LMFDB - Embedded newform 361.3.f.k.299.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(116,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("361.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			299.11
Character	$\chi$	$=$	361.299
Dual form			361.3.f.k.262.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.172450 - 0.473803i) q^{2} +(5.47876 + 0.966054i) q^{3} +(2.86943 - 2.40774i) q^{4} +(2.53204 + 2.12463i) q^{5} +(-0.487095 - 2.76245i) q^{6} +(-2.51371 - 4.35388i) q^{7} +(-3.38227 - 1.95275i) q^{8} +(20.6264 + 7.50738i) q^{9} +O(q^{10})$	\(q+(-0.172450 - 0.473803i) q^{2} +(5.47876 + 0.966054i) q^{3} +(2.86943 - 2.40774i) q^{4} +(2.53204 + 2.12463i) q^{5} +(-0.487095 - 2.76245i) q^{6} +(-2.51371 - 4.35388i) q^{7} +(-3.38227 - 1.95275i) q^{8} +(20.6264 + 7.50738i) q^{9} +(0.570007 - 1.56608i) q^{10} +(-5.32930 + 9.23062i) q^{11} +(18.0469 - 10.4194i) q^{12} +(-4.09063 + 0.721288i) q^{13} +(-1.62939 + 1.94183i) q^{14} +(11.8199 + 14.0864i) q^{15} +(2.25984 - 12.8162i) q^{16} +(1.92127 - 0.699283i) q^{17} -11.0675i q^{18} +12.3811 q^{20} +(-9.56595 - 26.2822i) q^{21} +(5.29254 + 0.933217i) q^{22} +(7.37523 - 6.18855i) q^{23} +(-16.6442 - 13.9661i) q^{24} +(-2.44405 - 13.8609i) q^{25} +(1.04718 + 1.81377i) q^{26} +(62.3929 + 36.0225i) q^{27} +(-17.6959 - 6.44078i) q^{28} +(-9.32536 + 25.6212i) q^{29} +(4.63585 - 8.02954i) q^{30} +(-26.7556 + 15.4473i) q^{31} +(-21.8467 + 3.85217i) q^{32} +(-38.1152 + 45.4240i) q^{33} +(-0.662646 - 0.789711i) q^{34} +(2.88557 - 16.3649i) q^{35} +(77.2616 - 28.1209i) q^{36} +19.3174i q^{37} -23.1084 q^{39} +(-4.41515 - 12.1305i) q^{40} +(-62.7733 - 11.0686i) q^{41} +(-10.8030 + 9.06476i) q^{42} +(-51.1046 - 42.8818i) q^{43} +(6.93285 + 39.3181i) q^{44} +(36.2763 + 62.8324i) q^{45} +(-4.20402 - 2.42719i) q^{46} +(23.4295 + 8.52763i) q^{47} +(24.7622 - 68.0337i) q^{48} +(11.8625 - 20.5465i) q^{49} +(-6.14586 + 3.54832i) q^{50} +(11.2017 - 1.97516i) q^{51} +(-10.0011 + 11.9188i) q^{52} +(40.0061 + 47.6775i) q^{53} +(6.30793 - 35.7741i) q^{54} +(-33.1057 + 12.0495i) q^{55} +19.6346i q^{56} +13.7476 q^{58} +(5.40126 + 14.8398i) q^{59} +(67.8328 + 11.9608i) q^{60} +(51.6764 - 43.3616i) q^{61} +(11.9330 + 10.0130i) q^{62} +(-19.1625 - 108.676i) q^{63} +(-20.4351 - 35.3947i) q^{64} +(-11.8901 - 6.86475i) q^{65} +(28.0950 + 10.2258i) q^{66} +(-19.7767 + 54.3360i) q^{67} +(3.82924 - 6.63244i) q^{68} +(46.3856 - 26.7808i) q^{69} +(-8.25136 + 1.45494i) q^{70} +(72.7304 - 86.6767i) q^{71} +(-55.1038 - 65.6701i) q^{72} +(-16.7860 + 95.1980i) q^{73} +(9.15264 - 3.33129i) q^{74} -78.3016i q^{75} +53.5853 q^{77} +(3.98505 + 10.9488i) q^{78} +(48.6512 + 8.57853i) q^{79} +(32.9517 - 27.6497i) q^{80} +(155.703 + 130.651i) q^{81} +(5.58092 + 31.6510i) q^{82} +(-48.0685 - 83.2571i) q^{83} +(-90.7295 - 52.3827i) q^{84} +(6.35044 + 2.31137i) q^{85} +(-11.5046 + 31.6085i) q^{86} +(-75.8429 + 131.364i) q^{87} +(36.0502 - 20.8136i) q^{88} +(-48.5394 + 8.55881i) q^{89} +(23.5143 - 28.0233i) q^{90} +(13.4231 + 15.9970i) q^{91} +(6.26229 - 35.5152i) q^{92} +(-161.510 + 58.7849i) q^{93} -12.5716i q^{94} -123.415 q^{96} +(-13.4988 - 37.0877i) q^{97} +(-11.7807 - 2.07725i) q^{98} +(-179.222 + 150.385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 24 q^{7}+O(q^{10}) $ 144 * q - 24 * q^7	$ 144 q - 24 q^{7} + 192 q^{11} + 528 q^{20} - 228 q^{26} + 1440 q^{30} + 408 q^{39} + 264 q^{45} - 336 q^{49} + 216 q^{58} + 24 q^{64} + 480 q^{68} - 144 q^{77} + 1704 q^{83} - 3216 q^{87} - 3624 q^{96}+O(q^{100}) $ 144 * q - 24 * q^7 + 192 * q^11 + 528 * q^20 - 228 * q^26 + 1440 * q^30 + 408 * q^39 + 264 * q^45 - 336 * q^49 + 216 * q^58 + 24 * q^64 + 480 * q^68 - 144 * q^77 + 1704 * q^83 - 3216 * q^87 - 3624 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.172450	−	0.473803i	−0.0862252	−	0.236902i	0.889085	−	0.457743i	$-0.151342\pi$
$2$	−0.172450	−	0.473803i	−0.0862252	−	0.236902i	−0.975310	+	0.220841i	$0.929120\pi$
$3$	5.47876	+	0.966054i	1.82625	+	0.322018i	0.978164	−	0.207834i	$-0.0666413\pi$
$3$	5.47876	+	0.966054i	1.82625	+	0.322018i	0.848090	+	0.529852i	$0.177752\pi$
$4$	2.86943	−	2.40774i	0.717357	−	0.601934i
$5$	2.53204	+	2.12463i	0.506408	+	0.424926i	0.859863	−	0.510525i	$-0.170549\pi$
$5$	2.53204	+	2.12463i	0.506408	+	0.424926i	−0.353455	+	0.935451i	$0.614993\pi$
$6$	−0.487095	−	2.76245i	−0.0811825	−	0.460409i
$7$	−2.51371	−	4.35388i	−0.359102	−	0.621982i	0.628709	−	0.777640i	$-0.283584\pi$
$7$	−2.51371	−	4.35388i	−0.359102	−	0.621982i	−0.987811	+	0.155658i	$0.950250\pi$
$8$	−3.38227	−	1.95275i	−0.422783	−	0.244094i
$9$	20.6264	+	7.50738i	2.29182	+	0.834153i
$10$	0.570007	−	1.56608i	0.0570007	−	0.156608i
$11$	−5.32930	+	9.23062i	−0.484482	+	0.839147i	−0.999841	−	0.0178271i	$-0.994325\pi$
$11$	−5.32930	+	9.23062i	−0.484482	+	0.839147i	0.515359	+	0.856974i	$0.327658\pi$
$12$	18.0469	−	10.4194i	1.50391	−	0.868283i
$13$	−4.09063	+	0.721288i	−0.314664	+	0.0554837i	−0.328750	−	0.944417i	$-0.606627\pi$
$13$	−4.09063	+	0.721288i	−0.314664	+	0.0554837i	0.0140861	+	0.999901i	$0.495516\pi$
$14$	−1.62939	+	1.94183i	−0.116385	+	0.138702i
$15$	11.8199	+	14.0864i	0.787995	+	0.939096i
$16$	2.25984	−	12.8162i	0.141240	−	0.801011i
$17$	1.92127	−	0.699283i	0.113016	−	0.0411343i	−0.284893	−	0.958559i	$-0.591958\pi$
$17$	1.92127	−	0.699283i	0.113016	−	0.0411343i	0.397909	+	0.917425i	$0.369736\pi$
$18$		−	11.0675i		−	0.614860i
$19$		0			0
$19$		0			0
$20$	12.3811			0.619053
$21$	−9.56595	−	26.2822i	−0.455521	−	1.25153i
$22$	5.29254	+	0.933217i	0.240570	+	0.0424190i
$23$	7.37523	−	6.18855i	0.320662	−	0.269068i	−0.468220	−	0.883612i	$-0.655105\pi$
$23$	7.37523	−	6.18855i	0.320662	−	0.269068i	0.788882	+	0.614544i	$0.210660\pi$
$24$	−16.6442	−	13.9661i	−0.693507	−	0.581922i
$25$	−2.44405	−	13.8609i	−0.0977620	−	0.554436i
$26$	1.04718	+	1.81377i	0.0402761	+	0.0697603i
$27$	62.3929	+	36.0225i	2.31085	+	1.33417i
$28$	−17.6959	−	6.44078i	−0.631996	−	0.230028i
$29$	−9.32536	+	25.6212i	−0.321564	+	0.883490i	0.668605	+	0.743617i	$0.266892\pi$
$29$	−9.32536	+	25.6212i	−0.321564	+	0.883490i	−0.990169	+	0.139873i	$0.955331\pi$
$30$	4.63585	−	8.02954i	0.154528	−	0.267651i
$31$	−26.7556	+	15.4473i	−0.863082	+	0.498301i	−0.865043	−	0.501697i	$-0.832709\pi$
$31$	−26.7556	+	15.4473i	−0.863082	+	0.498301i	0.00196095	+	0.999998i	$0.499376\pi$
$32$	−21.8467	+	3.85217i	−0.682711	+	0.120380i
$33$	−38.1152	+	45.4240i	−1.15501	+	1.37648i
$34$	−0.662646	−	0.789711i	−0.0194896	−	0.0232268i
$35$	2.88557	−	16.3649i	0.0824449	−	0.467568i
$36$	77.2616	−	28.1209i	2.14616	−	0.781137i
$37$			19.3174i			0.522091i	0.965326	+	0.261046i	$0.0840673\pi$
$37$			19.3174i			0.522091i	−0.965326	+	0.261046i	$0.915933\pi$
$38$		0			0
$39$	−23.1084			−0.592522
$40$	−4.41515	−	12.1305i	−0.110379	−	0.303263i
$41$	−62.7733	−	11.0686i	−1.53106	−	0.269966i	−0.656288	−	0.754510i	$-0.727874\pi$
$41$	−62.7733	−	11.0686i	−1.53106	−	0.269966i	−0.874767	+	0.484544i	$0.838986\pi$
$42$	−10.8030	+	9.06476i	−0.257213	+	0.215828i
$43$	−51.1046	−	42.8818i	−1.18848	−	0.997252i	−0.999885	−	0.0151965i	$-0.995163\pi$
$43$	−51.1046	−	42.8818i	−1.18848	−	0.997252i	−0.188594	−	0.982055i	$-0.560393\pi$
$44$	6.93285	+	39.3181i	0.157565	+	0.893594i
$45$	36.2763	+	62.8324i	0.806140	+	1.39628i
$46$	−4.20402	−	2.42719i	−0.0913917	−	0.0527650i
$47$	23.4295	+	8.52763i	0.498500	+	0.181439i	0.579019	−	0.815314i	$-0.303436\pi$
$47$	23.4295	+	8.52763i	0.498500	+	0.181439i	−0.0805194	+	0.996753i	$0.525658\pi$
$48$	24.7622	−	68.0337i	0.515880	−	1.41737i
$49$	11.8625	−	20.5465i	0.242092	−	0.419316i
$50$	−6.14586	+	3.54832i	−0.122917	+	0.0709663i
$51$	11.2017	−	1.97516i	0.219641	−	0.0387287i
$52$	−10.0011	+	11.9188i	−0.192329	+	0.229208i
$53$	40.0061	+	47.6775i	0.754833	+	0.899575i	0.997509	−	0.0705325i	$-0.0224698\pi$
$53$	40.0061	+	47.6775i	0.754833	+	0.899575i	−0.242677	+	0.970107i	$0.578025\pi$
$54$	6.30793	−	35.7741i	0.116814	−	0.662483i
$55$	−33.1057	+	12.0495i	−0.601921	+	0.219081i
$56$			19.6346i			0.350618i
$57$		0			0
$58$	13.7476			0.237027
$59$	5.40126	+	14.8398i	0.0915468	+	0.251523i	0.977013	−	0.213182i	$-0.0683827\pi$
$59$	5.40126	+	14.8398i	0.0915468	+	0.251523i	−0.885466	+	0.464705i	$0.846160\pi$
$60$	67.8328	+	11.9608i	1.13055	+	0.199346i
$61$	51.6764	−	43.3616i	0.847154	−	0.710846i	−0.112007	−	0.993707i	$-0.535728\pi$
$61$	51.6764	−	43.3616i	0.847154	−	0.710846i	0.959161	+	0.282861i	$0.0912835\pi$
$62$	11.9330	+	10.0130i	0.192468	+	0.161500i
$63$	−19.1625	−	108.676i	−0.304167	−	1.72502i
$64$	−20.4351	−	35.3947i	−0.319299	−	0.553042i
$65$	−11.8901	−	6.86475i	−0.182925	−	0.105612i
$66$	28.0950	+	10.2258i	0.425682	+	0.154936i
$67$	−19.7767	+	54.3360i	−0.295174	+	0.810985i	0.700115	+	0.714031i	$0.253132\pi$
$67$	−19.7767	+	54.3360i	−0.295174	+	0.810985i	−0.995289	+	0.0969542i	$0.969090\pi$
$68$	3.82924	−	6.63244i	0.0563124	−	0.0975359i
$69$	46.3856	−	26.7808i	0.672256	−	0.388127i
$70$	−8.25136	+	1.45494i	−0.117877	+	0.0207848i
$71$	72.7304	−	86.6767i	1.02437	−	1.22080i	0.0493284	−	0.998783i	$-0.484292\pi$
$71$	72.7304	−	86.6767i	1.02437	−	1.22080i	0.975043	−	0.222016i	$-0.0712637\pi$
$72$	−55.1038	−	65.6701i	−0.765330	−	0.912085i
$73$	−16.7860	+	95.1980i	−0.229945	+	1.30408i	0.623058	+	0.782176i	$0.285890\pi$
$73$	−16.7860	+	95.1980i	−0.229945	+	1.30408i	−0.853003	+	0.521907i	$0.825221\pi$
$74$	9.15264	−	3.33129i	0.123684	−	0.0450174i
$75$		−	78.3016i		−	1.04402i
$76$		0			0
$77$	53.5853			0.695913
$78$	3.98505	+	10.9488i	0.0510904	+	0.140370i
$79$	48.6512	+	8.57853i	0.615839	+	0.108589i	0.472861	−	0.881137i	$-0.343221\pi$
$79$	48.6512	+	8.57853i	0.615839	+	0.108589i	0.142977	+	0.989726i	$0.454332\pi$
$80$	32.9517	−	27.6497i	0.411896	−	0.345622i
$81$	155.703	+	130.651i	1.92226	+	1.61297i
$82$	5.58092	+	31.6510i	0.0680600	+	0.385987i
$83$	−48.0685	−	83.2571i	−0.579139	−	1.00310i	−0.995578	−	0.0939343i	$-0.970056\pi$
$83$	−48.0685	−	83.2571i	−0.579139	−	1.00310i	0.416440	−	0.909163i	$-0.363278\pi$
$84$	−90.7295	−	52.3827i	−1.08011	−	0.623603i
$85$	6.35044	+	2.31137i	0.0747110	+	0.0271926i
$86$	−11.5046	+	31.6085i	−0.133774	+	0.367541i
$87$	−75.8429	+	131.364i	−0.871758	+	1.50993i
$88$	36.0502	−	20.8136i	0.409662	−	0.236518i
$89$	−48.5394	+	8.55881i	−0.545387	+	0.0961664i	−0.439552	−	0.898217i	$-0.644863\pi$
$89$	−48.5394	+	8.55881i	−0.545387	+	0.0961664i	−0.105835	+	0.994384i	$0.533752\pi$
$90$	23.5143	−	28.0233i	0.261270	−	0.311370i
$91$	13.4231	+	15.9970i	0.147506	+	0.175791i
$92$	6.26229	−	35.5152i	0.0680684	−	0.386035i
$93$	−161.510	+	58.7849i	−1.73667	+	0.632096i
$94$		−	12.5716i		−	0.133740i
$95$		0			0
$96$	−123.415			−1.28557
$97$	−13.4988	−	37.0877i	−0.139163	−	0.382348i	0.850459	−	0.526041i	$-0.176324\pi$
$97$	−13.4988	−	37.0877i	−0.139163	−	0.382348i	−0.989622	+	0.143694i	$0.954102\pi$
$98$	−11.7807	−	2.07725i	−0.120211	−	0.0211965i
$99$	−179.222	+	150.385i	−1.81032	+	1.51904i
$100$	−40.3864	−	33.8882i	−0.403864	−	0.338882i
$101$	32.7132	+	185.526i	0.323893	+	1.83689i	0.517342	+	0.855779i	$0.326922\pi$
$101$	32.7132	+	185.526i	0.323893	+	1.83689i	−0.193448	+	0.981110i	$0.561967\pi$
$102$	−2.86758	−	4.96679i	−0.0281135	−	0.0486940i
$103$	−70.5875	−	40.7537i	−0.685316	−	0.395667i	0.116539	−	0.993186i	$-0.462820\pi$
$103$	−70.5875	−	40.7537i	−0.685316	−	0.395667i	−0.801855	+	0.597519i	$0.796153\pi$
$104$	15.2441	+	5.54839i	0.146578	+	0.0533499i
$105$	31.6187	−	86.8717i	0.301131	−	0.827350i
$106$	15.6907	−	27.1770i	0.148025	−	0.256387i
$107$	−64.7149	+	37.3632i	−0.604812	+	0.349188i	−0.770932	−	0.636917i	$-0.780209\pi$
$107$	−64.7149	+	37.3632i	−0.604812	+	0.349188i	0.166120	+	0.986105i	$0.446876\pi$
$108$	265.765	−	46.8615i	2.46078	−	0.433902i
$109$	25.9796	−	30.9613i	0.238345	−	0.284049i	−0.633591	−	0.773668i	$-0.718420\pi$
$109$	25.9796	−	30.9613i	0.238345	−	0.284049i	0.871936	+	0.489619i	$0.162864\pi$
$110$	11.4182	+	13.6076i	0.103802	+	0.123706i
$111$	−18.6616	+	105.835i	−0.168123	+	0.953472i
$112$	−61.4806	+	22.3771i	−0.548934	+	0.199796i
$113$		−	30.5747i		−	0.270573i	−0.990807	−	0.135286i	$-0.956805\pi$
$113$		−	30.5747i		−	0.270573i	0.990807	−	0.135286i	$-0.0431955\pi$
$114$		0			0
$115$	31.8228			0.276720
$116$	34.9307	+	95.9712i	0.301126	+	0.827338i
$117$	−89.7897	−	15.8323i	−0.767433	−	0.135319i
$118$	6.09972	−	5.11827i	0.0516926	−	0.0433752i
$119$	−7.87410	−	6.60715i	−0.0661689	−	0.0555223i
$120$	−12.4708	−	70.7255i	−0.103923	−	0.589379i
$121$	3.69713	+	6.40361i	0.0305548	+	0.0529224i
$122$	−29.4565	−	17.0067i	−0.241447	−	0.139399i
$123$	−333.227	−	121.285i	−2.70916	−	0.986054i
$124$	−39.5800	+	108.745i	−0.319194	+	0.876978i
$125$	64.5776	−	111.852i	0.516621	−	0.894814i
$126$	−48.1865	+	27.8205i	−0.382432	+	0.220797i
$127$	−120.929	+	21.3230i	−0.952195	+	0.167898i	−0.628105	−	0.778128i	$-0.716169\pi$
$127$	−120.929	+	21.3230i	−0.952195	+	0.167898i	−0.324090	+	0.946026i	$0.605058\pi$
$128$	−70.2839	+	83.7610i	−0.549093	+	0.654383i
$129$	−238.564	−	284.309i	−1.84933	−	2.20395i
$130$	−1.20209	+	6.81740i	−0.00924685	+	0.0524415i
$131$	109.105	−	39.7109i	0.832862	−	0.303137i	0.109829	−	0.993951i	$-0.464970\pi$
$131$	109.105	−	39.7109i	0.832862	−	0.303137i	0.723033	+	0.690814i	$0.242747\pi$
$132$			222.112i			1.68267i
$133$		0			0
$134$	29.1551			0.217575
$135$	81.4465	+	223.772i	0.603307	+	1.65757i
$136$	−7.86376	−	1.38659i	−0.0578217	−	0.0101955i
$137$	31.3176	−	26.2786i	0.228595	−	0.191814i	−0.521295	−	0.853377i	$-0.674551\pi$
$137$	31.3176	−	26.2786i	0.228595	−	0.191814i	0.749890	+	0.661562i	$0.230106\pi$
$138$	−20.6880	−	17.3593i	−0.149913	−	0.125792i
$139$	2.12250	+	12.0373i	0.0152698	+	0.0865992i	0.991490	−	0.130181i	$-0.0415557\pi$
$139$	2.12250	+	12.0373i	0.0152698	+	0.0865992i	−0.976221	+	0.216780i	$0.930445\pi$
$140$	−31.1224	−	53.9056i	−0.222303	−	0.385040i
$141$	120.126	+	69.3550i	0.851960	+	0.491880i
$142$	−53.6101	−	19.5125i	−0.377536	−	0.137412i
$143$	15.1422	−	41.6030i	0.105890	−	0.290930i
$144$	142.828	−	247.386i	0.991862	−	1.71795i
$145$	−78.0478	+	45.0609i	−0.538261	+	0.310765i
$146$	47.9999	−	8.46368i	0.328767	−	0.0579704i
$147$	84.8409	−	101.109i	0.577149	−	0.687819i
$148$	46.5111	+	55.4298i	0.314265	+	0.374526i
$149$	14.2515	−	80.8245i	0.0956480	−	0.542447i	−0.898899	−	0.438156i	$-0.855632\pi$
$149$	14.2515	−	80.8245i	0.0956480	−	0.542447i	0.994547	−	0.104290i	$-0.0332572\pi$
$150$	−37.0996	+	13.5031i	−0.247331	+	0.0900210i
$151$			137.096i			0.907922i	0.891022	+	0.453961i	$0.149989\pi$
$151$			137.096i			0.907922i	−0.891022	+	0.453961i	$0.850011\pi$
$152$		0			0
$153$	44.8785			0.293323
$154$	−9.24080	−	25.3889i	−0.0600052	−	0.164863i
$155$	−100.566	−	17.7325i	−0.648813	−	0.114403i
$156$	−66.3078	+	55.6388i	−0.425050	+	0.356659i
$157$	−46.9093	−	39.3616i	−0.298785	−	0.250711i	0.481053	−	0.876691i	$-0.340254\pi$
$157$	−46.9093	−	39.3616i	−0.298785	−	0.250711i	−0.779838	+	0.625981i	$0.784699\pi$
$158$	−4.32539	−	24.5305i	−0.0273759	−	0.155256i
$159$	173.125	+	299.862i	1.08884	+	1.88592i
$160$	−63.5012	−	36.6624i	−0.396883	−	0.229140i
$161$	−45.4834	−	16.5546i	−0.282506	−	0.102824i
$162$	35.0516	−	96.3035i	0.216368	−	0.594466i
$163$	−101.260	+	175.388i	−0.621229	+	1.07600i	0.368028	+	0.929815i	$0.380033\pi$
$163$	−101.260	+	175.388i	−0.621229	+	1.07600i	−0.989257	+	0.146186i	$0.953300\pi$
$164$	−206.774	+	119.381i	−1.26081	+	0.727932i
$165$	−193.019	+	34.0344i	−1.16981	+	0.206269i
$166$	−31.1581	+	37.1327i	−0.187699	+	0.223691i
$167$	140.912	+	167.932i	0.843782	+	1.00558i	0.999841	+	0.0178321i	$0.00567643\pi$
$167$	140.912	+	167.932i	0.843782	+	1.00558i	−0.156059	+	0.987748i	$0.549879\pi$
$168$	−18.9681	+	107.573i	−0.112905	+	0.640318i
$169$	−142.595	+	51.9004i	−0.843758	+	0.307103i
$170$		−	3.40746i		−	0.0200439i
$171$		0			0
$172$	−249.889			−1.45284
$173$	24.4636	+	67.2132i	0.141408	+	0.388516i	0.990099	−	0.140374i	$-0.0448306\pi$
$173$	24.4636	+	67.2132i	0.141408	+	0.388516i	−0.848690	+	0.528890i	$0.822608\pi$
$174$	75.3197	+	13.2809i	0.432872	+	0.0763270i
$175$	−54.2050	+	45.4834i	−0.309743	+	0.259905i
$176$	106.258	+	89.1609i	0.603738	+	0.506596i
$177$	15.2561	+	86.5219i	0.0861929	+	0.488824i
$178$	12.4258	+	21.5222i	0.0698081	+	0.120911i
$179$	−114.387	−	66.0413i	−0.639033	−	0.368946i	0.145209	−	0.989401i	$-0.453614\pi$
$179$	−114.387	−	66.0413i	−0.639033	−	0.368946i	−0.784242	+	0.620455i	$0.786948\pi$
$180$	255.376	+	92.9492i	1.41876	+	0.516385i
$181$	49.3067	−	135.469i	0.272413	−	0.748448i	−0.725756	−	0.687953i	$-0.758510\pi$
$181$	49.3067	−	135.469i	0.272413	−	0.748448i	0.998168	−	0.0604957i	$-0.0192681\pi$
$182$	5.26461	−	9.11857i	0.0289264	−	0.0501020i
$183$	325.012	−	187.646i	1.77602	−	1.02539i
$184$	−37.0297	+	6.52934i	−0.201248	+	0.0354855i
$185$	−41.0423	+	48.9124i	−0.221850	+	0.264391i
$186$	55.7050	+	66.3866i	0.299489	+	0.356917i
$187$	−3.78418	+	21.4612i	−0.0202363	+	0.114766i
$188$	87.7615	−	31.9426i	0.466816	−	0.169907i
$189$		−	362.201i		−	1.91641i
$190$		0			0
$191$	331.007			1.73302			0.866511	−	0.499158i	$-0.166357\pi$
$191$	331.007			1.73302			0.866511	+	0.499158i	$0.166357\pi$
$192$	−77.7660	−	213.660i	−0.405031	−	1.11281i
$193$	−73.2615	−	12.9180i	−0.379593	−	0.0669325i	−0.0194039	−	0.999812i	$-0.506177\pi$
$193$	−73.2615	−	12.9180i	−0.379593	−	0.0669325i	−0.360189	+	0.932879i	$0.617288\pi$
$194$	−15.2444	+	12.7916i	−0.0785794	+	0.0659360i
$195$	−58.5113	−	49.0968i	−0.300058	−	0.251778i
$196$	−15.4319	−	87.5184i	−0.0787339	−	0.446522i
$197$	−133.136	−	230.599i	−0.675820	−	1.17055i	−0.976229	−	0.216744i	$-0.930456\pi$
$197$	−133.136	−	230.599i	−0.675820	−	1.17055i	0.300409	−	0.953811i	$-0.402877\pi$
$198$	102.160	+	58.9820i	0.515958	+	0.297889i
$199$	246.727	+	89.8012i	1.23983	+	0.451262i	0.876954	−	0.480574i	$-0.159572\pi$
$199$	246.727	+	89.8012i	1.23983	+	0.451262i	0.362879	+	0.931836i	$0.381794\pi$
$200$	−18.8005	+	51.6538i	−0.0940023	+	0.258269i
$201$	−160.843	+	278.589i	−0.800215	+	1.38601i
$202$	82.2614	−	47.4936i	0.407235	−	0.235117i
$203$	134.993	−	23.8029i	0.664989	−	0.117256i
$204$	27.3868	−	32.6383i	0.134249	−	0.159992i
$205$	−135.428	−	161.396i	−0.660622	−	0.787299i
$206$	−7.13641	+	40.4726i	−0.0346428	+	0.196469i
$207$	198.584	−	72.2787i	0.959343	−	0.349172i
$208$			54.0562i			0.259885i
$209$		0			0
$210$	−46.6128			−0.221966
$211$	−93.0362	−	255.615i	−0.440930	−	1.21145i	−0.938882	−	0.344240i	$-0.888137\pi$
$211$	−93.0362	−	255.615i	−0.440930	−	1.21145i	0.497952	−	0.867205i	$-0.334086\pi$
$212$	229.589	+	40.4828i	1.08297	+	0.190957i
$213$	482.207	−	404.620i	2.26388	−	1.89962i
$214$	28.8629	+	24.2188i	0.134873	+	0.113172i
$215$	−38.2906	−	217.157i	−0.178096	−	1.01003i
$216$	−140.686	−	243.676i	−0.651325	−	1.12813i
$217$	134.511	+	77.6602i	0.619869	+	0.357881i
$218$	−19.1498	−	6.96995i	−0.0878430	−	0.0319722i
$219$	−183.933	+	505.351i	−0.839876	+	2.30754i
$220$	−65.9823	+	114.285i	−0.299920	+	0.519476i
$221$	−7.35479	+	4.24629i	−0.0332796	+	0.0192140i
$222$	53.3634	−	9.40940i	0.240376	−	0.0423847i
$223$	73.6284	−	87.7470i	0.330172	−	0.393484i	−0.575263	−	0.817969i	$-0.695100\pi$
$223$	73.6284	−	87.7470i	0.330172	−	0.393484i	0.905435	+	0.424485i	$0.139545\pi$
$224$	71.6883	+	85.4348i	0.320037	+	0.381405i
$225$	53.6471	−	304.248i	0.238432	−	1.35221i
$226$	−14.4864	+	5.27262i	−0.0640992	+	0.0233302i
$227$		−	403.991i		−	1.77970i	−0.456258	−	0.889848i	$-0.650811\pi$
$227$		−	403.991i		−	1.77970i	0.456258	−	0.889848i	$-0.349189\pi$
$228$		0			0
$229$	−109.482			−0.478087			−0.239043	−	0.971009i	$-0.576834\pi$
$229$	−109.482			−0.478087			−0.239043	+	0.971009i	$0.576834\pi$
$230$	−5.48785	−	15.0777i	−0.0238602	−	0.0655554i
$231$	293.581	+	51.7663i	1.27091	+	0.224096i
$232$	81.5727	−	68.4476i	0.351607	−	0.295033i
$233$	139.678	+	117.204i	0.599476	+	0.503020i	0.891277	−	0.453459i	$-0.149810\pi$
$233$	139.678	+	117.204i	0.599476	+	0.503020i	−0.291801	+	0.956479i	$0.594255\pi$
$234$	7.98284	+	45.2730i	0.0341147	+	0.193474i
$235$	41.2063	+	71.3713i	0.175346	+	0.303708i
$236$	51.2290	+	29.5770i	0.217072	+	0.125326i
$237$	258.261	+	93.9994i	1.08971	+	0.396622i
$238$	−1.77260	+	4.87018i	−0.00744790	+	0.0204630i
$239$	138.117	−	239.226i	0.577895	−	1.00094i	−0.417825	−	0.908527i	$-0.637208\pi$
$239$	138.117	−	239.226i	0.577895	−	1.00094i	0.995720	−	0.0924165i	$-0.0294591\pi$
$240$	207.245	−	119.653i	0.863523	−	0.498555i
$241$	148.185	−	26.1290i	0.614874	−	0.108419i	0.142467	−	0.989800i	$-0.454496\pi$
$241$	148.185	−	26.1290i	0.614874	−	0.108419i	0.472407	+	0.881381i	$0.343385\pi$
$242$	2.39648	−	2.85602i	0.00990282	−	0.0118017i
$243$	310.059	+	369.514i	1.27596	+	1.52063i
$244$	43.8783	−	248.846i	0.179829	−	1.01986i
$245$	73.6900	−	26.8210i	0.300776	−	0.109473i
$246$			178.800i			0.726828i
$247$		0			0
$248$	120.659			0.486529
$249$	−182.925	−	502.583i	−0.734639	−	2.01840i
$250$	−64.1322	−	11.3082i	−0.256529	−	0.0452329i
$251$	−295.638	+	248.070i	−1.17784	+	0.988325i	−0.177849	+	0.984058i	$0.556914\pi$
$251$	−295.638	+	248.070i	−1.17784	+	0.988325i	−0.999991	+	0.00426763i	$0.998642\pi$
$252$	−316.648	−	265.700i	−1.25654	−	1.05436i
$253$	17.8194	+	101.059i	0.0704323	+	0.399441i
$254$	30.9571	+	53.6193i	0.121878	+	0.211100i
$255$	32.5596	+	18.7983i	0.127685	+	0.0737189i
$256$	−101.815	−	37.0577i	−0.397715	−	0.144757i
$257$	136.415	−	374.797i	0.530798	−	1.45836i	−0.327325	−	0.944912i	$-0.606147\pi$
$257$	136.415	−	374.797i	0.530798	−	1.45836i	0.858123	−	0.513444i	$-0.171631\pi$
$258$	−93.5663	+	162.062i	−0.362660	+	0.628145i
$259$	84.1055	−	48.5583i	0.324732	−	0.187484i
$260$	−50.6463	+	8.93030i	−0.194793	+	0.0343473i
$261$	−384.696	+	458.463i	−1.47393	+	1.75656i
$262$	−37.6304	−	44.8461i	−0.143627	−	0.171168i
$263$	−10.5913	+	60.0664i	−0.0402712	+	0.228389i	−0.998300	−	0.0582822i	$-0.981438\pi$
$263$	−10.5913	+	60.0664i	−0.0402712	+	0.228389i	0.958029	+	0.286671i	$0.0925488\pi$
$264$	217.618	−	79.2063i	0.824309	−	0.300024i
$265$			205.719i			0.776300i
$266$		0			0
$267$	−274.204			−1.02698
$268$	74.0789	+	203.530i	0.276414	+	0.759441i
$269$	−163.601	−	28.8472i	−0.608181	−	0.107239i	−0.138928	−	0.990302i	$-0.544366\pi$
$269$	−163.601	−	28.8472i	−0.608181	−	0.107239i	−0.469253	+	0.883064i	$0.655477\pi$
$270$	91.9787	−	77.1793i	0.340662	−	0.285849i
$271$	−145.965	−	122.479i	−0.538616	−	0.451952i	0.332449	−	0.943121i	$-0.392125\pi$
$271$	−145.965	−	122.479i	−0.538616	−	0.451952i	−0.871064	+	0.491169i	$0.836570\pi$
$272$	−4.62039	−	26.2035i	−0.0169867	−	0.0963366i
$273$	58.0878	+	100.611i	0.212776	+	0.368538i
$274$	−17.8516	−	10.3066i	−0.0651518	−	0.0376154i
$275$	140.970	+	51.3088i	0.512617	+	0.186577i
$276$	68.6192	−	188.530i	0.248620	−	0.683079i
$277$	48.8669	−	84.6399i	0.176415	−	0.305559i	−0.764235	−	0.644938i	$-0.776883\pi$
$277$	48.8669	−	84.6399i	0.176415	−	0.305559i	0.940650	+	0.339378i	$0.110217\pi$
$278$	5.33728	−	3.08148i	0.0191989	−	0.0110845i
$279$	−667.838	+	117.758i	−2.39369	+	0.422071i
$280$	−41.7163	+	49.7156i	−0.148987	+	0.177556i
$281$	167.672	+	199.824i	0.596699	+	0.711118i	0.976879	−	0.213795i	$-0.0685824\pi$
$281$	167.672	+	199.824i	0.596699	+	0.711118i	−0.380180	+	0.924913i	$0.624138\pi$
$282$	12.1448	−	68.8766i	0.0430667	−	0.244243i
$283$	281.096	−	102.311i	0.993273	−	0.361522i	0.206286	−	0.978492i	$-0.433862\pi$
$283$	281.096	−	102.311i	0.993273	−	0.361522i	0.786987	+	0.616970i	$0.211640\pi$
$284$		−	423.828i		−	1.49235i
$285$		0			0
$286$	−22.3229			−0.0780521
$287$	109.602	+	301.130i	0.381890	+	1.04923i
$288$	−479.538	−	84.5555i	−1.66506	−	0.293596i
$289$	−218.185	+	183.079i	−0.754964	+	0.633490i
$290$	34.8094	+	29.2086i	0.120032	+	0.100719i
$291$	−38.1281	−	216.235i	−0.131024	−	0.743077i
$292$	181.046	+	313.580i	0.620019	+	1.07390i
$293$	439.492	+	253.741i	1.49997	+	0.866010i	1.00000		3.02106e-5i	$-9.61633e-6\pi$
$293$	439.492	+	253.741i	1.49997	+	0.866010i	0.499974	+	0.866041i	$0.333343\pi$
$294$	−62.5368	−	22.7615i	−0.212710	−	0.0774202i
$295$	−17.8530	+	49.0508i	−0.0605187	+	0.166274i
$296$	37.7221	−	65.3365i	0.127439	−	0.220732i
$297$	−665.021	+	383.950i	−2.23913	+	1.29276i
$298$	−40.7526	+	7.18579i	−0.136754	+	0.0241134i
$299$	−25.7056	+	30.6347i	−0.0859719	+	0.102457i
$300$	−188.530	−	224.681i	−0.628432	−	0.748936i
$301$	−58.2400	+	330.295i	−0.193488	+	1.09733i
$302$	64.9566	−	23.6423i	0.215088	−	0.0782857i
$303$			1048.05i			3.45893i
$304$		0			0
$305$	222.974			0.731063
$306$	−7.73931	−	21.2636i	−0.0252919	−	0.0694888i
$307$	46.2556	+	8.15611i	0.150670	+	0.0265671i	0.248474	−	0.968639i	$-0.420071\pi$
$307$	46.2556	+	8.15611i	0.150670	+	0.0265671i	−0.0978045	+	0.995206i	$0.531182\pi$
$308$	153.759	−	129.019i	0.499218	−	0.418893i
$309$	−347.362	−	291.471i	−1.12415	−	0.943273i
$310$	8.94092	+	50.7065i	0.0288417	+	0.163569i
$311$	48.0701	+	83.2599i	0.154566	+	0.267717i	0.932901	−	0.360133i	$-0.117269\pi$
$311$	48.0701	+	83.2599i	0.154566	+	0.267717i	−0.778335	+	0.627850i	$0.783935\pi$
$312$	78.1587	+	45.1249i	0.250509	+	0.144631i
$313$	−52.3716	−	19.0617i	−0.167322	−	0.0609001i	0.257001	−	0.966411i	$-0.417266\pi$
$313$	−52.3716	−	19.0617i	−0.167322	−	0.0609001i	−0.424323	+	0.905511i	$0.639488\pi$
$314$	−10.5601	+	29.0137i	−0.0336310	+	0.0924003i
$315$	182.376	−	315.885i	0.578972	−	1.00281i
$316$	160.256	−	92.5239i	0.507139	−	0.292797i
$317$	363.697	−	64.1296i	1.14731	−	0.202301i	0.432508	−	0.901630i	$-0.357629\pi$
$317$	363.697	−	64.1296i	1.14731	−	0.202301i	0.714800	+	0.699329i	$0.246518\pi$
$318$	112.220	−	133.739i	0.352893	−	0.420561i
$319$	−186.802	−	222.622i	−0.585586	−	0.697875i
$320$	23.4581	−	133.038i	0.0733067	−	0.415743i
$321$	−390.652	+	142.186i	−1.21699	+	0.442946i
$322$			24.4050i			0.0757921i
$323$		0			0
$324$	761.351			2.34985
$325$	19.9954	+	54.9369i	0.0615243	+	0.169037i
$326$	100.562	+	17.7318i	0.308472	+	0.0543920i
$327$	172.247	−	144.532i	0.526748	−	0.441994i
$328$	190.702	+	160.018i	0.581407	+	0.487859i
$329$	−21.7667	−	123.445i	−0.0661602	−	0.375213i
$330$	49.4117	+	85.5836i	0.149732	+	0.259344i
$331$	319.730	+	184.596i	0.965951	+	0.557692i	0.898000	−	0.439996i	$-0.145020\pi$
$331$	319.730	+	184.596i	0.965951	+	0.557692i	0.0679517	+	0.997689i	$0.478354\pi$
$332$	−338.390	−	123.164i	−1.01925	−	0.370976i
$333$	−145.023	+	398.447i	−0.435504	+	1.19654i
$334$	55.2664	−	95.7243i	0.165468	−	0.286600i
$335$	−165.519	+	95.5626i	−0.494087	+	0.285262i
$336$	−358.455	+	63.2053i	−1.06683	+	0.188111i
$337$	−78.9897	+	94.1363i	−0.234391	+	0.279336i	−0.870400	−	0.492345i	$-0.836140\pi$
$337$	−78.9897	+	94.1363i	−0.234391	+	0.279336i	0.636009	+	0.771682i	$0.280584\pi$
$338$	49.1811	+	58.6118i	0.145506	+	0.173408i
$339$	29.5368	−	167.512i	0.0871293	−	0.494135i
$340$	23.7873	−	8.65786i	0.0699626	−	0.0254643i
$341$		−	329.294i		−	0.965671i
$342$		0			0
$343$	−365.619			−1.06595
$344$	89.1117	+	244.832i	0.259046	+	0.711722i
$345$	174.349	+	30.7425i	0.505361	+	0.0891087i
$346$	27.6271	−	23.1819i	0.0798471	−	0.0669997i
$347$	204.857	+	171.895i	0.590366	+	0.495376i	0.888333	−	0.459201i	$-0.151864\pi$
$347$	204.857	+	171.895i	0.590366	+	0.495376i	−0.297967	+	0.954576i	$0.596309\pi$
$348$	98.6635	+	559.548i	0.283516	+	1.60790i
$349$	116.771	+	202.253i	0.334586	+	0.579521i	0.983405	−	0.181422i	$-0.0580700\pi$
$349$	116.771	+	202.253i	0.334586	+	0.579521i	−0.648819	+	0.760943i	$0.724737\pi$
$350$	30.8978	+	17.8389i	0.0882796	+	0.0509682i
$351$	−281.209	−	102.352i	−0.801164	−	0.291600i
$352$	80.8699	−	222.188i	0.229744	−	0.631217i
$353$	−20.6612	+	35.7862i	−0.0585302	+	0.101377i	−0.893806	−	0.448454i	$-0.851975\pi$
$353$	−20.6612	+	35.7862i	−0.0585302	+	0.101377i	0.835276	+	0.549831i	$0.185308\pi$
$354$	38.3635	−	22.1492i	0.108371	−	0.0625682i
$355$	368.312	−	64.9434i	1.03750	−	0.182939i
$356$	−118.673	+	141.429i	−0.333351	+	0.397272i
$357$	−36.7575	−	43.8058i	−0.102962	−	0.122705i
$358$	−11.5645	+	65.5857i	−0.0323032	+	0.183200i
$359$	−228.417	+	83.1371i	−0.636260	+	0.231580i	−0.639954	−	0.768414i	$-0.721046\pi$
$359$	−228.417	+	83.1371i	−0.636260	+	0.231580i	0.00369384	+	0.999993i	$0.498824\pi$
$360$		−	283.354i		−	0.787096i
$361$		0			0
$362$	−72.6887			−0.200798
$363$	14.0694	+	38.6555i	0.0387588	+	0.106489i
$364$	77.0329	+	13.5830i	0.211629	+	0.0373159i
$365$	−244.764	+	205.381i	−0.670585	+	0.562688i
$366$	−144.956	−	121.632i	−0.396054	−	0.332329i
$367$	−69.7402	−	395.516i	−0.190028	−	1.07770i	−0.919323	−	0.393503i	$-0.871263\pi$
$367$	−69.7402	−	395.516i	−0.190028	−	1.07770i	0.729296	−	0.684199i	$-0.239848\pi$
$368$	−62.6468	−	108.507i	−0.170236	−	0.294857i
$369$	−1211.69	−	699.568i	−3.28370	−	1.89585i
$370$	30.2526	+	11.0110i	0.0817638	+	0.0297596i
$371$	107.018	−	294.029i	0.288458	−	0.792531i
$372$	−321.903	+	557.553i	−0.865332	+	1.49880i
$373$	523.753	−	302.389i	1.40416	−	0.810694i	0.409347	−	0.912379i	$-0.365756\pi$
$373$	523.753	−	302.389i	1.40416	−	0.810694i	0.994817	+	0.101684i	$0.0324232\pi$
$374$	10.8210	−	1.90803i	0.0289330	−	0.00510167i
$375$	461.860	−	550.424i	1.23163	−	1.46780i
$376$	−62.5924	−	74.5947i	−0.166469	−	0.198390i
$377$	19.6663	−	111.533i	0.0521652	−	0.295844i
$378$	−171.612	+	62.4617i	−0.454000	+	0.165243i
$379$		−	31.3786i		−	0.0827931i	−0.999143	−	0.0413965i	$-0.986819\pi$
$379$		−	31.3786i		−	0.0827931i	0.999143	−	0.0413965i	$-0.0131807\pi$
$380$		0			0
$381$	−683.139			−1.79302
$382$	−57.0823	−	156.832i	−0.149430	−	0.410556i
$383$	−423.205	−	74.6225i	−1.10497	−	0.194837i	−0.408739	−	0.912651i	$-0.634032\pi$
$383$	−423.205	−	74.6225i	−1.10497	−	0.194837i	−0.696234	+	0.717814i	$0.745143\pi$
$384$	−465.986	+	391.009i	−1.21351	+	1.01825i
$385$	135.680	+	113.849i	0.352416	+	0.295712i
$386$	6.51339	+	36.9393i	0.0168741	+	0.0956976i
$387$	−732.171	−	1268.16i	−1.89191	−	3.27689i
$388$	−128.031	−	73.9189i	−0.329978	−	0.190513i
$389$	570.787	+	207.750i	1.46732	+	0.534061i	0.947371	−	0.320137i	$-0.103729\pi$
$389$	570.787	+	207.750i	1.46732	+	0.534061i	0.519948	+	0.854198i	$0.325951\pi$
$390$	−13.1719	+	36.1896i	−0.0337742	+	0.0927939i
$391$	9.84223	−	17.0472i	0.0251719	−	0.0435991i
$392$	−80.2443	+	46.3291i	−0.204705	+	0.118186i
$393$	636.123	−	112.166i	1.61863	−	0.285409i
$394$	−86.2993	+	102.847i	−0.219034	+	0.261034i
$395$	104.961	+	125.087i	0.265723	+	0.316676i
$396$	−152.177	+	863.037i	−0.384285	+	2.17939i
$397$	−199.534	+	72.6245i	−0.502605	+	0.182933i	−0.580865	−	0.814000i	$-0.697286\pi$
$397$	−199.534	+	72.6245i	−0.502605	+	0.182933i	0.0782602	+	0.996933i	$0.475064\pi$
$398$		−	132.386i		−	0.332629i
$399$		0			0
$400$	−183.167			−0.457917
$401$	103.856	+	285.343i	0.258993	+	0.711578i	0.999230	+	0.0392316i	$0.0124910\pi$
$401$	103.856	+	285.343i	0.258993	+	0.711578i	−0.740237	+	0.672346i	$0.765287\pi$
$402$	159.734	+	28.1654i	0.397348	+	0.0700631i
$403$	98.3050	−	82.4877i	0.243933	−	0.204684i
$404$	540.565	+	453.588i	1.33803	+	1.12274i
$405$	116.662	+	661.624i	0.288055	+	1.63364i
$406$	−34.5575	−	59.8553i	−0.0851169	−	0.147427i
$407$	−178.311	−	102.948i	−0.438112	−	0.252944i
$408$	−41.7441	−	15.1936i	−0.102314	−	0.0372393i
$409$	−167.768	+	460.940i	−0.410191	+	1.12699i	0.546898	+	0.837199i	$0.315808\pi$
$409$	−167.768	+	460.940i	−0.410191	+	1.12699i	−0.957090	+	0.289792i	$0.906414\pi$
$410$	−53.1156	+	91.9989i	−0.129550	+	0.224388i
$411$	196.968	−	113.720i	0.479241	−	0.276690i
$412$	−300.670	+	53.0162i	−0.729781	+	0.128680i
$413$	51.0336	−	60.8195i	0.123568	−	0.147263i
$414$	−68.4918	−	81.6253i	−0.165439	−	0.197163i
$415$	55.1794	−	312.938i	0.132962	−	0.754068i
$416$	86.5883	−	31.5156i	0.208145	−	0.0757586i
$417$			67.9999i			0.163069i
$418$		0			0
$419$	−20.9810			−0.0500739			−0.0250370	−	0.999687i	$-0.507970\pi$
$419$	−20.9810			−0.0500739			−0.0250370	+	0.999687i	$0.507970\pi$
$420$	−118.437	−	325.402i	−0.281992	−	0.774766i
$421$	687.520	+	121.228i	1.63306	+	0.287953i	0.913612	−	0.406588i	$-0.133281\pi$
$421$	687.520	+	121.228i	1.63306	+	0.287953i	0.719453	+	0.694541i	$0.244393\pi$
$422$	−105.067	+	88.1618i	−0.248974	+	0.208914i
$423$	419.245	+	351.788i	0.991122	+	0.831650i
$424$	−42.2091	−	239.380i	−0.0995499	−	0.564575i
$425$	−14.3884	−	24.9214i	−0.0338550	−	0.0586385i
$426$	−274.867	−	158.694i	−0.645227	−	0.372522i
$427$	−318.691	−	115.994i	−0.746348	−	0.271648i
$428$	−95.7340	+	263.027i	−0.223678	+	0.614549i
$429$	123.151	−	213.305i	0.287066	−	0.497213i
$430$	−96.2864	+	55.5910i	−0.223922	+	0.129281i
$431$	459.184	−	80.9665i	1.06539	−	0.187857i	0.386644	−	0.922229i	$-0.373634\pi$
$431$	459.184	−	80.9665i	1.06539	−	0.187857i	0.678748	+	0.734371i	$0.262523\pi$
$432$	602.669	−	718.233i	1.39507	−	1.66258i
$433$	−311.126	−	370.786i	−0.718537	−	0.856319i	0.275951	−	0.961172i	$-0.411007\pi$
$433$	−311.126	−	370.786i	−0.718537	−	0.856319i	−0.994488	+	0.104853i	$0.966563\pi$
$434$	13.5991	−	77.1245i	0.0313344	−	0.177706i
$435$	−471.137	+	171.480i	−1.08307	+	0.394206i
$436$		−	151.393i		−	0.347232i
$437$		0			0
$438$	271.157			0.619079
$439$	−118.849	−	326.535i	−0.270726	−	0.743815i	−0.998327	−	0.0578142i	$-0.981587\pi$
$439$	−118.849	−	326.535i	−0.270726	−	0.743815i	0.727601	−	0.686001i	$-0.240635\pi$
$440$	135.502	+	23.8926i	0.307959	+	0.0543014i
$441$	398.930	−	334.742i	0.904604	−	0.759053i
$442$	3.28024	+	2.75245i	0.00742137	+	0.00622727i
$443$	14.4340	+	81.8592i	0.0325824	+	0.184784i	0.996755	−	0.0804904i	$-0.0256486\pi$
$443$	14.4340	+	81.8592i	0.0325824	+	0.184784i	−0.964173	+	0.265274i	$0.914538\pi$
$444$	201.275	+	348.619i	0.453323	+	0.785178i
$445$	−141.088	−	81.4572i	−0.317052	−	0.183050i
$446$	−54.2721	−	19.7534i	−0.121686	−	0.0442902i
$447$	156.162	−	429.051i	0.349355	−	0.959845i
$448$	−102.736	+	177.944i	−0.229321	+	0.397196i
$449$	−108.702	+	62.7592i	−0.242098	+	0.139775i	−0.616141	−	0.787636i	$-0.711305\pi$
$449$	−108.702	+	62.7592i	−0.242098	+	0.139775i	0.374042	+	0.927412i	$0.377971\pi$
$450$	−153.405	+	27.0495i	−0.340901	+	0.0601100i
$451$	436.708	−	520.448i	0.968310	−	1.15399i
$452$	−73.6159	−	87.7320i	−0.162867	−	0.194097i
$453$	−132.442	+	751.117i	−0.292367	+	1.65810i
$454$	−191.412	+	69.6684i	−0.421613	+	0.153455i
$455$			69.0240i			0.151701i
$456$		0			0
$457$	763.151			1.66992			0.834958	−	0.550314i	$-0.185492\pi$
$457$	763.151			1.66992			0.834958	+	0.550314i	$0.185492\pi$
$458$	18.8802	+	51.8729i	0.0412231	+	0.113260i
$459$	145.063	+	25.5786i	0.316042	+	0.0557267i
$460$	91.3131	−	76.6208i	0.198507	−	0.166567i
$461$	83.5506	+	70.1073i	0.181238	+	0.152077i	0.728893	−	0.684627i	$-0.240035\pi$
$461$	83.5506	+	70.1073i	0.181238	+	0.152077i	−0.547655	+	0.836704i	$0.684480\pi$
$462$	−26.1011	−	148.027i	−0.0564959	−	0.320404i
$463$	−0.476643	−	0.825570i	−0.00102947	−	0.00178309i	0.865510	−	0.500891i	$-0.166994\pi$
$463$	−0.476643	−	0.825570i	−0.00102947	−	0.00178309i	−0.866540	+	0.499108i	$0.833661\pi$
$464$	307.292	+	177.415i	0.662268	+	0.382360i
$465$	−533.847	−	194.304i	−1.14806	−	0.417859i
$466$	31.4440	−	86.3917i	0.0674764	−	0.185390i
$467$	185.392	−	321.108i	0.396984	−	0.687597i	−0.596368	−	0.802711i	$-0.703390\pi$
$467$	185.392	−	321.108i	0.396984	−	0.687597i	0.993352	+	0.115114i	$0.0367234\pi$
$468$	−295.765	+	170.760i	−0.631977	+	0.364872i
$469$	286.285	−	50.4798i	0.610416	−	0.107633i
$470$	26.7099	−	31.8317i	0.0568297	−	0.0677270i
$471$	−218.979	−	260.970i	−0.464925	−	0.554076i
$472$	10.7100	−	60.7396i	0.0226908	−	0.128686i
$473$	668.177	−	243.197i	1.41264	−	0.514158i
$474$		−	138.575i		−	0.292353i
$475$		0			0
$476$	−38.5024			−0.0808875
$477$	467.248	+	1283.75i	0.979556	+	2.69131i
$478$	−137.164	−	24.1858i	−0.286955	−	0.0505978i
$479$	−48.5574	+	40.7445i	−0.101373	+	0.0850617i	−0.692065	−	0.721835i	$-0.743299\pi$
$479$	−48.5574	+	40.7445i	−0.101373	+	0.0850617i	0.590693	+	0.806897i	$0.298855\pi$
$480$	−312.490	−	262.210i	−0.651021	−	0.546272i
$481$	−13.9334	−	79.0202i	−0.0289676	−	0.164283i
$482$	−37.9345	−	65.7045i	−0.0787023	−	0.136316i
$483$	−233.200	−	134.638i	−0.482816	−	0.278754i
$484$	26.0268	+	9.47299i	0.0537745	+	0.0195723i
$485$	44.6182	−	122.588i	0.0919963	−	0.252758i
$486$	121.607	−	210.630i	0.250220	−	0.433394i
$487$	−299.678	+	173.019i	−0.615355	+	0.355275i	−0.775058	−	0.631890i	$-0.782280\pi$
$487$	−299.678	+	173.019i	−0.615355	+	0.355275i	0.159704	+	0.987165i	$0.448946\pi$
$488$	−259.458	+	45.7494i	−0.531676	+	0.0937488i
$489$	−724.216	+	863.087i	−1.48101	+	1.76500i
$490$	−25.4157	−	30.2893i	−0.0518689	−	0.0618149i
$491$	46.4760	−	263.579i	0.0946559	−	0.536820i	−0.900196	−	0.435484i	$-0.856577\pi$
$491$	46.4760	−	263.579i	0.0946559	−	0.536820i	0.994852	−	0.101336i	$-0.0323117\pi$
$492$	−1248.19	+	454.305i	−2.53698	+	0.923383i
$493$			55.7462i			0.113076i
$494$		0			0
$495$	−773.309			−1.56224
$496$	137.512	+	377.812i	0.277243	+	0.761718i
$497$	−560.203	−	98.7789i	−1.12717	−	0.198750i
$498$	−206.580	+	173.341i	−0.414819	+	0.348075i
$499$	−178.799	−	150.030i	−0.358315	−	0.300662i	0.445804	−	0.895131i	$-0.352918\pi$
$499$	−178.799	−	150.030i	−0.358315	−	0.300662i	−0.804119	+	0.594469i	$0.797362\pi$
$500$	−84.0086	−	476.436i	−0.168017	−	0.952873i
$501$	609.790	+	1056.19i	1.21715	+	2.10816i
$502$	168.519	+	97.2946i	0.335695	+	0.193814i
$503$	−111.957	−	40.7489i	−0.222578	−	0.0810118i	0.228324	−	0.973585i	$-0.426675\pi$
$503$	−111.957	−	40.7489i	−0.222578	−	0.0810118i	−0.450902	+	0.892573i	$0.648898\pi$
$504$	−147.405	+	404.991i	−0.292469	+	0.803553i
$505$	−311.343	+	539.262i	−0.616521	+	1.06785i
$506$	44.8090	−	25.8705i	0.0885553	−	0.0511274i
$507$	−831.383	+	146.595i	−1.63981	+	0.289143i
$508$	−295.656	+	352.349i	−0.582000	+	0.693601i
$509$	108.711	+	129.557i	0.213578	+	0.254533i	0.862188	−	0.506588i	$-0.169094\pi$
$509$	108.711	+	129.557i	0.213578	+	0.254533i	−0.648610	+	0.761121i	$0.724649\pi$
$510$	3.29179	−	18.6686i	0.00645448	−	0.0366052i
$511$	456.676	−	166.216i	0.893690	−	0.325277i
$512$			492.000i			0.960938i
$513$		0			0
$514$	−201.105			−0.391255
$515$	−92.1436	−	253.162i	−0.178920	−	0.491578i
$516$	−1369.08	−	241.406i	−2.65326	−	0.467841i
$517$	−203.578	+	170.822i	−0.393768	+	0.330411i
$518$	−37.5111	−	31.4756i	−0.0724153	−	0.0607637i
$519$	69.0988	+	391.878i	0.133138	+	0.755065i
$520$	26.8103	+	46.4368i	0.0515583	+	0.0893015i
$521$	−434.924	−	251.104i	−0.834787	−	0.481965i	0.0207018	−	0.999786i	$-0.493410\pi$
$521$	−434.924	−	251.104i	−0.834787	−	0.481965i	−0.855489	+	0.517821i	$0.826743\pi$
$522$	283.562	+	103.208i	0.543223	+	0.197717i
$523$	347.341	−	954.311i	0.664132	−	1.82469i	0.107007	−	0.994258i	$-0.465873\pi$
$523$	347.341	−	954.311i	0.664132	−	1.82469i	0.557125	−	0.830429i	$-0.311904\pi$
$524$	217.455	−	376.643i	0.414991	−	0.718785i
$525$	−340.916	+	196.828i	−0.649363	+	0.374910i
$526$	30.2861	−	5.34026i	0.0575782	−	0.0101526i
$527$	−40.6025	+	48.3881i	−0.0770445	+	0.0918181i
$528$	496.027	+	591.142i	0.939446	+	1.11959i
$529$	−75.7640	+	429.679i	−0.143221	+	0.812248i
$530$	97.4706	−	35.4764i	0.183907	−	0.0669366i
$531$			346.641i			0.652808i
$532$		0			0
$533$	264.766			0.496746
$534$	47.2866	+	129.919i	0.0885517	+	0.243294i
$535$	−243.243	−	42.8904i	−0.454661	−	0.0801690i
$536$	172.995	−	145.160i	0.322751	−	0.270820i
$537$	−562.899	−	472.328i	−1.04823	−	0.879569i
$538$	14.5451	+	82.4893i	0.0270355	+	0.153326i
$539$	126.438	+	218.997i	0.234578	+	0.406302i
$540$	772.489	+	445.997i	1.43054	+	0.825920i
$541$	−236.435	−	86.0552i	−0.437033	−	0.159067i	0.114128	−	0.993466i	$-0.463593\pi$
$541$	−236.435	−	86.0552i	−0.437033	−	0.159067i	−0.551161	+	0.834399i	$0.685815\pi$
$542$	−32.8593	+	90.2802i	−0.0606260	+	0.166569i
$543$	401.010	−	694.571i	0.738509	−	1.27914i
$544$	−39.2796	+	22.6781i	−0.0722052	+	0.0416877i
$545$	131.563	−	23.1981i	0.241400	−	0.0425653i
$546$	37.6526	−	44.8726i	0.0689608	−	0.0821842i
$547$	−145.283	−	173.141i	−0.265599	−	0.316529i	0.616718	−	0.787184i	$-0.288462\pi$
$547$	−145.283	−	173.141i	−0.265599	−	0.316529i	−0.882317	+	0.470655i	$0.844017\pi$
$548$	26.5917	−	150.809i	0.0485249	−	0.275199i
$549$	1391.43	−	506.438i	2.53448	−	0.922474i
$550$		−	75.6401i		−	0.137528i
$551$		0			0
$552$	−209.185			−0.378958
$553$	−84.9453	−	233.385i	−0.153608	−	0.422035i
$554$	−48.5298	−	8.55712i	−0.0875989	−	0.0154461i
$555$	−272.113	+	228.330i	−0.490294	+	0.411406i
$556$	35.0730	+	29.4297i	0.0630809	+	0.0529311i
$557$	175.784	+	996.923i	0.315591	+	1.78981i	0.568883	+	0.822418i	$0.307376\pi$
$557$	175.784	+	996.923i	0.315591	+	1.78981i	−0.253292	+	0.967390i	$0.581513\pi$
$558$	170.963	+	296.117i	0.306385	+	0.530675i
$559$	239.980	+	138.552i	0.429302	+	0.247858i
$560$	−203.214	−	73.9640i	−0.362883	−	0.132079i
$561$	−41.4653	+	113.925i	−0.0739131	+	0.203075i
$562$	65.7622	−	113.903i	0.117015	−	0.202675i
$563$	231.065	−	133.406i	0.410418	−	0.236955i	−0.280551	−	0.959839i	$-0.590517\pi$
$563$	231.065	−	133.406i	0.410418	−	0.236955i	0.690969	+	0.722884i	$0.257184\pi$
$564$	511.683	−	90.2234i	0.907239	−	0.159971i
$565$	64.9601	−	77.4164i	0.114974	−	0.137020i
$566$	−96.9503	−	115.541i	−0.171290	−	0.204136i
$567$	177.443	−	1006.33i	0.312951	−	1.77483i
$568$	−415.252	+	151.139i	−0.731077	+	0.266090i
$569$			883.651i			1.55299i	0.630124	+	0.776494i	$0.283004\pi$
$569$			883.651i			1.55299i	−0.630124	+	0.776494i	$0.716996\pi$
$570$		0			0
$571$	365.568			0.640224			0.320112	−	0.947380i	$-0.396280\pi$
$571$	365.568			0.640224			0.320112	+	0.947380i	$0.396280\pi$
$572$	−56.7194	−	155.835i	−0.0991597	−	0.272439i
$573$	1813.51	+	319.771i	3.16494	+	0.558064i
$574$	123.776	−	103.860i	0.215637	−	0.180941i
$575$	−103.804	−	87.1022i	−0.180529	−	0.151482i
$576$	−155.781	−	883.477i	−0.270453	−	1.53381i
$577$	−316.678	−	548.503i	−0.548836	−	0.950612i	−0.998355	−	0.0573410i	$-0.981738\pi$
$577$	−316.678	−	548.503i	−0.548836	−	0.950612i	0.449519	−	0.893271i	$-0.351596\pi$
$578$	124.369	+	71.8046i	0.215172	+	0.124229i
$579$	−388.903	−	141.549i	−0.671680	−	0.244472i
$580$	−115.458	+	317.218i	−0.199065	+	0.546927i
$581$	−241.661	+	418.569i	−0.415939	+	0.720428i
$582$	−95.8779	+	55.3551i	−0.164739	+	0.0951119i
$583$	−653.297	+	115.194i	−1.12058	+	0.197588i
$584$	242.673	−	289.206i	0.415536	−	0.495216i
$585$	−193.713	−	230.858i	−0.331133	−	0.394629i
$586$	44.4328	−	251.991i	0.0758238	−	0.430018i
$587$	125.370	−	45.6308i	0.213577	−	0.0777357i	−0.233016	−	0.972473i	$-0.574859\pi$
$587$	125.370	−	45.6308i	0.213577	−	0.0777357i	0.446593	+	0.894737i	$0.352637\pi$
$588$		−	494.400i		−	0.840817i
$589$		0			0
$590$	26.3192			0.0446088
$591$	−506.652	−	1392.02i	−0.857279	−	2.35536i
$592$	247.575	+	43.6542i	0.418201	+	0.0737401i
$593$	−12.0571	+	10.1171i	−0.0203324	+	0.0170609i	−0.652897	−	0.757447i	$-0.726447\pi$
$593$	−12.0571	+	10.1171i	−0.0203324	+	0.0170609i	0.632565	+	0.774507i	$0.282002\pi$
$594$	296.600	+	248.877i	0.499326	+	0.418985i
$595$	−5.89975	−	33.4591i	−0.00991554	−	0.0562338i
$596$	−153.710	−	266.234i	−0.257903	−	0.446701i
$597$	1265.00	+	730.351i	2.11894	+	1.22337i
$598$	18.9478	+	6.89643i	0.0316853	+	0.0115325i
$599$	−82.9276	+	227.842i	−0.138443	+	0.380370i	−0.989467	−	0.144757i	$-0.953760\pi$
$599$	−82.9276	+	227.842i	−0.138443	+	0.380370i	0.851024	+	0.525127i	$0.175982\pi$
$600$	−152.904	+	264.837i	−0.254839	+	0.441395i
$601$	23.1113	−	13.3433i	0.0384548	−	0.0222019i	−0.480649	−	0.876913i	$-0.659599\pi$
$601$	23.1113	−	13.3433i	0.0384548	−	0.0222019i	0.519104	+	0.854711i	$0.326266\pi$
$602$	166.539	−	29.3653i	0.276642	−	0.0487795i
$603$	−815.842	+	972.282i	−1.35297	+	1.61241i
$604$	330.091	+	393.387i	0.546509	+	0.651304i
$605$	−4.24405	+	24.0692i	−0.00701496	+	0.0397838i
$606$	496.572	−	180.737i	0.819426	−	0.298247i
$607$		−	705.287i		−	1.16192i	−0.813931	−	0.580961i	$-0.802677\pi$
$607$		−	705.287i		−	1.16192i	0.813931	−	0.580961i	$-0.197323\pi$
$608$		0			0
$609$	762.589			1.25220
$610$	−38.4520	−	105.646i	−0.0630360	−	0.173190i
$611$	−101.992	−	17.9840i	−0.166927	−	0.0294337i
$612$	128.776	−	108.056i	0.210418	−	0.176561i
$613$	−608.313	−	510.435i	−0.992353	−	0.832683i	−0.00644655	−	0.999979i	$-0.502052\pi$
$613$	−608.313	−	510.435i	−0.992353	−	0.832683i	−0.985907	+	0.167296i	$0.946496\pi$
$614$	−4.11240	−	23.3226i	−0.00669772	−	0.0379846i
$615$	−586.058	−	1015.08i	−0.952940	−	1.65054i
$616$	−181.240	−	104.639i	−0.294220	−	0.169868i
$617$	965.168	+	351.293i	1.56429	+	0.569356i	0.971715	−	0.236158i	$-0.0758882\pi$
$617$	965.168	+	351.293i	1.56429	+	0.569356i	0.592577	+	0.805513i	$0.298110\pi$
$618$	−78.1974	+	214.846i	−0.126533	+	0.347647i
$619$	340.432	−	589.645i	0.549971	−	0.952577i	−0.448305	−	0.893880i	$-0.647972\pi$
$619$	340.432	−	589.645i	0.549971	−	0.952577i	0.998276	−	0.0586965i	$-0.0186944\pi$
$620$	−331.262	+	191.254i	−0.534293	+	0.308474i
$621$	683.089	−	120.447i	1.09998	−	0.193957i
$622$	31.1591	−	37.1340i	0.0500951	−	0.0597010i
$623$	159.278	+	189.820i	0.255663	+	0.304687i
$624$	−52.2212	+	296.161i	−0.0836878	+	0.474617i
$625$	70.5091	−	25.6632i	0.112815	−	0.0410611i
$626$			28.1011i			0.0448899i
$627$		0			0
$628$	−229.375			−0.365247
$629$	13.5083	+	37.1138i	0.0214759	+	0.0590045i
$630$	−181.118	−	31.9360i	−0.287489	−	0.0506921i
$631$	470.453	−	394.757i	0.745568	−	0.625606i	−0.188759	−	0.982024i	$-0.560446\pi$
$631$	470.453	−	394.757i	0.745568	−	0.625606i	0.934327	+	0.356418i	$0.116002\pi$
$632$	−147.800	−	124.019i	−0.233860	−	0.196232i
$633$	−262.786	−	1490.33i	−0.415143	−	2.35439i
$634$	−93.1044	−	161.262i	−0.146852	−	0.254356i
$635$	−351.500	−	202.939i	−0.553543	−	0.319588i
$636$	1218.76	+	443.591i	1.91629	+	0.697471i
$637$	−33.7052	+	92.6042i	−0.0529124	+	0.145376i
$638$	−73.2650	+	126.899i	−0.114835	+	0.198901i
$639$	2150.88	−	1241.81i	3.36600	−	1.94336i
$640$	−355.923	+	62.7588i	−0.556129	+	0.0980606i
$641$	161.007	−	191.881i	0.251181	−	0.299346i	−0.625690	−	0.780072i	$-0.715182\pi$
$641$	161.007	−	191.881i	0.251181	−	0.299346i	0.876871	+	0.480726i	$0.159627\pi$
$642$	134.736	+	160.572i	0.209870	+	0.250113i
$643$	−65.1381	+	369.417i	−0.101303	+	0.574521i	0.891329	+	0.453357i	$0.149774\pi$
$643$	−65.1381	+	369.417i	−0.101303	+	0.574521i	−0.992633	+	0.121164i	$0.961337\pi$
$644$	−170.370	+	62.0098i	−0.264550	+	0.0962885i
$645$		−	1226.74i		−	1.90192i
$646$		0			0
$647$	−862.929			−1.33374			−0.666869	−	0.745175i	$-0.732366\pi$
$647$	−862.929			−1.33374			−0.666869	+	0.745175i	$0.732366\pi$
$648$	−271.502	−	745.945i	−0.418984	−	1.15115i
$649$	−165.766	−	29.2290i	−0.255417	−	0.0450370i
$650$	22.5811	−	18.9478i	0.0347401	−	0.0291504i
$651$	661.933	+	555.427i	1.01679	+	0.853191i
$652$	131.729	+	747.072i	0.202038	+	1.14582i
$653$	−41.8448	−	72.4774i	−0.0640809	−	0.110991i	0.832205	−	0.554468i	$-0.187078\pi$
$653$	−41.8448	−	72.4774i	−0.0640809	−	0.110991i	−0.896286	+	0.443477i	$0.853745\pi$
$654$	−98.1837	−	56.6864i	−0.150128	−	0.0866765i
$655$	360.629	+	131.258i	0.550578	+	0.200394i
$656$	−283.715	+	779.500i	−0.432492	+	1.18826i
$657$	−1060.92	+	1837.57i	−1.61480	+	2.79691i
$658$	−54.7350	+	31.6013i	−0.0831839	+	0.0480263i
$659$	−430.241	+	75.8630i	−0.652869	+	0.115118i	−0.490266	−	0.871573i	$-0.663100\pi$
$659$	−430.241	+	75.8630i	−0.652869	+	0.115118i	−0.162603	+	0.986692i	$0.551989\pi$
$660$	−471.907	+	562.397i	−0.715010	+	0.852116i
$661$	524.591	+	625.183i	0.793632	+	0.945813i	0.999463	−	0.0327741i	$-0.0104342\pi$
$661$	524.591	+	625.183i	0.793632	+	0.945813i	−0.205831	+	0.978588i	$0.565990\pi$
$662$	32.3248	−	183.323i	0.0488289	−	0.276923i
$663$	−44.3973	+	16.1593i	−0.0669643	+	0.0243730i
$664$			375.464i			0.565457i
$665$		0			0
$666$	213.795			0.321013
$667$	89.7816	+	246.673i	0.134605	+	0.369824i
$668$	808.671	+	142.590i	1.21058	+	0.213459i
$669$	488.161	−	409.616i	0.729688	−	0.612281i
$670$	73.8218	+	61.9438i	0.110182	+	0.0924534i
$671$	124.856	+	708.092i	0.186074	+	1.05528i
$672$	310.228	+	537.332i	0.461650	+	0.799600i
$673$	−741.181	−	427.921i	−1.10131	−	0.635841i	−0.164745	−	0.986336i	$-0.552680\pi$
$673$	−741.181	−	427.921i	−1.10131	−	0.635841i	−0.936565	+	0.350495i	$0.886013\pi$
$674$	58.2239	+	21.1918i	0.0863856	+	0.0314418i
$675$	346.813	−	952.862i	0.513798	−	1.41165i
$676$	−284.204	+	492.256i	−0.420420	+	0.728189i
$677$	62.9559	−	36.3476i	0.0929924	−	0.0536892i	−0.452783	−	0.891621i	$-0.649569\pi$
$677$	62.9559	−	36.3476i	0.0929924	−	0.0536892i	0.545775	+	0.837932i	$0.316235\pi$
$678$	−84.4613	+	14.8928i	−0.124574	+	0.0219658i
$679$	−127.543	+	152.000i	−0.187840	+	0.223859i
$680$	−16.9653	−	20.2185i	−0.0249490	−	0.0297331i
$681$	390.277	−	2213.37i	0.573094	−	3.25018i
$682$	−156.021	+	56.7868i	−0.228769	+	0.0832651i
$683$		−	593.349i		−	0.868739i	−0.900735	−	0.434370i	$-0.856971\pi$
$683$		−	593.349i		−	0.868739i	0.900735	−	0.434370i	$-0.143029\pi$
$684$		0			0
$685$	135.130			0.197269
$686$	63.0512	+	173.232i	0.0919114	+	0.252524i
$687$	−599.825	−	105.765i	−0.873108	−	0.153953i
$688$	−665.069	+	558.059i	−0.966670	+	0.811132i
$689$	−198.039	−	166.175i	−0.287430	−	0.241182i
$690$	−15.5007	−	87.9089i	−0.0224648	−	0.127404i
$691$	174.163	+	301.659i	0.252045	+	0.436554i	0.964089	−	0.265581i	$-0.0855637\pi$
$691$	174.163	+	301.659i	0.252045	+	0.436554i	−0.712044	+	0.702135i	$0.752230\pi$
$692$	232.028	+	133.962i	0.335301	+	0.193586i
$693$	1105.27	+	402.285i	1.59490	+	0.580498i
$694$	46.1170	−	126.705i	0.0664509	−	0.182572i
$695$	−20.2006	+	34.9884i	−0.0290656	+	0.0503430i
$696$	513.042	−	296.205i	0.737129	−	0.425582i
$697$	−128.344	+	22.6305i	−0.184138	+	0.0324685i
$698$	75.6909	−	90.2049i	0.108440	−	0.129233i
$699$	652.037	+	777.067i	0.932814	+	1.11168i
$700$	−46.0253	+	261.022i	−0.0657504	+	0.372889i
$701$	−707.962	+	257.677i	−1.00993	+	0.367585i	−0.793407	−	0.608692i	$-0.791694\pi$
$701$	−707.962	+	257.677i	−1.00993	+	0.367585i	−0.216525	+	0.976277i	$0.569472\pi$
$702$			150.888i			0.214940i
$703$		0			0
$704$	435.620			0.618778
$705$	156.811	+	430.834i	0.222427	+	0.611112i
$706$	20.5186	+	3.61799i	0.0290632	+	0.00512463i
$707$	725.525	−	608.788i	1.02620	−	0.861086i
$708$	252.098	+	211.536i	0.356071	+	0.298779i
$709$	28.5620	+	161.983i	0.0402849	+	0.228467i	0.998302	−	0.0582424i	$-0.0185496\pi$
$709$	28.5620	+	161.983i	0.0402849	+	0.228467i	−0.958018	+	0.286710i	$0.907439\pi$
$710$	−94.2860	−	163.308i	−0.132797	−	0.230011i
$711$	939.095	+	542.187i	1.32081	+	0.762570i
$712$	180.886	+	65.8373i	0.254054	+	0.0924681i
$713$	−101.732	+	279.506i	−0.142681	+	0.392014i
$714$	−14.4165	+	24.9701i	−0.0201912	+	0.0349722i
$715$	126.732	−	73.1686i	0.177247	−	0.102334i
$716$	−487.235	+	85.9126i	−0.680495	+	0.119990i
$717$	987.815	−	1177.23i	1.37771	−	1.64189i
$718$	78.7813	+	93.8879i	0.109723	+	0.130763i
$719$	−174.454	+	989.379i	−0.242635	+	1.37605i	0.583288	+	0.812265i	$0.301766\pi$
$719$	−174.454	+	989.379i	−0.242635	+	1.37605i	−0.825922	+	0.563784i	$0.809345\pi$
$720$	887.249	−	322.932i	1.23229	−	0.448517i
$721$			409.772i			0.568339i
$722$		0			0
$723$	837.111			1.15783
$724$	−184.692	−	507.436i	−0.255099	−	0.700879i
$725$	377.925	+	66.6383i	0.521275	+	0.0919149i
$726$	15.8888	−	13.3323i	0.0218854	−	0.0183641i
$727$	−30.8730	−	25.9055i	−0.0424663	−	0.0356334i	0.621308	−	0.783567i	$-0.286602\pi$
$727$	−30.8730	−	25.9055i	−0.0424663	−	0.0356334i	−0.663774	+	0.747933i	$0.731046\pi$
$728$	−14.1622	−	80.3179i	−0.0194536	−	0.110327i
$729$	427.115	+	739.785i	0.585892	+	1.01479i
$730$	139.520	+	80.5518i	0.191123	+	0.110345i
$731$	−128.172	−	46.6508i	−0.175338	−	0.0638178i
$732$	480.797	−	1320.98i	0.656827	−	1.80462i
$733$	401.131	−	694.780i	0.547246	−	0.947858i	−0.451216	−	0.892415i	$-0.649010\pi$
$733$	401.131	−	694.780i	0.547246	−	0.947858i	0.998462	−	0.0554428i	$-0.0176570\pi$
$734$	−175.370	+	101.250i	−0.238924	+	0.137943i
$735$	429.641	−	75.7572i	0.584545	−	0.103071i
$736$	−137.285	+	163.610i	−0.186529	+	0.222297i
$737$	−396.159	−	472.124i	−0.537529	−	0.640602i
$738$	−122.502	+	694.742i	−0.165992	+	0.941385i
$739$	72.2707	−	26.3044i	0.0977952	−	0.0355945i	−0.292659	−	0.956217i	$-0.594540\pi$
$739$	72.2707	−	26.3044i	0.0977952	−	0.0355945i	0.390454	+	0.920622i	$0.372318\pi$
$740$			239.170i			0.323202i
$741$		0			0
$742$	−157.767			−0.212624
$743$	−316.949	−	870.810i	−0.426580	−	1.17202i	−0.947875	−	0.318642i	$-0.896773\pi$
$743$	−316.949	−	870.810i	−0.426580	−	1.17202i	0.521295	−	0.853376i	$-0.325449\pi$
$744$	661.063	+	116.563i	0.888526	+	0.156671i
$745$	207.808	−	174.372i	0.278937	−	0.234056i
$746$	−233.594	−	196.009i	−0.313129	−	0.262747i
$747$	−366.435	−	2078.16i	−0.490543	−	2.78201i
$748$	40.8144	+	70.6925i	0.0545646	+	0.0945087i
$749$	325.349	+	187.840i	0.434378	+	0.250788i
$750$	−340.441	−	123.910i	−0.453921	−	0.165214i
$751$	−442.411	+	1215.52i	−0.589096	+	1.61853i	0.183064	+	0.983101i	$0.441398\pi$
$751$	−442.411	+	1215.52i	−0.589096	+	1.61853i	−0.772160	+	0.635428i	$0.780824\pi$
$752$	162.238	−	281.005i	0.215743	−	0.373677i
$753$	−1859.38	+	1073.51i	−2.46929	+	1.42565i
$754$	−56.2362	+	9.91596i	−0.0745838	+	0.0131511i
$755$	−291.279	+	347.133i	−0.385800	+	0.459778i
$756$	−872.084	−	1039.31i	−1.15355	−	1.37475i
$757$	84.6662	−	480.166i	0.111844	−	0.634301i	−0.876420	−	0.481548i	$-0.840075\pi$
$757$	84.6662	−	480.166i	0.111844	−	0.634301i	0.988264	−	0.152754i	$-0.0488141\pi$
$758$	−14.8673	+	5.41125i	−0.0196138	+	0.00713885i
$759$			570.891i			0.752162i
$760$		0			0
$761$	−271.919			−0.357318			−0.178659	−	0.983911i	$-0.557176\pi$
$761$	−271.919			−0.357318			−0.178659	+	0.983911i	$0.557176\pi$
$762$	117.808	+	323.674i	0.154603	+	0.424769i
$763$	−200.107	−	35.2843i	−0.262263	−	0.0462441i
$764$	949.801	−	796.978i	1.24320	−	1.04316i
$765$	113.634	+	95.3503i	0.148541	+	0.124641i
$766$	37.6255	+	213.385i	0.0491194	+	0.278570i
$767$	−32.7983	−	56.8084i	−0.0427619	−	0.0740657i
$768$	−522.021	−	301.389i	−0.679715	−	0.392434i
$769$	−720.325	−	262.177i	−0.936703	−	0.340932i	−0.171840	−	0.985125i	$-0.554971\pi$
$769$	−720.325	−	262.177i	−0.936703	−	0.340932i	−0.764863	+	0.644193i	$0.777193\pi$
$770$	30.5440	−	83.9190i	0.0396675	−	0.108986i
$771$	1109.46	−	1921.64i	1.43899	−	2.49240i
$772$	−241.322	+	139.327i	−0.312593	+	0.180476i
$773$	−1022.72	+	180.334i	−1.32306	+	0.233291i	−0.790166	−	0.612893i	$-0.790006\pi$
$773$	−1022.72	+	180.334i	−1.32306	+	0.233291i	−0.532892	+	0.846184i	$0.678895\pi$
$774$	−474.594	+	565.599i	−0.613171	+	0.730748i
$775$	279.506	+	333.102i	0.360652	+	0.429809i
$776$	−26.7665	+	151.800i	−0.0344929	+	0.195619i
$777$	507.704	−	184.789i	0.653416	−	0.237824i
$778$		−	306.268i		−	0.393660i
$779$		0			0
$780$	−286.106			−0.366803
$781$	412.477	+	1133.27i	0.528140	+	1.45105i
$782$	−9.77433	−	1.72348i	−0.0124991	−	0.00220394i
$783$	−1504.78	+	1262.66i	−1.92181	+	1.61259i
$784$	−236.520	−	198.464i	−0.301683	−	0.253142i
$785$	−35.1473	−	199.330i	−0.0447736	−	0.253924i
$786$	−162.844	−	282.054i	−0.207181	−	0.358848i
$787$	−164.535	−	94.9942i	−0.209066	−	0.120704i	0.391811	−	0.920046i	$-0.371849\pi$
$787$	−164.535	−	94.9942i	−0.209066	−	0.120704i	−0.600877	+	0.799341i	$0.705182\pi$
$788$	−937.247	−	341.130i	−1.18940	−	0.432906i
$789$	−116.055	+	318.858i	−0.147091	+	0.404129i
$790$	41.1662	−	71.3020i	0.0521092	−	0.0902557i
$791$	−133.119	+	76.8561i	−0.168292	+	0.0971631i
$792$	899.840	−	158.666i	1.13616	−	0.200336i
$793$	−180.113	+	214.650i	−0.227128	+	0.270681i
$794$	68.8195	+	82.0159i	0.0866745	+	0.103295i
$795$	−198.736	+	1127.09i	−0.249982	+	1.41772i
$796$	924.182	−	336.375i	1.16103	−	0.422581i
$797$			753.381i			0.945270i	0.881258	+	0.472635i	$0.156697\pi$
$797$			753.381i			0.945270i	−0.881258	+	0.472635i	$0.843303\pi$
$798$		0			0
$799$	50.9775			0.0638016
$800$	106.789	+	293.400i	0.133486	+	0.366751i
$801$	−1065.45	−	187.867i	−1.33014	−	0.234540i
$802$	117.286	−	98.4149i	0.146242	−	0.122712i
$803$	−789.279	−	662.284i	−0.982913	−	0.824762i
$804$	209.240	+	1186.66i	0.260248	+	1.47594i
$805$	−79.9933	−	138.552i	−0.0993705	−	0.172115i
$806$	−56.0357	−	32.3522i	−0.0695232	−	0.0401392i
$807$	−868.461	−	316.094i	−1.07616	−	0.391690i
$808$	251.641	−	691.378i	0.311437	−	0.855666i
$809$	−579.462	+	1003.66i	−0.716270	+	1.24062i	0.246198	+	0.969220i	$0.420819\pi$
$809$	−579.462	+	1003.66i	−0.716270	+	1.24062i	−0.962468	+	0.271396i	$0.912515\pi$
$810$	293.361	−	169.372i	0.362175	−	0.209102i
$811$	−290.044	+	51.1425i	−0.357637	+	0.0630611i	−0.349580	−	0.936906i	$-0.613676\pi$
$811$	−290.044	+	51.1425i	−0.357637	+	0.0630611i	−0.00805699	+	0.999968i	$0.502565\pi$
$812$	330.041	−	393.328i	0.406455	−	0.484394i
$813$	−681.385	−	812.043i	−0.838112	−	0.998823i
$814$	−18.0273	+	102.238i	−0.0221466	+	0.125600i
$815$	−629.030	+	228.948i	−0.771817	+	0.280918i
$816$		−	148.027i		−	0.181405i
$817$		0			0
$818$	247.326			0.302355
$819$	156.773	+	430.731i	0.191420	+	0.525923i
$820$	−777.199	−	137.041i	−0.947804	−	0.167123i
$821$	−903.558	+	758.175i	−1.10056	+	0.923478i	−0.997463	−	0.0711937i	$-0.977319\pi$
$821$	−903.558	+	758.175i	−1.10056	+	0.923478i	−0.103095	+	0.994671i	$0.532875\pi$
$822$	−87.8479	−	73.7132i	−0.106871	−	0.0896754i
$823$	158.036	+	896.265i	0.192024	+	1.08902i	0.916594	+	0.399820i	$0.130927\pi$
$823$	158.036	+	896.265i	0.192024	+	1.08902i	−0.724570	+	0.689202i	$0.757961\pi$
$824$	159.164	+	275.680i	0.193160	+	0.334563i
$825$	722.773	+	417.293i	0.876088	+	0.505810i
$826$	−37.6173	−	13.6916i	−0.0455415	−	0.0165757i
$827$	199.831	−	549.032i	0.241634	−	0.663884i	−0.758294	−	0.651913i	$-0.773967\pi$
$827$	199.831	−	549.032i	0.241634	−	0.663884i	0.999928	−	0.0119719i	$-0.00381086\pi$
$828$	395.794	−	685.536i	0.478013	−	0.827942i
$829$	−594.252	+	343.092i	−0.716830	+	0.413862i	−0.813585	−	0.581446i	$-0.802487\pi$
$829$	−594.252	+	343.092i	−0.716830	+	0.413862i	0.0967546	+	0.995308i	$0.469154\pi$
$830$	−157.787	+	27.8221i	−0.190105	+	0.0335206i
$831$	349.497	−	416.514i	0.420574	−	0.501220i
$832$	109.122	+	130.047i	0.131156	+	0.156306i
$833$	8.42322	−	47.7705i	0.0101119	−	0.0573475i
$834$	32.2186	−	11.7266i	0.0386314	−	0.0140607i
$835$			724.595i			0.867778i
$836$		0			0
$837$	−2225.81			−2.65927
$838$	3.61818	+	9.94086i	0.00431763	+	0.0118626i
$839$	−827.540	−	145.918i	−0.986341	−	0.173919i	−0.342865	−	0.939385i	$-0.611397\pi$
$839$	−827.540	−	145.918i	−0.986341	−	0.173919i	−0.643476	+	0.765466i	$0.722508\pi$
$840$	−276.582	+	232.080i	−0.329264	+	0.276285i
$841$	74.7590	+	62.7303i	0.0888930	+	0.0745901i
$842$	−61.1247	−	346.655i	−0.0725947	−	0.411705i
$843$	725.596	+	1256.77i	0.860731	+	1.49083i
$844$	−882.414	−	509.462i	−1.04551	−	0.603628i
$845$	−471.325	−	171.548i	−0.557782	−	0.203016i
$846$	94.3795	−	259.305i	0.111560	−	0.306508i
$847$	18.5870	−	32.1937i	0.0219445	−	0.0380090i
$848$	701.450	−	404.982i	0.827182	−	0.477574i
$849$	1638.90	−	288.982i	1.93039	−	0.340379i
$850$	−9.32656	+	11.1150i	−0.0109724	+	0.0130764i
$851$	119.547	+	142.470i	0.140478	+	0.167415i
$852$	409.441	−	2322.05i	0.480564	−	2.72541i
$853$	−332.733	+	121.105i	−0.390074	+	0.141975i	−0.529609	−	0.848242i	$-0.677661\pi$
$853$	−332.733	+	121.105i	−0.390074	+	0.141975i	0.139535	+	0.990217i	$0.455439\pi$
$854$			171.000i			0.200234i
$855$		0			0
$856$	291.844			0.340939
$857$	−358.527	−	985.044i	−0.418351	−	1.14941i	−0.952638	−	0.304106i	$-0.901642\pi$
$857$	−358.527	−	985.044i	−0.418351	−	1.14941i	0.534287	−	0.845303i	$-0.320580\pi$
$858$	−122.302	−	21.5651i	−0.142543	−	0.0251342i
$859$	260.638	−	218.701i	0.303420	−	0.254600i	−0.478346	−	0.878171i	$-0.658764\pi$
$859$	260.638	−	218.701i	0.303420	−	0.254600i	0.781766	+	0.623572i	$0.214319\pi$
$860$	−632.728	−	530.922i	−0.735731	−	0.617351i
$861$	309.578	+	1755.70i	0.359556	+	2.03914i
$862$	−117.549	−	203.600i	−0.136367	−	0.236195i
$863$	−973.829	−	562.241i	−1.12842	−	0.651495i	−0.184885	−	0.982760i	$-0.559191\pi$
$863$	−973.829	−	562.241i	−1.12842	−	0.651495i	−0.943538	+	0.331265i	$0.892525\pi$
$864$	−1501.85	−	546.627i	−1.73825	−	0.632670i
$865$	−80.8606	+	222.163i	−0.0934804	+	0.256835i
$866$	−122.026	+	211.355i	−0.140907	+	0.244059i
$867$	−1372.25	+	792.266i	−1.58275	+	0.913802i
$868$	572.956	−	101.028i	0.660088	−	0.116391i
$869$	−338.462	+	403.363i	−0.389485	+	0.464170i
$870$	162.495	+	193.655i	0.186776	+	0.222591i
$871$	41.7071	−	236.533i	0.0478842	−	0.271565i
$872$	−148.330	+	53.9876i	−0.170103	+	0.0619124i
$873$		−	866.325i		−	0.992354i
$874$		0			0
$875$	−649.318			−0.742078
$876$	688.970	+	1892.93i	0.786496	+	2.16088i
$877$	−629.747	−	111.041i	−0.718070	−	0.126615i	−0.197338	−	0.980336i	$-0.563230\pi$
$877$	−629.747	−	111.041i	−0.718070	−	0.126615i	−0.520732	+	0.853720i	$0.674341\pi$
$878$	−134.218	+	112.622i	−0.152868	+	0.128271i
$879$	2162.75	+	1814.76i	2.46046	+	2.06457i
$880$	79.6148	+	451.518i	0.0904713	+	0.513088i
$881$	160.656	+	278.264i	0.182356	+	0.315851i	0.942683	−	0.333691i	$-0.108294\pi$
$881$	160.656	+	278.264i	0.182356	+	0.315851i	−0.760326	+	0.649542i	$0.774961\pi$
$882$	−227.398	−	131.288i	−0.257821	−	0.148853i
$883$	583.163	+	212.254i	0.660434	+	0.240378i	0.650424	−	0.759572i	$-0.274591\pi$
$883$	583.163	+	212.254i	0.660434	+	0.240378i	0.0100104	+	0.999950i	$0.496814\pi$
$884$	−10.8801	+	29.8928i	−0.0123078	+	0.0338154i
$885$	−145.198	+	251.490i	−0.164066	+	0.284170i
$886$	36.2960	−	20.9555i	0.0409662	−	0.0236518i
$887$	−246.815	+	43.5201i	−0.278258	+	0.0490644i	−0.311036	−	0.950398i	$-0.600676\pi$
$887$	−246.815	+	43.5201i	−0.278258	+	0.0490644i	0.0327774	+	0.999463i	$0.489565\pi$
$888$	269.789	−	321.522i	0.303816	−	0.362074i
$889$	396.818	+	472.909i	0.446364	+	0.531956i
$890$	−14.2640	+	80.8953i	−0.0160270	+	0.0908936i
$891$	−2035.77	+	740.961i	−2.28482	+	0.831607i
$892$		−	429.061i		−	0.481010i
$893$		0			0
$894$	−230.216			−0.257512
$895$	−149.318	−	410.249i	−0.166836	−	0.458379i
$896$	541.359	+	95.4561i	0.604195	+	0.106536i
$897$	−170.430	+	143.007i	−0.190000	+	0.159429i
$898$	48.4812	+	40.6806i	0.0539880	+	0.0453013i
$899$	−146.274	−	829.562i	−0.162708	−	0.922760i
$900$	−578.612	−	1002.19i	−0.642903	−	1.11354i
$901$	110.202	+	63.6254i	0.122311	+	0.0706165i
$902$	−321.900	−	117.162i	−0.356874	−	0.129892i
$903$	−638.166	+	1753.35i	−0.706718	+	1.94169i
$904$	−59.7049	+	103.412i	−0.0660452	+	0.114394i
$905$	412.669	−	238.254i	0.455988	−	0.263265i
$906$	378.722	−	66.7789i	0.418015	−	0.0737074i
$907$	487.169	−	580.585i	0.537121	−	0.640116i	−0.427419	−	0.904054i	$-0.640577\pi$
$907$	487.169	−	580.585i	0.537121	−	0.640116i	0.964540	+	0.263938i	$0.0850214\pi$
$908$	−972.703	−	1159.22i	−1.07126	−	1.27668i
$909$	−718.058	+	4072.31i	−0.789943	+	4.47999i
$910$	32.7038	−	11.9032i	0.0359382	−	0.0130805i
$911$		−	410.330i		−	0.450417i	−0.974311	−	0.225208i	$-0.927694\pi$
$911$		−	410.330i		−	0.450417i	0.974311	−	0.225208i	$-0.0723063\pi$
$912$		0			0
$913$	1024.69			1.12233
$914$	−131.606	−	361.584i	−0.143989	−	0.395606i
$915$	1221.62	+	215.405i	1.33511	+	0.235415i
$916$	−314.150	+	263.603i	−0.342959	+	0.287777i
$917$	−447.155	−	375.207i	−0.487628	−	0.409168i
$918$	−12.8970	−	73.1425i	−0.0140490	−	0.0796759i
$919$	−498.853	−	864.038i	−0.542821	−	0.940194i	−0.998741	−	0.0501729i	$-0.984023\pi$
$919$	−498.853	−	864.038i	−0.542821	−	0.940194i	0.455919	−	0.890021i	$-0.349311\pi$
$920$	−107.633	−	62.1420i	−0.116992	−	0.0675456i
$921$	245.544	+	89.3707i	0.266606	+	0.0970366i
$922$	18.8088	−	51.6766i	0.0203999	−	0.0560484i
$923$	−234.994	+	407.021i	−0.254598	+	0.440977i
$924$	967.049	−	558.326i	1.04659	−	0.604249i
$925$	267.756	−	47.2126i	0.289466	−	0.0510407i
$926$	−0.308961	+	0.368205i	−0.000333651	+	0.000397630i
$927$	−1150.01	−	1370.53i	−1.24057	−	1.47845i
$928$	105.031	−	595.663i	0.113180	−	0.641878i
$929$	−1247.32	+	453.987i	−1.34265	+	0.488684i	−0.910645	−	0.413189i	$-0.864415\pi$
$929$	−1247.32	+	453.987i	−1.34265	+	0.488684i	−0.432002	+	0.901873i	$0.642193\pi$
$930$			286.446i			0.308007i
$931$		0			0
$932$	682.991			0.732823
$933$	182.931	+	502.600i	0.196068	+	0.538692i
$934$	−184.113	−	32.4641i	−0.197123	−	0.0347581i
$935$	−55.1788	+	46.3005i	−0.0590147	+	0.0495192i
$936$	272.776	+	228.886i	0.291427	+	0.244536i
$937$	−140.090	−	794.488i	−0.149509	−	0.847906i	−0.963636	−	0.267219i	$-0.913895\pi$
$937$	−140.090	−	794.488i	−0.149509	−	0.847906i	0.814127	−	0.580687i	$-0.197216\pi$
$938$	−73.2874	−	126.938i	−0.0781316	−	0.135328i
$939$	−268.517	−	155.028i	−0.285961	−	0.165100i
$940$	290.082	+	105.581i	0.308597	+	0.112320i
$941$	−132.578	+	364.256i	−0.140891	+	0.387095i	−0.989990	−	0.141139i	$-0.954923\pi$
$941$	−132.578	+	364.256i	−0.140891	+	0.387095i	0.849099	+	0.528234i	$0.177146\pi$
$942$	−85.8852	+	148.758i	−0.0911733	+	0.157917i
$943$	−531.466	+	306.842i	−0.563591	+	0.325389i
$944$	202.396	−	35.6879i	0.214403	−	0.0378050i
$945$	769.544	−	917.107i	0.814332	−	0.970484i
$946$	−230.455	−	274.645i	−0.243610	−	0.290323i
$947$	−90.8468	+	515.218i	−0.0959312	+	0.544053i	0.898527	+	0.438918i	$0.144638\pi$
$947$	−90.8468	+	515.218i	−0.0959312	+	0.544053i	−0.994458	+	0.105134i	$0.966473\pi$
$948$	967.388	−	352.100i	1.02045	−	0.371414i
$949$		−	401.527i		−	0.423106i
$950$		0			0
$951$	2054.56			2.16042
$952$	13.7302	+	37.7233i	0.0144224	+	0.0396253i
$953$	508.409	+	89.6462i	0.533483	+	0.0940674i	0.433898	−	0.900962i	$-0.357138\pi$
$953$	508.409	+	89.6462i	0.533483	+	0.0940674i	0.0995841	+	0.995029i	$0.468249\pi$
$954$	527.670	−	442.767i	0.553113	−	0.464117i
$955$	838.123	+	703.269i	0.877616	+	0.736407i
$956$	−179.675	−	1018.99i	−0.187945	−	1.06589i
$957$	−808.379	−	1400.15i	−0.844701	−	1.46307i
$958$	27.6787	+	15.9803i	0.0288921	+	0.0166809i
$959$	−193.137	−	70.2961i	−0.201394	−	0.0733015i
$960$	257.043	−	706.221i	0.267753	−	0.735646i
$961$	−3.26030	+	5.64700i	−0.00339261	+	0.00587617i
$962$	−35.0372	+	20.2288i	−0.0364212	+	0.0210278i
$963$	−1615.33	+	284.826i	−1.67739	+	0.295770i
$964$	362.293	−	431.765i	0.375823	−	0.447889i
$965$	−158.055	−	188.363i	−0.163788	−	0.195194i
$966$	−23.5766	+	133.709i	−0.0244064	+	0.138416i
$967$	−463.682	+	168.766i	−0.479506	+	0.174526i	−0.570454	−	0.821330i	$-0.693233\pi$
$967$	−463.682	+	168.766i	−0.479506	+	0.174526i	0.0909479	+	0.995856i	$0.471010\pi$
$968$		−	28.8783i		−	0.0298329i
$969$		0			0
$970$	−65.7768			−0.0678112
$971$	45.9990	+	126.381i	0.0473728	+	0.130156i	0.961123	−	0.276121i	$-0.0890491\pi$
$971$	45.9990	+	126.381i	0.0473728	+	0.130156i	−0.913750	+	0.406277i	$0.866827\pi$
$972$	1779.38	+	313.753i	1.83064	+	0.322791i
$973$	47.0735	−	39.4994i	0.0483798	−	0.0405954i
$974$	133.657	+	112.151i	0.137224	+	0.115145i
$975$	56.4780	+	320.303i	0.0579262	+	0.328516i
$976$	−438.950	−	760.284i	−0.449744	−	0.778979i
$977$	−605.791	−	349.754i	−0.620053	−	0.357988i	0.156837	−	0.987625i	$-0.449870\pi$
$977$	−605.791	−	349.754i	−0.620053	−	0.357988i	−0.776890	+	0.629637i	$0.783204\pi$
$978$	533.825	+	194.296i	0.545833	+	0.198667i
$979$	179.678	−	493.661i	0.183532	−	0.504251i
$980$	146.870	−	254.387i	0.149868	−	0.259578i
$981$	768.303	−	443.580i	0.783184	−	0.452171i
$982$	−132.899	+	23.4337i	−0.135335	+	0.0238633i
$983$	391.375	−	466.423i	0.398143	−	0.474489i	−0.529309	−	0.848429i	$-0.677549\pi$
$983$	391.375	−	466.423i	0.398143	−	0.474489i	0.927453	+	0.373940i	$0.121993\pi$
$984$	890.223	+	1060.93i	0.904698	+	1.07818i
$985$	152.832	−	866.752i	0.155159	−	0.879951i
$986$	26.4128	−	9.61346i	0.0267878	−	0.00974996i
$987$		−	697.354i		−	0.706539i
$988$		0			0
$989$	−642.285			−0.649428
$990$	133.357	+	366.396i	0.134704	+	0.370097i
$991$	916.252	+	161.560i	0.924573	+	0.163027i	0.615614	−	0.788048i	$-0.288908\pi$
$991$	916.252	+	161.560i	0.924573	+	0.163027i	0.308959	+	0.951075i	$0.400019\pi$
$992$	525.016	−	440.541i	0.529250	−	0.444093i
$993$	1573.39	+	1320.23i	1.58449	+	1.32954i
$994$	49.8054	+	282.460i	0.0501060	+	0.284165i
$995$	433.927	+	751.583i	0.436107	+	0.755360i
$996$	−1734.98	−	1001.69i	−1.74194	−	1.00571i
$997$	1215.70	+	442.480i	1.21936	+	0.443811i	0.869941	−	0.493155i	$-0.164156\pi$
$997$	1215.70	+	442.480i	1.21936	+	0.443811i	0.349420	+	0.936966i	$0.386379\pi$
$998$	−40.2509	+	110.589i	−0.0403316	+	0.110810i
$999$	−695.861	+	1205.27i	−0.696558	+	1.20647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.f.k.299.11		144
19.2	odd	18		361.3.b.d.360.11	✓	24
19.3	odd	18		361.3.d.g.69.11		48
19.4	even	9	inner	361.3.f.k.262.14		144
19.5	even	9		361.3.d.g.293.11		48
19.6	even	9	inner	361.3.f.k.333.11		144
19.7	even	3	inner	361.3.f.k.116.14		144
19.8	odd	6	inner	361.3.f.k.307.14		144
19.9	even	9	inner	361.3.f.k.127.14		144
19.10	odd	18	inner	361.3.f.k.127.11		144
19.11	even	3	inner	361.3.f.k.307.11		144
19.12	odd	6	inner	361.3.f.k.116.11		144
19.13	odd	18	inner	361.3.f.k.333.14		144
19.14	odd	18		361.3.d.g.293.14		48
19.15	odd	18	inner	361.3.f.k.262.11		144
19.16	even	9		361.3.d.g.69.14		48
19.17	even	9		361.3.b.d.360.14	yes	24
19.18	odd	2	inner	361.3.f.k.299.14		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.3.b.d.360.11	✓	24	19.2	odd	18
361.3.b.d.360.14	yes	24	19.17	even	9
361.3.d.g.69.11		48	19.3	odd	18
361.3.d.g.69.14		48	19.16	even	9
361.3.d.g.293.11		48	19.5	even	9
361.3.d.g.293.14		48	19.14	odd	18
361.3.f.k.116.11		144	19.12	odd	6	inner
361.3.f.k.116.14		144	19.7	even	3	inner
361.3.f.k.127.11		144	19.10	odd	18	inner
361.3.f.k.127.14		144	19.9	even	9	inner
361.3.f.k.262.11		144	19.15	odd	18	inner
361.3.f.k.262.14		144	19.4	even	9	inner
361.3.f.k.299.11		144	1.1	even	1	trivial
361.3.f.k.299.14		144	19.18	odd	2	inner
361.3.f.k.307.11		144	19.11	even	3	inner
361.3.f.k.307.14		144	19.8	odd	6	inner
361.3.f.k.333.11		144	19.6	even	9	inner
361.3.f.k.333.14		144	19.13	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.172450 - 0.473803i) q^{2} +(5.47876 + 0.966054i) q^{3} +(2.86943 - 2.40774i) q^{4} +(2.53204 + 2.12463i) q^{5} +(-0.487095 - 2.76245i) q^{6} +(-2.51371 - 4.35388i) q^{7} +(-3.38227 - 1.95275i) q^{8} +(20.6264 + 7.50738i) q^{9} +O(q^{10})\)	\(q+(-0.172450 - 0.473803i) q^{2} +(5.47876 + 0.966054i) q^{3} +(2.86943 - 2.40774i) q^{4} +(2.53204 + 2.12463i) q^{5} +(-0.487095 - 2.76245i) q^{6} +(-2.51371 - 4.35388i) q^{7} +(-3.38227 - 1.95275i) q^{8} +(20.6264 + 7.50738i) q^{9} +(0.570007 - 1.56608i) q^{10} +(-5.32930 + 9.23062i) q^{11} +(18.0469 - 10.4194i) q^{12} +(-4.09063 + 0.721288i) q^{13} +(-1.62939 + 1.94183i) q^{14} +(11.8199 + 14.0864i) q^{15} +(2.25984 - 12.8162i) q^{16} +(1.92127 - 0.699283i) q^{17} -11.0675i q^{18} +12.3811 q^{20} +(-9.56595 - 26.2822i) q^{21} +(5.29254 + 0.933217i) q^{22} +(7.37523 - 6.18855i) q^{23} +(-16.6442 - 13.9661i) q^{24} +(-2.44405 - 13.8609i) q^{25} +(1.04718 + 1.81377i) q^{26} +(62.3929 + 36.0225i) q^{27} +(-17.6959 - 6.44078i) q^{28} +(-9.32536 + 25.6212i) q^{29} +(4.63585 - 8.02954i) q^{30} +(-26.7556 + 15.4473i) q^{31} +(-21.8467 + 3.85217i) q^{32} +(-38.1152 + 45.4240i) q^{33} +(-0.662646 - 0.789711i) q^{34} +(2.88557 - 16.3649i) q^{35} +(77.2616 - 28.1209i) q^{36} +19.3174i q^{37} -23.1084 q^{39} +(-4.41515 - 12.1305i) q^{40} +(-62.7733 - 11.0686i) q^{41} +(-10.8030 + 9.06476i) q^{42} +(-51.1046 - 42.8818i) q^{43} +(6.93285 + 39.3181i) q^{44} +(36.2763 + 62.8324i) q^{45} +(-4.20402 - 2.42719i) q^{46} +(23.4295 + 8.52763i) q^{47} +(24.7622 - 68.0337i) q^{48} +(11.8625 - 20.5465i) q^{49} +(-6.14586 + 3.54832i) q^{50} +(11.2017 - 1.97516i) q^{51} +(-10.0011 + 11.9188i) q^{52} +(40.0061 + 47.6775i) q^{53} +(6.30793 - 35.7741i) q^{54} +(-33.1057 + 12.0495i) q^{55} +19.6346i q^{56} +13.7476 q^{58} +(5.40126 + 14.8398i) q^{59} +(67.8328 + 11.9608i) q^{60} +(51.6764 - 43.3616i) q^{61} +(11.9330 + 10.0130i) q^{62} +(-19.1625 - 108.676i) q^{63} +(-20.4351 - 35.3947i) q^{64} +(-11.8901 - 6.86475i) q^{65} +(28.0950 + 10.2258i) q^{66} +(-19.7767 + 54.3360i) q^{67} +(3.82924 - 6.63244i) q^{68} +(46.3856 - 26.7808i) q^{69} +(-8.25136 + 1.45494i) q^{70} +(72.7304 - 86.6767i) q^{71} +(-55.1038 - 65.6701i) q^{72} +(-16.7860 + 95.1980i) q^{73} +(9.15264 - 3.33129i) q^{74} -78.3016i q^{75} +53.5853 q^{77} +(3.98505 + 10.9488i) q^{78} +(48.6512 + 8.57853i) q^{79} +(32.9517 - 27.6497i) q^{80} +(155.703 + 130.651i) q^{81} +(5.58092 + 31.6510i) q^{82} +(-48.0685 - 83.2571i) q^{83} +(-90.7295 - 52.3827i) q^{84} +(6.35044 + 2.31137i) q^{85} +(-11.5046 + 31.6085i) q^{86} +(-75.8429 + 131.364i) q^{87} +(36.0502 - 20.8136i) q^{88} +(-48.5394 + 8.55881i) q^{89} +(23.5143 - 28.0233i) q^{90} +(13.4231 + 15.9970i) q^{91} +(6.26229 - 35.5152i) q^{92} +(-161.510 + 58.7849i) q^{93} -12.5716i q^{94} -123.415 q^{96} +(-13.4988 - 37.0877i) q^{97} +(-11.7807 - 2.07725i) q^{98} +(-179.222 + 150.385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 24 q^{7}+O(q^{10}) \) 144 * q - 24 * q^7	\( 144 q - 24 q^{7} + 192 q^{11} + 528 q^{20} - 228 q^{26} + 1440 q^{30} + 408 q^{39} + 264 q^{45} - 336 q^{49} + 216 q^{58} + 24 q^{64} + 480 q^{68} - 144 q^{77} + 1704 q^{83} - 3216 q^{87} - 3624 q^{96}+O(q^{100}) \) 144 * q - 24 * q^7 + 192 * q^11 + 528 * q^20 - 228 * q^26 + 1440 * q^30 + 408 * q^39 + 264 * q^45 - 336 * q^49 + 216 * q^58 + 24 * q^64 + 480 * q^68 - 144 * q^77 + 1704 * q^83 - 3216 * q^87 - 3624 * q^96

Introduction

L-functions

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