LMFDB - Embedded newform 950.2.w.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(-0.341841 + 0.670901i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.0404826 - 2.23570i) q^{5} +(0.232680 - 0.716117i) q^{6} +(2.21716 + 2.21716i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.43010 + 1.96837i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.341841 + 0.670901i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.0404826 - 2.23570i) q^{5} +(0.232680 - 0.716117i) q^{6} +(2.21716 + 2.21716i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.43010 + 1.96837i) q^{9} +(0.309757 + 2.21451i) q^{10} +(3.84997 + 2.79717i) q^{11} +(-0.117790 + 0.743699i) q^{12} +(-1.16183 - 0.184015i) q^{13} +(-2.53670 - 1.84302i) q^{14} +(1.48610 + 0.791414i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.49738 + 0.762954i) q^{17} +(-1.72042 - 1.72042i) q^{18} +(-1.80511 - 3.96757i) q^{19} +(-0.652368 - 2.13879i) q^{20} +(-2.24541 + 0.729578i) q^{21} +(-4.24015 - 2.16046i) q^{22} +(-0.197560 + 0.0312905i) q^{23} -0.752970i q^{24} +(-4.99672 - 0.181014i) q^{25} +1.17631 q^{26} +(-4.04055 + 0.639960i) q^{27} +(2.79378 + 1.42350i) q^{28} +(2.01959 + 6.21566i) q^{29} +(-1.59160 - 0.549194i) q^{30} +(2.40087 + 0.780090i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.19270 + 1.62676i) q^{33} +(1.35959 - 0.987803i) q^{34} +(5.04666 - 4.86715i) q^{35} +(1.96837 + 1.43010i) q^{36} +(0.759275 - 4.79387i) q^{37} +(2.40355 + 3.63634i) q^{38} +(0.520616 - 0.716567i) q^{39} +(0.978917 + 2.01040i) q^{40} +(5.72588 + 7.88100i) q^{41} +(2.10363 - 1.07186i) q^{42} +(5.92897 - 5.92897i) q^{43} +(4.52592 + 1.47056i) q^{44} +(4.45858 - 3.11760i) q^{45} +(0.190233 - 0.0618105i) q^{46} +(-2.73681 + 5.37129i) q^{47} +(0.117790 + 0.743699i) q^{48} +2.83159i q^{49} +(4.96352 - 0.602874i) q^{50} -1.26540i q^{51} +(-1.16183 + 0.184015i) q^{52} +(-3.57346 + 7.01331i) q^{53} +(3.89069 - 1.26416i) q^{54} +(6.40949 - 8.49416i) q^{55} +(-2.98207 - 0.968934i) q^{56} +(3.27890 + 0.145229i) q^{57} +(-2.96707 - 5.82320i) q^{58} +(3.89777 - 2.83189i) q^{59} +(1.65792 + 0.293451i) q^{60} +(0.253460 + 0.184149i) q^{61} +(-2.49334 - 0.394907i) q^{62} +(-1.19342 + 7.53495i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.458437 + 2.59005i) q^{65} +(2.89891 - 2.10618i) q^{66} +(6.31454 + 12.3930i) q^{67} +(-1.18833 + 1.18833i) q^{68} +(0.0465414 - 0.143240i) q^{69} +(-4.22314 + 5.59670i) q^{70} +(-2.92382 + 0.950007i) q^{71} +(-2.16785 - 1.10458i) q^{72} +(-9.51003 + 1.50624i) q^{73} +4.85363i q^{74} +(1.82953 - 3.29043i) q^{75} +(-2.94281 - 3.21557i) q^{76} +(2.33423 + 14.7378i) q^{77} +(-0.402111 + 0.789187i) q^{78} +(-0.745446 - 2.29425i) q^{79} +(-1.28136 - 1.83252i) q^{80} +(-1.30367 + 4.01230i) q^{81} +(-6.88825 - 6.88825i) q^{82} +(-0.730424 - 1.43354i) q^{83} +(-1.91006 + 1.38774i) q^{84} +(1.64512 + 3.37859i) q^{85} +(-4.92848 + 6.78347i) q^{86} +(-4.86047 - 0.769823i) q^{87} +(-4.70024 - 0.744445i) q^{88} +(8.14363 + 5.91669i) q^{89} +(-3.91599 + 3.77669i) q^{90} +(-2.16796 - 2.98395i) q^{91} +(-0.178222 + 0.0908086i) q^{92} +(-1.34408 + 1.34408i) q^{93} +(1.86286 - 5.73329i) q^{94} +(-8.94337 + 3.87506i) q^{95} +(-0.232680 - 0.716117i) q^{96} +(8.29029 + 4.22411i) q^{97} +(-0.442958 - 2.79673i) q^{98} +11.5784i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

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 $

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	−0.341841	+	0.670901i	−0.197362	+	0.387345i	−0.968384	−	0.249464i	$-0.919746\pi$
$3$	−0.341841	+	0.670901i	−0.197362	+	0.387345i	0.771022	+	0.636808i	$0.219746\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	0.0404826	−	2.23570i	0.0181044	−	0.999836i
$5$	0.0404826	−	2.23570i	0.0181044	−	0.999836i
$6$	0.232680	−	0.716117i	0.0949914	−	0.292353i
$7$	2.21716	+	2.21716i	0.838007	+	0.838007i	0.988596	−	0.150589i	$-0.0481170\pi$
$7$	2.21716	+	2.21716i	0.838007	+	0.838007i	−0.150589	+	0.988596i	$0.548117\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	1.43010	+	1.96837i	0.476701	+	0.656123i
$10$	0.309757	+	2.21451i	0.0979536	+	0.700289i
$11$	3.84997	+	2.79717i	1.16081	+	0.843378i	0.989880	−	0.141905i	$-0.0453226\pi$
$11$	3.84997	+	2.79717i	1.16081	+	0.843378i	0.170931	+	0.985283i	$0.445323\pi$
$12$	−0.117790	+	0.743699i	−0.0340032	+	0.214687i
$13$	−1.16183	−	0.184015i	−0.322233	−	0.0510367i	−0.00677733	−	0.999977i	$-0.502157\pi$
$13$	−1.16183	−	0.184015i	−0.322233	−	0.0510367i	−0.315456	+	0.948940i	$0.602157\pi$
$14$	−2.53670	−	1.84302i	−0.677962	−	0.492568i
$15$	1.48610	+	0.791414i	0.383708	+	0.204342i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−1.49738	+	0.762954i	−0.363169	+	0.185044i	−0.626047	−	0.779785i	$-0.715328\pi$
$17$	−1.49738	+	0.762954i	−0.363169	+	0.185044i	0.262878	+	0.964829i	$0.415328\pi$
$18$	−1.72042	−	1.72042i	−0.405506	−	0.405506i
$19$	−1.80511	−	3.96757i	−0.414120	−	0.910222i
$19$	−1.80511	−	3.96757i	−0.414120	−	0.910222i
$20$	−0.652368	−	2.13879i	−0.145874	−	0.478248i
$21$	−2.24541	+	0.729578i	−0.489989	+	0.159207i
$22$	−4.24015	−	2.16046i	−0.904003	−	0.460612i
$23$	−0.197560	+	0.0312905i	−0.0411942	+	0.00652452i	−0.176998	−	0.984211i	$-0.556638\pi$
$23$	−0.197560	+	0.0312905i	−0.0411942	+	0.00652452i	0.135803	+	0.990736i	$0.456638\pi$
$24$		−	0.752970i		−	0.153699i
$25$	−4.99672	−	0.181014i	−0.999344	−	0.0362028i
$26$	1.17631			0.230693
$27$	−4.04055	+	0.639960i	−0.777603	+	0.123160i
$28$	2.79378	+	1.42350i	0.527975	+	0.269017i
$29$	2.01959	+	6.21566i	0.375028	+	1.15422i	0.943459	+	0.331488i	$0.107551\pi$
$29$	2.01959	+	6.21566i	0.375028	+	1.15422i	−0.568431	+	0.822731i	$0.692449\pi$
$30$	−1.59160	−	0.549194i	−0.290586	−	0.100269i
$31$	2.40087	+	0.780090i	0.431209	+	0.140108i	0.516576	−	0.856241i	$-0.327206\pi$
$31$	2.40087	+	0.780090i	0.431209	+	0.140108i	−0.0853672	+	0.996350i	$0.527206\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−3.19270	+	1.62676i	−0.555778	+	0.283183i
$34$	1.35959	−	0.987803i	0.233169	−	0.169407i
$35$	5.04666	−	4.86715i	0.853042	−	0.822698i
$36$	1.96837	+	1.43010i	0.328061	+	0.238351i
$37$	0.759275	−	4.79387i	0.124824	−	0.788108i	−0.843264	−	0.537499i	$-0.819369\pi$
$37$	0.759275	−	4.79387i	0.124824	−	0.788108i	0.968088	−	0.250609i	$-0.0806308\pi$
$38$	2.40355	+	3.63634i	0.389907	+	0.589892i
$39$	0.520616	−	0.716567i	0.0833653	−	0.114743i
$40$	0.978917	+	2.01040i	0.154780	+	0.317873i
$41$	5.72588	+	7.88100i	0.894232	+	1.23081i	0.972271	+	0.233855i	$0.0751341\pi$
$41$	5.72588	+	7.88100i	0.894232	+	1.23081i	−0.0780391	+	0.996950i	$0.524866\pi$
$42$	2.10363	−	1.07186i	0.324598	−	0.165391i
$43$	5.92897	−	5.92897i	0.904160	−	0.904160i	−0.0916329	−	0.995793i	$-0.529209\pi$
$43$	5.92897	−	5.92897i	0.904160	−	0.904160i	0.995793	+	0.0916329i	$0.0292086\pi$
$44$	4.52592	+	1.47056i	0.682307	+	0.221695i
$45$	4.45858	−	3.11760i	0.664646	−	0.464744i
$46$	0.190233	−	0.0618105i	0.0280484	−	0.00911346i
$47$	−2.73681	+	5.37129i	−0.399205	+	0.783484i	−0.999872	−	0.0160158i	$-0.994902\pi$
$47$	−2.73681	+	5.37129i	−0.399205	+	0.783484i	0.600667	+	0.799499i	$0.294902\pi$
$48$	0.117790	+	0.743699i	0.0170016	+	0.107344i
$49$			2.83159i			0.404513i
$50$	4.96352	−	0.602874i	0.701948	−	0.0852593i
$51$		−	1.26540i		−	0.177192i
$52$	−1.16183	+	0.184015i	−0.161116	+	0.0255183i
$53$	−3.57346	+	7.01331i	−0.490852	+	0.963352i	0.504161	+	0.863610i	$0.331802\pi$
$53$	−3.57346	+	7.01331i	−0.490852	+	0.963352i	−0.995013	+	0.0997421i	$0.968198\pi$
$54$	3.89069	−	1.26416i	0.529456	−	0.172031i
$55$	6.40949	−	8.49416i	0.864256	−	1.14535i
$56$	−2.98207	−	0.968934i	−0.398496	−	0.129479i
$57$	3.27890	+	0.145229i	0.434301	+	0.0192360i
$58$	−2.96707	−	5.82320i	−0.389595	−	0.764624i
$59$	3.89777	−	2.83189i	0.507446	−	0.368681i	−0.304408	−	0.952542i	$-0.598459\pi$
$59$	3.89777	−	2.83189i	0.507446	−	0.368681i	0.811854	+	0.583861i	$0.198459\pi$
$60$	1.65792	+	0.293451i	0.214037	+	0.0378844i
$61$	0.253460	+	0.184149i	0.0324522	+	0.0235779i	0.603893	−	0.797065i	$-0.293615\pi$
$61$	0.253460	+	0.184149i	0.0324522	+	0.0235779i	−0.571441	+	0.820643i	$0.693615\pi$
$62$	−2.49334	−	0.394907i	−0.316655	−	0.0501532i
$63$	−1.19342	+	7.53495i	−0.150357	+	0.949315i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−0.458437	+	2.59005i	−0.0568621	+	0.321256i
$66$	2.89891	−	2.10618i	0.356832	−	0.259253i
$67$	6.31454	+	12.3930i	0.771444	+	1.51404i	0.855627	+	0.517593i	$0.173172\pi$
$67$	6.31454	+	12.3930i	0.771444	+	1.51404i	−0.0841831	+	0.996450i	$0.526828\pi$
$68$	−1.18833	+	1.18833i	−0.144106	+	0.144106i
$69$	0.0465414	−	0.143240i	0.00560293	−	0.0172440i
$70$	−4.22314	+	5.59670i	−0.504762	+	0.668933i
$71$	−2.92382	+	0.950007i	−0.346994	+	0.112745i	−0.477329	−	0.878725i	$-0.658395\pi$
$71$	−2.92382	+	0.950007i	−0.346994	+	0.112745i	0.130335	+	0.991470i	$0.458395\pi$
$72$	−2.16785	−	1.10458i	−0.255484	−	0.130175i
$73$	−9.51003	+	1.50624i	−1.11306	+	0.176292i	−0.685769	−	0.727820i	$-0.740534\pi$
$73$	−9.51003	+	1.50624i	−1.11306	+	0.176292i	−0.427296	+	0.904112i	$0.640534\pi$
$74$			4.85363i			0.564223i
$75$	1.82953	−	3.29043i	0.211256	−	0.379946i
$76$	−2.94281	−	3.21557i	−0.337563	−	0.368851i
$77$	2.33423	+	14.7378i	0.266011	+	1.67953i
$78$	−0.402111	+	0.789187i	−0.0455301	+	0.0893578i
$79$	−0.745446	−	2.29425i	−0.0838693	−	0.258123i	0.900324	−	0.435220i	$-0.143329\pi$
$79$	−0.745446	−	2.29425i	−0.0838693	−	0.258123i	−0.984193	+	0.177097i	$0.943329\pi$
$80$	−1.28136	−	1.83252i	−0.143261	−	0.204881i
$81$	−1.30367	+	4.01230i	−0.144853	+	0.445811i
$82$	−6.88825	−	6.88825i	−0.760680	−	0.760680i
$83$	−0.730424	−	1.43354i	−0.0801745	−	0.157351i	0.847439	−	0.530893i	$-0.178143\pi$
$83$	−0.730424	−	1.43354i	−0.0801745	−	0.157351i	−0.927613	+	0.373542i	$0.878143\pi$
$84$	−1.91006	+	1.38774i	−0.208405	+	0.151415i
$85$	1.64512	+	3.37859i	0.178438	+	0.366459i
$86$	−4.92848	+	6.78347i	−0.531452	+	0.731481i
$87$	−4.86047	−	0.769823i	−0.521097	−	0.0825337i
$88$	−4.70024	−	0.744445i	−0.501047	−	0.0793581i
$89$	8.14363	+	5.91669i	0.863223	+	0.627168i	0.928760	−	0.370682i	$-0.120876\pi$
$89$	8.14363	+	5.91669i	0.863223	+	0.627168i	−0.0655371	+	0.997850i	$0.520876\pi$
$90$	−3.91599	+	3.77669i	−0.412781	+	0.398098i
$91$	−2.16796	−	2.98395i	−0.227264	−	0.312803i
$92$	−0.178222	+	0.0908086i	−0.0185809	+	0.00946745i
$93$	−1.34408	+	1.34408i	−0.139374	+	0.139374i
$94$	1.86286	−	5.73329i	0.192139	−	0.591344i
$95$	−8.94337	+	3.87506i	−0.917570	+	0.397573i
$96$	−0.232680	−	0.716117i	−0.0237478	−	0.0730883i
$97$	8.29029	+	4.22411i	0.841751	+	0.428894i	0.821026	−	0.570891i	$-0.193402\pi$
$97$	8.29029	+	4.22411i	0.841751	+	0.428894i	0.0207259	+	0.999785i	$0.493402\pi$
$98$	−0.442958	−	2.79673i	−0.0447455	−	0.282512i
$99$			11.5784i			1.16367i
$100$	−4.80810	+	1.37192i	−0.480810	+	0.137192i
$101$	7.96110			0.792160			0.396080	−	0.918216i	$-0.370370\pi$
$101$	7.96110			0.792160			0.396080	+	0.918216i	$0.370370\pi$
$102$	0.197953	+	1.24982i	0.0196003	+	0.123751i
$103$	7.04561	−	13.8278i	0.694225	−	1.36249i	−0.227166	−	0.973856i	$-0.572946\pi$
$103$	7.04561	−	13.8278i	0.694225	−	1.36249i	0.921391	−	0.388637i	$-0.127054\pi$
$104$	1.11874	−	0.363500i	0.109701	−	0.0356441i
$105$	1.54022	+	5.04960i	0.150310	+	0.492791i
$106$	2.43234	−	7.48597i	0.236250	−	0.727102i
$107$	0.809842	−	0.809842i	0.0782904	−	0.0782904i	−0.666877	−	0.745168i	$-0.732369\pi$
$107$	0.809842	−	0.809842i	0.0782904	−	0.0782904i	0.745168	+	0.666877i	$0.232369\pi$
$108$	−3.64503	+	1.85723i	−0.350743	+	0.178713i
$109$	12.5546	−	9.12142i	1.20251	−	0.873674i	0.207980	−	0.978133i	$-0.433311\pi$
$109$	12.5546	−	9.12142i	1.20251	−	0.873674i	0.994529	+	0.104459i	$0.0333112\pi$
$110$	−5.00180	+	9.39224i	−0.476903	+	0.895515i
$111$	2.95666	+	2.14814i	0.280634	+	0.203892i
$112$	3.09693	+	0.490506i	0.292633	+	0.0463485i
$113$	−15.7570	−	2.49566i	−1.48229	−	0.234772i	−0.637744	−	0.770248i	$-0.720132\pi$
$113$	−15.7570	−	2.49566i	−1.48229	−	0.234772i	−0.844551	+	0.535476i	$0.820132\pi$
$114$	−3.26125	+	0.369493i	−0.305444	+	0.0346062i
$115$	0.0619584	+	0.442953i	0.00577765	+	0.0413056i
$116$	3.84149	+	5.28735i	0.356673	+	0.490919i
$117$	−1.29932	−	2.55006i	−0.120122	−	0.235754i
$118$	−3.40677	+	3.40677i	−0.313619	+	0.313619i
$119$	−5.01153	−	1.62834i	−0.459406	−	0.149270i
$120$	−1.68342	−	0.0304822i	−0.153674	−	0.00278263i
$121$	3.59895	+	11.0764i	0.327178	+	1.00695i
$122$	−0.279146	−	0.142232i	−0.0252727	−	0.0128771i
$123$	−7.24471	+	1.14745i	−0.653234	+	0.103462i
$124$	2.52442			0.226700
$125$	−0.606974	+	11.1639i	−0.0542894	+	0.998525i
$126$		−	7.62888i		−	0.679634i
$127$	−8.75886	+	1.38727i	−0.777223	+	0.123100i	−0.532429	−	0.846475i	$-0.678720\pi$
$127$	−8.75886	+	1.38727i	−0.777223	+	0.123100i	−0.244794	+	0.969575i	$0.578720\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	1.95099	+	6.00452i	0.171775	+	0.528668i
$130$	0.0476201	−	2.62988i	0.00417656	−	0.230655i
$131$	3.11471	−	9.58609i	0.272133	−	0.837540i	−0.717830	−	0.696218i	$-0.754865\pi$
$131$	3.11471	−	9.58609i	0.272133	−	0.837540i	0.989964	−	0.141322i	$-0.0451354\pi$
$132$	−2.53374	+	2.53374i	−0.220534	+	0.220534i
$133$	4.79452	−	12.7989i	0.415737	−	1.10981i
$134$	−8.17549	−	11.2526i	−0.706254	−	0.972076i
$135$	1.26719	+	9.05936i	0.109062	+	0.779706i
$136$	0.987803	−	1.35959i	0.0847034	−	0.116584i
$137$	4.63285	+	0.733771i	0.395811	+	0.0626903i	0.351167	−	0.936313i	$-0.385785\pi$
$137$	4.63285	+	0.733771i	0.395811	+	0.0626903i	0.0446435	+	0.999003i	$0.485785\pi$
$138$	−0.0235608	+	0.148757i	−0.00200563	+	0.0126630i
$139$	−2.67588	+	3.68304i	−0.226965	+	0.312391i	−0.907278	−	0.420531i	$-0.861844\pi$
$139$	−2.67588	+	3.68304i	−0.226965	+	0.312391i	0.680313	+	0.732922i	$0.261844\pi$
$140$	3.29563	−	6.18844i	0.278532	−	0.523019i
$141$	−2.66805	−	3.67226i	−0.224690	−	0.309260i
$142$	2.73921	−	1.39570i	0.229869	−	0.117124i
$143$	−3.95828	−	3.95828i	−0.331008	−	0.331008i
$144$	2.31396	+	0.751850i	0.192830	+	0.0626541i
$145$	13.9781	−	4.26357i	1.16082	−	0.354071i
$146$	9.15732	−	2.97539i	0.757865	−	0.246245i
$147$	−1.89972	−	0.967954i	−0.156686	−	0.0798355i
$148$	−0.759275	−	4.79387i	−0.0624120	−	0.394054i
$149$		−	7.02350i		−	0.575388i	−0.957722	−	0.287694i	$-0.907111\pi$
$149$		−	7.02350i		−	0.575388i	0.957722	−	0.287694i	$-0.0928886\pi$
$150$	−1.29227	+	3.53612i	−0.105513	+	0.288723i
$151$			0.345128i			0.0280861i	0.999901	+	0.0140430i	$0.00447019\pi$
$151$			0.345128i			0.0280861i	−0.999901	+	0.0140430i	$0.995530\pi$
$152$	3.40960	+	2.71563i	0.276555	+	0.220266i
$153$	−3.64319	−	1.85630i	−0.294534	−	0.150073i
$154$	−4.61099	−	14.1912i	−0.371564	−	1.14356i
$155$	1.84124	−	5.33605i	0.147892	−	0.428602i
$156$	0.273704	−	0.842375i	0.0219139	−	0.0674440i
$157$	13.8483	+	13.8483i	1.10522	+	1.10522i	0.993770	+	0.111447i	$0.0355486\pi$
$157$	13.8483	+	13.8483i	1.10522	+	1.10522i	0.111447	+	0.993770i	$0.464451\pi$
$158$	1.09517	+	2.14939i	0.0871269	+	0.170996i
$159$	−3.48368	−	4.79487i	−0.276274	−	0.380258i
$160$	1.55225	+	1.60951i	0.122716	+	0.127243i
$161$	−0.507399	−	0.368647i	−0.0399886	−	0.0290534i
$162$	0.659962	−	4.16684i	0.0518515	−	0.327378i
$163$	−0.329833	+	2.08248i	−0.0258345	+	0.163113i	−0.997233	−	0.0743438i	$-0.976314\pi$
$163$	−0.329833	+	2.08248i	−0.0258345	+	0.163113i	0.971398	+	0.237457i	$0.0763138\pi$
$164$	7.88100	+	5.72588i	0.615403	+	0.447116i
$165$	3.50771	+	7.20379i	0.273075	+	0.560814i
$166$	0.945686	+	1.30163i	0.0733995	+	0.101026i
$167$	4.46692	+	8.76682i	0.345660	+	0.678397i	0.996746	−	0.0806076i	$-0.0256861\pi$
$167$	4.46692	+	8.76682i	0.345660	+	0.678397i	−0.651085	+	0.759004i	$0.725686\pi$
$168$	1.66945	−	1.66945i	0.128801	−	0.128801i
$169$	−11.0478	−	3.58963i	−0.849827	−	0.276126i
$170$	−2.15339	−	3.07964i	−0.165158	−	0.236197i
$171$	5.22814	−	9.22715i	0.399806	−	0.705618i
$172$	3.80664	−	7.47094i	0.290253	−	0.569654i
$173$	−1.77684	−	11.2185i	−0.135091	−	0.852930i	−0.958419	−	0.285365i	$-0.907885\pi$
$173$	−1.77684	−	11.2185i	−0.135091	−	0.852930i	0.823328	−	0.567566i	$-0.192115\pi$
$174$	4.92106			0.373064
$175$	−10.6772	−	11.4799i	−0.807120	−	0.867796i
$176$	4.75883			0.358710
$177$	0.567503	+	3.58307i	0.0426561	+	0.269320i
$178$	−8.96894	−	4.56990i	−0.672250	−	0.342529i
$179$	−1.92621	−	5.92828i	−0.143972	−	0.443100i	0.852905	−	0.522065i	$-0.174838\pi$
$179$	−1.92621	−	5.92828i	−0.143972	−	0.443100i	−0.996877	+	0.0789654i	$0.974838\pi$
$180$	3.27697	−	4.34279i	0.244251	−	0.323692i
$181$	13.6007	+	4.41915i	1.01093	+	0.328473i	0.767227	−	0.641376i	$-0.221636\pi$
$181$	13.6007	+	4.41915i	1.01093	+	0.328473i	0.243708	+	0.969849i	$0.421636\pi$
$182$	2.60807	+	2.60807i	0.193323	+	0.193323i
$183$	−0.210189	+	0.107096i	−0.0155376	+	0.00791680i
$184$	0.161822	−	0.117571i	0.0119297	−	0.00866742i
$185$	−10.6869	−	1.89158i	−0.785719	−	0.139072i
$186$	1.11727	−	1.53779i	0.0819223	−	0.112756i
$187$	−7.89900	−	1.25108i	−0.577632	−	0.0914879i
$188$	−0.943041	+	5.95412i	−0.0687783	+	0.434249i
$189$	−10.3774	−	7.53964i	−0.754847	−	0.548428i
$190$	8.22707	−	5.22641i	0.596854	−	0.379163i
$191$	15.1557	−	11.0113i	1.09663	−	0.796749i	0.116125	−	0.993235i	$-0.462953\pi$
$191$	15.1557	−	11.0113i	1.09663	−	0.796749i	0.980507	+	0.196485i	$0.0629528\pi$
$192$	0.341841	+	0.670901i	0.0246703	+	0.0484181i
$193$	−7.06390	−	7.06390i	−0.508470	−	0.508470i	0.405586	−	0.914057i	$-0.367067\pi$
$193$	−7.06390	−	7.06390i	−0.508470	−	0.508470i	−0.914057	+	0.405586i	$0.867067\pi$
$194$	−8.84902	−	2.87522i	−0.635323	−	0.206429i
$195$	−1.58095	−	1.19295i	−0.113214	−	0.0854290i
$196$	0.875010	+	2.69300i	0.0625007	+	0.192357i
$197$	0.626273	−	1.22913i	0.0446201	−	0.0875719i	−0.867620	−	0.497228i	$-0.834351\pi$
$197$	0.626273	−	1.22913i	0.0446201	−	0.0875719i	0.912240	+	0.409656i	$0.134351\pi$
$198$	−1.81126	−	11.4359i	−0.128721	−	0.812711i
$199$		−	25.0452i		−	1.77541i	−0.460415	−	0.887704i	$-0.652300\pi$
$199$		−	25.0452i		−	1.77541i	0.460415	−	0.887704i	$-0.347700\pi$
$200$	4.53429	−	2.10718i	0.320623	−	0.149000i
$201$	−10.4730			−0.738711
$202$	−7.86309	+	1.24539i	−0.553245	+	0.0876254i
$203$	−9.30335	+	18.2589i	−0.652967	+	1.28152i
$204$	−0.391031	−	1.20347i	−0.0273777	−	0.0842598i
$205$	17.8514	−	12.4823i	1.24679	−	0.871803i
$206$	−4.79573	+	14.7597i	−0.334134	+	1.02836i
$207$	−0.344123	−	0.344123i	−0.0239182	−	0.0239182i
$208$	−1.04810	+	0.534033i	−0.0726726	+	0.0370285i
$209$	4.14834	−	20.3242i	0.286947	−	1.40586i
$210$	−2.31119	−	4.74649i	−0.159487	−	0.327539i
$211$	−13.8446	+	19.0554i	−0.953101	+	1.31183i	−0.00296506	+	0.999996i	$0.500944\pi$
$211$	−13.8446	+	19.0554i	−0.953101	+	1.31183i	−0.950136	+	0.311836i	$0.899056\pi$
$212$	−1.23133	+	7.77431i	−0.0845681	+	0.533942i
$213$	0.362122	−	2.28635i	0.0248122	−	0.156658i
$214$	−0.673185	+	0.926559i	−0.0460180	+	0.0633383i
$215$	−13.0154	−	13.4954i	−0.887643	−	0.920381i
$216$	3.30962	−	2.40458i	0.225191	−	0.163611i
$217$	3.59353	+	7.05269i	0.243944	+	0.478768i
$218$	−10.9731	+	10.9731i	−0.743191	+	0.743191i
$219$	2.24038	−	6.89518i	0.151391	−	0.465933i
$220$	3.47095	−	10.0591i	0.234012	−	0.678182i
$221$	1.88009	−	0.610880i	0.126469	−	0.0410922i
$222$	−3.25630	−	1.65917i	−0.218549	−	0.111356i
$223$	−2.37422	−	14.9902i	−0.158989	−	1.00382i	−0.930150	−	0.367179i	$-0.880324\pi$
$223$	−2.37422	−	14.9902i	−0.158989	−	1.00382i	0.771161	−	0.636640i	$-0.219676\pi$
$224$	−3.13554			−0.209502
$225$	−6.78953	−	10.0943i	−0.452635	−	0.672951i
$226$	15.9534			1.06121
$227$	−21.9638	+	3.47872i	−1.45779	+	0.230891i	−0.834459	−	0.551071i	$-0.814220\pi$
$227$	−21.9638	+	3.47872i	−1.45779	+	0.230891i	−0.623327	+	0.781961i	$0.714220\pi$
$228$	3.16330	−	0.875116i	0.209495	−	0.0579560i
$229$	−7.84539	+	2.54912i	−0.518438	+	0.168451i	−0.556536	−	0.830823i	$-0.687870\pi$
$229$	−7.84539	+	2.54912i	−0.518438	+	0.168451i	0.0380985	+	0.999274i	$0.487870\pi$
$230$	−0.130489	−	0.427807i	−0.00860417	−	0.0282088i
$231$	−10.6855	−	3.47194i	−0.703056	−	0.228437i
$232$	−4.62132	−	4.62132i	−0.303404	−	0.303404i
$233$	7.04884	+	13.8341i	0.461785	+	0.906304i	0.998060	+	0.0622609i	$0.0198311\pi$
$233$	7.04884	+	13.8341i	0.461785	+	0.906304i	−0.536275	+	0.844043i	$0.680169\pi$
$234$	1.68224	+	2.31541i	0.109972	+	0.151363i
$235$	11.8978	+	6.33613i	0.776128	+	0.413324i
$236$	2.83189	−	3.89777i	0.184341	−	0.253723i
$237$	1.79404	+	0.284148i	0.116535	+	0.0184574i
$238$	5.20456	+	0.824321i	0.337361	+	0.0534328i
$239$	−9.90533	+	13.6335i	−0.640722	+	0.881879i	−0.998654	−	0.0518692i	$-0.983482\pi$
$239$	−9.90533	+	13.6335i	−0.640722	+	0.881879i	0.357932	+	0.933748i	$0.383482\pi$
$240$	1.66746	−	0.233237i	0.107634	−	0.0150554i
$241$	−0.132321	−	0.182125i	−0.00852356	−	0.0117317i	0.804734	−	0.593636i	$-0.202308\pi$
$241$	−0.132321	−	0.182125i	−0.00852356	−	0.0117317i	−0.813258	+	0.581904i	$0.802308\pi$
$242$	−5.28738	−	10.3771i	−0.339886	−	0.667063i
$243$	−10.9243	−	10.9243i	−0.700797	−	0.700797i
$244$	0.297960	+	0.0968129i	0.0190749	+	0.00619781i
$245$	6.33059	+	0.114630i	0.404447	+	0.00732346i
$246$	6.97601	−	2.26664i	0.444774	−	0.144516i
$247$	1.36713	+	4.94179i	0.0869884	+	0.314439i
$248$	−2.49334	+	0.394907i	−0.158327	+	0.0250766i
$249$	1.21145			0.0767726
$250$	−1.14691	−	11.1214i	−0.0725369	−	0.703376i
$251$	−10.6970			−0.675190			−0.337595	−	0.941292i	$-0.609613\pi$
$251$	−10.6970			−0.675190			−0.337595	+	0.941292i	$0.609613\pi$
$252$	1.19342	+	7.53495i	0.0751783	+	0.474657i
$253$	−0.848127	−	0.432142i	−0.0533213	−	0.0271686i
$254$	8.43401	−	2.74037i	0.529197	−	0.171946i
$255$	−2.82907	−	0.0512269i	−0.177163	−	0.00320795i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.78330	−	5.78330i	0.360753	−	0.360753i	−0.503337	−	0.864090i	$-0.667895\pi$
$257$	5.78330	−	5.78330i	0.360753	−	0.360753i	0.864090	+	0.503337i	$0.167895\pi$
$258$	−2.86628	−	5.62539i	−0.178447	−	0.350222i
$259$	12.3122	−	8.94534i	0.765044	−	0.555837i
$260$	0.364370	+	2.60495i	0.0225972	+	0.161552i
$261$	−9.34648	+	12.8643i	−0.578533	+	0.796282i
$262$	−1.57677	+	9.95532i	−0.0974130	+	0.615041i
$263$	−0.906535	+	5.72364i	−0.0558993	+	0.352934i	0.943846	+	0.330385i	$0.107178\pi$
$263$	−0.906535	+	5.72364i	−0.0558993	+	0.352934i	−0.999746	+	0.0225499i	$0.992822\pi$
$264$	2.10618	−	2.89891i	0.129627	−	0.178416i
$265$	15.5350	+	8.27310i	0.954307	+	0.508213i
$266$	−2.73329	+	13.3914i	−0.167589	+	0.821079i
$267$	−6.75334	+	3.44100i	−0.413298	+	0.210586i
$268$	9.83512	+	9.83512i	0.600776	+	0.600776i
$269$	9.83129	−	30.2576i	0.599424	−	1.84484i	0.0680828	−	0.997680i	$-0.478312\pi$
$269$	9.83129	−	30.2576i	0.599424	−	1.84484i	0.531341	−	0.847158i	$-0.321688\pi$
$270$	−2.66878	−	8.74959i	−0.162417	−	0.532483i
$271$	−7.43131	−	22.8712i	−0.451420	−	1.38933i	−0.875287	−	0.483603i	$-0.839328\pi$
$271$	−7.43131	−	22.8712i	−0.451420	−	1.38933i	0.423867	−	0.905724i	$-0.360672\pi$
$272$	−0.762954	+	1.49738i	−0.0462609	+	0.0907921i
$273$	2.74303	−	0.434454i	0.166016	−	0.0262943i
$274$	−4.69060			−0.283369
$275$	−18.7309	−	14.6736i	−1.12952	−	0.884850i
$276$		−	0.150611i		−	0.00906573i
$277$	2.63335	+	16.6263i	0.158223	+	0.998979i	0.931190	+	0.364534i	$0.118772\pi$
$277$	2.63335	+	16.6263i	0.158223	+	0.998979i	−0.772967	+	0.634446i	$0.781228\pi$
$278$	2.06678	−	4.05629i	0.123957	−	0.243280i
$279$	1.89799	+	5.84140i	0.113630	+	0.349716i
$280$	−2.28697	+	6.62780i	−0.136673	+	0.396087i
$281$	−20.7686	−	6.74814i	−1.23895	−	0.402560i	−0.385003	−	0.922915i	$-0.625800\pi$
$281$	−20.7686	−	6.74814i	−1.23895	−	0.402560i	−0.853950	+	0.520355i	$0.825800\pi$
$282$	3.20967	+	3.20967i	0.191133	+	0.191133i
$283$	−3.11751	−	6.11846i	−0.185317	−	0.363705i	0.779593	−	0.626287i	$-0.215426\pi$
$283$	−3.11751	−	6.11846i	−0.185317	−	0.363705i	−0.964910	+	0.262582i	$0.915426\pi$
$284$	−2.48715	+	1.80702i	−0.147585	+	0.107227i
$285$	0.457427	−	7.32477i	0.0270956	−	0.433882i
$286$	4.52876	+	3.29034i	0.267791	+	0.194562i
$287$	−4.77824	+	30.1686i	−0.282051	+	1.78080i
$288$	−2.40308	−	0.380611i	−0.141603	−	0.0224277i
$289$	−8.33229	+	11.4684i	−0.490135	+	0.674613i
$290$	−13.1391	+	6.39774i	−0.771552	+	0.375688i
$291$	−5.66792	+	4.11799i	−0.332260	+	0.241401i
$292$	−8.57912	+	4.37128i	−0.502055	+	0.255810i
$293$	−4.45582	−	4.45582i	−0.260312	−	0.260312i	0.564869	−	0.825181i	$-0.308927\pi$
$293$	−4.45582	−	4.45582i	−0.260312	−	0.260312i	−0.825181	+	0.564869i	$0.808927\pi$
$294$	2.02775	+	0.658856i	0.118261	+	0.0384252i
$295$	−6.17348	−	8.82889i	−0.359434	−	0.514038i
$296$	1.49985	+	4.61607i	0.0871772	+	0.268304i
$297$	−17.3461	−	8.83826i	−1.00652	−	0.512848i
$298$	1.09872	+	6.93703i	0.0636470	+	0.401851i
$299$	0.235289			0.0136071
$300$	0.723186	−	3.69474i	0.0417532	−	0.213316i
$301$	26.2910			1.51539
$302$	−0.0539898	−	0.340878i	−0.00310677	−	0.0196153i
$303$	−2.72143	+	5.34111i	−0.156342	+	0.306839i
$304$	−3.79244	−	2.14881i	−0.217511	−	0.123243i
$305$	0.421963	−	0.559205i	0.0241615	−	0.0320200i
$306$	3.88872	+	1.26352i	0.222303	+	0.0722308i
$307$	19.5114	−	19.5114i	1.11357	−	1.11357i	0.120912	−	0.992663i	$-0.461418\pi$
$307$	19.5114	−	19.5114i	1.11357	−	1.11357i	0.992663	−	0.120912i	$-0.0385818\pi$
$308$	6.77421	+	13.2951i	0.385997	+	0.757561i
$309$	6.86860	+	9.45382i	0.390741	+	0.537809i
$310$	−0.983831	+	5.55839i	−0.0558778	+	0.315695i
$311$	4.96071	+	3.60417i	0.281296	+	0.204374i	0.719483	−	0.694511i	$-0.244379\pi$
$311$	4.96071	+	3.60417i	0.281296	+	0.204374i	−0.438186	+	0.898884i	$0.644379\pi$
$312$	−0.138558	+	0.874820i	−0.00784430	+	0.0495270i
$313$	2.07360	−	13.0922i	0.117207	−	0.740013i	−0.857160	−	0.515049i	$-0.827774\pi$
$313$	2.07360	−	13.0922i	0.117207	−	0.740013i	0.974367	−	0.224964i	$-0.0722265\pi$
$314$	−15.8442	−	11.5115i	−0.894140	−	0.649631i
$315$	16.7976	+	2.97316i	0.946437	+	0.167519i
$316$	−1.41792	−	1.95160i	−0.0797644	−	0.109786i
$317$	−13.8724	−	27.2262i	−0.779153	−	1.52917i	−0.847069	−	0.531483i	$-0.821635\pi$
$317$	−13.8724	−	27.2262i	−0.779153	−	1.52917i	0.0679164	−	0.997691i	$-0.478365\pi$
$318$	4.19087	+	4.19087i	0.235012	+	0.235012i
$319$	−9.61088	+	29.5793i	−0.538106	+	1.65612i
$320$	−1.78493	−	1.34686i	−0.0997804	−	0.0752920i
$321$	0.266487	+	0.820161i	0.0148738	+	0.0457769i
$322$	0.558821	+	0.284734i	0.0311419	+	0.0158676i
$323$	5.73001	+	4.56375i	0.318826	+	0.253934i
$324$			4.21878i			0.234377i
$325$	5.77202	+	1.12978i	0.320174	+	0.0626690i
$326$		−	2.10844i		−	0.116776i
$327$	1.82791	+	11.5409i	0.101083	+	0.638216i
$328$	−8.67970	−	4.42253i	−0.479256	−	0.244193i
$329$	−17.9770	+	5.84107i	−0.991102	+	0.322028i
$330$	−4.59144	−	6.56637i	−0.252751	−	0.361467i
$331$	−23.9708	−	7.78859i	−1.31756	−	0.428100i	−0.435901	−	0.899995i	$-0.643570\pi$
$331$	−23.9708	−	7.78859i	−1.31756	−	0.428100i	−0.881655	+	0.471895i	$0.843570\pi$
$332$	−1.13766	−	1.13766i	−0.0624373	−	0.0624373i
$333$	10.5219	−	5.36120i	0.576599	−	0.293792i
$334$	−5.78335	−	7.96010i	−0.316451	−	0.435558i
$335$	27.9626	−	13.6157i	1.52776	−	0.743906i
$336$	−1.38774	+	1.91006i	−0.0757074	+	0.104202i
$337$	−1.33347	+	8.41922i	−0.0726389	+	0.458624i	0.924380	+	0.381472i	$0.124583\pi$
$337$	−1.33347	+	8.41922i	−0.0726389	+	0.458624i	−0.997019	+	0.0771522i	$0.975417\pi$
$338$	11.4733	+	1.81719i	0.624064	+	0.0988421i
$339$	7.06074	−	9.71827i	0.383487	−	0.527824i
$340$	2.60864	+	2.70486i	0.141474	+	0.146691i
$341$	7.06124	+	9.71897i	0.382388	+	0.526311i
$342$	−3.72033	+	9.93141i	−0.201172	+	0.537029i
$343$	9.24203	−	9.24203i	0.499023	−	0.499023i
$344$	−2.59106	+	7.97445i	−0.139700	+	0.429954i
$345$	−0.318357	−	0.109851i	−0.0171398	−	0.00591421i
$346$	3.50994	+	10.8025i	0.188695	+	0.580744i
$347$	7.08595	−	13.9070i	0.380394	−	0.746564i	−0.618848	−	0.785511i	$-0.712400\pi$
$347$	7.08595	−	13.9070i	0.380394	−	0.746564i	0.999241	+	0.0389466i	$0.0124002\pi$
$348$	−4.86047	+	0.769823i	−0.260548	+	0.0412668i
$349$		−	23.7572i		−	1.27169i	−0.771815	−	0.635847i	$-0.780651\pi$
$349$		−	23.7572i		−	1.27169i	0.771815	−	0.635847i	$-0.219349\pi$
$350$	12.3416	+	9.66825i	0.659685	+	0.516790i
$351$	4.81218			0.256855
$352$	−4.70024	+	0.744445i	−0.250524	+	0.0396790i
$353$	−11.1523	−	5.68237i	−0.593576	−	0.302442i	0.131277	−	0.991346i	$-0.458092\pi$
$353$	−11.1523	−	5.68237i	−0.593576	−	0.302442i	−0.724853	+	0.688904i	$0.758092\pi$
$354$	−1.12103	−	3.45018i	−0.0595822	−	0.183375i
$355$	2.00557	+	6.57525i	0.106445	+	0.348978i
$356$	9.57341	+	3.11059i	0.507390	+	0.164861i
$357$	2.80560	−	2.80560i	0.148488	−	0.148488i
$358$	2.82989	+	5.55396i	0.149564	+	0.293536i
$359$	−13.2155	−	18.1895i	−0.697486	−	0.960007i	−0.999977	−	0.00685459i	$-0.997818\pi$
$359$	−13.2155	−	18.1895i	−0.697486	−	0.960007i	0.302491	−	0.953152i	$-0.402182\pi$
$360$	−2.55726	+	4.80195i	−0.134780	+	0.253085i
$361$	−12.4832	+	14.3238i	−0.657009	+	0.753883i
$362$	−14.1246	−	2.23712i	−0.742372	−	0.117580i
$363$	−8.66146	−	1.37184i	−0.454609	−	0.0720030i
$364$	−2.98395	−	2.16796i	−0.156401	−	0.113632i
$365$	2.98251	+	21.3226i	0.156112	+	1.11607i
$366$	0.190847	−	0.138659i	0.00997575	−	0.00724781i
$367$	−9.52628	+	4.85388i	−0.497268	+	0.253371i	−0.684590	−	0.728928i	$-0.740019\pi$
$367$	−9.52628	+	4.85388i	−0.497268	+	0.253371i	0.187323	+	0.982298i	$0.440019\pi$
$368$	−0.141438	+	0.141438i	−0.00737295	+	0.00737295i
$369$	−7.32411	+	22.5413i	−0.381278	+	1.17345i
$370$	10.8513	+	0.196488i	0.564130	+	0.0102149i
$371$	−23.4725	+	7.62669i	−1.21863	+	0.395958i
$372$	−0.862952	+	1.69364i	−0.0447420	+	0.0878110i
$373$	−1.64656	−	10.3960i	−0.0852556	−	0.538283i	−0.992939	−	0.118627i	$-0.962151\pi$
$373$	−1.64656	−	10.3960i	−0.0852556	−	0.538283i	0.907683	−	0.419656i	$-0.137849\pi$
$374$	7.99746			0.413539
$375$	−7.28235	−	4.22348i	−0.376059	−	0.218100i
$376$		−	6.02834i		−	0.310888i
$377$	−1.20264	−	7.59316i	−0.0619390	−	0.391067i
$378$	11.4291	+	5.82343i	0.587851	+	0.299525i
$379$	2.82947	+	8.70821i	0.145340	+	0.447310i	0.997055	−	0.0766955i	$-0.0244369\pi$
$379$	2.82947	+	8.70821i	0.145340	+	0.447310i	−0.851715	+	0.524006i	$0.824437\pi$
$380$	−7.30819	+	6.44906i	−0.374902	+	0.330830i
$381$	2.06342	−	6.35055i	0.105712	−	0.325349i
$382$	−13.2466	+	13.2466i	−0.677755	+	0.677755i
$383$	3.09810	−	1.57856i	0.158306	−	0.0806608i	−0.373043	−	0.927814i	$-0.621686\pi$
$383$	3.09810	−	1.57856i	0.158306	−	0.0806608i	0.531348	+	0.847153i	$0.321686\pi$
$384$	−0.442584	−	0.609165i	−0.0225855	−	0.0310863i
$385$	33.0438	−	4.62203i	1.68407	−	0.235560i
$386$	8.08197	+	5.87189i	0.411361	+	0.298871i
$387$	20.1494	+	3.19136i	1.02425	+	0.162226i
$388$	9.18986	+	1.45553i	0.466544	+	0.0738934i
$389$	−12.5722	+	17.3041i	−0.637434	+	0.877353i	−0.998475	−	0.0551970i	$-0.982421\pi$
$389$	−12.5722	+	17.3041i	−0.637434	+	0.877353i	0.361041	+	0.932550i	$0.382421\pi$
$390$	1.74811	+	0.930948i	0.0885189	+	0.0471404i
$391$	0.271950	−	0.197583i	0.0137531	−	0.00999222i
$392$	−1.28552	−	2.52297i	−0.0649283	−	0.127429i
$393$	5.36658	+	5.36658i	0.270708	+	0.270708i
$394$	−0.426284	+	1.31197i	−0.0214759	+	0.0660960i
$395$	−5.15943	+	1.57372i	−0.259599	+	0.0791824i
$396$	3.57792	+	11.0117i	0.179797	+	0.553360i
$397$	11.3921	−	22.3583i	0.571754	−	1.12213i	−0.406292	−	0.913743i	$-0.633179\pi$
$397$	11.3921	−	22.3583i	0.571754	−	1.12213i	0.978046	−	0.208387i	$-0.0668214\pi$
$398$	3.91793	+	24.7369i	0.196388	+	1.23995i
$399$	6.94786	+	7.59185i	0.347828	+	0.380068i
$400$	−4.14883	+	2.79056i	−0.207442	+	0.139528i
$401$			25.7199i			1.28439i	0.766541	+	0.642196i	$0.221976\pi$
$401$			25.7199i			1.28439i	−0.766541	+	0.642196i	$0.778024\pi$
$402$	10.3441	−	1.63834i	0.515916	−	0.0817131i
$403$	−2.64585	−	1.34813i	−0.131799	−	0.0671550i
$404$	7.57146	−	2.46012i	0.376694	−	0.122395i
$405$	8.91752	+	3.07705i	0.443115	+	0.152900i
$406$	6.33250	−	19.4894i	0.314277	−	0.967244i
$407$	16.3325	−	16.3325i	0.809570	−	0.809570i
$408$	0.574481	+	1.12748i	0.0284411	+	0.0558187i
$409$	−7.73763	+	5.62172i	−0.382601	+	0.277976i	−0.762417	−	0.647086i	$-0.775987\pi$
$409$	−7.73763	+	5.62172i	−0.382601	+	0.277976i	0.379816	+	0.925062i	$0.375987\pi$
$410$	−15.6789	+	15.1212i	−0.774326	+	0.746783i
$411$	−2.07599	+	2.85735i	−0.102401	+	0.140943i
$412$	2.42775	−	15.3282i	0.119607	−	0.755168i
$413$	14.9207	+	2.36321i	0.734201	+	0.116286i
$414$	0.393719	+	0.286054i	0.0193502	+	0.0140588i
$415$	−3.23453	+	1.57498i	−0.158777	+	0.0773126i
$416$	0.951654	−	0.691417i	0.0466587	−	0.0338995i
$417$	−1.55623	−	3.05426i	−0.0762087	−	0.149568i
$418$	−0.917858	+	20.7229i	−0.0448939	+	1.01359i
$419$	34.6518	+	11.2591i	1.69285	+	0.550041i	0.987335	−	0.158651i	$-0.0507143\pi$
$419$	34.6518	+	11.2591i	1.69285	+	0.550041i	0.705518	+	0.708692i	$0.250714\pi$
$420$	3.02525	+	4.32650i	0.147617	+	0.211112i
$421$	34.1211	−	11.0866i	1.66296	−	0.540329i	0.681471	−	0.731845i	$-0.261341\pi$
$421$	34.1211	−	11.0866i	1.66296	−	0.540329i	0.981489	+	0.191516i	$0.0613405\pi$
$422$	10.6932	−	20.9866i	0.520538	−	1.02161i
$423$	−14.4866	+	2.29445i	−0.704363	+	0.111560i
$424$		−	7.87122i		−	0.382260i
$425$	7.62011	−	3.54122i	0.369630	−	0.171775i
$426$			2.31485i			0.112155i
$427$	0.153672	+	0.970248i	0.00743672	+	0.0469536i
$428$	0.519951	−	1.02046i	0.0251328	−	0.0493258i
$429$	4.00872	−	1.30251i	0.193543	−	0.0628858i
$430$	14.9663	+	11.2932i	0.721739	+	0.544608i
$431$	12.3641	+	4.01734i	0.595557	+	0.193508i	0.591258	−	0.806483i	$-0.298632\pi$
$431$	12.3641	+	4.01734i	0.595557	+	0.193508i	0.00429919	+	0.999991i	$0.498632\pi$
$432$	−2.89271	+	2.89271i	−0.139176	+	0.139176i
$433$	6.73531	−	3.43181i	0.323678	−	0.164922i	−0.284600	−	0.958646i	$-0.591861\pi$
$433$	6.73531	−	3.43181i	0.323678	−	0.164922i	0.608278	+	0.793724i	$0.291861\pi$
$434$	−4.65257	−	6.40371i	−0.223330	−	0.307388i
$435$	−1.91786	+	10.8354i	−0.0919543	+	0.519517i
$436$	9.12142	−	12.5546i	0.436837	−	0.601254i
$437$	0.480765	+	0.727351i	0.0229981	+	0.0347939i
$438$	−1.13415	+	7.16076i	−0.0541920	+	0.342155i
$439$	−24.9358	−	18.1169i	−1.19012	−	0.864672i	−0.196843	−	0.980435i	$-0.563069\pi$
$439$	−24.9358	−	18.1169i	−1.19012	−	0.864672i	−0.993277	+	0.115763i	$0.963069\pi$
$440$	−1.85463	+	10.4782i	−0.0884162	+	0.499528i
$441$	−5.57361	+	4.04947i	−0.265410	+	0.192832i
$442$	−1.76138	+	0.897470i	−0.0837805	+	0.0426883i
$443$	19.7192	−	19.7192i	0.936888	−	0.936888i	−0.0612351	−	0.998123i	$-0.519504\pi$
$443$	19.7192	−	19.7192i	0.936888	−	0.936888i	0.998123	+	0.0612351i	$0.0195039\pi$
$444$	3.47576	+	1.12934i	0.164952	+	0.0535963i
$445$	13.5576	−	17.9672i	0.642693	−	0.851727i
$446$	4.68998	+	14.4343i	0.222077	+	0.683482i
$447$	4.71207	+	2.40092i	0.222873	+	0.113560i
$448$	3.09693	−	0.490506i	0.146316	−	0.0231742i
$449$	17.6030			0.830738			0.415369	−	0.909653i	$-0.363653\pi$
$449$	17.6030			0.830738			0.415369	+	0.909653i	$0.363653\pi$
$450$	8.28503	+	8.90786i	0.390560	+	0.419921i
$451$			46.3579i			2.18291i
$452$	−15.7570	+	2.49566i	−0.741147	+	0.117386i
$453$	−0.231546	−	0.117979i	−0.0108790	−	0.00554313i
$454$	21.1492	−	6.87178i	0.992579	−	0.322508i
$455$	−6.75898	+	4.72612i	−0.316866	+	0.221564i
$456$	−2.98746	+	1.35919i	−0.139900	+	0.0636500i
$457$	7.84845	+	7.84845i	0.367135	+	0.367135i	0.866431	−	0.499296i	$-0.166408\pi$
$457$	7.84845	+	7.84845i	0.367135	+	0.367135i	−0.499296	+	0.866431i	$0.666408\pi$
$458$	7.35003	−	3.74503i	0.343444	−	0.174994i
$459$	5.56198	−	4.04102i	0.259611	−	0.188618i
$460$	0.195806	+	0.402127i	0.00912950	+	0.0187493i
$461$	7.47099	+	5.42799i	0.347959	+	0.252807i	0.748012	−	0.663685i	$-0.231008\pi$
$461$	7.47099	+	5.42799i	0.347959	+	0.252807i	−0.400054	+	0.916492i	$0.631008\pi$
$462$	11.0971	+	1.75761i	0.516284	+	0.0817713i
$463$	−1.11274	+	7.02553i	−0.0517132	+	0.326504i	0.948247	+	0.317535i	$0.102855\pi$
$463$	−1.11274	+	7.02553i	−0.0517132	+	0.326504i	−0.999960	+	0.00896933i	$0.997145\pi$
$464$	5.28735	+	3.84149i	0.245459	+	0.178337i
$465$	2.95055	+	3.05937i	0.136828	+	0.141875i
$466$	−9.12620	−	12.5611i	−0.422763	−	0.581883i
$467$	−21.8638	+	11.1402i	−1.01174	+	0.515505i	−0.879594	−	0.475725i	$-0.842186\pi$
$467$	−21.8638	+	11.1402i	−1.01174	+	0.515505i	−0.132142	+	0.991231i	$0.542186\pi$
$468$	−2.02374	−	2.02374i	−0.0935475	−	0.0935475i
$469$	−13.4769	+	41.4775i	−0.622304	+	1.91526i
$470$	−12.7425	−	4.39690i	−0.587769	−	0.202814i
$471$	−14.0248	+	4.55693i	−0.646228	+	0.209972i
$472$	−2.18728	+	4.29278i	−0.100678	+	0.197591i
$473$	39.4107	−	6.24205i	1.81211	−	0.287010i
$474$	−1.81640			−0.0834300
$475$	8.30144	+	20.1516i	0.380896	+	0.924618i
$476$	−5.26943			−0.241524
$477$	−18.9152	+	2.99587i	−0.866067	+	0.137171i
$478$	7.65062	−	15.0152i	0.349931	−	0.686779i
$479$	−7.15073	+	2.32341i	−0.326725	+	0.106159i	−0.467787	−	0.883841i	$-0.654948\pi$
$479$	−7.15073	+	2.32341i	−0.326725	+	0.106159i	0.141062	+	0.990001i	$0.454948\pi$
$480$	−1.61044	+	0.491214i	−0.0735063	+	0.0224207i
$481$	−1.76429	+	5.42993i	−0.0804448	+	0.247584i
$482$	0.159183	+	0.159183i	0.00725057	+	0.00725057i
$483$	0.420775	−	0.214396i	0.0191459	−	0.00975534i
$484$	6.84562	+	9.42218i	0.311164	+	0.428281i
$485$	9.77947	−	18.3636i	0.444063	−	0.833849i
$486$	12.4988	+	9.08090i	0.566956	+	0.411918i
$487$	−2.62191	+	16.5541i	−0.118810	+	0.750136i	0.854297	+	0.519784i	$0.173988\pi$
$487$	−2.62191	+	16.5541i	−0.118810	+	0.750136i	−0.973107	+	0.230352i	$0.926012\pi$
$488$	−0.309436	−	0.0490099i	−0.0140075	−	0.00221857i
$489$	−1.28439	−	0.933164i	−0.0580821	−	0.0421991i
$490$	−6.27058	+	0.877104i	−0.283276	+	0.0396235i
$491$	−14.1326	+	10.2680i	−0.637797	+	0.463387i	−0.859093	−	0.511820i	$-0.828971\pi$
$491$	−14.1326	+	10.2680i	−0.637797	+	0.463387i	0.221295	+	0.975207i	$0.428971\pi$
$492$	−6.53555	+	3.33003i	−0.294645	+	0.150129i
$493$	−7.76636	−	7.76636i	−0.349779	−	0.349779i
$494$	−2.12337	−	4.66709i	−0.0955347	−	0.209982i
$495$	25.8859	+	0.468724i	1.16348	+	0.0210676i
$496$	2.40087	−	0.780090i	0.107802	−	0.0350271i
$497$	−8.58890	−	4.37626i	−0.385265	−	0.196302i
$498$	−1.19654	+	0.189513i	−0.0536181	+	0.00849227i
$499$		−	11.8414i		−	0.530095i	−0.964235	−	0.265047i	$-0.914612\pi$
$499$		−	11.8414i		−	0.530095i	0.964235	−	0.265047i	$-0.0853876\pi$
$500$	2.87255	+	10.8050i	0.128464	+	0.483215i
$501$	−7.40864			−0.330994
$502$	10.5653	−	1.67338i	0.471553	−	0.0746867i
$503$	−1.57553	−	0.802773i	−0.0702495	−	0.0357939i	0.418513	−	0.908211i	$-0.362551\pi$
$503$	−1.57553	−	0.802773i	−0.0702495	−	0.0357939i	−0.488762	+	0.872417i	$0.662551\pi$
$504$	−2.35745	−	7.25549i	−0.105009	−	0.323185i
$505$	0.322287	−	17.7987i	0.0143416	−	0.792030i
$506$	0.905287	+	0.294146i	0.0402449	+	0.0130764i
$507$	6.18486	−	6.18486i	0.274679	−	0.274679i
$508$	−7.90148	+	4.02601i	−0.350571	+	0.178625i
$509$	−18.3607	+	13.3398i	−0.813823	+	0.591277i	−0.914937	−	0.403598i	$-0.867760\pi$
$509$	−18.3607	+	13.3398i	−0.813823	+	0.591277i	0.101113	+	0.994875i	$0.467760\pi$
$510$	2.80225	−	0.391967i	0.124086	−	0.0173566i
$511$	−24.4248	−	17.7457i	−1.08049	−	0.785023i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	9.83270	+	14.8759i	0.434124	+	0.656789i
$514$	−4.80739	+	6.61681i	−0.212045	+	0.291855i
$515$	−30.6296	−	16.3117i	−1.34970	−	0.718778i
$516$	3.71100	+	5.10775i	0.163368	+	0.224856i
$517$	−25.5611	+	13.0240i	−1.12417	+	0.572795i
$518$	−10.7613	+	10.7613i	−0.472823	+	0.472823i
$519$	8.13393	+	2.64287i	0.357040	+	0.116009i
$520$	−0.767387	−	2.51588i	−0.0336522	−	0.110328i
$521$	1.76107	−	0.572206i	0.0771538	−	0.0250688i	−0.270186	−	0.962808i	$-0.587085\pi$
$521$	1.76107	−	0.572206i	0.0771538	−	0.0250688i	0.347340	+	0.937739i	$0.387085\pi$
$522$	7.21899	−	14.1681i	0.315966	−	0.620119i
$523$	−6.16835	−	38.9454i	−0.269723	−	1.70297i	−0.635367	−	0.772210i	$-0.719151\pi$
$523$	−6.16835	−	38.9454i	−0.269723	−	1.70297i	0.365644	−	0.930755i	$-0.380849\pi$
$524$		−	10.0794i		−	0.440321i
$525$	11.3518	−	3.23905i	0.495431	−	0.141364i
$526$		−	5.79498i		−	0.252673i
$527$	−4.19019	+	0.663661i	−0.182528	+	0.0289095i
$528$	−1.62676	+	3.19270i	−0.0707958	+	0.138945i
$529$	−21.8362	+	7.09503i	−0.949402	+	0.308479i
$530$	−16.6379	−	5.74104i	−0.722706	−	0.249375i
$531$	11.1484	+	3.62234i	0.483800	+	0.157196i
$532$	0.604766	−	13.6541i	0.0262199	−	0.591980i
$533$	−5.20226	−	10.2100i	−0.225335	−	0.442245i
$534$	6.13190	−	4.45509i	0.265353	−	0.192791i
$535$	−1.77778	−	1.84335i	−0.0768602	−	0.0796950i
$536$	−11.2526	−	8.17549i	−0.486038	−	0.353127i
$537$	4.63574	+	0.734230i	0.200047	+	0.0316843i
$538$	−4.97692	+	31.4230i	−0.214570	+	1.35474i
$539$	−7.92044	+	10.9015i	−0.341157	+	0.469563i
$540$	4.00466	+	8.22438i	0.172333	+	0.353921i
$541$	−27.1720	+	19.7416i	−1.16822	+	0.848759i	−0.990794	−	0.135375i	$-0.956776\pi$
$541$	−27.1720	+	19.7416i	−1.16822	+	0.848759i	−0.177423	+	0.984135i	$0.556776\pi$
$542$	10.9177	+	21.4271i	0.468954	+	0.920374i
$543$	−7.61410	+	7.61410i	−0.326752	+	0.326752i
$544$	0.519319	−	1.59830i	0.0222656	−	0.0685265i
$545$	−19.8845	−	28.4375i	−0.851760	−	1.21813i
$546$	−2.64130	+	0.858209i	−0.113037	+	0.0367280i
$547$	7.65795	+	3.90192i	0.327430	+	0.166834i	0.609976	−	0.792420i	$-0.291179\pi$
$547$	7.65795	+	3.90192i	0.327430	+	0.166834i	−0.282546	+	0.959254i	$0.591179\pi$
$548$	4.63285	−	0.733771i	0.197905	−	0.0313452i
$549$			0.762254i			0.0325322i
$550$	20.7958	+	11.5628i	0.886735	+	0.493038i
$551$	21.0155	−	19.2328i	0.895289	−	0.819344i
$552$	0.0235608	+	0.148757i	0.00100281	+	0.00633152i
$553$	3.43394	−	6.73949i	0.146026	−	0.286592i
$554$	−5.20186	−	16.0097i	−0.221006	−	0.680186i
$555$	4.92229	−	6.52325i	0.208940	−	0.276897i
$556$	−1.40679	+	4.32967i	−0.0596614	+	0.183619i
$557$	5.90556	+	5.90556i	0.250226	+	0.250226i	0.821063	−	0.570837i	$-0.193381\pi$
$557$	5.90556	+	5.90556i	0.250226	+	0.250226i	−0.570837	+	0.821063i	$0.693381\pi$
$558$	−2.78842	−	5.47258i	−0.118043	−	0.231673i
$559$	−7.97946	+	5.79742i	−0.337495	+	0.245205i
$560$	1.22200	−	6.90396i	0.0516388	−	0.291746i
$561$	3.53955	−	4.87177i	0.149440	−	0.205686i
$562$	21.5686	+	3.41613i	0.909816	+	0.144101i
$563$	−23.8440	−	3.77651i	−1.00490	−	0.159161i	−0.367772	−	0.929916i	$-0.619879\pi$
$563$	−23.8440	−	3.77651i	−1.00490	−	0.159161i	−0.637132	+	0.770755i	$0.719879\pi$
$564$	−3.67226	−	2.66805i	−0.154630	−	0.112345i
$565$	−6.21745	+	35.1269i	−0.261570	+	1.47780i
$566$	4.03627	+	5.55544i	0.169657	+	0.233513i
$567$	−11.7864	+	6.00545i	−0.494980	+	0.252205i
$568$	2.17385	−	2.17385i	0.0912127	−	0.0912127i
$569$	−12.5024	+	38.4783i	−0.524127	+	1.61310i	0.241910	+	0.970299i	$0.422226\pi$
$569$	−12.5024	+	38.4783i	−0.524127	+	1.61310i	−0.766037	+	0.642797i	$0.777774\pi$
$570$	0.694051	+	7.30615i	0.0290706	+	0.306021i
$571$	−8.50999	−	26.1911i	−0.356132	−	1.09606i	−0.955350	−	0.295476i	$-0.904522\pi$
$571$	−8.50999	−	26.1911i	−0.356132	−	1.09606i	0.599218	−	0.800586i	$-0.295478\pi$
$572$	−4.98773	−	2.54137i	−0.208547	−	0.106260i
$573$	2.20663	+	13.9321i	0.0921833	+	0.582023i
$574$		−	30.5447i		−	1.27491i
$575$	0.992819	−	0.120589i	0.0414034	−	0.00502890i
$576$	2.43304			0.101377
$577$	−2.03064	−	12.8209i	−0.0845366	−	0.533743i	−0.993219	−	0.116256i	$-0.962911\pi$
$577$	−2.03064	−	12.8209i	−0.0845366	−	0.533743i	0.908683	−	0.417487i	$-0.137089\pi$
$578$	6.43565	−	12.6307i	0.267688	−	0.525367i
$579$	7.15390	−	2.32444i	0.297306	−	0.0966006i
$580$	11.9765	−	8.37437i	0.497295	−	0.347727i
$581$	1.55892	−	4.79785i	0.0646747	−	0.199048i
$582$	4.95395	−	4.95395i	0.205348	−	0.205348i
$583$	−33.3751	+	17.0055i	−1.38226	+	0.704295i
$584$	7.78968	−	5.65953i	0.322339	−	0.234193i
$585$	−5.75378	+	2.80166i	−0.237890	+	0.115835i
$586$	5.09801	+	3.70392i	0.210597	+	0.153008i
$587$	40.4801	+	6.41141i	1.67079	+	0.264627i	0.918851	−	0.394604i	$-0.129118\pi$
$587$	40.4801	+	6.41141i	1.67079	+	0.264627i	0.751940	+	0.659232i	$0.229118\pi$
$588$	−2.10585	−	0.333534i	−0.0868439	−	0.0137547i
$589$	−1.23877	−	10.9338i	−0.0510426	−	0.450518i
$590$	7.47861	+	7.75444i	0.307890	+	0.319245i
$591$	0.610539	+	0.840334i	0.0251142	+	0.0345667i
$592$	−2.20350	−	4.32461i	−0.0905633	−	0.177741i
$593$	−15.6586	+	15.6586i	−0.643022	+	0.643022i	−0.951297	−	0.308275i	$-0.900248\pi$
$593$	−15.6586	+	15.6586i	−0.643022	+	0.643022i	0.308275	+	0.951297i	$0.400248\pi$
$594$	18.5151	+	6.01593i	0.759685	+	0.246837i
$595$	−3.84337	+	11.1384i	−0.157563	+	0.456628i
$596$	−2.17038	−	6.67975i	−0.0889023	−	0.273613i
$597$	16.8028	+	8.56148i	0.687695	+	0.350398i
$598$	−0.232392	+	0.0368073i	−0.00950322	+	0.00150516i
$599$	−14.4633			−0.590956			−0.295478	−	0.955350i	$-0.595479\pi$
$599$	−14.4633			−0.590956			−0.295478	+	0.955350i	$0.595479\pi$
$600$	−0.136298	+	3.76238i	−0.00556435	+	0.153599i
$601$		−	13.8508i		−	0.564984i	−0.959270	−	0.282492i	$-0.908839\pi$
$601$		−	13.8508i		−	0.564984i	0.959270	−	0.282492i	$-0.0911611\pi$
$602$	−25.9673	+	4.11281i	−1.05835	+	0.167626i
$603$	−15.3635	+	30.1526i	−0.625650	+	1.22791i
$604$	0.106650	+	0.328236i	0.00433954	+	0.0133557i
$605$	24.9093	−	7.59778i	1.01271	−	0.308894i
$606$	1.85239	−	5.70108i	0.0752483	−	0.231591i
$607$	12.8728	−	12.8728i	0.522492	−	0.522492i	−0.395831	−	0.918323i	$-0.629543\pi$
$607$	12.8728	−	12.8728i	0.522492	−	0.522492i	0.918323	+	0.395831i	$0.129543\pi$
$608$	4.08190	+	1.52909i	0.165543	+	0.0620128i
$609$	−9.06961	−	12.4833i	−0.367519	−	0.505847i
$610$	−0.329289	+	0.618330i	−0.0133325	+	0.0250354i
$611$	4.16810	−	5.73690i	0.168623	−	0.232090i
$612$	−4.03850	−	0.639636i	−0.163247	−	0.0258558i
$613$	−6.09668	+	38.4929i	−0.246243	+	1.55472i	0.486176	+	0.873861i	$0.338391\pi$
$613$	−6.09668	+	38.4929i	−0.246243	+	1.55472i	−0.732419	+	0.680854i	$0.761609\pi$
$614$	−16.2189	+	22.3234i	−0.654543	+	0.900901i
$615$	2.27207	+	16.2435i	0.0916187	+	0.655000i
$616$	−8.77063	−	12.0717i	−0.353379	−	0.486384i
$617$	22.4669	−	11.4474i	0.904482	−	0.460857i	0.0610759	−	0.998133i	$-0.480547\pi$
$617$	22.4669	−	11.4474i	0.904482	−	0.460857i	0.843406	+	0.537276i	$0.180547\pi$
$618$	−8.26294	−	8.26294i	−0.332384	−	0.332384i
$619$	−9.96020	−	3.23626i	−0.400334	−	0.130076i	0.101928	−	0.994792i	$-0.467499\pi$
$619$	−9.96020	−	3.23626i	−0.400334	−	0.130076i	−0.502262	+	0.864715i	$0.667499\pi$
$620$	0.102195	−	5.64386i	0.00410426	−	0.226663i
$621$	0.778227	−	0.252861i	0.0312292	−	0.0101470i
$622$	−5.46345	−	2.78377i	−0.219065	−	0.111619i
$623$	4.93747	+	31.1740i	0.197816	+	1.24896i
$624$		−	0.885725i		−	0.0354574i
$625$	24.9345	+	1.80896i	0.997379	+	0.0723582i
$626$			13.2554i			0.529791i
$627$	12.2175	+	9.73078i	0.487919	+	0.388610i
$628$	17.4499	+	8.89118i	0.696328	+	0.354797i
$629$	2.52058	+	7.75755i	0.100502	+	0.309314i
$630$	−17.0559	−	0.308837i	−0.679523	−	0.0123044i
$631$	10.0546	−	30.9448i	0.400267	−	1.23189i	−0.524517	−	0.851400i	$-0.675754\pi$
$631$	10.0546	−	30.9448i	0.400267	−	1.23189i	0.924784	−	0.380494i	$-0.124246\pi$
$632$	1.70576	+	1.70576i	0.0678517	+	0.0678517i
$633$	−8.05167	−	15.8023i	−0.320025	−	0.628084i
$634$	17.9607	+	24.7208i	0.713312	+	0.981790i
$635$	2.74693	+	19.6384i	0.109009	+	0.779324i
$636$	−4.79487	−	3.48368i	−0.190129	−	0.138137i
$637$	0.521056	−	3.28982i	0.0206450	−	0.130347i
$638$	4.86534	−	30.7186i	0.192621	−	1.21616i
$639$	−6.05133	−	4.39655i	−0.239387	−	0.173925i
$640$	1.97365	+	1.05106i	0.0780152	+	0.0415467i
$641$	9.32482	+	12.8345i	0.368308	+	0.506933i	0.952440	−	0.304726i	$-0.0985649\pi$
$641$	9.32482	+	12.8345i	0.368308	+	0.506933i	−0.584132	+	0.811659i	$0.698565\pi$
$642$	−0.391507	−	0.768376i	−0.0154516	−	0.0303254i
$643$	17.3651	−	17.3651i	0.684812	−	0.684812i	−0.276268	−	0.961081i	$-0.589098\pi$
$643$	17.3651	−	17.3651i	0.684812	−	0.684812i	0.961081	+	0.276268i	$0.0890978\pi$
$644$	−0.596483	−	0.193809i	−0.0235047	−	0.00763715i
$645$	13.5033	−	4.11875i	0.531692	−	0.162175i
$646$	−6.37339	−	3.61119i	−0.250758	−	0.142080i
$647$	7.96416	−	15.6305i	0.313103	−	0.614500i	−0.679803	−	0.733394i	$-0.737935\pi$
$647$	7.96416	−	15.6305i	0.313103	−	0.614500i	0.992907	+	0.118894i	$0.0379349\pi$
$648$	−0.659962	−	4.16684i	−0.0259258	−	0.163689i
$649$	22.9276			0.899987
$650$	−5.87769	−	0.212929i	−0.230542	−	0.00835175i
$651$	−5.96007			−0.233594
$652$	0.329833	+	2.08248i	0.0129173	+	0.0815564i
$653$	25.7166	+	13.1033i	1.00637	+	0.512770i	0.877849	−	0.478937i	$-0.158978\pi$
$653$	25.7166	+	13.1033i	1.00637	+	0.512770i	0.128519	+	0.991707i	$0.458978\pi$
$654$	−3.61080	−	11.1129i	−0.141194	−	0.434549i
$655$	−21.3055	−	7.35163i	−0.832476	−	0.287252i
$656$	9.26467	+	3.01027i	0.361725	+	0.117531i
$657$	−16.5652	−	16.5652i	−0.646269	−	0.646269i
$658$	16.8419	−	8.58137i	0.656565	−	0.334537i
$659$	20.4489	−	14.8570i	0.796575	−	0.578746i	−0.113332	−	0.993557i	$-0.536152\pi$
$659$	20.4489	−	14.8570i	0.796575	−	0.578746i	0.909907	+	0.414811i	$0.136152\pi$
$660$	5.56212	+	5.76727i	0.216505	+	0.224491i
$661$	−10.6427	+	14.6485i	−0.413954	+	0.569759i	−0.964177	−	0.265259i	$-0.914543\pi$
$661$	−10.6427	+	14.6485i	−0.413954	+	0.569759i	0.550223	+	0.835018i	$0.314543\pi$
$662$	24.8941	+	3.94284i	0.967537	+	0.153243i
$663$	−0.232854	+	1.47018i	−0.00904329	+	0.0570971i
$664$	1.30163	+	0.945686i	0.0505129	+	0.0366998i
$665$	−28.4205	−	11.2372i	−1.10210	−	0.435762i
$666$	−9.55373	+	6.94119i	−0.370199	+	0.268966i
$667$	−0.593482	−	1.16477i	−0.0229797	−	0.0451002i
$668$	6.95739	+	6.95739i	0.269189	+	0.269189i
$669$	10.8686	+	3.53141i	0.420203	+	0.136532i
$670$	−25.4884	+	17.8224i	−0.984703	+	0.688540i
$671$	0.460716	+	1.41794i	0.0177858	+	0.0547389i
$672$	1.07186	−	2.10363i	0.0413477	−	0.0811494i
$673$	−5.69461	−	35.9543i	−0.219511	−	1.38594i	−0.813547	−	0.581499i	$-0.802466\pi$
$673$	−5.69461	−	35.9543i	−0.219511	−	1.38594i	0.594036	−	0.804439i	$-0.297534\pi$
$674$		−	8.52417i		−	0.328339i
$675$	20.3053	−	2.46630i	0.781552	−	0.0949281i
$676$	−11.6163			−0.446781
$677$	5.12347	−	0.811478i	0.196911	−	0.0311876i	−0.0571999	−	0.998363i	$-0.518217\pi$
$677$	5.12347	−	0.811478i	0.196911	−	0.0311876i	0.254111	+	0.967175i	$0.418217\pi$
$678$	−5.45353	+	10.7032i	−0.209442	+	0.411053i
$679$	9.01536	+	27.7464i	0.345978	+	1.06481i
$680$	−2.99966	−	2.26347i	−0.115032	−	0.0868002i
$681$	5.17424	−	15.9247i	0.198277	−	0.610235i
$682$	−8.49469	−	8.49469i	−0.325278	−	0.325278i
$683$	−33.0960	+	16.8632i	−1.26638	+	0.645254i	−0.952595	−	0.304240i	$-0.901597\pi$
$683$	−33.0960	+	16.8632i	−1.26638	+	0.645254i	−0.313786	+	0.949494i	$0.601597\pi$
$684$	2.12091	−	10.3911i	0.0810951	−	0.397314i
$685$	1.82804	−	10.3280i	0.0698459	−	0.394611i
$686$	−7.68247	+	10.5740i	−0.293318	+	0.403718i
$687$	0.971668	−	6.13487i	0.0370714	−	0.234060i
$688$	1.31168	−	8.28160i	0.0500072	−	0.315733i
$689$	5.44230	−	7.49068i	0.207335	−	0.285372i
$690$	0.331622	+	0.0586970i	0.0126247	+	0.00223456i
$691$	1.06519	−	0.773906i	0.0405217	−	0.0294408i	−0.567340	−	0.823484i	$-0.692027\pi$
$691$	1.06519	−	0.773906i	0.0405217	−	0.0294408i	0.607862	+	0.794043i	$0.292027\pi$
$692$	−5.15660	−	10.1204i	−0.196025	−	0.384720i
$693$	−25.6712	+	25.6712i	−0.975167	+	0.975167i
$694$	−4.82318	+	14.8442i	−0.183085	+	0.563479i
$695$	8.12584	+	6.13157i	0.308231	+	0.232584i
$696$	4.68020	−	1.52069i	0.177403	−	0.0576416i
$697$	−14.5867	−	7.43228i	−0.552510	−	0.281518i
$698$	3.71645	+	23.4647i	0.140670	+	0.888153i
$699$	−11.6909			−0.442191
$700$	−13.7021	−	7.61857i	−0.517890	−	0.287955i
$701$	−12.4469			−0.470114			−0.235057	−	0.971982i	$-0.575528\pi$
$701$	−12.4469			−0.470114			−0.235057	+	0.971982i	$0.575528\pi$
$702$	−4.75293	+	0.752790i	−0.179388	+	0.0284122i
$703$	−20.3906	+	5.64098i	−0.769045	+	0.212754i
$704$	4.52592	−	1.47056i	0.170577	−	0.0554238i
$705$	−8.31808	+	5.81630i	−0.313277	+	0.219055i
$706$	11.9039	+	3.86781i	0.448009	+	0.145567i
$707$	17.6510	+	17.6510i	0.663836	+	0.663836i
$708$	1.64696	+	3.23234i	0.0618965	+	0.121479i
$709$	−22.5946	−	31.0988i	−0.848558	−	1.16794i	−0.984179	−	0.177178i	$-0.943303\pi$
$709$	−22.5946	−	31.0988i	−0.848558	−	1.16794i	0.135621	−	0.990761i	$-0.456697\pi$
$710$	−3.00947	−	6.18056i	−0.112944	−	0.231952i
$711$	3.44986	−	4.74832i	0.129380	−	0.178076i
$712$	−9.94215	−	1.57468i	−0.372598	−	0.0590137i
$713$	−0.498726	−	0.0789905i	−0.0186774	−	0.00295822i
$714$	−2.33217	+	3.20995i	−0.0872792	+	0.120130i
$715$	−9.00978	+	8.68930i	−0.336947	+	0.324961i
$716$	−3.66388	−	5.04289i	−0.136925	−	0.188462i
$717$	−5.76069	−	11.3060i	−0.215137	−	0.422230i
$718$	15.8982	+	15.8982i	0.593317	+	0.593317i
$719$	38.9337	+	12.6503i	1.45198	+	0.471777i	0.925610	−	0.378478i	$-0.123552\pi$
$719$	38.9337	+	12.6503i	1.45198	+	0.471777i	0.526371	+	0.850255i	$0.323552\pi$
$720$	1.77459	−	5.14288i	0.0661349	−	0.191664i
$721$	46.2797	−	15.0372i	1.72355	−	0.560014i
$722$	10.0888	−	16.1002i	0.375464	−	0.599188i
$723$	0.167420	−	0.0265168i	0.00622643	−	0.000986170i
$724$	14.3007			0.531480
$725$	−8.96621	−	31.4235i	−0.332997	−	1.16704i
$726$	8.76943			0.325464
$727$	−6.88620	−	43.4778i	−0.255395	−	1.61250i	−0.698213	−	0.715890i	$-0.746021\pi$
$727$	−6.88620	−	43.4778i	−0.255395	−	1.61250i	0.442818	−	0.896612i	$-0.353979\pi$
$728$	3.28635	+	1.67448i	0.121800	+	0.0620604i
$729$	−0.973356	+	0.316263i	−0.0360502	+	0.0117134i
$730$	−6.28138	−	20.5935i	−0.232484	−	0.762199i
$731$	−4.35440	+	13.4015i	−0.161053	+	0.495672i
$732$	−0.166807	+	0.166807i	−0.00616535	+	0.00616535i
$733$	23.4306	+	45.9851i	0.865429	+	1.69850i	0.702283	+	0.711898i	$0.252164\pi$
$733$	23.4306	+	45.9851i	0.865429	+	1.69850i	0.163146	+	0.986602i	$0.447836\pi$
$734$	8.64968	−	6.28436i	0.319265	−	0.231960i
$735$	−2.24096	+	4.20801i	−0.0826591	+	0.155215i
$736$	0.117571	−	0.161822i	0.00433371	−	0.00596484i
$737$	−10.3545	+	65.3755i	−0.381411	+	2.40814i
$738$	3.70770	−	23.4095i	0.136482	−	0.861716i
$739$	−25.5677	+	35.1909i	−0.940522	+	1.29452i	0.0150885	+	0.999886i	$0.495197\pi$
$739$	−25.5677	+	35.1909i	−0.940522	+	1.29452i	−0.955611	+	0.294632i	$0.904803\pi$
$740$	−10.7484	+	1.50344i	−0.395119	+	0.0552677i
$741$	−3.78279	−	0.772099i	−0.138964	−	0.0283638i
$742$	21.9905	−	11.2047i	0.807296	−	0.411338i
$743$	1.26655	+	1.26655i	0.0464653	+	0.0464653i	0.729958	−	0.683492i	$-0.239540\pi$
$743$	1.26655	+	1.26655i	0.0464653	+	0.0464653i	−0.683492	+	0.729958i	$0.739540\pi$
$744$	0.587384	−	1.80778i	0.0215345	−	0.0662765i
$745$	−15.7025	−	0.284330i	−0.575293	−	0.0104170i
$746$	3.25258	+	10.0104i	0.119085	+	0.366507i
$747$	1.77715	−	3.48785i	0.0650225	−	0.127614i
$748$	−7.89900	+	1.25108i	−0.288816	+	0.0457439i
$749$	3.59110			0.131216
$750$	7.85339	+	3.03227i	0.286765	+	0.110723i
$751$		−	42.5546i		−	1.55284i	−0.630215	−	0.776420i	$-0.717033\pi$
$751$		−	42.5546i		−	1.55284i	0.630215	−	0.776420i	$-0.282967\pi$
$752$	0.943041	+	5.95412i	0.0343891	+	0.217125i
$753$	3.65668	−	7.17664i	0.133257	−	0.261531i
$754$	2.37566	+	7.31154i	0.0865165	+	0.266270i
$755$	0.771602	+	0.0139717i	0.0280815	+	0.000508481i
$756$	−12.1994	−	3.96382i	−0.443688	−	0.144163i
$757$	−34.1964	−	34.1964i	−1.24289	−	1.24289i	−0.958797	−	0.284093i	$-0.908307\pi$
$757$	−34.1964	−	34.1964i	−1.24289	−	1.24289i	−0.284093	−	0.958797i	$-0.591693\pi$
$758$	−4.15690	−	8.15837i	−0.150985	−	0.296325i
$759$	0.579849	−	0.421285i	0.0210472	−	0.0152917i
$760$	6.20936	−	7.51291i	0.225237	−	0.272522i
$761$	−40.7469	−	29.6043i	−1.47707	−	1.07316i	−0.978485	−	0.206317i	$-0.933852\pi$
$761$	−40.7469	−	29.6043i	−1.47707	−	1.07316i	−0.498587	−	0.866839i	$-0.666148\pi$
$762$	−1.04457	+	6.59515i	−0.0378408	+	0.238917i
$763$	48.0591	+	7.61182i	1.73986	+	0.275566i
$764$	11.0113	−	15.1557i	0.398375	−	0.548316i
$765$	−4.29761	+	8.06993i	−0.155380	+	0.291769i
$766$	−2.81302	+	2.04378i	−0.101638	+	0.0738447i
$767$	−5.04964	+	2.57292i	−0.182332	+	0.0929028i
$768$	0.532430	+	0.532430i	0.0192124	+	0.0192124i
$769$	29.7734	+	9.67395i	1.07366	+	0.348852i	0.791910	−	0.610638i	$-0.209087\pi$
$769$	29.7734	+	9.67395i	1.07366	+	0.348852i	0.281745	+	0.959489i	$0.409087\pi$
$770$	−31.9139	+	9.73431i	−1.15010	+	0.350800i
$771$	1.90305	+	5.85699i	0.0685368	+	0.210934i
$772$	−8.90103	−	4.53530i	−0.320355	−	0.163229i
$773$	−1.02730	−	6.48612i	−0.0369494	−	0.233289i	0.962302	−	0.271984i	$-0.0876799\pi$
$773$	−1.02730	−	6.48612i	−0.0369494	−	0.233289i	−0.999251	+	0.0386950i	$0.987680\pi$
$774$	−20.4006			−0.733285
$775$	−11.8553	−	4.33248i	−0.425854	−	0.155627i
$776$	−9.30441			−0.334009
$777$	1.79262	+	11.3182i	0.0643099	+	0.406037i
$778$	9.71042	−	19.0578i	0.348136	−	0.683255i
$779$	20.9326	−	36.9439i	0.749987	−	1.32365i
$780$	−1.87222	−	0.646022i	−0.0670362	−	0.0231313i
$781$	−13.9140	−	4.52092i	−0.497881	−	0.161771i
$782$	−0.237693	+	0.237693i	−0.00849989	+	0.00849989i
$783$	−12.1380	−	23.8222i	−0.433777	−	0.851336i
$784$	1.66437	+	2.29080i	0.0594417	+	0.0818145i
$785$	31.5214	−	30.4001i	1.12505	−	1.08503i
$786$	−6.14003	−	4.46099i	−0.219007	−	0.159118i
$787$	3.74935	−	23.6725i	0.133650	−	0.843833i	−0.826212	−	0.563359i	$-0.809509\pi$
$787$	3.74935	−	23.6725i	0.133650	−	0.843833i	0.959862	−	0.280473i	$-0.0904914\pi$
$788$	0.215799	−	1.36250i	0.00768752	−	0.0485371i
$789$	−3.53010	−	2.56477i	−0.125675	−	0.0913082i
$790$	4.84973	−	2.36146i	0.172546	−	0.0840168i
$791$	−29.4025	−	40.4691i	−1.04543	−	1.43891i
$792$	−5.25649	−	10.3164i	−0.186781	−	0.366579i
$793$	−0.260590	−	0.260590i	−0.00925382	−	0.00925382i
$794$	−7.75425	+	23.8651i	−0.275188	+	0.846942i
$795$	−10.8609	+	7.59436i	−0.385198	+	0.269344i
$796$	−7.73939	−	23.8194i	−0.274315	−	0.844256i
$797$	24.5668	+	12.5174i	0.870202	+	0.443390i	0.831281	−	0.555852i	$-0.187608\pi$
$797$	24.5668	+	12.5174i	0.870202	+	0.443390i	0.0389206	+	0.999242i	$0.487608\pi$
$798$	−8.04994	−	6.41149i	−0.284965	−	0.226964i
$799$		−	10.1309i		−	0.358407i
$800$	3.66121	−	3.40522i	0.129443	−	0.120393i
$801$			24.4911i			0.865352i
$802$	−4.02348	−	25.4033i	−0.142074	−	0.897020i
$803$	−40.8266	−	20.8022i	−1.44074	−	0.734093i
$804$	−9.96044	+	3.23634i	−0.351278	+	0.114137i
$805$	−0.844725	+	1.11947i	−0.0297727	+	0.0394561i
$806$	2.82417	+	0.917627i	0.0994770	+	0.0323220i
$807$	16.9391	+	16.9391i	0.596285	+	0.596285i
$808$	−7.09340	+	3.61427i	−0.249545	+	0.127149i
$809$	−14.7779	−	20.3400i	−0.519563	−	0.715118i	0.465932	−	0.884821i	$-0.345719\pi$
$809$	−14.7779	−	20.3400i	−0.519563	−	0.715118i	−0.985495	+	0.169703i	$0.945719\pi$
$810$	−9.28909	−	1.64416i	−0.326385	−	0.0577700i
$811$	23.0146	−	31.6769i	0.808152	−	1.11233i	−0.183454	−	0.983028i	$-0.558728\pi$
$811$	23.0146	−	31.6769i	0.808152	−	1.11233i	0.991606	−	0.129297i	$-0.0412722\pi$
$812$	−3.20572	+	20.2401i	−0.112499	+	0.710288i
$813$	17.8846	+	2.83265i	0.627242	+	0.0993454i
$814$	−13.5764	+	18.6863i	−0.475853	+	0.654956i
$815$	4.64246	+	0.821713i	0.162618	+	0.0287834i
$816$	−0.743786	−	1.02373i	−0.0260377	−	0.0358378i
$817$	−34.2260	−	12.8212i	−1.19742	−	0.448556i
$818$	6.76293	−	6.76293i	0.236460	−	0.236460i
$819$	2.77309	−	8.53470i	0.0968997	−	0.298227i
$820$	13.1204	−	17.3878i	0.458184	−	0.607207i
$821$	14.6932	+	45.2209i	0.512795	+	1.57822i	0.787258	+	0.616623i	$0.211500\pi$
$821$	14.6932	+	45.2209i	0.512795	+	1.57822i	−0.274463	+	0.961598i	$0.588500\pi$
$822$	1.60344	−	3.14693i	0.0559264	−	0.109762i
$823$	39.3983	−	6.24008i	1.37334	−	0.217516i	0.574226	−	0.818697i	$-0.305303\pi$
$823$	39.3983	−	6.24008i	1.37334	−	0.217516i	0.799113	+	0.601181i	$0.205303\pi$
$824$			15.5193i			0.540640i
$825$	16.2475	−	7.55056i	0.565666	−	0.262877i
$826$	−15.1067			−0.525630
$827$	21.1911	−	3.35635i	0.736888	−	0.116712i	0.223302	−	0.974749i	$-0.428317\pi$
$827$	21.1911	−	3.35635i	0.736888	−	0.116712i	0.513587	+	0.858038i	$0.328317\pi$
$828$	−0.433620	−	0.220941i	−0.0150693	−	0.00767822i
$829$	6.32396	+	19.4632i	0.219640	+	0.675984i	0.998792	+	0.0491475i	$0.0156504\pi$
$829$	6.32396	+	19.4632i	0.219640	+	0.675984i	−0.779151	+	0.626836i	$0.784350\pi$
$830$	2.94833	−	2.06158i	0.102338	−	0.0715585i
$831$	−12.0548	−	3.91684i	−0.418177	−	0.135874i
$832$	−0.831776	+	0.831776i	−0.0288367	+	0.0288367i
$833$	−2.16037	−	4.23997i	−0.0748525	−	0.146906i
$834$	2.01486	+	2.77321i	0.0697688	+	0.0960286i
$835$	19.7808	−	9.63179i	0.684544	−	0.333322i
$836$	−2.33522	−	20.6114i	−0.0807654	−	0.712860i
$837$	−10.2000	−	1.61553i	−0.352565	−	0.0558409i
$838$	−35.9865	−	5.69970i	−1.24313	−	0.196893i
$839$	−17.3068	−	12.5741i	−0.597497	−	0.434107i	0.247493	−	0.968890i	$-0.420393\pi$
$839$	−17.3068	−	12.5741i	−0.597497	−	0.434107i	−0.844989	+	0.534783i	$0.820393\pi$
$840$	−3.66482	−	3.79998i	−0.126448	−	0.131112i
$841$	−11.0942	+	8.06039i	−0.382558	+	0.277944i
$842$	−31.9667	+	16.2878i	−1.10164	+	0.561316i
$843$	11.6269	−	11.6269i	0.400452	−	0.400452i
$844$	−7.27853	+	22.4010i	−0.250537	+	0.771075i
$845$	−8.47259	+	24.5542i	−0.291466	+	0.844689i
$846$	13.9493	−	4.53241i	0.479587	−	0.155827i
$847$	−16.5788	+	32.5377i	−0.569654	+	1.11801i
$848$	1.23133	+	7.77431i	0.0422840	+	0.266971i
$849$	5.17057			0.177454
$850$	−6.97232	+	4.68967i	−0.239149	+	0.160854i
$851$			0.970837i			0.0332799i
$852$	−0.362122	−	2.28635i	−0.0124061	−	0.0783289i
$853$	3.89574	+	1.98498i	0.133388	+	0.0679644i	0.519411	−	0.854525i	$-0.326151\pi$
$853$	3.89574	+	1.98498i	0.133388	+	0.0679644i	−0.386023	+	0.922489i	$0.626151\pi$
$854$	−0.303560	−	0.934263i	−0.0103876	−	0.0319698i
$855$	−20.4175	−	12.0621i	−0.698264	−	0.412515i
$856$	−0.353914	+	1.08924i	−0.0120965	+	0.0372293i
$857$	2.14693	−	2.14693i	0.0733378	−	0.0733378i	−0.669486	−	0.742824i	$-0.733486\pi$
$857$	2.14693	−	2.14693i	0.0733378	−	0.0733378i	0.742824	+	0.669486i	$0.233486\pi$
$858$	−3.75561	+	1.91358i	−0.128214	+	0.0653284i
$859$	19.8813	+	27.3643i	0.678341	+	0.933656i	0.999912	−	0.0132290i	$-0.00421104\pi$
$859$	19.8813	+	27.3643i	0.678341	+	0.933656i	−0.321571	+	0.946885i	$0.604211\pi$
$860$	−16.5487	−	8.81294i	−0.564306	−	0.300519i
$861$	−18.6068	−	13.5186i	−0.634116	−	0.460713i
$862$	−12.8403	−	2.03371i	−0.437343	−	0.0692683i
$863$	56.3395	+	8.92331i	1.91782	+	0.303753i	0.996397	−	0.0848077i	$-0.0270276\pi$
$863$	56.3395	+	8.92331i	1.91782	+	0.303753i	0.921423	+	0.388561i	$0.127028\pi$
$864$	2.40458	−	3.30962i	0.0818054	−	0.112595i
$865$	−25.1533	+	3.51834i	−0.855236	+	0.119627i
$866$	−6.11553	+	4.44319i	−0.207814	+	0.150986i
$867$	−4.84585	−	9.51052i	−0.164574	−	0.322994i
$868$	5.59705	+	5.59705i	0.189976	+	0.189976i
$869$	3.54745	−	10.9179i	0.120339	−	0.370366i
$870$	0.199217	−	11.0020i	0.00675410	−	0.373003i
$871$	−5.05590	−	15.5605i	−0.171313	−	0.527246i
$872$	−7.04516	+	13.8269i	−0.238579	+	0.468238i
$873$	3.54136	+	22.3593i	0.119857	+	0.756746i
$874$	−0.588629	−	0.643188i	−0.0199107	−	0.0217562i
$875$	−26.0978	+	23.4063i	−0.882267	+	0.791277i
$876$		−	7.25002i		−	0.244956i
$877$	31.8182	−	5.03951i	1.07442	−	0.170172i	0.405941	−	0.913899i	$-0.366944\pi$
$877$	31.8182	−	5.03951i	1.07442	−	0.170172i	0.668483	+	0.743727i	$0.266944\pi$
$878$	27.4629	+	13.9930i	0.926827	+	0.472242i
$879$	4.51260	−	1.46623i	0.152206	−	0.0494548i
$880$	0.192650	−	10.6393i	0.00649423	−	0.358651i
$881$	−11.8876	+	36.5864i	−0.400505	+	1.23263i	0.524086	+	0.851666i	$0.324407\pi$
$881$	−11.8876	+	36.5864i	−0.400505	+	1.23263i	−0.924591	+	0.380962i	$0.875593\pi$
$882$	4.87152	−	4.87152i	0.164032	−	0.164032i
$883$	−7.10877	−	13.9518i	−0.239229	−	0.469514i	0.739910	−	0.672706i	$-0.234868\pi$
$883$	−7.10877	−	13.9518i	−0.239229	−	0.469514i	−0.979139	+	0.203193i	$0.934868\pi$
$884$	1.59930	−	1.16196i	0.0537904	−	0.0390810i
$885$	8.03365	−	1.12371i	0.270048	−	0.0377733i
$886$	−16.3917	+	22.5612i	−0.550689	+	0.757959i
$887$	4.77841	−	30.1697i	0.160443	−	1.01300i	−0.767709	−	0.640798i	$-0.778603\pi$
$887$	4.77841	−	30.1697i	0.160443	−	1.01300i	0.928152	−	0.372200i	$-0.121397\pi$
$888$	−3.60964	−	0.571711i	−0.121132	−	0.0191854i
$889$	−22.4956	−	16.3440i	−0.754477	−	0.548160i
$890$	−10.5800	+	19.8669i	−0.354643	+	0.665939i
$891$	−16.2422	+	11.8006i	−0.544134	+	0.395336i
$892$	−6.89025	−	13.5229i	−0.230703	−	0.452779i
$893$	26.2512	+	1.16272i	0.878463	+	0.0389088i
$894$	−5.02965	−	1.63423i	−0.168217	−	0.0546569i
$895$	−13.3318	+	4.06645i	−0.445634	+	0.135926i
$896$	−2.98207	+	0.968934i	−0.0996241	+	0.0323698i
$897$	−0.0804314	+	0.157856i	−0.00268553	+	0.00527064i
$898$	−17.3863	+	2.75372i	−0.580188	+	0.0918928i
$899$			16.4984i			0.550254i
$900$	−9.57652	−	7.50213i	−0.319217	−	0.250071i
$901$		−	13.2280i		−	0.440688i
$902$	−7.25197	−	45.7872i	−0.241464	−	1.52455i
$903$	−8.98733	+	17.6386i	−0.299080	+	0.586977i
$904$	15.1726	−	4.92988i	0.504633	−	0.163965i
$905$	10.4305	−	30.2283i	0.346721	−	1.00482i
$906$	0.247152	+	0.0803044i	0.00821106	+	0.00266794i
$907$	16.4614	−	16.4614i	0.546592	−	0.546592i	−0.378861	−	0.925453i	$-0.623684\pi$
$907$	16.4614	−	16.4614i	0.546592	−	0.546592i	0.925453	+	0.378861i	$0.123684\pi$
$908$	−19.8138	+	10.0956i	−0.657544	+	0.335035i
$909$	11.3852	+	15.6704i	0.377623	+	0.519754i
$910$	5.93644	−	5.72527i	0.196791	−	0.189791i
$911$	25.0733	−	34.5104i	0.830714	−	1.14338i	−0.157075	−	0.987587i	$-0.550207\pi$
$911$	25.0733	−	34.5104i	0.830714	−	1.14338i	0.987790	−	0.155794i	$-0.0497935\pi$
$912$	2.73805	−	1.80980i	0.0906660	−	0.0599284i
$913$	1.19774	−	7.56221i	0.0396393	−	0.250273i
$914$	−8.97960	−	6.52406i	−0.297019	−	0.215797i
$915$	0.230927	+	0.474255i	0.00763420	+	0.0156784i
$916$	−6.67368	+	4.84872i	−0.220505	+	0.160206i
$917$	28.1597	−	14.3481i	0.929915	−	0.473815i
$918$	−4.86135	+	4.86135i	−0.160448	+	0.160448i
$919$	4.03170	+	1.30998i	0.132994	+	0.0432122i	0.374758	−	0.927123i	$-0.377726\pi$
$919$	4.03170	+	1.30998i	0.132994	+	0.0432122i	−0.241764	+	0.970335i	$0.577726\pi$
$920$	−0.256302	−	0.366545i	−0.00845002	−	0.0120846i
$921$	6.42042	+	19.7600i	0.211560	+	0.651115i
$922$	−8.22813	−	4.19244i	−0.270979	−	0.138071i
$923$	3.57179	−	0.565716i	0.117567	−	0.0186208i
$924$	−11.2354			−0.369618
$925$	−4.66164	+	23.8162i	−0.153274	+	0.783072i
$926$		−	7.11311i		−	0.233751i
$927$	37.2942	−	5.90681i	1.22490	−	0.194005i
$928$	−5.82320	−	2.96707i	−0.191156	−	0.0973988i
$929$	−5.60531	+	1.82127i	−0.183904	+	0.0597541i	−0.399521	−	0.916724i	$-0.630824\pi$
$929$	−5.60531	+	1.82127i	−0.183904	+	0.0597541i	0.215617	+	0.976478i	$0.430824\pi$
$930$	−3.39281	−	2.56014i	−0.111255	−	0.0839502i
$931$	11.2345	−	5.11133i	0.368197	−	0.167517i
$932$	10.9788	+	10.9788i	0.359624	+	0.359624i
$933$	−4.11381	+	2.09609i	−0.134680	+	0.0686230i
$934$	19.8519	−	14.4233i	0.649575	−	0.471944i
$935$	−3.11681	+	17.6092i	−0.101931	+	0.575881i
$936$	2.31541	+	1.68224i	0.0756815	+	0.0549859i
$937$	−46.8587	−	7.42169i	−1.53081	−	0.242456i	−0.666533	−	0.745476i	$-0.732222\pi$
$937$	−46.8587	−	7.42169i	−1.53081	−	0.242456i	−0.864275	+	0.503020i	$0.832222\pi$
$938$	6.82243	−	43.0751i	0.222760	−	1.40645i
$939$	8.07471	+	5.86662i	0.263508	+	0.191450i
$940$	13.2735	+	2.34940i	0.432933	+	0.0766288i
$941$	−3.40738	−	4.68986i	−0.111077	−	0.152885i	0.749859	−	0.661598i	$-0.230121\pi$
$941$	−3.40738	−	4.68986i	−0.111077	−	0.152885i	−0.860936	+	0.508713i	$0.830121\pi$
$942$	13.1393	−	6.69479i	0.428100	−	0.218128i
$943$	−1.37781	−	1.37781i	−0.0448676	−	0.0448676i
$944$	1.48881	−	4.58210i	0.0484568	−	0.149135i
$945$	−17.2765	+	22.8956i	−0.562004	+	0.744794i
$946$	−37.9491	+	12.3304i	−1.23383	+	0.400896i
$947$	20.8280	−	40.8773i	0.676819	−	1.32833i	−0.255540	−	0.966799i	$-0.582253\pi$
$947$	20.8280	−	40.8773i	0.676819	−	1.32833i	0.932359	−	0.361534i	$-0.117747\pi$
$948$	1.79404	−	0.284148i	0.0582676	−	0.00922868i
$949$	11.3262			0.367663
$950$	−11.3516	−	18.6048i	−0.368296	−	0.603621i
$951$	23.0082			0.746093
$952$	5.20456	−	0.824321i	0.168681	−	0.0267164i
$953$	14.2777	−	28.0216i	0.462501	−	0.907710i	−0.535501	−	0.844535i	$-0.679877\pi$
$953$	14.2777	−	28.0216i	0.462501	−	0.907710i	0.998002	−	0.0631755i	$-0.0201228\pi$
$954$	18.2136	−	5.91797i	0.589689	−	0.191601i
$955$	−24.0044	−	34.3295i	−0.776765	−	1.11088i
$956$	−5.20754	+	16.0272i	−0.168424	+	0.518355i
$957$	−16.5594	−	16.5594i	−0.535288	−	0.535288i
$958$	6.69923	−	3.41343i	0.216442	−	0.110283i
$959$	8.64488	+	11.8987i	0.279158	+	0.384227i
$960$	1.51377	−	0.737095i	0.0488568	−	0.0237896i
$961$	−19.9239	−	14.4756i	−0.642706	−	0.466953i
$962$	0.893142	−	5.63908i	0.0287961	−	0.181811i
$963$	2.75223	+	0.435910i	0.0886892	+	0.0140470i
$964$	−0.182125	−	0.132321i	−0.00586584	−	0.00426178i
$965$	−16.0787	+	15.5068i	−0.517593	+	0.499182i
$966$	−0.382056	+	0.277580i	−0.0122924	+	0.00893099i
$967$	−50.4170	+	25.6887i	−1.62130	+	0.826094i	−0.622237	+	0.782829i	$0.713776\pi$
$967$	−50.4170	+	25.6887i	−1.62130	+	0.826094i	−0.999064	+	0.0432649i	$0.986224\pi$
$968$	−8.23529	−	8.23529i	−0.264692	−	0.264692i
$969$	−5.02058	+	2.28419i	−0.161284	+	0.0733788i
$970$	−6.78637	+	19.6674i	−0.217897	+	0.631481i
$971$	−40.5480	+	13.1749i	−1.30125	+	0.422801i	−0.876016	−	0.482283i	$-0.839808\pi$
$971$	−40.5480	+	13.1749i	−1.30125	+	0.422801i	−0.425233	+	0.905084i	$0.639808\pi$
$972$	−13.7655	−	7.01386i	−0.441528	−	0.224970i
$973$	−14.0987	+	2.23302i	−0.451985	+	0.0715874i
$974$		−	16.7604i		−	0.537038i
$975$	−2.73108	+	3.48625i	−0.0874647	+	0.111649i
$976$	0.313293			0.0100283
$977$	−4.48900	+	0.710987i	−0.143616	+	0.0227465i	−0.227828	−	0.973701i	$-0.573163\pi$
$977$	−4.48900	+	0.710987i	−0.143616	+	0.0227465i	0.0842126	+	0.996448i	$0.473163\pi$
$978$	1.41456	+	0.720752i	0.0452325	+	0.0230471i
$979$	14.8028	+	45.5582i	0.473098	+	1.45605i
$980$	6.05617	−	1.84724i	0.193457	−	0.0590079i
$981$	35.9086	+	11.6674i	1.14647	+	0.372512i
$982$	12.3524	−	12.3524i	0.394180	−	0.394180i
$983$	10.5326	−	5.36665i	0.335939	−	0.171169i	−0.277881	−	0.960616i	$-0.589632\pi$
$983$	10.5326	−	5.36665i	0.335939	−	0.171169i	0.613820	+	0.789446i	$0.289632\pi$
$984$	5.93415	−	4.31141i	0.189174	−	0.137443i
$985$	−2.72261	−	1.44992i	−0.0867497	−	0.0461982i
$986$	8.88567	+	6.45582i	0.282977	+	0.205595i
$987$	2.22648	−	14.0575i	0.0708698	−	0.447454i
$988$	2.82732	+	4.27746i	0.0899489	+	0.136084i
$989$	−0.985810	+	1.35685i	−0.0313469	+	0.0431454i
$990$	−25.6405	+	3.58649i	−0.814908	+	0.113986i
$991$	1.71226	+	2.35672i	0.0543916	+	0.0748636i	0.835346	−	0.549724i	$-0.185267\pi$
$991$	1.71226	+	2.35672i	0.0543916	+	0.0748636i	−0.780955	+	0.624588i	$0.785267\pi$
$992$	−2.24928	+	1.14606i	−0.0714146	+	0.0363876i
$993$	13.4196	−	13.4196i	0.425858	−	0.425858i
$994$	9.16775	+	2.97878i	0.290783	+	0.0944813i
$995$	−55.9936	−	1.01390i	−1.77512	−	0.0321427i
$996$	1.15216	−	0.374359i	0.0365075	−	0.0118620i
$997$	8.26155	−	16.2142i	0.261646	−	0.513509i	−0.722389	−	0.691487i	$-0.756956\pi$
$997$	8.26155	−	16.2142i	0.261646	−	0.513509i	0.984034	+	0.177979i	$0.0569558\pi$
$998$	1.85241	+	11.6956i	0.0586369	+	0.370219i
$999$			19.8558i			0.628209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.10	✓	400
19.18	odd	2	inner	950.2.w.a.37.41	yes	400
25.23	odd	20	inner	950.2.w.a.873.41	yes	400
475.398	even	20	inner	950.2.w.a.873.10	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.10	✓	400	1.1	even	1	trivial
950.2.w.a.37.41	yes	400	19.18	odd	2	inner
950.2.w.a.873.10	yes	400	475.398	even	20	inner
950.2.w.a.873.41	yes	400	25.23	odd	20	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.341841 + 0.670901i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.0404826 - 2.23570i) q^{5} +(0.232680 - 0.716117i) q^{6} +(2.21716 + 2.21716i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.43010 + 1.96837i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.341841 + 0.670901i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.0404826 - 2.23570i) q^{5} +(0.232680 - 0.716117i) q^{6} +(2.21716 + 2.21716i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.43010 + 1.96837i) q^{9} +(0.309757 + 2.21451i) q^{10} +(3.84997 + 2.79717i) q^{11} +(-0.117790 + 0.743699i) q^{12} +(-1.16183 - 0.184015i) q^{13} +(-2.53670 - 1.84302i) q^{14} +(1.48610 + 0.791414i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.49738 + 0.762954i) q^{17} +(-1.72042 - 1.72042i) q^{18} +(-1.80511 - 3.96757i) q^{19} +(-0.652368 - 2.13879i) q^{20} +(-2.24541 + 0.729578i) q^{21} +(-4.24015 - 2.16046i) q^{22} +(-0.197560 + 0.0312905i) q^{23} -0.752970i q^{24} +(-4.99672 - 0.181014i) q^{25} +1.17631 q^{26} +(-4.04055 + 0.639960i) q^{27} +(2.79378 + 1.42350i) q^{28} +(2.01959 + 6.21566i) q^{29} +(-1.59160 - 0.549194i) q^{30} +(2.40087 + 0.780090i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.19270 + 1.62676i) q^{33} +(1.35959 - 0.987803i) q^{34} +(5.04666 - 4.86715i) q^{35} +(1.96837 + 1.43010i) q^{36} +(0.759275 - 4.79387i) q^{37} +(2.40355 + 3.63634i) q^{38} +(0.520616 - 0.716567i) q^{39} +(0.978917 + 2.01040i) q^{40} +(5.72588 + 7.88100i) q^{41} +(2.10363 - 1.07186i) q^{42} +(5.92897 - 5.92897i) q^{43} +(4.52592 + 1.47056i) q^{44} +(4.45858 - 3.11760i) q^{45} +(0.190233 - 0.0618105i) q^{46} +(-2.73681 + 5.37129i) q^{47} +(0.117790 + 0.743699i) q^{48} +2.83159i q^{49} +(4.96352 - 0.602874i) q^{50} -1.26540i q^{51} +(-1.16183 + 0.184015i) q^{52} +(-3.57346 + 7.01331i) q^{53} +(3.89069 - 1.26416i) q^{54} +(6.40949 - 8.49416i) q^{55} +(-2.98207 - 0.968934i) q^{56} +(3.27890 + 0.145229i) q^{57} +(-2.96707 - 5.82320i) q^{58} +(3.89777 - 2.83189i) q^{59} +(1.65792 + 0.293451i) q^{60} +(0.253460 + 0.184149i) q^{61} +(-2.49334 - 0.394907i) q^{62} +(-1.19342 + 7.53495i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.458437 + 2.59005i) q^{65} +(2.89891 - 2.10618i) q^{66} +(6.31454 + 12.3930i) q^{67} +(-1.18833 + 1.18833i) q^{68} +(0.0465414 - 0.143240i) q^{69} +(-4.22314 + 5.59670i) q^{70} +(-2.92382 + 0.950007i) q^{71} +(-2.16785 - 1.10458i) q^{72} +(-9.51003 + 1.50624i) q^{73} +4.85363i q^{74} +(1.82953 - 3.29043i) q^{75} +(-2.94281 - 3.21557i) q^{76} +(2.33423 + 14.7378i) q^{77} +(-0.402111 + 0.789187i) q^{78} +(-0.745446 - 2.29425i) q^{79} +(-1.28136 - 1.83252i) q^{80} +(-1.30367 + 4.01230i) q^{81} +(-6.88825 - 6.88825i) q^{82} +(-0.730424 - 1.43354i) q^{83} +(-1.91006 + 1.38774i) q^{84} +(1.64512 + 3.37859i) q^{85} +(-4.92848 + 6.78347i) q^{86} +(-4.86047 - 0.769823i) q^{87} +(-4.70024 - 0.744445i) q^{88} +(8.14363 + 5.91669i) q^{89} +(-3.91599 + 3.77669i) q^{90} +(-2.16796 - 2.98395i) q^{91} +(-0.178222 + 0.0908086i) q^{92} +(-1.34408 + 1.34408i) q^{93} +(1.86286 - 5.73329i) q^{94} +(-8.94337 + 3.87506i) q^{95} +(-0.232680 - 0.716117i) q^{96} +(8.29029 + 4.22411i) q^{97} +(-0.442958 - 2.79673i) q^{98} +11.5784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

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Database

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