LMFDB - Embedded newform 450.2.l.d.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.2
Root			$0.644389 + 0.983224i$ of defining polynomial
Character	$\chi$	$=$	450.109
Dual form			450.2.l.d.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(2.23347 - 0.107666i) q^{5} -0.992398i q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(2.23347 - 0.107666i) q^{5} -0.992398i q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.22570 + 1.87020i) q^{10} +(2.58148 + 1.87556i) q^{11} +(-2.26510 - 3.11764i) q^{13} +(0.802867 + 0.583317i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.15854 + 0.701351i) q^{17} +(1.45140 - 4.46695i) q^{19} +(-0.792578 - 2.09089i) q^{20} +(-3.03472 + 0.986039i) q^{22} +(3.29138 - 4.53019i) q^{23} +(4.97682 - 0.480938i) q^{25} +3.85361 q^{26} +(-0.943827 + 0.306668i) q^{28} +(2.25903 + 6.95256i) q^{29} +(-1.80729 + 5.56226i) q^{31} -1.00000i q^{32} +(-1.83616 + 1.33405i) q^{34} +(-0.106847 - 2.21650i) q^{35} +(3.07223 + 4.22856i) q^{37} +(2.76073 + 3.79981i) q^{38} +(2.15743 + 0.587785i) q^{40} +(-0.919147 + 0.667799i) q^{41} -6.88806i q^{43} +(0.986039 - 3.03472i) q^{44} +(1.73038 + 5.32556i) q^{46} +(-6.88191 + 2.23607i) q^{47} +6.01515 q^{49} +(-2.53621 + 4.30902i) q^{50} +(-2.26510 + 3.11764i) q^{52} +(4.00902 - 1.30261i) q^{53} +(5.96761 + 3.91107i) q^{55} +(0.306668 - 0.943827i) q^{56} +(-6.95256 - 2.25903i) q^{58} +(-5.55591 + 4.03660i) q^{59} +(8.95256 + 6.50442i) q^{61} +(-3.43767 - 4.73154i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-5.39470 - 6.71929i) q^{65} +(-12.4631 - 4.04950i) q^{67} -2.26962i q^{68} +(1.85599 + 1.21638i) q^{70} +(0.675441 + 2.07879i) q^{71} +(1.67716 - 2.30841i) q^{73} -5.22679 q^{74} -4.69683 q^{76} +(1.86130 - 2.56186i) q^{77} +(-3.44678 - 10.6081i) q^{79} +(-1.74363 + 1.39991i) q^{80} -1.13613i q^{82} +(-9.87934 - 3.20999i) q^{83} +(4.89655 + 1.33405i) q^{85} +(5.57255 + 4.04870i) q^{86} +(1.87556 + 2.58148i) q^{88} +(1.56046 + 1.13374i) q^{89} +(-3.09394 + 2.24788i) q^{91} +(-5.32556 - 1.73038i) q^{92} +(2.23607 - 6.88191i) q^{94} +(2.76073 - 10.1331i) q^{95} +(-15.7543 + 5.11887i) q^{97} +(-3.53561 + 4.86635i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	2.23347	−	0.107666i	0.998840	−	0.0481496i
$5$	2.23347	−	0.107666i	0.998840	−	0.0481496i
$6$		0			0
$7$		−	0.992398i		−	0.375091i	−0.982256	−	0.187546i	$-0.939947\pi$
$7$		−	0.992398i		−	0.375091i	0.982256	−	0.187546i	$-0.0600533\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$		0			0
$10$	−1.22570	+	1.87020i	−0.387600	+	0.591410i
$11$	2.58148	+	1.87556i	0.778347	+	0.565502i	0.904482	−	0.426511i	$-0.140257\pi$
$11$	2.58148	+	1.87556i	0.778347	+	0.565502i	−0.126136	+	0.992013i	$0.540257\pi$
$12$		0			0
$13$	−2.26510	−	3.11764i	−0.628225	−	0.864677i	0.369694	−	0.929153i	$-0.379462\pi$
$13$	−2.26510	−	3.11764i	−0.628225	−	0.864677i	−0.997919	+	0.0644761i	$0.979462\pi$
$14$	0.802867	+	0.583317i	0.214575	+	0.155898i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.15854	+	0.701351i	0.523522	+	0.170103i	0.558843	−	0.829273i	$-0.311245\pi$
$17$	2.15854	+	0.701351i	0.523522	+	0.170103i	−0.0353211	+	0.999376i	$0.511245\pi$
$18$		0			0
$19$	1.45140	−	4.46695i	0.332974	−	1.02479i	−0.634738	−	0.772728i	$-0.718892\pi$
$19$	1.45140	−	4.46695i	0.332974	−	1.02479i	0.967711	−	0.252061i	$-0.0811082\pi$
$20$	−0.792578	−	2.09089i	−0.177226	−	0.467537i
$21$		0			0
$22$	−3.03472	+	0.986039i	−0.647004	+	0.210224i
$23$	3.29138	−	4.53019i	0.686300	−	0.944611i	−0.313688	−	0.949526i	$-0.601565\pi$
$23$	3.29138	−	4.53019i	0.686300	−	0.944611i	0.999988	+	0.00491540i	$0.00156463\pi$
$24$		0			0
$25$	4.97682	−	0.480938i	0.995363	−	0.0961876i
$26$	3.85361			0.755756
$27$		0			0
$28$	−0.943827	+	0.306668i	−0.178367	+	0.0579548i
$29$	2.25903	+	6.95256i	0.419490	+	1.29106i	0.908172	+	0.418597i	$0.137478\pi$
$29$	2.25903	+	6.95256i	0.419490	+	1.29106i	−0.488682	+	0.872462i	$0.662522\pi$
$30$		0			0
$31$	−1.80729	+	5.56226i	−0.324599	+	0.999012i	0.647023	+	0.762471i	$0.276014\pi$
$31$	−1.80729	+	5.56226i	−0.324599	+	0.999012i	−0.971621	+	0.236541i	$0.923986\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−1.83616	+	1.33405i	−0.314899	+	0.228788i
$35$	−0.106847	−	2.21650i	−0.0180605	−	0.374656i
$36$		0			0
$37$	3.07223	+	4.22856i	0.505071	+	0.695171i	0.983078	−	0.183185i	$-0.0586407\pi$
$37$	3.07223	+	4.22856i	0.505071	+	0.695171i	−0.478007	+	0.878356i	$0.658641\pi$
$38$	2.76073	+	3.79981i	0.447849	+	0.616411i
$39$		0			0
$40$	2.15743	+	0.587785i	0.341120	+	0.0929370i
$41$	−0.919147	+	0.667799i	−0.143547	+	0.104293i	−0.657241	−	0.753681i	$-0.728277\pi$
$41$	−0.919147	+	0.667799i	−0.143547	+	0.104293i	0.513694	+	0.857973i	$0.328277\pi$
$42$		0			0
$43$		−	6.88806i		−	1.05042i	−0.850973	−	0.525209i	$-0.823987\pi$
$43$		−	6.88806i		−	1.05042i	0.850973	−	0.525209i	$-0.176013\pi$
$44$	0.986039	−	3.03472i	0.148651	−	0.457501i
$45$		0			0
$46$	1.73038	+	5.32556i	0.255131	+	0.785211i
$47$	−6.88191	+	2.23607i	−1.00383	+	0.326164i	−0.764395	−	0.644748i	$-0.776962\pi$
$47$	−6.88191	+	2.23607i	−1.00383	+	0.326164i	−0.239435	+	0.970912i	$0.576962\pi$
$48$		0			0
$49$	6.01515			0.859306
$50$	−2.53621	+	4.30902i	−0.358675	+	0.609387i
$51$		0			0
$52$	−2.26510	+	3.11764i	−0.314112	+	0.432339i
$53$	4.00902	−	1.30261i	0.550681	−	0.178927i	−0.0204428	−	0.999791i	$-0.506508\pi$
$53$	4.00902	−	1.30261i	0.550681	−	0.178927i	0.571124	+	0.820864i	$0.306508\pi$
$54$		0			0
$55$	5.96761	+	3.91107i	0.804673	+	0.527369i
$56$	0.306668	−	0.943827i	0.0409802	−	0.126124i
$57$		0			0
$58$	−6.95256	−	2.25903i	−0.912916	−	0.296625i
$59$	−5.55591	+	4.03660i	−0.723317	+	0.525521i	−0.887442	−	0.460919i	$-0.847520\pi$
$59$	−5.55591	+	4.03660i	−0.723317	+	0.525521i	0.164125	+	0.986440i	$0.447520\pi$
$60$		0			0
$61$	8.95256	+	6.50442i	1.14626	+	0.832805i	0.987979	−	0.154589i	$-0.0494053\pi$
$61$	8.95256	+	6.50442i	1.14626	+	0.832805i	0.158280	+	0.987394i	$0.449405\pi$
$62$	−3.43767	−	4.73154i	−0.436584	−	0.600907i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−5.39470	−	6.71929i	−0.669130	−	0.833426i
$66$		0			0
$67$	−12.4631	−	4.04950i	−1.52261	−	0.494726i	−0.576093	−	0.817384i	$-0.695423\pi$
$67$	−12.4631	−	4.04950i	−1.52261	−	0.494726i	−0.946515	+	0.322658i	$0.895423\pi$
$68$		−	2.26962i		−	0.275232i
$69$		0			0
$70$	1.85599	+	1.21638i	0.221833	+	0.145386i
$71$	0.675441	+	2.07879i	0.0801601	+	0.246707i	0.983103	−	0.183053i	$-0.0585980\pi$
$71$	0.675441	+	2.07879i	0.0801601	+	0.246707i	−0.902943	+	0.429760i	$0.858598\pi$
$72$		0			0
$73$	1.67716	−	2.30841i	0.196297	−	0.270179i	−0.699510	−	0.714623i	$-0.746598\pi$
$73$	1.67716	−	2.30841i	0.196297	−	0.270179i	0.895807	+	0.444443i	$0.146598\pi$
$74$	−5.22679			−0.607602
$75$		0			0
$76$	−4.69683			−0.538763
$77$	1.86130	−	2.56186i	0.212115	−	0.291951i
$78$		0			0
$79$	−3.44678	−	10.6081i	−0.387793	−	1.19350i	−0.934434	−	0.356137i	$-0.884094\pi$
$79$	−3.44678	−	10.6081i	−0.387793	−	1.19350i	0.546641	−	0.837367i	$-0.315906\pi$
$80$	−1.74363	+	1.39991i	−0.194944	+	0.156514i
$81$		0			0
$82$		−	1.13613i		−	0.125464i
$83$	−9.87934	−	3.20999i	−1.08440	−	0.352342i	−0.288319	−	0.957534i	$-0.593096\pi$
$83$	−9.87934	−	3.20999i	−1.08440	−	0.352342i	−0.796079	+	0.605192i	$0.793096\pi$
$84$		0			0
$85$	4.89655	+	1.33405i	0.531105	+	0.144698i
$86$	5.57255	+	4.04870i	0.600904	+	0.436582i
$87$		0			0
$88$	1.87556	+	2.58148i	0.199935	+	0.275187i
$89$	1.56046	+	1.13374i	0.165409	+	0.120176i	0.667410	−	0.744690i	$-0.267403\pi$
$89$	1.56046	+	1.13374i	0.165409	+	0.120176i	−0.502001	+	0.864867i	$0.667403\pi$
$90$		0			0
$91$	−3.09394	+	2.24788i	−0.324333	+	0.235642i
$92$	−5.32556	−	1.73038i	−0.555228	−	0.180405i
$93$		0			0
$94$	2.23607	−	6.88191i	0.230633	−	0.709815i
$95$	2.76073	−	10.1331i	0.283245	−	1.03963i
$96$		0			0
$97$	−15.7543	+	5.11887i	−1.59960	+	0.519743i	−0.967009	−	0.254741i	$-0.918010\pi$
$97$	−15.7543	+	5.11887i	−1.59960	+	0.519743i	−0.632594	+	0.774484i	$0.718010\pi$
$98$	−3.53561	+	4.86635i	−0.357151	+	0.491576i
$99$		0			0
$100$	−1.99532	−	4.58462i	−0.199532	−	0.458462i
$101$	−16.4535			−1.63719			−0.818593	−	0.574374i	$-0.805246\pi$
$101$	−16.4535			−1.63719			−0.818593	+	0.574374i	$0.805246\pi$
$102$		0			0
$103$	−8.91260	+	2.89588i	−0.878185	+	0.285340i	−0.713203	−	0.700957i	$-0.752756\pi$
$103$	−8.91260	+	2.89588i	−0.878185	+	0.285340i	−0.164982	+	0.986297i	$0.552756\pi$
$104$	−1.19083	−	3.66500i	−0.116771	−	0.359383i
$105$		0			0
$106$	−1.30261	+	4.00902i	−0.126521	+	0.389390i
$107$			8.47591i			0.819397i	0.912221	+	0.409698i	$0.134366\pi$
$107$			8.47591i			0.819397i	−0.912221	+	0.409698i	$0.865634\pi$
$108$		0			0
$109$	12.2467	−	8.89774i	1.17302	−	0.852249i	0.181653	−	0.983363i	$-0.441855\pi$
$109$	12.2467	−	8.89774i	1.17302	−	0.852249i	0.991367	+	0.131114i	$0.0418553\pi$
$110$	−6.67180	+	2.52903i	−0.636131	+	0.241133i
$111$		0			0
$112$	0.583317	+	0.802867i	0.0551183	+	0.0758638i
$113$	−3.00083	−	4.13029i	−0.282294	−	0.388545i	0.644198	−	0.764859i	$-0.277191\pi$
$113$	−3.00083	−	4.13029i	−0.282294	−	0.388545i	−0.926492	+	0.376314i	$0.877191\pi$
$114$		0			0
$115$	6.86346	−	10.4724i	0.640021	−	0.976560i
$116$	5.91420	−	4.29692i	0.549120	−	0.398959i
$117$		0			0
$118$		−	6.86748i		−	0.632202i
$119$	0.696020	−	2.14213i	0.0638040	−	0.196369i
$120$		0			0
$121$	−0.252844	−	0.778174i	−0.0229858	−	0.0707431i
$122$	−10.5244	+	3.41958i	−0.952832	+	0.309594i
$123$		0			0
$124$	5.84851			0.525212
$125$	11.0638	−	1.61000i	0.989577	−	0.144002i
$126$		0			0
$127$	−2.57239	+	3.54059i	−0.228262	+	0.314176i	−0.907751	−	0.419510i	$-0.862202\pi$
$127$	−2.57239	+	3.54059i	−0.228262	+	0.314176i	0.679488	+	0.733686i	$0.262202\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$		0			0
$130$	8.60695	−	0.414902i	0.754879	−	0.0363894i
$131$	1.56629	−	4.82055i	0.136848	−	0.421173i	−0.859025	−	0.511933i	$-0.828930\pi$
$131$	1.56629	−	4.82055i	0.136848	−	0.421173i	0.995873	+	0.0907598i	$0.0289295\pi$
$132$		0			0
$133$	−4.43299	−	1.44037i	−0.384389	−	0.124896i
$134$	10.6017	−	7.70261i	0.915851	−	0.665404i
$135$		0			0
$136$	1.83616	+	1.33405i	0.157450	+	0.114394i
$137$	−1.37475	−	1.89218i	−0.117453	−	0.161660i	0.746243	−	0.665674i	$-0.231856\pi$
$137$	−1.37475	−	1.89218i	−0.117453	−	0.161660i	−0.863695	+	0.504014i	$0.831856\pi$
$138$		0			0
$139$	1.47591	+	1.07231i	0.125185	+	0.0909520i	0.648616	−	0.761116i	$-0.275348\pi$
$139$	1.47591	+	1.07231i	0.125185	+	0.0909520i	−0.523431	+	0.852068i	$0.675348\pi$
$140$	−2.07500	+	0.786553i	−0.175369	+	0.0664759i
$141$		0			0
$142$	−2.07879	−	0.675441i	−0.174449	−	0.0566818i
$143$		−	12.2965i		−	1.02828i
$144$		0			0
$145$	5.79403	+	15.2852i	0.481168	+	1.26936i
$146$	0.881735	+	2.71370i	0.0729729	+	0.224587i
$147$		0			0
$148$	3.07223	−	4.22856i	0.252536	−	0.347586i
$149$	−23.8922			−1.95732			−0.978661	−	0.205483i	$-0.934123\pi$
$149$	−23.8922			−1.95732			−0.978661	+	0.205483i	$0.934123\pi$
$150$		0			0
$151$	−7.99856			−0.650914			−0.325457	−	0.945557i	$-0.605518\pi$
$151$	−7.99856			−0.650914			−0.325457	+	0.945557i	$0.605518\pi$
$152$	2.76073	−	3.79981i	0.223924	−	0.308206i
$153$		0			0
$154$	0.978544	+	3.01165i	0.0788533	+	0.242686i
$155$	−3.43767	+	12.6178i	−0.276120	+	1.01348i
$156$		0			0
$157$			5.20135i			0.415113i	0.978223	+	0.207557i	$0.0665511\pi$
$157$			5.20135i			0.415113i	−0.978223	+	0.207557i	$0.933449\pi$
$158$	10.6081	+	3.44678i	0.843935	+	0.274211i
$159$		0			0
$160$	−0.107666	−	2.23347i	−0.00851173	−	0.176572i
$161$	−4.49576	−	3.26636i	−0.354315	−	0.257425i
$162$		0			0
$163$	−10.7791	−	14.8361i	−0.844283	−	1.16206i	−0.985094	−	0.172019i	$-0.944971\pi$
$163$	−10.7791	−	14.8361i	−0.844283	−	1.16206i	0.140811	−	0.990036i	$-0.455029\pi$
$164$	0.919147	+	0.667799i	0.0717733	+	0.0521464i
$165$		0			0
$166$	8.40387	−	6.10577i	0.652267	−	0.473899i
$167$	22.8298	+	7.41785i	1.76662	+	0.574010i	0.997852	−	0.0655146i	$-0.0208689\pi$
$167$	22.8298	+	7.41785i	1.76662	+	0.574010i	0.768770	+	0.639525i	$0.220869\pi$
$168$		0			0
$169$	−0.571784	+	1.75977i	−0.0439834	+	0.135367i
$170$	−3.95739	+	3.17726i	−0.303518	+	0.243684i
$171$		0			0
$172$	−6.55093	+	2.12853i	−0.499504	+	0.162299i
$173$	−8.99653	+	12.3827i	−0.683994	+	0.941437i	−0.999973	−	0.00732946i	$-0.997667\pi$
$173$	−8.99653	+	12.3827i	−0.683994	+	0.941437i	0.315979	+	0.948766i	$0.397667\pi$
$174$		0			0
$175$	−0.477282	−	4.93898i	−0.0360791	−	0.373352i
$176$	−3.19089			−0.240522
$177$		0			0
$178$	−1.83443	+	0.596044i	−0.137497	+	0.0446754i
$179$	7.23182	+	22.2572i	0.540532	+	1.66358i	0.731384	+	0.681966i	$0.238875\pi$
$179$	7.23182	+	22.2572i	0.540532	+	1.66358i	−0.190852	+	0.981619i	$0.561125\pi$
$180$		0			0
$181$	−7.36808	+	22.6766i	−0.547665	+	1.68554i	0.166902	+	0.985974i	$0.446624\pi$
$181$	−7.36808	+	22.6766i	−0.547665	+	1.68554i	−0.714567	+	0.699567i	$0.753376\pi$
$182$		−	3.82432i		−	0.283477i
$183$		0			0
$184$	4.53019	−	3.29138i	0.333970	−	0.242644i
$185$	7.31702	+	9.11361i	0.537958	+	0.670046i
$186$		0			0
$187$	4.25680	+	5.85899i	0.311288	+	0.428452i
$188$	4.25325	+	5.85410i	0.310200	+	0.426954i
$189$		0			0
$190$	6.57512	+	8.18955i	0.477009	+	0.594132i
$191$	−10.1616	+	7.38286i	−0.735270	+	0.534205i	−0.891226	−	0.453559i	$-0.850154\pi$
$191$	−10.1616	+	7.38286i	−0.735270	+	0.534205i	0.155956	+	0.987764i	$0.450154\pi$
$192$		0			0
$193$			5.70634i			0.410751i	0.978683	+	0.205376i	$0.0658416\pi$
$193$			5.70634i			0.410751i	−0.978683	+	0.205376i	$0.934158\pi$
$194$	5.11887	−	15.7543i	0.367513	−	1.13109i
$195$		0			0
$196$	−1.85878	−	5.72074i	−0.132770	−	0.408625i
$197$	15.8269	−	5.14248i	1.12762	−	0.366387i	0.314950	−	0.949108i	$-0.398012\pi$
$197$	15.8269	−	5.14248i	1.12762	−	0.366387i	0.812672	+	0.582722i	$0.198012\pi$
$198$		0			0
$199$	−10.6260			−0.753254			−0.376627	−	0.926365i	$-0.622916\pi$
$199$	−10.6260			−0.753254			−0.376627	+	0.926365i	$0.622916\pi$
$200$	4.88185	+	1.08052i	0.345199	+	0.0764044i
$201$		0			0
$202$	9.67114	−	13.3112i	0.680459	−	0.936571i
$203$	6.89971	−	2.24185i	0.484265	−	0.157347i
$204$		0			0
$205$	−1.98099	+	1.59047i	−0.138358	+	0.111083i
$206$	2.89588	−	8.91260i	0.201766	−	0.620971i
$207$		0			0
$208$	3.66500	+	1.19083i	0.254122	+	0.0825693i
$209$	12.1248	−	8.80917i	0.838689	−	0.609343i
$210$		0			0
$211$	0.651586	+	0.473405i	0.0448570	+	0.0325905i	0.609988	−	0.792411i	$-0.291174\pi$
$211$	0.651586	+	0.473405i	0.0448570	+	0.0325905i	−0.565131	+	0.825001i	$0.691174\pi$
$212$	−2.47771	−	3.41027i	−0.170170	−	0.234219i
$213$		0			0
$214$	−6.85715	−	4.98201i	−0.468745	−	0.340563i
$215$	−0.741608	−	15.3843i	−0.0505773	−	1.04920i
$216$		0			0
$217$	5.51998	+	1.79355i	0.374721	+	0.121754i
$218$			15.1377i			1.02526i
$219$		0			0
$220$	1.87556	−	6.88413i	0.126450	−	0.464128i
$221$	−2.70274	−	8.31817i	−0.181806	−	0.559540i
$222$		0			0
$223$	−9.46004	+	13.0206i	−0.633491	+	0.871926i	−0.998247	−	0.0591772i	$-0.981152\pi$
$223$	−9.46004	+	13.0206i	−0.633491	+	0.871926i	0.364756	+	0.931103i	$0.381152\pi$
$224$	−0.992398			−0.0663074
$225$		0			0
$226$	5.10532			0.339601
$227$	8.08813	−	11.1324i	0.536828	−	0.738881i	−0.451323	−	0.892360i	$-0.649048\pi$
$227$	8.08813	−	11.1324i	0.536828	−	0.738881i	0.988152	+	0.153480i	$0.0490479\pi$
$228$		0			0
$229$	4.58275	+	14.1043i	0.302837	+	0.932036i	0.980476	+	0.196641i	$0.0630034\pi$
$229$	4.58275	+	14.1043i	0.302837	+	0.932036i	−0.677639	+	0.735395i	$0.736997\pi$
$230$	4.43814	+	11.7082i	0.292642	+	0.772016i
$231$		0			0
$232$			7.31036i			0.479949i
$233$	−0.842292	−	0.273677i	−0.0551804	−	0.0179292i	0.281297	−	0.959621i	$-0.409235\pi$
$233$	−0.842292	−	0.273677i	−0.0551804	−	0.0179292i	−0.336477	+	0.941692i	$0.609235\pi$
$234$		0			0
$235$	−15.1298	+	5.73515i	−0.986961	+	0.374120i
$236$	5.55591	+	4.03660i	0.361659	+	0.262760i
$237$		0			0
$238$	1.32391	+	1.82220i	0.0858162	+	0.118116i
$239$	17.6874	+	12.8506i	1.14410	+	0.831239i	0.987686	−	0.156452i	$-0.0500056\pi$
$239$	17.6874	+	12.8506i	1.14410	+	0.831239i	0.156417	+	0.987691i	$0.450006\pi$
$240$		0			0
$241$	9.21929	−	6.69821i	0.593867	−	0.431469i	−0.249830	−	0.968290i	$-0.580375\pi$
$241$	9.21929	−	6.69821i	0.593867	−	0.431469i	0.843697	+	0.536820i	$0.180375\pi$
$242$	0.778174	+	0.252844i	0.0500229	+	0.0162534i
$243$		0			0
$244$	3.41958	−	10.5244i	0.218916	−	0.673754i
$245$	13.4347	−	0.647626i	0.858310	−	0.0413753i
$246$		0			0
$247$	−17.2139	+	5.59313i	−1.09529	+	0.355883i
$248$	−3.43767	+	4.73154i	−0.218292	+	0.300453i
$249$		0			0
$250$	−5.20063	+	9.89714i	−0.328917	+	0.625950i
$251$	10.3970			0.656250			0.328125	−	0.944634i	$-0.393583\pi$
$251$	10.3970			0.656250			0.328125	+	0.944634i	$0.393583\pi$
$252$		0			0
$253$	16.9933	−	5.52145i	1.06836	−	0.347131i
$254$	−1.35238	−	4.16221i	−0.0848561	−	0.261160i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$			19.6467i			1.22553i	0.790266	+	0.612763i	$0.209942\pi$
$257$			19.6467i			1.22553i	−0.790266	+	0.612763i	$0.790058\pi$
$258$		0			0
$259$	4.19642	−	3.04888i	0.260753	−	0.189448i
$260$	−4.72337	+	7.20704i	−0.292931	+	0.446962i
$261$		0			0
$262$	2.97926	+	4.10060i	0.184060	+	0.253336i
$263$	−5.32150	−	7.32442i	−0.328138	−	0.451643i	0.612792	−	0.790244i	$-0.290046\pi$
$263$	−5.32150	−	7.32442i	−0.328138	−	0.451643i	−0.940930	+	0.338601i	$0.890046\pi$
$264$		0			0
$265$	8.81379	−	3.34098i	0.541427	−	0.205235i
$266$	3.77093	−	2.73974i	0.231210	−	0.167984i
$267$		0			0
$268$			13.1045i			0.800483i
$269$	9.18078	−	28.2555i	0.559762	−	1.72277i	−0.123263	−	0.992374i	$-0.539336\pi$
$269$	9.18078	−	28.2555i	0.559762	−	1.72277i	0.683024	−	0.730395i	$-0.260664\pi$
$270$		0			0
$271$	1.29803	+	3.99491i	0.0788495	+	0.242674i	0.982709	−	0.185155i	$-0.0592787\pi$
$271$	1.29803	+	3.99491i	0.0788495	+	0.242674i	−0.903860	+	0.427829i	$0.859279\pi$
$272$	−2.15854	+	0.701351i	−0.130881	+	0.0425257i
$273$		0			0
$274$	2.33886			0.141296
$275$	13.7496	+	8.09277i	0.829132	+	0.488013i
$276$		0			0
$277$	13.2634	−	18.2555i	0.796919	−	1.09686i	−0.196293	−	0.980545i	$-0.562890\pi$
$277$	13.2634	−	18.2555i	0.796919	−	1.09686i	0.993212	−	0.116319i	$-0.0371095\pi$
$278$	−1.73503	+	0.563746i	−0.104060	+	0.0338112i
$279$		0			0
$280$	0.583317	−	2.14103i	0.0348599	−	0.127951i
$281$	−2.08103	+	6.40474i	−0.124144	+	0.382075i	−0.993744	−	0.111681i	$-0.964376\pi$
$281$	−2.08103	+	6.40474i	−0.124144	+	0.382075i	0.869600	+	0.493756i	$0.164376\pi$
$282$		0			0
$283$	8.89142	+	2.88900i	0.528540	+	0.171733i	0.561118	−	0.827736i	$-0.310372\pi$
$283$	8.89142	+	2.88900i	0.528540	+	0.171733i	−0.0325774	+	0.999469i	$0.510372\pi$
$284$	1.76833	−	1.28477i	0.104931	−	0.0762368i
$285$		0			0
$286$	9.94804	+	7.22768i	0.588240	+	0.427381i
$287$	0.662723	+	0.912160i	0.0391193	+	0.0538431i
$288$		0			0
$289$	−9.58590	−	6.96456i	−0.563877	−	0.409680i
$290$	−15.7716	−	4.29692i	−0.926140	−	0.252324i
$291$		0			0
$292$	−2.71370	−	0.881735i	−0.158807	−	0.0515996i
$293$			5.03444i			0.294115i	0.989128	+	0.147058i	$0.0469803\pi$
$293$			5.03444i			0.294115i	−0.989128	+	0.147058i	$0.953020\pi$
$294$		0			0
$295$	−11.9744	+	9.61383i	−0.697175	+	0.559739i
$296$	1.61517	+	4.97097i	0.0938796	+	0.288932i
$297$		0			0
$298$	14.0435	−	19.3292i	0.813515	−	1.11971i
$299$	−21.5788			−1.24793
$300$		0			0
$301$	−6.83570			−0.394003
$302$	4.70144	−	6.47097i	0.270537	−	0.372363i
$303$		0			0
$304$	1.45140	+	4.46695i	0.0832435	+	0.256197i
$305$	20.6956	+	13.5636i	1.18503	+	0.776648i
$306$		0			0
$307$		−	24.3696i		−	1.39085i	−0.718600	−	0.695424i	$-0.755217\pi$
$307$		−	24.3696i		−	1.39085i	0.718600	−	0.695424i	$-0.244783\pi$
$308$	−3.01165	−	0.978544i	−0.171605	−	0.0557577i
$309$		0			0
$310$	−8.18737	−	10.1977i	−0.465011	−	0.579188i
$311$	−13.9864	−	10.1617i	−0.793098	−	0.576219i	0.115783	−	0.993275i	$-0.463062\pi$
$311$	−13.9864	−	10.1617i	−0.793098	−	0.576219i	−0.908881	+	0.417055i	$0.863062\pi$
$312$		0			0
$313$	−0.0734148	−	0.101047i	−0.00414965	−	0.00571151i	0.806937	−	0.590637i	$-0.201124\pi$
$313$	−0.0734148	−	0.101047i	−0.00414965	−	0.00571151i	−0.811087	+	0.584926i	$0.801124\pi$
$314$	−4.20798	−	3.05728i	−0.237470	−	0.172532i
$315$		0			0
$316$	−9.02379	+	6.55616i	−0.507628	+	0.368813i
$317$	20.3368	+	6.60782i	1.14223	+	0.371132i	0.818210	−	0.574919i	$-0.194966\pi$
$317$	20.3368	+	6.60782i	1.14223	+	0.371132i	0.324017	+	0.946051i	$0.394966\pi$
$318$		0			0
$319$	−7.20830	+	22.1849i	−0.403587	+	1.24211i
$320$	1.87020	+	1.22570i	0.104548	+	0.0685187i
$321$		0			0
$322$	5.28508	−	1.71723i	0.294526	−	0.0956973i
$323$	6.26580	−	8.62413i	0.348638	−	0.479860i
$324$		0			0
$325$	−12.7724	−	14.4265i	−0.708483	−	0.800241i
$326$	18.3385			1.01567
$327$		0			0
$328$	−1.08052	+	0.351083i	−0.0596618	+	0.0193853i
$329$	2.21907	+	6.82960i	0.122341	+	0.376528i
$330$		0			0
$331$	9.25913	−	28.4967i	0.508928	−	1.56632i	−0.285137	−	0.958487i	$-0.592039\pi$
$331$	9.25913	−	28.4967i	0.508928	−	1.56632i	0.794065	−	0.607833i	$-0.207961\pi$
$332$			10.3878i			0.570102i
$333$		0			0
$334$	−19.4202	+	14.1096i	−1.06262	+	0.772042i
$335$	−28.2720	−	7.70261i	−1.54466	−	0.420839i
$336$		0			0
$337$	9.17918	+	12.6341i	0.500022	+	0.688221i	0.982197	−	0.187854i	$-0.0601532\pi$
$337$	9.17918	+	12.6341i	0.500022	+	0.688221i	−0.482175	+	0.876075i	$0.660153\pi$
$338$	−1.08760	−	1.49695i	−0.0591575	−	0.0814234i
$339$		0			0
$340$	−0.244361	−	5.06914i	−0.0132523	−	0.274913i
$341$	−15.0978	+	10.9692i	−0.817594	+	0.594017i
$342$		0			0
$343$		−	12.9162i		−	0.697410i
$344$	2.12853	−	6.55093i	0.114762	−	0.353202i
$345$		0			0
$346$	−4.72976	−	14.5567i	−0.254273	−	0.782573i
$347$	−32.8612	+	10.6773i	−1.76408	+	0.573185i	−0.997610	−	0.0690922i	$-0.977990\pi$
$347$	−32.8612	+	10.6773i	−1.76408	+	0.573185i	−0.766472	+	0.642277i	$0.777990\pi$
$348$		0			0
$349$	−18.9109			−1.01228			−0.506139	−	0.862452i	$-0.668928\pi$
$349$	−18.9109			−1.01228			−0.506139	+	0.862452i	$0.668928\pi$
$350$	4.27626	+	2.51693i	0.228576	+	0.134536i
$351$		0			0
$352$	1.87556	−	2.58148i	0.0999676	−	0.137594i
$353$	−29.1745	+	9.47936i	−1.55280	+	0.504535i	−0.954873	−	0.297015i	$-0.904009\pi$
$353$	−29.1745	+	9.47936i	−1.55280	+	0.504535i	−0.597928	+	0.801550i	$0.704009\pi$
$354$		0			0
$355$	1.73240	+	4.57021i	0.0919460	+	0.242562i
$356$	0.596044	−	1.83443i	0.0315902	−	0.0972248i
$357$		0			0
$358$	−22.2572	−	7.23182i	−1.17633	−	0.382213i
$359$	−3.02381	+	2.19693i	−0.159590	+	0.115949i	−0.664714	−	0.747098i	$-0.731447\pi$
$359$	−3.02381	+	2.19693i	−0.159590	+	0.115949i	0.505124	+	0.863047i	$0.331447\pi$
$360$		0			0
$361$	−2.47575	−	1.79874i	−0.130303	−	0.0946703i
$362$	−14.0149	−	19.2899i	−0.736608	−	1.01385i
$363$		0			0
$364$	3.09394	+	2.24788i	0.162166	+	0.117821i
$365$	3.49736	−	5.33635i	0.183060	−	0.279317i
$366$		0			0
$367$	16.3640	+	5.31699i	0.854194	+	0.277544i	0.703202	−	0.710990i	$-0.251753\pi$
$367$	16.3640	+	5.31699i	0.854194	+	0.277544i	0.150992	+	0.988535i	$0.451753\pi$
$368$			5.59963i			0.291901i
$369$		0			0
$370$	−11.6739	+	0.562747i	−0.606897	+	0.0292558i
$371$	−1.29271	−	3.97854i	−0.0671140	−	0.206556i
$372$		0			0
$373$	−15.4109	+	21.2113i	−0.797948	+	1.09828i	0.195124	+	0.980778i	$0.437489\pi$
$373$	−15.4109	+	21.2113i	−0.797948	+	1.09828i	−0.993073	+	0.117503i	$0.962511\pi$
$374$	−7.24211			−0.374480
$375$		0			0
$376$	−7.23607			−0.373172
$377$	16.5587	−	22.7911i	0.852815	−	1.17380i
$378$		0			0
$379$	−5.77908	−	17.7862i	−0.296851	−	0.913614i	−0.982593	−	0.185770i	$-0.940522\pi$
$379$	−5.77908	−	17.7862i	−0.296851	−	0.913614i	0.685742	−	0.727845i	$-0.259478\pi$
$380$	−10.4902	+	0.505688i	−0.538138	+	0.0259412i
$381$		0			0
$382$		−	12.5605i		−	0.642649i
$383$	0.620541	+	0.201626i	0.0317082	+	0.0103026i	0.324828	−	0.945773i	$-0.394694\pi$
$383$	0.620541	+	0.201626i	0.0317082	+	0.0103026i	−0.293120	+	0.956076i	$0.594694\pi$
$384$		0			0
$385$	3.88134	−	5.92225i	0.197812	−	0.301826i
$386$	−4.61653	−	3.35410i	−0.234975	−	0.170719i
$387$		0			0
$388$	9.73667	+	13.4014i	0.494305	+	0.680352i
$389$	2.20848	+	1.60456i	0.111974	+	0.0813542i	0.642363	−	0.766400i	$-0.277954\pi$
$389$	2.20848	+	1.60456i	0.111974	+	0.0813542i	−0.530389	+	0.847755i	$0.677954\pi$
$390$		0			0
$391$	10.2818	−	7.47018i	0.519974	−	0.377783i
$392$	5.72074	+	1.85878i	0.288941	+	0.0938827i
$393$		0			0
$394$	−5.14248	+	15.8269i	−0.259074	+	0.797349i
$395$	−8.84042	−	23.3218i	−0.444810	−	1.17345i
$396$		0			0
$397$	21.5908	−	7.01527i	1.08361	−	0.352086i	0.287836	−	0.957680i	$-0.407064\pi$
$397$	21.5908	−	7.01527i	1.08361	−	0.352086i	0.795774	+	0.605594i	$0.207064\pi$
$398$	6.24578	−	8.59658i	0.313073	−	0.430908i
$399$		0			0
$400$	−3.74364	+	3.31439i	−0.187182	+	0.165719i
$401$	−26.1671			−1.30672			−0.653362	−	0.757045i	$-0.726642\pi$
$401$	−26.1671			−1.30672			−0.653362	+	0.757045i	$0.726642\pi$
$402$		0			0
$403$	21.4348	−	6.96459i	1.06774	−	0.346931i
$404$	5.08442	+	15.6482i	0.252959	+	0.778528i
$405$		0			0
$406$	−2.24185	+	6.89971i	−0.111261	+	0.342427i
$407$			16.6781i			0.826703i
$408$		0			0
$409$	−7.05454	+	5.12543i	−0.348825	+	0.253436i	−0.748376	−	0.663275i	$-0.769166\pi$
$409$	−7.05454	+	5.12543i	−0.348825	+	0.253436i	0.399551	+	0.916711i	$0.369166\pi$
$410$	−0.122322	−	2.53751i	−0.00604106	−	0.125319i
$411$		0			0
$412$	5.50829	+	7.58151i	0.271374	+	0.373514i
$413$	4.00592	+	5.51367i	0.197118	+	0.271310i
$414$		0			0
$415$	−22.4109	−	6.10577i	−1.10011	−	0.299720i
$416$	−3.11764	+	2.26510i	−0.152855	+	0.111056i
$417$		0			0
$418$			14.9871i			0.733041i
$419$	3.24062	−	9.97361i	0.158315	−	0.487243i	−0.840167	−	0.542328i	$-0.817543\pi$
$419$	3.24062	−	9.97361i	0.158315	−	0.487243i	0.998482	+	0.0550852i	$0.0175430\pi$
$420$		0			0
$421$	−7.49324	−	23.0618i	−0.365198	−	1.12397i	−0.949857	−	0.312685i	$-0.898771\pi$
$421$	−7.49324	−	23.0618i	−0.365198	−	1.12397i	0.584658	−	0.811280i	$-0.301229\pi$
$422$	−0.765985	+	0.248884i	−0.0372876	+	0.0121155i
$423$		0			0
$424$	4.21533			0.204715
$425$	11.0799	+	2.45237i	0.537456	+	0.118958i
$426$		0			0
$427$	6.45498	−	8.88451i	0.312378	−	0.429952i
$428$	8.06107	−	2.61920i	0.389646	−	0.126604i
$429$		0			0
$430$	12.8821	+	8.44269i	0.621228	+	0.407143i
$431$	−0.741608	+	2.28244i	−0.0357220	+	0.109941i	−0.967328	−	0.253530i	$-0.918408\pi$
$431$	−0.741608	+	2.28244i	−0.0357220	+	0.109941i	0.931606	+	0.363471i	$0.118408\pi$
$432$		0			0
$433$	37.4703	+	12.1748i	1.80071	+	0.585086i	0.999904	−	0.0138396i	$-0.00440543\pi$
$433$	37.4703	+	12.1748i	1.80071	+	0.585086i	0.800805	+	0.598925i	$0.204405\pi$
$434$	−4.69558	+	3.41154i	−0.225395	+	0.163759i
$435$		0			0
$436$	−12.2467	−	8.89774i	−0.586510	−	0.426125i
$437$	−15.4590	−	21.2775i	−0.739506	−	1.01784i
$438$		0			0
$439$	32.2528	+	23.4330i	1.53934	+	1.11840i	0.950746	+	0.309972i	$0.100320\pi$
$439$	32.2528	+	23.4330i	1.53934	+	1.11840i	0.588598	+	0.808426i	$0.299680\pi$
$440$	4.46695	+	5.56375i	0.212953	+	0.265241i
$441$		0			0
$442$	8.31817	+	2.70274i	0.395655	+	0.128556i
$443$		−	20.2834i		−	0.963696i	−0.876255	−	0.481848i	$-0.839966\pi$
$443$		−	20.2834i		−	0.963696i	0.876255	−	0.481848i	$-0.160034\pi$
$444$		0			0
$445$	3.60732	+	2.36418i	0.171003	+	0.112073i
$446$	−4.97344	−	15.3067i	−0.235499	−	0.724792i
$447$		0			0
$448$	0.583317	−	0.802867i	0.0275591	−	0.0379319i
$449$	−41.6650			−1.96629			−0.983147	−	0.182819i	$-0.941478\pi$
$449$	−41.6650			−1.96629			−0.983147	+	0.182819i	$0.941478\pi$
$450$		0			0
$451$	−3.62526			−0.170707
$452$	−3.00083	+	4.13029i	−0.141147	+	0.194272i
$453$		0			0
$454$	4.25218	+	13.0869i	0.199565	+	0.614198i
$455$	−6.66821	+	5.35369i	−0.312611	+	0.250985i
$456$		0			0
$457$		−	2.32297i		−	0.108664i	−0.998523	−	0.0543319i	$-0.982697\pi$
$457$		−	2.32297i		−	0.108664i	0.998523	−	0.0543319i	$-0.0173029\pi$
$458$	−14.1043	−	4.58275i	−0.659049	−	0.214138i
$459$		0			0
$460$	−12.0808	−	3.29138i	−0.563271	−	0.153461i
$461$	4.25272	+	3.08979i	0.198069	+	0.143906i	0.682399	−	0.730980i	$-0.260937\pi$
$461$	4.25272	+	3.08979i	0.198069	+	0.143906i	−0.484330	+	0.874885i	$0.660937\pi$
$462$		0			0
$463$	16.6900	+	22.9718i	0.775650	+	1.06759i	0.995749	+	0.0921126i	$0.0293620\pi$
$463$	16.6900	+	22.9718i	0.775650	+	1.06759i	−0.220099	+	0.975478i	$0.570638\pi$
$464$	−5.91420	−	4.29692i	−0.274560	−	0.199480i
$465$		0			0
$466$	0.716497	−	0.520565i	0.0331911	−	0.0241147i
$467$	−21.5655	−	7.00707i	−0.997934	−	0.324249i	−0.235895	−	0.971779i	$-0.575802\pi$
$467$	−21.5655	−	7.00707i	−0.997934	−	0.324249i	−0.762040	+	0.647530i	$0.775802\pi$
$468$		0			0
$469$	−4.01872	+	12.3684i	−0.185567	+	0.571117i
$470$	4.25325	−	15.6113i	0.196188	−	0.720096i
$471$		0			0
$472$	−6.53136	+	2.12217i	−0.300630	+	0.0976807i
$473$	12.9189	−	17.7814i	0.594014	−	0.817590i
$474$		0			0
$475$	5.07502	−	22.9292i	0.232858	−	1.05206i
$476$	−2.25237			−0.103237
$477$		0			0
$478$	−20.7928	+	6.75598i	−0.951040	+	0.309012i
$479$	12.8774	+	39.6326i	0.588383	+	1.81086i	0.585236	+	0.810863i	$0.301002\pi$
$479$	12.8774	+	39.6326i	0.588383	+	1.81086i	0.00314730	+	0.999995i	$0.498998\pi$
$480$		0			0
$481$	6.22423	−	19.1562i	0.283800	−	0.873447i
$482$			11.3957i			0.519059i
$483$		0			0
$484$	−0.661954	+	0.480938i	−0.0300888	+	0.0218608i
$485$	−34.6356	+	13.1291i	−1.57272	+	0.596160i
$486$		0			0
$487$	13.5877	+	18.7019i	0.615719	+	0.847464i	0.997033	−	0.0769816i	$-0.0245283\pi$
$487$	13.5877	+	18.7019i	0.615719	+	0.847464i	−0.381314	+	0.924446i	$0.624528\pi$
$488$	6.50442	+	8.95256i	0.294441	+	0.405264i
$489$		0			0
$490$	−7.37276	+	11.2495i	−0.333067	+	0.508203i
$491$	33.1199	−	24.0630i	1.49468	−	1.08595i	0.522237	−	0.852800i	$-0.325098\pi$
$491$	33.1199	−	24.0630i	1.49468	−	1.08595i	0.972441	−	0.233147i	$-0.0749025\pi$
$492$		0			0
$493$			16.5917i			0.747254i
$494$	5.59313	−	17.2139i	0.251647	−	0.774490i
$495$		0			0
$496$	−1.80729	−	5.56226i	−0.0811497	−	0.249753i
$497$	2.06299	−	0.670307i	0.0925378	−	0.0300674i
$498$		0			0
$499$	7.87697			0.352622			0.176311	−	0.984335i	$-0.443584\pi$
$499$	7.87697			0.352622			0.176311	+	0.984335i	$0.443584\pi$
$500$	−4.95010	−	10.0248i	−0.221375	−	0.448322i
$501$		0			0
$502$	−6.11118	+	8.41132i	−0.272755	+	0.375416i
$503$	6.58276	−	2.13887i	0.293511	−	0.0953674i	−0.158561	−	0.987349i	$-0.550685\pi$
$503$	6.58276	−	2.13887i	0.293511	−	0.0953674i	0.452071	+	0.891982i	$0.350685\pi$
$504$		0			0
$505$	−36.7485	+	1.77148i	−1.63529	+	0.0788299i
$506$	−5.52145	+	16.9933i	−0.245459	+	0.755444i
$507$		0			0
$508$	4.16221	+	1.35238i	0.184668	+	0.0600023i
$509$	−8.20925	+	5.96437i	−0.363869	+	0.264366i	−0.754664	−	0.656112i	$-0.772200\pi$
$509$	−8.20925	+	5.96437i	−0.363869	+	0.264366i	0.390795	+	0.920478i	$0.372200\pi$
$510$		0			0
$511$	−2.29086	−	1.66441i	−0.101342	−	0.0736292i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$		0			0
$514$	−15.8945	−	11.5480i	−0.701077	−	0.509362i
$515$	−19.5943	+	7.42746i	−0.863427	+	0.327293i
$516$		0			0
$517$	−21.9594	−	7.13505i	−0.965774	−	0.313799i
$518$			5.18706i			0.227906i
$519$		0			0
$520$	−3.05429	−	8.05748i	−0.133939	−	0.353344i
$521$	4.12922	+	12.7084i	0.180904	+	0.556766i	0.999854	−	0.0170994i	$-0.00544318\pi$
$521$	4.12922	+	12.7084i	0.180904	+	0.556766i	−0.818949	+	0.573866i	$0.805443\pi$
$522$		0			0
$523$	−4.34954	+	5.98663i	−0.190192	+	0.261777i	−0.893455	−	0.449153i	$-0.851726\pi$
$523$	−4.34954	+	5.98663i	−0.190192	+	0.261777i	0.703263	+	0.710930i	$0.251726\pi$
$524$	−5.06863			−0.221424
$525$		0			0
$526$	9.05348			0.394750
$527$	−7.80220	+	10.7388i	−0.339869	+	0.467790i
$528$		0			0
$529$	−2.58209	−	7.94686i	−0.112265	−	0.345516i
$530$	−2.47771	+	9.09429i	−0.107625	+	0.395031i
$531$		0			0
$532$			4.66112i			0.202085i
$533$	4.16391	+	1.35294i	0.180359	+	0.0586022i
$534$		0			0
$535$	0.912566	+	18.9307i	0.0394536	+	0.818446i
$536$	−10.6017	−	7.70261i	−0.457925	−	0.332702i
$537$		0			0
$538$	17.4629	+	24.0356i	0.752878	+	1.03625i
$539$	15.5280	+	11.2818i	0.668838	+	0.485940i
$540$		0			0
$541$	20.6625	−	15.0122i	0.888350	−	0.645424i	−0.0470972	−	0.998890i	$-0.514997\pi$
$541$	20.6625	−	15.0122i	0.888350	−	0.645424i	0.935447	+	0.353466i	$0.114997\pi$
$542$	−3.99491	−	1.29803i	−0.171596	−	0.0557550i
$543$		0			0
$544$	0.701351	−	2.15854i	0.0300702	−	0.0925465i
$545$	26.3947	−	21.1914i	1.13062	−	0.907741i
$546$		0			0
$547$	24.9282	−	8.09966i	1.06585	−	0.346317i	0.276982	−	0.960875i	$-0.410666\pi$
$547$	24.9282	−	8.09966i	1.06585	−	0.346317i	0.788871	+	0.614559i	$0.210666\pi$
$548$	−1.37475	+	1.89218i	−0.0587263	+	0.0808298i
$549$		0			0
$550$	−14.6290	+	6.36685i	−0.623783	+	0.271483i
$551$	34.3355			1.46274
$552$		0			0
$553$	−10.5275	+	3.42058i	−0.447673	+	0.145458i
$554$	6.97297	+	21.4606i	0.296253	+	0.911773i
$555$		0			0
$556$	0.563746	−	1.73503i	0.0239081	−	0.0735817i
$557$			5.75884i			0.244010i	0.992529	+	0.122005i	$0.0389324\pi$
$557$			5.75884i			0.244010i	−0.992529	+	0.122005i	$0.961068\pi$
$558$		0			0
$559$	−21.4745	+	15.6021i	−0.908273	+	0.659899i
$560$	1.38927	+	1.73038i	0.0587072	+	0.0731219i
$561$		0			0
$562$	−3.95835	−	5.44820i	−0.166973	−	0.229818i
$563$	−3.71075	−	5.10741i	−0.156390	−	0.215252i	0.723631	−	0.690187i	$-0.242472\pi$
$563$	−3.71075	−	5.10741i	−0.156390	−	0.215252i	−0.880021	+	0.474935i	$0.842472\pi$
$564$		0			0
$565$	−7.14697	−	8.90180i	−0.300675	−	0.374502i
$566$	−7.56350	+	5.49520i	−0.317917	+	0.230981i
$567$		0			0
$568$			2.18577i			0.0917130i
$569$	9.21364	−	28.3567i	0.386256	−	1.18877i	−0.549309	−	0.835619i	$-0.685109\pi$
$569$	9.21364	−	28.3567i	0.386256	−	1.18877i	0.935565	−	0.353154i	$-0.114891\pi$
$570$		0			0
$571$	−9.34861	−	28.7721i	−0.391227	−	1.20407i	−0.931861	−	0.362815i	$-0.881816\pi$
$571$	−9.34861	−	28.7721i	−0.391227	−	1.20407i	0.540634	−	0.841258i	$-0.318184\pi$
$572$	−11.6946	+	3.79981i	−0.488977	+	0.158878i
$573$		0			0
$574$	−1.12749			−0.0470606
$575$	14.2018	−	24.1289i	0.592258	−	1.00624i
$576$		0			0
$577$	18.2932	−	25.1784i	0.761554	−	1.04819i	−0.235529	−	0.971867i	$-0.575682\pi$
$577$	18.2932	−	25.1784i	0.761554	−	1.04819i	0.997083	−	0.0763219i	$-0.0243177\pi$
$578$	11.2689	−	3.66149i	0.468725	−	0.152298i
$579$		0			0
$580$	12.7466	−	10.2338i	0.529273	−	0.424936i
$581$	−3.18559	+	9.80424i	−0.132161	+	0.406748i
$582$		0			0
$583$	12.7923	+	4.15648i	0.529805	+	0.172144i
$584$	2.30841	−	1.67716i	0.0955228	−	0.0694014i
$585$		0			0
$586$	−4.07295	−	2.95917i	−0.168252	−	0.122242i
$587$	−4.55905	−	6.27500i	−0.188172	−	0.258997i	0.704499	−	0.709705i	$-0.251172\pi$
$587$	−4.55905	−	6.27500i	−0.188172	−	0.258997i	−0.892672	+	0.450708i	$0.851172\pi$
$588$		0			0
$589$	22.2233	+	16.1461i	0.915693	+	0.665290i
$590$	−0.739393	−	15.3383i	−0.0304403	−	0.631469i
$591$		0			0
$592$	−4.97097	−	1.61517i	−0.204306	−	0.0663829i
$593$			24.6122i			1.01070i	0.862914	+	0.505351i	$0.168637\pi$
$593$			24.6122i			1.01070i	−0.862914	+	0.505351i	$0.831363\pi$
$594$		0			0
$595$	1.32391	−	4.85933i	0.0542749	−	0.199213i
$596$	7.38308	+	22.7228i	0.302423	+	0.930762i
$597$		0			0
$598$	12.6837	−	17.4576i	0.518675	−	0.713895i
$599$	−18.4703			−0.754675			−0.377337	−	0.926076i	$-0.623160\pi$
$599$	−18.4703			−0.754675			−0.377337	+	0.926076i	$0.623160\pi$
$600$		0			0
$601$	−14.2568			−0.581547			−0.290774	−	0.956792i	$-0.593913\pi$
$601$	−14.2568			−0.581547			−0.290774	+	0.956792i	$0.593913\pi$
$602$	4.01792	−	5.53019i	0.163758	−	0.225394i
$603$		0			0
$604$	2.47169	+	7.60708i	0.100572	+	0.309528i
$605$	−0.648503	−	1.71081i	−0.0263654	−	0.0695543i
$606$		0			0
$607$		−	1.70894i		−	0.0693637i	−0.999398	−	0.0346819i	$-0.988958\pi$
$607$		−	1.70894i		−	0.0693637i	0.999398	−	0.0346819i	$-0.0110418\pi$
$608$	−4.46695	−	1.45140i	−0.181159	−	0.0588620i
$609$		0			0
$610$	−23.1377	+	8.77065i	−0.936820	+	0.355113i
$611$	22.5594	+	16.3904i	0.912657	+	0.663084i
$612$		0			0
$613$	−17.1588	−	23.6171i	−0.693038	−	0.953885i	−0.999998	−	0.00216283i	$-0.999312\pi$
$613$	−17.1588	−	23.6171i	−0.693038	−	0.953885i	0.306959	−	0.951723i	$-0.400688\pi$
$614$	19.7154	+	14.3241i	0.795650	+	0.578074i
$615$		0			0
$616$	2.56186	−	1.86130i	0.103220	−	0.0749940i
$617$	20.1736	+	6.55479i	0.812158	+	0.263886i	0.685511	−	0.728062i	$-0.259579\pi$
$617$	20.1736	+	6.55479i	0.812158	+	0.263886i	0.126646	+	0.991948i	$0.459579\pi$
$618$		0			0
$619$	−2.59372	+	7.98266i	−0.104251	+	0.320850i	−0.989554	−	0.144164i	$-0.953951\pi$
$619$	−2.59372	+	7.98266i	−0.104251	+	0.320850i	0.885303	+	0.465014i	$0.153951\pi$
$620$	13.0625	−	0.629685i	0.524603	−	0.0252888i
$621$		0			0
$622$	16.4420	−	5.34234i	0.659266	−	0.214208i
$623$	1.12512	−	1.54860i	0.0450771	−	0.0620434i
$624$		0			0
$625$	24.5374	−	4.78708i	0.981496	−	0.191483i
$626$	0.124901			0.00499204
$627$		0			0
$628$	4.94678	−	1.60731i	0.197398	−	0.0641385i
$629$	3.66581	+	11.2822i	0.146166	+	0.449851i
$630$		0			0
$631$	−6.42507	+	19.7743i	−0.255778	+	0.787204i	0.737897	+	0.674913i	$0.235819\pi$
$631$	−6.42507	+	19.7743i	−0.255778	+	0.787204i	−0.993675	+	0.112291i	$0.964181\pi$
$632$		−	11.1540i		−	0.443683i
$633$		0			0
$634$	−17.2995	+	12.5688i	−0.687051	+	0.499172i
$635$	−5.36416	+	8.18477i	−0.212870	+	0.324803i
$636$		0			0
$637$	−13.6249	−	18.7530i	−0.539838	−	0.743023i
$638$	−13.7110	−	18.8716i	−0.542824	−	0.747133i
$639$		0			0
$640$	−2.09089	+	0.792578i	−0.0826497	+	0.0313294i
$641$	6.22913	−	4.52573i	0.246036	−	0.178756i	−0.457932	−	0.888987i	$-0.651410\pi$
$641$	6.22913	−	4.52573i	0.246036	−	0.178756i	0.703968	+	0.710232i	$0.251410\pi$
$642$		0			0
$643$			18.3706i			0.724467i	0.932087	+	0.362234i	$0.117986\pi$
$643$			18.3706i			0.724467i	−0.932087	+	0.362234i	$0.882014\pi$
$644$	−1.71723	+	5.28508i	−0.0676682	+	0.208261i
$645$		0			0
$646$	3.29413	+	10.1383i	0.129606	+	0.398885i
$647$	−40.8863	+	13.2848i	−1.60741	+	0.522278i	−0.968924	−	0.247358i	$-0.920437\pi$
$647$	−40.8863	+	13.2848i	−1.60741	+	0.522278i	−0.638482	+	0.769636i	$0.720437\pi$
$648$		0			0
$649$	−21.9134			−0.860175
$650$	19.1787	−	1.85335i	0.752251	−	0.0726943i
$651$		0			0
$652$	−10.7791	+	14.8361i	−0.422141	+	0.581028i
$653$	9.30596	−	3.02369i	0.364170	−	0.118326i	−0.121215	−	0.992626i	$-0.538679\pi$
$653$	9.30596	−	3.02369i	0.364170	−	0.118326i	0.485386	+	0.874300i	$0.338679\pi$
$654$		0			0
$655$	2.97926	−	10.9352i	0.116409	−	0.427274i
$656$	0.351083	−	1.08052i	0.0137075	−	0.0421873i
$657$		0			0
$658$	−6.82960	−	2.21907i	−0.266245	−	0.0865084i
$659$	35.4038	−	25.7224i	1.37914	−	1.00200i	0.382177	−	0.924089i	$-0.375175\pi$
$659$	35.4038	−	25.7224i	1.37914	−	1.00200i	0.996960	−	0.0779123i	$-0.0248254\pi$
$660$		0			0
$661$	−20.8527	−	15.1503i	−0.811075	−	0.589280i	0.103067	−	0.994674i	$-0.467134\pi$
$661$	−20.8527	−	15.1503i	−0.811075	−	0.589280i	−0.914142	+	0.405394i	$0.867134\pi$
$662$	17.6119	+	24.2407i	0.684507	+	0.942143i
$663$		0			0
$664$	−8.40387	−	6.10577i	−0.326133	−	0.236950i
$665$	−10.0561	−	2.73974i	−0.389957	−	0.106243i
$666$		0			0
$667$	38.9318	+	12.6497i	1.50744	+	0.489798i
$668$		−	24.0047i		−	0.928768i
$669$		0			0
$670$	22.8494	−	18.3450i	0.882749	−	0.708731i
$671$	10.9115	+	33.5821i	0.421233	+	1.29642i
$672$		0			0
$673$	−1.83966	+	2.53207i	−0.0709135	+	0.0976041i	−0.843000	−	0.537913i	$-0.819213\pi$
$673$	−1.83966	+	2.53207i	−0.0709135	+	0.0976041i	0.772087	+	0.635517i	$0.219213\pi$
$674$	−15.6165			−0.601527
$675$		0			0
$676$	1.85033			0.0711666
$677$	20.4250	−	28.1126i	0.784996	−	1.08045i	−0.209717	−	0.977762i	$-0.567254\pi$
$677$	20.4250	−	28.1126i	0.784996	−	1.08045i	0.994713	−	0.102692i	$-0.0327456\pi$
$678$		0			0
$679$	5.07996	+	15.6345i	0.194951	+	0.599997i
$680$	4.24465	+	2.78187i	0.162775	+	0.106680i
$681$		0			0
$682$		−	18.6620i		−	0.714603i
$683$	39.7609	+	12.9191i	1.52141	+	0.494336i	0.946176	−	0.323653i	$-0.104911\pi$
$683$	39.7609	+	12.9191i	1.52141	+	0.494336i	0.575234	+	0.817989i	$0.304911\pi$
$684$		0			0
$685$	−3.27419	−	4.07812i	−0.125100	−	0.155817i
$686$	10.4494	+	7.59196i	0.398961	+	0.289862i
$687$		0			0
$688$	4.04870	+	5.57255i	0.154355	+	0.212452i
$689$	−13.1419	−	9.54813i	−0.500666	−	0.363755i
$690$		0			0
$691$	−10.5080	+	7.63452i	−0.399744	+	0.290431i	−0.769437	−	0.638723i	$-0.779463\pi$
$691$	−10.5080	+	7.63452i	−0.399744	+	0.290431i	0.369693	+	0.929154i	$0.379463\pi$
$692$	14.5567	+	4.72976i	0.553363	+	0.179798i
$693$		0			0
$694$	10.6773	−	32.8612i	0.405303	−	1.24739i
$695$	3.41185	+	2.23607i	0.129419	+	0.0848189i
$696$		0			0
$697$	−2.45237	+	0.796825i	−0.0928903	+	0.0301819i
$698$	11.1156	−	15.2993i	0.420730	−	0.579085i
$699$		0			0
$700$	−4.54977	+	1.98015i	−0.171965	+	0.0748427i
$701$	19.9966			0.755261			0.377630	−	0.925956i	$-0.376739\pi$
$701$	19.9966			0.755261			0.377630	+	0.925956i	$0.376739\pi$
$702$		0			0
$703$	23.3478	−	7.58616i	0.880579	−	0.286117i
$704$	0.986039	+	3.03472i	0.0371628	+	0.114375i
$705$		0			0
$706$	9.47936	−	29.1745i	0.356760	−	1.09800i
$707$			16.3284i			0.614094i
$708$		0			0
$709$	3.75564	−	2.72863i	0.141046	−	0.102476i	−0.515025	−	0.857175i	$-0.672217\pi$
$709$	3.75564	−	2.72863i	0.141046	−	0.102476i	0.656071	+	0.754699i	$0.272217\pi$
$710$	−4.71566	−	1.28477i	−0.176975	−	0.0482164i
$711$		0			0
$712$	1.13374	+	1.56046i	0.0424888	+	0.0584808i
$713$	19.2497	+	26.4949i	0.720906	+	0.992241i
$714$		0			0
$715$	−1.32391	−	27.4638i	−0.0495114	−	1.02709i
$716$	18.9331	−	13.7557i	0.707565	−	0.514076i
$717$		0			0
$718$		−	3.73763i		−	0.139487i
$719$	−3.34562	+	10.2968i	−0.124771	+	0.384005i	−0.993859	−	0.110652i	$-0.964706\pi$
$719$	−3.34562	+	10.2968i	−0.124771	+	0.384005i	0.869089	+	0.494657i	$0.164706\pi$
$720$		0			0
$721$	2.87387	+	8.84485i	0.107028	+	0.329400i
$722$	2.91042	−	0.945652i	0.108314	−	0.0351935i
$723$		0			0
$724$	23.8436			0.886141
$725$	14.5865	+	33.5152i	0.541729	+	1.24472i
$726$		0			0
$727$	−16.3513	+	22.5057i	−0.606437	+	0.834689i	−0.996278	−	0.0861932i	$-0.972530\pi$
$727$	−16.3513	+	22.5057i	−0.606437	+	0.834689i	0.389842	+	0.920882i	$0.372530\pi$
$728$	−3.63714	+	1.18178i	−0.134802	+	0.0437997i
$729$		0			0
$730$	2.26151	+	5.96605i	0.0837021	+	0.220813i
$731$	4.83095	−	14.8681i	0.178679	−	0.549917i
$732$		0			0
$733$	10.1351	+	3.29309i	0.374348	+	0.121633i	0.490148	−	0.871639i	$-0.336943\pi$
$733$	10.1351	+	3.29309i	0.374348	+	0.121633i	−0.115799	+	0.993273i	$0.536943\pi$
$734$	−13.9201	+	10.1135i	−0.513799	+	0.373296i
$735$		0			0
$736$	−4.53019	−	3.29138i	−0.166985	−	0.121322i
$737$	−24.5782	−	33.8290i	−0.905349	−	1.24611i
$738$		0			0
$739$	−21.4485	−	15.5832i	−0.788994	−	0.573238i	0.118671	−	0.992934i	$-0.462137\pi$
$739$	−21.4485	−	15.5832i	−0.788994	−	0.573238i	−0.907665	+	0.419696i	$0.862137\pi$
$740$	6.40647	−	9.77516i	0.235507	−	0.359342i
$741$		0			0
$742$	3.97854	+	1.29271i	0.146057	+	0.0474568i
$743$		−	4.29218i		−	0.157465i	−0.996896	−	0.0787325i	$-0.974913\pi$
$743$		−	4.29218i		−	0.157465i	0.996896	−	0.0787325i	$-0.0250873\pi$
$744$		0			0
$745$	−53.3625	+	2.57237i	−1.95505	+	0.0942443i
$746$	−8.10201	−	24.9354i	−0.296636	−	0.912951i
$747$		0			0
$748$	4.25680	−	5.85899i	0.155644	−	0.214226i
$749$	8.41148			0.307349
$750$		0			0
$751$	24.1035			0.879549			0.439774	−	0.898108i	$-0.355058\pi$
$751$	24.1035			0.879549			0.439774	+	0.898108i	$0.355058\pi$
$752$	4.25325	−	5.85410i	0.155100	−	0.213477i
$753$		0			0
$754$	8.70541	+	26.7925i	0.317032	+	0.975725i
$755$	−17.8646	+	0.861172i	−0.650159	+	0.0313412i
$756$		0			0
$757$			37.3911i			1.35900i	0.733674	+	0.679502i	$0.237804\pi$
$757$			37.3911i			1.35900i	−0.733674	+	0.679502i	$0.762196\pi$
$758$	17.7862	+	5.77908i	0.646023	+	0.209906i
$759$		0			0
$760$	5.75690	−	8.78402i	0.208825	−	0.318630i
$761$	−28.5644	−	20.7533i	−1.03546	−	0.752305i	−0.0660654	−	0.997815i	$-0.521045\pi$
$761$	−28.5644	−	20.7533i	−1.03546	−	0.752305i	−0.969394	+	0.245510i	$0.921045\pi$
$762$		0			0
$763$	−8.83010	−	12.1536i	−0.319671	−	0.439990i
$764$	10.1616	+	7.38286i	0.367635	+	0.267102i
$765$		0			0
$766$	−0.527864	+	0.383516i	−0.0190725	+	0.0138570i
$767$	25.1693	+	8.17801i	0.908812	+	0.295291i
$768$		0			0
$769$	−4.66718	+	14.3641i	−0.168303	+	0.517982i	−0.999264	−	0.0383471i	$-0.987791\pi$
$769$	−4.66718	+	14.3641i	−0.168303	+	0.517982i	0.830962	+	0.556329i	$0.187791\pi$
$770$	2.50980	+	6.62108i	0.0904471	+	0.238607i
$771$		0			0
$772$	5.42705	−	1.76336i	0.195324	−	0.0634646i
$773$	−20.9839	+	28.8818i	−0.754737	+	1.03881i	0.242897	+	0.970052i	$0.421902\pi$
$773$	−20.9839	+	28.8818i	−0.754737	+	1.03881i	−0.997634	+	0.0687538i	$0.978098\pi$
$774$		0			0
$775$	−6.31944	+	28.5516i	−0.227001	+	1.02560i
$776$	−16.5650			−0.594649
$777$		0			0
$778$	−2.59623	+	0.843565i	−0.0930792	+	0.0302433i
$779$	1.64898	+	5.07502i	0.0590807	+	0.181832i
$780$		0			0
$781$	−2.15526	+	6.63320i	−0.0771212	+	0.237355i
$782$			12.7090i			0.454474i
$783$		0			0
$784$	−4.86635	+	3.53561i	−0.173798	+	0.126272i
$785$	0.560008	+	11.6171i	0.0199875	+	0.414632i
$786$		0			0
$787$	−19.7169	−	27.1379i	−0.702830	−	0.967363i	−0.999922	−	0.0125140i	$-0.996017\pi$
$787$	−19.7169	−	27.1379i	−0.702830	−	0.967363i	0.297091	−	0.954849i	$-0.403983\pi$
$788$	−9.78158	−	13.4632i	−0.348454	−	0.479606i
$789$		0			0
$790$	24.0640	+	6.55616i	0.856159	+	0.233258i
$791$	−4.09889	+	2.97802i	−0.145740	+	0.105886i
$792$		0			0
$793$		−	42.6440i		−	1.51433i
$794$	−7.01527	+	21.5908i	−0.248963	+	0.766228i
$795$		0			0
$796$	3.28360	+	10.1059i	0.116384	+	0.358194i
$797$	−4.41143	+	1.43336i	−0.156261	+	0.0507723i	−0.386103	−	0.922456i	$-0.626179\pi$
$797$	−4.41143	+	1.43336i	−0.156261	+	0.0507723i	0.229842	+	0.973228i	$0.426179\pi$
$798$		0			0
$799$	−16.4231			−0.581008
$800$	−0.480938	−	4.97682i	−0.0170037	−	0.175957i
$801$		0			0
$802$	15.3807	−	21.1697i	0.543110	−	0.747527i
$803$	8.65912	−	2.81352i	0.305574	−	0.0992869i
$804$		0			0
$805$	−10.3928	−	6.81129i	−0.366299	−	0.240066i
$806$	−6.96459	+	21.4348i	−0.245317	+	0.755009i
$807$		0			0
$808$	−15.6482	−	5.08442i	−0.550503	−	0.178869i
$809$	9.20558	−	6.68825i	0.323651	−	0.235146i	−0.414081	−	0.910240i	$-0.635897\pi$
$809$	9.20558	−	6.68825i	0.323651	−	0.235146i	0.737732	+	0.675094i	$0.235897\pi$
$810$		0			0
$811$	25.9772	+	18.8735i	0.912183	+	0.662740i	0.941566	−	0.336828i	$-0.109354\pi$
$811$	25.9772	+	18.8735i	0.912183	+	0.662740i	−0.0293830	+	0.999568i	$0.509354\pi$
$812$	−4.26426	−	5.86925i	−0.149646	−	0.205970i
$813$		0			0
$814$	−13.4929	−	9.80315i	−0.472925	−	0.343600i
$815$	−25.6721	−	31.9756i	−0.899256	−	1.12006i
$816$		0			0
$817$	−30.7686	−	9.99732i	−1.07646	−	0.349762i
$818$		−	8.71989i		−	0.304884i
$819$		0			0
$820$	2.12479	+	1.39255i	0.0742009	+	0.0486300i
$821$	−16.0525	−	49.4045i	−0.560236	−	1.72423i	−0.681697	−	0.731634i	$-0.738758\pi$
$821$	−16.0525	−	49.4045i	−0.560236	−	1.72423i	0.121461	−	0.992596i	$-0.461242\pi$
$822$		0			0
$823$	−32.1554	+	44.2582i	−1.12087	+	1.54274i	−0.316518	+	0.948587i	$0.602514\pi$
$823$	−32.1554	+	44.2582i	−1.12087	+	1.54274i	−0.804350	+	0.594155i	$0.797486\pi$
$824$	−9.37127			−0.326464
$825$		0			0
$826$	−6.81527			−0.237134
$827$	−20.9773	+	28.8727i	−0.729451	+	1.00400i	0.269705	+	0.962943i	$0.413074\pi$
$827$	−20.9773	+	28.8727i	−0.729451	+	1.00400i	−0.999157	+	0.0410607i	$0.986926\pi$
$828$		0			0
$829$	−10.8942	−	33.5288i	−0.378370	−	1.16450i	−0.941177	−	0.337914i	$-0.890279\pi$
$829$	−10.8942	−	33.5288i	−0.378370	−	1.16450i	0.562807	−	0.826588i	$-0.309721\pi$
$830$	18.1124	−	14.5419i	0.628692	−	0.504756i
$831$		0			0
$832$		−	3.85361i		−	0.133600i
$833$	12.9839	+	4.21873i	0.449866	+	0.146170i
$834$		0			0
$835$	51.7884	+	14.1096i	1.79221	+	0.488282i
$836$	−12.1248	−	8.80917i	−0.419345	−	0.304672i
$837$		0			0
$838$	6.16403	+	8.48406i	0.212933	+	0.293077i
$839$	30.1946	+	21.9377i	1.04243	+	0.757373i	0.970759	−	0.240055i	$-0.0771656\pi$
$839$	30.1946	+	21.9377i	1.04243	+	0.757373i	0.0716748	+	0.997428i	$0.477166\pi$
$840$		0			0
$841$	−19.7735	+	14.3663i	−0.681844	+	0.495388i
$842$	23.0618	+	7.49324i	0.794763	+	0.258234i
$843$		0			0
$844$	0.248884	−	0.765985i	0.00856693	−	0.0263663i
$845$	−1.08760	+	3.99196i	−0.0374145	+	0.137328i
$846$		0			0
$847$	−0.772258	+	0.250922i	−0.0265351	+	0.00862178i
$848$	−2.47771	+	3.41027i	−0.0850849	+	0.117109i
$849$		0			0
$850$	−8.49664	+	7.52240i	−0.291432	+	0.258016i
$851$	29.2681			1.00330
$852$		0			0
$853$	−20.7438	+	6.74007i	−0.710254	+	0.230776i	−0.641793	−	0.766878i	$-0.721809\pi$
$853$	−20.7438	+	6.74007i	−0.710254	+	0.230776i	−0.0684615	+	0.997654i	$0.521809\pi$
$854$	3.39358	+	10.4444i	0.116126	+	0.357399i
$855$		0			0
$856$	−2.61920	+	8.06107i	−0.0895224	+	0.275522i
$857$		−	19.1130i		−	0.652889i	−0.945216	−	0.326445i	$-0.894149\pi$
$857$		−	19.1130i		−	0.652889i	0.945216	−	0.326445i	$-0.105851\pi$
$858$		0			0
$859$	24.5197	−	17.8146i	0.836602	−	0.607827i	−0.0848177	−	0.996396i	$-0.527031\pi$
$859$	24.5197	−	17.8146i	0.836602	−	0.607827i	0.921419	+	0.388570i	$0.127031\pi$
$860$	−14.4022	+	5.45932i	−0.491110	+	0.186161i
$861$		0			0
$862$	−1.41062	−	1.94156i	−0.0480460	−	0.0661297i
$863$	−25.6283	−	35.2743i	−0.872396	−	1.20075i	−0.978469	−	0.206392i	$-0.933828\pi$
$863$	−25.6283	−	35.2743i	−0.872396	−	1.20075i	0.106073	−	0.994358i	$-0.466172\pi$
$864$		0			0
$865$	−18.7603	+	28.6250i	−0.637871	+	0.973279i
$866$	−31.8742	+	23.1579i	−1.08313	+	0.786939i
$867$		0			0
$868$		−	5.80405i		−	0.197002i
$869$	10.9983	−	33.8493i	0.373092	−	1.14826i
$870$		0			0
$871$	15.6052	+	48.0279i	0.528763	+	1.62736i
$872$	14.3968	−	4.67782i	0.487539	−	0.158411i
$873$		0			0
$874$	26.3005			0.889627
$875$	−1.59776	−	10.9797i	−0.0540140	−	0.371182i
$876$		0			0
$877$	−10.8557	+	14.9416i	−0.366570	+	0.504541i	−0.951965	−	0.306208i	$-0.900940\pi$
$877$	−10.8557	+	14.9416i	−0.366570	+	0.504541i	0.585394	+	0.810749i	$0.300940\pi$
$878$	−37.9155	+	12.3195i	−1.27959	+	0.415762i
$879$		0			0
$880$	−7.12677	+	0.343550i	−0.240243	+	0.0115811i
$881$	−9.98946	+	30.7444i	−0.336553	+	1.03581i	0.629398	+	0.777083i	$0.283301\pi$
$881$	−9.98946	+	30.7444i	−0.336553	+	1.03581i	−0.965952	+	0.258722i	$0.916699\pi$
$882$		0			0
$883$	22.7220	+	7.38283i	0.764657	+	0.248452i	0.665276	−	0.746597i	$-0.268314\pi$
$883$	22.7220	+	7.38283i	0.764657	+	0.248452i	0.0993809	+	0.995049i	$0.468314\pi$
$884$	−7.07585	+	5.14091i	−0.237987	+	0.172907i
$885$		0			0
$886$	16.4097	+	11.9223i	0.551293	+	0.400538i
$887$	−13.4359	−	18.4929i	−0.451132	−	0.620930i	0.521508	−	0.853246i	$-0.325370\pi$
$887$	−13.4359	−	18.4929i	−0.451132	−	0.620930i	−0.972640	+	0.232316i	$0.925370\pi$
$888$		0			0
$889$	3.51367	+	2.55283i	0.117845	+	0.0856192i
$890$	−4.03299	+	1.52875i	−0.135186	+	0.0512439i
$891$		0			0
$892$	15.3067	+	4.97344i	0.512505	+	0.166523i
$893$			33.9866i			1.13732i
$894$		0			0
$895$	18.5484	+	48.9324i	0.620006	+	1.63563i
$896$	0.306668	+	0.943827i	0.0102451	+	0.0315310i
$897$		0			0
$898$	24.4901	−	33.7077i	0.817244	−	1.12484i
$899$	−42.7547			−1.42595
$900$		0			0
$901$	9.56720			0.318730
$902$	2.13087	−	2.93290i	0.0709503	−	0.0976548i
$903$		0			0
$904$	−1.57763	−	4.85544i	−0.0524712	−	0.161490i
$905$	−14.0149	+	51.4410i	−0.465872	+	1.70996i
$906$		0			0
$907$		−	7.20307i		−	0.239174i	−0.992824	−	0.119587i	$-0.961843\pi$
$907$		−	7.20307i		−	0.239174i	0.992824	−	0.119587i	$-0.0381570\pi$
$908$	−13.0869	−	4.25218i	−0.434303	−	0.141114i
$909$		0			0
$910$	−0.411749	−	8.54152i	−0.0136493	−	0.283149i
$911$	20.3748	+	14.8031i	0.675047	+	0.490450i	0.871711	−	0.490021i	$-0.163011\pi$
$911$	20.3748	+	14.8031i	0.675047	+	0.490450i	−0.196664	+	0.980471i	$0.563011\pi$
$912$		0			0
$913$	−19.4828	−	26.8158i	−0.644788	−	0.887474i
$914$	1.87932	+	1.36541i	0.0621623	+	0.0451636i
$915$		0			0
$916$	11.9978	−	8.71692i	0.396419	−	0.288015i
$917$	−4.78391	−	1.55439i	−0.157979	−	0.0513303i
$918$		0			0
$919$	4.59171	−	14.1318i	0.151466	−	0.466166i	−0.846319	−	0.532676i	$-0.821186\pi$
$919$	4.59171	−	14.1318i	0.151466	−	0.466166i	0.997786	+	0.0665102i	$0.0211865\pi$
$920$	9.76370	−	7.83896i	0.321900	−	0.258443i
$921$		0			0
$922$	−4.99938	+	1.62440i	−0.164646	+	0.0534966i
$923$	4.95099	−	6.81445i	0.162964	−	0.224300i
$924$		0			0
$925$	17.3236	+	19.5672i	0.569596	+	0.643366i
$926$	−28.3947			−0.933108
$927$		0			0
$928$	6.95256	−	2.25903i	0.228229	−	0.0741561i
$929$	−18.3634	−	56.5166i	−0.602482	−	1.85425i	−0.513252	−	0.858238i	$-0.671559\pi$
$929$	−18.3634	−	56.5166i	−0.602482	−	1.85425i	−0.0892298	−	0.996011i	$-0.528441\pi$
$930$		0			0
$931$	8.73038	−	26.8693i	0.286127	−	0.880607i
$932$			0.885638i			0.0290101i
$933$		0			0
$934$	18.3447	−	13.3282i	0.600258	−	0.436113i
$935$	10.1383	+	12.6276i	0.331557	+	0.412966i
$936$		0			0
$937$	8.76118	+	12.0587i	0.286215	+	0.393941i	0.927780	−	0.373127i	$-0.121715\pi$
$937$	8.76118	+	12.0587i	0.286215	+	0.393941i	−0.641565	+	0.767069i	$0.721715\pi$
$938$	−7.64406	−	10.5211i	−0.249587	−	0.343528i
$939$		0			0
$940$	10.1298	+	12.6171i	0.330398	+	0.411523i
$941$	−5.12951	+	3.72681i	−0.167217	+	0.121490i	−0.668247	−	0.743940i	$-0.732955\pi$
$941$	−5.12951	+	3.72681i	−0.167217	+	0.121490i	0.501029	+	0.865430i	$0.332955\pi$
$942$		0			0
$943$			6.36189i			0.207172i
$944$	2.12217	−	6.53136i	0.0690707	−	0.212578i
$945$		0			0
$946$	6.79189	+	20.9033i	0.220823	+	0.679625i
$947$	−17.0473	+	5.53899i	−0.553961	+	0.179993i	−0.572602	−	0.819833i	$-0.694066\pi$
$947$	−17.0473	+	5.53899i	−0.553961	+	0.179993i	0.0186409	+	0.999826i	$0.494066\pi$
$948$		0			0
$949$	−10.9957			−0.356936
$950$	15.5671	+	17.5832i	0.505063	+	0.570476i
$951$		0			0
$952$	1.32391	−	1.82220i	0.0429081	−	0.0590580i
$953$	−6.52939	+	2.12153i	−0.211508	+	0.0687230i	−0.412855	−	0.910797i	$-0.635468\pi$
$953$	−6.52939	+	2.12153i	−0.211508	+	0.0687230i	0.201347	+	0.979520i	$0.435468\pi$
$954$		0			0
$955$	−21.9009	+	17.5835i	−0.708695	+	0.568988i
$956$	6.75598	−	20.7928i	0.218504	−	0.672487i
$957$		0			0
$958$	−39.6326	−	12.8774i	−1.28047	−	0.416050i
$959$	−1.87779	+	1.36430i	−0.0606371	+	0.0440554i
$960$		0			0
$961$	−2.59297	−	1.88390i	−0.0836440	−	0.0607710i
$962$	11.8392	+	16.2952i	0.381711	+	0.525379i
$963$		0			0
$964$	−9.21929	−	6.69821i	−0.296933	−	0.215735i
$965$	0.614378	+	12.7450i	0.0197775	+	0.410275i
$966$		0			0
$967$	8.38555	+	2.72463i	0.269661	+	0.0876182i	0.440726	−	0.897641i	$-0.354721\pi$
$967$	8.38555	+	2.72463i	0.269661	+	0.0876182i	−0.171065	+	0.985260i	$0.554721\pi$
$968$		−	0.818220i		−	0.0262986i
$969$		0			0
$970$	9.73667	−	35.7379i	0.312626	−	1.14747i
$971$	−8.37280	−	25.7688i	−0.268696	−	0.826961i	−0.990819	−	0.135197i	$-0.956833\pi$
$971$	−8.37280	−	25.7688i	−0.268696	−	0.826961i	0.722123	−	0.691765i	$-0.243167\pi$
$972$		0			0
$973$	1.06416	−	1.46469i	0.0341153	−	0.0469557i
$974$	−23.1168			−0.740711
$975$		0			0
$976$	−11.0660			−0.354213
$977$	12.3606	−	17.0130i	0.395452	−	0.544293i	−0.564144	−	0.825677i	$-0.690794\pi$
$977$	12.3606	−	17.0130i	0.395452	−	0.544293i	0.959595	+	0.281384i	$0.0907935\pi$
$978$		0			0
$979$	1.90191	+	5.85348i	0.0607853	+	0.187078i
$980$	−4.76747	−	12.5770i	−0.152291	−	0.401758i
$981$		0			0
$982$			40.9384i			1.30640i
$983$	−44.7399	−	14.5369i	−1.42698	−	0.463654i	−0.509168	−	0.860667i	$-0.670047\pi$
$983$	−44.7399	−	14.5369i	−1.42698	−	0.463654i	−0.917813	+	0.397013i	$0.870047\pi$
$984$		0			0
$985$	34.7954	−	13.1896i	1.10867	−	0.420256i
$986$	−13.4230	−	9.75238i	−0.427475	−	0.310579i
$987$		0			0
$988$	10.6388	+	14.6430i	0.338464	+	0.465856i
$989$	−31.2042	−	22.6712i	−0.992237	−	0.720902i
$990$		0			0
$991$	−40.2778	+	29.2635i	−1.27947	+	0.929586i	−0.999537	−	0.0304345i	$-0.990311\pi$
$991$	−40.2778	+	29.2635i	−1.27947	+	0.929586i	−0.279929	+	0.960021i	$0.590311\pi$
$992$	5.56226	+	1.80729i	0.176602	+	0.0573815i
$993$		0			0
$994$	−0.670307	+	2.06299i	−0.0212608	+	0.0654341i
$995$	−23.7328	+	1.14405i	−0.752380	+	0.0362689i
$996$		0			0
$997$	−21.5340	+	6.99681i	−0.681987	+	0.221591i	−0.629465	−	0.777029i	$-0.716726\pi$
$997$	−21.5340	+	6.99681i	−0.681987	+	0.221591i	−0.0525222	+	0.998620i	$0.516726\pi$
$998$	−4.62997	+	6.37261i	−0.146559	+	0.201721i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.d.109.2	✓	16
3.2	odd	2	inner	450.2.l.d.109.3	yes	16
25.14	even	10	inner	450.2.l.d.289.2	yes	16
75.14	odd	10	inner	450.2.l.d.289.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.l.d.109.2	✓	16	1.1	even	1	trivial
450.2.l.d.109.3	yes	16	3.2	odd	2	inner
450.2.l.d.289.2	yes	16	25.14	even	10	inner
450.2.l.d.289.3	yes	16	75.14	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(2.23347 - 0.107666i) q^{5} -0.992398i q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(2.23347 - 0.107666i) q^{5} -0.992398i q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.22570 + 1.87020i) q^{10} +(2.58148 + 1.87556i) q^{11} +(-2.26510 - 3.11764i) q^{13} +(0.802867 + 0.583317i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.15854 + 0.701351i) q^{17} +(1.45140 - 4.46695i) q^{19} +(-0.792578 - 2.09089i) q^{20} +(-3.03472 + 0.986039i) q^{22} +(3.29138 - 4.53019i) q^{23} +(4.97682 - 0.480938i) q^{25} +3.85361 q^{26} +(-0.943827 + 0.306668i) q^{28} +(2.25903 + 6.95256i) q^{29} +(-1.80729 + 5.56226i) q^{31} -1.00000i q^{32} +(-1.83616 + 1.33405i) q^{34} +(-0.106847 - 2.21650i) q^{35} +(3.07223 + 4.22856i) q^{37} +(2.76073 + 3.79981i) q^{38} +(2.15743 + 0.587785i) q^{40} +(-0.919147 + 0.667799i) q^{41} -6.88806i q^{43} +(0.986039 - 3.03472i) q^{44} +(1.73038 + 5.32556i) q^{46} +(-6.88191 + 2.23607i) q^{47} +6.01515 q^{49} +(-2.53621 + 4.30902i) q^{50} +(-2.26510 + 3.11764i) q^{52} +(4.00902 - 1.30261i) q^{53} +(5.96761 + 3.91107i) q^{55} +(0.306668 - 0.943827i) q^{56} +(-6.95256 - 2.25903i) q^{58} +(-5.55591 + 4.03660i) q^{59} +(8.95256 + 6.50442i) q^{61} +(-3.43767 - 4.73154i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-5.39470 - 6.71929i) q^{65} +(-12.4631 - 4.04950i) q^{67} -2.26962i q^{68} +(1.85599 + 1.21638i) q^{70} +(0.675441 + 2.07879i) q^{71} +(1.67716 - 2.30841i) q^{73} -5.22679 q^{74} -4.69683 q^{76} +(1.86130 - 2.56186i) q^{77} +(-3.44678 - 10.6081i) q^{79} +(-1.74363 + 1.39991i) q^{80} -1.13613i q^{82} +(-9.87934 - 3.20999i) q^{83} +(4.89655 + 1.33405i) q^{85} +(5.57255 + 4.04870i) q^{86} +(1.87556 + 2.58148i) q^{88} +(1.56046 + 1.13374i) q^{89} +(-3.09394 + 2.24788i) q^{91} +(-5.32556 - 1.73038i) q^{92} +(2.23607 - 6.88191i) q^{94} +(2.76073 - 10.1331i) q^{95} +(-15.7543 + 5.11887i) q^{97} +(-3.53561 + 4.86635i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

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