LMFDB - Embedded newform 845.2.t.f.188.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(188,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.188"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$845 = 5 \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	845.t (of order $12$ , degree $4$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [20,6,-2,6,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1$ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.5
Root			$2.64975i$ of defining polynomial
Character	$\chi$	$=$	845.188
Dual form			845.2.t.f.427.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29475 + 1.32488i) q^{2} +(-1.25278 + 0.335680i) q^{3} +(2.51060 + 4.34849i) q^{4} +(1.81654 + 1.30391i) q^{5} +(-3.31955 - 0.889471i) q^{6} +(0.0561740 + 0.0972962i) q^{7} +8.00544i q^{8} +(-1.14131 + 0.658935i) q^{9} +(2.44100 + 5.39885i) q^{10} +(-1.78976 + 0.479564i) q^{11} +(-4.60492 - 4.60492i) q^{12} +0.297695i q^{14} +(-2.71342 - 1.02373i) q^{15} +(-5.58502 + 9.67354i) q^{16} +(0.706500 - 2.63669i) q^{17} -3.49203 q^{18} +(1.80138 - 6.72284i) q^{19} +(-1.10942 + 11.1728i) q^{20} +(-0.103034 - 0.103034i) q^{21} +(-4.74241 - 1.27073i) q^{22} +(0.831519 + 3.10327i) q^{23} +(-2.68727 - 10.0290i) q^{24} +(1.59964 + 4.73721i) q^{25} +(3.95990 - 3.95990i) q^{27} +(-0.282061 + 0.488544i) q^{28} +(4.03134 + 2.32749i) q^{29} +(-4.87031 - 5.94415i) q^{30} +(-0.624367 + 0.624367i) q^{31} +(-11.7667 + 6.79350i) q^{32} +(2.08118 - 1.20157i) q^{33} +(5.11454 - 5.11454i) q^{34} +(-0.0248231 + 0.249988i) q^{35} +(-5.73074 - 3.30864i) q^{36} +(-0.737435 + 1.27728i) q^{37} +(13.0407 - 13.0407i) q^{38} +(-10.4384 + 14.5422i) q^{40} +(1.40424 + 5.24069i) q^{41} +(-0.0999302 - 0.372945i) q^{42} +(-3.76415 - 1.00860i) q^{43} +(-6.57874 - 6.57874i) q^{44} +(-2.93243 - 0.291181i) q^{45} +(-2.20332 + 8.22291i) q^{46} -0.345095 q^{47} +(3.74956 - 13.9936i) q^{48} +(3.49369 - 6.05125i) q^{49} +(-2.60544 + 12.9901i) q^{50} +3.54034i q^{51} +(-3.59144 - 3.59144i) q^{53} +(14.3334 - 3.84062i) q^{54} +(-3.87647 - 1.46253i) q^{55} +(-0.778898 + 0.449697i) q^{56} +9.02691i q^{57} +(6.16729 + 10.6821i) q^{58} +(-1.24088 - 0.332494i) q^{59} +(-2.36063 - 14.3694i) q^{60} +(1.39151 + 2.41016i) q^{61} +(-2.25998 + 0.605559i) q^{62} +(-0.128224 - 0.0740300i) q^{63} -13.6621 q^{64} +6.36774 q^{66} +(-0.124992 - 0.0721643i) q^{67} +(13.2394 - 3.54747i) q^{68} +(-2.08342 - 3.60858i) q^{69} +(-0.388167 + 0.540774i) q^{70} +(5.28713 + 1.41668i) q^{71} +(-5.27506 - 9.13667i) q^{72} +9.06221i q^{73} +(-3.38447 + 1.95402i) q^{74} +(-3.59418 - 5.39770i) q^{75} +(33.7567 - 9.04509i) q^{76} +(-0.147197 - 0.147197i) q^{77} -15.1689i q^{79} +(-22.7588 + 10.2900i) q^{80} +(-1.65480 + 2.86620i) q^{81} +(-3.72089 + 13.8865i) q^{82} +8.53853 q^{83} +(0.189365 - 0.706718i) q^{84} +(4.72139 - 3.86845i) q^{85} +(-7.30152 - 7.30152i) q^{86} +(-5.83166 - 1.56259i) q^{87} +(-3.83912 - 14.3278i) q^{88} +(-0.147301 - 0.549735i) q^{89} +(-6.34342 - 4.55329i) q^{90} +(-11.4069 + 11.4069i) q^{92} +(0.572604 - 0.991779i) q^{93} +(-0.791908 - 0.457208i) q^{94} +(12.0383 - 9.86348i) q^{95} +(12.4606 - 12.4606i) q^{96} +(12.9596 - 7.48223i) q^{97} +(16.0343 - 9.25742i) q^{98} +(1.72666 - 1.72666i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100})$ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$ .

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	2.29475	+	1.32488i	1.62264	+	0.936830i	0.986211	+	0.165491i	$0.0529210\pi$
$2$	2.29475	+	1.32488i	1.62264	+	0.936830i	0.636425	+	0.771338i	$0.280412\pi$
$3$	−1.25278	+	0.335680i	−0.723291	+	0.193805i	−0.601640	−	0.798768i	$-0.705486\pi$
$3$	−1.25278	+	0.335680i	−0.723291	+	0.193805i	−0.121651	+	0.992573i	$0.538819\pi$
$4$	2.51060	+	4.34849i	1.25530	+	2.17424i
$5$	1.81654	+	1.30391i	0.812382	+	0.583126i
$5$	1.81654	+	1.30391i	0.812382	+	0.583126i
$6$	−3.31955	−	0.889471i	−1.35520	−	0.363125i
$7$	0.0561740	+	0.0972962i	0.0212318	+	0.0367745i	0.876446	−	0.481500i	$-0.159908\pi$
$7$	0.0561740	+	0.0972962i	0.0212318	+	0.0367745i	−0.855214	+	0.518275i	$0.826575\pi$
$8$			8.00544i			2.83035i
$9$	−1.14131	+	0.658935i	−0.380436	+	0.219645i
$10$	2.44100	+	5.39885i	0.771911	+	1.70726i
$11$	−1.78976	+	0.479564i	−0.539632	+	0.144594i	−0.518332	−	0.855179i	$-0.673447\pi$
$11$	−1.78976	+	0.479564i	−0.539632	+	0.144594i	−0.0212994	+	0.999773i	$0.506780\pi$
$12$	−4.60492	−	4.60492i	−1.32933	−	1.32933i
$13$		0			0
$13$		0			0
$14$			0.297695i			0.0795622i
$15$	−2.71342	−	1.02373i	−0.700601	−	0.264326i
$16$	−5.58502	+	9.67354i	−1.39626	+	2.41838i
$17$	0.706500	−	2.63669i	0.171351	−	0.639492i	−0.825793	−	0.563973i	$-0.809272\pi$
$17$	0.706500	−	2.63669i	0.171351	−	0.639492i	0.997144	−	0.0755186i	$-0.0240612\pi$
$18$	−3.49203			−0.823080
$19$	1.80138	−	6.72284i	0.413265	−	1.54233i	−0.375021	−	0.927016i	$-0.622364\pi$
$19$	1.80138	−	6.72284i	0.413265	−	1.54233i	0.788286	−	0.615309i	$-0.210969\pi$
$20$	−1.10942	+	11.1728i	−0.248075	+	2.49831i
$21$	−0.103034	−	0.103034i	−0.0224838	−	0.0224838i
$22$	−4.74241	−	1.27073i	−1.01109	−	0.270920i
$23$	0.831519	+	3.10327i	0.173384	+	0.647077i	0.996821	+	0.0796701i	$0.0253867\pi$
$23$	0.831519	+	3.10327i	0.173384	+	0.647077i	−0.823438	+	0.567407i	$0.807947\pi$
$24$	−2.68727	−	10.0290i	−0.548536	−	2.04717i
$25$	1.59964	+	4.73721i	0.319928	+	0.947442i
$26$		0			0
$27$	3.95990	−	3.95990i	0.762083	−	0.762083i
$28$	−0.282061	+	0.488544i	−0.0533045	+	0.0923261i
$29$	4.03134	+	2.32749i	0.748601	+	0.432205i	0.825188	−	0.564858i	$-0.191069\pi$
$29$	4.03134	+	2.32749i	0.748601	+	0.432205i	−0.0765874	+	0.997063i	$0.524402\pi$
$30$	−4.87031	−	5.94415i	−0.889193	−	1.08525i
$31$	−0.624367	+	0.624367i	−0.112140	+	0.112140i	−0.760950	−	0.648810i	$-0.775267\pi$
$31$	−0.624367	+	0.624367i	−0.112140	+	0.112140i	0.648810	+	0.760950i	$0.275267\pi$
$32$	−11.7667	+	6.79350i	−2.08008	+	1.20093i
$33$	2.08118	−	1.20157i	0.362288	−	0.209167i
$34$	5.11454	−	5.11454i	0.877136	−	0.877136i
$35$	−0.0248231	+	0.249988i	−0.00419587	+	0.0422557i
$36$	−5.73074	−	3.30864i	−0.955123	−	0.551441i
$37$	−0.737435	+	1.27728i	−0.121234	+	0.209983i	−0.920254	−	0.391321i	$-0.872018\pi$
$37$	−0.737435	+	1.27728i	−0.121234	+	0.209983i	0.799021	+	0.601303i	$0.205352\pi$
$38$	13.0407	−	13.0407i	2.11548	−	2.11548i
$39$		0			0
$40$	−10.4384	+	14.5422i	−1.65045	+	2.29932i
$41$	1.40424	+	5.24069i	0.219305	+	0.818458i	0.984606	+	0.174786i	$0.0559233\pi$
$41$	1.40424	+	5.24069i	0.219305	+	0.818458i	−0.765301	+	0.643672i	$0.777410\pi$
$42$	−0.0999302	−	0.372945i	−0.0154196	−	0.0575466i
$43$	−3.76415	−	1.00860i	−0.574027	−	0.153810i	−0.0398840	−	0.999204i	$-0.512699\pi$
$43$	−3.76415	−	1.00860i	−0.574027	−	0.153810i	−0.534143	+	0.845394i	$0.679366\pi$
$44$	−6.57874	−	6.57874i	−0.991782	−	0.991782i
$45$	−2.93243	−	0.291181i	−0.437140	−	0.0434067i
$46$	−2.20332	+	8.22291i	−0.324862	+	1.21240i
$47$	−0.345095			−0.0503372			−0.0251686	−	0.999683i	$-0.508012\pi$
$47$	−0.345095			−0.0503372			−0.0251686	+	0.999683i	$0.508012\pi$
$48$	3.74956	−	13.9936i	0.541203	−	2.01980i
$49$	3.49369	−	6.05125i	0.499098	−	0.864464i
$50$	−2.60544	+	12.9901i	−0.368464	+	1.83707i
$51$			3.54034i			0.495747i
$52$		0			0
$53$	−3.59144	−	3.59144i	−0.493322	−	0.493322i	0.416029	−	0.909351i	$-0.363421\pi$
$53$	−3.59144	−	3.59144i	−0.493322	−	0.493322i	−0.909351	+	0.416029i	$0.863421\pi$
$54$	14.3334	−	3.84062i	1.95053	−	0.522642i
$55$	−3.87647	−	1.46253i	−0.522703	−	0.197208i
$56$	−0.778898	+	0.449697i	−0.104085	+	0.0600933i
$57$			9.02691i			1.19564i
$58$	6.16729	+	10.6821i	0.809805	+	1.40262i
$59$	−1.24088	−	0.332494i	−0.161549	−	0.0432870i	0.177138	−	0.984186i	$-0.443316\pi$
$59$	−1.24088	−	0.332494i	−0.161549	−	0.0432870i	−0.338687	+	0.940899i	$0.609983\pi$
$60$	−2.36063	−	14.3694i	−0.304756	−	1.85508i
$61$	1.39151	+	2.41016i	0.178164	+	0.308589i	0.941252	−	0.337706i	$-0.109651\pi$
$61$	1.39151	+	2.41016i	0.178164	+	0.308589i	−0.763088	+	0.646295i	$0.776318\pi$
$62$	−2.25998	+	0.605559i	−0.287017	+	0.0769061i
$63$	−0.128224	−	0.0740300i	−0.0161547	−	0.00932691i
$64$	−13.6621			−1.70776
$65$		0			0
$66$	6.36774			0.783815
$67$	−0.124992	−	0.0721643i	−0.0152702	−	0.00881627i	0.492345	−	0.870400i	$-0.336140\pi$
$67$	−0.124992	−	0.0721643i	−0.0152702	−	0.00881627i	−0.507616	+	0.861584i	$0.669473\pi$
$68$	13.2394	−	3.54747i	1.60551	−	0.430194i
$69$	−2.08342	−	3.60858i	−0.250814	−	0.434422i
$70$	−0.388167	+	0.540774i	−0.0463948	+	0.0646349i
$71$	5.28713	+	1.41668i	0.627467	+	0.168129i	0.558520	−	0.829491i	$-0.311369\pi$
$71$	5.28713	+	1.41668i	0.627467	+	0.168129i	0.0689472	+	0.997620i	$0.478036\pi$
$72$	−5.27506	−	9.13667i	−0.621672	−	1.07677i
$73$			9.06221i			1.06065i	0.847794	+	0.530326i	$0.177930\pi$
$73$			9.06221i			1.06065i	−0.847794	+	0.530326i	$0.822070\pi$
$74$	−3.38447	+	1.95402i	−0.393436	+	0.227151i
$75$	−3.59418	−	5.39770i	−0.415020	−	0.623272i
$76$	33.7567	−	9.04509i	3.87216	−	1.03754i
$77$	−0.147197	−	0.147197i	−0.0167747	−	0.0167747i
$78$		0			0
$79$		−	15.1689i		−	1.70664i	−0.521388	−	0.853320i	$-0.674586\pi$
$79$		−	15.1689i		−	1.70664i	0.521388	−	0.853320i	$-0.325414\pi$
$80$	−22.7588	+	10.2900i	−2.54451	+	1.15046i
$81$	−1.65480	+	2.86620i	−0.183867	+	0.318467i
$82$	−3.72089	+	13.8865i	−0.410903	+	1.53351i
$83$	8.53853			0.937226			0.468613	−	0.883404i	$-0.344754\pi$
$83$	8.53853			0.937226			0.468613	+	0.883404i	$0.344754\pi$
$84$	0.189365	−	0.706718i	0.0206614	−	0.0771093i
$85$	4.72139	−	3.86845i	0.512107	−	0.419592i
$86$	−7.30152	−	7.30152i	−0.787343	−	0.787343i
$87$	−5.83166	−	1.56259i	−0.625219	−	0.167527i
$88$	−3.83912	−	14.3278i	−0.409251	−	1.52735i
$89$	−0.147301	−	0.549735i	−0.0156139	−	0.0582718i	0.957679	−	0.287837i	$-0.0929362\pi$
$89$	−0.147301	−	0.549735i	−0.0156139	−	0.0582718i	−0.973293	+	0.229565i	$0.926270\pi$
$90$	−6.34342	−	4.55329i	−0.668655	−	0.479959i
$91$		0			0
$92$	−11.4069	+	11.4069i	−1.18925	+	1.18925i
$93$	0.572604	−	0.991779i	0.0593763	−	0.102843i
$94$	−0.791908	−	0.457208i	−0.0816791	−	0.0471574i
$95$	12.0383	−	9.86348i	1.23510	−	1.01197i
$96$	12.4606	−	12.4606i	1.27175	−	1.27175i
$97$	12.9596	−	7.48223i	1.31585	−	0.759705i	0.332790	−	0.943001i	$-0.392010\pi$
$97$	12.9596	−	7.48223i	1.31585	−	0.759705i	0.983058	+	0.183296i	$0.0586766\pi$
$98$	16.0343	−	9.25742i	1.61971	−	0.935140i
$99$	1.72666	−	1.72666i	0.173536	−	0.173536i
$100$	−16.5836	+	18.8493i	−1.65836	+	1.88493i
$101$	−7.19717	−	4.15529i	−0.716146	−	0.413467i	0.0971867	−	0.995266i	$-0.469016\pi$
$101$	−7.19717	−	4.15529i	−0.716146	−	0.413467i	−0.813332	+	0.581799i	$0.802349\pi$
$102$	−4.69052	+	8.12422i	−0.464431	+	0.804418i
$103$	−7.72940	+	7.72940i	−0.761600	+	0.761600i	−0.976612	−	0.215011i	$-0.931021\pi$
$103$	−7.72940	+	7.72940i	−0.761600	+	0.761600i	0.215011	+	0.976612i	$0.431021\pi$
$104$		0			0
$105$	−0.0528184	−	0.321512i	−0.00515455	−	0.0313764i
$106$	−3.48325	−	12.9997i	−0.338324	−	1.26264i
$107$	−1.91631	−	7.15177i	−0.185257	−	0.691388i	−0.994575	−	0.104018i	$-0.966830\pi$
$107$	−1.91631	−	7.15177i	−0.185257	−	0.691388i	0.809318	−	0.587370i	$-0.199837\pi$
$108$	27.1613	+	7.27785i	2.61360	+	0.700311i
$109$	3.34544	+	3.34544i	0.320435	+	0.320435i	0.848934	−	0.528499i	$-0.177245\pi$
$109$	3.34544	+	3.34544i	0.320435	+	0.320435i	−0.528499	+	0.848934i	$0.677245\pi$
$110$	−6.95788	−	8.49200i	−0.663408	−	0.809681i
$111$	0.495085	−	1.84768i	0.0469914	−	0.175374i
$112$	−1.25493			−0.118580
$113$	1.58274	−	5.90688i	0.148892	−	0.555672i	−0.850659	−	0.525717i	$-0.823797\pi$
$113$	1.58274	−	5.90688i	0.148892	−	0.555672i	0.999551	−	0.0299550i	$-0.00953640\pi$
$114$	−11.9595	+	20.7145i	−1.12011	+	1.94009i
$115$	−2.53590	+	6.72145i	−0.236474	+	0.626778i
$116$			23.3736i			2.17019i
$117$		0			0
$118$	−2.40701	−	2.40701i	−0.221583	−	0.221583i
$119$	0.296227	−	0.0793738i	0.0271551	−	0.00727618i
$120$	8.19540	−	21.7221i	0.748134	−	1.98295i
$121$	−6.55303	+	3.78340i	−0.595730	+	0.343945i
$122$			7.37430i			0.667638i
$123$	−3.51839	−	6.09404i	−0.317243	−	0.549481i
$124$	−4.28258	−	1.14751i	−0.384587	−	0.103050i
$125$	−3.27108	+	10.6911i	−0.292574	+	0.956243i
$126$	−0.196161	−	0.339761i	−0.0174754	−	0.0302684i
$127$	11.2706	−	3.01994i	1.00010	−	0.267976i	0.278613	−	0.960403i	$-0.410125\pi$
$127$	11.2706	−	3.01994i	1.00010	−	0.267976i	0.721488	+	0.692427i	$0.243459\pi$
$128$	−7.81784	−	4.51363i	−0.691006	−	0.398953i
$129$	5.05420			0.444997
$130$		0			0
$131$	7.46380			0.652115			0.326058	−	0.945350i	$-0.394280\pi$
$131$	7.46380			0.652115			0.326058	+	0.945350i	$0.394280\pi$
$132$	10.4500	+	6.03333i	0.909559	+	0.525134i
$133$	0.755298	−	0.202381i	0.0654926	−	0.0175487i
$134$	−0.191218	−	0.331199i	−0.0165187	−	0.0286112i
$135$	12.3567	−	2.02997i	1.06349	−	0.174712i
$136$	21.1079	+	5.65584i	1.80998	+	0.484984i
$137$	9.24213	+	16.0078i	0.789608	+	1.36764i	0.926207	+	0.377015i	$0.123050\pi$
$137$	9.24213	+	16.0078i	0.789608	+	1.36764i	−0.136599	+	0.990626i	$0.543617\pi$
$138$		−	11.0411i		−	0.939879i
$139$	9.44862	−	5.45516i	0.801421	−	0.462701i	−0.0425466	−	0.999094i	$-0.513547\pi$
$139$	9.44862	−	5.45516i	0.801421	−	0.462701i	0.843968	+	0.536394i	$0.180214\pi$
$140$	−1.14939	+	0.519678i	−0.0971413	+	0.0439208i
$141$	0.432327	−	0.115842i	0.0364085	−	0.00975562i
$142$	10.2557	+	10.2557i	0.860643	+	0.860643i
$143$		0			0
$144$		−	14.7207i		−	1.22672i
$145$	4.28825	+	9.48449i	0.356120	+	0.787644i
$146$	−12.0063	+	20.7955i	−0.993650	+	1.72105i
$147$	−2.34553	+	8.75362i	−0.193456	+	0.721987i
$148$	−7.40562			−0.608738
$149$	−3.60307	+	13.4468i	−0.295175	+	1.10161i	0.645903	+	0.763419i	$0.276481\pi$
$149$	−3.60307	+	13.4468i	−0.295175	+	1.10161i	−0.941078	+	0.338189i	$0.890186\pi$
$150$	−1.09648	−	17.1482i	−0.0895272	−	1.40015i
$151$	−8.49593	−	8.49593i	−0.691389	−	0.691389i	0.271149	−	0.962537i	$-0.412596\pi$
$151$	−8.49593	−	8.49593i	−0.691389	−	0.691389i	−0.962537	+	0.271149i	$0.912596\pi$
$152$	53.8193	+	14.4208i	4.36532	+	1.16968i
$153$	0.931075	+	3.47482i	0.0752729	+	0.280922i
$154$	−0.142763	−	0.532801i	−0.0115042	−	0.0429343i
$155$	−1.94830	+	0.320070i	−0.156492	+	0.0257086i
$156$		0			0
$157$	−5.14491	+	5.14491i	−0.410609	+	0.410609i	−0.881951	−	0.471342i	$-0.843770\pi$
$157$	−5.14491	+	5.14491i	−0.410609	+	0.410609i	0.471342	+	0.881951i	$0.343770\pi$
$158$	20.0970	−	34.8090i	1.59883	−	2.76926i
$159$	5.70484	+	3.29369i	0.452423	+	0.261207i
$160$	−30.2328	−	3.00202i	−2.39011	−	0.237331i
$161$	−0.255227	+	0.255227i	−0.0201147	+	0.0201147i
$162$	−7.59474	+	4.38482i	−0.596699	+	0.344504i
$163$	−17.7686	+	10.2587i	−1.39175	+	0.803526i	−0.993509	−	0.113756i	$-0.963712\pi$
$163$	−17.7686	+	10.2587i	−1.39175	+	0.803526i	−0.398239	+	0.917282i	$0.630379\pi$
$164$	−19.2636	+	19.2636i	−1.50423	+	1.50423i
$165$	5.34730	+	0.530970i	0.416286	+	0.0413360i
$166$	19.5938	+	11.3125i	1.52078	+	0.878021i
$167$	1.27050	−	2.20058i	0.0983146	−	0.170286i	−0.812673	−	0.582721i	$-0.801988\pi$
$167$	1.27050	−	2.20058i	0.0983146	−	0.170286i	0.910987	+	0.412435i	$0.135322\pi$
$168$	0.824831	−	0.824831i	0.0636371	−	0.0636371i
$169$		0			0
$170$	15.9597	−	2.62187i	1.22405	−	0.201088i
$171$	2.37398	+	8.85983i	0.181543	+	0.677528i
$172$	−5.06438	−	18.9005i	−0.386155	−	1.44115i
$173$	−0.0762079	−	0.0204199i	−0.00579398	−	0.00155249i	0.255921	−	0.966698i	$-0.417621\pi$
$173$	−0.0762079	−	0.0204199i	−0.00579398	−	0.00155249i	−0.261715	+	0.965145i	$0.584288\pi$
$174$	−11.3120	−	11.3120i	−0.857560	−	0.857560i
$175$	−0.371054	+	0.421747i	−0.0280491	+	0.0318811i
$176$	5.35675	−	19.9916i	0.403780	−	1.50693i
$177$	1.66616			0.125236
$178$	0.390312	−	1.45666i	0.0292551	−	0.109182i
$179$	10.6120	−	18.3806i	0.793181	−	1.37383i	−0.130808	−	0.991408i	$-0.541757\pi$
$179$	10.6120	−	18.3806i	0.793181	−	1.37383i	0.923988	−	0.382421i	$-0.124910\pi$
$180$	−6.09595	−	13.4827i	−0.454365	−	1.00494i
$181$		−	22.5267i		−	1.67440i	−0.546899	−	0.837198i	$-0.684192\pi$
$181$		−	22.5267i		−	1.67440i	0.546899	−	0.837198i	$-0.315808\pi$
$182$		0			0
$183$	−2.55229	−	2.55229i	−0.188671	−	0.188671i
$184$	−24.8430	+	6.65667i	−1.83145	+	0.490737i
$185$	−3.00503	+	1.35867i	−0.220934	+	0.0998917i
$186$	2.62797	−	1.51726i	0.192692	−	0.111251i
$187$			5.05785i			0.369866i
$188$	−0.866395	−	1.50064i	−0.0631883	−	0.109445i
$189$	0.607727	+	0.162840i	0.0442056	+	0.0118449i
$190$	40.6927	−	6.68506i	2.95216	−	0.484985i
$191$	−9.80326	−	16.9797i	−0.709339	−	1.22861i	−0.965103	−	0.261872i	$-0.915660\pi$
$191$	−9.80326	−	16.9797i	−0.709339	−	1.22861i	0.255764	−	0.966739i	$-0.417673\pi$
$192$	17.1156	−	4.58610i	1.23521	−	0.330974i
$193$	−14.4730	−	8.35601i	−1.04179	−	0.601479i	−0.121451	−	0.992597i	$-0.538755\pi$
$193$	−14.4730	−	8.35601i	−1.04179	−	0.601479i	−0.920340	+	0.391119i	$0.872088\pi$
$194$	39.6521			2.84686
$195$		0			0
$196$	35.0850			2.50607
$197$	−13.1517	−	7.59315i	−0.937021	−	0.540990i	−0.0479960	−	0.998848i	$-0.515283\pi$
$197$	−13.1517	−	7.59315i	−0.937021	−	0.540990i	−0.889025	+	0.457858i	$0.848617\pi$
$198$	6.24989	−	1.67465i	0.444160	−	0.119012i
$199$	−6.97357	−	12.0786i	−0.494343	−	0.856228i	0.505636	−	0.862747i	$-0.331258\pi$
$199$	−6.97357	−	12.0786i	−0.494343	−	0.856228i	−0.999979	+	0.00651960i	$0.997925\pi$
$200$	−37.9234	+	12.8058i	−2.68159	+	0.905508i
$201$	0.180811	+	0.0484483i	0.0127535	+	0.00341728i
$202$	−11.0105	−	19.0707i	−0.774696	−	1.34181i
$203$			0.522979i			0.0367059i
$204$	−15.3951	+	8.88838i	−1.07787	+	0.622311i
$205$	−4.28253	+	11.3509i	−0.299105	+	0.792783i
$206$	−27.9776	+	7.49657i	−1.94929	+	0.522311i
$207$	−2.99388	−	2.99388i	−0.208089	−	0.208089i
$208$		0			0
$209$			12.8961i			0.892044i
$210$	0.304759	−	0.807769i	0.0210304	−	0.0557414i
$211$	11.8091	−	20.4539i	0.812969	−	1.40810i	−0.0978083	−	0.995205i	$-0.531183\pi$
$211$	11.8091	−	20.4539i	0.812969	−	1.40810i	0.910777	−	0.412898i	$-0.135483\pi$
$212$	6.60065	−	24.6340i	0.453335	−	1.69187i
$213$	−7.09915			−0.486426
$214$	5.07776	−	18.9504i	0.347108	−	1.29543i
$215$	−5.52260	−	6.74027i	−0.376638	−	0.459682i
$216$	31.7007	+	31.7007i	2.15696	+	2.15696i
$217$	−0.0958217	−	0.0256753i	−0.00650480	−	0.00174296i
$218$	3.24467	+	12.1093i	0.219757	+	0.820143i
$219$	−3.04201	−	11.3529i	−0.205560	−	0.767159i
$220$	−3.37247	−	20.5286i	−0.227372	−	1.38404i
$221$		0			0
$222$	3.58405	−	3.58405i	0.240546	−	0.240546i
$223$	−4.86319	+	8.42330i	−0.325664	+	0.564066i	−0.981646	−	0.190710i	$-0.938921\pi$
$223$	−4.86319	+	8.42330i	−0.325664	+	0.564066i	0.655983	+	0.754776i	$0.272254\pi$
$224$	−1.32196	−	0.763236i	−0.0883274	−	0.0509958i
$225$	−4.94720	−	4.35256i	−0.329813	−	0.290171i
$226$	11.4579	−	11.4579i	0.762168	−	0.762168i
$227$	−7.94647	+	4.58790i	−0.527426	+	0.304510i	−0.739968	−	0.672642i	$-0.765159\pi$
$227$	−7.94647	+	4.58790i	−0.527426	+	0.304510i	0.212542	+	0.977152i	$0.431826\pi$
$228$	−39.2534	+	22.6629i	−2.59962	+	1.50089i
$229$	12.5270	−	12.5270i	0.827811	−	0.827811i	−0.159403	−	0.987214i	$-0.550957\pi$
$229$	12.5270	−	12.5270i	0.827811	−	0.827811i	0.987214	+	0.159403i	$0.0509569\pi$
$230$	−14.7244	+	12.0643i	−0.970895	+	0.795498i
$231$	0.233817	+	0.134994i	0.0153840	+	0.00888197i
$232$	−18.6326	+	32.2726i	−1.22329	+	2.11880i
$233$	−11.8637	+	11.8637i	−0.777214	+	0.777214i	−0.979356	−	0.202142i	$-0.935210\pi$
$233$	−11.8637	+	11.8637i	−0.777214	+	0.777214i	0.202142	+	0.979356i	$0.435210\pi$
$234$		0			0
$235$	−0.626879	−	0.449972i	−0.0408931	−	0.0293530i
$236$	−1.66952	−	6.23072i	−0.108676	−	0.405585i
$237$	5.09192	+	19.0033i	0.330756	+	1.23440i
$238$	0.784929	+	0.210321i	0.0508794	+	0.0136331i
$239$	−18.2161	−	18.2161i	−1.17830	−	1.17830i	−0.980177	−	0.198124i	$-0.936515\pi$
$239$	−18.2161	−	18.2161i	−1.17830	−	1.17830i	−0.198124	−	0.980177i	$-0.563485\pi$
$240$	25.0576	−	20.5308i	1.61746	−	1.32526i
$241$	1.41585	−	5.28403i	0.0912030	−	0.340374i	−0.905213	−	0.424957i	$-0.860289\pi$
$241$	1.41585	−	5.28403i	0.0912030	−	0.340374i	0.996416	+	0.0845830i	$0.0269558\pi$
$242$	−20.0501			−1.28887
$243$	−3.23730	+	12.0818i	−0.207673	+	0.775046i
$244$	−6.98703	+	12.1019i	−0.447299	+	0.774744i
$245$	14.2367	−	6.43688i	0.909550	−	0.411237i
$246$		−	18.6458i		−	1.18881i
$247$		0			0
$248$	−4.99833	−	4.99833i	−0.317394	−	0.317394i
$249$	−10.6969	+	2.86622i	−0.677887	+	0.181639i
$250$	−21.6707	+	20.1997i	−1.37058	+	1.27754i
$251$	−11.3169	+	6.53384i	−0.714319	+	0.412412i	−0.812658	−	0.582741i	$-0.801980\pi$
$251$	−11.3169	+	6.53384i	−0.714319	+	0.412412i	0.0983394	+	0.995153i	$0.468647\pi$
$252$		−	0.743439i		−	0.0468322i
$253$	−2.97643	−	5.15533i	−0.187127	−	0.324113i
$254$	29.8642	+	8.00209i	1.87385	+	0.502096i
$255$	−4.61629	+	6.43118i	−0.289083	+	0.402736i
$256$	1.70209	+	2.94811i	0.106381	+	0.184257i
$257$	−16.8541	+	4.51603i	−1.05133	+	0.281702i	−0.742800	−	0.669513i	$-0.766503\pi$
$257$	−16.8541	+	4.51603i	−1.05133	+	0.281702i	−0.308528	+	0.951215i	$0.599836\pi$
$258$	11.5981	+	6.69619i	0.722069	+	0.416887i
$259$	−0.165699			−0.0102960
$260$		0			0
$261$	−6.13467			−0.379727
$262$	17.1276	+	9.88862i	1.05815	+	0.610921i
$263$	−20.1379	+	5.39593i	−1.24175	+	0.332727i	−0.819146	−	0.573585i	$-0.805552\pi$
$263$	−20.1379	+	5.39593i	−1.24175	+	0.332727i	−0.422608	+	0.906312i	$0.638885\pi$
$264$	9.61911	+	16.6608i	0.592015	+	1.02540i
$265$	−1.84108	−	11.2069i	−0.113097	−	0.688434i
$266$	2.00135	+	0.536261i	0.122711	+	0.0328803i
$267$	0.369071	+	0.639249i	0.0225868	+	0.0391214i
$268$		−	0.724703i		−	0.0442683i
$269$	9.15088	−	5.28326i	0.557939	−	0.322126i	−0.194379	−	0.980927i	$-0.562269\pi$
$269$	9.15088	−	5.28326i	0.557939	−	0.322126i	0.752318	+	0.658800i	$0.228936\pi$
$270$	31.0450	+	11.7128i	1.88934	+	0.712818i
$271$	7.64095	−	2.04739i	0.464155	−	0.124370i	−0.0191601	−	0.999816i	$-0.506099\pi$
$271$	7.64095	−	2.04739i	0.464155	−	0.124370i	0.483315	+	0.875446i	$0.339433\pi$
$272$	21.5603	+	21.5603i	1.30729	+	1.30729i
$273$		0			0
$274$			48.9787i			2.95891i
$275$	−5.13476	−	7.71132i	−0.309638	−	0.465010i
$276$	10.4612	−	18.1194i	0.629693	−	1.09066i
$277$	−2.64361	+	9.86609i	−0.158839	+	0.592796i	0.839907	+	0.542731i	$0.182610\pi$
$277$	−2.64361	+	9.86609i	−0.158839	+	0.592796i	−0.998746	+	0.0500653i	$0.984057\pi$
$278$	28.9097			1.73389
$279$	0.301178	−	1.12401i	0.0180311	−	0.0672929i
$280$	−2.00127	−	0.198720i	−0.119598	−	0.0118758i
$281$	12.4763	+	12.4763i	0.744271	+	0.744271i	0.973397	−	0.229126i	$-0.0735867\pi$
$281$	12.4763	+	12.4763i	0.744271	+	0.744271i	−0.229126	+	0.973397i	$0.573587\pi$
$282$	1.14556	+	0.306952i	0.0682171	+	0.0182787i
$283$	2.13952	+	7.98478i	0.127181	+	0.474646i	0.999908	−	0.0135626i	$-0.00431723\pi$
$283$	2.13952	+	7.98478i	0.127181	+	0.474646i	−0.872727	+	0.488208i	$0.837651\pi$
$284$	7.11345	+	26.5478i	0.422105	+	1.57532i
$285$	−11.7703	+	16.3977i	−0.697210	+	0.971318i
$286$		0			0
$287$	−0.431018	+	0.431018i	−0.0254422	+	0.0254422i
$288$	8.95295	−	15.5070i	0.527557	−	0.913756i
$289$	8.26943	+	4.77436i	0.486437	+	0.280844i
$290$	−2.72530	+	27.4460i	−0.160035	+	1.61168i
$291$	−13.7238	+	13.7238i	−0.804506	+	0.804506i
$292$	−39.4069	+	22.7516i	−2.30611	+	1.33144i
$293$	5.52378	−	3.18916i	0.322703	−	0.186313i	−0.329894	−	0.944018i	$-0.607013\pi$
$293$	5.52378	−	3.18916i	0.322703	−	0.186313i	0.652597	+	0.757705i	$0.273680\pi$
$294$	−16.9799	+	16.9799i	−0.990287	+	0.990287i
$295$	−1.82057	−	2.22199i	−0.105998	−	0.129369i
$296$	−10.2251	−	5.90349i	−0.594325	−	0.343133i
$297$	−5.18823	+	8.98628i	−0.301052	+	0.521437i
$298$	−26.0836	+	26.0836i	−1.51098	+	1.51098i
$299$		0			0
$300$	14.4483	−	29.1807i	0.834170	−	1.68475i
$301$	−0.113314	−	0.422894i	−0.00653132	−	0.0243752i
$302$	−8.24001	−	30.7521i	−0.474159	−	1.76959i
$303$	10.4113	+	2.78970i	0.598114	+	0.160264i
$304$	54.9729	+	54.9729i	3.15291	+	3.15291i
$305$	−0.614902	+	6.19255i	−0.0352092	+	0.354584i
$306$	−2.46712	+	9.20741i	−0.141036	+	0.526353i
$307$	−26.5460			−1.51506			−0.757530	−	0.652801i	$-0.773594\pi$
$307$	−26.5460			−1.51506			−0.757530	+	0.652801i	$0.773594\pi$
$308$	0.270532	−	1.00964i	0.0154150	−	0.0575296i
$309$	7.08860	−	12.2778i	0.403256	−	0.698460i
$310$	−4.89494	−	1.84678i	−0.278014	−	0.104890i
$311$		−	3.54417i		−	0.200972i	−0.994938	−	0.100486i	$-0.967960\pi$
$311$		−	3.54417i		−	0.200972i	0.994938	−	0.100486i	$-0.0320397\pi$
$312$		0			0
$313$	−6.21088	−	6.21088i	−0.351060	−	0.351060i	0.509444	−	0.860504i	$-0.329851\pi$
$313$	−6.21088	−	6.21088i	−0.351060	−	0.351060i	−0.860504	+	0.509444i	$0.829851\pi$
$314$	−18.6227	+	4.98993i	−1.05094	+	0.281598i
$315$	−0.136395	−	0.301671i	−0.00768500	−	0.0169972i
$316$	65.9619	−	38.0831i	3.71065	−	2.14234i
$317$			8.52812i			0.478987i	0.970898	+	0.239494i	$0.0769814\pi$
$317$			8.52812i			0.478987i	−0.970898	+	0.239494i	$0.923019\pi$
$318$	8.72748	+	15.1164i	0.489413	+	0.847688i
$319$	−8.33129	−	2.23236i	−0.466463	−	0.124988i
$320$	−24.8178	−	17.8142i	−1.38736	−	0.995842i
$321$	4.80142	+	8.31631i	0.267989	+	0.464171i
$322$	−0.923827	+	0.247539i	−0.0514829	+	0.0137948i
$323$	−16.4534	−	9.49937i	−0.915491	−	0.528559i
$324$	−16.6182			−0.923233
$325$		0			0
$326$	−54.3663			−3.01107
$327$	−5.31409	−	3.06809i	−0.293870	−	0.169666i
$328$	−41.9540	+	11.2415i	−2.31652	+	0.620710i
$329$	−0.0193853	−	0.0335764i	−0.00106875	−	0.00185113i
$330$	11.5673	+	8.30296i	0.636757	+	0.457063i
$331$	−17.3934	−	4.66054i	−0.956026	−	0.256166i	−0.253109	−	0.967438i	$-0.581453\pi$
$331$	−17.3934	−	4.66054i	−0.956026	−	0.256166i	−0.702917	+	0.711271i	$0.748120\pi$
$332$	21.4368	+	37.1297i	1.17650	+	2.03776i
$333$		−	1.94369i		−	0.106513i
$334$	5.83099	−	3.36652i	0.319058	−	0.184208i
$335$	−0.132958	−	0.294068i	−0.00726426	−	0.0160666i
$336$	1.57215	−	0.421256i	0.0857677	−	0.0229814i
$337$	−20.0865	−	20.0865i	−1.09418	−	1.09418i	−0.995077	−	0.0991030i	$-0.968403\pi$
$337$	−20.0865	−	20.0865i	−1.09418	−	1.09418i	−0.0991030	−	0.995077i	$-0.531597\pi$
$338$		0			0
$339$			7.93129i			0.430769i
$340$	28.6754	+	10.8188i	1.55514	+	0.586731i
$341$	0.818040	−	1.41689i	0.0442994	−	0.0767288i
$342$	−6.29048	+	23.4764i	−0.340150	+	1.26946i
$343$	1.57145			0.0848505
$344$	8.07428	−	30.1336i	0.435336	−	1.62470i
$345$	0.920654	−	9.27172i	0.0495663	−	0.499173i
$346$	−0.147825	−	0.147825i	−0.00794710	−	0.00794710i
$347$	6.93201	+	1.85743i	0.372130	+	0.0997119i	0.440037	−	0.897980i	$-0.354965\pi$
$347$	6.93201	+	1.85743i	0.372130	+	0.0997119i	−0.0679068	+	0.997692i	$0.521632\pi$
$348$	−7.84607	−	29.2819i	−0.420593	−	1.56968i
$349$	−0.945552	−	3.52885i	−0.0506143	−	0.188895i	0.935990	−	0.352026i	$-0.114507\pi$
$349$	−0.945552	−	3.52885i	−0.0506143	−	0.188895i	−0.986604	+	0.163131i	$0.947841\pi$
$350$	−1.41024	+	0.476204i	−0.0753806	+	0.0254542i
$351$		0			0
$352$	17.8016	−	17.8016i	0.948827	−	0.948827i
$353$	−0.881628	+	1.52702i	−0.0469243	+	0.0812753i	−0.888534	−	0.458812i	$-0.848275\pi$
$353$	−0.881628	+	1.52702i	−0.0469243	+	0.0812753i	0.841609	+	0.540087i	$0.181609\pi$
$354$	3.82343	+	2.20746i	0.203213	+	0.117325i
$355$	7.75707	+	9.46741i	0.411702	+	0.502478i
$356$	2.02070	−	2.02070i	0.107097	−	0.107097i
$357$	−0.344462	+	0.198875i	−0.0182309	+	0.0105256i
$358$	48.7040	−	28.1193i	2.57409	−	1.48615i
$359$	8.58021	−	8.58021i	0.452846	−	0.452846i	−0.443452	−	0.896298i	$-0.646246\pi$
$359$	8.58021	−	8.58021i	0.452846	−	0.452846i	0.896298	+	0.443452i	$0.146246\pi$
$360$	2.33103	−	23.4753i	0.122856	−	1.23726i
$361$	−25.4972	−	14.7208i	−1.34196	−	0.774778i
$362$	29.8451	−	51.6933i	1.56862	−	2.71694i
$363$	6.93947	−	6.93947i	0.364228	−	0.364228i
$364$		0			0
$365$	−11.8163	+	16.4619i	−0.618493	+	0.861654i
$366$	−2.47541	−	9.23835i	−0.129392	−	0.482896i
$367$	−3.62635	−	13.5337i	−0.189294	−	0.706454i	−0.993670	−	0.112334i	$-0.964167\pi$
$367$	−3.62635	−	13.5337i	−0.189294	−	0.706454i	0.804377	−	0.594120i	$-0.202499\pi$
$368$	−34.6637	−	9.28811i	−1.80697	−	0.484176i
$369$	−5.05594	−	5.05594i	−0.263202	−	0.263202i
$370$	−8.69589	−	0.863475i	−0.452078	−	0.0448900i
$371$	0.147688	−	0.551179i	0.00766757	−	0.0286158i
$372$	5.75032			0.298140
$373$	−7.47789	+	27.9078i	−0.387190	+	1.44501i	0.447495	+	0.894286i	$0.352316\pi$
$373$	−7.47789	+	27.9078i	−0.387190	+	1.44501i	−0.834685	+	0.550727i	$0.814350\pi$
$374$	−6.70103	+	11.6065i	−0.346502	+	0.600159i
$375$	0.509129	−	14.4916i	0.0262913	−	0.748344i
$376$		−	2.76263i		−	0.142472i
$377$		0			0
$378$	1.17884	+	1.17884i	0.0606330	+	0.0606330i
$379$	−9.15390	+	2.45278i	−0.470204	+	0.125991i	−0.486138	−	0.873882i	$-0.661595\pi$
$379$	−9.15390	+	2.45278i	−0.470204	+	0.125991i	0.0159336	+	0.999873i	$0.494928\pi$
$380$	73.1144	+	27.5849i	3.75069	+	1.41508i
$381$	−13.1058	+	7.56661i	−0.671428	+	0.387649i
$382$		−	51.9525i		−	2.65812i
$383$	10.5361	+	18.2490i	0.538369	+	0.932483i	0.998992	+	0.0448868i	$0.0142927\pi$
$383$	10.5361	+	18.2490i	0.538369	+	0.932483i	−0.460623	+	0.887596i	$0.652374\pi$
$384$	11.3091	+	3.03028i	0.577118	+	0.154638i
$385$	−0.0754581	−	0.459322i	−0.00384570	−	0.0234092i
$386$	−22.1414	−	38.3500i	−1.12697	−	1.95196i
$387$	4.96065	−	1.32920i	0.252164	−	0.0675672i
$388$	65.0727	+	37.5698i	3.30357	+	1.90732i
$389$	0.0604806			0.00306649			0.00153324	−	0.999999i	$-0.499512\pi$
$389$	0.0604806			0.00306649			0.00153324	+	0.999999i	$0.499512\pi$
$390$		0			0
$391$	8.76984			0.443510
$392$	48.4429	+	27.9685i	2.44673	+	1.41262i
$393$	−9.35047	+	2.50545i	−0.471669	+	0.126383i
$394$	−20.1200	−	34.8488i	−1.01363	−	1.75566i
$395$	19.7789	−	27.5550i	0.995186	−	1.38644i
$396$	11.8433	+	3.17341i	0.595150	+	0.159470i
$397$	−4.10812	−	7.11548i	−0.206181	−	0.357116i	0.744327	−	0.667815i	$-0.232770\pi$
$397$	−4.10812	−	7.11548i	−0.206181	−	0.357116i	−0.950508	+	0.310699i	$0.899437\pi$
$398$		−	36.9565i		−	1.85246i
$399$	−0.878284	+	0.507077i	−0.0439692	+	0.0253856i
$400$	−54.7596	−	10.9832i	−2.73798	−	0.549161i
$401$	8.69210	−	2.32904i	0.434063	−	0.116307i	−0.0351698	−	0.999381i	$-0.511197\pi$
$401$	8.69210	−	2.32904i	0.434063	−	0.116307i	0.469233	+	0.883075i	$0.344531\pi$
$402$	0.350730	+	0.350730i	0.0174928	+	0.0174928i
$403$		0			0
$404$		−	41.7291i		−	2.07610i
$405$	−6.74329	+	3.04886i	−0.335077	+	0.151499i
$406$	−0.692882	+	1.20011i	−0.0343872	+	0.0595603i
$407$	0.707294	−	2.63966i	0.0350593	−	0.130843i
$408$	−28.3420			−1.40314
$409$	−9.27138	+	34.6013i	−0.458440	+	1.71092i	0.219332	+	0.975650i	$0.429612\pi$
$409$	−9.27138	+	34.6013i	−0.458440	+	1.71092i	−0.677772	+	0.735272i	$0.737054\pi$
$410$	−24.8659	+	20.3738i	−1.22804	+	1.00619i
$411$	−16.9518	−	16.9518i	−0.836173	−	0.836173i
$412$	−53.0166	−	14.2058i	−2.61194	−	0.699867i
$413$	−0.0373550	−	0.139411i	−0.00183812	−	0.00685995i
$414$	−2.90369	−	10.8367i	−0.142709	−	0.532596i
$415$	15.5106	+	11.1335i	0.761385	+	0.546521i
$416$		0			0
$417$	−10.0058	+	10.0058i	−0.489987	+	0.489987i
$418$	−17.0858	+	29.5934i	−0.835693	+	1.44746i
$419$	11.3282	+	6.54037i	0.553421	+	0.319518i	0.750501	−	0.660870i	$-0.229812\pi$
$419$	11.3282	+	6.54037i	0.553421	+	0.319518i	−0.197080	+	0.980387i	$0.563146\pi$
$420$	1.26548	−	1.03687i	0.0617493	−	0.0505940i
$421$	−13.7924	+	13.7924i	−0.672203	+	0.672203i	−0.958223	−	0.286021i	$-0.907667\pi$
$421$	−13.7924	+	13.7924i	−0.672203	+	0.672203i	0.286021	+	0.958223i	$0.407667\pi$
$422$	54.1978	−	31.2911i	2.63831	−	1.52323i
$423$	0.393860	−	0.227395i	0.0191501	−	0.0110563i
$424$	28.7510	−	28.7510i	1.39627	−	1.39627i
$425$	13.6207	−	0.870925i	0.660701	−	0.0422461i
$426$	−16.2908	−	9.40550i	−0.789292	−	0.455698i
$427$	−0.156333	+	0.270777i	−0.00756548	+	0.0131038i
$428$	26.2883	−	26.2883i	1.27069	−	1.27069i
$429$		0			0
$430$	−3.74299	−	22.7840i	−0.180503	−	1.09874i
$431$	−5.75070	−	21.4619i	−0.277002	−	1.03378i	−0.954488	−	0.298249i	$-0.903597\pi$
$431$	−5.75070	−	21.4619i	−0.277002	−	1.03378i	0.677487	−	0.735535i	$-0.263069\pi$
$432$	16.1901	+	60.4224i	0.778948	+	2.90707i
$433$	−0.177294	−	0.0475058i	−0.00852021	−	0.00228298i	0.254556	−	0.967058i	$-0.418071\pi$
$433$	−0.177294	−	0.0475058i	−0.00852021	−	0.00228298i	−0.263077	+	0.964775i	$0.584737\pi$
$434$	−0.185871	−	0.185871i	−0.00892207	−	0.00892207i
$435$	−8.55597	−	10.4425i	−0.410228	−	0.500678i
$436$	−6.14854	+	22.9467i	−0.294462	+	1.09895i
$437$	22.3607			1.06966
$438$	8.06057	−	30.0825i	0.385149	−	1.43740i
$439$	−8.64682	+	14.9767i	−0.412690	+	0.714800i	−0.995183	−	0.0980356i	$-0.968744\pi$
$439$	−8.64682	+	14.9767i	−0.412690	+	0.714800i	0.582493	+	0.812836i	$0.302077\pi$
$440$	11.7082	−	31.0328i	0.558167	−	1.47943i
$441$			9.20846i			0.438498i
$442$		0			0
$443$	24.4472	+	24.4472i	1.16152	+	1.16152i	0.984143	+	0.177377i	$0.0567611\pi$
$443$	24.4472	+	24.4472i	1.16152	+	1.16152i	0.177377	+	0.984143i	$0.443239\pi$
$444$	9.27758	−	2.48592i	0.440295	−	0.117977i
$445$	0.449226	−	1.19068i	0.0212954	−	0.0564438i
$446$	−22.3197	+	12.8863i	−1.05687	+	0.610183i
$447$		−	18.0554i		−	0.853989i
$448$	−0.767456	−	1.32927i	−0.0362589	−	0.0628022i
$449$	−35.9175	−	9.62407i	−1.69505	−	0.454188i	−0.723366	−	0.690465i	$-0.757406\pi$
$449$	−35.9175	−	9.62407i	−1.69505	−	0.454188i	−0.971686	+	0.236277i	$0.924073\pi$
$450$	−5.58600	−	16.5425i	−0.263326	−	0.779820i
$451$	−5.02649	−	8.70613i	−0.236688	−	0.409956i
$452$	29.6596	−	7.94727i	1.39507	−	0.373808i
$453$	13.4954	+	7.79158i	0.634070	+	0.366080i
$454$	−24.3136			−1.14109
$455$		0			0
$456$	−72.2643			−3.38409
$457$	8.16394	+	4.71345i	0.381893	+	0.220486i	0.678642	−	0.734470i	$-0.262569\pi$
$457$	8.16394	+	4.71345i	0.381893	+	0.220486i	−0.296749	+	0.954956i	$0.595902\pi$
$458$	45.3433	−	12.1497i	2.11875	−	0.567718i
$459$	−7.64337	−	13.2387i	−0.356762	−	0.617930i
$460$	−35.5947	+	5.84755i	−1.65961	+	0.272643i
$461$	31.7653	+	8.51149i	1.47946	+	0.396419i	0.906162	−	0.422930i	$-0.138998\pi$
$461$	31.7653	+	8.51149i	1.47946	+	0.396419i	0.573295	+	0.819349i	$0.305665\pi$
$462$	0.357701	+	0.619557i	0.0166418	+	0.0288244i
$463$			18.6729i			0.867805i	0.900960	+	0.433903i	$0.142864\pi$
$463$			18.6729i			0.867805i	−0.900960	+	0.433903i	$0.857136\pi$
$464$	−45.0302	+	25.9982i	−2.09047	+	1.20694i
$465$	2.33335	−	1.05498i	0.108206	−	0.0489237i
$466$	−42.9421	+	11.5063i	−1.98925	+	0.533019i
$467$	−12.1678	−	12.1678i	−0.563057	−	0.563057i	0.367118	−	0.930175i	$-0.380345\pi$
$467$	−12.1678	−	12.1678i	−0.563057	−	0.563057i	−0.930175	+	0.367118i	$0.880345\pi$
$468$		0			0
$469$		−	0.0162150i		−	0.000748740i
$470$	−0.842375	−	1.86311i	−0.0388559	−	0.0859390i
$471$	4.71838	−	8.17247i	0.217411	−	0.376568i
$472$	2.66176	−	9.93381i	0.122517	−	0.457241i
$473$	7.22059			0.332003
$474$	−13.4923	+	50.3541i	−0.619723	+	2.31284i
$475$	34.7291	−	2.22062i	1.59348	−	0.101889i
$476$	1.08886	+	1.08886i	0.0499080	+	0.0499080i
$477$	6.46546	+	1.73242i	0.296033	+	0.0793219i
$478$	−17.6674	−	65.9355i	−0.808087	−	3.01582i
$479$	8.53158	+	31.8403i	0.389818	+	1.45482i	0.830430	+	0.557123i	$0.188095\pi$
$479$	8.53158	+	31.8403i	0.389818	+	1.45482i	−0.440612	+	0.897697i	$0.645239\pi$
$480$	38.8826	−	6.38768i	1.77474	−	0.291557i
$481$		0			0
$482$	10.2497	−	10.2497i	0.466862	−	0.466862i
$483$	0.234068	−	0.405417i	0.0106504	−	0.0184471i
$484$	−32.9041	−	18.9972i	−1.49564	−	0.863508i
$485$	33.2978	+	3.30637i	1.51197	+	0.150134i
$486$	−23.4357	+	23.4357i	−1.06306	+	1.06306i
$487$	−28.5670	+	16.4931i	−1.29449	+	0.747376i	−0.979447	−	0.201701i	$-0.935353\pi$
$487$	−28.5670	+	16.4931i	−1.29449	+	0.747376i	−0.315045	+	0.949077i	$0.602020\pi$
$488$	−19.2944	+	11.1396i	−0.873415	+	0.504267i
$489$	18.8165	−	18.8165i	0.850911	−	0.850911i
$490$	41.1978	+	4.09082i	1.86113	+	0.184804i
$491$	18.4427	+	10.6479i	0.832307	+	0.480533i	0.854642	−	0.519218i	$-0.173777\pi$
$491$	18.4427	+	10.6479i	0.832307	+	0.480533i	−0.0223350	+	0.999751i	$0.507110\pi$
$492$	17.6666	−	30.5994i	0.796470	−	1.37953i
$493$	8.98502	−	8.98502i	0.404665	−	0.404665i
$494$		0			0
$495$	5.38797	−	0.885142i	0.242171	−	0.0397842i
$496$	−2.55273	−	9.52693i	−0.114621	−	0.427772i
$497$	0.159161	+	0.593999i	0.00713937	+	0.0266445i
$498$	−28.3441	−	7.59477i	−1.27013	−	0.340330i
$499$	−14.9199	−	14.9199i	−0.667904	−	0.667904i	0.289326	−	0.957231i	$-0.406569\pi$
$499$	−14.9199	−	14.9199i	−0.667904	−	0.667904i	−0.957231	+	0.289326i	$0.906569\pi$
$500$	−54.7025	+	12.6169i	−2.44637	+	0.564244i
$501$	−0.852967	+	3.18332i	−0.0381077	+	0.142220i
$502$	−34.6261			−1.54544
$503$	11.3059	−	42.1943i	0.504106	−	1.88135i	0.0326345	−	0.999467i	$-0.489610\pi$
$503$	11.3059	−	42.1943i	0.504106	−	1.88135i	0.471471	−	0.881881i	$-0.343723\pi$
$504$	0.592643	−	1.02649i	0.0263984	−	0.0457234i
$505$	−7.65584	−	16.9327i	−0.340680	−	0.753496i
$506$		−	15.7736i		−	0.701224i
$507$		0			0
$508$	41.4280	+	41.4280i	1.83807	+	1.83807i
$509$	36.0898	−	9.67023i	1.59965	−	0.428626i	0.654715	−	0.755876i	$-0.272789\pi$
$509$	36.0898	−	9.67023i	1.59965	−	0.428626i	0.944938	+	0.327250i	$0.106122\pi$
$510$	−19.1138	+	8.64196i	−0.846372	+	0.382673i
$511$	−0.881719	+	0.509060i	−0.0390049	+	0.0225195i
$512$			27.0748i			1.19655i
$513$	−19.4885	−	33.7551i	−0.860438	−	1.49032i
$514$	−44.6591	−	11.9664i	−1.96983	−	0.527814i
$515$	−24.1192	+	3.96233i	−1.06282	+	0.174601i
$516$	12.6891	+	21.9781i	0.558605	+	0.967533i
$517$	0.617635	−	0.165495i	0.0271636	−	0.00727846i
$518$	−0.380238	−	0.219530i	−0.0167067	−	0.00964562i
$519$	0.102326			0.00449161
$520$		0			0
$521$	−35.6853			−1.56340			−0.781701	−	0.623653i	$-0.785648\pi$
$521$	−35.6853			−1.56340			−0.781701	+	0.623653i	$0.785648\pi$
$522$	−14.0776	−	8.12768i	−0.616158	−	0.355739i
$523$	4.16849	−	1.11694i	0.182275	−	0.0488406i	−0.166527	−	0.986037i	$-0.553255\pi$
$523$	4.16849	−	1.11694i	0.182275	−	0.0488406i	0.348802	+	0.937196i	$0.386589\pi$
$524$	18.7386	+	32.4562i	0.818600	+	1.41786i
$525$	0.323276	−	0.652910i	0.0141089	−	0.0284953i
$526$	−53.3604	−	14.2979i	−2.32662	−	0.623417i
$527$	1.20515	+	2.08738i	0.0524971	+	0.0909276i
$528$			26.8432i			1.16820i
$529$	10.9797	−	6.33914i	0.477379	−	0.275615i
$530$	10.6229	−	28.1563i	0.461431	−	1.22303i
$531$	1.63532	−	0.438183i	0.0709670	−	0.0190155i
$532$	2.77630	+	2.77630i	0.120368	+	0.120368i
$533$		0			0
$534$			1.95589i			0.0846398i
$535$	5.84421	−	15.4902i	0.252667	−	0.669699i
$536$	0.577707	−	1.00062i	0.0249531	−	0.0432201i
$537$	−7.12450	+	26.5890i	−0.307445	+	1.14740i
$538$	27.9987			1.20711
$539$	−3.35089	+	12.5057i	−0.144333	+	0.538659i
$540$	39.8500	+	48.6364i	1.71487	+	2.09298i
$541$	−5.42748	−	5.42748i	−0.233345	−	0.233345i	0.580742	−	0.814088i	$-0.302762\pi$
$541$	−5.42748	−	5.42748i	−0.233345	−	0.233345i	−0.814088	+	0.580742i	$0.802762\pi$
$542$	20.2467	+	5.42507i	0.869668	+	0.233027i
$543$	7.56177	+	28.2209i	0.324507	+	1.21108i
$544$	9.59920	+	35.8247i	0.411563	+	1.53597i
$545$	1.71498	+	10.4393i	0.0734616	+	0.447170i
$546$		0			0
$547$	11.6940	−	11.6940i	0.500000	−	0.500000i	−0.411438	−	0.911438i	$-0.634973\pi$
$547$	11.6940	−	11.6940i	0.500000	−	0.500000i	0.911438	+	0.411438i	$0.134973\pi$
$548$	−46.4066	+	80.3785i	−1.98239	+	3.43360i
$549$	−3.17628	−	1.83382i	−0.135560	−	0.0782657i
$550$	−1.56647	−	24.4985i	−0.0667943	−	1.04462i
$551$	22.9093	−	22.9093i	0.975971	−	0.975971i
$552$	28.8883	−	16.6786i	1.22957	−	0.709890i
$553$	1.47588	−	0.852100i	0.0627608	−	0.0362350i
$554$	−19.1378	+	19.1378i	−0.813087	+	0.813087i
$555$	3.30855	−	2.71085i	0.140440	−	0.115069i
$556$	47.4434	+	27.3915i	2.01205	+	1.16166i
$557$	2.43751	−	4.22190i	0.103281	−	0.178888i	−0.809754	−	0.586770i	$-0.800399\pi$
$557$	2.43751	−	4.22190i	0.103281	−	0.178888i	0.913034	+	0.407882i	$0.133733\pi$
$558$	2.18031	−	2.18031i	0.0922998	−	0.0922998i
$559$		0			0
$560$	−2.27963	−	1.63632i	−0.0963321	−	0.0691470i
$561$	−1.69782	−	6.33635i	−0.0716820	−	0.267521i
$562$	12.1004	+	45.1595i	0.510426	+	1.90494i
$563$	37.6390	+	10.0853i	1.58630	+	0.425047i	0.940868	−	0.338774i	$-0.110012\pi$
$563$	37.6390	+	10.0853i	1.58630	+	0.425047i	0.645428	+	0.763821i	$0.276679\pi$
$564$	1.58913	+	1.58913i	0.0669146	+	0.0669146i
$565$	10.5772	−	8.66633i	0.444984	−	0.364595i
$566$	−5.66919	+	21.1577i	−0.238294	+	0.889325i
$567$	−0.371828			−0.0156153
$568$	−11.3412	+	42.3258i	−0.475865	+	1.77595i
$569$	1.84104	−	3.18877i	0.0771804	−	0.133680i	−0.824852	−	0.565349i	$-0.808742\pi$
$569$	1.84104	−	3.18877i	0.0771804	−	0.133680i	0.902032	+	0.431668i	$0.142075\pi$
$570$	−48.7349	+	22.0346i	−2.04128	+	0.922929i
$571$		−	2.96698i		−	0.124164i	−0.998071	−	0.0620821i	$-0.980226\pi$
$571$		−	2.96698i		−	0.124164i	0.998071	−	0.0620821i	$-0.0197741\pi$
$572$		0			0
$573$	17.9811	+	17.9811i	0.751170	+	0.751170i
$574$	−1.56012	+	0.418034i	−0.0651184	+	0.0174484i
$575$	−13.3707	+	8.90320i	−0.557598	+	0.371289i
$576$	15.5927	−	9.00245i	0.649696	−	0.375102i
$577$			35.0533i			1.45929i	0.683827	+	0.729644i	$0.260314\pi$
$577$			35.0533i			1.45929i	−0.683827	+	0.729644i	$0.739686\pi$
$578$	12.6509	+	21.9120i	0.526207	+	0.911417i
$579$	20.9364	+	5.60990i	0.870088	+	0.233139i
$580$	−30.4771	+	42.4591i	−1.26549	+	1.76302i
$581$	0.479643	+	0.830767i	0.0198990	+	0.0344660i
$582$	−49.6753	+	13.3104i	−2.05911	+	0.551736i
$583$	8.15012	+	4.70547i	0.337543	+	0.194881i
$584$	−72.5469			−3.00201
$585$		0			0
$586$	16.9010			0.698173
$587$	6.10926	+	3.52719i	0.252156	+	0.145583i	0.620751	−	0.784008i	$-0.286828\pi$
$587$	6.10926	+	3.52719i	0.252156	+	0.145583i	−0.368595	+	0.929590i	$0.620161\pi$
$588$	−43.9537	+	11.7774i	−1.81262	+	0.485690i
$589$	3.07280	+	5.32224i	0.126612	+	0.219299i
$590$	−1.23391	−	7.51095i	−0.0507992	−	0.309221i
$591$	19.0250	+	5.09774i	0.782585	+	0.209693i
$592$	−8.23718	−	14.2672i	−0.338546	−	0.586379i
$593$			40.0169i			1.64330i	0.569993	+	0.821649i	$0.306946\pi$
$593$			40.0169i			1.64330i	−0.569993	+	0.821649i	$0.693054\pi$
$594$	−23.8114	+	13.7475i	−0.976995	+	0.564068i
$595$	0.641605	+	0.242067i	0.0263032	+	0.00992380i
$596$	−67.5192	+	18.0917i	−2.76570	+	0.741066i
$597$	12.7909	+	12.7909i	0.523495	+	0.523495i
$598$		0			0
$599$		−	13.9207i		−	0.568784i	−0.958708	−	0.284392i	$-0.908208\pi$
$599$		−	13.9207i		−	0.568784i	0.958708	−	0.284392i	$-0.0917918\pi$
$600$	43.2109	−	28.7730i	1.76408	−	1.17465i
$601$	1.15689	−	2.00379i	0.0471906	−	0.0817365i	−0.841465	−	0.540311i	$-0.818307\pi$
$601$	1.15689	−	2.00379i	0.0471906	−	0.0817365i	0.888656	+	0.458575i	$0.151640\pi$
$602$	0.300255	−	1.12057i	0.0122375	−	0.0456708i
$603$	0.190206			0.00774580
$604$	15.6145	−	58.2743i	0.635347	−	2.37115i
$605$	−16.8371	−	1.67187i	−0.684524	−	0.0679711i
$606$	20.1954	+	20.1954i	0.820381	+	0.820381i
$607$	−22.7965	−	6.10830i	−0.925282	−	0.247928i	−0.235440	−	0.971889i	$-0.575653\pi$
$607$	−22.7965	−	6.10830i	−0.925282	−	0.247928i	−0.689842	+	0.723960i	$0.742320\pi$
$608$	24.4753	+	91.3432i	0.992606	+	3.70446i
$609$	−0.175554	−	0.655175i	−0.00711379	−	0.0265490i
$610$	−9.61542	+	13.3957i	−0.389317	+	0.542377i
$611$		0			0
$612$	−12.7726	+	12.7726i	−0.516303	+	0.516303i
$613$	5.32964	−	9.23121i	0.215262	−	0.372845i	−0.738091	−	0.674701i	$-0.764273\pi$
$613$	5.32964	−	9.23121i	0.215262	−	0.372845i	0.953354	+	0.301856i	$0.0976060\pi$
$614$	−60.9165	−	35.1702i	−2.45839	−	1.41935i
$615$	1.55477	−	15.6577i	0.0626942	−	0.631381i
$616$	1.17838	−	1.17838i	0.0474783	−	0.0474783i
$617$	11.8892	−	6.86421i	0.478639	−	0.276343i	−0.241210	−	0.970473i	$-0.577544\pi$
$617$	11.8892	−	6.86421i	0.478639	−	0.276343i	0.719849	+	0.694130i	$0.244211\pi$
$618$	32.5332	−	18.7830i	1.30868	−	0.755565i
$619$	16.8604	−	16.8604i	0.677679	−	0.677679i	−0.281796	−	0.959474i	$-0.590930\pi$
$619$	16.8604	−	16.8604i	0.677679	−	0.677679i	0.959474	+	0.281796i	$0.0909301\pi$
$620$	−6.28323	−	7.66861i	−0.252341	−	0.307979i
$621$	15.5814	+	8.99592i	0.625260	+	0.360994i
$622$	4.69560	−	8.13301i	0.188276	−	0.326104i
$623$	0.0452127	−	0.0452127i	0.00181141	−	0.00181141i
$624$		0			0
$625$	−19.8823	+	15.1557i	−0.795292	+	0.606227i
$626$	−6.02379	−	22.4811i	−0.240759	−	0.898526i
$627$	−4.32898	−	16.1560i	−0.172883	−	0.645207i
$628$	−35.2894	−	9.45576i	−1.40820	−	0.377326i
$629$	2.84678	+	2.84678i	0.113509	+	0.113509i
$630$	0.0866830	−	0.872967i	0.00345353	−	0.0347798i
$631$	−7.91879	+	29.5533i	−0.315242	+	1.17650i	0.608522	+	0.793537i	$0.291763\pi$
$631$	−7.91879	+	29.5533i	−0.315242	+	1.17650i	−0.923764	+	0.382962i	$0.874904\pi$
$632$	121.434			4.83038
$633$	−7.92814	+	29.5882i	−0.315115	+	1.17603i
$634$	−11.2987	+	19.5700i	−0.448729	+	0.777222i
$635$	24.4112	+	9.20995i	0.968727	+	0.365486i
$636$			33.0766i			1.31157i
$637$		0			0
$638$	−16.1607	−	16.1607i	−0.639807	−	0.639807i
$639$	−6.96776	+	1.86700i	−0.275640	+	0.0738576i
$640$	−8.31606	−	18.3930i	−0.328721	−	0.727046i
$641$	13.2495	−	7.64957i	0.523322	−	0.302140i	−0.214971	−	0.976620i	$-0.568966\pi$
$641$	13.2495	−	7.64957i	0.523322	−	0.302140i	0.738293	+	0.674480i	$0.235632\pi$
$642$			25.4452i			1.00424i
$643$	−11.1740	−	19.3539i	−0.440660	−	0.763245i	0.557079	−	0.830460i	$-0.311922\pi$
$643$	−11.1740	−	19.3539i	−0.440660	−	0.763245i	−0.997739	+	0.0672147i	$0.978589\pi$
$644$	−1.75062	−	0.469078i	−0.0689842	−	0.0184843i
$645$	9.18116	+	6.59022i	0.361508	+	0.259490i
$646$	−25.1710	−	43.5974i	−0.990340	−	1.71532i
$647$	−4.51668	+	1.21024i	−0.177569	+	0.0475795i	−0.346508	−	0.938047i	$-0.612633\pi$
$647$	−4.51668	+	1.21024i	−0.177569	+	0.0475795i	0.168939	+	0.985627i	$0.445966\pi$
$648$	−22.9452	−	13.2474i	−0.901373	−	0.520408i
$649$	2.38033			0.0934361
$650$		0			0
$651$	0.128662			0.00504265
$652$	−89.2199	−	51.5111i	−3.49412	−	2.01733i
$653$	−23.6714	+	6.34274i	−0.926335	+	0.248211i	−0.690291	−	0.723532i	$-0.742518\pi$
$653$	−23.6714	+	6.34274i	−0.926335	+	0.248211i	−0.236044	+	0.971742i	$0.575851\pi$
$654$	−8.12969	−	14.0810i	−0.317896	−	0.550612i
$655$	13.5583	+	9.73212i	0.529766	+	0.380265i
$656$	−58.5387	−	15.6854i	−2.28555	−	0.612412i
$657$	−5.97141	−	10.3428i	−0.232967	−	0.403510i
$658$		−	0.102733i		−	0.00400494i
$659$	−35.2803	+	20.3691i	−1.37433	+	0.793467i	−0.991469	−	0.130341i	$-0.958393\pi$
$659$	−35.2803	+	20.3691i	−1.37433	+	0.793467i	−0.382856	+	0.923808i	$0.625059\pi$
$660$	11.1160	+	24.5857i	0.432690	+	0.956997i
$661$	−16.5152	+	4.42523i	−0.642367	+	0.172122i	−0.565275	−	0.824902i	$-0.691230\pi$
$661$	−16.5152	+	4.42523i	−0.642367	+	0.172122i	−0.0770916	+	0.997024i	$0.524563\pi$
$662$	−33.7389	−	33.7389i	−1.31130	−	1.31130i
$663$		0			0
$664$			68.3547i			2.65268i
$665$	1.63592	+	0.617206i	0.0634381	+	0.0239342i
$666$	2.57515	−	4.46029i	0.0997850	−	0.172833i
$667$	−3.87071	+	14.4457i	−0.149875	+	0.559340i
$668$	12.7589			0.493657
$669$	3.26496	−	12.1850i	0.126231	−	0.471099i
$670$	0.0844984	−	0.850967i	0.00326446	−	0.0328757i
$671$	−3.64628	−	3.64628i	−0.140763	−	0.140763i
$672$	1.91233	+	0.512407i	0.0737696	+	0.0197665i
$673$	6.16392	+	23.0041i	0.237602	+	0.886742i	0.976959	+	0.213428i	$0.0684630\pi$
$673$	6.16392	+	23.0041i	0.237602	+	0.886742i	−0.739357	+	0.673314i	$0.764870\pi$
$674$	−19.4814	−	72.7057i	−0.750396	−	2.80052i
$675$	25.0933	+	12.4245i	0.965842	+	0.478218i
$676$		0			0
$677$	26.1344	−	26.1344i	1.00443	−	1.00443i	0.00443504	−	0.999990i	$-0.498588\pi$
$677$	26.1344	−	26.1344i	1.00443	−	1.00443i	0.999990	−	0.00443504i	$-0.00141172\pi$
$678$	−10.5080	+	18.2004i	−0.403557	+	0.698981i
$679$	1.45598	+	0.840613i	0.0558756	+	0.0322598i
$680$	30.9686	+	37.7968i	1.18759	+	1.44944i
$681$	8.41509	−	8.41509i	0.322467	−	0.322467i
$682$	3.75440	−	2.16761i	0.143764	−	0.0830019i
$683$	23.1988	−	13.3938i	0.887676	−	0.512500i	0.0144941	−	0.999895i	$-0.495386\pi$
$683$	23.1988	−	13.3938i	0.887676	−	0.512500i	0.873181	+	0.487395i	$0.162053\pi$
$684$	−32.5667	+	32.5667i	−1.24522	+	1.24522i
$685$	−4.08406	+	41.1298i	−0.156044	+	1.57149i
$686$	3.60610	+	2.08198i	0.137682	+	0.0794905i
$687$	−11.4885	+	19.8987i	−0.438314	+	0.759182i
$688$	30.7796	−	30.7796i	1.17346	−	1.17346i
$689$		0			0
$690$	14.3966	−	20.0566i	0.548068	−	0.763541i
$691$	10.4473	+	38.9899i	0.397435	+	1.48325i	0.817593	+	0.575796i	$0.195308\pi$
$691$	10.4473	+	38.9899i	0.397435	+	1.48325i	−0.420158	+	0.907451i	$0.638025\pi$
$692$	−0.102532	−	0.382655i	−0.00389769	−	0.0145464i
$693$	0.264991	+	0.0710042i	0.0100662	+	0.00269723i
$694$	13.4464	+	13.4464i	0.510419	+	0.510419i
$695$	24.2768	+	2.41062i	0.920873	+	0.0914399i
$696$	12.5092	−	46.6850i	0.474160	−	1.76959i
$697$	14.8102			0.560976
$698$	2.50548	−	9.35058i	0.0948339	−	0.353925i
$699$	10.8801	−	18.8449i	0.411524	−	0.712780i
$700$	−2.76553	−	0.554686i	−0.104527	−	0.0209652i
$701$		−	24.9781i		−	0.943410i	−0.881756	−	0.471705i	$-0.843639\pi$
$701$		−	24.9781i		−	0.943410i	0.881756	−	0.471705i	$-0.156361\pi$
$702$		0			0
$703$	7.25852	+	7.25852i	0.273760	+	0.273760i
$704$	24.4519	−	6.55185i	0.921564	−	0.246932i
$705$	0.936386	+	0.353284i	0.0352663	+	0.0133054i
$706$	−4.04624	+	2.33610i	−0.152282	+	0.0879202i
$707$		−	0.933677i		−	0.0351145i
$708$	4.18306	+	7.24528i	0.157209	+	0.272294i
$709$	9.85779	+	2.64139i	0.370217	+	0.0991993i	0.439130	−	0.898423i	$-0.355287\pi$
$709$	9.85779	+	2.64139i	0.370217	+	0.0991993i	−0.0689135	+	0.997623i	$0.521953\pi$
$710$	5.25742	+	32.0025i	0.197307	+	1.20103i
$711$	9.99535	+	17.3124i	0.374855	+	0.649268i
$712$	4.40087	−	1.17921i	0.164930	−	0.0441927i
$713$	−2.45675	−	1.41841i	−0.0920061	−	0.0531198i
$714$	−1.05394			−0.0394428
$715$		0			0
$716$	106.570			3.98272
$717$	28.9355	+	16.7059i	1.08061	+	0.623893i
$718$	31.0572	−	8.32175i	1.15904	−	0.310565i
$719$	−14.2117	−	24.6153i	−0.530005	−	0.917996i	−0.999387	−	0.0350008i	$-0.988857\pi$
$719$	−14.2117	−	24.6153i	−0.530005	−	0.917996i	0.469382	−	0.882995i	$-0.344477\pi$
$720$	19.1944	−	26.7407i	0.715333	−	0.996566i
$721$	−1.18623	−	0.317850i	−0.0441776	−	0.0118373i
$722$	−39.0065	−	67.5612i	−1.45167	−	2.51437i
$723$			7.09498i			0.263865i
$724$	97.9570	−	56.5555i	3.64054	−	2.10187i
$725$	−4.57713	+	22.8204i	−0.169990	+	0.847530i
$726$	25.1183	−	6.73044i	0.932229	−	0.249790i
$727$	−8.56116	−	8.56116i	−0.317516	−	0.317516i	0.530296	−	0.847812i	$-0.322081\pi$
$727$	−8.56116	−	8.56116i	−0.317516	−	0.317516i	−0.847812	+	0.530296i	$0.822081\pi$
$728$		0			0
$729$		−	26.1513i		−	0.968566i
$730$	−48.9255	+	22.1208i	−1.81081	+	0.818728i
$731$	−5.31873	+	9.21232i	−0.196720	+	0.340730i
$732$	4.69082	−	17.5064i	0.173378	−	0.647054i
$733$	−17.2200			−0.636036			−0.318018	−	0.948085i	$-0.603017\pi$
$733$	−17.2200			−0.636036			−0.318018	+	0.948085i	$0.603017\pi$
$734$	9.60893	−	35.8610i	0.354672	−	1.32365i
$735$	−15.6747	+	12.8430i	−0.578169	+	0.473720i
$736$	−30.8663	−	30.8663i	−1.13775	−	1.13775i
$737$	0.258313	+	0.0692148i	0.00951508	+	0.00254956i
$738$	−4.90365	−	18.3007i	−0.180506	−	0.673656i
$739$	4.22013	+	15.7497i	0.155240	+	0.579364i	0.999085	+	0.0427762i	$0.0136202\pi$
$739$	4.22013	+	15.7497i	0.155240	+	0.579364i	−0.843845	+	0.536588i	$0.819713\pi$
$740$	−13.4526	−	9.65626i	−0.494528	−	0.354971i
$741$		0			0
$742$	1.06915	−	1.06915i	0.0392498	−	0.0392498i
$743$	16.5599	−	28.6826i	0.607525	−	1.05226i	−0.384122	−	0.923282i	$-0.625496\pi$
$743$	16.5599	−	28.6826i	0.607525	−	1.05226i	0.991647	−	0.128982i	$-0.0411708\pi$
$744$	7.93963	+	4.58395i	0.291081	+	0.168056i
$745$	−24.0786	+	19.7287i	−0.882171	+	0.722802i
$746$	−54.1344	+	54.1344i	−1.98200	+	1.98200i
$747$	−9.74510	+	5.62634i	−0.356555	+	0.205857i
$748$	−21.9940	+	12.6982i	−0.804179	+	0.464293i
$749$	0.588194	−	0.588194i	0.0214921	−	0.0214921i
$750$	20.3679	−	32.5802i	0.743732	−	1.18966i
$751$	−18.9961	−	10.9674i	−0.693176	−	0.400205i	0.111625	−	0.993750i	$-0.464395\pi$
$751$	−18.9961	−	10.9674i	−0.693176	−	0.400205i	−0.804801	+	0.593545i	$0.797728\pi$
$752$	1.92736	−	3.33829i	0.0702836	−	0.121735i
$753$	11.9843	−	11.9843i	0.436732	−	0.436732i
$754$		0			0
$755$	−4.35528	−	26.5111i	−0.158505	−	0.964838i
$756$	0.817652	+	3.05152i	0.0297377	+	0.110983i
$757$	0.762791	+	2.84678i	0.0277241	+	0.103468i	0.978401	−	0.206714i	$-0.0662768\pi$
$757$	0.762791	+	2.84678i	0.0277241	+	0.103468i	−0.950677	+	0.310181i	$0.899610\pi$
$758$	−24.2556	−	6.49926i	−0.881002	−	0.236064i
$759$	5.45935	+	5.45935i	0.198162	+	0.198162i
$760$	78.9615	+	96.3715i	2.86423	+	3.49576i
$761$	5.70396	−	21.2875i	0.206768	−	0.771670i	−0.782135	−	0.623109i	$-0.785869\pi$
$761$	5.70396	−	21.2875i	0.206768	−	0.771670i	0.988903	−	0.148561i	$-0.0474640\pi$
$762$	−40.0993			−1.45265
$763$	−0.137572	+	0.513426i	−0.00498044	+	0.0185873i
$764$	49.2241	−	85.2587i	1.78087	−	3.08455i
$765$	−2.83951	+	7.52619i	−0.102663	+	0.272110i
$766$			55.8361i			2.01744i
$767$		0			0
$768$	−3.12197	−	3.12197i	−0.112654	−	0.112654i
$769$	20.4038	−	5.46718i	0.735780	−	0.197152i	0.128578	−	0.991699i	$-0.458959\pi$
$769$	20.4038	−	5.46718i	0.735780	−	0.197152i	0.607202	+	0.794548i	$0.292292\pi$
$770$	0.435388	−	1.15400i	0.0156903	−	0.0415874i
$771$	19.5984	−	11.3152i	0.705820	−	0.407506i
$772$		−	83.9143i		−	3.02014i
$773$	−9.34781	−	16.1909i	−0.336217	−	0.582346i	0.647500	−	0.762065i	$-0.275814\pi$
$773$	−9.34781	−	16.1909i	−0.336217	−	0.582346i	−0.983718	+	0.179719i	$0.942481\pi$
$774$	13.1445	+	3.52206i	0.472470	+	0.126598i
$775$	−3.95652	−	1.95899i	−0.142122	−	0.0703691i
$776$	59.8985	+	103.747i	2.15023	+	3.72431i
$777$	0.207583	−	0.0556218i	0.00744702	−	0.00199542i
$778$	0.138788	+	0.0801293i	0.00497579	+	0.00287278i
$779$	37.7619			1.35296
$780$		0			0
$781$	−10.1421			−0.362912
$782$	20.1246	+	11.6190i	0.719656	+	0.415493i
$783$	25.1803	−	6.74705i	0.899872	−	0.241120i
$784$	39.0246	+	67.5927i	1.39374	+	2.41402i
$785$	−16.0544	+	2.63744i	−0.573008	+	0.0941344i
$786$	−24.7764	−	6.63883i	−0.883747	−	0.236799i
$787$	21.6615	+	37.5189i	0.772150	+	1.33740i	0.936382	+	0.350981i	$0.114152\pi$
$787$	21.6615	+	37.5189i	0.772150	+	1.33740i	−0.164232	+	0.986422i	$0.552515\pi$
$788$		−	76.2534i		−	2.71642i
$789$	23.4169	−	13.5198i	0.833665	−	0.481317i
$790$	81.8948	−	37.0273i	2.91369	−	1.31737i
$791$	0.663626	−	0.177818i	0.0235958	−	0.00632248i
$792$	13.8227	+	13.8227i	0.491168	+	0.491168i
$793$		0			0
$794$		−	21.7710i		−	0.772625i
$795$	6.06840	+	13.4217i	0.215224	+	0.476020i
$796$	35.0157	−	60.6489i	1.24110	−	2.14964i
$797$	9.10089	−	33.9650i	0.322370	−	1.20310i	−0.594559	−	0.804052i	$-0.702673\pi$
$797$	9.10089	−	33.9650i	0.322370	−	1.20310i	0.916929	−	0.399050i	$-0.130660\pi$
$798$	−2.68726			−0.0951280
$799$	−0.243809	+	0.909909i	−0.00862535	+	0.0321903i
$800$	−51.0047	−	44.8741i	−1.80329	−	1.58654i
$801$	0.530356	+	0.530356i	0.0187392	+	0.0187392i
$802$	23.0319	+	6.17139i	0.813286	+	0.217919i
$803$	−4.34591	−	16.2191i	−0.153364	−	0.572361i
$804$	0.243268	+	0.907890i	0.00857942	+	0.0320188i
$805$	−0.796423	+	0.130837i	−0.0280702	+	0.00461141i
$806$		0			0
$807$	−9.69052	+	9.69052i	−0.341122	+	0.341122i
$808$	33.2649	−	57.6165i	1.17026	−	2.02694i
$809$	17.8779	+	10.3218i	0.628554	+	0.362896i	0.780192	−	0.625540i	$-0.215121\pi$
$809$	17.8779	+	10.3218i	0.628554	+	0.362896i	−0.151638	+	0.988436i	$0.548455\pi$
$810$	−19.5136	−	1.93764i	−0.685637	−	0.0680817i
$811$	−22.0471	+	22.0471i	−0.774178	+	0.774178i	−0.978834	−	0.204656i	$-0.934392\pi$
$811$	−22.0471	+	22.0471i	−0.774178	+	0.774178i	0.204656	+	0.978834i	$0.434392\pi$
$812$	−2.27416	+	1.31299i	−0.0798075	+	0.0460769i
$813$	−8.88514	+	5.12984i	−0.311615	+	0.179911i
$814$	5.12029	−	5.12029i	0.179466	−	0.179466i
$815$	−45.6539	−	4.53330i	−1.59919	−	0.158794i
$816$	−34.2477	−	19.7729i	−1.19891	−	0.692190i
$817$	−13.5613	+	23.4889i	−0.474450	+	0.821772i
$818$	−67.1180	+	67.1180i	−2.34672	+	2.34672i
$819$		0			0
$820$	−60.1111	+	9.87512i	−2.09917	+	0.344854i
$821$	−9.49818	−	35.4477i	−0.331489	−	1.23713i	−0.907626	−	0.419780i	$-0.862107\pi$
$821$	−9.49818	−	35.4477i	−0.331489	−	1.23713i	0.576137	−	0.817353i	$-0.304559\pi$
$822$	−16.4412	−	61.3594i	−0.573453	−	2.14016i
$823$	−22.8038	−	6.11025i	−0.794889	−	0.212990i	−0.161550	−	0.986865i	$-0.551649\pi$
$823$	−22.8038	−	6.11025i	−0.794889	−	0.212990i	−0.633339	+	0.773875i	$0.718316\pi$
$824$	−61.8772	−	61.8772i	−2.15559	−	2.15559i
$825$	9.02125	+	7.93692i	0.314079	+	0.276328i
$826$	0.0989816	−	0.369404i	0.00344401	−	0.0128532i
$827$	−4.44429			−0.154543			−0.0772716	−	0.997010i	$-0.524621\pi$
$827$	−4.44429			−0.154543			−0.0772716	+	0.997010i	$0.524621\pi$
$828$	5.50240	−	20.5352i	0.191222	−	0.713649i
$829$	−14.6685	+	25.4065i	−0.509457	+	0.882406i	0.490483	+	0.871451i	$0.336820\pi$
$829$	−14.6685	+	25.4065i	−0.509457	+	0.882406i	−0.999940	+	0.0109548i	$0.996513\pi$
$830$	20.8425	+	46.0982i	0.723454	+	1.60009i
$831$		−	13.2474i		−	0.459548i
$832$		0			0
$833$	−13.4870	−	13.4870i	−0.467296	−	0.467296i
$834$	−36.2174	+	9.70441i	−1.25410	+	0.336036i
$835$	5.17728	−	2.34082i	0.179167	−	0.0810073i
$836$	−56.0786	+	32.3770i	−1.93952	+	1.11978i
$837$			4.94486i			0.170919i
$838$	17.3304	+	30.0171i	0.598668	+	1.03692i
$839$	8.19766	+	2.19656i	0.283015	+	0.0758336i	0.397534	−	0.917587i	$-0.369866\pi$
$839$	8.19766	+	2.19656i	0.283015	+	0.0758336i	−0.114519	+	0.993421i	$0.536533\pi$
$840$	2.57384	−	0.422834i	0.0888061	−	0.0145892i
$841$	−3.66554	−	6.34891i	−0.126398	−	0.218928i
$842$	−49.9236	+	13.3770i	−1.72048	+	0.461001i
$843$	−19.8180	−	11.4419i	−0.682568	−	0.394081i
$844$	118.591			4.08208
$845$		0			0
$846$	1.20508			0.0414316
$847$	−0.736220	−	0.425057i	−0.0252968	−	0.0146051i
$848$	54.8002	−	14.6837i	1.88185	−	0.504239i
$849$	−5.36067	−	9.28495i	−0.183978	−	0.318659i
$850$	32.4101	+	16.0472i	1.11166	+	0.550415i
$851$	−4.57693	−	1.22638i	−0.156895	−	0.0420399i
$852$	−17.8231	−	30.8705i	−0.610610	−	1.05761i
$853$		−	34.3415i		−	1.17583i	−0.808923	−	0.587915i	$-0.799949\pi$
$853$		−	34.3415i		−	1.17583i	0.808923	−	0.587915i	$-0.200051\pi$
$854$	−0.717491	+	0.414244i	−0.0245521	+	0.0141751i
$855$	−7.23998	+	19.1897i	−0.247602	+	0.656274i
$856$	57.2531	−	15.3409i	1.95687	−	0.524342i
$857$	24.6090	+	24.6090i	0.840626	+	0.840626i	0.988940	−	0.148314i	$-0.0473847\pi$
$857$	24.6090	+	24.6090i	0.840626	+	0.840626i	−0.148314	+	0.988940i	$0.547385\pi$
$858$		0			0
$859$			12.8606i			0.438798i	0.975635	+	0.219399i	$0.0704097\pi$
$859$			12.8606i			0.438798i	−0.975635	+	0.219399i	$0.929590\pi$
$860$	15.4449	−	40.9371i	0.526667	−	1.39594i
$861$	0.395284	−	0.684653i	0.0134713	−	0.0233329i
$862$	15.2379	−	56.8688i	0.519007	−	1.93696i
$863$	−2.75373			−0.0937379			−0.0468690	−	0.998901i	$-0.514924\pi$
$863$	−2.75373			−0.0937379			−0.0468690	+	0.998901i	$0.514924\pi$
$864$	−19.6933	+	73.4965i	−0.669980	+	2.50040i
$865$	−0.111809	−	0.136462i	−0.00380163	−	0.00463984i
$866$	−0.343907	−	0.343907i	−0.0116864	−	0.0116864i
$867$	−11.9624	−	3.20532i	−0.406264	−	0.108858i
$868$	−0.128921	−	0.481140i	−0.00437586	−	0.0163309i
$869$	7.27447	+	27.1487i	0.246770	+	0.920957i
$870$	−5.79888	−	35.2985i	−0.196601	−	1.19673i
$871$		0			0
$872$	−26.7817	+	26.7817i	−0.906944	+	0.906944i
$873$	−9.86060	+	17.0791i	−0.333731	+	0.578039i
$874$	51.3123	+	29.6252i	1.73566	+	1.00209i
$875$	−1.22395	+	0.282299i	−0.0413772	+	0.00954346i
$876$	41.7308	−	41.7308i	1.40995	−	1.40995i
$877$	40.9311	−	23.6316i	1.38214	−	0.797981i	0.389730	−	0.920929i	$-0.372568\pi$
$877$	40.9311	−	23.6316i	1.38214	−	0.797981i	0.992413	+	0.122948i	$0.0392349\pi$
$878$	−39.6847	+	22.9119i	−1.33929	+	0.773241i
$879$	−5.84953	+	5.84953i	−0.197300	+	0.197300i
$880$	35.7980	−	29.3309i	1.20675	−	0.988745i
$881$	−35.7854	−	20.6607i	−1.20564	−	0.696077i	−0.243837	−	0.969816i	$-0.578406\pi$
$881$	−35.7854	−	20.6607i	−1.20564	−	0.696077i	−0.961804	+	0.273739i	$0.911739\pi$
$882$	−12.2001	+	21.1311i	−0.410798	+	0.711523i
$883$	13.4808	−	13.4808i	0.453666	−	0.453666i	−0.442903	−	0.896569i	$-0.646051\pi$
$883$	13.4808	−	13.4808i	0.453666	−	0.453666i	0.896569	+	0.442903i	$0.146051\pi$
$884$		0			0
$885$	3.02665	+	2.17252i	0.101740	+	0.0730285i
$886$	23.7108	+	88.4897i	0.796578	+	2.97287i
$887$	5.93341	+	22.1438i	0.199225	+	0.743516i	0.991133	+	0.132876i	$0.0424212\pi$
$887$	5.93341	+	22.1438i	0.199225	+	0.743516i	−0.791908	+	0.610640i	$0.790912\pi$
$888$	14.7915	+	3.96337i	0.496371	+	0.133002i
$889$	0.926941	+	0.926941i	0.0310886	+	0.0310886i
$890$	2.60837	−	2.13716i	0.0874329	−	0.0716377i
$891$	1.58717	−	5.92339i	0.0531721	−	0.198441i
$892$	−48.8381			−1.63522
$893$	−0.621647	+	2.32002i	−0.0208026	+	0.0776364i
$894$	23.9211	−	41.4326i	0.800042	−	1.38571i
$895$	43.2438	−	19.5519i	1.44548	−	0.653549i
$896$		−	1.01420i		−	0.0338819i
$897$		0			0
$898$	−69.6712	−	69.6712i	−2.32496	−	2.32496i
$899$	−3.97024	+	1.06382i	−0.132415	+	0.0354805i
$900$	6.50661	−	32.4404i	0.216887	−	1.08135i
$901$	−12.0069	+	6.93217i	−0.400007	+	0.230944i
$902$		−	26.6379i		−	0.886946i
$903$	0.283915	+	0.491754i	0.00944808	+	0.0163646i
$904$	47.2871	+	12.6705i	1.57275	+	0.421416i
$905$	29.3728	−	40.9207i	0.976384	−	1.36025i
$906$	20.6458	+	35.7595i	0.685910	+	1.18803i
$907$	23.2963	−	6.24222i	0.773541	−	0.207270i	0.149606	−	0.988746i	$-0.452200\pi$
$907$	23.2963	−	6.24222i	0.773541	−	0.207270i	0.623935	+	0.781476i	$0.285533\pi$
$908$	−39.9008	−	23.0367i	−1.32416	−	0.764501i
$909$	10.9523			0.363264
$910$		0			0
$911$	58.5135			1.93864			0.969320	−	0.245803i	$-0.0790515\pi$
$911$	58.5135			1.93864			0.969320	+	0.245803i	$0.0790515\pi$
$912$	−87.3221	−	50.4154i	−2.89152	−	1.66942i
$913$	−15.2819	+	4.09477i	−0.505757	+	0.135517i
$914$	12.4895	+	21.6324i	0.413116	+	0.715537i
$915$	−1.30838	−	7.96429i	−0.0432538	−	0.263291i
$916$	85.9241	+	23.0233i	2.83901	+	0.760711i
$917$	0.419271	+	0.726199i	0.0138456	+	0.0239812i
$918$		−	40.5061i		−	1.33690i
$919$	−38.8451	+	22.4272i	−1.28138	+	0.739806i	−0.977101	−	0.212776i	$-0.931749\pi$
$919$	−38.8451	+	22.4272i	−1.28138	+	0.739806i	−0.304281	+	0.952582i	$0.598416\pi$
$920$	−53.8081	−	20.3010i	−1.77400	−	0.669303i
$921$	33.2562	−	8.91097i	1.09583	−	0.293626i
$922$	61.6169	+	61.6169i	2.02924	+	2.02924i
$923$		0			0
$924$			1.35567i			0.0445981i
$925$	−7.23035	−	1.45020i	−0.237733	−	0.0476824i
$926$	−24.7394	+	42.8498i	−0.812986	+	1.40813i
$927$	3.72846	−	13.9148i	0.122459	−	0.457022i
$928$	−63.2473			−2.07619
$929$	7.26384	−	27.1090i	0.238319	−	0.889418i	−0.738306	−	0.674466i	$-0.764374\pi$
$929$	7.26384	−	27.1090i	0.238319	−	0.889418i	0.976625	−	0.214952i	$-0.0689595\pi$
$930$	6.75219	+	0.670472i	0.221413	+	0.0219856i
$931$	−34.3881	−	34.3881i	−1.12702	−	1.12702i
$932$	−81.3738	−	21.8041i	−2.66549	−	0.714215i
$933$	1.18971	+	4.44006i	0.0389493	+	0.145361i
$934$	−11.8012	−	44.0428i	−0.386148	−	1.44113i
$935$	−6.59497	+	9.18779i	−0.215679	+	0.300473i
$936$		0			0
$937$	20.7545	−	20.7545i	0.678019	−	0.678019i	−0.281533	−	0.959552i	$-0.590843\pi$
$937$	20.7545	−	20.7545i	0.678019	−	0.678019i	0.959552	+	0.281533i	$0.0908428\pi$
$938$	0.0214829	−	0.0372095i	0.000701442	−	0.00121493i
$939$	9.86572	+	5.69597i	0.321955	+	0.185881i
$940$	0.382857	−	3.85567i	0.0124874	−	0.125758i
$941$	−6.70533	+	6.70533i	−0.218588	+	0.218588i	−0.807903	−	0.589315i	$-0.799398\pi$
$941$	−6.70533	+	6.70533i	−0.218588	+	0.218588i	0.589315	+	0.807903i	$0.299398\pi$
$942$	21.6550	−	12.5025i	0.705559	−	0.407355i
$943$	−15.0956	+	8.71547i	−0.491582	+	0.283815i
$944$	10.1467	−	10.1467i	0.330249	−	0.330249i
$945$	0.891632	+	1.08823i	0.0290048	+	0.0354000i
$946$	16.5695	+	9.56639i	0.538720	+	0.311030i
$947$	−2.25542	+	3.90651i	−0.0732915	+	0.126945i	−0.900342	−	0.435183i	$-0.856684\pi$
$947$	−2.25542	+	3.90651i	−0.0732915	+	0.126945i	0.827051	+	0.562128i	$0.190017\pi$
$948$	−69.8518	+	69.8518i	−2.26868	+	2.26868i
$949$		0			0
$950$	82.6367	+	40.9160i	2.68109	+	1.32749i
$951$	−2.86272	−	10.6838i	−0.0928302	−	0.346447i
$952$	0.635422	+	2.37143i	0.0205941	+	0.0768584i
$953$	5.54756	+	1.48646i	0.179703	+	0.0481513i	0.347548	−	0.937662i	$-0.387014\pi$
$953$	5.54756	+	1.48646i	0.179703	+	0.0481513i	−0.167845	+	0.985813i	$0.553681\pi$
$954$	12.5414	+	12.5414i	0.406043	+	0.406043i
$955$	4.33202	−	43.6270i	0.140181	−	1.41174i
$956$	33.4791	−	124.946i	1.08279	−	4.04103i
$957$	11.1866			0.361612
$958$	−22.6066	+	84.3690i	−0.730386	+	2.72584i
$959$	−1.03833	+	1.79845i	−0.0335296	+	0.0580749i
$960$	37.0710	+	13.9863i	1.19646	+	0.451406i
$961$			30.2203i			0.974849i
$962$		0			0
$963$	6.89966	+	6.89966i	0.222338	+	0.222338i
$964$	26.5322	−	7.10927i	0.854543	−	0.228974i
$965$	−15.3954	−	34.0505i	−0.495595	−	1.09613i
$966$	1.07426	−	0.620222i	0.0345636	−	0.0199553i
$967$			17.6414i			0.567310i	0.958926	+	0.283655i	$0.0915470\pi$
$967$			17.6414i			0.567310i	−0.958926	+	0.283655i	$0.908453\pi$
$968$	−30.2877	−	52.4599i	−0.973485	−	1.68612i
$969$	23.8012	+	6.37750i	0.764604	+	0.204875i
$970$	72.0297	+	51.7028i	2.31273	+	1.66008i
$971$	−16.6987	−	28.9229i	−0.535886	−	0.928181i	−0.999120	−	0.0419454i	$-0.986644\pi$
$971$	−16.6987	−	28.9229i	−0.535886	−	0.928181i	0.463234	−	0.886236i	$-0.346689\pi$
$972$	−60.6650	+	16.2551i	−1.94583	+	0.521384i
$973$	1.06153	+	0.612876i	0.0340312	+	0.0196479i
$974$	−87.4056			−2.80065
$975$		0			0
$976$	−31.0864			−0.995050
$977$	−13.2886	−	7.67217i	−0.425139	−	0.245454i	0.272134	−	0.962259i	$-0.412270\pi$
$977$	−13.2886	−	7.67217i	−0.425139	−	0.245454i	−0.697274	+	0.716805i	$0.745604\pi$
$978$	68.1088	−	18.2497i	2.17788	−	0.583561i
$979$	0.527266	+	0.913252i	0.0168515	+	0.0291877i
$980$	63.7334	+	45.7477i	2.03589	+	1.46136i
$981$	−6.02261	−	1.61375i	−0.192287	−	0.0515232i
$982$	28.2143	+	48.8686i	0.900354	+	1.55946i
$983$		−	4.80751i		−	0.153336i	−0.997057	−	0.0766679i	$-0.975572\pi$
$983$		−	4.80751i		−	0.153336i	0.997057	−	0.0766679i	$-0.0244281\pi$
$984$	48.7854	−	28.1663i	1.55522	−	0.897908i
$985$	−13.9899	−	30.9419i	−0.445754	−	0.985891i
$986$	32.5225	−	8.71437i	1.03573	−	0.277522i
$987$	0.0355565	+	0.0355565i	0.00113177	+	0.00113177i
$988$		0			0
$989$		−	12.5198i		−	0.398108i
$990$	13.5368	+	5.10721i	0.430227	+	0.162318i
$991$	−0.219558	+	0.380286i	−0.00697450	+	0.0120802i	−0.869492	−	0.493948i	$-0.835553\pi$
$991$	−0.219558	+	0.380286i	−0.00697450	+	0.0120802i	0.862517	+	0.506028i	$0.168887\pi$
$992$	3.10509	−	11.5884i	0.0985867	−	0.367931i
$993$	23.3545			0.741131
$994$	−0.421739	+	1.57395i	−0.0133767	+	0.0499227i
$995$	3.08159	−	31.0341i	0.0976931	−	0.983848i
$996$	−39.3193	−	39.3193i	−1.24588	−	1.24588i
$997$	6.34461	+	1.70003i	0.200936	+	0.0538406i	0.357883	−	0.933766i	$-0.383499\pi$
$997$	6.34461	+	1.70003i	0.200936	+	0.0538406i	−0.156947	+	0.987607i	$0.550165\pi$
$998$	−14.4704	−	54.0044i	−0.458053	−	1.70948i
$999$	2.13771	+	7.97806i	0.0676343	+	0.252415i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.f.188.5		20
5.2	odd	4		845.2.o.e.357.1		20
13.2	odd	12		845.2.o.f.258.5		20
13.3	even	3		65.2.t.a.28.1	yes	20
13.4	even	6		845.2.f.d.408.10		20
13.5	odd	4		845.2.o.g.488.5		20
13.6	odd	12		845.2.k.d.268.1		20
13.7	odd	12		845.2.k.e.268.10		20
13.8	odd	4		65.2.o.a.33.1	yes	20
13.9	even	3		845.2.f.e.408.1		20
13.10	even	6		845.2.t.g.418.5		20
13.11	odd	12		845.2.o.e.258.1		20
13.12	even	2		845.2.t.e.188.1		20
39.8	even	4		585.2.cf.a.163.5		20
39.29	odd	6		585.2.dp.a.28.5		20
65.2	even	12		845.2.t.e.427.1		20
65.3	odd	12		325.2.s.b.132.5		20
65.7	even	12		845.2.f.e.437.10		20
65.8	even	4		325.2.x.b.7.5		20
65.12	odd	4		845.2.o.f.357.5		20
65.17	odd	12		845.2.k.d.577.1		20
65.22	odd	12		845.2.k.e.577.10		20
65.29	even	6		325.2.x.b.93.5		20
65.32	even	12		845.2.f.d.437.1		20
65.34	odd	4		325.2.s.b.293.5		20
65.37	even	12	inner	845.2.t.f.427.5		20
65.42	odd	12		65.2.o.a.2.1	✓	20
65.47	even	4		65.2.t.a.7.1	yes	20
65.57	even	4		845.2.t.g.657.5		20
65.62	odd	12		845.2.o.g.587.5		20
195.47	odd	4		585.2.dp.a.397.5		20
195.107	even	12		585.2.cf.a.262.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.1	✓	20	65.42	odd	12
65.2.o.a.33.1	yes	20	13.8	odd	4
65.2.t.a.7.1	yes	20	65.47	even	4
65.2.t.a.28.1	yes	20	13.3	even	3
325.2.s.b.132.5		20	65.3	odd	12
325.2.s.b.293.5		20	65.34	odd	4
325.2.x.b.7.5		20	65.8	even	4
325.2.x.b.93.5		20	65.29	even	6
585.2.cf.a.163.5		20	39.8	even	4
585.2.cf.a.262.5		20	195.107	even	12
585.2.dp.a.28.5		20	39.29	odd	6
585.2.dp.a.397.5		20	195.47	odd	4
845.2.f.d.408.10		20	13.4	even	6
845.2.f.d.437.1		20	65.32	even	12
845.2.f.e.408.1		20	13.9	even	3
845.2.f.e.437.10		20	65.7	even	12
845.2.k.d.268.1		20	13.6	odd	12
845.2.k.d.577.1		20	65.17	odd	12
845.2.k.e.268.10		20	13.7	odd	12
845.2.k.e.577.10		20	65.22	odd	12
845.2.o.e.258.1		20	13.11	odd	12
845.2.o.e.357.1		20	5.2	odd	4
845.2.o.f.258.5		20	13.2	odd	12
845.2.o.f.357.5		20	65.12	odd	4
845.2.o.g.488.5		20	13.5	odd	4
845.2.o.g.587.5		20	65.62	odd	12
845.2.t.e.188.1		20	13.12	even	2
845.2.t.e.427.1		20	65.2	even	12
845.2.t.f.188.5		20	1.1	even	1	trivial
845.2.t.f.427.5		20	65.37	even	12	inner
845.2.t.g.418.5		20	13.10	even	6
845.2.t.g.657.5		20	65.57	even	4

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	845.2.t.f.188.5

Level	$845$
Weight	$2$
Character	845.188
Analytic conductor	$6.747$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$