LMFDB - Embedded newform 363.2.j.a.32.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,2,Mod(32,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$42$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			32.18
Character	$\chi$	$=$	363.32
Dual form			363.2.j.a.329.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0793462 + 0.551865i) q^{2} +(1.63436 - 0.573475i) q^{3} +(1.62073 + 0.475888i) q^{4} +(-0.495271 + 0.226183i) q^{5} +(0.186801 + 0.947448i) q^{6} +(-1.05566 - 1.64263i) q^{7} +(-0.854445 + 1.87097i) q^{8} +(2.34225 - 1.87453i) q^{9} +(-0.0855244 - 0.291270i) q^{10} +(2.40236 + 2.28663i) q^{11} +(2.92176 - 0.151675i) q^{12} +(0.250539 - 0.853257i) q^{13} +(0.990274 - 0.452243i) q^{14} +(-0.679740 + 0.653690i) q^{15} +(1.87728 + 1.20645i) q^{16} +(0.325125 - 0.375214i) q^{17} +(0.848638 + 1.44134i) q^{18} +(-1.81382 + 1.57168i) q^{19} +(-0.910337 + 0.130887i) q^{20} +(-2.66733 - 2.07926i) q^{21} +(-1.45253 + 1.14434i) q^{22} +(2.61290 - 4.06575i) q^{23} +(-0.323512 + 3.54785i) q^{24} +(-3.08017 + 3.55470i) q^{25} +(0.451003 + 0.205966i) q^{26} +(2.75308 - 4.40687i) q^{27} +(-0.929221 - 3.16464i) q^{28} +(-4.83034 - 5.57451i) q^{29} +(-0.306813 - 0.426992i) q^{30} +(-4.86195 + 1.42760i) q^{31} +(-3.50865 + 4.04920i) q^{32} +(5.23764 + 2.35947i) q^{33} +(0.181270 + 0.209197i) q^{34} +(0.894372 + 0.574778i) q^{35} +(4.68822 - 1.92345i) q^{36} +(0.276430 - 0.0811670i) q^{37} +(-0.723436 - 1.12569i) q^{38} +(-0.0798518 - 1.53821i) q^{39} -1.11990i q^{40} +(-0.926082 + 6.44104i) q^{41} +(1.35911 - 1.30703i) q^{42} +(-4.21125 - 1.92321i) q^{43} +(2.80539 + 4.84925i) q^{44} +(-0.736064 + 1.45818i) q^{45} +(2.03642 + 1.76457i) q^{46} +(4.65031 - 0.668613i) q^{47} +(3.76002 + 0.895203i) q^{48} +(1.32407 - 2.89931i) q^{49} +(-1.71732 - 1.98189i) q^{50} +(0.316195 - 0.799686i) q^{51} +(0.812110 - 1.26367i) q^{52} +(2.31955 + 3.60929i) q^{53} +(2.21355 + 1.86900i) q^{54} +(-1.70702 - 0.589127i) q^{55} +(3.97533 - 0.571566i) q^{56} +(-2.06310 + 3.60887i) q^{57} +(3.45965 - 2.22338i) q^{58} +(-8.48547 + 1.22003i) q^{59} +(-1.41276 + 0.735972i) q^{60} +(-5.96857 + 0.858151i) q^{61} +(-0.402064 - 2.79641i) q^{62} +(-5.55178 - 1.86860i) q^{63} +(0.966462 + 1.11536i) q^{64} +(0.0689074 + 0.479261i) q^{65} +(-1.71769 + 2.70326i) q^{66} +(-0.125710 + 0.874334i) q^{67} +(0.705499 - 0.453397i) q^{68} +(1.93881 - 8.14333i) q^{69} +(-0.388165 + 0.447966i) q^{70} +(-4.68574 + 4.06022i) q^{71} +(1.50587 + 5.98398i) q^{72} +(4.18299 - 6.50886i) q^{73} +(0.0228596 + 0.158992i) q^{74} +(-2.99556 + 7.57606i) q^{75} +(-3.68764 + 1.68409i) q^{76} +(1.22002 - 6.36009i) q^{77} +(0.855217 + 0.0779833i) q^{78} +(-13.4786 + 6.15546i) q^{79} +(-1.20264 - 0.172914i) q^{80} +(1.97229 - 8.78123i) q^{81} +(-3.48111 - 1.02214i) q^{82} +(7.17381 - 4.61032i) q^{83} +(-3.33352 - 4.63926i) q^{84} +(-0.0761581 + 0.259371i) q^{85} +(1.39550 - 2.17144i) q^{86} +(-11.0914 - 6.34067i) q^{87} +(-6.33090 + 2.54096i) q^{88} +(-7.26380 - 6.29412i) q^{89} +(-0.746313 - 0.521909i) q^{90} +(-1.66607 + 0.489203i) q^{91} +(6.16964 - 5.34603i) q^{92} +(-7.12747 + 5.12141i) q^{93} +2.61939i q^{94} +(0.542844 - 1.18866i) q^{95} +(-3.41228 + 8.62997i) q^{96} +(-0.898875 + 1.96826i) q^{97} +(1.49497 + 0.960756i) q^{98} +(9.91328 + 0.852556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 22 q^{3} - 58 q^{4} + 11 q^{6} - 22 q^{7} - 18 q^{9} - 44 q^{10} - 5 q^{12} - 44 q^{13} + 36 q^{15} - 70 q^{16} + 11 q^{18} - 22 q^{19} - 44 q^{21} + 22 q^{22} - 66 q^{24} + 24 q^{25} - 10 q^{27}+ \cdots + 99 q^{99}+O(q^{100}) $ 420 * q - 22 * q^3 - 58 * q^4 + 11 * q^6 - 22 * q^7 - 18 * q^9 - 44 * q^10 - 5 * q^12 - 44 * q^13 + 36 * q^15 - 70 * q^16 + 11 * q^18 - 22 * q^19 - 44 * q^21 + 22 * q^22 - 66 * q^24 + 24 * q^25 - 10 * q^27 - 22 * q^28 - 44 * q^30 - 48 * q^31 + 33 * q^33 - 26 * q^34 - 59 * q^36 - 6 * q^37 - 44 * q^39 + 12 * q^42 - 22 * q^43 + 42 * q^45 - 22 * q^46 - 48 * q^48 + 44 * q^49 + 11 * q^51 - 143 * q^54 + 44 * q^55 - 121 * q^57 + 14 * q^58 + 50 * q^60 - 22 * q^61 - 143 * q^63 + 142 * q^64 - 55 * q^66 + 2 * q^67 + 6 * q^69 + 26 * q^70 + 77 * q^72 - 44 * q^73 - 38 * q^75 + 176 * q^76 + 20 * q^78 + 22 * q^79 - 26 * q^81 - 70 * q^82 - 44 * q^84 - 154 * q^85 + 22 * q^87 + 176 * q^88 - 22 * q^90 - 154 * q^91 - 19 * q^93 + 22 * q^96 - 58 * q^97 + 99 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{1}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0793462	+	0.551865i	−0.0561062	+	0.390227i	0.942347	+	0.334636i	$0.108613\pi$
$2$	−0.0793462	+	0.551865i	−0.0561062	+	0.390227i	−0.998454	+	0.0555912i	$0.982296\pi$
$3$	1.63436	−	0.573475i	0.943597	−	0.331096i
$3$	1.63436	−	0.573475i	0.943597	−	0.331096i
$4$	1.62073	+	0.475888i	0.810363	+	0.237944i
$5$	−0.495271	+	0.226183i	−0.221492	+	0.101152i	−0.523071	−	0.852289i	$-0.675214\pi$
$5$	−0.495271	+	0.226183i	−0.221492	+	0.101152i	0.301579	+	0.953441i	$0.402486\pi$
$6$	0.186801	+	0.947448i	0.0762611	+	0.386794i
$7$	−1.05566	−	1.64263i	−0.399001	−	0.620857i	0.582383	−	0.812915i	$-0.302120\pi$
$7$	−1.05566	−	1.64263i	−0.399001	−	0.620857i	−0.981384	+	0.192057i	$0.938484\pi$
$8$	−0.854445	+	1.87097i	−0.302092	+	0.661489i
$9$	2.34225	−	1.87453i	0.780751	−	0.624843i
$10$	−0.0855244	−	0.291270i	−0.0270452	−	0.0921075i
$11$	2.40236	+	2.28663i	0.724339	+	0.689444i
$11$	2.40236	+	2.28663i	0.724339	+	0.689444i
$12$	2.92176	−	0.151675i	0.843439	−	0.0437849i
$13$	0.250539	−	0.853257i	0.0694870	−	0.236651i	−0.917426	−	0.397908i	$-0.869736\pi$
$13$	0.250539	−	0.853257i	0.0694870	−	0.236651i	0.986913	+	0.161257i	$0.0515547\pi$
$14$	0.990274	−	0.452243i	0.264662	−	0.120867i
$15$	−0.679740	+	0.653690i	−0.175508	+	0.168782i
$16$	1.87728	+	1.20645i	0.469319	+	0.301613i
$17$	0.325125	−	0.375214i	0.0788544	−	0.0910029i	−0.714951	−	0.699174i	$-0.753551\pi$
$17$	0.325125	−	0.375214i	0.0788544	−	0.0910029i	0.793806	+	0.608171i	$0.208097\pi$
$18$	0.848638	+	1.44134i	0.200026	+	0.339728i
$19$	−1.81382	+	1.57168i	−0.416118	+	0.360568i	−0.837615	−	0.546262i	$-0.816050\pi$
$19$	−1.81382	+	1.57168i	−0.416118	+	0.360568i	0.421497	+	0.906830i	$0.361505\pi$
$20$	−0.910337	+	0.130887i	−0.203558	+	0.0292672i
$21$	−2.66733	−	2.07926i	−0.582059	−	0.453731i
$22$	−1.45253	+	1.14434i	−0.309680	+	0.243975i
$23$	2.61290	−	4.06575i	0.544827	−	0.847768i	−0.454243	−	0.890878i	$-0.650090\pi$
$23$	2.61290	−	4.06575i	0.544827	−	0.847768i	0.999070	+	0.0431098i	$0.0137265\pi$
$24$	−0.323512	+	3.54785i	−0.0660365	+	0.724201i
$25$	−3.08017	+	3.55470i	−0.616034	+	0.710941i
$26$	0.451003	+	0.205966i	0.0884490	+	0.0403933i
$27$	2.75308	−	4.40687i	0.529831	−	0.848103i
$28$	−0.929221	−	3.16464i	−0.175606	−	0.598060i
$29$	−4.83034	−	5.57451i	−0.896972	−	1.03516i	−0.999184	−	0.0403982i	$-0.987137\pi$
$29$	−4.83034	−	5.57451i	−0.896972	−	1.03516i	0.102212	−	0.994763i	$-0.467408\pi$
$30$	−0.306813	−	0.426992i	−0.0560162	−	0.0779578i
$31$	−4.86195	+	1.42760i	−0.873232	+	0.256404i	−0.687489	−	0.726194i	$-0.741287\pi$
$31$	−4.86195	+	1.42760i	−0.873232	+	0.256404i	−0.185743	+	0.982598i	$0.559469\pi$
$32$	−3.50865	+	4.04920i	−0.620248	+	0.715804i
$33$	5.23764	+	2.35947i	0.911757	+	0.410731i
$34$	0.181270	+	0.209197i	0.0310876	+	0.0358770i
$35$	0.894372	+	0.574778i	0.151176	+	0.0971552i
$36$	4.68822	−	1.92345i	0.781369	−	0.320575i
$37$	0.276430	−	0.0811670i	0.0454447	−	0.0133438i	−0.258931	−	0.965896i	$-0.583370\pi$
$37$	0.276430	−	0.0811670i	0.0454447	−	0.0133438i	0.304376	+	0.952552i	$0.401552\pi$
$38$	−0.723436	−	1.12569i	−0.117357	−	0.182611i
$39$	−0.0798518	−	1.53821i	−0.0127865	−	0.246310i
$40$		−	1.11990i		−	0.177072i
$41$	−0.926082	+	6.44104i	−0.144630	+	1.00592i	0.780197	+	0.625534i	$0.215119\pi$
$41$	−0.926082	+	6.44104i	−0.144630	+	1.00592i	−0.924827	+	0.380388i	$0.875790\pi$
$42$	1.35911	−	1.30703i	0.209716	−	0.201678i
$43$	−4.21125	−	1.92321i	−0.642209	−	0.293287i	0.0675665	−	0.997715i	$-0.478477\pi$
$43$	−4.21125	−	1.92321i	−0.642209	−	0.293287i	−0.709776	+	0.704428i	$0.751204\pi$
$44$	2.80539	+	4.84925i	0.422929	+	0.731052i
$45$	−0.736064	+	1.45818i	−0.109726	+	0.217372i
$46$	2.03642	+	1.76457i	0.300254	+	0.260172i
$47$	4.65031	−	0.668613i	0.678317	−	0.0975272i	0.205459	−	0.978666i	$-0.434131\pi$
$47$	4.65031	−	0.668613i	0.678317	−	0.0975272i	0.472858	+	0.881139i	$0.343222\pi$
$48$	3.76002	+	0.895203i	0.542711	+	0.129211i
$49$	1.32407	−	2.89931i	0.189153	−	0.414187i
$50$	−1.71732	−	1.98189i	−0.242865	−	0.280281i
$51$	0.316195	−	0.799686i	0.0442761	−	0.111978i
$52$	0.812110	−	1.26367i	0.112619	−	0.175239i
$53$	2.31955	+	3.60929i	0.318615	+	0.495774i	0.963210	−	0.268750i	$-0.0866104\pi$
$53$	2.31955	+	3.60929i	0.318615	+	0.495774i	−0.644595	+	0.764524i	$0.722974\pi$
$54$	2.21355	+	1.86900i	0.301226	+	0.254338i
$55$	−1.70702	−	0.589127i	−0.230174	−	0.0794378i
$56$	3.97533	−	0.571566i	0.531226	−	0.0763787i
$57$	−2.06310	+	3.60887i	−0.273265	+	0.478006i
$58$	3.45965	−	2.22338i	0.454274	−	0.291944i
$59$	−8.48547	+	1.22003i	−1.10471	+	0.158834i	−0.670452	−	0.741953i	$-0.733900\pi$
$59$	−8.48547	+	1.22003i	−1.10471	+	0.158834i	−0.434262	+	0.900787i	$0.642991\pi$
$60$	−1.41276	+	0.735972i	−0.182386	+	0.0950136i
$61$	−5.96857	+	0.858151i	−0.764198	+	0.109875i	−0.513382	−	0.858160i	$-0.671608\pi$
$61$	−5.96857	+	0.858151i	−0.764198	+	0.109875i	−0.250815	+	0.968035i	$0.580699\pi$
$62$	−0.402064	−	2.79641i	−0.0510621	−	0.355145i
$63$	−5.55178	−	1.86860i	−0.699458	−	0.235422i
$64$	0.966462	+	1.11536i	0.120808	+	0.139420i
$65$	0.0689074	+	0.479261i	0.00854691	+	0.0594450i
$66$	−1.71769	+	2.70326i	−0.211434	+	0.332748i
$67$	−0.125710	+	0.874334i	−0.0153579	+	0.106817i	−0.996058	−	0.0886991i	$-0.971729\pi$
$67$	−0.125710	+	0.874334i	−0.0153579	+	0.106817i	0.980701	+	0.195516i	$0.0626381\pi$
$68$	0.705499	−	0.453397i	0.0855544	−	0.0549825i
$69$	1.93881	−	8.14333i	0.233405	−	0.980342i
$70$	−0.388165	+	0.447966i	−0.0463946	+	0.0535422i
$71$	−4.68574	+	4.06022i	−0.556096	+	0.481860i	−0.886978	−	0.461813i	$-0.847199\pi$
$71$	−4.68574	+	4.06022i	−0.556096	+	0.481860i	0.330882	+	0.943672i	$0.392654\pi$
$72$	1.50587	+	5.98398i	0.177468	+	0.705218i
$73$	4.18299	−	6.50886i	0.489582	−	0.761805i	−0.505289	−	0.862950i	$-0.668614\pi$
$73$	4.18299	−	6.50886i	0.489582	−	0.761805i	0.994872	+	0.101145i	$0.0322506\pi$
$74$	0.0228596	+	0.158992i	0.00265737	+	0.0184824i
$75$	−2.99556	+	7.57606i	−0.345898	+	0.874808i
$76$	−3.68764	+	1.68409i	−0.423002	+	0.193178i
$77$	1.22002	−	6.36009i	0.139034	−	0.724800i
$78$	0.855217	+	0.0779833i	0.0968343	+	0.00882987i
$79$	−13.4786	+	6.15546i	−1.51646	+	0.692543i	−0.987719	−	0.156241i	$-0.950062\pi$
$79$	−13.4786	+	6.15546i	−1.51646	+	0.692543i	−0.528739	+	0.848784i	$0.677335\pi$
$80$	−1.20264	−	0.172914i	−0.134459	−	0.0193323i
$81$	1.97229	−	8.78123i	0.219143	−	0.975693i
$82$	−3.48111	−	1.02214i	−0.384424	−	0.112877i
$83$	7.17381	−	4.61032i	0.787427	−	0.506049i	−0.0840635	−	0.996460i	$-0.526790\pi$
$83$	7.17381	−	4.61032i	0.787427	−	0.506049i	0.871491	+	0.490411i	$0.163154\pi$
$84$	−3.33352	−	4.63926i	−0.363717	−	0.506185i
$85$	−0.0761581	+	0.259371i	−0.00826051	+	0.0281327i
$86$	1.39550	−	2.17144i	0.150481	−	0.234152i
$87$	−11.0914	−	6.34067i	−1.18912	−	0.679791i
$88$	−6.33090	+	2.54096i	−0.674877	+	0.270867i
$89$	−7.26380	−	6.29412i	−0.769961	−	0.667175i	0.178546	−	0.983932i	$-0.442861\pi$
$89$	−7.26380	−	6.29412i	−0.769961	−	0.667175i	−0.948507	+	0.316757i	$0.897406\pi$
$90$	−0.746313	−	0.521909i	−0.0786683	−	0.0550140i
$91$	−1.66607	+	0.489203i	−0.174652	+	0.0512824i
$92$	6.16964	−	5.34603i	0.643230	−	0.557362i
$93$	−7.12747	+	5.12141i	−0.739085	+	0.531066i
$94$			2.61939i			0.270170i
$95$	0.542844	−	1.18866i	0.0556946	−	0.121954i
$96$	−3.41228	+	8.62997i	−0.348264	+	0.880792i
$97$	−0.898875	+	1.96826i	−0.0912670	+	0.199847i	−0.949761	−	0.312978i	$-0.898674\pi$
$97$	−0.898875	+	1.96826i	−0.0912670	+	0.199847i	0.858494	+	0.512824i	$0.171401\pi$
$98$	1.49497	+	0.960756i	0.151014	+	0.0970511i
$99$	9.91328	+	0.852556i	0.996322	+	0.0856851i
$100$	−6.68375	+	4.29539i	−0.668375	+	0.429539i
$101$	−1.06500	−	7.40723i	−0.105971	−	0.737047i	−0.971646	−	0.236440i	$-0.924019\pi$
$101$	−1.06500	−	7.40723i	−0.105971	−	0.737047i	0.865675	−	0.500607i	$-0.166890\pi$
$102$	0.416230	+	0.237949i	0.0412129	+	0.0235604i
$103$	2.44127	−	16.9794i	0.240546	−	1.67303i	−0.408866	−	0.912594i	$-0.634076\pi$
$103$	2.44127	−	16.9794i	0.240546	−	1.67303i	0.649412	−	0.760437i	$-0.275015\pi$
$104$	1.38235	+	1.19781i	0.135551	+	0.117455i
$105$	1.79135	+	0.426493i	0.174817	+	0.0416214i
$106$	−2.17589	+	0.993695i	−0.211341	+	0.0965162i
$107$	0.710049	+	1.55479i	0.0686430	+	0.150307i	0.940844	−	0.338841i	$-0.110035\pi$
$107$	0.710049	+	1.55479i	0.0686430	+	0.150307i	−0.872201	+	0.489148i	$0.837308\pi$
$108$	6.55917	−	5.83218i	0.631157	−	0.561202i
$109$	0.583885	−	1.98853i	0.0559261	−	0.190467i	−0.926792	−	0.375575i	$-0.877445\pi$
$109$	0.583885	−	1.98853i	0.0559261	−	0.190467i	0.982718	+	0.185108i	$0.0592635\pi$
$110$	0.460564	−	0.895297i	0.0439130	−	0.0853632i
$111$	0.405237	−	0.291182i	0.0384634	−	0.0276377i
$112$		−	4.35728i		−	0.411724i
$113$	8.63880	+	3.94521i	0.812670	+	0.371134i	0.778000	−	0.628265i	$-0.216234\pi$
$113$	8.63880	+	3.94521i	0.812670	+	0.371134i	0.0346707	+	0.999399i	$0.488962\pi$
$114$	−1.82791	−	1.42490i	−0.171199	−	0.133455i
$115$	−0.374491	+	2.60464i	−0.0349215	+	0.242884i
$116$	−5.17582	−	11.3335i	−0.480563	−	1.05229i
$117$	−1.01263	−	2.46819i	−0.0936176	−	0.228184i
$118$		−	4.77964i		−	0.440001i
$119$	−0.959561	−	0.137964i	−0.0879628	−	0.0126471i
$120$	−0.642236	−	1.83032i	−0.0586278	−	0.167084i
$121$	0.542688	+	10.9866i	0.0493353	+	0.998782i
$122$		−	3.36194i		−	0.304376i
$123$	2.18023	+	11.0581i	0.196585	+	0.997072i
$124$	−8.55927			−0.768645
$125$	1.48849	−	5.06932i	0.133134	−	0.453414i
$126$	1.47173	−	2.91556i	0.131112	−	0.259739i
$127$	−0.535863	−	0.0770454i	−0.0475501	−	0.00683667i	0.118499	−	0.992954i	$-0.462192\pi$
$127$	−0.535863	−	0.0770454i	−0.0475501	−	0.00683667i	−0.166049	+	0.986118i	$0.553101\pi$
$128$	−9.70685	+	6.23821i	−0.857972	+	0.551385i
$129$	−7.98560	−	0.728170i	−0.703093	−	0.0641118i
$130$	−0.269955			−0.0236766
$131$	−11.3115	+	3.32137i	−0.988293	+	0.290189i	−0.735644	−	0.677369i	$-0.763120\pi$
$131$	−11.3115	+	3.32137i	−0.988293	+	0.290189i	−0.252650	+	0.967558i	$0.581302\pi$
$132$	7.36595	+	6.31659i	0.641123	+	0.549788i
$133$	4.49646	+	1.32028i	0.389893	+	0.114483i
$134$	−0.472539	−	0.138750i	−0.0408212	−	0.0119862i
$135$	−0.366763	+	2.80530i	−0.0315659	+	0.241442i
$136$	0.424215	+	0.928901i	0.0363761	+	0.0796526i
$137$	−10.4813	+	16.3092i	−0.895474	+	1.39339i	0.0237783	+	0.999717i	$0.492430\pi$
$137$	−10.4813	+	16.3092i	−0.895474	+	1.39339i	−0.919253	+	0.393668i	$0.871206\pi$
$138$	4.34018	+	1.71610i	0.369461	+	0.146084i
$139$	15.7812	+	2.26899i	1.33854	+	0.192454i	0.774124	−	0.633034i	$-0.218191\pi$
$139$	15.7812	+	2.26899i	1.33854	+	0.192454i	0.564420	+	0.825488i	$0.309100\pi$
$140$	1.17600	+	1.35718i	0.0993904	+	0.114703i
$141$	7.21683	−	3.75959i	0.607767	−	0.316615i
$142$	−1.86890	−	2.90806i	−0.156834	−	0.244039i
$143$	2.55296	−	1.47694i	0.213490	−	0.123508i
$144$	6.65859	−	0.693194i	0.554882	−	0.0577661i
$145$	3.65319	+	1.66836i	0.303381	+	0.138549i
$146$	3.26011	+	2.82490i	0.269809	+	0.233790i
$147$	0.501322	−	5.49783i	0.0413483	−	0.453453i
$148$	0.486643			0.0400018
$149$	22.5677	−	6.62648i	1.84882	−	0.542862i	0.848921	−	0.528519i	$-0.177253\pi$
$149$	22.5677	−	6.62648i	1.84882	−	0.542862i	0.999897	−	0.0143429i	$-0.00456565\pi$
$150$	−3.94327	−	2.25428i	−0.321967	−	0.184061i
$151$	0.338242	+	1.15195i	0.0275258	+	0.0937442i	0.972110	−	0.234524i	$-0.0753532\pi$
$151$	0.338242	+	1.15195i	0.0275258	+	0.0937442i	−0.944585	+	0.328268i	$0.893535\pi$
$152$	−1.39077	−	4.73652i	−0.112806	−	0.384182i
$153$	0.0581748	−	1.48830i	0.00470316	−	0.120322i
$154$	3.41311	+	1.17793i	0.275036	+	0.0949207i
$155$	2.08509	−	1.80674i	0.167478	−	0.145121i
$156$	0.602596	−	2.53101i	0.0482463	−	0.202643i
$157$	5.47357	+	1.60718i	0.436838	+	0.128267i	0.492755	−	0.870168i	$-0.335990\pi$
$157$	5.47357	+	1.60718i	0.436838	+	0.128267i	−0.0559166	+	0.998435i	$0.517808\pi$
$158$	−2.32751	−	7.92676i	−0.185167	−	0.630619i
$159$	5.86082	+	4.56867i	0.464793	+	0.362319i
$160$	0.821875	−	2.79905i	0.0649749	−	0.221284i
$161$	−9.43687			−0.743730
$162$	4.68956	+	1.78519i	0.368447	+	0.140258i
$163$	2.17414	+	4.76071i	0.170292	+	0.372887i	0.975466	−	0.220152i	$-0.0706552\pi$
$163$	2.17414	+	4.76071i	0.170292	+	0.372887i	−0.805174	+	0.593039i	$0.797928\pi$
$164$	−4.56615	+	9.99846i	−0.356556	+	0.780749i
$165$	−3.12773	+	0.0160879i	−0.243493	+	0.00125244i
$166$	1.97506	+	4.32478i	0.153295	+	0.335668i
$167$	−7.52246	+	8.68139i	−0.582106	+	0.671786i	−0.968056	−	0.250734i	$-0.919328\pi$
$167$	−7.52246	+	8.68139i	−0.582106	+	0.671786i	0.385950	+	0.922520i	$0.373874\pi$
$168$	6.16933	−	3.21390i	0.475974	−	0.247957i
$169$	10.2710	+	6.60078i	0.790078	+	0.507752i
$170$	−0.137095	−	0.0626091i	−0.0105147	−	0.00480189i
$171$	−1.30225	+	7.08132i	−0.0995858	+	0.541522i
$172$	−5.91005	−	5.12109i	−0.450637	−	0.390479i
$173$	12.5594	+	8.07141i	0.954871	+	0.613658i	0.922574	−	0.385820i	$-0.126081\pi$
$173$	12.5594	+	8.07141i	0.954871	+	0.613658i	0.0322968	+	0.999478i	$0.489718\pi$
$174$	4.37925	−	5.61782i	0.331990	−	0.425886i
$175$	9.09068	+	1.30704i	0.687191	+	0.0988031i
$176$	1.75119	+	7.19097i	0.132001	+	0.542040i
$177$	−13.1686	+	6.86017i	−0.989815	+	0.515642i
$178$	4.04986	−	3.50922i	0.303550	−	0.263027i
$179$	12.4505	+	19.3733i	0.930591	+	1.44803i	0.893678	+	0.448710i	$0.148116\pi$
$179$	12.4505	+	19.3733i	0.930591	+	1.44803i	0.0369135	+	0.999318i	$0.488247\pi$
$180$	−1.88689	+	2.01302i	−0.140640	+	0.150042i
$181$	−0.790341	−	5.49694i	−0.0587456	−	0.408584i	−0.997883	−	0.0650415i	$-0.979282\pi$
$181$	−0.790341	−	5.49694i	−0.0587456	−	0.408584i	0.939137	−	0.343543i	$-0.111627\pi$
$182$	−0.137777	−	0.958263i	−0.0102127	−	0.0710312i
$183$	−9.26266	+	4.82536i	−0.684715	+	0.356701i
$184$	5.37434	+	8.36263i	0.396202	+	0.616502i
$185$	−0.118549	+	0.102723i	−0.00871590	+	0.00755237i
$186$	−2.26079	−	4.33977i	−0.165769	−	0.318207i
$187$	1.63904	−	0.157962i	0.119859	−	0.0115513i
$188$	7.85506	+	1.12939i	0.572889	+	0.0823690i
$189$	−10.1452	+	0.129842i	−0.737954	+	0.00944458i
$190$	0.612908	+	0.393892i	0.0444650	+	0.0285759i
$191$	−13.7811	−	11.9414i	−0.997166	−	0.864049i	−0.00644730	−	0.999979i	$-0.502052\pi$
$191$	−13.7811	−	11.9414i	−0.997166	−	0.864049i	−0.990718	+	0.135930i	$0.956598\pi$
$192$	2.21918	+	1.26865i	0.160155	+	0.0915569i
$193$	21.4210	+	9.78262i	1.54191	+	0.704168i	0.991425	−	0.130674i	$-0.0417142\pi$
$193$	21.4210	+	9.78262i	1.54191	+	0.704168i	0.550488	+	0.834843i	$0.314442\pi$
$194$	−1.01489	−	0.652232i	−0.0728650	−	0.0468275i
$195$	0.387464	+	0.743768i	0.0277469	+	0.0532623i
$196$	3.52570	−	4.06888i	0.251836	−	0.290634i
$197$	0.887347	+	1.94302i	0.0632209	+	0.138434i	0.938605	−	0.344993i	$-0.112119\pi$
$197$	0.887347	+	1.94302i	0.0632209	+	0.138434i	−0.875384	+	0.483428i	$0.839392\pi$
$198$	−1.25708	+	5.40314i	−0.0893366	+	0.383985i
$199$	6.73639	−	14.7506i	0.477530	−	1.04565i	−0.505605	−	0.862765i	$-0.668731\pi$
$199$	6.73639	−	14.7506i	0.477530	−	1.04565i	0.983135	−	0.182880i	$-0.0585421\pi$
$200$	−4.01892	−	8.80022i	−0.284181	−	0.622269i
$201$	0.295953	+	1.50107i	0.0208749	+	0.105877i
$202$	4.17229			0.293562
$203$	−4.05770	+	13.8193i	−0.284795	+	0.969922i
$204$	0.893026	−	1.14560i	0.0625244	−	0.0802080i
$205$	−0.998192	−	3.39953i	−0.0697167	−	0.237433i
$206$	9.17663	+	2.69450i	0.639366	+	0.187735i
$207$	−1.50130	−	14.4210i	−0.104347	−	1.00233i
$208$	1.49975	−	1.29954i	0.103989	−	0.0901067i
$209$	−7.95129	−	0.371772i	−0.550002	−	0.0257160i
$210$	−0.377503	+	0.954740i	−0.0260502	+	0.0658833i
$211$	−2.87866	−	9.80382i	−0.198175	−	0.674923i	−0.997278	−	0.0737288i	$-0.976510\pi$
$211$	−2.87866	−	9.80382i	−0.198175	−	0.674923i	0.799103	−	0.601194i	$-0.205308\pi$
$212$	2.04174	+	6.95352i	0.140227	+	0.477570i
$213$	−5.32975	+	9.32301i	−0.365188	+	0.638802i
$214$	−0.914374	+	0.268484i	−0.0625053	+	0.0183532i
$215$	2.52071			0.171911
$216$	5.89279	+	8.91638i	0.400954	+	0.606683i
$217$	7.47757	+	6.47935i	0.507611	+	0.439847i
$218$	1.05107	+	0.480008i	0.0711875	+	0.0325103i
$219$	3.10383	−	13.0367i	0.209738	−	0.880936i
$220$	−2.48625	−	1.76716i	−0.167623	−	0.119142i
$221$	−0.238698	−	0.371421i	−0.0160566	−	0.0249845i
$222$	0.128539	+	0.246740i	0.00862696	+	0.0165601i
$223$	−6.48994	−	7.48979i	−0.434598	−	0.501553i	0.495630	−	0.868534i	$-0.334937\pi$
$223$	−6.48994	−	7.48979i	−0.434598	−	0.501553i	−0.930229	+	0.366980i	$0.880392\pi$
$224$	10.3553	+	1.48887i	0.691892	+	0.0994790i
$225$	−0.551136	+	14.0999i	−0.0367424	+	0.939992i
$226$	−2.86268	+	4.45442i	−0.190423	+	0.296303i
$227$	−5.12741	−	11.2275i	−0.340318	−	0.745192i	0.659662	−	0.751563i	$-0.270700\pi$
$227$	−5.12741	−	11.2275i	−0.340318	−	0.745192i	−0.999980	+	0.00637018i	$0.997972\pi$
$228$	−5.06115	+	4.86718i	−0.335183	+	0.322337i
$229$	27.8341	+	8.17282i	1.83933	+	0.540075i	0.999994	−	0.00354331i	$-0.00112787\pi$
$229$	27.8341	+	8.17282i	1.83933	+	0.540075i	0.839333	+	0.543618i	$0.182946\pi$
$230$	−1.40770	−	0.413337i	−0.0928208	−	0.0272546i
$231$	−1.65341	−	11.0943i	−0.108786	−	0.729953i
$232$	14.5570	−	4.27433i	0.955716	−	0.280624i
$233$	−24.9601			−1.63519			−0.817594	−	0.575795i	$-0.804693\pi$
$233$	−24.9601			−1.63519			−0.817594	+	0.575795i	$0.804693\pi$
$234$	1.44245	−	0.362994i	0.0942961	−	0.0237296i
$235$	−2.15193	+	1.38296i	−0.140377	+	0.0902146i
$236$	−14.3332	−	2.06081i	−0.933013	−	0.134147i
$237$	−18.4988	+	17.7899i	−1.20163	+	1.15558i
$238$	0.152275	−	0.518601i	0.00987052	−	0.0336159i
$239$	29.5724			1.91288			0.956440	−	0.291929i	$-0.0942970\pi$
$239$	29.5724			1.91288			0.956440	+	0.291929i	$0.0942970\pi$
$240$	−2.06471	+	0.407082i	−0.133276	+	0.0262770i
$241$			5.69198i			0.366653i	0.983052	+	0.183326i	$0.0586865\pi$
$241$			5.69198i			0.366653i	−0.983052	+	0.183326i	$0.941314\pi$
$242$	−6.10618	−	0.572255i	−0.392520	−	0.0367859i
$243$	−1.81240	−	15.4827i	−0.116266	−	0.993218i
$244$	−10.0818	−	1.44955i	−0.645422	−	0.0927977i
$245$			1.73543i			0.110872i
$246$	−6.27555	+	0.325778i	−0.400114	+	0.0207709i
$247$	0.886616	+	1.94142i	0.0564140	+	0.123529i
$248$	1.48327	−	10.3164i	0.0941879	−	0.655091i
$249$	9.08066	−	11.6489i	0.575463	−	0.738221i
$250$	2.67947	+	1.22367i	0.169465	+	0.0773920i
$251$		−	25.8791i		−	1.63348i	−0.577009	−	0.816738i	$-0.695780\pi$
$251$		−	25.8791i		−	1.63348i	0.577009	−	0.816738i	$-0.304220\pi$
$252$	−8.10867	−	5.67052i	−0.510798	−	0.357209i
$253$	15.5740	−	3.79269i	0.979128	−	0.238444i
$254$	0.0850373	−	0.289610i	0.00533572	−	0.0181718i
$255$	0.0242731	+	0.467579i	0.00152004	+	0.0292810i
$256$	−1.44629	−	3.16692i	−0.0903928	−	0.197933i
$257$	5.07060	−	2.31567i	0.316296	−	0.144447i	−0.250941	−	0.968002i	$-0.580740\pi$
$257$	5.07060	−	2.31567i	0.316296	−	0.144447i	0.567236	+	0.823555i	$0.308013\pi$
$258$	1.03548	−	4.34920i	0.0644661	−	0.270769i
$259$	−0.425142	−	0.368388i	−0.0264171	−	0.0228905i
$260$	−0.116395	+	0.809544i	−0.00721850	+	0.0502058i
$261$	−21.7635	−	4.00230i	−1.34712	−	0.247736i
$262$	−0.935418	−	6.50598i	−0.0577903	−	0.401941i
$263$	15.5708	−	10.0068i	0.960138	−	0.617043i	0.0361019	−	0.999348i	$-0.488506\pi$
$263$	15.5708	−	10.0068i	0.960138	−	0.617043i	0.924036	+	0.382305i	$0.124870\pi$
$264$	−8.88979	+	7.78346i	−0.547128	+	0.479039i
$265$	−1.96517	−	1.26294i	−0.120719	−	0.0775815i
$266$	−1.08539	+	2.37668i	−0.0665498	+	0.145724i
$267$	−15.4812	−	6.12123i	−0.947432	−	0.374613i
$268$	−0.619827	+	1.35723i	−0.0378620	+	0.0829061i
$269$			21.7666i			1.32713i	0.748118	+	0.663566i	$0.230958\pi$
$269$			21.7666i			1.32713i	−0.748118	+	0.663566i	$0.769042\pi$
$270$	−1.51904	−	0.424993i	−0.0924461	−	0.0258643i
$271$	−11.9424	+	10.3481i	−0.725447	+	0.628604i	−0.937230	−	0.348713i	$-0.886619\pi$
$271$	−11.9424	+	10.3481i	−0.725447	+	0.628604i	0.211782	+	0.977317i	$0.432073\pi$
$272$	1.06303	−	0.312133i	0.0644556	−	0.0189259i
$273$	−2.44241	+	1.75498i	−0.147822	+	0.106216i
$274$	−8.16880	−	7.07831i	−0.493495	−	0.427616i
$275$	−15.5280	+	1.49650i	−0.936371	+	0.0902420i
$276$	7.01759	−	12.2755i	0.422409	−	0.738896i
$277$	12.9235	−	20.1094i	0.776501	−	1.20826i	−0.197186	−	0.980366i	$-0.563180\pi$
$277$	12.9235	−	20.1094i	0.776501	−	1.20826i	0.973686	−	0.227893i	$-0.0731835\pi$
$278$	−2.50436	+	8.52905i	−0.150201	+	0.511539i
$279$	−8.71184	+	12.4577i	−0.521564	+	0.745820i
$280$	−1.83959	+	1.18223i	−0.109936	+	0.0706518i
$281$	11.8563	+	3.48132i	0.707286	+	0.207678i	0.615541	−	0.788105i	$-0.288937\pi$
$281$	11.8563	+	3.48132i	0.707286	+	0.207678i	0.0917448	+	0.995783i	$0.470756\pi$
$282$	1.50216	+	4.28102i	0.0894522	+	0.254931i
$283$	−3.02547	−	0.434998i	−0.179846	−	0.0258579i	0.0518034	−	0.998657i	$-0.483503\pi$
$283$	−3.02547	−	0.434998i	−0.179846	−	0.0258579i	−0.231649	+	0.972799i	$0.574412\pi$
$284$	−9.52652	+	4.35062i	−0.565295	+	0.258162i
$285$	0.205532	−	2.25401i	0.0121747	−	0.133516i
$286$	0.612506	+	1.52608i	0.0362182	+	0.0902391i
$287$	11.5579	−	5.27832i	0.682242	−	0.311569i
$288$	−0.627805	+	16.0613i	−0.0369938	+	0.946422i
$289$	2.38427	+	16.5830i	0.140251	+	0.975469i
$290$	−1.21057	+	1.88369i	−0.0710873	+	0.110614i
$291$	−0.340334	+	3.73233i	−0.0199507	+	0.218793i
$292$	9.87698	−	8.55845i	0.578007	−	0.500846i
$293$	−3.38471	+	3.90616i	−0.197737	+	0.228200i	−0.845955	−	0.533254i	$-0.820969\pi$
$293$	−3.38471	+	3.90616i	−0.197737	+	0.228200i	0.648218	+	0.761454i	$0.275514\pi$
$294$	2.99428	+	0.712893i	0.174630	+	0.0415768i
$295$	3.92666	−	2.52351i	0.228619	−	0.146924i
$296$	−0.0843325	+	0.586545i	−0.00490173	+	0.0340923i
$297$	16.6908	−	4.29164i	0.968497	−	0.249026i
$298$	1.86626	+	12.9801i	0.108109	+	0.751918i
$299$	−2.81450	−	3.24811i	−0.162767	−	0.187843i
$300$	−8.46035	+	10.8532i	−0.488458	+	0.626608i
$301$	1.28650	+	8.94779i	0.0741525	+	0.515742i
$302$	−0.662558	+	0.0952614i	−0.0381259	+	0.00548168i
$303$	−5.98846	−	11.4953i	−0.344028	−	0.660389i
$304$	−5.30119	+	0.762197i	−0.304044	+	0.0437150i
$305$	2.76196	−	1.77501i	0.158150	−	0.101637i
$306$	0.816726	+	0.150196i	0.0466891	+	0.00858612i
$307$	11.4167	−	1.64147i	0.651584	−	0.0936836i	0.191407	−	0.981511i	$-0.438695\pi$
$307$	11.4167	−	1.64147i	0.651584	−	0.0936836i	0.460177	+	0.887827i	$0.347786\pi$
$308$	5.00401	−	9.72738i	0.285130	−	0.554269i
$309$	−5.74737	−	29.1504i	−0.326956	−	1.65831i
$310$	0.831631	+	1.29404i	0.0472335	+	0.0734967i
$311$	−3.59001	+	5.58616i	−0.203571	+	0.316762i	−0.927995	−	0.372592i	$-0.878469\pi$
$311$	−3.59001	+	5.58616i	−0.203571	+	0.316762i	0.724425	+	0.689354i	$0.242105\pi$
$312$	2.94617	+	1.16491i	0.166794	+	0.0659501i
$313$	−2.29297	−	2.64623i	−0.129606	−	0.149574i	0.687237	−	0.726433i	$-0.258823\pi$
$313$	−2.29297	−	2.64623i	−0.129606	−	0.149574i	−0.816843	+	0.576860i	$0.804278\pi$
$314$	−1.32126	+	2.89315i	−0.0745628	+	0.163270i
$315$	3.17228	−	0.330251i	0.178738	−	0.0186075i
$316$	−24.7744	+	3.56202i	−1.39367	+	0.200379i
$317$	−11.9740	−	10.3755i	−0.672525	−	0.582746i	0.250205	−	0.968193i	$-0.419502\pi$
$317$	−11.9740	−	10.3755i	−0.672525	−	0.582746i	−0.922730	+	0.385447i	$0.874047\pi$
$318$	−2.98632	+	2.87187i	−0.167465	+	0.161047i
$319$	1.14259	−	24.4372i	0.0639727	−	1.36822i
$320$	−0.730936	−	0.333807i	−0.0408605	−	0.0186604i
$321$	2.05211	+	2.13389i	0.114538	+	0.119102i
$322$	0.748780	−	5.20788i	0.0417279	−	0.290224i
$323$			1.19156i			0.0663003i
$324$	7.37542	−	13.2934i	0.409746	−	0.738522i
$325$	2.26137	+	3.51877i	0.125438	+	0.195186i
$326$	−2.79978	+	0.822089i	−0.155065	+	0.0455313i
$327$	−0.186096	−	3.58482i	−0.0102911	−	0.198241i
$328$	−11.2597	−	7.23620i	−0.621715	−	0.399552i
$329$	−6.00741	−	6.93292i	−0.331199	−	0.382224i
$330$	0.239295	−	1.72736i	0.0131727	−	0.0950879i
$331$	−14.8916	+	17.1858i	−0.818514	+	0.944616i	−0.999242	−	0.0389173i	$-0.987609\pi$
$331$	−14.8916	+	17.1858i	−0.818514	+	0.944616i	0.180728	+	0.983533i	$0.442155\pi$
$332$	13.8208	−	4.05815i	0.758514	−	0.222720i
$333$	0.495318	−	0.708289i	0.0271432	−	0.0388140i
$334$	−4.19407	−	4.84022i	−0.229489	−	0.264845i
$335$	−0.135499	−	0.461466i	−0.00740308	−	0.0252126i
$336$	−2.49879	−	7.12136i	−0.136320	−	0.388502i
$337$	20.5385	+	9.37963i	1.11880	+	0.510941i	0.886976	−	0.461816i	$-0.152802\pi$
$337$	20.5385	+	9.37963i	1.11880	+	0.510941i	0.231828	+	0.972757i	$0.425529\pi$
$338$	−4.45771	+	5.14447i	−0.242467	+	0.279822i
$339$	16.3814	+	1.49374i	0.889714	+	0.0811289i
$340$	−0.246863	+	0.384126i	−0.0133880	+	0.0208322i
$341$	−14.9445	−	7.68785i	−0.809292	−	0.416320i
$342$	−3.80460	−	1.28054i	−0.205729	−	0.0692439i
$343$	−19.6894	+	2.83090i	−1.06313	+	0.152854i
$344$	7.19656	−	6.23586i	0.388013	−	0.336215i
$345$	0.881647	+	4.47168i	0.0474663	+	0.240747i
$346$	−5.45087	+	6.29064i	−0.293040	+	0.338187i
$347$	21.7640	+	13.9869i	1.16835	+	0.750854i	0.973209	−	0.229921i	$-0.0738467\pi$
$347$	21.7640	+	13.9869i	1.16835	+	0.750854i	0.195143	+	0.980775i	$0.437483\pi$
$348$	−14.9586	−	15.5547i	−0.801866	−	0.833821i
$349$	8.34577	−	3.81138i	0.446739	−	0.204019i	−0.179326	−	0.983790i	$-0.557392\pi$
$349$	8.34577	−	3.81138i	0.446739	−	0.204019i	0.626065	+	0.779771i	$0.284664\pi$
$350$	−1.44262	+	4.91312i	−0.0771114	+	0.262617i
$351$	−3.07044	−	3.45318i	−0.163888	−	0.184317i
$352$	−17.6881	+	1.70467i	−0.942776	+	0.0908594i
$353$	3.49531	+	11.9039i	0.186036	+	0.633582i	0.998706	+	0.0508570i	$0.0161953\pi$
$353$	3.49531	+	11.9039i	0.186036	+	0.633582i	−0.812670	+	0.582725i	$0.801987\pi$
$354$	−2.74100	−	7.81164i	−0.145683	−	0.415184i
$355$	1.40236	−	3.07075i	0.0744297	−	0.162978i
$356$	−8.77734	−	13.6578i	−0.465198	−	0.723862i
$357$	−1.64738	+	0.324802i	−0.0871889	+	0.0171903i
$358$	−11.6793	+	5.33377i	−0.617272	+	0.281899i
$359$	−7.48977	−	2.19919i	−0.395295	−	0.116069i	0.0780430	−	0.996950i	$-0.475133\pi$
$359$	−7.48977	−	2.19919i	−0.395295	−	0.116069i	−0.473338	+	0.880881i	$0.656951\pi$
$360$	−2.09929	−	2.62309i	−0.110642	−	0.138249i
$361$	−1.88423	+	13.1051i	−0.0991702	+	0.689744i
$362$	3.09628			0.162737
$363$	7.18750	+	17.6448i	0.377246	+	0.926113i
$364$	−2.93305			−0.153734
$365$	−0.599523	+	4.16977i	−0.0313805	+	0.218256i
$366$	−1.92799	−	5.49461i	−0.100778	−	0.287208i
$367$	−21.4169	−	6.28857i	−1.11795	−	0.328261i	−0.329991	−	0.943984i	$-0.607046\pi$
$367$	−21.4169	−	6.28857i	−1.11795	−	0.328261i	−0.787963	+	0.615723i	$0.788864\pi$
$368$	9.81028	−	4.48021i	0.511396	−	0.233547i
$369$	9.90480	+	16.8225i	0.515623	+	0.875745i
$370$	−0.0472830	−	0.0735737i	−0.00245812	−	0.00382492i
$371$	3.48010	−	7.62035i	0.180678	−	0.395629i
$372$	−13.9889	+	4.90853i	−0.725291	+	0.254495i
$373$	8.83969	+	30.1052i	0.457702	+	1.55879i	0.788467	+	0.615077i	$0.210875\pi$
$373$	8.83969	+	30.1052i	0.457702	+	1.55879i	−0.330765	+	0.943713i	$0.607307\pi$
$374$	−0.0428784	+	0.917064i	−0.00221719	+	0.0474203i
$375$	−0.474411	−	9.13869i	−0.0244985	−	0.471920i
$376$	−2.72247	+	9.27190i	−0.140401	+	0.478161i
$377$	−5.96668	+	2.72489i	−0.307300	+	0.140339i
$378$	0.733327	−	5.60908i	0.0377183	−	0.288500i
$379$	−20.3671	−	13.0892i	−1.04619	−	0.672344i	−0.0996787	−	0.995020i	$-0.531781\pi$
$379$	−20.3671	−	13.0892i	−1.04619	−	0.672344i	−0.946510	+	0.322675i	$0.895418\pi$
$380$	1.44547	−	1.66816i	0.0741511	−	0.0855750i
$381$	−0.919975	+	0.181384i	−0.0471317	+	0.00929260i
$382$	7.68351	−	6.65780i	0.393123	−	0.340643i
$383$	4.38460	−	0.630411i	0.224043	−	0.0322125i	−0.0293791	−	0.999568i	$-0.509353\pi$
$383$	4.38460	−	0.630411i	0.224043	−	0.0322125i	0.253422	+	0.967356i	$0.418444\pi$
$384$	−12.2870	+	15.7621i	−0.627018	+	0.804357i
$385$	0.834304	+	3.42592i	0.0425200	+	0.174601i
$386$	−7.09836	+	11.0453i	−0.361297	+	0.562189i
$387$	−13.4689	+	3.38946i	−0.684664	+	0.172296i
$388$	−2.39350	+	2.76225i	−0.121512	+	0.140232i
$389$	−9.48665	−	4.33241i	−0.480992	−	0.219662i	0.160137	−	0.987095i	$-0.448806\pi$
$389$	−9.48665	−	4.33241i	−0.480992	−	0.219662i	−0.641129	+	0.767433i	$0.721534\pi$
$390$	−0.441203	+	0.154813i	−0.0223412	+	0.00783924i
$391$	−0.676010	−	2.30228i	−0.0341873	−	0.116431i
$392$	4.29319	+	4.95460i	0.216839	+	0.250245i
$393$	−16.5824	+	11.9152i	−0.836470	+	0.601042i
$394$	−1.14269	+	0.335525i	−0.0575680	+	0.0169035i
$395$	5.28329	−	6.09724i	0.265831	−	0.306786i
$396$	15.6610	+	6.09938i	0.786995	+	0.306505i
$397$	−20.1093	−	23.2074i	−1.00926	−	1.16475i	−0.986292	−	0.165009i	$-0.947235\pi$
$397$	−20.1093	−	23.2074i	−1.00926	−	1.16475i	−0.0229656	−	0.999736i	$-0.507311\pi$
$398$	7.60586	+	4.88799i	0.381247	+	0.245013i
$399$	8.10598	−	0.420800i	0.405806	−	0.0210664i
$400$	−10.0709	+	2.95709i	−0.503546	+	0.147854i
$401$	11.5571	+	17.9832i	0.577135	+	0.898040i	0.999967	−	0.00816860i	$-0.00260018\pi$
$401$	11.5571	+	17.9832i	0.577135	+	0.898040i	−0.422832	+	0.906208i	$0.638964\pi$
$402$	−0.851868	+	0.0442225i	−0.0424873	+	0.00220562i
$403$			4.50616i			0.224468i
$404$	1.79894	−	12.5119i	0.0895008	−	0.622491i
$405$	1.00935	+	4.79519i	0.0501549	+	0.238275i
$406$	−7.30440	−	3.33581i	−0.362511	−	0.165553i
$407$	0.849682	+	0.437098i	0.0421172	+	0.0216662i
$408$	1.22602	+	1.27488i	0.0606971	+	0.0631160i
$409$	10.1824	+	8.82313i	0.503489	+	0.436276i	0.869206	−	0.494450i	$-0.164631\pi$
$409$	10.1824	+	8.82313i	0.503489	+	0.436276i	−0.365717	+	0.930726i	$0.619176\pi$
$410$	1.95528	−	0.281127i	0.0965645	−	0.0138839i
$411$	−7.77723	+	32.6657i	−0.383622	+	1.61128i
$412$	12.0369	−	26.3572i	0.593017	−	1.29853i
$413$	10.9618	+	12.6506i	0.539395	+	0.622495i
$414$	8.07755	+	0.315736i	0.396990	+	0.0155176i
$415$	−2.51020	+	3.90595i	−0.123221	+	0.191736i
$416$	2.57595	+	4.00826i	0.126297	+	0.196521i
$417$	27.0933	−	5.34178i	1.32677	−	0.261588i
$418$	0.836072	−	4.35854i	0.0408936	−	0.213183i
$419$	−30.0872	+	4.32589i	−1.46986	+	0.211334i	−0.830260	−	0.557376i	$-0.811808\pi$
$419$	−30.0872	+	4.32589i	−1.46986	+	0.211334i	−0.639598	+	0.768710i	$0.720899\pi$
$420$	2.70032	+	1.54371i	0.131762	+	0.0753253i
$421$	9.40077	−	6.04151i	0.458165	−	0.294445i	−0.291127	−	0.956684i	$-0.594030\pi$
$421$	9.40077	−	6.04151i	0.458165	−	0.294445i	0.749292	+	0.662239i	$0.230394\pi$
$422$	5.63880	−	0.810736i	0.274492	−	0.0394660i
$423$	9.63885	−	10.2832i	0.468657	−	0.499986i
$424$	−8.73482	+	1.25588i	−0.424200	+	0.0609908i
$425$	0.332336	+	2.31145i	0.0161207	+	0.112122i
$426$	−4.72215	−	3.68105i	−0.228789	−	0.178347i
$427$	7.71040	+	8.89827i	0.373132	+	0.430618i
$428$	0.410889	+	2.85780i	0.0198611	+	0.138137i
$429$	3.32547	−	3.87792i	0.160555	−	0.187228i
$430$	−0.200009	+	1.39109i	−0.00964527	+	0.0670843i
$431$	−5.09868	+	3.27672i	−0.245595	+	0.157834i	−0.657647	−	0.753326i	$-0.728448\pi$
$431$	−5.09868	+	3.27672i	−0.245595	+	0.157834i	0.412053	+	0.911160i	$0.364812\pi$
$432$	10.4850	−	4.95146i	0.504459	−	0.238227i
$433$	2.39404	−	2.76287i	0.115050	−	0.132775i	−0.695303	−	0.718717i	$-0.744730\pi$
$433$	2.39404	−	2.76287i	0.115050	−	0.132775i	0.810353	+	0.585942i	$0.199275\pi$
$434$	−4.16904	+	3.61250i	−0.200120	+	0.173405i
$435$	6.92738	+	0.631676i	0.332142	+	0.0302865i
$436$	1.89264	−	2.94500i	0.0906409	−	0.141040i
$437$	1.65074	+	11.4812i	0.0789658	+	0.549219i
$438$	6.94820	+	2.74731i	0.331998	+	0.131271i
$439$	0.968648	−	0.442367i	0.0462311	−	0.0211130i	−0.392165	−	0.919895i	$-0.628274\pi$
$439$	0.968648	−	0.442367i	0.0462311	−	0.0211130i	0.438396	+	0.898782i	$0.355547\pi$
$440$	2.56079	−	2.69041i	0.122081	−	0.128260i
$441$	−2.33353	−	9.27291i	−0.111121	−	0.441567i
$442$	0.223914	−	0.102258i	0.0106505	−	0.00486392i
$443$	−12.4210	−	1.78587i	−0.590140	−	0.0848494i	−0.159226	−	0.987242i	$-0.550900\pi$
$443$	−12.4210	−	1.78587i	−0.590140	−	0.0848494i	−0.430914	+	0.902393i	$0.641809\pi$
$444$	0.795349	−	0.279078i	0.0377456	−	0.0132445i
$445$	5.02117	+	1.47435i	0.238026	+	0.0698908i
$446$	4.64830	−	2.98728i	0.220104	−	0.141452i
$447$	33.0836	−	23.7721i	1.56480	−	1.12438i
$448$	0.811871	−	2.76498i	0.0383573	−	0.130633i
$449$	15.9661	−	24.8437i	0.753486	−	1.17245i	−0.226622	−	0.973983i	$-0.572768\pi$
$449$	15.9661	−	24.8437i	0.753486	−	1.17245i	0.980108	−	0.198464i	$-0.0635954\pi$
$450$	−7.73750	−	1.42292i	−0.364749	−	0.0670773i
$451$	−16.9530	+	13.3561i	−0.798288	+	0.628915i
$452$	12.1237	+	10.5052i	0.570249	+	0.494124i
$453$	1.21342	+	1.68872i	0.0570116	+	0.0793431i
$454$	6.60288	−	1.93878i	0.309888	−	0.0909915i
$455$	0.714508	−	0.619125i	0.0334967	−	0.0290250i
$456$	−4.98929	−	6.94359i	−0.233645	−	0.325164i
$457$			8.75834i			0.409698i	0.978794	+	0.204849i	$0.0656703\pi$
$457$			8.75834i			0.409698i	−0.978794	+	0.204849i	$0.934330\pi$
$458$	−6.71882	+	14.7122i	−0.313950	+	0.687454i
$459$	−0.758427	−	2.46578i	−0.0354003	−	0.115093i
$460$	−1.84647	+	4.04320i	−0.0860920	+	0.188515i
$461$	8.37860	+	5.38460i	0.390230	+	0.250786i	0.721013	−	0.692921i	$-0.243677\pi$
$461$	8.37860	+	5.38460i	0.390230	+	0.250786i	−0.330783	+	0.943707i	$0.607313\pi$
$462$	6.25376	−	0.0321672i	0.290951	−	0.00149655i
$463$	16.6193	−	10.6806i	0.772363	−	0.496368i	−0.0941281	−	0.995560i	$-0.530006\pi$
$463$	16.6193	−	10.6806i	0.772363	−	0.496368i	0.866491	+	0.499193i	$0.166370\pi$
$464$	−2.34251	−	16.2925i	−0.108748	−	0.756360i
$465$	2.37166	−	4.14860i	0.109983	−	0.192387i
$466$	1.98049	−	13.7746i	0.0917442	−	0.638095i
$467$	−15.2980	−	13.2558i	−0.707906	−	0.613404i	0.224646	−	0.974440i	$-0.427877\pi$
$467$	−15.2980	−	13.2558i	−0.707906	−	0.613404i	−0.932552	+	0.361037i	$0.882423\pi$
$468$	−0.466615	−	4.48215i	−0.0215693	−	0.207188i
$469$	1.56892	−	0.716500i	0.0724459	−	0.0330849i
$470$	−0.592461	−	1.29731i	−0.0273282	−	0.0598404i
$471$	9.86745	−	0.512242i	0.454668	−	0.0236029i
$472$	4.96773	−	16.9185i	0.228658	−	0.778739i
$473$	−5.71928	−	14.2498i	−0.262973	−	0.655207i
$474$	−8.34978	−	11.6204i	−0.383518	−	0.533743i
$475$		−	11.2886i		−	0.517957i
$476$	−1.48953	−	0.680246i	−0.0682725	−	0.0311790i
$477$	12.1987	+	4.10581i	0.558540	+	0.187992i
$478$	−2.34646	+	16.3200i	−0.107324	+	0.746458i
$479$	−11.4309	−	25.0303i	−0.522293	−	1.14366i	−0.968564	−	0.248765i	$-0.919975\pi$
$479$	−11.4309	−	25.0303i	−0.522293	−	1.14366i	0.446271	−	0.894898i	$-0.352752\pi$
$480$	−0.261948	−	5.04597i	−0.0119562	−	0.230316i
$481$		−	0.256201i		−	0.0116818i
$482$	−3.14120	−	0.451637i	−0.143078	−	0.0205715i
$483$	−15.4232	+	5.41181i	−0.701781	+	0.246246i
$484$	−4.34885	+	18.0645i	−0.197675	+	0.821116i
$485$		−	1.17813i		−	0.0534963i
$486$	8.68819	+	0.228296i	0.394104	+	0.0103557i
$487$	−19.7878			−0.896671			−0.448335	−	0.893865i	$-0.647983\pi$
$487$	−19.7878			−0.896671			−0.448335	+	0.893865i	$0.647983\pi$
$488$	3.49424	−	11.9003i	0.158177	−	0.538701i
$489$	6.28348	+	6.53388i	0.284149	+	0.295472i
$490$	−0.957720	−	0.137699i	−0.0432654	−	0.00622062i
$491$	2.08091	−	1.33732i	0.0939104	−	0.0603525i	−0.492843	−	0.870118i	$-0.664042\pi$
$491$	2.08091	−	1.33732i	0.0939104	−	0.0603525i	0.586753	+	0.809766i	$0.300406\pi$
$492$	−1.72884	+	18.9596i	−0.0779422	+	0.854767i
$493$	−3.66210			−0.164933
$494$	−1.14175	+	0.335248i	−0.0513698	+	0.0150835i
$495$	−5.10260	+	1.81997i	−0.229345	+	0.0818014i
$496$	−10.8496	−	3.18572i	−0.487160	−	0.143043i
$497$	11.6160	+	3.41076i	0.521049	+	0.152994i
$498$	5.70812	+	5.93559i	0.255787	+	0.265980i
$499$	−1.92941	−	4.22482i	−0.0863723	−	0.189129i	0.861517	−	0.507729i	$-0.169515\pi$
$499$	−1.92941	−	4.22482i	−0.0863723	−	0.189129i	−0.947889	+	0.318600i	$0.896787\pi$
$500$	4.82486	−	7.50763i	0.215774	−	0.335751i
$501$	−7.31584	+	18.5024i	−0.326847	+	0.826628i
$502$	14.2818	+	2.05341i	0.637427	+	0.0916482i
$503$	−2.57734	−	2.97441i	−0.114918	−	0.132622i	0.695376	−	0.718646i	$-0.255238\pi$
$503$	−2.57734	−	2.97441i	−0.114918	−	0.132622i	−0.810294	+	0.586024i	$0.800692\pi$
$504$	8.23980	−	8.79062i	0.367030	−	0.391565i
$505$	2.20285	+	3.42770i	0.0980256	+	0.152531i
$506$	0.857314	+	8.89567i	0.0381122	+	0.395461i
$507$	20.5719	+	4.89786i	0.913630	+	0.217522i
$508$	−0.831822	−	0.379880i	−0.0369061	−	0.0168545i
$509$	−7.85769	−	6.80873i	−0.348286	−	0.301792i	0.463096	−	0.886308i	$-0.346739\pi$
$509$	−7.85769	−	6.80873i	−0.348286	−	0.301792i	−0.811382	+	0.584517i	$0.801284\pi$
$510$	−0.259967	−	0.0237051i	−0.0115115	−	0.00104968i
$511$	−15.1075			−0.668316
$512$	−20.2798	+	5.95470i	−0.896251	+	0.263163i
$513$	1.93261	+	12.3202i	0.0853270	+	0.543951i
$514$	0.875602	+	2.98203i	0.0386212	+	0.131532i
$515$	2.63136	+	8.96159i	0.115952	+	0.394895i
$516$	−12.5960	−	4.98042i	−0.554506	−	0.219251i
$517$	12.7006	+	9.02726i	0.558571	+	0.397018i
$518$	0.237034	−	0.205391i	0.0104147	−	0.00902436i
$519$	25.1553	+	5.98909i	1.10419	+	0.262892i
$520$	−0.955563	−	0.280579i	−0.0419042	−	0.0123042i
$521$	−1.85108	−	6.30420i	−0.0810972	−	0.276192i	0.908955	−	0.416895i	$-0.136882\pi$
$521$	−1.85108	−	6.30420i	−0.0810972	−	0.276192i	−0.990052	+	0.140703i	$0.955064\pi$
$522$	3.93557	−	11.6929i	0.172255	−	0.511785i
$523$	10.5603	−	35.9652i	0.461771	−	1.57265i	−0.318952	−	0.947771i	$-0.603331\pi$
$523$	10.5603	−	35.9652i	0.461771	−	1.57265i	0.780723	−	0.624877i	$-0.214851\pi$
$524$	−19.9135			−0.869926
$525$	15.6070	−	3.07711i	0.681145	−	0.134296i
$526$	4.28689	+	9.38699i	0.186917	+	0.409292i
$527$	−1.04509	+	2.28842i	−0.0455247	+	0.0996852i
$528$	6.98592	+	10.7483i	0.304023	+	0.467762i
$529$	−0.148552	−	0.325283i	−0.00645878	−	0.0141428i
$530$	0.852898	−	0.984297i	0.0370475	−	0.0427551i
$531$	−17.5881	+	18.7639i	−0.763260	+	0.814282i
$532$	6.65923	+	4.27963i	0.288714	+	0.185545i
$533$	5.26385	+	2.40392i	0.228003	+	0.104125i
$534$	4.60646	−	8.05782i	0.199341	−	0.348696i
$535$	−0.703334	−	0.609442i	−0.0304078	−	0.0263485i
$536$	−1.52844	−	0.982271i	−0.0660187	−	0.0424276i
$537$	31.4586	+	24.5229i	1.35754	+	1.05824i
$538$	−12.0122	−	1.72709i	−0.517883	−	0.0744603i
$539$	9.81053	−	3.93754i	0.422569	−	0.169602i
$540$	−1.92943	+	4.37208i	−0.0830295	+	0.188145i
$541$	−23.3982	+	20.2747i	−1.00597	+	0.871676i	−0.991745	−	0.128223i	$-0.959073\pi$
$541$	−23.3982	+	20.2747i	−1.00597	+	0.871676i	−0.0142223	+	0.999899i	$0.504527\pi$
$542$	−4.76318	−	7.41166i	−0.204596	−	0.318358i
$543$	−4.44406	−	8.53073i	−0.190713	−	0.366089i
$544$	0.378567	+	2.63299i	0.0162309	+	0.112889i
$545$	0.160590	+	1.11693i	0.00687891	+	0.0478439i
$546$	−0.774718	−	1.48713i	−0.0331549	−	0.0636434i
$547$	−14.4892	−	22.5456i	−0.619513	−	0.963981i	−0.999244	−	0.0388843i	$-0.987620\pi$
$547$	−14.4892	−	22.5456i	−0.619513	−	0.963981i	0.379730	−	0.925097i	$-0.376017\pi$
$548$	−24.7486	+	21.4448i	−1.05721	+	0.916076i
$549$	−12.3713	+	13.1983i	−0.527993	+	0.563288i
$550$	0.406221	−	8.68808i	0.0173213	−	0.370461i
$551$	17.5227	+	2.51938i	0.746492	+	0.107329i
$552$	13.5794	+	10.5855i	0.577976	+	0.450548i
$553$	24.3399	+	15.6423i	1.03504	+	0.665179i
$554$	10.0723	+	8.72766i	0.427929	+	0.370803i
$555$	−0.134842	+	0.235872i	−0.00572373	+	0.0100122i
$556$	24.4972	+	11.1875i	1.03891	+	0.474456i
$557$	14.5708	+	9.36407i	0.617384	+	0.396768i	0.811620	−	0.584186i	$-0.198586\pi$
$557$	14.5708	+	9.36407i	0.617384	+	0.396768i	−0.194236	+	0.980955i	$0.562223\pi$
$558$	−6.18369	−	5.79622i	−0.261776	−	0.245374i
$559$	−2.69608	+	3.11144i	−0.114032	+	0.131600i
$560$	0.985542	+	2.15804i	0.0416468	+	0.0911937i
$561$	2.58820	−	1.19812i	0.109274	−	0.0505845i
$562$	−2.86197	+	6.26683i	−0.120725	+	0.264350i
$563$	−9.11363	−	19.9561i	−0.384094	−	0.841048i	−0.998638	−	0.0521662i	$-0.983387\pi$
$563$	−9.11363	−	19.9561i	−0.384094	−	0.841048i	0.614545	−	0.788882i	$-0.289340\pi$
$564$	13.4857	−	2.65886i	0.567849	−	0.111958i
$565$	−5.17089			−0.217541
$566$	0.480120	−	1.63514i	0.0201809	−	0.0687300i
$567$	−16.5064	+	6.03023i	−0.693204	+	0.253246i
$568$	−3.59286	−	12.2361i	−0.150753	−	0.513417i
$569$	−26.8989	−	7.89824i	−1.12766	−	0.331111i	−0.335873	−	0.941907i	$-0.609031\pi$
$569$	−26.8989	−	7.89824i	−1.12766	−	0.331111i	−0.791788	+	0.610796i	$0.790850\pi$
$570$	1.22760	+	0.292273i	0.0514185	+	0.0122420i
$571$	3.30109	−	2.86041i	0.138147	−	0.119705i	−0.583047	−	0.812439i	$-0.698139\pi$
$571$	3.30109	−	2.86041i	0.138147	−	0.119705i	0.721193	+	0.692734i	$0.243594\pi$
$572$	4.84052	−	1.17880i	0.202392	−	0.0492880i
$573$	−29.3714	−	11.6134i	−1.22701	−	0.485156i
$574$	1.99584	+	6.79722i	0.0833049	+	0.283710i
$575$	6.40437	+	21.8113i	0.267081	+	0.909594i
$576$	4.35447	+	0.800786i	0.181436	+	0.0333661i
$577$	29.9167	−	8.78434i	1.24545	−	0.365697i	0.408389	−	0.912808i	$-0.366091\pi$
$577$	29.9167	−	8.78434i	1.24545	−	0.365697i	0.837060	+	0.547111i	$0.184272\pi$
$578$	−9.34075			−0.388524
$579$	40.6196	+	3.70391i	1.68809	+	0.153929i
$580$	5.12687	+	4.44246i	0.212882	+	0.184463i
$581$	−15.1462	−	6.91702i	−0.628368	−	0.286966i
$582$	−2.03274	−	0.483964i	−0.0842597	−	0.0200610i
$583$	−2.68070	+	13.9748i	−0.111023	+	0.578776i
$584$	8.60378	+	13.3877i	0.356027	+	0.553989i
$585$	1.05979	+	0.993382i	0.0438168	+	0.0410713i
$586$	−1.88711	−	2.17784i	−0.0779557	−	0.0899657i
$587$	18.9321	+	2.72202i	0.781411	+	0.112350i	0.521464	−	0.853273i	$-0.325386\pi$
$587$	18.9321	+	2.72202i	0.781411	+	0.112350i	0.259947	+	0.965623i	$0.416295\pi$
$588$	3.42886	−	8.67190i	0.141404	−	0.357623i
$589$	6.57495	−	10.2308i	0.270916	−	0.421554i
$590$	1.08107	+	2.36722i	0.0445070	+	0.0974567i
$591$	2.56452	+	2.66672i	0.105490	+	0.109694i
$592$	0.616859	+	0.181126i	0.0253528	+	0.00744424i
$593$	14.5326	+	4.26717i	0.596784	+	0.175231i	0.566154	−	0.824299i	$-0.308431\pi$
$593$	14.5326	+	4.26717i	0.596784	+	0.175231i	0.0306294	+	0.999531i	$0.490249\pi$
$594$	1.04406	+	9.55157i	0.0428382	+	0.391906i
$595$	0.506448	−	0.148707i	0.0207623	−	0.00609637i
$596$	39.7296			1.62739
$597$	2.55055	−	27.9710i	0.104387	−	1.14478i
$598$	2.01584	−	1.29550i	0.0824336	−	0.0529769i
$599$	0.00823764	+	0.00118439i	0.000336581	+	4.83930e-5i	0.142483	−	0.989797i	$-0.454491\pi$
$599$	0.00823764	+	0.00118439i	0.000336581	+	4.83930e-5i	−0.142147	+	0.989846i	$0.545400\pi$
$600$	−11.6151	−	12.0780i	−0.474183	−	0.493080i
$601$	−6.71586	+	22.8721i	−0.273946	+	0.932973i	0.701488	+	0.712681i	$0.252519\pi$
$601$	−6.71586	+	22.8721i	−0.273946	+	0.932973i	−0.975434	+	0.220292i	$0.929299\pi$
$602$	−5.04005			−0.205417
$603$	1.34452	+	2.28356i	0.0547530	+	0.0929936i
$604$			2.02796i			0.0825165i
$605$	−2.75376	−	5.31860i	−0.111956	−	0.216232i
$606$	6.81902	−	2.39271i	0.277004	−	0.0971972i
$607$	37.5338	+	5.39654i	1.52345	+	0.219039i	0.852604	−	0.522558i	$-0.175022\pi$
$607$	37.5338	+	5.39654i	1.52345	+	0.219039i	0.670846	+	0.741597i	$0.265931\pi$
$608$		−	12.8590i		−	0.521500i
$609$	1.29327	+	24.9126i	0.0524060	+	1.00951i
$610$	0.760412	+	1.66507i	0.0307882	+	0.0674168i
$611$	0.594584	−	4.13542i	0.0240543	−	0.167301i
$612$	0.802552	−	2.38445i	0.0324412	−	0.0963856i
$613$	−10.7763	−	4.92138i	−0.435251	−	0.198773i	0.185725	−	0.982602i	$-0.440537\pi$
$613$	−10.7763	−	4.92138i	−0.435251	−	0.198773i	−0.620977	+	0.783829i	$0.713264\pi$
$614$			6.43071i			0.259522i
$615$	−3.58095	−	4.98361i	−0.144398	−	0.200958i
$616$	10.8571	+	7.71698i	0.437446	+	0.310926i
$617$	−6.26831	+	21.3479i	−0.252353	+	0.859435i	0.731710	+	0.681616i	$0.238722\pi$
$617$	−6.26831	+	21.3479i	−0.252353	+	0.859435i	−0.984063	+	0.177819i	$0.943096\pi$
$618$	16.5431	−	0.858793i	0.665463	−	0.0345457i
$619$	−10.9197	−	23.9107i	−0.438898	−	0.961053i	−0.991799	−	0.127806i	$-0.959207\pi$
$619$	−10.9197	−	23.9107i	−0.438898	−	0.961053i	0.552901	−	0.833247i	$-0.313521\pi$
$620$	4.23916	−	1.93596i	0.170249	−	0.0777500i
$621$	−10.7237	−	22.7081i	−0.430329	−	0.911244i
$622$	−2.79795	−	2.42444i	−0.112188	−	0.0972111i
$623$	−2.67085	+	18.5762i	−0.107005	+	0.744239i
$624$	1.70587	−	2.98398i	0.0682894	−	0.119455i
$625$	−2.93753	−	20.4310i	−0.117501	−	0.817240i
$626$	1.64230	−	1.05544i	0.0656395	−	0.0421840i
$627$	−13.2084	+	3.95226i	−0.527495	+	0.157838i
$628$	8.10632	+	5.20961i	0.323477	+	0.207886i
$629$	0.0594192	−	0.130110i	0.00236920	−	0.00518782i
$630$	−0.0694545	+	1.77688i	−0.00276714	+	0.0707924i
$631$	−12.6038	+	27.5985i	−0.501751	+	1.09868i	0.474146	+	0.880446i	$0.342757\pi$
$631$	−12.6038	+	27.5985i	−0.501751	+	1.09868i	−0.975896	+	0.218234i	$0.929970\pi$
$632$		−	30.4776i		−	1.21233i
$633$	−10.3270	−	14.3721i	−0.410462	−	0.571240i
$634$	6.67596	−	5.78475i	0.265136	−	0.229742i
$635$	0.282824	−	0.0830445i	0.0112235	−	0.00329552i
$636$	7.32461	+	10.1937i	0.290440	+	0.404205i
$637$	−2.14212	−	1.85616i	−0.0848740	−	0.0735438i
$638$	13.3954	+	2.56955i	0.530327	+	0.101730i
$639$	−3.36419	+	18.2936i	−0.133085	+	0.723684i
$640$	3.39655	−	5.28513i	0.134260	−	0.208913i
$641$	5.17895	−	17.6379i	0.204556	−	0.696655i	−0.791755	−	0.610839i	$-0.790832\pi$
$641$	5.17895	−	17.6379i	0.204556	−	0.696655i	0.996311	−	0.0858158i	$-0.0273496\pi$
$642$	−1.34045	+	0.963171i	−0.0529032	+	0.0380133i
$643$	20.2503	−	13.0141i	0.798594	−	0.513225i	−0.0765627	−	0.997065i	$-0.524395\pi$
$643$	20.2503	−	13.0141i	0.798594	−	0.513225i	0.875157	+	0.483840i	$0.160758\pi$
$644$	−15.2946	−	4.49090i	−0.602691	−	0.176966i
$645$	4.11974	−	1.44556i	0.162215	−	0.0569190i
$646$	−0.657582	−	0.0945460i	−0.0258722	−	0.00371986i
$647$	−2.26135	+	1.03273i	−0.0889029	+	0.0406006i	−0.459370	−	0.888245i	$-0.651925\pi$
$647$	−2.26135	+	1.03273i	−0.0889029	+	0.0406006i	0.370467	+	0.928846i	$0.379198\pi$
$648$	14.7443	+	11.1932i	0.579209	+	0.439710i
$649$	−23.1749	−	16.4721i	−0.909695	−	0.646588i
$650$	−2.12132	+	0.968772i	−0.0832048	+	0.0379984i
$651$	15.9368	+	6.30138i	0.624611	+	0.246970i
$652$	1.25813	+	8.75046i	0.0492720	+	0.342694i
$653$	18.6294	−	28.9879i	0.729025	−	1.13438i	−0.256777	−	0.966471i	$-0.582661\pi$
$653$	18.6294	−	28.9879i	0.729025	−	1.13438i	0.985802	−	0.167914i	$-0.0537030\pi$
$654$	1.99310	+	0.181742i	0.0779364	+	0.00710666i
$655$	4.85104	−	4.20345i	0.189546	−	0.164242i
$656$	−9.50933	+	10.9744i	−0.371277	+	0.428477i
$657$	−2.40343	−	23.0865i	−0.0937667	−	0.900692i
$658$	4.30270	−	2.76518i	0.167737	−	0.107798i
$659$	−1.94626	+	13.5365i	−0.0758154	+	0.527308i	0.916154	+	0.400827i	$0.131277\pi$
$659$	−1.94626	+	13.5365i	−0.0758154	+	0.527308i	−0.991969	+	0.126481i	$0.959632\pi$
$660$	−5.07684	−	1.46237i	−0.197616	−	0.0569228i
$661$	0.524568	+	3.64845i	0.0204033	+	0.141908i	0.997477	−	0.0709946i	$-0.0226173\pi$
$661$	0.524568	+	3.64845i	0.0204033	+	0.141908i	−0.977073	+	0.212903i	$0.931708\pi$
$662$	−8.30264	−	9.58176i	−0.322691	−	0.372405i
$663$	−0.603119	−	0.470148i	−0.0234232	−	0.0182590i
$664$	2.49617	+	17.3613i	0.0968704	+	0.673748i
$665$	−2.52559	+	0.363125i	−0.0979383	+	0.0140814i
$666$	0.351578	+	0.329548i	0.0136234	+	0.0127697i
$667$	−35.2858	+	5.07333i	−1.36627	+	0.196440i
$668$	−16.3232	+	10.4903i	−0.631565	+	0.405882i
$669$	−14.9021	−	8.51917i	−0.576148	−	0.329370i
$670$	0.265418	−	0.0381614i	0.0102540	−	0.00147430i
$671$	−16.3009	−	11.5863i	−0.629291	−	0.447284i
$672$	17.7781	−	3.50516i	0.685804	−	0.135215i
$673$	−5.89821	−	9.17779i	−0.227359	−	0.353778i	0.708767	−	0.705443i	$-0.249252\pi$
$673$	−5.89821	−	9.17779i	−0.227359	−	0.353778i	−0.936126	+	0.351665i	$0.885616\pi$
$674$	−6.80594	+	10.5902i	−0.262155	+	0.407921i
$675$	7.18518	+	23.3603i	0.276558	+	0.899139i
$676$	13.5053	+	15.5859i	0.519434	+	0.599459i
$677$	−14.3373	+	31.3944i	−0.551029	+	1.20659i	0.405271	+	0.914197i	$0.367177\pi$
$677$	−14.3373	+	31.3944i	−0.551029	+	1.20659i	−0.956300	+	0.292388i	$0.905550\pi$
$678$	−2.12414	+	8.92178i	−0.0815773	+	0.342639i
$679$	4.18204	−	0.601287i	0.160492	−	0.0230753i
$680$	−0.420203	−	0.364108i	−0.0161140	−	0.0139629i
$681$	−14.8187	−	15.4092i	−0.567853	−	0.590483i
$682$	5.42845	−	7.63737i	0.207866	−	0.292450i
$683$	26.1768	+	11.9546i	1.00163	+	0.457428i	0.847599	−	0.530638i	$-0.178048\pi$
$683$	26.1768	+	11.9546i	1.00163	+	0.457428i	0.154030	+	0.988066i	$0.450775\pi$
$684$	−5.48052	+	10.8572i	−0.209553	+	0.415134i
$685$	1.50222	−	10.4481i	0.0573967	−	0.399203i
$686$		−	11.0905i		−	0.423437i
$687$	50.1777	−	2.60484i	1.91440	−	0.0993809i
$688$	−5.58542	−	8.69108i	−0.212942	−	0.331344i
$689$	3.66079	−	1.07491i	0.139465	−	0.0409506i
$690$	−2.53772	+	0.131739i	−0.0966093	+	0.00501521i
$691$	−43.8923	−	28.2078i	−1.66974	−	1.07308i	−0.901346	−	0.433100i	$-0.857420\pi$
$691$	−43.8923	−	28.2078i	−1.66974	−	1.07308i	−0.768395	−	0.639976i	$-0.778944\pi$
$692$	16.5142	+	19.0584i	0.627776	+	0.724492i
$693$	−9.06459	−	17.1839i	−0.344335	−	0.652762i
$694$	−9.44575	+	10.9010i	−0.358556	+	0.413795i
$695$	−8.32918	+	2.44567i	−0.315944	+	0.0927695i
$696$	21.3402	−	15.3339i	0.808897	−	0.581230i
$697$	2.11568	+	2.44163i	0.0801371	+	0.0924832i
$698$	1.44116	+	4.90815i	0.0545489	+	0.185776i
$699$	−40.7937	+	14.3140i	−1.54296	+	0.541405i
$700$	14.1115	+	6.44451i	0.533365	+	0.243580i
$701$	27.8052	−	32.0889i	1.05019	−	1.21198i	0.0735040	−	0.997295i	$-0.476582\pi$
$701$	27.8052	−	32.0889i	1.05019	−	1.21198i	0.976683	−	0.214686i	$-0.0688727\pi$
$702$	2.14932	−	1.42047i	0.0811207	−	0.0536123i
$703$	−0.373824	+	0.581681i	−0.0140990	+	0.0219385i
$704$	−0.228611	+	4.88943i	−0.00861610	+	0.184277i
$705$	−2.72393	+	3.49434i	−0.102589	+	0.131604i
$706$	−6.84670	+	0.984406i	−0.257679	+	0.0370486i
$707$	−11.0431	+	9.56890i	−0.415319	+	0.359876i
$708$	−24.6074	+	4.85166i	−0.924804	+	0.182336i
$709$	−30.1925	+	34.8440i	−1.13390	+	1.30860i	−0.188730	+	0.982029i	$0.560437\pi$
$709$	−30.1925	+	34.8440i	−1.13390	+	1.30860i	−0.945174	+	0.326566i	$0.894108\pi$
$710$	1.58336	+	1.01757i	0.0594226	+	0.0381886i
$711$	−20.0316	+	39.6836i	−0.751245	+	1.48825i
$712$	17.9826	−	8.21240i	0.673928	−	0.307773i
$713$	−6.89953	+	23.4977i	−0.258390	+	0.879994i
$714$	−0.0485331	−	0.934906i	−0.00181631	−	0.0349880i
$715$	−0.930351	+	1.30892i	−0.0347931	+	0.0489510i
$716$	10.9593	+	37.3239i	0.409567	+	1.39486i
$717$	48.3319	−	16.9591i	1.80499	−	0.633347i
$718$	1.80794	−	3.95884i	0.0674718	−	0.147743i
$719$	9.12846	+	14.2042i	0.340434	+	0.529726i	0.968688	−	0.248283i	$-0.0798663\pi$
$719$	9.12846	+	14.2042i	0.340434	+	0.529726i	−0.628254	+	0.778009i	$0.716230\pi$
$720$	−3.14102	+	1.84938i	−0.117059	+	0.0689222i
$721$	−30.4681	+	13.9143i	−1.13469	+	0.518196i
$722$	−7.08275	−	2.07968i	−0.263593	−	0.0773978i
$723$	3.26421	+	9.30273i	0.121397	+	0.345972i
$724$	1.33500	−	9.28515i	0.0496150	−	0.345080i
$725$	34.6940			1.28850
$726$	−10.3079	+	2.56648i	−0.382561	+	0.0952509i
$727$	−34.7398			−1.28843			−0.644214	−	0.764846i	$-0.722815\pi$
$727$	−34.7398			−1.28843			−0.644214	+	0.764846i	$0.722815\pi$
$728$	0.508282	−	3.53518i	0.0188382	−	0.131022i
$729$	−11.8411	−	24.2650i	−0.438559	−	0.898703i
$730$	−2.25358	−	0.661711i	−0.0834088	−	0.0244910i
$731$	−2.09080	+	0.954836i	−0.0773310	+	0.0353159i
$732$	−17.3086	+	3.41260i	−0.639743	+	0.126133i
$733$	−28.6843	−	44.6337i	−1.05948	−	1.64858i	−0.697822	−	0.716271i	$-0.745847\pi$
$733$	−28.6843	−	44.6337i	−1.05948	−	1.64858i	−0.361658	−	0.932311i	$-0.617789\pi$
$734$	5.16979	−	11.3203i	0.190821	−	0.417839i
$735$	0.995224	+	2.83631i	0.0367094	+	0.104619i
$736$	7.29529	+	24.8455i	0.268908	+	0.915816i
$737$	−2.30127	+	1.81301i	−0.0847686	+	0.0667832i
$738$	−10.0697	+	4.13131i	−0.370669	+	0.152076i
$739$	2.43239	−	8.28397i	0.0894770	−	0.304731i	−0.902580	−	0.430523i	$-0.858329\pi$
$739$	2.43239	−	8.28397i	0.0894770	−	0.304731i	0.992057	+	0.125792i	$0.0401473\pi$
$740$	−0.241020	+	0.110070i	−0.00886009	+	0.00404627i
$741$	2.56240	+	2.66452i	0.0941322	+	0.0978836i
$742$	3.92927	+	2.52519i	0.144248	+	0.0927026i
$743$	6.42393	−	7.41361i	0.235671	−	0.271979i	−0.625578	−	0.780161i	$-0.715137\pi$
$743$	6.42393	−	7.41361i	0.235671	−	0.271979i	0.861250	+	0.508182i	$0.169682\pi$
$744$	−3.49200	−	17.7113i	−0.128023	−	0.649327i
$745$	−9.67834	+	8.38633i	−0.354587	+	0.307251i
$746$	−17.3154	+	2.48958i	−0.633962	+	0.0911500i
$747$	8.16067	−	24.2460i	0.298583	−	0.887116i
$748$	2.73161	+	0.523989i	0.0998777	+	0.0191589i
$749$	1.80438	−	2.80768i	0.0659308	−	0.102590i
$750$	5.08097	+	0.463310i	0.185531	+	0.0169177i
$751$	−20.0088	+	23.0914i	−0.730131	+	0.842617i	−0.992486	−	0.122355i	$-0.960955\pi$
$751$	−20.0088	+	23.0914i	−0.730131	+	0.842617i	0.262355	+	0.964971i	$0.415501\pi$
$752$	9.53656	+	4.35520i	0.347763	+	0.158818i
$753$	−14.8410	−	42.2957i	−0.540838	−	1.54134i
$754$	−1.03034	−	3.50901i	−0.0375227	−	0.127791i
$755$	−0.428073	−	0.494022i	−0.0155792	−	0.0179793i
$756$	−16.5044	−	4.61754i	−0.600258	−	0.167938i
$757$	−32.3100	+	9.48707i	−1.17433	+	0.344814i	−0.809984	−	0.586451i	$-0.800525\pi$
$757$	−32.3100	+	9.48707i	−1.17433	+	0.344814i	−0.364343	+	0.931265i	$0.618706\pi$
$758$	8.83949	−	10.2013i	0.321065	−	0.370529i
$759$	23.2785	−	15.1299i	0.844955	−	0.549181i
$760$	1.76013	+	2.03129i	0.0638465	+	0.0736828i
$761$	−30.6024	−	19.6670i	−1.10934	−	0.712928i	−0.148189	−	0.988959i	$-0.547344\pi$
$761$	−30.6024	−	19.6670i	−1.10934	−	0.712928i	−0.961149	+	0.276031i	$0.910981\pi$
$762$	−0.0271031	−	0.522094i	−0.000981842	−	0.0189135i
$763$	−3.88281	+	1.14010i	−0.140567	+	0.0412743i
$764$	−16.6526	−	25.9120i	−0.602471	−	0.937464i
$765$	0.307816	+	0.750272i	0.0111291	+	0.0271261i
$766$			2.46973i			0.0892349i
$767$	−1.08494	+	7.54595i	−0.0391751	+	0.272468i
$768$	−4.17990	−	4.34648i	−0.150829	−	0.156840i
$769$	−30.1590	−	13.7732i	−1.08756	−	0.496673i	−0.210766	−	0.977537i	$-0.567596\pi$
$769$	−30.1590	−	13.7732i	−1.08756	−	0.496673i	−0.876795	+	0.480864i	$0.840323\pi$
$770$	−1.95684	+	0.188589i	−0.0705197	+	0.00679628i
$771$	6.95920	−	6.69250i	0.250630	−	0.241024i
$772$	30.0621	+	26.0489i	1.08196	+	0.937522i
$773$	−52.1600	+	7.49947i	−1.87606	+	0.269737i	−0.983463	−	0.181110i	$-0.942031\pi$
$773$	−52.1600	+	7.49947i	−1.87606	+	0.269737i	−0.892601	+	0.450847i	$0.851122\pi$
$774$	−0.801814	−	7.70196i	−0.0288206	−	0.276841i
$775$	9.90094	−	21.6800i	0.355652	−	0.778770i
$776$	−2.91453	−	3.36355i	−0.104625	−	0.120744i
$777$	−0.906096	−	0.358269i	−0.0325060	−	0.0128528i
$778$	3.14363	−	4.89159i	0.112705	−	0.175372i
$779$	−8.44352	−	13.1384i	−0.302520	−	0.470731i
$780$	0.274023	+	1.38983i	0.00981159	+	0.0497640i
$781$	−20.5411	−	0.960422i	−0.735017	−	0.0343666i
$782$	1.32418	−	0.190389i	0.0473527	−	0.00680830i
$783$	−37.8645	+	5.93963i	−1.35317	+	0.212265i
$784$	5.98352	−	3.84538i	0.213697	−	0.137335i
$785$	−3.07442	+	0.442035i	−0.109731	+	0.0157769i
$786$	−5.25983	−	10.0967i	−0.187612	−	0.360136i
$787$	−41.9046	+	6.02498i	−1.49374	+	0.214767i	−0.840263	−	0.542180i	$-0.817599\pi$
$787$	−41.9046	+	6.02498i	−1.49374	+	0.214767i	−0.653476	+	0.756947i	$0.726690\pi$
$788$	0.513487	+	3.57138i	0.0182922	+	0.127225i
$789$	19.7097	−	25.2841i	0.701683	−	0.900138i
$790$	2.94564	+	3.39946i	0.104801	+	0.120947i
$791$	−2.63908	−	18.3552i	−0.0938348	−	0.652635i
$792$	−10.0655	+	17.8190i	−0.357661	+	0.633172i
$793$	−0.763136	+	5.30773i	−0.0270998	+	0.188483i
$794$	14.4029	−	9.25621i	0.511141	−	0.328491i
$795$	−3.93605	−	0.937114i	−0.139597	−	0.0332360i
$796$	17.9375	−	20.7010i	0.635778	−	0.733727i
$797$	6.25674	−	5.42150i	0.221625	−	0.192039i	−0.536970	−	0.843601i	$-0.680431\pi$
$797$	6.25674	−	5.42150i	0.221625	−	0.192039i	0.758596	+	0.651562i	$0.225886\pi$
$798$	−0.410954	+	4.50679i	−0.0145476	+	0.159539i
$799$	1.26106	−	1.96224i	0.0446130	−	0.0694192i
$800$	−3.58647	−	24.9444i	−0.126801	−	0.881919i
$801$	−28.8121	−	1.12621i	−1.01803	−	0.0397927i
$802$	−10.8413	+	4.95107i	−0.382821	+	0.174828i
$803$	24.9324	−	6.07171i	0.879845	−	0.214266i
$804$	−0.234680	+	2.57366i	−0.00827653	+	0.0907659i
$805$	4.67381	−	2.13446i	0.164730	−	0.0752298i
$806$	−2.48679	−	0.357547i	−0.0875935	−	0.0125940i
$807$	12.4826	+	35.5744i	0.439408	+	1.25228i
$808$	14.7687	+	4.33649i	0.519562	+	0.152557i
$809$	8.52326	−	5.47756i	0.299662	−	0.192581i	−0.382166	−	0.924094i	$-0.624822\pi$
$809$	8.52326	−	5.47756i	0.299662	−	0.192581i	0.681828	+	0.731513i	$0.261185\pi$
$810$	−2.72638	+	0.176543i	−0.0957954	+	0.00620310i
$811$	−12.7349	+	43.3712i	−0.447184	+	1.52297i	0.360161	+	0.932890i	$0.382722\pi$
$811$	−12.7349	+	43.3712i	−0.447184	+	1.52297i	−0.807345	+	0.590079i	$0.799097\pi$
$812$	−13.1528	+	20.4662i	−0.461574	+	0.718224i
$813$	−13.5837	+	23.7612i	−0.476402	+	0.833342i
$814$	−0.308638	+	0.434228i	−0.0108178	+	0.0152197i
$815$	−2.15358	−	1.86609i	−0.0754366	−	0.0653662i
$816$	1.55837	−	1.11976i	0.0545538	−	0.0391994i
$817$	10.6611	−	3.13038i	0.372985	−	0.109518i
$818$	−5.67712	+	4.91925i	−0.198496	+	0.171998i
$819$	−2.98534	+	4.26894i	−0.104316	+	0.149169i
$820$		−	5.98473i		−	0.208996i
$821$	−1.01821	+	2.22957i	−0.0355358	+	0.0778125i	−0.926567	−	0.376129i	$-0.877255\pi$
$821$	−1.01821	+	2.22957i	−0.0355358	+	0.0778125i	0.891032	+	0.453941i	$0.149982\pi$
$822$	−17.4100	−	6.88388i	−0.607243	−	0.240103i
$823$	10.2822	−	22.5149i	0.358415	−	0.784819i	−0.641429	−	0.767182i	$-0.721658\pi$
$823$	10.2822	−	22.5149i	0.358415	−	0.784819i	0.999844	−	0.0176373i	$-0.00561442\pi$
$824$	29.6821	+	19.0755i	1.03403	+	0.664528i
$825$	−24.5200	+	11.3507i	−0.853678	+	0.395181i
$826$	−7.85119	+	5.04566i	−0.273178	+	0.175561i
$827$	−5.77163	−	40.1426i	−0.200699	−	1.39589i	−0.802216	−	0.597034i	$-0.796346\pi$
$827$	−5.77163	−	40.1426i	−0.200699	−	1.39589i	0.601517	−	0.798860i	$-0.294563\pi$
$828$	4.42958	−	24.0869i	0.153939	−	0.837078i
$829$	3.83400	−	26.6660i	0.133160	−	0.926150i	−0.808239	−	0.588855i	$-0.799579\pi$
$829$	3.83400	−	26.6660i	0.133160	−	0.926150i	0.941399	−	0.337295i	$-0.109512\pi$
$830$	−1.95638	−	1.69522i	−0.0679070	−	0.0588418i
$831$	9.58944	−	40.2774i	0.332654	−	1.39721i
$832$	1.19382	−	0.545201i	0.0413884	−	0.0189014i
$833$	−0.657374	−	1.43945i	−0.0227767	−	0.0498739i
$834$	0.798189	+	15.3757i	0.0276390	+	0.532417i
$835$	1.76208	−	6.00109i	0.0609793	−	0.207676i
$836$	−12.7099	−	4.38647i	−0.439583	−	0.151709i
$837$	−7.09410	+	25.3563i	−0.245208	+	0.876442i
$838$		−	16.9473i		−	0.585436i
$839$	−3.71640	−	1.69722i	−0.128304	−	0.0585946i	0.350228	−	0.936664i	$-0.386104\pi$
$839$	−3.71640	−	1.69722i	−0.128304	−	0.0585946i	−0.478533	+	0.878070i	$0.658831\pi$
$840$	−2.32856	+	2.98715i	−0.0803431	+	0.103066i
$841$	−3.61585	+	25.1488i	−0.124684	+	0.867199i
$842$	2.58818	+	5.66732i	0.0891946	+	0.195309i
$843$	21.3738	−	1.10957i	0.736154	−	0.0382155i
$844$		−	17.2592i		−	0.594087i
$845$	−6.57992	−	0.946050i	−0.226356	−	0.0325451i
$846$	4.91012	+	6.13528i	0.168814	+	0.210935i
$847$	17.4741	−	12.4895i	0.600417	−	0.429145i
$848$			9.57407i			0.328775i
$849$	−5.19417	+	1.02409i	−0.178263	+	0.0351468i
$850$	−1.30198			−0.0446574
$851$	0.392278	−	1.33598i	0.0134471	−	0.0457967i
$852$	−13.0748	+	12.5737i	−0.447935	+	0.430768i
$853$	−16.9650	−	2.43920i	−0.580871	−	0.0835167i	−0.154385	−	0.988011i	$-0.549340\pi$
$853$	−16.9650	−	2.43920i	−0.580871	−	0.0835167i	−0.426486	+	0.904494i	$0.640249\pi$
$854$	−5.52243	+	3.54905i	−0.188974	+	0.121446i
$855$	−0.956704	−	3.80172i	−0.0327186	−	0.130016i
$856$	−3.51567			−0.120163
$857$	39.6603	−	11.6453i	1.35477	−	0.397797i	0.477855	−	0.878439i	$-0.341415\pi$
$857$	39.6603	−	11.6453i	1.35477	−	0.397797i	0.876917	+	0.480642i	$0.159596\pi$
$858$	1.87622	+	2.14291i	0.0640532	+	0.0731576i
$859$	34.5624	+	10.1484i	1.17926	+	0.346261i	0.811887	−	0.583815i	$-0.198441\pi$
$859$	34.5624	+	10.1484i	1.17926	+	0.346261i	0.367369	+	0.930075i	$0.380259\pi$
$860$	4.08538	+	1.19958i	0.139310	+	0.0409052i
$861$	15.8628	−	15.2548i	0.540602	−	0.519883i
$862$	−1.40375	−	3.07377i	−0.0478118	−	0.104693i
$863$	19.8757	−	30.9272i	0.676578	−	1.05278i	−0.317930	−	0.948114i	$-0.602988\pi$
$863$	19.8757	−	30.9272i	0.676578	−	1.05278i	0.994508	−	0.104661i	$-0.0333758\pi$
$864$	8.18471	+	26.6100i	0.278450	+	0.905289i
$865$	−8.04591	−	1.15683i	−0.273569	−	0.0393333i
$866$	1.33477	+	1.54041i	0.0453574	+	0.0523452i
$867$	13.4067	+	25.7352i	0.455315	+	0.874013i
$868$	9.03565	+	14.0597i	0.306690	+	0.477219i
$869$	−46.4556	−	16.0328i	−1.57590	−	0.543876i
$870$	−0.898261	+	3.77286i	−0.0304539	+	0.127912i
$871$	0.714536	+	0.326318i	0.0242111	+	0.0110569i
$872$	3.22159	+	2.79153i	0.109097	+	0.0945330i
$873$	1.58417	+	6.29513i	0.0536161	+	0.213058i
$874$	−6.46704			−0.218751
$875$	−9.89837	+	2.90642i	−0.334626	+	0.0982550i
$876$	11.2345	−	19.6518i	0.379577	−	0.663972i
$877$	−1.44194	−	4.91078i	−0.0486907	−	0.165825i	0.931559	−	0.363591i	$-0.118450\pi$
$877$	−1.44194	−	4.91078i	−0.0486907	−	0.165825i	−0.980249	+	0.197766i	$0.936631\pi$
$878$	0.167268	+	0.569663i	0.00564503	+	0.0192252i
$879$	−3.29174	+	8.32511i	−0.111027	+	0.280799i
$880$	−2.49379	−	3.16539i	−0.0840656	−	0.106705i
$881$	−2.69276	+	2.33329i	−0.0907212	+	0.0786104i	−0.699041	−	0.715082i	$-0.746389\pi$
$881$	−2.69276	+	2.33329i	−0.0907212	+	0.0786104i	0.608319	+	0.793692i	$0.291844\pi$
$882$	5.30255	−	0.552023i	0.178546	−	0.0185876i
$883$	−16.3182	−	4.79145i	−0.549150	−	0.161245i	−0.00462478	−	0.999989i	$-0.501472\pi$
$883$	−16.3182	−	4.79145i	−0.549150	−	0.161245i	−0.544526	+	0.838744i	$0.683290\pi$
$884$	−0.210109	−	0.715566i	−0.00706673	−	0.0240671i
$885$	4.97040	−	6.37616i	0.167078	−	0.214332i
$886$	1.97112	−	6.71302i	0.0662211	−	0.225528i
$887$	15.9268			0.534770			0.267385	−	0.963590i	$-0.413840\pi$
$887$	15.9268			0.534770			0.267385	+	0.963590i	$0.413840\pi$
$888$	0.198540	+	1.00699i	0.00666256	+	0.0337923i
$889$	0.439130	+	0.961560i	0.0147279	+	0.0322497i
$890$	−1.21205	+	2.65402i	−0.0406281	+	0.0889631i
$891$	24.8175	−	16.5858i	0.831419	−	0.555646i
$892$	−6.95412	−	15.2274i	−0.232841	−	0.509851i
$893$	−7.38395	+	8.52153i	−0.247094	+	0.285162i
$894$	10.4939	+	20.1439i	0.350969	+	0.673713i
$895$	−10.5483	−	6.77896i	−0.352589	−	0.226595i
$896$	20.4942	+	9.35939i	0.684663	+	0.312675i
$897$	−6.46261	−	3.69452i	−0.215780	−	0.123356i
$898$	12.4435	+	10.7824i	0.415246	+	0.359812i
$899$	31.4430	+	20.2072i	1.04868	+	0.673948i
$900$	−7.60321	+	22.5898i	−0.253440	+	0.752992i
$901$	2.10840	+	0.303143i	0.0702411	+	0.0100991i
$902$	−6.02561	−	10.4155i	−0.200631	−	0.346800i
$903$	7.23394	+	13.8861i	0.240730	+	0.462101i
$904$	−14.7628	+	12.7920i	−0.491003	+	0.425456i
$905$	1.63475	+	2.54371i	0.0543408	+	0.0845559i
$906$	−1.02823	+	0.535652i	−0.0341605	+	0.0177958i
$907$	−1.11042	−	7.72315i	−0.0368709	−	0.256443i	0.963046	−	0.269337i	$-0.0868046\pi$
$907$	−1.11042	−	7.72315i	−0.0368709	−	0.256443i	−0.999917	+	0.0128942i	$0.995896\pi$
$908$	−2.96711	−	20.6367i	−0.0984671	−	0.684853i
$909$	−16.3796	−	15.3532i	−0.543276	−	0.509235i
$910$	0.284980	+	0.443437i	0.00944699	+	0.0146998i
$911$	−32.8747	+	28.4861i	−1.08919	+	0.943786i	−0.998642	−	0.0521062i	$-0.983407\pi$
$911$	−32.8747	+	28.4861i	−1.08919	+	0.943786i	−0.0905457	+	0.995892i	$0.528861\pi$
$912$	−8.22695	+	4.28581i	−0.272421	+	0.141917i
$913$	27.7762	+	5.32814i	0.919257	+	0.176336i
$914$	−4.83342	−	0.694941i	−0.159875	−	0.0229866i
$915$	3.49612	−	4.48491i	0.115578	−	0.148267i
$916$	41.2221	+	26.4918i	1.36202	+	0.875314i
$917$	17.3969	+	15.0745i	0.574496	+	0.497804i
$918$	1.42096	−	0.222899i	0.0468986	−	0.00735676i
$919$	48.3152	+	22.0648i	1.59377	+	0.727851i	0.997205	−	0.0747137i	$-0.0238043\pi$
$919$	48.3152	+	22.0648i	1.59377	+	0.727851i	0.596566	+	0.802564i	$0.296532\pi$
$920$	−4.55324	−	2.92619i	−0.150116	−	0.0964736i
$921$	17.7176	−	9.22993i	0.583814	−	0.304137i
$922$	−3.63638	+	4.19661i	−0.119758	+	0.138208i
$923$	2.29045	+	5.01539i	0.0753911	+	0.165084i
$924$	2.59993	−	18.7677i	0.0855315	−	0.617412i
$925$	−0.562925	+	1.23263i	−0.0185089	+	0.0405287i
$926$	4.57555	+	10.0191i	0.150362	+	0.329247i
$927$	−26.1103	−	44.3463i	−0.857575	−	1.45652i
$928$	39.5203			1.29732
$929$	−14.2555	+	48.5497i	−0.467707	+	1.59286i	0.301238	+	0.953549i	$0.402600\pi$
$929$	−14.2555	+	48.5497i	−0.467707	+	1.59286i	−0.768945	+	0.639315i	$0.779218\pi$
$930$	2.10128	+	1.63801i	0.0689038	+	0.0537125i
$931$	2.15517	+	7.33982i	0.0706327	+	0.240553i
$932$	−40.4534	−	11.8782i	−1.32510	−	0.389083i
$933$	−2.66383	+	11.1886i	−0.0872099	+	0.366297i
$934$	8.52923	−	7.39062i	0.279085	−	0.241828i
$935$	−0.776043	+	0.448957i	−0.0253793	+	0.0146825i
$936$	5.48315	+	0.214325i	0.179222	+	0.00700545i
$937$	9.52603	+	32.4427i	0.311202	+	1.05986i	0.955478	+	0.295063i	$0.0953406\pi$
$937$	9.52603	+	32.4427i	0.311202	+	1.05986i	−0.644276	+	0.764793i	$0.722841\pi$
$938$	0.270924	+	0.922682i	0.00884598	+	0.0301266i
$939$	−5.26509	−	3.00993i	−0.171820	−	0.0982252i
$940$	−4.14583	+	1.21733i	−0.135222	+	0.0397048i
$941$	39.4014			1.28445			0.642224	−	0.766517i	$-0.278012\pi$
$941$	39.4014			1.28445			0.642224	+	0.766517i	$0.278012\pi$
$942$	−0.500256	+	5.48614i	−0.0162992	+	0.178748i
$943$	23.7679	+	20.5950i	0.773991	+	0.670667i
$944$	−17.4015	−	7.94699i	−0.566370	−	0.258653i
$945$	4.99525	−	2.35897i	0.162496	−	0.0767374i
$946$	8.31777	−	2.02560i	0.270434	−	0.0658580i
$947$	11.5124	+	17.9136i	0.374101	+	0.582113i	0.976350	−	0.216195i	$-0.0693648\pi$
$947$	11.5124	+	17.9136i	0.374101	+	0.582113i	−0.602249	+	0.798309i	$0.705728\pi$
$948$	−38.4475	+	20.0291i	−1.24872	+	0.650516i
$949$	−4.50573	−	5.19989i	−0.146262	−	0.168796i
$950$	6.22979	+	0.895709i	0.202121	+	0.0290606i
$951$	−25.5198	−	10.0905i	−0.827537	−	0.327207i
$952$	1.07802	−	1.67743i	0.0349388	−	0.0543659i
$953$	−3.04189	−	6.66080i	−0.0985364	−	0.215765i	0.853944	−	0.520365i	$-0.174204\pi$
$953$	−3.04189	−	6.66080i	−0.0985364	−	0.215765i	−0.952480	+	0.304601i	$0.901477\pi$
$954$	−3.23377	+	6.40625i	−0.104697	+	0.207410i
$955$	9.52632	+	2.79718i	0.308265	+	0.0905146i
$956$	47.9288	+	14.0732i	1.55013	+	0.455159i
$957$	−12.1467	−	40.5943i	−0.392648	−	1.31223i
$958$	14.7203	−	4.32228i	0.475593	−	0.139647i
$959$	37.8546			1.22239
$960$	−1.38604	−	0.126387i	−0.0447343	−	0.00407911i
$961$	−4.47834	+	2.87806i	−0.144463	+	0.0928405i
$962$	0.141388	+	0.0203286i	0.00455854	+	0.000655419i
$963$	4.57761	+	2.31070i	0.147512	+	0.0744614i
$964$	−2.70875	+	9.22514i	−0.0872428	+	0.297122i
$965$	−12.8218			−0.412750
$966$	−1.76282	−	8.94094i	−0.0567177	−	0.287670i
$967$			8.45882i			0.272017i	0.990708	+	0.136009i	$0.0434275\pi$
$967$			8.45882i			0.272017i	−0.990708	+	0.136009i	$0.956573\pi$
$968$	−21.0194	−	8.37210i	−0.675588	−	0.269089i
$969$	0.683332	+	1.94744i	0.0219518	+	0.0625608i
$970$	0.650171	+	0.0934804i	0.0208757	+	0.00300148i
$971$			38.7854i			1.24468i	0.782746	+	0.622342i	$0.213819\pi$
$971$			38.7854i			1.24468i	−0.782746	+	0.622342i	$0.786181\pi$
$972$	4.43065	−	25.9558i	0.142113	−	0.832532i
$973$	−12.9324	−	28.3180i	−0.414594	−	0.907834i
$974$	1.57009	−	10.9202i	0.0503088	−	0.349905i
$975$	5.71382	+	4.45408i	0.182989	+	0.142645i
$976$	−12.2400	−	5.58982i	−0.391793	−	0.178926i
$977$			4.20787i			0.134622i	0.997732	+	0.0673109i	$0.0214419\pi$
$977$			4.20787i			0.134622i	−0.997732	+	0.0673109i	$0.978558\pi$
$978$	−4.10439	+	2.94919i	−0.131244	+	0.0943047i
$979$	−3.05799	−	31.7303i	−0.0977337	−	1.01411i
$980$	−0.825869	+	2.81265i	−0.0263814	+	0.0898468i
$981$	−2.35995	−	5.75215i	−0.0753475	−	0.183652i
$982$	0.572909	+	1.25450i	0.0182823	+	0.0400326i
$983$	−36.1994	+	16.5317i	−1.15458	+	0.527280i	−0.898326	−	0.439329i	$-0.855216\pi$
$983$	−36.1994	+	16.5317i	−1.15458	+	0.527280i	−0.256256	+	0.966609i	$0.582489\pi$
$984$	−22.5522	−	5.36935i	−0.718939	−	0.171169i
$985$	−0.878955	−	0.761619i	−0.0280058	−	0.0242672i
$986$	0.290574	−	2.02099i	0.00925376	−	0.0643613i
$987$	−13.7941	−	7.88578i	−0.439072	−	0.251007i
$988$	0.513064	+	3.56844i	0.0163227	+	0.113527i
$989$	−18.8229	+	12.0967i	−0.598533	+	0.384654i
$990$	−0.599504	−	2.96035i	−0.0190535	−	0.0940861i
$991$	−3.01192	−	1.93564i	−0.0956766	−	0.0614876i	0.491928	−	0.870636i	$-0.336292\pi$
$991$	−3.01192	−	1.93564i	−0.0956766	−	0.0614876i	−0.587604	+	0.809148i	$0.699929\pi$
$992$	11.2783	−	24.6959i	0.358085	−	0.784097i
$993$	−14.4825	+	36.6277i	−0.459589	+	1.16234i
$994$	−2.80397	+	6.13983i	−0.0889364	+	0.194744i
$995$			8.82923i			0.279905i
$996$	20.2609	−	14.5583i	0.641990	−	0.461299i
$997$	31.9613	−	27.6946i	1.01223	−	0.877098i	0.0197821	−	0.999804i	$-0.493703\pi$
$997$	31.9613	−	27.6946i	1.01223	−	0.877098i	0.992443	+	0.122706i	$0.0391573\pi$
$998$	2.48462	−	0.729551i	0.0786494	−	0.0230935i
$999$	0.403340	−	1.44165i	0.0127611	−	0.0456118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.j.a.32.18	✓	420
3.2	odd	2	inner	363.2.j.a.32.25	yes	420
121.87	odd	22	inner	363.2.j.a.329.25	yes	420
363.329	even	22	inner	363.2.j.a.329.18	yes	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.j.a.32.18	✓	420	1.1	even	1	trivial
363.2.j.a.32.25	yes	420	3.2	odd	2	inner
363.2.j.a.329.18	yes	420	363.329	even	22	inner
363.2.j.a.329.25	yes	420	121.87	odd	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0793462 + 0.551865i) q^{2} +(1.63436 - 0.573475i) q^{3} +(1.62073 + 0.475888i) q^{4} +(-0.495271 + 0.226183i) q^{5} +(0.186801 + 0.947448i) q^{6} +(-1.05566 - 1.64263i) q^{7} +(-0.854445 + 1.87097i) q^{8} +(2.34225 - 1.87453i) q^{9} +(-0.0855244 - 0.291270i) q^{10} +(2.40236 + 2.28663i) q^{11} +(2.92176 - 0.151675i) q^{12} +(0.250539 - 0.853257i) q^{13} +(0.990274 - 0.452243i) q^{14} +(-0.679740 + 0.653690i) q^{15} +(1.87728 + 1.20645i) q^{16} +(0.325125 - 0.375214i) q^{17} +(0.848638 + 1.44134i) q^{18} +(-1.81382 + 1.57168i) q^{19} +(-0.910337 + 0.130887i) q^{20} +(-2.66733 - 2.07926i) q^{21} +(-1.45253 + 1.14434i) q^{22} +(2.61290 - 4.06575i) q^{23} +(-0.323512 + 3.54785i) q^{24} +(-3.08017 + 3.55470i) q^{25} +(0.451003 + 0.205966i) q^{26} +(2.75308 - 4.40687i) q^{27} +(-0.929221 - 3.16464i) q^{28} +(-4.83034 - 5.57451i) q^{29} +(-0.306813 - 0.426992i) q^{30} +(-4.86195 + 1.42760i) q^{31} +(-3.50865 + 4.04920i) q^{32} +(5.23764 + 2.35947i) q^{33} +(0.181270 + 0.209197i) q^{34} +(0.894372 + 0.574778i) q^{35} +(4.68822 - 1.92345i) q^{36} +(0.276430 - 0.0811670i) q^{37} +(-0.723436 - 1.12569i) q^{38} +(-0.0798518 - 1.53821i) q^{39} -1.11990i q^{40} +(-0.926082 + 6.44104i) q^{41} +(1.35911 - 1.30703i) q^{42} +(-4.21125 - 1.92321i) q^{43} +(2.80539 + 4.84925i) q^{44} +(-0.736064 + 1.45818i) q^{45} +(2.03642 + 1.76457i) q^{46} +(4.65031 - 0.668613i) q^{47} +(3.76002 + 0.895203i) q^{48} +(1.32407 - 2.89931i) q^{49} +(-1.71732 - 1.98189i) q^{50} +(0.316195 - 0.799686i) q^{51} +(0.812110 - 1.26367i) q^{52} +(2.31955 + 3.60929i) q^{53} +(2.21355 + 1.86900i) q^{54} +(-1.70702 - 0.589127i) q^{55} +(3.97533 - 0.571566i) q^{56} +(-2.06310 + 3.60887i) q^{57} +(3.45965 - 2.22338i) q^{58} +(-8.48547 + 1.22003i) q^{59} +(-1.41276 + 0.735972i) q^{60} +(-5.96857 + 0.858151i) q^{61} +(-0.402064 - 2.79641i) q^{62} +(-5.55178 - 1.86860i) q^{63} +(0.966462 + 1.11536i) q^{64} +(0.0689074 + 0.479261i) q^{65} +(-1.71769 + 2.70326i) q^{66} +(-0.125710 + 0.874334i) q^{67} +(0.705499 - 0.453397i) q^{68} +(1.93881 - 8.14333i) q^{69} +(-0.388165 + 0.447966i) q^{70} +(-4.68574 + 4.06022i) q^{71} +(1.50587 + 5.98398i) q^{72} +(4.18299 - 6.50886i) q^{73} +(0.0228596 + 0.158992i) q^{74} +(-2.99556 + 7.57606i) q^{75} +(-3.68764 + 1.68409i) q^{76} +(1.22002 - 6.36009i) q^{77} +(0.855217 + 0.0779833i) q^{78} +(-13.4786 + 6.15546i) q^{79} +(-1.20264 - 0.172914i) q^{80} +(1.97229 - 8.78123i) q^{81} +(-3.48111 - 1.02214i) q^{82} +(7.17381 - 4.61032i) q^{83} +(-3.33352 - 4.63926i) q^{84} +(-0.0761581 + 0.259371i) q^{85} +(1.39550 - 2.17144i) q^{86} +(-11.0914 - 6.34067i) q^{87} +(-6.33090 + 2.54096i) q^{88} +(-7.26380 - 6.29412i) q^{89} +(-0.746313 - 0.521909i) q^{90} +(-1.66607 + 0.489203i) q^{91} +(6.16964 - 5.34603i) q^{92} +(-7.12747 + 5.12141i) q^{93} +2.61939i q^{94} +(0.542844 - 1.18866i) q^{95} +(-3.41228 + 8.62997i) q^{96} +(-0.898875 + 1.96826i) q^{97} +(1.49497 + 0.960756i) q^{98} +(9.91328 + 0.852556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 22 q^{3} - 58 q^{4} + 11 q^{6} - 22 q^{7} - 18 q^{9} - 44 q^{10} - 5 q^{12} - 44 q^{13} + 36 q^{15} - 70 q^{16} + 11 q^{18} - 22 q^{19} - 44 q^{21} + 22 q^{22} - 66 q^{24} + 24 q^{25} - 10 q^{27}+ \cdots + 99 q^{99}+O(q^{100}) \) 420 * q - 22 * q^3 - 58 * q^4 + 11 * q^6 - 22 * q^7 - 18 * q^9 - 44 * q^10 - 5 * q^12 - 44 * q^13 + 36 * q^15 - 70 * q^16 + 11 * q^18 - 22 * q^19 - 44 * q^21 + 22 * q^22 - 66 * q^24 + 24 * q^25 - 10 * q^27 - 22 * q^28 - 44 * q^30 - 48 * q^31 + 33 * q^33 - 26 * q^34 - 59 * q^36 - 6 * q^37 - 44 * q^39 + 12 * q^42 - 22 * q^43 + 42 * q^45 - 22 * q^46 - 48 * q^48 + 44 * q^49 + 11 * q^51 - 143 * q^54 + 44 * q^55 - 121 * q^57 + 14 * q^58 + 50 * q^60 - 22 * q^61 - 143 * q^63 + 142 * q^64 - 55 * q^66 + 2 * q^67 + 6 * q^69 + 26 * q^70 + 77 * q^72 - 44 * q^73 - 38 * q^75 + 176 * q^76 + 20 * q^78 + 22 * q^79 - 26 * q^81 - 70 * q^82 - 44 * q^84 - 154 * q^85 + 22 * q^87 + 176 * q^88 - 22 * q^90 - 154 * q^91 - 19 * q^93 + 22 * q^96 - 58 * q^97 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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