LMFDB - Embedded newform 845.2.o.g.488.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [20,4,-2,-6,6,8] 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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			488.5
Root			$-2.64975i$ of defining polynomial
Character	$\chi$	$=$	845.488
Dual form			845.2.o.g.587.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32488 - 2.29475i) q^{2} +(-1.25278 + 0.335680i) q^{3} +(-2.51060 - 4.34849i) q^{4} +(1.30391 - 1.81654i) q^{5} +(-0.889471 + 3.31955i) q^{6} +(-0.0972962 + 0.0561740i) q^{7} -8.00544 q^{8} +(-1.14131 + 0.658935i) q^{9} +(-2.44100 - 5.39885i) q^{10} +(-0.479564 - 1.78976i) q^{11} +(4.60492 + 4.60492i) q^{12} +0.297695i q^{14} +(-1.02373 + 2.71342i) q^{15} +(-5.58502 + 9.67354i) q^{16} +(-0.706500 + 2.63669i) q^{17} +3.49203i q^{18} +(-6.72284 - 1.80138i) q^{19} +(-11.1728 - 1.10942i) q^{20} +(0.103034 - 0.103034i) q^{21} +(-4.74241 - 1.27073i) q^{22} +(-0.831519 - 3.10327i) q^{23} +(10.0290 - 2.68727i) q^{24} +(-1.59964 - 4.73721i) q^{25} +(3.95990 - 3.95990i) q^{27} +(0.488544 + 0.282061i) q^{28} +(4.03134 + 2.32749i) q^{29} +(4.87031 + 5.94415i) q^{30} +(0.624367 + 0.624367i) q^{31} +(6.79350 + 11.7667i) q^{32} +(1.20157 + 2.08118i) q^{33} +(5.11454 + 5.11454i) q^{34} +(-0.0248231 + 0.249988i) q^{35} +(5.73074 + 3.30864i) q^{36} +(-1.27728 - 0.737435i) q^{37} +(-13.0407 + 13.0407i) q^{38} +(-10.4384 + 14.5422i) q^{40} +(5.24069 - 1.40424i) q^{41} +(-0.0999302 - 0.372945i) q^{42} +(3.76415 + 1.00860i) q^{43} +(-6.57874 + 6.57874i) q^{44} +(-0.291181 + 2.93243i) q^{45} +(-8.22291 - 2.20332i) q^{46} -0.345095i q^{47} +(3.74956 - 13.9936i) q^{48} +(-3.49369 + 6.05125i) q^{49} +(-12.9901 - 2.60544i) q^{50} -3.54034i q^{51} +(-3.59144 - 3.59144i) q^{53} +(-3.84062 - 14.3334i) q^{54} +(-3.87647 - 1.46253i) q^{55} +(0.778898 - 0.449697i) q^{56} +9.02691 q^{57} +(10.6821 - 6.16729i) q^{58} +(0.332494 - 1.24088i) q^{59} +(14.3694 - 2.36063i) q^{60} +(1.39151 + 2.41016i) q^{61} +(2.25998 - 0.605559i) q^{62} +(0.0740300 - 0.128224i) q^{63} +13.6621 q^{64} +6.36774 q^{66} +(-0.0721643 + 0.124992i) q^{67} +(13.2394 - 3.54747i) q^{68} +(2.08342 + 3.60858i) q^{69} +(0.540774 + 0.388167i) q^{70} +(1.41668 - 5.28713i) q^{71} +(9.13667 - 5.27506i) q^{72} -9.06221 q^{73} +(-3.38447 + 1.95402i) q^{74} +(3.59418 + 5.39770i) q^{75} +(9.04509 + 33.7567i) q^{76} +(0.147197 + 0.147197i) q^{77} -15.1689i q^{79} +(10.2900 + 22.7588i) q^{80} +(-1.65480 + 2.86620i) q^{81} +(3.72089 - 13.8865i) q^{82} -8.53853i q^{83} +(-0.706718 - 0.189365i) q^{84} +(3.86845 + 4.72139i) q^{85} +(7.30152 - 7.30152i) q^{86} +(-5.83166 - 1.56259i) q^{87} +(3.83912 + 14.3278i) q^{88} +(0.549735 - 0.147301i) q^{89} +(6.34342 + 4.55329i) q^{90} +(-11.4069 + 11.4069i) q^{92} +(-0.991779 - 0.572604i) q^{93} +(-0.791908 - 0.457208i) q^{94} +(-12.0383 + 9.86348i) q^{95} +(-12.4606 - 12.4606i) q^{96} +(-7.48223 - 12.9596i) q^{97} +(9.25742 + 16.0343i) q^{98} +(1.72666 + 1.72666i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100})$ 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 + 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 10 * q^10 + 16 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 10 * q^17 - 20 * q^19 - 14 * q^20 - 4 * q^21 + 16 * q^22 - 2 * q^23 + 32 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 14 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 - 20 * q^35 + 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 - 56 * q^42 - 22 * q^43 - 36 * q^44 - 52 * q^45 - 4 * q^46 + 28 * q^48 - 18 * q^49 - 44 * q^50 - 10 * q^53 - 48 * q^54 + 26 * q^55 + 12 * q^57 + 90 * q^58 - 16 * q^59 + 92 * q^60 - 16 * q^61 - 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 28 * q^68 + 16 * q^69 - 32 * q^70 + 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 34 * q^75 + 64 * q^76 + 28 * q^77 + 34 * q^80 - 14 * q^81 + 22 * q^82 - 40 * q^84 + 6 * q^85 - 60 * q^86 + 62 * q^87 + 50 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 + 48 * q^94 + 14 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	1.32488	−	2.29475i	0.936830	−	1.62264i	0.165491	−	0.986211i	$-0.447079\pi$
$2$	1.32488	−	2.29475i	0.936830	−	1.62264i	0.771338	−	0.636425i	$-0.219588\pi$
$3$	−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
$5$	1.30391	−	1.81654i	0.583126	−	0.812382i
$5$	1.30391	−	1.81654i	0.583126	−	0.812382i
$6$	−0.889471	+	3.31955i	−0.363125	+	1.35520i
$7$	−0.0972962	+	0.0561740i	−0.0367745	+	0.0212318i	−0.518275	−	0.855214i	$-0.673425\pi$
$7$	−0.0972962	+	0.0561740i	−0.0367745	+	0.0212318i	0.481500	+	0.876446i	$0.340092\pi$
$8$	−8.00544			−2.83035
$9$	−1.14131	+	0.658935i	−0.380436	+	0.219645i
$10$	−2.44100	−	5.39885i	−0.771911	−	1.70726i
$11$	−0.479564	−	1.78976i	−0.144594	−	0.539632i	−0.999773	−	0.0212994i	$-0.993220\pi$
$11$	−0.479564	−	1.78976i	−0.144594	−	0.539632i	0.855179	−	0.518332i	$-0.173447\pi$
$12$	4.60492	+	4.60492i	1.32933	+	1.32933i
$13$		0			0
$13$		0			0
$14$			0.297695i			0.0795622i
$15$	−1.02373	+	2.71342i	−0.264326	+	0.700601i
$16$	−5.58502	+	9.67354i	−1.39626	+	2.41838i
$17$	−0.706500	+	2.63669i	−0.171351	+	0.639492i	0.825793	+	0.563973i	$0.190728\pi$
$17$	−0.706500	+	2.63669i	−0.171351	+	0.639492i	−0.997144	+	0.0755186i	$0.975939\pi$
$18$			3.49203i			0.823080i
$19$	−6.72284	−	1.80138i	−1.54233	−	0.413265i	−0.615309	−	0.788286i	$-0.710969\pi$
$19$	−6.72284	−	1.80138i	−1.54233	−	0.413265i	−0.927016	+	0.375021i	$0.877636\pi$
$20$	−11.1728	−	1.10942i	−2.49831	−	0.248075i
$21$	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	$-0.974613\pi$
$23$	−0.831519	−	3.10327i	−0.173384	−	0.647077i	0.823438	−	0.567407i	$-0.192053\pi$
$24$	10.0290	−	2.68727i	2.04717	−	0.548536i
$25$	−1.59964	−	4.73721i	−0.319928	−	0.947442i
$26$		0			0
$27$	3.95990	−	3.95990i	0.762083	−	0.762083i
$28$	0.488544	+	0.282061i	0.0923261	+	0.0533045i
$29$	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	$-0.224733\pi$
$31$	0.624367	+	0.624367i	0.112140	+	0.112140i	−0.648810	+	0.760950i	$0.724733\pi$
$32$	6.79350	+	11.7667i	1.20093	+	2.08008i
$33$	1.20157	+	2.08118i	0.209167	+	0.362288i
$34$	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
$37$	−1.27728	−	0.737435i	−0.209983	−	0.121234i	0.391321	−	0.920254i	$-0.372018\pi$
$37$	−1.27728	−	0.737435i	−0.209983	−	0.121234i	−0.601303	+	0.799021i	$0.705352\pi$
$38$	−13.0407	+	13.0407i	−2.11548	+	2.11548i
$39$		0			0
$40$	−10.4384	+	14.5422i	−1.65045	+	2.29932i
$41$	5.24069	−	1.40424i	0.818458	−	0.219305i	0.174786	−	0.984606i	$-0.444077\pi$
$41$	5.24069	−	1.40424i	0.818458	−	0.219305i	0.643672	+	0.765301i	$0.277410\pi$
$42$	−0.0999302	−	0.372945i	−0.0154196	−	0.0575466i
$43$	3.76415	+	1.00860i	0.574027	+	0.153810i	0.534143	−	0.845394i	$-0.320634\pi$
$43$	3.76415	+	1.00860i	0.574027	+	0.153810i	0.0398840	+	0.999204i	$0.487301\pi$
$44$	−6.57874	+	6.57874i	−0.991782	+	0.991782i
$45$	−0.291181	+	2.93243i	−0.0434067	+	0.437140i
$46$	−8.22291	−	2.20332i	−1.21240	−	0.324862i
$47$		−	0.345095i		−	0.0503372i	−0.999683	−	0.0251686i	$-0.991988\pi$
$47$		−	0.345095i		−	0.0503372i	0.999683	−	0.0251686i	$-0.00801227\pi$
$48$	3.74956	−	13.9936i	0.541203	−	2.01980i
$49$	−3.49369	+	6.05125i	−0.499098	+	0.864464i
$50$	−12.9901	−	2.60544i	−1.83707	−	0.368464i
$51$		−	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	$0.863421\pi$
$54$	−3.84062	−	14.3334i	−0.522642	−	1.95053i
$55$	−3.87647	−	1.46253i	−0.522703	−	0.197208i
$56$	0.778898	−	0.449697i	0.104085	−	0.0600933i
$57$	9.02691			1.19564
$58$	10.6821	−	6.16729i	1.40262	−	0.809805i
$59$	0.332494	−	1.24088i	0.0432870	−	0.161549i	−0.940899	−	0.338687i	$-0.890017\pi$
$59$	0.332494	−	1.24088i	0.0432870	−	0.161549i	0.984186	+	0.177138i	$0.0566839\pi$
$60$	14.3694	−	2.36063i	1.85508	−	0.304756i
$61$	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
$63$	0.0740300	−	0.128224i	0.00932691	−	0.0161547i
$64$	13.6621			1.70776
$65$		0			0
$66$	6.36774			0.783815
$67$	−0.0721643	+	0.124992i	−0.00881627	+	0.0152702i	−0.870400	−	0.492345i	$-0.836140\pi$
$67$	−0.0721643	+	0.124992i	−0.00881627	+	0.0152702i	0.861584	+	0.507616i	$0.169473\pi$
$68$	13.2394	−	3.54747i	1.60551	−	0.430194i
$69$	2.08342	+	3.60858i	0.250814	+	0.434422i
$70$	0.540774	+	0.388167i	0.0646349	+	0.0463948i
$71$	1.41668	−	5.28713i	0.168129	−	0.627467i	−0.829491	−	0.558520i	$-0.811369\pi$
$71$	1.41668	−	5.28713i	0.168129	−	0.627467i	0.997620	−	0.0689472i	$-0.0219640\pi$
$72$	9.13667	−	5.27506i	1.07677	−	0.621672i
$73$	−9.06221			−1.06065			−0.530326	−	0.847794i	$-0.677930\pi$
$73$	−9.06221			−1.06065			−0.530326	+	0.847794i	$0.677930\pi$
$74$	−3.38447	+	1.95402i	−0.393436	+	0.227151i
$75$	3.59418	+	5.39770i	0.415020	+	0.623272i
$76$	9.04509	+	33.7567i	1.03754	+	3.87216i
$77$	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	$-0.325414\pi$
$80$	10.2900	+	22.7588i	1.15046	+	2.54451i
$81$	−1.65480	+	2.86620i	−0.183867	+	0.318467i
$82$	3.72089	−	13.8865i	0.410903	−	1.53351i
$83$		−	8.53853i		−	0.937226i	−0.883404	−	0.468613i	$-0.844754\pi$
$83$		−	8.53853i		−	0.937226i	0.883404	−	0.468613i	$-0.155246\pi$
$84$	−0.706718	−	0.189365i	−0.0771093	−	0.0206614i
$85$	3.86845	+	4.72139i	0.419592	+	0.512107i
$86$	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
$89$	0.549735	−	0.147301i	0.0582718	−	0.0156139i	−0.229565	−	0.973293i	$-0.573730\pi$
$89$	0.549735	−	0.147301i	0.0582718	−	0.0156139i	0.287837	+	0.957679i	$0.407064\pi$
$90$	6.34342	+	4.55329i	0.668655	+	0.479959i
$91$		0			0
$92$	−11.4069	+	11.4069i	−1.18925	+	1.18925i
$93$	−0.991779	−	0.572604i	−0.102843	−	0.0593763i
$94$	−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
$97$	−7.48223	−	12.9596i	−0.759705	−	1.31585i	−0.943001	−	0.332790i	$-0.892010\pi$
$97$	−7.48223	−	12.9596i	−0.759705	−	1.31585i	0.183296	−	0.983058i	$-0.441323\pi$
$98$	9.25742	+	16.0343i	0.935140	+	1.61971i
$99$	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	0.813332	−	0.581799i	$-0.197651\pi$
$101$	7.19717	+	4.15529i	0.716146	+	0.413467i	−0.0971867	+	0.995266i	$0.530984\pi$
$102$	−8.12422	−	4.69052i	−0.804418	−	0.464431i
$103$	7.72940	−	7.72940i	0.761600	−	0.761600i	−0.215011	−	0.976612i	$-0.568979\pi$
$103$	7.72940	−	7.72940i	0.761600	−	0.761600i	0.976612	+	0.215011i	$0.0689789\pi$
$104$		0			0
$105$	−0.0528184	−	0.321512i	−0.00515455	−	0.0313764i
$106$	−12.9997	+	3.48325i	−1.26264	+	0.338324i
$107$	−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	−0.528499	−	0.848934i	$-0.677245\pi$
$109$	3.34544	−	3.34544i	0.320435	−	0.320435i	0.848934	+	0.528499i	$0.177245\pi$
$110$	−8.49200	+	6.95788i	−0.809681	+	0.663408i
$111$	1.84768	+	0.495085i	0.175374	+	0.0469914i
$112$		−	1.25493i		−	0.118580i
$113$	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
$115$	−6.72145	−	2.53590i	−0.626778	−	0.236474i
$116$		−	23.3736i		−	2.17019i
$117$		0			0
$118$	−2.40701	−	2.40701i	−0.221583	−	0.221583i
$119$	−0.0793738	−	0.296227i	−0.00727618	−	0.0271551i
$120$	8.19540	−	21.7221i	0.748134	−	1.98295i
$121$	6.55303	−	3.78340i	0.595730	−	0.343945i
$122$	7.37430			0.667638
$123$	−6.09404	+	3.51839i	−0.549481	+	0.317243i
$124$	1.14751	−	4.28258i	0.103050	−	0.384587i
$125$	−10.6911	−	3.27108i	−0.956243	−	0.292574i
$126$	−0.196161	−	0.339761i	−0.0174754	−	0.0302684i
$127$	−11.2706	+	3.01994i	−1.00010	+	0.267976i	−0.721488	−	0.692427i	$-0.756541\pi$
$127$	−11.2706	+	3.01994i	−1.00010	+	0.267976i	−0.278613	+	0.960403i	$0.589875\pi$
$128$	4.51363	−	7.81784i	0.398953	−	0.691006i
$129$	−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	$0.394280\pi$
$132$	6.03333	−	10.4500i	0.525134	−	0.909559i
$133$	0.755298	−	0.202381i	0.0654926	−	0.0175487i
$134$	0.191218	+	0.331199i	0.0165187	+	0.0286112i
$135$	−2.02997	−	12.3567i	−0.174712	−	1.06349i
$136$	5.65584	−	21.1079i	0.484984	−	1.80998i
$137$	−16.0078	+	9.24213i	−1.36764	+	0.789608i	−0.990626	−	0.136599i	$-0.956383\pi$
$137$	−16.0078	+	9.24213i	−1.36764	+	0.789608i	−0.377015	+	0.926207i	$0.623050\pi$
$138$	11.0411			0.939879
$139$	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
$141$	0.115842	+	0.432327i	0.00975562	+	0.0364085i
$142$	−10.2557	−	10.2557i	−0.860643	−	0.860643i
$143$		0			0
$144$		−	14.7207i		−	1.22672i
$145$	9.48449	−	4.28825i	0.787644	−	0.356120i
$146$	−12.0063	+	20.7955i	−0.993650	+	1.72105i
$147$	2.34553	−	8.75362i	0.193456	−	0.721987i
$148$			7.40562i			0.608738i
$149$	13.4468	+	3.60307i	1.10161	+	0.295175i	0.763419	−	0.645903i	$-0.223519\pi$
$149$	13.4468	+	3.60307i	1.10161	+	0.295175i	0.338189	+	0.941078i	$0.390186\pi$
$150$	17.1482	−	1.09648i	1.40015	−	0.0895272i
$151$	8.49593	−	8.49593i	0.691389	−	0.691389i	−0.271149	−	0.962537i	$-0.587404\pi$
$151$	8.49593	−	8.49593i	0.691389	−	0.691389i	0.962537	+	0.271149i	$0.0874035\pi$
$152$	53.8193	+	14.4208i	4.36532	+	1.16968i
$153$	−0.931075	−	3.47482i	−0.0752729	−	0.280922i
$154$	0.532801	−	0.142763i	0.0429343	−	0.0115042i
$155$	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	$0.343770\pi$
$158$	−34.8090	−	20.0970i	−2.76926	−	1.59883i
$159$	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
$162$	4.38482	+	7.59474i	0.344504	+	0.596699i
$163$	−10.2587	−	17.7686i	−0.803526	−	1.39175i	−0.917282	−	0.398239i	$-0.869621\pi$
$163$	−10.2587	−	17.7686i	−0.803526	−	1.39175i	0.113756	−	0.993509i	$-0.463712\pi$
$164$	−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
$167$	2.20058	+	1.27050i	0.170286	+	0.0983146i	0.582721	−	0.812673i	$-0.301988\pi$
$167$	2.20058	+	1.27050i	0.170286	+	0.0983146i	−0.412435	+	0.910987i	$0.635322\pi$
$168$	−0.824831	+	0.824831i	−0.0636371	+	0.0636371i
$169$		0			0
$170$	15.9597	−	2.62187i	1.22405	−	0.201088i
$171$	8.85983	−	2.37398i	0.677528	−	0.181543i
$172$	−5.06438	−	18.9005i	−0.386155	−	1.44115i
$173$	0.0762079	+	0.0204199i	0.00579398	+	0.00155249i	0.261715	−	0.965145i	$-0.415712\pi$
$173$	0.0762079	+	0.0204199i	0.00579398	+	0.00155249i	−0.255921	+	0.966698i	$0.582379\pi$
$174$	−11.3120	+	11.3120i	−0.857560	+	0.857560i
$175$	0.421747	+	0.371054i	0.0318811	+	0.0280491i
$176$	19.9916	+	5.35675i	1.50693	+	0.403780i
$177$			1.66616i			0.125236i
$178$	0.390312	−	1.45666i	0.0292551	−	0.109182i
$179$	−10.6120	+	18.3806i	−0.793181	+	1.37383i	0.130808	+	0.991408i	$0.458243\pi$
$179$	−10.6120	+	18.3806i	−0.793181	+	1.37383i	−0.923988	+	0.382421i	$0.875090\pi$
$180$	13.4827	−	6.09595i	1.00494	−	0.454365i
$181$			22.5267i			1.67440i	0.546899	+	0.837198i	$0.315808\pi$
$181$			22.5267i			1.67440i	−0.546899	+	0.837198i	$0.684192\pi$
$182$		0			0
$183$	−2.55229	−	2.55229i	−0.188671	−	0.188671i
$184$	6.65667	+	24.8430i	0.490737	+	1.83145i
$185$	−3.00503	+	1.35867i	−0.220934	+	0.0998917i
$186$	−2.62797	+	1.51726i	−0.192692	+	0.111251i
$187$	5.05785			0.369866
$188$	−1.50064	+	0.866395i	−0.109445	+	0.0631883i
$189$	−0.162840	+	0.607727i	−0.0118449	+	0.0442056i
$190$	6.68506	+	40.6927i	0.484985	+	2.95216i
$191$	−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
$193$	8.35601	−	14.4730i	0.601479	−	1.04179i	−0.391119	−	0.920340i	$-0.627912\pi$
$193$	8.35601	−	14.4730i	0.601479	−	1.04179i	0.992597	−	0.121451i	$-0.0387548\pi$
$194$	−39.6521			−2.84686
$195$		0			0
$196$	35.0850			2.50607
$197$	−7.59315	+	13.1517i	−0.540990	+	0.937021i	0.457858	+	0.889025i	$0.348617\pi$
$197$	−7.59315	+	13.1517i	−0.540990	+	0.937021i	−0.998848	+	0.0479960i	$0.984717\pi$
$198$	6.24989	−	1.67465i	0.444160	−	0.119012i
$199$	6.97357	+	12.0786i	0.494343	+	0.856228i	0.999979	−	0.00651960i	$-0.00207527\pi$
$199$	6.97357	+	12.0786i	0.494343	+	0.856228i	−0.505636	+	0.862747i	$0.668742\pi$
$200$	12.8058	+	37.9234i	0.905508	+	2.68159i
$201$	0.0484483	−	0.180811i	0.00341728	−	0.0127535i
$202$	19.0707	−	11.0105i	1.34181	−	0.774696i
$203$	−0.522979			−0.0367059
$204$	−15.3951	+	8.88838i	−1.07787	+	0.622311i
$205$	4.28253	−	11.3509i	0.299105	−	0.792783i
$206$	−7.49657	−	27.9776i	−0.522311	−	1.94929i
$207$	2.99388	+	2.99388i	0.208089	+	0.208089i
$208$		0			0
$209$			12.8961i			0.892044i
$210$	−0.807769	−	0.304759i	−0.0557414	−	0.0210304i
$211$	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
$213$			7.09915i			0.486426i
$214$	−18.9504	−	5.07776i	−1.29543	−	0.347108i
$215$	6.74027	−	5.52260i	0.459682	−	0.376638i
$216$	−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
$219$	11.3529	−	3.04201i	0.767159	−	0.205560i
$220$	3.37247	+	20.5286i	0.227372	+	1.38404i
$221$		0			0
$222$	3.58405	−	3.58405i	0.240546	−	0.240546i
$223$	8.42330	+	4.86319i	0.564066	+	0.325664i	0.754776	−	0.655983i	$-0.227746\pi$
$223$	8.42330	+	4.86319i	0.564066	+	0.325664i	−0.190710	+	0.981646i	$0.561079\pi$
$224$	−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
$227$	4.58790	+	7.94647i	0.304510	+	0.527426i	0.977152	−	0.212542i	$-0.0681741\pi$
$227$	4.58790	+	7.94647i	0.304510	+	0.527426i	−0.672642	+	0.739968i	$0.734841\pi$
$228$	−22.6629	−	39.2534i	−1.50089	−	2.59962i
$229$	12.5270	+	12.5270i	0.827811	+	0.827811i	0.987214	−	0.159403i	$-0.0509569\pi$
$229$	12.5270	+	12.5270i	0.827811	+	0.827811i	−0.159403	+	0.987214i	$0.550957\pi$
$230$	−14.7244	+	12.0643i	−0.970895	+	0.795498i
$231$	−0.233817	−	0.134994i	−0.0153840	−	0.00888197i
$232$	−32.2726	−	18.6326i	−2.11880	−	1.22329i
$233$	11.8637	−	11.8637i	0.777214	−	0.777214i	−0.202142	−	0.979356i	$-0.564790\pi$
$233$	11.8637	−	11.8637i	0.777214	−	0.777214i	0.979356	+	0.202142i	$0.0647903\pi$
$234$		0			0
$235$	−0.626879	−	0.449972i	−0.0408931	−	0.0293530i
$236$	−6.23072	+	1.66952i	−0.405585	+	0.108676i
$237$	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	−0.198124	+	0.980177i	$0.563485\pi$
$239$	−18.2161	+	18.2161i	−1.17830	+	1.17830i	−0.980177	+	0.198124i	$0.936515\pi$
$240$	−20.5308	−	25.0576i	−1.32526	−	1.61746i
$241$	5.28403	+	1.41585i	0.340374	+	0.0912030i	0.424957	−	0.905213i	$-0.360289\pi$
$241$	5.28403	+	1.41585i	0.340374	+	0.0912030i	−0.0845830	+	0.996416i	$0.526956\pi$
$242$		−	20.0501i		−	1.28887i
$243$	−3.23730	+	12.0818i	−0.207673	+	0.775046i
$244$	6.98703	−	12.1019i	0.447299	−	0.774744i
$245$	6.43688	+	14.2367i	0.411237	+	0.909550i
$246$			18.6458i			1.18881i
$247$		0			0
$248$	−4.99833	−	4.99833i	−0.317394	−	0.317394i
$249$	2.86622	+	10.6969i	0.181639	+	0.677887i
$250$	−21.6707	+	20.1997i	−1.37058	+	1.27754i
$251$	11.3169	−	6.53384i	0.714319	−	0.412412i	−0.0983394	−	0.995153i	$-0.531353\pi$
$251$	11.3169	−	6.53384i	0.714319	−	0.412412i	0.812658	+	0.582741i	$0.198020\pi$
$252$	−0.743439			−0.0468322
$253$	−5.15533	+	2.97643i	−0.324113	+	0.187127i
$254$	−8.00209	+	29.8642i	−0.502096	+	1.87385i
$255$	−6.43118	−	4.61629i	−0.402736	−	0.289083i
$256$	1.70209	+	2.94811i	0.106381	+	0.184257i
$257$	16.8541	−	4.51603i	1.05133	−	0.281702i	0.308528	−	0.951215i	$-0.400164\pi$
$257$	16.8541	−	4.51603i	1.05133	−	0.281702i	0.742800	+	0.669513i	$0.233497\pi$
$258$	−6.69619	+	11.5981i	−0.416887	+	0.722069i
$259$	0.165699			0.0102960
$260$		0			0
$261$	−6.13467			−0.379727
$262$	9.88862	−	17.1276i	0.610921	−	1.05815i
$263$	−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
$265$	−11.2069	+	1.84108i	−0.688434	+	0.113097i
$266$	0.536261	−	2.00135i	0.0328803	−	0.122711i
$267$	−0.639249	+	0.369071i	−0.0391214	+	0.0225868i
$268$	0.724703			0.0442683
$269$	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
$271$	2.04739	+	7.64095i	0.124370	+	0.464155i	0.999816	−	0.0191601i	$-0.00609923\pi$
$271$	2.04739	+	7.64095i	0.124370	+	0.464155i	−0.875446	+	0.483315i	$0.839433\pi$
$272$	−21.5603	−	21.5603i	−1.30729	−	1.30729i
$273$		0			0
$274$			48.9787i			2.95891i
$275$	−7.71132	+	5.13476i	−0.465010	+	0.309638i
$276$	10.4612	−	18.1194i	0.629693	−	1.09066i
$277$	2.64361	−	9.86609i	0.158839	−	0.592796i	−0.839907	−	0.542731i	$-0.817390\pi$
$277$	2.64361	−	9.86609i	0.158839	−	0.592796i	0.998746	−	0.0500653i	$-0.0159429\pi$
$278$		−	28.9097i		−	1.73389i
$279$	−1.12401	−	0.301178i	−0.0672929	−	0.0180311i
$280$	0.198720	−	2.00127i	0.0118758	−	0.119598i
$281$	−12.4763	+	12.4763i	−0.744271	+	0.744271i	−0.973397	−	0.229126i	$-0.926413\pi$
$281$	−12.4763	+	12.4763i	−0.744271	+	0.744271i	0.229126	+	0.973397i	$0.426413\pi$
$282$	1.14556	+	0.306952i	0.0682171	+	0.0182787i
$283$	−2.13952	−	7.98478i	−0.127181	−	0.474646i	0.872727	−	0.488208i	$-0.162349\pi$
$283$	−2.13952	−	7.98478i	−0.127181	−	0.474646i	−0.999908	+	0.0135626i	$0.995683\pi$
$284$	−26.5478	+	7.11345i	−1.57532	+	0.422105i
$285$	11.7703	−	16.3977i	0.697210	−	0.971318i
$286$		0			0
$287$	−0.431018	+	0.431018i	−0.0254422	+	0.0254422i
$288$	−15.5070	−	8.95295i	−0.913756	−	0.527557i
$289$	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
$292$	22.7516	+	39.4069i	1.33144	+	2.30611i
$293$	3.18916	+	5.52378i	0.186313	+	0.322703i	0.944018	−	0.329894i	$-0.107013\pi$
$293$	3.18916	+	5.52378i	0.186313	+	0.322703i	−0.757705	+	0.652597i	$0.773680\pi$
$294$	−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
$297$	−8.98628	−	5.18823i	−0.521437	−	0.301052i
$298$	26.0836	−	26.0836i	1.51098	−	1.51098i
$299$		0			0
$300$	14.4483	−	29.1807i	0.834170	−	1.68475i
$301$	−0.422894	+	0.113314i	−0.0243752	+	0.00653132i
$302$	−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
$305$	6.19255	+	0.614902i	0.354584	+	0.0352092i
$306$	−9.20741	−	2.46712i	−0.526353	−	0.141036i
$307$		−	26.5460i		−	1.51506i	−0.652801	−	0.757530i	$-0.726406\pi$
$307$		−	26.5460i		−	1.51506i	0.652801	−	0.757530i	$-0.273594\pi$
$308$	0.270532	−	1.00964i	0.0154150	−	0.0575296i
$309$	−7.08860	+	12.2778i	−0.403256	+	0.698460i
$310$	1.84678	−	4.89494i	0.104890	−	0.278014i
$311$			3.54417i			0.200972i	0.994938	+	0.100486i	$0.0320397\pi$
$311$			3.54417i			0.200972i	−0.994938	+	0.100486i	$0.967960\pi$
$312$		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	$0.829851\pi$
$314$	4.98993	+	18.6227i	0.281598	+	1.05094i
$315$	−0.136395	−	0.301671i	−0.00768500	−	0.0169972i
$316$	−65.9619	+	38.0831i	−3.71065	+	2.14234i
$317$	8.52812			0.478987			0.239494	−	0.970898i	$-0.423019\pi$
$317$	8.52812			0.478987			0.239494	+	0.970898i	$0.423019\pi$
$318$	15.1164	−	8.72748i	0.847688	−	0.489413i
$319$	2.23236	−	8.33129i	0.124988	−	0.466463i
$320$	17.8142	−	24.8178i	0.995842	−	1.38736i
$321$	4.80142	+	8.31631i	0.267989	+	0.464171i
$322$	0.923827	−	0.247539i	0.0514829	−	0.0137948i
$323$	9.49937	−	16.4534i	0.528559	−	0.915491i
$324$	16.6182			0.923233
$325$		0			0
$326$	−54.3663			−3.01107
$327$	−3.06809	+	5.31409i	−0.169666	+	0.293870i
$328$	−41.9540	+	11.2415i	−2.31652	+	0.620710i
$329$	0.0193853	+	0.0335764i	0.00106875	+	0.00185113i
$330$	8.30296	−	11.5673i	0.457063	−	0.636757i
$331$	−4.66054	+	17.3934i	−0.256166	+	0.956026i	0.711271	+	0.702917i	$0.248120\pi$
$331$	−4.66054	+	17.3934i	−0.256166	+	0.956026i	−0.967438	+	0.253109i	$0.918547\pi$
$332$	−37.1297	+	21.4368i	−2.03776	+	1.17650i
$333$	1.94369			0.106513
$334$	5.83099	−	3.36652i	0.319058	−	0.184208i
$335$	0.132958	+	0.294068i	0.00726426	+	0.0160666i
$336$	0.421256	+	1.57215i	0.0229814	+	0.0857677i
$337$	20.0865	+	20.0865i	1.09418	+	1.09418i	0.995077	+	0.0991030i	$0.0315973\pi$
$337$	20.0865	+	20.0865i	1.09418	+	1.09418i	0.0991030	+	0.995077i	$0.468403\pi$
$338$		0			0
$339$			7.93129i			0.430769i
$340$	10.8188	−	28.6754i	0.586731	−	1.55514i
$341$	0.818040	−	1.41689i	0.0442994	−	0.0767288i
$342$	6.29048	−	23.4764i	0.340150	−	1.26946i
$343$		−	1.57145i		−	0.0848505i
$344$	−30.1336	−	8.07428i	−1.62470	−	0.435336i
$345$	9.27172	+	0.920654i	0.499173	+	0.0495663i
$346$	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
$349$	3.52885	−	0.945552i	0.188895	−	0.0506143i	−0.163131	−	0.986604i	$-0.552159\pi$
$349$	3.52885	−	0.945552i	0.188895	−	0.0506143i	0.352026	+	0.935990i	$0.385493\pi$
$350$	1.41024	−	0.476204i	0.0753806	−	0.0254542i
$351$		0			0
$352$	17.8016	−	17.8016i	0.948827	−	0.948827i
$353$	1.52702	+	0.881628i	0.0812753	+	0.0469243i	0.540087	−	0.841609i	$-0.318391\pi$
$353$	1.52702	+	0.881628i	0.0812753	+	0.0469243i	−0.458812	+	0.888534i	$0.651725\pi$
$354$	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
$357$	0.198875	+	0.344462i	0.0105256	+	0.0182309i
$358$	28.1193	+	48.7040i	1.48615	+	2.57409i
$359$	8.58021	+	8.58021i	0.452846	+	0.452846i	0.896298	−	0.443452i	$-0.146246\pi$
$359$	8.58021	+	8.58021i	0.452846	+	0.452846i	−0.443452	+	0.896298i	$0.646246\pi$
$360$	2.33103	−	23.4753i	0.122856	−	1.23726i
$361$	25.4972	+	14.7208i	1.34196	+	0.774778i
$362$	51.6933	+	29.8451i	2.71694	+	1.56862i
$363$	−6.93947	+	6.93947i	−0.364228	+	0.364228i
$364$		0			0
$365$	−11.8163	+	16.4619i	−0.618493	+	0.861654i
$366$	−9.23835	+	2.47541i	−0.482896	+	0.129392i
$367$	−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
$370$	−0.863475	+	8.69589i	−0.0448900	+	0.452078i
$371$	0.551179	+	0.147688i	0.0286158	+	0.00766757i
$372$			5.75032i			0.298140i
$373$	−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
$375$	14.4916	+	0.509129i	0.748344	+	0.0262913i
$376$			2.76263i			0.142472i
$377$		0			0
$378$	1.17884	+	1.17884i	0.0606330	+	0.0606330i
$379$	2.45278	+	9.15390i	0.125991	+	0.470204i	0.999873	−	0.0159336i	$-0.00507204\pi$
$379$	2.45278	+	9.15390i	0.125991	+	0.470204i	−0.873882	+	0.486138i	$0.838405\pi$
$380$	73.1144	+	27.5849i	3.75069	+	1.41508i
$381$	13.1058	−	7.56661i	0.671428	−	0.387649i
$382$	−51.9525			−2.65812
$383$	18.2490	−	10.5361i	0.932483	−	0.538369i	0.0448868	−	0.998992i	$-0.485707\pi$
$383$	18.2490	−	10.5361i	0.932483	−	0.538369i	0.887596	+	0.460623i	$0.152374\pi$
$384$	−3.03028	+	11.3091i	−0.154638	+	0.577118i
$385$	0.459322	−	0.0754581i	0.0234092	−	0.00384570i
$386$	−22.1414	−	38.3500i	−1.12697	−	1.95196i
$387$	−4.96065	+	1.32920i	−0.252164	+	0.0675672i
$388$	−37.5698	+	65.0727i	−1.90732	+	3.30357i
$389$	−0.0604806			−0.00306649			−0.00153324	−	0.999999i	$-0.500488\pi$
$389$	−0.0604806			−0.00306649			−0.00153324	+	0.999999i	$0.500488\pi$
$390$		0			0
$391$	8.76984			0.443510
$392$	27.9685	−	48.4429i	1.41262	−	2.44673i
$393$	−9.35047	+	2.50545i	−0.471669	+	0.126383i
$394$	20.1200	+	34.8488i	1.01363	+	1.75566i
$395$	−27.5550	−	19.7789i	−1.38644	−	0.995186i
$396$	3.17341	−	11.8433i	0.159470	−	0.595150i
$397$	7.11548	−	4.10812i	0.357116	−	0.206181i	−0.310699	−	0.950508i	$-0.600563\pi$
$397$	7.11548	−	4.10812i	0.357116	−	0.206181i	0.667815	+	0.744327i	$0.267230\pi$
$398$	36.9565			1.85246
$399$	−0.878284	+	0.507077i	−0.0439692	+	0.0253856i
$400$	54.7596	+	10.9832i	2.73798	+	0.549161i
$401$	2.32904	+	8.69210i	0.116307	+	0.434063i	0.999381	−	0.0351698i	$-0.0111972\pi$
$401$	2.32904	+	8.69210i	0.116307	+	0.434063i	−0.883075	+	0.469233i	$0.844531\pi$
$402$	−0.350730	−	0.350730i	−0.0174928	−	0.0174928i
$403$		0			0
$404$		−	41.7291i		−	2.07610i
$405$	3.04886	+	6.74329i	0.151499	+	0.335077i
$406$	−0.692882	+	1.20011i	−0.0343872	+	0.0595603i
$407$	−0.707294	+	2.63966i	−0.0350593	+	0.130843i
$408$			28.3420i			1.40314i
$409$	34.6013	+	9.27138i	1.71092	+	0.458440i	0.975650	−	0.219332i	$-0.0703877\pi$
$409$	34.6013	+	9.27138i	1.71092	+	0.458440i	0.735272	+	0.677772i	$0.237054\pi$
$410$	−20.3738	−	24.8659i	−1.00619	−	1.22804i
$411$	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
$414$	10.8367	−	2.90369i	0.532596	−	0.142709i
$415$	−15.5106	−	11.1335i	−0.761385	−	0.546521i
$416$		0			0
$417$	−10.0058	+	10.0058i	−0.489987	+	0.489987i
$418$	29.5934	+	17.0858i	1.44746	+	0.835693i
$419$	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	$-0.0923326\pi$
$421$	13.7924	+	13.7924i	0.672203	+	0.672203i	−0.286021	+	0.958223i	$0.592333\pi$
$422$	−31.2911	−	54.1978i	−1.52323	−	2.63831i
$423$	0.227395	+	0.393860i	0.0110563	+	0.0191501i
$424$	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
$427$	−0.270777	−	0.156333i	−0.0131038	−	0.00756548i
$428$	−26.2883	+	26.2883i	−1.27069	+	1.27069i
$429$		0			0
$430$	−3.74299	−	22.7840i	−0.180503	−	1.09874i
$431$	−21.4619	+	5.75070i	−1.03378	+	0.277002i	−0.735535	−	0.677487i	$-0.763069\pi$
$431$	−21.4619	+	5.75070i	−1.03378	+	0.277002i	−0.298249	+	0.954488i	$0.596403\pi$
$432$	16.1901	+	60.4224i	0.778948	+	2.90707i
$433$	0.177294	+	0.0475058i	0.00852021	+	0.00228298i	0.263077	−	0.964775i	$-0.415263\pi$
$433$	0.177294	+	0.0475058i	0.00852021	+	0.00228298i	−0.254556	+	0.967058i	$0.581929\pi$
$434$	−0.185871	+	0.185871i	−0.00892207	+	0.00892207i
$435$	−10.4425	+	8.55597i	−0.500678	+	0.410228i
$436$	−22.9467	−	6.14854i	−1.09895	−	0.294462i
$437$			22.3607i			1.06966i
$438$	8.06057	−	30.0825i	0.385149	−	1.43740i
$439$	8.64682	−	14.9767i	0.412690	−	0.714800i	−0.582493	−	0.812836i	$-0.697923\pi$
$439$	8.64682	−	14.9767i	0.412690	−	0.714800i	0.995183	+	0.0980356i	$0.0312559\pi$
$440$	31.0328	+	11.7082i	1.47943	+	0.558167i
$441$		−	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	$0.443239\pi$
$444$	−2.48592	−	9.27758i	−0.117977	−	0.440295i
$445$	0.449226	−	1.19068i	0.0212954	−	0.0564438i
$446$	22.3197	−	12.8863i	1.05687	−	0.610183i
$447$	−18.0554			−0.853989
$448$	−1.32927	+	0.767456i	−0.0628022	+	0.0362589i
$449$	9.62407	−	35.9175i	0.454188	−	1.69505i	−0.236277	−	0.971686i	$-0.575927\pi$
$449$	9.62407	−	35.9175i	0.454188	−	1.69505i	0.690465	−	0.723366i	$-0.257406\pi$
$450$	16.5425	−	5.58600i	0.779820	−	0.263326i
$451$	−5.02649	−	8.70613i	−0.236688	−	0.409956i
$452$	−29.6596	+	7.94727i	−1.39507	+	0.373808i
$453$	−7.79158	+	13.4954i	−0.366080	+	0.634070i
$454$	24.3136			1.14109
$455$		0			0
$456$	−72.2643			−3.38409
$457$	4.71345	−	8.16394i	0.220486	−	0.381893i	−0.734470	−	0.678642i	$-0.762569\pi$
$457$	4.71345	−	8.16394i	0.220486	−	0.381893i	0.954956	+	0.296749i	$0.0959023\pi$
$458$	45.3433	−	12.1497i	2.11875	−	0.567718i
$459$	7.64337	+	13.2387i	0.356762	+	0.617930i
$460$	5.84755	+	35.5947i	0.272643	+	1.65961i
$461$	8.51149	−	31.7653i	0.396419	−	1.47946i	−0.422930	−	0.906162i	$-0.638998\pi$
$461$	8.51149	−	31.7653i	0.396419	−	1.47946i	0.819349	−	0.573295i	$-0.194335\pi$
$462$	−0.619557	+	0.357701i	−0.0288244	+	0.0166418i
$463$	−18.6729			−0.867805			−0.433903	−	0.900960i	$-0.642864\pi$
$463$	−18.6729			−0.867805			−0.433903	+	0.900960i	$0.642864\pi$
$464$	−45.0302	+	25.9982i	−2.09047	+	1.20694i
$465$	−2.33335	+	1.05498i	−0.108206	+	0.0489237i
$466$	−11.5063	−	42.9421i	−0.533019	−	1.98925i
$467$	12.1678	+	12.1678i	0.563057	+	0.563057i	0.930175	−	0.367118i	$-0.119655\pi$
$467$	12.1678	+	12.1678i	0.563057	+	0.563057i	−0.367118	+	0.930175i	$0.619655\pi$
$468$		0			0
$469$		−	0.0162150i		−	0.000748740i
$470$	−1.86311	+	0.842375i	−0.0859390	+	0.0388559i
$471$	4.71838	−	8.17247i	0.217411	−	0.376568i
$472$	−2.66176	+	9.93381i	−0.122517	+	0.457241i
$473$		−	7.22059i		−	0.332003i
$474$	50.3541	+	13.4923i	2.31284	+	0.619723i
$475$	2.22062	+	34.7291i	0.101889	+	1.59348i
$476$	−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
$479$	−31.8403	+	8.53158i	−1.45482	+	0.389818i	−0.897697	−	0.440612i	$-0.854761\pi$
$479$	−31.8403	+	8.53158i	−1.45482	+	0.389818i	−0.557123	+	0.830430i	$0.688095\pi$
$480$	−38.8826	+	6.38768i	−1.77474	+	0.291557i
$481$		0			0
$482$	10.2497	−	10.2497i	0.466862	−	0.466862i
$483$	−0.405417	−	0.234068i	−0.0184471	−	0.0106504i
$484$	−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
$487$	16.4931	+	28.5670i	0.747376	+	1.29449i	0.949077	+	0.315045i	$0.102020\pi$
$487$	16.4931	+	28.5670i	0.747376	+	1.29449i	−0.201701	+	0.979447i	$0.564647\pi$
$488$	−11.1396	−	19.2944i	−0.504267	−	0.873415i
$489$	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	0.0223350	−	0.999751i	$-0.492890\pi$
$491$	−18.4427	−	10.6479i	−0.832307	−	0.480533i	−0.854642	+	0.519218i	$0.826223\pi$
$492$	30.5994	+	17.6666i	1.37953	+	0.796470i
$493$	−8.98502	+	8.98502i	−0.404665	+	0.404665i
$494$		0			0
$495$	5.38797	−	0.885142i	0.242171	−	0.0397842i
$496$	−9.52693	+	2.55273i	−0.427772	+	0.114621i
$497$	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	−0.957231	−	0.289326i	$-0.906569\pi$
$499$	−14.9199	+	14.9199i	−0.667904	+	0.667904i	0.289326	+	0.957231i	$0.406569\pi$
$500$	12.6169	+	54.7025i	0.564244	+	2.44637i
$501$	−3.18332	−	0.852967i	−0.142220	−	0.0381077i
$502$		−	34.6261i		−	1.54544i
$503$	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
$505$	16.9327	−	7.65584i	0.753496	−	0.340680i
$506$			15.7736i			0.701224i
$507$		0			0
$508$	41.4280	+	41.4280i	1.83807	+	1.83807i
$509$	−9.67023	−	36.0898i	−0.428626	−	1.59965i	−0.755876	−	0.654715i	$-0.772789\pi$
$509$	−9.67023	−	36.0898i	−0.428626	−	1.59965i	0.327250	−	0.944938i	$-0.393878\pi$
$510$	−19.1138	+	8.64196i	−0.846372	+	0.382673i
$511$	0.881719	−	0.509060i	0.0390049	−	0.0225195i
$512$	27.0748			1.19655
$513$	−33.7551	+	19.4885i	−1.49032	+	0.860438i
$514$	11.9664	−	44.6591i	0.527814	−	1.96983i
$515$	−3.96233	−	24.1192i	−0.174601	−	1.06282i
$516$	12.6891	+	21.9781i	0.558605	+	0.967533i
$517$	−0.617635	+	0.165495i	−0.0271636	+	0.00727846i
$518$	0.219530	−	0.380238i	0.00964562	−	0.0167067i
$519$	−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	$0.785648\pi$
$522$	−8.12768	+	14.0776i	−0.355739	+	0.616158i
$523$	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
$525$	−0.652910	−	0.323276i	−0.0284953	−	0.0141089i
$526$	−14.2979	+	53.3604i	−0.623417	+	2.32662i
$527$	−2.08738	+	1.20515i	−0.0909276	+	0.0524971i
$528$	−26.8432			−1.16820
$529$	10.9797	−	6.33914i	0.477379	−	0.275615i
$530$	−10.6229	+	28.1563i	−0.461431	+	1.22303i
$531$	0.438183	+	1.63532i	0.0190155	+	0.0709670i
$532$	−2.77630	−	2.77630i	−0.120368	−	0.120368i
$533$		0			0
$534$			1.95589i			0.0846398i
$535$	−15.4902	−	5.84421i	−0.669699	−	0.252667i
$536$	0.577707	−	1.00062i	0.0249531	−	0.0432201i
$537$	7.12450	−	26.5890i	0.307445	−	1.14740i
$538$		−	27.9987i		−	1.20711i
$539$	12.5057	+	3.35089i	0.538659	+	0.144333i
$540$	−48.6364	+	39.8500i	−2.09298	+	1.71487i
$541$	5.42748	−	5.42748i	0.233345	−	0.233345i	−0.580742	−	0.814088i	$-0.697238\pi$
$541$	5.42748	−	5.42748i	0.233345	−	0.233345i	0.814088	+	0.580742i	$0.197238\pi$
$542$	20.2467	+	5.42507i	0.869668	+	0.233027i
$543$	−7.56177	−	28.2209i	−0.324507	−	1.21108i
$544$	−35.8247	+	9.59920i	−1.53597	+	0.411563i
$545$	−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	$0.134973\pi$
$548$	80.3785	+	46.4066i	3.43360	+	1.98239i
$549$	−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
$552$	−16.6786	−	28.8883i	−0.709890	−	1.22957i
$553$	0.852100	+	1.47588i	0.0362350	+	0.0627608i
$554$	−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
$557$	4.22190	+	2.43751i	0.178888	+	0.103281i	0.586770	−	0.809754i	$-0.300399\pi$
$557$	4.22190	+	2.43751i	0.178888	+	0.103281i	−0.407882	+	0.913034i	$0.633733\pi$
$558$	−2.18031	+	2.18031i	−0.0922998	+	0.0922998i
$559$		0			0
$560$	−2.27963	−	1.63632i	−0.0963321	−	0.0691470i
$561$	−6.33635	+	1.69782i	−0.267521	+	0.0716820i
$562$	12.1004	+	45.1595i	0.510426	+	1.90494i
$563$	−37.6390	−	10.0853i	−1.58630	−	0.425047i	−0.645428	−	0.763821i	$-0.723321\pi$
$563$	−37.6390	−	10.0853i	−1.58630	−	0.425047i	−0.940868	+	0.338774i	$0.889988\pi$
$564$	1.58913	−	1.58913i	0.0669146	−	0.0669146i
$565$	−8.66633	−	10.5772i	−0.364595	−	0.444984i
$566$	−21.1577	−	5.66919i	−0.889325	−	0.238294i
$567$		−	0.371828i		−	0.0156153i
$568$	−11.3412	+	42.3258i	−0.475865	+	1.77595i
$569$	−1.84104	+	3.18877i	−0.0771804	+	0.133680i	−0.902032	−	0.431668i	$-0.857925\pi$
$569$	−1.84104	+	3.18877i	−0.0771804	+	0.133680i	0.824852	+	0.565349i	$0.191258\pi$
$570$	−22.0346	−	48.7349i	−0.922929	−	2.04128i
$571$			2.96698i			0.124164i	0.998071	+	0.0620821i	$0.0197741\pi$
$571$			2.96698i			0.124164i	−0.998071	+	0.0620821i	$0.980226\pi$
$572$		0			0
$573$	17.9811	+	17.9811i	0.751170	+	0.751170i
$574$	0.418034	+	1.56012i	0.0174484	+	0.0651184i
$575$	−13.3707	+	8.90320i	−0.557598	+	0.371289i
$576$	−15.5927	+	9.00245i	−0.649696	+	0.375102i
$577$	35.0533			1.45929			0.729644	−	0.683827i	$-0.239686\pi$
$577$	35.0533			1.45929			0.729644	+	0.683827i	$0.239686\pi$
$578$	21.9120	−	12.6509i	0.911417	−	0.526207i
$579$	−5.60990	+	20.9364i	−0.233139	+	0.870088i
$580$	−42.4591	−	30.4771i	−1.76302	−	1.26549i
$581$	0.479643	+	0.830767i	0.0198990	+	0.0344660i
$582$	49.6753	−	13.3104i	2.05911	−	0.551736i
$583$	−4.70547	+	8.15012i	−0.194881	+	0.337543i
$584$	72.5469			3.00201
$585$		0			0
$586$	16.9010			0.698173
$587$	3.52719	−	6.10926i	0.145583	−	0.252156i	−0.784008	−	0.620751i	$-0.786828\pi$
$587$	3.52719	−	6.10926i	0.145583	−	0.252156i	0.929590	+	0.368595i	$0.120161\pi$
$588$	−43.9537	+	11.7774i	−1.81262	+	0.485690i
$589$	−3.07280	−	5.32224i	−0.126612	−	0.219299i
$590$	−7.51095	+	1.23391i	−0.309221	+	0.0507992i
$591$	5.09774	−	19.0250i	0.209693	−	0.782585i
$592$	14.2672	−	8.23718i	0.586379	−	0.338546i
$593$	−40.0169			−1.64330			−0.821649	−	0.569993i	$-0.806946\pi$
$593$	−40.0169			−1.64330			−0.821649	+	0.569993i	$0.806946\pi$
$594$	−23.8114	+	13.7475i	−0.976995	+	0.564068i
$595$	−0.641605	−	0.242067i	−0.0263032	−	0.00992380i
$596$	−18.0917	−	67.5192i	−0.741066	−	2.76570i
$597$	−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	$-0.0917918\pi$
$600$	−28.7730	−	43.2109i	−1.17465	−	1.76408i
$601$	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
$603$		−	0.190206i		−	0.00774580i
$604$	−58.2743	−	15.6145i	−2.37115	−	0.635347i
$605$	1.67187	−	16.8371i	0.0679711	−	0.684524i
$606$	−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
$609$	0.655175	−	0.175554i	0.0265490	−	0.00711379i
$610$	9.61542	−	13.3957i	0.389317	−	0.542377i
$611$		0			0
$612$	−12.7726	+	12.7726i	−0.516303	+	0.516303i
$613$	−9.23121	−	5.32964i	−0.372845	−	0.215262i	0.301856	−	0.953354i	$-0.402394\pi$
$613$	−9.23121	−	5.32964i	−0.372845	−	0.215262i	−0.674701	+	0.738091i	$0.735727\pi$
$614$	−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
$617$	−6.86421	−	11.8892i	−0.276343	−	0.478639i	0.694130	−	0.719849i	$-0.255789\pi$
$617$	−6.86421	−	11.8892i	−0.276343	−	0.478639i	−0.970473	+	0.241210i	$0.922456\pi$
$618$	18.7830	+	32.5332i	0.755565	+	1.30868i
$619$	16.8604	+	16.8604i	0.677679	+	0.677679i	0.959474	−	0.281796i	$-0.0909301\pi$
$619$	16.8604	+	16.8604i	0.677679	+	0.677679i	−0.281796	+	0.959474i	$0.590930\pi$
$620$	−6.28323	−	7.66861i	−0.252341	−	0.307979i
$621$	−15.5814	−	8.99592i	−0.625260	−	0.360994i
$622$	8.13301	+	4.69560i	0.326104	+	0.188276i
$623$	−0.0452127	+	0.0452127i	−0.00181141	+	0.00181141i
$624$		0			0
$625$	−19.8823	+	15.1557i	−0.795292	+	0.606227i
$626$	−22.4811	+	6.02379i	−0.898526	+	0.240759i
$627$	−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
$630$	−0.872967	−	0.0866830i	−0.0347798	−	0.00345353i
$631$	−29.5533	−	7.91879i	−1.17650	−	0.315242i	−0.382962	−	0.923764i	$-0.625096\pi$
$631$	−29.5533	−	7.91879i	−1.17650	−	0.315242i	−0.793537	+	0.608522i	$0.791763\pi$
$632$			121.434i			4.83038i
$633$	−7.92814	+	29.5882i	−0.315115	+	1.17603i
$634$	11.2987	−	19.5700i	0.448729	−	0.777222i
$635$	−9.20995	+	24.4112i	−0.365486	+	0.968727i
$636$		−	33.0766i		−	1.31157i
$637$		0			0
$638$	−16.1607	−	16.1607i	−0.639807	−	0.639807i
$639$	1.86700	+	6.96776i	0.0738576	+	0.275640i
$640$	−8.31606	−	18.3930i	−0.328721	−	0.727046i
$641$	−13.2495	+	7.64957i	−0.523322	+	0.302140i	−0.738293	−	0.674480i	$-0.764368\pi$
$641$	−13.2495	+	7.64957i	−0.523322	+	0.302140i	0.214971	+	0.976620i	$0.431034\pi$
$642$	25.4452			1.00424
$643$	−19.3539	+	11.1740i	−0.763245	+	0.440660i	−0.830460	−	0.557079i	$-0.811922\pi$
$643$	−19.3539	+	11.1740i	−0.763245	+	0.440660i	0.0672147	+	0.997739i	$0.478589\pi$
$644$	0.469078	−	1.75062i	0.0184843	−	0.0689842i
$645$	−6.59022	+	9.18116i	−0.259490	+	0.361508i
$646$	−25.1710	−	43.5974i	−0.990340	−	1.71532i
$647$	4.51668	−	1.21024i	0.177569	−	0.0475795i	−0.168939	−	0.985627i	$-0.554034\pi$
$647$	4.51668	−	1.21024i	0.177569	−	0.0475795i	0.346508	+	0.938047i	$0.387367\pi$
$648$	13.2474	−	22.9452i	0.520408	−	0.901373i
$649$	−2.38033			−0.0934361
$650$		0			0
$651$	0.128662			0.00504265
$652$	−51.5111	+	89.2199i	−2.01733	+	3.49412i
$653$	−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
$655$	9.73212	−	13.5583i	0.380265	−	0.529766i
$656$	−15.6854	+	58.5387i	−0.612412	+	2.28555i
$657$	10.3428	−	5.97141i	0.403510	−	0.232967i
$658$	0.102733			0.00400494
$659$	−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
$661$	−4.42523	−	16.5152i	−0.172122	−	0.642367i	−0.997024	−	0.0770916i	$-0.975437\pi$
$661$	−4.42523	−	16.5152i	−0.172122	−	0.642367i	0.824902	−	0.565275i	$-0.191230\pi$
$662$	33.7389	+	33.7389i	1.31130	+	1.31130i
$663$		0			0
$664$			68.3547i			2.65268i
$665$	0.617206	−	1.63592i	0.0239342	−	0.0634381i
$666$	2.57515	−	4.46029i	0.0997850	−	0.172833i
$667$	3.87071	−	14.4457i	0.149875	−	0.559340i
$668$		−	12.7589i		−	0.493657i
$669$	−12.1850	−	3.26496i	−0.471099	−	0.126231i
$670$	0.850967	+	0.0844984i	0.0328757	+	0.00326446i
$671$	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	$-0.931537\pi$
$673$	−6.16392	−	23.0041i	−0.237602	−	0.886742i	0.739357	−	0.673314i	$-0.235130\pi$
$674$	72.7057	−	19.4814i	2.80052	−	0.750396i
$675$	−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	$-0.00141172\pi$
$678$	18.2004	+	10.5080i	0.698981	+	0.403557i
$679$	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
$682$	−2.16761	−	3.75440i	−0.0830019	−	0.143764i
$683$	13.3938	+	23.1988i	0.512500	+	0.887676i	0.999895	+	0.0144941i	$0.00461378\pi$
$683$	13.3938	+	23.1988i	0.512500	+	0.887676i	−0.487395	+	0.873181i	$0.662053\pi$
$684$	−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
$687$	−19.8987	−	11.4885i	−0.759182	−	0.438314i
$688$	−30.7796	+	30.7796i	−1.17346	+	1.17346i
$689$		0			0
$690$	14.3966	−	20.0566i	0.548068	−	0.763541i
$691$	38.9899	−	10.4473i	1.48325	−	0.397435i	0.575796	−	0.817593i	$-0.304692\pi$
$691$	38.9899	−	10.4473i	1.48325	−	0.397435i	0.907451	+	0.420158i	$0.138025\pi$
$692$	−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
$695$	2.41062	−	24.2768i	0.0914399	−	0.920873i
$696$	46.6850	+	12.5092i	1.76959	+	0.474160i
$697$			14.8102i			0.560976i
$698$	2.50548	−	9.35058i	0.0948339	−	0.353925i
$699$	−10.8801	+	18.8449i	−0.411524	+	0.712780i
$700$	0.554686	−	2.76553i	0.0209652	−	0.104527i
$701$			24.9781i			0.943410i	0.881756	+	0.471705i	$0.156361\pi$
$701$			24.9781i			0.943410i	−0.881756	+	0.471705i	$0.843639\pi$
$702$		0			0
$703$	7.25852	+	7.25852i	0.273760	+	0.273760i
$704$	−6.55185	−	24.4519i	−0.246932	−	0.921564i
$705$	0.936386	+	0.353284i	0.0352663	+	0.0133054i
$706$	4.04624	−	2.33610i	0.152282	−	0.0879202i
$707$	−0.933677			−0.0351145
$708$	7.24528	−	4.18306i	0.272294	−	0.157209i
$709$	−2.64139	+	9.85779i	−0.0991993	+	0.370217i	−0.997623	−	0.0689135i	$-0.978047\pi$
$709$	−2.64139	+	9.85779i	−0.0991993	+	0.370217i	0.898423	+	0.439130i	$0.144713\pi$
$710$	−32.0025	+	5.25742i	−1.20103	+	0.197307i
$711$	9.99535	+	17.3124i	0.374855	+	0.649268i
$712$	−4.40087	+	1.17921i	−0.164930	+	0.0441927i
$713$	1.41841	−	2.45675i	0.0531198	−	0.0920061i
$714$	1.05394			0.0394428
$715$		0			0
$716$	106.570			3.98272
$717$	16.7059	−	28.9355i	0.623893	−	1.08061i
$718$	31.0572	−	8.32175i	1.15904	−	0.310565i
$719$	14.2117	+	24.6153i	0.530005	+	0.917996i	0.999387	+	0.0350008i	$0.0111434\pi$
$719$	14.2117	+	24.6153i	0.530005	+	0.917996i	−0.469382	+	0.882995i	$0.655523\pi$
$720$	−26.7407	−	19.1944i	−0.996566	−	0.715333i
$721$	−0.317850	+	1.18623i	−0.0118373	+	0.0441776i
$722$	67.5612	−	39.0065i	2.51437	−	1.45167i
$723$	−7.09498			−0.263865
$724$	97.9570	−	56.5555i	3.64054	−	2.10187i
$725$	4.57713	−	22.8204i	0.169990	−	0.847530i
$726$	6.73044	+	25.1183i	0.249790	+	0.932229i
$727$	8.56116	+	8.56116i	0.317516	+	0.317516i	0.847812	−	0.530296i	$-0.177919\pi$
$727$	8.56116	+	8.56116i	0.317516	+	0.317516i	−0.530296	+	0.847812i	$0.677919\pi$
$728$		0			0
$729$		−	26.1513i		−	0.968566i
$730$	22.1208	+	48.9255i	0.818728	+	1.81081i
$731$	−5.31873	+	9.21232i	−0.196720	+	0.340730i
$732$	−4.69082	+	17.5064i	−0.173378	+	0.647054i
$733$			17.2200i			0.636036i	0.948085	+	0.318018i	$0.103017\pi$
$733$			17.2200i			0.636036i	−0.948085	+	0.318018i	$0.896983\pi$
$734$	−35.8610	−	9.60893i	−1.32365	−	0.354672i
$735$	−12.8430	−	15.6747i	−0.473720	−	0.578169i
$736$	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
$739$	−15.7497	+	4.22013i	−0.579364	+	0.155240i	−0.536588	−	0.843845i	$-0.680287\pi$
$739$	−15.7497	+	4.22013i	−0.579364	+	0.155240i	−0.0427762	+	0.999085i	$0.513620\pi$
$740$	13.4526	+	9.65626i	0.494528	+	0.354971i
$741$		0			0
$742$	1.06915	−	1.06915i	0.0392498	−	0.0392498i
$743$	−28.6826	−	16.5599i	−1.05226	−	0.607525i	−0.128982	−	0.991647i	$-0.541171\pi$
$743$	−28.6826	−	16.5599i	−1.05226	−	0.607525i	−0.923282	+	0.384122i	$0.874504\pi$
$744$	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
$747$	5.62634	+	9.74510i	0.205857	+	0.356555i
$748$	−12.6982	−	21.9940i	−0.464293	−	0.804179i
$749$	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	0.804801	−	0.593545i	$-0.202272\pi$
$751$	18.9961	+	10.9674i	0.693176	+	0.400205i	−0.111625	+	0.993750i	$0.535605\pi$
$752$	3.33829	+	1.92736i	0.121735	+	0.0702836i
$753$	−11.9843	+	11.9843i	−0.436732	+	0.436732i
$754$		0			0
$755$	−4.35528	−	26.5111i	−0.158505	−	0.964838i
$756$	3.05152	−	0.817652i	0.110983	−	0.0297377i
$757$	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
$760$	96.3715	−	78.9615i	3.49576	−	2.86423i
$761$	21.2875	+	5.70396i	0.771670	+	0.206768i	0.623109	−	0.782135i	$-0.285869\pi$
$761$	21.2875	+	5.70396i	0.771670	+	0.206768i	0.148561	+	0.988903i	$0.452536\pi$
$762$		−	40.0993i		−	1.45265i
$763$	−0.137572	+	0.513426i	−0.00498044	+	0.0185873i
$764$	−49.2241	+	85.2587i	−1.78087	+	3.08455i
$765$	−7.52619	−	2.83951i	−0.272110	−	0.102663i
$766$		−	55.8361i		−	2.01744i
$767$		0			0
$768$	−3.12197	−	3.12197i	−0.112654	−	0.112654i
$769$	−5.46718	−	20.4038i	−0.197152	−	0.735780i	−0.991699	−	0.128578i	$-0.958959\pi$
$769$	−5.46718	−	20.4038i	−0.197152	−	0.735780i	0.794548	−	0.607202i	$-0.207708\pi$
$770$	0.435388	−	1.15400i	0.0156903	−	0.0415874i
$771$	−19.5984	+	11.3152i	−0.705820	+	0.407506i
$772$	−83.9143			−3.02014
$773$	−16.1909	+	9.34781i	−0.582346	+	0.336217i	−0.762065	−	0.647500i	$-0.775814\pi$
$773$	−16.1909	+	9.34781i	−0.582346	+	0.336217i	0.179719	+	0.983718i	$0.442481\pi$
$774$	−3.52206	+	13.1445i	−0.126598	+	0.472470i
$775$	1.95899	−	3.95652i	0.0703691	−	0.142122i
$776$	59.8985	+	103.747i	2.15023	+	3.72431i
$777$	−0.207583	+	0.0556218i	−0.00744702	+	0.00199542i
$778$	−0.0801293	+	0.138788i	−0.00287278	+	0.00497579i
$779$	−37.7619			−1.35296
$780$		0			0
$781$	−10.1421			−0.362912
$782$	11.6190	−	20.1246i	0.415493	−	0.719656i
$783$	25.1803	−	6.74705i	0.899872	−	0.241120i
$784$	−39.0246	−	67.5927i	−1.39374	−	2.41402i
$785$	2.63744	+	16.0544i	0.0941344	+	0.573008i
$786$	−6.63883	+	24.7764i	−0.236799	+	0.883747i
$787$	−37.5189	+	21.6615i	−1.33740	+	0.772150i	−0.986422	−	0.164232i	$-0.947485\pi$
$787$	−37.5189	+	21.6615i	−1.33740	+	0.772150i	−0.350981	+	0.936382i	$0.614152\pi$
$788$	76.2534			2.71642
$789$	23.4169	−	13.5198i	0.833665	−	0.481317i
$790$	−81.8948	+	37.0273i	−2.91369	+	1.31737i
$791$	0.177818	+	0.663626i	0.00632248	+	0.0235958i
$792$	−13.8227	−	13.8227i	−0.491168	−	0.491168i
$793$		0			0
$794$		−	21.7710i		−	0.772625i
$795$	13.4217	−	6.06840i	0.476020	−	0.215224i
$796$	35.0157	−	60.6489i	1.24110	−	2.14964i
$797$	−9.10089	+	33.9650i	−0.322370	+	1.20310i	0.594559	+	0.804052i	$0.297327\pi$
$797$	−9.10089	+	33.9650i	−0.322370	+	1.20310i	−0.916929	+	0.399050i	$0.869340\pi$
$798$			2.68726i			0.0951280i
$799$	0.909909	+	0.243809i	0.0321903	+	0.00862535i
$800$	44.8741	−	51.0047i	1.58654	−	1.80329i
$801$	−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
$804$	−0.907890	+	0.243268i	−0.0320188	+	0.00857942i
$805$	0.796423	−	0.130837i	0.0280702	−	0.00461141i
$806$		0			0
$807$	−9.69052	+	9.69052i	−0.341122	+	0.341122i
$808$	−57.6165	−	33.2649i	−2.02694	−	1.17026i
$809$	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	$-0.0656076\pi$
$811$	22.0471	+	22.0471i	0.774178	+	0.774178i	−0.204656	+	0.978834i	$0.565608\pi$
$812$	1.31299	+	2.27416i	0.0460769	+	0.0798075i
$813$	−5.12984	−	8.88514i	−0.179911	−	0.311615i
$814$	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
$817$	−23.4889	−	13.5613i	−0.821772	−	0.474450i
$818$	67.1180	−	67.1180i	2.34672	−	2.34672i
$819$		0			0
$820$	−60.1111	+	9.87512i	−2.09917	+	0.344854i
$821$	−35.4477	+	9.49818i	−1.23713	+	0.331489i	−0.817353	−	0.576137i	$-0.804559\pi$
$821$	−35.4477	+	9.49818i	−1.23713	+	0.331489i	−0.419780	+	0.907626i	$0.637893\pi$
$822$	−16.4412	−	61.3594i	−0.573453	−	2.14016i
$823$	22.8038	+	6.11025i	0.794889	+	0.212990i	0.633339	−	0.773875i	$-0.281684\pi$
$823$	22.8038	+	6.11025i	0.794889	+	0.212990i	0.161550	+	0.986865i	$0.448351\pi$
$824$	−61.8772	+	61.8772i	−2.15559	+	2.15559i
$825$	7.93692	−	9.02125i	0.276328	−	0.314079i
$826$	0.369404	+	0.0989816i	0.0128532	+	0.00344401i
$827$		−	4.44429i		−	0.154543i	−0.997010	−	0.0772716i	$-0.975379\pi$
$827$		−	4.44429i		−	0.154543i	0.997010	−	0.0772716i	$-0.0246209\pi$
$828$	5.50240	−	20.5352i	0.191222	−	0.713649i
$829$	14.6685	−	25.4065i	0.509457	−	0.882406i	−0.490483	−	0.871451i	$-0.663180\pi$
$829$	14.6685	−	25.4065i	0.509457	−	0.882406i	0.999940	−	0.0109548i	$-0.00348709\pi$
$830$	−46.0982	+	20.8425i	−1.60009	+	0.723454i
$831$			13.2474i			0.459548i
$832$		0			0
$833$	−13.4870	−	13.4870i	−0.467296	−	0.467296i
$834$	9.70441	+	36.2174i	0.336036	+	1.25410i
$835$	5.17728	−	2.34082i	0.179167	−	0.0810073i
$836$	56.0786	−	32.3770i	1.93952	−	1.11978i
$837$	4.94486			0.170919
$838$	30.0171	−	17.3304i	1.03692	−	0.598668i
$839$	−2.19656	+	8.19766i	−0.0758336	+	0.283015i	−0.993421	−	0.114519i	$-0.963467\pi$
$839$	−2.19656	+	8.19766i	−0.0758336	+	0.283015i	0.917587	+	0.397534i	$0.130134\pi$
$840$	0.422834	+	2.57384i	0.0145892	+	0.0888061i
$841$	−3.66554	−	6.34891i	−0.126398	−	0.218928i
$842$	49.9236	−	13.3770i	1.72048	−	0.461001i
$843$	11.4419	−	19.8180i	0.394081	−	0.682568i
$844$	−118.591			−4.08208
$845$		0			0
$846$	1.20508			0.0414316
$847$	−0.425057	+	0.736220i	−0.0146051	+	0.0252968i
$848$	54.8002	−	14.6837i	1.88185	−	0.504239i
$849$	5.36067	+	9.28495i	0.183978	+	0.318659i
$850$	16.0472	−	32.4101i	0.550415	−	1.11166i
$851$	−1.22638	+	4.57693i	−0.0420399	+	0.156895i
$852$	30.8705	−	17.8231i	1.05761	−	0.610610i
$853$	34.3415			1.17583			0.587915	−	0.808923i	$-0.299949\pi$
$853$	34.3415			1.17583			0.587915	+	0.808923i	$0.299949\pi$
$854$	−0.717491	+	0.414244i	−0.0245521	+	0.0141751i
$855$	7.23998	−	19.1897i	0.247602	−	0.656274i
$856$	15.3409	+	57.2531i	0.524342	+	1.95687i
$857$	−24.6090	−	24.6090i	−0.840626	−	0.840626i	0.148314	−	0.988940i	$-0.452615\pi$
$857$	−24.6090	−	24.6090i	−0.840626	−	0.840626i	−0.988940	+	0.148314i	$0.952615\pi$
$858$		0			0
$859$			12.8606i			0.438798i	0.975635	+	0.219399i	$0.0704097\pi$
$859$			12.8606i			0.438798i	−0.975635	+	0.219399i	$0.929590\pi$
$860$	−40.9371	−	15.4449i	−1.39594	−	0.526667i
$861$	0.395284	−	0.684653i	0.0134713	−	0.0233329i
$862$	−15.2379	+	56.8688i	−0.519007	+	1.93696i
$863$			2.75373i			0.0937379i	0.998901	+	0.0468690i	$0.0149243\pi$
$863$			2.75373i			0.0937379i	−0.998901	+	0.0468690i	$0.985076\pi$
$864$	73.4965	+	19.6933i	2.50040	+	0.669980i
$865$	0.136462	−	0.111809i	0.00463984	−	0.00380163i
$866$	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
$869$	−27.1487	+	7.27447i	−0.920957	+	0.246770i
$870$	5.79888	+	35.2985i	0.196601	+	1.19673i
$871$		0			0
$872$	−26.7817	+	26.7817i	−0.906944	+	0.906944i
$873$	17.0791	+	9.86060i	0.578039	+	0.333731i
$874$	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
$877$	−23.6316	−	40.9311i	−0.797981	−	1.38214i	−0.920929	−	0.389730i	$-0.872568\pi$
$877$	−23.6316	−	40.9311i	−0.797981	−	1.38214i	0.122948	−	0.992413i	$-0.460765\pi$
$878$	−22.9119	−	39.6847i	−0.773241	−	1.33929i
$879$	−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	0.961804	−	0.273739i	$-0.0882605\pi$
$881$	35.7854	+	20.6607i	1.20564	+	0.696077i	0.243837	+	0.969816i	$0.421594\pi$
$882$	−21.1311	−	12.2001i	−0.711523	−	0.410798i
$883$	−13.4808	+	13.4808i	−0.453666	+	0.453666i	−0.896569	−	0.442903i	$-0.853949\pi$
$883$	−13.4808	+	13.4808i	−0.453666	+	0.453666i	0.442903	+	0.896569i	$0.353949\pi$
$884$		0			0
$885$	3.02665	+	2.17252i	0.101740	+	0.0730285i
$886$	88.4897	−	23.7108i	2.97287	−	0.796578i
$887$	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
$890$	−2.13716	−	2.60837i	−0.0716377	−	0.0874329i
$891$	5.92339	+	1.58717i	0.198441	+	0.0531721i
$892$		−	48.8381i		−	1.63522i
$893$	−0.621647	+	2.32002i	−0.0208026	+	0.0776364i
$894$	−23.9211	+	41.4326i	−0.800042	+	1.38571i
$895$	19.5519	+	43.2438i	0.653549	+	1.44548i
$896$			1.01420i			0.0338819i
$897$		0			0
$898$	−69.6712	−	69.6712i	−2.32496	−	2.32496i
$899$	1.06382	+	3.97024i	0.0354805	+	0.132415i
$900$	6.50661	−	32.4404i	0.216887	−	1.08135i
$901$	12.0069	−	6.93217i	0.400007	−	0.230944i
$902$	−26.6379			−0.886946
$903$	0.491754	−	0.283915i	0.0163646	−	0.00944808i
$904$	−12.6705	+	47.2871i	−0.421416	+	1.57275i
$905$	40.9207	+	29.3728i	1.36025	+	0.976384i
$906$	20.6458	+	35.7595i	0.685910	+	1.18803i
$907$	−23.2963	+	6.24222i	−0.773541	+	0.207270i	−0.623935	−	0.781476i	$-0.714467\pi$
$907$	−23.2963	+	6.24222i	−0.773541	+	0.207270i	−0.149606	+	0.988746i	$0.547800\pi$
$908$	23.0367	−	39.9008i	0.764501	−	1.32416i
$909$	−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	$0.0790515\pi$
$912$	−50.4154	+	87.3221i	−1.66942	+	2.89152i
$913$	−15.2819	+	4.09477i	−0.505757	+	0.135517i
$914$	−12.4895	−	21.6324i	−0.413116	−	0.715537i
$915$	−7.96429	+	1.30838i	−0.263291	+	0.0432538i
$916$	23.0233	−	85.9241i	0.760711	−	2.83901i
$917$	−0.726199	+	0.419271i	−0.0239812	+	0.0138456i
$918$	40.5061			1.33690
$919$	−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
$921$	8.91097	+	33.2562i	0.293626	+	1.09583i
$922$	−61.6169	−	61.6169i	−2.02924	−	2.02924i
$923$		0			0
$924$			1.35567i			0.0445981i
$925$	−1.45020	+	7.23035i	−0.0476824	+	0.237733i
$926$	−24.7394	+	42.8498i	−0.812986	+	1.40813i
$927$	−3.72846	+	13.9148i	−0.122459	+	0.457022i
$928$			63.2473i			2.07619i
$929$	−27.1090	−	7.26384i	−0.889418	−	0.238319i	−0.214952	−	0.976625i	$-0.568960\pi$
$929$	−27.1090	−	7.26384i	−0.889418	−	0.238319i	−0.674466	+	0.738306i	$0.735626\pi$
$930$	−0.670472	+	6.75219i	−0.0219856	+	0.221413i
$931$	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
$934$	44.0428	−	11.8012i	1.44113	−	0.386148i
$935$	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	$0.0908428\pi$
$938$	−0.0372095	−	0.0214829i	−0.00121493	−	0.000701442i
$939$	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	$-0.200602\pi$
$941$	6.70533	+	6.70533i	0.218588	+	0.218588i	−0.589315	+	0.807903i	$0.700602\pi$
$942$	−12.5025	−	21.6550i	−0.407355	−	0.705559i
$943$	−8.71547	−	15.0956i	−0.283815	−	0.491582i
$944$	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
$947$	−3.90651	−	2.25542i	−0.126945	−	0.0732915i	0.435183	−	0.900342i	$-0.356684\pi$
$947$	−3.90651	−	2.25542i	−0.126945	−	0.0732915i	−0.562128	+	0.827051i	$0.690017\pi$
$948$	69.8518	−	69.8518i	2.26868	−	2.26868i
$949$		0			0
$950$	82.6367	+	40.9160i	2.68109	+	1.32749i
$951$	−10.6838	+	2.86272i	−0.346447	+	0.0928302i
$952$	0.635422	+	2.37143i	0.0205941	+	0.0768584i
$953$	−5.54756	−	1.48646i	−0.179703	−	0.0481513i	0.167845	−	0.985813i	$-0.446319\pi$
$953$	−5.54756	−	1.48646i	−0.179703	−	0.0481513i	−0.347548	+	0.937662i	$0.612986\pi$
$954$	12.5414	−	12.5414i	0.406043	−	0.406043i
$955$	−43.6270	−	4.33202i	−1.41174	−	0.140181i
$956$	124.946	+	33.4791i	4.04103	+	1.08279i
$957$			11.1866i			0.361612i
$958$	−22.6066	+	84.3690i	−0.730386	+	2.72584i
$959$	1.03833	−	1.79845i	0.0335296	−	0.0580749i
$960$	−13.9863	+	37.0710i	−0.451406	+	1.19646i
$961$		−	30.2203i		−	0.974849i
$962$		0			0
$963$	6.89966	+	6.89966i	0.222338	+	0.222338i
$964$	−7.10927	−	26.5322i	−0.228974	−	0.854543i
$965$	−15.3954	−	34.0505i	−0.495595	−	1.09613i
$966$	−1.07426	+	0.620222i	−0.0345636	+	0.0199553i
$967$	17.6414			0.567310			0.283655	−	0.958926i	$-0.408453\pi$
$967$	17.6414			0.567310			0.283655	+	0.958926i	$0.408453\pi$
$968$	−52.4599	+	30.2877i	−1.68612	+	0.973485i
$969$	−6.37750	+	23.8012i	−0.204875	+	0.764604i
$970$	−51.7028	+	72.0297i	−1.66008	+	2.31273i
$971$	−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
$973$	−0.612876	+	1.06153i	−0.0196479	+	0.0340312i
$974$	87.4056			2.80065
$975$		0			0
$976$	−31.0864			−0.995050
$977$	−7.67217	+	13.2886i	−0.245454	+	0.425139i	−0.962259	−	0.272134i	$-0.912270\pi$
$977$	−7.67217	+	13.2886i	−0.245454	+	0.425139i	0.716805	+	0.697274i	$0.245604\pi$
$978$	68.1088	−	18.2497i	2.17788	−	0.583561i
$979$	−0.527266	−	0.913252i	−0.0168515	−	0.0291877i
$980$	45.7477	−	63.7334i	1.46136	−	2.03589i
$981$	−1.61375	+	6.02261i	−0.0515232	+	0.192287i
$982$	−48.8686	+	28.2143i	−1.55946	+	0.900354i
$983$	4.80751			0.153336			0.0766679	−	0.997057i	$-0.475572\pi$
$983$	4.80751			0.153336			0.0766679	+	0.997057i	$0.475572\pi$
$984$	48.7854	−	28.1663i	1.55522	−	0.897908i
$985$	13.9899	+	30.9419i	0.445754	+	0.985891i
$986$	8.71437	+	32.5225i	0.277522	+	1.03573i
$987$	−0.0355565	−	0.0355565i	−0.00113177	−	0.00113177i
$988$		0			0
$989$		−	12.5198i		−	0.398108i
$990$	5.10721	−	13.5368i	0.162318	−	0.430227i
$991$	−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
$993$		−	23.3545i		−	0.741131i
$994$	1.57395	+	0.421739i	0.0499227	+	0.0133767i
$995$	31.0341	+	3.08159i	0.983848	+	0.0976931i
$996$	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
$999$	−7.97806	+	2.13771i	−0.252415	+	0.0676343i

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.o.g.488.5		20
5.2	odd	4		845.2.t.g.657.5		20
13.2	odd	12		845.2.t.g.418.5		20
13.3	even	3		845.2.o.f.258.5		20
13.4	even	6		845.2.k.e.268.10		20
13.5	odd	4		845.2.t.e.188.1		20
13.6	odd	12		845.2.f.d.408.10		20
13.7	odd	12		845.2.f.e.408.1		20
13.8	odd	4		845.2.t.f.188.5		20
13.9	even	3		845.2.k.d.268.1		20
13.10	even	6		845.2.o.e.258.1		20
13.11	odd	12		65.2.t.a.28.1	yes	20
13.12	even	2		65.2.o.a.33.1	yes	20
39.11	even	12		585.2.dp.a.28.5		20
39.38	odd	2		585.2.cf.a.163.5		20
65.2	even	12	inner	845.2.o.g.587.5		20
65.7	even	12		845.2.k.e.577.10		20
65.12	odd	4		65.2.t.a.7.1	yes	20
65.17	odd	12		845.2.f.e.437.10		20
65.22	odd	12		845.2.f.d.437.1		20
65.24	odd	12		325.2.x.b.93.5		20
65.32	even	12		845.2.k.d.577.1		20
65.37	even	12		65.2.o.a.2.1	✓	20
65.38	odd	4		325.2.x.b.7.5		20
65.42	odd	12		845.2.t.e.427.1		20
65.47	even	4		845.2.o.e.357.1		20
65.57	even	4		845.2.o.f.357.5		20
65.62	odd	12		845.2.t.f.427.5		20
65.63	even	12		325.2.s.b.132.5		20
65.64	even	2		325.2.s.b.293.5		20
195.77	even	4		585.2.dp.a.397.5		20
195.167	odd	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	65.37	even	12
65.2.o.a.33.1	yes	20	13.12	even	2
65.2.t.a.7.1	yes	20	65.12	odd	4
65.2.t.a.28.1	yes	20	13.11	odd	12
325.2.s.b.132.5		20	65.63	even	12
325.2.s.b.293.5		20	65.64	even	2
325.2.x.b.7.5		20	65.38	odd	4
325.2.x.b.93.5		20	65.24	odd	12
585.2.cf.a.163.5		20	39.38	odd	2
585.2.cf.a.262.5		20	195.167	odd	12
585.2.dp.a.28.5		20	39.11	even	12
585.2.dp.a.397.5		20	195.77	even	4
845.2.f.d.408.10		20	13.6	odd	12
845.2.f.d.437.1		20	65.22	odd	12
845.2.f.e.408.1		20	13.7	odd	12
845.2.f.e.437.10		20	65.17	odd	12
845.2.k.d.268.1		20	13.9	even	3
845.2.k.d.577.1		20	65.32	even	12
845.2.k.e.268.10		20	13.4	even	6
845.2.k.e.577.10		20	65.7	even	12
845.2.o.e.258.1		20	13.10	even	6
845.2.o.e.357.1		20	65.47	even	4
845.2.o.f.258.5		20	13.3	even	3
845.2.o.f.357.5		20	65.57	even	4
845.2.o.g.488.5		20	1.1	even	1	trivial
845.2.o.g.587.5		20	65.2	even	12	inner
845.2.t.e.188.1		20	13.5	odd	4
845.2.t.e.427.1		20	65.42	odd	12
845.2.t.f.188.5		20	13.8	odd	4
845.2.t.f.427.5		20	65.62	odd	12
845.2.t.g.418.5		20	13.2	odd	12
845.2.t.g.657.5		20	5.2	odd	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

Database

Properties

Related objects

Downloads

Learn more

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.o.g.488.5

Level	$845$
Weight	$2$
Character	845.488
Analytic conductor	$6.747$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$