LMFDB - Embedded newform 675.2.u.e.49.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.17
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.860644 + 1.02568i) q^{2} +(1.52697 - 0.817526i) q^{3} +(0.0359939 - 0.204131i) q^{4} +(2.15270 + 0.862581i) q^{6} +(-0.340915 + 0.0601126i) q^{7} +(2.55944 - 1.47769i) q^{8} +(1.66330 - 2.49668i) q^{9} +(-0.377953 - 0.137564i) q^{11} +(-0.111921 - 0.341129i) q^{12} +(-0.483102 + 0.575738i) q^{13} +(-0.355063 - 0.297933i) q^{14} +(3.32884 + 1.21160i) q^{16} +(1.16198 + 0.670872i) q^{17} +(3.99230 - 0.442749i) q^{18} +(-1.87243 - 3.24314i) q^{19} +(-0.471425 + 0.370498i) q^{21} +(-0.184187 - 0.506050i) q^{22} +(3.04247 + 0.536470i) q^{23} +(2.70014 - 4.34880i) q^{24} -1.00630 q^{26} +(0.498713 - 5.17216i) q^{27} +0.0717552i q^{28} +(-3.79094 + 3.18098i) q^{29} +(-0.774172 + 4.39054i) q^{31} +(-0.399363 - 1.09724i) q^{32} +(-0.689586 + 0.0989303i) q^{33} +(0.311958 + 1.76920i) q^{34} +(-0.449783 - 0.429397i) q^{36} +(2.16657 + 1.25087i) q^{37} +(1.71492 - 4.71170i) q^{38} +(-0.267003 + 1.27409i) q^{39} +(1.73862 + 1.45887i) q^{41} +(-0.785740 - 0.164663i) q^{42} +(-2.92375 + 8.03293i) q^{43} +(-0.0416850 + 0.0722005i) q^{44} +(2.06824 + 3.58230i) q^{46} +(12.1171 - 2.13658i) q^{47} +(6.07356 - 0.871334i) q^{48} +(-6.46524 + 2.35315i) q^{49} +(2.32278 + 0.0744513i) q^{51} +(0.100137 + 0.119339i) q^{52} -10.1571i q^{53} +(5.73418 - 3.93988i) q^{54} +(-0.783723 + 0.657622i) q^{56} +(-5.51051 - 3.42144i) q^{57} +(-6.52530 - 1.15059i) q^{58} +(-12.7550 + 4.64243i) q^{59} +(2.31667 + 13.1385i) q^{61} +(-5.16956 + 2.98465i) q^{62} +(-0.416963 + 0.951143i) q^{63} +(4.32418 - 7.48970i) q^{64} +(-0.694958 - 0.622148i) q^{66} +(7.89073 - 9.40381i) q^{67} +(0.178770 - 0.213050i) q^{68} +(5.08436 - 1.66813i) q^{69} +(-1.14446 + 1.98226i) q^{71} +(0.567785 - 8.84795i) q^{72} +(-10.8000 + 6.23540i) q^{73} +(0.581658 + 3.29875i) q^{74} +(-0.729423 + 0.265488i) q^{76} +(0.137119 + 0.0241778i) q^{77} +(-1.53659 + 0.822676i) q^{78} +(-9.11223 + 7.64607i) q^{79} +(-3.46686 - 8.30547i) q^{81} +3.03883i q^{82} +(-3.11961 - 3.71780i) q^{83} +(0.0586617 + 0.109568i) q^{84} +(-10.7555 + 3.91468i) q^{86} +(-3.18814 + 7.95646i) q^{87} +(-1.17062 + 0.206412i) q^{88} +(0.197409 + 0.341923i) q^{89} +(0.130088 - 0.225318i) q^{91} +(0.219021 - 0.601754i) q^{92} +(2.40725 + 7.33715i) q^{93} +(12.6200 + 10.5894i) q^{94} +(-1.50684 - 1.34897i) q^{96} +(-5.07158 + 13.9340i) q^{97} +(-7.97784 - 4.60601i) q^{98} +(-0.972102 + 0.714819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.860644	+	1.02568i	0.608567	+	0.725262i	0.979060	−	0.203573i	$-0.0652555\pi$
$2$	0.860644	+	1.02568i	0.608567	+	0.725262i	−0.370492	+	0.928836i	$0.620811\pi$
$3$	1.52697	−	0.817526i	0.881599	−	0.471999i
$3$	1.52697	−	0.817526i	0.881599	−	0.471999i
$4$	0.0359939	−	0.204131i	0.0179969	−	0.102066i
$5$		0			0
$5$		0			0
$6$	2.15270	+	0.862581i	0.878836	+	0.352147i
$7$	−0.340915	+	0.0601126i	−0.128854	+	0.0227204i	−0.237703	−	0.971338i	$-0.576395\pi$
$7$	−0.340915	+	0.0601126i	−0.128854	+	0.0227204i	0.108849	+	0.994058i	$0.465283\pi$
$8$	2.55944	−	1.47769i	0.904897	−	0.522443i
$9$	1.66330	−	2.49668i	0.554434	−	0.832228i
$10$		0			0
$11$	−0.377953	−	0.137564i	−0.113957	−	0.0414770i	0.284412	−	0.958702i	$-0.408202\pi$
$11$	−0.377953	−	0.137564i	−0.113957	−	0.0414770i	−0.398369	+	0.917225i	$0.630424\pi$
$12$	−0.111921	−	0.341129i	−0.0323088	−	0.0984755i
$13$	−0.483102	+	0.575738i	−0.133988	+	0.159681i	−0.828867	−	0.559446i	$-0.811014\pi$
$13$	−0.483102	+	0.575738i	−0.133988	+	0.159681i	0.694878	+	0.719127i	$0.255458\pi$
$14$	−0.355063	−	0.297933i	−0.0948945	−	0.0796260i
$15$		0			0
$16$	3.32884	+	1.21160i	0.832209	+	0.302899i
$17$	1.16198	+	0.670872i	0.281823	+	0.162710i	0.634248	−	0.773129i	$-0.281310\pi$
$17$	1.16198	+	0.670872i	0.281823	+	0.162710i	−0.352426	+	0.935840i	$0.614643\pi$
$18$	3.99230	−	0.442749i	0.940994	−	0.104357i
$19$	−1.87243	−	3.24314i	−0.429565	−	0.744028i	0.567270	−	0.823532i	$-0.308000\pi$
$19$	−1.87243	−	3.24314i	−0.429565	−	0.744028i	−0.996835	+	0.0795040i	$0.974666\pi$
$20$		0			0
$21$	−0.471425	+	0.370498i	−0.102873	+	0.0808492i
$22$	−0.184187	−	0.506050i	−0.0392688	−	0.107890i
$23$	3.04247	+	0.536470i	0.634399	+	0.111862i	0.481594	−	0.876395i	$-0.340058\pi$
$23$	3.04247	+	0.536470i	0.634399	+	0.111862i	0.152806	+	0.988256i	$0.451169\pi$
$24$	2.70014	−	4.34880i	0.551164	−	0.887696i
$25$		0			0
$26$	−1.00630			−0.197352
$27$	0.498713	−	5.17216i	0.0959773	−	0.995384i
$28$			0.0717552i			0.0135605i
$29$	−3.79094	+	3.18098i	−0.703960	+	0.590693i	−0.922897	−	0.385046i	$-0.874185\pi$
$29$	−3.79094	+	3.18098i	−0.703960	+	0.590693i	0.218937	+	0.975739i	$0.429741\pi$
$30$		0			0
$31$	−0.774172	+	4.39054i	−0.139045	+	0.788565i	0.832912	+	0.553406i	$0.186672\pi$
$31$	−0.774172	+	4.39054i	−0.139045	+	0.788565i	−0.971957	+	0.235159i	$0.924439\pi$
$32$	−0.399363	−	1.09724i	−0.0705980	−	0.193966i
$33$	−0.689586	+	0.0989303i	−0.120041	+	0.0172216i
$34$	0.311958	+	1.76920i	0.0535003	+	0.303415i
$35$		0			0
$36$	−0.449783	−	0.429397i	−0.0749638	−	0.0715662i
$37$	2.16657	+	1.25087i	0.356181	+	0.205641i	0.667404	−	0.744696i	$-0.267405\pi$
$37$	2.16657	+	1.25087i	0.356181	+	0.205641i	−0.311223	+	0.950337i	$0.600739\pi$
$38$	1.71492	−	4.71170i	0.278196	−	0.764338i
$39$	−0.267003	+	1.27409i	−0.0427546	+	0.204017i
$40$		0			0
$41$	1.73862	+	1.45887i	0.271526	+	0.227838i	0.768376	−	0.639999i	$-0.221065\pi$
$41$	1.73862	+	1.45887i	0.271526	+	0.227838i	−0.496849	+	0.867837i	$0.665510\pi$
$42$	−0.785740	−	0.164663i	−0.121242	−	0.0254080i
$43$	−2.92375	+	8.03293i	−0.445867	+	1.22501i	0.489709	+	0.871886i	$0.337103\pi$
$43$	−2.92375	+	8.03293i	−0.445867	+	1.22501i	−0.935576	+	0.353124i	$0.885119\pi$
$44$	−0.0416850	+	0.0722005i	−0.00628425	+	0.0108846i
$45$		0			0
$46$	2.06824	+	3.58230i	0.304946	+	0.528181i
$47$	12.1171	−	2.13658i	1.76746	−	0.311652i	0.807103	−	0.590411i	$-0.201034\pi$
$47$	12.1171	−	2.13658i	1.76746	−	0.311652i	0.960361	+	0.278760i	$0.0899233\pi$
$48$	6.07356	−	0.871334i	0.876643	−	0.125766i
$49$	−6.46524	+	2.35315i	−0.923606	+	0.336165i
$50$		0			0
$51$	2.32278	+	0.0744513i	0.325254	+	0.0104253i
$52$	0.100137	+	0.119339i	0.0138866	+	0.0165494i
$53$		−	10.1571i		−	1.39519i	−0.716494	−	0.697593i	$-0.754254\pi$
$53$		−	10.1571i		−	1.39519i	0.716494	−	0.697593i	$-0.245746\pi$
$54$	5.73418	−	3.93988i	0.780323	−	0.536149i
$55$		0			0
$56$	−0.783723	+	0.657622i	−0.104729	+	0.0878784i
$57$	−5.51051	−	3.42144i	−0.729884	−	0.453180i
$58$	−6.52530	−	1.15059i	−0.856814	−	0.151079i
$59$	−12.7550	+	4.64243i	−1.66055	+	0.604392i	−0.990450	−	0.137874i	$-0.955973\pi$
$59$	−12.7550	+	4.64243i	−1.66055	+	0.604392i	−0.670105	+	0.742266i	$0.733751\pi$
$60$		0			0
$61$	2.31667	+	13.1385i	0.296619	+	1.68221i	0.660546	+	0.750785i	$0.270325\pi$
$61$	2.31667	+	13.1385i	0.296619	+	1.68221i	−0.363927	+	0.931427i	$0.618564\pi$
$62$	−5.16956	+	2.98465i	−0.656535	+	0.379051i
$63$	−0.416963	+	0.951143i	−0.0525324	+	0.119833i
$64$	4.32418	−	7.48970i	0.540522	−	0.936212i
$65$		0			0
$66$	−0.694958	−	0.622148i	−0.0855435	−	0.0765811i
$67$	7.89073	−	9.40381i	0.964006	−	1.14886i	−0.0248058	−	0.999692i	$-0.507897\pi$
$67$	7.89073	−	9.40381i	0.964006	−	1.14886i	0.988812	−	0.149166i	$-0.0476588\pi$
$68$	0.178770	−	0.213050i	0.0216791	−	0.0258361i
$69$	5.08436	−	1.66813i	0.612085	−	0.200819i
$70$		0			0
$71$	−1.14446	+	1.98226i	−0.135822	+	0.235251i	−0.925911	−	0.377741i	$-0.876701\pi$
$71$	−1.14446	+	1.98226i	−0.135822	+	0.235251i	0.790089	+	0.612992i	$0.210034\pi$
$72$	0.567785	−	8.84795i	0.0669141	−	1.04274i
$73$	−10.8000	+	6.23540i	−1.26405	+	0.729799i	−0.973855	−	0.227169i	$-0.927053\pi$
$73$	−10.8000	+	6.23540i	−1.26405	+	0.729799i	−0.290194	+	0.956968i	$0.593720\pi$
$74$	0.581658	+	3.29875i	0.0676164	+	0.383471i
$75$		0			0
$76$	−0.729423	+	0.265488i	−0.0836705	+	0.0304536i
$77$	0.137119	+	0.0241778i	0.0156262	+	0.00275532i
$78$	−1.53659	+	0.822676i	−0.173985	+	0.0931498i
$79$	−9.11223	+	7.64607i	−1.02521	+	0.860250i	−0.990273	−	0.139140i	$-0.955566\pi$
$79$	−9.11223	+	7.64607i	−1.02521	+	0.860250i	−0.0349328	+	0.999390i	$0.511122\pi$
$80$		0			0
$81$	−3.46686	−	8.30547i	−0.385207	−	0.922830i
$82$			3.03883i			0.335583i
$83$	−3.11961	−	3.71780i	−0.342421	−	0.408082i	0.567160	−	0.823608i	$-0.308042\pi$
$83$	−3.11961	−	3.71780i	−0.342421	−	0.408082i	−0.909581	+	0.415526i	$0.863598\pi$
$84$	0.0586617	+	0.109568i	0.00640052	+	0.0119549i
$85$		0			0
$86$	−10.7555	+	3.91468i	−1.15979	+	0.422130i
$87$	−3.18814	+	7.95646i	−0.341804	+	0.853022i
$88$	−1.17062	+	0.206412i	−0.124789	+	0.0220036i
$89$	0.197409	+	0.341923i	0.0209253	+	0.0362438i	0.876298	−	0.481769i	$-0.160005\pi$
$89$	0.197409	+	0.341923i	0.0209253	+	0.0362438i	−0.855373	+	0.518012i	$0.826672\pi$
$90$		0			0
$91$	0.130088	−	0.225318i	0.0136369	−	0.0236198i
$92$	0.219021	−	0.601754i	0.0228345	−	0.0627372i
$93$	2.40725	+	7.33715i	0.249620	+	0.760827i
$94$	12.6200	+	10.5894i	1.30165	+	1.09221i
$95$		0			0
$96$	−1.50684	−	1.34897i	−0.153791	−	0.137678i
$97$	−5.07158	+	13.9340i	−0.514941	+	1.41479i	0.361089	+	0.932531i	$0.382405\pi$
$97$	−5.07158	+	13.9340i	−0.514941	+	1.41479i	−0.876030	+	0.482257i	$0.839817\pi$
$98$	−7.97784	−	4.60601i	−0.805884	−	0.465277i
$99$	−0.972102	+	0.714819i	−0.0976999	+	0.0718420i
$100$		0			0
$101$	−2.32075	−	13.1616i	−0.230924	−	1.30963i	−0.851031	−	0.525116i	$-0.824022\pi$
$101$	−2.32075	−	13.1616i	−0.230924	−	1.30963i	0.620107	−	0.784517i	$-0.287089\pi$
$102$	1.92272	+	2.44649i	0.190378	+	0.242239i
$103$	2.46244	+	6.76551i	0.242632	+	0.666625i	0.999908	+	0.0135311i	$0.00430721\pi$
$103$	2.46244	+	6.76551i	0.242632	+	0.666625i	−0.757277	+	0.653094i	$0.773471\pi$
$104$	−0.385705	+	2.18744i	−0.0378215	+	0.214496i
$105$		0			0
$106$	10.4179	−	8.74166i	1.01188	−	0.849065i
$107$			8.94985i			0.865215i	0.901582	+	0.432607i	$0.142406\pi$
$107$			8.94985i			0.865215i	−0.901582	+	0.432607i	$0.857594\pi$
$108$	−1.03785	−	0.287969i	−0.0998672	−	0.0277098i
$109$	7.74154			0.741505			0.370752	−	0.928732i	$-0.379100\pi$
$109$	7.74154			0.741505			0.370752	+	0.928732i	$0.379100\pi$
$110$		0			0
$111$	4.33091	+	0.138817i	0.411072	+	0.0131760i
$112$	−1.20768	−	0.212947i	−0.114115	−	0.0201216i
$113$	1.41376	+	3.88427i	0.132995	+	0.365401i	0.988258	−	0.152793i	$-0.0488267\pi$
$113$	1.41376	+	3.88427i	0.132995	+	0.365401i	−0.855263	+	0.518194i	$0.826604\pi$
$114$	−1.23330	−	8.59663i	−0.115509	−	0.805148i
$115$		0			0
$116$	0.512886	+	0.888345i	0.0476203	+	0.0824808i
$117$	0.633893	+	2.16378i	0.0586034	+	0.200041i
$118$	−15.7391	−	9.08698i	−1.44890	−	0.836524i
$119$	−0.436466	−	0.158861i	−0.0400108	−	0.0145627i
$120$		0			0
$121$	−8.30256	−	6.96668i	−0.754779	−	0.633334i
$122$	−11.4820	+	13.6837i	−1.03953	+	1.23887i
$123$	3.84749	+	0.806296i	0.346917	+	0.0727013i
$124$	0.868382	+	0.316065i	0.0779830	+	0.0283835i
$125$		0			0
$126$	−1.33442	+	0.390927i	−0.118880	+	0.0348266i
$127$	1.96206	−	1.13280i	0.174105	−	0.100519i	−0.410415	−	0.911899i	$-0.634616\pi$
$127$	1.96206	−	1.13280i	0.174105	−	0.100519i	0.584520	+	0.811379i	$0.301283\pi$
$128$	9.10374	−	1.60524i	0.804665	−	0.141884i
$129$	2.10265	+	14.6563i	0.185128	+	1.29042i
$130$		0			0
$131$	−0.0505139	+	0.286479i	−0.00441342	+	0.0250298i	−0.986935	−	0.161119i	$-0.948490\pi$
$131$	−0.0505139	+	0.286479i	−0.00441342	+	0.0250298i	0.982522	+	0.186149i	$0.0596007\pi$
$132$	−0.00462607	+	0.144327i	−0.000402648	+	0.0125620i
$133$	0.833294	+	0.993081i	0.0722557	+	0.0861110i
$134$	16.4364			1.41989
$135$		0			0
$136$	3.96537			0.340027
$137$	6.21395	+	7.40550i	0.530893	+	0.632694i	0.963120	−	0.269071i	$-0.0867165\pi$
$137$	6.21395	+	7.40550i	0.530893	+	0.632694i	−0.432227	+	0.901765i	$0.642272\pi$
$138$	6.08678	+	3.77924i	0.518141	+	0.321710i
$139$	−0.516258	+	2.92785i	−0.0437885	+	0.248337i	−0.998843	−	0.0480940i	$-0.984685\pi$
$139$	−0.516258	+	2.92785i	−0.0437885	+	0.248337i	0.955054	+	0.296431i	$0.0957964\pi$
$140$		0			0
$141$	16.7558	−	13.1686i	1.41109	−	1.10899i
$142$	−3.01813	+	0.532177i	−0.253275	+	0.0446593i
$143$	0.261790	−	0.151145i	0.0218920	−	0.0126393i
$144$	8.56183	−	6.29580i	0.713486	−	0.524650i
$145$		0			0
$146$	−15.6905	−	5.71087i	−1.29855	−	0.472635i
$147$	−7.94849	+	8.87871i	−0.655580	+	0.732304i
$148$	0.333324	−	0.397240i	0.0273991	−	0.0326530i
$149$	−12.7219	−	10.6749i	−1.04221	−	0.874522i	−0.0499614	−	0.998751i	$-0.515910\pi$
$149$	−12.7219	−	10.6749i	−1.04221	−	0.874522i	−0.992254	+	0.124229i	$0.960354\pi$
$150$		0			0
$151$	−8.75299	−	3.18583i	−0.712308	−	0.259259i	−0.0396512	−	0.999214i	$-0.512625\pi$
$151$	−8.75299	−	3.18583i	−0.712308	−	0.259259i	−0.672657	+	0.739955i	$0.734847\pi$
$152$	−9.58473	−	5.53375i	−0.777424	−	0.448846i
$153$	3.60768	−	1.78525i	0.291664	−	0.144329i
$154$	0.0932122	+	0.161448i	0.00751125	+	0.0130099i
$155$		0			0
$156$	0.250470	+	0.100363i	0.0200537	+	0.00803546i
$157$	−5.25541	−	14.4391i	−0.419427	−	1.15237i	−0.952031	−	0.306002i	$-0.901008\pi$
$157$	−5.25541	−	14.4391i	−0.419427	−	1.15237i	0.532603	−	0.846365i	$-0.321214\pi$
$158$	−15.6848	−	2.76565i	−1.24781	−	0.220023i
$159$	−8.30371	−	15.5096i	−0.658527	−	1.23000i
$160$		0			0
$161$	−1.06947			−0.0842864
$162$	5.53499	−	10.7039i	0.434870	−	0.840980i
$163$			4.28453i			0.335590i	0.985822	+	0.167795i	$0.0536647\pi$
$163$			4.28453i			0.335590i	−0.985822	+	0.167795i	$0.946335\pi$
$164$	0.360381	−	0.302396i	0.0281411	−	0.0236131i
$165$		0			0
$166$	1.12839	−	6.39941i	0.0875799	−	0.496690i
$167$	−4.47320	−	12.2900i	−0.346147	−	0.951030i	−0.983572	−	0.180518i	$-0.942223\pi$
$167$	−4.47320	−	12.2900i	−0.346147	−	0.951030i	0.637425	−	0.770512i	$-0.280000\pi$
$168$	−0.659102	+	1.64489i	−0.0508508	+	0.126906i
$169$	2.15934	+	12.2462i	0.166103	+	0.942017i
$170$		0			0
$171$	−11.2115	−	0.719459i	−0.857366	−	0.0550184i
$172$	1.53453	+	0.885964i	0.117007	+	0.0675541i
$173$	0.375420	−	1.03146i	0.0285426	−	0.0784202i	−0.924603	−	0.380932i	$-0.875603\pi$
$173$	0.375420	−	1.03146i	0.0285426	−	0.0784202i	0.953146	+	0.302512i	$0.0978253\pi$
$174$	−10.9046	+	3.57769i	−0.826676	+	0.271224i
$175$		0			0
$176$	−1.09147	−	0.915853i	−0.0822727	−	0.0690350i
$177$	−15.6812	+	17.5164i	−1.17867	+	1.31661i
$178$	−0.180803	+	0.496752i	−0.0135518	+	0.0372331i
$179$	8.45761	−	14.6490i	0.632151	−	1.09492i	−0.354960	−	0.934882i	$-0.615505\pi$
$179$	8.45761	−	14.6490i	0.632151	−	1.09492i	0.987111	−	0.160037i	$-0.0511612\pi$
$180$		0			0
$181$	−1.06581	−	1.84604i	−0.0792210	−	0.137215i	0.823693	−	0.567036i	$-0.191910\pi$
$181$	−1.06581	−	1.84604i	−0.0792210	−	0.137215i	−0.902914	+	0.429821i	$0.858577\pi$
$182$	0.343063	−	0.0604912i	0.0254295	−	0.00448391i
$183$	14.2786	+	18.1682i	1.05550	+	1.34303i
$184$	8.57975	−	3.12277i	0.632508	−	0.230214i
$185$		0			0
$186$	−5.45376	+	8.78373i	−0.399889	+	0.644055i
$187$	−0.346887	−	0.413404i	−0.0253669	−	0.0302311i
$188$		−	2.55039i		−	0.186006i
$189$	0.140893	+	1.79325i	0.0102485	+	0.130440i
$190$		0			0
$191$	10.3330	−	8.67044i	0.747671	−	0.627371i	−0.187214	−	0.982319i	$-0.559946\pi$
$191$	10.3330	−	8.67044i	0.747671	−	0.627371i	0.934886	+	0.354948i	$0.115501\pi$
$192$	0.479884	−	14.9717i	0.0346326	−	1.08049i
$193$	9.25860	+	1.63254i	0.666448	+	0.117513i	0.496630	−	0.867963i	$-0.334571\pi$
$193$	9.25860	+	1.63254i	0.666448	+	0.117513i	0.169819	+	0.985475i	$0.445682\pi$
$194$	−18.6566	+	6.79046i	−1.33947	+	0.487527i
$195$		0			0
$196$	0.247644	+	1.40446i	0.0176888	+	0.100318i
$197$	−7.31619	+	4.22400i	−0.521257	+	0.300948i	−0.737449	−	0.675403i	$-0.763970\pi$
$197$	−7.31619	+	4.22400i	−0.521257	+	0.300948i	0.216192	+	0.976351i	$0.430636\pi$
$198$	−1.56981	−	0.381857i	−0.111561	−	0.0271374i
$199$	6.77278	−	11.7308i	0.480109	−	0.831574i	−0.519630	−	0.854391i	$-0.673930\pi$
$199$	6.77278	−	11.7308i	0.480109	−	0.831574i	0.999740	+	0.0228175i	$0.00726365\pi$
$200$		0			0
$201$	4.36108	−	20.8103i	0.307607	−	1.46784i
$202$	11.5022	−	13.7078i	0.809295	−	0.964480i
$203$	1.10117	−	1.31233i	0.0772872	−	0.0921073i
$204$	0.0988035	−	0.471471i	0.00691763	−	0.0330096i
$205$		0			0
$206$	−4.81993	+	8.34836i	−0.335820	+	0.581658i
$207$	6.39994	−	6.70378i	0.444827	−	0.465945i
$208$	−2.30573	+	1.33121i	−0.159874	+	0.0923031i
$209$	0.261552	+	1.48333i	0.0180919	+	0.102604i
$210$		0			0
$211$	−10.4837	+	3.81575i	−0.721726	+	0.262687i	−0.676658	−	0.736297i	$-0.736573\pi$
$211$	−10.4837	+	3.81575i	−0.721726	+	0.262687i	−0.0450677	+	0.998984i	$0.514350\pi$
$212$	−2.07338	−	0.365594i	−0.142401	−	0.0251091i
$213$	−0.127008	+	3.96248i	−0.00870247	+	0.271505i
$214$	−9.17964	+	7.70264i	−0.627508	+	0.526541i
$215$		0			0
$216$	−6.36644	−	13.9748i	−0.433181	−	0.950863i
$217$		−	1.54334i		−	0.104769i
$218$	6.66271	+	7.94031i	0.451256	+	0.537785i
$219$	−11.3938	+	18.3506i	−0.769920	+	1.24002i
$220$		0			0
$221$	−0.947603	+	0.344899i	−0.0637427	+	0.0232004i
$222$	3.58499	+	4.56158i	0.240609	+	0.306153i
$223$	18.9381	−	3.33930i	1.26819	−	0.223616i	0.501231	−	0.865314i	$-0.332881\pi$
$223$	18.9381	−	3.33930i	1.26819	−	0.223616i	0.766957	+	0.641698i	$0.221770\pi$
$224$	0.202107	+	0.350059i	0.0135038	+	0.0233893i
$225$		0			0
$226$	−2.76726	+	4.79303i	−0.184075	+	0.318828i
$227$	5.28423	−	14.5183i	0.350727	−	0.963614i	−0.631411	−	0.775449i	$-0.717524\pi$
$227$	5.28423	−	14.5183i	0.350727	−	0.963614i	0.982137	−	0.188165i	$-0.0602540\pi$
$228$	−0.896766	+	1.00172i	−0.0593898	+	0.0663403i
$229$	9.01052	+	7.56072i	0.595432	+	0.499627i	0.889974	−	0.456012i	$-0.150723\pi$
$229$	9.01052	+	7.56072i	0.595432	+	0.499627i	−0.294542	+	0.955639i	$0.595167\pi$
$230$		0			0
$231$	0.229143	−	0.0751796i	0.0150765	−	0.00494646i
$232$	−5.00217	+	13.7433i	−0.328408	+	0.902295i
$233$	−13.9975	−	8.08145i	−0.917006	−	0.529434i	−0.0343274	−	0.999411i	$-0.510929\pi$
$233$	−13.9975	−	8.08145i	−0.917006	−	0.529434i	−0.882679	+	0.469977i	$0.844262\pi$
$234$	−1.67378	+	2.51241i	−0.109418	+	0.164241i
$235$		0			0
$236$	0.488564	+	2.77079i	0.0318028	+	0.180363i
$237$	−7.66327	+	19.1248i	−0.497783	+	1.24229i
$238$	−0.212702	−	0.584395i	−0.0137875	−	0.0378807i
$239$	3.74110	−	21.2168i	0.241992	−	1.37240i	−0.585386	−	0.810755i	$-0.699057\pi$
$239$	3.74110	−	21.2168i	0.241992	−	1.37240i	0.827377	−	0.561647i	$-0.189832\pi$
$240$		0			0
$241$	3.36630	−	2.82466i	0.216842	−	0.181952i	−0.527896	−	0.849309i	$-0.677019\pi$
$241$	3.36630	−	2.82466i	0.216842	−	0.181952i	0.744738	+	0.667357i	$0.232574\pi$
$242$		−	14.5116i		−	0.932839i
$243$	−12.0837	−	9.84799i	−0.775173	−	0.631749i
$244$	2.76537			0.177034
$245$		0			0
$246$	2.48432	+	4.64021i	0.158395	+	0.295849i
$247$	2.77178	+	0.488739i	0.176364	+	0.0310977i
$248$	4.50643	+	12.3813i	0.286158	+	0.786214i
$249$	−7.80296	−	3.12663i	−0.494492	−	0.198142i
$250$		0			0
$251$	2.98966	+	5.17825i	0.188706	+	0.326848i	0.944819	−	0.327593i	$-0.106237\pi$
$251$	2.98966	+	5.17825i	0.188706	+	0.326848i	−0.756113	+	0.654441i	$0.772904\pi$
$252$	0.179150	+	0.119350i	0.0112854	+	0.00751837i
$253$	−1.07611	−	0.621293i	−0.0676546	−	0.0390604i
$254$	2.85052	+	1.03750i	0.178857	+	0.0650988i
$255$		0			0
$256$	−3.76852	−	3.16216i	−0.235532	−	0.197635i
$257$	−11.3252	+	13.4968i	−0.706446	+	0.841909i	−0.993239	−	0.116083i	$-0.962966\pi$
$257$	−11.3252	+	13.4968i	−0.706446	+	0.841909i	0.286794	+	0.957992i	$0.407411\pi$
$258$	−13.2230	+	14.7705i	−0.823228	+	0.919571i
$259$	−0.813808	−	0.296202i	−0.0505676	−	0.0184051i
$260$		0			0
$261$	1.63642	+	14.7557i	0.101292	+	0.913355i
$262$	−0.337309	+	0.194745i	−0.0208390	+	0.0120314i
$263$	−3.99237	+	0.703963i	−0.246180	+	0.0434082i	−0.295377	−	0.955381i	$-0.595445\pi$
$263$	−3.99237	+	0.703963i	−0.246180	+	0.0434082i	0.0491964	+	0.998789i	$0.484334\pi$
$264$	−1.61876	+	1.27220i	−0.0996279	+	0.0782985i
$265$		0			0
$266$	−0.301409	+	1.70938i	−0.0184806	+	0.104809i
$267$	0.580970	+	0.360720i	0.0355548	+	0.0220757i
$268$	−1.63559	−	1.94922i	−0.0999098	−	0.119068i
$269$	13.0325			0.794604			0.397302	−	0.917688i	$-0.369946\pi$
$269$	13.0325			0.794604			0.397302	+	0.917688i	$0.369946\pi$
$270$		0			0
$271$	−5.58778			−0.339434			−0.169717	−	0.985493i	$-0.554285\pi$
$271$	−5.58778			−0.339434			−0.169717	+	0.985493i	$0.554285\pi$
$272$	3.05523	+	3.64108i	0.185250	+	0.220773i
$273$	0.0144367	−	0.450406i	0.000873751	−	0.0272598i
$274$	−2.24764	+	12.7470i	−0.135785	+	0.770074i
$275$		0			0
$276$	−0.157511	−	1.09792i	−0.00948106	−	0.0660869i
$277$	18.9280	−	3.33752i	1.13728	−	0.200532i	0.426862	−	0.904317i	$-0.359619\pi$
$277$	18.9280	−	3.33752i	1.13728	−	0.200532i	0.710413	+	0.703785i	$0.248508\pi$
$278$	−3.44734	+	1.99032i	−0.206758	+	0.119372i
$279$	9.67412	+	9.23566i	0.579175	+	0.552924i
$280$		0			0
$281$	10.9339	+	3.97961i	0.652261	+	0.237404i	0.646892	−	0.762582i	$-0.276069\pi$
$281$	10.9339	+	3.97961i	0.652261	+	0.237404i	0.00536937	+	0.999986i	$0.498291\pi$
$282$	27.9275	+	5.85260i	1.66306	+	0.348517i
$283$	18.1048	−	21.5765i	1.07622	−	1.28259i	0.119105	−	0.992882i	$-0.461998\pi$
$283$	18.1048	−	21.5765i	1.07622	−	1.28259i	0.957115	−	0.289707i	$-0.0935580\pi$
$284$	0.363447	+	0.304969i	0.0215666	+	0.0180966i
$285$		0			0
$286$	0.380334	+	0.138430i	0.0224896	+	0.00818554i
$287$	−0.680418	−	0.392840i	−0.0401638	−	0.0231886i
$288$	−3.40372	−	0.827958i	−0.200566	−	0.0487879i
$289$	−7.59986	−	13.1633i	−0.447051	−	0.774315i
$290$		0			0
$291$	3.64728	+	25.4231i	0.213807	+	1.49033i
$292$	0.884106	+	2.42906i	0.0517384	+	0.142150i
$293$	−0.0818497	−	0.0144323i	−0.00478171	−	0.000843144i	0.171257	−	0.985226i	$-0.445217\pi$
$293$	−0.0818497	−	0.0144323i	−0.00478171	−	0.000843144i	−0.176039	+	0.984383i	$0.556328\pi$
$294$	−15.9475	−	0.511161i	−0.930077	−	0.0298115i
$295$		0			0
$296$	7.39358			0.429743
$297$	−0.899991	+	1.88623i	−0.0522228	+	0.109450i
$298$		−	22.2358i		−	1.28809i
$299$	−1.77869	+	1.49250i	−0.102864	+	0.0863134i
$300$		0			0
$301$	0.513870	−	2.91430i	0.0296190	−	0.167978i
$302$	−4.26558	−	11.7196i	−0.245457	−	0.674387i
$303$	−14.3037	−	18.2002i	−0.821728	−	1.04558i
$304$	−2.30363	−	13.0645i	−0.132122	−	0.749302i
$305$		0			0
$306$	4.93602	+	2.16385i	0.282173	+	0.123699i
$307$	−13.9629	−	8.06146i	−0.796902	−	0.460092i	0.0454847	−	0.998965i	$-0.485517\pi$
$307$	−13.9629	−	8.06146i	−0.796902	−	0.460092i	−0.842387	+	0.538873i	$0.818850\pi$
$308$	0.00987089	−	0.0271201i	0.000562446	−	0.00154531i
$309$	9.29107	+	8.31764i	0.528550	+	0.473174i
$310$		0			0
$311$	25.8269	+	21.6714i	1.46451	+	1.22887i	0.921056	+	0.389431i	$0.127328\pi$
$311$	25.8269	+	21.6714i	1.46451	+	1.22887i	0.543454	+	0.839439i	$0.317116\pi$
$312$	1.19933	+	3.65549i	0.0678986	+	0.206951i
$313$	−8.53543	+	23.4509i	−0.482451	+	1.32552i	0.424935	+	0.905224i	$0.360297\pi$
$313$	−8.53543	+	23.4509i	−0.482451	+	1.32552i	−0.907386	+	0.420299i	$0.861925\pi$
$314$	10.2868	−	17.8173i	0.580519	−	1.00549i
$315$		0			0
$316$	1.23282	+	2.13530i	0.0693514	+	0.120120i
$317$	15.4564	−	2.72538i	0.868119	−	0.153073i	0.278188	−	0.960527i	$-0.410266\pi$
$317$	15.4564	−	2.72538i	0.868119	−	0.153073i	0.589931	+	0.807454i	$0.299155\pi$
$318$	8.76134	−	21.8652i	0.491311	−	1.22614i
$319$	1.87038	−	0.680763i	0.104721	−	0.0381154i
$320$		0			0
$321$	7.31674	+	13.6662i	0.408381	+	0.762772i
$322$	−0.920437	−	1.09693i	−0.0512939	−	0.0611297i
$323$		−	5.02464i		−	0.279578i
$324$	−1.82019	+	0.408749i	−0.101122	+	0.0227083i
$325$		0			0
$326$	−4.39454	+	3.68746i	−0.243391	+	0.204229i
$327$	11.8211	−	6.32891i	0.653710	−	0.349990i
$328$	6.60565	+	1.16475i	0.364736	+	0.0643128i
$329$	−4.00248	+	1.45678i	−0.220664	+	0.0803150i
$330$		0			0
$331$	5.25148	+	29.7826i	0.288647	+	1.63700i	0.691959	+	0.721937i	$0.256748\pi$
$331$	5.25148	+	29.7826i	0.288647	+	1.63700i	−0.403312	+	0.915063i	$0.632141\pi$
$332$	−0.871206	+	0.502991i	−0.0478136	+	0.0276052i
$333$	6.72667	−	3.32866i	0.368619	−	0.182410i
$334$	8.75574	−	15.1654i	0.479093	−	0.829813i
$335$		0			0
$336$	−2.01819	+	0.662148i	−0.110101	+	0.0361232i
$337$	4.43304	−	5.28309i	0.241483	−	0.287788i	−0.631667	−	0.775240i	$-0.717629\pi$
$337$	4.43304	−	5.28309i	0.241483	−	0.287788i	0.873150	+	0.487452i	$0.162073\pi$
$338$	−10.7022	+	12.7544i	−0.582125	+	0.693749i
$339$	5.33427	+	4.77540i	0.289718	+	0.259364i
$340$		0			0
$341$	0.896579	−	1.55292i	0.0485525	−	0.0840953i
$342$	−8.91120	−	12.1186i	−0.481862	−	0.655298i
$343$	4.16122	−	2.40248i	0.224685	−	0.129722i
$344$	4.38704	+	24.8802i	0.236534	+	1.34145i
$345$		0			0
$346$	1.38104	−	0.502659i	0.0742453	−	0.0270231i
$347$	34.9269	+	6.15856i	1.87497	+	0.330609i	0.990668	−	0.136298i	$-0.0435204\pi$
$347$	34.9269	+	6.15856i	1.87497	+	0.330609i	0.884307	+	0.466906i	$0.154631\pi$
$348$	1.50941	+	0.937182i	0.0809129	+	0.0502382i
$349$	−18.7347	+	15.7203i	−1.00285	+	0.841488i	−0.987376	−	0.158392i	$-0.949369\pi$
$349$	−18.7347	+	15.7203i	−1.00285	+	0.841488i	−0.0154704	+	0.999880i	$0.504925\pi$
$350$		0			0
$351$	2.73688	+	2.78581i	0.146084	+	0.148696i
$352$			0.469642i			0.0250320i
$353$	−5.96325	−	7.10672i	−0.317392	−	0.378253i	0.583635	−	0.812016i	$-0.301630\pi$
$353$	−5.96325	−	7.10672i	−0.317392	−	0.378253i	−0.901027	+	0.433763i	$0.857185\pi$
$354$	−31.4621	−	1.00845i	−1.67219	−	0.0535983i
$355$		0			0
$356$	0.0769027	−	0.0279903i	0.00407584	−	0.00148348i
$357$	−0.796345	+	0.114246i	−0.0421471	+	0.00604656i
$358$	22.3041	−	3.93282i	1.17881	−	0.207856i
$359$	−3.57306	−	6.18872i	−0.188579	−	0.326628i	0.756198	−	0.654343i	$-0.227055\pi$
$359$	−3.57306	−	6.18872i	−0.188579	−	0.326628i	−0.944777	+	0.327715i	$0.893721\pi$
$360$		0			0
$361$	2.48802	−	4.30937i	0.130948	−	0.226809i
$362$	0.976152	−	2.68196i	0.0513054	−	0.140961i
$363$	−18.3732	−	3.85037i	−0.964345	−	0.202092i
$364$	−0.0413122	−	0.0346650i	−0.00216535	−	0.00181694i
$365$		0			0
$366$	−6.34593	+	30.2816i	−0.331707	+	1.58284i
$367$	−3.94110	+	10.8281i	−0.205724	+	0.565222i	−0.999050	−	0.0435748i	$-0.986125\pi$
$367$	−3.94110	+	10.8281i	−0.205724	+	0.565222i	0.793326	+	0.608797i	$0.208348\pi$
$368$	9.47791	+	5.47207i	0.494070	+	0.285252i
$369$	6.53419	−	1.91423i	0.340156	−	0.0996510i
$370$		0			0
$371$	0.610570	+	3.46272i	0.0316992	+	0.179775i
$372$	1.58439	−	0.227302i	0.0821467	−	0.0117851i
$373$	−10.5687	−	29.0373i	−0.547227	−	1.50349i	−0.837439	−	0.546531i	$-0.815948\pi$
$373$	−10.5687	−	29.0373i	−0.547227	−	1.50349i	0.290213	−	0.956962i	$-0.406274\pi$
$374$	0.125472	−	0.711588i	0.00648801	−	0.0367954i
$375$		0			0
$376$	27.8558	−	23.3738i	1.43655	−	1.20541i
$377$		−	3.71932i		−	0.191555i
$378$	−1.71803	+	1.68786i	−0.0883661	+	0.0868142i
$379$	2.84713			0.146247			0.0731236	−	0.997323i	$-0.476703\pi$
$379$	2.84713			0.146247			0.0731236	+	0.997323i	$0.476703\pi$
$380$		0			0
$381$	2.06992	−	3.33379i	0.106045	−	0.170795i
$382$	17.7861	+	3.13617i	0.910017	+	0.160461i
$383$	11.9857	+	32.9304i	0.612439	+	1.68266i	0.724769	+	0.688992i	$0.241947\pi$
$383$	11.9857	+	32.9304i	0.612439	+	1.68266i	−0.112329	+	0.993671i	$0.535831\pi$
$384$	12.5889	−	9.89370i	0.642422	−	0.504886i
$385$		0			0
$386$	6.29390	+	10.9014i	0.320351	+	0.554864i
$387$	15.1926	+	20.6608i	0.772284	+	1.05025i
$388$	2.66183	+	1.53681i	0.135134	+	0.0780196i
$389$	17.3917	+	6.33006i	0.881795	+	0.320947i	0.742934	−	0.669365i	$-0.233434\pi$
$389$	17.3917	+	6.33006i	0.881795	+	0.320947i	0.138861	+	0.990312i	$0.455656\pi$
$390$		0			0
$391$	3.17540	+	2.66448i	0.160587	+	0.134748i
$392$	−13.0701	+	15.5764i	−0.660141	+	0.786726i
$393$	0.157071	+	0.478742i	0.00792316	+	0.0241494i
$394$	−10.6291	−	3.86867i	−0.535486	−	0.194901i
$395$		0			0
$396$	0.110927	+	0.224165i	0.00557430	+	0.0112647i
$397$	−25.5478	+	14.7500i	−1.28221	+	0.740284i	−0.977252	−	0.212083i	$-0.931975\pi$
$397$	−25.5478	+	14.7500i	−1.28221	+	0.740284i	−0.304957	+	0.952366i	$0.598642\pi$
$398$	17.8609	−	3.14937i	0.895288	−	0.157863i
$399$	2.08429	+	0.835169i	0.104345	+	0.0418107i
$400$		0			0
$401$	4.06740	−	23.0673i	0.203116	−	1.15193i	−0.697261	−	0.716817i	$-0.745598\pi$
$401$	4.06740	−	23.0673i	0.203116	−	1.15193i	0.900377	−	0.435111i	$-0.143291\pi$
$402$	25.0979	−	13.4372i	1.25177	−	0.670185i
$403$	−2.15380	−	2.56680i	−0.107288	−	0.127861i
$404$	−2.77024			−0.137824
$405$		0			0
$406$	2.29374			0.113836
$407$	−0.646786	−	0.770809i	−0.0320600	−	0.0382076i
$408$	6.05501	−	3.24179i	0.299768	−	0.160493i
$409$	−1.34566	+	7.63161i	−0.0665386	+	0.377359i	0.933295	+	0.359111i	$0.116920\pi$
$409$	−1.34566	+	7.63161i	−0.0665386	+	0.377359i	−0.999833	+	0.0182481i	$0.994191\pi$
$410$		0			0
$411$	15.5427	+	6.22793i	0.766666	+	0.307201i
$412$	1.46968	−	0.259145i	0.0724062	−	0.0127672i
$413$	4.06929	−	2.34941i	0.200237	−	0.115607i
$414$	12.3840	+	0.794697i	0.608639	+	0.0390572i
$415$		0			0
$416$	0.824656	+	0.300150i	0.0404321	+	0.0147161i
$417$	1.60528	+	4.89280i	0.0786109	+	0.239602i
$418$	−1.29632	+	1.54489i	−0.0634049	+	0.0755630i
$419$	13.6412	+	11.4463i	0.666415	+	0.559189i	0.912002	−	0.410186i	$-0.134536\pi$
$419$	13.6412	+	11.4463i	0.666415	+	0.559189i	−0.245587	+	0.969375i	$0.578981\pi$
$420$		0			0
$421$	−28.5312	−	10.3845i	−1.39053	−	0.506110i	−0.465175	−	0.885219i	$-0.654009\pi$
$421$	−28.5312	−	10.3845i	−1.39053	−	0.506110i	−0.925352	+	0.379108i	$0.876231\pi$
$422$	−12.9364	−	7.46885i	−0.629736	−	0.363578i
$423$	14.8201	−	33.8064i	0.720576	−	1.64372i
$424$	−15.0091	−	25.9965i	−0.728905	−	1.26250i
$425$		0			0
$426$	−4.17353	+	3.28002i	−0.202208	+	0.158917i
$427$	−1.57958	−	4.33985i	−0.0764411	−	0.210020i
$428$	1.82694	+	0.322140i	0.0883087	+	0.0155712i
$429$	0.276182	−	0.444814i	0.0133342	−	0.0214758i
$430$		0			0
$431$	−22.4604			−1.08188			−0.540939	−	0.841062i	$-0.681931\pi$
$431$	−22.4604			−1.08188			−0.540939	+	0.841062i	$0.681931\pi$
$432$	7.92672	−	16.6131i	0.381374	−	0.799296i
$433$			9.65028i			0.463763i	0.972744	+	0.231882i	$0.0744882\pi$
$433$			9.65028i			0.463763i	−0.972744	+	0.231882i	$0.925512\pi$
$434$	1.58297	−	1.32827i	0.0759849	−	0.0637589i
$435$		0			0
$436$	0.278648	−	1.58029i	0.0133448	−	0.0756821i
$437$	−3.95697	−	10.8717i	−0.189287	−	0.520063i
$438$	−28.6278	+	4.10704i	−1.36789	+	0.196242i
$439$	−5.34208	−	30.2964i	−0.254963	−	1.44597i	−0.796167	−	0.605077i	$-0.793142\pi$
$439$	−5.34208	−	30.2964i	−0.254963	−	1.44597i	0.541203	−	0.840892i	$-0.317969\pi$
$440$		0			0
$441$	−4.87856	+	20.0557i	−0.232312	+	0.955031i
$442$	−1.16930	−	0.675098i	−0.0556181	−	0.0321111i
$443$	−5.84380	+	16.0557i	−0.277647	+	0.762830i	0.719981	+	0.693994i	$0.244151\pi$
$443$	−5.84380	+	16.0557i	−0.277647	+	0.762830i	−0.997628	+	0.0688358i	$0.978072\pi$
$444$	0.184223	−	0.879077i	0.00874284	−	0.0417192i
$445$		0			0
$446$	19.7240	+	16.5504i	0.933958	+	0.783684i
$447$	−28.1530	−	5.89985i	−1.33159	−	0.279053i
$448$	−1.02395	+	2.81329i	−0.0483773	+	0.132915i
$449$	3.63246	−	6.29160i	0.171426	−	0.296919i	−0.767492	−	0.641058i	$-0.778496\pi$
$449$	3.63246	−	6.29160i	0.171426	−	0.296919i	0.938919	+	0.344139i	$0.111829\pi$
$450$		0			0
$451$	−0.456427	−	0.790555i	−0.0214923	−	0.0372258i
$452$	0.843788	−	0.148783i	0.0396884	−	0.00699814i
$453$	−15.9701	+	2.29112i	−0.750340	+	0.107646i
$454$	19.4389	−	7.07519i	0.912314	−	0.332055i
$455$		0			0
$456$	−19.1596	−	0.614118i	−0.897231	−	0.0287587i
$457$	−6.41352	−	7.64333i	−0.300012	−	0.357540i	0.594887	−	0.803809i	$-0.297197\pi$
$457$	−6.41352	−	7.64333i	−0.300012	−	0.357540i	−0.894899	+	0.446269i	$0.852752\pi$
$458$			15.7490i			0.735901i
$459$	4.04936	−	5.67540i	0.189008	−	0.264905i
$460$		0			0
$461$	4.66867	−	3.91748i	0.217441	−	0.182455i	−0.527560	−	0.849518i	$-0.676893\pi$
$461$	4.66867	−	3.91748i	0.217441	−	0.182455i	0.745002	+	0.667063i	$0.232449\pi$
$462$	0.274321	+	0.170324i	0.0127626	+	0.00792419i
$463$	24.9689	+	4.40269i	1.16040	+	0.204611i	0.720514	−	0.693441i	$-0.243906\pi$
$463$	24.9689	+	4.40269i	1.16040	+	0.204611i	0.439891	+	0.898051i	$0.355017\pi$
$464$	−16.4735	+	5.99586i	−0.764762	+	0.278351i
$465$		0			0
$466$	−3.75791	−	21.3121i	−0.174082	−	0.987266i
$467$	23.9220	−	13.8113i	1.10698	−	0.639113i	0.168932	−	0.985628i	$-0.445968\pi$
$467$	23.9220	−	13.8113i	1.10698	−	0.639113i	0.938044	+	0.346515i	$0.112635\pi$
$468$	0.464511	−	0.0515146i	0.0214720	−	0.00238126i
$469$	−2.12478	+	3.68023i	−0.0981134	+	0.169937i
$470$		0			0
$471$	−19.8292	−	17.7517i	−0.913683	−	0.817957i
$472$	−25.7854	+	30.7299i	−1.18687	+	1.41446i
$473$	2.21008	−	2.63387i	0.101619	−	0.121105i
$474$	−26.2112	+	8.59964i	−1.20392	+	0.394995i
$475$		0			0
$476$	−0.0481385	+	0.0833784i	−0.00220643	+	0.00382164i
$477$	−25.3591	−	16.8943i	−1.16111	−	0.773538i
$478$	24.9813	−	14.4230i	1.14262	−	0.659692i
$479$	4.94905	+	28.0675i	0.226128	+	1.28244i	0.860517	+	0.509422i	$0.170141\pi$
$479$	4.94905	+	28.0675i	0.226128	+	1.28244i	−0.634389	+	0.773014i	$0.718748\pi$
$480$		0			0
$481$	−1.76684	+	0.643079i	−0.0805611	+	0.0293219i
$482$	5.79437	+	1.02170i	0.263926	+	0.0465374i
$483$	−1.63306	+	0.874323i	−0.0743068	+	0.0397831i
$484$	−1.72096	+	1.44406i	−0.0782254	+	0.0656389i
$485$		0			0
$486$	−0.298959	−	20.8696i	−0.0135611	−	0.946666i
$487$		−	24.3015i		−	1.10121i	−0.834767	−	0.550603i	$-0.814398\pi$
$487$		−	24.3015i		−	1.10121i	0.834767	−	0.550603i	$-0.185602\pi$
$488$	25.3440	+	30.2038i	1.14727	+	1.36726i
$489$	3.50272	+	6.54237i	0.158398	+	0.295856i
$490$		0			0
$491$	14.9080	−	5.42607i	0.672789	−	0.244875i	0.0170405	−	0.999855i	$-0.494576\pi$
$491$	14.9080	−	5.42607i	0.672789	−	0.244875i	0.655748	+	0.754980i	$0.272353\pi$
$492$	0.303076	−	0.756372i	0.0136637	−	0.0340999i
$493$	−6.53904	+	1.15301i	−0.294504	+	0.0519289i
$494$	1.88422	+	3.26357i	0.0847753	+	0.146835i
$495$		0			0
$496$	−7.89666	+	13.6774i	−0.354571	+	0.614134i
$497$	0.271004	−	0.744578i	0.0121562	−	0.0333989i
$498$	−3.50867	−	10.6942i	−0.157227	−	0.479219i
$499$	−26.8594	−	22.5377i	−1.20239	−	1.00893i	−0.999558	−	0.0297149i	$-0.990540\pi$
$499$	−26.8594	−	22.5377i	−1.20239	−	1.00893i	−0.202835	−	0.979213i	$-0.565015\pi$
$500$		0			0
$501$	−16.8779	−	15.1096i	−0.754048	−	0.675046i
$502$	−2.73817	+	7.52305i	−0.122210	+	0.335770i
$503$	6.27881	+	3.62507i	0.279958	+	0.161634i	0.633405	−	0.773821i	$-0.281657\pi$
$503$	6.27881	+	3.62507i	0.279958	+	0.161634i	−0.353446	+	0.935455i	$0.614990\pi$
$504$	0.338306	+	3.05053i	0.0150694	+	0.135881i
$505$		0			0
$506$	−0.288904	−	1.63845i	−0.0128433	−	0.0728382i
$507$	13.3089	+	16.9343i	0.591067	+	0.752081i
$508$	−0.160617	−	0.441292i	−0.00712623	−	0.0195791i
$509$	6.17449	−	35.0173i	0.273679	−	1.55211i	−0.469446	−	0.882961i	$-0.655546\pi$
$509$	6.17449	−	35.0173i	0.273679	−	1.55211i	0.743126	−	0.669152i	$-0.233343\pi$
$510$		0			0
$511$	3.30707	−	2.77496i	0.146296	−	0.122757i
$512$		−	25.0751i		−	1.10817i
$513$	−17.7079	+	8.06712i	−0.781822	+	0.356172i
$514$	−23.5903			−1.04052
$515$		0			0
$516$	3.06749	+	0.0983216i	0.135039	+	0.00432837i
$517$	−4.87361	−	0.859349i	−0.214341	−	0.0377941i
$518$	−0.396592	−	1.08963i	−0.0174253	−	0.0478755i
$519$	−0.269987	−	1.88192i	−0.0118511	−	0.0826073i
$520$		0			0
$521$	−19.0101	−	32.9265i	−0.832849	−	1.44254i	−0.895770	−	0.444519i	$-0.853375\pi$
$521$	−19.0101	−	32.9265i	−0.832849	−	1.44254i	0.0629204	−	0.998019i	$-0.479959\pi$
$522$	−13.7262	+	14.3778i	−0.600779	+	0.629301i
$523$	13.9242	+	8.03916i	0.608864	+	0.351528i	0.772521	−	0.634990i	$-0.218996\pi$
$523$	13.9242	+	8.03916i	0.608864	+	0.351528i	−0.163657	+	0.986517i	$0.552329\pi$
$524$	0.0566611	+	0.0206230i	0.00247525	+	0.000900918i
$525$		0			0
$526$	−4.15805	−	3.48902i	−0.181300	−	0.152128i
$527$	−3.84507	+	4.58237i	−0.167494	+	0.199611i
$528$	−2.41538	−	0.506177i	−0.105116	−	0.0220285i
$529$	−12.6441	−	4.60207i	−0.549743	−	0.200090i
$530$		0			0
$531$	−9.62467	+	39.5669i	−0.417675	+	1.71706i
$532$	0.232712	−	0.134356i	0.0100894	−	0.00582509i
$533$	−1.67986	+	0.296204i	−0.0727627	+	0.0128300i
$534$	0.130026	+	0.906339i	0.00562680	+	0.0392211i
$535$		0			0
$536$	6.29990	−	35.7285i	0.272114	−	1.54324i
$537$	0.938599	−	29.2830i	0.0405036	−	1.26365i
$538$	11.2163	+	13.3671i	0.483570	+	0.576297i
$539$	2.76726			0.119194
$540$		0			0
$541$	−17.0592			−0.733433			−0.366717	−	0.930333i	$-0.619518\pi$
$541$	−17.0592			−0.733433			−0.366717	+	0.930333i	$0.619518\pi$
$542$	−4.80909	−	5.73125i	−0.206568	−	0.246178i
$543$	−3.13665	−	1.94752i	−0.134606	−	0.0835762i
$544$	0.272054	−	1.54290i	0.0116642	−	0.0661511i
$545$		0			0
$546$	0.474395	−	0.372832i	0.0203022	−	0.0159557i
$547$	18.3900	−	3.24265i	0.786298	−	0.138646i	0.233938	−	0.972251i	$-0.424839\pi$
$547$	18.3900	−	3.24265i	0.786298	−	0.138646i	0.552360	+	0.833606i	$0.313727\pi$
$548$	1.73536	−	1.00191i	0.0741308	−	0.0427994i
$549$	36.6560	+	16.0693i	1.56444	+	0.685820i
$550$		0			0
$551$	17.4146	+	6.33841i	0.741888	+	0.270025i
$552$	10.5481	−	11.7826i	0.448957	−	0.501499i
$553$	2.64687	−	3.15442i	0.112556	−	0.134140i
$554$	19.7135	+	16.5416i	0.837547	+	0.702786i
$555$		0			0
$556$	0.579083	+	0.210769i	0.0245586	+	0.00893860i
$557$	4.66802	+	2.69508i	0.197790	+	0.114194i	0.595624	−	0.803263i	$-0.296905\pi$
$557$	4.66802	+	2.69508i	0.197790	+	0.114194i	−0.397834	+	0.917457i	$0.630238\pi$
$558$	−1.14682	+	17.8711i	−0.0485486	+	0.756545i
$559$	−3.21240	−	5.56403i	−0.135870	−	0.235334i
$560$		0			0
$561$	−0.867657	−	0.347668i	−0.0366325	−	0.0146786i
$562$	5.32840	+	14.6396i	0.224765	+	0.617536i
$563$	−0.845464	−	0.149078i	−0.0356321	−	0.00628289i	0.155804	−	0.987788i	$-0.450203\pi$
$563$	−0.845464	−	0.149078i	−0.0356321	−	0.00628289i	−0.191436	+	0.981505i	$0.561314\pi$
$564$	−2.08501	−	3.89438i	−0.0877947	−	0.163983i
$565$		0			0
$566$	37.7123			1.58517
$567$	1.68117	+	2.62306i	0.0706025	+	0.110158i
$568$			6.76462i			0.283837i
$569$	−22.5944	+	18.9589i	−0.947206	+	0.794800i	−0.978825	−	0.204700i	$-0.934378\pi$
$569$	−22.5944	+	18.9589i	−0.947206	+	0.794800i	0.0316187	+	0.999500i	$0.489934\pi$
$570$		0			0
$571$	2.15888	−	12.2436i	0.0903464	−	0.512380i	−0.905728	−	0.423860i	$-0.860675\pi$
$571$	2.15888	−	12.2436i	0.0903464	−	0.512380i	0.996074	−	0.0885205i	$-0.0282139\pi$
$572$	−0.0214305	−	0.0588798i	−0.000896054	−	0.00246189i
$573$	8.68995	−	21.6871i	0.363028	−	0.905990i
$574$	−0.182672	−	1.03598i	−0.00762458	−	0.0432411i
$575$		0			0
$576$	−11.5070	−	23.2537i	−0.479458	−	0.968905i
$577$	−28.9597	−	16.7199i	−1.20561	−	0.696057i	−0.243810	−	0.969823i	$-0.578397\pi$
$577$	−28.9597	−	16.7199i	−1.20561	−	0.696057i	−0.961796	+	0.273766i	$0.911731\pi$
$578$	6.96055	−	19.1240i	0.289521	−	0.795452i
$579$	15.4723	−	5.07630i	0.643006	−	0.210964i
$580$		0			0
$581$	1.28701	+	1.07993i	0.0533941	+	0.0448030i
$582$	−22.9368	+	25.6212i	−0.950762	+	1.06203i
$583$	−1.39725	+	3.83891i	−0.0578681	+	0.158991i
$584$	−18.4280	+	31.9182i	−0.762556	+	1.32079i
$585$		0			0
$586$	−0.0556406	−	0.0963723i	−0.00229849	−	0.00398110i
$587$	−21.6109	+	3.81058i	−0.891977	+	0.157280i	−0.600809	−	0.799392i	$-0.705155\pi$
$587$	−21.6109	+	3.81058i	−0.891977	+	0.157280i	−0.291168	+	0.956672i	$0.594044\pi$
$588$	1.52633	+	1.94211i	0.0629446	+	0.0800914i
$589$	15.6887	−	5.71024i	0.646444	−	0.235286i
$590$		0			0
$591$	−7.71840	+	12.4311i	−0.317493	+	0.511348i
$592$	5.69660	+	6.78894i	0.234129	+	0.279024i
$593$			11.2798i			0.463205i	0.972811	+	0.231602i	$0.0743968\pi$
$593$			11.2798i			0.463205i	−0.972811	+	0.231602i	$0.925603\pi$
$594$	−2.70923	+	0.700273i	−0.111161	+	0.0287325i
$595$		0			0
$596$	−2.63699	+	2.21270i	−0.108015	+	0.0906356i
$597$	0.751622	−	23.4495i	0.0307618	−	0.959726i
$598$	−3.06164	−	0.539850i	−0.125200	−	0.0220761i
$599$	5.06912	−	1.84501i	0.207119	−	0.0753850i	−0.236378	−	0.971661i	$-0.575960\pi$
$599$	5.06912	−	1.84501i	0.207119	−	0.0753850i	0.443496	+	0.896276i	$0.353738\pi$
$600$		0			0
$601$	1.30738	+	7.41452i	0.0533291	+	0.302445i	0.999793	−	0.0203664i	$-0.00648328\pi$
$601$	1.30738	+	7.41452i	0.0533291	+	0.302445i	−0.946463	+	0.322811i	$0.895372\pi$
$602$	3.43139	−	1.98111i	0.139853	−	0.0807441i
$603$	−10.3537	−	35.3420i	−0.421634	−	1.43924i
$604$	−0.965381	+	1.67209i	−0.0392808	+	0.0680363i
$605$		0			0
$606$	6.35711	−	30.3349i	0.258240	−	1.23227i
$607$	−13.9285	+	16.5993i	−0.565339	+	0.673745i	−0.970667	−	0.240427i	$-0.922713\pi$
$607$	−13.9285	+	16.5993i	−0.565339	+	0.673745i	0.405329	+	0.914171i	$0.367157\pi$
$608$	−2.81073	+	3.34969i	−0.113990	+	0.135848i
$609$	0.608601	−	2.90413i	0.0246618	−	0.117681i
$610$		0			0
$611$	−4.62369	+	8.00847i	−0.187055	+	0.323988i
$612$	−0.234570	−	0.800699i	−0.00948193	−	0.0323663i
$613$	−32.4185	+	18.7168i	−1.30937	+	0.755965i	−0.981991	−	0.188928i	$-0.939499\pi$
$613$	−32.4185	+	18.7168i	−1.30937	+	0.755965i	−0.327379	+	0.944893i	$0.606165\pi$
$614$	−3.74861	−	21.2594i	−0.151281	−	0.857960i
$615$		0			0
$616$	0.386675	−	0.140738i	0.0155796	−	0.00567050i
$617$	36.6531	+	6.46292i	1.47560	+	0.260187i	0.852817	−	0.522210i	$-0.174892\pi$
$617$	36.6531	+	6.46292i	1.47560	+	0.260187i	0.622780	+	0.782397i	$0.286003\pi$
$618$	−0.534901	+	16.6882i	−0.0215169	+	0.671296i
$619$	7.26024	−	6.09206i	0.291814	−	0.244861i	−0.485114	−	0.874451i	$-0.661222\pi$
$619$	7.26024	−	6.09206i	0.291814	−	0.244861i	0.776927	+	0.629591i	$0.216777\pi$
$620$		0			0
$621$	4.29203	−	15.4686i	0.172233	−	0.620735i
$622$			45.1414i			1.81000i
$623$	−0.0878537	−	0.104700i	−0.00351979	−	0.00419472i
$624$	−2.43249	+	3.91772i	−0.0973774	+	0.156834i
$625$		0			0
$626$	−31.3990	+	11.4283i	−1.25496	+	0.456766i
$627$	1.61205	+	2.05119i	0.0643789	+	0.0819164i
$628$	−3.13664	+	0.553074i	−0.125166	+	0.0220701i
$629$	1.67834	+	2.90698i	0.0669199	+	0.115909i
$630$		0			0
$631$	9.32426	−	16.1501i	0.371193	−	0.642925i	−0.618556	−	0.785740i	$-0.712282\pi$
$631$	9.32426	−	16.1501i	0.371193	−	0.642925i	0.989749	+	0.142815i	$0.0456155\pi$
$632$	−12.0236	+	33.0347i	−0.478275	+	1.31405i
$633$	−12.8888	+	14.3972i	−0.512285	+	0.572238i
$634$	16.0978	+	13.5077i	0.639327	+	0.536459i
$635$		0			0
$636$	−3.46489	+	1.13679i	−0.137392	+	0.0450768i
$637$	1.76857	−	4.85910i	0.0700732	−	0.192524i
$638$	2.30798	+	1.33251i	0.0913737	+	0.0527546i
$639$	3.04549	+	6.15444i	0.120478	+	0.243466i
$640$		0			0
$641$	−4.29405	−	24.3528i	−0.169605	−	0.961876i	−0.944189	−	0.329405i	$-0.893152\pi$
$641$	−4.29405	−	24.3528i	−0.169605	−	0.961876i	0.774584	−	0.632471i	$-0.217959\pi$
$642$	−7.71997	+	19.2663i	−0.304683	+	0.760381i
$643$	−2.70994	−	7.44549i	−0.106870	−	0.293622i	0.874719	−	0.484631i	$-0.161046\pi$
$643$	−2.70994	−	7.44549i	−0.106870	−	0.293622i	−0.981588	+	0.191009i	$0.938824\pi$
$644$	−0.0384945	+	0.218313i	−0.00151690	+	0.00860274i
$645$		0			0
$646$	5.15365	−	4.32443i	0.202768	−	0.170142i
$647$		−	3.79376i		−	0.149148i	−0.997215	−	0.0745741i	$-0.976240\pi$
$647$		−	3.79376i		−	0.149148i	0.997215	−	0.0745741i	$-0.0237597\pi$
$648$	−21.1461	−	16.1344i	−0.830698	−	0.633818i
$649$	5.45940			0.214300
$650$		0			0
$651$	−1.26172	−	2.35664i	−0.0494508	−	0.0923641i
$652$	0.874607	+	0.154217i	0.0342522	+	0.00603959i
$653$	−5.05580	−	13.8907i	−0.197849	−	0.543585i	0.800604	−	0.599194i	$-0.204512\pi$
$653$	−5.05580	−	13.8907i	−0.197849	−	0.543585i	−0.998453	+	0.0556090i	$0.982290\pi$
$654$	16.6652	+	6.67770i	0.651661	+	0.261119i
$655$		0			0
$656$	4.02001	+	6.96286i	0.156955	+	0.271854i
$657$	−2.39588	+	37.3356i	−0.0934722	+	1.45660i
$658$	−4.93889	−	2.85147i	−0.192538	−	0.111162i
$659$	38.5064	+	14.0152i	1.49999	+	0.545953i	0.956059	−	0.293174i	$-0.0947114\pi$
$659$	38.5064	+	14.0152i	1.49999	+	0.545953i	0.543935	+	0.839127i	$0.316934\pi$
$660$		0			0
$661$	12.0162	+	10.0828i	0.467375	+	0.392174i	0.845836	−	0.533443i	$-0.179102\pi$
$661$	12.0162	+	10.0828i	0.467375	+	0.392174i	−0.378461	+	0.925617i	$0.623547\pi$
$662$	−26.0276	+	31.0185i	−1.01159	+	1.20557i
$663$	−1.16500	+	1.30134i	−0.0452449	+	0.0505400i
$664$	−13.4782	−	4.90566i	−0.523055	−	0.190377i
$665$		0			0
$666$	9.20340	+	4.03459i	0.356624	+	0.156337i
$667$	−13.2403	+	7.64431i	−0.512668	+	0.295989i
$668$	−2.66978	+	0.470755i	−0.103297	+	0.0182141i
$669$	26.1880	−	20.5814i	1.01249	−	0.795723i
$670$		0			0
$671$	0.931786	−	5.28442i	0.0359712	−	0.204003i
$672$	0.594794	+	0.369304i	0.0229447	+	0.0142462i
$673$	−15.3802	−	18.3294i	−0.592861	−	0.706545i	0.383292	−	0.923627i	$-0.374790\pi$
$673$	−15.3802	−	18.3294i	−0.592861	−	0.706545i	−0.976153	+	0.217083i	$0.930346\pi$
$674$	9.23400			0.355681
$675$		0			0
$676$	2.57756			0.0991369
$677$	−16.4295	−	19.5799i	−0.631437	−	0.752518i	0.351554	−	0.936167i	$-0.385653\pi$
$677$	−16.4295	−	19.5799i	−0.631437	−	0.752518i	−0.982992	+	0.183650i	$0.941209\pi$
$678$	−0.307102	+	9.58115i	−0.0117942	+	0.367962i
$679$	0.891367	−	5.05520i	0.0342075	−	0.194001i
$680$		0			0
$681$	−3.80021	−	26.4891i	−0.145625	−	1.01506i
$682$	2.36443	−	0.416913i	0.0905386	−	0.0159644i
$683$	−37.4638	+	21.6297i	−1.43351	+	0.827639i	−0.997387	−	0.0722470i	$-0.976983\pi$
$683$	−37.4638	+	21.6297i	−1.43351	+	0.827639i	−0.436126	+	0.899886i	$0.643650\pi$
$684$	−0.550410	+	2.26273i	−0.0210454	+	0.0865175i
$685$		0			0
$686$	6.04549	+	2.20038i	0.230818	+	0.0840109i
$687$	19.9399	+	4.17869i	0.760756	+	0.159427i
$688$	−19.4654	+	23.1979i	−0.742110	+	0.884412i
$689$	5.84784	+	4.90692i	0.222785	+	0.186939i
$690$		0			0
$691$	−42.4251	−	15.4415i	−1.61393	−	0.587422i	−0.631716	−	0.775200i	$-0.717649\pi$
$691$	−42.4251	−	15.4415i	−1.61393	−	0.587422i	−0.982211	+	0.187778i	$0.939871\pi$
$692$	−0.197040	−	0.113761i	−0.00749033	−	0.00432454i
$693$	0.288435	−	0.302128i	0.0109567	−	0.0114769i
$694$	23.7430	+	41.1240i	0.901270	+	1.56105i
$695$		0			0
$696$	3.59737	+	25.0751i	0.136358	+	0.950471i
$697$	1.04153	+	2.86158i	0.0394507	+	0.108390i
$698$	−32.2479	−	5.68617i	−1.22060	−	0.215225i
$699$	−27.9806	−	0.896855i	−1.05832	−	0.0339222i
$700$		0			0
$701$	−52.1690			−1.97039			−0.985197	−	0.171425i	$-0.945163\pi$
$701$	−52.1690			−1.97039			−0.985197	+	0.171425i	$0.945163\pi$
$702$	−0.501854	+	5.20475i	−0.0189413	+	0.196441i
$703$		−	9.36864i		−	0.353345i
$704$	−2.66464	+	2.23590i	−0.100428	+	0.0842687i
$705$		0			0
$706$	2.15696	−	12.2327i	0.0811782	−	0.460384i
$707$	1.58236	+	4.34750i	0.0595108	+	0.163505i
$708$	3.01122	+	3.83150i	0.113168	+	0.143997i
$709$	−0.837721	−	4.75095i	−0.0314613	−	0.178426i	0.965028	−	0.262147i	$-0.0844306\pi$
$709$	−0.837721	−	4.75095i	−0.0314613	−	0.178426i	−0.996489	+	0.0837213i	$0.973319\pi$
$710$		0			0
$711$	3.93343	+	35.4681i	0.147515	+	1.33016i
$712$	1.01051	+	0.583420i	0.0378706	+	0.0218646i
$713$	−4.71079	+	12.9428i	−0.176421	+	0.484711i
$714$	−0.802550	−	0.718467i	−0.0300347	−	0.0268879i
$715$		0			0
$716$	−2.68590	−	2.25374i	−0.100377	−	0.0842261i
$717$	−11.6328	−	35.4560i	−0.434433	−	1.32413i
$718$	3.27249	−	8.99108i	0.122128	−	0.335544i
$719$	4.65459	−	8.06199i	0.173587	−	0.300662i	−0.766084	−	0.642740i	$-0.777798\pi$
$719$	4.65459	−	8.06199i	0.173587	−	0.300662i	0.939671	+	0.342078i	$0.111131\pi$
$720$		0			0
$721$	−1.24618	−	2.15844i	−0.0464100	−	0.0803846i
$722$	6.56131	−	1.15694i	0.244187	−	0.0430567i
$723$	2.83102	−	7.06522i	0.105287	−	0.262758i
$724$	−0.415197	+	0.151119i	−0.0154307	+	0.00561630i
$725$		0			0
$726$	−11.8636	−	22.1588i	−0.440299	−	0.822390i
$727$	−4.22289	−	5.03265i	−0.156618	−	0.186651i	0.682029	−	0.731325i	$-0.261098\pi$
$727$	−4.22289	−	5.03265i	−0.156618	−	0.186651i	−0.838648	+	0.544674i	$0.816653\pi$
$728$		−	0.768918i		−	0.0284980i
$729$	−26.5026	−	5.15885i	−0.981577	−	0.191068i
$730$		0			0
$731$	−8.78641	+	7.37268i	−0.324977	+	0.272688i
$732$	4.22264	−	2.26076i	0.156073	−	0.0835601i
$733$	−14.8900	−	2.62552i	−0.549976	−	0.0969756i	−0.108247	−	0.994124i	$-0.534524\pi$
$733$	−14.8900	−	2.62552i	−0.549976	−	0.0969756i	−0.441729	+	0.897148i	$0.645635\pi$
$734$	−14.4980	+	5.27684i	−0.535131	+	0.194772i
$735$		0			0
$736$	−0.626414	−	3.55257i	−0.0230899	−	0.130949i
$737$	−4.27594	+	2.46872i	−0.157506	+	0.0909364i
$738$	7.58700	+	5.05449i	0.279281	+	0.186058i
$739$	−19.1802	+	33.2210i	−0.705554	+	1.22206i	0.260937	+	0.965356i	$0.415968\pi$
$739$	−19.1802	+	33.2210i	−0.705554	+	1.22206i	−0.966491	+	0.256700i	$0.917365\pi$
$740$		0			0
$741$	4.63199	−	1.51971i	0.170160	−	0.0558279i
$742$	−3.02614	+	3.60641i	−0.111093	+	0.132396i
$743$	16.4495	−	19.6038i	0.603474	−	0.719192i	−0.374661	−	0.927162i	$-0.622241\pi$
$743$	16.4495	−	19.6038i	0.603474	−	0.719192i	0.978135	+	0.207970i	$0.0666855\pi$
$744$	17.0032	+	15.2218i	0.623369	+	0.558059i
$745$		0			0
$746$	20.6869	−	35.8308i	0.757403	−	1.31186i
$747$	−14.4710	+	1.60485i	−0.529467	+	0.0587183i
$748$	−0.0968746	+	0.0559306i	−0.00354209	+	0.00204502i
$749$	−0.537998	−	3.05114i	−0.0196580	−	0.111486i
$750$		0			0
$751$	40.5586	−	14.7621i	1.48000	−	0.538677i	0.529207	−	0.848493i	$-0.322490\pi$
$751$	40.5586	−	14.7621i	1.48000	−	0.538677i	0.950797	+	0.309816i	$0.100267\pi$
$752$	42.9246	+	7.56876i	1.56530	+	0.276004i
$753$	8.79849	+	5.46292i	0.320635	+	0.199080i
$754$	3.81482	−	3.20102i	0.138928	−	0.116574i
$755$		0			0
$756$	0.371130	+	0.0357852i	0.0134978	+	0.00130150i
$757$		−	40.4910i		−	1.47167i	−0.677161	−	0.735835i	$-0.736790\pi$
$757$		−	40.4910i		−	1.47167i	0.677161	−	0.735835i	$-0.263210\pi$
$758$	2.45037	+	2.92023i	0.0890013	+	0.106068i
$759$	−2.15112	−	0.0689492i	−0.0780807	−	0.00250270i
$760$		0			0
$761$	−10.7121	+	3.89889i	−0.388314	+	0.141335i	−0.528797	−	0.848748i	$-0.677357\pi$
$761$	−10.7121	+	3.89889i	−0.388314	+	0.141335i	0.140483	+	0.990083i	$0.455134\pi$
$762$	5.20085	−	0.746132i	0.188407	−	0.0270295i
$763$	−2.63921	+	0.465364i	−0.0955457	+	0.0168473i
$764$	−1.39798	−	2.42138i	−0.0505772	−	0.0876023i
$765$		0			0
$766$	−23.4605	+	40.6348i	−0.847662	+	1.46819i
$767$	3.48912	−	9.58628i	0.125985	−	0.346141i
$768$	−8.33958	−	1.74768i	−0.300929	−	0.0630638i
$769$	5.73459	+	4.81189i	0.206795	+	0.173521i	0.740303	−	0.672274i	$-0.234682\pi$
$769$	5.73459	+	4.81189i	0.206795	+	0.173521i	−0.533508	+	0.845795i	$0.679127\pi$
$770$		0			0
$771$	−6.25925	+	29.8680i	−0.225421	+	1.07567i
$772$	0.666505	−	1.83121i	0.0239880	−	0.0659066i
$773$	−3.97889	−	2.29721i	−0.143111	−	0.0826250i	0.426735	−	0.904377i	$-0.359664\pi$
$773$	−3.97889	−	2.29721i	−0.143111	−	0.0826250i	−0.569846	+	0.821752i	$0.692997\pi$
$774$	−8.11590	+	33.3643i	−0.291720	+	1.19926i
$775$		0			0
$776$	7.60984	+	43.1575i	0.273177	+	1.54927i
$777$	−1.48482	+	0.213017i	−0.0532675	+	0.00764194i
$778$	8.47548	+	23.2862i	0.303861	+	0.834850i
$779$	1.47590	−	8.37022i	0.0528795	−	0.299894i
$780$		0			0
$781$	0.705237	−	0.591764i	0.0252354	−	0.0211750i
$782$			5.55010i			0.198471i
$783$	14.5619	+	21.1938i	0.520401	+	0.757403i
$784$	−24.3728			−0.870457
$785$		0			0
$786$	−0.355853	+	0.573130i	−0.0126928	+	0.0204429i
$787$	−6.94491	−	1.22457i	−0.247559	−	0.0436514i	0.0484915	−	0.998824i	$-0.484559\pi$
$787$	−6.94491	−	1.22457i	−0.247559	−	0.0436514i	−0.296051	+	0.955172i	$0.595670\pi$
$788$	0.598914	+	1.64550i	0.0213354	+	0.0586186i
$789$	−5.52074	+	4.33880i	−0.196544	+	0.154465i
$790$		0			0
$791$	−0.715465	−	1.23922i	−0.0254390	−	0.0440617i
$792$	−1.43175	+	3.26600i	−0.0508750	+	0.116052i
$793$	−8.68353	−	5.01344i	−0.308361	−	0.178032i
$794$	−37.1164	−	13.5092i	−1.31721	−	0.479425i
$795$		0			0
$796$	−2.15084	−	1.80477i	−0.0762346	−	0.0639684i
$797$	−15.8724	+	18.9160i	−0.562230	+	0.670040i	−0.970017	−	0.243037i	$-0.921856\pi$
$797$	−15.8724	+	18.9160i	−0.562230	+	0.670040i	0.407787	+	0.913077i	$0.366301\pi$
$798$	0.937217	+	2.85659i	0.0331771	+	0.101122i
$799$	15.5133	+	5.64637i	0.548820	+	0.199754i
$800$		0			0
$801$	1.18202	+	0.0758522i	0.0417648	+	0.00268011i
$802$	27.1602	−	15.6810i	0.959060	−	0.553714i
$803$	4.93967	−	0.870997i	0.174317	−	0.0307368i
$804$	−4.09105	−	1.63927i	−0.144280	−	0.0578128i
$805$		0			0
$806$	0.779048	−	4.41820i	0.0274408	−	0.155625i
$807$	19.9003	−	10.6544i	0.700522	−	0.375053i
$808$	−25.3887	−	30.2570i	−0.893171	−	1.06444i
$809$	−31.8679			−1.12042			−0.560208	−	0.828352i	$-0.689279\pi$
$809$	−31.8679			−1.12042			−0.560208	+	0.828352i	$0.689279\pi$
$810$		0			0
$811$	−3.58217			−0.125787			−0.0628936	−	0.998020i	$-0.520033\pi$
$811$	−3.58217			−0.125787			−0.0628936	+	0.998020i	$0.520033\pi$
$812$	−0.228252	−	0.272020i	−0.00801006	−	0.00954602i
$813$	−8.53240	+	4.56816i	−0.299244	+	0.160212i
$814$	0.233948	−	1.32678i	0.00819987	−	0.0465038i
$815$		0			0
$816$	7.64194	+	3.06211i	0.267521	+	0.107195i
$817$	31.5264	−	5.55896i	1.10297	−	0.194483i
$818$	−8.98570	+	5.18789i	−0.314177	+	0.181390i
$819$	−0.346174	−	0.699560i	−0.0120963	−	0.0244446i
$820$		0			0
$821$	−19.9338	−	7.25531i	−0.695694	−	0.253212i	−0.0301230	−	0.999546i	$-0.509590\pi$
$821$	−19.9338	−	7.25531i	−0.695694	−	0.253212i	−0.665571	+	0.746334i	$0.731812\pi$
$822$	6.98892	+	21.3018i	0.243767	+	0.742987i
$823$	18.9052	−	22.5304i	0.658995	−	0.785359i	−0.328246	−	0.944592i	$-0.606458\pi$
$823$	18.9052	−	22.5304i	0.658995	−	0.785359i	0.987241	+	0.159233i	$0.0509021\pi$
$824$	16.2998	+	13.6772i	0.567830	+	0.476466i
$825$		0			0
$826$	5.91195	+	2.15177i	0.205703	+	0.0748697i
$827$	6.74365	+	3.89345i	0.234500	+	0.135388i	0.612646	−	0.790357i	$-0.290105\pi$
$827$	6.74365	+	3.89345i	0.234500	+	0.135388i	−0.378146	+	0.925746i	$0.623438\pi$
$828$	−1.13809	−	1.54772i	−0.0395515	−	0.0537871i
$829$	14.0422	+	24.3217i	0.487704	+	0.844728i	0.999900	−	0.0141403i	$-0.00450114\pi$
$829$	14.0422	+	24.3217i	0.487704	+	0.844728i	−0.512196	+	0.858869i	$0.671168\pi$
$830$		0			0
$831$	26.1741	−	20.5705i	0.907970	−	0.713582i
$832$	2.22309	+	6.10788i	0.0770716	+	0.211753i
$833$	−9.09117	−	1.60302i	−0.314990	−	0.0555413i
$834$	−3.63685	+	5.85746i	−0.125934	+	0.202827i
$835$		0			0
$836$	0.312209			0.0107980
$837$	22.3225	+	6.19376i	0.771580	+	0.214088i
$838$			23.8426i			0.823630i
$839$	25.5662	−	21.4526i	0.882643	−	0.740625i	−0.0840781	−	0.996459i	$-0.526795\pi$
$839$	25.5662	−	21.4526i	0.882643	−	0.740625i	0.966721	+	0.255834i	$0.0823501\pi$
$840$		0			0
$841$	−0.783180	+	4.44164i	−0.0270062	+	0.153160i
$842$	−13.9041	−	38.2012i	−0.479167	−	1.31650i
$843$	19.9492	−	2.86198i	0.687087	−	0.0985718i
$844$	0.401565	+	2.27739i	0.0138224	+	0.0783910i
$845$		0			0
$846$	47.4292	−	13.8947i	1.63065	−	0.477709i
$847$	3.24926	+	1.87596i	0.111646	+	0.0644587i
$848$	12.3063	−	33.8114i	0.422601	−	1.16109i
$849$	10.0063	−	47.7479i	0.343414	−	1.63870i
$850$		0			0
$851$	5.92066	+	4.96803i	0.202958	+	0.170302i
$852$	0.804295	+	0.168551i	0.0275547	+	0.00577447i
$853$	−8.16758	+	22.4403i	−0.279653	+	0.768340i	0.717749	+	0.696302i	$0.245172\pi$
$853$	−8.16758	+	22.4403i	−0.279653	+	0.768340i	−0.997402	+	0.0720379i	$0.977050\pi$
$854$	3.09183	−	5.35521i	0.105800	−	0.183251i
$855$		0			0
$856$	13.2251	+	22.9066i	0.452025	+	0.782930i
$857$	−54.6748	+	9.64065i	−1.86766	+	0.329318i	−0.988974	−	0.148087i	$-0.952688\pi$
$857$	−54.6748	+	9.64065i	−1.86766	+	0.329318i	−0.878683	+	0.477406i	$0.841577\pi$
$858$	0.693930	−	0.0995535i	0.0236904	−	0.00339870i
$859$	−12.9170	+	4.70141i	−0.440723	+	0.160410i	−0.552844	−	0.833284i	$-0.686458\pi$
$859$	−12.9170	+	4.70141i	−0.440723	+	0.160410i	0.112122	+	0.993695i	$0.464235\pi$
$860$		0			0
$861$	−1.36014	−	0.0435961i	−0.0463534	−	0.00148575i
$862$	−19.3304	−	23.0370i	−0.658395	−	0.784645i
$863$			14.2240i			0.484192i	0.970252	+	0.242096i	$0.0778349\pi$
$863$			14.2240i			0.484192i	−0.970252	+	0.242096i	$0.922165\pi$
$864$	−5.87427	+	1.51836i	−0.199847	+	0.0516557i
$865$		0			0
$866$	−9.89806	+	8.30546i	−0.336350	+	0.282231i
$867$	−22.3662	−	13.8870i	−0.759595	−	0.471627i
$868$	−0.315044	−	0.0555508i	−0.0106933	−	0.00188552i
$869$	4.49581	−	1.63634i	0.152510	−	0.0555091i
$870$		0			0
$871$	1.60211	+	9.08599i	0.0542853	+	0.307867i
$872$	19.8140	−	11.4396i	0.670986	−	0.387394i
$873$	26.3533	+	35.8386i	0.891926	+	1.21295i
$874$	7.74528	−	13.4152i	0.261988	−	0.453776i
$875$		0			0
$876$	3.33583	+	2.98633i	0.112707	+	0.100899i
$877$	16.9111	−	20.1538i	0.571046	−	0.680546i	−0.400799	−	0.916166i	$-0.631268\pi$
$877$	16.9111	−	20.1538i	0.571046	−	0.680546i	0.971845	+	0.235620i	$0.0757120\pi$
$878$	26.4767	−	31.5537i	0.893545	−	1.06489i
$879$	−0.136781	+	0.0448765i	−0.00461351	+	0.00151365i
$880$		0			0
$881$	−17.3061	+	29.9751i	−0.583058	+	1.00989i	0.412057	+	0.911158i	$0.364811\pi$
$881$	−17.3061	+	29.9751i	−0.583058	+	1.00989i	−0.995115	+	0.0987274i	$0.968523\pi$
$882$	−24.7693	+	12.2570i	−0.834026	+	0.412714i
$883$	10.9832	−	6.34115i	0.369614	−	0.213397i	−0.303676	−	0.952775i	$-0.598214\pi$
$883$	10.9832	−	6.34115i	0.369614	−	0.213397i	0.673290	+	0.739379i	$0.264881\pi$
$884$	0.0362969	+	0.205850i	0.00122080	+	0.00692347i
$885$		0			0
$886$	−21.4974	+	7.82441i	−0.722219	+	0.262866i
$887$	21.1857	+	3.73561i	0.711347	+	0.125430i	0.517601	−	0.855622i	$-0.326825\pi$
$887$	21.1857	+	3.73561i	0.711347	+	0.125430i	0.193746	+	0.981052i	$0.437936\pi$
$888$	11.2898	−	6.04445i	0.378861	−	0.202838i
$889$	−0.600801	+	0.504132i	−0.0201502	+	0.0169080i
$890$		0			0
$891$	0.167779	+	3.61599i	0.00562080	+	0.121140i
$892$		−	3.98605i		−	0.133463i
$893$	−29.6177	−	35.2970i	−0.991118	−	1.18117i
$894$	−18.1784	−	33.9535i	−0.607975	−	1.13557i
$895$		0			0
$896$	−3.00711	+	1.09450i	−0.100460	+	0.0365646i
$897$	−1.49586	+	3.73313i	−0.0499452	+	0.124646i
$898$	9.57940	−	1.68911i	0.319669	−	0.0563662i
$899$	−11.0314	−	19.1069i	−0.367917	−	0.637251i
$900$		0			0
$901$	6.81412	−	11.8024i	0.227011	−	0.393195i
$902$	0.418032	−	1.14853i	0.0139189	−	0.0382420i
$903$	−1.59785	−	4.87017i	−0.0531732	−	0.162069i
$904$	9.35818	+	7.85244i	0.311248	+	0.261168i
$905$		0			0
$906$	−16.0945	−	14.4083i	−0.534704	−	0.478683i
$907$	9.72036	−	26.7065i	0.322759	−	0.886774i	−0.667131	−	0.744940i	$-0.732478\pi$
$907$	9.72036	−	26.7065i	0.322759	−	0.886774i	0.989891	−	0.141833i	$-0.0452997\pi$
$908$	−2.77344	−	1.60125i	−0.0920399	−	0.0531392i
$909$	−36.7206	−	16.0976i	−1.21795	−	0.533924i
$910$		0			0
$911$	0.330416	+	1.87388i	0.0109472	+	0.0620845i	0.989792	−	0.142520i	$-0.0455204\pi$
$911$	0.330416	+	1.87388i	0.0109472	+	0.0620845i	−0.978845	+	0.204604i	$0.934409\pi$
$912$	−14.1982	−	18.0659i	−0.470149	−	0.598222i
$913$	0.667629	+	1.83430i	0.0220953	+	0.0607064i
$914$	2.31982	−	13.1564i	0.0767330	−	0.435174i
$915$		0			0
$916$	1.86770	−	1.56719i	0.0617107	−	0.0517814i
$917$		−	0.100702i		−	0.00332546i
$918$	9.30618	−	0.731174i	0.307150	−	0.0241323i
$919$	44.1735			1.45715			0.728575	−	0.684966i	$-0.240183\pi$
$919$	44.1735			1.45715			0.728575	+	0.684966i	$0.240183\pi$
$920$		0			0
$921$	−27.9114	−	0.894636i	−0.919711	−	0.0294792i
$922$	8.03612	+	1.41699i	0.264656	+	0.0466659i
$923$	−0.588372	−	1.61654i	−0.0193665	−	0.0532091i
$924$	−0.00709876	−	0.0494813i	−0.000233532	−	0.00162782i
$925$		0			0
$926$	16.9736	+	29.3992i	0.557788	+	0.966117i
$927$	20.9871	+	5.10513i	0.689307	+	0.167675i
$928$	5.00425	+	2.88921i	0.164273	+	0.0948429i
$929$	−46.6343	−	16.9735i	−1.53002	−	0.556883i	−0.566396	−	0.824133i	$-0.691663\pi$
$929$	−46.6343	−	16.9735i	−1.53002	−	0.556883i	−0.963627	+	0.267250i	$0.913885\pi$
$930$		0			0
$931$	19.7373	+	16.5616i	0.646865	+	0.542784i
$932$	−2.15350	+	2.56644i	−0.0705403	+	0.0840666i
$933$	57.1539	+	11.9774i	1.87114	+	0.392123i
$934$	34.7543	+	12.6495i	1.13719	+	0.413905i
$935$		0			0
$936$	4.81980	+	4.60135i	0.157540	+	0.150400i
$937$	−2.62661	+	1.51647i	−0.0858076	+	0.0495410i	−0.542290	−	0.840191i	$-0.682443\pi$
$937$	−2.62661	+	1.51647i	−0.0858076	+	0.0495410i	0.456482	+	0.889733i	$0.349109\pi$
$938$	−5.60341	+	0.988033i	−0.182958	+	0.0322604i
$939$	6.13835	+	42.7868i	0.200317	+	1.39630i
$940$		0			0
$941$	1.59606	−	9.05168i	0.0520299	−	0.295076i	−0.947678	−	0.319227i	$-0.896577\pi$
$941$	1.59606	−	9.05168i	0.0520299	−	0.295076i	0.999708	+	0.0241502i	$0.00768801\pi$
$942$	1.14160	−	35.6163i	0.0371953	−	1.16044i
$943$	4.50706	+	5.37130i	0.146770	+	0.174914i
$944$	−48.0839			−1.56500
$945$		0			0
$946$	4.60358			0.149675
$947$	7.86967	+	9.37871i	0.255730	+	0.304767i	0.878600	−	0.477558i	$-0.158478\pi$
$947$	7.86967	+	9.37871i	0.255730	+	0.304767i	−0.622870	+	0.782325i	$0.714034\pi$
$948$	3.62815	+	2.25269i	0.117837	+	0.0731640i
$949$	1.62756	−	9.23033i	0.0528327	−	0.299629i
$950$		0			0
$951$	21.3735	−	16.7976i	0.693082	−	0.544700i
$952$	−1.35185	+	0.238368i	−0.0438138	+	0.00772556i
$953$	51.2135	−	29.5681i	1.65897	−	0.957805i	0.685774	−	0.727814i	$-0.259464\pi$
$953$	51.2135	−	29.5681i	1.65897	−	0.957805i	0.973193	−	0.229991i	$-0.0738697\pi$
$954$	−4.49705	−	40.5502i	−0.145597	−	1.31286i
$955$		0			0
$956$	−4.19636	−	1.52735i	−0.135720	−	0.0493980i
$957$	2.29948	−	2.56860i	0.0743317	−	0.0830309i
$958$	−24.5288	+	29.2322i	−0.792488	+	0.944451i
$959$	−2.56359	−	2.15111i	−0.0827828	−	0.0694630i
$960$		0			0
$961$	10.4529	+	3.80456i	0.337191	+	0.122728i
$962$	−2.18021	−	1.25875i	−0.0702929	−	0.0405836i
$963$	22.3449	+	14.8863i	0.720056	+	0.479704i
$964$	−0.455436	−	0.788838i	−0.0146686	−	0.0254067i
$965$		0			0
$966$	−2.30226	−	0.922508i	−0.0740739	−	0.0296812i
$967$	5.11684	+	14.0584i	0.164546	+	0.452087i	0.994373	−	0.105934i	$-0.0337831\pi$
$967$	5.11684	+	14.0584i	0.164546	+	0.452087i	−0.829827	+	0.558021i	$0.811561\pi$
$968$	−31.5445	−	5.56214i	−1.01388	−	0.178774i
$969$	−4.10778	−	7.67250i	−0.131961	−	0.246476i
$970$		0			0
$971$	16.4454			0.527757			0.263878	−	0.964556i	$-0.414998\pi$
$971$	16.4454			0.527757			0.263878	+	0.964556i	$0.414998\pi$
$972$	−2.44522	+	2.11220i	−0.0784306	+	0.0677490i
$973$		−	1.02918i		−	0.0329940i
$974$	24.9255	−	20.9150i	0.798664	−	0.670158i
$975$		0			0
$976$	−8.20675	+	46.5428i	−0.262692	+	1.48980i
$977$	−15.1521	−	41.6300i	−0.484758	−	1.33186i	−0.905371	−	0.424622i	$-0.860407\pi$
$977$	−15.1521	−	41.6300i	−0.484758	−	1.33186i	0.420613	−	0.907240i	$-0.361815\pi$
$978$	−3.69576	+	9.22330i	−0.118177	+	0.294929i
$979$	−0.0275753	−	0.156387i	−0.000881309	−	0.00499815i
$980$		0			0
$981$	12.8765	−	19.3282i	0.411115	−	0.617101i
$982$	18.3959	+	10.6209i	0.587036	+	0.338925i
$983$	−8.82999	+	24.2602i	−0.281633	+	0.773780i	0.715535	+	0.698577i	$0.246183\pi$
$983$	−8.82999	+	24.2602i	−0.281633	+	0.773780i	−0.997168	+	0.0752034i	$0.976039\pi$
$984$	11.0389	−	3.62174i	0.351906	−	0.115457i
$985$		0			0
$986$	−6.81040	−	5.71461i	−0.216887	−	0.181990i
$987$	−4.92072	+	5.49660i	−0.156628	+	0.174959i
$988$	0.199534	−	0.548214i	0.00634801	−	0.0174410i
$989$	−13.2048	+	22.8715i	−0.419890	+	0.727270i
$990$		0			0
$991$	−6.60807	−	11.4455i	−0.209912	−	0.363579i	0.741774	−	0.670649i	$-0.233984\pi$
$991$	−6.60807	−	11.4455i	−0.209912	−	0.363579i	−0.951687	+	0.307071i	$0.900651\pi$
$992$	5.12666	−	0.903968i	0.162771	−	0.0287010i
$993$	32.3669	+	41.1840i	1.02713	+	1.30694i
$994$	0.996935	−	0.362854i	0.0316208	−	0.0115090i
$995$		0			0
$996$	−0.919101	+	1.48029i	−0.0291228	+	0.0469047i
$997$	15.5008	+	18.4731i	0.490914	+	0.585049i	0.953450	−	0.301552i	$-0.0975046\pi$
$997$	15.5008	+	18.4731i	0.490914	+	0.585049i	−0.462535	+	0.886601i	$0.653060\pi$
$998$		−	46.9461i		−	1.48605i
$999$	7.55019	−	10.5820i	0.238877	−	0.334800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.17		132
5.2	odd	4		675.2.l.g.76.3	yes	66
5.3	odd	4		675.2.l.f.76.9	✓	66
5.4	even	2	inner	675.2.u.e.49.6		132
27.16	even	9	inner	675.2.u.e.124.6		132
135.43	odd	36		675.2.l.f.151.9	yes	66
135.97	odd	36		675.2.l.g.151.3	yes	66
135.124	even	18	inner	675.2.u.e.124.17		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.9	✓	66	5.3	odd	4
675.2.l.f.151.9	yes	66	135.43	odd	36
675.2.l.g.76.3	yes	66	5.2	odd	4
675.2.l.g.151.3	yes	66	135.97	odd	36
675.2.u.e.49.6		132	5.4	even	2	inner
675.2.u.e.49.17		132	1.1	even	1	trivial
675.2.u.e.124.6		132	27.16	even	9	inner
675.2.u.e.124.17		132	135.124	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.860644 + 1.02568i) q^{2} +(1.52697 - 0.817526i) q^{3} +(0.0359939 - 0.204131i) q^{4} +(2.15270 + 0.862581i) q^{6} +(-0.340915 + 0.0601126i) q^{7} +(2.55944 - 1.47769i) q^{8} +(1.66330 - 2.49668i) q^{9} +(-0.377953 - 0.137564i) q^{11} +(-0.111921 - 0.341129i) q^{12} +(-0.483102 + 0.575738i) q^{13} +(-0.355063 - 0.297933i) q^{14} +(3.32884 + 1.21160i) q^{16} +(1.16198 + 0.670872i) q^{17} +(3.99230 - 0.442749i) q^{18} +(-1.87243 - 3.24314i) q^{19} +(-0.471425 + 0.370498i) q^{21} +(-0.184187 - 0.506050i) q^{22} +(3.04247 + 0.536470i) q^{23} +(2.70014 - 4.34880i) q^{24} -1.00630 q^{26} +(0.498713 - 5.17216i) q^{27} +0.0717552i q^{28} +(-3.79094 + 3.18098i) q^{29} +(-0.774172 + 4.39054i) q^{31} +(-0.399363 - 1.09724i) q^{32} +(-0.689586 + 0.0989303i) q^{33} +(0.311958 + 1.76920i) q^{34} +(-0.449783 - 0.429397i) q^{36} +(2.16657 + 1.25087i) q^{37} +(1.71492 - 4.71170i) q^{38} +(-0.267003 + 1.27409i) q^{39} +(1.73862 + 1.45887i) q^{41} +(-0.785740 - 0.164663i) q^{42} +(-2.92375 + 8.03293i) q^{43} +(-0.0416850 + 0.0722005i) q^{44} +(2.06824 + 3.58230i) q^{46} +(12.1171 - 2.13658i) q^{47} +(6.07356 - 0.871334i) q^{48} +(-6.46524 + 2.35315i) q^{49} +(2.32278 + 0.0744513i) q^{51} +(0.100137 + 0.119339i) q^{52} -10.1571i q^{53} +(5.73418 - 3.93988i) q^{54} +(-0.783723 + 0.657622i) q^{56} +(-5.51051 - 3.42144i) q^{57} +(-6.52530 - 1.15059i) q^{58} +(-12.7550 + 4.64243i) q^{59} +(2.31667 + 13.1385i) q^{61} +(-5.16956 + 2.98465i) q^{62} +(-0.416963 + 0.951143i) q^{63} +(4.32418 - 7.48970i) q^{64} +(-0.694958 - 0.622148i) q^{66} +(7.89073 - 9.40381i) q^{67} +(0.178770 - 0.213050i) q^{68} +(5.08436 - 1.66813i) q^{69} +(-1.14446 + 1.98226i) q^{71} +(0.567785 - 8.84795i) q^{72} +(-10.8000 + 6.23540i) q^{73} +(0.581658 + 3.29875i) q^{74} +(-0.729423 + 0.265488i) q^{76} +(0.137119 + 0.0241778i) q^{77} +(-1.53659 + 0.822676i) q^{78} +(-9.11223 + 7.64607i) q^{79} +(-3.46686 - 8.30547i) q^{81} +3.03883i q^{82} +(-3.11961 - 3.71780i) q^{83} +(0.0586617 + 0.109568i) q^{84} +(-10.7555 + 3.91468i) q^{86} +(-3.18814 + 7.95646i) q^{87} +(-1.17062 + 0.206412i) q^{88} +(0.197409 + 0.341923i) q^{89} +(0.130088 - 0.225318i) q^{91} +(0.219021 - 0.601754i) q^{92} +(2.40725 + 7.33715i) q^{93} +(12.6200 + 10.5894i) q^{94} +(-1.50684 - 1.34897i) q^{96} +(-5.07158 + 13.9340i) q^{97} +(-7.97784 - 4.60601i) q^{98} +(-0.972102 + 0.714819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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