LMFDB - Embedded newform 100.9.d.c.99.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(99,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.99"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,104] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.24
Character	$\chi$	$=$	100.99
Dual form			100.9.d.c.99.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(11.0540 + 11.5676i) q^{2} +27.2434 q^{3} +(-11.6196 + 255.736i) q^{4} +(301.148 + 315.141i) q^{6} +3325.58 q^{7} +(-3086.70 + 2692.49i) q^{8} -5818.80 q^{9} -6361.21i q^{11} +(-316.557 + 6967.12i) q^{12} +30777.4i q^{13} +(36760.8 + 38469.0i) q^{14} +(-65266.0 - 5943.09i) q^{16} +122375. i q^{17} +(-64320.8 - 67309.6i) q^{18} -7554.43i q^{19} +90600.1 q^{21} +(73584.1 - 70316.6i) q^{22} +406311. q^{23} +(-84092.2 + 73352.6i) q^{24} +(-356021. + 340213. i) q^{26} -337268. q^{27} +(-38641.8 + 850471. i) q^{28} -828838. q^{29} +1.39549e6i q^{31} +(-652701. - 820666. i) q^{32} -173301. i q^{33} +(-1.41559e6 + 1.35273e6i) q^{34} +(67611.9 - 1.48808e6i) q^{36} -386059. i q^{37} +(87386.8 - 83506.4i) q^{38} +838482. i q^{39} -972335. q^{41} +(1.00149e6 + 1.04803e6i) q^{42} -4.61450e6 q^{43} +(1.62679e6 + 73914.5i) q^{44} +(4.49135e6 + 4.70005e6i) q^{46} +1.87219e6 q^{47} +(-1.77807e6 - 161910. i) q^{48} +5.29467e6 q^{49} +3.33392e6i q^{51} +(-7.87090e6 - 357620. i) q^{52} +8.01944e6i q^{53} +(-3.72815e6 - 3.90139e6i) q^{54} +(-1.02651e7 + 8.95408e6i) q^{56} -205808. i q^{57} +(-9.16195e6 - 9.58768e6i) q^{58} -6.18263e6i q^{59} +9.79320e6 q^{61} +(-1.61425e7 + 1.54257e7i) q^{62} -1.93509e7 q^{63} +(2.27822e6 - 1.66218e7i) q^{64} +(2.00468e6 - 1.91566e6i) q^{66} -1.19411e6 q^{67} +(-3.12958e7 - 1.42195e6i) q^{68} +1.10693e7 q^{69} +3.62332e7i q^{71} +(1.79609e7 - 1.56670e7i) q^{72} -3.35548e7i q^{73} +(4.46578e6 - 4.26748e6i) q^{74} +(1.93194e6 + 87779.2i) q^{76} -2.11547e7i q^{77} +(-9.69923e6 + 9.26855e6i) q^{78} +1.22874e6i q^{79} +2.89888e7 q^{81} +(-1.07482e7 - 1.12476e7i) q^{82} -6.96923e7 q^{83} +(-1.05273e6 + 2.31697e7i) q^{84} +(-5.10086e7 - 5.33788e7i) q^{86} -2.25804e7 q^{87} +(1.71275e7 + 1.96352e7i) q^{88} -5.58347e7 q^{89} +1.02353e8i q^{91} +(-4.72116e6 + 1.03908e8i) q^{92} +3.80180e7i q^{93} +(2.06951e7 + 2.16567e7i) q^{94} +(-1.77818e7 - 2.23578e7i) q^{96} -5.97582e7i q^{97} +(5.85271e7 + 6.12467e7i) q^{98} +3.70146e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) $ 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

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 $

$2$	11.0540	+	11.5676i	0.690873	+	0.722976i
$2$	11.0540	+	11.5676i	0.690873	+	0.722976i
$3$	27.2434			0.336338			0.168169	−	0.985758i	$-0.446215\pi$
$3$	27.2434			0.336338			0.168169	+	0.985758i	$0.446215\pi$
$4$	−11.6196	+	255.736i	−0.0453889	+	0.998969i
$5$		0			0
$5$		0			0
$6$	301.148	+	315.141i	0.232367	+	0.243165i
$7$	3325.58			1.38508			0.692540	−	0.721379i	$-0.256492\pi$
$7$	3325.58			1.38508			0.692540	+	0.721379i	$0.256492\pi$
$8$	−3086.70	+	2692.49i	−0.753589	+	0.657346i
$9$	−5818.80			−0.886877
$10$		0			0
$11$		−	6361.21i		−	0.434479i	−0.976118	−	0.217240i	$-0.930295\pi$
$11$		−	6361.21i		−	0.434479i	0.976118	−	0.217240i	$-0.0697053\pi$
$12$	−316.557	+	6967.12i	−0.0152660	+	0.335992i
$13$			30777.4i			1.07760i	0.842433	+	0.538801i	$0.181123\pi$
$13$			30777.4i			1.07760i	−0.842433	+	0.538801i	$0.818877\pi$
$14$	36760.8	+	38469.0i	0.956915	+	1.00138i
$15$		0			0
$16$	−65266.0	−	5943.09i	−0.995880	−	0.0906843i
$17$			122375.i			1.46520i	0.680658	+	0.732601i	$0.261694\pi$
$17$			122375.i			1.46520i	−0.680658	+	0.732601i	$0.738306\pi$
$18$	−64320.8	−	67309.6i	−0.612719	−	0.641191i
$19$		−	7554.43i		−	0.0579679i	−0.999580	−	0.0289839i	$-0.990773\pi$
$19$		−	7554.43i		−	0.0579679i	0.999580	−	0.0289839i	$-0.00922717\pi$
$20$		0			0
$21$	90600.1			0.465856
$22$	73584.1	−	70316.6i	0.314118	−	0.300170i
$23$	406311.			1.45194			0.725968	−	0.687729i	$-0.241392\pi$
$23$	406311.			1.45194			0.725968	+	0.687729i	$0.241392\pi$
$24$	−84092.2	+	73352.6i	−0.253461	+	0.221091i
$25$		0			0
$26$	−356021.	+	340213.i	−0.779081	+	0.744487i
$27$	−337268.			−0.634629
$28$	−38641.8	+	850471.i	−0.0628673	+	1.38365i
$29$	−828838.			−1.17187			−0.585933	−	0.810360i	$-0.699272\pi$
$29$	−828838.			−1.17187			−0.585933	+	0.810360i	$0.699272\pi$
$30$		0			0
$31$			1.39549e6i			1.51106i	0.655116	+	0.755528i	$0.272620\pi$
$31$			1.39549e6i			1.51106i	−0.655116	+	0.755528i	$0.727380\pi$
$32$	−652701.	−	820666.i	−0.622464	−	0.782649i
$33$		−	173301.i		−	0.146132i
$34$	−1.41559e6	+	1.35273e6i	−1.05931	+	1.01227i
$35$		0			0
$36$	67611.9	−	1.48808e6i	0.0402544	−	0.885962i
$37$		−	386059.i		−	0.205990i	−0.994682	−	0.102995i	$-0.967157\pi$
$37$		−	386059.i		−	0.205990i	0.994682	−	0.102995i	$-0.0328426\pi$
$38$	87386.8	−	83506.4i	0.0419094	−	0.0400484i
$39$			838482.i			0.362439i
$40$		0			0
$41$	−972335.			−0.344097			−0.172048	−	0.985089i	$-0.555039\pi$
$41$	−972335.			−0.344097			−0.172048	+	0.985089i	$0.555039\pi$
$42$	1.00149e6	+	1.04803e6i	0.321847	+	0.336803i
$43$	−4.61450e6			−1.34974			−0.674871	−	0.737935i	$-0.735801\pi$
$43$	−4.61450e6			−1.34974			−0.674871	+	0.737935i	$0.735801\pi$
$44$	1.62679e6	+	73914.5i	0.434032	+	0.0197205i
$45$		0			0
$46$	4.49135e6	+	4.70005e6i	1.00310	+	1.04971i
$47$	1.87219e6			0.383670			0.191835	−	0.981427i	$-0.438556\pi$
$47$	1.87219e6			0.383670			0.191835	+	0.981427i	$0.438556\pi$
$48$	−1.77807e6	−	161910.i	−0.334953	−	0.0305006i
$49$	5.29467e6			0.918447
$50$		0			0
$51$			3.33392e6i			0.492804i
$52$	−7.87090e6	−	357620.i	−1.07649	−	0.0489112i
$53$			8.01944e6i			1.01634i	0.861256	+	0.508172i	$0.169678\pi$
$53$			8.01944e6i			1.01634i	−0.861256	+	0.508172i	$0.830322\pi$
$54$	−3.72815e6	−	3.90139e6i	−0.438448	−	0.458822i
$55$		0			0
$56$	−1.02651e7	+	8.95408e6i	−1.04378	+	0.910477i
$57$		−	205808.i		−	0.0194968i
$58$	−9.16195e6	−	9.58768e6i	−0.809610	−	0.847231i
$59$		−	6.18263e6i		−	0.510229i	−0.966911	−	0.255115i	$-0.917887\pi$
$59$		−	6.18263e6i		−	0.510229i	0.966911	−	0.255115i	$-0.0821132\pi$
$60$		0			0
$61$	9.79320e6			0.707303			0.353651	−	0.935377i	$-0.384940\pi$
$61$	9.79320e6			0.707303			0.353651	+	0.935377i	$0.384940\pi$
$62$	−1.61425e7	+	1.54257e7i	−1.09246	+	1.04395i
$63$	−1.93509e7			−1.22840
$64$	2.27822e6	−	1.66218e7i	0.135793	−	0.990737i
$65$		0			0
$66$	2.00468e6	−	1.91566e6i	0.105650	−	0.100959i
$67$	−1.19411e6			−0.0592579			−0.0296290	−	0.999561i	$-0.509433\pi$
$67$	−1.19411e6			−0.0592579			−0.0296290	+	0.999561i	$0.509433\pi$
$68$	−3.12958e7	−	1.42195e6i	−1.46369	−	0.0665039i
$69$	1.10693e7			0.488342
$70$		0			0
$71$			3.62332e7i			1.42585i	0.701242	+	0.712923i	$0.252629\pi$
$71$			3.62332e7i			1.42585i	−0.701242	+	0.712923i	$0.747371\pi$
$72$	1.79609e7	−	1.56670e7i	0.668340	−	0.582985i
$73$		−	3.35548e7i		−	1.18158i	−0.806826	−	0.590790i	$-0.798816\pi$
$73$		−	3.35548e7i		−	1.18158i	0.806826	−	0.590790i	$-0.201184\pi$
$74$	4.46578e6	−	4.26748e6i	0.148926	−	0.142313i
$75$		0			0
$76$	1.93194e6	+	87779.2i	0.0579081	+	0.00263110i
$77$		−	2.11547e7i		−	0.601789i
$78$	−9.69923e6	+	9.26855e6i	−0.262035	+	0.250399i
$79$			1.22874e6i			0.0315466i	0.999876	+	0.0157733i	$0.00502101\pi$
$79$			1.22874e6i			0.0315466i	−0.999876	+	0.0157733i	$0.994979\pi$
$80$		0			0
$81$	2.89888e7			0.673426
$82$	−1.07482e7	−	1.12476e7i	−0.237727	−	0.248774i
$83$	−6.96923e7			−1.46849			−0.734247	−	0.678882i	$-0.762465\pi$
$83$	−6.96923e7			−1.46849			−0.734247	+	0.678882i	$0.762465\pi$
$84$	−1.05273e6	+	2.31697e7i	−0.0211447	+	0.465376i
$85$		0			0
$86$	−5.10086e7	−	5.33788e7i	−0.932501	−	0.975832i
$87$	−2.25804e7			−0.394143
$88$	1.71275e7	+	1.96352e7i	0.285603	+	0.327419i
$89$	−5.58347e7			−0.889907			−0.444953	−	0.895554i	$-0.646780\pi$
$89$	−5.58347e7			−0.889907			−0.444953	+	0.895554i	$0.646780\pi$
$90$		0			0
$91$			1.02353e8i			1.49257i
$92$	−4.72116e6	+	1.03908e8i	−0.0659018	+	1.45044i
$93$			3.80180e7i			0.508226i
$94$	2.06951e7	+	2.16567e7i	0.265067	+	0.277384i
$95$		0			0
$96$	−1.77818e7	−	2.23578e7i	−0.209358	−	0.263235i
$97$		−	5.97582e7i		−	0.675010i	−0.941324	−	0.337505i	$-0.890417\pi$
$97$		−	5.97582e7i		−	0.675010i	0.941324	−	0.337505i	$-0.109583\pi$
$98$	5.85271e7	+	6.12467e7i	0.634531	+	0.664016i
$99$			3.70146e7i			0.385329i
$100$		0			0
$101$	9.62751e7			0.925185			0.462593	−	0.886571i	$-0.346919\pi$
$101$	9.62751e7			0.925185			0.462593	+	0.886571i	$0.346919\pi$
$102$	−3.85655e7	+	3.68530e7i	−0.356285	+	0.340465i
$103$	1.96312e8			1.74421			0.872104	−	0.489320i	$-0.162755\pi$
$103$	1.96312e8			1.74421			0.872104	+	0.489320i	$0.162755\pi$
$104$	−8.28678e7	−	9.50006e7i	−0.708358	−	0.812070i
$105$		0			0
$106$	−9.27658e7	+	8.86466e7i	−0.734792	+	0.702164i
$107$	1.64435e8			1.25447			0.627233	−	0.778832i	$-0.284187\pi$
$107$	1.64435e8			1.25447			0.627233	+	0.778832i	$0.284187\pi$
$108$	3.91891e6	−	8.62516e7i	0.0288051	−	0.633975i
$109$	1.81680e8			1.28707			0.643534	−	0.765417i	$-0.277467\pi$
$109$	1.81680e8			1.28707			0.643534	+	0.765417i	$0.277467\pi$
$110$		0			0
$111$		−	1.05176e7i		−	0.0692824i
$112$	−2.17047e8	−	1.97642e7i	−1.37937	−	0.125605i
$113$			1.30629e8i			0.801172i	0.916259	+	0.400586i	$0.131193\pi$
$113$			1.30629e8i			0.801172i	−0.916259	+	0.400586i	$0.868807\pi$
$114$	2.38071e6	−	2.27500e6i	0.0140957	−	0.0134698i
$115$		0			0
$116$	9.63074e6	−	2.11964e8i	0.0531897	−	1.17066i
$117$		−	1.79087e8i		−	0.955700i
$118$	7.15183e7	−	6.83426e7i	0.368883	−	0.352504i
$119$			4.06968e8i			2.02942i
$120$		0			0
$121$	1.73894e8			0.811228
$122$	1.08254e8	+	1.13284e8i	0.488656	+	0.511363i
$123$	−2.64897e7			−0.115733
$124$	−3.56878e8	−	1.62150e7i	−1.50950	−	0.0685852i
$125$		0			0
$126$	−2.13904e8	−	2.23843e8i	−0.848665	−	0.888100i
$127$	4.45982e8			1.71436			0.857181	−	0.515015i	$-0.172214\pi$
$127$	4.45982e8			1.71436			0.857181	+	0.515015i	$0.172214\pi$
$128$	2.17458e8	−	1.57383e8i	0.810095	−	0.586299i
$129$	−1.25715e8			−0.453970
$130$		0			0
$131$		−	1.31555e8i		−	0.446707i	−0.974738	−	0.223353i	$-0.928300\pi$
$131$		−	1.31555e8i		−	0.446707i	0.974738	−	0.223353i	$-0.0717004\pi$
$132$	4.43194e7	+	2.01368e6i	0.145981	+	0.00663278i
$133$		−	2.51228e7i		−	0.0802902i
$134$	−1.31997e7	−	1.38130e7i	−0.0409397	−	0.0428421i
$135$		0			0
$136$	−3.29494e8	−	3.77735e8i	−0.963145	−	1.10416i
$137$		−	3.26396e8i		−	0.926536i	−0.886218	−	0.463268i	$-0.846677\pi$
$137$		−	3.26396e8i		−	0.926536i	0.886218	−	0.463268i	$-0.153323\pi$
$138$	1.22360e8	+	1.28045e8i	0.337382	+	0.353059i
$139$		−	6.48927e8i		−	1.73835i	−0.494506	−	0.869174i	$-0.664651\pi$
$139$		−	6.48927e8i		−	1.73835i	0.494506	−	0.869174i	$-0.335349\pi$
$140$		0			0
$141$	5.10048e7			0.129043
$142$	−4.19131e8	+	4.00520e8i	−1.03085	+	0.985079i
$143$	1.95782e8			0.468196
$144$	3.79769e8	+	3.45816e7i	0.883222	+	0.0804258i
$145$		0			0
$146$	3.88149e8	−	3.70913e8i	0.854253	−	0.816321i
$147$	1.44245e8			0.308909
$148$	9.87292e7	+	4.48584e6i	0.205778	+	0.00934968i
$149$	7.30660e8			1.48242			0.741208	−	0.671276i	$-0.234253\pi$
$149$	7.30660e8			1.48242			0.741208	+	0.671276i	$0.234253\pi$
$150$		0			0
$151$			7.74114e8i			1.48901i	0.667618	+	0.744504i	$0.267314\pi$
$151$			7.74114e8i			1.48901i	−0.667618	+	0.744504i	$0.732686\pi$
$152$	2.03402e7	+	2.33183e7i	0.0381049	+	0.0436840i
$153$		−	7.12076e8i		−	1.29945i
$154$	2.44710e8	−	2.33843e8i	0.435079	−	0.415760i
$155$		0			0
$156$	−2.14430e8	−	9.74279e6i	−0.362066	−	0.0164507i
$157$			3.17523e8i			0.522609i	0.965256	+	0.261304i	$0.0841526\pi$
$157$			3.17523e8i			0.522609i	−0.965256	+	0.261304i	$0.915847\pi$
$158$	−1.42136e7	+	1.35825e7i	−0.0228075	+	0.0217947i
$159$			2.18477e8i			0.341835i
$160$		0			0
$161$	1.35122e9			2.01105
$162$	3.20441e8	+	3.35331e8i	0.465252	+	0.486871i
$163$	2.02004e7			0.0286161			0.0143081	−	0.999898i	$-0.495445\pi$
$163$	2.02004e7			0.0286161			0.0143081	+	0.999898i	$0.495445\pi$
$164$	1.12981e7	−	2.48661e8i	0.0156182	−	0.343742i
$165$		0			0
$166$	−7.70376e8	−	8.06174e8i	−1.01454	−	1.06169i
$167$	−5.65743e7			−0.0727366			−0.0363683	−	0.999338i	$-0.511579\pi$
$167$	−5.65743e7			−0.0727366			−0.0363683	+	0.999338i	$0.511579\pi$
$168$	−2.79655e8	+	2.43940e8i	−0.351064	+	0.306228i
$169$	−1.31518e8			−0.161228
$170$		0			0
$171$			4.39577e7i			0.0514103i
$172$	5.36185e7	−	1.18009e9i	0.0612634	−	1.34835i
$173$			1.09785e9i			1.22563i	0.790228	+	0.612813i	$0.209962\pi$
$173$			1.09785e9i			1.22563i	−0.790228	+	0.612813i	$0.790038\pi$
$174$	−2.49603e8	−	2.61201e8i	−0.272303	−	0.284956i
$175$		0			0
$176$	−3.78052e7	+	4.15171e8i	−0.0394004	+	0.432689i
$177$		−	1.68436e8i		−	0.171610i
$178$	−6.17196e8	−	6.45875e8i	−0.614813	−	0.643381i
$179$			6.44793e8i			0.628070i	0.949411	+	0.314035i	$0.101681\pi$
$179$			6.44793e8i			0.628070i	−0.949411	+	0.314035i	$0.898319\pi$
$180$		0			0
$181$	−6.79018e8			−0.632655			−0.316328	−	0.948650i	$-0.602450\pi$
$181$	−6.79018e8			−0.632655			−0.316328	+	0.948650i	$0.602450\pi$
$182$	−1.18398e9	+	1.13140e9i	−1.07909	+	1.03117i
$183$	2.66800e8			0.237893
$184$	−1.25416e9	+	1.09399e9i	−1.09416	+	0.954424i
$185$		0			0
$186$	−4.39777e8	+	4.20250e8i	−0.367436	+	0.351120i
$187$	7.78454e8			0.636600
$188$	−2.17540e7	+	4.78786e8i	−0.0174144	+	0.383275i
$189$	−1.12161e9			−0.879012
$190$		0			0
$191$		−	1.53738e8i		−	0.115518i	−0.998331	−	0.0577588i	$-0.981605\pi$
$191$		−	1.53738e8i		−	0.115518i	0.998331	−	0.0577588i	$-0.0183954\pi$
$192$	6.20666e7	−	4.52835e8i	0.0456723	−	0.333223i
$193$		−	9.67761e7i		−	0.0697491i	−0.999392	−	0.0348746i	$-0.988897\pi$
$193$		−	9.67761e7i		−	0.0697491i	0.999392	−	0.0348746i	$-0.0111032\pi$
$194$	6.91259e8	−	6.60565e8i	0.488016	−	0.466346i
$195$		0			0
$196$	−6.15217e7	+	1.35404e9i	−0.0416873	+	0.917501i
$197$		−	2.84766e9i		−	1.89070i	−0.326051	−	0.945352i	$-0.605718\pi$
$197$		−	2.84766e9i		−	1.89070i	0.326051	−	0.945352i	$-0.394282\pi$
$198$	−4.28171e8	+	4.09158e8i	−0.278584	+	0.266214i
$199$			8.71254e8i			0.555562i	0.960644	+	0.277781i	$0.0895990\pi$
$199$			8.71254e8i			0.555562i	−0.960644	+	0.277781i	$0.910401\pi$
$200$		0			0
$201$	−3.25317e7			−0.0199307
$202$	1.06422e9	+	1.11367e9i	0.639185	+	0.668887i
$203$	−2.75637e9			−1.62313
$204$	−8.52603e8	−	3.87387e7i	−0.492296	−	0.0223678i
$205$		0			0
$206$	2.17003e9	+	2.27087e9i	1.20503	+	1.26102i
$207$	−2.36424e9			−1.28769
$208$	1.82913e8	−	2.00872e9i	0.0977216	−	1.07316i
$209$	−4.80553e7			−0.0251858
$210$		0			0
$211$			2.22378e9i			1.12192i	0.827843	+	0.560960i	$0.189568\pi$
$211$			2.22378e9i			1.12192i	−0.827843	+	0.560960i	$0.810432\pi$
$212$	−2.05086e9	−	9.31824e7i	−1.01530	−	0.0461307i
$213$			9.87114e8i			0.479567i
$214$	1.81766e9	+	1.90212e9i	0.866676	+	0.906949i
$215$		0			0
$216$	1.04104e9	−	9.08090e8i	0.478249	−	0.417171i
$217$			4.64082e9i			2.09293i
$218$	2.00829e9	+	2.10161e9i	0.889201	+	0.930520i
$219$		−	9.14146e8i		−	0.397410i
$220$		0			0
$221$	−3.76639e9			−1.57891
$222$	1.21663e8	−	1.16261e8i	0.0500895	−	0.0478654i
$223$	−1.76089e9			−0.712054			−0.356027	−	0.934476i	$-0.615869\pi$
$223$	−1.76089e9			−0.712054			−0.356027	+	0.934476i	$0.615869\pi$
$224$	−2.17061e9	−	2.72919e9i	−0.862162	−	1.08403i
$225$		0			0
$226$	−1.51107e9	+	1.44397e9i	−0.579228	+	0.553508i
$227$	−1.85447e9			−0.698418			−0.349209	−	0.937045i	$-0.613550\pi$
$227$	−1.85447e9			−0.698418			−0.349209	+	0.937045i	$0.613550\pi$
$228$	5.26327e7	+	2.39140e6i	0.0194767	+	0.000884940i
$229$	1.13087e9			0.411218			0.205609	−	0.978634i	$-0.434083\pi$
$229$	1.13087e9			0.411218			0.205609	+	0.978634i	$0.434083\pi$
$230$		0			0
$231$		−	5.76326e8i		−	0.202405i
$232$	2.55837e9	−	2.23164e9i	0.883105	−	0.770321i
$233$		−	2.24935e9i		−	0.763191i	−0.924329	−	0.381596i	$-0.875375\pi$
$233$		−	2.24935e9i		−	0.763191i	0.924329	−	0.381596i	$-0.124625\pi$
$234$	2.07162e9	−	1.97963e9i	0.690949	−	0.660268i
$235$		0			0
$236$	1.58112e9	+	7.18395e7i	0.509703	+	0.0231587i
$237$			3.34752e7i			0.0106103i
$238$	−4.70765e9	+	4.49861e9i	−1.46722	+	1.40207i
$239$		−	2.77234e9i		−	0.849679i	−0.905269	−	0.424840i	$-0.860331\pi$
$239$		−	2.77234e9i		−	0.849679i	0.905269	−	0.424840i	$-0.139669\pi$
$240$		0			0
$241$	−1.60515e8			−0.0475826			−0.0237913	−	0.999717i	$-0.507574\pi$
$241$	−1.60515e8			−0.0475826			−0.0237913	+	0.999717i	$0.507574\pi$
$242$	1.92222e9	+	2.01154e9i	0.560455	+	0.586498i
$243$	3.00257e9			0.861128
$244$	−1.13793e8	+	2.50448e9i	−0.0321037	+	0.706574i
$245$		0			0
$246$	−2.92817e8	−	3.06423e8i	−0.0799568	−	0.0836721i
$247$	2.32506e8			0.0624663
$248$	−3.75735e9	−	4.30747e9i	−0.993287	−	1.13872i
$249$	−1.89866e9			−0.493911
$250$		0			0
$251$		−	5.77680e9i		−	1.45543i	−0.685877	−	0.727717i	$-0.740581\pi$
$251$		−	5.77680e9i		−	1.45543i	0.685877	−	0.727717i	$-0.259419\pi$
$252$	2.24849e8	−	4.94871e9i	0.0557555	−	1.22713i
$253$		−	2.58463e9i		−	0.630836i
$254$	4.92987e9	+	5.15895e9i	1.18441	+	1.23944i
$255$		0			0
$256$	4.22433e9	+	7.75762e8i	0.983553	+	0.180621i
$257$			4.57743e9i			1.04928i	0.851326	+	0.524638i	$0.175799\pi$
$257$			4.57743e9i			1.04928i	−0.851326	+	0.524638i	$0.824201\pi$
$258$	−1.38965e9	−	1.45422e9i	−0.313636	−	0.328210i
$259$		−	1.28387e9i		−	0.285313i
$260$		0			0
$261$	4.82284e9			1.03930
$262$	1.52178e9	−	1.45421e9i	0.322958	−	0.308618i
$263$	4.85941e8			0.101569			0.0507844	−	0.998710i	$-0.483828\pi$
$263$	4.85941e8			0.101569			0.0507844	+	0.998710i	$0.483828\pi$
$264$	4.66611e8	+	5.34929e8i	0.0960593	+	0.110124i
$265$		0			0
$266$	2.90612e8	−	2.77707e8i	0.0580479	−	0.0554703i
$267$	−1.52113e9			−0.299310
$268$	1.38751e7	−	3.05378e8i	0.00268965	−	0.0591968i
$269$	1.48731e9			0.284049			0.142024	−	0.989863i	$-0.454639\pi$
$269$	1.48731e9			0.284049			0.142024	+	0.989863i	$0.454639\pi$
$270$		0			0
$271$		−	6.79398e9i		−	1.25964i	−0.776740	−	0.629821i	$-0.783128\pi$
$271$		−	6.79398e9i		−	1.25964i	0.776740	−	0.629821i	$-0.216872\pi$
$272$	7.27286e8	−	7.98693e9i	0.132871	−	1.45917i
$273$			2.78844e9i			0.502007i
$274$	3.77562e9	−	3.60797e9i	0.669863	−	0.640118i
$275$		0			0
$276$	−1.28620e8	+	2.83082e9i	−0.0221653	+	0.487838i
$277$			1.54730e9i			0.262818i	0.991328	+	0.131409i	$0.0419501\pi$
$277$			1.54730e9i			0.262818i	−0.991328	+	0.131409i	$0.958050\pi$
$278$	7.50654e9	−	7.17322e9i	1.25678	−	1.20098i
$279$		−	8.12009e9i		−	1.34012i
$280$		0			0
$281$	−9.33090e9			−1.49657			−0.748287	−	0.663375i	$-0.769123\pi$
$281$	−9.33090e9			−1.49657			−0.748287	+	0.663375i	$0.769123\pi$
$282$	5.63805e8	+	5.90004e8i	0.0891523	+	0.0932950i
$283$	7.43824e9			1.15964			0.579822	−	0.814743i	$-0.303122\pi$
$283$	7.43824e9			1.15964			0.579822	+	0.814743i	$0.303122\pi$
$284$	−9.26613e9	−	4.21013e8i	−1.42438	−	0.0647176i
$285$		0			0
$286$	2.16416e9	+	2.26473e9i	0.323464	+	0.338495i
$287$	−3.23358e9			−0.476602
$288$	3.79793e9	+	4.77529e9i	0.552049	+	0.694113i
$289$	−7.99992e9			−1.14682
$290$		0			0
$291$		−	1.62802e9i		−	0.227032i
$292$	8.58117e9	+	3.89892e8i	1.18036	+	0.0536306i
$293$			1.59214e9i			0.216028i	0.994149	+	0.108014i	$0.0344492\pi$
$293$			1.59214e9i			0.216028i	−0.994149	+	0.108014i	$0.965551\pi$
$294$	1.59448e9	+	1.66857e9i	0.213417	+	0.223334i
$295$		0			0
$296$	1.03946e9	+	1.19165e9i	0.135407	+	0.155232i
$297$			2.14543e9i			0.275733i
$298$	8.07669e9	+	8.45199e9i	1.02416	+	1.07175i
$299$			1.25052e10i			1.56461i
$300$		0			0
$301$	−1.53459e10			−1.86950
$302$	−8.95465e9	+	8.55703e9i	−1.07652	+	1.02872i
$303$	2.62286e9			0.311175
$304$	−4.48966e7	+	4.93047e8i	−0.00525678	+	0.0577290i
$305$		0			0
$306$	8.23702e9	−	7.87127e9i	0.939474	−	0.897757i
$307$	3.36362e9			0.378663			0.189332	−	0.981913i	$-0.439368\pi$
$307$	3.36362e9			0.378663			0.189332	+	0.981913i	$0.439368\pi$
$308$	5.41002e9	+	2.45808e8i	0.601169	+	0.0273145i
$309$	5.34821e9			0.586644
$310$		0			0
$311$		−	1.23254e10i		−	1.31752i	−0.752352	−	0.658761i	$-0.771081\pi$
$311$		−	1.23254e10i		−	1.31752i	0.752352	−	0.658761i	$-0.228919\pi$
$312$	−2.25760e9	−	2.58814e9i	−0.238248	−	0.273130i
$313$		−	2.77987e9i		−	0.289633i	−0.989459	−	0.144816i	$-0.953741\pi$
$313$		−	2.77987e9i		−	0.289633i	0.989459	−	0.144816i	$-0.0462591\pi$
$314$	−3.67299e9	+	3.50989e9i	−0.377834	+	0.361056i
$315$		0			0
$316$	−3.14234e8	−	1.42775e7i	−0.0315141	−	0.00143187i
$317$		−	5.40177e8i		−	0.0534933i	−0.999642	−	0.0267466i	$-0.991485\pi$
$317$		−	5.40177e8i		−	0.0534933i	0.999642	−	0.0267466i	$-0.00851474\pi$
$318$	−2.52726e9	+	2.41504e9i	−0.247139	+	0.236165i
$319$			5.27241e9i			0.509151i
$320$		0			0
$321$	4.47977e9			0.421925
$322$	1.49363e10	+	1.56304e10i	1.38938	+	1.45394i
$323$	9.24475e8			0.0849347
$324$	−3.36837e8	+	7.41348e9i	−0.0305661	+	0.672732i
$325$		0			0
$326$	2.23295e8	+	2.33671e8i	0.0197701	+	0.0206888i
$327$	4.94959e9			0.432891
$328$	3.00131e9	−	2.61800e9i	0.259307	−	0.226191i
$329$	6.22610e9			0.531414
$330$		0			0
$331$			1.21115e10i			1.00899i	0.863414	+	0.504495i	$0.168321\pi$
$331$			1.21115e10i			1.00899i	−0.863414	+	0.504495i	$0.831679\pi$
$332$	8.09794e8	−	1.78228e10i	0.0666534	−	1.46698i
$333$			2.24640e9i			0.182688i
$334$	−6.25370e8	−	6.54429e8i	−0.0502518	−	0.0525868i
$335$		0			0
$336$	−5.91310e9	−	5.38444e8i	−0.463936	−	0.0422458i
$337$		−	9.48812e9i		−	0.735632i	−0.929899	−	0.367816i	$-0.880106\pi$
$337$		−	9.48812e9i		−	0.735632i	0.929899	−	0.367816i	$-0.119894\pi$
$338$	−1.45380e9	−	1.52135e9i	−0.111388	−	0.116564i
$339$			3.55878e9i			0.269465i
$340$		0			0
$341$	8.87702e9			0.656523
$342$	−5.08486e8	+	4.85907e8i	−0.0371685	+	0.0355180i
$343$	−1.56347e9			−0.112957
$344$	1.42436e10	−	1.24245e10i	1.01715	−	0.887248i
$345$		0			0
$346$	−1.26995e10	+	1.21356e10i	−0.886099	+	0.846752i
$347$	−9.01032e9			−0.621473			−0.310737	−	0.950496i	$-0.600576\pi$
$347$	−9.01032e9			−0.621473			−0.310737	+	0.950496i	$0.600576\pi$
$348$	2.62374e8	−	5.77462e9i	0.0178897	−	0.393737i
$349$	−2.17409e10			−1.46547			−0.732733	−	0.680517i	$-0.761755\pi$
$349$	−2.17409e10			−1.46547			−0.732733	+	0.680517i	$0.761755\pi$
$350$		0			0
$351$		−	1.03802e10i		−	0.683878i
$352$	−5.22043e9	+	4.15197e9i	−0.340045	+	0.270448i
$353$			5.60018e9i			0.360664i	0.983606	+	0.180332i	$0.0577173\pi$
$353$			5.60018e9i			0.360664i	−0.983606	+	0.180332i	$0.942283\pi$
$354$	1.94840e9	−	1.86189e9i	0.124070	−	0.118560i
$355$		0			0
$356$	6.48775e8	−	1.42790e10i	0.0403919	−	0.888990i
$357$			1.10872e10i			0.682573i
$358$	−7.45872e9	+	7.12752e9i	−0.454080	+	0.433917i
$359$		−	1.31213e10i		−	0.789952i	−0.918692	−	0.394976i	$-0.870753\pi$
$359$		−	1.31213e10i		−	0.789952i	0.918692	−	0.394976i	$-0.129247\pi$
$360$		0			0
$361$	1.69265e10			0.996640
$362$	−7.50585e9	−	7.85462e9i	−0.437085	−	0.457395i
$363$	4.73746e9			0.272847
$364$	−2.61753e10	−	1.18929e9i	−1.49103	−	0.0677460i
$365$		0			0
$366$	2.94920e9	+	3.08624e9i	0.164354	+	0.171991i
$367$	−9.89380e9			−0.545379			−0.272690	−	0.962102i	$-0.587913\pi$
$367$	−9.89380e9			−0.545379			−0.272690	+	0.962102i	$0.587913\pi$
$368$	−2.65183e10	−	2.41474e9i	−1.44595	−	0.131668i
$369$	5.65782e9			0.305171
$370$		0			0
$371$			2.66693e10i			1.40772i
$372$	−9.72257e9	−	4.41752e8i	−0.507703	−	0.0230678i
$373$		−	1.01496e10i		−	0.524339i	−0.965022	−	0.262170i	$-0.915562\pi$
$373$		−	1.01496e10i		−	0.524339i	0.965022	−	0.262170i	$-0.0844380\pi$
$374$	8.60501e9	+	9.00486e9i	0.439810	+	0.460247i
$375$		0			0
$376$	−5.77888e9	+	5.04084e9i	−0.289129	+	0.252204i
$377$		−	2.55095e10i		−	1.26281i
$378$	−1.23982e10	−	1.29744e10i	−0.607286	−	0.635505i
$379$		−	1.39748e10i		−	0.677312i	−0.940910	−	0.338656i	$-0.890028\pi$
$379$		−	1.39748e10i		−	0.677312i	0.940910	−	0.338656i	$-0.109972\pi$
$380$		0			0
$381$	1.21501e10			0.576606
$382$	1.77838e9	−	1.69942e9i	0.0835165	−	0.0798080i
$383$	−2.31617e10			−1.07640			−0.538201	−	0.842816i	$-0.680896\pi$
$383$	−2.31617e10			−1.07640			−0.538201	+	0.842816i	$0.680896\pi$
$384$	5.92430e9	−	4.28766e9i	0.272466	−	0.197195i
$385$		0			0
$386$	1.11947e9	−	1.06976e9i	0.0504269	−	0.0481878i
$387$	2.68508e10			1.19706
$388$	1.52823e10	+	6.94364e8i	0.674314	+	0.0306380i
$389$	1.13177e10			0.494267			0.247133	−	0.968981i	$-0.420511\pi$
$389$	1.13177e10			0.494267			0.247133	+	0.968981i	$0.420511\pi$
$390$		0			0
$391$			4.97224e10i			2.12738i
$392$	−1.63430e10	+	1.42558e10i	−0.692132	+	0.603738i
$393$		−	3.58401e9i		−	0.150245i
$394$	3.29407e10	−	3.14780e10i	1.36693	−	1.30624i
$395$		0			0
$396$	−9.46597e9	−	4.30093e8i	−0.384932	−	0.0174897i
$397$			1.01291e10i			0.407765i	0.978995	+	0.203882i	$0.0653560\pi$
$397$			1.01291e10i			0.407765i	−0.978995	+	0.203882i	$0.934644\pi$
$398$	−1.00783e10	+	9.63082e9i	−0.401658	+	0.383823i
$399$		−	6.84432e8i		−	0.0270047i
$400$		0			0
$401$	1.52259e10			0.588850			0.294425	−	0.955675i	$-0.404872\pi$
$401$	1.52259e10			0.588850			0.294425	+	0.955675i	$0.404872\pi$
$402$	−3.59605e8	−	3.76315e8i	−0.0137696	−	0.0144094i
$403$	−4.29496e10			−1.62832
$404$	−1.11867e9	+	2.46210e10i	−0.0419931	+	0.924232i
$405$		0			0
$406$	−3.04688e10	−	3.18846e10i	−1.12137	−	1.17348i
$407$	−2.45580e9			−0.0894985
$408$	−8.97653e9	−	1.02908e10i	−0.323942	−	0.371371i
$409$	5.16482e10			1.84570			0.922851	−	0.385156i	$-0.125852\pi$
$409$	5.16482e10			1.84570			0.922851	+	0.385156i	$0.125852\pi$
$410$		0			0
$411$		−	8.89213e9i		−	0.311629i
$412$	−2.28106e9	+	5.02041e10i	−0.0791678	+	1.74241i
$413$		−	2.05608e10i		−	0.706708i
$414$	−2.61343e10	−	2.73487e10i	−0.889629	−	0.930968i
$415$		0			0
$416$	2.52580e10	−	2.00884e10i	0.843384	−	0.670769i
$417$		−	1.76790e10i		−	0.584673i
$418$	−5.31202e8	−	5.55886e8i	−0.0174002	−	0.0182088i
$419$			2.90780e10i			0.943427i	0.881752	+	0.471714i	$0.156364\pi$
$419$			2.90780e10i			0.943427i	−0.881752	+	0.471714i	$0.843636\pi$
$420$		0			0
$421$	−2.02634e9			−0.0645037			−0.0322519	−	0.999480i	$-0.510268\pi$
$421$	−2.02634e9			−0.0645037			−0.0322519	+	0.999480i	$0.510268\pi$
$422$	−2.57239e10	+	2.45816e10i	−0.811122	+	0.775105i
$423$	−1.08939e10			−0.340268
$424$	−2.15923e10	−	2.47536e10i	−0.668089	−	0.765905i
$425$		0			0
$426$	−1.14186e10	+	1.09115e10i	−0.346715	+	0.331320i
$427$	3.25681e10			0.979671
$428$	−1.91066e9	+	4.20519e10i	−0.0569388	+	1.25317i
$429$	5.33376e9			0.157472
$430$		0			0
$431$			2.31188e10i			0.669972i	0.942223	+	0.334986i	$0.108732\pi$
$431$			2.31188e10i			0.669972i	−0.942223	+	0.334986i	$0.891268\pi$
$432$	2.20121e10	+	2.00441e9i	0.632014	+	0.0575509i
$433$			5.16117e10i			1.46824i	0.679021	+	0.734119i	$0.262405\pi$
$433$			5.16117e10i			1.46824i	−0.679021	+	0.734119i	$0.737595\pi$
$434$	−5.36832e10	+	5.12995e10i	−1.51314	+	1.44595i
$435$		0			0
$436$	−2.11105e9	+	4.64622e10i	−0.0584187	+	1.28574i
$437$		−	3.06945e9i		−	0.0841656i
$438$	1.05745e10	−	1.01049e10i	0.287318	−	0.274560i
$439$			4.07914e10i			1.09827i	0.835733	+	0.549137i	$0.185043\pi$
$439$			4.07914e10i			1.09827i	−0.835733	+	0.549137i	$0.814957\pi$
$440$		0			0
$441$	−3.08086e10			−0.814549
$442$	−4.16336e10	−	4.35682e10i	−1.09082	−	1.14151i
$443$	1.78192e9			0.0462671			0.0231336	−	0.999732i	$-0.492636\pi$
$443$	1.78192e9			0.0462671			0.0231336	+	0.999732i	$0.492636\pi$
$444$	2.68972e9	+	1.22209e8i	0.0692110	+	0.00314466i
$445$		0			0
$446$	−1.94648e10	−	2.03693e10i	−0.491939	−	0.514798i
$447$	1.99057e10			0.498593
$448$	7.57641e9	−	5.52771e10i	0.188084	−	1.37225i
$449$	−5.74811e10			−1.41429			−0.707147	−	0.707067i	$-0.750018\pi$
$449$	−5.74811e10			−1.41429			−0.707147	+	0.707067i	$0.750018\pi$
$450$		0			0
$451$			6.18523e9i			0.149503i
$452$	−3.34066e10	−	1.51785e9i	−0.800347	−	0.0363643i
$453$			2.10895e10i			0.500811i
$454$	−2.04992e10	−	2.14518e10i	−0.482518	−	0.504940i
$455$		0			0
$456$	5.54137e8	+	6.35269e8i	0.0128162	+	0.0146926i
$457$		−	4.50957e10i		−	1.03388i	−0.856021	−	0.516941i	$-0.827071\pi$
$457$		−	4.50957e10i		−	1.03388i	0.856021	−	0.516941i	$-0.172929\pi$
$458$	1.25006e10	+	1.30815e10i	0.284099	+	0.297301i
$459$		−	4.12732e10i		−	0.929860i
$460$		0			0
$461$	7.73092e10			1.71170			0.855850	−	0.517225i	$-0.173035\pi$
$461$	7.73092e10			1.71170			0.855850	+	0.517225i	$0.173035\pi$
$462$	6.66672e9	−	6.37069e9i	0.146334	−	0.139836i
$463$	8.52854e10			1.85588			0.927941	−	0.372726i	$-0.121577\pi$
$463$	8.52854e10			1.85588			0.927941	+	0.372726i	$0.121577\pi$
$464$	5.40949e10	+	4.92586e9i	1.16704	+	0.106270i
$465$		0			0
$466$	2.60196e10	−	2.48643e10i	0.551769	−	0.527268i
$467$	−3.20726e10			−0.674320			−0.337160	−	0.941447i	$-0.609466\pi$
$467$	−3.20726e10			−0.674320			−0.337160	+	0.941447i	$0.609466\pi$
$468$	4.57991e10	+	2.08092e9i	0.954716	+	0.0433782i
$469$	−3.97112e9			−0.0820770
$470$		0			0
$471$			8.65041e9i			0.175773i
$472$	1.66467e10	+	1.90839e10i	0.335397	+	0.384503i
$473$			2.93538e10i			0.586435i
$474$	−3.87228e8	+	3.70033e8i	−0.00767102	+	0.00733040i
$475$		0			0
$476$	−1.04076e11	−	4.72879e9i	−2.02733	−	0.0921133i
$477$		−	4.66635e10i		−	0.901371i
$478$	3.20694e10	−	3.06454e10i	0.614298	−	0.587020i
$479$			3.58893e10i			0.681746i	0.940109	+	0.340873i	$0.110723\pi$
$479$			3.58893e10i			0.681746i	−0.940109	+	0.340873i	$0.889277\pi$
$480$		0			0
$481$	1.18819e10			0.221976
$482$	−1.77433e9	−	1.85678e9i	−0.0328735	−	0.0344010i
$483$	3.68118e10			0.676393
$484$	−2.02057e9	+	4.44710e10i	−0.0368208	+	0.810392i
$485$		0			0
$486$	3.31903e10	+	3.47326e10i	0.594930	+	0.622575i
$487$	5.98567e10			1.06414			0.532068	−	0.846702i	$-0.321415\pi$
$487$	5.98567e10			1.06414			0.532068	+	0.846702i	$0.321415\pi$
$488$	−3.02287e10	+	2.63681e10i	−0.533016	+	0.464943i
$489$	5.50329e8			0.00962470
$490$		0			0
$491$		−	3.00275e10i		−	0.516645i	−0.966059	−	0.258323i	$-0.916830\pi$
$491$		−	3.00275e10i		−	0.516645i	0.966059	−	0.258323i	$-0.0831698\pi$
$492$	3.07799e8	−	6.77438e9i	0.00525299	−	0.115614i
$493$		−	1.01429e11i		−	1.71702i
$494$	2.57011e9	+	2.68954e9i	0.0431563	+	0.0451617i
$495$		0			0
$496$	8.29353e9	−	9.10782e10i	0.137029	−	1.50483i
$497$			1.20496e11i			1.97491i
$498$	−2.09877e10	−	2.19629e10i	−0.341230	−	0.357086i
$499$		−	2.32602e10i		−	0.375156i	−0.982250	−	0.187578i	$-0.939936\pi$
$499$		−	2.32602e10i		−	0.375156i	0.982250	−	0.187578i	$-0.0600637\pi$
$500$		0			0
$501$	−1.54128e9			−0.0244641
$502$	6.68238e10	−	6.38566e10i	1.05224	−	1.00552i
$503$	2.16574e10			0.338326			0.169163	−	0.985588i	$-0.445894\pi$
$503$	2.16574e10			0.338326			0.169163	+	0.985588i	$0.445894\pi$
$504$	5.97303e10	−	5.21020e10i	0.925705	−	0.807481i
$505$		0			0
$506$	2.98980e10	−	2.85704e10i	0.456079	−	0.435828i
$507$	−3.58300e9			−0.0542270
$508$	−5.18212e9	+	1.14054e11i	−0.0778131	+	1.71260i
$509$	−1.21565e10			−0.181108			−0.0905541	−	0.995892i	$-0.528864\pi$
$509$	−1.21565e10			−0.181108			−0.0905541	+	0.995892i	$0.528864\pi$
$510$		0			0
$511$		−	1.11589e11i		−	1.63658i
$512$	3.77219e10	+	5.74407e10i	0.548925	+	0.835871i
$513$			2.54787e9i			0.0367881i
$514$	−5.29500e10	+	5.05988e10i	−0.758601	+	0.724916i
$515$		0			0
$516$	1.46075e9	−	3.21498e10i	0.0206052	−	0.453502i
$517$		−	1.19094e10i		−	0.166697i
$518$	1.48513e10	−	1.41918e10i	0.206275	−	0.197115i
$519$			2.99091e10i			0.412225i
$520$		0			0
$521$	−5.20805e10			−0.706845			−0.353422	−	0.935464i	$-0.614982\pi$
$521$	−5.20805e10			−0.706845			−0.353422	+	0.935464i	$0.614982\pi$
$522$	5.33115e10	+	5.57888e10i	0.718024	+	0.751389i
$523$	−2.42007e10			−0.323461			−0.161731	−	0.986835i	$-0.551708\pi$
$523$	−2.42007e10			−0.323461			−0.161731	+	0.986835i	$0.551708\pi$
$524$	3.36434e10	+	1.52861e9i	0.446246	+	0.0202755i
$525$		0			0
$526$	5.37158e9	+	5.62118e9i	0.0701712	+	0.0734319i
$527$	−1.70774e11			−2.21400
$528$	−1.02994e9	+	1.13107e10i	−0.0132519	+	0.145530i
$529$	8.67778e10			1.10812
$530$		0			0
$531$			3.59755e10i			0.452510i
$532$	6.42482e9	+	2.91917e8i	0.0802074	+	0.00364428i
$533$		−	2.99260e10i		−	0.370800i
$534$	−1.68145e10	−	1.75958e10i	−0.206785	−	0.216394i
$535$		0			0
$536$	3.68587e9	−	3.21514e9i	0.0446561	−	0.0389530i
$537$			1.75664e10i			0.211244i
$538$	1.64407e10	+	1.72047e10i	0.196242	+	0.205361i
$539$		−	3.36805e10i		−	0.399046i
$540$		0			0
$541$	−7.39316e10			−0.863060			−0.431530	−	0.902099i	$-0.642026\pi$
$541$	−7.39316e10			−0.863060			−0.431530	+	0.902099i	$0.642026\pi$
$542$	7.85902e10	−	7.51005e10i	0.910692	−	0.870253i
$543$	−1.84988e10			−0.212786
$544$	1.00429e11	−	7.98743e10i	1.14674	−	0.912035i
$545$		0			0
$546$	−3.22556e10	+	3.08233e10i	−0.362939	+	0.346823i
$547$	9.08736e10			1.01505			0.507526	−	0.861636i	$-0.330560\pi$
$547$	9.08736e10			1.01505			0.507526	+	0.861636i	$0.330560\pi$
$548$	8.34712e10	+	3.79257e9i	0.925581	+	0.0420544i
$549$	−5.69847e10			−0.627290
$550$		0			0
$551$			6.26140e9i			0.0679305i
$552$	−3.41676e10	+	2.98040e10i	−0.368009	+	0.321009i
$553$			4.08628e9i			0.0436946i
$554$	−1.78985e10	+	1.71038e10i	−0.190011	+	0.181574i
$555$		0			0
$556$	1.65954e11	+	7.54025e9i	1.73656	+	0.0789018i
$557$		−	7.25820e9i		−	0.0754064i	−0.999289	−	0.0377032i	$-0.987996\pi$
$557$		−	7.25820e9i		−	0.0754064i	0.999289	−	0.0377032i	$-0.0120041\pi$
$558$	9.39301e10	−	8.97592e10i	0.968875	−	0.925853i
$559$		−	1.42022e11i		−	1.45449i
$560$		0			0
$561$	2.12077e10			0.214113
$562$	−1.03143e11	−	1.07936e11i	−1.03394	−	1.08199i
$563$	−4.02851e10			−0.400969			−0.200485	−	0.979697i	$-0.564252\pi$
$563$	−4.02851e10			−0.400969			−0.200485	+	0.979697i	$0.564252\pi$
$564$	−5.92653e8	+	1.30438e10i	−0.00585712	+	0.128910i
$565$		0			0
$566$	8.22221e10	+	8.60427e10i	0.801166	+	0.838394i
$567$	9.64045e10			0.932750
$568$	−9.75574e10	−	1.11841e11i	−0.937274	−	1.07450i
$569$	−4.42204e10			−0.421866			−0.210933	−	0.977501i	$-0.567650\pi$
$569$	−4.42204e10			−0.421866			−0.210933	+	0.977501i	$0.567650\pi$
$570$		0			0
$571$		−	1.92416e11i		−	1.81008i	−0.425327	−	0.905040i	$-0.639841\pi$
$571$		−	1.92416e11i		−	1.81008i	0.425327	−	0.905040i	$-0.360159\pi$
$572$	−2.27490e9	+	5.00684e10i	−0.0212509	+	0.467714i
$573$		−	4.18835e9i		−	0.0388530i
$574$	−3.57438e10	−	3.74048e10i	−0.329271	−	0.344572i
$575$		0			0
$576$	−1.32565e10	+	9.67190e10i	−0.120431	+	0.878662i
$577$			5.62180e10i			0.507192i	0.967310	+	0.253596i	$0.0816134\pi$
$577$			5.62180e10i			0.507192i	−0.967310	+	0.253596i	$0.918387\pi$
$578$	−8.84309e10	−	9.25400e10i	−0.792305	−	0.829122i
$579$		−	2.63651e9i		−	0.0234593i
$580$		0			0
$581$	−2.31767e11			−2.03398
$582$	1.88323e10	−	1.79960e10i	0.164139	−	0.156850i
$583$	5.10133e10			0.441580
$584$	9.03458e10	+	1.03574e11i	0.776706	+	0.890425i
$585$		0			0
$586$	−1.84172e10	+	1.75994e10i	−0.156183	+	0.149248i
$587$	−2.12589e11			−1.79056			−0.895278	−	0.445508i	$-0.853023\pi$
$587$	−2.12589e11			−1.79056			−0.895278	+	0.445508i	$0.853023\pi$
$588$	−1.67606e9	+	3.68886e10i	−0.0140211	+	0.308591i
$589$	1.05422e10			0.0875927
$590$		0			0
$591$		−	7.75800e10i		−	0.635916i
$592$	−2.29438e9	+	2.51965e10i	−0.0186801	+	0.205142i
$593$			3.64674e10i			0.294908i	0.989069	+	0.147454i	$0.0471078\pi$
$593$			3.64674e10i			0.294908i	−0.989069	+	0.147454i	$0.952892\pi$
$594$	−2.48175e10	+	2.37155e10i	−0.199348	+	0.190497i
$595$		0			0
$596$	−8.48995e9	+	1.86856e11i	−0.0672853	+	1.48089i
$597$			2.37359e10i			0.186857i
$598$	−1.44655e11	+	1.38232e11i	−1.13118	+	1.08095i
$599$			1.54791e11i			1.20237i	0.799111	+	0.601184i	$0.205304\pi$
$599$			1.54791e11i			1.20237i	−0.799111	+	0.601184i	$0.794696\pi$
$600$		0			0
$601$	1.37850e11			1.05659			0.528297	−	0.849059i	$-0.322831\pi$
$601$	1.37850e11			1.05659			0.528297	+	0.849059i	$0.322831\pi$
$602$	−1.69633e11	−	1.77515e11i	−1.29159	−	1.35161i
$603$	6.94830e9			0.0525545
$604$	−1.97969e11	−	8.99487e9i	−1.48747	−	0.0675845i
$605$		0			0
$606$	2.89930e10	+	3.03403e10i	0.214983	+	0.224972i
$607$	−4.21916e10			−0.310793			−0.155396	−	0.987852i	$-0.549665\pi$
$607$	−4.21916e10			−0.310793			−0.155396	+	0.987852i	$0.549665\pi$
$608$	−6.19967e9	+	4.93078e9i	−0.0453685	+	0.0360829i
$609$	−7.50928e10			−0.545920
$610$		0			0
$611$			5.76211e10i			0.413444i
$612$	1.82104e11	+	8.27401e9i	1.29811	+	0.0589808i
$613$			1.76436e11i			1.24953i	0.780815	+	0.624763i	$0.214804\pi$
$613$			1.76436e11i			1.24953i	−0.780815	+	0.624763i	$0.785196\pi$
$614$	3.71813e10	+	3.89091e10i	0.261608	+	0.273765i
$615$		0			0
$616$	5.69588e10	+	6.52982e10i	0.395583	+	0.453501i
$617$			3.80722e10i			0.262705i	0.991336	+	0.131352i	$0.0419319\pi$
$617$			3.80722e10i			0.262705i	−0.991336	+	0.131352i	$0.958068\pi$
$618$	5.91190e10	+	6.18661e10i	0.405297	+	0.424130i
$619$			4.67363e10i			0.318340i	0.987251	+	0.159170i	$0.0508818\pi$
$619$			4.67363e10i			0.318340i	−0.987251	+	0.159170i	$0.949118\pi$
$620$		0			0
$621$	−1.37036e11			−0.921441
$622$	1.42575e11	−	1.36244e11i	0.952537	−	0.910240i
$623$	−1.85683e11			−1.23259
$624$	4.98317e9	−	5.47243e10i	0.0328675	−	0.360946i
$625$		0			0
$626$	3.21565e10	−	3.07286e10i	0.209398	−	0.200099i
$627$	−1.30919e9			−0.00847096
$628$	−8.12021e10	−	3.68948e9i	−0.522070	−	0.0237206i
$629$	4.72440e10			0.301817
$630$		0			0
$631$			1.82629e11i			1.15200i	0.817450	+	0.576000i	$0.195387\pi$
$631$			1.82629e11i			1.15200i	−0.817450	+	0.576000i	$0.804613\pi$
$632$	−3.30838e9	−	3.79276e9i	−0.0207370	−	0.0237732i
$633$			6.05834e10i			0.377345i
$634$	6.24857e9	−	5.97110e9i	0.0386744	−	0.0369571i
$635$		0			0
$636$	−5.58724e10	−	2.53861e9i	−0.341483	−	0.0155155i
$637$			1.62956e11i			0.989721i
$638$	−6.09893e10	+	5.82811e10i	−0.368104	+	0.351759i
$639$		−	2.10833e11i		−	1.26455i
$640$		0			0
$641$	1.05531e11			0.625100			0.312550	−	0.949901i	$-0.398817\pi$
$641$	1.05531e11			0.625100			0.312550	+	0.949901i	$0.398817\pi$
$642$	4.95192e10	+	5.18202e10i	0.291497	+	0.305042i
$643$	1.09834e11			0.642528			0.321264	−	0.946990i	$-0.395892\pi$
$643$	1.09834e11			0.642528			0.321264	+	0.946990i	$0.395892\pi$
$644$	−1.57006e10	+	3.45556e11i	−0.0912793	+	2.00898i
$645$		0			0
$646$	1.02191e10	+	1.06940e10i	0.0586791	+	0.0614057i
$647$	−4.48807e9			−0.0256119			−0.0128060	−	0.999918i	$-0.504076\pi$
$647$	−4.48807e9			−0.0256119			−0.0128060	+	0.999918i	$0.504076\pi$
$648$	−8.94797e10	+	7.80520e10i	−0.507487	+	0.442674i
$649$	−3.93290e10			−0.221684
$650$		0			0
$651$			1.26432e11i			0.703934i
$652$	−2.34720e8	+	5.16599e9i	−0.00129885	+	0.0285866i
$653$		−	2.96586e11i		−	1.63117i	−0.578640	−	0.815583i	$-0.696416\pi$
$653$		−	2.96586e11i		−	1.63117i	0.578640	−	0.815583i	$-0.303584\pi$
$654$	5.47126e10	+	5.72550e10i	0.299072	+	0.312970i
$655$		0			0
$656$	6.34604e10	+	5.77867e9i	0.342679	+	0.0312042i
$657$			1.95248e11i			1.04791i
$658$	6.88232e10	+	7.20212e10i	0.367139	+	0.384199i
$659$			8.22505e10i			0.436111i	0.975936	+	0.218056i	$0.0699714\pi$
$659$			8.22505e10i			0.436111i	−0.975936	+	0.218056i	$0.930029\pi$
$660$		0			0
$661$	−1.54172e11			−0.807608			−0.403804	−	0.914845i	$-0.632312\pi$
$661$	−1.54172e11			−0.807608			−0.403804	+	0.914845i	$0.632312\pi$
$662$	−1.40102e11	+	1.33881e11i	−0.729476	+	0.697085i
$663$	−1.02609e11			−0.531047
$664$	2.15119e11	−	1.87646e11i	1.10664	−	0.965309i
$665$		0			0
$666$	−2.59855e10	+	2.48316e10i	−0.132079	+	0.126214i
$667$	−3.36766e11			−1.70147
$668$	6.57368e8	−	1.44681e10i	0.00330144	−	0.0726616i
$669$	−4.79726e10			−0.239491
$670$		0			0
$671$		−	6.22966e10i		−	0.307308i
$672$	−5.91347e10	−	7.43524e10i	−0.289978	−	0.364601i
$673$		−	2.82157e11i		−	1.37541i	−0.725992	−	0.687703i	$-0.758619\pi$
$673$		−	2.82157e11i		−	1.37541i	0.725992	−	0.687703i	$-0.241381\pi$
$674$	1.09755e11	−	1.04881e11i	0.531844	−	0.508228i
$675$		0			0
$676$	1.52818e9	−	3.36340e10i	0.00731794	−	0.161061i
$677$		−	2.70699e11i		−	1.28864i	−0.764756	−	0.644320i	$-0.777140\pi$
$677$		−	2.70699e11i		−	1.28864i	0.764756	−	0.644320i	$-0.222860\pi$
$678$	−4.11666e10	+	3.93386e10i	−0.194817	+	0.186166i
$679$		−	1.98730e11i		−	0.934943i
$680$		0			0
$681$	−5.05220e10			−0.234905
$682$	9.81263e10	+	1.02686e11i	0.453574	+	0.474650i
$683$	−3.96155e10			−0.182046			−0.0910232	−	0.995849i	$-0.529014\pi$
$683$	−3.96155e10			−0.182046			−0.0910232	+	0.995849i	$0.529014\pi$
$684$	−1.12416e10	−	5.10769e8i	−0.0513574	−	0.00233346i
$685$		0			0
$686$	−1.72825e10	−	1.80856e10i	−0.0780389	−	0.0816651i
$687$	3.08088e10			0.138308
$688$	3.01170e11	+	2.74244e10i	1.34418	+	0.122400i
$689$	−2.46818e11			−1.09521
$690$		0			0
$691$			1.26869e11i			0.556472i	0.960513	+	0.278236i	$0.0897497\pi$
$691$			1.26869e11i			0.556472i	−0.960513	+	0.278236i	$0.910250\pi$
$692$	−2.80760e11	−	1.27565e10i	−1.22436	−	0.0556299i
$693$			1.23095e11i			0.533712i
$694$	−9.95998e10	−	1.04228e11i	−0.429359	−	0.449310i
$695$		0			0
$696$	6.96988e10	−	6.07974e10i	0.297022	−	0.259088i
$697$		−	1.18990e11i		−	0.504171i
$698$	−2.40323e11	−	2.51490e11i	−1.01245	−	1.05950i
$699$		−	6.12800e10i		−	0.256691i
$700$		0			0
$701$	−6.26836e10			−0.259587			−0.129793	−	0.991541i	$-0.541431\pi$
$701$	−6.26836e10			−0.259587			−0.129793	+	0.991541i	$0.541431\pi$
$702$	1.20075e11	−	1.14743e11i	0.494427	−	0.472473i
$703$	−2.91646e9			−0.0119408
$704$	−1.05735e11	−	1.44923e10i	−0.430455	−	0.0589991i
$705$		0			0
$706$	−6.47808e10	+	6.19042e10i	−0.260752	+	0.249173i
$707$	3.20170e11			1.28146
$708$	4.30752e10	+	1.95715e9i	0.171433	+	0.00778918i
$709$	3.57762e11			1.41582			0.707912	−	0.706300i	$-0.249637\pi$
$709$	3.57762e11			1.41582			0.707912	+	0.706300i	$0.249637\pi$
$710$		0			0
$711$		−	7.14981e9i		−	0.0279780i
$712$	1.72345e11	−	1.50334e11i	0.670624	−	0.584977i
$713$			5.67004e11i			2.19396i
$714$	−1.28252e11	+	1.22558e11i	−0.493484	+	0.471571i
$715$		0			0
$716$	−1.64897e11	−	7.49222e9i	−0.627423	−	0.0285074i
$717$		−	7.55280e10i		−	0.285780i
$718$	1.51783e11	−	1.45043e11i	0.571116	−	0.545756i
$719$			1.70342e11i			0.637392i	0.947857	+	0.318696i	$0.103245\pi$
$719$			1.70342e11i			0.637392i	−0.947857	+	0.318696i	$0.896755\pi$
$720$		0			0
$721$	6.52852e11			2.41587
$722$	1.87105e11	+	1.95799e11i	0.688552	+	0.720547i
$723$	−4.37298e9			−0.0160038
$724$	7.88990e9	−	1.73650e11i	0.0287155	−	0.632003i
$725$		0			0
$726$	5.23678e10	+	5.48011e10i	0.188503	+	0.197262i
$727$	6.56094e10			0.234870			0.117435	−	0.993081i	$-0.462533\pi$
$727$	6.56094e10			0.234870			0.117435	+	0.993081i	$0.462533\pi$
$728$	−2.75583e11	−	3.15932e11i	−0.981132	−	1.12478i
$729$	−1.08395e11			−0.383796
$730$		0			0
$731$		−	5.64700e11i		−	1.97765i
$732$	−3.10010e9	+	6.82305e10i	−0.0107977	+	0.237648i
$733$		−	2.60967e11i		−	0.904003i	−0.892017	−	0.452001i	$-0.850710\pi$
$733$		−	2.60967e11i		−	0.904003i	0.892017	−	0.452001i	$-0.149290\pi$
$734$	−1.09366e11	−	1.14448e11i	−0.376788	−	0.394296i
$735$		0			0
$736$	−2.65200e11	−	3.33446e11i	−0.903778	−	1.13636i
$737$			7.59601e9i			0.0257463i
$738$	6.25414e10	+	6.54475e10i	0.210835	+	0.220632i
$739$			4.19763e11i			1.40743i	0.710483	+	0.703715i	$0.248477\pi$
$739$			4.19763e11i			1.40743i	−0.710483	+	0.703715i	$0.751523\pi$
$740$		0			0
$741$	6.33425e9			0.0210098
$742$	−3.08500e11	+	2.94801e11i	−1.01775	+	0.972554i
$743$	−1.42604e11			−0.467925			−0.233962	−	0.972246i	$-0.575169\pi$
$743$	−1.42604e11			−0.467925			−0.233962	+	0.972246i	$0.575169\pi$
$744$	−1.02363e11	−	1.17350e11i	−0.334081	−	0.382994i
$745$		0			0
$746$	1.17406e11	−	1.12193e11i	0.379085	−	0.362252i
$747$	4.05525e11			1.30237
$748$	−9.04530e9	+	1.99079e11i	−0.0288946	+	0.635944i
$749$	5.46841e11			1.73754
$750$		0			0
$751$		−	3.26311e10i		−	0.102582i	−0.998684	−	0.0512911i	$-0.983666\pi$
$751$		−	3.26311e10i		−	0.102582i	0.998684	−	0.0512911i	$-0.0163336\pi$
$752$	−1.22190e11	−	1.11266e10i	−0.382089	−	0.0347928i
$753$		−	1.57380e11i		−	0.489518i
$754$	2.95084e11	−	2.81981e11i	0.912978	−	0.872438i
$755$		0			0
$756$	1.30326e10	−	2.86836e11i	0.0398974	−	0.878106i
$757$		−	4.36612e11i		−	1.32957i	−0.747033	−	0.664787i	$-0.768522\pi$
$757$		−	4.36612e11i		−	1.32957i	0.747033	−	0.664787i	$-0.231478\pi$
$758$	1.61655e11	−	1.54477e11i	0.489680	−	0.467937i
$759$		−	7.04142e10i		−	0.212174i
$760$		0			0
$761$	−1.98059e11			−0.590548			−0.295274	−	0.955413i	$-0.595411\pi$
$761$	−1.98059e11			−0.590548			−0.295274	+	0.955413i	$0.595411\pi$
$762$	1.34307e11	+	1.40547e11i	0.398361	+	0.416872i
$763$	6.04192e11			1.78269
$764$	3.93164e10	+	1.78637e9i	0.115399	+	0.00524322i
$765$		0			0
$766$	−2.56028e11	−	2.67925e11i	−0.743657	−	0.778213i
$767$	1.90285e11			0.549824
$768$	1.15085e11	+	2.11344e10i	0.330807	+	0.0607499i
$769$	1.42097e10			0.0406329			0.0203165	−	0.999794i	$-0.493533\pi$
$769$	1.42097e10			0.0406329			0.0203165	+	0.999794i	$0.493533\pi$
$770$		0			0
$771$			1.24705e11i			0.352912i
$772$	2.47491e10	+	1.12450e9i	0.0696772	+	0.00316584i
$773$		−	6.62483e10i		−	0.185548i	−0.995687	−	0.0927741i	$-0.970427\pi$
$773$		−	6.62483e10i		−	0.185548i	0.995687	−	0.0927741i	$-0.0295734\pi$
$774$	2.96808e11	+	3.10600e11i	0.827013	+	0.865442i
$775$		0			0
$776$	1.60898e11	+	1.84456e11i	0.443715	+	0.508680i
$777$		−	3.49770e10i		−	0.0959617i
$778$	1.25106e11	+	1.30919e11i	0.341476	+	0.357343i
$779$			7.34544e9i			0.0199466i
$780$		0			0
$781$	2.30487e11			0.619501
$782$	−5.75170e11	+	5.49630e11i	−1.53804	+	1.46975i
$783$	2.79540e11			0.743700
$784$	−3.45562e11	−	3.14667e10i	−0.914663	−	0.0832887i
$785$		0			0
$786$	4.14584e10	−	3.96175e10i	0.108623	−	0.103800i
$787$	7.13437e10			0.185976			0.0929880	−	0.995667i	$-0.470358\pi$
$787$	7.13437e10			0.185976			0.0929880	+	0.995667i	$0.470358\pi$
$788$	7.28250e11	+	3.30886e10i	1.88876	+	0.0858170i
$789$	1.32387e10			0.0341615
$790$		0			0
$791$			4.34417e11i			1.10969i
$792$	−9.96614e10	−	1.14253e11i	−0.253295	−	0.290380i
$793$			3.01409e11i			0.762191i
$794$	−1.17170e11	+	1.11967e11i	−0.294804	+	0.281714i
$795$		0			0
$796$	−2.22811e11	−	1.01236e10i	−0.554990	−	0.0252164i
$797$			1.11980e11i			0.277527i	0.990326	+	0.138764i	$0.0443128\pi$
$797$			1.11980e11i			0.277527i	−0.990326	+	0.138764i	$0.955687\pi$
$798$	7.91725e9	−	7.56569e9i	0.0195237	−	0.0186568i
$799$			2.29109e11i			0.562154i
$800$		0			0
$801$	3.24891e11			0.789237
$802$	1.68306e11	+	1.76127e11i	0.406821	+	0.425725i
$803$	−2.13449e11			−0.513372
$804$	3.78004e8	−	8.31954e9i	0.000904634	−	0.0199102i
$805$		0			0
$806$	−4.74764e11	−	4.96825e11i	−1.12496	−	1.17724i
$807$	4.05195e10			0.0955365
$808$	−2.97172e11	+	2.59220e11i	−0.697209	+	0.608167i
$809$	−5.57023e10			−0.130041			−0.0650203	−	0.997884i	$-0.520711\pi$
$809$	−5.57023e10			−0.130041			−0.0650203	+	0.997884i	$0.520711\pi$
$810$		0			0
$811$			7.06448e11i			1.63304i	0.577317	+	0.816520i	$0.304100\pi$
$811$			7.06448e11i			1.63304i	−0.577317	+	0.816520i	$0.695900\pi$
$812$	3.20278e10	−	7.04902e11i	0.0736720	−	1.62145i
$813$		−	1.85091e11i		−	0.423666i
$814$	−2.71464e10	−	2.84078e10i	−0.0618321	−	0.0647053i
$815$		0			0
$816$	1.98137e10	−	2.17591e11i	0.0446896	−	0.490773i
$817$			3.48599e10i			0.0782417i
$818$	5.70917e11	+	5.97446e11i	1.27515	+	1.33440i
$819$		−	5.95569e11i		−	1.32372i
$820$		0			0
$821$	−8.39733e10			−0.184828			−0.0924142	−	0.995721i	$-0.529458\pi$
$821$	−8.39733e10			−0.184828			−0.0924142	+	0.995721i	$0.529458\pi$
$822$	1.02861e11	−	9.82933e10i	0.225301	−	0.215296i
$823$	1.90143e11			0.414459			0.207229	−	0.978292i	$-0.433555\pi$
$823$	1.90143e11			0.414459			0.207229	+	0.978292i	$0.433555\pi$
$824$	−6.05957e11	+	5.28569e11i	−1.31442	+	1.14655i
$825$		0			0
$826$	2.37840e11	−	2.27279e11i	0.510933	−	0.488246i
$827$	−3.98982e11			−0.852965			−0.426483	−	0.904496i	$-0.640247\pi$
$827$	−3.98982e11			−0.852965			−0.426483	+	0.904496i	$0.640247\pi$
$828$	2.74715e10	−	6.04622e11i	0.0584468	−	1.28636i
$829$	−9.18641e11			−1.94504			−0.972518	−	0.232827i	$-0.925202\pi$
$829$	−9.18641e11			−1.94504			−0.972518	+	0.232827i	$0.925202\pi$
$830$		0			0
$831$			4.21536e10i			0.0883957i
$832$	5.11576e11	+	7.01178e10i	1.06762	+	0.146331i
$833$			6.47936e11i			1.34571i
$834$	2.04504e11	−	1.95423e11i	0.422705	−	0.403935i
$835$		0			0
$836$	5.58382e8	−	1.22895e10i	0.00114316	−	0.0251599i
$837$		−	4.70655e11i		−	0.958960i
$838$	−3.36363e11	+	3.21427e11i	−0.682075	+	0.651789i
$839$			4.31925e11i			0.871688i	0.900022	+	0.435844i	$0.143550\pi$
$839$			4.31925e11i			0.871688i	−0.900022	+	0.435844i	$0.856450\pi$
$840$		0			0
$841$	1.86726e11			0.373268
$842$	−2.23991e10	−	2.34400e10i	−0.0445639	−	0.0466347i
$843$	−2.54205e11			−0.503355
$844$	−5.68701e11	−	2.58394e10i	−1.12076	−	0.0509228i
$845$		0			0
$846$	−1.20421e11	−	1.26016e11i	−0.235082	−	0.246006i
$847$	5.78298e11			1.12362
$848$	4.76602e10	−	5.23396e11i	0.0921664	−	1.01216i
$849$	2.02643e11			0.390033
$850$		0			0
$851$		−	1.56860e11i		−	0.299085i
$852$	−2.52441e11	−	1.14698e10i	−0.479073	−	0.0217670i
$853$		−	9.29871e11i		−	1.75641i	−0.478282	−	0.878206i	$-0.658740\pi$
$853$		−	9.29871e11i		−	1.75641i	0.478282	−	0.878206i	$-0.341260\pi$
$854$	3.60006e11	+	3.76735e11i	0.676828	+	0.708279i
$855$		0			0
$856$	−5.07561e11	+	4.42739e11i	−0.945351	+	0.824618i
$857$			1.19713e11i			0.221931i	0.993824	+	0.110965i	$0.0353943\pi$
$857$			1.19713e11i			0.221931i	−0.993824	+	0.110965i	$0.964606\pi$
$858$	5.89592e10	+	6.16989e10i	0.108793	+	0.113849i
$859$			4.22514e11i			0.776012i	0.921657	+	0.388006i	$0.126836\pi$
$859$			4.22514e11i			0.776012i	−0.921657	+	0.388006i	$0.873164\pi$
$860$		0			0
$861$	−8.80936e10			−0.160299
$862$	−2.67430e11	+	2.55555e11i	−0.484374	+	0.462865i
$863$	2.84698e11			0.513264			0.256632	−	0.966509i	$-0.417387\pi$
$863$	2.84698e11			0.513264			0.256632	+	0.966509i	$0.417387\pi$
$864$	2.20135e11	+	2.76784e11i	0.395034	+	0.496691i
$865$		0			0
$866$	−5.97024e11	+	5.70514e11i	−1.06150	+	1.01437i
$867$	−2.17945e11			−0.385719
$868$	−1.18683e12	−	5.39243e10i	−2.09078	−	0.0949961i
$869$	7.81630e9			0.0137064
$870$		0			0
$871$		−	3.67517e10i		−	0.0638565i
$872$	−5.60793e11	+	4.89172e11i	−0.969921	+	0.846049i
$873$			3.47721e11i			0.598651i
$874$	3.55062e10	−	3.39296e10i	0.0608497	−	0.0581478i
$875$		0			0
$876$	2.33780e11	+	1.06220e10i	0.397001	+	0.0180380i
$877$			1.94476e11i			0.328752i	0.986398	+	0.164376i	$0.0525610\pi$
$877$			1.94476e11i			0.328752i	−0.986398	+	0.164376i	$0.947439\pi$
$878$	−4.71859e11	+	4.50907e11i	−0.794025	+	0.758767i
$879$			4.33753e10i			0.0726585i
$880$		0			0
$881$	9.06691e11			1.50507			0.752533	−	0.658555i	$-0.228832\pi$
$881$	9.06691e11			1.50507			0.752533	+	0.658555i	$0.228832\pi$
$882$	−3.40557e11	−	3.56382e11i	−0.562750	−	0.588900i
$883$	−2.26542e11			−0.372654			−0.186327	−	0.982488i	$-0.559658\pi$
$883$	−2.26542e11			−0.372654			−0.186327	+	0.982488i	$0.559658\pi$
$884$	4.37638e10	−	9.63202e11i	0.0716648	−	1.57728i
$885$		0			0
$886$	1.96973e10	+	2.06125e10i	0.0319647	+	0.0334500i
$887$	1.70744e11			0.275837			0.137918	−	0.990444i	$-0.455959\pi$
$887$	1.70744e11			0.275837			0.137918	+	0.990444i	$0.455959\pi$
$888$	2.83184e10	+	3.24646e10i	0.0455425	+	0.0522105i
$889$	1.48315e12			2.37453
$890$		0			0
$891$		−	1.84404e11i		−	0.292590i
$892$	2.04608e10	−	4.50323e11i	0.0323193	−	0.711320i
$893$		−	1.41433e10i		−	0.0222405i
$894$	2.20037e11	+	2.30261e11i	0.344465	+	0.360471i
$895$		0			0
$896$	7.23174e11	−	5.23391e11i	1.12205	−	0.812071i
$897$			3.40684e11i			0.526238i
$898$	−6.35394e11	−	6.64919e11i	−0.977097	−	1.02250i
$899$		−	1.15664e12i		−	1.77075i
$900$		0			0
$901$	−9.81380e11			−1.48915
$902$	−7.15484e10	+	6.83713e10i	−0.108087	+	0.103288i
$903$	−4.18074e11			−0.628785
$904$	−3.51717e11	−	4.03213e11i	−0.526647	−	0.603755i
$905$		0			0
$906$	−2.43955e11	+	2.33123e11i	−0.362074	+	0.345997i
$907$	5.20431e11			0.769013			0.384507	−	0.923122i	$-0.374372\pi$
$907$	5.20431e11			0.769013			0.384507	+	0.923122i	$0.374372\pi$
$908$	2.15481e10	−	4.74254e11i	0.0317004	−	0.697698i
$909$	−5.60205e11			−0.820525
$910$		0			0
$911$			5.42499e11i			0.787635i	0.919189	+	0.393818i	$0.128846\pi$
$911$			5.42499e11i			0.787635i	−0.919189	+	0.393818i	$0.871154\pi$
$912$	−1.22314e9	+	1.34323e10i	−0.00176806	+	0.0194165i
$913$			4.43327e11i			0.638030i
$914$	5.21650e11	−	4.98487e11i	0.747472	−	0.714281i
$915$		0			0
$916$	−1.31403e10	+	2.89205e11i	−0.0186647	+	0.410794i
$917$		−	4.37497e11i		−	0.618725i
$918$	4.77433e11	−	4.56233e11i	0.672266	−	0.642415i
$919$			6.49225e11i			0.910192i	0.890442	+	0.455096i	$0.150395\pi$
$919$			6.49225e11i			0.910192i	−0.890442	+	0.455096i	$0.849605\pi$
$920$		0			0
$921$	9.16364e10			0.127359
$922$	8.54573e11	+	8.94283e11i	1.18257	+	1.23752i
$923$	−1.11516e12			−1.53650
$924$	1.47387e11	+	6.69666e9i	0.202196	+	0.00918693i
$925$		0			0
$926$	9.42742e11	+	9.86549e11i	1.28218	+	1.34176i
$927$	−1.14230e12			−1.54690
$928$	5.40983e11	+	6.80200e11i	0.729444	+	0.917159i
$929$	−4.98636e11			−0.669455			−0.334727	−	0.942315i	$-0.608644\pi$
$929$	−4.98636e11			−0.669455			−0.334727	+	0.942315i	$0.608644\pi$
$930$		0			0
$931$		−	3.99982e10i		−	0.0532404i
$932$	5.75240e11	+	2.61365e10i	0.762405	+	0.0346404i
$933$		−	3.35785e11i		−	0.443133i
$934$	−3.54529e11	−	3.71003e11i	−0.465870	−	0.487518i
$935$		0			0
$936$	4.82191e11	+	5.52789e11i	0.628226	+	0.720205i
$937$			4.01408e11i			0.520748i	0.965508	+	0.260374i	$0.0838459\pi$
$937$			4.01408e11i			0.520748i	−0.965508	+	0.260374i	$0.916154\pi$
$938$	−4.38966e10	−	4.59364e10i	−0.0567048	−	0.0593397i
$939$		−	7.57332e10i		−	0.0974146i
$940$		0			0
$941$	−2.64682e10			−0.0337572			−0.0168786	−	0.999858i	$-0.505373\pi$
$941$	−2.64682e10			−0.0337572			−0.0168786	+	0.999858i	$0.505373\pi$
$942$	−1.00065e11	+	9.56214e10i	−0.127080	+	0.121437i
$943$	−3.95071e11			−0.499606
$944$	−3.67439e10	+	4.03515e11i	−0.0462698	+	0.508127i
$945$		0			0
$946$	−3.39554e11	+	3.24476e11i	−0.423979	+	0.405152i
$947$	−5.71352e11			−0.710401			−0.355201	−	0.934790i	$-0.615587\pi$
$947$	−5.71352e11			−0.710401			−0.355201	+	0.934790i	$0.615587\pi$
$948$	−8.56081e9	−	3.88967e8i	−0.0105994	−	0.000481592i
$949$	1.03273e12			1.27327
$950$		0			0
$951$		−	1.47163e10i		−	0.0179918i
$952$	−1.09576e12	−	1.25619e12i	−1.33403	−	1.52935i
$953$			1.09917e12i			1.33258i	0.745694	+	0.666288i	$0.232118\pi$
$953$			1.09917e12i			1.33258i	−0.745694	+	0.666288i	$0.767882\pi$
$954$	5.39785e11	−	5.15817e11i	0.651670	−	0.622733i
$955$		0			0
$956$	7.08988e11	+	3.22134e10i	0.848803	+	0.0385660i
$957$			1.43639e11i			0.171247i
$958$	−4.15153e11	+	3.96719e11i	−0.492886	+	0.471000i
$959$		−	1.08545e12i		−	1.28333i
$960$		0			0
$961$	−1.09451e12			−1.28329
$962$	1.31342e11	+	1.37445e11i	0.153357	+	0.160483i
$963$	−9.56813e11			−1.11256
$964$	1.86512e9	−	4.10495e10i	0.00215972	−	0.0475335i
$965$		0			0
$966$	4.06917e11	+	4.25825e11i	0.467301	+	0.489016i
$967$	−8.78566e11			−1.00477			−0.502387	−	0.864643i	$-0.667545\pi$
$967$	−8.78566e11			−1.00477			−0.502387	+	0.864643i	$0.667545\pi$
$968$	−5.36758e11	+	4.68207e11i	−0.611332	+	0.533257i
$969$	2.51858e10			0.0285668
$970$		0			0
$971$		−	7.91945e11i		−	0.890878i	−0.895312	−	0.445439i	$-0.853048\pi$
$971$		−	7.91945e11i		−	0.890878i	0.895312	−	0.445439i	$-0.146952\pi$
$972$	−3.48885e10	+	7.67865e11i	−0.0390857	+	0.860241i
$973$		−	2.15806e12i		−	2.40775i
$974$	6.61654e11	+	6.92399e11i	0.735182	+	0.769344i
$975$		0			0
$976$	−6.39163e11	−	5.82018e10i	−0.704389	−	0.0641413i
$977$		−	5.46919e11i		−	0.600268i	−0.953897	−	0.300134i	$-0.902969\pi$
$977$		−	5.46919e11i		−	0.600268i	0.953897	−	0.300134i	$-0.0970313\pi$
$978$	6.08332e9	+	6.36600e9i	0.00664944	+	0.00695843i
$979$			3.55177e11i			0.386646i
$980$		0			0
$981$	−1.05716e12			−1.14147
$982$	3.47346e11	−	3.31923e11i	0.373522	−	0.356936i
$983$	7.38083e11			0.790481			0.395240	−	0.918578i	$-0.370661\pi$
$983$	7.38083e11			0.790481			0.395240	+	0.918578i	$0.370661\pi$
$984$	8.17658e10	−	7.13233e10i	0.0872151	−	0.0760766i
$985$		0			0
$986$	1.17329e12	−	1.12119e12i	1.24136	−	1.18624i
$987$	1.69620e11			0.178735
$988$	−2.70162e9	+	5.94601e10i	−0.00283528	+	0.0624020i
$989$	−1.87492e12			−1.95974
$990$		0			0
$991$		−	3.73877e11i		−	0.387645i	−0.981037	−	0.193823i	$-0.937911\pi$
$991$		−	3.73877e11i		−	0.387645i	0.981037	−	0.193823i	$-0.0620886\pi$
$992$	1.14523e12	−	9.10839e11i	1.18263	−	0.940578i
$993$			3.29959e11i			0.339362i
$994$	−1.39385e12	+	1.33196e12i	−1.42781	+	1.36441i
$995$		0			0
$996$	2.20615e10	−	4.85555e11i	0.0224181	−	0.493402i
$997$			1.14224e12i			1.15605i	0.816019	+	0.578025i	$0.196177\pi$
$997$			1.14224e12i			1.15605i	−0.816019	+	0.578025i	$0.803823\pi$
$998$	2.69066e11	−	2.57118e11i	0.271229	−	0.259185i
$999$			1.30205e11i			0.130727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.c.99.24		32
4.3	odd	2	inner	100.9.d.c.99.10		32
5.2	odd	4		100.9.b.d.51.4		16
5.3	odd	4		20.9.b.a.11.13	✓	16
5.4	even	2	inner	100.9.d.c.99.9		32
15.8	even	4		180.9.c.a.91.4		16
20.3	even	4		20.9.b.a.11.14	yes	16
20.7	even	4		100.9.b.d.51.3		16
20.19	odd	2	inner	100.9.d.c.99.23		32
40.3	even	4		320.9.b.d.191.10		16
40.13	odd	4		320.9.b.d.191.7		16
60.23	odd	4		180.9.c.a.91.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.13	✓	16	5.3	odd	4
20.9.b.a.11.14	yes	16	20.3	even	4
100.9.b.d.51.3		16	20.7	even	4
100.9.b.d.51.4		16	5.2	odd	4
100.9.d.c.99.9		32	5.4	even	2	inner
100.9.d.c.99.10		32	4.3	odd	2	inner
100.9.d.c.99.23		32	20.19	odd	2	inner
100.9.d.c.99.24		32	1.1	even	1	trivial
180.9.c.a.91.3		16	60.23	odd	4
180.9.c.a.91.4		16	15.8	even	4
320.9.b.d.191.7		16	40.13	odd	4
320.9.b.d.191.10		16	40.3	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(11.0540 + 11.5676i) q^{2} +27.2434 q^{3} +(-11.6196 + 255.736i) q^{4} +(301.148 + 315.141i) q^{6} +3325.58 q^{7} +(-3086.70 + 2692.49i) q^{8} -5818.80 q^{9} -6361.21i q^{11} +(-316.557 + 6967.12i) q^{12} +30777.4i q^{13} +(36760.8 + 38469.0i) q^{14} +(-65266.0 - 5943.09i) q^{16} +122375. i q^{17} +(-64320.8 - 67309.6i) q^{18} -7554.43i q^{19} +90600.1 q^{21} +(73584.1 - 70316.6i) q^{22} +406311. q^{23} +(-84092.2 + 73352.6i) q^{24} +(-356021. + 340213. i) q^{26} -337268. q^{27} +(-38641.8 + 850471. i) q^{28} -828838. q^{29} +1.39549e6i q^{31} +(-652701. - 820666. i) q^{32} -173301. i q^{33} +(-1.41559e6 + 1.35273e6i) q^{34} +(67611.9 - 1.48808e6i) q^{36} -386059. i q^{37} +(87386.8 - 83506.4i) q^{38} +838482. i q^{39} -972335. q^{41} +(1.00149e6 + 1.04803e6i) q^{42} -4.61450e6 q^{43} +(1.62679e6 + 73914.5i) q^{44} +(4.49135e6 + 4.70005e6i) q^{46} +1.87219e6 q^{47} +(-1.77807e6 - 161910. i) q^{48} +5.29467e6 q^{49} +3.33392e6i q^{51} +(-7.87090e6 - 357620. i) q^{52} +8.01944e6i q^{53} +(-3.72815e6 - 3.90139e6i) q^{54} +(-1.02651e7 + 8.95408e6i) q^{56} -205808. i q^{57} +(-9.16195e6 - 9.58768e6i) q^{58} -6.18263e6i q^{59} +9.79320e6 q^{61} +(-1.61425e7 + 1.54257e7i) q^{62} -1.93509e7 q^{63} +(2.27822e6 - 1.66218e7i) q^{64} +(2.00468e6 - 1.91566e6i) q^{66} -1.19411e6 q^{67} +(-3.12958e7 - 1.42195e6i) q^{68} +1.10693e7 q^{69} +3.62332e7i q^{71} +(1.79609e7 - 1.56670e7i) q^{72} -3.35548e7i q^{73} +(4.46578e6 - 4.26748e6i) q^{74} +(1.93194e6 + 87779.2i) q^{76} -2.11547e7i q^{77} +(-9.69923e6 + 9.26855e6i) q^{78} +1.22874e6i q^{79} +2.89888e7 q^{81} +(-1.07482e7 - 1.12476e7i) q^{82} -6.96923e7 q^{83} +(-1.05273e6 + 2.31697e7i) q^{84} +(-5.10086e7 - 5.33788e7i) q^{86} -2.25804e7 q^{87} +(1.71275e7 + 1.96352e7i) q^{88} -5.58347e7 q^{89} +1.02353e8i q^{91} +(-4.72116e6 + 1.03908e8i) q^{92} +3.80180e7i q^{93} +(2.06951e7 + 2.16567e7i) q^{94} +(-1.77818e7 - 2.23578e7i) q^{96} -5.97582e7i q^{97} +(5.85271e7 + 6.12467e7i) q^{98} +3.70146e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) \) 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more