LMFDB - Embedded newform 325.2.x.b.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(7,325)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("325.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.59513806569$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.5
Root			$2.64975i$ of defining polynomial
Character	$\chi$	$=$	325.7
Dual form			325.2.x.b.93.5

$q$-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} +(0.889471 - 3.31955i) q^{6} +(-0.0561740 - 0.0972962i) q^{7} +8.00544i q^{8} +(1.14131 - 0.658935i) q^{9} +(0.479564 + 1.78976i) q^{11} +(4.60492 - 4.60492i) q^{12} +(-2.96279 - 2.05471i) q^{13} -0.297695i q^{14} +(-5.58502 + 9.67354i) q^{16} +(2.63669 + 0.706500i) q^{17} +3.49203 q^{18} +(-6.72284 - 1.80138i) q^{19} +(-0.103034 + 0.103034i) q^{21} +(-1.27073 + 4.74241i) q^{22} +(3.10327 - 0.831519i) q^{23} +(10.0290 - 2.68727i) q^{24} +(-4.07664 - 8.64040i) q^{26} +(-3.95990 - 3.95990i) q^{27} +(0.282061 - 0.488544i) q^{28} +(-4.03134 - 2.32749i) q^{29} +(-0.624367 - 0.624367i) q^{31} +(-11.7667 + 6.79350i) q^{32} +(2.08118 - 1.20157i) q^{33} +(5.11454 + 5.11454i) q^{34} +(5.73074 + 3.30864i) q^{36} +(0.737435 - 1.27728i) q^{37} +(-13.0407 - 13.0407i) q^{38} +(-1.57955 + 4.40145i) q^{39} +(-5.24069 + 1.40424i) q^{41} +(-0.372945 + 0.0999302i) q^{42} +(-1.00860 + 3.76415i) q^{43} +(-6.57874 + 6.57874i) q^{44} +(8.22291 + 2.20332i) q^{46} +0.345095 q^{47} +(13.9936 + 3.74956i) q^{48} +(3.49369 - 6.05125i) q^{49} -3.54034i q^{51} +(1.49651 - 18.0422i) q^{52} +(3.59144 - 3.59144i) q^{53} +(-3.84062 - 14.3334i) q^{54} +(0.778898 - 0.449697i) q^{56} +9.02691i q^{57} +(-6.16729 - 10.6821i) q^{58} +(0.332494 - 1.24088i) q^{59} +(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} +(-1.41668 + 5.28713i) q^{71} +(5.27506 + 9.13667i) q^{72} +9.06221i q^{73} +(3.38447 - 1.95402i) q^{74} +(-9.04509 - 33.7567i) q^{76} +(0.147197 - 0.147197i) q^{77} +(-9.45605 + 8.00753i) q^{78} +15.1689i q^{79} +(-1.65480 + 2.86620i) q^{81} +(-13.8865 - 3.72089i) q^{82} -8.53853 q^{83} +(-0.706718 - 0.189365i) q^{84} +(-7.30152 + 7.30152i) q^{86} +(-1.56259 + 5.83166i) q^{87} +(-14.3278 + 3.83912i) q^{88} +(0.549735 - 0.147301i) q^{89} +(-0.0334840 + 0.403690i) q^{91} +(11.4069 + 11.4069i) q^{92} +(-0.572604 + 0.991779i) q^{93} +(0.791908 + 0.457208i) q^{94} +(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} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27}+ \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 - 16 * q^11 + 24 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^23 + 32 * q^24 - 24 * q^26 - 4 * q^27 - 18 * q^28 - 48 * q^32 - 18 * q^33 + 2 * q^34 + 36 * q^36 + 4 * q^37 + 8 * q^38 + 4 * q^39 + 10 * q^41 - 40 * q^42 - 10 * q^43 - 36 * q^44 + 4 * q^46 + 40 * q^47 + 56 * q^48 + 18 * q^49 + 30 * q^52 + 10 * q^53 - 48 * q^54 - 16 * q^59 - 16 * q^61 + 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 - 22 * q^68 - 16 * q^69 - 16 * q^71 - 4 * q^72 + 18 * q^74 - 64 * q^76 + 28 * q^77 - 68 * q^78 - 14 * q^81 - 56 * q^82 - 48 * q^83 - 40 * q^84 + 60 * q^86 + 34 * q^87 - 82 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 48 * q^94 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	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	$-0.961181\pi$
$3$	−0.335680	−	1.25278i	−0.193805	−	0.723291i	0.798768	−	0.601640i	$-0.205486\pi$
$4$	2.51060	+	4.34849i	1.25530	+	2.17424i
$5$		0			0
$5$		0			0
$6$	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
$10$		0			0
$11$	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
$13$	−2.96279	−	2.05471i	−0.821731	−	0.569875i
$13$	−2.96279	−	2.05471i	−0.821731	−	0.569875i
$14$		−	0.297695i		−	0.0795622i
$15$		0			0
$16$	−5.58502	+	9.67354i	−1.39626	+	2.41838i
$17$	2.63669	+	0.706500i	0.639492	+	0.171351i	0.563973	−	0.825793i	$-0.309272\pi$
$17$	2.63669	+	0.706500i	0.639492	+	0.171351i	0.0755186	+	0.997144i	$0.475939\pi$
$18$	3.49203			0.823080
$19$	−6.72284	−	1.80138i	−1.54233	−	0.413265i	−0.615309	−	0.788286i	$-0.710969\pi$
$19$	−6.72284	−	1.80138i	−1.54233	−	0.413265i	−0.927016	+	0.375021i	$0.877636\pi$
$20$		0			0
$21$	−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	0.0796701	−	0.996821i	$-0.474613\pi$
$23$	3.10327	−	0.831519i	0.647077	−	0.173384i	0.567407	+	0.823438i	$0.307947\pi$
$24$	10.0290	−	2.68727i	2.04717	−	0.548536i
$25$		0			0
$26$	−4.07664	−	8.64040i	−0.799495	−	1.69452i
$27$	−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	$0.808931\pi$
$30$		0			0
$31$	−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	$0.775267\pi$
$32$	−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			0
$36$	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
$39$	−1.57955	+	4.40145i	−0.252930	+	0.704795i
$40$		0			0
$41$	−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	$0.555923\pi$
$42$	−0.372945	+	0.0999302i	−0.0575466	+	0.0154196i
$43$	−1.00860	+	3.76415i	−0.153810	+	0.574027i	0.845394	+	0.534143i	$0.179366\pi$
$43$	−1.00860	+	3.76415i	−0.153810	+	0.574027i	−0.999204	+	0.0398840i	$0.987301\pi$
$44$	−6.57874	+	6.57874i	−0.991782	+	0.991782i
$45$		0			0
$46$	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
$50$		0			0
$51$		−	3.54034i		−	0.495747i
$52$	1.49651	−	18.0422i	0.207528	−	2.50201i
$53$	3.59144	−	3.59144i	0.493322	−	0.493322i	−0.416029	−	0.909351i	$-0.636579\pi$
$53$	3.59144	−	3.59144i	0.493322	−	0.493322i	0.909351	+	0.416029i	$0.136579\pi$
$54$	−3.84062	−	14.3334i	−0.522642	−	1.95053i
$55$		0			0
$56$	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	−0.940899	−	0.338687i	$-0.890017\pi$
$59$	0.332494	−	1.24088i	0.0432870	−	0.161549i	0.984186	+	0.177138i	$0.0566839\pi$
$60$		0			0
$61$	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			0
$71$	−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	$0.978036\pi$
$72$	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
$75$		0			0
$76$	−9.04509	−	33.7567i	−1.03754	−	3.87216i
$77$	0.147197	−	0.147197i	0.0167747	−	0.0167747i
$78$	−9.45605	+	8.00753i	−1.07069	+	0.906675i
$79$			15.1689i			1.70664i	0.521388	+	0.853320i	$0.325414\pi$
$79$			15.1689i			1.70664i	−0.521388	+	0.853320i	$0.674586\pi$
$80$		0			0
$81$	−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
$85$		0			0
$86$	−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	−0.229565	−	0.973293i	$-0.573730\pi$
$89$	0.549735	−	0.147301i	0.0582718	−	0.0156139i	0.287837	+	0.957679i	$0.407064\pi$
$90$		0			0
$91$	−0.0334840	+	0.403690i	−0.00351007	+	0.0423182i
$92$	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
$95$		0			0
$96$	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
$100$		0			0
$101$	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	0.976612	−	0.215011i	$-0.0689789\pi$
$103$	7.72940	+	7.72940i	0.761600	+	0.761600i	−0.215011	+	0.976612i	$0.568979\pi$
$104$	16.4489	−	23.7185i	1.61295	−	2.32579i
$105$		0			0
$106$	12.9997	−	3.48325i	1.26264	−	0.338324i
$107$	−7.15177	+	1.91631i	−0.691388	+	0.185257i	−0.587370	−	0.809318i	$-0.699837\pi$
$107$	−7.15177	+	1.91631i	−0.691388	+	0.185257i	−0.104018	+	0.994575i	$0.533170\pi$
$108$	7.27785	−	27.1613i	0.700311	−	2.61360i
$109$	3.34544	−	3.34544i	0.320435	−	0.320435i	−0.528499	−	0.848934i	$-0.677245\pi$
$109$	3.34544	−	3.34544i	0.320435	−	0.320435i	0.848934	+	0.528499i	$0.177245\pi$
$110$		0			0
$111$	−1.84768	−	0.495085i	−0.175374	−	0.0469914i
$112$	1.25493			0.118580
$113$	5.90688	+	1.58274i	0.555672	+	0.148892i	0.525717	−	0.850659i	$-0.323797\pi$
$113$	5.90688	+	1.58274i	0.555672	+	0.148892i	0.0299550	+	0.999551i	$0.490464\pi$
$114$	−11.9595	+	20.7145i	−1.12011	+	1.94009i
$115$		0			0
$116$		−	23.3736i		−	2.17019i
$117$	−4.73539	−	0.392775i	−0.437787	−	0.0363121i
$118$	2.40701	−	2.40701i	0.221583	−	0.221583i
$119$	−0.0793738	−	0.296227i	−0.00727618	−	0.0271551i
$120$		0			0
$121$	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
$125$		0			0
$126$	−0.196161	−	0.339761i	−0.0174754	−	0.0302684i
$127$	3.01994	+	11.2706i	0.267976	+	1.00010i	0.960403	+	0.278613i	$0.0898747\pi$
$127$	3.01994	+	11.2706i	0.267976	+	1.00010i	−0.692427	+	0.721488i	$0.743459\pi$
$128$	−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
$135$		0			0
$136$	−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			0
$141$	−0.115842	−	0.432327i	−0.00975562	−	0.0364085i
$142$	−10.2557	+	10.2557i	−0.860643	+	0.860643i
$143$	2.25659	−	6.28804i	0.188705	−	0.525833i
$144$			14.7207i			1.22672i
$145$		0			0
$146$	−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	0.763419	−	0.645903i	$-0.223519\pi$
$149$	13.4468	+	3.60307i	1.10161	+	0.295175i	0.338189	+	0.941078i	$0.390186\pi$
$150$		0			0
$151$	−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	$0.412596\pi$
$152$	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
$155$		0			0
$156$	−23.1052	+	4.18163i	−1.84990	+	0.334799i
$157$	5.14491	+	5.14491i	0.410609	+	0.410609i	0.881951	−	0.471342i	$-0.156230\pi$
$157$	5.14491	+	5.14491i	0.410609	+	0.410609i	−0.471342	+	0.881951i	$0.656230\pi$
$158$	−20.0970	+	34.8090i	−1.59883	+	2.76926i
$159$	−5.70484	−	3.29369i	−0.452423	−	0.261207i
$160$		0			0
$161$	−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
$165$		0			0
$166$	−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
$169$	4.55630	+	12.1754i	0.350484	+	0.936569i
$170$		0			0
$171$	−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	−0.966698	−	0.255921i	$-0.917621\pi$
$173$	−0.0204199	+	0.0762079i	−0.00155249	+	0.00579398i	0.965145	+	0.261715i	$0.0842880\pi$
$174$	−11.3120	+	11.3120i	−0.857560	+	0.857560i
$175$		0			0
$176$	−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	$-0.124910\pi$
$180$		0			0
$181$			22.5267i			1.67440i	0.546899	+	0.837198i	$0.315808\pi$
$181$			22.5267i			1.67440i	−0.546899	+	0.837198i	$0.684192\pi$
$182$	−0.611677	+	0.882008i	−0.0453405	+	0.0653788i
$183$	2.55229	−	2.55229i	0.188671	−	0.188671i
$184$	6.65667	+	24.8430i	0.490737	+	1.83145i
$185$		0			0
$186$	−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
$190$		0			0
$191$	−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	$0.997925\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	7.49657	+	27.9776i	0.522311	+	1.94929i
$207$	2.99388	−	2.99388i	0.208089	−	0.208089i
$208$	36.4236	−	17.1851i	2.52552	−	1.19157i
$209$		−	12.8961i		−	0.892044i
$210$		0			0
$211$	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
$215$		0			0
$216$	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
$220$		0			0
$221$	−6.36032	−	7.51086i	−0.427841	−	0.505235i
$222$	−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
$225$		0			0
$226$	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	0.987214	−	0.159403i	$-0.0509569\pi$
$229$	12.5270	+	12.5270i	0.827811	+	0.827811i	−0.159403	+	0.987214i	$0.550957\pi$
$230$		0			0
$231$	−0.233817	−	0.134994i	−0.0153840	−	0.00888197i
$232$	18.6326	−	32.2726i	1.22329	−	2.11880i
$233$	11.8637	+	11.8637i	0.777214	+	0.777214i	0.979356	−	0.202142i	$-0.0647903\pi$
$233$	11.8637	+	11.8637i	0.777214	+	0.777214i	−0.202142	+	0.979356i	$0.564790\pi$
$234$	−10.3462	−	7.17513i	−0.676350	−	0.469053i
$235$		0			0
$236$	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	$0.563485\pi$
$239$	−18.2161	+	18.2161i	−1.17830	+	1.17830i	−0.980177	+	0.198124i	$0.936515\pi$
$240$		0			0
$241$	−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	$0.639711\pi$
$242$	20.0501			1.28887
$243$	−12.0818	−	3.23730i	−0.775046	−	0.207673i
$244$	−6.98703	+	12.1019i	−0.447299	+	0.774744i
$245$		0			0
$246$			18.6458i			1.18881i
$247$	16.2171	+	19.1506i	1.03187	+	1.21853i
$248$	4.99833	−	4.99833i	0.317394	−	0.317394i
$249$	2.86622	+	10.6969i	0.181639	+	0.677887i
$250$		0			0
$251$	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
$255$		0			0
$256$	1.70209	+	2.94811i	0.106381	+	0.184257i
$257$	−4.51603	−	16.8541i	−0.281702	−	1.05133i	−0.951215	−	0.308528i	$-0.900164\pi$
$257$	−4.51603	−	16.8541i	−0.281702	−	1.05133i	0.669513	−	0.742800i	$-0.266503\pi$
$258$	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	$-0.861115\pi$
$263$	−5.39593	−	20.1379i	−0.332727	−	1.24175i	0.573585	−	0.819146i	$-0.305552\pi$
$264$	9.61911	+	16.6608i	0.592015	+	1.02540i
$265$		0			0
$266$	−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	$0.437731\pi$
$270$		0			0
$271$	−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
$273$	0.516973	−	0.0935629i	0.0312887	−	0.00566269i
$274$		−	48.9787i		−	2.95891i
$275$		0			0
$276$	10.4612	−	18.1194i	0.629693	−	1.09066i
$277$	−9.86609	−	2.64361i	−0.592796	−	0.158839i	−0.0500653	−	0.998746i	$-0.515943\pi$
$277$	−9.86609	−	2.64361i	−0.592796	−	0.158839i	−0.542731	+	0.839907i	$0.682610\pi$
$278$	−28.9097			−1.73389
$279$	−1.12401	−	0.301178i	−0.0672929	−	0.0180311i
$280$		0			0
$281$	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	$0.0735867\pi$
$282$	0.306952	−	1.14556i	0.0182787	−	0.0682171i
$283$	7.98478	−	2.13952i	0.474646	−	0.127181i	−0.0135626	−	0.999908i	$-0.504317\pi$
$283$	7.98478	−	2.13952i	0.474646	−	0.127181i	0.488208	+	0.872727i	$0.337651\pi$
$284$	−26.5478	+	7.11345i	−1.57532	+	0.422105i
$285$		0			0
$286$	13.5092	−	11.4398i	0.798816	−	0.676451i
$287$	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
$290$		0			0
$291$	−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
$295$		0			0
$296$	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
$299$	−10.9029	−	3.91272i	−0.630531	−	0.226278i
$300$		0			0
$301$	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
$305$		0			0
$306$	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
$310$		0			0
$311$			3.54417i			0.200972i	0.994938	+	0.100486i	$0.0320397\pi$
$311$			3.54417i			0.200972i	−0.994938	+	0.100486i	$0.967960\pi$
$312$	−35.2355	−	12.6450i	−1.99482	−	0.715879i
$313$	6.21088	−	6.21088i	0.351060	−	0.351060i	−0.509444	−	0.860504i	$-0.670149\pi$
$313$	6.21088	−	6.21088i	0.351060	−	0.351060i	0.860504	+	0.509444i	$0.170149\pi$
$314$	4.98993	+	18.6227i	0.281598	+	1.05094i
$315$		0			0
$316$	−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
$320$		0			0
$321$	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
$330$		0			0
$331$	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	$-0.0814530\pi$
$332$	−21.4368	−	37.1297i	−1.17650	−	2.03776i
$333$		−	1.94369i		−	0.106513i
$334$	−5.83099	+	3.36652i	−0.319058	+	0.184208i
$335$		0			0
$336$	−0.421256	−	1.57215i	−0.0229814	−	0.0857677i
$337$	20.0865	−	20.0865i	1.09418	−	1.09418i	0.0991030	−	0.995077i	$-0.468403\pi$
$337$	20.0865	−	20.0865i	1.09418	−	1.09418i	0.995077	−	0.0991030i	$-0.0315973\pi$
$338$	−5.67532	+	33.9761i	−0.308697	+	1.84805i
$339$		−	7.93129i		−	0.430769i
$340$		0			0
$341$	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
$345$		0			0
$346$	−0.147825	+	0.147825i	−0.00794710	+	0.00794710i
$347$	1.85743	−	6.93201i	0.0997119	−	0.372130i	−0.897980	−	0.440037i	$-0.854965\pi$
$347$	1.85743	−	6.93201i	0.0997119	−	0.372130i	0.997692	+	0.0679068i	$0.0216321\pi$
$348$	−29.2819	+	7.84607i	−1.56968	+	0.420593i
$349$	3.52885	−	0.945552i	0.188895	−	0.0506143i	−0.163131	−	0.986604i	$-0.552159\pi$
$349$	3.52885	−	0.945552i	0.188895	−	0.0506143i	0.352026	+	0.935990i	$0.385493\pi$
$350$		0			0
$351$	3.59590	+	19.8688i	0.191935	+	1.06052i
$352$	−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
$355$		0			0
$356$	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	0.896298	−	0.443452i	$-0.146246\pi$
$359$	8.58021	+	8.58021i	0.452846	+	0.452846i	−0.443452	+	0.896298i	$0.646246\pi$
$360$		0			0
$361$	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
$364$	−1.83951	+	0.867900i	−0.0964163	+	0.0454903i
$365$		0			0
$366$	9.23835	−	2.47541i	0.482896	−	0.129392i
$367$	−13.5337	+	3.62635i	−0.706454	+	0.189294i	−0.594120	−	0.804377i	$-0.702499\pi$
$367$	−13.5337	+	3.62635i	−0.706454	+	0.189294i	−0.112334	+	0.993670i	$0.535833\pi$
$368$	−9.28811	+	34.6637i	−0.484176	+	1.80697i
$369$	−5.05594	+	5.05594i	−0.263202	+	0.263202i
$370$		0			0
$371$	−0.551179	−	0.147688i	−0.0286158	−	0.00766757i
$372$	−5.75032			−0.298140
$373$	−27.9078	−	7.47789i	−1.44501	−	0.387190i	−0.550727	−	0.834685i	$-0.685650\pi$
$373$	−27.9078	−	7.47789i	−1.44501	−	0.387190i	−0.894286	+	0.447495i	$0.852316\pi$
$374$	−6.70103	+	11.6065i	−0.346502	+	0.600159i
$375$		0			0
$376$			2.76263i			0.142472i
$377$	7.16169	+	15.1791i	0.368846	+	0.781765i
$378$	−1.17884	+	1.17884i	−0.0606330	+	0.0606330i
$379$	2.45278	+	9.15390i	0.125991	+	0.470204i	0.999873	−	0.0159336i	$-0.00507204\pi$
$379$	2.45278	+	9.15390i	0.125991	+	0.470204i	−0.873882	+	0.486138i	$0.838405\pi$
$380$		0			0
$381$	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			0
$386$	−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
$395$		0			0
$396$	−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
$400$		0			0
$401$	−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
$403$	0.566974	+	3.13276i	0.0282430	+	0.156054i
$404$			41.7291i			2.07610i
$405$		0			0
$406$	−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	0.975650	−	0.219332i	$-0.0703877\pi$
$409$	34.6013	+	9.27138i	1.71092	+	0.458440i	0.735272	+	0.677772i	$0.237054\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	48.8209	+	4.04944i	2.39364	+	0.198540i
$417$	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	$0.770188\pi$
$420$		0			0
$421$	−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	$0.907667\pi$
$422$	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
$425$		0			0
$426$	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
$429$	−8.63501	−	0.716228i	−0.416902	−	0.0345798i
$430$		0			0
$431$	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	$0.236931\pi$
$432$	60.4224	−	16.1901i	2.90707	−	0.778948i
$433$	−0.0475058	+	0.177294i	−0.00228298	+	0.00852021i	−0.967058	−	0.254556i	$-0.918071\pi$
$433$	−0.0475058	+	0.177294i	−0.00228298	+	0.00852021i	0.964775	+	0.263077i	$0.0847372\pi$
$434$	−0.185871	+	0.185871i	−0.00892207	+	0.00892207i
$435$		0			0
$436$	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	$0.302077\pi$
$440$		0			0
$441$		−	9.20846i		−	0.438498i
$442$	−4.64440	−	25.6622i	−0.220912	−	1.22063i
$443$	−24.4472	+	24.4472i	−1.16152	+	1.16152i	−0.177377	+	0.984143i	$0.556761\pi$
$443$	−24.4472	+	24.4472i	−1.16152	+	1.16152i	−0.984143	+	0.177377i	$0.943239\pi$
$444$	−2.48592	−	9.27758i	−0.117977	−	0.440295i
$445$		0			0
$446$	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	$-0.575927\pi$
$449$	9.62407	−	35.9175i	0.454188	−	1.69505i	0.690465	−	0.723366i	$-0.257406\pi$
$450$		0			0
$451$	−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
$460$		0			0
$461$	−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	$0.805665\pi$
$462$	−0.357701	−	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			0
$466$	11.5063	+	42.9421i	0.533019	+	1.98925i
$467$	12.1678	−	12.1678i	0.563057	−	0.563057i	−0.367118	−	0.930175i	$-0.619655\pi$
$467$	12.1678	−	12.1678i	0.563057	−	0.563057i	0.930175	+	0.367118i	$0.119655\pi$
$468$	−10.1807	−	21.5779i	−0.470602	−	0.997437i
$469$			0.0162150i			0.000748740i
$470$		0			0
$471$	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
$475$		0			0
$476$	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	−0.897697	−	0.440612i	$-0.854761\pi$
$479$	−31.8403	+	8.53158i	−1.45482	+	0.389818i	−0.557123	+	0.830430i	$0.688095\pi$
$480$		0			0
$481$	−4.80931	+	2.26908i	−0.219285	+	0.103461i
$482$	−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
$485$		0			0
$486$	−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
$490$		0			0
$491$	−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
$494$	11.8420	+	65.4317i	0.532795	+	2.94391i
$495$		0			0
$496$	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	−0.957231	−	0.289326i	$-0.906569\pi$
$499$	−14.9199	+	14.9199i	−0.667904	+	0.667904i	0.289326	+	0.957231i	$0.406569\pi$
$500$		0			0
$501$	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	$0.0103897\pi$
$503$	42.1943	+	11.3059i	1.88135	+	0.504106i	0.881881	+	0.471471i	$0.156277\pi$
$504$	0.592643	−	1.02649i	0.0263984	−	0.0457234i
$505$		0			0
$506$			15.7736i			0.701224i
$507$	13.7236	−	9.79506i	0.609486	−	0.435014i
$508$	−41.4280	+	41.4280i	−1.83807	+	1.83807i
$509$	−9.67023	−	36.0898i	−0.428626	−	1.59965i	−0.755876	−	0.654715i	$-0.772789\pi$
$509$	−9.67023	−	36.0898i	−0.428626	−	1.59965i	0.327250	−	0.944938i	$-0.393878\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	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	0.986037	−	0.166527i	$-0.0532552\pi$
$523$	1.11694	+	4.16849i	0.0488406	+	0.182275i	−0.937196	+	0.348802i	$0.886589\pi$
$524$	18.7386	+	32.4562i	0.818600	+	1.41786i
$525$		0			0
$526$	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
$530$		0			0
$531$	−0.438183	−	1.63532i	−0.0190155	−	0.0709670i
$532$	−2.77630	+	2.77630i	−0.120368	+	0.120368i
$533$	18.4124	+	6.60765i	0.797529	+	0.286209i
$534$		−	1.95589i		−	0.0846398i
$535$		0			0
$536$	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
$540$		0			0
$541$	−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	$0.302762\pi$
$542$	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
$545$		0			0
$546$	1.31029	+	0.470222i	0.0560751	+	0.0201237i
$547$	−11.6940	−	11.6940i	−0.500000	−	0.500000i	0.411438	−	0.911438i	$-0.365027\pi$
$547$	−11.6940	−	11.6940i	−0.500000	−	0.500000i	−0.911438	+	0.411438i	$0.865027\pi$
$548$	46.4066	−	80.3785i	1.98239	−	3.43360i
$549$	3.17628	+	1.83382i	0.135560	+	0.0782657i
$550$		0			0
$551$	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
$555$		0			0
$556$	−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
$559$	10.7225	−	9.08000i	0.453514	−	0.384043i
$560$		0			0
$561$	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	$-0.610012\pi$
$563$	10.0853	−	37.6390i	0.425047	−	1.58630i	0.763821	−	0.645428i	$-0.223321\pi$
$564$	1.58913	−	1.58913i	0.0669146	−	0.0669146i
$565$		0			0
$566$	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	$0.142075\pi$
$570$		0			0
$571$			2.96698i			0.124164i	0.998071	+	0.0620821i	$0.0197741\pi$
$571$			2.96698i			0.124164i	−0.998071	+	0.0620821i	$0.980226\pi$
$572$	33.0089	−	5.97401i	1.38017	−	0.249786i
$573$	−17.9811	+	17.9811i	−0.751170	+	0.751170i
$574$	0.418034	+	1.56012i	0.0174484	+	0.0651184i
$575$		0			0
$576$	−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
$580$		0			0
$581$	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
$590$		0			0
$591$	−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			0
$596$	18.0917	+	67.5192i	0.741066	+	2.76570i
$597$	−12.7909	+	12.7909i	−0.523495	+	0.523495i
$598$	−19.8356	−	23.4237i	−0.811138	−	0.957867i
$599$			13.9207i			0.568784i	0.958708	+	0.284392i	$0.0917918\pi$
$599$			13.9207i			0.568784i	−0.958708	+	0.284392i	$0.908208\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	20.1954	−	20.1954i	0.820381	−	0.820381i
$607$	−6.10830	+	22.7965i	−0.247928	+	0.925282i	0.723960	+	0.689842i	$0.242320\pi$
$607$	−6.10830	+	22.7965i	−0.247928	+	0.925282i	−0.971889	+	0.235440i	$0.924347\pi$
$608$	91.3432	−	24.4753i	3.70446	−	0.992606i
$609$	0.655175	−	0.175554i	0.0265490	−	0.00711379i
$610$		0			0
$611$	−1.02244	−	0.709071i	−0.0413637	−	0.0286860i
$612$	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
$615$		0			0
$616$	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	0.959474	−	0.281796i	$-0.0909301\pi$
$619$	16.8604	+	16.8604i	0.677679	+	0.677679i	−0.281796	+	0.959474i	$0.590930\pi$
$620$		0			0
$621$	−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
$624$	−33.7558	−	39.8620i	−1.35131	−	1.59576i
$625$		0			0
$626$	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			0
$631$	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	$0.374904\pi$
$632$	−121.434			−4.83038
$633$	−29.5882	−	7.92814i	−1.17603	−	0.315115i
$634$	−11.2987	+	19.5700i	−0.448729	+	0.777222i
$635$		0			0
$636$		−	33.0766i		−	1.31157i
$637$	−22.7847	+	10.7501i	−0.902761	+	0.425933i
$638$	16.1607	−	16.1607i	0.639807	−	0.639807i
$639$	1.86700	+	6.96776i	0.0738576	+	0.275640i
$640$		0			0
$641$	−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
$645$		0			0
$646$	−25.1710	−	43.5974i	−0.990340	−	1.71532i
$647$	−1.21024	−	4.51668i	−0.0475795	−	0.177569i	0.938047	−	0.346508i	$-0.112633\pi$
$647$	−1.21024	−	4.51668i	−0.0475795	−	0.177569i	−0.985627	+	0.168939i	$0.945966\pi$
$648$	−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	$-0.924149\pi$
$653$	−6.34274	−	23.6714i	−0.248211	−	0.926335i	0.723532	−	0.690291i	$-0.242518\pi$
$654$	−8.12969	−	14.0810i	−0.317896	−	0.550612i
$655$		0			0
$656$	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	$0.0416072\pi$
$660$		0			0
$661$	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
$663$	−7.27440	+	10.4893i	−0.282514	+	0.407371i
$664$		−	68.3547i		−	2.65268i
$665$		0			0
$666$	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			0
$671$	−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	0.213428	−	0.976959i	$-0.431537\pi$
$673$	23.0041	−	6.16392i	0.886742	−	0.237602i	0.673314	+	0.739357i	$0.264870\pi$
$674$	72.7057	−	19.4814i	2.80052	−	0.750396i
$675$		0			0
$676$	−41.5055	+	50.3805i	−1.59636	+	1.93771i
$677$	−26.1344	−	26.1344i	−1.00443	−	1.00443i	−0.999990	−	0.00443504i	$-0.998588\pi$
$677$	−26.1344	−	26.1344i	−1.00443	−	1.00443i	−0.00443504	−	0.999990i	$-0.501412\pi$
$678$	10.5080	−	18.2004i	0.403557	−	0.698981i
$679$	−1.45598	−	0.840613i	−0.0558756	−	0.0322598i
$680$		0			0
$681$	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
$685$		0			0
$686$	−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
$689$	−18.0201	+	3.26131i	−0.686510	+	0.124246i
$690$		0			0
$691$	−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	$0.695308\pi$
$692$	−0.382655	+	0.102532i	−0.0145464	+	0.00389769i
$693$	0.0710042	−	0.264991i	0.00269723	−	0.0100662i
$694$	13.4464	−	13.4464i	0.510419	−	0.510419i
$695$		0			0
$696$	−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
$700$		0			0
$701$			24.9781i			0.943410i	0.881756	+	0.471705i	$0.156361\pi$
$701$			24.9781i			0.943410i	−0.881756	+	0.471705i	$0.843639\pi$
$702$	−18.0721	+	50.3582i	−0.682086	+	1.90065i
$703$	−7.25852	+	7.25852i	−0.273760	+	0.273760i
$704$	−6.55185	−	24.4519i	−0.246932	−	0.921564i
$705$		0			0
$706$	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	−0.997623	−	0.0689135i	$-0.978047\pi$
$709$	−2.64139	+	9.85779i	−0.0991993	+	0.370217i	0.898423	+	0.439130i	$0.144713\pi$
$710$		0			0
$711$	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	$-0.344477\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−6.73044	−	25.1183i	−0.249790	−	0.932229i
$727$	8.56116	−	8.56116i	0.317516	−	0.317516i	−0.530296	−	0.847812i	$-0.677919\pi$
$727$	8.56116	−	8.56116i	0.317516	−	0.317516i	0.847812	+	0.530296i	$0.177919\pi$
$728$	−3.23172	−	0.268054i	−0.119775	−	0.00993473i
$729$			26.1513i			0.968566i
$730$		0			0
$731$	−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
$735$		0			0
$736$	−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	−0.536588	−	0.843845i	$-0.680287\pi$
$739$	−15.7497	+	4.22013i	−0.579364	+	0.155240i	−0.0427762	+	0.999085i	$0.513620\pi$
$740$		0			0
$741$	18.5477	−	26.7449i	0.681367	−	0.982497i
$742$	−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
$745$		0			0
$746$	−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
$750$		0			0
$751$	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
$754$	−3.67617	+	44.3207i	−0.133878	+	1.61407i
$755$		0			0
$756$	−3.05152	+	0.817652i	−0.110983	+	0.0297377i
$757$	2.84678	−	0.762791i	0.103468	−	0.0277241i	−0.206714	−	0.978401i	$-0.566277\pi$
$757$	2.84678	−	0.762791i	0.103468	−	0.0277241i	0.310181	+	0.950677i	$0.399610\pi$
$758$	−6.49926	+	24.2556i	−0.236064	+	0.881002i
$759$	5.45935	−	5.45935i	0.198162	−	0.198162i
$760$		0			0
$761$	−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	$0.714131\pi$
$762$	40.0993			1.45265
$763$	−0.513426	−	0.137572i	−0.0185873	−	0.00498044i
$764$	49.2241	−	85.2587i	1.78087	−	3.08455i
$765$		0			0
$766$		−	55.8361i		−	2.01744i
$767$	−3.53477	+	2.99330i	−0.127633	+	0.108082i
$768$	3.12197	−	3.12197i	0.112654	−	0.112654i
$769$	−5.46718	−	20.4038i	−0.197152	−	0.735780i	−0.991699	−	0.128578i	$-0.958959\pi$
$769$	−5.46718	−	20.4038i	−0.197152	−	0.735780i	0.794548	−	0.607202i	$-0.207708\pi$
$770$		0			0
$771$	−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
$775$		0			0
$776$	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
$785$		0			0
$786$	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
$790$		0			0
$791$	−0.177818	−	0.663626i	−0.00632248	−	0.0235958i
$792$	−13.8227	+	13.8227i	−0.491168	+	0.491168i
$793$	0.829444	−	9.99995i	0.0294544	−	0.355109i
$794$			21.7710i			0.772625i
$795$		0			0
$796$	35.0157	−	60.6489i	1.24110	−	2.14964i
$797$	33.9650	+	9.10089i	1.20310	+	0.322370i	0.804052	−	0.594559i	$-0.202673\pi$
$797$	33.9650	+	9.10089i	1.20310	+	0.322370i	0.399050	+	0.916929i	$0.369340\pi$
$798$	2.68726			0.0951280
$799$	0.909909	+	0.243809i	0.0321903	+	0.00862535i
$800$		0			0
$801$	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			0
$806$	−2.84946	+	7.94010i	−0.100368	+	0.279678i
$807$	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	$0.784879\pi$
$810$		0			0
$811$	−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	$0.934392\pi$
$812$	−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
$815$		0			0
$816$	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
$819$	0.227790	+	0.482799i	0.00795963	+	0.0168704i
$820$		0			0
$821$	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	$0.195441\pi$
$822$	−61.3594	+	16.4412i	−2.14016	+	0.573453i
$823$	−6.11025	+	22.8038i	−0.212990	+	0.794889i	0.773875	+	0.633339i	$0.218316\pi$
$823$	−6.11025	+	22.8038i	−0.212990	+	0.794889i	−0.986865	+	0.161550i	$0.948351\pi$
$824$	−61.8772	+	61.8772i	−2.15559	+	2.15559i
$825$		0			0
$826$	−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	$0.996513\pi$
$830$		0			0
$831$			13.2474i			0.459548i
$832$	40.4780	+	28.0718i	1.40332	+	0.973213i
$833$	13.4870	−	13.4870i	0.467296	−	0.467296i
$834$	9.70441	+	36.2174i	0.336036	+	1.25410i
$835$		0			0
$836$	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	−0.993421	−	0.114519i	$-0.963467\pi$
$839$	−2.19656	+	8.19766i	−0.0758336	+	0.283015i	0.917587	+	0.397534i	$0.130134\pi$
$840$		0			0
$841$	−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
$850$		0			0
$851$	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
$855$		0			0
$856$	−15.3409	−	57.2531i	−0.524342	−	1.95687i
$857$	−24.6090	+	24.6090i	−0.840626	+	0.840626i	−0.988940	−	0.148314i	$-0.952615\pi$
$857$	−24.6090	+	24.6090i	−0.840626	+	0.840626i	0.148314	+	0.988940i	$0.452615\pi$
$858$	−18.8663	−	13.0839i	−0.644085	−	0.446677i
$859$		−	12.8606i		−	0.438798i	−0.975635	−	0.219399i	$-0.929590\pi$
$859$		−	12.8606i		−	0.438798i	0.975635	−	0.219399i	$-0.0704097\pi$
$860$		0			0
$861$	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			0
$866$	−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
$870$		0			0
$871$	0.222049	+	0.470631i	0.00752385	+	0.0159467i
$872$	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			0
$876$	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
$880$		0			0
$881$	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	0.442903	−	0.896569i	$-0.353949\pi$
$883$	−13.4808	−	13.4808i	−0.453666	−	0.453666i	−0.896569	+	0.442903i	$0.853949\pi$
$884$	16.6927	−	46.5145i	0.561435	−	1.56445i
$885$		0			0
$886$	−88.4897	+	23.7108i	−2.97287	+	0.796578i
$887$	22.1438	−	5.93341i	0.743516	−	0.199225i	0.132876	−	0.991133i	$-0.457579\pi$
$887$	22.1438	−	5.93341i	0.743516	−	0.199225i	0.610640	+	0.791908i	$0.290912\pi$
$888$	3.96337	−	14.7915i	0.133002	−	0.496371i
$889$	0.926941	−	0.926941i	0.0310886	−	0.0310886i
$890$		0			0
$891$	−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
$895$		0			0
$896$			1.01420i			0.0338819i
$897$	−1.24187	+	14.9723i	−0.0414650	+	0.499911i
$898$	69.6712	−	69.6712i	2.32496	−	2.32496i
$899$	1.06382	+	3.97024i	0.0354805	+	0.132415i
$900$		0			0
$901$	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
$905$		0			0
$906$	20.6458	+	35.7595i	0.685910	+	1.18803i
$907$	6.24222	+	23.2963i	0.207270	+	0.773541i	0.988746	+	0.149606i	$0.0478004\pi$
$907$	6.24222	+	23.2963i	0.207270	+	0.773541i	−0.781476	+	0.623935i	$0.785533\pi$
$908$	−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
$915$		0			0
$916$	−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	$0.0682506\pi$
$920$		0			0
$921$	−8.91097	−	33.2562i	−0.293626	−	1.09583i
$922$	−61.6169	+	61.6169i	−2.02924	+	2.02924i
$923$	15.0609	−	12.7538i	0.495735	−	0.419797i
$924$		−	1.35567i		−	0.0445981i
$925$		0			0
$926$	−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	−0.214952	−	0.976625i	$-0.568960\pi$
$929$	−27.1090	−	7.26384i	−0.889418	−	0.238319i	−0.674466	+	0.738306i	$0.735626\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	3.14434	−	37.9088i	0.102776	−	1.23909i
$937$	−20.7545	−	20.7545i	−0.678019	−	0.678019i	0.281533	−	0.959552i	$-0.409157\pi$
$937$	−20.7545	−	20.7545i	−0.678019	−	0.678019i	−0.959552	+	0.281533i	$0.909157\pi$
$938$	−0.0214829	+	0.0372095i	−0.000701442	+	0.00121493i
$939$	−9.86572	−	5.69597i	−0.321955	−	0.185881i
$940$		0			0
$941$	−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	$0.799398\pi$
$942$	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			0
$946$	−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
$949$	18.6203	−	26.8495i	0.604439	−	0.871570i
$950$		0			0
$951$	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	−0.937662	−	0.347548i	$-0.887014\pi$
$953$	1.48646	−	5.54756i	0.0481513	−	0.179703i	0.985813	+	0.167845i	$0.0536809\pi$
$954$	12.5414	−	12.5414i	0.406043	−	0.406043i
$955$		0			0
$956$	−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
$960$		0			0
$961$		−	30.2203i		−	0.974849i
$962$	−14.0424	−	1.16475i	−0.452746	−	0.0375529i
$963$	−6.89966	+	6.89966i	−0.222338	+	0.222338i
$964$	−7.10927	−	26.5322i	−0.228974	−	0.854543i
$965$		0			0
$966$	−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
$970$		0			0
$971$	−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
$980$		0			0
$981$	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
$985$		0			0
$986$	−8.71437	−	32.5225i	−0.277522	−	1.03573i
$987$	−0.0355565	+	0.0355565i	−0.00113177	+	0.00113177i
$988$	−42.5617	+	118.599i	−1.35407	+	3.77315i
$989$			12.5198i			0.398108i
$990$		0			0
$991$	−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
$995$		0			0
$996$	−39.3193	+	39.3193i	−1.24588	+	1.24588i
$997$	1.70003	−	6.34461i	0.0538406	−	0.200936i	−0.933766	−	0.357883i	$-0.883499\pi$
$997$	1.70003	−	6.34461i	0.0538406	−	0.200936i	0.987607	+	0.156947i	$0.0501653\pi$
$998$	−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	325.2.x.b.7.5		20
5.2	odd	4		65.2.o.a.33.1	yes	20
5.3	odd	4		325.2.s.b.293.5		20
5.4	even	2		65.2.t.a.7.1	yes	20
13.2	odd	12		325.2.s.b.132.5		20
15.2	even	4		585.2.cf.a.163.5		20
15.14	odd	2		585.2.dp.a.397.5		20
65.2	even	12		65.2.t.a.28.1	yes	20
65.4	even	6		845.2.f.d.437.1		20
65.7	even	12		845.2.f.d.408.10		20
65.9	even	6		845.2.f.e.437.10		20
65.12	odd	4		845.2.o.g.488.5		20
65.17	odd	12		845.2.k.d.268.1		20
65.19	odd	12		845.2.k.e.577.10		20
65.22	odd	12		845.2.k.e.268.10		20
65.24	odd	12		845.2.o.g.587.5		20
65.28	even	12	inner	325.2.x.b.93.5		20
65.29	even	6		845.2.t.f.427.5		20
65.32	even	12		845.2.f.e.408.1		20
65.34	odd	4		845.2.o.f.357.5		20
65.37	even	12		845.2.t.g.418.5		20
65.42	odd	12		845.2.o.e.258.1		20
65.44	odd	4		845.2.o.e.357.1		20
65.47	even	4		845.2.t.e.188.1		20
65.49	even	6		845.2.t.e.427.1		20
65.54	odd	12		65.2.o.a.2.1	✓	20
65.57	even	4		845.2.t.f.188.5		20
65.59	odd	12		845.2.k.d.577.1		20
65.62	odd	12		845.2.o.f.258.5		20
65.64	even	2		845.2.t.g.657.5		20
195.2	odd	12		585.2.dp.a.28.5		20
195.119	even	12		585.2.cf.a.262.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.1	✓	20	65.54	odd	12
65.2.o.a.33.1	yes	20	5.2	odd	4
65.2.t.a.7.1	yes	20	5.4	even	2
65.2.t.a.28.1	yes	20	65.2	even	12
325.2.s.b.132.5		20	13.2	odd	12
325.2.s.b.293.5		20	5.3	odd	4
325.2.x.b.7.5		20	1.1	even	1	trivial
325.2.x.b.93.5		20	65.28	even	12	inner
585.2.cf.a.163.5		20	15.2	even	4
585.2.cf.a.262.5		20	195.119	even	12
585.2.dp.a.28.5		20	195.2	odd	12
585.2.dp.a.397.5		20	15.14	odd	2
845.2.f.d.408.10		20	65.7	even	12
845.2.f.d.437.1		20	65.4	even	6
845.2.f.e.408.1		20	65.32	even	12
845.2.f.e.437.10		20	65.9	even	6
845.2.k.d.268.1		20	65.17	odd	12
845.2.k.d.577.1		20	65.59	odd	12
845.2.k.e.268.10		20	65.22	odd	12
845.2.k.e.577.10		20	65.19	odd	12
845.2.o.e.258.1		20	65.42	odd	12
845.2.o.e.357.1		20	65.44	odd	4
845.2.o.f.258.5		20	65.62	odd	12
845.2.o.f.357.5		20	65.34	odd	4
845.2.o.g.488.5		20	65.12	odd	4
845.2.o.g.587.5		20	65.24	odd	12
845.2.t.e.188.1		20	65.47	even	4
845.2.t.e.427.1		20	65.49	even	6
845.2.t.f.188.5		20	65.57	even	4
845.2.t.f.427.5		20	65.29	even	6
845.2.t.g.418.5		20	65.37	even	12
845.2.t.g.657.5		20	65.64	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29475 + 1.32488i) q^{2} +(-0.335680 - 1.25278i) q^{3} +(2.51060 + 4.34849i) q^{4} +(0.889471 - 3.31955i) q^{6} +(-0.0561740 - 0.0972962i) q^{7} +8.00544i q^{8} +(1.14131 - 0.658935i) q^{9} +(0.479564 + 1.78976i) q^{11} +(4.60492 - 4.60492i) q^{12} +(-2.96279 - 2.05471i) q^{13} -0.297695i q^{14} +(-5.58502 + 9.67354i) q^{16} +(2.63669 + 0.706500i) q^{17} +3.49203 q^{18} +(-6.72284 - 1.80138i) q^{19} +(-0.103034 + 0.103034i) q^{21} +(-1.27073 + 4.74241i) q^{22} +(3.10327 - 0.831519i) q^{23} +(10.0290 - 2.68727i) q^{24} +(-4.07664 - 8.64040i) q^{26} +(-3.95990 - 3.95990i) q^{27} +(0.282061 - 0.488544i) q^{28} +(-4.03134 - 2.32749i) q^{29} +(-0.624367 - 0.624367i) q^{31} +(-11.7667 + 6.79350i) q^{32} +(2.08118 - 1.20157i) q^{33} +(5.11454 + 5.11454i) q^{34} +(5.73074 + 3.30864i) q^{36} +(0.737435 - 1.27728i) q^{37} +(-13.0407 - 13.0407i) q^{38} +(-1.57955 + 4.40145i) q^{39} +(-5.24069 + 1.40424i) q^{41} +(-0.372945 + 0.0999302i) q^{42} +(-1.00860 + 3.76415i) q^{43} +(-6.57874 + 6.57874i) q^{44} +(8.22291 + 2.20332i) q^{46} +0.345095 q^{47} +(13.9936 + 3.74956i) q^{48} +(3.49369 - 6.05125i) q^{49} -3.54034i q^{51} +(1.49651 - 18.0422i) q^{52} +(3.59144 - 3.59144i) q^{53} +(-3.84062 - 14.3334i) q^{54} +(0.778898 - 0.449697i) q^{56} +9.02691i q^{57} +(-6.16729 - 10.6821i) q^{58} +(0.332494 - 1.24088i) q^{59} +(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} +(-1.41668 + 5.28713i) q^{71} +(5.27506 + 9.13667i) q^{72} +9.06221i q^{73} +(3.38447 - 1.95402i) q^{74} +(-9.04509 - 33.7567i) q^{76} +(0.147197 - 0.147197i) q^{77} +(-9.45605 + 8.00753i) q^{78} +15.1689i q^{79} +(-1.65480 + 2.86620i) q^{81} +(-13.8865 - 3.72089i) q^{82} -8.53853 q^{83} +(-0.706718 - 0.189365i) q^{84} +(-7.30152 + 7.30152i) q^{86} +(-1.56259 + 5.83166i) q^{87} +(-14.3278 + 3.83912i) q^{88} +(0.549735 - 0.147301i) q^{89} +(-0.0334840 + 0.403690i) q^{91} +(11.4069 + 11.4069i) q^{92} +(-0.572604 + 0.991779i) q^{93} +(0.791908 + 0.457208i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^11 + 24 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^23 + 32 * q^24 - 24 * q^26 - 4 * q^27 - 18 * q^28 - 48 * q^32 - 18 * q^33 + 2 * q^34 + 36 * q^36 + 4 * q^37 + 8 * q^38 + 4 * q^39 + 10 * q^41 - 40 * q^42 - 10 * q^43 - 36 * q^44 + 4 * q^46 + 40 * q^47 + 56 * q^48 + 18 * q^49 + 30 * q^52 + 10 * q^53 - 48 * q^54 - 16 * q^59 - 16 * q^61 + 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 - 22 * q^68 - 16 * q^69 - 16 * q^71 - 4 * q^72 + 18 * q^74 - 64 * q^76 + 28 * q^77 - 68 * q^78 - 14 * q^81 - 56 * q^82 - 48 * q^83 - 40 * q^84 + 60 * q^86 + 34 * q^87 - 82 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 48 * q^94 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more