LMFDB - Embedded newform 100.9.d.c.99.2

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			99.2
Character	$\chi$	$=$	100.99
Dual form			100.9.d.c.99.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-15.9375 + 1.41320i) q^{2} -39.9624 q^{3} +(252.006 - 45.0455i) q^{4} +(636.899 - 56.4746i) q^{6} +2633.20 q^{7} +(-3952.68 + 1074.04i) q^{8} -4964.01 q^{9} -2484.31i q^{11} +(-10070.7 + 1800.13i) q^{12} +41319.8i q^{13} +(-41966.5 + 3721.22i) q^{14} +(61477.8 - 22703.5i) q^{16} +48625.0i q^{17} +(79113.7 - 7015.11i) q^{18} -241516. i q^{19} -105229. q^{21} +(3510.82 + 39593.7i) q^{22} -57735.4 q^{23} +(157958. - 42921.4i) q^{24} +(-58392.9 - 658533. i) q^{26} +460567. q^{27} +(663581. - 118614. i) q^{28} +729286. q^{29} +134865. i q^{31} +(-947716. + 448716. i) q^{32} +99279.1i q^{33} +(-68716.6 - 774960. i) q^{34} +(-1.25096e6 + 223606. i) q^{36} -1.68171e6i q^{37} +(341309. + 3.84915e6i) q^{38} -1.65124e6i q^{39} -761790. q^{41} +(1.67708e6 - 148709. i) q^{42} +2.54364e6 q^{43} +(-111907. - 626061. i) q^{44} +(920156. - 81591.4i) q^{46} -5.65990e6 q^{47} +(-2.45680e6 + 907284. i) q^{48} +1.16893e6 q^{49} -1.94317e6i q^{51} +(1.86127e6 + 1.04128e7i) q^{52} +1.14302e7i q^{53} +(-7.34027e6 + 650871. i) q^{54} +(-1.04082e7 + 2.82817e6i) q^{56} +9.65155e6i q^{57} +(-1.16230e7 + 1.03062e6i) q^{58} +2.12902e7i q^{59} -2.63701e7 q^{61} +(-190590. - 2.14940e6i) q^{62} -1.30712e7 q^{63} +(1.44701e7 - 8.49070e6i) q^{64} +(-140301. - 1.58226e6i) q^{66} -1.53982e6 q^{67} +(2.19034e6 + 1.22538e7i) q^{68} +2.30724e6 q^{69} +2.06597e7i q^{71} +(1.96211e7 - 5.33157e6i) q^{72} +2.51296e7i q^{73} +(2.37658e6 + 2.68022e7i) q^{74} +(-1.08792e7 - 6.08634e7i) q^{76} -6.54169e6i q^{77} +(2.33352e6 + 2.63165e7i) q^{78} -1.95344e7i q^{79} +1.41635e7 q^{81} +(1.21410e7 - 1.07656e6i) q^{82} -2.37076e7 q^{83} +(-2.65183e7 + 4.74009e6i) q^{84} +(-4.05392e7 + 3.59466e6i) q^{86} -2.91440e7 q^{87} +(2.66826e6 + 9.81968e6i) q^{88} -3.86749e7 q^{89} +1.08803e8i q^{91} +(-1.45497e7 + 2.60072e6i) q^{92} -5.38951e6i q^{93} +(9.02045e7 - 7.99855e6i) q^{94} +(3.78730e7 - 1.79317e7i) q^{96} +9.46443e7i q^{97} +(-1.86298e7 + 1.65192e6i) q^{98} +1.23322e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.9375	+	1.41320i	−0.996092	+	0.0883247i
$2$	−15.9375	+	1.41320i	−0.996092	+	0.0883247i
$3$	−39.9624			−0.493363			−0.246681	−	0.969097i	$-0.579340\pi$
$3$	−39.9624			−0.493363			−0.246681	+	0.969097i	$0.579340\pi$
$4$	252.006	−	45.0455i	0.984397	−	0.175959i
$5$		0			0
$5$		0			0
$6$	636.899	−	56.4746i	0.491435	−	0.0435761i
$7$	2633.20			1.09671			0.548354	−	0.836246i	$-0.315255\pi$
$7$	2633.20			1.09671			0.548354	+	0.836246i	$0.315255\pi$
$8$	−3952.68	+	1074.04i	−0.965009	+	0.262218i
$9$	−4964.01			−0.756593
$10$		0			0
$11$		−	2484.31i		−	0.169682i	−0.996395	−	0.0848410i	$-0.972962\pi$
$11$		−	2484.31i		−	0.169682i	0.996395	−	0.0848410i	$-0.0270382\pi$
$12$	−10070.7	+	1800.13i	−0.485665	+	0.0868116i
$13$			41319.8i			1.44672i	0.690471	+	0.723360i	$0.257403\pi$
$13$			41319.8i			1.44672i	−0.690471	+	0.723360i	$0.742597\pi$
$14$	−41966.5	+	3721.22i	−1.09242	+	0.0968665i
$15$		0			0
$16$	61477.8	−	22703.5i	0.938077	−	0.346427i
$17$			48625.0i			0.582189i	0.956694	+	0.291095i	$0.0940194\pi$
$17$			48625.0i			0.582189i	−0.956694	+	0.291095i	$0.905981\pi$
$18$	79113.7	−	7015.11i	0.753636	−	0.0668259i
$19$		−	241516.i		−	1.85324i	−0.376002	−	0.926619i	$-0.622701\pi$
$19$		−	241516.i		−	1.85324i	0.376002	−	0.926619i	$-0.377299\pi$
$20$		0			0
$21$	−105229.			−0.541075
$22$	3510.82	+	39593.7i	0.0149871	+	0.169019i
$23$	−57735.4			−0.206315			−0.103158	−	0.994665i	$-0.532895\pi$
$23$	−57735.4			−0.206315			−0.103158	+	0.994665i	$0.532895\pi$
$24$	157958.	−	42921.4i	0.476099	−	0.129369i
$25$		0			0
$26$	−58392.9	−	658533.i	−0.127781	−	1.44107i
$27$	460567.			0.866638
$28$	663581.	−	118614.i	1.07960	−	0.192976i
$29$	729286.			1.03111			0.515556	−	0.856856i	$-0.327585\pi$
$29$	729286.			1.03111			0.515556	+	0.856856i	$0.327585\pi$
$30$		0			0
$31$			134865.i			0.146033i	0.997331	+	0.0730165i	$0.0232626\pi$
$31$			134865.i			0.146033i	−0.997331	+	0.0730165i	$0.976737\pi$
$32$	−947716.	+	448716.i	−0.903813	+	0.427929i
$33$			99279.1i			0.0837147i
$34$	−68716.6	−	774960.i	−0.0514217	−	0.579914i
$35$		0			0
$36$	−1.25096e6	+	223606.i	−0.744788	+	0.133129i
$37$		−	1.68171e6i		−	0.897313i	−0.893704	−	0.448656i	$-0.851903\pi$
$37$		−	1.68171e6i		−	0.897313i	0.893704	−	0.448656i	$-0.148097\pi$
$38$	341309.	+	3.84915e6i	0.163687	+	1.84599i
$39$		−	1.65124e6i		−	0.713758i
$40$		0			0
$41$	−761790.			−0.269588			−0.134794	−	0.990874i	$-0.543037\pi$
$41$	−761790.			−0.269588			−0.134794	+	0.990874i	$0.543037\pi$
$42$	1.67708e6	−	148709.i	0.538961	−	0.0477903i
$43$	2.54364e6			0.744016			0.372008	−	0.928230i	$-0.378669\pi$
$43$	2.54364e6			0.744016			0.372008	+	0.928230i	$0.378669\pi$
$44$	−111907.	−	626061.i	−0.0298571	−	0.167034i
$45$		0			0
$46$	920156.	−	81591.4i	0.205509	−	0.0182227i
$47$	−5.65990e6			−1.15989			−0.579946	−	0.814655i	$-0.696926\pi$
$47$	−5.65990e6			−1.15989			−0.579946	+	0.814655i	$0.696926\pi$
$48$	−2.45680e6	+	907284.i	−0.462812	+	0.170914i
$49$	1.16893e6			0.202770
$50$		0			0
$51$		−	1.94317e6i		−	0.287230i
$52$	1.86127e6	+	1.04128e7i	0.254564	+	1.42415i
$53$			1.14302e7i			1.44861i	0.689480	+	0.724305i	$0.257839\pi$
$53$			1.14302e7i			1.44861i	−0.689480	+	0.724305i	$0.742161\pi$
$54$	−7.34027e6	+	650871.i	−0.863251	+	0.0765455i
$55$		0			0
$56$	−1.04082e7	+	2.82817e6i	−1.05833	+	0.287577i
$57$			9.65155e6i			0.914318i
$58$	−1.16230e7	+	1.03062e6i	−1.02708	+	0.0910727i
$59$			2.12902e7i			1.75700i	0.477740	+	0.878501i	$0.341456\pi$
$59$			2.12902e7i			1.75700i	−0.477740	+	0.878501i	$0.658544\pi$
$60$		0			0
$61$	−2.63701e7			−1.90455			−0.952276	−	0.305238i	$-0.901264\pi$
$61$	−2.63701e7			−1.90455			−0.952276	+	0.305238i	$0.901264\pi$
$62$	−190590.	−	2.14940e6i	−0.0128983	−	0.145462i
$63$	−1.30712e7			−0.829762
$64$	1.44701e7	−	8.49070e6i	0.862483	−	0.506085i
$65$		0			0
$66$	−140301.	−	1.58226e6i	−0.00739408	−	0.0833876i
$67$	−1.53982e6			−0.0764137			−0.0382068	−	0.999270i	$-0.512165\pi$
$67$	−1.53982e6			−0.0764137			−0.0382068	+	0.999270i	$0.512165\pi$
$68$	2.19034e6	+	1.22538e7i	0.102441	+	0.573105i
$69$	2.30724e6			0.101788
$70$		0			0
$71$			2.06597e7i			0.813002i	0.913650	+	0.406501i	$0.133251\pi$
$71$			2.06597e7i			0.813002i	−0.913650	+	0.406501i	$0.866749\pi$
$72$	1.96211e7	−	5.33157e6i	0.730119	−	0.198392i
$73$			2.51296e7i			0.884899i	0.896793	+	0.442449i	$0.145890\pi$
$73$			2.51296e7i			0.884899i	−0.896793	+	0.442449i	$0.854110\pi$
$74$	2.37658e6	+	2.68022e7i	0.0792549	+	0.893806i
$75$		0			0
$76$	−1.08792e7	−	6.08634e7i	−0.326094	−	1.82432i
$77$		−	6.54169e6i		−	0.186092i
$78$	2.33352e6	+	2.63165e7i	0.0630425	+	0.710968i
$79$		−	1.95344e7i		−	0.501525i	−0.968049	−	0.250762i	$-0.919319\pi$
$79$		−	1.95344e7i		−	0.501525i	0.968049	−	0.250762i	$-0.0806812\pi$
$80$		0			0
$81$	1.41635e7			0.329027
$82$	1.21410e7	−	1.07656e6i	0.268534	−	0.0238113i
$83$	−2.37076e7			−0.499547			−0.249773	−	0.968304i	$-0.580356\pi$
$83$	−2.37076e7			−0.499547			−0.249773	+	0.968304i	$0.580356\pi$
$84$	−2.65183e7	+	4.74009e6i	−0.532633	+	0.0952071i
$85$		0			0
$86$	−4.05392e7	+	3.59466e6i	−0.741108	+	0.0657150i
$87$	−2.91440e7			−0.508712
$88$	2.66826e6	+	9.81968e6i	0.0444937	+	0.163745i
$89$	−3.86749e7			−0.616410			−0.308205	−	0.951320i	$-0.599728\pi$
$89$	−3.86749e7			−0.616410			−0.308205	+	0.951320i	$0.599728\pi$
$90$		0			0
$91$			1.08803e8i			1.58663i
$92$	−1.45497e7	+	2.60072e6i	−0.203096	+	0.0363030i
$93$		−	5.38951e6i		−	0.0720473i
$94$	9.02045e7	−	7.99855e6i	1.15536	−	0.102447i
$95$		0			0
$96$	3.78730e7	−	1.79317e7i	0.445907	−	0.211124i
$97$			9.46443e7i			1.06907i	0.845145	+	0.534537i	$0.179514\pi$
$97$			9.46443e7i			1.06907i	−0.845145	+	0.534537i	$0.820486\pi$
$98$	−1.86298e7	+	1.65192e6i	−0.201978	+	0.0179096i
$99$			1.23322e7i			0.128380i
$100$		0			0
$101$	−6.52649e7			−0.627183			−0.313591	−	0.949558i	$-0.601532\pi$
$101$	−6.52649e7			−0.627183			−0.313591	+	0.949558i	$0.601532\pi$
$102$	2.74608e6	+	3.09692e7i	0.0253695	+	0.286108i
$103$	1.47000e8			1.30607			0.653037	−	0.757326i	$-0.273495\pi$
$103$	1.47000e8			1.30607			0.653037	+	0.757326i	$0.273495\pi$
$104$	−4.43793e7	−	1.63324e8i	−0.379356	−	1.39610i
$105$		0			0
$106$	−1.61531e7	−	1.82169e8i	−0.127948	−	1.44295i
$107$	−2.42429e8			−1.84948			−0.924739	−	0.380603i	$-0.875716\pi$
$107$	−2.42429e8			−1.84948			−0.924739	+	0.380603i	$0.875716\pi$
$108$	1.16065e8	−	2.07465e7i	0.853116	−	0.152493i
$109$	5.93486e7			0.420440			0.210220	−	0.977654i	$-0.432582\pi$
$109$	5.93486e7			0.420440			0.210220	+	0.977654i	$0.432582\pi$
$110$		0			0
$111$			6.72051e7i			0.442701i
$112$	1.61883e8	−	5.97827e7i	1.02880	−	0.379930i
$113$			5.46199e7i			0.334994i	0.985873	+	0.167497i	$0.0535685\pi$
$113$			5.46199e7i			0.334994i	−0.985873	+	0.167497i	$0.946432\pi$
$114$	−1.36395e7	−	1.53821e8i	−0.0807569	−	0.910745i
$115$		0			0
$116$	1.83784e8	−	3.28511e7i	1.01502	−	0.181434i
$117$		−	2.05112e8i		−	1.09458i
$118$	−3.00873e7	−	3.39312e8i	−0.155187	−	1.75014i
$119$			1.28039e8i			0.638492i
$120$		0			0
$121$	2.08187e8			0.971208
$122$	4.20273e8	−	3.72661e7i	1.89711	−	0.168219i
$123$	3.04430e7			0.133005
$124$	6.07505e6	+	3.39867e7i	0.0256958	+	0.143755i
$125$		0			0
$126$	2.08322e8	−	1.84722e7i	0.826519	−	0.0732885i
$127$	−2.01099e8			−0.773026			−0.386513	−	0.922284i	$-0.626321\pi$
$127$	−2.01099e8			−0.773026			−0.386513	+	0.922284i	$0.626321\pi$
$128$	−2.18617e8	+	1.55769e8i	−0.814413	+	0.580286i
$129$	−1.01650e8			−0.367070
$130$		0			0
$131$			4.36365e8i			1.48172i	0.671662	+	0.740858i	$0.265581\pi$
$131$			4.36365e8i			1.48172i	−0.671662	+	0.740858i	$0.734419\pi$
$132$	4.47208e6	+	2.50189e7i	0.0147304	+	0.0824086i
$133$		−	6.35959e8i		−	2.03246i
$134$	2.45409e7	−	2.17607e6i	0.0761151	−	0.00674922i
$135$		0			0
$136$	−5.22254e7	−	1.92199e8i	−0.152660	−	0.561818i
$137$		−	4.48301e8i		−	1.27259i	−0.771447	−	0.636293i	$-0.780467\pi$
$137$		−	4.48301e8i		−	1.27259i	0.771447	−	0.636293i	$-0.219533\pi$
$138$	−3.67716e7	+	3.26059e6i	−0.101390	+	0.00899041i
$139$			4.73879e8i			1.26943i	0.772747	+	0.634714i	$0.218882\pi$
$139$			4.73879e8i			1.26943i	−0.772747	+	0.634714i	$0.781118\pi$
$140$		0			0
$141$	2.26183e8			0.572248
$142$	−2.91963e7	−	3.29264e8i	−0.0718082	−	0.809825i
$143$	1.02651e8			0.245482
$144$	−3.05176e8	+	1.12700e8i	−0.709743	+	0.262105i
$145$		0			0
$146$	−3.55130e7	−	4.00502e8i	−0.0781584	−	0.881440i
$147$	−4.67132e7			−0.100039
$148$	−7.57534e7	−	4.23800e8i	−0.157890	−	0.883312i
$149$	2.98504e8			0.605627			0.302814	−	0.953050i	$-0.402074\pi$
$149$	2.98504e8			0.605627			0.302814	+	0.953050i	$0.402074\pi$
$150$		0			0
$151$			7.25032e8i			1.39460i	0.716780	+	0.697299i	$0.245615\pi$
$151$			7.25032e8i			1.39460i	−0.716780	+	0.697299i	$0.754385\pi$
$152$	2.59399e8	+	9.54634e8i	0.485952	+	1.78839i
$153$		−	2.41375e8i		−	0.440480i
$154$	9.24468e6	+	1.04258e8i	0.0164365	+	0.185364i
$155$		0			0
$156$	−7.43808e7	−	4.16121e8i	−0.125592	−	0.702621i
$157$			6.70288e8i			1.10322i	0.834101	+	0.551611i	$0.185987\pi$
$157$			6.70288e8i			1.10322i	−0.834101	+	0.551611i	$0.814013\pi$
$158$	2.76060e7	+	3.11329e8i	0.0442970	+	0.499564i
$159$		−	4.56779e8i		−	0.714690i
$160$		0			0
$161$	−1.52029e8			−0.226268
$162$	−2.25731e8	+	2.00158e7i	−0.327741	+	0.0290612i
$163$	−9.70735e8			−1.37515			−0.687575	−	0.726113i	$-0.741325\pi$
$163$	−9.70735e8			−1.37515			−0.687575	+	0.726113i	$0.741325\pi$
$164$	−1.91976e8	+	3.43152e7i	−0.265381	+	0.0474364i
$165$		0			0
$166$	3.77840e8	−	3.35035e7i	0.497594	−	0.0441223i
$167$	−7.98683e8			−1.02685			−0.513427	−	0.858133i	$-0.671624\pi$
$167$	−7.98683e8			−1.02685			−0.513427	+	0.858133i	$0.671624\pi$
$168$	4.15935e8	−	1.13020e8i	0.522142	−	0.141880i
$169$	−8.91594e8			−1.09300
$170$		0			0
$171$			1.19889e9i			1.40215i
$172$	6.41013e8	−	1.14580e8i	0.732408	−	0.130916i
$173$			6.00425e8i			0.670308i	0.942163	+	0.335154i	$0.108788\pi$
$173$			6.00425e8i			0.670308i	−0.942163	+	0.335154i	$0.891212\pi$
$174$	4.64482e8	−	4.11862e7i	0.506724	−	0.0449319i
$175$		0			0
$176$	−5.64025e7	−	1.52730e8i	−0.0587824	−	0.159175i
$177$		−	8.50809e8i		−	0.866840i
$178$	6.16380e8	−	5.46552e7i	0.614001	−	0.0544442i
$179$			1.15845e9i			1.12840i	0.825637	+	0.564202i	$0.190816\pi$
$179$			1.15845e9i			1.12840i	−0.825637	+	0.564202i	$0.809184\pi$
$180$		0			0
$181$	−7.96493e8			−0.742109			−0.371055	−	0.928611i	$-0.621004\pi$
$181$	−7.96493e8			−0.742109			−0.371055	+	0.928611i	$0.621004\pi$
$182$	−1.53760e8	−	1.73405e9i	−0.140139	−	1.58043i
$183$	1.05381e9			0.939635
$184$	2.28209e8	−	6.20104e7i	0.199096	−	0.0540995i
$185$		0			0
$186$	7.61643e6	+	8.58952e7i	0.00636355	+	0.0717657i
$187$	1.20800e8			0.0987870
$188$	−1.42633e9	+	2.54953e8i	−1.14180	+	0.204094i
$189$	1.21276e9			0.950449
$190$		0			0
$191$		−	1.84245e9i		−	1.38440i	−0.721706	−	0.692200i	$-0.756642\pi$
$191$		−	1.84245e9i		−	1.38440i	0.721706	−	0.692200i	$-0.243358\pi$
$192$	−5.78258e8	+	3.39309e8i	−0.425517	+	0.249684i
$193$			2.34201e9i			1.68795i	0.536382	+	0.843975i	$0.319791\pi$
$193$			2.34201e9i			1.68795i	−0.536382	+	0.843975i	$0.680209\pi$
$194$	−1.33751e8	−	1.50839e9i	−0.0944256	−	1.06490i
$195$		0			0
$196$	2.94577e8	−	5.26550e7i	0.199606	−	0.0356792i
$197$			1.86381e9i			1.23747i	0.785598	+	0.618737i	$0.212356\pi$
$197$			1.86381e9i			1.23747i	−0.785598	+	0.618737i	$0.787644\pi$
$198$	−1.74277e7	−	1.96543e8i	−0.0113391	−	0.127878i
$199$		−	1.82005e9i		−	1.16057i	−0.814413	−	0.580286i	$-0.802941\pi$
$199$		−	1.82005e9i		−	1.16057i	0.814413	−	0.580286i	$-0.197059\pi$
$200$		0			0
$201$	6.15349e7			0.0376997
$202$	1.04016e9	−	9.22320e7i	0.624732	−	0.0553957i
$203$	1.92035e9			1.13083
$204$	−8.75311e7	−	4.89690e8i	−0.0505408	−	0.282749i
$205$		0			0
$206$	−2.34280e9	+	2.07739e8i	−1.30097	+	0.115359i
$207$	2.86599e8			0.156097
$208$	9.38102e8	+	2.54025e9i	0.501183	+	1.35713i
$209$	−6.00001e8			−0.314461
$210$		0			0
$211$		−	2.89129e9i		−	1.45869i	−0.684148	−	0.729344i	$-0.739826\pi$
$211$		−	2.89129e9i		−	1.45869i	0.684148	−	0.729344i	$-0.260174\pi$
$212$	5.14880e8	+	2.88048e9i	0.254896	+	1.42601i
$213$		−	8.25613e8i		−	0.401105i
$214$	3.86370e9	−	3.42599e8i	1.84225	−	0.163355i
$215$		0			0
$216$	−1.82047e9	+	4.94669e8i	−0.836313	+	0.227248i
$217$			3.55125e8i			0.160156i
$218$	−9.45866e8	+	8.38711e7i	−0.418797	+	0.0371353i
$219$		−	1.00424e9i		−	0.436576i
$220$		0			0
$221$	−2.00917e9			−0.842265
$222$	−9.49739e7	−	1.07108e9i	−0.0391014	−	0.440970i
$223$	−2.26023e9			−0.913973			−0.456986	−	0.889474i	$-0.651071\pi$
$223$	−2.26023e9			−0.913973			−0.456986	+	0.889474i	$0.651071\pi$
$224$	−2.49552e9	+	1.18156e9i	−0.991219	+	0.469313i
$225$		0			0
$226$	−7.71886e7	−	8.70503e8i	−0.0295882	−	0.333685i
$227$	−1.08021e9			−0.406823			−0.203412	−	0.979093i	$-0.565203\pi$
$227$	−1.08021e9			−0.406823			−0.203412	+	0.979093i	$0.565203\pi$
$228$	4.34759e8	+	2.43225e9i	0.160883	+	0.900053i
$229$	−6.30352e8			−0.229214			−0.114607	−	0.993411i	$-0.536561\pi$
$229$	−6.30352e8			−0.229214			−0.114607	+	0.993411i	$0.536561\pi$
$230$		0			0
$231$			2.61421e8i			0.0918107i
$232$	−2.88263e9	+	7.83286e8i	−0.995032	+	0.270376i
$233$			1.17430e9i			0.398435i	0.979955	+	0.199217i	$0.0638400\pi$
$233$			1.17430e9i			0.398435i	−0.979955	+	0.199217i	$0.936160\pi$
$234$	2.89863e8	+	3.26896e9i	0.0966784	+	1.09030i
$235$		0			0
$236$	9.59030e8	+	5.36526e9i	0.309161	+	1.72959i
$237$			7.80642e8i			0.247434i
$238$	−1.80944e8	−	2.04062e9i	−0.0563946	−	0.635996i
$239$			3.05182e9i			0.935334i	0.883905	+	0.467667i	$0.154905\pi$
$239$			3.05182e9i			0.935334i	−0.883905	+	0.467667i	$0.845095\pi$
$240$		0			0
$241$	2.81871e9			0.835570			0.417785	−	0.908546i	$-0.362807\pi$
$241$	2.81871e9			0.835570			0.417785	+	0.908546i	$0.362807\pi$
$242$	−3.31797e9	+	2.94209e8i	−0.967412	+	0.0857817i
$243$	−3.58779e9			−1.02897
$244$	−6.64542e9	+	1.18786e9i	−1.87484	+	0.335123i
$245$		0			0
$246$	−4.85184e8	+	4.30218e7i	−0.132485	+	0.0117476i
$247$	9.97938e9			2.68112
$248$	−1.44851e8	−	5.33076e8i	−0.0382925	−	0.140923i
$249$	9.47414e8			0.246458
$250$		0			0
$251$			2.92571e8i			0.0737116i	0.999321	+	0.0368558i	$0.0117342\pi$
$251$			2.92571e8i			0.0737116i	−0.999321	+	0.0368558i	$0.988266\pi$
$252$	−3.29402e9	+	5.88800e8i	−0.816816	+	0.146004i
$253$			1.43433e8i			0.0350079i
$254$	3.20500e9	−	2.84192e8i	0.770005	−	0.0682773i
$255$		0			0
$256$	3.26407e9	−	2.79152e9i	0.759976	−	0.649951i
$257$		−	3.03746e9i		−	0.696270i	−0.937444	−	0.348135i	$-0.886815\pi$
$257$		−	3.03746e9i		−	0.696270i	0.937444	−	0.348135i	$-0.113185\pi$
$258$	1.62004e9	−	1.43651e8i	0.365635	−	0.0324213i
$259$		−	4.42827e9i		−	0.984091i
$260$		0			0
$261$	−3.62018e9			−0.780133
$262$	−6.16669e8	−	6.95456e9i	−0.130872	−	1.47593i
$263$	−1.69827e9			−0.354964			−0.177482	−	0.984124i	$-0.556795\pi$
$263$	−1.69827e9			−0.354964			−0.177482	+	0.984124i	$0.556795\pi$
$264$	−1.06630e8	−	3.92418e8i	−0.0219515	−	0.0807855i
$265$		0			0
$266$	8.98734e8	+	1.01356e10i	0.179517	+	2.02452i
$267$	1.54554e9			0.304114
$268$	−3.88044e8	+	6.93621e7i	−0.0752215	+	0.0134457i
$269$	8.70547e8			0.166258			0.0831291	−	0.996539i	$-0.473509\pi$
$269$	8.70547e8			0.166258			0.0831291	+	0.996539i	$0.473509\pi$
$270$		0			0
$271$		−	7.36841e9i		−	1.36614i	−0.730351	−	0.683072i	$-0.760643\pi$
$271$		−	7.36841e9i		−	1.36614i	0.730351	−	0.683072i	$-0.239357\pi$
$272$	1.10396e9	+	2.98936e9i	0.201686	+	0.546138i
$273$		−	4.34803e9i		−	0.782785i
$274$	6.33537e8	+	7.14478e9i	0.112401	+	1.26761i
$275$		0			0
$276$	5.81439e8	−	1.03931e8i	0.100200	−	0.0179105i
$277$		−	2.37339e9i		−	0.403135i	−0.979475	−	0.201568i	$-0.935396\pi$
$277$		−	2.37339e9i		−	0.403135i	0.979475	−	0.201568i	$-0.0646036\pi$
$278$	−6.69684e8	−	7.55243e9i	−0.112122	−	1.26447i
$279$		−	6.69469e8i		−	0.110488i
$280$		0			0
$281$	5.50733e9			0.883315			0.441657	−	0.897184i	$-0.354391\pi$
$281$	5.50733e9			0.883315			0.441657	+	0.897184i	$0.354391\pi$
$282$	−3.60479e9	+	3.19641e8i	−0.570011	+	0.0505436i
$283$	4.55904e9			0.710768			0.355384	−	0.934720i	$-0.384350\pi$
$283$	4.55904e9			0.710768			0.355384	+	0.934720i	$0.384350\pi$
$284$	9.30629e8	+	5.20638e9i	0.143055	+	0.800317i
$285$		0			0
$286$	−1.63600e9	+	1.45066e8i	−0.244523	+	0.0216822i
$287$	−2.00594e9			−0.295659
$288$	4.70447e9	−	2.22743e9i	0.683818	−	0.323768i
$289$	4.61137e9			0.661056
$290$		0			0
$291$		−	3.78221e9i		−	0.527441i
$292$	1.13197e9	+	6.33280e9i	0.155706	+	0.871092i
$293$		−	8.27611e9i		−	1.12294i	−0.827498	−	0.561469i	$-0.810237\pi$
$293$		−	8.27611e9i		−	1.12294i	0.827498	−	0.561469i	$-0.189763\pi$
$294$	7.44490e8	−	6.60148e7i	0.0996482	−	0.00883593i
$295$		0			0
$296$	1.80623e9	+	6.64725e9i	0.235291	+	0.865914i
$297$		−	1.14419e9i		−	0.147053i
$298$	−4.75740e9	+	4.21845e8i	−0.603260	+	0.0534918i
$299$		−	2.38562e9i		−	0.298480i
$300$		0			0
$301$	6.69791e9			0.815969
$302$	−1.02461e9	−	1.15552e10i	−0.123178	−	1.38915i
$303$	2.60814e9			0.309429
$304$	−5.48324e9	−	1.48479e10i	−0.642012	−	1.73848i
$305$		0			0
$306$	3.41110e8	+	3.84691e9i	0.0389053	+	0.438759i
$307$	7.73582e9			0.870869			0.435434	−	0.900221i	$-0.356595\pi$
$307$	7.73582e9			0.870869			0.435434	+	0.900221i	$0.356595\pi$
$308$	−2.94674e8	−	1.64854e9i	−0.0327445	−	0.183188i
$309$	−5.87446e9			−0.644368
$310$		0			0
$311$		−	1.08068e10i		−	1.15520i	−0.816321	−	0.577599i	$-0.803990\pi$
$311$		−	1.08068e10i		−	1.15520i	0.816321	−	0.577599i	$-0.196010\pi$
$312$	1.77350e9	+	6.52680e9i	0.187160	+	0.688783i
$313$		−	4.73025e9i		−	0.492841i	−0.969163	−	0.246421i	$-0.920746\pi$
$313$		−	4.73025e9i		−	0.492841i	0.969163	−	0.246421i	$-0.0792544\pi$
$314$	−9.47248e8	−	1.06827e10i	−0.0974418	−	1.09891i
$315$		0			0
$316$	−8.79938e8	−	4.92279e9i	−0.0882478	−	0.493700i
$317$			5.44758e9i			0.539469i	0.962935	+	0.269735i	$0.0869360\pi$
$317$			5.44758e9i			0.539469i	−0.962935	+	0.269735i	$0.913064\pi$
$318$	6.45518e8	+	7.27990e9i	0.0631248	+	0.711897i
$319$		−	1.81178e9i		−	0.174961i
$320$		0			0
$321$	9.68803e9			0.912463
$322$	2.42295e9	−	2.14846e8i	0.225383	−	0.0199850i
$323$	1.17437e10			1.07893
$324$	3.56929e9	−	6.38003e8i	0.323893	−	0.0578952i
$325$		0			0
$326$	1.54711e10	−	1.37184e9i	1.36978	−	0.121460i
$327$	−2.37171e9			−0.207429
$328$	3.01111e9	−	8.18197e8i	0.260154	−	0.0706907i
$329$	−1.49036e10			−1.27206
$330$		0			0
$331$		−	8.65354e8i		−	0.0720911i	−0.999350	−	0.0360456i	$-0.988524\pi$
$331$		−	8.65354e8i		−	0.0720911i	0.999350	−	0.0360456i	$-0.0114761\pi$
$332$	−5.97446e9	+	1.06792e9i	−0.491752	+	0.0878997i
$333$			8.34801e9i			0.678901i
$334$	1.27290e10	−	1.12870e9i	1.02284	−	0.0906966i
$335$		0			0
$336$	−6.46924e9	+	2.38906e9i	−0.507570	+	0.187443i
$337$		−	8.64475e8i		−	0.0670244i	−0.999438	−	0.0335122i	$-0.989331\pi$
$337$		−	8.64475e8i		−	0.0670244i	0.999438	−	0.0335122i	$-0.0106693\pi$
$338$	1.42097e10	−	1.26000e9i	1.08873	−	0.0965389i
$339$		−	2.18274e9i		−	0.165274i
$340$		0			0
$341$	3.35046e8			0.0247792
$342$	−1.69426e9	−	1.91072e10i	−0.123844	−	1.39667i
$343$	−1.21018e10			−0.874329
$344$	−1.00542e10	+	2.73199e9i	−0.717982	+	0.195094i
$345$		0			0
$346$	−8.48518e8	−	9.56926e9i	−0.0592048	−	0.667689i
$347$	−1.10077e10			−0.759239			−0.379620	−	0.925143i	$-0.623945\pi$
$347$	−1.10077e10			−0.759239			−0.379620	+	0.925143i	$0.623945\pi$
$348$	−7.34446e9	+	1.31281e9i	−0.500775	+	0.0895125i
$349$	1.99631e10			1.34563			0.672816	−	0.739810i	$-0.265085\pi$
$349$	1.99631e10			1.34563			0.672816	+	0.739810i	$0.265085\pi$
$350$		0			0
$351$			1.90305e10i			1.25378i
$352$	1.11475e9	+	2.35442e9i	0.0726118	+	0.153361i
$353$			1.32468e10i			0.853126i	0.904458	+	0.426563i	$0.140276\pi$
$353$			1.32468e10i			0.853126i	−0.904458	+	0.426563i	$0.859724\pi$
$354$	1.20236e9	+	1.35597e10i	0.0765634	+	0.863452i
$355$		0			0
$356$	−9.74630e9	+	1.74213e9i	−0.606792	+	0.108463i
$357$		−	5.11675e9i		−	0.315008i
$358$	−1.63711e9	−	1.84627e10i	−0.0996659	−	1.12399i
$359$		−	2.59685e9i		−	0.156340i	−0.996940	−	0.0781699i	$-0.975092\pi$
$359$		−	2.59685e9i		−	0.156340i	0.996940	−	0.0781699i	$-0.0249076\pi$
$360$		0			0
$361$	−4.13463e10			−2.43449
$362$	1.26941e10	−	1.12560e9i	0.739209	−	0.0655466i
$363$	−8.31965e9			−0.479158
$364$	4.90109e9	+	2.74190e10i	0.279182	+	1.56188i
$365$		0			0
$366$	−1.67951e10	+	1.48924e9i	−0.935963	+	0.0829930i
$367$	3.62330e9			0.199728			0.0998642	−	0.995001i	$-0.468159\pi$
$367$	3.62330e9			0.199728			0.0998642	+	0.995001i	$0.468159\pi$
$368$	−3.54945e9	+	1.31079e9i	−0.193539	+	0.0714732i
$369$	3.78153e9			0.203968
$370$		0			0
$371$			3.00981e10i			1.58870i
$372$	−2.42773e8	−	1.35819e9i	−0.0126774	−	0.0709232i
$373$			4.15162e9i			0.214478i	0.994233	+	0.107239i	$0.0342009\pi$
$373$			4.15162e9i			0.214478i	−0.994233	+	0.107239i	$0.965799\pi$
$374$	−1.92524e9	+	1.70714e8i	−0.0984009	+	0.00872533i
$375$		0			0
$376$	2.23718e10	−	6.07899e9i	1.11931	−	0.304145i
$377$			3.01339e10i			1.49173i
$378$	−1.93284e10	+	1.71387e9i	−0.946734	+	0.0839481i
$379$			1.89551e10i			0.918692i	0.888257	+	0.459346i	$0.151916\pi$
$379$			1.89551e10i			0.918692i	−0.888257	+	0.459346i	$0.848084\pi$
$380$		0			0
$381$	8.03638e9			0.381382
$382$	2.60374e9	+	2.93639e10i	0.122277	+	1.37899i
$383$	−8.87673e9			−0.412532			−0.206266	−	0.978496i	$-0.566131\pi$
$383$	−8.87673e9			−0.412532			−0.206266	+	0.978496i	$0.566131\pi$
$384$	8.73647e9	−	6.22491e9i	0.401801	−	0.286291i
$385$		0			0
$386$	−3.30972e9	−	3.73257e10i	−0.149088	−	1.68135i
$387$	−1.26267e10			−0.562918
$388$	4.26330e9	+	2.38509e10i	0.188113	+	1.05239i
$389$	−2.05595e10			−0.897872			−0.448936	−	0.893564i	$-0.648197\pi$
$389$	−2.05595e10			−0.897872			−0.448936	+	0.893564i	$0.648197\pi$
$390$		0			0
$391$		−	2.80739e9i		−	0.120114i
$392$	−4.62040e9	+	1.25548e9i	−0.195675	+	0.0531699i
$393$		−	1.74382e10i		−	0.731023i
$394$	−2.63393e9	−	2.97044e10i	−0.109300	−	1.23264i
$395$		0			0
$396$	5.55508e8	+	3.10777e9i	0.0225897	+	0.126377i
$397$		−	2.04868e10i		−	0.824733i	−0.911018	−	0.412366i	$-0.864702\pi$
$397$		−	2.04868e10i		−	0.824733i	0.911018	−	0.412366i	$-0.135298\pi$
$398$	2.57209e9	+	2.90071e10i	0.102507	+	1.15604i
$399$			2.54144e10i			1.00274i
$400$		0			0
$401$	−7.30576e9			−0.282545			−0.141273	−	0.989971i	$-0.545119\pi$
$401$	−7.30576e9			−0.282545			−0.141273	+	0.989971i	$0.545119\pi$
$402$	−9.80711e8	+	8.69609e7i	−0.0375523	+	0.00332981i
$403$	−5.57258e9			−0.211269
$404$	−1.64471e10	+	2.93989e9i	−0.617397	+	0.110358i
$405$		0			0
$406$	−3.06056e10	+	2.71384e9i	−1.12641	+	0.0998802i
$407$	−4.17789e9			−0.152258
$408$	2.08705e9	+	7.68073e9i	0.0753170	+	0.277180i
$409$	1.05889e10			0.378406			0.189203	−	0.981938i	$-0.439410\pi$
$409$	1.05889e10			0.378406			0.189203	+	0.981938i	$0.439410\pi$
$410$		0			0
$411$			1.79152e10i			0.627847i
$412$	3.70448e10	−	6.62168e9i	1.28570	−	0.229815i
$413$			5.60614e10i			1.92692i
$414$	−4.56766e9	+	4.05021e8i	−0.155487	+	0.0137872i
$415$		0			0
$416$	−1.85408e10	−	3.91594e10i	−0.619093	−	1.30756i
$417$		−	1.89373e10i		−	0.626289i
$418$	9.56250e9	−	8.47919e8i	0.313232	−	0.0277747i
$419$			2.61037e9i			0.0846928i	0.999103	+	0.0423464i	$0.0134833\pi$
$419$			2.61037e9i			0.0846928i	−0.999103	+	0.0423464i	$0.986517\pi$
$420$		0			0
$421$	9.29505e9			0.295885			0.147943	−	0.988996i	$-0.452735\pi$
$421$	9.29505e9			0.295885			0.147943	+	0.988996i	$0.452735\pi$
$422$	4.08596e9	+	4.60799e10i	0.128838	+	1.45299i
$423$	2.80958e10			0.877567
$424$	−1.22766e10	−	4.51800e10i	−0.379852	−	1.39792i
$425$		0			0
$426$	1.16675e9	+	1.31582e10i	0.0354275	+	0.399537i
$427$	−6.94377e10			−2.08874
$428$	−6.10934e10	+	1.09203e10i	−1.82062	+	0.325432i
$429$	−4.10219e9			−0.121112
$430$		0			0
$431$			1.86560e10i			0.540642i	0.962770	+	0.270321i	$0.0871298\pi$
$431$			1.86560e10i			0.540642i	−0.962770	+	0.270321i	$0.912870\pi$
$432$	2.83146e10	−	1.04565e10i	0.812973	−	0.300227i
$433$		−	1.66970e10i		−	0.474994i	−0.971388	−	0.237497i	$-0.923673\pi$
$433$		−	1.66970e10i		−	0.474994i	0.971388	−	0.237497i	$-0.0763270\pi$
$434$	−5.01861e8	−	5.65980e9i	−0.0141457	−	0.159530i
$435$		0			0
$436$	1.49562e10	−	2.67339e9i	0.413880	−	0.0739802i
$437$			1.39440e10i			0.382351i
$438$	1.41918e9	+	1.60050e10i	0.0385605	+	0.434870i
$439$		−	5.48360e9i		−	0.147641i	−0.997272	−	0.0738206i	$-0.976481\pi$
$439$		−	5.48360e9i		−	0.147641i	0.997272	−	0.0738206i	$-0.0235192\pi$
$440$		0			0
$441$	−5.80257e9			−0.153414
$442$	3.20212e10	−	2.83936e9i	0.838973	−	0.0743928i
$443$	−5.97812e9			−0.155221			−0.0776104	−	0.996984i	$-0.524729\pi$
$443$	−5.97812e9			−0.155221			−0.0776104	+	0.996984i	$0.524729\pi$
$444$	3.02729e9	+	1.69361e10i	0.0778972	+	0.435793i
$445$		0			0
$446$	3.60223e10	−	3.19415e9i	0.910401	−	0.0807264i
$447$	−1.19289e10			−0.298794
$448$	3.81026e10	−	2.23577e10i	0.945893	−	0.555028i
$449$	3.11696e10			0.766913			0.383456	−	0.923559i	$-0.374734\pi$
$449$	3.11696e10			0.766913			0.383456	+	0.923559i	$0.374734\pi$
$450$		0			0
$451$			1.89253e9i			0.0457442i
$452$	2.46038e9	+	1.37645e10i	0.0589452	+	0.329767i
$453$		−	2.89740e10i		−	0.688043i
$454$	1.72158e10	−	1.52655e9i	0.405233	−	0.0359325i
$455$		0			0
$456$	−1.03662e10	−	3.81494e10i	−0.239751	−	0.882325i
$457$			4.33966e9i			0.0994927i	0.998762	+	0.0497463i	$0.0158413\pi$
$457$			4.33966e9i			0.0994927i	−0.998762	+	0.0497463i	$0.984159\pi$
$458$	1.00462e10	−	8.90810e8i	0.228318	−	0.0202453i
$459$			2.23951e10i			0.504547i
$460$		0			0
$461$	−5.16164e10			−1.14284			−0.571418	−	0.820659i	$-0.693607\pi$
$461$	−5.16164e10			−1.14284			−0.571418	+	0.820659i	$0.693607\pi$
$462$	−3.69440e8	−	4.16640e9i	−0.00810915	−	0.0914519i
$463$	6.86820e10			1.49458			0.747289	−	0.664499i	$-0.231355\pi$
$463$	6.86820e10			1.49458			0.747289	+	0.664499i	$0.231355\pi$
$464$	4.48349e10	−	1.65573e10i	0.967263	−	0.357205i
$465$		0			0
$466$	−1.65952e9	−	1.87154e10i	−0.0351916	−	0.396877i
$467$	2.14596e10			0.451185			0.225592	−	0.974222i	$-0.427568\pi$
$467$	2.14596e10			0.451185			0.225592	+	0.974222i	$0.427568\pi$
$468$	−9.23936e9	−	5.16893e10i	−0.192601	−	1.07750i
$469$	−4.05465e9			−0.0838036
$470$		0			0
$471$		−	2.67863e10i		−	0.544289i
$472$	−2.28667e10	−	8.41534e10i	−0.460718	−	1.69552i
$473$		−	6.31921e9i		−	0.126246i
$474$	−1.10320e9	−	1.24415e10i	−0.0218545	−	0.246466i
$475$		0			0
$476$	5.76759e9	+	3.22666e10i	0.112348	+	0.628530i
$477$		−	5.67397e10i		−	1.09601i
$478$	−4.31281e9	−	4.86382e10i	−0.0826131	−	0.931679i
$479$		−	8.24617e10i		−	1.56643i	−0.621753	−	0.783213i	$-0.713579\pi$
$479$		−	8.24617e10i		−	1.56643i	0.621753	−	0.783213i	$-0.286421\pi$
$480$		0			0
$481$	6.94878e10			1.29816
$482$	−4.49231e10	+	3.98339e9i	−0.832304	+	0.0738014i
$483$	6.07543e9			0.111632
$484$	5.24643e10	−	9.37789e9i	0.956055	−	0.170893i
$485$		0			0
$486$	5.71802e10	−	5.07024e9i	1.02495	−	0.0908832i
$487$	2.94674e9			0.0523874			0.0261937	−	0.999657i	$-0.491661\pi$
$487$	2.94674e9			0.0523874			0.0261937	+	0.999657i	$0.491661\pi$
$488$	1.04233e11	−	2.83227e10i	1.83791	−	0.499408i
$489$	3.87929e10			0.678448
$490$		0			0
$491$			8.17812e10i			1.40711i	0.710642	+	0.703554i	$0.248405\pi$
$491$			8.17812e10i			1.40711i	−0.710642	+	0.703554i	$0.751595\pi$
$492$	7.67180e9	−	1.37132e9i	0.130929	−	0.0234033i
$493$			3.54616e10i			0.600302i
$494$	−1.59046e11	+	1.41028e10i	−2.67064	+	0.236809i
$495$		0			0
$496$	3.06189e9	+	8.29118e9i	0.0505898	+	0.136990i
$497$			5.44012e10i			0.891626i
$498$	−1.50994e10	+	1.33888e9i	−0.245494	+	0.0217683i
$499$			4.69562e10i			0.757340i	0.925532	+	0.378670i	$0.123618\pi$
$499$			4.69562e10i			0.757340i	−0.925532	+	0.378670i	$0.876382\pi$
$500$		0			0
$501$	3.19173e10			0.506612
$502$	−4.13460e8	−	4.66284e9i	−0.00651056	−	0.0734236i
$503$	−8.89245e10			−1.38915			−0.694575	−	0.719420i	$-0.744408\pi$
$503$	−8.89245e10			−1.38915			−0.694575	+	0.719420i	$0.744408\pi$
$504$	5.16663e10	−	1.40391e10i	0.800728	−	0.217579i
$505$		0			0
$506$	−2.02699e8	−	2.28596e9i	−0.00309207	−	0.0348711i
$507$	3.56302e10			0.539245
$508$	−5.06780e10	+	9.05859e9i	−0.760965	+	0.136021i
$509$	−1.30873e11			−1.94975			−0.974877	−	0.222745i	$-0.928498\pi$
$509$	−1.30873e11			−1.94975			−0.974877	+	0.222745i	$0.928498\pi$
$510$		0			0
$511$			6.61711e10i			0.970476i
$512$	−4.80761e10	+	4.91025e10i	−0.699599	+	0.714535i
$513$		−	1.11234e11i		−	1.60609i
$514$	4.29252e9	+	4.84094e10i	0.0614978	+	0.693549i
$515$		0			0
$516$	−2.56164e10	+	4.57888e9i	−0.361343	+	0.0645892i
$517$			1.40610e10i			0.196813i
$518$	6.25801e9	+	7.05754e10i	0.0869195	+	0.980245i
$519$		−	2.39944e10i		−	0.330705i
$520$		0			0
$521$	7.03085e10			0.954238			0.477119	−	0.878839i	$-0.341681\pi$
$521$	7.03085e10			0.954238			0.477119	+	0.878839i	$0.341681\pi$
$522$	5.76966e10	−	5.11603e9i	0.777084	−	0.0689050i
$523$	−7.40744e10			−0.990060			−0.495030	−	0.868876i	$-0.664843\pi$
$523$	−7.40744e10			−0.990060			−0.495030	+	0.868876i	$0.664843\pi$
$524$	1.96563e10	+	1.09967e11i	0.260721	+	1.45860i
$525$		0			0
$526$	2.70661e10	−	2.39999e9i	0.353577	−	0.0313521i
$527$	−6.55779e9			−0.0850189
$528$	2.25398e9	+	6.10346e9i	0.0290011	+	0.0785309i
$529$	−7.49776e10			−0.957434
$530$		0			0
$531$		−	1.05685e11i		−	1.32934i
$532$	−2.86471e10	−	1.60265e11i	−0.357630	−	2.00075i
$533$		−	3.14770e10i		−	0.390018i
$534$	−2.46320e10	+	2.18415e9i	−0.302925	+	0.0268607i
$535$		0			0
$536$	6.08642e9	−	1.65384e9i	0.0737399	−	0.0200370i
$537$		−	4.62943e10i		−	0.556712i
$538$	−1.38743e10	+	1.23025e9i	−0.165608	+	0.0146847i
$539$		−	2.90399e9i		−	0.0344064i
$540$		0			0
$541$	3.35458e9			0.0391605			0.0195803	−	0.999808i	$-0.493767\pi$
$541$	3.35458e9			0.0391605			0.0195803	+	0.999808i	$0.493767\pi$
$542$	1.04130e10	+	1.17434e11i	0.120664	+	1.36081i
$543$	3.18298e10			0.366129
$544$	−2.18188e10	−	4.60827e10i	−0.249135	−	0.526190i
$545$		0			0
$546$	6.14462e9	+	6.92966e10i	0.0691392	+	0.779725i
$547$	1.13812e11			1.27128			0.635638	−	0.771987i	$-0.280737\pi$
$547$	1.13812e11			1.27128			0.635638	+	0.771987i	$0.280737\pi$
$548$	−2.01939e10	−	1.12974e11i	−0.223923	−	1.25273i
$549$	1.30902e11			1.44097
$550$		0			0
$551$		−	1.76134e11i		−	1.91090i
$552$	−9.11979e9	+	2.47808e9i	−0.0982265	+	0.0266907i
$553$		−	5.14380e10i		−	0.550026i
$554$	3.35407e9	+	3.78259e10i	0.0356068	+	0.401560i
$555$		0			0
$556$	2.13461e10	+	1.19420e11i	0.223367	+	1.24962i
$557$			1.05403e11i			1.09505i	0.836790	+	0.547524i	$0.184430\pi$
$557$			1.05403e11i			1.09505i	−0.836790	+	0.547524i	$0.815570\pi$
$558$	9.46091e8	+	1.06696e10i	0.00975879	+	0.110056i
$559$			1.05103e11i			1.07638i
$560$		0			0
$561$	−4.82745e9			−0.0487378
$562$	−8.77728e10	+	7.78293e9i	−0.879862	+	0.0780185i
$563$	7.97945e10			0.794217			0.397108	−	0.917772i	$-0.370014\pi$
$563$	7.97945e10			0.794217			0.397108	+	0.917772i	$0.370014\pi$
$564$	5.69995e10	−	1.01885e10i	0.563319	−	0.100692i
$565$		0			0
$566$	−7.26596e10	+	6.44282e9i	−0.707990	+	0.0627784i
$567$	3.72953e10			0.360846
$568$	−2.21895e10	−	8.16613e10i	−0.213184	−	0.784554i
$569$	4.57243e10			0.436212			0.218106	−	0.975925i	$-0.430012\pi$
$569$	4.57243e10			0.436212			0.218106	+	0.975925i	$0.430012\pi$
$570$		0			0
$571$		−	2.16780e10i		−	0.203927i	−0.994788	−	0.101964i	$-0.967487\pi$
$571$		−	2.16780e10i		−	0.203927i	0.994788	−	0.101964i	$-0.0325126\pi$
$572$	2.58687e10	−	4.62398e9i	0.241652	−	0.0431948i
$573$			7.36286e10i			0.683011i
$574$	3.19697e10	−	2.83479e9i	0.294504	−	0.0261140i
$575$		0			0
$576$	−7.18296e10	+	4.21479e10i	−0.652549	+	0.382901i
$577$		−	1.69273e11i		−	1.52716i	−0.645715	−	0.763579i	$-0.723440\pi$
$577$		−	1.69273e11i		−	1.52716i	0.645715	−	0.763579i	$-0.276560\pi$
$578$	−7.34935e10	+	6.51676e9i	−0.658472	+	0.0583876i
$579$		−	9.35923e10i		−	0.832772i
$580$		0			0
$581$	−6.24269e10			−0.547857
$582$	5.34500e9	+	6.02789e10i	0.0465861	+	0.525380i
$583$	2.83963e10			0.245803
$584$	−2.69903e10	−	9.93290e10i	−0.232036	−	0.853935i
$585$		0			0
$586$	1.16958e10	+	1.31900e11i	0.0991831	+	1.11855i
$587$	3.75401e10			0.316187			0.158093	−	0.987424i	$-0.449465\pi$
$587$	3.75401e10			0.316187			0.158093	+	0.987424i	$0.449465\pi$
$588$	−1.17720e10	+	2.10422e9i	−0.0984783	+	0.0176028i
$589$	3.25719e10			0.270634
$590$		0			0
$591$		−	7.44822e10i		−	0.610524i
$592$	−3.81806e10	−	1.03388e11i	−0.310854	−	0.841748i
$593$			1.04118e11i			0.841994i	0.907062	+	0.420997i	$0.138320\pi$
$593$			1.04118e11i			0.841994i	−0.907062	+	0.420997i	$0.861680\pi$
$594$	1.61697e9	+	1.82355e10i	0.0129884	+	0.146478i
$595$		0			0
$596$	7.52248e10	−	1.34463e10i	0.596178	−	0.106566i
$597$			7.27337e10i			0.572583i
$598$	3.37134e9	+	3.80207e10i	0.0263632	+	0.297314i
$599$		−	4.81442e10i		−	0.373970i	−0.982363	−	0.186985i	$-0.940128\pi$
$599$		−	4.81442e10i		−	0.373970i	0.982363	−	0.186985i	$-0.0598716\pi$
$600$		0			0
$601$	−1.48443e11			−1.13779			−0.568896	−	0.822410i	$-0.692629\pi$
$601$	−1.48443e11			−1.13779			−0.568896	+	0.822410i	$0.692629\pi$
$602$	−1.06748e11	+	9.46546e9i	−0.812780	+	0.0720702i
$603$	7.64369e9			0.0578141
$604$	3.26594e10	+	1.82712e11i	0.245392	+	1.37284i
$605$		0			0
$606$	−4.15672e10	+	3.68581e9i	−0.308219	+	0.0273302i
$607$	−5.44460e10			−0.401062			−0.200531	−	0.979687i	$-0.564267\pi$
$607$	−5.44460e10			−0.401062			−0.200531	+	0.979687i	$0.564267\pi$
$608$	1.08372e11	+	2.28888e11i	0.793054	+	1.67498i
$609$	−7.67419e10			−0.557909
$610$		0			0
$611$		−	2.33866e11i		−	1.67804i
$612$	−1.08729e10	−	6.08279e10i	−0.0775065	−	0.433608i
$613$			1.16278e11i			0.823484i	0.911301	+	0.411742i	$0.135079\pi$
$613$			1.16278e11i			0.823484i	−0.911301	+	0.411742i	$0.864921\pi$
$614$	−1.23289e11	+	1.09322e10i	−0.867465	+	0.0769192i
$615$		0			0
$616$	7.02607e9	+	2.58572e10i	0.0487966	+	0.179580i
$617$			4.87411e10i			0.336321i	0.985760	+	0.168161i	$0.0537828\pi$
$617$			4.87411e10i			0.336321i	−0.985760	+	0.168161i	$0.946217\pi$
$618$	9.36240e10	−	8.30176e9i	0.641850	−	0.0569136i
$619$		−	4.92280e10i		−	0.335312i	−0.985846	−	0.167656i	$-0.946380\pi$
$619$		−	4.92280e10i		−	0.335312i	0.985846	−	0.167656i	$-0.0536198\pi$
$620$		0			0
$621$	−2.65910e10			−0.178800
$622$	1.52721e10	+	1.72233e11i	0.102033	+	1.15068i
$623$	−1.01839e11			−0.676022
$624$	−3.74888e10	−	1.01514e11i	−0.247265	−	0.669560i
$625$		0			0
$626$	6.68477e9	+	7.53882e10i	0.0435300	+	0.490915i
$627$	2.39775e10			0.155143
$628$	3.01935e10	+	1.68916e11i	0.194122	+	1.08601i
$629$	8.17731e10			0.522406
$630$		0			0
$631$			1.10376e11i			0.696240i	0.937450	+	0.348120i	$0.113180\pi$
$631$			1.10376e11i			0.696240i	−0.937450	+	0.348120i	$0.886820\pi$
$632$	2.09808e10	+	7.72132e10i	0.131509	+	0.483976i
$633$			1.15543e11i			0.719662i
$634$	−7.69850e9	−	8.68207e10i	−0.0476485	−	0.537361i
$635$		0			0
$636$	−2.05758e10	−	1.15111e11i	−0.125756	−	0.703539i
$637$			4.82999e10i			0.293352i
$638$	2.56039e9	+	2.88751e10i	0.0154534	+	0.174277i
$639$		−	1.02555e11i		−	0.615112i
$640$		0			0
$641$	2.15342e11			1.27554			0.637772	−	0.770225i	$-0.279856\pi$
$641$	2.15342e11			1.27554			0.637772	+	0.770225i	$0.279856\pi$
$642$	−1.54403e11	+	1.36911e10i	−0.908897	+	0.0805930i
$643$	−1.22051e11			−0.713996			−0.356998	−	0.934105i	$-0.616200\pi$
$643$	−1.22051e11			−0.713996			−0.356998	+	0.934105i	$0.616200\pi$
$644$	−3.83121e10	+	6.84821e9i	−0.222737	+	0.0398138i
$645$		0			0
$646$	−1.87165e11	+	1.65962e10i	−1.07472	+	0.0952966i
$647$	2.92452e11			1.66893			0.834463	−	0.551064i	$-0.185778\pi$
$647$	2.92452e11			1.66893			0.834463	+	0.551064i	$0.185778\pi$
$648$	−5.59838e10	+	1.52122e10i	−0.317514	+	0.0862767i
$649$	5.28916e10			0.298132
$650$		0			0
$651$		−	1.41916e10i		−	0.0790149i
$652$	−2.44631e11	+	4.37272e10i	−1.35369	+	0.241970i
$653$		−	2.80990e10i		−	0.154539i	−0.997010	−	0.0772696i	$-0.975380\pi$
$653$		−	2.80990e10i		−	0.154539i	0.997010	−	0.0772696i	$-0.0246202\pi$
$654$	3.77990e10	−	3.35169e9i	0.206619	−	0.0183211i
$655$		0			0
$656$	−4.68332e10	+	1.72953e10i	−0.252894	+	0.0933925i
$657$		−	1.24743e11i		−	0.669509i
$658$	2.37526e11	−	2.10618e10i	1.26709	−	0.112355i
$659$		−	2.51394e11i		−	1.33295i	−0.745529	−	0.666473i	$-0.767803\pi$
$659$		−	2.51394e11i		−	1.33295i	0.745529	−	0.666473i	$-0.232197\pi$
$660$		0			0
$661$	−2.53415e11			−1.32748			−0.663738	−	0.747965i	$-0.731031\pi$
$661$	−2.53415e11			−1.32748			−0.663738	+	0.747965i	$0.731031\pi$
$662$	1.22291e9	+	1.37915e10i	0.00636743	+	0.0718094i
$663$	8.02914e10			0.415542
$664$	9.37086e10	−	2.54631e10i	0.482067	−	0.130990i
$665$		0			0
$666$	−1.17974e10	−	1.33046e11i	−0.0599637	−	0.676247i
$667$	−4.21056e10			−0.212734
$668$	−2.01273e11	+	3.59771e10i	−1.01083	+	0.180684i
$669$	9.03242e10			0.450920
$670$		0			0
$671$			6.55116e10i			0.323168i
$672$	9.97271e10	−	4.72178e10i	0.489031	−	0.231542i
$673$		−	1.77857e11i		−	0.866981i	−0.901158	−	0.433491i	$-0.857282\pi$
$673$		−	1.77857e11i		−	0.866981i	0.901158	−	0.433491i	$-0.142718\pi$
$674$	1.22167e9	+	1.37775e10i	0.00591991	+	0.0667624i
$675$		0			0
$676$	−2.24687e11	+	4.01623e10i	−1.07595	+	0.192323i
$677$			2.43910e11i			1.16111i	0.814220	+	0.580556i	$0.197165\pi$
$677$			2.43910e11i			1.16111i	−0.814220	+	0.580556i	$0.802835\pi$
$678$	3.08464e9	+	3.47874e10i	0.0145977	+	0.164628i
$679$			2.49217e11i			1.17246i
$680$		0			0
$681$	4.31678e10			0.200711
$682$	−5.33978e9	+	4.73485e8i	−0.0246823	+	0.00218861i
$683$	2.74209e11			1.26008			0.630041	−	0.776562i	$-0.283038\pi$
$683$	2.74209e11			1.26008			0.630041	+	0.776562i	$0.283038\pi$
$684$	5.40045e10	+	3.02126e11i	0.246720	+	1.38027i
$685$		0			0
$686$	1.92873e11	−	1.71023e10i	0.870912	−	0.0772249i
$687$	2.51904e10			0.113086
$688$	1.56378e11	−	5.77495e10i	0.697944	−	0.257747i
$689$	−4.72295e11			−2.09573
$690$		0			0
$691$		−	1.07912e11i		−	0.473323i	−0.971592	−	0.236661i	$-0.923947\pi$
$691$		−	1.07912e11i		−	0.473323i	0.971592	−	0.236661i	$-0.0760532\pi$
$692$	2.70465e10	+	1.51311e11i	0.117947	+	0.659850i
$693$			3.24730e10i			0.140796i
$694$	1.75435e11	−	1.55560e10i	0.756272	−	0.0670596i
$695$		0			0
$696$	1.15197e11	−	3.13020e10i	0.490912	−	0.133394i
$697$		−	3.70421e10i		−	0.156951i
$698$	−3.18161e11	+	2.82118e10i	−1.34037	+	0.118853i
$699$		−	4.69280e10i		−	0.196573i
$700$		0			0
$701$	−1.00364e11			−0.415630			−0.207815	−	0.978168i	$-0.566635\pi$
$701$	−1.00364e11			−0.415630			−0.207815	+	0.978168i	$0.566635\pi$
$702$	−2.68938e10	−	3.03298e11i	−0.110740	−	1.24888i
$703$	−4.06159e11			−1.66293
$704$	−2.10936e10	−	3.59482e10i	−0.0858735	−	0.146348i
$705$		0			0
$706$	−1.87204e10	−	2.11121e11i	−0.0753521	−	0.849791i
$707$	−1.71855e11			−0.687837
$708$	−3.83251e10	−	2.14409e11i	−0.152528	−	0.853315i
$709$	4.36108e11			1.72587			0.862937	−	0.505311i	$-0.168622\pi$
$709$	4.36108e11			1.72587			0.862937	+	0.505311i	$0.168622\pi$
$710$		0			0
$711$			9.69690e10i			0.379450i
$712$	1.52869e11	−	4.15386e10i	0.594841	−	0.161634i
$713$		−	7.78647e9i		−	0.0301288i
$714$	7.23097e9	+	8.15481e10i	0.0278230	+	0.313777i
$715$		0			0
$716$	5.21829e10	+	2.91936e11i	0.198553	+	1.11080i
$717$		−	1.21958e11i		−	0.461459i
$718$	3.66986e9	+	4.13872e10i	0.0138087	+	0.155729i
$719$			3.29910e11i			1.23447i	0.786780	+	0.617234i	$0.211747\pi$
$719$			3.29910e11i			1.23447i	−0.786780	+	0.617234i	$0.788253\pi$
$720$		0			0
$721$	3.87079e11			1.43238
$722$	6.58956e11	−	5.84304e10i	2.42498	−	0.215026i
$723$	−1.12642e11			−0.412239
$724$	−2.00721e11	+	3.58784e10i	−0.730531	+	0.130581i
$725$		0			0
$726$	1.32594e11	−	1.17573e10i	0.477285	−	0.0423215i
$727$	−2.87638e11			−1.02969			−0.514847	−	0.857282i	$-0.672151\pi$
$727$	−2.87638e11			−1.02969			−0.514847	+	0.857282i	$0.672151\pi$
$728$	−1.16859e11	−	4.30064e11i	−0.416043	−	1.53111i
$729$	5.04496e10			0.178627
$730$		0			0
$731$			1.23685e11i			0.433158i
$732$	2.65567e11	−	4.74695e10i	0.924974	−	0.165337i
$733$			7.34639e10i			0.254483i	0.991872	+	0.127241i	$0.0406123\pi$
$733$			7.34639e10i			0.254483i	−0.991872	+	0.127241i	$0.959388\pi$
$734$	−5.77462e10	+	5.12043e9i	−0.198948	+	0.0176410i
$735$		0			0
$736$	5.47168e10	−	2.59068e10i	0.186470	−	0.0882881i
$737$			3.82540e9i			0.0129660i
$738$	−6.02681e10	+	5.34405e9i	−0.203171	+	0.0180154i
$739$			3.53166e11i			1.18413i	0.805889	+	0.592067i	$0.201688\pi$
$739$			3.53166e11i			1.18413i	−0.805889	+	0.592067i	$0.798312\pi$
$740$		0			0
$741$	−3.98800e11			−1.32276
$742$	−4.25344e10	−	4.79687e11i	−0.140322	−	1.58249i
$743$	2.51184e11			0.824208			0.412104	−	0.911137i	$-0.364794\pi$
$743$	2.51184e11			0.824208			0.412104	+	0.911137i	$0.364794\pi$
$744$	5.78858e9	+	2.13030e10i	0.0188921	+	0.0695263i
$745$		0			0
$746$	−5.86705e9	−	6.61663e10i	−0.0189437	−	0.213639i
$747$	1.17685e11			0.377954
$748$	3.04422e10	−	5.44149e9i	0.0972456	−	0.0173825i
$749$	−6.38363e11			−2.02834
$750$		0			0
$751$			5.06685e11i			1.59286i	0.604729	+	0.796431i	$0.293281\pi$
$751$			5.06685e11i			1.59286i	−0.604729	+	0.796431i	$0.706719\pi$
$752$	−3.47958e11	+	1.28499e11i	−1.08807	+	0.401818i
$753$		−	1.16918e10i		−	0.0363666i
$754$	−4.25852e10	−	4.80259e11i	−0.131757	−	1.48590i
$755$		0			0
$756$	3.05623e11	−	5.46295e10i	0.935620	−	0.167240i
$757$		−	9.66712e10i		−	0.294384i	−0.989108	−	0.147192i	$-0.952977\pi$
$757$		−	9.66712e10i		−	0.294384i	0.989108	−	0.147192i	$-0.0470235\pi$
$758$	−2.67873e10	−	3.02097e11i	−0.0811432	−	0.915102i
$759$		−	5.73192e9i		−	0.0172716i
$760$		0			0
$761$	5.18752e11			1.54675			0.773376	−	0.633947i	$-0.218566\pi$
$761$	5.18752e11			1.54675			0.773376	+	0.633947i	$0.218566\pi$
$762$	−1.28079e11	+	1.13570e10i	−0.379892	+	0.0336855i
$763$	1.56276e11			0.461100
$764$	−8.29940e10	−	4.64307e11i	−0.243598	−	1.36280i
$765$		0			0
$766$	1.41473e11	−	1.25446e10i	0.410920	−	0.0364368i
$767$	−8.79708e11			−2.54189
$768$	−1.30440e11	+	1.11556e11i	−0.374944	+	0.320661i
$769$	−1.06291e11			−0.303943			−0.151972	−	0.988385i	$-0.548562\pi$
$769$	−1.06291e11			−0.303943			−0.151972	+	0.988385i	$0.548562\pi$
$770$		0			0
$771$			1.21384e11i			0.343514i
$772$	1.05497e11	+	5.90200e11i	0.297010	+	1.66161i
$773$		−	9.89630e10i		−	0.277176i	−0.990350	−	0.138588i	$-0.955744\pi$
$773$		−	9.89630e10i		−	0.277176i	0.990350	−	0.138588i	$-0.0442563\pi$
$774$	2.01237e11	−	1.78439e10i	0.560717	−	0.0497195i
$775$		0			0
$776$	−1.01652e11	−	3.74098e11i	−0.280330	−	1.03167i
$777$			1.76964e11i			0.485514i
$778$	3.27666e11	−	2.90546e10i	0.894363	−	0.0793043i
$779$			1.83984e11i			0.499610i
$780$		0			0
$781$	5.13253e10			0.137952
$782$	3.96738e9	+	4.47426e10i	0.0106091	+	0.119645i
$783$	3.35885e11			0.893601
$784$	7.18632e10	−	2.65387e10i	0.190214	−	0.0702451i
$785$		0			0
$786$	2.46436e10	+	2.77921e11i	0.0645674	+	0.728166i
$787$	3.29755e11			0.859592			0.429796	−	0.902926i	$-0.358585\pi$
$787$	3.29755e11			0.859592			0.429796	+	0.902926i	$0.358585\pi$
$788$	8.39562e10	+	4.69690e11i	0.217745	+	1.21817i
$789$	6.78670e10			0.175126
$790$		0			0
$791$			1.43825e11i			0.367391i
$792$	−1.32453e10	−	4.87450e10i	−0.0336636	−	0.123888i
$793$		−	1.08961e12i		−	2.75535i
$794$	2.89519e10	+	3.26509e11i	0.0728443	+	0.821509i
$795$		0			0
$796$	−8.19853e10	−	4.58664e11i	−0.204213	−	1.14246i
$797$		−	6.85369e10i		−	0.169860i	−0.996387	−	0.0849300i	$-0.972933\pi$
$797$		−	6.85369e10i		−	0.169860i	0.996387	−	0.0849300i	$-0.0270667\pi$
$798$	−3.59156e10	−	4.05042e11i	−0.0885668	−	0.998822i
$799$		−	2.75213e11i		−	0.675277i
$800$		0			0
$801$	1.91983e11			0.466371
$802$	1.16435e11	−	1.03245e10i	0.281441	−	0.0249557i
$803$	6.24297e10			0.150151
$804$	1.55072e10	−	2.77187e9i	0.0371115	−	0.00663360i
$805$		0			0
$806$	8.88128e10	−	7.87514e9i	0.210443	−	0.0186603i
$807$	−3.47891e10			−0.0820256
$808$	2.57971e11	−	7.00974e10i	0.605237	−	0.164459i
$809$	7.62508e11			1.78012			0.890062	−	0.455840i	$-0.150661\pi$
$809$	7.62508e11			1.78012			0.890062	+	0.455840i	$0.150661\pi$
$810$		0			0
$811$			4.40805e11i			1.01897i	0.860478	+	0.509487i	$0.170165\pi$
$811$			4.40805e11i			1.01897i	−0.860478	+	0.509487i	$0.829835\pi$
$812$	4.83940e11	−	8.65034e10i	1.11319	−	0.198980i
$813$			2.94459e11i			0.674005i
$814$	6.65850e10	−	5.90418e9i	0.151663	−	0.0134481i
$815$		0			0
$816$	−4.41167e10	−	1.19462e11i	−0.0995044	−	0.269444i
$817$		−	6.14330e11i		−	1.37884i
$818$	−1.68761e11	+	1.49642e10i	−0.376927	+	0.0334226i
$819$		−	5.40100e11i		−	1.20043i
$820$		0			0
$821$	−2.67657e11			−0.589123			−0.294562	−	0.955632i	$-0.595174\pi$
$821$	−2.67657e11			−0.589123			−0.294562	+	0.955632i	$0.595174\pi$
$822$	−2.53176e10	−	2.85522e11i	−0.0554544	−	0.625393i
$823$	−3.84869e11			−0.838906			−0.419453	−	0.907777i	$-0.637778\pi$
$823$	−3.84869e11			−0.838906			−0.419453	+	0.907777i	$0.637778\pi$
$824$	−5.81042e11	+	1.57884e11i	−1.26037	+	0.342476i
$825$		0			0
$826$	−7.92257e10	−	8.93477e11i	−0.170195	−	1.91939i
$827$	−4.88174e11			−1.04364			−0.521822	−	0.853054i	$-0.674747\pi$
$827$	−4.88174e11			−1.04364			−0.521822	+	0.853054i	$0.674747\pi$
$828$	7.22246e10	−	1.29100e10i	0.153661	−	0.0274666i
$829$	1.47134e11			0.311526			0.155763	−	0.987794i	$-0.450216\pi$
$829$	1.47134e11			0.311526			0.155763	+	0.987794i	$0.450216\pi$
$830$		0			0
$831$			9.48464e10i			0.198892i
$832$	3.50834e11	+	5.97900e11i	0.732164	+	1.24777i
$833$			5.68392e10i			0.118050i
$834$	2.67622e10	+	3.01813e11i	0.0553168	+	0.623841i
$835$		0			0
$836$	−1.51204e11	+	2.70273e10i	−0.309555	+	0.0553323i
$837$			6.21142e10i			0.126558i
$838$	−3.68896e9	−	4.16027e10i	−0.00748046	−	0.0843617i
$839$		−	4.39919e11i		−	0.887821i	−0.896071	−	0.443910i	$-0.853591\pi$
$839$		−	4.39919e11i		−	0.887821i	0.896071	−	0.443910i	$-0.146409\pi$
$840$		0			0
$841$	3.16120e10			0.0631929
$842$	−1.48140e11	+	1.31357e10i	−0.294729	+	0.0261340i
$843$	−2.20086e11			−0.435794
$844$	−1.30240e11	−	7.28622e11i	−0.256669	−	1.43593i
$845$		0			0
$846$	−4.47776e11	+	3.97049e10i	−0.874137	+	0.0775108i
$847$	5.48198e11			1.06513
$848$	2.59506e11	+	7.02705e11i	0.501838	+	1.35891i
$849$	−1.82190e11			−0.350666
$850$		0			0
$851$			9.70941e10i			0.185129i
$852$	−3.71901e10	−	2.08059e11i	−0.0705780	−	0.394847i
$853$			6.98819e11i			1.31998i	0.751273	+	0.659992i	$0.229440\pi$
$853$			6.98819e11i			1.31998i	−0.751273	+	0.659992i	$0.770560\pi$
$854$	1.10666e12	−	9.81291e10i	2.08058	−	0.184487i
$855$		0			0
$856$	9.58242e11	−	2.60379e11i	1.78476	−	0.484966i
$857$		−	3.28226e10i		−	0.0608485i	−0.999537	−	0.0304242i	$-0.990314\pi$
$857$		−	3.28226e10i		−	0.0608485i	0.999537	−	0.0304242i	$-0.00968583\pi$
$858$	6.53785e10	−	5.79719e9i	0.120638	−	0.0106972i
$859$			6.28697e11i			1.15470i	0.816497	+	0.577349i	$0.195913\pi$
$859$			6.28697e11i			1.15470i	−0.816497	+	0.577349i	$0.804087\pi$
$860$		0			0
$861$	8.01623e10			0.145867
$862$	−2.63646e10	−	2.97330e11i	−0.0477521	−	0.538529i
$863$	7.90308e11			1.42480			0.712399	−	0.701775i	$-0.247609\pi$
$863$	7.90308e11			1.42480			0.712399	+	0.701775i	$0.247609\pi$
$864$	−4.36487e11	+	2.06664e11i	−0.783278	+	0.370859i
$865$		0			0
$866$	2.35962e10	+	2.66109e11i	0.0419537	+	0.473138i
$867$	−1.84281e11			−0.326140
$868$	1.59968e10	+	8.94936e10i	0.0281809	+	0.157657i
$869$	−4.85296e10			−0.0850997
$870$		0			0
$871$		−	6.36251e10i		−	0.110549i
$872$	−2.34586e11	+	6.37430e10i	−0.405728	+	0.110247i
$873$		−	4.69815e11i		−	0.808854i
$874$	−1.97056e10	−	2.22232e11i	−0.0337710	−	0.380857i
$875$		0			0
$876$	−4.52364e10	−	2.53074e11i	−0.0768195	−	0.429764i
$877$		−	7.21024e10i		−	0.121885i	−0.998141	−	0.0609427i	$-0.980589\pi$
$877$		−	7.21024e10i		−	0.121885i	0.998141	−	0.0609427i	$-0.0194107\pi$
$878$	7.74940e9	+	8.73947e10i	0.0130404	+	0.147064i
$879$			3.30733e11i			0.554015i
$880$		0			0
$881$	−5.33265e11			−0.885196			−0.442598	−	0.896720i	$-0.645943\pi$
$881$	−5.33265e11			−0.885196			−0.442598	+	0.896720i	$0.645943\pi$
$882$	9.24783e10	−	8.20017e9i	0.152815	−	0.0135503i
$883$	−3.49301e11			−0.574589			−0.287295	−	0.957842i	$-0.592756\pi$
$883$	−3.49301e11			−0.574589			−0.287295	+	0.957842i	$0.592756\pi$
$884$	−5.06324e11	+	9.05043e10i	−0.829123	+	0.148204i
$885$		0			0
$886$	9.52761e10	−	8.44825e9i	0.154614	−	0.0137098i
$887$	2.17981e11			0.352148			0.176074	−	0.984377i	$-0.443660\pi$
$887$	2.17981e11			0.352148			0.176074	+	0.984377i	$0.443660\pi$
$888$	−7.21812e10	−	2.65640e11i	−0.116084	−	0.427210i
$889$	−5.29532e11			−0.847784
$890$		0			0
$891$		−	3.51866e10i		−	0.0558299i
$892$	−5.69591e11	+	1.01813e11i	−0.899712	+	0.160822i
$893$			1.36696e12i			2.14956i
$894$	1.90117e11	−	1.68579e10i	0.297626	−	0.0263909i
$895$		0			0
$896$	−5.75663e11	+	4.10171e11i	−0.893174	+	0.636405i
$897$			9.53348e10i			0.147259i
$898$	−4.96765e11	+	4.40488e10i	−0.763916	+	0.0677374i
$899$			9.83549e10i			0.150577i
$900$		0			0
$901$	−5.55795e11			−0.843365
$902$	−2.67451e9	−	3.01621e10i	−0.00404034	−	0.0455654i
$903$	−2.67665e11			−0.402569
$904$	−5.86642e10	−	2.15895e11i	−0.0878414	−	0.323272i
$905$		0			0
$906$	4.09459e10	+	4.61772e11i	0.0607712	+	0.685354i
$907$	6.26742e9			0.00926104			0.00463052	−	0.999989i	$-0.498526\pi$
$907$	6.26742e9			0.00926104			0.00463052	+	0.999989i	$0.498526\pi$
$908$	−2.72220e11	+	4.86587e10i	−0.400476	+	0.0715842i
$909$	3.23975e11			0.474522
$910$		0			0
$911$		−	6.22008e11i		−	0.903073i	−0.892253	−	0.451536i	$-0.850876\pi$
$911$		−	6.22008e11i		−	0.903073i	0.892253	−	0.451536i	$-0.149124\pi$
$912$	2.19123e11	+	5.93356e11i	0.316745	+	0.857701i
$913$			5.88972e10i			0.0847640i
$914$	−6.13279e9	−	6.91632e10i	−0.00878766	−	0.0991038i
$915$		0			0
$916$	−1.58852e11	+	2.83945e10i	−0.225638	+	0.0403323i
$917$			1.14904e12i			1.62501i
$918$	−3.16486e10	−	3.56921e11i	−0.0445640	−	0.502575i
$919$			8.27760e11i			1.16049i	0.814441	+	0.580246i	$0.197044\pi$
$919$			8.27760e11i			1.16049i	−0.814441	+	0.580246i	$0.802956\pi$
$920$		0			0
$921$	−3.09142e11			−0.429654
$922$	8.22635e11	−	7.29441e10i	1.13837	−	0.100941i
$923$	−8.53656e11			−1.17619
$924$	1.17759e10	+	6.58797e10i	0.0161549	+	0.0903782i
$925$		0			0
$926$	−1.09462e12	+	9.70610e10i	−1.48874	+	0.132008i
$927$	−7.29708e11			−0.988167
$928$	−6.91156e11	+	3.27242e11i	−0.931932	+	0.441243i
$929$	6.50031e11			0.872713			0.436356	−	0.899774i	$-0.356269\pi$
$929$	6.50031e11			0.872713			0.436356	+	0.899774i	$0.356269\pi$
$930$		0			0
$931$		−	2.82315e11i		−	0.375781i
$932$	5.28971e10	+	2.95931e11i	0.0701082	+	0.392218i
$933$			4.31866e11i			0.569932i
$934$	−3.42012e11	+	3.03266e10i	−0.449421	+	0.0398508i
$935$		0			0
$936$	2.20299e11	+	8.10740e11i	0.287018	+	1.05628i
$937$			6.60322e11i			0.856639i	0.903627	+	0.428319i	$0.140894\pi$
$937$			6.60322e11i			0.856639i	−0.903627	+	0.428319i	$0.859106\pi$
$938$	6.46209e10	−	5.73002e9i	0.0834760	−	0.00740193i
$939$			1.89032e11i			0.243149i
$940$		0			0
$941$	−2.13315e11			−0.272059			−0.136029	−	0.990705i	$-0.543434\pi$
$941$	−2.13315e11			−0.272059			−0.136029	+	0.990705i	$0.543434\pi$
$942$	3.78543e10	+	4.26906e11i	0.0480741	+	0.542161i
$943$	4.39823e10			0.0556200
$944$	4.83362e11	+	1.30888e12i	0.608674	+	1.64820i
$945$		0			0
$946$	8.93027e9	+	1.00712e11i	0.0111506	+	0.125753i
$947$	−1.23955e10			−0.0154121			−0.00770607	−	0.999970i	$-0.502453\pi$
$947$	−1.23955e10			−0.0154121			−0.00770607	+	0.999970i	$0.502453\pi$
$948$	3.51644e10	+	1.96726e11i	0.0435382	+	0.243573i
$949$	−1.03835e12			−1.28020
$950$		0			0
$951$		−	2.17698e11i		−	0.266154i
$952$	−1.37520e11	−	5.06098e11i	−0.167424	−	0.616150i
$953$		−	1.59801e12i		−	1.93734i	−0.248344	−	0.968672i	$-0.579886\pi$
$953$		−	1.59801e12i		−	1.93734i	0.248344	−	0.968672i	$-0.420114\pi$
$954$	8.01843e10	+	9.04288e11i	0.0968046	+	1.09172i
$955$		0			0
$956$	1.37471e11	+	7.69076e11i	0.164581	+	0.920741i
$957$			7.24029e10i			0.0863193i
$958$	1.16534e11	+	1.31423e12i	0.138354	+	1.56030i
$959$		−	1.18046e12i		−	1.39566i
$960$		0			0
$961$	8.34703e11			0.978674
$962$	−1.10746e12	+	9.81999e10i	−1.29309	+	0.114660i
$963$	1.20342e12			1.39930
$964$	7.10332e11	−	1.26970e11i	0.822533	−	0.147026i
$965$		0			0
$966$	−9.68270e10	+	8.58577e9i	−0.111196	+	0.00985986i
$967$	4.54304e11			0.519566			0.259783	−	0.965667i	$-0.416349\pi$
$967$	4.54304e11			0.519566			0.259783	+	0.965667i	$0.416349\pi$
$968$	−8.22896e11	+	2.23602e11i	−0.937224	+	0.254668i
$969$	−4.69307e11			−0.532306
$970$		0			0
$971$		−	3.98175e11i		−	0.447917i	−0.974599	−	0.223958i	$-0.928102\pi$
$971$		−	3.98175e11i		−	0.447917i	0.974599	−	0.223958i	$-0.0718979\pi$
$972$	−9.04143e11	+	1.61614e11i	−1.01291	+	0.181056i
$973$			1.24782e12i			1.39219i
$974$	−4.69636e10	+	4.16432e9i	−0.0521826	+	0.00462710i
$975$		0			0
$976$	−1.62118e12	+	5.98693e11i	−1.78662	+	0.659789i
$977$		−	1.61846e12i		−	1.77633i	−0.459525	−	0.888165i	$-0.651980\pi$
$977$		−	1.61846e12i		−	1.77633i	0.459525	−	0.888165i	$-0.348020\pi$
$978$	−6.18260e11	+	5.48219e10i	−0.675796	+	0.0599237i
$979$			9.60806e10i			0.104594i
$980$		0			0
$981$	−2.94607e11			−0.318102
$982$	−1.15573e11	−	1.30339e12i	−0.124282	−	1.40161i
$983$	−7.83368e10			−0.0838980			−0.0419490	−	0.999120i	$-0.513357\pi$
$983$	−7.83368e10			−0.0838980			−0.0419490	+	0.999120i	$0.513357\pi$
$984$	−1.20331e11	+	3.26971e10i	−0.128351	+	0.0348762i
$985$		0			0
$986$	−5.01141e10	−	5.65167e11i	−0.0530215	−	0.597956i
$987$	5.95585e11			0.627589
$988$	2.51486e12	−	4.49526e11i	2.63929	−	0.471767i
$989$	−1.46858e11			−0.153502
$990$		0			0
$991$		−	1.11925e12i		−	1.16046i	−0.814451	−	0.580232i	$-0.802962\pi$
$991$		−	1.11925e12i		−	1.16046i	0.814451	−	0.580232i	$-0.197038\pi$
$992$	−6.05159e10	−	1.27813e11i	−0.0624917	−	0.131987i
$993$			3.45816e10i			0.0355671i
$994$	−7.68795e10	−	8.67017e11i	−0.0787526	−	0.888142i
$995$		0			0
$996$	2.38754e11	−	4.26767e10i	0.242612	−	0.0433665i
$997$			8.38483e11i			0.848621i	0.905517	+	0.424311i	$0.139483\pi$
$997$			8.38483e11i			0.848621i	−0.905517	+	0.424311i	$0.860517\pi$
$998$	−6.63583e10	−	7.48363e11i	−0.0668918	−	0.754380i
$999$		−	7.74539e11i		−	0.777645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.c.99.2		32
4.3	odd	2	inner	100.9.d.c.99.32		32
5.2	odd	4		20.9.b.a.11.7	✓	16
5.3	odd	4		100.9.b.d.51.10		16
5.4	even	2	inner	100.9.d.c.99.31		32
15.2	even	4		180.9.c.a.91.10		16
20.3	even	4		100.9.b.d.51.9		16
20.7	even	4		20.9.b.a.11.8	yes	16
20.19	odd	2	inner	100.9.d.c.99.1		32
40.27	even	4		320.9.b.d.191.11		16
40.37	odd	4		320.9.b.d.191.6		16
60.47	odd	4		180.9.c.a.91.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.7	✓	16	5.2	odd	4
20.9.b.a.11.8	yes	16	20.7	even	4
100.9.b.d.51.9		16	20.3	even	4
100.9.b.d.51.10		16	5.3	odd	4
100.9.d.c.99.1		32	20.19	odd	2	inner
100.9.d.c.99.2		32	1.1	even	1	trivial
100.9.d.c.99.31		32	5.4	even	2	inner
100.9.d.c.99.32		32	4.3	odd	2	inner
180.9.c.a.91.9		16	60.47	odd	4
180.9.c.a.91.10		16	15.2	even	4
320.9.b.d.191.6		16	40.37	odd	4
320.9.b.d.191.11		16	40.27	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)

\(f(q)\)	\(=\)	\(q+(-15.9375 + 1.41320i) q^{2} -39.9624 q^{3} +(252.006 - 45.0455i) q^{4} +(636.899 - 56.4746i) q^{6} +2633.20 q^{7} +(-3952.68 + 1074.04i) q^{8} -4964.01 q^{9} -2484.31i q^{11} +(-10070.7 + 1800.13i) q^{12} +41319.8i q^{13} +(-41966.5 + 3721.22i) q^{14} +(61477.8 - 22703.5i) q^{16} +48625.0i q^{17} +(79113.7 - 7015.11i) q^{18} -241516. i q^{19} -105229. q^{21} +(3510.82 + 39593.7i) q^{22} -57735.4 q^{23} +(157958. - 42921.4i) q^{24} +(-58392.9 - 658533. i) q^{26} +460567. q^{27} +(663581. - 118614. i) q^{28} +729286. q^{29} +134865. i q^{31} +(-947716. + 448716. i) q^{32} +99279.1i q^{33} +(-68716.6 - 774960. i) q^{34} +(-1.25096e6 + 223606. i) q^{36} -1.68171e6i q^{37} +(341309. + 3.84915e6i) q^{38} -1.65124e6i q^{39} -761790. q^{41} +(1.67708e6 - 148709. i) q^{42} +2.54364e6 q^{43} +(-111907. - 626061. i) q^{44} +(920156. - 81591.4i) q^{46} -5.65990e6 q^{47} +(-2.45680e6 + 907284. i) q^{48} +1.16893e6 q^{49} -1.94317e6i q^{51} +(1.86127e6 + 1.04128e7i) q^{52} +1.14302e7i q^{53} +(-7.34027e6 + 650871. i) q^{54} +(-1.04082e7 + 2.82817e6i) q^{56} +9.65155e6i q^{57} +(-1.16230e7 + 1.03062e6i) q^{58} +2.12902e7i q^{59} -2.63701e7 q^{61} +(-190590. - 2.14940e6i) q^{62} -1.30712e7 q^{63} +(1.44701e7 - 8.49070e6i) q^{64} +(-140301. - 1.58226e6i) q^{66} -1.53982e6 q^{67} +(2.19034e6 + 1.22538e7i) q^{68} +2.30724e6 q^{69} +2.06597e7i q^{71} +(1.96211e7 - 5.33157e6i) q^{72} +2.51296e7i q^{73} +(2.37658e6 + 2.68022e7i) q^{74} +(-1.08792e7 - 6.08634e7i) q^{76} -6.54169e6i q^{77} +(2.33352e6 + 2.63165e7i) q^{78} -1.95344e7i q^{79} +1.41635e7 q^{81} +(1.21410e7 - 1.07656e6i) q^{82} -2.37076e7 q^{83} +(-2.65183e7 + 4.74009e6i) q^{84} +(-4.05392e7 + 3.59466e6i) q^{86} -2.91440e7 q^{87} +(2.66826e6 + 9.81968e6i) q^{88} -3.86749e7 q^{89} +1.08803e8i q^{91} +(-1.45497e7 + 2.60072e6i) q^{92} -5.38951e6i q^{93} +(9.02045e7 - 7.99855e6i) q^{94} +(3.78730e7 - 1.79317e7i) q^{96} +9.46443e7i q^{97} +(-1.86298e7 + 1.65192e6i) q^{98} +1.23322e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) \) 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