LMFDB - Embedded newform 952.2.cw.a.129.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(73,952)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("952.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 0, 8, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.cw (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [288,0,0,0,0,0,0,0,0,0,0,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			129.16
Character	$\chi$	$=$	952.129
Dual form			952.2.cw.a.369.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06671 + 2.16308i) q^{3} +(2.76046 - 2.42086i) q^{5} +(1.17475 - 2.37064i) q^{7} +(-1.71474 + 2.23469i) q^{9} +(-2.29799 + 0.150618i) q^{11} +(1.99304 + 1.99304i) q^{13} +(8.18112 + 3.38873i) q^{15} +(-4.11201 - 0.302263i) q^{17} +(0.0932516 + 0.708317i) q^{19} +(6.38101 + 0.0122885i) q^{21} +(6.79424 + 3.35055i) q^{23} +(1.10695 - 8.40815i) q^{25} +(0.433420 + 0.0862126i) q^{27} +(-0.349440 - 1.75675i) q^{29} +(4.43893 - 2.18904i) q^{31} +(-2.77708 - 4.81005i) q^{33} +(-2.49614 - 9.38798i) q^{35} +(0.510302 - 7.78570i) q^{37} +(-2.18510 + 6.43711i) q^{39} +(0.0118819 - 0.0597346i) q^{41} +(2.85983 + 6.90424i) q^{43} +(0.676404 + 10.3199i) q^{45} +(-2.68726 + 10.0290i) q^{47} +(-4.23991 - 5.56985i) q^{49} +(-3.73251 - 9.21702i) q^{51} +(-3.29512 - 4.29429i) q^{53} +(-5.97887 + 5.97887i) q^{55} +(-1.43267 + 0.957279i) q^{57} +(8.47313 + 1.11551i) q^{59} +(-1.00282 - 2.95422i) q^{61} +(3.28327 + 6.69026i) q^{63} +(10.3266 + 0.676841i) q^{65} +(-1.98621 - 1.14674i) q^{67} +18.2705i q^{69} +(-10.2996 - 6.88195i) q^{71} +(-4.04953 - 1.37463i) q^{73} +(19.3683 - 6.57464i) q^{75} +(-2.34250 + 5.62464i) q^{77} +(-3.14173 + 6.37079i) q^{79} +(2.46295 + 9.19186i) q^{81} +(-5.44666 + 13.1494i) q^{83} +(-12.0828 + 9.12022i) q^{85} +(3.42724 - 2.62982i) q^{87} +(5.78735 + 1.55072i) q^{89} +(7.06613 - 2.38346i) q^{91} +(9.47010 + 7.26667i) q^{93} +(1.97215 + 1.72953i) q^{95} +(-18.5103 + 3.68192i) q^{97} +(3.60387 - 5.39357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 32 q^{15} - 48 q^{21} + 32 q^{29} + 72 q^{31} + 32 q^{35} + 48 q^{37} + 32 q^{39} - 32 q^{43} - 24 q^{47} + 48 q^{49} + 16 q^{53} + 128 q^{57} - 72 q^{61} + 184 q^{63} - 32 q^{65} - 80 q^{71} - 96 q^{73}+ \cdots + 64 q^{99}+O(q^{100}) $ 288 * q - 32 * q^15 - 48 * q^21 + 32 * q^29 + 72 * q^31 + 32 * q^35 + 48 * q^37 + 32 * q^39 - 32 * q^43 - 24 * q^47 + 48 * q^49 + 16 * q^53 + 128 * q^57 - 72 * q^61 + 184 * q^63 - 32 * q^65 - 80 * q^71 - 96 * q^73 - 216 * q^75 + 56 * q^77 - 32 * q^79 - 64 * q^81 + 160 * q^85 - 144 * q^87 + 144 * q^89 - 32 * q^93 - 64 * q^95 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{16}\right)$

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			0
$2$		0			0
$3$	1.06671	+	2.16308i	0.615866	+	1.24885i	0.951728	+	0.306942i	$0.0993056\pi$
$3$	1.06671	+	2.16308i	0.615866	+	1.24885i	−0.335862	+	0.941911i	$0.609028\pi$
$4$		0			0
$5$	2.76046	−	2.42086i	1.23452	−	1.08264i	0.240815	−	0.970571i	$-0.422585\pi$
$5$	2.76046	−	2.42086i	1.23452	−	1.08264i	0.993700	−	0.112070i	$-0.0357482\pi$
$6$		0			0
$7$	1.17475	−	2.37064i	0.444015	−	0.896019i
$7$	1.17475	−	2.37064i	0.444015	−	0.896019i
$8$		0			0
$9$	−1.71474	+	2.23469i	−0.571581	+	0.744898i
$10$		0			0
$11$	−2.29799	+	0.150618i	−0.692869	+	0.0454130i	−0.407769	−	0.913085i	$-0.633693\pi$
$11$	−2.29799	+	0.150618i	−0.692869	+	0.0454130i	−0.285099	+	0.958498i	$0.592027\pi$
$12$		0			0
$13$	1.99304	+	1.99304i	0.552771	+	0.552771i	0.927240	−	0.374469i	$-0.122175\pi$
$13$	1.99304	+	1.99304i	0.552771	+	0.552771i	−0.374469	+	0.927240i	$0.622175\pi$
$14$		0			0
$15$	8.18112	+	3.38873i	2.11236	+	0.874966i
$16$		0			0
$17$	−4.11201	−	0.302263i	−0.997309	−	0.0733095i
$17$	−4.11201	−	0.302263i	−0.997309	−	0.0733095i
$18$		0			0
$19$	0.0932516	+	0.708317i	0.0213934	+	0.162499i	0.998807	−	0.0488377i	$-0.0155517\pi$
$19$	0.0932516	+	0.708317i	0.0213934	+	0.162499i	−0.977413	+	0.211337i	$0.932218\pi$
$20$		0			0
$21$	6.38101	+	0.0122885i	1.39245	+	0.00268158i
$22$		0			0
$23$	6.79424	+	3.35055i	1.41670	+	0.698637i	0.979634	−	0.200794i	$-0.0643520\pi$
$23$	6.79424	+	3.35055i	1.41670	+	0.698637i	0.437063	+	0.899431i	$0.356019\pi$
$24$		0			0
$25$	1.10695	−	8.40815i	0.221391	−	1.68163i
$26$		0			0
$27$	0.433420	+	0.0862126i	0.0834117	+	0.0165916i
$28$		0			0
$29$	−0.349440	−	1.75675i	−0.0648894	−	0.326221i	0.934682	−	0.355484i	$-0.115684\pi$
$29$	−0.349440	−	1.75675i	−0.0648894	−	0.326221i	−0.999572	+	0.0292629i	$0.990684\pi$
$30$		0			0
$31$	4.43893	−	2.18904i	0.797255	−	0.393163i	0.00242653	−	0.999997i	$-0.499228\pi$
$31$	4.43893	−	2.18904i	0.797255	−	0.393163i	0.794828	+	0.606835i	$0.207561\pi$
$32$		0			0
$33$	−2.77708	−	4.81005i	−0.483428	−	0.837322i
$34$		0			0
$35$	−2.49614	−	9.38798i	−0.421924	−	1.58686i
$36$		0			0
$37$	0.510302	−	7.78570i	0.0838931	−	1.27996i	−0.723656	−	0.690161i	$-0.757540\pi$
$37$	0.510302	−	7.78570i	0.0838931	−	1.27996i	0.807549	−	0.589800i	$-0.200794\pi$
$38$		0			0
$39$	−2.18510	+	6.43711i	−0.349897	+	1.03076i
$40$		0			0
$41$	0.0118819	−	0.0597346i	0.00185565	−	0.00932897i	−0.979846	−	0.199753i	$-0.935986\pi$
$41$	0.0118819	−	0.0597346i	0.00185565	−	0.00932897i	0.981702	+	0.190424i	$0.0609862\pi$
$42$		0			0
$43$	2.85983	+	6.90424i	0.436120	+	1.05289i	0.977277	+	0.211965i	$0.0679864\pi$
$43$	2.85983	+	6.90424i	0.436120	+	1.05289i	−0.541157	+	0.840921i	$0.682014\pi$
$44$		0			0
$45$	0.676404	+	10.3199i	0.100832	+	1.53841i
$46$		0			0
$47$	−2.68726	+	10.0290i	−0.391978	+	1.46288i	0.434889	+	0.900484i	$0.356787\pi$
$47$	−2.68726	+	10.0290i	−0.391978	+	1.46288i	−0.826867	+	0.562397i	$0.809879\pi$
$48$		0			0
$49$	−4.23991	−	5.56985i	−0.605701	−	0.795692i
$50$		0			0
$51$	−3.73251	−	9.21702i	−0.522656	−	1.29064i
$52$		0			0
$53$	−3.29512	−	4.29429i	−0.452620	−	0.589866i	0.510185	−	0.860065i	$-0.329577\pi$
$53$	−3.29512	−	4.29429i	−0.452620	−	0.589866i	−0.962804	+	0.270199i	$0.912910\pi$
$54$		0			0
$55$	−5.97887	+	5.97887i	−0.806191	+	0.806191i
$56$		0			0
$57$	−1.43267	+	0.957279i	−0.189762	+	0.126795i
$58$		0			0
$59$	8.47313	+	1.11551i	1.10311	+	0.145227i	0.660018	−	0.751250i	$-0.270549\pi$
$59$	8.47313	+	1.11551i	1.10311	+	0.145227i	0.443090	+	0.896477i	$0.353882\pi$
$60$		0			0
$61$	−1.00282	−	2.95422i	−0.128398	−	0.378249i	0.863653	−	0.504087i	$-0.168171\pi$
$61$	−1.00282	−	2.95422i	−0.128398	−	0.378249i	−0.992051	+	0.125839i	$0.959838\pi$
$62$		0			0
$63$	3.28327	+	6.69026i	0.413653	+	0.842893i
$64$		0			0
$65$	10.3266	+	0.676841i	1.28086	+	0.0839518i
$66$		0			0
$67$	−1.98621	−	1.14674i	−0.242654	−	0.140096i	0.373742	−	0.927533i	$-0.378075\pi$
$67$	−1.98621	−	1.14674i	−0.242654	−	0.140096i	−0.616396	+	0.787436i	$0.711408\pi$
$68$		0			0
$69$			18.2705i			2.19951i
$70$		0			0
$71$	−10.2996	−	6.88195i	−1.22233	−	0.816737i	−0.234479	−	0.972121i	$-0.575338\pi$
$71$	−10.2996	−	6.88195i	−1.22233	−	0.816737i	−0.987854	+	0.155384i	$0.950338\pi$
$72$		0			0
$73$	−4.04953	−	1.37463i	−0.473962	−	0.160888i	0.0742295	−	0.997241i	$-0.476350\pi$
$73$	−4.04953	−	1.37463i	−0.473962	−	0.160888i	−0.548192	+	0.836353i	$0.684684\pi$
$74$		0			0
$75$	19.3683	−	6.57464i	2.23646	−	0.759174i
$76$		0			0
$77$	−2.34250	+	5.62464i	−0.266953	+	0.640988i
$78$		0			0
$79$	−3.14173	+	6.37079i	−0.353472	+	0.716770i	−0.998892	−	0.0470574i	$-0.985016\pi$
$79$	−3.14173	+	6.37079i	−0.353472	+	0.716770i	0.645420	+	0.763828i	$0.276682\pi$
$80$		0			0
$81$	2.46295	+	9.19186i	0.273661	+	1.02132i
$82$		0			0
$83$	−5.44666	+	13.1494i	−0.597849	+	1.44333i	0.277921	+	0.960604i	$0.410355\pi$
$83$	−5.44666	+	13.1494i	−0.597849	+	1.44333i	−0.875769	+	0.482730i	$0.839645\pi$
$84$		0			0
$85$	−12.0828	+	9.12022i	−1.31056	+	0.989226i
$86$		0			0
$87$	3.42724	−	2.62982i	0.367439	−	0.281946i
$88$		0			0
$89$	5.78735	+	1.55072i	0.613458	+	0.164376i	0.552152	−	0.833743i	$-0.313807\pi$
$89$	5.78735	+	1.55072i	0.613458	+	0.164376i	0.0613061	+	0.998119i	$0.480473\pi$
$90$		0			0
$91$	7.06613	−	2.38346i	0.740732	−	0.249855i
$92$		0			0
$93$	9.47010	+	7.26667i	0.982004	+	0.753518i
$94$		0			0
$95$	1.97215	+	1.72953i	0.202339	+	0.177446i
$96$		0			0
$97$	−18.5103	+	3.68192i	−1.87943	+	0.373843i	−0.995580	−	0.0939192i	$-0.970060\pi$
$97$	−18.5103	+	3.68192i	−1.87943	+	0.373843i	−0.883854	+	0.467762i	$0.845060\pi$
$98$		0			0
$99$	3.60387	−	5.39357i	0.362202	−	0.542074i
$100$		0			0
$101$	−6.21702	+	10.7682i	−0.618616	+	1.07147i	0.371122	+	0.928584i	$0.378973\pi$
$101$	−6.21702	+	10.7682i	−0.618616	+	1.07147i	−0.989738	+	0.142891i	$0.954360\pi$
$102$		0			0
$103$	−1.29780	+	0.749287i	−0.127876	+	0.0738295i	−0.562574	−	0.826747i	$-0.690189\pi$
$103$	−1.29780	+	0.749287i	−0.127876	+	0.0738295i	0.434697	+	0.900577i	$0.356855\pi$
$104$		0			0
$105$	17.6443	−	15.4136i	1.72190	−	1.50421i
$106$		0			0
$107$	−7.31692	−	8.34335i	−0.707354	−	0.806582i	0.280846	−	0.959753i	$-0.409385\pi$
$107$	−7.31692	−	8.34335i	−0.707354	−	0.806582i	−0.988200	+	0.153171i	$0.951052\pi$
$108$		0			0
$109$	6.70687	−	7.64772i	0.642402	−	0.732519i	−0.335394	−	0.942078i	$-0.608870\pi$
$109$	6.70687	−	7.64772i	0.642402	−	0.732519i	0.977796	+	0.209559i	$0.0672029\pi$
$110$		0			0
$111$	17.3854	−	7.20127i	1.65015	−	0.683514i
$112$		0			0
$113$	5.88874	+	8.81312i	0.553966	+	0.829068i	0.997749	−	0.0670662i	$-0.0213639\pi$
$113$	5.88874	+	8.81312i	0.553966	+	0.829068i	−0.443783	+	0.896134i	$0.646364\pi$
$114$		0			0
$115$	26.8664	−	7.19884i	2.50531	−	0.671295i
$116$		0			0
$117$	−7.87140	+	1.03629i	−0.727711	+	0.0958050i
$118$		0			0
$119$	−5.54716	+	9.39303i	−0.508507	+	0.861058i
$120$		0			0
$121$	−5.64784	+	0.743553i	−0.513440	+	0.0675957i
$122$		0			0
$123$	0.141885	−	0.0380180i	0.0127933	−	0.00342797i
$124$		0			0
$125$	−7.10007	−	10.6260i	−0.635049	−	0.950418i
$126$		0			0
$127$	−7.27881	+	3.01498i	−0.645890	+	0.267536i	−0.681487	−	0.731830i	$-0.738667\pi$
$127$	−7.27881	+	3.01498i	−0.645890	+	0.267536i	0.0355975	+	0.999366i	$0.488667\pi$
$128$		0			0
$129$	−11.8838	+	13.5509i	−1.04631	+	1.19309i
$130$		0			0
$131$	−12.1642	−	13.8707i	−1.06279	−	1.21188i	−0.976478	−	0.215617i	$-0.930824\pi$
$131$	−12.1642	−	13.8707i	−1.06279	−	1.21188i	−0.0863159	−	0.996268i	$-0.527509\pi$
$132$		0			0
$133$	1.78871	+	0.611031i	0.155101	+	0.0529831i
$134$		0			0
$135$	1.40515	−	0.811262i	0.120936	−	0.0698223i
$136$		0			0
$137$	0.700565	−	1.21341i	0.0598533	−	0.103669i	−0.834546	−	0.550938i	$-0.814270\pi$
$137$	0.700565	−	1.21341i	0.0598533	−	0.103669i	0.894399	+	0.447269i	$0.147603\pi$
$138$		0			0
$139$	0.153609	−	0.229892i	0.0130290	−	0.0194992i	−0.824898	−	0.565282i	$-0.808767\pi$
$139$	0.153609	−	0.229892i	0.0130290	−	0.0194992i	0.837927	+	0.545782i	$0.183767\pi$
$140$		0			0
$141$	−24.5600	+	4.88530i	−2.06833	+	0.411416i
$142$		0			0
$143$	−4.88017	−	4.27980i	−0.408101	−	0.357895i
$144$		0			0
$145$	−5.21747	−	4.00351i	−0.433288	−	0.332473i
$146$		0			0
$147$	7.52524	−	15.1127i	0.620671	−	1.24647i
$148$		0			0
$149$	−6.14659	−	1.64697i	−0.503548	−	0.134925i	−0.00190188	−	0.999998i	$-0.500605\pi$
$149$	−6.14659	−	1.64697i	−0.503548	−	0.134925i	−0.501646	+	0.865073i	$0.667272\pi$
$150$		0			0
$151$	−5.82110	+	4.46669i	−0.473714	+	0.363494i	−0.817855	−	0.575424i	$-0.804837\pi$
$151$	−5.82110	+	4.46669i	−0.473714	+	0.363494i	0.344141	+	0.938918i	$0.388170\pi$
$152$		0			0
$153$	7.72650	−	8.67079i	0.624651	−	0.700992i
$154$		0			0
$155$	6.95413	−	16.7888i	0.558570	−	1.34851i
$156$		0			0
$157$	−5.39247	−	20.1250i	−0.430366	−	1.60615i	−0.751918	−	0.659256i	$-0.770871\pi$
$157$	−5.39247	−	20.1250i	−0.430366	−	1.60615i	0.321552	−	0.946892i	$-0.395795\pi$
$158$		0			0
$159$	5.77392	−	11.7084i	0.457902	−	0.928533i
$160$		0			0
$161$	15.9245	−	12.1707i	1.25503	−	0.959182i
$162$		0			0
$163$	−16.8990	+	5.73643i	−1.32363	+	0.449312i	−0.891713	−	0.452602i	$-0.850496\pi$
$163$	−16.8990	+	5.73643i	−1.32363	+	0.449312i	−0.431917	+	0.901914i	$0.642162\pi$
$164$		0			0
$165$	−19.3105	−	6.55503i	−1.50332	−	0.510308i
$166$		0			0
$167$	−2.16897	−	1.44926i	−0.167840	−	0.112147i	0.468813	−	0.883297i	$-0.344682\pi$
$167$	−2.16897	−	1.44926i	−0.167840	−	0.112147i	−0.636653	+	0.771150i	$0.719682\pi$
$168$		0			0
$169$		−	5.05556i		−	0.388889i
$170$		0			0
$171$	−1.74277	−	1.00619i	−0.133273	−	0.0769453i
$172$		0			0
$173$	8.72033	+	0.571560i	0.662994	+	0.0434549i	0.393186	−	0.919459i	$-0.371373\pi$
$173$	8.72033	+	0.571560i	0.662994	+	0.0434549i	0.269808	+	0.962914i	$0.413040\pi$
$174$		0			0
$175$	−18.6323	−	12.5017i	−1.40847	−	0.945040i
$176$		0			0
$177$	6.62546	+	19.5180i	0.498000	+	1.46706i
$178$		0			0
$179$	−5.37530	−	0.707672i	−0.401769	−	0.0528939i	−0.0730657	−	0.997327i	$-0.523278\pi$
$179$	−5.37530	−	0.707672i	−0.401769	−	0.0528939i	−0.328703	+	0.944433i	$0.606612\pi$
$180$		0			0
$181$	5.85329	−	3.91104i	0.435071	−	0.290705i	−0.318683	−	0.947861i	$-0.603241\pi$
$181$	5.85329	−	3.91104i	0.435071	−	0.290705i	0.753755	+	0.657156i	$0.228241\pi$
$182$		0			0
$183$	5.32047	−	5.32047i	0.393301	−	0.393301i
$184$		0			0
$185$	−17.4394	−	22.7275i	−1.28217	−	1.67096i
$186$		0			0
$187$	9.49487	+	0.0752526i	0.694334	+	0.00550302i
$188$		0			0
$189$	0.713541	−	0.926206i	0.0519025	−	0.0673716i
$190$		0			0
$191$	−5.38266	+	20.0883i	−0.389475	+	1.45354i	0.441514	+	0.897254i	$0.354441\pi$
$191$	−5.38266	+	20.0883i	−0.389475	+	1.45354i	−0.830990	+	0.556288i	$0.812225\pi$
$192$		0			0
$193$	1.72538	+	26.3242i	0.124195	+	1.89485i	0.375314	+	0.926898i	$0.377535\pi$
$193$	1.72538	+	26.3242i	0.124195	+	1.89485i	−0.251119	+	0.967956i	$0.580799\pi$
$194$		0			0
$195$	9.55144	+	23.0592i	0.683993	+	1.65130i
$196$		0			0
$197$	−3.03736	+	15.2698i	−0.216403	+	1.08793i	0.707912	+	0.706301i	$0.249637\pi$
$197$	−3.03736	+	15.2698i	−0.216403	+	1.08793i	−0.924315	+	0.381630i	$0.875363\pi$
$198$		0			0
$199$	8.88399	−	26.1714i	0.629769	−	1.85524i	0.124628	−	0.992203i	$-0.460226\pi$
$199$	8.88399	−	26.1714i	0.629769	−	1.85524i	0.505141	−	0.863037i	$-0.331441\pi$
$200$		0			0
$201$	0.361771	−	5.51955i	0.0255173	−	0.389319i
$202$		0			0
$203$	−4.57515	−	1.23536i	−0.321112	−	0.0867049i
$204$		0			0
$205$	−0.111809	−	0.193659i	−0.00780910	−	0.0135258i
$206$		0			0
$207$	−19.1378	+	9.43772i	−1.33017	+	0.655967i
$208$		0			0
$209$	−0.320976	−	1.61366i	−0.0222024	−	0.111619i
$210$		0			0
$211$	6.87193	+	1.36691i	0.473083	+	0.0941020i	0.425873	−	0.904783i	$-0.359967\pi$
$211$	6.87193	+	1.36691i	0.473083	+	0.0941020i	0.0472099	+	0.998885i	$0.484967\pi$
$212$		0			0
$213$	3.89952	−	29.6198i	0.267191	−	2.02951i
$214$		0			0
$215$	24.6086	+	12.1356i	1.67830	+	0.827644i
$216$		0			0
$217$	0.0252177	−	13.0947i	0.00171189	−	0.888926i
$218$		0			0
$219$	−1.34625	−	10.2258i	−0.0909712	−	0.690995i
$220$		0			0
$221$	−7.59299	−	8.79784i	−0.510760	−	0.591807i
$222$		0			0
$223$	22.6463	+	9.38040i	1.51651	+	0.628158i	0.976888	−	0.213751i	$-0.0685682\pi$
$223$	22.6463	+	9.38040i	1.51651	+	0.628158i	0.539619	+	0.841909i	$0.318568\pi$
$224$		0			0
$225$	16.8915	+	16.8915i	1.12610	+	1.12610i
$226$		0			0
$227$	−23.3216	+	1.52858i	−1.54791	+	0.101455i	−0.815238	−	0.579126i	$-0.803394\pi$
$227$	−23.3216	+	1.52858i	−1.54791	+	0.101455i	−0.732672	+	0.680582i	$0.761727\pi$
$228$		0			0
$229$	3.13646	−	4.08751i	0.207263	−	0.270110i	−0.678142	−	0.734931i	$-0.737215\pi$
$229$	3.13646	−	4.08751i	0.207263	−	0.270110i	0.885405	+	0.464821i	$0.153881\pi$
$230$		0			0
$231$	−14.6653	+	0.932855i	−0.964907	+	0.0613774i
$232$		0			0
$233$	16.4571	−	14.4325i	1.07814	−	0.945504i	0.0794590	−	0.996838i	$-0.474681\pi$
$233$	16.4571	−	14.4325i	1.07814	−	0.945504i	0.998682	+	0.0513343i	$0.0163474\pi$
$234$		0			0
$235$	16.8607	+	34.1902i	1.09987	+	2.23032i
$236$		0			0
$237$	−17.1318			−1.11283
$238$		0			0
$239$	10.0530			0.650277			0.325139	−	0.945666i	$-0.394589\pi$
$239$	10.0530			0.650277			0.325139	+	0.945666i	$0.394589\pi$
$240$		0			0
$241$	−0.258197	−	0.523573i	−0.0166320	−	0.0337263i	0.888398	−	0.459074i	$-0.151819\pi$
$241$	−0.258197	−	0.523573i	−0.0166320	−	0.0337263i	−0.905030	+	0.425347i	$0.860152\pi$
$242$		0			0
$243$	−16.2587	+	14.2585i	−1.04300	+	0.914683i
$244$		0			0
$245$	−25.1879	−	5.11112i	−1.60920	−	0.326537i
$246$		0			0
$247$	−1.22585	+	1.59756i	−0.0779990	+	0.101650i
$248$		0			0
$249$	−34.2532	+	2.24507i	−2.17071	+	0.142276i
$250$		0			0
$251$	5.44772	+	5.44772i	0.343857	+	0.343857i	0.857815	−	0.513958i	$-0.171821\pi$
$251$	5.44772	+	5.44772i	0.343857	+	0.343857i	−0.513958	+	0.857815i	$0.671821\pi$
$252$		0			0
$253$	−16.1177	−	6.67617i	−1.01331	−	0.419727i
$254$		0			0
$255$	−32.6166	−	16.4073i	−2.04253	−	1.02747i
$256$		0			0
$257$	0.765321	+	5.81319i	0.0477394	+	0.362617i	0.998595	+	0.0529834i	$0.0168730\pi$
$257$	0.765321	+	5.81319i	0.0477394	+	0.362617i	−0.950856	+	0.309634i	$0.899794\pi$
$258$		0			0
$259$	−17.8576	−	10.3560i	−1.10962	−	0.643492i
$260$		0			0
$261$	4.52501	+	2.23149i	0.280091	+	0.138126i
$262$		0			0
$263$	−0.392045	+	2.97788i	−0.0241745	+	0.183624i	−0.999272	−	0.0381534i	$-0.987852\pi$
$263$	−0.392045	+	2.97788i	−0.0241745	+	0.183624i	0.975097	+	0.221777i	$0.0711858\pi$
$264$		0			0
$265$	−19.4919	−	3.87718i	−1.19738	−	0.238173i
$266$		0			0
$267$	2.81912	+	14.1727i	0.172527	+	0.867352i
$268$		0			0
$269$	−7.91352	+	3.90252i	−0.482496	+	0.237941i	−0.667235	−	0.744847i	$-0.732522\pi$
$269$	−7.91352	+	3.90252i	−0.482496	+	0.237941i	0.184740	+	0.982787i	$0.440856\pi$
$270$		0			0
$271$	2.04973	+	3.55024i	0.124513	+	0.215662i	0.921542	−	0.388278i	$-0.126930\pi$
$271$	2.04973	+	3.55024i	0.124513	+	0.215662i	−0.797030	+	0.603940i	$0.793597\pi$
$272$		0			0
$273$	12.6931	+	12.7421i	0.768223	+	0.771188i
$274$		0			0
$275$	−1.27735	+	19.4885i	−0.0770269	+	1.17520i
$276$		0			0
$277$	−4.30274	+	12.6755i	−0.258526	+	0.761594i	0.737726	+	0.675100i	$0.235900\pi$
$277$	−4.30274	+	12.6755i	−0.258526	+	0.761594i	−0.996252	+	0.0864939i	$0.972434\pi$
$278$		0			0
$279$	−2.71978	+	13.6733i	−0.162829	+	0.818598i
$280$		0			0
$281$	9.63060	+	23.2503i	0.574514	+	1.38700i	0.897676	+	0.440655i	$0.145254\pi$
$281$	9.63060	+	23.2503i	0.574514	+	1.38700i	−0.323163	+	0.946343i	$0.604746\pi$
$282$		0			0
$283$	−0.128960	−	1.96755i	−0.00766587	−	0.116959i	0.992311	−	0.123770i	$-0.0394985\pi$
$283$	−0.128960	−	1.96755i	−0.00766587	−	0.116959i	−0.999977	+	0.00681146i	$0.997832\pi$
$284$		0			0
$285$	−1.63739	+	6.11083i	−0.0969907	+	0.361974i
$286$		0			0
$287$	−0.127651	−	0.0983412i	−0.00753500	−	0.00580490i
$288$		0			0
$289$	16.8173	+	2.48582i	0.989251	+	0.146224i
$290$		0			0
$291$	−27.7094	−	36.1116i	−1.62435	−	2.11690i
$292$		0			0
$293$	−9.26976	+	9.26976i	−0.541545	+	0.541545i	−0.923982	−	0.382437i	$-0.875085\pi$
$293$	−9.26976	+	9.26976i	−0.541545	+	0.541545i	0.382437	+	0.923982i	$0.375085\pi$
$294$		0			0
$295$	26.0902	−	17.4329i	1.51903	−	1.01499i
$296$		0			0
$297$	−1.00898	−	0.132834i	−0.0585468	−	0.00770784i
$298$		0			0
$299$	6.86342	+	20.2190i	0.396922	+	1.16929i
$300$		0			0
$301$	19.7271	+	1.33114i	1.13705	+	0.0767257i
$302$		0			0
$303$	−29.9242	−	1.96133i	−1.71910	−	0.112676i
$304$		0			0
$305$	−9.91999	−	5.72731i	−0.568017	−	0.327945i
$306$		0			0
$307$		−	15.6482i		−	0.893089i	−0.894761	−	0.446545i	$-0.852654\pi$
$307$		−	15.6482i		−	0.893089i	0.894761	−	0.446545i	$-0.147346\pi$
$308$		0			0
$309$	−3.00515	−	2.00797i	−0.170957	−	0.114230i
$310$		0			0
$311$	−23.6213	−	8.01836i	−1.33944	−	0.454679i	−0.442477	−	0.896780i	$-0.645900\pi$
$311$	−23.6213	−	8.01836i	−1.33944	−	0.454679i	−0.896966	+	0.442100i	$0.854233\pi$
$312$		0			0
$313$	32.3702	−	10.9882i	1.82967	−	0.621090i	0.831861	−	0.554985i	$-0.187276\pi$
$313$	32.3702	−	10.9882i	1.82967	−	0.621090i	0.997813	−	0.0661056i	$-0.0210574\pi$
$314$		0			0
$315$	25.2595	+	10.5199i	1.42321	+	0.592727i
$316$		0			0
$317$	−2.01295	+	4.08186i	−0.113058	+	0.229260i	−0.946046	−	0.324031i	$-0.894962\pi$
$317$	−2.01295	+	4.08186i	−0.113058	+	0.229260i	0.832988	+	0.553291i	$0.186628\pi$
$318$		0			0
$319$	1.06761	+	3.98437i	0.0597745	+	0.223082i
$320$		0			0
$321$	10.2423	−	24.7270i	0.571667	−	1.38013i
$322$		0			0
$323$	−0.169354	−	2.94079i	−0.00942312	−	0.163630i
$324$		0			0
$325$	18.9640	−	14.5516i	1.05193	−	0.807178i
$326$		0			0
$327$	23.6969	+	6.34956i	1.31044	+	0.351132i
$328$		0			0
$329$	20.6183	+	18.1522i	1.13673	+	1.00076i
$330$		0			0
$331$	−9.92203	−	7.61344i	−0.545364	−	0.418472i	0.298992	−	0.954256i	$-0.403350\pi$
$331$	−9.92203	−	7.61344i	−0.545364	−	0.418472i	−0.844356	+	0.535783i	$0.820016\pi$
$332$		0			0
$333$	16.5236	+	14.4908i	0.905489	+	0.794093i
$334$		0			0
$335$	−8.25893	+	1.64280i	−0.451234	+	0.0897560i
$336$		0			0
$337$	17.4862	−	26.1700i	0.952535	−	1.42557i	0.0481559	−	0.998840i	$-0.484666\pi$
$337$	17.4862	−	26.1700i	0.952535	−	1.42557i	0.904379	−	0.426730i	$-0.140334\pi$
$338$		0			0
$339$	−12.7819	+	22.1388i	−0.694215	+	1.20242i
$340$		0			0
$341$	−9.87088	+	5.69896i	−0.534538	+	0.308616i
$342$		0			0
$343$	−18.1850	+	3.50812i	−0.981896	+	0.189421i
$344$		0			0
$345$	44.2304	+	50.4351i	2.38128	+	2.71533i
$346$		0			0
$347$	−4.69736	+	5.35632i	−0.252168	+	0.287542i	−0.864049	−	0.503407i	$-0.832080\pi$
$347$	−4.69736	+	5.35632i	−0.252168	+	0.287542i	0.611882	+	0.790949i	$0.290413\pi$
$348$		0			0
$349$	21.9119	−	9.07621i	1.17292	−	0.485838i	0.290761	−	0.956796i	$-0.406091\pi$
$349$	21.9119	−	9.07621i	1.17292	−	0.485838i	0.882156	+	0.470957i	$0.156091\pi$
$350$		0			0
$351$	0.691999	+	1.03565i	0.0369362	+	0.0552789i
$352$		0			0
$353$	17.3686	−	4.65391i	0.924439	−	0.247703i	0.234957	−	0.972006i	$-0.424505\pi$
$353$	17.3686	−	4.65391i	0.924439	−	0.247703i	0.689482	+	0.724303i	$0.257838\pi$
$354$		0			0
$355$	−45.0918	+	5.93644i	−2.39322	+	0.315074i
$356$		0			0
$357$	−26.2351	−	1.97927i	−1.38851	−	0.104754i
$358$		0			0
$359$	−29.9869	+	3.94785i	−1.58265	+	0.208360i	−0.869961	−	0.493121i	$-0.835856\pi$
$359$	−29.9869	+	3.94785i	−1.58265	+	0.208360i	−0.712689	+	0.701481i	$0.752523\pi$
$360$		0			0
$361$	17.8596	−	4.78546i	0.939978	−	0.251866i
$362$		0			0
$363$	−7.63298	−	11.4236i	−0.400627	−	0.599581i
$364$		0			0
$365$	−14.5064	+	6.00874i	−0.759298	+	0.314512i
$366$		0			0
$367$	19.7614	−	22.5335i	1.03153	−	1.17624i	0.0473892	−	0.998877i	$-0.484910\pi$
$367$	19.7614	−	22.5335i	1.03153	−	1.17624i	0.984145	−	0.177363i	$-0.0567568\pi$
$368$		0			0
$369$	0.113114	+	0.128982i	0.00588848	+	0.00671453i
$370$		0			0
$371$	−14.0512	+	2.76683i	−0.729501	+	0.143647i
$372$		0			0
$373$	19.3065	−	11.1466i	0.999651	−	0.577149i	0.0915058	−	0.995805i	$-0.470832\pi$
$373$	19.3065	−	11.1466i	0.999651	−	0.577149i	0.908145	+	0.418656i	$0.137499\pi$
$374$		0			0
$375$	15.4111	−	26.6929i	0.795827	−	1.37841i
$376$		0			0
$377$	2.80484	−	4.19774i	0.144457	−	0.216195i
$378$		0			0
$379$	−11.8997	+	2.36700i	−0.611248	+	0.121585i	−0.491001	−	0.871159i	$-0.663369\pi$
$379$	−11.8997	+	2.36700i	−0.611248	+	0.121585i	−0.120247	+	0.992744i	$0.538369\pi$
$380$		0			0
$381$	−14.2860	−	12.5285i	−0.731895	−	0.641855i
$382$		0			0
$383$	1.15285	+	0.884613i	0.0589079	+	0.0452016i	0.637796	−	0.770206i	$-0.279846\pi$
$383$	1.15285	+	0.884613i	0.0589079	+	0.0452016i	−0.578888	+	0.815407i	$0.696513\pi$
$384$		0			0
$385$	7.15008	+	21.1975i	0.364402	+	1.08032i
$386$		0			0
$387$	−20.3327	−	5.44814i	−1.03357	−	0.276945i
$388$		0			0
$389$	−29.3380	+	22.5119i	−1.48750	+	1.14140i	−0.531866	+	0.846828i	$0.678509\pi$
$389$	−29.3380	+	22.5119i	−1.48750	+	1.14140i	−0.955631	+	0.294568i	$0.904824\pi$
$390$		0			0
$391$	−26.9252	−	15.8311i	−1.36167	−	0.800615i
$392$		0			0
$393$	17.0275	−	41.1081i	0.858926	−	2.07363i
$394$		0			0
$395$	6.75018	+	25.1920i	0.339638	+	1.26755i
$396$		0			0
$397$	−3.41712	+	6.92923i	−0.171500	+	0.347768i	−0.965605	−	0.260012i	$-0.916273\pi$
$397$	−3.41712	+	6.92923i	−0.171500	+	0.347768i	0.794105	+	0.607781i	$0.207940\pi$
$398$		0			0
$399$	0.586335	+	4.52092i	0.0293535	+	0.226329i
$400$		0			0
$401$	−27.1512	+	9.21658i	−1.35586	+	0.460254i	−0.902353	−	0.430997i	$-0.858162\pi$
$401$	−27.1512	+	9.21658i	−1.35586	+	0.460254i	−0.453511	+	0.891251i	$0.649829\pi$
$402$		0			0
$403$	13.2098	+	4.48413i	0.658028	+	0.223370i
$404$		0			0
$405$	29.0511	+	19.4113i	1.44356	+	0.964556i
$406$		0			0
$407$			17.9683i			0.890655i
$408$		0			0
$409$	6.22083	+	3.59160i	0.307600	+	0.177593i	0.645852	−	0.763462i	$-0.276502\pi$
$409$	6.22083	+	3.59160i	0.307600	+	0.177593i	−0.338252	+	0.941056i	$0.609836\pi$
$410$		0			0
$411$	3.37201	+	0.221013i	0.166329	+	0.0109018i
$412$		0			0
$413$	12.5983	−	18.7763i	0.619923	−	0.923923i
$414$		0			0
$415$	16.7976	+	49.4840i	0.824560	+	2.42907i
$416$		0			0
$417$	0.661131	+	0.0870395i	0.0323757	+	0.00426234i
$418$		0			0
$419$	21.7169	−	14.5108i	1.06094	−	0.708898i	0.102658	−	0.994717i	$-0.467265\pi$
$419$	21.7169	−	14.5108i	1.06094	−	0.708898i	0.958284	+	0.285818i	$0.0922654\pi$
$420$		0			0
$421$	1.79698	−	1.79698i	0.0875794	−	0.0875794i	−0.661960	−	0.749539i	$-0.730275\pi$
$421$	1.79698	−	1.79698i	0.0875794	−	0.0875794i	0.749539	+	0.661960i	$0.230275\pi$
$422$		0			0
$423$	−17.8038	−	23.2024i	−0.865651	−	1.12814i
$424$		0			0
$425$	−7.09328	+	34.2398i	−0.344075	+	1.66088i
$426$		0			0
$427$	−8.18146	−	1.09314i	−0.395929	−	0.0529009i
$428$		0			0
$429$	4.05179	−	15.1215i	0.195622	−	0.730072i
$430$		0			0
$431$	−2.14118	−	32.6681i	−0.103137	−	1.57357i	−0.665323	−	0.746555i	$-0.731706\pi$
$431$	−2.14118	−	32.6681i	−0.103137	−	1.57357i	0.562187	−	0.827010i	$-0.309960\pi$
$432$		0			0
$433$	−3.82740	−	9.24017i	−0.183933	−	0.444054i	0.804837	−	0.593495i	$-0.202253\pi$
$433$	−3.82740	−	9.24017i	−0.183933	−	0.444054i	−0.988771	+	0.149441i	$0.952253\pi$
$434$		0			0
$435$	3.09436	−	15.5564i	0.148363	−	0.745871i
$436$		0			0
$437$	−1.73967	+	5.12491i	−0.0832199	+	0.245158i
$438$		0			0
$439$	−1.04997	+	16.0195i	−0.0501126	+	0.764570i	0.896671	+	0.442698i	$0.145979\pi$
$439$	−1.04997	+	16.0195i	−0.0501126	+	0.764570i	−0.946783	+	0.321872i	$0.895688\pi$
$440$		0			0
$441$	19.7173	+	0.0759432i	0.938917	+	0.00361634i
$442$		0			0
$443$	−13.3181	−	23.0677i	−0.632764	−	1.09598i	−0.986984	−	0.160817i	$-0.948587\pi$
$443$	−13.3181	−	23.0677i	−0.632764	−	1.09598i	0.354220	−	0.935162i	$-0.384746\pi$
$444$		0			0
$445$	19.7298	−	9.72967i	0.935284	−	0.461231i
$446$		0			0
$447$	−2.99410	−	15.0524i	−0.141616	−	0.711953i
$448$		0			0
$449$	31.7904	+	6.32351i	1.50028	+	0.298425i	0.875823	−	0.482632i	$-0.160319\pi$
$449$	31.7904	+	6.32351i	1.50028	+	0.298425i	0.624460	+	0.781057i	$0.285319\pi$
$450$		0			0
$451$	−0.0183074	+	0.139059i	−0.000862064	+	0.00654802i
$452$		0			0
$453$	−15.8712	−	7.82682i	−0.745695	−	0.367736i
$454$		0			0
$455$	13.7358	−	23.6856i	0.643942	−	1.11040i
$456$		0			0
$457$	−2.00306	−	15.2147i	−0.0936992	−	0.711716i	−0.972230	−	0.234029i	$-0.924809\pi$
$457$	−2.00306	−	15.2147i	−0.0936992	−	0.711716i	0.878530	−	0.477686i	$-0.158525\pi$
$458$		0			0
$459$	−1.75617	−	0.485514i	−0.0819709	−	0.0226618i
$460$		0			0
$461$	1.44901	+	0.600201i	0.0674873	+	0.0279542i	0.416172	−	0.909286i	$-0.363372\pi$
$461$	1.44901	+	0.600201i	0.0674873	+	0.0279542i	−0.348684	+	0.937240i	$0.613372\pi$
$462$		0			0
$463$	25.2907	+	25.2907i	1.17536	+	1.17536i	0.980913	+	0.194445i	$0.0622907\pi$
$463$	25.2907	+	25.2907i	1.17536	+	1.17536i	0.194445	+	0.980913i	$0.437709\pi$
$464$		0			0
$465$	43.7334	−	2.86644i	2.02809	−	0.132928i
$466$		0			0
$467$	17.8060	−	23.2052i	0.823964	−	1.07381i	−0.172092	−	0.985081i	$-0.555053\pi$
$467$	17.8060	−	23.2052i	0.823964	−	1.07381i	0.996056	−	0.0887295i	$-0.0282807\pi$
$468$		0			0
$469$	−5.05181	+	3.36146i	−0.233271	+	0.155218i
$470$		0			0
$471$	37.7796	−	33.1319i	1.74079	−	1.52664i
$472$		0			0
$473$	−7.61175	−	15.4351i	−0.349989	−	0.709707i
$474$		0			0
$475$	6.05886			0.277999
$476$		0			0
$477$	15.2467			0.698098
$478$		0			0
$479$	6.85778	+	13.9062i	0.313340	+	0.635391i	0.995390	−	0.0959153i	$-0.0305778\pi$
$479$	6.85778	+	13.9062i	0.313340	+	0.635391i	−0.682049	+	0.731306i	$0.738911\pi$
$480$		0			0
$481$	16.5343	−	14.5002i	0.753899	−	0.661151i
$482$		0			0
$483$	43.3129	+	21.4634i	1.97081	+	0.976616i
$484$		0			0
$485$	−42.1835	+	54.9746i	−1.91545	+	2.49627i
$486$		0			0
$487$	15.1242	−	0.991289i	0.685341	−	0.0449196i	0.281245	−	0.959636i	$-0.409253\pi$
$487$	15.1242	−	0.991289i	0.685341	−	0.0449196i	0.404096	+	0.914717i	$0.367586\pi$
$488$		0			0
$489$	−30.4346	−	30.4346i	−1.37630	−	1.37630i
$490$		0			0
$491$	25.3990	+	10.5206i	1.14624	+	0.474789i	0.873272	−	0.487233i	$-0.161994\pi$
$491$	25.3990	+	10.5206i	1.14624	+	0.474789i	0.272970	+	0.962022i	$0.411994\pi$
$492$		0			0
$493$	0.905901	+	7.32942i	0.0407997	+	0.330100i
$494$		0			0
$495$	−3.10873	−	23.6132i	−0.139727	−	1.06133i
$496$		0			0
$497$	−28.4141	+	16.3320i	−1.27455	+	0.732591i
$498$		0			0
$499$	12.9955	+	6.40866i	0.581757	+	0.286891i	0.709260	−	0.704947i	$-0.249029\pi$
$499$	12.9955	+	6.40866i	0.581757	+	0.286891i	−0.127502	+	0.991838i	$0.540696\pi$
$500$		0			0
$501$	0.821194	−	6.23759i	0.0366883	−	0.278675i
$502$		0			0
$503$	21.3666	+	4.25008i	0.952688	+	0.189501i	0.646880	−	0.762592i	$-0.276073\pi$
$503$	21.3666	+	4.25008i	0.952688	+	0.189501i	0.305808	+	0.952093i	$0.401073\pi$
$504$		0			0
$505$	8.90644	+	44.7757i	0.396331	+	1.99249i
$506$		0			0
$507$	10.9356	−	5.39282i	0.485665	−	0.239504i
$508$		0			0
$509$	−15.8527	−	27.4576i	−0.702657	−	1.21704i	−0.967530	−	0.252755i	$-0.918663\pi$
$509$	−15.8527	−	27.4576i	−0.702657	−	1.21704i	0.264873	−	0.964283i	$-0.414670\pi$
$510$		0			0
$511$	−8.01597	+	7.98515i	−0.354606	+	0.353242i
$512$		0			0
$513$	−0.0206487	+	0.315038i	−0.000911661	+	0.0139093i
$514$		0			0
$515$	−1.76862	+	5.21018i	−0.0779346	+	0.229588i
$516$		0			0
$517$	4.66475	−	23.4513i	0.205155	−	1.03139i
$518$		0			0
$519$	8.06574	+	19.4724i	0.354047	+	0.854744i
$520$		0			0
$521$	0.0305083	+	0.465467i	0.00133659	+	0.0203925i	0.998475	−	0.0552035i	$-0.0175807\pi$
$521$	0.0305083	+	0.465467i	0.00133659	+	0.0203925i	−0.997139	+	0.0755960i	$0.975914\pi$
$522$		0			0
$523$	1.36510	−	5.09461i	0.0596915	−	0.222772i	−0.929636	−	0.368478i	$-0.879879\pi$
$523$	1.36510	−	5.09461i	0.0596915	−	0.222772i	0.989328	+	0.145707i	$0.0465455\pi$
$524$		0			0
$525$	7.16681	−	53.6389i	0.312785	−	2.34099i
$526$		0			0
$527$	−18.9146	+	7.65962i	−0.823932	+	0.333658i
$528$		0			0
$529$	20.9340	+	27.2817i	0.910173	+	1.18616i
$530$		0			0
$531$	−17.0221	+	17.0221i	−0.738694	+	0.738694i
$532$		0			0
$533$	0.142735	−	0.0953723i	0.00618253	−	0.00413103i
$534$		0			0
$535$	−40.3962	−	5.31825i	−1.74648	−	0.229928i
$536$		0			0
$537$	−4.20315	−	12.3821i	−0.181379	−	0.534326i
$538$		0			0
$539$	10.5822	+	12.1608i	0.455806	+	0.523803i
$540$		0			0
$541$	10.9965	+	0.720747i	0.472775	+	0.0309873i	0.299929	−	0.953961i	$-0.403037\pi$
$541$	10.9965	+	0.720747i	0.472775	+	0.0309873i	0.172846	+	0.984949i	$0.444704\pi$
$542$		0			0
$543$	14.7036	+	8.48915i	0.630994	+	0.364304i
$544$		0			0
$545$		−	37.3476i		−	1.59980i
$546$		0			0
$547$	17.2118	+	11.5005i	0.735922	+	0.491727i	0.866167	−	0.499754i	$-0.166576\pi$
$547$	17.2118	+	11.5005i	0.735922	+	0.491727i	−0.130245	+	0.991482i	$0.541576\pi$
$548$		0			0
$549$	8.32135	+	2.82472i	0.355147	+	0.120556i
$550$		0			0
$551$	1.21175	−	0.411335i	0.0516224	−	0.0175234i
$552$		0			0
$553$	11.4121	+	14.9320i	0.485293	+	0.634974i
$554$		0			0
$555$	30.5585	−	61.9665i	1.29713	−	2.63033i
$556$		0			0
$557$	0.879762	+	3.28332i	0.0372767	+	0.139119i	0.982056	−	0.188588i	$-0.0603910\pi$
$557$	0.879762	+	3.28332i	0.0372767	+	0.139119i	−0.944780	+	0.327706i	$0.893724\pi$
$558$		0			0
$559$	−8.06068	+	19.4602i	−0.340931	+	0.823079i
$560$		0			0
$561$	9.96550	+	20.6184i	0.420744	+	0.870509i
$562$		0			0
$563$	−2.41821	+	1.85556i	−0.101915	+	0.0782024i	−0.658462	−	0.752614i	$-0.728793\pi$
$563$	−2.41821	+	1.85556i	−0.101915	+	0.0782024i	0.556547	+	0.830816i	$0.312126\pi$
$564$		0			0
$565$	37.5909	+	10.0725i	1.58146	+	0.423752i
$566$		0			0
$567$	24.6840	+	4.95939i	1.03663	+	0.208275i
$568$		0			0
$569$	−32.9796	−	25.3061i	−1.38258	−	1.06089i	−0.989985	−	0.141175i	$-0.954912\pi$
$569$	−32.9796	−	25.3061i	−1.38258	−	1.06089i	−0.392592	−	0.919713i	$-0.628421\pi$
$570$		0			0
$571$	−6.23157	−	5.46494i	−0.260783	−	0.228701i	0.518963	−	0.854797i	$-0.326318\pi$
$571$	−6.23157	−	5.46494i	−0.260783	−	0.228701i	−0.779746	+	0.626096i	$0.784652\pi$
$572$		0			0
$573$	−49.1944	+	9.78537i	−2.05512	+	0.408790i
$574$		0			0
$575$	35.6928	−	53.4181i	1.48849	−	2.22769i
$576$		0			0
$577$	7.57427	−	13.1190i	0.315321	−	0.546152i	−0.664185	−	0.747569i	$-0.731221\pi$
$577$	7.57427	−	13.1190i	0.315321	−	0.546152i	0.979506	+	0.201416i	$0.0645545\pi$
$578$		0			0
$579$	−55.1007	+	31.8124i	−2.28991	+	1.32208i
$580$		0			0
$581$	24.7741	+	28.3594i	1.02780	+	1.17655i
$582$		0			0
$583$	8.21894	+	9.37190i	0.340394	+	0.388145i
$584$		0			0
$585$	−19.2200	+	21.9162i	−0.794648	+	0.906123i
$586$		0			0
$587$	−12.7221	+	5.26966i	−0.525097	+	0.217502i	−0.629454	−	0.777038i	$-0.716721\pi$
$587$	−12.7221	+	5.26966i	−0.525097	+	0.217502i	0.104357	+	0.994540i	$0.466721\pi$
$588$		0			0
$589$	1.96447	+	2.94003i	0.0809445	+	0.121142i
$590$		0			0
$591$	−36.2698	+	9.71847i	−1.49194	+	0.399764i
$592$		0			0
$593$	12.2388	−	1.61127i	0.502587	−	0.0661668i	0.125029	−	0.992153i	$-0.460097\pi$
$593$	12.2388	−	1.61127i	0.502587	−	0.0661668i	0.377557	+	0.925986i	$0.376764\pi$
$594$		0			0
$595$	7.42650	+	39.3580i	0.304457	+	1.61352i
$596$		0			0
$597$	66.0874	−	8.70056i	2.70478	−	0.356090i
$598$		0			0
$599$	−29.1444	+	7.80921i	−1.19081	+	0.319076i	−0.799205	−	0.601059i	$-0.794746\pi$
$599$	−29.1444	+	7.80921i	−1.19081	+	0.319076i	−0.391602	+	0.920135i	$0.628079\pi$
$600$		0			0
$601$	−12.6028	−	18.8614i	−0.514078	−	0.769372i	0.480089	−	0.877220i	$-0.340604\pi$
$601$	−12.6028	−	18.8614i	−0.514078	−	0.769372i	−0.994167	+	0.107847i	$0.965604\pi$
$602$		0			0
$603$	5.96844	−	2.47221i	0.243054	−	0.100676i
$604$		0			0
$605$	−13.7906	+	15.7252i	−0.560668	+	0.639319i
$606$		0			0
$607$	21.6670	+	24.7065i	0.879438	+	1.00281i	0.999949	+	0.0100951i	$0.00321343\pi$
$607$	21.6670	+	24.7065i	0.879438	+	1.00281i	−0.120511	+	0.992712i	$0.538453\pi$
$608$		0			0
$609$	−2.20819	−	11.2142i	−0.0894805	−	0.454421i
$610$		0			0
$611$	−25.3441	+	14.6324i	−1.02531	+	0.591964i
$612$		0			0
$613$	−15.6837	+	27.1649i	−0.633457	+	1.09718i	0.353382	+	0.935479i	$0.385031\pi$
$613$	−15.6837	+	27.1649i	−0.633457	+	1.09718i	−0.986840	+	0.161701i	$0.948302\pi$
$614$		0			0
$615$	0.299632	−	0.448431i	0.0120823	−	0.0180825i
$616$		0			0
$617$	5.21544	−	1.03741i	0.209966	−	0.0417647i	−0.0889867	−	0.996033i	$-0.528363\pi$
$617$	5.21544	−	1.03741i	0.209966	−	0.0417647i	0.298952	+	0.954268i	$0.403363\pi$
$618$		0			0
$619$	−10.7629	−	9.43881i	−0.432598	−	0.379378i	0.415172	−	0.909743i	$-0.363721\pi$
$619$	−10.7629	−	9.43881i	−0.432598	−	0.379378i	−0.847769	+	0.530365i	$0.822055\pi$
$620$		0			0
$621$	2.65590	+	2.03794i	0.106578	+	0.0817798i
$622$		0			0
$623$	10.4749	−	11.8980i	0.419668	−	0.476685i
$624$		0			0
$625$	−4.36485	−	1.16956i	−0.174594	−	0.0467824i
$626$		0			0
$627$	3.14807	−	2.41560i	0.125722	−	0.0964698i
$628$		0			0
$629$	−4.45169	+	31.8606i	−0.177501	+	1.27037i
$630$		0			0
$631$	6.51666	−	15.7326i	0.259424	−	0.626305i	−0.739477	−	0.673182i	$-0.764927\pi$
$631$	6.51666	−	15.7326i	0.259424	−	0.626305i	0.998901	+	0.0468773i	$0.0149270\pi$
$632$		0			0
$633$	4.37363	+	16.3226i	0.173836	+	0.648765i
$634$		0			0
$635$	−12.7940	+	25.9437i	−0.507715	+	1.02954i
$636$		0			0
$637$	2.65062	−	19.5513i	0.105021	−	0.774649i
$638$		0			0
$639$	33.0401	−	11.2156i	1.30705	−	0.443683i
$640$		0			0
$641$	−13.6409	−	4.63047i	−0.538784	−	0.182893i	0.0387651	−	0.999248i	$-0.487658\pi$
$641$	−13.6409	−	4.63047i	−0.538784	−	0.182893i	−0.577549	+	0.816356i	$0.695991\pi$
$642$		0			0
$643$	10.4968	+	7.01373i	0.413953	+	0.276595i	0.745058	−	0.666999i	$-0.232422\pi$
$643$	10.4968	+	7.01373i	0.413953	+	0.276595i	−0.331105	+	0.943594i	$0.607422\pi$
$644$		0			0
$645$			66.1756i			2.60566i
$646$		0			0
$647$	24.9088	+	14.3811i	0.979266	+	0.565379i	0.902048	−	0.431635i	$-0.142063\pi$
$647$	24.9088	+	14.3811i	0.979266	+	0.565379i	0.0772175	+	0.997014i	$0.475396\pi$
$648$		0			0
$649$	−19.6392	−	1.28722i	−0.770904	−	0.0505277i
$650$		0			0
$651$	28.3517	−	13.9137i	1.11119	−	0.545321i
$652$		0			0
$653$	5.15957	+	15.1996i	0.201910	+	0.594807i	0.999970	−	0.00777114i	$-0.00247365\pi$
$653$	5.15957	+	15.1996i	0.201910	+	0.594807i	−0.798060	+	0.602578i	$0.794140\pi$
$654$		0			0
$655$	−67.1578	−	8.84149i	−2.62407	−	0.345466i
$656$		0			0
$657$	10.0158	−	6.69234i	0.390753	−	0.261093i
$658$		0			0
$659$	−24.7581	+	24.7581i	−0.964437	+	0.964437i	−0.999389	−	0.0349516i	$-0.988872\pi$
$659$	−24.7581	+	24.7581i	−0.964437	+	0.964437i	0.0349516	+	0.999389i	$0.488872\pi$
$660$		0			0
$661$	−2.24056	−	2.91996i	−0.0871478	−	0.113573i	0.747744	−	0.663987i	$-0.231137\pi$
$661$	−2.24056	−	2.91996i	−0.0871478	−	0.113573i	−0.834892	+	0.550413i	$0.814470\pi$
$662$		0			0
$663$	10.9309	−	25.8090i	0.424520	−	1.00234i
$664$		0			0
$665$	6.41690	−	2.64350i	0.248837	−	0.102510i
$666$		0			0
$667$	3.51191	−	13.1066i	0.135982	−	0.507491i
$668$		0			0
$669$	3.86653	+	58.9918i	0.149489	+	2.28076i
$670$		0			0
$671$	2.74943	+	6.63770i	0.106140	+	0.256246i
$672$		0			0
$673$	3.20669	−	16.1211i	0.123609	−	0.621423i	−0.868463	−	0.495753i	$-0.834892\pi$
$673$	3.20669	−	16.1211i	0.123609	−	0.621423i	0.992072	−	0.125670i	$-0.0401079\pi$
$674$		0			0
$675$	1.20466	−	3.54883i	0.0463676	−	0.136594i
$676$		0			0
$677$	1.67787	−	25.5994i	0.0644860	−	0.983866i	−0.835930	−	0.548836i	$-0.815071\pi$
$677$	1.67787	−	25.5994i	0.0644860	−	0.983866i	0.900416	−	0.435030i	$-0.143262\pi$
$678$		0			0
$679$	−13.0165	+	48.2066i	−0.499527	+	1.85000i
$680$		0			0
$681$	−28.1839	−	48.8159i	−1.08001	−	1.87063i
$682$		0			0
$683$	5.53174	−	2.72795i	0.211666	−	0.104382i	−0.333366	−	0.942798i	$-0.608184\pi$
$683$	5.53174	−	2.72795i	0.211666	−	0.104382i	0.545032	+	0.838416i	$0.316518\pi$
$684$		0			0
$685$	−1.00362	−	5.04556i	−0.0383465	−	0.192781i
$686$		0			0
$687$	12.1873	+	2.42420i	0.464974	+	0.0924892i
$688$		0			0
$689$	1.99138	−	15.1260i	0.0758655	−	0.576255i
$690$		0			0
$691$	−37.4507	−	18.4687i	−1.42469	−	0.702581i	−0.443619	−	0.896215i	$-0.646306\pi$
$691$	−37.4507	−	18.4687i	−1.42469	−	0.702581i	−0.981074	+	0.193635i	$0.937972\pi$
$692$		0			0
$693$	−8.55257	−	14.8796i	−0.324885	−	0.565229i
$694$		0			0
$695$	−0.132505	−	1.00647i	−0.00502620	−	0.0381777i
$696$		0			0
$697$	−0.0669142	+	0.242038i	−0.00253456	+	0.00916783i
$698$		0			0
$699$	48.7735	+	20.2027i	1.84478	+	0.764135i
$700$		0			0
$701$	−23.3027	−	23.3027i	−0.880132	−	0.880132i	0.113416	−	0.993548i	$-0.463821\pi$
$701$	−23.3027	−	23.3027i	−0.880132	−	0.880132i	−0.993548	+	0.113416i	$0.963821\pi$
$702$		0			0
$703$	5.56233	−	0.364574i	0.209787	−	0.0137502i
$704$		0			0
$705$	−55.9704	+	72.9421i	−2.10797	+	2.74716i
$706$		0			0
$707$	18.2241	+	27.3883i	0.685387	+	1.03004i
$708$		0			0
$709$	−29.3207	+	25.7136i	−1.10116	+	0.965693i	−0.999576	−	0.0291337i	$-0.990725\pi$
$709$	−29.3207	+	25.7136i	−1.10116	+	0.965693i	−0.101586	+	0.994827i	$0.532392\pi$
$710$		0			0
$711$	−8.84953	−	17.9451i	−0.331883	−	0.672993i
$712$		0			0
$713$	37.4936			1.40415
$714$		0			0
$715$	−23.8323			−0.891278
$716$		0			0
$717$	10.7237	+	21.7455i	0.400484	+	0.812100i
$718$		0			0
$719$	22.7923	−	19.9883i	0.850009	−	0.745438i	−0.118887	−	0.992908i	$-0.537933\pi$
$719$	22.7923	−	19.9883i	0.850009	−	0.745438i	0.968896	+	0.247470i	$0.0795992\pi$
$720$		0			0
$721$	0.251694	+	3.95686i	0.00937359	+	0.147361i
$722$		0			0
$723$	0.857105	−	1.11700i	0.0318761	−	0.0415417i
$724$		0			0
$725$	−15.1579	+	0.993500i	−0.562949	+	0.0368977i
$726$		0			0
$727$	−5.84869	−	5.84869i	−0.216916	−	0.216916i	0.590282	−	0.807197i	$-0.299017\pi$
$727$	−5.84869	−	5.84869i	−0.216916	−	0.216916i	−0.807197	+	0.590282i	$0.799017\pi$
$728$		0			0
$729$	−21.8103	−	9.03413i	−0.807789	−	0.334597i
$730$		0			0
$731$	−9.67276	−	29.2547i	−0.357760	−	1.08203i
$732$		0			0
$733$	−2.88268	−	21.8962i	−0.106474	−	0.808753i	−0.958468	−	0.285201i	$-0.907940\pi$
$733$	−2.88268	−	21.8962i	−0.106474	−	0.808753i	0.851994	−	0.523552i	$-0.175394\pi$
$734$		0			0
$735$	−15.8125	−	59.9355i	−0.583253	−	2.21075i
$736$		0			0
$737$	4.73699	+	2.33603i	0.174489	+	0.0860486i
$738$		0			0
$739$	−2.10461	+	15.9861i	−0.0774195	+	0.588059i	0.908132	+	0.418684i	$0.137508\pi$
$739$	−2.10461	+	15.9861i	−0.0774195	+	0.588059i	−0.985552	+	0.169376i	$0.945825\pi$
$740$		0			0
$741$	−4.76327	−	0.947474i	−0.174983	−	0.0348063i
$742$		0			0
$743$	2.89689	+	14.5636i	0.106277	+	0.534288i	0.996840	+	0.0794301i	$0.0253101\pi$
$743$	2.89689	+	14.5636i	0.106277	+	0.534288i	−0.890564	+	0.454858i	$0.849690\pi$
$744$		0			0
$745$	−20.9545	+	10.3336i	−0.767714	+	0.378594i
$746$		0			0
$747$	−20.0453	−	34.7194i	−0.733418	−	1.27032i
$748$		0			0
$749$	−28.3747	+	7.54444i	−1.03679	+	0.275668i
$750$		0			0
$751$	−1.08634	+	16.5744i	−0.0396413	+	0.604809i	0.931113	+	0.364732i	$0.118839\pi$
$751$	−1.08634	+	16.5744i	−0.0396413	+	0.604809i	−0.970754	+	0.240077i	$0.922827\pi$
$752$		0			0
$753$	−5.97269	+	17.5950i	−0.217657	+	0.641197i
$754$		0			0
$755$	−5.25570	+	26.4222i	−0.191274	+	0.961601i
$756$		0			0
$757$	−0.893771	−	2.15775i	−0.0324846	−	0.0784249i	0.906805	−	0.421551i	$-0.138514\pi$
$757$	−0.893771	−	2.15775i	−0.0324846	−	0.0784249i	−0.939289	+	0.343126i	$0.888514\pi$
$758$		0			0
$759$	−2.75187	−	41.9854i	−0.0998865	−	1.52397i
$760$		0			0
$761$	−13.1671	+	49.1402i	−0.477307	+	1.78133i	0.135146	+	0.990826i	$0.456850\pi$
$761$	−13.1671	+	49.1402i	−0.477307	+	1.78133i	−0.612453	+	0.790507i	$0.709817\pi$
$762$		0			0
$763$	−10.2511	−	24.8838i	−0.371115	−	0.900853i
$764$		0			0
$765$	0.337949	−	42.6401i	0.0122186	−	1.54166i
$766$		0			0
$767$	14.6641	+	19.1106i	0.529489	+	0.690043i
$768$		0			0
$769$	−15.2609	+	15.2609i	−0.550323	+	0.550323i	−0.926534	−	0.376211i	$-0.877227\pi$
$769$	−15.2609	+	15.2609i	−0.550323	+	0.550323i	0.376211	+	0.926534i	$0.377227\pi$
$770$		0			0
$771$	−11.7580	+	7.85644i	−0.423454	+	0.282943i
$772$		0			0
$773$	−37.8948	−	4.98895i	−1.36298	−	0.179440i	−0.586689	−	0.809812i	$-0.699569\pi$
$773$	−37.8948	−	4.98895i	−1.36298	−	0.179440i	−0.776293	+	0.630372i	$0.782902\pi$
$774$		0			0
$775$	−13.4921	−	39.7463i	−0.484649	−	1.42773i
$776$		0			0
$777$	3.35191	−	49.6743i	0.120249	−	1.78206i
$778$		0			0
$779$	0.0434190	+	0.00284583i	0.00155565	+	0.000101962i
$780$		0			0
$781$	24.7048	+	14.2633i	0.884007	+	0.510382i
$782$		0			0
$783$		−	0.791539i		−	0.0282873i
$784$		0			0
$785$	−63.6054	−	42.4998i	−2.27018	−	1.51688i
$786$		0			0
$787$	−0.421478	−	0.143073i	−0.0150241	−	0.00509999i	0.313917	−	0.949450i	$-0.398359\pi$
$787$	−0.421478	−	0.143073i	−0.0150241	−	0.00509999i	−0.328941	+	0.944350i	$0.606692\pi$
$788$		0			0
$789$	−6.85957	+	2.32851i	−0.244207	+	0.0828972i
$790$		0			0
$791$	27.8106	−	3.60686i	0.988830	−	0.128245i
$792$		0			0
$793$	3.88921	−	7.88655i	0.138110	−	0.280059i
$794$		0			0
$795$	−12.4056	−	46.2983i	−0.439981	−	1.64203i
$796$		0			0
$797$	18.9454	−	45.7383i	0.671081	−	1.62013i	−0.108696	−	0.994075i	$-0.534668\pi$
$797$	18.9454	−	45.7383i	0.671081	−	1.62013i	0.779777	−	0.626057i	$-0.215332\pi$
$798$		0			0
$799$	14.0815	−	40.4271i	0.498166	−	1.43021i
$800$		0			0
$801$	−13.3892	+	10.2739i	−0.473084	+	0.363010i
$802$		0			0
$803$	9.51282	+	2.54895i	0.335700	+	0.0899505i
$804$		0			0
$805$	14.4955	−	72.1476i	0.510901	−	2.54287i
$806$		0			0
$807$	−16.8829	−	12.9547i	−0.594305	−	0.456027i
$808$		0			0
$809$	20.5371	+	18.0105i	0.722046	+	0.633217i	0.939379	−	0.342880i	$-0.111403\pi$
$809$	20.5371	+	18.0105i	0.722046	+	0.633217i	−0.217333	+	0.976097i	$0.569736\pi$
$810$		0			0
$811$	2.32146	−	0.461767i	0.0815174	−	0.0162148i	−0.154163	−	0.988045i	$-0.549268\pi$
$811$	2.32146	−	0.461767i	0.0815174	−	0.0162148i	0.235681	+	0.971831i	$0.424268\pi$
$812$		0			0
$813$	−5.49297	+	8.22082i	−0.192647	+	0.288317i
$814$		0			0
$815$	−32.7619	+	56.7452i	−1.14760	+	1.98770i
$816$		0			0
$817$	−4.62370	+	2.66950i	−0.161763	+	0.0933939i
$818$		0			0
$819$	−6.79028	+	19.8777i	−0.237272	+	0.694582i
$820$		0			0
$821$	8.22923	+	9.38364i	0.287202	+	0.327491i	0.877393	−	0.479773i	$-0.159281\pi$
$821$	8.22923	+	9.38364i	0.287202	+	0.327491i	−0.590191	+	0.807264i	$0.700948\pi$
$822$		0			0
$823$	0.743288	−	0.847557i	0.0259094	−	0.0295440i	−0.738740	−	0.673991i	$-0.764579\pi$
$823$	0.743288	−	0.847557i	0.0259094	−	0.0295440i	0.764649	+	0.644447i	$0.222912\pi$
$824$		0			0
$825$	−43.5177	+	18.0256i	−1.51509	+	0.627572i
$826$		0			0
$827$	−10.8571	−	16.2488i	−0.377538	−	0.565025i	0.593234	−	0.805030i	$-0.297851\pi$
$827$	−10.8571	−	16.2488i	−0.377538	−	0.565025i	−0.970772	+	0.240005i	$0.922851\pi$
$828$		0			0
$829$	35.7717	−	9.58500i	1.24240	−	0.332901i	0.423006	−	0.906127i	$-0.360975\pi$
$829$	35.7717	−	9.58500i	1.24240	−	0.332901i	0.819397	+	0.573226i	$0.194308\pi$
$830$		0			0
$831$	−32.0077	+	4.21390i	−1.11034	+	0.146179i
$832$		0			0
$833$	15.7510	+	24.1848i	0.545740	+	0.837955i
$834$		0			0
$835$	−9.49581	+	1.25015i	−0.328616	+	0.0432631i
$836$		0			0
$837$	2.11264	−	0.566081i	0.0730236	−	0.0195666i
$838$		0			0
$839$	12.9021	+	19.3094i	0.445432	+	0.666636i	0.984451	−	0.175658i	$-0.0562052\pi$
$839$	12.9021	+	19.3094i	0.445432	+	0.666636i	−0.539020	+	0.842293i	$0.681205\pi$
$840$		0			0
$841$	23.8284	−	9.87006i	0.821670	−	0.340347i
$842$		0			0
$843$	−40.0192	+	45.6331i	−1.37833	+	1.57169i
$844$		0			0
$845$	−12.2388	−	13.9557i	−0.421027	−	0.480090i
$846$		0			0
$847$	−4.87212	+	14.2625i	−0.167408	+	0.490066i
$848$		0			0
$849$	4.11839	−	2.37775i	0.141343	−	0.0816043i
$850$		0			0
$851$	29.5535	−	51.1881i	1.01308	−	1.75471i
$852$		0			0
$853$	−0.769738	+	1.15199i	−0.0263553	+	0.0394435i	−0.844413	−	0.535692i	$-0.820051\pi$
$853$	−0.769738	+	1.15199i	−0.0263553	+	0.0394435i	0.818058	+	0.575136i	$0.195051\pi$
$854$		0			0
$855$	−7.24671	+	1.44146i	−0.247832	+	0.0492969i
$856$		0			0
$857$	38.0628	+	33.3801i	1.30020	+	1.14024i	0.981306	+	0.192453i	$0.0616443\pi$
$857$	38.0628	+	33.3801i	1.30020	+	1.14024i	0.318893	+	0.947791i	$0.396689\pi$
$858$		0			0
$859$	8.11484	+	6.22673i	0.276875	+	0.212453i	0.737859	−	0.674955i	$-0.235837\pi$
$859$	8.11484	+	6.22673i	0.276875	+	0.212453i	−0.460984	+	0.887408i	$0.652504\pi$
$860$		0			0
$861$	0.0765528	−	0.381021i	0.00260891	−	0.0129851i
$862$		0			0
$863$	5.09774	+	1.36594i	0.173529	+	0.0464970i	0.344537	−	0.938773i	$-0.388036\pi$
$863$	5.09774	+	1.36594i	0.173529	+	0.0464970i	−0.171008	+	0.985270i	$0.554702\pi$
$864$		0			0
$865$	25.4558	−	19.5329i	0.865523	−	0.664139i
$866$		0			0
$867$	12.5622	+	39.0287i	0.426634	+	1.32548i
$868$		0			0
$869$	6.26009	−	15.1132i	0.212359	−	0.512680i
$870$		0			0
$871$	−1.67310	−	6.24409i	−0.0566908	−	0.211573i
$872$		0			0
$873$	23.5124	−	47.6784i	0.795773	−	1.61367i
$874$		0			0
$875$	−33.5313	+	4.34880i	−1.13356	+	0.147016i
$876$		0			0
$877$	−20.3787	+	6.91762i	−0.688139	+	0.233592i	−0.643539	−	0.765413i	$-0.722535\pi$
$877$	−20.3787	+	6.91762i	−0.688139	+	0.233592i	−0.0445996	+	0.999005i	$0.514201\pi$
$878$		0			0
$879$	−29.9393	−	10.1630i	−1.00983	−	0.342791i
$880$		0			0
$881$	19.2029	+	12.8310i	0.646963	+	0.432287i	0.835283	−	0.549821i	$-0.185304\pi$
$881$	19.2029	+	12.8310i	0.646963	+	0.432287i	−0.188320	+	0.982108i	$0.560304\pi$
$882$		0			0
$883$		−	10.1303i		−	0.340911i	−0.985365	−	0.170455i	$-0.945476\pi$
$883$		−	10.1303i		−	0.340911i	0.985365	−	0.170455i	$-0.0545239\pi$
$884$		0			0
$885$	65.5395	+	37.8393i	2.20309	+	1.27195i
$886$		0			0
$887$	50.2716	+	3.29497i	1.68795	+	0.110634i	0.878871	−	0.477059i	$-0.158297\pi$
$887$	50.2716	+	3.29497i	1.68795	+	0.110634i	0.809084	+	0.587694i	$0.199964\pi$
$888$		0			0
$889$	−1.40336	+	20.7973i	−0.0470671	+	0.697520i
$890$		0			0
$891$	−7.04429	−	20.7518i	−0.235992	−	0.695211i
$892$		0			0
$893$	−7.35430	−	0.968212i	−0.246102	−	0.0324000i
$894$		0			0
$895$	−16.5515	+	11.0594i	−0.553255	+	0.369673i
$896$		0			0
$897$	−36.4139	+	36.4139i	−1.21583	+	1.21583i
$898$		0			0
$899$	−5.39674	−	7.03317i	−0.179991	−	0.234569i
$900$		0			0
$901$	12.2516	+	18.6541i	0.408159	+	0.621460i
$902$		0			0
$903$	18.1638	+	44.0911i	0.604452	+	1.46726i
$904$		0			0
$905$	6.68969	−	24.9663i	0.222373	−	0.829906i
$906$		0			0
$907$	0.886502	+	13.5254i	0.0294358	+	0.449104i	0.986983	+	0.160826i	$0.0514159\pi$
$907$	0.886502	+	13.5254i	0.0294358	+	0.449104i	−0.957547	+	0.288278i	$0.906917\pi$
$908$		0			0
$909$	−13.4030	−	32.3578i	−0.444551	−	1.07324i
$910$		0			0
$911$	−0.450078	+	2.26269i	−0.0149117	+	0.0749664i	−0.987525	−	0.157465i	$-0.949668\pi$
$911$	−0.450078	+	2.26269i	−0.0149117	+	0.0749664i	0.972613	+	0.232431i	$0.0746680\pi$
$912$		0			0
$913$	10.5358	−	31.0375i	0.348684	−	1.02719i
$914$		0			0
$915$	1.80684	−	27.5671i	0.0597323	−	0.911340i
$916$		0			0
$917$	−47.1724	+	12.5425i	−1.55777	+	0.414189i
$918$		0			0
$919$	−8.73139	−	15.1232i	−0.288022	−	0.498868i	0.685316	−	0.728246i	$-0.259664\pi$
$919$	−8.73139	−	15.1232i	−0.288022	−	0.498868i	−0.973337	+	0.229378i	$0.926331\pi$
$920$		0			0
$921$	33.8482	−	16.6921i	1.11534	−	0.550023i
$922$		0			0
$923$	−6.81145	−	34.2435i	−0.224202	−	1.12714i
$924$		0			0
$925$	−64.8985	−	12.9091i	−2.13385	−	0.424449i
$926$		0			0
$927$	0.550969	−	4.18503i	0.0180962	−	0.137454i
$928$		0			0
$929$	−48.0656	−	23.7033i	−1.57698	−	0.777681i	−0.577725	−	0.816232i	$-0.696059\pi$
$929$	−48.0656	−	23.7033i	−1.57698	−	0.777681i	−0.999257	+	0.0385508i	$0.987726\pi$
$930$		0			0
$931$	3.54983	−	3.52259i	0.116341	−	0.115448i
$932$		0			0
$933$	−7.85281	−	59.6480i	−0.257089	−	1.95279i
$934$		0			0
$935$	26.3924	−	22.7780i	0.863123	−	0.744921i
$936$		0			0
$937$	−47.4988	−	19.6746i	−1.55172	−	0.642742i	−0.568091	−	0.822966i	$-0.692318\pi$
$937$	−47.4988	−	19.6746i	−1.55172	−	0.642742i	−0.983626	+	0.180223i	$0.942318\pi$
$938$		0			0
$939$	58.2980	+	58.2980i	1.90248	+	1.90248i
$940$		0			0
$941$	34.1774	−	2.24010i	1.11415	−	0.0730253i	0.502813	−	0.864395i	$-0.332299\pi$
$941$	34.1774	−	2.24010i	1.11415	−	0.0730253i	0.611337	+	0.791370i	$0.290632\pi$
$942$		0			0
$943$	0.280872	−	0.366040i	0.00914646	−	0.0119199i
$944$		0			0
$945$	−0.272512	−	4.28414i	−0.00886483	−	0.139363i
$946$		0			0
$947$	14.1910	−	12.4452i	0.461147	−	0.404415i	−0.397000	−	0.917818i	$-0.629949\pi$
$947$	14.1910	−	12.4452i	0.461147	−	0.404415i	0.858147	+	0.513403i	$0.171616\pi$
$948$		0			0
$949$	−5.33120	−	10.8106i	−0.173058	−	0.350927i
$950$		0			0
$951$	−10.9766			−0.355941
$952$		0			0
$953$	4.74186			0.153604			0.0768020	−	0.997046i	$-0.475529\pi$
$953$	4.74186			0.153604			0.0768020	+	0.997046i	$0.475529\pi$
$954$		0			0
$955$	33.7725	+	68.4838i	1.09285	+	2.21608i
$956$		0			0
$957$	−7.47966	+	6.55948i	−0.241783	+	0.212038i
$958$		0			0
$959$	−2.05358	−	3.08625i	−0.0663137	−	0.0996604i
$960$		0			0
$961$	−3.95942	+	5.16001i	−0.127723	+	0.166452i
$962$		0			0
$963$	31.1915	−	2.04440i	1.00513	−	0.0658798i
$964$		0			0
$965$	68.4899	+	68.4899i	2.20477	+	2.20477i
$966$		0			0
$967$	−23.1024	−	9.56934i	−0.742924	−	0.307729i	−0.0210734	−	0.999778i	$-0.506708\pi$
$967$	−23.1024	−	9.56934i	−0.742924	−	0.307729i	−0.721851	+	0.692049i	$0.756708\pi$
$968$		0			0
$969$	6.18051	−	3.50330i	0.198546	−	0.112542i
$970$		0			0
$971$	−1.09714	−	8.33358i	−0.0352088	−	0.267437i	−0.999990	−	0.00438512i	$-0.998604\pi$
$971$	−1.09714	−	8.33358i	−0.0352088	−	0.267437i	0.964782	−	0.263052i	$-0.0847292\pi$
$972$		0			0
$973$	−0.364540	−	0.634219i	−0.0116866	−	0.0203321i
$974$		0			0
$975$	51.7053	+	25.4983i	1.65590	+	0.816598i
$976$		0			0
$977$	3.61261	−	27.4405i	0.115578	−	0.877899i	−0.831192	−	0.555986i	$-0.812341\pi$
$977$	3.61261	−	27.4405i	0.115578	−	0.877899i	0.946769	−	0.321913i	$-0.104326\pi$
$978$		0			0
$979$	−13.5328	−	2.69184i	−0.432511	−	0.0860317i
$980$		0			0
$981$	5.58977	+	28.1017i	0.178468	+	0.897217i
$982$		0			0
$983$	−9.58744	+	4.72800i	−0.305792	+	0.150800i	−0.588710	−	0.808344i	$-0.700364\pi$
$983$	−9.58744	+	4.72800i	−0.305792	+	0.150800i	0.282918	+	0.959144i	$0.408697\pi$
$984$		0			0
$985$	28.5816	+	49.5048i	0.910686	+	1.57735i
$986$		0			0
$987$	−17.2707	+	63.9621i	−0.549732	+	2.03594i
$988$		0			0
$989$	−3.70262	+	56.4910i	−0.117736	+	1.79631i
$990$		0			0
$991$	−6.12893	+	18.0553i	−0.194692	+	0.573544i	−0.999808	−	0.0195726i	$-0.993769\pi$
$991$	−6.12893	+	18.0553i	−0.194692	+	0.573544i	0.805116	+	0.593117i	$0.202103\pi$
$992$		0			0
$993$	5.88451	−	29.5834i	0.186739	−	0.938802i
$994$		0			0
$995$	−38.8333	−	93.7520i	−1.23110	−	2.97214i
$996$		0			0
$997$	−3.47145	−	52.9641i	−0.109942	−	1.67739i	−0.595631	−	0.803258i	$-0.703098\pi$
$997$	−3.47145	−	52.9641i	−0.109942	−	1.67739i	0.485690	−	0.874131i	$-0.338569\pi$
$998$		0			0
$999$	0.892400	−	3.33048i	0.0282343	−	0.105372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.cw.a.129.16	✓	288
7.5	odd	6	inner	952.2.cw.a.537.16	yes	288
17.12	odd	16	inner	952.2.cw.a.913.16	yes	288
119.12	even	48	inner	952.2.cw.a.369.16	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.cw.a.129.16	✓	288	1.1	even	1	trivial
952.2.cw.a.369.16	yes	288	119.12	even	48	inner
952.2.cw.a.537.16	yes	288	7.5	odd	6	inner
952.2.cw.a.913.16	yes	288	17.12	odd	16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.cw (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06671 + 2.16308i) q^{3} +(2.76046 - 2.42086i) q^{5} +(1.17475 - 2.37064i) q^{7} +(-1.71474 + 2.23469i) q^{9} +(-2.29799 + 0.150618i) q^{11} +(1.99304 + 1.99304i) q^{13} +(8.18112 + 3.38873i) q^{15} +(-4.11201 - 0.302263i) q^{17} +(0.0932516 + 0.708317i) q^{19} +(6.38101 + 0.0122885i) q^{21} +(6.79424 + 3.35055i) q^{23} +(1.10695 - 8.40815i) q^{25} +(0.433420 + 0.0862126i) q^{27} +(-0.349440 - 1.75675i) q^{29} +(4.43893 - 2.18904i) q^{31} +(-2.77708 - 4.81005i) q^{33} +(-2.49614 - 9.38798i) q^{35} +(0.510302 - 7.78570i) q^{37} +(-2.18510 + 6.43711i) q^{39} +(0.0118819 - 0.0597346i) q^{41} +(2.85983 + 6.90424i) q^{43} +(0.676404 + 10.3199i) q^{45} +(-2.68726 + 10.0290i) q^{47} +(-4.23991 - 5.56985i) q^{49} +(-3.73251 - 9.21702i) q^{51} +(-3.29512 - 4.29429i) q^{53} +(-5.97887 + 5.97887i) q^{55} +(-1.43267 + 0.957279i) q^{57} +(8.47313 + 1.11551i) q^{59} +(-1.00282 - 2.95422i) q^{61} +(3.28327 + 6.69026i) q^{63} +(10.3266 + 0.676841i) q^{65} +(-1.98621 - 1.14674i) q^{67} +18.2705i q^{69} +(-10.2996 - 6.88195i) q^{71} +(-4.04953 - 1.37463i) q^{73} +(19.3683 - 6.57464i) q^{75} +(-2.34250 + 5.62464i) q^{77} +(-3.14173 + 6.37079i) q^{79} +(2.46295 + 9.19186i) q^{81} +(-5.44666 + 13.1494i) q^{83} +(-12.0828 + 9.12022i) q^{85} +(3.42724 - 2.62982i) q^{87} +(5.78735 + 1.55072i) q^{89} +(7.06613 - 2.38346i) q^{91} +(9.47010 + 7.26667i) q^{93} +(1.97215 + 1.72953i) q^{95} +(-18.5103 + 3.68192i) q^{97} +(3.60387 - 5.39357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 32 q^{15} - 48 q^{21} + 32 q^{29} + 72 q^{31} + 32 q^{35} + 48 q^{37} + 32 q^{39} - 32 q^{43} - 24 q^{47} + 48 q^{49} + 16 q^{53} + 128 q^{57} - 72 q^{61} + 184 q^{63} - 32 q^{65} - 80 q^{71} - 96 q^{73}+ \cdots + 64 q^{99}+O(q^{100}) \) 288 * q - 32 * q^15 - 48 * q^21 + 32 * q^29 + 72 * q^31 + 32 * q^35 + 48 * q^37 + 32 * q^39 - 32 * q^43 - 24 * q^47 + 48 * q^49 + 16 * q^53 + 128 * q^57 - 72 * q^61 + 184 * q^63 - 32 * q^65 - 80 * q^71 - 96 * q^73 - 216 * q^75 + 56 * q^77 - 32 * q^79 - 64 * q^81 + 160 * q^85 - 144 * q^87 + 144 * q^89 - 32 * q^93 - 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more