LMFDB - Embedded newform 668.2.e.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			21.1
Character	$\chi$	$=$	668.21
Dual form			668.2.e.a.509.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.30940 - 0.504914i) q^{3} +(-2.26577 - 2.68874i) q^{5} +(1.34830 - 1.87063i) q^{7} +(7.83367 + 2.44733i) q^{9} +O(q^{10})$	\(q+(-3.30940 - 0.504914i) q^{3} +(-2.26577 - 2.68874i) q^{5} +(1.34830 - 1.87063i) q^{7} +(7.83367 + 2.44733i) q^{9} +(4.12227 - 3.89463i) q^{11} +(0.147148 - 1.10424i) q^{13} +(6.14075 + 10.0421i) q^{15} +(2.68317 - 4.03629i) q^{17} +(-7.00893 - 1.61969i) q^{19} +(-5.40658 + 5.50988i) q^{21} +(-0.971946 - 4.60119i) q^{23} +(-1.24807 + 7.25647i) q^{25} +(-15.6642 - 7.64811i) q^{27} +(-1.17751 + 5.57434i) q^{29} +(-0.811528 + 0.155444i) q^{31} +(-15.6087 + 10.8075i) q^{33} +(-8.08457 + 0.613182i) q^{35} +(6.51057 - 2.03398i) q^{37} +(-1.04451 + 3.58006i) q^{39} +(6.16653 - 2.45231i) q^{41} +(-5.99079 - 2.12358i) q^{43} +(-11.1691 - 26.6077i) q^{45} +(-0.401377 + 1.59837i) q^{47} +(0.532123 + 1.59648i) q^{49} +(-10.9177 + 12.0029i) q^{51} +(2.67386 + 2.00522i) q^{53} +(-19.8117 - 2.25937i) q^{55} +(22.3775 + 8.89911i) q^{57} +(5.27120 + 7.92946i) q^{59} +(-3.18062 - 4.07808i) q^{61} +(15.1402 - 11.3541i) q^{63} +(-3.30240 + 2.10631i) q^{65} +(0.337603 - 0.400625i) q^{67} +(0.893356 + 15.7179i) q^{69} +(-0.366451 - 3.86105i) q^{71} +(3.53031 - 6.29683i) q^{73} +(7.79424 - 23.3844i) q^{75} +(-1.72733 - 12.9624i) q^{77} +(-9.00987 - 0.341191i) q^{79} +(27.7351 + 19.2038i) q^{81} +(2.05692 - 0.558109i) q^{83} +(-16.9320 + 1.93096i) q^{85} +(6.71142 - 17.8532i) q^{87} +(-8.86736 + 14.5010i) q^{89} +(-1.86722 - 1.76410i) q^{91} +(2.76416 - 0.104675i) q^{93} +(11.5257 + 22.5150i) q^{95} +(-15.2582 - 2.92263i) q^{97} +(41.8239 - 20.4207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{23}{83}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−3.30940	−	0.504914i	−1.91068	−	0.291512i	−0.916570	−	0.399873i	$-0.869054\pi$
$3$	−3.30940	−	0.504914i	−1.91068	−	0.291512i	−0.994112	+	0.108361i	$0.965440\pi$
$4$		0			0
$5$	−2.26577	−	2.68874i	−1.01328	−	1.20244i	−0.979174	−	0.203021i	$-0.934924\pi$
$5$	−2.26577	−	2.68874i	−1.01328	−	1.20244i	−0.0341086	−	0.999418i	$-0.510859\pi$
$6$		0			0
$7$	1.34830	−	1.87063i	0.509611	−	0.707031i	−0.475353	−	0.879795i	$-0.657679\pi$
$7$	1.34830	−	1.87063i	0.509611	−	0.707031i	0.984963	+	0.172764i	$0.0552699\pi$
$8$		0			0
$9$	7.83367	+	2.44733i	2.61122	+	0.815776i
$10$		0			0
$11$	4.12227	−	3.89463i	1.24291	−	1.17427i	0.265228	−	0.964186i	$-0.414553\pi$
$11$	4.12227	−	3.89463i	1.24291	−	1.17427i	0.977682	−	0.210088i	$-0.0673751\pi$
$12$		0			0
$13$	0.147148	−	1.10424i	0.0408114	−	0.306260i	−0.958933	−	0.283634i	$-0.908460\pi$
$13$	0.147148	−	1.10424i	0.0408114	−	0.306260i	0.999744	−	0.0226262i	$-0.00720275\pi$
$14$		0			0
$15$	6.14075	+	10.0421i	1.58554	+	2.59286i
$16$		0			0
$17$	2.68317	−	4.03629i	0.650765	−	0.978944i	−0.348370	−	0.937357i	$-0.613265\pi$
$17$	2.68317	−	4.03629i	0.650765	−	0.978944i	0.999135	−	0.0415872i	$-0.0132414\pi$
$18$		0			0
$19$	−7.00893	−	1.61969i	−1.60796	−	0.371583i	−0.676792	−	0.736174i	$-0.736630\pi$
$19$	−7.00893	−	1.61969i	−1.60796	−	0.371583i	−0.931168	+	0.364591i	$0.881209\pi$
$20$		0			0
$21$	−5.40658	+	5.50988i	−1.17981	+	1.20235i
$22$		0			0
$23$	−0.971946	−	4.60119i	−0.202665	−	0.959414i	−0.954073	−	0.299575i	$-0.903155\pi$
$23$	−0.971946	−	4.60119i	−0.202665	−	0.959414i	0.751408	−	0.659838i	$-0.229375\pi$
$24$		0			0
$25$	−1.24807	+	7.25647i	−0.249613	+	1.45129i
$26$		0			0
$27$	−15.6642	−	7.64811i	−3.01458	−	1.47188i
$28$		0			0
$29$	−1.17751	+	5.57434i	−0.218659	+	1.03513i	0.720979	+	0.692957i	$0.243692\pi$
$29$	−1.17751	+	5.57434i	−0.218659	+	1.03513i	−0.939638	+	0.342171i	$0.888838\pi$
$30$		0			0
$31$	−0.811528	+	0.155444i	−0.145755	+	0.0279186i	−0.260484	−	0.965478i	$-0.583882\pi$
$31$	−0.811528	+	0.155444i	−0.145755	+	0.0279186i	0.114729	+	0.993397i	$0.463400\pi$
$32$		0			0
$33$	−15.6087	+	10.8075i	−2.71712	+	1.88134i
$34$		0			0
$35$	−8.08457	+	0.613182i	−1.36654	+	0.103647i
$36$		0			0
$37$	6.51057	−	2.03398i	1.07033	−	0.334384i	0.288247	−	0.957556i	$-0.406928\pi$
$37$	6.51057	−	2.03398i	1.07033	−	0.334384i	0.782085	+	0.623172i	$0.214156\pi$
$38$		0			0
$39$	−1.04451	+	3.58006i	−0.167256	+	0.573269i
$40$		0			0
$41$	6.16653	−	2.45231i	0.963050	−	0.382986i	0.165480	−	0.986213i	$-0.447083\pi$
$41$	6.16653	−	2.45231i	0.963050	−	0.382986i	0.797570	+	0.603227i	$0.206119\pi$
$42$		0			0
$43$	−5.99079	−	2.12358i	−0.913587	−	0.323842i	−0.164548	−	0.986369i	$-0.552617\pi$
$43$	−5.99079	−	2.12358i	−0.913587	−	0.323842i	−0.749038	+	0.662527i	$0.769484\pi$
$44$		0			0
$45$	−11.1691	−	26.6077i	−1.66499	−	3.96645i
$46$		0			0
$47$	−0.401377	+	1.59837i	−0.0585468	+	0.233147i	−0.992130	−	0.125215i	$-0.960038\pi$
$47$	−0.401377	+	1.59837i	−0.0585468	+	0.233147i	0.933583	+	0.358362i	$0.116665\pi$
$48$		0			0
$49$	0.532123	+	1.59648i	0.0760176	+	0.228069i
$50$		0			0
$51$	−10.9177	+	12.0029i	−1.52878	+	1.68075i
$52$		0			0
$53$	2.67386	+	2.00522i	0.367283	+	0.275438i	0.767587	−	0.640944i	$-0.221457\pi$
$53$	2.67386	+	2.00522i	0.367283	+	0.275438i	−0.400305	+	0.916382i	$0.631096\pi$
$54$		0			0
$55$	−19.8117	−	2.25937i	−2.67141	−	0.304654i
$56$		0			0
$57$	22.3775	+	8.89911i	2.96398	+	1.17872i
$58$		0			0
$59$	5.27120	+	7.92946i	0.686252	+	1.03233i	0.996655	+	0.0817225i	$0.0260421\pi$
$59$	5.27120	+	7.92946i	0.686252	+	1.03233i	−0.310403	+	0.950605i	$0.600464\pi$
$60$		0			0
$61$	−3.18062	−	4.07808i	−0.407237	−	0.522144i	0.540437	−	0.841385i	$-0.318259\pi$
$61$	−3.18062	−	4.07808i	−0.407237	−	0.522144i	−0.947674	+	0.319240i	$0.896572\pi$
$62$		0			0
$63$	15.1402	−	11.3541i	1.90749	−	1.43049i
$64$		0			0
$65$	−3.30240	+	2.10631i	−0.409613	+	0.261255i
$66$		0			0
$67$	0.337603	−	0.400625i	0.0412447	−	0.0489442i	−0.743677	−	0.668539i	$-0.766920\pi$
$67$	0.337603	−	0.400625i	0.0412447	−	0.0489442i	0.784922	+	0.619595i	$0.212703\pi$
$68$		0			0
$69$	0.893356	+	15.7179i	0.107547	+	1.89221i
$70$		0			0
$71$	−0.366451	−	3.86105i	−0.0434897	−	0.458222i	−0.990549	−	0.137162i	$-0.956202\pi$
$71$	−0.366451	−	3.86105i	−0.0434897	−	0.458222i	0.947059	−	0.321060i	$-0.104039\pi$
$72$		0			0
$73$	3.53031	−	6.29683i	0.413192	−	0.736988i	−0.584010	−	0.811746i	$-0.698517\pi$
$73$	3.53031	−	6.29683i	0.413192	−	0.736988i	0.997202	+	0.0747579i	$0.0238184\pi$
$74$		0			0
$75$	7.79424	−	23.3844i	0.900001	−	2.70019i
$76$		0			0
$77$	−1.72733	−	12.9624i	−0.196848	−	1.47720i
$78$		0			0
$79$	−9.00987	−	0.341191i	−1.01369	−	0.0383870i	−0.474232	−	0.880400i	$-0.657274\pi$
$79$	−9.00987	−	0.341191i	−1.01369	−	0.0383870i	−0.539457	+	0.842013i	$0.681371\pi$
$80$		0			0
$81$	27.7351	+	19.2038i	3.08168	+	2.13376i
$82$		0			0
$83$	2.05692	−	0.558109i	0.225776	−	0.0612604i	−0.147179	−	0.989110i	$-0.547019\pi$
$83$	2.05692	−	0.558109i	0.225776	−	0.0612604i	0.372955	+	0.927849i	$0.378345\pi$
$84$		0			0
$85$	−16.9320	+	1.93096i	−1.83653	+	0.209442i
$86$		0			0
$87$	6.71142	−	17.8532i	0.719539	−	1.91406i
$88$		0			0
$89$	−8.86736	+	14.5010i	−0.939938	+	1.53710i	−0.0996089	+	0.995027i	$0.531759\pi$
$89$	−8.86736	+	14.5010i	−0.939938	+	1.53710i	−0.840329	+	0.542076i	$0.817638\pi$
$90$		0			0
$91$	−1.86722	−	1.76410i	−0.195738	−	0.184928i
$92$		0			0
$93$	2.76416	−	0.104675i	0.286630	−	0.0108543i
$94$		0			0
$95$	11.5257	+	22.5150i	1.18251	+	2.30999i
$96$		0			0
$97$	−15.2582	−	2.92263i	−1.54924	−	0.296748i	−0.658963	−	0.752176i	$-0.729004\pi$
$97$	−15.2582	−	2.92263i	−1.54924	−	0.296748i	−0.890273	+	0.455428i	$0.849486\pi$
$98$		0			0
$99$	41.8239	−	20.4207i	4.20346	−	2.05235i
$100$		0			0
$101$	5.42940	−	1.92458i	0.540245	−	0.191503i	−0.0499669	−	0.998751i	$-0.515912\pi$
$101$	5.42940	−	1.92458i	0.540245	−	0.191503i	0.590212	+	0.807248i	$0.299044\pi$
$102$		0			0
$103$	−0.0153314	+	0.810008i	−0.00151065	+	0.0798124i	0.998269	+	0.0588153i	$0.0187323\pi$
$103$	−0.0153314	+	0.810008i	−0.00151065	+	0.0798124i	−0.999780	+	0.0209972i	$0.993316\pi$
$104$		0			0
$105$	27.0647	+	2.05275i	2.64124	+	0.200328i
$106$		0			0
$107$	−0.0607041	−	3.20719i	−0.00586849	−	0.310051i	−0.990663	−	0.136330i	$-0.956469\pi$
$107$	−0.0607041	−	3.20719i	−0.00586849	−	0.310051i	0.984795	−	0.173721i	$-0.0555789\pi$
$108$		0			0
$109$	−5.67399	+	11.0839i	−0.543470	+	1.06165i	0.442818	+	0.896612i	$0.353979\pi$
$109$	−5.67399	+	11.0839i	−0.543470	+	1.06165i	−0.986288	+	0.165036i	$0.947226\pi$
$110$		0			0
$111$	−22.5731	+	3.44396i	−2.14254	+	0.326887i
$112$		0			0
$113$	2.25512	+	1.97454i	0.212144	+	0.185749i	0.758245	−	0.651970i	$-0.226057\pi$
$113$	2.25512	+	1.97454i	0.212144	+	0.185749i	−0.546101	+	0.837719i	$0.683888\pi$
$114$		0			0
$115$	−10.1692	+	13.0385i	−0.948280	+	1.21585i
$116$		0			0
$117$	3.85513	−	8.29011i	0.356407	−	0.766421i
$118$		0			0
$119$	−3.93267	−	10.4614i	−0.360507	−	0.958992i
$120$		0			0
$121$	1.20080	−	21.1271i	0.109163	−	1.92065i
$122$		0			0
$123$	−21.6457	+	5.00210i	−1.95173	+	0.451024i
$124$		0			0
$125$	7.16912	−	4.19961i	0.641225	−	0.375625i
$126$		0			0
$127$	−0.400413	+	4.21888i	−0.0355309	+	0.374365i	0.960005	+	0.279982i	$0.0903286\pi$
$127$	−0.400413	+	4.21888i	−0.0355309	+	0.374365i	−0.995536	+	0.0943825i	$0.969912\pi$
$128$		0			0
$129$	18.7537	+	10.0526i	1.65117	+	0.885081i
$130$		0			0
$131$	9.22210	+	10.1388i	0.805738	+	0.885832i	0.995379	−	0.0960219i	$-0.0306119\pi$
$131$	9.22210	+	10.1388i	0.805738	+	0.885832i	−0.189641	+	0.981854i	$0.560732\pi$
$132$		0			0
$133$	−12.4800	+	10.9273i	−1.08215	+	0.947515i
$134$		0			0
$135$	14.9278	+	59.4458i	1.28478	+	5.11628i
$136$		0			0
$137$	−0.198479	−	0.680284i	−0.0169572	−	0.0581205i	0.951058	−	0.309013i	$-0.0999988\pi$
$137$	−0.198479	−	0.680284i	−0.0169572	−	0.0581205i	−0.968015	+	0.250893i	$0.919276\pi$
$138$		0			0
$139$	6.65483	−	2.94282i	0.564456	−	0.249607i	−0.102464	−	0.994737i	$-0.532673\pi$
$139$	6.65483	−	2.94282i	0.564456	−	0.249607i	0.666920	+	0.745130i	$0.267612\pi$
$140$		0			0
$141$	2.13536	−	5.08700i	0.179829	−	0.428402i
$142$		0			0
$143$	−3.69401	−	5.12505i	−0.308908	−	0.428578i
$144$		0			0
$145$	17.6559	−	9.46414i	1.46624	−	0.785954i
$146$		0			0
$147$	−0.954922	−	5.55207i	−0.0787606	−	0.457927i
$148$		0			0
$149$	−13.6922	−	8.73303i	−1.12171	−	0.715438i	−0.159352	−	0.987222i	$-0.550941\pi$
$149$	−13.6922	−	8.73303i	−1.12171	−	0.715438i	−0.962358	+	0.271784i	$0.912386\pi$
$150$		0			0
$151$	−5.27725	−	9.41277i	−0.429457	−	0.766000i	0.568953	−	0.822370i	$-0.307349\pi$
$151$	−5.27725	−	9.41277i	−0.429457	−	0.766000i	−0.998410	+	0.0563699i	$0.982047\pi$
$152$		0			0
$153$	30.8972	−	25.0524i	2.49789	−	2.02536i
$154$		0			0
$155$	2.25668	+	1.82978i	0.181261	+	0.146972i
$156$		0			0
$157$	4.98514	+	10.7201i	0.397858	+	0.855556i	0.998432	+	0.0559868i	$0.0178305\pi$
$157$	4.98514	+	10.7201i	0.397858	+	0.855556i	−0.600574	+	0.799569i	$0.705061\pi$
$158$		0			0
$159$	−7.83640	−	7.98613i	−0.621467	−	0.633341i
$160$		0			0
$161$	−9.91759	−	4.38564i	−0.781615	−	0.345637i
$162$		0			0
$163$	7.17641	+	4.20389i	0.562100	+	0.329274i	0.758939	−	0.651162i	$-0.225718\pi$
$163$	7.17641	+	4.20389i	0.562100	+	0.329274i	−0.196839	+	0.980436i	$0.563068\pi$
$164$		0			0
$165$	64.4241	+	17.4804i	5.01541	+	1.36085i
$166$		0			0
$167$	3.89992	−	12.3203i	0.301785	−	0.953376i
$167$	3.89992	−	12.3203i	0.301785	−	0.953376i
$168$		0			0
$169$	11.3487	+	3.07927i	0.872975	+	0.236867i
$170$		0			0
$171$	−50.9417	−	29.8413i	−3.89561	−	2.28202i
$172$		0			0
$173$	3.04011	+	1.34436i	0.231135	+	0.102210i	0.516756	−	0.856133i	$-0.327139\pi$
$173$	3.04011	+	1.34436i	0.231135	+	0.102210i	−0.285621	+	0.958343i	$0.592200\pi$
$174$		0			0
$175$	11.8914	+	12.1186i	0.898904	+	0.916079i
$176$		0			0
$177$	−13.4408	−	28.9032i	−1.01027	−	2.17250i
$178$		0			0
$179$	11.7859	+	9.55638i	0.880922	+	0.714277i	0.959222	−	0.282653i	$-0.0912144\pi$
$179$	11.7859	+	9.55638i	0.880922	+	0.714277i	−0.0783003	+	0.996930i	$0.524949\pi$
$180$		0			0
$181$	13.2762	−	10.7647i	0.986810	−	0.800135i	0.00698214	−	0.999976i	$-0.497777\pi$
$181$	13.2762	−	10.7647i	0.986810	−	0.800135i	0.979828	+	0.199841i	$0.0640426\pi$
$182$		0			0
$183$	8.46687	+	15.1019i	0.625889	+	1.11637i
$184$		0			0
$185$	−20.2203	−	12.8967i	−1.48662	−	0.948184i
$186$		0			0
$187$	−4.65908	−	27.0886i	−0.340705	−	1.98092i
$188$		0			0
$189$	−35.4269	+	18.9900i	−2.57693	+	1.38132i
$190$		0			0
$191$	4.87078	+	6.75769i	0.352437	+	0.488969i	0.949737	−	0.313049i	$-0.101350\pi$
$191$	4.87078	+	6.75769i	0.352437	+	0.488969i	−0.597300	+	0.802018i	$0.703760\pi$
$192$		0			0
$193$	−2.13416	+	5.08414i	−0.153620	+	0.365964i	−0.980530	−	0.196370i	$-0.937085\pi$
$193$	−2.13416	+	5.08414i	−0.153620	+	0.365964i	0.826910	+	0.562334i	$0.190097\pi$
$194$		0			0
$195$	11.9925	−	5.30317i	0.858799	−	0.379768i
$196$		0			0
$197$	−6.50828	−	22.3071i	−0.463696	−	1.58931i	−0.770435	−	0.637519i	$-0.779961\pi$
$197$	−6.50828	−	22.3071i	−0.463696	−	1.58931i	0.306739	−	0.951794i	$-0.400762\pi$
$198$		0			0
$199$	4.19675	+	16.7124i	0.297500	+	1.18471i	0.916732	+	0.399504i	$0.130818\pi$
$199$	4.19675	+	16.7124i	0.297500	+	1.18471i	−0.619232	+	0.785208i	$0.712556\pi$
$200$		0			0
$201$	−1.31954	+	1.15537i	−0.0930734	+	0.0814935i
$202$		0			0
$203$	8.83987	+	9.71858i	0.620437	+	0.682111i
$204$		0			0
$205$	−20.5655	−	11.0238i	−1.43636	−	0.769936i
$206$		0			0
$207$	3.64670	−	38.4228i	0.253463	−	2.67057i
$208$		0			0
$209$	−35.2008	+	20.6204i	−2.43489	+	1.42634i
$210$		0			0
$211$	−1.52894	+	0.353322i	−0.105256	+	0.0243237i	−0.277455	−	0.960738i	$-0.589491\pi$
$211$	−1.52894	+	0.353322i	−0.105256	+	0.0243237i	0.172199	+	0.985062i	$0.444913\pi$
$212$		0			0
$213$	−0.736763	+	12.9628i	−0.0504822	+	0.888195i
$214$		0			0
$215$	7.86401	+	20.9192i	0.536321	+	1.42668i
$216$		0			0
$217$	−0.803408	+	1.72765i	−0.0545389	+	0.117281i
$218$		0			0
$219$	−14.8626	+	19.0562i	−1.00432	+	1.28770i
$220$		0			0
$221$	−4.06220	−	3.55679i	−0.273253	−	0.239256i
$222$		0			0
$223$	−16.6984	+	2.54767i	−1.11821	+	0.170605i	−0.683489	−	0.729960i	$-0.739538\pi$
$223$	−16.6984	+	2.54767i	−1.11821	+	0.170605i	−0.434721	+	0.900565i	$0.643153\pi$
$224$		0			0
$225$	−27.5359	+	53.7903i	−1.83573	+	3.58602i
$226$		0			0
$227$	−0.0715253	−	3.77891i	−0.00474730	−	0.250815i	−0.994298	−	0.106633i	$-0.965993\pi$
$227$	−0.0715253	−	3.77891i	−0.00474730	−	0.250815i	0.989551	−	0.144182i	$-0.0460551\pi$
$228$		0			0
$229$	−0.695324	−	0.0527375i	−0.0459483	−	0.00348499i	0.0526345	−	0.998614i	$-0.483238\pi$
$229$	−0.695324	−	0.0527375i	−0.0459483	−	0.00348499i	−0.0985828	+	0.995129i	$0.531431\pi$
$230$		0			0
$231$	−0.828454	+	43.7698i	−0.0545082	+	2.87984i
$232$		0			0
$233$	1.10063	−	0.390145i	0.0721048	−	0.0255592i	−0.297807	−	0.954626i	$-0.596255\pi$
$233$	1.10063	−	0.390145i	0.0721048	−	0.0255592i	0.369912	+	0.929067i	$0.379388\pi$
$234$		0			0
$235$	5.20703	−	2.54235i	0.339669	−	0.165845i
$236$		0			0
$237$	29.6450	+	5.67834i	1.92565	+	0.368848i
$238$		0			0
$239$	−6.96856	−	13.6128i	−0.450759	−	0.880540i	−0.999021	−	0.0442337i	$-0.985915\pi$
$239$	−6.96856	−	13.6128i	−0.450759	−	0.880540i	0.548263	−	0.836306i	$-0.315289\pi$
$240$		0			0
$241$	−8.66768	+	0.328233i	−0.558334	+	0.0211433i	−0.315502	−	0.948925i	$-0.602173\pi$
$241$	−8.66768	+	0.328233i	−0.558334	+	0.0211433i	−0.242832	+	0.970068i	$0.578076\pi$
$242$		0			0
$243$	−44.0775	−	41.6434i	−2.82757	−	2.67142i
$244$		0			0
$245$	3.08685	−	5.04800i	0.197212	−	0.322505i
$246$		0			0
$247$	−2.81987	+	7.50119i	−0.179424	+	0.477289i
$248$		0			0
$249$	−7.08896	+	0.808440i	−0.449244	+	0.0512328i
$250$		0			0
$251$	22.0124	−	5.97269i	1.38941	−	0.376993i	0.512930	−	0.858430i	$-0.328560\pi$
$251$	22.0124	−	5.97269i	1.38941	−	0.376993i	0.876480	+	0.481438i	$0.159885\pi$
$252$		0			0
$253$	−21.9265	−	15.1820i	−1.37851	−	0.954482i
$254$		0			0
$255$	57.0096	+	2.15887i	3.57008	+	0.135194i
$256$		0			0
$257$	0.532118	+	3.99316i	0.0331926	+	0.249087i	0.999979	−	0.00649958i	$-0.00206890\pi$
$257$	0.532118	+	3.99316i	0.0331926	+	0.249087i	−0.966786	+	0.255586i	$0.917732\pi$
$258$		0			0
$259$	4.97341	−	14.9213i	0.309033	−	0.927163i
$260$		0			0
$261$	−22.8665	+	40.7857i	−1.41540	+	2.52457i
$262$		0			0
$263$	−1.22990	−	12.9586i	−0.0758389	−	0.799064i	−0.949757	−	0.312990i	$-0.898669\pi$
$263$	−1.22990	−	12.9586i	−0.0758389	−	0.799064i	0.873918	−	0.486074i	$-0.161571\pi$
$264$		0			0
$265$	−0.666848	−	11.7327i	−0.0409641	−	0.720732i
$266$		0			0
$267$	36.6674	−	43.5123i	2.24401	−	2.66291i
$268$		0			0
$269$	8.33654	−	5.31713i	0.508288	−	0.324191i	−0.258586	−	0.965988i	$-0.583257\pi$
$269$	8.33654	−	5.31713i	0.508288	−	0.324191i	0.766874	+	0.641797i	$0.221811\pi$
$270$		0			0
$271$	−4.45396	+	3.34018i	−0.270559	+	0.202901i	−0.726606	−	0.687054i	$-0.758903\pi$
$271$	−4.45396	+	3.34018i	−0.270559	+	0.202901i	0.456047	+	0.889956i	$0.349265\pi$
$272$		0			0
$273$	5.28865	+	6.78091i	0.320083	+	0.410399i
$274$		0			0
$275$	23.1163	+	34.7739i	1.39397	+	2.09694i
$276$		0			0
$277$	12.6802	+	5.04267i	0.761879	+	0.302984i	0.717991	−	0.696052i	$-0.245062\pi$
$277$	12.6802	+	5.04267i	0.761879	+	0.302984i	0.0438878	+	0.999036i	$0.486026\pi$
$278$		0			0
$279$	−6.73767	−	0.768378i	−0.403373	−	0.0460016i
$280$		0			0
$281$	−1.60592	−	1.20433i	−0.0958009	−	0.0718443i	0.550989	−	0.834512i	$-0.314251\pi$
$281$	−1.60592	−	1.20433i	−0.0958009	−	0.0718443i	−0.646790	+	0.762668i	$0.723889\pi$
$282$		0			0
$283$	−4.47658	+	4.92157i	−0.266105	+	0.292557i	−0.858204	−	0.513308i	$-0.828420\pi$
$283$	−4.47658	+	4.92157i	−0.266105	+	0.292557i	0.592099	+	0.805865i	$0.298299\pi$
$284$		0			0
$285$	−26.7750	−	80.3307i	−1.58601	−	4.75838i
$286$		0			0
$287$	3.72699	−	14.8417i	0.219997	−	0.876080i
$288$		0			0
$289$	−2.51237	−	5.98514i	−0.147786	−	0.352067i
$290$		0			0
$291$	49.0198	+	17.3762i	2.87359	+	1.01861i
$292$		0			0
$293$	−2.95635	+	1.17568i	−0.172712	+	0.0686841i	−0.454288	−	0.890855i	$-0.650106\pi$
$293$	−2.95635	+	1.17568i	−0.172712	+	0.0686841i	0.281577	+	0.959539i	$0.409143\pi$
$294$		0			0
$295$	9.37689	−	32.1392i	0.545944	−	1.87122i
$296$		0			0
$297$	−94.3587	+	29.4787i	−5.47525	+	1.71053i
$298$		0			0
$299$	−5.22382	+	0.396206i	−0.302101	+	0.0229132i
$300$		0			0
$301$	−12.0498	+	8.34332i	−0.694540	+	0.480901i
$302$		0			0
$303$	−18.9398	+	3.62782i	−1.08806	+	0.208413i
$304$		0			0
$305$	−3.75832	+	17.7918i	−0.215201	+	1.01876i
$306$		0			0
$307$	2.37699	+	1.16057i	0.135662	+	0.0662373i	0.505328	−	0.862927i	$-0.331371\pi$
$307$	2.37699	+	1.16057i	0.135662	+	0.0662373i	−0.369666	+	0.929165i	$0.620528\pi$
$308$		0			0
$309$	0.459722	−	2.67290i	0.0261527	−	0.152056i
$310$		0			0
$311$	6.65397	+	31.4998i	0.377312	+	1.78619i	0.588237	+	0.808689i	$0.299822\pi$
$311$	6.65397	+	31.4998i	0.377312	+	1.78619i	−0.210925	+	0.977502i	$0.567648\pi$
$312$		0			0
$313$	8.77629	−	8.94398i	0.496065	−	0.505543i	−0.419477	−	0.907766i	$-0.637786\pi$
$313$	8.77629	−	8.94398i	0.496065	−	0.505543i	0.915542	+	0.402223i	$0.131762\pi$
$314$		0			0
$315$	−64.8325	−	14.9821i	−3.65290	−	0.844147i
$316$		0			0
$317$	−1.26069	+	1.89646i	−0.0708076	+	0.106516i	−0.866481	−	0.499211i	$-0.833623\pi$
$317$	−1.26069	+	1.89646i	−0.0708076	+	0.106516i	0.795673	+	0.605726i	$0.207117\pi$
$318$		0			0
$319$	16.8559	+	27.5649i	0.943751	+	1.54334i
$320$		0			0
$321$	−1.41846	+	10.6445i	−0.0791706	+	0.594119i
$322$		0			0
$323$	−25.3437	+	23.9442i	−1.41016	+	1.33229i
$324$		0			0
$325$	7.82921	+	2.44593i	0.434286	+	0.135676i
$326$		0			0
$327$	24.3739	−	33.8163i	1.34788	−	1.87004i
$328$		0			0
$329$	2.44879	+	2.90592i	0.135006	+	0.160209i
$330$		0			0
$331$	9.96725	+	1.52070i	0.547849	+	0.0835852i	0.418843	−	0.908059i	$-0.362436\pi$
$331$	9.96725	+	1.52070i	0.547849	+	0.0835852i	0.129006	+	0.991644i	$0.458821\pi$
$332$		0			0
$333$	55.9795			3.06766
$334$		0			0
$335$	−1.84211			−0.100645
$336$		0			0
$337$	−13.6385	−	2.08082i	−0.742935	−	0.113349i	−0.231697	−	0.972788i	$-0.574428\pi$
$337$	−13.6385	−	2.08082i	−0.742935	−	0.113349i	−0.511239	+	0.859439i	$0.670813\pi$
$338$		0			0
$339$	−6.46612	−	7.67319i	−0.351191	−	0.416751i
$340$		0			0
$341$	−2.73994	+	3.80138i	−0.148376	+	0.205856i
$342$		0			0
$343$	19.1108	+	5.97044i	1.03189	+	0.322373i
$344$		0			0
$345$	40.2372	−	38.0152i	2.16630	−	2.04667i
$346$		0			0
$347$	0.706071	−	5.29855i	0.0379039	−	0.284441i	−0.962030	−	0.272944i	$-0.912003\pi$
$347$	0.706071	−	5.29855i	0.0379039	−	0.284441i	0.999934	−	0.0114977i	$-0.00365990\pi$
$348$		0			0
$349$	−15.6077	−	25.5237i	−0.835463	−	1.36625i	−0.928786	−	0.370617i	$-0.879146\pi$
$349$	−15.6077	−	25.5237i	−0.835463	−	1.36625i	0.0933224	−	0.995636i	$-0.470251\pi$
$350$		0			0
$351$	−10.7503	+	16.1716i	−0.573808	+	0.863177i
$352$		0			0
$353$	28.8286	+	6.66200i	1.53439	+	0.354582i	0.905988	−	0.423303i	$-0.139130\pi$
$353$	28.8286	+	6.66200i	1.53439	+	0.354582i	0.628405	+	0.777886i	$0.283708\pi$
$354$		0			0
$355$	−9.55105	+	9.73354i	−0.506917	+	0.516602i
$356$		0			0
$357$	7.73269	+	36.6065i	0.409257	+	1.93742i
$358$		0			0
$359$	5.52899	−	32.1465i	0.291809	−	1.69663i	−0.355726	−	0.934590i	$-0.615767\pi$
$359$	5.52899	−	32.1465i	0.291809	−	1.69663i	0.647535	−	0.762035i	$-0.275800\pi$
$360$		0			0
$361$	29.4282	+	14.3684i	1.54885	+	0.756231i
$362$		0			0
$363$	−14.6413	+	69.3117i	−0.768468	+	3.63792i
$364$		0			0
$365$	−24.9294	+	4.77510i	−1.30486	+	0.249940i
$366$		0			0
$367$	−23.9060	+	16.5526i	−1.24788	+	0.864038i	−0.994643	−	0.103366i	$-0.967039\pi$
$367$	−23.9060	+	16.5526i	−1.24788	+	0.864038i	−0.253241	+	0.967403i	$0.581497\pi$
$368$		0			0
$369$	54.3081	−	4.11905i	2.82717	−	0.214429i
$370$		0			0
$371$	7.35619	−	2.29816i	0.381914	−	0.119314i
$372$		0			0
$373$	−4.19884	+	14.3915i	−0.217408	+	0.745164i	0.776020	+	0.630708i	$0.217235\pi$
$373$	−4.19884	+	14.3915i	−0.217408	+	0.745164i	−0.993428	+	0.114456i	$0.963488\pi$
$374$		0			0
$375$	−25.8459	+	10.2784i	−1.33468	+	0.530775i
$376$		0			0
$377$	5.98212	+	2.12050i	0.308095	+	0.109211i
$378$		0			0
$379$	0.775805	+	1.84818i	0.0398504	+	0.0949345i	0.940761	−	0.339070i	$-0.110112\pi$
$379$	0.775805	+	1.84818i	0.0398504	+	0.0949345i	−0.900911	+	0.434004i	$0.857100\pi$
$380$		0			0
$381$	3.45529	−	13.7598i	0.177020	−	0.704935i
$382$		0			0
$383$	−4.95810	−	14.8754i	−0.253347	−	0.760095i	−0.995913	−	0.0903218i	$-0.971210\pi$
$383$	−4.95810	−	14.8754i	−0.253347	−	0.760095i	0.742565	−	0.669774i	$-0.233609\pi$
$384$		0			0
$385$	−30.9387	+	34.0141i	−1.57678	+	1.73352i
$386$		0			0
$387$	−41.7328	−	31.2968i	−2.12140	−	1.59091i
$388$		0			0
$389$	−35.2019	−	4.01449i	−1.78481	−	0.203543i	−0.842591	−	0.538554i	$-0.818971\pi$
$389$	−35.2019	−	4.01449i	−1.78481	−	0.203543i	−0.942214	+	0.335011i	$0.891260\pi$
$390$		0			0
$391$	−21.1796	−	8.42272i	−1.07110	−	0.425955i
$392$		0			0
$393$	−25.4004	−	38.2097i	−1.28128	−	1.92743i
$394$		0			0
$395$	19.4969	+	24.9982i	0.980996	+	1.25780i
$396$		0			0
$397$	15.4911	−	11.6173i	0.777477	−	0.583056i	−0.135638	−	0.990758i	$-0.543308\pi$
$397$	15.4911	−	11.6173i	0.777477	−	0.583056i	0.913115	+	0.407702i	$0.133670\pi$
$398$		0			0
$399$	46.8187	−	29.8614i	2.34386	−	1.49494i
$400$		0			0
$401$	10.3243	−	12.2516i	0.515570	−	0.611815i	−0.443053	−	0.896496i	$-0.646104\pi$
$401$	10.3243	−	12.2516i	0.515570	−	0.611815i	0.958622	+	0.284681i	$0.0918876\pi$
$402$		0			0
$403$	0.0522327	+	0.918993i	0.00260189	+	0.0457783i
$404$		0			0
$405$	−11.2073	−	118.084i	−0.556895	−	5.86763i
$406$		0			0
$407$	18.9168	−	33.7408i	0.937669	−	1.67247i
$408$		0			0
$409$	8.21608	−	24.6500i	0.406259	−	1.21886i	−0.523923	−	0.851765i	$-0.675532\pi$
$409$	8.21608	−	24.6500i	0.406259	−	1.21886i	0.930182	−	0.367098i	$-0.119649\pi$
$410$		0			0
$411$	0.313360	+	2.35154i	0.0154569	+	0.115993i
$412$		0			0
$413$	21.9403	+	0.830847i	1.07961	+	0.0408833i
$414$		0			0
$415$	−6.16111	−	4.26596i	−0.302437	−	0.209408i
$416$		0			0
$417$	−23.5094	+	6.37886i	−1.15126	+	0.312374i
$418$		0			0
$419$	−13.6930	+	1.56157i	−0.668945	+	0.0762879i	−0.441167	−	0.897425i	$-0.645435\pi$
$419$	−13.6930	+	1.56157i	−0.668945	+	0.0762879i	−0.227778	+	0.973713i	$0.573146\pi$
$420$		0			0
$421$	−9.95704	+	26.4869i	−0.485276	+	1.29089i	0.435285	+	0.900293i	$0.356648\pi$
$421$	−9.95704	+	26.4869i	−0.485276	+	1.29089i	−0.920561	+	0.390599i	$0.872268\pi$
$422$		0			0
$423$	−7.05600	+	11.5388i	−0.343074	+	0.561037i
$424$		0			0
$425$	25.9404	+	24.5079i	1.25830	+	1.18881i
$426$		0			0
$427$	−11.9170	+	0.451281i	−0.576705	+	0.0218390i
$428$		0			0
$429$	9.63724	+	18.8260i	0.465290	+	0.908927i
$430$		0			0
$431$	7.71498	+	1.47777i	0.371618	+	0.0711815i	0.370536	−	0.928818i	$-0.379174\pi$
$431$	7.71498	+	1.47777i	0.371618	+	0.0711815i	0.00108128	+	0.999999i	$0.499656\pi$
$432$		0			0
$433$	−10.8131	+	5.27953i	−0.519645	+	0.253718i	−0.679831	−	0.733369i	$-0.737947\pi$
$433$	−10.8131	+	5.27953i	−0.519645	+	0.253718i	0.160187	+	0.987087i	$0.448790\pi$
$434$		0			0
$435$	−63.2090	+	22.4059i	−3.03064	+	1.07428i
$436$		0			0
$437$	−0.640198	+	33.8237i	−0.0306248	+	1.61801i
$438$		0			0
$439$	−21.3183	−	1.61690i	−1.01747	−	0.0771706i	−0.443687	−	0.896182i	$-0.646330\pi$
$439$	−21.3183	−	1.61690i	−1.01747	−	0.0771706i	−0.573778	+	0.819011i	$0.694523\pi$
$440$		0			0
$441$	0.261362	+	13.8086i	0.0124458	+	0.657552i
$442$		0			0
$443$	14.9090	−	29.1241i	0.708346	−	1.38373i	−0.205903	−	0.978572i	$-0.566013\pi$
$443$	14.9090	−	29.1241i	0.708346	−	1.38373i	0.914248	−	0.405154i	$-0.132782\pi$
$444$		0			0
$445$	59.0808	−	9.01393i	2.80070	−	0.427301i
$446$		0			0
$447$	40.9036	+	35.8145i	1.93467	+	1.69397i
$448$		0			0
$449$	14.6060	−	18.7273i	0.689301	−	0.883796i	−0.308422	−	0.951250i	$-0.599801\pi$
$449$	14.6060	−	18.7273i	0.689301	−	0.883796i	0.997722	+	0.0674538i	$0.0214875\pi$
$450$		0			0
$451$	15.8693	−	34.1254i	0.747255	−	1.60690i
$452$		0			0
$453$	12.7119	+	33.8152i	0.597257	+	1.58877i
$454$		0			0
$455$	−0.512527	+	9.01751i	−0.0240276	+	0.422747i
$456$		0			0
$457$	−28.1146	+	6.49699i	−1.31514	+	0.303916i	−0.823716	−	0.567002i	$-0.808103\pi$
$457$	−28.1146	+	6.49699i	−1.31514	+	0.303916i	−0.491428	+	0.870918i	$0.663525\pi$
$458$		0			0
$459$	−72.8999	+	42.7042i	−3.40267	+	1.99326i
$460$		0			0
$461$	2.52060	−	26.5578i	0.117396	−	1.23692i	−0.721416	−	0.692502i	$-0.756509\pi$
$461$	2.52060	−	26.5578i	0.117396	−	1.23692i	0.838812	−	0.544421i	$-0.183250\pi$
$462$		0			0
$463$	−8.37309	−	4.48825i	−0.389131	−	0.208587i	0.266219	−	0.963913i	$-0.414226\pi$
$463$	−8.37309	−	4.48825i	−0.389131	−	0.208587i	−0.655349	+	0.755326i	$0.727479\pi$
$464$		0			0
$465$	−6.54438	−	7.19492i	−0.303488	−	0.333656i
$466$		0			0
$467$	−25.6899	+	22.4936i	−1.18879	+	1.04088i	−0.190540	+	0.981679i	$0.561024\pi$
$467$	−25.6899	+	22.4936i	−1.18879	+	1.04088i	−0.998246	+	0.0592005i	$0.981145\pi$
$468$		0			0
$469$	−0.294231	−	1.17169i	−0.0135863	−	0.0541038i
$470$		0			0
$471$	−11.0851	−	37.9941i	−0.510775	−	1.75068i
$472$		0			0
$473$	−32.9662	+	14.5779i	−1.51579	+	0.670294i
$474$		0			0
$475$	20.5009	−	48.8386i	0.940644	−	2.24087i
$476$		0			0
$477$	16.0387	+	22.2520i	0.734362	+	1.01885i
$478$		0			0
$479$	14.4110	−	7.72477i	0.658456	−	0.352954i	−0.109013	−	0.994040i	$-0.534769\pi$
$479$	14.4110	−	7.72477i	0.658456	−	0.352954i	0.767469	+	0.641087i	$0.221516\pi$
$480$		0			0
$481$	−1.28798	−	7.48851i	−0.0587267	−	0.341447i
$482$		0			0
$483$	30.6069	+	19.5214i	1.39266	+	0.888253i
$484$		0			0
$485$	26.7134	+	47.6473i	1.21299	+	2.16355i
$486$		0			0
$487$	−10.1498	+	8.22972i	−0.459930	+	0.372924i	−0.831540	−	0.555464i	$-0.812541\pi$
$487$	−10.1498	+	8.22972i	−0.459930	+	0.372924i	0.371611	+	0.928389i	$0.378806\pi$
$488$		0			0
$489$	−21.6270	−	17.5358i	−0.978007	−	0.792997i
$490$		0			0
$491$	6.96144	+	14.9699i	0.314165	+	0.675583i	0.998567	−	0.0535223i	$-0.0170448\pi$
$491$	6.96144	+	14.9699i	0.314165	+	0.675583i	−0.684401	+	0.729105i	$0.739936\pi$
$492$		0			0
$493$	19.3402	+	19.7097i	0.871037	+	0.887680i
$494$		0			0
$495$	−149.669	−	66.1850i	−6.72713	−	2.97479i
$496$		0			0
$497$	−7.71667	−	4.52037i	−0.346140	−	0.202766i
$498$		0			0
$499$	3.09404	+	0.839514i	0.138508	+	0.0375818i	0.330443	−	0.943826i	$-0.392802\pi$
$499$	3.09404	+	0.839514i	0.138508	+	0.0375818i	−0.191935	+	0.981408i	$0.561476\pi$
$500$		0			0
$501$	−19.1271	+	38.8038i	−0.854536	+	1.73362i
$502$		0			0
$503$	3.19719	+	0.867504i	0.142556	+	0.0386801i	0.332427	−	0.943129i	$-0.392132\pi$
$503$	3.19719	+	0.867504i	0.142556	+	0.0386801i	−0.189871	+	0.981809i	$0.560807\pi$
$504$		0			0
$505$	−17.4764	−	10.2376i	−0.777691	−	0.455566i
$506$		0			0
$507$	−36.0025	−	15.9206i	−1.59893	−	0.707060i
$508$		0			0
$509$	8.73975	+	8.90674i	0.387383	+	0.394784i	0.879620	−	0.475677i	$-0.157797\pi$
$509$	8.73975	+	8.90674i	0.387383	+	0.394784i	−0.492237	+	0.870461i	$0.663821\pi$
$510$		0			0
$511$	−7.01911	−	15.0939i	−0.310507	−	0.667716i
$512$		0			0
$513$	97.4020	+	78.9763i	4.30040	+	3.48689i
$514$		0			0
$515$	2.21263	−	1.79407i	0.0975003	−	0.0790561i
$516$		0			0
$517$	4.57049	+	8.15214i	0.201010	+	0.358531i
$518$		0			0
$519$	−9.38215	−	5.98402i	−0.411830	−	0.262669i
$520$		0			0
$521$	−3.60855	−	20.9807i	−0.158094	−	0.919181i	−0.950852	−	0.309646i	$-0.899790\pi$
$521$	−3.60855	−	20.9807i	−0.158094	−	0.919181i	0.792759	−	0.609536i	$-0.208644\pi$
$522$		0			0
$523$	32.2562	−	17.2904i	1.41046	−	0.756055i	0.421870	−	0.906656i	$-0.361374\pi$
$523$	32.2562	−	17.2904i	1.41046	−	0.756055i	0.988595	+	0.150601i	$0.0481209\pi$
$524$		0			0
$525$	−33.2345	−	46.1093i	−1.45047	−	2.01238i
$526$		0			0
$527$	−1.55005	+	3.69265i	−0.0675214	+	0.160854i
$528$		0			0
$529$	0.808852	−	0.357681i	0.0351675	−	0.0155514i
$530$		0			0
$531$	21.8869	+	75.0171i	0.949810	+	3.25547i
$532$		0			0
$533$	−1.80054	−	7.17016i	−0.0779900	−	0.310574i
$534$		0			0
$535$	−8.48574	+	7.42996i	−0.366871	+	0.321225i
$536$		0			0
$537$	−34.1792	−	37.5767i	−1.47494	−	1.62156i
$538$		0			0
$539$	8.41125	+	4.50871i	0.362298	+	0.194204i
$540$		0			0
$541$	2.40541	−	25.3442i	0.103417	−	1.08963i	−0.781507	−	0.623896i	$-0.785549\pi$
$541$	2.40541	−	25.3442i	0.103417	−	1.08963i	0.884924	−	0.465736i	$-0.154210\pi$
$542$		0			0
$543$	−49.3714	+	28.9214i	−2.11873	+	1.24114i
$544$		0			0
$545$	42.6577	−	9.85776i	1.82726	−	0.422260i
$546$		0			0
$547$	0.00580676	−	0.102165i	0.000248279	−	0.00436828i	−0.998262	−	0.0589293i	$-0.981231\pi$
$547$	0.00580676	−	0.102165i	0.000248279	−	0.00436828i	0.998510	+	0.0545610i	$0.0173759\pi$
$548$		0			0
$549$	−14.9356	−	39.7303i	−0.637434	−	1.69565i
$550$		0			0
$551$	17.2818	−	37.1629i	0.736230	−	1.58319i
$552$		0			0
$553$	−12.7863	+	16.3941i	−0.543728	+	0.697148i
$554$		0			0
$555$	60.4053	+	52.8898i	2.56406	+	2.24505i
$556$		0			0
$557$	−35.4807	+	5.41328i	−1.50337	+	0.229368i	−0.849640	−	0.527363i	$-0.823181\pi$
$557$	−35.4807	+	5.41328i	−1.50337	+	0.229368i	−0.653726	+	0.756731i	$0.726795\pi$
$558$		0			0
$559$	−3.22646	+	6.30277i	−0.136465	+	0.266579i
$560$		0			0
$561$	1.74132	+	91.9995i	0.0735187	+	3.88422i
$562$		0			0
$563$	−8.18269	−	0.620624i	−0.344859	−	0.0261562i	−0.0979403	−	0.995192i	$-0.531225\pi$
$563$	−8.18269	−	0.620624i	−0.344859	−	0.0261562i	−0.246919	+	0.969036i	$0.579418\pi$
$564$		0			0
$565$	0.199445	−	10.5373i	0.00839070	−	0.443307i
$566$		0			0
$567$	73.3186	−	25.9895i	3.07909	−	1.09146i
$568$		0			0
$569$	23.7907	−	11.6159i	0.997359	−	0.486964i	0.133690	−	0.991023i	$-0.457317\pi$
$569$	23.7907	−	11.6159i	0.997359	−	0.486964i	0.863669	+	0.504059i	$0.168161\pi$
$570$		0			0
$571$	3.71556	+	0.711696i	0.155491	+	0.0297836i	0.265280	−	0.964171i	$-0.414536\pi$
$571$	3.71556	+	0.711696i	0.155491	+	0.0297836i	−0.109789	+	0.993955i	$0.535017\pi$
$572$		0			0
$573$	−12.7073	−	24.8232i	−0.530855	−	1.03700i
$574$		0			0
$575$	34.6014	−	1.31031i	1.44298	−	0.0546436i
$576$		0			0
$577$	2.97004	+	2.80603i	0.123644	+	0.116816i	0.746085	−	0.665850i	$-0.231931\pi$
$577$	2.97004	+	2.80603i	0.123644	+	0.116816i	−0.622441	+	0.782667i	$0.713859\pi$
$578$		0			0
$579$	9.62983	−	15.7479i	0.400202	−	0.654459i
$580$		0			0
$581$	1.72933	−	4.60023i	0.0717448	−	0.190850i
$582$		0			0
$583$	18.8319	−	2.14763i	0.779939	−	0.0889459i
$584$		0			0
$585$	−31.0248	+	8.41803i	−1.28272	+	0.348043i
$586$		0			0
$587$	30.5404	+	21.1462i	1.26054	+	0.872797i	0.995803	−	0.0915250i	$-0.0291741\pi$
$587$	30.5404	+	21.1462i	1.26054	+	0.872797i	0.264733	+	0.964322i	$0.414716\pi$
$588$		0			0
$589$	5.93972	+	0.224929i	0.244742	+	0.00926803i
$590$		0			0
$591$	10.2753	+	77.1091i	0.422671	+	3.17184i
$592$		0			0
$593$	9.27485	−	27.8265i	0.380872	−	1.14270i	−0.566910	−	0.823780i	$-0.691861\pi$
$593$	9.27485	−	27.8265i	0.380872	−	1.14270i	0.947782	−	0.318918i	$-0.103319\pi$
$594$		0			0
$595$	−19.2173	+	34.2770i	−0.787834	+	1.40522i
$596$		0			0
$597$	−5.45039	−	57.4271i	−0.223069	−	2.35033i
$598$		0			0
$599$	0.555744	+	9.77787i	0.0227071	+	0.399513i	0.989555	+	0.144159i	$0.0460476\pi$
$599$	0.555744	+	9.77787i	0.0227071	+	0.399513i	−0.966848	+	0.255354i	$0.917808\pi$
$600$		0			0
$601$	−10.7169	+	12.7175i	−0.437150	+	0.518756i	−0.937933	−	0.346817i	$-0.887262\pi$
$601$	−10.7169	+	12.7175i	−0.437150	+	0.518756i	0.500783	+	0.865573i	$0.333046\pi$
$602$		0			0
$603$	3.62513	−	2.31214i	0.147627	−	0.0941577i
$604$		0			0
$605$	−59.5260	+	44.6405i	−2.42007	+	1.81490i
$606$		0			0
$607$	−24.7609	−	31.7476i	−1.00502	−	1.28859i	−0.957105	−	0.289743i	$-0.906430\pi$
$607$	−24.7609	−	31.7476i	−1.00502	−	1.28859i	−0.0479113	−	0.998852i	$-0.515256\pi$
$608$		0			0
$609$	−24.3476	−	36.6260i	−0.986615	−	1.48416i
$610$		0			0
$611$	1.70592	+	0.678412i	0.0690142	+	0.0274456i
$612$		0			0
$613$	−32.4487	−	3.70052i	−1.31059	−	0.149462i	−0.570125	−	0.821558i	$-0.693105\pi$
$613$	−32.4487	−	3.70052i	−1.31059	−	0.149462i	−0.740464	+	0.672095i	$0.765394\pi$
$614$		0			0
$615$	62.4935	+	46.8660i	2.51998	+	1.88982i
$616$		0			0
$617$	24.3612	−	26.7828i	0.980744	−	1.07823i	−0.0161810	−	0.999869i	$-0.505151\pi$
$617$	24.3612	−	26.7828i	0.980744	−	1.07823i	0.996925	−	0.0783642i	$-0.0249697\pi$
$618$		0			0
$619$	2.94919	+	8.84821i	0.118538	+	0.355639i	0.991145	−	0.132784i	$-0.0423916\pi$
$619$	2.94919	+	8.84821i	0.118538	+	0.355639i	−0.872607	+	0.488423i	$0.837572\pi$
$620$		0			0
$621$	−19.9656	+	79.5076i	−0.801192	+	3.19053i
$622$		0			0
$623$	15.1701	+	36.1393i	0.607777	+	1.44789i
$624$		0			0
$625$	7.16431	+	2.53956i	0.286572	+	0.101582i
$626$		0			0
$627$	126.905	−	50.4676i	5.06810	−	2.01548i
$628$		0			0
$629$	9.25928	−	31.7361i	0.369191	−	1.26540i
$630$		0			0
$631$	18.0386	−	5.63545i	0.718104	−	0.224344i	0.0827562	−	0.996570i	$-0.473628\pi$
$631$	18.0386	−	5.63545i	0.718104	−	0.224344i	0.635348	+	0.772226i	$0.280857\pi$
$632$		0			0
$633$	5.23827	−	0.397301i	0.208202	−	0.0157913i
$634$		0			0
$635$	12.2507	−	8.48240i	0.486154	−	0.336614i
$636$		0			0
$637$	1.84119	−	0.352671i	0.0729508	−	0.0139733i
$638$		0			0
$639$	6.57859	−	31.1430i	0.260245	−	1.23200i
$640$		0			0
$641$	−1.86950	−	0.912791i	−0.0738409	−	0.0360531i	0.401458	−	0.915877i	$-0.368504\pi$
$641$	−1.86950	−	0.912791i	−0.0738409	−	0.0360531i	−0.475299	+	0.879824i	$0.657660\pi$
$642$		0			0
$643$	−4.89226	+	28.4444i	−0.192932	+	1.12174i	0.713901	+	0.700247i	$0.246927\pi$
$643$	−4.89226	+	28.4444i	−0.192932	+	1.12174i	−0.906833	+	0.421491i	$0.861507\pi$
$644$		0			0
$645$	−15.4628	−	73.2006i	−0.608845	−	2.88227i
$646$		0			0
$647$	3.42184	−	3.48722i	0.134527	−	0.137097i	−0.643204	−	0.765695i	$-0.722395\pi$
$647$	3.42184	−	3.48722i	0.134527	−	0.137097i	0.777730	+	0.628598i	$0.216371\pi$
$648$		0			0
$649$	52.6116	+	12.1580i	2.06519	+	0.477243i
$650$		0			0
$651$	3.53111	−	5.31184i	0.138395	−	0.208188i
$652$		0			0
$653$	−23.0132	−	37.6340i	−0.900577	−	1.47273i	−0.881104	−	0.472923i	$-0.843199\pi$
$653$	−23.0132	−	37.6340i	−0.900577	−	1.47273i	−0.0194731	−	0.999810i	$-0.506199\pi$
$654$		0			0
$655$	6.36543	−	47.7680i	0.248718	−	1.86645i
$656$		0			0
$657$	43.0657	−	40.6875i	1.68015	−	1.58737i
$658$		0			0
$659$	28.9743	+	9.05190i	1.12868	+	0.352612i	0.804835	−	0.593499i	$-0.202254\pi$
$659$	28.9743	+	9.05190i	1.12868	+	0.352612i	0.323843	+	0.946111i	$0.395025\pi$
$660$		0			0
$661$	23.0064	−	31.9190i	0.894846	−	1.24150i	−0.0748518	−	0.997195i	$-0.523848\pi$
$661$	23.0064	−	31.9190i	0.894846	−	1.24150i	0.969697	−	0.244309i	$-0.0785613\pi$
$662$		0			0
$663$	11.6476	+	13.8219i	0.452354	+	0.536798i
$664$		0			0
$665$	57.6574	+	8.79676i	2.23586	+	0.341124i
$666$		0			0
$667$	26.7930			1.03743
$668$		0			0
$669$	56.5481			2.18628
$670$		0			0
$671$	−28.9940	−	4.42360i	−1.11930	−	0.170771i
$672$		0			0
$673$	20.5300	+	24.3624i	0.791372	+	0.939102i	0.999237	−	0.0390551i	$-0.0124348\pi$
$673$	20.5300	+	24.3624i	0.791372	+	0.939102i	−0.207866	+	0.978157i	$0.566652\pi$
$674$		0			0
$675$	75.0483	−	104.122i	2.88861	−	4.00764i
$676$		0			0
$677$	10.4341	+	3.25973i	0.401015	+	0.125282i	0.492052	−	0.870566i	$-0.336247\pi$
$677$	10.4341	+	3.25973i	0.401015	+	0.125282i	−0.0910367	+	0.995848i	$0.529018\pi$
$678$		0			0
$679$	−26.0398	+	24.6018i	−0.999317	+	0.944132i
$680$		0			0
$681$	−1.67132	+	12.5420i	−0.0640450	+	0.480611i
$682$		0			0
$683$	20.1523	+	32.9555i	0.771105	+	1.26101i	0.960273	+	0.279061i	$0.0900232\pi$
$683$	20.1523	+	32.9555i	0.771105	+	1.26101i	−0.189168	+	0.981945i	$0.560579\pi$
$684$		0			0
$685$	−1.37940	+	2.07502i	−0.0527040	+	0.0792825i
$686$		0			0
$687$	2.27447	+	0.525608i	0.0867766	+	0.0200532i
$688$		0			0
$689$	2.60769	−	2.65751i	0.0993450	−	0.101243i
$690$		0			0
$691$	7.16553	+	33.9215i	0.272590	+	1.29044i	0.871807	+	0.489850i	$0.162948\pi$
$691$	7.16553	+	33.9215i	0.272590	+	1.29044i	−0.599217	+	0.800586i	$0.704521\pi$
$692$		0			0
$693$	18.1918	−	105.770i	0.691050	−	4.01788i
$694$		0			0
$695$	−22.9908	−	11.2253i	−0.872091	−	0.425801i
$696$		0			0
$697$	6.64764	−	31.4699i	0.251797	−	1.19201i
$698$		0			0
$699$	−3.83942	+	0.735421i	−0.145220	+	0.0278162i
$700$		0			0
$701$	18.2359	−	12.6265i	0.688759	−	0.476898i	−0.172536	−	0.985003i	$-0.555196\pi$
$701$	18.2359	−	12.6265i	0.688759	−	0.476898i	0.861295	+	0.508106i	$0.169654\pi$
$702$		0			0
$703$	−48.9266	+	3.71088i	−1.84530	+	0.139959i
$704$		0			0
$705$	−18.5158	+	5.78455i	−0.697346	+	0.217859i
$706$		0			0
$707$	3.72030	−	12.7513i	0.139916	−	0.479562i
$708$		0			0
$709$	−38.7065	+	15.3928i	−1.45365	+	0.578089i	−0.957059	−	0.289894i	$-0.906380\pi$
$709$	−38.7065	+	15.3928i	−1.45365	+	0.578089i	−0.496594	+	0.867983i	$0.665416\pi$
$710$		0			0
$711$	−69.7453	−	24.7229i	−2.61565	−	0.927180i
$712$		0			0
$713$	1.50399	+	3.58291i	0.0563248	+	0.134181i
$714$		0			0
$715$	−5.41013	+	21.5444i	−0.202327	+	0.805714i
$716$		0			0
$717$	16.1884	+	48.5688i	0.604568	+	1.81383i
$718$		0			0
$719$	12.2373	−	13.4537i	0.456373	−	0.501738i	−0.467736	−	0.883868i	$-0.654930\pi$
$719$	12.2373	−	13.4537i	0.456373	−	0.501738i	0.924108	+	0.382131i	$0.124810\pi$
$720$		0			0
$721$	1.49455	+	1.12082i	0.0556600	+	0.0417413i
$722$		0			0
$723$	28.8505	+	3.29018i	1.07296	+	0.122363i
$724$		0			0
$725$	−38.9804	−	15.5017i	−1.44769	−	0.575720i
$726$		0			0
$727$	7.90749	+	11.8952i	0.293273	+	0.441169i	0.949673	−	0.313244i	$-0.101416\pi$
$727$	7.90749	+	11.8952i	0.293273	+	0.441169i	−0.656400	+	0.754413i	$0.727922\pi$
$728$		0			0
$729$	62.6034	+	80.2678i	2.31865	+	2.97288i
$730$		0			0
$731$	−24.6457	+	18.4826i	−0.911554	+	0.683605i
$732$		0			0
$733$	24.3116	−	15.5062i	0.897971	−	0.572734i	−0.00616451	−	0.999981i	$-0.501962\pi$
$733$	24.3116	−	15.5062i	0.897971	−	0.572734i	0.904135	+	0.427247i	$0.140516\pi$
$734$		0			0
$735$	−12.7644	+	15.1472i	−0.470823	+	0.558714i
$736$		0			0
$737$	−0.168596	−	2.96632i	−0.00621033	−	0.109266i
$738$		0			0
$739$	−3.67552	−	38.7265i	−0.135206	−	1.42458i	−0.763101	−	0.646279i	$-0.776324\pi$
$739$	−3.67552	−	38.7265i	−0.135206	−	1.42458i	0.627895	−	0.778298i	$-0.283917\pi$
$740$		0			0
$741$	13.1195	−	23.4006i	0.481958	−	0.859644i
$742$		0			0
$743$	6.32404	−	18.9735i	0.232006	−	0.696069i	−0.766541	−	0.642195i	$-0.778024\pi$
$743$	6.32404	−	18.9735i	0.232006	−	0.696069i	0.998548	−	0.0538736i	$-0.0171568\pi$
$744$		0			0
$745$	7.54260	+	56.6018i	0.276340	+	2.07373i
$746$		0			0
$747$	17.4791	+	0.661909i	0.639526	+	0.0242180i
$748$		0			0
$749$	−6.08130	−	4.21071i	−0.222206	−	0.153856i
$750$		0			0
$751$	−6.48009	+	1.75826i	−0.236462	+	0.0641598i	−0.378123	−	0.925755i	$-0.623430\pi$
$751$	−6.48009	+	1.75826i	−0.236462	+	0.0641598i	0.141661	+	0.989915i	$0.454756\pi$
$752$		0			0
$753$	−75.8635	+	8.65164i	−2.76462	+	0.315283i
$754$		0			0
$755$	−13.3514	+	35.5163i	−0.485907	+	1.29257i
$756$		0			0
$757$	−8.71101	+	14.2453i	−0.316607	+	0.517755i	−0.971212	−	0.238216i	$-0.923437\pi$
$757$	−8.71101	+	14.2453i	−0.316607	+	0.517755i	0.654605	+	0.755971i	$0.272835\pi$
$758$		0			0
$759$	64.8980	+	61.3142i	2.35565	+	2.22556i
$760$		0			0
$761$	−26.7491	+	1.01295i	−0.969654	+	0.0367194i	−0.517916	−	0.855431i	$-0.673292\pi$
$761$	−26.7491	+	1.01295i	−0.969654	+	0.0367194i	−0.451738	+	0.892151i	$0.649196\pi$
$762$		0			0
$763$	13.0837	+	25.5584i	0.473660	+	0.925277i
$764$		0			0
$765$	−137.365	−	26.3116i	−4.96645	−	0.951298i
$766$		0			0
$767$	9.53165	−	4.65386i	0.344168	−	0.168041i
$768$		0			0
$769$	−21.1714	+	7.50470i	−0.763460	+	0.270626i	−0.687207	−	0.726462i	$-0.741163\pi$
$769$	−21.1714	+	7.50470i	−0.763460	+	0.270626i	−0.0762535	+	0.997088i	$0.524296\pi$
$770$		0			0
$771$	0.255212	−	13.4836i	0.00919123	−	0.485601i
$772$		0			0
$773$	30.2998	+	2.29812i	1.08981	+	0.0826577i	0.608242	−	0.793751i	$-0.291875\pi$
$773$	30.2998	+	2.29812i	1.08981	+	0.0826577i	0.481567	+	0.876409i	$0.340068\pi$
$774$		0			0
$775$	−0.115133	−	6.08283i	−0.00413570	−	0.218502i
$776$		0			0
$777$	−23.9930	+	46.8693i	−0.860742	+	1.68143i
$778$		0			0
$779$	−47.1928	+	7.20018i	−1.69086	+	0.257973i
$780$		0			0
$781$	−16.5479	−	14.4891i	−0.592132	−	0.518460i
$782$		0			0
$783$	61.0780	−	78.3119i	2.18275	−	2.79864i
$784$		0			0
$785$	17.5283	−	37.6930i	0.625612	−	1.34532i
$786$		0			0
$787$	16.0589	+	42.7184i	0.572436	+	1.52275i	0.830727	+	0.556681i	$0.187925\pi$
$787$	16.0589	+	42.7184i	0.572436	+	1.52275i	−0.258290	+	0.966067i	$0.583159\pi$
$788$		0			0
$789$	−2.47276	+	43.5063i	−0.0880326	+	1.54886i
$790$		0			0
$791$	6.73422	−	1.55621i	0.239441	−	0.0553324i
$792$		0			0
$793$	−4.97119	+	2.91208i	−0.176532	+	0.103411i
$794$		0			0
$795$	−3.71712	+	39.1648i	−0.131833	+	1.38903i
$796$		0			0
$797$	−22.6167	−	12.1233i	−0.801124	−	0.429429i	0.0202669	−	0.999795i	$-0.493548\pi$
$797$	−22.6167	−	12.1233i	−0.801124	−	0.429429i	−0.821391	+	0.570366i	$0.806801\pi$
$798$		0			0
$799$	5.37454	+	5.90879i	0.190138	+	0.209038i
$800$		0			0
$801$	−104.953	+	91.8947i	−3.70832	+	3.24694i
$802$		0			0
$803$	−9.97091	−	39.7065i	−0.351866	−	1.40121i
$804$		0			0
$805$	10.6791	+	36.6026i	0.376390	+	1.29007i
$806$		0			0
$807$	−30.2736	+	13.3873i	−1.06568	+	0.471254i
$808$		0			0
$809$	−3.94768	+	9.40445i	−0.138793	+	0.330643i	−0.976513	−	0.215457i	$-0.930876\pi$
$809$	−3.94768	+	9.40445i	−0.138793	+	0.330643i	0.837720	+	0.546100i	$0.183888\pi$
$810$		0			0
$811$	−2.34068	−	3.24745i	−0.0821923	−	0.114033i	0.768134	−	0.640290i	$-0.221186\pi$
$811$	−2.34068	−	3.24745i	−0.0821923	−	0.114033i	−0.850326	+	0.526256i	$0.823595\pi$
$812$		0			0
$813$	16.4264	−	8.80511i	0.576100	−	0.308809i
$814$		0			0
$815$	−4.95695	−	28.8205i	−0.173634	−	1.00954i
$816$		0			0
$817$	38.5495	+	24.5872i	1.34868	+	0.860199i
$818$		0			0
$819$	−10.3098	−	18.3891i	−0.360254	−	0.642567i
$820$		0			0
$821$	−16.3632	+	13.2678i	−0.571080	+	0.463048i	−0.871251	−	0.490837i	$-0.836691\pi$
$821$	−16.3632	+	13.2678i	−0.571080	+	0.463048i	0.300172	+	0.953885i	$0.402956\pi$
$822$		0			0
$823$	11.7070	+	9.49234i	0.408079	+	0.330882i	0.811732	−	0.584030i	$-0.198525\pi$
$823$	11.7070	+	9.49234i	0.408079	+	0.330882i	−0.403653	+	0.914912i	$0.632260\pi$
$824$		0			0
$825$	−58.9434	−	126.752i	−2.05215	−	4.41295i
$826$		0			0
$827$	22.8946	+	23.3320i	0.796124	+	0.811335i	0.985340	−	0.170601i	$-0.0545708\pi$
$827$	22.8946	+	23.3320i	0.796124	+	0.811335i	−0.189217	+	0.981935i	$0.560595\pi$
$828$		0			0
$829$	34.6141	+	15.3066i	1.20220	+	0.531622i	0.905907	−	0.423476i	$-0.139190\pi$
$829$	34.6141	+	15.3066i	1.20220	+	0.531622i	0.296290	+	0.955098i	$0.404251\pi$
$830$		0			0
$831$	−39.4177	−	23.0906i	−1.36739	−	0.801004i
$832$		0			0
$833$	7.87164	+	2.13583i	0.272736	+	0.0740023i
$834$		0			0
$835$	−41.9625	+	17.4292i	−1.45217	+	0.603161i
$836$		0			0
$837$	13.9008	+	3.77175i	0.480483	+	0.130371i
$838$		0			0
$839$	−43.9449	−	25.7426i	−1.51715	−	0.888734i	−0.999450	−	0.0331704i	$-0.989440\pi$
$839$	−43.9449	−	25.7426i	−1.51715	−	0.888734i	−0.517698	−	0.855563i	$-0.673211\pi$
$840$		0			0
$841$	−3.16418	−	1.39923i	−0.109110	−	0.0482493i
$842$		0			0
$843$	4.70653	+	4.79646i	0.162102	+	0.165199i
$844$		0			0
$845$	−17.4341	−	37.4905i	−0.599753	−	1.28971i
$846$		0			0
$847$	−37.9019	−	30.7320i	−1.30233	−	1.05596i
$848$		0			0
$849$	17.2998	−	14.0271i	0.593726	−	0.481411i
$850$		0			0
$851$	−15.6866	−	27.9794i	−0.537731	−	0.959123i
$852$		0			0
$853$	−41.7147	−	26.6060i	−1.42828	−	0.910973i	−0.999973	−	0.00734226i	$-0.997663\pi$
$853$	−41.7147	−	26.6060i	−1.42828	−	0.910973i	−0.428311	−	0.903631i	$-0.640891\pi$
$854$		0			0
$855$	35.1869	+	204.582i	1.20337	+	6.99657i
$856$		0			0
$857$	−6.32251	+	3.38907i	−0.215973	+	0.115768i	−0.576866	−	0.816838i	$-0.695725\pi$
$857$	−6.32251	+	3.38907i	−0.215973	+	0.115768i	0.360894	+	0.932607i	$0.382472\pi$
$858$		0			0
$859$	−17.5017	−	24.2818i	−0.597151	−	0.828484i	0.398925	−	0.916983i	$-0.369383\pi$
$859$	−17.5017	−	24.2818i	−0.597151	−	0.828484i	−0.996076	+	0.0884994i	$0.971793\pi$
$860$		0			0
$861$	−19.8279	+	47.2354i	−0.675733	+	1.60978i
$862$		0			0
$863$	2.25447	−	0.996945i	0.0767430	−	0.0339364i	−0.365703	−	0.930732i	$-0.619171\pi$
$863$	2.25447	−	0.996945i	0.0767430	−	0.0339364i	0.442446	+	0.896795i	$0.354111\pi$
$864$		0			0
$865$	−3.27355	−	11.2201i	−0.111304	−	0.381494i
$866$		0			0
$867$	5.29245	+	21.0758i	0.179741	+	0.715770i
$868$		0			0
$869$	−38.4699	+	33.6836i	−1.30500	+	1.14264i
$870$		0			0
$871$	−0.392708	−	0.431745i	−0.0133064	−	0.0146291i
$872$		0			0
$873$	−112.375	−	60.2367i	−3.80332	−	2.03870i
$874$		0			0
$875$	1.81022	−	19.0731i	0.0611967	−	0.644789i
$876$		0			0
$877$	19.9383	−	11.6797i	0.673269	−	0.394396i	−0.128765	−	0.991675i	$-0.541101\pi$
$877$	19.9383	−	11.6797i	0.673269	−	0.394396i	0.802033	+	0.597280i	$0.203752\pi$
$878$		0			0
$879$	10.3774	−	2.39810i	0.350020	−	0.0808859i
$880$		0			0
$881$	−1.06698	+	18.7726i	−0.0359473	+	0.632465i	0.929009	+	0.370056i	$0.120662\pi$
$881$	−1.06698	+	18.7726i	−0.0359473	+	0.632465i	−0.964957	+	0.262409i	$0.915483\pi$
$882$		0			0
$883$	−7.60085	−	20.2191i	−0.255789	−	0.680428i	−0.999923	−	0.0123983i	$-0.996053\pi$
$883$	−7.60085	−	20.2191i	−0.255789	−	0.680428i	0.744134	−	0.668030i	$-0.232862\pi$
$884$		0			0
$885$	−47.2594	+	101.627i	−1.58861	+	3.41615i
$886$		0			0
$887$	−23.3556	+	29.9457i	−0.784205	+	1.00548i	0.215376	+	0.976531i	$0.430902\pi$
$887$	−23.3556	+	29.9457i	−0.784205	+	1.00548i	−0.999581	+	0.0289471i	$0.990785\pi$
$888$		0			0
$889$	7.35208	+	6.43735i	0.246581	+	0.215902i
$890$		0			0
$891$	189.123	−	28.8545i	6.33587	−	0.966661i
$892$		0			0
$893$	5.40210	−	10.5528i	0.180774	−	0.353136i
$894$		0			0
$895$	−1.00963	−	53.3418i	−0.0337481	−	1.78302i
$896$		0			0
$897$	17.4877	+	1.32638i	0.583899	+	0.0442864i
$898$		0			0
$899$	0.0890874	−	4.70677i	0.00297123	−	0.156980i
$900$		0			0
$901$	15.2681	−	5.41213i	0.508653	−	0.180304i
$902$		0			0
$903$	44.0903	−	21.5272i	1.46723	−	0.716382i
$904$		0			0
$905$	−59.0242	−	11.3058i	−1.96203	−	0.375817i
$906$		0			0
$907$	−18.2562	−	35.6628i	−0.606187	−	1.18416i	−0.967773	−	0.251824i	$-0.918969\pi$
$907$	−18.2562	−	35.6628i	−0.606187	−	1.18416i	0.361586	−	0.932339i	$-0.382235\pi$
$908$		0			0
$909$	47.2422	−	1.78899i	1.56692	−	0.0593372i
$910$		0			0
$911$	−9.53146	−	9.00510i	−0.315791	−	0.298352i	0.512458	−	0.858712i	$-0.328735\pi$
$911$	−9.53146	−	9.00510i	−0.315791	−	0.298352i	−0.828249	+	0.560360i	$0.810663\pi$
$912$		0			0
$913$	6.30554	−	10.3116i	0.208683	−	0.341264i
$914$		0			0
$915$	21.4211	−	56.9827i	0.708160	−	1.88379i
$916$		0			0
$917$	31.4001	−	3.58094i	1.03692	−	0.118253i
$918$		0			0
$919$	−4.61851	+	1.25315i	−0.152350	+	0.0413377i	−0.337223	−	0.941425i	$-0.609488\pi$
$919$	−4.61851	+	1.25315i	−0.152350	+	0.0413377i	0.184872	+	0.982763i	$0.440813\pi$
$920$		0			0
$921$	−7.28041	−	5.04097i	−0.239898	−	0.166106i
$922$		0			0
$923$	−4.31743	−	0.163495i	−0.142110	−	0.00538151i
$924$		0			0
$925$	6.63385	+	49.7823i	0.218120	+	1.63683i
$926$		0			0
$927$	−2.10246	+	6.30781i	−0.0690537	+	0.207176i
$928$		0			0
$929$	0.611885	−	1.09139i	0.0200753	−	0.0358073i	−0.862043	−	0.506835i	$-0.830815\pi$
$929$	0.611885	−	1.09139i	0.0200753	−	0.0358073i	0.882119	+	0.471027i	$0.156117\pi$
$930$		0			0
$931$	−1.14381	−	12.0515i	−0.0374867	−	0.394972i
$932$		0			0
$933$	−6.11594	−	107.605i	−0.200227	−	3.52283i
$934$		0			0
$935$	−62.2778	+	73.9036i	−2.03670	+	2.41691i
$936$		0			0
$937$	−38.7188	+	24.6952i	−1.26489	+	0.806758i	−0.988046	−	0.154157i	$-0.950734\pi$
$937$	−38.7188	+	24.6952i	−1.26489	+	0.806758i	−0.276842	+	0.960915i	$0.589288\pi$
$938$		0			0
$939$	−33.5602	+	25.1679i	−1.09520	+	0.821324i
$940$		0			0
$941$	11.4982	+	14.7426i	0.374831	+	0.480594i	0.938437	−	0.345449i	$-0.112273\pi$
$941$	11.4982	+	14.7426i	0.374831	+	0.480594i	−0.563607	+	0.826043i	$0.690587\pi$
$942$		0			0
$943$	−17.2771	−	25.9898i	−0.562618	−	0.846345i
$944$		0			0
$945$	131.328	+	52.2267i	4.27211	+	1.69893i
$946$		0			0
$947$	−50.4442	−	5.75277i	−1.63922	−	0.186940i	−0.755562	−	0.655078i	$-0.772636\pi$
$947$	−50.4442	−	5.75277i	−1.63922	−	0.186940i	−0.883655	+	0.468138i	$0.844925\pi$
$948$		0			0
$949$	−6.43372	−	4.82486i	−0.208847	−	0.156622i
$950$		0			0
$951$	5.12968	−	5.63959i	0.166341	−	0.182876i
$952$		0			0
$953$	8.52015	+	25.5623i	0.275995	+	0.828043i	0.991578	+	0.129515i	$0.0413419\pi$
$953$	8.52015	+	25.5623i	0.275995	+	0.828043i	−0.715583	+	0.698528i	$0.753839\pi$
$954$		0			0
$955$	7.13359	−	28.4076i	0.230838	−	0.919248i
$956$		0			0
$957$	−41.8651	−	99.7340i	−1.35331	−	3.22394i
$958$		0			0
$959$	−1.54017	−	0.545949i	−0.0497346	−	0.0176296i
$960$		0			0
$961$	−28.1713	+	11.2032i	−0.908753	+	0.361393i
$962$		0			0
$963$	7.37350	−	25.2726i	0.237608	−	0.814398i
$964$		0			0
$965$	18.5054	−	5.78130i	0.595710	−	0.186107i
$966$		0			0
$967$	54.5811	−	4.13975i	1.75521	−	0.133126i	0.841701	−	0.539945i	$-0.181555\pi$
$967$	54.5811	−	4.13975i	1.75521	−	0.133126i	0.913509	+	0.406819i	$0.133362\pi$
$968$		0			0
$969$	95.9623	−	66.4444i	3.08275	−	2.13450i
$970$		0			0
$971$	−23.8810	+	4.57428i	−0.766378	+	0.146796i	−0.556405	−	0.830911i	$-0.687820\pi$
$971$	−23.8810	+	4.57428i	−0.766378	+	0.146796i	−0.209973	+	0.977707i	$0.567338\pi$
$972$		0			0
$973$	3.46780	−	16.4165i	0.111173	−	0.526290i
$974$		0			0
$975$	−24.6750	−	12.0476i	−0.790232	−	0.385833i
$976$		0			0
$977$	8.78944	−	51.1032i	0.281199	−	1.63494i	−0.409866	−	0.912146i	$-0.634425\pi$
$977$	8.78944	−	51.1032i	0.281199	−	1.63494i	0.691066	−	0.722792i	$-0.257142\pi$
$978$		0			0
$979$	19.9223	+	94.3121i	0.636720	+	3.01423i
$980$		0			0
$981$	−71.5741	+	72.9417i	−2.28519	+	2.32885i
$982$		0			0
$983$	−51.1410	−	11.8182i	−1.63115	−	0.376941i	−0.692390	−	0.721524i	$-0.743442\pi$
$983$	−51.1410	−	11.8182i	−1.63115	−	0.376941i	−0.938756	+	0.344583i	$0.888020\pi$
$984$		0			0
$985$	−45.2316	+	68.0417i	−1.44120	+	2.16799i
$986$		0			0
$987$	−6.63677	−	10.8533i	−0.211251	−	0.345463i
$988$		0			0
$989$	−3.94824	+	29.6287i	−0.125547	+	0.942139i
$990$		0			0
$991$	−0.00782630	+	0.00739411i	−0.000248611	+	0.000234882i	−0.686876	−	0.726775i	$-0.741018\pi$
$991$	−0.00782630	+	0.00739411i	−0.000248611	+	0.000234882i	0.686627	+	0.727010i	$0.259091\pi$
$992$		0			0
$993$	−32.2178	−	10.0652i	−1.02240	−	0.319409i
$994$		0			0
$995$	35.4264	−	49.1504i	1.12309	−	1.55817i
$996$		0			0
$997$	16.8940	+	20.0478i	0.535040	+	0.634919i	0.963201	−	0.268783i	$-0.0866215\pi$
$997$	16.8940	+	20.0478i	0.535040	+	0.634919i	−0.428161	+	0.903702i	$0.640838\pi$
$998$		0			0
$999$	−117.539	−	17.9329i	−3.71878	−	0.567372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.21.1	✓	1148
167.8	even	83	inner	668.2.e.a.509.1	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.21.1	✓	1148	1.1	even	1	trivial
668.2.e.a.509.1	yes	1148	167.8	even	83	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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.30940 - 0.504914i) q^{3} +(-2.26577 - 2.68874i) q^{5} +(1.34830 - 1.87063i) q^{7} +(7.83367 + 2.44733i) q^{9} +O(q^{10})\)	\(q+(-3.30940 - 0.504914i) q^{3} +(-2.26577 - 2.68874i) q^{5} +(1.34830 - 1.87063i) q^{7} +(7.83367 + 2.44733i) q^{9} +(4.12227 - 3.89463i) q^{11} +(0.147148 - 1.10424i) q^{13} +(6.14075 + 10.0421i) q^{15} +(2.68317 - 4.03629i) q^{17} +(-7.00893 - 1.61969i) q^{19} +(-5.40658 + 5.50988i) q^{21} +(-0.971946 - 4.60119i) q^{23} +(-1.24807 + 7.25647i) q^{25} +(-15.6642 - 7.64811i) q^{27} +(-1.17751 + 5.57434i) q^{29} +(-0.811528 + 0.155444i) q^{31} +(-15.6087 + 10.8075i) q^{33} +(-8.08457 + 0.613182i) q^{35} +(6.51057 - 2.03398i) q^{37} +(-1.04451 + 3.58006i) q^{39} +(6.16653 - 2.45231i) q^{41} +(-5.99079 - 2.12358i) q^{43} +(-11.1691 - 26.6077i) q^{45} +(-0.401377 + 1.59837i) q^{47} +(0.532123 + 1.59648i) q^{49} +(-10.9177 + 12.0029i) q^{51} +(2.67386 + 2.00522i) q^{53} +(-19.8117 - 2.25937i) q^{55} +(22.3775 + 8.89911i) q^{57} +(5.27120 + 7.92946i) q^{59} +(-3.18062 - 4.07808i) q^{61} +(15.1402 - 11.3541i) q^{63} +(-3.30240 + 2.10631i) q^{65} +(0.337603 - 0.400625i) q^{67} +(0.893356 + 15.7179i) q^{69} +(-0.366451 - 3.86105i) q^{71} +(3.53031 - 6.29683i) q^{73} +(7.79424 - 23.3844i) q^{75} +(-1.72733 - 12.9624i) q^{77} +(-9.00987 - 0.341191i) q^{79} +(27.7351 + 19.2038i) q^{81} +(2.05692 - 0.558109i) q^{83} +(-16.9320 + 1.93096i) q^{85} +(6.71142 - 17.8532i) q^{87} +(-8.86736 + 14.5010i) q^{89} +(-1.86722 - 1.76410i) q^{91} +(2.76416 - 0.104675i) q^{93} +(11.5257 + 22.5150i) q^{95} +(-15.2582 - 2.92263i) q^{97} +(41.8239 - 20.4207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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