LMFDB - Embedded newform 676.2.f.h.99.6

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			99.6
Root			$1.08916 + 0.902074i$ of defining polynomial
Character	$\chi$	$=$	676.99
Dual form			676.2.f.h.239.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.492201 - 1.32580i) q^{2} +0.850043i q^{3} +(-1.51548 - 1.30512i) q^{4} +(-0.166404 - 0.166404i) q^{5} +(1.12698 + 0.418392i) q^{6} +(1.86977 + 1.86977i) q^{7} +(-2.47624 + 1.36683i) 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} +(1.12095 - 3.01941i) q^{18} +(-3.94713 + 3.94713i) q^{19} +(0.0350045 + 0.469358i) q^{20} +(-1.58939 + 1.58939i) q^{21} +(1.85387 - 0.850043i) q^{22} +8.74431 q^{23} +(-1.16187 - 2.10491i) q^{24} -4.94462i q^{25} +4.48604i q^{27} +(-0.393323 - 5.27387i) q^{28} +4.22047 q^{29} +(-0.117912 - 0.257157i) q^{30} +(3.88100 - 3.88100i) q^{31} +(5.53656 + 1.16038i) q^{32} +(-0.866814 + 0.866814i) q^{33} +(1.85511 + 0.688709i) 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} +(-0.214509 - 2.87624i) q^{44} +(-0.378973 - 0.378973i) q^{45} +(4.30396 - 11.5932i) q^{46} +(-2.80318 - 2.80318i) q^{47} +(-3.36256 + 0.504362i) q^{48} -0.00790080i q^{49} +(-6.55556 - 2.43375i) q^{50} -1.18942 q^{51} -5.94462 q^{53} +(5.94758 + 2.20803i) q^{54} -0.339374i q^{55} +(-7.18567 - 2.07434i) q^{56} +(-3.35523 - 3.35523i) q^{57} +(2.07732 - 5.59549i) q^{58} +(6.02449 + 6.02449i) q^{59} +(-0.398974 + 0.0297554i) 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} +(-0.825010 - 0.306284i) q^{70} +(-7.68668 + 7.68668i) q^{71} +(-5.63946 + 3.11287i) q^{72} +(5.05407 - 5.05407i) q^{73} +(0.305117 + 0.665434i) q^{74} +4.20314 q^{75} +(11.1333 - 0.830315i) q^{76} +3.81333i q^{77} +8.51654i q^{79} +(0.559518 - 0.756985i) q^{80} +3.01896 q^{81} +(-7.45030 + 3.41614i) q^{82} +(-6.91195 + 6.91195i) q^{83} +(4.48301 - 0.334342i) q^{84} +(0.232839 - 0.232839i) q^{85} +(4.52197 - 12.1804i) 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} +(-0.986372 + 4.70632i) q^{96} +(-10.9412 - 10.9412i) q^{97} +(-0.0104749 - 0.00388878i) 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 $

$2$	0.492201	−	1.32580i	0.348039	−	0.937480i
$2$	0.492201	−	1.32580i	0.348039	−	0.937480i
$3$			0.850043i			0.490772i	0.969425	+	0.245386i	$0.0789148\pi$
$3$			0.850043i			0.490772i	−0.969425	+	0.245386i	$0.921085\pi$
$4$	−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	$0.766758\pi$
$6$	1.12698	+	0.418392i	0.460089	+	0.170808i
$7$	1.86977	+	1.86977i	0.706708	+	0.706708i	0.965841	−	0.259134i	$-0.0834371\pi$
$7$	1.86977	+	1.86977i	0.706708	+	0.706708i	−0.259134	+	0.965841i	$0.583437\pi$
$8$	−2.47624	+	1.36683i	−0.875483	+	0.483249i
$9$	2.27743			0.759142
$10$	−0.302522	+	0.138714i	−0.0956658	+	0.0438651i
$11$	1.01973	+	1.01973i	0.307460	+	0.307460i	0.843924	−	0.536463i	$-0.180240\pi$
$11$	1.01973	+	1.01973i	0.307460	+	0.307460i	−0.536463	+	0.843924i	$0.680240\pi$
$12$	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	$0.945726\pi$
$18$	1.12095	−	3.01941i	0.264211	−	0.711681i
$19$	−3.94713	+	3.94713i	−0.905535	+	0.905535i	−0.995908	−	0.0903734i	$-0.971194\pi$
$19$	−3.94713	+	3.94713i	−0.905535	+	0.905535i	0.0903734	+	0.995908i	$0.471194\pi$
$20$	0.0350045	+	0.469358i	0.00782725	+	0.104952i
$21$	−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	$-0.134803\pi$
$23$	8.74431			1.82331			0.911657	+	0.410951i	$0.134803\pi$
$24$	−1.16187	−	2.10491i	−0.237165	−	0.429663i
$25$		−	4.94462i		−	0.988924i
$26$		0			0
$27$			4.48604i			0.863339i
$28$	−0.393323	−	5.27387i	−0.0743311	−	0.996668i
$29$	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	−0.266725	−	0.963773i	$-0.585942\pi$
$31$	3.88100	−	3.88100i	0.697047	−	0.697047i	0.963773	+	0.266725i	$0.0859416\pi$
$32$	5.53656	+	1.16038i	0.978735	+	0.205128i
$33$	−0.866814	+	0.866814i	−0.150893	+	0.150893i
$34$	1.85511	+	0.688709i	0.318149	+	0.118113i
$35$		−	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	$-0.252951\pi$
$43$	9.18723			1.40104			0.700520	+	0.713633i	$0.252951\pi$
$44$	−0.214509	−	2.87624i	−0.0323385	−	0.433610i
$45$	−0.378973	−	0.378973i	−0.0564939	−	0.0564939i
$46$	4.30396	−	11.5932i	0.634584	−	1.70932i
$47$	−2.80318	−	2.80318i	−0.408886	−	0.408886i	0.472464	−	0.881350i	$-0.343365\pi$
$47$	−2.80318	−	2.80318i	−0.408886	−	0.408886i	−0.881350	+	0.472464i	$0.843365\pi$
$48$	−3.36256	+	0.504362i	−0.485343	+	0.0727984i
$49$		−	0.00790080i		−	0.00112869i
$50$	−6.55556	−	2.43375i	−0.927097	−	0.344184i
$51$	−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	$0.633871\pi$
$54$	5.94758	+	2.20803i	0.809363	+	0.300475i
$55$		−	0.339374i		−	0.0457612i
$56$	−7.18567	−	2.07434i	−0.960226	−	0.277195i
$57$	−3.35523	−	3.35523i	−0.444411	−	0.444411i
$58$	2.07732	−	5.59549i	0.272765	−	0.734723i
$59$	6.02449	+	6.02449i	0.784322	+	0.784322i	0.980557	−	0.196235i	$-0.0628714\pi$
$59$	6.02449	+	6.02449i	0.784322	+	0.784322i	−0.196235	+	0.980557i	$0.562871\pi$
$60$	−0.398974	+	0.0297554i	−0.0515073	+	0.00384140i
$61$	−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	−0.807606	−	0.589722i	$-0.799237\pi$
$67$	−1.78345	+	1.78345i	−0.217884	+	0.217884i	0.589722	+	0.807606i	$0.299237\pi$
$68$	1.82618	−	2.12052i	0.221456	−	0.257151i
$69$			7.43304i			0.894833i
$70$	−0.825010	−	0.306284i	−0.0986075	−	0.0366080i
$71$	−7.68668	+	7.68668i	−0.912241	+	0.912241i	−0.996448	−	0.0842073i	$-0.973164\pi$
$71$	−7.68668	+	7.68668i	−0.912241	+	0.912241i	0.0842073	+	0.996448i	$0.473164\pi$
$72$	−5.63946	+	3.11287i	−0.664616	+	0.366855i
$73$	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
$76$	11.1333	−	0.830315i	1.27707	−	0.0952437i
$77$			3.81333i			0.434569i
$78$		0			0
$79$			8.51654i			0.958186i	0.877764	+	0.479093i	$0.159034\pi$
$79$			8.51654i			0.958186i	−0.877764	+	0.479093i	$0.840966\pi$
$80$	0.559518	−	0.756985i	0.0625560	−	0.0846335i
$81$	3.01896			0.335440
$82$	−7.45030	+	3.41614i	−0.822747	+	0.377250i
$83$	−6.91195	+	6.91195i	−0.758685	+	0.758685i	−0.976083	−	0.217398i	$-0.930243\pi$
$83$	−6.91195	+	6.91195i	−0.758685	+	0.758685i	0.217398	+	0.976083i	$0.430243\pi$
$84$	4.48301	−	0.334342i	0.489137	−	0.0364797i
$85$	0.232839	−	0.232839i	0.0252550	−	0.0252550i
$86$	4.52197	−	12.1804i	0.487616	−	1.31345i
$87$			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
$96$	−0.986372	+	4.70632i	−0.100671	+	0.480336i
$97$	−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	$-0.537609\pi$
$98$	−0.0104749	−	0.00388878i	−0.00105812	−	0.000392826i
$99$	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	$0.849120\pi$
$102$	−0.585432	+	1.57693i	−0.0579664	+	0.156139i
$103$	−10.9080			−1.07480			−0.537398	−	0.843329i	$-0.680593\pi$
$103$	−10.9080			−1.07480			−0.537398	+	0.843329i	$0.680593\pi$
$104$		0			0
$105$	0.528960			0.0516212
$106$	−2.92595	+	7.88136i	−0.284193	+	0.765505i
$107$		−	9.85658i		−	0.952872i	−0.879209	−	0.476436i	$-0.841928\pi$
$107$		−	9.85658i		−	0.952872i	0.879209	−	0.476436i	$-0.158072\pi$
$108$	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	$0.749476\pi$
$110$	−0.449941	−	0.167040i	−0.0429002	−	0.0159267i
$111$	−0.311137	−	0.311137i	−0.0295318	−	0.0295318i
$112$	−6.28695	+	8.50576i	−0.594061	+	0.803718i
$113$	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
$122$	−3.55470	+	9.57497i	−0.321827	+	0.866877i
$123$	3.48354	−	3.48354i	0.314100	−	0.314100i
$124$	−10.9467	+	0.816402i	−0.983044	+	0.0733151i
$125$	−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	$-0.576199\pi$
$127$	−5.34414			−0.474216			−0.237108	+	0.971483i	$0.576199\pi$
$128$	−6.87610	−	8.98439i	−0.607767	−	0.794115i
$129$			7.80954i			0.687592i
$130$		0			0
$131$		−	11.2254i		−	0.980764i	−0.871508	−	0.490382i	$-0.836857\pi$
$131$		−	11.2254i		−	0.980764i	0.871508	−	0.490382i	$-0.163143\pi$
$132$	2.44493	−	0.182342i	0.212804	−	0.0158708i
$133$	−14.7605			−1.27990
$134$	1.48668	+	3.24232i	0.128430	+	0.280094i
$135$	0.746494	−	0.746494i	0.0642480	−	0.0642480i
$136$	−1.91253	−	3.46486i	−0.163998	−	0.297109i
$137$	−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	$0.315846\pi$
$138$	9.85470	+	3.65855i	0.838888	+	0.311436i
$139$		−	6.94068i		−	0.588700i	−0.955698	−	0.294350i	$-0.904897\pi$
$139$		−	6.94068i		−	0.588700i	0.955698	−	0.294350i	$-0.0951032\pi$
$140$	−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
$148$	1.03241	−	0.0769967i	0.0848635	−	0.00632909i
$149$	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	$0.536782\pi$
$150$	2.06879	−	5.57251i	0.168916	−	0.454993i
$151$	−0.480824	−	0.480824i	−0.0391289	−	0.0391289i	0.687272	−	0.726401i	$-0.258808\pi$
$151$	−0.480824	−	0.480824i	−0.0391289	−	0.0391289i	−0.726401	+	0.687272i	$0.758808\pi$
$152$	4.37897	−	15.1691i	0.355182	−	1.23038i
$153$			3.18667i			0.257627i
$154$	5.05570	+	1.87692i	0.407400	+	0.151247i
$155$	−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	$0.424295\pi$
$158$	11.2912	+	4.19185i	0.898280	+	0.333486i
$159$		−	5.05318i		−	0.400743i
$160$	−0.728214	−	1.11440i	−0.0575703	−	0.0881008i
$161$	16.3499	+	16.3499i	1.28855	+	1.28855i
$162$	1.48593	−	4.00252i	0.116746	−	0.314468i
$163$	−11.1248	−	11.1248i	−0.871358	−	0.871358i	0.121263	−	0.992620i	$-0.461306\pi$
$163$	−11.1248	−	11.1248i	−0.871358	−	0.871358i	−0.992620	+	0.121263i	$0.961306\pi$
$164$	0.862067	+	11.5590i	0.0673161	+	0.902607i
$165$	0.288482			0.0224583
$166$	5.76177	+	12.5659i	0.447200	+	0.975304i
$167$	−3.96436	−	3.96436i	−0.306772	−	0.306772i	0.536884	−	0.843656i	$-0.319601\pi$
$167$	−3.96436	−	3.96436i	−0.306772	−	0.306772i	−0.843656	+	0.536884i	$0.819601\pi$
$168$	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	$0.973824\pi$
$174$	4.75640	+	1.76581i	0.360582	+	0.133866i
$175$	9.24531	−	9.24531i	0.698880	−	0.698880i
$176$	−3.42875	+	4.63884i	−0.258452	+	0.349666i
$177$	−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	$-0.623622\pi$
$179$	−10.1328			−0.757359			−0.378679	+	0.925528i	$0.623622\pi$
$180$	0.0797203	+	1.06893i	0.00594200	+	0.0796732i
$181$		−	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
$184$	−21.6530	+	11.9520i	−1.59628	+	0.881115i
$185$	0.121816			0.00895609
$186$	5.99760	−	2.75004i	0.439765	−	0.201643i
$187$	−1.42685	+	1.42685i	−0.104342	+	0.104342i
$188$	0.589675	+	7.90664i	0.0430065	+	0.576651i
$189$	−8.38787	+	8.38787i	−0.610128	+	0.610128i
$190$	0.646573	−	1.74162i	0.0469073	−	0.126350i
$191$		−	3.87048i		−	0.280058i	−0.990147	−	0.140029i	$-0.955280\pi$
$191$		−	3.87048i		−	0.280058i	0.990147	−	0.140029i	$-0.0447196\pi$
$192$	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	$-0.527495\pi$
$199$	−2.43397			−0.172539			−0.0862696	+	0.996272i	$0.527495\pi$
$200$	6.75848	+	12.2441i	0.477896	+	0.865786i
$201$	−1.51601	−	1.51601i	−0.106931	−	0.106931i
$202$	12.1636	+	4.51573i	0.855829	+	0.317726i
$203$	7.89132	+	7.89132i	0.553862	+	0.553862i
$204$	1.80253	+	1.55233i	0.126203	+	0.108685i
$205$			1.36387i			0.0952569i
$206$	−5.36892	+	14.4618i	−0.374071	+	1.00760i
$207$	19.9145			1.38416
$208$		0			0
$209$	−8.05002			−0.556831
$210$	0.260355	−	0.701294i	0.0179662	−	0.0483939i
$211$			4.19052i			0.288488i	0.989542	+	0.144244i	$0.0460750\pi$
$211$			4.19052i			0.288488i	−0.989542	+	0.144244i	$0.953925\pi$
$212$	9.00893	+	7.75843i	0.618736	+	0.532851i
$213$	−6.53401	−	6.53401i	−0.447703	−	0.447703i
$214$	−13.0678	−	4.85142i	−0.893298	−	0.331636i
$215$	−1.52879	−	1.52879i	−0.104263	−	0.104263i
$216$	−6.13167	−	11.1085i	−0.417207	−	0.755838i
$217$	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	−0.103117	−	0.994669i	$-0.532882\pi$
$223$	13.3137	−	13.3137i	0.891553	−	0.891553i	0.994669	+	0.103117i	$0.0328815\pi$
$224$	8.18247	+	12.5218i	0.546714	+	0.836645i
$225$		−	11.2610i		−	0.750734i
$226$	2.24113	−	6.03672i	0.149078	−	0.401557i
$227$	5.26077	−	5.26077i	0.349170	−	0.349170i	−0.510631	−	0.859800i	$-0.670588\pi$
$227$	5.26077	−	5.26077i	0.349170	−	0.349170i	0.859800	+	0.510631i	$0.170588\pi$
$228$	0.705803	+	9.46375i	0.0467430	+	0.626752i
$229$	−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
$232$	−10.4509	+	5.76868i	−0.686135	+	0.378733i
$233$			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
$236$	−1.26731	−	16.9927i	−0.0824946	−	1.10613i
$237$	−7.23943			−0.470251
$238$	2.18091	+	4.75637i	0.141367	+	0.308310i
$239$	−5.96641	+	5.96641i	−0.385935	+	0.385935i	−0.873235	−	0.487300i	$-0.837982\pi$
$239$	−5.96641	+	5.96641i	−0.385935	+	0.385935i	0.487300	+	0.873235i	$0.337982\pi$
$240$	0.643470	+	0.475614i	0.0415358	+	0.0307008i
$241$	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	$0.0840018\pi$
$242$	−11.8265	−	4.39058i	−0.760237	−	0.282237i
$243$			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	$-0.834071\pi$
$251$	−27.4775			−1.73436			−0.867182	+	0.497992i	$0.834071\pi$
$252$	−0.895766	−	12.0109i	−0.0564279	−	0.756613i
$253$	8.91683	+	8.91683i	0.560597	+	0.560597i
$254$	−2.63039	+	7.08524i	−0.165045	+	0.444568i
$255$	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	$-0.334696\pi$
$258$	10.3539	+	3.84386i	0.644604	+	0.239309i
$259$	−1.36877			−0.0850511
$260$		0			0
$261$	9.61181			0.594956
$262$	−14.8825	−	5.52513i	−0.919446	−	0.341344i
$263$			23.8060i			1.46794i	0.679180	+	0.733972i	$0.262336\pi$
$263$			23.8060i			1.46794i	−0.679180	+	0.733972i	$0.737664\pi$
$264$	0.961648	−	3.33123i	0.0591854	−	0.205023i
$265$	0.989207	+	0.989207i	0.0607665	+	0.0607665i
$266$	−7.26513	+	19.5694i	−0.445453	+	1.19988i
$267$	−3.99309	−	3.99309i	−0.244373	−	0.244373i
$268$	5.03040	−	0.375166i	0.307281	−	0.0229169i
$269$	−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	0.344993	−	0.938605i	$-0.387881\pi$
$271$	−9.77210	−	9.77210i	−0.593613	−	0.593613i	−0.938605	+	0.344993i	$0.887881\pi$
$272$	−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	$0.875048\pi$
$278$	−9.20193	−	3.41621i	−0.551895	−	0.204891i
$279$	8.83868	−	8.83868i	0.529158	−	0.529158i
$280$	0.850546	+	1.54090i	0.0508299	+	0.0920865i
$281$	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	$-0.710819\pi$
$283$	−20.6898			−1.22988			−0.614939	+	0.788575i	$0.710819\pi$
$284$	21.6810	−	1.61696i	1.28653	−	0.0959490i
$285$			1.11665i			0.0661445i
$286$		0			0
$287$		−	15.3249i		−	0.904603i
$288$	12.6091	+	2.64268i	0.742999	+	0.155721i
$289$	15.0421			0.884830
$290$	−1.27678	+	0.585436i	−0.0749753	+	0.0343780i
$291$	9.30045	−	9.30045i	0.545202	−	0.545202i
$292$	−14.2555	+	1.06317i	−0.834238	+	0.0622172i
$293$	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	$0.0147621\pi$
$294$	0.00330563	−	0.00890407i	0.000192788	−	0.000519296i
$295$		−	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
$304$	−17.9559	−	13.2719i	−1.02984	−	0.761195i
$305$	1.20178	+	1.20178i	0.0688135	+	0.0688135i
$306$	4.22488	+	1.56848i	0.241521	+	0.0896643i
$307$	−16.3164	−	16.3164i	−0.931228	−	0.931228i	0.0665547	−	0.997783i	$-0.478799\pi$
$307$	−16.3164	−	16.3164i	−0.931228	−	0.931228i	−0.997783	+	0.0665547i	$0.978799\pi$
$308$	4.97684	−	5.77900i	0.283582	−	0.329289i
$309$		−	9.27226i		−	0.527480i
$310$	−0.635739	+	1.71243i	−0.0361076	+	0.0972596i
$311$	8.54527			0.484558			0.242279	−	0.970207i	$-0.422105\pi$
$311$	8.54527			0.484558			0.242279	+	0.970207i	$0.422105\pi$
$312$		0			0
$313$	5.88378			0.332571			0.166285	−	0.986078i	$-0.446823\pi$
$313$	5.88378			0.332571			0.166285	+	0.986078i	$0.446823\pi$
$314$	2.90599	−	7.82761i	0.163995	−	0.441738i
$315$		−	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	$0.977532\pi$
$318$	−6.69949	−	2.48718i	−0.375689	−	0.139474i
$319$	4.30374	+	4.30374i	0.240963	+	0.240963i
$320$	−1.83589	+	0.416956i	−0.102629	+	0.0233086i
$321$	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
$330$	0.141991	−	0.382469i	0.00781636	−	0.0210542i
$331$	10.1585	−	10.1585i	0.558364	−	0.558364i	−0.370477	−	0.928842i	$-0.620806\pi$
$331$	10.1585	−	10.1585i	0.558364	−	0.558364i	0.928842	+	0.370477i	$0.120806\pi$
$332$	19.4958	−	1.45399i	1.06997	−	0.0797981i
$333$	−0.833596	+	0.833596i	−0.0456808	+	0.0456808i
$334$	−7.20721	+	3.30468i	−0.394361	+	0.180824i
$335$	0.593547			0.0324290
$336$	−7.23026	−	5.34417i	−0.394443	−	0.291549i
$337$		−	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
$340$	−0.656745	+	0.0489799i	−0.0356170	+	0.00265631i
$341$	7.91513			0.428629
$342$	7.49345	+	16.3425i	0.405200	+	0.883704i
$343$	13.1032	−	13.1032i	0.707505	−	0.707505i
$344$	−22.7498	+	12.5574i	−1.22659	+	0.677051i
$345$	1.23689	−	1.23689i	0.0665917	−	0.0665917i
$346$	2.86476	+	1.06354i	0.154010	+	0.0571762i
$347$			0.470309i			0.0252475i	0.999920	+	0.0126238i	$0.00401838\pi$
$347$			0.470309i			0.0252475i	−0.999920	+	0.0126238i	$0.995982\pi$
$348$	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
$356$	13.2498	−	0.988165i	0.702238	−	0.0523726i
$357$	−2.22394	−	2.22394i	−0.117703	−	0.117703i
$358$	−4.98736	+	13.4340i	−0.263590	+	0.710009i
$359$	11.7167	+	11.7167i	0.618383	+	0.618383i	0.945117	−	0.326733i	$-0.105948\pi$
$359$	11.7167	+	11.7167i	0.618383	+	0.618383i	−0.326733	+	0.945117i	$0.605948\pi$
$360$	1.45642	+	0.420434i	0.0767601	+	0.0221588i
$361$		−	12.1597i		−	0.639986i
$362$	−18.3660	−	6.81837i	−0.965297	−	0.358366i
$363$	7.58264			0.397985
$364$		0			0
$365$	−1.68203			−0.0880416
$366$	−8.13913	−	3.02165i	−0.425439	−	0.157944i
$367$			10.1556i			0.530118i	0.964232	+	0.265059i	$0.0853914\pi$
$367$			10.1556i			0.530118i	−0.964232	+	0.265059i	$0.914609\pi$
$368$	5.18832	+	34.5903i	0.270460	+	1.80314i
$369$	−9.33307	−	9.33307i	−0.485860	−	0.485860i
$370$	0.0599580	−	0.161503i	0.00311707	−	0.00839616i
$371$	−11.1151	−	11.1151i	−0.577067	−	0.577067i
$372$	−0.693977	−	9.30517i	−0.0359810	−	0.482451i
$373$	−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	$-0.422504\pi$
$379$	23.5868	−	23.5868i	1.21157	−	1.21157i	0.970509	−	0.241064i	$-0.0774965\pi$
$380$	−1.99078	−	1.71445i	−0.102125	−	0.0879494i
$381$		−	4.54275i		−	0.232732i
$382$	−5.13147	−	1.90505i	−0.262549	−	0.0974711i
$383$	−14.8033	+	14.8033i	−0.756412	+	0.756412i	−0.975667	−	0.219256i	$-0.929637\pi$
$383$	−14.8033	+	14.8033i	−0.756412	+	0.756412i	0.219256	+	0.975667i	$0.429637\pi$
$384$	7.63712	−	5.84498i	0.389730	−	0.298275i
$385$	0.634552	−	0.634552i	0.0323398	−	0.0323398i
$386$	−4.84776	−	10.5725i	−0.246745	−	0.538128i
$387$	20.9233			1.06359
$388$	2.30157	+	30.8605i	0.116844	+	1.56671i
$389$			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
$392$	0.0107991	+	0.0195643i	0.000545436	+	0.000988145i
$393$	9.54203			0.481332
$394$	15.9156	−	7.29770i	0.801817	−	0.367653i
$395$	1.41718	−	1.41718i	0.0713063	−	0.0713063i
$396$	−0.488529	−	6.55043i	−0.0245495	−	0.329172i
$397$	−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	$0.270645\pi$
$398$	−1.19800	+	3.22694i	−0.0600503	+	0.161752i
$399$		−	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
$408$	2.94528	−	1.62574i	0.145813	−	0.0804859i
$409$	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	$0.712178\pi$
$410$	1.80822	+	0.671299i	0.0893014	+	0.0331531i
$411$	−2.88999	−	2.88999i	−0.142553	−	0.142553i
$412$	16.5308	+	14.2362i	0.814414	+	0.701368i
$413$			22.5289i			1.10857i
$414$	9.80195	−	26.4026i	0.481740	−	1.29762i
$415$	2.30035			0.112920
$416$		0			0
$417$	5.89987			0.288918
$418$	−3.96223	+	10.6727i	−0.193799	+	0.522018i
$419$			5.60503i			0.273824i	0.990583	+	0.136912i	$0.0437177\pi$
$419$			5.60503i			0.273824i	−0.990583	+	0.136912i	$0.956282\pi$
$420$	−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	$0.710921\pi$
$422$	5.55579	+	2.06258i	0.270451	+	0.100405i
$423$	−6.38405	−	6.38405i	−0.310403	−	0.310403i
$424$	14.7203	−	8.12531i	0.714881	−	0.394600i
$425$	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	−0.763536	−	0.645766i	$-0.776538\pi$
$431$	−2.44497	+	2.44497i	−0.117770	+	0.117770i	0.645766	+	0.763536i	$0.276538\pi$
$432$	−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	$-0.0419789\pi$
$434$	7.14339	−	19.2415i	0.342894	−	0.923622i
$435$	0.596987	−	0.596987i	0.0286233	−	0.0286233i
$436$	−0.00511532	−	0.0685887i	−0.000244980	−	0.00328480i
$437$	−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	$-0.759547\pi$
$439$	−30.5063			−1.45599			−0.727994	+	0.685584i	$0.759547\pi$
$440$	0.463868	+	0.840371i	0.0221140	+	0.0400631i
$441$		−	0.0179935i		−	0.000856833i
$442$		0			0
$443$		−	12.8994i		−	0.612869i	−0.951892	−	0.306434i	$-0.900864\pi$
$443$		−	12.8994i		−	0.612869i	0.951892	−	0.306434i	$-0.0991360\pi$
$444$	0.0654505	+	0.877592i	0.00310614	+	0.0416487i
$445$	1.56337			0.0741108
$446$	−11.0983	−	24.2043i	−0.525518	−	1.14611i
$447$	−9.11058	+	9.11058i	−0.430916	+	0.430916i
$448$	20.6287	−	4.68507i	0.974616	−	0.221349i
$449$	−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	$0.324821\pi$
$450$	−14.9298	−	5.54268i	−0.703798	−	0.261284i
$451$		−	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
$460$	0.306091	+	4.10421i	0.0142715	+	0.191360i
$461$	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	$0.516656\pi$
$462$	−1.59546	+	4.29756i	−0.0742277	+	0.199941i
$463$	−5.89061	−	5.89061i	−0.273760	−	0.273760i	0.556852	−	0.830612i	$-0.312009\pi$
$463$	−5.89061	−	5.89061i	−0.273760	−	0.273760i	−0.830612	+	0.556852i	$0.812009\pi$
$464$	2.50416	+	16.6951i	0.116253	+	0.775051i
$465$		−	1.09794i		−	0.0509156i
$466$	17.6603	+	6.55637i	0.818097	+	0.303718i
$467$	3.30334			0.152860			0.0764301	−	0.997075i	$-0.475648\pi$
$467$	3.30334			0.152860			0.0764301	+	0.997075i	$0.475648\pi$
$468$		0			0
$469$	−6.66931			−0.307960
$470$	1.23686	+	0.459185i	0.0570523	+	0.0211806i
$471$			5.01872i			0.231250i
$472$	−23.1526	−	6.68361i	−1.06568	−	0.307638i
$473$	9.36849	+	9.36849i	0.430764	+	0.430764i
$474$	−3.56325	+	9.59801i	−0.163666	+	0.440851i
$475$	19.5171	+	19.5171i	0.895505	+	0.895505i
$476$	7.37943	−	0.550355i	0.338235	−	0.0252255i
$477$	−13.5384			−0.619882
$478$	4.97358	+	10.8469i	0.227486	+	0.496127i
$479$	19.6666	+	19.6666i	0.898589	+	0.898589i	0.995311	−	0.0967224i	$-0.0308359\pi$
$479$	19.6666	+	19.6666i	0.898589	+	0.898589i	−0.0967224	+	0.995311i	$0.530836\pi$
$480$	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
$486$	21.2451	+	7.88721i	0.963695	+	0.357771i
$487$	7.29545	−	7.29545i	0.330588	−	0.330588i	−0.522222	−	0.852810i	$-0.674897\pi$
$487$	7.29545	−	7.29545i	0.330588	−	0.330588i	0.852810	+	0.522222i	$0.174897\pi$
$488$	17.8835	−	9.87134i	0.809549	−	0.446855i
$489$	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	$-0.400527\pi$
$491$	13.6249			0.614881			0.307441	+	0.951567i	$0.400527\pi$
$492$	−9.82565	+	0.732794i	−0.442975	+	0.0330369i
$493$			5.90546i			0.265969i
$494$		0			0
$495$		−	0.772899i		−	0.0347392i
$496$	17.6550	+	13.0495i	0.792732	+	0.585940i
$497$	−28.7447			−1.28938
$498$	−10.6816	+	4.89775i	−0.478652	+	0.219474i
$499$	11.2288	−	11.2288i	0.502670	−	0.502670i	−0.409597	−	0.912267i	$-0.634331\pi$
$499$	11.2288	−	11.2288i	0.502670	−	0.502670i	0.912267	+	0.409597i	$0.134331\pi$
$500$	4.66758	−	0.348107i	0.208741	−	0.0155678i
$501$	3.36988	−	3.36988i	0.150555	−	0.150555i
$502$	−13.5244	+	36.4296i	−0.603625	+	1.62593i
$503$			22.8605i			1.01930i	0.860382	+	0.509650i	$0.170225\pi$
$503$			22.8605i			1.01930i	−0.860382	+	0.509650i	$0.829775\pi$
$504$	−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
$512$	−1.30512	+	22.5897i	−0.0576787	+	0.998335i
$513$	−17.7070	−	17.7070i	−0.781783	−	0.781783i
$514$	−36.9039	−	13.7005i	−1.62776	−	0.604305i
$515$	1.81513	+	1.81513i	0.0799842	+	0.0799842i
$516$	10.1924	−	11.8352i	0.448694	−	0.521015i
$517$		−	5.71698i		−	0.251433i
$518$	−0.673709	+	1.81471i	−0.0296011	+	0.0797338i
$519$	−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	$0.386609\pi$
$522$	4.73094	−	12.7433i	0.207068	−	0.557760i
$523$		−	2.15778i		−	0.0943532i	−0.998887	−	0.0471766i	$-0.984978\pi$
$523$		−	2.15778i		−	0.0943532i	0.998887	−	0.0471766i	$-0.0150224\pi$
$524$	−14.6504	+	17.0118i	−0.640006	+	0.743162i
$525$	7.85891	+	7.85891i	0.342991	+	0.342991i
$526$	31.5620	+	11.7174i	1.37617	+	0.510901i
$527$	5.43046	+	5.43046i	0.236554	+	0.236554i
$528$	−3.94321	−	2.91459i	−0.171606	−	0.126841i
$529$	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
$538$	−10.1944	+	27.4597i	−0.439512	+	1.18387i
$539$	0.00805668	−	0.00805668i	0.000347026	−	0.000347026i
$540$	−2.10556	+	0.157032i	−0.0906087	+	0.00675757i
$541$	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
$544$	−1.62365	+	7.74700i	−0.0696135	+	0.332150i
$545$		−	0.00809292i		−	0.000346663i
$546$		0			0
$547$			8.11076i			0.346791i	0.984852	+	0.173396i	$0.0554739\pi$
$547$			8.11076i			0.346791i	−0.984852	+	0.173396i	$0.944526\pi$
$548$	9.58951	−	0.715183i	0.409644	−	0.0305511i
$549$	−16.4477			−0.701970
$550$	−4.20314	−	9.16667i	−0.179222	−	0.390868i
$551$	−16.6588	+	16.6588i	−0.709687	+	0.709687i
$552$	−10.1597	−	18.4060i	−0.432427	−	0.783411i
$553$	−15.9240	+	15.9240i	−0.677157	+	0.677157i
$554$	16.8822	+	6.26750i	0.717256	+	0.266281i
$555$			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	$-0.458006\pi$
$563$	6.24260			0.263094			0.131547	+	0.991310i	$0.458006\pi$
$564$	−6.72099	+	0.501249i	−0.283005	+	0.0211064i
$565$	−0.757683	−	0.757683i	−0.0318759	−	0.0318759i
$566$	−10.1835	+	27.4304i	−0.428045	+	1.15299i
$567$	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	$0.764053\pi$
$570$	1.48045	+	0.549615i	0.0620091	+	0.0230208i
$571$	−41.4189			−1.73333			−0.866663	−	0.498894i	$-0.833740\pi$
$571$	−41.4189			−1.73333			−0.866663	+	0.498894i	$0.833740\pi$
$572$		0			0
$573$	3.29007			0.137445
$574$	−20.3178	−	7.54295i	−0.848047	−	0.314837i
$575$		−	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	$0.631657\pi$
$578$	7.40375	−	19.9428i	0.307955	−	0.829511i
$579$	4.94341	+	4.94341i	0.205441	+	0.205441i
$580$	0.147736	+	1.98091i	0.00613439	+	0.0822528i
$581$	−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	−0.958713	−	0.284374i	$-0.908214\pi$
$587$	−16.3380	+	16.3380i	−0.674340	+	0.674340i	0.284374	+	0.958713i	$0.408214\pi$
$588$	−0.0101780	−	0.00876519i	−0.000419732	−	0.000361470i
$589$			30.6376i			1.26240i
$590$	−2.65822	−	0.986862i	−0.109437	−	0.0406285i
$591$	−7.44168	+	7.44168i	−0.306110	+	0.306110i
$592$	−1.66508	−	1.23073i	−0.0684344	−	0.0505826i
$593$	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
$596$	−2.25458	−	30.2305i	−0.0923513	−	1.23829i
$597$		−	2.06898i		−	0.0846775i
$598$		0			0
$599$			10.6090i			0.433471i	0.976230	+	0.216735i	$0.0695409\pi$
$599$			10.6090i			0.433471i	−0.976230	+	0.216735i	$0.930459\pi$
$600$	−10.4080	+	5.74499i	−0.424904	+	0.234538i
$601$	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
$604$	0.101146	+	1.35621i	0.00411556	+	0.0551834i
$605$	−1.48437	+	1.48437i	−0.0603483	+	0.0603483i
$606$	−3.83856	+	10.3396i	−0.155931	+	0.420017i
$607$		−	10.2708i		−	0.416878i	−0.978035	−	0.208439i	$-0.933162\pi$
$607$		−	10.2708i		−	0.416878i	0.978035	−	0.208439i	$-0.0668383\pi$
$608$	−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
$616$	−5.21218	−	9.44271i	−0.210005	−	0.380458i
$617$	−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	$-0.569588\pi$
$618$	−12.2931	−	4.56381i	−0.494502	−	0.183584i
$619$	12.0880	+	12.0880i	0.485858	+	0.485858i	0.906996	−	0.421138i	$-0.138369\pi$
$619$	12.0880	+	12.0880i	0.485858	+	0.485858i	−0.421138	+	0.906996i	$0.638369\pi$
$620$	1.95743	+	1.68572i	0.0786122	+	0.0677002i
$621$			39.2273i			1.57414i
$622$	4.20599	−	11.3293i	0.168645	−	0.454263i
$623$	−17.5666			−0.703790
$624$		0			0
$625$	−24.1724			−0.966894
$626$	2.89600	−	7.80069i	0.115747	−	0.311778i
$627$		−	6.84286i		−	0.273278i
$628$	−8.94749	−	7.70552i	−0.357044	−	0.307484i
$629$	−0.512159	−	0.512159i	−0.0204211	−	0.0204211i
$630$	−1.87890	−	0.697540i	−0.0748572	−	0.0277907i
$631$	−8.52621	−	8.52621i	−0.339423	−	0.339423i	0.516727	−	0.856150i	$-0.327150\pi$
$631$	−8.52621	−	8.52621i	−0.339423	−	0.339423i	−0.856150	+	0.516727i	$0.827150\pi$
$632$	−11.6407	−	21.0890i	−0.463042	−	0.838875i
$633$	−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	$-0.0131880\pi$
$642$	4.12391	−	11.1082i	0.162758	−	0.438406i
$643$	−29.9695	+	29.9695i	−1.18188	+	1.18188i	−0.202627	+	0.979256i	$0.564948\pi$
$643$	−29.9695	+	29.9695i	−1.18188	+	1.18188i	−0.979256	+	0.202627i	$0.935052\pi$
$644$	−3.43934	−	46.1163i	−0.135529	−	1.81724i
$645$	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	$-0.178512\pi$
$647$	43.0799			1.69365			0.846824	+	0.531874i	$0.178512\pi$
$648$	−7.47566	+	4.12641i	−0.293672	+	0.162101i
$649$			12.2867i			0.482296i
$650$		0			0
$651$			12.3368i			0.483518i
$652$	2.34019	+	31.3784i	0.0916490	+	1.22887i
$653$	−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
$656$	13.7794	−	18.6425i	0.537996	−	0.727867i
$657$	11.5103	−	11.5103i	0.449058	−	0.449058i
$658$	−13.8978	−	5.15956i	−0.541795	−	0.201141i
$659$		−	15.2432i		−	0.593792i	−0.954910	−	0.296896i	$-0.904048\pi$
$659$		−	15.2432i		−	0.593792i	0.954910	−	0.296896i	$-0.0959515\pi$
$660$	−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
$668$	0.833940	+	11.1819i	0.0322661	+	0.432639i
$669$	11.3172	+	11.3172i	0.437549	+	0.437549i
$670$	0.292145	−	0.786923i	0.0112865	−	0.0304015i
$671$	−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	$-0.194707\pi$
$674$	−19.0155	−	7.05950i	−0.732451	−	0.271922i
$675$	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	$0.688908\pi$
$678$	5.13147	+	1.90505i	0.197073	+	0.0731632i
$679$		−	40.9149i		−	1.57017i
$680$	−0.258313	+	0.894819i	−0.00990586	+	0.0343147i
$681$	4.47188	+	4.47188i	0.171363	+	0.171363i
$682$	3.89584	−	10.4939i	0.149179	−	0.401831i
$683$	−3.56874	−	3.56874i	−0.136554	−	0.136554i	0.635526	−	0.772080i	$-0.280783\pi$
$683$	−3.56874	−	3.56874i	−0.136554	−	0.136554i	−0.772080	+	0.635526i	$0.780783\pi$
$684$	25.3552	−	1.89098i	0.969480	−	0.0723035i
$685$	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	−0.540623	−	0.841265i	$-0.681811\pi$
$691$	7.90295	−	7.90295i	0.300642	−	0.300642i	0.841265	+	0.540623i	$0.181811\pi$
$692$	2.82007	−	3.27461i	0.107203	−	0.124482i
$693$			8.68457i			0.329900i
$694$	0.623535	+	0.231487i	0.0236691	+	0.00878711i
$695$	−1.15495	+	1.15495i	−0.0438099	+	0.0438099i
$696$	−4.90363	−	8.88371i	−0.185872	−	0.336736i
$697$	5.73421	−	5.73421i	0.217199	−	0.217199i
$698$	−16.6711	−	36.3583i	−0.631012	−	1.37618i
$699$	−11.3230			−0.428275
$700$	−26.0773	+	1.94483i	−0.985628	+	0.0735078i
$701$		−	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
$704$	11.2504	−	2.55513i	0.424016	−	0.0963000i
$705$	−0.793023			−0.0298670
$706$	−46.2170	+	21.1916i	−1.73940	+	0.797557i
$707$	−17.1544	+	17.1544i	−0.645156	+	0.645156i
$708$	14.4445	−	1.07726i	0.542857	−	0.0404861i
$709$	−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	$0.956537\pi$
$710$	1.25914	−	3.39163i	0.0472547	−	0.127286i
$711$			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	$-0.400878\pi$
$719$	16.4313			0.612785			0.306392	+	0.951905i	$0.400878\pi$
$720$	1.27426	−	1.72398i	0.0474889	−	0.0642489i
$721$	−20.3955	−	20.3955i	−0.759567	−	0.759567i
$722$	−16.1213	−	5.98503i	−0.599974	−	0.222740i
$723$	9.29717	+	9.29717i	0.345765	+	0.345765i
$724$	−18.0795	+	20.9936i	−0.671921	+	0.780221i
$725$		−	20.8686i		−	0.775041i
$726$	3.73218	−	10.0530i	0.138514	−	0.373103i
$727$	−32.1429			−1.19211			−0.596057	−	0.802942i	$-0.703267\pi$
$727$	−32.1429			−1.19211			−0.596057	+	0.802942i	$0.703267\pi$
$728$		0			0
$729$	−4.56452			−0.169056
$730$	−0.827898	+	2.23003i	−0.0306419	+	0.0825372i
$731$			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	$0.917248\pi$
$734$	13.4643	+	4.99860i	0.496975	+	0.184502i
$735$	−0.00111757	−	0.00111757i	−4.12222e−5	−	4.12222e-5i
$736$	48.4134	+	10.1467i	1.78454	+	0.374013i
$737$	−3.63728			−0.133981
$738$	−16.9675	+	7.78001i	−0.624582	+	0.286386i
$739$	16.4275	+	16.4275i	0.604297	+	0.604297i	0.941450	−	0.337153i	$-0.109464\pi$
$739$	16.4275	+	16.4275i	0.604297	+	0.604297i	−0.337153	+	0.941450i	$0.609464\pi$
$740$	−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	$0.500340\pi$
$743$	−27.2871	+	27.2871i	−1.00107	+	1.00107i	−0.999999	+	0.00106799i	$0.999660\pi$
$744$	−12.6783	−	3.65994i	−0.464811	−	0.134180i
$745$		−	3.56696i		−	0.130683i
$746$	−7.39079	+	19.9079i	−0.270596	+	0.728880i
$747$	−15.7415	+	15.7415i	−0.575950	+	0.575950i
$748$	4.02456	−	0.300151i	0.147153	−	0.0109746i
$749$	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	$-0.492485\pi$
$751$	1.29395			0.0472168			0.0236084	+	0.999721i	$0.492485\pi$
$752$	9.42546	−	12.7519i	0.343711	−	0.465015i
$753$		−	23.3570i		−	0.851178i
$754$		0			0
$755$			0.160022i			0.00582380i
$756$	23.6588	−	1.76446i	0.860462	−	0.0641730i
$757$	−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
$760$	−3.25288	+	1.79552i	−0.117994	+	0.0651305i
$761$	−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	$0.300397\pi$
$762$	−6.02276	−	2.23594i	−0.218182	−	0.0809997i
$763$			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
$772$	−16.4031	+	1.22334i	−0.590361	+	0.0440289i
$773$	−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	$0.862218\pi$
$774$	10.2984	−	27.7400i	0.370170	−	0.997093i
$775$	−19.1900	−	19.1900i	−0.689327	−	0.689327i
$776$	42.0477	+	12.1382i	1.50942	+	0.435735i
$777$		−	1.16351i		−	0.0417408i
$778$	12.7331	+	4.72715i	0.456504	+	0.169477i
$779$	32.3513			1.15911
$780$		0			0
$781$	−15.6767			−0.560955
$782$	16.2217	+	6.02228i	0.580086	+	0.215356i
$783$			18.9332i			0.676617i
$784$	0.0312536	−	0.00468784i	0.00111620	−	0.000167423i
$785$	−0.982461	−	0.982461i	−0.0350655	−	0.0350655i
$786$	4.69660	−	12.6508i	0.167522	−	0.451239i
$787$	21.1389	+	21.1389i	0.753520	+	0.753520i	0.975134	−	0.221614i	$-0.0711325\pi$
$787$	21.1389	+	21.1389i	0.753520	+	0.753520i	−0.221614	+	0.975134i	$0.571133\pi$
$788$	−1.84158	−	24.6928i	−0.0656037	−	0.879645i
$789$	−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	$0.770698\pi$
$798$	−16.6348	−	6.17567i	−0.588867	−	0.218616i
$799$	3.92234	−	3.92234i	0.138762	−	0.138762i
$800$	5.73763	−	27.3762i	0.202856	−	0.967895i
$801$	−10.6983	+	10.6983i	−0.378004	+	0.378004i
$802$	15.9451	+	34.7748i	0.563041	+	1.22794i
$803$	10.3076			0.363746
$804$	0.318907	+	4.27606i	0.0112470	+	0.150805i
$805$		−	5.44136i		−	0.191783i
$806$		0			0
$807$		−	17.6060i		−	0.619759i
$808$	−12.5401	−	22.7184i	−0.441160	−	0.799232i
$809$	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	−0.778502	−	0.627643i	$-0.784020\pi$
$811$	−4.29617	+	4.29617i	−0.150859	+	0.150859i	0.627643	+	0.778502i	$0.284020\pi$
$812$	−1.66001	−	22.2582i	−0.0582549	−	0.781110i
$813$	8.30670	−	8.30670i	0.291329	−	0.291329i
$814$	−0.367425	+	0.989700i	−0.0128782	+	0.0346890i
$815$			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	$-0.576225\pi$
$823$	−13.6087			−0.474371			−0.237185	+	0.971464i	$0.576225\pi$
$824$	27.0108	−	14.9094i	0.940966	−	0.519394i
$825$	4.28607	+	4.28607i	0.149222	+	0.149222i
$826$	29.8687	+	11.0887i	1.03927	+	0.385826i
$827$	−17.0815	−	17.0815i	−0.593982	−	0.593982i	0.344723	−	0.938705i	$-0.387973\pi$
$827$	−17.0815	−	17.0815i	−0.593982	−	0.593982i	−0.938705	+	0.344723i	$0.887973\pi$
$828$	−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	$0.841626\pi$
$830$	1.13223	−	3.04980i	0.0393004	−	0.105860i
$831$	−10.8241			−0.375485
$832$		0			0
$833$	0.0110551			0.000383038
$834$	2.90392	−	7.82203i	0.100555	−	0.270855i
$835$			1.31937i			0.0456587i
$836$	12.1996	+	10.5062i	0.421932	+	0.363365i
$837$	17.4103	+	17.4103i	0.601788	+	0.601788i
$838$	7.43113	+	2.75880i	0.256704	+	0.0953012i
$839$	28.2374	+	28.2374i	0.974865	+	0.974865i	0.999692	−	0.0248272i	$-0.00790354\pi$
$839$	28.2374	+	28.2374i	0.974865	+	0.974865i	−0.0248272	+	0.999692i	$0.507904\pi$
$840$	−1.30983	+	0.723001i	−0.0451935	+	0.0249459i
$841$	−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
$850$	3.40540	−	9.17283i	0.116804	−	0.314625i
$851$	−3.20064	+	3.20064i	−0.109717	+	0.109717i
$852$	1.37449	+	18.4298i	0.0470891	+	0.631394i
$853$	−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
$856$	13.4723	+	24.4073i	0.460474	+	0.834223i
$857$			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	$0.345244\pi$
$859$			51.8251i			1.76825i	−0.467252	+	0.884124i	$0.654756\pi$
$860$	0.321595	+	4.31210i	0.0109663	+	0.147041i
$861$	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	$-0.429347\pi$
$863$	35.1233	−	35.1233i	1.19561	−	1.19561i	0.975467	−	0.220144i	$-0.0706527\pi$
$864$	−5.20550	+	24.8372i	−0.177095	+	0.844980i
$865$	0.359562	−	0.359562i	0.0122255	−	0.0122255i
$866$	−7.25558	−	2.69363i	−0.246555	−	0.0915332i
$867$			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
$876$	−0.903738	−	12.1178i	−0.0305345	−	0.409421i
$877$	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	$0.534256\pi$
$878$	−15.0152	+	40.4452i	−0.506740	+	1.36496i
$879$	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	$0.989286\pi$
$882$	−0.0238557	−	0.00885641i	−0.000803264	−	0.000298211i
$883$	−16.1625			−0.543913			−0.271956	−	0.962310i	$-0.587671\pi$
$883$	−16.1625			−0.543913			−0.271956	+	0.962310i	$0.587671\pi$
$884$		0			0
$885$	1.70433			0.0572906
$886$	−17.1020	−	6.34909i	−0.574552	−	0.213302i
$887$		−	17.6060i		−	0.591150i	−0.955319	−	0.295575i	$-0.904489\pi$
$887$		−	17.6060i		−	0.591150i	0.955319	−	0.295575i	$-0.0955113\pi$
$888$	1.19572	+	0.345177i	0.0401259	+	0.0115834i
$889$	−9.99232	−	9.99232i	−0.335132	−	0.335132i
$890$	0.769492	−	2.07271i	0.0257934	−	0.0694774i
$891$	3.07852	+	3.07852i	0.103134	+	0.103134i
$892$	−37.5526	+	2.80066i	−1.25735	+	0.0937730i
$893$	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
$902$	−11.0808	−	4.11375i	−0.368951	−	0.136973i
$903$	−14.6021	+	14.6021i	−0.485926	+	0.485926i
$904$	−11.2750	+	6.22358i	−0.375001	+	0.206993i
$905$	−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	$-0.337623\pi$
$907$	29.4107			0.976567			0.488283	+	0.872685i	$0.337623\pi$
$908$	−14.8385	+	1.10665i	−0.492433	+	0.0367255i
$909$			20.8944i			0.693024i
$910$		0			0
$911$			20.5091i			0.679495i	0.940517	+	0.339748i	$0.110342\pi$
$911$			20.5091i			0.679495i	−0.940517	+	0.339748i	$0.889658\pi$
$912$	11.2817	−	15.2632i	0.373574	−	0.505416i
$913$	−14.0966			−0.466531
$914$	−13.3464	+	6.11967i	−0.441461	+	0.202421i
$915$	−1.02156	+	1.02156i	−0.0337718	+	0.0337718i
$916$	8.96158	−	0.668352i	0.296099	−	0.0220830i
$917$	20.9889	−	20.9889i	0.693113	−	0.693113i
$918$	−3.08958	+	8.32211i	−0.101971	+	0.274671i
$919$		−	48.9751i		−	1.61554i	−0.589498	−	0.807770i	$-0.700674\pi$
$919$		−	48.9751i		−	1.61554i	0.589498	−	0.807770i	$-0.299326\pi$
$920$	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
$928$	23.3669	+	4.89734i	0.767056	+	0.160763i
$929$	−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	$0.785849\pi$
$930$	−1.45564	−	0.540405i	−0.0477324	−	0.0177206i
$931$	0.0311855	+	0.0311855i	0.00102206	+	0.00102206i
$932$	17.3848	−	20.1869i	0.569459	−	0.661244i
$933$			7.26384i			0.237808i
$934$	1.62591	−	4.37956i	0.0532013	−	0.143303i
$935$	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	$0.441910\pi$
$938$	−3.28264	+	8.84215i	−0.107182	+	0.288706i
$939$			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	$0.907473\pi$
$942$	6.65380	+	2.47022i	0.216793	+	0.0804841i
$943$	−35.8348	−	35.8348i	−1.16694	−	1.16694i
$944$	−20.2568	+	27.4059i	−0.659304	+	0.891988i
$945$	2.79155			0.0908091
$946$	17.0319	−	7.80954i	0.553755	−	0.253910i
$947$	−20.7444	−	20.7444i	−0.674102	−	0.674102i	0.284557	−	0.958659i	$-0.408154\pi$
$947$	−20.7444	−	20.7444i	−0.674102	−	0.674102i	−0.958659	+	0.284557i	$0.908154\pi$
$948$	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	$-0.0681699\pi$
$954$	−6.66363	+	17.9492i	−0.215743	+	0.581128i
$955$	−0.644063	+	0.644063i	−0.0208414	+	0.0208414i
$956$	16.8288	−	1.25509i	0.544283	−	0.0405925i
$957$	−3.65836	+	3.65836i	−0.118258	+	0.118258i
$958$	35.7538	−	16.3940i	1.15515	−	0.529666i
$959$	−12.7138			−0.410549
$960$	−0.354431	−	1.56059i	−0.0114392	−	0.0503677i
$961$			0.875747i			0.0282499i
$962$		0			0
$963$		−	22.4477i		−	0.723365i
$964$	−30.8497	+	2.30076i	−0.993601	+	0.0741024i
$965$	−1.93544			−0.0623039
$966$	11.5854	+	25.2667i	0.372754	+	0.812943i
$967$	13.0476	−	13.0476i	0.419581	−	0.419581i	−0.465478	−	0.885059i	$-0.654118\pi$
$967$	13.0476	−	13.0476i	0.419581	−	0.419581i	0.885059	+	0.465478i	$0.154118\pi$
$968$	12.1926	+	22.0888i	0.391884	+	0.709961i
$969$	4.69479	−	4.69479i	0.150818	−	0.150818i
$970$	4.82762	+	1.79225i	0.155006	+	0.0575457i
$971$			44.2841i			1.42115i	0.703624	+	0.710573i	$0.251564\pi$
$971$			44.2841i			1.42115i	−0.703624	+	0.710573i	$0.748436\pi$
$972$	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
$980$	0.00370830		0.000276564i	0.000118457		8.83450e-6i
$981$	0.0553805	+	0.0553805i	0.00176816	+	0.00176816i
$982$	6.70617	−	18.0638i	0.214002	−	0.576439i
$983$	8.44991	+	8.44991i	0.269510	+	0.269510i	0.828903	−	0.559393i	$-0.188966\pi$
$983$	8.44991	+	8.44991i	0.269510	+	0.269510i	−0.559393	+	0.828903i	$0.688966\pi$
$984$	−3.86466	+	13.3875i	−0.123201	+	0.426778i
$985$		−	2.91356i		−	0.0928336i
$986$	7.82945	+	2.90667i	0.249340	+	0.0925674i
$987$	8.91069			0.283630
$988$		0			0
$989$	80.3360			2.55454
$990$	−1.02471	−	0.380422i	−0.0325673	−	0.0120906i
$991$			41.8295i			1.32876i	0.747396	+	0.664379i	$0.231304\pi$
$991$			41.8295i			1.32876i	−0.747396	+	0.664379i	$0.768696\pi$
$992$	25.9908	−	16.9839i	0.825209	−	0.539241i
$993$	8.63520	+	8.63520i	0.274030	+	0.274030i
$994$	−14.1482	+	38.1096i	−0.448752	+	1.20876i
$995$	0.405021	+	0.405021i	0.0128400	+	0.0128400i
$996$	1.23595	+	16.5723i	0.0391627	+	0.525112i
$997$	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.99.6		16
4.3	odd	2	inner	676.2.f.h.99.1		16
13.2	odd	12		676.2.l.m.19.3		16
13.3	even	3		52.2.l.b.7.4	yes	16
13.4	even	6		676.2.l.i.427.4		16
13.5	odd	4	inner	676.2.f.h.239.1		16
13.6	odd	12		52.2.l.b.15.3	yes	16
13.7	odd	12		676.2.l.k.587.2		16
13.8	odd	4		676.2.f.i.239.8		16
13.9	even	3		676.2.l.m.427.1		16
13.10	even	6		676.2.l.k.319.1		16
13.11	odd	12		676.2.l.i.19.2		16
13.12	even	2		676.2.f.i.99.3		16
39.29	odd	6		468.2.cb.f.163.1		16
39.32	even	12		468.2.cb.f.379.2		16
52.3	odd	6		52.2.l.b.7.3	✓	16
52.7	even	12		676.2.l.k.587.1		16
52.11	even	12		676.2.l.i.19.4		16
52.15	even	12		676.2.l.m.19.1		16
52.19	even	12		52.2.l.b.15.4	yes	16
52.23	odd	6		676.2.l.k.319.2		16
52.31	even	4	inner	676.2.f.h.239.6		16
52.35	odd	6		676.2.l.m.427.3		16
52.43	odd	6		676.2.l.i.427.2		16
52.47	even	4		676.2.f.i.239.3		16
52.51	odd	2		676.2.f.i.99.8		16
104.3	odd	6		832.2.bu.n.319.2		16
104.19	even	12		832.2.bu.n.639.3		16
104.29	even	6		832.2.bu.n.319.3		16
104.45	odd	12		832.2.bu.n.639.2		16
156.71	odd	12		468.2.cb.f.379.1		16
156.107	even	6		468.2.cb.f.163.2		16

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

\(f(q)\)	\(=\)	\(q+(0.492201 - 1.32580i) q^{2} +0.850043i q^{3} +(-1.51548 - 1.30512i) q^{4} +(-0.166404 - 0.166404i) q^{5} +(1.12698 + 0.418392i) q^{6} +(1.86977 + 1.86977i) q^{7} +(-2.47624 + 1.36683i) 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} +(1.12095 - 3.01941i) q^{18} +(-3.94713 + 3.94713i) q^{19} +(0.0350045 + 0.469358i) q^{20} +(-1.58939 + 1.58939i) q^{21} +(1.85387 - 0.850043i) q^{22} +8.74431 q^{23} +(-1.16187 - 2.10491i) q^{24} -4.94462i q^{25} +4.48604i q^{27} +(-0.393323 - 5.27387i) q^{28} +4.22047 q^{29} +(-0.117912 - 0.257157i) q^{30} +(3.88100 - 3.88100i) q^{31} +(5.53656 + 1.16038i) q^{32} +(-0.866814 + 0.866814i) q^{33} +(1.85511 + 0.688709i) 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} +(-0.214509 - 2.87624i) q^{44} +(-0.378973 - 0.378973i) q^{45} +(4.30396 - 11.5932i) q^{46} +(-2.80318 - 2.80318i) q^{47} +(-3.36256 + 0.504362i) q^{48} -0.00790080i q^{49} +(-6.55556 - 2.43375i) q^{50} -1.18942 q^{51} -5.94462 q^{53} +(5.94758 + 2.20803i) q^{54} -0.339374i q^{55} +(-7.18567 - 2.07434i) q^{56} +(-3.35523 - 3.35523i) q^{57} +(2.07732 - 5.59549i) q^{58} +(6.02449 + 6.02449i) q^{59} +(-0.398974 + 0.0297554i) 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} +(-0.825010 - 0.306284i) q^{70} +(-7.68668 + 7.68668i) q^{71} +(-5.63946 + 3.11287i) q^{72} +(5.05407 - 5.05407i) q^{73} +(0.305117 + 0.665434i) q^{74} +4.20314 q^{75} +(11.1333 - 0.830315i) q^{76} +3.81333i q^{77} +8.51654i q^{79} +(0.559518 - 0.756985i) q^{80} +3.01896 q^{81} +(-7.45030 + 3.41614i) q^{82} +(-6.91195 + 6.91195i) q^{83} +(4.48301 - 0.334342i) q^{84} +(0.232839 - 0.232839i) q^{85} +(4.52197 - 12.1804i) 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} +(-0.986372 + 4.70632i) q^{96} +(-10.9412 - 10.9412i) q^{97} +(-0.0104749 - 0.00388878i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more