LMFDB - Embedded newform 192.2.r.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	192.37
Dual form			192.2.r.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35486 - 0.405391i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.67132 + 1.09850i) q^{4} +(-0.550464 + 2.76737i) q^{5} +(-1.08979 + 0.901306i) q^{6} +(-1.44187 + 3.48098i) q^{7} +(-1.81909 - 2.16585i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(-1.35486 - 0.405391i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.67132 + 1.09850i) q^{4} +(-0.550464 + 2.76737i) q^{5} +(-1.08979 + 0.901306i) q^{6} +(-1.44187 + 3.48098i) q^{7} +(-1.81909 - 2.16585i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(1.86767 - 3.52626i) q^{10} +(-5.04042 + 3.36790i) q^{11} +(1.84190 - 0.779355i) q^{12} +(0.117455 + 0.590485i) q^{13} +(3.36469 - 4.13173i) q^{14} +(1.99516 + 1.99516i) q^{15} +(1.58660 + 3.67188i) q^{16} +(2.77708 - 2.77708i) q^{17} +(0.143952 + 1.40687i) q^{18} +(4.75841 - 0.946507i) q^{19} +(-3.95995 + 4.02046i) q^{20} +(2.09327 + 3.13280i) q^{21} +(8.19440 - 2.51971i) q^{22} +(-2.21894 + 0.919113i) q^{23} +(-2.81147 + 0.309231i) q^{24} +(-2.73591 - 1.13325i) q^{25} +(0.0802419 - 0.847643i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-6.23367 + 4.23393i) q^{28} +(6.64945 + 4.44302i) q^{29} +(-1.89435 - 3.51199i) q^{30} -1.09090i q^{31} +(-0.661079 - 5.61809i) q^{32} +6.06206i q^{33} +(-4.88838 + 2.63677i) q^{34} +(-8.83945 - 5.90633i) q^{35} +(0.375296 - 1.96447i) q^{36} +(0.0776136 + 0.0154383i) q^{37} +(-6.83071 - 0.646628i) q^{38} +(0.556225 + 0.230396i) q^{39} +(6.99506 - 3.84186i) q^{40} +(5.07471 - 2.10201i) q^{41} +(-1.56609 - 5.09311i) q^{42} +(-4.35589 - 6.51905i) q^{43} +(-12.1238 + 0.0919304i) q^{44} +(2.76737 - 0.550464i) q^{45} +(3.37896 - 0.345738i) q^{46} +(7.14806 - 7.14806i) q^{47} +(3.93452 + 0.720779i) q^{48} +(-5.08848 - 5.08848i) q^{49} +(3.24738 + 2.64452i) q^{50} +(-0.766196 - 3.85193i) q^{51} +(-0.452343 + 1.11591i) q^{52} +(0.192204 - 0.128427i) q^{53} +(1.24974 + 0.661922i) q^{54} +(-6.54565 - 15.8026i) q^{55} +(10.1622 - 3.20932i) q^{56} +(1.85664 - 4.48233i) q^{57} +(-7.20795 - 8.71532i) q^{58} +(-2.74884 + 13.8193i) q^{59} +(1.14286 + 5.52623i) q^{60} +(-4.68943 + 7.01823i) q^{61} +(-0.442241 + 1.47802i) q^{62} +3.76778 q^{63} +(-1.38185 + 7.87975i) q^{64} -1.69874 q^{65} +(2.45750 - 8.21327i) q^{66} +(-6.50973 + 9.74250i) q^{67} +(7.69201 - 1.59076i) q^{68} +(-0.468560 + 2.35561i) q^{69} +(9.58189 + 11.5857i) q^{70} +(0.823076 - 1.98708i) q^{71} +(-1.30485 + 2.50945i) q^{72} +(1.38827 + 3.35157i) q^{73} +(-0.0988974 - 0.0523807i) q^{74} +(-2.46226 + 1.64523i) q^{75} +(8.99255 + 3.64520i) q^{76} +(-4.45597 - 22.4017i) q^{77} +(-0.660209 - 0.537644i) q^{78} +(2.20249 + 2.20249i) q^{79} +(-11.0348 + 2.36946i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(-7.72768 + 0.790704i) q^{82} +(6.00359 - 1.19419i) q^{83} +(0.0571380 + 7.53535i) q^{84} +(6.15653 + 9.21390i) q^{85} +(3.25888 + 10.5983i) q^{86} +(7.38848 - 3.06041i) q^{87} +(16.4633 + 4.79031i) q^{88} +(6.97098 + 2.88747i) q^{89} +(-3.97256 - 0.376062i) q^{90} +(-2.22482 - 0.442544i) q^{91} +(-4.71819 - 0.901370i) q^{92} +(-0.907050 - 0.606072i) q^{93} +(-12.5824 + 6.78690i) q^{94} +13.6893i q^{95} +(-5.03855 - 2.57158i) q^{96} -11.7711i q^{97} +(4.83138 + 8.95702i) q^{98} +(5.04042 + 3.36790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	−1.35486	−	0.405391i	−0.958034	−	0.286655i
$2$	−1.35486	−	0.405391i	−0.958034	−	0.286655i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$4$	1.67132	+	1.09850i	0.835658	+	0.549250i
$5$	−0.550464	+	2.76737i	−0.246175	+	1.23760i	0.637849	+	0.770162i	$0.279825\pi$
$5$	−0.550464	+	2.76737i	−0.246175	+	1.23760i	−0.884023	+	0.467443i	$0.845175\pi$
$6$	−1.08979	+	0.901306i	−0.444906	+	0.367957i
$7$	−1.44187	+	3.48098i	−0.544975	+	1.31569i	0.376200	+	0.926538i	$0.377230\pi$
$7$	−1.44187	+	3.48098i	−0.544975	+	1.31569i	−0.921175	+	0.389148i	$0.872770\pi$
$8$	−1.81909	−	2.16585i	−0.643144	−	0.765745i
$9$	−0.382683	−	0.923880i	−0.127561	−	0.307960i
$10$	1.86767	−	3.52626i	0.590609	−	1.11510i
$11$	−5.04042	+	3.36790i	−1.51974	+	1.01546i	−0.534332	+	0.845275i	$0.679437\pi$
$11$	−5.04042	+	3.36790i	−1.51974	+	1.01546i	−0.985412	+	0.170185i	$0.945563\pi$
$12$	1.84190	−	0.779355i	0.531711	−	0.224981i
$13$	0.117455	+	0.590485i	0.0325761	+	0.163771i	0.993649	−	0.112524i	$-0.0358934\pi$
$13$	0.117455	+	0.590485i	0.0325761	+	0.163771i	−0.961073	+	0.276295i	$0.910893\pi$
$14$	3.36469	−	4.13173i	0.899252	−	1.10425i
$15$	1.99516	+	1.99516i	0.515148	+	0.515148i
$16$	1.58660	+	3.67188i	0.396650	+	0.917970i
$17$	2.77708	−	2.77708i	0.673542	−	0.673542i	−0.284989	−	0.958531i	$-0.591990\pi$
$17$	2.77708	−	2.77708i	0.673542	−	0.673542i	0.958531	+	0.284989i	$0.0919899\pi$
$18$	0.143952	+	1.40687i	0.0339298	+	0.331602i
$19$	4.75841	−	0.946507i	1.09165	−	0.217144i	0.383740	−	0.923441i	$-0.374636\pi$
$19$	4.75841	−	0.946507i	1.09165	−	0.217144i	0.707915	+	0.706298i	$0.249636\pi$
$20$	−3.95995	+	4.02046i	−0.885472	+	0.899003i
$21$	2.09327	+	3.13280i	0.456789	+	0.683633i
$22$	8.19440	−	2.51971i	1.74705	−	0.537204i
$23$	−2.21894	+	0.919113i	−0.462680	+	0.191648i	−0.601832	−	0.798623i	$-0.705562\pi$
$23$	−2.21894	+	0.919113i	−0.462680	+	0.191648i	0.139152	+	0.990271i	$0.455562\pi$
$24$	−2.81147	+	0.309231i	−0.573889	+	0.0631214i
$25$	−2.73591	−	1.13325i	−0.547183	−	0.226651i
$26$	0.0802419	−	0.847643i	0.0157367	−	0.166236i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	−6.23367	+	4.23393i	−1.17805	+	0.800137i
$29$	6.64945	+	4.44302i	1.23477	+	0.825048i	0.989518	−	0.144410i	$-0.0461285\pi$
$29$	6.64945	+	4.44302i	1.23477	+	0.825048i	0.245254	+	0.969459i	$0.421129\pi$
$30$	−1.89435	−	3.51199i	−0.345860	−	0.641199i
$31$		−	1.09090i		−	0.195931i	−0.995190	−	0.0979657i	$-0.968766\pi$
$31$		−	1.09090i		−	0.195931i	0.995190	−	0.0979657i	$-0.0312336\pi$
$32$	−0.661079	−	5.61809i	−0.116863	−	0.993148i
$33$			6.06206i			1.05527i
$34$	−4.88838	+	2.63677i	−0.838350	+	0.452202i
$35$	−8.83945	−	5.90633i	−1.49414	−	0.998352i
$36$	0.375296	−	1.96447i	0.0625493	−	0.327412i
$37$	0.0776136	+	0.0154383i	0.0127596	+	0.00253804i	0.201466	−	0.979496i	$-0.435429\pi$
$37$	0.0776136	+	0.0154383i	0.0127596	+	0.00253804i	−0.188706	+	0.982034i	$0.560429\pi$
$38$	−6.83071	−	0.646628i	−1.10809	−	0.104897i
$39$	0.556225	+	0.230396i	0.0890673	+	0.0368929i
$40$	6.99506	−	3.84186i	1.10602	−	0.607451i
$41$	5.07471	−	2.10201i	0.792537	−	0.328279i	0.0505738	−	0.998720i	$-0.483895\pi$
$41$	5.07471	−	2.10201i	0.792537	−	0.328279i	0.741963	+	0.670441i	$0.233895\pi$
$42$	−1.56609	−	5.09311i	−0.241653	−	0.785884i
$43$	−4.35589	−	6.51905i	−0.664267	−	0.994146i	−0.998662	−	0.0517132i	$-0.983532\pi$
$43$	−4.35589	−	6.51905i	−0.664267	−	0.994146i	0.334395	−	0.942433i	$-0.391468\pi$
$44$	−12.1238	+	0.0919304i	−1.82773	+	0.0138590i
$45$	2.76737	−	0.550464i	0.412535	−	0.0820583i
$46$	3.37896	−	0.345738i	0.498200	−	0.0509763i
$47$	7.14806	−	7.14806i	1.04265	−	1.04265i	0.0436028	−	0.999049i	$-0.486116\pi$
$47$	7.14806	−	7.14806i	1.04265	−	1.04265i	0.999049	−	0.0436028i	$-0.0138836\pi$
$48$	3.93452	+	0.720779i	0.567900	+	0.104036i
$49$	−5.08848	−	5.08848i	−0.726926	−	0.726926i
$50$	3.24738	+	2.64452i	0.459249	+	0.373991i
$51$	−0.766196	−	3.85193i	−0.107289	−	0.539378i
$52$	−0.452343	+	1.11591i	−0.0627287	+	0.154749i
$53$	0.192204	−	0.128427i	0.0264012	−	0.0176408i	−0.542300	−	0.840185i	$-0.682446\pi$
$53$	0.192204	−	0.128427i	0.0264012	−	0.0176408i	0.568701	+	0.822544i	$0.307446\pi$
$54$	1.24974	+	0.661922i	0.170069	+	0.0900762i
$55$	−6.54565	−	15.8026i	−0.882615	−	2.13082i
$56$	10.1622	−	3.20932i	1.35798	−	0.428864i
$57$	1.85664	−	4.48233i	0.245918	−	0.593698i
$58$	−7.20795	−	8.71532i	−0.946450	−	1.14438i
$59$	−2.74884	+	13.8193i	−0.357868	+	1.79913i	0.211868	+	0.977298i	$0.432045\pi$
$59$	−2.74884	+	13.8193i	−0.357868	+	1.79913i	−0.569736	+	0.821828i	$0.692955\pi$
$60$	1.14286	+	5.52623i	0.147543	+	0.713433i
$61$	−4.68943	+	7.01823i	−0.600421	+	0.898593i	−0.999835	−	0.0181777i	$-0.994214\pi$
$61$	−4.68943	+	7.01823i	−0.600421	+	0.898593i	0.399414	+	0.916771i	$0.369214\pi$
$62$	−0.442241	+	1.47802i	−0.0561646	+	0.187709i
$63$	3.76778			0.474696
$64$	−1.38185	+	7.87975i	−0.172731	+	0.984969i
$65$	−1.69874			−0.210703
$66$	2.45750	−	8.21327i	0.302498	−	1.01098i
$67$	−6.50973	+	9.74250i	−0.795290	+	1.19024i	0.183024	+	0.983108i	$0.441411\pi$
$67$	−6.50973	+	9.74250i	−0.795290	+	1.19024i	−0.978314	+	0.207127i	$0.933589\pi$
$68$	7.69201	−	1.59076i	0.932793	−	0.192908i
$69$	−0.468560	+	2.35561i	−0.0564080	+	0.283582i
$70$	9.58189	+	11.5857i	1.14525	+	1.38476i
$71$	0.823076	−	1.98708i	0.0976811	−	0.235823i	−0.867484	−	0.497466i	$-0.834264\pi$
$71$	0.823076	−	1.98708i	0.0976811	−	0.235823i	0.965165	+	0.261642i	$0.0842641\pi$
$72$	−1.30485	+	2.50945i	−0.153779	+	0.295742i
$73$	1.38827	+	3.35157i	0.162484	+	0.392272i	0.984062	−	0.177824i	$-0.0569059\pi$
$73$	1.38827	+	3.35157i	0.162484	+	0.392272i	−0.821578	+	0.570096i	$0.806906\pi$
$74$	−0.0988974	−	0.0523807i	−0.0114966	−	0.00608913i
$75$	−2.46226	+	1.64523i	−0.284317	+	0.189975i
$76$	8.99255	+	3.64520i	1.03152	+	0.418133i
$77$	−4.45597	−	22.4017i	−0.507805	−	2.55291i
$78$	−0.660209	−	0.537644i	−0.0747540	−	0.0608762i
$79$	2.20249	+	2.20249i	0.247799	+	0.247799i	0.820067	−	0.572268i	$-0.193936\pi$
$79$	2.20249	+	2.20249i	0.247799	+	0.247799i	−0.572268	+	0.820067i	$0.693936\pi$
$80$	−11.0348	+	2.36946i	−1.23373	+	0.264914i
$81$	−0.707107	+	0.707107i	−0.0785674	+	0.0785674i
$82$	−7.72768	+	0.790704i	−0.853380	+	0.0873186i
$83$	6.00359	−	1.19419i	0.658980	−	0.131079i	0.145738	−	0.989323i	$-0.453444\pi$
$83$	6.00359	−	1.19419i	0.658980	−	0.131079i	0.513242	+	0.858244i	$0.328444\pi$
$84$	0.0571380	+	7.53535i	0.00623426	+	0.822174i
$85$	6.15653	+	9.21390i	0.667769	+	0.999387i
$86$	3.25888	+	10.5983i	0.351414	+	1.14284i
$87$	7.38848	−	3.06041i	0.792128	−	0.328110i
$88$	16.4633	+	4.79031i	1.75500	+	0.510649i
$89$	6.97098	+	2.88747i	0.738922	+	0.306072i	0.720213	−	0.693753i	$-0.244044\pi$
$89$	6.97098	+	2.88747i	0.738922	+	0.306072i	0.0187096	+	0.999825i	$0.494044\pi$
$90$	−3.97256	−	0.376062i	−0.418745	−	0.0396404i
$91$	−2.22482	−	0.442544i	−0.233225	−	0.0463913i
$92$	−4.71819	−	0.901370i	−0.491905	−	0.0939743i
$93$	−0.907050	−	0.606072i	−0.0940567	−	0.0628467i
$94$	−12.5824	+	6.78690i	−1.29778	+	0.700015i
$95$			13.6893i			1.40449i
$96$	−5.03855	−	2.57158i	−0.514245	−	0.262461i
$97$		−	11.7711i		−	1.19517i	−0.801804	−	0.597587i	$-0.796126\pi$
$97$		−	11.7711i		−	1.19517i	0.801804	−	0.597587i	$-0.203874\pi$
$98$	4.83138	+	8.95702i	0.488043	+	0.904796i
$99$	5.04042	+	3.36790i	0.506581	+	0.338487i
$100$	−3.32770	−	4.89942i	−0.332770	−	0.489942i
$101$	8.53142	+	1.69700i	0.848908	+	0.168858i	0.600329	−	0.799753i	$-0.295036\pi$
$101$	8.53142	+	1.69700i	0.848908	+	0.168858i	0.248579	+	0.968612i	$0.420036\pi$
$102$	−0.523444	+	5.52945i	−0.0518287	+	0.547497i
$103$	−6.36742	−	2.63747i	−0.627400	−	0.259878i	0.0462477	−	0.998930i	$-0.485274\pi$
$103$	−6.36742	−	2.63747i	−0.627400	−	0.259878i	−0.673648	+	0.739052i	$0.735274\pi$
$104$	1.06524	−	1.32853i	0.104456	−	0.130273i
$105$	−9.82187	+	4.06835i	−0.958516	+	0.397031i
$106$	−0.312473	+	0.0960829i	−0.0303501	+	0.00933240i
$107$	−0.240788	−	0.360365i	−0.0232779	−	0.0348378i	0.819648	−	0.572867i	$-0.194169\pi$
$107$	−0.240788	−	0.360365i	−0.0232779	−	0.0348378i	−0.842926	+	0.538029i	$0.819169\pi$
$108$	−1.42490	−	1.40345i	−0.137111	−	0.135047i
$109$	−1.46005	+	0.290421i	−0.139847	+	0.0278173i	−0.264517	−	0.964381i	$-0.585213\pi$
$109$	−1.46005	+	0.290421i	−0.139847	+	0.0278173i	0.124670	+	0.992198i	$0.460213\pi$
$110$	2.46224	+	24.0639i	0.234766	+	2.29441i
$111$	0.0559563	−	0.0559563i	0.00531114	−	0.00531114i
$112$	−15.0694	+	0.228545i	−1.42392	+	0.0215955i
$113$	−6.17742	−	6.17742i	−0.581122	−	0.581122i	0.354089	−	0.935212i	$-0.384791\pi$
$113$	−6.17742	−	6.17742i	−0.581122	−	0.581122i	−0.935212	+	0.354089i	$0.884791\pi$
$114$	−4.33259	+	5.32028i	−0.405784	+	0.498290i
$115$	−1.32208	−	6.64655i	−0.123285	−	0.619794i
$116$	6.23268	+	14.7301i	0.578690	+	1.36766i
$117$	0.500589	−	0.334483i	0.0462795	−	0.0309230i
$118$	9.32654	−	17.6090i	0.858578	−	1.62104i
$119$	5.66278	+	13.6712i	0.519106	+	1.25323i
$120$	0.691858	−	7.95060i	0.0631577	−	0.725787i
$121$	9.85356	−	23.7886i	0.895778	−	2.16260i
$122$	9.19868	−	7.60770i	0.832809	−	0.688769i
$123$	1.07160	−	5.38728i	0.0966227	−	0.485755i
$124$	1.19835	−	1.82324i	0.107615	−	0.163732i
$125$	−3.19579	+	4.78284i	−0.285840	+	0.427790i
$126$	−5.10484	−	1.52743i	−0.454775	−	0.136074i
$127$	16.9371			1.50292			0.751462	−	0.659776i	$-0.229349\pi$
$127$	16.9371			1.50292			0.751462	+	0.659776i	$0.229349\pi$
$128$	5.06660	−	10.1158i	0.447828	−	0.894120i
$129$	−7.84040			−0.690309
$130$	2.30157	+	0.688655i	0.201861	+	0.0603991i
$131$	0.342417	−	0.512463i	0.0299171	−	0.0447741i	−0.816210	−	0.577756i	$-0.803929\pi$
$131$	0.342417	−	0.512463i	0.0299171	−	0.0447741i	0.846127	+	0.532982i	$0.178929\pi$
$132$	−6.65917	+	10.1316i	−0.579606	+	0.881845i
$133$	−3.56623	+	17.9287i	−0.309232	+	1.55461i
$134$	12.7693	−	10.5608i	1.10310	−	0.912313i
$135$	1.07977	−	2.60680i	0.0929321	−	0.224358i
$136$	−11.0665	−	0.963004i	−0.948946	−	0.0825769i
$137$	2.65094	+	6.39994i	0.226485	+	0.546783i	0.995745	−	0.0921527i	$-0.0293748\pi$
$137$	2.65094	+	6.39994i	0.226485	+	0.546783i	−0.769260	+	0.638936i	$0.779375\pi$
$138$	1.58978	−	3.00158i	0.135331	−	0.255512i
$139$	12.2417	−	8.17964i	1.03833	−	0.693788i	0.0852017	−	0.996364i	$-0.472847\pi$
$139$	12.2417	−	8.17964i	1.03833	−	0.693788i	0.953125	+	0.302576i	$0.0978465\pi$
$140$	−8.28542	−	19.5815i	−0.700246	−	1.65494i
$141$	−1.97215	−	9.91464i	−0.166085	−	0.834964i
$142$	−1.92070	+	2.35856i	−0.161182	+	0.197926i
$143$	−2.58072	−	2.58072i	−0.215810	−	0.215810i
$144$	2.78521	−	2.87099i	0.232101	−	0.239249i
$145$	−15.9558	+	15.9558i	−1.32505	+	1.32505i
$146$	−0.522217	−	5.10372i	−0.0432190	−	0.422387i
$147$	−7.05792	+	1.40391i	−0.582128	+	0.115792i
$148$	0.112758	+	0.111061i	0.00926865	+	0.00912914i
$149$	7.18228	+	10.7490i	0.588395	+	0.880596i	0.999520	−	0.0309834i	$-0.00986389\pi$
$149$	7.18228	+	10.7490i	0.588395	+	0.880596i	−0.411125	+	0.911579i	$0.634864\pi$
$150$	4.00299	−	1.23088i	0.326843	−	0.100501i
$151$	−1.77465	+	0.735084i	−0.144419	+	0.0598203i	−0.453722	−	0.891143i	$-0.649904\pi$
$151$	−1.77465	+	0.735084i	−0.144419	+	0.0598203i	0.309303	+	0.950963i	$0.399904\pi$
$152$	−10.7060	−	8.58425i	−0.868368	−	0.696274i
$153$	−3.62844	−	1.50295i	−0.293342	−	0.121506i
$154$	−3.04420	+	32.1576i	−0.245308	+	2.59134i
$155$	3.01892	+	0.600501i	0.242486	+	0.0482334i
$156$	0.676538	+	0.996077i	0.0541664	+	0.0797500i
$157$	−18.5396	−	12.3877i	−1.47962	−	0.988650i	−0.993386	−	0.114821i	$-0.963371\pi$
$157$	−18.5396	−	12.3877i	−1.47962	−	0.988650i	−0.486233	−	0.873829i	$-0.661629\pi$
$158$	−2.09120	−	3.87694i	−0.166367	−	0.308433i
$159$		−	0.231162i		−	0.0183323i
$160$	15.9112	+	1.26311i	1.25789	+	0.0998574i
$161$		−	9.04931i		−	0.713185i
$162$	1.24469	−	0.671379i	0.0977920	−	0.0527485i
$163$	9.25935	+	6.18690i	0.725248	+	0.484595i	0.862574	−	0.505931i	$-0.168851\pi$
$163$	9.25935	+	6.18690i	0.725248	+	0.484595i	−0.137326	+	0.990526i	$0.543851\pi$
$164$	10.7905	+	2.06144i	0.842597	+	0.160971i
$165$	−16.7760	−	3.33694i	−1.30601	−	0.259781i
$166$	−8.61817	−	0.815837i	−0.668900	−	0.0633212i
$167$	0.366293	+	0.151723i	0.0283446	+	0.0117407i	0.396811	−	0.917900i	$-0.370117\pi$
$167$	0.366293	+	0.151723i	0.0283446	+	0.0117407i	−0.368466	+	0.929641i	$0.620117\pi$
$168$	2.97735	−	10.2325i	0.229707	−	0.789458i
$169$	11.6756	−	4.83617i	0.898120	−	0.372013i
$170$	−4.60603	−	14.9794i	−0.353267	−	1.14887i
$171$	−2.69542	−	4.03399i	−0.206124	−	0.308487i
$172$	−0.118899	−	15.6803i	−0.00906594	−	1.19562i
$173$	−3.64204	+	0.724447i	−0.276899	+	0.0550787i	−0.331586	−	0.943425i	$-0.607584\pi$
$173$	−3.64204	+	0.724447i	−0.276899	+	0.0550787i	0.0546871	+	0.998504i	$0.482584\pi$
$174$	−11.2510	+	1.15122i	−0.852940	+	0.0872735i
$175$	7.88966	−	7.88966i	0.596402	−	0.596402i
$176$	−20.3636	−	13.1643i	−1.53497	−	0.992297i
$177$	9.96320	+	9.96320i	0.748880	+	0.748880i
$178$	−8.27418	−	6.73811i	−0.620176	−	0.505043i
$179$	−3.14338	−	15.8029i	−0.234947	−	1.18116i	−0.900516	−	0.434824i	$-0.856811\pi$
$179$	−3.14338	−	15.8029i	−0.234947	−	1.18116i	0.665568	−	0.746337i	$-0.268189\pi$
$180$	5.22983	+	2.11995i	0.389809	+	0.158012i
$181$	−8.62490	+	5.76298i	−0.641084	+	0.428359i	−0.833168	−	0.553020i	$-0.813475\pi$
$181$	−8.62490	+	5.76298i	−0.641084	+	0.428359i	0.192084	+	0.981378i	$0.438475\pi$
$182$	2.83493	+	1.50151i	0.210139	+	0.111299i
$183$	3.23014	+	7.79824i	0.238779	+	0.576463i
$184$	6.02710	+	3.13394i	0.444324	+	0.231037i
$185$	−0.0854469	+	0.206287i	−0.00628218	+	0.0151665i
$186$	0.983234	+	1.18885i	0.0720943	+	0.0871711i
$187$	−4.64473	+	23.3506i	−0.339656	+	1.70757i
$188$	19.7988	−	4.09453i	1.44398	−	0.298624i
$189$	2.09327	−	3.13280i	0.152263	−	0.227878i
$190$	5.54951	−	18.5471i	0.402604	−	1.34555i
$191$	−11.7019			−0.846723			−0.423361	−	0.905961i	$-0.639150\pi$
$191$	−11.7019			−0.846723			−0.423361	+	0.905961i	$0.639150\pi$
$192$	5.78406	+	5.52672i	0.417429	+	0.398857i
$193$	2.49273			0.179431			0.0897155	−	0.995967i	$-0.471404\pi$
$193$	2.49273			0.179431			0.0897155	+	0.995967i	$0.471404\pi$
$194$	−4.77190	+	15.9483i	−0.342602	+	1.14502i
$195$	−0.943772	+	1.41245i	−0.0675849	+	0.101148i
$196$	−2.91477	−	14.0942i	−0.208198	−	1.00673i
$197$	4.59529	−	23.1021i	0.327401	−	1.64596i	−0.369822	−	0.929102i	$-0.620581\pi$
$197$	4.59529	−	23.1021i	0.327401	−	1.64596i	0.697223	−	0.716854i	$-0.254419\pi$
$198$	−5.46377	−	6.60639i	−0.388293	−	0.469496i
$199$	−2.65580	+	6.41167i	−0.188265	+	0.454511i	−0.989626	−	0.143670i	$-0.954110\pi$
$199$	−2.65580	+	6.41167i	−0.188265	+	0.454511i	0.801361	+	0.598181i	$0.204110\pi$
$200$	2.52240	+	7.98708i	0.178361	+	0.564772i
$201$	4.48398	+	10.8253i	0.316275	+	0.763557i
$202$	−10.8710	−	5.75777i	−0.764878	−	0.405115i
$203$	−25.0537	+	16.7403i	−1.75842	+	1.17494i
$204$	2.95078	−	7.27945i	0.206596	−	0.509664i
$205$	3.02360	+	15.2007i	0.211178	+	1.06166i
$206$	7.55778	+	6.15471i	0.526576	+	0.428819i
$207$	1.69830	+	1.69830i	0.118040	+	0.118040i
$208$	−1.98184	+	1.36814i	−0.137416	+	0.0948636i
$209$	−20.7966	+	20.7966i	−1.43853	+	1.43853i
$210$	14.9566	−	1.53037i	1.03210	−	0.105606i
$211$	23.9112	−	4.75623i	1.64611	−	0.327433i	0.716957	−	0.697117i	$-0.245534\pi$
$211$	23.9112	−	4.75623i	1.64611	−	0.327433i	0.929157	+	0.369684i	$0.120534\pi$
$212$	0.462310	−	0.00350554i	0.0317516	−	0.000240761i
$213$	−1.19492	−	1.78833i	−0.0818746	−	0.122534i
$214$	0.180147	+	0.585859i	0.0123146	+	0.0400485i
$215$	20.4384	−	8.46585i	1.39389	−	0.577366i
$216$	1.36160	+	2.47912i	0.0926449	+	0.168683i
$217$	3.79740	+	1.57293i	0.257784	+	0.106778i
$218$	2.09590	+	0.198408i	0.141952	+	0.0134379i
$219$	3.55801	+	0.707732i	0.240428	+	0.0478241i
$220$	6.41929	−	33.6015i	0.432789	−	2.26542i
$221$	1.96601	+	1.31365i	0.132248	+	0.0883653i
$222$	−0.0984974	+	0.0531290i	−0.00661071	+	0.00356579i
$223$			13.5536i			0.907614i	0.891100	+	0.453807i	$0.149935\pi$
$223$			13.5536i			0.907614i	−0.891100	+	0.453807i	$0.850065\pi$
$224$	20.5097	+	5.79935i	1.37036	+	0.387485i
$225$			2.96133i			0.197422i
$226$	5.86529	+	10.8738i	0.390154	+	0.723316i
$227$	−3.47886	−	2.32450i	−0.230900	−	0.154282i	0.434739	−	0.900557i	$-0.356841\pi$
$227$	−3.47886	−	2.32450i	−0.230900	−	0.154282i	−0.665638	+	0.746274i	$0.731841\pi$
$228$	8.02686	−	5.45187i	0.531592	−	0.361059i
$229$	−18.7134	−	3.72233i	−1.23662	−	0.245978i	−0.466869	−	0.884327i	$-0.654618\pi$
$229$	−18.7134	−	3.72233i	−1.23662	−	0.245978i	−0.769748	+	0.638348i	$0.779618\pi$
$230$	−0.903209	+	9.54113i	−0.0595558	+	0.629124i
$231$	−21.1019	−	8.74070i	−1.38840	−	0.575096i
$232$	−2.47299	−	22.4840i	−0.162360	−	1.47615i
$233$	5.58686	−	2.31415i	0.366007	−	0.151605i	−0.192097	−	0.981376i	$-0.561529\pi$
$233$	5.58686	−	2.31415i	0.366007	−	0.151605i	0.558104	+	0.829771i	$0.311529\pi$
$234$	−0.813827	+	0.250245i	−0.0532015	+	0.0163590i
$235$	15.8466	+	23.7161i	1.03372	+	1.54706i
$236$	−19.7747	+	20.0769i	−1.28723	+	1.30690i
$237$	3.05494	−	0.607665i	0.198439	−	0.0394721i
$238$	−2.13014	−	20.8182i	−0.138076	−	1.34944i
$239$	−9.71480	+	9.71480i	−0.628398	+	0.628398i	−0.947665	−	0.319266i	$-0.896563\pi$
$239$	−9.71480	+	9.71480i	−0.628398	+	0.628398i	0.319266	+	0.947665i	$0.396563\pi$
$240$	−4.16047	+	10.4915i	−0.268557	+	0.677224i
$241$	5.14170	+	5.14170i	0.331206	+	0.331206i	0.853044	−	0.521838i	$-0.174754\pi$
$241$	5.14170	+	5.14170i	0.331206	+	0.331206i	−0.521838	+	0.853044i	$0.674754\pi$
$242$	−22.9939	+	28.2358i	−1.47810	+	1.81506i
$243$	0.195090	+	0.980785i	0.0125150	+	0.0629174i
$244$	−15.5471	+	6.57835i	−0.995298	+	0.421136i
$245$	16.8827	−	11.2807i	1.07860	−	0.720696i
$246$	−3.63583	+	6.86463i	−0.231812	+	0.437673i
$247$	1.11780	+	2.69860i	0.0711237	+	0.171708i
$248$	−2.36273	+	1.98444i	−0.150034	+	0.126012i
$249$	2.34249	−	5.65526i	0.148449	−	0.358388i
$250$	6.26878	−	5.18455i	0.396473	−	0.327900i
$251$	3.71646	−	18.6839i	0.234581	−	1.17932i	−0.666446	−	0.745553i	$-0.732185\pi$
$251$	3.71646	−	18.6839i	0.234581	−	1.17932i	0.901027	−	0.433764i	$-0.142815\pi$
$252$	6.29716	+	4.13891i	0.396684	+	0.260727i
$253$	8.08888	−	12.1059i	0.508544	−	0.761089i
$254$	−22.9475	−	6.86614i	−1.43985	−	0.430820i
$255$	11.0815			0.693948
$256$	−10.9654	+	11.6516i	−0.685338	+	0.728225i
$257$	−0.0837045			−0.00522134			−0.00261067	−	0.999997i	$-0.500831\pi$
$257$	−0.0837045			−0.00522134			−0.00261067	+	0.999997i	$0.500831\pi$
$258$	10.6227	+	3.17843i	0.661339	+	0.197880i
$259$	−0.165649	+	0.247911i	−0.0102929	+	0.0154045i
$260$	−2.83914	−	1.86607i	−0.176076	−	0.115729i
$261$	1.56018	−	7.84356i	0.0965728	−	0.485504i
$262$	−0.671677	+	0.555506i	−0.0414963	+	0.0343193i
$263$	−1.14721	+	2.76961i	−0.0707399	+	0.170781i	−0.955295	−	0.295655i	$-0.904462\pi$
$263$	−1.14721	+	2.76961i	−0.0707399	+	0.170781i	0.884555	+	0.466436i	$0.154462\pi$
$264$	13.1295	−	11.0274i	0.808067	−	0.678690i
$265$	0.249602	+	0.602593i	0.0153329	+	0.0370170i
$266$	12.0999	−	22.8452i	0.741891	−	1.40073i
$267$	6.27372	−	4.19196i	0.383945	−	0.256544i
$268$	−21.5819	+	9.13186i	−1.31833	+	0.557817i
$269$	0.365152	+	1.83574i	0.0222637	+	0.111927i	0.990319	−	0.138809i	$-0.0443274\pi$
$269$	0.365152	+	1.83574i	0.0222637	+	0.111927i	−0.968056	+	0.250736i	$0.919327\pi$
$270$	−2.51972	+	3.09414i	−0.153345	+	0.188303i
$271$	0.608631	+	0.608631i	0.0369717	+	0.0369717i	0.725351	−	0.688379i	$-0.241677\pi$
$271$	0.608631	+	0.608631i	0.0369717	+	0.0369717i	−0.688379	+	0.725351i	$0.741677\pi$
$272$	14.6032	+	5.79100i	0.885451	+	0.351131i
$273$	−1.60401	+	1.60401i	−0.0970789	+	0.0970789i
$274$	−0.997190	−	9.74571i	−0.0602425	−	0.588760i
$275$	17.6068	−	3.50222i	1.06173	−	0.211192i
$276$	−3.37075	+	3.42226i	−0.202895	+	0.205996i
$277$	4.87782	+	7.30017i	0.293080	+	0.438624i	0.948565	−	0.316584i	$-0.102536\pi$
$277$	4.87782	+	7.30017i	0.293080	+	0.438624i	−0.655485	+	0.755208i	$0.727536\pi$
$278$	−19.9018	+	6.11963i	−1.19363	+	0.367031i
$279$	−1.00786	+	0.417469i	−0.0603390	+	0.0249932i
$280$	3.28747	+	29.8891i	0.196464	+	1.78621i
$281$	−22.0912	−	9.15048i	−1.31785	−	0.545872i	−0.390686	−	0.920524i	$-0.627762\pi$
$281$	−22.0912	−	9.15048i	−1.31785	−	0.545872i	−0.927166	+	0.374652i	$0.877762\pi$
$282$	−1.34732	+	14.2325i	−0.0802315	+	0.847532i
$283$	17.5023	+	3.48143i	1.04041	+	0.206949i	0.685591	−	0.727987i	$-0.259544\pi$
$283$	17.5023	+	3.48143i	1.04041	+	0.206949i	0.354815	+	0.934937i	$0.384544\pi$
$284$	3.55843	−	2.41689i	0.211154	−	0.143416i
$285$	11.3822	+	7.60536i	0.674225	+	0.450503i
$286$	2.45032	+	4.54272i	0.144891	+	0.268617i
$287$			20.6958i			1.22163i
$288$	−4.93746	+	2.76071i	−0.290942	+	0.162676i
$289$			1.57561i			0.0926828i
$290$	28.0862	−	15.1496i	1.64928	−	0.889614i
$291$	−9.78732	−	6.53968i	−0.573743	−	0.383363i
$292$	−1.36147	+	7.12655i	−0.0796738	+	0.417050i
$293$	−9.40188	−	1.87015i	−0.549263	−	0.109255i	−0.0873457	−	0.996178i	$-0.527838\pi$
$293$	−9.40188	−	1.87015i	−0.549263	−	0.109255i	−0.461918	+	0.886923i	$0.652838\pi$
$294$	10.1317	+	0.959112i	0.590891	+	0.0559365i
$295$	−36.7301	−	15.2141i	−2.13851	−	0.885799i
$296$	−0.107749	−	0.196183i	−0.00626277	−	0.0114029i
$297$	5.60061	−	2.31985i	0.324981	−	0.134611i
$298$	−5.37345	−	17.4751i	−0.311276	−	1.01231i
$299$	−0.803347	−	1.20229i	−0.0464588	−	0.0695305i
$300$	−5.92250	+	0.0449082i	−0.341935	+	0.00259278i
$301$	28.9733	−	5.76315i	1.66999	−	0.332182i
$302$	2.70241	−	0.276513i	0.155506	−	0.0159115i
$303$	6.15081	−	6.15081i	0.353355	−	0.353355i
$304$	11.0251	+	15.9706i	0.632336	+	0.915976i
$305$	−16.8407	−	16.8407i	−0.964294	−	0.964294i
$306$	4.30676	+	3.50722i	0.246201	+	0.200495i
$307$	−2.86680	−	14.4124i	−0.163617	−	0.822559i	−0.972196	−	0.234171i	$-0.924763\pi$
$307$	−2.86680	−	14.4124i	−0.163617	−	0.822559i	0.808578	−	0.588389i	$-0.200237\pi$
$308$	17.1609	−	42.3351i	0.977832	−	2.41227i
$309$	−5.73053	+	3.82901i	−0.325998	+	0.217825i
$310$	−3.84679	−	2.03744i	−0.218483	−	0.115719i
$311$	−3.68959	−	8.90746i	−0.209218	−	0.505096i	0.784083	−	0.620656i	$-0.213134\pi$
$311$	−3.68959	−	8.90746i	−0.209218	−	0.505096i	−0.993300	+	0.115560i	$0.963134\pi$
$312$	−0.512817	−	1.62381i	−0.0290325	−	0.0919303i
$313$	−7.49331	+	18.0905i	−0.423547	+	1.02253i	0.557746	+	0.830012i	$0.311666\pi$
$313$	−7.49331	+	18.0905i	−0.423547	+	1.02253i	−0.981293	+	0.192521i	$0.938334\pi$
$314$	20.0967	+	24.2995i	1.13412	+	1.37130i
$315$	−2.07403	+	10.4268i	−0.116858	+	0.587486i
$316$	1.26162	+	6.10048i	0.0709718	+	0.343179i
$317$	−11.9224	+	17.8432i	−0.669631	+	1.00217i	0.328701	+	0.944434i	$0.393389\pi$
$317$	−11.9224	+	17.8432i	−0.669631	+	1.00217i	−0.998332	+	0.0577394i	$0.981611\pi$
$318$	−0.0937109	+	0.313193i	−0.00525504	+	0.0175630i
$319$	−48.4797			−2.71434
$320$	−21.0455	−	8.16161i	−1.17648	−	0.456248i
$321$	−0.433407			−0.0241904
$322$	−3.66851	+	12.2606i	−0.204438	+	0.683256i
$323$	10.5860	−	15.8430i	0.589020	−	0.881530i
$324$	−1.95856	+	0.405043i	−0.108809	+	0.0225024i
$325$	0.347823	−	1.74862i	0.0192937	−	0.0969962i
$326$	−10.0371	−	12.1361i	−0.555901	−	0.672154i
$327$	−0.569682	+	1.37533i	−0.0315035	+	0.0760561i
$328$	−13.7840	−	7.16734i	−0.761094	−	0.395750i
$329$	14.5757	+	35.1888i	0.803583	+	1.94002i
$330$	21.3764	+	11.3219i	1.17673	+	0.623251i
$331$	11.2967	−	7.54823i	0.620924	−	0.414888i	−0.204926	−	0.978777i	$-0.565695\pi$
$331$	11.2967	−	7.54823i	0.620924	−	0.414888i	0.825850	+	0.563889i	$0.190695\pi$
$332$	11.3457	+	4.59908i	0.622677	+	0.252407i
$333$	−0.0154383	−	0.0776136i	−0.000846014	−	0.00425320i
$334$	−0.434770	−	0.354057i	−0.0237896	−	0.0193731i
$335$	−23.3777	−	23.3777i	−1.27726	−	1.27726i
$336$	−8.18208	+	12.6567i	−0.446369	+	0.690481i
$337$	2.34753	−	2.34753i	0.127878	−	0.127878i	−0.640271	−	0.768149i	$-0.721178\pi$
$337$	2.34753	−	2.34753i	0.127878	−	0.127878i	0.768149	+	0.640271i	$0.221178\pi$
$338$	−17.7793	+	1.81920i	−0.967069	+	0.0989513i
$339$	−8.56832	+	1.70435i	−0.465367	+	0.0925673i
$340$	0.168049	+	22.1623i	0.00911373	+	1.20192i
$341$	3.67404	+	5.49859i	0.198961	+	0.297766i
$342$	2.01659	+	6.55821i	0.109045	+	0.354627i
$343$	0.682957	−	0.282890i	0.0368762	−	0.0152746i
$344$	−6.19558	+	21.2929i	−0.334043	+	1.14804i
$345$	−6.26091	−	2.59335i	−0.337076	−	0.139621i
$346$	5.22816	+	0.494923i	0.281068	+	0.0266072i
$347$	12.1004	+	2.40692i	0.649583	+	0.129210i	0.508874	−	0.860841i	$-0.330062\pi$
$347$	12.1004	+	2.40692i	0.649583	+	0.129210i	0.140709	+	0.990051i	$0.455062\pi$
$348$	15.7103	+	3.00133i	0.842162	+	0.160888i
$349$	12.8952	+	8.61632i	0.690266	+	0.461221i	0.850580	−	0.525845i	$-0.176251\pi$
$349$	12.8952	+	8.61632i	0.690266	+	0.461221i	−0.160314	+	0.987066i	$0.551251\pi$
$350$	−13.8878	+	7.49102i	−0.742335	+	0.400412i
$351$		−	0.602053i		−	0.0321352i
$352$	22.2533	+	26.0911i	1.18610	+	1.39066i
$353$			13.8287i			0.736029i	0.929820	+	0.368014i	$0.119962\pi$
$353$			13.8287i			0.736029i	−0.929820	+	0.368014i	$0.880038\pi$
$354$	−9.45979	−	17.5378i	−0.502782	−	0.932122i
$355$	5.04591	+	3.37157i	0.267809	+	0.178944i
$356$	8.47882	+	12.4835i	0.449377	+	0.661624i
$357$	14.5132	+	2.88686i	0.768121	+	0.152789i
$358$	−2.14747	+	22.6850i	−0.113497	+	1.19894i
$359$	−11.7924	−	4.88459i	−0.622381	−	0.257799i	0.0491309	−	0.998792i	$-0.484355\pi$
$359$	−11.7924	−	4.88459i	−0.622381	−	0.257799i	−0.671512	+	0.740994i	$0.734355\pi$
$360$	−6.22630	−	4.99237i	−0.328155	−	0.263121i
$361$	4.19289	−	1.73675i	0.220678	−	0.0914080i
$362$	14.0218	−	4.31160i	0.736971	−	0.226612i
$363$	−14.3051	−	21.4092i	−0.750826	−	1.12369i
$364$	−3.23224	−	3.18360i	−0.169416	−	0.166866i
$365$	−10.0392	+	1.99693i	−0.525477	+	0.104524i
$366$	−1.21506	−	11.8750i	−0.0635124	−	0.620718i
$367$	13.0798	−	13.0798i	0.682759	−	0.682759i	−0.277862	−	0.960621i	$-0.589626\pi$
$367$	13.0798	−	13.0798i	0.682759	−	0.682759i	0.960621	+	0.277862i	$0.0896257\pi$
$368$	−6.89543	−	6.68940i	−0.359449	−	0.348709i
$369$	−3.88402	−	3.88402i	−0.202194	−	0.202194i
$370$	0.199396	−	0.244852i	0.0103661	−	0.0127292i
$371$	0.169917	+	0.854232i	0.00882167	+	0.0443495i
$372$	−0.850199	−	2.00933i	−0.0440808	−	0.104179i
$373$	22.5169	−	15.0453i	1.16588	−	0.779018i	0.186783	−	0.982401i	$-0.440194\pi$
$373$	22.5169	−	15.0453i	1.16588	−	0.779018i	0.979099	+	0.203384i	$0.0651938\pi$
$374$	15.7591	−	29.7540i	0.814884	−	1.53854i
$375$	2.20130	+	5.31440i	0.113675	+	0.274435i
$376$	−28.4846	−	2.47872i	−1.46898	−	0.127830i
$377$	−1.84253	+	4.44826i	−0.0948950	+	0.229097i
$378$	−4.10610	+	3.39593i	−0.211195	+	0.174668i
$379$	3.23641	−	16.2705i	0.166243	−	0.835761i	−0.804186	−	0.594377i	$-0.797399\pi$
$379$	3.23641	−	16.2705i	0.166243	−	0.835761i	0.970430	−	0.241384i	$-0.0776014\pi$
$380$	−15.0377	+	22.8791i	−0.771417	+	1.17367i
$381$	9.40975	−	14.0827i	0.482076	−	0.721478i
$382$	15.8546	+	4.74386i	0.811189	+	0.242717i
$383$	19.0363			0.972711			0.486355	−	0.873761i	$-0.338326\pi$
$383$	19.0363			0.972711			0.486355	+	0.873761i	$0.338326\pi$
$384$	−5.59613	−	9.83277i	−0.285577	−	0.501776i
$385$	64.4465			3.28450
$386$	−3.37732	−	1.01053i	−0.171901	−	0.0514347i
$387$	−4.35589	+	6.51905i	−0.221422	+	0.331382i
$388$	12.9306	−	19.6732i	0.656449	−	0.998758i
$389$	6.19646	−	31.1517i	0.314173	−	1.57945i	−0.424524	−	0.905417i	$-0.639559\pi$
$389$	6.19646	−	31.1517i	0.314173	−	1.57945i	0.738697	−	0.674037i	$-0.235441\pi$
$390$	1.85128	−	1.53109i	0.0937431	−	0.0775296i
$391$	−3.60972	+	8.71462i	−0.182551	+	0.440717i
$392$	−1.76452	+	20.2773i	−0.0891219	+	1.02416i
$393$	−0.235861	−	0.569419i	−0.0118976	−	0.0287234i
$394$	−15.5914	+	29.4373i	−0.785482	+	1.48303i
$395$	−7.30748	+	4.88270i	−0.367679	+	0.245675i
$396$	4.72450	+	11.1657i	0.237415	+	0.561099i
$397$	−3.96471	−	19.9320i	−0.198983	−	1.00036i	−0.943151	−	0.332364i	$-0.892154\pi$
$397$	−3.96471	−	19.9320i	−0.198983	−	1.00036i	0.744168	−	0.667993i	$-0.232846\pi$
$398$	6.19748	−	7.61031i	0.310652	−	0.381470i
$399$	12.9258	+	12.9258i	0.647102	+	0.647102i
$400$	−0.179628	−	11.8440i	−0.00898139	−	0.592198i
$401$	12.5193	−	12.5193i	0.625185	−	0.625185i	−0.321668	−	0.946853i	$-0.604243\pi$
$401$	12.5193	−	12.5193i	0.625185	−	0.625185i	0.946853	+	0.321668i	$0.104243\pi$
$402$	−1.68671	−	16.4846i	−0.0841257	−	0.822175i
$403$	0.644160	−	0.128131i	0.0320879	−	0.00638268i
$404$	12.3945	+	12.2080i	0.616651	+	0.607370i
$405$	−1.56759	−	2.34606i	−0.0778941	−	0.116577i
$406$	40.7308	−	12.5244i	2.02143	−	0.621574i
$407$	−0.443200	+	0.183579i	−0.0219686	+	0.00909969i
$408$	−6.94894	+	8.66645i	−0.344024	+	0.429053i
$409$	−21.7659	−	9.01574i	−1.07626	−	0.445800i	−0.227061	−	0.973880i	$-0.572912\pi$
$409$	−21.7659	−	9.01574i	−1.07626	−	0.445800i	−0.849194	+	0.528081i	$0.822912\pi$
$410$	2.06564	−	21.8206i	0.102015	−	1.07764i
$411$	6.79414	+	1.35144i	0.335130	+	0.0666615i
$412$	−7.74471	−	11.4027i	−0.381555	−	0.561769i
$413$	−44.1414	−	29.4943i	−2.17206	−	1.45132i
$414$	−1.61249	−	2.98944i	−0.0792496	−	0.146923i
$415$			17.2715i			0.847825i
$416$	3.23975	−	1.05023i	0.158842	−	0.0514917i
$417$		−	14.7230i		−	0.720987i
$418$	36.6074	−	19.7459i	1.79053	−	0.965802i
$419$	3.93884	+	2.63185i	0.192425	+	0.128574i	0.648051	−	0.761597i	$-0.275585\pi$
$419$	3.93884	+	2.63185i	0.192425	+	0.128574i	−0.455626	+	0.890171i	$0.650585\pi$
$420$	−20.8845	−	3.98982i	−1.01906	−	0.194683i
$421$	−18.2760	−	3.63532i	−0.890718	−	0.177175i	−0.271541	−	0.962427i	$-0.587533\pi$
$421$	−18.2760	−	3.63532i	−0.890718	−	0.177175i	−0.619176	+	0.785252i	$0.712533\pi$
$422$	−34.3246	−	3.24933i	−1.67089	−	0.158175i
$423$	−9.33939	−	3.86850i	−0.454097	−	0.188093i
$424$	−0.627789	−	0.182667i	−0.0304881	−	0.00887108i
$425$	−10.7450	+	4.45073i	−0.521209	+	0.215892i
$426$	0.893986	+	2.90735i	0.0433137	+	0.140862i
$427$	−17.6688	−	26.4432i	−0.855052	−	1.27968i
$428$	−0.00657256	−	0.866789i	−0.000317697	−	0.0418978i
$429$	−3.57956	+	0.712018i	−0.172823	+	0.0343766i
$430$	−31.1232	+	3.18455i	−1.50089	+	0.153573i
$431$	3.02256	−	3.02256i	0.145592	−	0.145592i	−0.630554	−	0.776146i	$-0.717172\pi$
$431$	3.02256	−	3.02256i	0.145592	−	0.145592i	0.776146	+	0.630554i	$0.217172\pi$
$432$	−0.839764	−	3.91086i	−0.0404032	−	0.188161i
$433$	6.03583	+	6.03583i	0.290064	+	0.290064i	0.837105	−	0.547042i	$-0.184246\pi$
$433$	6.03583	+	6.03583i	0.290064	+	0.290064i	−0.547042	+	0.837105i	$0.684246\pi$
$434$	−4.50731	−	3.67054i	−0.216358	−	0.176192i
$435$	4.40218	+	22.1313i	0.211069	+	1.06111i
$436$	−2.75923	−	1.11847i	−0.132143	−	0.0535652i
$437$	−9.68866	+	6.47375i	−0.463471	+	0.309682i
$438$	−4.53371	−	2.40127i	−0.216629	−	0.114737i
$439$	0.640152	+	1.54546i	0.0305528	+	0.0737610i	0.938420	−	0.345498i	$-0.112290\pi$
$439$	0.640152	+	1.54546i	0.0305528	+	0.0737610i	−0.907867	+	0.419259i	$0.862290\pi$
$440$	−22.3190	+	42.9232i	−1.06402	+	2.04628i
$441$	−2.75387	+	6.64842i	−0.131136	+	0.316591i
$442$	−2.13114	−	2.57681i	−0.101368	−	0.122567i
$443$	−3.99653	+	20.0919i	−0.189881	+	0.954597i	0.761871	+	0.647729i	$0.224281\pi$
$443$	−3.99653	+	20.0919i	−0.189881	+	0.954597i	−0.951752	+	0.306868i	$0.900719\pi$
$444$	0.154989	−	0.0320527i	0.00735544	−	0.00152116i
$445$	−11.8280	+	17.7018i	−0.560700	+	0.839146i
$446$	5.49449	−	18.3633i	0.260172	−	0.869525i
$447$	12.9278			0.611462
$448$	−25.4368	−	16.1718i	−1.20178	−	0.764044i
$449$	23.3415			1.10155			0.550776	−	0.834653i	$-0.314332\pi$
$449$	23.3415			1.10155			0.550776	+	0.834653i	$0.314332\pi$
$450$	1.20050	−	4.01220i	0.0565920	−	0.189137i
$451$	−18.4993	+	27.6862i	−0.871098	+	1.30369i
$452$	−3.53853	−	17.1103i	−0.166438	−	0.804801i
$453$	−0.374743	+	1.88396i	−0.0176069	+	0.0885161i
$454$	3.77105	+	4.55967i	0.176984	+	0.213996i
$455$	2.44937	−	5.91329i	0.114828	−	0.277219i
$456$	−13.0855	+	4.13252i	−0.612782	+	0.193523i
$457$	−10.2245	−	24.6841i	−0.478282	−	1.15467i	−0.960414	−	0.278576i	$-0.910137\pi$
$457$	−10.2245	−	24.6841i	−0.478282	−	1.15467i	0.482132	−	0.876099i	$-0.339863\pi$
$458$	23.8451	+	12.6295i	1.11421	+	0.590137i
$459$	−3.26551	+	2.18194i	−0.152421	+	0.101844i
$460$	5.09161	−	12.5608i	0.237398	−	0.585650i
$461$	−1.67676	−	8.42964i	−0.0780945	−	0.392608i	−0.999987	−	0.00516111i	$-0.998357\pi$
$461$	−1.67676	−	8.42964i	−0.0780945	−	0.392608i	0.921892	−	0.387447i	$-0.126643\pi$
$462$	25.0468	+	20.3970i	1.16528	+	0.948953i
$463$	−23.6019	−	23.6019i	−1.09687	−	1.09687i	−0.994774	−	0.102099i	$-0.967444\pi$
$463$	−23.6019	−	23.6019i	−1.09687	−	1.09687i	−0.102099	−	0.994774i	$-0.532556\pi$
$464$	−5.76424	+	31.4653i	−0.267598	+	1.46074i
$465$	2.17652	−	2.17652i	0.100934	−	0.100934i
$466$	−8.50757	+	0.870502i	−0.394106	+	0.0403252i
$467$	−21.5869	+	4.29389i	−0.998920	+	0.198698i	−0.667359	−	0.744736i	$-0.732575\pi$
$467$	−21.5869	+	4.29389i	−0.998920	+	0.198698i	−0.331561	+	0.943434i	$0.607575\pi$
$468$	1.20407	−	0.00913007i	0.0556583	−	0.000422037i
$469$	−24.5273	−	36.7076i	−1.13256	−	1.69500i
$470$	−11.8557	−	38.5561i	−0.546862	−	1.77846i
$471$	−20.6001	+	8.53283i	−0.949201	+	0.393172i
$472$	34.9311	−	19.1850i	1.60783	−	0.883061i
$473$	43.9110	+	18.1886i	2.01903	+	0.836311i
$474$	−4.38537	−	0.415140i	−0.201427	−	0.0190680i
$475$	−14.0912	−	2.80292i	−0.646550	−	0.128607i
$476$	−5.55346	+	29.0694i	−0.254543	+	1.33239i
$477$	−0.192204	−	0.128427i	−0.00880042	−	0.00588025i
$478$	17.1005	−	9.22395i	0.782160	−	0.421894i
$479$		−	38.0097i		−	1.73671i	−0.495943	−	0.868355i	$-0.665178\pi$
$479$		−	38.0097i		−	1.73671i	0.495943	−	0.868355i	$-0.334822\pi$
$480$	9.89004	−	12.5280i	0.451417	−	0.571820i
$481$			0.0476430i			0.00217233i
$482$	−4.88191	−	9.05071i	−0.222365	−	0.412249i
$483$	−7.52422	−	5.02753i	−0.342364	−	0.228760i
$484$	42.6002	−	28.9341i	1.93637	−	1.31519i
$485$	32.5750	+	6.47957i	1.47915	+	0.294222i
$486$	0.133280	−	1.40792i	0.00604572	−	0.0638645i
$487$	35.0866	+	14.5333i	1.58992	+	0.658568i	0.989946	−	0.141447i	$-0.0451755\pi$
$487$	35.0866	+	14.5333i	1.58992	+	0.658568i	0.599979	+	0.800016i	$0.295176\pi$
$488$	23.7310	−	2.61014i	1.07425	−	0.118156i
$489$	10.2884	−	4.26161i	0.465259	−	0.192717i
$490$	−27.4469	+	8.43968i	−1.23992	+	0.381266i
$491$	−18.6979	−	27.9834i	−0.843824	−	1.26287i	−0.962865	−	0.269982i	$-0.912982\pi$
$491$	−18.6979	−	27.9834i	−0.843824	−	1.26287i	0.119041	−	0.992889i	$-0.462018\pi$
$492$	7.70891	−	7.82671i	0.347544	−	0.352855i
$493$	30.8047	−	6.12744i	1.38738	−	0.275966i
$494$	−0.420476	−	4.10938i	−0.0189181	−	0.184890i
$495$	−12.0948	+	12.0948i	−0.543620	+	0.543620i
$496$	4.00565	−	1.73082i	0.179859	−	0.0777161i
$497$	5.73022	+	5.73022i	0.257035	+	0.257035i
$498$	−5.46634	+	6.71249i	−0.244953	+	0.300794i
$499$	2.18143	+	10.9668i	0.0976544	+	0.490942i	0.998398	+	0.0565897i	$0.0180227\pi$
$499$	2.18143	+	10.9668i	0.0976544	+	0.490942i	−0.900743	+	0.434352i	$0.856977\pi$
$500$	−10.5951	+	4.48306i	−0.473828	+	0.200489i
$501$	0.329655	−	0.220268i	0.0147279	−	0.00984087i
$502$	−12.6096	+	23.8075i	−0.562793	+	1.06258i
$503$	8.36416	+	20.1929i	0.372940	+	0.900356i	0.993249	+	0.115999i	$0.0370069\pi$
$503$	8.36416	+	20.1929i	0.372940	+	0.900356i	−0.620310	+	0.784357i	$0.712993\pi$
$504$	−6.85392	−	8.16047i	−0.305298	−	0.363496i
$505$	−9.39247	+	22.6754i	−0.417959	+	1.00904i
$506$	−15.8670	+	13.1227i	−0.705372	+	0.583373i
$507$	2.46546	−	12.3947i	0.109495	−	0.550468i
$508$	28.3073	+	18.6054i	1.25593	+	0.825481i
$509$	−17.7455	+	26.5580i	−0.786554	+	1.17716i	0.194018	+	0.980998i	$0.437848\pi$
$509$	−17.7455	+	26.5580i	−0.786554	+	1.17716i	−0.980571	+	0.196163i	$0.937152\pi$
$510$	−15.0139	−	4.49232i	−0.664826	−	0.198923i
$511$	−13.6684			−0.604657
$512$	19.5801	−	11.3411i	0.865326	−	0.501209i
$513$	−4.85163			−0.214205
$514$	0.113408	+	0.0339330i	0.00500222	+	0.00149672i
$515$	10.8039	−	16.1692i	0.476076	−	0.712498i
$516$	−13.1038	−	8.61267i	−0.576862	−	0.379152i
$517$	−11.9553	+	60.1032i	−0.525792	+	2.64333i
$518$	0.324933	−	0.268734i	0.0142767	−	0.0118075i
$519$	−1.42105	+	3.43073i	−0.0623774	+	0.150592i
$520$	3.09016	+	3.67923i	0.135513	+	0.161345i
$521$	11.4166	+	27.5621i	0.500170	+	1.20752i	0.949391	+	0.314097i	$0.101702\pi$
$521$	11.4166	+	27.5621i	0.500170	+	1.20752i	−0.449221	+	0.893421i	$0.648298\pi$
$522$	−5.29354	+	9.99448i	−0.231692	+	0.437447i
$523$	−9.91414	+	6.62442i	−0.433515	+	0.289666i	−0.753117	−	0.657886i	$-0.771451\pi$
$523$	−9.91414	+	6.62442i	−0.433515	+	0.289666i	0.319602	+	0.947552i	$0.396451\pi$
$524$	1.13523	−	0.480344i	0.0495927	−	0.0209839i
$525$	−2.17675	−	10.9433i	−0.0950012	−	0.477603i
$526$	2.67708	−	3.28737i	0.116726	−	0.143336i
$527$	−3.02952	−	3.02952i	−0.131968	−	0.131968i
$528$	−22.2592	+	9.61806i	−0.968706	+	0.418572i
$529$	−12.1846	+	12.1846i	−0.529763	+	0.529763i
$530$	−0.0938916	−	0.917619i	−0.00407839	−	0.0398588i
$531$	13.8193	−	2.74884i	0.599709	−	0.119289i
$532$	−25.6549	+	26.0470i	−1.11228	+	1.12928i
$533$	1.83726	+	2.74965i	0.0795805	+	0.119101i
$534$	−10.1994	+	3.13624i	−0.441372	+	0.135718i
$535$	1.12981	−	0.467981i	0.0488458	−	0.0202326i
$536$	32.9426	−	3.62332i	1.42290	−	0.156504i
$537$	−14.8860	−	6.16597i	−0.642377	−	0.266081i
$538$	0.249462	−	2.63521i	0.0107550	−	0.113612i
$539$	42.7856	+	8.51058i	1.84290	+	0.366577i
$540$	4.66821	−	3.17066i	0.200888	−	0.136444i
$541$	10.5683	+	7.06150i	0.454366	+	0.303598i	0.761613	−	0.648032i	$-0.224408\pi$
$541$	10.5683	+	7.06150i	0.454366	+	0.303598i	−0.307247	+	0.951630i	$0.599408\pi$
$542$	−0.577880	−	1.07135i	−0.0248221	−	0.0460183i
$543$			10.3731i			0.445152i
$544$	−17.4378	−	13.7660i	−0.747639	−	0.590214i
$545$		−	4.20035i		−	0.179923i
$546$	2.82346	−	1.52296i	0.120833	−	0.0651768i
$547$	−2.55309	−	1.70592i	−0.109162	−	0.0729398i	0.499791	−	0.866146i	$-0.333410\pi$
$547$	−2.55309	−	1.70592i	−0.109162	−	0.0729398i	−0.608953	+	0.793206i	$0.708410\pi$
$548$	−2.59977	+	13.6084i	−0.111056	+	0.581321i
$549$	8.27857	+	1.64671i	0.353321	+	0.0702799i
$550$	−25.2747	−	2.39262i	−1.07771	−	0.102022i
$551$	35.8462	+	14.8480i	1.52710	+	0.632545i
$552$	5.95426	−	3.27022i	0.253430	−	0.139190i
$553$	−10.8425	+	4.49111i	−0.461070	+	0.190982i
$554$	−3.64936	−	11.8682i	−0.155046	−	0.504230i
$555$	0.124050	+	0.185654i	0.00526562	+	0.00788055i
$556$	29.4451	−	0.223272i	1.24875	−	0.00946884i
$557$	−12.3147	+	2.44954i	−0.521790	+	0.103790i	−0.448956	−	0.893554i	$-0.648204\pi$
$557$	−12.3147	+	2.44954i	−0.521790	+	0.103790i	−0.0728334	+	0.997344i	$0.523204\pi$
$558$	1.53475	−	0.157037i	0.0649713	−	0.00664792i
$559$	3.33778	−	3.33778i	0.141173	−	0.141173i
$560$	7.66269	−	41.8284i	0.323808	−	1.76757i
$561$	16.8349	+	16.8349i	0.710768	+	0.710768i
$562$	26.2211	+	21.3532i	1.10607	+	0.900732i
$563$	3.64998	+	18.3497i	0.153828	+	0.773347i	0.978260	+	0.207385i	$0.0664951\pi$
$563$	3.64998	+	18.3497i	0.153828	+	0.773347i	−0.824431	+	0.565962i	$0.808505\pi$
$564$	7.59515	−	18.7369i	0.319814	−	0.788966i
$565$	20.4956	−	13.6947i	0.862257	−	0.576142i
$566$	−22.3019	−	11.8121i	−0.937421	−	0.496502i
$567$	−1.44187	−	3.48098i	−0.0605528	−	0.146187i
$568$	−5.80097	+	1.83201i	−0.243403	+	0.0768694i
$569$	3.19075	−	7.70316i	0.133763	−	0.322933i	−0.842779	−	0.538260i	$-0.819082\pi$
$569$	3.19075	−	7.70316i	0.133763	−	0.322933i	0.976542	+	0.215327i	$0.0690818\pi$
$570$	−12.3382	−	14.9185i	−0.516792	−	0.624867i
$571$	5.13034	−	25.7920i	0.214698	−	1.07936i	−0.711605	−	0.702580i	$-0.752031\pi$
$571$	5.13034	−	25.7920i	0.214698	−	1.07936i	0.926303	−	0.376780i	$-0.122969\pi$
$572$	−1.47828	−	7.14811i	−0.0618100	−	0.298878i
$573$	−6.50125	+	9.72981i	−0.271594	+	0.406469i
$574$	8.38988	−	28.0400i	0.350187	−	1.17037i
$575$	7.11240			0.296608
$576$	7.80875	−	1.73879i	0.325365	−	0.0724495i
$577$	−12.2974			−0.511949			−0.255974	−	0.966684i	$-0.582396\pi$
$577$	−12.2974			−0.511949			−0.255974	+	0.966684i	$0.582396\pi$
$578$	0.638737	−	2.13474i	0.0265680	−	0.0887933i
$579$	1.38489	−	2.07263i	0.0575540	−	0.0861357i
$580$	−44.1945	+	9.13973i	−1.83508	+	0.379507i
$581$	−4.49945	+	22.6202i	−0.186668	+	0.938446i
$582$	10.6094	+	12.8281i	0.439772	+	0.531740i
$583$	−0.536261	+	1.29465i	−0.0222097	+	0.0536188i
$584$	4.73364	−	9.10358i	0.195879	−	0.376709i
$585$	0.650081	+	1.56943i	0.0268775	+	0.0648881i
$586$	11.9801	+	6.34523i	0.494895	+	0.262119i
$587$	29.7892	−	19.9045i	1.22953	−	0.821547i	0.240703	−	0.970599i	$-0.422622\pi$
$587$	29.7892	−	19.9045i	1.22953	−	0.821547i	0.988829	+	0.149051i	$0.0476220\pi$
$588$	−13.3382	−	5.40675i	−0.550059	−	0.222971i
$589$	−1.03254	−	5.19095i	−0.0425452	−	0.213889i
$590$	43.5966	+	35.5031i	1.79484	+	1.46164i
$591$	−16.6557	−	16.6557i	−0.685123	−	0.685123i
$592$	0.0664540	+	0.309482i	0.00273124	+	0.0127196i
$593$	−2.29194	+	2.29194i	−0.0941186	+	0.0941186i	−0.752598	−	0.658480i	$-0.771200\pi$
$593$	−2.29194	+	2.29194i	−0.0941186	+	0.0941186i	0.658480	+	0.752598i	$0.271200\pi$
$594$	−8.52852	+	0.872646i	−0.349929	+	0.0358051i
$595$	−40.9503	+	8.14552i	−1.67880	+	0.333934i
$596$	0.196048	+	25.8548i	0.00803043	+	1.05905i
$597$	3.85563	+	5.77035i	0.157800	+	0.236165i
$598$	0.601028	+	1.95462i	0.0245779	+	0.0799302i
$599$	23.2038	−	9.61133i	0.948082	−	0.392708i	0.145572	−	0.989348i	$-0.453498\pi$
$599$	23.2038	−	9.61133i	0.948082	−	0.392708i	0.802510	+	0.596639i	$0.203498\pi$
$600$	8.04238	+	2.34008i	0.328329	+	0.0955334i
$601$	24.9791	+	10.3467i	1.01892	+	0.422051i	0.828701	−	0.559691i	$-0.189080\pi$
$601$	24.9791	+	10.3467i	1.01892	+	0.422051i	0.190219	+	0.981742i	$0.439080\pi$
$602$	−41.5912	−	3.93723i	−1.69513	−	0.160469i
$603$	11.4921	+	2.28591i	0.467993	+	0.0930896i
$604$	−3.77349	−	0.720894i	−0.153541	−	0.0293328i
$605$	60.4078	+	40.3632i	2.45592	+	1.64100i
$606$	−10.8270	+	5.84003i	−0.439817	+	0.237235i
$607$			33.7894i			1.37147i	0.727852	+	0.685734i	$0.240519\pi$
$607$			33.7894i			1.37147i	−0.727852	+	0.685734i	$0.759481\pi$
$608$	−8.46325	−	26.1075i	−0.343230	−	1.05880i
$609$			30.1318i			1.22100i
$610$	15.9898	+	29.6439i	0.647407	+	1.20025i
$611$	5.06040	+	3.38125i	0.204722	+	0.136791i
$612$	−4.41328	−	6.49773i	−0.178396	−	0.262655i
$613$	−43.2175	−	8.59650i	−1.74554	−	0.347209i	−0.783766	−	0.621057i	$-0.786704\pi$
$613$	−43.2175	−	8.59650i	−1.74554	−	0.347209i	−0.961773	+	0.273847i	$0.911704\pi$
$614$	−1.95852	+	20.6890i	−0.0790395	+	0.834941i
$615$	14.3187	+	5.93101i	0.577387	+	0.239161i
$616$	−40.4130	+	50.4015i	−1.62828	+	2.03074i
$617$	−32.0494	+	13.2753i	−1.29026	+	0.534443i	−0.919063	−	0.394111i	$-0.871053\pi$
$617$	−32.0494	+	13.2753i	−1.29026	+	0.534443i	−0.371197	+	0.928554i	$0.621053\pi$
$618$	9.31633	−	2.86469i	0.374758	−	0.115235i
$619$	−0.0516343	−	0.0772762i	−0.00207536	−	0.00310599i	0.830430	−	0.557122i	$-0.188095\pi$
$619$	−0.0516343	−	0.0772762i	−0.00207536	−	0.00310599i	−0.832506	+	0.554016i	$0.813095\pi$
$620$	4.38592	+	4.31991i	0.176143	+	0.173492i
$621$	2.35561	−	0.468560i	0.0945273	−	0.0188027i
$622$	1.38789	+	13.5641i	0.0556495	+	0.543872i
$623$	−20.1025	+	20.1025i	−0.805389	+	0.805389i
$624$	0.0365192	+	2.40794i	0.00146194	+	0.0963946i
$625$	−21.9466	−	21.9466i	−0.877864	−	0.877864i
$626$	17.4861	−	21.4724i	0.698886	−	0.858210i
$627$	5.73778	+	28.8458i	0.229145	+	1.15199i
$628$	−17.3776	−	41.0696i	−0.693440	−	1.63885i
$629$	0.258413	−	0.172666i	0.0103036	−	0.00688465i
$630$	7.03697	−	13.2862i	0.280360	−	0.529334i
$631$	−8.48348	−	20.4809i	−0.337722	−	0.815333i	−0.997934	−	0.0642535i	$-0.979533\pi$
$631$	−8.48348	−	20.4809i	−0.337722	−	0.815333i	0.660212	−	0.751080i	$-0.270467\pi$
$632$	0.763752	−	8.77678i	0.0303804	−	0.349122i
$633$	9.32969	−	22.5239i	0.370822	−	0.895243i
$634$	23.3868	−	19.3419i	0.928807	−	0.768164i
$635$	−9.32326	+	46.8712i	−0.369982	+	1.86003i
$636$	0.253931	−	0.386345i	0.0100690	−	0.0153196i
$637$	2.40701	−	3.60234i	0.0953690	−	0.142730i
$638$	65.6834	+	19.6532i	2.60043	+	0.778078i
$639$	−2.15080			−0.0850844
$640$	25.2052	+	19.5895i	0.996322	+	0.774344i
$641$	−43.7205			−1.72685			−0.863427	−	0.504473i	$-0.831687\pi$
$641$	−43.7205			−1.72685			−0.863427	+	0.504473i	$0.831687\pi$
$642$	0.587208	+	0.175699i	0.0231753	+	0.00693430i
$643$	−19.3695	+	28.9885i	−0.763858	+	1.14319i	0.221907	+	0.975068i	$0.428772\pi$
$643$	−19.3695	+	28.9885i	−0.763858	+	1.14319i	−0.985765	+	0.168127i	$0.946228\pi$
$644$	9.94066	−	15.1243i	0.391717	−	0.595979i
$645$	4.31585	−	21.6973i	0.169937	−	0.854329i
$646$	−20.7652	+	17.1737i	−0.816995	+	0.675691i
$647$	4.63457	−	11.1888i	0.182204	−	0.439879i	−0.806216	−	0.591621i	$-0.798488\pi$
$647$	4.63457	−	11.1888i	0.182204	−	0.439879i	0.988420	+	0.151742i	$0.0484883\pi$
$648$	2.81778	+	0.245202i	0.110693	+	0.00963245i
$649$	−32.6869	−	78.9131i	−1.28307	−	3.09761i
$650$	−1.18013	+	2.22814i	−0.0462884	+	0.0873950i
$651$	3.41757	−	2.28355i	0.133945	−	0.0894993i
$652$	8.67900	+	20.5117i	0.339896	+	0.803298i
$653$	6.73650	+	33.8666i	0.263619	+	1.32530i	0.854881	+	0.518824i	$0.173630\pi$
$653$	6.73650	+	33.8666i	0.263619	+	1.32530i	−0.591261	+	0.806480i	$0.701370\pi$
$654$	1.32939	−	1.63245i	0.0519832	−	0.0638337i
$655$	1.22969	+	1.22969i	0.0480478	+	0.0480478i
$656$	15.7699	+	15.2987i	0.615710	+	0.597313i
$657$	2.56518	−	2.56518i	0.100077	−	0.100077i
$658$	−5.48286	−	53.5849i	−0.213744	−	2.08896i
$659$	21.2180	−	4.22052i	0.826536	−	0.164408i	0.236342	−	0.971670i	$-0.424051\pi$
$659$	21.2180	−	4.22052i	0.826536	−	0.164408i	0.590194	+	0.807262i	$0.299051\pi$
$660$	−24.3723	−	24.0055i	−0.948690	−	0.934411i
$661$	18.4026	+	27.5414i	0.715778	+	1.07124i	0.993856	+	0.110679i	$0.0353025\pi$
$661$	18.4026	+	27.5414i	0.715778	+	1.07124i	−0.278078	+	0.960558i	$0.589697\pi$
$662$	−18.3655	+	5.64724i	−0.713796	+	0.219486i
$663$	2.18451	−	0.904854i	0.0848394	−	0.0351416i
$664$	−13.5075	−	10.8306i	−0.524192	−	0.420308i
$665$	−47.6521	−	19.7382i	−1.84787	−	0.765413i
$666$	−0.0105470	+	0.111414i	−0.000408689	+	0.00431722i
$667$	−18.8383	−	3.74718i	−0.729424	−	0.145091i
$668$	0.445523	+	0.655951i	0.0172378	+	0.0253795i
$669$	11.2694	+	7.52996i	0.435700	+	0.291125i
$670$	22.1965	+	41.1507i	0.857526	+	1.58979i
$671$		−	51.1684i		−	1.97533i
$672$	16.2165	−	13.8312i	0.625566	−	0.533550i
$673$			36.9171i			1.42305i	0.702661	+	0.711525i	$0.251995\pi$
$673$			36.9171i			1.42305i	−0.702661	+	0.711525i	$0.748005\pi$
$674$	−4.13225	+	2.22892i	−0.159168	+	0.0858547i
$675$	2.46226	+	1.64523i	0.0947724	+	0.0633249i
$676$	24.8261	+	4.74281i	0.954849	+	0.182416i
$677$	−43.3887	−	8.63055i	−1.66756	−	0.331699i	−0.731048	−	0.682326i	$-0.760969\pi$
$677$	−43.3887	−	8.63055i	−1.66756	−	0.331699i	−0.936515	+	0.350627i	$0.885969\pi$
$678$	12.2998	+	1.16436i	0.472373	+	0.0447170i
$679$	40.9750	+	16.9724i	1.57248	+	0.651341i
$680$	8.75670	−	30.0950i	0.335804	−	1.15409i
$681$	−3.86550	+	1.60114i	−0.148126	+	0.0613559i
$682$	−2.74875	−	8.93927i	−0.105255	−	0.342303i
$683$	9.01636	+	13.4939i	0.345002	+	0.516331i	0.962876	−	0.269946i	$-0.0870058\pi$
$683$	9.01636	+	13.4939i	0.345002	+	0.516331i	−0.617874	+	0.786277i	$0.712006\pi$
$684$	−0.0735744	−	9.70299i	−0.00281319	−	0.371003i
$685$	−19.1702	+	3.81319i	−0.732456	+	0.145695i
$686$	−1.04000	+	0.106413i	−0.0397072	+	0.00406288i
$687$	−13.4916	+	13.4916i	−0.514737	+	0.514737i
$688$	17.0261	−	26.3374i	0.649115	−	1.00411i
$689$	0.0984093	+	0.0984093i	0.00374910	+	0.00374910i
$690$	7.43136	+	6.05176i	0.282907	+	0.230387i
$691$	−5.17138	−	25.9983i	−0.196729	−	0.989022i	−0.945358	−	0.326033i	$-0.894288\pi$
$691$	−5.17138	−	25.9983i	−0.196729	−	0.989022i	0.748630	−	0.662988i	$-0.230712\pi$
$692$	−6.88281	−	2.79000i	−0.261645	−	0.106060i
$693$	−18.9912	+	12.6895i	−0.721417	+	0.482035i
$694$	−15.4186	−	8.16643i	−0.585284	−	0.309994i
$695$	15.8975	+	38.3799i	0.603025	+	1.45583i
$696$	−20.0687	−	10.4352i	−0.760701	−	0.395546i
$697$	8.25543	−	19.9304i	0.312697	−	0.754917i
$698$	−13.9783	−	16.9016i	−0.529087	−	0.639733i
$699$	1.17974	−	5.93098i	0.0446220	−	0.224330i
$700$	21.8529	−	4.51933i	0.825962	−	0.170815i
$701$	6.89392	−	10.3175i	0.260380	−	0.389686i	−0.678128	−	0.734944i	$-0.737209\pi$
$701$	6.89392	−	10.3175i	0.260380	−	0.389686i	0.938508	+	0.345258i	$0.112209\pi$
$702$	−0.244067	+	0.815701i	−0.00921171	+	0.0307866i
$703$	0.383930			0.0144802
$704$	−19.5731	−	44.3712i	−0.737690	−	1.67230i
$705$	28.5231			1.07424
$706$	5.60604	−	18.7361i	0.210986	−	0.705141i
$707$	−18.2084	+	27.2508i	−0.684798	+	1.02487i
$708$	5.70709	+	27.5962i	0.214486	+	1.03713i
$709$	9.84519	−	49.4951i	0.369744	−	1.85883i	−0.128384	−	0.991725i	$-0.540979\pi$
$709$	9.84519	−	49.4951i	0.369744	−	1.85883i	0.498128	−	0.867104i	$-0.334021\pi$
$710$	−5.46972	−	6.61359i	−0.205275	−	0.248203i
$711$	1.19198	−	2.87769i	0.0447026	−	0.107922i
$712$	−6.42696	−	20.3507i	−0.240861	−	0.762674i
$713$	1.00266	+	2.42064i	0.0375499	+	0.0906535i
$714$	−18.4932	−	9.79483i	−0.692089	−	0.366562i
$715$	8.56238	−	5.72120i	0.320215	−	0.213961i
$716$	12.1058	−	29.8646i	0.452416	−	1.11609i
$717$	2.68031	+	13.4748i	0.100098	+	0.503226i
$718$	13.9970	+	11.3985i	0.522363	+	0.425388i
$719$	−3.68068	−	3.68068i	−0.137266	−	0.137266i	0.635135	−	0.772401i	$-0.280944\pi$
$719$	−3.68068	−	3.68068i	−0.137266	−	0.137266i	−0.772401	+	0.635135i	$0.780944\pi$
$720$	6.41194	+	9.28808i	0.238959	+	0.346146i
$721$	18.3620	−	18.3620i	0.683835	−	0.683835i
$722$	−6.38486	+	0.653305i	−0.237620	+	0.0243135i
$723$	7.13175	−	1.41859i	0.265232	−	0.0527580i
$724$	−20.7456	+	0.157306i	−0.771003	+	0.00584625i
$725$	−13.1573	−	19.6912i	−0.488649	−	0.731314i
$726$	10.7025	+	34.8057i	0.397206	+	1.29176i
$727$	−6.50895	+	2.69610i	−0.241404	+	0.0999926i	−0.500105	−	0.865965i	$-0.666705\pi$
$727$	−6.50895	+	2.69610i	−0.241404	+	0.0999926i	0.258702	+	0.965957i	$0.416705\pi$
$728$	3.08865	+	5.62366i	0.114473	+	0.208427i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	14.4113	+	1.36424i	0.533387	+	0.0504930i
$731$	−30.2006	−	6.00728i	−1.11701	−	0.222187i
$732$	−3.16778	+	16.5816i	−0.117085	+	0.612875i
$733$	−34.6820	−	23.1738i	−1.28101	−	0.855943i	−0.286246	−	0.958156i	$-0.592407\pi$
$733$	−34.6820	−	23.1738i	−1.28101	−	0.855943i	−0.994762	+	0.102214i	$0.967407\pi$
$734$	−23.0238	+	12.4189i	−0.849823	+	0.458390i
$735$		−	20.3047i		−	0.748949i
$736$	6.63055	+	11.8586i	0.244405	+	0.437113i
$737$		−	71.0304i		−	2.61644i
$738$	3.68777	+	6.83686i	0.135749	+	0.251668i
$739$	16.3428	+	10.9199i	0.601181	+	0.401697i	0.818585	−	0.574385i	$-0.194759\pi$
$739$	16.3428	+	10.9199i	0.601181	+	0.401697i	−0.217404	+	0.976082i	$0.569759\pi$
$740$	−0.369415	+	0.250908i	−0.0135800	+	0.00922355i
$741$	2.86482	+	0.569848i	0.105242	+	0.0209339i
$742$	0.116083	−	1.22625i	0.00426154	−	0.0450171i
$743$	3.56517	+	1.47674i	0.130793	+	0.0541764i	0.447120	−	0.894474i	$-0.352450\pi$
$743$	3.56517	+	1.47674i	0.130793	+	0.0541764i	−0.316327	+	0.948650i	$0.602450\pi$
$744$	0.337340	+	3.06704i	0.0123675	+	0.112443i
$745$	−33.7001	+	13.9591i	−1.23468	+	0.511420i
$746$	−36.6066	+	11.2562i	−1.34026	+	0.412120i
$747$	−3.40076	−	5.08960i	−0.124427	−	0.186219i
$748$	−33.4134	+	33.9240i	−1.22172	+	1.24039i
$749$	1.60161	−	0.318579i	0.0585214	−	0.0116406i
$750$	−0.828051	−	8.09268i	−0.0302361	−	0.295503i
$751$	36.2282	−	36.2282i	1.32199	−	1.32199i	0.409821	−	0.912166i	$-0.365591\pi$
$751$	36.2282	−	36.2282i	1.32199	−	1.32199i	0.912166	−	0.409821i	$-0.134409\pi$
$752$	37.5879	+	14.9057i	1.37069	+	0.543556i
$753$	−13.4703	−	13.4703i	−0.490887	−	0.490887i
$754$	4.29966	−	5.27984i	0.156584	−	0.192281i
$755$	−1.05737	−	5.31575i	−0.0384816	−	0.193460i
$756$	6.93989	−	2.93644i	0.252401	−	0.106797i
$757$	21.9214	−	14.6474i	0.796746	−	0.532369i	−0.0892787	−	0.996007i	$-0.528456\pi$
$757$	21.9214	−	14.6474i	0.796746	−	0.532369i	0.886025	+	0.463638i	$0.153456\pi$
$758$	−10.9808	+	20.7324i	−0.398841	+	0.753033i
$759$	−5.57172	−	13.4513i	−0.202241	−	0.488252i
$760$	29.6490	−	24.9020i	1.07548	−	0.903290i
$761$	−1.29032	+	3.11511i	−0.0467741	+	0.112923i	−0.945540	−	0.325507i	$-0.894465\pi$
$761$	−1.29032	+	3.11511i	−0.0467741	+	0.112923i	0.898766	+	0.438429i	$0.144465\pi$
$762$	−18.4579	+	15.2655i	−0.668660	+	0.553011i
$763$	1.09424	−	5.50114i	0.0396143	−	0.199155i
$764$	−19.5577	−	12.8546i	−0.707571	−	0.465062i
$765$	6.15653	−	9.21390i	0.222590	−	0.333129i
$766$	−25.7916	−	7.71715i	−0.931890	−	0.278832i
$767$	−8.48299			−0.306303
$768$	3.59589	+	15.5907i	0.129756	+	0.562580i
$769$	8.42713			0.303890			0.151945	−	0.988389i	$-0.451446\pi$
$769$	8.42713			0.303890			0.151945	+	0.988389i	$0.451446\pi$
$770$	−87.3163	−	26.1260i	−3.14666	−	0.941516i
$771$	−0.0465037	+	0.0695977i	−0.00167479	+	0.00250650i
$772$	4.16615	+	2.73827i	0.149943	+	0.0985524i
$773$	−0.694550	+	3.49174i	−0.0249812	+	0.125589i	−0.991264	−	0.131896i	$-0.957894\pi$
$773$	−0.694550	+	3.49174i	−0.0249812	+	0.125589i	0.966282	+	0.257485i	$0.0828937\pi$
$774$	8.54441	−	7.06660i	0.307122	−	0.254004i
$775$	−1.23627	+	2.98461i	−0.0444080	+	0.107210i
$776$	−25.4945	+	21.4127i	−0.915199	+	0.768670i
$777$	0.114101	+	0.275464i	0.00409335	+	0.00988223i
$778$	−21.0240	+	39.6944i	−0.753746	+	1.42311i
$779$	22.1580	−	14.8055i	0.793892	−	0.530462i
$780$	−3.12892	+	1.32393i	−0.112033	+	0.0474041i
$781$	2.54364	+	12.7878i	0.0910187	+	0.457582i
$782$	8.42350	−	10.3438i	0.301224	−	0.369893i
$783$	−5.65489	−	5.65489i	−0.202089	−	0.202089i
$784$	10.6109	−	26.7577i	0.378961	−	0.955631i
$785$	44.4868	−	44.4868i	1.58780	−	1.58780i
$786$	0.0887226	+	0.867101i	0.00316463	+	0.0309285i
$787$	32.0181	−	6.36879i	1.14132	−	0.227023i	0.411993	−	0.911187i	$-0.364833\pi$
$787$	32.0181	−	6.36879i	1.14132	−	0.227023i	0.729328	+	0.684164i	$0.239833\pi$
$788$	33.0578	−	33.5630i	1.17764	−	1.19563i
$789$	1.66549	+	2.49258i	0.0592929	+	0.0887382i
$790$	11.8800	−	3.65301i	0.422673	−	0.129968i
$791$	30.4105	−	12.5964i	1.08127	−	0.447877i
$792$	−1.87458	−	17.0433i	−0.0666101	−	0.605608i
$793$	−4.69496	−	1.94472i	−0.166723	−	0.0690589i
$794$	−2.70858	+	28.6124i	−0.0961241	+	1.01542i
$795$	0.639710	+	0.127246i	0.0226882	+	0.00451296i
$796$	−11.4819	+	7.79854i	−0.406965	+	0.276412i
$797$	−3.35716	−	2.24318i	−0.118917	−	0.0794575i	0.494690	−	0.869070i	$-0.335282\pi$
$797$	−3.35716	−	2.24318i	−0.118917	−	0.0794575i	−0.613606	+	0.789612i	$0.710282\pi$
$798$	−12.2728	−	22.7528i	−0.434451	−	0.805440i
$799$		−	39.7015i		−	1.40454i
$800$	−4.55806	+	16.1198i	−0.161152	+	0.569921i
$801$		−	7.54533i		−	0.266601i
$802$	−22.0372	+	11.8868i	−0.778160	+	0.419736i
$803$	−18.2852	−	12.2178i	−0.645271	−	0.431156i
$804$	−4.39742	+	23.0181i	−0.155085	+	0.811787i
$805$	25.0428	+	4.98131i	0.882641	+	0.175568i
$806$	−0.924693	−	0.0875359i	−0.0325709	−	0.00308332i
$807$	1.72923	+	0.716270i	0.0608718	+	0.0252139i
$808$	−11.8439	−	21.5648i	−0.416668	−	0.758647i
$809$	0.549987	−	0.227812i	0.0193365	−	0.00800944i	−0.372994	−	0.927834i	$-0.621669\pi$
$809$	0.549987	−	0.227812i	0.0193365	−	0.00800944i	0.392331	+	0.919824i	$0.371669\pi$
$810$	1.17280	+	3.81408i	0.0412079	+	0.134013i
$811$	13.6598	+	20.4433i	0.479660	+	0.717862i	0.989837	−	0.142207i	$-0.0454200\pi$
$811$	13.6598	+	20.4433i	0.479660	+	0.717862i	−0.510177	+	0.860070i	$0.670420\pi$
$812$	−60.2619	+	0.456945i	−2.11478	+	0.0160356i
$813$	0.844196	−	0.167921i	0.0296072	−	0.00588925i
$814$	0.674897	−	0.0690561i	0.0236551	−	0.00242041i
$815$	−22.2184	+	22.2184i	−0.778275	+	0.778275i
$816$	12.9282	−	8.92484i	0.452576	−	0.312432i
$817$	−26.8975	−	26.8975i	−0.941023	−	0.941023i
$818$	25.8350	+	21.0388i	0.903299	+	0.735605i
$819$	0.442544	+	2.22482i	0.0154638	+	0.0777415i
$820$	−11.6445	+	28.7266i	−0.406645	+	1.00318i
$821$	6.22025	−	4.15624i	0.217088	−	0.145054i	−0.442272	−	0.896881i	$-0.645827\pi$
$821$	6.22025	−	4.15624i	0.217088	−	0.145054i	0.659360	+	0.751827i	$0.270827\pi$
$822$	−8.65727	−	4.58530i	−0.301957	−	0.159931i
$823$	10.8907	+	26.2924i	0.379625	+	0.916496i	0.992036	+	0.125956i	$0.0401999\pi$
$823$	10.8907	+	26.2924i	0.379625	+	0.916496i	−0.612411	+	0.790540i	$0.709800\pi$
$824$	5.87051	+	18.5887i	0.204509	+	0.647568i
$825$	6.86985	−	16.5853i	0.239177	−	0.577425i
$826$	47.8489	+	57.8553i	1.66488	+	2.01305i
$827$	7.40445	−	37.2247i	0.257478	−	1.29443i	−0.608183	−	0.793797i	$-0.708101\pi$
$827$	7.40445	−	37.2247i	0.257478	−	1.29443i	0.865660	−	0.500632i	$-0.166899\pi$
$828$	0.972815	+	4.70398i	0.0338077	+	0.163474i
$829$	−8.99896	+	13.4679i	−0.312547	+	0.467759i	−0.954172	−	0.299259i	$-0.903261\pi$
$829$	−8.99896	+	13.4679i	−0.312547	+	0.467759i	0.641625	+	0.767018i	$0.278261\pi$
$830$	7.00171	−	23.4006i	0.243033	−	0.812245i
$831$	8.77984			0.304569
$832$	−4.81518	+	0.109552i	−0.166936	+	0.00379805i
$833$	−28.2623			−0.979230
$834$	−5.96855	+	19.9476i	−0.206674	+	0.690730i
$835$	−0.621506	+	0.930149i	−0.0215081	+	0.0321891i
$836$	−57.6029	+	11.9127i	−1.99224	+	0.412009i
$837$	−0.212824	+	1.06994i	−0.00735628	+	0.0369825i
$838$	−4.26966	−	5.16256i	−0.147493	−	0.178338i
$839$	−12.6494	+	30.5385i	−0.436707	+	1.05430i	0.540372	+	0.841427i	$0.318284\pi$
$839$	−12.6494	+	30.5385i	−0.436707	+	1.05430i	−0.977079	+	0.212878i	$0.931716\pi$
$840$	26.6783	+	13.8721i	0.920488	+	0.478632i
$841$	13.3770	+	32.2948i	0.461274	+	1.11361i
$842$	23.2878	+	12.3343i	0.802550	+	0.425068i
$843$	−19.8816	+	13.2844i	−0.684758	+	0.457541i
$844$	45.1879	+	18.3173i	1.55543	+	0.630506i
$845$	6.95650	+	34.9727i	0.239311	+	1.20310i
$846$	11.0854	+	9.02740i	0.381122	+	0.310368i
$847$	68.6000	+	68.6000i	2.35713	+	2.35713i
$848$	0.776518	+	0.501989i	0.0266657	+	0.0172384i
$849$	12.6185	−	12.6185i	0.433065	−	0.433065i
$850$	16.3623	−	1.67421i	0.561223	−	0.0574248i
$851$	−0.186409	+	0.0370791i	−0.00639002	+	0.00127105i
$852$	−0.0326166	−	4.30148i	−0.00111743	−	0.147366i
$853$	−0.0242934	−	0.0363577i	−0.000831791	−	0.00124486i	0.831053	−	0.556193i	$-0.187738\pi$
$853$	−0.0242934	−	0.0363577i	−0.000831791	−	0.00124486i	−0.831885	+	0.554948i	$0.812738\pi$
$854$	13.2190	+	42.9897i	0.452344	+	1.47108i
$855$	12.6473	−	5.23866i	0.432527	−	0.179159i
$856$	−0.342483	+	1.17705i	−0.0117058	+	0.0402306i
$857$	−19.0816	−	7.90384i	−0.651814	−	0.269990i	0.0321753	−	0.999482i	$-0.489757\pi$
$857$	−19.0816	−	7.90384i	−0.651814	−	0.269990i	−0.683989	+	0.729492i	$0.739757\pi$
$858$	5.13846	+	0.486431i	0.175424	+	0.0166065i
$859$	−51.2782	−	10.1999i	−1.74959	−	0.348015i	−0.786582	−	0.617486i	$-0.788151\pi$
$859$	−51.2782	−	10.1999i	−1.74959	−	0.348015i	−0.963009	+	0.269471i	$0.913151\pi$
$860$	43.4587	+	8.30242i	1.48193	+	0.283110i
$861$	17.2079	+	11.4980i	0.586444	+	0.391850i
$862$	−5.32048	+	2.86985i	−0.181216	+	0.0977473i
$863$		−	16.4653i		−	0.560487i	−0.959929	−	0.280243i	$-0.909585\pi$
$863$		−	16.4653i		−	0.560487i	0.959929	−	0.280243i	$-0.0904152\pi$
$864$	−0.447659	+	5.63911i	−0.0152297	+	0.191847i
$865$		−	10.4777i		−	0.356251i
$866$	−5.73086	−	10.6246i	−0.194743	−	0.361039i
$867$	1.31007	+	0.875361i	0.0444923	+	0.0297288i
$868$	4.61879	+	6.80031i	0.156772	+	0.230818i
$869$	−18.5192	−	3.68370i	−0.628221	−	0.124961i
$870$	3.00745	−	31.7695i	0.101962	−	1.07709i
$871$	−6.51740	−	2.69960i	−0.220834	−	0.0914723i
$872$	3.28496	+	2.63395i	0.111243	+	0.0891966i
$873$	−10.8751	+	4.50461i	−0.368066	+	0.152458i
$874$	15.7512	−	4.84337i	0.532793	−	0.163829i
$875$	−12.0410	−	18.0207i	−0.407062	−	0.609211i
$876$	5.16912	+	5.09132i	0.174648	+	0.172020i
$877$	−9.33591	+	1.85703i	−0.315251	+	0.0627074i	−0.350180	−	0.936682i	$-0.613880\pi$
$877$	−9.33591	+	1.85703i	−0.315251	+	0.0627074i	0.0349288	+	0.999390i	$0.488880\pi$
$878$	−0.240803	−	2.35341i	−0.00812669	−	0.0794236i
$879$	−6.77837	+	6.77837i	−0.228629	+	0.228629i
$880$	47.6399	−	49.1072i	1.60594	−	1.65540i
$881$	37.8427	+	37.8427i	1.27495	+	1.27495i	0.943457	+	0.331495i	$0.107553\pi$
$881$	37.8427	+	37.8427i	1.27495	+	1.27495i	0.331495	+	0.943457i	$0.392447\pi$
$882$	6.42632	−	7.89132i	0.216386	−	0.265714i
$883$	−0.278940	−	1.40233i	−0.00938708	−	0.0471920i	0.975808	−	0.218630i	$-0.0701587\pi$
$883$	−0.278940	−	1.40233i	−0.00938708	−	0.0471920i	−0.985195	+	0.171438i	$0.945159\pi$
$884$	1.84278	+	4.35518i	0.0619796	+	0.146480i
$885$	−33.0562	+	22.0874i	−1.11117	+	0.742461i
$886$	13.5598	−	25.6017i	0.455552	−	0.860106i
$887$	−0.611836	−	1.47710i	−0.0205434	−	0.0495962i	0.913275	−	0.407344i	$-0.133545\pi$
$887$	−0.611836	−	1.47710i	−0.0205434	−	0.0495962i	−0.933818	+	0.357747i	$0.883545\pi$
$888$	−0.222983	−	0.0194039i	−0.00748280	−	0.000651151i
$889$	−24.4211	+	58.9577i	−0.819056	+	1.97738i
$890$	23.2015	−	19.1886i	0.777715	−	0.643204i
$891$	1.18265	−	5.94558i	0.0396202	−	0.199184i
$892$	−14.8886	+	22.6523i	−0.498507	+	0.758456i
$893$	27.2477	−	40.7791i	0.911810	−	1.36462i
$894$	−17.5154	−	5.24080i	−0.585802	−	0.175278i
$895$	45.4626			1.51965
$896$	27.9075	+	32.2224i	0.932325	+	1.07647i
$897$	−1.44599			−0.0482801
$898$	−31.6245	−	9.46242i	−1.05532	−	0.315765i
$899$	4.84689	−	7.25389i	0.161653	−	0.241931i
$900$	−3.25302	+	4.94932i	−0.108434	+	0.164977i
$901$	0.177115	−	0.890418i	0.00590056	−	0.0296641i
$902$	36.2878	−	30.0116i	1.20825	−	0.999275i
$903$	11.3048	−	27.2923i	0.376201	−	0.908230i
$904$	−2.14213	+	24.6166i	−0.0712462	+	0.818737i
$905$	−11.2006	−	27.0406i	−0.372320	−	0.898859i
$906$	1.27147	−	2.40059i	0.0422416	−	0.0797543i
$907$	−10.8204	+	7.22998i	−0.359286	+	0.240068i	−0.722092	−	0.691798i	$-0.756819\pi$
$907$	−10.8204	+	7.22998i	−0.359286	+	0.240068i	0.362805	+	0.931865i	$0.381819\pi$
$908$	−3.26081	−	7.70649i	−0.108214	−	0.255749i
$909$	−1.69700	−	8.53142i	−0.0562861	−	0.282969i
$910$	−5.71575	+	7.01876i	−0.189475	+	0.232670i
$911$	20.9362	+	20.9362i	0.693646	+	0.693646i	0.963032	−	0.269386i	$-0.0868208\pi$
$911$	20.9362	+	20.9362i	0.693646	+	0.693646i	−0.269386	+	0.963032i	$0.586821\pi$
$912$	19.4043	−	0.294289i	0.642541	−	0.00974489i
$913$	−26.2387	+	26.2387i	−0.868375	+	0.868375i
$914$	3.84610	+	37.5886i	0.127218	+	1.24332i
$915$	−23.3587	+	4.64633i	−0.772214	+	0.153603i
$916$	−27.1870	−	26.7778i	−0.898285	−	0.884765i
$917$	1.29015	+	1.93085i	0.0426046	+	0.0637623i
$918$	5.30886	−	1.63243i	0.175218	−	0.0538782i
$919$	16.6832	−	6.91041i	0.550328	−	0.227953i	−0.0901522	−	0.995928i	$-0.528735\pi$
$919$	16.6832	−	6.91041i	0.550328	−	0.227953i	0.640480	+	0.767975i	$0.278735\pi$
$920$	−11.9905	+	14.9541i	−0.395314	+	0.493021i
$921$	−13.5762	−	5.62344i	−0.447351	−	0.185299i
$922$	−1.14552	+	12.1008i	−0.0377256	+	0.398518i
$923$	1.27002	+	0.252622i	0.0418031	+	0.00831515i
$924$	−25.6663	−	37.7889i	−0.844360	−	1.24316i
$925$	−0.194849	−	0.130194i	−0.00640659	−	0.00428074i
$926$	22.4094	+	41.5454i	0.736418	+	1.36527i
$927$			6.89204i			0.226364i
$928$	20.5655	−	40.2944i	0.675096	−	1.32273i
$929$		−	14.7778i		−	0.484845i	−0.970171	−	0.242422i	$-0.922058\pi$
$929$		−	14.7778i		−	0.484845i	0.970171	−	0.242422i	$-0.0779419\pi$
$930$	−3.83123	+	2.06655i	−0.125631	+	0.0677648i
$931$	−29.0294	−	19.3968i	−0.951399	−	0.635704i
$932$	11.8795	+	2.26948i	0.389126	+	0.0743393i
$933$	−9.45611	−	1.88094i	−0.309579	−	0.0615791i
$934$	30.9880	+	2.93347i	1.01396	+	0.0959861i
$935$	−62.0630	−	25.7073i	−2.02968	−	0.840719i
$936$	−1.63506	−	0.475750i	−0.0534435	−	0.0155504i
$937$	33.0196	−	13.6772i	1.07870	−	0.446813i	0.228649	−	0.973509i	$-0.426569\pi$
$937$	33.0196	−	13.6772i	1.07870	−	0.446813i	0.850054	+	0.526696i	$0.176569\pi$
$938$	18.3502	+	59.6770i	0.599154	+	1.94852i
$939$	10.8786	+	16.2810i	0.355010	+	0.531310i
$940$	0.432549	+	57.0445i	0.0141082	+	1.86059i
$941$	−56.9668	+	11.3314i	−1.85706	+	0.369393i	−0.991361	−	0.131164i	$-0.958129\pi$
$941$	−56.9668	+	11.3314i	−1.85706	+	0.369393i	−0.865704	+	0.500557i	$0.833129\pi$
$942$	31.3694	−	3.20975i	1.02207	−	0.104579i
$943$	−9.32847	+	9.32847i	−0.303777	+	0.303777i
$944$	−55.1043	+	11.8323i	−1.79349	+	0.385110i
$945$	7.51733	+	7.51733i	0.244539	+	0.244539i
$946$	−52.1201	−	42.4442i	−1.69457	−	1.37998i
$947$	−7.78461	−	39.1359i	−0.252966	−	1.27174i	−0.873213	−	0.487339i	$-0.837968\pi$
$947$	−7.78461	−	39.1359i	−0.252966	−	1.27174i	0.620247	−	0.784406i	$-0.287032\pi$
$948$	5.77329	+	2.34025i	0.187508	+	0.0760077i
$949$	−1.81600	+	1.21341i	−0.0589497	+	0.0393889i
$950$	17.9554	+	9.51004i	0.582551	+	0.308546i
$951$	8.21232	+	19.8263i	0.266303	+	0.642912i
$952$	19.3087	−	37.1338i	0.625797	−	1.20351i
$953$	1.77520	−	4.28572i	0.0575045	−	0.138828i	−0.892516	−	0.451016i	$-0.851062\pi$
$953$	1.77520	−	4.28572i	0.0575045	−	0.138828i	0.950020	+	0.312188i	$0.101062\pi$
$954$	0.208347	+	0.251918i	0.00674550	+	0.00815616i
$955$	6.44149	−	32.3836i	0.208442	−	1.04791i
$956$	−26.9082	+	5.56481i	−0.870274	+	0.179979i
$957$	−26.9339	+	40.3094i	−0.870648	+	1.30302i
$958$	−15.4088	+	51.4981i	−0.497836	+	1.66383i
$959$	−26.1003			−0.842824
$960$	−18.4784	+	12.9644i	−0.596387	+	0.418423i
$961$	29.8099			0.961611
$962$	0.0193140	−	0.0645498i	0.000622709	−	0.00208117i
$963$	−0.240788	+	0.360365i	−0.00775929	+	0.0116126i
$964$	2.94526	+	14.2416i	0.0948603	+	0.458690i
$965$	−1.37216	+	6.89831i	−0.0441714	+	0.222065i
$966$	8.15619	+	9.86187i	0.262421	+	0.317300i
$967$	6.23882	−	15.0619i	0.200627	−	0.484357i	−0.791260	−	0.611480i	$-0.790574\pi$
$967$	6.23882	−	15.0619i	0.200627	−	0.484357i	0.991887	+	0.127124i	$0.0405745\pi$
$968$	−69.4471	+	21.9321i	−2.23211	+	0.704925i
$969$	−7.29175	−	17.6038i	−0.234245	−	0.565517i
$970$	−41.5079	−	21.9845i	−1.33274	−	0.705881i
$971$	−5.11342	+	3.41668i	−0.164098	+	0.109646i	−0.634907	−	0.772588i	$-0.718962\pi$
$971$	−5.11342	+	3.41668i	−0.164098	+	0.109646i	0.470810	+	0.882235i	$0.343962\pi$
$972$	−0.751334	+	1.85351i	−0.0240991	+	0.0594513i
$973$	10.8222	+	54.4070i	0.346945	+	1.74421i
$974$	−41.6459	−	33.9145i	−1.33442	−	1.08669i
$975$	−1.26069	−	1.26069i	−0.0403743	−	0.0403743i
$976$	−33.2104	−	6.08392i	−1.06304	−	0.194742i
$977$	18.3458	−	18.3458i	0.586935	−	0.586935i	−0.349865	−	0.936800i	$-0.613773\pi$
$977$	18.3458	−	18.3458i	0.586935	−	0.586935i	0.936800	+	0.349865i	$0.113773\pi$
$978$	−15.6671	+	1.60307i	−0.500977	+	0.0512604i
$979$	−44.8614	+	8.92349i	−1.43378	+	0.285196i
$980$	40.6082	−	0.307918i	1.29718	−	0.00983607i
$981$	0.827049	+	1.23777i	0.0264057	+	0.0395189i
$982$	13.9889	+	45.4936i	0.446404	+	1.45176i
$983$	−23.7807	+	9.85030i	−0.758487	+	0.314176i	−0.728199	−	0.685366i	$-0.759642\pi$
$983$	−23.7807	+	9.85030i	−0.758487	+	0.314176i	−0.0302880	+	0.999541i	$0.509642\pi$
$984$	−13.6174	+	7.47901i	−0.434107	+	0.238422i
$985$	61.4025	+	25.4337i	1.95644	+	0.810386i
$986$	−44.2203	−	4.18610i	−1.40826	−	0.133313i
$987$	37.3562	+	7.43062i	1.18906	+	0.236519i
$988$	−1.09622	+	5.73811i	−0.0348753	+	0.182554i
$989$	15.6572	+	10.4618i	0.497870	+	0.332666i
$990$	21.2899	−	11.4837i	0.676638	−	0.364975i
$991$			3.06925i			0.0974979i	0.998811	+	0.0487490i	$0.0155234\pi$
$991$			3.06925i			0.0974979i	−0.998811	+	0.0487490i	$0.984477\pi$
$992$	−6.12878	+	0.721171i	−0.194589	+	0.0228972i
$993$		−	13.5865i		−	0.431153i
$994$	−5.44069	−	10.0867i	−0.172568	−	0.319929i
$995$	−16.2815	−	10.8790i	−0.516159	−	0.344887i
$996$	10.1273	−	6.87851i	0.320897	−	0.217954i
$997$	52.5656	+	10.4559i	1.66477	+	0.331143i	0.935565	−	0.353153i	$-0.114891\pi$
$997$	52.5656	+	10.4559i	1.66477	+	0.331143i	0.729204	+	0.684297i	$0.239891\pi$
$998$	1.49030	−	15.7429i	0.0471745	−	0.498332i
$999$	−0.0731104	−	0.0302833i	−0.00231311	−	0.000958122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.37.2	✓	128
3.2	odd	2		576.2.bd.b.37.15		128
4.3	odd	2		768.2.r.a.241.2		128
64.19	odd	16		768.2.r.a.529.2		128
64.45	even	16	inner	192.2.r.a.109.2	yes	128
192.173	odd	16		576.2.bd.b.109.15		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.37.2	✓	128	1.1	even	1	trivial
192.2.r.a.109.2	yes	128	64.45	even	16	inner
576.2.bd.b.37.15		128	3.2	odd	2
576.2.bd.b.109.15		128	192.173	odd	16
768.2.r.a.241.2		128	4.3	odd	2
768.2.r.a.529.2		128	64.19	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35486 - 0.405391i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.67132 + 1.09850i) q^{4} +(-0.550464 + 2.76737i) q^{5} +(-1.08979 + 0.901306i) q^{6} +(-1.44187 + 3.48098i) q^{7} +(-1.81909 - 2.16585i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(-1.35486 - 0.405391i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.67132 + 1.09850i) q^{4} +(-0.550464 + 2.76737i) q^{5} +(-1.08979 + 0.901306i) q^{6} +(-1.44187 + 3.48098i) q^{7} +(-1.81909 - 2.16585i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(1.86767 - 3.52626i) q^{10} +(-5.04042 + 3.36790i) q^{11} +(1.84190 - 0.779355i) q^{12} +(0.117455 + 0.590485i) q^{13} +(3.36469 - 4.13173i) q^{14} +(1.99516 + 1.99516i) q^{15} +(1.58660 + 3.67188i) q^{16} +(2.77708 - 2.77708i) q^{17} +(0.143952 + 1.40687i) q^{18} +(4.75841 - 0.946507i) q^{19} +(-3.95995 + 4.02046i) q^{20} +(2.09327 + 3.13280i) q^{21} +(8.19440 - 2.51971i) q^{22} +(-2.21894 + 0.919113i) q^{23} +(-2.81147 + 0.309231i) q^{24} +(-2.73591 - 1.13325i) q^{25} +(0.0802419 - 0.847643i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-6.23367 + 4.23393i) q^{28} +(6.64945 + 4.44302i) q^{29} +(-1.89435 - 3.51199i) q^{30} -1.09090i q^{31} +(-0.661079 - 5.61809i) q^{32} +6.06206i q^{33} +(-4.88838 + 2.63677i) q^{34} +(-8.83945 - 5.90633i) q^{35} +(0.375296 - 1.96447i) q^{36} +(0.0776136 + 0.0154383i) q^{37} +(-6.83071 - 0.646628i) q^{38} +(0.556225 + 0.230396i) q^{39} +(6.99506 - 3.84186i) q^{40} +(5.07471 - 2.10201i) q^{41} +(-1.56609 - 5.09311i) q^{42} +(-4.35589 - 6.51905i) q^{43} +(-12.1238 + 0.0919304i) q^{44} +(2.76737 - 0.550464i) q^{45} +(3.37896 - 0.345738i) q^{46} +(7.14806 - 7.14806i) q^{47} +(3.93452 + 0.720779i) q^{48} +(-5.08848 - 5.08848i) q^{49} +(3.24738 + 2.64452i) q^{50} +(-0.766196 - 3.85193i) q^{51} +(-0.452343 + 1.11591i) q^{52} +(0.192204 - 0.128427i) q^{53} +(1.24974 + 0.661922i) q^{54} +(-6.54565 - 15.8026i) q^{55} +(10.1622 - 3.20932i) q^{56} +(1.85664 - 4.48233i) q^{57} +(-7.20795 - 8.71532i) q^{58} +(-2.74884 + 13.8193i) q^{59} +(1.14286 + 5.52623i) q^{60} +(-4.68943 + 7.01823i) q^{61} +(-0.442241 + 1.47802i) q^{62} +3.76778 q^{63} +(-1.38185 + 7.87975i) q^{64} -1.69874 q^{65} +(2.45750 - 8.21327i) q^{66} +(-6.50973 + 9.74250i) q^{67} +(7.69201 - 1.59076i) q^{68} +(-0.468560 + 2.35561i) q^{69} +(9.58189 + 11.5857i) q^{70} +(0.823076 - 1.98708i) q^{71} +(-1.30485 + 2.50945i) q^{72} +(1.38827 + 3.35157i) q^{73} +(-0.0988974 - 0.0523807i) q^{74} +(-2.46226 + 1.64523i) q^{75} +(8.99255 + 3.64520i) q^{76} +(-4.45597 - 22.4017i) q^{77} +(-0.660209 - 0.537644i) q^{78} +(2.20249 + 2.20249i) q^{79} +(-11.0348 + 2.36946i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(-7.72768 + 0.790704i) q^{82} +(6.00359 - 1.19419i) q^{83} +(0.0571380 + 7.53535i) q^{84} +(6.15653 + 9.21390i) q^{85} +(3.25888 + 10.5983i) q^{86} +(7.38848 - 3.06041i) q^{87} +(16.4633 + 4.79031i) q^{88} +(6.97098 + 2.88747i) q^{89} +(-3.97256 - 0.376062i) q^{90} +(-2.22482 - 0.442544i) q^{91} +(-4.71819 - 0.901370i) q^{92} +(-0.907050 - 0.606072i) q^{93} +(-12.5824 + 6.78690i) q^{94} +13.6893i q^{95} +(-5.03855 - 2.57158i) q^{96} -11.7711i q^{97} +(4.83138 + 8.95702i) q^{98} +(5.04042 + 3.36790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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