LMFDB - Embedded newform 207.2.i.c.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	207.55
Dual form			207.2.i.c.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.226900 - 0.0666238i) q^{2} +(-1.63546 + 1.05105i) q^{4} +(0.215370 + 1.49793i) q^{5} +(-1.05773 + 2.31611i) q^{7} +(-0.610783 + 0.704881i) q^{8} +O(q^{10})$	\(q+(0.226900 - 0.0666238i) q^{2} +(-1.63546 + 1.05105i) q^{4} +(0.215370 + 1.49793i) q^{5} +(-1.05773 + 2.31611i) q^{7} +(-0.610783 + 0.704881i) q^{8} +(0.148666 + 0.325532i) q^{10} +(-3.23616 - 0.950224i) q^{11} +(1.36745 + 2.99430i) q^{13} +(-0.0856910 + 0.595994i) q^{14} +(1.52357 - 3.33616i) q^{16} +(5.28043 + 3.39353i) q^{17} +(-3.55928 + 2.28741i) q^{19} +(-1.92663 - 2.22345i) q^{20} -0.797593 q^{22} +(4.72041 - 0.847210i) q^{23} +(2.60004 - 0.763442i) q^{25} +(0.509766 + 0.588302i) q^{26} +(-0.704460 - 4.89963i) q^{28} +(-5.28830 - 3.39858i) q^{29} +(3.10538 - 3.58380i) q^{31} +(0.388902 - 2.70488i) q^{32} +(1.42422 + 0.418188i) q^{34} +(-3.69718 - 1.08559i) q^{35} +(-0.00540403 + 0.0375858i) q^{37} +(-0.655203 + 0.756145i) q^{38} +(-1.18741 - 0.763102i) q^{40} +(0.462048 + 3.21361i) q^{41} +(-0.844033 - 0.974066i) q^{43} +(6.29135 - 1.84731i) q^{44} +(1.01462 - 0.506723i) q^{46} -3.41741 q^{47} +(0.338474 + 0.390620i) q^{49} +(0.539086 - 0.346450i) q^{50} +(-5.38357 - 3.45981i) q^{52} +(2.79399 - 6.11799i) q^{53} +(0.726398 - 5.05221i) q^{55} +(-0.986535 - 2.16021i) q^{56} +(-1.42634 - 0.418811i) q^{58} +(4.32805 + 9.47711i) q^{59} +(-2.35737 + 2.72055i) q^{61} +(0.465844 - 1.02006i) q^{62} +(0.951939 + 6.62088i) q^{64} +(-4.19075 + 2.69323i) q^{65} +(6.54316 - 1.92124i) q^{67} -12.2027 q^{68} -0.911214 q^{70} +(3.92408 - 1.15221i) q^{71} +(3.66912 - 2.35800i) q^{73} +(0.00127794 + 0.00888826i) q^{74} +(3.41689 - 7.48194i) q^{76} +(5.62381 - 6.49022i) q^{77} +(0.997820 + 2.18492i) q^{79} +(5.32548 + 1.56370i) q^{80} +(0.318941 + 0.698384i) q^{82} +(0.420847 - 2.92705i) q^{83} +(-3.94603 + 8.64060i) q^{85} +(-0.256407 - 0.164783i) q^{86} +(2.64639 - 1.70073i) q^{88} +(8.09455 + 9.34161i) q^{89} -8.38151 q^{91} +(-6.82959 + 6.34695i) q^{92} +(-0.775410 + 0.227681i) q^{94} +(-4.19295 - 4.83892i) q^{95} +(1.51088 + 10.5084i) q^{97} +(0.102824 + 0.0660811i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 7 q^{2} - 3 q^{4} + 3 q^{5} - 5 q^{7} - 4 q^{8}+O(q^{10}) $ 10 * q + 7 * q^2 - 3 * q^4 + 3 * q^5 - 5 * q^7 - 4 * q^8	$ 10 q + 7 q^{2} - 3 q^{4} + 3 q^{5} - 5 q^{7} - 4 q^{8} + q^{10} - 7 q^{11} - 3 q^{13} - 9 q^{14} + q^{16} + 10 q^{17} + 2 q^{19} + 9 q^{20} - 6 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{26} + 7 q^{28} - 14 q^{29} + 10 q^{31} - 21 q^{32} + 29 q^{34} - 7 q^{35} - 19 q^{37} + 8 q^{38} + q^{40} - 7 q^{41} - 11 q^{43} + 34 q^{44} - 29 q^{46} + 18 q^{47} - 18 q^{49} - 16 q^{50} - 20 q^{52} - 29 q^{53} - q^{55} + 2 q^{56} - 23 q^{58} + 21 q^{59} + 3 q^{61} - 4 q^{62} + 24 q^{64} - 2 q^{65} + 45 q^{67} + 30 q^{68} + 38 q^{70} + 14 q^{71} + 19 q^{73} - 10 q^{74} - 16 q^{76} - 2 q^{77} - 15 q^{79} + 52 q^{80} + 16 q^{82} - 18 q^{83} - 19 q^{85} + 11 q^{86} + 27 q^{88} - 25 q^{89} - 4 q^{91} - 52 q^{92} + 17 q^{94} - 6 q^{95} - 34 q^{97} - 17 q^{98}+O(q^{100}) $ 10 * q + 7 * q^2 - 3 * q^4 + 3 * q^5 - 5 * q^7 - 4 * q^8 + q^10 - 7 * q^11 - 3 * q^13 - 9 * q^14 + q^16 + 10 * q^17 + 2 * q^19 + 9 * q^20 - 6 * q^22 + 12 * q^23 - 4 * q^25 - 12 * q^26 + 7 * q^28 - 14 * q^29 + 10 * q^31 - 21 * q^32 + 29 * q^34 - 7 * q^35 - 19 * q^37 + 8 * q^38 + q^40 - 7 * q^41 - 11 * q^43 + 34 * q^44 - 29 * q^46 + 18 * q^47 - 18 * q^49 - 16 * q^50 - 20 * q^52 - 29 * q^53 - q^55 + 2 * q^56 - 23 * q^58 + 21 * q^59 + 3 * q^61 - 4 * q^62 + 24 * q^64 - 2 * q^65 + 45 * q^67 + 30 * q^68 + 38 * q^70 + 14 * q^71 + 19 * q^73 - 10 * q^74 - 16 * q^76 - 2 * q^77 - 15 * q^79 + 52 * q^80 + 16 * q^82 - 18 * q^83 - 19 * q^85 + 11 * q^86 + 27 * q^88 - 25 * q^89 - 4 * q^91 - 52 * q^92 + 17 * q^94 - 6 * q^95 - 34 * q^97 - 17 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	0.226900	−	0.0666238i	0.160442	−	0.0471101i	−0.200525	−	0.979689i	$-0.564265\pi$
$2$	0.226900	−	0.0666238i	0.160442	−	0.0471101i	0.360967	+	0.932578i	$0.382447\pi$
$3$		0			0
$3$		0			0
$4$	−1.63546	+	1.05105i	−0.817731	+	0.525524i
$5$	0.215370	+	1.49793i	0.0963165	+	0.669896i	0.979585	+	0.201029i	$0.0644286\pi$
$5$	0.215370	+	1.49793i	0.0963165	+	0.669896i	−0.883269	+	0.468867i	$0.844662\pi$
$6$		0			0
$7$	−1.05773	+	2.31611i	−0.399784	+	0.875406i	0.597508	+	0.801863i	$0.296158\pi$
$7$	−1.05773	+	2.31611i	−0.399784	+	0.875406i	−0.997292	+	0.0735424i	$0.976570\pi$
$8$	−0.610783	+	0.704881i	−0.215944	+	0.249213i
$9$		0			0
$10$	0.148666	+	0.325532i	0.0470122	+	0.102942i
$11$	−3.23616	−	0.950224i	−0.975740	−	0.286503i	−0.245275	−	0.969453i	$-0.578878\pi$
$11$	−3.23616	−	0.950224i	−0.975740	−	0.286503i	−0.730465	+	0.682950i	$0.760697\pi$
$12$		0			0
$13$	1.36745	+	2.99430i	0.379263	+	0.830470i	0.998959	+	0.0456275i	$0.0145287\pi$
$13$	1.36745	+	2.99430i	0.379263	+	0.830470i	−0.619696	+	0.784842i	$0.712744\pi$
$14$	−0.0856910	+	0.595994i	−0.0229019	+	0.159286i
$15$		0			0
$16$	1.52357	−	3.33616i	0.380893	−	0.834040i
$17$	5.28043	+	3.39353i	1.28069	+	0.823051i	0.990973	−	0.134061i	$-0.0428018\pi$
$17$	5.28043	+	3.39353i	1.28069	+	0.823051i	0.289719	+	0.957112i	$0.406438\pi$
$18$		0			0
$19$	−3.55928	+	2.28741i	−0.816554	+	0.524767i	−0.880979	−	0.473155i	$-0.843115\pi$
$19$	−3.55928	+	2.28741i	−0.816554	+	0.524767i	0.0644252	+	0.997923i	$0.479479\pi$
$20$	−1.92663	−	2.22345i	−0.430808	−	0.497178i
$21$		0			0
$22$	−0.797593			−0.170047
$23$	4.72041	−	0.847210i	0.984273	−	0.176655i
$23$	4.72041	−	0.847210i	0.984273	−	0.176655i
$24$		0			0
$25$	2.60004	−	0.763442i	0.520009	−	0.152688i
$26$	0.509766	+	0.588302i	0.0999734	+	0.115375i
$27$		0			0
$28$	−0.704460	−	4.89963i	−0.133130	−	0.925943i
$29$	−5.28830	−	3.39858i	−0.982012	−	0.631101i	−0.0520069	−	0.998647i	$-0.516562\pi$
$29$	−5.28830	−	3.39858i	−0.982012	−	0.631101i	−0.930005	+	0.367546i	$0.880198\pi$
$30$		0			0
$31$	3.10538	−	3.58380i	0.557742	−	0.643669i	−0.404927	−	0.914349i	$-0.632703\pi$
$31$	3.10538	−	3.58380i	0.557742	−	0.643669i	0.962669	+	0.270680i	$0.0872485\pi$
$32$	0.388902	−	2.70488i	0.0687489	−	0.478159i
$33$		0			0
$34$	1.42422	+	0.418188i	0.244251	+	0.0717187i
$35$	−3.69718	−	1.08559i	−0.624937	−	0.183498i
$36$		0			0
$37$	−0.00540403	+	0.0375858i	−0.000888417	+	0.00617907i	−0.990261	−	0.139225i	$-0.955539\pi$
$37$	−0.00540403	+	0.0375858i	−0.000888417	+	0.00617907i	0.989372	+	0.145404i	$0.0464481\pi$
$38$	−0.655203	+	0.756145i	−0.106288	+	0.122663i
$39$		0			0
$40$	−1.18741	−	0.763102i	−0.187746	−	0.120657i
$41$	0.462048	+	3.21361i	0.0721597	+	0.501882i	0.993564	+	0.113275i	$0.0361343\pi$
$41$	0.462048	+	3.21361i	0.0721597	+	0.501882i	−0.921404	+	0.388606i	$0.872957\pi$
$42$		0			0
$43$	−0.844033	−	0.974066i	−0.128714	−	0.148544i	0.687734	−	0.725963i	$-0.258605\pi$
$43$	−0.844033	−	0.974066i	−0.128714	−	0.148544i	−0.816448	+	0.577419i	$0.804060\pi$
$44$	6.29135	−	1.84731i	0.948457	−	0.278492i
$45$		0			0
$46$	1.01462	−	0.506723i	0.149597	−	0.0747123i
$47$	−3.41741			−0.498480			−0.249240	−	0.968442i	$-0.580181\pi$
$47$	−3.41741			−0.498480			−0.249240	+	0.968442i	$0.580181\pi$
$48$		0			0
$49$	0.338474	+	0.390620i	0.0483534	+	0.0558028i
$50$	0.539086	−	0.346450i	0.0762383	−	0.0489954i
$51$		0			0
$52$	−5.38357	−	3.45981i	−0.746567	−	0.479789i
$53$	2.79399	−	6.11799i	0.383784	−	0.840370i	−0.614876	−	0.788624i	$-0.710794\pi$
$53$	2.79399	−	6.11799i	0.383784	−	0.840370i	0.998660	−	0.0517465i	$-0.0164788\pi$
$54$		0			0
$55$	0.726398	−	5.05221i	0.0979475	−	0.681240i
$56$	−0.986535	−	2.16021i	−0.131831	−	0.288670i
$57$		0			0
$58$	−1.42634	−	0.418811i	−0.187288	−	0.0549926i
$59$	4.32805	+	9.47711i	0.563464	+	1.23381i	0.950205	+	0.311626i	$0.100874\pi$
$59$	4.32805	+	9.47711i	0.563464	+	1.23381i	−0.386741	+	0.922188i	$0.626399\pi$
$60$		0			0
$61$	−2.35737	+	2.72055i	−0.301830	+	0.348331i	−0.886322	−	0.463069i	$-0.846748\pi$
$61$	−2.35737	+	2.72055i	−0.301830	+	0.348331i	0.584492	+	0.811399i	$0.301294\pi$
$62$	0.465844	−	1.02006i	0.0591622	−	0.129547i
$63$		0			0
$64$	0.951939	+	6.62088i	0.118992	+	0.827610i
$65$	−4.19075	+	2.69323i	−0.519799	+	0.334055i
$66$		0			0
$67$	6.54316	−	1.92124i	0.799374	−	0.234717i	0.143562	−	0.989641i	$-0.454144\pi$
$67$	6.54316	−	1.92124i	0.799374	−	0.234717i	0.655812	+	0.754924i	$0.272326\pi$
$68$	−12.2027			−1.47979
$69$		0			0
$70$	−0.911214			−0.108911
$71$	3.92408	−	1.15221i	0.465702	−	0.136742i	−0.0404594	−	0.999181i	$-0.512882\pi$
$71$	3.92408	−	1.15221i	0.465702	−	0.136742i	0.506161	+	0.862439i	$0.331064\pi$
$72$		0			0
$73$	3.66912	−	2.35800i	0.429438	−	0.275983i	−0.308015	−	0.951381i	$-0.599665\pi$
$73$	3.66912	−	2.35800i	0.429438	−	0.275983i	0.737453	+	0.675399i	$0.236028\pi$
$74$	0.00127794	+	0.00888826i	0.000148557	+	0.00103324i
$75$		0			0
$76$	3.41689	−	7.48194i	0.391944	−	0.858237i
$77$	5.62381	−	6.49022i	0.640892	−	0.739629i
$78$		0			0
$79$	0.997820	+	2.18492i	0.112263	+	0.245823i	0.957421	−	0.288694i	$-0.0932210\pi$
$79$	0.997820	+	2.18492i	0.112263	+	0.245823i	−0.845158	+	0.534517i	$0.820494\pi$
$80$	5.32548	+	1.56370i	0.595407	+	0.174827i
$81$		0			0
$82$	0.318941	+	0.698384i	0.0352212	+	0.0771237i
$83$	0.420847	−	2.92705i	0.0461939	−	0.321286i	−0.953602	−	0.301071i	$-0.902656\pi$
$83$	0.420847	−	2.92705i	0.0461939	−	0.321286i	0.999796	−	0.0202149i	$-0.00643503\pi$
$84$		0			0
$85$	−3.94603	+	8.64060i	−0.428007	+	0.937204i
$86$	−0.256407	−	0.164783i	−0.0276491	−	0.0177690i
$87$		0			0
$88$	2.64639	−	1.70073i	0.282106	−	0.181298i
$89$	8.09455	+	9.34161i	0.858020	+	0.990208i	1.00000		0.000338824i	$0.000107851\pi$
$89$	8.09455	+	9.34161i	0.858020	+	0.990208i	−0.141979	+	0.989870i	$0.545347\pi$
$90$		0			0
$91$	−8.38151			−0.878621
$92$	−6.82959	+	6.34695i	−0.712034	+	0.661716i
$93$		0			0
$94$	−0.775410	+	0.227681i	−0.0799774	+	0.0234835i
$95$	−4.19295	−	4.83892i	−0.430187	−	0.496463i
$96$		0			0
$97$	1.51088	+	10.5084i	0.153407	+	1.06697i	0.910454	+	0.413610i	$0.135732\pi$
$97$	1.51088	+	10.5084i	0.153407	+	1.06697i	−0.757047	+	0.653360i	$0.773359\pi$
$98$	0.102824	+	0.0660811i	0.0103868	+	0.00667520i
$99$		0			0
$100$	−3.44986	+	3.98135i	−0.344986	+	0.398135i
$101$	1.30916	−	9.10538i	0.130266	−	0.906019i	−0.814940	−	0.579545i	$-0.803230\pi$
$101$	1.30916	−	9.10538i	0.130266	−	0.906019i	0.945206	−	0.326474i	$-0.105861\pi$
$102$		0			0
$103$	−14.1707	−	4.16088i	−1.39628	−	0.409984i	−0.504873	−	0.863193i	$-0.668461\pi$
$103$	−14.1707	−	4.16088i	−1.39628	−	0.409984i	−0.891404	+	0.453209i	$0.850279\pi$
$104$	−2.94584	−	0.864977i	−0.288863	−	0.0848180i
$105$		0			0
$106$	0.226353	−	1.57432i	0.0219853	−	0.152911i
$107$	−10.6131	+	12.2481i	−1.02600	+	1.18407i	−0.0432669	+	0.999064i	$0.513777\pi$
$107$	−10.6131	+	12.2481i	−1.02600	+	1.18407i	−0.982737	+	0.185008i	$0.940769\pi$
$108$		0			0
$109$	12.6437	+	8.12562i	1.21105	+	0.778293i	0.980834	−	0.194847i	$-0.0624210\pi$
$109$	12.6437	+	8.12562i	1.21105	+	0.778293i	0.230214	+	0.973140i	$0.426057\pi$
$110$	−0.171778	−	1.19474i	−0.0163784	−	0.113914i
$111$		0			0
$112$	6.11537	+	7.05751i	0.577848	+	0.666872i
$113$	−1.10866	+	0.325532i	−0.104294	+	0.0306235i	−0.333463	−	0.942763i	$-0.608217\pi$
$113$	−1.10866	+	0.325532i	−0.104294	+	0.0306235i	0.229169	+	0.973387i	$0.426399\pi$
$114$		0			0
$115$	2.28570	+	6.88839i	0.213143	+	0.642346i
$116$	12.2209			1.13468
$117$		0			0
$118$	1.61343	+	1.86200i	0.148529	+	0.171411i
$119$	−13.4450	+	8.64060i	−1.23250	+	0.792082i
$120$		0			0
$121$	0.316044	+	0.203109i	0.0287313	+	0.0184645i
$122$	−0.353634	+	0.774349i	−0.0320165	+	0.0701063i
$123$		0			0
$124$	−1.31199	+	9.12507i	−0.117820	+	0.819455i
$125$	4.84687	+	10.6132i	0.433517	+	0.949271i
$126$		0			0
$127$	−10.0205	−	2.94228i	−0.889173	−	0.261085i	−0.194923	−	0.980819i	$-0.562446\pi$
$127$	−10.0205	−	2.94228i	−0.889173	−	0.261085i	−0.694250	+	0.719734i	$0.744264\pi$
$128$	2.92750	+	6.41034i	0.258757	+	0.566599i
$129$		0			0
$130$	−0.771448	+	0.890298i	−0.0676605	+	0.0780843i
$131$	6.31204	−	13.8214i	0.551485	−	1.20758i	−0.404600	−	0.914494i	$-0.632589\pi$
$131$	6.31204	−	13.8214i	0.551485	−	1.20758i	0.956085	−	0.293090i	$-0.0946836\pi$
$132$		0			0
$133$	−1.53312	−	10.6631i	−0.132939	−	0.924610i
$134$	1.35664	−	0.871860i	0.117196	−	0.0753173i
$135$		0			0
$136$	−5.61723	+	1.64937i	−0.481673	+	0.141432i
$137$	−1.22243			−0.104439			−0.0522196	−	0.998636i	$-0.516630\pi$
$137$	−1.22243			−0.104439			−0.0522196	+	0.998636i	$0.516630\pi$
$138$		0			0
$139$	2.18447			0.185284			0.0926420	−	0.995699i	$-0.470469\pi$
$139$	2.18447			0.185284			0.0926420	+	0.995699i	$0.470469\pi$
$140$	7.18760	−	2.11047i	0.607463	−	0.178367i
$141$		0			0
$142$	0.813607	−	0.522874i	0.0682764	−	0.0438786i
$143$	−1.58004	−	10.9894i	−0.132130	−	0.918983i
$144$		0			0
$145$	3.95191	−	8.65347i	0.328188	−	0.718632i
$146$	0.675423	−	0.779480i	0.0558984	−	0.0645102i
$147$		0			0
$148$	−0.0306664	−	0.0671501i	−0.00252076	−	0.00551970i
$149$	−3.97217	−	1.16634i	−0.325413	−	0.0955499i	0.114946	−	0.993372i	$-0.463331\pi$
$149$	−3.97217	−	1.16634i	−0.325413	−	0.0955499i	−0.440359	+	0.897822i	$0.645149\pi$
$150$		0			0
$151$	−2.82316	−	6.18185i	−0.229745	−	0.503072i	0.759290	−	0.650753i	$-0.225546\pi$
$151$	−2.82316	−	6.18185i	−0.229745	−	0.503072i	−0.989035	+	0.147681i	$0.952819\pi$
$152$	0.561594	−	3.90597i	0.0455513	−	0.316816i
$153$		0			0
$154$	0.843637	−	1.84731i	0.0679822	−	0.148860i
$155$	6.03710	+	3.87981i	0.484911	+	0.311634i
$156$		0			0
$157$	8.19158	−	5.26441i	0.653759	−	0.420146i	−0.171279	−	0.985223i	$-0.554790\pi$
$157$	8.19158	−	5.26441i	0.653759	−	0.420146i	0.825038	+	0.565077i	$0.191154\pi$
$158$	0.371973	+	0.429279i	0.0295926	+	0.0341516i
$159$		0			0
$160$	4.13548			0.326939
$161$	−3.03069	+	11.8291i	−0.238852	+	0.932262i
$162$		0			0
$163$	5.78457	−	1.69850i	0.453083	−	0.133037i	−0.0472260	−	0.998884i	$-0.515038\pi$
$163$	5.78457	−	1.69850i	0.453083	−	0.133037i	0.500309	+	0.865847i	$0.333220\pi$
$164$	−4.13332	−	4.77011i	−0.322758	−	0.372483i
$165$		0			0
$166$	−0.0995214	−	0.692186i	−0.00772436	−	0.0537241i
$167$	−1.48029	−	0.951323i	−0.114548	−	0.0736155i	0.482112	−	0.876109i	$-0.339870\pi$
$167$	−1.48029	−	0.951323i	−0.114548	−	0.0736155i	−0.596660	+	0.802494i	$0.703506\pi$
$168$		0			0
$169$	1.41728	−	1.63562i	0.109021	−	0.125817i
$170$	−0.319684	+	2.22345i	−0.0245186	+	0.170531i
$171$		0			0
$172$	2.40417	+	0.705929i	0.183317	+	0.0538266i
$173$	−9.79801	−	2.87696i	−0.744929	−	0.218731i	−0.112825	−	0.993615i	$-0.535990\pi$
$173$	−9.79801	−	2.87696i	−0.744929	−	0.218731i	−0.632104	+	0.774884i	$0.717808\pi$
$174$		0			0
$175$	−0.981933	+	6.82949i	−0.0742271	+	0.516261i
$176$	−8.10063	+	9.34863i	−0.610608	+	0.704679i
$177$		0			0
$178$	2.45903	+	1.58032i	0.184312	+	0.118450i
$179$	−1.46662	−	10.2006i	−0.109620	−	0.762426i	−0.968278	−	0.249876i	$-0.919610\pi$
$179$	−1.46662	−	10.2006i	−0.109620	−	0.762426i	0.858658	−	0.512550i	$-0.171299\pi$
$180$		0			0
$181$	−6.08462	−	7.02203i	−0.452266	−	0.521943i	0.483128	−	0.875550i	$-0.339501\pi$
$181$	−6.08462	−	7.02203i	−0.452266	−	0.521943i	−0.935394	+	0.353607i	$0.884955\pi$
$182$	−1.90176	+	0.558408i	−0.140968	+	0.0413920i
$183$		0			0
$184$	−2.28596	+	3.84479i	−0.168523	+	0.283441i
$185$	−0.0574649			−0.00422491
$186$		0			0
$187$	−13.8637	−	15.9996i	−1.01382	−	1.17001i
$188$	5.58904	−	3.59186i	0.407623	−	0.261963i
$189$		0			0
$190$	−1.27377	−	0.818600i	−0.0924087	−	0.0593875i
$191$	8.52854	−	18.6749i	0.617104	−	1.35127i	−0.300504	−	0.953781i	$-0.597155\pi$
$191$	8.52854	−	18.6749i	0.617104	−	1.35127i	0.917607	−	0.397488i	$-0.130118\pi$
$192$		0			0
$193$	1.95491	−	13.5967i	0.140718	−	0.978713i	−0.790034	−	0.613063i	$-0.789937\pi$
$193$	1.95491	−	13.5967i	0.140718	−	0.978713i	0.930752	−	0.365651i	$-0.119154\pi$
$194$	1.04293	+	2.28370i	0.0748781	+	0.163960i
$195$		0			0
$196$	−0.964121	−	0.283091i	−0.0688658	−	0.0202208i
$197$	−0.955220	−	2.09164i	−0.0680566	−	0.149023i	0.872547	−	0.488531i	$-0.162467\pi$
$197$	−0.955220	−	2.09164i	−0.0680566	−	0.149023i	−0.940603	+	0.339507i	$0.889740\pi$
$198$		0			0
$199$	−1.12023	+	1.29281i	−0.0794109	+	0.0916450i	−0.794065	−	0.607833i	$-0.792039\pi$
$199$	−1.12023	+	1.29281i	−0.0794109	+	0.0916450i	0.714654	+	0.699478i	$0.246584\pi$
$200$	−1.04993	+	2.29902i	−0.0742410	+	0.162565i
$201$		0			0
$202$	−0.309588	−	2.15323i	−0.0217825	−	0.151501i
$203$	13.4651	−	8.65347i	0.945062	−	0.607355i
$204$		0			0
$205$	−4.71426	+	1.38423i	−0.329259	+	0.0966790i
$206$	−3.49254			−0.243337
$207$		0			0
$208$	12.0729			0.837104
$209$	13.6919	−	4.02032i	0.947092	−	0.278091i
$210$		0			0
$211$	−6.73249	+	4.32671i	−0.463484	+	0.297863i	−0.751465	−	0.659773i	$-0.770652\pi$
$211$	−6.73249	+	4.32671i	−0.463484	+	0.297863i	0.287981	+	0.957636i	$0.407016\pi$
$212$	1.86083	+	12.9424i	0.127802	+	0.888885i
$213$		0			0
$214$	−1.59209	+	3.48618i	−0.108833	+	0.238310i
$215$	1.27731	−	1.47409i	0.0871116	−	0.100532i
$216$		0			0
$217$	5.01580	+	10.9831i	0.340495	+	0.745580i
$218$	3.41021	+	1.00133i	0.230969	+	0.0678186i
$219$		0			0
$220$	4.12212	+	9.02618i	0.277913	+	0.608545i
$221$	−2.94051	+	20.4517i	−0.197800	+	1.37573i
$222$		0			0
$223$	11.8489	−	25.9455i	0.793463	−	1.73744i	0.127000	−	0.991903i	$-0.459465\pi$
$223$	11.8489	−	25.9455i	0.793463	−	1.73744i	0.666463	−	0.745538i	$-0.267808\pi$
$224$	5.85342	+	3.76177i	0.391098	+	0.251344i
$225$		0			0
$226$	−0.229867	+	0.147726i	−0.0152905	+	0.00982661i
$227$	−6.14462	−	7.09127i	−0.407833	−	0.470664i	0.514259	−	0.857635i	$-0.328067\pi$
$227$	−6.14462	−	7.09127i	−0.407833	−	0.470664i	−0.922092	+	0.386971i	$0.873521\pi$
$228$		0			0
$229$	−6.65292			−0.439637			−0.219819	−	0.975541i	$-0.570547\pi$
$229$	−6.65292			−0.439637			−0.219819	+	0.975541i	$0.570547\pi$
$230$	0.977556	+	1.41069i	0.0644581	+	0.0930183i
$231$		0			0
$232$	5.62560	−	1.65182i	0.369339	−	0.108448i
$233$	−16.7901	−	19.3768i	−1.09996	−	1.26942i	−0.960224	−	0.279229i	$-0.909921\pi$
$233$	−16.7901	−	19.3768i	−1.09996	−	1.26942i	−0.139733	−	0.990189i	$-0.544624\pi$
$234$		0			0
$235$	−0.736009	−	5.11905i	−0.0480119	−	0.333930i
$236$	−17.0393	−	10.9505i	−1.10916	−	0.712815i
$237$		0			0
$238$	−2.47501	+	2.85631i	−0.160431	+	0.185147i
$239$	−0.218040	+	1.51650i	−0.0141038	+	0.0980943i	−0.995657	−	0.0930929i	$-0.970325\pi$
$239$	−0.218040	+	1.51650i	−0.0141038	+	0.0980943i	0.981554	+	0.191187i	$0.0612337\pi$
$240$		0			0
$241$	26.7753	+	7.86194i	1.72475	+	0.506432i	0.985885	−	0.167422i	$-0.0535442\pi$
$241$	26.7753	+	7.86194i	1.72475	+	0.506432i	0.738864	+	0.673854i	$0.235362\pi$
$242$	0.0852423	+	0.0250294i	0.00547958	+	0.00160895i
$243$		0			0
$244$	0.995962	−	6.92707i	0.0637599	−	0.443460i
$245$	−0.512225	+	0.591139i	−0.0327249	+	0.0377665i
$246$		0			0
$247$	−11.7163	−	7.52962i	−0.745492	−	0.479098i
$248$	0.629439	+	4.37784i	0.0399694	+	0.277993i
$249$		0			0
$250$	1.80684	+	2.08521i	0.114275	+	0.131880i
$251$	−10.8108	+	3.17435i	−0.682374	+	0.200363i	−0.604506	−	0.796601i	$-0.706629\pi$
$251$	−10.8108	+	3.17435i	−0.682374	+	0.200363i	−0.0778679	+	0.996964i	$0.524811\pi$
$252$		0			0
$253$	−16.0810	−	1.74373i	−1.01101	−	0.109627i
$254$	−2.46967			−0.154961
$255$		0			0
$256$	−7.66935	−	8.85090i	−0.479334	−	0.553181i
$257$	13.8310	−	8.88867i	0.862756	−	0.554460i	−0.0327727	−	0.999463i	$-0.510434\pi$
$257$	13.8310	−	8.88867i	0.862756	−	0.554460i	0.895529	+	0.445003i	$0.146797\pi$
$258$		0			0
$259$	−0.0813368	−	0.0522720i	−0.00505402	−	0.00324802i
$260$	4.02310	−	8.80937i	0.249502	−	0.546334i
$261$		0			0
$262$	0.511364	−	3.55661i	0.0315921	−	0.219728i
$263$	9.76148	+	21.3747i	0.601919	+	1.31802i	0.927966	+	0.372665i	$0.121556\pi$
$263$	9.76148	+	21.3747i	0.601919	+	1.31802i	−0.326048	+	0.945353i	$0.605717\pi$
$264$		0			0
$265$	9.76608	+	2.86758i	0.599926	+	0.176154i
$266$	−1.05828	−	2.31732i	−0.0648875	−	0.142084i
$267$		0			0
$268$	−8.68177	+	10.0193i	−0.530323	+	0.612026i
$269$	−1.84523	+	4.04049i	−0.112506	+	0.246353i	−0.957506	−	0.288412i	$-0.906873\pi$
$269$	−1.84523	+	4.04049i	−0.112506	+	0.246353i	0.845001	+	0.534765i	$0.179600\pi$
$270$		0			0
$271$	2.80373	+	19.5004i	0.170315	+	1.18456i	0.878220	+	0.478257i	$0.158731\pi$
$271$	2.80373	+	19.5004i	0.170315	+	1.18456i	−0.707905	+	0.706308i	$0.750360\pi$
$272$	19.3665	−	12.4461i	1.17426	−	0.754654i
$273$		0			0
$274$	−0.277369	+	0.0814429i	−0.0167565	+	0.00492015i
$275$	−9.13961			−0.551139
$276$		0			0
$277$	−18.8580			−1.13307			−0.566535	−	0.824038i	$-0.691716\pi$
$277$	−18.8580			−1.13307			−0.566535	+	0.824038i	$0.691716\pi$
$278$	0.495655	−	0.145537i	0.0297274	−	0.00872876i
$279$		0			0
$280$	3.02338	−	1.94301i	0.180682	−	0.116117i
$281$	2.73137	+	18.9971i	0.162940	+	1.13327i	0.893055	+	0.449948i	$0.148558\pi$
$281$	2.73137	+	18.9971i	0.162940	+	1.13327i	−0.730114	+	0.683325i	$0.760533\pi$
$282$		0			0
$283$	0.452826	−	0.991551i	0.0269177	−	0.0589416i	−0.895696	−	0.444668i	$-0.853322\pi$
$283$	0.452826	−	0.991551i	0.0269177	−	0.0589416i	0.922613	+	0.385726i	$0.126049\pi$
$284$	−5.20665	+	6.00879i	−0.308958	+	0.356556i
$285$		0			0
$286$	−1.09067	−	2.38823i	−0.0644926	−	0.141219i
$287$	−7.93178	−	2.32898i	−0.468198	−	0.137475i
$288$		0			0
$289$	9.30486	+	20.3748i	0.547345	+	1.19852i
$290$	0.320160	−	2.22676i	0.0188005	−	0.130760i
$291$		0			0
$292$	−3.52233	+	7.71283i	−0.206129	+	0.451359i
$293$	11.7264	+	7.53613i	0.685066	+	0.440265i	0.836329	−	0.548228i	$-0.184698\pi$
$293$	11.7264	+	7.53613i	0.685066	+	0.440265i	−0.151262	+	0.988494i	$0.548334\pi$
$294$		0			0
$295$	−13.2639	+	8.52422i	−0.772257	+	0.496299i
$296$	−0.0231929	−	0.0267660i	−0.00134806	−	0.00155574i
$297$		0			0
$298$	−0.978991			−0.0567114
$299$	8.99173	+	12.9758i	0.520005	+	0.750410i
$300$		0			0
$301$	3.14880	−	0.924571i	0.181494	−	0.0532914i
$302$	−1.05243	−	1.21457i	−0.0605607	−	0.0698907i
$303$		0			0
$304$	2.20834	+	15.3593i	0.126657	+	0.880919i
$305$	−4.58291	−	2.94526i	−0.262417	−	0.168645i
$306$		0			0
$307$	16.7842	−	19.3701i	0.957928	−	1.10551i	−0.0364203	−	0.999337i	$-0.511595\pi$
$307$	16.7842	−	19.3701i	0.957928	−	1.10551i	0.994348	−	0.106171i	$-0.0338590\pi$
$308$	−2.37599	+	16.5254i	−0.135385	+	0.941622i
$309$		0			0
$310$	1.62830	+	0.478113i	0.0924814	+	0.0271550i
$311$	−3.56322	−	1.04626i	−0.202052	−	0.0593277i	0.179141	−	0.983823i	$-0.442668\pi$
$311$	−3.56322	−	1.04626i	−0.202052	−	0.0593277i	−0.381192	+	0.924496i	$0.624486\pi$
$312$		0			0
$313$	−2.23843	+	15.5687i	−0.126524	+	0.879992i	0.823389	+	0.567477i	$0.192081\pi$
$313$	−2.23843	+	15.5687i	−0.126524	+	0.879992i	−0.949913	+	0.312515i	$0.898829\pi$
$314$	1.50793	−	1.74025i	0.0850976	−	0.0982078i
$315$		0			0
$316$	−3.92835	−	2.52460i	−0.220987	−	0.142020i
$317$	−0.470339	−	3.27128i	−0.0264169	−	0.183733i	0.972341	−	0.233567i	$-0.0750399\pi$
$317$	−0.470339	−	3.27128i	−0.0264169	−	0.183733i	−0.998758	+	0.0498339i	$0.984131\pi$
$318$		0			0
$319$	13.8844	+	16.0234i	0.777376	+	0.897140i
$320$	−9.71262	+	2.85188i	−0.542952	+	0.159425i
$321$		0			0
$322$	0.100436	+	2.88593i	0.00559706	+	0.160827i
$323$	−26.5569			−1.47766
$324$		0			0
$325$	5.84141	+	6.74135i	0.324023	+	0.373943i
$326$	1.19936	−	0.770780i	0.0664263	−	0.0426896i
$327$		0			0
$328$	−2.54742	−	1.63713i	−0.140658	−	0.0903954i
$329$	3.61470	−	7.91508i	0.199285	−	0.436373i
$330$		0			0
$331$	−1.13861	+	7.91923i	−0.0625838	+	0.435280i	0.934306	+	0.356472i	$0.116021\pi$
$331$	−1.13861	+	7.91923i	−0.0625838	+	0.435280i	−0.996890	+	0.0788080i	$0.974889\pi$
$332$	2.38819	+	5.22942i	0.131069	+	0.287001i
$333$		0			0
$334$	−0.399258	−	0.117233i	−0.0218464	−	0.00641468i
$335$	4.28710	+	9.38744i	0.234229	+	0.512891i
$336$		0			0
$337$	−0.911733	+	1.05220i	−0.0496653	+	0.0573168i	−0.780039	−	0.625731i	$-0.784801\pi$
$337$	−0.911733	+	1.05220i	−0.0496653	+	0.0573168i	0.730373	+	0.683048i	$0.239346\pi$
$338$	0.212608	−	0.465547i	0.0115644	−	0.0253224i
$339$		0			0
$340$	−2.62810	−	18.2788i	−0.142529	−	0.991309i
$341$	−13.4549	+	8.64695i	−0.728625	+	0.468259i
$342$		0			0
$343$	−18.3642	+	5.39220i	−0.991571	+	0.291152i
$344$	1.20212			0.0648141
$345$		0			0
$346$	−2.41484			−0.129823
$347$	16.1469	−	4.74116i	0.866811	−	0.254519i	0.182052	−	0.983289i	$-0.441726\pi$
$347$	16.1469	−	4.74116i	0.866811	−	0.254519i	0.684758	+	0.728770i	$0.259908\pi$
$348$		0			0
$349$	−16.0913	+	10.3412i	−0.861347	+	0.553554i	−0.895095	−	0.445876i	$-0.852892\pi$
$349$	−16.0913	+	10.3412i	−0.861347	+	0.553554i	0.0337478	+	0.999430i	$0.489256\pi$
$350$	0.232206	+	1.61503i	0.0124120	+	0.0863270i
$351$		0			0
$352$	−3.82879	+	8.38388i	−0.204075	+	0.446862i
$353$	22.0360	−	25.4309i	1.17286	−	1.35355i	0.250076	−	0.968226i	$-0.419544\pi$
$353$	22.0360	−	25.4309i	1.17286	−	1.35355i	0.922781	−	0.385324i	$-0.125910\pi$
$354$		0			0
$355$	2.57107	+	5.62985i	0.136458	+	0.298801i
$356$	−23.0568	−	6.77009i	−1.22201	−	0.358814i
$357$		0			0
$358$	−1.01238	−	2.21679i	−0.0535057	−	0.117161i
$359$	−2.79386	+	19.4317i	−0.147454	+	1.02557i	0.772914	+	0.634511i	$0.218799\pi$
$359$	−2.79386	+	19.4317i	−0.147454	+	1.02557i	−0.920368	+	0.391054i	$0.872110\pi$
$360$		0			0
$361$	−0.456674	+	0.999978i	−0.0240355	+	0.0526304i
$362$	−1.84843	−	1.18792i	−0.0971515	−	0.0624355i
$363$		0			0
$364$	13.7076	−	8.80937i	0.718476	−	0.461736i
$365$	4.32234	+	4.98825i	0.226242	+	0.261097i
$366$		0			0
$367$	6.73062			0.351336			0.175668	−	0.984449i	$-0.443792\pi$
$367$	6.73062			0.351336			0.175668	+	0.984449i	$0.443792\pi$
$368$	4.36546	−	17.0388i	0.227565	−	0.888210i
$369$		0			0
$370$	−0.0130388	+	0.00382853i	−0.000677854	+	0.000199036i
$371$	11.2146	+	12.9424i	0.582234	+	0.671934i
$372$		0			0
$373$	−3.60455	−	25.0702i	−0.186637	−	1.29809i	−0.840640	−	0.541595i	$-0.817821\pi$
$373$	−3.60455	−	25.0702i	−0.186637	−	1.29809i	0.654003	−	0.756492i	$-0.273088\pi$
$374$	−4.21163	−	2.70665i	−0.217778	−	0.139958i
$375$		0			0
$376$	2.08729	−	2.40887i	0.107644	−	0.124228i
$377$	2.94489	−	20.4822i	0.151669	−	1.05488i
$378$		0			0
$379$	−27.6884	−	8.13003i	−1.42226	−	0.417612i	−0.521989	−	0.852952i	$-0.674810\pi$
$379$	−27.6884	−	8.13003i	−1.42226	−	0.417612i	−0.900266	+	0.435340i	$0.856628\pi$
$380$	11.9433	+	3.50688i	0.612680	+	0.179899i
$381$		0			0
$382$	0.690932	−	4.80554i	0.0353512	−	0.245873i
$383$	−8.44472	+	9.74573i	−0.431505	+	0.497983i	−0.929307	−	0.369307i	$-0.879595\pi$
$383$	−8.44472	+	9.74573i	−0.431505	+	0.497983i	0.497802	+	0.867290i	$0.334140\pi$
$384$		0			0
$385$	10.9331	+	7.02629i	0.557203	+	0.358093i
$386$	−0.462296	−	3.21534i	−0.0235302	−	0.163656i
$387$		0			0
$388$	−13.5159	−	15.5981i	−0.686164	−	0.791875i
$389$	2.01154	−	0.590642i	0.101989	−	0.0299467i	−0.230340	−	0.973110i	$-0.573984\pi$
$389$	2.01154	−	0.590642i	0.101989	−	0.0299467i	0.332329	+	0.943164i	$0.392166\pi$
$390$		0			0
$391$	27.8008	+	11.5452i	1.40595	+	0.583865i
$392$	−0.482074			−0.0243484
$393$		0			0
$394$	−0.356092	−	0.410953i	−0.0179397	−	0.0207035i
$395$	−3.05796	+	1.96523i	−0.153863	+	0.0988817i
$396$		0			0
$397$	1.58072	+	1.01587i	0.0793341	+	0.0509849i	0.579707	−	0.814825i	$-0.303167\pi$
$397$	1.58072	+	1.01587i	0.0793341	+	0.0509849i	−0.500372	+	0.865810i	$0.666804\pi$
$398$	−0.168047	+	0.367973i	−0.00842346	+	0.0184448i
$399$		0			0
$400$	1.41439	−	9.83733i	0.0707197	−	0.491866i
$401$	−7.00168	−	15.3315i	−0.349647	−	0.765620i	−0.999982	−	0.00597275i	$-0.998099\pi$
$401$	−7.00168	−	15.3315i	−0.349647	−	0.765620i	0.650335	−	0.759647i	$-0.274628\pi$
$402$		0			0
$403$	14.9774	+	4.39777i	0.746079	+	0.219068i
$404$	7.42911	+	16.2675i	0.369612	+	0.809338i
$405$		0			0
$406$	2.47869	−	2.86057i	0.123016	−	0.141967i
$407$	0.0532033	−	0.116499i	0.00263719	−	0.00577464i
$408$		0			0
$409$	−1.85146	−	12.8772i	−0.0915489	−	0.636736i	−0.982998	−	0.183616i	$-0.941220\pi$
$409$	−1.85146	−	12.8772i	−0.0915489	−	0.636736i	0.891449	−	0.453121i	$-0.149689\pi$
$410$	−0.977443	+	0.628164i	−0.0482725	+	0.0310228i
$411$		0			0
$412$	27.5489	−	8.08908i	1.35724	−	0.398520i
$413$	−26.5279			−1.30535
$414$		0			0
$415$	4.47517			0.219677
$416$	8.63102	−	2.53430i	0.423170	−	0.124254i
$417$		0			0
$418$	2.83885	−	1.82442i	0.138853	−	0.0892353i
$419$	−4.18557	−	29.1113i	−0.204479	−	1.42218i	−0.790787	−	0.612092i	$-0.790328\pi$
$419$	−4.18557	−	29.1113i	−0.204479	−	1.42218i	0.586308	−	0.810088i	$-0.300581\pi$
$420$		0			0
$421$	9.26262	−	20.2823i	0.451432	−	0.988499i	−0.537925	−	0.842993i	$-0.680792\pi$
$421$	9.26262	−	20.2823i	0.451432	−	0.988499i	0.989357	−	0.145506i	$-0.0464811\pi$
$422$	−1.23934	+	1.43027i	−0.0603301	+	0.0696247i
$423$		0			0
$424$	2.60593	+	5.70619i	0.126555	+	0.277117i
$425$	16.3201	+	4.79202i	0.791642	+	0.232447i
$426$		0			0
$427$	−3.80762	−	8.33753i	−0.184264	−	0.403481i
$428$	4.48390	−	31.1862i	0.216737	−	1.50744i
$429$		0			0
$430$	0.191611	−	0.419570i	0.00924031	−	0.0202335i
$431$	1.48190	+	0.952360i	0.0713807	+	0.0458736i	0.575844	−	0.817559i	$-0.304673\pi$
$431$	1.48190	+	0.952360i	0.0713807	+	0.0458736i	−0.504464	+	0.863433i	$0.668310\pi$
$432$		0			0
$433$	11.6083	−	7.46017i	0.557857	−	0.358513i	−0.231130	−	0.972923i	$-0.574242\pi$
$433$	11.6083	−	7.46017i	0.557857	−	0.358513i	0.788987	+	0.614410i	$0.210606\pi$
$434$	1.86982	+	2.15789i	0.0897542	+	0.103582i
$435$		0			0
$436$	−29.2187			−1.39932
$437$	−14.8633	+	13.8129i	−0.711009	+	0.660763i
$438$		0			0
$439$	−6.89730	+	2.02523i	−0.329190	+	0.0966590i	−0.442151	−	0.896940i	$-0.645785\pi$
$439$	−6.89730	+	2.02523i	−0.329190	+	0.0966590i	0.112961	+	0.993599i	$0.463966\pi$
$440$	3.11753	+	3.59783i	0.148623	+	0.171520i
$441$		0			0
$442$	0.695368	+	4.83639i	0.0330753	+	0.230044i
$443$	19.6782	+	12.6464i	0.934939	+	0.600849i	0.916956	−	0.398989i	$-0.130639\pi$
$443$	19.6782	+	12.6464i	0.934939	+	0.600849i	0.0179838	+	0.999838i	$0.494275\pi$
$444$		0			0
$445$	−12.2498	+	14.1370i	−0.580695	+	0.670158i
$446$	0.959929	−	6.67646i	0.0454540	−	0.316139i
$447$		0			0
$448$	−16.3415	−	4.79831i	−0.772066	−	0.226699i
$449$	6.47903	+	1.90241i	0.305764	+	0.0897804i	0.431015	−	0.902345i	$-0.358155\pi$
$449$	6.47903	+	1.90241i	0.305764	+	0.0897804i	−0.125251	+	0.992125i	$0.539974\pi$
$450$		0			0
$451$	1.55839	−	10.8388i	0.0733816	−	0.510380i
$452$	1.47102	−	1.69765i	0.0691911	−	0.0798508i
$453$		0			0
$454$	−1.86666	−	1.19963i	−0.0876067	−	0.0563014i
$455$	−1.80513	−	12.5549i	−0.0846257	−	0.588585i
$456$		0			0
$457$	−4.73128	−	5.46019i	−0.221320	−	0.255417i	0.634221	−	0.773152i	$-0.281321\pi$
$457$	−4.73128	−	5.46019i	−0.221320	−	0.255417i	−0.855541	+	0.517735i	$0.826775\pi$
$458$	−1.50955	+	0.443242i	−0.0705364	+	0.0207114i
$459$		0			0
$460$	−10.9782	−	8.86332i	−0.511861	−	0.413255i
$461$	32.1800			1.49877			0.749385	−	0.662134i	$-0.230349\pi$
$461$	32.1800			1.49877			0.749385	+	0.662134i	$0.230349\pi$
$462$		0			0
$463$	12.2945	+	14.1886i	0.571373	+	0.659399i	0.965727	−	0.259559i	$-0.0835773\pi$
$463$	12.2945	+	14.1886i	0.571373	+	0.659399i	−0.394355	+	0.918958i	$0.629032\pi$
$464$	−19.3953	+	12.4646i	−0.900406	+	0.578656i
$465$		0			0
$466$	−5.10063	−	3.27798i	−0.236282	−	0.151849i
$467$	−11.8290	+	25.9018i	−0.547379	+	1.19859i	0.410617	+	0.911808i	$0.365313\pi$
$467$	−11.8290	+	25.9018i	−0.547379	+	1.19859i	−0.957995	+	0.286784i	$0.907414\pi$
$468$		0			0
$469$	−2.47109	+	17.1868i	−0.114104	+	0.793613i
$470$	−0.508051	−	1.11248i	−0.0234346	−	0.0513147i
$471$		0			0
$472$	−9.32373	−	2.73769i	−0.429160	−	0.126013i
$473$	1.80585	+	3.95426i	0.0830330	+	0.181817i
$474$		0			0
$475$	−7.50797	+	8.66466i	−0.344489	+	0.397562i
$476$	12.9072	−	28.2627i	0.591599	−	1.29542i
$477$		0			0
$478$	0.0515618	+	0.358621i	0.00235838	+	0.0164029i
$479$	−3.97699	+	2.55585i	−0.181713	+	0.116780i	−0.628335	−	0.777943i	$-0.716263\pi$
$479$	−3.97699	+	2.55585i	−0.181713	+	0.116780i	0.446622	+	0.894723i	$0.352627\pi$
$480$		0			0
$481$	−0.119933	+	0.0352155i	−0.00546848	+	0.00160569i
$482$	6.59911			0.300581
$483$		0			0
$484$	−0.730356			−0.0331980
$485$	−15.4155	+	4.52641i	−0.699983	+	0.205534i
$486$		0			0
$487$	26.6479	−	17.1256i	1.20753	−	0.776034i	0.227288	−	0.973827i	$-0.427014\pi$
$487$	26.6479	−	17.1256i	1.20753	−	0.776034i	0.980244	+	0.197794i	$0.0633776\pi$
$488$	−0.477823	−	3.32333i	−0.0216300	−	0.150440i
$489$		0			0
$490$	−0.0768398	+	0.168256i	−0.00347127	+	0.00760102i
$491$	−4.71421	+	5.44049i	−0.212749	+	0.245526i	−0.852087	−	0.523400i	$-0.824663\pi$
$491$	−4.71421	+	5.44049i	−0.212749	+	0.245526i	0.639338	+	0.768926i	$0.279209\pi$
$492$		0			0
$493$	−16.3913	−	35.8920i	−0.738227	−	1.61649i
$494$	−3.16008	−	0.927884i	−0.142179	−	0.0417475i
$495$		0			0
$496$	−7.22485	−	15.8202i	−0.324405	−	0.710349i
$497$	−1.48197	+	10.3073i	−0.0664753	+	0.462346i
$498$		0			0
$499$	−9.46867	+	20.7335i	−0.423876	+	0.928159i	0.570405	+	0.821364i	$0.306786\pi$
$499$	−9.46867	+	20.7335i	−0.423876	+	0.928159i	−0.994281	+	0.106795i	$0.965941\pi$
$500$	−19.0818	−	12.2631i	−0.853365	−	0.548425i
$501$		0			0
$502$	−2.24149	+	1.44052i	−0.100043	+	0.0642935i
$503$	−15.9978	−	18.4625i	−0.713308	−	0.823201i	0.277177	−	0.960819i	$-0.410601\pi$
$503$	−15.9978	−	18.4625i	−0.713308	−	0.823201i	−0.990485	+	0.137617i	$0.956056\pi$
$504$		0			0
$505$	13.9212			0.619485
$506$	−3.76496	+	0.675728i	−0.167373	+	0.0300398i
$507$		0			0
$508$	19.4806	−	5.72001i	0.864311	−	0.253785i
$509$	−5.12772	−	5.91771i	−0.227282	−	0.262298i	0.630642	−	0.776074i	$-0.282792\pi$
$509$	−5.12772	−	5.91771i	−0.227282	−	0.262298i	−0.857924	+	0.513776i	$0.828246\pi$
$510$		0			0
$511$	1.58044	+	10.9922i	0.0699144	+	0.486266i
$512$	−14.1868	−	9.11729i	−0.626973	−	0.402931i
$513$		0			0
$514$	2.54606	−	2.93831i	0.112302	−	0.129603i
$515$	3.18079	−	22.1229i	0.140162	−	0.974849i
$516$		0			0
$517$	11.0593	+	3.24730i	0.486387	+	0.142816i
$518$	−0.0219379	−	0.00644153i	−0.000963894	−	0.000283025i
$519$		0			0
$520$	0.661231	−	4.59896i	0.0289969	−	0.201678i
$521$	1.98664	−	2.29270i	0.0870361	−	0.100445i	−0.710561	−	0.703636i	$-0.751559\pi$
$521$	1.98664	−	2.29270i	0.0870361	−	0.100445i	0.797597	+	0.603191i	$0.206104\pi$
$522$		0			0
$523$	24.9421	+	16.0293i	1.09064	+	0.700913i	0.956992	−	0.290115i	$-0.0936937\pi$
$523$	24.9421	+	16.0293i	1.09064	+	0.700913i	0.133650	+	0.991029i	$0.457330\pi$
$524$	4.20389	+	29.2387i	0.183648	+	1.27730i
$525$		0			0
$526$	3.63894	+	4.19956i	0.158665	+	0.183109i
$527$	28.5594	−	8.38581i	1.24407	−	0.365292i
$528$		0			0
$529$	21.5645	−	7.99835i	0.937586	−	0.347754i
$530$	2.40697			0.104552
$531$		0			0
$532$	13.7148	+	15.8277i	0.594613	+	0.686219i
$533$	−8.99069	+	5.77797i	−0.389430	+	0.250271i
$534$		0			0
$535$	−20.6326	−	13.2598i	−0.892026	−	0.573270i
$536$	−2.64220	+	5.78561i	−0.114126	+	0.249900i
$537$		0			0
$538$	−0.149489	+	1.03972i	−0.00644494	+	0.0448256i
$539$	−0.724181	−	1.58573i	−0.0311927	−	0.0683024i
$540$		0			0
$541$	−22.8021	−	6.69531i	−0.980341	−	0.287854i	−0.247976	−	0.968766i	$-0.579765\pi$
$541$	−22.8021	−	6.69531i	−0.980341	−	0.287854i	−0.732365	+	0.680912i	$0.761584\pi$
$542$	1.93536	+	4.23784i	0.0831307	+	0.182031i
$543$		0			0
$544$	11.2326	−	12.9632i	0.481595	−	0.555791i
$545$	−9.44856	+	20.6895i	−0.404732	+	0.886239i
$546$		0			0
$547$	2.72007	+	18.9185i	0.116302	+	0.808896i	0.961571	+	0.274556i	$0.0885308\pi$
$547$	2.72007	+	18.9185i	0.116302	+	0.808896i	−0.845269	+	0.534340i	$0.820560\pi$
$548$	1.99924	−	1.28483i	0.0854032	−	0.0548853i
$549$		0			0
$550$	−2.07378	+	0.608916i	−0.0884261	+	0.0259642i
$551$	26.5965			1.13305
$552$		0			0
$553$	−6.11593			−0.260076
$554$	−4.27888	+	1.25639i	−0.181792	+	0.0533790i
$555$		0			0
$556$	−3.57261	+	2.29598i	−0.151513	+	0.0973712i
$557$	−2.79304	−	19.4260i	−0.118345	−	0.823106i	−0.959378	−	0.282123i	$-0.908961\pi$
$557$	−2.79304	−	19.4260i	−0.118345	−	0.823106i	0.841033	−	0.540983i	$-0.181948\pi$
$558$		0			0
$559$	1.76247	−	3.85928i	0.0745447	−	0.163230i
$560$	−9.25462	+	10.6804i	−0.391079	+	0.451329i
$561$		0			0
$562$	1.88541	+	4.12847i	0.0795312	+	0.174149i
$563$	42.8697	+	12.5877i	1.80674	+	0.530507i	0.998312	−	0.0580848i	$-0.0184994\pi$
$563$	42.8697	+	12.5877i	1.80674	+	0.530507i	0.808430	+	0.588592i	$0.200318\pi$
$564$		0			0
$565$	−0.726398	−	1.59059i	−0.0305598	−	0.0669166i
$566$	0.0366853	−	0.255152i	0.00154200	−	0.0107248i
$567$		0			0
$568$	−1.58458	+	3.46976i	−0.0664877	+	0.145588i
$569$	−3.48719	−	2.24108i	−0.146191	−	0.0939510i	0.465501	−	0.885047i	$-0.345874\pi$
$569$	−3.48719	−	2.24108i	−0.146191	−	0.0939510i	−0.611691	+	0.791096i	$0.709511\pi$
$570$		0			0
$571$	−11.2629	+	7.23824i	−0.471339	+	0.302911i	−0.754662	−	0.656113i	$-0.772199\pi$
$571$	−11.2629	+	7.23824i	−0.471339	+	0.302911i	0.283324	+	0.959024i	$0.408563\pi$
$572$	14.1345	+	16.3121i	0.590994	+	0.682043i
$573$		0			0
$574$	−1.95489			−0.0815954
$575$	11.6265	−	5.80654i	0.484857	−	0.242149i
$576$		0			0
$577$	−22.4790	+	6.60044i	−0.935814	+	0.274780i	−0.713869	−	0.700279i	$-0.753059\pi$
$577$	−22.4790	+	6.60044i	−0.935814	+	0.274780i	−0.221945	+	0.975059i	$0.571241\pi$
$578$	3.46872	+	4.00311i	0.144280	+	0.166508i
$579$		0			0
$580$	2.63202	+	18.3061i	0.109289	+	0.760118i
$581$	6.33422	+	4.07076i	0.262788	+	0.168883i
$582$		0			0
$583$	−14.8553	+	17.1439i	−0.615242	+	0.710028i
$584$	−0.578925	+	4.02651i	−0.0239561	+	0.166618i
$585$		0			0
$586$	3.16281	+	0.928686i	0.130655	+	0.0383637i
$587$	−38.4429	−	11.2879i	−1.58671	−	0.465899i	−0.634900	−	0.772594i	$-0.718959\pi$
$587$	−38.4429	−	11.2879i	−1.58671	−	0.465899i	−0.951808	+	0.306695i	$0.900777\pi$
$588$		0			0
$589$	−2.85529	+	19.8590i	−0.117650	+	0.818276i
$590$	−2.44167	+	2.81784i	−0.100522	+	0.116009i
$591$		0			0
$592$	0.117159	+	0.0752935i	0.00481520	+	0.00309454i
$593$	0.831288	+	5.78174i	0.0341369	+	0.237427i	0.999745	−	0.0225738i	$-0.00718609\pi$
$593$	0.831288	+	5.78174i	0.0341369	+	0.237427i	−0.965608	+	0.260001i	$0.916277\pi$
$594$		0			0
$595$	−15.8387	−	18.2788i	−0.649323	−	0.749359i
$596$	7.72221	−	2.26745i	0.316314	−	0.0928782i
$597$		0			0
$598$	2.90472	+	2.34514i	0.118783	+	0.0959000i
$599$	5.01179			0.204776			0.102388	−	0.994745i	$-0.467352\pi$
$599$	5.01179			0.204776			0.102388	+	0.994745i	$0.467352\pi$
$600$		0			0
$601$	−8.34466	−	9.63025i	−0.340386	−	0.392826i	0.559587	−	0.828771i	$-0.310960\pi$
$601$	−8.34466	−	9.63025i	−0.340386	−	0.392826i	−0.899973	+	0.435945i	$0.856414\pi$
$602$	0.652864	−	0.419570i	0.0266087	−	0.0171004i
$603$		0			0
$604$	11.1146	+	7.14291i	0.452246	+	0.290641i
$605$	−0.236178	+	0.517157i	−0.00960199	+	0.0210254i
$606$		0			0
$607$	0.0879598	−	0.611774i	0.00357018	−	0.0248311i	−0.987958	−	0.154719i	$-0.950553\pi$
$607$	0.0879598	−	0.611774i	0.00357018	−	0.0248311i	0.991529	+	0.129888i	$0.0414618\pi$
$608$	4.80294	+	10.5170i	0.194785	+	0.426520i
$609$		0			0
$610$	−1.23609	−	0.362948i	−0.0500477	−	0.0146953i
$611$	−4.67314	−	10.2328i	−0.189055	−	0.413973i
$612$		0			0
$613$	−20.8291	+	24.0381i	−0.841281	+	0.970890i	−0.999865	−	0.0164557i	$-0.994762\pi$
$613$	−20.8291	+	24.0381i	−0.841281	+	0.970890i	0.158584	+	0.987346i	$0.449307\pi$
$614$	2.51784	−	5.51329i	0.101612	−	0.222498i
$615$		0			0
$616$	1.13991	+	7.92823i	0.0459282	+	0.319437i
$617$	−33.6295	+	21.6123i	−1.35387	+	0.870080i	−0.997923	−	0.0644251i	$-0.979479\pi$
$617$	−33.6295	+	21.6123i	−1.35387	+	0.870080i	−0.355949	+	0.934505i	$0.615842\pi$
$618$		0			0
$619$	33.7104	−	9.89827i	1.35494	−	0.397845i	0.477961	−	0.878381i	$-0.341376\pi$
$619$	33.7104	−	9.89827i	1.35494	−	0.397845i	0.876975	+	0.480536i	$0.159558\pi$
$620$	−13.9513			−0.560298
$621$		0			0
$622$	−0.878199			−0.0352126
$623$	−30.1980	+	8.86693i	−1.20986	+	0.355246i
$624$		0			0
$625$	−3.45576	+	2.22088i	−0.138230	+	0.0888353i
$626$	0.529342	+	3.68166i	0.0211568	+	0.147149i
$627$		0			0
$628$	−7.86387	+	17.2195i	−0.313803	+	0.687132i
$629$	−0.156084	+	0.180131i	−0.00622348	+	0.00718228i
$630$		0			0
$631$	19.6170	+	42.9552i	0.780941	+	1.71002i	0.700933	+	0.713227i	$0.252767\pi$
$631$	19.6170	+	42.9552i	0.780941	+	1.71002i	0.0800078	+	0.996794i	$0.474505\pi$
$632$	−2.14956	−	0.631168i	−0.0855049	−	0.0251065i
$633$		0			0
$634$	−0.324665	−	0.710917i	−0.0128941	−	0.0282341i
$635$	2.24922	−	15.6437i	0.0892576	−	0.620800i
$636$		0			0
$637$	−0.706786	+	1.54765i	−0.0280039	+	0.0613200i
$638$	4.21791	+	2.71068i	0.166989	+	0.107317i
$639$		0			0
$640$	−8.97177	+	5.76580i	−0.354640	+	0.227913i
$641$	4.52524	+	5.22241i	0.178736	+	0.206273i	0.838047	−	0.545598i	$-0.183697\pi$
$641$	4.52524	+	5.22241i	0.178736	+	0.206273i	−0.659311	+	0.751870i	$0.729152\pi$
$642$		0			0
$643$	38.9219			1.53493			0.767465	−	0.641091i	$-0.221518\pi$
$643$	38.9219			1.53493			0.767465	+	0.641091i	$0.221518\pi$
$644$	−7.47635	−	22.5314i	−0.294609	−	0.887862i
$645$		0			0
$646$	−6.02575	+	1.76932i	−0.237080	+	0.0696130i
$647$	7.63135	+	8.80704i	0.300019	+	0.346241i	0.885664	−	0.464328i	$-0.153704\pi$
$647$	7.63135	+	8.80704i	0.300019	+	0.346241i	−0.585644	+	0.810568i	$0.699158\pi$
$648$		0			0
$649$	−5.00091	−	34.7821i	−0.196303	−	1.36532i
$650$	1.77455	+	1.14043i	0.0696035	+	0.0447315i
$651$		0			0
$652$	−7.67524	+	8.85770i	−0.300586	+	0.346894i
$653$	−5.61467	+	39.0509i	−0.219719	+	1.52818i	0.519357	+	0.854557i	$0.326171\pi$
$653$	−5.61467	+	39.0509i	−0.219719	+	1.52818i	−0.739076	+	0.673622i	$0.764738\pi$
$654$		0			0
$655$	22.0630	+	6.47828i	0.862073	+	0.253127i
$656$	11.4251	+	3.35471i	0.446075	+	0.130979i
$657$		0			0
$658$	0.292841	−	2.03676i	0.0114161	−	0.0794010i
$659$	−0.488601	+	0.563876i	−0.0190332	+	0.0219655i	−0.765186	−	0.643809i	$-0.777353\pi$
$659$	−0.488601	+	0.563876i	−0.0190332	+	0.0219655i	0.746153	+	0.665774i	$0.231899\pi$
$660$		0			0
$661$	−24.5667	−	15.7881i	−0.955534	−	0.614085i	−0.0327757	−	0.999463i	$-0.510435\pi$
$661$	−24.5667	−	15.7881i	−0.955534	−	0.614085i	−0.922759	+	0.385378i	$0.874071\pi$
$662$	0.269258	+	1.87273i	0.0104650	+	0.0727857i
$663$		0			0
$664$	1.80618	+	2.08444i	0.0700933	+	0.0808920i
$665$	15.6425	−	4.59304i	0.606588	−	0.178110i
$666$		0			0
$667$	−27.8422	−	11.5624i	−1.07806	−	0.447698i
$668$	3.42084			0.132356
$669$		0			0
$670$	1.59817	+	1.84439i	0.0617427	+	0.0712548i
$671$	10.2140	−	6.56412i	0.394306	−	0.253405i
$672$		0			0
$673$	14.0784	+	9.04766i	0.542683	+	0.348762i	0.783088	−	0.621911i	$-0.213644\pi$
$673$	14.0784	+	9.04766i	0.542683	+	0.348762i	−0.240404	+	0.970673i	$0.577280\pi$
$674$	−0.136771	+	0.299486i	−0.00526821	+	0.0115358i
$675$		0			0
$676$	−0.598783	+	4.16463i	−0.0230301	+	0.160178i
$677$	−18.7888	−	41.1418i	−0.722113	−	1.58121i	−0.810919	−	0.585159i	$-0.801032\pi$
$677$	−18.7888	−	41.1418i	−0.722113	−	1.58121i	0.0888053	−	0.996049i	$-0.471695\pi$
$678$		0			0
$679$	−25.9367	−	7.61572i	−0.995361	−	0.292264i
$680$	−3.68043	−	8.05901i	−0.141138	−	0.309049i
$681$		0			0
$682$	−2.47683	+	2.85841i	−0.0948426	+	0.109454i
$683$	−14.4581	+	31.6589i	−0.553225	+	1.21139i	0.402034	+	0.915625i	$0.368303\pi$
$683$	−14.4581	+	31.6589i	−0.553225	+	1.21139i	−0.955259	+	0.295769i	$0.904424\pi$
$684$		0			0
$685$	−0.263275	−	1.83112i	−0.0100592	−	0.0699634i
$686$	−3.80758	+	2.44698i	−0.145374	+	0.0934261i
$687$		0			0
$688$	−4.53559	+	1.33177i	−0.172918	+	0.0507732i
$689$	22.1397			0.843457
$690$		0			0
$691$	10.7550			0.409140			0.204570	−	0.978852i	$-0.434420\pi$
$691$	10.7550			0.409140			0.204570	+	0.978852i	$0.434420\pi$
$692$	19.0481	−	5.59303i	0.724100	−	0.212615i
$693$		0			0
$694$	3.34785	−	2.15153i	0.127083	−	0.0816711i
$695$	0.470469	+	3.27219i	0.0178459	+	0.124121i
$696$		0			0
$697$	−8.46566	+	18.5372i	−0.320660	+	0.702147i
$698$	−2.96214	+	3.41849i	−0.112119	+	0.129392i
$699$		0			0
$700$	−5.57221	−	12.2014i	−0.210610	−	0.461171i
$701$	−19.4393	−	5.70790i	−0.734214	−	0.215585i	−0.106811	−	0.994279i	$-0.534064\pi$
$701$	−19.4393	−	5.70790i	−0.734214	−	0.215585i	−0.627403	+	0.778695i	$0.715882\pi$
$702$		0			0
$703$	−0.0667397	−	0.146140i	−0.00251714	−	0.00551176i
$704$	3.21069	−	22.3308i	0.121007	−	0.841624i
$705$		0			0
$706$	3.30566	−	7.23839i	0.124410	−	0.272420i
$707$	19.7043	+	12.6632i	0.741056	+	0.476248i
$708$		0			0
$709$	−11.0641	+	7.11045i	−0.415520	+	0.267038i	−0.731654	−	0.681676i	$-0.761251\pi$
$709$	−11.0641	+	7.11045i	−0.415520	+	0.267038i	0.316134	+	0.948714i	$0.397615\pi$
$710$	0.958457	+	1.10612i	0.0359702	+	0.0415119i
$711$		0			0
$712$	−11.5287			−0.432057
$713$	11.6224	−	19.5479i	0.435263	−	0.732074i
$714$		0			0
$715$	16.1211	−	4.73360i	0.602897	−	0.177026i
$716$	13.1199	+	15.1412i	0.490313	+	0.565851i
$717$		0			0
$718$	0.660688	+	4.59519i	0.0246567	+	0.171491i
$719$	24.1781	+	15.5383i	0.901692	+	0.579482i	0.907292	−	0.420502i	$-0.138146\pi$
$719$	24.1781	+	15.5383i	0.901692	+	0.579482i	−0.00559955	+	0.999984i	$0.501782\pi$
$720$		0			0
$721$	24.6258	−	28.4197i	0.917112	−	1.05840i
$722$	−0.0369970	+	0.257320i	−0.00137689	+	0.00957646i
$723$		0			0
$724$	17.3317	+	5.08903i	0.644126	+	0.189132i
$725$	−16.3444	−	4.79916i	−0.607017	−	0.178236i
$726$		0			0
$727$	3.96330	−	27.5653i	0.146991	−	1.02234i	−0.774120	−	0.633039i	$-0.781807\pi$
$727$	3.96330	−	27.5653i	0.146991	−	1.02234i	0.921110	−	0.389302i	$-0.127284\pi$
$728$	5.11928	−	5.90797i	0.189733	−	0.218964i
$729$		0			0
$730$	1.31308	+	0.843862i	0.0485991	+	0.0312327i
$731$	−1.15134	−	8.00774i	−0.0425838	−	0.296177i
$732$		0			0
$733$	16.3812	+	18.9049i	0.605052	+	0.698267i	0.972797	−	0.231660i	$-0.0744156\pi$
$733$	16.3812	+	18.9049i	0.605052	+	0.698267i	−0.367745	+	0.929927i	$0.619870\pi$
$734$	1.52718	−	0.448420i	0.0563691	−	0.0165515i
$735$		0			0
$736$	−0.455820	−	13.0976i	−0.0168017	−	0.482784i
$737$	−23.0003			−0.847229
$738$		0			0
$739$	−4.18350	−	4.82801i	−0.153892	−	0.177601i	0.673568	−	0.739125i	$-0.264761\pi$
$739$	−4.18350	−	4.82801i	−0.153892	−	0.177601i	−0.827461	+	0.561524i	$0.810215\pi$
$740$	0.0939818	−	0.0603984i	0.00345484	−	0.00222029i
$741$		0			0
$742$	3.40686	+	2.18946i	0.125070	+	0.0803775i
$743$	12.0136	−	26.3062i	0.440738	−	0.965081i	−0.550725	−	0.834687i	$-0.685649\pi$
$743$	12.0136	−	26.3062i	0.440738	−	0.965081i	0.991462	−	0.130394i	$-0.0416241\pi$
$744$		0			0
$745$	0.891604	−	6.20124i	0.0326659	−	0.227196i
$746$	−2.48815	−	5.44828i	−0.0910975	−	0.199476i
$747$		0			0
$748$	39.4899	+	11.5953i	1.44390	+	0.423966i
$749$	−17.1422	−	37.5362i	−0.626363	−	1.37154i
$750$		0			0
$751$	32.9193	−	37.9909i	1.20124	−	1.38631i	0.299465	−	0.954107i	$-0.403192\pi$
$751$	32.9193	−	37.9909i	1.20124	−	1.38631i	0.901778	−	0.432200i	$-0.142263\pi$
$752$	−5.20667	+	11.4010i	−0.189868	+	0.415753i
$753$		0			0
$754$	−0.696404	−	4.84360i	−0.0253615	−	0.176393i
$755$	8.65198	−	5.56029i	0.314878	−	0.202360i
$756$		0			0
$757$	−33.7498	+	9.90983i	−1.22666	+	0.360179i	−0.829987	−	0.557782i	$-0.811652\pi$
$757$	−33.7498	+	9.90983i	−1.22666	+	0.360179i	−0.396670	+	0.917961i	$0.629834\pi$
$758$	−6.82414			−0.247864
$759$		0			0
$760$	5.97184			0.216621
$761$	−33.8907	+	9.95120i	−1.22854	+	0.360731i	−0.830697	−	0.556725i	$-0.812058\pi$
$761$	−33.8907	+	9.95120i	−1.22854	+	0.360731i	−0.397839	+	0.917455i	$0.630240\pi$
$762$		0			0
$763$	−32.1934	+	20.6895i	−1.16548	+	0.749008i
$764$	5.68011	+	39.5060i	0.205499	+	1.42928i
$765$		0			0
$766$	−1.26681	+	2.77392i	−0.0457716	+	0.100226i
$767$	−22.4589	+	25.9190i	−0.810944	+	0.935880i
$768$		0			0
$769$	−20.4810	−	44.8471i	−0.738563	−	1.61723i	−0.785904	−	0.618349i	$-0.787802\pi$
$769$	−20.4810	−	44.8471i	−0.738563	−	1.61723i	0.0473404	−	0.998879i	$-0.484925\pi$
$770$	2.94884	+	0.865857i	0.106269	+	0.0312033i
$771$		0			0
$772$	11.0936	+	24.2916i	0.399268	+	0.874275i
$773$	0.532931	−	3.70661i	0.0191682	−	0.133318i	−0.977990	−	0.208651i	$-0.933093\pi$
$773$	0.532931	−	3.70661i	0.0191682	−	0.133318i	0.997158	+	0.0753329i	$0.0240020\pi$
$774$		0			0
$775$	5.33810	−	11.6888i	0.191750	−	0.419874i
$776$	−8.33002	−	5.35338i	−0.299030	−	0.192175i
$777$		0			0
$778$	0.417068	−	0.268033i	0.0149526	−	0.00960945i
$779$	−8.99539	−	10.3812i	−0.322293	−	0.371946i
$780$		0			0
$781$	−13.7938			−0.493581
$782$	7.07718	+	0.767407i	0.253079	+	0.0274424i
$783$		0			0
$784$	1.81886	−	0.534065i	0.0649593	−	0.0190738i
$785$	9.64996	+	11.1366i	0.344422	+	0.397484i
$786$		0			0
$787$	−1.65608	−	11.5183i	−0.0590330	−	0.410584i	−0.997815	−	0.0660715i	$-0.978953\pi$
$787$	−1.65608	−	11.5183i	−0.0590330	−	0.410584i	0.938782	−	0.344512i	$-0.111956\pi$
$788$	3.76064	+	2.41682i	0.133967	+	0.0860956i
$789$		0			0
$790$	−0.562920	+	0.649645i	−0.0200278	+	0.0231133i
$791$	0.418697	−	2.91210i	0.0148871	−	0.103542i
$792$		0			0
$793$	−11.3697	−	3.33846i	−0.403751	−	0.118552i
$794$	0.426346	+	0.125187i	0.0151305	+	0.00444270i
$795$		0			0
$796$	0.473283	−	3.29176i	0.0167751	−	0.116673i
$797$	32.7798	−	37.8299i	1.16112	−	1.34000i	0.230910	−	0.972975i	$-0.425830\pi$
$797$	32.7798	−	37.8299i	1.16112	−	1.34000i	0.930210	−	0.367029i	$-0.119625\pi$
$798$		0			0
$799$	−18.0454	−	11.5971i	−0.638400	−	0.410275i
$800$	−1.05385	−	7.32970i	−0.0372593	−	0.259144i
$801$		0			0
$802$	−2.61012	−	3.01224i	−0.0921667	−	0.106366i
$803$	−14.1145	+	4.14439i	−0.498090	+	0.146252i
$804$		0			0
$805$	−18.3719	−	1.99214i	−0.647524	−	0.0702136i
$806$	3.69137			0.130023
$807$		0			0
$808$	5.61860	+	6.48421i	0.197662	+	0.228114i
$809$	26.9667	−	17.3305i	0.948100	−	0.609307i	0.0274196	−	0.999624i	$-0.491271\pi$
$809$	26.9667	−	17.3305i	0.948100	−	0.609307i	0.920681	+	0.390317i	$0.127635\pi$
$810$		0			0
$811$	40.6899	+	26.1498i	1.42882	+	0.918244i	0.999889	+	0.0149043i	$0.00474437\pi$
$811$	40.6899	+	26.1498i	1.42882	+	0.918244i	0.428926	+	0.903339i	$0.358892\pi$
$812$	−12.9264	+	28.3049i	−0.453628	+	0.993306i
$813$		0			0
$814$	0.00431021	−	0.0299782i	0.000151073	−	0.00105073i
$815$	3.79007	+	8.29910i	0.132760	+	0.290705i
$816$		0			0
$817$	5.23223	+	1.53632i	0.183053	+	0.0537491i
$818$	−1.27802	−	2.79848i	−0.0446851	−	0.0978466i
$819$		0			0
$820$	6.25511	−	7.21878i	0.218438	−	0.252091i
$821$	4.37202	−	9.57340i	0.152585	−	0.334114i	−0.817868	−	0.575406i	$-0.804844\pi$
$821$	4.37202	−	9.57340i	0.152585	−	0.334114i	0.970452	+	0.241292i	$0.0775712\pi$
$822$		0			0
$823$	−6.76894	−	47.0790i	−0.235950	−	1.64107i	−0.671571	−	0.740940i	$-0.734380\pi$
$823$	−6.76894	−	47.0790i	−0.235950	−	1.64107i	0.435620	−	0.900131i	$-0.356529\pi$
$824$	11.5881	−	7.44724i	0.403692	−	0.259437i
$825$		0			0
$826$	−6.01917	+	1.76739i	−0.209434	+	0.0614953i
$827$	52.9294			1.84053			0.920267	−	0.391291i	$-0.127971\pi$
$827$	52.9294			1.84053			0.920267	+	0.391291i	$0.127971\pi$
$828$		0			0
$829$	12.4245			0.431522			0.215761	−	0.976446i	$-0.430777\pi$
$829$	12.4245			0.431522			0.215761	+	0.976446i	$0.430777\pi$
$830$	1.01542	−	0.298153i	0.0352456	−	0.0103490i
$831$		0			0
$832$	−18.5232	+	11.9041i	−0.642176	+	0.412701i
$833$	0.461709	+	3.21126i	0.0159973	+	0.111264i
$834$		0			0
$835$	1.10621	−	2.42226i	0.0382819	−	0.0838257i
$836$	−18.1671	+	20.9660i	−0.628323	+	0.725123i
$837$		0			0
$838$	−2.88921	−	6.32649i	−0.0998061	−	0.218545i
$839$	−41.9145	−	12.3072i	−1.44705	−	0.424892i	−0.538484	−	0.842636i	$-0.681003\pi$
$839$	−41.9145	−	12.3072i	−1.44705	−	0.424892i	−0.908565	+	0.417744i	$0.862821\pi$
$840$		0			0
$841$	4.36870	+	9.56611i	0.150645	+	0.329866i
$842$	0.750402	−	5.21916i	0.0258606	−	0.179864i
$843$		0			0
$844$	6.46316	−	14.1523i	0.222471	−	0.487144i
$845$	2.75529	+	1.77072i	0.0947850	+	0.0609146i
$846$		0			0
$847$	−0.804712	+	0.517157i	−0.0276502	+	0.0177697i
$848$	−16.1537	−	18.6424i	−0.554722	−	0.640183i
$849$		0			0
$850$	4.02229			0.137963
$851$	0.00633388	+	0.181999i	0.000217123	+	0.00623884i
$852$		0			0
$853$	−28.6213	+	8.40397i	−0.979975	+	0.287746i	−0.732214	−	0.681075i	$-0.761513\pi$
$853$	−28.6213	+	8.40397i	−0.979975	+	0.287746i	−0.247761	+	0.968821i	$0.579695\pi$
$854$	−1.41943	−	1.63810i	−0.0485718	−	0.0560548i
$855$		0			0
$856$	−2.15120	−	14.9619i	−0.0735264	−	0.511387i
$857$	5.53260	+	3.55559i	0.188990	+	0.121457i	0.631714	−	0.775201i	$-0.282352\pi$
$857$	5.53260	+	3.55559i	0.188990	+	0.121457i	−0.442724	+	0.896658i	$0.645988\pi$
$858$		0			0
$859$	−12.0994	+	13.9634i	−0.412825	+	0.476425i	−0.923638	−	0.383267i	$-0.874799\pi$
$859$	−12.0994	+	13.9634i	−0.412825	+	0.476425i	0.510813	+	0.859692i	$0.329344\pi$
$860$	−0.539647	+	3.75333i	−0.0184018	+	0.127987i
$861$		0			0
$862$	0.399693	+	0.117360i	0.0136136	+	0.00399731i
$863$	28.3383	+	8.32088i	0.964648	+	0.283246i	0.725873	−	0.687829i	$-0.241436\pi$
$863$	28.3383	+	8.32088i	0.964648	+	0.283246i	0.238775	+	0.971075i	$0.423254\pi$
$864$		0			0
$865$	2.19929	−	15.2964i	0.0747780	−	0.520093i
$866$	2.13689	−	2.46610i	0.0726144	−	0.0838014i
$867$		0			0
$868$	−19.7469	−	12.6906i	−0.670253	−	0.430746i
$869$	−1.15295	−	8.01891i	−0.0391110	−	0.272023i
$870$		0			0
$871$	14.7002	+	16.9650i	0.498099	+	0.574836i
$872$	−13.4502	+	3.94932i	−0.455480	+	0.133741i
$873$		0			0
$874$	−2.45221	+	4.12441i	−0.0829473	+	0.139510i
$875$	−29.7079			−1.00431
$876$		0			0
$877$	−5.63716	−	6.50563i	−0.190353	−	0.219680i	0.652548	−	0.757747i	$-0.273700\pi$
$877$	−5.63716	−	6.50563i	−0.190353	−	0.219680i	−0.842902	+	0.538068i	$0.819155\pi$
$878$	−1.43007	+	0.919049i	−0.0482625	+	0.0310164i
$879$		0			0
$880$	−15.7483	−	10.1208i	−0.530874	−	0.341172i
$881$	2.08959	−	4.57555i	0.0703999	−	0.154154i	−0.871161	−	0.490998i	$-0.836632\pi$
$881$	2.08959	−	4.57555i	0.0703999	−	0.154154i	0.941561	+	0.336844i	$0.109359\pi$
$882$		0			0
$883$	3.07912	−	21.4157i	0.103621	−	0.720696i	−0.870088	−	0.492897i	$-0.835938\pi$
$883$	3.07912	−	21.4157i	0.103621	−	0.720696i	0.973708	−	0.227799i	$-0.0731530\pi$
$884$	−16.6866	−	36.5386i	−0.561231	−	1.22892i
$885$		0			0
$886$	5.30753	+	1.55843i	0.178310	+	0.0523565i
$887$	−11.4298	−	25.0277i	−0.383774	−	0.840349i	−0.998661	−	0.0517330i	$-0.983526\pi$
$887$	−11.4298	−	25.0277i	−0.383774	−	0.840349i	0.614887	−	0.788616i	$-0.289202\pi$
$888$		0			0
$889$	17.4136	−	20.0963i	0.584032	−	0.674009i
$890$	−1.83761	+	4.02381i	−0.0615969	+	0.134878i
$891$		0			0
$892$	7.89152	+	54.8867i	0.264228	+	1.83774i
$893$	12.1635	−	7.81701i	0.407036	−	0.261586i
$894$		0			0
$895$	14.9639	−	4.39380i	0.500188	−	0.146868i
$896$	−17.9435			−0.599451
$897$		0			0
$898$	1.59684			0.0532871
$899$	−28.6020	+	8.39831i	−0.953930	+	0.280099i
$900$		0			0
$901$	35.5150	−	22.8241i	1.18318	−	0.760382i
$902$	−0.368526	−	2.56315i	−0.0122706	−	0.0853436i
$903$		0			0
$904$	0.447689	−	0.980303i	0.0148899	−	0.0326044i
$905$	9.20809	−	10.6267i	0.306087	−	0.353243i
$906$		0			0
$907$	0.791937	+	1.73410i	0.0262959	+	0.0575799i	0.922324	−	0.386417i	$-0.126287\pi$
$907$	0.791937	+	1.73410i	0.0262959	+	0.0575799i	−0.896028	+	0.443997i	$0.853560\pi$
$908$	17.5026	+	5.13922i	0.580843	+	0.170551i
$909$		0			0
$910$	−1.24604	−	2.72845i	−0.0413059	−	0.0904472i
$911$	−5.36602	+	37.3215i	−0.177784	+	1.23652i	0.684091	+	0.729397i	$0.260199\pi$
$911$	−5.36602	+	37.3215i	−0.177784	+	1.23652i	−0.861875	+	0.507120i	$0.830710\pi$
$912$		0			0
$913$	−4.14328	+	9.07253i	−0.137123	+	0.300257i
$914$	−1.43731	−	0.923700i	−0.0475418	−	0.0305533i
$915$		0			0
$916$	10.8806	−	6.99253i	0.359505	−	0.231040i
$917$	25.3355	+	29.2387i	0.836651	+	0.965546i
$918$		0			0
$919$	−1.89744			−0.0625909			−0.0312955	−	0.999510i	$-0.509963\pi$
$919$	−1.89744			−0.0625909			−0.0312955	+	0.999510i	$0.509963\pi$
$920$	−6.25156	−	2.59616i	−0.206108	−	0.0855930i
$921$		0			0
$922$	7.30163	−	2.14395i	0.240466	−	0.0706073i
$923$	8.81605	+	10.1743i	0.290184	+	0.334890i
$924$		0			0
$925$	0.0146439	+	0.101851i	0.000481488	+	0.00334882i
$926$	3.73491	+	2.40028i	0.122737	+	0.0788781i
$927$		0			0
$928$	−11.2494	+	12.9825i	−0.369279	+	0.426171i
$929$	−3.96319	+	27.5646i	−0.130028	+	0.904366i	0.815484	+	0.578779i	$0.196471\pi$
$929$	−3.96319	+	27.5646i	−0.130028	+	0.904366i	−0.945512	+	0.325586i	$0.894438\pi$
$930$		0			0
$931$	−2.09823	−	0.616095i	−0.0687666	−	0.0201917i
$932$	47.8256	+	14.0429i	1.56658	+	0.459989i
$933$		0			0
$934$	−0.958311	+	6.66520i	−0.0313569	+	0.218092i
$935$	20.9805	−	24.2128i	0.686135	−	0.791843i
$936$		0			0
$937$	12.0534	+	7.74624i	0.393767	+	0.253059i	0.722510	−	0.691361i	$-0.242989\pi$
$937$	12.0534	+	7.74624i	0.393767	+	0.253059i	−0.328743	+	0.944420i	$0.606625\pi$
$938$	0.584360	+	4.06432i	0.0190800	+	0.132705i
$939$		0			0
$940$	6.58408	+	7.59844i	0.214749	+	0.247834i
$941$	−33.6359	+	9.87638i	−1.09650	+	0.321961i	−0.779460	−	0.626452i	$-0.784506\pi$
$941$	−33.6359	+	9.87638i	−1.09650	+	0.321961i	−0.317038	+	0.948413i	$0.602688\pi$
$942$		0			0
$943$	4.90365	+	14.7781i	0.159685	+	0.481241i
$944$	38.2113			1.24367
$945$		0			0
$946$	0.673195	+	0.776908i	0.0218874	+	0.0252595i
$947$	6.65862	−	4.27924i	0.216376	−	0.139057i	−0.427963	−	0.903796i	$-0.640769\pi$
$947$	6.65862	−	4.27924i	0.216376	−	0.139057i	0.644339	+	0.764740i	$0.277132\pi$
$948$		0			0
$949$	12.0779	+	7.76199i	0.392065	+	0.251965i
$950$	−1.12628	+	2.46622i	−0.0365415	+	0.0800147i
$951$		0			0
$952$	2.12140	−	14.7547i	0.0687550	−	0.478202i
$953$	−7.32967	−	16.0497i	−0.237431	−	0.519902i	0.752982	−	0.658042i	$-0.228615\pi$
$953$	−7.32967	−	16.0497i	−0.237431	−	0.519902i	−0.990413	+	0.138140i	$0.955888\pi$
$954$		0			0
$955$	29.8106	+	8.75317i	0.964647	+	0.283246i
$956$	−1.23732	−	2.70935i	−0.0400178	−	0.0876267i
$957$		0			0
$958$	−0.732097	+	0.844885i	−0.0236530	+	0.0272970i
$959$	1.29300	−	2.83128i	0.0417532	−	0.0914267i
$960$		0			0
$961$	1.21153	+	8.42636i	0.0390816	+	0.271818i
$962$	−0.0248666	+	0.0159808i	−0.000801731	+	0.000515241i
$963$		0			0
$964$	−52.0533	+	15.2842i	−1.67652	+	0.492272i
$965$	20.7880			0.669190
$966$		0			0
$967$	−18.1226			−0.582785			−0.291392	−	0.956604i	$-0.594119\pi$
$967$	−18.1226			−0.582785			−0.291392	+	0.956604i	$0.594119\pi$
$968$	−0.336202	+	0.0987179i	−0.0108060	+	0.00317291i
$969$		0			0
$970$	−3.19622	+	2.05408i	−0.102624	+	0.0659526i
$971$	−1.50925	−	10.4971i	−0.0484342	−	0.336867i	−0.999602	−	0.0281944i	$-0.991024\pi$
$971$	−1.50925	−	10.4971i	−0.0484342	−	0.336867i	0.951168	−	0.308673i	$-0.0998848\pi$
$972$		0			0
$973$	−2.31058	+	5.05946i	−0.0740737	+	0.162199i
$974$	4.90544	−	5.66117i	0.157180	−	0.181396i
$975$		0			0
$976$	5.48457	+	12.0095i	0.175557	+	0.384416i
$977$	6.30869	+	1.85240i	0.201833	+	0.0592635i	0.381086	−	0.924539i	$-0.375550\pi$
$977$	6.30869	+	1.85240i	0.201833	+	0.0592635i	−0.179253	+	0.983803i	$0.557368\pi$
$978$		0			0
$979$	−17.3187	−	37.9226i	−0.553507	−	1.21201i
$980$	0.216409	−	1.50516i	0.00691294	−	0.0480805i
$981$		0			0
$982$	−0.707187	+	1.54852i	−0.0225672	+	0.0494154i
$983$	−36.7725	−	23.6323i	−1.17286	−	0.753752i	−0.198800	−	0.980040i	$-0.563705\pi$
$983$	−36.7725	−	23.6323i	−1.17286	−	0.753752i	−0.974060	+	0.226288i	$0.927341\pi$
$984$		0			0
$985$	2.92741	−	1.88133i	0.0932751	−	0.0599443i
$986$	−6.11044	−	7.05183i	−0.194596	−	0.224576i
$987$		0			0
$988$	27.0756			0.861390
$989$	−4.80942	−	3.88292i	−0.152931	−	0.123470i
$990$		0			0
$991$	−52.0340	+	15.2786i	−1.65291	+	0.485339i	−0.969582	−	0.244768i	$-0.921288\pi$
$991$	−52.0340	+	15.2786i	−1.65291	+	0.485339i	−0.683333	+	0.730107i	$0.739470\pi$
$992$	−8.48604	−	9.79341i	−0.269432	−	0.310941i
$993$		0			0
$994$	0.350454	+	2.43746i	0.0111157	+	0.0773115i
$995$	−2.17781	−	1.39959i	−0.0690412	−	0.0443701i
$996$		0			0
$997$	−0.450373	+	0.519758i	−0.0142635	+	0.0164609i	−0.762836	−	0.646591i	$-0.776194\pi$
$997$	−0.450373	+	0.519758i	−0.0142635	+	0.0164609i	0.748573	+	0.663052i	$0.230739\pi$
$998$	−0.767096	+	5.33527i	−0.0242820	+	0.168885i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.c.55.1		10
3.2	odd	2		23.2.c.a.9.1	✓	10
12.11	even	2		368.2.m.c.193.1		10
15.2	even	4		575.2.p.b.124.1		20
15.8	even	4		575.2.p.b.124.2		20
15.14	odd	2		575.2.k.b.101.1		10
23.8	even	11		4761.2.a.bo.1.4		5
23.15	odd	22		4761.2.a.bn.1.4		5
23.18	even	11	inner	207.2.i.c.64.1		10
69.2	odd	22		529.2.c.g.266.1		10
69.5	even	22		529.2.c.a.501.1		10
69.8	odd	22		529.2.a.i.1.2		5
69.11	even	22		529.2.c.e.399.1		10
69.14	even	22		529.2.c.f.177.1		10
69.17	even	22		529.2.c.c.255.1		10
69.20	even	22		529.2.c.c.334.1		10
69.26	odd	22		529.2.c.b.334.1		10
69.29	odd	22		529.2.c.b.255.1		10
69.32	odd	22		529.2.c.g.177.1		10
69.35	odd	22		529.2.c.d.399.1		10
69.38	even	22		529.2.a.j.1.2		5
69.41	odd	22		23.2.c.a.18.1	yes	10
69.44	even	22		529.2.c.f.266.1		10
69.50	odd	22		529.2.c.i.466.1		10
69.53	even	22		529.2.c.h.487.1		10
69.56	even	22		529.2.c.e.118.1		10
69.59	odd	22		529.2.c.d.118.1		10
69.62	odd	22		529.2.c.i.487.1		10
69.65	even	22		529.2.c.h.466.1		10
69.68	even	2		529.2.c.a.170.1		10
276.107	odd	22		8464.2.a.bt.1.3		5
276.179	even	22		368.2.m.c.225.1		10
276.215	even	22		8464.2.a.bs.1.3		5
345.179	odd	22		575.2.k.b.501.1		10
345.248	even	44		575.2.p.b.524.1		20
345.317	even	44		575.2.p.b.524.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.9.1	✓	10	3.2	odd	2
23.2.c.a.18.1	yes	10	69.41	odd	22
207.2.i.c.55.1		10	1.1	even	1	trivial
207.2.i.c.64.1		10	23.18	even	11	inner
368.2.m.c.193.1		10	12.11	even	2
368.2.m.c.225.1		10	276.179	even	22
529.2.a.i.1.2		5	69.8	odd	22
529.2.a.j.1.2		5	69.38	even	22
529.2.c.a.170.1		10	69.68	even	2
529.2.c.a.501.1		10	69.5	even	22
529.2.c.b.255.1		10	69.29	odd	22
529.2.c.b.334.1		10	69.26	odd	22
529.2.c.c.255.1		10	69.17	even	22
529.2.c.c.334.1		10	69.20	even	22
529.2.c.d.118.1		10	69.59	odd	22
529.2.c.d.399.1		10	69.35	odd	22
529.2.c.e.118.1		10	69.56	even	22
529.2.c.e.399.1		10	69.11	even	22
529.2.c.f.177.1		10	69.14	even	22
529.2.c.f.266.1		10	69.44	even	22
529.2.c.g.177.1		10	69.32	odd	22
529.2.c.g.266.1		10	69.2	odd	22
529.2.c.h.466.1		10	69.65	even	22
529.2.c.h.487.1		10	69.53	even	22
529.2.c.i.466.1		10	69.50	odd	22
529.2.c.i.487.1		10	69.62	odd	22
575.2.k.b.101.1		10	15.14	odd	2
575.2.k.b.501.1		10	345.179	odd	22
575.2.p.b.124.1		20	15.2	even	4
575.2.p.b.124.2		20	15.8	even	4
575.2.p.b.524.1		20	345.248	even	44
575.2.p.b.524.2		20	345.317	even	44
4761.2.a.bn.1.4		5	23.15	odd	22
4761.2.a.bo.1.4		5	23.8	even	11
8464.2.a.bs.1.3		5	276.215	even	22
8464.2.a.bt.1.3		5	276.107	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.226900 - 0.0666238i) q^{2} +(-1.63546 + 1.05105i) q^{4} +(0.215370 + 1.49793i) q^{5} +(-1.05773 + 2.31611i) q^{7} +(-0.610783 + 0.704881i) q^{8} +O(q^{10})\)	\(q+(0.226900 - 0.0666238i) q^{2} +(-1.63546 + 1.05105i) q^{4} +(0.215370 + 1.49793i) q^{5} +(-1.05773 + 2.31611i) q^{7} +(-0.610783 + 0.704881i) q^{8} +(0.148666 + 0.325532i) q^{10} +(-3.23616 - 0.950224i) q^{11} +(1.36745 + 2.99430i) q^{13} +(-0.0856910 + 0.595994i) q^{14} +(1.52357 - 3.33616i) q^{16} +(5.28043 + 3.39353i) q^{17} +(-3.55928 + 2.28741i) q^{19} +(-1.92663 - 2.22345i) q^{20} -0.797593 q^{22} +(4.72041 - 0.847210i) q^{23} +(2.60004 - 0.763442i) q^{25} +(0.509766 + 0.588302i) q^{26} +(-0.704460 - 4.89963i) q^{28} +(-5.28830 - 3.39858i) q^{29} +(3.10538 - 3.58380i) q^{31} +(0.388902 - 2.70488i) q^{32} +(1.42422 + 0.418188i) q^{34} +(-3.69718 - 1.08559i) q^{35} +(-0.00540403 + 0.0375858i) q^{37} +(-0.655203 + 0.756145i) q^{38} +(-1.18741 - 0.763102i) q^{40} +(0.462048 + 3.21361i) q^{41} +(-0.844033 - 0.974066i) q^{43} +(6.29135 - 1.84731i) q^{44} +(1.01462 - 0.506723i) q^{46} -3.41741 q^{47} +(0.338474 + 0.390620i) q^{49} +(0.539086 - 0.346450i) q^{50} +(-5.38357 - 3.45981i) q^{52} +(2.79399 - 6.11799i) q^{53} +(0.726398 - 5.05221i) q^{55} +(-0.986535 - 2.16021i) q^{56} +(-1.42634 - 0.418811i) q^{58} +(4.32805 + 9.47711i) q^{59} +(-2.35737 + 2.72055i) q^{61} +(0.465844 - 1.02006i) q^{62} +(0.951939 + 6.62088i) q^{64} +(-4.19075 + 2.69323i) q^{65} +(6.54316 - 1.92124i) q^{67} -12.2027 q^{68} -0.911214 q^{70} +(3.92408 - 1.15221i) q^{71} +(3.66912 - 2.35800i) q^{73} +(0.00127794 + 0.00888826i) q^{74} +(3.41689 - 7.48194i) q^{76} +(5.62381 - 6.49022i) q^{77} +(0.997820 + 2.18492i) q^{79} +(5.32548 + 1.56370i) q^{80} +(0.318941 + 0.698384i) q^{82} +(0.420847 - 2.92705i) q^{83} +(-3.94603 + 8.64060i) q^{85} +(-0.256407 - 0.164783i) q^{86} +(2.64639 - 1.70073i) q^{88} +(8.09455 + 9.34161i) q^{89} -8.38151 q^{91} +(-6.82959 + 6.34695i) q^{92} +(-0.775410 + 0.227681i) q^{94} +(-4.19295 - 4.83892i) q^{95} +(1.51088 + 10.5084i) q^{97} +(0.102824 + 0.0660811i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 7 q^{2} - 3 q^{4} + 3 q^{5} - 5 q^{7} - 4 q^{8}+O(q^{10}) \) 10 * q + 7 * q^2 - 3 * q^4 + 3 * q^5 - 5 * q^7 - 4 * q^8	\( 10 q + 7 q^{2} - 3 q^{4} + 3 q^{5} - 5 q^{7} - 4 q^{8} + q^{10} - 7 q^{11} - 3 q^{13} - 9 q^{14} + q^{16} + 10 q^{17} + 2 q^{19} + 9 q^{20} - 6 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{26} + 7 q^{28} - 14 q^{29} + 10 q^{31} - 21 q^{32} + 29 q^{34} - 7 q^{35} - 19 q^{37} + 8 q^{38} + q^{40} - 7 q^{41} - 11 q^{43} + 34 q^{44} - 29 q^{46} + 18 q^{47} - 18 q^{49} - 16 q^{50} - 20 q^{52} - 29 q^{53} - q^{55} + 2 q^{56} - 23 q^{58} + 21 q^{59} + 3 q^{61} - 4 q^{62} + 24 q^{64} - 2 q^{65} + 45 q^{67} + 30 q^{68} + 38 q^{70} + 14 q^{71} + 19 q^{73} - 10 q^{74} - 16 q^{76} - 2 q^{77} - 15 q^{79} + 52 q^{80} + 16 q^{82} - 18 q^{83} - 19 q^{85} + 11 q^{86} + 27 q^{88} - 25 q^{89} - 4 q^{91} - 52 q^{92} + 17 q^{94} - 6 q^{95} - 34 q^{97} - 17 q^{98}+O(q^{100}) \) 10 * q + 7 * q^2 - 3 * q^4 + 3 * q^5 - 5 * q^7 - 4 * q^8 + q^10 - 7 * q^11 - 3 * q^13 - 9 * q^14 + q^16 + 10 * q^17 + 2 * q^19 + 9 * q^20 - 6 * q^22 + 12 * q^23 - 4 * q^25 - 12 * q^26 + 7 * q^28 - 14 * q^29 + 10 * q^31 - 21 * q^32 + 29 * q^34 - 7 * q^35 - 19 * q^37 + 8 * q^38 + q^40 - 7 * q^41 - 11 * q^43 + 34 * q^44 - 29 * q^46 + 18 * q^47 - 18 * q^49 - 16 * q^50 - 20 * q^52 - 29 * q^53 - q^55 + 2 * q^56 - 23 * q^58 + 21 * q^59 + 3 * q^61 - 4 * q^62 + 24 * q^64 - 2 * q^65 + 45 * q^67 + 30 * q^68 + 38 * q^70 + 14 * q^71 + 19 * q^73 - 10 * q^74 - 16 * q^76 - 2 * q^77 - 15 * q^79 + 52 * q^80 + 16 * q^82 - 18 * q^83 - 19 * q^85 + 11 * q^86 + 27 * q^88 - 25 * q^89 - 4 * q^91 - 52 * q^92 + 17 * q^94 - 6 * q^95 - 34 * q^97 - 17 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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