LMFDB - Embedded newform 65.2.o.a.33.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,2,Mod(2,65)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("65.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$65 = 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	65.o (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.519027613138$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.1
Root			$-2.64975i$ of defining polynomial
Character	$\chi$	$=$	65.33
Dual form			65.2.o.a.2.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32488 + 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} +(-2.05471 + 2.96279i) q^{13} +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} +(-4.07664 - 8.64040i) q^{26} +(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} +(1.57955 - 4.40145i) q^{39} +(-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} +(18.0422 + 1.49651i) q^{52} +(-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} +(-2.70287 - 7.59569i) q^{65} +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} +(8.00753 + 9.45605i) q^{78} -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} +(-0.0334840 + 0.403690i) q^{91} +(-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})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21}+ \cdots - 60 q^{99}+O(q^{100})$ 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 + 2 * q^13 + 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 - 24 * q^26 + 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 - 4 * q^39 - 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 + 46 * q^52 - 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 + 8 * q^65 - 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 + 32 * q^78 - 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^91 - 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 $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$ .

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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	$0.552921\pi$
$2$	−1.32488	+	2.29475i	−0.936830	+	1.62264i	−0.771338	+	0.636425i	$0.780412\pi$
$3$	−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	−0.481500	−	0.876446i	$-0.659908\pi$
$7$	0.0972962	−	0.0561740i	0.0367745	−	0.0212318i	0.518275	+	0.855214i	$0.326575\pi$
$8$	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	$0.00678031\pi$
$11$	0.479564	+	1.78976i	0.144594	+	0.539632i	−0.855179	+	0.518332i	$0.826553\pi$
$12$	4.60492	+	4.60492i	1.32933	+	1.32933i
$13$	−2.05471	+	2.96279i	−0.569875	+	0.821731i
$13$	−2.05471	+	2.96279i	−0.569875	+	0.821731i
$14$			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	0.927016	−	0.375021i	$-0.122364\pi$
$19$	6.72284	+	1.80138i	1.54233	+	0.413265i	0.615309	+	0.788286i	$0.289031\pi$
$20$	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
$26$	−4.07664	−	8.64040i	−0.799495	−	1.69452i
$27$	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	0.648810	−	0.760950i	$-0.275267\pi$
$31$	−0.624367	−	0.624367i	−0.112140	−	0.112140i	−0.760950	+	0.648810i	$0.775267\pi$
$32$	−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	0.601303	−	0.799021i	$-0.294648\pi$
$37$	1.27728	+	0.737435i	0.209983	+	0.121234i	−0.391321	+	0.920254i	$0.627982\pi$
$38$	−13.0407	+	13.0407i	−2.11548	+	2.11548i
$39$	1.57955	−	4.40145i	0.252930	−	0.704795i
$40$	−10.4384	+	14.5422i	−1.65045	+	2.29932i
$41$	−5.24069	+	1.40424i	−0.818458	+	0.219305i	−0.643672	−	0.765301i	$-0.722590\pi$
$41$	−5.24069	+	1.40424i	−0.818458	+	0.219305i	−0.174786	+	0.984606i	$0.555923\pi$
$42$	−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	$0.00801227\pi$
$47$			0.345095i			0.0503372i	−0.999683	+	0.0251686i	$0.991988\pi$
$48$	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
$52$	18.0422	+	1.49651i	2.50201	+	0.207528i
$53$	−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	−0.984186	−	0.177138i	$-0.943316\pi$
$59$	−0.332494	+	1.24088i	−0.0432870	+	0.161549i	0.940899	+	0.338687i	$0.109983\pi$
$60$	−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
$65$	−2.70287	−	7.59569i	−0.335250	−	0.942129i
$66$	6.36774			0.783815
$67$	0.0721643	−	0.124992i	0.00881627	−	0.0152702i	−0.861584	−	0.507616i	$-0.830527\pi$
$67$	0.0721643	−	0.124992i	0.00881627	−	0.0152702i	0.870400	+	0.492345i	$0.163860\pi$
$68$	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	$0.188631\pi$
$71$	−1.41668	+	5.28713i	−0.168129	+	0.627467i	−0.997620	+	0.0689472i	$0.978036\pi$
$72$	−9.13667	+	5.27506i	−1.07677	+	0.621672i
$73$	9.06221			1.06065			0.530326	−	0.847794i	$-0.322070\pi$
$73$	9.06221			1.06065			0.530326	+	0.847794i	$0.322070\pi$
$74$	−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
$78$	8.00753	+	9.45605i	0.906675	+	1.07069i
$79$		−	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	$0.155246\pi$
$83$			8.53853i			0.937226i	−0.883404	+	0.468613i	$0.844754\pi$
$84$	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	−0.287837	−	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
$91$	−0.0334840	+	0.403690i	−0.00351007	+	0.0423182i
$92$	−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	$0.107990\pi$
$97$	7.48223	+	12.9596i	0.759705	+	1.31585i	−0.183296	+	0.983058i	$0.558677\pi$
$98$	−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	$0.0689789\pi$
$104$	−16.4489	+	23.7185i	−1.61295	+	2.32579i
$105$	−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	−0.848934	−	0.528499i	$-0.822755\pi$
$109$	−3.34544	+	3.34544i	−0.320435	+	0.320435i	0.528499	+	0.848934i	$0.322755\pi$
$110$	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
$117$	0.392775	−	4.73539i	0.0363121	−	0.437787i
$118$	−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
$130$	21.0112	+	3.86092i	1.84281	+	0.338625i
$131$	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	0.377015	−	0.926207i	$-0.376950\pi$
$137$	16.0078	−	9.24213i	1.36764	−	0.789608i	0.990626	+	0.136599i	$0.0436170\pi$
$138$	−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
$143$	−6.28804	−	2.25659i	−0.525833	−	0.188705i
$144$		−	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	−0.338189	−	0.941078i	$-0.609814\pi$
$149$	−13.4468	−	3.60307i	−1.10161	−	0.295175i	−0.763419	+	0.645903i	$0.776481\pi$
$150$	−17.1482	+	1.09648i	−1.40015	+	0.0895272i
$151$	−8.49593	+	8.49593i	−0.691389	+	0.691389i	−0.962537	−	0.271149i	$-0.912596\pi$
$151$	−8.49593	+	8.49593i	−0.691389	+	0.691389i	0.271149	+	0.962537i	$0.412596\pi$
$152$	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
$156$	−23.1052	+	4.18163i	−1.84990	+	0.334799i
$157$	−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	$0.130379\pi$
$163$	10.2587	+	17.7686i	0.803526	+	1.39175i	−0.113756	+	0.993509i	$0.536288\pi$
$164$	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	0.412435	−	0.910987i	$-0.364678\pi$
$167$	−2.20058	−	1.27050i	−0.170286	−	0.0983146i	−0.582721	+	0.812673i	$0.698012\pi$
$168$	−0.824831	+	0.824831i	−0.0636371	+	0.0636371i
$169$	−4.55630	−	12.1754i	−0.350484	−	0.936569i
$170$	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	$0.684192\pi$
$182$	−0.882008	−	0.611677i	−0.0653788	−	0.0453405i
$183$	−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	$0.372088\pi$
$193$	−8.35601	+	14.4730i	−0.601479	+	1.04179i	−0.992597	+	0.121451i	$0.961245\pi$
$194$	−39.6521			−2.84686
$195$	5.93582	+	8.60840i	0.425073	+	0.616460i
$196$	35.0850			2.50607
$197$	7.59315	−	13.1517i	0.540990	−	0.937021i	−0.457858	−	0.889025i	$-0.651383\pi$
$197$	7.59315	−	13.1517i	0.540990	−	0.937021i	0.998848	−	0.0479960i	$-0.0152835\pi$
$198$	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
$208$	−17.1851	−	36.4236i	−1.19157	−	2.52552i
$209$			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
$221$	−6.36032	−	7.51086i	−0.427841	−	0.505235i
$222$	3.58405	−	3.58405i	0.240546	−	0.240546i
$223$	−8.42330	−	4.86319i	−0.564066	−	0.325664i	0.190710	−	0.981646i	$-0.438921\pi$
$223$	−8.42330	−	4.86319i	−0.564066	−	0.325664i	−0.754776	+	0.655983i	$0.772254\pi$
$224$	−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	0.672642	−	0.739968i	$-0.265159\pi$
$227$	−4.58790	−	7.94647i	−0.304510	−	0.527426i	−0.977152	+	0.212542i	$0.931826\pi$
$228$	22.6629	+	39.2534i	1.50089	+	2.59962i
$229$	−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	$0.949043\pi$
$230$	−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	$0.0647903\pi$
$234$	10.3462	+	7.17513i	0.676350	+	0.469053i
$235$	−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	$-0.436515\pi$
$239$	18.2161	−	18.2161i	1.17830	−	1.17830i	0.980177	−	0.198124i	$-0.0634848\pi$
$240$	20.5308	+	25.0576i	1.32526	+	1.61746i
$241$	−5.28403	−	1.41585i	−0.340374	−	0.0912030i	0.0845830	−	0.996416i	$-0.473044\pi$
$241$	−5.28403	−	1.41585i	−0.340374	−	0.0912030i	−0.424957	+	0.905213i	$0.639711\pi$
$242$			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
$247$	−19.1506	+	16.2171i	−1.21853	+	1.03187i
$248$	−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
$260$	−26.2439	+	30.8231i	−1.62758	+	1.91157i
$261$	−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	0.875446	−	0.483315i	$-0.160567\pi$
$271$	−2.04739	−	7.64095i	−0.124370	−	0.464155i	−0.999816	+	0.0191601i	$0.993901\pi$
$272$	−21.5603	−	21.5603i	−1.30729	−	1.30729i
$273$	−0.0935629	−	0.516973i	−0.00566269	−	0.0312887i
$274$			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	−0.229126	−	0.973397i	$-0.573587\pi$
$281$	12.4763	−	12.4763i	0.744271	−	0.744271i	0.973397	+	0.229126i	$0.0735867\pi$
$282$	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
$286$	13.5092	−	11.4398i	0.798816	−	0.676451i
$287$	−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	0.757705	−	0.652597i	$-0.226320\pi$
$293$	−3.18916	−	5.52378i	−0.186313	−	0.322703i	−0.944018	+	0.329894i	$0.892987\pi$
$294$	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
$299$	10.9029	+	3.91272i	0.630531	+	0.226278i
$300$	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	$0.273594\pi$
$307$			26.5460i			1.51506i	−0.652801	+	0.757530i	$0.726406\pi$
$308$	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	$0.967960\pi$
$312$	12.6450	−	35.2355i	0.715879	−	1.99482i
$313$	−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	$-0.576981\pi$
$317$	−8.52812			−0.478987			−0.239494	+	0.970898i	$0.576981\pi$
$318$	−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
$325$	17.3222	+	4.99421i	0.960862	+	0.277029i
$326$	−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	$-0.751880\pi$
$331$	4.66054	−	17.3934i	0.256166	−	0.956026i	0.967438	−	0.253109i	$-0.0814530\pi$
$332$	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	$0.468403\pi$
$338$	33.9761	+	5.67532i	1.84805	+	0.308697i
$339$			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	−0.352026	−	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
$351$	3.59590	+	19.8688i	0.191935	+	1.06052i
$352$	17.8016	−	17.8016i	0.948827	−	0.948827i
$353$	−1.52702	−	0.881628i	−0.0812753	−	0.0469243i	0.458812	−	0.888534i	$-0.348275\pi$
$353$	−1.52702	−	0.881628i	−0.0812753	−	0.0469243i	−0.540087	+	0.841609i	$0.681609\pi$
$354$	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	0.443452	−	0.896298i	$-0.353754\pi$
$359$	−8.58021	−	8.58021i	−0.452846	−	0.452846i	−0.896298	+	0.443452i	$0.853754\pi$
$360$	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
$364$	1.83951	−	0.867900i	0.0964163	−	0.0454903i
$365$	−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
$377$	−15.1791	+	7.16169i	−0.781765	+	0.368846i
$378$	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	$0.994928\pi$
$380$	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	−0.887596	−	0.460623i	$-0.847626\pi$
$383$	−18.2490	+	10.5361i	−0.932483	+	0.538369i	−0.0448868	+	0.998992i	$0.514293\pi$
$384$	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	$0.500488\pi$
$390$	−27.6184	+	2.21619i	−1.39851	+	0.112221i
$391$	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	−0.667815	−	0.744327i	$-0.732770\pi$
$397$	−7.11548	+	4.10812i	−0.357116	+	0.206181i	0.310699	+	0.950508i	$0.399437\pi$
$398$	−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	0.883075	−	0.469233i	$-0.155469\pi$
$401$	−2.32904	−	8.69210i	−0.116307	−	0.434063i	−0.999381	+	0.0351698i	$0.988803\pi$
$402$	−0.350730	−	0.350730i	−0.0174928	−	0.0174928i
$403$	3.13276	−	0.566974i	0.156054	−	0.0282430i
$404$		−	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	−0.735272	−	0.677772i	$-0.762946\pi$
$409$	−34.6013	−	9.27138i	−1.71092	−	0.458440i	−0.975650	+	0.219332i	$0.929612\pi$
$410$	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
$416$	48.8209	+	4.04944i	2.39364	+	0.198540i
$417$	−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	0.286021	−	0.958223i	$-0.407667\pi$
$421$	−13.7924	−	13.7924i	−0.672203	−	0.672203i	−0.958223	+	0.286021i	$0.907667\pi$
$422$	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
$429$	8.63501	+	0.716228i	0.416902	+	0.0345798i
$430$	−3.74299	−	22.7840i	−0.180503	−	1.09874i
$431$	21.4619	−	5.75070i	1.03378	−	0.277002i	0.298249	−	0.954488i	$-0.403597\pi$
$431$	21.4619	−	5.75070i	1.03378	−	0.277002i	0.735535	+	0.677487i	$0.236931\pi$
$432$	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
$442$	25.6622	−	4.64440i	1.22063	−	0.220912i
$443$	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	$0.424073\pi$
$449$	−9.62407	+	35.9175i	−0.454188	+	1.69505i	−0.690465	+	0.723366i	$0.742594\pi$
$450$	−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
$455$	−0.689660	−	0.587200i	−0.0323317	−	0.0275284i
$456$	−72.2643			−3.38409
$457$	−4.71345	+	8.16394i	−0.220486	+	0.381893i	−0.954956	−	0.296749i	$-0.904098\pi$
$457$	−4.71345	+	8.16394i	−0.220486	+	0.381893i	0.734470	+	0.678642i	$0.237431\pi$
$458$	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	$0.361002\pi$
$461$	−8.51149	+	31.7653i	−0.396419	+	1.47946i	−0.819349	+	0.573295i	$0.805665\pi$
$462$	0.619557	−	0.357701i	0.0288244	−	0.0166418i
$463$	18.6729			0.867805			0.433903	−	0.900960i	$-0.357136\pi$
$463$	18.6729			0.867805			0.433903	+	0.900960i	$0.357136\pi$
$464$	−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	$0.619655\pi$
$468$	−21.5779	+	10.1807i	−0.997437	+	0.470602i
$469$		−	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	0.557123	−	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
$481$	−4.80931	+	2.26908i	−0.219285	+	0.103461i
$482$	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	$-0.897980\pi$
$487$	−16.4931	−	28.5670i	−0.747376	−	1.29449i	0.201701	−	0.979447i	$-0.435353\pi$
$488$	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
$494$	−11.8420	−	65.4317i	−0.532795	−	2.94391i
$495$	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	−0.289326	−	0.957231i	$-0.593431\pi$
$499$	14.9199	−	14.9199i	0.667904	−	0.667904i	0.957231	+	0.289326i	$0.0934312\pi$
$500$	−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
$507$	9.79506	+	13.7236i	0.435014	+	0.609486i
$508$	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	$0.606122\pi$
$510$	−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
$520$	−21.6377	−	60.8068i	−0.948875	−	2.66655i
$521$	−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
$533$	6.60765	−	18.4124i	0.286209	−	0.797529i
$534$			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	−0.814088	−	0.580742i	$-0.802762\pi$
$541$	−5.42748	+	5.42748i	−0.233345	+	0.233345i	0.580742	+	0.814088i	$0.302762\pi$
$542$	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
$546$	1.31029	+	0.470222i	0.0560751	+	0.0201237i
$547$	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	0.407882	−	0.913034i	$-0.366267\pi$
$557$	−4.22190	−	2.43751i	−0.178888	−	0.103281i	−0.586770	+	0.809754i	$0.699601\pi$
$558$	−2.18031	+	2.18031i	−0.0922998	+	0.0922998i
$559$	−10.7225	+	9.08000i	−0.453514	+	0.384043i
$560$	−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	$0.980226\pi$
$572$	5.97401	+	33.0089i	0.249786	+	1.38017i
$573$	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	$-0.760314\pi$
$577$	−35.0533			−1.45929			−0.729644	+	0.683827i	$0.760314\pi$
$578$	−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
$585$	8.08988	+	6.88801i	0.334475	+	0.284784i
$586$	16.9010			0.698173
$587$	−3.52719	+	6.10926i	−0.145583	+	0.252156i	−0.929590	−	0.368595i	$-0.879839\pi$
$587$	−3.52719	+	6.10926i	−0.145583	+	0.252156i	0.784008	+	0.620751i	$0.213172\pi$
$588$	−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	$-0.193054\pi$
$593$	40.0169			1.64330			0.821649	+	0.569993i	$0.193054\pi$
$594$	−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
$598$	−23.4237	+	19.8356i	−0.957867	+	0.811138i
$599$		−	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
$611$	−1.02244	−	0.709071i	−0.0413637	−	0.0286860i
$612$	−12.7726	+	12.7726i	−0.516303	+	0.516303i
$613$	9.23121	+	5.32964i	0.372845	+	0.215262i	0.674701	−	0.738091i	$-0.264273\pi$
$613$	9.23121	+	5.32964i	0.372845	+	0.215262i	−0.301856	+	0.953354i	$0.597606\pi$
$614$	−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	0.970473	−	0.241210i	$-0.0775442\pi$
$617$	6.86421	+	11.8892i	0.276343	+	0.478639i	−0.694130	+	0.719849i	$0.744211\pi$
$618$	−18.7830	−	32.5332i	−0.755565	−	1.30868i
$619$	−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	$0.909070\pi$
$620$	−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
$624$	33.7558	+	39.8620i	1.35131	+	1.59576i
$625$	−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	0.793537	−	0.608522i	$-0.208237\pi$
$631$	29.5533	+	7.91879i	1.17650	+	0.315242i	0.382962	+	0.923764i	$0.374904\pi$
$632$		−	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
$637$	−10.7501	−	22.7847i	−0.425933	−	0.902761i
$638$	−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	−0.0672147	−	0.997739i	$-0.521411\pi$
$643$	19.3539	−	11.1740i	0.763245	−	0.440660i	0.830460	+	0.557079i	$0.188078\pi$
$644$	−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
$650$	−34.4102	+	33.1334i	−1.34968	+	1.29960i
$651$	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	$0.0245634\pi$
$661$	4.42523	+	16.5152i	0.172122	+	0.642367i	−0.824902	+	0.565275i	$0.808770\pi$
$662$	33.7389	+	33.7389i	1.31130	+	1.31130i
$663$	10.4893	+	7.27440i	0.407371	+	0.282514i
$664$			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
$676$	−41.5055	+	50.3805i	−1.59636	+	1.93771i
$677$	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	$-0.995386\pi$
$683$	−13.3938	−	23.1988i	−0.512500	−	0.887676i	0.487395	−	0.873181i	$-0.337947\pi$
$684$	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
$689$	18.0201	−	3.26131i	0.686510	−	0.124246i
$690$	14.3966	−	20.0566i	0.548068	−	0.763541i
$691$	−38.9899	+	10.4473i	−1.48325	+	0.397435i	−0.907451	−	0.420158i	$-0.861975\pi$
$691$	−38.9899	+	10.4473i	−1.48325	+	0.397435i	−0.575796	+	0.817593i	$0.695308\pi$
$692$	−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	$0.843639\pi$
$702$	−50.3582	−	18.0721i	−1.90065	−	0.682086i
$703$	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	−0.898423	−	0.439130i	$-0.855287\pi$
$709$	2.64139	−	9.85779i	0.0991993	−	0.370217i	0.997623	+	0.0689135i	$0.0219533\pi$
$710$	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
$715$	12.2982	−	8.48010i	0.459928	−	0.317138i
$716$	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	$0.677919\pi$
$728$	−0.268054	+	3.23172i	−0.00993473	+	0.119775i
$729$		−	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	$-0.896983\pi$
$733$		−	17.2200i		−	0.636036i	0.948085	−	0.318018i	$-0.103017\pi$
$734$	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	0.0427762	−	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
$741$	18.5477	−	26.7449i	0.681367	−	0.982497i
$742$	1.06915	−	1.06915i	0.0392498	−	0.0392498i
$743$	28.6826	+	16.5599i	1.05226	+	0.607525i	0.923282	−	0.384122i	$-0.125496\pi$
$743$	28.6826	+	16.5599i	1.05226	+	0.607525i	0.128982	+	0.991647i	$0.458829\pi$
$744$	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
$754$	3.67617	−	44.3207i	0.133878	−	1.61407i
$755$	−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	−0.148561	−	0.988903i	$-0.547464\pi$
$761$	−21.2875	−	5.70396i	−0.771670	−	0.206768i	−0.623109	+	0.782135i	$0.714131\pi$
$762$			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
$767$	−2.99330	−	3.53477i	−0.108082	−	0.127633i
$768$	−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	$0.792292\pi$
$770$	0.435388	−	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	−0.179719	−	0.983718i	$-0.557519\pi$
$773$	16.1909	−	9.34781i	0.582346	−	0.336217i	0.762065	+	0.647500i	$0.224186\pi$
$774$	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
$780$	22.5310	−	47.4241i	0.806740	−	1.69805i
$781$	−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	0.350981	−	0.936382i	$-0.385848\pi$
$787$	37.5189	−	21.6615i	1.33740	−	0.772150i	0.986422	+	0.164232i	$0.0525147\pi$
$788$	−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
$793$	−9.99995	−	0.829444i	−0.355109	−	0.0294544i
$794$		−	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
$806$	−2.84946	+	7.94010i	−0.100368	+	0.279678i
$807$	−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	0.204656	−	0.978834i	$-0.434392\pi$
$811$	−22.0471	−	22.0471i	−0.774178	−	0.774178i	−0.978834	+	0.204656i	$0.934392\pi$
$812$	−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
$819$	−0.227790	−	0.482799i	−0.00795963	−	0.0168704i
$820$	−60.1111	+	9.87512i	−2.09917	+	0.344854i
$821$	35.4477	−	9.49818i	1.23713	−	0.331489i	0.419780	−	0.907626i	$-0.362107\pi$
$821$	35.4477	−	9.49818i	1.23713	−	0.331489i	0.817353	+	0.576137i	$0.195441\pi$
$822$	−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	$0.0246209\pi$
$827$			4.44429i			0.154543i	−0.997010	+	0.0772716i	$0.975379\pi$
$828$	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
$832$	−28.0718	+	40.4780i	−0.973213	+	1.40332i
$833$	−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	−0.917587	−	0.397534i	$-0.869866\pi$
$839$	2.19656	−	8.19766i	0.0758336	−	0.283015i	0.993421	+	0.114519i	$0.0365327\pi$
$840$	−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
$845$	28.0581	+	7.59891i	0.965228	+	0.261410i
$846$	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	$-0.700051\pi$
$853$	−34.3415			−1.17583			−0.587915	+	0.808923i	$0.700051\pi$
$854$	−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	$0.952615\pi$
$858$	−13.0839	+	18.8663i	−0.446677	+	0.644085i
$859$			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	$-0.985076\pi$
$863$		−	2.75373i		−	0.0937379i	0.998901	−	0.0468690i	$-0.0149243\pi$
$864$	−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
$871$	0.222049	+	0.470631i	0.00752385	+	0.0159467i
$872$	−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	$0.127432\pi$
$877$	23.6316	+	40.9311i	0.797981	+	1.38214i	−0.122948	+	0.992413i	$0.539235\pi$
$878$	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	$0.353949\pi$
$884$	−16.6927	+	46.5145i	−0.561435	+	1.56445i
$885$	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
$897$	−14.9723	−	1.24187i	−0.499911	−	0.0414650i
$898$	−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
$910$	2.26119	−	0.804631i	0.0749579	−	0.0266733i
$911$	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
$923$	−12.7538	−	15.0609i	−0.419797	−	0.495735i
$924$			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	0.674466	−	0.738306i	$-0.264374\pi$
$929$	27.1090	+	7.26384i	0.889418	+	0.238319i	0.214952	+	0.976625i	$0.431040\pi$
$930$	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
$936$	3.14434	−	37.9088i	0.102776	−	1.23909i
$937$	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	0.589315	−	0.807903i	$-0.299398\pi$
$941$	−6.70533	−	6.70533i	−0.218588	−	0.218588i	−0.807903	+	0.589315i	$0.799398\pi$
$942$	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	0.562128	−	0.827051i	$-0.309983\pi$
$947$	3.90651	+	2.25542i	0.126945	+	0.0732915i	−0.435183	+	0.900342i	$0.643316\pi$
$948$	69.8518	−	69.8518i	2.26868	−	2.26868i
$949$	−18.6203	+	26.8495i	−0.604439	+	0.871570i
$950$	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
$962$	1.16475	−	14.0424i	0.0375529	−	0.452746i
$963$	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	$-0.591547\pi$
$967$	−17.6414			−0.567310			−0.283655	+	0.958926i	$0.591547\pi$
$968$	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
$975$	−23.3773	−	0.441906i	−0.748672	−	0.0141523i
$976$	−31.0864			−0.995050
$977$	7.67217	−	13.2886i	0.245454	−	0.425139i	−0.716805	−	0.697274i	$-0.754396\pi$
$977$	7.67217	−	13.2886i	0.245454	−	0.425139i	0.962259	+	0.272134i	$0.0877295\pi$
$978$	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	$-0.524428\pi$
$983$	−4.80751			−0.153336			−0.0766679	+	0.997057i	$0.524428\pi$
$984$	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
$988$	118.599	+	42.5617i	3.77315	+	1.35407i
$989$		−	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	65.2.o.a.33.1	yes	20
3.2	odd	2		585.2.cf.a.163.5		20
5.2	odd	4		65.2.t.a.7.1	yes	20
5.3	odd	4		325.2.x.b.7.5		20
5.4	even	2		325.2.s.b.293.5		20
13.2	odd	12		65.2.t.a.28.1	yes	20
13.3	even	3		845.2.o.e.258.1		20
13.4	even	6		845.2.k.d.268.1		20
13.5	odd	4		845.2.t.f.188.5		20
13.6	odd	12		845.2.f.e.408.1		20
13.7	odd	12		845.2.f.d.408.10		20
13.8	odd	4		845.2.t.e.188.1		20
13.9	even	3		845.2.k.e.268.10		20
13.10	even	6		845.2.o.f.258.5		20
13.11	odd	12		845.2.t.g.418.5		20
13.12	even	2		845.2.o.g.488.5		20
15.2	even	4		585.2.dp.a.397.5		20
39.2	even	12		585.2.dp.a.28.5		20
65.2	even	12	inner	65.2.o.a.2.1	✓	20
65.7	even	12		845.2.k.d.577.1		20
65.12	odd	4		845.2.t.g.657.5		20
65.17	odd	12		845.2.f.d.437.1		20
65.22	odd	12		845.2.f.e.437.10		20
65.28	even	12		325.2.s.b.132.5		20
65.32	even	12		845.2.k.e.577.10		20
65.37	even	12		845.2.o.g.587.5		20
65.42	odd	12		845.2.t.f.427.5		20
65.47	even	4		845.2.o.f.357.5		20
65.54	odd	12		325.2.x.b.93.5		20
65.57	even	4		845.2.o.e.357.1		20
65.62	odd	12		845.2.t.e.427.1		20
195.2	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	65.2	even	12	inner
65.2.o.a.33.1	yes	20	1.1	even	1	trivial
65.2.t.a.7.1	yes	20	5.2	odd	4
65.2.t.a.28.1	yes	20	13.2	odd	12
325.2.s.b.132.5		20	65.28	even	12
325.2.s.b.293.5		20	5.4	even	2
325.2.x.b.7.5		20	5.3	odd	4
325.2.x.b.93.5		20	65.54	odd	12
585.2.cf.a.163.5		20	3.2	odd	2
585.2.cf.a.262.5		20	195.2	odd	12
585.2.dp.a.28.5		20	39.2	even	12
585.2.dp.a.397.5		20	15.2	even	4
845.2.f.d.408.10		20	13.7	odd	12
845.2.f.d.437.1		20	65.17	odd	12
845.2.f.e.408.1		20	13.6	odd	12
845.2.f.e.437.10		20	65.22	odd	12
845.2.k.d.268.1		20	13.4	even	6
845.2.k.d.577.1		20	65.7	even	12
845.2.k.e.268.10		20	13.9	even	3
845.2.k.e.577.10		20	65.32	even	12
845.2.o.e.258.1		20	13.3	even	3
845.2.o.e.357.1		20	65.57	even	4
845.2.o.f.258.5		20	13.10	even	6
845.2.o.f.357.5		20	65.47	even	4
845.2.o.g.488.5		20	13.12	even	2
845.2.o.g.587.5		20	65.37	even	12
845.2.t.e.188.1		20	13.8	odd	4
845.2.t.e.427.1		20	65.62	odd	12
845.2.t.f.188.5		20	13.5	odd	4
845.2.t.f.427.5		20	65.42	odd	12
845.2.t.g.418.5		20	13.11	odd	12
845.2.t.g.657.5		20	65.12	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

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Fields

Representations

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Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	65.2.o.a.33.1

Level	$65$
Weight	$2$
Character	65.33
Analytic conductor	$0.519$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$