LMFDB - Embedded newform 1512.2.c.f.757.19

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			757.19
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.f.757.20

$q$-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	$-0.884702\pi$
$5$		−	1.58470i		−	0.708700i	0.935113	−	0.354350i	$-0.115298\pi$
$6$		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	$0.0380257\pi$
$11$			0.790533i			0.238355i	−0.992873	+	0.119177i	$0.961974\pi$
$12$		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	$-0.682340\pi$
$17$	−4.46962			−1.08404			−0.542021	+	0.840365i	$0.682340\pi$
$18$		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	$-0.527900\pi$
$23$	−0.839644			−0.175078			−0.0875390	+	0.996161i	$0.527900\pi$
$24$		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	$-0.917376\pi$
$29$		−	2.76437i		−	0.513331i	0.966500	−	0.256665i	$-0.0826238\pi$
$30$		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	$-0.346749\pi$
$41$	5.93014			0.926132			0.463066	+	0.886324i	$0.346749\pi$
$42$		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	$-0.614083\pi$
$47$	−4.80964			−0.701558			−0.350779	+	0.936458i	$0.614083\pi$
$48$		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	$0.0969833\pi$
$53$			4.36792i			0.599980i	−0.953942	+	0.299990i	$0.903017\pi$
$54$		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	$0.0948016\pi$
$59$			4.50798i			0.586889i	−0.955976	+	0.293445i	$0.905198\pi$
$60$		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	$-0.691291\pi$
$71$	−9.52886			−1.13087			−0.565434	+	0.824794i	$0.691291\pi$
$72$		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	$-0.868615\pi$
$83$		−	7.30905i		−	0.802273i	0.916018	−	0.401136i	$-0.131385\pi$
$84$		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	$-0.709278\pi$
$89$	−11.5305			−1.22223			−0.611114	+	0.791543i	$0.709278\pi$
$90$		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	$-0.661676\pi$
$101$		−	17.5623i		−	1.74752i	0.486362	−	0.873758i	$-0.338324\pi$
$102$		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	$0.362032\pi$
$107$			18.7750i			1.81505i	−0.419996	+	0.907526i	$0.637968\pi$
$108$		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	$-0.329544\pi$
$113$	10.8486			1.02055			0.510275	+	0.860012i	$0.329544\pi$
$114$		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	$-0.927344\pi$
$131$		−	5.17978i		−	0.452560i	0.974062	−	0.226280i	$-0.0726564\pi$
$132$		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	$-0.386098\pi$
$137$	8.19905			0.700492			0.350246	+	0.936658i	$0.386098\pi$
$138$		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	$-0.951435\pi$
$149$		−	3.71034i		−	0.303963i	0.988383	−	0.151981i	$-0.0485654\pi$
$150$		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	$-0.566447\pi$
$167$	−5.35614			−0.414471			−0.207235	+	0.978291i	$0.566447\pi$
$168$		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	$-0.801136\pi$
$173$		−	15.3862i		−	1.16979i	0.811110	−	0.584894i	$-0.198864\pi$
$174$		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	$0.260524\pi$
$179$			19.5360i			1.46019i	−0.683347	+	0.730094i	$0.739476\pi$
$180$		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	$-0.278756\pi$
$191$	17.7019			1.28086			0.640431	+	0.768016i	$0.278756\pi$
$192$		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	$-0.818440\pi$
$197$		−	15.1573i		−	1.07991i	0.841692	−	0.539957i	$-0.181560\pi$
$198$		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	$0.0973579\pi$
$227$			9.07343i			0.602224i	−0.953589	+	0.301112i	$0.902642\pi$
$228$		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	$-0.189747\pi$
$233$	25.2633			1.65505			0.827527	+	0.561426i	$0.189747\pi$
$234$		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	$-0.532361\pi$
$239$	−3.13797			−0.202979			−0.101489	+	0.994837i	$0.532361\pi$
$240$		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	$0.132582\pi$
$251$			12.8195i			0.809158i	−0.914503	+	0.404579i	$0.867418\pi$
$252$		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	$-0.386752\pi$
$257$	11.1680			0.696639			0.348319	+	0.937376i	$0.386752\pi$
$258$		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	$-0.654452\pi$
$263$	−15.1277			−0.932817			−0.466408	+	0.884570i	$0.654452\pi$
$264$		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	$-0.954179\pi$
$269$		−	4.70567i		−	0.286910i	0.989657	−	0.143455i	$-0.0458212\pi$
$270$		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	$-0.173519\pi$
$281$	28.6669			1.71013			0.855063	+	0.518525i	$0.173519\pi$
$282$		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	$0.246313\pi$
$293$			23.9254i			1.39774i	−0.715250	+	0.698868i	$0.753687\pi$
$294$		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	$-0.942882\pi$
$311$	−34.7041			−1.96789			−0.983944	+	0.178480i	$0.942882\pi$
$312$		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	$0.323781\pi$
$317$			30.2902i			1.70127i	−0.525761	+	0.850633i	$0.676219\pi$
$318$		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	$0.0507598\pi$
$347$			5.91592i			0.317583i	−0.987312	+	0.158792i	$0.949240\pi$
$348$		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	$-0.302162\pi$
$353$	21.8800			1.16455			0.582277	+	0.812990i	$0.302162\pi$
$354$		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	$-0.337814\pi$
$359$	18.4834			0.975519			0.487759	+	0.872978i	$0.337814\pi$
$360$		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	$-0.498427\pi$
$383$	0.193380			0.00988125			0.00494063	+	0.999988i	$0.498427\pi$
$384$		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	$-0.722314\pi$
$389$		−	30.2102i		−	1.53172i	0.643008	−	0.765859i	$-0.277686\pi$
$390$		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	$-0.181979\pi$
$401$	33.6813			1.68196			0.840981	+	0.541065i	$0.181979\pi$
$402$		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	$0.126324\pi$
$419$			15.8239i			0.773048i	−0.922279	+	0.386524i	$0.873676\pi$
$420$		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	$-0.326332\pi$
$431$	21.5464			1.03785			0.518927	+	0.854819i	$0.326332\pi$
$432$		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	$-0.992955\pi$
$443$		−	0.931584i		−	0.0442609i	0.999755	−	0.0221304i	$-0.00704492\pi$
$444$		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	$-0.663895\pi$
$449$	−20.8693			−0.984883			−0.492441	+	0.870346i	$0.663895\pi$
$450$		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	$-0.985844\pi$
$461$		−	1.90910i		−	0.0889156i	0.999011	−	0.0444578i	$-0.0141560\pi$
$462$		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	$-0.864908\pi$
$467$		−	17.7972i		−	0.823554i	0.911285	−	0.411777i	$-0.135092\pi$
$468$		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	$-0.664886\pi$
$479$	−21.6737			−0.990294			−0.495147	+	0.868809i	$0.664886\pi$
$480$		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	$0.132357\pi$
$491$			17.9010i			0.807863i	−0.914789	+	0.403931i	$0.867643\pi$
$492$		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	$-0.199772\pi$
$503$	36.3076			1.61888			0.809438	+	0.587205i	$0.199772\pi$
$504$		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	$0.0220539\pi$
$509$			3.12375i			0.138458i	−0.997601	+	0.0692290i	$0.977946\pi$
$510$		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	$-0.511720\pi$
$521$	−1.68044			−0.0736213			−0.0368107	+	0.999322i	$0.511720\pi$
$522$		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	$-0.690800\pi$
$557$		−	38.9728i		−	1.65133i	0.564161	−	0.825665i	$-0.309200\pi$
$558$		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	$-0.891662\pi$
$563$		−	15.8415i		−	0.667642i	0.942637	−	0.333821i	$-0.108338\pi$
$564$		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	$-0.619403\pi$
$569$	−17.4790			−0.732758			−0.366379	+	0.930466i	$0.619403\pi$
$570$		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	$-0.836319\pi$
$587$		−	23.8334i		−	0.983709i	0.870677	−	0.491855i	$-0.163681\pi$
$588$		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	$-0.695587\pi$
$593$	−28.0780			−1.15302			−0.576512	+	0.817088i	$0.695587\pi$
$594$		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	$-0.646039\pi$
$599$	−21.6780			−0.885738			−0.442869	+	0.896586i	$0.646039\pi$
$600$		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	$-0.261439\pi$
$617$	33.8435			1.36249			0.681244	+	0.732056i	$0.261439\pi$
$618$		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	$-0.426285\pi$
$641$	11.6219			0.459039			0.229519	+	0.973304i	$0.426285\pi$
$642$		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	$-0.700691\pi$
$647$	−29.9913			−1.17908			−0.589540	+	0.807739i	$0.700691\pi$
$648$		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	$0.0943390\pi$
$653$			14.9263i			0.584110i	−0.956402	+	0.292055i	$0.905661\pi$
$654$		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	$0.178883\pi$
$659$			27.3581i			1.06572i	−0.846204	+	0.532859i	$0.821117\pi$
$660$		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	$0.315798\pi$
$677$			43.5656i			1.67436i	−0.546926	+	0.837181i	$0.684202\pi$
$678$		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	$-0.894821\pi$
$683$		−	16.9585i		−	0.648898i	0.945903	−	0.324449i	$-0.105179\pi$
$684$		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	$-0.811605\pi$
$701$		−	29.5427i		−	1.11581i	0.829905	−	0.557905i	$-0.188395\pi$
$702$		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	$-0.401225\pi$
$719$	16.3756			0.610708			0.305354	+	0.952239i	$0.401225\pi$
$720$		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	$-0.638062\pi$
$743$	−22.9110			−0.840524			−0.420262	+	0.907403i	$0.638062\pi$
$744$		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	$-0.517222\pi$
$761$	−2.98366			−0.108158			−0.0540789	+	0.998537i	$0.517222\pi$
$762$		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	$-0.951727\pi$
$773$		−	8.40051i		−	0.302145i	0.988523	−	0.151073i	$-0.0482728\pi$
$774$		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	$0.277128\pi$
$797$			43.1786i			1.52946i	−0.644349	+	0.764731i	$0.722872\pi$
$798$		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	$-0.641940\pi$
$809$	−24.5341			−0.862573			−0.431287	+	0.902215i	$0.641940\pi$
$810$		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	$-0.993212\pi$
$821$		−	1.22205i		−	0.0426499i	0.999773	−	0.0213250i	$-0.00678846\pi$
$822$		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	$0.209794\pi$
$827$			35.2221i			1.22479i	−0.790551	+	0.612396i	$0.790206\pi$
$828$		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	$-0.542891\pi$
$839$	−7.78246			−0.268680			−0.134340	+	0.990935i	$0.542891\pi$
$840$		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	$-0.807656\pi$
$857$	−48.1812			−1.64584			−0.822919	+	0.568159i	$0.807656\pi$
$858$		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	$-0.376238\pi$
$863$	22.2727			0.758173			0.379086	+	0.925361i	$0.376238\pi$
$864$		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	$-0.644000\pi$
$881$	−25.9486			−0.874229			−0.437115	+	0.899406i	$0.644000\pi$
$882$		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	$-0.459245\pi$
$887$	7.60567			0.255373			0.127687	+	0.991815i	$0.459245\pi$
$888$		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	$-0.793390\pi$
$911$	−48.0894			−1.59327			−0.796637	+	0.604458i	$0.793390\pi$
$912$		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	$-0.700517\pi$
$929$	−35.9109			−1.17820			−0.589100	+	0.808060i	$0.700517\pi$
$930$		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	$-0.969764\pi$
$941$		−	5.81896i		−	0.189693i	0.995492	−	0.0948464i	$-0.0302360\pi$
$942$		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	$0.120876\pi$
$947$			22.8143i			0.741365i	−0.928760	+	0.370682i	$0.879124\pi$
$948$		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	$-0.496599\pi$
$953$	0.659700			0.0213698			0.0106849	+	0.999943i	$0.496599\pi$
$954$		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	$0.0145133\pi$
$971$			2.84056i			0.0911580i	−0.998961	+	0.0455790i	$0.985487\pi$
$972$		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	$-0.589683\pi$
$977$	−17.3811			−0.556071			−0.278035	+	0.960571i	$0.589683\pi$
$978$		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	$-0.160924\pi$
$983$	54.8615			1.74981			0.874905	+	0.484294i	$0.160924\pi$
$984$		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.757.19	yes	24
3.2	odd	2	inner	1512.2.c.f.757.6	yes	24
4.3	odd	2		6048.2.c.g.3025.7		24
8.3	odd	2		6048.2.c.g.3025.18		24
8.5	even	2	inner	1512.2.c.f.757.20	yes	24
12.11	even	2		6048.2.c.g.3025.17		24
24.5	odd	2	inner	1512.2.c.f.757.5	✓	24
24.11	even	2		6048.2.c.g.3025.8		24

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