LMFDB - Embedded newform 637.2.x.b.80.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.1
Character	$\chi$	$=$	637.80
Dual form			637.2.x.b.215.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433802 - 1.61897i) q^{2} -0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(0.520288 - 1.94174i) q^{5} +(-1.03250 + 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} +O(q^{10})$	\(q+(-0.433802 - 1.61897i) q^{2} -0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(0.520288 - 1.94174i) q^{5} +(-1.03250 + 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} -3.36932 q^{10} +(0.694217 + 0.694217i) q^{11} +(0.258049 + 0.446954i) q^{12} +(1.60977 - 3.22624i) q^{13} +(-1.23834 - 0.331813i) q^{15} +(-2.48181 + 4.29862i) q^{16} +(-2.99281 - 5.18370i) q^{17} +(-1.12497 - 4.19844i) q^{18} +(1.98532 + 1.98532i) q^{19} +(0.421043 + 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 - 1.49448i) q^{23} +(-0.900016 + 0.900016i) q^{24} +(0.830467 + 0.479471i) q^{25} +(-5.92151 - 1.20663i) q^{26} -3.56710i q^{27} +(3.65708 + 6.33425i) q^{29} +2.14878i q^{30} +(-8.34708 + 2.23659i) q^{31} +(4.18037 + 1.12013i) q^{32} +(0.442736 - 0.442736i) q^{33} +(-7.09397 + 7.09397i) q^{34} +(-1.81745 + 1.04931i) q^{36} +(4.63309 - 1.24143i) q^{37} +(2.35294 - 4.07541i) q^{38} +(-2.05753 - 1.02663i) q^{39} +(-3.47451 + 2.00601i) q^{40} +(0.886060 - 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.767427 - 0.205631i) q^{44} +(1.34925 - 5.03547i) q^{45} +(-1.29661 + 4.83903i) q^{46} +(-2.96429 - 0.794280i) q^{47} +(2.74144 + 1.58277i) q^{48} +(0.415990 - 1.55250i) q^{50} +(-3.30589 + 1.90866i) q^{51} +(0.177238 + 2.91241i) q^{52} +(-3.16223 + 5.47715i) q^{53} +(-5.77504 + 1.54742i) q^{54} +(1.70918 - 0.986797i) q^{55} +(1.26614 - 1.26614i) q^{57} +(8.66852 - 8.66852i) q^{58} +(-0.491481 - 0.131692i) q^{59} +(1.00213 - 0.268520i) q^{60} +13.0284i q^{61} +(7.24196 + 12.5434i) q^{62} +2.67342i q^{64} +(-5.42698 - 4.80434i) q^{65} +(-0.908836 - 0.524717i) q^{66} +(0.606011 - 0.606011i) q^{67} +(4.19491 + 2.42193i) q^{68} +(-0.953100 + 1.65082i) q^{69} +(-3.01121 - 11.2380i) q^{71} +(-3.65973 - 3.65973i) q^{72} +(0.377014 + 1.40704i) q^{73} +(-4.01968 - 6.96230i) q^{74} +(0.305782 - 0.529629i) q^{75} +(-2.19469 - 0.588064i) q^{76} +(-0.769526 + 3.77644i) q^{78} +(5.80137 + 10.0483i) q^{79} +(7.05555 + 7.05555i) q^{80} +5.50492 q^{81} -5.73802 q^{82} +(1.23779 + 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(-0.374999 + 1.39951i) q^{86} +(4.03966 - 2.33230i) q^{87} -1.95941i q^{88} +(-2.07729 - 7.75255i) q^{89} -8.73759 q^{90} +2.41881 q^{92} +(1.42638 + 5.32334i) q^{93} +5.14367i q^{94} +(4.88792 - 2.82204i) q^{95} +(0.714359 - 2.66602i) q^{96} +(12.0756 - 3.23566i) q^{97} +(1.80030 + 1.80030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.433802	−	1.61897i	−0.306744	−	1.14479i	−0.931433	−	0.363912i	$-0.881441\pi$
$2$	−0.433802	−	1.61897i	−0.306744	−	1.14479i	0.624689	−	0.780873i	$-0.285226\pi$
$3$		−	0.637748i		−	0.368204i	−0.982907	−	0.184102i	$-0.941062\pi$
$3$		−	0.637748i		−	0.368204i	0.982907	−	0.184102i	$-0.0589377\pi$
$4$	−0.700831	+	0.404625i	−0.350416	+	0.202313i
$5$	0.520288	−	1.94174i	0.232680	−	0.868373i	−0.746501	−	0.665384i	$-0.768268\pi$
$5$	0.520288	−	1.94174i	0.232680	−	0.868373i	0.979181	−	0.202989i	$-0.0650656\pi$
$6$	−1.03250	+	0.276656i	−0.421515	+	0.112945i
$7$		0			0
$7$		0			0
$8$	−1.41124	−	1.41124i	−0.498948	−	0.498948i
$9$	2.59328			0.864426
$10$	−3.36932			−1.06547
$11$	0.694217	+	0.694217i	0.209314	+	0.209314i	0.803976	−	0.594662i	$-0.202714\pi$
$11$	0.694217	+	0.694217i	0.209314	+	0.209314i	−0.594662	+	0.803976i	$0.702714\pi$
$12$	0.258049	+	0.446954i	0.0744924	+	0.129025i
$13$	1.60977	−	3.22624i	0.446471	−	0.894798i
$13$	1.60977	−	3.22624i	0.446471	−	0.894798i
$14$		0			0
$15$	−1.23834	−	0.331813i	−0.319739	−	0.0856737i
$16$	−2.48181	+	4.29862i	−0.620452	+	1.07465i
$17$	−2.99281	−	5.18370i	−0.725863	−	1.25723i	−0.958618	−	0.284696i	$-0.908107\pi$
$17$	−2.99281	−	5.18370i	−0.725863	−	1.25723i	0.232755	−	0.972535i	$-0.425226\pi$
$18$	−1.12497	−	4.19844i	−0.265158	−	0.989582i
$19$	1.98532	+	1.98532i	0.455464	+	0.455464i	0.897163	−	0.441699i	$-0.145624\pi$
$19$	1.98532	+	1.98532i	0.455464	+	0.455464i	−0.441699	+	0.897163i	$0.645624\pi$
$20$	0.421043	+	1.57135i	0.0941481	+	0.351366i
$21$		0			0
$22$	0.822765	−	1.42507i	0.175414	−	0.303826i
$23$	−2.58851	−	1.49448i	−0.539742	−	0.311620i	0.205233	−	0.978713i	$-0.434205\pi$
$23$	−2.58851	−	1.49448i	−0.539742	−	0.311620i	−0.744974	+	0.667093i	$0.767538\pi$
$24$	−0.900016	+	0.900016i	−0.183715	+	0.183715i
$25$	0.830467	+	0.479471i	0.166093	+	0.0958941i
$26$	−5.92151	−	1.20663i	−1.16130	−	0.236639i
$27$		−	3.56710i		−	0.686489i
$28$		0			0
$29$	3.65708	+	6.33425i	0.679103	+	1.17624i	0.975251	+	0.221099i	$0.0709645\pi$
$29$	3.65708	+	6.33425i	0.679103	+	1.17624i	−0.296148	+	0.955142i	$0.595702\pi$
$30$			2.14878i			0.392312i
$31$	−8.34708	+	2.23659i	−1.49918	+	0.401704i	−0.912825	−	0.408351i	$-0.866104\pi$
$31$	−8.34708	+	2.23659i	−1.49918	+	0.401704i	−0.586354	+	0.810055i	$0.699437\pi$
$32$	4.18037	+	1.12013i	0.738992	+	0.198012i
$33$	0.442736	−	0.442736i	0.0770704	−	0.0770704i
$34$	−7.09397	+	7.09397i	−1.21661	+	1.21661i
$35$		0			0
$36$	−1.81745	+	1.04931i	−0.302908	+	0.174884i
$37$	4.63309	−	1.24143i	0.761675	−	0.204090i	0.142984	−	0.989725i	$-0.454330\pi$
$37$	4.63309	−	1.24143i	0.761675	−	0.204090i	0.618690	+	0.785635i	$0.287664\pi$
$38$	2.35294	−	4.07541i	0.381697	−	0.661119i
$39$	−2.05753	−	1.02663i	−0.329468	−	0.164393i
$40$	−3.47451	+	2.00601i	−0.549369	+	0.317178i
$41$	0.886060	−	3.30682i	0.138379	−	0.516439i	−0.861582	−	0.507619i	$-0.830526\pi$
$41$	0.886060	−	3.30682i	0.138379	−	0.516439i	0.999961	−	0.00881984i	$-0.00280748\pi$
$42$		0			0
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	0.441830	−	0.897099i	$-0.354329\pi$
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	−0.555995	+	0.831185i	$0.687663\pi$
$44$	−0.767427	−	0.205631i	−0.115694	−	0.0310001i
$45$	1.34925	−	5.03547i	0.201134	−	0.750644i
$46$	−1.29661	+	4.83903i	−0.191175	+	0.713476i
$47$	−2.96429	−	0.794280i	−0.432387	−	0.115858i	0.0360596	−	0.999350i	$-0.488519\pi$
$47$	−2.96429	−	0.794280i	−0.432387	−	0.115858i	−0.468446	+	0.883492i	$0.655186\pi$
$48$	2.74144	+	1.58277i	0.395692	+	0.228453i
$49$		0			0
$50$	0.415990	−	1.55250i	0.0588299	−	0.219556i
$51$	−3.30589	+	1.90866i	−0.462918	+	0.267266i
$52$	0.177238	+	2.91241i	0.0245784	+	0.403878i
$53$	−3.16223	+	5.47715i	−0.434366	+	0.752344i	−0.997244	−	0.0741963i	$-0.976361\pi$
$53$	−3.16223	+	5.47715i	−0.434366	+	0.752344i	0.562878	+	0.826540i	$0.309694\pi$
$54$	−5.77504	+	1.54742i	−0.785883	+	0.210577i
$55$	1.70918	−	0.986797i	0.230466	−	0.133060i
$56$		0			0
$57$	1.26614	−	1.26614i	0.167704	−	0.167704i
$58$	8.66852	−	8.66852i	1.13823	−	1.13823i
$59$	−0.491481	−	0.131692i	−0.0639854	−	0.0171448i	0.226684	−	0.973968i	$-0.427211\pi$
$59$	−0.491481	−	0.131692i	−0.0639854	−	0.0171448i	−0.290670	+	0.956823i	$0.593878\pi$
$60$	1.00213	−	0.268520i	0.129374	−	0.0346657i
$61$			13.0284i			1.66811i	0.551679	+	0.834057i	$0.313988\pi$
$61$			13.0284i			1.66811i	−0.551679	+	0.834057i	$0.686012\pi$
$62$	7.24196	+	12.5434i	0.919729	+	1.59302i
$63$		0			0
$64$			2.67342i			0.334178i
$65$	−5.42698	−	4.80434i	−0.673134	−	0.595905i
$66$	−0.908836	−	0.524717i	−0.111870	−	0.0645882i
$67$	0.606011	−	0.606011i	0.0740361	−	0.0740361i	−0.669119	−	0.743155i	$-0.733328\pi$
$67$	0.606011	−	0.606011i	0.0740361	−	0.0740361i	0.743155	+	0.669119i	$0.233328\pi$
$68$	4.19491	+	2.42193i	0.508707	+	0.293702i
$69$	−0.953100	+	1.65082i	−0.114740	+	0.198735i
$70$		0			0
$71$	−3.01121	−	11.2380i	−0.357365	−	1.33370i	−0.877482	−	0.479609i	$-0.840778\pi$
$71$	−3.01121	−	11.2380i	−0.357365	−	1.33370i	0.520117	−	0.854095i	$-0.325888\pi$
$72$	−3.65973	−	3.65973i	−0.431304	−	0.431304i
$73$	0.377014	+	1.40704i	0.0441262	+	0.164681i	0.984473	−	0.175536i	$-0.0561660\pi$
$73$	0.377014	+	1.40704i	0.0441262	+	0.164681i	−0.940347	+	0.340217i	$0.889499\pi$
$74$	−4.01968	−	6.96230i	−0.467279	−	0.809350i
$75$	0.305782	−	0.529629i	0.0353086	−	0.0611563i
$76$	−2.19469	−	0.588064i	−0.251748	−	0.0674556i
$77$		0			0
$78$	−0.769526	+	3.77644i	−0.0871316	+	0.427597i
$79$	5.80137	+	10.0483i	0.652705	+	1.13052i	0.982464	+	0.186454i	$0.0596994\pi$
$79$	5.80137	+	10.0483i	0.652705	+	1.13052i	−0.329758	+	0.944065i	$0.606967\pi$
$80$	7.05555	+	7.05555i	0.788834	+	0.788834i
$81$	5.50492			0.611657
$82$	−5.73802			−0.633658
$83$	1.23779	+	1.23779i	0.135865	+	0.135865i	0.771768	−	0.635904i	$-0.219372\pi$
$83$	1.23779	+	1.23779i	0.135865	+	0.135865i	−0.635904	+	0.771768i	$0.719372\pi$
$84$		0			0
$85$	−11.6225	+	3.11424i	−1.26064	+	0.337787i
$86$	−0.374999	+	1.39951i	−0.0404372	+	0.150914i
$87$	4.03966	−	2.33230i	0.433097	−	0.250049i
$88$		−	1.95941i		−	0.208874i
$89$	−2.07729	−	7.75255i	−0.220192	−	0.821769i	−0.984274	−	0.176649i	$-0.943474\pi$
$89$	−2.07729	−	7.75255i	−0.220192	−	0.821769i	0.764082	−	0.645120i	$-0.223193\pi$
$90$	−8.73759			−0.921023
$91$		0			0
$92$	2.41881			0.252179
$93$	1.42638	+	5.32334i	0.147909	+	0.552004i
$94$			5.14367i			0.530529i
$95$	4.88792	−	2.82204i	0.501490	−	0.289535i
$96$	0.714359	−	2.66602i	0.0729090	−	0.272100i
$97$	12.0756	−	3.23566i	1.22609	−	0.328531i	0.413037	−	0.910714i	$-0.364468\pi$
$97$	12.0756	−	3.23566i	1.22609	−	0.328531i	0.813058	+	0.582183i	$0.197801\pi$
$98$		0			0
$99$	1.80030	+	1.80030i	0.180937	+	0.180937i
$100$	−0.776023			−0.0776023
$101$	7.99635			0.795667			0.397833	−	0.917458i	$-0.369762\pi$
$101$	7.99635			0.795667			0.397833	+	0.917458i	$0.369762\pi$
$102$	4.52417	+	4.52417i	0.447959	+	0.447959i
$103$	5.16928	+	8.95345i	0.509344	+	0.882210i	0.999941	+	0.0108235i	$0.00344528\pi$
$103$	5.16928	+	8.95345i	0.509344	+	0.882210i	−0.490597	+	0.871386i	$0.663221\pi$
$104$	−6.82477	+	2.28122i	−0.669224	+	0.223692i
$105$		0			0
$106$	10.2391	+	2.74356i	0.994511	+	0.266479i
$107$	−6.52593	+	11.3032i	−0.630885	+	1.09273i	0.356486	+	0.934301i	$0.383975\pi$
$107$	−6.52593	+	11.3032i	−0.630885	+	1.09273i	−0.987371	+	0.158425i	$0.949358\pi$
$108$	1.44334	+	2.49994i	0.138885	+	0.240557i
$109$	−3.03074	−	11.3109i	−0.290292	−	1.08339i	−0.944885	−	0.327403i	$-0.893826\pi$
$109$	−3.03074	−	11.3109i	−0.290292	−	1.08339i	0.654592	−	0.755982i	$-0.272840\pi$
$110$	−2.33904	−	2.33904i	−0.223019	−	0.223019i
$111$	−0.791721	−	2.95474i	−0.0751468	−	0.280452i
$112$		0			0
$113$	4.05748	−	7.02777i	0.381696	−	0.661117i	−0.609609	−	0.792702i	$-0.708674\pi$
$113$	4.05748	−	7.02777i	0.381696	−	0.661117i	0.991305	+	0.131586i	$0.0420069\pi$
$114$	−2.59909	−	1.50058i	−0.243427	−	0.140543i
$115$	−4.24866	+	4.24866i	−0.396189	+	0.396189i
$116$	−5.12600	−	2.95950i	−0.475937	−	0.274782i
$117$	4.17459	−	8.36653i	0.385941	−	0.773486i
$118$			0.852822i			0.0785086i
$119$		0			0
$120$	1.27933	+	2.21587i	0.116786	+	0.202280i
$121$		−	10.0361i		−	0.912375i
$122$	21.0926	−	5.65174i	1.90963	−	0.511684i
$123$	−2.10892	−	0.565083i	−0.190155	−	0.0509518i
$124$	4.94491	−	4.94491i	0.444066	−	0.444066i
$125$	8.47036	−	8.47036i	0.757612	−	0.757612i
$126$		0			0
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	−0.165977	−	0.986130i	$-0.553078\pi$
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	0.771024	+	0.636805i	$0.219745\pi$
$128$	12.6889	−	3.39999i	1.12155	−	0.300519i
$129$	−0.275650	+	0.477440i	−0.0242696	+	0.0420362i
$130$	−5.42385	+	10.8702i	−0.475703	+	0.953384i
$131$	17.2856	−	9.97987i	1.51025	−	0.871945i	0.510325	−	0.859982i	$-0.329525\pi$
$131$	17.2856	−	9.97987i	1.51025	−	0.871945i	0.999928	−	0.0119634i	$-0.00380815\pi$
$132$	−0.131141	+	0.489425i	−0.0114144	+	0.0425990i
$133$		0			0
$134$	−1.24400	−	0.718226i	−0.107466	−	0.0620452i
$135$	−6.92639	−	1.85592i	−0.596129	−	0.159732i
$136$	−3.09187	+	11.5390i	−0.265125	+	0.989461i
$137$	−2.78324	+	10.3872i	−0.237788	+	0.887437i	0.739084	+	0.673613i	$0.235259\pi$
$137$	−2.78324	+	10.3872i	−0.237788	+	0.887437i	−0.976872	+	0.213824i	$0.931408\pi$
$138$	3.08608	+	0.826913i	0.262705	+	0.0703915i
$139$	−14.1096	−	8.14616i	−1.19676	−	0.690949i	−0.236927	−	0.971527i	$-0.576140\pi$
$139$	−14.1096	−	8.14616i	−1.19676	−	0.690949i	−0.959831	+	0.280579i	$0.909474\pi$
$140$		0			0
$141$	−0.506551	+	1.89047i	−0.0426593	+	0.159207i
$142$	−16.8877	+	9.75012i	−1.41719	+	0.818212i
$143$	3.35724	−	1.12218i	0.280747	−	0.0938413i
$144$	−6.43601	+	11.1475i	−0.536334	+	0.928959i
$145$	14.2022	−	3.80547i	1.17943	−	0.316027i
$146$	2.11440	−	1.22075i	0.174989	−	0.101030i
$147$		0			0
$148$	−2.74470	+	2.74470i	−0.225613	+	0.225613i
$149$	13.2274	−	13.2274i	1.08363	−	1.08363i	0.0874634	−	0.996168i	$-0.472124\pi$
$149$	13.2274	−	13.2274i	1.08363	−	1.08363i	0.996168	−	0.0874634i	$-0.0278761\pi$
$150$	−0.990103	−	0.265297i	−0.0808416	−	0.0216614i
$151$	0.0351934	−	0.00943004i	0.00286400	−	0.000767406i	−0.257387	−	0.966308i	$-0.582861\pi$
$151$	0.0351934	−	0.00943004i	0.00286400	−	0.000767406i	0.260251	+	0.965541i	$0.416195\pi$
$152$		−	5.60353i		−	0.454506i
$153$	−7.76118	−	13.4428i	−0.627454	−	1.08678i
$154$		0			0
$155$			17.3715i			1.39532i
$156$	1.85738	−	0.113033i	0.148710	−	0.00904988i
$157$	−6.22554	−	3.59432i	−0.496852	−	0.286858i	0.230560	−	0.973058i	$-0.425944\pi$
$157$	−6.22554	−	3.59432i	−0.496852	−	0.286858i	−0.727413	+	0.686200i	$0.759277\pi$
$158$	13.7512	−	13.7512i	1.09399	−	1.09399i
$159$	3.49304	+	2.01671i	0.277016	+	0.159935i
$160$	4.34999	−	7.53441i	0.343897	−	0.595647i
$161$		0			0
$162$	−2.38804	−	8.91230i	−0.187622	−	0.700216i
$163$	−11.6359	−	11.6359i	−0.911397	−	0.911397i	0.0849855	−	0.996382i	$-0.472916\pi$
$163$	−11.6359	−	11.6359i	−0.911397	−	0.911397i	−0.996382	+	0.0849855i	$0.972916\pi$
$164$	0.717044	+	2.67605i	0.0559918	+	0.208964i
$165$	−0.629328	−	1.09003i	−0.0489932	−	0.0848586i
$166$	1.46699	−	2.54090i	0.113860	−	0.197212i
$167$	6.49344	+	1.73991i	0.502478	+	0.134638i	0.501150	−	0.865361i	$-0.332911\pi$
$167$	6.49344	+	1.73991i	0.502478	+	0.134638i	0.00132801	+	0.999999i	$0.499577\pi$
$168$		0			0
$169$	−7.81725	−	10.3870i	−0.601327	−	0.799003i
$170$	10.0837	+	17.4656i	0.773388	+	1.33955i
$171$	5.14849	+	5.14849i	0.393715	+	0.393715i
$172$	0.699554			0.0533405
$173$	9.51731			0.723587			0.361794	−	0.932258i	$-0.382164\pi$
$173$	9.51731			0.723587			0.361794	+	0.932258i	$0.382164\pi$
$174$	−5.52834	−	5.52834i	−0.419102	−	0.419102i
$175$		0			0
$176$	−4.70709	+	1.26126i	−0.354810	+	0.0950711i
$177$	−0.0839864	+	0.313441i	−0.00631280	+	0.0235597i
$178$	−11.6500	+	6.72614i	−0.873206	+	0.504146i
$179$		−	6.00707i		−	0.448989i	−0.974475	−	0.224495i	$-0.927927\pi$
$179$		−	6.00707i		−	0.448989i	0.974475	−	0.224495i	$-0.0720731\pi$
$180$	1.09188	+	4.07496i	0.0813841	+	0.303729i
$181$	6.05960			0.450407			0.225203	−	0.974312i	$-0.427695\pi$
$181$	6.05960			0.450407			0.225203	+	0.974312i	$0.427695\pi$
$182$		0			0
$183$	8.30883			0.614207
$184$	1.54394	+	5.76207i	0.113821	+	0.424786i
$185$		−	9.64216i		−	0.708905i
$186$	7.99956	−	4.61855i	0.586556	−	0.338648i
$187$	1.52095	−	5.67627i	0.111223	−	0.415090i
$188$	2.39886	−	0.642771i	0.174955	−	0.0468789i
$189$		0			0
$190$	−6.68919	−	6.68919i	−0.485285	−	0.485285i
$191$	21.6273			1.56490			0.782449	−	0.622715i	$-0.213970\pi$
$191$	21.6273			1.56490			0.782449	+	0.622715i	$0.213970\pi$
$192$	1.70497			0.123046
$193$	6.85258	+	6.85258i	0.493260	+	0.493260i	0.909332	−	0.416072i	$-0.136594\pi$
$193$	6.85258	+	6.85258i	0.493260	+	0.493260i	−0.416072	+	0.909332i	$0.636594\pi$
$194$	−10.4769	−	18.1465i	−0.752195	−	1.30284i
$195$	−3.06396	+	3.46105i	−0.219415	+	0.247851i
$196$		0			0
$197$	−4.47322	−	1.19859i	−0.318704	−	0.0853964i	0.0959210	−	0.995389i	$-0.469420\pi$
$197$	−4.47322	−	1.19859i	−0.318704	−	0.0853964i	−0.414624	+	0.909993i	$0.636087\pi$
$198$	2.13366	−	3.69560i	0.151632	−	0.262635i
$199$	10.7801	+	18.6717i	0.764182	+	1.32360i	0.940678	+	0.339300i	$0.110190\pi$
$199$	10.7801	+	18.6717i	0.764182	+	1.32360i	−0.176496	+	0.984301i	$0.556476\pi$
$200$	−0.495341	−	1.84864i	−0.0350259	−	0.130718i
$201$	−0.386483	−	0.386483i	−0.0272604	−	0.0272604i
$202$	−3.46883	−	12.9459i	−0.244066	−	0.910868i
$203$		0			0
$204$	1.54458	−	2.67530i	0.108142	−	0.187308i
$205$	−5.95998	−	3.44100i	−0.416263	−	0.240330i
$206$	12.2529	−	12.2529i	0.853702	−	0.853702i
$207$	−6.71272	−	3.87559i	−0.466566	−	0.269372i
$208$	9.87322	+	14.9267i	0.684585	+	1.03498i
$209$			2.75649i			0.190670i
$210$		0			0
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	0.999945	+	0.0105352i	$0.00335353\pi$
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	−0.490848	+	0.871245i	$0.663313\pi$
$212$		−	5.11807i		−	0.351511i
$213$	−7.16701	+	1.92039i	−0.491076	+	0.131583i
$214$	21.1306	+	5.66192i	1.44446	+	0.387041i
$215$	−1.22877	+	1.22877i	−0.0838015	+	0.0838015i
$216$	−5.03404	+	5.03404i	−0.342523	+	0.342523i
$217$		0			0
$218$	−16.9972	+	9.81336i	−1.15120	+	0.664644i
$219$	0.897335	−	0.240440i	0.0606363	−	0.0162474i
$220$	−0.798566	+	1.38316i	−0.0538393	+	0.0932524i
$221$	−21.5416	+	1.31094i	−1.44904	+	0.0881832i
$222$	−4.44019	+	2.56355i	−0.298006	+	0.172054i
$223$	−5.52568	+	20.6221i	−0.370027	+	1.38096i	0.490450	+	0.871469i	$0.336832\pi$
$223$	−5.52568	+	20.6221i	−0.370027	+	1.38096i	−0.860477	+	0.509490i	$0.829834\pi$
$224$		0			0
$225$	2.15363	+	1.24340i	0.143575	+	0.0828933i
$226$	−13.1379	−	3.52029i	−0.873919	−	0.234166i
$227$	3.49849	−	13.0566i	0.232203	−	0.866594i	−0.747186	−	0.664615i	$-0.768596\pi$
$227$	3.49849	−	13.0566i	0.232203	−	0.866594i	0.979390	−	0.201980i	$-0.0647375\pi$
$228$	−0.375037	+	1.39966i	−0.0248374	+	0.0926946i
$229$	−6.94692	−	1.86142i	−0.459066	−	0.123006i	0.0218726	−	0.999761i	$-0.493037\pi$
$229$	−6.94692	−	1.86142i	−0.459066	−	0.123006i	−0.480938	+	0.876755i	$0.659704\pi$
$230$	8.72153	+	5.03538i	0.575081	+	0.332023i
$231$		0			0
$232$	3.77813	−	14.1002i	0.248046	−	0.925721i
$233$	−20.0959	+	11.6024i	−1.31653	+	0.760097i	−0.983168	−	0.182702i	$-0.941515\pi$
$233$	−20.0959	+	11.6024i	−1.31653	+	0.760097i	−0.333359	+	0.942800i	$0.608182\pi$
$234$	−15.3561	−	3.12912i	−1.00386	−	0.204557i
$235$	−3.08457	+	5.34264i	−0.201215	+	0.348515i
$236$	0.397731	−	0.106572i	0.0258901	−	0.00693723i
$237$	6.40827	−	3.69982i	0.416262	−	0.240329i
$238$		0			0
$239$	−2.77302	+	2.77302i	−0.179372	+	0.179372i	−0.791082	−	0.611710i	$-0.790482\pi$
$239$	−2.77302	+	2.77302i	−0.179372	+	0.179372i	0.611710	+	0.791082i	$0.290482\pi$
$240$	4.49966	−	4.49966i	0.290452	−	0.290452i
$241$	3.08037	+	0.825382i	0.198424	+	0.0531675i	0.356662	−	0.934233i	$-0.383915\pi$
$241$	3.08037	+	0.825382i	0.198424	+	0.0531675i	−0.158238	+	0.987401i	$0.550581\pi$
$242$	−16.2482	+	4.35369i	−1.04447	+	0.279866i
$243$		−	14.2121i		−	0.911704i
$244$	−5.27161	−	9.13070i	−0.337480	−	0.584533i
$245$		0			0
$246$			3.65941i			0.233316i
$247$	9.60104	−	3.20920i	0.610900	−	0.204197i
$248$	14.9361	+	8.62336i	0.948443	+	0.547584i
$249$	0.789397	−	0.789397i	0.0500260	−	0.0500260i
$250$	−17.3877	−	10.0388i	−1.09970	−	0.634910i
$251$	−5.89697	+	10.2138i	−0.372213	+	0.644692i	−0.989906	−	0.141727i	$-0.954734\pi$
$251$	−5.89697	+	10.2138i	−0.372213	+	0.644692i	0.617692	+	0.786420i	$0.288068\pi$
$252$		0			0
$253$	−0.759496	−	2.83448i	−0.0477491	−	0.178202i
$254$	−9.33127	−	9.33127i	−0.585496	−	0.585496i
$255$	1.98610	+	7.41224i	0.124375	+	0.464173i
$256$	−8.33554	−	14.4376i	−0.520971	−	0.902349i
$257$	−8.34519	+	14.4543i	−0.520559	+	0.901634i	0.479156	+	0.877730i	$0.340943\pi$
$257$	−8.34519	+	14.4543i	−0.520559	+	0.901634i	−0.999714	+	0.0239041i	$0.992390\pi$
$258$	0.892538	+	0.239155i	0.0555670	+	0.0148891i
$259$		0			0
$260$	5.74735	+	1.17114i	0.356436	+	0.0726310i
$261$	9.48383	+	16.4265i	0.587034	+	1.01677i
$262$	−23.6557	−	23.6557i	−1.46145	−	1.46145i
$263$	9.51537			0.586743			0.293371	−	0.955999i	$-0.405223\pi$
$263$	9.51537			0.586743			0.293371	+	0.955999i	$0.405223\pi$
$264$	−1.24961			−0.0769083
$265$	8.98993	+	8.98993i	0.552247	+	0.552247i
$266$		0			0
$267$	−4.94418	+	1.32479i	−0.302579	+	0.0810758i
$268$	−0.179504	+	0.669919i	−0.0109650	+	0.0409218i
$269$	0.275945	−	0.159317i	0.0168247	−	0.00971373i	−0.491564	−	0.870841i	$-0.663575\pi$
$269$	0.275945	−	0.159317i	0.0168247	−	0.00971373i	0.508389	+	0.861128i	$0.330241\pi$
$270$			12.0187i			0.731437i
$271$	6.94654	+	25.9248i	0.421972	+	1.57482i	0.770447	+	0.637504i	$0.220033\pi$
$271$	6.94654	+	25.9248i	0.421972	+	1.57482i	−0.348475	+	0.937318i	$0.613300\pi$
$272$	29.7103			1.80145
$273$		0			0
$274$	18.0239			1.08886
$275$	0.243668	+	0.909381i	0.0146937	+	0.0548378i
$276$		−	1.54259i		−	0.0928532i
$277$	13.1218	−	7.57587i	0.788412	−	0.455190i	−0.0509909	−	0.998699i	$-0.516238\pi$
$277$	13.1218	−	7.57587i	0.788412	−	0.455190i	0.839403	+	0.543509i	$0.182905\pi$
$278$	−7.06764	+	26.3768i	−0.423889	+	1.58198i
$279$	−21.6463	+	5.80010i	−1.29593	+	0.347243i
$280$		0			0
$281$	5.40600	+	5.40600i	0.322495	+	0.322495i	0.849724	−	0.527228i	$-0.176769\pi$
$281$	5.40600	+	5.40600i	0.322495	+	0.322495i	−0.527228	+	0.849724i	$0.676769\pi$
$282$	3.28036			0.195343
$283$	−1.79244			−0.106549			−0.0532746	−	0.998580i	$-0.516966\pi$
$283$	−1.79244			−0.106549			−0.0532746	+	0.998580i	$0.516966\pi$
$284$	6.65752	+	6.65752i	0.395051	+	0.395051i
$285$	−1.79975	−	3.11726i	−0.106608	−	0.184651i
$286$	−3.27315	−	4.94848i	−0.193546	−	0.292610i
$287$		0			0
$288$	10.8409	+	2.90480i	0.638803	+	0.171167i
$289$	−9.41380	+	16.3052i	−0.553753	+	0.959128i
$290$	−12.3219	−	21.3422i	−0.723567	−	1.25325i
$291$	−2.06353	−	7.70122i	−0.120967	−	0.451453i
$292$	−0.833545	−	0.833545i	−0.0487796	−	0.0487796i
$293$	6.85691	+	25.5903i	0.400585	+	1.49500i	0.812055	+	0.583580i	$0.198349\pi$
$293$	6.85691	+	25.5903i	0.400585	+	1.49500i	−0.411471	+	0.911423i	$0.634985\pi$
$294$		0			0
$295$	−0.511424	+	0.885812i	−0.0297762	+	0.0515739i
$296$	−8.29035	−	4.78644i	−0.481867	−	0.278206i
$297$	2.47634	−	2.47634i	0.143692	−	0.143692i
$298$	−27.1529	−	15.6767i	−1.57292	−	0.908127i
$299$	−8.98846	+	5.94538i	−0.519816	+	0.343830i
$300$			0.494908i			0.0285735i
$301$		0			0
$302$	−0.0305339	−	0.0528863i	−0.00175703	−	0.00304327i
$303$		−	5.09966i		−	0.292968i
$304$	−13.4613	+	3.60695i	−0.772059	+	0.206873i
$305$	25.2978	+	6.77851i	1.44855	+	0.388136i
$306$	−18.3966	+	18.3966i	−1.05166	+	1.05166i
$307$	−1.54710	+	1.54710i	−0.0882978	+	0.0882978i	−0.749876	−	0.661578i	$-0.769887\pi$
$307$	−1.54710	+	1.54710i	−0.0882978	+	0.0882978i	0.661578	+	0.749876i	$0.269887\pi$
$308$		0			0
$309$	5.71005	−	3.29670i	0.324833	−	0.187543i
$310$	28.1240	−	7.53581i	1.59734	−	0.428005i
$311$	−14.6672	+	25.4043i	−0.831699	+	1.44055i	0.0649904	+	0.997886i	$0.479298\pi$
$311$	−14.6672	+	25.4043i	−0.831699	+	1.44055i	−0.896690	+	0.442660i	$0.854035\pi$
$312$	1.45484	+	4.35249i	0.0823644	+	0.246411i
$313$	−24.2354	+	13.9923i	−1.36987	+	0.790893i	−0.990911	−	0.134521i	$-0.957050\pi$
$313$	−24.2354	+	13.9923i	−1.36987	+	0.790893i	−0.378957	+	0.925414i	$0.623717\pi$
$314$	−3.11844	+	11.6382i	−0.175984	+	0.656781i
$315$		0			0
$316$	−8.13157	−	4.69476i	−0.457436	−	0.264101i
$317$	−7.59654	−	2.03549i	−0.426664	−	0.114324i	0.0390957	−	0.999235i	$-0.487552\pi$
$317$	−7.59654	−	2.03549i	−0.426664	−	0.114324i	−0.465760	+	0.884911i	$0.654219\pi$
$318$	1.74970	−	6.52998i	0.0981185	−	0.366183i
$319$	−1.85854	+	6.93616i	−0.104058	+	0.388350i
$320$	5.19109	+	1.39095i	0.290191	+	0.0777564i
$321$	7.20862	+	4.16190i	0.402346	+	0.232295i
$322$		0			0
$323$	4.34961	−	16.2330i	0.242019	−	0.903227i
$324$	−3.85802	+	2.22743i	−0.214334	+	0.123746i
$325$	2.88375	−	1.90745i	0.159962	−	0.105806i
$326$	−13.7905	+	23.8859i	−0.763788	+	1.32292i
$327$	−7.21349	+	1.93285i	−0.398907	+	0.106887i
$328$	−5.91716	+	3.41627i	−0.326720	+	0.188632i
$329$		0			0
$330$	−1.49172	+	1.49172i	−0.0821165	+	0.0821165i
$331$	11.5133	−	11.5133i	0.632826	−	0.632826i	−0.315950	−	0.948776i	$-0.602323\pi$
$331$	11.5133	−	11.5133i	0.632826	−	0.632826i	0.948776	+	0.315950i	$0.102323\pi$
$332$	−1.36832	−	0.366640i	−0.0750963	−	0.0201220i
$333$	12.0149	−	3.21938i	0.658411	−	0.176421i
$334$		−	11.2675i		−	0.616529i
$335$	−0.861417	−	1.49202i	−0.0470642	−	0.0815176i
$336$		0			0
$337$			11.0114i			0.599827i	0.953966	+	0.299913i	$0.0969578\pi$
$337$			11.0114i			0.599827i	−0.953966	+	0.299913i	$0.903042\pi$
$338$	−13.4252	+	17.1618i	−0.730233	+	0.933480i
$339$	−4.48195	−	2.58765i	−0.243426	−	0.140542i
$340$	6.88532	−	6.88532i	0.373409	−	0.373409i
$341$	−7.34737	−	4.24200i	−0.397882	−	0.229717i
$342$	6.10183	−	10.5687i	0.329949	−	0.571488i
$343$		0			0
$344$	0.446530	+	1.66647i	0.0240753	+	0.0898501i
$345$	2.70957	+	2.70957i	0.145879	+	0.145879i
$346$	−4.12863	−	15.4082i	−0.221956	−	0.828352i
$347$	−2.36362	−	4.09391i	−0.126886	−	0.219772i	0.795583	−	0.605845i	$-0.207165\pi$
$347$	−2.36362	−	4.09391i	−0.126886	−	0.219772i	−0.922468	+	0.386073i	$0.873831\pi$
$348$	−1.88741	+	3.26910i	−0.101176	+	0.175242i
$349$	−22.4353	−	6.01151i	−1.20093	−	0.321789i	−0.397734	−	0.917501i	$-0.630203\pi$
$349$	−22.4353	−	6.01151i	−1.20093	−	0.321789i	−0.803198	+	0.595712i	$0.796870\pi$
$350$		0			0
$351$	−11.5083	−	5.74223i	−0.614269	−	0.306498i
$352$	2.12447	+	3.67970i	0.113235	+	0.196128i
$353$	−9.29908	−	9.29908i	−0.494940	−	0.494940i	0.414919	−	0.909859i	$-0.363810\pi$
$353$	−9.29908	−	9.29908i	−0.494940	−	0.494940i	−0.909859	+	0.414919i	$0.863810\pi$
$354$	0.543886			0.0289072
$355$	−23.3880			−1.24130
$356$	4.59271	+	4.59271i	0.243413	+	0.243413i
$357$		0			0
$358$	−9.72526	+	2.60588i	−0.513996	+	0.137725i
$359$	2.43301	−	9.08010i	0.128409	−	0.479229i	−0.871529	−	0.490344i	$-0.836871\pi$
$359$	2.43301	−	9.08010i	0.128409	−	0.479229i	0.999938	+	0.0111144i	$0.00353790\pi$
$360$	−9.01037	+	5.20214i	−0.474888	+	0.274177i
$361$		−	11.1170i		−	0.585105i
$362$	−2.62867	−	9.81032i	−0.138160	−	0.515619i
$363$	−6.40052			−0.335940
$364$		0			0
$365$	2.92826			0.153272
$366$	−3.60439	−	13.4518i	−0.188404	−	0.703135i
$367$		−	7.31961i		−	0.382081i	−0.981582	−	0.191040i	$-0.938814\pi$
$367$		−	7.31961i		−	0.382081i	0.981582	−	0.191040i	$-0.0611861\pi$
$368$	12.8484	−	7.41801i	0.669767	−	0.386690i
$369$	2.29780	−	8.57550i	0.119619	−	0.446423i
$370$	−15.6104	+	4.18279i	−0.811544	+	0.217453i
$371$		0			0
$372$	−3.15361	−	3.15361i	−0.163507	−	0.163507i
$373$	−1.08512			−0.0561856			−0.0280928	−	0.999605i	$-0.508943\pi$
$373$	−1.08512			−0.0561856			−0.0280928	+	0.999605i	$0.508943\pi$
$374$	−9.84951			−0.509306
$375$	−5.40196	−	5.40196i	−0.278956	−	0.278956i
$376$	3.06241	+	5.30425i	0.157932	+	0.273546i
$377$	26.3229	−	1.60191i	1.35570	−	0.0825025i
$378$		0			0
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.454119	−	0.890941i	$-0.650046\pi$
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.838749	+	0.544518i	$0.816713\pi$
$380$	−2.28374	+	3.95555i	−0.117153	+	0.202915i
$381$	−2.51061	−	4.34851i	−0.128623	−	0.222781i
$382$	−9.38197	−	35.0140i	−0.480023	−	1.79147i
$383$	3.76918	+	3.76918i	0.192596	+	0.192596i	0.796817	−	0.604221i	$-0.206516\pi$
$383$	3.76918	+	3.76918i	0.192596	+	0.192596i	−0.604221	+	0.796817i	$0.706516\pi$
$384$	−2.16834	−	8.09234i	−0.110652	−	0.412961i
$385$		0			0
$386$	8.12146	−	14.0668i	0.413372	−	0.715981i
$387$	−1.94141	−	1.12088i	−0.0986876	−	0.0569773i
$388$	−7.15375	+	7.15375i	−0.363177	+	0.363177i
$389$	−2.97841	−	1.71958i	−0.151011	−	0.0871864i	0.422590	−	0.906321i	$-0.361121\pi$
$389$	−2.97841	−	1.71958i	−0.151011	−	0.0871864i	−0.573602	+	0.819134i	$0.694454\pi$
$390$	6.93249	+	3.45905i	0.351040	+	0.175156i
$391$			17.8907i			0.904773i
$392$		0			0
$393$	−6.36465	−	11.0239i	−0.321054	−	0.556082i
$394$			7.76196i			0.391042i
$395$	22.5295	−	6.03677i	1.13358	−	0.303743i
$396$	−1.99015	−	0.533259i	−0.100009	−	0.0267973i
$397$	0.424872	−	0.424872i	0.0213237	−	0.0213237i	−0.696365	−	0.717688i	$-0.745200\pi$
$397$	0.424872	−	0.424872i	0.0213237	−	0.0213237i	0.717688	+	0.696365i	$0.245200\pi$
$398$	25.5525	−	25.5525i	1.28083	−	1.28083i
$399$		0			0
$400$	−4.12212	+	2.37991i	−0.206106	+	0.118995i
$401$	−11.5834	+	3.10377i	−0.578448	+	0.154995i	−0.536168	−	0.844111i	$-0.680129\pi$
$401$	−11.5834	+	3.10377i	−0.578448	+	0.154995i	−0.0422800	+	0.999106i	$0.513462\pi$
$402$	−0.458047	+	0.793361i	−0.0228453	+	0.0395693i
$403$	−6.22113	+	30.5301i	−0.309896	+	1.52081i
$404$	−5.60409	+	3.23553i	−0.278814	+	0.160973i
$405$	2.86414	−	10.6891i	0.142320	−	0.531147i
$406$		0			0
$407$	4.07819	+	2.35454i	0.202148	+	0.116710i
$408$	7.35898	+	1.97183i	0.364324	+	0.0976203i
$409$	−3.00424	+	11.2120i	−0.148550	+	0.554396i	0.851022	+	0.525131i	$0.175984\pi$
$409$	−3.00424	+	11.2120i	−0.148550	+	0.554396i	−0.999572	+	0.0292657i	$0.990683\pi$
$410$	−2.98542	+	11.1418i	−0.147440	+	0.550252i
$411$	6.62441	+	1.77501i	0.326758	+	0.0875546i
$412$	−7.24558	−	4.18324i	−0.356964	−	0.206093i
$413$		0			0
$414$	−3.36248	+	12.5489i	−0.165257	+	0.616747i
$415$	3.04747	−	1.75946i	0.149594	−	0.0863683i
$416$	10.3432	−	11.6837i	0.507119	−	0.572842i
$417$	−5.19520	+	8.99836i	−0.254410	+	0.440651i
$418$	4.46267	−	1.19577i	0.218276	−	0.0584870i
$419$	−30.9881	+	17.8910i	−1.51387	+	0.874032i	−0.513999	+	0.857791i	$0.671836\pi$
$419$	−30.9881	+	17.8910i	−1.51387	+	0.874032i	−0.999868	+	0.0162408i	$0.994830\pi$
$420$		0			0
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	−0.786646	−	0.617404i	$-0.788184\pi$
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	0.617404	+	0.786646i	$0.288184\pi$
$422$	17.5288	−	17.5288i	0.853287	−	0.853287i
$423$	−7.68723	−	2.05979i	−0.373766	−	0.100150i
$424$	12.1922	−	3.26690i	0.592107	−	0.158655i
$425$		−	5.73985i		−	0.278424i
$426$	6.21813	+	10.7701i	0.301269	+	0.521814i
$427$		0			0
$428$		−	10.5622i		−	0.510544i
$429$	−0.715668	−	2.14108i	−0.0345528	−	0.103372i
$430$	2.52239	+	1.45630i	0.121640	+	0.0702291i
$431$	0.347144	−	0.347144i	0.0167213	−	0.0167213i	−0.698697	−	0.715418i	$-0.746236\pi$
$431$	0.347144	−	0.347144i	0.0167213	−	0.0167213i	0.715418	+	0.698697i	$0.246236\pi$
$432$	15.3336	+	8.85286i	0.737739	+	0.425934i
$433$	8.89347	−	15.4039i	0.427393	−	0.740266i	−0.569248	−	0.822166i	$-0.692765\pi$
$433$	8.89347	−	15.4039i	0.427393	−	0.740266i	0.996641	+	0.0818999i	$0.0260988\pi$
$434$		0			0
$435$	−2.42693	−	9.05744i	−0.116363	−	0.434271i
$436$	6.70070	+	6.70070i	0.320905	+	0.320905i
$437$	−2.17201	−	8.10604i	−0.103901	−	0.387764i
$438$	−0.778531	−	1.34846i	−0.0371997	−	0.0644317i
$439$	14.3012	−	24.7704i	0.682559	−	1.18223i	−0.291639	−	0.956529i	$-0.594200\pi$
$439$	14.3012	−	24.7704i	0.682559	−	1.18223i	0.974197	−	0.225698i	$-0.0724662\pi$
$440$	−3.80467	−	1.01946i	−0.181381	−	0.0486008i
$441$		0			0
$442$	11.4672	+	34.3065i	0.545437	+	1.63179i
$443$	3.68575	+	6.38391i	0.175115	+	0.303309i	0.940201	−	0.340620i	$-0.110637\pi$
$443$	3.68575	+	6.38391i	0.175115	+	0.303309i	−0.765086	+	0.643928i	$0.777304\pi$
$444$	1.75043	+	1.75043i	0.0830716	+	0.0830716i
$445$	−16.1342			−0.764836
$446$	35.7837			1.69441
$447$	−8.43576	−	8.43576i	−0.398998	−	0.398998i
$448$		0			0
$449$	22.5220	−	6.03476i	1.06288	−	0.284798i	0.315315	−	0.948987i	$-0.397890\pi$
$449$	22.5220	−	6.03476i	1.06288	−	0.284798i	0.747565	+	0.664189i	$0.231223\pi$
$450$	1.07878	−	4.02606i	0.0508541	−	0.189790i
$451$	2.91077	−	1.68053i	0.137063	−	0.0791332i
$452$			6.56704i			0.308887i
$453$	−0.00601399	−	0.0224445i	−0.000282562	−	0.00105454i
$454$	−22.6558			−1.06329
$455$		0			0
$456$	−3.57364			−0.167351
$457$	−1.16783	−	4.35841i	−0.0546289	−	0.203878i	0.933217	−	0.359313i	$-0.116989\pi$
$457$	−1.16783	−	4.35841i	−0.0546289	−	0.203878i	−0.987846	+	0.155435i	$0.950322\pi$
$458$			12.0544i			0.563263i
$459$	−18.4908	+	10.6757i	−0.863076	+	0.498297i
$460$	1.25848	−	4.69671i	0.0586769	−	0.218985i
$461$	32.1809	−	8.62285i	1.49882	−	0.401606i	0.586112	−	0.810230i	$-0.300658\pi$
$461$	32.1809	−	8.62285i	1.49882	−	0.401606i	0.912703	+	0.408623i	$0.133991\pi$
$462$		0			0
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.883028	+	0.469321i	$0.155501\pi$
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.469321	+	0.883028i	$0.344499\pi$
$464$	−36.3047			−1.68540
$465$	11.0787			0.513761
$466$	27.5016	+	27.5016i	1.27399	+	1.27399i
$467$	−2.85866	−	4.95135i	−0.132283	−	0.229121i	0.792273	−	0.610167i	$-0.208897\pi$
$467$	−2.85866	−	4.95135i	−0.132283	−	0.229121i	−0.924556	+	0.381045i	$0.875564\pi$
$468$	0.459626	+	7.55267i	0.0212462	+	0.349122i
$469$		0			0
$470$	9.98767	+	2.67619i	0.460697	+	0.123443i
$471$	−2.29227	+	3.97033i	−0.105622	+	0.182943i
$472$	0.507749	+	0.879447i	0.0233710	+	0.0404798i
$473$	−0.219657	−	0.819771i	−0.0100998	−	0.0376931i
$474$	−8.76981	−	8.76981i	−0.402811	−	0.402811i
$475$	0.696841	+	2.60065i	0.0319733	+	0.119326i
$476$		0			0
$477$	−8.20054	+	14.2038i	−0.375477	+	0.650345i
$478$	5.69239	+	3.28650i	0.260364	+	0.150321i
$479$	−23.5643	+	23.5643i	−1.07668	+	1.07668i	−0.0798746	+	0.996805i	$0.525452\pi$
$479$	−23.5643	+	23.5643i	−1.07668	+	1.07668i	−0.996805	+	0.0798746i	$0.974548\pi$
$480$	−4.80506	−	2.77420i	−0.219320	−	0.126624i
$481$	3.45307	−	16.9459i	0.157446	−	0.772665i
$482$		−	5.34507i		−	0.243461i
$483$		0			0
$484$	4.06087	+	7.03363i	0.184585	+	0.319711i
$485$		−	25.1312i		−	1.14115i
$486$	−23.0089	+	6.16522i	−1.04371	+	0.279660i
$487$	14.6038	+	3.91309i	0.661763	+	0.177319i	0.574041	−	0.818826i	$-0.305375\pi$
$487$	14.6038	+	3.91309i	0.661763	+	0.177319i	0.0877214	+	0.996145i	$0.472041\pi$
$488$	18.3862	−	18.3862i	0.832303	−	0.832303i
$489$	−7.42080	+	7.42080i	−0.335580	+	0.335580i
$490$		0			0
$491$	−3.79911	+	2.19342i	−0.171451	+	0.0989875i	−0.583270	−	0.812278i	$-0.698227\pi$
$491$	−3.79911	+	2.19342i	−0.171451	+	0.0989875i	0.411819	+	0.911266i	$0.364894\pi$
$492$	1.70664	−	0.457294i	0.0769415	−	0.0206164i
$493$	21.8899	−	37.9144i	0.985871	−	1.70758i
$494$	−9.36056	−	14.1516i	−0.421151	−	0.636713i
$495$	4.43238	−	2.55904i	0.199221	−	0.115020i
$496$	11.1016	−	41.4317i	0.498476	−	1.86034i
$497$		0			0
$498$	−1.62045	−	0.935569i	−0.0726142	−	0.0419238i
$499$	−19.3575	−	5.18682i	−0.866560	−	0.232194i	−0.201960	−	0.979394i	$-0.564731\pi$
$499$	−19.3575	−	5.18682i	−0.866560	−	0.232194i	−0.664599	+	0.747200i	$0.731398\pi$
$500$	−2.50897	+	9.36361i	−0.112205	+	0.418753i
$501$	1.10963	−	4.14118i	0.0495745	−	0.185014i
$502$	19.0940	+	5.11623i	0.852209	+	0.228349i
$503$	−0.917016	−	0.529439i	−0.0408877	−	0.0236065i	0.479417	−	0.877587i	$-0.340848\pi$
$503$	−0.917016	−	0.529439i	−0.0408877	−	0.0236065i	−0.520305	+	0.853981i	$0.674182\pi$
$504$		0			0
$505$	4.16041	−	15.5268i	0.185136	−	0.690936i
$506$	−4.25947	+	2.45920i	−0.189356	+	0.109325i
$507$	−6.62432	+	4.98544i	−0.294196	+	0.221411i
$508$	−3.18576	+	5.51790i	−0.141345	+	0.244817i
$509$	−10.8606	+	2.91008i	−0.481387	+	0.128987i	−0.491348	−	0.870963i	$-0.663496\pi$
$509$	−10.8606	+	2.91008i	−0.481387	+	0.128987i	0.00996149	+	0.999950i	$0.496829\pi$
$510$	11.1386	−	6.43089i	0.493227	−	0.284765i
$511$		0			0
$512$	−1.18017	+	1.18017i	−0.0521565	+	0.0521565i
$513$	7.08184	−	7.08184i	0.312671	−	0.312671i
$514$	27.0212	+	7.24032i	1.19186	+	0.319357i
$515$	20.0748	−	5.37903i	0.884601	−	0.237028i
$516$		−	0.446140i		−	0.0196402i
$517$	−1.50646	−	2.60927i	−0.0662541	−	0.114755i
$518$		0			0
$519$		−	6.06965i		−	0.266428i
$520$	0.878691	+	14.4388i	0.0385332	+	0.633185i
$521$	−14.6510	−	8.45874i	−0.641871	−	0.370584i	0.143464	−	0.989656i	$-0.454176\pi$
$521$	−14.6510	−	8.45874i	−0.641871	−	0.370584i	−0.785335	+	0.619071i	$0.787509\pi$
$522$	22.4799	−	22.4799i	0.983917	−	0.983917i
$523$	0.268849	+	0.155220i	0.0117560	+	0.00678731i	0.505866	−	0.862612i	$-0.331173\pi$
$523$	0.268849	+	0.155220i	0.0117560	+	0.00678731i	−0.494111	+	0.869399i	$0.664506\pi$
$524$	−8.07621	+	13.9884i	−0.352811	+	0.611086i
$525$		0			0
$526$	−4.12779	−	15.4051i	−0.179980	−	0.671695i
$527$	36.5750	+	36.5750i	1.59323	+	1.59323i
$528$	0.804367	+	3.00194i	0.0350056	+	0.130643i
$529$	−7.03308	−	12.1816i	−0.305786	−	0.529637i
$530$	10.6546	−	18.4543i	0.462806	−	0.801603i
$531$	−1.27455	−	0.341514i	−0.0553106	−	0.0148204i
$532$		0			0
$533$	−9.24224	−	8.18188i	−0.400326	−	0.354396i
$534$	4.28959	+	7.42978i	0.185629	+	0.321518i
$535$	18.5526	+	18.5526i	0.802099	+	0.802099i
$536$	−1.71045			−0.0738803
$537$	−3.83100			−0.165320
$538$	−0.377635	−	0.377635i	−0.0162810	−	0.0162810i
$539$		0			0
$540$	5.60519	−	1.50190i	0.241209	−	0.0646317i
$541$	−8.05676	+	30.0682i	−0.346387	+	1.29273i	0.544597	+	0.838698i	$0.316683\pi$
$541$	−8.05676	+	30.0682i	−0.346387	+	1.29273i	−0.890984	+	0.454036i	$0.849984\pi$
$542$	38.9581	−	22.4925i	1.67340	−	0.966135i
$543$		−	3.86450i		−	0.165842i
$544$	−6.70465	−	25.0221i	−0.287459	−	1.07281i
$545$	−23.5396			−1.00833
$546$		0			0
$547$	−13.8672			−0.592920			−0.296460	−	0.955045i	$-0.595806\pi$
$547$	−13.8672			−0.592920			−0.296460	+	0.955045i	$0.595806\pi$
$548$	−2.25234	−	8.40583i	−0.0962150	−	0.359079i
$549$			33.7862i			1.44196i
$550$	1.36656	−	0.788983i	0.0582702	−	0.0336423i
$551$	−5.31504	+	19.8360i	−0.226428	+	0.845042i
$552$	3.67475	−	0.984647i	0.156408	−	0.0419094i
$553$		0			0
$554$	−17.9574	−	17.9574i	−0.762936	−	0.762936i
$555$	−6.14927			−0.261022
$556$	13.1846			0.559150
$557$	−16.0453	−	16.0453i	−0.679860	−	0.679860i	0.280108	−	0.959968i	$-0.409630\pi$
$557$	−16.0453	−	16.0453i	−0.679860	−	0.679860i	−0.959968	+	0.280108i	$0.909630\pi$
$558$	18.7804	+	32.5286i	0.795038	+	1.37705i
$559$	−2.59959	+	1.71949i	−0.109951	+	0.0727266i
$560$		0			0
$561$	−3.62003	−	0.969985i	−0.152838	−	0.0409528i
$562$	6.40703	−	11.0973i	0.270264	−	0.468111i
$563$	11.2217	+	19.4366i	0.472940	+	0.819156i	0.999520	−	0.0309690i	$-0.00985932\pi$
$563$	11.2217	+	19.4366i	0.472940	+	0.819156i	−0.526580	+	0.850125i	$0.676526\pi$
$564$	−0.409927	−	1.52987i	−0.0172610	−	0.0644190i
$565$	−11.5350	−	11.5350i	−0.485283	−	0.485283i
$566$	0.777562	+	2.90190i	0.0326834	+	0.121976i
$567$		0			0
$568$	−11.6100	+	20.1090i	−0.487143	+	0.843756i
$569$	11.1921	+	6.46175i	0.469196	+	0.270891i	0.715903	−	0.698200i	$-0.246015\pi$
$569$	11.1921	+	6.46175i	0.469196	+	0.270891i	−0.246707	+	0.969090i	$0.579349\pi$
$570$	−4.26602	+	4.26602i	−0.178684	+	0.178684i
$571$	15.1053	+	8.72106i	0.632138	+	0.364965i	0.781580	−	0.623805i	$-0.214414\pi$
$571$	15.1053	+	8.72106i	0.632138	+	0.364965i	−0.149442	+	0.988771i	$0.547748\pi$
$572$	−1.89880	+	2.14488i	−0.0793928	+	0.0896821i
$573$		−	13.7928i		−	0.576202i
$574$		0			0
$575$	−1.43312	−	2.48223i	−0.0597650	−	0.103516i
$576$			6.93292i			0.288872i
$577$	13.9338	−	3.73355i	0.580071	−	0.155430i	0.0431598	−	0.999068i	$-0.486258\pi$
$577$	13.9338	−	3.73355i	0.580071	−	0.155430i	0.536912	+	0.843639i	$0.319591\pi$
$578$	30.4813	+	8.16745i	1.26786	+	0.339721i
$579$	4.37022	−	4.37022i	0.181620	−	0.181620i
$580$	−8.41357	+	8.41357i	−0.349354	+	0.349354i
$581$		0			0
$582$	−11.5729	+	6.68160i	−0.479711	+	0.276961i
$583$	−5.99760	+	1.60705i	−0.248395	+	0.0665573i
$584$	1.45361	−	2.51772i	0.0601507	−	0.104184i
$585$	−14.0737	−	12.4590i	−0.581874	−	0.515116i
$586$	38.4555	−	22.2023i	1.58858	−	0.917167i
$587$	4.97130	−	18.5532i	0.205188	−	0.765771i	−0.784205	−	0.620502i	$-0.786929\pi$
$587$	4.97130	−	18.5532i	0.205188	−	0.765771i	0.989392	−	0.145268i	$-0.0464046\pi$
$588$		0			0
$589$	−21.0120	−	12.1313i	−0.865783	−	0.499860i
$590$	1.65596	+	0.443713i	0.0681748	+	0.0182674i
$591$	−0.764402	+	2.85279i	−0.0314433	+	0.117348i
$592$	−6.16199	+	22.9969i	−0.253256	+	0.945165i
$593$	−2.51561	−	0.674056i	−0.103304	−	0.0276802i	0.206797	−	0.978384i	$-0.433696\pi$
$593$	−2.51561	−	0.674056i	−0.103304	−	0.0276802i	−0.310101	+	0.950704i	$0.600363\pi$
$594$	−5.08337	−	2.93489i	−0.208573	−	0.120420i
$595$		0			0
$596$	−3.91804	+	14.6223i	−0.160489	+	0.598954i
$597$	11.9078	−	6.87500i	0.487356	−	0.281375i
$598$	13.5246	+	11.9729i	0.553063	+	0.489610i
$599$	−12.4050	+	21.4861i	−0.506855	+	0.877898i	0.493114	+	0.869965i	$0.335859\pi$
$599$	−12.4050	+	21.4861i	−0.506855	+	0.877898i	−0.999969	+	0.00793343i	$0.997475\pi$
$600$	−1.17896	+	0.315903i	−0.0481310	+	0.0128967i
$601$	15.2889	−	8.82708i	0.623649	−	0.360064i	−0.154639	−	0.987971i	$-0.549422\pi$
$601$	15.2889	−	8.82708i	0.623649	−	0.360064i	0.778288	+	0.627907i	$0.216088\pi$
$602$		0			0
$603$	1.57155	−	1.57155i	0.0639987	−	0.0639987i
$604$	−0.0208490	+	0.0208490i	−0.000848334	+	0.000848334i
$605$	−19.4876	−	5.22168i	−0.792282	−	0.212291i
$606$	−8.25620	+	2.21224i	−0.335385	+	0.0898662i
$607$			15.0740i			0.611835i	0.952058	+	0.305917i	$0.0989631\pi$
$607$			15.0740i			0.611835i	−0.952058	+	0.305917i	$0.901037\pi$
$608$	6.07556	+	10.5232i	0.246397	+	0.426771i
$609$		0			0
$610$		−	43.8969i		−	1.77733i
$611$	−7.33438	+	8.28491i	−0.296717	+	0.335172i
$612$	10.8786	+	6.28074i	0.439740	+	0.253884i
$613$	−24.8050	+	24.8050i	−1.00186	+	1.00186i	−0.00186450	+	0.999998i	$0.500593\pi$
$613$	−24.8050	+	24.8050i	−1.00186	+	1.00186i	−0.999998	+	0.00186450i	$0.999407\pi$
$614$	3.17585	+	1.83358i	0.128167	+	0.0739972i
$615$	−2.19449	+	3.80097i	−0.0884904	+	0.153270i
$616$		0			0
$617$	9.01921	+	33.6601i	0.363100	+	1.35511i	0.869979	+	0.493089i	$0.164132\pi$
$617$	9.01921	+	33.6601i	0.363100	+	1.35511i	−0.506879	+	0.862017i	$0.669201\pi$
$618$	−7.81429	−	7.81429i	−0.314337	−	0.314337i
$619$	−2.05655	−	7.67515i	−0.0826597	−	0.308490i	0.912201	−	0.409743i	$-0.134382\pi$
$619$	−2.05655	−	7.67515i	−0.0826597	−	0.308490i	−0.994861	+	0.101253i	$0.967715\pi$
$620$	−7.02896	−	12.1745i	−0.282290	−	0.488940i
$621$	−5.33095	+	9.23348i	−0.213924	+	0.370527i
$622$	47.4915	+	12.7253i	1.90423	+	0.510238i
$623$		0			0
$624$	9.51949	−	6.29663i	0.381084	−	0.252067i
$625$	−9.64286	−	16.7019i	−0.385715	−	0.668077i
$626$	33.1665	+	33.1665i	1.32560	+	1.32560i
$627$	1.75795			0.0702056
$628$	5.81741			0.232140
$629$	−20.3011	−	20.3011i	−0.809460	−	0.809460i
$630$		0			0
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.677559	−	0.735469i	$-0.263038\pi$
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.954517	+	0.298155i	$0.0963713\pi$
$632$	5.99339	−	22.3676i	0.238404	−	0.889737i
$633$	8.16866	−	4.71618i	0.324675	−	0.187451i
$634$			13.1816i			0.523507i
$635$	−4.09642	−	15.2880i	−0.162561	−	0.606687i
$636$	−3.26404			−0.129428
$637$		0			0
$638$	12.0357			0.476497
$639$	−7.80890	−	29.1432i	−0.308915	−	1.15289i
$640$		−	26.4076i		−	1.04385i
$641$	17.7415	−	10.2431i	0.700748	−	0.404577i	−0.106878	−	0.994272i	$-0.534085\pi$
$641$	17.7415	−	10.2431i	0.700748	−	0.404577i	0.807626	+	0.589695i	$0.200752\pi$
$642$	3.61088	−	13.4760i	0.142510	−	0.531855i
$643$	−20.9593	+	5.61604i	−0.826556	+	0.221475i	−0.647211	−	0.762311i	$-0.724065\pi$
$643$	−20.9593	+	5.61604i	−0.826556	+	0.221475i	−0.179345	+	0.983786i	$0.557398\pi$
$644$		0			0
$645$	0.783647	+	0.783647i	0.0308561	+	0.0308561i
$646$	−28.1676			−1.10824
$647$	−39.1337			−1.53850			−0.769252	−	0.638945i	$-0.779371\pi$
$647$	−39.1337			−1.53850			−0.769252	+	0.638945i	$0.779371\pi$
$648$	−7.76875	−	7.76875i	−0.305185	−	0.305185i
$649$	−0.249772	−	0.432618i	−0.00980440	−	0.0169817i
$650$	−4.33908	−	3.84126i	−0.170193	−	0.150666i
$651$		0			0
$652$	12.8630	+	3.44664i	0.503755	+	0.134981i
$653$	14.8092	−	25.6503i	0.579528	−	1.00377i	−0.416005	−	0.909362i	$-0.636570\pi$
$653$	14.8092	−	25.6503i	0.579528	−	1.00377i	0.995533	−	0.0944103i	$-0.0300966\pi$
$654$	6.25845	+	10.8400i	0.244725	+	0.423876i
$655$	−10.3848	−	38.7566i	−0.405768	−	1.51435i
$656$	12.0157	+	12.0157i	0.469135	+	0.469135i
$657$	0.977702	+	3.64883i	0.0381438	+	0.142355i
$658$		0			0
$659$	1.87682	−	3.25074i	0.0731104	−	0.126631i	−0.827153	−	0.561977i	$-0.810041\pi$
$659$	1.87682	−	3.25074i	0.0731104	−	0.126631i	0.900263	+	0.435346i	$0.143374\pi$
$660$	0.882106	+	0.509284i	0.0343359	+	0.0198239i
$661$	30.7260	−	30.7260i	1.19510	−	1.19510i	0.219487	−	0.975615i	$-0.429562\pi$
$661$	30.7260	−	30.7260i	1.19510	−	1.19510i	0.975615	−	0.219487i	$-0.0704385\pi$
$662$	−23.6341	−	13.6452i	−0.918566	−	0.530334i
$663$	0.836048	+	13.7381i	0.0324694	+	0.533544i
$664$		−	3.49363i		−	0.135579i
$665$		0			0
$666$	−10.4242	−	18.0552i	−0.403928	−	0.699623i
$667$		−	21.8617i		−	0.846488i
$668$	−5.25482	+	1.40802i	−0.203315	+	0.0544781i
$669$	13.1517	+	3.52399i	0.508475	+	0.136245i
$670$	−2.04185	+	2.04185i	−0.0788835	+	0.0788835i
$671$	−9.04453	+	9.04453i	−0.349160	+	0.349160i
$672$		0			0
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.0186390	−	0.999826i	$-0.494067\pi$
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.875194	+	0.483771i	$0.160733\pi$
$674$	17.8271	−	4.77675i	0.686673	−	0.183993i
$675$	1.71032	−	2.96236i	0.0658303	−	0.114021i
$676$	9.68143	+	4.11651i	0.372363	+	0.158327i
$677$	−18.0711	+	10.4333i	−0.694527	+	0.400985i	−0.805306	−	0.592860i	$-0.797999\pi$
$677$	−18.0711	+	10.4333i	−0.694527	+	0.400985i	0.110779	+	0.993845i	$0.464666\pi$
$678$	−2.24506	+	8.37867i	−0.0862209	+	0.321781i
$679$		0			0
$680$	20.7971	+	12.0072i	0.797532	+	0.460456i
$681$	−8.32680	−	2.23116i	−0.319084	−	0.0854982i
$682$	−3.68038	+	13.7354i	−0.140929	+	0.525954i
$683$	8.48852	−	31.6796i	0.324804	−	1.21219i	−0.589704	−	0.807619i	$-0.700756\pi$
$683$	8.48852	−	31.6796i	0.324804	−	1.21219i	0.914509	−	0.404567i	$-0.132578\pi$
$684$	−5.69143	−	1.52501i	−0.217617	−	0.0583103i
$685$	18.7211	+	10.8087i	0.715298	+	0.412977i
$686$		0			0
$687$	−1.18712	+	4.43039i	−0.0452914	+	0.169030i
$688$	3.71593	−	2.14539i	0.141668	−	0.0817923i
$689$	12.5801	+	19.0191i	0.479264	+	0.724570i
$690$	3.21130	−	5.56214i	0.122252	−	0.211747i
$691$	−43.4491	+	11.6421i	−1.65288	+	0.442888i	−0.960418	−	0.278564i	$-0.910141\pi$
$691$	−43.4491	+	11.6421i	−1.65288	+	0.442888i	−0.692464	+	0.721453i	$0.743475\pi$
$692$	−6.67003	+	3.85094i	−0.253556	+	0.146391i
$693$		0			0
$694$	−5.60257	+	5.60257i	−0.212671	+	0.212671i
$695$	−23.1588	+	23.1588i	−0.878463	+	0.878463i
$696$	−8.99236	−	2.40950i	−0.340855	−	0.0913317i
$697$	−19.7934	+	5.30361i	−0.749727	+	0.200889i
$698$			38.9298i			1.47352i
$699$	7.39940	+	12.8161i	0.279871	+	0.484751i
$700$		0			0
$701$			38.7293i			1.46279i	0.681956	+	0.731393i	$0.261129\pi$
$701$			38.7293i			1.46279i	−0.681956	+	0.731393i	$0.738871\pi$
$702$	−4.30417	+	21.1226i	−0.162450	+	0.797223i
$703$	11.6628	+	6.73352i	0.439871	+	0.253960i
$704$	−1.85593	+	1.85593i	−0.0699482	+	0.0699482i
$705$	3.40726	+	1.96718i	0.128325	+	0.0740884i
$706$	−11.0210	+	19.0889i	−0.414780	+	0.718420i
$707$		0			0
$708$	−0.0679660	−	0.253653i	−0.00255432	−	0.00953285i
$709$	20.8624	+	20.8624i	0.783504	+	0.783504i	0.980420	−	0.196917i	$-0.0630928\pi$
$709$	20.8624	+	20.8624i	0.783504	+	0.783504i	−0.196917	+	0.980420i	$0.563093\pi$
$710$	10.1457	+	37.8644i	0.380763	+	1.42103i
$711$	15.0446	+	26.0580i	0.564215	+	0.977250i
$712$	−8.00915	+	13.8723i	−0.300156	+	0.519885i
$713$	24.9490	+	6.68507i	0.934348	+	0.250358i
$714$		0			0
$715$	−0.432246	−	7.10276i	−0.0161651	−	0.265628i
$716$	2.43061	+	4.20994i	0.0908362	+	0.157333i
$717$	1.76849	+	1.76849i	0.0660455	+	0.0660455i
$718$	−15.7559			−0.588003
$719$	−8.46228			−0.315590			−0.157795	−	0.987472i	$-0.550438\pi$
$719$	−8.46228			−0.315590			−0.157795	+	0.987472i	$0.550438\pi$
$720$	18.2970	+	18.2970i	0.681888	+	0.681888i
$721$		0			0
$722$	−17.9981	+	4.82258i	−0.669820	+	0.179478i
$723$	0.526386	−	1.96450i	0.0195765	−	0.0730605i
$724$	−4.24676	+	2.45187i	−0.157830	+	0.0911229i
$725$			7.01385i			0.260488i
$726$	2.77656	+	10.3623i	0.103048	+	0.384580i
$727$	3.27056			0.121299			0.0606493	−	0.998159i	$-0.480683\pi$
$727$	3.27056			0.121299			0.0606493	+	0.998159i	$0.480683\pi$
$728$		0			0
$729$	7.45103			0.275964
$730$	−1.27028	−	4.74076i	−0.0470153	−	0.175463i
$731$			5.17425i			0.191376i
$732$	−5.82309	+	3.36196i	−0.215228	+	0.124262i
$733$	3.57318	−	13.3353i	0.131979	−	0.492551i	−0.868014	−	0.496541i	$-0.834603\pi$
$733$	3.57318	−	13.3353i	0.131979	−	0.492551i	0.999992	+	0.00399003i	$0.00127007\pi$
$734$	−11.8502	+	3.17526i	−0.437400	+	0.117201i
$735$		0			0
$736$	−9.14692	−	9.14692i	−0.337160	−	0.337160i
$737$	0.841407			0.0309936
$738$	−14.8803			−0.547750
$739$	30.0608	+	30.0608i	1.10580	+	1.10580i	0.993696	+	0.112109i	$0.0357605\pi$
$739$	30.0608	+	30.0608i	1.10580	+	1.10580i	0.112109	+	0.993696i	$0.464240\pi$
$740$	3.90146	+	6.75753i	0.143420	+	0.248412i
$741$	−2.04666	−	6.12305i	−0.0751861	−	0.224936i
$742$		0			0
$743$	−47.1919	−	12.6450i	−1.73130	−	0.463901i	−0.750820	−	0.660507i	$-0.770341\pi$
$743$	−47.1919	−	12.6450i	−1.73130	−	0.463901i	−0.980482	+	0.196606i	$0.937008\pi$
$744$	5.49953	−	9.52547i	0.201623	−	0.349221i
$745$	−18.8021	−	32.5663i	−0.688857	−	1.19314i
$746$	0.470729	+	1.75678i	0.0172346	+	0.0643204i
$747$	3.20993	+	3.20993i	0.117445	+	0.117445i
$748$	1.23083	+	4.59352i	0.0450036	+	0.167956i
$749$		0			0
$750$	−6.40223	+	11.0890i	−0.233776	+	0.404913i
$751$	9.96838	+	5.75525i	0.363751	+	0.210012i	0.670725	−	0.741706i	$-0.265983\pi$
$751$	9.96838	+	5.75525i	0.363751	+	0.210012i	−0.306974	+	0.951718i	$0.599316\pi$
$752$	10.7711	−	10.7711i	0.392782	−	0.392782i
$753$	6.51387	+	3.76078i	0.237379	+	0.137051i
$754$	−14.0124	−	41.9211i	−0.510300	−	1.52668i
$755$		−	0.0732428i		−	0.00266558i
$756$		0			0
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	0.655562	−	0.755141i	$-0.272432\pi$
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	−0.981753	+	0.190163i	$0.939098\pi$
$758$			43.6743i			1.58632i
$759$	−1.80768	+	0.484368i	−0.0656148	+	0.0175814i
$760$	−10.8806	−	2.91545i	−0.394681	−	0.105754i
$761$	−7.83029	+	7.83029i	−0.283848	+	0.283848i	−0.834641	−	0.550794i	$-0.814325\pi$
$761$	−7.83029	+	7.83029i	−0.283848	+	0.283848i	0.550794	+	0.834641i	$0.314325\pi$
$762$	−5.95100	+	5.95100i	−0.215582	+	0.215582i
$763$		0			0
$764$	−15.1571	+	8.75096i	−0.548365	+	0.316599i
$765$	−30.1404	+	8.07610i	−1.08973	+	0.291992i
$766$	4.46711	−	7.73726i	0.161403	−	0.279559i
$767$	−1.21604	+	1.37364i	−0.0439088	+	0.0495993i
$768$	−9.20755	+	5.31598i	−0.332249	+	0.191824i
$769$	−2.87361	+	10.7245i	−0.103625	+	0.386734i	−0.998186	−	0.0602130i	$-0.980822\pi$
$769$	−2.87361	+	10.7245i	−0.103625	+	0.386734i	0.894561	+	0.446947i	$0.147489\pi$
$770$		0			0
$771$	9.21820	+	5.32213i	0.331986	+	0.191672i
$772$	−7.57523	−	2.02978i	−0.272638	−	0.0730533i
$773$	−0.718001	+	2.67962i	−0.0258247	+	0.0963792i	−0.977635	−	0.210307i	$-0.932554\pi$
$773$	−0.718001	+	2.67962i	−0.0258247	+	0.0963792i	0.951811	+	0.306686i	$0.0992203\pi$
$774$	−0.972476	+	3.62933i	−0.0349549	+	0.130454i
$775$	−8.00436	−	2.14476i	−0.287525	−	0.0770421i
$776$	−21.6079	−	12.4753i	−0.775678	−	0.447838i
$777$		0			0
$778$	−1.49192	+	5.56791i	−0.0534879	+	0.199619i
$779$	8.32421	−	4.80599i	0.298246	−	0.172192i
$780$	0.746893	−	3.66537i	0.0267431	−	0.131241i
$781$	5.71117	−	9.89204i	0.204362	−	0.353965i
$782$	28.9646	−	7.76103i	1.03577	−	0.277534i
$783$	22.5949	−	13.0452i	0.807477	−	0.466197i
$784$		0			0
$785$	−10.2183	+	10.2183i	−0.364707	+	0.364707i
$786$	−15.0864	+	15.0864i	−0.538113	+	0.538113i
$787$	37.6817	+	10.0968i	1.34321	+	0.359912i	0.857624	−	0.514278i	$-0.171940\pi$
$787$	37.6817	+	10.0968i	1.34321	+	0.359912i	0.485585	+	0.874189i	$0.338607\pi$
$788$	3.61995	−	0.969963i	0.128955	−	0.0345535i
$789$		−	6.06841i		−	0.216041i
$790$	−19.5467	−	33.8559i	−0.695441	−	1.20454i
$791$		0			0
$792$		−	5.08130i		−	0.180556i
$793$	42.0327	+	20.9728i	1.49262	+	0.744765i
$794$	−0.872166	−	0.503545i	−0.0309520	−	0.0178701i
$795$	5.73331	−	5.73331i	0.203340	−	0.203340i
$796$	−15.1101	−	8.72381i	−0.535563	−	0.309207i
$797$	−16.0998	+	27.8857i	−0.570285	+	0.987763i	0.426251	+	0.904605i	$0.359834\pi$
$797$	−16.0998	+	27.8857i	−0.570285	+	0.987763i	−0.996536	+	0.0831583i	$0.973499\pi$
$798$		0			0
$799$	4.75426	+	17.7431i	0.168193	+	0.627707i
$800$	2.93459	+	2.93459i	0.103754	+	0.103754i
$801$	−5.38699	−	20.1045i	−0.190340	−	0.710358i
$802$	10.0498	+	17.4068i	0.354871	+	0.614655i
$803$	−0.715059	+	1.23852i	−0.0252339	+	0.0437064i
$804$	0.427240	+	0.114479i	0.0150676	+	0.00403735i
$805$		0			0
$806$	52.1261	−	3.17219i	1.83606	−	0.111736i
$807$	−0.101604	−	0.175984i	−0.00357664	−	0.00619492i
$808$	−11.2848	−	11.2848i	−0.396997	−	0.396997i
$809$	11.7932			0.414629			0.207314	−	0.978274i	$-0.433528\pi$
$809$	11.7932			0.414629			0.207314	+	0.978274i	$0.433528\pi$
$810$	−18.5478			−0.651705
$811$	14.4330	+	14.4330i	0.506811	+	0.506811i	0.913546	−	0.406735i	$-0.133333\pi$
$811$	14.4330	+	14.4330i	0.506811	+	0.506811i	−0.406735	+	0.913546i	$0.633333\pi$
$812$		0			0
$813$	16.5335	−	4.43015i	0.579856	−	0.155372i
$814$	2.04281	−	7.62388i	0.0716005	−	0.267217i
$815$	−28.6480	+	16.5399i	−1.00350	+	0.579369i
$816$		−	18.9477i		−	0.663302i
$817$	−0.628174	−	2.34438i	−0.0219770	−	0.0820194i
$818$	19.4551			0.680232
$819$		0			0
$820$	5.56926			0.194487
$821$	−2.34685	−	8.75856i	−0.0819056	−	0.305676i	0.912805	−	0.408396i	$-0.133912\pi$
$821$	−2.34685	−	8.75856i	−0.0819056	−	0.305676i	−0.994710	+	0.102721i	$0.967245\pi$
$822$		−	11.4947i		−	0.400925i
$823$	14.1019	−	8.14175i	0.491562	−	0.283804i	−0.233660	−	0.972318i	$-0.575070\pi$
$823$	14.1019	−	8.14175i	0.491562	−	0.283804i	0.725222	+	0.688515i	$0.241737\pi$
$824$	5.34038	−	19.9306i	0.186041	−	0.694314i
$825$	0.579957	−	0.155399i	0.0201915	−	0.00541030i
$826$		0			0
$827$	−27.1227	−	27.1227i	−0.943148	−	0.943148i	0.0553203	−	0.998469i	$-0.482382\pi$
$827$	−27.1227	−	27.1227i	−0.943148	−	0.943148i	−0.998469	+	0.0553203i	$0.982382\pi$
$828$	6.27265			0.217990
$829$	2.81059			0.0976158			0.0488079	−	0.998808i	$-0.484458\pi$
$829$	2.81059			0.0976158			0.0488079	+	0.998808i	$0.484458\pi$
$830$	−4.17051	−	4.17051i	−0.144760	−	0.144760i
$831$	−4.83150	−	8.36841i	−0.167603	−	0.290297i
$832$	8.62510	+	4.30360i	0.299021	+	0.149201i
$833$		0			0
$834$	16.8218	+	4.50738i	0.582490	+	0.156078i
$835$	6.75692	−	11.7033i	0.233833	−	0.405010i
$836$	−1.11534	−	1.93183i	−0.0385750	−	0.0668138i
$837$	7.97816	+	29.7749i	0.275765	+	1.02917i
$838$	42.4077	+	42.4077i	1.46495	+	1.46495i
$839$	−9.79321	−	36.5488i	−0.338099	−	1.26180i	−0.900470	−	0.434918i	$-0.856777\pi$
$839$	−9.79321	−	36.5488i	−0.338099	−	1.26180i	0.562371	−	0.826885i	$-0.309889\pi$
$840$		0			0
$841$	−12.2485	+	21.2150i	−0.422363	+	0.731553i
$842$	7.12836	+	4.11556i	0.245660	+	0.141832i
$843$	3.44767	−	3.44767i	0.118744	−	0.118744i
$844$	−10.3654	−	5.98444i	−0.356790	−	0.205993i
$845$	−24.2362	+	9.77483i	−0.833749	+	0.336264i
$846$			13.3389i			0.458602i
$847$		0			0
$848$	−15.6961	−	27.1864i	−0.539006	−	0.933586i
$849$			1.14312i			0.0392319i
$850$	−9.29265	+	2.48996i	−0.318735	+	0.0854049i
$851$	−13.8481	−	3.71058i	−0.474706	−	0.127197i
$852$	4.24583	−	4.24583i	0.145460	−	0.145460i
$853$	7.88711	−	7.88711i	0.270050	−	0.270050i	−0.559070	−	0.829120i	$-0.688842\pi$
$853$	7.88711	−	7.88711i	0.270050	−	0.270050i	0.829120	+	0.559070i	$0.188842\pi$
$854$		0			0
$855$	12.6757	−	7.31833i	0.433501	−	0.250282i
$856$	25.1612	−	6.74193i	0.859993	−	0.230434i
$857$	−8.86465	+	15.3540i	−0.302811	+	0.524483i	−0.976771	−	0.214284i	$-0.931258\pi$
$857$	−8.86465	+	15.3540i	−0.302811	+	0.524483i	0.673961	+	0.738767i	$0.264592\pi$
$858$	−3.15588	+	2.08745i	−0.107740	+	0.0712643i
$859$	−3.20832	+	1.85233i	−0.109467	+	0.0632005i	−0.553734	−	0.832694i	$-0.686797\pi$
$859$	−3.20832	+	1.85233i	−0.109467	+	0.0632005i	0.444267	+	0.895894i	$0.353464\pi$
$860$	0.363970	−	1.35835i	0.0124113	−	0.0463195i
$861$		0			0
$862$	−0.712607	−	0.411424i	−0.0242715	−	0.0140132i
$863$	−38.0906	−	10.2063i	−1.29662	−	0.347428i	−0.456448	−	0.889750i	$-0.650879\pi$
$863$	−38.0906	−	10.2063i	−1.29662	−	0.347428i	−0.840171	+	0.542322i	$0.817545\pi$
$864$	3.99561	−	14.9118i	0.135933	−	0.507310i
$865$	4.95174	−	18.4801i	0.168364	−	0.628344i
$866$	−28.7965	−	7.71601i	−0.978546	−	0.262201i
$867$	10.3986	+	6.00364i	0.353155	+	0.203894i
$868$		0			0
$869$	−2.94827	+	11.0031i	−0.100013	+	0.373254i
$870$	−13.6109	+	7.85827i	−0.461454	+	0.266420i
$871$	−0.979596	−	2.93068i	−0.0331924	−	0.0993023i
$872$	−11.6853	+	20.2395i	−0.395713	+	0.685394i
$873$	31.3155	−	8.39095i	1.05987	−	0.283991i
$874$	−12.1812	+	7.03283i	−0.412036	+	0.237889i
$875$		0			0
$876$	−0.531592	+	0.531592i	−0.0179608	+	0.0179608i
$877$	−28.1504	+	28.1504i	−0.950570	+	0.950570i	−0.998835	−	0.0482643i	$-0.984631\pi$
$877$	−28.1504	+	28.1504i	−0.950570	+	0.950570i	0.0482643	+	0.998835i	$0.484631\pi$
$878$	−46.3064	−	12.4078i	−1.56277	−	0.418742i
$879$	16.3202	−	4.37298i	0.550467	−	0.147497i
$880$			9.79616i			0.330229i
$881$	−1.49665	−	2.59227i	−0.0504233	−	0.0873357i	0.839712	−	0.543032i	$-0.182724\pi$
$881$	−1.49665	−	2.59227i	−0.0504233	−	0.0873357i	−0.890135	+	0.455696i	$0.849390\pi$
$882$		0			0
$883$			1.38623i			0.0466504i	0.999728	+	0.0233252i	$0.00742531\pi$
$883$			1.38623i			0.0466504i	−0.999728	+	0.0233252i	$0.992575\pi$
$884$	14.5666	−	9.63502i	0.489927	−	0.324061i
$885$	0.564925	+	0.326160i	0.0189897	+	0.0109637i
$886$	8.73647	−	8.73647i	0.293508	−	0.293508i
$887$	30.8094	+	17.7878i	1.03448	+	0.597256i	0.918264	−	0.395968i	$-0.129591\pi$
$887$	30.8094	+	17.7878i	1.03448	+	0.597256i	0.116214	+	0.993224i	$0.462924\pi$
$888$	−3.05254	+	5.28716i	−0.102437	+	0.177425i
$889$		0			0
$890$	6.99906	+	26.1209i	0.234609	+	0.875573i
$891$	3.82161	+	3.82161i	0.128029	+	0.128029i
$892$	−4.47166	−	16.6885i	−0.149722	−	0.558771i
$893$	−4.30817	−	7.46197i	−0.144168	−	0.249705i
$894$	−9.99780	+	17.3167i	−0.334376	+	0.579157i
$895$	−11.6642	−	3.12540i	−0.389890	−	0.104471i
$896$		0			0
$897$	3.79166	+	5.73238i	0.126600	+	0.191398i
$898$	−19.5402	−	33.8446i	−0.652065	−	1.12941i
$899$	−44.6931	−	44.6931i	−1.49060	−	1.49060i
$900$	−2.01244			−0.0670815
$901$	37.8558			1.26116
$902$	−3.98343	−	3.98343i	−0.132634	−	0.132634i
$903$		0			0
$904$	−15.6439	+	4.19178i	−0.520310	+	0.139417i
$905$	3.15274	−	11.7662i	0.104801	−	0.391121i
$906$	−0.0337282	+	0.0194730i	−0.00112054	+	0.000646946i
$907$		−	49.8113i		−	1.65396i	−0.562233	−	0.826979i	$-0.690058\pi$
$907$		−	49.8113i		−	1.65396i	0.562233	−	0.826979i	$-0.309942\pi$
$908$	2.83116	+	10.5660i	0.0939553	+	0.350646i
$909$	20.7368			0.687795
$910$		0			0
$911$	−55.7036			−1.84554			−0.922772	−	0.385347i	$-0.874082\pi$
$911$	−55.7036			−1.84554			−0.922772	+	0.385347i	$0.874082\pi$
$912$	2.30033	+	8.58493i	0.0761714	+	0.284276i
$913$			1.71859i			0.0568769i
$914$	−6.54953	+	3.78137i	−0.216639	+	0.125077i
$915$	4.32299	−	16.1336i	0.142914	−	0.533360i
$916$	5.62180	−	1.50636i	0.185749	−	0.0497714i
$917$		0			0
$918$	25.3049	+	25.3049i	0.835187	+	0.835187i
$919$	−20.0645			−0.661867			−0.330934	−	0.943654i	$-0.607364\pi$
$919$	−20.0645			−0.661867			−0.330934	+	0.943654i	$0.607364\pi$
$920$	11.9917			0.395356
$921$	0.986663	+	0.986663i	0.0325116	+	0.0325116i
$922$	−27.9203	−	48.3594i	−0.919506	−	1.59263i
$923$	−41.1038	−	8.37574i	−1.35295	−	0.275691i
$924$		0			0
$925$	4.44286	+	1.19046i	0.146080	+	0.0391421i
$926$	34.4873	−	59.7338i	1.13332	−	1.96297i
$927$	13.4054	+	23.2188i	0.440290	+	0.762605i
$928$	8.19279	+	30.5759i	0.268942	+	1.00370i
$929$	−22.3969	−	22.3969i	−0.734818	−	0.734818i	0.236752	−	0.971570i	$-0.423917\pi$
$929$	−22.3969	−	22.3969i	−0.734818	−	0.734818i	−0.971570	+	0.236752i	$0.923917\pi$
$930$	−4.80595	−	17.9360i	−0.157593	−	0.588146i
$931$		0			0
$932$	9.38923	−	16.2626i	0.307555	−	0.532700i
$933$	16.2016	+	9.35397i	0.530415	+	0.306235i
$934$	−6.77600	+	6.77600i	−0.221717	+	0.221717i
$935$	−10.2305	−	5.90659i	−0.334574	−	0.193166i
$936$	−17.6985	+	5.91584i	−0.578495	+	0.193365i
$937$		−	43.3600i		−	1.41651i	−0.705957	−	0.708255i	$-0.749483\pi$
$937$		−	43.3600i		−	1.41651i	0.705957	−	0.708255i	$-0.250517\pi$
$938$		0			0
$939$	8.92359	+	15.4561i	0.291210	+	0.504391i
$940$		−	4.99238i		−	0.162834i
$941$	−37.4931	+	10.0463i	−1.22224	+	0.327499i	−0.811554	−	0.584277i	$-0.801378\pi$
$941$	−37.4931	+	10.0463i	−1.22224	+	0.327499i	−0.410688	+	0.911776i	$0.634711\pi$
$942$	7.42224	+	1.98878i	0.241830	+	0.0647980i
$943$	−7.23554	+	7.23554i	−0.235622	+	0.235622i
$944$	1.78586	−	1.78586i	0.0581246	−	0.0581246i
$945$		0			0
$946$	−1.23190	+	0.711236i	−0.0400524	+	0.0231243i
$947$	−39.8444	+	10.6763i	−1.29477	+	0.346932i	−0.839470	−	0.543406i	$-0.817134\pi$
$947$	−39.8444	+	10.6763i	−1.29477	+	0.346932i	−0.455299	+	0.890339i	$0.650468\pi$
$948$	−2.99408	+	5.18590i	−0.0972431	+	0.168430i
$949$	5.14634	+	1.04867i	0.167057	+	0.0340413i
$950$	3.90808	−	2.25633i	0.126795	−	0.0732050i
$951$	−1.29813	+	4.84468i	−0.0420947	+	0.157100i
$952$		0			0
$953$	−9.00364	−	5.19825i	−0.291656	−	0.168388i	0.347032	−	0.937853i	$-0.387189\pi$
$953$	−9.00364	−	5.19825i	−0.291656	−	0.168388i	−0.638689	+	0.769465i	$0.720523\pi$
$954$	26.5529	+	7.11482i	0.859681	+	0.230351i
$955$	11.2524	−	41.9947i	0.364120	−	1.35892i
$956$	0.821387	−	3.06546i	0.0265655	−	0.0991439i
$957$	4.42352	+	1.18528i	0.142992	+	0.0383146i
$958$	48.3721	+	27.9277i	1.56283	+	0.902301i
$959$		0			0
$960$	0.887075	−	3.31061i	0.0286302	−	0.106850i
$961$	37.8246	−	21.8380i	1.22015	−	0.704452i
$962$	−28.9328	+	1.76074i	−0.932832	+	0.0567685i
$963$	−16.9235	+	29.3124i	−0.545353	+	0.944580i
$964$	−2.49279	+	0.667940i	−0.0802873	+	0.0215129i
$965$	16.8713	−	9.74062i	0.543105	−	0.313562i
$966$		0			0
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	−0.420775	−	0.907165i	$-0.638242\pi$
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	0.907165	+	0.420775i	$0.138242\pi$
$968$	−14.1634	+	14.1634i	−0.455228	+	0.455228i
$969$	−10.3526	−	2.77396i	−0.332572	−	0.0891124i
$970$	−40.6867	+	10.9020i	−1.30637	+	0.350041i
$971$		−	17.4624i		−	0.560396i	−0.959942	−	0.280198i	$-0.909600\pi$
$971$		−	17.4624i		−	0.560396i	0.959942	−	0.280198i	$-0.0904002\pi$
$972$	5.75056	+	9.96026i	0.184449	+	0.319475i
$973$		0			0
$974$		−	25.3407i		−	0.811968i
$975$	−1.21647	−	1.83911i	−0.0389583	−	0.0588986i
$976$	−56.0040	−	32.3339i	−1.79265	−	1.03498i
$977$	−8.45756	+	8.45756i	−0.270581	+	0.270581i	−0.829334	−	0.558753i	$-0.811280\pi$
$977$	−8.45756	+	8.45756i	−0.270581	+	0.270581i	0.558753	+	0.829334i	$0.311280\pi$
$978$	15.2332	+	8.79490i	0.487104	+	0.281230i
$979$	3.93986	−	6.82405i	0.125919	−	0.218097i
$980$		0			0
$981$	−7.85955	−	29.3322i	−0.250936	−	0.936506i
$982$	5.19914	+	5.19914i	0.165911	+	0.165911i
$983$	−3.18140	−	11.8732i	−0.101471	−	0.378695i	0.896450	−	0.443145i	$-0.146137\pi$
$983$	−3.18140	−	11.8732i	−0.101471	−	0.378695i	−0.997921	+	0.0644501i	$0.979471\pi$
$984$	2.17872	+	3.77366i	0.0694551	+	0.120300i
$985$	−4.65472	+	8.06222i	−0.148312	+	0.256884i
$986$	−70.8782	−	18.9918i	−2.25722	−	0.604821i
$987$		0			0
$988$	−5.43019	+	6.13393i	−0.172757	+	0.195146i
$989$	1.29190	+	2.23763i	0.0410799	+	0.0711525i
$990$	−6.06579	−	6.06579i	−0.192783	−	0.192783i
$991$	−38.3547			−1.21838			−0.609189	−	0.793025i	$-0.708505\pi$
$991$	−38.3547			−1.21838			−0.609189	+	0.793025i	$0.708505\pi$
$992$	−37.3991			−1.18742
$993$	−7.34257	−	7.34257i	−0.233009	−	0.233009i
$994$		0			0
$995$	41.8644	−	11.2175i	1.32719	−	0.355619i
$996$	−0.233824	+	0.872644i	−0.00740901	+	0.0276508i
$997$	−33.1334	+	19.1296i	−1.04935	+	0.605840i	−0.922466	−	0.386078i	$-0.873829\pi$
$997$	−33.1334	+	19.1296i	−1.04935	+	0.605840i	−0.126879	+	0.991918i	$0.540496\pi$
$998$			33.5892i			1.06325i
$999$	−4.42832	−	16.5267i	−0.140106	−	0.522882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.80.1		32
7.2	even	3		637.2.bb.b.509.2		32
7.3	odd	6		91.2.bc.a.41.8	yes	32
7.4	even	3		91.2.bc.a.41.7	yes	32
7.5	odd	6		637.2.bb.b.509.1		32
7.6	odd	2	inner	637.2.x.b.80.2		32
13.7	odd	12		637.2.bb.b.423.1		32
21.11	odd	6		819.2.fm.g.496.1		32
21.17	even	6		819.2.fm.g.496.2		32
91.20	even	12		637.2.bb.b.423.2		32
91.33	even	12	inner	637.2.x.b.215.2		32
91.46	odd	12		91.2.bc.a.20.8	yes	32
91.59	even	12		91.2.bc.a.20.7	✓	32
91.72	odd	12	inner	637.2.x.b.215.1		32
273.59	odd	12		819.2.fm.g.748.1		32
273.137	even	12		819.2.fm.g.748.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.7	✓	32	91.59	even	12
91.2.bc.a.20.8	yes	32	91.46	odd	12
91.2.bc.a.41.7	yes	32	7.4	even	3
91.2.bc.a.41.8	yes	32	7.3	odd	6
637.2.x.b.80.1		32	1.1	even	1	trivial
637.2.x.b.80.2		32	7.6	odd	2	inner
637.2.x.b.215.1		32	91.72	odd	12	inner
637.2.x.b.215.2		32	91.33	even	12	inner
637.2.bb.b.423.1		32	13.7	odd	12
637.2.bb.b.423.2		32	91.20	even	12
637.2.bb.b.509.1		32	7.5	odd	6
637.2.bb.b.509.2		32	7.2	even	3
819.2.fm.g.496.1		32	21.11	odd	6
819.2.fm.g.496.2		32	21.17	even	6
819.2.fm.g.748.1		32	273.59	odd	12
819.2.fm.g.748.2		32	273.137	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.433802 - 1.61897i) q^{2} -0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(0.520288 - 1.94174i) q^{5} +(-1.03250 + 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} +O(q^{10})\)	\(q+(-0.433802 - 1.61897i) q^{2} -0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(0.520288 - 1.94174i) q^{5} +(-1.03250 + 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} -3.36932 q^{10} +(0.694217 + 0.694217i) q^{11} +(0.258049 + 0.446954i) q^{12} +(1.60977 - 3.22624i) q^{13} +(-1.23834 - 0.331813i) q^{15} +(-2.48181 + 4.29862i) q^{16} +(-2.99281 - 5.18370i) q^{17} +(-1.12497 - 4.19844i) q^{18} +(1.98532 + 1.98532i) q^{19} +(0.421043 + 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 - 1.49448i) q^{23} +(-0.900016 + 0.900016i) q^{24} +(0.830467 + 0.479471i) q^{25} +(-5.92151 - 1.20663i) q^{26} -3.56710i q^{27} +(3.65708 + 6.33425i) q^{29} +2.14878i q^{30} +(-8.34708 + 2.23659i) q^{31} +(4.18037 + 1.12013i) q^{32} +(0.442736 - 0.442736i) q^{33} +(-7.09397 + 7.09397i) q^{34} +(-1.81745 + 1.04931i) q^{36} +(4.63309 - 1.24143i) q^{37} +(2.35294 - 4.07541i) q^{38} +(-2.05753 - 1.02663i) q^{39} +(-3.47451 + 2.00601i) q^{40} +(0.886060 - 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.767427 - 0.205631i) q^{44} +(1.34925 - 5.03547i) q^{45} +(-1.29661 + 4.83903i) q^{46} +(-2.96429 - 0.794280i) q^{47} +(2.74144 + 1.58277i) q^{48} +(0.415990 - 1.55250i) q^{50} +(-3.30589 + 1.90866i) q^{51} +(0.177238 + 2.91241i) q^{52} +(-3.16223 + 5.47715i) q^{53} +(-5.77504 + 1.54742i) q^{54} +(1.70918 - 0.986797i) q^{55} +(1.26614 - 1.26614i) q^{57} +(8.66852 - 8.66852i) q^{58} +(-0.491481 - 0.131692i) q^{59} +(1.00213 - 0.268520i) q^{60} +13.0284i q^{61} +(7.24196 + 12.5434i) q^{62} +2.67342i q^{64} +(-5.42698 - 4.80434i) q^{65} +(-0.908836 - 0.524717i) q^{66} +(0.606011 - 0.606011i) q^{67} +(4.19491 + 2.42193i) q^{68} +(-0.953100 + 1.65082i) q^{69} +(-3.01121 - 11.2380i) q^{71} +(-3.65973 - 3.65973i) q^{72} +(0.377014 + 1.40704i) q^{73} +(-4.01968 - 6.96230i) q^{74} +(0.305782 - 0.529629i) q^{75} +(-2.19469 - 0.588064i) q^{76} +(-0.769526 + 3.77644i) q^{78} +(5.80137 + 10.0483i) q^{79} +(7.05555 + 7.05555i) q^{80} +5.50492 q^{81} -5.73802 q^{82} +(1.23779 + 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(-0.374999 + 1.39951i) q^{86} +(4.03966 - 2.33230i) q^{87} -1.95941i q^{88} +(-2.07729 - 7.75255i) q^{89} -8.73759 q^{90} +2.41881 q^{92} +(1.42638 + 5.32334i) q^{93} +5.14367i q^{94} +(4.88792 - 2.82204i) q^{95} +(0.714359 - 2.66602i) q^{96} +(12.0756 - 3.23566i) q^{97} +(1.80030 + 1.80030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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