LMFDB - Embedded newform 676.2.f.h.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(99,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("676.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.f (of order $4$, degree $2$, 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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.1
Root			$-1.39427 + 0.236640i$ of defining polynomial
Character	$\chi$	$=$	676.99
Dual form			676.2.f.h.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32580 + 0.492201i) q^{2} -0.850043i q^{3} +(1.51548 - 1.30512i) q^{4} +(-0.166404 - 0.166404i) q^{5} +(0.418392 + 1.12698i) q^{6} +(-1.86977 - 1.86977i) q^{7} +(-1.36683 + 2.47624i) q^{8} +2.27743 q^{9} +(0.302522 + 0.138714i) q^{10} +(-1.01973 - 1.01973i) q^{11} +(-1.10941 - 1.28822i) q^{12} +(3.39924 + 1.55864i) q^{14} +(-0.141450 + 0.141450i) q^{15} +(0.593337 - 3.95575i) q^{16} +1.39924i q^{17} +(-3.01941 + 1.12095i) q^{18} +(3.94713 - 3.94713i) q^{19} +(-0.469358 - 0.0350045i) q^{20} +(-1.58939 + 1.58939i) q^{21} +(1.85387 + 0.850043i) q^{22} -8.74431 q^{23} +(2.10491 + 1.16187i) q^{24} -4.94462i q^{25} -4.48604i q^{27} +(-5.27387 - 0.393323i) q^{28} +4.22047 q^{29} +(0.117912 - 0.257157i) q^{30} +(-3.88100 + 3.88100i) q^{31} +(1.16038 + 5.53656i) q^{32} +(-0.866814 + 0.866814i) q^{33} +(-0.688709 - 1.85511i) q^{34} +0.622275i q^{35} +(3.45139 - 2.97231i) q^{36} +(-0.366025 + 0.366025i) q^{37} +(-3.29032 + 7.17588i) q^{38} +(0.639502 - 0.184609i) q^{40} +(-4.09808 - 4.09808i) q^{41} +(1.32491 - 2.88950i) q^{42} -9.18723 q^{43} +(-2.87624 - 0.214509i) q^{44} +(-0.378973 - 0.378973i) q^{45} +(11.5932 - 4.30396i) q^{46} +(2.80318 + 2.80318i) q^{47} +(-3.36256 - 0.504362i) q^{48} -0.00790080i q^{49} +(2.43375 + 6.55556i) q^{50} +1.18942 q^{51} -5.94462 q^{53} +(2.20803 + 5.94758i) q^{54} +0.339374i q^{55} +(7.18567 - 2.07434i) q^{56} +(-3.35523 - 3.35523i) q^{57} +(-5.59549 + 2.07732i) q^{58} +(-6.02449 - 6.02449i) q^{59} +(-0.0297554 + 0.398974i) q^{60} -7.22205 q^{61} +(3.23518 - 7.05564i) q^{62} +(-4.25827 - 4.25827i) q^{63} +(-4.26353 - 6.76922i) q^{64} +(0.722573 - 1.57587i) q^{66} +(1.78345 - 1.78345i) q^{67} +(1.82618 + 2.12052i) q^{68} +7.43304i q^{69} +(-0.306284 - 0.825010i) q^{70} +(7.68668 - 7.68668i) q^{71} +(-3.11287 + 5.63946i) q^{72} +(5.05407 - 5.05407i) q^{73} +(0.305117 - 0.665434i) q^{74} -4.20314 q^{75} +(0.830315 - 11.1333i) q^{76} +3.81333i q^{77} -8.51654i q^{79} +(-0.756985 + 0.559518i) q^{80} +3.01896 q^{81} +(7.45030 + 3.41614i) q^{82} +(6.91195 - 6.91195i) q^{83} +(-0.334342 + 4.48301i) q^{84} +(0.232839 - 0.232839i) q^{85} +(12.1804 - 4.52197i) q^{86} -3.58758i q^{87} +(3.91890 - 1.13129i) q^{88} +(-4.69752 + 4.69752i) q^{89} +(0.688971 + 0.315910i) q^{90} +(-13.2518 + 11.4124i) q^{92} +(3.29901 + 3.29901i) q^{93} +(-5.09618 - 2.33672i) q^{94} -1.31364 q^{95} +(4.70632 - 0.986372i) q^{96} +(-10.9412 - 10.9412i) q^{97} +(0.00388878 + 0.0104749i) q^{98} +(-2.32236 - 2.32236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 12 q^{5} + 4 q^{6} + 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} - 6 q^{18} - 22 q^{20} - 28 q^{21} + 4 q^{24} - 36 q^{28} + 16 q^{29} - 2 q^{32} + 28 q^{33} + 14 q^{34} + 8 q^{37} - 40 q^{40}+ \cdots + 70 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 12 * q^5 + 4 * q^6 + 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 - 6 * q^18 - 22 * q^20 - 28 * q^21 + 4 * q^24 - 36 * q^28 + 16 * q^29 - 2 * q^32 + 28 * q^33 + 14 * q^34 + 8 * q^37 - 40 * q^40 - 24 * q^41 + 56 * q^42 - 8 * q^44 + 20 * q^45 + 56 * q^46 + 20 * q^48 - 32 * q^50 - 32 * q^53 + 44 * q^54 + 12 * q^57 + 30 * q^58 - 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 + 28 * q^70 - 46 * q^72 + 20 * q^73 - 8 * q^74 - 8 * q^76 - 22 * q^80 - 96 * q^81 - 48 * q^84 - 52 * q^85 + 16 * q^86 + 44 * q^89 - 12 * q^92 + 112 * q^93 + 76 * q^94 - 72 * q^96 - 52 * q^97 + 70 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.32580	+	0.492201i	−0.937480	+	0.348039i
$2$	−1.32580	+	0.492201i	−0.937480	+	0.348039i
$3$		−	0.850043i		−	0.490772i	−0.969425	−	0.245386i	$-0.921085\pi$
$3$		−	0.850043i		−	0.490772i	0.969425	−	0.245386i	$-0.0789148\pi$
$4$	1.51548	−	1.30512i	0.757738	−	0.652559i
$5$	−0.166404	−	0.166404i	−0.0744180	−	0.0744180i	0.668918	−	0.743336i	$-0.266758\pi$
$5$	−0.166404	−	0.166404i	−0.0744180	−	0.0744180i	−0.743336	+	0.668918i	$0.766758\pi$
$6$	0.418392	+	1.12698i	0.170808	+	0.460089i
$7$	−1.86977	−	1.86977i	−0.706708	−	0.706708i	0.259134	−	0.965841i	$-0.416563\pi$
$7$	−1.86977	−	1.86977i	−0.706708	−	0.706708i	−0.965841	+	0.259134i	$0.916563\pi$
$8$	−1.36683	+	2.47624i	−0.483249	+	0.875483i
$9$	2.27743			0.759142
$10$	0.302522	+	0.138714i	0.0956658	+	0.0438651i
$11$	−1.01973	−	1.01973i	−0.307460	−	0.307460i	0.536463	−	0.843924i	$-0.319760\pi$
$11$	−1.01973	−	1.01973i	−0.307460	−	0.307460i	−0.843924	+	0.536463i	$0.819760\pi$
$12$	−1.10941	−	1.28822i	−0.320258	−	0.371877i
$13$		0			0
$13$		0			0
$14$	3.39924	+	1.55864i	0.908486	+	0.416563i
$15$	−0.141450	+	0.141450i	−0.0365223	+	0.0365223i
$16$	0.593337	−	3.95575i	0.148334	−	0.988937i
$17$			1.39924i			0.339366i	0.985499	+	0.169683i	$0.0542744\pi$
$17$			1.39924i			0.339366i	−0.985499	+	0.169683i	$0.945726\pi$
$18$	−3.01941	+	1.12095i	−0.711681	+	0.264211i
$19$	3.94713	−	3.94713i	0.905535	−	0.905535i	−0.0903734	−	0.995908i	$-0.528806\pi$
$19$	3.94713	−	3.94713i	0.905535	−	0.905535i	0.995908	+	0.0903734i	$0.0288060\pi$
$20$	−0.469358	−	0.0350045i	−0.104952	−	0.00782725i
$21$	−1.58939	+	1.58939i	−0.346833	+	0.346833i
$22$	1.85387	+	0.850043i	0.395246	+	0.181230i
$23$	−8.74431			−1.82331			−0.911657	−	0.410951i	$-0.865197\pi$
$23$	−8.74431			−1.82331			−0.911657	+	0.410951i	$0.865197\pi$
$24$	2.10491	+	1.16187i	0.429663	+	0.237165i
$25$		−	4.94462i		−	0.988924i
$26$		0			0
$27$		−	4.48604i		−	0.863339i
$28$	−5.27387	−	0.393323i	−0.996668	−	0.0743311i
$29$	4.22047			0.783722			0.391861	−	0.920025i	$-0.371831\pi$
$29$	4.22047			0.783722			0.391861	+	0.920025i	$0.371831\pi$
$30$	0.117912	−	0.257157i	0.0215278	−	0.0469501i
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	−0.963773	−	0.266725i	$-0.914058\pi$
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	0.266725	+	0.963773i	$0.414058\pi$
$32$	1.16038	+	5.53656i	0.205128	+	0.978735i
$33$	−0.866814	+	0.866814i	−0.150893	+	0.150893i
$34$	−0.688709	−	1.85511i	−0.118113	−	0.318149i
$35$			0.622275i			0.105184i
$36$	3.45139	−	2.97231i	0.575231	−	0.495385i
$37$	−0.366025	+	0.366025i	−0.0601742	+	0.0601742i	−0.736553	−	0.676379i	$-0.763548\pi$
$37$	−0.366025	+	0.366025i	−0.0601742	+	0.0601742i	0.676379	+	0.736553i	$0.263548\pi$
$38$	−3.29032	+	7.17588i	−0.533760	+	1.16408i
$39$		0			0
$40$	0.639502	−	0.184609i	0.101114	−	0.0291893i
$41$	−4.09808	−	4.09808i	−0.640012	−	0.640012i	0.310546	−	0.950558i	$-0.399488\pi$
$41$	−4.09808	−	4.09808i	−0.640012	−	0.640012i	−0.950558	+	0.310546i	$0.899488\pi$
$42$	1.32491	−	2.88950i	0.204438	−	0.445860i
$43$	−9.18723			−1.40104			−0.700520	−	0.713633i	$-0.747049\pi$
$43$	−9.18723			−1.40104			−0.700520	+	0.713633i	$0.747049\pi$
$44$	−2.87624	−	0.214509i	−0.433610	−	0.0323385i
$45$	−0.378973	−	0.378973i	−0.0564939	−	0.0564939i
$46$	11.5932	−	4.30396i	1.70932	−	0.634584i
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	0.881350	−	0.472464i	$-0.156635\pi$
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	−0.472464	+	0.881350i	$0.656635\pi$
$48$	−3.36256	−	0.504362i	−0.485343	−	0.0727984i
$49$		−	0.00790080i		−	0.00112869i
$50$	2.43375	+	6.55556i	0.344184	+	0.927097i
$51$	1.18942			0.166552
$52$		0			0
$53$	−5.94462			−0.816556			−0.408278	−	0.912858i	$-0.633871\pi$
$53$	−5.94462			−0.816556			−0.408278	+	0.912858i	$0.633871\pi$
$54$	2.20803	+	5.94758i	0.300475	+	0.809363i
$55$			0.339374i			0.0457612i
$56$	7.18567	−	2.07434i	0.960226	−	0.277195i
$57$	−3.35523	−	3.35523i	−0.444411	−	0.444411i
$58$	−5.59549	+	2.07732i	−0.734723	+	0.272765i
$59$	−6.02449	−	6.02449i	−0.784322	−	0.784322i	0.196235	−	0.980557i	$-0.437129\pi$
$59$	−6.02449	−	6.02449i	−0.784322	−	0.784322i	−0.980557	+	0.196235i	$0.937129\pi$
$60$	−0.0297554	+	0.398974i	−0.00384140	+	0.0515073i
$61$	−7.22205			−0.924688			−0.462344	−	0.886701i	$-0.652992\pi$
$61$	−7.22205			−0.924688			−0.462344	+	0.886701i	$0.652992\pi$
$62$	3.23518	−	7.05564i	0.410869	−	0.896068i
$63$	−4.25827	−	4.25827i	−0.536492	−	0.536492i
$64$	−4.26353	−	6.76922i	−0.532941	−	0.846152i
$65$		0			0
$66$	0.722573	−	1.57587i	0.0889426	−	0.193976i
$67$	1.78345	−	1.78345i	0.217884	−	0.217884i	−0.589722	−	0.807606i	$-0.700763\pi$
$67$	1.78345	−	1.78345i	0.217884	−	0.217884i	0.807606	+	0.589722i	$0.200763\pi$
$68$	1.82618	+	2.12052i	0.221456	+	0.257151i
$69$			7.43304i			0.894833i
$70$	−0.306284	−	0.825010i	−0.0366080	−	0.0986075i
$71$	7.68668	−	7.68668i	0.912241	−	0.912241i	−0.0842073	−	0.996448i	$-0.526836\pi$
$71$	7.68668	−	7.68668i	0.912241	−	0.912241i	0.996448	+	0.0842073i	$0.0268358\pi$
$72$	−3.11287	+	5.63946i	−0.366855	+	0.664616i
$73$	5.05407	−	5.05407i	0.591534	−	0.591534i	−0.346512	−	0.938046i	$-0.612634\pi$
$73$	5.05407	−	5.05407i	0.591534	−	0.591534i	0.938046	+	0.346512i	$0.112634\pi$
$74$	0.305117	−	0.665434i	0.0354692	−	0.0773551i
$75$	−4.20314			−0.485337
$76$	0.830315	−	11.1333i	0.0952437	−	1.27707i
$77$			3.81333i			0.434569i
$78$		0			0
$79$		−	8.51654i		−	0.958186i	−0.877764	−	0.479093i	$-0.840966\pi$
$79$		−	8.51654i		−	0.958186i	0.877764	−	0.479093i	$-0.159034\pi$
$80$	−0.756985	+	0.559518i	−0.0846335	+	0.0625560i
$81$	3.01896			0.335440
$82$	7.45030	+	3.41614i	0.822747	+	0.377250i
$83$	6.91195	−	6.91195i	0.758685	−	0.758685i	−0.217398	−	0.976083i	$-0.569757\pi$
$83$	6.91195	−	6.91195i	0.758685	−	0.758685i	0.976083	+	0.217398i	$0.0697570\pi$
$84$	−0.334342	+	4.48301i	−0.0364797	+	0.489137i
$85$	0.232839	−	0.232839i	0.0252550	−	0.0252550i
$86$	12.1804	−	4.52197i	1.31345	−	0.487616i
$87$		−	3.58758i		−	0.384629i
$88$	3.91890	−	1.13129i	0.417756	−	0.120596i
$89$	−4.69752	+	4.69752i	−0.497936	+	0.497936i	−0.910795	−	0.412859i	$-0.864530\pi$
$89$	−4.69752	+	4.69752i	−0.497936	+	0.497936i	0.412859	+	0.910795i	$0.364530\pi$
$90$	0.688971	+	0.315910i	0.0726240	+	0.0332998i
$91$		0			0
$92$	−13.2518	+	11.4124i	−1.38160	+	1.18982i
$93$	3.29901	+	3.29901i	0.342092	+	0.342092i
$94$	−5.09618	−	2.33672i	−0.525631	−	0.241015i
$95$	−1.31364			−0.134776
$96$	4.70632	−	0.986372i	0.480336	−	0.100671i
$97$	−10.9412	−	10.9412i	−1.11091	−	1.11091i	−0.993028	−	0.117877i	$-0.962391\pi$
$97$	−10.9412	−	10.9412i	−1.11091	−	1.11091i	−0.117877	−	0.993028i	$-0.537609\pi$
$98$	0.00388878	+	0.0104749i	0.000392826	+	0.00105812i
$99$	−2.32236	−	2.32236i	−0.233406	−	0.233406i
$100$	−6.45331	−	7.49345i	−0.645331	−	0.749345i
$101$			9.17457i			0.912904i	0.889748	+	0.456452i	$0.150880\pi$
$101$			9.17457i			0.912904i	−0.889748	+	0.456452i	$0.849120\pi$
$102$	−1.57693	+	0.585432i	−0.156139	+	0.0579664i
$103$	10.9080			1.07480			0.537398	−	0.843329i	$-0.319407\pi$
$103$	10.9080			1.07480			0.537398	+	0.843329i	$0.319407\pi$
$104$		0			0
$105$	0.528960			0.0516212
$106$	7.88136	−	2.92595i	0.765505	−	0.284193i
$107$			9.85658i			0.952872i	0.879209	+	0.476436i	$0.158072\pi$
$107$			9.85658i			0.952872i	−0.879209	+	0.476436i	$0.841928\pi$
$108$	−5.85481	−	6.79849i	−0.563379	−	0.654185i
$109$	0.0243171	+	0.0243171i	0.00232916	+	0.00232916i	0.708270	−	0.705941i	$-0.249476\pi$
$109$	0.0243171	+	0.0243171i	0.00232916	+	0.00232916i	−0.705941	+	0.708270i	$0.749476\pi$
$110$	−0.167040	−	0.449941i	−0.0159267	−	0.0429002i
$111$	0.311137	+	0.311137i	0.0295318	+	0.0295318i
$112$	−8.50576	+	6.28695i	−0.803718	+	0.594061i
$113$	4.55328			0.428336			0.214168	−	0.976797i	$-0.431296\pi$
$113$	4.55328			0.428336			0.214168	+	0.976797i	$0.431296\pi$
$114$	6.09981	+	2.79691i	0.571299	+	0.261955i
$115$	1.45509	+	1.45509i	0.135688	+	0.135688i
$116$	6.39602	−	5.50821i	0.593856	−	0.511424i
$117$		0			0
$118$	10.9525	+	5.02200i	1.00826	+	0.462312i
$119$	2.61627	−	2.61627i	0.239833	−	0.239833i
$120$	−0.156926	−	0.543604i	−0.0143253	−	0.0496241i
$121$		−	8.92030i		−	0.810937i
$122$	9.57497	−	3.55470i	0.866877	−	0.321827i
$123$	−3.48354	+	3.48354i	−0.314100	+	0.314100i
$124$	−0.816402	+	10.9467i	−0.0733151	+	0.983044i
$125$	−1.65482	+	1.65482i	−0.148012	+	0.148012i
$126$	7.74153	+	3.54968i	0.689670	+	0.316230i
$127$	5.34414			0.474216			0.237108	−	0.971483i	$-0.423801\pi$
$127$	5.34414			0.474216			0.237108	+	0.971483i	$0.423801\pi$
$128$	8.98439	+	6.87610i	0.794115	+	0.607767i
$129$			7.80954i			0.687592i
$130$		0			0
$131$			11.2254i			0.980764i	0.871508	+	0.490382i	$0.163143\pi$
$131$			11.2254i			0.980764i	−0.871508	+	0.490382i	$0.836857\pi$
$132$	−0.182342	+	2.44493i	−0.0158708	+	0.212804i
$133$	−14.7605			−1.27990
$134$	−1.48668	+	3.24232i	−0.128430	+	0.280094i
$135$	−0.746494	+	0.746494i	−0.0642480	+	0.0642480i
$136$	−3.46486	−	1.91253i	−0.297109	−	0.163998i
$137$	−3.39982	+	3.39982i	−0.290466	+	0.290466i	−0.837264	−	0.546798i	$-0.815846\pi$
$137$	−3.39982	+	3.39982i	−0.290466	+	0.290466i	0.546798	+	0.837264i	$0.315846\pi$
$138$	−3.65855	−	9.85470i	−0.311436	−	0.838888i
$139$			6.94068i			0.588700i	0.955698	+	0.294350i	$0.0951032\pi$
$139$			6.94068i			0.588700i	−0.955698	+	0.294350i	$0.904897\pi$
$140$	0.812141	+	0.943042i	0.0686385	+	0.0797016i
$141$	2.38283	−	2.38283i	0.200670	−	0.200670i
$142$	−6.40759	+	13.9744i	−0.537713	+	1.17270i
$143$		0			0
$144$	1.35128	−	9.00893i	0.112607	−	0.750744i
$145$	−0.702302	−	0.702302i	−0.0583230	−	0.0583230i
$146$	−4.21305	+	9.18828i	−0.348674	+	0.760428i
$147$	−0.00671601			−0.000553928
$148$	−0.0769967	+	1.03241i	−0.00632909	+	0.0848635i
$149$	10.7178	+	10.7178i	0.878035	+	0.878035i	0.993331	−	0.115296i	$-0.0367816\pi$
$149$	10.7178	+	10.7178i	0.878035	+	0.878035i	−0.115296	+	0.993331i	$0.536782\pi$
$150$	5.57251	−	2.06879i	0.454993	−	0.168916i
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	0.726401	−	0.687272i	$-0.241192\pi$
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	−0.687272	+	0.726401i	$0.741192\pi$
$152$	4.37897	+	15.1691i	0.355182	+	1.23038i
$153$			3.18667i			0.257627i
$154$	−1.87692	−	5.05570i	−0.151247	−	0.407400i
$155$	1.29162			0.103746
$156$		0			0
$157$	5.90408			0.471197			0.235598	−	0.971851i	$-0.424295\pi$
$157$	5.90408			0.471197			0.235598	+	0.971851i	$0.424295\pi$
$158$	4.19185	+	11.2912i	0.333486	+	0.898280i
$159$			5.05318i			0.400743i
$160$	0.728214	−	1.11440i	0.0575703	−	0.0881008i
$161$	16.3499	+	16.3499i	1.28855	+	1.28855i
$162$	−4.00252	+	1.48593i	−0.314468	+	0.116746i
$163$	11.1248	+	11.1248i	0.871358	+	0.871358i	0.992620	−	0.121263i	$-0.0386943\pi$
$163$	11.1248	+	11.1248i	0.871358	+	0.871358i	−0.121263	+	0.992620i	$0.538694\pi$
$164$	−11.5590	−	0.862067i	−0.902607	−	0.0673161i
$165$	0.288482			0.0224583
$166$	−5.76177	+	12.5659i	−0.447200	+	0.975304i
$167$	3.96436	+	3.96436i	0.306772	+	0.306772i	0.843656	−	0.536884i	$-0.180399\pi$
$167$	3.96436	+	3.96436i	0.306772	+	0.306772i	−0.536884	+	0.843656i	$0.680399\pi$
$168$	−1.76327	−	6.10813i	−0.136040	−	0.471253i
$169$		0			0
$170$	−0.194094	+	0.423302i	−0.0148863	+	0.0324658i
$171$	8.98931	−	8.98931i	0.687430	−	0.687430i
$172$	−13.9230	+	11.9904i	−1.06162	+	0.914261i
$173$			2.16078i			0.164281i	0.996621	+	0.0821405i	$0.0261756\pi$
$173$			2.16078i			0.164281i	−0.996621	+	0.0821405i	$0.973824\pi$
$174$	1.76581	+	4.75640i	0.133866	+	0.360582i
$175$	−9.24531	+	9.24531i	−0.698880	+	0.698880i
$176$	−4.63884	+	3.42875i	−0.349666	+	0.258452i
$177$	−5.12108	+	5.12108i	−0.384924	+	0.384924i
$178$	3.91583	−	8.54008i	0.293504	−	0.640106i
$179$	10.1328			0.757359			0.378679	−	0.925528i	$-0.376378\pi$
$179$	10.1328			0.757359			0.378679	+	0.925528i	$0.376378\pi$
$180$	−1.06893	−	0.0797203i	−0.0796732	−	0.00594200i
$181$		−	13.8528i		−	1.02967i	−0.857289	−	0.514836i	$-0.827853\pi$
$181$		−	13.8528i		−	1.02967i	0.857289	−	0.514836i	$-0.172147\pi$
$182$		0			0
$183$			6.13905i			0.453812i
$184$	11.9520	−	21.6530i	0.881115	−	1.59628i
$185$	0.121816			0.00895609
$186$	−5.99760	−	2.75004i	−0.439765	−	0.201643i
$187$	1.42685	−	1.42685i	0.104342	−	0.104342i
$188$	7.90664	+	0.589675i	0.576651	+	0.0430065i
$189$	−8.38787	+	8.38787i	−0.610128	+	0.610128i
$190$	1.74162	−	0.646573i	0.126350	−	0.0469073i
$191$			3.87048i			0.280058i	0.990147	+	0.140029i	$0.0447196\pi$
$191$			3.87048i			0.280058i	−0.990147	+	0.140029i	$0.955280\pi$
$192$	−5.75413	+	3.62418i	−0.415268	+	0.261553i
$193$	5.81548	−	5.81548i	0.418607	−	0.418607i	−0.466116	−	0.884724i	$-0.654347\pi$
$193$	5.81548	−	5.81548i	0.418607	−	0.418607i	0.884724	+	0.466116i	$0.154347\pi$
$194$	19.8910	+	9.12050i	1.42809	+	0.654814i
$195$		0			0
$196$	−0.0103115	−	0.0119735i	−0.000736533	−	0.000855248i
$197$	8.75448	+	8.75448i	0.623731	+	0.623731i	0.946483	−	0.322753i	$-0.104608\pi$
$197$	8.75448	+	8.75448i	0.623731	+	0.623731i	−0.322753	+	0.946483i	$0.604608\pi$
$198$	4.22205	+	1.93591i	0.300048	+	0.137579i
$199$	2.43397			0.172539			0.0862696	−	0.996272i	$-0.472505\pi$
$199$	2.43397			0.172539			0.0862696	+	0.996272i	$0.472505\pi$
$200$	12.2441	+	6.75848i	0.865786	+	0.477896i
$201$	−1.51601	−	1.51601i	−0.106931	−	0.106931i
$202$	−4.51573	−	12.1636i	−0.317726	−	0.855829i
$203$	−7.89132	−	7.89132i	−0.553862	−	0.553862i
$204$	1.80253	−	1.55233i	0.126203	−	0.108685i
$205$			1.36387i			0.0952569i
$206$	−14.4618	+	5.36892i	−1.00760	+	0.374071i
$207$	−19.9145			−1.38416
$208$		0			0
$209$	−8.05002			−0.556831
$210$	−0.701294	+	0.260355i	−0.0483939	+	0.0179662i
$211$		−	4.19052i		−	0.288488i	−0.989542	−	0.144244i	$-0.953925\pi$
$211$		−	4.19052i		−	0.288488i	0.989542	−	0.144244i	$-0.0460750\pi$
$212$	−9.00893	+	7.75843i	−0.618736	+	0.532851i
$213$	−6.53401	−	6.53401i	−0.447703	−	0.447703i
$214$	−4.85142	−	13.0678i	−0.331636	−	0.893298i
$215$	1.52879	+	1.52879i	0.104263	+	0.104263i
$216$	11.1085	+	6.13167i	0.755838	+	0.417207i
$217$	14.5132			0.985217
$218$	−0.0442085	−	0.0202707i	−0.00299418	−	0.00137290i
$219$	−4.29617	−	4.29617i	−0.290308	−	0.290308i
$220$	0.442923	+	0.514313i	0.0298618	+	0.0346750i
$221$		0			0
$222$	−0.565647	−	0.259363i	−0.0379637	−	0.0174073i
$223$	−13.3137	+	13.3137i	−0.891553	+	0.891553i	−0.994669	−	0.103117i	$-0.967118\pi$
$223$	−13.3137	+	13.3137i	−0.891553	+	0.891553i	0.103117	+	0.994669i	$0.467118\pi$
$224$	8.18247	−	12.5218i	0.546714	−	0.836645i
$225$		−	11.2610i		−	0.750734i
$226$	−6.03672	+	2.24113i	−0.401557	+	0.149078i
$227$	−5.26077	+	5.26077i	−0.349170	+	0.349170i	−0.859800	−	0.510631i	$-0.829412\pi$
$227$	−5.26077	+	5.26077i	−0.349170	+	0.349170i	0.510631	+	0.859800i	$0.329412\pi$
$228$	−9.46375	−	0.705803i	−0.626752	−	0.0467430i
$229$	−3.17720	+	3.17720i	−0.209955	+	0.209955i	−0.804248	−	0.594293i	$-0.797432\pi$
$229$	−3.17720	+	3.17720i	−0.209955	+	0.209955i	0.594293	+	0.804248i	$0.297432\pi$
$230$	−2.64534	−	1.21295i	−0.174429	−	0.0799799i
$231$	3.24149			0.213274
$232$	−5.76868	+	10.4509i	−0.378733	+	0.686135i
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$		0			0
$235$		−	0.932921i		−	0.0608571i
$236$	−16.9927	−	1.26731i	−1.10613	−	0.0824946i
$237$	−7.23943			−0.470251
$238$	−2.18091	+	4.75637i	−0.141367	+	0.308310i
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	−0.487300	−	0.873235i	$-0.662018\pi$
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	0.873235	+	0.487300i	$0.162018\pi$
$240$	0.475614	+	0.643470i	0.0307008	+	0.0415358i
$241$	10.9373	−	10.9373i	0.704533	−	0.704533i	−0.260847	−	0.965380i	$-0.584002\pi$
$241$	10.9373	−	10.9373i	0.704533	−	0.704533i	0.965380	+	0.260847i	$0.0840018\pi$
$242$	4.39058	+	11.8265i	0.282237	+	0.760237i
$243$		−	16.0244i		−	1.02796i
$244$	−10.9448	+	9.42562i	−0.700672	+	0.603413i
$245$	−0.00131472	+	0.00131472i	−8.39945e−5	+	8.39945e-5i
$246$	2.90387	−	6.33307i	0.185144	−	0.403782i
$247$		0			0
$248$	−4.30560	−	14.9150i	−0.273406	−	0.947101i
$249$	−5.87545	−	5.87545i	−0.372342	−	0.372342i
$250$	1.37945	−	3.00846i	0.0872443	−	0.190272i
$251$	27.4775			1.73436			0.867182	−	0.497992i	$-0.165929\pi$
$251$	27.4775			1.73436			0.867182	+	0.497992i	$0.165929\pi$
$252$	−12.0109	−	0.895766i	−0.756613	−	0.0564279i
$253$	8.91683	+	8.91683i	0.560597	+	0.560597i
$254$	−7.08524	+	2.63039i	−0.444568	+	0.165045i
$255$	−0.197923	−	0.197923i	−0.0123944	−	0.0123944i
$256$	−15.2959	−	4.69419i	−0.955994	−	0.293387i
$257$		−	27.8352i		−	1.73631i	−0.496289	−	0.868157i	$-0.665304\pi$
$257$		−	27.8352i		−	1.73631i	0.496289	−	0.868157i	$-0.334696\pi$
$258$	−3.84386	−	10.3539i	−0.239309	−	0.644604i
$259$	1.36877			0.0850511
$260$		0			0
$261$	9.61181			0.594956
$262$	−5.52513	−	14.8825i	−0.341344	−	0.919446i
$263$		−	23.8060i		−	1.46794i	−0.679180	−	0.733972i	$-0.737664\pi$
$263$		−	23.8060i		−	1.46794i	0.679180	−	0.733972i	$-0.262336\pi$
$264$	−0.961648	−	3.33123i	−0.0591854	−	0.205023i
$265$	0.989207	+	0.989207i	0.0607665	+	0.0607665i
$266$	19.5694	−	7.26513i	1.19988	−	0.445453i
$267$	3.99309	+	3.99309i	0.244373	+	0.244373i
$268$	0.375166	−	5.03040i	0.0229169	−	0.307281i
$269$	−20.7119			−1.26282			−0.631412	−	0.775448i	$-0.717524\pi$
$269$	−20.7119			−1.26282			−0.631412	+	0.775448i	$0.717524\pi$
$270$	0.622275	−	1.35712i	0.0378704	−	0.0825920i
$271$	9.77210	+	9.77210i	0.593613	+	0.593613i	0.938605	−	0.344993i	$-0.112119\pi$
$271$	9.77210	+	9.77210i	0.593613	+	0.593613i	−0.344993	+	0.938605i	$0.612119\pi$
$272$	5.53506	+	0.830223i	0.335612	+	0.0503397i
$273$		0			0
$274$	2.83408	−	6.18087i	0.171213	−	0.373400i
$275$	−5.04218	+	5.04218i	−0.304055	+	0.304055i
$276$	9.70099	+	11.2646i	0.583931	+	0.678049i
$277$			12.7336i			0.765090i	0.923937	+	0.382545i	$0.124952\pi$
$277$			12.7336i			0.765090i	−0.923937	+	0.382545i	$0.875048\pi$
$278$	−3.41621	−	9.20193i	−0.204891	−	0.551895i
$279$	−8.83868	+	8.83868i	−0.529158	+	0.529158i
$280$	−1.54090	−	0.850546i	−0.0920865	−	0.0508299i
$281$	15.4454	−	15.4454i	0.921396	−	0.921396i	−0.0757324	−	0.997128i	$-0.524129\pi$
$281$	15.4454	−	15.4454i	0.921396	−	0.921396i	0.997128	+	0.0757324i	$0.0241295\pi$
$282$	−1.98632	+	4.33197i	−0.118283	+	0.257965i
$283$	20.6898			1.22988			0.614939	−	0.788575i	$-0.289181\pi$
$283$	20.6898			1.22988			0.614939	+	0.788575i	$0.289181\pi$
$284$	1.61696	−	21.6810i	0.0959490	−	1.28653i
$285$			1.11665i			0.0661445i
$286$		0			0
$287$			15.3249i			0.904603i
$288$	2.64268	+	12.6091i	0.155721	+	0.742999i
$289$	15.0421			0.884830
$290$	1.27678	+	0.585436i	0.0749753	+	0.0343780i
$291$	−9.30045	+	9.30045i	−0.545202	+	0.545202i
$292$	1.06317	−	14.2555i	0.0622172	−	0.834238i
$293$	16.3053	−	16.3053i	0.952565	−	0.952565i	−0.0463600	−	0.998925i	$-0.514762\pi$
$293$	16.3053	−	16.3053i	0.952565	−	0.952565i	0.998925	+	0.0463600i	$0.0147621\pi$
$294$	0.00890407	−	0.00330563i	0.000519296	−	0.000192788i
$295$			2.00500i			0.116735i
$296$	−0.406071	−	1.40666i	−0.0236024	−	0.0817606i
$297$	−4.57455	+	4.57455i	−0.265442	+	0.265442i
$298$	−19.4849	−	8.93431i	−1.12873	−	0.517551i
$299$		0			0
$300$	−6.36976	+	5.48559i	−0.367758	+	0.316711i
$301$	17.1780	+	17.1780i	0.990126	+	0.990126i
$302$	−0.874138	−	0.400813i	−0.0503010	−	0.0230642i
$303$	7.79878			0.448028
$304$	−13.2719	−	17.9559i	−0.761195	−	1.02984i
$305$	1.20178	+	1.20178i	0.0688135	+	0.0688135i
$306$	−1.56848	−	4.22488i	−0.0896643	−	0.241521i
$307$	16.3164	+	16.3164i	0.931228	+	0.931228i	0.997783	−	0.0665547i	$-0.0212007\pi$
$307$	16.3164	+	16.3164i	0.931228	+	0.931228i	−0.0665547	+	0.997783i	$0.521201\pi$
$308$	4.97684	+	5.77900i	0.283582	+	0.329289i
$309$		−	9.27226i		−	0.527480i
$310$	−1.71243	+	0.635739i	−0.0972596	+	0.0361076i
$311$	−8.54527			−0.484558			−0.242279	−	0.970207i	$-0.577895\pi$
$311$	−8.54527			−0.484558			−0.242279	+	0.970207i	$0.577895\pi$
$312$		0			0
$313$	5.88378			0.332571			0.166285	−	0.986078i	$-0.446823\pi$
$313$	5.88378			0.332571			0.166285	+	0.986078i	$0.446823\pi$
$314$	−7.82761	+	2.90599i	−0.441738	+	0.163995i
$315$			1.41718i			0.0798493i
$316$	−11.1151	−	12.9066i	−0.625272	−	0.726054i
$317$	−16.5045	−	16.5045i	−0.926984	−	0.926984i	0.0705258	−	0.997510i	$-0.477532\pi$
$317$	−16.5045	−	16.5045i	−0.926984	−	0.926984i	−0.997510	+	0.0705258i	$0.977532\pi$
$318$	−2.48718	−	6.69949i	−0.139474	−	0.375689i
$319$	−4.30374	−	4.30374i	−0.240963	−	0.240963i
$320$	−0.416956	+	1.83589i	−0.0233086	+	0.102629i
$321$	8.37852			0.467643
$322$	−29.7240	−	13.6292i	−1.65646	−	0.759525i
$323$	5.52300	+	5.52300i	0.307308	+	0.307308i
$324$	4.57516	−	3.94009i	0.254175	−	0.218894i
$325$		0			0
$326$	−20.2248	−	9.27355i	−1.12015	−	0.513614i
$327$	0.0206706	−	0.0206706i	0.00114309	−	0.00114309i
$328$	15.7492	−	4.54643i	0.869605	−	0.251035i
$329$		−	10.4826i		−	0.577926i
$330$	−0.382469	+	0.141991i	−0.0210542	+	0.00781636i
$331$	−10.1585	+	10.1585i	−0.558364	+	0.558364i	−0.928842	−	0.370477i	$-0.879194\pi$
$331$	−10.1585	+	10.1585i	−0.558364	+	0.558364i	0.370477	+	0.928842i	$0.379194\pi$
$332$	1.45399	−	19.4958i	0.0797981	−	1.06997i
$333$	−0.833596	+	0.833596i	−0.0456808	+	0.0456808i
$334$	−7.20721	−	3.30468i	−0.394361	−	0.180824i
$335$	−0.593547			−0.0324290
$336$	5.34417	+	7.23026i	0.291549	+	0.394443i
$337$		−	14.3427i		−	0.781297i	−0.920540	−	0.390649i	$-0.872251\pi$
$337$		−	14.3427i		−	0.781297i	0.920540	−	0.390649i	$-0.127749\pi$
$338$		0			0
$339$		−	3.87048i		−	0.210216i
$340$	0.0489799	−	0.656745i	0.00265631	−	0.0356170i
$341$	7.91513			0.428629
$342$	−7.49345	+	16.3425i	−0.405200	+	0.883704i
$343$	−13.1032	+	13.1032i	−0.707505	+	0.707505i
$344$	12.5574	−	22.7498i	0.677051	−	1.22659i
$345$	1.23689	−	1.23689i	0.0665917	−	0.0665917i
$346$	−1.06354	−	2.86476i	−0.0571762	−	0.154010i
$347$		−	0.470309i		−	0.0252475i	−0.999920	−	0.0126238i	$-0.995982\pi$
$347$		−	0.470309i		−	0.0252475i	0.999920	−	0.0126238i	$-0.00401838\pi$
$348$	−4.68221	−	5.43689i	−0.250993	−	0.291448i
$349$	19.9991	−	19.9991i	1.07053	−	1.07053i	0.0732091	−	0.997317i	$-0.476676\pi$
$349$	19.9991	−	19.9991i	1.07053	−	1.07053i	0.997317	−	0.0732091i	$-0.0233240\pi$
$350$	7.70686	−	16.8080i	0.411949	−	0.898423i
$351$		0			0
$352$	4.46252	−	6.82907i	0.237853	−	0.363991i
$353$	−25.4219	−	25.4219i	−1.35307	−	1.35307i	−0.882202	−	0.470871i	$-0.843940\pi$
$353$	−25.4219	−	25.4219i	−1.35307	−	1.35307i	−0.470871	−	0.882202i	$-0.656060\pi$
$354$	4.26891	−	9.31011i	0.226890	−	0.494827i
$355$	−2.55819			−0.135774
$356$	−0.988165	+	13.2498i	−0.0523726	+	0.702238i
$357$	−2.22394	−	2.22394i	−0.117703	−	0.117703i
$358$	−13.4340	+	4.98736i	−0.710009	+	0.263590i
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	0.326733	−	0.945117i	$-0.394052\pi$
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	−0.945117	+	0.326733i	$0.894052\pi$
$360$	1.45642	−	0.420434i	0.0767601	−	0.0221588i
$361$		−	12.1597i		−	0.639986i
$362$	6.81837	+	18.3660i	0.358366	+	0.965297i
$363$	−7.58264			−0.397985
$364$		0			0
$365$	−1.68203			−0.0880416
$366$	−3.02165	−	8.13913i	−0.157944	−	0.425439i
$367$		−	10.1556i		−	0.530118i	−0.964232	−	0.265059i	$-0.914609\pi$
$367$		−	10.1556i		−	0.530118i	0.964232	−	0.265059i	$-0.0853914\pi$
$368$	−5.18832	+	34.5903i	−0.270460	+	1.80314i
$369$	−9.33307	−	9.33307i	−0.485860	−	0.485860i
$370$	−0.161503	+	0.0599580i	−0.00839616	+	0.00311707i
$371$	11.1151	+	11.1151i	0.577067	+	0.577067i
$372$	9.30517	+	0.693977i	0.482451	+	0.0359810i
$373$	−15.0158			−0.777489			−0.388744	−	0.921346i	$-0.627091\pi$
$373$	−15.0158			−0.777489			−0.388744	+	0.921346i	$0.627091\pi$
$374$	−1.18942	+	2.59401i	−0.0615033	+	0.134133i
$375$	1.40667	+	1.40667i	0.0726401	+	0.0726401i
$376$	−10.7728	+	3.10987i	−0.555567	+	0.160379i
$377$		0			0
$378$	6.99210	−	15.2491i	0.359635	−	0.784331i
$379$	−23.5868	+	23.5868i	−1.21157	+	1.21157i	−0.241064	+	0.970509i	$0.577496\pi$
$379$	−23.5868	+	23.5868i	−1.21157	+	1.21157i	−0.970509	+	0.241064i	$0.922504\pi$
$380$	−1.99078	+	1.71445i	−0.102125	+	0.0879494i
$381$		−	4.54275i		−	0.232732i
$382$	−1.90505	−	5.13147i	−0.0974711	−	0.262549i
$383$	14.8033	−	14.8033i	0.756412	−	0.756412i	−0.219256	−	0.975667i	$-0.570363\pi$
$383$	14.8033	−	14.8033i	0.756412	−	0.756412i	0.975667	+	0.219256i	$0.0703629\pi$
$384$	5.84498	−	7.63712i	0.298275	−	0.389730i
$385$	0.634552	−	0.634552i	0.0323398	−	0.0323398i
$386$	−4.84776	+	10.5725i	−0.246745	+	0.538128i
$387$	−20.9233			−1.06359
$388$	−30.8605	−	2.30157i	−1.56671	−	0.116844i
$389$			9.60410i			0.486947i	0.969908	+	0.243474i	$0.0782870\pi$
$389$			9.60410i			0.486947i	−0.969908	+	0.243474i	$0.921713\pi$
$390$		0			0
$391$		−	12.2354i		−	0.618772i
$392$	0.0195643	+	0.0107991i	0.000988145	+	0.000545436i
$393$	9.54203			0.481332
$394$	−15.9156	−	7.29770i	−0.801817	−	0.367653i
$395$	−1.41718	+	1.41718i	−0.0713063	+	0.0713063i
$396$	−6.55043	−	0.488529i	−0.329172	−	0.0245495i
$397$	−1.82627	+	1.82627i	−0.0916580	+	0.0916580i	−0.751449	−	0.659791i	$-0.770645\pi$
$397$	−1.82627	+	1.82627i	−0.0916580	+	0.0916580i	0.659791	+	0.751449i	$0.270645\pi$
$398$	−3.22694	+	1.19800i	−0.161752	+	0.0600503i
$399$			12.5470i			0.628138i
$400$	−19.5597	−	2.93383i	−0.977984	−	0.146691i
$401$	−19.1281	+	19.1281i	−0.955211	+	0.955211i	−0.999039	−	0.0438280i	$-0.986045\pi$
$401$	−19.1281	+	19.1281i	−0.955211	+	0.955211i	0.0438280	+	0.999039i	$0.486045\pi$
$402$	2.75611	+	1.26374i	0.137462	+	0.0630298i
$403$		0			0
$404$	11.9739	+	13.9038i	0.595723	+	0.691742i
$405$	−0.502366	−	0.502366i	−0.0249628	−	0.0249628i
$406$	14.3464	+	6.57817i	0.712000	+	0.326469i
$407$	0.746494			0.0370023
$408$	−1.62574	+	2.94528i	−0.0804859	+	0.145813i
$409$	3.39034	+	3.39034i	0.167642	+	0.167642i	0.785942	−	0.618300i	$-0.212178\pi$
$409$	3.39034	+	3.39034i	0.167642	+	0.167642i	−0.618300	+	0.785942i	$0.712178\pi$
$410$	−0.671299	−	1.80822i	−0.0331531	−	0.0893014i
$411$	2.88999	+	2.88999i	0.142553	+	0.142553i
$412$	16.5308	−	14.2362i	0.814414	−	0.701368i
$413$			22.5289i			1.10857i
$414$	26.4026	−	9.80195i	1.29762	−	0.481740i
$415$	−2.30035			−0.112920
$416$		0			0
$417$	5.89987			0.288918
$418$	10.6727	−	3.96223i	0.522018	−	0.193799i
$419$		−	5.60503i		−	0.273824i	−0.990583	−	0.136912i	$-0.956282\pi$
$419$		−	5.60503i		−	0.273824i	0.990583	−	0.136912i	$-0.0437177\pi$
$420$	0.801626	−	0.690355i	0.0391154	−	0.0336859i
$421$	3.55354	+	3.55354i	0.173189	+	0.173189i	0.788379	−	0.615190i	$-0.210921\pi$
$421$	3.55354	+	3.55354i	0.173189	+	0.173189i	−0.615190	+	0.788379i	$0.710921\pi$
$422$	2.06258	+	5.55579i	0.100405	+	0.270451i
$423$	6.38405	+	6.38405i	0.310403	+	0.310403i
$424$	8.12531	−	14.7203i	0.394600	−	0.714881i
$425$	6.91873			0.335607
$426$	11.8788	+	5.44672i	0.575530	+	0.263895i
$427$	13.5036	+	13.5036i	0.653484	+	0.653484i
$428$	12.8640	+	14.9374i	0.621805	+	0.722027i
$429$		0			0
$430$	−2.77934	−	1.27439i	−0.134032	−	0.0614567i
$431$	2.44497	−	2.44497i	0.117770	−	0.117770i	−0.645766	−	0.763536i	$-0.723462\pi$
$431$	2.44497	−	2.44497i	0.117770	−	0.117770i	0.763536	+	0.645766i	$0.223462\pi$
$432$	−17.7456	−	2.66173i	−0.853788	−	0.128063i
$433$		−	5.47262i		−	0.262997i	−0.991316	−	0.131499i	$-0.958021\pi$
$433$		−	5.47262i		−	0.262997i	0.991316	−	0.131499i	$-0.0419789\pi$
$434$	−19.2415	+	7.14339i	−0.923622	+	0.342894i
$435$	−0.596987	+	0.596987i	−0.0286233	+	0.0286233i
$436$	0.0685887	+	0.00511532i	0.00328480	+	0.000244980i
$437$	−34.5150	+	34.5150i	−1.65107	+	1.65107i
$438$	7.81043	+	3.58127i	0.373197	+	0.171120i
$439$	30.5063			1.45599			0.727994	−	0.685584i	$-0.240453\pi$
$439$	30.5063			1.45599			0.727994	+	0.685584i	$0.240453\pi$
$440$	−0.840371	−	0.463868i	−0.0400631	−	0.0221140i
$441$		−	0.0179935i		−	0.000856833i
$442$		0			0
$443$			12.8994i			0.612869i	0.951892	+	0.306434i	$0.0991360\pi$
$443$			12.8994i			0.612869i	−0.951892	+	0.306434i	$0.900864\pi$
$444$	0.877592	+	0.0654505i	0.0416487	+	0.00310614i
$445$	1.56337			0.0741108
$446$	11.0983	−	24.2043i	0.525518	−	1.14611i
$447$	9.11058	−	9.11058i	0.430916	−	0.430916i
$448$	−4.68507	+	20.6287i	−0.221349	+	0.974616i
$449$	−6.97915	+	6.97915i	−0.329367	+	0.329367i	−0.852346	−	0.522979i	$-0.824821\pi$
$449$	−6.97915	+	6.97915i	−0.329367	+	0.329367i	0.522979	+	0.852346i	$0.324821\pi$
$450$	5.54268	+	14.9298i	0.261284	+	0.703798i
$451$			8.35786i			0.393556i
$452$	6.90038	−	5.94256i	0.324567	−	0.279515i
$453$	0.408721	−	0.408721i	0.0192034	−	0.0192034i
$454$	4.38536	−	9.56407i	0.205815	−	0.448864i
$455$		0			0
$456$	12.8944	−	3.72231i	0.603836	−	0.174313i
$457$	−7.34129	−	7.34129i	−0.343411	−	0.343411i	0.514237	−	0.857648i	$-0.328075\pi$
$457$	−7.34129	−	7.34129i	−0.343411	−	0.343411i	−0.857648	+	0.514237i	$0.828075\pi$
$458$	2.64850	−	5.77614i	0.123756	−	0.269901i
$459$	6.27706			0.292988
$460$	4.10421	+	0.306091i	0.191360	+	0.0142715i
$461$	20.3185	+	20.3185i	0.946329	+	0.946329i	0.998631	−	0.0523023i	$-0.0166559\pi$
$461$	20.3185	+	20.3185i	0.946329	+	0.946329i	−0.0523023	+	0.998631i	$0.516656\pi$
$462$	−4.29756	+	1.59546i	−0.199941	+	0.0742277i
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	0.830612	−	0.556852i	$-0.187991\pi$
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	−0.556852	+	0.830612i	$0.687991\pi$
$464$	2.50416	−	16.6951i	0.116253	−	0.775051i
$465$		−	1.09794i		−	0.0509156i
$466$	−6.55637	−	17.6603i	−0.303718	−	0.818097i
$467$	−3.30334			−0.152860			−0.0764301	−	0.997075i	$-0.524352\pi$
$467$	−3.30334			−0.152860			−0.0764301	+	0.997075i	$0.524352\pi$
$468$		0			0
$469$	−6.66931			−0.307960
$470$	0.459185	+	1.23686i	0.0211806	+	0.0570523i
$471$		−	5.01872i		−	0.231250i
$472$	23.1526	−	6.68361i	1.06568	−	0.307638i
$473$	9.36849	+	9.36849i	0.430764	+	0.430764i
$474$	9.59801	−	3.56325i	0.440851	−	0.163666i
$475$	−19.5171	−	19.5171i	−0.895505	−	0.895505i
$476$	0.550355	−	7.37943i	0.0252255	−	0.338235i
$477$	−13.5384			−0.619882
$478$	−4.97358	+	10.8469i	−0.227486	+	0.496127i
$479$	−19.6666	−	19.6666i	−0.898589	−	0.898589i	0.0967224	−	0.995311i	$-0.469164\pi$
$479$	−19.6666	−	19.6666i	−0.898589	−	0.898589i	−0.995311	+	0.0967224i	$0.969164\pi$
$480$	−0.947285	−	0.619013i	−0.0432374	−	0.0282539i
$481$		0			0
$482$	−9.11729	+	19.8840i	−0.415281	+	0.905691i
$483$	13.8981	−	13.8981i	0.632385	−	0.632385i
$484$	−11.6420	−	13.5185i	−0.529184	−	0.614478i
$485$			3.64130i			0.165343i
$486$	7.88721	+	21.2451i	0.357771	+	0.963695i
$487$	−7.29545	+	7.29545i	−0.330588	+	0.330588i	−0.852810	−	0.522222i	$-0.825103\pi$
$487$	−7.29545	+	7.29545i	−0.330588	+	0.330588i	0.522222	+	0.852810i	$0.325103\pi$
$488$	9.87134	−	17.8835i	0.446855	−	0.809549i
$489$	9.45652	−	9.45652i	0.427638	−	0.427638i
$490$	0.00109595	−	0.00239016i	4.95099e−5	−	0.000107977i
$491$	−13.6249			−0.614881			−0.307441	−	0.951567i	$-0.599473\pi$
$491$	−13.6249			−0.614881			−0.307441	+	0.951567i	$0.599473\pi$
$492$	−0.732794	+	9.82565i	−0.0330369	+	0.442975i
$493$			5.90546i			0.265969i
$494$		0			0
$495$			0.772899i			0.0347392i
$496$	13.0495	+	17.6550i	0.585940	+	0.792732i
$497$	−28.7447			−1.28938
$498$	10.6816	+	4.89775i	0.478652	+	0.219474i
$499$	−11.2288	+	11.2288i	−0.502670	+	0.502670i	−0.912267	−	0.409597i	$-0.865669\pi$
$499$	−11.2288	+	11.2288i	−0.502670	+	0.502670i	0.409597	+	0.912267i	$0.365669\pi$
$500$	−0.348107	+	4.66758i	−0.0155678	+	0.208741i
$501$	3.36988	−	3.36988i	0.150555	−	0.150555i
$502$	−36.4296	+	13.5244i	−1.62593	+	0.603625i
$503$		−	22.8605i		−	1.01930i	−0.860382	−	0.509650i	$-0.829775\pi$
$503$		−	22.8605i		−	1.01930i	0.860382	−	0.509650i	$-0.170225\pi$
$504$	16.3649	−	4.72415i	0.728948	−	0.210430i
$505$	1.52668	−	1.52668i	0.0679365	−	0.0679365i
$506$	−16.2108	−	7.43304i	−0.720657	−	0.330439i
$507$		0			0
$508$	8.09892	−	6.97473i	0.359331	−	0.309454i
$509$	6.97468	+	6.97468i	0.309147	+	0.309147i	0.844579	−	0.535431i	$-0.179851\pi$
$509$	6.97468	+	6.97468i	0.309147	+	0.309147i	−0.535431	+	0.844579i	$0.679851\pi$
$510$	0.359824	+	0.164988i	0.0159333	+	0.00730580i
$511$	−18.8999			−0.836083
$512$	22.5897	−	1.30512i	0.998335	−	0.0576787i
$513$	−17.7070	−	17.7070i	−0.781783	−	0.781783i
$514$	13.7005	+	36.9039i	0.604305	+	1.62776i
$515$	−1.81513	−	1.81513i	−0.0799842	−	0.0799842i
$516$	10.1924	+	11.8352i	0.448694	+	0.521015i
$517$		−	5.71698i		−	0.251433i
$518$	−1.81471	+	0.673709i	−0.0797338	+	0.0296011i
$519$	1.83676			0.0806246
$520$		0			0
$521$	15.9204			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$521$	15.9204			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$522$	−12.7433	+	4.73094i	−0.557760	+	0.207068i
$523$			2.15778i			0.0943532i	0.998887	+	0.0471766i	$0.0150224\pi$
$523$			2.15778i			0.0943532i	−0.998887	+	0.0471766i	$0.984978\pi$
$524$	14.6504	+	17.0118i	0.640006	+	0.743162i
$525$	7.85891	+	7.85891i	0.342991	+	0.342991i
$526$	11.7174	+	31.5620i	0.510901	+	1.37617i
$527$	−5.43046	−	5.43046i	−0.236554	−	0.236554i
$528$	2.91459	+	3.94321i	0.126841	+	0.171606i
$529$	53.4630			2.32448
$530$	−1.79838	−	0.824599i	−0.0781165	−	0.0358183i
$531$	−13.7203	−	13.7203i	−0.595412	−	0.595412i
$532$	−22.3692	+	19.2642i	−0.969826	+	0.835207i
$533$		0			0
$534$	−7.25943	−	3.32863i	−0.314146	−	0.144044i
$535$	1.64017	−	1.64017i	0.0709109	−	0.0709109i
$536$	1.97857	+	6.85395i	0.0854614	+	0.296045i
$537$		−	8.61329i		−	0.371691i
$538$	27.4597	−	10.1944i	1.18387	−	0.439512i
$539$	−0.00805668	+	0.00805668i	−0.000347026	+	0.000347026i
$540$	−0.157032	+	2.10556i	−0.00675757	+	0.0906087i
$541$	8.15947	−	8.15947i	0.350803	−	0.350803i	−0.509605	−	0.860408i	$-0.670209\pi$
$541$	8.15947	−	8.15947i	0.350803	−	0.350803i	0.860408	+	0.509605i	$0.170209\pi$
$542$	−17.7657	−	8.14598i	−0.763100	−	0.349900i
$543$	−11.7755			−0.505334
$544$	−7.74700	+	1.62365i	−0.332150	+	0.0696135i
$545$		−	0.00809292i		−	0.000346663i
$546$		0			0
$547$		−	8.11076i		−	0.346791i	−0.984852	−	0.173396i	$-0.944526\pi$
$547$		−	8.11076i		−	0.346791i	0.984852	−	0.173396i	$-0.0554739\pi$
$548$	−0.715183	+	9.58951i	−0.0305511	+	0.409644i
$549$	−16.4477			−0.701970
$550$	4.20314	−	9.16667i	0.179222	−	0.390868i
$551$	16.6588	−	16.6588i	0.709687	−	0.709687i
$552$	−18.4060	−	10.1597i	−0.783411	−	0.432427i
$553$	−15.9240	+	15.9240i	−0.677157	+	0.677157i
$554$	−6.26750	−	16.8822i	−0.266281	−	0.717256i
$555$		−	0.103549i		−	0.00439540i
$556$	9.05840	+	10.5184i	0.384162	+	0.446081i
$557$	−2.42571	+	2.42571i	−0.102781	+	0.102781i	−0.756627	−	0.653846i	$-0.773154\pi$
$557$	−2.42571	+	2.42571i	−0.102781	+	0.102781i	0.653846	+	0.756627i	$0.273154\pi$
$558$	7.36789	−	16.0687i	0.311908	−	0.680243i
$559$		0			0
$560$	2.46156	+	0.369219i	0.104020	+	0.0156023i
$561$	−1.21288	−	1.21288i	−0.0512080	−	0.0512080i
$562$	−12.8752	+	28.0797i	−0.543109	+	1.18447i
$563$	−6.24260			−0.263094			−0.131547	−	0.991310i	$-0.541994\pi$
$563$	−6.24260			−0.263094			−0.131547	+	0.991310i	$0.541994\pi$
$564$	0.501249	−	6.72099i	0.0211064	−	0.283005i
$565$	−0.757683	−	0.757683i	−0.0318759	−	0.0318759i
$566$	−27.4304	+	10.1835i	−1.15299	+	0.428045i
$567$	−5.64476	−	5.64476i	−0.237058	−	0.237058i
$568$	8.52765	+	29.5405i	0.357812	+	1.23949i
$569$			32.2126i			1.35042i	0.737625	+	0.675211i	$0.235947\pi$
$569$			32.2126i			1.35042i	−0.737625	+	0.675211i	$0.764053\pi$
$570$	−0.549615	−	1.48045i	−0.0230208	−	0.0620091i
$571$	41.4189			1.73333			0.866663	−	0.498894i	$-0.166260\pi$
$571$	41.4189			1.73333			0.866663	+	0.498894i	$0.166260\pi$
$572$		0			0
$573$	3.29007			0.137445
$574$	−7.54295	−	20.3178i	−0.314837	−	0.848047i
$575$			43.2373i			1.80312i
$576$	−9.70988	−	15.4164i	−0.404578	−	0.642350i
$577$	12.3408	+	12.3408i	0.513753	+	0.513753i	0.915674	−	0.401921i	$-0.131657\pi$
$577$	12.3408	+	12.3408i	0.513753	+	0.513753i	−0.401921	+	0.915674i	$0.631657\pi$
$578$	−19.9428	+	7.40375i	−0.829511	+	0.307955i
$579$	−4.94341	−	4.94341i	−0.205441	−	0.205441i
$580$	−1.98091	−	0.147736i	−0.0822528	−	0.00613439i
$581$	−25.8475			−1.07234
$582$	7.75282	−	16.9082i	0.321365	−	0.700867i
$583$	6.06191	+	6.06191i	0.251058	+	0.251058i
$584$	5.60701	+	19.4231i	0.232020	+	0.803736i
$585$		0			0
$586$	−13.5920	+	29.6430i	−0.561481	+	1.22454i
$587$	16.3380	−	16.3380i	0.674340	−	0.674340i	−0.284374	−	0.958713i	$-0.591786\pi$
$587$	16.3380	−	16.3380i	0.674340	−	0.674340i	0.958713	+	0.284374i	$0.0917857\pi$
$588$	−0.0101780	+	0.00876519i	−0.000419732	+	0.000361470i
$589$			30.6376i			1.26240i
$590$	−0.986862	−	2.65822i	−0.0406285	−	0.109437i
$591$	7.44168	−	7.44168i	0.306110	−	0.306110i
$592$	1.23073	+	1.66508i	0.0505826	+	0.0684344i
$593$	11.0244	−	11.0244i	0.452717	−	0.452717i	−0.443538	−	0.896255i	$-0.646277\pi$
$593$	11.0244	−	11.0244i	0.452717	−	0.452717i	0.896255	+	0.443538i	$0.146277\pi$
$594$	3.81333	−	8.31652i	0.156463	−	0.341231i
$595$	−0.870713			−0.0356958
$596$	30.2305	+	2.25458i	1.23829	+	0.0923513i
$597$		−	2.06898i		−	0.0846775i
$598$		0			0
$599$		−	10.6090i		−	0.433471i	−0.976230	−	0.216735i	$-0.930459\pi$
$599$		−	10.6090i		−	0.433471i	0.976230	−	0.216735i	$-0.0695409\pi$
$600$	5.74499	−	10.4080i	0.234538	−	0.424904i
$601$	28.2503			1.15235			0.576177	−	0.817325i	$-0.304544\pi$
$601$	28.2503			1.15235			0.576177	+	0.817325i	$0.304544\pi$
$602$	−31.2296	−	14.3195i	−1.27283	−	0.583621i
$603$	4.06169	−	4.06169i	0.165405	−	0.165405i
$604$	1.35621	+	0.101146i	0.0551834	+	0.00411556i
$605$	−1.48437	+	1.48437i	−0.0603483	+	0.0603483i
$606$	−10.3396	+	3.83856i	−0.420017	+	0.155931i
$607$			10.2708i			0.416878i	0.978035	+	0.208439i	$0.0668383\pi$
$607$			10.2708i			0.416878i	−0.978035	+	0.208439i	$0.933162\pi$
$608$	26.4337	+	17.2734i	1.07203	+	0.700528i
$609$	−6.70796	+	6.70796i	−0.271820	+	0.271820i
$610$	−2.18483	−	1.00180i	−0.0884610	−	0.0405615i
$611$		0			0
$612$	4.15898	+	4.82933i	0.168117	+	0.195214i
$613$	25.0553	+	25.0553i	1.01198	+	1.01198i	0.999927	+	0.0120477i	$0.00383501\pi$
$613$	25.0553	+	25.0553i	1.01198	+	1.01198i	0.0120477	+	0.999927i	$0.496165\pi$
$614$	−29.6632	−	13.6013i	−1.19711	−	0.548905i
$615$	1.15935			0.0467495
$616$	−9.44271	−	5.21218i	−0.380458	−	0.210005i
$617$	−29.6355	−	29.6355i	−1.19308	−	1.19308i	−0.976198	−	0.216881i	$-0.930412\pi$
$617$	−29.6355	−	29.6355i	−1.19308	−	1.19308i	−0.216881	−	0.976198i	$-0.569588\pi$
$618$	4.56381	+	12.2931i	0.183584	+	0.494502i
$619$	−12.0880	−	12.0880i	−0.485858	−	0.485858i	0.421138	−	0.906996i	$-0.361631\pi$
$619$	−12.0880	−	12.0880i	−0.485858	−	0.485858i	−0.906996	+	0.421138i	$0.861631\pi$
$620$	1.95743	−	1.68572i	0.0786122	−	0.0677002i
$621$			39.2273i			1.57414i
$622$	11.3293	−	4.20599i	0.454263	−	0.168645i
$623$	17.5666			0.703790
$624$		0			0
$625$	−24.1724			−0.966894
$626$	−7.80069	+	2.89600i	−0.311778	+	0.115747i
$627$			6.84286i			0.273278i
$628$	8.94749	−	7.70552i	0.357044	−	0.307484i
$629$	−0.512159	−	0.512159i	−0.0204211	−	0.0204211i
$630$	−0.697540	−	1.87890i	−0.0277907	−	0.0748572i
$631$	8.52621	+	8.52621i	0.339423	+	0.339423i	0.856150	−	0.516727i	$-0.172850\pi$
$631$	8.52621	+	8.52621i	0.339423	+	0.339423i	−0.516727	+	0.856150i	$0.672850\pi$
$632$	21.0890	+	11.6407i	0.838875	+	0.463042i
$633$	−3.56213			−0.141582
$634$	30.0051	+	13.7581i	1.19166	+	0.546403i
$635$	−0.889285	−	0.889285i	−0.0352902	−	0.0352902i
$636$	6.59499	+	7.65798i	0.261509	+	0.303659i
$637$		0			0
$638$	7.82419	+	3.58758i	0.309763	+	0.142034i
$639$	17.5059	−	17.5059i	0.692521	−	0.692521i
$640$	−0.350828	−	2.63925i	−0.0138677	−	0.104325i
$641$		−	2.09731i		−	0.0828386i	−0.999142	−	0.0414193i	$-0.986812\pi$
$641$		−	2.09731i		−	0.0828386i	0.999142	−	0.0414193i	$-0.0131880\pi$
$642$	−11.1082	+	4.12391i	−0.438406	+	0.162758i
$643$	29.9695	−	29.9695i	1.18188	−	1.18188i	0.202627	−	0.979256i	$-0.435052\pi$
$643$	29.9695	−	29.9695i	1.18188	−	1.18188i	0.979256	−	0.202627i	$-0.0649478\pi$
$644$	46.1163	+	3.43934i	1.81724	+	0.135529i
$645$	1.29954	−	1.29954i	0.0511692	−	0.0511692i
$646$	−10.0408	−	4.60395i	−0.395050	−	0.181140i
$647$	−43.0799			−1.69365			−0.846824	−	0.531874i	$-0.821488\pi$
$647$	−43.0799			−1.69365			−0.846824	+	0.531874i	$0.821488\pi$
$648$	−4.12641	+	7.47566i	−0.162101	+	0.293672i
$649$			12.2867i			0.482296i
$650$		0			0
$651$		−	12.3368i		−	0.483518i
$652$	31.3784	+	2.34019i	1.22887	+	0.0916490i
$653$	−11.1212			−0.435206			−0.217603	−	0.976037i	$-0.569824\pi$
$653$	−11.1212			−0.435206			−0.217603	+	0.976037i	$0.569824\pi$
$654$	−0.0172309	+	0.0375791i	−0.000673782	+	0.00146946i
$655$	1.86794	−	1.86794i	0.0729865	−	0.0729865i
$656$	−18.6425	+	13.7794i	−0.727867	+	0.537996i
$657$	11.5103	−	11.5103i	0.449058	−	0.449058i
$658$	5.15956	+	13.8978i	0.201141	+	0.541795i
$659$			15.2432i			0.593792i	0.954910	+	0.296896i	$0.0959515\pi$
$659$			15.2432i			0.593792i	−0.954910	+	0.296896i	$0.904048\pi$
$660$	0.437188	−	0.376503i	0.0170175	−	0.0146554i
$661$	−7.30232	+	7.30232i	−0.284027	+	0.284027i	−0.834713	−	0.550685i	$-0.814366\pi$
$661$	−7.30232	+	7.30232i	−0.284027	+	0.284027i	0.550685	+	0.834713i	$0.314366\pi$
$662$	8.46813	−	18.4682i	0.329123	−	0.717788i
$663$		0			0
$664$	7.66815	+	26.5631i	0.297582	+	1.03085i
$665$	2.45620	+	2.45620i	0.0952474	+	0.0952474i
$666$	0.694883	−	1.51548i	0.0269262	−	0.0587235i
$667$	−36.9051			−1.42897
$668$	11.1819	+	0.833940i	0.432639	+	0.0322661i
$669$	11.3172	+	11.3172i	0.437549	+	0.437549i
$670$	0.786923	−	0.292145i	0.0304015	−	0.0112865i
$671$	7.36454	+	7.36454i	0.284305	+	0.284305i
$672$	−10.6440	−	6.95545i	−0.410602	−	0.268312i
$673$		−	29.7947i		−	1.14850i	−0.818680	−	0.574251i	$-0.805293\pi$
$673$		−	29.7947i		−	1.14850i	0.818680	−	0.574251i	$-0.194707\pi$
$674$	7.05950	+	19.0155i	0.271922	+	0.732451i
$675$	−22.1818			−0.853776
$676$		0			0
$677$	−29.1021			−1.11849			−0.559243	−	0.829004i	$-0.688908\pi$
$677$	−29.1021			−1.11849			−0.559243	+	0.829004i	$0.688908\pi$
$678$	1.90505	+	5.13147i	0.0731632	+	0.197073i
$679$			40.9149i			1.57017i
$680$	0.258313	+	0.894819i	0.00990586	+	0.0343147i
$681$	4.47188	+	4.47188i	0.171363	+	0.171363i
$682$	−10.4939	+	3.89584i	−0.401831	+	0.149179i
$683$	3.56874	+	3.56874i	0.136554	+	0.136554i	0.772080	−	0.635526i	$-0.219217\pi$
$683$	3.56874	+	3.56874i	0.136554	+	0.136554i	−0.635526	+	0.772080i	$0.719217\pi$
$684$	1.89098	−	25.3552i	0.0723035	−	0.969480i
$685$	1.13149			0.0432319
$686$	10.9228	−	23.8216i	0.417033	−	0.909511i
$687$	2.70075	+	2.70075i	0.103040	+	0.103040i
$688$	−5.45113	+	36.3424i	−0.207822	+	1.38554i
$689$		0			0
$690$	−1.03106	+	2.24866i	−0.0392519	+	0.0856049i
$691$	−7.90295	+	7.90295i	−0.300642	+	0.300642i	−0.841265	−	0.540623i	$-0.818189\pi$
$691$	−7.90295	+	7.90295i	−0.300642	+	0.300642i	0.540623	+	0.841265i	$0.318189\pi$
$692$	2.82007	+	3.27461i	0.107203	+	0.124482i
$693$			8.68457i			0.329900i
$694$	0.231487	+	0.623535i	0.00878711	+	0.0236691i
$695$	1.15495	−	1.15495i	0.0438099	−	0.0438099i
$696$	8.88371	+	4.90363i	0.336736	+	0.185872i
$697$	5.73421	−	5.73421i	0.217199	−	0.217199i
$698$	−16.6711	+	36.3583i	−0.631012	+	1.37618i
$699$	11.3230			0.428275
$700$	−1.94483	+	26.0773i	−0.0735078	+	0.985628i
$701$		−	27.1476i		−	1.02535i	−0.858582	−	0.512676i	$-0.828654\pi$
$701$		−	27.1476i		−	1.02535i	0.858582	−	0.512676i	$-0.171346\pi$
$702$		0			0
$703$			2.88950i			0.108980i
$704$	−2.55513	+	11.2504i	−0.0963000	+	0.424016i
$705$	−0.793023			−0.0298670
$706$	46.2170	+	21.1916i	1.73940	+	0.797557i
$707$	17.1544	−	17.1544i	0.645156	−	0.645156i
$708$	−1.07726	+	14.4445i	−0.0404861	+	0.542857i
$709$	−30.0036	+	30.0036i	−1.12681	+	1.12681i	−0.136118	+	0.990693i	$0.543463\pi$
$709$	−30.0036	+	30.0036i	−1.12681	+	1.12681i	−0.990693	+	0.136118i	$0.956537\pi$
$710$	3.39163	−	1.25914i	0.127286	−	0.0472547i
$711$		−	19.3958i		−	0.727399i
$712$	−5.21145	−	18.0529i	−0.195307	−	0.676561i
$713$	33.9366	−	33.9366i	1.27094	−	1.27094i
$714$	4.04312	+	1.85387i	0.151310	+	0.0693792i
$715$		0			0
$716$	15.3560	−	13.2245i	0.573880	−	0.494221i
$717$	−5.07171	−	5.07171i	−0.189406	−	0.189406i
$718$	21.3009	+	9.76699i	0.794943	+	0.364501i
$719$	−16.4313			−0.612785			−0.306392	−	0.951905i	$-0.599122\pi$
$719$	−16.4313			−0.612785			−0.306392	+	0.951905i	$0.599122\pi$
$720$	−1.72398	+	1.27426i	−0.0642489	+	0.0474889i
$721$	−20.3955	−	20.3955i	−0.759567	−	0.759567i
$722$	5.98503	+	16.1213i	0.222740	+	0.599974i
$723$	−9.29717	−	9.29717i	−0.345765	−	0.345765i
$724$	−18.0795	−	20.9936i	−0.671921	−	0.780221i
$725$		−	20.8686i		−	0.775041i
$726$	10.0530	−	3.73218i	0.373103	−	0.138514i
$727$	32.1429			1.19211			0.596057	−	0.802942i	$-0.296733\pi$
$727$	32.1429			1.19211			0.596057	+	0.802942i	$0.296733\pi$
$728$		0			0
$729$	−4.56452			−0.169056
$730$	2.23003	−	0.827898i	0.0825372	−	0.0306419i
$731$		−	12.8552i		−	0.475466i
$732$	8.01218	+	9.30358i	0.296139	+	0.343870i
$733$	−19.2047	−	19.2047i	−0.709343	−	0.709343i	0.257054	−	0.966397i	$-0.417248\pi$
$733$	−19.2047	−	19.2047i	−0.709343	−	0.709343i	−0.966397	+	0.257054i	$0.917248\pi$
$734$	4.99860	+	13.4643i	0.184502	+	0.496975i
$735$	0.00111757	+	0.00111757i	4.12222e−5	+	4.12222e-5i
$736$	−10.1467	−	48.4134i	−0.374013	−	1.78454i
$737$	−3.63728			−0.133981
$738$	16.9675	+	7.78001i	0.624582	+	0.286386i
$739$	−16.4275	−	16.4275i	−0.604297	−	0.604297i	0.337153	−	0.941450i	$-0.390536\pi$
$739$	−16.4275	−	16.4275i	−0.604297	−	0.604297i	−0.941450	+	0.337153i	$0.890536\pi$
$740$	0.184609	−	0.158984i	0.00678637	−	0.00584438i
$741$		0			0
$742$	−20.2072	−	9.26549i	−0.741830	−	0.340147i
$743$	27.2871	−	27.2871i	1.00107	−	1.00107i	0.00106799	−	0.999999i	$-0.499660\pi$
$743$	27.2871	−	27.2871i	1.00107	−	1.00107i	0.999999	−	0.00106799i	$-0.000339950\pi$
$744$	−12.6783	+	3.65994i	−0.464811	+	0.134180i
$745$		−	3.56696i		−	0.130683i
$746$	19.9079	−	7.39079i	0.728880	−	0.270596i
$747$	15.7415	−	15.7415i	0.575950	−	0.575950i
$748$	0.300151	−	4.02456i	0.0109746	−	0.147153i
$749$	18.4296	−	18.4296i	0.673402	−	0.673402i
$750$	−2.55732	−	1.17259i	−0.0933803	−	0.0428171i
$751$	−1.29395			−0.0472168			−0.0236084	−	0.999721i	$-0.507515\pi$
$751$	−1.29395			−0.0472168			−0.0236084	+	0.999721i	$0.507515\pi$
$752$	12.7519	−	9.42546i	0.465015	−	0.343711i
$753$		−	23.3570i		−	0.851178i
$754$		0			0
$755$		−	0.160022i		−	0.00582380i
$756$	−1.76446	+	23.6588i	−0.0641730	+	0.860462i
$757$	−22.5600			−0.819958			−0.409979	−	0.912095i	$-0.634464\pi$
$757$	−22.5600			−0.819958			−0.409979	+	0.912095i	$0.634464\pi$
$758$	19.6619	−	42.8808i	0.714152	−	1.55750i
$759$	7.57969	−	7.57969i	0.275125	−	0.275125i
$760$	1.79552	−	3.25288i	0.0651305	−	0.117994i
$761$	−6.15099	+	6.15099i	−0.222973	+	0.222973i	−0.809749	−	0.586776i	$-0.800397\pi$
$761$	−6.15099	+	6.15099i	−0.222973	+	0.222973i	0.586776	+	0.809749i	$0.300397\pi$
$762$	2.23594	+	6.02276i	0.0809997	+	0.218182i
$763$		−	0.0909349i		−	0.00329207i
$764$	5.05143	+	5.86562i	0.182754	+	0.212211i
$765$	0.530275	−	0.530275i	0.0191721	−	0.0191721i
$766$	−12.3399	+	26.9123i	−0.445860	+	0.972381i
$767$		0			0
$768$	−3.99026	+	13.0022i	−0.143986	+	0.469175i
$769$	6.84481	+	6.84481i	0.246830	+	0.246830i	0.819668	−	0.572838i	$-0.194158\pi$
$769$	6.84481	+	6.84481i	0.246830	+	0.246830i	−0.572838	+	0.819668i	$0.694158\pi$
$770$	−0.528960	+	1.15361i	−0.0190624	+	0.0415734i
$771$	−23.6611			−0.852135
$772$	1.22334	−	16.4031i	0.0440289	−	0.590361i
$773$	−13.5763	−	13.5763i	−0.488306	−	0.488306i	0.419465	−	0.907771i	$-0.362218\pi$
$773$	−13.5763	−	13.5763i	−0.488306	−	0.488306i	−0.907771	+	0.419465i	$0.862218\pi$
$774$	27.7400	−	10.2984i	0.997093	−	0.370170i
$775$	19.1900	+	19.1900i	0.689327	+	0.689327i
$776$	42.0477	−	12.1382i	1.50942	−	0.435735i
$777$		−	1.16351i		−	0.0417408i
$778$	−4.72715	−	12.7331i	−0.169477	−	0.456504i
$779$	−32.3513			−1.15911
$780$		0			0
$781$	−15.6767			−0.560955
$782$	6.02228	+	16.2217i	0.215356	+	0.580086i
$783$		−	18.9332i		−	0.676617i
$784$	−0.0312536	−	0.00468784i	−0.00111620	−	0.000167423i
$785$	−0.982461	−	0.982461i	−0.0350655	−	0.0350655i
$786$	−12.6508	+	4.69660i	−0.451239	+	0.167522i
$787$	−21.1389	−	21.1389i	−0.753520	−	0.753520i	0.221614	−	0.975134i	$-0.428867\pi$
$787$	−21.1389	−	21.1389i	−0.753520	−	0.753520i	−0.975134	+	0.221614i	$0.928867\pi$
$788$	24.6928	+	1.84158i	0.879645	+	0.0656037i
$789$	−20.2362			−0.720426
$790$	1.18136	−	2.57644i	0.0420309	−	0.0916656i
$791$	−8.51359	−	8.51359i	−0.302709	−	0.302709i
$792$	8.92500	−	2.57644i	0.317136	−	0.0915498i
$793$		0			0
$794$	1.52237	−	3.32016i	0.0540270	−	0.117828i
$795$	0.840869	−	0.840869i	0.0298225	−	0.0298225i
$796$	3.68862	−	3.17661i	0.130740	−	0.112592i
$797$			37.2463i			1.31933i	0.751559	+	0.659665i	$0.229302\pi$
$797$			37.2463i			1.31933i	−0.751559	+	0.659665i	$0.770698\pi$
$798$	−6.17567	−	16.6348i	−0.218616	−	0.588867i
$799$	−3.92234	+	3.92234i	−0.138762	+	0.138762i
$800$	27.3762	−	5.73763i	0.967895	−	0.202856i
$801$	−10.6983	+	10.6983i	−0.378004	+	0.378004i
$802$	15.9451	−	34.7748i	0.563041	−	1.22794i
$803$	−10.3076			−0.363746
$804$	−4.27606	−	0.318907i	−0.150805	−	0.0112470i
$805$		−	5.44136i		−	0.191783i
$806$		0			0
$807$			17.6060i			0.619759i
$808$	−22.7184	−	12.5401i	−0.799232	−	0.441160i
$809$	41.8180			1.47024			0.735121	−	0.677936i	$-0.237125\pi$
$809$	41.8180			1.47024			0.735121	+	0.677936i	$0.237125\pi$
$810$	0.913300	+	0.418770i	0.0320901	+	0.0147141i
$811$	4.29617	−	4.29617i	0.150859	−	0.150859i	−0.627643	−	0.778502i	$-0.715980\pi$
$811$	4.29617	−	4.29617i	0.150859	−	0.150859i	0.778502	+	0.627643i	$0.215980\pi$
$812$	−22.2582	−	1.66001i	−0.781110	−	0.0582549i
$813$	8.30670	−	8.30670i	0.291329	−	0.291329i
$814$	−0.989700	+	0.367425i	−0.0346890	+	0.0128782i
$815$		−	3.70240i		−	0.129689i
$816$	0.705725	−	4.70503i	0.0247053	−	0.164709i
$817$	−36.2632	+	36.2632i	−1.26869	+	1.26869i
$818$	−6.16364	−	2.82618i	−0.215506	−	0.0988149i
$819$		0			0
$820$	1.78001	+	2.06691i	0.0621607	+	0.0721798i
$821$	−13.3510	−	13.3510i	−0.465954	−	0.465954i	0.434647	−	0.900601i	$-0.356873\pi$
$821$	−13.3510	−	13.3510i	−0.465954	−	0.465954i	−0.900601	+	0.434647i	$0.856873\pi$
$822$	−5.25400	−	2.40909i	−0.183254	−	0.0840266i
$823$	13.6087			0.474371			0.237185	−	0.971464i	$-0.423775\pi$
$823$	13.6087			0.474371			0.237185	+	0.971464i	$0.423775\pi$
$824$	−14.9094	+	27.0108i	−0.519394	+	0.940966i
$825$	4.28607	+	4.28607i	0.149222	+	0.149222i
$826$	−11.0887	−	29.8687i	−0.385826	−	1.03927i
$827$	17.0815	+	17.0815i	0.593982	+	0.593982i	0.938705	−	0.344723i	$-0.112027\pi$
$827$	17.0815	+	17.0815i	0.593982	+	0.593982i	−0.344723	+	0.938705i	$0.612027\pi$
$828$	−30.1800	+	25.9908i	−1.04883	+	0.903243i
$829$			27.4835i			0.954541i	0.878757	+	0.477270i	$0.158374\pi$
$829$			27.4835i			0.954541i	−0.878757	+	0.477270i	$0.841626\pi$
$830$	3.04980	−	1.13223i	0.105860	−	0.0393004i
$831$	10.8241			0.375485
$832$		0			0
$833$	0.0110551			0.000383038
$834$	−7.82203	+	2.90392i	−0.270855	+	0.100555i
$835$		−	1.31937i		−	0.0456587i
$836$	−12.1996	+	10.5062i	−0.421932	+	0.363365i
$837$	17.4103	+	17.4103i	0.601788	+	0.601788i
$838$	2.75880	+	7.43113i	0.0953012	+	0.256704i
$839$	−28.2374	−	28.2374i	−0.974865	−	0.974865i	0.0248272	−	0.999692i	$-0.492096\pi$
$839$	−28.2374	−	28.2374i	−0.974865	−	0.974865i	−0.999692	+	0.0248272i	$0.992096\pi$
$840$	−0.723001	+	1.30983i	−0.0249459	+	0.0451935i
$841$	−11.1876			−0.385781
$842$	−6.46033	−	2.96222i	−0.222638	−	0.102085i
$843$	−13.1293	−	13.1293i	−0.452196	−	0.452196i
$844$	−5.46913	−	6.35064i	−0.188255	−	0.218598i
$845$		0			0
$846$	−11.6062	−	5.32172i	−0.399029	−	0.182964i
$847$	−16.6789	+	16.6789i	−0.573095	+	0.573095i
$848$	−3.52716	+	23.5154i	−0.121123	+	0.807523i
$849$		−	17.5872i		−	0.603590i
$850$	−9.17283	+	3.40540i	−0.314625	+	0.116804i
$851$	3.20064	−	3.20064i	0.109717	−	0.109717i
$852$	−18.4298	−	1.37449i	−0.631394	−	0.0470891i
$853$	−6.78242	+	6.78242i	−0.232226	+	0.232226i	−0.813621	−	0.581395i	$-0.802507\pi$
$853$	−6.78242	+	6.78242i	−0.232226	+	0.232226i	0.581395	+	0.813621i	$0.302507\pi$
$854$	−24.5495	−	11.2565i	−0.840066	−	0.385191i
$855$	−2.99171			−0.102314
$856$	−24.4073	−	13.4723i	−0.834223	−	0.460474i
$857$			25.7579i			0.879872i	0.898029	+	0.439936i	$0.144999\pi$
$857$			25.7579i			0.879872i	−0.898029	+	0.439936i	$0.855001\pi$
$858$		0			0
$859$		−	51.8251i		−	1.76825i	−0.467252	−	0.884124i	$-0.654756\pi$
$859$		−	51.8251i		−	1.76825i	0.467252	−	0.884124i	$-0.345244\pi$
$860$	4.31210	+	0.321595i	0.147041	+	0.0109663i
$861$	13.0269			0.443954
$862$	−2.03812	+	4.44495i	−0.0694186	+	0.151396i
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.220144	+	0.975467i	$0.570653\pi$
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.975467	+	0.220144i	$0.929347\pi$
$864$	24.8372	−	5.20550i	0.844980	−	0.177095i
$865$	0.359562	−	0.359562i	0.0122255	−	0.0122255i
$866$	2.69363	+	7.25558i	0.0915332	+	0.246555i
$867$		−	12.7864i		−	0.434250i
$868$	21.9943	−	18.9414i	0.746537	−	0.642912i
$869$	−8.68457	+	8.68457i	−0.294604	+	0.294604i
$870$	0.497646	−	1.08532i	0.0168718	−	0.0367958i
$871$		0			0
$872$	−0.0934525	+	0.0269775i	−0.00316470	+	0.000913575i
$873$	−24.9177	−	24.9177i	−0.843335	−	0.843335i
$874$	28.7715	−	62.7481i	0.973212	−	2.12249i
$875$	6.18828			0.209202
$876$	−12.1178	−	0.903738i	−0.409421	−	0.0305345i
$877$	26.2620	+	26.2620i	0.886805	+	0.886805i	0.994215	−	0.107410i	$-0.0342557\pi$
$877$	26.2620	+	26.2620i	0.886805	+	0.886805i	−0.107410	+	0.994215i	$0.534256\pi$
$878$	−40.4452	+	15.0152i	−1.36496	+	0.506740i
$879$	−13.8602	−	13.8602i	−0.467493	−	0.467493i
$880$	1.34248	+	0.201363i	0.0452549	+	0.00678795i
$881$			1.99779i			0.0673074i	0.999434	+	0.0336537i	$0.0107143\pi$
$881$			1.99779i			0.0673074i	−0.999434	+	0.0336537i	$0.989286\pi$
$882$	0.00885641	+	0.0238557i	0.000298211	+	0.000803264i
$883$	16.1625			0.543913			0.271956	−	0.962310i	$-0.412329\pi$
$883$	16.1625			0.543913			0.271956	+	0.962310i	$0.412329\pi$
$884$		0			0
$885$	1.70433			0.0572906
$886$	−6.34909	−	17.1020i	−0.213302	−	0.574552i
$887$			17.6060i			0.591150i	0.955319	+	0.295575i	$0.0955113\pi$
$887$			17.6060i			0.591150i	−0.955319	+	0.295575i	$0.904489\pi$
$888$	−1.19572	+	0.345177i	−0.0401259	+	0.0115834i
$889$	−9.99232	−	9.99232i	−0.335132	−	0.335132i
$890$	−2.07271	+	0.769492i	−0.0694774	+	0.0257934i
$891$	−3.07852	−	3.07852i	−0.103134	−	0.103134i
$892$	−2.80066	+	37.5526i	−0.0937730	+	1.25735i
$893$	22.1291			0.740522
$894$	−7.59454	+	16.5630i	−0.254000	+	0.553950i
$895$	−1.68613	−	1.68613i	−0.0563611	−	0.0563611i
$896$	−3.94203	−	29.6555i	−0.131694	−	0.990721i
$897$		0			0
$898$	5.81779	−	12.6881i	0.194142	−	0.423407i
$899$	−16.3796	+	16.3796i	−0.546291	+	0.546291i
$900$	−14.6969	−	17.0658i	−0.489898	−	0.568860i
$901$		−	8.31797i		−	0.277112i
$902$	−4.11375	−	11.0808i	−0.136973	−	0.368951i
$903$	14.6021	−	14.6021i	0.485926	−	0.485926i
$904$	−6.22358	+	11.2750i	−0.206993	+	0.375001i
$905$	−2.30516	+	2.30516i	−0.0766261	+	0.0766261i
$906$	−0.340708	+	0.743054i	−0.0113193	+	0.0246863i
$907$	−29.4107			−0.976567			−0.488283	−	0.872685i	$-0.662377\pi$
$907$	−29.4107			−0.976567			−0.488283	+	0.872685i	$0.662377\pi$
$908$	−1.10665	+	14.8385i	−0.0367255	+	0.492433i
$909$			20.8944i			0.693024i
$910$		0			0
$911$		−	20.5091i		−	0.679495i	−0.940517	−	0.339748i	$-0.889658\pi$
$911$		−	20.5091i		−	0.679495i	0.940517	−	0.339748i	$-0.110342\pi$
$912$	−15.2632	+	11.2817i	−0.505416	+	0.373574i
$913$	−14.0966			−0.466531
$914$	13.3464	+	6.11967i	0.441461	+	0.202421i
$915$	1.02156	−	1.02156i	0.0337718	−	0.0337718i
$916$	−0.668352	+	8.96158i	−0.0220830	+	0.296099i
$917$	20.9889	−	20.9889i	0.693113	−	0.693113i
$918$	−8.32211	+	3.08958i	−0.274671	+	0.101971i
$919$			48.9751i			1.61554i	0.589498	+	0.807770i	$0.299326\pi$
$919$			48.9751i			1.61554i	−0.589498	+	0.807770i	$0.700674\pi$
$920$	−5.59201	+	1.61428i	−0.184363	+	0.0532213i
$921$	13.8697	−	13.8697i	0.457021	−	0.457021i
$922$	−36.9391	−	16.9375i	−1.21652	−	0.557806i
$923$		0			0
$924$	4.91240	−	4.23053i	0.161606	−	0.139174i
$925$	1.80986	+	1.80986i	0.0595077	+	0.0595077i
$926$	−10.7091	−	4.91039i	−0.351923	−	0.161365i
$927$	24.8422			0.815923
$928$	4.89734	+	23.3669i	0.160763	+	0.767056i
$929$	−4.84435	−	4.84435i	−0.158938	−	0.158938i	0.623158	−	0.782096i	$-0.285849\pi$
$929$	−4.84435	−	4.84435i	−0.158938	−	0.158938i	−0.782096	+	0.623158i	$0.785849\pi$
$930$	0.540405	+	1.45564i	0.0177206	+	0.0477324i
$931$	−0.0311855	−	0.0311855i	−0.00102206	−	0.00102206i
$932$	17.3848	+	20.1869i	0.569459	+	0.661244i
$933$			7.26384i			0.237808i
$934$	4.37956	−	1.62591i	0.143303	−	0.0532013i
$935$	−0.474867			−0.0155298
$936$		0			0
$937$	11.1107			0.362970			0.181485	−	0.983394i	$-0.441910\pi$
$937$	11.1107			0.362970			0.181485	+	0.983394i	$0.441910\pi$
$938$	8.84215	−	3.28264i	0.288706	−	0.107182i
$939$		−	5.00146i		−	0.163217i
$940$	−1.21757	−	1.41382i	−0.0397128	−	0.0461137i
$941$	−20.5970	−	20.5970i	−0.671442	−	0.671442i	0.286606	−	0.958048i	$-0.407473\pi$
$941$	−20.5970	−	20.5970i	−0.671442	−	0.671442i	−0.958048	+	0.286606i	$0.907473\pi$
$942$	2.47022	+	6.65380i	0.0804841	+	0.216793i
$943$	35.8348	+	35.8348i	1.16694	+	1.16694i
$944$	−27.4059	+	20.2568i	−0.891988	+	0.659304i
$945$	2.79155			0.0908091
$946$	−17.0319	−	7.80954i	−0.553755	−	0.253910i
$947$	20.7444	+	20.7444i	0.674102	+	0.674102i	0.958659	−	0.284557i	$-0.0918465\pi$
$947$	20.7444	+	20.7444i	0.674102	+	0.674102i	−0.284557	+	0.958659i	$0.591846\pi$
$948$	−10.9712	+	9.44830i	−0.356327	+	0.306867i
$949$		0			0
$950$	35.4820	+	16.2694i	1.15119	+	0.527848i
$951$	−14.0295	+	14.0295i	−0.454938	+	0.454938i
$952$	2.90250	+	10.0545i	0.0940706	+	0.325868i
$953$		−	13.1218i		−	0.425057i	−0.977155	−	0.212529i	$-0.931830\pi$
$953$		−	13.1218i		−	0.425057i	0.977155	−	0.212529i	$-0.0681699\pi$
$954$	17.9492	−	6.66363i	0.581128	−	0.215743i
$955$	0.644063	−	0.644063i	0.0208414	−	0.0208414i
$956$	1.25509	−	16.8288i	0.0405925	−	0.544283i
$957$	−3.65836	+	3.65836i	−0.118258	+	0.118258i
$958$	35.7538	+	16.3940i	1.15515	+	0.529666i
$959$	12.7138			0.410549
$960$	1.56059	+	0.354431i	0.0503677	+	0.0114392i
$961$			0.875747i			0.0282499i
$962$		0			0
$963$			22.4477i			0.723365i
$964$	2.30076	−	30.8497i	0.0741024	−	0.993601i
$965$	−1.93544			−0.0623039
$966$	−11.5854	+	25.2667i	−0.372754	+	0.812943i
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	−0.885059	−	0.465478i	$-0.845882\pi$
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	0.465478	+	0.885059i	$0.345882\pi$
$968$	22.0888	+	12.1926i	0.709961	+	0.391884i
$969$	4.69479	−	4.69479i	0.150818	−	0.150818i
$970$	−1.79225	−	4.82762i	−0.0575457	−	0.155006i
$971$		−	44.2841i		−	1.42115i	−0.703624	−	0.710573i	$-0.748436\pi$
$971$		−	44.2841i		−	1.42115i	0.703624	−	0.710573i	$-0.251564\pi$
$972$	−20.9137	−	24.2845i	−0.670806	−	0.778927i
$973$	12.9775	−	12.9775i	0.416039	−	0.416039i
$974$	6.08146	−	13.2631i	0.194862	−	0.424978i
$975$		0			0
$976$	−4.28511	+	28.5686i	−0.137163	+	0.914459i
$977$	−0.175234	−	0.175234i	−0.00560624	−	0.00560624i	0.704298	−	0.709904i	$-0.251262\pi$
$977$	−0.175234	−	0.175234i	−0.00560624	−	0.00560624i	−0.709904	+	0.704298i	$0.751262\pi$
$978$	−7.88292	+	17.1919i	−0.252068	+	0.549737i
$979$	9.58040			0.306191
$980$	−0.000276564		0.00370830i	−8.83450e−6		0.000118457i
$981$	0.0553805	+	0.0553805i	0.00176816	+	0.00176816i
$982$	18.0638	−	6.70617i	0.576439	−	0.214002i
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	0.559393	−	0.828903i	$-0.311034\pi$
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	−0.828903	+	0.559393i	$0.811034\pi$
$984$	−3.86466	−	13.3875i	−0.123201	−	0.426778i
$985$		−	2.91356i		−	0.0928336i
$986$	−2.90667	−	7.82945i	−0.0925674	−	0.249340i
$987$	−8.91069			−0.283630
$988$		0			0
$989$	80.3360			2.55454
$990$	−0.380422	−	1.02471i	−0.0120906	−	0.0325673i
$991$		−	41.8295i		−	1.32876i	−0.747396	−	0.664379i	$-0.768696\pi$
$991$		−	41.8295i		−	1.32876i	0.747396	−	0.664379i	$-0.231304\pi$
$992$	−25.9908	−	16.9839i	−0.825209	−	0.539241i
$993$	8.63520	+	8.63520i	0.274030	+	0.274030i
$994$	38.1096	−	14.1482i	1.20876	−	0.448752i
$995$	−0.405021	−	0.405021i	−0.0128400	−	0.0128400i
$996$	−16.5723	−	1.23595i	−0.525112	−	0.0391627i
$997$	12.7618			0.404169			0.202085	−	0.979368i	$-0.435228\pi$
$997$	12.7618			0.404169			0.202085	+	0.979368i	$0.435228\pi$
$998$	9.36028	−	20.4139i	0.296294	−	0.646191i
$999$	1.64200	+	1.64200i	0.0519507	+	0.0519507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.f.h.99.1		16
4.3	odd	2	inner	676.2.f.h.99.6		16
13.2	odd	12		676.2.l.m.19.1		16
13.3	even	3		52.2.l.b.7.3	✓	16
13.4	even	6		676.2.l.i.427.2		16
13.5	odd	4	inner	676.2.f.h.239.6		16
13.6	odd	12		52.2.l.b.15.4	yes	16
13.7	odd	12		676.2.l.k.587.1		16
13.8	odd	4		676.2.f.i.239.3		16
13.9	even	3		676.2.l.m.427.3		16
13.10	even	6		676.2.l.k.319.2		16
13.11	odd	12		676.2.l.i.19.4		16
13.12	even	2		676.2.f.i.99.8		16
39.29	odd	6		468.2.cb.f.163.2		16
39.32	even	12		468.2.cb.f.379.1		16
52.3	odd	6		52.2.l.b.7.4	yes	16
52.7	even	12		676.2.l.k.587.2		16
52.11	even	12		676.2.l.i.19.2		16
52.15	even	12		676.2.l.m.19.3		16
52.19	even	12		52.2.l.b.15.3	yes	16
52.23	odd	6		676.2.l.k.319.1		16
52.31	even	4	inner	676.2.f.h.239.1		16
52.35	odd	6		676.2.l.m.427.1		16
52.43	odd	6		676.2.l.i.427.4		16
52.47	even	4		676.2.f.i.239.8		16
52.51	odd	2		676.2.f.i.99.3		16
104.3	odd	6		832.2.bu.n.319.3		16
104.19	even	12		832.2.bu.n.639.2		16
104.29	even	6		832.2.bu.n.319.2		16
104.45	odd	12		832.2.bu.n.639.3		16
156.71	odd	12		468.2.cb.f.379.2		16
156.107	even	6		468.2.cb.f.163.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.3	✓	16	13.3	even	3
52.2.l.b.7.4	yes	16	52.3	odd	6
52.2.l.b.15.3	yes	16	52.19	even	12
52.2.l.b.15.4	yes	16	13.6	odd	12
468.2.cb.f.163.1		16	156.107	even	6
468.2.cb.f.163.2		16	39.29	odd	6
468.2.cb.f.379.1		16	39.32	even	12
468.2.cb.f.379.2		16	156.71	odd	12
676.2.f.h.99.1		16	1.1	even	1	trivial
676.2.f.h.99.6		16	4.3	odd	2	inner
676.2.f.h.239.1		16	52.31	even	4	inner
676.2.f.h.239.6		16	13.5	odd	4	inner
676.2.f.i.99.3		16	52.51	odd	2
676.2.f.i.99.8		16	13.12	even	2
676.2.f.i.239.3		16	13.8	odd	4
676.2.f.i.239.8		16	52.47	even	4
676.2.l.i.19.2		16	52.11	even	12
676.2.l.i.19.4		16	13.11	odd	12
676.2.l.i.427.2		16	13.4	even	6
676.2.l.i.427.4		16	52.43	odd	6
676.2.l.k.319.1		16	52.23	odd	6
676.2.l.k.319.2		16	13.10	even	6
676.2.l.k.587.1		16	13.7	odd	12
676.2.l.k.587.2		16	52.7	even	12
676.2.l.m.19.1		16	13.2	odd	12
676.2.l.m.19.3		16	52.15	even	12
676.2.l.m.427.1		16	52.35	odd	6
676.2.l.m.427.3		16	13.9	even	3
832.2.bu.n.319.2		16	104.29	even	6
832.2.bu.n.319.3		16	104.3	odd	6
832.2.bu.n.639.2		16	104.19	even	12
832.2.bu.n.639.3		16	104.45	odd	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32580 + 0.492201i) q^{2} -0.850043i q^{3} +(1.51548 - 1.30512i) q^{4} +(-0.166404 - 0.166404i) q^{5} +(0.418392 + 1.12698i) q^{6} +(-1.86977 - 1.86977i) q^{7} +(-1.36683 + 2.47624i) q^{8} +2.27743 q^{9} +(0.302522 + 0.138714i) q^{10} +(-1.01973 - 1.01973i) q^{11} +(-1.10941 - 1.28822i) q^{12} +(3.39924 + 1.55864i) q^{14} +(-0.141450 + 0.141450i) q^{15} +(0.593337 - 3.95575i) q^{16} +1.39924i q^{17} +(-3.01941 + 1.12095i) q^{18} +(3.94713 - 3.94713i) q^{19} +(-0.469358 - 0.0350045i) q^{20} +(-1.58939 + 1.58939i) q^{21} +(1.85387 + 0.850043i) q^{22} -8.74431 q^{23} +(2.10491 + 1.16187i) q^{24} -4.94462i q^{25} -4.48604i q^{27} +(-5.27387 - 0.393323i) q^{28} +4.22047 q^{29} +(0.117912 - 0.257157i) q^{30} +(-3.88100 + 3.88100i) q^{31} +(1.16038 + 5.53656i) q^{32} +(-0.866814 + 0.866814i) q^{33} +(-0.688709 - 1.85511i) q^{34} +0.622275i q^{35} +(3.45139 - 2.97231i) q^{36} +(-0.366025 + 0.366025i) q^{37} +(-3.29032 + 7.17588i) q^{38} +(0.639502 - 0.184609i) q^{40} +(-4.09808 - 4.09808i) q^{41} +(1.32491 - 2.88950i) q^{42} -9.18723 q^{43} +(-2.87624 - 0.214509i) q^{44} +(-0.378973 - 0.378973i) q^{45} +(11.5932 - 4.30396i) q^{46} +(2.80318 + 2.80318i) q^{47} +(-3.36256 - 0.504362i) q^{48} -0.00790080i q^{49} +(2.43375 + 6.55556i) q^{50} +1.18942 q^{51} -5.94462 q^{53} +(2.20803 + 5.94758i) q^{54} +0.339374i q^{55} +(7.18567 - 2.07434i) q^{56} +(-3.35523 - 3.35523i) q^{57} +(-5.59549 + 2.07732i) q^{58} +(-6.02449 - 6.02449i) q^{59} +(-0.0297554 + 0.398974i) q^{60} -7.22205 q^{61} +(3.23518 - 7.05564i) q^{62} +(-4.25827 - 4.25827i) q^{63} +(-4.26353 - 6.76922i) q^{64} +(0.722573 - 1.57587i) q^{66} +(1.78345 - 1.78345i) q^{67} +(1.82618 + 2.12052i) q^{68} +7.43304i q^{69} +(-0.306284 - 0.825010i) q^{70} +(7.68668 - 7.68668i) q^{71} +(-3.11287 + 5.63946i) q^{72} +(5.05407 - 5.05407i) q^{73} +(0.305117 - 0.665434i) q^{74} -4.20314 q^{75} +(0.830315 - 11.1333i) q^{76} +3.81333i q^{77} -8.51654i q^{79} +(-0.756985 + 0.559518i) q^{80} +3.01896 q^{81} +(7.45030 + 3.41614i) q^{82} +(6.91195 - 6.91195i) q^{83} +(-0.334342 + 4.48301i) q^{84} +(0.232839 - 0.232839i) q^{85} +(12.1804 - 4.52197i) q^{86} -3.58758i q^{87} +(3.91890 - 1.13129i) q^{88} +(-4.69752 + 4.69752i) q^{89} +(0.688971 + 0.315910i) q^{90} +(-13.2518 + 11.4124i) q^{92} +(3.29901 + 3.29901i) q^{93} +(-5.09618 - 2.33672i) q^{94} -1.31364 q^{95} +(4.70632 - 0.986372i) q^{96} +(-10.9412 - 10.9412i) q^{97} +(0.00388878 + 0.0104749i) q^{98} +(-2.32236 - 2.32236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 12 q^{5} + 4 q^{6} + 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} - 6 q^{18} - 22 q^{20} - 28 q^{21} + 4 q^{24} - 36 q^{28} + 16 q^{29} - 2 q^{32} + 28 q^{33} + 14 q^{34} + 8 q^{37} - 40 q^{40}+ \cdots + 70 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 12 * q^5 + 4 * q^6 + 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 - 6 * q^18 - 22 * q^20 - 28 * q^21 + 4 * q^24 - 36 * q^28 + 16 * q^29 - 2 * q^32 + 28 * q^33 + 14 * q^34 + 8 * q^37 - 40 * q^40 - 24 * q^41 + 56 * q^42 - 8 * q^44 + 20 * q^45 + 56 * q^46 + 20 * q^48 - 32 * q^50 - 32 * q^53 + 44 * q^54 + 12 * q^57 + 30 * q^58 - 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 + 28 * q^70 - 46 * q^72 + 20 * q^73 - 8 * q^74 - 8 * q^76 - 22 * q^80 - 96 * q^81 - 48 * q^84 - 52 * q^85 + 16 * q^86 + 44 * q^89 - 12 * q^92 + 112 * q^93 + 76 * q^94 - 72 * q^96 - 52 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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