LMFDB - Embedded newform 91.10.q.a.36.11

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			36.11
Character	$\chi$	$=$	91.36
Dual form			91.10.q.a.43.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-29.7427 + 17.1720i) q^{2} +(-63.0297 - 109.171i) q^{3} +(333.753 - 578.077i) q^{4} +894.218i q^{5} +(3749.35 + 2164.69i) q^{6} +(-2079.33 - 1200.50i) q^{7} +5340.70i q^{8} +(1896.02 - 3284.00i) q^{9} +O(q^{10})$	\(q+(-29.7427 + 17.1720i) q^{2} +(-63.0297 - 109.171i) q^{3} +(333.753 - 578.077i) q^{4} +894.218i q^{5} +(3749.35 + 2164.69i) q^{6} +(-2079.33 - 1200.50i) q^{7} +5340.70i q^{8} +(1896.02 - 3284.00i) q^{9} +(-15355.5 - 26596.5i) q^{10} +(27666.2 - 15973.1i) q^{11} -84145.4 q^{12} +(-27651.7 - 99196.2i) q^{13} +82459.8 q^{14} +(97622.3 - 56362.2i) q^{15} +(79171.3 + 137129. i) q^{16} +(34404.7 - 59590.7i) q^{17} +130234. i q^{18} +(411953. + 237841. i) q^{19} +(516927. + 298448. i) q^{20} +302668. i q^{21} +(-548579. + 950167. i) q^{22} +(62398.3 + 108077. i) q^{23} +(583047. - 336623. i) q^{24} +1.15350e6 q^{25} +(2.52583e6 + 2.47553e6i) q^{26} -2.95925e6 q^{27} +(-1.38796e6 + 801341. i) q^{28} +(-466094. - 807298. i) q^{29} +(-1.93570e6 + 3.35273e6i) q^{30} +1.00238e7i q^{31} +(-7.07763e6 - 4.08627e6i) q^{32} +(-3.48758e6 - 2.01356e6i) q^{33} +2.36319e6i q^{34} +(1.07351e6 - 1.85937e6i) q^{35} +(-1.26561e6 - 2.19209e6i) q^{36} +(4.50111e6 - 2.59872e6i) q^{37} -1.63368e7 q^{38} +(-9.08643e6 + 9.27106e6i) q^{39} -4.77575e6 q^{40} +(-2.79105e7 + 1.61141e7i) q^{41} +(-5.19741e6 - 9.00219e6i) q^{42} +(1.68063e7 - 2.91094e7i) q^{43} -2.13243e7i q^{44} +(2.93661e6 + 1.69546e6i) q^{45} +(-3.71179e6 - 2.14300e6i) q^{46} +2.60287e7i q^{47} +(9.98028e6 - 1.72863e7i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(-3.43082e7 + 1.98079e7i) q^{50} -8.67407e6 q^{51} +(-6.65719e7 - 1.71222e7i) q^{52} +6.33814e7 q^{53} +(8.80161e7 - 5.08161e7i) q^{54} +(1.42834e7 + 2.47396e7i) q^{55} +(6.41151e6 - 1.11051e7i) q^{56} -5.99642e7i q^{57} +(2.77258e7 + 1.60075e7i) q^{58} +(1.27905e8 + 7.38459e7i) q^{59} -7.52443e7i q^{60} +(7.29737e7 - 1.26394e8i) q^{61} +(-1.72128e8 - 2.98135e8i) q^{62} +(-7.88489e6 + 4.55235e6i) q^{63} +1.99606e8 q^{64} +(8.87030e7 - 2.47267e7i) q^{65} +1.38307e8 q^{66} +(1.80937e8 - 1.04464e8i) q^{67} +(-2.29654e7 - 3.97772e7i) q^{68} +(7.86588e6 - 1.36241e7i) q^{69} +7.37370e7i q^{70} +(-2.70152e8 - 1.55972e8i) q^{71} +(1.75389e7 + 1.01261e7i) q^{72} -1.14181e6i q^{73} +(-8.92502e7 + 1.54586e8i) q^{74} +(-7.27047e7 - 1.25928e8i) q^{75} +(2.74981e8 - 1.58760e8i) q^{76} -7.67028e7 q^{77} +(1.11053e8 - 4.31778e8i) q^{78} -5.29459e8 q^{79} +(-1.22623e8 + 7.07963e7i) q^{80} +(1.49201e8 + 2.58424e8i) q^{81} +(5.53422e8 - 9.58555e8i) q^{82} -6.57330e8i q^{83} +(1.74966e8 + 1.01017e8i) q^{84} +(5.32871e7 + 3.07653e7i) q^{85} +1.15439e9i q^{86} +(-5.87555e7 + 1.01767e8i) q^{87} +(8.53075e7 + 1.47757e8i) q^{88} +(3.36332e7 - 1.94182e7i) q^{89} -1.16457e8 q^{90} +(-6.15880e7 + 2.39457e8i) q^{91} +8.33025e7 q^{92} +(1.09430e9 - 6.31796e8i) q^{93} +(-4.46964e8 - 7.74164e8i) q^{94} +(-2.12682e8 + 3.68375e8i) q^{95} +1.03023e9i q^{96} +(-3.27858e8 - 1.89289e8i) q^{97} +(-1.71461e8 - 9.89930e7i) q^{98} -1.21141e8i 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 $

$2$	−29.7427	+	17.1720i	−1.31446	+	0.758901i	−0.982831	−	0.184510i	$-0.940930\pi$
$2$	−29.7427	+	17.1720i	−1.31446	+	0.758901i	−0.331625	+	0.943411i	$0.607597\pi$
$3$	−63.0297	−	109.171i	−0.449262	−	0.778144i	0.549076	−	0.835772i	$-0.314980\pi$
$3$	−63.0297	−	109.171i	−0.449262	−	0.778144i	−0.998338	+	0.0576280i	$0.981646\pi$
$4$	333.753	−	578.077i	0.651862	−	1.12906i
$5$			894.218i			0.639850i	0.947443	+	0.319925i	$0.103658\pi$
$5$			894.218i			0.639850i	−0.947443	+	0.319925i	$0.896342\pi$
$6$	3749.35	+	2164.69i	1.18107	+	0.681890i
$7$	−2079.33	−	1200.50i	−0.327327	−	0.188982i
$7$	−2079.33	−	1200.50i	−0.327327	−	0.188982i
$8$			5340.70i			0.460992i
$9$	1896.02	−	3284.00i	0.0963278	−	0.166845i
$10$	−15355.5	−	26596.5i	−0.485583	−	0.841054i
$11$	27666.2	−	15973.1i	0.569748	−	0.328944i	−0.187301	−	0.982303i	$-0.559974\pi$
$11$	27666.2	−	15973.1i	0.569748	−	0.328944i	0.757049	+	0.653359i	$0.226641\pi$
$12$	−84145.4			−1.17143
$13$	−27651.7	−	99196.2i	−0.268520	−	0.963274i
$13$	−27651.7	−	99196.2i	−0.268520	−	0.963274i
$14$	82459.8			0.573675
$15$	97622.3	−	56362.2i	0.497896	−	0.287460i
$16$	79171.3	+	137129.i	0.302014	+	0.523104i
$17$	34404.7	−	59590.7i	0.0999074	−	0.173045i	−0.811739	−	0.584021i	$-0.801479\pi$
$17$	34404.7	−	59590.7i	0.0999074	−	0.173045i	0.911646	+	0.410976i	$0.134812\pi$
$18$			130234.i			0.292413i
$19$	411953.	+	237841.i	0.725197	+	0.418693i	0.816663	−	0.577115i	$-0.195822\pi$
$19$	411953.	+	237841.i	0.725197	+	0.418693i	−0.0914654	+	0.995808i	$0.529155\pi$
$20$	516927.	+	298448.i	0.722427	+	0.417094i
$21$			302668.i			0.339610i
$22$	−548579.	+	950167.i	−0.499272	+	0.864764i
$23$	62398.3	+	108077.i	0.0464940	+	0.0805300i	0.888336	−	0.459194i	$-0.151862\pi$
$23$	62398.3	+	108077.i	0.0464940	+	0.0805300i	−0.841842	+	0.539724i	$0.818528\pi$
$24$	583047.	−	336623.i	0.358718	−	0.207106i
$25$	1.15350e6			0.590592
$26$	2.52583e6	+	2.47553e6i	1.08399	+	1.06240i
$27$	−2.95925e6			−1.07163
$28$	−1.38796e6	+	801341.i	−0.426744	+	0.246381i
$29$	−466094.	−	807298.i	−0.122372	−	0.211955i	0.798331	−	0.602219i	$-0.205717\pi$
$29$	−466094.	−	807298.i	−0.122372	−	0.211955i	−0.920703	+	0.390265i	$0.872383\pi$
$30$	−1.93570e6	+	3.35273e6i	−0.436308	+	0.755707i
$31$			1.00238e7i			1.94941i	0.223485	+	0.974707i	$0.428257\pi$
$31$			1.00238e7i			1.94941i	−0.223485	+	0.974707i	$0.571743\pi$
$32$	−7.07763e6	−	4.08627e6i	−1.19320	−	0.688894i
$33$	−3.48758e6	−	2.01356e6i	−0.511932	−	0.295564i
$34$			2.36319e6i			0.303279i
$35$	1.07351e6	−	1.85937e6i	0.120920	−	0.209440i
$36$	−1.26561e6	−	2.19209e6i	−0.125585	−	0.217519i
$37$	4.50111e6	−	2.59872e6i	0.394832	−	0.227956i	−0.289420	−	0.957202i	$-0.593462\pi$
$37$	4.50111e6	−	2.59872e6i	0.394832	−	0.227956i	0.684252	+	0.729246i	$0.260129\pi$
$38$	−1.63368e7			−1.27099
$39$	−9.08643e6	+	9.27106e6i	−0.628930	+	0.641710i
$40$	−4.77575e6			−0.294966
$41$	−2.79105e7	+	1.61141e7i	−1.54255	+	0.890593i	−0.543875	+	0.839166i	$0.683043\pi$
$41$	−2.79105e7	+	1.61141e7i	−1.54255	+	0.890593i	−0.998677	+	0.0514263i	$0.983623\pi$
$42$	−5.19741e6	−	9.00219e6i	−0.257730	−	0.446402i
$43$	1.68063e7	−	2.91094e7i	0.749659	−	1.29845i	−0.198327	−	0.980136i	$-0.563551\pi$
$43$	1.68063e7	−	2.91094e7i	0.749659	−	1.29845i	0.947986	−	0.318312i	$-0.103116\pi$
$44$		−	2.13243e7i		−	0.857704i
$45$	2.93661e6	+	1.69546e6i	0.106756	+	0.0616354i
$46$	−3.71179e6	−	2.14300e6i	−0.122229	−	0.0705687i
$47$			2.60287e7i			0.778058i	0.921226	+	0.389029i	$0.127189\pi$
$47$			2.60287e7i			0.778058i	−0.921226	+	0.389029i	$0.872811\pi$
$48$	9.98028e6	−	1.72863e7i	0.271367	−	0.470022i
$49$	2.88240e6	+	4.99246e6i	0.0714286	+	0.123718i
$50$	−3.43082e7	+	1.98079e7i	−0.776307	+	0.448201i
$51$	−8.67407e6			−0.179538
$52$	−6.65719e7	−	1.71222e7i	−1.26263	−	0.324746i
$53$	6.33814e7			1.10337			0.551684	−	0.834053i	$-0.313985\pi$
$53$	6.33814e7			1.10337			0.551684	+	0.834053i	$0.313985\pi$
$54$	8.80161e7	−	5.08161e7i	1.40861	−	0.813260i
$55$	1.42834e7	+	2.47396e7i	0.210475	+	0.364553i
$56$	6.41151e6	−	1.11051e7i	0.0871193	−	0.150895i
$57$		−	5.99642e7i		−	0.752411i
$58$	2.77258e7	+	1.60075e7i	0.321705	+	0.185737i
$59$	1.27905e8	+	7.38459e7i	1.37421	+	0.793401i	0.991455	−	0.130449i	$-0.0416420\pi$
$59$	1.27905e8	+	7.38459e7i	1.37421	+	0.793401i	0.382755	+	0.923850i	$0.374975\pi$
$60$		−	7.52443e7i		−	0.749537i
$61$	7.29737e7	−	1.26394e8i	0.674811	−	1.16881i	−0.301714	−	0.953399i	$-0.597559\pi$
$61$	7.29737e7	−	1.26394e8i	0.674811	−	1.16881i	0.976524	−	0.215408i	$-0.0691080\pi$
$62$	−1.72128e8	−	2.98135e8i	−1.47941	−	2.56242i
$63$	−7.88489e6	+	4.55235e6i	−0.0630614	+	0.0364085i
$64$	1.99606e8			1.48718
$65$	8.87030e7	−	2.47267e7i	0.616351	−	0.171813i
$66$	1.38307e8			0.897215
$67$	1.80937e8	−	1.04464e8i	1.09696	−	0.633331i	0.161541	−	0.986866i	$-0.448354\pi$
$67$	1.80937e8	−	1.04464e8i	1.09696	−	0.633331i	0.935421	+	0.353535i	$0.115020\pi$
$68$	−2.29654e7	−	3.97772e7i	−0.130252	−	0.225602i
$69$	7.86588e6	−	1.36241e7i	0.0417760	−	0.0723581i
$70$			7.37370e7i			0.367066i
$71$	−2.70152e8	−	1.55972e8i	−1.26167	−	0.728426i	−0.288273	−	0.957548i	$-0.593081\pi$
$71$	−2.70152e8	−	1.55972e8i	−1.26167	−	0.728426i	−0.973398	+	0.229123i	$0.926414\pi$
$72$	1.75389e7	+	1.01261e7i	0.0769141	+	0.0444063i
$73$		−	1.14181e6i		−	0.00470587i	−0.999997	−	0.00235294i	$-0.999251\pi$
$73$		−	1.14181e6i		−	0.00470587i	0.999997	−	0.00235294i	$-0.000748964\pi$
$74$	−8.92502e7	+	1.54586e8i	−0.345992	+	0.599276i
$75$	−7.27047e7	−	1.25928e8i	−0.265330	−	0.459566i
$76$	2.74981e8	−	1.58760e8i	0.945456	−	0.545860i
$77$	−7.67028e7			−0.248658
$78$	1.11053e8	−	4.31778e8i	0.339706	−	1.32079i
$79$	−5.29459e8			−1.52936			−0.764681	−	0.644409i	$-0.777103\pi$
$79$	−5.29459e8			−1.52936			−0.764681	+	0.644409i	$0.777103\pi$
$80$	−1.22623e8	+	7.07963e7i	−0.334708	+	0.193244i
$81$	1.49201e8	+	2.58424e8i	0.385114	+	0.667037i
$82$	5.53422e8	−	9.58555e8i	1.35174	−	2.34129i
$83$		−	6.57330e8i		−	1.52031i	−0.649742	−	0.760155i	$-0.725123\pi$
$83$		−	6.57330e8i		−	1.52031i	0.649742	−	0.760155i	$-0.274877\pi$
$84$	1.74966e8	+	1.01017e8i	0.383439	+	0.221379i
$85$	5.32871e7	+	3.07653e7i	0.110723	+	0.0639258i
$86$			1.15439e9i			2.27567i
$87$	−5.87555e7	+	1.01767e8i	−0.109954	+	0.190446i
$88$	8.53075e7	+	1.47757e8i	0.151640	+	0.262649i
$89$	3.36332e7	−	1.94182e7i	0.0568216	−	0.0328060i	−0.471320	−	0.881962i	$-0.656222\pi$
$89$	3.36332e7	−	1.94182e7i	0.0568216	−	0.0328060i	0.528142	+	0.849156i	$0.322889\pi$
$90$	−1.16457e8			−0.187101
$91$	−6.15880e7	+	2.39457e8i	−0.0941478	+	0.366051i
$92$	8.33025e7			0.121231
$93$	1.09430e9	−	6.31796e8i	1.51693	−	0.875797i
$94$	−4.46964e8	−	7.74164e8i	−0.590469	−	1.02272i
$95$	−2.12682e8	+	3.68375e8i	−0.267901	+	0.464017i
$96$			1.03023e9i			1.23797i
$97$	−3.27858e8	−	1.89289e8i	−0.376022	−	0.217096i	0.300064	−	0.953919i	$-0.402992\pi$
$97$	−3.27858e8	−	1.89289e8i	−0.376022	−	0.217096i	−0.676086	+	0.736823i	$0.736325\pi$
$98$	−1.71461e8	−	9.89930e7i	−0.187779	−	0.108414i
$99$		−	1.21141e8i		−	0.126746i
$100$	3.84984e8	−	6.66812e8i	0.384984	−	0.666812i
$101$	−7.43058e8	−	1.28701e9i	−0.710521	−	1.23066i	−0.964662	−	0.263491i	$-0.915126\pi$
$101$	−7.43058e8	−	1.28701e9i	−0.710521	−	1.23066i	0.254141	−	0.967167i	$-0.418207\pi$
$102$	2.57990e8	−	1.48951e8i	0.235995	−	0.136252i
$103$	3.57738e8			0.313183			0.156591	−	0.987663i	$-0.449949\pi$
$103$	3.57738e8			0.313183			0.156591	+	0.987663i	$0.449949\pi$
$104$	5.29777e8	−	1.47680e8i	0.444061	−	0.123786i
$105$	−2.70651e8			−0.217299
$106$	−1.88514e9	+	1.08838e9i	−1.45033	+	0.837347i
$107$	2.96608e8	+	5.13740e8i	0.218754	+	0.378893i	0.954427	−	0.298444i	$-0.0964675\pi$
$107$	2.96608e8	+	5.13740e8i	0.218754	+	0.378893i	−0.735673	+	0.677337i	$0.763134\pi$
$108$	−9.87658e8	+	1.71067e9i	−0.698554	+	1.20993i
$109$		−	1.50599e9i		−	1.02188i	−0.859615	−	0.510942i	$-0.829297\pi$
$109$		−	1.50599e9i		−	1.02188i	0.859615	−	0.510942i	$-0.170703\pi$
$110$	−8.49656e8	−	4.90549e8i	−0.553319	−	0.319459i
$111$	−5.67407e8	−	3.27593e8i	−0.354765	−	0.204824i
$112$		−	3.80180e8i		−	0.228301i
$113$	3.62253e8	−	6.27441e8i	0.209006	−	0.362009i	−0.742395	−	0.669962i	$-0.766310\pi$
$113$	3.62253e8	−	6.27441e8i	0.209006	−	0.362009i	0.951402	+	0.307952i	$0.0996438\pi$
$114$	1.02970e9	+	1.78350e9i	0.571005	+	0.989010i
$115$	−9.66443e7	+	5.57976e7i	−0.0515271	+	0.0297492i
$116$	−6.22241e8			−0.319079
$117$	−3.78189e8	−	9.72696e7i	−0.186583	−	0.0479889i
$118$	−5.07232e9			−2.40845
$119$	−1.43077e8	+	8.26057e7i	−0.0654048	+	0.0377615i
$120$	3.01014e8	+	5.21371e8i	0.132517	+	0.229526i
$121$	−6.68695e8	+	1.15821e9i	−0.283592	+	0.491195i
$122$			5.01241e9i			2.04846i
$123$	3.51838e9	+	2.03133e9i	1.38602	+	0.800218i
$124$	5.79453e9	+	3.34547e9i	2.20100	+	1.27075i
$125$			2.77800e9i			1.01774i
$126$	1.56346e8	−	2.70798e8i	0.0552609	−	0.0957147i
$127$	−1.87159e9	−	3.24169e9i	−0.638401	−	1.10574i	−0.985784	−	0.168020i	$-0.946263\pi$
$127$	−1.87159e9	−	3.24169e9i	−0.638401	−	1.10574i	0.347382	−	0.937724i	$-0.387071\pi$
$128$	−2.31308e9	+	1.33546e9i	−0.761633	+	0.439729i
$129$	−4.23718e9			−1.34717
$130$	−2.21366e9	+	2.25864e9i	−0.679777	+	0.693590i
$131$	3.08622e9			0.915600			0.457800	−	0.889055i	$-0.348638\pi$
$131$	3.08622e9			0.915600			0.457800	+	0.889055i	$0.348638\pi$
$132$	−2.32798e9	+	1.34406e9i	−0.667417	+	0.385333i
$133$	−5.71056e8	−	9.89098e8i	−0.158251	−	0.274099i
$134$	−3.58771e9	+	6.21410e9i	−0.961272	+	1.66497i
$135$		−	2.64621e9i		−	0.685682i
$136$	3.18256e8	+	1.83745e8i	0.0797722	+	0.0460565i
$137$	3.06275e9	+	1.76828e9i	0.742794	+	0.428852i	0.823084	−	0.567919i	$-0.192251\pi$
$137$	3.06275e9	+	1.76828e9i	0.742794	+	0.428852i	−0.0802904	+	0.996772i	$0.525585\pi$
$138$			5.40291e8i			0.126815i
$139$	3.05467e9	−	5.29084e9i	0.694060	−	1.20215i	−0.276437	−	0.961032i	$-0.589154\pi$
$139$	3.05467e9	−	5.29084e9i	0.694060	−	1.20215i	0.970497	−	0.241115i	$-0.0775131\pi$
$140$	−7.16574e8	−	1.24114e9i	−0.157647	−	0.273052i
$141$	2.84157e9	−	1.64058e9i	0.605441	−	0.349552i
$142$	1.07134e10			2.21121
$143$	−2.34949e9	−	2.30270e9i	−0.469852	−	0.460495i
$144$	6.00442e8			0.116370
$145$	7.21900e8	−	4.16789e8i	0.135619	−	0.0782997i
$146$	1.96071e7	+	3.39605e7i	0.00357129	+	0.00618566i
$147$	3.63354e8	−	6.29347e8i	0.0641802	−	0.111163i
$148$		−	3.46932e9i		−	0.594383i
$149$	7.83991e8	+	4.52637e8i	0.130309	+	0.0752337i	0.563737	−	0.825954i	$-0.309363\pi$
$149$	7.83991e8	+	4.52637e8i	0.130309	+	0.0752337i	−0.433429	+	0.901188i	$0.642696\pi$
$150$	4.32487e9	+	2.49697e9i	0.697530	+	0.402719i
$151$		−	5.85096e9i		−	0.915864i	−0.888987	−	0.457932i	$-0.848590\pi$
$151$		−	5.85096e9i		−	0.915864i	0.888987	−	0.457932i	$-0.151410\pi$
$152$	−1.27024e9	+	2.20012e9i	−0.193014	+	0.334310i
$153$	−1.30464e8	−	2.25970e8i	−0.0192477	−	0.0333380i
$154$	2.28135e9	−	1.31714e9i	0.326850	−	0.188707i
$155$	−8.96345e9			−1.24733
$156$	2.32677e9	+	8.34690e9i	0.314552	+	1.12840i
$157$	−1.09025e9			−0.143212			−0.0716060	−	0.997433i	$-0.522812\pi$
$157$	−1.09025e9			−0.143212			−0.0716060	+	0.997433i	$0.522812\pi$
$158$	1.57475e10	−	9.09185e9i	2.01028	−	1.16063i
$159$	−3.99491e9	−	6.91938e9i	−0.495701	−	0.858579i
$160$	3.65402e9	−	6.32894e9i	0.440789	−	0.763469i
$161$		−	2.99636e8i		−	0.0351462i
$162$	−8.87529e9	−	5.12415e9i	−1.01243	−	0.584527i
$163$	3.44813e9	+	1.99078e9i	0.382596	+	0.220892i	0.678947	−	0.734187i	$-0.262437\pi$
$163$	3.44813e9	+	1.99078e9i	0.382596	+	0.220892i	−0.296351	+	0.955079i	$0.595770\pi$
$164$			2.15125e10i			2.32217i
$165$	1.80056e9	−	3.11866e9i	0.189117	−	0.327559i
$166$	1.12877e10	+	1.95508e10i	1.15376	+	1.99838i
$167$	4.81801e9	−	2.78168e9i	0.479340	−	0.276747i	−0.240801	−	0.970574i	$-0.577410\pi$
$167$	4.81801e9	−	2.78168e9i	0.479340	−	0.276747i	0.720141	+	0.693827i	$0.244077\pi$
$168$	−1.61646e9			−0.156557
$169$	−9.07526e9	+	5.48589e9i	−0.855794	+	0.517317i
$170$	−2.11320e9			−0.194053
$171$	1.56214e9	−	9.01903e8i	0.139713	−	0.0806635i
$172$	−1.12183e10	−	1.94307e10i	−0.977348	−	1.69282i
$173$	−7.21646e9	+	1.24993e10i	−0.612515	+	1.06091i	0.378300	+	0.925683i	$0.376509\pi$
$173$	−7.21646e9	+	1.24993e10i	−0.612515	+	1.06091i	−0.990815	+	0.135224i	$0.956825\pi$
$174$		−	4.03579e9i		−	0.333777i
$175$	−2.39850e9	−	1.38478e9i	−0.193317	−	0.111611i
$176$	4.38074e9	+	2.52922e9i	0.344144	+	0.198692i
$177$		−	1.86179e10i		−	1.42578i
$178$	−6.66896e8	+	1.15510e9i	−0.0497930	+	0.0862439i
$179$	−1.18650e9	−	2.05507e9i	−0.0863829	−	0.149620i	0.819597	−	0.572941i	$-0.194198\pi$
$179$	−1.18650e9	−	2.05507e9i	−0.0863829	−	0.149620i	−0.905980	+	0.423321i	$0.860864\pi$
$180$	1.96021e9	−	1.13173e9i	0.139180	−	0.0803555i
$181$	−8.67348e9			−0.600675			−0.300338	−	0.953833i	$-0.597099\pi$
$181$	−8.67348e9			−0.600675			−0.300338	+	0.953833i	$0.597099\pi$
$182$	−2.28016e9	−	8.17970e9i	−0.154043	−	0.552606i
$183$	−1.83980e10			−1.21267
$184$	−5.77207e8	+	3.33250e8i	−0.0371237	+	0.0214334i
$185$	2.32382e9	+	4.02497e9i	0.145858	+	0.252633i
$186$	−2.16984e10	+	3.75827e10i	−1.32929	+	2.30239i
$187$		−	2.19820e9i		−	0.131456i
$188$	1.50466e10	+	8.68715e9i	0.878472	+	0.507186i
$189$	6.15325e9	+	3.55258e9i	0.350773	+	0.202519i
$190$		−	1.46086e10i		−	0.813240i
$191$	−3.15375e9	+	5.46246e9i	−0.171466	+	0.296988i	−0.938933	−	0.344101i	$-0.888184\pi$
$191$	−3.15375e9	+	5.46246e9i	−0.171466	+	0.296988i	0.767467	+	0.641089i	$0.221517\pi$
$192$	−1.25811e10	−	2.17911e10i	−0.668133	−	1.15724i
$193$	9.99658e8	−	5.77153e8i	0.0518613	−	0.0299421i	−0.473845	−	0.880608i	$-0.657134\pi$
$193$	9.99658e8	−	5.77153e8i	0.0518613	−	0.0299421i	0.525706	+	0.850666i	$0.323801\pi$
$194$	1.30018e10			0.659018
$195$	−8.29034e9	−	8.12524e9i	−0.410598	−	0.402421i
$196$	3.84804e9			0.186246
$197$	−3.06073e10	+	1.76711e10i	−1.44786	+	0.835923i	−0.998354	−	0.0573541i	$-0.981734\pi$
$197$	−3.06073e10	+	1.76711e10i	−1.44786	+	0.835923i	−0.449507	+	0.893277i	$0.648400\pi$
$198$	2.08023e9	+	3.60307e9i	0.0961875	+	0.166602i
$199$	−5.86839e9	+	1.01643e10i	−0.265265	+	0.459452i	−0.967633	−	0.252362i	$-0.918793\pi$
$199$	−5.86839e9	+	1.01643e10i	−0.265265	+	0.459452i	0.702368	+	0.711814i	$0.252126\pi$
$200$			6.16050e9i			0.272258i
$201$	−2.28088e10	−	1.31687e10i	−0.985646	−	0.569063i
$202$	4.42012e10	+	2.55196e10i	1.86790	+	1.07843i
$203$			2.23818e9i			0.0925046i
$204$	−2.89500e9	+	5.01428e9i	−0.117034	+	0.202709i
$205$	−1.44095e10	−	2.49580e10i	−0.569846	−	0.987002i
$206$	−1.06401e10	+	6.14307e9i	−0.411664	+	0.237675i
$207$	4.73234e8			0.0179147
$208$	1.14134e10	−	1.16453e10i	0.422796	−	0.431387i
$209$	1.51962e10			0.550906
$210$	8.04991e9	−	4.64762e9i	0.285630	−	0.164909i
$211$	−2.59778e10	−	4.49948e10i	−0.902258	−	1.56276i	−0.824557	−	0.565779i	$-0.808575\pi$
$211$	−2.59778e10	−	4.49948e10i	−0.902258	−	1.56276i	−0.0777008	−	0.996977i	$-0.524758\pi$
$212$	2.11537e10	−	3.66394e10i	0.719243	−	1.24577i
$213$			3.93236e10i			1.30902i
$214$	−1.76439e10	−	1.01867e10i	−0.575085	−	0.332025i
$215$	2.60301e10	+	1.50285e10i	0.830812	+	0.479670i
$216$		−	1.58045e10i		−	0.494012i
$217$	1.20336e10	−	2.08427e10i	0.368405	−	0.638096i
$218$	2.58607e10	+	4.47921e10i	0.775509	+	1.34322i
$219$	−1.24652e8	+	7.19678e7i	−0.00366185	+	0.00211417i
$220$	1.90685e10			0.548802
$221$	−6.86252e9	−	1.76503e9i	−0.193517	−	0.0497722i
$222$	2.25016e10			0.621764
$223$	5.56548e10	−	3.21323e10i	1.50706	−	0.870101i	0.507094	−	0.861891i	$-0.330720\pi$
$223$	5.56548e10	−	3.21323e10i	1.50706	−	0.870101i	0.999966	−	0.00821043i	$-0.00261349\pi$
$224$	9.81114e9	+	1.69934e10i	0.260377	+	0.450987i
$225$	2.18706e9	−	3.78810e9i	0.0568904	−	0.0985371i
$226$			2.48824e10i			0.634460i
$227$	−3.23223e10	−	1.86613e10i	−0.807952	−	0.466471i	0.0382922	−	0.999267i	$-0.487808\pi$
$227$	−3.23223e10	−	1.86613e10i	−0.807952	−	0.466471i	−0.846244	+	0.532795i	$0.821142\pi$
$228$	−3.46639e10	−	2.00132e10i	−0.849515	−	0.490468i
$229$		−	3.22501e10i		−	0.774945i	−0.921881	−	0.387473i	$-0.873348\pi$
$229$		−	3.22501e10i		−	0.774945i	0.921881	−	0.387473i	$-0.126652\pi$
$230$	1.91631e9	−	3.31915e9i	0.0451534	−	0.0782080i
$231$	4.83455e9	+	8.37369e9i	0.111713	+	0.193492i
$232$	4.31154e9	−	2.48927e9i	0.0977093	−	0.0564125i
$233$	2.07868e10			0.462047			0.231023	−	0.972948i	$-0.425793\pi$
$233$	2.07868e10			0.462047			0.231023	+	0.972948i	$0.425793\pi$
$234$	1.29187e10	−	3.60119e9i	0.281674	−	0.0785189i
$235$	−2.32753e10			−0.497840
$236$	8.53773e10	−	4.92926e10i	1.79159	−	1.03437i
$237$	3.33716e10	+	5.78013e10i	0.687084	+	1.19006i
$238$	2.83701e9	−	4.91384e9i	0.0573144	−	0.0992715i
$239$		−	2.38596e9i		−	0.0473012i	−0.999720	−	0.0236506i	$-0.992471\pi$
$239$		−	2.38596e9i		−	0.0473012i	0.999720	−	0.0236506i	$-0.00752892\pi$
$240$	1.54578e10	+	8.92454e9i	0.300743	+	0.173634i
$241$	4.12681e10	+	2.38262e10i	0.788022	+	0.454964i	0.839266	−	0.543722i	$-0.182985\pi$
$241$	4.12681e10	+	2.38262e10i	0.788022	+	0.454964i	−0.0512440	+	0.998686i	$0.516319\pi$
$242$		−	4.59312e10i		−	0.860872i
$243$	−1.03153e10	+	1.78665e10i	−0.189781	+	0.328710i
$244$	−4.87104e10	−	8.43689e10i	−0.879766	−	1.52380i
$245$	−4.46435e9	+	2.57749e9i	−0.0791609	+	0.0457036i
$246$	−1.39528e11			−2.42915
$247$	1.22017e10	−	4.74408e10i	0.208586	−	0.810991i
$248$	−5.35340e10			−0.898664
$249$	−7.17611e10	+	4.14313e10i	−1.18302	+	0.683017i
$250$	−4.77037e10	−	8.26253e10i	−0.772364	−	1.33777i
$251$	5.82299e9	−	1.00857e10i	0.0926007	−	0.160389i	−0.816004	−	0.578046i	$-0.803815\pi$
$251$	5.82299e9	−	1.00857e10i	0.0926007	−	0.160389i	0.908605	+	0.417657i	$0.137149\pi$
$252$			6.07744e9i			0.0949332i
$253$	3.45265e9	+	1.99339e9i	0.0529797	+	0.0305879i
$254$	1.11332e11	+	6.42777e10i	1.67830	+	0.968967i
$255$		−	7.75651e9i		−	0.114878i
$256$	−5.23427e9	+	9.06603e9i	−0.0761687	+	0.131928i
$257$	−5.00282e10	−	8.66514e10i	−0.715346	−	1.23902i	−0.962826	−	0.270122i	$-0.912936\pi$
$257$	−5.00282e10	−	8.66514e10i	−0.715346	−	1.23902i	0.247480	−	0.968893i	$-0.420397\pi$
$258$	1.26025e11	−	7.27608e10i	1.77080	−	1.02237i
$259$	−1.24790e10			−0.172319
$260$	1.53110e10	−	5.95298e10i	0.207789	−	0.807894i
$261$	−3.53489e9			−0.0471513
$262$	−9.17926e10	+	5.29965e10i	−1.20352	+	0.694850i
$263$	−3.65678e10	−	6.33373e10i	−0.471301	−	0.816317i	0.528160	−	0.849145i	$-0.322882\pi$
$263$	−3.65678e10	−	6.33373e10i	−0.471301	−	0.816317i	−0.999461	+	0.0328280i	$0.989549\pi$
$264$	1.07538e10	−	1.86261e10i	0.136253	−	0.235996i
$265$			5.66768e10i			0.705990i
$266$	3.39695e10	+	1.96123e10i	0.416028	+	0.240194i
$267$	−4.23978e9	−	2.44784e9i	−0.0510555	−	0.0294769i
$268$		−	1.39461e11i		−	1.65138i
$269$	−4.71586e9	+	8.16811e9i	−0.0549131	+	0.0951123i	−0.892175	−	0.451689i	$-0.850822\pi$
$269$	−4.71586e9	+	8.16811e9i	−0.0549131	+	0.0951123i	0.837262	+	0.546802i	$0.184155\pi$
$270$	4.54407e10	+	7.87056e10i	0.520365	+	0.901298i
$271$	1.07730e11	−	6.21982e10i	1.21332	−	0.700513i	0.249842	−	0.968287i	$-0.419621\pi$
$271$	1.07730e11	−	6.21982e10i	1.21332	−	0.700513i	0.963482	+	0.267774i	$0.0862881\pi$
$272$	1.08955e10			0.120694
$273$	3.00236e10	−	8.36931e9i	0.327137	−	0.0911922i
$274$	−1.21459e11			−1.30183
$275$	3.19130e10	−	1.84250e10i	0.336488	−	0.194272i
$276$	−5.25053e9	−	9.09418e9i	−0.0544643	−	0.0943350i
$277$	−2.18238e10	+	3.78000e10i	−0.222727	+	0.385774i	−0.955635	−	0.294553i	$-0.904829\pi$
$277$	−2.18238e10	+	3.78000e10i	−0.222727	+	0.385774i	0.732908	+	0.680327i	$0.238162\pi$
$278$			2.09818e11i			2.10689i
$279$	3.29182e10	+	1.90053e10i	0.325250	+	0.187783i
$280$	9.93034e9	+	5.73329e9i	0.0965502	+	0.0557433i
$281$		−	7.09067e8i		−	0.00678436i	−0.999994	−	0.00339218i	$-0.998920\pi$
$281$		−	7.09067e8i		−	0.00678436i	0.999994	−	0.00339218i	$-0.00107977\pi$
$282$	−5.63440e10	+	9.75906e10i	−0.530550	+	0.918940i
$283$	1.41977e10	+	2.45911e10i	0.131577	+	0.227898i	0.924285	−	0.381704i	$-0.124663\pi$
$283$	1.41977e10	+	2.45911e10i	0.131577	+	0.227898i	−0.792708	+	0.609602i	$0.791329\pi$
$284$	−1.80328e11	+	1.04113e11i	−1.64487	+	0.949666i
$285$	5.36210e10			0.481430
$286$	1.09422e11	+	2.81432e10i	0.967069	+	0.248729i
$287$	7.73800e10			0.673225
$288$	−2.68387e10	+	1.54953e10i	−0.229877	+	0.132719i
$289$	5.69266e10	+	9.85997e10i	0.480037	+	0.831449i
$290$	−1.43142e10	+	2.47929e10i	−0.118844	+	0.205843i
$291$			4.77232e10i			0.390132i
$292$	−6.60053e8	−	3.81082e8i	−0.00531320	−	0.00306758i
$293$	1.23999e11	+	7.15907e10i	0.982908	+	0.567482i	0.903147	−	0.429332i	$-0.141251\pi$
$293$	1.23999e11	+	7.15907e10i	0.982908	+	0.567482i	0.0797614	+	0.996814i	$0.474584\pi$
$294$			2.49580e10i			0.194826i
$295$	−6.60343e10	+	1.14375e11i	−0.507657	+	0.879288i
$296$	1.38790e10	+	2.40391e10i	0.105086	+	0.182014i
$297$	−8.18712e10	+	4.72683e10i	−0.610558	+	0.352506i
$298$	−3.10907e10			−0.228380
$299$	8.99540e9	−	9.17818e9i	0.0650879	−	0.0664104i
$300$	−9.70617e10			−0.691835
$301$	−6.98916e10	+	4.03519e10i	−0.490767	+	0.283345i
$302$	1.00473e11	+	1.74024e11i	0.695050	+	1.20386i
$303$	−9.36694e10	+	1.62240e11i	−0.638419	+	1.10577i
$304$			7.53207e10i			0.505805i
$305$	1.13024e11	+	6.52543e10i	0.747861	+	0.431778i
$306$	7.76071e9	+	4.48065e9i	0.0506006	+	0.0292142i
$307$		−	1.97180e11i		−	1.26690i	−0.773785	−	0.633448i	$-0.781639\pi$
$307$		−	1.97180e11i		−	1.26690i	0.773785	−	0.633448i	$-0.218361\pi$
$308$	−2.55998e10	+	4.43401e10i	−0.162091	+	0.280749i
$309$	−2.25481e10	−	3.90545e10i	−0.140701	−	0.243701i
$310$	2.66597e11	−	1.53920e11i	1.63956	−	0.946602i
$311$	−2.78673e11			−1.68917			−0.844584	−	0.535423i	$-0.820152\pi$
$311$	−2.78673e11			−1.68917			−0.844584	+	0.535423i	$0.820152\pi$
$312$	−4.95139e10	−	4.85279e10i	−0.295823	−	0.289932i
$313$	−9.16942e10			−0.539999			−0.269999	−	0.962861i	$-0.587023\pi$
$313$	−9.16942e10			−0.539999			−0.269999	+	0.962861i	$0.587023\pi$
$314$	3.24271e10	−	1.87218e10i	0.188246	−	0.108684i
$315$	−4.07079e9	−	7.05081e9i	−0.0232960	−	0.0403498i
$316$	−1.76709e11	+	3.06068e11i	−0.996932	+	1.72674i
$317$		−	1.19322e11i		−	0.663675i	−0.943337	−	0.331838i	$-0.892331\pi$
$317$		−	1.19322e11i		−	0.663675i	0.943337	−	0.331838i	$-0.107669\pi$
$318$	2.37639e11	+	1.37201e11i	1.30315	+	0.752376i
$319$	−2.57901e10	−	1.48899e10i	−0.139442	−	0.0805071i
$320$			1.78491e11i			0.951573i
$321$	3.73902e10	−	6.47618e10i	0.196556	−	0.340444i
$322$	5.14535e9	+	8.91200e9i	0.0266725	+	0.0461981i
$323$	2.83462e10	−	1.63657e10i	0.144905	−	0.0836610i
$324$	1.99185e11			1.00416
$325$	−3.18963e10	−	1.14423e11i	−0.158586	−	0.568902i
$326$	−1.36743e11			−0.670540
$327$	−1.64409e11	+	9.49217e10i	−0.795173	+	0.459093i
$328$	−8.60607e10	−	1.49061e11i	−0.410556	−	0.711104i
$329$	3.12474e10	−	5.41221e10i	0.147039	−	0.254679i
$330$			1.23677e11i			0.574083i
$331$	−2.60520e11	−	1.50412e11i	−1.19293	−	0.688740i	−0.233962	−	0.972246i	$-0.575169\pi$
$331$	−2.60520e11	−	1.50412e11i	−1.19293	−	0.688740i	−0.958970	+	0.283506i	$0.908502\pi$
$332$	−3.79988e11	−	2.19386e11i	−1.71652	−	0.991032i
$333$		−	1.97089e10i		−	0.0878341i
$334$	−9.55339e10	+	1.65470e11i	−0.420047	+	0.727543i
$335$	9.34137e10	+	1.61797e11i	0.405237	+	0.701891i
$336$	−4.15045e10	+	2.39626e10i	−0.177651	+	0.102567i
$337$	−3.59943e11			−1.52020			−0.760098	−	0.649808i	$-0.774849\pi$
$337$	−3.59943e11			−1.52020			−0.760098	+	0.649808i	$0.774849\pi$
$338$	1.75719e11	−	3.19006e11i	0.732310	−	1.32945i
$339$	−9.13308e10			−0.375594
$340$	3.55694e10	−	2.05360e10i	0.144352	−	0.0833415i
$341$	1.60111e11	+	2.77320e11i	0.641248	+	1.11067i
$342$	−3.09749e10	+	5.36501e10i	−0.122431	+	0.212057i
$343$		−	1.38413e10i		−	0.0539949i
$344$	1.55464e11	+	8.97574e10i	0.598574	+	0.345587i
$345$	1.21829e10	+	7.03381e9i	0.0462983	+	0.0267304i
$346$		−	4.95683e11i		−	1.85935i
$347$	−2.04097e10	+	3.53507e10i	−0.0755710	+	0.130893i	−0.901334	−	0.433124i	$-0.857411\pi$
$347$	−2.04097e10	+	3.53507e10i	−0.0755710	+	0.130893i	0.825763	+	0.564017i	$0.190745\pi$
$348$	3.92196e10	+	6.79304e10i	0.143350	+	0.248289i
$349$	−2.92262e11	+	1.68738e11i	−1.05453	+	0.608833i	−0.923914	−	0.382601i	$-0.875029\pi$
$349$	−2.92262e11	+	1.68738e11i	−1.05453	+	0.608833i	−0.130615	+	0.991433i	$0.541695\pi$
$350$	9.51174e10			0.338808
$351$	8.18283e10	+	2.93546e11i	0.287754	+	1.03227i
$352$	−2.61082e11			−0.906430
$353$	−2.10206e10	+	1.21362e10i	−0.0720540	+	0.0416004i	−0.535594	−	0.844476i	$-0.679912\pi$
$353$	−2.10206e10	+	1.21362e10i	−0.0720540	+	0.0416004i	0.463540	+	0.886076i	$0.346579\pi$
$354$	3.19707e11	+	5.53748e11i	1.08202	+	1.87412i
$355$	1.39473e11	−	2.41575e11i	0.466083	−	0.807280i
$356$		−	2.59235e10i		−	0.0855398i
$357$	1.80362e10	+	1.04132e10i	0.0587677	+	0.0339296i
$358$	7.05793e10	+	4.07490e10i	0.227093	+	0.131112i
$359$		−	5.15811e11i		−	1.63895i	−0.573115	−	0.819475i	$-0.694265\pi$
$359$		−	5.15811e11i		−	1.63895i	0.573115	−	0.819475i	$-0.305735\pi$
$360$	−9.05492e9	+	1.56836e10i	−0.0284134	+	0.0492135i
$361$	−4.82072e10	−	8.34973e10i	−0.149393	−	0.258756i
$362$	2.57973e11	−	1.48941e11i	0.789561	−	0.455853i
$363$	1.68590e11			0.509628
$364$	1.17870e11	+	1.15522e11i	0.351921	+	0.344913i
$365$	1.02102e9			0.00301105
$366$	5.47207e11	−	3.15930e11i	1.59400	−	0.920294i
$367$	−2.27139e11	−	3.93417e11i	−0.653575	−	1.13202i	−0.982249	−	0.187581i	$-0.939935\pi$
$367$	−2.27139e11	−	3.93417e11i	−0.653575	−	1.13202i	0.328674	−	0.944443i	$-0.393398\pi$
$368$	−9.88030e9	+	1.71132e10i	−0.0280837	+	0.0486425i
$369$			1.22211e11i			0.343155i
$370$	−1.38233e11	−	7.98091e10i	−0.383447	−	0.221383i
$371$	−1.31791e11	−	7.60894e10i	−0.361162	−	0.208517i
$372$		−	8.43456e11i		−	2.28359i
$373$	2.36407e11	−	4.09469e11i	0.632369	−	1.09530i	−0.354697	−	0.934981i	$-0.615416\pi$
$373$	2.36407e11	−	4.09469e11i	0.632369	−	1.09530i	0.987066	−	0.160314i	$-0.0512507\pi$
$374$	3.77474e10	+	6.53804e10i	0.0997619	+	0.172793i
$375$	3.03276e11	−	1.75096e11i	0.791949	−	0.457232i
$376$	−1.39011e11			−0.358678
$377$	−6.71926e10	+	6.85579e10i	−0.171311	+	0.174792i
$378$	−2.44019e11			−0.614767
$379$	3.03172e11	−	1.75036e11i	0.754765	−	0.435764i	−0.0726478	−	0.997358i	$-0.523145\pi$
$379$	3.03172e11	−	1.75036e11i	0.754765	−	0.435764i	0.827413	+	0.561594i	$0.189812\pi$
$380$	1.41966e11	+	2.45893e11i	0.349268	+	0.604950i
$381$	−2.35931e11	+	4.08645e11i	−0.573619	+	0.993536i
$382$		−	2.16625e11i		−	0.520503i
$383$	7.60757e10	+	4.39224e10i	0.180656	+	0.104302i	0.587601	−	0.809151i	$-0.300073\pi$
$383$	7.60757e10	+	4.39224e10i	0.180656	+	0.104302i	−0.406945	+	0.913453i	$0.633406\pi$
$384$	2.91585e11	+	1.68347e11i	0.684345	+	0.395107i
$385$		−	6.85890e10i		−	0.159104i
$386$	−1.98217e10	+	3.43322e10i	−0.0454462	+	0.0787152i
$387$	−6.37302e10	−	1.10384e11i	−0.144426	−	0.250153i
$388$	−2.18847e11	+	1.26351e11i	−0.490228	+	0.283033i
$389$	4.62172e11			1.02336			0.511682	−	0.859175i	$-0.329023\pi$
$389$	4.62172e11			1.02336			0.511682	+	0.859175i	$0.329023\pi$
$390$	3.86104e11	+	9.93053e10i	0.845110	+	0.217361i
$391$	8.58717e9			0.0185804
$392$	−2.66633e10	+	1.53940e10i	−0.0570330	+	0.0329280i
$393$	−1.94523e11	−	3.36924e11i	−0.411344	−	0.712469i
$394$	6.06896e11	−	1.05117e12i	1.26877	−	2.19757i
$395$		−	4.73451e11i		−	0.978562i
$396$	−7.00290e10	−	4.04313e10i	−0.143103	−	0.0826207i
$397$	1.20376e11	+	6.94990e10i	0.243210	+	0.140417i	0.616651	−	0.787236i	$-0.288489\pi$
$397$	1.20376e11	+	6.94990e10i	0.243210	+	0.140417i	−0.373441	+	0.927654i	$0.621822\pi$
$398$		−	4.03087e11i		−	0.805239i
$399$	−7.19870e10	+	1.24685e11i	−0.142192	+	0.246284i
$400$	9.13240e10	+	1.58178e11i	0.178367	+	0.308941i
$401$	−4.74803e11	+	2.74127e11i	−0.916987	+	0.529423i	−0.882673	−	0.469988i	$-0.844258\pi$
$401$	−4.74803e11	+	2.74127e11i	−0.916987	+	0.529423i	−0.0343146	+	0.999411i	$0.510925\pi$
$402$	9.04530e11			1.72745
$403$	9.94321e11	−	2.77175e11i	1.87782	−	0.523457i
$404$	−9.91992e11			−1.85264
$405$	−2.31087e11	+	1.33418e11i	−0.426804	+	0.246415i
$406$	−3.84340e10	−	6.65696e10i	−0.0702018	−	0.121593i
$407$	8.30191e10	−	1.43793e11i	0.149970	−	0.259755i
$408$		−	4.63256e10i		−	0.0827657i
$409$	2.04454e10	+	1.18041e10i	0.0361277	+	0.0208583i	0.517955	−	0.855408i	$-0.326693\pi$
$409$	2.04454e10	+	1.18041e10i	0.0361277	+	0.0208583i	−0.481827	+	0.876266i	$0.660027\pi$
$410$	8.57157e11	+	4.94880e11i	1.49807	+	0.864913i
$411$		−	4.45816e11i		−	0.770668i
$412$	1.19396e11	−	2.06800e11i	0.204152	−	0.353601i
$413$	−1.77304e11	−	3.07100e11i	−0.299877	−	0.519403i
$414$	−1.40753e10	+	8.12635e9i	−0.0235480	+	0.0135955i
$415$	5.87796e11			0.972770
$416$	−2.09634e11	+	8.15067e11i	−0.343195	+	1.33436i
$417$	−7.70138e11			−1.24726
$418$	−4.51977e11	+	2.60949e11i	−0.724141	+	0.418083i
$419$	1.71749e11	+	2.97478e11i	0.272227	+	0.471511i	0.969432	−	0.245361i	$-0.0789065\pi$
$419$	1.71749e11	+	2.97478e11i	0.272227	+	0.471511i	−0.697205	+	0.716872i	$0.745573\pi$
$420$	−9.03308e10	+	1.56458e11i	−0.141649	+	0.245344i
$421$		−	1.06853e12i		−	1.65774i	−0.559439	−	0.828872i	$-0.688983\pi$
$421$		−	1.06853e12i		−	1.65774i	0.559439	−	0.828872i	$-0.311017\pi$
$422$	1.54530e12	+	8.92178e11i	2.37195	+	1.36945i
$423$	8.54783e10	+	4.93509e10i	0.129815	+	0.0749486i
$424$			3.38501e11i			0.508644i
$425$	3.96858e10	−	6.87379e10i	0.0590045	−	0.102199i
$426$	−6.75263e11	−	1.16959e12i	−0.993413	−	1.72064i
$427$	−3.03472e11	+	1.75210e11i	−0.441767	+	0.255054i
$428$	3.95975e11			0.570389
$429$	−1.03299e11	+	4.01633e11i	−0.147245	+	0.572495i
$430$	−1.03228e12			−1.45609
$431$	−1.07786e12	+	6.22303e11i	−1.50458	+	0.868669i	−0.504593	+	0.863358i	$0.668357\pi$
$431$	−1.07786e12	+	6.22303e11i	−1.50458	+	0.868669i	−0.999986	+	0.00531128i	$0.998309\pi$
$432$	−2.34287e11	−	4.05798e11i	−0.323647	−	0.560574i
$433$	3.36252e11	−	5.82406e11i	0.459695	−	0.796214i	−0.539250	−	0.842146i	$-0.681292\pi$
$433$	3.36252e11	−	5.82406e11i	0.459695	−	0.796214i	0.998945	+	0.0459314i	$0.0146256\pi$
$434$			8.26560e11i			1.11833i
$435$	−9.10022e10	−	5.25402e10i	−0.121857	−	0.0703542i
$436$	−8.70576e11	−	5.02627e11i	−1.15377	−	0.666127i
$437$			5.93634e10i			0.0778669i
$438$	2.47166e9	−	4.28104e9i	0.00320889	−	0.00555796i
$439$	−3.11478e11	−	5.39496e11i	−0.400256	−	0.693263i	0.593501	−	0.804833i	$-0.297745\pi$
$439$	−3.11478e11	−	5.39496e11i	−0.400256	−	0.693263i	−0.993757	+	0.111570i	$0.964412\pi$
$440$	−1.32127e11	+	7.62835e10i	−0.168056	+	0.0970272i
$441$	2.18604e10			0.0275222
$442$	2.34419e11	−	6.53462e10i	0.292141	−	0.0814367i
$443$	−8.63622e11			−1.06539			−0.532693	−	0.846308i	$-0.678820\pi$
$443$	−8.63622e11			−1.06539			−0.532693	+	0.846308i	$0.678820\pi$
$444$	−3.78748e11	+	2.18670e11i	−0.462516	+	0.267034i
$445$	1.73641e10	+	3.00754e10i	0.0209909	+	0.0363573i
$446$	−1.10355e12	+	1.91140e12i	−1.32064	+	2.28742i
$447$		−	1.14118e11i		−	0.135198i
$448$	−4.15046e11	−	2.39627e11i	−0.486794	−	0.281051i
$449$	1.13455e12	+	6.55035e11i	1.31740	+	0.760599i	0.983309	−	0.181943i	$-0.0582386\pi$
$449$	1.13455e12	+	6.55035e11i	1.31740	+	0.760599i	0.334087	+	0.942542i	$0.391572\pi$
$450$			1.50224e11i			0.172697i
$451$	−5.14784e11	+	8.91633e11i	−0.585910	+	1.01483i
$452$	−2.41806e11	−	4.18821e11i	−0.272486	−	0.471960i
$453$	−6.38753e11	+	3.68784e11i	−0.712674	+	0.411463i
$454$	1.28180e12			1.41602
$455$	−2.14127e11	−	5.50731e10i	−0.234218	−	0.0602404i
$456$	3.20251e11			0.346855
$457$	−9.68890e11	+	5.59389e11i	−1.03909	+	0.599917i	−0.919574	−	0.392916i	$-0.871466\pi$
$457$	−9.68890e11	+	5.59389e11i	−1.03909	+	0.599917i	−0.119512	+	0.992833i	$0.538133\pi$
$458$	5.53797e11	+	9.59205e11i	0.588107	+	1.01863i
$459$	−1.01812e11	+	1.76344e11i	−0.107064	+	0.185440i
$460$			7.44905e10i			0.0775695i
$461$	4.10778e11	+	2.37163e11i	0.423597	+	0.244564i	0.696615	−	0.717445i	$-0.254689\pi$
$461$	4.10778e11	+	2.37163e11i	0.423597	+	0.244564i	−0.273018	+	0.962009i	$0.588022\pi$
$462$	−2.87585e11	−	1.66038e11i	−0.293682	−	0.169558i
$463$		−	9.33201e11i		−	0.943758i	−0.881663	−	0.471879i	$-0.843576\pi$
$463$		−	9.33201e11i		−	0.943758i	0.881663	−	0.471879i	$-0.156424\pi$
$464$	7.38024e10	−	1.27830e11i	0.0739162	−	0.128027i
$465$	5.64963e11	+	9.78545e11i	0.560379	+	0.970605i
$466$	−6.18256e11	+	3.56950e11i	−0.607339	+	0.350648i
$467$	8.07708e11			0.785830			0.392915	−	0.919575i	$-0.371467\pi$
$467$	8.07708e11			0.785830			0.392915	+	0.919575i	$0.371467\pi$
$468$	−1.82451e11	+	1.86158e11i	−0.175809	+	0.179381i
$469$	−5.01637e11			−0.478753
$470$	6.92271e11	−	3.99683e11i	0.654389	−	0.377811i
$471$	6.87184e10	+	1.19024e11i	0.0643397	+	0.111440i
$472$	−3.94389e11	+	6.83102e11i	−0.365751	+	0.633500i
$473$		−	1.07379e12i		−	0.986384i
$474$	−1.98513e12	−	1.14611e12i	−1.80628	−	1.04286i
$475$	4.75187e11	+	2.74350e11i	0.428296	+	0.247277i
$476$			1.10280e11i			0.0984610i
$477$	1.20172e11	−	2.08145e11i	0.106285	−	0.184091i
$478$	4.09716e10	+	7.09649e10i	0.0358969	+	0.0621753i
$479$	7.48107e11	−	4.31920e11i	0.649313	−	0.374881i	−0.138880	−	0.990309i	$-0.544350\pi$
$479$	7.48107e11	−	4.31920e11i	0.649313	−	0.374881i	0.788193	+	0.615428i	$0.211017\pi$
$480$	−9.21246e11			−0.792118
$481$	−3.82246e11	−	3.74634e11i	−0.325605	−	0.319120i
$482$	−1.63657e12			−1.38109
$483$	−3.27115e10	+	1.88860e10i	−0.0273488	+	0.0157898i
$484$	4.46358e11	+	7.73114e11i	0.369725	+	0.640383i
$485$	1.69265e11	−	2.93176e11i	0.138909	−	0.240597i
$486$		−	7.08533e11i		−	0.576099i
$487$	−2.46302e11	−	1.42202e11i	−0.198421	−	0.114558i	0.397498	−	0.917603i	$-0.369879\pi$
$487$	−2.46302e11	−	1.42202e11i	−0.198421	−	0.114558i	−0.595919	+	0.803045i	$0.703212\pi$
$488$	6.75033e11	+	3.89730e11i	0.538810	+	0.311082i
$489$		−	5.01913e11i		−	0.396953i
$490$	8.85213e10	−	1.53323e11i	0.0693690	−	0.120151i
$491$	2.30955e11	+	4.00026e11i	0.179333	+	0.310614i	0.941652	−	0.336587i	$-0.109273\pi$
$491$	2.30955e11	+	4.00026e11i	0.179333	+	0.310614i	−0.762319	+	0.647201i	$0.775939\pi$
$492$	2.34854e12	−	1.35593e12i	1.80699	−	1.04326i
$493$	−6.41433e10			−0.0489035
$494$	4.51741e11	+	1.62055e12i	0.341285	+	1.22431i
$495$	1.08327e11			0.0810983
$496$	−1.37455e12	+	7.93596e11i	−1.01975	+	0.588751i
$497$	3.74490e11	+	6.48635e11i	0.275319	+	0.476867i
$498$	1.42291e12	−	2.46456e12i	1.03668	−	1.79559i
$499$		−	9.73615e11i		−	0.702967i	−0.936194	−	0.351483i	$-0.885677\pi$
$499$		−	9.73615e11i		−	0.702967i	0.936194	−	0.351483i	$-0.114323\pi$
$500$	1.60590e12	+	9.27166e11i	1.14909	+	0.663426i
$501$	−6.07355e11	−	3.50657e11i	−0.430698	−	0.248664i
$502$			3.99969e11i			0.281099i
$503$	−1.76310e11	+	3.05378e11i	−0.122806	+	0.212707i	−0.920873	−	0.389862i	$-0.872523\pi$
$503$	−1.76310e11	+	3.05378e11i	−0.122806	+	0.212707i	0.798067	+	0.602569i	$0.205856\pi$
$504$	−2.43127e10	−	4.21109e10i	−0.0167840	−	0.0290708i
$505$	1.15087e12	−	6.64456e11i	0.787437	−	0.454627i
$506$	−1.36921e11			−0.0928526
$507$	1.17091e12	+	6.44978e11i	0.787023	+	0.433520i
$508$	−2.49860e12			−1.66460
$509$	−2.19429e12	+	1.26687e12i	−1.44898	+	0.836571i	−0.998421	−	0.0561740i	$-0.982110\pi$
$509$	−2.19429e12	+	1.26687e12i	−1.44898	+	0.836571i	−0.450562	+	0.892745i	$0.648777\pi$
$510$	1.33194e11	+	2.30700e11i	0.0871807	+	0.151001i
$511$	−1.37074e9	+	2.37419e9i	−0.000889326	+	0.00154036i
$512$		−	1.72704e12i		−	1.11068i
$513$	−1.21907e12	−	7.03830e11i	−0.777142	−	0.448683i
$514$	2.97595e12	+	1.71817e12i	1.88058	+	1.08575i
$515$			3.19896e11i			0.200390i
$516$	−1.41417e12	+	2.44942e12i	−0.878170	+	1.52104i
$517$	4.15758e11	+	7.20115e11i	0.255937	+	0.443296i
$518$	3.71161e11	−	2.14290e11i	0.226505	−	0.130773i
$519$	1.81940e12			1.10072
$520$	1.32058e11	+	4.73736e11i	0.0792043	+	0.284133i
$521$	−9.81423e11			−0.583561			−0.291781	−	0.956485i	$-0.594248\pi$
$521$	−9.81423e11			−0.583561			−0.291781	+	0.956485i	$0.594248\pi$
$522$	1.05137e11	−	6.07011e10i	0.0619783	−	0.0357832i
$523$	1.22840e12	+	2.12764e12i	0.717928	+	1.24349i	0.961819	+	0.273685i	$0.0882426\pi$
$523$	1.22840e12	+	2.12764e12i	0.717928	+	1.24349i	−0.243892	+	0.969803i	$0.578424\pi$
$524$	1.03004e12	−	1.78407e12i	0.596845	−	1.03377i
$525$			3.49128e11i			0.200571i
$526$	2.17525e12	+	1.25588e12i	1.23901	+	0.715341i
$527$	5.97325e11	+	3.44865e11i	0.337336	+	0.194761i
$528$		−	6.37664e11i		−	0.357058i
$529$	8.92789e11	−	1.54636e12i	0.495677	−	0.858537i
$530$	−9.73252e11	−	1.68572e12i	−0.535777	−	0.927992i
$531$	4.85021e11	−	2.80027e11i	0.264749	−	0.152853i
$532$	−7.62367e11			−0.412631
$533$	2.37023e12	+	2.32303e12i	1.27209	+	1.24676i
$534$	1.68137e11			0.0894803
$535$	−4.59396e11	+	2.65232e11i	−0.242435	+	0.139970i
$536$	5.57912e11	+	9.66332e11i	0.291961	+	0.505691i
$537$	−1.49569e11	+	2.59061e11i	−0.0776171	+	0.134437i
$538$		−	3.23923e11i		−	0.166694i
$539$	1.59490e11	+	9.20817e10i	0.0813925	+	0.0469920i
$540$	−1.52972e12	−	8.83182e11i	−0.774174	−	0.446970i
$541$		−	9.09308e11i		−	0.456376i	−0.973617	−	0.228188i	$-0.926720\pi$
$541$		−	9.09308e11i		−	0.456376i	0.973617	−	0.228188i	$-0.0732802\pi$
$542$	−2.13613e12	+	3.69989e12i	−1.06324	+	1.84158i
$543$	5.46687e11	+	9.46889e11i	0.269860	+	0.467412i
$544$	−4.87008e11	+	2.81174e11i	−0.238419	+	0.137651i
$545$	1.34668e12			0.653852
$546$	−7.49265e11	+	7.64490e11i	−0.360802	+	0.368133i
$547$	1.95429e12			0.933353			0.466676	−	0.884428i	$-0.345451\pi$
$547$	1.95429e12			0.933353			0.466676	+	0.884428i	$0.345451\pi$
$548$	2.04440e12	−	1.18034e12i	0.968398	−	0.559105i
$549$	−2.76719e11	−	4.79292e11i	−0.130006	−	0.225177i
$550$	−6.32786e11	+	1.09602e12i	−0.294866	+	0.510723i
$551$		−	4.43425e11i		−	0.204945i
$552$	7.27623e10	+	4.20093e10i	0.0333565	+	0.0192584i
$553$	1.10092e12	+	6.35615e11i	0.500601	+	0.289022i
$554$		−	1.49903e12i		−	0.676110i
$555$	2.92939e11	−	5.07385e11i	0.131057	−	0.226997i
$556$	−2.03901e12	−	3.53167e12i	−0.904862	−	1.56727i
$557$	−4.38606e11	+	2.53229e11i	−0.193075	+	0.111472i	−0.593421	−	0.804892i	$-0.702223\pi$
$557$	−4.38606e11	+	2.53229e11i	−0.193075	+	0.111472i	0.400346	+	0.916364i	$0.368890\pi$
$558$	−1.30543e12			−0.570035
$559$	−3.35226e12	−	8.62196e11i	−1.45206	−	0.373468i
$560$	3.39964e11			0.146079
$561$	−2.39979e11	+	1.38552e11i	−0.102292	+	0.0590580i
$562$	1.21761e10	+	2.10896e10i	0.00514866	+	0.00891773i
$563$	5.23643e11	−	9.06976e11i	0.219658	−	0.380459i	−0.735045	−	0.678018i	$-0.762839\pi$
$563$	5.23643e11	−	9.06976e11i	0.219658	−	0.380459i	0.954703	+	0.297559i	$0.0961725\pi$
$564$		−	2.19019e12i		−	0.911437i
$565$	5.61069e11	+	3.23933e11i	0.231632	+	0.133733i
$566$	−8.44557e11	−	4.87605e11i	−0.345903	−	0.199707i
$567$		−	7.16464e11i		−	0.291119i
$568$	8.33002e11	−	1.44280e12i	0.335798	−	0.581620i
$569$	1.30595e12	+	2.26198e12i	0.522303	+	0.904655i	0.999663	+	0.0259472i	$0.00826017\pi$
$569$	1.30595e12	+	2.26198e12i	0.522303	+	0.904655i	−0.477361	+	0.878707i	$0.658406\pi$
$570$	−1.59483e12	+	9.20778e11i	−0.632818	+	0.365358i
$571$	−1.83045e12			−0.720604			−0.360302	−	0.932836i	$-0.617326\pi$
$571$	−1.83045e12			−0.720604			−0.360302	+	0.932836i	$0.617326\pi$
$572$	−2.11529e12	+	5.89653e11i	−0.826204	+	0.230311i
$573$	7.95121e11			0.308132
$574$	−2.30149e12	+	1.32877e12i	−0.884924	+	0.510911i
$575$	7.19764e10	+	1.24667e11i	0.0274590	+	0.0475604i
$576$	3.78457e11	−	6.55507e11i	0.143257	−	0.248128i
$577$			1.28518e12i			0.482694i	0.970439	+	0.241347i	$0.0775893\pi$
$577$			1.28518e12i			0.482694i	−0.970439	+	0.241347i	$0.922411\pi$
$578$	−3.38630e12	−	1.95508e12i	−1.26197	−	0.728601i
$579$	−1.26016e11	−	7.27555e10i	−0.0465986	−	0.0269037i
$580$		−	5.56419e11i		−	0.204162i
$581$	−7.89125e11	+	1.36680e12i	−0.287312	+	0.497638i
$582$	−8.19502e11	−	1.41942e12i	−0.296072	−	0.512811i
$583$	1.75352e12	−	1.01240e12i	0.628641	−	0.362946i
$584$	6.09805e9			0.00216937
$585$	8.69802e10	−	3.38183e11i	0.0307057	−	0.119385i
$586$	−4.91741e12			−1.72265
$587$	−5.35780e11	+	3.09333e11i	−0.186258	+	0.107536i	−0.590230	−	0.807235i	$-0.700963\pi$
$587$	−5.35780e11	+	3.09333e11i	−0.186258	+	0.107536i	0.403972	+	0.914772i	$0.367629\pi$
$588$	−2.42541e11	−	4.20093e11i	−0.0836733	−	0.144926i
$589$	−2.38407e12	+	4.12933e12i	−0.816206	+	1.41371i
$590$		−	4.53576e12i		−	1.54105i
$591$	3.85833e12	+	2.22761e12i	1.30094	+	0.751096i
$592$	7.12717e11	+	4.11488e11i	0.238490	+	0.137692i
$593$		−	1.42064e11i		−	0.0471780i	−0.999722	−	0.0235890i	$-0.992491\pi$
$593$		−	1.42064e11i		−	0.0471780i	0.999722	−	0.0235890i	$-0.00750930\pi$
$594$	1.62338e12	−	2.81178e12i	0.535034	−	0.926706i
$595$	−7.38675e10	−	1.27942e11i	−0.0241617	−	0.0418492i
$596$	5.23319e11	−	3.02138e11i	0.169886	−	0.0980839i
$597$	1.47953e12			0.476694
$598$	−1.09940e11	+	4.27453e11i	−0.0351562	+	0.136689i
$599$	1.07524e12			0.341260			0.170630	−	0.985335i	$-0.445420\pi$
$599$	1.07524e12			0.341260			0.170630	+	0.985335i	$0.445420\pi$
$600$	6.72545e11	−	3.88294e11i	0.211856	−	0.122315i
$601$	1.24262e12	+	2.15228e12i	0.388511	+	0.672921i	0.992250	−	0.124261i	$-0.0396561\pi$
$601$	1.24262e12	+	2.15228e12i	0.388511	+	0.672921i	−0.603738	+	0.797183i	$0.706323\pi$
$602$	1.38584e12	−	2.40035e12i	0.430061	−	0.744888i
$603$		−	7.92265e11i		−	0.244030i
$604$	−3.38231e12	−	1.95278e12i	−1.03406	−	0.597017i
$605$	−1.03569e12	−	5.97958e11i	−0.314291	−	0.181456i
$606$		−	6.43396e12i		−	1.93799i
$607$	−2.75949e12	+	4.77957e12i	−0.825048	+	1.42903i	0.0768346	+	0.997044i	$0.475519\pi$
$607$	−2.75949e12	+	4.77957e12i	−0.825048	+	1.42903i	−0.901883	+	0.431981i	$0.857815\pi$
$608$	−1.94377e12	−	3.36670e12i	−0.576870	−	0.999168i
$609$	2.44344e11	−	1.41072e11i	0.0719819	−	0.0415588i
$610$	−4.48218e12			−1.31071
$611$	2.58195e12	−	7.19738e11i	0.749483	−	0.208924i
$612$	−1.74171e11			−0.0501874
$613$	4.64562e12	−	2.68215e12i	1.32884	−	0.767205i	0.343717	−	0.939073i	$-0.388314\pi$
$613$	4.64562e12	−	2.68215e12i	1.32884	−	0.767205i	0.985120	+	0.171869i	$0.0549804\pi$
$614$	3.38598e12	+	5.86468e12i	0.961449	+	1.66528i
$615$	−1.81646e12	+	3.14619e12i	−0.512020	+	0.886844i
$616$		−	4.09647e11i		−	0.114629i
$617$	1.51893e12	+	8.76956e11i	0.421944	+	0.243610i	0.695909	−	0.718130i	$-0.255002\pi$
$617$	1.51893e12	+	8.76956e11i	0.421944	+	0.243610i	−0.273965	+	0.961740i	$0.588335\pi$
$618$	1.34128e12	+	7.74391e11i	0.369890	+	0.213556i
$619$		−	1.08127e12i		−	0.296024i	−0.988986	−	0.148012i	$-0.952713\pi$
$619$		−	1.08127e12i		−	0.296024i	0.988986	−	0.148012i	$-0.0472874\pi$
$620$	−2.99158e12	+	5.18157e12i	−0.813089	+	1.40831i
$621$	−1.84652e11	−	3.19827e11i	−0.0498244	−	0.0862983i
$622$	8.28849e12	−	4.78536e12i	2.22034	−	1.28191i
$623$	−9.32460e10			−0.0247990
$624$	−1.99071e12	−	5.12008e11i	−0.525627	−	0.135190i
$625$	−2.31206e11			−0.0606093
$626$	2.72724e12	−	1.57457e12i	0.709804	−	0.409805i
$627$	−9.57813e11	−	1.65898e12i	−0.247501	−	0.428684i
$628$	−3.63876e11	+	6.30252e11i	−0.0933544	+	0.161695i
$629$		−	3.57632e11i		−	0.0910980i
$630$	2.42153e11	+	1.39807e11i	0.0612430	+	0.0353587i
$631$	4.16702e12	+	2.40583e12i	1.04639	+	0.604134i	0.921637	−	0.388054i	$-0.126853\pi$
$631$	4.16702e12	+	2.40583e12i	1.04639	+	0.604134i	0.124754	+	0.992188i	$0.460186\pi$
$632$		−	2.82768e12i		−	0.705023i
$633$	−3.27474e12	+	5.67201e12i	−0.810700	+	1.40417i
$634$	2.04900e12	+	3.54898e12i	0.503664	+	0.872371i
$635$	2.89877e12	−	1.67361e12i	0.707510	−	0.408481i
$636$	−5.33325e12			−1.29251
$637$	4.15530e11	−	4.23973e11i	0.0999942	−	0.102026i
$638$	1.02276e12			0.244388
$639$	−1.02443e12	+	5.91454e11i	−0.243068	+	0.140335i
$640$	−1.19419e12	−	2.06840e12i	−0.281361	−	0.487331i
$641$	−2.31271e11	+	4.00572e11i	−0.0541077	+	0.0937173i	−0.891811	−	0.452409i	$-0.850565\pi$
$641$	−2.31271e11	+	4.00572e11i	−0.0541077	+	0.0937173i	0.837703	+	0.546126i	$0.183898\pi$
$642$			2.56825e12i			0.596665i
$643$	−4.86705e11	−	2.80999e11i	−0.112284	−	0.0648269i	0.442806	−	0.896617i	$-0.353983\pi$
$643$	−4.86705e11	−	2.80999e11i	−0.112284	−	0.0648269i	−0.555090	+	0.831790i	$0.687316\pi$
$644$	−1.73213e11	−	1.00005e11i	−0.0396821	−	0.0229104i
$645$		−	3.78896e12i		−	0.861989i
$646$	−5.62063e11	+	9.73521e11i	−0.126981	+	0.219937i
$647$	−4.53813e11	−	7.86028e11i	−0.101814	−	0.176347i	0.810618	−	0.585575i	$-0.199131\pi$
$647$	−4.53813e11	−	7.86028e11i	−0.101814	−	0.176347i	−0.912432	+	0.409228i	$0.865798\pi$
$648$	−1.38016e12	+	7.96838e11i	−0.307499	+	0.177534i
$649$	4.71819e12			1.04394
$650$	2.91355e12	+	2.85552e12i	0.640194	+	0.627445i
$651$	−3.03388e12			−0.662041
$652$	2.30165e12	−	1.32886e12i	0.498799	−	0.287982i
$653$	−1.09249e12	−	1.89225e12i	−0.235131	−	0.407258i	0.724180	−	0.689611i	$-0.242219\pi$
$653$	−1.09249e12	−	1.89225e12i	−0.235131	−	0.407258i	−0.959311	+	0.282353i	$0.908885\pi$
$654$	3.25999e12	−	5.64646e12i	0.696813	−	1.20691i
$655$			2.75975e12i			0.585847i
$656$	−4.41941e12	−	2.55155e12i	−0.931746	−	0.537944i
$657$	−3.74970e9	−	2.16489e9i	−0.000785150	−	0.000453307i
$658$			2.14632e12i			0.446352i
$659$	−3.22521e12	+	5.58623e12i	−0.666153	+	1.15381i	0.312819	+	0.949813i	$0.398727\pi$
$659$	−3.22521e12	+	5.58623e12i	−0.666153	+	1.15381i	−0.978971	+	0.203998i	$0.934606\pi$
$660$	−1.20188e12	−	2.08172e12i	−0.246556	−	0.427047i
$661$	−7.16703e12	+	4.13789e12i	−1.46027	+	0.843087i	−0.999023	−	0.0441856i	$-0.985931\pi$
$661$	−7.16703e12	+	4.13789e12i	−1.46027	+	0.843087i	−0.461246	+	0.887272i	$0.652597\pi$
$662$	1.03315e13			2.09074
$663$	2.39853e11	+	8.60435e11i	0.0482097	+	0.172945i
$664$	3.51060e12			0.700850
$665$	8.84469e11	−	5.10648e11i	0.175382	−	0.101257i
$666$	3.38440e11	+	5.86196e11i	0.0666574	+	0.115454i
$667$	5.81669e10	−	1.00748e11i	0.0113791	−	0.0197092i
$668$		−	3.71358e12i		−	0.721603i
$669$	−7.01580e12	−	4.05058e12i	−1.35413	−	0.781807i
$670$	−5.55676e12	−	3.20820e12i	−1.06533	−	0.615070i
$671$		−	4.66246e12i		−	0.887899i
$672$	1.23679e12	−	2.14218e12i	0.233955	−	0.405222i
$673$	−1.55006e12	−	2.68478e12i	−0.291260	−	0.504477i	0.682848	−	0.730561i	$-0.260741\pi$
$673$	−1.55006e12	−	2.68478e12i	−0.291260	−	0.504477i	−0.974108	+	0.226083i	$0.927408\pi$
$674$	1.07057e13	−	6.18094e12i	1.99823	−	1.15368i
$675$	−3.41349e12			−0.632895
$676$	1.42372e11	+	7.07714e12i	0.0262220	+	1.30346i
$677$	7.49406e12			1.37110			0.685548	−	0.728027i	$-0.259562\pi$
$677$	7.49406e12			1.37110			0.685548	+	0.728027i	$0.259562\pi$
$678$	2.71643e12	−	1.56833e12i	0.493702	−	0.285039i
$679$	4.54482e11	+	7.87187e11i	0.0820546	+	0.142123i
$680$	−1.64308e11	+	2.84590e11i	−0.0294693	+	0.0510423i
$681$			4.70486e12i			0.838271i
$682$	−9.52427e12	−	5.49884e12i	−1.68578	−	0.973288i
$683$	−1.00633e12	−	5.81006e11i	−0.176949	−	0.102162i	0.408909	−	0.912575i	$-0.365909\pi$
$683$	−1.00633e12	−	5.81006e11i	−0.176949	−	0.102162i	−0.585858	+	0.810413i	$0.699243\pi$
$684$		−	1.20405e12i		−	0.210326i
$685$	−1.58122e12	+	2.73876e12i	−0.274401	+	0.475277i
$686$	2.37682e11	+	4.11678e11i	0.0409768	+	0.0709739i
$687$	−3.52076e12	+	2.03271e12i	−0.603019	+	0.348153i
$688$	5.32230e12			0.905632
$689$	−1.75261e12	−	6.28719e12i	−0.296277	−	1.06285i
$690$	−4.83138e11			−0.0811428
$691$	8.97751e12	−	5.18317e12i	1.49798	−	0.864856i	0.497978	−	0.867190i	$-0.334076\pi$
$691$	8.97751e12	−	5.18317e12i	1.49798	−	0.864856i	0.999997	+	0.00233343i	$0.000742754\pi$
$692$	4.81703e12	+	8.34334e12i	0.798550	+	1.38313i
$693$	−1.45430e11	+	2.51892e11i	−0.0239527	+	0.0414873i
$694$		−	1.40190e12i		−	0.229404i
$695$	4.73116e12	+	2.73154e12i	0.769194	+	0.444094i
$696$	−5.43509e11	−	3.13795e11i	−0.0877941	−	0.0506880i
$697$			2.21761e12i			0.355907i
$698$	5.79512e12	−	1.00374e13i	0.924087	−	1.60057i
$699$	−1.31018e12	−	2.26931e12i	−0.207580	−	0.359539i
$700$	−1.60102e12	+	9.24347e11i	−0.252031	+	0.145510i
$701$	−1.10550e13			−1.72912			−0.864562	−	0.502526i	$-0.832404\pi$
$701$	−1.10550e13			−1.72912			−0.864562	+	0.502526i	$0.832404\pi$
$702$	−7.47456e12	−	7.32571e12i	−1.16163	−	1.13850i
$703$	2.47233e12			0.381774
$704$	5.52234e12	−	3.18833e12i	0.847318	−	0.489199i
$705$	1.46703e12	+	2.54098e12i	0.223661	+	0.387391i
$706$	4.16806e11	−	7.21929e11i	0.0631412	−	0.109364i
$707$			3.56817e12i			0.537103i
$708$	−1.07626e13	−	6.21380e12i	−1.60979	−	0.929410i
$709$	6.44535e12	+	3.72122e12i	0.957940	+	0.553067i	0.895538	−	0.444984i	$-0.146791\pi$
$709$	6.44535e12	+	3.72122e12i	0.957940	+	0.553067i	0.0624014	+	0.998051i	$0.480124\pi$
$710$			9.58013e12i			1.41484i
$711$	−1.00386e12	+	1.73874e12i	−0.147320	+	0.255166i
$712$	1.03707e11	+	1.79625e11i	0.0151233	+	0.0261943i
$713$	−1.08334e12	+	6.25467e11i	−0.156986	+	0.0906361i
$714$	−7.15262e11			−0.102997
$715$	2.05911e12	−	2.10095e12i	0.294648	−	0.300635i
$716$	−1.58399e12			−0.225239
$717$	−2.60476e11	+	1.50386e11i	−0.0368071	+	0.0212506i
$718$	8.85749e12	+	1.53416e13i	1.24380	+	2.15433i
$719$	3.70941e12	−	6.42488e12i	0.517636	−	0.896572i	−0.482154	−	0.876086i	$-0.660145\pi$
$719$	3.70941e12	−	6.42488e12i	0.517636	−	0.896572i	0.999790	−	0.0204855i	$-0.00652120\pi$
$720$			5.36925e11i			0.0744591i
$721$	−7.43854e11	−	4.29464e11i	−0.102513	−	0.0591859i
$722$	2.86763e12	+	1.65563e12i	0.392740	+	0.226749i
$723$		−	6.00702e12i		−	0.817593i
$724$	−2.89480e12	+	5.01394e12i	−0.391557	+	0.678197i
$725$	−5.37639e11	−	9.31218e11i	−0.0722719	−	0.125179i
$726$	−5.01434e12	+	2.89503e12i	−0.669883	+	0.386757i
$727$	−4.69664e12			−0.623566			−0.311783	−	0.950153i	$-0.600926\pi$
$727$	−4.69664e12			−0.623566			−0.311783	+	0.950153i	$0.600926\pi$
$728$	−1.27887e12	−	3.28923e11i	−0.168747	−	0.0434014i
$729$	8.47412e12			1.11127
$730$	−3.03681e10	+	1.75330e10i	−0.00395789	+	0.00228509i
$731$	−1.15643e12	−	2.00300e12i	−0.149793	−	0.259449i
$732$	−6.14040e12	+	1.06355e13i	−0.790491	+	1.36917i
$733$		−	1.20741e13i		−	1.54485i	−0.635108	−	0.772424i	$-0.719044\pi$
$733$		−	1.20741e13i		−	1.54485i	0.635108	−	0.772424i	$-0.280956\pi$
$734$	1.35115e13	+	7.80086e12i	1.71819	+	0.991997i
$735$	5.62773e11	+	3.24917e11i	0.0711279	+	0.0410657i
$736$		−	1.01991e12i		−	0.128118i
$737$	3.33723e12	−	5.78026e12i	0.416661	−	0.721678i
$738$	−2.09860e12	−	3.63488e12i	−0.260421	−	0.451062i
$739$	2.20677e12	−	1.27408e12i	0.272181	−	0.157144i	−0.357697	−	0.933838i	$-0.616438\pi$
$739$	2.20677e12	−	1.27408e12i	0.272181	−	0.157144i	0.629878	+	0.776694i	$0.283105\pi$
$740$	3.10233e12			0.380316
$741$	−5.94821e12	+	1.65811e12i	−0.724777	+	0.202038i
$742$	5.22642e12			0.632975
$743$	−6.60508e12	+	3.81345e12i	−0.795113	+	0.459058i	−0.841759	−	0.539853i	$-0.818480\pi$
$743$	−6.60508e12	+	3.81345e12i	−0.795113	+	0.459058i	0.0466467	+	0.998911i	$0.485146\pi$
$744$	3.37423e12	+	5.84434e12i	0.403735	+	0.699290i
$745$	−4.04756e11	+	7.01058e11i	−0.0481383	+	0.0833779i
$746$			1.62383e13i			1.91962i
$747$	−2.15867e12	−	1.24631e12i	−0.253656	−	0.146448i
$748$	−1.27073e12	−	7.33656e11i	−0.148421	−	0.0856910i
$749$		−	1.42431e12i		−	0.165362i
$750$	−6.01350e12	+	1.04157e13i	−0.693987	+	1.20202i
$751$	6.40304e11	+	1.10904e12i	0.0734525	+	0.127224i	0.900412	−	0.435038i	$-0.143265\pi$
$751$	6.40304e11	+	1.10904e12i	0.0734525	+	0.127224i	−0.826960	+	0.562261i	$0.809932\pi$
$752$	−3.56928e12	+	2.06072e12i	−0.407005	+	0.234985i
$753$	−1.46808e12			−0.166408
$754$	8.21216e11	−	3.19293e12i	0.0925308	−	0.359764i
$755$	5.23204e12			0.586016
$756$	4.10733e12	−	2.37137e12i	0.457311	−	0.264029i
$757$	−2.93119e12	−	5.07698e12i	−0.324424	−	0.561919i	0.656972	−	0.753915i	$-0.271837\pi$
$757$	−2.93119e12	−	5.07698e12i	−0.324424	−	0.561919i	−0.981396	+	0.191996i	$0.938504\pi$
$758$	−6.01143e12	+	1.04121e13i	−0.661404	+	1.14558i
$759$		−	5.02570e11i		−	0.0549678i
$760$	−1.96738e12	−	1.13587e12i	−0.213908	−	0.123500i
$761$	5.25991e12	+	3.03681e12i	0.568522	+	0.328236i	0.756559	−	0.653926i	$-0.226879\pi$
$761$	5.25991e12	+	3.03681e12i	0.568522	+	0.328236i	−0.188037	+	0.982162i	$0.560212\pi$
$762$		−	1.62056e13i		−	1.74128i
$763$	−1.80793e12	+	3.13144e12i	−0.193118	+	0.334490i
$764$	2.10515e12	+	3.64623e12i	0.223544	+	0.387190i
$765$	2.02067e11	−	1.16663e11i	0.0213314	−	0.0123157i
$766$	−3.01693e12			−0.316618
$767$	3.78844e12	−	1.47296e13i	0.395259	−	1.53679i
$768$	1.31966e12			0.136879
$769$	−4.55813e12	+	2.63164e12i	−0.470022	+	0.271367i	−0.716249	−	0.697845i	$-0.754142\pi$
$769$	−4.55813e12	+	2.63164e12i	−0.470022	+	0.271367i	0.246227	+	0.969212i	$0.420809\pi$
$770$	1.17781e12	+	2.04002e12i	0.120744	+	0.209135i
$771$	−6.30652e12	+	1.09232e13i	−0.642755	+	1.11328i
$772$		−	7.70506e11i		−	0.0780725i
$773$	−9.19166e12	−	5.30680e12i	−0.925947	−	0.534596i	−0.0404194	−	0.999183i	$-0.512869\pi$
$773$	−9.19166e12	−	5.30680e12i	−0.925947	−	0.534596i	−0.885527	+	0.464587i	$0.846203\pi$
$774$	3.79102e12	+	2.18875e12i	0.379683	+	0.219210i
$775$			1.15624e13i			1.15131i
$776$	1.01093e12	−	1.75099e12i	0.100080	−	0.173343i
$777$	7.86550e11	+	1.36234e12i	0.0774162	+	0.134089i
$778$	−1.37463e13	+	7.93640e12i	−1.34517	+	0.776632i
$779$	−1.53304e13			−1.49154
$780$	−7.46395e12	+	2.08064e12i	−0.722009	+	0.201266i
$781$	−9.96545e12			−0.958445
$782$	−2.55406e11	+	1.47459e11i	−0.0244231	+	0.0141007i
$783$	1.37929e12	+	2.38899e12i	0.131137	+	0.227137i
$784$	−4.56407e11	+	7.90519e11i	−0.0431449	+	0.0747292i
$785$		−	9.74925e11i		−	0.0916342i
$786$	1.15713e13	+	6.68070e12i	1.08139	+	0.624339i
$787$	4.84898e12	+	2.79956e12i	0.450572	+	0.260138i	0.708072	−	0.706141i	$-0.249565\pi$
$787$	4.84898e12	+	2.79956e12i	0.450572	+	0.260138i	−0.257500	+	0.966278i	$0.582899\pi$
$788$			2.35912e13i			2.17962i
$789$	−4.60971e12	+	7.98426e12i	−0.423475	+	0.733480i
$790$	8.13009e12	+	1.40817e13i	0.742632	+	1.28628i
$791$	−1.50649e12	+	8.69770e11i	−0.136827	+	0.0789969i
$792$	6.46979e11			0.0584288
$793$	−1.45557e13	−	3.74369e12i	−1.30708	−	0.336179i
$794$	−4.77374e12			−0.426252
$795$	6.18744e12	−	3.57232e12i	0.549362	−	0.317174i
$796$	3.91719e12	+	6.78476e12i	0.345832	+	0.598999i
$797$	8.09005e12	−	1.40124e13i	0.710213	−	1.23013i	−0.254564	−	0.967056i	$-0.581932\pi$
$797$	8.09005e12	−	1.40124e13i	0.710213	−	1.23013i	0.964777	−	0.263069i	$-0.0847348\pi$
$798$		−	4.94463e12i		−	0.431639i
$799$	1.55107e12	+	8.95509e11i	0.134639	+	0.0777337i
$800$	−8.16405e12	−	4.71351e12i	−0.704694	−	0.406855i
$801$		−	1.47269e11i		−	0.0126405i
$802$	9.41461e12	−	1.63066e13i	0.803559	−	1.39181i
$803$	−1.82382e10	−	3.15895e10i	−0.00154797	−	0.00268116i
$804$	−1.52250e13	+	8.79018e12i	−1.28501	+	0.741901i
$805$	2.67940e11			0.0224883
$806$	−2.48142e13	+	2.53184e13i	−2.07106	+	2.11314i
$807$	1.18896e12			0.0986814
$808$	6.87356e12	−	3.96845e12i	0.567323	−	0.327544i
$809$	−2.73250e12	−	4.73283e12i	−0.224281	−	0.388466i	0.731823	−	0.681495i	$-0.238670\pi$
$809$	−2.73250e12	−	4.73283e12i	−0.224281	−	0.388466i	−0.956103	+	0.293029i	$0.905337\pi$
$810$	4.58211e12	−	7.93644e12i	0.374010	−	0.647804i
$811$			6.52841e12i			0.529924i	0.964259	+	0.264962i	$0.0853594\pi$
$811$			6.52841e12i			0.529924i	−0.964259	+	0.264962i	$0.914641\pi$
$812$	1.29384e12	+	7.47000e11i	0.104443	+	0.0603002i
$813$	−1.35804e13	−	7.84066e12i	−1.09020	−	0.629427i
$814$			5.70241e12i			0.455248i
$815$	−1.78019e12	+	3.08338e12i	−0.141338	+	0.244804i
$816$	−6.86737e11	−	1.18946e12i	−0.0542232	−	0.0939173i
$817$	1.38468e13	−	7.99445e12i	1.08730	−	0.627754i
$818$	−8.10802e11			−0.0633176
$819$	6.69606e11	+	6.56271e11i	0.0520046	+	0.0509690i
$820$	−1.92369e13			−1.48584
$821$	−2.90840e12	+	1.67917e12i	−0.223414	+	0.128988i	−0.607530	−	0.794297i	$-0.707840\pi$
$821$	−2.90840e12	+	1.67917e12i	−0.223414	+	0.128988i	0.384116	+	0.923285i	$0.374506\pi$
$822$	7.65553e12	+	1.32598e13i	0.584860	+	1.01301i
$823$	3.68329e12	−	6.37964e12i	0.279857	−	0.484727i	−0.691492	−	0.722384i	$-0.743046\pi$
$823$	3.68329e12	−	6.37964e12i	0.279857	−	0.484727i	0.971349	+	0.237657i	$0.0763795\pi$
$824$			1.91057e12i			0.144375i
$825$	−4.02293e12	−	2.32264e12i	−0.302343	−	0.174558i
$826$	1.05470e13	+	6.08932e12i	0.788350	+	0.455154i
$827$			7.77133e12i			0.577724i	0.957371	+	0.288862i	$0.0932769\pi$
$827$			7.77133e12i			0.577724i	−0.957371	+	0.288862i	$0.906723\pi$
$828$	1.57943e11	−	2.73566e11i	0.0116779	−	0.0202267i
$829$	4.60721e12	+	7.97992e12i	0.338799	+	0.586818i	0.984207	−	0.177020i	$-0.0566459\pi$
$829$	4.60721e12	+	7.97992e12i	0.338799	+	0.586818i	−0.645408	+	0.763838i	$0.723313\pi$
$830$	−1.74827e13	+	1.00936e13i	−1.27866	+	0.738236i
$831$	5.50220e12			0.400250
$832$	−5.51945e12	−	1.98002e13i	−0.399338	−	1.43256i
$833$	3.96673e11			0.0285450
$834$	2.29060e13	−	1.32248e13i	1.63947	−	0.946546i
$835$	2.48743e12	+	4.30835e12i	0.177077	+	0.306706i
$836$	5.07179e12	−	8.78459e12i	0.359114	−	0.622004i
$837$		−	2.96629e13i		−	2.08905i
$838$	−1.02166e13	−	5.89854e12i	−0.715661	−	0.413187i
$839$	1.82125e13	+	1.05150e13i	1.26894	+	0.732623i	0.974787	−	0.223136i	$-0.0716294\pi$
$839$	1.82125e13	+	1.05150e13i	1.26894	+	0.732623i	0.294152	+	0.955759i	$0.404963\pi$
$840$		−	1.44547e12i		−	0.100173i
$841$	6.81909e12	−	1.18110e13i	0.470050	−	0.814151i
$842$	1.83488e13	+	3.17810e13i	1.25806	+	2.17903i
$843$	−7.74092e10	+	4.46922e10i	−0.00527921	+	0.00304795i
$844$	−3.46806e13			−2.35259
$845$	−4.90558e12	−	8.11526e12i	−0.331006	−	0.547580i
$846$	−3.38981e12			−0.227514
$847$	2.78087e12	−	1.60554e12i	0.185654	−	0.107188i
$848$	5.01799e12	+	8.69141e12i	0.333233	+	0.577177i
$849$	1.78975e12	−	3.09994e12i	0.118225	−	0.204771i
$850$			2.72594e12i			0.179114i
$851$	5.61723e11	+	3.24311e11i	0.0367146	+	0.0211972i
$852$	2.27321e13	+	1.31244e13i	1.47795	+	0.853297i
$853$			1.90117e13i			1.22956i	0.788698	+	0.614780i	$0.210755\pi$
$853$			1.90117e13i			1.22956i	−0.788698	+	0.614780i	$0.789245\pi$
$854$	6.01739e12	−	1.04224e13i	0.387122	−	0.670515i
$855$	8.06497e11	+	1.39689e12i	0.0516126	+	0.0893956i
$856$	−2.74373e12	+	1.58409e12i	−0.174667	+	0.100844i
$857$	8.64689e12			0.547578			0.273789	−	0.961790i	$-0.411723\pi$
$857$	8.64689e12			0.547578			0.273789	+	0.961790i	$0.411723\pi$
$858$	−3.82443e12	−	1.37195e13i	−0.240920	−	0.864264i
$859$	1.28512e13			0.805329			0.402664	−	0.915348i	$-0.368084\pi$
$859$	1.28512e13			0.805329			0.402664	+	0.915348i	$0.368084\pi$
$860$	1.73753e13	−	1.00316e13i	1.08315	−	0.625356i
$861$	−4.87723e12	−	8.44762e12i	−0.302454	−	0.523866i
$862$	2.13723e13	−	3.70180e13i	1.31847	−	2.28365i
$863$		−	2.42676e13i		−	1.48929i	−0.667463	−	0.744643i	$-0.732620\pi$
$863$		−	2.42676e13i		−	1.48929i	0.667463	−	0.744643i	$-0.267380\pi$
$864$	2.09445e13	+	1.20923e13i	1.27867	+	0.738239i
$865$	−1.11771e13	−	6.45308e12i	−0.678821	−	0.391918i
$866$			2.30964e13i			1.39545i
$867$	7.17613e12	−	1.24294e13i	0.431324	−	0.747076i
$868$	−8.03248e12	−	1.39127e13i	−0.480298	−	0.831900i
$869$	−1.46481e13	+	8.45709e12i	−0.871350	+	0.503074i
$870$	3.60887e12			0.213567
$871$	−1.53657e13	−	1.50597e13i	−0.904628	−	0.886613i
$872$	8.04301e12			0.471080
$873$	−1.24325e12	+	7.17791e11i	−0.0724427	+	0.0418248i
$874$	−1.01939e12	−	1.76563e12i	−0.0590932	−	0.102352i
$875$	3.33499e12	−	5.77637e12i	0.192335	−	0.333134i
$876$			9.60779e10i			0.00551258i
$877$	−4.34035e12	−	2.50590e12i	−0.247757	−	0.143043i	0.370980	−	0.928641i	$-0.379022\pi$
$877$	−4.34035e12	−	2.50590e12i	−0.247757	−	0.143043i	−0.618737	+	0.785598i	$0.712355\pi$
$878$	1.85284e13	+	1.06974e13i	1.05224	+	0.607509i
$879$		−	1.80494e13i		−	1.01979i
$880$	−2.26167e12	+	3.91733e12i	−0.127133	+	0.220201i
$881$	6.36181e12	+	1.10190e13i	0.355786	+	0.616240i	0.987252	−	0.159164i	$-0.0508798\pi$
$881$	6.36181e12	+	1.10190e13i	0.355786	+	0.616240i	−0.631466	+	0.775404i	$0.717547\pi$
$882$	−6.50187e11	+	3.75386e11i	−0.0361767	+	0.0208867i
$883$	2.81330e13			1.55737			0.778687	−	0.627412i	$-0.215886\pi$
$883$	2.81330e13			1.55737			0.778687	+	0.627412i	$0.215886\pi$
$884$	−3.31071e12	+	3.37798e12i	−0.182342	+	0.186047i
$885$	1.66485e13			0.912284
$886$	2.56865e13	−	1.48301e13i	1.40040	−	0.808523i
$887$	−1.55041e13	−	2.68539e13i	−0.840989	−	1.45664i	−0.889059	−	0.457792i	$-0.848640\pi$
$887$	−1.55041e13	−	2.68539e13i	−0.840989	−	1.45664i	0.0480701	−	0.998844i	$-0.484693\pi$
$888$	1.74957e12	−	3.03035e12i	0.0944222	−	0.163544i
$889$			8.98737e12i			0.482586i
$890$	−1.03291e12	−	5.96350e11i	−0.0551832	−	0.0318600i
$891$	8.25566e12	+	4.76640e12i	0.438836	+	0.253362i
$892$		−	4.28970e13i		−	2.26874i
$893$	−6.19069e12	+	1.07226e13i	−0.325767	+	0.564245i
$894$	1.95964e12	+	3.39419e12i	0.102602	+	0.177712i
$895$	1.83768e12	−	1.06099e12i	0.0957341	−	0.0552721i
$896$	6.41287e12			0.332404
$897$	−1.56896e12	−	4.03535e11i	−0.0809184	−	0.0208121i
$898$	−4.49930e13			−2.30888
$899$	8.09218e12	−	4.67202e12i	0.413187	−	0.238554i
$900$	−1.45988e12	−	2.52858e12i	−0.0741694	−	0.128465i
$901$	2.18062e12	−	3.77694e12i	0.110235	−	0.190932i
$902$		−	3.53595e13i		−	1.77859i
$903$	8.81049e12	+	5.08674e12i	0.440966	+	0.254592i
$904$	3.35097e12	+	1.93469e12i	0.166883	+	0.0963502i
$905$		−	7.75598e12i		−	0.384342i
$906$	1.26655e13	−	2.19373e13i	0.624519	−	1.08170i
$907$	−1.70773e13	−	2.95787e13i	−0.837889	−	1.45127i	−0.891657	−	0.452712i	$-0.850457\pi$
$907$	−1.70773e13	−	2.95787e13i	−0.837889	−	1.45127i	0.0537682	−	0.998553i	$-0.482877\pi$
$908$	−2.15753e13	+	1.24565e13i	−1.05335	+	0.608149i
$909$	−5.63542e12			−0.273772
$910$	7.31443e12	−	2.03896e12i	0.353585	−	0.0985647i
$911$	−1.87203e13			−0.900491			−0.450246	−	0.892905i	$-0.648664\pi$
$911$	−1.87203e13			−0.900491			−0.450246	+	0.892905i	$0.648664\pi$
$912$	8.22280e12	−	4.74744e12i	0.393589	−	0.227239i
$913$	−1.04996e13	−	1.81858e13i	−0.500097	−	0.866193i
$914$	1.92116e13	−	3.32755e13i	0.910555	−	1.57713i
$915$		−	1.64518e13i		−	0.775925i
$916$	−1.86430e13	−	1.07636e13i	−0.874957	−	0.505157i
$917$	−6.41726e12	−	3.70501e12i	−0.299701	−	0.173032i
$918$		−	6.99326e12i		−	0.325003i
$919$	1.70679e13	−	2.95624e13i	0.789332	−	1.36716i	−0.137045	−	0.990565i	$-0.543760\pi$
$919$	1.70679e13	−	2.95624e13i	0.789332	−	1.36716i	0.926377	−	0.376598i	$-0.122906\pi$
$920$	−2.97998e11	−	5.16148e11i	−0.0137141	−	0.0237536i
$921$	−2.15263e13	+	1.24282e13i	−0.985828	+	0.569168i
$922$	−1.62902e13			−0.742399
$923$	−8.00169e12	+	3.11110e13i	−0.362889	+	1.41093i
$924$	6.45419e12			0.291285
$925$	5.19203e12	−	2.99762e12i	0.233184	−	0.134629i
$926$	1.60249e13	+	2.77559e13i	0.716219	+	1.24053i
$927$	6.78279e11	−	1.17481e12i	0.0301682	−	0.0522528i
$928$			7.61834e12i			0.337205i
$929$	7.61229e12	+	4.39496e12i	0.335309	+	0.193590i	0.658195	−	0.752847i	$-0.271320\pi$
$929$	7.61229e12	+	4.39496e12i	0.335309	+	0.193590i	−0.322887	+	0.946438i	$0.604653\pi$
$930$	−3.36071e13	−	1.94031e13i	−1.47319	−	0.850544i
$931$			2.74221e12i			0.119627i
$932$	6.93766e12	−	1.20164e13i	0.301190	−	0.521677i
$933$	1.75647e13	+	3.04229e13i	0.758879	+	1.31442i
$934$	−2.40234e13	+	1.38699e13i	−1.03294	+	0.596367i
$935$	1.96567e12			0.0841120
$936$	5.19488e11	−	2.01979e12i	0.0221225	−	0.0860133i
$937$	8.37684e12			0.355020			0.177510	−	0.984119i	$-0.443196\pi$
$937$	8.37684e12			0.355020			0.177510	+	0.984119i	$0.443196\pi$
$938$	1.49201e13	−	8.61410e12i	0.629300	−	0.363327i
$939$	5.77946e12	+	1.00103e13i	0.242601	+	0.420197i
$940$	−7.76821e12	+	1.34549e13i	−0.324523	+	0.562090i
$941$			3.25371e13i			1.35277i	0.736546	+	0.676387i	$0.236455\pi$
$941$			3.25371e13i			1.35277i	−0.736546	+	0.676387i	$0.763545\pi$
$942$	−4.08774e12	−	2.36006e12i	−0.169143	−	0.0976549i
$943$	−3.48313e12	−	2.01099e12i	−0.143439	−	0.0828145i
$944$			2.33859e13i			0.958474i
$945$	−3.17678e12	+	5.50234e12i	−0.129582	+	0.224442i
$946$	1.84392e13	+	3.19376e13i	0.748568	+	1.29656i
$947$	−2.58062e13	+	1.48992e13i	−1.04268	+	0.601989i	−0.920590	−	0.390531i	$-0.872291\pi$
$947$	−2.58062e13	+	1.48992e13i	−1.04268	+	0.601989i	−0.122085	+	0.992520i	$0.538958\pi$
$948$	4.45515e13			1.79153
$949$	−1.13263e11	+	3.15730e10i	−0.00453304	+	0.00126362i
$950$	−1.88445e13			−0.750634
$951$	−1.30265e13	+	7.52086e12i	−0.516435	+	0.298164i
$952$	−4.41172e11	−	7.64133e11i	−0.0174077	−	0.0301511i
$953$	−7.92094e12	+	1.37195e13i	−0.311071	+	0.538790i	−0.978594	−	0.205798i	$-0.934021\pi$
$953$	−7.92094e12	+	1.37195e13i	−0.311071	+	0.538790i	0.667524	+	0.744588i	$0.267354\pi$
$954$			8.25439e12i			0.322639i
$955$	−4.88463e12	−	2.82014e12i	−0.190028	−	0.109712i
$956$	−1.37927e12	−	7.96321e11i	−0.0534058	−	0.0308338i
$957$			3.75402e12i			0.144675i
$958$	−1.48338e13	+	2.56930e13i	−0.568995	+	0.985529i
$959$	−4.24563e12	−	7.35365e12i	−0.162091	−	0.280750i
$960$	1.94860e13	−	1.12502e13i	0.740461	−	0.427505i
$961$	−7.40367e13			−2.80022
$962$	1.78023e13	+	4.57871e12i	0.670173	+	0.172368i
$963$	2.24950e12			0.0842884
$964$	2.75467e13	−	1.59041e13i	1.02736	−	0.593148i
$965$	5.16100e11	+	8.93912e11i	0.0191585	+	0.0331835i
$966$	6.48619e11	−	1.12344e12i	0.0239658	−	0.0415101i
$967$			8.16413e12i			0.300255i	0.988667	+	0.150128i	$0.0479685\pi$
$967$			8.16413e12i			0.300255i	−0.988667	+	0.150128i	$0.952032\pi$
$968$	−6.18567e12	−	3.57130e12i	−0.226437	−	0.130734i
$969$	−3.57331e12	−	2.06305e12i	−0.130201	−	0.0751714i
$970$			1.16265e13i			0.421673i
$971$	−6.82811e12	+	1.18266e13i	−0.246498	+	0.426948i	−0.962552	−	0.271098i	$-0.912613\pi$
$971$	−6.82811e12	+	1.18266e13i	−0.246498	+	0.426948i	0.716053	+	0.698046i	$0.245947\pi$
$972$	6.88550e12	+	1.19260e13i	0.247421	+	0.428546i
$973$	−1.27033e13	+	7.33425e12i	−0.454369	+	0.262330i
$974$	9.76759e12			0.347754
$975$	−1.04812e13	+	1.06942e13i	−0.371441	+	0.378989i
$976$	2.31097e13			0.815210
$977$	2.51952e13	−	1.45465e13i	0.884693	−	0.510778i	0.0124903	−	0.999922i	$-0.496024\pi$
$977$	2.51952e13	−	1.45465e13i	0.884693	−	0.510778i	0.872203	+	0.489144i	$0.162691\pi$
$978$	8.61884e12	+	1.49283e13i	0.301248	+	0.521776i
$979$	6.20336e11	−	1.07445e12i	0.0215826	−	0.0373822i
$980$			3.44099e12i			0.119170i
$981$	−4.94566e12	−	2.85538e12i	−0.170496	−	0.0984358i
$982$	−1.37385e13	−	7.93190e12i	−0.471451	−	0.272192i
$983$			3.29711e13i			1.12627i	0.826365	+	0.563135i	$0.190405\pi$
$983$			3.29711e13i			1.12627i	−0.826365	+	0.563135i	$0.809595\pi$
$984$	−1.08487e13	+	1.87906e13i	−0.368894	+	0.638943i
$985$	−1.58018e13	−	2.73696e13i	−0.534865	−	0.926414i
$986$	1.90780e12	−	1.10147e12i	0.0642814	−	0.0371129i
$987$	−7.87806e12			−0.264236
$988$	−2.33521e13	−	2.28871e13i	−0.779687	−	0.764159i
$989$	4.19473e12			0.139419
$990$	−3.22193e12	+	1.86018e12i	−0.106600	+	0.0615456i
$991$	5.86402e12	+	1.01568e13i	0.193136	+	0.334522i	0.946288	−	0.323325i	$-0.104801\pi$
$991$	5.86402e12	+	1.01568e13i	0.193136	+	0.334522i	−0.753152	+	0.657847i	$0.771467\pi$
$992$	4.09599e13	−	7.09447e13i	1.34294	−	2.32604i
$993$			3.79216e13i			1.23770i
$994$	−2.22767e13	−	1.28615e13i	−0.723789	−	0.417880i
$995$	−9.08914e12	−	5.24761e12i	−0.293981	−	0.169730i
$996$			5.53113e13i			1.78093i
$997$	−1.38218e13	+	2.39400e13i	−0.443032	+	0.767354i	−0.997913	−	0.0645760i	$-0.979431\pi$
$997$	−1.38218e13	+	2.39400e13i	−0.443032	+	0.767354i	0.554881	+	0.831930i	$0.312764\pi$
$998$	1.67189e13	+	2.89580e13i	0.533482	+	0.924018i
$999$	−1.33199e13	+	7.69025e12i	−0.423113	+	0.244284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.q.a.36.11	✓	124
13.4	even	6	inner	91.10.q.a.43.11	yes	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.q.a.36.11	✓	124	1.1	even	1	trivial
91.10.q.a.43.11	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)

\(f(q)\)	\(=\)	\(q+(-29.7427 + 17.1720i) q^{2} +(-63.0297 - 109.171i) q^{3} +(333.753 - 578.077i) q^{4} +894.218i q^{5} +(3749.35 + 2164.69i) q^{6} +(-2079.33 - 1200.50i) q^{7} +5340.70i q^{8} +(1896.02 - 3284.00i) q^{9} +O(q^{10})\)	\(q+(-29.7427 + 17.1720i) q^{2} +(-63.0297 - 109.171i) q^{3} +(333.753 - 578.077i) q^{4} +894.218i q^{5} +(3749.35 + 2164.69i) q^{6} +(-2079.33 - 1200.50i) q^{7} +5340.70i q^{8} +(1896.02 - 3284.00i) q^{9} +(-15355.5 - 26596.5i) q^{10} +(27666.2 - 15973.1i) q^{11} -84145.4 q^{12} +(-27651.7 - 99196.2i) q^{13} +82459.8 q^{14} +(97622.3 - 56362.2i) q^{15} +(79171.3 + 137129. i) q^{16} +(34404.7 - 59590.7i) q^{17} +130234. i q^{18} +(411953. + 237841. i) q^{19} +(516927. + 298448. i) q^{20} +302668. i q^{21} +(-548579. + 950167. i) q^{22} +(62398.3 + 108077. i) q^{23} +(583047. - 336623. i) q^{24} +1.15350e6 q^{25} +(2.52583e6 + 2.47553e6i) q^{26} -2.95925e6 q^{27} +(-1.38796e6 + 801341. i) q^{28} +(-466094. - 807298. i) q^{29} +(-1.93570e6 + 3.35273e6i) q^{30} +1.00238e7i q^{31} +(-7.07763e6 - 4.08627e6i) q^{32} +(-3.48758e6 - 2.01356e6i) q^{33} +2.36319e6i q^{34} +(1.07351e6 - 1.85937e6i) q^{35} +(-1.26561e6 - 2.19209e6i) q^{36} +(4.50111e6 - 2.59872e6i) q^{37} -1.63368e7 q^{38} +(-9.08643e6 + 9.27106e6i) q^{39} -4.77575e6 q^{40} +(-2.79105e7 + 1.61141e7i) q^{41} +(-5.19741e6 - 9.00219e6i) q^{42} +(1.68063e7 - 2.91094e7i) q^{43} -2.13243e7i q^{44} +(2.93661e6 + 1.69546e6i) q^{45} +(-3.71179e6 - 2.14300e6i) q^{46} +2.60287e7i q^{47} +(9.98028e6 - 1.72863e7i) q^{48} +(2.88240e6 + 4.99246e6i) q^{49} +(-3.43082e7 + 1.98079e7i) q^{50} -8.67407e6 q^{51} +(-6.65719e7 - 1.71222e7i) q^{52} +6.33814e7 q^{53} +(8.80161e7 - 5.08161e7i) q^{54} +(1.42834e7 + 2.47396e7i) q^{55} +(6.41151e6 - 1.11051e7i) q^{56} -5.99642e7i q^{57} +(2.77258e7 + 1.60075e7i) q^{58} +(1.27905e8 + 7.38459e7i) q^{59} -7.52443e7i q^{60} +(7.29737e7 - 1.26394e8i) q^{61} +(-1.72128e8 - 2.98135e8i) q^{62} +(-7.88489e6 + 4.55235e6i) q^{63} +1.99606e8 q^{64} +(8.87030e7 - 2.47267e7i) q^{65} +1.38307e8 q^{66} +(1.80937e8 - 1.04464e8i) q^{67} +(-2.29654e7 - 3.97772e7i) q^{68} +(7.86588e6 - 1.36241e7i) q^{69} +7.37370e7i q^{70} +(-2.70152e8 - 1.55972e8i) q^{71} +(1.75389e7 + 1.01261e7i) q^{72} -1.14181e6i q^{73} +(-8.92502e7 + 1.54586e8i) q^{74} +(-7.27047e7 - 1.25928e8i) q^{75} +(2.74981e8 - 1.58760e8i) q^{76} -7.67028e7 q^{77} +(1.11053e8 - 4.31778e8i) q^{78} -5.29459e8 q^{79} +(-1.22623e8 + 7.07963e7i) q^{80} +(1.49201e8 + 2.58424e8i) q^{81} +(5.53422e8 - 9.58555e8i) q^{82} -6.57330e8i q^{83} +(1.74966e8 + 1.01017e8i) q^{84} +(5.32871e7 + 3.07653e7i) q^{85} +1.15439e9i q^{86} +(-5.87555e7 + 1.01767e8i) q^{87} +(8.53075e7 + 1.47757e8i) q^{88} +(3.36332e7 - 1.94182e7i) q^{89} -1.16457e8 q^{90} +(-6.15880e7 + 2.39457e8i) q^{91} +8.33025e7 q^{92} +(1.09430e9 - 6.31796e8i) q^{93} +(-4.46964e8 - 7.74164e8i) q^{94} +(-2.12682e8 + 3.68375e8i) q^{95} +1.03023e9i q^{96} +(-3.27858e8 - 1.89289e8i) q^{97} +(-1.71461e8 - 9.89930e7i) q^{98} -1.21141e8i 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

Varieties

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Representations

Groups

Database

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