LMFDB - Embedded newform 384.2.v.a.157.16

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			157.16
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0869984 - 1.41154i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.98486 + 0.245602i) q^{4} +(-0.678042 + 0.362421i) q^{5} +(1.41327 + 0.0517752i) q^{6} +(-0.110208 - 0.554052i) q^{7} +(0.519356 + 2.78034i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(-0.0869984 - 1.41154i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.98486 + 0.245602i) q^{4} +(-0.678042 + 0.362421i) q^{5} +(1.41327 + 0.0517752i) q^{6} +(-0.110208 - 0.554052i) q^{7} +(0.519356 + 2.78034i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(0.570558 + 0.925550i) q^{10} +(3.39910 - 4.14181i) q^{11} +(-0.0498693 - 1.99938i) q^{12} +(2.37520 - 4.44368i) q^{13} +(-0.772476 + 0.203764i) q^{14} +(-0.294216 - 0.710300i) q^{15} +(3.87936 - 0.974974i) q^{16} +(1.50219 - 3.62661i) q^{17} +(-0.190050 + 1.40139i) q^{18} +(1.06633 + 3.51523i) q^{19} +(1.25681 - 0.885885i) q^{20} +(0.562186 - 0.0553705i) q^{21} +(-6.14203 - 4.43762i) q^{22} +(6.43758 - 4.30145i) q^{23} +(-2.81785 + 0.244335i) q^{24} +(-2.44946 + 3.66587i) q^{25} +(-6.47905 - 2.96608i) q^{26} +(0.290285 - 0.956940i) q^{27} +(0.354824 + 1.07265i) q^{28} +(0.104844 - 0.0860430i) q^{29} +(-0.977018 + 0.477091i) q^{30} +(-0.250209 + 0.250209i) q^{31} +(-1.71371 - 5.39103i) q^{32} +(3.78870 + 3.78870i) q^{33} +(-5.24978 - 1.80489i) q^{34} +(0.275525 + 0.335729i) q^{35} +(1.99464 + 0.146344i) q^{36} +(-8.81530 - 2.67409i) q^{37} +(4.86910 - 1.81099i) q^{38} +(4.18947 + 2.79931i) q^{39} +(-1.35980 - 1.69696i) q^{40} +(0.174404 + 0.261014i) q^{41} +(-0.127067 - 0.788728i) q^{42} +(0.800053 + 8.12307i) q^{43} +(-5.72950 + 9.05576i) q^{44} +(0.735718 - 0.223178i) q^{45} +(-6.63171 - 8.71265i) q^{46} +(7.48036 + 3.09847i) q^{47} +(0.590036 + 3.95624i) q^{48} +(6.17233 - 2.55666i) q^{49} +(5.38761 + 3.13857i) q^{50} +(3.46191 + 1.85043i) q^{51} +(-3.62306 + 9.40344i) q^{52} +(-5.71984 - 4.69415i) q^{53} +(-1.37601 - 0.326495i) q^{54} +(-0.803651 + 4.04023i) q^{55} +(1.48321 - 0.594165i) q^{56} +(-3.60282 + 0.716646i) q^{57} +(-0.130574 - 0.140505i) q^{58} +(-2.98807 - 5.59029i) q^{59} +(0.758430 + 1.33759i) q^{60} +(-14.5584 - 1.43387i) q^{61} +(0.374946 + 0.331410i) q^{62} +0.564906i q^{63} +(-7.46054 + 2.88797i) q^{64} +3.87382i q^{65} +(5.01827 - 5.67749i) q^{66} +(0.526102 + 0.0518166i) q^{67} +(-2.09094 + 7.56727i) q^{68} +(3.64975 + 6.82820i) q^{69} +(0.449923 - 0.418122i) q^{70} +(-4.44436 + 0.884037i) q^{71} +(0.0330397 - 2.82823i) q^{72} +(-1.65631 + 8.32681i) q^{73} +(-3.00766 + 12.6757i) q^{74} +(-3.40813 - 2.79698i) q^{75} +(-2.97987 - 6.71535i) q^{76} +(-2.66939 - 1.42682i) q^{77} +(3.58685 - 6.15712i) q^{78} +(12.2655 - 5.08055i) q^{79} +(-2.27702 + 2.06703i) q^{80} +(0.923880 + 0.382683i) q^{81} +(0.353258 - 0.268885i) q^{82} +(5.70222 - 1.72975i) q^{83} +(-1.10226 + 0.247977i) q^{84} +(0.295811 + 3.00342i) q^{85} +(11.3964 - 1.83600i) q^{86} +(0.0753522 + 0.112772i) q^{87} +(13.2810 + 7.29956i) q^{88} +(12.2367 + 8.17628i) q^{89} +(-0.379029 - 1.01908i) q^{90} +(-2.72379 - 0.826253i) q^{91} +(-11.7213 + 10.1189i) q^{92} +(-0.224479 - 0.273528i) q^{93} +(3.72281 - 10.8284i) q^{94} +(-1.99701 - 1.99701i) q^{95} +(5.53304 - 1.17704i) q^{96} +(-0.824257 + 0.824257i) q^{97} +(-4.14580 - 8.49003i) q^{98} +(-4.14181 + 3.39910i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	−0.0869984	−	1.41154i	−0.0615171	−	0.998106i
$2$	−0.0869984	−	1.41154i	−0.0615171	−	0.998106i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	−1.98486	+	0.245602i	−0.992431	+	0.122801i
$5$	−0.678042	+	0.362421i	−0.303230	+	0.162080i	−0.615993	−	0.787751i	$-0.711245\pi$
$5$	−0.678042	+	0.362421i	−0.303230	+	0.162080i	0.312764	+	0.949831i	$0.398745\pi$
$6$	1.41327	+	0.0517752i	0.576963	+	0.0211371i
$7$	−0.110208	−	0.554052i	−0.0416546	−	0.209412i	0.954353	−	0.298681i	$-0.0965468\pi$
$7$	−0.110208	−	0.554052i	−0.0416546	−	0.209412i	−0.996008	+	0.0892695i	$0.971547\pi$
$8$	0.519356	+	2.78034i	0.183620	+	0.982997i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	0.570558	+	0.925550i	0.180426	+	0.292685i
$11$	3.39910	−	4.14181i	1.02487	−	1.24880i	0.0567278	−	0.998390i	$-0.481933\pi$
$11$	3.39910	−	4.14181i	1.02487	−	1.24880i	0.968139	−	0.250414i	$-0.0805667\pi$
$12$	−0.0498693	−	1.99938i	−0.0143960	−	0.577171i
$13$	2.37520	−	4.44368i	0.658761	−	1.23245i	−0.301531	−	0.953456i	$-0.597498\pi$
$13$	2.37520	−	4.44368i	0.658761	−	1.23245i	0.960292	−	0.278998i	$-0.0900023\pi$
$14$	−0.772476	+	0.203764i	−0.206453	+	0.0544581i
$15$	−0.294216	−	0.710300i	−0.0759663	−	0.183399i
$16$	3.87936	−	0.974974i	0.969840	−	0.243744i
$17$	1.50219	−	3.62661i	0.364335	−	0.879583i	−0.630321	−	0.776335i	$-0.717077\pi$
$17$	1.50219	−	3.62661i	0.364335	−	0.879583i	0.994656	−	0.103248i	$-0.0329234\pi$
$18$	−0.190050	+	1.40139i	−0.0447952	+	0.330310i
$19$	1.06633	+	3.51523i	0.244634	+	0.806449i	0.990156	+	0.139968i	$0.0447000\pi$
$19$	1.06633	+	3.51523i	0.244634	+	0.806449i	−0.745522	+	0.666480i	$0.767800\pi$
$20$	1.25681	−	0.885885i	0.281031	−	0.198090i
$21$	0.562186	−	0.0553705i	0.122679	−	0.0120828i
$22$	−6.14203	−	4.43762i	−1.30949	−	0.946103i
$23$	6.43758	−	4.30145i	1.34233	−	0.896915i	0.343225	−	0.939253i	$-0.388481\pi$
$23$	6.43758	−	4.30145i	1.34233	−	0.896915i	0.999103	+	0.0423380i	$0.0134806\pi$
$24$	−2.81785	+	0.244335i	−0.575192	+	0.0498746i
$25$	−2.44946	+	3.66587i	−0.489892	+	0.733175i
$26$	−6.47905	−	2.96608i	−1.27065	−	0.581696i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	0.354824	+	1.07265i	0.0670554	+	0.202712i
$29$	0.104844	−	0.0860430i	0.0194690	−	0.0159778i	−0.624608	−	0.780938i	$-0.714741\pi$
$29$	0.104844	−	0.0860430i	0.0194690	−	0.0159778i	0.644077	+	0.764960i	$0.277241\pi$
$30$	−0.977018	+	0.477091i	−0.178378	+	0.0871046i
$31$	−0.250209	+	0.250209i	−0.0449388	+	0.0449388i	−0.729219	−	0.684280i	$-0.760116\pi$
$31$	−0.250209	+	0.250209i	−0.0449388	+	0.0449388i	0.684280	+	0.729219i	$0.260116\pi$
$32$	−1.71371	−	5.39103i	−0.302944	−	0.953008i
$33$	3.78870	+	3.78870i	0.659528	+	0.659528i
$34$	−5.24978	−	1.80489i	−0.900329	−	0.309536i
$35$	0.275525	+	0.335729i	0.0465723	+	0.0567485i
$36$	1.99464	+	0.146344i	0.332440	+	0.0243907i
$37$	−8.81530	−	2.67409i	−1.44923	−	0.439618i	−0.535011	−	0.844845i	$-0.679692\pi$
$37$	−8.81530	−	2.67409i	−1.44923	−	0.439618i	−0.914216	+	0.405227i	$0.867192\pi$
$38$	4.86910	−	1.81099i	0.789872	−	0.293781i
$39$	4.18947	+	2.79931i	0.670852	+	0.448249i
$40$	−1.35980	−	1.69696i	−0.215003	−	0.268313i
$41$	0.174404	+	0.261014i	0.0272374	+	0.0407636i	0.844838	−	0.535021i	$-0.179696\pi$
$41$	0.174404	+	0.261014i	0.0272374	+	0.0407636i	−0.817601	+	0.575785i	$0.804696\pi$
$42$	−0.127067	−	0.788728i	−0.0196068	−	0.121703i
$43$	0.800053	+	8.12307i	0.122007	+	1.23876i	0.839953	+	0.542658i	$0.182582\pi$
$43$	0.800053	+	8.12307i	0.122007	+	1.23876i	−0.717947	+	0.696098i	$0.754918\pi$
$44$	−5.72950	+	9.05576i	−0.863755	+	1.36521i
$45$	0.735718	−	0.223178i	0.109674	−	0.0332694i
$46$	−6.63171	−	8.71265i	−0.977793	−	1.28461i
$47$	7.48036	+	3.09847i	1.09112	+	0.451958i	0.854398	−	0.519619i	$-0.173926\pi$
$47$	7.48036	+	3.09847i	1.09112	+	0.451958i	0.236724	+	0.971577i	$0.423926\pi$
$48$	0.590036	+	3.95624i	0.0851643	+	0.571034i
$49$	6.17233	−	2.55666i	0.881761	−	0.365237i
$50$	5.38761	+	3.13857i	0.761923	+	0.443861i
$51$	3.46191	+	1.85043i	0.484764	+	0.259112i
$52$	−3.62306	+	9.40344i	−0.502428	+	1.30402i
$53$	−5.71984	−	4.69415i	−0.785680	−	0.644791i	0.153526	−	0.988145i	$-0.450937\pi$
$53$	−5.71984	−	4.69415i	−0.785680	−	0.644791i	−0.939206	+	0.343354i	$0.888437\pi$
$54$	−1.37601	−	0.326495i	−0.187251	−	0.0444303i
$55$	−0.803651	+	4.04023i	−0.108364	+	0.544784i
$56$	1.48321	−	0.594165i	0.198203	−	0.0793986i
$57$	−3.60282	+	0.716646i	−0.477205	+	0.0949220i
$58$	−0.130574	−	0.140505i	−0.0171452	−	0.0184492i
$59$	−2.98807	−	5.59029i	−0.389014	−	0.727794i	0.608839	−	0.793294i	$-0.291636\pi$
$59$	−2.98807	−	5.59029i	−0.389014	−	0.727794i	−0.997853	+	0.0655002i	$0.979136\pi$
$60$	0.758430	+	1.33759i	0.0979129	+	0.172682i
$61$	−14.5584	−	1.43387i	−1.86401	−	0.183589i	−0.897636	−	0.440738i	$-0.854717\pi$
$61$	−14.5584	−	1.43387i	−1.86401	−	0.183589i	−0.966372	+	0.257150i	$0.917217\pi$
$62$	0.374946	+	0.331410i	0.0476182	+	0.0420892i
$63$			0.564906i			0.0711715i
$64$	−7.46054	+	2.88797i	−0.932567	+	0.360996i
$65$			3.87382i			0.480488i
$66$	5.01827	−	5.67749i	0.617706	−	0.698851i
$67$	0.526102	+	0.0518166i	0.0642736	+	0.00633040i	0.130103	−	0.991501i	$-0.458469\pi$
$67$	0.526102	+	0.0518166i	0.0642736	+	0.00633040i	−0.0658292	+	0.997831i	$0.520969\pi$
$68$	−2.09094	+	7.56727i	−0.253564	+	0.917666i
$69$	3.64975	+	6.82820i	0.439378	+	0.822019i
$70$	0.449923	−	0.418122i	0.0537760	−	0.0499751i
$71$	−4.44436	+	0.884037i	−0.527448	+	0.104916i	−0.451629	−	0.892206i	$-0.649157\pi$
$71$	−4.44436	+	0.884037i	−0.527448	+	0.104916i	−0.0758187	+	0.997122i	$0.524157\pi$
$72$	0.0330397	−	2.82823i	0.00389377	−	0.333311i
$73$	−1.65631	+	8.32681i	−0.193856	+	0.974580i	0.754241	+	0.656598i	$0.228005\pi$
$73$	−1.65631	+	8.32681i	−0.193856	+	0.974580i	−0.948097	+	0.317982i	$0.896995\pi$
$74$	−3.00766	+	12.6757i	−0.349633	+	1.47353i
$75$	−3.40813	−	2.79698i	−0.393537	−	0.322968i
$76$	−2.97987	−	6.71535i	−0.341815	−	0.770304i
$77$	−2.66939	−	1.42682i	−0.304205	−	0.162601i
$78$	3.58685	−	6.15712i	0.406131	−	0.697157i
$79$	12.2655	−	5.08055i	1.37998	−	0.571607i	0.435504	−	0.900187i	$-0.356570\pi$
$79$	12.2655	−	5.08055i	1.37998	−	0.571607i	0.944476	+	0.328580i	$0.106570\pi$
$80$	−2.27702	+	2.06703i	−0.254578	+	0.231101i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	0.353258	−	0.268885i	0.0390108	−	0.0296934i
$83$	5.70222	−	1.72975i	0.625900	−	0.189865i	0.0386272	−	0.999254i	$-0.487702\pi$
$83$	5.70222	−	1.72975i	0.625900	−	0.189865i	0.587273	+	0.809389i	$0.300202\pi$
$84$	−1.10226	+	0.247977i	−0.120267	+	0.0270565i
$85$	0.295811	+	3.00342i	0.0320852	+	0.325767i
$86$	11.3964	−	1.83600i	1.22890	−	0.197981i
$87$	0.0753522	+	0.112772i	0.00807860	+	0.0120905i
$88$	13.2810	+	7.29956i	1.41576	+	0.778136i
$89$	12.2367	+	8.17628i	1.29708	+	0.866684i	0.996210	−	0.0869792i	$-0.0277214\pi$
$89$	12.2367	+	8.17628i	1.29708	+	0.866684i	0.300875	+	0.953664i	$0.402721\pi$
$90$	−0.379029	−	1.01908i	−0.0399532	−	0.107420i
$91$	−2.72379	−	0.826253i	−0.285531	−	0.0866149i
$92$	−11.7213	+	10.1189i	−1.22203	+	1.05497i
$93$	−0.224479	−	0.273528i	−0.0232774	−	0.0283636i
$94$	3.72281	−	10.8284i	0.383979	−	1.11686i
$95$	−1.99701	−	1.99701i	−0.204889	−	0.204889i
$96$	5.53304	−	1.17704i	0.564714	−	0.120131i
$97$	−0.824257	+	0.824257i	−0.0836907	+	0.0836907i	−0.747713	−	0.664022i	$-0.768848\pi$
$97$	−0.824257	+	0.824257i	−0.0836907	+	0.0836907i	0.664022	+	0.747713i	$0.268848\pi$
$98$	−4.14580	−	8.49003i	−0.418789	−	0.857623i
$99$	−4.14181	+	3.39910i	−0.416268	+	0.341622i
$100$	3.96149	−	7.87785i	0.396149	−	0.787785i
$101$	1.10150	−	3.63117i	0.109604	−	0.361315i	−0.884931	−	0.465722i	$-0.845795\pi$
$101$	1.10150	−	3.63117i	0.109604	−	0.361315i	0.994535	+	0.104407i	$0.0332945\pi$
$102$	2.31076	−	5.04759i	0.228800	−	0.499786i
$103$	1.11450	−	1.66796i	0.109814	−	0.164349i	−0.772492	−	0.635025i	$-0.780990\pi$
$103$	1.11450	−	1.66796i	0.109814	−	0.164349i	0.882306	+	0.470676i	$0.155990\pi$
$104$	13.5885	+	4.29599i	1.33246	+	0.421256i
$105$	−0.361118	+	0.241292i	−0.0352415	+	0.0235476i
$106$	−6.12834	+	8.48214i	−0.595237	+	0.823858i
$107$	7.51669	−	0.740329i	0.726666	−	0.0715703i	0.272082	−	0.962274i	$-0.412288\pi$
$107$	7.51669	−	0.740329i	0.726666	−	0.0715703i	0.454584	+	0.890704i	$0.349788\pi$
$108$	−0.341148	+	1.97069i	−0.0328270	+	0.189630i
$109$	0.167835	+	0.553279i	0.0160757	+	0.0529945i	0.964611	−	0.263676i	$-0.0849350\pi$
$109$	0.167835	+	0.553279i	0.0160757	+	0.0529945i	−0.948536	+	0.316671i	$0.897435\pi$
$110$	5.77284	+	0.782889i	0.550419	+	0.0746455i
$111$	3.52527	−	8.51075i	0.334604	−	0.807804i
$112$	−0.967722	−	2.04192i	−0.0914411	−	0.192943i
$113$	4.89839	+	11.8258i	0.460802	+	1.11247i	0.968069	+	0.250686i	$0.0806560\pi$
$113$	4.89839	+	11.8258i	0.460802	+	1.11247i	−0.507266	+	0.861789i	$0.669344\pi$
$114$	1.32501	+	5.02316i	0.124099	+	0.470462i
$115$	−2.80601	+	5.24968i	−0.261662	+	0.489535i
$116$	−0.186968	+	0.196533i	−0.0173595	+	0.0182477i
$117$	−3.19648	+	3.89492i	−0.295514	+	0.360085i
$118$	−7.63093	+	4.70412i	−0.702484	+	0.433049i
$119$	−2.17488	−	0.432611i	−0.199371	−	0.0396574i
$120$	1.82207	−	1.18692i	0.166332	−	0.108350i
$121$	−3.45475	−	17.3682i	−0.314069	−	1.57893i
$122$	−0.757409	+	20.6744i	−0.0685726	+	1.87177i
$123$	−0.276852	+	0.147981i	−0.0249629	+	0.0133430i
$124$	0.435178	−	0.558081i	0.0390801	−	0.0501172i
$125$	0.709036	−	7.19896i	0.0634181	−	0.643895i
$126$	0.797385	−	0.0491459i	0.0710367	−	0.00437827i
$127$	3.16801			0.281116			0.140558	−	0.990072i	$-0.455110\pi$
$127$	3.16801			0.281116			0.140558	+	0.990072i	$0.455110\pi$
$128$	4.72553	+	10.2796i	0.417681	+	0.908594i
$129$	−8.16237			−0.718657
$130$	5.46803	−	0.337016i	0.479578	−	0.0295583i
$131$	−1.12670	+	11.4396i	−0.0984406	+	0.999484i	0.811390	+	0.584505i	$0.198711\pi$
$131$	−1.12670	+	11.4396i	−0.0984406	+	0.999484i	−0.909831	+	0.414979i	$0.863789\pi$
$132$	−8.45056	−	6.58953i	−0.735527	−	0.573545i
$133$	1.83010	−	0.978209i	0.158690	−	0.0848215i
$134$	0.0273709	−	0.747120i	0.00236448	−	0.0645413i
$135$	0.149990	+	0.754051i	0.0129091	+	0.0648984i
$136$	10.8634	+	2.29309i	0.931527	+	0.196631i
$137$	−17.7983	−	3.54030i	−1.52061	−	0.302468i	−0.637064	−	0.770811i	$-0.719851\pi$
$137$	−17.7983	−	3.54030i	−1.52061	−	0.302468i	−0.883547	+	0.468343i	$0.844851\pi$
$138$	9.32072	−	5.74579i	0.793432	−	0.489114i
$139$	−7.80612	+	9.51178i	−0.662106	+	0.806779i	−0.990464	−	0.137775i	$-0.956005\pi$
$139$	−7.80612	+	9.51178i	−0.662106	+	0.806779i	0.328357	+	0.944554i	$0.393505\pi$
$140$	−0.629336	−	0.598706i	−0.0531886	−	0.0505999i
$141$	−3.81675	+	7.14064i	−0.321428	+	0.601350i
$142$	1.63450	+	6.19645i	0.137164	+	0.519995i
$143$	−10.3314	−	24.9421i	−0.863952	−	2.08576i
$144$	−3.99503	+	0.199415i	−0.332919	+	0.0166179i
$145$	−0.0399046	+	0.0963383i	−0.00331390	+	0.00800046i
$146$	11.8977	+	1.61352i	0.984660	+	0.133535i
$147$	1.93936	+	6.39320i	0.159955	+	0.527303i
$148$	18.1539	+	3.14265i	1.49224	+	0.258324i
$149$	−19.9947	+	1.96931i	−1.63803	+	0.161332i	−0.874696	−	0.484672i	$-0.838939\pi$
$149$	−19.9947	+	1.96931i	−1.63803	+	0.161332i	−0.763334	+	0.646004i	$0.776439\pi$
$150$	−3.65154	+	5.05403i	−0.298147	+	0.412660i
$151$	−1.42347	+	0.951133i	−0.115840	+	0.0774021i	−0.612141	−	0.790749i	$-0.709691\pi$
$151$	−1.42347	+	0.951133i	−0.115840	+	0.0774021i	0.496300	+	0.868151i	$0.334691\pi$
$152$	−9.21971	+	4.79042i	−0.747817	+	0.388554i
$153$	−2.18084	+	3.26386i	−0.176311	+	0.263868i
$154$	−1.78177	+	3.89206i	−0.143579	+	0.313631i
$155$	0.0789711	−	0.260333i	0.00634311	−	0.0209104i
$156$	−9.00304	−	4.52731i	−0.720820	−	0.362475i
$157$	9.69310	−	7.95493i	0.773594	−	0.634872i	−0.162465	−	0.986714i	$-0.551945\pi$
$157$	9.69310	−	7.95493i	0.773594	−	0.634872i	0.936059	+	0.351842i	$0.114445\pi$
$158$	−8.23846	−	16.8712i	−0.655416	−	1.34220i
$159$	5.23219	−	5.23219i	0.414940	−	0.414940i
$160$	3.11579	+	3.03426i	0.246325	+	0.239879i
$161$	−3.09270	−	3.09270i	−0.243739	−	0.243739i
$162$	0.459795	−	1.33738i	0.0361249	−	0.105075i
$163$	10.4001	+	12.6725i	0.814595	+	0.992587i	0.999951	+	0.00991570i	$0.00315632\pi$
$163$	10.4001	+	12.6725i	0.814595	+	0.992587i	−0.185356	+	0.982672i	$0.559344\pi$
$164$	−0.410274	−	0.475244i	−0.0320370	−	0.0371103i
$165$	−3.94200	−	1.19579i	−0.306884	−	0.0930924i
$166$	−2.93769	−	7.89840i	−0.228009	−	0.613035i
$167$	1.35660	+	0.906453i	0.104977	+	0.0701435i	0.606951	−	0.794739i	$-0.292393\pi$
$167$	1.35660	+	0.906453i	0.104977	+	0.0701435i	−0.501974	+	0.864883i	$0.667393\pi$
$168$	0.445923	+	1.53431i	0.0344037	+	0.118375i
$169$	−6.88231	−	10.3001i	−0.529408	−	0.792316i
$170$	4.21370	−	0.678840i	0.323176	−	0.0520647i
$171$	−0.360057	−	3.65572i	−0.0275342	−	0.279560i
$172$	−3.58304	−	15.9267i	−0.273204	−	1.21440i
$173$	1.23338	−	0.374141i	0.0937720	−	0.0284454i	−0.243050	−	0.970014i	$-0.578148\pi$
$173$	1.23338	−	0.374141i	0.0937720	−	0.0284454i	0.336822	+	0.941568i	$0.390648\pi$
$174$	0.152627	−	0.116173i	0.0115706	−	0.00880707i
$175$	2.30103	+	0.953119i	0.173942	+	0.0720490i
$176$	9.14816	−	19.3816i	0.689569	−	1.46094i
$177$	5.85625	−	2.42574i	0.440183	−	0.182330i
$178$	10.4765	−	17.9838i	0.785250	−	1.34794i
$179$	−19.5643	−	10.4573i	−1.46230	−	0.781617i	−0.467553	−	0.883965i	$-0.654864\pi$
$179$	−19.5643	−	10.4573i	−1.46230	−	0.781617i	−0.994749	+	0.102348i	$0.967364\pi$
$180$	−1.40549	+	0.623671i	−0.104759	+	0.0464857i
$181$	14.3971	+	11.8154i	1.07013	+	0.878234i	0.992921	−	0.118781i	$-0.0378986\pi$
$181$	14.3971	+	11.8154i	1.07013	+	0.878234i	0.0772108	+	0.997015i	$0.475399\pi$
$182$	−0.929320	+	3.91661i	−0.0688858	+	0.290319i
$183$	2.85394	−	14.3477i	0.210969	−	1.06061i
$184$	15.3029	+	15.6647i	1.12814	+	1.15481i
$185$	6.94629	−	1.38170i	0.510702	−	0.101585i
$186$	−0.366566	+	0.340656i	−0.0268779	+	0.0249781i
$187$	−9.91465	−	18.5490i	−0.725031	−	1.35644i
$188$	−15.6085	−	4.31283i	−1.13837	−	0.314546i
$189$	−0.562186	−	0.0553705i	−0.0408930	−	0.00402761i
$190$	−2.64511	+	2.99259i	−0.191897	+	0.217105i
$191$			7.27164i			0.526158i	0.964774	+	0.263079i	$0.0847379\pi$
$191$			7.27164i			0.526158i	−0.964774	+	0.263079i	$0.915262\pi$
$192$	−2.14280	−	7.70768i	−0.154643	−	0.556254i
$193$			4.50922i			0.324581i	0.986743	+	0.162291i	$0.0518882\pi$
$193$			4.50922i			0.324581i	−0.986743	+	0.162291i	$0.948112\pi$
$194$	1.23518	+	1.09176i	0.0886806	+	0.0783838i
$195$	−3.85517	−	0.379701i	−0.276074	−	0.0271909i
$196$	−11.6233	+	6.59056i	−0.830236	+	0.470754i
$197$	−3.80216	−	7.11334i	−0.270893	−	0.506804i	0.709286	−	0.704921i	$-0.249018\pi$
$197$	−3.80216	−	7.11334i	−0.270893	−	0.506804i	−0.980178	+	0.198117i	$0.936518\pi$
$198$	5.15828	+	5.55060i	0.366583	+	0.394464i
$199$	−27.2866	+	5.42764i	−1.93430	+	0.384755i	−0.934728	+	0.355365i	$0.884357\pi$
$199$	−27.2866	+	5.42764i	−1.93430	+	0.384755i	−0.999568	+	0.0293905i	$0.990643\pi$
$200$	−11.4645	−	4.90643i	−0.810663	−	0.346937i
$201$	−0.103134	+	0.518490i	−0.00727452	+	0.0365715i
$202$	−5.22136	−	1.23891i	−0.367373	−	0.0871691i
$203$	−0.0592268	−	0.0486062i	−0.00415691	−	0.00341149i
$204$	−7.32588	−	2.82259i	−0.512914	−	0.197621i
$205$	−0.212850	−	0.113771i	−0.0148661	−	0.00794611i
$206$	−2.45134	−	1.42804i	−0.170793	−	0.0994962i
$207$	−7.15306	+	2.96289i	−0.497172	+	0.205935i
$208$	4.88176	−	19.5544i	0.338489	−	1.35585i
$209$	18.1840	+	7.53205i	1.25781	+	0.521003i
$210$	0.372008	+	0.488739i	0.0256710	+	0.0337262i
$211$	−18.8208	+	5.70922i	−1.29568	+	0.393039i	−0.861486	−	0.507782i	$-0.830466\pi$
$211$	−18.8208	+	5.70922i	−1.29568	+	0.393039i	−0.434191	+	0.900821i	$0.642966\pi$
$212$	12.5060	+	7.91244i	0.858915	+	0.543428i
$213$	−0.444157	−	4.50961i	−0.0304332	−	0.308993i
$214$	−1.69894	−	10.5457i	−0.116137	−	0.720887i
$215$	−3.48644	−	5.21783i	−0.237773	−	0.355853i
$216$	2.81138	+	0.310096i	0.191290	+	0.0210994i
$217$	0.166203	+	0.111054i	0.0112826	+	0.00753881i
$218$	0.766371	−	0.285040i	0.0519052	−	0.0193053i
$219$	−8.12437	−	2.46450i	−0.548994	−	0.166536i
$220$	0.602847	−	8.21667i	0.0406440	−	0.553968i
$221$	−12.5475	−	15.2892i	−0.844036	−	1.02846i
$222$	−12.3199	−	4.23562i	−0.826858	−	0.284276i
$223$	16.3326	+	16.3326i	1.09371	+	1.09371i	0.995129	+	0.0985838i	$0.0314312\pi$
$223$	16.3326	+	16.3326i	1.09371	+	1.09371i	0.0985838	+	0.995129i	$0.468569\pi$
$224$	−2.79805	+	1.54362i	−0.186952	+	0.103137i
$225$	3.11757	−	3.11757i	0.207838	−	0.207838i
$226$	16.2663	−	7.94308i	1.08202	−	0.528366i
$227$	15.7450	−	12.9216i	1.04503	−	0.857634i	0.0549989	−	0.998486i	$-0.482484\pi$
$227$	15.7450	−	12.9216i	1.04503	−	0.857634i	0.990031	+	0.140853i	$0.0449845\pi$
$228$	6.97509	−	2.30730i	0.461937	−	0.152805i
$229$	0.103506	−	0.341213i	0.00683985	−	0.0225480i	−0.953454	−	0.301539i	$-0.902500\pi$
$229$	0.103506	−	0.341213i	0.00683985	−	0.0225480i	0.960294	+	0.278991i	$0.0899998\pi$
$230$	7.65423	+	3.50407i	0.504705	+	0.231052i
$231$	1.68159	−	2.51668i	0.110641	−	0.165585i
$232$	0.293680	+	0.246814i	0.0192810	+	0.0162041i
$233$	−11.5601	+	7.72421i	−0.757327	+	0.506030i	−0.873276	−	0.487225i	$-0.838009\pi$
$233$	−11.5601	+	7.72421i	−0.757327	+	0.506030i	0.115949	+	0.993255i	$0.463009\pi$
$234$	5.77590	+	4.17309i	0.377582	+	0.272803i
$235$	−6.19495	+	0.610149i	−0.404114	+	0.0398017i
$236$	7.30390	+	10.3621i	0.475444	+	0.674514i
$237$	3.85385	+	12.7045i	0.250335	+	0.825243i
$238$	−0.421435	+	3.10756i	−0.0273176	+	0.201433i
$239$	2.22623	−	5.37459i	0.144003	−	0.347653i	−0.835378	−	0.549675i	$-0.814751\pi$
$239$	2.22623	−	5.37459i	0.144003	−	0.347653i	0.979381	+	0.202022i	$0.0647514\pi$
$240$	−1.83389	−	2.46866i	−0.118377	−	0.159351i
$241$	−1.11027	−	2.68043i	−0.0715189	−	0.172662i	0.884078	−	0.467340i	$-0.154788\pi$
$241$	−1.11027	−	2.68043i	−0.0715189	−	0.172662i	−0.955597	+	0.294678i	$0.904788\pi$
$242$	−24.2153	+	6.38751i	−1.55662	+	0.410605i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	29.2485	−	0.729528i	1.87244	−	0.0467032i
$245$	−3.25851	+	3.97051i	−0.208179	+	0.253666i
$246$	0.232965	+	0.377912i	0.0148533	+	0.0240948i
$247$	18.1533	+	3.61091i	1.15507	+	0.229757i
$248$	−0.825611	−	0.565716i	−0.0524264	−	0.0359230i
$249$	1.16251	+	5.84431i	0.0736708	+	0.370368i
$250$	−10.2233	−	0.374531i	−0.646576	−	0.0236874i
$251$	−10.0797	+	5.38769i	−0.636223	+	0.340068i	−0.757774	−	0.652517i	$-0.773713\pi$
$251$	−10.0797	+	5.38769i	−0.636223	+	0.340068i	0.121551	+	0.992585i	$0.461213\pi$
$252$	−0.138742	−	1.12126i	−0.00873995	−	0.0706328i
$253$	4.06615	−	41.2843i	0.255637	−	2.59552i
$254$	−0.275612	−	4.47176i	−0.0172934	−	0.280583i
$255$	−3.01795			−0.188992
$256$	14.0989	−	7.56455i	0.881178	−	0.472784i
$257$	28.9773			1.80755			0.903777	−	0.428003i	$-0.140783\pi$
$257$	28.9773			1.80755			0.903777	+	0.428003i	$0.140783\pi$
$258$	0.710113	+	11.5215i	0.0442097	+	0.717296i
$259$	−0.510071	+	5.17884i	−0.0316943	+	0.321797i
$260$	−0.951420	−	7.68900i	−0.0590046	−	0.476852i
$261$	−0.119615	+	0.0639357i	−0.00740400	+	0.00395752i
$262$	16.2454	+	0.595154i	1.00365	+	0.0367687i
$263$	−0.370034	−	1.86029i	−0.0228173	−	0.114710i	0.967698	−	0.252112i	$-0.0811250\pi$
$263$	−0.370034	−	1.86029i	−0.0228173	−	0.114710i	−0.990515	+	0.137401i	$0.956125\pi$
$264$	−8.56617	+	12.5015i	−0.527211	+	0.769417i
$265$	5.57955	+	1.10984i	0.342749	+	0.0681770i
$266$	−1.53999	−	2.49815i	−0.0944230	−	0.153171i
$267$	−9.33632	+	11.3763i	−0.571373	+	0.696220i
$268$	−1.05697	+	0.0263633i	−0.0645646	+	0.00161039i
$269$	−2.18738	+	4.09230i	−0.133367	+	0.249512i	−0.939736	−	0.341900i	$-0.888929\pi$
$269$	−2.18738	+	4.09230i	−0.133367	+	0.249512i	0.806369	+	0.591412i	$0.201429\pi$
$270$	1.05132	−	0.277317i	0.0639813	−	0.0168770i
$271$	−0.873615	−	2.10909i	−0.0530683	−	0.128118i	0.895122	−	0.445822i	$-0.147088\pi$
$271$	−0.873615	−	2.10909i	−0.0530683	−	0.128118i	−0.948190	+	0.317703i	$0.897088\pi$
$272$	2.29169	−	15.5335i	0.138954	−	0.941858i
$273$	1.08925	−	2.62969i	0.0659246	−	0.159156i
$274$	−3.44884	+	25.4309i	−0.208352	+	1.53634i
$275$	6.85742	+	22.6059i	0.413518	+	1.36319i
$276$	−8.92127	−	12.6566i	−0.536997	−	0.761841i
$277$	−0.331568	+	0.0326566i	−0.0199220	+	0.00196215i	−0.107973	−	0.994154i	$-0.534436\pi$
$277$	−0.331568	+	0.0326566i	−0.0199220	+	0.00196215i	0.0880512	+	0.996116i	$0.471936\pi$
$278$	14.1053	+	10.1911i	0.845982	+	0.611222i
$279$	0.294214	−	0.196588i	0.0176141	−	0.0117694i
$280$	−0.790343	+	0.940416i	−0.0472320	+	0.0562006i
$281$	−9.70045	+	14.5178i	−0.578681	+	0.866057i	−0.999149	−	0.0412506i	$-0.986866\pi$
$281$	−9.70045	+	14.5178i	−0.578681	+	0.866057i	0.420468	+	0.907307i	$0.361866\pi$
$282$	10.4113	+	4.76625i	0.619984	+	0.283826i
$283$	−5.50354	+	18.1427i	−0.327151	+	1.07847i	0.626967	+	0.779045i	$0.284296\pi$
$283$	−5.50354	+	18.1427i	−0.327151	+	1.07847i	−0.954119	+	0.299428i	$0.903204\pi$
$284$	8.60431	−	2.84624i	0.510572	−	0.168893i
$285$	2.18314	−	1.79165i	0.129318	−	0.106128i
$286$	−34.3079	+	16.7530i	−2.02867	+	0.990626i
$287$	0.125395	−	0.125395i	0.00740182	−	0.00740182i
$288$	0.629042	+	5.62177i	0.0370667	+	0.331266i
$289$	1.12508	+	1.12508i	0.0661813	+	0.0661813i
$290$	0.139456	+	0.0479455i	0.00818917	+	0.00281546i
$291$	−0.739497	−	0.901080i	−0.0433501	−	0.0528222i
$292$	1.24245	−	16.9344i	0.0727092	−	0.991009i
$293$	4.10730	+	1.24593i	0.239951	+	0.0727883i	0.407970	−	0.912996i	$-0.366237\pi$
$293$	4.10730	+	1.24593i	0.239951	+	0.0727883i	−0.168019	+	0.985784i	$0.553737\pi$
$294$	8.85551	−	3.29367i	0.516464	−	0.192091i
$295$	4.05208	+	2.70751i	0.235921	+	0.157637i
$296$	2.85659	−	25.8983i	0.166036	−	1.50531i
$297$	−2.97676	−	4.45504i	−0.172729	−	0.258508i
$298$	4.51925	+	28.0519i	0.261793	+	1.62500i
$299$	−3.82376	−	38.8233i	−0.221134	−	2.24521i
$300$	7.45162	+	4.71458i	0.430220	+	0.272196i
$301$	4.41243	−	1.33850i	0.254328	−	0.0771496i
$302$	1.46640	+	1.92653i	0.0843817	+	0.110860i
$303$	3.50572	+	1.45212i	0.201398	+	0.0834219i
$304$	7.56394	+	12.5972i	0.433822	+	0.722498i
$305$	10.3908	−	4.30403i	0.594978	−	0.246448i
$306$	4.79679	+	2.79439i	0.274214	+	0.159745i
$307$	18.0677	+	9.65741i	1.03118	+	0.551177i	0.898037	−	0.439919i	$-0.144993\pi$
$307$	18.0677	+	9.65741i	1.03118	+	0.551177i	0.133143	+	0.991097i	$0.457493\pi$
$308$	5.64879	+	2.17643i	0.321870	+	0.124013i
$309$	1.55069	+	1.27262i	0.0882156	+	0.0723967i
$310$	−0.374339	−	0.0888219i	−0.0212610	−	0.00504474i
$311$	−3.06114	+	15.3894i	−0.173581	+	0.872651i	0.791594	+	0.611047i	$0.209251\pi$
$311$	−3.06114	+	15.3894i	−0.173581	+	0.872651i	−0.965175	+	0.261604i	$0.915749\pi$
$312$	−5.60721	+	13.1020i	−0.317446	+	0.741753i
$313$	16.3046	−	3.24318i	0.921590	−	0.183316i	0.288577	−	0.957457i	$-0.406818\pi$
$313$	16.3046	−	3.24318i	0.921590	−	0.183316i	0.633013	+	0.774141i	$0.281818\pi$
$314$	−12.0719	−	12.9901i	−0.681259	−	0.733073i
$315$	−0.204734	−	0.383030i	−0.0115354	−	0.0215813i
$316$	−23.0976	+	13.0966i	−1.29934	+	0.736743i
$317$	18.1111	+	1.78379i	1.01722	+	0.100188i	0.592861	−	0.805305i	$-0.297998\pi$
$317$	18.1111	+	1.78379i	1.01722	+	0.100188i	0.424362	+	0.905493i	$0.360498\pi$
$318$	−7.84061	−	6.93023i	−0.439680	−	0.388628i
$319$		−	0.726711i		−	0.0406880i
$320$	4.01190	−	4.66202i	0.224272	−	0.260615i
$321$			7.55306i			0.421571i
$322$	−4.09639	+	4.63451i	−0.228283	+	0.258271i
$323$	14.3502	+	1.41337i	0.798467	+	0.0786421i
$324$	−1.92776	−	0.532667i	−0.107098	−	0.0295926i
$325$	10.4720	+	19.5918i	0.580883	+	1.08676i
$326$	16.9829	−	15.7825i	0.940596	−	0.874114i
$327$	−0.567066	+	0.112796i	−0.0313588	+	0.00623765i
$328$	−0.635130	+	0.620462i	−0.0350692	+	0.0342593i
$329$	0.892317	−	4.48598i	0.0491950	−	0.247320i
$330$	−1.34496	+	5.66830i	−0.0740374	+	0.312030i
$331$	12.5302	+	10.2833i	0.688723	+	0.565220i	0.912328	−	0.409459i	$-0.134283\pi$
$331$	12.5302	+	10.2833i	0.688723	+	0.565220i	−0.223605	+	0.974680i	$0.571783\pi$
$332$	−10.8933	+	4.83380i	−0.597847	+	0.265289i
$333$	8.12423	+	4.34249i	0.445205	+	0.237967i
$334$	1.16147	−	1.99375i	0.0635527	−	0.109093i
$335$	−0.375499	+	0.155537i	−0.0205157	+	0.00849788i
$336$	2.12694	−	0.762919i	0.116034	−	0.0416206i
$337$	−6.03044	−	2.49789i	−0.328499	−	0.136069i	0.212338	−	0.977196i	$-0.431892\pi$
$337$	−6.03044	−	2.49789i	−0.328499	−	0.136069i	−0.540837	+	0.841128i	$0.681892\pi$
$338$	−13.9402	+	10.6107i	−0.758247	+	0.577147i
$339$	−12.2490	+	3.71568i	−0.665272	+	0.201808i
$340$	−1.32479	−	5.88873i	−0.0718469	−	0.319361i
$341$	0.185834	+	1.88680i	0.0100635	+	0.102176i
$342$	−5.12885	+	0.826274i	−0.277336	+	0.0446798i
$343$	−4.29368	−	6.42594i	−0.231837	−	0.346968i
$344$	−22.1694	+	6.44318i	−1.19529	+	0.347393i
$345$	−4.94936	−	3.30706i	−0.266465	−	0.178046i
$346$	−0.635415	−	1.70841i	−0.0341601	−	0.0918445i
$347$	−9.19567	−	2.78948i	−0.493649	−	0.149747i	0.0336377	−	0.999434i	$-0.489291\pi$
$347$	−9.19567	−	2.78948i	−0.493649	−	0.149747i	−0.527287	+	0.849687i	$0.676791\pi$
$348$	−0.177261	−	0.205331i	−0.00950218	−	0.0110069i
$349$	6.52196	+	7.94703i	0.349113	+	0.425395i	0.917729	−	0.397208i	$-0.130021\pi$
$349$	6.52196	+	7.94703i	0.349113	+	0.425395i	−0.568616	+	0.822603i	$0.692521\pi$
$350$	1.14518	−	3.33091i	0.0612122	−	0.178045i
$351$	−3.56285	−	3.56285i	−0.190171	−	0.190171i
$352$	−28.1537	−	11.2268i	−1.50060	−	0.598389i
$353$	3.14211	−	3.14211i	0.167238	−	0.167238i	−0.618526	−	0.785764i	$-0.712270\pi$
$353$	3.14211	−	3.14211i	0.167238	−	0.167238i	0.785764	+	0.618526i	$0.212270\pi$
$354$	−3.93350	−	8.05527i	−0.209063	−	0.428133i
$355$	2.69307	−	2.21014i	0.142933	−	0.117302i
$356$	−26.2962	−	13.2234i	−1.39370	−	0.700841i
$357$	0.643704	−	2.12201i	0.0340684	−	0.112309i
$358$	−13.0588	+	28.5254i	−0.690180	+	1.50762i
$359$	−19.5683	+	29.2860i	−1.03277	+	1.54565i	−0.209662	+	0.977774i	$0.567236\pi$
$359$	−19.5683	+	29.2860i	−1.03277	+	1.54565i	−0.823111	+	0.567880i	$0.807764\pi$
$360$	1.00261	+	1.92964i	0.0528421	+	0.101701i
$361$	4.57816	−	3.05903i	0.240956	−	0.161001i
$362$	15.4254	−	21.3500i	0.810739	−	1.12213i
$363$	17.6232	−	1.73573i	0.924979	−	0.0911025i
$364$	5.60928	+	0.971029i	0.294006	+	0.0508958i
$365$	−1.89477	−	6.24621i	−0.0991766	−	0.326942i
$366$	−20.5006	−	2.78021i	−1.07158	−	0.145324i
$367$	8.32737	−	20.1041i	0.434685	−	1.04942i	−0.543072	−	0.839686i	$-0.682739\pi$
$367$	8.32737	−	20.1041i	0.434685	−	1.04942i	0.977758	−	0.209738i	$-0.0672609\pi$
$368$	20.7799	−	22.9634i	1.08323	−	1.19705i
$369$	−0.120132	−	0.290024i	−0.00625381	−	0.0150980i
$370$	−2.55464	−	9.68473i	−0.132809	−	0.503485i
$371$	−1.97043	+	3.68642i	−0.102300	+	0.191389i
$372$	0.512739	+	0.487784i	0.0265843	+	0.0252904i
$373$	−15.1125	+	18.4146i	−0.782493	+	0.953471i	−0.999744	−	0.0226451i	$-0.992791\pi$
$373$	−15.1125	+	18.4146i	−0.782493	+	0.953471i	0.217250	+	0.976116i	$0.430291\pi$
$374$	−25.3200	+	15.6086i	−1.30927	+	0.807102i
$375$	7.09480	+	1.41124i	0.366374	+	0.0728763i
$376$	−4.72981	+	22.4071i	−0.243921	+	1.15556i
$377$	−0.133323	−	0.670260i	−0.00686649	−	0.0345202i
$378$	−0.0292481	+	0.798362i	−0.00150436	+	0.0410633i
$379$	−11.4668	+	6.12912i	−0.589009	+	0.314832i	−0.738841	−	0.673880i	$-0.764627\pi$
$379$	−11.4668	+	6.12912i	−0.589009	+	0.314832i	0.149832	+	0.988711i	$0.452127\pi$
$380$	4.45426	+	3.47332i	0.228499	+	0.178178i
$381$	−0.310520	+	3.15276i	−0.0159084	+	0.161521i
$382$	10.2642	−	0.632621i	0.525161	−	0.0323677i
$383$	14.1821			0.724673			0.362336	−	0.932047i	$-0.381979\pi$
$383$	14.1821			0.724673			0.362336	+	0.932047i	$0.381979\pi$
$384$	−10.6932	+	3.69520i	−0.545687	+	0.188570i
$385$	2.32706			0.118598
$386$	6.36493	−	0.392295i	0.323966	−	0.0199673i
$387$	0.800053	−	8.12307i	0.0406690	−	0.412919i
$388$	1.43360	−	1.83848i	0.0727799	−	0.0933346i
$389$	−3.61396	+	1.93170i	−0.183235	+	0.0979411i	−0.560464	−	0.828179i	$-0.689377\pi$
$389$	−3.61396	+	1.93170i	−0.183235	+	0.0979411i	0.377229	+	0.926120i	$0.376877\pi$
$390$	−0.200568	+	5.47474i	−0.0101561	+	0.277224i
$391$	−5.92922	−	29.8082i	−0.299854	−	1.50747i
$392$	10.3140	+	15.8333i	0.520937	+	0.799704i
$393$	−11.2741	−	2.24256i	−0.568703	−	0.113122i
$394$	−9.70995	+	5.98573i	−0.489180	+	0.301557i
$395$	−6.47525	+	7.89011i	−0.325805	+	0.396995i
$396$	7.38610	−	7.76398i	0.371166	−	0.390155i
$397$	2.93991	−	5.50019i	0.147550	−	0.276047i	−0.797279	−	0.603611i	$-0.793728\pi$
$397$	2.93991	−	5.50019i	0.147550	−	0.276047i	0.944829	+	0.327565i	$0.106228\pi$
$398$	10.0352	+	38.0438i	0.503019	+	1.90696i
$399$	0.794117	+	1.91717i	0.0397556	+	0.0959785i
$400$	−5.92820	+	16.6094i	−0.296410	+	0.830470i
$401$	5.76850	−	13.9264i	0.288065	−	0.695451i	−0.711912	−	0.702269i	$-0.752170\pi$
$401$	5.76850	−	13.9264i	0.288065	−	0.695451i	0.999977	+	0.00681829i	$0.00217035\pi$
$402$	0.740840	+	0.100470i	0.0369497	+	0.00501097i
$403$	0.517552	+	1.70614i	0.0257811	+	0.0849889i
$404$	−1.29451	+	7.47791i	−0.0644042	+	0.372040i
$405$	−0.765122	+	0.0753579i	−0.0380192	+	0.00374456i
$406$	−0.0634567	+	0.0878294i	−0.00314930	+	0.00435890i
$407$	−41.0397	+	27.4218i	−2.03426	+	1.35925i
$408$	−3.34685	+	10.5863i	−0.165694	+	0.524100i
$409$	17.2597	−	25.8309i	0.853436	−	1.27726i	−0.105724	−	0.994396i	$-0.533716\pi$
$409$	17.2597	−	25.8309i	0.853436	−	1.27726i	0.959161	−	0.282862i	$-0.0912840\pi$
$410$	−0.142074	+	0.310344i	−0.00701654	+	0.0153268i
$411$	5.26779	−	17.3656i	0.259841	−	0.856581i
$412$	−1.80246	+	3.58439i	−0.0888011	+	0.176590i
$413$	−2.76800	+	2.27164i	−0.136204	+	0.111780i
$414$	4.80453	+	9.83902i	0.236130	+	0.483562i
$415$	−3.23945	+	3.23945i	−0.159018	+	0.159018i
$416$	−28.0264	−	5.18958i	−1.37411	−	0.254440i
$417$	−8.70085	−	8.70085i	−0.426082	−	0.426082i
$418$	9.04978	−	26.3226i	0.442639	−	1.28748i
$419$	−2.39171	−	2.91431i	−0.116843	−	0.142373i	0.711304	−	0.702884i	$-0.248105\pi$
$419$	−2.39171	−	2.91431i	−0.116843	−	0.142373i	−0.828147	+	0.560511i	$0.810605\pi$
$420$	0.657508	−	0.567622i	0.0320831	−	0.0276971i
$421$	19.2267	+	5.83235i	0.937051	+	0.284251i	0.721637	−	0.692271i	$-0.243390\pi$
$421$	19.2267	+	5.83235i	0.937051	+	0.284251i	0.215414	+	0.976523i	$0.430890\pi$
$422$	9.69615	+	26.0695i	0.472001	+	1.26904i
$423$	−6.73215	−	4.49828i	−0.327328	−	0.218714i
$424$	10.0807	−	18.3410i	0.489561	−	0.890718i
$425$	9.61515	+	14.3901i	0.466403	+	0.698022i
$426$	−6.32683	+	1.01927i	−0.306536	+	0.0493839i
$427$	0.810004	+	8.22411i	0.0391988	+	0.397993i
$428$	−14.7378	+	3.31557i	−0.712377	+	0.160264i
$429$	25.8347	−	7.83686i	1.24731	−	0.378367i
$430$	−7.06183	+	5.37518i	−0.340552	+	0.259214i
$431$	−6.03774	−	2.50091i	−0.290828	−	0.120465i	0.232500	−	0.972596i	$-0.425310\pi$
$431$	−6.03774	−	2.50091i	−0.290828	−	0.120465i	−0.523327	+	0.852132i	$0.675310\pi$
$432$	0.193126	−	3.99534i	0.00929179	−	0.192226i
$433$	−3.87401	+	1.60467i	−0.186173	+	0.0771154i	−0.473823	−	0.880620i	$-0.657126\pi$
$433$	−3.87401	+	1.60467i	−0.186173	+	0.0771154i	0.287649	+	0.957736i	$0.407126\pi$
$434$	0.142297	−	0.244263i	0.00683045	−	0.0117250i
$435$	−0.0919630	−	0.0491553i	−0.00440929	−	0.00235681i
$436$	−0.469017	−	1.05696i	−0.0224618	−	0.0506193i
$437$	21.9852	+	18.0428i	1.05169	+	0.863103i
$438$	−2.77192	+	11.6822i	−0.132448	+	0.558199i
$439$	2.74784	−	13.8143i	0.131147	−	0.659321i	−0.858149	−	0.513400i	$-0.828386\pi$
$439$	2.74784	−	13.8143i	0.131147	−	0.659321i	0.989296	−	0.145921i	$-0.0466144\pi$
$440$	−11.6506	−	0.136103i	−0.555419	−	0.00648846i
$441$	−6.55251	+	1.30338i	−0.312024	+	0.0620655i
$442$	−20.4896	+	19.0414i	−0.974590	+	0.905705i
$443$	−7.60926	−	14.2359i	−0.361527	−	0.676369i	0.633740	−	0.773546i	$-0.281519\pi$
$443$	−7.60926	−	14.2359i	−0.361527	−	0.676369i	−0.995267	+	0.0971768i	$0.969019\pi$
$444$	−4.90691	+	17.7585i	−0.232872	+	0.842780i
$445$	−11.2602	−	1.10904i	−0.533786	−	0.0525734i
$446$	21.6331	−	24.4750i	1.02436	−	1.15892i
$447$		−	20.0914i		−	0.950293i
$448$	2.42229	+	3.81525i	0.114443	+	0.180253i
$449$			40.1659i			1.89554i	0.318949	+	0.947772i	$0.396670\pi$
$449$			40.1659i			1.89554i	−0.318949	+	0.947772i	$0.603330\pi$
$450$	−4.67178	−	4.12934i	−0.220230	−	0.194659i
$451$	1.67389	+	0.164864i	0.0788204	+	0.00776313i
$452$	−12.6271	−	22.2695i	−0.593928	−	1.04747i
$453$	−0.807029	−	1.50984i	−0.0379175	−	0.0709387i
$454$	−19.6090	−	21.1004i	−0.920296	−	0.990291i
$455$	2.14630	−	0.426925i	0.100620	−	0.0200146i
$456$	−3.86366	−	9.64486i	−0.180933	−	0.451662i
$457$	4.88732	−	24.5702i	0.228619	−	1.14935i	−0.680480	−	0.732767i	$-0.738229\pi$
$457$	4.88732	−	24.5702i	0.228619	−	1.14935i	0.909099	−	0.416580i	$-0.136771\pi$
$458$	−0.490638	−	0.116417i	−0.0229260	−	0.00543981i
$459$	−3.03439	−	2.49026i	−0.141633	−	0.116235i
$460$	4.28022	−	11.1091i	0.199566	−	0.517963i
$461$	4.83020	+	2.58180i	0.224965	+	0.120246i	0.580029	−	0.814596i	$-0.303041\pi$
$461$	4.83020	+	2.58180i	0.224965	+	0.120246i	−0.355064	+	0.934842i	$0.615541\pi$
$462$	−3.69868	−	2.15468i	−0.172078	−	0.100245i
$463$	−0.530514	+	0.219746i	−0.0246551	+	0.0102125i	−0.394977	−	0.918691i	$-0.629247\pi$
$463$	−0.530514	+	0.219746i	−0.0246551	+	0.0102125i	0.370322	+	0.928904i	$0.379247\pi$
$464$	0.322836	−	0.436011i	0.0149873	−	0.0202413i
$465$	0.251339	+	0.104108i	0.0116555	+	0.00482789i
$466$	11.9087	+	15.6455i	0.551660	+	0.724763i
$467$	−9.65498	+	2.92881i	−0.446779	+	0.135529i	−0.505654	−	0.862736i	$-0.668749\pi$
$467$	−9.65498	+	2.92881i	−0.446779	+	0.135529i	0.0588748	+	0.998265i	$0.481249\pi$
$468$	5.38796	−	8.51594i	0.249059	−	0.393649i
$469$	−0.0292715	−	0.297199i	−0.00135163	−	0.0137234i
$470$	1.40020	+	8.69130i	0.0645863	+	0.400900i
$471$	6.96653	+	10.4261i	0.321001	+	0.480412i
$472$	13.9910	−	11.2112i	0.643989	−	0.516037i
$473$	36.3637	+	24.2974i	1.67200	+	1.11720i
$474$	17.5975	−	6.54512i	0.808280	−	0.300627i
$475$	−15.4983	−	4.70137i	−0.711112	−	0.215713i
$476$	4.42310	+	0.324517i	0.202732	+	0.0148742i
$477$	4.69415	+	5.71984i	0.214930	+	0.261893i
$478$	−7.78009	−	2.67482i	−0.355853	−	0.122343i
$479$	3.25170	+	3.25170i	0.148574	+	0.148574i	0.777481	−	0.628907i	$-0.216497\pi$
$479$	3.25170	+	3.25170i	0.148574	+	0.148574i	−0.628907	+	0.777481i	$0.716497\pi$
$480$	−3.32505	+	2.80338i	−0.151767	+	0.127956i
$481$	−32.8209	+	32.8209i	−1.49650	+	1.49650i
$482$	−3.68693	+	1.80038i	−0.167935	+	0.0820051i
$483$	3.38094	−	2.77467i	0.153838	−	0.126252i
$484$	11.1229	+	33.6250i	0.505586	+	1.52841i
$485$	0.260153	−	0.857609i	0.0118129	−	0.0389420i
$486$	1.28587	+	0.588667i	0.0583284	+	0.0267025i
$487$	−17.6732	+	26.4498i	−0.800848	+	1.19855i	0.175952	+	0.984399i	$0.443700\pi$
$487$	−17.6732	+	26.4498i	−0.800848	+	1.19855i	−0.976800	+	0.214155i	$0.931300\pi$
$488$	−3.57433	−	41.2218i	−0.161802	−	1.86602i
$489$	−13.6309	+	9.10785i	−0.616409	+	0.411871i
$490$	5.88799	+	4.25407i	0.265992	+	0.192179i
$491$	31.4993	−	3.10241i	1.42154	−	0.140010i	0.642166	−	0.766566i	$-0.278036\pi$
$491$	31.4993	−	3.10241i	1.42154	−	0.140010i	0.779376	+	0.626556i	$0.215536\pi$
$492$	0.513169	−	0.361717i	0.0231354	−	0.0163074i
$493$	−0.154549	−	0.509480i	−0.00696054	−	0.0229458i
$494$	3.51763	−	25.9382i	0.158265	−	1.16701i
$495$	1.57642	−	3.80581i	0.0708547	−	0.171058i
$496$	−0.726702	+	1.21460i	−0.0326299	+	0.0545369i
$497$	0.979605	+	2.36498i	0.0439413	+	0.106084i
$498$	8.14831	−	2.14936i	0.365135	−	0.0963152i
$499$	18.6847	−	34.9566i	0.836442	−	1.56487i	0.0113074	−	0.999936i	$-0.496401\pi$
$499$	18.6847	−	34.9566i	0.836442	−	1.56487i	0.825134	−	0.564936i	$-0.191099\pi$
$500$	0.360744	+	14.4631i	0.0161330	+	0.646809i
$501$	−1.03506	+	1.26122i	−0.0462430	+	0.0563473i
$502$	8.48184	+	13.7591i	0.378563	+	0.614098i
$503$	12.7928	+	2.54464i	0.570402	+	0.113460i	0.471861	−	0.881673i	$-0.343582\pi$
$503$	12.7928	+	2.54464i	0.570402	+	0.113460i	0.0985411	+	0.995133i	$0.468582\pi$
$504$	−1.57063	+	0.293388i	−0.0699614	+	0.0130685i
$505$	0.569147	+	2.86129i	0.0253267	+	0.127326i
$506$	−58.6280	−	2.14785i	−2.60633	−	0.0954834i
$507$	10.9251	−	5.83958i	0.485200	−	0.259345i
$508$	−6.28807	+	0.778072i	−0.278988	+	0.0345214i
$509$	2.18155	−	22.1497i	0.0966955	−	0.981766i	−0.817346	−	0.576147i	$-0.804556\pi$
$509$	2.18155	−	22.1497i	0.0966955	−	0.981766i	0.914042	−	0.405620i	$-0.132944\pi$
$510$	0.262557	+	4.25995i	0.0116262	+	0.188634i
$511$	4.79602			0.212164
$512$	−11.9042	−	19.2429i	−0.526096	−	0.850425i
$513$	3.67340			0.162185
$514$	−2.52098	−	40.9025i	−0.111196	−	1.80413i
$515$	−0.151171	+	1.53486i	−0.00666138	+	0.0676341i
$516$	16.2012	−	2.00470i	0.713218	−	0.0882520i
$517$	38.2597	−	20.4503i	1.68266	−	0.899401i
$518$	7.35449	+	0.269433i	0.323138	+	0.0118382i
$519$	0.251447	+	1.26411i	0.0110373	+	0.0554883i
$520$	−10.7705	+	2.01189i	−0.472319	+	0.0882273i
$521$	−35.6060	−	7.08248i	−1.55993	−	0.310289i	−0.661683	−	0.749784i	$-0.730157\pi$
$521$	−35.6060	−	7.08248i	−1.55993	−	0.310289i	−0.898245	+	0.439495i	$0.855157\pi$
$522$	0.100654	+	0.163279i	0.00440550	+	0.00714652i
$523$	−10.3490	+	12.6102i	−0.452528	+	0.551407i	−0.948436	−	0.316968i	$-0.897335\pi$
$523$	−10.3490	+	12.6102i	−0.452528	+	0.551407i	0.495908	+	0.868375i	$0.334835\pi$
$524$	−0.573245	−	22.9828i	−0.0250423	−	1.00401i
$525$	−1.17407	+	2.19653i	−0.0512406	+	0.0958645i
$526$	−2.59367	+	0.684159i	−0.113089	+	0.0298307i
$527$	0.531548	+	1.28327i	0.0231546	+	0.0559001i
$528$	18.3916	+	11.0038i	0.800392	+	0.478881i
$529$	14.1382	−	34.1327i	0.614705	−	1.48403i
$530$	1.08117	−	7.97228i	0.0469629	−	0.346294i
$531$	1.84005	+	6.06582i	0.0798512	+	0.263234i
$532$	−3.39225	+	2.39109i	−0.147073	+	0.103667i
$533$	1.57411	−	0.155036i	0.0681822	−	0.00671536i
$534$	16.8703	+	12.1888i	0.730051	+	0.527462i
$535$	−4.82832	+	3.22618i	−0.208746	+	0.139480i
$536$	0.129167	+	1.48965i	0.00557917	+	0.0643432i
$537$	12.3246	−	18.4451i	0.531846	−	0.795963i
$538$	5.96673	+	2.73154i	0.257244	+	0.117765i
$539$	10.3911	−	34.2550i	0.447578	−	1.47547i
$540$	−0.482906	−	1.45985i	−0.0207810	−	0.0628219i
$541$	−17.0432	+	13.9870i	−0.732745	+	0.601348i	−0.924987	−	0.379999i	$-0.875924\pi$
$541$	−17.0432	+	13.9870i	−0.732745	+	0.601348i	0.192242	+	0.981348i	$0.438424\pi$
$542$	−2.90105	+	1.41663i	−0.124611	+	0.0608493i
$543$	−13.1697	+	13.1697i	−0.565166	+	0.565166i
$544$	−22.1255	−	1.88341i	−0.948623	−	0.0807504i
$545$	−0.314319	−	0.314319i	−0.0134640	−	0.0134640i
$546$	−3.80666	−	1.30874i	−0.162910	−	0.0560089i
$547$	−26.6198	−	32.4364i	−1.13818	−	1.38688i	−0.910685	−	0.413101i	$-0.864446\pi$
$547$	−26.6198	−	32.4364i	−1.13818	−	1.38688i	−0.227497	−	0.973779i	$-0.573054\pi$
$548$	36.1967	+	2.65571i	1.54624	+	0.113446i
$549$	13.9989	+	4.24652i	0.597458	+	0.181237i
$550$	31.3124	−	11.6462i	1.33517	−	0.496594i
$551$	0.414259	+	0.276799i	0.0176480	+	0.0117920i
$552$	−17.0892	+	13.6938i	−0.727363	+	0.582847i
$553$	−4.16664	−	6.23582i	−0.177184	−	0.265174i
$554$	0.0749419	+	0.465179i	0.00318398	+	0.0197636i
$555$	0.694194	+	7.04827i	0.0294669	+	0.299183i
$556$	13.1580	−	20.7968i	0.558022	−	0.881980i
$557$	−14.1459	+	4.29110i	−0.599379	+	0.181820i	−0.575372	−	0.817892i	$-0.695143\pi$
$557$	−14.1459	+	4.29110i	−0.599379	+	0.181820i	−0.0240076	+	0.999712i	$0.507643\pi$
$558$	−0.303086	−	0.398191i	−0.0128307	−	0.0168568i
$559$	37.9966	+	15.7387i	1.60708	+	0.665676i
$560$	1.39619	+	1.03378i	0.0589997	+	0.0436853i
$561$	19.4315	−	8.04879i	0.820398	−	0.339820i
$562$	21.3362	+	12.4295i	0.900015	+	0.524307i
$563$	34.3690	+	18.3706i	1.44848	+	0.774229i	0.993233	−	0.116136i	$-0.0370510\pi$
$563$	34.3690	+	18.3706i	1.44848	+	0.774229i	0.455247	+	0.890365i	$0.349551\pi$
$564$	5.82197	−	15.1106i	0.245149	−	0.636270i
$565$	−7.60722	−	6.24309i	−0.320038	−	0.262649i
$566$	26.0879	+	6.19005i	1.09656	+	0.260187i
$567$	0.110208	−	0.554052i	0.00462829	−	0.0232680i
$568$	−4.76612	−	11.8977i	−0.199982	−	0.499215i
$569$	−37.7207	+	7.50312i	−1.58134	+	0.314547i	−0.906103	−	0.423058i	$-0.860957\pi$
$569$	−37.7207	+	7.50312i	−1.58134	+	0.314547i	−0.675233	+	0.737605i	$0.735957\pi$
$570$	−2.71891	−	2.92570i	−0.113883	−	0.122544i
$571$	−4.88472	−	9.13866i	−0.204419	−	0.382441i	0.758732	−	0.651403i	$-0.225819\pi$
$571$	−4.88472	−	9.13866i	−0.204419	−	0.382441i	−0.963151	+	0.268962i	$0.913319\pi$
$572$	26.6322	+	46.9693i	1.11355	+	1.96388i
$573$	−7.23663	−	0.712745i	−0.302314	−	0.0297754i
$574$	−0.187908	−	0.166090i	−0.00784314	−	0.00693246i
$575$			34.1356i			1.42355i
$576$	7.88060	−	1.37700i	0.328358	−	0.0573750i
$577$			17.7108i			0.737312i	0.929566	+	0.368656i	$0.120182\pi$
$577$			17.7108i			0.737312i	−0.929566	+	0.368656i	$0.879818\pi$
$578$	1.49021	−	1.68597i	0.0619847	−	0.0701273i
$579$	−4.48751	−	0.441981i	−0.186495	−	0.0183681i
$580$	0.0555443	−	0.201019i	0.00230635	−	0.00834685i
$581$	−1.58680	−	2.96869i	−0.0658315	−	0.123162i
$582$	−1.20757	+	1.12222i	−0.0500554	+	0.0465175i
$583$	−38.8846	+	7.73462i	−1.61043	+	0.320335i
$584$	−24.0116	−	0.280505i	−0.993605	−	0.0116074i
$585$	0.755745	−	3.79939i	0.0312462	−	0.157085i
$586$	1.40135	−	5.90599i	0.0578893	−	0.243974i
$587$	21.9534	+	18.0167i	0.906114	+	0.743629i	0.967070	−	0.254512i	$-0.0819148\pi$
$587$	21.9534	+	18.0167i	0.906114	+	0.743629i	−0.0609555	+	0.998140i	$0.519415\pi$
$588$	−5.41954	−	12.2133i	−0.223498	−	0.503669i
$589$	−1.14635	−	0.612734i	−0.0472343	−	0.0252473i
$590$	3.46922	−	5.95520i	0.142826	−	0.245172i
$591$	7.45176	−	3.08662i	0.306525	−	0.126967i
$592$	−36.8049	−	1.77907i	−1.51267	−	0.0731194i
$593$	−16.8707	−	6.98808i	−0.692797	−	0.286966i	0.00836802	−	0.999965i	$-0.497336\pi$
$593$	−16.8707	−	6.98808i	−0.692797	−	0.286966i	−0.701165	+	0.712999i	$0.747336\pi$
$594$	−6.02947	+	4.58938i	−0.247392	+	0.188305i
$595$	1.63145	−	0.494895i	0.0668829	−	0.0202887i
$596$	39.2031	−	8.81955i	1.60582	−	0.361263i
$597$	−2.72695	−	27.6872i	−0.111607	−	1.13316i
$598$	−54.4678	+	8.77494i	−2.22736	+	0.358834i
$599$	6.42648	+	9.61790i	0.262579	+	0.392977i	0.939209	−	0.343346i	$-0.111560\pi$
$599$	6.42648	+	9.61790i	0.262579	+	0.392977i	−0.676630	+	0.736323i	$0.736560\pi$
$600$	6.00652	−	10.9284i	0.245215	−	0.446150i
$601$	−2.78554	−	1.86124i	−0.113624	−	0.0759214i	0.497460	−	0.867487i	$-0.334266\pi$
$601$	−2.78554	−	1.86124i	−0.113624	−	0.0759214i	−0.611084	+	0.791566i	$0.709266\pi$
$602$	−2.27321	−	6.11185i	−0.0926490	−	0.249100i
$603$	−0.505885	−	0.153458i	−0.0206012	−	0.00624931i
$604$	2.59180	−	2.23748i	0.105459	−	0.0910417i
$605$	8.63707	+	10.5243i	0.351147	+	0.427874i
$606$	1.74472	−	5.07478i	0.0708745	−	0.206149i
$607$	5.02161	+	5.02161i	0.203821	+	0.203821i	0.801635	−	0.597814i	$-0.203964\pi$
$607$	5.02161	+	5.02161i	0.203821	+	0.203821i	−0.597814	+	0.801635i	$0.703964\pi$
$608$	17.1233	−	11.7727i	0.694442	−	0.477446i
$609$	0.0541774	−	0.0541774i	0.00219538	−	0.00219538i
$610$	−6.97927	−	14.2926i	−0.282583	−	0.578690i
$611$	31.5359	−	25.8808i	1.27581	−	1.04703i
$612$	3.52706	−	7.01394i	0.142573	−	0.283522i
$613$	−10.2547	+	33.8052i	−0.414183	+	1.36538i	0.463483	+	0.886106i	$0.346600\pi$
$613$	−10.2547	+	33.8052i	−0.414183	+	1.36538i	−0.877666	+	0.479273i	$0.840900\pi$
$614$	12.0599	−	26.3434i	0.486698	−	1.06313i
$615$	0.134086	−	0.200674i	0.00540687	−	0.00809196i
$616$	2.58067	−	8.16282i	0.103978	−	0.328889i
$617$	21.1821	−	14.1534i	0.852759	−	0.569795i	−0.0505816	−	0.998720i	$-0.516108\pi$
$617$	21.1821	−	14.1534i	0.852759	−	0.569795i	0.903340	+	0.428925i	$0.141108\pi$
$618$	1.66144	−	2.29957i	0.0668328	−	0.0925021i
$619$	23.1712	−	2.28216i	0.931329	−	0.0917279i	0.379040	−	0.925380i	$-0.376254\pi$
$619$	23.1712	−	2.28216i	0.931329	−	0.0917279i	0.552289	+	0.833652i	$0.313754\pi$
$620$	−0.0928083	+	0.536120i	−0.00372727	+	0.0215311i
$621$	−2.24750	−	7.40903i	−0.0901892	−	0.297314i
$622$	21.9889	+	2.98205i	0.881676	+	0.119569i
$623$	3.18151	−	7.68084i	0.127464	−	0.307726i
$624$	18.9817	+	6.77492i	0.759877	+	0.271214i
$625$	−6.30779	−	15.2283i	−0.252311	−	0.609134i
$626$	−5.99634	−	22.7323i	−0.239662	−	0.908567i
$627$	−9.27813	+	17.3582i	−0.370533	+	0.693218i
$628$	−17.2857	+	18.1701i	−0.689776	+	0.725065i
$629$	−22.9402	+	27.9527i	−0.914684	+	1.11455i
$630$	−0.522849	+	0.322312i	−0.0208308	+	0.0128412i
$631$	−15.5589	−	3.09486i	−0.619391	−	0.123204i	−0.124586	−	0.992209i	$-0.539760\pi$
$631$	−15.5589	−	3.09486i	−0.619391	−	0.123204i	−0.494804	+	0.869004i	$0.664760\pi$
$632$	20.4958	+	31.4637i	0.815280	+	1.25156i
$633$	−3.83697	−	19.2898i	−0.152506	−	0.766699i
$634$	0.942245	−	25.7197i	0.0374213	−	1.02146i
$635$	−2.14805	+	1.14815i	−0.0852426	+	0.0455631i
$636$	−9.10014	+	11.6702i	−0.360844	+	0.462754i
$637$	3.29950	−	33.5004i	0.130731	−	1.32733i
$638$	−1.02578	+	0.0632227i	−0.0406110	+	0.00250301i
$639$	4.53143			0.179260
$640$	−6.92963	−	5.25735i	−0.273918	−	0.207815i
$641$	26.6288			1.05177			0.525887	−	0.850555i	$-0.323734\pi$
$641$	26.6288			1.05177			0.525887	+	0.850555i	$0.323734\pi$
$642$	10.6614	−	0.657104i	0.420772	−	0.0259338i
$643$	2.98043	−	30.2608i	0.117537	−	1.19337i	−0.737698	−	0.675131i	$-0.764087\pi$
$643$	2.98043	−	30.2608i	0.117537	−	1.19337i	0.855235	−	0.518241i	$-0.173413\pi$
$644$	6.89816	+	5.37901i	0.271825	+	0.211963i
$645$	5.53443	−	2.95822i	0.217918	−	0.116480i
$646$	0.746580	−	20.3788i	0.0293738	−	0.801792i
$647$	−2.88117	−	14.4846i	−0.113271	−	0.569449i	−0.995183	−	0.0980359i	$-0.968744\pi$
$647$	−2.88117	−	14.4846i	−0.113271	−	0.569449i	0.881912	−	0.471413i	$-0.156256\pi$
$648$	−0.584166	+	2.76744i	−0.0229482	+	0.108715i
$649$	−33.3107	−	6.62591i	−1.30756	−	0.260090i
$650$	26.7434	−	16.4861i	1.04896	−	0.646637i
$651$	−0.126810	+	0.154518i	−0.00497006	+	0.00605603i
$652$	−23.7551	−	22.5989i	−0.930321	−	0.885041i
$653$	−12.5896	+	23.5535i	−0.492669	+	0.921718i	0.505592	+	0.862772i	$0.331274\pi$
$653$	−12.5896	+	23.5535i	−0.492669	+	0.921718i	−0.998261	+	0.0589459i	$0.981226\pi$
$654$	0.208550	+	0.790620i	0.00815494	+	0.0309157i
$655$	−3.38200	−	8.16488i	−0.132146	−	0.319028i
$656$	0.931059	+	0.842529i	0.0363517	+	0.0328952i
$657$	3.24896	−	7.84369i	0.126754	−	0.306011i
$658$	−6.40975	−	0.869264i	−0.249878	−	0.0338874i
$659$	−6.76071	−	22.2871i	−0.263360	−	0.868181i	−0.984499	−	0.175391i	$-0.943881\pi$
$659$	−6.76071	−	22.2871i	−0.263360	−	0.868181i	0.721139	−	0.692790i	$-0.243619\pi$
$660$	8.11802	+	1.40532i	0.315993	+	0.0547020i
$661$	−26.3034	+	2.59066i	−1.02308	+	0.100765i	−0.595618	−	0.803268i	$-0.703093\pi$
$661$	−26.3034	+	2.59066i	−1.02308	+	0.100765i	−0.427464	+	0.904032i	$0.640593\pi$
$662$	13.4251	−	18.5815i	0.521782	−	0.722189i
$663$	16.4454	−	10.9885i	0.638687	−	0.426757i
$664$	7.77077	+	14.9557i	0.301564	+	0.580395i
$665$	−0.886361	+	1.32653i	−0.0343716	+	0.0514408i
$666$	5.42278	−	11.8454i	0.210129	−	0.459001i
$667$	0.304830	−	1.00489i	0.0118030	−	0.0389094i
$668$	−2.91530	−	1.46600i	−0.112796	−	0.0567213i
$669$	−17.8548	+	14.6531i	−0.690308	+	0.566521i
$670$	0.252213	+	0.516498i	0.00974385	+	0.0199541i
$671$	−55.4241	+	55.4241i	−2.13962	+	2.13962i
$672$	−1.26193	−	2.93587i	−0.0486799	−	0.113254i
$673$	−21.2101	−	21.2101i	−0.817590	−	0.817590i	0.168169	−	0.985758i	$-0.446215\pi$
$673$	−21.2101	−	21.2101i	−0.817590	−	0.817590i	−0.985758	+	0.168169i	$0.946215\pi$
$674$	−3.00122	+	8.72949i	−0.115603	+	0.336247i
$675$	2.79698	+	3.40813i	0.107656	+	0.131179i
$676$	16.1902	+	18.7540i	0.622699	+	0.721307i
$677$	−28.0845	−	8.51934i	−1.07937	−	0.327425i	−0.299972	−	0.953948i	$-0.596977\pi$
$677$	−28.0845	−	8.51934i	−1.07937	−	0.327425i	−0.779403	+	0.626523i	$0.784477\pi$
$678$	6.31045	+	16.9666i	0.242351	+	0.651597i
$679$	0.547521	+	0.365842i	0.0210119	+	0.0140397i
$680$	−8.19689	+	2.38230i	−0.314336	+	0.0913570i
$681$	11.3161	+	16.9357i	0.433632	+	0.648976i
$682$	2.64712	−	0.426459i	0.101363	−	0.0163300i
$683$	−0.171946	−	1.74580i	−0.00657934	−	0.0668011i	0.991334	−	0.131362i	$-0.0419352\pi$
$683$	−0.171946	−	1.74580i	−0.00657934	−	0.0668011i	−0.997914	+	0.0645614i	$0.979435\pi$
$684$	1.61252	+	7.16766i	0.0616561	+	0.274062i
$685$	13.3511	−	4.05000i	0.510118	−	0.154743i
$686$	−8.69690	+	6.61972i	−0.332049	+	0.252742i
$687$	0.329424	+	0.136452i	0.0125683	+	0.00520597i
$688$	11.0235	+	30.7323i	0.420266	+	1.17166i
$689$	−34.4450	+	14.2676i	−1.31225	+	0.543552i
$690$	−4.23744	+	7.27391i	−0.161317	+	0.276913i
$691$	−41.1799	−	22.0111i	−1.56656	−	0.837342i	−0.999910	−	0.0133813i	$-0.995740\pi$
$691$	−41.1799	−	22.0111i	−1.56656	−	0.837342i	−0.566647	−	0.823961i	$-0.691760\pi$
$692$	−2.35620	+	1.04554i	−0.0895692	+	0.0397455i
$693$	2.33974	+	1.92017i	0.0888792	+	0.0729413i
$694$	−3.13743	+	13.2227i	−0.119095	+	0.501926i
$695$	1.84561	−	9.27849i	0.0700078	−	0.351953i
$696$	−0.274411	+	0.268073i	−0.0104015	+	0.0101613i
$697$	1.20859	−	0.240403i	0.0457785	−	0.00910590i
$698$	10.6501	−	9.89736i	0.403113	−	0.374620i
$699$	−6.55393	−	12.2615i	−0.247892	−	0.463774i
$700$	−4.80132	−	1.32667i	−0.181473	−	0.0501435i
$701$	−31.4250	−	3.09510i	−1.18691	−	0.116900i	−0.514771	−	0.857328i	$-0.672123\pi$
$701$	−31.4250	−	3.09510i	−1.18691	−	0.116900i	−0.672136	+	0.740427i	$0.734623\pi$
$702$	−4.71913	+	5.33905i	−0.178112	+	0.201510i
$703$		−	33.8393i		−	1.27627i
$704$	−13.3977	+	40.7166i	−0.504944	+	1.53457i
$705$		−	6.22492i		−	0.234444i
$706$	−4.70855	−	4.16184i	−0.177209	−	0.156633i
$707$	−2.13325	−	0.210107i	−0.0802292	−	0.00790188i
$708$	−11.0281	+	6.25307i	−0.414461	+	0.235005i
$709$	19.4631	+	36.4128i	0.730951	+	1.36751i	0.922487	+	0.386027i	$0.126153\pi$
$709$	19.4631	+	36.4128i	0.730951	+	1.36751i	−0.191537	+	0.981485i	$0.561347\pi$
$710$	−3.35399	−	3.60908i	−0.125873	−	0.135446i
$711$	−13.0210	+	2.59004i	−0.488326	+	0.0971342i
$712$	−16.3776	+	38.2685i	−0.613777	+	1.43417i
$713$	−0.534477	+	2.68700i	−0.0200163	+	0.100629i
$714$	−3.05129	−	0.724000i	−0.114192	−	0.0270950i
$715$	16.0446	+	13.1675i	0.600036	+	0.492436i
$716$	41.4007	+	15.9513i	1.54722	+	0.596128i
$717$	5.13050	+	2.74231i	0.191602	+	0.102413i
$718$	43.0406	+	25.0734i	1.60626	+	0.935733i
$719$	−25.1026	+	10.3978i	−0.936169	+	0.387774i	−0.798016	−	0.602637i	$-0.794117\pi$
$719$	−25.1026	+	10.3978i	−0.936169	+	0.387774i	−0.138154	+	0.990411i	$0.544117\pi$
$720$	2.63652	−	1.58309i	0.0982574	−	0.0589984i
$721$	−1.04696	−	0.433666i	−0.0389909	−	0.0161506i
$722$	−4.71622	−	6.19610i	−0.175519	−	0.230595i
$723$	2.77635	−	0.842197i	0.103254	−	0.0313216i
$724$	−31.4783	−	19.9160i	−1.16988	−	0.740173i
$725$	0.0586125	+	0.595102i	0.00217681	+	0.0221015i
$726$	−3.98324	−	24.7248i	−0.147832	−	0.917622i
$727$	0.380516	+	0.569483i	0.0141126	+	0.0211209i	0.838459	−	0.544965i	$-0.183457\pi$
$727$	0.380516	+	0.569483i	0.0141126	+	0.0211209i	−0.824346	+	0.566086i	$0.808457\pi$
$728$	0.882644	−	8.00218i	0.0327129	−	0.296580i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−8.65190	+	3.21794i	−0.320221	+	0.119101i
$731$	30.6611	+	9.30093i	1.13404	+	0.344007i
$732$	−2.14084	+	29.1792i	−0.0791277	+	1.07849i
$733$	13.6150	+	16.5900i	0.502883	+	0.612765i	0.961142	−	0.276054i	$-0.0890268\pi$
$733$	13.6150	+	16.5900i	0.502883	+	0.612765i	−0.458259	+	0.888819i	$0.651527\pi$
$734$	−29.1021	−	10.0054i	−1.07418	−	0.369305i
$735$	−3.63200	−	3.63200i	−0.133968	−	0.133968i
$736$	−34.2214	−	27.3338i	−1.26142	−	1.00754i
$737$	2.00289	−	2.00289i	0.0737773	−	0.0737773i
$738$	−0.398927	+	0.194802i	−0.0146847	+	0.00717075i
$739$	29.4477	−	24.1671i	1.08325	−	0.889003i	0.0889971	−	0.996032i	$-0.471634\pi$
$739$	29.4477	−	24.1671i	1.08325	−	0.889003i	0.994256	+	0.107029i	$0.0341338\pi$
$740$	−13.4481	+	4.44852i	−0.494361	+	0.163531i
$741$	−5.37286	+	17.7119i	−0.197377	+	0.650665i
$742$	5.37493	+	2.46062i	0.197320	+	0.0903322i
$743$	5.64843	−	8.45347i	0.207221	−	0.310128i	−0.713272	−	0.700887i	$-0.752788\pi$
$743$	5.64843	−	8.45347i	0.207221	−	0.310128i	0.920493	+	0.390760i	$0.127788\pi$
$744$	0.643916	−	0.766186i	0.0236071	−	0.0280897i
$745$	12.8435	−	8.58177i	0.470550	−	0.314412i
$746$	27.3076	+	19.7297i	0.999802	+	0.722356i
$747$	−5.93011	+	0.584065i	−0.216971	+	0.0213698i
$748$	24.2349	+	34.3822i	0.886116	+	1.25714i
$749$	−1.23858	−	4.08304i	−0.0452567	−	0.149191i
$750$	1.37478	−	10.1373i	0.0502000	−	0.370163i
$751$	−17.5500	+	42.3695i	−0.640409	+	1.54609i	0.185719	+	0.982603i	$0.440539\pi$
$751$	−17.5500	+	42.3695i	−0.640409	+	1.54609i	−0.826128	+	0.563482i	$0.809461\pi$
$752$	32.0399	+	4.72690i	1.16838	+	0.172372i
$753$	−4.37377	−	10.5592i	−0.159389	−	0.384799i
$754$	−0.934497	+	0.246502i	−0.0340324	+	0.00897706i
$755$	0.620463	−	1.16080i	0.0225810	−	0.0422460i
$756$	1.12946	−	0.0281715i	0.0410781	−	0.00102459i
$757$	−6.62011	+	8.06663i	−0.240612	+	0.293187i	−0.879289	−	0.476288i	$-0.841982\pi$
$757$	−6.62011	+	8.06663i	−0.240612	+	0.293187i	0.638677	+	0.769475i	$0.279482\pi$
$758$	9.64906	+	15.6525i	0.350470	+	0.568526i
$759$	40.6870	+	8.09314i	1.47684	+	0.293762i
$760$	4.51520	−	6.58952i	0.163784	−	0.239027i
$761$	−3.75966	−	18.9011i	−0.136288	−	0.685165i	−0.987153	−	0.159780i	$-0.948921\pi$
$761$	−3.75966	−	18.9011i	−0.136288	−	0.685165i	0.850865	−	0.525385i	$-0.176079\pi$
$762$	4.47724	+	0.164024i	0.162193	+	0.00594198i
$763$	0.288048	−	0.153965i	0.0104281	−	0.00557391i
$764$	−1.78593	−	14.4332i	−0.0646128	−	0.522175i
$765$	0.295811	−	3.00342i	0.0106951	−	0.108589i
$766$	−1.23382	−	20.0186i	−0.0445798	−	0.723300i
$767$	−31.9387			−1.15324
$768$	6.14620	+	14.7724i	0.221782	+	0.533054i
$769$	−43.1766			−1.55699			−0.778494	−	0.627651i	$-0.784016\pi$
$769$	−43.1766			−1.55699			−0.778494	+	0.627651i	$0.784016\pi$
$770$	−0.202451	−	3.28473i	−0.00729582	−	0.118374i
$771$	−2.84027	+	28.8378i	−0.102290	+	1.03857i
$772$	−1.10748	−	8.95019i	−0.0398590	−	0.322124i
$773$	42.3885	−	22.6571i	1.52461	−	0.814920i	0.525257	−	0.850944i	$-0.323969\pi$
$773$	42.3885	−	22.6571i	1.52461	−	0.814920i	0.999351	+	0.0360235i	$0.0114691\pi$
$774$	−11.5356	−	0.422609i	−0.414639	−	0.0151904i
$775$	−0.304358	−	1.53011i	−0.0109328	−	0.0549631i
$776$	−2.71980	−	1.86363i	−0.0976350	−	0.0669004i
$777$	−5.10391	−	1.01523i	−0.183102	−	0.0364212i
$778$	3.04107	+	4.93317i	0.109028	+	0.176863i
$779$	−0.731552	+	0.891399i	−0.0262106	+	0.0319377i
$780$	7.74523	−	0.193185i	0.277324	−	0.00691712i
$781$	−11.4453	+	21.4126i	−0.409544	+	0.766204i
$782$	−41.5595	+	10.9626i	−1.48617	+	0.392021i
$783$	−0.0519035	−	0.125306i	−0.00185488	−	0.00447807i
$784$	21.4520	−	15.9361i	0.766143	−	0.569145i
$785$	−3.68930	+	8.90676i	−0.131677	+	0.317896i
$786$	−2.18462	+	16.1089i	−0.0779228	+	0.574585i
$787$	13.0791	+	43.1160i	0.466220	+	1.53692i	0.803377	+	0.595471i	$0.203035\pi$
$787$	13.0791	+	43.1160i	0.466220	+	1.53692i	−0.337157	+	0.941448i	$0.609465\pi$
$788$	9.29382	+	13.1852i	0.331078	+	0.469703i
$789$	1.88760	−	0.185912i	0.0672004	−	0.00661866i
$790$	11.7005	+	8.45361i	0.416285	+	0.300766i
$791$	6.01225	−	4.01726i	0.213771	−	0.142837i
$792$	−11.6017	−	9.75029i	−0.412249	−	0.346461i
$793$	−40.9506	+	61.2869i	−1.45420	+	2.17636i
$794$	−8.01948	−	3.67128i	−0.284601	−	0.130289i
$795$	−1.65139	+	5.44390i	−0.0585687	+	0.193075i
$796$	52.8271	−	17.4748i	1.87241	−	0.619377i
$797$	35.6117	−	29.2257i	1.26143	−	1.03523i	0.263932	−	0.964541i	$-0.414981\pi$
$797$	35.6117	−	29.2257i	1.26143	−	1.03523i	0.997499	−	0.0706875i	$-0.0225193\pi$
$798$	2.63706	−	1.28772i	0.0933511	−	0.0455846i
$799$	22.4739	−	22.4739i	0.795068	−	0.795068i
$800$	23.9605	+	6.92287i	0.847132	+	0.244760i
$801$	−10.4064	−	10.4064i	−0.367693	−	0.367693i
$802$	−20.1594	−	6.93087i	−0.711855	−	0.244737i
$803$	28.8582	+	35.1638i	1.01838	+	1.24090i
$804$	0.0773646	−	1.05446i	0.00272844	−	0.0371880i
$805$	3.21784	+	0.976121i	0.113414	+	0.0344037i
$806$	2.36325	−	0.878974i	0.0832420	−	0.0309605i
$807$	−3.85820	−	2.57797i	−0.135815	−	0.0907487i
$808$	10.6680	+	1.17668i	0.375297	+	0.0413954i
$809$	−20.8744	−	31.2408i	−0.733906	−	1.09837i	−0.991244	−	0.132046i	$-0.957845\pi$
$809$	−20.8744	−	31.2408i	−0.733906	−	1.09837i	0.257338	−	0.966322i	$-0.417155\pi$
$810$	0.172935	+	1.07344i	0.00607630	+	0.0377168i
$811$	−1.76520	−	17.9224i	−0.0619845	−	0.629339i	−0.975119	−	0.221681i	$-0.928846\pi$
$811$	−1.76520	−	17.9224i	−0.0619845	−	0.629339i	0.913135	−	0.407658i	$-0.133654\pi$
$812$	0.129495	+	0.0819304i	0.00454438	+	0.00287519i
$813$	2.18457	−	0.662681i	0.0766161	−	0.0232412i
$814$	42.2773	+	55.5433i	1.48182	+	1.94679i
$815$	−11.6445	−	4.82329i	−0.407888	−	0.168953i
$816$	15.2341	+	3.80320i	0.533300	+	0.133139i
$817$	−27.7013	+	11.4743i	−0.969147	+	0.401434i
$818$	−37.9628	−	22.1154i	−1.32734	−	0.773247i
$819$	2.51026	+	1.34176i	0.0877156	+	0.0468850i
$820$	0.450421	+	0.173543i	0.0157294	+	0.00606039i
$821$	−26.3595	−	21.6327i	−0.919952	−	0.754985i	0.0498807	−	0.998755i	$-0.484116\pi$
$821$	−26.3595	−	21.6327i	−0.919952	−	0.754985i	−0.969833	+	0.243770i	$0.921616\pi$
$822$	−24.9704	−	5.92489i	−0.870943	−	0.206654i
$823$	0.688730	−	3.46248i	0.0240076	−	0.120694i	−0.966923	−	0.255068i	$-0.917902\pi$
$823$	0.688730	−	3.46248i	0.0240076	−	0.120694i	0.990931	+	0.134373i	$0.0429022\pi$
$824$	5.21631	+	2.23241i	0.181719	+	0.0777695i
$825$	−23.1692	+	4.60863i	−0.806647	+	0.160452i
$826$	3.44731	+	3.70950i	0.119947	+	0.129070i
$827$	−1.02984	−	1.92669i	−0.0358109	−	0.0669975i	0.863379	−	0.504555i	$-0.168344\pi$
$827$	−1.02984	−	1.92669i	−0.0358109	−	0.0669975i	−0.899190	+	0.437558i	$0.855844\pi$
$828$	13.4701	−	7.63774i	0.468120	−	0.265430i
$829$	−39.6591	−	3.90608i	−1.37742	−	0.135664i	−0.617955	−	0.786214i	$-0.712038\pi$
$829$	−39.6591	−	3.90608i	−1.37742	−	0.135664i	−0.759464	+	0.650550i	$0.774538\pi$
$830$	4.85442	+	4.29077i	0.168499	+	0.148935i
$831$		−	0.333173i		−	0.0115576i
$832$	−4.88703	+	40.0117i	−0.169427	+	1.38716i
$833$		−	26.2252i		−	0.908651i
$834$	−11.5246	+	13.0385i	−0.399064	+	0.451487i
$835$	−1.24835	−	0.122952i	−0.0432010	−	0.00425493i
$836$	−37.9426	−	10.4841i	−1.31227	−	0.362599i
$837$	0.166803	+	0.312066i	0.00576555	+	0.0107866i
$838$	−3.90557	+	3.62952i	−0.134916	+	0.125380i
$839$	30.6784	−	6.10232i	1.05914	−	0.210675i	0.365361	−	0.930866i	$-0.380946\pi$
$839$	30.6784	−	6.10232i	1.05914	−	0.210675i	0.693776	+	0.720191i	$0.255946\pi$
$840$	−0.858421	−	0.878714i	−0.0296183	−	0.0303185i
$841$	−5.65403	+	28.4247i	−0.194967	+	0.980163i
$842$	6.55988	−	27.6465i	0.226068	−	0.952763i
$843$	−13.4970	−	11.0767i	−0.464863	−	0.381503i
$844$	35.9545	−	15.9545i	1.23760	−	0.549175i
$845$	8.39947	+	4.48961i	0.288950	+	0.154447i
$846$	−5.76379	+	9.89400i	−0.198163	+	0.340163i
$847$	−9.24215	+	3.82822i	−0.317564	+	0.131539i
$848$	−26.7660	−	12.6336i	−0.919148	−	0.433839i
$849$	−17.5159	−	7.25534i	−0.601145	−	0.249003i
$850$	19.4756	−	14.8240i	0.668008	−	0.508460i
$851$	−68.2517	+	20.7039i	−2.33964	+	0.709722i
$852$	1.98916	+	8.84186i	0.0681476	+	0.302917i
$853$	−1.26140	−	12.8072i	−0.0431896	−	0.438511i	−0.992326	−	0.123647i	$-0.960541\pi$
$853$	−1.26140	−	12.8072i	−0.0431896	−	0.438511i	0.949137	−	0.314864i	$-0.101959\pi$
$854$	11.5381	−	1.85883i	0.394827	−	0.0636080i
$855$	1.56904	+	2.34824i	0.0536601	+	0.0803080i
$856$	5.96220	+	20.5144i	0.203784	+	0.701169i
$857$	15.6084	+	10.4292i	0.533173	+	0.356255i	0.792827	−	0.609447i	$-0.208608\pi$
$857$	15.6084	+	10.4292i	0.533173	+	0.356255i	−0.259654	+	0.965702i	$0.583608\pi$
$858$	−13.3096	−	35.7847i	−0.454381	−	1.22167i
$859$	21.6453	+	6.56603i	0.738528	+	0.224030i	0.637066	−	0.770809i	$-0.280148\pi$
$859$	21.6453	+	6.56603i	0.738528	+	0.224030i	0.101462	+	0.994839i	$0.467648\pi$
$860$	8.20162	+	9.50039i	0.279673	+	0.323961i
$861$	0.112500	+	0.137082i	0.00383399	+	0.00467173i
$862$	−3.00485	+	8.74006i	−0.102346	+	0.297688i
$863$	25.0967	+	25.0967i	0.854303	+	0.854303i	0.990660	−	0.136357i	$-0.0435394\pi$
$863$	25.0967	+	25.0967i	0.854303	+	0.854303i	−0.136357	+	0.990660i	$0.543539\pi$
$864$	−5.65636	+	0.0749831i	−0.192433	+	0.00255098i
$865$	−0.700686	+	0.700686i	−0.0238240	+	0.0238240i
$866$	2.60208	+	5.32870i	0.0884222	+	0.181077i
$867$	−1.22994	+	1.00939i	−0.0417710	+	0.0342806i
$868$	−0.357166	−	0.179606i	−0.0121230	−	0.00609623i
$869$	20.6491	−	68.0708i	0.700471	−	2.30914i
$870$	−0.0613837	+	0.134085i	−0.00208110	+	0.00454592i
$871$	1.47985	−	2.21476i	0.0501429	−	0.0750441i
$872$	−1.45114	+	0.753988i	−0.0491416	+	0.0255332i
$873$	0.969224	−	0.647615i	0.0328033	−	0.0219184i
$874$	23.5553	−	32.6026i	0.796772	−	1.10280i
$875$	−4.06674	+	0.400539i	−0.137481	+	0.0135407i
$876$	16.7311	+	2.89633i	0.565290	+	0.0978580i
$877$	8.45224	+	27.8633i	0.285412	+	0.940877i	0.976026	+	0.217654i	$0.0698404\pi$
$877$	8.45224	+	27.8633i	0.285412	+	0.940877i	−0.690614	+	0.723224i	$0.742660\pi$
$878$	−19.7384	−	2.67685i	−0.666140	−	0.0903392i
$879$	−1.64252	+	3.96540i	−0.0554009	+	0.133749i
$880$	0.821466	+	16.4570i	0.0276916	+	0.554766i
$881$	−12.0632	−	29.1232i	−0.406420	−	0.981185i	−0.986072	−	0.166321i	$-0.946811\pi$
$881$	−12.0632	−	29.1232i	−0.406420	−	0.981185i	0.579652	−	0.814864i	$-0.303189\pi$
$882$	2.40982	+	9.13571i	0.0811428	+	0.307615i
$883$	−1.52644	+	2.85577i	−0.0513688	+	0.0961043i	−0.906296	−	0.422644i	$-0.861102\pi$
$883$	−1.52644	+	2.85577i	−0.0513688	+	0.0961043i	0.854927	+	0.518749i	$0.173602\pi$
$884$	28.6601	+	27.2652i	0.963944	+	0.917028i
$885$	−3.09165	+	3.76718i	−0.103925	+	0.126632i
$886$	−19.4325	+	11.9792i	−0.652848	+	0.402450i
$887$	35.8161	+	7.12426i	1.20259	+	0.239209i	0.755420	−	0.655241i	$-0.227433\pi$
$887$	35.8161	+	7.12426i	1.20259	+	0.239209i	0.447167	+	0.894451i	$0.352433\pi$
$888$	25.4936	+	5.38132i	0.855509	+	0.180585i
$889$	−0.349140	−	1.75524i	−0.0117098	−	0.0588690i
$890$	−0.585822	+	15.9907i	−0.0196368	+	0.536010i
$891$	4.72536	−	2.52576i	0.158306	−	0.0846161i
$892$	−36.4293	−	28.4067i	−1.21974	−	0.951125i
$893$	−2.91526	+	29.5992i	−0.0975556	+	0.990498i
$894$	−28.3598	+	1.74792i	−0.948493	+	0.0584593i
$895$	17.0553			0.570097
$896$	5.17462	−	3.75107i	0.172872	−	0.125315i
$897$	39.0112			1.30255
$898$	56.6955	−	3.49436i	1.89195	−	0.116608i
$899$	−0.00470409	+	0.0477614i	−0.000156890	+	0.00159293i
$900$	−5.42227	+	6.95363i	−0.180742	+	0.231788i
$901$	−25.6162	+	13.6921i	−0.853398	+	0.456151i
$902$	0.0870853	−	2.37710i	0.00289962	−	0.0791487i
$903$	0.899557	+	4.52238i	0.0299354	+	0.150495i
$904$	−30.3356	+	19.7610i	−1.00895	+	0.657240i
$905$	−14.0440	−	2.79353i	−0.466839	−	0.0928601i
$906$	−2.06099	+	1.27050i	−0.0684718	+	0.0422097i
$907$	−5.81518	+	7.08582i	−0.193090	+	0.235281i	−0.860551	−	0.509364i	$-0.829881\pi$
$907$	−5.81518	+	7.08582i	−0.193090	+	0.235281i	0.667462	+	0.744644i	$0.267381\pi$
$908$	−28.0780	+	29.5145i	−0.931801	+	0.979473i
$909$	−1.78875	+	3.34651i	−0.0593289	+	0.110997i
$910$	−0.789344	−	2.99243i	−0.0261665	−	0.0991981i
$911$	−19.0322	−	45.9479i	−0.630566	−	1.52232i	−0.838913	−	0.544266i	$-0.816808\pi$
$911$	−19.0322	−	45.9479i	−0.630566	−	1.52232i	0.208347	−	0.978055i	$-0.433192\pi$
$912$	−13.2779	+	6.29278i	−0.439676	+	0.208375i
$913$	12.2181	−	29.4971i	0.404360	−	0.976212i
$914$	−35.1069	−	4.76106i	−1.16123	−	0.157482i
$915$	3.26482	+	10.7627i	0.107932	+	0.355803i
$916$	−0.121642	+	0.702681i	−0.00401916	+	0.0232172i
$917$	6.46231	−	0.636482i	0.213404	−	0.0210185i
$918$	−3.25110	+	4.49979i	−0.107302	+	0.148515i
$919$	22.7406	−	15.1948i	0.750144	−	0.501230i	−0.120761	−	0.992682i	$-0.538534\pi$
$919$	22.7406	−	15.1948i	0.750144	−	0.501230i	0.870905	+	0.491452i	$0.163534\pi$
$920$	−16.0532	−	5.07520i	−0.529258	−	0.167325i
$921$	−11.3819	+	17.0341i	−0.375045	+	0.561294i
$922$	3.22408	−	7.04261i	0.106179	−	0.231936i
$923$	−6.62784	+	21.8490i	−0.218158	+	0.719170i
$924$	−2.71963	+	5.40827i	−0.0894691	+	0.177919i
$925$	31.3956	−	25.7657i	1.03228	−	0.847171i
$926$	0.356333	+	0.729722i	0.0117098	+	0.0239802i
$927$	−1.41848	+	1.41848i	−0.0465891	+	0.0465891i
$928$	−0.643532	−	0.417763i	−0.0211250	−	0.0137137i
$929$	−0.966877	−	0.966877i	−0.0317222	−	0.0317222i	0.691068	−	0.722790i	$-0.257141\pi$
$929$	−0.966877	−	0.966877i	−0.0317222	−	0.0317222i	−0.722790	+	0.691068i	$0.757141\pi$
$930$	0.125086	−	0.363830i	0.00410173	−	0.0119305i
$931$	15.5690	+	18.9709i	0.510254	+	0.621746i
$932$	21.0481	−	18.1707i	0.689454	−	0.595201i
$933$	−15.0152	−	4.55482i	−0.491576	−	0.149118i
$934$	4.97408	+	13.3735i	0.162757	+	0.437596i
$935$	13.4451	+	8.98373i	0.439702	+	0.293799i
$936$	−12.4893	−	6.86443i	−0.408225	−	0.224371i
$937$	1.33151	+	1.99275i	0.0434986	+	0.0651003i	0.852582	−	0.522594i	$-0.175036\pi$
$937$	1.33151	+	1.99275i	0.0434986	+	0.0651003i	−0.809083	+	0.587694i	$0.800036\pi$
$938$	−0.416960	+	0.0671735i	−0.0136142	+	0.00219329i
$939$	1.62944	+	16.5440i	0.0531747	+	0.539892i
$940$	12.1463	−	2.73256i	0.396167	−	0.0891261i
$941$	3.41403	−	1.03564i	0.111294	−	0.0337608i	−0.234146	−	0.972201i	$-0.575229\pi$
$941$	3.41403	−	1.03564i	0.111294	−	0.0337608i	0.345441	+	0.938441i	$0.387729\pi$
$942$	14.1108	−	10.7406i	0.459755	−	0.349946i
$943$	2.24548	+	0.930109i	0.0731230	+	0.0302885i
$944$	−17.0422	−	18.7734i	−0.554676	−	0.611024i
$945$	0.401253	−	0.166204i	0.0130528	−	0.00540663i
$946$	31.1331	−	53.4425i	1.01222	−	1.73756i
$947$	−29.9478	−	16.0074i	−0.973173	−	0.520172i	−0.0934323	−	0.995626i	$-0.529784\pi$
$947$	−29.9478	−	16.0074i	−0.973173	−	0.520172i	−0.879741	+	0.475454i	$0.842284\pi$
$948$	−10.7696	−	24.2701i	−0.349781	−	0.788255i
$949$	33.0676	+	27.1379i	1.07342	+	0.880934i
$950$	−5.28781	+	22.2854i	−0.171559	+	0.723035i
$951$	−3.55040	+	17.8491i	−0.115130	+	0.578796i
$952$	0.0732653	−	6.27159i	0.00237454	−	0.203263i
$953$	46.4075	−	9.23104i	1.50329	−	0.299023i	0.626318	−	0.779568i	$-0.284561\pi$
$953$	46.4075	−	9.23104i	1.50329	−	0.299023i	0.876970	+	0.480545i	$0.159561\pi$
$954$	7.66537	−	7.12357i	0.248175	−	0.230634i
$955$	−2.63540	−	4.93048i	−0.0852794	−	0.159547i
$956$	−3.09874	+	11.2146i	−0.100220	+	0.362705i
$957$	0.723212	+	0.0712302i	0.0233781	+	0.00230254i
$958$	4.30700	−	4.87278i	0.139153	−	0.157432i
$959$			10.2513i			0.331033i
$960$	4.24634	+	4.44954i	0.137050	+	0.143608i
$961$			30.8748i			0.995961i
$962$	49.1832	+	43.4724i	1.58573	+	1.40161i
$963$	−7.51669	−	0.740329i	−0.242222	−	0.0238568i
$964$	2.86206	+	5.04760i	0.0921806	+	0.162572i
$965$	−1.63424	−	3.05744i	−0.0526080	−	0.0984226i
$966$	−4.21068	−	4.53093i	−0.135476	−	0.145780i
$967$	−0.708786	+	0.140986i	−0.0227930	+	0.00453382i	−0.206474	−	0.978452i	$-0.566199\pi$
$967$	−0.708786	+	0.140986i	−0.0227930	+	0.00453382i	0.183681	+	0.982986i	$0.441199\pi$
$968$	46.4952	−	18.6257i	1.49441	−	0.598652i
$969$	−2.81313	+	14.1426i	−0.0903708	+	0.454325i
$970$	−1.23318	−	0.292604i	−0.0395950	−	0.00939496i
$971$	−23.0134	−	18.8866i	−0.738536	−	0.606101i	0.188060	−	0.982157i	$-0.439780\pi$
$971$	−23.0134	−	18.8866i	−0.738536	−	0.606101i	−0.926597	+	0.376056i	$0.877280\pi$
$972$	0.719056	−	1.86627i	0.0230637	−	0.0598606i
$973$	6.13031	+	3.27672i	0.196529	+	0.105047i
$974$	38.8723	+	22.6452i	1.24555	+	0.725600i
$975$	−20.5239	+	8.50127i	−0.657290	+	0.272258i
$976$	−57.8751	+	8.63152i	−1.85254	+	0.276288i
$977$	−19.8727	−	8.23154i	−0.635784	−	0.263350i	0.0414243	−	0.999142i	$-0.486810\pi$
$977$	−19.8727	−	8.23154i	−0.635784	−	0.263350i	−0.677208	+	0.735791i	$0.736810\pi$
$978$	14.0419	+	18.4481i	0.449011	+	0.589905i
$979$	75.4583	−	22.8900i	2.41166	−	0.731568i
$980$	5.49253	−	8.68121i	0.175452	−	0.277311i
$981$	−0.0566711	−	0.575391i	−0.00180937	−	0.0183708i
$982$	−7.11954	−	44.1924i	−0.227194	−	1.41024i
$983$	12.4540	+	18.6388i	0.397222	+	0.594484i	0.975134	−	0.221614i	$-0.0711326\pi$
$983$	12.4540	+	18.6388i	0.397222	+	0.594484i	−0.577913	+	0.816099i	$0.696133\pi$
$984$	−0.555220	−	0.692887i	−0.0176998	−	0.0220884i
$985$	5.15605	+	3.44516i	0.164285	+	0.109772i
$986$	−0.705704	+	0.262475i	−0.0224742	+	0.00835892i
$987$	4.37692	+	1.32772i	0.139319	+	0.0422619i
$988$	−36.9186	−	2.70868i	−1.17454	−	0.0861744i
$989$	40.0914	+	48.8515i	1.27483	+	1.55339i
$990$	−5.50918	−	1.89407i	−0.175093	−	0.0601975i
$991$	37.7252	+	37.7252i	1.19838	+	1.19838i	0.974651	+	0.223731i	$0.0718237\pi$
$991$	37.7252	+	37.7252i	1.19838	+	1.19838i	0.223731	+	0.974651i	$0.428176\pi$
$992$	1.77767	+	0.920097i	0.0564410	+	0.0292131i
$993$	−11.4619	+	11.4619i	−0.363734	+	0.363734i
$994$	3.25302	−	1.58850i	0.103180	−	0.0503840i
$995$	16.5344	−	13.5694i	0.524175	−	0.430179i
$996$	−3.74279	−	11.3146i	−0.118595	−	0.358518i
$997$	15.8918	−	52.3881i	0.503297	−	1.65915i	−0.225365	−	0.974274i	$-0.572357\pi$
$997$	15.8918	−	52.3881i	0.503297	−	1.65915i	0.728662	−	0.684874i	$-0.240143\pi$
$998$	−50.9680	−	23.3329i	−1.61336	−	0.738591i
$999$	−5.11789	+	7.65947i	−0.161923	+	0.242335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.16	✓	512
128.53	even	32	inner	384.2.v.a.181.16	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.16	✓	512	1.1	even	1	trivial
384.2.v.a.181.16	yes	512	128.53	even	32	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.0869984 - 1.41154i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.98486 + 0.245602i) q^{4} +(-0.678042 + 0.362421i) q^{5} +(1.41327 + 0.0517752i) q^{6} +(-0.110208 - 0.554052i) q^{7} +(0.519356 + 2.78034i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(-0.0869984 - 1.41154i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.98486 + 0.245602i) q^{4} +(-0.678042 + 0.362421i) q^{5} +(1.41327 + 0.0517752i) q^{6} +(-0.110208 - 0.554052i) q^{7} +(0.519356 + 2.78034i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(0.570558 + 0.925550i) q^{10} +(3.39910 - 4.14181i) q^{11} +(-0.0498693 - 1.99938i) q^{12} +(2.37520 - 4.44368i) q^{13} +(-0.772476 + 0.203764i) q^{14} +(-0.294216 - 0.710300i) q^{15} +(3.87936 - 0.974974i) q^{16} +(1.50219 - 3.62661i) q^{17} +(-0.190050 + 1.40139i) q^{18} +(1.06633 + 3.51523i) q^{19} +(1.25681 - 0.885885i) q^{20} +(0.562186 - 0.0553705i) q^{21} +(-6.14203 - 4.43762i) q^{22} +(6.43758 - 4.30145i) q^{23} +(-2.81785 + 0.244335i) q^{24} +(-2.44946 + 3.66587i) q^{25} +(-6.47905 - 2.96608i) q^{26} +(0.290285 - 0.956940i) q^{27} +(0.354824 + 1.07265i) q^{28} +(0.104844 - 0.0860430i) q^{29} +(-0.977018 + 0.477091i) q^{30} +(-0.250209 + 0.250209i) q^{31} +(-1.71371 - 5.39103i) q^{32} +(3.78870 + 3.78870i) q^{33} +(-5.24978 - 1.80489i) q^{34} +(0.275525 + 0.335729i) q^{35} +(1.99464 + 0.146344i) q^{36} +(-8.81530 - 2.67409i) q^{37} +(4.86910 - 1.81099i) q^{38} +(4.18947 + 2.79931i) q^{39} +(-1.35980 - 1.69696i) q^{40} +(0.174404 + 0.261014i) q^{41} +(-0.127067 - 0.788728i) q^{42} +(0.800053 + 8.12307i) q^{43} +(-5.72950 + 9.05576i) q^{44} +(0.735718 - 0.223178i) q^{45} +(-6.63171 - 8.71265i) q^{46} +(7.48036 + 3.09847i) q^{47} +(0.590036 + 3.95624i) q^{48} +(6.17233 - 2.55666i) q^{49} +(5.38761 + 3.13857i) q^{50} +(3.46191 + 1.85043i) q^{51} +(-3.62306 + 9.40344i) q^{52} +(-5.71984 - 4.69415i) q^{53} +(-1.37601 - 0.326495i) q^{54} +(-0.803651 + 4.04023i) q^{55} +(1.48321 - 0.594165i) q^{56} +(-3.60282 + 0.716646i) q^{57} +(-0.130574 - 0.140505i) q^{58} +(-2.98807 - 5.59029i) q^{59} +(0.758430 + 1.33759i) q^{60} +(-14.5584 - 1.43387i) q^{61} +(0.374946 + 0.331410i) q^{62} +0.564906i q^{63} +(-7.46054 + 2.88797i) q^{64} +3.87382i q^{65} +(5.01827 - 5.67749i) q^{66} +(0.526102 + 0.0518166i) q^{67} +(-2.09094 + 7.56727i) q^{68} +(3.64975 + 6.82820i) q^{69} +(0.449923 - 0.418122i) q^{70} +(-4.44436 + 0.884037i) q^{71} +(0.0330397 - 2.82823i) q^{72} +(-1.65631 + 8.32681i) q^{73} +(-3.00766 + 12.6757i) q^{74} +(-3.40813 - 2.79698i) q^{75} +(-2.97987 - 6.71535i) q^{76} +(-2.66939 - 1.42682i) q^{77} +(3.58685 - 6.15712i) q^{78} +(12.2655 - 5.08055i) q^{79} +(-2.27702 + 2.06703i) q^{80} +(0.923880 + 0.382683i) q^{81} +(0.353258 - 0.268885i) q^{82} +(5.70222 - 1.72975i) q^{83} +(-1.10226 + 0.247977i) q^{84} +(0.295811 + 3.00342i) q^{85} +(11.3964 - 1.83600i) q^{86} +(0.0753522 + 0.112772i) q^{87} +(13.2810 + 7.29956i) q^{88} +(12.2367 + 8.17628i) q^{89} +(-0.379029 - 1.01908i) q^{90} +(-2.72379 - 0.826253i) q^{91} +(-11.7213 + 10.1189i) q^{92} +(-0.224479 - 0.273528i) q^{93} +(3.72281 - 10.8284i) q^{94} +(-1.99701 - 1.99701i) q^{95} +(5.53304 - 1.17704i) q^{96} +(-0.824257 + 0.824257i) q^{97} +(-4.14580 - 8.49003i) q^{98} +(-4.14181 + 3.39910i) 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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