LMFDB - Embedded newform 100.9.b.c.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,9,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, 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:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-39}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 10 $ x^2 - x + 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.2
Root			$0.500000 - 3.12250i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.9.b.c.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.0000 + 12.4900i) q^{2} +99.9200i q^{3} +(-56.0000 + 249.800i) q^{4} +(-1248.00 + 999.200i) q^{6} +1398.88i q^{7} +(-3680.00 + 1798.56i) q^{8} -3423.00 q^{9} +18485.2i q^{11} +(-24960.0 - 5595.52i) q^{12} +5470.00 q^{13} +(-17472.0 + 13988.8i) q^{14} +(-59264.0 - 27977.6i) q^{16} -73090.0 q^{17} +(-34230.0 - 42753.3i) q^{18} +19484.4i q^{19} -139776. q^{21} +(-230880. + 184852. i) q^{22} -237210. i q^{23} +(-179712. - 367705. i) q^{24} +(54700.0 + 68320.3i) q^{26} +313549. i q^{27} +(-349440. - 78337.3i) q^{28} -128222. q^{29} +67945.6i q^{31} +(-243200. - 1.01998e6i) q^{32} -1.84704e6 q^{33} +(-730900. - 912894. i) q^{34} +(191688. - 855065. i) q^{36} +3.47203e6 q^{37} +(-243360. + 194844. i) q^{38} +546562. i q^{39} +2.14688e6 q^{41} +(-1.39776e6 - 1.74580e6i) q^{42} -5.92815e6i q^{43} +(-4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 - 2.37210e6i) q^{46} +7.62629e6i q^{47} +(2.79552e6 - 5.92166e6i) q^{48} +3.80794e6 q^{49} -7.30315e6i q^{51} +(-306320. + 1.36641e6i) q^{52} -824290. q^{53} +(-3.91622e6 + 3.13549e6i) q^{54} +(-2.51597e6 - 5.14788e6i) q^{56} -1.94688e6 q^{57} +(-1.28222e6 - 1.60149e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. + 679456. i) q^{62} -4.78836e6i q^{63} +(1.03076e7 - 1.32374e7i) q^{64} +(-1.84704e7 - 2.30695e7i) q^{66} +1.52567e7i q^{67} +(4.09304e6 - 1.82579e7i) q^{68} +2.37020e7 q^{69} +1.19604e6i q^{71} +(1.25966e7 - 6.15647e6i) q^{72} +5.72563e6 q^{73} +(3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 - 1.09113e6i) q^{76} -2.58586e7 q^{77} +(-6.82656e6 + 5.46562e6i) q^{78} -3.59132e7i q^{79} -5.37881e7 q^{81} +(2.14688e7 + 2.68145e7i) q^{82} -5.19603e7i q^{83} +(7.82746e6 - 3.49160e7i) q^{84} +(7.40426e7 - 5.92815e7i) q^{86} -1.28119e7i q^{87} +(-3.32467e7 - 6.80255e7i) q^{88} -8.33242e7 q^{89} +7.65187e6i q^{91} +(5.92550e7 + 1.32838e7i) q^{92} -6.78912e6 q^{93} +(-9.52524e7 + 7.62629e7i) q^{94} +(1.01917e8 - 2.43005e7i) q^{96} -1.20619e8 q^{97} +(3.80794e7 + 4.75611e7i) q^{98} -6.32748e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 20 q^{2} - 112 q^{4} - 2496 q^{6} - 7360 q^{8} - 6846 q^{9} - 49920 q^{12} + 10940 q^{13} - 34944 q^{14} - 118528 q^{16} - 146180 q^{17} - 68460 q^{18} - 279552 q^{21} - 461760 q^{22} - 359424 q^{24}+ \cdots + 76158740 q^{98}+O(q^{100}) $ 2 * q + 20 * q^2 - 112 * q^4 - 2496 * q^6 - 7360 * q^8 - 6846 * q^9 - 49920 * q^12 + 10940 * q^13 - 34944 * q^14 - 118528 * q^16 - 146180 * q^17 - 68460 * q^18 - 279552 * q^21 - 461760 * q^22 - 359424 * q^24 + 109400 * q^26 - 698880 * q^28 - 256444 * q^29 - 486400 * q^32 - 3694080 * q^33 - 1461800 * q^34 + 383376 * q^36 + 6944060 * q^37 - 486720 * q^38 + 4293764 * q^41 - 2795520 * q^42 - 9235200 * q^44 + 5925504 * q^46 + 5591040 * q^48 + 7615874 * q^49 - 612640 * q^52 - 1648580 * q^53 - 7832448 * q^54 - 5031936 * q^56 - 3893760 * q^57 - 2564440 * q^58 - 29492156 * q^61 - 1697280 * q^62 + 20615168 * q^64 - 36940800 * q^66 + 8186080 * q^68 + 47404032 * q^69 + 25193280 * q^72 + 11451260 * q^73 + 69440600 * q^74 - 9734400 * q^76 - 51717120 * q^77 - 13653120 * q^78 - 107576190 * q^81 + 42937640 * q^82 + 15654912 * q^84 + 148085184 * q^86 - 66493440 * q^88 - 166648444 * q^89 + 118510080 * q^92 - 13578240 * q^93 - 190504704 * q^94 + 203833344 * q^96 - 241238020 * q^97 + 76158740 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	10.0000	+	12.4900i	0.625000	+	0.780625i
$2$	10.0000	+	12.4900i	0.625000	+	0.780625i
$3$			99.9200i			1.23358i	0.787128	+	0.616790i	$0.211567\pi$
$3$			99.9200i			1.23358i	−0.787128	+	0.616790i	$0.788433\pi$
$4$	−56.0000	+	249.800i	−0.218750	+	0.975781i
$5$		0			0
$5$		0			0
$6$	−1248.00	+	999.200i	−0.962963	+	0.770987i
$7$			1398.88i			0.582624i	0.956628	+	0.291312i	$0.0940917\pi$
$7$			1398.88i			0.582624i	−0.956628	+	0.291312i	$0.905908\pi$
$8$	−3680.00	+	1798.56i	−0.898438	+	0.439101i
$9$	−3423.00			−0.521719
$10$		0			0
$11$			18485.2i			1.26256i	0.775554	+	0.631282i	$0.217471\pi$
$11$			18485.2i			1.26256i	−0.775554	+	0.631282i	$0.782529\pi$
$12$	−24960.0	−	5595.52i	−1.20370	−	0.269846i
$13$	5470.00			0.191520			0.0957600	−	0.995404i	$-0.469472\pi$
$13$	5470.00			0.191520			0.0957600	+	0.995404i	$0.469472\pi$
$14$	−17472.0	+	13988.8i	−0.454810	+	0.364140i
$15$		0			0
$16$	−59264.0	−	27977.6i	−0.904297	−	0.426904i
$17$	−73090.0			−0.875109			−0.437555	−	0.899192i	$-0.644155\pi$
$17$	−73090.0			−0.875109			−0.437555	+	0.899192i	$0.644155\pi$
$18$	−34230.0	−	42753.3i	−0.326075	−	0.407267i
$19$			19484.4i			0.149511i	0.997202	+	0.0747554i	$0.0238176\pi$
$19$			19484.4i			0.149511i	−0.997202	+	0.0747554i	$0.976182\pi$
$20$		0			0
$21$	−139776.			−0.718713
$22$	−230880.	+	184852.i	−0.985588	+	0.789102i
$23$		−	237210.i		−	0.847660i	−0.905742	−	0.423830i	$-0.860685\pi$
$23$		−	237210.i		−	0.847660i	0.905742	−	0.423830i	$-0.139315\pi$
$24$	−179712.	−	367705.i	−0.541667	−	1.10829i
$25$		0			0
$26$	54700.0	+	68320.3i	0.119700	+	0.149505i
$27$			313549.i			0.589997i
$28$	−349440.	−	78337.3i	−0.568513	−	0.127449i
$29$	−128222.			−0.181289			−0.0906443	−	0.995883i	$-0.528893\pi$
$29$	−128222.			−0.181289			−0.0906443	+	0.995883i	$0.528893\pi$
$30$		0			0
$31$			67945.6i			0.0735723i	0.999323	+	0.0367862i	$0.0117120\pi$
$31$			67945.6i			0.0735723i	−0.999323	+	0.0367862i	$0.988288\pi$
$32$	−243200.	−	1.01998e6i	−0.231934	−	0.972732i
$33$	−1.84704e6			−1.55747
$34$	−730900.	−	912894.i	−0.546943	−	0.683132i
$35$		0			0
$36$	191688.	−	855065.i	0.114126	−	0.509084i
$37$	3.47203e6			1.85258			0.926289	−	0.376813i	$-0.122980\pi$
$37$	3.47203e6			1.85258			0.926289	+	0.376813i	$0.122980\pi$
$38$	−243360.	+	194844.i	−0.116712	+	0.0934442i
$39$			546562.i			0.236255i
$40$		0			0
$41$	2.14688e6			0.759754			0.379877	−	0.925037i	$-0.375966\pi$
$41$	2.14688e6			0.759754			0.379877	+	0.925037i	$0.375966\pi$
$42$	−1.39776e6	−	1.74580e6i	−0.449196	−	0.561045i
$43$		−	5.92815e6i		−	1.73399i	−0.498321	−	0.866993i	$-0.666050\pi$
$43$		−	5.92815e6i		−	1.73399i	0.498321	−	0.866993i	$-0.333950\pi$
$44$	−4.61760e6	−	1.03517e6i	−1.23199	−	0.276186i
$45$		0			0
$46$	2.96275e6	−	2.37210e6i	0.661704	−	0.529787i
$47$			7.62629e6i			1.56287i	0.623989	+	0.781433i	$0.285511\pi$
$47$			7.62629e6i			1.56287i	−0.623989	+	0.781433i	$0.714489\pi$
$48$	2.79552e6	−	5.92166e6i	0.526620	−	1.11552i
$49$	3.80794e6			0.660550
$50$		0			0
$51$		−	7.30315e6i		−	1.07952i
$52$	−306320.	+	1.36641e6i	−0.0418950	+	0.186881i
$53$	−824290.			−0.104466			−0.0522332	−	0.998635i	$-0.516634\pi$
$53$	−824290.			−0.104466			−0.0522332	+	0.998635i	$0.516634\pi$
$54$	−3.91622e6	+	3.13549e6i	−0.460567	+	0.368748i
$55$		0			0
$56$	−2.51597e6	−	5.14788e6i	−0.255831	−	0.523451i
$57$	−1.94688e6			−0.184433
$58$	−1.28222e6	−	1.60149e6i	−0.113305	−	0.141518i
$59$			3.72552e6i			0.307453i	0.988113	+	0.153726i	$0.0491274\pi$
$59$			3.72552e6i			0.307453i	−0.988113	+	0.153726i	$0.950873\pi$
$60$		0			0
$61$	−1.47461e7			−1.06502			−0.532509	−	0.846424i	$-0.678751\pi$
$61$	−1.47461e7			−1.06502			−0.532509	+	0.846424i	$0.678751\pi$
$62$	−848640.	+	679456.i	−0.0574324	+	0.0459827i
$63$		−	4.78836e6i		−	0.303966i
$64$	1.03076e7	−	1.32374e7i	0.614380	−	0.789010i
$65$		0			0
$66$	−1.84704e7	−	2.30695e7i	−0.973421	−	1.21580i
$67$			1.52567e7i			0.757113i	0.925578	+	0.378557i	$0.123579\pi$
$67$			1.52567e7i			0.757113i	−0.925578	+	0.378557i	$0.876421\pi$
$68$	4.09304e6	−	1.82579e7i	0.191430	−	0.853915i
$69$	2.37020e7			1.04566
$70$		0			0
$71$			1.19604e6i			0.0470666i	0.999723	+	0.0235333i	$0.00749158\pi$
$71$			1.19604e6i			0.0470666i	−0.999723	+	0.0235333i	$0.992508\pi$
$72$	1.25966e7	−	6.15647e6i	0.468732	−	0.229088i
$73$	5.72563e6			0.201619			0.100810	−	0.994906i	$-0.467857\pi$
$73$	5.72563e6			0.201619			0.100810	+	0.994906i	$0.467857\pi$
$74$	3.47203e7	+	4.33656e7i	1.15786	+	1.44617i
$75$		0			0
$76$	−4.86720e6	−	1.09113e6i	−0.145890	−	0.0327055i
$77$	−2.58586e7			−0.735600
$78$	−6.82656e6	+	5.46562e6i	−0.184427	+	0.147659i
$79$		−	3.59132e7i		−	0.922032i	−0.887392	−	0.461016i	$-0.847485\pi$
$79$		−	3.59132e7i		−	0.922032i	0.887392	−	0.461016i	$-0.152515\pi$
$80$		0			0
$81$	−5.37881e7			−1.24953
$82$	2.14688e7	+	2.68145e7i	0.474846	+	0.593082i
$83$		−	5.19603e7i		−	1.09486i	−0.836851	−	0.547431i	$-0.815606\pi$
$83$		−	5.19603e7i		−	1.09486i	0.836851	−	0.547431i	$-0.184394\pi$
$84$	7.82746e6	−	3.49160e7i	0.157218	−	0.701306i
$85$		0			0
$86$	7.40426e7	−	5.92815e7i	1.35359	−	1.08374i
$87$		−	1.28119e7i		−	0.223634i
$88$	−3.32467e7	−	6.80255e7i	−0.554393	−	1.13433i
$89$	−8.33242e7			−1.32804			−0.664020	−	0.747715i	$-0.731151\pi$
$89$	−8.33242e7			−1.32804			−0.664020	+	0.747715i	$0.731151\pi$
$90$		0			0
$91$			7.65187e6i			0.111584i
$92$	5.92550e7	+	1.32838e7i	0.827130	+	0.185426i
$93$	−6.78912e6			−0.0907573
$94$	−9.52524e7	+	7.62629e7i	−1.22001	+	0.976792i
$95$		0			0
$96$	1.01917e8	−	2.43005e7i	1.19994	−	0.286109i
$97$	−1.20619e8			−1.36248			−0.681238	−	0.732062i	$-0.738558\pi$
$97$	−1.20619e8			−1.36248			−0.681238	+	0.732062i	$0.738558\pi$
$98$	3.80794e7	+	4.75611e7i	0.412844	+	0.515641i
$99$		−	6.32748e7i		−	0.658704i
$100$		0			0
$101$	2.77246e7			0.266428			0.133214	−	0.991087i	$-0.457470\pi$
$101$	2.77246e7			0.266428			0.133214	+	0.991087i	$0.457470\pi$
$102$	9.12163e7	−	7.30315e7i	0.842698	−	0.674698i
$103$			1.04501e8i			0.928477i	0.885710	+	0.464238i	$0.153672\pi$
$103$			1.04501e8i			0.928477i	−0.885710	+	0.464238i	$0.846328\pi$
$104$	−2.01296e7	+	9.83812e6i	−0.172069	+	0.0840967i
$105$		0			0
$106$	−8.24290e6	−	1.02954e7i	−0.0652915	−	0.0815490i
$107$			1.00328e8i			0.765394i	0.923874	+	0.382697i	$0.125005\pi$
$107$			1.00328e8i			0.765394i	−0.923874	+	0.382697i	$0.874995\pi$
$108$	−7.83245e7	−	1.75587e7i	−0.575708	−	0.129062i
$109$	−5.90716e7			−0.418478			−0.209239	−	0.977865i	$-0.567099\pi$
$109$	−5.90716e7			−0.418478			−0.209239	+	0.977865i	$0.567099\pi$
$110$		0			0
$111$			3.46925e8i			2.28530i
$112$	3.91373e7	−	8.29032e7i	0.248724	−	0.526865i
$113$	−5.50849e7			−0.337846			−0.168923	−	0.985629i	$-0.554029\pi$
$113$	−5.50849e7			−0.337846			−0.168923	+	0.985629i	$0.554029\pi$
$114$	−1.94688e7	−	2.43165e7i	−0.115271	−	0.143973i
$115$		0			0
$116$	7.18043e6	−	3.20298e7i	0.0396569	−	0.176898i
$117$	−1.87238e7			−0.0999196
$118$	−4.65317e7	+	3.72552e7i	−0.240005	+	0.192158i
$119$		−	1.02244e8i		−	0.509859i
$120$		0			0
$121$	−1.27344e8			−0.594067
$122$	−1.47461e8	−	1.84178e8i	−0.665637	−	0.831380i
$123$			2.14516e8i			0.937217i
$124$	−1.69728e7	−	3.80495e6i	−0.0717905	−	0.0160939i
$125$		0			0
$126$	5.98067e7	−	4.78836e7i	0.237283	−	0.189979i
$127$			2.57160e8i			0.988529i	0.869312	+	0.494264i	$0.164562\pi$
$127$			2.57160e8i			0.988529i	−0.869312	+	0.494264i	$0.835438\pi$
$128$	2.68411e8	−	3.63229e6i	0.999908	−	0.0135313i
$129$	5.92341e8			2.13901
$130$		0			0
$131$			3.12175e8i			1.06002i	0.847992	+	0.530009i	$0.177812\pi$
$131$			3.12175e8i			1.06002i	−0.847992	+	0.530009i	$0.822188\pi$
$132$	1.03434e8	−	4.61390e8i	0.340697	−	1.51975i
$133$	−2.72563e7			−0.0871085
$134$	−1.90556e8	+	1.52567e8i	−0.591021	+	0.473196i
$135$		0			0
$136$	2.68971e8	−	1.31457e8i	0.786231	−	0.384262i
$137$	−2.21980e8			−0.630132			−0.315066	−	0.949070i	$-0.602027\pi$
$137$	−2.21980e8			−0.630132			−0.315066	+	0.949070i	$0.602027\pi$
$138$	2.37020e8	+	2.96038e8i	0.653535	+	0.816265i
$139$			2.95030e8i			0.790328i	0.918611	+	0.395164i	$0.129312\pi$
$139$			2.95030e8i			0.790328i	−0.918611	+	0.395164i	$0.870688\pi$
$140$		0			0
$141$	−7.62019e8			−1.92792
$142$	−1.49386e7	+	1.19604e7i	−0.0367414	+	0.0294166i
$143$			1.01114e8i			0.241806i
$144$	2.02861e8	+	9.57673e7i	0.471789	+	0.222724i
$145$		0			0
$146$	5.72563e7	+	7.15131e7i	0.126012	+	0.157389i
$147$			3.80489e8i			0.814841i
$148$	−1.94434e8	+	8.67313e8i	−0.405252	+	1.80771i
$149$	4.03603e8			0.818859			0.409429	−	0.912342i	$-0.365728\pi$
$149$	4.03603e8			0.818859			0.409429	+	0.912342i	$0.365728\pi$
$150$		0			0
$151$			8.36985e8i			1.60994i	0.593316	+	0.804970i	$0.297819\pi$
$151$			8.36985e8i			1.60994i	−0.593316	+	0.804970i	$0.702181\pi$
$152$	−3.50438e7	−	7.17026e7i	−0.0656504	−	0.134326i
$153$	2.50187e8			0.456561
$154$	−2.58586e8	−	3.22973e8i	−0.459750	−	0.574227i
$155$		0			0
$156$	−1.36531e8	−	3.06075e7i	−0.230533	−	0.0516808i
$157$	2.71319e8			0.446561			0.223281	−	0.974754i	$-0.428323\pi$
$157$	2.71319e8			0.446561			0.223281	+	0.974754i	$0.428323\pi$
$158$	4.48556e8	−	3.59132e8i	0.719761	−	0.576270i
$159$		−	8.23630e7i		−	0.128868i
$160$		0			0
$161$	3.31828e8			0.493867
$162$	−5.37881e8	−	6.71813e8i	−0.780955	−	0.975413i
$163$			5.78509e8i			0.819520i	0.912193	+	0.409760i	$0.134388\pi$
$163$			5.78509e8i			0.819520i	−0.912193	+	0.409760i	$0.865612\pi$
$164$	−1.20225e8	+	5.36291e8i	−0.166196	+	0.741353i
$165$		0			0
$166$	6.48984e8	−	5.19603e8i	0.854676	−	0.684288i
$167$			4.68118e8i			0.601852i	0.953647	+	0.300926i	$0.0972958\pi$
$167$			4.68118e8i			0.601852i	−0.953647	+	0.300926i	$0.902704\pi$
$168$	5.14376e8	−	2.51395e8i	0.645719	−	0.315588i
$169$	−7.85810e8			−0.963320
$170$		0			0
$171$		−	6.66951e7i		−	0.0780026i
$172$	1.48085e9	+	3.31976e8i	1.69199	+	0.379309i
$173$	2.06197e8			0.230196			0.115098	−	0.993354i	$-0.463282\pi$
$173$	2.06197e8			0.230196			0.115098	+	0.993354i	$0.463282\pi$
$174$	1.60021e8	−	1.28119e8i	0.174574	−	0.139771i
$175$		0			0
$176$	5.17171e8	−	1.09551e9i	0.538994	−	1.14173i
$177$	−3.72253e8			−0.379268
$178$	−8.33242e8	−	1.04072e9i	−0.830025	−	1.03670i
$179$		−	1.41911e8i		−	0.138230i	−0.997609	−	0.0691152i	$-0.977982\pi$
$179$		−	1.41911e8i		−	0.138230i	0.997609	−	0.0691152i	$-0.0220176\pi$
$180$		0			0
$181$	4.82566e8			0.449616			0.224808	−	0.974403i	$-0.427824\pi$
$181$	4.82566e8			0.449616			0.224808	+	0.974403i	$0.427824\pi$
$182$	−9.55718e7	+	7.65187e7i	−0.0871053	+	0.0697400i
$183$		−	1.47343e9i		−	1.31379i
$184$	4.26636e8	+	8.72933e8i	0.372209	+	0.761569i
$185$		0			0
$186$	−6.78912e7	−	8.47961e7i	−0.0567233	−	0.0708474i
$187$		−	1.35108e9i		−	1.10488i
$188$	−1.90505e9	−	4.27072e8i	−1.52502	−	0.341877i
$189$	−4.38617e8			−0.343747
$190$		0			0
$191$		−	9.92461e8i		−	0.745727i	−0.927886	−	0.372864i	$-0.878376\pi$
$191$		−	9.92461e8i		−	0.745727i	0.927886	−	0.372864i	$-0.121624\pi$
$192$	1.32268e9	+	1.02993e9i	0.973307	+	0.757887i
$193$	−1.17593e9			−0.847526			−0.423763	−	0.905773i	$-0.639291\pi$
$193$	−1.17593e9			−0.847526			−0.423763	+	0.905773i	$0.639291\pi$
$194$	−1.20619e9	−	1.50653e9i	−0.851547	−	1.06358i
$195$		0			0
$196$	−2.13244e8	+	9.51222e8i	−0.144495	+	0.644552i
$197$	−1.70538e9			−1.13229			−0.566144	−	0.824306i	$-0.691565\pi$
$197$	−1.70538e9			−1.13229			−0.566144	+	0.824306i	$0.691565\pi$
$198$	7.90302e8	−	6.32748e8i	0.514200	−	0.411690i
$199$		−	2.49036e9i		−	1.58800i	−0.607919	−	0.793999i	$-0.707996\pi$
$199$		−	2.49036e9i		−	1.58800i	0.607919	−	0.793999i	$-0.292004\pi$
$200$		0			0
$201$	−1.52445e9			−0.933960
$202$	2.77246e8	+	3.46281e8i	0.166518	+	0.207981i
$203$		−	1.79367e8i		−	0.105623i
$204$	1.82433e9	+	4.08976e8i	1.05337	+	0.236144i
$205$		0			0
$206$	−1.30522e9	+	1.04501e9i	−0.724792	+	0.580298i
$207$			8.11970e8i			0.442241i
$208$	−3.24174e8	−	1.53037e8i	−0.173191	−	0.0817606i
$209$	−3.60173e8			−0.188767
$210$		0			0
$211$		−	1.46774e9i		−	0.740491i	−0.928934	−	0.370245i	$-0.879274\pi$
$211$		−	1.46774e9i		−	0.740491i	0.928934	−	0.370245i	$-0.120726\pi$
$212$	4.61602e7	−	2.05908e8i	0.0228520	−	0.101936i
$213$	−1.19508e8			−0.0580604
$214$	−1.25309e9	+	1.00328e9i	−0.597486	+	0.478371i
$215$		0			0
$216$	−5.63936e8	−	1.15386e9i	−0.259069	−	0.530076i
$217$	−9.50477e7			−0.0428650
$218$	−5.90716e8	−	7.37804e8i	−0.261549	−	0.326674i
$219$			5.72105e8i			0.248713i
$220$		0			0
$221$	−3.99802e8			−0.167601
$222$	−4.33309e9	+	3.46925e9i	−1.78396	+	1.42831i
$223$		−	1.47920e9i		−	0.598147i	−0.954230	−	0.299073i	$-0.903322\pi$
$223$		−	1.47920e9i		−	0.598147i	0.954230	−	0.299073i	$-0.0966776\pi$
$224$	1.42683e9	−	3.40208e8i	0.566737	−	0.135130i
$225$		0			0
$226$	−5.50849e8	−	6.88011e8i	−0.211154	−	0.263731i
$227$		−	7.50054e8i		−	0.282481i	−0.989975	−	0.141241i	$-0.954891\pi$
$227$		−	7.50054e8i		−	0.282481i	0.989975	−	0.141241i	$-0.0451091\pi$
$228$	1.09025e8	−	4.86330e8i	0.0403448	−	0.179967i
$229$	−2.84784e9			−1.03556			−0.517778	−	0.855515i	$-0.673241\pi$
$229$	−2.84784e9			−1.03556			−0.517778	+	0.855515i	$0.673241\pi$
$230$		0			0
$231$		−	2.58379e9i		−	0.907421i
$232$	4.71857e8	−	2.30615e8i	0.162876	−	0.0796041i
$233$	−2.20621e8			−0.0748553			−0.0374276	−	0.999299i	$-0.511916\pi$
$233$	−2.20621e8			−0.0748553			−0.0374276	+	0.999299i	$0.511916\pi$
$234$	−1.87238e8	−	2.33860e8i	−0.0624498	−	0.0779997i
$235$		0			0
$236$	−9.30634e8	−	2.08629e8i	−0.300007	−	0.0672553i
$237$	3.58845e9			1.13740
$238$	1.27703e9	−	1.02244e9i	0.398009	−	0.318662i
$239$			4.04493e9i			1.23971i	0.784717	+	0.619855i	$0.212808\pi$
$239$			4.04493e9i			1.23971i	−0.784717	+	0.619855i	$0.787192\pi$
$240$		0			0
$241$	6.17983e9			1.83193			0.915964	−	0.401260i	$-0.131427\pi$
$241$	6.17983e9			1.83193			0.915964	+	0.401260i	$0.131427\pi$
$242$	−1.27344e9	−	1.59052e9i	−0.371292	−	0.463743i
$243$		−	3.31731e9i		−	0.951395i
$244$	8.25780e8	−	3.68357e9i	0.232973	−	1.03922i
$245$		0			0
$246$	−2.67931e9	+	2.14516e9i	−0.731615	+	0.585760i
$247$			1.06580e8i			0.0286343i
$248$	−1.22204e8	−	2.50040e8i	−0.0323057	−	0.0661001i
$249$	5.19187e9			1.35060
$250$		0			0
$251$		−	5.21367e9i		−	1.31356i	−0.754084	−	0.656778i	$-0.771919\pi$
$251$		−	5.21367e9i		−	1.31356i	0.754084	−	0.656778i	$-0.228081\pi$
$252$	1.19613e9	+	2.68148e8i	0.296604	+	0.0664926i
$253$	4.38487e9			1.07022
$254$	−3.21193e9	+	2.57160e9i	−0.771670	+	0.617830i
$255$		0			0
$256$	2.72948e9	+	3.31613e9i	0.635506	+	0.772096i
$257$	6.13693e9			1.40676			0.703378	−	0.710816i	$-0.251674\pi$
$257$	6.13693e9			1.40676			0.703378	+	0.710816i	$0.251674\pi$
$258$	5.92341e9	+	7.39833e9i	1.33688	+	1.66976i
$259$			4.85695e9i			1.07936i
$260$		0			0
$261$	4.38904e8			0.0945818
$262$	−3.89907e9	+	3.12175e9i	−0.827477	+	0.662512i
$263$			6.96916e9i			1.45666i	0.685228	+	0.728329i	$0.259703\pi$
$263$			6.96916e9i			1.45666i	−0.685228	+	0.728329i	$0.740297\pi$
$264$	6.79711e9	−	3.32201e9i	1.39929	−	0.683889i
$265$		0			0
$266$	−2.72563e8	−	3.40431e8i	−0.0544428	−	0.0679991i
$267$		−	8.32575e9i		−	1.63824i
$268$	−3.81112e9	−	8.54374e8i	−0.738777	−	0.165619i
$269$	2.70720e9			0.517025			0.258513	−	0.966008i	$-0.416768\pi$
$269$	2.70720e9			0.517025			0.258513	+	0.966008i	$0.416768\pi$
$270$		0			0
$271$			7.99032e9i			1.48145i	0.671808	+	0.740725i	$0.265518\pi$
$271$			7.99032e9i			1.48145i	−0.671808	+	0.740725i	$0.734482\pi$
$272$	4.33161e9	+	2.04488e9i	0.791359	+	0.373588i
$273$	−7.64575e8			−0.137648
$274$	−2.21980e9	−	2.77253e9i	−0.393832	−	0.491897i
$275$		0			0
$276$	−1.32731e9	+	5.92076e9i	−0.228737	+	1.02033i
$277$	8.22965e9			1.39786			0.698928	−	0.715192i	$-0.253661\pi$
$277$	8.22965e9			1.39786			0.698928	+	0.715192i	$0.253661\pi$
$278$	−3.68493e9	+	2.95030e9i	−0.616949	+	0.493955i
$279$		−	2.32578e8i		−	0.0383841i
$280$		0			0
$281$	3.08105e9			0.494167			0.247083	−	0.968994i	$-0.420528\pi$
$281$	3.08105e9			0.494167			0.247083	+	0.968994i	$0.420528\pi$
$282$	−7.62019e9	−	9.51761e9i	−1.20495	−	1.50498i
$283$			1.17112e9i			0.182582i	0.995824	+	0.0912908i	$0.0290993\pi$
$283$			1.17112e9i			0.182582i	−0.995824	+	0.0912908i	$0.970901\pi$
$284$	−2.98771e8	−	6.69784e7i	−0.0459267	−	0.0102958i
$285$		0			0
$286$	−1.26291e9	+	1.01114e9i	−0.188760	+	0.151129i
$287$			3.00323e9i			0.442650i
$288$	8.32474e8	+	3.49140e9i	0.121004	+	0.507493i
$289$	−1.63361e9			−0.234184
$290$		0			0
$291$		−	1.20522e10i		−	1.68072i
$292$	−3.20635e8	+	1.43026e9i	−0.0441042	+	0.196736i
$293$	−4.80980e9			−0.652614			−0.326307	−	0.945264i	$-0.605804\pi$
$293$	−4.80980e9			−0.652614			−0.326307	+	0.945264i	$0.605804\pi$
$294$	−4.75231e9	+	3.80489e9i	−0.636085	+	0.509275i
$295$		0			0
$296$	−1.27771e10	+	6.24465e9i	−1.66443	+	0.813470i
$297$	−5.79601e9			−0.744909
$298$	4.03603e9	+	5.04100e9i	0.511787	+	0.639221i
$299$		−	1.29754e9i		−	0.162344i
$300$		0			0
$301$	8.29277e9			1.01026
$302$	−1.04539e10	+	8.36985e9i	−1.25676	+	1.00621i
$303$			2.77025e9i			0.328661i
$304$	5.45126e8	−	1.15472e9i	0.0638268	−	0.135202i
$305$		0			0
$306$	2.50187e9	+	3.12484e9i	0.285351	+	0.356403i
$307$		−	3.49176e9i		−	0.393089i	−0.980495	−	0.196545i	$-0.937028\pi$
$307$		−	3.49176e9i		−	0.393089i	0.980495	−	0.196545i	$-0.0629721\pi$
$308$	1.44808e9	−	6.45947e9i	0.160912	−	0.717784i
$309$	−1.04417e10			−1.14535
$310$		0			0
$311$			1.29807e10i			1.38757i	0.720182	+	0.693785i	$0.244058\pi$
$311$			1.29807e10i			1.38757i	−0.720182	+	0.693785i	$0.755942\pi$
$312$	−9.83025e8	−	2.01135e9i	−0.103740	−	0.212260i
$313$	6.31165e9			0.657606			0.328803	−	0.944399i	$-0.393355\pi$
$313$	6.31165e9			0.657606			0.328803	+	0.944399i	$0.393355\pi$
$314$	2.71319e9	+	3.38877e9i	0.279101	+	0.348597i
$315$		0			0
$316$	8.97112e9	+	2.01114e9i	0.899702	+	0.201695i
$317$	−1.65902e10			−1.64291			−0.821455	−	0.570273i	$-0.806837\pi$
$317$	−1.65902e10			−1.64291			−0.821455	+	0.570273i	$0.806837\pi$
$318$	1.02871e9	−	8.23630e8i	0.100597	−	0.0805423i
$319$		−	2.37021e9i		−	0.228888i
$320$		0			0
$321$	−1.00247e10			−0.944175
$322$	3.31828e9	+	4.14453e9i	0.308667	+	0.385525i
$323$		−	1.42411e9i		−	0.130838i
$324$	3.01213e9	−	1.34363e10i	0.273334	−	1.21927i
$325$		0			0
$326$	−7.22557e9	+	5.78509e9i	−0.639738	+	0.512200i
$327$		−	5.90243e9i		−	0.516226i
$328$	−7.90053e9	+	3.86129e9i	−0.682591	+	0.333609i
$329$	−1.06683e10			−0.910563
$330$		0			0
$331$		−	5.48640e9i		−	0.457062i	−0.973537	−	0.228531i	$-0.926608\pi$
$331$		−	5.48640e9i		−	0.457062i	0.973537	−	0.228531i	$-0.0733922\pi$
$332$	1.29797e10	+	2.90978e9i	1.06834	+	0.239501i
$333$	−1.18848e10			−0.966526
$334$	−5.84680e9	+	4.68118e9i	−0.469821	+	0.376158i
$335$		0			0
$336$	8.28368e9	+	3.91060e9i	0.649930	+	0.306822i
$337$	3.56226e8			0.0276189			0.0138095	−	0.999905i	$-0.495604\pi$
$337$	3.56226e8			0.0276189			0.0138095	+	0.999905i	$0.495604\pi$
$338$	−7.85810e9	−	9.81476e9i	−0.602075	−	0.751992i
$339$		−	5.50408e9i		−	0.416760i
$340$		0			0
$341$	−1.25599e9			−0.0928897
$342$	8.33021e8	−	6.66951e8i	0.0608908	−	0.0487517i
$343$			1.33911e10i			0.967476i
$344$	1.06621e10	+	2.18156e10i	0.761396	+	1.55788i
$345$		0			0
$346$	2.06197e9	+	2.57540e9i	0.143872	+	0.179697i
$347$		−	1.59731e10i		−	1.10172i	−0.834599	−	0.550859i	$-0.814300\pi$
$347$		−	1.59731e10i		−	1.10172i	0.834599	−	0.550859i	$-0.185700\pi$
$348$	3.20042e9	+	7.17469e8i	0.218218	+	0.0489199i
$349$	1.03634e10			0.698553			0.349277	−	0.937020i	$-0.386427\pi$
$349$	1.03634e10			0.698553			0.349277	+	0.937020i	$0.386427\pi$
$350$		0			0
$351$			1.71511e9i			0.112996i
$352$	1.88546e10	−	4.49560e9i	1.22814	−	0.292831i
$353$	1.30979e10			0.843536			0.421768	−	0.906704i	$-0.361410\pi$
$353$	1.30979e10			0.843536			0.421768	+	0.906704i	$0.361410\pi$
$354$	−3.72253e9	−	4.64944e9i	−0.237042	−	0.296066i
$355$		0			0
$356$	4.66616e9	−	2.08144e10i	0.290509	−	1.29588i
$357$	1.02162e10			0.628952
$358$	1.77247e9	−	1.41911e9i	0.107906	−	0.0863940i
$359$		−	3.31454e9i		−	0.199547i	−0.995010	−	0.0997737i	$-0.968188\pi$
$359$		−	3.31454e9i		−	0.199547i	0.995010	−	0.0997737i	$-0.0318119\pi$
$360$		0			0
$361$	1.66039e10			0.977647
$362$	4.82566e9	+	6.02724e9i	0.281010	+	0.350982i
$363$		−	1.27242e10i		−	0.732829i
$364$	−1.91144e9	−	4.28505e8i	−0.108882	−	0.0244090i
$365$		0			0
$366$	1.84031e10	−	1.47343e10i	1.02557	−	0.821116i
$367$			1.96628e10i			1.08388i	0.840418	+	0.541939i	$0.182309\pi$
$367$			1.96628e10i			1.08388i	−0.840418	+	0.541939i	$0.817691\pi$
$368$	−6.63656e9	+	1.40580e10i	−0.361870	+	0.766536i
$369$	−7.34878e9			−0.396378
$370$		0			0
$371$		−	1.15308e9i		−	0.0608646i
$372$	3.80191e8	−	1.69592e9i	0.0198532	−	0.0885593i
$373$	2.10063e10			1.08521			0.542606	−	0.839987i	$-0.317438\pi$
$373$	2.10063e10			1.08521			0.542606	+	0.839987i	$0.317438\pi$
$374$	1.68750e10	−	1.35108e10i	0.862498	−	0.690551i
$375$		0			0
$376$	−1.37163e10	−	2.80648e10i	−0.686257	−	1.40414i
$377$	−7.01374e8			−0.0347204
$378$	−4.38617e9	−	5.47833e9i	−0.214842	−	0.268337i
$379$		−	3.04816e9i		−	0.147734i	−0.997268	−	0.0738670i	$-0.976466\pi$
$379$		−	3.04816e9i		−	0.147734i	0.997268	−	0.0738670i	$-0.0235340\pi$
$380$		0			0
$381$	−2.56955e10			−1.21943
$382$	1.23958e10	−	9.92461e9i	0.582133	−	0.466080i
$383$		−	2.23357e10i		−	1.03802i	−0.854770	−	0.519008i	$-0.826302\pi$
$383$		−	2.23357e10i		−	1.03802i	0.854770	−	0.519008i	$-0.173698\pi$
$384$	3.62938e8	+	2.68196e10i	0.0166920	+	1.23347i
$385$		0			0
$386$	−1.17593e10	−	1.46874e10i	−0.529704	−	0.661599i
$387$			2.02921e10i			0.904654i
$388$	6.75466e9	−	3.01306e10i	0.298042	−	1.32948i
$389$	3.13680e10			1.36990			0.684948	−	0.728592i	$-0.259825\pi$
$389$	3.13680e10			1.36990			0.684948	+	0.728592i	$0.259825\pi$
$390$		0			0
$391$			1.73377e10i			0.741795i
$392$	−1.40132e10	+	6.84880e9i	−0.593463	+	0.290048i
$393$	−3.11926e10			−1.30762
$394$	−1.70538e10	−	2.13002e10i	−0.707680	−	0.883892i
$395$		0			0
$396$	1.58060e10	+	3.54339e9i	0.642751	+	0.144091i
$397$	−7.65788e9			−0.308281			−0.154140	−	0.988049i	$-0.549261\pi$
$397$	−7.65788e9			−0.308281			−0.154140	+	0.988049i	$0.549261\pi$
$398$	3.11046e10	−	2.49036e10i	1.23963	−	0.992499i
$399$		−	2.72345e9i		−	0.107455i
$400$		0			0
$401$	−3.26120e10			−1.26125			−0.630623	−	0.776089i	$-0.717201\pi$
$401$	−3.26120e10			−1.26125			−0.630623	+	0.776089i	$0.717201\pi$
$402$	−1.52445e10	−	1.90403e10i	−0.583725	−	0.729072i
$403$			3.71662e8i			0.0140906i
$404$	−1.55258e9	+	6.92561e9i	−0.0582812	+	0.259976i
$405$		0			0
$406$	2.24029e9	−	1.79367e9i	0.0824520	−	0.0660144i
$407$			6.41811e10i			2.33900i
$408$	1.31352e10	+	2.68756e10i	0.474018	+	0.969879i
$409$	2.26168e10			0.808236			0.404118	−	0.914707i	$-0.367578\pi$
$409$	2.26168e10			0.808236			0.404118	+	0.914707i	$0.367578\pi$
$410$		0			0
$411$		−	2.21802e10i		−	0.777318i
$412$	−2.61043e10	−	5.85205e9i	−0.905990	−	0.203104i
$413$	−5.21155e9			−0.179129
$414$	−1.01415e10	+	8.11970e9i	−0.345224	+	0.276400i
$415$		0			0
$416$	−1.33030e9	−	5.57931e9i	−0.0444199	−	0.186297i
$417$	−2.94794e10			−0.974932
$418$	−3.60173e9	−	4.49856e9i	−0.117979	−	0.147356i
$419$			4.94503e10i			1.60440i	0.597054	+	0.802201i	$0.296338\pi$
$419$			4.94503e10i			1.60440i	−0.597054	+	0.802201i	$0.703662\pi$
$420$		0			0
$421$	−3.34077e10			−1.06345			−0.531726	−	0.846916i	$-0.678457\pi$
$421$	−3.34077e10			−1.06345			−0.531726	+	0.846916i	$0.678457\pi$
$422$	1.83321e10	−	1.46774e10i	0.578045	−	0.462807i
$423$		−	2.61048e10i		−	0.815378i
$424$	3.03339e9	−	1.48253e9i	0.0938565	−	0.0458713i
$425$		0			0
$426$	−1.19508e9	−	1.49266e9i	−0.0362878	−	0.0453234i
$427$		−	2.06280e10i		−	0.620505i
$428$	−2.50618e10	−	5.61834e9i	−0.746857	−	0.167430i
$429$	−1.01033e10			−0.298287
$430$		0			0
$431$			3.06956e10i			0.889544i	0.895644	+	0.444772i	$0.146715\pi$
$431$			3.06956e10i			0.889544i	−0.895644	+	0.444772i	$0.853285\pi$
$432$	8.77234e9	−	1.85822e10i	0.251872	−	0.533533i
$433$	−2.88433e9			−0.0820529			−0.0410265	−	0.999158i	$-0.513063\pi$
$433$	−2.88433e9			−0.0820529			−0.0410265	+	0.999158i	$0.513063\pi$
$434$	−9.50477e8	−	1.18715e9i	−0.0267906	−	0.0334615i
$435$		0			0
$436$	3.30801e9	−	1.47561e10i	0.0915421	−	0.408343i
$437$	4.62189e9			0.126734
$438$	−7.14559e9	+	5.72105e9i	−0.194152	+	0.155446i
$439$		−	6.92422e10i		−	1.86429i	−0.362088	−	0.932144i	$-0.617936\pi$
$439$		−	6.92422e10i		−	1.86429i	0.362088	−	0.932144i	$-0.382064\pi$
$440$		0			0
$441$	−1.30346e10			−0.344621
$442$	−3.99802e9	−	4.99353e9i	−0.104751	−	0.130833i
$443$			2.06609e10i			0.536455i	0.963356	+	0.268228i	$0.0864379\pi$
$443$			2.06609e10i			0.536455i	−0.963356	+	0.268228i	$0.913562\pi$
$444$	−8.66619e10	−	1.94278e10i	−2.22996	−	0.499910i
$445$		0			0
$446$	1.84752e10	−	1.47920e10i	0.466928	−	0.373842i
$447$			4.03280e10i			1.01013i
$448$	1.85175e10	+	1.44191e10i	0.459696	+	0.357952i
$449$	2.11092e10			0.519382			0.259691	−	0.965692i	$-0.416379\pi$
$449$	2.11092e10			0.519382			0.259691	+	0.965692i	$0.416379\pi$
$450$		0			0
$451$			3.96855e10i			0.959237i
$452$	3.08476e9	−	1.37602e10i	0.0739039	−	0.329664i
$453$	−8.36315e10			−1.98599
$454$	9.36818e9	−	7.50054e9i	0.220512	−	0.176551i
$455$		0			0
$456$	7.16452e9	−	3.50158e9i	0.165702	−	0.0809850i
$457$	2.06831e10			0.474188			0.237094	−	0.971487i	$-0.423805\pi$
$457$	2.06831e10			0.474188			0.237094	+	0.971487i	$0.423805\pi$
$458$	−2.84784e10	−	3.55695e10i	−0.647223	−	0.808381i
$459$		−	2.29173e10i		−	0.516312i
$460$		0			0
$461$	7.65072e10			1.69394			0.846971	−	0.531640i	$-0.178424\pi$
$461$	7.65072e10			1.69394			0.846971	+	0.531640i	$0.178424\pi$
$462$	3.22715e10	−	2.58379e10i	0.708355	−	0.567138i
$463$			3.41303e9i			0.0742704i	0.999310	+	0.0371352i	$0.0118232\pi$
$463$			3.41303e9i			0.0742704i	−0.999310	+	0.0371352i	$0.988177\pi$
$464$	7.59895e9	+	3.58734e9i	0.163939	+	0.0773929i
$465$		0			0
$466$	−2.20621e9	−	2.75555e9i	−0.0467845	−	0.0584339i
$467$			1.92903e10i			0.405576i	0.979223	+	0.202788i	$0.0650002\pi$
$467$			1.92903e10i			0.405576i	−0.979223	+	0.202788i	$0.935000\pi$
$468$	1.04853e9	−	4.67721e9i	0.0218574	−	0.0974997i
$469$	−2.13423e10			−0.441112
$470$		0			0
$471$			2.71102e10i			0.550869i
$472$	−6.70056e9	−	1.37099e10i	−0.135003	−	0.276227i
$473$	1.09583e11			2.18927
$474$	3.58845e10	+	4.48197e10i	0.710875	+	0.887883i
$475$		0			0
$476$	2.55406e10	+	5.72567e9i	0.497511	+	0.111532i
$477$	2.82154e9			0.0545021
$478$	−5.05212e10	+	4.04493e10i	−0.967748	+	0.774818i
$479$			2.43887e10i			0.463282i	0.972801	+	0.231641i	$0.0744095\pi$
$479$			2.43887e10i			0.463282i	−0.972801	+	0.231641i	$0.925590\pi$
$480$		0			0
$481$	1.89920e10			0.354806
$482$	6.17983e10	+	7.71861e10i	1.14496	+	1.43005i
$483$			3.31563e10i			0.609224i
$484$	7.13124e9	−	3.18104e10i	0.129952	−	0.579679i
$485$		0			0
$486$	4.14332e10	−	3.31731e10i	0.742683	−	0.594622i
$487$		−	9.30801e10i		−	1.65478i	−0.561626	−	0.827391i	$-0.689824\pi$
$487$		−	9.30801e10i		−	1.65478i	0.561626	−	0.827391i	$-0.310176\pi$
$488$	5.42656e10	−	2.65217e10i	0.956853	−	0.467651i
$489$	−5.78046e10			−1.01094
$490$		0			0
$491$			2.12850e9i			0.0366225i	0.999832	+	0.0183113i	$0.00582898\pi$
$491$			2.12850e9i			0.0366225i	−0.999832	+	0.0183113i	$0.994171\pi$
$492$	−5.35862e10	−	1.20129e10i	−0.914518	−	0.205016i
$493$	9.37175e9			0.158647
$494$	−1.33118e9	+	1.06580e9i	−0.0223526	+	0.0178964i
$495$		0			0
$496$	1.90095e9	−	4.02673e9i	0.0314083	−	0.0665312i
$497$	−1.67312e9			−0.0274221
$498$	5.19187e10	+	6.48464e10i	0.844124	+	1.05431i
$499$		−	1.04101e10i		−	0.167901i	−0.996470	−	0.0839503i	$-0.973246\pi$
$499$		−	1.04101e10i		−	0.167901i	0.996470	−	0.0839503i	$-0.0267537\pi$
$500$		0			0
$501$	−4.67744e10			−0.742433
$502$	6.51187e10	−	5.21367e10i	1.02539	−	0.820973i
$503$			3.93019e10i			0.613962i	0.951716	+	0.306981i	$0.0993188\pi$
$503$			3.93019e10i			0.613962i	−0.951716	+	0.306981i	$0.900681\pi$
$504$	8.61216e9	+	1.76212e10i	0.133472	+	0.273094i
$505$		0			0
$506$	4.38487e10	+	5.47670e10i	0.668890	+	0.835444i
$507$		−	7.85181e10i		−	1.18833i
$508$	−6.42387e10	−	1.44010e10i	−0.964587	−	0.216241i
$509$	−3.25113e10			−0.484354			−0.242177	−	0.970232i	$-0.577861\pi$
$509$	−3.25113e10			−0.484354			−0.242177	+	0.970232i	$0.577861\pi$
$510$		0			0
$511$			8.00947e9i			0.117468i
$512$	−1.41237e10	+	6.72524e10i	−0.205526	+	0.978652i
$513$	−6.10931e9			−0.0882110
$514$	6.13693e10	+	7.66503e10i	0.879223	+	1.09815i
$515$		0			0
$516$	−3.31711e10	+	1.47967e11i	−0.467908	+	2.08720i
$517$	−1.40973e11			−1.97322
$518$	−6.06633e10	+	4.85695e10i	−0.842572	+	0.674598i
$519$			2.06032e10i			0.283965i
$520$		0			0
$521$	1.84550e9			0.0250475			0.0125237	−	0.999922i	$-0.496013\pi$
$521$	1.84550e9			0.0250475			0.0125237	+	0.999922i	$0.496013\pi$
$522$	4.38904e9	+	5.48191e9i	0.0591136	+	0.0738329i
$523$			6.23770e10i			0.833715i	0.908972	+	0.416858i	$0.136869\pi$
$523$			6.23770e10i			0.833715i	−0.908972	+	0.416858i	$0.863131\pi$
$524$	−7.79814e10	−	1.74818e10i	−1.03435	−	0.231879i
$525$		0			0
$526$	−8.70448e10	+	6.96916e10i	−1.13710	+	0.910411i
$527$		−	4.96614e9i		−	0.0643838i
$528$	1.09463e11	+	5.16757e10i	1.40842	+	0.664892i
$529$	2.20424e10			0.281473
$530$		0			0
$531$		−	1.27524e10i		−	0.160404i
$532$	1.52635e9	−	6.80863e9i	0.0190550	−	0.0849988i
$533$	1.17434e10			0.145508
$534$	1.03989e11	−	8.32575e10i	1.27885	−	1.02390i
$535$		0			0
$536$	−2.74400e10	−	5.61446e10i	−0.332449	−	0.680219i
$537$	1.41797e10			0.170518
$538$	2.70720e10	+	3.38130e10i	0.323141	+	0.403603i
$539$			7.03905e10i			0.833986i
$540$		0			0
$541$	−7.45917e10			−0.870766			−0.435383	−	0.900245i	$-0.643387\pi$
$541$	−7.45917e10			−0.870766			−0.435383	+	0.900245i	$0.643387\pi$
$542$	−9.97991e10	+	7.99032e10i	−1.15646	+	0.925907i
$543$			4.82179e10i			0.554638i
$544$	1.77755e10	+	7.45506e10i	0.202967	+	0.851246i
$545$		0			0
$546$	−7.64575e9	−	9.54954e9i	−0.0860299	−	0.107451i
$547$			1.41531e9i			0.0158089i	0.999969	+	0.00790445i	$0.00251609\pi$
$547$			1.41531e9i			0.0158089i	−0.999969	+	0.00790445i	$0.997484\pi$
$548$	1.24309e10	−	5.54506e10i	0.137841	−	0.614871i
$549$	5.04758e10			0.555641
$550$		0			0
$551$		−	2.49833e9i		−	0.0271046i
$552$	−8.72234e10	+	4.26295e10i	−0.939457	+	0.459149i
$553$	5.02383e10			0.537198
$554$	8.22965e10	+	1.02788e11i	0.873660	+	1.09120i
$555$		0			0
$556$	−7.36985e10	−	1.65217e10i	−0.771187	−	0.172884i
$557$	1.37543e11			1.42895			0.714475	−	0.699661i	$-0.246666\pi$
$557$	1.37543e11			1.42895			0.714475	+	0.699661i	$0.246666\pi$
$558$	2.90489e9	−	2.32578e9i	0.0299636	−	0.0239901i
$559$		−	3.24270e10i		−	0.332093i
$560$		0			0
$561$	1.35000e11			1.36296
$562$	3.08105e10	+	3.84823e10i	0.308854	+	0.385759i
$563$		−	1.06415e11i		−	1.05918i	−0.848255	−	0.529589i	$-0.822346\pi$
$563$		−	1.06415e11i		−	1.05918i	0.848255	−	0.529589i	$-0.177654\pi$
$564$	4.26731e10	−	1.90352e11i	0.421733	−	1.88123i
$565$		0			0
$566$	−1.46273e10	+	1.17112e10i	−0.142528	+	0.114113i
$567$		−	7.52431e10i		−	0.728005i
$568$	−2.15115e9	−	4.40143e9i	−0.0206670	−	0.0422864i
$569$	4.02429e10			0.383919			0.191960	−	0.981403i	$-0.438516\pi$
$569$	4.02429e10			0.383919			0.191960	+	0.981403i	$0.438516\pi$
$570$		0			0
$571$		−	1.50341e11i		−	1.41427i	−0.707077	−	0.707137i	$-0.749986\pi$
$571$		−	1.50341e11i		−	1.41427i	0.707077	−	0.707137i	$-0.250014\pi$
$572$	−2.52583e10	−	5.66238e9i	−0.235950	−	0.0528951i
$573$	9.91667e10			0.919914
$574$	−3.75103e10	+	3.00323e10i	−0.345544	+	0.276657i
$575$		0			0
$576$	−3.52829e10	+	4.53116e10i	−0.320534	+	0.411642i
$577$	−4.96477e9			−0.0447915			−0.0223958	−	0.999749i	$-0.507129\pi$
$577$	−4.96477e9			−0.0447915			−0.0223958	+	0.999749i	$0.507129\pi$
$578$	−1.63361e10	−	2.04038e10i	−0.146365	−	0.182810i
$579$		−	1.17499e11i		−	1.04549i
$580$		0			0
$581$	7.26862e10			0.637892
$582$	1.50533e11	−	1.20522e11i	1.31201	−	1.05045i
$583$		−	1.52372e10i		−	0.131895i
$584$	−2.10703e10	+	1.02979e10i	−0.181142	+	0.0885313i
$585$		0			0
$586$	−4.80980e10	−	6.00743e10i	−0.407884	−	0.509446i
$587$			1.53440e11i			1.29237i	0.763181	+	0.646185i	$0.223637\pi$
$587$			1.53440e11i			1.29237i	−0.763181	+	0.646185i	$0.776363\pi$
$588$	−9.50461e10	−	2.13074e10i	−0.795106	−	0.178246i
$589$	−1.32388e9			−0.0109999
$590$		0			0
$591$		−	1.70402e11i		−	1.39677i
$592$	−2.05766e11	−	9.71390e10i	−1.67528	−	0.790873i
$593$	−2.06036e11			−1.66619			−0.833094	−	0.553131i	$-0.813433\pi$
$593$	−2.06036e11			−1.66619			−0.833094	+	0.553131i	$0.813433\pi$
$594$	−5.79601e10	−	7.23922e10i	−0.465568	−	0.581495i
$595$		0			0
$596$	−2.26017e10	+	1.00820e11i	−0.179125	+	0.799027i
$597$	2.48837e11			1.95892
$598$	1.62063e10	−	1.29754e10i	0.126730	−	0.101465i
$599$			2.30634e11i			1.79150i	0.444558	+	0.895750i	$0.353361\pi$
$599$			2.30634e11i			1.79150i	−0.444558	+	0.895750i	$0.646639\pi$
$600$		0			0
$601$	1.01422e11			0.777382			0.388691	−	0.921368i	$-0.372927\pi$
$601$	1.01422e11			0.777382			0.388691	+	0.921368i	$0.372927\pi$
$602$	8.29277e10	+	1.03577e11i	0.631413	+	0.788635i
$603$		−	5.22236e10i		−	0.395001i
$604$	−2.09079e11	−	4.68711e10i	−1.57095	−	0.352174i
$605$		0			0
$606$	−3.46004e10	+	2.77025e10i	−0.256561	+	0.205413i
$607$		−	1.97883e11i		−	1.45765i	−0.684700	−	0.728825i	$-0.740067\pi$
$607$		−	1.97883e11i		−	1.45765i	0.684700	−	0.728825i	$-0.259933\pi$
$608$	1.98738e10	−	4.73860e9i	0.145434	−	0.0346766i
$609$	1.79224e10			0.130294
$610$		0			0
$611$			4.17158e10i			0.299320i
$612$	−1.40105e10	+	6.24967e10i	−0.0998728	+	0.445504i
$613$	−1.27158e11			−0.900538			−0.450269	−	0.892893i	$-0.648672\pi$
$613$	−1.27158e11			−0.900538			−0.450269	+	0.892893i	$0.648672\pi$
$614$	4.36121e10	−	3.49176e10i	0.306855	−	0.245681i
$615$		0			0
$616$	9.51595e10	−	4.65082e10i	0.660890	−	0.323003i
$617$	5.06702e10			0.349632			0.174816	−	0.984601i	$-0.444067\pi$
$617$	5.06702e10			0.349632			0.174816	+	0.984601i	$0.444067\pi$
$618$	−1.04417e11	−	1.30417e11i	−0.715844	−	0.894089i
$619$			7.06748e10i			0.481395i	0.970600	+	0.240698i	$0.0773762\pi$
$619$			7.06748e10i			0.481395i	−0.970600	+	0.240698i	$0.922624\pi$
$620$		0			0
$621$	7.43769e10			0.500117
$622$	−1.62128e11	+	1.29807e11i	−1.08317	+	0.867231i
$623$		−	1.16561e11i		−	0.773748i
$624$	1.52915e10	−	3.23915e10i	0.100858	−	0.213645i
$625$		0			0
$626$	6.31165e10	+	7.88325e10i	0.411004	+	0.513343i
$627$		−	3.59885e10i		−	0.232859i
$628$	−1.51938e10	+	6.77754e10i	−0.0976853	+	0.435746i
$629$	−2.53771e11			−1.62121
$630$		0			0
$631$		−	1.65273e11i		−	1.04252i	−0.853399	−	0.521259i	$-0.825463\pi$
$631$		−	1.65273e11i		−	1.04252i	0.853399	−	0.521259i	$-0.174537\pi$
$632$	6.45921e10	+	1.32161e11i	0.404866	+	0.828388i
$633$	1.46657e11			0.913454
$634$	−1.65902e11	−	2.07211e11i	−1.02682	−	1.28250i
$635$		0			0
$636$	2.05743e10	+	4.61233e9i	0.125747	+	0.0281898i
$637$	2.08294e10			0.126508
$638$	2.96039e10	−	2.37021e10i	0.178676	−	0.143055i
$639$		−	4.09405e9i		−	0.0245556i
$640$		0			0
$641$	1.12013e11			0.663490			0.331745	−	0.943369i	$-0.392363\pi$
$641$	1.12013e11			0.663490			0.331745	+	0.943369i	$0.392363\pi$
$642$	−1.00247e11	−	1.25209e11i	−0.590109	−	0.737046i
$643$		−	2.65913e11i		−	1.55559i	−0.628518	−	0.777795i	$-0.716338\pi$
$643$		−	2.65913e11i		−	1.55559i	0.628518	−	0.777795i	$-0.283662\pi$
$644$	−1.85824e10	+	8.28907e10i	−0.108033	+	0.481906i
$645$		0			0
$646$	1.77872e10	−	1.42411e10i	0.102136	−	0.0817739i
$647$			2.71996e11i			1.55219i	0.630614	+	0.776097i	$0.282803\pi$
$647$			2.71996e11i			1.55219i	−0.630614	+	0.776097i	$0.717197\pi$
$648$	1.97940e11	−	9.67411e10i	1.12262	−	0.548670i
$649$	−6.88669e10			−0.388179
$650$		0			0
$651$		−	9.49716e9i		−	0.0528774i
$652$	−1.44511e11	−	3.23965e10i	−0.799672	−	0.179270i
$653$	−3.03789e11			−1.67078			−0.835391	−	0.549656i	$-0.814759\pi$
$653$	−3.03789e11			−1.67078			−0.835391	+	0.549656i	$0.814759\pi$
$654$	7.37213e10	−	5.90243e10i	0.402979	−	0.322641i
$655$		0			0
$656$	−1.27233e11	−	6.00646e10i	−0.687043	−	0.324342i
$657$	−1.95988e10			−0.105189
$658$	−1.06683e11	−	1.33247e11i	−0.569102	−	0.710808i
$659$		−	4.18575e10i		−	0.221938i	−0.993824	−	0.110969i	$-0.964605\pi$
$659$		−	4.18575e10i		−	0.221938i	0.993824	−	0.110969i	$-0.0353954\pi$
$660$		0			0
$661$	−2.46529e11			−1.29141			−0.645703	−	0.763589i	$-0.723435\pi$
$661$	−2.46529e11			−1.29141			−0.645703	+	0.763589i	$0.723435\pi$
$662$	6.85251e10	−	5.48640e10i	0.356794	−	0.285664i
$663$		−	3.99482e10i		−	0.206749i
$664$	9.34537e10	+	1.91214e11i	0.480755	+	0.983665i
$665$		0			0
$666$	−1.18848e11	−	1.48441e11i	−0.604079	−	0.754494i
$667$			3.04155e10i			0.153671i
$668$	−1.16936e11	−	2.62146e10i	−0.587276	−	0.131655i
$669$	1.47802e11			0.737862
$670$		0			0
$671$		−	2.72584e11i		−	1.34465i
$672$	3.39935e10	+	1.42569e11i	0.166694	+	0.699115i
$673$	3.15336e11			1.53714			0.768569	−	0.639767i	$-0.220969\pi$
$673$	3.15336e11			1.53714			0.768569	+	0.639767i	$0.220969\pi$
$674$	3.56226e9	+	4.44927e9i	0.0172618	+	0.0215600i
$675$		0			0
$676$	4.40053e10	−	1.96295e11i	0.210726	−	0.939989i
$677$	2.47236e10			0.117695			0.0588475	−	0.998267i	$-0.481257\pi$
$677$	2.47236e10			0.117695			0.0588475	+	0.998267i	$0.481257\pi$
$678$	6.87460e10	−	5.50408e10i	0.325333	−	0.260475i
$679$		−	1.68731e11i		−	0.793811i
$680$		0			0
$681$	7.49454e10			0.348463
$682$	−1.25599e10	−	1.56873e10i	−0.0580561	−	0.0725120i
$683$			7.20843e10i			0.331251i	0.986189	+	0.165626i	$0.0529644\pi$
$683$			7.20843e10i			0.331251i	−0.986189	+	0.165626i	$0.947036\pi$
$684$	1.66604e10	+	3.73492e9i	0.0761135	+	0.0170631i
$685$		0			0
$686$	−1.67255e11	+	1.33911e11i	−0.755235	+	0.604672i
$687$		−	2.84556e11i		−	1.27744i
$688$	−1.65855e11	+	3.51326e11i	−0.740246	+	1.56804i
$689$	−4.50887e9			−0.0200074
$690$		0			0
$691$			2.95424e11i			1.29578i	0.761732	+	0.647892i	$0.224349\pi$
$691$			2.95424e11i			1.29578i	−0.761732	+	0.647892i	$0.775651\pi$
$692$	−1.15470e10	+	5.15080e10i	−0.0503554	+	0.224621i
$693$	8.85139e10			0.383776
$694$	1.99503e11	−	1.59731e11i	0.860028	−	0.688573i
$695$		0			0
$696$	2.30430e10	+	4.71479e10i	0.0981980	+	0.200921i
$697$	−1.56916e11			−0.664867
$698$	1.03634e11	+	1.29438e11i	0.436596	+	0.545308i
$699$		−	2.20444e10i		−	0.0923400i
$700$		0			0
$701$	−2.87925e11			−1.19236			−0.596180	−	0.802851i	$-0.703315\pi$
$701$	−2.87925e11			−1.19236			−0.596180	+	0.802851i	$0.703315\pi$
$702$	−2.14217e10	+	1.71511e10i	−0.0882077	+	0.0706227i
$703$			6.76504e10i			0.276980i
$704$	2.44696e11	+	1.90538e11i	0.996176	+	0.775694i
$705$		0			0
$706$	1.30979e11	+	1.63593e11i	0.527210	+	0.658485i
$707$			3.87834e10i			0.155227i
$708$	2.08462e10	−	9.29889e10i	0.0829648	−	0.370082i
$709$	2.51685e11			0.996030			0.498015	−	0.867168i	$-0.334062\pi$
$709$	2.51685e11			0.996030			0.498015	+	0.867168i	$0.334062\pi$
$710$		0			0
$711$			1.22931e11i			0.481042i
$712$	3.06633e11	−	1.49864e11i	1.19316	−	0.583144i
$713$	1.61174e10			0.0623643
$714$	1.02162e11	+	1.27601e11i	0.393095	+	0.490976i
$715$		0			0
$716$	3.54493e10	+	7.94701e9i	0.134883	+	0.0302379i
$717$	−4.04170e11			−1.52928
$718$	4.13986e10	−	3.31454e10i	0.155772	−	0.124717i
$719$			1.38856e11i			0.519574i	0.965666	+	0.259787i	$0.0836524\pi$
$719$			1.38856e11i			0.519574i	−0.965666	+	0.259787i	$0.916348\pi$
$720$		0			0
$721$	−1.46184e11			−0.540953
$722$	1.66039e11	+	2.07383e11i	0.611029	+	0.763175i
$723$			6.17489e11i			2.25983i
$724$	−2.70237e10	+	1.20545e11i	−0.0983536	+	0.438727i
$725$		0			0
$726$	1.58925e11	−	1.27242e11i	0.572064	−	0.458018i
$727$		−	1.79083e11i		−	0.641088i	−0.947234	−	0.320544i	$-0.896134\pi$
$727$		−	1.79083e11i		−	0.641088i	0.947234	−	0.320544i	$-0.103866\pi$
$728$	−1.37623e10	−	2.81589e10i	−0.0489967	−	0.100251i
$729$	−2.14381e10			−0.0759061
$730$		0			0
$731$			4.33289e11i			1.51743i
$732$	3.68062e11	+	8.25119e10i	1.28197	+	0.287391i
$733$	−2.17618e11			−0.753839			−0.376920	−	0.926246i	$-0.623017\pi$
$733$	−2.17618e11			−0.753839			−0.376920	+	0.926246i	$0.623017\pi$
$734$	−2.45588e11	+	1.96628e11i	−0.846101	+	0.677423i
$735$		0			0
$736$	−2.41950e11	+	5.76895e10i	−0.824546	+	0.196601i
$737$	−2.82023e11			−0.955904
$738$	−7.34878e10	−	9.17862e10i	−0.247736	−	0.309423i
$739$		−	4.84950e11i		−	1.62599i	−0.582268	−	0.812997i	$-0.697834\pi$
$739$		−	4.84950e11i		−	1.62599i	0.582268	−	0.812997i	$-0.302166\pi$
$740$		0			0
$741$	−1.06494e10			−0.0353227
$742$	1.44020e10	−	1.15308e10i	0.0475124	−	0.0380404i
$743$			2.03509e11i			0.667771i	0.942614	+	0.333886i	$0.108360\pi$
$743$			2.03509e11i			0.667771i	−0.942614	+	0.333886i	$0.891640\pi$
$744$	2.49840e10	−	1.22106e10i	0.0815398	−	0.0398517i
$745$		0			0
$746$	2.10063e11	+	2.62369e11i	0.678258	+	0.847144i
$747$			1.77860e11i			0.571210i
$748$	3.37500e11	+	7.56606e10i	1.07812	+	0.241693i
$749$	−1.40346e11			−0.445937
$750$		0			0
$751$		−	2.34693e11i		−	0.737804i	−0.929468	−	0.368902i	$-0.879734\pi$
$751$		−	2.34693e11i		−	0.737804i	0.929468	−	0.368902i	$-0.120266\pi$
$752$	2.13365e11	−	4.51965e11i	0.667194	−	1.41330i
$753$	5.20950e11			1.62038
$754$	−7.01374e9	−	8.76016e9i	−0.0217002	−	0.0271036i
$755$		0			0
$756$	2.45626e10	−	1.09567e11i	0.0751946	−	0.335421i
$757$	3.84882e11			1.17204			0.586022	−	0.810295i	$-0.300693\pi$
$757$	3.84882e11			1.17204			0.586022	+	0.810295i	$0.300693\pi$
$758$	3.80715e10	−	3.04816e10i	0.115325	−	0.0923338i
$759$			4.38136e11i			1.32021i
$760$		0			0
$761$	2.39209e11			0.713244			0.356622	−	0.934249i	$-0.383928\pi$
$761$	2.39209e11			0.713244			0.356622	+	0.934249i	$0.383928\pi$
$762$	−2.56955e11	−	3.20936e11i	−0.762143	−	0.951916i
$763$		−	8.26340e10i		−	0.243815i
$764$	2.47917e11	+	5.55778e10i	0.727666	+	0.163128i
$765$		0			0
$766$	2.78972e11	−	2.23357e11i	0.810301	−	0.648760i
$767$			2.03786e10i			0.0588833i
$768$	−3.31347e11	+	2.72729e11i	−0.952442	+	0.783947i
$769$	2.08457e11			0.596089			0.298045	−	0.954552i	$-0.403666\pi$
$769$	2.08457e11			0.596089			0.298045	+	0.954552i	$0.403666\pi$
$770$		0			0
$771$			6.13202e11i			1.73535i
$772$	6.58522e10	−	2.93748e11i	0.185396	−	0.826999i
$773$	5.54469e10			0.155296			0.0776478	−	0.996981i	$-0.475259\pi$
$773$	5.54469e10			0.155296			0.0776478	+	0.996981i	$0.475259\pi$
$774$	−2.53448e11	+	2.02921e11i	−0.706195	+	0.565409i
$775$		0			0
$776$	4.43878e11	−	2.16940e11i	1.22410	−	0.598265i
$777$	−4.85306e11			−1.33147
$778$	3.13680e11	+	3.91786e11i	0.856185	+	1.06938i
$779$			4.18307e10i			0.113591i
$780$		0			0
$781$	−2.21091e10			−0.0594246
$782$	−2.16548e11	+	1.73377e11i	−0.579064	+	0.463622i
$783$		−	4.02039e10i		−	0.106960i
$784$	−2.25674e11	−	1.06537e11i	−0.597333	−	0.281991i
$785$		0			0
$786$	−3.11926e11	−	3.89595e11i	−0.817261	−	1.02076i
$787$			4.05908e11i			1.05811i	0.848589	+	0.529053i	$0.177453\pi$
$787$			4.05908e11i			1.05811i	−0.848589	+	0.529053i	$0.822547\pi$
$788$	9.55014e10	−	4.26005e11i	0.247688	−	1.10487i
$789$	−6.96358e11			−1.79690
$790$		0			0
$791$		−	7.70572e10i		−	0.196837i
$792$	1.13804e11	+	2.32851e11i	0.289238	+	0.591804i
$793$	−8.06610e10			−0.203972
$794$	−7.65788e10	−	9.56469e10i	−0.192676	−	0.240652i
$795$		0			0
$796$	6.22092e11	+	1.39460e11i	1.54954	+	0.347375i
$797$	3.09015e11			0.765855			0.382927	−	0.923778i	$-0.374916\pi$
$797$	3.09015e11			0.765855			0.382927	+	0.923778i	$0.374916\pi$
$798$	3.40159e10	−	2.72345e10i	0.0838823	−	0.0671596i
$799$		−	5.57406e11i		−	1.36768i
$800$		0			0
$801$	2.85219e11			0.692864
$802$	−3.26120e11	−	4.07324e11i	−0.788279	−	0.984560i
$803$			1.05839e11i			0.254557i
$804$	8.53690e10	−	3.80807e11i	0.204304	−	0.911340i
$805$		0			0
$806$	−4.64206e9	+	3.71662e9i	−0.0109994	+	0.00880660i
$807$			2.70504e11i			0.637792i
$808$	−1.02027e11	+	4.98644e10i	−0.239369	+	0.116989i
$809$	4.77958e11			1.11582			0.557912	−	0.829900i	$-0.311603\pi$
$809$	4.77958e11			1.11582			0.557912	+	0.829900i	$0.311603\pi$
$810$		0			0
$811$			6.37503e11i			1.47366i	0.676075	+	0.736832i	$0.263679\pi$
$811$			6.37503e11i			1.47366i	−0.676075	+	0.736832i	$0.736321\pi$
$812$	4.48059e10	+	1.00446e10i	0.103065	+	0.0231050i
$813$	−7.98393e11			−1.82749
$814$	−8.01622e11	+	6.41811e11i	−1.82588	+	1.46187i
$815$		0			0
$816$	−2.04325e11	+	4.32814e11i	−0.460850	+	0.976204i
$817$	1.15506e11			0.259250
$818$	2.26168e11	+	2.82484e11i	0.505148	+	0.630929i
$819$		−	2.61924e10i		−	0.0582155i
$820$		0			0
$821$	−8.43824e11			−1.85729			−0.928644	−	0.370973i	$-0.879024\pi$
$821$	−8.43824e11			−1.85729			−0.928644	+	0.370973i	$0.879024\pi$
$822$	2.77031e11	−	2.21802e11i	0.606794	−	0.485824i
$823$		−	2.60916e11i		−	0.568723i	−0.958717	−	0.284362i	$-0.908218\pi$
$823$		−	2.60916e11i		−	0.568723i	0.958717	−	0.284362i	$-0.0917817\pi$
$824$	−1.87951e11	−	3.84563e11i	−0.407696	−	0.834179i
$825$		0			0
$826$	−5.21155e10	−	6.50922e10i	−0.111956	−	0.139833i
$827$			2.78675e11i			0.595765i	0.954602	+	0.297883i	$0.0962804\pi$
$827$			2.78675e11i			0.595765i	−0.954602	+	0.297883i	$0.903720\pi$
$828$	−2.02830e11	−	4.54703e10i	−0.431530	−	0.0967401i
$829$	4.75156e11			1.00605			0.503023	−	0.864273i	$-0.332221\pi$
$829$	4.75156e11			1.00605			0.503023	+	0.864273i	$0.332221\pi$
$830$		0			0
$831$			8.22306e11i			1.72437i
$832$	5.63825e10	−	7.24086e10i	0.117666	−	0.151111i
$833$	−2.78322e11			−0.578053
$834$	−2.94794e11	−	3.68198e11i	−0.609333	−	0.761056i
$835$		0			0
$836$	2.01697e10	−	8.99711e10i	0.0412928	−	0.184195i
$837$	−2.13043e10			−0.0434075
$838$	−6.17635e11	+	4.94503e11i	−1.25244	+	1.00275i
$839$			3.35440e11i			0.676966i	0.940973	+	0.338483i	$0.109914\pi$
$839$			3.35440e11i			0.676966i	−0.940973	+	0.338483i	$0.890086\pi$
$840$		0			0
$841$	−4.83806e11			−0.967134
$842$	−3.34077e11	−	4.17262e11i	−0.664658	−	0.830157i
$843$			3.07858e11i			0.609594i
$844$	3.66642e11	+	8.21935e10i	0.722557	+	0.161982i
$845$		0			0
$846$	3.26049e11	−	2.61048e11i	0.636504	−	0.509611i
$847$		−	1.78138e11i		−	0.346117i
$848$	4.88507e10	+	2.30616e10i	0.0944686	+	0.0445971i
$849$	−1.17019e11			−0.225229
$850$		0			0
$851$		−	8.23600e11i		−	1.57036i
$852$	6.69247e9	−	2.98532e10i	0.0127007	−	0.0566543i
$853$	9.75408e10			0.184243			0.0921213	−	0.995748i	$-0.470635\pi$
$853$	9.75408e10			0.184243			0.0921213	+	0.995748i	$0.470635\pi$
$854$	2.57643e11	−	2.06280e11i	0.484382	−	0.387816i
$855$		0			0
$856$	−1.80445e11	−	3.69205e11i	−0.336086	−	0.687659i
$857$	7.94769e10			0.147339			0.0736695	−	0.997283i	$-0.476529\pi$
$857$	7.94769e10			0.147339			0.0736695	+	0.997283i	$0.476529\pi$
$858$	−1.01033e11	−	1.26190e11i	−0.186429	−	0.232850i
$859$			4.15618e11i			0.763347i	0.924297	+	0.381673i	$0.124652\pi$
$859$			4.15618e11i			0.763347i	−0.924297	+	0.381673i	$0.875348\pi$
$860$		0			0
$861$	−3.00083e11			−0.546045
$862$	−3.83388e11	+	3.06956e11i	−0.694400	+	0.555965i
$863$		−	4.80012e11i		−	0.865383i	−0.901542	−	0.432692i	$-0.857564\pi$
$863$		−	4.80012e11i		−	0.865383i	0.901542	−	0.432692i	$-0.142436\pi$
$864$	3.19815e11	−	7.62551e10i	0.573909	−	0.136840i
$865$		0			0
$866$	−2.88433e10	−	3.60253e10i	−0.0512831	−	0.0640525i
$867$		−	1.63230e11i		−	0.288884i
$868$	5.32267e9	−	2.37429e10i	0.00937671	−	0.0418268i
$869$	6.63863e11			1.16412
$870$		0			0
$871$			8.34540e10i			0.145002i
$872$	2.17383e11	−	1.06244e11i	0.375976	−	0.183754i
$873$	4.12879e11			0.710830
$874$	4.62189e10	+	5.77274e10i	0.0792089	+	0.0989319i
$875$		0			0
$876$	−1.42912e11	−	3.20379e10i	−0.242690	−	0.0544060i
$877$	−2.74155e11			−0.463444			−0.231722	−	0.972782i	$-0.574436\pi$
$877$	−2.74155e11			−0.463444			−0.231722	+	0.972782i	$0.574436\pi$
$878$	8.64835e11	−	6.92422e11i	1.45531	−	1.16518i
$879$		−	4.80595e11i		−	0.805051i
$880$		0			0
$881$	8.01838e11			1.33101			0.665507	−	0.746391i	$-0.268215\pi$
$881$	8.01838e11			1.33101			0.665507	+	0.746391i	$0.268215\pi$
$882$	−1.30346e11	−	1.62802e11i	−0.215388	−	0.269020i
$883$		−	9.95008e11i		−	1.63676i	−0.574681	−	0.818378i	$-0.694874\pi$
$883$		−	9.95008e11i		−	1.63676i	0.574681	−	0.818378i	$-0.305126\pi$
$884$	2.23889e10	−	9.98706e10i	0.0366627	−	0.163542i
$885$		0			0
$886$	−2.58054e11	+	2.06609e11i	−0.418770	+	0.335284i
$887$			5.46038e11i			0.882122i	0.897477	+	0.441061i	$0.145398\pi$
$887$			5.46038e11i			0.882122i	−0.897477	+	0.441061i	$0.854602\pi$
$888$	−6.23965e11	−	1.27668e12i	−1.00348	−	2.05320i
$889$	−3.59736e11			−0.575940
$890$		0			0
$891$		−	9.94283e11i		−	1.57761i
$892$	3.69504e11	+	8.28353e10i	0.583660	+	0.130845i
$893$	−1.48594e11			−0.233665
$894$	−5.03696e11	+	4.03280e11i	−0.788531	+	0.631330i
$895$		0			0
$896$	5.08114e9	+	3.75474e11i	0.00788368	+	0.582570i
$897$	1.29650e11			0.200264
$898$	2.11092e11	+	2.63654e11i	0.324614	+	0.405442i
$899$		−	8.71212e9i		−	0.0133378i
$900$		0			0
$901$	6.02474e10			0.0914195
$902$	−4.95672e11	+	3.96855e11i	−0.748804	+	0.599523i
$903$			8.28613e11i			1.24624i
$904$	2.02713e11	−	9.90735e10i	0.303534	−	0.148349i
$905$		0			0
$906$	−8.36315e11	−	1.04456e12i	−1.24124	−	1.55031i
$907$			6.55018e11i			0.967886i	0.875100	+	0.483943i	$0.160796\pi$
$907$			6.55018e11i			0.967886i	−0.875100	+	0.483943i	$0.839204\pi$
$908$	1.87364e11	+	4.20030e10i	0.275640	+	0.0617927i
$909$	−9.49014e10			−0.139001
$910$		0			0
$911$			1.19425e11i			0.173389i	0.996235	+	0.0866943i	$0.0276304\pi$
$911$			1.19425e11i			0.173389i	−0.996235	+	0.0866943i	$0.972370\pi$
$912$	1.15380e11	+	5.44690e10i	0.166783	+	0.0787354i
$913$	9.60496e11			1.38233
$914$	2.06831e11	+	2.58332e11i	0.296368	+	0.370163i
$915$		0			0
$916$	1.59479e11	−	7.11390e11i	0.226528	−	1.01048i
$917$	−4.36696e11			−0.617592
$918$	2.86237e11	−	2.29173e11i	0.403046	−	0.322695i
$919$		−	5.33989e10i		−	0.0748635i	−0.999299	−	0.0374318i	$-0.988082\pi$
$919$		−	5.33989e10i		−	0.0748635i	0.999299	−	0.0374318i	$-0.0119177\pi$
$920$		0			0
$921$	3.48897e11			0.484907
$922$	7.65072e11	+	9.55574e11i	1.05871	+	1.32233i
$923$			6.54235e9i			0.00901420i
$924$	6.45430e11	+	1.44692e11i	0.885444	+	0.198498i
$925$		0			0
$926$	−4.26287e10	+	3.41303e10i	−0.0579773	+	0.0464190i
$927$		−	3.57707e11i		−	0.484404i
$928$	3.11836e10	+	1.30784e11i	0.0420469	+	0.176345i
$929$	−6.30991e11			−0.847150			−0.423575	−	0.905861i	$-0.639225\pi$
$929$	−6.30991e11			−0.847150			−0.423575	+	0.905861i	$0.639225\pi$
$930$		0			0
$931$			7.41953e10i			0.0987593i
$932$	1.23548e10	−	5.51110e10i	0.0163746	−	0.0730423i
$933$	−1.29703e12			−1.71168
$934$	−2.40936e11	+	1.92903e11i	−0.316603	+	0.253485i
$935$		0			0
$936$	6.89036e10	−	3.36759e10i	0.0897715	−	0.0438748i
$937$	8.41436e11			1.09160			0.545799	−	0.837916i	$-0.316226\pi$
$937$	8.41436e11			1.09160			0.545799	+	0.837916i	$0.316226\pi$
$938$	−2.13423e11	−	2.66565e11i	−0.275695	−	0.344343i
$939$			6.30660e11i			0.811209i
$940$		0			0
$941$	−4.52935e11			−0.577666			−0.288833	−	0.957379i	$-0.593267\pi$
$941$	−4.52935e11			−0.577666			−0.288833	+	0.957379i	$0.593267\pi$
$942$	−3.38606e11	+	2.71102e11i	−0.430022	+	0.344293i
$943$		−	5.09262e11i		−	0.644013i
$944$	1.04231e11	−	2.20789e11i	0.131253	−	0.278029i
$945$		0			0
$946$	1.09583e12	+	1.36869e12i	1.36829	+	1.70900i
$947$		−	1.00309e12i		−	1.24721i	−0.781739	−	0.623605i	$-0.785667\pi$
$947$		−	1.00309e12i		−	1.24721i	0.781739	−	0.623605i	$-0.214333\pi$
$948$	−2.00953e11	+	8.96394e11i	−0.248806	+	1.10985i
$949$	3.13192e10			0.0386141
$950$		0			0
$951$		−	1.65769e12i		−	2.02666i
$952$	1.83892e11	+	3.76258e11i	0.223880	+	0.458077i
$953$	1.39040e12			1.68565			0.842826	−	0.538186i	$-0.180890\pi$
$953$	1.39040e12			1.68565			0.842826	+	0.538186i	$0.180890\pi$
$954$	2.82154e10	+	3.52411e10i	0.0340638	+	0.0425457i
$955$		0			0
$956$	−1.01042e12	−	2.26516e11i	−1.20968	−	0.271186i
$957$	2.36831e11			0.282352
$958$	−3.04614e11	+	2.43887e11i	−0.361650	+	0.289551i
$959$		−	3.10523e11i		−	0.367130i
$960$		0			0
$961$	8.48274e11			0.994587
$962$	1.89920e11	+	2.37210e11i	0.221754	+	0.276970i
$963$		−	3.43421e11i		−	0.399321i
$964$	−3.46071e11	+	1.54372e12i	−0.400734	+	1.78756i
$965$		0			0
$966$	−4.14122e11	+	3.31563e11i	−0.475575	+	0.380765i
$967$		−	9.01843e11i		−	1.03140i	−0.856771	−	0.515698i	$-0.827533\pi$
$967$		−	9.01843e11i		−	1.03140i	0.856771	−	0.515698i	$-0.172467\pi$
$968$	4.68624e11	−	2.29035e11i	0.533732	−	0.260856i
$969$	1.42297e11			0.161399
$970$		0			0
$971$		−	1.28411e12i		−	1.44452i	−0.691621	−	0.722261i	$-0.743103\pi$
$971$		−	1.28411e12i		−	1.44452i	0.691621	−	0.722261i	$-0.256897\pi$
$972$	8.28664e11	+	1.85769e11i	0.928354	+	0.208118i
$973$	−4.12712e11			−0.460464
$974$	1.16257e12	−	9.30801e11i	1.29176	−	1.03424i
$975$		0			0
$976$	8.73912e11	+	4.12560e11i	0.963093	+	0.454661i
$977$	−1.20120e12			−1.31837			−0.659183	−	0.751983i	$-0.729098\pi$
$977$	−1.20120e12			−1.31837			−0.659183	+	0.751983i	$0.729098\pi$
$978$	−5.78046e11	−	7.21979e11i	−0.631840	−	0.789167i
$979$		−	1.54026e12i		−	1.67674i
$980$		0			0
$981$	2.02202e11			0.218328
$982$	−2.65850e10	+	2.12850e10i	−0.0285884	+	0.0228891i
$983$			3.77388e11i			0.404179i	0.979367	+	0.202090i	$0.0647733\pi$
$983$			3.77388e11i			0.404179i	−0.979367	+	0.202090i	$0.935227\pi$
$984$	−3.85820e11	−	7.89420e11i	−0.411533	−	0.842031i
$985$		0			0
$986$	9.37175e10	+	1.17053e11i	0.0991546	+	0.123844i
$987$		−	1.06597e12i		−	1.12325i
$988$	−2.66236e10	−	5.96846e9i	−0.0279408	−	0.00626375i
$989$	−1.40622e12			−1.46983
$990$		0			0
$991$			3.35563e11i			0.347920i	0.984753	+	0.173960i	$0.0556563\pi$
$991$			3.35563e11i			0.347920i	−0.984753	+	0.173960i	$0.944344\pi$
$992$	6.93033e10	−	1.65244e10i	0.0715661	−	0.0170639i
$993$	5.48200e11			0.563822
$994$	−1.67312e10	−	2.08972e10i	−0.0171388	−	0.0214064i
$995$		0			0
$996$	−2.90745e11	+	1.29693e12i	−0.295444	+	1.31789i
$997$	1.03163e12			1.04410			0.522050	−	0.852915i	$-0.325167\pi$
$997$	1.03163e12			1.04410			0.522050	+	0.852915i	$0.325167\pi$
$998$	1.30022e11	−	1.04101e11i	0.131067	−	0.104938i
$999$			1.08865e12i			1.09302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.b.c.51.2		2
4.3	odd	2	inner	100.9.b.c.51.1		2
5.2	odd	4		100.9.d.b.99.2		4
5.3	odd	4		100.9.d.b.99.3		4
5.4	even	2		4.9.b.b.3.1	✓	2
15.14	odd	2		36.9.d.b.19.2		2
20.3	even	4		100.9.d.b.99.1		4
20.7	even	4		100.9.d.b.99.4		4
20.19	odd	2		4.9.b.b.3.2	yes	2
40.19	odd	2		64.9.c.b.63.1		2
40.29	even	2		64.9.c.b.63.2		2
60.59	even	2		36.9.d.b.19.1		2
80.19	odd	4		256.9.d.e.127.1		4
80.29	even	4		256.9.d.e.127.3		4
80.59	odd	4		256.9.d.e.127.4		4
80.69	even	4		256.9.d.e.127.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.9.b.b.3.1	✓	2	5.4	even	2
4.9.b.b.3.2	yes	2	20.19	odd	2
36.9.d.b.19.1		2	60.59	even	2
36.9.d.b.19.2		2	15.14	odd	2
64.9.c.b.63.1		2	40.19	odd	2
64.9.c.b.63.2		2	40.29	even	2
100.9.b.c.51.1		2	4.3	odd	2	inner
100.9.b.c.51.2		2	1.1	even	1	trivial
100.9.d.b.99.1		4	20.3	even	4
100.9.d.b.99.2		4	5.2	odd	4
100.9.d.b.99.3		4	5.3	odd	4
100.9.d.b.99.4		4	20.7	even	4
256.9.d.e.127.1		4	80.19	odd	4
256.9.d.e.127.2		4	80.69	even	4
256.9.d.e.127.3		4	80.29	even	4
256.9.d.e.127.4		4	80.59	odd	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(10.0000 + 12.4900i) q^{2} +99.9200i q^{3} +(-56.0000 + 249.800i) q^{4} +(-1248.00 + 999.200i) q^{6} +1398.88i q^{7} +(-3680.00 + 1798.56i) q^{8} -3423.00 q^{9} +18485.2i q^{11} +(-24960.0 - 5595.52i) q^{12} +5470.00 q^{13} +(-17472.0 + 13988.8i) q^{14} +(-59264.0 - 27977.6i) q^{16} -73090.0 q^{17} +(-34230.0 - 42753.3i) q^{18} +19484.4i q^{19} -139776. q^{21} +(-230880. + 184852. i) q^{22} -237210. i q^{23} +(-179712. - 367705. i) q^{24} +(54700.0 + 68320.3i) q^{26} +313549. i q^{27} +(-349440. - 78337.3i) q^{28} -128222. q^{29} +67945.6i q^{31} +(-243200. - 1.01998e6i) q^{32} -1.84704e6 q^{33} +(-730900. - 912894. i) q^{34} +(191688. - 855065. i) q^{36} +3.47203e6 q^{37} +(-243360. + 194844. i) q^{38} +546562. i q^{39} +2.14688e6 q^{41} +(-1.39776e6 - 1.74580e6i) q^{42} -5.92815e6i q^{43} +(-4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 - 2.37210e6i) q^{46} +7.62629e6i q^{47} +(2.79552e6 - 5.92166e6i) q^{48} +3.80794e6 q^{49} -7.30315e6i q^{51} +(-306320. + 1.36641e6i) q^{52} -824290. q^{53} +(-3.91622e6 + 3.13549e6i) q^{54} +(-2.51597e6 - 5.14788e6i) q^{56} -1.94688e6 q^{57} +(-1.28222e6 - 1.60149e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. + 679456. i) q^{62} -4.78836e6i q^{63} +(1.03076e7 - 1.32374e7i) q^{64} +(-1.84704e7 - 2.30695e7i) q^{66} +1.52567e7i q^{67} +(4.09304e6 - 1.82579e7i) q^{68} +2.37020e7 q^{69} +1.19604e6i q^{71} +(1.25966e7 - 6.15647e6i) q^{72} +5.72563e6 q^{73} +(3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 - 1.09113e6i) q^{76} -2.58586e7 q^{77} +(-6.82656e6 + 5.46562e6i) q^{78} -3.59132e7i q^{79} -5.37881e7 q^{81} +(2.14688e7 + 2.68145e7i) q^{82} -5.19603e7i q^{83} +(7.82746e6 - 3.49160e7i) q^{84} +(7.40426e7 - 5.92815e7i) q^{86} -1.28119e7i q^{87} +(-3.32467e7 - 6.80255e7i) q^{88} -8.33242e7 q^{89} +7.65187e6i q^{91} +(5.92550e7 + 1.32838e7i) q^{92} -6.78912e6 q^{93} +(-9.52524e7 + 7.62629e7i) q^{94} +(1.01917e8 - 2.43005e7i) q^{96} -1.20619e8 q^{97} +(3.80794e7 + 4.75611e7i) q^{98} -6.32748e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 20 q^{2} - 112 q^{4} - 2496 q^{6} - 7360 q^{8} - 6846 q^{9} - 49920 q^{12} + 10940 q^{13} - 34944 q^{14} - 118528 q^{16} - 146180 q^{17} - 68460 q^{18} - 279552 q^{21} - 461760 q^{22} - 359424 q^{24}+ \cdots + 76158740 q^{98}+O(q^{100}) \) 2 * q + 20 * q^2 - 112 * q^4 - 2496 * q^6 - 7360 * q^8 - 6846 * q^9 - 49920 * q^12 + 10940 * q^13 - 34944 * q^14 - 118528 * q^16 - 146180 * q^17 - 68460 * q^18 - 279552 * q^21 - 461760 * q^22 - 359424 * q^24 + 109400 * q^26 - 698880 * q^28 - 256444 * q^29 - 486400 * q^32 - 3694080 * q^33 - 1461800 * q^34 + 383376 * q^36 + 6944060 * q^37 - 486720 * q^38 + 4293764 * q^41 - 2795520 * q^42 - 9235200 * q^44 + 5925504 * q^46 + 5591040 * q^48 + 7615874 * q^49 - 612640 * q^52 - 1648580 * q^53 - 7832448 * q^54 - 5031936 * q^56 - 3893760 * q^57 - 2564440 * q^58 - 29492156 * q^61 - 1697280 * q^62 + 20615168 * q^64 - 36940800 * q^66 + 8186080 * q^68 + 47404032 * q^69 + 25193280 * q^72 + 11451260 * q^73 + 69440600 * q^74 - 9734400 * q^76 - 51717120 * q^77 - 13653120 * q^78 - 107576190 * q^81 + 42937640 * q^82 + 15654912 * q^84 + 148085184 * q^86 - 66493440 * q^88 - 166648444 * q^89 + 118510080 * q^92 - 13578240 * q^93 - 190504704 * q^94 + 203833344 * q^96 - 241238020 * q^97 + 76158740 * q^98

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