LMFDB - Embedded newform 845.2.t.g.657.5

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,-2,6,0,8] 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			657.5
Root			$2.64975i$ of defining polynomial
Character	$\chi$	$=$	845.657
Dual form			845.2.t.g.418.5

$q$-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} +(0.335680 + 1.25278i) q^{3} +(2.51060 + 4.34849i) q^{4} +(-1.81654 + 1.30391i) q^{5} +(-0.889471 + 3.31955i) q^{6} +(-0.0561740 - 0.0972962i) q^{7} +8.00544i q^{8} +(1.14131 - 0.658935i) q^{9} +(-5.89604 + 0.585458i) q^{10} +(-0.479564 - 1.78976i) q^{11} +(-4.60492 + 4.60492i) q^{12} -0.297695i q^{14} +(-2.24328 - 1.83802i) q^{15} +(-5.58502 + 9.67354i) q^{16} +(-2.63669 - 0.706500i) q^{17} +3.49203 q^{18} +(6.72284 + 1.80138i) q^{19} +(-10.2306 - 4.62561i) q^{20} +(0.103034 - 0.103034i) q^{21} +(1.27073 - 4.74241i) q^{22} +(-3.10327 + 0.831519i) q^{23} +(-10.0290 + 2.68727i) 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} +(-2.71263 - 7.18989i) 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} +(0.228908 + 0.103497i) 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} +(5.24069 - 1.40424i) q^{41} +(0.372945 - 0.0999302i) q^{42} +(1.00860 - 3.76415i) q^{43} +(6.57874 - 6.57874i) q^{44} +(-1.21404 + 2.68515i) q^{45} +(-8.22291 - 2.20332i) q^{46} +0.345095 q^{47} +(-13.9936 - 3.74956i) q^{48} +(3.49369 - 6.05125i) q^{49} +(9.94700 - 8.75140i) q^{50} -3.54034i q^{51} +(-3.59144 + 3.59144i) q^{53} +(3.84062 + 14.3334i) q^{54} +(3.20483 + 2.62586i) q^{55} +(0.778898 - 0.449697i) q^{56} +9.02691i q^{57} +(-6.16729 - 10.6821i) q^{58} +(-0.332494 + 1.24088i) q^{59} +(2.36063 - 14.3694i) q^{60} +(1.39151 + 2.41016i) q^{61} +(0.605559 + 2.25998i) q^{62} +(-0.128224 - 0.0740300i) q^{63} -13.6621 q^{64} +6.36774 q^{66} +(-0.124992 - 0.0721643i) q^{67} +(-3.54747 - 13.2394i) q^{68} +(-2.08342 - 3.60858i) q^{69} +(0.388167 + 0.540774i) q^{70} +(1.41668 - 5.28713i) q^{71} +(5.27506 + 9.13667i) q^{72} +9.06221i q^{73} +(3.38447 - 1.95402i) q^{74} +(6.47163 + 0.413804i) q^{75} +(9.04509 + 33.7567i) q^{76} +(-0.147197 + 0.147197i) q^{77} +15.1689i q^{79} +(-2.46800 - 24.8547i) q^{80} +(-1.65480 + 2.86620i) q^{81} +(13.8865 + 3.72089i) q^{82} -8.53853 q^{83} +(0.706718 + 0.189365i) q^{84} +(5.71087 - 2.15462i) q^{85} +(7.30152 - 7.30152i) q^{86} +(1.56259 - 5.83166i) q^{87} +(14.3278 - 3.83912i) q^{88} +(-0.549735 + 0.147301i) 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} +(-14.5612 + 5.49370i) 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} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 8 * q^6 + 2 * q^7 + 12 * q^9 - 2 * q^10 + 16 * q^11 - 24 * q^12 + 20 * q^15 - 2 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^21 + 16 * q^22 - 10 * q^23 - 32 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 26 * q^30 - 48 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 + 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 + 40 * q^42 + 10 * q^43 + 36 * q^44 - 4 * q^46 + 40 * q^47 - 56 * q^48 + 18 * q^49 - 36 * q^50 - 10 * q^53 + 48 * q^54 - 10 * q^55 + 16 * q^59 - 28 * q^60 - 16 * q^61 - 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 22 * q^68 - 16 * q^69 + 12 * q^70 + 16 * q^71 - 4 * q^72 + 18 * q^74 - 38 * q^75 + 64 * q^76 - 28 * q^77 + 2 * q^80 - 14 * q^81 + 56 * q^82 - 48 * q^83 + 40 * q^84 + 26 * q^85 - 60 * q^86 - 34 * q^87 + 82 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 - 48 * q^94 - 26 * 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	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	$0.280412\pi$
$3$	0.335680	+	1.25278i	0.193805	+	0.723291i	0.992573	+	0.121651i	$0.0388189\pi$
$3$	0.335680	+	1.25278i	0.193805	+	0.723291i	−0.798768	+	0.601640i	$0.794514\pi$
$4$	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
$6$	−0.889471	+	3.31955i	−0.363125	+	1.35520i
$7$	−0.0561740	−	0.0972962i	−0.0212318	−	0.0367745i	0.855214	−	0.518275i	$-0.173425\pi$
$7$	−0.0561740	−	0.0972962i	−0.0212318	−	0.0367745i	−0.876446	+	0.481500i	$0.840092\pi$
$8$			8.00544i			2.83035i
$9$	1.14131	−	0.658935i	0.380436	−	0.219645i
$10$	−5.89604	+	0.585458i	−1.86449	+	0.185138i
$11$	−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
$15$	−2.24328	−	1.83802i	−0.579213	−	0.474575i
$16$	−5.58502	+	9.67354i	−1.39626	+	2.41838i
$17$	−2.63669	−	0.706500i	−0.639492	−	0.171351i	−0.0755186	−	0.997144i	$-0.524061\pi$
$17$	−2.63669	−	0.706500i	−0.639492	−	0.171351i	−0.563973	+	0.825793i	$0.690728\pi$
$18$	3.49203			0.823080
$19$	6.72284	+	1.80138i	1.54233	+	0.413265i	0.927016	−	0.375021i	$-0.122364\pi$
$19$	6.72284	+	1.80138i	1.54233	+	0.413265i	0.615309	+	0.788286i	$0.289031\pi$
$20$	−10.2306	−	4.62561i	−2.28764	−	1.03432i
$21$	0.103034	−	0.103034i	0.0224838	−	0.0224838i
$22$	1.27073	−	4.74241i	0.270920	−	1.01109i
$23$	−3.10327	+	0.831519i	−0.647077	+	0.173384i	−0.567407	−	0.823438i	$-0.692053\pi$
$23$	−3.10327	+	0.831519i	−0.647077	+	0.173384i	−0.0796701	+	0.996821i	$0.525387\pi$
$24$	−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
$28$	0.282061	−	0.488544i	0.0533045	−	0.0923261i
$29$	−4.03134	−	2.32749i	−0.748601	−	0.432205i	0.0765874	−	0.997063i	$-0.475598\pi$
$29$	−4.03134	−	2.32749i	−0.748601	−	0.432205i	−0.825188	+	0.564858i	$0.808931\pi$
$30$	−2.71263	−	7.18989i	−0.495257	−	1.31269i
$31$	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	$0.724733\pi$
$32$	−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
$35$	0.228908	+	0.103497i	0.0386925	+	0.0174941i
$36$	5.73074	+	3.30864i	0.955123	+	0.551441i
$37$	0.737435	−	1.27728i	0.121234	−	0.209983i	−0.799021	−	0.601303i	$-0.794648\pi$
$37$	0.737435	−	1.27728i	0.121234	−	0.209983i	0.920254	+	0.391321i	$0.127982\pi$
$38$	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	$0.277410\pi$
$42$	0.372945	−	0.0999302i	0.0575466	−	0.0154196i
$43$	1.00860	−	3.76415i	0.153810	−	0.574027i	−0.845394	−	0.534143i	$-0.820634\pi$
$43$	1.00860	−	3.76415i	0.153810	−	0.574027i	0.999204	−	0.0398840i	$-0.0126989\pi$
$44$	6.57874	−	6.57874i	0.991782	−	0.991782i
$45$	−1.21404	+	2.68515i	−0.180979	+	0.400278i
$46$	−8.22291	−	2.20332i	−1.21240	−	0.324862i
$47$	0.345095			0.0503372			0.0251686	−	0.999683i	$-0.491988\pi$
$47$	0.345095			0.0503372			0.0251686	+	0.999683i	$0.491988\pi$
$48$	−13.9936	−	3.74956i	−2.01980	−	0.541203i
$49$	3.49369	−	6.05125i	0.499098	−	0.864464i
$50$	9.94700	−	8.75140i	1.40672	−	1.23764i
$51$		−	3.54034i		−	0.495747i
$52$		0			0
$53$	−3.59144	+	3.59144i	−0.493322	+	0.493322i	−0.909351	−	0.416029i	$-0.863421\pi$
$53$	−3.59144	+	3.59144i	−0.493322	+	0.493322i	0.416029	+	0.909351i	$0.363421\pi$
$54$	3.84062	+	14.3334i	0.522642	+	1.95053i
$55$	3.20483	+	2.62586i	0.432139	+	0.354071i
$56$	0.778898	−	0.449697i	0.104085	−	0.0600933i
$57$			9.02691i			1.19564i
$58$	−6.16729	−	10.6821i	−0.809805	−	1.40262i
$59$	−0.332494	+	1.24088i	−0.0432870	+	0.161549i	−0.984186	−	0.177138i	$-0.943316\pi$
$59$	−0.332494	+	1.24088i	−0.0432870	+	0.161549i	0.940899	+	0.338687i	$0.109983\pi$
$60$	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	$0.776318\pi$
$62$	0.605559	+	2.25998i	0.0769061	+	0.287017i
$63$	−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	$0.669473\pi$
$68$	−3.54747	−	13.2394i	−0.430194	−	1.60551i
$69$	−2.08342	−	3.60858i	−0.250814	−	0.434422i
$70$	0.388167	+	0.540774i	0.0463948	+	0.0646349i
$71$	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	$-0.0219640\pi$
$72$	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
$75$	6.47163	+	0.413804i	0.747280	+	0.0477820i
$76$	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	$0.325414\pi$
$79$			15.1689i			1.70664i	−0.521388	+	0.853320i	$0.674586\pi$
$80$	−2.46800	−	24.8547i	−0.275931	−	2.77884i
$81$	−1.65480	+	2.86620i	−0.183867	+	0.318467i
$82$	13.8865	+	3.72089i	1.53351	+	0.410903i
$83$	−8.53853			−0.937226			−0.468613	−	0.883404i	$-0.655246\pi$
$83$	−8.53853			−0.937226			−0.468613	+	0.883404i	$0.655246\pi$
$84$	0.706718	+	0.189365i	0.0771093	+	0.0206614i
$85$	5.71087	−	2.15462i	0.619431	−	0.233702i
$86$	7.30152	−	7.30152i	0.787343	−	0.787343i
$87$	1.56259	−	5.83166i	0.167527	−	0.625219i
$88$	14.3278	−	3.83912i	1.52735	−	0.409251i
$89$	−0.549735	+	0.147301i	−0.0582718	+	0.0156139i	−0.287837	−	0.957679i	$-0.592936\pi$
$89$	−0.549735	+	0.147301i	−0.0582718	+	0.0156139i	0.229565	+	0.973293i	$0.426270\pi$
$90$	−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
$95$	−14.5612	+	5.49370i	−1.49394	+	0.563641i
$96$	−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
$100$	24.6157	−	4.93722i	2.46157	−	0.493722i
$101$	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	$0.530984\pi$
$102$	4.69052	−	8.12422i	0.464431	−	0.804418i
$103$	−7.72940	−	7.72940i	−0.761600	−	0.761600i	0.215011	−	0.976612i	$-0.431021\pi$
$103$	−7.72940	−	7.72940i	−0.761600	−	0.761600i	−0.976612	+	0.215011i	$0.931021\pi$
$104$		0			0
$105$	−0.0528184	+	0.321512i	−0.00515455	+	0.0313764i
$106$	−12.9997	+	3.48325i	−1.26264	+	0.338324i
$107$	7.15177	−	1.91631i	0.691388	−	0.185257i	0.104018	−	0.994575i	$-0.466830\pi$
$107$	7.15177	−	1.91631i	0.691388	−	0.185257i	0.587370	+	0.809318i	$0.300163\pi$
$108$	−7.27785	+	27.1613i	−0.700311	+	2.61360i
$109$	−3.34544	+	3.34544i	−0.320435	+	0.320435i	−0.848934	−	0.528499i	$-0.822755\pi$
$109$	−3.34544	+	3.34544i	−0.320435	+	0.320435i	0.528499	+	0.848934i	$0.322755\pi$
$110$	3.87535	+	10.2717i	0.369500	+	0.979368i
$111$	1.84768	+	0.495085i	0.175374	+	0.0469914i
$112$	1.25493			0.118580
$113$	−5.90688	−	1.58274i	−0.555672	−	0.148892i	−0.0299550	−	0.999551i	$-0.509536\pi$
$113$	−5.90688	−	1.58274i	−0.555672	−	0.148892i	−0.525717	+	0.850659i	$0.676203\pi$
$114$	−11.9595	+	20.7145i	−1.12011	+	1.94009i
$115$	4.55300	−	5.55688i	0.424569	−	0.518181i
$116$		−	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
$120$	14.7142	−	17.9585i	1.34321	−	1.63938i
$121$	6.55303	−	3.78340i	0.595730	−	0.343945i
$122$			7.37430i			0.667638i
$123$	3.51839	+	6.09404i	0.317243	+	0.549481i
$124$	−1.14751	+	4.28258i	−0.103050	+	0.384587i
$125$	3.27108	+	10.6911i	0.292574	+	0.956243i
$126$	−0.196161	−	0.339761i	−0.0174754	−	0.0302684i
$127$	−3.01994	−	11.2706i	−0.267976	−	1.00010i	−0.960403	−	0.278613i	$-0.910125\pi$
$127$	−3.01994	−	11.2706i	−0.267976	−	1.00010i	0.692427	−	0.721488i	$-0.256541\pi$
$128$	−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
$133$	−0.202381	−	0.755298i	−0.0175487	−	0.0654926i
$134$	−0.191218	−	0.331199i	−0.0165187	−	0.0286112i
$135$	−12.3567	−	2.02997i	−1.06349	−	0.174712i
$136$	5.65584	−	21.1079i	0.484984	−	1.80998i
$137$	−9.24213	−	16.0078i	−0.789608	−	1.36764i	−0.926207	−	0.377015i	$-0.876950\pi$
$137$	−9.24213	−	16.0078i	−0.789608	−	1.36764i	0.136599	−	0.990626i	$-0.456383\pi$
$138$		−	11.0411i		−	0.939879i
$139$	−9.44862	+	5.45516i	−0.801421	+	0.462701i	−0.843968	−	0.536394i	$-0.819786\pi$
$139$	−9.44862	+	5.45516i	−0.801421	+	0.462701i	0.0425466	+	0.999094i	$0.486453\pi$
$140$	0.124642	+	1.25524i	0.0105341	+	0.106087i
$141$	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
$145$	10.3579	−	1.02851i	0.860179	−	0.0854132i
$146$	−12.0063	+	20.7955i	−0.993650	+	1.72105i
$147$	8.75362	+	2.34553i	0.721987	+	0.193456i
$148$	7.40562			0.608738
$149$	−13.4468	−	3.60307i	−1.10161	−	0.295175i	−0.338189	−	0.941078i	$-0.609814\pi$
$149$	−13.4468	−	3.60307i	−1.10161	−	0.295175i	−0.763419	+	0.645903i	$0.776481\pi$
$150$	14.3026	+	9.52370i	1.16780	+	0.777607i
$151$	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	$0.0874035\pi$
$152$	−14.4208	+	53.8193i	−1.16968	+	4.36532i
$153$	−3.47482	+	0.931075i	−0.280922	+	0.0752729i
$154$	−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	0.471342	−	0.881951i	$-0.343770\pi$
$157$	−5.14491	−	5.14491i	−0.410609	−	0.410609i	−0.881951	+	0.471342i	$0.843770\pi$
$158$	−20.0970	+	34.8090i	−1.59883	+	2.76926i
$159$	−5.70484	−	3.29369i	−0.452423	−	0.261207i
$160$	12.5166	−	27.6833i	0.989520	−	2.18856i
$161$	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
$165$	−2.21381	+	4.89638i	−0.172345	+	0.381183i
$166$	−19.5938	−	11.3125i	−1.52078	−	0.878021i
$167$	−1.27050	+	2.20058i	−0.0983146	+	0.170286i	−0.910987	−	0.412435i	$-0.864678\pi$
$167$	−1.27050	+	2.20058i	−0.0983146	+	0.170286i	0.812673	+	0.582721i	$0.198012\pi$
$168$	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
$172$	18.9005	−	5.06438i	1.44115	−	0.386155i
$173$	0.0204199	−	0.0762079i	0.00155249	−	0.00579398i	−0.965145	−	0.261715i	$-0.915712\pi$
$173$	0.0204199	−	0.0762079i	0.00155249	−	0.00579398i	0.966698	+	0.255921i	$0.0823787\pi$
$174$	11.3120	−	11.3120i	0.857560	−	0.857560i
$175$	−0.550771	+	0.110469i	−0.0416343	+	0.00835067i
$176$	19.9916	+	5.35675i	1.50693	+	0.403780i
$177$	−1.66616			−0.125236
$178$	−1.45666	−	0.390312i	−0.109182	−	0.0292551i
$179$	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	$-0.124910\pi$
$180$	−14.7243	+	1.46208i	−1.09748	+	0.108977i
$181$			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
$185$	0.325870	+	3.28177i	0.0239584	+	0.241281i
$186$	−2.62797	+	1.51726i	−0.192692	+	0.111251i
$187$			5.05785i			0.369866i
$188$	0.866395	+	1.50064i	0.0631883	+	0.109445i
$189$	0.162840	−	0.607727i	0.0118449	−	0.0442056i
$190$	−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	$-0.417673\pi$
$192$	−4.58610	−	17.1156i	−0.330974	−	1.23521i
$193$	−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	$0.848617\pi$
$198$	−1.67465	−	6.24989i	−0.119012	−	0.444160i
$199$	−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
$201$	0.0484483	−	0.180811i	0.00341728	−	0.0127535i
$202$	11.0105	+	19.0707i	0.774696	+	1.34181i
$203$			0.522979i			0.0367059i
$204$	15.3951	−	8.88838i	1.07787	−	0.622311i
$205$	−7.68893	+	9.38424i	−0.537018	+	0.655424i
$206$	−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
$210$	−0.547169	+	0.667813i	−0.0377583	+	0.0460835i
$211$	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	$-0.135483\pi$
$212$	−24.6340	−	6.60065i	−1.69187	−	0.453335i
$213$	7.09915			0.486426
$214$	18.9504	+	5.07776i	1.29543	+	0.347108i
$215$	3.07594	+	8.15285i	0.209777	+	0.556019i
$216$	−31.7007	+	31.7007i	−2.15696	+	2.15696i
$217$	0.0256753	−	0.0958217i	0.00174296	−	0.00650480i
$218$	−12.1093	+	3.24467i	−0.820143	+	0.219757i
$219$	−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
$223$	4.86319	−	8.42330i	0.325664	−	0.564066i	−0.655983	−	0.754776i	$-0.727746\pi$
$223$	4.86319	−	8.42330i	0.325664	−	0.564066i	0.981646	+	0.190710i	$0.0610790\pi$
$224$	1.32196	+	0.763236i	0.0883274	+	0.0509958i
$225$	−1.29583	−	6.46068i	−0.0863886	−	0.430712i
$226$	−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	$-0.449043\pi$
$229$	−12.5270	−	12.5270i	−0.827811	−	0.827811i	−0.987214	+	0.159403i	$0.949043\pi$
$230$	17.8102	−	6.71950i	1.17437	−	0.443071i
$231$	−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	0.202142	−	0.979356i	$-0.435210\pi$
$233$	−11.8637	−	11.8637i	−0.777214	−	0.777214i	−0.979356	+	0.202142i	$0.935210\pi$
$234$		0			0
$235$	−0.626879	+	0.449972i	−0.0408931	+	0.0293530i
$236$	−6.23072	+	1.66952i	−0.405585	+	0.108676i
$237$	−19.0033	+	5.09192i	−1.23440	+	0.330756i
$238$	−0.210321	+	0.784929i	−0.0136331	+	0.0508794i
$239$	18.2161	−	18.2161i	1.17830	−	1.17830i	0.198124	−	0.980177i	$-0.436515\pi$
$239$	18.2161	−	18.2161i	1.17830	−	1.17830i	0.980177	−	0.198124i	$-0.0634848\pi$
$240$	30.3090	−	11.4351i	1.95644	−	0.738133i
$241$	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	$0.526956\pi$
$242$	20.0501			1.28887
$243$	12.0818	+	3.23730i	0.775046	+	0.207673i
$244$	−6.98703	+	12.1019i	−0.447299	+	0.774744i
$245$	1.54385	+	15.5478i	0.0986329	+	0.993312i
$246$			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
$250$	−6.65810	+	28.8673i	−0.421095	+	1.82573i
$251$	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	$0.198020\pi$
$252$		−	0.743439i		−	0.0468322i
$253$	2.97643	+	5.15533i	0.187127	+	0.324113i
$254$	8.00209	−	29.8642i	0.502096	−	1.87385i
$255$	4.61629	+	6.43118i	0.289083	+	0.402736i
$256$	1.70209	+	2.94811i	0.106381	+	0.184257i
$257$	4.51603	+	16.8541i	0.281702	+	1.05133i	0.951215	+	0.308528i	$0.0998362\pi$
$257$	4.51603	+	16.8541i	0.281702	+	1.05133i	−0.669513	+	0.742800i	$0.733497\pi$
$258$	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
$263$	5.39593	+	20.1379i	0.332727	+	1.24175i	0.906312	+	0.422608i	$0.138885\pi$
$263$	5.39593	+	20.1379i	0.332727	+	1.24175i	−0.573585	+	0.819146i	$0.694448\pi$
$264$	9.61911	+	16.6608i	0.592015	+	1.02540i
$265$	1.84108	−	11.2069i	0.113097	−	0.688434i
$266$	0.536261	−	2.00135i	0.0328803	−	0.122711i
$267$	−0.369071	−	0.639249i	−0.0225868	−	0.0391214i
$268$		−	0.724703i		−	0.0442683i
$269$	−9.15088	+	5.28326i	−0.557939	+	0.322126i	−0.752318	−	0.658800i	$-0.771064\pi$
$269$	−9.15088	+	5.28326i	−0.557939	+	0.322126i	0.194379	+	0.980927i	$0.437731\pi$
$270$	−25.6661	−	21.0294i	−1.56199	−	1.27981i
$271$	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
$275$	−9.24558	−	0.591174i	−0.557529	−	0.0356491i
$276$	10.4612	−	18.1194i	0.629693	−	1.09066i
$277$	9.86609	+	2.64361i	0.592796	+	0.158839i	0.542731	−	0.839907i	$-0.317390\pi$
$277$	9.86609	+	2.64361i	0.592796	+	0.158839i	0.0500653	+	0.998746i	$0.484057\pi$
$278$	−28.9097			−1.73389
$279$	1.12401	+	0.301178i	0.0672929	+	0.0180311i
$280$	−0.828536	+	1.83251i	−0.0495145	+	0.109513i
$281$	−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	$0.426413\pi$
$282$	−0.306952	+	1.14556i	−0.0182787	+	0.0682171i
$283$	−7.98478	+	2.13952i	−0.474646	+	0.127181i	−0.488208	−	0.872727i	$-0.662349\pi$
$283$	−7.98478	+	2.13952i	−0.474646	+	0.127181i	0.0135626	+	0.999908i	$0.495683\pi$
$284$	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
$288$	−8.95295	+	15.5070i	−0.527557	+	0.913756i
$289$	−8.26943	−	4.77436i	−0.486437	−	0.280844i
$290$	25.1316	+	11.3628i	1.47578	+	0.667247i
$291$	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
$295$	−1.01401	−	2.68766i	−0.0590380	−	0.156481i
$296$	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
$301$	−0.422894	+	0.113314i	−0.0243752	+	0.00653132i
$302$	30.7521	−	8.24001i	1.76959	−	0.474159i
$303$	−2.78970	+	10.4113i	−0.160264	+	0.598114i
$304$	−54.9729	+	54.9729i	−3.15291	+	3.15291i
$305$	−5.67036	−	2.56376i	−0.324684	−	0.146800i
$306$	−9.20741	−	2.46712i	−0.526353	−	0.141036i
$307$	26.5460			1.51506			0.757530	−	0.652801i	$-0.226406\pi$
$307$	26.5460			1.51506			0.757530	+	0.652801i	$0.226406\pi$
$308$	−1.00964	−	0.270532i	−0.0575296	−	0.0154150i
$309$	7.08860	−	12.2778i	0.403256	−	0.698460i
$310$	−4.04683	−	3.31575i	−0.229844	−	0.188322i
$311$			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	−0.860504	−	0.509444i	$-0.829851\pi$
$313$	−6.21088	+	6.21088i	−0.351060	+	0.351060i	0.509444	+	0.860504i	$0.329851\pi$
$314$	−4.98993	−	18.6227i	−0.281598	−	1.05094i
$315$	0.329452	−	0.0327136i	0.0185625	−	0.00184320i
$316$	−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
$319$	−2.23236	+	8.33129i	−0.124988	+	0.466463i
$320$	24.8178	−	17.8142i	1.38736	−	0.995842i
$321$	4.80142	+	8.31631i	0.267989	+	0.464171i
$322$	0.247539	+	0.923827i	0.0137948	+	0.0514829i
$323$	−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
$328$	11.2415	+	41.9540i	0.620710	+	2.31652i
$329$	−0.0193853	−	0.0335764i	−0.00106875	−	0.00185113i
$330$	−11.5673	+	8.30296i	−0.636757	+	0.457063i
$331$	−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	$0.918547\pi$
$332$	−21.4368	−	37.1297i	−1.17650	−	2.03776i
$333$		−	1.94369i		−	0.106513i
$334$	−5.83099	+	3.36652i	−0.319058	+	0.184208i
$335$	0.321149	−	0.0318891i	0.0175463	−	0.00174229i
$336$	0.421256	+	1.57215i	0.0229814	+	0.0857677i
$337$	−20.0865	+	20.0865i	−1.09418	+	1.09418i	−0.0991030	+	0.995077i	$0.531597\pi$
$337$	−20.0865	+	20.0865i	−1.09418	+	1.09418i	−0.995077	+	0.0991030i	$0.968403\pi$
$338$		0			0
$339$		−	7.93129i		−	0.430769i
$340$	23.7071	+	19.4242i	1.28570	+	1.05343i
$341$	0.818040	−	1.41689i	0.0442994	−	0.0767288i
$342$	23.4764	+	6.29048i	1.26946	+	0.340150i
$343$	−1.57145			−0.0848505
$344$	30.1336	+	8.07428i	1.62470	+	0.435336i
$345$	8.48987	+	3.83855i	0.457079	+	0.206661i
$346$	0.147825	−	0.147825i	0.00794710	−	0.00794710i
$347$	−1.85743	+	6.93201i	−0.0997119	+	0.372130i	−0.997692	−	0.0679068i	$-0.978368\pi$
$347$	−1.85743	+	6.93201i	−0.0997119	+	0.372130i	0.897980	+	0.440037i	$0.145035\pi$
$348$	29.2819	−	7.84607i	1.56968	−	0.420593i
$349$	−3.52885	+	0.945552i	−0.188895	+	0.0506143i	−0.352026	−	0.935990i	$-0.614507\pi$
$349$	−3.52885	+	0.945552i	−0.188895	+	0.0506143i	0.163131	+	0.986604i	$0.447841\pi$
$350$	−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	−0.841609	−	0.540087i	$-0.818391\pi$
$353$	0.881628	−	1.52702i	0.0469243	−	0.0812753i	0.888534	+	0.458812i	$0.151725\pi$
$354$	−3.82343	−	2.20746i	−0.203213	−	0.117325i
$355$	4.32048	+	11.4515i	0.229307	+	0.607784i
$356$	−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	$-0.353754\pi$
$359$	−8.58021	−	8.58021i	−0.452846	−	0.452846i	−0.896298	+	0.443452i	$0.853754\pi$
$360$	−21.4958	−	9.71894i	−1.13293	−	0.512233i
$361$	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
$366$	−9.23835	+	2.47541i	−0.482896	+	0.129392i
$367$	13.5337	−	3.62635i	0.706454	−	0.189294i	0.112334	−	0.993670i	$-0.464167\pi$
$367$	13.5337	−	3.62635i	0.706454	−	0.189294i	0.594120	+	0.804377i	$0.297501\pi$
$368$	9.28811	−	34.6637i	0.484176	−	1.80697i
$369$	5.05594	−	5.05594i	0.263202	−	0.263202i
$370$	−3.60015	+	7.96260i	−0.187163	+	0.413956i
$371$	0.551179	+	0.147688i	0.0286158	+	0.00766757i
$372$	−5.75032			−0.298140
$373$	27.9078	+	7.47789i	1.44501	+	0.387190i	0.894286	−	0.447495i	$-0.147684\pi$
$373$	27.9078	+	7.47789i	1.44501	+	0.387190i	0.550727	+	0.834685i	$0.314350\pi$
$374$	−6.70103	+	11.6065i	−0.346502	+	0.600159i
$375$	−12.2955	+	7.68673i	−0.634939	+	0.396941i
$376$			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	0.873882	−	0.486138i	$-0.161595\pi$
$379$	−2.45278	−	9.15390i	−0.125991	−	0.470204i	−0.999873	+	0.0159336i	$0.994928\pi$
$380$	−60.4465	−	49.5265i	−3.10084	−	2.54066i
$381$	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	$-0.985707\pi$
$383$	−10.5361	−	18.2490i	−0.538369	−	0.932483i	0.460623	−	0.887596i	$-0.347626\pi$
$384$	3.03028	−	11.3091i	0.154638	−	0.577118i
$385$	0.0754581	−	0.459322i	0.00384570	−	0.0234092i
$386$	−22.1414	−	38.3500i	−1.12697	−	1.95196i
$387$	−1.32920	−	4.96065i	−0.0675672	−	0.252164i
$388$	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
$393$	2.50545	+	9.35047i	0.126383	+	0.471669i
$394$	−20.1200	−	34.8488i	−1.01363	−	1.75566i
$395$	−19.7789	−	27.5550i	−0.995186	−	1.38644i
$396$	3.17341	−	11.8433i	0.159470	−	0.595150i
$397$	4.10812	+	7.11548i	0.206181	+	0.357116i	0.950508	−	0.310699i	$-0.100563\pi$
$397$	4.10812	+	7.11548i	0.206181	+	0.357116i	−0.744327	+	0.667815i	$0.767230\pi$
$398$		−	36.9565i		−	1.85246i
$399$	0.878284	−	0.507077i	0.0439692	−	0.0253856i
$400$	36.8915	+	41.9316i	1.84458	+	2.09658i
$401$	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
$405$	−0.731252	−	7.36429i	−0.0363362	−	0.365935i
$406$	−0.692882	+	1.20011i	−0.0343872	+	0.0595603i
$407$	−2.63966	−	0.707294i	−0.130843	−	0.0350593i
$408$	28.3420			1.40314
$409$	−34.6013	−	9.27138i	−1.71092	−	0.458440i	−0.735272	−	0.677772i	$-0.762946\pi$
$409$	−34.6013	−	9.27138i	−1.71092	−	0.458440i	−0.975650	+	0.219332i	$0.929612\pi$
$410$	−30.0772	+	11.3476i	−1.48541	+	0.560420i
$411$	16.9518	−	16.9518i	0.836173	−	0.836173i
$412$	14.2058	−	53.0166i	0.699867	−	2.61194i
$413$	0.139411	−	0.0373550i	0.00685995	−	0.00183812i
$414$	−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
$418$	17.0858	−	29.5934i	0.835693	−	1.44746i
$419$	−11.3282	−	6.54037i	−0.553421	−	0.319518i	0.197080	−	0.980387i	$-0.436854\pi$
$419$	−11.3282	−	6.54037i	−0.553421	−	0.319518i	−0.750501	+	0.660870i	$0.770188\pi$
$420$	−1.53070	+	0.577508i	−0.0746903	+	0.0281795i
$421$	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	$0.592333\pi$
$422$	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
$425$	−7.56460	+	11.3604i	−0.366937	+	0.551061i
$426$	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
$431$	−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	$0.596403\pi$
$432$	−60.4224	+	16.1901i	−2.90707	+	0.778948i
$433$	0.0475058	−	0.177294i	0.00228298	−	0.00852021i	−0.964775	−	0.263077i	$-0.915263\pi$
$433$	0.0475058	−	0.177294i	0.00228298	−	0.00852021i	0.967058	+	0.254556i	$0.0819295\pi$
$434$	0.185871	−	0.185871i	0.00892207	−	0.00892207i
$435$	4.76545	+	12.6309i	0.228486	+	0.605606i
$436$	−22.9467	−	6.14854i	−1.09895	−	0.294462i
$437$	−22.3607			−1.06966
$438$	−30.0825	−	8.06057i	−1.43740	−	0.385149i
$439$	−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	$0.302077\pi$
$440$	−21.0211	+	25.6560i	−1.00214	+	1.22310i
$441$		−	9.20846i		−	0.438498i
$442$		0			0
$443$	24.4472	−	24.4472i	1.16152	−	1.16152i	0.177377	−	0.984143i	$-0.443239\pi$
$443$	24.4472	−	24.4472i	1.16152	−	1.16152i	0.984143	−	0.177377i	$-0.0567611\pi$
$444$	2.48592	+	9.27758i	0.117977	+	0.440295i
$445$	0.806549	−	0.984383i	0.0382341	−	0.0466643i
$446$	22.3197	−	12.8863i	1.05687	−	0.610183i
$447$		−	18.0554i		−	0.853989i
$448$	0.767456	+	1.32927i	0.0362589	+	0.0628022i
$449$	−9.62407	+	35.9175i	−0.454188	+	1.69505i	0.236277	+	0.971686i	$0.424073\pi$
$449$	−9.62407	+	35.9175i	−0.454188	+	1.69505i	−0.690465	+	0.723366i	$0.742594\pi$
$450$	5.58600	−	16.5425i	0.263326	−	0.779820i
$451$	−5.02649	−	8.70613i	−0.236688	−	0.409956i
$452$	−7.94727	−	29.6596i	−0.373808	−	1.39507i
$453$	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	$0.595902\pi$
$458$	−12.1497	−	45.3433i	−0.567718	−	2.11875i
$459$	−7.64337	−	13.2387i	−0.356762	−	0.617930i
$460$	35.5947	+	5.84755i	1.65961	+	0.272643i
$461$	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	$-0.194335\pi$
$462$	−0.357701	−	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
$465$	−0.253032	−	2.54823i	−0.0117341	−	0.118171i
$466$	−11.5063	−	42.9421i	−0.533019	−	1.98925i
$467$	−12.1678	+	12.1678i	−0.563057	+	0.563057i	−0.930175	−	0.367118i	$-0.880345\pi$
$467$	−12.1678	+	12.1678i	−0.563057	+	0.563057i	0.367118	+	0.930175i	$0.380345\pi$
$468$		0			0
$469$			0.0162150i			0.000748740i
$470$	−2.03469	+	0.202039i	−0.0938533	+	0.00931935i
$471$	4.71838	−	8.17247i	0.217411	−	0.376568i
$472$	−9.93381	−	2.66176i	−0.457241	−	0.122517i
$473$	−7.22059			−0.332003
$474$	−50.3541	−	13.4923i	−2.31284	−	0.619723i
$475$	19.2876	−	28.9659i	0.884978	−	1.32905i
$476$	−1.08886	+	1.08886i	−0.0499080	+	0.0499080i
$477$	−1.73242	+	6.46546i	−0.0793219	+	0.296033i
$478$	65.9355	−	17.6674i	3.01582	−	0.808087i
$479$	31.8403	−	8.53158i	1.45482	−	0.389818i	0.557123	−	0.830430i	$-0.311905\pi$
$479$	31.8403	−	8.53158i	1.45482	−	0.389818i	0.897697	+	0.440612i	$0.145239\pi$
$480$	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
$485$	−13.7855	+	30.4899i	−0.625967	+	1.38448i
$486$	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
$490$	−17.0562	+	37.7238i	−0.770519	+	1.70419i
$491$	−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	$0.826223\pi$
$492$	−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
$496$	−9.52693	+	2.55273i	−0.427772	+	0.114621i
$497$	−0.593999	+	0.159161i	−0.0266445	+	0.00713937i
$498$	7.59477	−	28.3441i	0.340330	−	1.27013i
$499$	14.9199	−	14.9199i	0.667904	−	0.667904i	−0.289326	−	0.957231i	$-0.593431\pi$
$499$	14.9199	−	14.9199i	0.667904	−	0.667904i	0.957231	+	0.289326i	$0.0934312\pi$
$500$	−38.2778	+	41.0654i	−1.71184	+	1.83650i
$501$	−3.18332	−	0.852967i	−0.142220	−	0.0381077i
$502$	34.6261			1.54544
$503$	−42.1943	−	11.3059i	−1.88135	−	0.504106i	−0.999467	−	0.0326345i	$-0.989610\pi$
$503$	−42.1943	−	11.3059i	−1.88135	−	0.504106i	−0.881881	−	0.471471i	$-0.843723\pi$
$504$	0.592643	−	1.02649i	0.0263984	−	0.0457234i
$505$	−18.4921	+	1.83621i	−0.822887	+	0.0817102i
$506$			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	$0.227211\pi$
$509$	9.67023	+	36.0898i	0.428626	+	1.59965i	−0.327250	+	0.944938i	$0.606122\pi$
$510$	2.07272	+	20.8740i	0.0917818	+	0.924316i
$511$	0.881719	−	0.509060i	0.0390049	−	0.0225195i
$512$			27.0748i			1.19655i
$513$	19.4885	+	33.7551i	0.860438	+	1.49032i
$514$	−11.9664	+	44.6591i	−0.527814	+	1.96983i
$515$	24.1192	+	3.96233i	1.06282	+	0.174601i
$516$	12.6891	+	21.9781i	0.558605	+	0.967533i
$517$	−0.165495	−	0.617635i	−0.00727846	−	0.0271636i
$518$	−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
$523$	−1.11694	−	4.16849i	−0.0488406	−	0.182275i	0.937196	−	0.348802i	$-0.113411\pi$
$523$	−1.11694	−	4.16849i	−0.0488406	−	0.182275i	−0.986037	+	0.166527i	$0.946745\pi$
$524$	18.7386	+	32.4562i	0.818600	+	1.41786i
$525$	−0.323276	−	0.652910i	−0.0141089	−	0.0284953i
$526$	−14.2979	+	53.3604i	−0.623417	+	2.32662i
$527$	−1.20515	−	2.08738i	−0.0524971	−	0.0909276i
$528$			26.8432i			1.16820i
$529$	−10.9797	+	6.33914i	−0.477379	+	0.275615i
$530$	19.0726	−	23.2779i	0.828461	−	1.01113i
$531$	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
$535$	−10.4928	+	12.8063i	−0.453643	+	0.553666i
$536$	0.577707	−	1.00062i	0.0249531	−	0.0432201i
$537$	26.5890	+	7.12450i	1.14740	+	0.307445i
$538$	−27.9987			−1.20711
$539$	−12.5057	−	3.35089i	−0.538659	−	0.144333i
$540$	−22.1954	−	58.8293i	−0.955136	−	2.53161i
$541$	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	$0.197238\pi$
$542$	−5.42507	+	20.2467i	−0.233027	+	0.869668i
$543$	−28.2209	+	7.56177i	−1.21108	+	0.324507i
$544$	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	0.911438	−	0.411438i	$-0.134973\pi$
$547$	11.6940	+	11.6940i	0.500000	+	0.500000i	−0.411438	+	0.911438i	$0.634973\pi$
$548$	46.4066	−	80.3785i	1.98239	−	3.43360i
$549$	3.17628	+	1.83382i	0.135560	+	0.0782657i
$550$	−20.4331	−	13.6059i	−0.871270	−	0.580156i
$551$	−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
$555$	−4.00194	+	1.50987i	−0.169873	+	0.0640904i
$556$	−47.4434	−	27.3915i	−2.01205	−	1.16166i
$557$	−2.43751	+	4.22190i	−0.103281	+	0.178888i	−0.913034	−	0.407882i	$-0.866267\pi$
$557$	−2.43751	+	4.22190i	−0.103281	+	0.178888i	0.809754	+	0.586770i	$0.199601\pi$
$558$	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
$562$	−45.1595	+	12.1004i	−1.90494	+	0.510426i
$563$	−10.0853	+	37.6390i	−0.425047	+	1.58630i	0.338774	+	0.940868i	$0.389988\pi$
$563$	−10.0853	+	37.6390i	−0.425047	+	1.58630i	−0.763821	+	0.645428i	$0.776679\pi$
$564$	−1.58913	+	1.58913i	−0.0669146	+	0.0669146i
$565$	12.7938	−	4.82692i	0.538241	−	0.203070i
$566$	−21.1577	−	5.66919i	−0.889325	−	0.238294i
$567$	0.371828			0.0156153
$568$	42.3258	+	11.3412i	1.77595	+	0.475865i
$569$	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	$0.142075\pi$
$570$	−5.28488	−	53.2230i	−0.221359	−	2.22926i
$571$			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
$575$	−1.02504	+	16.0310i	−0.0427472	+	0.668538i
$576$	−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
$579$	5.60990	−	20.9364i	0.233139	−	0.870088i
$580$	30.4771	+	42.4591i	1.26549	+	1.76302i
$581$	0.479643	+	0.830767i	0.0198990	+	0.0344660i
$582$	13.3104	+	49.6753i	0.551736	+	2.05911i
$583$	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	$0.620161\pi$
$588$	11.7774	+	43.9537i	0.485690	+	1.81262i
$589$	3.07280	+	5.32224i	0.126612	+	0.219299i
$590$	1.23391	−	7.51095i	0.0507992	−	0.309221i
$591$	5.09774	−	19.0250i	0.209693	−	0.782585i
$592$	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
$595$	−0.530439	−	0.434612i	−0.0217459	−	0.0178174i
$596$	−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	$0.0917918\pi$
$599$			13.9207i			0.568784i	−0.958708	+	0.284392i	$0.908208\pi$
$600$	−3.31268	+	51.8082i	−0.135240	+	2.11506i
$601$	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	$0.151640\pi$
$602$	−1.12057	−	0.300255i	−0.0456708	−	0.0122375i
$603$	−0.190206			−0.00774580
$604$	58.2743	+	15.6145i	2.37115	+	0.635347i
$605$	−6.97065	+	15.4173i	−0.283397	+	0.626801i
$606$	−20.1954	+	20.1954i	−0.820381	+	0.820381i
$607$	6.10830	−	22.7965i	0.247928	−	0.925282i	−0.723960	−	0.689842i	$-0.757680\pi$
$607$	6.10830	−	22.7965i	0.247928	−	0.925282i	0.971889	−	0.235440i	$-0.0756531\pi$
$608$	−91.3432	+	24.4753i	−3.70446	+	0.992606i
$609$	−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
$613$	−5.32964	+	9.23121i	−0.215262	+	0.372845i	−0.953354	−	0.301856i	$-0.902394\pi$
$613$	−5.32964	+	9.23121i	−0.215262	+	0.372845i	0.738091	+	0.674701i	$0.235727\pi$
$614$	60.9165	+	35.1702i	2.45839	+	1.41935i
$615$	−14.3374	−	6.48240i	−0.578139	−	0.261396i
$616$	−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	$-0.409070\pi$
$619$	−16.8604	−	16.8604i	−0.677679	−	0.677679i	−0.959474	+	0.281796i	$0.909070\pi$
$620$	−3.49959	−	9.27574i	−0.140547	−	0.372523i
$621$	−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
$626$	−22.4811	+	6.02379i	−0.898526	+	0.240759i
$627$	16.1560	−	4.32898i	0.645207	−	0.172883i
$628$	9.45576	−	35.2894i	0.377326	−	1.40820i
$629$	−2.84678	+	2.84678i	−0.113509	+	0.113509i
$630$	0.799353	+	0.361414i	0.0318470	+	0.0143991i
$631$	−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	$0.791763\pi$
$632$	−121.434			−4.83038
$633$	29.5882	+	7.92814i	1.17603	+	0.315115i
$634$	−11.2987	+	19.5700i	−0.448729	+	0.777222i
$635$	20.1816	+	16.5357i	0.800884	+	0.656200i
$636$		−	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
$640$	20.0868	−	1.99456i	0.794001	−	0.0788418i
$641$	−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	$0.431034\pi$
$642$			25.4452i			1.00424i
$643$	11.1740	+	19.3539i	0.440660	+	0.763245i	0.997739	−	0.0672147i	$-0.0214113\pi$
$643$	11.1740	+	19.3539i	0.440660	+	0.763245i	−0.557079	+	0.830460i	$0.688078\pi$
$644$	−0.469078	+	1.75062i	−0.0184843	+	0.0689842i
$645$	−9.18116	+	6.59022i	−0.361508	+	0.259490i
$646$	−25.1710	−	43.5974i	−0.990340	−	1.71532i
$647$	1.21024	+	4.51668i	0.0475795	+	0.177569i	0.985627	−	0.168939i	$-0.0540340\pi$
$647$	1.21024	+	4.51668i	0.0475795	+	0.177569i	−0.938047	+	0.346508i	$0.887367\pi$
$648$	−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
$653$	6.34274	+	23.6714i	0.248211	+	0.926335i	0.971742	+	0.236044i	$0.0758509\pi$
$653$	6.34274	+	23.6714i	0.248211	+	0.926335i	−0.723532	+	0.690291i	$0.757482\pi$
$654$	−8.12969	−	14.0810i	−0.317896	−	0.550612i
$655$	−13.5583	+	9.73212i	−0.529766	+	0.380265i
$656$	−15.6854	+	58.5387i	−0.612412	+	2.28555i
$657$	5.97141	+	10.3428i	0.232967	+	0.403510i
$658$		−	0.102733i		−	0.00400494i
$659$	35.2803	−	20.3691i	1.37433	−	0.793467i	0.382856	−	0.923808i	$-0.374941\pi$
$659$	35.2803	−	20.3691i	1.37433	−	0.793467i	0.991469	+	0.130341i	$0.0416072\pi$
$660$	−26.8498	+	2.66611i	−1.04513	+	0.103778i
$661$	−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
$665$	1.35247	+	1.10814i	0.0524467	+	0.0429719i
$666$	2.57515	−	4.46029i	0.0997850	−	0.172833i
$667$	14.4457	+	3.87071i	0.559340	+	0.149875i
$668$	−12.7589			−0.493657
$669$	12.1850	+	3.26496i	0.471099	+	0.126231i
$670$	0.779208	+	0.352306i	0.0301034	+	0.0136107i
$671$	3.64628	−	3.64628i	0.140763	−	0.140763i
$672$	−0.512407	+	1.91233i	−0.0197665	+	0.0737696i
$673$	−23.0041	+	6.16392i	−0.886742	+	0.237602i	−0.673314	−	0.739357i	$-0.735130\pi$
$673$	−23.0041	+	6.16392i	−0.886742	+	0.237602i	−0.213428	+	0.976959i	$0.568463\pi$
$674$	−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	0.999990	+	0.00443504i	$0.00141172\pi$
$677$	26.1344	+	26.1344i	1.00443	+	1.00443i	0.00443504	+	0.999990i	$0.498588\pi$
$678$	10.5080	−	18.2004i	0.403557	−	0.698981i
$679$	−1.45598	−	0.840613i	−0.0558756	−	0.0322598i
$680$	17.2487	+	45.7180i	0.661457	+	1.75321i
$681$	−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
$685$	37.6615	+	17.0280i	1.43897	+	0.650606i
$686$	−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
$691$	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	$0.138025\pi$
$692$	0.382655	−	0.102532i	0.0145464	−	0.00389769i
$693$	−0.0710042	+	0.264991i	−0.00269723	+	0.0100662i
$694$	−13.4464	+	13.4464i	−0.510419	+	0.510419i
$695$	10.0508	−	22.2297i	0.381247	−	0.843219i
$696$	46.6850	+	12.5092i	1.76959	+	0.474160i
$697$	−14.8102			−0.560976
$698$	−9.35058	−	2.50548i	−0.353925	−	0.0948339i
$699$	10.8801	−	18.8449i	0.411524	−	0.712780i
$700$	−1.86314	−	2.11768i	−0.0704200	−	0.0800406i
$701$			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
$705$	−0.774146	−	0.634292i	−0.0291560	−	0.0238888i
$706$	4.04624	−	2.33610i	0.152282	−	0.0879202i
$707$		−	0.933677i		−	0.0351145i
$708$	−4.18306	−	7.24528i	−0.157209	−	0.272294i
$709$	2.64139	−	9.85779i	0.0991993	−	0.370217i	−0.898423	−	0.439130i	$-0.855287\pi$
$709$	2.64139	−	9.85779i	0.0991993	−	0.370217i	0.997623	+	0.0689135i	$0.0219533\pi$
$710$	−5.25742	+	32.0025i	−0.197307	+	1.20103i
$711$	9.99535	+	17.3124i	0.374855	+	0.649268i
$712$	−1.17921	−	4.40087i	−0.0441927	−	0.164930i
$713$	−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
$718$	−8.32175	−	31.0572i	−0.310565	−	1.15904i
$719$	−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
$721$	−0.317850	+	1.18623i	−0.0118373	+	0.0441776i
$722$	39.0065	+	67.5612i	1.45167	+	2.51437i
$723$			7.09498i			0.263865i
$724$	−97.9570	+	56.5555i	−3.64054	+	2.10187i
$725$	−17.4745	+	15.3741i	−0.648987	+	0.570981i
$726$	6.73044	+	25.1183i	0.249790	+	0.932229i
$727$	−8.56116	+	8.56116i	−0.317516	+	0.317516i	−0.847812	−	0.530296i	$-0.822081\pi$
$727$	−8.56116	+	8.56116i	−0.317516	+	0.317516i	0.530296	+	0.847812i	$0.322081\pi$
$728$		0			0
$729$			26.1513i			0.968566i
$730$	−5.30555	−	53.4311i	−0.196367	−	1.97757i
$731$	−5.31873	+	9.21232i	−0.196720	+	0.340730i
$732$	−17.5064	−	4.69082i	−0.647054	−	0.173378i
$733$	17.2200			0.636036			0.318018	−	0.948085i	$-0.396983\pi$
$733$	17.2200			0.636036			0.318018	+	0.948085i	$0.396983\pi$
$734$	35.8610	+	9.60893i	1.32365	+	0.354672i
$735$	−18.9597	+	7.15319i	−0.699338	+	0.263849i
$736$	30.8663	−	30.8663i	1.13775	−	1.13775i
$737$	−0.0692148	+	0.258313i	−0.00254956	+	0.00951508i
$738$	18.3007	−	4.90365i	0.673656	−	0.180506i
$739$	15.7497	−	4.22013i	0.579364	−	0.155240i	0.0427762	−	0.999085i	$-0.486380\pi$
$739$	15.7497	−	4.22013i	0.579364	−	0.155240i	0.536588	+	0.843845i	$0.319713\pi$
$740$	−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	$0.374504\pi$
$743$	−16.5599	+	28.6826i	−0.607525	+	1.05226i	−0.991647	+	0.128982i	$0.958829\pi$
$744$	−7.93963	−	4.58395i	−0.291081	−	0.168056i
$745$	29.1248	−	10.9883i	1.06705	−	0.402581i
$746$	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
$750$	−38.3992	+	1.34907i	−1.40214	+	0.0492609i
$751$	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	$0.535605\pi$
$752$	−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
$756$	3.05152	−	0.817652i	0.110983	−	0.0297377i
$757$	−2.84678	+	0.762791i	−0.103468	+	0.0277241i	−0.310181	−	0.950677i	$-0.600390\pi$
$757$	−2.84678	+	0.762791i	−0.103468	+	0.0277241i	0.206714	+	0.978401i	$0.433723\pi$
$758$	6.49926	−	24.2556i	0.236064	−	0.881002i
$759$	−5.45935	+	5.45935i	−0.198162	+	0.198162i
$760$	−43.9794	−	116.568i	−1.59530	−	4.22838i
$761$	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	$0.452536\pi$
$762$	40.0993			1.45265
$763$	0.513426	+	0.137572i	0.0185873	+	0.00498044i
$764$	49.2241	−	85.2587i	1.78087	−	3.08455i
$765$	5.09811	−	6.22218i	0.184323	−	0.224963i
$766$		−	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	$0.0410413\pi$
$769$	5.46718	+	20.4038i	0.197152	+	0.735780i	−0.794548	+	0.607202i	$0.792292\pi$
$770$	0.781703	−	0.954059i	0.0281706	−	0.0343819i
$771$	−19.5984	+	11.3152i	−0.705820	+	0.407506i
$772$		−	83.9143i		−	3.02014i
$773$	9.34781	+	16.1909i	0.336217	+	0.582346i	0.983718	−	0.179719i	$-0.0575189\pi$
$773$	9.34781	+	16.1909i	0.336217	+	0.582346i	−0.647500	+	0.762065i	$0.724186\pi$
$774$	3.52206	−	13.1445i	0.126598	−	0.472470i
$775$	3.95652	−	1.95899i	0.142122	−	0.0703691i
$776$	59.8985	+	103.747i	2.15023	+	3.72431i
$777$	−0.0556218	−	0.207583i	−0.00199542	−	0.00744702i
$778$	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
$783$	−6.74705	−	25.1803i	−0.241120	−	0.899872i
$784$	39.0246	+	67.5927i	1.39374	+	2.41402i
$785$	16.0544	+	2.63744i	0.573008	+	0.0941344i
$786$	−6.63883	+	24.7764i	−0.236799	+	0.883747i
$787$	−21.6615	−	37.5189i	−0.772150	−	1.33740i	−0.936382	−	0.350981i	$-0.885848\pi$
$787$	−21.6615	−	37.5189i	−0.772150	−	1.33740i	0.164232	−	0.986422i	$-0.447485\pi$
$788$		−	76.2534i		−	2.71642i
$789$	−23.4169	+	13.5198i	−0.833665	+	0.481317i
$790$	−8.88078	−	89.4366i	−0.315964	−	3.18201i
$791$	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
$795$	14.6578	−	1.45547i	0.519857	−	0.0516202i
$796$	35.0157	−	60.6489i	1.24110	−	2.14964i
$797$	−33.9650	−	9.10089i	−1.20310	−	0.322370i	−0.399050	−	0.916929i	$-0.630660\pi$
$797$	−33.9650	−	9.10089i	−1.20310	−	0.322370i	−0.804052	+	0.594559i	$0.797327\pi$
$798$	2.68726			0.0951280
$799$	−0.909909	−	0.243809i	−0.0321903	−	0.00862535i
$800$	13.3597	+	66.6084i	0.472338	+	2.35496i
$801$	−0.530356	+	0.530356i	−0.0187392	+	0.0187392i
$802$	−6.17139	+	23.0319i	−0.217919	+	0.813286i
$803$	16.2191	−	4.34591i	0.572361	−	0.153364i
$804$	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
$808$	−33.2649	+	57.6165i	−1.17026	+	2.02694i
$809$	−17.8779	−	10.3218i	−0.628554	−	0.362896i	0.151638	−	0.988436i	$-0.451545\pi$
$809$	−17.8779	−	10.3218i	−0.628554	−	0.362896i	−0.780192	+	0.625540i	$0.784879\pi$
$810$	8.07874	−	17.8681i	0.283858	−	0.627820i
$811$	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	$0.565608\pi$
$812$	−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
$815$	18.9010	−	41.8041i	0.662074	−	1.46433i
$816$	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
$821$	−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	$0.637893\pi$
$822$	61.3594	−	16.4412i	2.14016	−	0.573453i
$823$	6.11025	−	22.8038i	0.212990	−	0.794889i	−0.773875	−	0.633339i	$-0.781684\pi$
$823$	6.11025	−	22.8038i	0.212990	−	0.794889i	0.986865	−	0.161550i	$-0.0516494\pi$
$824$	61.8772	−	61.8772i	2.15559	−	2.15559i
$825$	−2.36295	−	11.7811i	−0.0822674	−	0.410165i
$826$	0.369404	+	0.0989816i	0.0128532	+	0.00344401i
$827$	4.44429			0.154543			0.0772716	−	0.997010i	$-0.475379\pi$
$827$	4.44429			0.154543			0.0772716	+	0.997010i	$0.475379\pi$
$828$	−20.5352	−	5.50240i	−0.713649	−	0.191222i
$829$	−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	$0.996513\pi$
$830$	50.3435	−	4.99895i	1.74745	−	0.173516i
$831$			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
$835$	−0.561431	−	5.65406i	−0.0194291	−	0.195667i
$836$	56.0786	−	32.3770i	1.93952	−	1.11978i
$837$			4.94486i			0.170919i
$838$	−17.3304	−	30.0171i	−0.598668	−	1.03692i
$839$	2.19656	−	8.19766i	0.0758336	−	0.283015i	−0.917587	−	0.397534i	$-0.869866\pi$
$839$	2.19656	−	8.19766i	0.0758336	−	0.283015i	0.993421	+	0.114519i	$0.0365327\pi$
$840$	−2.57384	−	0.422834i	−0.0888061	−	0.0145892i
$841$	−3.66554	−	6.34891i	−0.126398	−	0.218928i
$842$	13.3770	+	49.9236i	0.461001	+	1.72048i
$843$	−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
$848$	−14.6837	−	54.8002i	−0.504239	−	1.88185i
$849$	−5.36067	−	9.28495i	−0.183978	−	0.318659i
$850$	−32.4101	+	16.0472i	−1.11166	+	0.550415i
$851$	−1.22638	+	4.57693i	−0.0420399	+	0.156895i
$852$	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
$855$	−12.9988	+	15.8649i	−0.444549	+	0.542567i
$856$	15.3409	+	57.2531i	0.524342	+	1.95687i
$857$	24.6090	−	24.6090i	0.840626	−	0.840626i	−0.148314	−	0.988940i	$-0.547385\pi$
$857$	24.6090	−	24.6090i	0.840626	−	0.840626i	0.988940	+	0.148314i	$0.0473847\pi$
$858$		0			0
$859$		−	12.8606i		−	0.438798i	−0.975635	−	0.219399i	$-0.929590\pi$
$859$		−	12.8606i		−	0.438798i	0.975635	−	0.219399i	$-0.0704097\pi$
$860$	−27.7301	+	33.8442i	−0.945588	+	1.15408i
$861$	0.395284	−	0.684653i	0.0134713	−	0.0233329i
$862$	−56.8688	−	15.2379i	−1.93696	−	0.519007i
$863$	2.75373			0.0937379			0.0468690	−	0.998901i	$-0.485076\pi$
$863$	2.75373			0.0937379			0.0468690	+	0.998901i	$0.485076\pi$
$864$	−73.4965	−	19.6933i	−2.50040	−	0.669980i
$865$	0.0622747	+	0.165060i	0.00211740	+	0.00561222i
$866$	0.343907	−	0.343907i	0.0116864	−	0.0116864i
$867$	3.20532	−	11.9624i	0.108858	−	0.406264i
$868$	0.481140	−	0.128921i	0.0163309	−	0.00437586i
$869$	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
$873$	9.86060	−	17.0791i	0.333731	−	0.578039i
$874$	−51.3123	−	29.6252i	−1.73566	−	1.00209i
$875$	0.856456	−	0.918826i	0.0289535	−	0.0310620i
$876$	−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
$880$	−43.3004	+	16.3365i	−1.45965	+	0.550705i
$881$	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	$0.421594\pi$
$882$	12.2001	−	21.1311i	0.410798	−	0.711523i
$883$	13.4808	+	13.4808i	0.453666	+	0.453666i	0.896569	−	0.442903i	$-0.146051\pi$
$883$	13.4808	+	13.4808i	0.453666	+	0.453666i	−0.442903	+	0.896569i	$0.646051\pi$
$884$		0			0
$885$	3.02665	−	2.17252i	0.101740	−	0.0730285i
$886$	88.4897	−	23.7108i	2.97287	−	0.796578i
$887$	−22.1438	+	5.93341i	−0.743516	+	0.199225i	−0.610640	−	0.791908i	$-0.709088\pi$
$887$	−22.1438	+	5.93341i	−0.743516	+	0.199225i	−0.132876	+	0.991133i	$0.542421\pi$
$888$	−3.96337	+	14.7915i	−0.133002	+	0.496371i
$889$	−0.926941	+	0.926941i	−0.0310886	+	0.0310886i
$890$	3.15502	−	1.19034i	0.105757	−	0.0399003i
$891$	5.92339	+	1.58717i	0.198441	+	0.0531721i
$892$	48.8381			1.63522
$893$	2.32002	+	0.621647i	0.0776364	+	0.0208026i
$894$	23.9211	−	41.4326i	0.800042	−	1.38571i
$895$	4.68942	+	47.2262i	0.156750	+	1.57860i
$896$			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
$900$	24.8409	−	21.8551i	0.828029	−	0.728502i
$901$	12.0069	−	6.93217i	0.400007	−	0.230944i
$902$		−	26.6379i		−	0.886946i
$903$	−0.283915	−	0.491754i	−0.00944808	−	0.0163646i
$904$	12.6705	−	47.2871i	0.421416	−	1.57275i
$905$	−29.3728	−	40.9207i	−0.976384	−	1.36025i
$906$	20.6458	+	35.7595i	0.685910	+	1.18803i
$907$	−6.24222	−	23.2963i	−0.207270	−	0.773541i	−0.988746	−	0.149606i	$-0.952200\pi$
$907$	−6.24222	−	23.2963i	−0.207270	−	0.773541i	0.781476	−	0.623935i	$-0.214467\pi$
$908$	−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
$913$	4.09477	+	15.2819i	0.135517	+	0.505757i
$914$	12.4895	+	21.6324i	0.413116	+	0.715537i
$915$	1.30838	−	7.96429i	0.0432538	−	0.263291i
$916$	23.0233	−	85.9241i	0.760711	−	2.83901i
$917$	−0.419271	−	0.726199i	−0.0138456	−	0.0239812i
$918$		−	40.5061i		−	1.33690i
$919$	38.8451	−	22.4272i	1.28138	−	0.739806i	0.304281	−	0.952582i	$-0.401584\pi$
$919$	38.8451	−	22.4272i	1.28138	−	0.739806i	0.977101	+	0.212776i	$0.0682506\pi$
$920$	44.4852	+	36.4487i	1.46663	+	1.20168i
$921$	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
$925$	−4.87109	−	5.53657i	−0.160160	−	0.182041i
$926$	−24.7394	+	42.8498i	−0.812986	+	1.40813i
$927$	−13.9148	−	3.72846i	−0.457022	−	0.122459i
$928$	63.2473			2.07619
$929$	27.1090	+	7.26384i	0.889418	+	0.238319i	0.674466	−	0.738306i	$-0.264374\pi$
$929$	27.1090	+	7.26384i	0.889418	+	0.238319i	0.214952	+	0.976625i	$0.431040\pi$
$930$	2.79545	−	6.18280i	0.0916664	−	0.202742i
$931$	34.3881	−	34.3881i	1.12702	−	1.12702i
$932$	21.8041	−	81.3738i	0.714215	−	2.66549i
$933$	−4.44006	+	1.18971i	−0.145361	+	0.0389493i
$934$	−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	0.959552	−	0.281533i	$-0.0908428\pi$
$937$	20.7545	+	20.7545i	0.678019	+	0.678019i	−0.281533	+	0.959552i	$0.590843\pi$
$938$	−0.0214829	+	0.0372095i	−0.000701442	+	0.00121493i
$939$	−9.86572	−	5.69597i	−0.321955	−	0.185881i
$940$	−3.53054	−	1.59627i	−0.115153	−	0.0520647i
$941$	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	$0.700602\pi$
$942$	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
$945$	0.496615	+	1.31629i	0.0161549	+	0.0428189i
$946$	−16.5695	−	9.56639i	−0.538720	−	0.311030i
$947$	2.25542	−	3.90651i	0.0732915	−	0.126945i	−0.827051	−	0.562128i	$-0.809983\pi$
$947$	2.25542	−	3.90651i	0.0732915	−	0.126945i	0.900342	+	0.435183i	$0.143316\pi$
$948$	−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
$952$	−2.37143	+	0.635422i	−0.0768584	+	0.0205941i
$953$	−1.48646	+	5.54756i	−0.0481513	+	0.179703i	−0.985813	−	0.167845i	$-0.946319\pi$
$953$	−1.48646	+	5.54756i	−0.0481513	+	0.179703i	0.937662	+	0.347548i	$0.112986\pi$
$954$	−12.5414	+	12.5414i	−0.406043	+	0.406043i
$955$	39.9481	+	18.0618i	1.29269	+	0.584467i
$956$	124.946	+	33.4791i	4.04103	+	1.08279i
$957$	−11.1866			−0.361612
$958$	84.3690	+	22.6066i	2.72584	+	0.730386i
$959$	−1.03833	+	1.79845i	−0.0335296	+	0.0580749i
$960$	30.6480	+	25.1113i	0.989160	+	0.810463i
$961$		−	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
$965$	37.1863	−	3.69249i	1.19707	−	0.118865i
$966$	−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
$969$	6.37750	−	23.8012i	0.204875	−	0.764604i
$970$	−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	$-0.346689\pi$
$972$	16.2551	+	60.6650i	0.521384	+	1.94583i
$973$	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	$0.745604\pi$
$978$	−18.2497	−	68.1088i	−0.583561	−	2.17788i
$979$	0.527266	+	0.913252i	0.0168515	+	0.0291877i
$980$	−63.7334	+	45.7477i	−2.03589	+	1.46136i
$981$	−1.61375	+	6.02261i	−0.0515232	+	0.192287i
$982$	−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
$985$	33.7914	−	3.35539i	1.07668	−	0.106911i
$986$	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
$990$	11.1914	+	9.16958i	0.355685	+	0.291428i
$991$	−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	$0.168887\pi$
$992$	−11.5884	−	3.10509i	−0.367931	−	0.0985867i
$993$	−23.3545			−0.741131
$994$	−1.57395	−	0.421739i	−0.0499227	−	0.0133767i
$995$	28.4171	+	12.8483i	0.900884	+	0.407319i
$996$	39.3193	−	39.3193i	1.24588	−	1.24588i
$997$	−1.70003	+	6.34461i	−0.0538406	+	0.200936i	−0.987607	−	0.156947i	$-0.949835\pi$
$997$	−1.70003	+	6.34461i	−0.0538406	+	0.200936i	0.933766	+	0.357883i	$0.116501\pi$
$998$	54.0044	−	14.4704i	1.70948	−	0.458053i
$999$	7.97806	−	2.13771i	0.252415	−	0.0676343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.g.657.5		20
5.3	odd	4		845.2.o.g.488.5		20
13.2	odd	12		845.2.o.g.587.5		20
13.3	even	3		845.2.t.e.427.1		20
13.4	even	6		845.2.f.e.437.10		20
13.5	odd	4		845.2.o.f.357.5		20
13.6	odd	12		845.2.k.d.577.1		20
13.7	odd	12		845.2.k.e.577.10		20
13.8	odd	4		845.2.o.e.357.1		20
13.9	even	3		845.2.f.d.437.1		20
13.10	even	6		845.2.t.f.427.5		20
13.11	odd	12		65.2.o.a.2.1	✓	20
13.12	even	2		65.2.t.a.7.1	yes	20
39.11	even	12		585.2.cf.a.262.5		20
39.38	odd	2		585.2.dp.a.397.5		20
65.3	odd	12		845.2.o.f.258.5		20
65.8	even	4		845.2.t.f.188.5		20
65.12	odd	4		325.2.s.b.293.5		20
65.18	even	4		845.2.t.e.188.1		20
65.23	odd	12		845.2.o.e.258.1		20
65.24	odd	12		325.2.s.b.132.5		20
65.28	even	12	inner	845.2.t.g.418.5		20
65.33	even	12		845.2.f.e.408.1		20
65.37	even	12		325.2.x.b.93.5		20
65.38	odd	4		65.2.o.a.33.1	yes	20
65.43	odd	12		845.2.k.e.268.10		20
65.48	odd	12		845.2.k.d.268.1		20
65.58	even	12		845.2.f.d.408.10		20
65.63	even	12		65.2.t.a.28.1	yes	20
65.64	even	2		325.2.x.b.7.5		20
195.38	even	4		585.2.cf.a.163.5		20
195.128	odd	12		585.2.dp.a.28.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.1	✓	20	13.11	odd	12
65.2.o.a.33.1	yes	20	65.38	odd	4
65.2.t.a.7.1	yes	20	13.12	even	2
65.2.t.a.28.1	yes	20	65.63	even	12
325.2.s.b.132.5		20	65.24	odd	12
325.2.s.b.293.5		20	65.12	odd	4
325.2.x.b.7.5		20	65.64	even	2
325.2.x.b.93.5		20	65.37	even	12
585.2.cf.a.163.5		20	195.38	even	4
585.2.cf.a.262.5		20	39.11	even	12
585.2.dp.a.28.5		20	195.128	odd	12
585.2.dp.a.397.5		20	39.38	odd	2
845.2.f.d.408.10		20	65.58	even	12
845.2.f.d.437.1		20	13.9	even	3
845.2.f.e.408.1		20	65.33	even	12
845.2.f.e.437.10		20	13.4	even	6
845.2.k.d.268.1		20	65.48	odd	12
845.2.k.d.577.1		20	13.6	odd	12
845.2.k.e.268.10		20	65.43	odd	12
845.2.k.e.577.10		20	13.7	odd	12
845.2.o.e.258.1		20	65.23	odd	12
845.2.o.e.357.1		20	13.8	odd	4
845.2.o.f.258.5		20	65.3	odd	12
845.2.o.f.357.5		20	13.5	odd	4
845.2.o.g.488.5		20	5.3	odd	4
845.2.o.g.587.5		20	13.2	odd	12
845.2.t.e.188.1		20	65.18	even	4
845.2.t.e.427.1		20	13.3	even	3
845.2.t.f.188.5		20	65.8	even	4
845.2.t.f.427.5		20	13.10	even	6
845.2.t.g.418.5		20	65.28	even	12	inner
845.2.t.g.657.5		20	1.1	even	1	trivial

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

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

\(f(q)\)	\(=\)	\(q+(2.29475 + 1.32488i) q^{2} +(0.335680 + 1.25278i) q^{3} +(2.51060 + 4.34849i) q^{4} +(-1.81654 + 1.30391i) q^{5} +(-0.889471 + 3.31955i) q^{6} +(-0.0561740 - 0.0972962i) q^{7} +8.00544i q^{8} +(1.14131 - 0.658935i) q^{9} +(-5.89604 + 0.585458i) q^{10} +(-0.479564 - 1.78976i) q^{11} +(-4.60492 + 4.60492i) q^{12} -0.297695i q^{14} +(-2.24328 - 1.83802i) q^{15} +(-5.58502 + 9.67354i) q^{16} +(-2.63669 - 0.706500i) q^{17} +3.49203 q^{18} +(6.72284 + 1.80138i) q^{19} +(-10.2306 - 4.62561i) q^{20} +(0.103034 - 0.103034i) q^{21} +(1.27073 - 4.74241i) q^{22} +(-3.10327 + 0.831519i) q^{23} +(-10.0290 + 2.68727i) 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} +(-2.71263 - 7.18989i) 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} +(0.228908 + 0.103497i) 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} +(5.24069 - 1.40424i) q^{41} +(0.372945 - 0.0999302i) q^{42} +(1.00860 - 3.76415i) q^{43} +(6.57874 - 6.57874i) q^{44} +(-1.21404 + 2.68515i) q^{45} +(-8.22291 - 2.20332i) q^{46} +0.345095 q^{47} +(-13.9936 - 3.74956i) q^{48} +(3.49369 - 6.05125i) q^{49} +(9.94700 - 8.75140i) q^{50} -3.54034i q^{51} +(-3.59144 + 3.59144i) q^{53} +(3.84062 + 14.3334i) q^{54} +(3.20483 + 2.62586i) q^{55} +(0.778898 - 0.449697i) q^{56} +9.02691i q^{57} +(-6.16729 - 10.6821i) q^{58} +(-0.332494 + 1.24088i) q^{59} +(2.36063 - 14.3694i) q^{60} +(1.39151 + 2.41016i) q^{61} +(0.605559 + 2.25998i) q^{62} +(-0.128224 - 0.0740300i) q^{63} -13.6621 q^{64} +6.36774 q^{66} +(-0.124992 - 0.0721643i) q^{67} +(-3.54747 - 13.2394i) q^{68} +(-2.08342 - 3.60858i) q^{69} +(0.388167 + 0.540774i) q^{70} +(1.41668 - 5.28713i) q^{71} +(5.27506 + 9.13667i) q^{72} +9.06221i q^{73} +(3.38447 - 1.95402i) q^{74} +(6.47163 + 0.413804i) q^{75} +(9.04509 + 33.7567i) q^{76} +(-0.147197 + 0.147197i) q^{77} +15.1689i q^{79} +(-2.46800 - 24.8547i) q^{80} +(-1.65480 + 2.86620i) q^{81} +(13.8865 + 3.72089i) q^{82} -8.53853 q^{83} +(0.706718 + 0.189365i) q^{84} +(5.71087 - 2.15462i) q^{85} +(7.30152 - 7.30152i) q^{86} +(1.56259 - 5.83166i) q^{87} +(14.3278 - 3.83912i) q^{88} +(-0.549735 + 0.147301i) 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} +(-14.5612 + 5.49370i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 8 * q^6 + 2 * q^7 + 12 * q^9 - 2 * q^10 + 16 * q^11 - 24 * q^12 + 20 * q^15 - 2 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^21 + 16 * q^22 - 10 * q^23 - 32 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 26 * q^30 - 48 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 + 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 + 40 * q^42 + 10 * q^43 + 36 * q^44 - 4 * q^46 + 40 * q^47 - 56 * q^48 + 18 * q^49 - 36 * q^50 - 10 * q^53 + 48 * q^54 - 10 * q^55 + 16 * q^59 - 28 * q^60 - 16 * q^61 - 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 22 * q^68 - 16 * q^69 + 12 * q^70 + 16 * q^71 - 4 * q^72 + 18 * q^74 - 38 * q^75 + 64 * q^76 - 28 * q^77 + 2 * q^80 - 14 * q^81 + 56 * q^82 - 48 * q^83 + 40 * q^84 + 26 * q^85 - 60 * q^86 - 34 * q^87 + 82 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 - 48 * q^94 - 26 * q^95 - 56 * q^96 - 66 * q^97 + 30 * q^98 - 60 * q^99

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