e34i	2.09105	−	3.62180i
$509$	−1.79627e33	−	3.11122e33i	−0.263268	−	0.455994i	0.703840	−	0.710358i	$-0.251467\pi$
$509$	−1.79627e33	−	3.11122e33i	−0.263268	−	0.455994i	−0.967108	+	0.254364i	$0.918134\pi$
$510$	1.72502e33			0.246699
$511$	−1.45983e33	−	5.10570e32i	−0.203724	−	0.0712515i
$512$	−1.51405e34			−2.06189
$513$	1.16851e33	+	2.02392e33i	0.155298	+	0.268984i
$514$	−7.22658e33	+	1.25168e34i	−0.937333	+	1.62351i
$515$	−8.47510e33	+	1.46793e34i	−1.07289	+	1.85830i
$516$	−1.87140e33	−	3.24137e33i	−0.231231	−	0.400504i
$517$	1.17613e34			1.41848
$518$	1.59700e34	+	5.58543e33i	1.88011	+	0.657559i
$519$	−2.79766e33			−0.321516
$520$	−1.76522e34	−	3.05745e34i	−1.98042	−	3.43018i
$521$	4.31368e33	−	7.47151e33i	0.472472	−	0.818345i	−0.527032	−	0.849846i	$-0.676695\pi$
$521$	4.31368e33	−	7.47151e33i	0.472472	−	0.818345i	0.999504	+	0.0315001i	$0.0100285\pi$
$522$	6.65655e32	−	1.15295e33i	0.0711816	−	0.123290i
$523$	4.11156e33	+	7.12144e33i	0.429275	+	0.743527i	0.996809	−	0.0798235i	$-0.0254357\pi$
$523$	4.11156e33	+	7.12144e33i	0.429275	+	0.743527i	−0.567534	+	0.823350i	$0.692102\pi$
$524$	2.10405e34			2.14493
$525$	2.95615e33	−	2.54476e33i	0.294263	−	0.253311i
$526$	−1.80413e34			−1.75366
$527$	−1.52975e33	−	2.64960e33i	−0.145207	−	0.251506i
$528$	−1.09127e34	+	1.89013e34i	−1.01160	+	1.75214i
$529$	2.22938e33	−	3.86140e33i	0.201831	−	0.349582i
$530$	−1.06202e33	−	1.83947e33i	−0.0939040	−	0.162647i
$531$	9.19984e33			0.794509
$532$	1.84181e33	+	9.72610e33i	0.155363	+	0.820434i
$533$	−3.52112e33			−0.290128
$534$	5.08128e33	+	8.80104e33i	0.408985	+	0.708383i
$535$	−4.79474e33	+	8.30473e33i	−0.377001	+	0.652985i
$536$	9.23645e32	−	1.59980e33i	0.0709488	−	0.122887i
$537$	−1.00052e33	−	1.73296e33i	−0.0750843	−	0.130050i
$538$	3.83569e33			0.281232
$539$	3.77066e33	−	2.50683e34i	0.270121	−	1.79583i
$540$	3.94574e34			2.76189
$541$	1.25786e34	+	2.17867e34i	0.860331	+	1.49014i	0.871610	+	0.490200i	$0.163076\pi$
$541$	1.25786e34	+	2.17867e34i	0.860331	+	1.49014i	−0.0112794	+	0.999936i	$0.503590\pi$
$542$	1.25500e34	−	2.17373e34i	0.838791	−	1.45283i
$543$	−1.11762e33	+	1.93578e33i	−0.0729958	+	0.126432i
$544$	2.46617e33	+	4.27153e33i	0.157412	+	0.272645i
$545$	2.00892e34			1.25316
$546$	−3.35265e33	−	1.77045e34i	−0.204400	−	1.07938i
$547$	−1.01748e34			−0.606298			−0.303149	−	0.952943i	$-0.598038\pi$
$547$	−1.01748e34			−0.606298			−0.303149	+	0.952943i	$0.598038\pi$
$548$	−3.34962e34	−	5.80171e34i	−1.95092	−	3.37909i
$549$	−6.52180e33	+	1.12961e34i	−0.371290	+	0.643093i
$550$	−2.31030e34	+	4.00156e34i	−1.28569	+	2.22687i
$551$	−3.37686e32	−	5.84890e32i	−0.0183704	−	0.0318185i
$552$	−1.82269e34			−0.969334
$553$	−7.32509e33	+	6.30569e33i	−0.380846	+	0.327845i
$554$	−4.28955e34			−2.18042
$555$	−7.31537e33	−	1.26706e34i	−0.363558	−	0.629701i
$556$	1.02611e34	−	1.77728e34i	0.498610	−	0.863618i
$557$	1.65298e32	−	2.86305e32i	0.00785378	−	0.0136032i	−0.862072	−	0.506786i	$-0.830833\pi$
$557$	1.65298e32	−	2.86305e32i	0.00785378	−	0.0136032i	0.869926	+	0.493183i	$0.164167\pi$
$558$	−2.13004e34	−	3.68933e34i	−0.989601	−	1.71404i
$559$	−1.02164e34			−0.464143
$560$	6.26747e34	+	2.19202e34i	2.78447	+	0.973853i
$561$	−4.22461e33			−0.183548
$562$	1.87961e34	+	3.25558e34i	0.798664	+	1.38333i
$563$	4.91804e33	−	8.51830e33i	0.204380	−	0.353996i	−0.745555	−	0.666444i	$-0.767816\pi$
$563$	4.91804e33	−	8.51830e33i	0.204380	−	0.353996i	0.949935	+	0.312448i	$0.101149\pi$
$564$	−1.14092e34	+	1.97613e34i	−0.463730	+	0.803204i
$565$	8.88496e33	+	1.53892e34i	0.353224	+	0.611802i
$566$	2.87805e34			1.11916
$567$	−7.58234e33	−	2.65188e33i	−0.288413	−	0.100871i
$568$	−8.76810e34			−3.26250
$569$	−1.24036e33	−	2.14837e33i	−0.0451487	−	0.0781998i	0.842568	−	0.538590i	$-0.181043\pi$
$569$	−1.24036e33	−	2.14837e33i	−0.0451487	−	0.0781998i	−0.887717	+	0.460390i	$0.847709\pi$
$570$	6.09252e33	−	1.05526e34i	0.216951	−	0.375770i
$571$	−6.01492e33	+	1.04181e34i	−0.209546	+	0.362944i	−0.951571	−	0.307428i	$-0.900532\pi$
$571$	−6.01492e33	+	1.04181e34i	−0.209546	+	0.362944i	0.742026	+	0.670371i	$0.233865\pi$
$572$	7.49784e34	+	1.29866e35i	2.55556	+	4.42636i
$573$	1.82680e34			0.609198
$574$	1.03679e34	−	8.92505e33i	0.338293	−	0.291214i
$575$	−1.86792e34			−0.596361
$576$	7.83999e33	+	1.35793e34i	0.244926	+	0.424224i
$577$	−2.13800e34	+	3.70313e34i	−0.653598	+	1.13206i	0.328646	+	0.944453i	$0.393408\pi$
$577$	−2.13800e34	+	3.70313e34i	−0.653598	+	1.13206i	−0.982243	+	0.187611i	$0.939926\pi$
$578$	2.94057e34	−	5.09321e34i	0.879697	−	1.52368i
$579$	−4.23137e33	−	7.32894e33i	−0.123879	−	0.214565i
$580$	−1.14027e34			−0.326707
$581$	3.57869e33	+	1.88981e34i	0.100351	+	0.529928i
$582$	3.26209e34			0.895278
$583$	2.60090e33	+	4.50489e33i	0.0698661	+	0.121012i
$584$	−1.02467e34	+	1.77478e34i	−0.269415	+	0.466641i
$585$	2.30303e34	−	3.98896e34i	0.592721	−	1.02662i
$586$	−5.05212e34	−	8.75053e34i	−1.27278	−	2.20452i
$587$	−4.35684e34			−1.07447			−0.537237	−	0.843431i	$-0.680532\pi$
$587$	−4.35684e34			−1.07447			−0.537237	+	0.843431i	$0.680532\pi$
$588$	3.84619e34	+	3.06533e34i	0.928570	+	0.740049i
$589$	−2.16113e34			−0.510788
$590$	−5.60809e34	−	9.71350e34i	−1.29767	−	2.24763i
$591$	−1.84658e33	+	3.19837e33i	−0.0418336	+	0.0724579i
$592$	5.42616e34	−	9.39838e34i	1.20357	−	2.08464i
$593$	3.62615e34	+	6.28068e34i	0.787522	+	1.36403i	0.927481	+	0.373871i	$0.121970\pi$
$593$	3.62615e34	+	6.28068e34i	0.787522	+	1.36403i	−0.139959	+	0.990157i	$0.544697\pi$
$594$	−1.37548e35			−2.92499
$595$	2.39128e33	+	1.26277e34i	0.0497930	+	0.262944i
$596$	1.03228e35			2.10483
$597$	−1.88272e34	−	3.26097e34i	−0.375931	−	0.651131i
$598$	−4.31450e34	+	7.47293e34i	−0.843656	+	1.46126i
$599$	−3.37158e34	+	5.83975e34i	−0.645652	+	1.11830i	0.338499	+	0.940967i	$0.390081\pi$
$599$	−3.37158e34	+	5.83975e34i	−0.645652	+	1.11830i	−0.984151	+	0.177335i	$0.943253\pi$
$600$	−2.58435e34	−	4.47622e34i	−0.484686	−	0.839501i
$601$	4.74903e34			0.872316			0.436158	−	0.899870i	$-0.356339\pi$
$601$	4.74903e34			0.872316			0.436158	+	0.899870i	$0.356339\pi$
$602$	3.00822e34	−	2.58958e34i	0.541195	−	0.465879i
$603$	2.41010e33			0.0424687
$604$	6.38810e33	+	1.10645e34i	0.110258	+	0.190972i
$605$	9.04736e34	−	1.56705e35i	1.52961	−	2.64936i
$606$	5.17475e34	−	8.96294e34i	0.857002	−	1.48437i
$607$	−3.06671e33	−	5.31169e33i	−0.0497524	−	0.0861736i	0.840077	−	0.542468i	$-0.182510\pi$
$607$	−3.06671e33	−	5.31169e33i	−0.0497524	−	0.0861736i	−0.889829	+	0.456294i	$0.849177\pi$
$608$	3.48405e34			0.553720
$609$	−3.16744e33	−	1.10780e33i	−0.0493165	−	0.0172482i
$610$	1.59024e35			2.42571
$611$	3.11427e34	+	5.39407e34i	0.465416	+	0.806123i
$612$	−1.21137e34	+	2.09816e34i	−0.177372	+	0.307218i
$613$	−4.83520e32	+	8.37481e32i	−0.00693678	+	0.0120149i	−0.869473	−	0.493981i	$-0.835541\pi$
$613$	−4.83520e32	+	8.37481e32i	−0.00693678	+	0.0120149i	0.862536	+	0.505995i	$0.168875\pi$
$614$	3.89124e34	+	6.73983e34i	0.546995	+	0.947423i
$615$	−1.18303e34			−0.162951
$616$	−3.17085e35	−	1.10899e35i	−4.27973	−	1.49681i
$617$	−1.38070e34			−0.182615			−0.0913073	−	0.995823i	$-0.529105\pi$
$617$	−1.38070e34			−0.182615			−0.0913073	+	0.995823i	$0.529105\pi$
$618$	5.73193e34	+	9.92800e34i	0.742925	+	1.28678i
$619$	7.48941e33	−	1.29720e34i	0.0951293	−	0.164769i	−0.814533	−	0.580117i	$-0.803007\pi$
$619$	7.48941e33	−	1.29720e34i	0.0951293	−	0.164769i	0.909663	+	0.415348i	$0.136340\pi$
$620$	−1.82439e35	+	3.15993e35i	−2.27102	+	3.93352i
$621$	−2.78025e34	−	4.81553e34i	−0.339186	−	0.587488i
$622$	1.98756e35			2.37651
$623$	−5.73826e34	+	4.93969e34i	−0.672481	+	0.578894i
$624$	−1.15583e35			−1.32765
$625$	5.22193e34	+	9.04465e34i	0.587937	+	1.01834i
$626$	−8.05028e33	+	1.39435e34i	−0.0888447	+	0.153884i
$627$	−1.49207e34	+	2.58434e34i	−0.161415	+	0.279579i
$628$	−1.24737e35	−	2.16052e35i	−1.32282	−	2.29119i
$629$	2.10062e34			0.218381
$630$	3.32965e34	+	1.75830e35i	0.339345	+	1.79199i
$631$	1.55673e35			1.55541			0.777706	−	0.628628i	$-0.216383\pi$
$631$	1.55673e35			1.55541			0.777706	+	0.628628i	$0.216383\pi$
$632$	6.40380e34	+	1.10917e35i	0.627298	+	1.08651i
$633$	−4.44191e34	+	7.69361e34i	−0.426603	+	0.738897i
$634$	−7.22960e33	+	1.25220e34i	−0.0680767	+	0.117912i
$635$	−1.27667e35	−	2.21126e35i	−1.17871	−	2.04159i
$636$	−1.00921e34			−0.0913627
$637$	1.24955e35	−	4.90850e34i	1.10920	−	0.435718i
$638$	3.97498e34			0.346000
$639$	−5.71973e34	−	9.90687e34i	−0.488219	−	0.845621i
$640$	−2.89545e34	+	5.01506e34i	−0.242363	+	0.419785i
$641$	7.70050e34	−	1.33376e35i	0.632111	−	1.09485i	−0.355008	−	0.934863i	$-0.615522\pi$
$641$	7.70050e34	−	1.33376e35i	0.632111	−	1.09485i	0.987119	−	0.159985i	$-0.0511446\pi$
$642$	3.24280e34	+	5.61670e34i	0.261056	+	0.452162i
$643$	−2.66772e34			−0.210622			−0.105311	−	0.994439i	$-0.533584\pi$
$643$	−2.66772e34			−0.210622			−0.105311	+	0.994439i	$0.533584\pi$
$644$	−4.38222e34	−	2.31414e35i	−0.339329	−	1.79191i
$645$	−3.43254e34			−0.260687
$646$	8.74739e33	+	1.51509e34i	0.0651586	+	0.112858i
$647$	6.79466e33	−	1.17687e34i	0.0496437	−	0.0859855i	−0.840136	−	0.542376i	$-0.817525\pi$
$647$	6.79466e33	−	1.17687e34i	0.0496437	−	0.0859855i	0.889779	+	0.456391i	$0.150858\pi$
$648$	−5.32209e34	+	9.21813e34i	−0.381412	+	0.660626i
$649$	1.37343e35	+	2.37885e35i	0.965489	+	1.67228i
$650$	−2.44698e35			−1.68738
$651$	−8.13770e34	+	7.00521e34i	−0.550477	+	0.473869i
$652$	1.35223e35			0.897335
$653$	−1.21342e35	−	2.10170e35i	−0.789943	−	1.36822i	−0.926001	−	0.377521i	$-0.876777\pi$
$653$	−1.21342e35	−	2.10170e35i	−0.789943	−	1.36822i	0.136058	−	0.990701i	$-0.456557\pi$
$654$	6.79343e34	−	1.17666e35i	0.433878	−	0.751498i
$655$	9.64815e34	−	1.67111e35i	0.604544	−	1.04710i
$656$	−4.38757e34	−	7.59949e34i	−0.269728	−	0.467182i
$657$	−2.67370e34			−0.161267
$658$	−2.28424e35	−	7.98902e34i	−1.35182	−	0.472792i
$659$	−1.83966e35			−1.06824			−0.534120	−	0.845409i	$-0.679357\pi$
$659$	−1.83966e35			−1.06824			−0.534120	+	0.845409i	$0.679357\pi$
$660$	2.51914e35	+	4.36329e35i	1.43534	+	2.48608i
$661$	−1.02951e35	+	1.78316e35i	−0.575587	+	0.996946i	0.420390	+	0.907343i	$0.361893\pi$
$661$	−1.02951e35	+	1.78316e35i	−0.575587	+	0.996946i	−0.995978	+	0.0896028i	$0.971440\pi$
$662$	7.51501e34	−	1.30164e35i	0.412292	−	0.714110i
$663$	−1.11863e34	−	1.93753e34i	−0.0602238	−	0.104311i
$664$	2.54871e35			1.34654
$665$	8.56938e34	+	2.99710e34i	0.444303	+	0.155393i
$666$	2.92493e35			1.48829
$667$	8.03459e33	+	1.39163e34i	0.0401228	+	0.0694947i
$668$	1.11797e35	−	1.93638e35i	0.547929	−	0.949041i
$669$	8.13219e34	−	1.40854e35i	0.391184	−	0.677550i
$670$	−1.46916e34	−	2.54467e34i	−0.0693642	−	0.120142i
$671$	−3.89451e35			−1.80477
$672$	1.31191e35	−	1.12934e35i	0.596745	−	0.513698i
$673$	−1.60111e35			−0.714878			−0.357439	−	0.933936i	$-0.616350\pi$
$673$	−1.60111e35			−0.714878			−0.357439	+	0.933936i	$0.616350\pi$
$674$	1.98268e35	+	3.43410e35i	0.868968	+	1.50510i
$675$	7.88411e34	−	1.36557e35i	0.339200	−	0.587511i
$676$	−1.17479e35	+	2.03479e35i	−0.496165	+	0.859383i
$677$	2.05082e35	+	3.55213e35i	0.850296	+	1.47276i	0.880942	+	0.473225i	$0.156910\pi$
$677$	2.05082e35	+	3.55213e35i	0.850296	+	1.47276i	−0.0306458	+	0.999530i	$0.509756\pi$
$678$	1.20183e35			0.489182
$679$	4.52200e34	+	2.38795e35i	0.180700	+	0.954231i
$680$	1.70305e35			0.668137
$681$	−3.79237e34	−	6.56859e34i	−0.146074	−	0.253007i
$682$	6.35980e35	−	1.10155e36i	2.40513	−	4.16581i
$683$	6.37661e34	−	1.10446e35i	0.236772	−	0.410102i	−0.723014	−	0.690834i	$-0.757244\pi$
$683$	6.37661e34	−	1.10446e35i	0.236772	−	0.410102i	0.959786	+	0.280732i	$0.0905771\pi$
$684$	8.55678e34	+	1.48208e35i	0.311967	+	0.540343i
$685$	−6.14390e35			−2.19944
$686$	−2.43513e35	+	4.61257e35i	−0.855993	+	1.62140i
$687$	−1.16398e35			−0.401779
$688$	−1.27304e35	−	2.20497e35i	−0.431506	−	0.747391i
$689$	−1.37738e34	+	2.38570e34i	−0.0458474	+	0.0794100i
$690$	−1.44960e35	+	2.51078e35i	−0.473842	+	0.820719i
$691$	2.22487e35	+	3.85359e35i	0.714215	+	1.23706i	0.963262	+	0.268565i	$0.0865495\pi$
$691$	2.22487e35	+	3.85359e35i	0.714215	+	1.23706i	−0.249047	+	0.968492i	$0.580117\pi$
$692$	−4.79041e35			−1.51024
$693$	−8.15435e34	−	4.30610e35i	−0.252478	−	1.33327i
$694$	−8.49428e35			−2.58305
$695$	−9.41054e34	−	1.62995e35i	−0.281063	−	0.486816i
$696$	−2.22325e34	+	3.85078e34i	−0.0652187	+	0.112962i
$697$	8.49276e33	−	1.47099e34i	0.0244703	−	0.0423838i
$698$	−7.75517e34	−	1.34323e35i	−0.219482	−	0.380154i
$699$	2.81707e32			0.000783128
$700$	5.06180e35	−	4.35737e35i	1.38223	−	1.18987i
$701$	1.56793e35			0.420584			0.210292	−	0.977639i	$-0.432559\pi$
$701$	1.56793e35			0.420584			0.210292	+	0.977639i	$0.432559\pi$
$702$	−3.64213e35	−	6.30836e35i	−0.959714	−	1.66227i
$703$	7.41907e34	−	1.28502e35i	0.192047	−	0.332635i
$704$	−2.34084e35	+	4.05445e35i	−0.595269	+	1.03104i
$705$	1.04634e35	+	1.81231e35i	0.261402	+	0.452762i
$706$	2.29012e35			0.562081
$707$	7.27850e35	+	2.54562e35i	1.75509	+	0.613833i
$708$	−5.32924e35			−1.26255
$709$	−5.94299e34	−	1.02936e35i	−0.138333	−	0.239600i	0.788533	−	0.614993i	$-0.210841\pi$
$709$	−5.94299e34	−	1.02936e35i	−0.138333	−	0.239600i	−0.926866	+	0.375393i	$0.877508\pi$
$710$	−6.97334e35	+	1.20782e36i	−1.59482	+	2.76231i
$711$	−8.35484e34	+	1.44710e35i	−0.187745	+	0.325184i
$712$	5.01655e35	+	8.68891e35i	1.10766	+	1.91852i
$713$	5.14200e35			1.11561
$714$	8.20490e34	+	2.86962e34i	0.174923	+	0.0611783i
$715$	1.37526e36			2.88111
$716$	−1.71319e35	−	2.96733e35i	−0.352690	−	0.610877i
$717$	−1.07205e34	+	1.85685e34i	−0.0216884	+	0.0375653i
$718$	−3.81621e35	+	6.60987e35i	−0.758712	+	1.31413i
$719$	−1.76868e35	−	3.06345e35i	−0.345572	−	0.598549i	0.639885	−	0.768471i	$-0.278982\pi$
$719$	−1.76868e35	−	3.06345e35i	−0.345572	−	0.598549i	−0.985458	+	0.169922i	$0.945649\pi$
$720$	1.14790e36			2.20417
$721$	−6.47304e35	+	5.57221e35i	−1.22157	+	1.05157i
$722$	−8.64959e35			−1.60428
$723$	7.92350e34	+	1.37239e35i	0.144440	+	0.250178i
$724$	−1.91370e35	+	3.31462e35i	−0.342880	+	0.593885i
$725$	−2.27842e34	+	3.94633e34i	−0.0401243	+	0.0694974i
$726$	−6.11896e35	−	1.05984e36i	−1.05918	−	1.83456i
$727$	−5.31713e35			−0.904685			−0.452342	−	0.891844i	$-0.649411\pi$
$727$	−5.31713e35			−0.904685			−0.452342	+	0.891844i	$0.649411\pi$
$728$	−3.30994e35	−	1.74789e36i	−0.553576	−	2.92329i
$729$	1.29782e35			0.213364
$730$	1.62985e35	+	2.82299e35i	0.263398	+	0.456219i
$731$	2.46415e34	−	4.26804e34i	0.0391472	−	0.0678049i
$732$	3.77792e35	−	6.54355e35i	0.590016	−	1.02194i
$733$	5.32969e35	+	9.23129e35i	0.818280	+	1.41730i	0.906948	+	0.421242i	$0.138406\pi$
$733$	5.32969e35	+	9.23129e35i	0.818280	+	1.41730i	−0.0886678	+	0.996061i	$0.528261\pi$
$734$	1.91457e36			2.88982
$735$	4.19827e35	−	1.64917e35i	0.622987	−	0.244722i
$736$	−8.28963e35			−1.20938
$737$	3.59800e34	+	6.23192e34i	0.0516081	+	0.0893878i
$738$	1.18254e35	−	2.04822e35i	0.166768	−	0.288850i
$739$	−3.73746e35	+	6.47347e35i	−0.518228	+	0.897598i	0.481548	+	0.876420i	$0.340075\pi$
$739$	−3.73746e35	+	6.47347e35i	−0.518228	+	0.897598i	−0.999776	+	0.0211776i	$0.993258\pi$
$740$	−1.25261e36	−	2.16958e36i	−1.70772	−	2.95787i
$741$	−1.58034e35			−0.211847
$742$	−1.99138e34	−	1.05160e35i	−0.0262485	−	0.138612i
$743$	−1.00025e35			−0.129643			−0.0648215	−	0.997897i	$-0.520648\pi$
$743$	−1.00025e35			−0.129643			−0.0648215	+	0.997897i	$0.520648\pi$
$744$	7.11420e35	+	1.23222e36i	0.906701	+	1.57045i
$745$	4.73352e35	−	8.19871e35i	0.593241	−	1.02752i
$746$	1.22622e36	−	2.12387e36i	1.51124	−	2.61754i
$747$	1.66261e35	+	2.87972e35i	0.201504	+	0.349014i
$748$	−7.23377e35			−0.862173
$749$	−3.66208e35	+	3.15244e35i	−0.429245	+	0.369509i
$750$	2.42451e35			0.279485
$751$	−3.90419e35	−	6.76225e35i	−0.442621	−	0.766641i	0.555262	−	0.831675i	$-0.312618\pi$
$751$	−3.90419e35	−	6.76225e35i	−0.442621	−	0.766641i	−0.997883	+	0.0650338i	$0.979284\pi$
$752$	−7.76121e35	+	1.34428e36i	−0.865379	+	1.49888i
$753$	−6.70536e34	+	1.16140e35i	−0.0735334	+	0.127364i
$754$	1.05253e35	+	1.82304e35i	0.113526	+	0.196632i
$755$	1.17171e35			0.124304
$756$	1.87675e36	+	6.56383e35i	1.95832	+	0.684913i
$757$	−1.18318e36			−1.21438			−0.607188	−	0.794558i	$-0.707703\pi$
$757$	−1.18318e36			−1.21438			−0.607188	+	0.794558i	$0.707703\pi$
$758$	−1.44730e35	−	2.50679e35i	−0.146114	−	0.253077i
$759$	3.55008e35	−	6.14892e35i	0.352546	−	0.610628i
$760$	6.01490e35	−	1.04181e36i	0.587569	−	1.01770i
$761$	−9.51667e35	−	1.64834e36i	−0.914486	−	1.58394i	−0.807653	−	0.589659i	$-0.799262\pi$
$761$	−9.51667e35	−	1.64834e36i	−0.914486	−	1.58394i	−0.106833	−	0.994277i	$-0.534071\pi$
$762$	−1.72689e36			−1.63240
$763$	9.55524e35	+	3.34190e35i	0.888556	+	0.310768i
$764$	3.12802e36			2.86156
$765$	1.11096e35	+	1.92423e35i	0.0999837	+	0.173177i
$766$	−1.86716e36	+	3.23401e36i	−1.65319	+	2.86340i
$767$	−7.27339e35	+	1.25979e36i	−0.633571	+	1.09738i
$768$	3.88127e35	+	6.72256e35i	0.332628	+	0.576128i
$769$	−1.73117e36			−1.45969			−0.729844	−	0.683614i	$-0.760407\pi$
$769$	−1.73117e36			−1.45969			−0.729844	+	0.683614i	$0.760407\pi$
$770$	−4.04945e36	+	3.48590e36i	−3.35940	+	2.89188i
$771$	6.29799e35			0.514070
$772$	−7.24534e35	−	1.25493e36i	−0.581892	−	1.00787i
$773$	−3.57212e35	+	6.18709e35i	−0.282281	+	0.488925i	−0.971946	−	0.235203i	$-0.924424\pi$
$773$	−3.57212e35	+	6.18709e35i	−0.282281	+	0.488925i	0.689665	+	0.724129i	$0.257758\pi$
$774$	3.43111e35	−	5.94286e35i	0.266792	−	0.462097i
$775$	7.29073e35	+	1.26279e36i	0.557828	+	0.966186i
$776$	3.22053e36			2.42469
$777$	−1.37169e35	−	7.24356e35i	−0.101624	−	0.536648i
$778$	3.40237e36			2.48049
$779$	−5.99902e34	−	1.03906e35i	−0.0430390	−	0.0745458i
$780$	−1.33409e36	+	2.31071e36i	−0.941893	+	1.63141i
$781$	1.70778e36	−	2.95796e36i	1.18657	−	2.05520i
$782$	−2.08127e35	−	3.60487e35i	−0.142313	−	0.246493i
$783$	−1.35650e35			−0.0912845
$784$	2.61641e36	+	2.08522e36i	1.73283	+	1.38102i
$785$	−2.28795e36			−1.49133
$786$	−6.52529e35	−	1.13021e36i	−0.418618	−	0.725068i
$787$	6.03740e35	−	1.04571e36i	0.381211	−	0.660277i	−0.610024	−	0.792383i	$-0.708840\pi$
$787$	6.03740e35	−	1.04571e36i	0.381211	−	0.660277i	0.991236	+	0.132105i	$0.0421737\pi$
$788$	−3.16189e35	+	5.47655e35i	−0.196503	+	0.340353i
$789$	3.93077e35	+	6.80829e35i	0.240444	+	0.416462i
$790$	2.03720e36			1.22658
$791$	1.66601e35	+	8.79776e35i	0.0987350	+	0.521394i
$792$	−5.80745e36			−3.38782
$793$	−1.03123e36	−	1.78614e36i	−0.592161	−	1.02565i
$794$	−6.20597e35	+	1.07491e36i	−0.350795	+	0.607595i
$795$	−4.62777e34	+	8.01553e34i	−0.0257503	+	0.0446008i
$796$	−3.22378e36	−	5.58375e36i	−1.76584	−	3.05853i
$797$	1.13770e34			0.00613476			0.00306738	−	0.999995i	$-0.499024\pi$
$797$	1.13770e34			0.00613476			0.00306738	+	0.999995i	$0.499024\pi$
$798$	4.65329e35	−	4.00571e35i	0.247015	−	0.212639i
$799$	−3.00458e35			−0.157018
$800$	−1.17537e36	−	2.03580e36i	−0.604713	−	1.04739i
$801$	−6.54493e35	+	1.13362e36i	−0.331512	+	0.574195i
$802$	−1.86553e36	+	3.23119e36i	−0.930298	+	1.61132i
$803$	−3.99153e35	−	6.91353e35i	−0.195972	−	0.339434i
$804$	−1.39611e35			−0.0674870
$805$	−2.03892e36	−	7.13101e35i	−0.970401	−	0.339393i
$806$	6.73604e36			3.15658
$807$	−8.35704e34	−	1.44748e35i	−0.0385597	−	0.0667873i
$808$	5.10883e36	−	8.84875e36i	2.32102	−	4.02013i
$809$	9.61175e35	−	1.66480e36i	0.429978	−	0.744743i	−0.566893	−	0.823791i	$-0.691855\pi$
$809$	9.61175e35	−	1.66480e36i	0.429978	−	0.744743i	0.996871	+	0.0790483i	$0.0251881\pi$
$810$	8.46541e35	+	1.46625e36i	0.372894	+	0.645871i
$811$	9.14531e35			0.396678			0.198339	−	0.980134i	$-0.436445\pi$
$811$	9.14531e35			0.396678			0.198339	+	0.980134i	$0.436445\pi$
$812$	−5.42359e35	−	1.89687e35i	−0.231652	−	0.0810191i
$813$	−1.09374e36			−0.460026
$814$	4.36657e36	+	7.56313e36i	1.80857	+	3.13254i
$815$	6.20066e35	−	1.07399e36i	0.252911	−	0.438055i
$816$	2.78779e35	−	4.82860e35i	0.111978	−	0.193952i
$817$	−1.74060e35	−	3.01481e35i	−0.0688531	−	0.119257i
$818$	−1.90651e36			−0.742718
$819$	1.75898e36	−	1.51419e36i	0.674859	−	0.580942i
$820$	−2.02570e36			−0.765424
$821$	2.63961e36	+	4.57193e36i	0.982312	+	1.70141i	0.653320	+	0.757082i	$0.273376\pi$
$821$	2.63961e36	+	4.57193e36i	0.982312	+	1.70141i	0.328992	+	0.944333i	$0.393291\pi$
$822$	−2.07764e36	+	3.59858e36i	−0.761505	+	1.31896i
$823$	−2.54232e35	+	4.40343e35i	−0.0917768	+	0.158962i	−0.908259	−	0.418409i	$-0.862588\pi$
$823$	−2.54232e35	+	4.40343e35i	−0.0917768	+	0.158962i	0.816482	+	0.577371i	$0.195921\pi$
$824$	5.65891e36	+	9.80151e36i	2.01207	+	3.48500i
$825$	2.01344e36			0.705120
$826$	−1.05157e36	−	5.55305e36i	−0.362732	−	1.91549i
$827$	−2.13937e36			−0.726888			−0.363444	−	0.931616i	$-0.618399\pi$
$827$	−2.13937e36			−0.726888			−0.363444	+	0.931616i	$0.618399\pi$
$828$	−2.03592e36	−	3.52632e36i	−0.681367	−	1.18016i
$829$	8.40540e35	−	1.45586e36i	0.277094	−	0.479940i	−0.693567	−	0.720392i	$-0.743962\pi$
$829$	8.40540e35	−	1.45586e36i	0.277094	−	0.479940i	0.970661	+	0.240451i	$0.0772954\pi$
$830$	2.02701e36	−	3.51088e36i	0.658232	−	1.14009i
$831$	9.34588e35	+	1.61875e36i	0.298956	+	0.517807i
$832$	−2.47932e36			−0.781251
$833$	−9.63268e34	+	6.40405e35i	−0.0299009	+	0.198789i
$834$	−1.27292e36			−0.389247
$835$	−1.02529e36	−	1.77586e36i	−0.308864	−	0.534969i
$836$	−2.55486e36	+	4.42514e36i	−0.758207	+	1.31325i
$837$	−2.17034e36	+	3.75914e36i	−0.634540	+	1.09906i
$838$	−4.16293e36	−	7.21041e36i	−1.19908	−	2.07687i
$839$	6.06533e36			1.72119			0.860597	−	0.509287i	$-0.170091\pi$
$839$	6.06533e36			1.72119			0.860597	+	0.509287i	$0.170091\pi$
$840$	−1.11208e36	−	5.87262e36i	−0.310918	−	1.64188i
$841$	−3.59116e36			−0.989202
$842$	−2.99674e36	−	5.19051e36i	−0.813295	−	1.40867i
$843$	8.19044e35	−	1.41863e36i	0.219009	−	0.379335i
$844$	−7.60585e36	+	1.31737e37i	−2.00386	+	3.47079i
$845$	1.07740e36	+	1.86612e36i	0.279685	+	0.484429i
$846$	−4.18362e36			−1.07009
$847$	6.91011e36	−	5.94846e36i	1.74158	−	1.49921i
$848$	−6.86528e35			−0.170494
$849$	−6.27057e35	−	1.08609e36i	−0.153448	−	0.265779i
$850$	5.90198e35	−	1.02225e36i	0.142319	−	0.246503i
$851$	−1.76522e36	+	3.05746e36i	−0.419450	+	0.726508i
$852$	3.31330e36	+	5.73881e36i	0.775829	+	1.34378i
$853$	−2.28852e36			−0.528071			−0.264035	−	0.964513i	$-0.585054\pi$
$853$	−2.28852e36			−0.528071			−0.264035	+	0.964513i	$0.585054\pi$
$854$	7.56381e36	+	2.64540e36i	1.71995	+	0.601545i
$855$	1.56949e36			0.351708
$856$	3.20149e36	+	5.54515e36i	0.707018	+	1.22459i
$857$	9.55524e35	−	1.65502e36i	0.207961	−	0.360199i	−0.743111	−	0.669168i	$-0.766651\pi$
$857$	9.55524e35	−	1.65502e36i	0.207961	−	0.360199i	0.951072	+	0.308969i	$0.0999841\pi$
$858$	4.65062e36	−	8.05511e36i	0.997516	−	1.72775i
$859$	8.69900e35	+	1.50671e36i	0.183889	+	0.318505i	0.943201	−	0.332221i	$-0.107798\pi$
$859$	8.69900e35	+	1.50671e36i	0.183889	+	0.318505i	−0.759313	+	0.650726i	$0.774465\pi$
$860$	−5.87752e36			−1.22451
$861$	−5.62698e35	−	1.96801e35i	−0.115541	−	0.0404099i
$862$	1.82694e36			0.369729
$863$	2.29038e36	+	3.96705e36i	0.456849	+	0.791285i	0.998792	−	0.0491297i	$-0.0156448\pi$
$863$	2.29038e36	+	3.96705e36i	0.456849	+	0.791285i	−0.541944	+	0.840415i	$0.682311\pi$
$864$	3.49889e36	−	6.06026e36i	0.687874	−	1.19143i
$865$	−2.19665e36	+	3.80472e36i	−0.425658	+	0.737260i
$866$	−8.14853e36	−	1.41137e37i	−1.55634	−	2.69567i
$867$	−2.56271e36			−0.482460
$868$	−1.39341e37	+	1.19950e37i	−2.58573	+	2.22588i
$869$	−4.98912e36			−0.912592
$870$	3.53633e35	+	6.12511e35i	0.0637621	+	0.110439i
$871$	−1.90543e35	+	3.30030e35i	−0.0338661	+	0.0586579i
$872$	6.70688e36	−	1.16167e37i	1.17507	−	2.03529i
$873$	2.10086e36	+	3.63880e36i	0.362843	+	0.628463i
$874$	−2.94029e36			−0.500608
$875$	3.36093e35	+	1.77482e36i	0.0564104	+	0.297888i
$876$	1.54881e36			0.256270
$877$	−9.44450e34	−	1.63583e35i	−0.0154058	−	0.0266836i	0.858220	−	0.513282i	$-0.171571\pi$
$877$	−9.44450e34	−	1.63583e35i	−0.0154058	−	0.0266836i	−0.873626	+	0.486599i	$0.838237\pi$
$878$	4.95582e36	−	8.58372e36i	0.796955	−	1.38037i
$879$	−2.20147e36	+	3.81306e36i	−0.349021	+	0.604523i
$880$	1.71367e37	+	2.96817e37i	2.67852	+	4.63933i
$881$	−2.30697e36			−0.355502			−0.177751	−	0.984075i	$-0.556882\pi$
$881$	−2.30697e36			−0.355502			−0.177751	+	0.984075i	$0.556882\pi$
$882$	−1.34127e36	+	8.91707e36i	−0.203778	+	1.35477i
$883$	3.61124e36			0.540938			0.270469	−	0.962729i	$-0.412821\pi$
$883$	3.61124e36			0.540938			0.270469	+	0.962729i	$0.412821\pi$
$884$	−1.91543e36	−	3.31762e36i	−0.282887	−	0.489974i
$885$	−2.44373e36	+	4.23267e36i	−0.355847	+	0.616345i
$886$	−6.60458e35	+	1.14395e36i	−0.0948251	+	0.164242i
$887$	−1.57413e36	−	2.72648e36i	−0.222841	−	0.385973i	0.732828	−	0.680414i	$-0.238200\pi$
$887$	−1.57413e36	−	2.72648e36i	−0.222841	−	0.385973i	−0.955670	+	0.294441i	$0.904867\pi$
$888$	−9.76908e36			−1.36361
$889$	−2.39387e36	−	1.26414e37i	−0.329479	−	1.73989i
$890$	1.59588e37			2.16583
$891$	−2.07319e36	−	3.59087e36i	−0.277439	−	0.480538i
$892$	1.39247e37	−	2.41183e37i	1.83749	−	3.18262i
$893$	−1.06117e36	+	1.83801e36i	−0.138084	+	0.239168i
$894$	−3.20140e36	−	5.54500e36i	−0.410792	−	0.711512i
$895$	−3.14235e36			−0.397619
$896$	−2.21146e36	+	1.90370e36i	−0.275949	+	0.237546i
$897$	3.76010e36			0.462694
$898$	3.81504e36	+	6.60784e36i	0.462961	+	0.801872i
$899$	6.27202e35	−	1.08635e36i	0.0750605	−	0.130009i
$900$	5.77338e36	−	9.99978e36i	0.681394	−	1.18021i
$901$	−6.64436e34	−	1.15084e35i	−0.00773380	−	0.0133953i
$902$	7.06158e36			0.810626
$903$	−1.63265e36	−	5.71012e35i	−0.184841	−	0.0646471i
$904$	1.18651e37			1.32485
$905$	1.75506e36	+	3.03986e36i	0.193279	+	0.334769i
$906$	3.96229e35	−	6.86289e35i	0.0430372	−	0.0745426i
$907$	−3.98597e36	+	6.90390e36i	−0.427015	+	0.739611i	−0.996606	−	0.0823169i	$-0.973768\pi$
$907$	−3.98597e36	+	6.90390e36i	−0.427015	+	0.739611i	0.569592	+	0.821928i	$0.307101\pi$
$908$	−6.49366e36	−	1.12473e37i	−0.686146	−	1.18844i
$909$	1.33307e37			1.38932
$910$	−2.67099e37	−	9.34165e36i	−2.74571	−	0.960298i
$911$	−1.37224e37			−1.39140			−0.695698	−	0.718334i	$-0.744905\pi$
$911$	−1.37224e37			−1.39140			−0.695698	+	0.718334i	$0.744905\pi$
$912$	−1.96921e36	−	3.41078e36i	−0.196950	−	0.341128i
$913$	−4.96416e36	+	8.59819e36i	−0.489735	+	0.848247i
$914$	4.57730e36	−	7.92811e36i	0.445432	−	0.771511i
$915$	−3.46474e36	−	6.00111e36i	−0.332589	−	0.576061i
$916$	−1.99308e37			−1.88726
$917$	7.36897e36	−	6.34346e36i	0.688320	−	0.592529i
$918$	3.51386e36			0.323780
$919$	−1.74950e36	−	3.03022e36i	−0.159027	−	0.275442i	0.775491	−	0.631358i	$-0.217502\pi$
$919$	−1.74950e36	−	3.03022e36i	−0.159027	−	0.275442i	−0.934518	+	0.355916i	$0.884169\pi$
$920$	−1.43113e37	+	2.47879e37i	−1.28331	+	2.22275i
$921$	1.69561e36	−	2.93689e36i	0.149997	−	0.259802i
$922$	−1.92035e37	−	3.32615e37i	−1.67589	−	2.90272i
$923$	1.80881e37			1.55730
$924$	4.72361e36	+	2.49442e37i	0.401213	+	2.11870i
$925$	−1.00115e37			−0.838933
$926$	1.86572e37	+	3.23152e37i	1.54244	+	2.67159i
$927$	−7.38300e36	+	1.27877e37i	−0.602194	+	1.04303i
$928$	−1.01114e36	+	1.75134e36i	−0.0813694	+	0.140936i
$929$	8.80697e36	+	1.52541e37i	0.699246	+	1.21113i	0.968728	+	0.248125i	$0.0798143\pi$
$929$	8.80697e36	+	1.52541e37i	0.699246	+	1.21113i	−0.269482	+	0.963006i	$0.586852\pi$
$930$	2.26319e37			1.77290
$931$	3.57736e36	+	2.85108e36i	0.276498	+	0.220363i
$932$	4.82365e34			0.00367855
$933$	−4.33041e36	−	7.50049e36i	−0.325843	−	0.564376i
$934$	−1.52134e37	+	2.63505e37i	−1.12951	+	1.95638i
$935$	−3.31706e36	+	5.74531e36i	−0.243001	+	0.420890i
$936$	−1.53775e37	−	2.66347e37i	−1.11157	−	1.92530i
$937$	2.25701e37			1.60986			0.804930	−	0.593370i	$-0.202203\pi$
$937$	2.25701e37			1.60986			0.804930	+	0.593370i	$0.202203\pi$
$938$	−2.75481e35	−	1.45474e36i	−0.0193890	−	0.102389i
$939$	7.01584e35			0.0487259
$940$	1.79164e37	+	3.10321e37i	1.22787	+	2.12674i
$941$	8.54887e36	−	1.48071e37i	0.578147	−	1.00138i	−0.417544	−	0.908657i	$-0.637109\pi$
$941$	8.54887e36	−	1.48071e37i	0.578147	−	1.00138i	0.995692	−	0.0927242i	$-0.0295575\pi$
$942$	−7.73698e36	+	1.34008e37i	−0.516339	+	0.894326i
$943$	1.42735e36	+	2.47224e36i	0.0940014	+	0.162815i
$944$	−3.62527e37			−2.35608
$945$	1.38191e37	−	1.18959e37i	0.886303	−	0.762960i
$946$	2.04890e37			1.29683
$947$	3.09004e36	+	5.35211e36i	0.193014	+	0.334311i	0.946248	−	0.323443i	$-0.104840\pi$
$947$	3.09004e36	+	5.35211e36i	0.193014	+	0.334311i	−0.753233	+	0.657753i	$0.771507\pi$
$948$	4.83975e36	−	8.38270e36i	0.298345	−	0.516749i
$949$	2.11383e36	−	3.66126e36i	0.128601	−	0.222743i
$950$	−4.16898e36	−	7.22089e36i	−0.250314	−	0.433556i
$951$	6.30062e35			0.0373359
$952$	8.10037e36	+	2.83306e36i	0.473743	+	0.165689i
$953$	−2.46578e37			−1.42329			−0.711645	−	0.702539i	$-0.752050\pi$
$953$	−2.46578e37			−1.42329			−0.711645	+	0.702539i	$0.752050\pi$
$954$	−9.25168e35	−	1.60244e36i	−0.0527067	−	0.0912907i
$955$	1.43436e37	−	2.48438e37i	0.806521	−	1.39694i
$956$	−1.83567e36	+	3.17947e36i	−0.101876	+	0.176454i
$957$	−8.66052e35	−	1.50005e36i	−0.0474400	−	0.0821685i
$958$	−2.88163e36			−0.155800
$959$	−2.92228e37	−	1.02205e37i	−1.55952	−	0.545433i
$960$	−8.33008e36			−0.438792
$961$	−1.04535e37	−	1.81061e37i	−0.543527	−	0.941416i
$962$	−2.31245e37	+	4.00528e37i	−1.18682	+	2.05563i
$963$	−4.17689e36	+	7.23458e36i	−0.211604	+	0.366509i
$964$	1.35674e37	+	2.34993e37i	0.678472	+	1.17515i
$965$	−1.32895e37			−0.656019
$966$	−1.10716e37	+	9.53081e36i	−0.539506	+	0.464425i
$967$	2.15136e37			1.03486			0.517432	−	0.855725i	$-0.326888\pi$
$967$	2.15136e37			1.03486			0.517432	+	0.855725i	$0.326888\pi$
$968$	−6.04101e37	−	1.04633e38i	−2.86858	−	4.96853i
$969$	3.81169e35	−	6.60204e35i	0.0178678	−	0.0309479i
$970$	2.56131e37	−	4.43632e37i	1.18527	−	2.05294i
$971$	1.07012e37	+	1.85351e37i	0.488870	+	0.846747i	0.999918	−	0.0128048i	$-0.00407600\pi$
$971$	1.07012e37	+	1.85351e37i	0.488870	+	0.846747i	−0.511048	+	0.859552i	$0.670743\pi$
$972$	5.40459e37			2.43744
$973$	−1.76456e36	−	9.31817e36i	−0.0785643	−	0.414878i
$974$	3.50549e37			1.54085
$975$	5.33137e36	+	9.23420e36i	0.231356	+	0.400721i
$976$	2.56997e37	−	4.45131e37i	1.10104	−	1.90707i
$977$	−1.36129e37	+	2.35783e37i	−0.575797	+	0.997309i	0.420158	+	0.907451i	$0.361975\pi$
$977$	−1.36129e37	+	2.35783e37i	−0.575797	+	0.997309i	−0.995955	+	0.0898583i	$0.971359\pi$
$978$	−4.19367e36	−	7.26365e36i	−0.175129	−	0.303333i
$979$	−3.90833e37			−1.61142
$980$	7.18867e37	−	2.82386e37i	2.92633	−	1.14952i
$981$	1.75005e37			0.703378
$982$	1.86822e37	+	3.23585e37i	0.741369	+	1.28409i
$983$	9.88557e36	−	1.71223e37i	0.387331	−	0.670878i	−0.604758	−	0.796409i	$-0.706730\pi$
$983$	9.88557e36	−	1.71223e37i	0.387331	−	0.670878i	0.992090	+	0.125531i	$0.0400636\pi$
$984$	−3.94961e36	+	6.84093e36i	−0.152797	+	0.264653i
$985$	2.89978e36	+	5.02257e36i	0.110768	+	0.191855i
$986$	−1.01546e36			−0.0383004
$987$	1.96198e36	+	1.03607e37i	0.0730684	+	0.385856i
$988$	−2.70600e37			−0.995098
$989$	4.14142e36	+	7.17315e36i	0.150382	+	0.260469i
$990$	−4.61871e37	+	7.99984e37i	−1.65608	+	2.86841i
$991$	1.61283e37	−	2.79350e37i	0.571041	−	0.989073i	−0.425418	−	0.904997i	$-0.639873\pi$
$991$	1.61283e37	−	2.79350e37i	0.571041	−	0.989073i	0.996459	−	0.0840758i	$-0.0267938\pi$
$992$	3.23556e37	+	5.60415e37i	1.13124	+	1.95936i
$993$	−6.54935e36			−0.226117
$994$	−5.32603e37	+	4.58483e37i	−1.81583	+	1.56312i
$995$	−5.91308e37			−1.99079
$996$	−9.63109e36	−	1.66815e37i	−0.320209	−	0.554618i
$997$	2.02839e37	−	3.51327e37i	0.665981	−	1.15351i	−0.313038	−	0.949741i	$-0.601347\pi$
$997$	2.02839e37	−	3.51327e37i	0.665981	−	1.15351i	0.979018	−	0.203772i	$-0.0653200\pi$
$998$	−1.57121e37	+	2.72141e37i	−0.509451	+	0.882395i
$999$	−1.49013e37	−	2.58099e37i	−0.477152	−	0.826451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.26.c.a.4.2	yes	32
7.2	even	3	inner	7.26.c.a.2.2	✓	32
7.3	odd	6		49.26.a.g.1.15		16
7.4	even	3		49.26.a.f.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.c.a.2.2	✓	32	7.2	even	3	inner
7.26.c.a.4.2	yes	32	1.1	even	1	trivial
49.26.a.f.1.15		16	7.4	even	3
49.26.a.g.1.15		16	7.3	odd	6

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5310.35 - 9197.79i) q^{2} +(-231399. + 400795. i) q^{3} +(-3.96223e7 + 6.86279e7i) q^{4} +(3.63378e8 + 6.29389e8i) q^{5} +4.91524e9 q^{6} +(6.81365e9 + 3.59811e10i) q^{7} +4.85262e11 q^{8} +(3.16553e11 + 5.48286e11i) q^{9} +O(q^{10})\)	\(q+(-5310.35 - 9197.79i) q^{2} +(-231399. + 400795. i) q^{3} +(-3.96223e7 + 6.86279e7i) q^{4} +(3.63378e8 + 6.29389e8i) q^{5} +4.91524e9 q^{6} +(6.81365e9 + 3.59811e10i) q^{7} +4.85262e11 q^{8} +(3.16553e11 + 5.48286e11i) q^{9} +(3.85933e12 - 6.68455e12i) q^{10} +(-9.45154e12 + 1.63705e13i) q^{11} +(-1.83371e13 - 3.17609e13i) q^{12} -1.00107e14 q^{13} +(2.94764e14 - 2.53743e14i) q^{14} -3.36342e14 q^{15} +(-1.24740e15 - 2.16057e15i) q^{16} +(2.41453e14 - 4.18208e14i) q^{17} +(3.36201e15 - 5.82318e15i) q^{18} +(-1.70555e15 - 2.95410e15i) q^{19} -5.75915e16 q^{20} +(-1.59977e16 - 5.59513e15i) q^{21} +2.00764e17 q^{22} +(4.05802e16 + 7.02869e16i) q^{23} +(-1.12289e17 + 1.94491e17i) q^{24} +(-1.15076e17 + 1.99317e17i) q^{25} +(5.31602e17 + 9.20761e17i) q^{26} -6.85124e17 q^{27} +(-2.73928e18 - 9.58050e17i) q^{28} +1.97993e17 q^{29} +(1.78609e18 + 3.09360e18i) q^{30} +(3.16780e18 - 5.48679e18i) q^{31} +(-5.10694e18 + 8.84549e18i) q^{32} +(-4.37416e18 - 7.57626e18i) q^{33} -5.12879e18 q^{34} +(-2.01702e19 + 1.73632e19i) q^{35} -5.01703e19 q^{36} +(2.17498e19 + 3.76718e19i) q^{37} +(-1.81141e19 + 3.13745e19i) q^{38} +(2.31646e19 - 4.01223e19i) q^{39} +(1.76333e20 + 3.05419e20i) q^{40} +3.51736e19 q^{41} +(3.34907e19 + 1.76856e20i) q^{42} +1.02055e20 q^{43} +(-7.48984e20 - 1.29728e21i) q^{44} +(-2.30057e20 + 3.98470e20i) q^{45} +(4.30990e20 - 7.46496e20i) q^{46} +(-3.11095e20 - 5.38832e20i) q^{47} +1.15459e21 q^{48} +(-1.24822e21 + 4.90326e20i) q^{49} +2.44437e21 q^{50} +(1.11744e20 + 1.93546e20i) q^{51} +(3.96647e21 - 6.87012e21i) q^{52} +(1.37591e20 - 2.38315e20i) q^{53} +(3.63825e21 + 6.30163e21i) q^{54} -1.37379e22 q^{55} +(3.30641e21 + 1.74603e22i) q^{56} +1.57865e21 q^{57} +(-1.05141e21 - 1.82110e21i) q^{58} +(7.26563e21 - 1.25844e22i) q^{59} +(1.33266e22 - 2.30824e22i) q^{60} +(1.03013e22 + 1.78423e22i) q^{61} -6.72885e22 q^{62} +(-1.75711e22 + 1.51258e22i) q^{63} +2.47667e22 q^{64} +(-3.63766e22 - 6.30062e22i) q^{65} +(-4.64566e22 + 8.04651e22i) q^{66} +(1.90339e21 - 3.29678e21i) q^{67} +(1.91338e22 + 3.31408e22i) q^{68} -3.75609e22 q^{69} +(2.66814e23 + 9.33168e22i) q^{70} -1.80688e23 q^{71} +(1.53611e23 + 2.66062e23i) q^{72} +(-2.11158e22 + 3.65736e22i) q^{73} +(2.30998e23 - 4.00100e23i) q^{74} +(-5.32568e22 - 9.22435e22i) q^{75} +2.70311e23 q^{76} +(-6.53431e23 - 2.28534e23i) q^{77} -4.92049e23 q^{78} +(1.31966e23 + 2.28571e23i) q^{79} +(9.06558e23 - 1.57020e24i) q^{80} +(-1.09675e23 + 1.89962e23i) q^{81} +(-1.86784e23 - 3.23519e23i) q^{82} +5.25223e23 q^{83} +(1.01785e24 - 8.76199e23i) q^{84} +3.50954e23 q^{85} +(-5.41949e23 - 9.38683e23i) q^{86} +(-4.58154e22 + 7.93546e22i) q^{87} +(-4.58647e24 + 7.94400e24i) q^{88} +(1.03378e24 + 1.79056e24i) q^{89} +4.88673e24 q^{90} +(-6.82093e23 - 3.60196e24i) q^{91} -6.43153e24 q^{92} +(1.46605e24 + 2.53928e24i) q^{93} +(-3.30404e24 + 5.72276e24i) q^{94} +(1.23952e24 - 2.14691e24i) q^{95} +(-2.36349e24 - 4.09368e24i) q^{96} +6.63668e24 q^{97} +(1.11384e25 + 8.87703e24i) q^{98} -1.19677e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4050 q^{2} + 531440 q^{3} - 286295596 q^{4} + 288173088 q^{5} - 13063290884 q^{6} - 55218840880 q^{7} + 274366746720 q^{8} - 5146896583216 q^{9}+O(q^{10}) \) 32 * q - 4050 * q^2 + 531440 * q^3 - 286295596 * q^4 + 288173088 * q^5 - 13063290884 * q^6 - 55218840880 * q^7 + 274366746720 * q^8 - 5146896583216 * q^9	\( 32 q - 4050 q^{2} + 531440 q^{3} - 286295596 q^{4} + 288173088 q^{5} - 13063290884 q^{6} - 55218840880 q^{7} + 274366746720 q^{8} - 5146896583216 q^{9} - 918803280822 q^{10} + 253661467680 q^{11} + 59498382182260 q^{12} + 136259290951840 q^{13} + 669930284417310 q^{14} - 28\!\cdots\!16 q^{15}+ \cdots + 42\!\cdots\!56 q^{99}+O(q^{100}) \) 32 * q - 4050 * q^2 + 531440 * q^3 - 286295596 * q^4 + 288173088 * q^5 - 13063290884 * q^6 - 55218840880 * q^7 + 274366746720 * q^8 - 5146896583216 * q^9 - 918803280822 * q^10 + 253661467680 * q^11 + 59498382182260 * q^12 + 136259290951840 * q^13 + 669930284417310 * q^14 - 2808664429278016 * q^15 - 5327562569765872 * q^16 + 5022112861130400 * q^17 + 1957025270033980 * q^18 + 10588631642557696 * q^19 + 24731206489166184 * q^20 + 8085415409820784 * q^21 - 189302943512898660 * q^22 + 20610047702550960 * q^23 + 573793671932159616 * q^24 - 958211520923613472 * q^25 + 2724774668939531124 * q^26 - 2206109587432690240 * q^27 + 9458322343110556580 * q^28 - 8689264986101232672 * q^29 - 2619504629356224458 * q^30 + 10841379318391039264 * q^31 + 6763645131553838880 * q^32 - 11546953084647657040 * q^33 + 13082632789597647612 * q^34 - 65806476706321130304 * q^35 + 282452039645146513456 * q^36 + 29321738000603330320 * q^37 - 70525127026788123690 * q^38 + 25840220465930531024 * q^39 - 85110519871079993136 * q^40 - 330540029228046240288 * q^41 + 315672536170051901120 * q^42 + 431015165468582915200 * q^43 - 879888416642398340460 * q^44 + 485170985786336771600 * q^45 + 1667203425207259516686 * q^46 + 2014371898465936816800 * q^47 - 11662563919658426657120 * q^48 + 1488998457641379674528 * q^49 - 1672792512944596205616 * q^50 - 7525441297042267778496 * q^51 + 6992249387859106251160 * q^52 + 8918984691607286334960 * q^53 + 34981309708344282421726 * q^54 - 65886425153156913843552 * q^55 - 6796685514980676446208 * q^56 + 56688134325496104699680 * q^57 - 26386021221286483940940 * q^58 - 10935316261765587024144 * q^59 + 139984946157807148568716 * q^60 - 17484129051186787701488 * q^61 - 262788504919801688816100 * q^62 - 63958098944828837939120 * q^63 + 331619102526249229604096 * q^64 - 60109967964600925224336 * q^65 + 61498292814044614748374 * q^66 + 218997561331718103994960 * q^67 + 482184105822238591781100 * q^68 - 815717958910888805206848 * q^69 + 590837748017767784846550 * q^70 - 556118852555986042838976 * q^71 - 332574755512105623952800 * q^72 + 181923789786333620742640 * q^73 - 788377165482644151934950 * q^74 - 66014699727433523602592 * q^75 + 1262772869625204941438344 * q^76 - 101350576550797077490560 * q^77 + 311390952582194080319080 * q^78 + 438039985868556642949360 * q^79 - 1229118480867135510718416 * q^80 - 738103636463171961601504 * q^81 - 4913051673767471255932260 * q^82 + 4355401847600512595234880 * q^83 - 4660353883629012393074068 * q^84 - 505677682638035696807712 * q^85 + 5848093469680723949747688 * q^86 - 2195492958449506107537040 * q^87 - 10064215655338142337197760 * q^88 + 449697822243925695740496 * q^89 + 41750741714541116033274904 * q^90 + 4132471530877362173570272 * q^91 - 18512115732486299505457080 * q^92 - 2539354660954665131215920 * q^93 - 1689612490320614160295890 * q^94 - 2244103526711501036678160 * q^95 - 3851732620967552391601888 * q^96 - 17074074602311685528685920 * q^97 + 12285904054220374515545790 * q^98 + 4273620815399973239951456 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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