LMFDB - Embedded newform 1512.2.c.f.757.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.6
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.f.757.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09864 + 0.890504i) q^{2} +(0.414007 - 1.95668i) q^{4} +1.58470i q^{5} +1.00000 q^{7} +(1.28759 + 2.51836i) q^{8} +O(q^{10})$	\(q+(-1.09864 + 0.890504i) q^{2} +(0.414007 - 1.95668i) q^{4} +1.58470i q^{5} +1.00000 q^{7} +(1.28759 + 2.51836i) q^{8} +(-1.41118 - 1.74101i) q^{10} -0.790533i q^{11} -0.494366i q^{13} +(-1.09864 + 0.890504i) q^{14} +(-3.65720 - 1.62016i) q^{16} +4.46962 q^{17} -7.55705i q^{19} +(3.10076 + 0.656077i) q^{20} +(0.703973 + 0.868509i) q^{22} +0.839644 q^{23} +2.48872 q^{25} +(0.440235 + 0.543129i) q^{26} +(0.414007 - 1.95668i) q^{28} +2.76437i q^{29} -0.568664 q^{31} +(5.46069 - 1.47678i) q^{32} +(-4.91049 + 3.98021i) q^{34} +1.58470i q^{35} -0.343650i q^{37} +(6.72958 + 8.30245i) q^{38} +(-3.99084 + 2.04044i) q^{40} -5.93014 q^{41} -3.16166i q^{43} +(-1.54682 - 0.327286i) q^{44} +(-0.922464 + 0.747706i) q^{46} +4.80964 q^{47} +1.00000 q^{49} +(-2.73420 + 2.21621i) q^{50} +(-0.967316 - 0.204671i) q^{52} -4.36792i q^{53} +1.25276 q^{55} +(1.28759 + 2.51836i) q^{56} +(-2.46168 - 3.03704i) q^{58} -4.50798i q^{59} -5.40103i q^{61} +(0.624755 - 0.506397i) q^{62} +(-4.68423 + 6.48521i) q^{64} +0.783423 q^{65} +7.57396i q^{67} +(1.85045 - 8.74561i) q^{68} +(-1.41118 - 1.74101i) q^{70} +9.52886 q^{71} +14.1344 q^{73} +(0.306022 + 0.377547i) q^{74} +(-14.7867 - 3.12867i) q^{76} -0.790533i q^{77} -3.71341 q^{79} +(2.56747 - 5.79557i) q^{80} +(6.51507 - 5.28081i) q^{82} +7.30905i q^{83} +7.08301i q^{85} +(2.81547 + 3.47352i) q^{86} +(1.99084 - 1.01788i) q^{88} +11.5305 q^{89} -0.494366i q^{91} +(0.347618 - 1.64292i) q^{92} +(-5.28405 + 4.28300i) q^{94} +11.9757 q^{95} +1.75839 q^{97} +(-1.09864 + 0.890504i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7}+O(q^{10}) $ 24 * q + 24 * q^7	$ 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.09864	+	0.890504i	−0.776854	+	0.629681i
$2$	−1.09864	+	0.890504i	−0.776854	+	0.629681i
$3$		0			0
$3$		0			0
$4$	0.414007	−	1.95668i	0.207003	−	0.978340i
$5$			1.58470i			0.708700i	0.935113	+	0.354350i	$0.115298\pi$
$5$			1.58470i			0.708700i	−0.935113	+	0.354350i	$0.884702\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.28759	+	2.51836i	0.455231	+	0.890373i
$9$		0			0
$10$	−1.41118	−	1.74101i	−0.446255	−	0.550557i
$11$		−	0.790533i		−	0.238355i	−0.992873	−	0.119177i	$-0.961974\pi$
$11$		−	0.790533i		−	0.238355i	0.992873	−	0.119177i	$-0.0380257\pi$
$12$		0			0
$13$		−	0.494366i		−	0.137112i	−0.997647	−	0.0685562i	$-0.978161\pi$
$13$		−	0.494366i		−	0.137112i	0.997647	−	0.0685562i	$-0.0218392\pi$
$14$	−1.09864	+	0.890504i	−0.293623	+	0.237997i
$15$		0			0
$16$	−3.65720	−	1.62016i	−0.914299	−	0.405039i
$17$	4.46962			1.08404			0.542021	−	0.840365i	$-0.317660\pi$
$17$	4.46962			1.08404			0.542021	+	0.840365i	$0.317660\pi$
$18$		0			0
$19$		−	7.55705i		−	1.73371i	−0.498564	−	0.866853i	$-0.666139\pi$
$19$		−	7.55705i		−	1.73371i	0.498564	−	0.866853i	$-0.333861\pi$
$20$	3.10076	+	0.656077i	0.693350	+	0.146703i
$21$		0			0
$22$	0.703973	+	0.868509i	0.150088	+	0.185167i
$23$	0.839644			0.175078			0.0875390	−	0.996161i	$-0.472100\pi$
$23$	0.839644			0.175078			0.0875390	+	0.996161i	$0.472100\pi$
$24$		0			0
$25$	2.48872			0.497744
$26$	0.440235	+	0.543129i	0.0863371	+	0.106516i
$27$		0			0
$28$	0.414007	−	1.95668i	0.0782399	−	0.369778i
$29$			2.76437i			0.513331i	0.966500	+	0.256665i	$0.0826238\pi$
$29$			2.76437i			0.513331i	−0.966500	+	0.256665i	$0.917376\pi$
$30$		0			0
$31$	−0.568664			−0.102135			−0.0510675	−	0.998695i	$-0.516262\pi$
$31$	−0.568664			−0.102135			−0.0510675	+	0.998695i	$0.516262\pi$
$32$	5.46069	−	1.47678i	0.965322	−	0.261061i
$33$		0			0
$34$	−4.91049	+	3.98021i	−0.842141	+	0.682600i
$35$			1.58470i			0.267864i
$36$		0			0
$37$		−	0.343650i		−	0.0564957i	−0.999601	−	0.0282479i	$-0.991007\pi$
$37$		−	0.343650i		−	0.0564957i	0.999601	−	0.0282479i	$-0.00899277\pi$
$38$	6.72958	+	8.30245i	1.09168	+	1.34684i
$39$		0			0
$40$	−3.99084	+	2.04044i	−0.631008	+	0.322622i
$41$	−5.93014			−0.926132			−0.463066	−	0.886324i	$-0.653251\pi$
$41$	−5.93014			−0.926132			−0.463066	+	0.886324i	$0.653251\pi$
$42$		0			0
$43$		−	3.16166i		−	0.482149i	−0.970507	−	0.241074i	$-0.922500\pi$
$43$		−	3.16166i		−	0.482149i	0.970507	−	0.241074i	$-0.0774998\pi$
$44$	−1.54682	−	0.327286i	−0.233192	−	0.0493402i
$45$		0			0
$46$	−0.922464	+	0.747706i	−0.136010	+	0.110243i
$47$	4.80964			0.701558			0.350779	−	0.936458i	$-0.385917\pi$
$47$	4.80964			0.701558			0.350779	+	0.936458i	$0.385917\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−2.73420	+	2.21621i	−0.386674	+	0.313420i
$51$		0			0
$52$	−0.967316	−	0.204671i	−0.134143	−	0.0283827i
$53$		−	4.36792i		−	0.599980i	−0.953942	−	0.299990i	$-0.903017\pi$
$53$		−	4.36792i		−	0.599980i	0.953942	−	0.299990i	$-0.0969833\pi$
$54$		0			0
$55$	1.25276			0.168922
$56$	1.28759	+	2.51836i	0.172061	+	0.336529i
$57$		0			0
$58$	−2.46168	−	3.03704i	−0.323235	−	0.398783i
$59$		−	4.50798i		−	0.586889i	−0.955976	−	0.293445i	$-0.905198\pi$
$59$		−	4.50798i		−	0.586889i	0.955976	−	0.293445i	$-0.0948016\pi$
$60$		0			0
$61$		−	5.40103i		−	0.691531i	−0.938321	−	0.345766i	$-0.887619\pi$
$61$		−	5.40103i		−	0.691531i	0.938321	−	0.345766i	$-0.112381\pi$
$62$	0.624755	−	0.506397i	0.0793440	−	0.0643125i
$63$		0			0
$64$	−4.68423	+	6.48521i	−0.585529	+	0.810651i
$65$	0.783423			0.0971716
$66$		0			0
$67$			7.57396i			0.925307i	0.886539	+	0.462653i	$0.153103\pi$
$67$			7.57396i			0.925307i	−0.886539	+	0.462653i	$0.846897\pi$
$68$	1.85045	−	8.74561i	0.224400	−	1.06056i
$69$		0			0
$70$	−1.41118	−	1.74101i	−0.168669	−	0.208091i
$71$	9.52886			1.13087			0.565434	−	0.824794i	$-0.308709\pi$
$71$	9.52886			1.13087			0.565434	+	0.824794i	$0.308709\pi$
$72$		0			0
$73$	14.1344			1.65431			0.827155	−	0.561975i	$-0.189958\pi$
$73$	14.1344			1.65431			0.827155	+	0.561975i	$0.189958\pi$
$74$	0.306022	+	0.377547i	0.0355743	+	0.0438889i
$75$		0			0
$76$	−14.7867	−	3.12867i	−1.69615	−	0.358883i
$77$		−	0.790533i		−	0.0900896i
$78$		0			0
$79$	−3.71341			−0.417791			−0.208896	−	0.977938i	$-0.566987\pi$
$79$	−3.71341			−0.417791			−0.208896	+	0.977938i	$0.566987\pi$
$80$	2.56747	−	5.79557i	0.287052	−	0.647964i
$81$		0			0
$82$	6.51507	−	5.28081i	0.719469	−	0.583168i
$83$			7.30905i			0.802273i	0.916018	+	0.401136i	$0.131385\pi$
$83$			7.30905i			0.802273i	−0.916018	+	0.401136i	$0.868615\pi$
$84$		0			0
$85$			7.08301i			0.768260i
$86$	2.81547	+	3.47352i	0.303600	+	0.374559i
$87$		0			0
$88$	1.99084	−	1.01788i	0.212225	−	0.108507i
$89$	11.5305			1.22223			0.611114	−	0.791543i	$-0.290722\pi$
$89$	11.5305			1.22223			0.611114	+	0.791543i	$0.290722\pi$
$90$		0			0
$91$		−	0.494366i		−	0.0518236i
$92$	0.347618	−	1.64292i	0.0362417	−	0.171286i
$93$		0			0
$94$	−5.28405	+	4.28300i	−0.545008	+	0.441758i
$95$	11.9757			1.22868
$96$		0			0
$97$	1.75839			0.178538			0.0892689	−	0.996008i	$-0.471547\pi$
$97$	1.75839			0.178538			0.0892689	+	0.996008i	$0.471547\pi$
$98$	−1.09864	+	0.890504i	−0.110979	+	0.0899544i
$99$		0			0
$100$	1.03035	−	4.86963i	0.103035	−	0.486963i
$101$			17.5623i			1.74752i	0.486362	+	0.873758i	$0.338324\pi$
$101$			17.5623i			1.74752i	−0.486362	+	0.873758i	$0.661676\pi$
$102$		0			0
$103$	8.30641			0.818454			0.409227	−	0.912432i	$-0.365798\pi$
$103$	8.30641			0.818454			0.409227	+	0.912432i	$0.365798\pi$
$104$	1.24499	−	0.636540i	0.122081	−	0.0624178i
$105$		0			0
$106$	3.88965	+	4.79876i	0.377796	+	0.466096i
$107$		−	18.7750i		−	1.81505i	−0.419996	−	0.907526i	$-0.637968\pi$
$107$		−	18.7750i		−	1.81505i	0.419996	−	0.907526i	$-0.362032\pi$
$108$		0			0
$109$			0.165074i			0.0158113i	0.999969	+	0.00790563i	$0.00251646\pi$
$109$			0.165074i			0.0158113i	−0.999969	+	0.00790563i	$0.997484\pi$
$110$	−1.37633	+	1.11559i	−0.131228	+	0.106367i
$111$		0			0
$112$	−3.65720	−	1.62016i	−0.345573	−	0.153090i
$113$	−10.8486			−1.02055			−0.510275	−	0.860012i	$-0.670456\pi$
$113$	−10.8486			−1.02055			−0.510275	+	0.860012i	$0.670456\pi$
$114$		0			0
$115$			1.33059i			0.124078i
$116$	5.40899	+	1.14447i	0.502212	+	0.106261i
$117$		0			0
$118$	4.01437	+	4.95263i	0.369553	+	0.455927i
$119$	4.46962			0.409729
$120$		0			0
$121$	10.3751			0.943187
$122$	4.80964	+	5.93377i	0.435444	+	0.537219i
$123$		0			0
$124$	−0.235431	+	1.11269i	−0.0211423	+	0.0999229i
$125$			11.8674i			1.06145i
$126$		0			0
$127$	21.0320			1.86629			0.933145	−	0.359499i	$-0.117052\pi$
$127$	21.0320			1.86629			0.933145	+	0.359499i	$0.117052\pi$
$128$	−0.628830	−	11.2962i	−0.0555813	−	0.998454i
$129$		0			0
$130$	−0.860697	+	0.697641i	−0.0754881	+	0.0611871i
$131$			5.17978i			0.452560i	0.974062	+	0.226280i	$0.0726564\pi$
$131$			5.17978i			0.452560i	−0.974062	+	0.226280i	$0.927344\pi$
$132$		0			0
$133$		−	7.55705i		−	0.655279i
$134$	−6.74464	−	8.32104i	−0.582648	−	0.718828i
$135$		0			0
$136$	5.75502	+	11.2561i	0.493489	+	0.965201i
$137$	−8.19905			−0.700492			−0.350246	−	0.936658i	$-0.613902\pi$
$137$	−8.19905			−0.700492			−0.350246	+	0.936658i	$0.613902\pi$
$138$		0			0
$139$		−	3.89763i		−	0.330593i	−0.986244	−	0.165296i	$-0.947142\pi$
$139$		−	3.89763i		−	0.330593i	0.986244	−	0.165296i	$-0.0528581\pi$
$140$	3.10076	+	0.656077i	0.262062	+	0.0554486i
$141$		0			0
$142$	−10.4688	+	8.48548i	−0.878518	+	0.712086i
$143$	−0.390813			−0.0326814
$144$		0			0
$145$	−4.38070			−0.363798
$146$	−15.5286	+	12.5868i	−1.28516	+	1.04169i
$147$		0			0
$148$	−0.672414	−	0.142273i	−0.0552721	−	0.0116948i
$149$			3.71034i			0.303963i	0.988383	+	0.151981i	$0.0485654\pi$
$149$			3.71034i			0.303963i	−0.988383	+	0.151981i	$0.951435\pi$
$150$		0			0
$151$	−4.08172			−0.332165			−0.166083	−	0.986112i	$-0.553112\pi$
$151$	−4.08172			−0.332165			−0.166083	+	0.986112i	$0.553112\pi$
$152$	19.0313	−	9.73036i	1.54365	−	0.789237i
$153$		0			0
$154$	0.703973	+	0.868509i	0.0567277	+	0.0699865i
$155$		−	0.901163i		−	0.0723832i
$156$		0			0
$157$			9.64250i			0.769555i	0.923009	+	0.384778i	$0.125722\pi$
$157$			9.64250i			0.769555i	−0.923009	+	0.384778i	$0.874278\pi$
$158$	4.07969	−	3.30680i	0.324563	−	0.263075i
$159$		0			0
$160$	2.34026	+	8.65356i	0.185014	+	0.684124i
$161$	0.839644			0.0661732
$162$		0			0
$163$		−	6.79301i		−	0.532069i	−0.963963	−	0.266035i	$-0.914286\pi$
$163$		−	6.79301i		−	0.532069i	0.963963	−	0.266035i	$-0.0857136\pi$
$164$	−2.45512	+	11.6034i	−0.191712	+	0.906072i
$165$		0			0
$166$	−6.50874	−	8.03000i	−0.505176	−	0.623249i
$167$	5.35614			0.414471			0.207235	−	0.978291i	$-0.433553\pi$
$167$	5.35614			0.414471			0.207235	+	0.978291i	$0.433553\pi$
$168$		0			0
$169$	12.7556			0.981200
$170$	−6.30745	−	7.78166i	−0.483759	−	0.596826i
$171$		0			0
$172$	−6.18636	−	1.30895i	−0.471705	−	0.0998064i
$173$			15.3862i			1.16979i	0.811110	+	0.584894i	$0.198864\pi$
$173$			15.3862i			1.16979i	−0.811110	+	0.584894i	$0.801136\pi$
$174$		0			0
$175$	2.48872			0.188129
$176$	−1.28079	+	2.89114i	−0.0965431	+	0.217928i
$177$		0			0
$178$	−12.6678	+	10.2679i	−0.949492	+	0.769614i
$179$		−	19.5360i		−	1.46019i	−0.683347	−	0.730094i	$-0.739476\pi$
$179$		−	19.5360i		−	1.46019i	0.683347	−	0.730094i	$-0.260524\pi$
$180$		0			0
$181$		−	1.07045i		−	0.0795657i	−0.999208	−	0.0397828i	$-0.987333\pi$
$181$		−	1.07045i		−	0.0795657i	0.999208	−	0.0397828i	$-0.0126666\pi$
$182$	0.440235	+	0.543129i	0.0326324	+	0.0402594i
$183$		0			0
$184$	1.08112	+	2.11452i	0.0797009	+	0.155885i
$185$	0.544583			0.0400386
$186$		0			0
$187$		−	3.53338i		−	0.258386i
$188$	1.99122	−	9.41093i	0.145225	−	0.686362i
$189$		0			0
$190$	−13.1569	+	10.6644i	−0.954503	+	0.773675i
$191$	−17.7019			−1.28086			−0.640431	−	0.768016i	$-0.721244\pi$
$191$	−17.7019			−1.28086			−0.640431	+	0.768016i	$0.721244\pi$
$192$		0			0
$193$	−10.5405			−0.758719			−0.379359	−	0.925249i	$-0.623856\pi$
$193$	−10.5405			−0.758719			−0.379359	+	0.925249i	$0.623856\pi$
$194$	−1.93184	+	1.56586i	−0.138698	+	0.112422i
$195$		0			0
$196$	0.414007	−	1.95668i	0.0295719	−	0.139763i
$197$			15.1573i			1.07991i	0.841692	+	0.539957i	$0.181560\pi$
$197$			15.1573i			1.07991i	−0.841692	+	0.539957i	$0.818440\pi$
$198$		0			0
$199$	19.8834			1.40950			0.704750	−	0.709456i	$-0.251059\pi$
$199$	19.8834			1.40950			0.704750	+	0.709456i	$0.251059\pi$
$200$	3.20444	+	6.26748i	0.226588	+	0.443178i
$201$		0			0
$202$	−15.6393	−	19.2946i	−1.10038	−	1.35756i
$203$			2.76437i			0.194021i
$204$		0			0
$205$		−	9.39751i		−	0.656350i
$206$	−9.12572	+	7.39688i	−0.635819	+	0.515365i
$207$		0			0
$208$	−0.800950	+	1.80799i	−0.0555359	+	0.125362i
$209$	−5.97410			−0.413237
$210$		0			0
$211$			26.0319i			1.79211i	0.443942	+	0.896055i	$0.353580\pi$
$211$			26.0319i			1.79211i	−0.443942	+	0.896055i	$0.646420\pi$
$212$	−8.54662	−	1.80835i	−0.586984	−	0.124198i
$213$		0			0
$214$	16.7192	+	20.6270i	1.14290	+	1.41003i
$215$	5.01029			0.341699
$216$		0			0
$217$	−0.568664			−0.0386034
$218$	−0.146999	−	0.181357i	−0.00995605	−	0.0122830i
$219$		0			0
$220$	0.518651	−	2.45125i	0.0349674	−	0.165263i
$221$		−	2.20963i		−	0.148635i
$222$		0			0
$223$	21.1231			1.41451			0.707255	−	0.706959i	$-0.249933\pi$
$223$	21.1231			1.41451			0.707255	+	0.706959i	$0.249933\pi$
$224$	5.46069	−	1.47678i	0.364858	−	0.0986717i
$225$		0			0
$226$	11.9187	−	9.66071i	0.792817	−	0.642621i
$227$		−	9.07343i		−	0.602224i	−0.953589	−	0.301112i	$-0.902642\pi$
$227$		−	9.07343i		−	0.602224i	0.953589	−	0.301112i	$-0.0973579\pi$
$228$		0			0
$229$			15.8950i			1.05037i	0.850987	+	0.525187i	$0.176005\pi$
$229$			15.8950i			1.05037i	−0.850987	+	0.525187i	$0.823995\pi$
$230$	−1.18489	−	1.46183i	−0.0781295	−	0.0963903i
$231$		0			0
$232$	−6.96167	+	3.55937i	−0.457056	+	0.233684i
$233$	−25.2633			−1.65505			−0.827527	−	0.561426i	$-0.810253\pi$
$233$	−25.2633			−1.65505			−0.827527	+	0.561426i	$0.810253\pi$
$234$		0			0
$235$			7.62185i			0.497194i
$236$	−8.82068	−	1.86633i	−0.574177	−	0.121488i
$237$		0			0
$238$	−4.91049	+	3.98021i	−0.318299	+	0.257999i
$239$	3.13797			0.202979			0.101489	−	0.994837i	$-0.467639\pi$
$239$	3.13797			0.202979			0.101489	+	0.994837i	$0.467639\pi$
$240$		0			0
$241$	7.05736			0.454604			0.227302	−	0.973824i	$-0.427009\pi$
$241$	7.05736			0.454604			0.227302	+	0.973824i	$0.427009\pi$
$242$	−11.3984	+	9.23903i	−0.732718	+	0.593907i
$243$		0			0
$244$	−10.5681	−	2.23606i	−0.676553	−	0.143149i
$245$			1.58470i			0.101243i
$246$		0			0
$247$	−3.73595			−0.237713
$248$	−0.732205	−	1.43210i	−0.0464951	−	0.0909384i
$249$		0			0
$250$	−10.5680	−	13.0380i	−0.668376	−	0.824593i
$251$		−	12.8195i		−	0.809158i	−0.914503	−	0.404579i	$-0.867418\pi$
$251$		−	12.8195i		−	0.809158i	0.914503	−	0.404579i	$-0.132582\pi$
$252$		0			0
$253$		−	0.663767i		−	0.0417307i
$254$	−23.1066	+	18.7291i	−1.44983	+	1.17517i
$255$		0			0
$256$	10.7502	+	11.8505i	0.671886	+	0.740654i
$257$	−11.1680			−0.696639			−0.348319	−	0.937376i	$-0.613248\pi$
$257$	−11.1680			−0.696639			−0.348319	+	0.937376i	$0.613248\pi$
$258$		0			0
$259$		−	0.343650i		−	0.0213534i
$260$	0.324342	−	1.53291i	0.0201148	−	0.0950669i
$261$		0			0
$262$	−4.61262	−	5.69070i	−0.284968	−	0.351573i
$263$	15.1277			0.932817			0.466408	−	0.884570i	$-0.345548\pi$
$263$	15.1277			0.932817			0.466408	+	0.884570i	$0.345548\pi$
$264$		0			0
$265$	6.92185			0.425206
$266$	6.72958	+	8.30245i	0.412617	+	0.509056i
$267$		0			0
$268$	14.8198	+	3.13567i	0.905265	+	0.191542i
$269$			4.70567i			0.286910i	0.989657	+	0.143455i	$0.0458212\pi$
$269$			4.70567i			0.286910i	−0.989657	+	0.143455i	$0.954179\pi$
$270$		0			0
$271$	−19.6194			−1.19179			−0.595897	−	0.803061i	$-0.703203\pi$
$271$	−19.6194			−1.19179			−0.595897	+	0.803061i	$0.703203\pi$
$272$	−16.3463	−	7.24148i	−0.991138	−	0.439079i
$273$		0			0
$274$	9.00778	−	7.30129i	0.544180	−	0.441087i
$275$		−	1.96742i		−	0.118640i
$276$		0			0
$277$		−	10.0661i		−	0.604811i	−0.953179	−	0.302406i	$-0.902210\pi$
$277$		−	10.0661i		−	0.604811i	0.953179	−	0.302406i	$-0.0977897\pi$
$278$	3.47086	+	4.28208i	0.208168	+	0.256822i
$279$		0			0
$280$	−3.99084	+	2.04044i	−0.238499	+	0.121940i
$281$	−28.6669			−1.71013			−0.855063	−	0.518525i	$-0.826481\pi$
$281$	−28.6669			−1.71013			−0.855063	+	0.518525i	$0.826481\pi$
$282$		0			0
$283$		−	8.69308i		−	0.516750i	−0.966045	−	0.258375i	$-0.916813\pi$
$283$		−	8.69308i		−	0.516750i	0.966045	−	0.258375i	$-0.0831870\pi$
$284$	3.94501	−	18.6449i	0.234093	−	1.10637i
$285$		0			0
$286$	0.429361	−	0.348020i	0.0253887	−	0.0205789i
$287$	−5.93014			−0.350045
$288$		0			0
$289$	2.97746			0.175145
$290$	4.81280	−	3.90103i	0.282618	−	0.229077i
$291$		0			0
$292$	5.85174	−	27.6565i	0.342447	−	1.61848i
$293$		−	23.9254i		−	1.39774i	−0.715250	−	0.698868i	$-0.753687\pi$
$293$		−	23.9254i		−	1.39774i	0.715250	−	0.698868i	$-0.246313\pi$
$294$		0			0
$295$	7.14381			0.415928
$296$	0.865434	−	0.442480i	0.0503023	−	0.0257186i
$297$		0			0
$298$	−3.30407	−	4.07631i	−0.191400	−	0.236134i
$299$		−	0.415091i		−	0.0240054i
$300$		0			0
$301$		−	3.16166i		−	0.182235i
$302$	4.48432	−	3.63478i	0.258044	−	0.209158i
$303$		0			0
$304$	−12.2436	+	27.6376i	−0.702219	+	1.58513i
$305$	8.55903			0.490089
$306$		0			0
$307$		−	7.88720i		−	0.450146i	−0.974342	−	0.225073i	$-0.927738\pi$
$307$		−	7.88720i		−	0.450146i	0.974342	−	0.225073i	$-0.0722621\pi$
$308$	−1.54682	−	0.327286i	−0.0881383	−	0.0186489i
$309$		0			0
$310$	0.802489	+	0.990051i	0.0455783	+	0.0562311i
$311$	34.7041			1.96789			0.983944	−	0.178480i	$-0.0571179\pi$
$311$	34.7041			1.96789			0.983944	+	0.178480i	$0.0571179\pi$
$312$		0			0
$313$	−11.2387			−0.635249			−0.317624	−	0.948217i	$-0.602885\pi$
$313$	−11.2387			−0.635249			−0.317624	+	0.948217i	$0.602885\pi$
$314$	−8.58668	−	10.5936i	−0.484574	−	0.597832i
$315$		0			0
$316$	−1.53738	+	7.26596i	−0.0864842	+	0.408742i
$317$		−	30.2902i		−	1.70127i	−0.525761	−	0.850633i	$-0.676219\pi$
$317$		−	30.2902i		−	1.70127i	0.525761	−	0.850633i	$-0.323781\pi$
$318$		0			0
$319$	2.18533			0.122355
$320$	−10.2771	−	7.42312i	−0.574509	−	0.414965i
$321$		0			0
$322$	−0.922464	+	0.747706i	−0.0514069	+	0.0416680i
$323$		−	33.7771i		−	1.87941i
$324$		0			0
$325$		−	1.23034i		−	0.0682469i
$326$	6.04920	+	7.46305i	0.335034	+	0.413340i
$327$		0			0
$328$	−7.63558	−	14.9342i	−0.421604	−	0.824603i
$329$	4.80964			0.265164
$330$		0			0
$331$		−	20.2855i		−	1.11499i	−0.830180	−	0.557495i	$-0.811763\pi$
$331$		−	20.2855i		−	1.11499i	0.830180	−	0.557495i	$-0.188237\pi$
$332$	14.3015	+	3.02600i	0.784896	+	0.166073i
$333$		0			0
$334$	−5.88445	+	4.76966i	−0.321983	+	0.260984i
$335$	−12.0025			−0.655765
$336$		0			0
$337$	2.73774			0.149134			0.0745671	−	0.997216i	$-0.476242\pi$
$337$	2.73774			0.149134			0.0745671	+	0.997216i	$0.476242\pi$
$338$	−14.0138	+	11.3589i	−0.762249	+	0.617843i
$339$		0			0
$340$	13.8592	+	2.93241i	0.751620	+	0.159032i
$341$			0.449548i			0.0243444i
$342$		0			0
$343$	1.00000			0.0539949
$344$	7.96219	−	4.07092i	0.429292	−	0.219489i
$345$		0			0
$346$	−13.7014	−	16.9038i	−0.736593	−	0.908754i
$347$		−	5.91592i		−	0.317583i	−0.987312	−	0.158792i	$-0.949240\pi$
$347$		−	5.91592i		−	0.317583i	0.987312	−	0.158792i	$-0.0507598\pi$
$348$		0			0
$349$		−	26.5968i		−	1.42370i	−0.702333	−	0.711848i	$-0.747858\pi$
$349$		−	26.5968i		−	1.42370i	0.702333	−	0.711848i	$-0.252142\pi$
$350$	−2.73420	+	2.21621i	−0.146149	+	0.118462i
$351$		0			0
$352$	−1.16745	−	4.31686i	−0.0622251	−	0.230089i
$353$	−21.8800			−1.16455			−0.582277	−	0.812990i	$-0.697838\pi$
$353$	−21.8800			−1.16455			−0.582277	+	0.812990i	$0.697838\pi$
$354$		0			0
$355$			15.1004i			0.801446i
$356$	4.77369	−	22.5615i	0.253005	−	1.19575i
$357$		0			0
$358$	17.3969	+	21.4630i	0.919453	+	1.13435i
$359$	−18.4834			−0.975519			−0.487759	−	0.872978i	$-0.662186\pi$
$359$	−18.4834			−0.975519			−0.487759	+	0.872978i	$0.662186\pi$
$360$		0			0
$361$	−38.1090			−2.00573
$362$	0.953237	+	1.17603i	0.0501010	+	0.0618109i
$363$		0			0
$364$	−0.967316	−	0.204671i	−0.0507011	−	0.0107277i
$365$			22.3989i			1.17241i
$366$		0			0
$367$	−32.8686			−1.71573			−0.857863	−	0.513878i	$-0.828208\pi$
$367$	−32.8686			−1.71573			−0.857863	+	0.513878i	$0.828208\pi$
$368$	−3.07074	−	1.36036i	−0.160074	−	0.0709134i
$369$		0			0
$370$	−0.598299	+	0.484953i	−0.0311041	+	0.0252115i
$371$		−	4.36792i		−	0.226771i
$372$		0			0
$373$			4.11202i			0.212912i	0.994317	+	0.106456i	$0.0339504\pi$
$373$			4.11202i			0.212912i	−0.994317	+	0.106456i	$0.966050\pi$
$374$	3.14649	+	3.88190i	0.162701	+	0.200728i
$375$		0			0
$376$	6.19283	+	12.1124i	0.319371	+	0.624649i
$377$	1.36661			0.0703840
$378$		0			0
$379$			10.6063i			0.544811i	0.962183	+	0.272406i	$0.0878192\pi$
$379$			10.6063i			0.544811i	−0.962183	+	0.272406i	$0.912181\pi$
$380$	4.95801	−	23.4326i	0.254340	−	1.20206i
$381$		0			0
$382$	19.4479	−	15.7636i	0.995042	−	0.806534i
$383$	−0.193380			−0.00988125			−0.00494063	−	0.999988i	$-0.501573\pi$
$383$	−0.193380			−0.00988125			−0.00494063	+	0.999988i	$0.501573\pi$
$384$		0			0
$385$	1.25276			0.0638466
$386$	11.5801	−	9.38631i	0.589413	−	0.477751i
$387$		0			0
$388$	0.727987	−	3.44062i	0.0369579	−	0.174671i
$389$			30.2102i			1.53172i	0.643008	+	0.765859i	$0.277686\pi$
$389$			30.2102i			1.53172i	−0.643008	+	0.765859i	$0.722314\pi$
$390$		0			0
$391$	3.75289			0.189792
$392$	1.28759	+	2.51836i	0.0650330	+	0.127196i
$393$		0			0
$394$	−13.4976	−	16.6524i	−0.680002	−	0.838935i
$395$		−	5.88465i		−	0.296089i
$396$		0			0
$397$		−	19.1773i		−	0.962480i	−0.876589	−	0.481240i	$-0.840186\pi$
$397$		−	19.1773i		−	0.962480i	0.876589	−	0.481240i	$-0.159814\pi$
$398$	−21.8447	+	17.7063i	−1.09497	+	0.887535i
$399$		0			0
$400$	−9.10174	−	4.03212i	−0.455087	−	0.201606i
$401$	−33.6813			−1.68196			−0.840981	−	0.541065i	$-0.818021\pi$
$401$	−33.6813			−1.68196			−0.840981	+	0.541065i	$0.818021\pi$
$402$		0			0
$403$			0.281128i			0.0140040i
$404$	34.3638	+	7.27091i	1.70966	+	0.361741i
$405$		0			0
$406$	−2.46168	−	3.03704i	−0.122171	−	0.150726i
$407$	−0.271667			−0.0134660
$408$		0			0
$409$	15.0414			0.743751			0.371876	−	0.928283i	$-0.378715\pi$
$409$	15.0414			0.743751			0.371876	+	0.928283i	$0.378715\pi$
$410$	8.36851	+	10.3244i	0.413291	+	0.509888i
$411$		0			0
$412$	3.43891	−	16.2530i	0.169423	−	0.800727i
$413$		−	4.50798i		−	0.221823i
$414$		0			0
$415$	−11.5827			−0.568571
$416$	−0.730071	−	2.69958i	−0.0357947	−	0.132358i
$417$		0			0
$418$	6.56336	−	5.31996i	0.321025	−	0.260208i
$419$		−	15.8239i		−	0.773048i	−0.922279	−	0.386524i	$-0.873676\pi$
$419$		−	15.8239i		−	0.773048i	0.922279	−	0.386524i	$-0.126324\pi$
$420$		0			0
$421$		−	2.62118i		−	0.127748i	−0.997958	−	0.0638742i	$-0.979654\pi$
$421$		−	2.62118i		−	0.127748i	0.997958	−	0.0638742i	$-0.0203457\pi$
$422$	−23.1815	−	28.5996i	−1.12846	−	1.39221i
$423$		0			0
$424$	11.0000	−	5.62408i	0.534206	−	0.273129i
$425$	11.1236			0.539575
$426$		0			0
$427$		−	5.40103i		−	0.261374i
$428$	−36.7368	−	7.77299i	−1.77574	−	0.375722i
$429$		0			0
$430$	−5.50449	+	4.46168i	−0.265450	+	0.215161i
$431$	−21.5464			−1.03785			−0.518927	−	0.854819i	$-0.673668\pi$
$431$	−21.5464			−1.03785			−0.518927	+	0.854819i	$0.673668\pi$
$432$		0			0
$433$	12.4258			0.597145			0.298572	−	0.954387i	$-0.403490\pi$
$433$	12.4258			0.597145			0.298572	+	0.954387i	$0.403490\pi$
$434$	0.624755	−	0.506397i	0.0299892	−	0.0243079i
$435$		0			0
$436$	0.322998	+	0.0683419i	0.0154688	+	0.00327298i
$437$		−	6.34523i		−	0.303534i
$438$		0			0
$439$	−24.2735			−1.15851			−0.579256	−	0.815146i	$-0.696657\pi$
$439$	−24.2735			−1.15851			−0.579256	+	0.815146i	$0.696657\pi$
$440$	1.61304	+	3.15490i	0.0768986	+	0.150404i
$441$		0			0
$442$	1.96768	+	2.42758i	0.0935930	+	0.115468i
$443$			0.931584i			0.0442609i	0.999755	+	0.0221304i	$0.00704492\pi$
$443$			0.931584i			0.0442609i	−0.999755	+	0.0221304i	$0.992955\pi$
$444$		0			0
$445$			18.2724i			0.866193i
$446$	−23.2067	+	18.8102i	−1.09887	+	0.890690i
$447$		0			0
$448$	−4.68423	+	6.48521i	−0.221309	+	0.306397i
$449$	20.8693			0.984883			0.492441	−	0.870346i	$-0.336105\pi$
$449$	20.8693			0.984883			0.492441	+	0.870346i	$0.336105\pi$
$450$		0			0
$451$			4.68797i			0.220748i
$452$	−4.49139	+	21.2272i	−0.211257	+	0.998444i
$453$		0			0
$454$	8.07992	+	9.96840i	0.379209	+	0.467840i
$455$	0.783423			0.0367274
$456$		0			0
$457$	−31.3346			−1.46577			−0.732885	−	0.680353i	$-0.761827\pi$
$457$	−31.3346			−1.46577			−0.732885	+	0.680353i	$0.761827\pi$
$458$	−14.1546	−	17.4629i	−0.661401	−	0.815987i
$459$		0			0
$460$	2.60353	+	0.550871i	0.121390	+	0.0256845i
$461$			1.90910i			0.0889156i	0.999011	+	0.0444578i	$0.0141560\pi$
$461$			1.90910i			0.0889156i	−0.999011	+	0.0444578i	$0.985844\pi$
$462$		0			0
$463$	18.6081			0.864793			0.432397	−	0.901683i	$-0.357668\pi$
$463$	18.6081			0.864793			0.432397	+	0.901683i	$0.357668\pi$
$464$	4.47872	−	10.1098i	0.207919	−	0.469338i
$465$		0			0
$466$	27.7552	−	22.4971i	1.28573	−	1.04216i
$467$			17.7972i			0.823554i	0.911285	+	0.411777i	$0.135092\pi$
$467$			17.7972i			0.823554i	−0.911285	+	0.411777i	$0.864908\pi$
$468$		0			0
$469$			7.57396i			0.349733i
$470$	−6.78728	−	8.37364i	−0.313074	−	0.386247i
$471$		0			0
$472$	11.3527	−	5.80442i	0.522550	−	0.267170i
$473$	−2.49940			−0.114922
$474$		0			0
$475$		−	18.8074i		−	0.862941i
$476$	1.85045	−	8.74561i	0.0848153	−	0.400854i
$477$		0			0
$478$	−3.44749	+	2.79438i	−0.157685	+	0.127812i
$479$	21.6737			0.990294			0.495147	−	0.868809i	$-0.335114\pi$
$479$	21.6737			0.990294			0.495147	+	0.868809i	$0.335114\pi$
$480$		0			0
$481$	−0.169889			−0.00774627
$482$	−7.75347	+	6.28460i	−0.353161	+	0.286256i
$483$		0			0
$484$	4.29534	−	20.3007i	0.195243	−	0.922758i
$485$			2.78653i			0.126530i
$486$		0			0
$487$	−38.6259			−1.75030			−0.875152	−	0.483848i	$-0.839239\pi$
$487$	−38.6259			−1.75030			−0.875152	+	0.483848i	$0.839239\pi$
$488$	13.6017	−	6.95431i	0.615721	−	0.314807i
$489$		0			0
$490$	−1.41118	−	1.74101i	−0.0637508	−	0.0786509i
$491$		−	17.9010i		−	0.807863i	−0.914789	−	0.403931i	$-0.867643\pi$
$491$		−	17.9010i		−	0.807863i	0.914789	−	0.403931i	$-0.132357\pi$
$492$		0			0
$493$			12.3557i			0.556472i
$494$	4.10445	−	3.32687i	0.184668	−	0.149683i
$495$		0			0
$496$	2.07972	+	0.921325i	0.0933820	+	0.0413687i
$497$	9.52886			0.427428
$498$		0			0
$499$			24.3201i			1.08872i	0.838853	+	0.544359i	$0.183227\pi$
$499$			24.3201i			1.08872i	−0.838853	+	0.544359i	$0.816773\pi$
$500$	23.2207	+	4.91318i	1.03846	+	0.219724i
$501$		0			0
$502$	11.4158	+	14.0840i	0.509512	+	0.628598i
$503$	−36.3076			−1.61888			−0.809438	−	0.587205i	$-0.800228\pi$
$503$	−36.3076			−1.61888			−0.809438	+	0.587205i	$0.800228\pi$
$504$		0			0
$505$	−27.8310			−1.23846
$506$	0.591087	+	0.729239i	0.0262770	+	0.0324186i
$507$		0			0
$508$	8.70740	−	41.1530i	0.386328	−	1.82587i
$509$		−	3.12375i		−	0.138458i	−0.997601	−	0.0692290i	$-0.977946\pi$
$509$		−	3.12375i		−	0.138458i	0.997601	−	0.0692290i	$-0.0220539\pi$
$510$		0			0
$511$	14.1344			0.625270
$512$	−22.3634	−	3.44629i	−0.988333	−	0.152306i
$513$		0			0
$514$	12.2695	−	9.94512i	0.541186	−	0.438660i
$515$			13.1632i			0.580039i
$516$		0			0
$517$		−	3.80218i		−	0.167220i
$518$	0.306022	+	0.377547i	0.0134458	+	0.0165885i
$519$		0			0
$520$	1.00873	+	1.97294i	0.0442355	+	0.0865190i
$521$	1.68044			0.0736213			0.0368107	−	0.999322i	$-0.488280\pi$
$521$	1.68044			0.0736213			0.0368107	+	0.999322i	$0.488280\pi$
$522$		0			0
$523$		−	26.5738i		−	1.16199i	−0.813906	−	0.580996i	$-0.802663\pi$
$523$		−	26.5738i		−	1.16199i	0.813906	−	0.580996i	$-0.197337\pi$
$524$	10.1352	+	2.14446i	0.442757	+	0.0936814i
$525$		0			0
$526$	−16.6199	+	13.4713i	−0.724662	+	0.587377i
$527$	−2.54171			−0.110719
$528$		0			0
$529$	−22.2950			−0.969348
$530$	−7.60460	+	6.16393i	−0.330323	+	0.267744i
$531$		0			0
$532$	−14.7867	−	3.12867i	−0.641086	−	0.135645i
$533$			2.93166i			0.126984i
$534$		0			0
$535$	29.7529			1.28633
$536$	−19.0739	+	9.75214i	−0.823868	+	0.421228i
$537$		0			0
$538$	−4.19041	−	5.16982i	−0.180662	−	0.222887i
$539$		−	0.790533i		−	0.0340507i
$540$		0			0
$541$			26.0022i			1.11792i	0.829194	+	0.558962i	$0.188800\pi$
$541$			26.0022i			1.11792i	−0.829194	+	0.558962i	$0.811200\pi$
$542$	21.5546	−	17.4712i	0.925850	−	0.750450i
$543$		0			0
$544$	24.4072	−	6.60065i	1.04645	−	0.283001i
$545$	−0.261594			−0.0112054
$546$		0			0
$547$		−	13.4108i		−	0.573406i	−0.958019	−	0.286703i	$-0.907441\pi$
$547$		−	13.4108i		−	0.573406i	0.958019	−	0.286703i	$-0.0925594\pi$
$548$	−3.39446	+	16.0429i	−0.145004	+	0.685320i
$549$		0			0
$550$	1.75199	+	2.16148i	0.0747051	+	0.0921656i
$551$	20.8905			0.889964
$552$		0			0
$553$	−3.71341			−0.157910
$554$	8.96387	+	11.0590i	0.380838	+	0.469850i
$555$		0			0
$556$	−7.62642	−	1.61365i	−0.323432	−	0.0684338i
$557$			38.9728i			1.65133i	0.564161	+	0.825665i	$0.309200\pi$
$557$			38.9728i			1.65133i	−0.564161	+	0.825665i	$0.690800\pi$
$558$		0			0
$559$	−1.56302			−0.0661086
$560$	2.56747	−	5.79557i	0.108495	−	0.244907i
$561$		0			0
$562$	31.4945	−	25.5280i	1.32852	−	1.07683i
$563$			15.8415i			0.667642i	0.942637	+	0.333821i	$0.108338\pi$
$563$			15.8415i			0.667642i	−0.942637	+	0.333821i	$0.891662\pi$
$564$		0			0
$565$		−	17.1918i		−	0.723264i
$566$	7.74122	+	9.55054i	0.325388	+	0.401439i
$567$		0			0
$568$	12.2692	+	23.9971i	0.514806	+	1.00689i
$569$	17.4790			0.732758			0.366379	−	0.930466i	$-0.380597\pi$
$569$	17.4790			0.732758			0.366379	+	0.930466i	$0.380597\pi$
$570$		0			0
$571$		−	11.4195i		−	0.477893i	−0.971033	−	0.238946i	$-0.923198\pi$
$571$		−	11.4195i		−	0.477893i	0.971033	−	0.238946i	$-0.0768020\pi$
$572$	−0.161799	+	0.764696i	−0.00676516	+	0.0319735i
$573$		0			0
$574$	6.51507	−	5.28081i	0.271934	−	0.220417i
$575$	2.08964			0.0871439
$576$		0			0
$577$	27.4108			1.14113			0.570564	−	0.821253i	$-0.306725\pi$
$577$	27.4108			1.14113			0.570564	+	0.821253i	$0.306725\pi$
$578$	−3.27115	+	2.65144i	−0.136062	+	0.110285i
$579$		0			0
$580$	−1.81364	+	8.57164i	−0.0753073	+	0.355918i
$581$			7.30905i			0.303231i
$582$		0			0
$583$	−3.45299			−0.143008
$584$	18.1993	+	35.5955i	0.753093	+	1.47295i
$585$		0			0
$586$	21.3057	+	26.2853i	0.880128	+	1.08584i
$587$			23.8334i			0.983709i	0.870677	+	0.491855i	$0.163681\pi$
$587$			23.8334i			0.983709i	−0.870677	+	0.491855i	$0.836319\pi$
$588$		0			0
$589$			4.29742i			0.177072i
$590$	−7.84845	+	6.36159i	−0.323116	+	0.261902i
$591$		0			0
$592$	−0.556767	+	1.25680i	−0.0228830	+	0.0516540i
$593$	28.0780			1.15302			0.576512	−	0.817088i	$-0.304413\pi$
$593$	28.0780			1.15302			0.576512	+	0.817088i	$0.304413\pi$
$594$		0			0
$595$			7.08301i			0.290375i
$596$	7.25994	+	1.53610i	0.297379	+	0.0629213i
$597$		0			0
$598$	0.369640	+	0.456035i	0.0151157	+	0.0186487i
$599$	21.6780			0.885738			0.442869	−	0.896586i	$-0.353961\pi$
$599$	21.6780			0.885738			0.442869	+	0.896586i	$0.353961\pi$
$600$		0			0
$601$	5.83369			0.237961			0.118981	−	0.992897i	$-0.462037\pi$
$601$	5.83369			0.237961			0.118981	+	0.992897i	$0.462037\pi$
$602$	2.81547	+	3.47352i	0.114750	+	0.141570i
$603$		0			0
$604$	−1.68986	+	7.98661i	−0.0687593	+	0.324971i
$605$			16.4414i			0.668437i
$606$		0			0
$607$	−29.5358			−1.19882			−0.599410	−	0.800442i	$-0.704598\pi$
$607$	−29.5358			−1.19882			−0.599410	+	0.800442i	$0.704598\pi$
$608$	−11.1601	−	41.2667i	−0.452602	−	1.67358i
$609$		0			0
$610$	−9.40327	+	7.62185i	−0.380727	+	0.308600i
$611$		−	2.37772i		−	0.0961923i
$612$		0			0
$613$			19.5561i			0.789861i	0.918711	+	0.394931i	$0.129231\pi$
$613$			19.5561i			0.789861i	−0.918711	+	0.394931i	$0.870769\pi$
$614$	7.02358	+	8.66516i	0.283448	+	0.349698i
$615$		0			0
$616$	1.99084	−	1.01788i	0.0802134	−	0.0410116i
$617$	−33.8435			−1.36249			−0.681244	−	0.732056i	$-0.738561\pi$
$617$	−33.8435			−1.36249			−0.681244	+	0.732056i	$0.738561\pi$
$618$		0			0
$619$		−	20.6581i		−	0.830320i	−0.909748	−	0.415160i	$-0.863726\pi$
$619$		−	20.6581i		−	0.830320i	0.909748	−	0.415160i	$-0.136274\pi$
$620$	−1.76329	−	0.373088i	−0.0708154	−	0.0149836i
$621$		0			0
$622$	−38.1272	+	30.9041i	−1.52876	+	1.23914i
$623$	11.5305			0.461959
$624$		0			0
$625$	−6.36268			−0.254507
$626$	12.3473	−	10.0081i	0.493495	−	0.400004i
$627$		0			0
$628$	18.8673	+	3.99206i	0.752887	+	0.159300i
$629$		−	1.53598i		−	0.0612437i
$630$		0			0
$631$	−42.3648			−1.68651			−0.843257	−	0.537510i	$-0.819365\pi$
$631$	−42.3648			−1.68651			−0.843257	+	0.537510i	$0.819365\pi$
$632$	−4.78134	−	9.35169i	−0.190192	−	0.371990i
$633$		0			0
$634$	26.9735	+	33.2779i	1.07125	+	1.32163i
$635$			33.3295i			1.32264i
$636$		0			0
$637$		−	0.494366i		−	0.0195875i
$638$	−2.40088	+	1.94604i	−0.0950518	+	0.0770445i
$639$		0			0
$640$	17.9011	−	0.996509i	0.707605	−	0.0393905i
$641$	−11.6219			−0.459039			−0.229519	−	0.973304i	$-0.573715\pi$
$641$	−11.6219			−0.459039			−0.229519	+	0.973304i	$0.573715\pi$
$642$		0			0
$643$			40.4455i			1.59502i	0.603309	+	0.797508i	$0.293849\pi$
$643$			40.4455i			1.59502i	−0.603309	+	0.797508i	$0.706151\pi$
$644$	0.347618	−	1.64292i	0.0136981	−	0.0647399i
$645$		0			0
$646$	30.0786	+	37.1088i	1.18343	+	1.46002i
$647$	29.9913			1.17908			0.589540	−	0.807739i	$-0.299309\pi$
$647$	29.9913			1.17908			0.589540	+	0.807739i	$0.299309\pi$
$648$		0			0
$649$	−3.56371			−0.139888
$650$	1.09562	+	1.35169i	0.0429738	+	0.0530178i
$651$		0			0
$652$	−13.2917	−	2.81235i	−0.520545	−	0.110140i
$653$		−	14.9263i		−	0.584110i	−0.956402	−	0.292055i	$-0.905661\pi$
$653$		−	14.9263i		−	0.584110i	0.956402	−	0.292055i	$-0.0943390\pi$
$654$		0			0
$655$	−8.20842			−0.320729
$656$	21.6877	+	9.60776i	0.846762	+	0.375120i
$657$		0			0
$658$	−5.28405	+	4.28300i	−0.205994	+	0.166969i
$659$		−	27.3581i		−	1.06572i	−0.846204	−	0.532859i	$-0.821117\pi$
$659$		−	27.3581i		−	1.06572i	0.846204	−	0.532859i	$-0.178883\pi$
$660$		0			0
$661$			14.3560i			0.558385i	0.960235	+	0.279192i	$0.0900667\pi$
$661$			14.3560i			0.558385i	−0.960235	+	0.279192i	$0.909933\pi$
$662$	18.0643	+	22.2864i	0.702088	+	0.866184i
$663$		0			0
$664$	−18.4068	+	9.41105i	−0.714322	+	0.365220i
$665$	11.9757			0.464397
$666$		0			0
$667$			2.32109i			0.0898729i
$668$	2.21748	−	10.4803i	0.0857968	−	0.405493i
$669$		0			0
$670$	13.1864	−	10.6882i	0.509434	−	0.412923i
$671$	−4.26970			−0.164830
$672$		0			0
$673$	20.5132			0.790727			0.395364	−	0.918525i	$-0.370619\pi$
$673$	20.5132			0.790727			0.395364	+	0.918525i	$0.370619\pi$
$674$	−3.00778	+	2.43797i	−0.115856	+	0.0939071i
$675$		0			0
$676$	5.28090	−	24.9586i	0.203112	−	0.959948i
$677$		−	43.5656i		−	1.67436i	−0.546926	−	0.837181i	$-0.684202\pi$
$677$		−	43.5656i		−	1.67436i	0.546926	−	0.837181i	$-0.315798\pi$
$678$		0			0
$679$	1.75839			0.0674810
$680$	−17.8375	+	9.12000i	−0.684038	+	0.349736i
$681$		0			0
$682$	−0.400324	−	0.493890i	−0.0153292	−	0.0189120i
$683$			16.9585i			0.648898i	0.945903	+	0.324449i	$0.105179\pi$
$683$			16.9585i			0.648898i	−0.945903	+	0.324449i	$0.894821\pi$
$684$		0			0
$685$		−	12.9931i		−	0.496439i
$686$	−1.09864	+	0.890504i	−0.0419462	+	0.0339996i
$687$		0			0
$688$	−5.12239	+	11.5628i	−0.195289	+	0.440828i
$689$	−2.15935			−0.0822647
$690$		0			0
$691$			27.7324i			1.05499i	0.849558	+	0.527495i	$0.176869\pi$
$691$			27.7324i			1.05499i	−0.849558	+	0.527495i	$0.823131\pi$
$692$	30.1058	+	6.36997i	1.14445	+	0.242150i
$693$		0			0
$694$	5.26815	+	6.49945i	0.199976	+	0.246716i
$695$	6.17659			0.234291
$696$		0			0
$697$	−26.5054			−1.00397
$698$	23.6846	+	29.2203i	0.896475	+	1.10600i
$699$		0			0
$700$	1.03035	−	4.86963i	0.0389434	−	0.184055i
$701$			29.5427i			1.11581i	0.829905	+	0.557905i	$0.188395\pi$
$701$			29.5427i			1.11581i	−0.829905	+	0.557905i	$0.811605\pi$
$702$		0			0
$703$	−2.59698			−0.0979470
$704$	5.12677	+	3.70304i	0.193223	+	0.139564i
$705$		0			0
$706$	24.0382	−	19.4842i	0.904688	−	0.733298i
$707$			17.5623i			0.660499i
$708$		0			0
$709$			45.9348i			1.72512i	0.505955	+	0.862560i	$0.331140\pi$
$709$			45.9348i			1.72512i	−0.505955	+	0.862560i	$0.668860\pi$
$710$	−13.4470	−	16.5899i	−0.504655	−	0.622606i
$711$		0			0
$712$	14.8465	+	29.0378i	0.556396	+	1.08824i
$713$	−0.477476			−0.0178816
$714$		0			0
$715$		−	0.619322i		−	0.0231613i
$716$	−38.2257	−	8.08803i	−1.42856	−	0.302264i
$717$		0			0
$718$	20.3066	−	16.4596i	0.757835	−	0.614266i
$719$	−16.3756			−0.610708			−0.305354	−	0.952239i	$-0.598775\pi$
$719$	−16.3756			−0.610708			−0.305354	+	0.952239i	$0.598775\pi$
$720$		0			0
$721$	8.30641			0.309347
$722$	41.8679	−	33.9362i	1.55816	−	1.26297i
$723$		0			0
$724$	−2.09452	−	0.443172i	−0.0778423	−	0.0164704i
$725$			6.87974i			0.255507i
$726$		0			0
$727$	3.43696			0.127470			0.0637348	−	0.997967i	$-0.479699\pi$
$727$	3.43696			0.127470			0.0637348	+	0.997967i	$0.479699\pi$
$728$	1.24499	−	0.636540i	0.0461424	−	0.0235917i
$729$		0			0
$730$	−19.9463	−	24.6082i	−0.738244	−	0.910791i
$731$		−	14.1314i		−	0.522669i
$732$		0			0
$733$			35.3171i			1.30447i	0.758019	+	0.652233i	$0.226167\pi$
$733$			35.3171i			1.30447i	−0.758019	+	0.652233i	$0.773833\pi$
$734$	36.1107	−	29.2696i	1.33287	−	1.08036i
$735$		0			0
$736$	4.58504	−	1.23997i	0.169007	−	0.0457060i
$737$	5.98747			0.220551
$738$		0			0
$739$			41.3212i			1.52003i	0.649908	+	0.760013i	$0.274807\pi$
$739$			41.3212i			1.52003i	−0.649908	+	0.760013i	$0.725193\pi$
$740$	0.225461	−	1.06558i	0.00828811	−	0.0391713i
$741$		0			0
$742$	3.88965	+	4.79876i	0.142793	+	0.176168i
$743$	22.9110			0.840524			0.420262	−	0.907403i	$-0.361938\pi$
$743$	22.9110			0.840524			0.420262	+	0.907403i	$0.361938\pi$
$744$		0			0
$745$	−5.87978			−0.215418
$746$	−3.66177	−	4.51762i	−0.134067	−	0.165402i
$747$		0			0
$748$	−6.91370	−	1.46284i	−0.252790	−	0.0534868i
$749$		−	18.7750i		−	0.686025i
$750$		0			0
$751$	−48.2764			−1.76163			−0.880815	−	0.473461i	$-0.843005\pi$
$751$	−48.2764			−1.76163			−0.880815	+	0.473461i	$0.843005\pi$
$752$	−17.5898	−	7.79237i	−0.641434	−	0.284159i
$753$		0			0
$754$	−1.50141	+	1.21697i	−0.0546781	+	0.0443195i
$755$		−	6.46830i		−	0.235406i
$756$		0			0
$757$		−	26.9389i		−	0.979112i	−0.871972	−	0.489556i	$-0.837159\pi$
$757$		−	26.9389i		−	0.979112i	0.871972	−	0.489556i	$-0.162841\pi$
$758$	−9.44498	−	11.6525i	−0.343057	−	0.423239i
$759$		0			0
$760$	15.4197	+	30.1590i	0.559332	+	1.09398i
$761$	2.98366			0.108158			0.0540789	−	0.998537i	$-0.482778\pi$
$761$	2.98366			0.108158			0.0540789	+	0.998537i	$0.482778\pi$
$762$		0			0
$763$			0.165074i			0.00597609i
$764$	−7.32869	+	34.6369i	−0.265143	+	1.25312i
$765$		0			0
$766$	0.212454	−	0.172206i	0.00767629	−	0.00622204i
$767$	−2.22859			−0.0804698
$768$		0			0
$769$	1.13907			0.0410760			0.0205380	−	0.999789i	$-0.493462\pi$
$769$	1.13907			0.0410760			0.0205380	+	0.999789i	$0.493462\pi$
$770$	−1.37633	+	1.11559i	−0.0495994	+	0.0402030i
$771$		0			0
$772$	−4.36382	+	20.6243i	−0.157057	+	0.742285i
$773$			8.40051i			0.302145i	0.988523	+	0.151073i	$0.0482728\pi$
$773$			8.40051i			0.302145i	−0.988523	+	0.151073i	$0.951727\pi$
$774$		0			0
$775$	−1.41525			−0.0508371
$776$	2.26409	+	4.42826i	0.0812760	+	0.158965i
$777$		0			0
$778$	−26.9023	−	33.1901i	−0.964494	−	1.18992i
$779$			44.8143i			1.60564i
$780$		0			0
$781$		−	7.53288i		−	0.269548i
$782$	−4.12306	+	3.34196i	−0.147440	+	0.119508i
$783$		0			0
$784$	−3.65720	−	1.62016i	−0.130614	−	0.0578628i
$785$	−15.2805			−0.545384
$786$		0			0
$787$		−	13.6837i		−	0.487771i	−0.969804	−	0.243886i	$-0.921578\pi$
$787$		−	13.6837i		−	0.487771i	0.969804	−	0.243886i	$-0.0784222\pi$
$788$	29.6580	+	6.27523i	1.05652	+	0.223546i
$789$		0			0
$790$	5.24030	+	6.46509i	0.186442	+	0.230018i
$791$	−10.8486			−0.385731
$792$		0			0
$793$	−2.67009			−0.0948175
$794$	17.0774	+	21.0689i	0.606056	+	0.747707i
$795$		0			0
$796$	8.23187	−	38.9055i	0.291771	−	1.37897i
$797$		−	43.1786i		−	1.52946i	−0.644349	−	0.764731i	$-0.722872\pi$
$797$		−	43.1786i		−	1.52946i	0.644349	−	0.764731i	$-0.277128\pi$
$798$		0			0
$799$	21.4972			0.760518
$800$	13.5901	−	3.67530i	0.480483	−	0.129941i
$801$		0			0
$802$	37.0035	−	29.9933i	1.30664	−	1.05910i
$803$		−	11.1737i		−	0.394312i
$804$		0			0
$805$			1.33059i			0.0468970i
$806$	−0.250346	−	0.308858i	−0.00881805	−	0.0108791i
$807$		0			0
$808$	−44.2281	+	22.6130i	−1.55594	+	0.795523i
$809$	24.5341			0.862573			0.431287	−	0.902215i	$-0.358060\pi$
$809$	24.5341			0.862573			0.431287	+	0.902215i	$0.358060\pi$
$810$		0			0
$811$		−	0.566589i		−	0.0198956i	−0.999951	−	0.00994781i	$-0.996833\pi$
$811$		−	0.566589i		−	0.0198956i	0.999951	−	0.00994781i	$-0.00316654\pi$
$812$	5.40899	+	1.14447i	0.189818	+	0.0401629i
$813$		0			0
$814$	0.298463	−	0.241920i	0.0104611	−	0.00847931i
$815$	10.7649			0.377078
$816$		0			0
$817$	−23.8928			−0.835904
$818$	−16.5251	+	13.3945i	−0.577786	+	0.468326i
$819$		0			0
$820$	−18.3879	−	3.89063i	−0.642134	−	0.135867i
$821$			1.22205i			0.0426499i	0.999773	+	0.0213250i	$0.00678846\pi$
$821$			1.22205i			0.0426499i	−0.999773	+	0.0213250i	$0.993212\pi$
$822$		0			0
$823$	−46.7218			−1.62862			−0.814309	−	0.580431i	$-0.802884\pi$
$823$	−46.7218			−1.62862			−0.814309	+	0.580431i	$0.802884\pi$
$824$	10.6952	+	20.9185i	0.372586	+	0.728730i
$825$		0			0
$826$	4.01437	+	4.95263i	0.139678	+	0.172324i
$827$		−	35.2221i		−	1.22479i	−0.790551	−	0.612396i	$-0.790206\pi$
$827$		−	35.2221i		−	1.22479i	0.790551	−	0.612396i	$-0.209794\pi$
$828$		0			0
$829$		−	1.09826i		−	0.0381443i	−0.999818	−	0.0190721i	$-0.993929\pi$
$829$		−	1.09826i		−	0.0381443i	0.999818	−	0.0190721i	$-0.00607122\pi$
$830$	12.7252	−	10.3144i	0.441697	−	0.358018i
$831$		0			0
$832$	3.20607	+	2.31573i	0.111150	+	0.0802833i
$833$	4.46962			0.154863
$834$		0			0
$835$			8.48789i			0.293735i
$836$	−2.47332	+	11.6894i	−0.0855414	+	0.404286i
$837$		0			0
$838$	14.0912	+	17.3847i	0.486774	+	0.600545i
$839$	7.78246			0.268680			0.134340	−	0.990935i	$-0.457109\pi$
$839$	7.78246			0.268680			0.134340	+	0.990935i	$0.457109\pi$
$840$		0			0
$841$	21.3583			0.736492
$842$	2.33417	+	2.87973i	0.0804408	+	0.0992419i
$843$		0			0
$844$	50.9361	+	10.7774i	1.75329	+	0.370973i
$845$			20.2138i			0.695377i
$846$		0			0
$847$	10.3751			0.356491
$848$	−7.07672	+	15.9743i	−0.243015	+	0.548561i
$849$		0			0
$850$	−12.2208	+	9.90562i	−0.419171	+	0.339760i
$851$		−	0.288544i		−	0.00989116i
$852$		0			0
$853$			35.3178i			1.20926i	0.796507	+	0.604630i	$0.206679\pi$
$853$			35.3178i			1.20926i	−0.796507	+	0.604630i	$0.793321\pi$
$854$	4.80964	+	5.93377i	0.164582	+	0.203050i
$855$		0			0
$856$	47.2822	−	24.1745i	1.61607	−	0.826268i
$857$	48.1812			1.64584			0.822919	−	0.568159i	$-0.192344\pi$
$857$	48.1812			1.64584			0.822919	+	0.568159i	$0.192344\pi$
$858$		0			0
$859$			23.2897i			0.794633i	0.917682	+	0.397317i	$0.130059\pi$
$859$			23.2897i			0.794633i	−0.917682	+	0.397317i	$0.869941\pi$
$860$	2.07429	−	9.80354i	0.0707328	−	0.334298i
$861$		0			0
$862$	23.6717	−	19.1871i	0.806260	−	0.653517i
$863$	−22.2727			−0.758173			−0.379086	−	0.925361i	$-0.623762\pi$
$863$	−22.2727			−0.758173			−0.379086	+	0.925361i	$0.623762\pi$
$864$		0			0
$865$	−24.3825			−0.829029
$866$	−13.6514	+	11.0652i	−0.463894	+	0.376011i
$867$		0			0
$868$	−0.235431	+	1.11269i	−0.00799104	+	0.0377673i
$869$			2.93557i			0.0995825i
$870$		0			0
$871$	3.74431			0.126871
$872$	−0.415716	+	0.212548i	−0.0140779	+	0.00719777i
$873$		0			0
$874$	5.65045	+	6.97111i	0.191129	+	0.235801i
$875$			11.8674i			0.401191i
$876$		0			0
$877$		−	52.5939i		−	1.77597i	−0.459872	−	0.887985i	$-0.652105\pi$
$877$		−	52.5939i		−	1.77597i	0.459872	−	0.887985i	$-0.347895\pi$
$878$	26.6678	−	21.6157i	0.899994	−	0.729493i
$879$		0			0
$880$	−4.58159	−	2.02967i	−0.154445	−	0.0684201i
$881$	25.9486			0.874229			0.437115	−	0.899406i	$-0.356000\pi$
$881$	25.9486			0.874229			0.437115	+	0.899406i	$0.356000\pi$
$882$		0			0
$883$		−	6.37782i		−	0.214631i	−0.994225	−	0.107315i	$-0.965775\pi$
$883$		−	6.37782i		−	0.214631i	0.994225	−	0.107315i	$-0.0342255\pi$
$884$	−4.32353	−	0.914800i	−0.145416	−	0.0307680i
$885$		0			0
$886$	−0.829579	−	1.02347i	−0.0278703	−	0.0343842i
$887$	−7.60567			−0.255373			−0.127687	−	0.991815i	$-0.540755\pi$
$887$	−7.60567			−0.255373			−0.127687	+	0.991815i	$0.540755\pi$
$888$		0			0
$889$	21.0320			0.705392
$890$	−16.2716	−	20.0747i	−0.545426	−	0.672905i
$891$		0			0
$892$	8.74511	−	41.3312i	0.292808	−	1.38387i
$893$		−	36.3467i		−	1.21629i
$894$		0			0
$895$	30.9587			1.03484
$896$	−0.628830	−	11.2962i	−0.0210077	−	0.377380i
$897$		0			0
$898$	−22.9278	+	18.5842i	−0.765110	+	0.620162i
$899$		−	1.57200i		−	0.0524291i
$900$		0			0
$901$		−	19.5229i		−	0.650403i
$902$	−4.17466	−	5.15038i	−0.139001	−	0.171489i
$903$		0			0
$904$	−13.9685	−	27.3206i	−0.464586	−	0.908670i
$905$	1.69634			0.0563882
$906$		0			0
$907$		−	21.2861i		−	0.706794i	−0.935473	−	0.353397i	$-0.885026\pi$
$907$		−	21.2861i		−	0.706794i	0.935473	−	0.353397i	$-0.114974\pi$
$908$	−17.7538	−	3.75646i	−0.589180	−	0.124662i
$909$		0			0
$910$	−0.860697	+	0.697641i	−0.0285318	+	0.0231266i
$911$	48.0894			1.59327			0.796637	−	0.604458i	$-0.206610\pi$
$911$	48.0894			1.59327			0.796637	+	0.604458i	$0.206610\pi$
$912$		0			0
$913$	5.77805			0.191226
$914$	34.4253	−	27.9036i	1.13869	−	0.922968i
$915$		0			0
$916$	31.1015	+	6.58066i	1.02762	+	0.217431i
$917$			5.17978i			0.171052i
$918$		0			0
$919$	33.6403			1.10969			0.554846	−	0.831953i	$-0.312777\pi$
$919$	33.6403			1.10969			0.554846	+	0.831953i	$0.312777\pi$
$920$	−3.35089	+	1.71325i	−0.110476	+	0.0564841i
$921$		0			0
$922$	−1.70006	−	2.09741i	−0.0559885	−	0.0690744i
$923$		−	4.71074i		−	0.155056i
$924$		0			0
$925$		−	0.855249i		−	0.0281204i
$926$	−20.4436	+	16.5706i	−0.671818	+	0.544544i
$927$		0			0
$928$	4.08237	+	15.0954i	0.134010	+	0.495530i
$929$	35.9109			1.17820			0.589100	−	0.808060i	$-0.299483\pi$
$929$	35.9109			1.17820			0.589100	+	0.808060i	$0.299483\pi$
$930$		0			0
$931$		−	7.55705i		−	0.247672i
$932$	−10.4592	+	49.4322i	−0.342602	+	1.61921i
$933$		0			0
$934$	−15.8484	−	19.5526i	−0.518577	−	0.639781i
$935$	5.59936			0.183119
$936$		0			0
$937$	6.70862			0.219161			0.109581	−	0.993978i	$-0.465049\pi$
$937$	6.70862			0.219161			0.109581	+	0.993978i	$0.465049\pi$
$938$	−6.74464	−	8.32104i	−0.220220	−	0.271691i
$939$		0			0
$940$	14.9135	+	3.15549i	0.486425	+	0.102921i
$941$			5.81896i			0.189693i	0.995492	+	0.0948464i	$0.0302360\pi$
$941$			5.81896i			0.189693i	−0.995492	+	0.0948464i	$0.969764\pi$
$942$		0			0
$943$	−4.97921			−0.162145
$944$	−7.30364	+	16.4866i	−0.237713	+	0.536592i
$945$		0			0
$946$	2.74593	−	2.22572i	0.0892779	−	0.0723645i
$947$		−	22.8143i		−	0.741365i	−0.928760	−	0.370682i	$-0.879124\pi$
$947$		−	22.8143i		−	0.741365i	0.928760	−	0.370682i	$-0.120876\pi$
$948$		0			0
$949$		−	6.98758i		−	0.226826i
$950$	16.7480	+	20.6625i	0.543378	+	0.670379i
$951$		0			0
$952$	5.75502	+	11.2561i	0.186521	+	0.364812i
$953$	−0.659700			−0.0213698			−0.0106849	−	0.999943i	$-0.503401\pi$
$953$	−0.659700			−0.0213698			−0.0106849	+	0.999943i	$0.503401\pi$
$954$		0			0
$955$		−	28.0522i		−	0.907747i
$956$	1.29914	−	6.14001i	0.0420173	−	0.198582i
$957$		0			0
$958$	−23.8115	+	19.3005i	−0.769314	+	0.623570i
$959$	−8.19905			−0.264761
$960$		0			0
$961$	−30.6766			−0.989568
$962$	0.186646	−	0.151287i	0.00601772	−	0.00487768i
$963$		0			0
$964$	2.92179	−	13.8090i	0.0941046	−	0.444758i
$965$		−	16.7035i		−	0.537704i
$966$		0			0
$967$	−3.46722			−0.111498			−0.0557491	−	0.998445i	$-0.517755\pi$
$967$	−3.46722			−0.111498			−0.0557491	+	0.998445i	$0.517755\pi$
$968$	13.3588	+	26.1281i	0.429368	+	0.839789i
$969$		0			0
$970$	−2.48142	−	3.06139i	−0.0796735	−	0.0982952i
$971$		−	2.84056i		−	0.0911580i	−0.998961	−	0.0455790i	$-0.985487\pi$
$971$		−	2.84056i		−	0.0911580i	0.998961	−	0.0455790i	$-0.0145133\pi$
$972$		0			0
$973$		−	3.89763i		−	0.124952i
$974$	42.4358	−	34.3965i	1.35973	−	1.10213i
$975$		0			0
$976$	−8.75052	+	19.7526i	−0.280097	+	0.632267i
$977$	17.3811			0.556071			0.278035	−	0.960571i	$-0.410317\pi$
$977$	17.3811			0.556071			0.278035	+	0.960571i	$0.410317\pi$
$978$		0			0
$979$		−	9.11522i		−	0.291324i
$980$	3.10076	+	0.656077i	0.0990500	+	0.0209576i
$981$		0			0
$982$	15.9409	+	19.6668i	0.508696	+	0.627591i
$983$	−54.8615			−1.74981			−0.874905	−	0.484294i	$-0.839076\pi$
$983$	−54.8615			−1.74981			−0.874905	+	0.484294i	$0.839076\pi$
$984$		0			0
$985$	−24.0198			−0.765336
$986$	−11.0028	−	13.5744i	−0.350400	−	0.432297i
$987$		0			0
$988$	−1.54671	+	7.31005i	−0.0492073	+	0.232564i
$989$		−	2.65467i		−	0.0844136i
$990$		0			0
$991$	−20.9952			−0.666933			−0.333467	−	0.942762i	$-0.608218\pi$
$991$	−20.9952			−0.666933			−0.333467	+	0.942762i	$0.608218\pi$
$992$	−3.10530	+	0.839793i	−0.0985933	+	0.0266635i
$993$		0			0
$994$	−10.4688	+	8.48548i	−0.332049	+	0.269143i
$995$			31.5093i			0.998913i
$996$		0			0
$997$		−	44.0239i		−	1.39425i	−0.716950	−	0.697125i	$-0.754462\pi$
$997$		−	44.0239i		−	1.39425i	0.716950	−	0.697125i	$-0.245538\pi$
$998$	−21.6571	−	26.7190i	−0.685545	−	0.845774i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.f.757.6	yes	24
3.2	odd	2	inner	1512.2.c.f.757.19	yes	24
4.3	odd	2		6048.2.c.g.3025.17		24
8.3	odd	2		6048.2.c.g.3025.8		24
8.5	even	2	inner	1512.2.c.f.757.5	✓	24
12.11	even	2		6048.2.c.g.3025.7		24
24.5	odd	2	inner	1512.2.c.f.757.20	yes	24
24.11	even	2		6048.2.c.g.3025.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.f.757.5	✓	24	8.5	even	2	inner
1512.2.c.f.757.6	yes	24	1.1	even	1	trivial
1512.2.c.f.757.19	yes	24	3.2	odd	2	inner
1512.2.c.f.757.20	yes	24	24.5	odd	2	inner
6048.2.c.g.3025.7		24	12.11	even	2
6048.2.c.g.3025.8		24	8.3	odd	2
6048.2.c.g.3025.17		24	4.3	odd	2
6048.2.c.g.3025.18		24	24.11	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09864 + 0.890504i) q^{2} +(0.414007 - 1.95668i) q^{4} +1.58470i q^{5} +1.00000 q^{7} +(1.28759 + 2.51836i) q^{8} +O(q^{10})\)	\(q+(-1.09864 + 0.890504i) q^{2} +(0.414007 - 1.95668i) q^{4} +1.58470i q^{5} +1.00000 q^{7} +(1.28759 + 2.51836i) q^{8} +(-1.41118 - 1.74101i) q^{10} -0.790533i q^{11} -0.494366i q^{13} +(-1.09864 + 0.890504i) q^{14} +(-3.65720 - 1.62016i) q^{16} +4.46962 q^{17} -7.55705i q^{19} +(3.10076 + 0.656077i) q^{20} +(0.703973 + 0.868509i) q^{22} +0.839644 q^{23} +2.48872 q^{25} +(0.440235 + 0.543129i) q^{26} +(0.414007 - 1.95668i) q^{28} +2.76437i q^{29} -0.568664 q^{31} +(5.46069 - 1.47678i) q^{32} +(-4.91049 + 3.98021i) q^{34} +1.58470i q^{35} -0.343650i q^{37} +(6.72958 + 8.30245i) q^{38} +(-3.99084 + 2.04044i) q^{40} -5.93014 q^{41} -3.16166i q^{43} +(-1.54682 - 0.327286i) q^{44} +(-0.922464 + 0.747706i) q^{46} +4.80964 q^{47} +1.00000 q^{49} +(-2.73420 + 2.21621i) q^{50} +(-0.967316 - 0.204671i) q^{52} -4.36792i q^{53} +1.25276 q^{55} +(1.28759 + 2.51836i) q^{56} +(-2.46168 - 3.03704i) q^{58} -4.50798i q^{59} -5.40103i q^{61} +(0.624755 - 0.506397i) q^{62} +(-4.68423 + 6.48521i) q^{64} +0.783423 q^{65} +7.57396i q^{67} +(1.85045 - 8.74561i) q^{68} +(-1.41118 - 1.74101i) q^{70} +9.52886 q^{71} +14.1344 q^{73} +(0.306022 + 0.377547i) q^{74} +(-14.7867 - 3.12867i) q^{76} -0.790533i q^{77} -3.71341 q^{79} +(2.56747 - 5.79557i) q^{80} +(6.51507 - 5.28081i) q^{82} +7.30905i q^{83} +7.08301i q^{85} +(2.81547 + 3.47352i) q^{86} +(1.99084 - 1.01788i) q^{88} +11.5305 q^{89} -0.494366i q^{91} +(0.347618 - 1.64292i) q^{92} +(-5.28405 + 4.28300i) q^{94} +11.9757 q^{95} +1.75839 q^{97} +(-1.09864 + 0.890504i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7}+O(q^{10}) \) 24 * q + 24 * q^7	\( 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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