LMFDB - Embedded newform 213.2.l.a.23.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [213,2,Mod(23,213)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("213.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 213 = 3 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	213.l (of order $14$, degree $6$, 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:	$1.70081356305$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	213.23
Dual form			213.2.l.a.176.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.208082 + 0.165940i) q^{2} +(1.72906 + 0.101725i) q^{3} +(-0.429280 + 1.88080i) q^{4} +0.782738i q^{5} +(-0.376667 + 0.265753i) q^{6} +(0.755976 + 0.602871i) q^{7} +(-0.453728 - 0.942175i) q^{8} +(2.97930 + 0.351777i) q^{9} +(-0.129888 - 0.162874i) q^{10} +(-4.96823 - 2.39257i) q^{11} +(-0.933575 + 3.20835i) q^{12} +(2.39142 + 4.96584i) q^{13} -0.257346 q^{14} +(-0.0796240 + 1.35340i) q^{15} +(-3.22548 - 1.55331i) q^{16} +3.44458 q^{17} +(-0.678314 + 0.421187i) q^{18} +(-0.924967 - 4.05255i) q^{19} +(-1.47217 - 0.336014i) q^{20} +(1.24580 + 1.11930i) q^{21} +(1.43082 - 0.326576i) q^{22} +(2.86273 - 3.58976i) q^{23} +(-0.688680 - 1.67523i) q^{24} +4.38732 q^{25} +(-1.32164 - 0.636470i) q^{26} +(5.11561 + 0.911314i) q^{27} +(-1.45840 + 1.16304i) q^{28} +(-4.55903 - 1.04057i) q^{29} +(-0.208015 - 0.294832i) q^{30} +(-0.355010 - 0.737186i) q^{31} +(2.96795 - 0.677416i) q^{32} +(-8.34699 - 4.64230i) q^{33} +(-0.716756 + 0.571594i) q^{34} +(-0.471890 + 0.591731i) q^{35} +(-1.94058 + 5.45246i) q^{36} +(-0.480127 - 0.602061i) q^{37} +(0.864948 + 0.689773i) q^{38} +(3.62977 + 8.82951i) q^{39} +(0.737477 - 0.355150i) q^{40} +(0.268596 - 0.129349i) q^{41} +(-0.444966 - 0.0261785i) q^{42} +(-3.99387 - 5.00816i) q^{43} +(6.63271 - 8.31715i) q^{44} +(-0.275349 + 2.33201i) q^{45} +1.22201i q^{46} +(1.50276 + 6.58403i) q^{47} +(-5.41904 - 3.01388i) q^{48} +(-1.34960 - 5.91298i) q^{49} +(-0.912923 + 0.728032i) q^{50} +(5.95589 + 0.350400i) q^{51} +(-10.3663 + 2.36605i) q^{52} +(-2.71989 - 11.9166i) q^{53} +(-1.21569 + 0.659257i) q^{54} +(1.87276 - 3.88882i) q^{55} +(0.225003 - 0.985801i) q^{56} +(-1.18708 - 7.10119i) q^{57} +(1.12132 - 0.540001i) q^{58} +(-1.68039 - 0.809235i) q^{59} +(-2.51129 - 0.730745i) q^{60} +(-3.93040 + 3.13439i) q^{61} +(0.196200 + 0.0944848i) q^{62} +(2.04021 + 2.06207i) q^{63} +(3.95903 - 4.96447i) q^{64} +(-3.88695 + 1.87186i) q^{65} +(2.50720 - 0.419120i) q^{66} +(-12.4773 - 2.84787i) q^{67} +(-1.47869 + 6.47856i) q^{68} +(5.31501 - 5.91570i) q^{69} -0.201434i q^{70} +(-6.06969 + 5.84456i) q^{71} +(-1.02036 - 2.96664i) q^{72} +(6.41916 + 8.04937i) q^{73} +(0.199812 + 0.0456057i) q^{74} +(7.58595 + 0.446300i) q^{75} +8.01909 q^{76} +(-2.31345 - 4.80393i) q^{77} +(-2.22046 - 1.23494i) q^{78} +(14.5615 - 7.01245i) q^{79} +(1.21583 - 2.52471i) q^{80} +(8.75251 + 2.09610i) q^{81} +(-0.0344259 + 0.0714861i) q^{82} +(-1.46007 + 3.03188i) q^{83} +(-2.63998 + 1.86261i) q^{84} +2.69621i q^{85} +(1.66211 + 0.379365i) q^{86} +(-7.77698 - 2.26297i) q^{87} +5.76652i q^{88} +(-8.62574 + 1.96877i) q^{89} +(-0.329679 - 0.530942i) q^{90} +(-1.18590 + 5.19578i) q^{91} +(5.52269 + 6.92523i) q^{92} +(-0.538844 - 1.31075i) q^{93} +(-1.40525 - 1.12065i) q^{94} +(3.17208 - 0.724007i) q^{95} +(5.20068 - 0.869379i) q^{96} +(0.981209 - 2.03750i) q^{97} +(1.26203 + 1.00643i) q^{98} +(-13.9602 - 8.87591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 10 q^{3} + 10 q^{4} - 15 q^{6} - 14 q^{7} - 14 q^{9} + 2 q^{10} + 20 q^{12} - 14 q^{13} + 22 q^{15} - 30 q^{16} + 8 q^{18} - 14 q^{19} - 28 q^{21} - 14 q^{22} + 8 q^{24} - 84 q^{25} - 7 q^{27} - 42 q^{28}+ \cdots + 49 q^{99}+O(q^{100}) $ 132 * q - 10 * q^3 + 10 * q^4 - 15 * q^6 - 14 * q^7 - 14 * q^9 + 2 * q^10 + 20 * q^12 - 14 * q^13 + 22 * q^15 - 30 * q^16 + 8 * q^18 - 14 * q^19 - 28 * q^21 - 14 * q^22 + 8 * q^24 - 84 * q^25 - 7 * q^27 - 42 * q^28 - 5 * q^30 + 14 * q^31 - 7 * q^33 - 42 * q^34 - 43 * q^36 + 22 * q^37 - 35 * q^39 + 64 * q^40 - 28 * q^42 + 16 * q^43 - 50 * q^45 + 55 * q^48 + 12 * q^49 - 98 * q^51 - 168 * q^52 - 38 * q^54 + 70 * q^55 + 48 * q^57 + 86 * q^58 + 116 * q^60 + 14 * q^61 + 105 * q^63 + 2 * q^64 - 42 * q^67 - 28 * q^69 + 266 * q^72 - 62 * q^73 + 18 * q^75 - 120 * q^76 + 21 * q^78 - 74 * q^79 - 22 * q^81 - 182 * q^82 + 42 * q^84 - 2 * q^87 + 15 * q^90 - 22 * q^91 + 14 * q^94 - 210 * q^96 - 42 * q^97 + 49 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/213\mathbb{Z}\right)^\times$.

$n$	$7$	$143$
$\chi(n)$	$e\left(\frac{3}{14}\right)$	$-1$

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 $

$2$	−0.208082	+	0.165940i	−0.147136	+	0.117337i	−0.694292	−	0.719694i	$-0.744282\pi$
$2$	−0.208082	+	0.165940i	−0.147136	+	0.117337i	0.547155	+	0.837031i	$0.315711\pi$
$3$	1.72906	+	0.101725i	0.998274	+	0.0587309i
$3$	1.72906	+	0.101725i	0.998274	+	0.0587309i
$4$	−0.429280	+	1.88080i	−0.214640	+	0.940399i
$5$			0.782738i			0.350051i	0.984564	+	0.175026i	$0.0560008\pi$
$5$			0.782738i			0.350051i	−0.984564	+	0.175026i	$0.943999\pi$
$6$	−0.376667	+	0.265753i	−0.153774	+	0.108493i
$7$	0.755976	+	0.602871i	0.285732	+	0.227864i	0.755858	−	0.654736i	$-0.227220\pi$
$7$	0.755976	+	0.602871i	0.285732	+	0.227864i	−0.470126	+	0.882599i	$0.655791\pi$
$8$	−0.453728	−	0.942175i	−0.160417	−	0.333109i
$9$	2.97930	+	0.351777i	0.993101	+	0.117259i
$10$	−0.129888	−	0.162874i	−0.0410740	−	0.0515052i
$11$	−4.96823	−	2.39257i	−1.49798	−	0.721388i	−0.507835	−	0.861454i	$-0.669554\pi$
$11$	−4.96823	−	2.39257i	−1.49798	−	0.721388i	−0.990142	+	0.140066i	$0.955269\pi$
$12$	−0.933575	+	3.20835i	−0.269500	+	0.926170i
$13$	2.39142	+	4.96584i	0.663261	+	1.37728i	0.912597	+	0.408859i	$0.134073\pi$
$13$	2.39142	+	4.96584i	0.663261	+	1.37728i	−0.249336	+	0.968417i	$0.580212\pi$
$14$	−0.257346			−0.0687785
$15$	−0.0796240	+	1.35340i	−0.0205588	+	0.349447i
$16$	−3.22548	−	1.55331i	−0.806370	−	0.388327i
$17$	3.44458			0.835434			0.417717	−	0.908577i	$-0.362830\pi$
$17$	3.44458			0.835434			0.417717	+	0.908577i	$0.362830\pi$
$18$	−0.678314	+	0.421187i	−0.159880	+	0.0992747i
$19$	−0.924967	−	4.05255i	−0.212202	−	0.929718i	−0.963067	−	0.269262i	$-0.913220\pi$
$19$	−0.924967	−	4.05255i	−0.212202	−	0.929718i	0.750865	−	0.660456i	$-0.229637\pi$
$20$	−1.47217	−	0.336014i	−0.329188	−	0.0751349i
$21$	1.24580	+	1.11930i	0.271856	+	0.244252i
$22$	1.43082	−	0.326576i	0.305053	−	0.0696262i
$23$	2.86273	−	3.58976i	0.596921	−	0.748516i	−0.387973	−	0.921671i	$-0.626825\pi$
$23$	2.86273	−	3.58976i	0.596921	−	0.748516i	0.984895	+	0.173155i	$0.0553961\pi$
$24$	−0.688680	−	1.67523i	−0.140576	−	0.341956i
$25$	4.38732			0.877464
$26$	−1.32164	−	0.636470i	−0.259196	−	0.124822i
$27$	5.11561	+	0.911314i	0.984500	+	0.175382i
$28$	−1.45840	+	1.16304i	−0.275612	+	0.219794i
$29$	−4.55903	−	1.04057i	−0.846590	−	0.193229i	−0.222842	−	0.974855i	$-0.571533\pi$
$29$	−4.55903	−	1.04057i	−0.846590	−	0.193229i	−0.623747	+	0.781626i	$0.714391\pi$
$30$	−0.208015	−	0.294832i	−0.0379782	−	0.0538286i
$31$	−0.355010	−	0.737186i	−0.0637617	−	0.132402i	0.866653	−	0.498912i	$-0.166267\pi$
$31$	−0.355010	−	0.737186i	−0.0637617	−	0.132402i	−0.930414	+	0.366510i	$0.880553\pi$
$32$	2.96795	−	0.677416i	0.524665	−	0.119751i
$33$	−8.34699	−	4.64230i	−1.45302	−	0.808120i
$34$	−0.716756	+	0.571594i	−0.122923	+	0.0980276i
$35$	−0.471890	+	0.591731i	−0.0797640	+	0.100021i
$36$	−1.94058	+	5.45246i	−0.323429	+	0.908743i
$37$	−0.480127	−	0.602061i	−0.0789324	−	0.0989782i	0.740797	−	0.671729i	$-0.234448\pi$
$37$	−0.480127	−	0.602061i	−0.0789324	−	0.0989782i	−0.819730	+	0.572750i	$0.805876\pi$
$38$	0.864948	+	0.689773i	0.140313	+	0.111896i
$39$	3.62977	+	8.82951i	0.581228	+	1.41385i
$40$	0.737477	−	0.355150i	0.116605	−	0.0561541i
$41$	0.268596	−	0.129349i	0.0419477	−	0.0202009i	−0.412792	−	0.910825i	$-0.635446\pi$
$41$	0.268596	−	0.129349i	0.0419477	−	0.0202009i	0.454740	+	0.890624i	$0.349732\pi$
$42$	−0.444966	−	0.0261785i	−0.0686598	−	0.00403942i
$43$	−3.99387	−	5.00816i	−0.609060	−	0.763737i	0.377700	−	0.925928i	$-0.376715\pi$
$43$	−3.99387	−	5.00816i	−0.609060	−	0.763737i	−0.986759	+	0.162192i	$0.948144\pi$
$44$	6.63271	−	8.31715i	0.999918	−	1.25386i
$45$	−0.275349	+	2.33201i	−0.0410467	+	0.347636i
$46$			1.22201i			0.180175i
$47$	1.50276	+	6.58403i	0.219200	+	0.960380i	0.958071	+	0.286532i	$0.0925025\pi$
$47$	1.50276	+	6.58403i	0.219200	+	0.960380i	−0.738870	+	0.673848i	$0.764640\pi$
$48$	−5.41904	−	3.01388i	−0.782171	−	0.435016i
$49$	−1.34960	−	5.91298i	−0.192800	−	0.844712i
$50$	−0.912923	+	0.728032i	−0.129107	+	0.102959i
$51$	5.95589	+	0.350400i	0.833992	+	0.0490658i
$52$	−10.3663	+	2.36605i	−1.43755	+	0.328112i
$53$	−2.71989	−	11.9166i	−0.373606	−	1.63687i	−0.716563	−	0.697522i	$-0.754286\pi$
$53$	−2.71989	−	11.9166i	−0.373606	−	1.63687i	0.342957	−	0.939351i	$-0.388571\pi$
$54$	−1.21569	+	0.659257i	−0.165435	+	0.0897135i
$55$	1.87276	−	3.88882i	0.252523	−	0.524369i
$56$	0.225003	−	0.985801i	0.0300673	−	0.131733i
$57$	−1.18708	−	7.10119i	−0.157233	−	0.940576i
$58$	1.12132	−	0.540001i	0.147237	−	0.0709056i
$59$	−1.68039	−	0.809235i	−0.218769	−	0.105353i	0.321290	−	0.946981i	$-0.395884\pi$
$59$	−1.68039	−	0.809235i	−0.218769	−	0.105353i	−0.540059	+	0.841627i	$0.681598\pi$
$60$	−2.51129	−	0.730745i	−0.324207	−	0.0943387i
$61$	−3.93040	+	3.13439i	−0.503236	+	0.401317i	−0.841936	−	0.539577i	$-0.818584\pi$
$61$	−3.93040	+	3.13439i	−0.503236	+	0.401317i	0.338700	+	0.940894i	$0.390013\pi$
$62$	0.196200	+	0.0944848i	0.0249174	+	0.0119996i
$63$	2.04021	+	2.06207i	0.257042	+	0.259797i
$64$	3.95903	−	4.96447i	0.494879	−	0.620559i
$65$	−3.88695	+	1.87186i	−0.482117	+	0.232175i
$66$	2.50720	−	0.419120i	0.308615	−	0.0515901i
$67$	−12.4773	−	2.84787i	−1.52435	−	0.347922i	−0.623418	−	0.781888i	$-0.714257\pi$
$67$	−12.4773	−	2.84787i	−1.52435	−	0.347922i	−0.900929	+	0.433966i	$0.857114\pi$
$68$	−1.47869	+	6.47856i	−0.179317	+	0.785641i
$69$	5.31501	−	5.91570i	0.639852	−	0.712166i
$70$		−	0.201434i		−	0.0240760i
$71$	−6.06969	+	5.84456i	−0.720340	+	0.693621i
$71$	−6.06969	+	5.84456i	−0.720340	+	0.693621i
$72$	−1.02036	−	2.96664i	−0.120250	−	0.349622i
$73$	6.41916	+	8.04937i	0.751306	+	0.942108i	0.999647	−	0.0265651i	$-0.00845691\pi$
$73$	6.41916	+	8.04937i	0.751306	+	0.942108i	−0.248341	+	0.968673i	$0.579885\pi$
$74$	0.199812	+	0.0456057i	0.0232276	+	0.00530156i
$75$	7.58595	+	0.446300i	0.875950	+	0.0515343i
$76$	8.01909			0.919853
$77$	−2.31345	−	4.80393i	−0.263642	−	0.547459i
$78$	−2.22046	−	1.23494i	−0.251417	−	0.139829i
$79$	14.5615	−	7.01245i	1.63830	−	0.788963i	0.638485	−	0.769635i	$-0.279562\pi$
$79$	14.5615	−	7.01245i	1.63830	−	0.788963i	0.999813	−	0.0193282i	$-0.00615273\pi$
$80$	1.21583	−	2.52471i	0.135934	−	0.282271i
$81$	8.75251	+	2.09610i	0.972501	+	0.232900i
$82$	−0.0344259	+	0.0714861i	−0.00380170	+	0.00789432i
$83$	−1.46007	+	3.03188i	−0.160264	+	0.332792i	−0.965602	−	0.260024i	$-0.916269\pi$
$83$	−1.46007	+	3.03188i	−0.160264	+	0.332792i	0.805338	+	0.592816i	$0.201984\pi$
$84$	−2.63998	+	1.86261i	−0.288045	+	0.203227i
$85$			2.69621i			0.292445i
$86$	1.66211	+	0.379365i	0.179230	+	0.0409080i
$87$	−7.77698	−	2.26297i	−0.833780	−	0.242616i
$88$			5.76652i			0.614713i
$89$	−8.62574	+	1.96877i	−0.914327	+	0.208689i	−0.653703	−	0.756751i	$-0.726785\pi$
$89$	−8.62574	+	1.96877i	−0.914327	+	0.208689i	−0.260624	+	0.965440i	$0.583928\pi$
$90$	−0.329679	−	0.530942i	−0.0347512	−	0.0559662i
$91$	−1.18590	+	5.19578i	−0.124316	+	0.544665i
$92$	5.52269	+	6.92523i	0.575780	+	0.722006i
$93$	−0.538844	−	1.31075i	−0.0558755	−	0.135919i
$94$	−1.40525	−	1.12065i	−0.144941	−	0.115586i
$95$	3.17208	−	0.724007i	0.325449	−	0.0742816i
$96$	5.20068	−	0.869379i	0.530793	−	0.0887306i
$97$	0.981209	−	2.03750i	0.0996267	−	0.206877i	−0.845198	−	0.534453i	$-0.820518\pi$
$97$	0.981209	−	2.03750i	0.0996267	−	0.206877i	0.944825	+	0.327576i	$0.106232\pi$
$98$	1.26203	+	1.00643i	0.127484	+	0.101665i
$99$	−13.9602	−	8.87591i	−1.40305	−	0.892063i
$100$	−1.88339	+	8.25166i	−0.188339	+	0.825166i
$101$	7.50147	+	15.5770i	0.746424	+	1.54997i	0.832719	+	0.553696i	$0.186783\pi$
$101$	7.50147	+	15.5770i	0.746424	+	1.54997i	−0.0862948	+	0.996270i	$0.527503\pi$
$102$	−1.29746	+	0.915409i	−0.128468	+	0.0906390i
$103$	−0.0567521	−	0.248647i	−0.00559195	−	0.0244999i	0.972055	−	0.234753i	$-0.0754282\pi$
$103$	−0.0567521	−	0.248647i	−0.00559195	−	0.0244999i	−0.977647	+	0.210253i	$0.932571\pi$
$104$	3.59364	−	4.50628i	0.352385	−	0.441877i
$105$	−0.876121	+	0.975137i	−0.0855006	+	0.0951636i
$106$	2.54340	+	2.02830i	0.247037	+	0.197006i
$107$	7.64363	+	6.09560i	0.738938	+	0.589283i	0.918947	−	0.394382i	$-0.129041\pi$
$107$	7.64363	+	6.09560i	0.738938	+	0.589283i	−0.180009	+	0.983665i	$0.557613\pi$
$108$	−3.91003	+	9.23023i	−0.376242	+	0.888179i
$109$	−3.93259	+	4.93131i	−0.376674	+	0.472334i	−0.933646	−	0.358197i	$-0.883392\pi$
$109$	−3.93259	+	4.93131i	−0.376674	+	0.472334i	0.556972	+	0.830531i	$0.311963\pi$
$110$	0.255624	+	1.11996i	0.0243727	+	0.106784i
$111$	−0.768925	−	1.08984i	−0.0729831	−	0.103443i
$112$	−1.50194	−	3.11881i	−0.141920	−	0.294700i
$113$	−1.71323	+	7.50615i	−0.161167	+	0.706119i	0.828170	+	0.560477i	$0.189382\pi$
$113$	−1.71323	+	7.50615i	−0.161167	+	0.706119i	−0.989337	+	0.145642i	$0.953475\pi$
$114$	1.42538	+	1.28065i	0.133499	+	0.119944i
$115$	2.80984	+	2.24077i	0.262019	+	0.208953i
$116$	3.91419	−	8.12791i	0.363424	−	0.754657i
$117$	5.37791	+	15.6360i	0.497188	+	1.44555i
$118$	0.483944	−	0.110457i	0.0445507	−	0.0101684i
$119$	2.60402	+	2.07664i	0.238710	+	0.190365i
$120$	1.31127	−	0.539056i	0.119702	−	0.0492089i
$121$	12.1005	+	15.1736i	1.10005	+	1.37941i
$122$	0.297725	−	1.30442i	0.0269548	−	0.118097i
$123$	0.477577	−	0.196330i	0.0430617	−	0.0177024i
$124$	1.53890	−	0.351243i	0.138197	−	0.0315425i
$125$			7.34781i			0.657208i
$126$	−0.766711	−	0.0905283i	−0.0683040	−	0.00806490i
$127$	−2.75931	−	0.629795i	−0.244849	−	0.0558853i	0.0983348	−	0.995153i	$-0.468648\pi$
$127$	−2.75931	−	0.629795i	−0.244849	−	0.0558853i	−0.343184	+	0.939268i	$0.611506\pi$
$128$			7.77854i			0.687532i
$129$	−6.39619	−	9.06568i	−0.563153	−	0.798189i
$130$	0.498189	−	1.03450i	0.0436941	−	0.0907317i
$131$	0.229726	−	0.477031i	0.0200712	−	0.0416784i	−0.890692	−	0.454607i	$-0.849780\pi$
$131$	0.229726	−	0.477031i	0.0200712	−	0.0416784i	0.910763	+	0.412928i	$0.135494\pi$
$132$	12.3144	−	13.7062i	1.07183	−	1.19297i
$133$	1.74391	−	3.62127i	0.151216	−	0.314004i
$134$	3.06888	−	1.47790i	0.265111	−	0.127671i
$135$	−0.713320	+	4.00419i	−0.0613928	+	0.344625i
$136$	−1.56290	−	3.24540i	−0.134018	−	0.278291i
$137$	−12.5983			−1.07635			−0.538173	−	0.842835i	$-0.680885\pi$
$137$	−12.5983			−1.07635			−0.538173	+	0.842835i	$0.680885\pi$
$138$	−0.124308	+	2.11292i	−0.0105818	+	0.179864i
$139$	−15.5592	−	3.55130i	−1.31972	−	0.301217i	−0.496052	−	0.868293i	$-0.665218\pi$
$139$	−15.5592	−	3.55130i	−1.31972	−	0.301217i	−0.823666	+	0.567076i	$0.808075\pi$
$140$	−0.910354	−	1.14155i	−0.0769390	−	0.0964784i
$141$	1.92861	+	11.5371i	0.162418	+	0.971596i
$142$	0.293148	−	2.22335i	0.0246005	−	0.186580i
$143$		−	30.3931i		−	2.54160i
$144$	−9.06327	−	5.76243i	−0.755272	−	0.480203i
$145$	0.814492	−	3.56852i	0.0676399	−	0.296350i
$146$	−2.67142	−	0.609735i	−0.221089	−	0.0504620i
$147$	−1.73204	−	10.3612i	−0.142856	−	0.854577i
$148$	1.33846	−	0.644570i	0.110021	−	0.0529833i
$149$	−4.41783	+	5.53978i	−0.361923	+	0.453837i	−0.929138	−	0.369733i	$-0.879449\pi$
$149$	−4.41783	+	5.53978i	−0.361923	+	0.453837i	0.567215	+	0.823569i	$0.308021\pi$
$150$	−1.65256	+	1.16594i	−0.134931	+	0.0951990i
$151$	9.81899	+	4.72858i	0.799058	+	0.384806i	0.788420	−	0.615137i	$-0.210899\pi$
$151$	9.81899	+	4.72858i	0.799058	+	0.384806i	0.0106380	+	0.999943i	$0.496614\pi$
$152$	−3.39853	+	2.71023i	−0.275657	+	0.219829i
$153$	10.2625	+	1.21173i	0.829671	+	0.0979622i
$154$	1.27855	+	0.615718i	0.103029	+	0.0496160i
$155$	0.577023	−	0.277880i	0.0463476	−	0.0223198i
$156$	−18.1647	+	3.03653i	−1.45434	+	0.243117i
$157$	2.13731	−	9.36415i	0.170576	−	0.747340i	−0.815187	−	0.579198i	$-0.803366\pi$
$157$	2.13731	−	9.36415i	0.170576	−	0.747340i	0.985763	−	0.168143i	$-0.0537769\pi$
$158$	−1.86634	+	3.87550i	−0.148478	+	0.308318i
$159$	−3.49064	−	20.8812i	−0.276826	−	1.65599i
$160$	0.530240	+	2.32313i	0.0419191	+	0.183660i
$161$	4.32832	−	0.987911i	0.341119	−	0.0778583i
$162$	−2.16907	+	1.01623i	−0.170418	+	0.0798425i
$163$	6.89447	−	5.49816i	0.540016	−	0.430649i	−0.315120	−	0.949052i	$-0.602045\pi$
$163$	6.89447	−	5.49816i	0.540016	−	0.430649i	0.855136	+	0.518403i	$0.173473\pi$
$164$	0.127977	+	0.560702i	0.00999330	+	0.0437835i
$165$	3.63370	−	6.53351i	0.282883	−	0.508633i
$166$	−0.199294	−	0.873164i	−0.0154682	−	0.0677707i
$167$			18.7990i			1.45471i	0.686262	+	0.727354i	$0.259250\pi$
$167$			18.7990i			1.45471i	−0.686262	+	0.727354i	$0.740750\pi$
$168$	0.489324	−	1.68162i	0.0377522	−	0.129740i
$169$	−10.8353	+	13.5870i	−0.833485	+	1.04516i
$170$	−0.447408	−	0.561032i	−0.0343147	−	0.0430292i
$171$	−1.33017	−	12.3992i	−0.101720	−	0.948187i
$172$	11.1338	−	5.36176i	0.848945	−	0.408831i
$173$	15.2198	−	7.32949i	1.15714	−	0.557251i	0.245971	−	0.969277i	$-0.420893\pi$
$173$	15.2198	−	7.32949i	1.15714	−	0.557251i	0.911172	+	0.412026i	$0.135179\pi$
$174$	1.99377	−	0.819628i	0.151147	−	0.0621358i
$175$	3.31671	+	2.64499i	0.250720	+	0.199942i
$176$	12.3085	+	15.4344i	0.927789	+	1.16341i
$177$	−2.82319	−	1.57016i	−0.212204	−	0.118020i
$178$	1.46816	−	1.84102i	0.110044	−	0.137990i
$179$	18.7489	−	14.9518i	1.40136	−	1.11755i	0.424073	−	0.905628i	$-0.360600\pi$
$179$	18.7489	−	14.9518i	1.40136	−	1.11755i	0.977287	−	0.211920i	$-0.0679715\pi$
$180$	−4.26785	−	1.51896i	−0.318106	−	0.113217i
$181$	−3.94735	+	0.900957i	−0.293404	+	0.0669676i	−0.366689	−	0.930343i	$-0.619509\pi$
$181$	−3.94735	+	0.900957i	−0.293404	+	0.0669676i	0.0732851	+	0.997311i	$0.476652\pi$
$182$	−0.615422	−	1.27794i	−0.0456181	−	0.0947270i
$183$	−7.11474	+	5.01973i	−0.525937	+	0.371069i
$184$	−4.68108	−	1.06843i	−0.345094	−	0.0787654i
$185$	0.471256	−	0.375814i	0.0346474	−	0.0276304i
$186$	0.329630	+	0.183328i	0.0241696	+	0.0134423i
$187$	−17.1135	−	8.24142i	−1.25146	−	0.602672i
$188$	−13.0283			−0.950189
$189$	3.31788	+	3.77299i	0.241340	+	0.274444i
$190$	−0.539912	+	0.677028i	−0.0391693	+	0.0491168i
$191$	−2.54874	+	0.581734i	−0.184421	+	0.0420928i	−0.313734	−	0.949511i	$-0.601580\pi$
$191$	−2.54874	+	0.581734i	−0.184421	+	0.0420928i	0.129313	+	0.991604i	$0.458723\pi$
$192$	7.35042	−	8.18114i	0.530471	−	0.590423i
$193$	−21.1862	−	4.83562i	−1.52502	−	0.348075i	−0.623850	−	0.781544i	$-0.714432\pi$
$193$	−21.1862	−	4.83562i	−1.52502	−	0.348075i	−0.901168	+	0.433469i	$0.857289\pi$
$194$	0.133931	+	0.586789i	0.00961567	+	0.0421290i
$195$	−6.91119	+	2.84116i	−0.494921	+	0.203459i
$196$	11.7005			0.835749
$197$	−5.58568	−	2.68992i	−0.397963	−	0.191649i	0.224188	−	0.974546i	$-0.428027\pi$
$197$	−5.58568	−	2.68992i	−0.397963	−	0.191649i	−0.622152	+	0.782897i	$0.713741\pi$
$198$	4.37774	−	0.469638i	0.311112	−	0.0333757i
$199$	−16.6621			−1.18114			−0.590571	−	0.806985i	$-0.701098\pi$
$199$	−16.6621			−1.18114			−0.590571	+	0.806985i	$0.701098\pi$
$200$	−1.99065	−	4.13363i	−0.140760	−	0.292291i
$201$	−21.2844	−	6.19339i	−1.50128	−	0.436848i
$202$	−4.14576	−	1.99649i	−0.291695	−	0.140473i
$203$	−2.81919	−	3.53515i	−0.197868	−	0.248119i
$204$	−3.21578	+	11.0514i	−0.225149	+	0.773754i
$205$	0.101247	+	0.210241i	0.00707136	+	0.0146838i
$206$	0.0530696	+	0.0423216i	0.00369754	+	0.00294869i
$207$	9.79175	−	9.68793i	0.680574	−	0.673358i
$208$		−	19.7318i		−	1.36816i
$209$	−5.10056	+	22.3470i	−0.352813	+	1.54578i
$210$	0.0204909	−	0.348292i	0.00141400	−	0.0240344i
$211$	−10.3277	+	8.23607i	−0.710988	+	0.566994i	−0.910804	−	0.412839i	$-0.864537\pi$
$211$	−10.3277	+	8.23607i	−0.710988	+	0.566994i	0.199815	+	0.979834i	$0.435966\pi$
$212$	23.5803			1.61950
$213$	−11.0894	+	9.48816i	−0.759833	+	0.650118i
$214$	−2.60201			−0.177869
$215$	3.92007	−	3.12615i	0.267347	−	0.213202i
$216$	−1.46248	−	5.23329i	−0.0995091	−	0.356081i
$217$	0.176049	−	0.771320i	0.0119510	−	0.0523606i
$218$		−	1.67869i		−	0.113695i
$219$	10.2803	+	14.5708i	0.694678	+	0.984606i
$220$	6.51015	+	5.19167i	0.438914	+	0.350022i
$221$	8.23746	+	17.1053i	0.554111	+	1.15062i
$222$	0.340848	+	0.0991809i	0.0228762	+	0.00665659i
$223$	−2.09611	−	2.62845i	−0.140366	−	0.176014i	0.706679	−	0.707534i	$-0.250192\pi$
$223$	−2.09611	−	2.62845i	−0.140366	−	0.176014i	−0.847046	+	0.531520i	$0.821621\pi$
$224$	2.65210	+	1.27718i	0.177201	+	0.0853354i
$225$	13.0712	+	1.54336i	0.871411	+	0.102891i
$226$	−0.889077	−	1.84619i	−0.0591405	−	0.122807i
$227$	−11.9785			−0.795040			−0.397520	−	0.917594i	$-0.630129\pi$
$227$	−11.9785			−0.795040			−0.397520	+	0.917594i	$0.630129\pi$
$228$	13.8655	+	0.815741i	0.918265	+	0.0540238i
$229$	17.0947	+	8.23238i	1.12965	+	0.544011i	0.902861	−	0.429933i	$-0.141463\pi$
$229$	17.0947	+	8.23238i	1.12965	+	0.544011i	0.226789	+	0.973944i	$0.427177\pi$
$230$	−0.956511			−0.0630704
$231$	−3.51142	−	8.54162i	−0.231034	−	0.561998i
$232$	1.08816	+	4.76754i	0.0714411	+	0.313004i
$233$	−8.21302	−	1.87457i	−0.538053	−	0.122807i	−0.0551451	−	0.998478i	$-0.517562\pi$
$233$	−8.21302	−	1.87457i	−0.538053	−	0.122807i	−0.482908	+	0.875671i	$0.660419\pi$
$234$	−3.71368	−	2.36116i	−0.242771	−	0.154354i
$235$	−5.15357	+	1.17627i	−0.336182	+	0.0767314i
$236$	2.24337	−	2.81309i	0.146031	−	0.183117i
$237$	25.8911	−	10.6437i	1.68181	−	0.691382i
$238$	−0.886448			−0.0574599
$239$	−11.0730	−	5.33249i	−0.716255	−	0.344930i	0.0400068	−	0.999199i	$-0.487262\pi$
$239$	−11.0730	−	5.33249i	−0.716255	−	0.344930i	−0.756262	+	0.654269i	$0.772976\pi$
$240$	2.35908	−	4.24169i	0.152278	−	0.273800i
$241$	−4.30331	+	3.43178i	−0.277201	+	0.221060i	−0.752215	−	0.658918i	$-0.771014\pi$
$241$	−4.30331	+	3.43178i	−0.277201	+	0.221060i	0.475014	+	0.879978i	$0.342443\pi$
$242$	−5.03580	−	1.14939i	−0.323713	−	0.0738855i
$243$	14.9204	+	4.51464i	0.957143	+	0.289614i
$244$	−4.20791	−	8.73781i	−0.269384	−	0.559381i
$245$	4.62832	−	1.05638i	0.295692	−	0.0674899i
$246$	−0.0667964	+	0.120102i	−0.00425878	+	0.00765741i
$247$	17.9123	−	14.2846i	1.13973	−	0.908907i
$248$	−0.533480	+	0.668963i	−0.0338760	+	0.0424792i
$249$	−2.83298	+	5.09377i	−0.179533	+	0.322805i
$250$	−1.21930	−	1.52895i	−0.0771150	−	0.0966992i
$251$	−15.7722	−	12.5779i	−0.995535	−	0.793913i	−0.0169713	−	0.999856i	$-0.505402\pi$
$251$	−15.7722	−	12.5779i	−0.995535	−	0.793913i	−0.978564	+	0.205943i	$0.933974\pi$
$252$	−4.75416	+	2.95201i	−0.299484	+	0.185959i
$253$	−22.8115	+	10.9854i	−1.43415	+	0.690648i
$254$	0.678672	−	0.326831i	0.0425837	−	0.0205072i
$255$	−0.274271	+	4.66191i	−0.0171755	+	0.291940i
$256$	6.62730	+	8.31037i	0.414206	+	0.519398i
$257$	−13.2550	+	16.6213i	−0.826825	+	1.03681i	0.171838	+	0.985125i	$0.445029\pi$
$257$	−13.2550	+	16.6213i	−0.826825	+	1.03681i	−0.998664	+	0.0516809i	$0.983542\pi$
$258$	2.83529	+	0.825023i	0.176518	+	0.0513637i
$259$		−	0.744598i		−	0.0462671i
$260$	−1.85200	−	8.11412i	−0.114856	−	0.503217i
$261$	−13.2167	−	4.70393i	−0.818092	−	0.291166i
$262$	0.0313566	+	0.137382i	0.00193722	+	0.00848750i
$263$	3.90925	−	3.11753i	0.241055	−	0.192235i	−0.495509	−	0.868603i	$-0.665018\pi$
$263$	3.90925	−	3.11753i	0.241055	−	0.192235i	0.736564	+	0.676368i	$0.236447\pi$
$264$	−0.586599	+	9.97067i	−0.0361027	+	0.613652i
$265$	9.32759	−	2.12896i	0.572989	−	0.130781i
$266$	0.238036	+	1.04290i	0.0145949	+	0.0639446i
$267$	−15.1147	+	2.52667i	−0.925005	+	0.154630i
$268$	10.7125	−	22.2448i	0.654372	−	1.35882i
$269$	3.73067	−	16.3451i	0.227463	−	0.996581i	−0.724237	−	0.689551i	$-0.757808\pi$
$269$	3.73067	−	16.3451i	0.227463	−	0.996581i	0.951700	−	0.307030i	$-0.0993352\pi$
$270$	−0.516025	−	0.951568i	−0.0314043	−	0.0579106i
$271$	23.9178	−	11.5182i	1.45290	−	0.699680i	0.469805	−	0.882770i	$-0.344324\pi$
$271$	23.9178	−	11.5182i	1.45290	−	0.699680i	0.983096	+	0.183090i	$0.0586100\pi$
$272$	−11.1104	−	5.35050i	−0.673669	−	0.324422i
$273$	−2.57904	+	8.86318i	−0.156090	+	0.536424i
$274$	2.62148	−	2.09056i	0.158369	−	0.126295i
$275$	−21.7972	−	10.4970i	−1.31442	−	0.632992i
$276$	8.84460	+	12.5359i	0.532382	+	0.754575i
$277$	7.55509	−	9.47379i	0.453942	−	0.569225i	−0.501216	−	0.865322i	$-0.667114\pi$
$277$	7.55509	−	9.47379i	0.453942	−	0.569225i	0.955158	+	0.296097i	$0.0956853\pi$
$278$	3.82690	−	1.84294i	0.229522	−	0.110532i
$279$	−0.798357	−	2.32118i	−0.0477964	−	0.138966i
$280$	0.771624	+	0.176118i	0.0461134	+	0.0105251i
$281$	−5.10751	+	22.3774i	−0.304688	+	1.33493i	0.558273	+	0.829657i	$0.311464\pi$
$281$	−5.10751	+	22.3774i	−0.304688	+	1.33493i	−0.862962	+	0.505269i	$0.831393\pi$
$282$	−2.31577	−	2.08062i	−0.137902	−	0.123899i
$283$			22.9101i			1.36186i	0.732348	+	0.680931i	$0.238425\pi$
$283$			22.9101i			1.36186i	−0.732348	+	0.680931i	$0.761575\pi$
$284$	−8.38683	−	13.9248i	−0.497667	−	0.826285i
$285$	5.55837	−	0.929173i	0.329250	−	0.0550394i
$286$	5.04343	+	6.32426i	0.298224	+	0.373961i
$287$	0.281033	+	0.0641440i	0.0165889	+	0.00378630i
$288$	9.08074	−	0.974170i	0.535088	−	0.0574035i
$289$	−5.13485			−0.302050
$290$	0.422679	+	0.877702i	0.0248206	+	0.0515405i
$291$	1.90383	−	3.42315i	0.111605	−	0.200669i
$292$	−17.8949	+	8.61771i	−1.04722	+	0.504313i
$293$	7.08866	−	14.7198i	0.414124	−	0.859937i	−0.584690	−	0.811257i	$-0.698784\pi$
$293$	7.08866	−	14.7198i	0.414124	−	0.859937i	0.998814	−	0.0486808i	$-0.0155017\pi$
$294$	2.07974	+	1.86856i	0.121293	+	0.108977i
$295$	0.633419	−	1.31531i	0.0368791	−	0.0765802i
$296$	−0.349400	+	0.725536i	−0.0203084	+	0.0421709i
$297$	−23.2352	−	16.7671i	−1.34824	−	0.972926i
$298$		−	1.88582i		−	0.109243i
$299$	24.6722	+	5.63126i	1.42683	+	0.325664i
$300$	−4.09589	+	14.0760i	−0.236476	+	0.812681i
$301$		−	6.19384i		−	0.357007i
$302$	−2.82782	+	0.645430i	−0.162722	+	0.0371403i
$303$	11.3859	+	27.6966i	0.654105	+	1.59113i
$304$	−3.31139	+	14.5082i	−0.189921	+	0.832100i
$305$	−2.45340	−	3.07647i	−0.140481	−	0.176158i
$306$	−2.33651	+	1.45081i	−0.133569	+	0.0829375i
$307$	10.7470	+	8.57043i	0.613363	+	0.489140i	0.880201	−	0.474601i	$-0.157408\pi$
$307$	10.7470	+	8.57043i	0.613363	+	0.489140i	−0.266838	+	0.963741i	$0.585979\pi$
$308$	10.0283	−	2.28890i	0.571418	−	0.130422i
$309$	−0.0728343	−	0.435699i	−0.00414340	−	0.0247861i
$310$	−0.0739569	+	0.153573i	−0.00420047	+	0.00872236i
$311$	−1.79572	−	1.43204i	−0.101826	−	0.0812034i	0.571254	−	0.820774i	$-0.306457\pi$
$311$	−1.79572	−	1.43204i	−0.101826	−	0.0812034i	−0.673079	+	0.739570i	$0.735029\pi$
$312$	6.67202	−	7.42607i	0.377729	−	0.420418i
$313$	3.28436	−	14.3897i	0.185643	−	0.813356i	−0.793236	−	0.608915i	$-0.791605\pi$
$313$	3.28436	−	14.3897i	0.185643	−	0.813356i	0.978879	−	0.204441i	$-0.0655376\pi$
$314$	1.10915	+	2.30318i	0.0625930	+	0.129976i
$315$	−1.61406	+	1.59695i	−0.0909421	+	0.0899778i
$316$	6.93804	+	30.3976i	0.390295	+	1.71000i
$317$	13.5882	−	17.0391i	0.763192	−	0.957012i	−0.236702	−	0.971582i	$-0.576066\pi$
$317$	13.5882	−	17.0391i	0.763192	−	0.957012i	0.999894	+	0.0145699i	$0.00463791\pi$
$318$	4.19137	+	3.76578i	0.235040	+	0.211174i
$319$	20.1606	+	16.0776i	1.12878	+	0.900172i
$320$	3.88588	+	3.09889i	0.217227	+	0.173233i
$321$	12.5962	+	11.3172i	0.703053	+	0.631665i
$322$	−0.736712	+	0.923808i	−0.0410554	+	0.0514818i
$323$	−3.18613	−	13.9593i	−0.177281	−	0.776718i
$324$	−7.69962	+	15.5619i	−0.427757	+	0.864549i
$325$	10.4919	+	21.7867i	0.581988	+	1.20851i
$326$	−0.522252	+	2.28814i	−0.0289249	+	0.126728i
$327$	−7.30132	+	8.12650i	−0.403764	+	0.449396i
$328$	−0.243739	−	0.194375i	−0.0134582	−	0.0107326i
$329$	−2.83327	+	5.88335i	−0.156203	+	0.324359i
$330$	0.328061	+	1.96248i	0.0180592	+	0.108031i
$331$	−3.07087	+	0.700906i	−0.168790	+	0.0385253i	−0.306081	−	0.952006i	$-0.599018\pi$
$331$	−3.07087	+	0.700906i	−0.168790	+	0.0385253i	0.137291	+	0.990531i	$0.456161\pi$
$332$	−5.07556	−	4.04763i	−0.278558	−	0.222142i
$333$	−1.21865	−	1.96262i	−0.0667818	−	0.107551i
$334$	−3.11950	−	3.91173i	−0.170692	−	0.214040i
$335$	2.22913	−	9.76648i	0.121791	−	0.533600i
$336$	−2.27969	−	5.54540i	−0.124367	−	0.302527i
$337$	−13.8768	+	3.16728i	−0.755916	+	0.172533i	−0.583077	−	0.812417i	$-0.698151\pi$
$337$	−13.8768	+	3.16728i	−0.755916	+	0.172533i	−0.172840	+	0.984950i	$0.555294\pi$
$338$		−	4.62523i		−	0.251579i
$339$	−3.72584	+	12.8043i	−0.202360	+	0.695435i
$340$	−5.07102	−	1.15743i	−0.275015	−	0.0627703i
$341$			4.51190i			0.244333i
$342$	2.33430	+	2.35931i	0.126224	+	0.127577i
$343$	5.48125	−	11.3819i	0.295960	−	0.614566i
$344$	−2.90643	+	6.03527i	−0.156704	+	0.325400i
$345$	4.63044	+	4.16026i	0.249295	+	0.223981i
$346$	−1.95072	+	4.05072i	−0.104871	+	0.217768i
$347$	−13.2810	+	6.39581i	−0.712964	+	0.343345i	−0.754958	−	0.655773i	$-0.772343\pi$
$347$	−13.2810	+	6.39581i	−0.712964	+	0.343345i	0.0419949	+	0.999118i	$0.486629\pi$
$348$	7.59469	−	13.6555i	0.407118	−	0.732010i
$349$	4.54702	+	9.44199i	0.243397	+	0.505418i	0.986501	−	0.163758i	$-0.0523616\pi$
$349$	4.54702	+	9.44199i	0.243397	+	0.505418i	−0.743104	+	0.669176i	$0.766647\pi$
$350$	−1.12906			−0.0603507
$351$	7.70816	+	27.5827i	0.411431	+	1.47225i
$352$	−16.3662	−	3.73549i	−0.872324	−	0.199102i
$353$	2.37444	+	2.97745i	0.126379	+	0.158474i	0.840995	−	0.541043i	$-0.181970\pi$
$353$	2.37444	+	2.97745i	0.126379	+	0.158474i	−0.714616	+	0.699516i	$0.753399\pi$
$354$	0.848006	−	0.141758i	0.0450710	−	0.00753435i
$355$	−4.57476	−	4.75098i	−0.242803	−	0.252156i
$356$		−	17.0684i		−	0.904625i
$357$	4.29127	+	3.85553i	0.227118	+	0.204056i
$358$	−1.42022	+	6.22239i	−0.0750610	+	0.328864i
$359$	16.6894	+	3.80924i	0.880832	+	0.201044i	0.638938	−	0.769259i	$-0.279374\pi$
$359$	16.6894	+	3.80924i	0.880832	+	0.201044i	0.241894	+	0.970303i	$0.422231\pi$
$360$	2.32210	−	0.798672i	0.122385	−	0.0420937i
$361$	1.55084	−	0.746845i	0.0816231	−	0.0393076i
$362$	0.671868	−	0.842496i	0.0353126	−	0.0442806i
$363$	19.3790	+	27.4669i	1.01713	+	1.44164i
$364$	−9.26312	−	4.46088i	−0.485520	−	0.233814i
$365$	−6.30055	+	5.02452i	−0.329786	+	0.262995i
$366$	0.647477	−	2.22513i	0.0338442	−	0.116310i
$367$	−14.4899	−	6.97795i	−0.756365	−	0.364246i	0.0156274	−	0.999878i	$-0.495025\pi$
$367$	−14.4899	−	6.97795i	−0.756365	−	0.364246i	−0.771992	+	0.635632i	$0.780740\pi$
$368$	−14.8097	+	7.13197i	−0.772009	+	0.371780i
$369$	0.845732	−	0.290884i	0.0440271	−	0.0151428i
$370$	−0.0356974	+	0.156400i	−0.00185582	+	0.00813087i
$371$	5.12801	−	10.6484i	0.266233	−	0.552839i
$372$	2.69657	−	0.450776i	0.139811	−	0.0233717i
$373$	−1.29448	−	5.67150i	−0.0670258	−	0.293659i	0.930295	−	0.366812i	$-0.119551\pi$
$373$	−1.29448	−	5.67150i	−0.0670258	−	0.293659i	−0.997321	+	0.0731533i	$0.976694\pi$
$374$	4.92859	−	1.12492i	0.254851	−	0.0581681i
$375$	−0.747456	+	12.7048i	−0.0385985	+	0.656074i
$376$	5.52147	−	4.40322i	0.284748	−	0.227079i
$377$	−5.73526	−	25.1278i	−0.295381	−	1.29415i
$378$	−1.31648	−	0.234522i	−0.0677124	−	0.0120625i
$379$	−4.38336	−	19.2047i	−0.225158	−	0.986481i	−0.953530	−	0.301299i	$-0.902580\pi$
$379$	−4.38336	−	19.2047i	−0.225158	−	0.986481i	0.728372	−	0.685182i	$-0.240277\pi$
$380$			6.27685i			0.321995i
$381$	−4.70696	−	1.36965i	−0.241145	−	0.0701691i
$382$	0.433815	−	0.543987i	0.0221959	−	0.0278328i
$383$	−16.5909	−	20.8043i	−0.847756	−	1.06305i	−0.997237	−	0.0742880i	$-0.976332\pi$
$383$	−16.5909	−	20.8043i	−0.847756	−	1.06305i	0.149481	−	0.988765i	$-0.452240\pi$
$384$	−0.791272	+	13.4496i	−0.0403794	+	0.686346i
$385$	3.76022	−	1.81083i	0.191639	−	0.0922883i
$386$	5.21090	−	2.50944i	0.265228	−	0.127727i
$387$	−10.1372	−	16.3258i	−0.515303	−	0.829886i
$388$	3.41091	+	2.72011i	0.173163	+	0.138093i
$389$	19.2344	+	24.1191i	0.975222	+	1.22289i	0.974844	+	0.222889i	$0.0715488\pi$
$389$	19.2344	+	24.1191i	0.975222	+	1.22289i	0.000377825		1.00000i	$0.499880\pi$
$390$	0.966634	−	1.73804i	0.0489474	−	0.0880089i
$391$	9.86093	−	12.3652i	0.498689	−	0.625336i
$392$	−4.95872	+	3.95444i	−0.250453	+	0.199730i
$393$	0.445736	−	0.801446i	0.0224844	−	0.0404276i
$394$	1.60865	−	0.367163i	0.0810424	−	0.0184974i
$395$	5.48892	+	11.3978i	0.276177	+	0.573488i
$396$	22.6866	−	22.4461i	1.14005	−	1.12796i
$397$	23.6124	+	5.38937i	1.18507	+	0.270485i	0.769242	−	0.638958i	$-0.220634\pi$
$397$	23.6124	+	5.38937i	1.18507	+	0.270485i	0.415830	+	0.909443i	$0.363491\pi$
$398$	3.46708	−	2.76490i	0.173789	−	0.138592i
$399$	3.38370	−	6.08399i	0.169397	−	0.304580i
$400$	−14.1512	−	6.81487i	−0.707561	−	0.340743i
$401$	31.4367			1.56988			0.784938	−	0.619575i	$-0.212695\pi$
$401$	31.4367			1.56988			0.784938	+	0.619575i	$0.212695\pi$
$402$	5.45662	−	2.24319i	0.272152	−	0.111880i
$403$	2.81177	−	3.52585i	0.140064	−	0.175635i
$404$	−32.5173	+	7.42187i	−1.61780	+	0.369252i
$405$	−1.64070	+	6.85092i	−0.0815270	+	0.340425i
$406$	1.17324	+	0.267785i	0.0582272	+	0.0132900i
$407$	0.944909	+	4.13992i	0.0468374	+	0.205208i
$408$	−2.37222	−	5.77048i	−0.117442	−	0.285681i
$409$	10.3718			0.512854			0.256427	−	0.966564i	$-0.417455\pi$
$409$	10.3718			0.512854			0.256427	+	0.966564i	$0.417455\pi$
$410$	−0.0559549	−	0.0269465i	−0.00276342	−	0.00133079i
$411$	−21.7832	−	1.28156i	−1.07449	−	0.0632147i
$412$	0.492018			0.0242400
$413$	−0.782474	−	1.62482i	−0.0385030	−	0.0799523i
$414$	−0.429874	+	3.64073i	−0.0211271	+	0.178932i
$415$	−2.37317	−	1.14286i	−0.116494	−	0.0561006i
$416$	10.4616	+	13.1184i	0.512921	+	0.643183i
$417$	−26.5416	−	7.72317i	−1.29975	−	0.378205i
$418$	−2.64693	−	5.49641i	−0.129466	−	0.268838i
$419$	−20.1902	−	16.1011i	−0.986354	−	0.786591i	−0.00938112	−	0.999956i	$-0.502986\pi$
$419$	−20.1902	−	16.1011i	−0.986354	−	0.786591i	−0.976973	+	0.213365i	$0.931558\pi$
$420$	−1.45793	−	2.06641i	−0.0711399	−	0.100831i
$421$			10.9723i			0.534758i	0.963591	+	0.267379i	$0.0861576\pi$
$421$			10.9723i			0.534758i	−0.963591	+	0.267379i	$0.913842\pi$
$422$	0.782318	−	3.42756i	0.0380826	−	0.166851i
$423$	2.16107	+	20.1445i	0.105075	+	0.979458i
$424$	−9.99345	+	7.96951i	−0.485325	+	0.387034i
$425$	15.1125			0.733064
$426$	0.733042	−	3.81449i	0.0355160	−	0.184813i
$427$	−4.86092			−0.235236
$428$	−14.7458	+	11.7594i	−0.712767	+	0.568413i
$429$	3.09174	−	52.5515i	0.149270	−	2.53721i
$430$	−0.296943	+	1.30099i	−0.0143199	+	0.0627395i
$431$		−	9.95961i		−	0.479738i	−0.970805	−	0.239869i	$-0.922896\pi$
$431$		−	9.95961i		−	0.479738i	0.970805	−	0.239869i	$-0.0771044\pi$
$432$	−15.0848	−	10.8856i	−0.725766	−	0.523731i
$433$	2.31848	+	1.84893i	0.111419	+	0.0888538i	0.677615	−	0.735417i	$-0.263014\pi$
$433$	2.31848	+	1.84893i	0.111419	+	0.0888538i	−0.566195	+	0.824271i	$0.691585\pi$
$434$	0.0913602	+	0.189711i	0.00438543	+	0.00910644i
$435$	1.77131	−	6.08734i	0.0849280	−	0.291866i
$436$	−7.58662	−	9.51332i	−0.363333	−	0.455605i
$437$	−17.1956	−	8.28096i	−0.822577	−	0.396132i
$438$	−4.55703	−	1.32602i	−0.217743	−	0.0633597i
$439$	7.41715	+	15.4019i	0.354001	+	0.735091i	0.999591	−	0.0285931i	$-0.00910270\pi$
$439$	7.41715	+	15.4019i	0.354001	+	0.735091i	−0.645590	+	0.763684i	$0.723388\pi$
$440$	−4.51368			−0.215181
$441$	−1.94082	−	18.0913i	−0.0924198	−	0.861492i
$442$	−4.55251	−	2.19237i	−0.216541	−	0.104281i
$443$	−16.7431			−0.795488			−0.397744	−	0.917497i	$-0.630207\pi$
$443$	−16.7431			−0.795488			−0.397744	+	0.917497i	$0.630207\pi$
$444$	2.37985	−	0.978346i	0.112943	−	0.0464302i
$445$	−1.54103	−	6.75170i	−0.0730519	−	0.320061i
$446$	0.872328	+	0.199103i	0.0413059	+	0.00942781i
$447$	−8.20223	+	9.12922i	−0.387952	+	0.431797i
$448$	5.98587	−	1.36624i	0.282806	−	0.0645486i
$449$	22.2873	−	27.9474i	1.05180	−	1.31892i	0.105934	−	0.994373i	$-0.466217\pi$
$449$	22.2873	−	27.9474i	1.05180	−	1.31892i	0.945870	−	0.324546i	$-0.105212\pi$
$450$	−2.97598	+	1.84788i	−0.140289	+	0.0871100i
$451$	−1.64393			−0.0774094
$452$	−13.3821	−	6.44447i	−0.629441	−	0.303123i
$453$	16.4966	+	9.17483i	0.775079	+	0.431071i
$454$	2.49251	−	1.98771i	0.116979	−	0.0932878i
$455$	−4.06693	−	0.928251i	−0.190661	−	0.0435171i
$456$	−6.15196	+	4.34045i	−0.288092	+	0.203260i
$457$	−5.61951	−	11.6690i	−0.262870	−	0.545854i	0.727201	−	0.686424i	$-0.240821\pi$
$457$	−5.61951	−	11.6690i	−0.262870	−	0.545854i	−0.990071	+	0.140570i	$0.955106\pi$
$458$	−4.92318	+	1.12368i	−0.230045	+	0.0525063i
$459$	17.6212	+	3.13910i	0.822485	+	0.146520i
$460$	−5.42065	+	4.32282i	−0.252739	+	0.201553i
$461$	−14.8335	+	18.6006i	−0.690865	+	0.866317i	−0.996304	−	0.0858944i	$-0.972625\pi$
$461$	−14.8335	+	18.6006i	−0.690865	+	0.866317i	0.305439	+	0.952212i	$0.401197\pi$
$462$	2.14806	+	1.19467i	0.0999368	+	0.0555813i
$463$	−0.162465	−	0.203725i	−0.00755039	−	0.00946789i	0.778042	−	0.628212i	$-0.216213\pi$
$463$	−0.162465	−	0.203725i	−0.00755039	−	0.00946789i	−0.785592	+	0.618744i	$0.787642\pi$
$464$	13.0887	+	10.4379i	0.607629	+	0.484568i
$465$	1.02598	−	0.421773i	0.0475785	−	0.0195593i
$466$	2.02005	−	0.972804i	0.0935769	−	0.0450643i
$467$	35.7160	−	17.1999i	1.65274	−	0.795916i	0.653498	−	0.756929i	$-0.273301\pi$
$467$	35.7160	−	17.1999i	1.65274	−	0.795916i	0.999240	−	0.0389878i	$-0.0124133\pi$
$468$	−31.7168	+	3.40254i	−1.46611	+	0.157282i
$469$	−7.71566	−	9.67514i	−0.356276	−	0.446756i
$470$	0.877176	−	1.09994i	0.0404611	−	0.0507367i
$471$	4.64810	−	15.9738i	0.214173	−	0.736032i
$472$			1.95040i			0.0897744i
$473$	7.86009	+	34.4373i	0.361407	+	1.58343i
$474$	−3.62126	+	6.51113i	−0.166330	+	0.299066i
$475$	−4.05813	−	17.7798i	−0.186200	−	0.815794i
$476$	−5.02359	+	4.00618i	−0.230256	+	0.183623i
$477$	−3.91139	−	36.4600i	−0.179090	−	1.66939i
$478$	3.18897	−	0.727862i	0.145860	−	0.0332916i
$479$	−3.20778	−	14.0542i	−0.146567	−	0.642152i	−0.993824	−	0.110969i	$-0.964605\pi$
$479$	−3.20778	−	14.0542i	−0.146567	−	0.642152i	0.847257	−	0.531184i	$-0.178253\pi$
$480$	0.680496	+	4.07077i	0.0310603	+	0.185805i
$481$	1.84155	−	3.82402i	0.0839674	−	0.174360i
$482$	0.325974	−	1.42818i	0.0148477	−	0.0650520i
$483$	7.58442	−	1.26786i	0.345103	−	0.0576896i
$484$	−33.7329	+	16.2449i	−1.53331	+	0.738405i
$485$	1.59483	+	0.768029i	0.0724175	+	0.0348744i
$486$	−3.85382	+	1.53647i	−0.174813	+	0.0696959i
$487$	−9.10134	+	7.25808i	−0.412421	+	0.328895i	−0.807623	−	0.589700i	$-0.799246\pi$
$487$	−9.10134	+	7.25808i	−0.412421	+	0.328895i	0.395202	+	0.918594i	$0.370675\pi$
$488$	4.73647	+	2.28096i	0.214410	+	0.103254i
$489$	12.4803	−	8.80531i	0.564377	−	0.398190i
$490$	−0.787774	+	0.987837i	−0.0355880	+	0.0446259i
$491$	−2.18580	+	1.05262i	−0.0986437	+	0.0475043i	−0.482555	−	0.875866i	$-0.660291\pi$
$491$	−2.18580	+	1.05262i	−0.0986437	+	0.0475043i	0.383911	+	0.923370i	$0.374577\pi$
$492$	0.164242	+	0.982507i	0.00740460	+	0.0442948i
$493$	−15.7039	−	3.58432i	−0.707270	−	0.161430i
$494$	−1.35685	+	5.94474i	−0.0610474	+	0.267466i
$495$	6.94752	−	10.9272i	0.312268	−	0.491141i
$496$			2.92922i			0.131526i
$497$	−8.11206	+	0.759107i	−0.363875	+	0.0340506i
$498$	−0.255769	−	1.53003i	−0.0114613	−	0.0685621i
$499$	−14.2454	−	17.8631i	−0.637710	−	0.799663i	0.353004	−	0.935622i	$-0.385160\pi$
$499$	−14.2454	−	17.8631i	−0.637710	−	0.799663i	−0.990715	+	0.135959i	$0.956589\pi$
$500$	−13.8198	−	3.15427i	−0.618038	−	0.141063i
$501$	−1.91232	+	32.5046i	−0.0854364	+	1.45220i
$502$	5.36911			0.239635
$503$	11.7952	+	24.4929i	0.525921	+	1.09209i	0.979607	+	0.200924i	$0.0643946\pi$
$503$	11.7952	+	24.4929i	0.525921	+	1.09209i	−0.453686	+	0.891162i	$0.649891\pi$
$504$	1.01713	−	2.85785i	0.0453068	−	0.127299i
$505$	−12.1927	+	5.87169i	−0.542567	+	0.261287i
$506$	2.92374	−	6.07121i	0.129976	−	0.269898i
$507$	−20.1170	+	22.3906i	−0.893429	+	0.994402i
$508$	2.36903	−	4.91935i	0.105109	−	0.218261i
$509$	−8.41328	+	17.4704i	−0.372912	+	0.774360i	−0.999989	−	0.00459699i	$-0.998537\pi$
$509$	−8.41328	+	17.4704i	−0.372912	+	0.774360i	0.627077	+	0.778957i	$0.284251\pi$
$510$	−0.716525	−	1.01557i	−0.0317283	−	0.0449703i
$511$			9.95506i			0.440386i
$512$	−17.9251	−	4.09128i	−0.792184	−	0.180811i
$513$	−1.03863	−	21.5742i	−0.0458568	−	0.952524i
$514$		−	5.65812i		−	0.249569i
$515$	0.194626	−	0.0444221i	0.00857623	−	0.00195747i
$516$	19.7965	−	8.13823i	0.871491	−	0.358266i
$517$	8.28671	−	36.3065i	0.364449	−	1.59676i
$518$	0.123559	+	0.154938i	0.00542885	+	0.00680757i
$519$	27.0616	−	11.1249i	1.18787	−	0.488329i
$520$	3.52724	+	2.81288i	0.154680	+	0.123353i
$521$	22.0586	−	5.03474i	0.966406	−	0.220576i	0.289936	−	0.957046i	$-0.406366\pi$
$521$	22.0586	−	5.03474i	0.966406	−	0.220576i	0.676470	+	0.736470i	$0.263509\pi$
$522$	3.53072	−	1.21437i	0.154536	−	0.0531516i
$523$	−0.143420	+	0.297814i	−0.00627130	+	0.0130225i	−0.904081	−	0.427361i	$-0.859443\pi$
$523$	−0.143420	+	0.297814i	−0.00627130	+	0.0130225i	0.897810	+	0.440384i	$0.145158\pi$
$524$	0.798581	+	0.636847i	0.0348862	+	0.0278208i
$525$	5.46573	+	4.91074i	0.238544	+	0.214322i
$526$	−0.296124	+	1.29740i	−0.0129116	+	0.0565695i
$527$	−1.22286	−	2.53930i	−0.0532687	−	0.110614i
$528$	19.7121	+	27.9391i	0.857860	+	1.21589i
$529$	0.426884	+	1.87030i	0.0185602	+	0.0813175i
$530$	−1.58762	+	1.99082i	−0.0689620	+	0.0864756i
$531$	−4.72174	−	3.00208i	−0.204906	−	0.130279i
$532$	6.06224	+	4.83448i	0.262832	+	0.209601i
$533$	1.28465	+	1.02448i	0.0556446	+	0.0443751i
$534$	2.72582	−	3.03389i	0.117958	−	0.131289i
$535$	−4.77125	+	5.98296i	−0.206279	+	0.258666i
$536$	2.97812	+	13.0480i	0.128635	+	0.563587i
$537$	33.9390	−	23.9453i	1.46458	−	1.03332i
$538$	1.93603	+	4.02020i	0.0834680	+	0.173323i
$539$	−7.44212	+	32.6061i	−0.320555	+	1.40444i
$540$	−7.22485	−	3.06053i	−0.310908	−	0.131704i
$541$	4.02601	+	3.21064i	0.173092	+	0.138036i	0.706204	−	0.708009i	$-0.250406\pi$
$541$	4.02601	+	3.21064i	0.173092	+	0.138036i	−0.533112	+	0.846045i	$0.678978\pi$
$542$	−3.06553	+	6.36564i	−0.131676	+	0.273428i
$543$	−6.91686	+	1.15627i	−0.296831	+	0.0496201i
$544$	10.2234	−	2.33342i	0.438323	−	0.100044i
$545$	−3.85993	−	3.07819i	−0.165341	−	0.131855i
$546$	−0.934104	−	2.27223i	−0.0399760	−	0.0972427i
$547$	7.62720	+	9.56421i	0.326116	+	0.408936i	0.917679	−	0.397322i	$-0.130061\pi$
$547$	7.62720	+	9.56421i	0.326116	+	0.408936i	−0.591563	+	0.806258i	$0.701489\pi$
$548$	5.40819	−	23.6948i	0.231027	−	1.01219i
$549$	−12.8125	+	7.95567i	−0.546822	+	0.339540i
$550$	6.27748	−	1.43279i	0.267673	−	0.0610945i
$551$			19.4382i			0.828093i
$552$	−7.98519	−	2.32356i	−0.339872	−	0.0988972i
$553$	15.2358	+	3.47746i	0.647890	+	0.147877i
$554$			3.22502i			0.137018i
$555$	0.853060	−	0.601867i	0.0362104	−	0.0255478i
$556$	13.3585	−	27.7393i	0.566528	−	1.17641i
$557$	−13.5491	+	28.1350i	−0.574094	+	1.19212i	0.388570	+	0.921419i	$0.372969\pi$
$557$	−13.5491	+	28.1350i	−0.574094	+	1.19212i	−0.962664	+	0.270699i	$0.912745\pi$
$558$	0.551301	+	0.350518i	0.0233384	+	0.0148386i
$559$	15.3187	−	31.8095i	0.647911	−	1.34540i
$560$	2.44121	−	1.17563i	0.103160	−	0.0496793i
$561$	−28.7519	−	15.9908i	−1.21391	−	0.675131i
$562$	−2.65053	−	5.50389i	−0.111806	−	0.232167i
$563$	39.9045			1.68177			0.840887	−	0.541211i	$-0.182034\pi$
$563$	39.9045			1.68177			0.840887	+	0.541211i	$0.182034\pi$
$564$	−22.5268	−	1.32531i	−0.948549	−	0.0558055i
$565$	−5.87535	−	1.34101i	−0.247178	−	0.0564167i
$566$	−3.80169	−	4.76717i	−0.159797	−	0.200379i
$567$	5.35301	+	6.86124i	0.224805	+	0.288145i
$568$	8.26058	+	3.06687i	0.346606	+	0.128683i
$569$			6.29941i			0.264085i	0.991244	+	0.132043i	$0.0421536\pi$
$569$			6.29941i			0.264085i	−0.991244	+	0.132043i	$0.957846\pi$
$570$	−1.00241	+	1.11570i	−0.0419864	+	0.0467316i
$571$	−8.53610	+	37.3991i	−0.357225	+	1.56510i	0.402848	+	0.915267i	$0.368020\pi$
$571$	−8.53610	+	37.3991i	−0.357225	+	1.56510i	−0.760073	+	0.649837i	$0.774837\pi$
$572$	57.1633	+	13.0471i	2.39012	+	0.545528i
$573$	−4.46611	+	0.746583i	−0.186574	+	0.0311890i
$574$	−0.0691220	+	0.0332874i	−0.00288510	+	0.00138939i
$575$	12.5597	−	15.7494i	0.523777	−	0.656796i
$576$	13.5416	−	13.3980i	0.564231	−	0.558249i
$577$	19.2682	+	9.27906i	0.802145	+	0.386292i	0.789595	−	0.613629i	$-0.210291\pi$
$577$	19.2682	+	9.27906i	0.802145	+	0.386292i	0.0125499	+	0.999921i	$0.496005\pi$
$578$	1.06847	−	0.852076i	0.0444425	−	0.0354417i
$579$	−36.1404	−	10.5162i	−1.50194	−	0.437040i
$580$	6.36202	+	3.06379i	0.264169	+	0.127217i
$581$	−2.93161	+	1.41179i	−0.121624	+	0.0585709i
$582$	0.171883	+	1.02822i	0.00712480	+	0.0426210i
$583$	−14.9983	+	65.7120i	−0.621168	+	2.72151i
$584$	4.67137	−	9.70019i	0.193303	−	0.401397i
$585$	−12.2389	+	4.20949i	−0.506016	+	0.174041i
$586$	0.967572	+	4.23921i	0.0399700	+	0.175120i
$587$	37.9597	−	8.66405i	1.56676	−	0.357604i	0.650923	−	0.759144i	$-0.274382\pi$
$587$	37.9597	−	8.66405i	1.56676	−	0.357604i	0.915841	+	0.401540i	$0.131525\pi$
$588$	20.2308	+	1.19023i	0.834306	+	0.0490843i
$589$	−2.65911	+	2.12057i	−0.109567	+	0.0873764i
$590$	0.0864590	+	0.378802i	0.00355946	+	0.0155950i
$591$	−9.38435	−	5.21924i	−0.386021	−	0.214691i
$592$	0.613455	+	2.68772i	0.0252128	+	0.110465i
$593$		−	28.4050i		−	1.16645i	−0.812310	−	0.583226i	$-0.801790\pi$
$593$		−	28.4050i		−	1.16645i	0.812310	−	0.583226i	$-0.198210\pi$
$594$	7.61715	−	0.366708i	0.312536	−	0.0150462i
$595$	−1.62546	+	2.03827i	−0.0666376	+	0.0835609i
$596$	−8.52273	−	10.6872i	−0.349105	−	0.437763i
$597$	−28.8097	−	1.69495i	−1.17910	−	0.0693696i
$598$	−6.06829	+	2.92233i	−0.248151	+	0.119503i
$599$	−7.80926	+	3.76074i	−0.319078	+	0.153660i	−0.586566	−	0.809901i	$-0.699521\pi$
$599$	−7.80926	+	3.76074i	−0.319078	+	0.153660i	0.267488	+	0.963561i	$0.413806\pi$
$600$	−3.02146	−	7.34979i	−0.123351	−	0.300054i
$601$	−32.3048	−	25.7622i	−1.31774	−	1.05086i	−0.994521	−	0.104539i	$-0.966663\pi$
$601$	−32.3048	−	25.7622i	−1.31774	−	1.05086i	−0.323219	−	0.946324i	$-0.604765\pi$
$602$	1.02780	+	1.28883i	0.0418902	+	0.0525286i
$603$	−36.1719	−	12.8739i	−1.47303	−	0.524266i
$604$	−13.1086	+	16.4376i	−0.533381	+	0.668838i
$605$	−11.8769	+	9.47153i	−0.482866	+	0.385073i
$606$	−6.96518	−	3.87379i	−0.282941	−	0.157362i
$607$	22.5826	−	5.15434i	0.916601	−	0.209208i	0.261899	−	0.965095i	$-0.415651\pi$
$607$	22.5826	−	5.15434i	0.916601	−	0.209208i	0.654702	+	0.755887i	$0.272794\pi$
$608$	−5.49052	−	11.4012i	−0.222670	−	0.462379i
$609$	−4.51493	−	6.39927i	−0.182954	−	0.259311i
$610$	1.02102	+	0.233041i	0.0413398	+	0.00943555i
$611$	−29.1015	+	23.2077i	−1.17732	+	0.938883i
$612$	−6.68448	+	18.7814i	−0.270204	+	0.759195i
$613$	4.16276	+	2.00468i	0.168132	+	0.0809683i	0.516057	−	0.856554i	$-0.327399\pi$
$613$	4.16276	+	2.00468i	0.168132	+	0.0809683i	−0.347925	+	0.937522i	$0.613114\pi$
$614$	−3.65843			−0.147642
$615$	0.153675	+	0.373818i	0.00619676	+	0.0150738i
$616$	−3.47647	+	4.35935i	−0.140071	+	0.175643i
$617$	23.7486	−	5.42046i	0.956082	−	0.218219i	0.284106	−	0.958793i	$-0.408303\pi$
$617$	23.7486	−	5.42046i	0.956082	−	0.218219i	0.671976	+	0.740573i	$0.265446\pi$
$618$	0.0874555	+	0.0785752i	0.00351797	+	0.00316076i
$619$	33.3245	+	7.60610i	1.33942	+	0.305715i	0.831422	−	0.555641i	$-0.187527\pi$
$619$	33.3245	+	7.60610i	1.33942	+	0.305715i	0.508002	+	0.861356i	$0.330384\pi$
$620$	0.274931	+	1.20455i	0.0110415	+	0.0483760i
$621$	17.9160	−	15.7550i	0.718946	−	0.632225i
$622$	0.611289			0.0245105
$623$	−7.70777	−	3.71187i	−0.308805	−	0.148713i
$624$	2.00722	−	34.1176i	0.0803531	−	1.36580i
$625$	16.1852			0.647408
$626$	1.70441	+	3.53925i	0.0681221	+	0.141457i
$627$	−11.0924	+	38.1205i	−0.442989	+	1.52239i
$628$	16.6946	+	8.03968i	0.666186	+	0.320818i
$629$	−1.65384	−	2.07385i	−0.0659429	−	0.0826897i
$630$	0.0708599	−	0.600134i	0.00282313	−	0.0239099i
$631$	6.87689	+	14.2800i	0.273764	+	0.568478i	0.991840	−	0.127487i	$-0.0406912\pi$
$631$	6.87689	+	14.2800i	0.273764	+	0.568478i	−0.718076	+	0.695965i	$0.754977\pi$
$632$	−13.2139	−	10.5378i	−0.525622	−	0.419169i
$633$	−18.6950	+	13.1901i	−0.743061	+	0.524259i
$634$			5.80037i			0.230362i
$635$	0.492965	−	2.15982i	0.0195627	−	0.0857098i
$636$	40.7718	+	2.39871i	1.61671	+	0.0951150i
$637$	26.1355	−	20.8423i	1.03553	−	0.825804i
$638$	−6.86298			−0.271708
$639$	−20.1394	+	15.2775i	−0.796704	+	0.604370i
$640$	−6.08856			−0.240672
$641$	−35.1959	+	28.0678i	−1.39015	+	1.10861i	−0.409621	+	0.912256i	$0.634339\pi$
$641$	−35.1959	+	28.0678i	−1.39015	+	1.10861i	−0.980533	+	0.196354i	$0.937090\pi$
$642$	−4.49903	−	0.264689i	−0.177562	−	0.0104464i
$643$	5.77410	−	25.2980i	0.227708	−	0.997655i	−0.723795	−	0.690015i	$-0.757604\pi$
$643$	5.77410	−	25.2980i	0.227708	−	0.997655i	0.951503	−	0.307639i	$-0.0995390\pi$
$644$			8.56478i			0.337500i
$645$	7.09606	−	5.00654i	0.279407	−	0.197132i
$646$	2.97939	+	2.37598i	0.117222	+	0.0934818i
$647$	15.3902	+	31.9582i	0.605053	+	1.25641i	0.948364	+	0.317184i	$0.102737\pi$
$647$	15.3902	+	31.9582i	0.605053	+	1.25641i	−0.343311	+	0.939222i	$0.611548\pi$
$648$	−1.99636	−	9.19745i	−0.0784244	−	0.361310i
$649$	6.41243	+	8.04093i	0.251710	+	0.315634i
$650$	−5.79848	−	2.79240i	−0.227435	−	0.109527i
$651$	0.382862	−	1.31575i	0.0150055	−	0.0515683i
$652$	7.38126	+	15.3273i	0.289072	+	0.600265i
$653$	−34.2763			−1.34134			−0.670668	−	0.741757i	$-0.733993\pi$
$653$	−34.2763			−1.34134			−0.670668	+	0.741757i	$0.733993\pi$
$654$	0.170765	−	2.90256i	0.00667743	−	0.113499i
$655$	0.373390	+	0.179815i	0.0145896	+	0.00702596i
$656$	−1.06727			−0.0416699
$657$	16.2930	+	26.2396i	0.635652	+	1.02371i
$658$	−0.386729	−	1.69437i	−0.0150763	−	0.0660535i
$659$	36.2871	+	8.28228i	1.41354	+	0.322632i	0.860045	−	0.510218i	$-0.170435\pi$
$659$	36.2871	+	8.28228i	1.41354	+	0.322632i	0.553498	+	0.832850i	$0.313293\pi$
$660$	10.7283	+	9.63896i	0.417600	+	0.375196i
$661$	−23.6201	+	5.39113i	−0.918715	+	0.209691i	−0.655630	−	0.755082i	$-0.727597\pi$
$661$	−23.6201	+	5.39113i	−0.918715	+	0.209691i	−0.263085	+	0.964773i	$0.584740\pi$
$662$	0.522685	−	0.655426i	0.0203147	−	0.0254738i
$663$	12.5030	+	30.4140i	0.485578	+	1.18118i
$664$	3.51904			0.136565
$665$	2.83450	+	1.36502i	0.109917	+	0.0529334i
$666$	0.579257	+	0.206163i	0.0224458	+	0.00798864i
$667$	−16.7867	+	13.3869i	−0.649982	+	0.518344i
$668$	−35.3571	−	8.07002i	−1.36801	−	0.312239i
$669$	−3.35693	−	4.75797i	−0.129787	−	0.183954i
$670$	1.15681	+	2.40213i	0.0446913	+	0.0928024i
$671$	27.0264	−	6.16859i	1.04334	−	0.238136i
$672$	4.45572	+	2.47811i	0.171883	+	0.0955952i
$673$	−28.2884	+	22.5592i	−1.09044	+	0.869594i	−0.992086	−	0.125558i	$-0.959928\pi$
$673$	−28.2884	+	22.5592i	−1.09044	+	0.869594i	−0.0983499	+	0.995152i	$0.531356\pi$
$674$	2.36193	−	2.96177i	0.0909782	−	0.114083i
$675$	22.4438	+	3.99823i	0.863864	+	0.153892i
$676$	−20.9031	−	26.2117i	−0.803965	−	1.00814i
$677$	−12.7465	−	10.1650i	−0.489890	−	0.390674i	0.347156	−	0.937808i	$-0.387148\pi$
$677$	−12.7465	−	10.1650i	−0.489890	−	0.390674i	−0.837045	+	0.547134i	$0.815719\pi$
$678$	−1.34947	−	3.28261i	−0.0518259	−	0.126068i
$679$	1.97012	−	0.948760i	0.0756063	−	0.0364101i
$680$	2.54030	−	1.22334i	0.0974160	−	0.0469131i
$681$	−20.7115	−	1.21851i	−0.793667	−	0.0466934i
$682$	−0.748704	−	0.938845i	−0.0286693	−	0.0359502i
$683$	7.43420	−	9.32219i	0.284462	−	0.356704i	−0.618986	−	0.785402i	$-0.712456\pi$
$683$	7.43420	−	9.32219i	0.284462	−	0.356704i	0.903448	+	0.428698i	$0.141028\pi$
$684$	23.8913	+	2.82093i	0.913507	+	0.107861i
$685$		−	9.86117i		−	0.376776i
$686$	0.748167	+	3.27793i	0.0285651	+	0.125152i
$687$	28.7204	+	15.9732i	1.09575	+	0.609417i
$688$	5.10293	+	22.3574i	0.194548	+	0.852369i
$689$	52.6716	−	42.0042i	2.00663	−	1.60023i
$690$	−1.65387	−	0.0973010i	−0.0629616	−	0.00370418i
$691$	−27.1195	+	6.18984i	−1.03167	+	0.235473i	−0.704658	−	0.709547i	$-0.748900\pi$
$691$	−27.1195	+	6.18984i	−1.03167	+	0.235473i	−0.327015	+	0.945019i	$0.606043\pi$
$692$	7.25172	+	31.7718i	0.275669	+	1.20778i
$693$	−5.20256	−	15.1262i	−0.197629	−	0.574596i
$694$	1.70223	−	3.53471i	0.0646156	−	0.134176i
$695$	2.77973	−	12.1788i	0.105441	−	0.461969i
$696$	1.39652	+	8.35405i	0.0529348	+	0.316660i
$697$	0.925202	−	0.445554i	0.0350445	−	0.0168766i
$698$	−2.51296	−	1.21018i	−0.0951168	−	0.0458058i
$699$	−14.0101	−	4.07671i	−0.529911	−	0.154195i
$700$	−6.39848	+	5.10262i	−0.241840	+	0.192861i
$701$	−20.1493	−	9.70340i	−0.761029	−	0.366492i	0.0127741	−	0.999918i	$-0.495934\pi$
$701$	−20.1493	−	9.70340i	−0.761029	−	0.366492i	−0.773803	+	0.633426i	$0.781648\pi$
$702$	−6.18100	−	4.46037i	−0.233287	−	0.168346i
$703$	−1.99578	+	2.50262i	−0.0752721	+	0.0943883i
$704$	−31.5473	+	15.1924i	−1.18898	+	0.572584i
$705$	−9.03050	+	1.50960i	−0.340108	+	0.0568546i
$706$	−0.988157	−	0.225540i	−0.0371898	−	0.00848833i
$707$	−3.71997	+	16.2982i	−0.139904	+	0.612958i
$708$	4.16508	−	4.63580i	0.156533	−	0.174224i
$709$		−	49.8732i		−	1.87303i	−0.350634	−	0.936513i	$-0.614034\pi$
$709$		−	49.8732i		−	1.87303i	0.350634	−	0.936513i	$-0.385966\pi$
$710$	1.74030	+	0.229458i	0.0653124	+	0.00861142i
$711$	45.8500	−	15.7698i	1.71951	−	0.591415i
$712$	5.76866	+	7.23367i	0.216190	+	0.271093i
$713$	−3.66262	−	0.835968i	−0.137166	−	0.0313073i
$714$	−1.53272	−	0.0901739i	−0.0573607	−	0.00337467i
$715$	23.7898			0.889689
$716$	20.0727	+	41.6814i	0.750153	+	1.55771i
$717$	−18.6035	−	10.3466i	−0.694760	−	0.386401i
$718$	−4.10487	+	1.97680i	−0.153192	+	0.0737735i
$719$	−7.19133	+	14.9330i	−0.268191	+	0.556905i	−0.990956	−	0.134189i	$-0.957157\pi$
$719$	−7.19133	+	14.9330i	−0.268191	+	0.556905i	0.722764	+	0.691095i	$0.242871\pi$
$720$	4.51047	−	7.09416i	0.168095	−	0.264384i
$721$	0.106999	−	0.222186i	0.00398485	−	0.00827463i
$722$	−0.198770	+	0.412751i	−0.00739747	+	0.0153610i
$723$	−7.78979	+	5.49600i	−0.289705	+	0.204398i
$724$		−	7.81093i		−	0.290291i
$725$	−20.0019	−	4.56530i	−0.742852	−	0.169551i
$726$	−8.59028	−	2.49963i	−0.318815	−	0.0927699i
$727$			10.3905i			0.385363i	0.981261	+	0.192682i	$0.0617185\pi$
$727$			10.3905i			0.385363i	−0.981261	+	0.192682i	$0.938282\pi$
$728$	5.43341	−	1.24014i	0.201376	−	0.0459627i
$729$	25.3390	+	9.32386i	0.938482	+	0.345328i
$730$	0.477263	−	2.09103i	0.0176643	−	0.0773923i
$731$	−13.7572	−	17.2510i	−0.508829	−	0.638052i
$732$	−6.38687	−	15.5363i	−0.236066	−	0.574236i
$733$	3.71583	+	2.96328i	0.137247	+	0.109451i	0.689707	−	0.724088i	$-0.257739\pi$
$733$	3.71583	+	2.96328i	0.137247	+	0.109451i	−0.552460	+	0.833540i	$0.686311\pi$
$734$	4.17300	−	0.952461i	0.154028	−	0.0351560i
$735$	8.11010	−	1.35574i	0.299146	−	0.0500071i
$736$	6.06471	−	12.5935i	0.223548	−	0.464202i
$737$	55.1765	+	44.0018i	2.03245	+	1.62083i
$738$	−0.127712	+	0.200869i	−0.00470116	+	0.00739407i
$739$	2.73515	−	11.9835i	0.100614	−	0.440819i	−0.899379	−	0.437169i	$-0.855981\pi$
$739$	2.73515	−	11.9835i	0.100614	−	0.440819i	0.999993	−	0.00364983i	$-0.00116178\pi$
$740$	0.504529	+	1.04767i	0.0185469	+	0.0385130i
$741$	32.4246	−	22.8768i	1.19115	−	0.840400i
$742$	0.699951	+	3.06669i	0.0256960	+	0.112582i
$743$	−9.90166	+	12.4163i	−0.363257	+	0.455509i	−0.929551	−	0.368694i	$-0.879805\pi$
$743$	−9.90166	+	12.4163i	−0.363257	+	0.455509i	0.566294	+	0.824203i	$0.308377\pi$
$744$	−0.990470	+	1.10241i	−0.0363124	+	0.0404163i
$745$	−4.33620	−	3.45800i	−0.158866	−	0.126691i
$746$	1.21049	+	0.965331i	0.0443191	+	0.0353433i
$747$	−5.41655	+	8.51926i	−0.198181	+	0.311703i
$748$	22.8469	−	28.6491i	0.835366	−	1.04752i
$749$	2.10355	+	9.21625i	0.0768620	+	0.336754i
$750$	−1.95270	−	2.76768i	−0.0713027	−	0.101061i
$751$	7.18657	+	14.9231i	0.262242	+	0.544550i	0.989964	−	0.141322i	$-0.0451352\pi$
$751$	7.18657	+	14.9231i	0.262242	+	0.544550i	−0.727722	+	0.685872i	$0.759421\pi$
$752$	5.37991	−	23.5709i	0.196185	−	0.859543i
$753$	−25.9917	−	23.3525i	−0.947190	−	0.851011i
$754$	5.36312	+	4.27694i	0.195313	+	0.155757i
$755$	−3.70124	+	7.68570i	−0.134702	+	0.279711i
$756$	−8.52052	+	4.62059i	−0.309888	+	0.168049i
$757$	−37.5429	+	8.56893i	−1.36452	+	0.311443i	−0.841215	−	0.540701i	$-0.818159\pi$
$757$	−37.5429	+	8.56893i	−1.36452	+	0.311443i	−0.523307	+	0.852144i	$0.675302\pi$
$758$	4.09893	+	3.26879i	0.148880	+	0.118728i
$759$	−40.5599	+	16.6740i	−1.47223	+	0.605227i
$760$	−2.12140	−	2.66016i	−0.0769514	−	0.0964940i
$761$	7.03406	−	30.8182i	0.254984	−	1.11716i	−0.671553	−	0.740956i	$-0.734372\pi$
$761$	7.03406	−	30.8182i	0.254984	−	1.11716i	0.926537	−	0.376203i	$-0.122770\pi$
$762$	1.20671	−	0.496073i	0.0437146	−	0.0179708i
$763$	−5.94589	+	1.35711i	−0.215256	+	0.0491307i
$764$		−	5.04340i		−	0.182464i
$765$	−0.948464	+	8.03282i	−0.0342918	+	0.290427i
$766$	6.90455	+	1.57592i	0.249471	+	0.0569402i
$767$		−	10.2798i		−	0.371182i
$768$	10.6136	+	15.0433i	0.382986	+	0.542828i
$769$	9.33868	−	19.3920i	0.336761	−	0.699292i	−0.661976	−	0.749525i	$-0.730282\pi$
$769$	9.33868	−	19.3920i	0.336761	−	0.699292i	0.998738	+	0.0502326i	$0.0159963\pi$
$770$	−0.481946	+	1.00077i	−0.0173681	+	0.0360653i
$771$	−24.6095	+	27.3908i	−0.886291	+	0.986456i
$772$	18.1896	−	37.7712i	0.654659	−	1.35941i
$773$	11.6961	−	5.63253i	0.420678	−	0.202588i	−0.211555	−	0.977366i	$-0.567853\pi$
$773$	11.6961	−	5.63253i	0.420678	−	0.202588i	0.632233	+	0.774778i	$0.282138\pi$
$774$	4.81847	+	1.71493i	0.173196	+	0.0616420i
$775$	−1.55754	−	3.23427i	−0.0559486	−	0.116178i
$776$	−2.36488			−0.0848944
$777$	0.0757442	−	1.28746i	0.00271731	−	0.0461872i
$778$	−8.00466	−	1.82701i	−0.286981	−	0.0655015i
$779$	−0.772636	−	0.968855i	−0.0276826	−	0.0347128i
$780$	−2.37680	−	14.2182i	−0.0851033	−	0.509094i
$781$	44.1392	−	14.5149i	1.57942	−	0.519385i
$782$			4.20930i			0.150524i
$783$	−22.3739	−	9.47784i	−0.799579	−	0.338711i
$784$	−4.83158	+	21.1686i	−0.172557	+	0.756020i
$785$	7.32968	+	1.67295i	0.261607	+	0.0597102i
$786$	0.0402423	+	0.240732i	0.00143539	+	0.00858663i
$787$	−45.1571	+	21.7465i	−1.60968	+	0.775180i	−0.999849	−	0.0173536i	$-0.994476\pi$
$787$	−45.1571	+	21.7465i	−1.60968	+	0.775180i	−0.609828	+	0.792534i	$0.708762\pi$
$788$	7.45702	−	9.35081i	0.265645	−	0.333109i
$789$	7.07647	−	4.99272i	0.251929	−	0.177746i
$790$	−3.03350	−	1.46086i	−0.107927	−	0.0519750i
$791$	−5.82040	+	4.64161i	−0.206950	+	0.165037i
$792$	−2.02853	+	17.1802i	−0.0720807	+	0.610472i
$793$	−24.9641	−	12.0221i	−0.886501	−	0.426917i
$794$	−5.80763	+	2.79681i	−0.206105	+	0.0992549i
$795$	16.3445	−	2.73226i	0.579681	−	0.0969031i
$796$	7.15269	−	31.3380i	0.253520	−	1.11075i
$797$	−8.09015	+	16.7994i	−0.286568	+	0.595065i	−0.993707	−	0.112010i	$-0.964271\pi$
$797$	−8.09015	+	16.7994i	−0.286568	+	0.595065i	0.707139	+	0.707074i	$0.249985\pi$
$798$	0.305490	+	1.82746i	0.0108142	+	0.0646914i
$799$	5.17639	+	22.6793i	0.183128	+	0.802334i
$800$	13.0214	−	2.97204i	0.460375	−	0.105078i
$801$	−26.3913	+	2.83122i	−0.932490	+	0.100036i
$802$	−6.54142	+	5.21661i	−0.230986	+	0.184205i
$803$	−12.6331	−	55.3494i	−0.445814	−	1.95324i
$804$	20.7855	−	37.3729i	0.733047	−	1.31804i
$805$	0.773275	+	3.38794i	0.0272544	+	0.119409i
$806$			1.20025i			0.0422770i
$807$	8.11327	−	27.8823i	0.285601	−	0.981502i
$808$	11.2726	−	14.1354i	0.396569	−	0.497282i
$809$	5.39805	+	6.76894i	0.189785	+	0.237983i	0.867616	−	0.497235i	$-0.165651\pi$
$809$	5.39805	+	6.76894i	0.189785	+	0.237983i	−0.677831	+	0.735218i	$0.737080\pi$
$810$	−0.795441	−	1.69781i	−0.0279490	−	0.0596550i
$811$	−39.2502	+	18.9019i	−1.37826	+	0.663736i	−0.968628	−	0.248515i	$-0.920058\pi$
$811$	−39.2502	+	18.9019i	−1.37826	+	0.663736i	−0.409633	+	0.912250i	$0.634343\pi$
$812$	7.85912	−	3.78475i	0.275801	−	0.132819i
$813$	42.5270	−	17.4826i	1.49149	−	0.613142i
$814$	−0.883596	−	0.704644i	−0.0309700	−	0.0246978i
$815$	4.30362	+	5.39656i	0.150749	+	0.189033i
$816$	−18.6663	−	10.3816i	−0.653452	−	0.363427i
$817$	−16.6016	+	20.8177i	−0.580816	+	0.728320i
$818$	−2.15819	+	1.72110i	−0.0754595	+	0.0601769i
$819$	−5.36092	+	15.0626i	−0.187326	+	0.526331i
$820$	−0.438883	+	0.100172i	−0.0153265	+	0.00349816i
$821$	1.33952	+	2.78155i	0.0467497	+	0.0970768i	0.923035	−	0.384715i	$-0.125700\pi$
$821$	1.33952	+	2.78155i	0.0467497	+	0.0970768i	−0.876286	+	0.481792i	$0.839986\pi$
$822$	4.74536	−	3.34804i	0.165513	−	0.116776i
$823$	13.3930	+	3.05686i	0.466850	+	0.106555i	0.449474	−	0.893294i	$-0.351612\pi$
$823$	13.3930	+	3.05686i	0.466850	+	0.106555i	0.0173761	+	0.999849i	$0.494469\pi$
$824$	−0.208519	+	0.166289i	−0.00726412	+	0.00579294i
$825$	−36.6209	−	20.3673i	−1.27498	−	0.709097i
$826$	0.432442	+	0.208253i	0.0150466	+	0.00724605i
$827$	−25.5703			−0.889167			−0.444584	−	0.895737i	$-0.646648\pi$
$827$	−25.5703			−0.889167			−0.444584	+	0.895737i	$0.646648\pi$
$828$	14.0176	+	22.5751i	0.487146	+	0.784540i
$829$	15.0223	−	18.8373i	0.521745	−	0.654248i	−0.449233	−	0.893414i	$-0.648303\pi$
$829$	15.0223	−	18.8373i	0.521745	−	0.654248i	0.970979	+	0.239167i	$0.0768742\pi$
$830$	0.683459	−	0.155995i	0.0237232	−	0.00541466i
$831$	14.0269	−	15.6122i	0.486589	−	0.541582i
$832$	34.1205	+	7.78778i	1.18292	+	0.269993i
$833$	−4.64881	−	20.3678i	−0.161072	−	0.705701i
$834$	6.80442	−	2.79726i	0.235618	−	0.0968613i
$835$	−14.7147			−0.509222
$836$	−39.8407	−	19.1863i	−1.37792	−	0.663571i
$837$	−1.14429	−	4.09468i	−0.0395523	−	0.141533i
$838$	6.87303			0.237425
$839$	−7.49299	−	15.5593i	−0.258687	−	0.537168i	0.730661	−	0.682740i	$-0.239212\pi$
$839$	−7.49299	−	15.5593i	−0.258687	−	0.537168i	−0.989348	+	0.145572i	$0.953498\pi$
$840$	1.31627	+	0.383013i	0.0454156	+	0.0132152i
$841$	−6.42617	−	3.09468i	−0.221592	−	0.106713i
$842$	−1.82075	−	2.28314i	−0.0627471	−	0.0786823i
$843$	−11.1075	+	38.1724i	−0.382564	+	1.31473i
$844$	−11.0569	−	22.9599i	−0.380594	−	0.790312i
$845$	−10.6351	−	8.48121i	−0.365858	−	0.291762i
$846$	−3.79245	−	3.83310i	−0.130387	−	0.131785i
$847$			18.7659i			0.644804i
$848$	−9.73724	+	42.6616i	−0.334378	+	1.46501i
$849$	−2.33052	+	39.6129i	−0.0799834	+	1.35951i
$850$	−3.14464	+	2.50777i	−0.107860	+	0.0860157i
$851$	−3.53573			−0.121203
$852$	−13.0848	−	24.9300i	−0.448280	−	0.854088i
$853$	−6.59212			−0.225710			−0.112855	−	0.993611i	$-0.536000\pi$
$853$	−6.59212			−0.225710			−0.112855	+	0.993611i	$0.536000\pi$
$854$	1.01147	−	0.806620i	0.0346118	−	0.0276020i
$855$	9.70529	−	1.04117i	0.331914	−	0.0356073i
$856$	2.27499	−	9.96738i	0.0777576	−	0.340678i
$857$		−	43.1896i		−	1.47533i	−0.675167	−	0.737665i	$-0.735929\pi$
$857$		−	43.1896i		−	1.47533i	0.675167	−	0.737665i	$-0.264071\pi$
$858$	8.07706	+	11.4481i	0.275746	+	0.390831i
$859$	4.44501	+	3.54478i	0.151662	+	0.120946i	0.696381	−	0.717672i	$-0.254792\pi$
$859$	4.44501	+	3.54478i	0.151662	+	0.120946i	−0.544719	+	0.838618i	$0.683364\pi$
$860$	4.19686	+	8.71486i	0.143112	+	0.297174i
$861$	0.479399	+	0.139497i	0.0163379	+	0.00475405i
$862$	1.65270	+	2.07242i	0.0562911	+	0.0705868i
$863$	−3.89743	−	1.87690i	−0.132670	−	0.0638906i	0.366371	−	0.930469i	$-0.380600\pi$
$863$	−3.89743	−	1.87690i	−0.132670	−	0.0638906i	−0.499041	+	0.866578i	$0.666314\pi$
$864$	15.8002	−	0.760662i	0.537535	−	0.0258783i
$865$	5.73707	+	11.9132i	0.195066	+	0.405059i
$866$	−0.789245			−0.0268196
$867$	−8.87846	−	0.522342i	−0.301528	−	0.0177397i
$868$	1.37512	+	0.662224i	0.0466747	+	0.0224774i
$869$	−89.1227			−3.02328
$870$	0.641554	+	1.56060i	0.0217507	+	0.0529092i
$871$	−15.6965	−	68.7709i	−0.531856	−	2.33021i
$872$	6.43048	+	1.46772i	0.217764	+	0.0497031i
$873$	3.64007	−	5.72517i	0.123198	−	0.193768i
$874$	4.95224	−	1.13032i	0.167512	−	0.0382335i
$875$	−4.42978	+	5.55477i	−0.149754	+	0.187786i
$876$	−31.8179	+	13.0802i	−1.07503	+	0.441939i
$877$	−51.1338			−1.72666			−0.863332	−	0.504636i	$-0.831627\pi$
$877$	−51.1338			−1.72666			−0.863332	+	0.504636i	$0.831627\pi$
$878$	−4.09916	−	1.97405i	−0.138340	−	0.0666210i
$879$	13.7541	−	24.7303i	0.463914	−	0.834131i
$880$	−12.0811	+	9.63435i	−0.407253	+	0.324774i
$881$	35.3659	+	8.07204i	1.19151	+	0.271954i	0.771896	−	0.635749i	$-0.219309\pi$
$881$	35.3659	+	8.07204i	1.19151	+	0.271954i	0.419613	+	0.907703i	$0.362166\pi$
$882$	3.40592	+	3.44242i	0.114683	+	0.115912i
$883$	−6.71184	−	13.9373i	−0.225871	−	0.469027i	0.756977	−	0.653441i	$-0.226675\pi$
$883$	−6.71184	−	13.9373i	−0.225871	−	0.469027i	−0.982849	+	0.184415i	$0.940961\pi$
$884$	−35.7077	+	8.15005i	−1.20098	+	0.274116i
$885$	1.22902	−	2.20981i	0.0413131	−	0.0742821i
$886$	3.48393	−	2.77835i	0.117045	−	0.0933403i
$887$	25.3289	−	31.7614i	0.850460	−	1.06644i	−0.146553	−	0.989203i	$-0.546818\pi$
$887$	25.3289	−	31.7614i	0.850460	−	1.06644i	0.997013	−	0.0772400i	$-0.0246108\pi$
$888$	−0.677938	+	1.21895i	−0.0227501	+	0.0409054i
$889$	−1.70629	−	2.13962i	−0.0572271	−	0.0717606i
$890$	1.44104	+	1.14919i	0.0483037	+	0.0385209i
$891$	−38.4694	−	31.3549i	−1.28877	−	1.05043i
$892$	5.84339	−	2.81403i	0.195651	−	0.0942207i
$893$	25.2921	−	12.1800i	0.846368	−	0.407589i
$894$	0.191835	−	3.26071i	0.00641593	−	0.109054i
$895$	11.7033	+	14.6755i	0.391199	+	0.490548i
$896$	−4.68946	+	5.88039i	−0.156664	+	0.196450i
$897$	42.0868	+	12.2466i	1.40524	+	0.408901i
$898$			9.51371i			0.317477i
$899$	0.851407	+	3.73026i	0.0283960	+	0.124411i
$900$	−8.51393	+	23.9217i	−0.283798	+	0.797389i
$901$	−9.36889	−	41.0478i	−0.312123	−	1.36750i
$902$	0.342071	−	0.272793i	0.0113897	−	0.00908301i
$903$	0.630067	−	10.7095i	0.0209673	−	0.356390i
$904$	7.84945	−	1.79158i	0.261069	−	0.0595872i
$905$	−0.705213	−	3.08974i	−0.0234421	−	0.102707i
$906$	−4.95512	+	0.828329i	−0.164623	+	0.0275194i
$907$	−9.37988	+	19.4775i	−0.311454	+	0.646740i	−0.996665	−	0.0816041i	$-0.973996\pi$
$907$	−9.37988	+	19.4775i	−0.311454	+	0.646740i	0.685211	+	0.728345i	$0.259710\pi$
$908$	5.14212	−	22.5291i	0.170647	−	0.747654i
$909$	16.8695	+	49.0474i	0.559527	+	1.62680i
$910$	1.00029	−	0.481714i	0.0331593	−	0.0159687i
$911$	8.26342	+	3.97945i	0.273779	+	0.131845i	0.565736	−	0.824586i	$-0.308592\pi$
$911$	8.26342	+	3.97945i	0.273779	+	0.131845i	−0.291957	+	0.956432i	$0.594306\pi$
$912$	−7.20144	+	24.7487i	−0.238464	+	0.819510i
$913$	14.5080	−	11.5697i	0.480144	−	0.382902i
$914$	3.10568	+	1.49562i	0.102727	+	0.0494706i
$915$	−3.92913	−	5.56898i	−0.129893	−	0.184105i
$916$	−22.8218	+	28.6177i	−0.754055	+	0.945555i
$917$	0.461255	−	0.222129i	0.0152320	−	0.00733534i
$918$	−4.18755	+	2.27086i	−0.138210	+	0.0749497i
$919$	46.5442	+	10.6234i	1.53535	+	0.350434i	0.904842	−	0.425747i	$-0.139989\pi$
$919$	46.5442	+	10.6234i	1.53535	+	0.350434i	0.630510	+	0.776181i	$0.282846\pi$
$920$	0.836298	−	3.66406i	0.0275719	−	0.120801i
$921$	17.7104	+	15.9120i	0.583576	+	0.524320i
$922$		−	6.33193i		−	0.208531i
$923$	−43.5383	−	16.1643i	−1.43308	−	0.532055i
$924$	17.5724	−	2.93752i	0.578091	−	0.0966373i
$925$	−2.10647	−	2.64143i	−0.0692604	−	0.0868498i
$926$	0.0676121	+	0.0154320i	0.00222187	+	0.000507128i
$927$	−0.0816134	−	0.760760i	−0.00268054	−	0.0249866i
$928$	−14.2359			−0.467316
$929$	10.9697	+	22.7789i	0.359905	+	0.747351i	0.999777	−	0.0211311i	$-0.00672673\pi$
$929$	10.9697	+	22.7789i	0.359905	+	0.747351i	−0.639872	+	0.768482i	$0.721012\pi$
$930$	−0.143498	+	0.258014i	−0.00470549	+	0.00846061i
$931$	−22.7143	+	10.9386i	−0.744431	+	0.358499i
$932$	7.05136	−	14.6423i	0.230975	−	0.479625i
$933$	−2.95923	−	2.65875i	−0.0968809	−	0.0870435i
$934$	−4.57770	+	9.50569i	−0.149787	+	0.311036i
$935$	6.45087	−	13.3954i	0.210966	−	0.438076i
$936$	12.2917	−	12.1614i	0.401768	−	0.397508i
$937$		−	24.8875i		−	0.813038i	−0.913642	−	0.406519i	$-0.866742\pi$
$937$		−	24.8875i		−	0.813038i	0.913642	−	0.406519i	$-0.133258\pi$
$938$	3.21098	+	0.732886i	0.104842	+	0.0239296i
$939$	7.14266	−	24.5466i	0.233092	−	0.801049i
$940$		−	10.1978i		−	0.332615i
$941$	46.3511	−	10.5793i	1.51100	−	0.344876i	0.614857	−	0.788639i	$-0.289214\pi$
$941$	46.3511	−	10.5793i	1.51100	−	0.344876i	0.896144	+	0.443763i	$0.146357\pi$
$942$	1.68350	+	4.09516i	0.0548514	+	0.133428i
$943$	0.304588	−	1.33449i	0.00991875	−	0.0434569i
$944$	4.16309	+	5.22034i	0.135497	+	0.169908i
$945$	−2.95326	+	2.59703i	−0.0960696	+	0.0844814i
$946$	−7.35007	−	5.86148i	−0.238971	−	0.190573i
$947$	30.4001	−	6.93862i	0.987870	−	0.225475i	0.302087	−	0.953280i	$-0.402317\pi$
$947$	30.4001	−	6.93862i	0.987870	−	0.225475i	0.685783	+	0.727806i	$0.259460\pi$
$948$	8.90411	+	53.2650i	0.289192	+	1.72997i
$949$	−24.6210	+	51.1260i	−0.799230	+	1.65962i
$950$	3.79481	+	3.02626i	0.123120	+	0.0981848i
$951$	25.2282	−	28.0794i	0.818081	−	0.910537i
$952$	0.775041	−	3.39568i	0.0251192	−	0.110054i
$953$	13.4466	+	27.9221i	0.435577	+	0.904486i	0.997033	+	0.0769787i	$0.0245274\pi$
$953$	13.4466	+	27.9221i	0.435577	+	0.904486i	−0.561455	+	0.827507i	$0.689758\pi$
$954$	6.86406	+	6.93762i	0.222232	+	0.224614i
$955$	−0.455346	−	1.99500i	−0.0147346	−	0.0645567i
$956$	14.7828	−	18.5370i	0.478109	−	0.599529i
$957$	33.2235	+	29.8500i	1.07396	+	0.964912i
$958$	2.99963	+	2.39213i	0.0969137	+	0.0772861i
$959$	−9.52401	−	7.59515i	−0.307546	−	0.245260i
$960$	6.40369	+	5.75346i	0.206678	+	0.185692i
$961$	18.9108	−	23.7134i	0.610025	−	0.764947i
$962$	0.251364	+	1.10130i	0.00810429	+	0.0355072i
$963$	20.6284	+	20.8495i	0.664742	+	0.671865i
$964$	−4.60715	−	9.56686i	−0.148386	−	0.308128i
$965$	3.78502	−	16.5833i	0.121844	−	0.533834i
$966$	−1.36779	+	1.52238i	−0.0440081	+	0.0489817i
$967$	24.7905	+	19.7697i	0.797208	+	0.635752i	0.934975	−	0.354713i	$-0.115421\pi$
$967$	24.7905	+	19.7697i	0.797208	+	0.635752i	−0.137768	+	0.990465i	$0.543993\pi$
$968$	8.80582	−	18.2855i	0.283030	−	0.587717i
$969$	−4.08900	−	24.4606i	−0.131357	−	0.785789i
$970$	−0.459302	+	0.104833i	−0.0147473	+	0.00336598i
$971$	5.75592	+	4.59019i	0.184716	+	0.147306i	0.711482	−	0.702704i	$-0.248024\pi$
$971$	5.75592	+	4.59019i	0.184716	+	0.147306i	−0.526766	+	0.850010i	$0.676596\pi$
$972$	−14.8961	+	26.1242i	−0.477794	+	0.837934i
$973$	−9.62145	−	12.0649i	−0.308449	−	0.386783i
$974$	0.689421	−	3.02055i	0.0220905	−	0.0967847i
$975$	15.9250	+	38.7379i	0.510007	+	1.24061i
$976$	17.5461	−	4.00478i	0.561636	−	0.128190i
$977$			16.6842i			0.533774i	0.963728	+	0.266887i	$0.0859950\pi$
$977$			16.6842i			0.533774i	−0.963728	+	0.266887i	$0.914005\pi$
$978$	−1.13577	+	3.90320i	−0.0363178	+	0.124811i
$979$	47.5651	+	10.8564i	1.52019	+	0.346973i
$980$			9.15841i			0.292555i
$981$	−13.4511	+	13.3085i	−0.429461	+	0.424907i
$982$	0.280153	−	0.581743i	0.00894004	−	0.0185642i
$983$	−15.0426	+	31.2363i	−0.479785	+	0.996283i	0.510841	+	0.859675i	$0.329334\pi$
$983$	−15.0426	+	31.2363i	−0.479785	+	0.996283i	−0.990625	+	0.136607i	$0.956380\pi$
$984$	−0.401667	−	0.360881i	−0.0128047	−	0.0115045i
$985$	2.10550	−	4.37213i	0.0670870	−	0.139308i
$986$	3.86249	−	1.86008i	0.123007	−	0.0592369i
$987$	−5.49738	+	9.88445i	−0.174984	+	0.314625i
$988$	19.1770	+	39.8215i	0.610103	+	1.26689i
$989$	−29.4114			−0.935230
$990$	0.367604	+	3.42662i	0.0116832	+	0.108905i
$991$	−11.6997	−	2.67038i	−0.371653	−	0.0848273i	0.0326150	−	0.999468i	$-0.489616\pi$
$991$	−11.6997	−	2.67038i	−0.371653	−	0.0848273i	−0.404268	+	0.914641i	$0.632474\pi$
$992$	−1.55303	−	1.94744i	−0.0493089	−	0.0618314i
$993$	−5.38102	+	0.899525i	−0.170761	+	0.0285456i
$994$	1.56201	−	1.50407i	0.0495439	−	0.0477062i
$995$		−	13.0420i		−	0.413460i
$996$	−8.36422	−	7.51491i	−0.265030	−	0.238119i
$997$	−11.3724	+	49.8257i	−0.360167	+	1.57800i	0.392600	+	0.919709i	$0.371576\pi$
$997$	−11.3724	+	49.8257i	−0.360167	+	1.57800i	−0.752767	+	0.658287i	$0.771281\pi$
$998$	5.92841	+	1.35312i	0.187661	+	0.0428323i
$999$	−1.90748	−	3.51746i	−0.0603500	−	0.111287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	213.2.l.a.23.11	✓	132
3.2	odd	2	inner	213.2.l.a.23.12	yes	132
71.34	odd	14	inner	213.2.l.a.176.12	yes	132
213.176	even	14	inner	213.2.l.a.176.11	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.l.a.23.11	✓	132	1.1	even	1	trivial
213.2.l.a.23.12	yes	132	3.2	odd	2	inner
213.2.l.a.176.11	yes	132	213.176	even	14	inner
213.2.l.a.176.12	yes	132	71.34	odd	14	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:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	213.l (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.208082 + 0.165940i) q^{2} +(1.72906 + 0.101725i) q^{3} +(-0.429280 + 1.88080i) q^{4} +0.782738i q^{5} +(-0.376667 + 0.265753i) q^{6} +(0.755976 + 0.602871i) q^{7} +(-0.453728 - 0.942175i) q^{8} +(2.97930 + 0.351777i) q^{9} +(-0.129888 - 0.162874i) q^{10} +(-4.96823 - 2.39257i) q^{11} +(-0.933575 + 3.20835i) q^{12} +(2.39142 + 4.96584i) q^{13} -0.257346 q^{14} +(-0.0796240 + 1.35340i) q^{15} +(-3.22548 - 1.55331i) q^{16} +3.44458 q^{17} +(-0.678314 + 0.421187i) q^{18} +(-0.924967 - 4.05255i) q^{19} +(-1.47217 - 0.336014i) q^{20} +(1.24580 + 1.11930i) q^{21} +(1.43082 - 0.326576i) q^{22} +(2.86273 - 3.58976i) q^{23} +(-0.688680 - 1.67523i) q^{24} +4.38732 q^{25} +(-1.32164 - 0.636470i) q^{26} +(5.11561 + 0.911314i) q^{27} +(-1.45840 + 1.16304i) q^{28} +(-4.55903 - 1.04057i) q^{29} +(-0.208015 - 0.294832i) q^{30} +(-0.355010 - 0.737186i) q^{31} +(2.96795 - 0.677416i) q^{32} +(-8.34699 - 4.64230i) q^{33} +(-0.716756 + 0.571594i) q^{34} +(-0.471890 + 0.591731i) q^{35} +(-1.94058 + 5.45246i) q^{36} +(-0.480127 - 0.602061i) q^{37} +(0.864948 + 0.689773i) q^{38} +(3.62977 + 8.82951i) q^{39} +(0.737477 - 0.355150i) q^{40} +(0.268596 - 0.129349i) q^{41} +(-0.444966 - 0.0261785i) q^{42} +(-3.99387 - 5.00816i) q^{43} +(6.63271 - 8.31715i) q^{44} +(-0.275349 + 2.33201i) q^{45} +1.22201i q^{46} +(1.50276 + 6.58403i) q^{47} +(-5.41904 - 3.01388i) q^{48} +(-1.34960 - 5.91298i) q^{49} +(-0.912923 + 0.728032i) q^{50} +(5.95589 + 0.350400i) q^{51} +(-10.3663 + 2.36605i) q^{52} +(-2.71989 - 11.9166i) q^{53} +(-1.21569 + 0.659257i) q^{54} +(1.87276 - 3.88882i) q^{55} +(0.225003 - 0.985801i) q^{56} +(-1.18708 - 7.10119i) q^{57} +(1.12132 - 0.540001i) q^{58} +(-1.68039 - 0.809235i) q^{59} +(-2.51129 - 0.730745i) q^{60} +(-3.93040 + 3.13439i) q^{61} +(0.196200 + 0.0944848i) q^{62} +(2.04021 + 2.06207i) q^{63} +(3.95903 - 4.96447i) q^{64} +(-3.88695 + 1.87186i) q^{65} +(2.50720 - 0.419120i) q^{66} +(-12.4773 - 2.84787i) q^{67} +(-1.47869 + 6.47856i) q^{68} +(5.31501 - 5.91570i) q^{69} -0.201434i q^{70} +(-6.06969 + 5.84456i) q^{71} +(-1.02036 - 2.96664i) q^{72} +(6.41916 + 8.04937i) q^{73} +(0.199812 + 0.0456057i) q^{74} +(7.58595 + 0.446300i) q^{75} +8.01909 q^{76} +(-2.31345 - 4.80393i) q^{77} +(-2.22046 - 1.23494i) q^{78} +(14.5615 - 7.01245i) q^{79} +(1.21583 - 2.52471i) q^{80} +(8.75251 + 2.09610i) q^{81} +(-0.0344259 + 0.0714861i) q^{82} +(-1.46007 + 3.03188i) q^{83} +(-2.63998 + 1.86261i) q^{84} +2.69621i q^{85} +(1.66211 + 0.379365i) q^{86} +(-7.77698 - 2.26297i) q^{87} +5.76652i q^{88} +(-8.62574 + 1.96877i) q^{89} +(-0.329679 - 0.530942i) q^{90} +(-1.18590 + 5.19578i) q^{91} +(5.52269 + 6.92523i) q^{92} +(-0.538844 - 1.31075i) q^{93} +(-1.40525 - 1.12065i) q^{94} +(3.17208 - 0.724007i) q^{95} +(5.20068 - 0.869379i) q^{96} +(0.981209 - 2.03750i) q^{97} +(1.26203 + 1.00643i) q^{98} +(-13.9602 - 8.87591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 10 q^{3} + 10 q^{4} - 15 q^{6} - 14 q^{7} - 14 q^{9} + 2 q^{10} + 20 q^{12} - 14 q^{13} + 22 q^{15} - 30 q^{16} + 8 q^{18} - 14 q^{19} - 28 q^{21} - 14 q^{22} + 8 q^{24} - 84 q^{25} - 7 q^{27} - 42 q^{28}+ \cdots + 49 q^{99}+O(q^{100}) \) 132 * q - 10 * q^3 + 10 * q^4 - 15 * q^6 - 14 * q^7 - 14 * q^9 + 2 * q^10 + 20 * q^12 - 14 * q^13 + 22 * q^15 - 30 * q^16 + 8 * q^18 - 14 * q^19 - 28 * q^21 - 14 * q^22 + 8 * q^24 - 84 * q^25 - 7 * q^27 - 42 * q^28 - 5 * q^30 + 14 * q^31 - 7 * q^33 - 42 * q^34 - 43 * q^36 + 22 * q^37 - 35 * q^39 + 64 * q^40 - 28 * q^42 + 16 * q^43 - 50 * q^45 + 55 * q^48 + 12 * q^49 - 98 * q^51 - 168 * q^52 - 38 * q^54 + 70 * q^55 + 48 * q^57 + 86 * q^58 + 116 * q^60 + 14 * q^61 + 105 * q^63 + 2 * q^64 - 42 * q^67 - 28 * q^69 + 266 * q^72 - 62 * q^73 + 18 * q^75 - 120 * q^76 + 21 * q^78 - 74 * q^79 - 22 * q^81 - 182 * q^82 + 42 * q^84 - 2 * q^87 + 15 * q^90 - 22 * q^91 + 14 * q^94 - 210 * q^96 - 42 * q^97 + 49 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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