LMFDB - Embedded newform 91.10.q.a.36.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, 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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$124$
Relative dimension:	$62$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.4
Character	$\chi$	$=$	91.36
Dual form			91.10.q.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-35.5029 + 20.4976i) q^{2} +(54.8657 + 95.0301i) q^{3} +(584.302 - 1012.04i) q^{4} +455.216i q^{5} +(-3895.78 - 2249.23i) q^{6} +(2079.33 + 1200.50i) q^{7} +26917.6i q^{8} +(3821.02 - 6618.20i) q^{9} +O(q^{10})$	\(q+(-35.5029 + 20.4976i) q^{2} +(54.8657 + 95.0301i) q^{3} +(584.302 - 1012.04i) q^{4} +455.216i q^{5} +(-3895.78 - 2249.23i) q^{6} +(2079.33 + 1200.50i) q^{7} +26917.6i q^{8} +(3821.02 - 6618.20i) q^{9} +(-9330.84 - 16161.5i) q^{10} +(11974.0 - 6913.22i) q^{11} +128233. q^{12} +(-82166.0 - 62074.5i) q^{13} -98429.4 q^{14} +(-43259.3 + 24975.7i) q^{15} +(-252584. - 437488. i) q^{16} +(-41239.0 + 71428.1i) q^{17} +313287. i q^{18} +(-936141. - 540482. i) q^{19} +(460698. + 265984. i) q^{20} +263465. i q^{21} +(-283409. + 490878. i) q^{22} +(-301927. - 522953. i) q^{23} +(-2.55799e6 + 1.47685e6i) q^{24} +1.74590e6 q^{25} +(4.18951e6 + 519618. i) q^{26} +2.99841e6 q^{27} +(2.42991e6 - 1.40291e6i) q^{28} +(3.23127e6 + 5.59672e6i) q^{29} +(1.02389e6 - 1.77342e6i) q^{30} +4.87040e6i q^{31} +(5.99949e6 + 3.46381e6i) q^{32} +(1.31393e6 + 758597. i) q^{33} -3.38120e6i q^{34} +(-546487. + 946544. i) q^{35} +(-4.46526e6 - 7.73406e6i) q^{36} +(1.24097e7 - 7.16472e6i) q^{37} +4.43143e7 q^{38} +(1.39086e6 - 1.12140e7i) q^{39} -1.22533e7 q^{40} +(4.84399e6 - 2.79668e6i) q^{41} +(-5.40040e6 - 9.35376e6i) q^{42} +(-5.88562e6 + 1.01942e7i) q^{43} -1.61576e7i q^{44} +(3.01271e6 + 1.73939e6i) q^{45} +(2.14386e7 + 1.23776e7i) q^{46} +5.34680e7i q^{47} +(2.77164e7 - 4.80062e7i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(-6.19846e7 + 3.57868e7i) q^{50} -9.05043e6 q^{51} +(-1.10832e8 + 4.68851e7i) q^{52} +8.06196e7 q^{53} +(-1.06452e8 + 6.14602e7i) q^{54} +(3.14701e6 + 5.45078e6i) q^{55} +(-3.23146e7 + 5.59706e7i) q^{56} -1.18616e8i q^{57} +(-2.29439e8 - 1.32466e8i) q^{58} +(3.36049e6 + 1.94018e6i) q^{59} +5.83736e7i q^{60} +(-9.64257e7 + 1.67014e8i) q^{61} +(-9.98314e7 - 1.72913e8i) q^{62} +(1.58903e7 - 9.17426e6i) q^{63} -2.53529e7 q^{64} +(2.82573e7 - 3.74033e7i) q^{65} -6.21976e7 q^{66} +(-1.81216e7 + 1.04625e7i) q^{67} +(4.81921e7 + 8.34712e7i) q^{68} +(3.31309e7 - 5.73843e7i) q^{69} -4.48067e7i q^{70} +(-1.85679e8 - 1.07202e8i) q^{71} +(1.78146e8 + 1.02853e8i) q^{72} +2.14646e8i q^{73} +(-2.93719e8 + 5.08736e8i) q^{74} +(9.57901e7 + 1.65913e8i) q^{75} +(-1.09398e9 + 6.31609e8i) q^{76} +3.31973e7 q^{77} +(1.80481e8 + 4.26639e8i) q^{78} +4.84095e8 q^{79} +(1.99152e8 - 1.14980e8i) q^{80} +(8.93008e7 + 1.54674e8i) q^{81} +(-1.14650e8 + 1.98580e8i) q^{82} -3.85707e8i q^{83} +(2.66637e8 + 1.53943e8i) q^{84} +(-3.25152e7 - 1.87727e7i) q^{85} -4.82564e8i q^{86} +(-3.54572e8 + 6.14136e8i) q^{87} +(1.86087e8 + 3.22313e8i) q^{88} +(-3.64684e7 + 2.10551e7i) q^{89} -1.42613e8 q^{90} +(-9.63295e7 - 2.27714e8i) q^{91} -7.05667e8 q^{92} +(-4.62834e8 + 2.67217e8i) q^{93} +(-1.09596e9 - 1.89827e9i) q^{94} +(2.46036e8 - 4.26147e8i) q^{95} +7.60176e8i q^{96} +(-9.63525e8 - 5.56291e8i) q^{97} +(-2.04667e8 - 1.18165e8i) q^{98} -1.05662e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9}+O(q^{10}) $ 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9	\( 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9} - 47368 q^{10} + 18420 q^{11} + 434316 q^{12} - 103730 q^{13} - 307328 q^{14} - 994308 q^{15} - 4327304 q^{16} + 826226 q^{17} - 832512 q^{20} - 2238874 q^{22} - 5178348 q^{23} + 13060272 q^{24} - 56263016 q^{25} + 12486810 q^{26} - 16794384 q^{27} + 8409710 q^{29} - 18091000 q^{30} + 30354048 q^{32} + 36508140 q^{33} + 8902908 q^{35} + 42350446 q^{36} + 26865678 q^{37} - 7473860 q^{38} - 21470652 q^{39} - 112860988 q^{40} - 109829778 q^{41} + 12446784 q^{42} - 53384856 q^{43} - 84576450 q^{45} + 160042176 q^{46} - 39524126 q^{48} + 357417662 q^{49} + 35767422 q^{50} + 121877584 q^{51} + 61751010 q^{52} - 252868460 q^{53} + 951692088 q^{54} - 414833028 q^{55} - 118013952 q^{56} - 342666540 q^{58} - 440088588 q^{59} + 264060146 q^{61} + 995887736 q^{62} - 383747028 q^{63} - 2239569444 q^{64} - 501903354 q^{65} + 304284804 q^{66} + 392937636 q^{67} - 3665660 q^{68} - 249969892 q^{69} - 375620748 q^{71} - 2829560808 q^{72} + 1336479018 q^{74} + 1306893216 q^{75} + 1652559990 q^{76} + 823754288 q^{77} + 857091302 q^{78} - 2357982776 q^{79} + 1107773136 q^{80} - 1492992434 q^{81} - 1984241462 q^{82} - 2156016366 q^{84} + 3060837654 q^{85} - 1286987624 q^{87} + 1904443442 q^{88} + 887446752 q^{89} + 7601525656 q^{90} - 86522436 q^{91} - 8365653336 q^{92} - 776657196 q^{93} + 6270763420 q^{94} - 6325568332 q^{95} - 5522676732 q^{97}+O(q^{100}) \) 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9 - 47368 * q^10 + 18420 * q^11 + 434316 * q^12 - 103730 * q^13 - 307328 * q^14 - 994308 * q^15 - 4327304 * q^16 + 826226 * q^17 - 832512 * q^20 - 2238874 * q^22 - 5178348 * q^23 + 13060272 * q^24 - 56263016 * q^25 + 12486810 * q^26 - 16794384 * q^27 + 8409710 * q^29 - 18091000 * q^30 + 30354048 * q^32 + 36508140 * q^33 + 8902908 * q^35 + 42350446 * q^36 + 26865678 * q^37 - 7473860 * q^38 - 21470652 * q^39 - 112860988 * q^40 - 109829778 * q^41 + 12446784 * q^42 - 53384856 * q^43 - 84576450 * q^45 + 160042176 * q^46 - 39524126 * q^48 + 357417662 * q^49 + 35767422 * q^50 + 121877584 * q^51 + 61751010 * q^52 - 252868460 * q^53 + 951692088 * q^54 - 414833028 * q^55 - 118013952 * q^56 - 342666540 * q^58 - 440088588 * q^59 + 264060146 * q^61 + 995887736 * q^62 - 383747028 * q^63 - 2239569444 * q^64 - 501903354 * q^65 + 304284804 * q^66 + 392937636 * q^67 - 3665660 * q^68 - 249969892 * q^69 - 375620748 * q^71 - 2829560808 * q^72 + 1336479018 * q^74 + 1306893216 * q^75 + 1652559990 * q^76 + 823754288 * q^77 + 857091302 * q^78 - 2357982776 * q^79 + 1107773136 * q^80 - 1492992434 * q^81 - 1984241462 * q^82 - 2156016366 * q^84 + 3060837654 * q^85 - 1286987624 * q^87 + 1904443442 * q^88 + 887446752 * q^89 + 7601525656 * q^90 - 86522436 * q^91 - 8365653336 * q^92 - 776657196 * q^93 + 6270763420 * q^94 - 6325568332 * q^95 - 5522676732 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−35.5029	+	20.4976i	−1.56902	+	0.905874i	−0.572736	+	0.819740i	$0.694118\pi$
$2$	−35.5029	+	20.4976i	−1.56902	+	0.905874i	−0.996284	+	0.0861345i	$0.972549\pi$
$3$	54.8657	+	95.0301i	0.391070	+	0.677354i	0.992591	−	0.121503i	$-0.0387715\pi$
$3$	54.8657	+	95.0301i	0.391070	+	0.677354i	−0.601521	+	0.798857i	$0.705438\pi$
$4$	584.302	−	1012.04i	1.14122	−	1.97664i
$5$			455.216i			0.325726i	0.986649	+	0.162863i	$0.0520729\pi$
$5$			455.216i			0.325726i	−0.986649	+	0.162863i	$0.947927\pi$
$6$	−3895.78	−	2249.23i	−1.22719	−	0.708521i
$7$	2079.33	+	1200.50i	0.327327	+	0.188982i
$7$	2079.33	+	1200.50i	0.327327	+	0.188982i
$8$			26917.6i			2.32344i
$9$	3821.02	−	6618.20i	0.194128	−	0.336239i
$10$	−9330.84	−	16161.5i	−0.295067	−	0.511071i
$11$	11974.0	−	6913.22i	0.246589	−	0.142368i	−0.371612	−	0.928388i	$-0.621195\pi$
$11$	11974.0	−	6913.22i	0.246589	−	0.142368i	0.618201	+	0.786020i	$0.287862\pi$
$12$	128233.			1.78518
$13$	−82166.0	−	62074.5i	−0.797898	−	0.602793i
$13$	−82166.0	−	62074.5i	−0.797898	−	0.602793i
$14$	−98429.4			−0.684776
$15$	−43259.3	+	24975.7i	−0.220632	+	0.127382i
$16$	−252584.	−	437488.i	−0.963531	−	1.66888i
$17$	−41239.0	+	71428.1i	−0.119754	+	0.207419i	−0.919670	−	0.392692i	$-0.871544\pi$
$17$	−41239.0	+	71428.1i	−0.119754	+	0.207419i	0.799916	+	0.600111i	$0.204877\pi$
$18$			313287.i			0.703421i
$19$	−936141.	−	540482.i	−1.64797	−	0.951458i	−0.977876	−	0.209185i	$-0.932919\pi$
$19$	−936141.	−	540482.i	−1.64797	−	0.951458i	−0.670098	−	0.742273i	$-0.733748\pi$
$20$	460698.	+	265984.i	0.643845	+	0.371724i
$21$			263465.i			0.295621i
$22$	−283409.	+	490878.i	−0.257935	+	0.446757i
$23$	−301927.	−	522953.i	−0.224971	−	0.389661i	0.731340	−	0.682013i	$-0.238895\pi$
$23$	−301927.	−	522953.i	−0.224971	−	0.389661i	−0.956311	+	0.292352i	$0.905562\pi$
$24$	−2.55799e6	+	1.47685e6i	−1.57379	+	0.908630i
$25$	1.74590e6			0.893902
$26$	4.18951e6	+	519618.i	1.79797	+	0.223000i
$27$	2.99841e6			1.08581
$28$	2.42991e6	−	1.40291e6i	0.747101	−	0.431339i
$29$	3.23127e6	+	5.59672e6i	0.848364	+	1.46941i	0.882668	+	0.469998i	$0.155745\pi$
$29$	3.23127e6	+	5.59672e6i	0.848364	+	1.46941i	−0.0343036	+	0.999411i	$0.510921\pi$
$30$	1.02389e6	−	1.77342e6i	0.230784	−	0.399730i
$31$			4.87040e6i			0.947189i	0.880743	+	0.473594i	$0.157044\pi$
$31$			4.87040e6i			0.947189i	−0.880743	+	0.473594i	$0.842956\pi$
$32$	5.99949e6	+	3.46381e6i	1.01144	+	0.583954i
$33$	1.31393e6	+	758597.i	0.192867	+	0.111352i
$34$		−	3.38120e6i		−	0.433926i
$35$	−546487.	+	946544.i	−0.0615565	+	0.106619i
$36$	−4.46526e6	−	7.73406e6i	−0.443083	−	0.767443i
$37$	1.24097e7	−	7.16472e6i	1.08856	−	0.628480i	0.155367	−	0.987857i	$-0.450344\pi$
$37$	1.24097e7	−	7.16472e6i	1.08856	−	0.628480i	0.933193	+	0.359377i	$0.117011\pi$
$38$	4.43143e7			3.44760
$39$	1.39086e6	−	1.12140e7i	0.0962701	−	0.776194i
$40$	−1.22533e7			−0.756806
$41$	4.84399e6	−	2.79668e6i	0.267717	−	0.154566i	−0.360133	−	0.932901i	$-0.617269\pi$
$41$	4.84399e6	−	2.79668e6i	0.267717	−	0.154566i	0.627850	+	0.778335i	$0.283935\pi$
$42$	−5.40040e6	−	9.35376e6i	−0.267796	−	0.463836i
$43$	−5.88562e6	+	1.01942e7i	−0.262533	+	0.454721i	−0.966914	−	0.255101i	$-0.917891\pi$
$43$	−5.88562e6	+	1.01942e7i	−0.262533	+	0.454721i	0.704381	+	0.709822i	$0.251225\pi$
$44$		−	1.61576e7i		−	0.649892i
$45$	3.01271e6	+	1.73939e6i	0.109522	+	0.0632325i
$46$	2.14386e7	+	1.23776e7i	0.705968	+	0.407591i
$47$			5.34680e7i			1.59828i	0.601144	+	0.799141i	$0.294712\pi$
$47$			5.34680e7i			1.59828i	−0.601144	+	0.799141i	$0.705288\pi$
$48$	2.77164e7	−	4.80062e7i	0.753617	−	1.30530i
$49$	2.88240e6	+	4.99246e6i	0.0714286	+	0.123718i
$50$	−6.19846e7	+	3.57868e7i	−1.40255	+	0.809763i
$51$	−9.05043e6			−0.187328
$52$	−1.10832e8	+	4.68851e7i	−2.10208	+	0.889242i
$53$	8.06196e7			1.40346			0.701729	−	0.712444i	$-0.252412\pi$
$53$	8.06196e7			1.40346			0.701729	+	0.712444i	$0.252412\pi$
$54$	−1.06452e8	+	6.14602e7i	−1.70366	+	0.983609i
$55$	3.14701e6	+	5.45078e6i	0.0463731	+	0.0803205i
$56$	−3.23146e7	+	5.59706e7i	−0.439089	+	0.760525i
$57$		−	1.18616e8i		−	1.48835i
$58$	−2.29439e8	−	1.32466e8i	−2.66220	−	1.53702i
$59$	3.36049e6	+	1.94018e6i	0.0361051	+	0.0208453i	0.517944	−	0.855415i	$-0.326698\pi$
$59$	3.36049e6	+	1.94018e6i	0.0361051	+	0.0208453i	−0.481839	+	0.876260i	$0.660031\pi$
$60$			5.83736e7i			0.581481i
$61$	−9.64257e7	+	1.67014e8i	−0.891679	+	1.54443i	−0.0538179	+	0.998551i	$0.517139\pi$
$61$	−9.64257e7	+	1.67014e8i	−0.891679	+	1.54443i	−0.837861	+	0.545883i	$0.816194\pi$
$62$	−9.98314e7	−	1.72913e8i	−0.858034	−	1.48616i
$63$	1.58903e7	−	9.17426e6i	0.127086	−	0.0733734i
$64$	−2.53529e7			−0.188894
$65$	2.82573e7	−	3.74033e7i	0.196346	−	0.259896i
$66$	−6.21976e7			−0.403484
$67$	−1.81216e7	+	1.04625e7i	−0.109865	+	0.0634305i	−0.553926	−	0.832566i	$-0.686871\pi$
$67$	−1.81216e7	+	1.04625e7i	−0.109865	+	0.0634305i	0.444061	+	0.895997i	$0.353537\pi$
$68$	4.81921e7	+	8.34712e7i	0.273329	+	0.473420i
$69$	3.31309e7	−	5.73843e7i	0.175959	−	0.304770i
$70$		−	4.48067e7i		−	0.223050i
$71$	−1.85679e8	−	1.07202e8i	−0.867162	−	0.500656i	−0.000757583	−	1.00000i	$-0.500241\pi$
$71$	−1.85679e8	−	1.07202e8i	−0.867162	−	0.500656i	−0.866404	+	0.499344i	$0.833574\pi$
$72$	1.78146e8	+	1.02853e8i	0.781233	+	0.451045i
$73$			2.14646e8i			0.884646i	0.896856	+	0.442323i	$0.145846\pi$
$73$			2.14646e8i			0.884646i	−0.896856	+	0.442323i	$0.854154\pi$
$74$	−2.93719e8	+	5.08736e8i	−1.13865	+	1.97220i
$75$	9.57901e7	+	1.65913e8i	0.349579	+	0.605488i
$76$	−1.09398e9	+	6.31609e8i	−3.76139	+	2.17164i
$77$	3.31973e7			0.107620
$78$	1.80481e8	+	4.26639e8i	0.552084	+	1.30507i
$79$	4.84095e8			1.39833			0.699164	−	0.714961i	$-0.253556\pi$
$79$	4.84095e8			1.39833			0.699164	+	0.714961i	$0.253556\pi$
$80$	1.99152e8	−	1.14980e8i	0.543600	−	0.313847i
$81$	8.93008e7	+	1.54674e8i	0.230501	+	0.399239i
$82$	−1.14650e8	+	1.98580e8i	−0.280035	+	0.485035i
$83$		−	3.85707e8i		−	0.892086i	−0.895012	−	0.446043i	$-0.852833\pi$
$83$		−	3.85707e8i		−	0.892086i	0.895012	−	0.446043i	$-0.147167\pi$
$84$	2.66637e8	+	1.53943e8i	0.584338	+	0.337368i
$85$	−3.25152e7	−	1.87727e7i	−0.0675619	−	0.0390069i
$86$		−	4.82564e8i		−	0.951288i
$87$	−3.54572e8	+	6.14136e8i	−0.663540	+	1.14929i
$88$	1.86087e8	+	3.22313e8i	0.330785	+	0.572936i
$89$	−3.64684e7	+	2.10551e7i	−0.0616115	+	0.0355714i	−0.530489	−	0.847692i	$-0.677992\pi$
$89$	−3.64684e7	+	2.10551e7i	−0.0616115	+	0.0355714i	0.468878	+	0.883263i	$0.344658\pi$
$90$	−1.42613e8			−0.229123
$91$	−9.63295e7	−	2.27714e8i	−0.147256	−	0.348099i
$92$	−7.05667e8			−1.02696
$93$	−4.62834e8	+	2.67217e8i	−0.641582	+	0.370418i
$94$	−1.09596e9	−	1.89827e9i	−1.44784	−	2.50774i
$95$	2.46036e8	−	4.26147e8i	0.309915	−	0.536788i
$96$			7.60176e8i			0.913469i
$97$	−9.63525e8	−	5.56291e8i	−1.10507	−	0.638013i	−0.167523	−	0.985868i	$-0.553577\pi$
$97$	−9.63525e8	−	5.56291e8i	−1.10507	−	0.638013i	−0.937548	+	0.347855i	$0.886910\pi$
$98$	−2.04667e8	−	1.18165e8i	−0.224146	−	0.129411i
$99$		−	1.05662e8i		−	0.110551i
$100$	1.02014e9	−	1.76693e9i	1.02014	−	1.76693i
$101$	1.23366e8	+	2.13676e8i	0.117964	+	0.204319i	0.918961	−	0.394349i	$-0.129030\pi$
$101$	1.23366e8	+	2.13676e8i	0.117964	+	0.204319i	−0.800997	+	0.598669i	$0.795697\pi$
$102$	3.21316e8	−	1.85512e8i	0.293922	−	0.169696i
$103$	2.23405e8			0.195580			0.0977902	−	0.995207i	$-0.468823\pi$
$103$	2.23405e8			0.195580			0.0977902	+	0.995207i	$0.468823\pi$
$104$	1.67090e9	−	2.21172e9i	1.40056	−	1.85387i
$105$	−1.19934e8			−0.0962917
$106$	−2.86223e9	+	1.65251e9i	−2.20205	+	1.27136i
$107$	7.19447e8	+	1.24612e9i	0.530606	+	0.919036i	0.999362	+	0.0357086i	$0.0113688\pi$
$107$	7.19447e8	+	1.24612e9i	0.530606	+	0.919036i	−0.468757	+	0.883327i	$0.655298\pi$
$108$	1.75198e9	−	3.03452e9i	1.23915	−	2.14626i
$109$			2.48258e9i			1.68455i	0.539047	+	0.842276i	$0.318785\pi$
$109$			2.48258e9i			1.68455i	−0.539047	+	0.842276i	$0.681215\pi$
$110$	−2.23456e8	−	1.29012e8i	−0.145521	−	0.0840163i
$111$	1.36173e9	+	7.86194e8i	0.851407	+	0.491560i
$112$		−	1.21291e9i		−	0.728361i
$113$	6.33933e8	−	1.09800e9i	0.365755	−	0.633506i	−0.623142	−	0.782109i	$-0.714144\pi$
$113$	6.33933e8	−	1.09800e9i	0.365755	−	0.633506i	0.988897	+	0.148602i	$0.0474775\pi$
$114$	2.43133e9	+	4.21119e9i	1.34826	+	2.33525i
$115$	2.38057e8	−	1.37442e8i	0.126923	−	0.0732790i
$116$	7.55216e9			3.87267
$117$	−7.24779e8	+	3.06603e8i	−0.357577	+	0.151266i
$118$	−1.59076e8			−0.0755329
$119$	−1.71499e8	+	9.90149e7i	−0.0783971	+	0.0452626i
$120$	−6.72288e8	−	1.16444e9i	−0.295965	−	0.512626i
$121$	−1.08339e9	+	1.87648e9i	−0.459463	+	0.795813i
$122$		−	7.90598e9i		−	3.23100i
$123$	5.31537e8	+	3.06883e8i	0.209392	+	0.120893i
$124$	4.92904e9	+	2.84578e9i	1.87225	+	1.08095i
$125$			1.68386e9i			0.616894i
$126$	−3.76101e8	+	6.51425e8i	−0.132934	+	0.230249i
$127$	−1.31343e7	−	2.27493e7i	−0.00448013	−	0.00775981i	0.863777	−	0.503875i	$-0.168093\pi$
$127$	−1.31343e7	−	2.27493e7i	−0.00448013	−	0.00775981i	−0.868257	+	0.496115i	$0.834759\pi$
$128$	−2.17164e9	+	1.25380e9i	−0.715060	+	0.412840i
$129$	−1.29167e9			−0.410676
$130$	−2.36539e8	+	1.90713e9i	−0.0726369	+	0.585647i
$131$	8.00771e8			0.237568			0.118784	−	0.992920i	$-0.462100\pi$
$131$	8.00771e8			0.237568			0.118784	+	0.992920i	$0.462100\pi$
$132$	1.53546e9	−	8.86500e8i	0.440207	−	0.254153i
$133$	−1.29770e9	−	2.24768e9i	−0.359617	−	0.622875i
$134$	4.28912e8	−	7.42897e8i	0.114920	−	0.199048i
$135$			1.36493e9i			0.353677i
$136$	−1.92268e9	−	1.11006e9i	−0.481927	−	0.278240i
$137$	2.79852e9	+	1.61573e9i	0.678713	+	0.391855i	0.799370	−	0.600839i	$-0.205167\pi$
$137$	2.79852e9	+	1.61573e9i	0.678713	+	0.391855i	−0.120657	+	0.992694i	$0.538500\pi$
$138$			2.71641e9i			0.637587i
$139$	−1.67857e9	+	2.90736e9i	−0.381392	+	0.660591i	−0.991262	−	0.131911i	$-0.957889\pi$
$139$	−1.67857e9	+	2.90736e9i	−0.381392	+	0.660591i	0.609869	+	0.792502i	$0.291222\pi$
$140$	6.38628e8	+	1.10614e9i	0.140498	+	0.243350i
$141$	−5.08107e9	+	2.93355e9i	−1.08260	+	0.625041i
$142$	8.78951e9			1.81413
$143$	−1.41299e9	−	1.75252e8i	−0.282571	−	0.0350469i
$144$	−3.86051e9			−0.748193
$145$	−2.54772e9	+	1.47093e9i	−0.478625	+	0.276334i
$146$	−4.39972e9	−	7.62054e9i	−0.801378	−	1.38803i
$147$	−3.16290e8	+	5.47830e8i	−0.0558672	+	0.0967648i
$148$		−	1.67455e10i		−	2.86893i
$149$	7.36626e9	+	4.25291e9i	1.22436	+	0.706884i	0.965844	−	0.259123i	$-0.0834335\pi$
$149$	7.36626e9	+	4.25291e9i	1.22436	+	0.706884i	0.258515	+	0.966007i	$0.416767\pi$
$150$	−6.80165e9	−	3.92693e9i	−1.09699	−	0.633349i
$151$			6.67311e9i			1.04456i	0.852775	+	0.522278i	$0.174918\pi$
$151$			6.67311e9i			1.04456i	−0.852775	+	0.522278i	$0.825082\pi$
$152$	1.45485e10	−	2.51987e10i	2.21066	−	3.82897i
$153$	3.15150e8	+	5.45856e8i	0.0464950	+	0.0805316i
$154$	−1.17860e9	+	6.80464e8i	−0.168858	+	0.0974904i
$155$	−2.21708e9			−0.308524
$156$	−1.05364e10	−	7.95998e9i	−1.42439	−	1.07610i
$157$	−4.23310e9			−0.556045			−0.278023	−	0.960575i	$-0.589679\pi$
$157$	−4.23310e9			−0.556045			−0.278023	+	0.960575i	$0.589679\pi$
$158$	−1.71868e10	+	9.92279e9i	−2.19400	+	1.26671i
$159$	4.42325e9	+	7.66129e9i	0.548851	+	0.950637i
$160$	−1.57678e9	+	2.73107e9i	−0.190209	+	0.329452i
$161$		−	1.44985e9i		−	0.170062i
$162$	−6.34087e9	−	3.66090e9i	−0.723321	−	0.417610i
$163$	−6.10006e9	−	3.52187e9i	−0.676846	−	0.390777i	0.121820	−	0.992552i	$-0.461127\pi$
$163$	−6.10006e9	−	3.52187e9i	−0.676846	−	0.390777i	−0.798666	+	0.601775i	$0.794460\pi$
$164$		−	6.53642e9i		−	0.705574i
$165$	−3.45326e8	+	5.98121e8i	−0.0362703	+	0.0628220i
$166$	7.90607e9	+	1.36937e10i	0.808117	+	1.39970i
$167$	−3.84139e9	+	2.21783e9i	−0.382177	+	0.220650i	−0.678765	−	0.734356i	$-0.737484\pi$
$167$	−3.84139e9	+	2.21783e9i	−0.382177	+	0.220650i	0.296588	+	0.955005i	$0.404151\pi$
$168$	−7.09185e9			−0.686860
$169$	2.89801e9	+	1.02008e10i	0.273281	+	0.961934i
$170$	1.53918e9			0.141341
$171$	−7.15402e9	+	4.13038e9i	−0.639835	+	0.369409i
$172$	6.87796e9	+	1.19130e10i	0.599214	+	1.03787i
$173$	3.58090e9	−	6.20230e9i	0.303938	−	0.526436i	−0.673086	−	0.739564i	$-0.735032\pi$
$173$	3.58090e9	−	6.20230e9i	0.303938	−	0.526436i	0.977024	+	0.213128i	$0.0683651\pi$
$174$		−	2.90714e10i		−	2.40434i
$175$	3.63030e9	+	2.09596e9i	0.292598	+	0.168932i
$176$	−6.04890e9	−	3.49233e9i	−0.475192	−	0.274352i
$177$			4.25797e8i			0.0326079i
$178$	8.63156e8	−	1.49503e9i	0.0644465	−	0.111625i
$179$	7.90641e8	+	1.36943e9i	0.0575626	+	0.0997014i	0.893371	−	0.449320i	$-0.148334\pi$
$179$	7.90641e8	+	1.36943e9i	0.0575626	+	0.0997014i	−0.835808	+	0.549022i	$0.815000\pi$
$180$	3.52067e9	−	2.03266e9i	0.249976	−	0.144324i
$181$	−2.42479e9			−0.167927			−0.0839634	−	0.996469i	$-0.526758\pi$
$181$	−2.42479e9			−0.167927			−0.0839634	+	0.996469i	$0.526758\pi$
$182$	8.08755e9	+	6.10996e9i	0.546381	+	0.412779i
$183$	−2.11618e10			−1.39484
$184$	1.40767e10	−	8.12716e9i	0.905356	−	0.522708i
$185$	3.26150e9	+	5.64908e9i	0.204712	+	0.354572i
$186$	1.09546e10	−	1.89740e10i	0.671103	−	1.16239i
$187$			1.14038e9i			0.0681964i
$188$	5.41118e10	+	3.12415e10i	3.15923	+	1.82398i
$189$	6.23468e9	+	3.59959e9i	0.355415	+	0.205199i
$190$			2.01726e10i			1.12298i
$191$	1.02732e10	−	1.77936e10i	0.558539	−	0.967418i	−0.439079	−	0.898448i	$-0.644695\pi$
$191$	1.02732e10	−	1.77936e10i	0.558539	−	0.967418i	0.997619	−	0.0689701i	$-0.0219713\pi$
$192$	−1.39100e9	−	2.40929e9i	−0.0738708	−	0.127948i
$193$	−7.59907e9	+	4.38733e9i	−0.394233	+	0.227610i	−0.683993	−	0.729489i	$-0.739758\pi$
$193$	−7.59907e9	+	4.38733e9i	−0.394233	+	0.227610i	0.289760	+	0.957099i	$0.406425\pi$
$194$	4.56105e10			2.31184
$195$	5.10480e9	+	6.33141e8i	0.252827	+	0.0313577i
$196$	6.73678e9			0.326062
$197$	9.04849e9	−	5.22415e9i	0.428034	−	0.247125i	−0.270475	−	0.962727i	$-0.587181\pi$
$197$	9.04849e9	−	5.22415e9i	0.428034	−	0.247125i	0.698509	+	0.715602i	$0.253847\pi$
$198$	2.16582e9	+	3.75131e9i	0.100145	+	0.173456i
$199$	−4.37562e9	+	7.57879e9i	−0.197788	+	0.342579i	−0.947811	−	0.318833i	$-0.896709\pi$
$199$	−4.37562e9	+	7.57879e9i	−0.197788	+	0.342579i	0.750023	+	0.661412i	$0.230043\pi$
$200$			4.69956e10i			2.07693i
$201$	−1.98850e9	−	1.14806e9i	−0.0859299	−	0.0496116i
$202$	−8.75968e9	−	5.05740e9i	−0.370175	−	0.213721i
$203$			1.55166e10i			0.641303i
$204$	−5.28819e9	+	9.15941e9i	−0.213782	+	0.370281i
$205$	1.27309e9	+	2.20506e9i	0.0503463	+	0.0872024i
$206$	−7.93152e9	+	4.57926e9i	−0.306870	+	0.177171i
$207$	−4.61467e9			−0.174693
$208$	−6.40306e9	+	5.16257e10i	−0.237193	+	1.91241i
$209$	−1.49459e10			−0.541830
$210$	4.25798e9	−	2.45835e9i	0.151084	−	0.0872281i
$211$	−1.50307e10	−	2.60340e10i	−0.522046	−	0.904210i	−0.999671	−	0.0256465i	$-0.991836\pi$
$211$	−1.50307e10	−	2.60340e10i	−0.522046	−	0.904210i	0.477625	−	0.878564i	$-0.341498\pi$
$212$	4.71062e10	−	8.15904e10i	1.60165	−	2.77413i
$213$		−	2.35268e10i		−	0.783167i
$214$	−5.10849e10	−	2.94939e10i	−1.66506	−	0.961324i
$215$	−4.64056e9	−	2.67923e9i	−0.148114	−	0.0855139i
$216$			8.07102e10i			2.52282i
$217$	−5.84691e9	+	1.01271e10i	−0.179002	+	0.310040i
$218$	−5.08869e10	−	8.81388e10i	−1.52599	−	2.64310i
$219$	−2.03978e10	+	1.17767e10i	−0.599219	+	0.345959i
$220$	7.35522e9			0.211687
$221$	7.82231e9	−	3.30907e9i	0.220582	−	0.0933126i
$222$	−6.44604e10			−1.78117
$223$	3.53473e10	−	2.04078e10i	0.957160	−	0.552617i	0.0618623	−	0.998085i	$-0.480296\pi$
$223$	3.53473e10	−	2.04078e10i	0.957160	−	0.552617i	0.895298	+	0.445468i	$0.146963\pi$
$224$	8.31660e9	+	1.44048e10i	0.220714	+	0.382288i
$225$	6.67113e9	−	1.15547e10i	0.173531	−	0.300565i
$226$			5.19764e10i			1.32531i
$227$	6.22658e10	+	3.59492e10i	1.55644	+	0.898613i	0.997593	+	0.0693455i	$0.0220911\pi$
$227$	6.22658e10	+	3.59492e10i	1.55644	+	0.898613i	0.558851	+	0.829268i	$0.311242\pi$
$228$	−1.20044e11	−	6.93073e10i	−2.94193	−	1.69853i
$229$			3.79587e10i			0.912118i	0.889949	+	0.456059i	$0.150739\pi$
$229$			3.79587e10i			0.912118i	−0.889949	+	0.456059i	$0.849261\pi$
$230$	−5.63447e9	+	9.75918e9i	−0.132763	+	0.229952i
$231$	1.82139e9	+	3.15474e9i	0.0420871	+	0.0728970i
$232$	−1.50651e11	+	8.69781e10i	−3.41409	+	1.97113i
$233$	−4.06760e10			−0.904142			−0.452071	−	0.891982i	$-0.649315\pi$
$233$	−4.06760e10			−0.904142			−0.452071	+	0.891982i	$0.649315\pi$
$234$	1.94471e10	−	2.57415e10i	0.424018	−	0.561258i
$235$	−2.43395e10			−0.520602
$236$	3.92709e9	−	2.26731e9i	0.0824075	−	0.0475780i
$237$	2.65602e10	+	4.60036e10i	0.546845	+	0.947163i
$238$	4.05913e9	−	7.03063e9i	0.0820044	−	0.142036i
$239$			4.19432e10i			0.831517i	0.909475	+	0.415758i	$0.136484\pi$
$239$			4.19432e10i			0.831517i	−0.909475	+	0.415758i	$0.863516\pi$
$240$	2.18532e10	+	1.26169e10i	0.425172	+	0.245473i
$241$	−8.09052e10	−	4.67106e10i	−1.54490	−	0.891947i	−0.998519	−	0.0544090i	$-0.982673\pi$
$241$	−8.09052e10	−	4.67106e10i	−1.54490	−	0.891947i	−0.546379	−	0.837538i	$-0.683994\pi$
$242$		−	8.88274e10i		−	1.66486i
$243$	1.97098e10	−	3.41383e10i	0.362621	−	0.628079i
$244$	1.12684e11	+	1.95174e11i	2.03520	+	3.52506i
$245$	−2.27265e9	+	1.31212e9i	−0.0402982	+	0.0232662i
$246$	−2.51615e10			−0.438054
$247$	4.33689e10	+	1.02520e11i	0.741382	+	1.75255i
$248$	−1.31100e11			−2.20074
$249$	3.66538e10	−	2.11621e10i	0.604258	−	0.348868i
$250$	−3.45150e10	−	5.97818e10i	−0.558828	−	0.967919i
$251$	4.12973e10	−	7.15291e10i	0.656735	−	1.13750i	−0.324721	−	0.945810i	$-0.605270\pi$
$251$	4.12973e10	−	7.15291e10i	0.656735	−	1.13750i	0.981456	−	0.191688i	$-0.0613963\pi$
$252$		−	2.14422e10i		−	0.334940i
$253$	−7.23058e9	−	4.17458e9i	−0.110951	−	0.0640575i
$254$	9.32611e8	+	5.38443e8i	0.0140588	+	0.00811687i
$255$		−	4.11990e9i		−	0.0610177i
$256$	5.78899e10	−	1.00268e11i	0.842409	−	1.45910i
$257$	−4.93316e9	−	8.54449e9i	−0.0705386	−	0.122176i	0.828599	−	0.559843i	$-0.189138\pi$
$257$	−4.93316e9	−	8.54449e9i	−0.0705386	−	0.122176i	−0.899137	+	0.437666i	$0.855805\pi$
$258$	4.58581e10	−	2.64762e10i	0.644358	−	0.372021i
$259$	3.44050e10			0.475086
$260$	−2.13429e10	−	5.04524e10i	−0.289650	−	0.684703i
$261$	4.93869e10			0.658764
$262$	−2.84297e10	+	1.64139e10i	−0.372749	+	0.215206i
$263$	−7.41596e9	−	1.28448e10i	−0.0955799	−	0.165549i	0.814271	−	0.580485i	$-0.197137\pi$
$263$	−7.41596e9	−	1.28448e10i	−0.0955799	−	0.165549i	−0.909850	+	0.414936i	$0.863804\pi$
$264$	−2.04196e10	+	3.53678e10i	−0.258720	+	0.448116i
$265$			3.66994e10i			0.457143i
$266$	9.21439e10	+	5.31993e10i	1.12849	+	0.651536i
$267$	−4.00173e9	−	2.31040e9i	−0.0481889	−	0.0278219i
$268$			2.44530e10i			0.289552i
$269$	−3.70364e10	+	6.41490e10i	−0.431265	+	0.746972i	−0.996982	−	0.0776267i	$-0.975266\pi$
$269$	−3.70364e10	+	6.41490e10i	−0.431265	+	0.746972i	0.565718	+	0.824599i	$0.308599\pi$
$270$	−2.79777e10	−	4.84588e10i	−0.320387	−	0.554927i
$271$	−2.47750e10	+	1.43038e10i	−0.279031	+	0.161098i	−0.632984	−	0.774165i	$-0.718170\pi$
$271$	−2.47750e10	+	1.43038e10i	−0.279031	+	0.161098i	0.353954	+	0.935263i	$0.384837\pi$
$272$	4.16653e10			0.461545
$273$	1.63545e10	−	2.16479e10i	0.178199	−	0.235876i
$274$	−1.32474e11			−1.41989
$275$	2.09055e10	−	1.20698e10i	0.220427	−	0.127263i
$276$	−3.87169e10	−	6.70596e10i	−0.401615	−	0.695617i
$277$	5.07377e10	−	8.78803e10i	0.517812	−	0.896876i	−0.481974	−	0.876185i	$-0.660080\pi$
$277$	5.07377e10	−	8.78803e10i	0.517812	−	0.896876i	0.999786	−	0.0206906i	$-0.00658649\pi$
$278$		−	1.37626e11i		−	1.38197i
$279$	3.22332e10	+	1.86099e10i	0.318482	+	0.183876i
$280$	−2.54787e10	−	1.47101e10i	−0.247723	−	0.143023i
$281$			1.70240e11i			1.62886i	0.580263	+	0.814429i	$0.302950\pi$
$281$			1.70240e11i			1.62886i	−0.580263	+	0.814429i	$0.697050\pi$
$282$	1.20262e11	−	2.08299e11i	1.13242	−	1.96140i
$283$	−6.00170e8	−	1.03952e9i	−0.00556205	−	0.00963376i	0.863231	−	0.504809i	$-0.168437\pi$
$283$	−6.00170e8	−	1.03952e9i	−0.00556205	−	0.00963376i	−0.868793	+	0.495175i	$0.835104\pi$
$284$	−2.16985e11	+	1.25277e11i	−1.97924	+	1.14271i
$285$	5.39957e10			0.484794
$286$	5.37576e10	−	2.27410e10i	0.475108	−	0.200985i
$287$	1.34296e10			0.116841
$288$	4.58483e10	−	2.64705e10i	0.392697	−	0.226723i
$289$	5.58926e10	+	9.68089e10i	0.471318	+	0.816347i
$290$	6.03009e10	−	1.04444e11i	0.500648	−	0.867148i
$291$		−	1.22085e11i		−	0.998032i
$292$	2.17230e11	+	1.25418e11i	1.74863	+	1.00957i
$293$	−1.58852e11	−	9.17130e10i	−1.25918	−	0.726987i	−0.286264	−	0.958151i	$-0.592413\pi$
$293$	−1.58852e11	−	9.17130e10i	−1.25918	−	0.726987i	−0.972915	+	0.231164i	$0.925747\pi$
$294$		−	2.59327e10i		−	0.202435i
$295$	−8.83202e8	+	1.52975e9i	−0.00678986	+	0.0117604i
$296$	1.92857e11	+	3.34039e11i	1.46024	+	2.52921i
$297$	3.59031e10	−	2.07287e10i	0.267749	−	0.154585i
$298$	−3.48698e11			−2.56139
$299$	−7.65392e9	+	6.17109e10i	−0.0553813	+	0.446521i
$300$	2.23882e11			1.59578
$301$	−2.44763e10	+	1.41314e10i	−0.171868	+	0.0992282i
$302$	−1.36783e11	−	2.36914e11i	−0.946236	−	1.63893i
$303$	−1.35371e10	+	2.34469e10i	−0.0922643	+	0.159806i
$304$			5.46068e11i			3.66704i
$305$	−7.60276e10	−	4.38946e10i	−0.503063	−	0.290443i
$306$	−2.23775e10	−	1.29196e10i	−0.145903	−	0.0842372i
$307$		−	1.21764e11i		−	0.782341i	−0.920318	−	0.391171i	$-0.872070\pi$
$307$		−	1.21764e11i		−	0.782341i	0.920318	−	0.391171i	$-0.127930\pi$
$308$	1.93972e10	−	3.35970e10i	0.122818	−	0.212727i
$309$	1.22573e10	+	2.12302e10i	0.0764857	+	0.132477i
$310$	7.87128e10	−	4.54449e10i	0.484081	−	0.279484i
$311$	2.12633e11			1.28887			0.644433	−	0.764661i	$-0.277093\pi$
$311$	2.12633e11			1.28887			0.644433	+	0.764661i	$0.277093\pi$
$312$	3.01855e11	+	3.74386e10i	1.80344	+	0.223678i
$313$	2.82810e11			1.66550			0.832752	−	0.553647i	$-0.186764\pi$
$313$	2.82810e11			1.66550			0.832752	+	0.553647i	$0.186764\pi$
$314$	1.50287e11	−	8.67684e10i	0.872446	−	0.503707i
$315$	4.17627e9	+	7.23352e9i	0.0238996	+	0.0413954i
$316$	2.82858e11	−	4.89925e11i	1.59579	−	2.76400i
$317$		−	2.01042e11i		−	1.11820i	−0.829100	−	0.559101i	$-0.811147\pi$
$317$		−	2.01042e11i		−	1.11820i	0.829100	−	0.559101i	$-0.188853\pi$
$318$	−3.14076e11	−	1.81332e11i	−1.72232	−	0.994379i
$319$	7.73827e10	+	4.46769e10i	0.418394	+	0.241560i
$320$		−	1.15411e10i		−	0.0615277i
$321$	−7.89459e10	+	1.36738e11i	−0.415008	+	0.718816i
$322$	2.97185e10	+	5.14740e10i	0.154055	+	0.266831i
$323$	7.72111e10	−	4.45779e10i	0.394701	−	0.227881i
$324$	2.08715e11			1.05221
$325$	−1.43454e11	−	1.08376e11i	−0.713242	−	0.538838i
$326$	2.88760e11			1.41598
$327$	−2.35920e11	+	1.36209e11i	−1.14104	+	0.658778i
$328$	7.52799e10	+	1.30389e11i	0.359126	+	0.622025i
$329$	−6.41883e10	+	1.11177e11i	−0.302047	+	0.523160i
$330$		−	2.83134e10i		−	0.131425i
$331$	1.03380e11	+	5.96864e10i	0.473380	+	0.273306i	0.717653	−	0.696400i	$-0.245216\pi$
$331$	1.03380e11	+	5.96864e10i	0.473380	+	0.273306i	−0.244274	+	0.969706i	$0.578550\pi$
$332$	−3.90352e11	−	2.25370e11i	−1.76334	−	1.01806i
$333$		−	1.09506e11i		−	0.488022i
$334$	9.09202e10	−	1.57478e11i	0.399762	−	0.692408i
$335$	−4.76270e9	−	8.24923e9i	−0.0206610	−	0.0357859i
$336$	1.15263e11	−	6.65470e10i	0.493358	−	0.284840i
$337$	1.38427e11			0.584635			0.292317	−	0.956321i	$-0.405574\pi$
$337$	1.38427e11			0.584635			0.292317	+	0.956321i	$0.405574\pi$
$338$	−3.11980e11	−	3.02757e11i	−1.30017	−	1.26174i
$339$	1.39125e11			0.572144
$340$	−3.79975e10	+	2.19378e10i	−0.154205	+	0.0890305i
$341$	3.36701e10	+	5.83183e10i	0.134850	+	0.233566i
$342$	1.69326e11	−	2.93281e11i	0.669276	−	1.15922i
$343$			1.38413e10i			0.0539949i
$344$	−2.74404e11	−	1.58427e11i	−1.05652	−	0.609981i
$345$	2.61223e10	+	1.50817e10i	0.0992717	+	0.0573145i
$346$			2.93599e11i			1.10132i
$347$	−6.93633e10	+	1.20141e11i	−0.256831	+	0.444844i	−0.965391	−	0.260806i	$-0.916012\pi$
$347$	−6.93633e10	+	1.20141e11i	−0.256831	+	0.444844i	0.708560	+	0.705650i	$0.249345\pi$
$348$	4.14354e11	+	7.17682e11i	1.51448	+	2.62316i
$349$	2.78597e11	−	1.60848e11i	1.00522	−	0.580366i	0.0954341	−	0.995436i	$-0.469576\pi$
$349$	2.78597e11	−	1.60848e11i	1.00522	−	0.580366i	0.909790	+	0.415070i	$0.136243\pi$
$350$	−1.71848e11			−0.612123
$351$	−2.46368e11	−	1.86125e11i	−0.866366	−	0.654520i
$352$	9.57842e10			0.332546
$353$	−2.46117e11	+	1.42096e11i	−0.843638	+	0.487075i	−0.858499	−	0.512815i	$-0.828603\pi$
$353$	−2.46117e11	+	1.42096e11i	−0.843638	+	0.487075i	0.0148612	+	0.999890i	$0.495269\pi$
$354$	−8.72782e9	−	1.51170e10i	−0.0295387	−	0.0511625i
$355$	4.88000e10	−	8.45241e10i	0.163077	−	0.282457i
$356$			4.92101e10i			0.162379i
$357$	−1.88188e10	−	1.08650e10i	−0.0613176	−	0.0354017i
$358$	−5.61400e10	−	3.24125e10i	−0.180634	−	0.104289i
$359$			2.25381e11i			0.716131i	0.933696	+	0.358065i	$0.116564\pi$
$359$			2.25381e11i			0.716131i	−0.933696	+	0.358065i	$0.883436\pi$
$360$	−4.68203e10	+	8.10951e10i	−0.146917	+	0.254468i
$361$	4.22897e11	+	7.32478e11i	1.31054	+	2.26993i
$362$	8.60869e10	−	4.97023e10i	0.263481	−	0.152121i
$363$	−2.37763e11			−0.718729
$364$	−2.86741e11	−	3.55641e10i	−0.856118	−	0.106183i
$365$	−9.77103e10			−0.288152
$366$	7.51306e11	−	4.33767e11i	2.18853	−	1.26355i
$367$	−1.51524e11	−	2.62447e11i	−0.435998	−	0.755170i	0.561379	−	0.827559i	$-0.310271\pi$
$367$	−1.51524e11	−	2.62447e11i	−0.435998	−	0.755170i	−0.997376	+	0.0723888i	$0.976938\pi$
$368$	−1.52524e11	+	2.64179e11i	−0.433533	+	0.750902i
$369$		−	4.27446e10i		−	0.120022i
$370$	−2.31585e11	−	1.33706e11i	−0.642396	−	0.370887i
$371$	1.67634e11	+	9.67838e10i	0.459389	+	0.265228i
$372$			6.24543e11i			1.69091i
$373$	−2.28081e11	+	3.95048e11i	−0.610098	+	1.05672i	0.381125	+	0.924524i	$0.375537\pi$
$373$	−2.28081e11	+	3.95048e11i	−0.610098	+	1.05672i	−0.991223	+	0.132198i	$0.957797\pi$
$374$	−2.33750e10	−	4.04867e10i	−0.0617773	−	0.107001i
$375$	−1.60017e11	+	9.23860e10i	−0.417855	+	0.241249i
$376$	−1.43923e12			−3.71352
$377$	8.19134e10	−	6.60440e11i	0.208842	−	1.68383i
$378$	−2.95132e11			−0.743538
$379$	−3.26411e11	+	1.88454e11i	−0.812622	+	0.469168i	−0.847866	−	0.530211i	$-0.822113\pi$
$379$	−3.26411e11	+	1.88454e11i	−0.812622	+	0.469168i	0.0352433	+	0.999379i	$0.488779\pi$
$380$	−2.87519e11	−	4.97997e11i	−0.707360	−	1.22518i
$381$	1.44125e9	−	2.49631e9i	0.00350409	−	0.00606927i
$382$			8.42300e11i			2.02386i
$383$	−1.06897e11	−	6.17173e10i	−0.253847	−	0.146559i	0.367677	−	0.929953i	$-0.380153\pi$
$383$	−1.06897e11	−	6.17173e10i	−0.253847	−	0.146559i	−0.621525	+	0.783395i	$0.713486\pi$
$384$	−2.38297e11	−	1.37581e11i	−0.559278	−	0.322899i
$385$			1.51119e10i			0.0350548i
$386$	1.79859e11	−	3.11525e11i	0.412373	−	0.714250i
$387$	4.49781e10	+	7.79043e10i	0.101930	+	0.176548i
$388$	−1.12598e12	+	6.50085e11i	−2.52225	+	1.45622i
$389$	−3.65780e11			−0.809929			−0.404964	−	0.914332i	$-0.632716\pi$
$389$	−3.65780e11			−0.809929			−0.404964	+	0.914332i	$0.632716\pi$
$390$	−1.94213e11	+	8.21578e10i	−0.425096	+	0.179828i
$391$	4.98047e10			0.107764
$392$	−1.34385e11	+	7.75874e10i	−0.287452	+	0.165960i
$393$	4.39348e10	+	7.60974e10i	0.0929057	+	0.160917i
$394$	−2.14165e11	+	3.70944e11i	−0.447729	+	0.775489i
$395$			2.20368e11i			0.455472i
$396$	−1.06934e11	−	6.17386e10i	−0.218519	−	0.126162i
$397$	4.79506e11	+	2.76843e11i	0.968805	+	0.559340i	0.898872	−	0.438212i	$-0.144388\pi$
$397$	4.79506e11	+	2.76843e11i	0.968805	+	0.559340i	0.0699335	+	0.997552i	$0.477721\pi$
$398$		−	3.58759e11i		−	0.716685i
$399$	1.42398e11	−	2.46640e11i	0.281271	−	0.487176i
$400$	−4.40987e11	−	7.63812e11i	−0.861303	−	1.49182i
$401$	−8.04568e11	+	4.64517e11i	−1.55386	+	0.897124i	−0.556042	+	0.831154i	$0.687681\pi$
$401$	−8.04568e11	+	4.64517e11i	−1.55386	+	0.897124i	−0.997822	+	0.0659696i	$0.978986\pi$
$402$	9.41301e10			0.179768
$403$	3.02327e11	−	4.00181e11i	0.570959	−	0.755760i
$404$	2.88332e11			0.538488
$405$	−7.04099e10	+	4.06512e10i	−0.130043	+	0.0750802i
$406$	−3.18052e11	−	5.50882e11i	−0.580940	−	1.00622i
$407$	9.90625e10	−	1.71581e11i	0.178951	−	0.309953i
$408$		−	2.43616e11i		−	0.435246i
$409$	−6.96075e11	−	4.01879e11i	−1.22999	−	0.710135i	−0.262962	−	0.964806i	$-0.584699\pi$
$409$	−6.96075e11	−	4.01879e11i	−1.22999	−	0.710135i	−0.967028	+	0.254672i	$0.918033\pi$
$410$	−9.03969e10	−	5.21907e10i	−0.157989	−	0.0912148i
$411$			3.54592e11i			0.612972i
$412$	1.30536e11	−	2.26095e11i	0.223199	−	0.386593i
$413$	4.65838e9	+	8.06854e9i	0.00787878	+	0.0136465i
$414$	1.63834e11	−	9.45897e10i	0.274096	−	0.158249i
$415$	1.75580e11			0.290576
$416$	−2.77940e11	−	6.57023e11i	−0.455021	−	1.07562i
$417$	−3.68383e11			−0.596605
$418$	5.30621e11	−	3.06354e11i	0.850142	−	0.490829i
$419$	−1.05723e11	−	1.83118e11i	−0.167574	−	0.290247i	0.769992	−	0.638053i	$-0.220260\pi$
$419$	−1.05723e11	−	1.83118e11i	−0.167574	−	0.290247i	−0.937566	+	0.347806i	$0.886927\pi$
$420$	−7.00775e10	+	1.21378e11i	−0.109890	+	0.190334i
$421$			9.84557e11i			1.52747i	0.645532	+	0.763733i	$0.276636\pi$
$421$			9.84557e11i			1.52747i	−0.645532	+	0.763733i	$0.723364\pi$
$422$	1.06727e12	+	6.16187e11i	1.63820	+	0.945816i
$423$	3.53861e11	+	2.04302e11i	0.537405	+	0.310271i
$424$			2.17009e12i			3.26085i
$425$	−7.19993e10	+	1.24707e11i	−0.107048	+	0.185412i
$426$	4.82242e11	+	8.35268e11i	0.709451	+	1.22880i
$427$	−4.01001e11	+	2.31518e11i	−0.583741	+	0.337023i
$428$	1.68150e12			2.42214
$429$	−6.08707e10	−	1.43892e11i	−0.0867662	−	0.205107i
$430$	2.19671e11			0.309859
$431$	9.74960e11	−	5.62893e11i	1.36094	−	0.785739i	0.371191	−	0.928557i	$-0.378950\pi$
$431$	9.74960e11	−	5.62893e11i	1.36094	−	0.785739i	0.989749	+	0.142818i	$0.0456163\pi$
$432$	−7.57351e11	−	1.31177e12i	−1.04621	−	1.81209i
$433$	−3.97611e11	+	6.88682e11i	−0.543579	+	0.941506i	0.455116	+	0.890432i	$0.349598\pi$
$433$	−3.97611e11	+	6.88682e11i	−0.543579	+	0.941506i	−0.998695	+	0.0510737i	$0.983736\pi$
$434$		−	4.79390e11i		−	0.648613i
$435$	−2.79565e11	−	1.61407e11i	−0.374352	−	0.216132i
$436$	2.51248e12	+	1.45058e12i	3.32976	+	1.92244i
$437$			6.52744e11i			0.856202i
$438$	4.82787e11	−	8.36212e11i	0.626791	−	1.08563i
$439$	−4.07342e11	−	7.05537e11i	−0.523442	−	0.906628i	−0.999628	−	0.0272836i	$-0.991314\pi$
$439$	−4.07342e11	−	7.05537e11i	−0.523442	−	0.906628i	0.476186	−	0.879345i	$-0.342019\pi$
$440$	−1.46722e11	+	8.47101e10i	−0.186620	+	0.107745i
$441$	4.40548e10			0.0554651
$442$	−2.09887e11	+	2.77820e11i	−0.261568	+	0.346229i
$443$	7.13160e11			0.879772			0.439886	−	0.898054i	$-0.355019\pi$
$443$	7.13160e11			0.879772			0.439886	+	0.898054i	$0.355019\pi$
$444$	1.59132e12	−	9.18751e11i	1.94328	−	1.12195i
$445$	−9.58460e9	−	1.66010e10i	−0.0115865	−	0.0200685i
$446$	−8.36621e11	+	1.44907e12i	−1.00120	+	1.73413i
$447$			9.33356e11i			1.10577i
$448$	−5.27170e10	−	3.04362e10i	−0.0618300	−	0.0356976i
$449$	1.14940e12	+	6.63608e11i	1.33464	+	0.770554i	0.986007	−	0.166705i	$-0.0533127\pi$
$449$	1.14940e12	+	6.63608e11i	1.33464	+	0.770554i	0.348633	+	0.937259i	$0.386646\pi$
$450$			5.46968e11i			0.628790i
$451$	3.86681e10	−	6.69751e10i	0.0440107	−	0.0762287i
$452$	−7.40817e11	−	1.28313e12i	−0.834811	−	1.44593i
$453$	−6.34146e11	+	3.66124e11i	−0.707534	+	0.408495i
$454$	−2.94749e12			−3.25612
$455$	1.03659e11	−	4.38508e10i	0.113385	−	0.0479652i
$456$	3.19285e12			3.45809
$457$	1.45908e11	−	8.42402e10i	0.156479	−	0.0903434i	−0.419716	−	0.907656i	$-0.637870\pi$
$457$	1.45908e11	−	8.42402e10i	0.156479	−	0.0903434i	0.576195	+	0.817312i	$0.304537\pi$
$458$	−7.78061e11	−	1.34764e12i	−0.826264	−	1.43113i
$459$	−1.23652e11	+	2.14171e11i	−0.130030	+	0.225218i
$460$		−	3.21231e11i		−	0.334509i
$461$	6.76314e11	+	3.90470e11i	0.697420	+	0.402655i	0.806386	−	0.591390i	$-0.201421\pi$
$461$	6.76314e11	+	3.90470e11i	0.697420	+	0.402655i	−0.108966	+	0.994045i	$0.534754\pi$
$462$	−1.29329e11	−	7.46682e10i	−0.132071	−	0.0762512i
$463$			5.66566e11i			0.572976i	0.958084	+	0.286488i	$0.0924878\pi$
$463$			5.66566e11i			0.572976i	−0.958084	+	0.286488i	$0.907512\pi$
$464$	1.63233e12	−	2.82728e12i	1.63485	−	2.83164i
$465$	−1.21642e11	−	2.10690e11i	−0.120655	−	0.208980i
$466$	1.44412e12	−	8.33760e11i	1.41862	−	0.819039i
$467$	2.70027e11			0.262713			0.131356	−	0.991335i	$-0.458067\pi$
$467$	2.70027e11			0.262713			0.131356	+	0.991335i	$0.458067\pi$
$468$	−1.13195e11	+	9.12655e11i	−0.109074	+	0.879428i
$469$	−5.02409e10			−0.0479490
$470$	8.64122e11	−	4.98901e11i	0.816835	−	0.471600i
$471$	−2.32252e11	−	4.02272e11i	−0.217453	−	0.376639i
$472$	−5.22251e10	+	9.04565e10i	−0.0484329	+	0.0838882i
$473$			1.62754e11i			0.149505i
$474$	−1.88593e12	−	1.08884e12i	−1.71602	−	0.990745i
$475$	−1.63441e12	−	9.43628e11i	−1.47313	−	0.850511i
$476$			2.31419e11i			0.206617i
$477$	3.08049e11	−	5.33556e11i	0.272450	−	0.471897i
$478$	−8.59734e11	−	1.48910e12i	−0.753249	−	1.30467i
$479$	1.50508e12	−	8.68957e11i	1.30632	−	0.754204i	0.324839	−	0.945769i	$-0.394690\pi$
$479$	1.50508e12	−	8.68957e11i	1.30632	−	0.754204i	0.981480	+	0.191566i	$0.0613565\pi$
$480$	−3.46045e11			−0.297541
$481$	−1.46440e12	−	1.81627e11i	−1.24740	−	0.154713i
$482$	3.82982e12			3.23197
$483$	1.37780e11	−	7.95472e10i	0.115192	−	0.0665063i
$484$	1.26605e12	+	2.19287e12i	1.04869	+	1.81639i
$485$	2.53233e11	−	4.38612e11i	0.207818	−	0.359951i
$486$			1.61601e12i			1.31396i
$487$	8.84243e11	+	5.10518e11i	0.712346	+	0.411273i	0.811929	−	0.583756i	$-0.198418\pi$
$487$	8.84243e11	+	5.10518e11i	0.712346	+	0.411273i	−0.0995830	+	0.995029i	$0.531751\pi$
$488$	−4.49563e12	−	2.59555e12i	−3.58840	−	2.07177i
$489$		−	7.72919e11i		−	0.611286i
$490$	5.37904e10	−	9.31677e10i	0.0421524	−	0.0730101i
$491$	−4.97452e11	−	8.61613e11i	−0.386265	−	0.669030i	0.605679	−	0.795709i	$-0.292902\pi$
$491$	−4.97452e11	−	8.61613e11i	−0.386265	−	0.669030i	−0.991944	+	0.126679i	$0.959568\pi$
$492$	6.21157e11	−	3.58625e11i	0.477923	−	0.275929i
$493$	−5.33018e11			−0.406378
$494$	−3.64113e12	−	2.75079e12i	−2.75084	−	2.07819i
$495$	4.80991e10			0.0360092
$496$	2.13074e12	−	1.23018e12i	1.58075	−	0.912646i
$497$	−2.57391e11	−	4.45815e11i	−0.189230	−	0.327756i
$498$	−8.67544e11	+	1.50263e12i	−0.632062	+	1.09476i
$499$		−	5.26045e9i		−	0.00379814i	−0.999998	−	0.00189907i	$-0.999396\pi$
$499$		−	5.26045e9i		−	0.00379814i	0.999998	−	0.00189907i	$-0.000604492\pi$
$500$	1.70413e12	+	9.83882e11i	1.21938	+	0.704009i
$501$	−4.21521e11	−	2.43365e11i	−0.298916	−	0.172579i
$502$			3.38598e12i			2.37968i
$503$	−4.62120e11	+	8.00415e11i	−0.321884	+	0.557519i	−0.980877	−	0.194630i	$-0.937649\pi$
$503$	−4.62120e11	+	8.00415e11i	−0.321884	+	0.557519i	0.658993	+	0.752149i	$0.270983\pi$
$504$	2.46949e11	+	4.27729e11i	0.170479	+	0.295278i
$505$	−9.72687e10	+	5.61581e10i	−0.0665521	+	0.0384239i
$506$	3.42275e11			0.232112
$507$	−8.10385e11	+	8.35073e11i	−0.544698	+	0.561292i
$508$	−3.06976e10			−0.0204512
$509$	7.30686e11	−	4.21862e11i	0.482504	−	0.278574i	−0.238955	−	0.971031i	$-0.576805\pi$
$509$	7.30686e11	−	4.21862e11i	0.482504	−	0.278574i	0.721459	+	0.692457i	$0.243472\pi$
$510$	8.44481e10	+	1.46268e11i	0.0552744	+	0.0957380i
$511$	−2.57682e11	+	4.46319e11i	−0.167182	+	0.289568i
$512$			3.46253e12i			2.22679i
$513$	−2.80694e12	−	1.62059e12i	−1.78939	−	1.03310i
$514$	3.50283e11	+	2.02236e11i	0.221353	+	0.127798i
$515$			1.01698e11i			0.0637057i
$516$	−7.54728e11	+	1.30723e12i	−0.468670	+	0.811760i
$517$	3.69636e11	+	6.40228e11i	0.227544	+	0.394119i
$518$	−1.22148e12	+	7.05219e11i	−0.745420	+	0.430368i
$519$	7.85874e11			0.475445
$520$	1.00681e12	+	7.60621e11i	0.603854	+	0.456198i
$521$	2.16905e12			1.28973			0.644867	−	0.764295i	$-0.276913\pi$
$521$	2.16905e12			1.28973			0.644867	+	0.764295i	$0.276913\pi$
$522$	−1.75338e12	+	1.01231e12i	−1.03361	+	0.596757i
$523$	−3.61076e11	−	6.25402e11i	−0.211028	−	0.365512i	0.741008	−	0.671496i	$-0.234348\pi$
$523$	−3.61076e11	−	6.25402e11i	−0.211028	−	0.365512i	−0.952037	+	0.305984i	$0.901015\pi$
$524$	4.67892e11	−	8.10414e11i	0.271116	−	0.469587i
$525$			4.59984e11i			0.264257i
$526$	5.26576e11	+	3.04019e11i	0.299934	+	0.173167i
$527$	−3.47883e11	−	2.00850e11i	−0.196465	−	0.113429i
$528$		−	7.66437e11i		−	0.429165i
$529$	7.18256e11	−	1.24406e12i	0.398776	−	0.690700i
$530$	−7.52248e11	−	1.30293e12i	−0.414114	−	0.717266i
$531$	2.56810e10	−	1.48269e10i	0.0140180	−	0.00809331i
$532$	−3.03299e12			−1.64160
$533$	−5.71613e11	−	7.08964e10i	−0.306782	−	0.0380497i
$534$	1.89430e11			0.100812
$535$	−5.67254e11	+	3.27504e11i	−0.299354	+	0.172832i
$536$	−2.81626e11	−	4.87790e11i	−0.147377	−	0.255265i
$537$	−8.67581e10	+	1.50269e11i	−0.0450221	+	0.0779806i
$538$		−	3.03663e12i		−	1.56269i
$539$	6.90280e10	+	3.98533e10i	0.0352270	+	0.0203383i
$540$	1.38136e12	+	7.97530e11i	0.699094	+	0.403622i
$541$		−	1.84396e12i		−	0.925473i	−0.886496	−	0.462737i	$-0.846868\pi$
$541$		−	1.84396e12i		−	0.925473i	0.886496	−	0.462737i	$-0.153132\pi$
$542$	5.86389e11	−	1.01566e12i	0.291870	−	0.505533i
$543$	−1.33038e11	−	2.30428e11i	−0.0656712	−	0.113746i
$544$	−4.94826e11	+	2.85688e11i	−0.242247	+	0.139861i
$545$	−1.13011e12			−0.548703
$546$	−1.36901e11	+	1.10379e12i	−0.0659235	+	0.531519i
$547$	1.62160e12			0.774463			0.387231	−	0.921983i	$-0.373431\pi$
$547$	1.62160e12			0.774463			0.387231	+	0.921983i	$0.373431\pi$
$548$	3.27037e12	−	1.88815e12i	1.54912	−	0.894382i
$549$	7.36889e11	+	1.27633e12i	0.346199	+	0.599635i
$550$	−4.94804e11	+	8.57026e11i	−0.230569	+	0.399357i
$551$		−	6.98577e12i		−	3.22873i
$552$	1.54465e12	+	8.91805e11i	0.708116	+	0.408831i
$553$	1.00659e12	+	5.81156e11i	0.457710	+	0.264259i
$554$			4.16000e12i			1.87629i
$555$	−3.57888e11	+	6.19881e11i	−0.160114	+	0.277326i
$556$	1.96158e12	+	3.39756e12i	0.870502	+	1.50775i
$557$	−9.15411e11	+	5.28513e11i	−0.402965	+	0.232652i	−0.687763	−	0.725936i	$-0.741407\pi$
$557$	−9.15411e11	+	5.28513e11i	−0.402965	+	0.232652i	0.284797	+	0.958588i	$0.408074\pi$
$558$	−1.52583e12			−0.666273
$559$	1.11640e12	−	4.72269e11i	0.483577	−	0.204567i
$560$	5.52135e11			0.237246
$561$	−1.08370e11	+	6.25676e10i	−0.0461931	+	0.0266696i
$562$	−3.48951e12	−	6.04401e12i	−1.47554	−	2.55571i
$563$	−1.39998e12	+	2.42484e12i	−0.587266	+	1.01718i	0.407322	+	0.913284i	$0.366463\pi$
$563$	−1.39998e12	+	2.42484e12i	−0.587266	+	1.01718i	−0.994589	+	0.103891i	$0.966871\pi$
$564$			6.85633e12i			2.85322i
$565$	4.99829e11	+	2.88577e11i	0.206350	+	0.119136i
$566$	4.26155e10	+	2.46041e10i	0.0174539	+	0.0100770i
$567$			4.28823e11i			0.174242i
$568$	2.88562e12	−	4.99804e12i	1.16325	−	2.01480i
$569$	2.04387e12	+	3.54008e12i	0.817423	+	1.41582i	0.907575	+	0.419891i	$0.137932\pi$
$569$	2.04387e12	+	3.54008e12i	0.817423	+	1.41582i	−0.0901513	+	0.995928i	$0.528735\pi$
$570$	−1.91700e12	+	1.10678e12i	−0.760652	+	0.439163i
$571$	4.07307e12			1.60347			0.801733	−	0.597683i	$-0.203912\pi$
$571$	4.07307e12			1.60347			0.801733	+	0.597683i	$0.203912\pi$
$572$	−1.00298e12	+	1.32761e12i	−0.391750	+	0.518547i
$573$	2.25457e12			0.873713
$574$	−4.76791e11	+	2.75275e11i	−0.183326	+	0.105843i
$575$	−5.27135e11	−	9.13025e11i	−0.201102	−	0.348319i
$576$	−9.68739e10	+	1.67790e11i	−0.0366695	+	0.0635135i
$577$		−	1.06291e12i		−	0.399212i	−0.979876	−	0.199606i	$-0.936034\pi$
$577$		−	1.06291e12i		−	0.399212i	0.979876	−	0.199606i	$-0.0639662\pi$
$578$	−3.96870e12	−	2.29133e12i	−1.47902	−	0.853910i
$579$	−8.33856e11	−	4.81427e11i	−0.308346	−	0.178023i
$580$			3.43786e12i			1.26143i
$581$	4.63042e11	−	8.02012e11i	0.168588	−	0.292004i
$582$	2.50245e12	+	4.33437e12i	0.904091	+	1.56593i
$583$	9.65342e11	−	5.57341e11i	0.346077	−	0.199808i
$584$	−5.77776e12			−2.05542
$585$	−1.39571e11	−	3.29931e11i	−0.0492712	−	0.116472i
$586$	7.51958e12			2.63423
$587$	−1.37403e12	+	7.93299e11i	−0.477668	+	0.275782i	−0.719444	−	0.694550i	$-0.755603\pi$
$587$	−1.37403e12	+	7.93299e11i	−0.477668	+	0.275782i	0.241776	+	0.970332i	$0.422270\pi$
$588$	3.69618e11	+	6.40197e11i	0.127513	+	0.220859i
$589$	2.63236e12	−	4.55938e12i	0.901210	−	1.56094i
$590$		−	7.24141e10i		−	0.0246030i
$591$	9.92903e11	+	5.73253e11i	0.334783	+	0.193287i
$592$	−6.26896e12	−	3.61939e12i	−2.09772	−	1.21112i
$593$		−	6.78780e11i		−	0.225415i	−0.993628	−	0.112708i	$-0.964048\pi$
$593$		−	6.78780e11i		−	0.225415i	0.993628	−	0.112708i	$-0.0359523\pi$
$594$	−8.49776e11	+	1.47186e12i	−0.280069	+	0.485094i
$595$	−4.50732e10	−	7.80691e10i	−0.0147432	−	0.0255360i
$596$	8.60825e12	−	4.96998e12i	2.79452	−	1.61341i
$597$	−9.60285e11			−0.309397
$598$	−9.93190e11	−	2.34780e12i	−0.317597	−	0.750769i
$599$	−4.97942e12			−1.58037			−0.790184	−	0.612870i	$-0.790015\pi$
$599$	−4.97942e12			−1.58037			−0.790184	+	0.612870i	$0.790015\pi$
$600$	−4.46600e12	+	2.57844e12i	−1.40682	+	0.812226i
$601$	−6.92640e11	−	1.19969e12i	−0.216557	−	0.375088i	0.737196	−	0.675679i	$-0.236149\pi$
$601$	−6.92640e11	−	1.19969e12i	−0.216557	−	0.375088i	−0.953753	+	0.300591i	$0.902816\pi$
$602$	5.79318e11	−	1.00341e12i	0.179776	−	0.311382i
$603$			1.59909e11i			0.0492545i
$604$	6.75346e12	+	3.89911e12i	2.06471	+	1.19206i
$605$	−8.54206e11	−	4.93176e11i	−0.259217	−	0.149659i
$606$		−	1.10991e12i		−	0.334319i
$607$	1.95478e11	−	3.38577e11i	0.0584451	−	0.101230i	−0.835322	−	0.549760i	$-0.814719\pi$
$607$	1.95478e11	−	3.38577e11i	0.0584451	−	0.101230i	0.893768	+	0.448530i	$0.148052\pi$
$608$	−3.74425e12	−	6.48523e12i	−1.11122	−	1.92468i
$609$	−1.47454e12	+	8.51326e11i	−0.434389	+	0.250795i
$610$	3.59893e12			1.05242
$611$	3.31900e12	−	4.39325e12i	0.963433	−	1.27526i
$612$	7.36572e11			0.212243
$613$	4.06991e12	−	2.34977e12i	1.16416	−	0.672129i	0.211864	−	0.977299i	$-0.432047\pi$
$613$	4.06991e12	−	2.34977e12i	1.16416	−	0.672129i	0.952298	+	0.305170i	$0.0987134\pi$
$614$	2.49587e12	+	4.32297e12i	0.708703	+	1.22751i
$615$	−1.39698e11	+	2.41964e11i	−0.0393779	+	0.0682045i
$616$			8.93592e11i			0.250050i
$617$	−4.05226e12	−	2.33957e12i	−1.12568	−	0.649910i	−0.182833	−	0.983144i	$-0.558527\pi$
$617$	−4.05226e12	−	2.33957e12i	−1.12568	−	0.649910i	−0.942844	+	0.333234i	$0.891860\pi$
$618$	−8.70336e11	−	5.02489e11i	−0.240015	−	0.138573i
$619$		−	1.11341e12i		−	0.304823i	−0.988317	−	0.152411i	$-0.951296\pi$
$619$		−	1.11341e12i		−	0.304823i	0.988317	−	0.152411i	$-0.0487038\pi$
$620$	−1.29545e12	+	2.24378e12i	−0.352093	+	0.609843i
$621$	−9.05302e11	−	1.56803e12i	−0.244276	−	0.423099i
$622$	−7.54907e12	+	4.35845e12i	−2.02226	+	1.16755i
$623$	−1.01106e11			−0.0268895
$624$	−5.25730e12	+	2.22399e12i	−1.38814	+	0.587223i
$625$	2.64345e12			0.692964
$626$	−1.00406e13	+	5.79693e12i	−2.61321	+	1.50874i
$627$	−8.20015e11	−	1.42031e12i	−0.211894	−	0.367010i
$628$	−2.47341e12	+	4.28407e12i	−0.634568	+	1.09910i
$629$			1.18186e12i			0.301051i
$630$	−2.96539e11	−	1.71207e11i	−0.0749980	−	0.0433001i
$631$	−3.61730e12	−	2.08845e12i	−0.908349	−	0.524435i	−0.0284491	−	0.999595i	$-0.509057\pi$
$631$	−3.61730e12	−	2.08845e12i	−0.908349	−	0.524435i	−0.879899	+	0.475160i	$0.842390\pi$
$632$			1.30307e13i			3.24893i
$633$	1.64934e12	−	2.85674e12i	0.408314	−	0.707220i
$634$	4.12088e12	+	7.13757e12i	1.01295	+	1.75448i
$635$	1.03558e10	−	5.97895e9i	0.00252757	−	0.00145930i
$636$	1.03381e13			2.50543
$637$	7.30695e10	−	5.89134e11i	0.0175836	−	0.141771i
$638$	−3.66308e12			−0.875292
$639$	−1.41896e12	+	8.19240e11i	−0.336680	+	0.194382i
$640$	−5.70748e11	−	9.88565e11i	−0.134473	−	0.232914i
$641$	3.70572e12	−	6.41850e12i	0.866986	−	1.50166i	0.00192353	−	0.999998i	$-0.499388\pi$
$641$	3.70572e12	−	6.41850e12i	0.866986	−	1.50166i	0.865062	−	0.501665i	$-0.167279\pi$
$642$		−	6.47280e12i		−	1.50378i
$643$	−4.56403e12	−	2.63505e12i	−1.05293	−	0.607909i	−0.129462	−	0.991584i	$-0.541325\pi$
$643$	−4.56403e12	−	2.63505e12i	−1.05293	−	0.607909i	−0.923468	+	0.383675i	$0.874658\pi$
$644$	−1.46731e12	−	8.47153e11i	−0.336152	−	0.194078i
$645$		−	5.87991e11i		−	0.133768i
$646$	−1.82748e12	+	3.16528e12i	−0.412863	+	0.715099i
$647$	1.63608e12	+	2.83378e12i	0.367059	+	0.635764i	0.989104	−	0.147217i	$-0.0470315\pi$
$647$	1.63608e12	+	2.83378e12i	0.367059	+	0.635764i	−0.622046	+	0.782981i	$0.713698\pi$
$648$	−4.16345e12	+	2.40377e12i	−0.927610	+	0.535556i
$649$	5.36516e10			0.0118708
$650$	7.31447e12	+	9.07203e11i	1.60721	+	0.199340i
$651$	−1.28318e12			−0.280009
$652$	−7.12856e12	+	4.11568e12i	−1.54486	+	0.891923i
$653$	2.28111e12	+	3.95100e12i	0.490950	+	0.850351i	0.999946	−	0.0104184i	$-0.00331635\pi$
$653$	2.28111e12	+	3.95100e12i	0.490950	+	0.850351i	−0.508995	+	0.860769i	$0.669983\pi$
$654$	5.58389e12	−	9.67159e12i	1.19354	−	2.06727i
$655$			3.64524e11i			0.0773821i
$656$	−2.44703e12	−	1.41279e12i	−0.515907	−	0.297859i
$657$	1.42057e12	+	8.20165e11i	0.297453	+	0.171734i
$658$		−	5.26282e12i		−	1.09447i
$659$	−1.64127e12	+	2.84276e12i	−0.338996	+	0.587158i	−0.984244	−	0.176815i	$-0.943421\pi$
$659$	−1.64127e12	+	2.84276e12i	−0.338996	+	0.587158i	0.645248	+	0.763973i	$0.276754\pi$
$660$	4.03549e11	+	6.98968e11i	0.0827844	+	0.143387i
$661$	−1.60091e12	+	9.24285e11i	−0.326182	+	0.188321i	−0.654145	−	0.756369i	$-0.726971\pi$
$661$	−1.60091e12	+	9.24285e11i	−0.326182	+	0.188321i	0.327963	+	0.944691i	$0.393638\pi$
$662$	−4.89371e12			−0.990323
$663$	7.43637e11	+	5.61801e11i	0.149469	+	0.112920i
$664$	1.03823e13			2.07271
$665$	1.02318e12	−	5.90732e11i	0.202887	−	0.117137i
$666$	2.24461e12	+	3.88778e12i	0.442086	+	0.765716i
$667$	1.95122e12	−	3.37960e12i	0.381715	−	0.661149i
$668$			5.18353e12i			1.00724i
$669$	3.87871e12	+	2.23937e12i	0.748634	+	0.432224i
$670$	3.38179e11	+	1.95248e11i	0.0648350	+	0.0374325i
$671$			2.66645e12i			0.507787i
$672$	−9.12592e11	+	1.58066e12i	−0.172629	+	0.299003i
$673$	−1.98365e12	−	3.43578e12i	−0.372732	−	0.645591i	0.617253	−	0.786765i	$-0.288246\pi$
$673$	−1.98365e12	−	3.43578e12i	−0.372732	−	0.645591i	−0.989985	+	0.141174i	$0.954912\pi$
$674$	−4.91454e12	+	2.83741e12i	−0.917304	+	0.529606i
$675$	5.23494e12			0.970609
$676$	1.20170e13	+	3.02747e12i	2.21327	+	0.557596i
$677$	7.33132e12			1.34132			0.670661	−	0.741764i	$-0.266011\pi$
$677$	7.33132e12			1.34132			0.670661	+	0.741764i	$0.266011\pi$
$678$	−4.93932e12	+	2.85172e12i	−0.897705	+	0.518290i
$679$	−1.33566e12	−	2.31342e12i	−0.241146	−	0.417678i
$680$	5.05316e11	−	8.75233e11i	0.0906302	−	0.156976i
$681$			7.88951e12i			1.40568i
$682$	−2.39077e12	−	1.38031e12i	−0.423163	−	0.244314i
$683$	6.16692e12	+	3.56047e12i	1.08436	+	0.626058i	0.932070	−	0.362277i	$-0.118001\pi$
$683$	6.16692e12	+	3.56047e12i	1.08436	+	0.626058i	0.152294	+	0.988335i	$0.451334\pi$
$684$			9.65356e12i			1.68630i
$685$	−7.35505e11	+	1.27393e12i	−0.127637	+	0.221075i
$686$	−2.83713e11	−	4.91405e11i	−0.0489126	−	0.0847191i
$687$	−3.60722e12	+	2.08263e12i	−0.617827	+	0.356703i
$688$	5.94645e12			1.01184
$689$	−6.62419e12	−	5.00442e12i	−1.11981	−	0.845994i
$690$	−1.23655e12			−0.207679
$691$	−4.15054e12	+	2.39632e12i	−0.692554	+	0.399846i	−0.804568	−	0.593860i	$-0.797603\pi$
$691$	−4.15054e12	+	2.39632e12i	−0.692554	+	0.399846i	0.112014	+	0.993707i	$0.464270\pi$
$692$	−4.18466e12	−	7.24804e12i	−0.693717	−	1.20155i
$693$	1.26847e11	−	2.19706e11i	0.0208921	−	0.0361862i
$694$		−	5.68712e12i		−	0.930625i
$695$	−1.32348e12	−	7.64111e11i	−0.215172	−	0.124230i
$696$	−1.65311e13	−	9.54423e12i	−2.67030	−	1.54170i
$697$			4.61329e11i			0.0740394i
$698$	−6.59401e12	+	1.14212e13i	−1.05148	+	1.82121i
$699$	−2.23172e12	−	3.86545e12i	−0.353583	−	0.612424i
$700$	4.24239e12	−	2.44935e12i	0.667835	−	0.385575i
$701$	−2.53783e12			−0.396947			−0.198473	−	0.980106i	$-0.563598\pi$
$701$	−2.53783e12			−0.396947			−0.198473	+	0.980106i	$0.563598\pi$
$702$	1.25619e13	+	1.55803e12i	1.95226	+	0.242136i
$703$	−1.54896e13			−2.39189
$704$	−3.03577e11	+	1.75270e11i	−0.0465792	+	0.0268925i
$705$	−1.33540e12	−	2.31298e12i	−0.203592	−	0.352632i
$706$	5.82525e12	−	1.00896e13i	0.882457	−	1.52846i
$707$			5.92402e11i			0.0891722i
$708$	4.30925e11	+	2.48794e11i	0.0644543	+	0.0372127i
$709$	−3.89654e12	−	2.24967e12i	−0.579123	−	0.334357i	0.181662	−	0.983361i	$-0.441852\pi$
$709$	−3.89654e12	−	2.24967e12i	−0.579123	−	0.334357i	−0.760785	+	0.649004i	$0.775186\pi$
$710$			4.00113e12i			0.590908i
$711$	1.84974e12	−	3.20384e12i	0.271454	−	0.470173i
$712$	−5.66752e11	−	9.81644e11i	−0.0826482	−	0.143151i
$713$	2.54699e12	−	1.47050e12i	0.369083	−	0.213090i
$714$	8.90828e11			0.128278
$715$	7.97774e10	−	6.43218e11i	0.0114157	−	0.0920409i
$716$	1.84789e12			0.262766
$717$	−3.98587e12	+	2.30124e12i	−0.563231	+	0.325182i
$718$	−4.61977e12	−	8.00167e12i	−0.648724	−	1.12362i
$719$	−1.04752e12	+	1.81436e12i	−0.146178	+	0.253188i	−0.929812	−	0.368035i	$-0.880031\pi$
$719$	−1.04752e12	+	1.81436e12i	−0.146178	+	0.253188i	0.783634	+	0.621223i	$0.213364\pi$
$720$		−	1.75737e12i		−	0.243706i
$721$	4.64532e11	+	2.68198e11i	0.0640187	+	0.0369612i
$722$	−3.00281e13	−	1.73367e13i	−4.11254	−	2.37438i
$723$		−	1.02512e13i		−	1.39526i
$724$	−1.41681e12	+	2.45399e12i	−0.191641	+	0.331932i
$725$	5.64148e12	+	9.77134e12i	0.758355	+	1.31351i
$726$	8.44128e12	−	4.87358e12i	1.12770	−	0.651078i
$727$	−6.97895e12			−0.926585			−0.463293	−	0.886205i	$-0.653332\pi$
$727$	−6.97895e12			−0.926585			−0.463293	+	0.886205i	$0.653332\pi$
$728$	6.12951e12	−	2.59296e12i	0.808788	−	0.342141i
$729$	7.84098e12			1.02824
$730$	3.46900e12	−	2.00283e12i	0.452117	−	0.261030i
$731$	−4.85434e11	−	8.40797e11i	−0.0628785	−	0.108909i
$732$	−1.23649e13	+	2.14167e13i	−1.59181	+	2.75710i
$733$		−	1.48444e13i		−	1.89930i	−0.313307	−	0.949652i	$-0.601437\pi$
$733$		−	1.48444e13i		−	1.89930i	0.313307	−	0.949652i	$-0.398563\pi$
$734$	1.07591e13	+	6.21176e12i	1.36818	+	0.789918i
$735$	−2.49381e11	−	1.43980e11i	−0.0315189	−	0.0181974i
$736$		−	4.18327e12i		−	0.525491i
$737$	−1.44659e11	+	2.50557e11i	−0.0180610	+	0.0312826i
$738$	8.76161e11	+	1.51756e12i	0.108725	+	0.188318i
$739$	−1.26113e11	+	7.28111e10i	−0.0155546	+	0.00898044i	−0.507757	−	0.861500i	$-0.669525\pi$
$739$	−1.26113e11	+	7.28111e10i	−0.0155546	+	0.00898044i	0.492203	+	0.870481i	$0.336192\pi$
$740$	7.62280e12			0.934484
$741$	−7.36300e12	+	9.74616e12i	−0.897166	+	1.18755i
$742$	−7.93534e12			−0.961054
$743$	−1.28025e13	+	7.39155e12i	−1.54116	+	0.889787i	−0.542390	+	0.840127i	$0.682480\pi$
$743$	−1.28025e13	+	7.39155e12i	−1.54116	+	0.889787i	−0.998766	+	0.0496597i	$0.984186\pi$
$744$	−7.19286e12	−	1.24584e13i	−0.860644	−	1.49068i
$745$	−1.93600e12	+	3.35324e12i	−0.230251	+	0.398806i
$746$		−	1.87005e13i		−	2.21069i
$747$	−2.55269e12	−	1.47379e12i	−0.299954	−	0.173179i
$748$	1.15411e12	+	6.66325e11i	0.134800	+	0.0778268i
$749$			3.45478e12i			0.401100i
$750$	3.78738e12	−	6.55994e12i	0.437082	−	0.757049i
$751$	4.60644e12	+	7.97859e12i	0.528428	+	0.915265i	0.999451	+	0.0331433i	$0.0105518\pi$
$751$	4.60644e12	+	7.97859e12i	0.528428	+	0.915265i	−0.471022	+	0.882121i	$0.656115\pi$
$752$	2.33916e13	−	1.35051e13i	2.66735	−	1.53999i
$753$	9.06322e12			1.02732
$754$	1.06293e13	+	2.51265e13i	1.19766	+	2.83114i
$755$	−3.03771e12			−0.340239
$756$	7.28588e12	−	4.20650e12i	0.811211	−	0.468353i
$757$	−4.06927e10	−	7.04818e10i	−0.00450386	−	0.00780092i	0.863765	−	0.503895i	$-0.168100\pi$
$757$	−4.06927e10	−	7.04818e10i	−0.00450386	−	0.00780092i	−0.868269	+	0.496094i	$0.834767\pi$
$758$	7.72569e12	−	1.33813e13i	0.850014	−	1.47227i
$759$		−	9.16163e11i		−	0.100204i
$760$	1.14709e13	+	6.62271e12i	1.24720	+	0.720070i
$761$	7.33199e12	+	4.23312e12i	0.792484	+	0.457541i	0.840836	−	0.541289i	$-0.182064\pi$
$761$	7.33199e12	+	4.23312e12i	0.792484	+	0.457541i	−0.0483520	+	0.998830i	$0.515397\pi$
$762$			1.18168e11i			0.0126971i
$763$	−2.98034e12	+	5.16210e12i	−0.318350	+	0.551399i
$764$	−1.20053e13	−	2.07937e13i	−1.27483	−	2.20807i
$765$	−2.48482e11	+	1.43461e11i	−0.0262313	+	0.0151446i
$766$	5.06022e12			0.531056
$767$	−1.55682e11	−	3.68018e11i	−0.0162428	−	0.0383963i
$768$	1.27047e13			1.31777
$769$	6.66882e11	−	3.85024e11i	0.0687670	−	0.0397027i	−0.465222	−	0.885194i	$-0.654026\pi$
$769$	6.66882e11	−	3.85024e11i	0.0687670	−	0.0397027i	0.533989	+	0.845491i	$0.320692\pi$
$770$	−3.09758e11	−	5.36517e11i	−0.0317552	−	0.0550016i
$771$	5.41323e11	−	9.37599e11i	0.0551711	−	0.0955591i
$772$			1.02541e13i			1.03901i
$773$	8.57834e12	+	4.95271e12i	0.864163	+	0.498925i	0.865404	−	0.501075i	$-0.167062\pi$
$773$	8.57834e12	+	4.95271e12i	0.864163	+	0.498925i	−0.00124131	+	0.999999i	$0.500395\pi$
$774$	−3.19370e12	−	1.84389e12i	−0.319860	−	0.184671i
$775$			8.50324e12i			0.846694i
$776$	1.49741e13	−	2.59358e13i	1.48239	−	2.56757i
$777$	1.88765e12	+	3.26951e12i	0.185792	+	0.321802i
$778$	1.29862e13	−	7.49761e12i	1.27079	−	0.733693i
$779$	−6.04621e12			−0.588253
$780$	3.62351e12	−	4.79632e12i	0.350513	−	0.463962i
$781$	−2.96444e12			−0.285110
$782$	−1.76821e12	+	1.02088e12i	−0.169084	+	0.0976209i
$783$	9.68868e12	+	1.67813e13i	0.921163	+	1.59550i
$784$	1.45610e12	−	2.52203e12i	0.137647	−	0.238412i
$785$		−	1.92698e12i		−	0.181119i
$786$	−3.11963e12	−	1.80112e12i	−0.291542	−	0.168322i
$787$	1.66042e13	+	9.58641e12i	1.54287	+	0.890779i	0.998656	+	0.0518353i	$0.0165071\pi$
$787$	1.66042e13	+	9.58641e12i	1.54287	+	0.890779i	0.544219	+	0.838943i	$0.316826\pi$
$788$		−	1.22099e13i		−	1.12809i
$789$	8.13763e11	−	1.40948e12i	0.0747569	−	0.129483i
$790$	−4.51701e12	−	7.82370e12i	−0.412600	−	0.714645i
$791$	2.63631e12	−	1.52207e12i	0.239443	−	0.138242i
$792$	2.84417e12			0.256858
$793$	1.82902e13	−	7.73731e12i	1.64244	−	0.694802i
$794$	−2.26984e13			−2.02677
$795$	−3.48754e12	+	2.01353e12i	−0.309648	+	0.178775i
$796$	5.11337e12	+	8.85662e12i	0.451438	+	0.781914i
$797$	−8.59106e12	+	1.48802e13i	−0.754196	+	1.30631i	0.191577	+	0.981478i	$0.438640\pi$
$797$	−8.59106e12	+	1.48802e13i	−0.754196	+	1.30631i	−0.945773	+	0.324829i	$0.894693\pi$
$798$			1.16753e13i			1.01919i
$799$	−3.81911e12	−	2.20497e12i	−0.331514	−	0.191400i
$800$	1.04745e13	+	6.04747e12i	0.904127	+	0.521998i
$801$			3.21807e11i			0.0276216i
$802$	1.90430e13	−	3.29834e13i	1.62536	−	2.81521i
$803$	1.48389e12	+	2.57018e12i	0.125946	+	0.218144i
$804$	−2.32377e12	+	1.34163e12i	−0.196129	+	0.113235i
$805$	6.59997e11			0.0553937
$806$	−2.53075e12	+	2.04046e13i	−0.211223	+	1.70302i
$807$	−8.12811e12			−0.674619
$808$	−5.75165e12	+	3.32072e12i	−0.474724	+	0.274082i
$809$	5.00052e12	+	8.66116e12i	0.410438	+	0.710899i	0.994938	−	0.100495i	$-0.0320426\pi$
$809$	5.00052e12	+	8.66116e12i	0.410438	+	0.710899i	−0.584500	+	0.811394i	$0.698709\pi$
$810$	1.66650e12	−	2.88647e12i	0.136026	−	0.235605i
$811$		−	8.44692e12i		−	0.685653i	−0.939399	−	0.342827i	$-0.888616\pi$
$811$		−	8.44692e12i		−	0.685653i	0.939399	−	0.342827i	$-0.111384\pi$
$812$	1.57034e13	+	9.06636e12i	1.26763	+	0.731865i
$813$	−2.71859e12	−	1.56958e12i	−0.218241	−	0.126002i
$814$			8.12217e12i			0.648429i
$815$	1.60321e12	−	2.77685e12i	0.127286	−	0.220467i
$816$	2.28599e12	+	3.95945e12i	0.180497	+	0.312629i
$817$	1.10195e13	−	6.36214e12i	0.865295	−	0.499578i
$818$	3.29502e13			2.57317
$819$	−1.87513e12	−	2.32570e11i	−0.145631	−	0.0180624i
$820$	2.97548e12			0.229824
$821$	5.92354e12	−	3.41996e12i	0.455027	−	0.262710i	−0.254924	−	0.966961i	$-0.582050\pi$
$821$	5.92354e12	−	3.41996e12i	0.455027	−	0.262710i	0.709951	+	0.704251i	$0.248717\pi$
$822$	−7.26828e12	−	1.25890e13i	−0.555275	−	0.961765i
$823$	−1.20196e12	+	2.08186e12i	−0.0913253	+	0.158180i	−0.908069	−	0.418821i	$-0.862444\pi$
$823$	−1.20196e12	+	2.08186e12i	−0.0913253	+	0.158180i	0.816744	+	0.577001i	$0.195777\pi$
$824$			6.01353e12i			0.454420i
$825$	2.29399e12	+	1.32444e12i	0.172405	+	0.0995378i
$826$	−3.30771e11	−	1.90971e11i	−0.0247239	−	0.0142744i
$827$		−	4.33245e12i		−	0.322077i	−0.986948	−	0.161038i	$-0.948516\pi$
$827$		−	4.33245e12i		−	0.322077i	0.986948	−	0.161038i	$-0.0514843\pi$
$828$	−2.69637e12	+	4.67024e12i	−0.199362	+	0.345305i
$829$	4.91860e12	+	8.51927e12i	0.361698	+	0.626480i	0.988240	−	0.152908i	$-0.0488637\pi$
$829$	4.91860e12	+	8.51927e12i	0.361698	+	0.626480i	−0.626542	+	0.779388i	$0.715530\pi$
$830$	−6.23360e12	+	3.59897e12i	−0.455919	+	0.263225i
$831$	1.11350e13			0.810003
$832$	2.08315e12	+	1.57377e12i	0.150718	+	0.113864i
$833$	−4.75470e11			−0.0342153
$834$	1.30786e13	−	7.55096e12i	0.936085	−	0.540449i
$835$	−1.00959e12	−	1.74866e12i	−0.0718714	−	0.124485i
$836$	−8.73291e12	+	1.51258e13i	−0.618345	+	1.07100i
$837$			1.46035e13i			1.02847i
$838$	7.50694e12	+	4.33414e12i	0.525854	+	0.303602i
$839$	3.28293e12	+	1.89540e12i	0.228735	+	0.132060i	0.609988	−	0.792410i	$-0.291174\pi$
$839$	3.28293e12	+	1.89540e12i	0.228735	+	0.132060i	−0.381253	+	0.924471i	$0.624507\pi$
$840$		−	3.22833e12i		−	0.223728i
$841$	−1.36286e13	+	2.36055e13i	−0.939443	+	1.62716i
$842$	−2.01810e13	−	3.49546e13i	−1.38369	−	2.39662i
$843$	−1.61779e13	+	9.34034e12i	−1.10331	+	0.636998i
$844$	−3.51300e13			−2.38307
$845$	−4.64359e12	+	1.31922e12i	−0.313327	+	0.0890148i
$846$	−1.67508e13			−1.12427
$847$	−4.50544e12	+	2.60122e12i	−0.300789	+	0.173661i
$848$	−2.03632e13	−	3.52701e13i	−1.35227	−	2.34221i
$849$	6.58574e10	−	1.14068e11i	0.00435031	−	0.00753496i
$850$		−	5.90325e12i		−	0.387888i
$851$	−7.49362e12	−	4.32645e12i	−0.489789	−	0.282780i
$852$	−2.38101e13	−	1.37468e13i	−1.54804	−	0.893763i
$853$			2.13503e13i			1.38081i	0.723423	+	0.690405i	$0.242567\pi$
$853$			2.13503e13i			1.38081i	−0.723423	+	0.690405i	$0.757433\pi$
$854$	9.49113e12	−	1.64391e13i	0.610601	−	1.05759i
$855$	−1.88022e12	−	3.25663e12i	−0.120326	−	0.208411i
$856$	−3.35426e13	+	1.93658e13i	−2.13533	+	1.23283i
$857$	−3.94898e12			−0.250075			−0.125038	−	0.992152i	$-0.539905\pi$
$857$	−3.94898e12			−0.250075			−0.125038	+	0.992152i	$0.539905\pi$
$858$	5.11053e12	+	3.86089e12i	0.321939	+	0.243217i
$859$	3.11813e12			0.195400			0.0977002	−	0.995216i	$-0.468851\pi$
$859$	3.11813e12			0.195400			0.0977002	+	0.995216i	$0.468851\pi$
$860$	−5.42298e12	+	3.13096e12i	−0.338061	+	0.195180i
$861$	7.36826e11	+	1.27622e12i	0.0456931	+	0.0791428i
$862$	−2.30759e13	+	3.99686e13i	−1.42356	+	2.46568i
$863$			2.49150e13i			1.52902i	0.644613	+	0.764509i	$0.277018\pi$
$863$			2.49150e13i			1.52902i	−0.644613	+	0.764509i	$0.722982\pi$
$864$	1.79889e13	+	1.03859e13i	1.09823	+	0.634064i
$865$	2.82339e12	+	1.63008e12i	0.171474	+	0.0990006i
$866$		−	3.26002e13i		−	1.96966i
$867$	−6.13317e12	+	1.06230e13i	−0.368637	+	0.638498i
$868$	6.83273e12	+	1.18346e13i	0.408560	+	0.707646i
$869$	5.79658e12	−	3.34666e12i	0.344812	−	0.199077i
$870$	1.32338e13			0.783155
$871$	2.13843e12	+	2.65226e11i	0.125896	+	0.0156147i
$872$	−6.68252e13			−3.91396
$873$	−7.36329e12	+	4.25120e12i	−0.429050	+	0.247712i
$874$	−1.33797e13	−	2.31743e13i	−0.775612	−	1.34340i
$875$	−2.02147e12	+	3.50129e12i	−0.116582	+	0.201926i
$876$			2.75246e13i			1.57926i
$877$	−8.16094e11	−	4.71172e11i	−0.0465845	−	0.0268956i	0.476527	−	0.879160i	$-0.341896\pi$
$877$	−8.16094e11	−	4.71172e11i	−0.0465845	−	0.0268956i	−0.523111	+	0.852264i	$0.675229\pi$
$878$	2.89236e13	+	1.66991e13i	1.64258	+	0.948345i
$879$		−	2.01276e13i		−	1.13721i
$880$	1.58977e12	−	2.75356e12i	0.0893638	−	0.154783i
$881$	−9.04625e12	−	1.56686e13i	−0.505914	−	0.876270i	−0.999977	−	0.00684292i	$-0.997822\pi$
$881$	−9.04625e12	−	1.56686e13i	−0.505914	−	0.876270i	0.494062	−	0.869427i	$-0.335512\pi$
$882$	−1.56407e12	+	9.03017e11i	−0.0870258	+	0.0502444i
$883$	−5.98940e12			−0.331559			−0.165779	−	0.986163i	$-0.553014\pi$
$883$	−5.98940e12			−0.331559			−0.165779	+	0.986163i	$0.553014\pi$
$884$	1.22168e12	−	9.85000e12i	0.0672857	−	0.542502i
$885$	−1.93830e11			−0.0106213
$886$	−2.53192e13	+	1.46181e13i	−1.38038	+	0.796962i
$887$	4.36900e12	+	7.56734e12i	0.236988	+	0.410475i	0.959849	−	0.280519i	$-0.0905065\pi$
$887$	4.36900e12	+	7.56734e12i	0.236988	+	0.410475i	−0.722861	+	0.690994i	$0.757173\pi$
$888$	−2.11625e13	+	3.66545e13i	−1.14211	+	1.97820i
$889$		−	6.30710e10i		−	0.00338666i
$890$	6.80562e11	+	3.92923e11i	0.0363591	+	0.0209919i
$891$	2.13858e12	+	1.23471e12i	0.113678	+	0.0656321i
$892$		−	4.76973e13i		−	2.52262i
$893$	2.88984e13	−	5.00536e13i	1.52070	−	2.63393i
$894$	−1.91315e13	−	3.31368e13i	−1.00168	−	1.73497i
$895$	−6.23387e11	+	3.59913e11i	−0.0324754	+	0.0187497i
$896$	−6.02073e12			−0.312078
$897$	−6.28434e12	+	2.65846e12i	−0.324111	+	0.137108i
$898$	−5.44095e13			−2.79210
$899$	−2.72583e13	+	1.57376e13i	−1.39181	+	0.803561i
$900$	−7.79591e12	−	1.35029e13i	−0.396073	−	0.686019i
$901$	−3.32467e12	+	5.75850e12i	−0.168069	+	0.291104i
$902$			3.17041e12i			0.159473i
$903$	−2.68581e12	−	1.55065e12i	−0.134425	−	0.0776104i
$904$	2.95557e13	+	1.70640e13i	1.47192	+	0.849811i
$905$		−	1.10380e12i		−	0.0546982i
$906$	1.50093e13	−	2.59969e13i	0.740090	−	1.28187i
$907$	−1.82571e13	−	3.16223e13i	−0.895777	−	1.55153i	−0.832840	−	0.553514i	$-0.813286\pi$
$907$	−1.82571e13	−	3.16223e13i	−0.895777	−	1.55153i	−0.0629377	−	0.998017i	$-0.520047\pi$
$908$	7.27642e13	−	4.20104e13i	3.55248	−	2.05102i
$909$	1.88553e12			0.0916001
$910$	−2.78135e12	+	3.68159e12i	−0.134453	+	0.177971i
$911$	5.09862e12			0.245256			0.122628	−	0.992453i	$-0.460868\pi$
$911$	5.09862e12			0.245256			0.122628	+	0.992453i	$0.460868\pi$
$912$	−5.18929e13	+	2.99604e13i	−2.48388	+	1.43407i
$913$	−2.66648e12	−	4.61848e12i	−0.127005	−	0.219979i
$914$	−3.45344e12	+	5.98154e12i	−0.163680	+	0.283501i
$915$		−	9.63322e12i		−	0.454335i
$916$	3.84157e13	+	2.21793e13i	1.80293	+	1.04092i
$917$	1.66506e12	+	9.61326e11i	0.0777623	+	0.0448961i
$918$		−	1.01382e13i		−	0.471162i
$919$	−1.31486e13	+	2.27740e13i	−0.608077	+	1.05322i	0.383480	+	0.923549i	$0.374725\pi$
$919$	−1.31486e13	+	2.27740e13i	−0.608077	+	1.05322i	−0.991557	+	0.129671i	$0.958608\pi$
$920$	3.69962e12	+	6.40793e12i	0.170260	+	0.294898i
$921$	1.15712e13	−	6.68066e12i	0.529922	−	0.305951i
$922$	−3.20148e13			−1.45902
$923$	8.60200e12	+	2.03343e13i	0.390114	+	0.922191i
$924$	4.25697e12			0.192122
$925$	2.16661e13	−	1.25089e13i	0.973066	−	0.561800i
$926$	−1.16132e13	−	2.01147e13i	−0.519044	−	0.899011i
$927$	8.53634e11	−	1.47854e12i	0.0379676	−	0.0657618i
$928$			4.47700e13i			1.98162i
$929$	−2.87199e13	−	1.65814e13i	−1.26506	−	0.730385i	−0.291014	−	0.956719i	$-0.593993\pi$
$929$	−2.87199e13	−	1.65814e13i	−1.26506	−	0.730385i	−0.974050	+	0.226334i	$0.927326\pi$
$930$	8.63726e12	+	4.98673e12i	0.378619	+	0.218596i
$931$		−	6.23154e12i		−	0.271845i
$932$	−2.37671e13	+	4.11658e13i	−1.03182	+	1.78717i
$933$	1.16662e13	+	2.02065e13i	0.504038	+	0.873019i
$934$	−9.58672e12	+	5.53490e12i	−0.412201	+	0.237984i
$935$	−5.19118e11			−0.0222134
$936$	−8.25303e12	−	1.95093e13i	−0.351457	−	0.830809i
$937$	7.49024e11			0.0317444			0.0158722	−	0.999874i	$-0.494948\pi$
$937$	7.49024e11			0.0317444			0.0158722	+	0.999874i	$0.494948\pi$
$938$	1.78370e12	−	1.02982e12i	0.0752329	−	0.0434357i
$939$	1.55166e13	+	2.68755e13i	0.651329	+	1.12814i
$940$	−1.42216e13	+	2.46326e13i	−0.594119	+	1.02905i
$941$			1.44448e13i			0.600563i	0.953851	+	0.300282i	$0.0970806\pi$
$941$			1.44448e13i			0.600563i	−0.953851	+	0.300282i	$0.902919\pi$
$942$	1.64912e13	+	9.52121e12i	0.682376	+	0.393970i
$943$	−2.92506e12	−	1.68878e12i	−0.120457	−	0.0695459i
$944$		−	1.96023e12i		−	0.0803404i
$945$	−1.63859e12	+	2.83813e12i	−0.0668387	+	0.115768i
$946$	−3.33607e12	−	5.77824e12i	−0.135433	−	0.234577i
$947$	1.51690e13	−	8.75784e12i	0.612891	−	0.353853i	−0.161205	−	0.986921i	$-0.551538\pi$
$947$	1.51690e13	−	8.75784e12i	0.612891	−	0.353853i	0.774096	+	0.633068i	$0.218205\pi$
$948$	6.20768e13			2.49627
$949$	1.33240e13	−	1.76366e13i	0.533259	−	0.705857i
$950$	7.73684e13			3.08182
$951$	1.91050e13	−	1.10303e13i	0.757418	−	0.437296i
$952$	−2.66525e12	−	4.61634e12i	−0.105165	−	0.182151i
$953$	−1.37363e13	+	2.37920e13i	−0.539450	+	0.934356i	0.459483	+	0.888186i	$0.348035\pi$
$953$	−1.37363e13	+	2.37920e13i	−0.539450	+	0.934356i	−0.998934	+	0.0461691i	$0.985299\pi$
$954$			2.52570e13i			0.987222i
$955$	8.09995e12	+	4.67651e12i	0.315114	+	0.181931i
$956$	4.24483e13	+	2.45075e13i	1.64361	+	0.948940i
$957$			9.80492e12i			0.377868i
$958$	−3.56231e13	+	6.17009e13i	−1.36643	+	2.36672i
$959$	3.87936e12	+	6.71925e12i	0.148107	+	0.256529i
$960$	1.09675e12	−	6.33208e11i	0.0416760	−	0.0240617i
$961$	2.71887e12			0.102833
$962$	5.57133e13	−	2.35684e13i	2.09735	−	0.887241i
$963$	1.09961e13			0.412021
$964$	−9.45462e13	+	5.45863e13i	−3.52612	+	2.03581i
$965$	−1.99718e12	−	3.45922e12i	−0.0741387	−	0.128412i
$966$	−3.26105e12	+	5.64831e12i	−0.120493	+	0.208699i
$967$		−	5.18455e13i		−	1.90674i	−0.301803	−	0.953370i	$-0.597588\pi$
$967$		−	5.18455e13i		−	1.90674i	0.301803	−	0.953370i	$-0.402412\pi$
$968$	−5.05105e13	−	2.91623e13i	−1.84903	−	1.06754i
$969$	8.47248e12	+	4.89159e12i	0.308712	+	0.178235i
$970$			2.07627e13i			0.753026i
$971$	2.45249e12	−	4.24784e12i	0.0885362	−	0.153349i	−0.818356	−	0.574711i	$-0.805114\pi$
$971$	2.45249e12	−	4.24784e12i	0.0885362	−	0.153349i	0.906893	+	0.421362i	$0.138448\pi$
$972$	−2.30329e13	−	3.98942e13i	−0.827659	−	1.43355i
$973$	−6.98058e12	+	4.03024e12i	−0.249680	+	0.144153i
$974$	−4.18575e13			−1.49025
$975$	2.42830e12	−	1.95786e13i	0.0860561	−	0.693841i
$976$	9.74223e13			3.43664
$977$	2.77961e13	−	1.60481e13i	0.976020	−	0.563505i	0.0749536	−	0.997187i	$-0.476119\pi$
$977$	2.77961e13	−	1.60481e13i	0.976020	−	0.563505i	0.901066	+	0.433682i	$0.142786\pi$
$978$	1.58430e13	+	2.74409e13i	0.553748	+	0.959120i
$979$	−2.91116e11	+	5.04228e11i	−0.0101285	+	0.0175430i
$980$			3.06669e12i			0.106207i
$981$	1.64302e13	+	9.48599e12i	0.566412	+	0.327018i
$982$	3.53220e13	+	2.03932e13i	1.21211	+	0.699814i
$983$		−	2.54443e13i		−	0.869161i	−0.900633	−	0.434581i	$-0.856897\pi$
$983$		−	2.54443e13i		−	0.869161i	0.900633	−	0.434581i	$-0.143103\pi$
$984$	−8.26057e12	+	1.43077e13i	−0.280887	+	0.486511i
$985$	2.37812e12	+	4.11902e12i	0.0804952	+	0.139422i
$986$	1.89237e13	−	1.09256e13i	0.637616	−	0.368127i
$987$	−1.40869e13			−0.472486
$988$	1.29095e14	+	1.60114e13i	4.31025	+	0.534594i
$989$	7.10811e12			0.236249
$990$	−1.70766e12	+	9.85916e11i	−0.0564992	+	0.0326198i
$991$	−2.81751e13	−	4.88007e13i	−0.927970	−	1.60729i	−0.786713	−	0.617319i	$-0.788219\pi$
$991$	−2.81751e13	−	4.88007e13i	−0.927970	−	1.60729i	−0.141258	−	0.989973i	$-0.545115\pi$
$992$	−1.68701e13	+	2.92199e13i	−0.553115	+	0.958023i
$993$			1.30989e13i			0.427528i
$994$	1.82763e13	+	1.05518e13i	0.593812	+	0.342837i
$995$	−3.44999e12	−	1.99185e12i	−0.111587	−	0.0644248i
$996$		−	4.94603e13i		−	1.59254i
$997$	−1.85713e13	+	3.21664e13i	−0.595269	+	1.03104i	0.398239	+	0.917282i	$0.369621\pi$
$997$	−1.85713e13	+	3.21664e13i	−0.595269	+	1.03104i	−0.993509	+	0.113755i	$0.963712\pi$
$998$	1.07827e11	+	1.86761e11i	0.00344063	+	0.00595935i
$999$	3.72093e13	−	2.14828e13i	1.18197	−	0.682411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.q.a.36.4	✓	124
13.4	even	6	inner	91.10.q.a.43.4	yes	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.q.a.36.4	✓	124	1.1	even	1	trivial
91.10.q.a.43.4	yes	124	13.4	even	6	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-35.5029 + 20.4976i) q^{2} +(54.8657 + 95.0301i) q^{3} +(584.302 - 1012.04i) q^{4} +455.216i q^{5} +(-3895.78 - 2249.23i) q^{6} +(2079.33 + 1200.50i) q^{7} +26917.6i q^{8} +(3821.02 - 6618.20i) q^{9} +O(q^{10})\)	\(q+(-35.5029 + 20.4976i) q^{2} +(54.8657 + 95.0301i) q^{3} +(584.302 - 1012.04i) q^{4} +455.216i q^{5} +(-3895.78 - 2249.23i) q^{6} +(2079.33 + 1200.50i) q^{7} +26917.6i q^{8} +(3821.02 - 6618.20i) q^{9} +(-9330.84 - 16161.5i) q^{10} +(11974.0 - 6913.22i) q^{11} +128233. q^{12} +(-82166.0 - 62074.5i) q^{13} -98429.4 q^{14} +(-43259.3 + 24975.7i) q^{15} +(-252584. - 437488. i) q^{16} +(-41239.0 + 71428.1i) q^{17} +313287. i q^{18} +(-936141. - 540482. i) q^{19} +(460698. + 265984. i) q^{20} +263465. i q^{21} +(-283409. + 490878. i) q^{22} +(-301927. - 522953. i) q^{23} +(-2.55799e6 + 1.47685e6i) q^{24} +1.74590e6 q^{25} +(4.18951e6 + 519618. i) q^{26} +2.99841e6 q^{27} +(2.42991e6 - 1.40291e6i) q^{28} +(3.23127e6 + 5.59672e6i) q^{29} +(1.02389e6 - 1.77342e6i) q^{30} +4.87040e6i q^{31} +(5.99949e6 + 3.46381e6i) q^{32} +(1.31393e6 + 758597. i) q^{33} -3.38120e6i q^{34} +(-546487. + 946544. i) q^{35} +(-4.46526e6 - 7.73406e6i) q^{36} +(1.24097e7 - 7.16472e6i) q^{37} +4.43143e7 q^{38} +(1.39086e6 - 1.12140e7i) q^{39} -1.22533e7 q^{40} +(4.84399e6 - 2.79668e6i) q^{41} +(-5.40040e6 - 9.35376e6i) q^{42} +(-5.88562e6 + 1.01942e7i) q^{43} -1.61576e7i q^{44} +(3.01271e6 + 1.73939e6i) q^{45} +(2.14386e7 + 1.23776e7i) q^{46} +5.34680e7i q^{47} +(2.77164e7 - 4.80062e7i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(-6.19846e7 + 3.57868e7i) q^{50} -9.05043e6 q^{51} +(-1.10832e8 + 4.68851e7i) q^{52} +8.06196e7 q^{53} +(-1.06452e8 + 6.14602e7i) q^{54} +(3.14701e6 + 5.45078e6i) q^{55} +(-3.23146e7 + 5.59706e7i) q^{56} -1.18616e8i q^{57} +(-2.29439e8 - 1.32466e8i) q^{58} +(3.36049e6 + 1.94018e6i) q^{59} +5.83736e7i q^{60} +(-9.64257e7 + 1.67014e8i) q^{61} +(-9.98314e7 - 1.72913e8i) q^{62} +(1.58903e7 - 9.17426e6i) q^{63} -2.53529e7 q^{64} +(2.82573e7 - 3.74033e7i) q^{65} -6.21976e7 q^{66} +(-1.81216e7 + 1.04625e7i) q^{67} +(4.81921e7 + 8.34712e7i) q^{68} +(3.31309e7 - 5.73843e7i) q^{69} -4.48067e7i q^{70} +(-1.85679e8 - 1.07202e8i) q^{71} +(1.78146e8 + 1.02853e8i) q^{72} +2.14646e8i q^{73} +(-2.93719e8 + 5.08736e8i) q^{74} +(9.57901e7 + 1.65913e8i) q^{75} +(-1.09398e9 + 6.31609e8i) q^{76} +3.31973e7 q^{77} +(1.80481e8 + 4.26639e8i) q^{78} +4.84095e8 q^{79} +(1.99152e8 - 1.14980e8i) q^{80} +(8.93008e7 + 1.54674e8i) q^{81} +(-1.14650e8 + 1.98580e8i) q^{82} -3.85707e8i q^{83} +(2.66637e8 + 1.53943e8i) q^{84} +(-3.25152e7 - 1.87727e7i) q^{85} -4.82564e8i q^{86} +(-3.54572e8 + 6.14136e8i) q^{87} +(1.86087e8 + 3.22313e8i) q^{88} +(-3.64684e7 + 2.10551e7i) q^{89} -1.42613e8 q^{90} +(-9.63295e7 - 2.27714e8i) q^{91} -7.05667e8 q^{92} +(-4.62834e8 + 2.67217e8i) q^{93} +(-1.09596e9 - 1.89827e9i) q^{94} +(2.46036e8 - 4.26147e8i) q^{95} +7.60176e8i q^{96} +(-9.63525e8 - 5.56291e8i) q^{97} +(-2.04667e8 - 1.18165e8i) q^{98} -1.05662e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9}+O(q^{10}) \) 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9	\( 124 q + 15360 q^{4} + 6570 q^{6} - 381386 q^{9} - 47368 q^{10} + 18420 q^{11} + 434316 q^{12} - 103730 q^{13} - 307328 q^{14} - 994308 q^{15} - 4327304 q^{16} + 826226 q^{17} - 832512 q^{20} - 2238874 q^{22} - 5178348 q^{23} + 13060272 q^{24} - 56263016 q^{25} + 12486810 q^{26} - 16794384 q^{27} + 8409710 q^{29} - 18091000 q^{30} + 30354048 q^{32} + 36508140 q^{33} + 8902908 q^{35} + 42350446 q^{36} + 26865678 q^{37} - 7473860 q^{38} - 21470652 q^{39} - 112860988 q^{40} - 109829778 q^{41} + 12446784 q^{42} - 53384856 q^{43} - 84576450 q^{45} + 160042176 q^{46} - 39524126 q^{48} + 357417662 q^{49} + 35767422 q^{50} + 121877584 q^{51} + 61751010 q^{52} - 252868460 q^{53} + 951692088 q^{54} - 414833028 q^{55} - 118013952 q^{56} - 342666540 q^{58} - 440088588 q^{59} + 264060146 q^{61} + 995887736 q^{62} - 383747028 q^{63} - 2239569444 q^{64} - 501903354 q^{65} + 304284804 q^{66} + 392937636 q^{67} - 3665660 q^{68} - 249969892 q^{69} - 375620748 q^{71} - 2829560808 q^{72} + 1336479018 q^{74} + 1306893216 q^{75} + 1652559990 q^{76} + 823754288 q^{77} + 857091302 q^{78} - 2357982776 q^{79} + 1107773136 q^{80} - 1492992434 q^{81} - 1984241462 q^{82} - 2156016366 q^{84} + 3060837654 q^{85} - 1286987624 q^{87} + 1904443442 q^{88} + 887446752 q^{89} + 7601525656 q^{90} - 86522436 q^{91} - 8365653336 q^{92} - 776657196 q^{93} + 6270763420 q^{94} - 6325568332 q^{95} - 5522676732 q^{97}+O(q^{100}) \) 124 * q + 15360 * q^4 + 6570 * q^6 - 381386 * q^9 - 47368 * q^10 + 18420 * q^11 + 434316 * q^12 - 103730 * q^13 - 307328 * q^14 - 994308 * q^15 - 4327304 * q^16 + 826226 * q^17 - 832512 * q^20 - 2238874 * q^22 - 5178348 * q^23 + 13060272 * q^24 - 56263016 * q^25 + 12486810 * q^26 - 16794384 * q^27 + 8409710 * q^29 - 18091000 * q^30 + 30354048 * q^32 + 36508140 * q^33 + 8902908 * q^35 + 42350446 * q^36 + 26865678 * q^37 - 7473860 * q^38 - 21470652 * q^39 - 112860988 * q^40 - 109829778 * q^41 + 12446784 * q^42 - 53384856 * q^43 - 84576450 * q^45 + 160042176 * q^46 - 39524126 * q^48 + 357417662 * q^49 + 35767422 * q^50 + 121877584 * q^51 + 61751010 * q^52 - 252868460 * q^53 + 951692088 * q^54 - 414833028 * q^55 - 118013952 * q^56 - 342666540 * q^58 - 440088588 * q^59 + 264060146 * q^61 + 995887736 * q^62 - 383747028 * q^63 - 2239569444 * q^64 - 501903354 * q^65 + 304284804 * q^66 + 392937636 * q^67 - 3665660 * q^68 - 249969892 * q^69 - 375620748 * q^71 - 2829560808 * q^72 + 1336479018 * q^74 + 1306893216 * q^75 + 1652559990 * q^76 + 823754288 * q^77 + 857091302 * q^78 - 2357982776 * q^79 + 1107773136 * q^80 - 1492992434 * q^81 - 1984241462 * q^82 - 2156016366 * q^84 + 3060837654 * q^85 - 1286987624 * q^87 + 1904443442 * q^88 + 887446752 * q^89 + 7601525656 * q^90 - 86522436 * q^91 - 8365653336 * q^92 - 776657196 * q^93 + 6270763420 * q^94 - 6325568332 * q^95 - 5522676732 * q^97

Introduction

L-functions

Modular forms

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Database

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