LMFDB - Embedded newform 414.2.i.a.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, 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("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.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:	$3.30580664368$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			325.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	414.325
Dual form			414.2.i.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(1.81440 - 2.09393i) q^{5} +(0.163423 - 0.105026i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.33083 - 1.49793i) q^{10} +(0.413293 - 2.87451i) q^{11} +(0.910738 + 0.585296i) q^{13} +(-0.127214 - 0.146813i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-4.45384 - 1.30777i) q^{17} +(4.24593 - 1.24672i) q^{19} +(-1.15098 + 2.52028i) q^{20} -2.90407 q^{22} +(4.73556 - 0.757939i) q^{23} +(-0.380916 - 2.64933i) q^{25} +(0.449727 - 0.984764i) q^{26} +(-0.127214 + 0.146813i) q^{28} +(-8.83766 - 2.59497i) q^{29} +(-2.85525 - 6.25212i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.660607 + 4.59462i) q^{34} +(0.0765987 - 0.532755i) q^{35} +(3.17329 + 3.66217i) q^{37} +(-1.83829 - 4.02529i) q^{38} +(2.65843 + 0.780586i) q^{40} +(-3.76214 + 4.34174i) q^{41} +(3.14342 - 6.88313i) q^{43} +(0.413293 + 2.87451i) q^{44} +(-1.42416 - 4.57949i) q^{46} +5.61457 q^{47} +(-2.89223 + 6.33310i) q^{49} +(-2.56815 + 0.754078i) q^{50} +(-1.03874 - 0.305003i) q^{52} +(3.48496 - 2.23965i) q^{53} +(-5.26914 - 6.08092i) q^{55} +(0.163423 + 0.105026i) q^{56} +(-1.31083 + 9.11701i) q^{58} +(9.01685 + 5.79478i) q^{59} +(-1.19623 - 2.61939i) q^{61} +(-5.78214 + 3.71596i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(2.87801 - 0.845060i) q^{65} +(2.08311 + 14.4884i) q^{67} +4.64187 q^{68} -0.538234 q^{70} +(1.81195 + 12.6024i) q^{71} +(-2.86708 + 0.841852i) q^{73} +(3.17329 - 3.66217i) q^{74} +(-3.72270 + 2.39243i) q^{76} +(-0.234356 - 0.513169i) q^{77} +(2.15275 + 1.38349i) q^{79} +(0.394306 - 2.74246i) q^{80} +(4.83295 + 3.10595i) q^{82} +(-0.531462 - 0.613340i) q^{83} +(-10.8194 + 6.95322i) q^{85} +(-7.26043 - 2.13185i) q^{86} +(2.78644 - 0.818172i) q^{88} +(-2.81645 + 6.16716i) q^{89} +0.210307 q^{91} +(-4.33020 + 2.06140i) q^{92} +(-0.799036 - 5.55742i) q^{94} +(5.09327 - 11.1527i) q^{95} +(8.09928 - 9.34707i) q^{97} +(6.68024 + 1.96150i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32}+ \cdots + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.81440	−	2.09393i	0.811424	−	0.936433i	−0.187526	−	0.982260i	$-0.560047\pi$
$5$	1.81440	−	2.09393i	0.811424	−	0.936433i	0.998949	+	0.0458269i	$0.0145923\pi$
$6$		0			0
$7$	0.163423	−	0.105026i	0.0617682	−	0.0396960i	−0.509392	−	0.860534i	$-0.670130\pi$
$7$	0.163423	−	0.105026i	0.0617682	−	0.0396960i	0.571160	+	0.820838i	$0.306493\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$		0			0
$10$	−2.33083	−	1.49793i	−0.737073	−	0.473688i
$11$	0.413293	−	2.87451i	0.124612	−	0.866698i	−0.827612	−	0.561300i	$-0.810301\pi$
$11$	0.413293	−	2.87451i	0.124612	−	0.866698i	0.952225	−	0.305398i	$-0.0987896\pi$
$12$		0			0
$13$	0.910738	+	0.585296i	0.252593	+	0.162332i	0.660810	−	0.750553i	$-0.270213\pi$
$13$	0.910738	+	0.585296i	0.252593	+	0.162332i	−0.408217	+	0.912885i	$0.633849\pi$
$14$	−0.127214	−	0.146813i	−0.0339995	−	0.0392375i
$15$		0			0
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−4.45384	−	1.30777i	−1.08022	−	0.317180i	−0.307251	−	0.951629i	$-0.599409\pi$
$17$	−4.45384	−	1.30777i	−1.08022	−	0.317180i	−0.772965	+	0.634449i	$0.781227\pi$
$18$		0			0
$19$	4.24593	−	1.24672i	0.974083	−	0.286017i	0.244303	−	0.969699i	$-0.421441\pi$
$19$	4.24593	−	1.24672i	0.974083	−	0.286017i	0.729780	+	0.683682i	$0.239623\pi$
$20$	−1.15098	+	2.52028i	−0.257366	+	0.563553i
$21$		0			0
$22$	−2.90407			−0.619150
$23$	4.73556	−	0.757939i	0.987433	−	0.158041i
$23$	4.73556	−	0.757939i	0.987433	−	0.158041i
$24$		0			0
$25$	−0.380916	−	2.64933i	−0.0761832	−	0.529866i
$26$	0.449727	−	0.984764i	0.0881987	−	0.193128i
$27$		0			0
$28$	−0.127214	+	0.146813i	−0.0240413	+	0.0277451i
$29$	−8.83766	−	2.59497i	−1.64111	−	0.481874i	−0.674533	−	0.738245i	$-0.735655\pi$
$29$	−8.83766	−	2.59497i	−1.64111	−	0.481874i	−0.966579	+	0.256371i	$0.917473\pi$
$30$		0			0
$31$	−2.85525	−	6.25212i	−0.512818	−	1.12291i	−0.972088	−	0.234617i	$-0.924616\pi$
$31$	−2.85525	−	6.25212i	−0.512818	−	1.12291i	0.459270	−	0.888297i	$-0.348111\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$		0			0
$34$	−0.660607	+	4.59462i	−0.113293	+	0.787972i
$35$	0.0765987	−	0.532755i	0.0129475	−	0.0900521i
$36$		0			0
$37$	3.17329	+	3.66217i	0.521685	+	0.602057i	0.954052	−	0.299641i	$-0.0968669\pi$
$37$	3.17329	+	3.66217i	0.521685	+	0.602057i	−0.432367	+	0.901698i	$0.642321\pi$
$38$	−1.83829	−	4.02529i	−0.298209	−	0.652988i
$39$		0			0
$40$	2.65843	+	0.780586i	0.420335	+	0.123421i
$41$	−3.76214	+	4.34174i	−0.587547	+	0.678065i	−0.969210	−	0.246236i	$-0.920806\pi$
$41$	−3.76214	+	4.34174i	−0.587547	+	0.678065i	0.381663	+	0.924302i	$0.375352\pi$
$42$		0			0
$43$	3.14342	−	6.88313i	0.479367	−	1.04967i	−0.503270	−	0.864129i	$-0.667870\pi$
$43$	3.14342	−	6.88313i	0.479367	−	1.04967i	0.982637	−	0.185538i	$-0.0594029\pi$
$44$	0.413293	+	2.87451i	0.0623062	+	0.433349i
$45$		0			0
$46$	−1.42416	−	4.57949i	−0.209982	−	0.675209i
$47$	5.61457			0.818969			0.409484	−	0.912317i	$-0.365709\pi$
$47$	5.61457			0.818969			0.409484	+	0.912317i	$0.365709\pi$
$48$		0			0
$49$	−2.89223	+	6.33310i	−0.413175	+	0.904728i
$50$	−2.56815	+	0.754078i	−0.363192	+	0.106643i
$51$		0			0
$52$	−1.03874	−	0.305003i	−0.144048	−	0.0422963i
$53$	3.48496	−	2.23965i	0.478697	−	0.307640i	−0.278949	−	0.960306i	$-0.589986\pi$
$53$	3.48496	−	2.23965i	0.478697	−	0.307640i	0.757645	+	0.652666i	$0.226350\pi$
$54$		0			0
$55$	−5.26914	−	6.08092i	−0.710491	−	0.819951i
$56$	0.163423	+	0.105026i	0.0218384	+	0.0140347i
$57$		0			0
$58$	−1.31083	+	9.11701i	−0.172120	+	1.19712i
$59$	9.01685	+	5.79478i	1.17389	+	0.754416i	0.974254	−	0.225453i	$-0.0723862\pi$
$59$	9.01685	+	5.79478i	1.17389	+	0.754416i	0.199640	+	0.979869i	$0.436023\pi$
$60$		0			0
$61$	−1.19623	−	2.61939i	−0.153162	−	0.335378i	0.817461	−	0.575984i	$-0.195381\pi$
$61$	−1.19623	−	2.61939i	−0.153162	−	0.335378i	−0.970623	+	0.240606i	$0.922654\pi$
$62$	−5.78214	+	3.71596i	−0.734332	+	0.471927i
$63$		0			0
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	2.87801	−	0.845060i	0.356973	−	0.104817i
$66$		0			0
$67$	2.08311	+	14.4884i	0.254493	+	1.77003i	0.570519	+	0.821284i	$0.306742\pi$
$67$	2.08311	+	14.4884i	0.254493	+	1.77003i	−0.316027	+	0.948750i	$0.602349\pi$
$68$	4.64187			0.562910
$69$		0			0
$70$	−0.538234			−0.0643313
$71$	1.81195	+	12.6024i	0.215038	+	1.49563i	0.755997	+	0.654576i	$0.227153\pi$
$71$	1.81195	+	12.6024i	0.215038	+	1.49563i	−0.540958	+	0.841050i	$0.681938\pi$
$72$		0			0
$73$	−2.86708	+	0.841852i	−0.335567	+	0.0985313i	−0.445175	−	0.895444i	$-0.646859\pi$
$73$	−2.86708	+	0.841852i	−0.335567	+	0.0985313i	0.109608	+	0.993975i	$0.465040\pi$
$74$	3.17329	−	3.66217i	0.368887	−	0.425718i
$75$		0			0
$76$	−3.72270	+	2.39243i	−0.427023	+	0.274431i
$77$	−0.234356	−	0.513169i	−0.0267074	−	0.0584811i
$78$		0			0
$79$	2.15275	+	1.38349i	0.242203	+	0.155654i	0.656111	−	0.754664i	$-0.272200\pi$
$79$	2.15275	+	1.38349i	0.242203	+	0.155654i	−0.413908	+	0.910319i	$0.635837\pi$
$80$	0.394306	−	2.74246i	0.0440848	−	0.306617i
$81$		0			0
$82$	4.83295	+	3.10595i	0.533710	+	0.342995i
$83$	−0.531462	−	0.613340i	−0.0583356	−	0.0673228i	0.725832	−	0.687872i	$-0.241455\pi$
$83$	−0.531462	−	0.613340i	−0.0583356	−	0.0673228i	−0.784167	+	0.620549i	$0.786910\pi$
$84$		0			0
$85$	−10.8194	+	6.95322i	−1.17353	+	0.754182i
$86$	−7.26043	−	2.13185i	−0.782912	−	0.229884i
$87$		0			0
$88$	2.78644	−	0.818172i	0.297035	−	0.0872174i
$89$	−2.81645	+	6.16716i	−0.298543	+	0.653717i	−0.998149	−	0.0608109i	$-0.980631\pi$
$89$	−2.81645	+	6.16716i	−0.298543	+	0.653717i	0.699607	+	0.714528i	$0.253359\pi$
$90$		0			0
$91$	0.210307			0.0220462
$92$	−4.33020	+	2.06140i	−0.451455	+	0.214916i
$93$		0			0
$94$	−0.799036	−	5.55742i	−0.0824143	−	0.573204i
$95$	5.09327	−	11.1527i	0.522559	−	1.14424i
$96$		0			0
$97$	8.09928	−	9.34707i	0.822357	−	0.949051i	−0.177024	−	0.984206i	$-0.556647\pi$
$97$	8.09928	−	9.34707i	0.822357	−	0.949051i	0.999382	+	0.0351554i	$0.0111926\pi$
$98$	6.68024	+	1.96150i	0.674806	+	0.198141i
$99$		0			0
$100$	1.11189	+	2.43470i	0.111189	+	0.243470i
$101$	10.2791	+	11.8628i	1.02281	+	1.18039i	0.983453	+	0.181163i	$0.0579862\pi$
$101$	10.2791	+	11.8628i	1.02281	+	1.18039i	0.0393592	+	0.999225i	$0.487468\pi$
$102$		0			0
$103$	−1.34415	+	9.34877i	−0.132443	+	0.921162i	0.809913	+	0.586550i	$0.199514\pi$
$103$	−1.34415	+	9.34877i	−0.132443	+	0.921162i	−0.942356	+	0.334612i	$0.891395\pi$
$104$	−0.154070	+	1.07158i	−0.0151078	+	0.105077i
$105$		0			0
$106$	−2.71282	−	3.13076i	−0.263492	−	0.304086i
$107$	−3.95144	−	8.65244i	−0.382000	−	0.836463i	−0.998783	−	0.0493295i	$-0.984292\pi$
$107$	−3.95144	−	8.65244i	−0.382000	−	0.836463i	0.616783	−	0.787133i	$-0.288436\pi$
$108$		0			0
$109$	19.4026	+	5.69711i	1.85843	+	0.545684i	0.999432	+	0.0337045i	$0.0107305\pi$
$109$	19.4026	+	5.69711i	1.85843	+	0.545684i	0.858998	+	0.511980i	$0.171088\pi$
$110$	−5.26914	+	6.08092i	−0.502393	+	0.579793i
$111$		0			0
$112$	0.0806993	−	0.176707i	0.00762536	−	0.0166972i
$113$	0.187381	+	1.30327i	0.0176274	+	0.122601i	0.996735	−	0.0807412i	$-0.0257287\pi$
$113$	0.187381	+	1.30327i	0.0176274	+	0.122601i	−0.979108	+	0.203342i	$0.934820\pi$
$114$		0			0
$115$	7.00512	−	11.2911i	0.653231	−	1.05290i
$116$	9.21076			0.855197
$117$		0			0
$118$	4.45257	−	9.74976i	0.409892	−	0.897538i
$119$	−0.865212	+	0.254049i	−0.0793138	+	0.0232886i
$120$		0			0
$121$	2.46241	+	0.723028i	0.223855	+	0.0657298i
$122$	−2.42248	+	1.55683i	−0.219321	+	0.140949i
$123$		0			0
$124$	4.50102	+	5.19445i	0.404203	+	0.466475i
$125$	5.41551	+	3.48034i	0.484378	+	0.311291i
$126$		0			0
$127$	0.685740	−	4.76943i	0.0608496	−	0.423218i	−0.936513	−	0.350634i	$-0.885966\pi$
$127$	0.685740	−	4.76943i	0.0608496	−	0.423218i	0.997362	−	0.0725845i	$-0.0231247\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$		0			0
$130$	−1.24604	−	2.72845i	−0.109285	−	0.239301i
$131$	−13.4413	+	8.63823i	−1.17438	+	0.754725i	−0.974344	−	0.225064i	$-0.927741\pi$
$131$	−13.4413	+	8.63823i	−1.17438	+	0.754725i	−0.200032	+	0.979789i	$0.564104\pi$
$132$		0			0
$133$	0.562947	−	0.649675i	0.0488137	−	0.0563340i
$134$	14.0444	−	4.12382i	1.21325	−	0.356243i
$135$		0			0
$136$	−0.660607	−	4.59462i	−0.0566466	−	0.393986i
$137$	−18.7720			−1.60380			−0.801898	−	0.597460i	$-0.796176\pi$
$137$	−18.7720			−1.60380			−0.801898	+	0.597460i	$0.796176\pi$
$138$		0			0
$139$	17.7540			1.50588			0.752938	−	0.658092i	$-0.228636\pi$
$139$	17.7540			1.50588			0.752938	+	0.658092i	$0.228636\pi$
$140$	0.0765987	+	0.532755i	0.00647377	+	0.0450261i
$141$		0			0
$142$	12.2162	−	3.58701i	1.02516	−	0.301015i
$143$	2.05884	−	2.37603i	0.172169	−	0.198694i
$144$		0			0
$145$	−21.4687	+	13.7971i	−1.78288	+	1.14579i
$146$	1.24131	+	2.71809i	0.102732	+	0.224951i
$147$		0			0
$148$	−4.07650	−	2.61981i	−0.335086	−	0.215347i
$149$	−1.35418	+	9.41852i	−0.110939	+	0.771595i	0.856072	+	0.516857i	$0.172898\pi$
$149$	−1.35418	+	9.41852i	−0.110939	+	0.771595i	−0.967010	+	0.254738i	$0.918011\pi$
$150$		0			0
$151$	−7.30101	−	4.69207i	−0.594148	−	0.381835i	0.208735	−	0.977972i	$-0.433065\pi$
$151$	−7.30101	−	4.69207i	−0.594148	−	0.381835i	−0.802883	+	0.596137i	$0.796702\pi$
$152$	2.89788	+	3.34433i	0.235049	+	0.271261i
$153$		0			0
$154$	−0.474593	+	0.305003i	−0.0382438	+	0.0245778i
$155$	−18.2720	−	5.36516i	−1.46765	−	0.430940i
$156$		0			0
$157$	−19.0136	+	5.58290i	−1.51745	+	0.445564i	−0.931183	−	0.364552i	$-0.881222\pi$
$157$	−19.0136	+	5.58290i	−1.51745	+	0.445564i	−0.586270	+	0.810116i	$0.699404\pi$
$158$	1.06304	−	2.32772i	0.0845706	−	0.185184i
$159$		0			0
$160$	−2.77066			−0.219040
$161$	0.694298	−	0.621221i	0.0547184	−	0.0489591i
$162$		0			0
$163$	−2.06377	−	14.3538i	−0.161647	−	1.12428i	−0.895530	−	0.445001i	$-0.853203\pi$
$163$	−2.06377	−	14.3538i	−0.161647	−	1.12428i	0.733883	−	0.679276i	$-0.237706\pi$
$164$	2.38653	−	5.22578i	0.186357	−	0.408065i
$165$		0			0
$166$	−0.531462	+	0.613340i	−0.0412495	+	0.0476044i
$167$	−9.49053	−	2.78667i	−0.734399	−	0.215639i	−0.106915	−	0.994268i	$-0.534097\pi$
$167$	−9.49053	−	2.78667i	−0.734399	−	0.215639i	−0.627484	+	0.778629i	$0.715915\pi$
$168$		0			0
$169$	−4.91352	−	10.7591i	−0.377963	−	0.827624i
$170$	8.42221	+	9.71974i	0.645954	+	0.745470i
$171$		0			0
$172$	−1.07689	+	7.48992i	−0.0821119	+	0.571101i
$173$	1.88474	−	13.1086i	0.143294	−	0.996631i	−0.783589	−	0.621280i	$-0.786613\pi$
$173$	1.88474	−	13.1086i	0.143294	−	0.996631i	0.926883	−	0.375351i	$-0.122478\pi$
$174$		0			0
$175$	−0.340499	−	0.392956i	−0.0257393	−	0.0297047i
$176$	−1.20640	−	2.64164i	−0.0909355	−	0.199121i
$177$		0			0
$178$	6.50521	+	1.91010i	0.487586	+	0.143168i
$179$	3.43495	−	3.96414i	0.256740	−	0.296294i	−0.612717	−	0.790302i	$-0.709923\pi$
$179$	3.43495	−	3.96414i	0.256740	−	0.296294i	0.869457	+	0.494009i	$0.164469\pi$
$180$		0			0
$181$	−6.75269	+	14.7863i	−0.501924	+	1.09906i	0.473916	+	0.880570i	$0.342840\pi$
$181$	−6.75269	+	14.7863i	−0.501924	+	1.09906i	−0.975839	+	0.218489i	$0.929887\pi$
$182$	−0.0299298	−	0.208166i	−0.00221855	−	0.0154303i
$183$		0			0
$184$	2.65667	+	3.99276i	0.195852	+	0.294350i
$185$	13.4259			0.987093
$186$		0			0
$187$	−5.59993	+	12.2621i	−0.409508	+	0.896697i
$188$	−5.38714	+	1.58181i	−0.392897	+	0.115365i
$189$		0			0
$190$	−11.7640	−	3.45423i	−0.853453	−	0.250596i
$191$	6.47147	−	4.15896i	0.468259	−	0.300932i	−0.285151	−	0.958483i	$-0.592044\pi$
$191$	6.47147	−	4.15896i	0.468259	−	0.300932i	0.753410	+	0.657551i	$0.228407\pi$
$192$		0			0
$193$	0.934780	+	1.07879i	0.0672869	+	0.0776533i	0.788395	−	0.615169i	$-0.210912\pi$
$193$	0.934780	+	1.07879i	0.0672869	+	0.0776533i	−0.721108	+	0.692823i	$0.756367\pi$
$194$	−10.4046	−	6.68662i	−0.747005	−	0.480071i
$195$		0			0
$196$	0.990833	−	6.89140i	0.0707738	−	0.492243i
$197$	−5.26265	−	3.38210i	−0.374948	−	0.240965i	0.339571	−	0.940580i	$-0.389718\pi$
$197$	−5.26265	−	3.38210i	−0.374948	−	0.240965i	−0.714519	+	0.699616i	$0.753354\pi$
$198$		0			0
$199$	0.358560	+	0.785136i	0.0254176	+	0.0556568i	0.921915	−	0.387392i	$-0.126624\pi$
$199$	0.358560	+	0.785136i	0.0254176	+	0.0556568i	−0.896497	+	0.443049i	$0.853897\pi$
$200$	2.25168	−	1.44706i	0.159218	−	0.102323i
$201$		0			0
$202$	10.2791	−	11.8628i	0.723237	−	0.834661i
$203$	−1.71682	+	0.504104i	−0.120497	+	0.0353811i
$204$		0			0
$205$	2.26527	+	15.7553i	0.158213	+	1.10040i
$206$	9.44491			0.658058
$207$		0			0
$208$	1.08260			0.0750646
$209$	−1.82889	−	12.7202i	−0.126507	−	0.879878i
$210$		0			0
$211$	−18.2924	+	5.37114i	−1.25930	+	0.369764i	−0.842234	−	0.539112i	$-0.818760\pi$
$211$	−18.2924	+	5.37114i	−1.25930	+	0.369764i	−0.417067	+	0.908876i	$0.636942\pi$
$212$	−2.71282	+	3.13076i	−0.186317	+	0.215021i
$213$		0			0
$214$	−8.00202	+	5.14259i	−0.547007	+	0.351540i
$215$	−8.70936	−	19.0708i	−0.593973	−	1.30062i
$216$		0			0
$217$	−1.12325	−	0.721868i	−0.0762511	−	0.0490036i
$218$	2.87785	−	20.0159i	0.194912	−	1.35565i
$219$		0			0
$220$	6.76890	+	4.35011i	0.456359	+	0.293284i
$221$	−3.29085	−	3.79785i	−0.221367	−	0.255471i
$222$		0			0
$223$	5.39879	−	3.46959i	0.361529	−	0.232341i	−0.347248	−	0.937774i	$-0.612884\pi$
$223$	5.39879	−	3.46959i	0.361529	−	0.232341i	0.708777	+	0.705433i	$0.249247\pi$
$224$	−0.186393	−	0.0547299i	−0.0124539	−	0.00365679i
$225$		0			0
$226$	1.26333	−	0.370948i	0.0840357	−	0.0246751i
$227$	0.497189	−	1.08869i	0.0329996	−	0.0722590i	−0.892414	−	0.451217i	$-0.850990\pi$
$227$	0.497189	−	1.08869i	0.0329996	−	0.0722590i	0.925414	+	0.378958i	$0.123717\pi$
$228$		0			0
$229$	−28.0856			−1.85595			−0.927974	−	0.372646i	$-0.878451\pi$
$229$	−28.0856			−1.85595			−0.927974	+	0.372646i	$0.878451\pi$
$230$	−12.1731	−	5.32693i	−0.802672	−	0.351247i
$231$		0			0
$232$	−1.31083	−	9.11701i	−0.0860600	−	0.598561i
$233$	6.81811	−	14.9296i	0.446669	−	0.978070i	−0.543656	−	0.839308i	$-0.682961\pi$
$233$	6.81811	−	14.9296i	0.446669	−	0.978070i	0.990326	−	0.138762i	$-0.0443122\pi$
$234$		0			0
$235$	10.1871	−	11.7565i	0.664531	−	0.766909i
$236$	−10.2842	−	3.01971i	−0.669444	−	0.196566i
$237$		0			0
$238$	0.374596	+	0.820250i	0.0242814	+	0.0531689i
$239$	6.76847	+	7.81123i	0.437816	+	0.505266i	0.931182	−	0.364556i	$-0.118779\pi$
$239$	6.76847	+	7.81123i	0.437816	+	0.505266i	−0.493366	+	0.869822i	$0.664234\pi$
$240$		0			0
$241$	3.12210	−	21.7147i	0.201112	−	1.39877i	−0.599879	−	0.800091i	$-0.704785\pi$
$241$	3.12210	−	21.7147i	0.201112	−	1.39877i	0.800991	−	0.598676i	$-0.204306\pi$
$242$	0.365231	−	2.54024i	0.0234780	−	0.163293i
$243$		0			0
$244$	1.88574	+	2.17626i	0.120722	+	0.139321i
$245$	8.01339	+	17.5469i	0.511957	+	1.12103i
$246$		0			0
$247$	4.59663	+	1.34969i	0.292476	+	0.0858788i
$248$	4.50102	−	5.19445i	0.285815	−	0.329848i
$249$		0			0
$250$	2.67421	−	5.85569i	0.169132	−	0.370347i
$251$	0.0385613	+	0.268200i	0.00243397	+	0.0169286i	0.991002	−	0.133845i	$-0.0427325\pi$
$251$	0.0385613	+	0.268200i	0.00243397	+	0.0169286i	−0.988568	+	0.150774i	$0.951823\pi$
$252$		0			0
$253$	−0.221534	−	13.9257i	−0.0139277	−	0.875500i
$254$	−4.81847			−0.302338
$255$		0			0
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	14.0118	−	4.11424i	0.874033	−	0.256639i	0.186203	−	0.982511i	$-0.440382\pi$
$257$	14.0118	−	4.11424i	0.874033	−	0.256639i	0.687830	+	0.725872i	$0.258564\pi$
$258$		0			0
$259$	0.903212	+	0.265207i	0.0561228	+	0.0164792i
$260$	−2.52335	+	1.62166i	−0.156491	+	0.100571i
$261$		0			0
$262$	10.4632	+	12.0752i	0.646419	+	0.746007i
$263$	14.3594	+	9.22820i	0.885436	+	0.569035i	0.902438	−	0.430820i	$-0.141776\pi$
$263$	14.3594	+	9.22820i	0.885436	+	0.569035i	−0.0170015	+	0.999855i	$0.505412\pi$
$264$		0			0
$265$	1.63345	−	11.3609i	0.100342	−	0.697893i
$266$	−0.723178	−	0.464758i	−0.0443409	−	0.0284962i
$267$		0			0
$268$	−6.08057	−	13.3146i	−0.371430	−	0.813318i
$269$	−27.1087	+	17.4217i	−1.65284	+	1.06222i	−0.725349	+	0.688381i	$0.758322\pi$
$269$	−27.1087	+	17.4217i	−1.65284	+	1.06222i	−0.927494	+	0.373837i	$0.878042\pi$
$270$		0			0
$271$	−2.00662	+	2.31576i	−0.121893	+	0.140672i	−0.813416	−	0.581682i	$-0.802395\pi$
$271$	−2.00662	+	2.31576i	−0.121893	+	0.140672i	0.691523	+	0.722355i	$0.256940\pi$
$272$	−4.45384	+	1.30777i	−0.270054	+	0.0792950i
$273$		0			0
$274$	2.67153	+	18.5809i	0.161393	+	1.12251i
$275$	−7.77296			−0.468727
$276$		0			0
$277$	−5.05736			−0.303867			−0.151934	−	0.988391i	$-0.548550\pi$
$277$	−5.05736			−0.303867			−0.151934	+	0.988391i	$0.548550\pi$
$278$	−2.52666	−	17.5733i	−0.151539	−	1.05398i
$279$		0			0
$280$	0.516432	−	0.151638i	0.0308627	−	0.00906210i
$281$	−5.50042	+	6.34782i	−0.328127	+	0.378679i	−0.895711	−	0.444636i	$-0.853333\pi$
$281$	−5.50042	+	6.34782i	−0.328127	+	0.378679i	0.567584	+	0.823316i	$0.307878\pi$
$282$		0			0
$283$	12.8122	−	8.23389i	0.761605	−	0.489454i	−0.101278	−	0.994858i	$-0.532293\pi$
$283$	12.8122	−	8.23389i	0.761605	−	0.489454i	0.862883	+	0.505404i	$0.168657\pi$
$284$	−5.28905	−	11.5814i	−0.313847	−	0.687229i
$285$		0			0
$286$	−2.64485	−	1.69974i	−0.156393	−	0.100508i
$287$	−0.158827	+	1.10466i	−0.00937524	+	0.0652062i
$288$		0			0
$289$	3.82516	+	2.45828i	0.225010	+	0.144605i
$290$	16.7120	+	19.2867i	0.981361	+	1.13255i
$291$		0			0
$292$	2.51377	−	1.61550i	0.147107	−	0.0945401i
$293$	27.7542	+	8.14937i	1.62142	+	0.476091i	0.961399	−	0.275158i	$-0.0887303\pi$
$293$	27.7542	+	8.14937i	1.62142	+	0.476091i	0.660018	+	0.751249i	$0.270548\pi$
$294$		0			0
$295$	28.4940	−	8.36660i	1.65899	−	0.487122i
$296$	−2.01299	+	4.40784i	−0.117003	+	0.256201i
$297$		0			0
$298$	9.51537			0.551211
$299$	4.75647	+	2.08142i	0.275074	+	0.120372i
$300$		0			0
$301$	−0.209198	−	1.45501i	−0.0120580	−	0.0838651i
$302$	−3.60527	+	7.89445i	−0.207460	+	0.454274i
$303$		0			0
$304$	2.89788	−	3.34433i	0.166205	−	0.191810i
$305$	−7.65525	−	2.24778i	−0.438338	−	0.128708i
$306$		0			0
$307$	−8.96612	−	19.6331i	−0.511724	−	1.12052i	−0.972479	−	0.232991i	$-0.925149\pi$
$307$	−8.96612	−	19.6331i	−0.511724	−	1.12052i	0.460755	−	0.887527i	$-0.347579\pi$
$308$	0.369440	+	0.426356i	0.0210508	+	0.0242939i
$309$		0			0
$310$	−2.71016	+	18.8496i	−0.153927	+	1.07059i
$311$	0.125077	−	0.869929i	0.00709246	−	0.0493291i	−0.985968	−	0.166935i	$-0.946613\pi$
$311$	0.125077	−	0.869929i	0.00709246	−	0.0493291i	0.993060	+	0.117606i	$0.0375220\pi$
$312$		0			0
$313$	3.57263	+	4.12304i	0.201937	+	0.233048i	0.847681	−	0.530506i	$-0.177998\pi$
$313$	3.57263	+	4.12304i	0.201937	+	0.233048i	−0.645744	+	0.763554i	$0.723453\pi$
$314$	8.23200	+	18.0256i	0.464559	+	1.01724i
$315$		0			0
$316$	−2.45532	−	0.720946i	−0.138122	−	0.0405564i
$317$	−3.33115	+	3.84435i	−0.187096	+	0.215920i	−0.841547	−	0.540184i	$-0.818355\pi$
$317$	−3.33115	+	3.84435i	−0.187096	+	0.215920i	0.654451	+	0.756105i	$0.272900\pi$
$318$		0			0
$319$	−11.1118	+	24.3315i	−0.622142	+	1.36230i
$320$	0.394306	+	2.74246i	0.0220424	+	0.153308i
$321$		0			0
$322$	−0.713707	−	0.598822i	−0.0397733	−	0.0333711i
$323$	−20.5411			−1.14294
$324$		0			0
$325$	1.20373	−	2.63579i	0.0667708	−	0.146208i
$326$	−13.9140	+	4.08552i	−0.770625	+	0.226276i
$327$		0			0
$328$	−5.51223	−	1.61854i	−0.304362	−	0.0893688i
$329$	0.917552	−	0.589675i	0.0505863	−	0.0325098i
$330$		0			0
$331$	23.3216	+	26.9146i	1.28187	+	1.47936i	0.795954	+	0.605356i	$0.206969\pi$
$331$	23.3216	+	26.9146i	1.28187	+	1.47936i	0.485919	+	0.874004i	$0.338485\pi$
$332$	0.682732	+	0.438765i	0.0374698	+	0.0240804i
$333$		0			0
$334$	−1.40766	+	9.79051i	−0.0770239	+	0.535713i
$335$	34.1172	+	21.9258i	1.86402	+	1.19793i
$336$		0			0
$337$	4.77911	+	10.4648i	0.260335	+	0.570053i	0.993990	−	0.109468i	$-0.0349147\pi$
$337$	4.77911	+	10.4648i	0.260335	+	0.570053i	−0.733656	+	0.679521i	$0.762187\pi$
$338$	−9.95033	+	6.39469i	−0.541227	+	0.347825i
$339$		0			0
$340$	8.42221	−	9.71974i	0.456758	−	0.527127i
$341$	−19.1519	+	5.62349i	−1.03713	+	0.304529i
$342$		0			0
$343$	0.386005	+	2.68473i	0.0208423	+	0.144962i
$344$	7.56694			0.407982
$345$		0			0
$346$	−13.2434			−0.711972
$347$	−2.24907	−	15.6426i	−0.120736	−	0.839740i	−0.956725	−	0.290993i	$-0.906014\pi$
$347$	−2.24907	−	15.6426i	−0.120736	−	0.839740i	0.835989	−	0.548747i	$-0.184895\pi$
$348$		0			0
$349$	−11.7351	+	3.44574i	−0.628167	+	0.184446i	−0.580294	−	0.814407i	$-0.697062\pi$
$349$	−11.7351	+	3.44574i	−0.628167	+	0.184446i	−0.0478727	+	0.998853i	$0.515244\pi$
$350$	−0.340499	+	0.392956i	−0.0182004	+	0.0210044i
$351$		0			0
$352$	−2.44306	+	1.57006i	−0.130216	+	0.0836845i
$353$	−1.51906	−	3.32628i	−0.0808514	−	0.177040i	0.864889	−	0.501963i	$-0.167389\pi$
$353$	−1.51906	−	3.32628i	−0.0808514	−	0.177040i	−0.945740	+	0.324923i	$0.894661\pi$
$354$		0			0
$355$	29.6760	+	19.0716i	1.57504	+	1.01222i
$356$	0.964871	−	6.71083i	0.0511381	−	0.355673i
$357$		0			0
$358$	−4.41264	−	2.83583i	−0.233215	−	0.149878i
$359$	−8.61646	−	9.94392i	−0.454759	−	0.524820i	0.481351	−	0.876528i	$-0.340146\pi$
$359$	−8.61646	−	9.94392i	−0.454759	−	0.524820i	−0.936110	+	0.351708i	$0.885601\pi$
$360$		0			0
$361$	0.489802	−	0.314776i	0.0257790	−	0.0165672i
$362$	15.5968	+	4.57965i	0.819752	+	0.240701i
$363$		0			0
$364$	−0.201788	+	0.0592504i	−0.0105766	+	0.00310556i
$365$	−3.43926	+	7.53092i	−0.180019	+	0.394186i
$366$		0			0
$367$	−12.3385			−0.644064			−0.322032	−	0.946729i	$-0.604366\pi$
$367$	−12.3385			−0.644064			−0.322032	+	0.946729i	$0.604366\pi$
$368$	3.57403	−	3.19786i	0.186309	−	0.166700i
$369$		0			0
$370$	−1.91071	−	13.2893i	−0.0993330	−	0.690876i
$371$	0.334303	−	0.732022i	0.0173562	−	0.0380047i
$372$		0			0
$373$	12.1475	−	14.0189i	0.628973	−	0.725873i	−0.348412	−	0.937341i	$-0.613279\pi$
$373$	12.1475	−	14.0189i	0.628973	−	0.725873i	0.977385	+	0.211468i	$0.0678244\pi$
$374$	12.9343	+	3.79785i	0.668816	+	0.196382i
$375$		0			0
$376$	2.33238	+	5.10719i	0.120283	+	0.263383i
$377$	−6.52997	−	7.53598i	−0.336310	−	0.388123i
$378$		0			0
$379$	−0.406982	+	2.83062i	−0.0209053	+	0.145399i	−0.997601	−	0.0692308i	$-0.977946\pi$
$379$	−0.406982	+	2.83062i	−0.0209053	+	0.145399i	0.976695	+	0.214630i	$0.0688546\pi$
$380$	−1.74488	+	12.1359i	−0.0895103	+	0.622558i
$381$		0			0
$382$	−5.03762	−	5.81372i	−0.257747	−	0.297456i
$383$	0.0334270	+	0.0731949i	0.00170804	+	0.00374009i	0.910484	−	0.413544i	$-0.135709\pi$
$383$	0.0334270	+	0.0731949i	0.00170804	+	0.00374009i	−0.908776	+	0.417284i	$0.862982\pi$
$384$		0			0
$385$	−1.49975	−	0.440368i	−0.0764346	−	0.0224432i
$386$	0.934780	−	1.07879i	0.0475791	−	0.0549092i
$387$		0			0
$388$	−5.13783	+	11.2503i	−0.260834	+	0.571146i
$389$	−1.95719	−	13.6126i	−0.0992337	−	0.690185i	−0.977333	−	0.211707i	$-0.932098\pi$
$389$	−1.95719	−	13.6126i	−0.0992337	−	0.690185i	0.878099	−	0.478478i	$-0.158811\pi$
$390$		0			0
$391$	−22.0827	−	2.81726i	−1.11677	−	0.142475i
$392$	−6.96226			−0.351647
$393$		0			0
$394$	−2.59872	+	5.69041i	−0.130922	+	0.286678i
$395$	6.80286	−	1.99750i	0.342289	−	0.100505i
$396$		0			0
$397$	6.36046	+	1.86760i	0.319222	+	0.0937321i	0.437418	−	0.899258i	$-0.355893\pi$
$397$	6.36046	+	1.86760i	0.319222	+	0.0937321i	−0.118196	+	0.992990i	$0.537711\pi$
$398$	0.726117	−	0.466647i	0.0363969	−	0.0233909i
$399$		0			0
$400$	−1.75278	−	2.02282i	−0.0876391	−	0.101141i
$401$	29.6875	+	19.0790i	1.48252	+	0.952759i	0.996907	+	0.0785860i	$0.0250405\pi$
$401$	29.6875	+	19.0790i	1.48252	+	0.952759i	0.485615	+	0.874173i	$0.338596\pi$
$402$		0			0
$403$	1.05896	−	7.36521i	0.0527504	−	0.366887i
$404$	−13.2049	−	8.48626i	−0.656967	−	0.422207i
$405$		0			0
$406$	0.743301	+	1.62760i	0.0368894	+	0.0807766i
$407$	11.8384	−	7.60811i	0.586810	−	0.377120i
$408$		0			0
$409$	19.1568	−	22.1082i	0.947244	−	1.09318i	−0.0482952	−	0.998833i	$-0.515379\pi$
$409$	19.1568	−	22.1082i	0.947244	−	1.09318i	0.995540	−	0.0943452i	$-0.0300757\pi$
$410$	15.2725	−	4.48442i	0.754257	−	0.221470i
$411$		0			0
$412$	−1.34415	−	9.34877i	−0.0662215	−	0.460581i
$413$	2.08217			0.102457
$414$		0			0
$415$	−2.24857			−0.110378
$416$	−0.154070	−	1.07158i	−0.00755388	−	0.0525384i
$417$		0			0
$418$	−12.3305	+	3.62056i	−0.603104	+	0.177087i
$419$	0.476760	−	0.550210i	0.0232912	−	0.0268795i	−0.743984	−	0.668197i	$-0.767066\pi$
$419$	0.476760	−	0.550210i	0.0232912	−	0.0268795i	0.767276	+	0.641317i	$0.221612\pi$
$420$		0			0
$421$	−28.4791	+	18.3024i	−1.38798	+	0.892004i	−0.999565	−	0.0294793i	$-0.990615\pi$
$421$	−28.4791	+	18.3024i	−1.38798	+	0.892004i	−0.388419	+	0.921483i	$0.626979\pi$
$422$	7.91975	+	17.3418i	0.385527	+	0.844187i
$423$		0			0
$424$	3.48496	+	2.23965i	0.169245	+	0.108767i
$425$	−1.76816	+	12.2979i	−0.0857685	+	0.596533i
$426$		0			0
$427$	−0.470596	−	0.302434i	−0.0227737	−	0.0146358i
$428$	6.22905	+	7.18871i	0.301092	+	0.347479i
$429$		0			0
$430$	−17.6373	+	11.3348i	−0.850544	+	0.546611i
$431$	1.42384	+	0.418077i	0.0685839	+	0.0201381i	0.315845	−	0.948811i	$-0.397712\pi$
$431$	1.42384	+	0.418077i	0.0685839	+	0.0201381i	−0.247261	+	0.968949i	$0.579530\pi$
$432$		0			0
$433$	6.69224	−	1.96502i	0.321608	−	0.0944327i	−0.116944	−	0.993139i	$-0.537310\pi$
$433$	6.69224	−	1.96502i	0.321608	−	0.0944327i	0.438552	+	0.898706i	$0.355492\pi$
$434$	−0.554666	+	1.21455i	−0.0266248	+	0.0583002i
$435$		0			0
$436$	−20.2217			−0.968443
$437$	19.1619	−	9.12206i	0.916639	−	0.436367i
$438$		0			0
$439$	−1.32651	−	9.22605i	−0.0633106	−	0.440335i	−0.996680	−	0.0814180i	$-0.974055\pi$
$439$	−1.32651	−	9.22605i	−0.0633106	−	0.440335i	0.933369	−	0.358917i	$-0.116854\pi$
$440$	3.34251	−	7.31909i	0.159348	−	0.348924i
$441$		0			0
$442$	−3.29085	+	3.79785i	−0.156530	+	0.180645i
$443$	30.3672	+	8.91661i	1.44279	+	0.423641i	0.907150	−	0.420807i	$-0.138253\pi$
$443$	30.3672	+	8.91661i	1.44279	+	0.423641i	0.535638	+	0.844448i	$0.320071\pi$
$444$		0			0
$445$	7.80342	+	17.0871i	0.369918	+	0.810007i
$446$	−4.20260	−	4.85006i	−0.198999	−	0.229657i
$447$		0			0
$448$	−0.0276463	+	0.192284i	−0.00130617	+	0.00908459i
$449$	−1.36062	+	9.46329i	−0.0642115	+	0.446600i	0.932199	+	0.361946i	$0.117888\pi$
$449$	−1.36062	+	9.46329i	−0.0642115	+	0.446600i	−0.996410	+	0.0846542i	$0.973021\pi$
$450$		0			0
$451$	10.9255	+	12.6087i	0.514463	+	0.593721i
$452$	−0.546964	−	1.19768i	−0.0257270	−	0.0563343i
$453$		0			0
$454$	−1.14837	−	0.337191i	−0.0538955	−	0.0158252i
$455$	0.381581	−	0.440368i	0.0178888	−	0.0206448i
$456$		0			0
$457$	−5.34240	+	11.6982i	−0.249907	+	0.547220i	−0.992460	−	0.122567i	$-0.960887\pi$
$457$	−5.34240	+	11.6982i	−0.249907	+	0.547220i	0.742553	+	0.669787i	$0.233615\pi$
$458$	3.99700	+	27.7997i	0.186767	+	1.29900i
$459$		0			0
$460$	−3.54029	+	12.8073i	−0.165067	+	0.597145i
$461$	−18.4038			−0.857151			−0.428575	−	0.903506i	$-0.640984\pi$
$461$	−18.4038			−0.857151			−0.428575	+	0.903506i	$0.640984\pi$
$462$		0			0
$463$	11.4891	−	25.1576i	0.533944	−	1.16917i	−0.429941	−	0.902857i	$-0.641466\pi$
$463$	11.4891	−	25.1576i	0.533944	−	1.16917i	0.963885	−	0.266318i	$-0.0858070\pi$
$464$	−8.83766	+	2.59497i	−0.410278	+	0.120468i
$465$		0			0
$466$	−15.7479	−	4.62401i	−0.729509	−	0.214203i
$467$	−20.4802	+	13.1618i	−0.947711	+	0.609057i	−0.920571	−	0.390575i	$-0.872276\pi$
$467$	−20.4802	+	13.1618i	−0.947711	+	0.609057i	−0.0271399	+	0.999632i	$0.508640\pi$
$468$		0			0
$469$	1.86208	+	2.14896i	0.0859829	+	0.0992296i
$470$	−13.0866	−	8.41025i	−0.603640	−	0.387936i
$471$		0			0
$472$	−1.52538	+	10.6093i	−0.0702114	+	0.488331i
$473$	−18.4865	−	11.8806i	−0.850010	−	0.546268i
$474$		0			0
$475$	−4.92031	−	10.7740i	−0.225759	−	0.494344i
$476$	0.758591	−	0.487517i	0.0347699	−	0.0223453i
$477$		0			0
$478$	6.76847	−	7.81123i	0.309582	−	0.357277i
$479$	−6.99671	+	2.05442i	−0.319688	+	0.0938689i	−0.437640	−	0.899150i	$-0.644185\pi$
$479$	−6.99671	+	2.05442i	−0.319688	+	0.0938689i	0.117952	+	0.993019i	$0.462367\pi$
$480$		0			0
$481$	0.746581	+	5.19259i	0.0340412	+	0.236762i
$482$	−21.9380			−0.999248
$483$		0			0
$484$	−2.56636			−0.116653
$485$	−4.87676	−	33.9186i	−0.221442	−	1.54016i
$486$		0			0
$487$	−21.5014	+	6.31339i	−0.974323	+	0.286087i	−0.729879	−	0.683576i	$-0.760424\pi$
$487$	−21.5014	+	6.31339i	−0.974323	+	0.286087i	−0.244444	+	0.969663i	$0.578605\pi$
$488$	1.88574	−	2.17626i	0.0853636	−	0.0985149i
$489$		0			0
$490$	16.2279	−	10.4290i	0.733100	−	0.471134i
$491$	−8.18375	−	17.9199i	−0.369328	−	0.808715i	−0.999480	−	0.0322432i	$-0.989735\pi$
$491$	−8.18375	−	17.9199i	−0.369328	−	0.808715i	0.630152	−	0.776471i	$-0.282992\pi$
$492$		0			0
$493$	35.9679	+	23.1152i	1.61991	+	1.04106i
$494$	0.681786	−	4.74192i	0.0306750	−	0.213349i
$495$		0			0
$496$	−5.78214	−	3.71596i	−0.259626	−	0.166851i
$497$	1.61969	+	1.86922i	0.0726529	+	0.0838460i
$498$		0			0
$499$	−14.5484	+	9.34971i	−0.651277	+	0.418550i	−0.824133	−	0.566397i	$-0.808337\pi$
$499$	−14.5484	+	9.34971i	−0.651277	+	0.418550i	0.172855	+	0.984947i	$0.444701\pi$
$500$	−6.17667	−	1.81363i	−0.276229	−	0.0811082i
$501$		0			0
$502$	0.259982	−	0.0763376i	0.0116036	−	0.00340711i
$503$	−6.82524	+	14.9452i	−0.304323	+	0.666373i	−0.998575	−	0.0533577i	$-0.983008\pi$
$503$	−6.82524	+	14.9452i	−0.304323	+	0.666373i	0.694253	+	0.719731i	$0.255735\pi$
$504$		0			0
$505$	43.4902			1.93529
$506$	−13.7524	+	2.20111i	−0.611369	+	0.0978513i
$507$		0			0
$508$	0.685740	+	4.76943i	0.0304248	+	0.211609i
$509$	−11.2142	+	24.5556i	−0.497059	+	1.08841i	0.480354	+	0.877074i	$0.340508\pi$
$509$	−11.2142	+	24.5556i	−0.497059	+	1.08841i	−0.977414	+	0.211334i	$0.932219\pi$
$510$		0			0
$511$	−0.380132	+	0.438696i	−0.0168161	+	0.0194068i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$		0			0
$514$	−6.06645	−	13.2837i	−0.267580	−	0.585918i
$515$	17.1368	+	19.7770i	0.755139	+	0.871477i
$516$		0			0
$517$	2.32046	−	16.1392i	0.102054	−	0.709799i
$518$	0.133967	−	0.931761i	0.00588617	−	0.0409392i
$519$		0			0
$520$	1.96426	+	2.26688i	0.0861386	+	0.0994092i
$521$	−9.75660	−	21.3640i	−0.427444	−	0.935973i	−0.993734	−	0.111767i	$-0.964349\pi$
$521$	−9.75660	−	21.3640i	−0.427444	−	0.935973i	0.566290	−	0.824206i	$-0.308378\pi$
$522$		0			0
$523$	−28.1477	−	8.26490i	−1.23081	−	0.361399i	−0.399255	−	0.916840i	$-0.630731\pi$
$523$	−28.1477	−	8.26490i	−1.23081	−	0.361399i	−0.831556	+	0.555441i	$0.812550\pi$
$524$	10.4632	−	12.0752i	0.457087	−	0.527507i
$525$		0			0
$526$	7.09072	−	15.5265i	0.309170	−	0.676988i
$527$	4.54051	+	31.5800i	0.197788	+	1.37565i
$528$		0			0
$529$	21.8511	−	7.17853i	0.950046	−	0.312110i
$530$	−11.4777			−0.498560
$531$		0			0
$532$	−0.357109	+	0.781959i	−0.0154826	+	0.0339022i
$533$	−5.96752	+	1.75222i	−0.258482	+	0.0758972i
$534$		0			0
$535$	−25.2871	−	7.42495i	−1.09326	−	0.321009i
$536$	−12.3137	+	7.91354i	−0.531872	+	0.341813i
$537$		0			0
$538$	21.1023	+	24.3534i	0.909785	+	1.04995i
$539$	17.0092	+	10.9312i	0.732640	+	0.470839i
$540$		0			0
$541$	0.682956	−	4.75006i	0.0293626	−	0.204221i	−0.969859	−	0.243666i	$-0.921650\pi$
$541$	0.682956	−	4.75006i	0.0293626	−	0.204221i	0.999222	+	0.0394449i	$0.0125590\pi$
$542$	2.57776	+	1.65662i	0.110724	+	0.0711581i
$543$		0			0
$544$	1.92830	+	4.22240i	0.0826753	+	0.181034i
$545$	47.1333	−	30.2908i	2.01897	−	1.29751i
$546$		0			0
$547$	−18.0000	+	20.7731i	−0.769622	+	0.888192i	−0.996315	−	0.0857749i	$-0.972663\pi$
$547$	−18.0000	+	20.7731i	−0.769622	+	0.888192i	0.226692	+	0.973966i	$0.427209\pi$
$548$	18.0116	−	5.28867i	0.769416	−	0.225921i
$549$		0			0
$550$	1.10621	+	7.69385i	0.0471689	+	0.328067i
$551$	−40.7593			−1.73640
$552$		0			0
$553$	0.497111			0.0211393
$554$	0.719737	+	5.00588i	0.0305787	+	0.212679i
$555$		0			0
$556$	−17.0348	+	5.00188i	−0.722438	+	0.212127i
$557$	−7.86165	+	9.07283i	−0.333109	+	0.384428i	−0.897452	−	0.441112i	$-0.854584\pi$
$557$	−7.86165	+	9.07283i	−0.333109	+	0.384428i	0.564343	+	0.825540i	$0.309130\pi$
$558$		0			0
$559$	6.89150	−	4.42890i	0.291479	−	0.187322i
$560$	−0.223590	−	0.489595i	−0.00944842	−	0.0206892i
$561$		0			0
$562$	7.06600	+	4.54104i	0.298061	+	0.191552i
$563$	−0.869255	+	6.04580i	−0.0366347	+	0.254800i	−0.999906	−	0.0137310i	$-0.995629\pi$
$563$	−0.869255	+	6.04580i	−0.0366347	+	0.254800i	0.963271	+	0.268531i	$0.0865382\pi$
$564$		0			0
$565$	3.06893	+	1.97228i	0.129111	+	0.0829745i
$566$	−9.97344	−	11.5100i	−0.419215	−	0.483800i
$567$		0			0
$568$	−10.7108	+	6.88341i	−0.449415	+	0.288822i
$569$	23.9950	+	7.04556i	1.00592	+	0.295365i	0.742884	−	0.669420i	$-0.233457\pi$
$569$	23.9950	+	7.04556i	1.00592	+	0.295365i	0.263038	+	0.964786i	$0.415276\pi$
$570$		0			0
$571$	22.4009	−	6.57751i	0.937450	−	0.275260i	0.222898	−	0.974842i	$-0.428448\pi$
$571$	22.4009	−	6.57751i	0.937450	−	0.275260i	0.714553	+	0.699582i	$0.246630\pi$
$572$	−1.30604	+	2.85983i	−0.0546082	+	0.119575i
$573$		0			0
$574$	1.11602			0.0465819
$575$	−3.81188	−	12.2573i	−0.158966	−	0.511167i
$576$		0			0
$577$	−5.23379	−	36.4018i	−0.217886	−	1.51543i	−0.745823	−	0.666145i	$-0.767943\pi$
$577$	−5.23379	−	36.4018i	−0.217886	−	1.51543i	0.527937	−	0.849284i	$-0.322966\pi$
$578$	1.88888	−	4.13608i	0.0785672	−	0.172038i
$579$		0			0
$580$	16.7120	−	19.2867i	0.693927	−	0.800835i
$581$	−0.151270	−	0.0444169i	−0.00627573	−	0.00184272i
$582$		0			0
$583$	−4.99759	−	10.9432i	−0.206979	−	0.453221i
$584$	−1.95680	−	2.25827i	−0.0809731	−	0.0934480i
$585$		0			0
$586$	4.11658	−	28.6315i	0.170055	−	1.18276i
$587$	3.37092	−	23.4453i	0.139133	−	0.967690i	−0.793938	−	0.607998i	$-0.791973\pi$
$587$	3.37092	−	23.4453i	0.139133	−	0.967690i	0.933071	−	0.359692i	$-0.117118\pi$
$588$		0			0
$589$	−19.9178	−	22.9864i	−0.820699	−	0.947137i
$590$	−12.3366	−	27.0133i	−0.507888	−	1.11212i
$591$		0			0
$592$	4.64946	+	1.36520i	0.191091	+	0.0561095i
$593$	17.0796	−	19.7109i	0.701376	−	0.809431i	−0.287562	−	0.957762i	$-0.592845\pi$
$593$	17.0796	−	19.7109i	0.701376	−	0.809431i	0.988938	+	0.148331i	$0.0473901\pi$
$594$		0			0
$595$	−1.03788	+	2.27264i	−0.0425489	+	0.0931690i
$596$	−1.35418	−	9.41852i	−0.0554693	−	0.385797i
$597$		0			0
$598$	1.38332	−	5.00428i	0.0565680	−	0.204640i
$599$	−11.2311			−0.458891			−0.229445	−	0.973322i	$-0.573691\pi$
$599$	−11.2311			−0.458891			−0.229445	+	0.973322i	$0.573691\pi$
$600$		0			0
$601$	9.43741	−	20.6650i	0.384960	−	0.842945i	−0.613616	−	0.789604i	$-0.710286\pi$
$601$	9.43741	−	20.6650i	0.384960	−	0.842945i	0.998576	−	0.0533404i	$-0.0169868\pi$
$602$	−1.41042	+	0.414138i	−0.0574846	+	0.0168790i
$603$		0			0
$604$	8.32718	+	2.44508i	0.338828	+	0.0994889i
$605$	5.98175	−	3.84424i	0.243193	−	0.156291i
$606$		0			0
$607$	−10.5182	−	12.1387i	−0.426922	−	0.492694i	0.501011	−	0.865441i	$-0.332962\pi$
$607$	−10.5182	−	12.1387i	−0.426922	−	0.492694i	−0.927933	+	0.372747i	$0.878416\pi$
$608$	−3.72270	−	2.39243i	−0.150975	−	0.0970260i
$609$		0			0
$610$	−1.13545	+	7.89722i	−0.0459730	+	0.319749i
$611$	5.11340	+	3.28618i	0.206866	+	0.132945i
$612$		0			0
$613$	2.61584	+	5.72789i	0.105653	+	0.231347i	0.955074	−	0.296369i	$-0.0957757\pi$
$613$	2.61584	+	5.72789i	0.105653	+	0.231347i	−0.849421	+	0.527716i	$0.823048\pi$
$614$	−18.1572	+	11.6689i	−0.732766	+	0.470920i
$615$		0			0
$616$	0.369440	−	0.426356i	0.0148852	−	0.0171784i
$617$	−9.23760	+	2.71240i	−0.371892	+	0.109197i	−0.462337	−	0.886704i	$-0.652989\pi$
$617$	−9.23760	+	2.71240i	−0.371892	+	0.109197i	0.0904455	+	0.995901i	$0.471171\pi$
$618$		0			0
$619$	−3.51921	−	24.4767i	−0.141449	−	0.983800i	−0.929666	−	0.368403i	$-0.879905\pi$
$619$	−3.51921	−	24.4767i	−0.141449	−	0.983800i	0.788217	−	0.615397i	$-0.211004\pi$
$620$	19.0434			0.764803
$621$		0			0
$622$	−0.878874			−0.0352396
$623$	0.187438	+	1.30366i	0.00750953	+	0.0522299i
$624$		0			0
$625$	29.9542	−	8.79536i	1.19817	−	0.351814i
$626$	3.57263	−	4.12304i	0.142791	−	0.164790i
$627$		0			0
$628$	16.6706	−	10.7135i	0.665228	−	0.427516i
$629$	−9.34406	−	20.4606i	−0.372572	−	0.815819i
$630$		0			0
$631$	30.1416	+	19.3708i	1.19992	+	0.771141i	0.978942	−	0.204138i	$-0.0654391\pi$
$631$	30.1416	+	19.3708i	1.19992	+	0.771141i	0.220977	+	0.975279i	$0.429076\pi$
$632$	−0.364180	+	2.53293i	−0.0144863	+	0.100754i
$633$		0			0
$634$	4.27930	+	2.75014i	0.169953	+	0.109222i
$635$	−8.74263	−	10.0895i	−0.346941	−	0.400391i
$636$		0			0
$637$	−6.34080	+	4.07498i	−0.251232	+	0.161457i
$638$	25.6652	+	7.53598i	1.01609	+	0.298352i
$639$		0			0
$640$	2.65843	−	0.780586i	0.105084	−	0.0308554i
$641$	5.26851	−	11.5364i	0.208094	−	0.455662i	−0.776591	−	0.630005i	$-0.783053\pi$
$641$	5.26851	−	11.5364i	0.208094	−	0.455662i	0.984685	+	0.174343i	$0.0557802\pi$
$642$		0			0
$643$	−27.3350			−1.07799			−0.538993	−	0.842310i	$-0.681195\pi$
$643$	−27.3350			−1.07799			−0.538993	+	0.842310i	$0.681195\pi$
$644$	−0.491156	+	0.791664i	−0.0193543	+	0.0311959i
$645$		0			0
$646$	2.92331	+	20.3320i	0.115016	+	0.799954i
$647$	1.94623	−	4.26166i	0.0765143	−	0.167543i	−0.867509	−	0.497421i	$-0.834280\pi$
$647$	1.94623	−	4.26166i	0.0765143	−	0.167543i	0.944024	+	0.329878i	$0.107008\pi$
$648$		0			0
$649$	20.3838	−	23.5241i	0.800133	−	0.923403i
$650$	−2.78027	−	0.816362i	−0.109051	−	0.0320204i
$651$		0			0
$652$	6.02410	+	13.1909i	0.235922	+	0.516597i
$653$	−18.8217	−	21.7214i	−0.736550	−	0.850024i	0.256643	−	0.966506i	$-0.417384\pi$
$653$	−18.8217	−	21.7214i	−0.736550	−	0.850024i	−0.993193	+	0.116482i	$0.962838\pi$
$654$		0			0
$655$	−6.30013	+	43.8184i	−0.246167	+	1.71213i
$656$	−0.817590	+	5.68647i	−0.0319215	+	0.222019i
$657$		0			0
$658$	−0.714254	−	0.824293i	−0.0278445	−	0.0321343i
$659$	−1.50370	−	3.29264i	−0.0585758	−	0.128263i	0.878081	−	0.478513i	$-0.158824\pi$
$659$	−1.50370	−	3.29264i	−0.0585758	−	0.128263i	−0.936656	+	0.350250i	$0.886097\pi$
$660$		0			0
$661$	16.3839	+	4.81074i	0.637259	+	0.187116i	0.584374	−	0.811485i	$-0.301340\pi$
$661$	16.3839	+	4.81074i	0.637259	+	0.187116i	0.0528849	+	0.998601i	$0.483158\pi$
$662$	23.3216	−	26.9146i	0.906421	−	1.04607i
$663$		0			0
$664$	0.337136	−	0.738226i	0.0130834	−	0.0286487i
$665$	−0.338963	−	2.35754i	−0.0131444	−	0.0914215i
$666$		0			0
$667$	−43.8181	−	5.59023i	−1.69664	−	0.216455i
$668$	9.89119			0.382702
$669$		0			0
$670$	16.8472	−	36.8903i	0.650865	−	1.42519i
$671$	−8.02385	+	2.35602i	−0.309757	+	0.0909530i
$672$		0			0
$673$	−42.8696	−	12.5877i	−1.65250	−	0.485219i	−0.683025	−	0.730395i	$-0.739336\pi$
$673$	−42.8696	−	12.5877i	−1.65250	−	0.485219i	−0.969478	+	0.245177i	$0.921154\pi$
$674$	9.67814	−	6.21976i	0.372788	−	0.239576i
$675$		0			0
$676$	7.74568	+	8.93899i	0.297911	+	0.343807i
$677$	−17.0221	−	10.9395i	−0.654214	−	0.420438i	0.170990	−	0.985273i	$-0.445303\pi$
$677$	−17.0221	−	10.9395i	−0.654214	−	0.420438i	−0.825204	+	0.564835i	$0.808940\pi$
$678$		0			0
$679$	0.341928	−	2.37816i	0.0131220	−	0.0912655i
$680$	−10.8194	−	6.95322i	−0.414906	−	0.266644i
$681$		0			0
$682$	8.29185	+	18.1566i	0.317511	+	0.695253i
$683$	34.6818	−	22.2886i	1.32706	−	0.852850i	0.331184	−	0.943566i	$-0.392552\pi$
$683$	34.6818	−	22.2886i	1.32706	−	0.852850i	0.995877	+	0.0907163i	$0.0289156\pi$
$684$		0			0
$685$	−34.0598	+	39.3071i	−1.30136	+	1.50185i
$686$	2.60247	−	0.764153i	0.0993626	−	0.0291755i
$687$		0			0
$688$	−1.07689	−	7.48992i	−0.0410560	−	0.285551i
$689$	4.48475			0.170855
$690$		0			0
$691$	−39.4196			−1.49959			−0.749795	−	0.661670i	$-0.769848\pi$
$691$	−39.4196			−1.49959			−0.749795	+	0.661670i	$0.769848\pi$
$692$	1.88474	+	13.1086i	0.0716470	+	0.498316i
$693$		0			0
$694$	−15.1633	+	4.45236i	−0.575592	+	0.169009i
$695$	32.2128	−	37.1756i	1.22190	−	1.41015i
$696$		0			0
$697$	22.4339	−	14.4174i	0.849746	−	0.546099i
$698$	5.08075	+	11.1253i	0.192309	+	0.421099i
$699$		0			0
$700$	0.437415	+	0.281109i	0.0165327	+	0.0106249i
$701$	−6.43057	+	44.7256i	−0.242879	+	1.68926i	0.394645	+	0.918834i	$0.370868\pi$
$701$	−6.43057	+	44.7256i	−0.242879	+	1.68926i	−0.637525	+	0.770430i	$0.720042\pi$
$702$		0			0
$703$	18.0392	+	11.5931i	0.680363	+	0.437243i
$704$	1.90176	+	2.19475i	0.0716754	+	0.0827178i
$705$		0			0
$706$	−3.07624	+	1.97698i	−0.115776	+	0.0744045i
$707$	2.92575	+	0.859077i	0.110034	+	0.0323089i
$708$		0			0
$709$	−30.6067	+	8.98694i	−1.14946	+	0.337511i	−0.800328	−	0.599563i	$-0.795341\pi$
$709$	−30.6067	+	8.98694i	−1.14946	+	0.337511i	−0.349131	+	0.937074i	$0.613523\pi$
$710$	14.6542	−	32.0881i	0.549961	−	1.20425i
$711$		0			0
$712$	−6.77984			−0.254085
$713$	−18.2599	−	27.4432i	−0.683840	−	1.02776i
$714$		0			0
$715$	−1.23968	−	8.62213i	−0.0463612	−	0.322449i
$716$	−2.17898	+	4.77130i	−0.0814323	+	0.178312i
$717$		0			0
$718$	−8.61646	+	9.94392i	−0.321563	+	0.371104i
$719$	−24.1545	−	7.09239i	−0.900809	−	0.264502i	−0.201642	−	0.979459i	$-0.564628\pi$
$719$	−24.1545	−	7.09239i	−0.900809	−	0.264502i	−0.699168	+	0.714958i	$0.746446\pi$
$720$		0			0
$721$	0.762197	+	1.66898i	0.0283857	+	0.0621560i
$722$	−0.381279	−	0.440019i	−0.0141897	−	0.0163758i
$723$		0			0
$724$	2.31337	−	16.0898i	0.0859757	−	0.597974i
$725$	−3.50853	+	24.4023i	−0.130303	+	0.906280i
$726$		0			0
$727$	−1.54963	−	1.78836i	−0.0574725	−	0.0663268i	0.726285	−	0.687393i	$-0.241245\pi$
$727$	−1.54963	−	1.78836i	−0.0574725	−	0.0663268i	−0.783758	+	0.621067i	$0.786700\pi$
$728$	0.0873647	+	0.191302i	0.00323795	+	0.00709013i
$729$		0			0
$730$	7.94372	+	2.33249i	0.294010	+	0.0863292i
$731$	−23.0018	+	26.5455i	−0.850754	+	0.981822i
$732$		0			0
$733$	−0.181280	+	0.396947i	−0.00669571	+	0.0146616i	−0.912950	−	0.408071i	$-0.866202\pi$
$733$	−0.181280	+	0.396947i	−0.00669571	+	0.0146616i	0.906255	+	0.422732i	$0.138929\pi$
$734$	1.75595	+	12.2129i	0.0648133	+	0.450786i
$735$		0			0
$736$	−3.67394	−	3.08255i	−0.135423	−	0.113624i
$737$	42.5079			1.56580
$738$		0			0
$739$	−14.5747	+	31.9141i	−0.536138	+	1.17398i	0.426822	+	0.904336i	$0.359633\pi$
$739$	−14.5747	+	31.9141i	−0.536138	+	1.17398i	−0.962960	+	0.269643i	$0.913094\pi$
$740$	−12.8821	+	3.78252i	−0.473555	+	0.139048i
$741$		0			0
$742$	−0.772148	−	0.226723i	−0.0283464	−	0.00832327i
$743$	−28.2800	+	18.1745i	−1.03749	+	0.666756i	−0.944366	−	0.328898i	$-0.893323\pi$
$743$	−28.2800	+	18.1745i	−1.03749	+	0.666756i	−0.0931277	+	0.995654i	$0.529686\pi$
$744$		0			0
$745$	17.2647	+	19.9245i	0.632529	+	0.729977i
$746$	−15.6050	−	10.0287i	−0.571340	−	0.367178i
$747$		0			0
$748$	1.91845	−	13.3431i	0.0701455	−	0.487873i
$749$	−1.55449	−	0.999008i	−0.0567997	−	0.0365030i
$750$		0			0
$751$	16.5189	+	36.1713i	0.602782	+	1.31991i	0.927403	+	0.374064i	$0.122036\pi$
$751$	16.5189	+	36.1713i	0.602782	+	1.31991i	−0.324621	+	0.945844i	$0.605237\pi$
$752$	4.72328	−	3.03546i	0.172240	−	0.110692i
$753$		0			0
$754$	−6.52997	+	7.53598i	−0.237807	+	0.274444i
$755$	−23.0718	+	6.77449i	−0.839669	+	0.246549i
$756$		0			0
$757$	3.53539	+	24.5892i	0.128496	+	0.893709i	0.947462	+	0.319868i	$0.103638\pi$
$757$	3.53539	+	24.5892i	0.128496	+	0.893709i	−0.818966	+	0.573842i	$0.805452\pi$
$758$	2.85973			0.103870
$759$		0			0
$760$	12.2607			0.444742
$761$	−3.46327	−	24.0876i	−0.125543	−	0.873174i	−0.951106	−	0.308864i	$-0.900051\pi$
$761$	−3.46327	−	24.0876i	−0.125543	−	0.873174i	0.825563	−	0.564310i	$-0.190858\pi$
$762$		0			0
$763$	3.76918	−	1.10673i	0.136453	−	0.0400663i
$764$	−5.03762	+	5.81372i	−0.182255	+	0.210333i
$765$		0			0
$766$	0.0676928	−	0.0435035i	0.00244584	−	0.00157185i
$767$	4.82033	+	10.5551i	0.174052	+	0.381121i
$768$		0			0
$769$	−22.2445	−	14.2957i	−0.802159	−	0.515516i	0.0741608	−	0.997246i	$-0.476372\pi$
$769$	−22.2445	−	14.2957i	−0.802159	−	0.515516i	−0.876320	+	0.481730i	$0.840009\pi$
$770$	−0.222448	+	1.54716i	−0.00801647	+	0.0557558i
$771$		0			0
$772$	−1.20085	−	0.771737i	−0.0432194	−	0.0277754i
$773$	14.4872	+	16.7191i	0.521067	+	0.601343i	0.953898	−	0.300132i	$-0.0970307\pi$
$773$	14.4872	+	16.7191i	0.521067	+	0.601343i	−0.432831	+	0.901475i	$0.642485\pi$
$774$		0			0
$775$	−15.4763	+	9.94603i	−0.555926	+	0.357272i
$776$	11.8670	+	3.48445i	0.425999	+	0.125085i
$777$		0			0
$778$	−13.1955	+	3.87455i	−0.473081	+	0.138909i
$779$	−10.5608	+	23.1250i	−0.378382	+	0.828540i
$780$		0			0
$781$	36.9745			1.32305
$782$	0.354100	+	22.2588i	0.0126626	+	0.795974i
$783$		0			0
$784$	0.990833	+	6.89140i	0.0353869	+	0.246121i
$785$	−22.8081	+	49.9428i	−0.814056	+	1.78253i
$786$		0			0
$787$	−2.95813	+	3.41387i	−0.105446	+	0.121691i	−0.806019	−	0.591889i	$-0.798382\pi$
$787$	−2.95813	+	3.41387i	−0.105446	+	0.121691i	0.700573	+	0.713581i	$0.252928\pi$
$788$	6.00232	+	1.76244i	0.213824	+	0.0627844i
$789$		0			0
$790$	−2.94532	−	6.44934i	−0.104790	−	0.229457i
$791$	0.167499	+	0.193304i	0.00595559	+	0.00687311i
$792$		0			0
$793$	0.443660	−	3.08572i	0.0157548	−	0.109577i
$794$	0.943402	−	6.56150i	0.0334801	−	0.232859i
$795$		0			0
$796$	−0.565234	−	0.652315i	−0.0200342	−	0.0231207i
$797$	12.5900	+	27.5683i	0.445961	+	0.976518i	0.990466	+	0.137760i	$0.0439903\pi$
$797$	12.5900	+	27.5683i	0.445961	+	0.976518i	−0.544505	+	0.838758i	$0.683282\pi$
$798$		0			0
$799$	−25.0064	−	7.34255i	−0.884663	−	0.259761i
$800$	−1.75278	+	2.02282i	−0.0619702	+	0.0715175i
$801$		0			0
$802$	14.6598	−	32.1005i	0.517656	−	1.13351i
$803$	1.23497	+	8.58940i	0.0435811	+	0.303113i
$804$		0			0
$805$	−0.0410586	−	2.58095i	−0.00144712	−	0.0909666i
$806$	−7.44095			−0.262096
$807$		0			0
$808$	−6.52063	+	14.2782i	−0.229395	+	0.502305i
$809$	27.2132	−	7.99050i	0.956764	−	0.280931i	0.234163	−	0.972197i	$-0.424765\pi$
$809$	27.2132	−	7.99050i	0.956764	−	0.280931i	0.722600	+	0.691266i	$0.242947\pi$
$810$		0			0
$811$	10.1871	+	2.99120i	0.357718	+	0.105035i	0.455653	−	0.890157i	$-0.349406\pi$
$811$	10.1871	+	2.99120i	0.357718	+	0.105035i	−0.0979355	+	0.995193i	$0.531224\pi$
$812$	1.50525	−	0.967368i	0.0528240	−	0.0339479i
$813$		0			0
$814$	−9.21546	−	10.6352i	−0.323002	−	0.372764i
$815$	−33.8003	−	21.7221i	−1.18397	−	0.760894i
$816$		0			0
$817$	4.76542	−	33.1443i	0.166721	−	1.15957i
$818$	−24.6094	−	15.8155i	−0.860449	−	0.552977i
$819$		0			0
$820$	−6.61228	−	14.4789i	−0.230911	−	0.505625i
$821$	−13.0634	+	8.39532i	−0.455915	+	0.292999i	−0.748371	−	0.663280i	$-0.769164\pi$
$821$	−13.0634	+	8.39532i	−0.455915	+	0.292999i	0.292456	+	0.956279i	$0.405527\pi$
$822$		0			0
$823$	32.8520	−	37.9133i	1.14515	−	1.32157i	0.205808	−	0.978592i	$-0.434018\pi$
$823$	32.8520	−	37.9133i	1.14515	−	1.32157i	0.939342	−	0.342981i	$-0.111437\pi$
$824$	−9.06232	+	2.66094i	−0.315701	+	0.0926982i
$825$		0			0
$826$	−0.296323	−	2.06097i	−0.0103104	−	0.0717104i
$827$	33.0620			1.14968			0.574839	−	0.818267i	$-0.305065\pi$
$827$	33.0620			1.14968			0.574839	+	0.818267i	$0.305065\pi$
$828$		0			0
$829$	−11.7345			−0.407556			−0.203778	−	0.979017i	$-0.565322\pi$
$829$	−11.7345			−0.407556			−0.203778	+	0.979017i	$0.565322\pi$
$830$	0.320005	+	2.22569i	0.0111076	+	0.0772547i
$831$		0			0
$832$	−1.03874	+	0.305003i	−0.0360120	+	0.0105741i
$833$	21.1637	−	24.4243i	0.733280	−	0.846251i
$834$		0			0
$835$	−23.0547	+	14.8163i	−0.797840	+	0.512741i
$836$	5.33852	+	11.6897i	0.184637	+	0.404298i
$837$		0			0
$838$	−0.612459	−	0.393604i	−0.0211571	−	0.0135968i
$839$	−1.09621	+	7.62430i	−0.0378453	+	0.263220i	−0.999955	−	0.00944127i	$-0.996995\pi$
$839$	−1.09621	+	7.62430i	−0.0378453	+	0.263220i	0.962110	+	0.272661i	$0.0879038\pi$
$840$		0			0
$841$	46.9740	+	30.1883i	1.61979	+	1.04098i
$842$	22.1691	+	25.5845i	0.763997	+	0.881700i
$843$		0			0
$844$	16.0382	−	10.3071i	0.552058	−	0.354786i
$845$	−31.4439	−	9.23276i	−1.08170	−	0.317617i
$846$		0			0
$847$	0.478351	−	0.140457i	0.0164364	−	0.00482615i
$848$	1.72089	−	3.76823i	0.0590957	−	0.129401i
$849$		0			0
$850$	12.4243			0.426150
$851$	17.8030	+	14.9373i	0.610279	+	0.512043i
$852$		0			0
$853$	6.01254	+	41.8181i	0.205865	+	1.43183i	0.786464	+	0.617636i	$0.211909\pi$
$853$	6.01254	+	41.8181i	0.205865	+	1.43183i	−0.580599	+	0.814190i	$0.697181\pi$
$854$	−0.232382	+	0.508847i	−0.00795196	+	0.0174124i
$855$		0			0
$856$	6.22905	−	7.18871i	0.212905	−	0.245705i
$857$	−18.5488	−	5.44641i	−0.633613	−	0.186046i	−0.0508744	−	0.998705i	$-0.516201\pi$
$857$	−18.5488	−	5.44641i	−0.633613	−	0.186046i	−0.582739	+	0.812659i	$0.698019\pi$
$858$		0			0
$859$	−8.34241	−	18.2673i	−0.284639	−	0.623273i	0.712264	−	0.701912i	$-0.247670\pi$
$859$	−8.34241	−	18.2673i	−0.284639	−	0.623273i	−0.996903	+	0.0786387i	$0.974943\pi$
$860$	13.7294	+	15.8446i	0.468170	+	0.540297i
$861$		0			0
$862$	0.211188	−	1.46885i	0.00719309	−	0.0500291i
$863$	0.826096	−	5.74562i	0.0281206	−	0.195583i	−0.970919	−	0.239410i	$-0.923046\pi$
$863$	0.826096	−	5.74562i	0.0281206	−	0.195583i	0.999039	+	0.0438270i	$0.0139550\pi$
$864$		0			0
$865$	−24.0289	−	27.7308i	−0.817006	−	0.942875i
$866$	−2.89742	−	6.34447i	−0.0984584	−	0.215594i
$867$		0			0
$868$	1.28112	+	0.376172i	0.0434841	+	0.0127681i
$869$	4.86656	−	5.61631i	0.165087	−	0.190520i
$870$		0			0
$871$	−6.58281	+	14.4143i	−0.223050	+	0.488411i
$872$	2.87785	+	20.0159i	0.0974562	+	0.677823i
$873$		0			0
$874$	−11.7562	−	17.6687i	−0.397661	−	0.597652i
$875$	1.25055			0.0422762
$876$		0			0
$877$	14.9519	−	32.7400i	0.504889	−	1.10555i	−0.469960	−	0.882688i	$-0.655732\pi$
$877$	14.9519	−	32.7400i	0.504889	−	1.10555i	0.974849	−	0.222865i	$-0.0715410\pi$
$878$	−8.94336	+	2.62601i	−0.301824	+	0.0886234i
$879$		0			0
$880$	−7.72028	−	2.26688i	−0.260251	−	0.0764165i
$881$	−31.4703	+	20.2247i	−1.06026	+	0.681388i	−0.949916	−	0.312506i	$-0.898832\pi$
$881$	−31.4703	+	20.2247i	−1.06026	+	0.681388i	−0.110344	+	0.993893i	$0.535195\pi$
$882$		0			0
$883$	32.9735	+	38.0535i	1.10965	+	1.28060i	0.956287	+	0.292431i	$0.0944643\pi$
$883$	32.9735	+	38.0535i	1.10965	+	1.28060i	0.153361	+	0.988170i	$0.450990\pi$
$884$	4.22753	+	2.71687i	0.142187	+	0.0913782i
$885$		0			0
$886$	4.50415	−	31.3270i	0.151320	−	1.05245i
$887$	−25.8216	−	16.5945i	−0.867004	−	0.557190i	0.0298308	−	0.999555i	$-0.490503\pi$
$887$	−25.8216	−	16.5945i	−0.867004	−	0.557190i	−0.896835	+	0.442365i	$0.854140\pi$
$888$		0			0
$889$	−0.388847	−	0.851456i	−0.0130415	−	0.0285569i
$890$	15.8026	−	10.1557i	0.529706	−	0.340421i
$891$		0			0
$892$	−4.20260	+	4.85006i	−0.140713	+	0.162392i
$893$	23.8391	−	6.99978i	0.797744	−	0.234239i
$894$		0			0
$895$	−2.06826	−	14.3851i	−0.0691343	−	0.480840i
$896$	0.194262			0.00648983
$897$		0			0
$898$	9.56061			0.319042
$899$	9.00963	+	62.6634i	0.300488	+	2.08994i
$900$		0			0
$901$	−18.4504	+	5.41753i	−0.614673	+	0.180484i
$902$	10.9255	−	12.6087i	0.363780	−	0.419824i
$903$		0			0
$904$	−1.10765	+	0.711845i	−0.0368400	+	0.0236756i
$905$	18.7094	+	40.9680i	0.621923	+	1.36182i
$906$		0			0
$907$	−4.54974	−	2.92394i	−0.151071	−	0.0970877i	0.462921	−	0.886399i	$-0.346801\pi$
$907$	−4.54974	−	2.92394i	−0.151071	−	0.0970877i	−0.613993	+	0.789312i	$0.710438\pi$
$908$	−0.170329	+	1.18467i	−0.00565257	+	0.0393145i
$909$		0			0
$910$	−0.490190	−	0.315026i	−0.0162496	−	0.0104430i
$911$	−29.6277	−	34.1922i	−0.981610	−	1.13284i	−0.991132	−	0.132883i	$-0.957576\pi$
$911$	−29.6277	−	34.1922i	−0.981610	−	1.13284i	0.00952202	−	0.999955i	$-0.496969\pi$
$912$		0			0
$913$	−1.98270	+	1.27421i	−0.0656179	+	0.0421701i
$914$	12.3395	+	3.62319i	0.408153	+	0.119845i
$915$		0			0
$916$	26.9479	−	7.91262i	0.890384	−	0.261440i
$917$	−1.28939	+	2.82338i	−0.0425795	+	0.0932361i
$918$		0			0
$919$	10.7793			0.355576			0.177788	−	0.984069i	$-0.443106\pi$
$919$	10.7793			0.355576			0.177788	+	0.984069i	$0.443106\pi$
$920$	13.1808	+	1.68158i	0.434558	+	0.0554401i
$921$		0			0
$922$	2.61914	+	18.2165i	0.0862566	+	0.599928i
$923$	−5.72590	+	12.5380i	−0.188470	+	0.412692i
$924$		0			0
$925$	8.49354	−	9.80206i	0.279266	−	0.322290i
$926$	−26.5366	−	7.79186i	−0.872048	−	0.256056i
$927$		0			0
$928$	3.82629	+	8.37840i	0.125604	+	0.275034i
$929$	−20.5270	−	23.6894i	−0.673470	−	0.777226i	0.311445	−	0.950264i	$-0.399187\pi$
$929$	−20.5270	−	23.6894i	−0.673470	−	0.777226i	−0.984915	+	0.173038i	$0.944642\pi$
$930$		0			0
$931$	−4.38462	+	30.4957i	−0.143700	+	0.999455i
$932$	−2.33578	+	16.2457i	−0.0765111	+	0.532146i
$933$		0			0
$934$	15.9425	+	18.3986i	0.521655	+	0.602022i
$935$	15.5155	+	33.9743i	0.507412	+	1.11108i
$936$		0			0
$937$	−15.5397	−	4.56287i	−0.507661	−	0.149063i	0.0178650	−	0.999840i	$-0.494313\pi$
$937$	−15.5397	−	4.56287i	−0.507661	−	0.149063i	−0.525526	+	0.850778i	$0.676131\pi$
$938$	1.86208	−	2.14896i	0.0607991	−	0.0701659i
$939$		0			0
$940$	−6.46223	+	14.1503i	−0.210775	+	0.461532i
$941$	−3.42607	−	23.8289i	−0.111687	−	0.776798i	−0.966279	−	0.257498i	$-0.917102\pi$
$941$	−3.42607	−	23.8289i	−0.111687	−	0.776798i	0.854592	−	0.519300i	$-0.173807\pi$
$942$		0			0
$943$	−14.5251	+	23.4120i	−0.473001	+	0.762400i
$944$	10.7184			0.348853
$945$		0			0
$946$	−9.12872	+	19.9891i	−0.296800	+	0.649902i
$947$	4.75553	−	1.39635i	0.154534	−	0.0453753i	−0.203551	−	0.979064i	$-0.565248\pi$
$947$	4.75553	−	1.39635i	0.154534	−	0.0453753i	0.358085	+	0.933689i	$0.383430\pi$
$948$		0			0
$949$	−3.10389	−	0.911386i	−0.100757	−	0.0295848i
$950$	−9.96408	+	6.40352i	−0.323277	+	0.207758i
$951$		0			0
$952$	−0.590513	−	0.681488i	−0.0191386	−	0.0220872i
$953$	32.4534	+	20.8566i	1.05127	+	0.675610i	0.947749	−	0.319017i	$-0.103353\pi$
$953$	32.4534	+	20.8566i	1.05127	+	0.675610i	0.103521	+	0.994627i	$0.466989\pi$
$954$		0			0
$955$	3.03326	−	21.0968i	0.0981541	−	0.682677i
$956$	−8.69497	−	5.58792i	−0.281215	−	0.180726i
$957$		0			0
$958$	3.02925	+	6.63312i	0.0978705	+	0.214306i
$959$	−3.06778	+	1.97154i	−0.0990637	+	0.0636644i
$960$		0			0
$961$	−10.6359	+	12.2745i	−0.343093	+	0.395951i
$962$	5.03349	−	1.47796i	0.162286	−	0.0476515i
$963$		0			0
$964$	3.12210	+	21.7147i	0.100556	+	0.699383i
$965$	3.95498			0.127315
$966$		0			0
$967$	47.2484			1.51940			0.759702	−	0.650271i	$-0.225345\pi$
$967$	47.2484			1.51940			0.759702	+	0.650271i	$0.225345\pi$
$968$	0.365231	+	2.54024i	0.0117390	+	0.0816464i
$969$		0			0
$970$	−32.8793	+	9.65424i	−1.05569	+	0.309979i
$971$	11.2136	−	12.9412i	0.359863	−	0.415304i	−0.546731	−	0.837308i	$-0.684128\pi$
$971$	11.2136	−	12.9412i	0.359863	−	0.415304i	0.906594	+	0.422005i	$0.138673\pi$
$972$		0			0
$973$	2.90142	−	1.86463i	0.0930153	−	0.0597773i
$974$	9.30911	+	20.3841i	0.298283	+	0.653149i
$975$		0			0
$976$	−2.42248	−	1.55683i	−0.0775418	−	0.0498331i
$977$	−3.35123	+	23.3083i	−0.107215	+	0.745699i	0.863306	+	0.504682i	$0.168390\pi$
$977$	−3.35123	+	23.3083i	−0.107215	+	0.745699i	−0.970521	+	0.241017i	$0.922519\pi$
$978$		0			0
$979$	16.5636	+	10.6448i	0.529374	+	0.340208i
$980$	−12.6323	−	14.5785i	−0.403525	−	0.465692i
$981$		0			0
$982$	−16.5729	+	10.6507i	−0.528861	+	0.339878i
$983$	−7.70621	−	2.26275i	−0.245790	−	0.0721704i	0.156517	−	0.987675i	$-0.449973\pi$
$983$	−7.70621	−	2.26275i	−0.245790	−	0.0721704i	−0.402307	+	0.915505i	$0.631792\pi$
$984$		0			0
$985$	−16.6304	+	4.88313i	−0.529889	+	0.155589i
$986$	17.7611	−	38.8915i	0.565630	−	1.23856i
$987$		0			0
$988$	−4.79069			−0.152412
$989$	9.66886	−	34.9780i	0.307452	−	1.11224i
$990$		0			0
$991$	7.56451	+	52.6123i	0.240294	+	1.67128i	0.650664	+	0.759365i	$0.274490\pi$
$991$	7.56451	+	52.6123i	0.240294	+	1.67128i	−0.410370	+	0.911919i	$0.634600\pi$
$992$	−2.85525	+	6.25212i	−0.0906542	+	0.198505i
$993$		0			0
$994$	1.61969	−	1.86922i	0.0513734	−	0.0592880i
$995$	2.29459	+	0.673752i	0.0727434	+	0.0213594i
$996$		0			0
$997$	−5.98347	−	13.1020i	−0.189498	−	0.414944i	0.790906	−	0.611937i	$-0.209610\pi$
$997$	−5.98347	−	13.1020i	−0.189498	−	0.414944i	−0.980405	+	0.196993i	$0.936882\pi$
$998$	11.3250	+	13.0697i	0.358487	+	0.413716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.a.325.1		10
3.2	odd	2		138.2.e.d.49.1	yes	10
23.8	even	11	inner	414.2.i.a.307.1		10
23.10	odd	22		9522.2.a.by.1.4		5
23.13	even	11		9522.2.a.bx.1.2		5
69.8	odd	22		138.2.e.d.31.1	✓	10
69.56	even	22		3174.2.a.w.1.2		5
69.59	odd	22		3174.2.a.x.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.31.1	✓	10	69.8	odd	22
138.2.e.d.49.1	yes	10	3.2	odd	2
414.2.i.a.307.1		10	23.8	even	11	inner
414.2.i.a.325.1		10	1.1	even	1	trivial
3174.2.a.w.1.2		5	69.56	even	22
3174.2.a.x.1.4		5	69.59	odd	22
9522.2.a.bx.1.2		5	23.13	even	11
9522.2.a.by.1.4		5	23.10	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(1.81440 - 2.09393i) q^{5} +(0.163423 - 0.105026i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.33083 - 1.49793i) q^{10} +(0.413293 - 2.87451i) q^{11} +(0.910738 + 0.585296i) q^{13} +(-0.127214 - 0.146813i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-4.45384 - 1.30777i) q^{17} +(4.24593 - 1.24672i) q^{19} +(-1.15098 + 2.52028i) q^{20} -2.90407 q^{22} +(4.73556 - 0.757939i) q^{23} +(-0.380916 - 2.64933i) q^{25} +(0.449727 - 0.984764i) q^{26} +(-0.127214 + 0.146813i) q^{28} +(-8.83766 - 2.59497i) q^{29} +(-2.85525 - 6.25212i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.660607 + 4.59462i) q^{34} +(0.0765987 - 0.532755i) q^{35} +(3.17329 + 3.66217i) q^{37} +(-1.83829 - 4.02529i) q^{38} +(2.65843 + 0.780586i) q^{40} +(-3.76214 + 4.34174i) q^{41} +(3.14342 - 6.88313i) q^{43} +(0.413293 + 2.87451i) q^{44} +(-1.42416 - 4.57949i) q^{46} +5.61457 q^{47} +(-2.89223 + 6.33310i) q^{49} +(-2.56815 + 0.754078i) q^{50} +(-1.03874 - 0.305003i) q^{52} +(3.48496 - 2.23965i) q^{53} +(-5.26914 - 6.08092i) q^{55} +(0.163423 + 0.105026i) q^{56} +(-1.31083 + 9.11701i) q^{58} +(9.01685 + 5.79478i) q^{59} +(-1.19623 - 2.61939i) q^{61} +(-5.78214 + 3.71596i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(2.87801 - 0.845060i) q^{65} +(2.08311 + 14.4884i) q^{67} +4.64187 q^{68} -0.538234 q^{70} +(1.81195 + 12.6024i) q^{71} +(-2.86708 + 0.841852i) q^{73} +(3.17329 - 3.66217i) q^{74} +(-3.72270 + 2.39243i) q^{76} +(-0.234356 - 0.513169i) q^{77} +(2.15275 + 1.38349i) q^{79} +(0.394306 - 2.74246i) q^{80} +(4.83295 + 3.10595i) q^{82} +(-0.531462 - 0.613340i) q^{83} +(-10.8194 + 6.95322i) q^{85} +(-7.26043 - 2.13185i) q^{86} +(2.78644 - 0.818172i) q^{88} +(-2.81645 + 6.16716i) q^{89} +0.210307 q^{91} +(-4.33020 + 2.06140i) q^{92} +(-0.799036 - 5.55742i) q^{94} +(5.09327 - 11.1527i) q^{95} +(8.09928 - 9.34707i) q^{97} +(6.68024 + 1.96150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32}+ \cdots + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more