LMFDB - Embedded newform 525.2.bg.a.16.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.12
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.a.361.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.246594 - 0.109791i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.28951 + 1.43214i) q^{4} +(-1.94989 + 1.09450i) q^{5} +(-0.0834131 + 0.256719i) q^{6} +(-2.11046 + 1.59561i) q^{7} +(-0.327575 + 1.00817i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.246594 - 0.109791i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.28951 + 1.43214i) q^{4} +(-1.94989 + 1.09450i) q^{5} +(-0.0834131 + 0.256719i) q^{6} +(-2.11046 + 1.59561i) q^{7} +(-0.327575 + 1.00817i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.360664 + 0.483977i) q^{10} +(0.155707 - 1.48145i) q^{11} +(-0.201441 - 1.91658i) q^{12} +(4.75723 - 3.45633i) q^{13} +(-0.345242 + 0.625176i) q^{14} +(0.491355 - 2.18141i) q^{15} +(-0.372972 - 3.54859i) q^{16} +(-1.86232 + 0.395847i) q^{17} +(-0.134965 - 0.233767i) q^{18} +(-2.23343 - 2.48048i) q^{19} +(0.946908 - 4.20389i) q^{20} +(0.226400 - 2.63605i) q^{21} +(-0.124253 - 0.382412i) q^{22} +(-1.38005 + 0.614439i) q^{23} +(-0.530027 - 0.918034i) q^{24} +(2.60412 - 4.26832i) q^{25} +(0.793630 - 1.37461i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.436303 - 5.08002i) q^{28} +(-0.319893 - 0.984530i) q^{29} +(-0.118334 - 0.591870i) q^{30} +(-4.54770 + 0.966644i) q^{31} +(-1.54163 - 2.67018i) q^{32} +(0.996746 + 1.10700i) q^{33} +(-0.415775 + 0.302078i) q^{34} +(2.36875 - 5.42117i) q^{35} +(1.55909 + 1.13274i) q^{36} +(0.829815 + 7.89516i) q^{37} +(-0.823083 - 0.366460i) q^{38} +(-0.614654 + 5.84804i) q^{39} +(-0.464713 - 2.32435i) q^{40} +(-9.88531 + 7.18210i) q^{41} +(-0.233585 - 0.674889i) q^{42} +4.05343 q^{43} +(1.92087 + 2.13334i) q^{44} +(1.29233 + 1.82480i) q^{45} +(-0.272853 + 0.303034i) q^{46} +(-6.33216 - 1.34594i) q^{47} +(2.88668 + 2.09730i) q^{48} +(1.90805 - 6.73494i) q^{49} +(0.173539 - 1.33845i) q^{50} +(0.951960 - 1.64884i) q^{51} +(-1.18452 + 11.2700i) q^{52} +(6.07462 - 6.74655i) q^{53} +(0.264032 + 0.0561217i) q^{54} +(1.31784 + 3.05909i) q^{55} +(-0.917318 - 2.65038i) q^{56} +3.33781 q^{57} +(-0.186976 - 0.207658i) q^{58} +(-11.6443 - 5.18437i) q^{59} +(2.49049 + 3.51664i) q^{60} +(2.09243 - 0.931610i) q^{61} +(-1.01531 + 0.737664i) q^{62} +(1.80747 + 1.93211i) q^{63} +(5.10005 + 3.70540i) q^{64} +(-5.49309 + 11.9463i) q^{65} +(0.367330 + 0.163546i) q^{66} +(-8.75498 + 1.86093i) q^{67} +(1.83456 - 3.17755i) q^{68} +(0.466818 - 1.43672i) q^{69} +(-0.0110745 - 1.59689i) q^{70} +(-2.89716 - 8.91654i) q^{71} +(1.03689 + 0.220398i) q^{72} +(0.591782 - 5.63043i) q^{73} +(1.07144 + 1.85579i) q^{74} +(1.42948 + 4.79130i) q^{75} +6.43242 q^{76} +(2.03521 + 3.37499i) q^{77} +(0.490490 + 1.50957i) q^{78} +(2.75252 + 0.585065i) q^{79} +(4.61119 + 6.51113i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-1.64913 + 2.85638i) q^{82} +(-2.56136 + 7.88306i) q^{83} +(3.48325 + 3.72344i) q^{84} +(3.19805 - 2.81017i) q^{85} +(0.999551 - 0.445029i) q^{86} +(0.945698 + 0.421052i) q^{87} +(1.44255 + 0.642266i) q^{88} +(-11.8858 + 5.29190i) q^{89} +(0.519026 + 0.308099i) q^{90} +(-4.52496 + 14.8851i) q^{91} +(0.899623 - 2.76876i) q^{92} +(2.32465 - 4.02641i) q^{93} +(-1.70924 + 0.363311i) q^{94} +(7.06983 + 2.39215i) q^{95} +(3.01588 + 0.641045i) q^{96} +(-1.63352 - 5.02747i) q^{97} +(-0.268921 - 1.87028i) q^{98} -1.48961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.246594	−	0.109791i	0.174368	−	0.0776337i	−0.317696	−	0.948193i	$-0.602909\pi$
$2$	0.246594	−	0.109791i	0.174368	−	0.0776337i	0.492064	+	0.870559i	$0.336243\pi$
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	−1.28951	+	1.43214i	−0.644753	+	0.716071i
$5$	−1.94989	+	1.09450i	−0.872016	+	0.489477i
$5$	−1.94989	+	1.09450i	−0.872016	+	0.489477i
$6$	−0.0834131	+	0.256719i	−0.0340533	+	0.104805i
$7$	−2.11046	+	1.59561i	−0.797677	+	0.603085i
$7$	−2.11046	+	1.59561i	−0.797677	+	0.603085i
$8$	−0.327575	+	1.00817i	−0.115815	+	0.356442i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−0.360664	+	0.483977i	−0.114052	+	0.153047i
$11$	0.155707	−	1.48145i	0.0469474	−	0.446675i	−0.945647	−	0.325196i	$-0.894570\pi$
$11$	0.155707	−	1.48145i	0.0469474	−	0.446675i	0.992594	−	0.121479i	$-0.0387637\pi$
$12$	−0.201441	−	1.91658i	−0.0581509	−	0.553269i
$13$	4.75723	−	3.45633i	1.31942	−	0.958613i	0.319478	−	0.947594i	$-0.396492\pi$
$13$	4.75723	−	3.45633i	1.31942	−	0.958613i	0.999939	−	0.0110190i	$-0.00350751\pi$
$14$	−0.345242	+	0.625176i	−0.0922698	+	0.167085i
$15$	0.491355	−	2.18141i	0.126867	−	0.563239i
$16$	−0.372972	−	3.54859i	−0.0932429	−	0.887147i
$17$	−1.86232	+	0.395847i	−0.451678	+	0.0960071i	−0.428133	−	0.903716i	$-0.640829\pi$
$17$	−1.86232	+	0.395847i	−0.451678	+	0.0960071i	−0.0235447	+	0.999723i	$0.507495\pi$
$18$	−0.134965	−	0.233767i	−0.0318116	−	0.0550993i
$19$	−2.23343	−	2.48048i	−0.512384	−	0.569060i	0.430326	−	0.902674i	$-0.358399\pi$
$19$	−2.23343	−	2.48048i	−0.512384	−	0.569060i	−0.942710	+	0.333613i	$0.891732\pi$
$20$	0.946908	−	4.20389i	0.211735	−	0.940018i
$21$	0.226400	−	2.63605i	0.0494045	−	0.575233i
$22$	−0.124253	−	0.382412i	−0.0264909	−	0.0815306i
$23$	−1.38005	+	0.614439i	−0.287761	+	0.128119i	−0.545541	−	0.838084i	$-0.683676\pi$
$23$	−1.38005	+	0.614439i	−0.287761	+	0.128119i	0.257780	+	0.966204i	$0.417009\pi$
$24$	−0.530027	−	0.918034i	−0.108191	−	0.187393i
$25$	2.60412	−	4.26832i	0.520825	−	0.853664i
$26$	0.793630	−	1.37461i	0.155644	−	0.269583i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.436303	−	5.08002i	0.0824536	−	0.960034i
$29$	−0.319893	−	0.984530i	−0.0594027	−	0.182823i	0.916952	−	0.398998i	$-0.130642\pi$
$29$	−0.319893	−	0.984530i	−0.0594027	−	0.182823i	−0.976355	+	0.216175i	$0.930642\pi$
$30$	−0.118334	−	0.591870i	−0.0216047	−	0.108060i
$31$	−4.54770	+	0.966644i	−0.816792	+	0.173614i	−0.597319	−	0.802004i	$-0.703767\pi$
$31$	−4.54770	+	0.966644i	−0.816792	+	0.173614i	−0.219473	+	0.975619i	$0.570434\pi$
$32$	−1.54163	−	2.67018i	−0.272524	−	0.472025i
$33$	0.996746	+	1.10700i	0.173511	+	0.192704i
$34$	−0.415775	+	0.302078i	−0.0713048	+	0.0518060i
$35$	2.36875	−	5.42117i	0.400392	−	0.916344i
$36$	1.55909	+	1.13274i	0.259848	+	0.188791i
$37$	0.829815	+	7.89516i	0.136421	+	1.29796i	0.821802	+	0.569773i	$0.192969\pi$
$37$	0.829815	+	7.89516i	0.136421	+	1.29796i	−0.685381	+	0.728184i	$0.740365\pi$
$38$	−0.823083	−	0.366460i	−0.133522	−	0.0594477i
$39$	−0.614654	+	5.84804i	−0.0984234	+	0.936436i
$40$	−0.464713	−	2.32435i	−0.0734776	−	0.367512i
$41$	−9.88531	+	7.18210i	−1.54383	+	1.12166i	−0.595948	+	0.803023i	$0.703224\pi$
$41$	−9.88531	+	7.18210i	−1.54383	+	1.12166i	−0.947878	+	0.318633i	$0.896776\pi$
$42$	−0.233585	−	0.674889i	−0.0360429	−	0.104138i
$43$	4.05343			0.618142			0.309071	−	0.951039i	$-0.399982\pi$
$43$	4.05343			0.618142			0.309071	+	0.951039i	$0.399982\pi$
$44$	1.92087	+	2.13334i	0.289582	+	0.321613i
$45$	1.29233	+	1.82480i	0.192649	+	0.272025i
$46$	−0.272853	+	0.303034i	−0.0402300	+	0.0446799i
$47$	−6.33216	−	1.34594i	−0.923640	−	0.196326i	−0.278541	−	0.960424i	$-0.589851\pi$
$47$	−6.33216	−	1.34594i	−0.923640	−	0.196326i	−0.645099	+	0.764099i	$0.723184\pi$
$48$	2.88668	+	2.09730i	0.416657	+	0.302719i
$49$	1.90805	−	6.73494i	0.272578	−	0.962134i
$50$	0.173539	−	1.33845i	0.0245422	−	0.189285i
$51$	0.951960	−	1.64884i	0.133301	−	0.230884i
$52$	−1.18452	+	11.2700i	−0.164264	+	1.56287i
$53$	6.07462	−	6.74655i	0.834414	−	0.926710i	−0.163798	−	0.986494i	$-0.552374\pi$
$53$	6.07462	−	6.74655i	0.834414	−	0.926710i	0.998211	+	0.0597837i	$0.0190411\pi$
$54$	0.264032	+	0.0561217i	0.0359302	+	0.00763720i
$55$	1.31784	+	3.05909i	0.177698	+	0.412488i
$56$	−0.917318	−	2.65038i	−0.122582	−	0.354172i
$57$	3.33781			0.442104
$58$	−0.186976	−	0.207658i	−0.0245511	−	0.0272668i
$59$	−11.6443	−	5.18437i	−1.51596	−	0.674947i	−0.530940	−	0.847409i	$-0.678161\pi$
$59$	−11.6443	−	5.18437i	−1.51596	−	0.674947i	−0.985016	+	0.172462i	$0.944828\pi$
$60$	2.49049	+	3.51664i	0.321521	+	0.453996i
$61$	2.09243	−	0.931610i	0.267908	−	0.119280i	−0.268386	−	0.963311i	$-0.586490\pi$
$61$	2.09243	−	0.931610i	0.267908	−	0.119280i	0.536294	+	0.844031i	$0.319824\pi$
$62$	−1.01531	+	0.737664i	−0.128944	+	0.0936834i
$63$	1.80747	+	1.93211i	0.227720	+	0.243423i
$64$	5.10005	+	3.70540i	0.637506	+	0.463175i
$65$	−5.49309	+	11.9463i	−0.681334	+	1.48175i
$66$	0.367330	+	0.163546i	0.0452151	+	0.0201311i
$67$	−8.75498	+	1.86093i	−1.06959	+	0.227349i	−0.708880	−	0.705329i	$-0.750799\pi$
$67$	−8.75498	+	1.86093i	−1.06959	+	0.227349i	−0.360711	+	0.932678i	$0.617466\pi$
$68$	1.83456	−	3.17755i	0.222473	−	0.385334i
$69$	0.466818	−	1.43672i	0.0561983	−	0.172961i
$70$	−0.0110745	−	1.59689i	−0.00132366	−	0.190865i
$71$	−2.89716	−	8.91654i	−0.343830	−	1.05820i	−0.962207	−	0.272318i	$-0.912210\pi$
$71$	−2.89716	−	8.91654i	−0.343830	−	1.05820i	0.618378	−	0.785881i	$-0.287790\pi$
$72$	1.03689	+	0.220398i	0.122199	+	0.0259741i
$73$	0.591782	−	5.63043i	0.0692629	−	0.658992i	−0.903721	−	0.428121i	$-0.859176\pi$
$73$	0.591782	−	5.63043i	0.0692629	−	0.658992i	0.972984	−	0.230871i	$-0.0741576\pi$
$74$	1.07144	+	1.85579i	0.124553	+	0.215732i
$75$	1.42948	+	4.79130i	0.165062	+	0.553252i
$76$	6.43242			0.737849
$77$	2.03521	+	3.37499i	0.231934	+	0.384616i
$78$	0.490490	+	1.50957i	0.0555371	+	0.170926i
$79$	2.75252	+	0.585065i	0.309682	+	0.0658250i	0.360131	−	0.932902i	$-0.382732\pi$
$79$	2.75252	+	0.585065i	0.309682	+	0.0658250i	−0.0504491	+	0.998727i	$0.516065\pi$
$80$	4.61119	+	6.51113i	0.515547	+	0.727966i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−1.64913	+	2.85638i	−0.182116	+	0.315434i
$83$	−2.56136	+	7.88306i	−0.281146	+	0.865279i	0.706381	+	0.707831i	$0.250326\pi$
$83$	−2.56136	+	7.88306i	−0.281146	+	0.865279i	−0.987527	+	0.157447i	$0.949674\pi$
$84$	3.48325	+	3.72344i	0.380054	+	0.406260i
$85$	3.19805	−	2.81017i	0.346877	−	0.304806i
$86$	0.999551	−	0.445029i	0.107784	−	0.0479887i
$87$	0.945698	+	0.421052i	0.101390	+	0.0451415i
$88$	1.44255	+	0.642266i	0.153777	+	0.0684658i
$89$	−11.8858	+	5.29190i	−1.25989	+	0.560941i	−0.924516	−	0.381143i	$-0.875531\pi$
$89$	−11.8858	+	5.29190i	−1.25989	+	0.560941i	−0.335377	+	0.942084i	$0.608864\pi$
$90$	0.519026	+	0.308099i	0.0547101	+	0.0324765i
$91$	−4.52496	+	14.8851i	−0.474344	+	1.56038i
$92$	0.899623	−	2.76876i	0.0937922	−	0.288663i
$93$	2.32465	−	4.02641i	0.241055	−	0.417520i
$94$	−1.70924	+	0.363311i	−0.176295	+	0.0374726i
$95$	7.06983	+	2.39215i	0.725349	+	0.245430i
$96$	3.01588	+	0.641045i	0.307807	+	0.0654264i
$97$	−1.63352	−	5.02747i	−0.165859	−	0.510462i	0.833239	−	0.552912i	$-0.186484\pi$
$97$	−1.63352	−	5.02747i	−0.165859	−	0.510462i	−0.999099	+	0.0424504i	$0.986484\pi$
$98$	−0.268921	−	1.87028i	−0.0271651	−	0.188927i
$99$	−1.48961			−0.149712
$100$	2.75480	+	9.23350i	0.275480	+	0.923350i
$101$	−6.32831	−	10.9610i	−0.629690	−	1.09066i	−0.987614	−	0.156905i	$-0.949848\pi$
$101$	−6.32831	−	10.9610i	−0.629690	−	1.09066i	0.357924	−	0.933751i	$-0.383485\pi$
$102$	0.0537199	−	0.511111i	0.00531906	−	0.0506075i
$103$	2.66187	+	0.565798i	0.262282	+	0.0557498i	0.337176	−	0.941442i	$-0.390528\pi$
$103$	2.66187	+	0.565798i	0.262282	+	0.0557498i	−0.0748936	+	0.997192i	$0.523862\pi$
$104$	1.92622	+	5.92831i	0.188882	+	0.581318i
$105$	2.44371	+	5.38779i	0.238482	+	0.525795i
$106$	0.757256	−	2.33059i	0.0735512	−	0.226367i
$107$	1.71354	−	2.96794i	0.165654	−	0.286922i	−0.771233	−	0.636553i	$-0.780360\pi$
$107$	1.71354	−	2.96794i	0.165654	−	0.286922i	0.936887	+	0.349631i	$0.113693\pi$
$108$	−1.88502	+	0.400674i	−0.181387	+	0.0385549i
$109$	−9.30773	−	4.14407i	−0.891519	−	0.396930i	−0.0907292	−	0.995876i	$-0.528920\pi$
$109$	−9.30773	−	4.14407i	−0.891519	−	0.396930i	−0.800789	+	0.598946i	$0.795586\pi$
$110$	0.660832	+	0.609666i	0.0630078	+	0.0581293i
$111$	−6.42251	−	4.66622i	−0.609597	−	0.442898i
$112$	6.44931	+	6.89402i	0.609402	+	0.651423i
$113$	−2.60554	+	1.89303i	−0.245108	+	0.178082i	−0.703556	−	0.710640i	$-0.748406\pi$
$113$	−2.60554	+	1.89303i	−0.245108	+	0.178082i	0.458448	+	0.888721i	$0.348406\pi$
$114$	0.823083	−	0.366460i	0.0770888	−	0.0343222i
$115$	2.01844	−	2.70856i	0.188221	−	0.252575i
$116$	1.82249	+	0.811425i	0.169214	+	0.0753389i
$117$	−3.93466	−	4.36988i	−0.363759	−	0.403996i
$118$	−3.44060			−0.316733
$119$	3.29871	−	3.80695i	0.302393	−	0.348983i
$120$	2.03828	+	1.20995i	0.186069	+	0.110452i
$121$	8.58916	+	1.82568i	0.780833	+	0.165971i
$122$	0.413698	−	0.459458i	0.0374545	−	0.0415974i
$123$	1.27722	−	12.1520i	0.115163	−	1.09571i
$124$	4.47992	−	7.75945i	0.402309	−	0.696820i
$125$	−0.406059	+	11.1730i	−0.0363190	+	0.999340i
$126$	0.657839	+	0.278002i	0.0586050	+	0.0247664i
$127$	4.31276	+	3.13340i	0.382696	+	0.278045i	0.762456	−	0.647040i	$-0.223993\pi$
$127$	4.31276	+	3.13340i	0.382696	+	0.278045i	−0.379760	+	0.925085i	$0.623993\pi$
$128$	7.69622	+	1.63588i	0.680256	+	0.144593i
$129$	−2.71227	+	3.01229i	−0.238802	+	0.265217i
$130$	−0.0429765	+	3.54896i	−0.00376929	+	0.311265i
$131$	−1.20783	−	1.34144i	−0.105529	−	0.117202i	0.688066	−	0.725648i	$-0.258460\pi$
$131$	−1.20783	−	1.34144i	−0.105529	−	0.117202i	−0.793595	+	0.608446i	$0.791793\pi$
$132$	−2.87069			−0.249862
$133$	8.67144	+	1.67125i	0.751909	+	0.144915i
$134$	−1.95461	+	1.42011i	−0.168853	+	0.122679i
$135$	−2.22083	−	0.260643i	−0.191138	−	0.0224326i
$136$	0.210965	−	2.00720i	0.0180901	−	0.172116i
$137$	5.17496	+	2.30404i	0.442127	+	0.196848i	0.615712	−	0.787971i	$-0.288869\pi$
$137$	5.17496	+	2.30404i	0.442127	+	0.196848i	−0.173585	+	0.984819i	$0.555535\pi$
$138$	−0.0426238	−	0.405538i	−0.00362838	−	0.0345217i
$139$	1.05827	+	0.768875i	0.0897609	+	0.0652151i	0.631761	−	0.775164i	$-0.282333\pi$
$139$	1.05827	+	0.768875i	0.0897609	+	0.0652151i	−0.542000	+	0.840379i	$0.682333\pi$
$140$	4.70936	+	10.3830i	0.398014	+	0.877525i
$141$	5.23727	−	3.80510i	0.441058	−	0.320447i
$142$	−1.69338	−	1.88068i	−0.142105	−	0.157823i
$143$	−4.37965	−	7.58578i	−0.366245	−	0.634355i
$144$	−3.49016	+	0.741857i	−0.290847	+	0.0618214i
$145$	1.70133	+	1.56960i	0.141288	+	0.130348i
$146$	−0.472239	−	1.45340i	−0.0390828	−	0.120284i
$147$	3.72830	+	5.92451i	0.307505	+	0.488645i
$148$	−12.3771	−	8.99245i	−1.01739	−	0.739175i
$149$	−4.95709	+	8.58593i	−0.406100	+	0.703386i	−0.994449	−	0.105221i	$-0.966445\pi$
$149$	−4.95709	+	8.58593i	−0.406100	+	0.703386i	0.588348	+	0.808607i	$0.299778\pi$
$150$	0.878541	+	1.02456i	0.0717326	+	0.0836552i
$151$	−6.24948	−	10.8244i	−0.508576	−	0.880879i	−0.999951	−	0.00993081i	$-0.996839\pi$
$151$	−6.24948	−	10.8244i	−0.508576	−	0.880879i	0.491375	−	0.870948i	$-0.336494\pi$
$152$	3.23236	−	1.43914i	0.262179	−	0.116730i
$153$	0.588344	+	1.81074i	0.0475648	+	0.146389i
$154$	0.872413	+	0.608804i	0.0703010	+	0.0490589i
$155$	7.80952	−	6.86233i	0.627276	−	0.551195i
$156$	−7.58263	−	8.42136i	−0.607096	−	0.674249i
$157$	10.7570	+	18.6317i	0.858502	+	1.48697i	0.873358	+	0.487079i	$0.161938\pi$
$157$	10.7570	+	18.6317i	0.858502	+	1.48697i	−0.0148559	+	0.999890i	$0.504729\pi$
$158$	0.742988	−	0.157927i	0.0591089	−	0.0125640i
$159$	0.948949	+	9.02865i	0.0752566	+	0.716018i
$160$	5.92852	+	3.51923i	0.468691	+	0.278220i
$161$	1.93213	−	3.49878i	0.152274	−	0.275742i
$162$	−0.218378	+	0.158661i	−0.0171574	+	0.0124656i
$163$	2.04802	+	19.4856i	0.160413	+	1.52623i	0.717960	+	0.696084i	$0.245076\pi$
$163$	2.04802	+	19.4856i	0.160413	+	1.52623i	−0.557547	+	0.830145i	$0.688257\pi$
$164$	2.46139	−	23.4185i	0.192202	−	1.82868i
$165$	−3.15516	−	1.06758i	−0.245629	−	0.0831111i
$166$	0.233870	+	2.22513i	0.0181519	+	0.172703i
$167$	−1.32784	+	4.08667i	−0.102751	+	0.316236i	−0.989196	−	0.146598i	$-0.953167\pi$
$167$	−1.32784	+	4.08667i	−0.102751	+	0.316236i	0.886445	+	0.462834i	$0.153167\pi$
$168$	2.58342	+	1.09175i	0.199316	+	0.0842305i
$169$	6.66778	−	20.5213i	0.512906	−	1.57856i
$170$	0.480089	−	1.04409i	0.0368211	−	0.0800777i
$171$	−2.23343	+	2.48048i	−0.170795	+	0.189687i
$172$	−5.22692	+	5.80509i	−0.398549	+	0.442634i
$173$	−6.77579	+	3.01678i	−0.515154	+	0.229361i	−0.647812	−	0.761801i	$-0.724316\pi$
$173$	−6.77579	+	3.01678i	−0.515154	+	0.229361i	0.132658	+	0.991162i	$0.457649\pi$
$174$	0.279431			0.0211836
$175$	1.31469	+	13.1633i	0.0993814	+	0.995049i
$176$	−5.31514			−0.400644
$177$	11.6443	−	5.18437i	0.875238	−	0.389681i
$178$	−2.34997	+	2.60990i	−0.176137	+	0.195620i
$179$	−15.8923	+	17.6502i	−1.18785	+	1.31924i	−0.251624	+	0.967825i	$0.580965\pi$
$179$	−15.8923	+	17.6502i	−1.18785	+	1.31924i	−0.936221	+	0.351411i	$0.885702\pi$
$180$	−4.27984	−	0.502295i	−0.319000	−	0.0374389i
$181$	−0.822348	+	2.53093i	−0.0611247	+	0.188122i	−0.976956	−	0.213441i	$-0.931533\pi$
$181$	−0.822348	+	2.53093i	−0.0611247	+	0.188122i	0.915831	+	0.401563i	$0.131533\pi$
$182$	0.518419	+	4.16737i	0.0384278	+	0.308906i
$183$	−0.707788	+	2.17835i	−0.0523212	+	0.161028i
$184$	−0.167390	−	1.59261i	−0.0123401	−	0.117408i
$185$	−10.2593	−	14.4864i	−0.754281	−	1.06506i
$186$	0.131182	−	1.24811i	0.00961873	−	0.0915161i
$187$	0.296454	+	2.82057i	0.0216788	+	0.206260i
$188$	10.0929	−	7.33295i	0.736103	−	0.534810i
$189$	−2.64527	+	0.0503825i	−0.192415	+	0.00366479i
$190$	2.00601	−	0.186311i	0.145531	−	0.0135164i
$191$	−1.60222	−	15.2441i	−0.115932	−	1.10302i	−0.885559	−	0.464527i	$-0.846224\pi$
$191$	−1.60222	−	15.2441i	−0.115932	−	1.10302i	0.769626	−	0.638494i	$-0.220442\pi$
$192$	−6.16625	+	1.31068i	−0.445010	+	0.0945899i
$193$	6.87991	+	11.9164i	0.495227	+	0.857758i	0.999985	−	0.00550278i	$-0.00175160\pi$
$193$	6.87991	+	11.9164i	0.495227	+	0.857758i	−0.504758	+	0.863261i	$0.668418\pi$
$194$	−0.954785	−	1.06040i	−0.0685496	−	0.0761320i
$195$	−5.20220	−	12.0758i	−0.372537	−	0.864764i
$196$	7.18495	+	11.4173i	0.513211	+	0.815524i
$197$	−2.64905	−	8.15295i	−0.188737	−	0.580874i	0.811255	−	0.584692i	$-0.198785\pi$
$197$	−2.64905	−	8.15295i	−0.188737	−	0.580874i	−0.999993	+	0.00381823i	$0.998785\pi$
$198$	−0.367330	+	0.163546i	−0.0261050	+	0.0116227i
$199$	−1.07599	−	1.86367i	−0.0762751	−	0.132112i	0.825365	−	0.564600i	$-0.190969\pi$
$199$	−1.07599	−	1.86367i	−0.0762751	−	0.132112i	−0.901640	+	0.432487i	$0.857636\pi$
$200$	3.45015	+	4.02360i	0.243963	+	0.284511i
$201$	4.47528	−	7.75142i	0.315662	−	0.546743i
$202$	−2.76393	−	2.00811i	−0.194470	−	0.141290i
$203$	2.24605	+	1.56738i	0.157642	+	0.110009i
$204$	1.13382	+	3.48954i	0.0793832	+	0.244316i
$205$	11.4144	−	24.8238i	0.797217	−	1.73377i
$206$	0.718520	−	0.152726i	0.0500617	−	0.0106409i
$207$	0.755328	+	1.30827i	0.0524989	+	0.0909308i
$208$	−14.0394	−	15.5923i	−0.973456	−	1.08113i
$209$	−4.02247	+	2.92250i	−0.278240	+	0.202153i
$210$	1.19413	+	1.06030i	0.0824030	+	0.0731676i
$211$	−7.99554	−	5.80910i	−0.550435	−	0.399915i	0.277511	−	0.960723i	$-0.410491\pi$
$211$	−7.99554	−	5.80910i	−0.550435	−	0.399915i	−0.827946	+	0.560808i	$0.810491\pi$
$212$	1.82876	+	17.3994i	0.125599	+	1.19500i
$213$	8.56486	+	3.81332i	0.586855	+	0.261285i
$214$	0.0966965	−	0.920006i	0.00661004	−	0.0628903i
$215$	−7.90373	+	4.43649i	−0.539030	+	0.302566i
$216$	−0.857602	+	0.623084i	−0.0583524	+	0.0423955i
$217$	8.05534	−	9.29643i	0.546832	−	0.631083i
$218$	−2.75021			−0.186268
$219$	3.78825	+	4.20728i	0.255986	+	0.284301i
$220$	−6.08042	−	2.05738i	−0.409942	−	0.138708i
$221$	−7.49128	+	8.31991i	−0.503918	+	0.559657i
$222$	−2.09606	−	0.445531i	−0.140678	−	0.0299021i
$223$	−23.4652	−	17.0484i	−1.57134	−	1.14165i	−0.925855	−	0.377879i	$-0.876654\pi$
$223$	−23.4652	−	17.0484i	−1.57134	−	1.14165i	−0.645489	−	0.763769i	$-0.723346\pi$
$224$	7.51411	+	3.17545i	0.502057	+	0.212169i
$225$	−4.51714	−	2.14370i	−0.301143	−	0.142913i
$226$	−0.434672	+	0.752874i	−0.0289139	+	0.0500804i
$227$	−2.30072	+	21.8899i	−0.152704	+	1.45288i	0.602880	+	0.797832i	$0.294020\pi$
$227$	−2.30072	+	21.8899i	−0.152704	+	1.45288i	−0.755584	+	0.655052i	$0.772647\pi$
$228$	−4.30413	+	4.78022i	−0.285048	+	0.316578i
$229$	−21.6597	−	4.60391i	−1.43131	−	0.304235i	−0.573925	−	0.818908i	$-0.694580\pi$
$229$	−21.6597	−	4.60391i	−1.43131	−	0.304235i	−0.857387	+	0.514673i	$0.827913\pi$
$230$	0.200361	−	0.889520i	0.0132114	−	0.0586532i
$231$	−3.86993	−	0.745852i	−0.254623	−	0.0490734i
$232$	1.09736			0.0720455
$233$	17.0554	+	18.9419i	1.11733	+	1.24093i	0.967678	+	0.252188i	$0.0811502\pi$
$233$	17.0554	+	18.9419i	1.11733	+	1.24093i	0.149657	+	0.988738i	$0.452183\pi$
$234$	−1.45003	−	0.645597i	−0.0947917	−	0.0422040i
$235$	13.8201	−	4.30613i	0.901526	−	0.280901i
$236$	22.4401	−	9.99099i	1.46073	−	0.650358i
$237$	−2.27658	+	1.65403i	−0.147880	+	0.107441i
$238$	0.395475	−	1.30094i	0.0256348	−	0.0843273i
$239$	1.86990	+	1.35856i	0.120954	+	0.0878779i	0.646617	−	0.762814i	$-0.276183\pi$
$239$	1.86990	+	1.35856i	0.120954	+	0.0878779i	−0.525664	+	0.850692i	$0.676183\pi$
$240$	−7.92420	−	0.930010i	−0.511505	−	0.0600319i
$241$	12.8739	+	5.73183i	0.829281	+	0.369220i	0.777068	−	0.629416i	$-0.216706\pi$
$241$	12.8739	+	5.73183i	0.829281	+	0.369220i	0.0522125	+	0.998636i	$0.483373\pi$
$242$	2.31848	−	0.492808i	0.149037	−	0.0316789i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.36400	+	4.19797i	−0.0873215	+	0.268748i
$245$	3.65094	+	15.2207i	0.233250	+	0.972417i
$246$	−1.01922	−	3.13683i	−0.0649830	−	0.199997i
$247$	−19.1983	−	4.08072i	−1.22156	−	0.259650i
$248$	0.515170	−	4.90151i	0.0327133	−	0.311247i
$249$	−4.14437	−	7.17826i	−0.262639	−	0.454904i
$250$	1.12656	+	2.79977i	0.0712496	+	0.177073i
$251$	7.96904			0.503002			0.251501	−	0.967857i	$-0.419076\pi$
$251$	7.96904			0.503002			0.251501	+	0.967857i	$0.419076\pi$
$252$	−5.09780	+	0.0970940i	−0.321131	+	0.00611635i
$253$	0.695379	+	2.14016i	0.0437181	+	0.134551i
$254$	1.40752	+	0.299177i	0.0883156	+	0.0187721i
$255$	−0.0515503	+	4.25698i	−0.00322821	+	0.266583i
$256$	−10.2550	+	2.17978i	−0.640940	+	0.136236i
$257$	12.4994	−	21.6496i	0.779692	−	1.35047i	−0.152428	−	0.988315i	$-0.548709\pi$
$257$	12.4994	−	21.6496i	0.779692	−	1.35047i	0.932119	−	0.362151i	$-0.117958\pi$
$258$	−0.338109	+	1.04059i	−0.0210498	+	0.0647845i
$259$	−14.3489	−	15.3383i	−0.891598	−	0.953077i
$260$	−10.0253	−	23.2717i	−0.621746	−	1.44325i
$261$	−0.945698	+	0.421052i	−0.0585373	+	0.0260625i
$262$	−0.445121	−	0.198181i	−0.0274997	−	0.0122437i
$263$	−1.93229	−	0.860309i	−0.119150	−	0.0530489i	0.346296	−	0.938125i	$-0.387439\pi$
$263$	−1.93229	−	0.860309i	−0.119150	−	0.0530489i	−0.465446	+	0.885076i	$0.654106\pi$
$264$	−1.44255	+	0.642266i	−0.0887830	+	0.0395288i
$265$	−4.46071	+	19.8037i	−0.274019	+	1.21653i
$266$	2.32181	−	0.539923i	0.142359	−	0.0331048i
$267$	4.02051	−	12.3739i	0.246051	−	0.757268i
$268$	8.62449	−	14.9381i	0.526824	−	0.912487i
$269$	−12.9268	+	2.74768i	−0.788162	+	0.167529i	−0.584373	−	0.811486i	$-0.698659\pi$
$269$	−12.9268	+	2.74768i	−0.788162	+	0.167529i	−0.203790	+	0.979015i	$0.565326\pi$
$270$	−0.576258	+	0.179553i	−0.0350699	+	0.0109272i
$271$	5.40672	+	1.14923i	0.328435	+	0.0698110i	0.369178	−	0.929359i	$-0.379639\pi$
$271$	5.40672	+	1.14923i	0.328435	+	0.0698110i	−0.0407432	+	0.999170i	$0.512973\pi$
$272$	2.09929	+	6.46095i	0.127288	+	0.391753i
$273$	−8.03401	−	13.3228i	−0.486240	−	0.806332i
$274$	1.52908			0.0923748
$275$	−5.91783	−	4.52250i	−0.356859	−	0.272717i
$276$	1.45562	+	2.52121i	0.0876181	+	0.151759i
$277$	3.07693	−	29.2750i	0.184875	−	1.75897i	−0.371871	−	0.928284i	$-0.621284\pi$
$277$	3.07693	−	29.2750i	0.184875	−	1.75897i	0.556746	−	0.830683i	$-0.312050\pi$
$278$	0.345377	+	0.0734122i	0.0207143	+	0.00440297i
$279$	1.43671	+	4.42175i	0.0860138	+	0.264723i
$280$	4.68952	+	4.16394i	0.280253	+	0.248843i
$281$	6.58540	−	20.2678i	0.392852	−	1.20908i	−0.537769	−	0.843092i	$-0.680733\pi$
$281$	6.58540	−	20.2678i	0.392852	−	1.20908i	0.930622	−	0.365983i	$-0.119267\pi$
$282$	0.873714	−	1.51332i	0.0520289	−	0.0901167i
$283$	−25.0452	+	5.32352i	−1.48878	+	0.316450i	−0.879269	−	0.476326i	$-0.841968\pi$
$283$	−25.0452	+	5.32352i	−1.48878	+	0.316450i	−0.609512	+	0.792777i	$0.708635\pi$
$284$	16.5057	+	7.34880i	0.979431	+	0.436071i
$285$	−6.50836	+	3.65325i	−0.385522	+	0.216400i
$286$	−1.91284	−	1.38976i	−0.113109	−	0.0821784i
$287$	9.40267	−	30.9306i	0.555022	−	1.82578i
$288$	−2.49441	+	1.81229i	−0.146984	+	0.106790i
$289$	−12.2188	+	5.44014i	−0.718750	+	0.320008i
$290$	0.591864	+	0.200263i	0.0347554	+	0.0117599i
$291$	4.82918	+	2.15009i	0.283091	+	0.126040i
$292$	7.30047	+	8.10800i	0.427228	+	0.474485i
$293$	26.1590			1.52823			0.764114	−	0.645081i	$-0.223177\pi$
$293$	26.1590			1.52823			0.764114	+	0.645081i	$0.223177\pi$
$294$	1.56983	+	1.05161i	0.0915544	+	0.0613314i
$295$	28.3794	−	2.63577i	1.65231	−	0.153461i
$296$	−8.23151	−	1.74966i	−0.478447	−	0.101697i
$297$	0.996746	−	1.10700i	0.0578371	−	0.0642346i
$298$	−0.279733	+	2.66148i	−0.0162045	+	0.154175i
$299$	−4.44152	+	7.69294i	−0.256860	+	0.444894i
$300$	−8.70515	−	4.13120i	−0.502592	−	0.238515i
$301$	−8.55458	+	6.46770i	−0.493078	+	0.372792i
$302$	−2.72950	−	1.98310i	−0.157065	−	0.114115i
$303$	12.3800	+	2.63146i	0.711215	+	0.151173i
$304$	−7.96918	+	8.85067i	−0.457064	+	0.507621i
$305$	−3.06035	+	4.10671i	−0.175235	+	0.235149i
$306$	0.343884	+	0.381922i	0.0196585	+	0.0218330i
$307$	−28.9558			−1.65259			−0.826297	−	0.563235i	$-0.809557\pi$
$307$	−28.9558			−1.65259			−0.826297	+	0.563235i	$0.809557\pi$
$308$	−7.45789	−	1.43736i	−0.424952	−	0.0819011i
$309$	−2.20161	+	1.59956i	−0.125245	+	0.0909960i
$310$	1.17236	−	2.54962i	0.0665855	−	0.144809i
$311$	−3.28730	+	31.2766i	−0.186406	+	1.77353i	0.357042	+	0.934088i	$0.383785\pi$
$311$	−3.28730	+	31.2766i	−0.186406	+	1.77353i	−0.543447	+	0.839443i	$0.682881\pi$
$312$	−5.69448	−	2.53535i	−0.322387	−	0.143536i
$313$	−3.54070	−	33.6875i	−0.200132	−	1.90413i	−0.387545	−	0.921851i	$-0.626677\pi$
$313$	−3.54070	−	33.6875i	−0.200132	−	1.90413i	0.187412	−	0.982281i	$-0.439990\pi$
$314$	4.69819	+	3.41344i	0.265134	+	0.192631i
$315$	−5.63907	−	1.78911i	−0.317726	−	0.100805i
$316$	−4.38728	+	3.18755i	−0.246804	+	0.179314i
$317$	0.219758	+	0.244066i	0.0123428	+	0.0137081i	0.749285	−	0.662248i	$-0.230398\pi$
$317$	0.219758	+	0.244066i	0.0123428	+	0.0137081i	−0.736942	+	0.675956i	$0.763731\pi$
$318$	1.22527	+	2.12222i	0.0687095	+	0.119008i
$319$	−1.50834	+	0.320609i	−0.0844511	+	0.0179506i
$320$	−14.0001	−	1.64310i	−0.782629	−	0.0918518i
$321$	1.05903	+	3.25935i	0.0591091	+	0.181919i
$322$	0.0923195	−	1.07491i	0.00514477	−	0.0599022i
$323$	5.14124	+	3.73533i	0.286066	+	0.207839i
$324$	0.963569	−	1.66895i	0.0535316	−	0.0927194i
$325$	−2.36430	−	29.3061i	−0.131148	−	1.62561i
$326$	2.64436	+	4.58017i	0.146458	+	0.253672i
$327$	9.30773	−	4.14407i	0.514719	−	0.229167i
$328$	−4.00261	−	12.3188i	−0.221007	−	0.680190i
$329$	15.5113	−	7.26312i	0.855168	−	0.400429i
$330$	−0.895253	+	0.0831479i	−0.0492820	+	0.00457714i
$331$	13.1714	+	14.6283i	0.723967	+	0.804046i	0.986997	−	0.160741i	$-0.0513885\pi$
$331$	13.1714	+	14.6283i	0.723967	+	0.804046i	−0.263030	+	0.964788i	$0.584722\pi$
$332$	−7.98677	−	13.8335i	−0.438331	−	0.759212i
$333$	7.76517	−	1.65054i	0.425529	−	0.0904490i
$334$	0.121241	+	1.15353i	0.00663401	+	0.0631184i
$335$	15.0344	−	13.2110i	0.821419	−	0.721792i
$336$	−9.43868	+	0.179771i	−0.514922	+	0.00980734i
$337$	−22.9612	+	16.6823i	−1.25078	+	0.908742i	−0.998267	−	0.0588526i	$-0.981256\pi$
$337$	−22.9612	+	16.6823i	−1.25078	+	0.908742i	−0.252509	+	0.967594i	$0.581256\pi$
$338$	−0.608815	−	5.79249i	−0.0331152	−	0.315070i
$339$	0.336646	−	3.20298i	0.0182841	−	0.173962i
$340$	−0.0993446	+	8.20379i	−0.00538772	+	0.444913i
$341$	0.723929	+	6.88773i	0.0392030	+	0.372991i
$342$	−0.278417	+	0.856880i	−0.0150551	+	0.0463348i
$343$	6.71950	+	17.2583i	0.362819	+	0.931860i
$344$	−1.32780	+	4.08655i	−0.0715903	+	0.220332i
$345$	0.662251	+	3.31238i	0.0356544	+	0.178332i
$346$	−1.33965	+	1.48784i	−0.0720203	+	0.0799866i
$347$	−1.30245	+	1.44651i	−0.0699189	+	0.0776528i	−0.777089	−	0.629390i	$-0.783305\pi$
$347$	−1.30245	+	1.44651i	−0.0699189	+	0.0776528i	0.707170	+	0.707043i	$0.249971\pi$
$348$	−1.82249	+	0.811425i	−0.0976958	+	0.0434970i
$349$	25.2081			1.34936			0.674679	−	0.738112i	$-0.264282\pi$
$349$	25.2081			1.34936			0.674679	+	0.738112i	$0.264282\pi$
$350$	1.76940	+	3.10164i	0.0945783	+	0.165790i
$351$	5.88026			0.313865
$352$	−4.19579	+	1.86809i	−0.223636	+	0.0995693i
$353$	3.13425	−	3.48094i	0.166820	−	0.185272i	−0.653939	−	0.756548i	$-0.726885\pi$
$353$	3.13425	−	3.48094i	0.166820	−	0.185272i	0.820758	+	0.571276i	$0.193551\pi$
$354$	2.30221	−	2.55687i	0.122361	−	0.135896i
$355$	15.4083	+	14.2153i	0.817789	+	0.754470i
$356$	7.74807	−	23.8461i	0.410647	−	1.26384i
$357$	0.621844	+	4.99877i	0.0329115	+	0.264563i
$358$	−1.98112	+	6.09725i	−0.104705	+	0.322250i
$359$	0.668372	+	6.35913i	0.0352753	+	0.335622i	0.997899	+	0.0647815i	$0.0206350\pi$
$359$	0.668372	+	6.35913i	0.0352753	+	0.335622i	−0.962624	+	0.270841i	$0.912698\pi$
$360$	−2.26304	+	0.705129i	−0.119273	+	0.0371635i
$361$	0.821491	−	7.81597i	0.0432364	−	0.411367i
$362$	0.0750862	+	0.714397i	0.00394644	+	0.0375479i
$363$	−7.10402	+	5.16137i	−0.372864	+	0.270902i
$364$	−15.4826	−	25.6748i	−0.811511	−	1.34573i
$365$	5.00862	+	11.6264i	0.262163	+	0.608555i
$366$	0.0646260	+	0.614875i	0.00337806	+	0.0321401i
$367$	−9.80499	+	2.08412i	−0.511816	+	0.108790i	−0.456578	−	0.889683i	$-0.650925\pi$
$367$	−9.80499	+	2.08412i	−0.511816	+	0.108790i	−0.0552382	+	0.998473i	$0.517592\pi$
$368$	2.69511	+	4.66807i	0.140492	+	0.243340i
$369$	8.17605	+	9.08043i	0.425628	+	0.472708i
$370$	−4.12036	−	2.44589i	−0.214208	−	0.127156i
$371$	−2.05534	+	23.9310i	−0.106708	+	1.24244i
$372$	2.76874	+	8.52132i	0.143553	+	0.441810i
$373$	2.25202	−	1.00266i	0.116605	−	0.0519159i	−0.347605	−	0.937641i	$-0.613005\pi$
$373$	2.25202	−	1.00266i	0.116605	−	0.0519159i	0.464210	+	0.885725i	$0.346338\pi$
$374$	0.382776	+	0.662987i	0.0197929	+	0.0342822i
$375$	−8.03142	−	7.77793i	−0.414741	−	0.401651i
$376$	3.43120	−	5.94301i	0.176950	−	0.306487i
$377$	−4.92466	−	3.57798i	−0.253633	−	0.184275i
$378$	−0.646776	+	0.302850i	−0.0332666	+	0.0155769i
$379$	3.29443	+	10.1392i	0.169223	+	0.520816i	0.999323	−	0.0367997i	$-0.0117163\pi$
$379$	3.29443	+	10.1392i	0.169223	+	0.520816i	−0.830099	+	0.557616i	$0.811716\pi$
$380$	−12.5425	+	7.04031i	−0.643416	+	0.361160i
$381$	−5.21437	+	1.10835i	−0.267140	+	0.0567824i
$382$	−2.06875	−	3.58318i	−0.105847	−	0.183332i
$383$	−8.75896	−	9.72781i	−0.447562	−	0.497068i	0.476573	−	0.879135i	$-0.341879\pi$
$383$	−8.75896	−	9.72781i	−0.447562	−	0.497068i	−0.924135	+	0.382067i	$0.875212\pi$
$384$	−6.36547	+	4.62479i	−0.324837	+	0.236008i
$385$	−7.66237	−	4.35330i	−0.390511	−	0.221865i
$386$	3.00485	+	2.18315i	0.152943	+	0.111119i
$387$	−0.423699	−	4.03122i	−0.0215378	−	0.204919i
$388$	9.30649	+	4.14351i	0.472465	+	0.210355i
$389$	2.29356	−	21.8218i	0.116288	−	1.10641i	−0.768317	−	0.640069i	$-0.778906\pi$
$389$	2.29356	−	21.8218i	0.116288	−	1.10641i	0.884606	−	0.466340i	$-0.154428\pi$
$390$	−2.60864	−	2.40666i	−0.132093	−	0.121866i
$391$	2.32687	−	1.69057i	0.117675	−	0.0854958i
$392$	6.16494	+	4.12983i	0.311377	+	0.208588i
$393$	1.80508			0.0910542
$394$	−1.54836	−	1.71963i	−0.0780052	−	0.0866335i
$395$	−6.00745	+	1.87183i	−0.302268	+	0.0941818i
$396$	1.92087	−	2.13334i	0.0965272	−	0.107204i
$397$	11.2307	+	2.38717i	0.563655	+	0.119809i	0.480922	−	0.876763i	$-0.340302\pi$
$397$	11.2307	+	2.38717i	0.563655	+	0.119809i	0.0827327	+	0.996572i	$0.473635\pi$
$398$	−0.469947	−	0.341436i	−0.0235563	−	0.0171147i
$399$	−7.04430	+	5.32585i	−0.352656	+	0.266626i
$400$	−16.1178	−	7.64900i	−0.805888	−	0.382450i
$401$	−12.1454	+	21.0364i	−0.606512	+	1.05051i	0.385298	+	0.922792i	$0.374099\pi$
$401$	−12.1454	+	21.0364i	−0.606512	+	1.05051i	−0.991811	+	0.127718i	$0.959235\pi$
$402$	0.252544	−	2.40280i	0.0125958	−	0.119841i
$403$	−18.2934	+	20.3169i	−0.911260	+	1.01206i
$404$	23.8580	+	5.07118i	1.18698	+	0.252301i
$405$	1.67972	−	1.47599i	0.0834658	−	0.0733426i
$406$	0.725945	+	0.139911i	0.0360281	+	0.00694369i
$407$	11.8255			0.586170
$408$	1.35048	+	1.49986i	0.0668587	+	0.0742541i
$409$	23.7309	+	10.5657i	1.17342	+	0.522438i	0.898476	−	0.439023i	$-0.144675\pi$
$409$	23.7309	+	10.5657i	1.17342	+	0.522438i	0.274940	+	0.961461i	$0.411342\pi$
$410$	0.0893033	−	7.37459i	0.00441038	−	0.364205i
$411$	−5.17496	+	2.30404i	−0.255262	+	0.113650i
$412$	−4.24281	+	3.08258i	−0.209028	+	0.151868i
$413$	32.8470	−	7.63838i	1.61629	−	0.375860i
$414$	0.329895	+	0.239683i	0.0162134	+	0.0117798i
$415$	−3.63367	−	18.1745i	−0.178370	−	0.892151i
$416$	−16.5629	−	7.37427i	−0.812062	−	0.361553i
$417$	−1.27950	+	0.271967i	−0.0626576	+	0.0133183i
$418$	−0.671054	+	1.16230i	−0.0328223	+	0.0568499i
$419$	3.69537	−	11.3732i	0.180531	−	0.555616i	−0.819312	−	0.573348i	$-0.805644\pi$
$419$	3.69537	−	11.3732i	0.180531	−	0.555616i	0.999843	+	0.0177317i	$0.00564448\pi$
$420$	−10.8673	−	3.44785i	−0.530268	−	0.168238i
$421$	−10.3067	−	31.7207i	−0.502317	−	1.54597i	−0.805234	−	0.592957i	$-0.797960\pi$
$421$	−10.3067	−	31.7207i	−0.502317	−	1.54597i	0.302917	−	0.953017i	$-0.402040\pi$
$422$	−2.60943	−	0.554652i	−0.127025	−	0.0270001i
$423$	−0.676678	+	6.43816i	−0.0329012	+	0.313034i
$424$	4.81179	+	8.33426i	0.233681	+	0.404748i
$425$	−3.16010	+	8.97979i	−0.153287	+	0.435584i
$426$	2.53071			0.122613
$427$	−2.92949	+	5.30483i	−0.141768	+	0.256719i
$428$	2.04089	+	6.28121i	0.0986501	+	0.303614i
$429$	8.56790	+	1.82116i	0.413662	+	0.0879266i
$430$	−1.46193	+	1.96177i	−0.0705003	+	0.0946048i
$431$	−6.07328	+	1.29092i	−0.292540	+	0.0621812i	−0.351844	−	0.936059i	$-0.614445\pi$
$431$	−6.07328	+	1.29092i	−0.292540	+	0.0621812i	0.0593041	+	0.998240i	$0.481112\pi$
$432$	1.78407	−	3.09009i	0.0858360	−	0.148672i
$433$	−6.23966	+	19.2037i	−0.299859	+	0.922871i	0.681687	+	0.731644i	$0.261247\pi$
$433$	−6.23966	+	19.2037i	−0.299859	+	0.922871i	−0.981546	+	0.191227i	$0.938753\pi$
$434$	0.965736	−	3.17684i	0.0463568	−	0.152493i
$435$	−2.30485	+	0.214066i	−0.110509	+	0.0102637i
$436$	17.9373	−	7.98619i	0.859040	−	0.382469i
$437$	4.60636	+	2.05088i	0.220352	+	0.0981070i
$438$	1.39608	+	0.621574i	0.0667072	+	0.0296999i
$439$	3.99484	−	1.77862i	0.190663	−	0.0848888i	−0.309184	−	0.951002i	$-0.600056\pi$
$439$	3.99484	−	1.77862i	0.190663	−	0.0848888i	0.499848	+	0.866113i	$0.333389\pi$
$440$	−3.51578	+	0.326533i	−0.167608	+	0.0155669i
$441$	−6.89749	−	1.19360i	−0.328452	−	0.0568381i
$442$	−0.933855	+	2.87411i	−0.0444189	+	0.136707i
$443$	−9.05599	+	15.6854i	−0.430263	+	0.745237i	−0.996896	−	0.0787332i	$-0.974912\pi$
$443$	−9.05599	+	15.6854i	−0.430263	+	0.745237i	0.566633	+	0.823970i	$0.308246\pi$
$444$	14.9646	−	3.18082i	0.710187	−	0.150955i
$445$	17.3840	−	23.3277i	0.824080	−	1.10584i
$446$	−7.65813	−	1.62778i	−0.362623	−	0.0770778i
$447$	−3.06365	−	9.42894i	−0.144906	−	0.445974i
$448$	−16.6758	+	0.317611i	−0.787857	+	0.0150057i
$449$	29.2820			1.38190			0.690951	−	0.722902i	$-0.257192\pi$
$449$	29.2820			1.38190			0.690951	+	0.722902i	$0.257192\pi$
$450$	−1.34926	−	0.0326827i	−0.0636046	−	0.00154068i
$451$	9.10073	+	15.7629i	0.428537	+	0.742248i
$452$	0.648764	−	6.17258i	0.0305153	−	0.290334i
$453$	12.2258	+	2.59868i	0.574420	+	0.122097i
$454$	1.83596	+	5.65051i	0.0861660	+	0.265192i
$455$	−7.46865	−	33.9769i	−0.350136	−	1.59286i
$456$	−1.09338	+	3.36509i	−0.0512023	+	0.157585i
$457$	−2.57826	+	4.46568i	−0.120606	+	0.208896i	−0.920007	−	0.391902i	$-0.871817\pi$
$457$	−2.57826	+	4.46568i	−0.120606	+	0.208896i	0.799401	+	0.600798i	$0.205150\pi$
$458$	−5.84661	+	1.24274i	−0.273194	+	0.0580692i
$459$	−1.73932	−	0.774394i	−0.0811844	−	0.0361456i
$460$	1.27625	+	6.38340i	0.0595054	+	0.297628i
$461$	20.8663	+	15.1602i	0.971840	+	0.706083i	0.955870	−	0.293790i	$-0.0949165\pi$
$461$	20.8663	+	15.1602i	0.971840	+	0.706083i	0.0159695	+	0.999872i	$0.494917\pi$
$462$	−1.03619	+	0.240960i	−0.0482078	+	0.0112105i
$463$	0.935795	−	0.679895i	0.0434901	−	0.0315974i	−0.565828	−	0.824523i	$-0.691443\pi$
$463$	0.935795	−	0.679895i	0.0434901	−	0.0315974i	0.609318	+	0.792926i	$0.291443\pi$
$464$	−3.37438	+	1.50237i	−0.156652	+	0.0697458i
$465$	−0.125884	+	10.3954i	−0.00583773	+	0.482075i
$466$	6.28540	+	2.79844i	0.291165	+	0.129635i
$467$	−2.13106	−	2.36678i	−0.0986138	−	0.109522i	0.691818	−	0.722072i	$-0.256810\pi$
$467$	−2.13106	−	2.36678i	−0.0986138	−	0.109522i	−0.790431	+	0.612551i	$0.790144\pi$
$468$	11.3321			0.523825
$469$	15.5077	−	17.8970i	0.716078	−	0.826404i
$470$	2.93519	−	2.57919i	0.135390	−	0.118969i
$471$	−21.0439	−	4.47301i	−0.969650	−	0.206105i
$472$	9.04111	−	10.0412i	0.416151	−	0.462182i
$473$	0.631148	−	6.00497i	0.0290202	−	0.276109i
$474$	−0.379793	+	0.657821i	−0.0174445	+	0.0302147i
$475$	−16.4036	+	3.07353i	−0.752649	+	0.141023i
$476$	1.19838	+	9.63332i	0.0549276	+	0.441542i
$477$	−7.34457	−	5.33614i	−0.336285	−	0.244325i
$478$	0.610262	+	0.129715i	0.0279127	+	0.00593303i
$479$	10.3802	−	11.5283i	0.474281	−	0.526743i	−0.457769	−	0.889071i	$-0.651351\pi$
$479$	10.3802	−	11.5283i	0.474281	−	0.526743i	0.932051	+	0.362328i	$0.118018\pi$
$480$	−6.58225	+	2.05093i	−0.300437	+	0.0936115i
$481$	31.2359	+	34.6910i	1.42423	+	1.58177i
$482$	3.80392			0.173264
$483$	1.30725	+	3.77699i	0.0594818	+	0.171859i
$484$	−13.6904	+	9.94667i	−0.622292	+	0.452122i
$485$	8.68777	+	8.01510i	0.394491	+	0.363947i
$486$	0.0282154	−	0.268452i	0.00127988	−	0.0121772i
$487$	4.75361	+	2.11644i	0.215407	+	0.0959052i	0.511603	−	0.859222i	$-0.329052\pi$
$487$	4.75361	+	2.11644i	0.215407	+	0.0959052i	−0.296197	+	0.955127i	$0.595718\pi$
$488$	0.253795	+	2.41470i	0.0114888	+	0.109308i
$489$	−15.8510	−	11.5164i	−0.716808	−	0.520791i
$490$	2.57139	+	3.35250i	0.116164	+	0.151450i
$491$	−18.5220	+	13.4570i	−0.835885	+	0.607306i	−0.921218	−	0.389047i	$-0.872804\pi$
$491$	−18.5220	+	13.4570i	−0.835885	+	0.607306i	0.0853333	+	0.996352i	$0.472804\pi$
$492$	15.7564	+	17.4992i	0.710352	+	0.788926i
$493$	0.985465	+	1.70688i	0.0443831	+	0.0768738i
$494$	−5.18220	+	1.10151i	−0.233158	+	0.0495593i
$495$	2.90458	−	1.63039i	0.130551	−	0.0732805i
$496$	5.12639	+	15.7774i	0.230182	+	0.708426i
$497$	20.3417	+	14.1952i	0.912449	+	0.636743i
$498$	−1.81008	−	1.31510i	−0.0811117	−	0.0589311i
$499$	10.4745	−	18.1423i	0.468902	−	0.812162i	−0.530466	−	0.847706i	$-0.677983\pi$
$499$	10.4745	−	18.1423i	0.468902	−	0.812162i	0.999368	+	0.0355440i	$0.0113164\pi$
$500$	−15.4777	−	14.9891i	−0.692182	−	0.670335i
$501$	−2.14849	−	3.72129i	−0.0959873	−	0.166255i
$502$	1.96512	−	0.874926i	0.0877075	−	0.0390499i
$503$	2.90854	+	8.95156i	0.129685	+	0.399131i	0.994726	−	0.102572i	$-0.0327072\pi$
$503$	2.90854	+	8.95156i	0.129685	+	0.399131i	−0.865040	+	0.501703i	$0.832707\pi$
$504$	−2.53998	+	1.18933i	−0.113140	+	0.0529771i
$505$	24.3363	+	14.4463i	1.08295	+	0.642850i
$506$	0.406445	+	0.451403i	0.0180687	+	0.0200673i
$507$	10.7887	+	18.6866i	0.479143	+	0.829900i
$508$	−10.0488	+	2.13594i	−0.445844	+	0.0947671i
$509$	4.28297	+	40.7498i	0.189839	+	1.80620i	0.511432	+	0.859324i	$0.329115\pi$
$509$	4.28297	+	40.7498i	0.189839	+	1.80620i	−0.321593	+	0.946878i	$0.604218\pi$
$510$	0.454665	+	1.05541i	0.0201329	+	0.0467341i
$511$	7.73506	+	12.8270i	0.342179	+	0.567435i
$512$	−15.0205	+	10.9130i	−0.663817	+	0.482291i
$513$	−0.348896	−	3.31953i	−0.0154041	−	0.146561i
$514$	0.705352	−	6.71098i	0.0311118	−	0.296009i
$515$	−5.80962	+	1.81019i	−0.256002	+	0.0797663i
$516$	−0.816526	−	7.76872i	−0.0359455	−	0.341999i
$517$	−2.97991	+	9.17123i	−0.131056	+	0.403350i
$518$	−5.22236	−	2.20696i	−0.229457	−	0.0969683i
$519$	2.29199	−	7.05401i	0.100607	−	0.309637i
$520$	−10.2445	−	9.45127i	−0.449250	−	0.414466i
$521$	16.8582	−	18.7230i	0.738572	−	0.820267i	−0.250435	−	0.968133i	$-0.580574\pi$
$521$	16.8582	−	18.7230i	0.738572	−	0.820267i	0.989007	+	0.147866i	$0.0472404\pi$
$522$	−0.186976	+	0.207658i	−0.00818371	+	0.00908893i
$523$	−38.6101	+	17.1903i	−1.68830	+	0.751680i	−0.688655	+	0.725089i	$0.741799\pi$
$523$	−38.6101	+	17.1903i	−1.68830	+	0.751680i	−0.999646	+	0.0265917i	$0.991535\pi$
$524$	3.47864			0.151965
$525$	−10.6619	−	7.83094i	−0.465324	−	0.341770i
$526$	−0.570944			−0.0248943
$527$	8.08662	−	3.60039i	0.352258	−	0.156836i
$528$	3.55652	−	3.94992i	0.154778	−	0.171898i
$529$	−13.8630	+	15.3964i	−0.602739	+	0.669409i
$530$	1.07428	+	5.37322i	0.0466637	+	0.233398i
$531$	−3.93881	+	12.1224i	−0.170930	+	0.526068i
$532$	−13.5753	+	10.2636i	−0.588565	+	0.444985i
$533$	−22.2030	+	68.3338i	−0.961718	+	2.95986i
$534$	−0.367101	−	3.49273i	−0.0158860	−	0.151145i
$535$	−0.0927913	+	7.66262i	−0.00401172	+	0.331284i
$536$	0.991775	−	9.43611i	0.0428382	−	0.407578i
$537$	−2.48262	−	23.6205i	−0.107133	−	1.01930i
$538$	−2.88601	+	2.09681i	−0.124425	+	0.0903997i
$539$	−9.68040	−	3.87536i	−0.416964	−	0.166923i
$540$	3.23705	−	2.84444i	0.139300	−	0.122405i
$541$	2.77650	+	26.4167i	0.119371	+	1.13574i	0.876139	+	0.482058i	$0.160111\pi$
$541$	2.77650	+	26.4167i	0.119371	+	1.13574i	−0.756768	+	0.653683i	$0.773223\pi$
$542$	1.45944	−	0.310213i	0.0626883	−	0.0133248i
$543$	−1.33059	−	2.30464i	−0.0571010	−	0.0989018i
$544$	3.92798	+	4.36246i	0.168411	+	0.187039i
$545$	22.6847	−	2.10688i	0.971707	−	0.0902486i
$546$	−3.44385	−	2.40326i	−0.147383	−	0.102850i
$547$	5.93080	+	18.2531i	0.253583	+	0.780447i	0.994106	+	0.108416i	$0.0345778\pi$
$547$	5.93080	+	18.2531i	0.253583	+	0.780447i	−0.740523	+	0.672031i	$0.765422\pi$
$548$	−9.97286	+	4.44020i	−0.426020	+	0.189676i
$549$	−1.14522	−	1.98359i	−0.0488770	−	0.0846575i
$550$	−1.95583	−	0.465497i	−0.0833968	−	0.0198488i
$551$	−1.72764	+	2.99237i	−0.0736001	+	0.127479i
$552$	1.29554	+	0.941266i	0.0551419	+	0.0400630i
$553$	−6.74260	+	3.15719i	−0.286724	+	0.134257i
$554$	−2.45537	−	7.55686i	−0.104319	−	0.321060i
$555$	17.6304	+	2.06916i	0.748367	+	0.0878308i
$556$	−2.46578	+	0.524118i	−0.104572	+	0.0222275i
$557$	−14.3849	−	24.9154i	−0.609508	−	1.05570i	−0.991322	−	0.131459i	$-0.958034\pi$
$557$	−14.3849	−	24.9154i	−0.609508	−	1.05570i	0.381814	−	0.924239i	$-0.375300\pi$
$558$	0.839751	+	0.932638i	0.0355495	+	0.0394817i
$559$	19.2831	−	14.0100i	0.815587	−	0.592559i
$560$	−20.1210	−	6.38377i	−0.850266	−	0.269764i
$561$	−2.29446	−	1.66702i	−0.0968721	−	0.0703817i
$562$	−0.601294	−	5.72093i	−0.0253640	−	0.241323i
$563$	32.3145	+	14.3874i	1.36190	+	0.606355i	0.952090	−	0.305818i	$-0.0989299\pi$
$563$	32.3145	+	14.3874i	1.36190	+	0.606355i	0.409805	+	0.912173i	$0.365597\pi$
$564$	−1.30405	+	12.4072i	−0.0549105	+	0.522438i
$565$	3.00857	−	6.54297i	0.126572	−	0.275265i
$566$	−5.59151	+	4.06247i	−0.235029	+	0.170758i
$567$	1.73259	−	1.99953i	0.0727620	−	0.0839725i
$568$	9.93844			0.417008
$569$	−7.77912	−	8.63958i	−0.326117	−	0.362190i	0.557683	−	0.830054i	$-0.311690\pi$
$569$	−7.77912	−	8.63958i	−0.326117	−	0.362190i	−0.883801	+	0.467864i	$0.845024\pi$
$570$	−1.20383	+	1.61542i	−0.0504228	+	0.0676627i
$571$	12.1172	−	13.4575i	0.507088	−	0.563178i	−0.434185	−	0.900824i	$-0.642964\pi$
$571$	12.1172	−	13.4575i	0.507088	−	0.563178i	0.941273	+	0.337645i	$0.109630\pi$
$572$	16.5115	+	3.50963i	0.690381	+	0.146745i
$573$	12.4006	+	9.00959i	0.518044	+	0.376381i
$574$	−1.07725	−	8.65963i	−0.0449637	−	0.361446i
$575$	−0.971207	+	7.49058i	−0.0405021	+	0.312379i
$576$	3.15200	−	5.45943i	0.131333	−	0.227476i
$577$	0.696078	−	6.62274i	0.0289781	−	0.275708i	−0.970432	−	0.241374i	$-0.922402\pi$
$577$	0.696078	−	6.62274i	0.0289781	−	0.275708i	0.999410	−	0.0343348i	$-0.0109313\pi$
$578$	−2.41579	+	2.68301i	−0.100484	+	0.111598i
$579$	−13.4591	−	2.86083i	−0.559343	−	0.118892i
$580$	−4.44176	+	0.412535i	−0.184434	+	0.0171296i
$581$	−7.17267	−	20.7238i	−0.297572	−	0.859768i
$582$	1.42690			0.0591471
$583$	−9.04884	−	10.0498i	−0.374765	−	0.416218i
$584$	5.48259	+	2.44101i	0.226871	+	0.101010i
$585$	12.4550	+	4.21428i	0.514951	+	0.174239i
$586$	6.45066	−	2.87202i	0.266474	−	0.118642i
$587$	14.4315	−	10.4851i	0.595654	−	0.432768i	−0.248680	−	0.968586i	$-0.579997\pi$
$587$	14.4315	−	10.4851i	0.595654	−	0.432768i	0.844333	+	0.535818i	$0.179997\pi$
$588$	−13.2924	−	2.30023i	−0.548170	−	0.0948600i
$589$	12.5547	+	9.12154i	0.517308	+	0.375847i
$590$	6.70879	−	3.76575i	0.276197	−	0.155034i
$591$	7.83139	+	3.48676i	0.322140	+	0.143426i
$592$	27.7072	−	5.88934i	1.13876	−	0.242051i
$593$	3.79069	−	6.56566i	0.155665	−	0.269619i	−0.777636	−	0.628715i	$-0.783581\pi$
$593$	3.79069	−	6.56566i	0.155665	−	0.269619i	0.933301	+	0.359095i	$0.116915\pi$
$594$	0.124253	−	0.382412i	0.00509818	−	0.0156906i
$595$	−2.26540	+	11.0336i	−0.0928724	+	0.452333i
$596$	−5.90407	−	18.1709i	−0.241840	−	0.744308i
$597$	2.10496	+	0.447423i	0.0861502	+	0.0183118i
$598$	−0.250639	+	2.38467i	−0.0102494	+	0.0975164i
$599$	19.4620	+	33.7092i	0.795197	+	1.37732i	0.922714	+	0.385486i	$0.125966\pi$
$599$	19.4620	+	33.7092i	0.795197	+	1.37732i	−0.127517	+	0.991836i	$0.540701\pi$
$600$	−5.29872	−	0.128349i	−0.216319	−	0.00523984i
$601$	−10.3213			−0.421015			−0.210507	−	0.977592i	$-0.567512\pi$
$601$	−10.3213			−0.421015			−0.210507	+	0.977592i	$0.567512\pi$
$602$	−1.39941	+	2.53411i	−0.0570359	+	0.103283i
$603$	2.76588	+	8.51250i	0.112635	+	0.346656i
$604$	23.5609	+	5.00802i	0.958678	+	0.203773i
$605$	−18.7461	+	5.84099i	−0.762138	+	0.237470i
$606$	3.34175	−	0.710311i	0.135749	−	0.0288544i
$607$	12.2859	−	21.2797i	0.498668	−	0.863718i	−0.501331	−	0.865256i	$-0.667156\pi$
$607$	12.2859	−	21.2797i	0.498668	−	0.863718i	0.999999	+	0.00153752i	$0.000489409\pi$
$608$	−3.18020	+	9.78763i	−0.128974	+	0.396941i
$609$	−2.66769	+	0.620356i	−0.108100	+	0.0251381i
$610$	−0.303786	+	1.34869i	−0.0122999	+	0.0546067i
$611$	−34.7755	+	15.4831i	−1.40687	+	0.626378i
$612$	−3.35190	−	1.49236i	−0.135493	−	0.0603252i
$613$	−19.3575	−	8.61849i	−0.781840	−	0.348098i	−0.0233038	−	0.999728i	$-0.507418\pi$
$613$	−19.3575	−	8.61849i	−0.781840	−	0.348098i	−0.758536	+	0.651631i	$0.774085\pi$
$614$	−7.14032	+	3.17907i	−0.288160	+	0.128297i
$615$	10.8099	+	25.0929i	0.435899	+	1.01184i
$616$	−4.06925	+	0.946281i	−0.163955	+	0.0381268i
$617$	−0.0510418	+	0.157091i	−0.00205487	+	0.00632423i	−0.952079	−	0.305853i	$-0.901058\pi$
$617$	−0.0510418	+	0.157091i	−0.00205487	+	0.00632423i	0.950024	+	0.312177i	$0.101058\pi$
$618$	−0.367286	+	0.636159i	−0.0147744	+	0.0255901i
$619$	27.6815	−	5.88389i	1.11261	−	0.236494i	0.385296	−	0.922793i	$-0.374099\pi$
$619$	27.6815	−	5.88389i	1.11261	−	0.236494i	0.727319	+	0.686300i	$0.240766\pi$
$620$	−0.242596	+	20.0334i	−0.00974288	+	0.804559i
$621$	−1.47764	−	0.314083i	−0.0592958	−	0.0126037i
$622$	2.62325	+	8.07352i	0.105183	+	0.323719i
$623$	16.6407	−	30.1335i	0.666694	−	1.20727i
$624$	20.9815			0.839934
$625$	−11.4371	−	22.2305i	−0.457483	−	0.889218i
$626$	−4.57169	−	7.91840i	−0.182722	−	0.316483i
$627$	0.519721	−	4.94481i	0.0207556	−	0.197477i
$628$	−40.5544	−	8.62011i	−1.61830	−	0.343980i
$629$	−4.67066	−	14.3748i	−0.186231	−	0.573161i
$630$	−1.58699	+	0.177935i	−0.0632271	+	0.00708908i
$631$	−0.123878	+	0.381258i	−0.00493152	+	0.0151776i	−0.953492	−	0.301418i	$-0.902540\pi$
$631$	−0.123878	+	0.381258i	−0.00493152	+	0.0151776i	0.948560	+	0.316596i	$0.102540\pi$
$632$	−1.49150	+	2.58335i	−0.0593287	+	0.102760i
$633$	9.66706	−	2.05480i	0.384231	−	0.0816708i
$634$	0.0809872	+	0.0360578i	0.00321641	+	0.00143204i
$635$	−11.8389	−	1.38945i	−0.469813	−	0.0551388i
$636$	−14.1540	−	10.2835i	−0.561242	−	0.407766i
$637$	−14.2011	−	38.6344i	−0.562670	−	1.53075i
$638$	−0.336749	+	0.244662i	−0.0133320	+	0.00968627i
$639$	−8.56486	+	3.81332i	−0.338821	+	0.150853i
$640$	−16.7972	+	5.23375i	−0.663969	+	0.206882i
$641$	44.1964	+	19.6775i	1.74565	+	0.777215i	0.992905	+	0.118908i	$0.0379392\pi$
$641$	44.1964	+	19.6775i	1.74565	+	0.777215i	0.752749	+	0.658308i	$0.228727\pi$
$642$	0.618995	+	0.687464i	0.0244298	+	0.0271320i
$643$	−0.370720			−0.0146198			−0.00730989	−	0.999973i	$-0.502327\pi$
$643$	−0.370720			−0.0146198			−0.00730989	+	0.999973i	$0.502327\pi$
$644$	2.51924	+	7.27879i	0.0992722	+	0.286824i
$645$	1.99167	−	8.84221i	0.0784220	−	0.348162i
$646$	1.67790	+	0.356649i	0.0660162	+	0.0140322i
$647$	32.4412	−	36.0296i	1.27539	−	1.41647i	0.412600	−	0.910912i	$-0.364621\pi$
$647$	32.4412	−	36.0296i	1.27539	−	1.41647i	0.862794	−	0.505556i	$-0.168713\pi$
$648$	0.110806	−	1.05425i	0.00435286	−	0.0414147i
$649$	−9.49350	+	16.4432i	−0.372652	+	0.645453i
$650$	−3.80055	−	6.96711i	−0.149070	−	0.273273i
$651$	1.51852	+	12.2068i	0.0595155	+	0.478423i
$652$	−30.5471	−	22.1938i	−1.19632	−	0.869174i
$653$	−44.2965	−	9.41550i	−1.73345	−	0.368457i	−0.770357	−	0.637612i	$-0.779922\pi$
$653$	−44.2965	−	9.41550i	−1.73345	−	0.368457i	−0.963097	+	0.269155i	$0.913255\pi$
$654$	1.84025	−	2.04380i	0.0719594	−	0.0799190i
$655$	3.82335	+	1.29367i	0.149390	+	0.0505479i
$656$	29.1733	+	32.4002i	1.13902	+	1.26501i
$657$	−5.66145			−0.220874
$658$	3.02758	−	3.49404i	0.118027	−	0.136212i
$659$	−24.8817	+	18.0776i	−0.969252	+	0.704203i	−0.955281	−	0.295700i	$-0.904447\pi$
$659$	−24.8817	+	18.0776i	−0.969252	+	0.704203i	−0.0139708	+	0.999902i	$0.504447\pi$
$660$	5.59752	−	3.14198i	0.217883	−	0.122301i
$661$	−2.99990	+	28.5422i	−0.116683	+	1.11016i	0.766861	+	0.641813i	$0.221818\pi$
$661$	−2.99990	+	28.5422i	−0.116683	+	1.11016i	−0.883544	+	0.468349i	$0.844849\pi$
$662$	4.85404	+	2.16116i	0.188658	+	0.0839959i
$663$	−1.17025	−	11.1342i	−0.0454488	−	0.432417i
$664$	−7.10844	−	5.16459i	−0.275861	−	0.200425i
$665$	−18.7375	+	6.23217i	−0.726609	+	0.241673i
$666$	1.73363	−	1.25956i	0.0671768	−	0.0488068i
$667$	1.04640	+	1.16215i	0.0405169	+	0.0449986i
$668$	−4.14043	−	7.17144i	−0.160198	−	0.277471i
$669$	28.3707	−	6.03038i	1.09688	−	0.233148i
$670$	2.25696	−	4.90838i	0.0871939	−	0.189627i
$671$	−1.05433	−	3.24490i	−0.0407020	−	0.125268i
$672$	−7.38774	+	3.45928i	−0.284988	+	0.133445i
$673$	9.71270	+	7.05669i	0.374397	+	0.272015i	0.759032	−	0.651053i	$-0.225673\pi$
$673$	9.71270	+	7.05669i	0.374397	+	0.272015i	−0.384635	+	0.923069i	$0.625673\pi$
$674$	−3.83053	+	6.63467i	−0.147546	+	0.255558i
$675$	4.61563	−	1.92248i	0.177656	−	0.0739962i
$676$	20.7913	+	36.0116i	0.799666	+	1.38506i
$677$	−18.6379	+	8.29811i	−0.716311	+	0.318922i	−0.732331	−	0.680949i	$-0.761567\pi$
$677$	−18.6379	+	8.29811i	−0.716311	+	0.318922i	0.0160192	+	0.999872i	$0.494901\pi$
$678$	−0.268642	−	0.826795i	−0.0103171	−	0.0317529i
$679$	11.4694	+	8.00378i	0.440154	+	0.307157i
$680$	1.78553	+	4.14472i	0.0684720	+	0.158943i
$681$	−14.7279	−	16.3570i	−0.564374	−	0.626800i
$682$	0.934724	+	1.61899i	0.0357924	+	0.0619943i
$683$	−44.8232	+	9.52746i	−1.71511	+	0.364558i	−0.957564	−	0.288222i	$-0.906936\pi$
$683$	−44.8232	+	9.52746i	−1.71511	+	0.364558i	−0.757547	+	0.652780i	$0.773602\pi$
$684$	−0.672371	−	6.39718i	−0.0257087	−	0.244602i
$685$	−12.6124	+	1.17139i	−0.481894	+	0.0447566i
$686$	3.55178	+	3.51805i	0.135608	+	0.134320i
$687$	17.9145	−	13.0157i	0.683482	−	0.496579i
$688$	−1.51181	−	14.3839i	−0.0576374	−	0.548383i
$689$	5.58006	−	53.0908i	0.212584	−	2.02260i
$690$	0.526975	+	0.744102i	0.0200616	+	0.0283275i
$691$	−3.16988	−	30.1594i	−0.120588	−	1.14732i	−0.872691	−	0.488273i	$-0.837627\pi$
$691$	−3.16988	−	30.1594i	−0.120588	−	1.14732i	0.752103	−	0.659045i	$-0.229040\pi$
$692$	4.41697	−	13.5941i	0.167908	−	0.516768i
$693$	3.14376	−	2.37685i	0.119422	−	0.0902889i
$694$	−0.162361	+	0.499697i	−0.00616316	+	0.0189682i
$695$	−2.90504	−	0.340944i	−0.110194	−	0.0129328i
$696$	−0.734280	+	0.815500i	−0.0278328	+	0.0309115i
$697$	15.5666	−	17.2884i	0.589625	−	0.654845i
$698$	6.21615	−	2.76761i	0.235285	−	0.104756i
$699$	−25.4889			−0.964077
$700$	−20.5470	−	15.0913i	−0.776603	−	0.570397i
$701$	−18.1682			−0.686204			−0.343102	−	0.939298i	$-0.611478\pi$
$701$	−18.1682			−0.686204			−0.343102	+	0.939298i	$0.611478\pi$
$702$	1.45003	−	0.645597i	0.0547280	−	0.0243665i
$703$	17.7304	−	19.6916i	0.668716	−	0.742684i
$704$	6.28349	−	6.97852i	0.236818	−	0.263013i
$705$	−6.04739	+	13.1517i	−0.227758	+	0.495323i
$706$	0.390713	−	1.20249i	0.0147047	−	0.0452563i
$707$	30.8450	+	13.0351i	1.16005	+	0.490235i
$708$	−7.59063	+	23.3615i	−0.285273	+	0.877981i
$709$	−3.44551	−	32.7818i	−0.129399	−	1.23115i	−0.845816	−	0.533475i	$-0.820886\pi$
$709$	−3.44551	−	32.7818i	−0.129399	−	1.23115i	0.716417	−	0.697672i	$-0.245781\pi$
$710$	5.36031	+	1.81372i	0.201169	+	0.0680676i
$711$	0.294144	−	2.79859i	0.0110313	−	0.104955i
$712$	−1.44166	−	13.7164i	−0.0540283	−	0.514045i
$713$	5.68213	−	4.12831i	0.212797	−	0.154606i
$714$	0.702161	+	1.16439i	0.0262777	+	0.0435763i
$715$	16.8425	+	9.99788i	0.629874	+	0.373899i
$716$	−4.78435	−	45.5200i	−0.178799	−	1.70116i
$717$	−2.26081	+	0.480550i	−0.0844315	+	0.0179465i
$718$	0.862990	+	1.49474i	0.0322065	+	0.0557833i
$719$	−30.0515	−	33.3756i	−1.12073	−	1.24470i	−0.966501	−	0.256664i	$-0.917377\pi$
$719$	−30.0515	−	33.3756i	−1.12073	−	1.24470i	−0.154231	−	0.988035i	$-0.549290\pi$
$720$	5.99346	−	5.26653i	0.223363	−	0.196272i
$721$	−6.52056	+	3.05322i	−0.242838	+	0.113708i
$722$	−0.655545	−	2.01756i	−0.0243969	−	0.0750859i
$723$	−12.8739	+	5.73183i	−0.478785	+	0.213169i
$724$	−2.56422	−	4.44137i	−0.0952987	−	0.165062i
$725$	−5.03533	−	1.19843i	−0.187007	−	0.0445086i
$726$	−1.18514	+	2.05272i	−0.0439846	+	0.0761835i
$727$	9.00669	+	6.54374i	0.334040	+	0.242694i	0.742143	−	0.670242i	$-0.233810\pi$
$727$	9.00669	+	6.54374i	0.334040	+	0.242694i	−0.408103	+	0.912936i	$0.633810\pi$
$728$	−13.5245	−	9.43792i	−0.501251	−	0.349793i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	2.51157	+	2.31710i	0.0929573	+	0.0857598i
$731$	−7.54876	+	1.60454i	−0.279201	+	0.0593460i
$732$	−2.20701	−	3.82265i	−0.0815733	−	0.141289i
$733$	10.1788	+	11.3047i	0.375962	+	0.417548i	0.901197	−	0.433409i	$-0.142689\pi$
$733$	10.1788	+	11.3047i	0.375962	+	0.417548i	−0.525235	+	0.850957i	$0.676023\pi$
$734$	−2.18903	+	1.59043i	−0.0807987	+	0.0587037i
$735$	−13.7542	−	7.47148i	−0.507330	−	0.275590i
$736$	3.76819	+	2.73775i	0.138897	+	0.100915i
$737$	1.39367	+	13.2599i	0.0513364	+	0.488433i
$738$	3.01311	+	1.34152i	0.110914	+	0.0493821i
$739$	−0.554290	+	5.27372i	−0.0203899	+	0.193997i	−0.999975	−	0.00703166i	$-0.997762\pi$
$739$	−0.554290	+	5.27372i	−0.0203899	+	0.193997i	0.979585	+	0.201029i	$0.0644284\pi$
$740$	33.9761	+	3.98755i	1.24899	+	0.146585i
$741$	15.8787	−	11.5366i	0.583319	−	0.423806i
$742$	2.12057	+	6.12690i	0.0778485	+	0.224926i
$743$	−7.80026			−0.286164			−0.143082	−	0.989711i	$-0.545701\pi$
$743$	−7.80026			−0.286164			−0.143082	+	0.989711i	$0.545701\pi$
$744$	3.29782	+	3.66260i	0.120904	+	0.134277i
$745$	0.268435	−	22.1671i	0.00983470	−	0.812141i
$746$	0.445250	−	0.494500i	0.0163018	−	0.0181049i
$747$	8.10761	+	1.72333i	0.296642	+	0.0630532i
$748$	−4.42174	−	3.21258i	−0.161675	−	0.117464i
$749$	1.11933	+	8.99785i	0.0408994	+	0.328774i
$750$	−2.83444	−	1.03621i	−0.103499	−	0.0378372i
$751$	3.30791	−	5.72946i	0.120707	−	0.209071i	−0.799340	−	0.600880i	$-0.794817\pi$
$751$	3.30791	−	5.72946i	0.120707	−	0.209071i	0.920047	+	0.391809i	$0.128150\pi$
$752$	−2.41448	+	22.9722i	−0.0880469	+	0.837710i
$753$	−5.33233	+	5.92215i	−0.194321	+	0.215815i
$754$	−1.60722	−	0.341625i	−0.0585315	−	0.0124412i
$755$	24.0332	+	14.2663i	0.874656	+	0.519205i
$756$	3.33894	−	3.85337i	0.121436	−	0.140146i
$757$	−29.7193			−1.08017			−0.540083	−	0.841612i	$-0.681607\pi$
$757$	−29.7193			−1.08017			−0.540083	+	0.841612i	$0.681607\pi$
$758$	1.92557	+	2.13857i	0.0699400	+	0.0776763i
$759$	−2.05575	−	0.915277i	−0.0746189	−	0.0332225i
$760$	−4.72760	+	6.34399i	−0.171488	+	0.230121i
$761$	−15.7558	+	7.01495i	−0.571148	+	0.254292i	−0.671927	−	0.740617i	$-0.734533\pi$
$761$	−15.7558	+	7.01495i	−0.571148	+	0.254292i	0.100779	+	0.994909i	$0.467867\pi$
$762$	−1.16415	+	0.845801i	−0.0421725	+	0.0306401i
$763$	26.2559	−	6.10565i	0.950526	−	0.221039i
$764$	23.8977	+	17.3627i	0.864590	+	0.628161i
$765$	−3.12906	−	2.88679i	−0.113131	−	0.104372i
$766$	−3.22793	−	1.43717i	−0.116630	−	0.0519269i
$767$	−73.3134	+	15.5832i	−2.64719	+	0.562678i
$768$	5.24208	−	9.07954i	0.189157	−	0.327630i
$769$	9.55359	−	29.4029i	0.344511	−	1.06030i	−0.617333	−	0.786702i	$-0.711787\pi$
$769$	9.55359	−	29.4029i	0.344511	−	1.06030i	0.961845	−	0.273595i	$-0.0882129\pi$
$770$	−2.36745	−	0.232241i	−0.0853168	−	0.00836938i
$771$	7.72506	+	23.7753i	0.278211	+	0.856246i
$772$	−25.9376	−	5.51321i	−0.933515	−	0.198425i
$773$	2.13131	−	20.2781i	0.0766579	−	0.729351i	−0.886920	−	0.461923i	$-0.847160\pi$
$773$	2.13131	−	20.2781i	0.0766579	−	0.729351i	0.963578	−	0.267428i	$-0.0861738\pi$
$774$	−0.547072	−	0.947557i	−0.0196641	−	0.0340592i
$775$	−7.71684	+	21.9283i	−0.277197	+	0.787688i
$776$	5.60365			0.201159
$777$	20.9999	−	0.399969i	0.753367	−	0.0143488i
$778$	−1.83025	−	5.63293i	−0.0656177	−	0.201950i
$779$	39.8932	+	8.47956i	1.42932	+	0.303812i
$780$	24.0025	+	8.12150i	0.859427	+	0.290796i
$781$	−13.6606	+	2.90364i	−0.488813	+	0.103900i
$782$	0.388183	−	0.672353i	0.0138814	−	0.0240433i
$783$	0.319893	−	0.984530i	0.0114320	−	0.0351842i
$784$	−24.6112	−	4.25893i	−0.878970	−	0.152105i
$785$	−41.3674	−	24.5561i	−1.47646	−	0.876444i
$786$	0.445121	−	0.198181i	0.0158770	−	0.00706888i
$787$	34.3709	+	15.3029i	1.22519	+	0.545490i	0.914332	−	0.404966i	$-0.132717\pi$
$787$	34.3709	+	15.3029i	1.22519	+	0.545490i	0.310859	+	0.950456i	$0.399383\pi$
$788$	15.0922	+	6.71946i	0.537636	+	0.239371i
$789$	1.93229	−	0.860309i	0.0687912	−	0.0306278i
$790$	−1.27589	+	1.12114i	−0.0453942	+	0.0398885i
$791$	2.47832	−	8.15259i	0.0881190	−	0.289873i
$792$	0.487960	−	1.50179i	0.0173389	−	0.0533636i
$793$	6.73421	−	11.6640i	0.239139	−	0.414201i
$794$	3.03152	−	0.644370i	0.107585	−	0.0228678i
$795$	−11.7322	−	16.5662i	−0.416099	−	0.587543i
$796$	4.05655	+	0.862245i	0.143780	+	0.0305615i
$797$	−8.27408	−	25.4650i	−0.293083	−	0.902016i	−0.983859	−	0.178947i	$-0.942731\pi$
$797$	−8.27408	−	25.4650i	−0.293083	−	0.902016i	0.690776	−	0.723069i	$-0.257269\pi$
$798$	−1.15235	+	2.08672i	−0.0407928	+	0.0738691i
$799$	12.3253			0.436036
$800$	−15.4118	−	0.373315i	−0.544888	−	0.0131987i
$801$	6.50532	+	11.2675i	0.229854	+	0.398119i
$802$	−0.685375	+	6.52091i	−0.0242014	+	0.230261i
$803$	−8.24908	−	1.75340i	−0.291104	−	0.0618760i
$804$	5.33023	+	16.4048i	0.187983	+	0.578551i
$805$	0.0619782	+	8.93695i	0.00218444	+	0.314986i
$806$	−2.28044	+	7.01847i	−0.0803250	+	0.247215i
$807$	6.60781	−	11.4451i	0.232606	−	0.402885i
$808$	13.1235	−	2.78949i	0.461684	−	0.0981339i
$809$	−15.1429	−	6.74207i	−0.532397	−	0.237039i	0.122887	−	0.992421i	$-0.460785\pi$
$809$	−15.1429	−	6.74207i	−0.532397	−	0.237039i	−0.655285	+	0.755382i	$0.727451\pi$
$810$	0.252158	−	0.548387i	0.00885993	−	0.0192684i
$811$	−44.6061	−	32.4082i	−1.56633	−	1.13801i	−0.930567	−	0.366122i	$-0.880685\pi$
$811$	−44.6061	−	32.4082i	−1.56633	−	1.13801i	−0.635763	−	0.771884i	$-0.719315\pi$
$812$	−5.14101	+	1.19551i	−0.180414	+	0.0419542i
$813$	−4.47185	+	3.24899i	−0.156835	+	0.113947i
$814$	2.91610	−	1.29833i	0.102209	−	0.0455065i
$815$	−25.3205	−	35.7532i	−0.886937	−	1.25238i
$816$	−6.20612	−	2.76314i	−0.217258	−	0.0967293i
$817$	−9.05306	−	10.0544i	−0.316726	−	0.351760i
$818$	7.01189			0.245165
$819$	15.2766	+	2.94425i	0.533806	+	0.102880i
$820$	20.8322	+	48.3575i	0.727494	+	1.68872i
$821$	−8.34979	−	1.77480i	−0.291410	−	0.0619411i	0.0598872	−	0.998205i	$-0.480926\pi$
$821$	−8.34979	−	1.77480i	−0.291410	−	0.0619411i	−0.351297	+	0.936264i	$0.614259\pi$
$822$	−1.02315	+	1.13632i	−0.0356865	+	0.0396339i
$823$	3.04911	−	29.0104i	0.106285	−	1.01124i	−0.803259	−	0.595630i	$-0.796902\pi$
$823$	3.04911	−	29.0104i	0.106285	−	1.01124i	0.909544	−	0.415607i	$-0.136431\pi$
$824$	−1.44238	+	2.49828i	−0.0502478	+	0.0870318i
$825$	7.32067	−	1.37167i	0.254873	−	0.0477554i
$826$	7.26124	−	5.48987i	0.252651	−	0.191017i
$827$	−23.4943	−	17.0696i	−0.816978	−	0.593569i	0.0988675	−	0.995101i	$-0.468478\pi$
$827$	−23.4943	−	17.0696i	−0.816978	−	0.593569i	−0.915845	+	0.401532i	$0.868478\pi$
$828$	−2.84762	−	0.605281i	−0.0989618	−	0.0210350i
$829$	−2.84749	+	3.16245i	−0.0988973	+	0.109837i	−0.790561	−	0.612383i	$-0.790211\pi$
$829$	−2.84749	+	3.16245i	−0.0988973	+	0.109837i	0.691664	+	0.722219i	$0.256878\pi$
$830$	−2.89143	−	4.08278i	−0.100363	−	0.141715i
$831$	19.6967	+	21.8754i	0.683272	+	0.758850i
$832$	37.0691			1.28514
$833$	−0.887375	+	13.2979i	−0.0307457	+	0.460744i
$834$	−0.285658	+	0.207543i	−0.00989154	+	0.00718662i
$835$	−1.88374	−	9.42186i	−0.0651893	−	0.326057i
$836$	1.00157	−	9.52933i	0.0346401	−	0.329579i
$837$	−4.24735	−	1.89104i	−0.146810	−	0.0653640i
$838$	−0.337413	−	3.21027i	−0.0116557	−	0.110897i
$839$	−18.9284	−	13.7523i	−0.653482	−	0.474782i	0.210974	−	0.977492i	$-0.432337\pi$
$839$	−18.9284	−	13.7523i	−0.653482	−	0.474782i	−0.864455	+	0.502709i	$0.832337\pi$
$840$	−6.23231	+	0.698773i	−0.215035	+	0.0241100i
$841$	22.5945	−	16.4159i	0.779122	−	0.566065i
$842$	−6.02421	−	6.69056i	−0.207608	−	0.230572i
$843$	10.6554	+	18.4557i	0.366992	+	0.635648i
$844$	18.6297	−	3.95988i	0.641262	−	0.136305i
$845$	9.45924	+	47.3122i	0.325408	+	1.62759i
$846$	0.539985	+	1.66190i	0.0185651	+	0.0571374i
$847$	−21.0401	+	9.85195i	−0.722947	+	0.338517i
$848$	−26.2064	−	19.0401i	−0.899931	−	0.653838i
$849$	12.8023	−	22.1743i	0.439375	−	0.761021i
$850$	0.206636	+	2.56131i	0.00708757	+	0.0878522i
$851$	−5.99629	−	10.3859i	−0.205550	−	0.356023i
$852$	−16.5057	+	7.34880i	−0.565475	+	0.251766i
$853$	13.9817	+	43.0311i	0.478723	+	1.47336i	0.840870	+	0.541237i	$0.182044\pi$
$853$	13.9817	+	43.0311i	0.478723	+	1.47336i	−0.362148	+	0.932121i	$0.617956\pi$
$854$	−0.139974	+	1.62977i	−0.00478983	+	0.0557695i
$855$	1.64005	−	7.28115i	0.0560885	−	0.249010i
$856$	2.43088	+	2.69976i	0.0830857	+	0.0922761i
$857$	−21.2943	−	36.8828i	−0.727399	−	1.25989i	−0.957979	−	0.286839i	$-0.907396\pi$
$857$	−21.2943	−	36.8828i	−0.727399	−	1.25989i	0.230580	−	0.973053i	$-0.425938\pi$
$858$	2.31274	−	0.491587i	0.0789555	−	0.0167825i
$859$	3.36202	+	31.9875i	0.114711	+	1.09140i	0.888792	+	0.458312i	$0.151546\pi$
$859$	3.36202	+	31.9875i	0.114711	+	1.09140i	−0.774081	+	0.633087i	$0.781788\pi$
$860$	3.83823	−	17.0402i	0.130882	−	0.581065i
$861$	16.6943	+	27.6842i	0.568941	+	0.943474i
$862$	−1.35590	+	0.985121i	−0.0461822	+	0.0335534i
$863$	−3.20588	−	30.5019i	−0.109129	−	1.03830i	−0.902833	−	0.429992i	$-0.858516\pi$
$863$	−3.20588	−	30.5019i	−0.109129	−	1.03830i	0.793703	−	0.608305i	$-0.208150\pi$
$864$	0.322288	−	3.06637i	0.0109645	−	0.104320i
$865$	9.91016	−	13.2985i	0.336956	−	0.452163i
$866$	0.569725	+	5.42057i	0.0193600	+	0.184198i
$867$	4.13313	−	12.7205i	0.140368	−	0.432010i
$868$	2.92640	+	23.5242i	0.0993285	+	0.798463i
$869$	1.29533	−	3.98662i	0.0439412	−	0.135237i
$870$	−0.544859	+	0.305838i	−0.0184724	+	0.0103689i
$871$	−35.2174	+	39.1129i	−1.19330	+	1.32529i
$872$	7.22691	−	8.02629i	0.244734	−	0.271805i
$873$	−4.82918	+	2.15009i	−0.163443	+	0.0727694i
$874$	1.36107			0.0460388
$875$	−16.9707	−	24.2280i	−0.573716	−	0.819054i
$876$	−10.9104			−0.368628
$877$	−20.2194	+	9.00225i	−0.682760	+	0.303984i	−0.718651	−	0.695371i	$-0.755240\pi$
$877$	−20.2194	+	9.00225i	−0.682760	+	0.303984i	0.0358904	+	0.999356i	$0.488573\pi$
$878$	0.789828	−	0.877193i	0.0266554	−	0.0296038i
$879$	−17.5038	+	19.4400i	−0.590389	+	0.655694i
$880$	10.3639	−	5.81744i	0.349368	−	0.196106i
$881$	4.34181	−	13.3627i	0.146279	−	0.450202i	−0.850894	−	0.525337i	$-0.823939\pi$
$881$	4.34181	−	13.3627i	0.146279	−	0.450202i	0.997173	+	0.0751359i	$0.0239391\pi$
$882$	−1.83192	+	0.462945i	−0.0616841	+	0.0155882i
$883$	−4.11155	+	12.6541i	−0.138365	+	0.425843i	−0.996098	−	0.0882519i	$-0.971872\pi$
$883$	−4.11155	+	12.6541i	−0.138365	+	0.425843i	0.857734	+	0.514095i	$0.171872\pi$
$884$	−2.25524	−	21.4571i	−0.0758518	−	0.721682i
$885$	−17.0307	+	22.8536i	−0.572482	+	0.768217i
$886$	−0.511037	+	4.86219i	−0.0171686	+	0.163349i
$887$	−4.22164	−	40.1662i	−0.141749	−	1.34865i	−0.801873	−	0.597494i	$-0.796163\pi$
$887$	−4.22164	−	40.1662i	−0.141749	−	1.34865i	0.660124	−	0.751156i	$-0.270504\pi$
$888$	6.80820	−	4.94645i	0.228468	−	0.165992i
$889$	−14.1016	+	0.268582i	−0.472952	+	0.00900796i
$890$	1.72562	−	7.66106i	0.0578430	−	0.256799i
$891$	0.155707	+	1.48145i	0.00521638	+	0.0496306i
$892$	54.6743	−	11.6214i	1.83063	−	0.389113i
$893$	10.8039	+	18.7128i	0.361537	+	0.626201i
$894$	−1.79069	−	1.98876i	−0.0598895	−	0.0665140i
$895$	11.6700	−	51.8100i	0.390085	−	1.73182i
$896$	−18.8528	+	8.82772i	−0.629826	+	0.294913i
$897$	−2.74501	−	8.44828i	−0.0916533	−	0.282080i
$898$	7.22075	−	3.21488i	0.240960	−	0.107282i
$899$	2.40647	+	4.16813i	0.0802602	+	0.139015i
$900$	8.89496	−	3.70488i	0.296499	−	0.123496i
$901$	−8.64226	+	14.9688i	−0.287915	+	0.498684i
$902$	3.97481	+	2.88787i	0.132347	+	0.0961554i
$903$	0.917695	−	10.6850i	0.0305390	−	0.355576i
$904$	−1.05499	−	3.24694i	−0.0350886	−	0.107992i
$905$	−1.16662	−	5.83509i	−0.0387799	−	0.193965i
$906$	3.30013	−	0.701463i	0.109639	−	0.0233046i
$907$	14.5733	+	25.2417i	0.483898	+	0.838136i	0.999829	−	0.0184945i	$-0.00588730\pi$
$907$	14.5733	+	25.2417i	0.483898	+	0.838136i	−0.515931	+	0.856630i	$0.672554\pi$
$908$	−28.3827	−	31.5221i	−0.941911	−	1.04610i
$909$	−10.2394	+	7.43937i	−0.339620	+	0.246748i
$910$	−5.57207	−	7.55850i	−0.184712	−	0.250562i
$911$	18.8728	+	13.7119i	0.625285	+	0.454296i	0.854764	−	0.519018i	$-0.173702\pi$
$911$	18.8728	+	13.7119i	0.625285	+	0.454296i	−0.229479	+	0.973314i	$0.573702\pi$
$912$	−1.24491	−	11.8445i	−0.0412230	−	0.392211i
$913$	11.2796	+	5.02199i	0.373299	+	0.166204i
$914$	−0.145493	+	1.38428i	−0.00481250	+	0.0457879i
$915$	−1.00410	−	5.02221i	−0.0331946	−	0.166029i
$916$	34.5238	−	25.0830i	1.14070	−	0.828765i
$917$	4.68949	+	0.903806i	0.154861	+	0.0298463i
$918$	−0.513926			−0.0169621
$919$	7.06606	+	7.84766i	0.233088	+	0.258870i	0.848330	−	0.529468i	$-0.177608\pi$
$919$	7.06606	+	7.84766i	0.233088	+	0.258870i	−0.615242	+	0.788338i	$0.710942\pi$
$920$	2.06950	+	2.92219i	0.0682295	+	0.0963418i
$921$	19.3752	−	21.5183i	0.638435	−	0.709053i
$922$	6.80995	+	1.44750i	0.224274	+	0.0476708i
$923$	−44.6009	−	32.4045i	−1.46806	−	1.06661i
$924$	6.05846	−	4.58051i	0.199309	−	0.150688i
$925$	35.8600	+	17.0181i	1.17907	+	0.559551i
$926$	0.156115	−	0.270399i	0.00513026	−	0.00888587i
$927$	0.284457	−	2.70643i	0.00934281	−	0.0888909i
$928$	−2.13571	+	2.37195i	−0.0701082	+	0.0778631i
$929$	−36.1250	−	7.67860i	−1.18522	−	0.251927i	−0.427200	−	0.904157i	$-0.640500\pi$
$929$	−36.1250	−	7.67860i	−1.18522	−	0.251927i	−0.758021	+	0.652230i	$0.773833\pi$
$930$	1.11027	+	2.57726i	0.0364073	+	0.0845117i
$931$	−20.9673	+	10.3092i	−0.687177	+	0.337869i
$932$	−49.1205			−1.60900
$933$	−21.0434	−	23.3711i	−0.688930	−	0.765134i
$934$	−0.785357	−	0.349664i	−0.0256977	−	0.0114413i
$935$	−3.66517	−	5.17532i	−0.119864	−	0.169251i
$936$	5.69448	−	2.53535i	0.186130	−	0.0828704i
$937$	−22.3694	+	16.2523i	−0.730777	+	0.530940i	−0.889809	−	0.456333i	$-0.849163\pi$
$937$	−22.3694	+	16.2523i	−0.730777	+	0.530940i	0.159032	+	0.987273i	$0.449163\pi$
$938$	1.85918	−	6.11587i	0.0607043	−	0.199690i
$939$	27.4039	+	19.9101i	0.894293	+	0.649742i
$940$	−11.6542	+	25.3452i	−0.380117	+	0.826669i
$941$	1.45892	+	0.649551i	0.0475593	+	0.0211748i	0.430378	−	0.902649i	$-0.358380\pi$
$941$	1.45892	+	0.649551i	0.0475593	+	0.0211748i	−0.382819	+	0.923823i	$0.625047\pi$
$942$	−5.68038	+	1.20740i	−0.185077	+	0.0393393i
$943$	9.22929	−	15.9856i	0.300547	−	0.520563i
$944$	−14.0542	+	43.2544i	−0.457425	+	1.40781i
$945$	5.10284	−	2.99350i	0.165995	−	0.0973785i
$946$	−0.503652	−	1.55008i	−0.0163751	−	0.0503975i
$947$	26.7239	+	5.68033i	0.868409	+	0.184586i	0.620509	−	0.784199i	$-0.286926\pi$
$947$	26.7239	+	5.68033i	0.868409	+	0.184586i	0.247900	+	0.968786i	$0.420259\pi$
$948$	0.566856	−	5.39327i	0.0184106	−	0.175165i
$949$	−16.6454	−	28.8306i	−0.540332	−	0.935882i
$950$	−3.70758	+	2.55887i	−0.120290	+	0.0830208i
$951$	−0.328423			−0.0106499
$952$	2.75748	+	4.57273i	0.0893705	+	0.148203i
$953$	0.911808	+	2.80626i	0.0295364	+	0.0909036i	0.964738	−	0.263212i	$-0.0847819\pi$
$953$	0.911808	+	2.80626i	0.0295364	+	0.0909036i	−0.935202	+	0.354116i	$0.884782\pi$
$954$	−2.39698	−	0.509494i	−0.0776052	−	0.0164955i
$955$	19.8088	+	27.9706i	0.640999	+	0.905107i
$956$	−4.35689	+	0.926087i	−0.140912	+	0.0299518i
$957$	0.771021	−	1.33545i	0.0249236	−	0.0431689i
$958$	1.29398	−	3.98246i	0.0418066	−	0.128667i
$959$	−14.5979	+	3.39465i	−0.471390	+	0.109619i
$960$	10.5889	−	9.30465i	0.341757	−	0.300306i
$961$	−8.57269	+	3.81681i	−0.276538	+	0.123123i
$962$	11.5113	+	5.12517i	0.371140	+	0.165242i
$963$	−3.13079	−	1.39392i	−0.100888	−	0.0449184i
$964$	−24.8098	+	11.0460i	−0.799069	+	0.355768i
$965$	−26.4576	−	15.7055i	−0.851699	−	0.505577i
$966$	0.737038	+	0.787860i	0.0237138	+	0.0253490i
$967$	−11.3302	+	34.8709i	−0.364356	+	1.12137i	0.586027	+	0.810291i	$0.300691\pi$
$967$	−11.3302	+	34.8709i	−0.364356	+	1.12137i	−0.950383	+	0.311081i	$0.899309\pi$
$968$	−4.65420	+	8.06130i	−0.149592	+	0.259100i
$969$	−6.21605	+	1.32126i	−0.199688	+	0.0424451i
$970$	3.02233	+	1.02264i	0.0970412	+	0.0328349i
$971$	48.7224	+	10.3563i	1.56358	+	0.332348i	0.906741	−	0.421687i	$-0.138562\pi$
$971$	48.7224	+	10.3563i	1.56358	+	0.332348i	0.656834	+	0.754035i	$0.271895\pi$
$972$	0.595518	+	1.83282i	0.0191013	+	0.0587876i
$973$	−3.46025	+	0.0659047i	−0.110930	+	0.00211281i
$974$	1.40458			0.0450055
$975$	23.3607	+	17.8526i	0.748140	+	0.571740i
$976$	−4.08632	−	7.07771i	−0.130800	−	0.226552i
$977$	−1.50092	+	14.2803i	−0.0480188	+	0.456869i	0.943922	+	0.330168i	$0.107105\pi$
$977$	−1.50092	+	14.2803i	−0.0480188	+	0.456869i	−0.991941	+	0.126701i	$0.959561\pi$
$978$	−5.17316	−	1.09959i	−0.165419	−	0.0351610i
$979$	5.98901	+	18.4323i	0.191409	+	0.589098i
$980$	−26.5062	−	14.3986i	−0.846708	−	0.459946i
$981$	−3.14844	+	9.68991i	−0.100522	+	0.309375i
$982$	−3.08995	+	5.35195i	−0.0986043	+	0.170788i
$983$	54.6410	−	11.6143i	1.74278	−	0.370438i	0.776936	−	0.629579i	$-0.216773\pi$
$983$	54.6410	−	11.6143i	1.74278	−	0.370438i	0.965840	+	0.259141i	$0.0834394\pi$
$984$	11.8329	+	5.26834i	0.377219	+	0.167949i
$985$	14.0888	+	12.9979i	0.448906	+	0.414149i
$986$	0.430409	+	0.312710i	0.0137070	+	0.00995872i
$987$	−4.98156	+	16.3871i	−0.158565	+	0.521609i
$988$	30.6005	−	22.2325i	0.973531	−	0.707312i
$989$	−5.59395	+	2.49059i	−0.177877	+	0.0791960i
$990$	0.537250	−	0.720939i	0.0170749	−	0.0229129i
$991$	−10.0797	−	4.48778i	−0.320193	−	0.142559i	0.240346	−	0.970687i	$-0.422739\pi$
$991$	−10.0797	−	4.48778i	−0.320193	−	0.142559i	−0.560539	+	0.828128i	$0.689406\pi$
$992$	9.59198	+	10.6530i	0.304546	+	0.338232i
$993$	−19.6844			−0.624665
$994$	6.57463	+	1.26713i	0.208535	+	0.0401909i
$995$	4.13786	+	2.45628i	0.131179	+	0.0778692i
$996$	15.6245	+	3.32109i	0.495081	+	0.105233i
$997$	−8.40846	+	9.33854i	−0.266299	+	0.295755i	−0.861433	−	0.507872i	$-0.830432\pi$
$997$	−8.40846	+	9.33854i	−0.266299	+	0.295755i	0.595134	+	0.803627i	$0.297099\pi$
$998$	0.591084	−	5.62379i	0.0187104	−	0.178018i
$999$	−3.96933	+	6.87508i	−0.125584	+	0.217518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.16.12	✓	160
7.4	even	3	inner	525.2.bg.a.466.9	yes	160
25.11	even	5	inner	525.2.bg.a.436.9	yes	160
175.11	even	15	inner	525.2.bg.a.361.12	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.12	✓	160	1.1	even	1	trivial
525.2.bg.a.361.12	yes	160	175.11	even	15	inner
525.2.bg.a.436.9	yes	160	25.11	even	5	inner
525.2.bg.a.466.9	yes	160	7.4	even	3	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.246594 - 0.109791i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.28951 + 1.43214i) q^{4} +(-1.94989 + 1.09450i) q^{5} +(-0.0834131 + 0.256719i) q^{6} +(-2.11046 + 1.59561i) q^{7} +(-0.327575 + 1.00817i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.246594 - 0.109791i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.28951 + 1.43214i) q^{4} +(-1.94989 + 1.09450i) q^{5} +(-0.0834131 + 0.256719i) q^{6} +(-2.11046 + 1.59561i) q^{7} +(-0.327575 + 1.00817i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.360664 + 0.483977i) q^{10} +(0.155707 - 1.48145i) q^{11} +(-0.201441 - 1.91658i) q^{12} +(4.75723 - 3.45633i) q^{13} +(-0.345242 + 0.625176i) q^{14} +(0.491355 - 2.18141i) q^{15} +(-0.372972 - 3.54859i) q^{16} +(-1.86232 + 0.395847i) q^{17} +(-0.134965 - 0.233767i) q^{18} +(-2.23343 - 2.48048i) q^{19} +(0.946908 - 4.20389i) q^{20} +(0.226400 - 2.63605i) q^{21} +(-0.124253 - 0.382412i) q^{22} +(-1.38005 + 0.614439i) q^{23} +(-0.530027 - 0.918034i) q^{24} +(2.60412 - 4.26832i) q^{25} +(0.793630 - 1.37461i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.436303 - 5.08002i) q^{28} +(-0.319893 - 0.984530i) q^{29} +(-0.118334 - 0.591870i) q^{30} +(-4.54770 + 0.966644i) q^{31} +(-1.54163 - 2.67018i) q^{32} +(0.996746 + 1.10700i) q^{33} +(-0.415775 + 0.302078i) q^{34} +(2.36875 - 5.42117i) q^{35} +(1.55909 + 1.13274i) q^{36} +(0.829815 + 7.89516i) q^{37} +(-0.823083 - 0.366460i) q^{38} +(-0.614654 + 5.84804i) q^{39} +(-0.464713 - 2.32435i) q^{40} +(-9.88531 + 7.18210i) q^{41} +(-0.233585 - 0.674889i) q^{42} +4.05343 q^{43} +(1.92087 + 2.13334i) q^{44} +(1.29233 + 1.82480i) q^{45} +(-0.272853 + 0.303034i) q^{46} +(-6.33216 - 1.34594i) q^{47} +(2.88668 + 2.09730i) q^{48} +(1.90805 - 6.73494i) q^{49} +(0.173539 - 1.33845i) q^{50} +(0.951960 - 1.64884i) q^{51} +(-1.18452 + 11.2700i) q^{52} +(6.07462 - 6.74655i) q^{53} +(0.264032 + 0.0561217i) q^{54} +(1.31784 + 3.05909i) q^{55} +(-0.917318 - 2.65038i) q^{56} +3.33781 q^{57} +(-0.186976 - 0.207658i) q^{58} +(-11.6443 - 5.18437i) q^{59} +(2.49049 + 3.51664i) q^{60} +(2.09243 - 0.931610i) q^{61} +(-1.01531 + 0.737664i) q^{62} +(1.80747 + 1.93211i) q^{63} +(5.10005 + 3.70540i) q^{64} +(-5.49309 + 11.9463i) q^{65} +(0.367330 + 0.163546i) q^{66} +(-8.75498 + 1.86093i) q^{67} +(1.83456 - 3.17755i) q^{68} +(0.466818 - 1.43672i) q^{69} +(-0.0110745 - 1.59689i) q^{70} +(-2.89716 - 8.91654i) q^{71} +(1.03689 + 0.220398i) q^{72} +(0.591782 - 5.63043i) q^{73} +(1.07144 + 1.85579i) q^{74} +(1.42948 + 4.79130i) q^{75} +6.43242 q^{76} +(2.03521 + 3.37499i) q^{77} +(0.490490 + 1.50957i) q^{78} +(2.75252 + 0.585065i) q^{79} +(4.61119 + 6.51113i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-1.64913 + 2.85638i) q^{82} +(-2.56136 + 7.88306i) q^{83} +(3.48325 + 3.72344i) q^{84} +(3.19805 - 2.81017i) q^{85} +(0.999551 - 0.445029i) q^{86} +(0.945698 + 0.421052i) q^{87} +(1.44255 + 0.642266i) q^{88} +(-11.8858 + 5.29190i) q^{89} +(0.519026 + 0.308099i) q^{90} +(-4.52496 + 14.8851i) q^{91} +(0.899623 - 2.76876i) q^{92} +(2.32465 - 4.02641i) q^{93} +(-1.70924 + 0.363311i) q^{94} +(7.06983 + 2.39215i) q^{95} +(3.01588 + 0.641045i) q^{96} +(-1.63352 - 5.02747i) q^{97} +(-0.268921 - 1.87028i) q^{98} -1.48961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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