LMFDB - Embedded newform 1170.2.q.c.359.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(359,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.359"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.q (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			359.8
Character	$\chi$	$=$	1170.359
Dual form			1170.2.q.c.629.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(2.23186 - 0.137134i) q^{5} +(1.96562 + 1.96562i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.67513 + 1.48119i) q^{10} +(2.64510 + 2.64510i) q^{11} +(0.770380 + 3.52229i) q^{13} +2.77980i q^{14} -1.00000 q^{16} -5.46226i q^{17} +(-5.64075 - 5.64075i) q^{19} +(0.137134 + 2.23186i) q^{20} +3.74074i q^{22} +6.48642i q^{23} +(4.96239 - 0.612127i) q^{25} +(-1.94589 + 3.03537i) q^{26} +(-1.96562 + 1.96562i) q^{28} -2.74241i q^{29} +(0.945844 + 0.945844i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.86240 - 3.86240i) q^{34} +(4.65654 + 4.11743i) q^{35} +(-6.10217 - 6.10217i) q^{37} -7.97722i q^{38} +(-1.48119 + 1.67513i) q^{40} +(-5.19926 + 5.19926i) q^{41} +1.08404 q^{43} +(-2.64510 + 2.64510i) q^{44} +(-4.58659 + 4.58659i) q^{46} +(-0.108579 + 0.108579i) q^{47} +0.727313i q^{49} +(3.94178 + 3.07610i) q^{50} +(-3.52229 + 0.770380i) q^{52} +12.5009 q^{53} +(6.26623 + 5.54076i) q^{55} -2.77980 q^{56} +(1.93918 - 1.93918i) q^{58} +(9.67063 + 9.67063i) q^{59} -11.6006 q^{61} +1.33763i q^{62} -1.00000i q^{64} +(2.20241 + 7.75561i) q^{65} +(4.45889 - 4.45889i) q^{67} +5.46226 q^{68} +(0.381205 + 6.20413i) q^{70} +(8.97120 - 8.97120i) q^{71} +(7.14966 + 7.14966i) q^{73} -8.62977i q^{74} +(5.64075 - 5.64075i) q^{76} +10.3985i q^{77} -17.7477 q^{79} +(-2.23186 + 0.137134i) q^{80} -7.35287 q^{82} +(1.82503 + 1.82503i) q^{83} +(-0.749061 - 12.1910i) q^{85} +(0.766529 + 0.766529i) q^{86} -3.74074 q^{88} +(2.49913 + 2.49913i) q^{89} +(-5.40920 + 8.43775i) q^{91} -6.48642 q^{92} -0.153554 q^{94} +(-13.3629 - 11.8158i) q^{95} +(0.837007 - 0.837007i) q^{97} +(-0.514288 + 0.514288i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) $ 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	2.23186	−	0.137134i	0.998118	−	0.0613281i
$5$	2.23186	−	0.137134i	0.998118	−	0.0613281i
$6$		0			0
$7$	1.96562	+	1.96562i	0.742934	+	0.742934i	0.973142	−	0.230208i	$-0.0739405\pi$
$7$	1.96562	+	1.96562i	0.742934	+	0.742934i	−0.230208	+	0.973142i	$0.573941\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	1.67513	+	1.48119i	0.529723	+	0.468395i
$11$	2.64510	+	2.64510i	0.797528	+	0.797528i	0.982705	−	0.185177i	$-0.0592859\pi$
$11$	2.64510	+	2.64510i	0.797528	+	0.797528i	−0.185177	+	0.982705i	$0.559286\pi$
$12$		0			0
$13$	0.770380	+	3.52229i	0.213665	+	0.976907i
$13$	0.770380	+	3.52229i	0.213665	+	0.976907i
$14$			2.77980i			0.742934i
$15$		0			0
$16$	−1.00000			−0.250000
$17$		−	5.46226i		−	1.32479i	−0.749154	−	0.662396i	$-0.769540\pi$
$17$		−	5.46226i		−	1.32479i	0.749154	−	0.662396i	$-0.230460\pi$
$18$		0			0
$19$	−5.64075	−	5.64075i	−1.29408	−	1.29408i	−0.932242	−	0.361834i	$-0.882151\pi$
$19$	−5.64075	−	5.64075i	−1.29408	−	1.29408i	−0.361834	−	0.932242i	$-0.617849\pi$
$20$	0.137134	+	2.23186i	0.0306641	+	0.499059i
$21$		0			0
$22$			3.74074i			0.797528i
$23$			6.48642i			1.35251i	0.736666	+	0.676256i	$0.236399\pi$
$23$			6.48642i			1.35251i	−0.736666	+	0.676256i	$0.763601\pi$
$24$		0			0
$25$	4.96239	−	0.612127i	0.992478	−	0.122425i
$26$	−1.94589	+	3.03537i	−0.381621	+	0.595286i
$27$		0			0
$28$	−1.96562	+	1.96562i	−0.371467	+	0.371467i
$29$		−	2.74241i		−	0.509253i	−0.967040	−	0.254626i	$-0.918048\pi$
$29$		−	2.74241i		−	0.509253i	0.967040	−	0.254626i	$-0.0819525\pi$
$30$		0			0
$31$	0.945844	+	0.945844i	0.169879	+	0.169879i	0.786926	−	0.617047i	$-0.211671\pi$
$31$	0.945844	+	0.945844i	0.169879	+	0.169879i	−0.617047	+	0.786926i	$0.711671\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	3.86240	−	3.86240i	0.662396	−	0.662396i
$35$	4.65654	+	4.11743i	0.787098	+	0.695973i
$36$		0			0
$37$	−6.10217	−	6.10217i	−1.00319	−	1.00319i	−0.999995	−	0.00319562i	$-0.998983\pi$
$37$	−6.10217	−	6.10217i	−1.00319	−	1.00319i	−0.00319562	−	0.999995i	$-0.501017\pi$
$38$		−	7.97722i		−	1.29408i
$39$		0			0
$40$	−1.48119	+	1.67513i	−0.234197	+	0.264861i
$41$	−5.19926	+	5.19926i	−0.811988	+	0.811988i	−0.984932	−	0.172944i	$-0.944672\pi$
$41$	−5.19926	+	5.19926i	−0.811988	+	0.811988i	0.172944	+	0.984932i	$0.444672\pi$
$42$		0			0
$43$	1.08404			0.165314			0.0826569	−	0.996578i	$-0.473659\pi$
$43$	1.08404			0.165314			0.0826569	+	0.996578i	$0.473659\pi$
$44$	−2.64510	+	2.64510i	−0.398764	+	0.398764i
$45$		0			0
$46$	−4.58659	+	4.58659i	−0.676256	+	0.676256i
$47$	−0.108579	+	0.108579i	−0.0158379	+	0.0158379i	−0.714981	−	0.699143i	$-0.753565\pi$
$47$	−0.108579	+	0.108579i	−0.0158379	+	0.0158379i	0.699143	+	0.714981i	$0.253565\pi$
$48$		0			0
$49$			0.727313i			0.103902i
$50$	3.94178	+	3.07610i	0.557452	+	0.435026i
$51$		0			0
$52$	−3.52229	+	0.770380i	−0.488453	+	0.106833i
$53$	12.5009			1.71713			0.858565	−	0.512704i	$-0.171356\pi$
$53$	12.5009			1.71713			0.858565	+	0.512704i	$0.171356\pi$
$54$		0			0
$55$	6.26623	+	5.54076i	0.844938	+	0.747116i
$56$	−2.77980			−0.371467
$57$		0			0
$58$	1.93918	−	1.93918i	0.254626	−	0.254626i
$59$	9.67063	+	9.67063i	1.25901	+	1.25901i	0.951567	+	0.307442i	$0.0994730\pi$
$59$	9.67063	+	9.67063i	1.25901	+	1.25901i	0.307442	+	0.951567i	$0.400527\pi$
$60$		0			0
$61$	−11.6006			−1.48531			−0.742653	−	0.669677i	$-0.766433\pi$
$61$	−11.6006			−1.48531			−0.742653	+	0.669677i	$0.766433\pi$
$62$			1.33763i			0.169879i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.20241	+	7.75561i	0.273175	+	0.961964i
$66$		0			0
$67$	4.45889	−	4.45889i	0.544740	−	0.544740i	−0.380174	−	0.924915i	$-0.624136\pi$
$67$	4.45889	−	4.45889i	0.544740	−	0.544740i	0.924915	+	0.380174i	$0.124136\pi$
$68$	5.46226			0.662396
$69$		0			0
$70$	0.381205	+	6.20413i	0.0455628	+	0.741536i
$71$	8.97120	−	8.97120i	1.06469	−	1.06469i	0.0669273	−	0.997758i	$-0.478680\pi$
$71$	8.97120	−	8.97120i	1.06469	−	1.06469i	0.997758	−	0.0669273i	$-0.0213196\pi$
$72$		0			0
$73$	7.14966	+	7.14966i	0.836804	+	0.836804i	0.988437	−	0.151633i	$-0.0484531\pi$
$73$	7.14966	+	7.14966i	0.836804	+	0.836804i	−0.151633	+	0.988437i	$0.548453\pi$
$74$		−	8.62977i		−	1.00319i
$75$		0			0
$76$	5.64075	−	5.64075i	0.647038	−	0.647038i
$77$			10.3985i			1.18502i
$78$		0			0
$79$	−17.7477			−1.99677			−0.998386	−	0.0567868i	$-0.981914\pi$
$79$	−17.7477			−1.99677			−0.998386	+	0.0567868i	$0.981914\pi$
$80$	−2.23186	+	0.137134i	−0.249529	+	0.0153320i
$81$		0			0
$82$	−7.35287			−0.811988
$83$	1.82503	+	1.82503i	0.200323	+	0.200323i	0.800138	−	0.599816i	$-0.204759\pi$
$83$	1.82503	+	1.82503i	0.200323	+	0.200323i	−0.599816	+	0.800138i	$0.704759\pi$
$84$		0			0
$85$	−0.749061	−	12.1910i	−0.0812470	−	1.32230i
$86$	0.766529	+	0.766529i	0.0826569	+	0.0826569i
$87$		0			0
$88$	−3.74074			−0.398764
$89$	2.49913	+	2.49913i	0.264907	+	0.264907i	0.827044	−	0.562137i	$-0.190021\pi$
$89$	2.49913	+	2.49913i	0.264907	+	0.264907i	−0.562137	+	0.827044i	$0.690021\pi$
$90$		0			0
$91$	−5.40920	+	8.43775i	−0.567038	+	0.884516i
$92$	−6.48642			−0.676256
$93$		0			0
$94$	−0.153554			−0.0158379
$95$	−13.3629	−	11.8158i	−1.37100	−	1.21228i
$96$		0			0
$97$	0.837007	−	0.837007i	0.0849852	−	0.0849852i	−0.663336	−	0.748321i	$-0.730860\pi$
$97$	0.837007	−	0.837007i	0.0849852	−	0.0849852i	0.748321	+	0.663336i	$0.230860\pi$
$98$	−0.514288	+	0.514288i	−0.0519510	+	0.0519510i
$99$		0			0
$100$	0.612127	+	4.96239i	0.0612127	+	0.496239i
$101$	−12.7572			−1.26939			−0.634694	−	0.772763i	$-0.718874\pi$
$101$	−12.7572			−1.26939			−0.634694	+	0.772763i	$0.718874\pi$
$102$		0			0
$103$	−3.99740			−0.393875			−0.196938	−	0.980416i	$-0.563100\pi$
$103$	−3.99740			−0.393875			−0.196938	+	0.980416i	$0.563100\pi$
$104$	−3.03537	−	1.94589i	−0.297643	−	0.190810i
$105$		0			0
$106$	8.83947	+	8.83947i	0.858565	+	0.858565i
$107$	−4.67233			−0.451691			−0.225846	−	0.974163i	$-0.572515\pi$
$107$	−4.67233			−0.451691			−0.225846	+	0.974163i	$0.572515\pi$
$108$		0			0
$109$	−10.2433	−	10.2433i	−0.981130	−	0.981130i	0.0186953	−	0.999825i	$-0.494049\pi$
$109$	−10.2433	−	10.2433i	−0.981130	−	0.981130i	−0.999825	+	0.0186953i	$0.994049\pi$
$110$	0.512982	+	8.34880i	0.0489109	+	0.796027i
$111$		0			0
$112$	−1.96562	−	1.96562i	−0.185734	−	0.185734i
$113$	2.65269			0.249544			0.124772	−	0.992185i	$-0.460180\pi$
$113$	2.65269			0.249544			0.124772	+	0.992185i	$0.460180\pi$
$114$		0			0
$115$	0.889508	+	14.4768i	0.0829471	+	1.34997i
$116$	2.74241			0.254626
$117$		0			0
$118$			13.6763i			1.25901i
$119$	10.7367	−	10.7367i	0.984233	−	0.984233i
$120$		0			0
$121$			2.99312i			0.272102i
$122$	−8.20287	−	8.20287i	−0.742653	−	0.742653i
$123$		0			0
$124$	−0.945844	+	0.945844i	−0.0849393	+	0.0849393i
$125$	10.9914	−	2.04669i	0.983101	−	0.183062i
$126$		0			0
$127$	0.680223			0.0603600			0.0301800	−	0.999544i	$-0.490392\pi$
$127$	0.680223			0.0603600			0.0301800	+	0.999544i	$0.490392\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−3.92671	+	7.04138i	−0.344395	+	0.617570i
$131$		−	5.94995i		−	0.519850i	−0.965629	−	0.259925i	$-0.916302\pi$
$131$		−	5.94995i		−	0.519850i	0.965629	−	0.259925i	$-0.0836978\pi$
$132$		0			0
$133$		−	22.1751i		−	1.92283i
$134$	6.30582			0.544740
$135$		0			0
$136$	3.86240	+	3.86240i	0.331198	+	0.331198i
$137$	6.79720	−	6.79720i	0.580724	−	0.580724i	−0.354378	−	0.935102i	$-0.615307\pi$
$137$	6.79720	−	6.79720i	0.580724	−	0.580724i	0.935102	+	0.354378i	$0.115307\pi$
$138$		0			0
$139$	9.52103			0.807563			0.403781	−	0.914855i	$-0.367696\pi$
$139$	9.52103			0.807563			0.403781	+	0.914855i	$0.367696\pi$
$140$	−4.11743	+	4.65654i	−0.347986	+	0.393549i
$141$		0			0
$142$	12.6872			1.06469
$143$	−7.27908	+	11.3545i	−0.608707	+	0.949515i
$144$		0			0
$145$	−0.376077	−	6.12067i	−0.0312315	−	0.508294i
$146$			10.1111i			0.836804i
$147$		0			0
$148$	6.10217	−	6.10217i	0.501595	−	0.501595i
$149$	6.89267	−	6.89267i	0.564669	−	0.564669i	−0.365961	−	0.930630i	$-0.619260\pi$
$149$	6.89267	−	6.89267i	0.564669	−	0.564669i	0.930630	+	0.365961i	$0.119260\pi$
$150$		0			0
$151$	13.8330	−	13.8330i	1.12571	−	1.12571i	0.134848	−	0.990866i	$-0.456945\pi$
$151$	13.8330	−	13.8330i	1.12571	−	1.12571i	0.990866	−	0.134848i	$-0.0430547\pi$
$152$	7.97722			0.647038
$153$		0			0
$154$	−7.35287	+	7.35287i	−0.592511	+	0.592511i
$155$	2.24070	+	1.98128i	0.179977	+	0.159141i
$156$		0			0
$157$			0.454032i			0.0362357i	0.999836	+	0.0181179i	$0.00576741\pi$
$157$			0.454032i			0.0362357i	−0.999836	+	0.0181179i	$0.994233\pi$
$158$	−12.5495	−	12.5495i	−0.998386	−	0.998386i
$159$		0			0
$160$	−1.67513	−	1.48119i	−0.132431	−	0.117099i
$161$	−12.7498	+	12.7498i	−1.00483	+	1.00483i
$162$		0			0
$163$	1.75837	+	1.75837i	0.137726	+	0.137726i	0.772609	−	0.634883i	$-0.218952\pi$
$163$	1.75837	+	1.75837i	0.137726	+	0.137726i	−0.634883	+	0.772609i	$0.718952\pi$
$164$	−5.19926	−	5.19926i	−0.405994	−	0.405994i
$165$		0			0
$166$			2.58098i			0.200323i
$167$	−7.24838	+	7.24838i	−0.560897	+	0.560897i	−0.929562	−	0.368665i	$-0.879815\pi$
$167$	−7.24838	+	7.24838i	−0.560897	+	0.560897i	0.368665	+	0.929562i	$0.379815\pi$
$168$		0			0
$169$	−11.8130	+	5.42700i	−0.908694	+	0.417462i
$170$	8.09067	−	9.15000i	0.620526	−	0.701773i
$171$		0			0
$172$			1.08404i			0.0826569i
$173$		−	1.44733i		−	0.110039i	−0.998485	−	0.0550194i	$-0.982478\pi$
$173$		−	1.44733i		−	0.110039i	0.998485	−	0.0550194i	$-0.0175221\pi$
$174$		0			0
$175$	10.9574	+	8.55096i	0.828299	+	0.646391i
$176$	−2.64510	−	2.64510i	−0.199382	−	0.199382i
$177$		0			0
$178$			3.53430i			0.264907i
$179$	1.75078			0.130859			0.0654296	−	0.997857i	$-0.479158\pi$
$179$	1.75078			0.130859			0.0654296	+	0.997857i	$0.479158\pi$
$180$		0			0
$181$			8.25471i			0.613568i	0.951779	+	0.306784i	$0.0992529\pi$
$181$			8.25471i			0.613568i	−0.951779	+	0.306784i	$0.900747\pi$
$182$	−9.79127	+	2.14151i	−0.725777	+	0.158739i
$183$		0			0
$184$	−4.58659	−	4.58659i	−0.338128	−	0.338128i
$185$	−14.4560	−	12.7824i	−1.06283	−	0.939778i
$186$		0			0
$187$	14.4482	−	14.4482i	1.05656	−	1.05656i
$188$	−0.108579	−	0.108579i	−0.00791895	−	0.00791895i
$189$		0			0
$190$	−1.09395	−	17.8040i	−0.0793633	−	1.29164i
$191$			0.580127i			0.0419765i	0.999780	+	0.0209883i	$0.00668127\pi$
$191$			0.580127i			0.0419765i	−0.999780	+	0.0209883i	$0.993319\pi$
$192$		0			0
$193$	−16.1005	−	16.1005i	−1.15894	−	1.15894i	−0.984704	−	0.174238i	$-0.944254\pi$
$193$	−16.1005	−	16.1005i	−1.15894	−	1.15894i	−0.174238	−	0.984704i	$-0.555746\pi$
$194$	1.18371			0.0849852
$195$		0			0
$196$	−0.727313			−0.0519510
$197$	−16.9646	−	16.9646i	−1.20868	−	1.20868i	−0.971455	−	0.237224i	$-0.923762\pi$
$197$	−16.9646	−	16.9646i	−1.20868	−	1.20868i	−0.237224	−	0.971455i	$-0.576238\pi$
$198$		0			0
$199$		−	14.1566i		−	1.00353i	−0.865003	−	0.501767i	$-0.832684\pi$
$199$		−	14.1566i		−	1.00353i	0.865003	−	0.501767i	$-0.167316\pi$
$200$	−3.07610	+	3.94178i	−0.217513	+	0.278726i
$201$		0			0
$202$	−9.02070	−	9.02070i	−0.634694	−	0.634694i
$203$	5.39053	−	5.39053i	0.378341	−	0.378341i
$204$		0			0
$205$	−10.8910	+	12.3170i	−0.760662	+	0.860257i
$206$	−2.82659	−	2.82659i	−0.196938	−	0.196938i
$207$		0			0
$208$	−0.770380	−	3.52229i	−0.0534163	−	0.244227i
$209$		−	29.8407i		−	2.06413i
$210$		0			0
$211$	7.57960			0.521801			0.260901	−	0.965366i	$-0.415980\pi$
$211$	7.57960			0.521801			0.260901	+	0.965366i	$0.415980\pi$
$212$			12.5009i			0.858565i
$213$		0			0
$214$	−3.30384	−	3.30384i	−0.225846	−	0.225846i
$215$	2.41941	−	0.148658i	0.165003	−	0.0101384i
$216$		0			0
$217$			3.71834i			0.252417i
$218$		−	14.4862i		−	0.981130i
$219$		0			0
$220$	−5.54076	+	6.26623i	−0.373558	+	0.422469i
$221$	19.2396	−	4.20802i	1.29420	−	0.283062i
$222$		0			0
$223$	−19.2433	+	19.2433i	−1.28862	+	1.28862i	−0.353001	+	0.935623i	$0.614839\pi$
$223$	−19.2433	+	19.2433i	−1.28862	+	1.28862i	−0.935623	+	0.353001i	$0.885161\pi$
$224$		−	2.77980i		−	0.185734i
$225$		0			0
$226$	1.87574	+	1.87574i	0.124772	+	0.124772i
$227$	12.3895	+	12.3895i	0.822322	+	0.822322i	0.986441	−	0.164119i	$-0.0524780\pi$
$227$	12.3895	+	12.3895i	0.822322	+	0.822322i	−0.164119	+	0.986441i	$0.552478\pi$
$228$		0			0
$229$	6.78591	−	6.78591i	0.448425	−	0.448425i	−0.446406	−	0.894831i	$-0.647296\pi$
$229$	6.78591	−	6.78591i	0.448425	−	0.448425i	0.894831	+	0.446406i	$0.147296\pi$
$230$	−9.60765	+	10.8656i	−0.633510	+	0.716457i
$231$		0			0
$232$	1.93918	+	1.93918i	0.127313	+	0.127313i
$233$		−	9.03392i		−	0.591832i	−0.955214	−	0.295916i	$-0.904375\pi$
$233$		−	9.03392i		−	0.591832i	0.955214	−	0.295916i	$-0.0956248\pi$
$234$		0			0
$235$	−0.227443	+	0.257223i	−0.0148368	+	0.0167794i
$236$	−9.67063	+	9.67063i	−0.629504	+	0.629504i
$237$		0			0
$238$	15.1840			0.984233
$239$	2.52590	−	2.52590i	0.163387	−	0.163387i	−0.620678	−	0.784065i	$-0.713143\pi$
$239$	2.52590	−	2.52590i	0.163387	−	0.163387i	0.784065	+	0.620678i	$0.213143\pi$
$240$		0			0
$241$	8.17058	−	8.17058i	0.526314	−	0.526314i	−0.393158	−	0.919471i	$-0.628617\pi$
$241$	8.17058	−	8.17058i	0.526314	−	0.526314i	0.919471	+	0.393158i	$0.128617\pi$
$242$	−2.11646	+	2.11646i	−0.136051	+	0.136051i
$243$		0			0
$244$		−	11.6006i		−	0.742653i
$245$	0.0997393	+	1.62326i	0.00637211	+	0.103706i
$246$		0			0
$247$	15.5228	−	24.2139i	0.987694	−	1.54069i
$248$	−1.33763			−0.0849393
$249$		0			0
$250$	9.21933	+	6.32487i	0.583082	+	0.400020i
$251$	8.23530			0.519807			0.259904	−	0.965635i	$-0.416309\pi$
$251$	8.23530			0.519807			0.259904	+	0.965635i	$0.416309\pi$
$252$		0			0
$253$	−17.1572	+	17.1572i	−1.07867	+	1.07867i
$254$	0.480990	+	0.480990i	0.0301800	+	0.0301800i
$255$		0			0
$256$	1.00000			0.0625000
$257$			22.8434i			1.42493i	0.701707	+	0.712466i	$0.252422\pi$
$257$			22.8434i			1.42493i	−0.701707	+	0.712466i	$0.747578\pi$
$258$		0			0
$259$		−	23.9891i		−	1.49061i
$260$	−7.75561	+	2.20241i	−0.480982	+	0.136587i
$261$		0			0
$262$	4.20725	−	4.20725i	0.259925	−	0.259925i
$263$	6.68091			0.411963			0.205981	−	0.978556i	$-0.433961\pi$
$263$	6.68091			0.411963			0.205981	+	0.978556i	$0.433961\pi$
$264$		0			0
$265$	27.9002	−	1.71430i	1.71390	−	0.105308i
$266$	15.6802	−	15.6802i	0.961414	−	0.961414i
$267$		0			0
$268$	4.45889	+	4.45889i	0.272370	+	0.272370i
$269$		−	27.5684i		−	1.68087i	−0.541910	−	0.840436i	$-0.682299\pi$
$269$		−	27.5684i		−	1.68087i	0.541910	−	0.840436i	$-0.317701\pi$
$270$		0			0
$271$	16.1517	−	16.1517i	0.981146	−	0.981146i	−0.0186793	−	0.999826i	$-0.505946\pi$
$271$	16.1517	−	16.1517i	0.981146	−	0.981146i	0.999826	+	0.0186793i	$0.00594615\pi$
$272$			5.46226i			0.331198i
$273$		0			0
$274$	9.61269			0.580724
$275$	14.7452	+	11.5069i	0.889167	+	0.693891i
$276$		0			0
$277$	−5.66115			−0.340146			−0.170073	−	0.985431i	$-0.554400\pi$
$277$	−5.66115			−0.340146			−0.170073	+	0.985431i	$0.554400\pi$
$278$	6.73238	+	6.73238i	0.403781	+	0.403781i
$279$		0			0
$280$	−6.20413	+	0.381205i	−0.370768	+	0.0227814i
$281$	−20.2028	−	20.2028i	−1.20520	−	1.20520i	−0.972564	−	0.232637i	$-0.925264\pi$
$281$	−20.2028	−	20.2028i	−1.20520	−	1.20520i	−0.232637	−	0.972564i	$-0.574736\pi$
$282$		0			0
$283$	11.2936			0.671334			0.335667	−	0.941981i	$-0.391038\pi$
$283$	11.2936			0.671334			0.335667	+	0.941981i	$0.391038\pi$
$284$	8.97120	+	8.97120i	0.532343	+	0.532343i
$285$		0			0
$286$	−13.1760	+	2.88179i	−0.779111	+	0.170404i
$287$	−20.4395			−1.20651
$288$		0			0
$289$	−12.8363			−0.755074
$290$	4.06204	−	4.59390i	0.238531	−	0.269763i
$291$		0			0
$292$	−7.14966	+	7.14966i	−0.418402	+	0.418402i
$293$	−11.2366	+	11.2366i	−0.656451	+	0.656451i	−0.954539	−	0.298088i	$-0.903651\pi$
$293$	−11.2366	+	11.2366i	−0.656451	+	0.656451i	0.298088	+	0.954539i	$0.403651\pi$
$294$		0			0
$295$	22.9097	+	20.2573i	1.33385	+	1.17943i
$296$	8.62977			0.501595
$297$		0			0
$298$	9.74770			0.564669
$299$	−22.8471	+	4.99701i	−1.32128	+	0.288985i
$300$		0			0
$301$	2.13080	+	2.13080i	0.122817	+	0.122817i
$302$	19.5628			1.12571
$303$		0			0
$304$	5.64075	+	5.64075i	0.323519	+	0.323519i
$305$	−25.8909	+	1.59084i	−1.48251	+	0.0910910i
$306$		0			0
$307$	6.11744	+	6.11744i	0.349141	+	0.349141i	0.859789	−	0.510649i	$-0.170595\pi$
$307$	6.11744	+	6.11744i	0.349141	+	0.349141i	−0.510649	+	0.859789i	$0.670595\pi$
$308$	−10.3985			−0.592511
$309$		0			0
$310$	0.183434	+	2.98539i	0.0104183	+	0.169559i
$311$	−16.1716			−0.917008			−0.458504	−	0.888692i	$-0.651614\pi$
$311$	−16.1716			−0.917008			−0.458504	+	0.888692i	$0.651614\pi$
$312$		0			0
$313$		−	14.4637i		−	0.817536i	−0.912638	−	0.408768i	$-0.865959\pi$
$313$		−	14.4637i		−	0.817536i	0.912638	−	0.408768i	$-0.134041\pi$
$314$	−0.321049	+	0.321049i	−0.0181179	+	0.0181179i
$315$		0			0
$316$		−	17.7477i		−	0.998386i
$317$	−20.8873	−	20.8873i	−1.17315	−	1.17315i	−0.981455	−	0.191694i	$-0.938602\pi$
$317$	−20.8873	−	20.8873i	−1.17315	−	1.17315i	−0.191694	−	0.981455i	$-0.561398\pi$
$318$		0			0
$319$	7.25395	−	7.25395i	0.406143	−	0.406143i
$320$	−0.137134	−	2.23186i	−0.00766602	−	0.124765i
$321$		0			0
$322$	−18.0310			−1.00483
$323$	−30.8112	+	30.8112i	−1.71438	+	1.71438i
$324$		0			0
$325$	5.97901	+	17.0074i	0.331656	+	0.943400i
$326$			2.48671i			0.137726i
$327$		0			0
$328$		−	7.35287i		−	0.405994i
$329$	−0.426850			−0.0235330
$330$		0			0
$331$	11.0069	+	11.0069i	0.604993	+	0.604993i	0.941633	−	0.336640i	$-0.109291\pi$
$331$	11.0069	+	11.0069i	0.604993	+	0.604993i	−0.336640	+	0.941633i	$0.609291\pi$
$332$	−1.82503	+	1.82503i	−0.100161	+	0.100161i
$333$		0			0
$334$	−10.2508			−0.560897
$335$	9.34015	−	10.5631i	0.510307	−	0.577123i
$336$		0			0
$337$	−6.28780			−0.342518			−0.171259	−	0.985226i	$-0.554784\pi$
$337$	−6.28780			−0.342518			−0.171259	+	0.985226i	$0.554784\pi$
$338$	−12.1905	−	4.51560i	−0.663078	−	0.245616i
$339$		0			0
$340$	12.1910	−	0.749061i	0.661149	−	0.0406235i
$341$			5.00371i			0.270966i
$342$		0			0
$343$	12.3297	−	12.3297i	0.665742	−	0.665742i
$344$	−0.766529	+	0.766529i	−0.0413285	+	0.0413285i
$345$		0			0
$346$	1.02342	−	1.02342i	0.0550194	−	0.0550194i
$347$	−23.0734			−1.23864			−0.619322	−	0.785137i	$-0.712592\pi$
$347$	−23.0734			−1.23864			−0.619322	+	0.785137i	$0.712592\pi$
$348$		0			0
$349$	−7.85542	+	7.85542i	−0.420491	+	0.420491i	−0.885373	−	0.464882i	$-0.846097\pi$
$349$	−7.85542	+	7.85542i	−0.420491	+	0.420491i	0.464882	+	0.885373i	$0.346097\pi$
$350$	1.70159	+	13.7945i	0.0909540	+	0.737345i
$351$		0			0
$352$		−	3.74074i		−	0.199382i
$353$	5.37052	+	5.37052i	0.285844	+	0.285844i	0.835434	−	0.549590i	$-0.185216\pi$
$353$	5.37052	+	5.37052i	0.285844	+	0.285844i	−0.549590	+	0.835434i	$0.685216\pi$
$354$		0			0
$355$	18.7922	−	21.2527i	0.997386	−	1.12798i
$356$	−2.49913	+	2.49913i	−0.132454	+	0.132454i
$357$		0			0
$358$	1.23799	+	1.23799i	0.0654296	+	0.0654296i
$359$	0.806713	+	0.806713i	0.0425767	+	0.0425767i	0.728075	−	0.685498i	$-0.240415\pi$
$359$	0.806713	+	0.806713i	0.0425767	+	0.0425767i	−0.685498	+	0.728075i	$0.740415\pi$
$360$		0			0
$361$			44.6361i			2.34927i
$362$	−5.83696	+	5.83696i	−0.306784	+	0.306784i
$363$		0			0
$364$	−8.43775	−	5.40920i	−0.442258	−	0.283519i
$365$	16.9375	+	14.9766i	0.886549	+	0.783909i
$366$		0			0
$367$			30.3706i			1.58533i	0.609658	+	0.792665i	$0.291307\pi$
$367$			30.3706i			1.58533i	−0.609658	+	0.792665i	$0.708693\pi$
$368$		−	6.48642i		−	0.338128i
$369$		0			0
$370$	−1.18343	−	19.2604i	−0.0615238	−	1.00130i
$371$	24.5720	+	24.5720i	1.27571	+	1.27571i
$372$		0			0
$373$			14.3157i			0.741237i	0.928785	+	0.370619i	$0.120854\pi$
$373$			14.3157i			0.741237i	−0.928785	+	0.370619i	$0.879146\pi$
$374$	20.4329			1.05656
$375$		0			0
$376$		−	0.153554i		−	0.00791895i
$377$	9.65956	−	2.11270i	0.497493	−	0.108810i
$378$		0			0
$379$	−24.9955	−	24.9955i	−1.28393	−	1.28393i	−0.938412	−	0.345519i	$-0.887703\pi$
$379$	−24.9955	−	24.9955i	−1.28393	−	1.28393i	−0.345519	−	0.938412i	$-0.612297\pi$
$380$	11.8158	−	13.3629i	0.606139	−	0.685502i
$381$		0			0
$382$	−0.410212	+	0.410212i	−0.0209883	+	0.0209883i
$383$	0.385931	+	0.385931i	0.0197201	+	0.0197201i	0.716898	−	0.697178i	$-0.245561\pi$
$383$	0.385931	+	0.385931i	0.0197201	+	0.0197201i	−0.697178	+	0.716898i	$0.745561\pi$
$384$		0			0
$385$	1.42599	+	23.2080i	0.0726752	+	1.18279i
$386$		−	22.7696i		−	1.15894i
$387$		0			0
$388$	0.837007	+	0.837007i	0.0424926	+	0.0424926i
$389$	13.6949			0.694360			0.347180	−	0.937798i	$-0.387139\pi$
$389$	13.6949			0.694360			0.347180	+	0.937798i	$0.387139\pi$
$390$		0			0
$391$	35.4305			1.79180
$392$	−0.514288	−	0.514288i	−0.0259755	−	0.0259755i
$393$		0			0
$394$		−	23.9916i		−	1.20868i
$395$	−39.6104	+	2.43381i	−1.99301	+	0.122458i
$396$		0			0
$397$	7.91126	+	7.91126i	0.397055	+	0.397055i	0.877193	−	0.480138i	$-0.159414\pi$
$397$	7.91126	+	7.91126i	0.397055	+	0.397055i	−0.480138	+	0.877193i	$0.659414\pi$
$398$	10.0102	−	10.0102i	0.501767	−	0.501767i
$399$		0			0
$400$	−4.96239	+	0.612127i	−0.248119	+	0.0306063i
$401$	16.8138	+	16.8138i	0.839642	+	0.839642i	0.988812	−	0.149169i	$-0.0476600\pi$
$401$	16.8138	+	16.8138i	0.839642	+	0.839642i	−0.149169	+	0.988812i	$0.547660\pi$
$402$		0			0
$403$	−2.60288	+	4.06020i	−0.129659	+	0.202253i
$404$		−	12.7572i		−	0.634694i
$405$		0			0
$406$	7.62336			0.378341
$407$		−	32.2817i		−	1.60015i
$408$		0			0
$409$	−6.83881	−	6.83881i	−0.338157	−	0.338157i	0.517516	−	0.855673i	$-0.326857\pi$
$409$	−6.83881	−	6.83881i	−0.338157	−	0.338157i	−0.855673	+	0.517516i	$0.826857\pi$
$410$	−16.4106	+	1.00833i	−0.810460	+	0.0497977i
$411$		0			0
$412$		−	3.99740i		−	0.196938i
$413$			38.0175i			1.87072i
$414$		0			0
$415$	4.32347	+	3.82293i	0.212231	+	0.187660i
$416$	1.94589	−	3.03537i	0.0954052	−	0.148822i
$417$		0			0
$418$	21.1006	−	21.1006i	1.03206	−	1.03206i
$419$		−	14.3477i		−	0.700932i	−0.936576	−	0.350466i	$-0.886023\pi$
$419$		−	14.3477i		−	0.700932i	0.936576	−	0.350466i	$-0.113977\pi$
$420$		0			0
$421$	−17.4452	−	17.4452i	−0.850228	−	0.850228i	0.139933	−	0.990161i	$-0.455311\pi$
$421$	−17.4452	−	17.4452i	−0.850228	−	0.850228i	−0.990161	+	0.139933i	$0.955311\pi$
$422$	5.35959	+	5.35959i	0.260901	+	0.260901i
$423$		0			0
$424$	−8.83947	+	8.83947i	−0.429283	+	0.429283i
$425$	−3.34359	−	27.1058i	−0.162188	−	1.31483i
$426$		0			0
$427$	−22.8024	−	22.8024i	−1.10348	−	1.10348i
$428$		−	4.67233i		−	0.225846i
$429$		0			0
$430$	1.81590	+	1.60567i	0.0875705	+	0.0774321i
$431$	−5.54989	+	5.54989i	−0.267329	+	0.267329i	−0.828023	−	0.560694i	$-0.810534\pi$
$431$	−5.54989	+	5.54989i	−0.267329	+	0.267329i	0.560694	+	0.828023i	$0.310534\pi$
$432$		0			0
$433$	−4.13768			−0.198844			−0.0994220	−	0.995045i	$-0.531699\pi$
$433$	−4.13768			−0.198844			−0.0994220	+	0.995045i	$0.531699\pi$
$434$	−2.62926	+	2.62926i	−0.126209	+	0.126209i
$435$		0			0
$436$	10.2433	−	10.2433i	0.490565	−	0.490565i
$437$	36.5883	−	36.5883i	1.75026	−	1.75026i
$438$		0			0
$439$			33.0671i			1.57821i	0.614262	+	0.789103i	$0.289454\pi$
$439$			33.0671i			1.57821i	−0.614262	+	0.789103i	$0.710546\pi$
$440$	−8.34880	+	0.512982i	−0.398013	+	0.0244555i
$441$		0			0
$442$	16.5800	+	10.6290i	0.788630	+	0.505568i
$443$	23.9819			1.13941			0.569707	−	0.821848i	$-0.307057\pi$
$443$	23.9819			1.13941			0.569707	+	0.821848i	$0.307057\pi$
$444$		0			0
$445$	5.92042	+	5.23499i	0.280655	+	0.248162i
$446$	−27.2141			−1.28862
$447$		0			0
$448$	1.96562	−	1.96562i	0.0928668	−	0.0928668i
$449$	−0.714936	−	0.714936i	−0.0337399	−	0.0337399i	0.690036	−	0.723775i	$-0.257595\pi$
$449$	−0.714936	−	0.714936i	−0.0337399	−	0.0337399i	−0.723775	+	0.690036i	$0.757595\pi$
$450$		0			0
$451$	−27.5051			−1.29517
$452$			2.65269i			0.124772i
$453$		0			0
$454$			17.5214i			0.822322i
$455$	−10.9155	+	19.5737i	−0.511725	+	0.917627i
$456$		0			0
$457$	−16.5043	+	16.5043i	−0.772038	+	0.772038i	−0.978462	−	0.206425i	$-0.933817\pi$
$457$	−16.5043	+	16.5043i	−0.772038	+	0.772038i	0.206425	+	0.978462i	$0.433817\pi$
$458$	9.59672			0.448425
$459$		0			0
$460$	−14.4768	+	0.889508i	−0.674983	+	0.0414735i
$461$	−5.07529	+	5.07529i	−0.236380	+	0.236380i	−0.815349	−	0.578969i	$-0.803455\pi$
$461$	−5.07529	+	5.07529i	−0.236380	+	0.236380i	0.578969	+	0.815349i	$0.303455\pi$
$462$		0			0
$463$	−10.7995	−	10.7995i	−0.501895	−	0.501895i	0.410132	−	0.912026i	$-0.365483\pi$
$463$	−10.7995	−	10.7995i	−0.501895	−	0.501895i	−0.912026	+	0.410132i	$0.865483\pi$
$464$			2.74241i			0.127313i
$465$		0			0
$466$	6.38795	−	6.38795i	0.295916	−	0.295916i
$467$			9.77705i			0.452428i	0.974078	+	0.226214i	$0.0726349\pi$
$467$			9.77705i			0.452428i	−0.974078	+	0.226214i	$0.927365\pi$
$468$		0			0
$469$	17.5290			0.809412
$470$	−0.342711	+	0.0210575i	−0.0158081	+	0.000971309i
$471$		0			0
$472$	−13.6763			−0.629504
$473$	2.86738	+	2.86738i	0.131842	+	0.131842i
$474$		0			0
$475$	−31.4444	−	24.5387i	−1.44277	−	1.12591i
$476$	10.7367	+	10.7367i	0.492117	+	0.492117i
$477$		0			0
$478$	3.57216			0.163387
$479$	7.77169	+	7.77169i	0.355098	+	0.355098i	0.862002	−	0.506904i	$-0.169210\pi$
$479$	7.77169	+	7.77169i	0.355098	+	0.355098i	−0.506904	+	0.862002i	$0.669210\pi$
$480$		0			0
$481$	16.7926	−	26.1946i	0.765677	−	1.19437i
$482$	11.5550			0.526314
$483$		0			0
$484$	−2.99312			−0.136051
$485$	1.75330	−	1.98286i	0.0796132	−	0.0900372i
$486$		0			0
$487$	−15.3878	+	15.3878i	−0.697288	+	0.697288i	−0.963825	−	0.266537i	$-0.914121\pi$
$487$	−15.3878	+	15.3878i	−0.697288	+	0.697288i	0.266537	+	0.963825i	$0.414121\pi$
$488$	8.20287	−	8.20287i	0.371326	−	0.371326i
$489$		0			0
$490$	−1.07729	+	1.21835i	−0.0486671	+	0.0550392i
$491$	11.3600			0.512669			0.256334	−	0.966588i	$-0.417485\pi$
$491$	11.3600			0.512669			0.256334	+	0.966588i	$0.417485\pi$
$492$		0			0
$493$	−14.9798			−0.674654
$494$	28.0981	−	6.14550i	1.26419	−	0.276499i
$495$		0			0
$496$	−0.945844	−	0.945844i	−0.0424697	−	0.0424697i
$497$	35.2679			1.58198
$498$		0			0
$499$	5.53890	+	5.53890i	0.247955	+	0.247955i	0.820131	−	0.572176i	$-0.193901\pi$
$499$	5.53890	+	5.53890i	0.247955	+	0.247955i	−0.572176	+	0.820131i	$0.693901\pi$
$500$	2.04669	+	10.9914i	0.0915309	+	0.491551i
$501$		0			0
$502$	5.82323	+	5.82323i	0.259904	+	0.259904i
$503$	8.56557			0.381920			0.190960	−	0.981598i	$-0.438840\pi$
$503$	8.56557			0.381920			0.190960	+	0.981598i	$0.438840\pi$
$504$		0			0
$505$	−28.4723	+	1.74944i	−1.26700	+	0.0778492i
$506$	−24.2640			−1.07867
$507$		0			0
$508$			0.680223i			0.0301800i
$509$	−9.27756	+	9.27756i	−0.411221	+	0.411221i	−0.882164	−	0.470943i	$-0.843914\pi$
$509$	−9.27756	+	9.27756i	−0.411221	+	0.411221i	0.470943	+	0.882164i	$0.343914\pi$
$510$		0			0
$511$			28.1070i			1.24338i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−16.1527	+	16.1527i	−0.712466	+	0.712466i
$515$	−8.92162	+	0.548178i	−0.393134	+	0.0241556i
$516$		0			0
$517$	−0.574406			−0.0252623
$518$	16.9628	−	16.9628i	0.745304	−	0.745304i
$519$		0			0
$520$	−7.04138	−	3.92671i	−0.308785	−	0.172197i
$521$			0.281155i			0.0123176i	0.999981	+	0.00615880i	$0.00196042\pi$
$521$			0.281155i			0.0123176i	−0.999981	+	0.00615880i	$0.998040\pi$
$522$		0			0
$523$			29.1354i			1.27400i	0.770863	+	0.637001i	$0.219825\pi$
$523$			29.1354i			1.27400i	−0.770863	+	0.637001i	$0.780175\pi$
$524$	5.94995			0.259925
$525$		0			0
$526$	4.72412	+	4.72412i	0.205981	+	0.205981i
$527$	5.16645	−	5.16645i	0.225054	−	0.225054i
$528$		0			0
$529$	−19.0737			−0.829291
$530$	20.9406	+	18.5163i	0.909603	+	0.804295i
$531$		0			0
$532$	22.1751			0.961414
$533$	−22.3187	−	14.3079i	−0.966730	−	0.619743i
$534$		0			0
$535$	−10.4280	+	0.640735i	−0.450841	+	0.0277014i
$536$			6.30582i			0.272370i
$537$		0			0
$538$	19.4938	−	19.4938i	0.840436	−	0.840436i
$539$	−1.92382	+	1.92382i	−0.0828647	+	0.0828647i
$540$		0			0
$541$	−19.7024	+	19.7024i	−0.847074	+	0.847074i	−0.989767	−	0.142693i	$-0.954424\pi$
$541$	−19.7024	+	19.7024i	−0.847074	+	0.847074i	0.142693	+	0.989767i	$0.454424\pi$
$542$	22.8420			0.981146
$543$		0			0
$544$	−3.86240	+	3.86240i	−0.165599	+	0.165599i
$545$	−24.2663	−	21.4569i	−1.03945	−	0.919112i
$546$		0			0
$547$			23.1700i			0.990679i	0.868699	+	0.495340i	$0.164956\pi$
$547$			23.1700i			0.990679i	−0.868699	+	0.495340i	$0.835044\pi$
$548$	6.79720	+	6.79720i	0.290362	+	0.290362i
$549$		0			0
$550$	2.28981	+	18.5630i	0.0976377	+	0.791529i
$551$	−15.4692	+	15.4692i	−0.659012	+	0.659012i
$552$		0			0
$553$	−34.8852	−	34.8852i	−1.48347	−	1.48347i
$554$	−4.00304	−	4.00304i	−0.170073	−	0.170073i
$555$		0			0
$556$			9.52103i			0.403781i
$557$	21.7682	−	21.7682i	0.922349	−	0.922349i	−0.0748464	−	0.997195i	$-0.523847\pi$
$557$	21.7682	−	21.7682i	0.922349	−	0.922349i	0.997195	+	0.0748464i	$0.0238466\pi$
$558$		0			0
$559$	0.835119	+	3.81828i	0.0353218	+	0.161496i
$560$	−4.65654	−	4.11743i	−0.196775	−	0.173993i
$561$		0			0
$562$		−	28.5711i		−	1.20520i
$563$		−	19.8520i		−	0.836660i	−0.908295	−	0.418330i	$-0.862616\pi$
$563$		−	19.8520i		−	0.836660i	0.908295	−	0.418330i	$-0.137384\pi$
$564$		0			0
$565$	5.92043	−	0.363774i	0.249074	−	0.0153041i
$566$	7.98577	+	7.98577i	0.335667	+	0.335667i
$567$		0			0
$568$			12.6872i			0.532343i
$569$	29.6118			1.24139			0.620696	−	0.784052i	$-0.286850\pi$
$569$	29.6118			1.24139			0.620696	+	0.784052i	$0.286850\pi$
$570$		0			0
$571$		−	2.28081i		−	0.0954491i	−0.998861	−	0.0477246i	$-0.984803\pi$
$571$		−	2.28081i		−	0.0954491i	0.998861	−	0.0477246i	$-0.0151970\pi$
$572$	−11.3545	−	7.27908i	−0.474757	−	0.304353i
$573$		0			0
$574$	−14.4529	−	14.4529i	−0.603254	−	0.603254i
$575$	3.97051	+	32.1882i	0.165582	+	1.34234i
$576$		0			0
$577$	−14.7512	+	14.7512i	−0.614100	+	0.614100i	−0.944012	−	0.329912i	$-0.892981\pi$
$577$	−14.7512	+	14.7512i	−0.614100	+	0.614100i	0.329912	+	0.944012i	$0.392981\pi$
$578$	−9.07661	−	9.07661i	−0.377537	−	0.377537i
$579$		0			0
$580$	6.12067	−	0.376077i	0.254147	−	0.0156158i
$581$			7.17461i			0.297653i
$582$		0			0
$583$	33.0661	+	33.0661i	1.36946	+	1.36946i
$584$	−10.1111			−0.418402
$585$		0			0
$586$	−15.8910			−0.656451
$587$	6.03336	+	6.03336i	0.249023	+	0.249023i	0.820570	−	0.571546i	$-0.193656\pi$
$587$	6.03336	+	6.03336i	0.249023	+	0.249023i	−0.571546	+	0.820570i	$0.693656\pi$
$588$		0			0
$589$		−	10.6705i		−	0.439672i
$590$	1.87549	+	30.5237i	0.0772127	+	1.25664i
$591$		0			0
$592$	6.10217	+	6.10217i	0.250798	+	0.250798i
$593$	−3.28068	+	3.28068i	−0.134721	+	0.134721i	−0.771252	−	0.636530i	$-0.780369\pi$
$593$	−3.28068	+	3.28068i	−0.134721	+	0.134721i	0.636530	+	0.771252i	$0.280369\pi$
$594$		0			0
$595$	22.4905	−	25.4352i	0.922019	−	1.04274i
$596$	6.89267	+	6.89267i	0.282335	+	0.282335i
$597$		0			0
$598$	−19.6887	−	12.6219i	−0.805132	−	0.516147i
$599$		−	5.00194i		−	0.204374i	−0.994765	−	0.102187i	$-0.967416\pi$
$599$		−	5.00194i		−	0.204374i	0.994765	−	0.102187i	$-0.0325840\pi$
$600$		0			0
$601$	−15.7393			−0.642021			−0.321010	−	0.947076i	$-0.604022\pi$
$601$	−15.7393			−0.642021			−0.321010	+	0.947076i	$0.604022\pi$
$602$			3.01341i			0.122817i
$603$		0			0
$604$	13.8330	+	13.8330i	0.562857	+	0.562857i
$605$	0.410459	+	6.68023i	0.0166875	+	0.271590i
$606$		0			0
$607$			0.932239i			0.0378384i	0.999821	+	0.0189192i	$0.00602253\pi$
$607$			0.932239i			0.0378384i	−0.999821	+	0.0189192i	$0.993977\pi$
$608$			7.97722i			0.323519i
$609$		0			0
$610$	−19.4325	−	17.1828i	−0.786801	−	0.695709i
$611$	−0.466094	−	0.298800i	−0.0188562	−	0.0120881i
$612$		0			0
$613$	−13.2136	+	13.2136i	−0.533691	+	0.533691i	−0.921669	−	0.387978i	$-0.873174\pi$
$613$	−13.2136	+	13.2136i	−0.533691	+	0.533691i	0.387978	+	0.921669i	$0.373174\pi$
$614$			8.65137i			0.349141i
$615$		0			0
$616$	−7.35287	−	7.35287i	−0.296255	−	0.296255i
$617$	22.6516	+	22.6516i	0.911920	+	0.911920i	0.996423	−	0.0845030i	$-0.0269303\pi$
$617$	22.6516	+	22.6516i	0.911920	+	0.911920i	−0.0845030	+	0.996423i	$0.526930\pi$
$618$		0			0
$619$	11.9427	−	11.9427i	0.480016	−	0.480016i	−0.425120	−	0.905137i	$-0.639768\pi$
$619$	11.9427	−	11.9427i	0.480016	−	0.480016i	0.905137	+	0.425120i	$0.139768\pi$
$620$	−1.98128	+	2.24070i	−0.0795703	+	0.0899886i
$621$		0			0
$622$	−11.4351	−	11.4351i	−0.458504	−	0.458504i
$623$			9.82466i			0.393617i
$624$		0			0
$625$	24.2506	−	6.07522i	0.970024	−	0.243009i
$626$	10.2274	−	10.2274i	0.408768	−	0.408768i
$627$		0			0
$628$	−0.454032			−0.0181179
$629$	−33.3316	+	33.3316i	−1.32902	+	1.32902i
$630$		0			0
$631$	−1.54916	+	1.54916i	−0.0616710	+	0.0616710i	−0.737270	−	0.675599i	$-0.763885\pi$
$631$	−1.54916	+	1.54916i	−0.0616710	+	0.0616710i	0.675599	+	0.737270i	$0.263885\pi$
$632$	12.5495	−	12.5495i	0.499193	−	0.499193i
$633$		0			0
$634$		−	29.5391i		−	1.17315i
$635$	1.51816	−	0.0932816i	0.0602464	−	0.00370177i
$636$		0			0
$637$	−2.56181	+	0.560308i	−0.101503	+	0.0222002i
$638$	10.2586			0.406143
$639$		0			0
$640$	1.48119	−	1.67513i	0.0585493	−	0.0662154i
$641$	−14.2386			−0.562389			−0.281195	−	0.959651i	$-0.590731\pi$
$641$	−14.2386			−0.562389			−0.281195	+	0.959651i	$0.590731\pi$
$642$		0			0
$643$	−3.35321	+	3.35321i	−0.132238	+	0.132238i	−0.770128	−	0.637890i	$-0.779808\pi$
$643$	−3.35321	+	3.35321i	−0.132238	+	0.132238i	0.637890	+	0.770128i	$0.279808\pi$
$644$	−12.7498	−	12.7498i	−0.502414	−	0.502414i
$645$		0			0
$646$	−43.5737			−1.71438
$647$			14.8434i			0.583553i	0.956487	+	0.291777i	$0.0942464\pi$
$647$			14.8434i			0.583553i	−0.956487	+	0.291777i	$0.905754\pi$
$648$		0			0
$649$			51.1596i			2.00819i
$650$	−7.79824	+	16.2538i	−0.305872	+	0.637528i
$651$		0			0
$652$	−1.75837	+	1.75837i	−0.0688630	+	0.0688630i
$653$	−17.0479			−0.667134			−0.333567	−	0.942726i	$-0.608252\pi$
$653$	−17.0479			−0.667134			−0.333567	+	0.942726i	$0.608252\pi$
$654$		0			0
$655$	−0.815940	−	13.2795i	−0.0318814	−	0.518871i
$656$	5.19926	−	5.19926i	0.202997	−	0.202997i
$657$		0			0
$658$	−0.301829	−	0.301829i	−0.0117665	−	0.0117665i
$659$			24.7994i			0.966047i	0.875607	+	0.483023i	$0.160461\pi$
$659$			24.7994i			0.966047i	−0.875607	+	0.483023i	$0.839539\pi$
$660$		0			0
$661$	−18.8061	+	18.8061i	−0.731474	+	0.731474i	−0.970912	−	0.239437i	$-0.923037\pi$
$661$	−18.8061	+	18.8061i	−0.731474	+	0.731474i	0.239437	+	0.970912i	$0.423037\pi$
$662$			15.5661i			0.604993i
$663$		0			0
$664$	−2.58098			−0.100161
$665$	−3.04096	−	49.4918i	−0.117923	−	1.91921i
$666$		0			0
$667$	17.7884			0.688771
$668$	−7.24838	−	7.24838i	−0.280448	−	0.280448i
$669$		0			0
$670$	14.0737	−	0.864742i	0.543715	−	0.0334079i
$671$	−30.6848	−	30.6848i	−1.18457	−	1.18457i
$672$		0			0
$673$	−11.7856			−0.454302			−0.227151	−	0.973860i	$-0.572941\pi$
$673$	−11.7856			−0.454302			−0.227151	+	0.973860i	$0.572941\pi$
$674$	−4.44614	−	4.44614i	−0.171259	−	0.171259i
$675$		0			0
$676$	−5.42700	−	11.8130i	−0.208731	−	0.454347i
$677$	29.8845			1.14856			0.574278	−	0.818661i	$-0.305283\pi$
$677$	29.8845			1.14856			0.574278	+	0.818661i	$0.305283\pi$
$678$		0			0
$679$	3.29047			0.126277
$680$	9.15000	+	8.09067i	0.350886	+	0.310263i
$681$		0			0
$682$	−3.53816	+	3.53816i	−0.135483	+	0.135483i
$683$	5.38081	−	5.38081i	0.205891	−	0.205891i	−0.596627	−	0.802518i	$-0.703493\pi$
$683$	5.38081	−	5.38081i	0.205891	−	0.205891i	0.802518	+	0.596627i	$0.203493\pi$
$684$		0			0
$685$	14.2383	−	16.1025i	0.544016	−	0.615246i
$686$	17.4368			0.665742
$687$		0			0
$688$	−1.08404			−0.0413285
$689$	9.63045	+	44.0318i	0.366891	+	1.67748i
$690$		0			0
$691$	−28.0782	−	28.0782i	−1.06814	−	1.06814i	−0.997502	−	0.0706416i	$-0.977495\pi$
$691$	−28.0782	−	28.0782i	−1.06814	−	1.06814i	−0.0706416	−	0.997502i	$-0.522505\pi$
$692$	1.44733			0.0550194
$693$		0			0
$694$	−16.3153	−	16.3153i	−0.619322	−	0.619322i
$695$	21.2496	−	1.30565i	0.806043	−	0.0495263i
$696$		0			0
$697$	28.3997	+	28.3997i	1.07572	+	1.07572i
$698$	−11.1092			−0.420491
$699$		0			0
$700$	−8.55096	+	10.9574i	−0.323196	+	0.414150i
$701$	−33.9767			−1.28328			−0.641641	−	0.767005i	$-0.721746\pi$
$701$	−33.9767			−1.28328			−0.641641	+	0.767005i	$0.721746\pi$
$702$		0			0
$703$			68.8416i			2.59641i
$704$	2.64510	−	2.64510i	0.0996910	−	0.0996910i
$705$		0			0
$706$			7.59507i			0.285844i
$707$	−25.0758	−	25.0758i	−0.943072	−	0.943072i
$708$		0			0
$709$	14.0038	−	14.0038i	0.525923	−	0.525923i	−0.393431	−	0.919354i	$-0.628712\pi$
$709$	14.0038	−	14.0038i	0.525923	−	0.525923i	0.919354	+	0.393431i	$0.128712\pi$
$710$	28.3160	−	1.73984i	1.06268	−	0.0652951i
$711$		0			0
$712$	−3.53430			−0.132454
$713$	−6.13515	+	6.13515i	−0.229763	+	0.229763i
$714$		0			0
$715$	−14.6888	+	26.3399i	−0.549329	+	0.985058i
$716$			1.75078i			0.0654296i
$717$		0			0
$718$			1.14087i			0.0425767i
$719$	−28.6769			−1.06947			−0.534734	−	0.845021i	$-0.679588\pi$
$719$	−28.6769			−1.06947			−0.534734	+	0.845021i	$0.679588\pi$
$720$		0			0
$721$	−7.85736	−	7.85736i	−0.292623	−	0.292623i
$722$	−31.5625	+	31.5625i	−1.17463	+	1.17463i
$723$		0			0
$724$	−8.25471			−0.306784
$725$	−1.67870	−	13.6089i	−0.0623455	−	0.505422i
$726$		0			0
$727$	27.5424			1.02149			0.510746	−	0.859732i	$-0.329369\pi$
$727$	27.5424			1.02149			0.510746	+	0.859732i	$0.329369\pi$
$728$	−2.14151	−	9.79127i	−0.0793695	−	0.362889i
$729$		0			0
$730$	1.38658	+	22.5666i	0.0513196	+	0.835229i
$731$		−	5.92128i		−	0.219006i
$732$		0			0
$733$	13.4697	−	13.4697i	0.497515	−	0.497515i	−0.413148	−	0.910664i	$-0.635571\pi$
$733$	13.4697	−	13.4697i	0.497515	−	0.497515i	0.910664	+	0.413148i	$0.135571\pi$
$734$	−21.4752	+	21.4752i	−0.792665	+	0.792665i
$735$		0			0
$736$	4.58659	−	4.58659i	0.169064	−	0.169064i
$737$	23.5884			0.868891
$738$		0			0
$739$	1.37770	−	1.37770i	0.0506797	−	0.0506797i	−0.681313	−	0.731992i	$-0.738591\pi$
$739$	1.37770	−	1.37770i	0.0506797	−	0.0506797i	0.731992	+	0.681313i	$0.238591\pi$
$740$	12.7824	−	14.4560i	0.469889	−	0.531413i
$741$		0			0
$742$			34.7501i			1.27571i
$743$	13.8710	+	13.8710i	0.508876	+	0.508876i	0.914181	−	0.405305i	$-0.132835\pi$
$743$	13.8710	+	13.8710i	0.508876	+	0.508876i	−0.405305	+	0.914181i	$0.632835\pi$
$744$		0			0
$745$	14.4382	−	16.3287i	0.528976	−	0.598237i
$746$	−10.1227	+	10.1227i	−0.370619	+	0.370619i
$747$		0			0
$748$	14.4482	+	14.4482i	0.528279	+	0.528279i
$749$	−9.18402	−	9.18402i	−0.335577	−	0.335577i
$750$		0			0
$751$			38.2290i			1.39500i	0.716586	+	0.697498i	$0.245704\pi$
$751$			38.2290i			1.39500i	−0.716586	+	0.697498i	$0.754296\pi$
$752$	0.108579	−	0.108579i	0.00395947	−	0.00395947i
$753$		0			0
$754$	8.32424	+	5.33644i	0.303151	+	0.194342i
$755$	28.9764	−	32.7703i	1.05456	−	1.19263i
$756$		0			0
$757$		−	21.6549i		−	0.787061i	−0.919311	−	0.393531i	$-0.871254\pi$
$757$		−	21.6549i		−	0.787061i	0.919311	−	0.393531i	$-0.128746\pi$
$758$		−	35.3489i		−	1.28393i
$759$		0			0
$760$	17.8040	−	1.09395i	0.645820	−	0.0396816i
$761$	16.0417	+	16.0417i	0.581511	+	0.581511i	0.935318	−	0.353807i	$-0.115113\pi$
$761$	16.0417	+	16.0417i	0.581511	+	0.581511i	−0.353807	+	0.935318i	$0.615113\pi$
$762$		0			0
$763$		−	40.2688i		−	1.45783i
$764$	−0.580127			−0.0209883
$765$		0			0
$766$			0.545789i			0.0197201i
$767$	−26.6127	+	41.5128i	−0.960928	+	1.49894i
$768$		0			0
$769$	1.04097	+	1.04097i	0.0375384	+	0.0375384i	0.725627	−	0.688088i	$-0.241550\pi$
$769$	1.04097	+	1.04097i	0.0375384	+	0.0375384i	−0.688088	+	0.725627i	$0.741550\pi$
$770$	−15.4022	+	17.4189i	−0.555058	+	0.627733i
$771$		0			0
$772$	16.1005	−	16.1005i	0.579471	−	0.579471i
$773$	9.70713	+	9.70713i	0.349141	+	0.349141i	0.859790	−	0.510648i	$-0.170595\pi$
$773$	9.70713	+	9.70713i	0.349141	+	0.349141i	−0.510648	+	0.859790i	$0.670595\pi$
$774$		0			0
$775$	5.27262	+	4.11467i	0.189398	+	0.147803i
$776$			1.18371i			0.0424926i
$777$		0			0
$778$	9.68377	+	9.68377i	0.347180	+	0.347180i
$779$	58.6555			2.10155
$780$		0			0
$781$	47.4595			1.69823
$782$	25.0532	+	25.0532i	0.895899	+	0.895899i
$783$		0			0
$784$		−	0.727313i		−	0.0259755i
$785$	0.0622632	+	1.01334i	0.00222227	+	0.0361675i
$786$		0			0
$787$	14.1991	+	14.1991i	0.506144	+	0.506144i	0.913341	−	0.407196i	$-0.133494\pi$
$787$	14.1991	+	14.1991i	0.506144	+	0.506144i	−0.407196	+	0.913341i	$0.633494\pi$
$788$	16.9646	−	16.9646i	0.604339	−	0.604339i
$789$		0			0
$790$	−29.7297	−	26.2878i	−1.05774	−	0.935278i
$791$	5.21418	+	5.21418i	0.185395	+	0.185395i
$792$		0			0
$793$	−8.93688	−	40.8607i	−0.317358	−	1.45101i
$794$			11.1882i			0.397055i
$795$		0			0
$796$	14.1566			0.501767
$797$		−	0.200056i		−	0.00708635i	−0.999994	−	0.00354318i	$-0.998872\pi$
$797$		−	0.200056i		−	0.00708635i	0.999994	−	0.00354318i	$-0.00112783\pi$
$798$		0			0
$799$	0.593087	+	0.593087i	0.0209819	+	0.0209819i
$800$	−3.94178	−	3.07610i	−0.139363	−	0.108757i
$801$		0			0
$802$			23.7783i			0.839642i
$803$			37.8231i			1.33475i
$804$		0			0
$805$	−26.7074	+	30.2043i	−0.941312	+	1.06456i
$806$	−4.71150	+	1.03048i	−0.165956	+	0.0362971i
$807$		0			0
$808$	9.02070	−	9.02070i	0.317347	−	0.317347i
$809$			16.7938i			0.590438i	0.955430	+	0.295219i	$0.0953926\pi$
$809$			16.7938i			0.590438i	−0.955430	+	0.295219i	$0.904607\pi$
$810$		0			0
$811$	−9.73805	−	9.73805i	−0.341949	−	0.341949i	0.515151	−	0.857100i	$-0.327736\pi$
$811$	−9.73805	−	9.73805i	−0.341949	−	0.341949i	−0.857100	+	0.515151i	$0.827736\pi$
$812$	5.39053	+	5.39053i	0.189171	+	0.189171i
$813$		0			0
$814$	22.8266	−	22.8266i	0.800073	−	0.800073i
$815$	4.16556	+	3.68330i	0.145913	+	0.129020i
$816$		0			0
$817$	−6.11477	−	6.11477i	−0.213929	−	0.213929i
$818$		−	9.67153i		−	0.338157i
$819$		0			0
$820$	−12.3170	−	10.8910i	−0.430129	−	0.380331i
$821$	5.09187	−	5.09187i	0.177708	−	0.177708i	−0.612648	−	0.790356i	$-0.709896\pi$
$821$	5.09187	−	5.09187i	0.177708	−	0.177708i	0.790356	+	0.612648i	$0.209896\pi$
$822$		0			0
$823$	−38.3300			−1.33610			−0.668050	−	0.744116i	$-0.732871\pi$
$823$	−38.3300			−1.33610			−0.668050	+	0.744116i	$0.732871\pi$
$824$	2.82659	−	2.82659i	0.0984688	−	0.0984688i
$825$		0			0
$826$	−26.8825	+	26.8825i	−0.935361	+	0.935361i
$827$	−21.1668	+	21.1668i	−0.736041	+	0.736041i	−0.971809	−	0.235768i	$-0.924239\pi$
$827$	−21.1668	+	21.1668i	−0.736041	+	0.736041i	0.235768	+	0.971809i	$0.424239\pi$
$828$		0			0
$829$			2.65197i			0.0921068i	0.998939	+	0.0460534i	$0.0146644\pi$
$829$			2.65197i			0.0921068i	−0.998939	+	0.0460534i	$0.985336\pi$
$830$	0.353939	+	5.76037i	0.0122854	+	0.199945i
$831$		0			0
$832$	3.52229	−	0.770380i	0.122113	−	0.0267081i
$833$	3.97277			0.137648
$834$		0			0
$835$	−15.1834	+	17.1714i	−0.525442	+	0.594240i
$836$	29.8407			1.03206
$837$		0			0
$838$	10.1454	−	10.1454i	0.350466	−	0.350466i
$839$	−1.62957	−	1.62957i	−0.0562591	−	0.0562591i	0.678417	−	0.734677i	$-0.262666\pi$
$839$	−1.62957	−	1.62957i	−0.0562591	−	0.0562591i	−0.734677	+	0.678417i	$0.762666\pi$
$840$		0			0
$841$	21.4792			0.740662
$842$		−	24.6713i		−	0.850228i
$843$		0			0
$844$			7.57960i			0.260901i
$845$	−25.6208	+	13.7323i	−0.881382	+	0.472404i
$846$		0			0
$847$	−5.88334	+	5.88334i	−0.202154	+	0.202154i
$848$	−12.5009			−0.429283
$849$		0			0
$850$	16.8024	−	21.5310i	0.576319	−	0.738507i
$851$	39.5813	−	39.5813i	1.35683	−	1.35683i
$852$		0			0
$853$	15.3255	+	15.3255i	0.524735	+	0.524735i	0.918998	−	0.394263i	$-0.129000\pi$
$853$	15.3255	+	15.3255i	0.524735	+	0.524735i	−0.394263	+	0.918998i	$0.629000\pi$
$854$		−	32.2474i		−	1.10348i
$855$		0			0
$856$	3.30384	−	3.30384i	0.112923	−	0.112923i
$857$			12.8053i			0.437422i	0.975790	+	0.218711i	$0.0701852\pi$
$857$			12.8053i			0.437422i	−0.975790	+	0.218711i	$0.929815\pi$
$858$		0			0
$859$	25.3058			0.863422			0.431711	−	0.902012i	$-0.357910\pi$
$859$	25.3058			0.863422			0.431711	+	0.902012i	$0.357910\pi$
$860$	0.148658	+	2.41941i	0.00506919	+	0.0825013i
$861$		0			0
$862$	−7.84872			−0.267329
$863$	−38.9537	−	38.9537i	−1.32600	−	1.32600i	−0.908829	−	0.417169i	$-0.863022\pi$
$863$	−38.9537	−	38.9537i	−1.32600	−	1.32600i	−0.417169	−	0.908829i	$-0.636978\pi$
$864$		0			0
$865$	−0.198478	−	3.23025i	−0.00674847	−	0.109832i
$866$	−2.92578	−	2.92578i	−0.0994220	−	0.0994220i
$867$		0			0
$868$	−3.71834			−0.126209
$869$	−46.9445	−	46.9445i	−1.59248	−	1.59248i
$870$		0			0
$871$	19.1405	+	12.2705i	0.648553	+	0.415769i
$872$	14.4862			0.490565
$873$		0			0
$874$	51.7437			1.75026
$875$	25.6279	+	17.5819i	0.866382	+	0.594377i
$876$		0			0
$877$	23.8344	−	23.8344i	0.804831	−	0.804831i	−0.179015	−	0.983846i	$-0.557291\pi$
$877$	23.8344	−	23.8344i	0.804831	−	0.804831i	0.983846	+	0.179015i	$0.0572912\pi$
$878$	−23.3819	+	23.3819i	−0.789103	+	0.789103i
$879$		0			0
$880$	−6.26623	−	5.54076i	−0.211234	−	0.186779i
$881$	30.9019			1.04111			0.520555	−	0.853828i	$-0.325725\pi$
$881$	30.9019			1.04111			0.520555	+	0.853828i	$0.325725\pi$
$882$		0			0
$883$	2.78159			0.0936080			0.0468040	−	0.998904i	$-0.485096\pi$
$883$	2.78159			0.0936080			0.0468040	+	0.998904i	$0.485096\pi$
$884$	4.20802	+	19.2396i	0.141531	+	0.647099i
$885$		0			0
$886$	16.9577	+	16.9577i	0.569707	+	0.569707i
$887$	9.96887			0.334722			0.167361	−	0.985896i	$-0.446476\pi$
$887$	9.96887			0.334722			0.167361	+	0.985896i	$0.446476\pi$
$888$		0			0
$889$	1.33706	+	1.33706i	0.0448435	+	0.0448435i
$890$	0.484672	+	7.88806i	0.0162463	+	0.264408i
$891$		0			0
$892$	−19.2433	−	19.2433i	−0.644312	−	0.644312i
$893$	1.22494			0.0409909
$894$		0			0
$895$	3.90749	−	0.240091i	0.130613	−	0.00802535i
$896$	2.77980			0.0928668
$897$		0			0
$898$		−	1.01107i		−	0.0337399i
$899$	2.59389	−	2.59389i	0.0865112	−	0.0865112i
$900$		0			0
$901$		−	68.2831i		−	2.27484i
$902$	−19.4491	−	19.4491i	−0.647583	−	0.647583i
$903$		0			0
$904$	−1.87574	+	1.87574i	−0.0623860	+	0.0623860i
$905$	1.13200	+	18.4233i	0.0376290	+	0.612413i
$906$		0			0
$907$	13.0402			0.432994			0.216497	−	0.976283i	$-0.430537\pi$
$907$	13.0402			0.432994			0.216497	+	0.976283i	$0.430537\pi$
$908$	−12.3895	+	12.3895i	−0.411161	+	0.411161i
$909$		0			0
$910$	−21.5591	+	6.12226i	−0.714676	+	0.202951i
$911$			44.0523i			1.45952i	0.683705	+	0.729759i	$0.260368\pi$
$911$			44.0523i			1.45952i	−0.683705	+	0.729759i	$0.739632\pi$
$912$		0			0
$913$			9.65475i			0.319526i
$914$	−23.3406			−0.772038
$915$		0			0
$916$	6.78591	+	6.78591i	0.224213	+	0.224213i
$917$	11.6953	−	11.6953i	0.386214	−	0.386214i
$918$		0			0
$919$	28.3309			0.934551			0.467275	−	0.884112i	$-0.345236\pi$
$919$	28.3309			0.934551			0.467275	+	0.884112i	$0.345236\pi$
$920$	−10.8656	−	9.60765i	−0.358228	−	0.316755i
$921$		0			0
$922$	−7.17755			−0.236380
$923$	38.5104	+	24.6879i	1.26758	+	0.812612i
$924$		0			0
$925$	−34.0166	−	26.5460i	−1.11846	−	0.872828i
$926$		−	15.2728i		−	0.501895i
$927$		0			0
$928$	−1.93918	+	1.93918i	−0.0636566	+	0.0636566i
$929$	−8.70178	+	8.70178i	−0.285496	+	0.285496i	−0.835296	−	0.549800i	$-0.814704\pi$
$929$	−8.70178	+	8.70178i	−0.285496	+	0.285496i	0.549800	+	0.835296i	$0.314704\pi$
$930$		0			0
$931$	4.10259	−	4.10259i	0.134457	−	0.134457i
$932$	9.03392			0.295916
$933$		0			0
$934$	−6.91342	+	6.91342i	−0.226214	+	0.226214i
$935$	30.2651	−	34.2277i	0.989773	−	1.11937i
$936$		0			0
$937$			45.8610i			1.49821i	0.662449	+	0.749107i	$0.269517\pi$
$937$			45.8610i			1.49821i	−0.662449	+	0.749107i	$0.730483\pi$
$938$	12.3948	+	12.3948i	0.404706	+	0.404706i
$939$		0			0
$940$	−0.257223	−	0.227443i	−0.00838970	−	0.00741839i
$941$	29.6637	−	29.6637i	0.967008	−	0.967008i	−0.0324645	−	0.999473i	$-0.510336\pi$
$941$	29.6637	−	29.6637i	0.967008	−	0.967008i	0.999473	+	0.0324645i	$0.0103356\pi$
$942$		0			0
$943$	−33.7246	−	33.7246i	−1.09822	−	1.09822i
$944$	−9.67063	−	9.67063i	−0.314752	−	0.314752i
$945$		0			0
$946$			4.05509i			0.131842i
$947$	24.8855	−	24.8855i	0.808669	−	0.808669i	−0.175764	−	0.984432i	$-0.556239\pi$
$947$	24.8855	−	24.8855i	0.808669	−	0.808669i	0.984432	+	0.175764i	$0.0562394\pi$
$948$		0			0
$949$	−19.6752	+	30.6911i	−0.638684	+	0.996276i
$950$	−4.88307	−	39.5861i	−0.158428	−	1.28434i
$951$		0			0
$952$			15.1840i			0.492117i
$953$		−	30.5350i		−	0.989127i	−0.869142	−	0.494563i	$-0.835328\pi$
$953$		−	30.5350i		−	0.989127i	0.869142	−	0.494563i	$-0.164672\pi$
$954$		0			0
$955$	0.0795551	+	1.29476i	0.00257434	+	0.0418975i
$956$	2.52590	+	2.52590i	0.0816935	+	0.0816935i
$957$		0			0
$958$			10.9908i			0.355098i
$959$	26.7214			0.862879
$960$		0			0
$961$		−	29.2108i		−	0.942282i
$962$	30.3965	−	6.64821i	0.980024	−	0.214347i
$963$		0			0
$964$	8.17058	+	8.17058i	0.263157	+	0.263157i
$965$	−38.1420	−	33.7262i	−1.22784	−	1.08568i
$966$		0			0
$967$	−20.6880	+	20.6880i	−0.665281	+	0.665281i	−0.956620	−	0.291339i	$-0.905899\pi$
$967$	−20.6880	+	20.6880i	−0.665281	+	0.665281i	0.291339	+	0.956620i	$0.405899\pi$
$968$	−2.11646	−	2.11646i	−0.0680256	−	0.0680256i
$969$		0			0
$970$	2.64187	−	0.162326i	0.0848252	−	0.00521198i
$971$		−	4.98561i		−	0.159996i	−0.996795	−	0.0799979i	$-0.974509\pi$
$971$		−	4.98561i		−	0.159996i	0.996795	−	0.0799979i	$-0.0254914\pi$
$972$		0			0
$973$	18.7147	+	18.7147i	0.599966	+	0.599966i
$974$	−21.7617			−0.697288
$975$		0			0
$976$	11.6006			0.371326
$977$	−43.1731	−	43.1731i	−1.38123	−	1.38123i	−0.842440	−	0.538791i	$-0.818881\pi$
$977$	−43.1731	−	43.1731i	−1.38123	−	1.38123i	−0.538791	−	0.842440i	$-0.681119\pi$
$978$		0			0
$979$			13.2209i			0.422542i
$980$	−1.62326	+	0.0997393i	−0.0518532	+	0.00318605i
$981$		0			0
$982$	8.03272	+	8.03272i	0.256334	+	0.256334i
$983$	−3.53204	+	3.53204i	−0.112655	+	0.112655i	−0.761187	−	0.648532i	$-0.775383\pi$
$983$	−3.53204	+	3.53204i	−0.112655	+	0.112655i	0.648532	+	0.761187i	$0.275383\pi$
$984$		0			0
$985$	−40.1891	−	35.5362i	−1.28053	−	1.13228i
$986$	−10.5923	−	10.5923i	−0.337327	−	0.337327i
$987$		0			0
$988$	24.2139	+	15.5228i	0.770346	+	0.493847i
$989$			7.03151i			0.223589i
$990$		0			0
$991$	7.85099			0.249395			0.124697	−	0.992195i	$-0.460204\pi$
$991$	7.85099			0.249395			0.124697	+	0.992195i	$0.460204\pi$
$992$		−	1.33763i		−	0.0424697i
$993$		0			0
$994$	24.9382	+	24.9382i	0.790991	+	0.790991i
$995$	−1.94135	−	31.5955i	−0.0615448	−	1.00164i
$996$		0			0
$997$		−	45.6170i		−	1.44470i	−0.691525	−	0.722352i	$-0.743061\pi$
$997$		−	45.6170i		−	1.44470i	0.691525	−	0.722352i	$-0.256939\pi$
$998$			7.83319i			0.247955i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.q.c.359.8	yes	24
3.2	odd	2	inner	1170.2.q.c.359.4	✓	24
5.4	even	2		1170.2.q.d.359.5	yes	24
13.5	odd	4		1170.2.q.d.629.9	yes	24
15.14	odd	2		1170.2.q.d.359.9	yes	24
39.5	even	4		1170.2.q.d.629.5	yes	24
65.44	odd	4	inner	1170.2.q.c.629.4	yes	24
195.44	even	4	inner	1170.2.q.c.629.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.q.c.359.4	✓	24	3.2	odd	2	inner
1170.2.q.c.359.8	yes	24	1.1	even	1	trivial
1170.2.q.c.629.4	yes	24	65.44	odd	4	inner
1170.2.q.c.629.8	yes	24	195.44	even	4	inner
1170.2.q.d.359.5	yes	24	5.4	even	2
1170.2.q.d.359.9	yes	24	15.14	odd	2
1170.2.q.d.629.5	yes	24	39.5	even	4
1170.2.q.d.629.9	yes	24	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(2.23186 - 0.137134i) q^{5} +(1.96562 + 1.96562i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.67513 + 1.48119i) q^{10} +(2.64510 + 2.64510i) q^{11} +(0.770380 + 3.52229i) q^{13} +2.77980i q^{14} -1.00000 q^{16} -5.46226i q^{17} +(-5.64075 - 5.64075i) q^{19} +(0.137134 + 2.23186i) q^{20} +3.74074i q^{22} +6.48642i q^{23} +(4.96239 - 0.612127i) q^{25} +(-1.94589 + 3.03537i) q^{26} +(-1.96562 + 1.96562i) q^{28} -2.74241i q^{29} +(0.945844 + 0.945844i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.86240 - 3.86240i) q^{34} +(4.65654 + 4.11743i) q^{35} +(-6.10217 - 6.10217i) q^{37} -7.97722i q^{38} +(-1.48119 + 1.67513i) q^{40} +(-5.19926 + 5.19926i) q^{41} +1.08404 q^{43} +(-2.64510 + 2.64510i) q^{44} +(-4.58659 + 4.58659i) q^{46} +(-0.108579 + 0.108579i) q^{47} +0.727313i q^{49} +(3.94178 + 3.07610i) q^{50} +(-3.52229 + 0.770380i) q^{52} +12.5009 q^{53} +(6.26623 + 5.54076i) q^{55} -2.77980 q^{56} +(1.93918 - 1.93918i) q^{58} +(9.67063 + 9.67063i) q^{59} -11.6006 q^{61} +1.33763i q^{62} -1.00000i q^{64} +(2.20241 + 7.75561i) q^{65} +(4.45889 - 4.45889i) q^{67} +5.46226 q^{68} +(0.381205 + 6.20413i) q^{70} +(8.97120 - 8.97120i) q^{71} +(7.14966 + 7.14966i) q^{73} -8.62977i q^{74} +(5.64075 - 5.64075i) q^{76} +10.3985i q^{77} -17.7477 q^{79} +(-2.23186 + 0.137134i) q^{80} -7.35287 q^{82} +(1.82503 + 1.82503i) q^{83} +(-0.749061 - 12.1910i) q^{85} +(0.766529 + 0.766529i) q^{86} -3.74074 q^{88} +(2.49913 + 2.49913i) q^{89} +(-5.40920 + 8.43775i) q^{91} -6.48642 q^{92} -0.153554 q^{94} +(-13.3629 - 11.8158i) q^{95} +(0.837007 - 0.837007i) q^{97} +(-0.514288 + 0.514288i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) \) 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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