LMFDB - Embedded newform 384.2.v.a.253.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

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("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			253.13
Character	$\chi$	$=$	384.253
Dual form			384.2.v.a.85.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540446 + 1.30687i) q^{2} +(0.634393 + 0.773010i) q^{3} +(-1.41584 - 1.41259i) q^{4} +(-3.76594 - 1.14238i) q^{5} +(-1.35308 + 0.411302i) q^{6} +(5.02585 - 0.999703i) q^{7} +(2.61126 - 1.08689i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})$	\(q+(-0.540446 + 1.30687i) q^{2} +(0.634393 + 0.773010i) q^{3} +(-1.41584 - 1.41259i) q^{4} +(-3.76594 - 1.14238i) q^{5} +(-1.35308 + 0.411302i) q^{6} +(5.02585 - 0.999703i) q^{7} +(2.61126 - 1.08689i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(3.52824 - 4.30421i) q^{10} +(4.06125 - 0.399998i) q^{11} +(0.193748 - 1.99059i) q^{12} +(-0.709129 - 2.33768i) q^{13} +(-1.40971 + 7.10843i) q^{14} +(-1.50601 - 3.63583i) q^{15} +(0.00918989 + 3.99999i) q^{16} +(-1.18238 + 2.85451i) q^{17} +(-1.17633 - 0.785019i) q^{18} +(1.81765 + 0.971557i) q^{19} +(3.71824 + 6.93715i) q^{20} +(3.96114 + 3.25083i) q^{21} +(-1.67214 + 5.52371i) q^{22} +(2.07867 + 3.11095i) q^{23} +(2.49674 + 1.32901i) q^{24} +(8.71990 + 5.82645i) q^{25} +(3.43830 + 0.336649i) q^{26} +(-0.881921 + 0.471397i) q^{27} +(-8.52795 - 5.68404i) q^{28} +(0.754197 - 7.65749i) q^{29} +(5.56549 - 0.00319664i) q^{30} +(1.31544 - 1.31544i) q^{31} +(-5.23245 - 2.14977i) q^{32} +(2.88563 + 2.88563i) q^{33} +(-3.09148 - 3.08793i) q^{34} +(-20.0691 - 1.97663i) q^{35} +(1.66166 - 1.11305i) q^{36} +(1.00278 + 1.87607i) q^{37} +(-2.25205 + 1.85037i) q^{38} +(1.35719 - 2.03117i) q^{39} +(-11.0755 + 1.11011i) q^{40} +(-0.465749 + 0.311203i) q^{41} +(-6.38920 + 3.41982i) q^{42} +(4.07158 - 4.96124i) q^{43} +(-6.31510 - 5.17054i) q^{44} +(1.85513 - 3.47071i) q^{45} +(-5.18903 + 1.03526i) q^{46} +(8.31103 + 3.44254i) q^{47} +(-3.08620 + 2.54467i) q^{48} +(17.7926 - 7.36993i) q^{49} +(-12.3271 + 8.24693i) q^{50} +(-2.95666 + 0.896893i) q^{51} +(-2.29817 + 4.31149i) q^{52} +(-0.366200 - 3.71809i) q^{53} +(-0.139426 - 1.40732i) q^{54} +(-15.7514 - 3.13314i) q^{55} +(12.0372 - 8.07304i) q^{56} +(0.402084 + 2.02142i) q^{57} +(9.59977 + 5.12410i) q^{58} +(0.620862 - 2.04671i) q^{59} +(-3.00367 + 7.27512i) q^{60} +(-1.85378 + 1.52136i) q^{61} +(1.00819 + 2.43004i) q^{62} +5.12431i q^{63} +(5.63733 - 5.67632i) q^{64} +9.61367i q^{65} +(-5.33068 + 2.21163i) q^{66} +(-10.0924 + 8.28263i) q^{67} +(5.70630 - 2.37131i) q^{68} +(-1.08610 + 3.58040i) q^{69} +(13.4295 - 25.1595i) q^{70} +(-1.13357 - 5.69887i) q^{71} +(0.556578 + 2.77312i) q^{72} +(-3.80329 - 0.756522i) q^{73} +(-2.99373 + 0.296593i) q^{74} +(1.02794 + 10.4368i) q^{75} +(-1.20109 - 3.94316i) q^{76} +(20.0113 - 6.07037i) q^{77} +(1.92100 + 2.87141i) q^{78} +(-1.75819 + 0.728267i) q^{79} +(4.53492 - 15.0742i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(-0.154992 - 0.776863i) q^{82} +(-1.95865 + 3.66437i) q^{83} +(-1.01626 - 10.1981i) q^{84} +(7.71371 - 9.39919i) q^{85} +(4.28324 + 8.00232i) q^{86} +(6.39778 - 4.27486i) q^{87} +(10.1702 - 5.45864i) q^{88} +(-7.24931 + 10.8494i) q^{89} +(3.53318 + 4.30015i) q^{90} +(-5.90096 - 11.0399i) q^{91} +(1.45143 - 7.34091i) q^{92} +(1.85136 + 0.182343i) q^{93} +(-8.99062 + 9.00096i) q^{94} +(-5.73528 - 5.73528i) q^{95} +(-1.65764 - 5.40853i) q^{96} +(-7.28783 + 7.28783i) q^{97} +(0.0156433 + 27.2357i) q^{98} +(-0.399998 + 4.06125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{32}\right)$	$1$

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 $

$2$	−0.540446	+	1.30687i	−0.382153	+	0.924099i
$2$	−0.540446	+	1.30687i	−0.382153	+	0.924099i
$3$	0.634393	+	0.773010i	0.366267	+	0.446298i
$3$	0.634393	+	0.773010i	0.366267	+	0.446298i
$4$	−1.41584	−	1.41259i	−0.707919	−	0.706294i
$5$	−3.76594	−	1.14238i	−1.68418	−	0.510890i	−0.704202	−	0.710000i	$-0.748695\pi$
$5$	−3.76594	−	1.14238i	−1.68418	−	0.510890i	−0.979977	+	0.199110i	$0.936195\pi$
$6$	−1.35308	+	0.411302i	−0.552393	+	0.167913i
$7$	5.02585	−	0.999703i	1.89959	−	0.377852i	0.901143	−	0.433523i	$-0.142730\pi$
$7$	5.02585	−	0.999703i	1.89959	−	0.377852i	0.998449	+	0.0556705i	$0.0177296\pi$
$8$	2.61126	−	1.08689i	0.923219	−	0.384275i
$9$	−0.195090	+	0.980785i	−0.0650301	+	0.326928i
$10$	3.52824	−	4.30421i	1.11573	−	1.36111i
$11$	4.06125	−	0.399998i	1.22451	−	0.120604i	0.534983	−	0.844863i	$-0.320318\pi$
$11$	4.06125	−	0.399998i	1.22451	−	0.120604i	0.689528	+	0.724259i	$0.257818\pi$
$12$	0.193748	−	1.99059i	0.0559302	−	0.574635i
$13$	−0.709129	−	2.33768i	−0.196677	−	0.648357i	−0.998696	−	0.0510581i	$-0.983741\pi$
$13$	−0.709129	−	2.33768i	−0.196677	−	0.648357i	0.802019	−	0.597299i	$-0.203759\pi$
$14$	−1.40971	+	7.10843i	−0.376761	+	1.89981i
$15$	−1.50601	−	3.63583i	−0.388850	−	0.938768i
$16$	0.00918989	+	3.99999i	0.00229747	+	0.999997i
$17$	−1.18238	+	2.85451i	−0.286769	+	0.692321i	−0.999963	−	0.00864586i	$-0.997248\pi$
$17$	−1.18238	+	2.85451i	−0.286769	+	0.692321i	0.713194	+	0.700967i	$0.247248\pi$
$18$	−1.17633	−	0.785019i	−0.277263	−	0.185031i
$19$	1.81765	+	0.971557i	0.416999	+	0.222890i	0.666533	−	0.745476i	$-0.267778\pi$
$19$	1.81765	+	0.971557i	0.416999	+	0.222890i	−0.249534	+	0.968366i	$0.580278\pi$
$20$	3.71824	+	6.93715i	0.831423	+	1.55119i
$21$	3.96114	+	3.25083i	0.864393	+	0.709389i
$22$	−1.67214	+	5.52371i	−0.356501	+	1.17766i
$23$	2.07867	+	3.11095i	0.433433	+	0.648678i	0.982318	−	0.187219i	$-0.0599476\pi$
$23$	2.07867	+	3.11095i	0.433433	+	0.648678i	−0.548885	+	0.835898i	$0.684948\pi$
$24$	2.49674	+	1.32901i	0.509646	+	0.271283i
$25$	8.71990	+	5.82645i	1.74398	+	1.16529i
$26$	3.43830	+	0.336649i	0.674307	+	0.0660224i
$27$	−0.881921	+	0.471397i	−0.169726	+	0.0907203i
$28$	−8.52795	−	5.68404i	−1.61163	−	1.07418i
$29$	0.754197	−	7.65749i	0.140051	−	1.42196i	−0.626322	−	0.779564i	$-0.715440\pi$
$29$	0.754197	−	7.65749i	0.140051	−	1.42196i	0.766373	−	0.642396i	$-0.222060\pi$
$30$	5.56549	−	0.00319664i	1.01611	−	0.000583624i
$31$	1.31544	−	1.31544i	0.236261	−	0.236261i	−0.579039	−	0.815300i	$-0.696572\pi$
$31$	1.31544	−	1.31544i	0.236261	−	0.236261i	0.815300	+	0.579039i	$0.196572\pi$
$32$	−5.23245	−	2.14977i	−0.924975	−	0.380029i
$33$	2.88563	+	2.88563i	0.502324	+	0.502324i
$34$	−3.09148	−	3.08793i	−0.530184	−	0.529575i
$35$	−20.0691	−	1.97663i	−3.39229	−	0.334112i
$36$	1.66166	−	1.11305i	0.276944	−	0.185508i
$37$	1.00278	+	1.87607i	0.164856	+	0.308424i	0.950762	−	0.309922i	$-0.100303\pi$
$37$	1.00278	+	1.87607i	0.164856	+	0.308424i	−0.785906	+	0.618346i	$0.787803\pi$
$38$	−2.25205	+	1.85037i	−0.365330	+	0.300170i
$39$	1.35719	−	2.03117i	0.217324	−	0.325248i
$40$	−11.0755	+	1.11011i	−1.75119	+	0.175524i
$41$	−0.465749	+	0.311203i	−0.0727377	+	0.0486018i	−0.591407	−	0.806373i	$-0.701427\pi$
$41$	−0.465749	+	0.311203i	−0.0727377	+	0.0486018i	0.518670	+	0.854975i	$0.326427\pi$
$42$	−6.38920	+	3.41982i	−0.985876	+	0.527690i
$43$	4.07158	−	4.96124i	0.620910	−	0.756582i	−0.363667	−	0.931529i	$-0.618476\pi$
$43$	4.07158	−	4.96124i	0.620910	−	0.756582i	0.984578	+	0.174947i	$0.0559755\pi$
$44$	−6.31510	−	5.17054i	−0.952037	−	0.779488i
$45$	1.85513	−	3.47071i	0.276547	−	0.517383i
$46$	−5.18903	+	1.03526i	−0.765081	+	0.152641i
$47$	8.31103	+	3.44254i	1.21229	+	0.502146i	0.894950	−	0.446166i	$-0.147211\pi$
$47$	8.31103	+	3.44254i	1.21229	+	0.502146i	0.317338	+	0.948313i	$0.397211\pi$
$48$	−3.08620	+	2.54467i	−0.445455	+	0.367292i
$49$	17.7926	−	7.36993i	2.54180	−	1.05285i
$50$	−12.3271	+	8.24693i	−1.74331	+	1.16629i
$51$	−2.95666	+	0.896893i	−0.414015	+	0.125590i
$52$	−2.29817	+	4.31149i	−0.318699	+	0.597896i
$53$	−0.366200	−	3.71809i	−0.0503015	−	0.510720i	−0.987016	−	0.160624i	$-0.948649\pi$
$53$	−0.366200	−	3.71809i	−0.0503015	−	0.510720i	0.936714	−	0.350095i	$-0.113851\pi$
$54$	−0.139426	−	1.40732i	−0.0189734	−	0.191513i
$55$	−15.7514	−	3.13314i	−2.12391	−	0.422472i
$56$	12.0372	−	8.07304i	1.60854	−	1.07881i
$57$	0.402084	+	2.02142i	0.0532574	+	0.267743i
$58$	9.59977	+	5.12410i	1.26051	+	0.672827i
$59$	0.620862	−	2.04671i	0.0808293	−	0.266459i	−0.907206	−	0.420687i	$-0.861789\pi$
$59$	0.620862	−	2.04671i	0.0808293	−	0.266459i	0.988035	+	0.154228i	$0.0492891\pi$
$60$	−3.00367	+	7.27512i	−0.387772	+	0.939214i
$61$	−1.85378	+	1.52136i	−0.237352	+	0.194790i	−0.745548	−	0.666451i	$-0.767812\pi$
$61$	−1.85378	+	1.52136i	−0.237352	+	0.194790i	0.508196	+	0.861241i	$0.330312\pi$
$62$	1.00819	+	2.43004i	0.128041	+	0.308616i
$63$			5.12431i			0.645602i
$64$	5.63733	−	5.67632i	0.704666	−	0.709539i
$65$			9.61367i			1.19243i
$66$	−5.33068	+	2.21163i	−0.656161	+	0.272233i
$67$	−10.0924	+	8.28263i	−1.23299	+	1.01188i	−0.233769	+	0.972292i	$0.575106\pi$
$67$	−10.0924	+	8.28263i	−1.23299	+	1.01188i	−0.999216	+	0.0395927i	$0.987394\pi$
$68$	5.70630	−	2.37131i	0.691991	−	0.287564i
$69$	−1.08610	+	3.58040i	−0.130751	+	0.431030i
$70$	13.4295	−	25.1595i	1.60513	−	3.00713i
$71$	−1.13357	−	5.69887i	−0.134531	−	0.676331i	−0.987908	−	0.155038i	$-0.950450\pi$
$71$	−1.13357	−	5.69887i	−0.134531	−	0.676331i	0.853378	−	0.521293i	$-0.174550\pi$
$72$	0.556578	+	2.77312i	0.0655933	+	0.326816i
$73$	−3.80329	−	0.756522i	−0.445142	−	0.0885442i	−0.0325702	−	0.999469i	$-0.510369\pi$
$73$	−3.80329	−	0.756522i	−0.445142	−	0.0885442i	−0.412571	+	0.910925i	$0.635369\pi$
$74$	−2.99373	+	0.296593i	−0.348014	+	0.0344783i
$75$	1.02794	+	10.4368i	0.118696	+	1.20514i
$76$	−1.20109	−	3.94316i	−0.137775	−	0.452312i
$77$	20.0113	−	6.07037i	2.28050	−	0.691783i
$78$	1.92100	+	2.87141i	0.217511	+	0.325123i
$79$	−1.75819	+	0.728267i	−0.197812	+	0.0819364i	−0.479390	−	0.877602i	$-0.659142\pi$
$79$	−1.75819	+	0.728267i	−0.197812	+	0.0819364i	0.281578	+	0.959538i	$0.409142\pi$
$80$	4.53492	−	15.0742i	0.507019	−	1.68535i
$81$	−0.923880	−	0.382683i	−0.102653	−	0.0425204i
$82$	−0.154992	−	0.776863i	−0.0171160	−	0.0857902i
$83$	−1.95865	+	3.66437i	−0.214989	+	0.402217i	−0.966180	−	0.257869i	$-0.916980\pi$
$83$	−1.95865	+	3.66437i	−0.214989	+	0.402217i	0.751191	+	0.660085i	$0.229480\pi$
$84$	−1.01626	−	10.1981i	−0.110883	−	1.11270i
$85$	7.71371	−	9.39919i	0.836670	−	1.01948i
$86$	4.28324	+	8.00232i	0.461874	+	0.862913i
$87$	6.39778	−	4.27486i	0.685914	−	0.458313i
$88$	10.1702	−	5.45864i	1.08415	−	0.581893i
$89$	−7.24931	+	10.8494i	−0.768426	+	1.15003i	0.216370	+	0.976312i	$0.430578\pi$
$89$	−7.24931	+	10.8494i	−0.768426	+	1.15003i	−0.984795	+	0.173719i	$0.944422\pi$
$90$	3.53318	+	4.30015i	0.372430	+	0.453276i
$91$	−5.90096	−	11.0399i	−0.618589	−	1.15730i
$92$	1.45143	−	7.34091i	0.151322	−	0.765343i
$93$	1.85136	+	0.182343i	0.191977	+	0.0189081i
$94$	−8.99062	+	9.00096i	−0.927312	+	0.928378i
$95$	−5.73528	−	5.73528i	−0.588428	−	0.588428i
$96$	−1.65764	−	5.40853i	−0.169182	−	0.552006i
$97$	−7.28783	+	7.28783i	−0.739967	+	0.739967i	−0.972571	−	0.232604i	$-0.925275\pi$
$97$	−7.28783	+	7.28783i	−0.739967	+	0.739967i	0.232604	+	0.972571i	$0.425275\pi$
$98$	0.0156433	+	27.2357i	0.00158022	+	2.75122i
$99$	−0.399998	+	4.06125i	−0.0402013	+	0.408171i
$100$	−4.11558	−	20.5669i	−0.411558	−	2.05669i
$101$	−4.56924	+	2.44231i	−0.454656	+	0.243019i	−0.682795	−	0.730610i	$-0.739236\pi$
$101$	−4.56924	+	2.44231i	−0.454656	+	0.243019i	0.228139	+	0.973629i	$0.426736\pi$
$102$	0.425788	−	4.34870i	0.0421593	−	0.430586i
$103$	−13.5286	−	9.03953i	−1.33301	−	0.890691i	−0.334354	−	0.942448i	$-0.608518\pi$
$103$	−13.5286	−	9.03953i	−1.33301	−	0.890691i	−0.998660	+	0.0517568i	$0.983518\pi$
$104$	−4.39253	−	5.33355i	−0.430723	−	0.522997i
$105$	−11.2037	−	16.7676i	−1.09337	−	1.63635i
$106$	5.05699	+	1.53085i	0.491178	+	0.148689i
$107$	13.4083	+	11.0039i	1.29623	+	1.06379i	0.993865	+	0.110599i	$0.0352768\pi$
$107$	13.4083	+	11.0039i	1.29623	+	1.06379i	0.302367	+	0.953192i	$0.402223\pi$
$108$	1.91455	+	0.578370i	0.184227	+	0.0556537i
$109$	−8.10861	−	4.33414i	−0.776664	−	0.415135i	0.0349063	−	0.999391i	$-0.488887\pi$
$109$	−8.10861	−	4.33414i	−0.776664	−	0.415135i	−0.811570	+	0.584255i	$0.801387\pi$
$110$	12.6074	−	18.8917i	1.20207	−	1.80126i
$111$	−0.814064	+	1.96533i	−0.0772676	+	0.186540i
$112$	4.04499	+	20.0941i	0.382216	+	1.89872i
$113$	−6.77999	−	16.3684i	−0.637808	−	1.53980i	−0.829593	−	0.558368i	$-0.811428\pi$
$113$	−6.77999	−	16.3684i	−0.637808	−	1.53980i	0.191785	−	0.981437i	$-0.438572\pi$
$114$	−2.85904	−	0.566991i	−0.267774	−	0.0531036i
$115$	−4.27424	−	14.0903i	−0.398575	−	1.31393i
$116$	−11.8847	+	9.77639i	−1.10347	+	0.907715i
$117$	2.43111	−	0.239443i	0.224756	−	0.0221366i
$118$	2.33925	+	1.91752i	0.215345	+	0.176522i
$119$	−3.08878	+	15.5284i	−0.283148	+	1.42348i
$120$	−7.88434	−	7.85722i	−0.719739	−	0.717262i
$121$	5.54509	−	1.10299i	0.504099	−	0.100271i
$122$	−0.986355	−	3.24486i	−0.0893003	−	0.293776i
$123$	−0.536031	−	0.162603i	−0.0483323	−	0.0146614i
$124$	−3.72063	+	0.00427403i	−0.334123	+	0.000383819i
$125$	−13.6996	−	16.6930i	−1.22533	−	1.49307i
$126$	−6.69682	−	2.76941i	−0.596601	−	0.246719i
$127$	5.01419			0.444938			0.222469	−	0.974940i	$-0.428588\pi$
$127$	5.01419			0.444938			0.222469	+	0.974940i	$0.428588\pi$
$128$	4.37156	+	10.4350i	0.386395	+	0.922333i
$129$	6.41807			0.565080
$130$	−12.5639	−	5.19567i	−1.10192	−	0.455690i
$131$	−2.99998	−	3.65549i	−0.262109	−	0.319381i	0.625281	−	0.780399i	$-0.284984\pi$
$131$	−2.99998	−	3.65549i	−0.262109	−	0.319381i	−0.887391	+	0.461018i	$0.847484\pi$
$132$	−0.00937576	−	8.16179i	−0.000816055	−	0.710393i
$133$	10.1065	+	3.06578i	0.876347	+	0.265837i
$134$	−5.36995	−	17.6658i	−0.463893	−	1.52610i
$135$	3.85978	−	0.767757i	0.332197	−	0.0660780i
$136$	0.0150582	+	8.73898i	0.00129123	+	0.749362i
$137$	2.18236	−	10.9715i	0.186452	−	0.937356i	−0.768331	−	0.640052i	$-0.778913\pi$
$137$	2.18236	−	10.9715i	0.186452	−	0.937356i	0.954783	−	0.297303i	$-0.0960873\pi$
$138$	−4.09215	−	3.35441i	−0.348347	−	0.285546i
$139$	−11.9285	+	1.17486i	−1.01176	+	0.0996499i	−0.590290	−	0.807191i	$-0.700987\pi$
$139$	−11.9285	+	1.17486i	−1.01176	+	0.0996499i	−0.421473	+	0.906841i	$0.638487\pi$
$140$	25.6224	+	31.1479i	2.16549	+	2.63248i
$141$	2.61134	+	8.60844i	0.219915	+	0.724961i
$142$	8.06033	+	1.59849i	0.676408	+	0.134142i
$143$	−3.81502	−	9.21026i	−0.319028	−	0.770201i
$144$	−3.92492	−	0.771346i	−0.327077	−	0.0642788i
$145$	−11.5881	+	27.9761i	−0.962336	+	2.32329i
$146$	3.04415	−	4.56156i	0.251936	−	0.377518i
$147$	16.9845	+	9.07842i	1.40086	+	0.748775i
$148$	1.23034	−	4.07272i	0.101133	−	0.334776i
$149$	−2.61530	−	2.14632i	−0.214253	−	0.175833i	0.521145	−	0.853468i	$-0.325505\pi$
$149$	−2.61530	−	2.14632i	−0.214253	−	0.175833i	−0.735399	+	0.677635i	$0.763005\pi$
$150$	−14.1952	−	4.29716i	−1.15903	−	0.350861i
$151$	−3.88355	−	5.81215i	−0.316039	−	0.472986i	0.639108	−	0.769117i	$-0.279304\pi$
$151$	−3.88355	−	5.81215i	−0.316039	−	0.472986i	−0.955147	+	0.296131i	$0.904304\pi$
$152$	5.80234	+	0.561388i	0.470632	+	0.0455345i
$153$	−2.56899	−	1.71655i	−0.207691	−	0.138775i
$154$	−2.88183	+	29.4330i	−0.232224	+	2.37178i
$155$	−6.45662	+	3.45113i	−0.518608	+	0.277202i
$156$	−4.79077	+	0.958666i	−0.383569	+	0.0767547i
$157$	−1.71590	+	17.4219i	−0.136944	+	1.39042i	0.643623	+	0.765343i	$0.277431\pi$
$157$	−1.71590	+	17.4219i	−0.136944	+	1.39042i	−0.780567	+	0.625072i	$0.785069\pi$
$158$	−0.00154581	−	2.69132i	−0.000122978	−	0.214110i
$159$	2.64181	−	2.64181i	0.209509	−	0.209509i
$160$	17.2492	+	14.0734i	1.36367	+	1.11260i
$161$	13.5571	+	13.5571i	1.06845	+	1.06845i
$162$	0.999425	−	1.00057i	0.0785223	−	0.0786125i
$163$	13.1535	+	1.29551i	1.03026	+	0.101472i	0.598995	−	0.800753i	$-0.295567\pi$
$163$	13.1535	+	1.29551i	1.03026	+	0.101472i	0.431266	+	0.902225i	$0.358067\pi$
$164$	1.09903	+	0.217298i	0.0858195	+	0.0169681i
$165$	−7.57060	−	14.1636i	−0.589371	−	1.10264i
$166$	−3.73033	−	4.54009i	−0.289529	−	0.352380i
$167$	2.97873	−	4.45799i	0.230501	−	0.344970i	−0.698132	−	0.715969i	$-0.745985\pi$
$167$	2.97873	−	4.45799i	0.230501	−	0.344970i	0.928633	+	0.371000i	$0.120985\pi$
$168$	13.8769	+	4.18340i	1.07062	+	0.322757i
$169$	5.84720	−	3.90698i	0.449785	−	0.300537i
$170$	8.11471	+	15.1606i	0.622370	+	1.16276i
$171$	−1.30750	+	1.59319i	−0.0999867	+	0.121834i
$172$	−12.7729	+	1.27284i	−0.973923	+	0.0970528i
$173$	−5.29367	+	9.90376i	−0.402470	+	0.752969i	−0.998759	−	0.0498012i	$-0.984141\pi$
$173$	−5.29367	+	9.90376i	−0.402470	+	0.752969i	0.596289	+	0.802770i	$0.296641\pi$
$174$	2.12905	+	10.6714i	0.161403	+	0.808998i
$175$	49.6496	+	20.5655i	3.75316	+	1.55461i
$176$	1.63731	+	16.2413i	0.123417	+	1.22423i
$177$	1.97600	−	0.818485i	0.148525	−	0.0615211i
$178$	−10.2609	−	15.3374i	−0.769086	−	1.14959i
$179$	−10.7040	+	3.24701i	−0.800051	+	0.242693i	−0.663730	−	0.747972i	$-0.731028\pi$
$179$	−10.7040	+	3.24701i	−0.800051	+	0.242693i	−0.136321	+	0.990665i	$0.543528\pi$
$180$	−7.52925	+	2.29342i	−0.561197	+	0.170941i
$181$	1.42092	+	14.4268i	0.105616	+	1.07234i	0.891208	+	0.453594i	$0.149858\pi$
$181$	1.42092	+	14.4268i	0.105616	+	1.07234i	−0.785592	+	0.618745i	$0.787642\pi$
$182$	17.6169	−	1.74533i	1.30585	−	0.129373i
$183$	−2.35205	−	0.467852i	−0.173868	−	0.0345846i
$184$	8.80922	+	5.86420i	0.649424	+	0.432315i
$185$	−1.63321	−	8.21072i	−0.120076	−	0.603664i
$186$	−1.23886	+	2.32095i	−0.0908375	+	0.170180i
$187$	−3.66013	+	12.0658i	−0.267655	+	0.882341i
$188$	−6.90417	−	16.6141i	−0.503538	−	1.21171i
$189$	−3.96114	+	3.25083i	−0.288131	+	0.236463i
$190$	10.5949	−	4.39568i	0.768635	−	0.318896i
$191$		−	4.65126i		−	0.336553i	−0.985740	−	0.168277i	$-0.946180\pi$
$191$		−	4.65126i		−	0.336553i	0.985740	−	0.168277i	$-0.0538202\pi$
$192$	7.96413	+	0.756696i	0.574762	+	0.0546098i
$193$			19.6126i			1.41174i	0.708339	+	0.705872i	$0.249445\pi$
$193$			19.6126i			1.41174i	−0.708339	+	0.705872i	$0.750555\pi$
$194$	−5.58560	−	13.4629i	−0.401022	−	0.966583i
$195$	−7.43147	+	6.09885i	−0.532179	+	0.436748i
$196$	−35.6021	−	14.6990i	−2.54300	−	1.04993i
$197$	0.532057	−	1.75396i	0.0379075	−	0.124964i	−0.935945	−	0.352147i	$-0.885452\pi$
$197$	0.532057	−	1.75396i	0.0379075	−	0.124964i	0.973852	+	0.227183i	$0.0729516\pi$
$198$	−5.09136	−	2.71763i	−0.361827	−	0.193134i
$199$	0.875615	+	4.40202i	0.0620707	+	0.312051i	0.999331	−	0.0365806i	$-0.0116466\pi$
$199$	0.875615	+	4.40202i	0.0620707	+	0.312051i	−0.937260	+	0.348631i	$0.886647\pi$
$200$	29.1026	+	5.73676i	2.05787	+	0.405650i
$201$	−12.8051	−	2.54710i	−0.903204	−	0.179658i
$202$	−0.722364	−	7.29135i	−0.0508254	−	0.513018i
$203$	−3.86474	−	39.2394i	−0.271252	−	2.75406i
$204$	5.45309	+	2.90669i	0.381793	+	0.203509i
$205$	2.10949	−	0.639908i	0.147333	−	0.0446931i
$206$	19.1250	−	12.7948i	1.33250	−	0.891456i
$207$	−3.45670	+	1.43181i	−0.240258	+	0.0995179i
$208$	9.34419	−	2.85799i	0.647903	−	0.198166i
$209$	7.77056	+	3.21867i	0.537501	+	0.222640i
$210$	27.9681	−	5.57990i	1.92998	−	0.385050i
$211$	−4.90361	+	9.17400i	−0.337578	+	0.631564i	−0.992237	−	0.124360i	$-0.960312\pi$
$211$	−4.90361	+	9.17400i	−0.337578	+	0.631564i	0.654659	+	0.755924i	$0.272812\pi$
$212$	−4.73366	+	5.78151i	−0.325109	+	0.397075i
$213$	3.68615	−	4.49159i	0.252571	−	0.307759i
$214$	−21.6272	+	11.5760i	−1.47841	+	0.791317i
$215$	−21.0010	+	14.0324i	−1.43225	+	0.957002i
$216$	−1.79057	+	2.18949i	−0.121833	+	0.148976i
$217$	5.29616	−	7.92627i	0.359527	−	0.538070i
$218$	10.0464	−	8.25456i	0.680430	−	0.559069i
$219$	−1.82798	−	3.41992i	−0.123524	−	0.231097i
$220$	17.8755	+	26.6862i	1.20517	+	1.79918i
$221$	7.51141	+	0.739809i	0.505272	+	0.0497649i
$222$	−2.12847	−	2.12603i	−0.142854	−	0.142690i
$223$	−6.46512	−	6.46512i	−0.432937	−	0.432937i	0.456689	−	0.889626i	$-0.349035\pi$
$223$	−6.46512	−	6.46512i	−0.432937	−	0.432937i	−0.889626	+	0.456689i	$0.849035\pi$
$224$	−28.4466	−	5.57350i	−1.90067	−	0.372395i
$225$	−7.41567	+	7.41567i	−0.494378	+	0.494378i
$226$	25.0556	−	0.0143911i	1.66667	−	0.000957285i
$227$	0.656937	−	6.67000i	0.0436025	−	0.442703i	−0.948454	−	0.316913i	$-0.897354\pi$
$227$	0.656937	−	6.67000i	0.0436025	−	0.442703i	0.992057	−	0.125790i	$-0.0401465\pi$
$228$	2.28614	−	3.42997i	0.151403	−	0.227156i
$229$	−9.38622	+	5.01704i	−0.620259	+	0.331535i	−0.751418	−	0.659826i	$-0.770630\pi$
$229$	−9.38622	+	5.01704i	−0.620259	+	0.331535i	0.131160	+	0.991361i	$0.458130\pi$
$230$	20.7242	+	2.02914i	1.36652	+	0.133798i
$231$	17.3875	+	11.6180i	1.14401	+	0.764406i
$232$	−6.35347	−	20.8154i	−0.417126	−	1.36660i
$233$	−2.06306	−	3.08758i	−0.135155	−	0.202274i	0.757718	−	0.652582i	$-0.226314\pi$
$233$	−2.06306	−	3.08758i	−0.135155	−	0.202274i	−0.892873	+	0.450308i	$0.851314\pi$
$234$	−1.00096	+	3.30656i	−0.0654348	+	0.216157i
$235$	−27.3661	−	22.4588i	−1.78517	−	1.46505i
$236$	−3.77019	+	2.02078i	−0.245419	+	0.131542i
$237$	−1.67834	−	0.897093i	−0.109020	−	0.0582725i
$238$	−18.6243	−	12.4289i	−1.20723	−	0.805645i
$239$	−11.4520	+	27.6475i	−0.740767	+	1.78837i	−0.138033	+	0.990428i	$0.544078\pi$
$239$	−11.4520	+	27.6475i	−0.740767	+	1.78837i	−0.602734	+	0.797942i	$0.705922\pi$
$240$	14.5294	−	6.05744i	0.937872	−	0.391006i
$241$	−2.19510	−	5.29944i	−0.141399	−	0.341367i	0.837277	−	0.546780i	$-0.184146\pi$
$241$	−2.19510	−	5.29944i	−0.141399	−	0.341367i	−0.978675	+	0.205412i	$0.934146\pi$
$242$	−1.55535	+	7.84283i	−0.0999819	+	0.504156i
$243$	−0.290285	−	0.956940i	−0.0186218	−	0.0613878i
$244$	4.77370	+	0.464632i	0.305605	+	0.0297450i
$245$	−75.4251	+	7.42872i	−4.81873	+	0.474603i
$246$	0.502198	−	0.612647i	0.0320189	−	0.0390609i
$247$	0.982242	−	4.93806i	0.0624985	−	0.314201i
$248$	2.00521	−	4.86471i	0.127331	−	0.308909i
$249$	−4.07515	+	0.810597i	−0.258252	+	0.0513695i
$250$	29.2196	−	8.88199i	1.84801	−	0.561746i
$251$	1.67257	+	0.507367i	0.105571	+	0.0320247i	0.342628	−	0.939471i	$-0.388683\pi$
$251$	1.67257	+	0.507367i	0.105571	+	0.0320247i	−0.237057	+	0.971496i	$0.576183\pi$
$252$	7.23854	−	7.25519i	0.455985	−	0.457034i
$253$	9.68637	+	11.8029i	0.608977	+	0.742041i
$254$	−2.70990	+	6.55291i	−0.170034	+	0.411166i
$255$	12.1592			0.761439
$256$	−15.9998	+	0.0735189i	−0.999989	+	0.00459493i
$257$	12.8263			0.800080			0.400040	−	0.916498i	$-0.368996\pi$
$257$	12.8263			0.800080			0.400040	+	0.916498i	$0.368996\pi$
$258$	−3.46862	+	8.38761i	−0.215947	+	0.522190i
$259$	6.91533	+	8.42636i	0.429698	+	0.523588i
$260$	13.5802	−	13.6114i	0.842206	−	0.844143i
$261$	7.36322	+	2.23361i	0.455772	+	0.138257i
$262$	6.39858	−	1.94500i	0.395306	−	0.120163i
$263$	22.5322	−	4.48193i	1.38939	−	0.276368i	0.556982	−	0.830524i	$-0.311959\pi$
$263$	22.5322	−	4.48193i	1.38939	−	0.276368i	0.832412	+	0.554157i	$0.186959\pi$
$264$	10.6715	+	4.39875i	0.656785	+	0.270724i
$265$	−2.86841	+	14.4205i	−0.176205	+	0.885842i
$266$	−9.46861	+	11.5511i	−0.580558	+	0.708241i
$267$	−12.9856	+	1.27897i	−0.794705	+	0.0782716i
$268$	25.9892	+	2.52957i	1.58754	+	0.154518i
$269$	0.972712	+	3.20660i	0.0593073	+	0.195510i	0.981588	−	0.191011i	$-0.0611767\pi$
$269$	0.972712	+	3.20660i	0.0593073	+	0.195510i	−0.922281	+	0.386521i	$0.873677\pi$
$270$	−1.08264	+	5.45917i	−0.0658872	+	0.332235i
$271$	2.21994	+	5.35941i	0.134852	+	0.325561i	0.976852	−	0.213916i	$-0.0686219\pi$
$271$	2.21994	+	5.35941i	0.134852	+	0.325561i	−0.842000	+	0.539477i	$0.818622\pi$
$272$	−11.4289	−	4.70327i	−0.692978	−	0.285177i
$273$	4.79045	−	11.5652i	0.289931	−	0.699955i
$274$	13.1589	+	8.78155i	0.794957	+	0.530513i
$275$	37.7442	+	20.1747i	2.27606	+	1.21658i
$276$	6.59538	−	3.53505i	0.396995	−	0.212785i
$277$	−2.74370	−	2.25170i	−0.164853	−	0.135292i	0.548350	−	0.836249i	$-0.315256\pi$
$277$	−2.74370	−	2.25170i	−0.164853	−	0.135292i	−0.713203	+	0.700958i	$0.752756\pi$
$278$	4.91132	−	16.2240i	0.294562	−	0.973051i
$279$	1.03354	+	1.54680i	0.0618762	+	0.0926043i
$280$	−54.5539	+	16.6515i	−3.26022	+	0.995115i
$281$	10.5721	+	7.06408i	0.630681	+	0.421408i	0.829405	−	0.558648i	$-0.188680\pi$
$281$	10.5721	+	7.06408i	0.630681	+	0.421408i	−0.198724	+	0.980056i	$0.563680\pi$
$282$	−12.6614	−	1.23970i	−0.753977	−	0.0738230i
$283$	−5.26463	+	2.81401i	−0.312950	+	0.167275i	−0.620393	−	0.784291i	$-0.713027\pi$
$283$	−5.26463	+	2.81401i	−0.312950	+	0.167275i	0.307443	+	0.951567i	$0.400527\pi$
$284$	−6.44519	+	9.66994i	−0.382452	+	0.573805i
$285$	0.795009	−	8.07186i	0.0470923	−	0.478136i
$286$	14.0985	−	0.00809771i	0.833659	−	0.000478828i
$287$	−2.02967	+	2.02967i	−0.119808	+	0.119808i
$288$	3.12926	−	4.71251i	0.184393	−	0.277687i
$289$	5.27059	+	5.27059i	0.310035	+	0.310035i
$290$	−30.2985	−	30.2637i	−1.77919	−	1.77714i
$291$	−10.2569	−	1.01022i	−0.601271	−	0.0592200i
$292$	4.31619	+	6.44359i	0.252586	+	0.377083i
$293$	−10.0949	−	18.8863i	−0.589753	−	1.10335i	−0.982946	−	0.183894i	$-0.941130\pi$
$293$	−10.0949	−	18.8863i	−0.589753	−	1.10335i	0.393193	−	0.919456i	$-0.371370\pi$
$294$	−21.0436	+	17.2902i	−1.22729	+	1.00839i
$295$	−4.67626	+	6.99851i	−0.272262	+	0.407469i
$296$	4.65760	+	3.80898i	0.270718	+	0.221393i
$297$	−3.39314	+	2.26722i	−0.196890	+	0.131558i
$298$	4.21839	−	2.25789i	0.244365	−	0.130796i
$299$	5.79838	−	7.06534i	0.335329	−	0.408599i
$300$	13.2876	−	16.2289i	0.767157	−	0.936977i
$301$	15.5034	−	29.0048i	0.893600	−	1.67181i
$302$	9.69459	−	1.93416i	0.557861	−	0.111299i
$303$	−4.78662	−	1.98268i	−0.274984	−	0.113902i
$304$	−3.86951	+	7.27953i	−0.221932	+	0.417510i
$305$	8.71919	−	3.61161i	0.499259	−	0.206800i
$306$	3.63171	−	2.42965i	0.207611	−	0.138894i
$307$	−7.40177	+	2.24530i	−0.422441	+	0.128146i	−0.494346	−	0.869265i	$-0.664592\pi$
$307$	−7.40177	+	2.24530i	−0.422441	+	0.128146i	0.0719044	+	0.997412i	$0.477092\pi$
$308$	−36.9077	−	19.6731i	−2.10301	−	1.12098i
$309$	−1.59481	−	16.1924i	−0.0907255	−	0.921152i
$310$	−1.02075	−	10.3031i	−0.0579745	−	0.585179i
$311$	−15.0497	−	2.99357i	−0.853390	−	0.169750i	−0.251035	−	0.967978i	$-0.580771\pi$
$311$	−15.0497	−	2.99357i	−0.853390	−	0.169750i	−0.602355	+	0.798228i	$0.705771\pi$
$312$	1.33630	−	6.77904i	0.0756528	−	0.383787i
$313$	−4.33204	−	21.7787i	−0.244862	−	1.23100i	−0.886039	−	0.463610i	$-0.846554\pi$
$313$	−4.33204	−	21.7787i	−0.244862	−	1.23100i	0.641178	−	0.767392i	$-0.278446\pi$
$314$	−21.8408	−	11.6580i	−1.23255	−	0.657901i
$315$	5.85393	−	19.2978i	0.329832	−	1.08731i
$316$	3.51806	+	1.45249i	0.197906	+	0.0817092i
$317$	−2.40787	+	1.97609i	−0.135240	+	0.110988i	−0.699581	−	0.714553i	$-0.746630\pi$
$317$	−2.40787	+	1.97609i	−0.135240	+	0.110988i	0.564342	+	0.825541i	$0.309130\pi$
$318$	2.02476	+	4.88027i	0.113543	+	0.273672i
$319$		−	31.4006i		−	1.75810i
$320$	−27.7144	+	14.9367i	−1.54928	+	0.834985i
$321$			17.3456i			0.968137i
$322$	−25.0443	+	10.3906i	−1.39567	+	0.579043i
$323$	−4.92248	+	4.03977i	−0.273894	+	0.224779i
$324$	0.767489	+	1.84688i	0.0426383	+	0.102604i
$325$	7.43687	−	24.5161i	0.412523	−	1.35991i
$326$	−8.80181	+	16.4898i	−0.487487	+	0.913286i
$327$	−1.79371	−	9.01759i	−0.0991924	−	0.498674i
$328$	−0.877944	+	1.31885i	−0.0484764	+	0.0728213i
$329$	45.2115	+	8.99312i	2.49259	+	0.495807i
$330$	22.6015	−	2.23917i	1.24417	−	0.123262i
$331$	0.623059	+	6.32602i	0.0342464	+	0.347710i	0.997004	+	0.0773450i	$0.0246443\pi$
$331$	0.623059	+	6.32602i	0.0342464	+	0.347710i	−0.962758	+	0.270365i	$0.912856\pi$
$332$	7.94937	−	2.42139i	0.436278	−	0.132891i
$333$	−2.03565	+	0.617509i	−0.111553	+	0.0338393i
$334$	4.21619	+	6.30213i	0.230699	+	0.344837i
$335$	47.4694	−	19.6625i	2.59353	−	1.07428i
$336$	−12.9669	+	15.8744i	−0.707401	+	0.866020i
$337$	−4.08828	−	1.69342i	−0.222703	−	0.0922464i	0.268542	−	0.963268i	$-0.413458\pi$
$337$	−4.08828	−	1.69342i	−0.222703	−	0.0922464i	−0.491245	+	0.871021i	$0.663458\pi$
$338$	1.94583	+	9.75306i	0.105839	+	0.530497i
$339$	8.35172	−	15.6250i	0.453603	−	0.848632i
$340$	−24.1985	+	2.41142i	−1.31235	+	0.130778i
$341$	4.81616	−	5.86851i	0.260810	−	0.317798i
$342$	−1.37546	−	2.56976i	−0.0743766	−	0.138957i
$343$	52.2301	−	34.8990i	2.82016	−	1.88437i
$344$	5.23961	−	17.3804i	0.282501	−	0.937090i
$345$	8.18039	−	12.2428i	0.440418	−	0.659132i
$346$	−10.0820	−	12.2706i	−0.542013	−	0.659671i
$347$	14.4060	+	26.9517i	0.773353	+	1.44684i	0.891104	+	0.453799i	$0.149932\pi$
$347$	14.4060	+	26.9517i	0.773353	+	1.44684i	−0.117751	+	0.993043i	$0.537568\pi$
$348$	−15.0968	−	2.98492i	−0.809275	−	0.160009i
$349$	6.72585	+	0.662439i	0.360027	+	0.0354595i	0.276414	−	0.961039i	$-0.410854\pi$
$349$	6.72585	+	0.662439i	0.360027	+	0.0354595i	0.0836131	+	0.996498i	$0.473354\pi$
$350$	−53.7095	+	53.7712i	−2.87089	+	2.87419i
$351$	1.72737	+	1.72737i	0.0922003	+	0.0922003i
$352$	−22.1102	−	6.63776i	−1.17848	−	0.353794i
$353$	−3.16205	+	3.16205i	−0.168299	+	0.168299i	−0.786231	−	0.617932i	$-0.787971\pi$
$353$	−3.16205	+	3.16205i	−0.168299	+	0.168299i	0.617932	+	0.786231i	$0.287971\pi$
$354$	0.00173731	+	3.02472i	9.23369e−5	+	0.160762i
$355$	−2.24133	+	22.7566i	−0.118957	+	1.20779i
$356$	25.5895	−	5.12064i	1.35624	−	0.271393i
$357$	−13.9631	+	7.46343i	−0.739005	+	0.395007i
$358$	1.54147	−	15.7435i	0.0814694	−	0.832072i
$359$	−12.2920	−	8.21322i	−0.648744	−	0.433477i	0.187177	−	0.982326i	$-0.440066\pi$
$359$	−12.2920	−	8.21322i	−0.648744	−	0.433477i	−0.835921	+	0.548849i	$0.815066\pi$
$360$	1.07194	−	11.0792i	0.0564961	−	0.583927i
$361$	−8.19589	−	12.2660i	−0.431363	−	0.645580i
$362$	−19.6220	−	5.93996i	−1.03131	−	0.312197i
$363$	4.37039	+	3.58668i	0.229386	+	0.188252i
$364$	−7.24006	+	23.9664i	−0.379482	+	1.25618i
$365$	13.4587	+	7.19384i	0.704462	+	0.376543i
$366$	1.88258	−	2.82098i	0.0984039	−	0.147455i
$367$	−4.38689	+	10.5909i	−0.228994	+	0.552839i	−0.996055	−	0.0887339i	$-0.971718\pi$
$367$	−4.38689	+	10.5909i	−0.228994	+	0.552839i	0.767062	+	0.641573i	$0.221718\pi$
$368$	−12.4247	+	8.34325i	−0.647681	+	0.434922i
$369$	−0.214361	−	0.517512i	−0.0111592	−	0.0269406i
$370$	11.6130	+	2.30304i	0.603733	+	0.119730i
$371$	−5.55746	−	18.3205i	−0.288529	−	0.951152i
$372$	−2.36365	−	2.87338i	−0.122549	−	0.148978i
$373$	−25.0702	+	2.46920i	−1.29809	+	0.127850i	−0.723346	−	0.690486i	$-0.757397\pi$
$373$	−25.0702	+	2.46920i	−1.29809	+	0.127850i	−0.574740	+	0.818336i	$0.694897\pi$
$374$	−13.7904	−	11.3042i	−0.713085	−	0.584529i
$375$	4.21294	−	21.1799i	0.217555	−	1.09372i
$376$	25.4439	−	0.0438426i	1.31217	−	0.00226101i
$377$	−18.4356	+	3.66707i	−0.949483	+	0.188864i
$378$	−2.10764	−	6.93361i	−0.108405	−	0.356626i
$379$	34.0005	+	10.3139i	1.74649	+	0.529791i	0.991968	−	0.126489i	$-0.0403707\pi$
$379$	34.0005	+	10.3139i	1.74649	+	0.529791i	0.754518	+	0.656279i	$0.227871\pi$
$380$	0.0186346	+	16.2218i	0.000955936	+	0.832162i
$381$	3.18097	+	3.87602i	0.162966	+	0.198575i
$382$	6.07861	+	2.51375i	0.311009	+	0.128615i
$383$	13.7405			0.702107			0.351054	−	0.936355i	$-0.385823\pi$
$383$	13.7405			0.702107			0.351054	+	0.936355i	$0.385823\pi$
$384$	−5.29309	+	9.99916i	−0.270112	+	0.510268i
$385$	−82.2961			−4.19420
$386$	−25.6312	−	10.5995i	−1.30459	−	0.539502i
$387$	4.07158	+	4.96124i	0.206970	+	0.252194i
$388$	20.6131	−	0.0236790i	1.04647	−	0.00120212i
$389$	9.32881	+	2.82986i	0.472990	+	0.143480i	0.517775	−	0.855517i	$-0.326760\pi$
$389$	9.32881	+	2.82986i	0.472990	+	0.143480i	−0.0447855	+	0.998997i	$0.514260\pi$
$390$	−3.95412	−	13.0081i	−0.200225	−	0.658690i
$391$	−11.3380	+	2.25527i	−0.573389	+	0.114054i
$392$	38.4507	−	38.5834i	1.94205	−	1.94876i
$393$	0.922562	−	4.63803i	0.0465371	−	0.233958i
$394$	2.00465	+	1.64325i	0.100993	+	0.0827856i
$395$	7.45320	−	0.734077i	0.375011	−	0.0369354i
$396$	6.30320	−	5.18503i	0.316748	−	0.260558i
$397$	1.92717	+	6.35302i	0.0967217	+	0.318849i	0.991928	−	0.126803i	$-0.0404718\pi$
$397$	1.92717	+	6.35302i	0.0967217	+	0.318849i	−0.895206	+	0.445652i	$0.852972\pi$
$398$	−6.22610	−	1.23473i	−0.312086	−	0.0618915i
$399$	4.04163	+	9.75736i	0.202335	+	0.488479i
$400$	−23.2256	+	34.9331i	−1.16128	+	1.74665i
$401$	−8.09466	+	19.5422i	−0.404228	+	0.975893i	0.582399	+	0.812903i	$0.302114\pi$
$401$	−8.09466	+	19.5422i	−0.404228	+	0.975893i	−0.986628	+	0.162991i	$0.947886\pi$
$402$	10.2492	−	15.3581i	0.511184	−	0.765993i
$403$	−4.00791	−	2.14227i	−0.199648	−	0.106714i
$404$	9.91927	+	2.99654i	0.493502	+	0.149083i
$405$	3.04210	+	2.49659i	0.151163	+	0.124056i
$406$	53.3696	+	16.1560i	2.64869	+	0.801809i
$407$	4.82296	+	7.21807i	0.239065	+	0.357786i
$408$	−6.74577	+	5.55559i	−0.333966	+	0.275043i
$409$	5.13865	+	3.43354i	0.254090	+	0.169777i	0.676092	−	0.736818i	$-0.263672\pi$
$409$	5.13865	+	3.43354i	0.254090	+	0.169777i	−0.422002	+	0.906595i	$0.638672\pi$
$410$	−0.303788	+	3.10268i	−0.0150030	+	0.153230i
$411$	9.86553	−	5.27324i	0.486631	−	0.260110i
$412$	6.38518	+	31.9088i	0.314575	+	1.57204i
$413$	1.07426	−	10.9071i	0.0528607	−	0.536704i
$414$	−0.00303915	−	5.29129i	−0.000149366	−	0.260053i
$415$	11.5623	−	11.5623i	0.567569	−	0.567569i
$416$	−1.31500	+	13.7563i	−0.0644730	+	0.674457i
$417$	−8.47554	−	8.47554i	−0.415049	−	0.415049i
$418$	−8.40597	+	8.41563i	−0.411149	+	0.411622i
$419$	15.3634	+	1.51316i	0.750549	+	0.0739226i	0.466056	−	0.884755i	$-0.345675\pi$
$419$	15.3634	+	1.51316i	0.750549	+	0.0739226i	0.284493	+	0.958678i	$0.408175\pi$
$420$	−7.82301	+	39.5664i	−0.381724	+	1.93064i
$421$	12.2531	+	22.9239i	0.597179	+	1.11724i	0.981031	+	0.193849i	$0.0620973\pi$
$421$	12.2531	+	22.9239i	0.597179	+	1.11724i	−0.383852	+	0.923395i	$0.625403\pi$
$422$	−9.33913	−	11.3664i	−0.454622	−	0.553310i
$423$	−4.99779	+	7.47973i	−0.243001	+	0.363677i
$424$	−4.99741	−	9.31088i	−0.242696	−	0.452176i
$425$	−26.9419	+	18.0020i	−1.30687	+	0.873225i
$426$	3.87777	+	7.24479i	0.187879	+	0.351011i
$427$	−7.79590	+	9.49934i	−0.377270	+	0.459705i
$428$	−3.43999	−	34.5202i	−0.166278	−	1.66860i
$429$	4.69941	−	8.79197i	0.226890	−	0.424481i
$430$	−6.98869	−	35.0294i	−0.337025	−	1.68927i
$431$	−32.2738	−	13.3683i	−1.55458	−	0.643926i	−0.570440	−	0.821340i	$-0.693227\pi$
$431$	−32.2738	−	13.3683i	−1.55458	−	0.643926i	−0.984136	+	0.177413i	$0.943227\pi$
$432$	−1.89369	−	3.52334i	−0.0911100	−	0.169517i
$433$	23.4669	−	9.72033i	1.12775	−	0.467129i	0.260734	−	0.965411i	$-0.416035\pi$
$433$	23.4669	−	9.72033i	1.12775	−	0.467129i	0.867015	+	0.498282i	$0.166035\pi$
$434$	7.49634	+	11.2051i	0.359836	+	0.537864i
$435$	−28.9772	+	8.79013i	−1.38935	+	0.421454i
$436$	5.35811	+	17.5906i	0.256607	+	0.842435i
$437$	0.755841	+	7.67418i	0.0361568	+	0.367106i
$438$	5.45732	−	0.540665i	0.260761	−	0.0258339i
$439$	−30.4892	−	6.06467i	−1.45517	−	0.289451i	−0.596761	−	0.802419i	$-0.703546\pi$
$439$	−30.4892	−	6.06467i	−1.45517	−	0.289451i	−0.858408	+	0.512968i	$0.828546\pi$
$440$	−44.5362	+	8.93861i	−2.12318	+	0.426132i
$441$	3.75716	+	18.8885i	0.178912	+	0.899452i
$442$	−5.02634	+	9.41663i	−0.239079	+	0.447903i
$443$	7.86970	−	25.9429i	0.373901	−	1.23259i	−0.545114	−	0.838362i	$-0.683514\pi$
$443$	7.86970	−	25.9429i	0.373901	−	1.23259i	0.919015	−	0.394223i	$-0.128986\pi$
$444$	3.92878	−	1.63264i	0.186452	−	0.0774818i
$445$	39.6946	−	32.5765i	1.88171	−	1.54428i
$446$	11.9431	−	4.95505i	0.565524	−	0.234629i
$447$		−	3.38326i		−	0.160023i
$448$	22.6577	−	34.1639i	1.07048	−	1.61409i
$449$		−	30.7136i		−	1.44947i	−0.689030	−	0.724733i	$-0.741963\pi$
$449$		−	30.7136i		−	1.44947i	0.689030	−	0.724733i	$-0.258037\pi$
$450$	−5.68357	−	13.6991i	−0.267926	−	0.645782i
$451$	−1.76704	+	1.45017i	−0.0832066	+	0.0682859i
$452$	−13.5224	+	32.7523i	−0.636039	+	1.54054i
$453$	2.02915	−	6.68921i	0.0953378	−	0.314287i
$454$	8.36181	+	4.46330i	0.392439	+	0.209473i
$455$	9.61082	+	48.3168i	0.450562	+	2.26513i
$456$	3.24701	+	4.84141i	0.152055	+	0.226720i
$457$	−34.9753	−	6.95701i	−1.63607	−	0.325435i	−0.710412	−	0.703786i	$-0.751491\pi$
$457$	−34.9753	−	6.95701i	−1.63607	−	0.325435i	−0.925662	+	0.378351i	$0.876491\pi$
$458$	−1.48390	−	14.9780i	−0.0693379	−	0.699878i
$459$	−0.302844	−	3.07482i	−0.0141355	−	0.143521i
$460$	−13.8521	+	25.9873i	−0.645860	+	1.21166i
$461$	−35.7040	+	10.8307i	−1.66290	+	0.504435i	−0.975156	−	0.221518i	$-0.928899\pi$
$461$	−35.7040	+	10.8307i	−1.66290	+	0.504435i	−0.687744	+	0.725953i	$0.741399\pi$
$462$	−24.5802	+	16.4444i	−1.14357	+	0.765063i
$463$	−10.7240	+	4.44201i	−0.498385	+	0.206438i	−0.617693	−	0.786419i	$-0.711933\pi$
$463$	−10.7240	+	4.44201i	−0.498385	+	0.206438i	0.119308	+	0.992857i	$0.461933\pi$
$464$	30.6368	+	2.94641i	1.42228	+	0.136784i
$465$	−6.76380	−	2.80166i	−0.313664	−	0.129924i
$466$	5.15005	−	1.02748i	0.238571	−	0.0475973i
$467$	3.54868	−	6.63912i	0.164213	−	0.307222i	−0.786334	−	0.617802i	$-0.788023\pi$
$467$	3.54868	−	6.63912i	0.164213	−	0.307222i	0.950547	+	0.310580i	$0.100523\pi$
$468$	−3.78029	−	3.09514i	−0.174744	−	0.143073i
$469$	−42.4428	+	51.7167i	−1.95983	+	2.38805i
$470$	44.1407	−	23.6263i	2.03606	−	1.08980i
$471$	−14.5558	+	9.72590i	−0.670697	+	0.448146i
$472$	−0.603323	−	6.01929i	−0.0277702	−	0.277060i
$473$	14.5512	−	21.7774i	0.669066	−	1.00133i
$474$	2.07944	−	1.70855i	0.0955119	−	0.0784764i
$475$	10.1890	+	19.0624i	0.467505	+	0.874641i
$476$	26.3084	−	17.6225i	1.20584	−	0.807724i
$477$	3.71809	+	0.366200i	0.170240	+	0.0167672i
$478$	−29.9427	−	29.9083i	−1.36955	−	1.36797i
$479$	7.01057	+	7.01057i	0.320321	+	0.320321i	0.848890	−	0.528569i	$-0.177271\pi$
$479$	7.01057	+	7.01057i	0.320321	+	0.320321i	−0.528569	+	0.848890i	$0.677271\pi$
$480$	0.0639328	+	22.2619i	0.00291812	+	1.01611i
$481$	3.67456	−	3.67456i	0.167545	−	0.167545i
$482$	8.11203	−	0.00465930i	0.369493	−	0.000212225i
$483$	−1.87925	+	19.0803i	−0.0855088	+	0.868185i
$484$	−9.40900	−	6.27127i	−0.427682	−	0.285058i
$485$	35.7710	−	19.1200i	1.62428	−	0.868195i
$486$	1.40748	+	0.137809i	0.0638447	+	0.00625113i
$487$	0.119775	+	0.0800311i	0.00542753	+	0.00362656i	0.558281	−	0.829652i	$-0.311461\pi$
$487$	0.119775	+	0.0800311i	0.00542753	+	0.00362656i	−0.552854	+	0.833278i	$0.686461\pi$
$488$	−3.18714	+	5.98751i	−0.144275	+	0.271042i
$489$	7.34305	+	10.9897i	0.332064	+	0.496969i
$490$	31.0547	−	102.586i	1.40291	−	4.63436i
$491$	−19.8103	−	16.2579i	−0.894025	−	0.733707i	0.0705523	−	0.997508i	$-0.477524\pi$
$491$	−19.8103	−	16.2579i	−0.894025	−	0.733707i	−0.964577	+	0.263801i	$0.915024\pi$
$492$	0.529241	+	0.987411i	0.0238600	+	0.0445159i
$493$	20.9667	+	11.2069i	0.944291	+	0.504734i
$494$	5.92257	+	3.95242i	0.266469	+	0.177828i
$495$	6.14587	−	14.8375i	0.276236	−	0.666894i
$496$	5.27385	+	5.24967i	0.236803	+	0.235717i
$497$	−11.3944	−	27.5084i	−0.511106	−	1.23392i
$498$	1.14305	−	5.76379i	0.0512212	−	0.258281i
$499$	−6.03347	−	19.8897i	−0.270095	−	0.890385i	−0.982124	−	0.188234i	$-0.939724\pi$
$499$	−6.03347	−	19.8897i	−0.270095	−	0.890385i	0.712029	−	0.702150i	$-0.247776\pi$
$500$	−4.18395	+	42.9865i	−0.187112	+	1.92242i
$501$	5.33576	−	0.525527i	0.238384	−	0.0234788i
$502$	−1.56700	+	1.91163i	−0.0699384	+	0.0853201i
$503$	−5.46684	+	27.4837i	−0.243755	+	1.22544i	0.643966	+	0.765054i	$0.277288\pi$
$503$	−5.46684	+	27.4837i	−0.243755	+	1.22544i	−0.887721	+	0.460383i	$0.847712\pi$
$504$	5.56958	+	13.3809i	0.248089	+	0.596032i
$505$	19.9975	−	3.97776i	0.889878	−	0.177008i
$506$	−20.6598	+	6.28005i	−0.918441	+	0.279182i
$507$	6.72956	+	2.04139i	0.298870	+	0.0906613i
$508$	−7.09928	−	7.08299i	−0.314980	−	0.314257i
$509$	−10.2476	−	12.4868i	−0.454218	−	0.553466i	0.494670	−	0.869081i	$-0.335289\pi$
$509$	−10.2476	−	12.4868i	−0.454218	−	0.553466i	−0.948887	+	0.315615i	$0.897789\pi$
$510$	−6.57138	+	15.8905i	−0.290986	+	0.703645i
$511$	−19.8711			−0.879044
$512$	8.55096	−	20.9495i	0.377903	−	0.925845i
$513$	−2.06102			−0.0909961
$514$	−6.93189	+	16.7623i	−0.305753	+	0.739353i
$515$	40.6213	+	49.4972i	1.78999	+	2.18111i
$516$	−9.08695	−	9.06609i	−0.400030	−	0.399112i
$517$	35.1301	+	10.6566i	1.54502	+	0.468677i
$518$	−14.7495	+	4.48348i	−0.648058	+	0.196993i
$519$	−11.0140	+	2.19082i	−0.483460	+	0.0961661i
$520$	10.4490	+	25.1038i	0.458221	+	1.10087i
$521$	−0.206346	+	1.03737i	−0.00904017	+	0.0454480i	−0.985042	−	0.172314i	$-0.944876\pi$
$521$	−0.206346	+	1.03737i	−0.00904017	+	0.0454480i	0.976002	+	0.217762i	$0.0698756\pi$
$522$	−6.89846	+	8.41565i	−0.301937	+	0.368343i
$523$	25.1096	−	2.47308i	1.09797	−	0.108140i	0.467229	−	0.884136i	$-0.345252\pi$
$523$	25.1096	−	2.47308i	1.09797	−	0.108140i	0.630738	+	0.775996i	$0.282752\pi$
$524$	−0.916213	+	9.41331i	−0.0400249	+	0.411222i
$525$	15.6000	+	51.4263i	0.680840	+	2.24443i
$526$	−6.32011	+	31.8690i	−0.275570	+	1.38955i
$527$	2.19960	+	5.31030i	0.0958160	+	0.231320i
$528$	−11.5160	+	11.5690i	−0.501168	+	0.503476i
$529$	3.44457	−	8.31594i	0.149764	−	0.361562i
$530$	−17.2955	−	11.5421i	−0.751268	−	0.501357i
$531$	1.88626	+	1.00823i	0.0818566	+	0.0437532i
$532$	−9.97851	−	18.6170i	−0.432623	−	0.807149i
$533$	1.05777	+	0.868090i	0.0458171	+	0.0376011i
$534$	5.34655	−	17.6617i	0.231368	−	0.764298i
$535$	−37.9242	−	56.7576i	−1.63961	−	2.45385i
$536$	−17.3516	+	32.5975i	−0.749473	+	1.40800i
$537$	−9.30049	−	6.21439i	−0.401346	−	0.268171i
$538$	−4.71632	−	0.461782i	−0.203335	−	0.0199088i
$539$	69.3121	−	37.0481i	2.98548	−	1.59577i
$540$	−6.54934	−	4.36526i	−0.281839	−	0.187851i
$541$	3.10875	−	31.5637i	0.133656	−	1.35703i	−0.661190	−	0.750219i	$-0.729948\pi$
$541$	3.10875	−	31.5637i	0.133656	−	1.35703i	0.794846	−	0.606812i	$-0.207552\pi$
$542$	−8.20383	+	0.00471202i	−0.352385	+	0.000202399i
$543$	−10.2507	+	10.2507i	−0.439899	+	0.439899i
$544$	12.3233	−	12.3942i	0.528356	−	0.531399i
$545$	25.5853	+	25.5853i	1.09595	+	1.09595i
$546$	12.5252	+	12.5108i	0.536030	+	0.535415i
$547$	4.22939	+	0.416559i	0.180836	+	0.0178108i	0.188030	−	0.982163i	$-0.439790\pi$
$547$	4.22939	+	0.416559i	0.180836	+	0.0178108i	−0.00719385	+	0.999974i	$0.502290\pi$
$548$	−18.5880	+	12.4510i	−0.794041	+	0.531882i
$549$	−1.13047	−	2.11496i	−0.0482473	−	0.0902643i
$550$	−46.7645	+	38.4236i	−1.99404	+	1.63839i
$551$	8.81056	−	13.1859i	0.375342	−	0.561740i
$552$	1.05542	+	10.5298i	0.0449217	+	0.448179i
$553$	−8.10835	+	5.41783i	−0.344802	+	0.230390i
$554$	4.42551	−	2.36875i	0.188022	−	0.100639i
$555$	5.31087	−	6.47132i	0.225434	−	0.274692i
$556$	18.5484	+	15.1867i	0.786628	+	0.644058i
$557$	14.9638	−	27.9952i	0.634035	−	1.18620i	−0.335685	−	0.941974i	$-0.608968\pi$
$557$	14.9638	−	27.9952i	0.634035	−	1.18620i	0.969720	−	0.244221i	$-0.0785323\pi$
$558$	−2.58004	+	0.514742i	−0.109222	+	0.0217908i
$559$	−14.4851	−	5.99992i	−0.612654	−	0.253769i
$560$	7.72207	−	80.2943i	0.326317	−	3.39305i
$561$	−11.6490	+	4.82516i	−0.491820	+	0.203718i
$562$	−14.9455	+	9.99871i	−0.630439	+	0.421770i
$563$	8.65406	−	2.62518i	0.364725	−	0.110638i	−0.102602	−	0.994722i	$-0.532717\pi$
$563$	8.65406	−	2.62518i	0.364725	−	0.110638i	0.467327	+	0.884084i	$0.345217\pi$
$564$	8.46294	−	15.8769i	0.356354	−	0.668538i
$565$	6.83408	+	69.3876i	0.287512	+	2.91916i
$566$	−0.832301	−	8.40103i	−0.0349842	−	0.353122i
$567$	−5.02585	−	0.999703i	−0.211066	−	0.0419836i
$568$	−9.15412	−	13.6491i	−0.384098	−	0.572705i
$569$	3.70781	+	18.6404i	0.155439	+	0.781447i	0.977317	+	0.211782i	$0.0679268\pi$
$569$	3.70781	+	18.6404i	0.155439	+	0.781447i	−0.821877	+	0.569664i	$0.807073\pi$
$570$	10.1192	+	5.40138i	0.423848	+	0.226239i
$571$	−13.3518	+	44.0149i	−0.558754	+	1.84196i	−0.0195186	+	0.999809i	$0.506213\pi$
$571$	−13.3518	+	44.0149i	−0.558754	+	1.84196i	−0.539235	+	0.842155i	$0.681287\pi$
$572$	−7.60886	+	18.4293i	−0.318143	+	0.770567i
$573$	3.59547	−	2.95073i	0.150203	−	0.123268i
$574$	−1.55560	−	3.74945i	−0.0649293	−	0.156499i
$575$			39.2385i			1.63636i
$576$	4.46746	+	6.63640i	0.186144	+	0.276517i
$577$		−	36.5677i		−	1.52233i	−0.648557	−	0.761166i	$-0.724627\pi$
$577$		−	36.5677i		−	1.52233i	0.648557	−	0.761166i	$-0.275373\pi$
$578$	−9.73646	+	4.03953i	−0.404984	+	0.168022i
$579$	−15.1607	+	12.4421i	−0.630058	+	0.517075i
$580$	55.9255	−	23.2404i	2.32218	−	0.965004i
$581$	−6.18057	+	20.3746i	−0.256413	+	0.845282i
$582$	6.86353	−	12.8585i	0.284503	−	0.533003i
$583$	−2.97446	−	14.9536i	−0.123190	−	0.619316i
$584$	−10.7536	+	2.15830i	−0.444988	+	0.0893111i
$585$	−9.42895	−	1.87553i	−0.389839	−	0.0775438i
$586$	30.1378	−	2.98579i	1.24498	−	0.123342i
$587$	−1.12091	−	11.3808i	−0.0462651	−	0.469737i	−0.990205	−	0.139620i	$-0.955412\pi$
$587$	−1.12091	−	11.3808i	−0.0462651	−	0.469737i	0.943940	−	0.330117i	$-0.107088\pi$
$588$	−11.2233	−	36.8457i	−0.462839	−	1.51949i
$589$	3.66905	−	1.11299i	0.151181	−	0.0458601i
$590$	−6.61891	−	9.89359i	−0.272496	−	0.407313i
$591$	1.69336	−	0.701412i	0.0696555	−	0.0288522i
$592$	−7.49504	+	4.02835i	−0.308044	+	0.165564i
$593$	34.5712	+	14.3199i	1.41967	+	0.588047i	0.954778	−	0.297321i	$-0.0960930\pi$
$593$	34.5712	+	14.3199i	1.41967	+	0.588047i	0.464892	+	0.885367i	$0.346093\pi$
$594$	−1.12917	−	5.65972i	−0.0463303	−	0.232221i
$595$	29.3715	−	54.9503i	1.20412	−	2.25274i
$596$	0.670970	+	6.73317i	0.0274840	+	0.275801i
$597$	−2.84732	+	3.46947i	−0.116533	+	0.141996i
$598$	6.09980	+	11.3962i	0.249439	+	0.466024i
$599$	−26.0679	+	17.4180i	−1.06510	+	0.711680i	−0.959209	−	0.282697i	$-0.908771\pi$
$599$	−26.0679	+	17.4180i	−1.06510	+	0.711680i	−0.105895	+	0.994377i	$0.533771\pi$
$600$	14.0279	+	26.1360i	0.572688	+	1.06700i
$601$	21.8203	−	32.6564i	0.890069	−	1.33208i	−0.0526911	−	0.998611i	$-0.516780\pi$
$601$	21.8203	−	32.6564i	0.890069	−	1.33208i	0.942760	−	0.333472i	$-0.108220\pi$
$602$	29.5269	+	35.9365i	1.20343	+	1.46466i
$603$	−6.15455	−	11.5144i	−0.250633	−	0.468901i
$604$	−2.71169	+	13.7149i	−0.110337	+	0.558052i
$605$	−22.1425	−	2.18084i	−0.900220	−	0.0886639i
$606$	5.17803	−	5.18398i	0.210343	−	0.210585i
$607$	7.65283	+	7.65283i	0.310619	+	0.310619i	0.845149	−	0.534531i	$-0.179512\pi$
$607$	7.65283	+	7.65283i	0.310619	+	0.310619i	−0.534531	+	0.845149i	$0.679512\pi$
$608$	−7.42216	−	8.99115i	−0.301008	−	0.364639i
$609$	27.8807	−	27.8807i	1.12978	−	1.12978i
$610$	0.00766596	+	13.3468i	0.000310386	+	0.540394i
$611$	2.15398	−	21.8698i	0.0871408	−	0.884756i
$612$	1.21250	+	6.05928i	0.0490125	+	0.244932i
$613$	23.1873	−	12.3939i	0.936526	−	0.500584i	0.0688022	−	0.997630i	$-0.478082\pi$
$613$	23.1873	−	12.3939i	0.936526	−	0.500584i	0.867724	+	0.497047i	$0.165582\pi$
$614$	1.06593	−	10.8866i	0.0430173	−	0.439349i
$615$	1.83290	+	1.22471i	0.0739098	+	0.0493850i
$616$	45.6569	−	37.6015i	1.83957	−	1.51501i
$617$	1.19874	+	1.79404i	0.0482593	+	0.0722251i	0.854815	−	0.518933i	$-0.173671\pi$
$617$	1.19874	+	1.79404i	0.0482593	+	0.0722251i	−0.806555	+	0.591159i	$0.798671\pi$
$618$	22.0233	+	6.66688i	0.885907	+	0.268181i
$619$	−14.7005	−	12.0644i	−0.590864	−	0.484909i	0.290802	−	0.956783i	$-0.406078\pi$
$619$	−14.7005	−	12.0644i	−0.590864	−	0.484909i	−0.881666	+	0.471874i	$0.843578\pi$
$620$	14.0166	+	4.23430i	0.562918	+	0.170054i
$621$	−3.29972	−	1.76374i	−0.132413	−	0.0707763i
$622$	12.0458	−	18.0502i	0.482991	−	0.723746i
$623$	−25.5878	+	61.7744i	−1.02515	+	2.47494i
$624$	8.13715	+	5.41007i	0.325747	+	0.216576i
$625$	12.4554	+	30.0700i	0.498216	+	1.20280i
$626$	30.8032	+	6.10874i	1.23114	+	0.244154i
$627$	2.44153	+	8.04863i	0.0975052	+	0.321431i
$628$	27.0393	−	22.2426i	1.07899	−	0.887578i
$629$	−6.54093	+	0.644225i	−0.260804	+	0.0256869i
$630$	22.0561	+	18.0798i	0.878736	+	0.720316i
$631$	−1.63934	+	8.24154i	−0.0652612	+	0.328090i	−0.999600	−	0.0282969i	$-0.990992\pi$
$631$	−1.63934	+	8.24154i	−0.0652612	+	0.328090i	0.934338	+	0.356387i	$0.115992\pi$
$632$	−3.79954	+	3.81266i	−0.151138	+	0.151659i
$633$	−10.2024	+	2.02939i	−0.405510	+	0.0806609i
$634$	−1.28118	−	4.21475i	−0.0508820	−	0.167389i
$635$	−18.8831	−	5.72814i	−0.749354	−	0.227314i
$636$	−7.47216	+	0.00858356i	−0.296291	+	0.000340360i
$637$	−29.8458	−	36.3672i	−1.18253	−	1.44092i
$638$	41.0367	+	16.9703i	1.62466	+	0.671862i
$639$	5.81051			0.229860
$640$	−4.54222	−	44.2916i	−0.179547	−	1.75078i
$641$	21.4050			0.845447			0.422723	−	0.906259i	$-0.361074\pi$
$641$	21.4050			0.845447			0.422723	+	0.906259i	$0.361074\pi$
$642$	−22.6685	−	9.37435i	−0.894655	−	0.369976i
$643$	−18.4740	−	22.5107i	−0.728545	−	0.887734i	0.268600	−	0.963252i	$-0.413439\pi$
$643$	−18.4740	−	22.5107i	−0.728545	−	0.887734i	−0.997144	+	0.0755174i	$0.975939\pi$
$644$	−0.0440487	−	38.3453i	−0.00173576	−	1.51102i
$645$	−24.1701	−	7.33191i	−0.951695	−	0.288694i
$646$	−2.61914	−	8.61633i	−0.103049	−	0.339005i
$647$	23.6653	−	4.70733i	0.930380	−	0.185064i	0.293440	−	0.955977i	$-0.405200\pi$
$647$	23.6653	−	4.70733i	0.930380	−	0.185064i	0.636940	+	0.770913i	$0.280200\pi$
$648$	−2.82842	+	0.00487368i	−0.111111	+	0.000191456i
$649$	1.70279	−	8.56053i	0.0668405	−	0.336030i
$650$	28.0202	+	22.9687i	1.09904	+	0.900905i
$651$	9.48694	−	0.934382i	0.371822	−	0.0366213i
$652$	−16.7932	−	20.4147i	−0.657672	−	0.799501i
$653$	4.91090	+	16.1891i	0.192178	+	0.633527i	0.999082	+	0.0428438i	$0.0136418\pi$
$653$	4.91090	+	16.1891i	0.192178	+	0.633527i	−0.806903	+	0.590683i	$0.798858\pi$
$654$	12.7542	+	2.52936i	0.498731	+	0.0989059i
$655$	7.12177	+	17.1935i	0.278270	+	0.671804i
$656$	−1.24909	−	1.86013i	−0.0487688	−	0.0726259i
$657$	1.48397	−	3.58262i	0.0578952	−	0.139771i
$658$	−36.1872	+	54.2254i	−1.41072	+	2.11393i
$659$	−42.5483	−	22.7426i	−1.65745	−	0.885924i	−0.989967	−	0.141296i	$-0.954873\pi$
$659$	−42.5483	−	22.7426i	−1.65745	−	0.885924i	−0.667480	−	0.744628i	$-0.732627\pi$
$660$	−9.28860	+	30.7475i	−0.361558	+	1.19684i
$661$	−24.1791	−	19.8432i	−0.940457	−	0.771813i	0.0332905	−	0.999446i	$-0.489401\pi$
$661$	−24.1791	−	19.8432i	−0.940457	−	0.771813i	−0.973747	+	0.227633i	$0.926901\pi$
$662$	−8.60404	−	2.60461i	−0.334406	−	0.101231i
$663$	4.19331	+	6.27573i	0.162854	+	0.243729i
$664$	−1.13175	+	11.6974i	−0.0439204	+	0.453949i
$665$	−34.5582	−	23.0911i	−1.34011	−	0.895434i
$666$	0.293154	−	2.99407i	0.0113595	−	0.116018i
$667$	25.3898	−	13.5711i	0.983098	−	0.525477i
$668$	−10.5147	+	2.10406i	−0.406826	+	0.0814087i
$669$	0.896177	−	9.09904i	0.0346482	−	0.351789i
$670$	0.0417353	+	72.6630i	0.00161238	+	2.80722i
$671$	−6.92011	+	6.92011i	−0.267148	+	0.267148i
$672$	−13.7380	−	25.5253i	−0.529953	−	0.984661i
$673$	15.7518	+	15.7518i	0.607187	+	0.607187i	0.942210	−	0.335023i	$-0.108744\pi$
$673$	15.7518	+	15.7518i	0.607187	+	0.607187i	−0.335023	+	0.942210i	$0.608744\pi$
$674$	4.42258	−	4.42766i	0.170351	−	0.170547i
$675$	−10.4368	−	1.02794i	−0.401714	−	0.0395654i
$676$	−13.7976	−	2.72805i	−0.530678	−	0.104925i
$677$	19.1099	+	35.7522i	0.734455	+	1.37407i	0.920192	+	0.391468i	$0.128033\pi$
$677$	19.1099	+	35.7522i	0.734455	+	1.37407i	−0.185737	+	0.982600i	$0.559467\pi$
$678$	15.9062	+	19.3591i	0.610875	+	0.743482i
$679$	−29.3419	+	43.9132i	−1.12604	+	1.68523i
$680$	9.92657	−	32.9277i	0.380667	−	1.26272i
$681$	5.57273	−	3.72358i	0.213548	−	0.142688i
$682$	5.06653	+	9.46573i	0.194007	+	0.362461i
$683$	−3.60525	+	4.39301i	−0.137951	+	0.168094i	−0.837403	−	0.546585i	$-0.815927\pi$
$683$	−3.60525	+	4.39301i	−0.137951	+	0.168094i	0.699452	+	0.714679i	$0.253427\pi$
$684$	4.10172	−	0.408742i	0.156833	−	0.0156286i
$685$	−20.7523	+	38.8248i	−0.792904	+	1.48342i
$686$	17.3811	+	87.1192i	0.663614	+	3.32623i
$687$	−9.83278	−	4.07287i	−0.375144	−	0.155390i
$688$	19.8823	+	16.2407i	0.758006	+	0.619171i
$689$	−8.43205	+	3.49267i	−0.321235	+	0.133060i
$690$	11.5788	+	17.3073i	0.440796	+	0.658878i
$691$	10.2924	−	3.12216i	0.391541	−	0.118773i	−0.0883747	−	0.996087i	$-0.528167\pi$
$691$	10.2924	−	3.12216i	0.391541	−	0.118773i	0.479916	+	0.877315i	$0.340667\pi$
$692$	21.4849	−	6.54433i	0.816733	−	0.248778i
$693$	2.04971	+	20.8111i	0.0778622	+	0.790548i
$694$	−43.0081	+	4.26087i	−1.63257	+	0.161740i
$695$	46.2642	+	9.20251i	1.75490	+	0.349071i
$696$	12.0599	−	18.1165i	0.457130	−	0.686703i
$697$	−0.337643	−	1.69744i	−0.0127891	−	0.0642953i
$698$	−4.50068	+	8.43183i	−0.170353	+	0.319149i
$699$	1.07794	−	3.55351i	0.0407716	−	0.134406i
$700$	−41.2451	−	99.2519i	−1.55892	−	3.75137i
$701$	−34.7865	+	28.5485i	−1.31387	+	1.07826i	−0.322581	+	0.946542i	$0.604550\pi$
$701$	−34.7865	+	28.5485i	−1.31387	+	1.07826i	−0.991287	+	0.131721i	$0.957950\pi$
$702$	−3.19101	+	1.32391i	−0.120437	+	0.0499676i
$703$			4.38430i			0.165357i
$704$	20.6241	−	25.3078i	0.777298	−	0.953825i
$705$		−	35.4020i		−	1.33332i
$706$	−2.42348	−	5.84132i	−0.0912091	−	0.219841i
$707$	−20.5227	+	16.8426i	−0.771836	+	0.633429i
$708$	−3.95387	−	1.63243i	−0.148596	−	0.0613504i
$709$	−13.6432	+	44.9755i	−0.512380	+	1.68909i	0.193786	+	0.981044i	$0.437923\pi$
$709$	−13.6432	+	44.9755i	−0.512380	+	1.68909i	−0.706166	+	0.708047i	$0.749577\pi$
$710$	−28.5286	−	15.2278i	−1.07066	−	0.571490i
$711$	−0.371267	−	1.86649i	−0.0139236	−	0.0699987i
$712$	−7.13772	+	36.2097i	−0.267497	+	1.35702i
$713$	6.82665	+	1.35791i	0.255660	+	0.0508540i
$714$	−2.20747	−	22.2816i	−0.0826124	−	0.833867i
$715$	3.84545	+	39.0435i	0.143812	+	1.46014i
$716$	19.7417	+	10.5230i	0.737784	+	0.393265i
$717$	−28.6369	+	8.68691i	−1.06946	+	0.324418i
$718$	17.3768	−	11.6252i	0.648495	−	0.433850i
$719$	−36.6450	+	15.1789i	−1.36663	+	0.566076i	−0.940872	−	0.338761i	$-0.889992\pi$
$719$	−36.6450	+	15.1789i	−1.36663	+	0.566076i	−0.425757	+	0.904838i	$0.639992\pi$
$720$	13.8998	+	7.38861i	0.518017	+	0.275357i
$721$	−77.0296	−	31.9067i	−2.86873	−	1.18827i
$722$	20.4596	−	4.08188i	0.761426	−	0.151912i
$723$	2.70397	−	5.05877i	0.100562	−	0.188138i
$724$	18.3674	−	22.4332i	0.682619	−	0.833725i
$725$	51.1925	−	62.3783i	1.90124	−	2.31667i
$726$	−7.04930	+	3.77313i	−0.261624	+	0.140034i
$727$	−5.17871	+	3.46031i	−0.192068	+	0.128336i	−0.647886	−	0.761737i	$-0.724347\pi$
$727$	−5.17871	+	3.46031i	−0.192068	+	0.128336i	0.455818	+	0.890073i	$0.349347\pi$
$728$	−27.4082	−	22.4144i	−1.01581	−	0.830732i
$729$	0.555570	−	0.831470i	0.0205767	−	0.0307952i
$730$	−16.6751	+	13.7010i	−0.617175	+	0.507096i
$731$	9.34776	+	17.4884i	0.345740	+	0.646833i
$732$	2.66924	+	3.98488i	0.0986578	+	0.147285i
$733$	−25.2585	−	2.48775i	−0.932945	−	0.0918871i	−0.379890	−	0.925032i	$-0.624038\pi$
$733$	−25.2585	−	2.48775i	−0.932945	−	0.0918871i	−0.553055	+	0.833145i	$0.686538\pi$
$734$	−11.4701	−	11.4569i	−0.423368	−	0.422882i
$735$	−53.5916	−	53.5916i	−1.97676	−	1.97676i
$736$	−4.18872	−	20.7465i	−0.154398	−	0.764728i
$737$	−37.6748	+	37.6748i	−1.38777	+	1.38777i
$738$	0.792173		0.000455000i	0.0291603		1.67488e-5i
$739$	4.70193	−	47.7395i	0.172963	−	1.75613i	−0.381918	−	0.924196i	$-0.624736\pi$
$739$	4.70193	−	47.7395i	0.172963	−	1.75613i	0.554881	−	0.831930i	$-0.312764\pi$
$740$	−9.28600	+	13.9321i	−0.341360	+	0.512154i
$741$	4.44030	−	2.37339i	0.163119	−	0.0871887i
$742$	26.9461	+	2.63833i	0.989221	+	0.0968561i
$743$	−31.1677	−	20.8256i	−1.14343	−	0.764016i	−0.168320	−	0.985732i	$-0.553834\pi$
$743$	−31.1677	−	20.8256i	−1.14343	−	0.764016i	−0.975111	+	0.221716i	$0.928834\pi$
$744$	5.03256	−	1.53609i	0.184503	−	0.0563156i
$745$	7.39712	+	11.0706i	0.271010	+	0.405594i
$746$	10.3221	−	34.0981i	0.377921	−	1.24842i
$747$	−3.21185	−	2.63589i	−0.117515	−	0.0964423i
$748$	22.2262	−	11.9130i	0.812670	−	0.435582i
$749$	78.3889	+	41.8997i	2.86427	+	1.53098i
$750$	25.4026	+	16.9524i	0.927571	+	0.619013i
$751$	−8.81055	+	21.2706i	−0.321502	+	0.776173i	0.677666	+	0.735370i	$0.262992\pi$
$751$	−8.81055	+	21.2706i	−0.321502	+	0.776173i	−0.999167	+	0.0408033i	$0.987008\pi$
$752$	−13.6937	+	33.2757i	−0.499360	+	1.21344i
$753$	0.668864	+	1.61478i	0.0243748	+	0.0588459i
$754$	5.17105	−	26.0749i	0.188318	−	0.949591i
$755$	7.98551	+	26.3247i	0.290622	+	0.958054i
$756$	10.2004	+	0.992823i	0.370986	+	0.0361086i
$757$	52.7973	−	5.20008i	1.91895	−	0.189000i	0.933453	−	0.358699i	$-0.116780\pi$
$757$	52.7973	−	5.20008i	1.91895	−	0.189000i	0.985496	+	0.169699i	$0.0542796\pi$
$758$	−31.8544	+	38.8602i	−1.15700	+	1.41147i
$759$	−2.97878	+	14.9753i	−0.108123	+	0.543570i
$760$	−21.2099	−	8.74266i	−0.769365	−	0.317130i
$761$	−16.9441	+	3.37040i	−0.614225	+	0.122177i	−0.492392	−	0.870374i	$-0.663877\pi$
$761$	−16.9441	+	3.37040i	−0.614225	+	0.122177i	−0.121833	+	0.992551i	$0.538877\pi$
$762$	−6.78461	+	2.06235i	−0.245781	+	0.0747109i
$763$	−45.0855	−	13.6765i	−1.63220	−	0.495124i
$764$	−6.57031	+	6.58542i	−0.237706	+	0.238252i
$765$	7.71371	+	9.39919i	0.278890	+	0.339828i
$766$	−7.42600	+	17.9571i	−0.268312	+	0.648817i
$767$	−5.22483			−0.188658
$768$	−10.2070	−	12.3214i	−0.368314	−	0.444610i
$769$	39.5594			1.42655			0.713275	−	0.700884i	$-0.247211\pi$
$769$	39.5594			1.42655			0.713275	+	0.700884i	$0.247211\pi$
$770$	44.4766	−	107.551i	1.60282	−	3.87586i
$771$	8.13689	+	9.91483i	0.293043	+	0.357074i
$772$	27.7045	−	27.7682i	0.997106	−	0.999400i
$773$	0.702428	+	0.213079i	0.0252646	+	0.00766393i	0.302892	−	0.953025i	$-0.402048\pi$
$773$	0.702428	+	0.213079i	0.0252646	+	0.00766393i	−0.277627	+	0.960689i	$0.589548\pi$
$774$	−8.68418	+	2.63976i	−0.312146	+	0.0948844i
$775$	19.1349	−	3.80617i	0.687346	−	0.136722i
$776$	−11.1093	+	26.9515i	−0.398801	+	0.967502i
$777$	−2.12662	+	10.6912i	−0.0762921	+	0.383546i
$778$	−8.73999	+	10.6622i	−0.313344	+	0.382258i
$779$	−1.14892	+	0.113159i	−0.0411644	+	0.00405434i
$780$	19.1369	+	1.86263i	0.685211	+	0.0666928i
$781$	−6.88326	−	22.6911i	−0.246302	−	0.811950i
$782$	3.18023	−	16.0362i	0.113725	−	0.573454i
$783$	2.94457	+	7.10883i	0.105230	+	0.254049i
$784$	29.6431	+	71.1024i	1.05868	+	2.53937i
$785$	26.3644	−	63.6494i	0.940987	−	2.27174i
$786$	5.56273	+	3.71227i	0.198416	+	0.132412i
$787$	17.1690	+	9.17701i	0.612008	+	0.327125i	0.748115	−	0.663569i	$-0.230959\pi$
$787$	17.1690	+	9.17701i	0.612008	+	0.327125i	−0.136107	+	0.990694i	$0.543459\pi$
$788$	−3.23092	+	1.73174i	−0.115097	+	0.0616906i
$789$	17.7589	+	14.5743i	0.632232	+	0.518859i
$790$	−3.06871	+	10.1371i	−0.109180	+	0.360663i
$791$	−50.4387	−	75.4869i	−1.79339	−	2.68400i
$792$	3.36964	+	11.0397i	0.119735	+	0.392279i
$793$	4.87102	+	3.25471i	0.172975	+	0.115578i
$794$	−9.34412	−	0.914897i	−0.331610	−	0.0324685i
$795$	−12.9669	+	6.93093i	−0.459887	+	0.245815i
$796$	4.97851	−	7.46942i	0.176458	−	0.264747i
$797$	−2.33124	+	23.6694i	−0.0825766	+	0.838414i	0.861296	+	0.508104i	$0.169653\pi$
$797$	−2.33124	+	23.6694i	−0.0825766	+	0.838414i	−0.943872	+	0.330310i	$0.892847\pi$
$798$	−14.9359	+	0.00857873i	−0.528726	+	0.000303684i
$799$	−19.6535	+	19.6535i	−0.695293	+	0.695293i
$800$	−33.1009	−	49.2323i	−1.17029	−	1.74063i
$801$	−9.22663	−	9.22663i	−0.326007	−	0.326007i
$802$	−21.1645	−	21.1402i	−0.747345	−	0.746487i
$803$	−15.7487	−	1.55111i	−0.555760	−	0.0547376i
$804$	14.5320	+	21.6946i	0.512503	+	0.765111i
$805$	−35.5678	−	66.5427i	−1.25360	−	2.34532i
$806$	4.96573	−	4.08005i	0.174911	−	0.143714i
$807$	−1.86165	+	2.78616i	−0.0655333	+	0.0980775i
$808$	−9.27693	+	11.3438i	−0.326361	+	0.399072i
$809$	−18.2852	+	12.2178i	−0.642872	+	0.429554i	−0.833812	−	0.552048i	$-0.813846\pi$
$809$	−18.2852	+	12.2178i	−0.642872	+	0.429554i	0.190940	+	0.981602i	$0.438846\pi$
$810$	−4.90682	+	2.62637i	−0.172408	+	0.0922813i
$811$	−22.8863	+	27.8871i	−0.803648	+	0.979248i	−0.999999	−	0.00128601i	$-0.999591\pi$
$811$	−22.8863	+	27.8871i	−0.803648	+	0.979248i	0.196351	+	0.980534i	$0.437091\pi$
$812$	−49.9572	+	61.0158i	−1.75315	+	2.14124i
$813$	−2.73457	+	5.11601i	−0.0959054	+	0.179426i
$814$	−12.0397	+	2.40203i	−0.421990	+	0.0841909i
$815$	−48.0553	−	19.9052i	−1.68330	−	0.697247i
$816$	−3.61473	−	11.8184i	−0.126541	−	0.413726i
$817$	12.2209	−	5.06204i	0.427554	−	0.177098i
$818$	−7.26436	+	4.85993i	−0.253992	+	0.169923i
$819$	11.9790	−	3.63380i	0.418581	−	0.126975i
$820$	−3.89063	−	2.07384i	−0.135867	−	0.0724217i
$821$	−0.797574	−	8.09791i	−0.0278355	−	0.282619i	−0.999019	−	0.0442855i	$-0.985899\pi$
$821$	−0.797574	−	8.09791i	−0.0278355	−	0.282619i	0.971183	−	0.238333i	$-0.0766011\pi$
$822$	1.55967	+	15.7429i	0.0543998	+	0.549097i
$823$	9.58365	+	1.90631i	0.334065	+	0.0664497i	0.359273	−	0.933233i	$-0.383025\pi$
$823$	9.58365	+	1.90631i	0.334065	+	0.0664497i	−0.0252078	+	0.999682i	$0.508025\pi$
$824$	−45.1517	−	8.90037i	−1.57293	−	0.310059i
$825$	8.34942	+	41.9754i	0.290690	+	1.46140i
$826$	13.6736	+	7.29862i	0.475767	+	0.253952i
$827$	−1.09706	+	3.61654i	−0.0381487	+	0.125759i	−0.973947	−	0.226778i	$-0.927181\pi$
$827$	−1.09706	+	3.61654i	−0.0381487	+	0.125759i	0.935798	+	0.352537i	$0.114681\pi$
$828$	6.91669	+	2.85568i	0.240372	+	0.0992419i
$829$	25.3652	−	20.8167i	0.880971	−	0.722994i	−0.0808349	−	0.996728i	$-0.525759\pi$
$829$	25.3652	−	20.8167i	0.880971	−	0.722994i	0.961806	+	0.273734i	$0.0882586\pi$
$830$	8.86164	+	21.3592i	0.307592	+	0.741388i
$831$		−	3.54937i		−	0.123126i
$832$	−17.2670	−	9.15305i	−0.598626	−	0.317325i
$833$			59.5032i			2.06166i
$834$	15.6570	−	6.49589i	0.542159	−	0.224934i
$835$	−16.3105	+	13.3857i	−0.564447	+	0.463230i
$836$	−6.45520	−	15.5337i	−0.223258	−	0.537245i
$837$	−0.540022	+	1.78021i	−0.0186659	+	0.0615331i
$838$	−10.2806	+	19.2602i	−0.355136	+	0.665332i
$839$	−9.12470	−	45.8729i	−0.315020	−	1.58371i	−0.736220	−	0.676742i	$-0.763391\pi$
$839$	−9.12470	−	45.8729i	−0.315020	−	1.58371i	0.421200	−	0.906968i	$-0.361609\pi$
$840$	−47.4804	−	31.6072i	−1.63823	−	1.09055i
$841$	−29.6256	−	5.89290i	−1.02157	−	0.203203i
$842$	−36.5808	+	3.62411i	−1.26066	+	0.124895i
$843$	1.24629	+	12.6538i	0.0429245	+	0.435820i
$844$	19.9018	−	6.06212i	0.685048	−	0.208667i
$845$	−26.4835	+	8.03367i	−0.911059	+	0.276367i
$846$	−7.07402	−	10.5739i	−0.243210	−	0.363537i
$847$	26.7661	−	11.0869i	0.919694	−	0.380950i
$848$	14.8690	−	1.49897i	0.510603	−	0.0514747i
$849$	−5.51510	−	2.28443i	−0.189278	−	0.0784015i
$850$	−8.96571	−	44.9387i	−0.307521	−	1.54139i
$851$	−3.75191	+	7.01933i	−0.128614	+	0.240620i
$852$	−11.5638	+	1.15234i	−0.396168	+	0.0394787i
$853$	−0.497593	+	0.606319i	−0.0170373	+	0.0207600i	−0.781459	−	0.623956i	$-0.785524\pi$
$853$	−0.497593	+	0.606319i	−0.0170373	+	0.0207600i	0.764422	+	0.644716i	$0.223024\pi$
$854$	−8.20117	−	15.3221i	−0.280638	−	0.524313i
$855$	6.74398	−	4.50618i	0.230639	−	0.154108i
$856$	46.9727	+	14.1607i	1.60549	+	0.484002i
$857$	1.21368	−	1.81641i	0.0414586	−	0.0620472i	−0.810161	−	0.586207i	$-0.800621\pi$
$857$	1.21368	−	1.81641i	0.0414586	−	0.0620472i	0.851620	+	0.524160i	$0.175621\pi$
$858$	8.95022	+	10.8931i	0.305556	+	0.371885i
$859$	1.00897	+	1.88765i	0.0344256	+	0.0644057i	0.898546	−	0.438880i	$-0.144625\pi$
$859$	1.00897	+	1.88765i	0.0344256	+	0.0644057i	−0.864120	+	0.503285i	$0.832125\pi$
$860$	49.5560	+	9.79813i	1.68984	+	0.334113i
$861$	−2.85657	−	0.281347i	−0.0973515	−	0.00958829i
$862$	34.9129	−	34.9530i	1.18914	−	1.19050i
$863$	19.1684	+	19.1684i	0.652501	+	0.652501i	0.953595	−	0.301093i	$-0.0973516\pi$
$863$	19.1684	+	19.1684i	0.652501	+	0.652501i	−0.301093	+	0.953595i	$0.597352\pi$
$864$	5.62800	−	0.570634i	0.191468	−	0.0194134i
$865$	31.2495	−	31.2495i	1.06252	−	1.06252i
$866$	0.0206323	+	35.9216i	0.000701113	+	1.22067i
$867$	−0.730594	+	7.41785i	−0.0248123	+	0.251923i
$868$	−18.6951	+	3.74101i	−0.634552	+	0.126978i
$869$	−6.84915	+	3.66094i	−0.232341	+	0.124189i
$870$	4.17300	−	42.6201i	0.141478	−	1.44496i
$871$	26.5190	+	17.7194i	0.898562	+	0.600400i
$872$	−25.8844	−	2.50436i	−0.876557	−	0.0848085i
$873$	−5.72601	−	8.56958i	−0.193796	−	0.290036i
$874$	−10.4377	−	3.15969i	−0.353060	−	0.106878i
$875$	−85.5403	−	70.2011i	−2.89179	−	2.37323i
$876$	−2.24281	+	7.42423i	−0.0757774	+	0.250842i
$877$	20.1868	+	10.7901i	0.681660	+	0.364355i	0.775602	−	0.631223i	$-0.217447\pi$
$877$	20.1868	+	10.7901i	0.681660	+	0.364355i	−0.0939412	+	0.995578i	$0.529947\pi$
$878$	24.4035	−	36.5679i	0.823578	−	1.23411i
$879$	8.19515	−	19.7848i	0.276416	−	0.667326i
$880$	12.3878	−	63.0340i	0.417592	−	2.12488i
$881$	8.20570	+	19.8103i	0.276457	+	0.667427i	0.999732	−	0.0231332i	$-0.00736419\pi$
$881$	8.20570	+	19.8103i	0.276457	+	0.667427i	−0.723275	+	0.690560i	$0.757364\pi$
$882$	−26.7154	−	5.29808i	−0.899555	−	0.178396i
$883$	−2.85403	−	9.40849i	−0.0960459	−	0.316621i	0.895732	−	0.444595i	$-0.146652\pi$
$883$	−2.85403	−	9.40849i	−0.0960459	−	0.316621i	−0.991777	+	0.127974i	$0.959152\pi$
$884$	−9.58988	−	11.6580i	−0.322543	−	0.392100i
$885$	−8.37651	+	0.825014i	−0.281573	+	0.0277325i
$886$	29.6510	+	24.3054i	0.996144	+	0.816557i
$887$	1.86280	−	9.36495i	0.0625468	−	0.314444i	−0.936828	−	0.349789i	$-0.886253\pi$
$887$	1.86280	−	9.36495i	0.0625468	−	0.314444i	0.999375	+	0.0353453i	$0.0112531\pi$
$888$	0.0103675	+	6.01677i	0.000347912	+	0.201910i
$889$	25.2006	−	5.01270i	0.845200	−	0.168121i
$890$	21.1206	+	69.4817i	0.707965	+	2.32903i
$891$	−3.90518	−	1.18462i	−0.130828	−	0.0396863i
$892$	0.0210060	+	18.2861i	0.000703332	+	0.612265i
$893$	11.7620	+	14.3320i	0.393599	+	0.479602i
$894$	4.42149	+	1.82847i	0.147877	+	0.0611531i
$895$	44.0198			1.47142
$896$	32.4027	+	48.0745i	1.08250	+	1.60606i
$897$	9.14004			0.305177
$898$	40.1388	+	16.5990i	1.33945	+	0.553917i
$899$	−9.08089	−	11.0651i	−0.302865	−	0.369042i
$900$	20.9747	−	0.0240944i	0.699155	−	0.000803146i
$901$	11.0463	+	3.35087i	0.368007	+	0.111634i
$902$	−0.940202	−	3.09304i	−0.0313053	−	0.102987i
$903$	32.2563	−	6.41617i	1.07342	−	0.213517i
$904$	−35.4950	−	35.3728i	−1.18054	−	1.17648i
$905$	11.1299	−	55.9538i	0.369971	−	1.85997i
$906$	7.64531	+	6.26700i	0.253998	+	0.208207i
$907$	28.3788	−	2.79507i	0.942302	−	0.0928087i	0.384815	−	0.922994i	$-0.374265\pi$
$907$	28.3788	−	2.79507i	0.942302	−	0.0928087i	0.557488	+	0.830185i	$0.311765\pi$
$908$	−10.3521	+	8.51565i	−0.343546	+	0.282602i
$909$	−1.50397	−	4.95791i	−0.0498834	−	0.164444i
$910$	−68.3381	−	13.5525i	−2.26539	−	0.449261i
$911$	−3.76912	−	9.09946i	−0.124877	−	0.301479i	0.849061	−	0.528295i	$-0.177168\pi$
$911$	−3.76912	−	9.09946i	−0.124877	−	0.301479i	−0.973938	+	0.226816i	$0.927168\pi$
$912$	−8.08194	+	1.62691i	−0.267620	+	0.0538724i
$913$	−6.48880	+	15.6654i	−0.214748	+	0.518448i
$914$	27.9942	−	41.9484i	0.925965	−	1.38753i
$915$	8.32321	+	4.44885i	0.275157	+	0.147074i
$916$	20.3764	+	6.15555i	0.673254	+	0.203385i
$917$	−18.7318	−	15.3728i	−0.618580	−	0.507655i
$918$	4.18208	+	1.26600i	0.138029	+	0.0417841i
$919$	13.7688	+	20.6065i	0.454192	+	0.679747i	0.985929	−	0.167163i	$-0.0534606\pi$
$919$	13.7688	+	20.6065i	0.454192	+	0.679747i	−0.531737	+	0.846909i	$0.678461\pi$
$920$	−26.4758	−	32.1477i	−0.872881	−	1.05988i
$921$	−6.43128	−	4.29724i	−0.211918	−	0.141599i
$922$	5.14172	−	52.5140i	0.169334	−	1.72946i
$923$	−12.5183	+	6.69117i	−0.412045	+	0.220243i
$924$	−8.20649	−	41.0105i	−0.269974	−	1.34915i
$925$	−2.18668	+	22.2018i	−0.0718978	+	0.729990i
$926$	−0.00942858	−	16.4155i	−0.000309842	−	0.539448i
$927$	11.5051	−	11.5051i	0.377878	−	0.377878i
$928$	−20.4081	+	38.4461i	−0.669929	+	1.26205i
$929$	6.19209	+	6.19209i	0.203156	+	0.203156i	0.801351	−	0.598195i	$-0.204115\pi$
$929$	6.19209	+	6.19209i	0.203156	+	0.203156i	−0.598195	+	0.801351i	$0.704115\pi$
$930$	7.31688	−	7.32529i	0.239930	−	0.240206i
$931$	39.5011	+	3.89052i	1.29460	+	0.127507i
$932$	−1.44053	+	7.28576i	−0.0471861	+	0.238653i
$933$	−7.23336	−	13.5327i	−0.236810	−	0.443040i
$934$	6.75862	+	8.22576i	0.221149	+	0.269155i
$935$	27.5676	−	41.2579i	0.901558	−	1.34928i
$936$	6.08800	−	3.26761i	0.198993	−	0.106805i
$937$	−16.0930	+	10.7530i	−0.525736	+	0.351286i	−0.789943	−	0.613180i	$-0.789890\pi$
$937$	−16.0930	+	10.7530i	−0.525736	+	0.351286i	0.264207	+	0.964466i	$0.414890\pi$
$938$	−44.6491	−	83.4174i	−1.45785	−	2.72367i
$939$	14.0869	−	17.1649i	0.459709	−	0.560157i
$940$	7.02094	+	70.4550i	0.228998	+	2.29799i
$941$	−11.1492	+	20.8586i	−0.363453	+	0.679972i	−0.995480	−	0.0949741i	$-0.969723\pi$
$941$	−11.1492	+	20.8586i	−0.363453	+	0.679972i	0.632027	+	0.774946i	$0.282223\pi$
$942$	−4.84388	−	24.2789i	−0.157822	−	0.791051i
$943$	−1.93628	−	0.802032i	−0.0630538	−	0.0261178i
$944$	8.19251	+	2.46463i	0.266644	+	0.0802169i
$945$	18.6311	−	7.71726i	0.606071	−	0.251043i
$946$	20.5962	+	30.7861i	0.669641	+	1.00094i
$947$	26.3986	−	8.00791i	0.857838	−	0.260222i	0.169426	−	0.985543i	$-0.445808\pi$
$947$	26.3986	−	8.00791i	0.857838	−	0.260222i	0.688411	+	0.725321i	$0.258308\pi$
$948$	1.10904	+	3.64095i	0.0360199	+	0.118252i
$949$	0.928514	+	9.42736i	0.0301408	+	0.306025i
$950$	−30.4187	+	3.01362i	−0.986913	+	0.0977749i
$951$	−3.05508	−	0.607692i	−0.0990676	−	0.0197058i
$952$	8.81207	+	43.9057i	0.285601	+	1.42299i
$953$	10.8210	+	54.4010i	0.350527	+	1.76222i	0.606059	+	0.795419i	$0.292749\pi$
$953$	10.8210	+	54.4010i	0.350527	+	1.76222i	−0.255532	+	0.966801i	$0.582251\pi$
$954$	−2.48801	+	4.66117i	−0.0805521	+	0.150911i
$955$	−5.31353	+	17.5164i	−0.171942	+	0.566816i
$956$	55.2687	−	22.9675i	1.78752	−	0.742821i
$957$	24.2730	−	19.9204i	0.784635	−	0.643934i
$958$	−12.9508	+	5.37310i	−0.418420	+	0.173597i
$959$		−	57.3226i		−	1.85104i
$960$	−29.1280	−	11.9478i	−0.940102	−	0.385613i
$961$			27.5392i			0.888362i
$962$	2.81628	+	6.78808i	0.0908006	+	0.218856i
$963$	−13.4083	+	11.0039i	−0.432077	+	0.354597i
$964$	−4.37802	+	10.6039i	−0.141007	+	0.341529i
$965$	22.4051	−	73.8597i	0.721246	−	2.37763i
$966$	−23.9200	−	12.7678i	−0.769612	−	0.410798i
$967$	−10.8993	−	54.7945i	−0.350498	−	1.76207i	−0.606197	−	0.795315i	$-0.707306\pi$
$967$	−10.8993	−	54.7945i	−0.350498	−	1.76207i	0.255699	−	0.966756i	$-0.417694\pi$
$968$	13.2808	−	8.90710i	0.426862	−	0.286285i
$969$	−6.24557	−	1.24232i	−0.200637	−	0.0399091i
$970$	5.65515	+	57.0815i	0.181576	+	1.83278i
$971$	1.38351	+	14.0470i	0.0443988	+	0.450788i	0.991524	+	0.129924i	$0.0414734\pi$
$971$	1.38351	+	14.0470i	0.0443988	+	0.450788i	−0.947125	+	0.320864i	$0.896027\pi$
$972$	−0.940767	+	1.76492i	−0.0301751	+	0.0566100i
$973$	−58.7764	+	17.8296i	−1.88428	+	0.571591i
$974$	−0.169322	+	0.113278i	−0.00542544	+	0.00362967i
$975$	23.6691	−	9.80406i	0.758017	−	0.313981i
$976$	−6.10245	−	7.40111i	−0.195335	−	0.236904i
$977$	2.63894	+	1.09309i	0.0844272	+	0.0349709i	0.424497	−	0.905429i	$-0.360451\pi$
$977$	2.63894	+	1.09309i	0.0844272	+	0.0349709i	−0.340070	+	0.940400i	$0.610451\pi$
$978$	−18.3306	+	3.65713i	−0.586148	+	0.116942i
$979$	−25.1015	+	46.9617i	−0.802248	+	1.50090i
$980$	117.283	+	96.0267i	3.74648	+	3.06746i
$981$	5.83277	−	7.10725i	0.186226	−	0.226917i
$982$	31.9533	−	17.1030i	1.01967	−	0.545779i
$983$	−32.1409	+	21.4759i	−1.02514	+	0.684974i	−0.950016	−	0.312201i	$-0.898934\pi$
$983$	−32.1409	+	21.4759i	−1.02514	+	0.684974i	−0.0751196	+	0.997175i	$0.523934\pi$
$984$	−1.57645	+	0.158010i	−0.0502553	+	0.00503717i
$985$	−4.00738	+	5.99747i	−0.127686	+	0.191095i
$986$	−25.9774	+	21.3440i	−0.827288	+	0.679733i
$987$	21.7301	+	40.6541i	0.691676	+	1.29403i
$988$	−8.36614	+	5.60399i	−0.266162	+	0.178287i
$989$	23.8977	+	2.35371i	0.759901	+	0.0748437i
$990$	16.0692	+	16.0507i	0.510712	+	0.510125i
$991$	7.19034	+	7.19034i	0.228409	+	0.228409i	0.812028	−	0.583619i	$-0.198364\pi$
$991$	7.19034	+	7.19034i	0.228409	+	0.228409i	−0.583619	+	0.812028i	$0.698364\pi$
$992$	−9.71088	+	4.05509i	−0.308321	+	0.128749i
$993$	−4.49482	+	4.49482i	−0.142639	+	0.142639i
$994$	42.1080	−	0.0241855i	1.33559	−	0.000767119i
$995$	1.73128	−	17.5780i	0.0548854	−	0.557260i
$996$	6.91478	+	4.60883i	0.219103	+	0.146036i
$997$	−41.3591	+	22.1069i	−1.30986	+	0.700133i	−0.970631	−	0.240573i	$-0.922665\pi$
$997$	−41.3591	+	22.1069i	−1.30986	+	0.700133i	−0.339225	+	0.940705i	$0.610165\pi$
$998$	29.2541	+	2.86431i	0.926021	+	0.0906681i
$999$	−1.76875	−	1.18184i	−0.0559606	−	0.0373917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.253.13	yes	512
128.85	even	32	inner	384.2.v.a.85.13	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.85.13	✓	512	128.85	even	32	inner
384.2.v.a.253.13	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540446 + 1.30687i) q^{2} +(0.634393 + 0.773010i) q^{3} +(-1.41584 - 1.41259i) q^{4} +(-3.76594 - 1.14238i) q^{5} +(-1.35308 + 0.411302i) q^{6} +(5.02585 - 0.999703i) q^{7} +(2.61126 - 1.08689i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})\)	\(q+(-0.540446 + 1.30687i) q^{2} +(0.634393 + 0.773010i) q^{3} +(-1.41584 - 1.41259i) q^{4} +(-3.76594 - 1.14238i) q^{5} +(-1.35308 + 0.411302i) q^{6} +(5.02585 - 0.999703i) q^{7} +(2.61126 - 1.08689i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(3.52824 - 4.30421i) q^{10} +(4.06125 - 0.399998i) q^{11} +(0.193748 - 1.99059i) q^{12} +(-0.709129 - 2.33768i) q^{13} +(-1.40971 + 7.10843i) q^{14} +(-1.50601 - 3.63583i) q^{15} +(0.00918989 + 3.99999i) q^{16} +(-1.18238 + 2.85451i) q^{17} +(-1.17633 - 0.785019i) q^{18} +(1.81765 + 0.971557i) q^{19} +(3.71824 + 6.93715i) q^{20} +(3.96114 + 3.25083i) q^{21} +(-1.67214 + 5.52371i) q^{22} +(2.07867 + 3.11095i) q^{23} +(2.49674 + 1.32901i) q^{24} +(8.71990 + 5.82645i) q^{25} +(3.43830 + 0.336649i) q^{26} +(-0.881921 + 0.471397i) q^{27} +(-8.52795 - 5.68404i) q^{28} +(0.754197 - 7.65749i) q^{29} +(5.56549 - 0.00319664i) q^{30} +(1.31544 - 1.31544i) q^{31} +(-5.23245 - 2.14977i) q^{32} +(2.88563 + 2.88563i) q^{33} +(-3.09148 - 3.08793i) q^{34} +(-20.0691 - 1.97663i) q^{35} +(1.66166 - 1.11305i) q^{36} +(1.00278 + 1.87607i) q^{37} +(-2.25205 + 1.85037i) q^{38} +(1.35719 - 2.03117i) q^{39} +(-11.0755 + 1.11011i) q^{40} +(-0.465749 + 0.311203i) q^{41} +(-6.38920 + 3.41982i) q^{42} +(4.07158 - 4.96124i) q^{43} +(-6.31510 - 5.17054i) q^{44} +(1.85513 - 3.47071i) q^{45} +(-5.18903 + 1.03526i) q^{46} +(8.31103 + 3.44254i) q^{47} +(-3.08620 + 2.54467i) q^{48} +(17.7926 - 7.36993i) q^{49} +(-12.3271 + 8.24693i) q^{50} +(-2.95666 + 0.896893i) q^{51} +(-2.29817 + 4.31149i) q^{52} +(-0.366200 - 3.71809i) q^{53} +(-0.139426 - 1.40732i) q^{54} +(-15.7514 - 3.13314i) q^{55} +(12.0372 - 8.07304i) q^{56} +(0.402084 + 2.02142i) q^{57} +(9.59977 + 5.12410i) q^{58} +(0.620862 - 2.04671i) q^{59} +(-3.00367 + 7.27512i) q^{60} +(-1.85378 + 1.52136i) q^{61} +(1.00819 + 2.43004i) q^{62} +5.12431i q^{63} +(5.63733 - 5.67632i) q^{64} +9.61367i q^{65} +(-5.33068 + 2.21163i) q^{66} +(-10.0924 + 8.28263i) q^{67} +(5.70630 - 2.37131i) q^{68} +(-1.08610 + 3.58040i) q^{69} +(13.4295 - 25.1595i) q^{70} +(-1.13357 - 5.69887i) q^{71} +(0.556578 + 2.77312i) q^{72} +(-3.80329 - 0.756522i) q^{73} +(-2.99373 + 0.296593i) q^{74} +(1.02794 + 10.4368i) q^{75} +(-1.20109 - 3.94316i) q^{76} +(20.0113 - 6.07037i) q^{77} +(1.92100 + 2.87141i) q^{78} +(-1.75819 + 0.728267i) q^{79} +(4.53492 - 15.0742i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(-0.154992 - 0.776863i) q^{82} +(-1.95865 + 3.66437i) q^{83} +(-1.01626 - 10.1981i) q^{84} +(7.71371 - 9.39919i) q^{85} +(4.28324 + 8.00232i) q^{86} +(6.39778 - 4.27486i) q^{87} +(10.1702 - 5.45864i) q^{88} +(-7.24931 + 10.8494i) q^{89} +(3.53318 + 4.30015i) q^{90} +(-5.90096 - 11.0399i) q^{91} +(1.45143 - 7.34091i) q^{92} +(1.85136 + 0.182343i) q^{93} +(-8.99062 + 9.00096i) q^{94} +(-5.73528 - 5.73528i) q^{95} +(-1.65764 - 5.40853i) q^{96} +(-7.28783 + 7.28783i) q^{97} +(0.0156433 + 27.2357i) q^{98} +(-0.399998 + 4.06125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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