LMFDB - Embedded newform 525.2.z.b.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	525.169
Dual form			525.2.z.b.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59414 + 0.842888i) q^{2} +(0.587785 + 0.809017i) q^{3} +(4.40108 - 3.19758i) q^{4} +(1.06976 + 1.96357i) q^{5} +(-2.20671 - 1.60327i) q^{6} +1.00000i q^{7} +(-5.51531 + 7.59117i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-2.59414 + 0.842888i) q^{2} +(0.587785 + 0.809017i) q^{3} +(4.40108 - 3.19758i) q^{4} +(1.06976 + 1.96357i) q^{5} +(-2.20671 - 1.60327i) q^{6} +1.00000i q^{7} +(-5.51531 + 7.59117i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-4.43019 - 4.19209i) q^{10} +(-0.0451431 - 0.138936i) q^{11} +(5.17379 + 1.68106i) q^{12} +(-6.24935 - 2.03054i) q^{13} +(-0.842888 - 2.59414i) q^{14} +(-0.959771 + 2.01961i) q^{15} +(4.54686 - 13.9938i) q^{16} +(-2.52683 + 3.47788i) q^{17} -2.72764i q^{18} +(-0.218037 - 0.158413i) q^{19} +(10.9868 + 5.22119i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(0.234215 + 0.322369i) q^{22} +(1.60816 - 0.522522i) q^{23} -9.38320 q^{24} +(-2.71121 + 4.20111i) q^{25} +17.9232 q^{26} +(-0.951057 + 0.309017i) q^{27} +(3.19758 + 4.40108i) q^{28} +(-7.58124 + 5.50810i) q^{29} +(0.787473 - 6.04815i) q^{30} +(3.38164 + 2.45691i) q^{31} +21.3680i q^{32} +(0.0858672 - 0.118186i) q^{33} +(3.62349 - 11.1520i) q^{34} +(-1.96357 + 1.06976i) q^{35} +(1.68106 + 5.17379i) q^{36} +(8.86730 + 2.88116i) q^{37} +(0.699145 + 0.227166i) q^{38} +(-2.03054 - 6.24935i) q^{39} +(-20.8059 - 2.70894i) q^{40} +(0.911073 - 2.80399i) q^{41} +(1.60327 - 2.20671i) q^{42} +4.72780i q^{43} +(-0.642937 - 0.467121i) q^{44} +(-2.19804 + 0.410629i) q^{45} +(-3.73136 + 2.71099i) q^{46} +(-6.69207 - 9.21084i) q^{47} +(13.9938 - 4.54686i) q^{48} -1.00000 q^{49} +(3.49221 - 13.1835i) q^{50} -4.29890 q^{51} +(-33.9967 + 11.0462i) q^{52} +(-0.0481219 - 0.0662342i) q^{53} +(2.20671 - 1.60327i) q^{54} +(0.224518 - 0.237270i) q^{55} +(-7.59117 - 5.51531i) q^{56} -0.269509i q^{57} +(15.0241 - 20.6789i) q^{58} +(-1.45299 + 4.47186i) q^{59} +(2.23384 + 11.9574i) q^{60} +(-2.91511 - 8.97178i) q^{61} +(-10.8434 - 3.52322i) q^{62} +(-0.951057 - 0.309017i) q^{63} +(-8.91713 - 27.4441i) q^{64} +(-2.69822 - 14.4432i) q^{65} +(-0.123134 + 0.378968i) q^{66} +(-4.22013 + 5.80851i) q^{67} +23.3862i q^{68} +(1.36798 + 0.993895i) q^{69} +(4.19209 - 4.43019i) q^{70} +(-4.77413 + 3.46861i) q^{71} +(-5.51531 - 7.59117i) q^{72} +(6.77150 - 2.20019i) q^{73} -25.4316 q^{74} +(-4.99238 + 0.275932i) q^{75} -1.46614 q^{76} +(0.138936 - 0.0451431i) q^{77} +(10.5350 + 14.5002i) q^{78} +(-12.5838 + 9.14269i) q^{79} +(32.3419 - 6.04197i) q^{80} +(-0.809017 - 0.587785i) q^{81} +8.04189i q^{82} +(3.86765 - 5.32337i) q^{83} +(-1.68106 + 5.17379i) q^{84} +(-9.53218 - 1.24110i) q^{85} +(-3.98500 - 12.2646i) q^{86} +(-8.91229 - 2.89578i) q^{87} +(1.30367 + 0.423587i) q^{88} +(1.68955 + 5.19990i) q^{89} +(5.35592 - 2.91793i) q^{90} +(2.03054 - 6.24935i) q^{91} +(5.40683 - 7.44186i) q^{92} +4.17994i q^{93} +(25.1239 + 18.2536i) q^{94} +(0.0778075 - 0.597596i) q^{95} +(-17.2871 + 12.5598i) q^{96} +(1.16626 + 1.60522i) q^{97} +(2.59414 - 0.842888i) q^{98} +0.146086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$1$

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 $

$2$	−2.59414	+	0.842888i	−1.83434	+	0.596012i	−0.835413	+	0.549623i	$0.814771\pi$
$2$	−2.59414	+	0.842888i	−1.83434	+	0.596012i	−0.998923	+	0.0463891i	$0.985229\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	4.40108	−	3.19758i	2.20054	−	1.59879i
$5$	1.06976	+	1.96357i	0.478413	+	0.878135i
$5$	1.06976	+	1.96357i	0.478413	+	0.878135i
$6$	−2.20671	−	1.60327i	−0.900886	−	0.654532i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−5.51531	+	7.59117i	−1.94996	+	2.68388i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−4.43019	−	4.19209i	−1.40095	−	1.32566i
$11$	−0.0451431	−	0.138936i	−0.0136111	−	0.0418908i	0.944020	−	0.329887i	$-0.107011\pi$
$11$	−0.0451431	−	0.138936i	−0.0136111	−	0.0418908i	−0.957631	+	0.287997i	$0.907011\pi$
$12$	5.17379	+	1.68106i	1.49354	+	0.485282i
$13$	−6.24935	−	2.03054i	−1.73326	−	0.563169i	−0.739343	−	0.673329i	$-0.764864\pi$
$13$	−6.24935	−	2.03054i	−1.73326	−	0.563169i	−0.993914	+	0.110160i	$0.964864\pi$
$14$	−0.842888	−	2.59414i	−0.225271	−	0.693314i
$15$	−0.959771	+	2.01961i	−0.247812	+	0.521462i
$16$	4.54686	−	13.9938i	1.13672	−	3.49845i
$17$	−2.52683	+	3.47788i	−0.612847	+	0.843511i	−0.996808	−	0.0798383i	$-0.974560\pi$
$17$	−2.52683	+	3.47788i	−0.612847	+	0.843511i	0.383961	+	0.923349i	$0.374560\pi$
$18$		−	2.72764i		−	0.642912i
$19$	−0.218037	−	0.158413i	−0.0500212	−	0.0363425i	0.562494	−	0.826802i	$-0.309842\pi$
$19$	−0.218037	−	0.158413i	−0.0500212	−	0.0363425i	−0.612515	+	0.790459i	$0.709842\pi$
$20$	10.9868	+	5.22119i	2.45672	+	1.16749i
$21$	−0.809017	+	0.587785i	−0.176542	+	0.128265i
$22$	0.234215	+	0.322369i	0.0499348	+	0.0687294i
$23$	1.60816	−	0.522522i	0.335324	−	0.108953i	−0.136515	−	0.990638i	$-0.543590\pi$
$23$	1.60816	−	0.522522i	0.335324	−	0.108953i	0.471839	+	0.881685i	$0.343590\pi$
$24$	−9.38320			−1.91534
$25$	−2.71121	+	4.20111i	−0.542243	+	0.840222i
$26$	17.9232			3.51503
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	3.19758	+	4.40108i	0.604285	+	0.831727i
$29$	−7.58124	+	5.50810i	−1.40780	+	1.02283i	−0.414164	+	0.910202i	$0.635926\pi$
$29$	−7.58124	+	5.50810i	−1.40780	+	1.02283i	−0.993637	+	0.112626i	$0.964074\pi$
$30$	0.787473	−	6.04815i	0.143772	−	1.10424i
$31$	3.38164	+	2.45691i	0.607361	+	0.441273i	0.848484	−	0.529221i	$-0.177516\pi$
$31$	3.38164	+	2.45691i	0.607361	+	0.441273i	−0.241123	+	0.970494i	$0.577516\pi$
$32$			21.3680i			3.77737i
$33$	0.0858672	−	0.118186i	0.0149476	−	0.0205736i
$34$	3.62349	−	11.1520i	0.621424	−	1.91255i
$35$	−1.96357	+	1.06976i	−0.331904	+	0.180823i
$36$	1.68106	+	5.17379i	0.280177	+	0.862298i
$37$	8.86730	+	2.88116i	1.45778	+	0.473660i	0.927390	−	0.374096i	$-0.122047\pi$
$37$	8.86730	+	2.88116i	1.45778	+	0.473660i	0.530386	+	0.847756i	$0.322047\pi$
$38$	0.699145	+	0.227166i	0.113416	+	0.0368512i
$39$	−2.03054	−	6.24935i	−0.325146	−	1.00070i
$40$	−20.8059	−	2.70894i	−3.28970	−	0.428321i
$41$	0.911073	−	2.80399i	0.142286	−	0.437910i	−0.854366	−	0.519671i	$-0.826054\pi$
$41$	0.911073	−	2.80399i	0.142286	−	0.437910i	0.996652	+	0.0817610i	$0.0260544\pi$
$42$	1.60327	−	2.20671i	0.247390	−	0.340503i
$43$			4.72780i			0.720982i	0.932763	+	0.360491i	$0.117391\pi$
$43$			4.72780i			0.720982i	−0.932763	+	0.360491i	$0.882609\pi$
$44$	−0.642937	−	0.467121i	−0.0969264	−	0.0704211i
$45$	−2.19804	+	0.410629i	−0.327665	+	0.0612129i
$46$	−3.73136	+	2.71099i	−0.550159	+	0.399714i
$47$	−6.69207	−	9.21084i	−0.976138	−	1.34354i	−0.938884	−	0.344233i	$-0.888139\pi$
$47$	−6.69207	−	9.21084i	−0.976138	−	1.34354i	−0.0372542	−	0.999306i	$-0.511861\pi$
$48$	13.9938	−	4.54686i	2.01983	−	0.656283i
$49$	−1.00000			−0.142857
$50$	3.49221	−	13.1835i	0.493873	−	1.86443i
$51$	−4.29890			−0.601967
$52$	−33.9967	+	11.0462i	−4.71449	+	1.53183i
$53$	−0.0481219	−	0.0662342i	−0.00661006	−	0.00909796i	0.805699	−	0.592325i	$-0.201790\pi$
$53$	−0.0481219	−	0.0662342i	−0.00661006	−	0.00909796i	−0.812309	+	0.583227i	$0.801790\pi$
$54$	2.20671	−	1.60327i	0.300295	−	0.218177i
$55$	0.224518	−	0.237270i	0.0302740	−	0.0319935i
$56$	−7.59117	−	5.51531i	−1.01441	−	0.737014i
$57$		−	0.269509i		−	0.0356973i
$58$	15.0241	−	20.6789i	1.97276	−	2.71528i
$59$	−1.45299	+	4.47186i	−0.189164	+	0.582186i	−0.999995	−	0.00309360i	$-0.999015\pi$
$59$	−1.45299	+	4.47186i	−0.189164	+	0.582186i	0.810831	+	0.585280i	$0.199015\pi$
$60$	2.23384	+	11.9574i	0.288387	+	1.54370i
$61$	−2.91511	−	8.97178i	−0.373241	−	1.14872i	−0.944657	−	0.328058i	$-0.893606\pi$
$61$	−2.91511	−	8.97178i	−0.373241	−	1.14872i	0.571416	−	0.820660i	$-0.306394\pi$
$62$	−10.8434	−	3.52322i	−1.37711	−	0.447449i
$63$	−0.951057	−	0.309017i	−0.119822	−	0.0389325i
$64$	−8.91713	−	27.4441i	−1.11464	−	3.43051i
$65$	−2.69822	−	14.4432i	−0.334673	−	1.79146i
$66$	−0.123134	+	0.378968i	−0.0151568	+	0.0466477i
$67$	−4.22013	+	5.80851i	−0.515571	+	0.709623i	−0.984846	−	0.173429i	$-0.944515\pi$
$67$	−4.22013	+	5.80851i	−0.515571	+	0.709623i	0.469275	+	0.883052i	$0.344515\pi$
$68$			23.3862i			2.83599i
$69$	1.36798	+	0.993895i	0.164685	+	0.119651i
$70$	4.19209	−	4.43019i	0.501051	−	0.529509i
$71$	−4.77413	+	3.46861i	−0.566585	+	0.411648i	−0.833863	−	0.551971i	$-0.813876\pi$
$71$	−4.77413	+	3.46861i	−0.566585	+	0.411648i	0.267278	+	0.963620i	$0.413876\pi$
$72$	−5.51531	−	7.59117i	−0.649985	−	0.894628i
$73$	6.77150	−	2.20019i	0.792544	−	0.257513i	0.115357	−	0.993324i	$-0.463199\pi$
$73$	6.77150	−	2.20019i	0.792544	−	0.257513i	0.677187	+	0.735811i	$0.263199\pi$
$74$	−25.4316			−2.95636
$75$	−4.99238	+	0.275932i	−0.576470	+	0.0318619i
$76$	−1.46614			−0.168178
$77$	0.138936	−	0.0451431i	0.0158332	−	0.00514453i
$78$	10.5350	+	14.5002i	1.19285	+	1.64182i
$79$	−12.5838	+	9.14269i	−1.41579	+	1.02863i	−0.423344	+	0.905969i	$0.639144\pi$
$79$	−12.5838	+	9.14269i	−1.41579	+	1.02863i	−0.992448	+	0.122664i	$0.960856\pi$
$80$	32.3419	−	6.04197i	3.61593	−	0.675513i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			8.04189i			0.888079i
$83$	3.86765	−	5.32337i	0.424530	−	0.584315i	−0.542157	−	0.840277i	$-0.682392\pi$
$83$	3.86765	−	5.32337i	0.424530	−	0.584315i	0.966687	+	0.255962i	$0.0823922\pi$
$84$	−1.68106	+	5.17379i	−0.183419	+	0.564506i
$85$	−9.53218	−	1.24110i	−1.03391	−	0.134616i
$86$	−3.98500	−	12.2646i	−0.429714	−	1.32252i
$87$	−8.91229	−	2.89578i	−0.955498	−	0.310460i
$88$	1.30367	+	0.423587i	0.138971	+	0.0451545i
$89$	1.68955	+	5.19990i	0.179092	+	0.551188i	0.999797	−	0.0201644i	$-0.00641896\pi$
$89$	1.68955	+	5.19990i	0.179092	+	0.551188i	−0.820705	+	0.571352i	$0.806419\pi$
$90$	5.35592	−	2.91793i	0.564563	−	0.307577i
$91$	2.03054	−	6.24935i	0.212858	−	0.655109i
$92$	5.40683	−	7.44186i	0.563701	−	0.775868i
$93$			4.17994i			0.433439i
$94$	25.1239	+	18.2536i	2.59133	+	1.88271i
$95$	0.0778075	−	0.597596i	0.00798288	−	0.0613121i
$96$	−17.2871	+	12.5598i	−1.76436	+	1.28188i
$97$	1.16626	+	1.60522i	0.118416	+	0.162985i	0.864110	−	0.503303i	$-0.167882\pi$
$97$	1.16626	+	1.60522i	0.118416	+	0.162985i	−0.745694	+	0.666288i	$0.767882\pi$
$98$	2.59414	−	0.842888i	0.262048	−	0.0851446i
$99$	0.146086			0.0146822
$100$	1.50108	+	27.1587i	0.150108	+	2.71587i
$101$	14.2302			1.41595			0.707977	−	0.706235i	$-0.249608\pi$
$101$	14.2302			1.41595			0.707977	+	0.706235i	$0.249608\pi$
$102$	11.1520	−	3.62349i	1.10421	−	0.358779i
$103$	8.35028	+	11.4932i	0.822778	+	1.13246i	0.989225	+	0.146406i	$0.0467706\pi$
$103$	8.35028	+	11.4932i	0.822778	+	1.13246i	−0.166447	+	0.986050i	$0.553229\pi$
$104$	49.8812	−	36.2408i	4.89125	−	3.55370i
$105$	−2.01961	−	0.959771i	−0.197094	−	0.0936640i
$106$	0.180663	+	0.131259i	0.0175476	+	0.0127490i
$107$			3.19584i			0.308953i	0.987996	+	0.154477i	$0.0493691\pi$
$107$			3.19584i			0.308953i	−0.987996	+	0.154477i	$0.950631\pi$
$108$	−3.19758	+	4.40108i	−0.307687	+	0.423495i
$109$	1.03048	−	3.17149i	0.0987019	−	0.303773i	−0.889499	−	0.456937i	$-0.848946\pi$
$109$	1.03048	−	3.17149i	0.0987019	−	0.303773i	0.988201	+	0.153164i	$0.0489463\pi$
$110$	−0.382440	+	0.804757i	−0.0364643	+	0.0767305i
$111$	2.88116	+	8.86730i	0.273468	+	0.841647i
$112$	13.9938	+	4.54686i	1.32229	+	0.429638i
$113$	−5.69522	−	1.85049i	−0.535761	−	0.174079i	0.0286253	−	0.999590i	$-0.490887\pi$
$113$	−5.69522	−	1.85049i	−0.535761	−	0.174079i	−0.564386	+	0.825511i	$0.690887\pi$
$114$	0.227166	+	0.699145i	0.0212760	+	0.0654809i
$115$	2.74635	+	2.59875i	0.256099	+	0.242335i
$116$	−15.7531	+	48.4832i	−1.46264	+	4.50155i
$117$	3.86231	−	5.31601i	0.357070	−	0.491465i
$118$		−	12.8253i		−	1.18067i
$119$	−3.47788	−	2.52683i	−0.318817	−	0.231634i
$120$	−10.0378	−	18.4246i	−0.916322	−	1.68193i
$121$	8.88192	−	6.45309i	0.807447	−	0.586645i
$122$	15.1244	+	20.8170i	1.36930	+	1.88468i
$123$	2.80399	−	0.911073i	0.252828	−	0.0821487i
$124$	22.7390			2.04203
$125$	−11.1495	−	0.829467i	−0.997244	−	0.0741898i
$126$	2.72764			0.242998
$127$	0.945723	−	0.307284i	0.0839193	−	0.0272670i	−0.266756	−	0.963764i	$-0.585952\pi$
$127$	0.945723	−	0.307284i	0.0839193	−	0.0272670i	0.350676	+	0.936497i	$0.385952\pi$
$128$	21.1450	+	29.1036i	1.86897	+	2.57242i
$129$	−3.82487	+	2.77893i	−0.336761	+	0.244671i
$130$	19.1736	+	35.1935i	1.68164	+	3.08667i
$131$	6.64041	+	4.82454i	0.580175	+	0.421522i	0.838787	−	0.544459i	$-0.183265\pi$
$131$	6.64041	+	4.82454i	0.580175	+	0.421522i	−0.258612	+	0.965981i	$0.583265\pi$
$132$		−	0.794714i		−	0.0691710i
$133$	0.158413	−	0.218037i	0.0137362	−	0.0189062i
$134$	6.05170	−	18.6252i	0.522787	−	1.60897i
$135$	−1.62418	−	1.53689i	−0.139787	−	0.132275i
$136$	−12.4650	−	38.3632i	−1.06886	−	3.28962i
$137$	−13.8019	−	4.48452i	−1.17918	−	0.383139i	−0.347118	−	0.937822i	$-0.612840\pi$
$137$	−13.8019	−	4.48452i	−1.17918	−	0.383139i	−0.832062	+	0.554683i	$0.812840\pi$
$138$	−4.38648	−	1.42525i	−0.373402	−	0.121326i
$139$	5.99240	+	18.4427i	0.508268	+	1.56429i	0.795206	+	0.606340i	$0.207363\pi$
$139$	5.99240	+	18.4427i	0.508268	+	1.56429i	−0.286937	+	0.957949i	$0.592637\pi$
$140$	−5.22119	+	10.9868i	−0.441271	+	0.928552i
$141$	3.51823	−	10.8280i	0.296288	−	0.911881i
$142$	9.46114	−	13.0221i	0.793961	−	1.09279i
$143$			0.959924i			0.0802729i
$144$	11.9038	+	8.64865i	0.991987	+	0.720720i
$145$	−18.9257	−	8.99395i	−1.57169	−	0.746907i
$146$	−15.7117	+	11.4152i	−1.30031	+	0.944731i
$147$	−0.587785	−	0.809017i	−0.0484797	−	0.0667266i
$148$	48.2385	−	15.6736i	3.96518	−	1.28836i
$149$	3.19810			0.261999			0.130999	−	0.991382i	$-0.458181\pi$
$149$	3.19810			0.261999			0.130999	+	0.991382i	$0.458181\pi$
$150$	12.7184	−	4.92383i	1.03845	−	0.402029i
$151$	−6.43573			−0.523732			−0.261866	−	0.965104i	$-0.584338\pi$
$151$	−6.43573			−0.523732			−0.261866	+	0.965104i	$0.584338\pi$
$152$	2.40509	−	0.781460i	0.195078	−	0.0633848i
$153$	−2.52683	−	3.47788i	−0.204282	−	0.281170i
$154$	−0.322369	+	0.234215i	−0.0259773	+	0.0188736i
$155$	−1.20675	+	9.26840i	−0.0969287	+	0.744455i
$156$	−28.9193	−	21.0111i	−2.31540	−	1.68224i
$157$		−	8.30203i		−	0.662574i	−0.943530	−	0.331287i	$-0.892517\pi$
$157$		−	8.30203i		−	0.662574i	0.943530	−	0.331287i	$-0.107483\pi$
$158$	24.9380	−	34.3242i	1.98396	−	2.73069i
$159$	0.0252992	−	0.0778629i	0.00200636	−	0.00617493i
$160$	−41.9576	+	22.8587i	−3.31704	+	1.80714i
$161$	0.522522	+	1.60816i	0.0411805	+	0.126741i
$162$	2.59414	+	0.842888i	0.203815	+	0.0662236i
$163$	−12.9518	−	4.20831i	−1.01447	−	0.329620i	−0.245835	−	0.969312i	$-0.579062\pi$
$163$	−12.9518	−	4.20831i	−1.01447	−	0.329620i	−0.768632	+	0.639692i	$0.779062\pi$
$164$	−4.95627	−	15.2538i	−0.387020	−	1.19112i
$165$	0.323924	+	0.0421752i	0.0252175	+	0.00328333i
$166$	−5.54624	+	17.0696i	−0.430472	+	1.32486i
$167$	8.09694	−	11.1445i	0.626560	−	0.862386i	−0.371250	−	0.928533i	$-0.621071\pi$
$167$	8.09694	−	11.1445i	0.626560	−	0.862386i	0.997810	+	0.0661472i	$0.0210707\pi$
$168$		−	9.38320i		−	0.723930i
$169$	24.4140	+	17.7378i	1.87800	+	1.36445i
$170$	25.7739	−	4.81498i	1.97677	−	0.369292i
$171$	0.218037	−	0.158413i	0.0166737	−	0.0121142i
$172$	15.1175	+	20.8074i	1.15270	+	1.58655i
$173$	5.86422	−	1.90540i	0.445848	−	0.144865i	−0.0774839	−	0.996994i	$-0.524689\pi$
$173$	5.86422	−	1.90540i	0.445848	−	0.144865i	0.523332	+	0.852129i	$0.324689\pi$
$174$	25.5606			1.93774
$175$	−4.20111	−	2.71121i	−0.317574	−	0.204949i
$176$	−2.14950			−0.162025
$177$	−4.47186	+	1.45299i	−0.336125	+	0.109214i
$178$	−8.76586	−	12.0652i	−0.657029	−	0.904323i
$179$	−9.60120	+	6.97568i	−0.717627	+	0.521387i	−0.885625	−	0.464401i	$-0.846270\pi$
$179$	−9.60120	+	6.97568i	−0.717627	+	0.521387i	0.167998	+	0.985787i	$0.446270\pi$
$180$	−8.36075	+	8.83561i	−0.623173	+	0.658568i
$181$	8.80554	+	6.39760i	0.654510	+	0.475530i	0.864805	−	0.502108i	$-0.167442\pi$
$181$	8.80554	+	6.39760i	0.654510	+	0.475530i	−0.210294	+	0.977638i	$0.567442\pi$
$182$			17.9232i			1.32856i
$183$	5.54487	−	7.63185i	0.409888	−	0.564163i
$184$	−4.90293	+	15.0897i	−0.361449	+	1.11242i
$185$	3.82855	+	20.4937i	0.281481	+	1.50673i
$186$	−3.52322	−	10.8434i	−0.258335	−	0.795074i
$187$	0.597272	+	0.194066i	0.0436769	+	0.0141915i
$188$	−58.9047	−	19.1393i	−4.29607	−	1.39588i
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	0.301863	+	1.61583i	0.0218995	+	0.117225i
$191$	−1.46114	+	4.49692i	−0.105724	+	0.325386i	−0.989900	−	0.141769i	$-0.954721\pi$
$191$	−1.46114	+	4.49692i	−0.105724	+	0.325386i	0.884176	+	0.467155i	$0.154721\pi$
$192$	16.9614	−	23.3453i	1.22408	−	1.68481i
$193$			2.93989i			0.211618i	0.994386	+	0.105809i	$0.0337432\pi$
$193$			2.93989i			0.211618i	−0.994386	+	0.105809i	$0.966257\pi$
$194$	−4.37846	−	3.18114i	−0.314355	−	0.228392i
$195$	10.0988	−	10.6724i	0.723193	−	0.764268i
$196$	−4.40108	+	3.19758i	−0.314363	+	0.228398i
$197$	10.9119	+	15.0189i	0.777438	+	1.07005i	0.995560	+	0.0941302i	$0.0300070\pi$
$197$	10.9119	+	15.0189i	0.777438	+	1.07005i	−0.218122	+	0.975922i	$0.569993\pi$
$198$	−0.378968	+	0.123134i	−0.0269321	+	0.00875077i
$199$	−2.88502			−0.204513			−0.102257	−	0.994758i	$-0.532606\pi$
$199$	−2.88502			−0.204513			−0.102257	+	0.994758i	$0.532606\pi$
$200$	−16.9382	−	43.7517i	−1.19771	−	3.09371i
$201$	−7.17971			−0.506418
$202$	−36.9151	+	11.9944i	−2.59734	+	0.843926i
$203$	−5.50810	−	7.58124i	−0.386593	−	0.532099i
$204$	−18.9198	+	13.7461i	−1.32465	+	0.962417i
$205$	6.48047	−	1.21065i	0.452616	−	0.0845557i
$206$	−31.3493	−	22.7766i	−2.18421	−	1.58692i
$207$			1.69092i			0.117527i
$208$	−56.8298	+	78.2195i	−3.94044	+	5.42355i
$209$	−0.0121665	+	0.0374445i	−0.000841572	+	0.00259009i
$210$	6.04815	+	0.787473i	0.417362	+	0.0543408i
$211$	7.06229	+	21.7355i	0.486188	+	1.49633i	0.830253	+	0.557386i	$0.188196\pi$
$211$	7.06229	+	21.7355i	0.486188	+	1.49633i	−0.344065	+	0.938946i	$0.611804\pi$
$212$	−0.423577	−	0.137629i	−0.0290914	−	0.00945238i
$213$	−5.61233	−	1.82356i	−0.384551	−	0.124948i
$214$	−2.69373	−	8.29046i	−0.184140	−	0.566724i
$215$	−9.28336	+	5.05762i	−0.633120	+	0.344927i
$216$	2.89957	−	8.92396i	0.197291	−	0.607198i
$217$	−2.45691	+	3.38164i	−0.166786	+	0.229561i
$218$			9.09587i			0.616050i
$219$	5.76018	+	4.18502i	0.389237	+	0.282797i
$220$	0.229435	−	1.76216i	0.0154685	−	0.118805i
$221$	22.8530	−	16.6037i	1.53726	−	1.11688i
$222$	−14.9483	−	20.5746i	−1.00326	−	1.38087i
$223$	12.2545	−	3.98171i	0.820619	−	0.266635i	0.131530	−	0.991312i	$-0.458011\pi$
$223$	12.2545	−	3.98171i	0.820619	−	0.266635i	0.689089	+	0.724677i	$0.258011\pi$
$224$	−21.3680			−1.42771
$225$	−3.15768	−	3.87673i	−0.210512	−	0.258449i
$226$	16.3340			1.08652
$227$	8.61278	−	2.79846i	0.571650	−	0.185741i	−0.00890619	−	0.999960i	$-0.502835\pi$
$227$	8.61278	−	2.79846i	0.571650	−	0.185741i	0.580557	+	0.814220i	$0.302835\pi$
$228$	−0.861775	−	1.18613i	−0.0570725	−	0.0785535i
$229$	22.2454	−	16.1622i	1.47002	−	1.06803i	0.489408	−	0.872055i	$-0.337213\pi$
$229$	22.2454	−	16.1622i	1.47002	−	1.06803i	0.980609	−	0.195975i	$-0.0627871\pi$
$230$	−9.31490	−	4.42667i	−0.614206	−	0.291886i
$231$	0.118186	+	0.0858672i	0.00777607	+	0.00564965i
$232$		−	87.9294i		−	5.77285i
$233$	2.94691	−	4.05607i	0.193058	−	0.265722i	−0.701504	−	0.712666i	$-0.747488\pi$
$233$	2.94691	−	4.05607i	0.193058	−	0.265722i	0.894562	+	0.446944i	$0.147488\pi$
$234$	−5.53858	+	17.0460i	−0.362068	+	1.11433i
$235$	10.9272	−	22.9938i	0.712812	−	1.49995i
$236$	7.90435	+	24.3271i	0.514529	+	1.58356i
$237$	−14.7932	−	4.80660i	−0.960921	−	0.312222i
$238$	11.1520	+	3.62349i	0.722875	+	0.234876i
$239$	−2.59667	−	7.99174i	−0.167965	−	0.516943i	0.831278	−	0.555857i	$-0.187610\pi$
$239$	−2.59667	−	7.99174i	−0.167965	−	0.516943i	−0.999243	+	0.0389146i	$0.987610\pi$
$240$	23.8981	+	22.6137i	1.54262	+	1.45971i
$241$	0.583320	−	1.79527i	0.0375749	−	0.115644i	−0.930510	−	0.366267i	$-0.880636\pi$
$241$	0.583320	−	1.79527i	0.0375749	−	0.115644i	0.968085	+	0.250623i	$0.0806356\pi$
$242$	−17.6017	+	24.2267i	−1.13148	+	1.55735i
$243$		−	1.00000i		−	0.0641500i
$244$	−41.5176	−	30.1643i	−2.65789	−	1.93107i
$245$	−1.06976	−	1.96357i	−0.0683447	−	0.125448i
$246$	−6.50603	+	4.72691i	−0.414809	+	0.301377i
$247$	1.04093	+	1.43271i	0.0662326	+	0.0911613i
$248$	−37.3016	+	12.1200i	−2.36865	+	0.769622i
$249$	6.58004			0.416993
$250$	29.6226	−	7.24605i	1.87350	−	0.458280i
$251$	−2.28853			−0.144451			−0.0722254	−	0.997388i	$-0.523010\pi$
$251$	−2.28853			−0.144451			−0.0722254	+	0.997388i	$0.523010\pi$
$252$	−5.17379	+	1.68106i	−0.325918	+	0.105897i
$253$	−0.145194	−	0.199843i	−0.00912828	−	0.0125640i
$254$	−2.19433	+	1.59428i	−0.137685	+	0.100034i
$255$	−4.59881	−	8.44119i	−0.287988	−	0.528608i
$256$	−32.6936	−	23.7533i	−2.04335	−	1.48458i
$257$		−	15.2948i		−	0.954064i	−0.878886	−	0.477032i	$-0.841713\pi$
$257$		−	15.2948i		−	0.954064i	0.878886	−	0.477032i	$-0.158287\pi$
$258$	7.57993	−	10.4329i	0.471906	−	0.649522i
$259$	−2.88116	+	8.86730i	−0.179027	+	0.550987i
$260$	−58.0584	−	54.9381i	−3.60063	−	3.40711i
$261$	−2.89578	−	8.91229i	−0.179244	−	0.551657i
$262$	−21.2927	−	6.91842i	−1.31547	−	0.427422i
$263$	21.1299	+	6.86551i	1.30292	+	0.423345i	0.876597	−	0.481224i	$-0.159808\pi$
$263$	21.1299	+	6.86551i	1.30292	+	0.423345i	0.426326	+	0.904570i	$0.359808\pi$
$264$	0.423587	+	1.30367i	0.0260699	+	0.0802350i
$265$	0.0785763	−	0.165346i	0.00482691	−	0.0101571i
$266$	−0.227166	+	0.699145i	−0.0139284	+	0.0428673i
$267$	−3.21371	+	4.42330i	−0.196676	+	0.270701i
$268$			39.0579i			2.38584i
$269$	−0.783982	−	0.569597i	−0.0478002	−	0.0347289i	0.563629	−	0.826028i	$-0.309405\pi$
$269$	−0.783982	−	0.569597i	−0.0478002	−	0.0347289i	−0.611429	+	0.791299i	$0.709405\pi$
$270$	5.50879	+	2.61791i	0.335254	+	0.159321i
$271$	17.2353	−	12.5221i	1.04697	−	0.760666i	0.0753338	−	0.997158i	$-0.475998\pi$
$271$	17.2353	−	12.5221i	1.04697	−	0.760666i	0.971633	+	0.236492i	$0.0759978\pi$
$272$	37.1797	+	51.1734i	2.25435	+	3.10285i
$273$	6.24935	−	2.03054i	0.378228	−	0.122894i
$274$	39.5842			2.39137
$275$	0.706078	+	0.187034i	0.0425781	+	0.0112786i
$276$	9.19865			0.553694
$277$	−20.4484	+	6.64407i	−1.22862	+	0.399204i	−0.850215	−	0.526435i	$-0.823528\pi$
$277$	−20.4484	+	6.64407i	−1.22862	+	0.399204i	−0.378407	+	0.925639i	$0.623528\pi$
$278$	−31.0903	−	42.7921i	−1.86467	−	2.56650i
$279$	−3.38164	+	2.45691i	−0.202454	+	0.147091i
$280$	2.70894	−	20.8059i	0.161890	−	1.24339i
$281$	26.9790	+	19.6014i	1.60943	+	1.16932i	0.865244	+	0.501351i	$0.167163\pi$
$281$	26.9790	+	19.6014i	1.60943	+	1.16932i	0.744188	+	0.667970i	$0.232837\pi$
$282$			31.0548i			1.84929i
$283$	−15.0042	+	20.6515i	−0.891908	+	1.22761i	0.0810697	+	0.996708i	$0.474166\pi$
$283$	−15.0042	+	20.6515i	−0.891908	+	1.22761i	−0.972978	+	0.230898i	$0.925834\pi$
$284$	−9.92022	+	30.5313i	−0.588657	+	1.81170i
$285$	0.529200	−	0.288311i	0.0313471	−	0.0170781i
$286$	−0.809109	−	2.49018i	−0.0478436	−	0.147247i
$287$	2.80399	+	0.911073i	0.165514	+	0.0537789i
$288$	−20.3222	−	6.60308i	−1.19750	−	0.389090i
$289$	−0.457516	−	1.40809i	−0.0269127	−	0.0828289i
$290$	56.6768	+	7.37936i	3.32818	+	0.433331i
$291$	−0.613138	+	1.88704i	−0.0359428	+	0.110621i
$292$	22.7667	−	31.3356i	1.33232	−	1.83378i
$293$		−	6.32909i		−	0.369749i	−0.982762	−	0.184875i	$-0.940812\pi$
$293$		−	6.32909i		−	0.369749i	0.982762	−	0.184875i	$-0.0591879\pi$
$294$	2.20671	+	1.60327i	0.128698	+	0.0935045i
$295$	−10.3352	+	1.93077i	−0.601736	+	0.112414i
$296$	−70.7773	+	51.4227i	−4.11385	+	2.98889i
$297$	0.0858672	+	0.118186i	0.00498252	+	0.00685785i
$298$	−8.29634	+	2.69564i	−0.480594	+	0.156154i
$299$	−11.1109			−0.642561
$300$	−21.0896	+	17.1779i	−1.21761	+	0.991767i
$301$	−4.72780			−0.272506
$302$	16.6952	−	5.42460i	0.960701	−	0.312151i
$303$	8.36428	+	11.5124i	0.480516	+	0.661373i
$304$	−3.20819	+	2.33089i	−0.184002	+	0.133686i
$305$	14.4982	−	15.3217i	0.830167	−	0.877318i
$306$	9.48643	+	6.89229i	0.542303	+	0.394006i
$307$			0.255783i			0.0145983i	0.999973	+	0.00729916i	$0.00232342\pi$
$307$			0.255783i			0.0145983i	−0.999973	+	0.00729916i	$0.997677\pi$
$308$	0.467121	−	0.642937i	0.0266167	−	0.0366347i
$309$	−4.39000	+	13.5110i	−0.249739	+	0.768616i
$310$	−4.68173	−	25.0607i	−0.265905	−	1.42335i
$311$	2.18435	+	6.72274i	0.123863	+	0.381212i	0.993692	−	0.112142i	$-0.0357710\pi$
$311$	2.18435	+	6.72274i	0.123863	+	0.381212i	−0.869829	+	0.493353i	$0.835771\pi$
$312$	58.6389	+	19.0529i	3.31977	+	1.07866i
$313$	14.7991	+	4.80853i	0.836496	+	0.271794i	0.695779	−	0.718256i	$-0.255059\pi$
$313$	14.7991	+	4.80853i	0.836496	+	0.271794i	0.140717	+	0.990050i	$0.455059\pi$
$314$	6.99769	+	21.5367i	0.394902	+	1.21538i
$315$	−0.410629	−	2.19804i	−0.0231363	−	0.123846i
$316$	−26.1481	+	80.4755i	−1.47094	+	4.52710i
$317$	−12.8285	+	17.6569i	−0.720521	+	0.991713i	0.278985	+	0.960295i	$0.410002\pi$
$317$	−12.8285	+	17.6569i	−0.720521	+	0.991713i	−0.999506	+	0.0314171i	$0.989998\pi$
$318$			0.223312i			0.0125227i
$319$	1.10751	+	0.804656i	0.0620089	+	0.0450521i
$320$	44.3492	−	46.8681i	2.47920	−	2.62001i
$321$	−2.58549	+	1.87847i	−0.144308	+	0.104846i
$322$	−2.71099	−	3.73136i	−0.151078	−	0.207941i
$323$	1.10189	−	0.358025i	0.0613106	−	0.0199210i
$324$	−5.44004			−0.302224
$325$	25.4738	−	20.7490i	1.41303	−	1.15095i
$326$	37.1461			2.05733
$327$	3.17149	−	1.03048i	0.175384	−	0.0569856i
$328$	16.2607	+	22.3810i	0.897849	+	1.23578i
$329$	9.21084	−	6.69207i	0.507810	−	0.368946i
$330$	−0.875855	+	0.163623i	−0.0482142	+	0.00900717i
$331$	−7.69845	−	5.59325i	−0.423145	−	0.307433i	0.355757	−	0.934578i	$-0.384223\pi$
$331$	−7.69845	−	5.59325i	−0.423145	−	0.307433i	−0.778902	+	0.627146i	$0.784223\pi$
$332$		−	35.7957i		−	1.96454i
$333$	−5.48030	+	7.54298i	−0.300318	+	0.413353i
$334$	−11.6111	+	35.7352i	−0.635329	+	1.95534i
$335$	−15.9200	−	2.07279i	−0.869800	−	0.113249i
$336$	4.54686	+	13.9938i	0.248052	+	0.763425i
$337$	5.02110	+	1.63145i	0.273517	+	0.0888709i	0.442564	−	0.896737i	$-0.354069\pi$
$337$	5.02110	+	1.63145i	0.273517	+	0.0888709i	−0.169047	+	0.985608i	$0.554069\pi$
$338$	−78.2845	−	25.4362i	−4.25811	−	1.38355i
$339$	−1.85049	−	5.69522i	−0.100505	−	0.309322i
$340$	−45.9204	+	25.0177i	−2.49039	+	1.35677i
$341$	0.188695	−	0.580744i	0.0102184	−	0.0314491i
$342$	−0.432095	+	0.594728i	−0.0233650	+	0.0321592i
$343$		−	1.00000i		−	0.0539949i
$344$	−35.8895	−	26.0752i	−1.93503	−	1.40588i
$345$	−0.488169	+	3.74936i	−0.0262821	+	0.201859i
$346$	−13.6066	+	9.88576i	−0.731495	+	0.531462i
$347$	16.5245	+	22.7440i	0.887080	+	1.22096i	0.974409	+	0.224781i	$0.0721668\pi$
$347$	16.5245	+	22.7440i	0.887080	+	1.22096i	−0.0873292	+	0.996180i	$0.527833\pi$
$348$	−48.4832	+	15.7531i	−2.59897	+	0.844457i
$349$	−29.9652			−1.60400			−0.801999	−	0.597325i	$-0.796230\pi$
$349$	−29.9652			−1.60400			−0.801999	+	0.597325i	$0.796230\pi$
$350$	13.1835	+	3.49221i	0.704689	+	0.186667i
$351$	6.57095			0.350731
$352$	2.96879	−	0.964618i	0.158237	−	0.0514143i
$353$	1.24850	+	1.71841i	0.0664509	+	0.0914618i	0.840949	−	0.541115i	$-0.181997\pi$
$353$	1.24850	+	1.71841i	0.0664509	+	0.0914618i	−0.774498	+	0.632576i	$0.781997\pi$
$354$	10.3759	−	7.53855i	0.551474	−	0.400669i
$355$	−11.9181	−	5.66375i	−0.632545	−	0.300601i
$356$	24.0629	+	17.4827i	1.27533	+	0.926583i
$357$		−	4.29890i		−	0.227522i
$358$	19.0272	−	26.1886i	1.00562	−	1.38411i
$359$	1.79348	−	5.51976i	0.0946563	−	0.291322i	−0.892508	−	0.451032i	$-0.851056\pi$
$359$	1.79348	−	5.51976i	0.0946563	−	0.291322i	0.987164	+	0.159710i	$0.0510560\pi$
$360$	9.00572	−	18.9504i	0.474643	−	0.998776i
$361$	−5.84888	−	18.0010i	−0.307836	−	0.947421i
$362$	−28.2353	−	9.17420i	−1.48401	−	0.482185i
$363$	10.4413	+	3.39259i	0.548027	+	0.178065i
$364$	−11.0462	−	33.9967i	−0.578978	−	1.78191i
$365$	11.5641	+	10.9426i	0.605294	+	0.572763i
$366$	−7.95138	+	24.4718i	−0.415625	+	1.27916i
$367$	−1.20632	+	1.66035i	−0.0629693	+	0.0866698i	−0.839340	−	0.543607i	$-0.817058\pi$
$367$	−1.20632	+	1.66035i	−0.0629693	+	0.0866698i	0.776371	+	0.630276i	$0.217058\pi$
$368$		−	24.8801i		−	1.29696i
$369$	2.38522	+	1.73296i	0.124170	+	0.0902145i
$370$	−27.2057	−	49.9366i	−1.41436	−	2.59608i
$371$	0.0662342	−	0.0481219i	0.00343871	−	0.00249837i
$372$	13.3657	+	18.3963i	0.692977	+	0.953802i
$373$	13.4480	−	4.36951i	0.696309	−	0.226244i	0.0605873	−	0.998163i	$-0.480703\pi$
$373$	13.4480	−	4.36951i	0.696309	−	0.226244i	0.635722	+	0.771918i	$0.280703\pi$
$374$	−1.71299			−0.0885764
$375$	−5.88248	−	9.50771i	−0.303770	−	0.490976i
$376$	106.830			5.50933
$377$	58.5622	−	19.0280i	3.01611	−	0.979993i
$378$	1.60327	+	2.20671i	0.0824632	+	0.113501i
$379$	−23.3881	+	16.9924i	−1.20137	+	0.872843i	−0.994418	−	0.105509i	$-0.966353\pi$
$379$	−23.3881	+	16.9924i	−1.20137	+	0.872843i	−0.206947	+	0.978352i	$0.566353\pi$
$380$	−1.56842	−	2.87887i	−0.0804584	−	0.147683i
$381$	0.804480	+	0.584489i	0.0412148	+	0.0299443i
$382$		−	12.8972i		−	0.659880i
$383$	4.93626	−	6.79418i	0.252231	−	0.347166i	−0.664060	−	0.747679i	$-0.731168\pi$
$383$	4.93626	−	6.79418i	0.252231	−	0.347166i	0.916291	+	0.400513i	$0.131168\pi$
$384$	−11.1166	+	34.2133i	−0.567291	+	1.74594i
$385$	0.237270	+	0.224518i	0.0120924	+	0.0114425i
$386$	−2.47800	−	7.62649i	−0.126127	−	0.388178i
$387$	−4.49640	−	1.46097i	−0.228565	−	0.0742652i
$388$	10.2656	+	3.33550i	0.521157	+	0.169334i
$389$	1.47885	+	4.55144i	0.0749808	+	0.230767i	0.981522	−	0.191351i	$-0.0612868\pi$
$389$	1.47885	+	4.55144i	0.0749808	+	0.230767i	−0.906541	+	0.422118i	$0.861287\pi$
$390$	−17.2022	+	36.1980i	−0.871066	+	1.83296i
$391$	−2.24627	+	6.91331i	−0.113599	+	0.349621i
$392$	5.51531	−	7.59117i	0.278565	−	0.383412i
$393$			8.20800i			0.414039i
$394$	−40.9662	−	29.7637i	−2.06385	−	1.49947i
$395$	−31.4140	−	14.9287i	−1.58061	−	0.751146i
$396$	0.642937	−	0.467121i	0.0323088	−	0.0234737i
$397$	−3.73784	−	5.14469i	−0.187597	−	0.258205i	0.704851	−	0.709355i	$-0.251014\pi$
$397$	−3.73784	−	5.14469i	−0.187597	−	0.258205i	−0.892448	+	0.451151i	$0.851014\pi$
$398$	7.48415	−	2.43175i	0.375146	−	0.121892i
$399$	0.269509			0.0134923
$400$	46.4620	+	57.0421i	2.32310	+	2.85210i
$401$	32.6938			1.63265			0.816326	−	0.577592i	$-0.196008\pi$
$401$	32.6938			1.63265			0.816326	+	0.577592i	$0.196008\pi$
$402$	18.6252	−	6.05170i	0.928941	−	0.301831i
$403$	−16.1442	−	22.2206i	−0.804200	−	1.10689i
$404$	62.6282	−	45.5020i	3.11587	−	2.26381i
$405$	0.288701	−	2.21735i	0.0143457	−	0.110181i
$406$	20.6789	+	15.0241i	1.02628	+	0.745635i
$407$		−	1.36205i		−	0.0675144i
$408$	23.7098	−	32.6337i	1.17381	−	1.61561i
$409$	1.17726	−	3.62322i	0.0582116	−	0.179157i	−0.917723	−	0.397222i	$-0.869974\pi$
$409$	1.17726	−	3.62322i	0.0582116	−	0.179157i	0.975934	+	0.218065i	$0.0699744\pi$
$410$	−15.7908	+	8.60292i	−0.779853	+	0.424868i
$411$	−4.48452	−	13.8019i	−0.221205	−	0.680800i
$412$	73.5006	+	23.8818i	3.62112	+	1.17657i
$413$	−4.47186	−	1.45299i	−0.220046	−	0.0714972i
$414$	−1.42525	−	4.38648i	−0.0700474	−	0.215584i
$415$	14.5903	+	1.89966i	0.716208	+	0.0932509i
$416$	43.3885	−	133.536i	2.12730	−	6.54715i
$417$	−11.3982	+	15.6883i	−0.558173	+	0.768259i
$418$		−	0.107391i		−	0.00525269i
$419$	7.92618	+	5.75871i	0.387219	+	0.281331i	0.764315	−	0.644843i	$-0.223077\pi$
$419$	7.92618	+	5.75871i	0.387219	+	0.281331i	−0.377096	+	0.926174i	$0.623077\pi$
$420$	−11.9574	+	2.23384i	−0.583463	+	0.109000i
$421$	−18.4128	+	13.3777i	−0.897383	+	0.651987i	−0.937793	−	0.347196i	$-0.887134\pi$
$421$	−18.4128	+	13.3777i	−0.897383	+	0.651987i	0.0404094	+	0.999183i	$0.487134\pi$
$422$	−36.6412	−	50.4322i	−1.78366	−	2.45500i
$423$	10.8280	−	3.51823i	0.526475	−	0.171062i
$424$	0.768202			0.0373072
$425$	−7.76019	−	20.0448i	−0.376425	−	0.972315i
$426$	16.0962			0.779866
$427$	8.97178	−	2.91511i	0.434175	−	0.141072i
$428$	10.2189	+	14.0651i	0.493950	+	0.679864i
$429$	−0.776595	+	0.564229i	−0.0374944	+	0.0272412i
$430$	19.8193	−	20.9450i	0.955774	−	1.01006i
$431$	9.47096	+	6.88106i	0.456200	+	0.331449i	0.792039	−	0.610471i	$-0.209020\pi$
$431$	9.47096	+	6.88106i	0.456200	+	0.331449i	−0.335839	+	0.941920i	$0.609020\pi$
$432$			14.7140i			0.707925i
$433$	−16.1254	+	22.1947i	−0.774936	+	1.06661i	0.220887	+	0.975299i	$0.429105\pi$
$433$	−16.1254	+	22.1947i	−0.774936	+	1.06661i	−0.995823	+	0.0913085i	$0.970895\pi$
$434$	3.52322	−	10.8434i	0.169120	−	0.520498i
$435$	−3.84797	−	20.5977i	−0.184496	−	0.987584i
$436$	−5.60584	−	17.2530i	−0.268471	−	0.826269i
$437$	−0.433413	−	0.140824i	−0.0207329	−	0.00673654i
$438$	−18.4702	−	6.00134i	−0.882542	−	0.286755i
$439$	−4.40711	−	13.5637i	−0.210340	−	0.647359i	−0.999452	−	0.0331098i	$-0.989459\pi$
$439$	−4.40711	−	13.5637i	−0.210340	−	0.647359i	0.789112	−	0.614249i	$-0.210541\pi$
$440$	0.562871	+	3.01298i	0.0268338	+	0.143638i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	−45.2889	+	62.3349i	−2.15417	+	2.96497i
$443$		−	13.4332i		−	0.638231i	−0.947716	−	0.319115i	$-0.896614\pi$
$443$		−	13.4332i		−	0.638231i	0.947716	−	0.319115i	$-0.103386\pi$
$444$	41.0341	+	29.8130i	1.94739	+	1.41486i
$445$	−8.40294	+	8.88021i	−0.398338	+	0.420962i
$446$	−28.4337	+	20.6583i	−1.34637	+	0.978198i
$447$	1.87980	+	2.58732i	0.0889114	+	0.122376i
$448$	27.4441	−	8.91713i	1.29661	−	0.421295i
$449$	0.219166			0.0103431			0.00517154	−	0.999987i	$-0.498354\pi$
$449$	0.219166			0.0103431			0.00517154	+	0.999987i	$0.498354\pi$
$450$	11.4591	+	7.39523i	0.540189	+	0.348614i
$451$	−0.430704			−0.0202811
$452$	−30.9822	+	10.0667i	−1.45728	+	0.473499i
$453$	−3.78283	−	5.20662i	−0.177733	−	0.244628i
$454$	−19.9840	+	14.5192i	−0.937896	+	0.681421i
$455$	14.4432	−	2.69822i	0.677109	−	0.126495i
$456$	2.04589	+	1.48643i	0.0958075	+	0.0696082i
$457$			21.1783i			0.990678i	0.868700	+	0.495339i	$0.164956\pi$
$457$			21.1783i			0.990678i	−0.868700	+	0.495339i	$0.835044\pi$
$458$	−44.0848	+	60.6775i	−2.05995	+	2.83527i
$459$	1.32843	−	4.08850i	0.0620060	−	0.190835i
$460$	20.3967	+	2.65566i	0.950999	+	0.123821i
$461$	−7.93318	−	24.4158i	−0.369485	−	1.13716i	−0.947125	−	0.320866i	$-0.896026\pi$
$461$	−7.93318	−	24.4158i	−0.369485	−	1.13716i	0.577639	−	0.816292i	$-0.303974\pi$
$462$	−0.378968	−	0.123134i	−0.0176312	−	0.00572872i
$463$	4.58123	+	1.48853i	0.212908	+	0.0691779i	0.413529	−	0.910491i	$-0.364296\pi$
$463$	4.58123	+	1.48853i	0.212908	+	0.0691779i	−0.200621	+	0.979669i	$0.564296\pi$
$464$	42.6083	+	131.135i	1.97804	+	6.08779i
$465$	−8.20760	+	4.47154i	−0.380618	+	0.207363i
$466$	−4.22588	+	13.0059i	−0.195760	+	0.602488i
$467$	−12.4529	+	17.1399i	−0.576250	+	0.793140i	−0.993278	−	0.115753i	$-0.963072\pi$
$467$	−12.4529	+	17.1399i	−0.576250	+	0.793140i	0.417028	+	0.908894i	$0.363072\pi$
$468$		−	35.7462i		−	1.65237i
$469$	−5.80851	−	4.22013i	−0.268212	−	0.194868i
$470$	−8.96556	+	68.8595i	−0.413551	+	3.17625i
$471$	6.71649	−	4.87981i	0.309479	−	0.224850i
$472$	−25.9329	−	35.6936i	−1.19366	−	1.64293i
$473$	0.656861	−	0.213427i	0.0302025	−	0.00981339i
$474$	42.4271			1.94874
$475$	1.25666	−	0.486506i	0.0576594	−	0.0223224i
$476$	−23.3862			−1.07190
$477$	0.0778629	−	0.0252992i	0.00356510	−	0.00115837i
$478$	13.4723	+	18.5430i	0.616208	+	0.848138i
$479$	−22.5122	+	16.3560i	−1.02861	+	0.747326i	−0.968029	−	0.250837i	$-0.919294\pi$
$479$	−22.5122	+	16.3560i	−1.02861	+	0.747326i	−0.0605771	+	0.998164i	$0.519294\pi$
$480$	−43.1551	−	20.5084i	−1.96975	−	0.936076i
$481$	−49.5645	−	36.0107i	−2.25995	−	1.64195i
$482$			5.14887i			0.234525i
$483$	−0.993895	+	1.36798i	−0.0452238	+	0.0622452i
$484$	18.4558	−	56.8012i	0.838902	−	2.58187i
$485$	−1.90433	+	4.00723i	−0.0864714	+	0.181959i
$486$	0.842888	+	2.59414i	0.0382342	+	0.117673i
$487$	18.9269	+	6.14973i	0.857660	+	0.278671i	0.704651	−	0.709554i	$-0.251104\pi$
$487$	18.9269	+	6.14973i	0.857660	+	0.278671i	0.153009	+	0.988225i	$0.451104\pi$
$488$	84.1840	+	27.3531i	3.81083	+	1.23821i
$489$	−4.20831	−	12.9518i	−0.190306	−	0.585702i
$490$	4.43019	+	4.19209i	0.200136	+	0.189379i
$491$	−1.44225	+	4.43879i	−0.0650878	+	0.200320i	−0.978312	−	0.207139i	$-0.933585\pi$
$491$	−1.44225	+	4.43879i	−0.0650878	+	0.200320i	0.913224	+	0.407458i	$0.133585\pi$
$492$	9.42739	−	12.9757i	0.425020	−	0.584989i
$493$		−	40.2847i		−	1.81433i
$494$	−3.90793	−	2.83928i	−0.175826	−	0.127745i
$495$	0.156277	+	0.286850i	0.00702415	+	0.0128930i
$496$	49.7573	−	36.1508i	2.23417	−	1.62322i
$497$	−3.46861	−	4.77413i	−0.155588	−	0.214149i
$498$	−17.0696	+	5.54624i	−0.764906	+	0.248533i
$499$	33.8269			1.51430			0.757151	−	0.653240i	$-0.226591\pi$
$499$	33.8269			1.51430			0.757151	+	0.653240i	$0.226591\pi$
$500$	−51.7223	+	32.0009i	−2.31309	+	1.43112i
$501$	13.7753			0.615437
$502$	5.93678	−	1.92898i	0.264972	−	0.0860945i
$503$	9.27949	+	12.7721i	0.413752	+	0.569481i	0.964129	−	0.265436i	$-0.0855158\pi$
$503$	9.27949	+	12.7721i	0.413752	+	0.569481i	−0.550377	+	0.834917i	$0.685516\pi$
$504$	7.59117	−	5.51531i	0.338138	−	0.245671i
$505$	15.2229	+	27.9419i	0.677411	+	1.24340i
$506$	0.545100	+	0.396038i	0.0242326	+	0.0176060i
$507$			30.1774i			1.34023i
$508$	3.17964	−	4.37640i	0.141074	−	0.194171i
$509$	−9.53886	+	29.3576i	−0.422803	+	1.30125i	0.482280	+	0.876017i	$0.339809\pi$
$509$	−9.53886	+	29.3576i	−0.422803	+	1.30125i	−0.905083	+	0.425235i	$0.860191\pi$
$510$	19.0449	+	18.0214i	0.843324	+	0.798000i
$511$	2.20019	+	6.77150i	0.0973308	+	0.299553i
$512$	36.4065	+	11.8292i	1.60895	+	0.522781i
$513$	0.256318	+	0.0832829i	0.0113167	+	0.00367703i
$514$	12.8918	+	39.6769i	0.568634	+	1.75007i
$515$	−13.6348	+	28.6913i	−0.600823	+	1.26429i
$516$	−7.94773	+	24.4606i	−0.349879	+	1.07682i
$517$	−0.977617	+	1.34557i	−0.0429956	+	0.0591783i
$518$		−	25.4316i		−	1.11740i
$519$	4.98840	+	3.62429i	0.218967	+	0.159089i
$520$	124.522	+	59.1762i	5.46067	+	2.59505i
$521$	21.7570	−	15.8074i	0.953193	−	0.692535i	0.00163318	−	0.999999i	$-0.499480\pi$
$521$	21.7570	−	15.8074i	0.953193	−	0.692535i	0.951560	+	0.307463i	$0.0994801\pi$
$522$	15.0241	+	20.6789i	0.657588	+	0.905092i
$523$	8.89439	−	2.88996i	0.388925	−	0.126369i	−0.108026	−	0.994148i	$-0.534453\pi$
$523$	8.89439	−	2.88996i	0.388925	−	0.126369i	0.496951	+	0.867779i	$0.334453\pi$
$524$	44.6518			1.95062
$525$	−0.275932	−	4.99238i	−0.0120427	−	0.217885i
$526$	−60.6007			−2.64232
$527$	−17.0897	+	5.55277i	−0.744438	+	0.241882i
$528$	−1.26345	−	1.73898i	−0.0549844	−	0.0756796i
$529$	−16.2943	+	11.8385i	−0.708446	+	0.514716i
$530$	−0.0644704	+	0.495161i	−0.00280041	+	0.0215084i
$531$	−3.80399	−	2.76376i	−0.165079	−	0.119937i
$532$		−	1.46614i		−	0.0635652i
$533$	−11.3872	+	15.6732i	−0.493235	+	0.678880i
$534$	4.60849	−	14.1835i	0.199429	−	0.613779i
$535$	−6.27525	+	3.41879i	−0.271303	+	0.147807i
$536$	−20.8181	−	64.0715i	−0.899204	−	2.76747i
$537$	−11.2869	−	3.66733i	−0.487065	−	0.158257i
$538$	2.51387	+	0.816805i	0.108381	+	0.0352150i
$539$	0.0451431	+	0.138936i	0.00194445	+	0.00598440i
$540$	−12.0625	−	1.57054i	−0.519087	−	0.0675855i
$541$	9.25850	−	28.4947i	0.398054	−	1.22508i	−0.528503	−	0.848931i	$-0.677247\pi$
$541$	9.25850	−	28.4947i	0.398054	−	1.22508i	0.926558	−	0.376153i	$-0.122753\pi$
$542$	−34.1560	+	47.0116i	−1.46712	+	2.01932i
$543$			10.8842i			0.467088i
$544$	−74.3155	−	53.9934i	−3.18625	−	2.31495i
$545$	7.32980	−	1.36932i	0.313974	−	0.0586553i
$546$	−14.5002	+	10.5350i	−0.620551	+	0.450856i
$547$	−10.5531	−	14.5251i	−0.451219	−	0.621050i	0.521440	−	0.853288i	$-0.325395\pi$
$547$	−10.5531	−	14.5251i	−0.451219	−	0.621050i	−0.972659	+	0.232238i	$0.925395\pi$
$548$	−75.0831	+	24.3960i	−3.20739	+	1.04214i
$549$	9.43349			0.402611
$550$	−1.98932	+	0.109951i	−0.0848248	+	0.00468831i
$551$	2.52555			0.107592
$552$	−15.0897	+	4.90293i	−0.642259	+	0.208682i
$553$	−9.14269	−	12.5838i	−0.388787	−	0.535119i
$554$	47.4458	−	34.4714i	2.01578	−	1.46455i
$555$	−14.3294	+	15.1433i	−0.608250	+	0.642796i
$556$	85.3450	+	62.0067i	3.61943	+	2.62967i
$557$		−	21.0909i		−	0.893651i	−0.894621	−	0.446826i	$-0.852554\pi$
$557$		−	21.0909i		−	0.893651i	0.894621	−	0.446826i	$-0.147446\pi$
$558$	6.70156	−	9.22391i	0.283700	−	0.390479i
$559$	9.59996	−	29.5456i	0.406035	−	1.24965i
$560$	6.04197	+	32.3419i	0.255320	+	1.36669i
$561$	0.194066	+	0.597272i	0.00819345	+	0.0252169i
$562$	−86.5092	−	28.1085i	−3.64917	−	1.18569i
$563$	−15.9051	−	5.16788i	−0.670320	−	0.217800i	−0.0459673	−	0.998943i	$-0.514637\pi$
$563$	−15.9051	−	5.16788i	−0.670320	−	0.217800i	−0.624352	+	0.781143i	$0.714637\pi$
$564$	−19.1393	−	58.9047i	−0.805910	−	2.48034i
$565$	−2.45897	−	13.1625i	−0.103450	−	0.553752i
$566$	21.5162	−	66.2199i	0.904392	−	2.78343i
$567$	0.587785	−	0.809017i	0.0246847	−	0.0339755i
$568$		−	55.3717i		−	2.32335i
$569$	−7.72842	−	5.61503i	−0.323992	−	0.235394i	0.413885	−	0.910329i	$-0.364172\pi$
$569$	−7.72842	−	5.61503i	−0.323992	−	0.235394i	−0.737877	+	0.674935i	$0.764172\pi$
$570$	−1.12981	+	1.19398i	−0.0473224	+	0.0500101i
$571$	−28.5956	+	20.7759i	−1.19669	+	0.869444i	−0.993955	−	0.109790i	$-0.964982\pi$
$571$	−28.5956	+	20.7759i	−1.19669	+	0.869444i	−0.202732	+	0.979234i	$0.564982\pi$
$572$	3.06943	+	4.22471i	0.128339	+	0.176644i
$573$	−4.49692	+	1.46114i	−0.187862	+	0.0610399i
$574$	−8.04189			−0.335662
$575$	−2.16489	+	8.17271i	−0.0902820	+	0.340826i
$576$	28.8564			1.20235
$577$	8.39058	−	2.72627i	0.349305	−	0.113496i	−0.129109	−	0.991630i	$-0.541212\pi$
$577$	8.39058	−	2.72627i	0.349305	−	0.113496i	0.478414	+	0.878134i	$0.341212\pi$
$578$	2.37373	+	3.26715i	0.0987340	+	0.135896i
$579$	−2.37842	+	1.72802i	−0.0988438	+	0.0718142i
$580$	−112.052	+	20.9331i	−4.65272	+	0.869201i
$581$	5.32337	+	3.86765i	0.220850	+	0.160457i
$582$		−	5.41207i		−	0.224338i
$583$	−0.00702994	+	0.00967589i	−0.000291150	+	0.000400734i
$584$	−20.6449	+	63.5383i	−0.854290	+	2.62923i
$585$	14.5701	+	1.89704i	0.602400	+	0.0784329i
$586$	5.33471	+	16.4186i	0.220375	+	0.678244i
$587$	−23.5643	−	7.65651i	−0.972604	−	0.316018i	−0.220737	−	0.975333i	$-0.570846\pi$
$587$	−23.5643	−	7.65651i	−0.972604	−	0.316018i	−0.751867	+	0.659315i	$0.770846\pi$
$588$	−5.17379	−	1.68106i	−0.213363	−	0.0693259i
$589$	−0.348117	−	1.07139i	−0.0143439	−	0.0441460i
$590$	25.1835	−	13.7201i	1.03679	−	0.564847i
$591$	−5.73671	+	17.6558i	−0.235977	+	0.726261i
$592$	80.6368	−	110.987i	3.31415	−	4.56154i
$593$		−	37.6324i		−	1.54538i	−0.634785	−	0.772689i	$-0.718911\pi$
$593$		−	37.6324i		−	1.54538i	0.634785	−	0.772689i	$-0.281089\pi$
$594$	−0.322369	−	0.234215i	−0.0132270	−	0.00960996i
$595$	1.24110	−	9.53218i	0.0508800	−	0.390781i
$596$	14.0751	−	10.2262i	0.576539	−	0.418880i
$597$	−1.69577	−	2.33403i	−0.0694033	−	0.0955254i
$598$	28.8233	−	9.36527i	1.17867	−	0.382974i
$599$	−26.7311			−1.09220			−0.546102	−	0.837719i	$-0.683889\pi$
$599$	−26.7311			−1.09220			−0.546102	+	0.837719i	$0.683889\pi$
$600$	25.4399	−	39.4199i	1.03858	−	1.60931i
$601$	−26.3895			−1.07645			−0.538225	−	0.842802i	$-0.680905\pi$
$601$	−26.3895			−1.07645			−0.538225	+	0.842802i	$0.680905\pi$
$602$	12.2646	−	3.98500i	0.499867	−	0.162417i
$603$	−4.22013	−	5.80851i	−0.171857	−	0.236541i
$604$	−28.3242	+	20.5787i	−1.15250	+	0.837337i
$605$	22.1727	+	10.5370i	0.901447	+	0.428390i
$606$	−31.4019	−	22.8148i	−1.27561	−	0.926787i
$607$		−	33.4522i		−	1.35778i	−0.734239	−	0.678891i	$-0.762461\pi$
$607$		−	33.4522i		−	1.35778i	0.734239	−	0.678891i	$-0.237539\pi$
$608$	3.38498	−	4.65903i	0.137279	−	0.188948i
$609$	2.89578	−	8.91229i	0.117343	−	0.361144i
$610$	−24.6960	+	51.9671i	−0.999914	+	2.10409i
$611$	23.1181	+	71.1502i	0.935258	+	2.87843i
$612$	−22.2416	−	7.22673i	−0.899063	−	0.292123i
$613$	21.1629	+	6.87623i	0.854760	+	0.277728i	0.703438	−	0.710756i	$-0.251647\pi$
$613$	21.1629	+	6.87623i	0.854760	+	0.277728i	0.151322	+	0.988485i	$0.451647\pi$
$614$	−0.215597	−	0.663538i	−0.00870078	−	0.0267782i
$615$	4.78856	+	4.53121i	0.193094	+	0.182716i
$616$	−0.423587	+	1.30367i	−0.0170668	+	0.0525262i
$617$	19.6532	−	27.0504i	0.791210	−	1.08901i	−0.202747	−	0.979231i	$-0.564987\pi$
$617$	19.6532	−	27.0504i	0.791210	−	1.08901i	0.993956	−	0.109776i	$-0.0350132\pi$
$618$		−	38.7499i		−	1.55875i
$619$	20.5472	+	14.9284i	0.825863	+	0.600024i	0.918386	−	0.395686i	$-0.129493\pi$
$619$	20.5472	+	14.9284i	0.825863	+	0.600024i	−0.0925231	+	0.995711i	$0.529493\pi$
$620$	24.3254	+	44.6497i	0.976930	+	1.79317i
$621$	−1.36798	+	0.993895i	−0.0548951	+	0.0398837i
$622$	−11.3330	−	15.5986i	−0.454413	−	0.625446i
$623$	−5.19990	+	1.68955i	−0.208329	+	0.0676904i
$624$	−96.6847			−3.87048
$625$	−10.2986	−	22.7802i	−0.411945	−	0.911208i
$626$	−42.4441			−1.69641
$627$	−0.0374445	+	0.0121665i	−0.00149539	+	0.000485882i
$628$	−26.5464	−	36.5380i	−1.05932	−	1.45802i
$629$	−32.4265	+	23.5592i	−1.29293	+	0.939369i
$630$	2.91793	+	5.35592i	0.116253	+	0.213385i
$631$	−21.7753	−	15.8207i	−0.866860	−	0.629811i	0.0628823	−	0.998021i	$-0.479971\pi$
$631$	−21.7753	−	15.8207i	−0.866860	−	0.629811i	−0.929743	+	0.368210i	$0.879971\pi$
$632$		−	145.951i		−	5.80561i
$633$	−13.4333	+	18.4893i	−0.533924	+	0.734884i
$634$	18.3962	−	56.6176i	0.730606	−	2.24857i
$635$	1.61507	+	1.52827i	0.0640922	+	0.0606476i
$636$	−0.137629	−	0.423577i	−0.00545733	−	0.0167959i
$637$	6.24935	+	2.03054i	0.247608	+	0.0804527i
$638$	−3.55128	−	1.15388i	−0.140597	−	0.0456826i
$639$	−1.82356	−	5.61233i	−0.0721388	−	0.222020i
$640$	−34.5268	+	72.6536i	−1.36479	+	2.87189i
$641$	−5.69964	+	17.5417i	−0.225122	+	0.692855i	0.773157	+	0.634215i	$0.218676\pi$
$641$	−5.69964	+	17.5417i	−0.225122	+	0.692855i	−0.998279	+	0.0586401i	$0.981324\pi$
$642$	5.12378	−	7.05228i	0.202220	−	0.278331i
$643$			30.4666i			1.20148i	0.799443	+	0.600742i	$0.205128\pi$
$643$			30.4666i			1.20148i	−0.799443	+	0.600742i	$0.794872\pi$
$644$	7.44186	+	5.40683i	0.293251	+	0.213059i
$645$	−9.54832	−	4.53760i	−0.375965	−	0.178668i
$646$	−2.55668	+	1.85754i	−0.100591	+	0.0730838i
$647$	−4.52354	−	6.22612i	−0.177839	−	0.244774i	0.710787	−	0.703407i	$-0.248339\pi$
$647$	−4.52354	−	6.22612i	−0.177839	−	0.244774i	−0.888625	+	0.458634i	$0.848339\pi$
$648$	8.92396	−	2.89957i	0.350566	−	0.113906i
$649$	0.686895			0.0269630
$650$	−48.5937	+	75.2974i	−1.90600	+	2.95341i
$651$	−4.17994			−0.163825
$652$	−70.4585	+	22.8934i	−2.75937	+	0.896573i
$653$	19.6969	+	27.1105i	0.770800	+	1.06092i	0.996238	+	0.0866576i	$0.0276186\pi$
$653$	19.6969	+	27.1105i	0.770800	+	1.06092i	−0.225438	+	0.974257i	$0.572381\pi$
$654$	−7.35871	+	5.34642i	−0.287748	+	0.209061i
$655$	−2.36966	+	18.2000i	−0.0925901	+	0.711134i
$656$	−35.0960	−	25.4987i	−1.37027	−	0.995559i
$657$			7.11997i			0.277777i
$658$	−18.2536	+	25.1239i	−0.711598	+	0.979431i
$659$	−6.21846	+	19.1384i	−0.242237	+	0.745528i	0.753842	+	0.657056i	$0.228198\pi$
$659$	−6.21846	+	19.1384i	−0.242237	+	0.745528i	−0.996079	+	0.0884722i	$0.971802\pi$
$660$	1.56048	−	0.850155i	0.0607414	−	0.0330923i
$661$	−3.20864	−	9.87519i	−0.124802	−	0.384100i	0.869063	−	0.494701i	$-0.164723\pi$
$661$	−3.20864	−	9.87519i	−0.124802	−	0.384100i	−0.993865	+	0.110601i	$0.964723\pi$
$662$	24.6854	+	8.02076i	0.959424	+	0.311736i
$663$	26.8653	+	8.72907i	1.04336	+	0.339009i
$664$	19.0793	+	58.7200i	0.740420	+	2.27878i
$665$	0.597596	+	0.0778075i	0.0231738	+	0.00301725i
$666$	7.85878	−	24.1868i	0.304522	−	0.937221i
$667$	−9.31373	+	12.8192i	−0.360629	+	0.496363i
$668$		−	74.9384i		−	2.89945i
$669$	10.4243	+	7.57367i	0.403025	+	0.292815i
$670$	43.0458	−	8.04163i	1.66300	−	0.310675i
$671$	−1.11491	+	0.810027i	−0.0430405	+	0.0312708i
$672$	−12.5598	−	17.2871i	−0.484505	−	0.666864i
$673$	−2.85053	+	0.926195i	−0.109880	+	0.0357022i	−0.363441	−	0.931617i	$-0.618398\pi$
$673$	−2.85053	+	0.926195i	−0.109880	+	0.0357022i	0.253561	+	0.967319i	$0.418398\pi$
$674$	−14.4006			−0.554690
$675$	1.28030	−	4.83330i	0.0492789	−	0.186034i
$676$	164.166			6.31409
$677$	−10.6176	+	3.44985i	−0.408066	+	0.132589i	−0.505855	−	0.862619i	$-0.668823\pi$
$677$	−10.6176	+	3.44985i	−0.408066	+	0.132589i	0.0977891	+	0.995207i	$0.468823\pi$
$678$	9.60086	+	13.2144i	0.368719	+	0.507498i
$679$	−1.60522	+	1.16626i	−0.0616025	+	0.0447569i
$680$	61.9943	−	65.5154i	2.37737	−	2.51240i
$681$	7.32647	+	5.32299i	0.280751	+	0.203978i
$682$			1.66558i			0.0637784i
$683$	8.90233	−	12.2530i	0.340638	−	0.468848i	−0.603990	−	0.796992i	$-0.706423\pi$
$683$	8.90233	−	12.2530i	0.340638	−	0.468848i	0.944628	+	0.328144i	$0.106423\pi$
$684$	0.453062	−	1.39438i	0.0173233	−	0.0533155i
$685$	−5.95913	−	31.8985i	−0.227687	−	1.21878i
$686$	0.842888	+	2.59414i	0.0321816	+	0.0990449i
$687$	26.1510	+	8.49698i	0.997724	+	0.324180i
$688$	66.1598	+	21.4966i	2.52232	+	0.819551i
$689$	0.166240	+	0.511633i	0.00633323	+	0.0194917i
$690$	−1.89391	−	10.1378i	−0.0720998	−	0.385941i
$691$	−0.301995	+	0.929446i	−0.0114884	+	0.0353578i	−0.956636	−	0.291285i	$-0.905917\pi$
$691$	−0.301995	+	0.929446i	−0.0114884	+	0.0353578i	0.945148	+	0.326642i	$0.105917\pi$
$692$	19.7163	−	27.1371i	0.749500	−	1.03160i
$693$			0.146086i			0.00554935i
$694$	−62.0375	−	45.0729i	−2.35491	−	1.71094i
$695$	−29.8031	+	31.4958i	−1.13050	+	1.19470i
$696$	71.1364	−	51.6836i	2.69642	−	1.95906i
$697$	7.44984	+	10.2538i	0.282183	+	0.388391i
$698$	77.7339	−	25.2573i	2.94227	−	0.956003i
$699$	5.01358			0.189631
$700$	−27.1587	+	1.50108i	−1.02650	+	0.0567355i
$701$	−45.2686			−1.70977			−0.854886	−	0.518816i	$-0.826373\pi$
$701$	−45.2686			−1.70977			−0.854886	+	0.518816i	$0.826373\pi$
$702$	−17.0460	+	5.53858i	−0.643359	+	0.209040i
$703$	−1.47699	−	2.03290i	−0.0557057	−	0.0766723i
$704$	−3.41043	+	2.47782i	−0.128535	+	0.0933864i
$705$	25.0252	−	4.67510i	0.942503	−	0.176074i
$706$	−4.68721	−	3.40546i	−0.176406	−	0.128166i
$707$			14.2302i			0.535181i
$708$	−15.0350	+	20.6938i	−0.565048	+	0.777722i
$709$	15.8895	−	48.9028i	0.596741	−	1.83658i	0.0508821	−	0.998705i	$-0.483797\pi$
$709$	15.8895	−	48.9028i	0.596741	−	1.83658i	0.545859	−	0.837877i	$-0.316203\pi$
$710$	35.6910	+	4.64700i	1.33946	+	0.174399i
$711$	−4.80660	−	14.7932i	−0.180262	−	0.554788i
$712$	−48.7917	−	15.8534i	−1.82855	−	0.594131i
$713$	6.72200	+	2.18411i	0.251741	+	0.0817955i
$714$	3.62349	+	11.1520i	0.135606	+	0.417352i
$715$	−1.88488	+	1.02689i	−0.0704904	+	0.0384036i
$716$	−19.9504	+	61.4011i	−0.745582	+	2.29467i
$717$	4.93917	−	6.79818i	0.184457	−	0.253883i
$718$			15.8308i			0.590799i
$719$	24.3694	+	17.7054i	0.908824	+	0.660300i	0.940717	−	0.339192i	$-0.110154\pi$
$719$	24.3694	+	17.7054i	0.908824	+	0.660300i	−0.0318929	+	0.999491i	$0.510154\pi$
$720$	−4.24793	+	32.6260i	−0.158311	+	1.21590i
$721$	−11.4932	+	8.35028i	−0.428028	+	0.310981i
$722$	30.3457	+	41.7672i	1.12935	+	1.55441i
$723$	1.79527	−	0.583320i	0.0667669	−	0.0216939i
$724$	59.2107			2.20055
$725$	−2.58574	−	46.7833i	−0.0960319	−	1.73749i
$726$	−29.9459			−1.11140
$727$	−3.64664	+	1.18486i	−0.135246	+	0.0439442i	−0.375858	−	0.926677i	$-0.622652\pi$
$727$	−3.64664	+	1.18486i	−0.135246	+	0.0439442i	0.240612	+	0.970621i	$0.422652\pi$
$728$	36.2408	+	49.8812i	1.34317	+	1.84872i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−39.2224	−	18.6395i	−1.45169	−	0.689878i
$731$	−16.4427	−	11.9463i	−0.608156	−	0.441851i
$732$		−	51.3186i		−	1.89679i
$733$	−12.6270	+	17.3796i	−0.466389	+	0.641930i	−0.975818	−	0.218583i	$-0.929857\pi$
$733$	−12.6270	+	17.3796i	−0.466389	+	0.641930i	0.509429	+	0.860513i	$0.329857\pi$
$734$	1.72987	−	5.32399i	0.0638506	−	0.196512i
$735$	0.959771	−	2.01961i	0.0354017	−	0.0744946i
$736$	11.1653	+	34.3631i	0.411557	+	1.26664i
$737$	0.997521	+	0.324114i	0.0367442	+	0.0119389i
$738$	−7.64829	−	2.48508i	−0.281538	−	0.0914771i
$739$	−9.77120	−	30.0727i	−0.359439	−	1.10624i	−0.953390	−	0.301740i	$-0.902433\pi$
$739$	−9.77120	−	30.0727i	−0.359439	−	1.10624i	0.593951	−	0.804501i	$-0.297567\pi$
$740$	82.3800	+	77.9526i	3.02835	+	2.86559i
$741$	−0.547248	+	1.68425i	−0.0201036	+	0.0618726i
$742$	−0.131259	+	0.180663i	−0.00481869	+	0.00663235i
$743$		−	5.58803i		−	0.205005i	−0.994733	−	0.102502i	$-0.967315\pi$
$743$		−	5.58803i		−	0.205005i	0.994733	−	0.102502i	$-0.0326850\pi$
$744$	−31.7306	−	23.0536i	−1.16330	−	0.845188i
$745$	3.42121	+	6.27970i	0.125343	+	0.230070i
$746$	−31.2029	+	22.6703i	−1.14242	+	0.830017i
$747$	3.86765	+	5.32337i	0.141510	+	0.194772i
$748$	3.24919	−	1.05572i	0.118802	−	0.0386011i
$749$	−3.19584			−0.116773
$750$	23.2739	+	19.7061i	0.849843	+	0.719564i
$751$	17.1967			0.627517			0.313758	−	0.949503i	$-0.398412\pi$
$751$	17.1967			0.627517			0.313758	+	0.949503i	$0.398412\pi$
$752$	−159.323	+	51.7670i	−5.80990	+	1.88775i
$753$	−1.34517	−	1.85146i	−0.0490206	−	0.0674710i
$754$	−135.880	+	98.7228i	−4.94847	+	3.59527i
$755$	−6.88471	−	12.6370i	−0.250560	−	0.459908i
$756$	−4.40108	−	3.19758i	−0.160066	−	0.116295i
$757$		−	4.82219i		−	0.175265i	−0.996153	−	0.0876327i	$-0.972070\pi$
$757$		−	4.82219i		−	0.175265i	0.996153	−	0.0876327i	$-0.0279302\pi$
$758$	46.3493	−	63.7944i	1.68348	−	2.31712i
$759$	0.0763331	−	0.234929i	0.00277072	−	0.00852739i
$760$	4.10732	+	3.88658i	0.148988	+	0.140981i
$761$	−11.1023	−	34.1693i	−0.402458	−	1.23864i	−0.922999	−	0.384801i	$-0.874270\pi$
$761$	−11.1023	−	34.1693i	−0.402458	−	1.23864i	0.520542	−	0.853836i	$-0.325730\pi$
$762$	−2.57959	−	0.838161i	−0.0934489	−	0.0303634i
$763$	3.17149	+	1.03048i	0.114816	+	0.0373058i
$764$	7.94865	+	24.4634i	0.287572	+	0.885056i
$765$	4.12596	−	8.68212i	0.149174	−	0.313903i
$766$	−7.07863	+	21.7858i	−0.255761	+	0.787152i
$767$	18.1605	−	24.9958i	0.655739	−	0.902547i
$768$		−	40.4115i		−	1.45822i
$769$	7.58602	+	5.51157i	0.273559	+	0.198752i	0.716103	−	0.697995i	$-0.245924\pi$
$769$	7.58602	+	5.51157i	0.273559	+	0.198752i	−0.442544	+	0.896747i	$0.645924\pi$
$770$	−0.804757	−	0.382440i	−0.0290014	−	0.0137822i
$771$	12.3738	−	8.99007i	0.445630	−	0.323769i
$772$	9.40051	+	12.9387i	0.338332	+	0.465674i
$773$	6.24323	−	2.02855i	0.224553	−	0.0729618i	−0.194579	−	0.980887i	$-0.562334\pi$
$773$	6.24323	−	2.02855i	0.224553	−	0.0729618i	0.419133	+	0.907925i	$0.362334\pi$
$774$	12.8957			0.463528
$775$	−19.4901	+	7.54544i	−0.700104	+	0.271040i
$776$	−18.6177			−0.668338
$777$	−8.86730	+	2.88116i	−0.318113	+	0.103361i
$778$	−7.67271	−	10.5606i	−0.275080	−	0.378615i
$779$	−0.642838	+	0.467049i	−0.0230321	+	0.0167338i
$780$	10.3200	−	79.2620i	0.369514	−	2.83803i
$781$	0.697434	+	0.506716i	0.0249562	+	0.0181317i
$782$		−	19.8275i		−	0.709029i
$783$	5.50810	−	7.58124i	0.196843	−	0.270932i
$784$	−4.54686	+	13.9938i	−0.162388	+	0.499779i
$785$	16.3016	−	8.88121i	0.581830	−	0.316984i
$786$	−6.91842	−	21.2927i	−0.246772	−	0.759486i
$787$	20.8956	+	6.78938i	0.744846	+	0.242015i	0.656762	−	0.754098i	$-0.271926\pi$
$787$	20.8956	+	6.78938i	0.744846	+	0.242015i	0.0880840	+	0.996113i	$0.471926\pi$
$788$	96.0481	+	31.2079i	3.42157	+	1.11174i
$789$	6.86551	+	21.1299i	0.244419	+	0.752243i
$790$	94.0758	+	12.2487i	3.34707	+	0.435791i
$791$	1.85049	−	5.69522i	0.0657958	−	0.202499i
$792$	−0.805709	+	1.10896i	−0.0286296	+	0.0394053i
$793$			61.9870i			2.20122i
$794$	14.0329	+	10.1955i	0.498008	+	0.361824i
$795$	0.179953	−	0.0336181i	0.00638229	−	0.00119231i
$796$	−12.6972	+	9.22506i	−0.450040	+	0.326973i
$797$	−4.54536	−	6.25616i	−0.161005	−	0.221604i	0.720891	−	0.693049i	$-0.243733\pi$
$797$	−4.54536	−	6.25616i	−0.161005	−	0.221604i	−0.881896	+	0.471444i	$0.843733\pi$
$798$	−0.699145	+	0.227166i	−0.0247495	+	0.00804159i
$799$	48.9440			1.73151
$800$	−89.7694	−	57.9333i	−3.17383	−	2.04825i
$801$	−5.46750			−0.193184
$802$	−84.8124	+	27.5572i	−2.99483	+	0.973080i
$803$	−0.611372	−	0.841482i	−0.0215749	−	0.0296952i
$804$	−31.5985	+	22.9577i	−1.11439	+	0.809655i
$805$	−2.59875	+	2.74635i	−0.0915940	+	0.0967963i
$806$	60.6099	+	44.0356i	2.13489	+	1.55109i
$807$		−	0.969055i		−	0.0341124i
$808$	−78.4838	+	108.024i	−2.76105	+	3.80026i
$809$	10.9295	−	33.6376i	0.384262	−	1.18264i	−0.552753	−	0.833345i	$-0.686423\pi$
$809$	10.9295	−	33.6376i	0.384262	−	1.18264i	0.937015	−	0.349290i	$-0.113577\pi$
$810$	1.12005	+	5.99547i	0.0393545	+	0.210659i
$811$	−1.62280	−	4.99446i	−0.0569841	−	0.175379i	0.918513	−	0.395390i	$-0.129391\pi$
$811$	−1.62280	−	4.99446i	−0.0569841	−	0.175379i	−0.975497	+	0.220011i	$0.929391\pi$
$812$	−48.4832	−	15.7531i	−1.70143	−	0.552827i
$813$	20.2613	+	6.58328i	0.710593	+	0.230886i
$814$	1.14806	+	3.53336i	0.0402394	+	0.123844i
$815$	−5.59209	−	29.9337i	−0.195882	−	1.04853i
$816$	−19.5465	+	60.1580i	−0.684265	+	2.10595i
$817$	0.748946	−	1.03084i	0.0262023	−	0.0360644i
$818$			10.3915i			0.363329i
$819$	5.31601	+	3.86231i	0.185756	+	0.134960i
$820$	24.6499	−	26.0500i	0.860813	−	0.909705i
$821$	40.4853	−	29.4143i	1.41295	−	1.02657i	0.420063	−	0.907495i	$-0.362008\pi$
$821$	40.4853	−	29.4143i	1.41295	−	1.02657i	0.992886	−	0.119072i	$-0.0379919\pi$
$822$	23.2670	+	32.0243i	0.811530	+	1.11697i
$823$	−48.3848	+	15.7212i	−1.68659	+	0.548005i	−0.986171	−	0.165730i	$-0.947002\pi$
$823$	−48.3848	+	15.7212i	−1.68659	+	0.548005i	−0.700416	+	0.713735i	$0.747002\pi$
$824$	−133.301			−4.64376
$825$	0.263708	+	0.681165i	0.00918114	+	0.0237151i
$826$	12.8253			0.446251
$827$	49.8105	−	16.1844i	1.73208	−	0.562787i	0.738332	−	0.674438i	$-0.235614\pi$
$827$	49.8105	−	16.1844i	1.73208	−	0.562787i	0.993747	+	0.111651i	$0.0356139\pi$
$828$	5.40683	+	7.44186i	0.187900	+	0.258623i
$829$	20.4546	−	14.8611i	0.710416	−	0.516148i	−0.172892	−	0.984941i	$-0.555311\pi$
$829$	20.4546	−	14.8611i	0.710416	−	0.516148i	0.883308	+	0.468793i	$0.155311\pi$
$830$	−39.4505	+	7.36997i	−1.36935	+	0.255815i
$831$	−17.3944	−	12.6378i	−0.603405	−	0.438400i
$832$			189.614i			6.57369i
$833$	2.52683	−	3.47788i	0.0875495	−	0.120502i
$834$	16.3451	−	50.3051i	0.565985	−	1.74192i
$835$	30.5448	+	3.97695i	1.05705	+	0.137628i
$836$	0.0661860	+	0.203700i	0.00228909	+	0.00704510i
$837$	−3.97536	−	1.29167i	−0.137408	−	0.0446467i
$838$	−25.4156	−	8.25803i	−0.877968	−	0.285269i
$839$	−5.17890	−	15.9390i	−0.178796	−	0.550276i	0.820991	−	0.570941i	$-0.193422\pi$
$839$	−5.17890	−	15.9390i	−0.178796	−	0.550276i	−0.999786	+	0.0206652i	$0.993422\pi$
$840$	18.4246	−	10.0378i	0.635708	−	0.346337i
$841$	18.1746	−	55.9358i	0.626712	−	1.92882i
$842$	36.4895	−	50.2235i	1.25751	−	1.73081i
$843$			33.3479i			1.14856i
$844$	100.583	+	73.0775i	3.46219	+	2.51543i
$845$	−8.71224	+	66.9139i	−0.299710	+	2.30191i
$846$	−25.1239	+	18.2536i	−0.863777	+	0.627571i
$847$	6.45309	+	8.88192i	0.221731	+	0.305186i
$848$	−1.14567	+	0.372251i	−0.0393425	+	0.0127832i
$849$	−25.5267			−0.876074
$850$	37.0266	+	45.4581i	1.27000	+	1.55920i
$851$	15.7655			0.540434
$852$	−30.5313	+	9.92022i	−1.04599	+	0.339861i
$853$	2.33430	+	3.21289i	0.0799250	+	0.110007i	0.847108	−	0.531422i	$-0.178342\pi$
$853$	2.33430	+	3.21289i	0.0799250	+	0.110007i	−0.767183	+	0.641429i	$0.778342\pi$
$854$	−20.8170	+	15.1244i	−0.712342	+	0.517547i
$855$	0.544304	+	0.258667i	0.0186148	+	0.00884622i
$856$	−24.2601	−	17.6260i	−0.829194	−	0.602445i
$857$		−	33.7339i		−	1.15233i	−0.817334	−	0.576164i	$-0.804549\pi$
$857$		−	33.7339i		−	1.15233i	0.817334	−	0.576164i	$-0.195451\pi$
$858$	1.53902	−	2.11827i	0.0525411	−	0.0723167i
$859$	−1.60931	+	4.95293i	−0.0549088	+	0.168992i	−0.974750	−	0.223299i	$-0.928317\pi$
$859$	−1.60931	+	4.95293i	−0.0549088	+	0.168992i	0.919841	+	0.392291i	$0.128317\pi$
$860$	−24.6847	+	51.9432i	−0.841742	+	1.77125i
$861$	0.911073	+	2.80399i	0.0310493	+	0.0955598i
$862$	−30.3690	−	9.86748i	−1.03437	−	0.336088i
$863$	−2.21872	−	0.720907i	−0.0755262	−	0.0245400i	0.271010	−	0.962576i	$-0.412642\pi$
$863$	−2.21872	−	0.720907i	−0.0755262	−	0.0245400i	−0.346536	+	0.938037i	$0.612642\pi$
$864$	−6.60308	−	20.3222i	−0.224641	−	0.691375i
$865$	10.0147	+	9.47648i	0.340510	+	0.322210i
$866$	23.1239	−	71.1681i	0.785782	−	2.41839i
$867$	0.870248	−	1.19779i	0.0295552	−	0.0406792i
$868$			22.7390i			0.771813i
$869$	1.83832	+	1.33562i	0.0623608	+	0.0453078i
$870$	27.3438	+	50.1900i	0.927040	+	1.70160i
$871$	38.1674	−	27.7303i	1.29325	−	0.939604i
$872$	18.3919	+	25.3143i	0.622828	+	0.857249i
$873$	−1.88704	+	0.613138i	−0.0638668	+	0.0207516i
$874$	1.24303			0.0420462
$875$	0.829467	−	11.1495i	0.0280411	−	0.376923i
$876$	38.7329			1.30866
$877$	12.8897	−	4.18811i	0.435254	−	0.141423i	−0.0831909	−	0.996534i	$-0.526511\pi$
$877$	12.8897	−	4.18811i	0.435254	−	0.141423i	0.518445	+	0.855111i	$0.326511\pi$
$878$	22.8653	+	31.4714i	0.771668	+	1.06211i
$879$	5.12034	−	3.72014i	0.172705	−	0.125477i
$880$	−2.29946	−	4.22070i	−0.0775147	−	0.142280i
$881$	15.5579	+	11.3035i	0.524159	+	0.380824i	0.818168	−	0.574979i	$-0.194990\pi$
$881$	15.5579	+	11.3035i	0.524159	+	0.380824i	−0.294009	+	0.955803i	$0.594990\pi$
$882$			2.72764i			0.0918445i
$883$	9.45756	−	13.0172i	0.318272	−	0.438064i	−0.619667	−	0.784865i	$-0.712732\pi$
$883$	9.45756	−	13.0172i	0.318272	−	0.438064i	0.937939	+	0.346801i	$0.112732\pi$
$884$	47.4865	−	146.148i	1.59714	−	4.91550i
$885$	−7.63688	−	7.22644i	−0.256711	−	0.242914i
$886$	11.3227	+	34.8477i	0.380393	+	1.17073i
$887$	12.4173	+	4.03463i	0.416933	+	0.135470i	0.509968	−	0.860193i	$-0.329657\pi$
$887$	12.4173	+	4.03463i	0.416933	+	0.135470i	−0.0930357	+	0.995663i	$0.529657\pi$
$888$	−83.2037	−	27.0345i	−2.79213	−	0.907219i
$889$	0.307284	+	0.945723i	0.0103060	+	0.0317185i
$890$	14.3134	−	30.1193i	0.479787	−	1.00960i
$891$	−0.0451431	+	0.138936i	−0.00151235	+	0.00465453i
$892$	41.2011	−	56.7084i	1.37951	−	1.89874i
$893$			3.06842i			0.102681i
$894$	−7.05728	−	5.12742i	−0.236031	−	0.171486i
$895$	−23.9682	−	11.3903i	−0.801170	−	0.380736i
$896$	−29.1036	+	21.1450i	−0.972283	+	0.706405i
$897$	−6.53084	−	8.98893i	−0.218058	−	0.300132i
$898$	−0.568547	+	0.184732i	−0.0189727	+	0.00616460i
$899$	−39.1699			−1.30639
$900$	−26.2934	−	6.96490i	−0.876445	−	0.232163i
$901$	0.351951			0.0117252
$902$	1.11731	−	0.363036i	0.0372023	−	0.0120878i
$903$	−2.77893	−	3.82487i	−0.0924769	−	0.127284i
$904$	45.4582	−	33.0273i	1.51192	−	1.09847i
$905$	−3.14229	+	24.1342i	−0.104453	+	0.802248i
$906$	14.2018	+	10.3182i	0.471823	+	0.342799i
$907$			43.0028i			1.42789i	0.700204	+	0.713943i	$0.253092\pi$
$907$			43.0028i			1.42789i	−0.700204	+	0.713943i	$0.746908\pi$
$908$	28.9573	−	39.8563i	0.960982	−	1.32268i
$909$	−4.39736	+	13.5337i	−0.145851	+	0.448884i
$910$	−35.1935	+	19.1736i	−1.16665	+	0.635598i
$911$	−12.0063	−	36.9516i	−0.397786	−	1.22426i	−0.926770	−	0.375628i	$-0.877427\pi$
$911$	−12.0063	−	36.9516i	−0.397786	−	1.22426i	0.528984	−	0.848632i	$-0.322573\pi$
$912$	−3.77146	−	1.22542i	−0.124885	−	0.0405777i
$913$	−0.914205	−	0.297043i	−0.0302558	−	0.00983070i
$914$	−17.8509	−	54.9395i	−0.590456	−	1.81724i
$915$	20.9174	+	2.72346i	0.691507	+	0.0900347i
$916$	46.2239	−	142.263i	1.52728	−	4.70049i
$917$	−4.82454	+	6.64041i	−0.159320	+	0.219286i
$918$			11.7259i			0.387011i
$919$	−8.20891	−	5.96412i	−0.270787	−	0.196738i	0.444102	−	0.895976i	$-0.353523\pi$
$919$	−8.20891	−	5.96412i	−0.270787	−	0.196738i	−0.714889	+	0.699238i	$0.753523\pi$
$920$	−34.8746	+	6.51512i	−1.14978	+	0.214797i
$921$	−0.206933	+	0.150346i	−0.00681867	+	0.00495406i
$922$	41.1596	+	56.6514i	1.35552	+	1.86571i
$923$	36.8784	−	11.9825i	1.21387	−	0.394409i
$924$	0.794714			0.0261442
$925$	−36.1452	+	29.4411i	−1.18845	+	0.968016i
$926$	−13.1390			−0.431775
$927$	−13.5110	+	4.39000i	−0.443761	+	0.144187i
$928$	−117.697	−	161.996i	−3.86360	−	5.31779i
$929$	−23.1146	+	16.7938i	−0.758367	+	0.550986i	−0.898409	−	0.439160i	$-0.855276\pi$
$929$	−23.1146	+	16.7938i	−0.758367	+	0.550986i	0.140042	+	0.990146i	$0.455276\pi$
$930$	17.5227	−	18.5179i	0.574591	−	0.607226i
$931$	0.218037	+	0.158413i	0.00714589	+	0.00519179i
$932$		−	27.2741i		−	0.893391i
$933$	−4.15488	+	5.71870i	−0.136025	+	0.187222i
$934$	17.8575	−	54.9597i	0.584315	−	1.79834i
$935$	0.257879	+	1.38039i	0.00843353	+	0.0451436i
$936$	19.0529	+	58.6389i	0.622764	+	1.91667i
$937$	5.83679	+	1.89649i	0.190680	+	0.0619556i	0.402800	−	0.915288i	$-0.368037\pi$
$937$	5.83679	+	1.89649i	0.190680	+	0.0619556i	−0.212120	+	0.977244i	$0.568037\pi$
$938$	18.6252	+	6.05170i	0.608135	+	0.197595i
$939$	4.80853	+	14.7991i	0.156920	+	0.482951i
$940$	−25.4327	−	136.138i	−0.829524	−	4.44033i
$941$	−6.44699	+	19.8418i	−0.210166	+	0.646824i	0.789296	+	0.614013i	$0.210446\pi$
$941$	−6.44699	+	19.8418i	−0.210166	+	0.646824i	−0.999462	+	0.0328110i	$0.989554\pi$
$942$	−13.3104	+	18.3202i	−0.433676	+	0.596904i
$943$		−	4.98532i		−	0.162344i
$944$	55.9717	+	40.6658i	1.82172	+	1.32356i
$945$	1.53689	−	1.62418i	0.0499951	−	0.0528346i
$946$	−1.52410	+	1.10732i	−0.0495527	+	0.0360021i
$947$	30.5414	+	42.0366i	0.992461	+	1.36600i	0.929839	+	0.367968i	$0.119946\pi$
$947$	30.5414	+	42.0366i	0.992461	+	1.36600i	0.0626221	+	0.998037i	$0.480054\pi$
$948$	−80.4755	+	26.1481i	−2.61372	+	0.849250i
$949$	−46.7850			−1.51871
$950$	−2.84988	+	2.32129i	−0.0924623	+	0.0753126i
$951$	−21.8252			−0.707730
$952$	38.3632	−	12.4650i	1.24336	−	0.403992i
$953$	−8.92714	−	12.2872i	−0.289178	−	0.398020i	0.639569	−	0.768734i	$-0.279113\pi$
$953$	−8.92714	−	12.2872i	−0.289178	−	0.398020i	−0.928747	+	0.370714i	$0.879113\pi$
$954$	−0.180663	+	0.131259i	−0.00584919	+	0.00424968i
$955$	−10.3931	+	1.94159i	−0.336312	+	0.0628285i
$956$	−36.9824	−	26.8693i	−1.19610	−	0.869015i
$957$			1.36896i			0.0442523i
$958$	44.6134	−	61.4051i	1.44139	−	1.98391i
$959$	4.48452	−	13.8019i	0.144813	−	0.445688i
$960$	63.9849	+	8.33088i	2.06510	+	0.268878i
$961$	−4.18042	−	12.8660i	−0.134852	−	0.415032i
$962$	158.931	+	51.6397i	5.12413	+	1.66493i
$963$	−3.03942	−	0.987568i	−0.0979440	−	0.0318239i
$964$	−3.17328	−	9.76636i	−0.102205	−	0.314553i
$965$	−5.77268	+	3.14498i	−0.185829	+	0.101241i
$966$	1.42525	−	4.38648i	0.0458568	−	0.141133i
$967$	−18.0283	+	24.8138i	−0.579750	+	0.797958i	−0.993668	−	0.112357i	$-0.964160\pi$
$967$	−18.0283	+	24.8138i	−0.579750	+	0.797958i	0.413918	+	0.910314i	$0.364160\pi$
$968$			103.015i			3.31103i
$969$	0.937321	+	0.681004i	0.0301111	+	0.0218770i
$970$	1.56247	−	12.0005i	0.0501679	−	0.385312i
$971$	−14.2880	+	10.3809i	−0.458525	+	0.333138i	−0.792952	−	0.609284i	$-0.791457\pi$
$971$	−14.2880	+	10.3809i	−0.458525	+	0.333138i	0.334428	+	0.942421i	$0.391457\pi$
$972$	−3.19758	−	4.40108i	−0.102562	−	0.141165i
$973$	−18.4427	+	5.99240i	−0.591246	+	0.192107i
$974$	−54.2827			−1.73933
$975$	31.7594	+	8.41281i	1.01711	+	0.269426i
$976$	−138.804			−4.44301
$977$	41.8409	−	13.5949i	1.33861	−	0.434941i	0.449764	−	0.893147i	$-0.351508\pi$
$977$	41.8409	−	13.5949i	1.33861	−	0.434941i	0.888846	+	0.458207i	$0.151508\pi$
$978$	21.8339	+	30.0518i	0.698171	+	0.960950i
$979$	0.646182	−	0.469479i	0.0206521	−	0.0150046i
$980$	−10.9868	−	5.22119i	−0.350960	−	0.166785i
$981$	2.69783	+	1.96009i	0.0861350	+	0.0625807i
$982$		−	12.7305i		−	0.406247i
$983$	−18.5943	+	25.5929i	−0.593066	+	0.816286i	−0.995052	−	0.0993604i	$-0.968320\pi$
$983$	−18.5943	+	25.5929i	−0.593066	+	0.816286i	0.401985	+	0.915646i	$0.368320\pi$
$984$	−8.54878	+	26.3104i	−0.272525	+	0.838746i
$985$	−17.8175	+	37.4929i	−0.567714	+	1.19462i
$986$	33.9555	+	104.504i	1.08136	+	3.32810i
$987$	10.8280	+	3.51823i	0.344659	+	0.111986i
$988$	9.16241	+	2.97705i	0.291495	+	0.0947125i
$989$	2.47038	+	7.60304i	0.0785534	+	0.241762i
$990$	−0.647189	−	0.612406i	−0.0205690	−	0.0194635i
$991$	−4.03869	+	12.4298i	−0.128293	+	0.394846i	−0.994487	−	0.104863i	$-0.966560\pi$
$991$	−4.03869	+	12.4298i	−0.128293	+	0.394846i	0.866194	+	0.499709i	$0.166560\pi$
$992$	−52.4992	+	72.2590i	−1.66685	+	2.29422i
$993$		−	9.51580i		−	0.301975i
$994$	13.0221	+	9.46114i	0.413037	+	0.300089i
$995$	−3.08628	−	5.66493i	−0.0978418	−	0.179590i
$996$	28.9593	−	21.0402i	0.917611	−	0.666684i
$997$	−10.8300	−	14.9063i	−0.342991	−	0.472086i	0.602321	−	0.798254i	$-0.294243\pi$
$997$	−10.8300	−	14.9063i	−0.342991	−	0.472086i	−0.945312	+	0.326168i	$0.894243\pi$
$998$	−87.7519	+	28.5123i	−2.77774	+	0.902542i
$999$	−9.32364			−0.294987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.169.1	✓	72
25.4	even	10	inner	525.2.z.b.379.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.169.1	✓	72	1.1	even	1	trivial
525.2.z.b.379.1	yes	72	25.4	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59414 + 0.842888i) q^{2} +(0.587785 + 0.809017i) q^{3} +(4.40108 - 3.19758i) q^{4} +(1.06976 + 1.96357i) q^{5} +(-2.20671 - 1.60327i) q^{6} +1.00000i q^{7} +(-5.51531 + 7.59117i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-2.59414 + 0.842888i) q^{2} +(0.587785 + 0.809017i) q^{3} +(4.40108 - 3.19758i) q^{4} +(1.06976 + 1.96357i) q^{5} +(-2.20671 - 1.60327i) q^{6} +1.00000i q^{7} +(-5.51531 + 7.59117i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-4.43019 - 4.19209i) q^{10} +(-0.0451431 - 0.138936i) q^{11} +(5.17379 + 1.68106i) q^{12} +(-6.24935 - 2.03054i) q^{13} +(-0.842888 - 2.59414i) q^{14} +(-0.959771 + 2.01961i) q^{15} +(4.54686 - 13.9938i) q^{16} +(-2.52683 + 3.47788i) q^{17} -2.72764i q^{18} +(-0.218037 - 0.158413i) q^{19} +(10.9868 + 5.22119i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(0.234215 + 0.322369i) q^{22} +(1.60816 - 0.522522i) q^{23} -9.38320 q^{24} +(-2.71121 + 4.20111i) q^{25} +17.9232 q^{26} +(-0.951057 + 0.309017i) q^{27} +(3.19758 + 4.40108i) q^{28} +(-7.58124 + 5.50810i) q^{29} +(0.787473 - 6.04815i) q^{30} +(3.38164 + 2.45691i) q^{31} +21.3680i q^{32} +(0.0858672 - 0.118186i) q^{33} +(3.62349 - 11.1520i) q^{34} +(-1.96357 + 1.06976i) q^{35} +(1.68106 + 5.17379i) q^{36} +(8.86730 + 2.88116i) q^{37} +(0.699145 + 0.227166i) q^{38} +(-2.03054 - 6.24935i) q^{39} +(-20.8059 - 2.70894i) q^{40} +(0.911073 - 2.80399i) q^{41} +(1.60327 - 2.20671i) q^{42} +4.72780i q^{43} +(-0.642937 - 0.467121i) q^{44} +(-2.19804 + 0.410629i) q^{45} +(-3.73136 + 2.71099i) q^{46} +(-6.69207 - 9.21084i) q^{47} +(13.9938 - 4.54686i) q^{48} -1.00000 q^{49} +(3.49221 - 13.1835i) q^{50} -4.29890 q^{51} +(-33.9967 + 11.0462i) q^{52} +(-0.0481219 - 0.0662342i) q^{53} +(2.20671 - 1.60327i) q^{54} +(0.224518 - 0.237270i) q^{55} +(-7.59117 - 5.51531i) q^{56} -0.269509i q^{57} +(15.0241 - 20.6789i) q^{58} +(-1.45299 + 4.47186i) q^{59} +(2.23384 + 11.9574i) q^{60} +(-2.91511 - 8.97178i) q^{61} +(-10.8434 - 3.52322i) q^{62} +(-0.951057 - 0.309017i) q^{63} +(-8.91713 - 27.4441i) q^{64} +(-2.69822 - 14.4432i) q^{65} +(-0.123134 + 0.378968i) q^{66} +(-4.22013 + 5.80851i) q^{67} +23.3862i q^{68} +(1.36798 + 0.993895i) q^{69} +(4.19209 - 4.43019i) q^{70} +(-4.77413 + 3.46861i) q^{71} +(-5.51531 - 7.59117i) q^{72} +(6.77150 - 2.20019i) q^{73} -25.4316 q^{74} +(-4.99238 + 0.275932i) q^{75} -1.46614 q^{76} +(0.138936 - 0.0451431i) q^{77} +(10.5350 + 14.5002i) q^{78} +(-12.5838 + 9.14269i) q^{79} +(32.3419 - 6.04197i) q^{80} +(-0.809017 - 0.587785i) q^{81} +8.04189i q^{82} +(3.86765 - 5.32337i) q^{83} +(-1.68106 + 5.17379i) q^{84} +(-9.53218 - 1.24110i) q^{85} +(-3.98500 - 12.2646i) q^{86} +(-8.91229 - 2.89578i) q^{87} +(1.30367 + 0.423587i) q^{88} +(1.68955 + 5.19990i) q^{89} +(5.35592 - 2.91793i) q^{90} +(2.03054 - 6.24935i) q^{91} +(5.40683 - 7.44186i) q^{92} +4.17994i q^{93} +(25.1239 + 18.2536i) q^{94} +(0.0778075 - 0.597596i) q^{95} +(-17.2871 + 12.5598i) q^{96} +(1.16626 + 1.60522i) q^{97} +(2.59414 - 0.842888i) q^{98} +0.146086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

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