LMFDB - Embedded newform 525.2.z.b.169.2

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			169.2
Character	$\chi$	$=$	525.169
Dual form			525.2.z.b.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47820 + 0.805216i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.87506 - 2.81540i) q^{4} +(1.64699 - 1.51242i) q^{5} +(2.10808 + 1.53161i) q^{6} -1.00000i q^{7} +(-4.27295 + 5.88121i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-2.47820 + 0.805216i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.87506 - 2.81540i) q^{4} +(1.64699 - 1.51242i) q^{5} +(2.10808 + 1.53161i) q^{6} -1.00000i q^{7} +(-4.27295 + 5.88121i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-2.86374 + 5.07427i) q^{10} +(1.87192 + 5.76118i) q^{11} +(-4.55541 - 1.48014i) q^{12} +(0.849893 + 0.276147i) q^{13} +(0.805216 + 2.47820i) q^{14} +(-2.19165 - 0.443462i) q^{15} +(2.89329 - 8.90464i) q^{16} +(-4.31197 + 5.93491i) q^{17} -2.60573i q^{18} +(4.29544 + 3.12082i) q^{19} +(2.12411 - 10.4977i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-9.27798 - 12.7700i) q^{22} +(4.01197 - 1.30357i) q^{23} +7.26958 q^{24} +(0.425146 - 4.98189i) q^{25} -2.32856 q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.81540 - 3.87506i) q^{28} +(-0.549000 + 0.398872i) q^{29} +(5.78843 - 0.665767i) q^{30} +(-0.525312 - 0.381661i) q^{31} +9.85803i q^{32} +(3.56060 - 4.90075i) q^{33} +(5.90703 - 18.1800i) q^{34} +(-1.51242 - 1.64699i) q^{35} +(1.48014 + 4.55541i) q^{36} +(5.90789 + 1.91959i) q^{37} +(-13.1579 - 4.27526i) q^{38} +(-0.276147 - 0.849893i) q^{39} +(1.85738 + 16.1488i) q^{40} +(-0.370998 + 1.14182i) q^{41} +(1.53161 - 2.10808i) q^{42} +5.67954i q^{43} +(23.4738 + 17.0547i) q^{44} +(0.929453 + 2.03374i) q^{45} +(-8.89280 + 6.46100i) q^{46} +(-4.12054 - 5.67143i) q^{47} +(-8.90464 + 2.89329i) q^{48} -1.00000 q^{49} +(2.95790 + 12.6885i) q^{50} +7.33596 q^{51} +(4.07085 - 1.32270i) q^{52} +(7.30230 + 10.0508i) q^{53} +(-2.10808 + 1.53161i) q^{54} +(11.7964 + 6.65746i) q^{55} +(5.88121 + 4.27295i) q^{56} -5.30946i q^{57} +(1.03935 - 1.43055i) q^{58} +(1.11715 - 3.43822i) q^{59} +(-9.74131 + 4.45193i) q^{60} +(0.488353 + 1.50300i) q^{61} +(1.60915 + 0.522843i) q^{62} +(0.951057 + 0.309017i) q^{63} +(-2.15126 - 6.62089i) q^{64} +(1.81742 - 0.830587i) q^{65} +(-4.87772 + 15.0121i) q^{66} +(3.20047 - 4.40506i) q^{67} +35.1381i q^{68} +(-3.41278 - 2.47953i) q^{69} +(5.07427 + 2.86374i) q^{70} +(4.32469 - 3.14207i) q^{71} +(-4.27295 - 5.88121i) q^{72} +(-13.3801 + 4.34747i) q^{73} -16.1866 q^{74} +(-4.28033 + 2.58433i) q^{75} +25.4315 q^{76} +(5.76118 - 1.87192i) q^{77} +(1.36869 + 1.88385i) q^{78} +(8.61771 - 6.26113i) q^{79} +(-8.70237 - 19.0417i) q^{80} +(-0.809017 - 0.587785i) q^{81} -3.12838i q^{82} +(-0.102448 + 0.141008i) q^{83} +(-1.48014 + 4.55541i) q^{84} +(1.87434 + 16.2963i) q^{85} +(-4.57325 - 14.0750i) q^{86} +(0.645388 + 0.209699i) q^{87} +(-41.8813 - 13.6081i) q^{88} +(-5.00533 - 15.4048i) q^{89} +(-3.94097 - 4.29161i) q^{90} +(0.276147 - 0.849893i) q^{91} +(11.8766 - 16.3467i) q^{92} +0.649321i q^{93} +(14.7782 + 10.7370i) q^{94} +(11.7945 - 1.35657i) q^{95} +(7.97532 - 5.79441i) q^{96} +(3.19971 + 4.40403i) q^{97} +(2.47820 - 0.805216i) q^{98} -6.05766 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 $

$2$	−2.47820	+	0.805216i	−1.75235	+	0.569373i	−0.996363	−	0.0852118i	$-0.972843\pi$
$2$	−2.47820	+	0.805216i	−1.75235	+	0.569373i	−0.755988	+	0.654585i	$0.772843\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	3.87506	−	2.81540i	1.93753	−	1.40770i
$5$	1.64699	−	1.51242i	0.736556	−	0.676377i
$5$	1.64699	−	1.51242i	0.736556	−	0.676377i
$6$	2.10808	+	1.53161i	0.860621	+	0.625278i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−4.27295	+	5.88121i	−1.51072	+	2.07932i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−2.86374	+	5.07427i	−0.905594	+	1.60462i
$11$	1.87192	+	5.76118i	0.564405	+	1.73706i	0.669712	+	0.742621i	$0.266418\pi$
$11$	1.87192	+	5.76118i	0.564405	+	1.73706i	−0.105307	+	0.994440i	$0.533582\pi$
$12$	−4.55541	−	1.48014i	−1.31503	−	0.427280i
$13$	0.849893	+	0.276147i	0.235718	+	0.0765894i	0.424494	−	0.905431i	$-0.360452\pi$
$13$	0.849893	+	0.276147i	0.235718	+	0.0765894i	−0.188776	+	0.982020i	$0.560452\pi$
$14$	0.805216	+	2.47820i	0.215203	+	0.662326i
$15$	−2.19165	−	0.443462i	−0.565882	−	0.114501i
$16$	2.89329	−	8.90464i	0.723323	−	2.22616i
$17$	−4.31197	+	5.93491i	−1.04581	+	1.43943i	−0.153416	+	0.988162i	$0.549028\pi$
$17$	−4.31197	+	5.93491i	−1.04581	+	1.43943i	−0.892389	+	0.451266i	$0.850972\pi$
$18$		−	2.60573i		−	0.614177i
$19$	4.29544	+	3.12082i	0.985442	+	0.715965i	0.958918	−	0.283683i	$-0.0915563\pi$
$19$	4.29544	+	3.12082i	0.985442	+	0.715965i	0.0265235	+	0.999648i	$0.491556\pi$
$20$	2.12411	−	10.4977i	0.474965	−	2.34735i
$21$	−0.809017	+	0.587785i	−0.176542	+	0.128265i
$22$	−9.27798	−	12.7700i	−1.97807	−	2.72258i
$23$	4.01197	−	1.30357i	0.836553	−	0.271813i	0.140750	−	0.990045i	$-0.455049\pi$
$23$	4.01197	−	1.30357i	0.836553	−	0.271813i	0.695803	+	0.718233i	$0.255049\pi$
$24$	7.26958			1.48390
$25$	0.425146	−	4.98189i	0.0850292	−	0.996378i
$26$	−2.32856			−0.456668
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−2.81540	−	3.87506i	−0.532060	−	0.732318i
$29$	−0.549000	+	0.398872i	−0.101947	+	0.0740687i	−0.637591	−	0.770375i	$-0.720069\pi$
$29$	−0.549000	+	0.398872i	−0.101947	+	0.0740687i	0.535644	+	0.844444i	$0.320069\pi$
$30$	5.78843	−	0.665767i	1.05682	−	0.121552i
$31$	−0.525312	−	0.381661i	−0.0943488	−	0.0685484i	0.539611	−	0.841915i	$-0.318571\pi$
$31$	−0.525312	−	0.381661i	−0.0943488	−	0.0685484i	−0.633960	+	0.773366i	$0.718571\pi$
$32$			9.85803i			1.74267i
$33$	3.56060	−	4.90075i	0.619822	−	0.853111i
$34$	5.90703	−	18.1800i	1.01305	−	3.11784i
$35$	−1.51242	−	1.64699i	−0.255646	−	0.278392i
$36$	1.48014	+	4.55541i	0.246690	+	0.759235i
$37$	5.90789	+	1.91959i	0.971252	+	0.315579i	0.751321	−	0.659937i	$-0.229417\pi$
$37$	5.90789	+	1.91959i	0.971252	+	0.315579i	0.219930	+	0.975516i	$0.429417\pi$
$38$	−13.1579	−	4.27526i	−2.13449	−	0.693538i
$39$	−0.276147	−	0.849893i	−0.0442189	−	0.136092i
$40$	1.85738	+	16.1488i	0.293678	+	2.55335i
$41$	−0.370998	+	1.14182i	−0.0579402	+	0.178322i	−0.975838	−	0.218495i	$-0.929885\pi$
$41$	−0.370998	+	1.14182i	−0.0579402	+	0.178322i	0.917898	+	0.396817i	$0.129885\pi$
$42$	1.53161	−	2.10808i	0.236333	−	0.325284i
$43$			5.67954i			0.866122i	0.901365	+	0.433061i	$0.142566\pi$
$43$			5.67954i			0.866122i	−0.901365	+	0.433061i	$0.857434\pi$
$44$	23.4738	+	17.0547i	3.53881	+	2.57110i
$45$	0.929453	+	2.03374i	0.138555	+	0.303173i
$46$	−8.89280	+	6.46100i	−1.31117	+	0.952622i
$47$	−4.12054	−	5.67143i	−0.601042	−	0.827263i	0.394761	−	0.918784i	$-0.370827\pi$
$47$	−4.12054	−	5.67143i	−0.601042	−	0.827263i	−0.995803	+	0.0915203i	$0.970827\pi$
$48$	−8.90464	+	2.89329i	−1.28527	+	0.417611i
$49$	−1.00000			−0.142857
$50$	2.95790	+	12.6885i	0.418310	+	1.79442i
$51$	7.33596			1.02724
$52$	4.07085	−	1.32270i	0.564525	−	0.183425i
$53$	7.30230	+	10.0508i	1.00305	+	1.38058i	0.923436	+	0.383752i	$0.125368\pi$
$53$	7.30230	+	10.0508i	1.00305	+	1.38058i	0.0796124	+	0.996826i	$0.474632\pi$
$54$	−2.10808	+	1.53161i	−0.286874	+	0.208426i
$55$	11.7964	+	6.65746i	1.59062	+	0.897692i
$56$	5.88121	+	4.27295i	0.785910	+	0.570997i
$57$		−	5.30946i		−	0.703255i
$58$	1.03935	−	1.43055i	0.136474	−	0.187840i
$59$	1.11715	−	3.43822i	0.145440	−	0.447618i	−0.851627	−	0.524148i	$-0.824384\pi$
$59$	1.11715	−	3.43822i	0.145440	−	0.447618i	0.997067	+	0.0765297i	$0.0243840\pi$
$60$	−9.74131	+	4.45193i	−1.25760	+	0.574742i
$61$	0.488353	+	1.50300i	0.0625272	+	0.192439i	0.977440	−	0.211212i	$-0.0677410\pi$
$61$	0.488353	+	1.50300i	0.0625272	+	0.192439i	−0.914913	+	0.403651i	$0.867741\pi$
$62$	1.60915	+	0.522843i	0.204362	+	0.0664012i
$63$	0.951057	+	0.309017i	0.119822	+	0.0389325i
$64$	−2.15126	−	6.62089i	−0.268907	−	0.827611i
$65$	1.81742	−	0.830587i	0.225423	−	0.103022i
$66$	−4.87772	+	15.0121i	−0.600406	+	1.84786i
$67$	3.20047	−	4.40506i	0.390999	−	0.538164i	−0.567457	−	0.823403i	$-0.692073\pi$
$67$	3.20047	−	4.40506i	0.390999	−	0.538164i	0.958457	+	0.285239i	$0.0920728\pi$
$68$			35.1381i			4.26112i
$69$	−3.41278	−	2.47953i	−0.410851	−	0.298501i
$70$	5.07427	+	2.86374i	0.606491	+	0.342282i
$71$	4.32469	−	3.14207i	0.513246	−	0.372895i	−0.300807	−	0.953685i	$-0.597256\pi$
$71$	4.32469	−	3.14207i	0.513246	−	0.372895i	0.814054	+	0.580790i	$0.197256\pi$
$72$	−4.27295	−	5.88121i	−0.503572	−	0.693107i
$73$	−13.3801	+	4.34747i	−1.56603	+	0.508833i	−0.958410	−	0.285397i	$-0.907875\pi$
$73$	−13.3801	+	4.34747i	−1.56603	+	0.508833i	−0.607618	+	0.794230i	$0.707875\pi$
$74$	−16.1866			−1.88166
$75$	−4.28033	+	2.58433i	−0.494250	+	0.298413i
$76$	25.4315			2.91719
$77$	5.76118	−	1.87192i	0.656547	−	0.213325i
$78$	1.36869	+	1.88385i	0.154974	+	0.213303i
$79$	8.61771	−	6.26113i	0.969568	−	0.704432i	0.0142149	−	0.999899i	$-0.495475\pi$
$79$	8.61771	−	6.26113i	0.969568	−	0.704432i	0.955353	+	0.295467i	$0.0954751\pi$
$80$	−8.70237	−	19.0417i	−0.972955	−	2.12893i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		−	3.12838i		−	0.345472i
$83$	−0.102448	+	0.141008i	−0.0112451	+	0.0154776i	−0.814603	−	0.580020i	$-0.803045\pi$
$83$	−0.102448	+	0.141008i	−0.0112451	+	0.0154776i	0.803357	+	0.595497i	$0.203045\pi$
$84$	−1.48014	+	4.55541i	−0.161497	+	0.497036i
$85$	1.87434	+	16.2963i	0.203301	+	1.76758i
$86$	−4.57325	−	14.0750i	−0.493147	−	1.51775i
$87$	0.645388	+	0.209699i	0.0691929	+	0.0224821i
$88$	−41.8813	−	13.6081i	−4.46457	−	1.45063i
$89$	−5.00533	−	15.4048i	−0.530564	−	1.63291i	−0.753044	−	0.657971i	$-0.771415\pi$
$89$	−5.00533	−	15.4048i	−0.530564	−	1.63291i	0.222480	−	0.974937i	$-0.428585\pi$
$90$	−3.94097	−	4.29161i	−0.415415	−	0.452376i
$91$	0.276147	−	0.849893i	0.0289481	−	0.0890930i
$92$	11.8766	−	16.3467i	1.23822	−	1.70426i
$93$			0.649321i			0.0673315i
$94$	14.7782	+	10.7370i	1.52426	+	1.10744i
$95$	11.7945	−	1.35657i	1.21010	−	0.139181i
$96$	7.97532	−	5.79441i	0.813977	−	0.591389i
$97$	3.19971	+	4.40403i	0.324882	+	0.447161i	0.939950	−	0.341313i	$-0.110872\pi$
$97$	3.19971	+	4.40403i	0.324882	+	0.447161i	−0.615068	+	0.788474i	$0.710872\pi$
$98$	2.47820	−	0.805216i	0.250336	−	0.0813391i
$99$	−6.05766			−0.608818
$100$	−12.3785	−	20.5021i	−1.23785	−	2.05021i
$101$	2.83084			0.281679			0.140839	−	0.990032i	$-0.455020\pi$
$101$	2.83084			0.281679			0.140839	+	0.990032i	$0.455020\pi$
$102$	−18.1800	+	5.90703i	−1.80008	+	0.584883i
$103$	3.41268	+	4.69715i	0.336261	+	0.462824i	0.943345	−	0.331814i	$-0.107661\pi$
$103$	3.41268	+	4.69715i	0.336261	+	0.462824i	−0.607084	+	0.794638i	$0.707661\pi$
$104$	−5.25563	+	3.81844i	−0.515357	+	0.374429i
$105$	−0.443462	+	2.19165i	−0.0432774	+	0.213883i
$106$	−26.1896	−	19.0278i	−2.54376	−	1.84815i
$107$		−	17.8695i		−	1.72751i	−0.503913	−	0.863754i	$-0.668107\pi$
$107$		−	17.8695i		−	1.72751i	0.503913	−	0.863754i	$-0.331893\pi$
$108$	2.81540	−	3.87506i	0.270912	−	0.372878i
$109$	−2.98953	+	9.20083i	−0.286345	+	0.881279i	0.699647	+	0.714488i	$0.253341\pi$
$109$	−2.98953	+	9.20083i	−0.286345	+	0.881279i	−0.985992	+	0.166791i	$0.946659\pi$
$110$	−34.5945	−	6.99988i	−3.29845	−	0.667413i
$111$	−1.91959	−	5.90789i	−0.182199	−	0.560752i
$112$	−8.90464	−	2.89329i	−0.841409	−	0.273390i
$113$	5.20317	+	1.69061i	0.489473	+	0.159040i	0.543347	−	0.839508i	$-0.317157\pi$
$113$	5.20317	+	1.69061i	0.489473	+	0.159040i	−0.0538736	+	0.998548i	$0.517157\pi$
$114$	4.27526	+	13.1579i	0.400415	+	1.23235i
$115$	4.63612	−	8.21476i	0.432320	−	0.766030i
$116$	−1.00443	+	3.09131i	−0.0932587	+	0.287021i
$117$	−0.525263	+	0.722962i	−0.0485605	+	0.0668379i
$118$			9.42013i			0.867193i
$119$	5.93491	+	4.31197i	0.544053	+	0.395277i
$120$	11.9729	−	10.9947i	1.09297	−	1.00367i
$121$	−20.7879	+	15.1033i	−1.88981	+	1.37303i
$122$	−2.42047	−	3.33149i	−0.219139	−	0.301619i
$123$	1.14182	−	0.370998i	0.102954	−	0.0334518i
$124$	−3.11014			−0.279299
$125$	−6.83452	−	8.84812i	−0.611298	−	0.791400i
$126$	−2.60573			−0.232137
$127$	14.9758	−	4.86592i	1.32888	−	0.431781i	0.443348	−	0.896350i	$-0.353791\pi$
$127$	14.9758	−	4.86592i	1.32888	−	0.431781i	0.885537	+	0.464569i	$0.153791\pi$
$128$	−0.926329	−	1.27498i	−0.0818767	−	0.112694i
$129$	4.59484	−	3.33835i	0.404553	−	0.293925i
$130$	−3.83511	+	3.52177i	−0.336362	+	0.308880i
$131$	7.16334	+	5.20447i	0.625864	+	0.454717i	0.854965	−	0.518686i	$-0.173579\pi$
$131$	7.16334	+	5.20447i	0.625864	+	0.454717i	−0.229101	+	0.973403i	$0.573579\pi$
$132$		−	29.0152i		−	2.52545i
$133$	3.12082	−	4.29544i	0.270609	−	0.372462i
$134$	−4.38436	+	13.4937i	−0.378751	+	1.16568i
$135$	1.09901	−	1.94735i	0.0945881	−	0.167601i
$136$	−16.4797	−	50.7192i	−1.41312	−	4.34913i
$137$	7.26956	+	2.36202i	0.621080	+	0.201801i	0.602620	−	0.798028i	$-0.294124\pi$
$137$	7.26956	+	2.36202i	0.621080	+	0.201801i	0.0184604	+	0.999830i	$0.494124\pi$
$138$	10.4541	+	3.39675i	0.889913	+	0.289150i
$139$	−4.41355	−	13.5835i	−0.374352	−	1.15214i	−0.943914	−	0.330190i	$-0.892887\pi$
$139$	−4.41355	−	13.5835i	−0.374352	−	1.15214i	0.569562	−	0.821948i	$-0.307113\pi$
$140$	−10.4977	−	2.12411i	−0.887215	−	0.179520i
$141$	−2.16629	+	6.66717i	−0.182435	+	0.561477i
$142$	−8.18740	+	11.2690i	−0.687071	+	0.945672i
$143$			5.41331i			0.452684i
$144$	7.57474	+	5.50337i	0.631228	+	0.458614i
$145$	−0.300934	+	1.48726i	−0.0249912	+	0.123510i
$146$	29.6580	−	21.5478i	2.45451	−	1.78331i
$147$	0.587785	+	0.809017i	0.0484797	+	0.0667266i
$148$	28.2979	−	9.19453i	2.32607	−	0.755786i
$149$	−16.8759			−1.38253			−0.691264	−	0.722603i	$-0.742946\pi$
$149$	−16.8759			−1.38253			−0.691264	+	0.722603i	$0.742946\pi$
$150$	8.52656	−	9.85108i	0.696191	−	0.804337i
$151$	3.34966			0.272591			0.136296	−	0.990668i	$-0.456480\pi$
$151$	3.34966			0.272591			0.136296	+	0.990668i	$0.456480\pi$
$152$	−36.7084	+	11.9273i	−2.97745	+	0.967431i
$153$	−4.31197	−	5.93491i	−0.348602	−	0.479809i
$154$	−12.7700	+	9.27798i	−1.02904	+	0.747641i
$155$	−1.44242	+	0.165902i	−0.115858	+	0.0133256i
$156$	−3.46287	−	2.51592i	−0.277252	−	0.201435i
$157$			19.7534i			1.57649i	0.615362	+	0.788245i	$0.289010\pi$
$157$			19.7534i			1.57649i	−0.615362	+	0.788245i	$0.710990\pi$
$158$	−16.3148	+	22.4554i	−1.29794	+	1.78646i
$159$	3.83905	−	11.8154i	0.304456	−	0.937020i
$160$	14.9095	+	16.2361i	1.17870	+	1.28357i
$161$	−1.30357	−	4.01197i	−0.102736	−	0.316187i
$162$	2.47820	+	0.805216i	0.194706	+	0.0632637i
$163$	12.5048	+	4.06304i	0.979448	+	0.318242i	0.754624	−	0.656157i	$-0.227819\pi$
$163$	12.5048	+	4.06304i	0.979448	+	0.318242i	0.224824	+	0.974399i	$0.427819\pi$
$164$	1.77702	+	5.46912i	0.138762	+	0.427066i
$165$	−1.54774	−	13.4566i	−0.120491	−	1.04760i
$166$	0.140345	−	0.431938i	0.0108929	−	0.0335249i
$167$	−3.66762	+	5.04804i	−0.283809	+	0.390629i	−0.926991	−	0.375084i	$-0.877614\pi$
$167$	−3.66762	+	5.04804i	−0.283809	+	0.390629i	0.643182	+	0.765713i	$0.277614\pi$
$168$		−	7.26958i		−	0.560860i
$169$	−9.87116	−	7.17182i	−0.759320	−	0.551678i
$170$	−17.7670	−	38.8761i	−1.36267	−	2.98166i
$171$	−4.29544	+	3.12082i	−0.328481	+	0.238655i
$172$	15.9902	+	22.0086i	1.21924	+	1.67814i
$173$	20.8162	−	6.76358i	1.58262	−	0.514226i	0.619893	−	0.784687i	$-0.287176\pi$
$173$	20.8162	−	6.76358i	1.58262	−	0.514226i	0.962731	+	0.270461i	$0.0871761\pi$
$174$	−1.76825			−0.134051
$175$	−4.98189	−	0.425146i	−0.376596	−	0.0321380i
$176$	56.7172			4.27522
$177$	−3.43822	+	1.11715i	−0.258432	+	0.0839698i
$178$	24.8084	+	34.1458i	1.85947	+	2.55934i
$179$	−10.3070	+	7.48850i	−0.770384	+	0.559717i	−0.902078	−	0.431574i	$-0.857959\pi$
$179$	−10.3070	+	7.48850i	−0.770384	+	0.559717i	0.131694	+	0.991290i	$0.457959\pi$
$180$	9.32749	+	5.26411i	0.695230	+	0.392363i
$181$	0.931053	+	0.676450i	0.0692047	+	0.0502801i	0.621850	−	0.783137i	$-0.286381\pi$
$181$	0.931053	+	0.676450i	0.0692047	+	0.0502801i	−0.552645	+	0.833417i	$0.686381\pi$
$182$			2.32856i			0.172604i
$183$	0.928903	−	1.27853i	0.0686665	−	0.0945113i
$184$	−9.47638	+	29.1653i	−0.698608	+	2.15010i
$185$	12.6335	−	5.77370i	0.928831	−	0.424491i
$186$	−0.522843	−	1.60915i	−0.0383367	−	0.117988i
$187$	−42.2638	−	13.7323i	−3.09063	−	1.00421i
$188$	−31.9347	−	10.3762i	−2.32908	−	0.756763i
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	−28.1369	+	12.8590i	−2.04127	+	0.932890i
$191$	1.10923	−	3.41387i	0.0802613	−	0.247019i	−0.902872	−	0.429910i	$-0.858545\pi$
$191$	1.10923	−	3.41387i	0.0802613	−	0.247019i	0.983133	+	0.182891i	$0.0585454\pi$
$192$	−4.09193	+	5.63206i	−0.295310	+	0.406459i
$193$		−	3.37691i		−	0.243075i	−0.992587	−	0.121538i	$-0.961217\pi$
$193$		−	3.37691i		−	0.243075i	0.992587	−	0.121538i	$-0.0387825\pi$
$194$	−11.4757	−	8.33759i	−0.823908	−	0.598604i
$195$	−1.74021	−	0.982113i	−0.124619	−	0.0703306i
$196$	−3.87506	+	2.81540i	−0.276790	+	0.201100i
$197$	−1.42113	−	1.95601i	−0.101251	−	0.139360i	0.755385	−	0.655281i	$-0.227450\pi$
$197$	−1.42113	−	1.95601i	−0.101251	−	0.139360i	−0.856636	+	0.515921i	$0.827450\pi$
$198$	15.0121	−	4.87772i	1.06686	−	0.346645i
$199$	−16.6370			−1.17937			−0.589683	−	0.807635i	$-0.700747\pi$
$199$	−16.6370			−1.17937			−0.589683	+	0.807635i	$0.700747\pi$
$200$	27.4829	+	23.7878i	1.94334	+	1.68205i
$201$	−5.44496			−0.384058
$202$	−7.01537	+	2.27943i	−0.493600	+	0.160380i
$203$	0.398872	+	0.549000i	0.0279953	+	0.0385323i
$204$	28.4273	−	20.6536i	1.99031	−	1.44604i
$205$	1.11588	+	2.44166i	0.0779364	+	0.170533i
$206$	−12.2395	−	8.89253i	−0.852768	−	0.619572i
$207$			4.21843i			0.293201i
$208$	4.91798	−	6.76901i	0.341000	−	0.469347i
$209$	−9.93888	+	30.5887i	−0.687487	+	2.11587i
$210$	−0.665767	−	5.78843i	−0.0459423	−	0.399440i
$211$	1.37707	+	4.23820i	0.0948017	+	0.291770i	0.987202	−	0.159475i	$-0.0509801\pi$
$211$	1.37707	+	4.23820i	0.0948017	+	0.291770i	−0.892400	+	0.451245i	$0.850980\pi$
$212$	56.5938	+	18.3884i	3.88688	+	1.26292i
$213$	−5.08398	−	1.65188i	−0.348349	−	0.113185i
$214$	14.3888	+	44.2841i	0.983597	+	3.02720i
$215$	8.58987	+	9.35414i	0.585824	+	0.637947i
$216$	−2.24642	+	6.91378i	−0.152850	+	0.470423i
$217$	−0.381661	+	0.525312i	−0.0259089	+	0.0356605i
$218$		−	25.2087i		−	1.70735i
$219$	11.3818	+	8.26938i	0.769113	+	0.558793i
$220$	64.4551	−	7.41342i	4.34556	−	0.499813i
$221$	−5.30362	+	3.85330i	−0.356760	+	0.259201i
$222$	9.51425	+	13.0952i	0.638555	+	0.878896i
$223$	6.10375	−	1.98323i	0.408737	−	0.132807i	−0.0974295	−	0.995242i	$-0.531062\pi$
$223$	6.10375	−	1.98323i	0.408737	−	0.132807i	0.506167	+	0.862436i	$0.331062\pi$
$224$	9.85803			0.658668
$225$	4.60668	+	1.94383i	0.307112	+	0.129588i
$226$	−14.2558			−0.948282
$227$	−12.7685	+	4.14875i	−0.847478	+	0.275362i	−0.700389	−	0.713761i	$-0.746990\pi$
$227$	−12.7685	+	4.14875i	−0.847478	+	0.275362i	−0.147089	+	0.989123i	$0.546990\pi$
$228$	−14.9482	−	20.5745i	−0.989971	−	1.36258i
$229$	5.34511	−	3.88345i	0.353215	−	0.256626i	−0.397002	−	0.917818i	$-0.629949\pi$
$229$	5.34511	−	3.88345i	0.353215	−	0.256626i	0.750216	+	0.661192i	$0.229949\pi$
$230$	−4.87458	+	24.0909i	−0.321420	+	1.58851i
$231$	−4.90075	−	3.56060i	−0.322446	−	0.234271i
$232$		−	4.93315i		−	0.323877i
$233$	−11.9796	+	16.4885i	−0.784809	+	1.08020i	0.209926	+	0.977717i	$0.432678\pi$
$233$	−11.9796	+	16.4885i	−0.784809	+	1.08020i	−0.994735	+	0.102480i	$0.967322\pi$
$234$	0.719565	−	2.21459i	0.0470394	−	0.144772i
$235$	−15.3641	−	3.10879i	−1.00224	−	0.202795i
$236$	−5.35095	−	16.4685i	−0.348317	−	1.07201i
$237$	−10.1307	−	3.29167i	−0.658061	−	0.213817i
$238$	−18.1800	−	5.90703i	−1.17843	−	0.382896i
$239$	1.94971	+	6.00059i	0.126116	+	0.388146i	0.994103	−	0.108442i	$-0.0345861\pi$
$239$	1.94971	+	6.00059i	0.126116	+	0.388146i	−0.867987	+	0.496588i	$0.834586\pi$
$240$	−10.2900	+	18.2328i	−0.664214	+	1.17692i
$241$	−5.28436	+	16.2636i	−0.340396	+	1.04763i	0.623607	+	0.781738i	$0.285667\pi$
$241$	−5.28436	+	16.2636i	−0.340396	+	1.04763i	−0.964003	+	0.265893i	$0.914333\pi$
$242$	39.3552	−	54.1677i	2.52985	−	3.48203i
$243$			1.00000i			0.0641500i
$244$	6.12393	+	4.44930i	0.392045	+	0.284837i
$245$	−1.64699	+	1.51242i	−0.105222	+	0.0966252i
$246$	−2.53091	+	1.83882i	−0.161365	+	0.117239i
$247$	2.78886	+	3.83854i	0.177451	+	0.244240i
$248$	4.48926	−	1.45865i	0.285068	−	0.0926244i
$249$	0.174295			0.0110455
$250$	24.0620	+	16.4241i	1.52181	+	1.03875i
$251$	−1.05013			−0.0662837			−0.0331418	−	0.999451i	$-0.510551\pi$
$251$	−1.05013			−0.0662837			−0.0331418	+	0.999451i	$0.510551\pi$
$252$	4.55541	−	1.48014i	0.286964	−	0.0932402i
$253$	15.0202	+	20.6735i	0.944310	+	1.29973i
$254$	−33.1948	+	24.1174i	−2.08283	+	1.51326i
$255$	12.0822	−	11.0951i	0.756619	−	0.694801i
$256$	14.5864	+	10.5976i	0.911650	+	0.662352i
$257$		−	24.0686i		−	1.50136i	−0.660667	−	0.750679i	$-0.729726\pi$
$257$		−	24.0686i		−	1.50136i	0.660667	−	0.750679i	$-0.270274\pi$
$258$	−8.69884	+	11.9729i	−0.541566	+	0.745402i
$259$	1.91959	−	5.90789i	0.119278	−	0.367099i
$260$	4.70416	−	8.33532i	0.291740	−	0.516935i
$261$	−0.209699	−	0.645388i	−0.0129801	−	0.0399485i
$262$	−21.9429	−	7.12968i	−1.35564	−	0.440473i
$263$	−26.1120	−	8.48431i	−1.61014	−	0.523165i	−0.640550	−	0.767916i	$-0.721294\pi$
$263$	−26.1120	−	8.48431i	−1.61014	−	0.523165i	−0.969586	+	0.244752i	$0.921294\pi$
$264$	13.6081	+	41.8813i	0.837519	+	2.57762i
$265$	27.2278	+	5.50931i	1.67259	+	0.338434i
$266$	−4.27526	+	13.1579i	−0.262133	+	0.806762i
$267$	−9.52070	+	13.1041i	−0.582658	+	0.801959i
$268$		−	26.0805i		−	1.59312i
$269$	−13.2054	−	9.59431i	−0.805150	−	0.584975i	0.107271	−	0.994230i	$-0.465789\pi$
$269$	−13.2054	−	9.59431i	−0.805150	−	0.584975i	−0.912420	+	0.409254i	$0.865789\pi$
$270$	−1.15554	+	5.71086i	−0.0703241	+	0.347552i
$271$	13.9016	−	10.1001i	0.844461	−	0.613537i	−0.0791525	−	0.996863i	$-0.525221\pi$
$271$	13.9016	−	10.1001i	0.844461	−	0.613537i	0.923613	+	0.383326i	$0.125221\pi$
$272$	40.3725	+	55.5680i	2.44794	+	3.36930i
$273$	−0.849893	+	0.276147i	−0.0514378	+	0.0167132i
$274$	−19.9173			−1.20325
$275$	29.4974	−	6.87636i	1.77876	−	0.414660i
$276$	−20.2056			−1.21624
$277$	14.4969	−	4.71031i	0.871032	−	0.283015i	0.160803	−	0.986987i	$-0.448592\pi$
$277$	14.4969	−	4.71031i	0.871032	−	0.283015i	0.710229	+	0.703971i	$0.248592\pi$
$278$	21.8753	+	30.1088i	1.31199	+	1.80580i
$279$	0.525312	−	0.381661i	0.0314496	−	0.0228495i
$280$	16.1488	−	1.85738i	0.965076	−	0.111000i
$281$	19.7276	+	14.3329i	1.17685	+	0.855029i	0.991813	−	0.127703i	$-0.0407603\pi$
$281$	19.7276	+	14.3329i	1.17685	+	0.855029i	0.185035	+	0.982732i	$0.440760\pi$
$282$		−	18.2669i		−	1.08778i
$283$	14.0370	−	19.3203i	0.834415	−	1.14847i	−0.152671	−	0.988277i	$-0.548787\pi$
$283$	14.0370	−	19.3203i	0.834415	−	1.14847i	0.987085	−	0.160196i	$-0.0512126\pi$
$284$	7.91227	−	24.3515i	0.469507	−	1.44499i
$285$	−8.03015	−	8.74462i	−0.475665	−	0.517986i
$286$	−4.35888	−	13.4153i	−0.257746	−	0.793261i
$287$	1.14182	+	0.370998i	0.0673992	+	0.0218993i
$288$	−9.37555	−	3.04630i	−0.552459	−	0.179505i
$289$	−11.3769	−	35.0144i	−0.669227	−	2.05967i
$290$	−0.451791	−	3.92804i	−0.0265301	−	0.230662i
$291$	1.68219	−	5.17724i	0.0986116	−	0.303495i
$292$	−39.6090	+	54.5171i	−2.31794	+	3.19037i
$293$		−	14.3649i		−	0.839207i	−0.907708	−	0.419603i	$-0.862169\pi$
$293$		−	14.3649i		−	0.839207i	0.907708	−	0.419603i	$-0.137831\pi$
$294$	−2.10808	−	1.53161i	−0.122946	−	0.0893254i
$295$	−3.36012	−	7.35231i	−0.195634	−	0.428068i
$296$	−36.5337	+	26.5433i	−2.12348	+	1.54280i
$297$	3.56060	+	4.90075i	0.206607	+	0.284370i
$298$	41.8218	−	13.5887i	2.42267	−	0.787174i
$299$	3.76972			0.218008
$300$	−9.31062	+	22.0653i	−0.537549	+	1.27394i
$301$	5.67954			0.327363
$302$	−8.30112	+	2.69720i	−0.477676	+	0.155206i
$303$	−1.66392	−	2.29019i	−0.0955899	−	0.131568i
$304$	40.2177	−	29.2199i	2.30665	−	1.67588i
$305$	3.07748	+	1.73682i	0.176216	+	0.0994501i
$306$	15.4648	+	11.2358i	0.884064	+	0.642310i
$307$		−	4.48761i		−	0.256122i	−0.991766	−	0.128061i	$-0.959125\pi$
$307$		−	4.48761i		−	0.256122i	0.991766	−	0.128061i	$-0.0408753\pi$
$308$	17.0547	−	23.4738i	0.971783	−	1.33754i
$309$	1.79415	−	5.52183i	0.102066	−	0.314126i
$310$	3.44101	−	1.57259i	0.195436	−	0.0893174i
$311$	−1.95303	−	6.01080i	−0.110746	−	0.340841i	0.880290	−	0.474436i	$-0.157348\pi$
$311$	−1.95303	−	6.01080i	−0.110746	−	0.340841i	−0.991036	+	0.133595i	$0.957348\pi$
$312$	6.17836	+	2.00747i	0.349781	+	0.113651i
$313$	−29.0084	−	9.42542i	−1.63965	−	0.532756i	−0.663193	−	0.748448i	$-0.730799\pi$
$313$	−29.0084	−	9.42542i	−1.63965	−	0.532756i	−0.976461	+	0.215692i	$0.930799\pi$
$314$	−15.9057	−	48.9528i	−0.897611	−	2.76256i
$315$	2.03374	−	0.929453i	0.114589	−	0.0523688i
$316$	15.7666	−	48.5246i	0.886940	−	2.72972i
$317$	−18.5477	+	25.5288i	−1.04174	+	1.43384i	−0.145992	+	0.989286i	$0.546637\pi$
$317$	−18.5477	+	25.5288i	−1.04174	+	1.43384i	−0.895753	+	0.444553i	$0.853363\pi$
$318$			32.3721i			1.81534i
$319$	−3.32566	−	2.41623i	−0.186201	−	0.135283i
$320$	−13.5567	−	7.65092i	−0.757842	−	0.427699i
$321$	−14.4567	+	10.5034i	−0.806895	+	0.586244i
$322$	6.46100	+	8.89280i	0.360057	+	0.495576i
$323$	−37.0436	+	12.0362i	−2.06116	+	0.669712i
$324$	−4.78984			−0.266102
$325$	1.73706	−	4.11667i	0.0963549	−	0.228352i
$326$	−34.2609			−1.89754
$327$	9.20083	−	2.98953i	0.508807	−	0.165321i
$328$	−5.13000	−	7.06084i	−0.283257	−	0.389870i
$329$	−5.67143	+	4.12054i	−0.312676	+	0.227173i
$330$	14.6711	+	32.1019i	0.807617	+	1.76715i
$331$	5.19899	+	3.77729i	0.285762	+	0.207618i	0.721427	−	0.692491i	$-0.243487\pi$
$331$	5.19899	+	3.77729i	0.285762	+	0.207618i	−0.435665	+	0.900109i	$0.643487\pi$
$332$			0.834846i			0.0458181i
$333$	−3.65128	+	5.02555i	−0.200089	+	0.275399i
$334$	5.02432	−	15.4633i	0.274919	−	0.846113i
$335$	−1.39119	−	12.0956i	−0.0760089	−	0.660851i
$336$	2.89329	+	8.90464i	0.157842	+	0.485788i
$337$	−13.8496	−	4.50000i	−0.754434	−	0.245130i	−0.0935460	−	0.995615i	$-0.529820\pi$
$337$	−13.8496	−	4.50000i	−0.754434	−	0.245130i	−0.660888	+	0.750484i	$0.729820\pi$
$338$	30.2376	+	9.82478i	1.64471	+	0.534397i
$339$	−1.69061	−	5.20317i	−0.0918215	−	0.282598i
$340$	53.1437	+	57.8720i	2.88212	+	3.13855i
$341$	1.21548	−	3.74085i	0.0658218	−	0.202579i
$342$	8.13202	−	11.1928i	0.439729	−	0.605236i
$343$			1.00000i			0.0539949i
$344$	−33.4026	−	24.2684i	−1.80095	−	1.30846i
$345$	−9.37092	+	1.07781i	−0.504514	+	0.0580275i
$346$	−46.1404	+	33.5230i	−2.48053	+	1.80221i
$347$	−5.36215	−	7.38036i	−0.287855	−	0.396199i	0.640461	−	0.767991i	$-0.278743\pi$
$347$	−5.36215	−	7.38036i	−0.287855	−	0.396199i	−0.928316	+	0.371792i	$0.878743\pi$
$348$	3.09131	−	1.00443i	0.165711	−	0.0538429i
$349$	−4.20075			−0.224861			−0.112430	−	0.993660i	$-0.535864\pi$
$349$	−4.20075			−0.224861			−0.112430	+	0.993660i	$0.535864\pi$
$350$	12.6885	−	2.95790i	0.678226	−	0.158106i
$351$	0.893630			0.0476984
$352$	−56.7939	+	18.4535i	−3.02713	+	0.983573i
$353$	7.07384	+	9.73631i	0.376503	+	0.518211i	0.954654	−	0.297718i	$-0.0962256\pi$
$353$	7.07384	+	9.73631i	0.376503	+	0.518211i	−0.578151	+	0.815930i	$0.696226\pi$
$354$	7.62105	−	5.53701i	0.405054	−	0.294289i
$355$	2.37057	−	11.7157i	0.125817	−	0.621806i
$356$	−62.7667	−	45.6027i	−3.32663	−	2.41694i
$357$		−	7.33596i		−	0.388260i
$358$	19.5130	−	26.8574i	1.03130	−	1.41946i
$359$	−3.05571	+	9.40452i	−0.161274	+	0.496352i	−0.998742	−	0.0501347i	$-0.984035\pi$
$359$	−3.05571	+	9.40452i	−0.161274	+	0.496352i	0.837468	+	0.546486i	$0.184035\pi$
$360$	−15.9324	−	3.22378i	−0.839711	−	0.169908i
$361$	2.83997	+	8.74052i	0.149472	+	0.460028i
$362$	−2.85202	−	0.926679i	−0.149899	−	0.0487051i
$363$	24.4377	+	7.94027i	1.28264	+	0.416756i
$364$	−1.32270	−	4.07085i	−0.0693283	−	0.213371i
$365$	−15.4617	+	27.3967i	−0.809304	+	1.43401i
$366$	−1.27252	+	3.91641i	−0.0665156	+	0.204714i
$367$	4.48604	−	6.17450i	0.234169	−	0.322306i	−0.675719	−	0.737159i	$-0.736167\pi$
$367$	4.48604	−	6.17450i	0.234169	−	0.322306i	0.909889	+	0.414853i	$0.136167\pi$
$368$		−	39.4967i		−	2.05891i
$369$	−0.971286	−	0.705681i	−0.0505632	−	0.0367363i
$370$	−26.6592	+	24.4810i	−1.38594	+	1.27271i
$371$	10.0508	−	7.30230i	0.521809	−	0.379117i
$372$	1.82810	+	2.51616i	0.0947824	+	0.130457i
$373$	−17.7900	+	5.78032i	−0.921131	+	0.299293i	−0.730931	−	0.682452i	$-0.760914\pi$
$373$	−17.7900	+	5.78032i	−0.921131	+	0.299293i	−0.190200	+	0.981745i	$0.560914\pi$
$374$	115.795			5.98764
$375$	−3.14105	+	10.7300i	−0.162203	+	0.554097i
$376$	50.9617			2.62815
$377$	−0.576739	+	0.187394i	−0.0297035	+	0.00965127i
$378$	1.53161	+	2.10808i	0.0787776	+	0.108428i
$379$	−9.34885	+	6.79234i	−0.480218	+	0.348899i	−0.801410	−	0.598115i	$-0.795917\pi$
$379$	−9.34885	+	6.79234i	−0.480218	+	0.348899i	0.321192	+	0.947014i	$0.395917\pi$
$380$	41.8853	−	38.4631i	2.14867	−	1.97312i
$381$	−12.7392	−	9.25554i	−0.652646	−	0.474175i
$382$			9.35342i			0.478563i
$383$	−7.09972	+	9.77192i	−0.362779	+	0.499322i	−0.950920	−	0.309436i	$-0.899860\pi$
$383$	−7.09972	+	9.77192i	−0.362779	+	0.499322i	0.588142	+	0.808758i	$0.299860\pi$
$384$	−0.487000	+	1.49883i	−0.0248521	+	0.0764869i
$385$	6.65746	−	11.7964i	0.339296	−	0.601199i
$386$	2.71914	+	8.36865i	0.138401	+	0.425953i
$387$	−5.40156	−	1.75507i	−0.274577	−	0.0892154i
$388$	24.7982	+	8.05741i	1.25894	+	0.409053i
$389$	−5.19366	−	15.9844i	−0.263329	−	0.810443i	−0.992074	−	0.125658i	$-0.959896\pi$
$389$	−5.19366	−	15.9844i	−0.263329	−	0.810443i	0.728745	−	0.684785i	$-0.240104\pi$
$390$	5.10340	+	1.03263i	0.258421	+	0.0522891i
$391$	−9.56291	+	29.4316i	−0.483617	+	1.48842i
$392$	4.27295	−	5.88121i	0.215817	−	0.297046i
$393$		−	8.85437i		−	0.446644i
$394$	5.09684	+	3.70307i	0.256775	+	0.186558i
$395$	4.72379	−	23.3456i	0.237679	−	1.17465i
$396$	−23.4738	+	17.0547i	−1.17960	+	0.857032i
$397$	−2.25326	−	3.10135i	−0.113088	−	0.155652i	0.748721	−	0.662885i	$-0.230668\pi$
$397$	−2.25326	−	3.10135i	−0.113088	−	0.155652i	−0.861809	+	0.507233i	$0.830668\pi$
$398$	41.2298	−	13.3964i	2.06666	−	0.671500i
$399$	−5.30946			−0.265805
$400$	−43.1319	−	18.1998i	−2.15659	−	0.909992i
$401$	24.7347			1.23519			0.617596	−	0.786495i	$-0.288107\pi$
$401$	24.7347			1.23519			0.617596	+	0.786495i	$0.288107\pi$
$402$	13.4937	−	4.38436i	0.673004	−	0.218672i
$403$	−0.341064	−	0.469434i	−0.0169896	−	0.0233842i
$404$	10.9697	−	7.96993i	0.545761	−	0.396519i
$405$	−2.22142	+	0.255501i	−0.110383	+	0.0126959i
$406$	−1.43055	−	1.03935i	−0.0709969	−	0.0515823i
$407$			37.6297i			1.86524i
$408$	−31.3462	+	43.1443i	−1.55187	+	2.13596i
$409$	−1.84449	+	5.67674i	−0.0912039	+	0.280697i	−0.986246	−	0.165285i	$-0.947146\pi$
$409$	−1.84449	+	5.67674i	−0.0912039	+	0.280697i	0.895042	+	0.445982i	$0.147146\pi$
$410$	−4.73144	−	5.15241i	−0.233669	−	0.254459i
$411$	−2.36202	−	7.26956i	−0.116510	−	0.358581i
$412$	26.4487	+	8.59370i	1.30303	+	0.423381i
$413$	−3.43822	−	1.11715i	−0.169184	−	0.0549711i
$414$	−3.39675	−	10.4541i	−0.166941	−	0.513792i
$415$	0.0445326	+	0.387183i	0.00218602	+	0.0190061i
$416$	−2.72227	+	8.37827i	−0.133470	+	0.410779i
$417$	−8.39507	+	11.5548i	−0.411108	+	0.565842i
$418$		−	83.8079i		−	4.09918i
$419$	19.4383	+	14.1228i	0.949624	+	0.689942i	0.950718	−	0.310057i	$-0.100348\pi$
$419$	19.4383	+	14.1228i	0.949624	+	0.689942i	−0.00109421	+	0.999999i	$0.500348\pi$
$420$	4.45193	+	9.74131i	0.217232	+	0.475327i
$421$	−25.6223	+	18.6157i	−1.24875	+	0.907272i	−0.998149	−	0.0608171i	$-0.980629\pi$
$421$	−25.6223	+	18.6157i	−1.24875	+	0.907272i	−0.250604	+	0.968090i	$0.580629\pi$
$422$	−6.82533	−	9.39426i	−0.332252	−	0.457305i
$423$	6.66717	−	2.16629i	0.324169	−	0.105329i
$424$	−90.3130			−4.38599
$425$	27.7339	+	24.0050i	1.34529	+	1.16441i
$426$	13.9292			0.674874
$427$	1.50300	−	0.488353i	0.0727351	−	0.0236331i
$428$	−50.3097	−	69.2454i	−2.43181	−	3.34710i
$429$	4.37946	−	3.18186i	0.211442	−	0.153622i
$430$	−28.8195	−	16.2647i	−1.38980	−	0.784354i
$431$	5.25895	+	3.82085i	0.253315	+	0.184044i	0.707195	−	0.707019i	$-0.249960\pi$
$431$	5.25895	+	3.82085i	0.253315	+	0.184044i	−0.453880	+	0.891063i	$0.649960\pi$
$432$		−	9.36289i		−	0.450472i
$433$	−2.52614	+	3.47693i	−0.121398	+	0.167090i	−0.865391	−	0.501097i	$-0.832930\pi$
$433$	−2.52614	+	3.47693i	−0.121398	+	0.167090i	0.743993	+	0.668188i	$0.232930\pi$
$434$	0.522843	−	1.60915i	0.0250973	−	0.0772415i
$435$	1.38010	−	0.630728i	0.0661708	−	0.0302411i
$436$	14.3194	+	44.0705i	0.685774	+	2.11059i
$437$	21.3014	+	6.92123i	1.01898	+	0.331088i
$438$	−34.8651	−	11.3283i	−1.66592	−	0.541289i
$439$	−4.07796	−	12.5507i	−0.194630	−	0.599011i	−0.999981	−	0.00621157i	$-0.998023\pi$
$439$	−4.07796	−	12.5507i	−0.194630	−	0.599011i	0.805350	−	0.592799i	$-0.201977\pi$
$440$	−89.5593	+	40.9300i	−4.26957	+	1.95126i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	10.0407	−	13.8198i	0.477586	−	0.657341i
$443$		−	0.0864068i		−	0.00410531i	−0.999998	−	0.00205266i	$-0.999347\pi$
$443$		−	0.0864068i		−	0.00410531i	0.999998	−	0.00205266i	$-0.000653381\pi$
$444$	−24.0716	−	17.4890i	−1.14239	−	0.829993i
$445$	−31.5423	−	17.8014i	−1.49525	−	0.843867i
$446$	−13.5294	+	9.82967i	−0.640634	+	0.465448i
$447$	9.91940	+	13.6529i	0.469172	+	0.645759i
$448$	−6.62089	+	2.15126i	−0.312808	+	0.101637i
$449$	−7.28830			−0.343956			−0.171978	−	0.985101i	$-0.555016\pi$
$449$	−7.28830			−0.343956			−0.171978	+	0.985101i	$0.555016\pi$
$450$	−12.9815	−	1.10782i	−0.611953	−	0.0522230i
$451$	−7.27268			−0.342457
$452$	24.9224	−	8.09777i	1.17225	−	0.380887i
$453$	−1.96888	−	2.70993i	−0.0925060	−	0.127324i
$454$	28.3023	−	20.5629i	1.32829	−	0.965063i
$455$	−0.830587	−	1.81742i	−0.0389385	−	0.0852017i
$456$	31.2260	+	22.6870i	1.46229	+	1.06242i
$457$			3.97488i			0.185937i	0.995669	+	0.0929685i	$0.0296356\pi$
$457$			3.97488i			0.185937i	−0.995669	+	0.0929685i	$0.970364\pi$
$458$	−10.1192	+	13.9279i	−0.472841	+	0.650809i
$459$	−2.26694	+	6.97691i	−0.105811	+	0.325654i
$460$	−5.16256	−	44.8852i	−0.240705	−	2.09278i
$461$	−8.39888	−	25.8491i	−0.391175	−	1.20391i	−0.931901	−	0.362714i	$-0.881850\pi$
$461$	−8.39888	−	25.8491i	−0.391175	−	1.20391i	0.540726	−	0.841199i	$-0.318150\pi$
$462$	15.0121	+	4.87772i	0.698426	+	0.226932i
$463$	15.7558	+	5.11937i	0.732234	+	0.237917i	0.651319	−	0.758804i	$-0.274216\pi$
$463$	15.7558	+	5.11937i	0.732234	+	0.237917i	0.0809148	+	0.996721i	$0.474216\pi$
$464$	1.96339	+	6.04270i	0.0911482	+	0.280525i
$465$	0.982049	+	1.06942i	0.0455414	+	0.0495934i
$466$	16.4110	−	50.5079i	0.760226	−	2.33973i
$467$	6.13343	−	8.44194i	0.283821	−	0.390646i	−0.643174	−	0.765720i	$-0.722383\pi$
$467$	6.13343	−	8.44194i	0.283821	−	0.390646i	0.926995	+	0.375074i	$0.122383\pi$
$468$			4.28035i			0.197859i
$469$	−4.40506	−	3.20047i	−0.203407	−	0.147784i
$470$	40.5785	−	4.66721i	1.87175	−	0.215282i
$471$	15.9808	−	11.6107i	0.736357	−	0.534994i
$472$	15.4474	+	21.2615i	0.711024	+	0.978640i
$473$	−32.7208	+	10.6316i	−1.50451	+	0.488844i
$474$	27.7565			1.27490
$475$	17.3738	−	20.0726i	0.797164	−	0.920995i
$476$	35.1381			1.61055
$477$	−11.8154	+	3.83905i	−0.540989	+	0.175778i
$478$	−9.66354	−	13.3007i	−0.442000	−	0.608361i
$479$	−17.9730	+	13.0582i	−0.821209	+	0.596643i	−0.917059	−	0.398753i	$-0.869443\pi$
$479$	−17.9730	+	13.0582i	−0.821209	+	0.596643i	0.0958495	+	0.995396i	$0.469443\pi$
$480$	4.37166	−	21.6054i	0.199538	−	0.986147i
$481$	4.49099	+	3.26289i	0.204771	+	0.148775i
$482$		−	44.5595i		−	2.02963i
$483$	−2.47953	+	3.41278i	−0.112823	+	0.155287i
$484$	−38.0326	+	117.052i	−1.72876	+	5.32057i
$485$	11.9306	+	2.41406i	0.541743	+	0.109617i
$486$	−0.805216	−	2.47820i	−0.0365253	−	0.112413i
$487$	16.7384	+	5.43863i	0.758488	+	0.246448i	0.662630	−	0.748947i	$-0.269440\pi$
$487$	16.7384	+	5.43863i	0.758488	+	0.246448i	0.0958584	+	0.995395i	$0.469440\pi$
$488$	−10.9262	−	3.55012i	−0.494604	−	0.160706i
$489$	−4.06304	−	12.5048i	−0.183737	−	0.565485i
$490$	2.86374	−	5.07427i	0.129371	−	0.229232i
$491$	−6.28477	+	19.3425i	−0.283628	+	0.872916i	0.703179	+	0.711013i	$0.251763\pi$
$491$	−6.28477	+	19.3425i	−0.283628	+	0.872916i	−0.986807	+	0.161903i	$0.948237\pi$
$492$	3.38010	−	4.65231i	0.152387	−	0.209742i
$493$		−	4.97819i		−	0.224206i
$494$	−10.0022	−	7.26702i	−0.450020	−	0.326959i
$495$	−9.97690	+	9.16175i	−0.448428	+	0.411790i
$496$	−4.91844	+	3.57345i	−0.220844	+	0.160453i
$497$	−3.14207	−	4.32469i	−0.140941	−	0.193989i
$498$	−0.431938	+	0.140345i	−0.0193556	+	0.00628902i
$499$	−25.2802			−1.13170			−0.565848	−	0.824510i	$-0.691451\pi$
$499$	−25.2802			−1.13170			−0.565848	+	0.824510i	$0.691451\pi$
$500$	−51.3952	−	15.0451i	−2.29846	−	0.672839i
$501$	6.23972			0.278770
$502$	2.60243	−	0.845582i	0.116152	−	0.0377402i
$503$	−10.0865	−	13.8829i	−0.449736	−	0.619009i	0.522605	−	0.852575i	$-0.324960\pi$
$503$	−10.0865	−	13.8829i	−0.449736	−	0.619009i	−0.972341	+	0.233566i	$0.924960\pi$
$504$	−5.88121	+	4.27295i	−0.261970	+	0.190332i
$505$	4.66235	−	4.28142i	0.207472	−	0.190521i
$506$	−53.8696	−	39.1385i	−2.39479	−	1.73992i
$507$			12.2014i			0.541884i
$508$	44.3325	−	61.0185i	1.96694	−	2.70726i
$509$	6.13918	−	18.8944i	0.272114	−	0.837482i	−0.717854	−	0.696193i	$-0.754876\pi$
$509$	6.13918	−	18.8944i	0.272114	−	0.837482i	0.989969	−	0.141288i	$-0.0451244\pi$
$510$	−21.0083	+	37.2246i	−0.930262	+	1.64833i
$511$	4.34747	+	13.3801i	0.192321	+	0.591903i
$512$	−41.6837	−	13.5439i	−1.84218	−	0.598559i
$513$	5.04959	+	1.64071i	0.222945	+	0.0724392i
$514$	19.3804	+	59.6468i	0.854834	+	2.63091i
$515$	12.7247	+	2.57474i	0.560719	+	0.113456i
$516$	8.40653	−	25.8726i	0.370077	−	1.13898i
$517$	24.9608	−	34.3556i	1.09778	−	1.51096i
$518$			16.1866i			0.711199i
$519$	−17.7073	−	12.8651i	−0.777264	−	0.564715i
$520$	−2.88087	+	14.2377i	−0.126334	+	0.624363i
$521$	27.9863	−	20.3332i	1.22610	−	0.890815i	0.229509	−	0.973306i	$-0.426288\pi$
$521$	27.9863	−	20.3332i	1.22610	−	0.890815i	0.996592	+	0.0824919i	$0.0262879\pi$
$522$	1.03935	+	1.43055i	0.0454913	+	0.0626134i
$523$	21.6253	−	7.02648i	0.945608	−	0.307247i	0.204678	−	0.978829i	$-0.434385\pi$
$523$	21.6253	−	7.02648i	0.945608	−	0.307247i	0.740929	+	0.671583i	$0.234385\pi$
$524$	42.4110			1.85273
$525$	2.58433	+	4.28033i	0.112790	+	0.186809i
$526$	71.5425			3.11940
$527$	4.53025	−	1.47197i	0.197341	−	0.0641200i
$528$	−33.3376	−	45.8852i	−1.45083	−	1.99690i
$529$	−4.21079	+	3.05932i	−0.183078	+	0.133014i
$530$	−71.9121	+	8.27110i	−3.12366	+	0.359274i
$531$	2.92472	+	2.12494i	0.126922	+	0.0922144i
$532$		−	25.4315i		−	1.10259i
$533$	−0.630618	+	0.867971i	−0.0273151	+	0.0375960i
$534$	13.0426	−	40.1408i	0.564406	−	1.73706i
$535$	−27.0262	−	29.4309i	−1.16845	−	1.27241i
$536$	12.2317	+	37.6452i	0.528328	+	1.62603i
$537$	12.1166	+	3.93694i	0.522872	+	0.169891i
$538$	40.4512	+	13.1434i	1.74397	+	0.566652i
$539$	−1.87192	−	5.76118i	−0.0806293	−	0.248152i
$540$	−1.22381	−	10.6403i	−0.0526643	−	0.457884i
$541$	5.29537	−	16.2975i	0.227666	−	0.700683i	−0.770344	−	0.637628i	$-0.779916\pi$
$541$	5.29537	−	16.2975i	0.227666	−	0.700683i	0.998010	−	0.0630551i	$-0.0200844\pi$
$542$	−26.3181	+	36.2238i	−1.13046	+	1.55594i
$543$		−	1.15085i		−	0.0493875i
$544$	−58.5066	−	42.5075i	−2.50845	−	1.82250i
$545$	8.99183	+	19.6751i	0.385168	+	0.842789i
$546$	1.88385	−	1.36869i	0.0806211	−	0.0585747i
$547$	9.21602	+	12.6848i	0.394049	+	0.542362i	0.959238	−	0.282600i	$-0.0911968\pi$
$547$	9.21602	+	12.6848i	0.394049	+	0.542362i	−0.565189	+	0.824961i	$0.691197\pi$
$548$	34.8200	−	11.3137i	1.48744	−	0.483298i
$549$	−1.58034			−0.0674475
$550$	−67.5635	+	40.7928i	−2.88092	+	1.73941i
$551$	−3.60301			−0.153493
$552$	29.1653	−	9.47638i	1.24136	−	0.403342i
$553$	−6.26113	−	8.61771i	−0.266250	−	0.366462i
$554$	−32.1333	+	23.3462i	−1.36521	+	0.991884i
$555$	−12.0968	−	6.82700i	−0.513480	−	0.289790i
$556$	−55.3458	−	40.2111i	−2.34718	−	1.70533i
$557$		−	13.0894i		−	0.554616i	−0.960781	−	0.277308i	$-0.910558\pi$
$557$		−	13.0894i		−	0.554616i	0.960781	−	0.277308i	$-0.0894423\pi$
$558$	−0.994507	+	1.36882i	−0.0421009	+	0.0579468i
$559$	−1.56839	+	4.82700i	−0.0663357	+	0.204160i
$560$	−19.0417	+	8.70237i	−0.804660	+	0.367742i
$561$	13.7323	+	42.2638i	0.579779	+	1.78438i
$562$	−60.4299	−	19.6349i	−2.54908	−	0.828246i
$563$	29.7274	+	9.65901i	1.25286	+	0.407079i	0.858945	−	0.512068i	$-0.171121\pi$
$563$	29.7274	+	9.65901i	1.25286	+	0.407079i	0.393915	+	0.919147i	$0.371121\pi$
$564$	10.3762	+	31.9347i	0.436917	+	1.34469i
$565$	11.1265	−	5.08498i	0.468095	−	0.213927i
$566$	−19.2295	+	59.1824i	−0.808277	+	2.48762i
$567$	−0.587785	+	0.809017i	−0.0246847	+	0.0339755i
$568$			38.8603i			1.63054i
$569$	27.9109	+	20.2784i	1.17008	+	0.850116i	0.991019	−	0.133721i	$-0.0426925\pi$
$569$	27.9109	+	20.2784i	1.17008	+	0.850116i	0.179066	+	0.983837i	$0.442693\pi$
$570$	26.9416	+	15.2049i	1.12846	+	0.636863i
$571$	13.7274	−	9.97356i	0.574475	−	0.417381i	−0.262253	−	0.964999i	$-0.584465\pi$
$571$	13.7274	−	9.97356i	0.574475	−	0.417381i	0.836728	+	0.547618i	$0.184465\pi$
$572$	15.2406	+	20.9769i	0.637242	+	0.877089i
$573$	−3.41387	+	1.10923i	−0.142616	+	0.0463389i
$574$	−3.12838			−0.130576
$575$	−4.78856	−	20.5414i	−0.199697	−	0.856636i
$576$	6.96161			0.290067
$577$	−12.7194	+	4.13279i	−0.529516	+	0.172050i	−0.561560	−	0.827436i	$-0.689799\pi$
$577$	−12.7194	+	4.13279i	−0.529516	+	0.172050i	0.0320434	+	0.999486i	$0.489799\pi$
$578$	56.3882	+	77.6117i	2.34544	+	3.22822i
$579$	−2.73198	+	1.98490i	−0.113537	+	0.0824895i
$580$	3.02109	+	6.61047i	0.125444	+	0.274485i
$581$	0.141008	+	0.102448i	0.00584999	+	0.00425026i
$582$			14.1848i			0.587977i
$583$	−44.2349	+	60.8841i	−1.83202	+	2.52156i
$584$	31.6043	−	97.2680i	1.30779	−	4.02498i
$585$	0.228323	+	1.98513i	0.00944001	+	0.0820750i
$586$	11.5668	+	35.5991i	0.477822	+	1.47058i
$587$	−6.55992	−	2.13145i	−0.270757	−	0.0879743i	0.170492	−	0.985359i	$-0.445464\pi$
$587$	−6.55992	−	2.13145i	−0.270757	−	0.0879743i	−0.441249	+	0.897385i	$0.645464\pi$
$588$	4.55541	+	1.48014i	0.187862	+	0.0610400i
$589$	−1.06535	−	3.27881i	−0.0438969	−	0.135101i
$590$	14.2472	+	15.5149i	0.586549	+	0.638736i
$591$	−0.747130	+	2.29943i	−0.0307328	+	0.0945859i
$592$	34.1865	−	47.0537i	1.40506	−	1.93390i
$593$			26.0399i			1.06933i	0.845064	+	0.534666i	$0.179562\pi$
$593$			26.0399i			1.06933i	−0.845064	+	0.534666i	$0.820438\pi$
$594$	−12.7700	−	9.27798i	−0.523961	−	0.380680i
$595$	16.2963	−	1.87434i	0.668082	−	0.0768406i
$596$	−65.3951	+	47.5123i	−2.67869	+	1.94618i
$597$	9.77899	+	13.4596i	0.400227	+	0.550866i
$598$	−9.34211	+	3.03544i	−0.382027	+	0.124128i
$599$	37.6439			1.53809			0.769044	−	0.639196i	$-0.220733\pi$
$599$	37.6439			1.53809			0.769044	+	0.639196i	$0.220733\pi$
$600$	3.09063	−	36.2163i	0.126175	−	1.47852i
$601$	16.3990			0.668929			0.334464	−	0.942408i	$-0.391445\pi$
$601$	16.3990			0.668929			0.334464	+	0.942408i	$0.391445\pi$
$602$	−14.0750	+	4.57325i	−0.573655	+	0.186392i
$603$	3.20047	+	4.40506i	0.130333	+	0.179388i
$604$	12.9801	−	9.43062i	0.528154	−	0.383727i
$605$	−11.3949	+	56.3151i	−0.463267	+	2.28953i
$606$	5.96763	+	4.33574i	0.242418	+	0.176127i
$607$			16.9442i			0.687745i	0.939016	+	0.343873i	$0.111739\pi$
$607$			16.9442i			0.687745i	−0.939016	+	0.343873i	$0.888261\pi$
$608$	−30.7652	+	42.3446i	−1.24769	+	1.71730i
$609$	0.209699	−	0.645388i	0.00849745	−	0.0261525i
$610$	−9.02513	−	1.82615i	−0.365417	−	0.0739388i
$611$	−1.93587	−	5.95798i	−0.0783168	−	0.241034i
$612$	−33.4183	−	10.8583i	−1.35085	−	0.438919i
$613$	23.6372	+	7.68019i	0.954697	+	0.310200i	0.744623	−	0.667485i	$-0.232629\pi$
$613$	23.6372	+	7.68019i	0.954697	+	0.310200i	0.210075	+	0.977685i	$0.432629\pi$
$614$	3.61350	+	11.1212i	0.145829	+	0.448815i
$615$	1.31945	−	2.33794i	0.0532054	−	0.0942748i
$616$	−13.6081	+	41.8813i	−0.548285	+	1.68745i
$617$	−3.59985	+	4.95477i	−0.144925	+	0.199471i	−0.875308	−	0.483566i	$-0.839341\pi$
$617$	−3.59985	+	4.95477i	−0.144925	+	0.199471i	0.730383	+	0.683037i	$0.239341\pi$
$618$			15.1289i			0.608573i
$619$	−0.127437	−	0.0925887i	−0.00512214	−	0.00372145i	0.585221	−	0.810874i	$-0.301008\pi$
$619$	−0.127437	−	0.0925887i	−0.00512214	−	0.00372145i	−0.590343	+	0.807152i	$0.701008\pi$
$620$	−5.12237	+	4.70386i	−0.205719	+	0.188911i
$621$	3.41278	−	2.47953i	0.136950	−	0.0995002i
$622$	9.67997	+	13.3233i	0.388132	+	0.534217i
$623$	−15.4048	+	5.00533i	−0.617181	+	0.200534i
$624$	−8.36696			−0.334947
$625$	−24.6385	−	4.23607i	−0.985540	−	0.169443i
$626$	79.4782			3.17659
$627$	30.5887	−	9.93888i	1.22160	−	0.396921i
$628$	55.6136	+	76.5455i	2.21922	+	3.05450i
$629$	−36.8672	+	26.7856i	−1.46999	+	1.06801i
$630$	−4.29161	+	3.94097i	−0.170982	+	0.157012i
$631$	−2.76261	−	2.00716i	−0.109978	−	0.0799036i	0.531437	−	0.847098i	$-0.321652\pi$
$631$	−2.76261	−	2.00716i	−0.109978	−	0.0799036i	−0.641415	+	0.767194i	$0.721652\pi$
$632$			77.4361i			3.08024i
$633$	2.61935	−	3.60523i	0.104110	−	0.143295i
$634$	25.4088	−	78.2003i	1.00911	−	3.10573i
$635$	17.3056	−	30.6638i	0.686751	−	1.21686i
$636$	−18.3884	−	56.5938i	−0.729149	−	2.24409i
$637$	−0.849893	−	0.276147i	−0.0336740	−	0.0109413i
$638$	10.1872	+	3.31003i	0.403316	+	0.131045i
$639$	1.65188	+	5.08398i	0.0653476	+	0.201119i
$640$	−3.45397	−	0.698880i	−0.136530	−	0.0276257i
$641$	3.18483	−	9.80191i	0.125793	−	0.387152i	−0.868251	−	0.496124i	$-0.834756\pi$
$641$	3.18483	−	9.80191i	0.125793	−	0.387152i	0.994045	+	0.108972i	$0.0347560\pi$
$642$	27.3691	−	37.6703i	1.08017	−	1.48673i
$643$		−	3.94322i		−	0.155505i	−0.996973	−	0.0777527i	$-0.975226\pi$
$643$		−	3.94322i		−	0.155505i	0.996973	−	0.0777527i	$-0.0247745\pi$
$644$	−16.3467	−	11.8766i	−0.644150	−	0.468002i
$645$	2.51866	−	12.4476i	0.0991720	−	0.490123i
$646$	82.1097	−	59.6562i	3.23056	−	2.34714i
$647$	−0.468671	−	0.645070i	−0.0184254	−	0.0253603i	0.799705	−	0.600393i	$-0.204989\pi$
$647$	−0.468671	−	0.645070i	−0.0184254	−	0.0253603i	−0.818130	+	0.575033i	$0.804989\pi$
$648$	6.91378	−	2.24642i	0.271599	−	0.0882478i
$649$	21.8994			0.859627
$650$	−0.989979	+	11.6006i	−0.0388302	+	0.455014i
$651$	0.649321			0.0254489
$652$	59.8958	−	19.4613i	2.34570	−	0.762164i
$653$	−10.1200	−	13.9290i	−0.396026	−	0.545082i	0.563715	−	0.825969i	$-0.309371\pi$
$653$	−10.1200	−	13.9290i	−0.396026	−	0.545082i	−0.959741	+	0.280887i	$0.909371\pi$
$654$	−20.3943	+	14.8173i	−0.797479	+	0.579402i
$655$	19.6693	−	2.26230i	0.768543	−	0.0883954i
$656$	9.09405	+	6.60721i	0.355063	+	0.257968i
$657$		−	14.0687i		−	0.548873i
$658$	10.7370	−	14.7782i	0.418572	−	0.576116i
$659$	10.3014	−	31.7044i	0.401285	−	1.23503i	−0.522672	−	0.852534i	$-0.675065\pi$
$659$	10.3014	−	31.7044i	0.401285	−	1.23503i	0.923957	−	0.382495i	$-0.124935\pi$
$660$	−43.8833	−	47.7878i	−1.70816	−	1.86014i
$661$	−11.9129	−	36.6640i	−0.463356	−	1.42606i	−0.861038	−	0.508541i	$-0.830185\pi$
$661$	−11.9129	−	36.6640i	−0.463356	−	1.42606i	0.397682	−	0.917523i	$-0.369815\pi$
$662$	−15.9257	−	5.17456i	−0.618968	−	0.201115i
$663$	6.23478	+	2.02580i	0.242139	+	0.0786756i
$664$	−0.391541	−	1.20504i	−0.0151947	−	0.0467645i
$665$	−1.35657	−	11.7945i	−0.0526056	−	0.457373i
$666$	5.00194	−	15.3944i	0.193821	−	0.596520i
$667$	−1.68261	+	2.31592i	−0.0651511	+	0.0896728i
$668$			29.8873i			1.15637i
$669$	−5.19216	−	3.77232i	−0.200740	−	0.145846i
$670$	13.1872	+	28.8550i	0.509465	+	1.11476i
$671$	−7.74487	+	5.62698i	−0.298988	+	0.217227i
$672$	−5.79441	−	7.97532i	−0.223524	−	0.307655i
$673$	−15.3237	+	4.97896i	−0.590684	+	0.191925i	−0.589081	−	0.808074i	$-0.700510\pi$
$673$	−15.3237	+	4.97896i	−0.590684	+	0.191925i	−0.00160290	+	0.999999i	$0.500510\pi$
$674$	37.9454			1.46160
$675$	−1.13515	−	4.86944i	−0.0436920	−	0.187425i
$676$	−58.4429			−2.24780
$677$	−9.70283	+	3.15264i	−0.372910	+	0.121166i	−0.489475	−	0.872017i	$-0.662812\pi$
$677$	−9.70283	+	3.15264i	−0.372910	+	0.121166i	0.116565	+	0.993183i	$0.462812\pi$
$678$	8.37935	+	11.5332i	0.321807	+	0.442929i
$679$	4.40403	−	3.19971i	0.169011	−	0.122794i
$680$	−103.851	−	58.6097i	−3.98249	−	2.24758i
$681$	10.8616	+	7.89139i	0.416216	+	0.302399i
$682$			10.2493i			0.392466i
$683$	−16.9795	+	23.3703i	−0.649704	+	0.894241i	−0.999086	−	0.0427394i	$-0.986391\pi$
$683$	−16.9795	+	23.3703i	−0.649704	+	0.894241i	0.349382	+	0.936980i	$0.386391\pi$
$684$	−7.85875	+	24.1867i	−0.300487	+	0.924803i
$685$	15.5453	−	7.10443i	0.593954	−	0.271446i
$686$	−0.805216	−	2.47820i	−0.0307433	−	0.0946181i
$687$	−6.28355	−	2.04165i	−0.239733	−	0.0778938i
$688$	50.5743	+	16.4326i	1.92813	+	0.626486i
$689$	3.43069	+	10.5586i	0.130699	+	0.402250i
$690$	22.3551	−	10.2166i	0.851045	−	0.388941i
$691$	−5.52236	+	16.9961i	−0.210080	+	0.646561i	0.789386	+	0.613897i	$0.210399\pi$
$691$	−5.52236	+	16.9961i	−0.210080	+	0.646561i	−0.999466	+	0.0326637i	$0.989601\pi$
$692$	61.6218	−	84.8151i	2.34251	−	3.22419i
$693$			6.05766i			0.230112i
$694$	19.2312	+	13.9723i	0.730008	+	0.530382i
$695$	−27.8131	−	15.6967i	−1.05501	−	0.595411i
$696$	−3.99100	+	2.89963i	−0.151278	+	0.109910i
$697$	−5.17684	−	7.12532i	−0.196087	−	0.269891i
$698$	10.4103	−	3.38251i	0.394035	−	0.128030i
$699$	20.3809			0.770877
$700$	−20.5021	+	12.3785i	−0.774907	+	0.467865i
$701$	25.2669			0.954316			0.477158	−	0.878818i	$-0.341667\pi$
$701$	25.2669			0.954316			0.477158	+	0.878818i	$0.341667\pi$
$702$	−2.21459	+	0.719565i	−0.0835844	+	0.0271582i
$703$	19.3863	+	26.6830i	0.731168	+	1.00637i
$704$	34.1171	−	24.7876i	1.28584	−	0.934216i
$705$	6.51572	+	14.2571i	0.245396	+	0.536954i
$706$	−25.3702	−	18.4325i	−0.954820	−	0.693718i
$707$		−	2.83084i		−	0.106465i
$708$	−10.1781	+	14.0090i	−0.382517	+	0.526489i
$709$	1.75000	−	5.38596i	0.0657228	−	0.202274i	−0.912802	−	0.408402i	$-0.866086\pi$
$709$	1.75000	−	5.38596i	0.0657228	−	0.202274i	0.978525	+	0.206128i	$0.0660863\pi$
$710$	3.55893	+	30.9427i	0.133564	+	1.16126i
$711$	3.29167	+	10.1307i	0.123447	+	0.379932i
$712$	111.987	+	36.3866i	4.19687	+	1.36365i
$713$	−2.60506	−	0.846434i	−0.0975601	−	0.0316992i
$714$	5.90703	+	18.1800i	0.221065	+	0.680368i
$715$	8.18722	+	8.91566i	0.306185	+	0.333427i
$716$	−18.8573	+	58.0368i	−0.704731	+	2.16894i
$717$	3.70857	−	5.10441i	0.138499	−	0.190628i
$718$		−	25.7668i		−	0.961608i
$719$	37.6019	+	27.3194i	1.40231	+	1.01884i	0.994385	+	0.105826i	$0.0337487\pi$
$719$	37.6019	+	27.3194i	1.40231	+	1.01884i	0.407928	+	0.913014i	$0.366251\pi$
$720$	20.7989	−	2.39223i	0.775131	−	0.0891531i
$721$	4.69715	−	3.41268i	0.174931	−	0.127095i
$722$	−14.0760	−	19.3740i	−0.523855	−	0.721024i
$723$	16.2636	−	5.28436i	0.604850	−	0.196528i
$724$	5.51237			0.204865
$725$	1.75373	+	2.90464i	0.0651320	+	0.107876i
$726$	−66.9550			−2.48493
$727$	−37.3725	+	12.1431i	−1.38607	+	0.450362i	−0.904660	−	0.426134i	$-0.859875\pi$
$727$	−37.3725	+	12.1431i	−1.38607	+	0.450362i	−0.481410	+	0.876495i	$0.659875\pi$
$728$	3.81844	+	5.25563i	0.141521	+	0.194787i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	16.2570	−	80.3445i	0.601698	−	2.97368i
$731$	−33.7076	−	24.4900i	−1.24672	−	0.905795i
$732$		−	7.56960i		−	0.279780i
$733$	4.34547	−	5.98103i	0.160504	−	0.220914i	−0.721189	−	0.692738i	$-0.756404\pi$
$733$	4.34547	−	5.98103i	0.160504	−	0.220914i	0.881693	+	0.471824i	$0.156404\pi$
$734$	−6.14549	+	18.9139i	−0.226834	+	0.698124i
$735$	2.19165	+	0.443462i	0.0808403	+	0.0163573i
$736$	12.8506	+	39.5501i	0.473680	+	1.45784i
$737$	31.3694	+	10.1925i	1.15551	+	0.375447i
$738$	2.97527	+	0.966723i	0.109521	+	0.0355855i
$739$	−8.03965	−	24.7435i	−0.295743	−	0.910205i	−0.982971	−	0.183762i	$-0.941172\pi$
$739$	−8.03965	−	24.7435i	−0.295743	−	0.910205i	0.687227	−	0.726442i	$-0.258828\pi$
$740$	32.7002	−	57.9417i	1.20208	−	2.12998i
$741$	1.46619	−	4.51247i	0.0538618	−	0.165770i
$742$	−19.0278	+	26.1896i	−0.698534	+	0.961450i
$743$		−	48.9391i		−	1.79540i	−0.440606	−	0.897700i	$-0.645237\pi$
$743$		−	48.9391i		−	1.79540i	0.440606	−	0.897700i	$-0.354763\pi$
$744$	−3.81879	−	2.77452i	−0.140004	−	0.101719i
$745$	−27.7944	+	25.5235i	−1.01831	+	0.935109i
$746$	39.4327	−	28.6495i	1.44373	−	1.04893i
$747$	−0.102448	−	0.141008i	−0.00374838	−	0.00515920i
$748$	−202.437	+	65.7757i	−7.40182	+	2.40500i
$749$	−17.8695			−0.652937
$750$	−0.855849	−	29.1204i	−0.0312512	−	1.06333i
$751$	−33.3763			−1.21792			−0.608959	−	0.793201i	$-0.708413\pi$
$751$	−33.3763			−1.21792			−0.608959	+	0.793201i	$0.708413\pi$
$752$	−62.4240	+	20.2828i	−2.27637	+	0.739637i
$753$	0.617251	+	0.849574i	0.0224939	+	0.0309602i
$754$	1.27838	−	0.928798i	0.0465559	−	0.0338248i
$755$	5.51685	−	5.06610i	0.200779	−	0.184374i
$756$	−3.87506	−	2.81540i	−0.140935	−	0.102395i
$757$		−	42.3093i		−	1.53776i	−0.639395	−	0.768878i	$-0.720815\pi$
$757$		−	42.3093i		−	1.53776i	0.639395	−	0.768878i	$-0.279185\pi$
$758$	17.6990	−	24.3606i	0.642857	−	0.884817i
$759$	7.89657	−	24.3031i	0.286627	−	0.882148i
$760$	−42.4192	+	75.1628i	−1.53871	+	2.72644i
$761$	6.66197	+	20.5034i	0.241496	+	0.743248i	0.996193	+	0.0871749i	$0.0277839\pi$
$761$	6.66197	+	20.5034i	0.241496	+	0.743248i	−0.754697	+	0.656074i	$0.772216\pi$
$762$	39.0228	+	12.6793i	1.41365	+	0.459322i
$763$	9.20083	+	2.98953i	0.333092	+	0.108228i
$764$	−5.31305	−	16.3519i	−0.192219	−	0.591591i
$765$	−16.0779	−	3.25321i	−0.581297	−	0.117620i
$766$	9.72601	−	29.9336i	0.351415	−	1.08154i
$767$	1.89891	−	2.61362i	0.0685656	−	0.0943724i
$768$		−	18.0298i		−	0.650593i
$769$	−2.05043	−	1.48972i	−0.0739404	−	0.0537208i	0.550201	−	0.835032i	$-0.314551\pi$
$769$	−2.05043	−	1.48972i	−0.0739404	−	0.0537208i	−0.624141	+	0.781311i	$0.714551\pi$
$770$	−6.99988	+	34.5945i	−0.252258	+	1.24670i
$771$	−19.4719	+	14.1472i	−0.701264	+	0.509498i
$772$	−9.50734	−	13.0857i	−0.342177	−	0.470966i
$773$	−29.4076	+	9.55510i	−1.05772	+	0.343673i	−0.785692	−	0.618617i	$-0.787693\pi$
$773$	−29.4076	+	9.55510i	−1.05772	+	0.343673i	−0.272024	+	0.962290i	$0.587693\pi$
$774$	14.7994			0.531952
$775$	−2.12473	+	2.45478i	−0.0763226	+	0.0881785i
$776$	−39.5732			−1.42060
$777$	−5.90789	+	1.91959i	−0.211944	+	0.0688649i
$778$	25.7418	+	35.4306i	0.922889	+	1.27025i
$779$	−5.15700	+	3.74678i	−0.184769	+	0.134242i
$780$	−9.50846	+	1.09363i	−0.340457	+	0.0391583i
$781$	26.1975	+	19.0336i	0.937421	+	0.681076i
$782$		−	80.6376i		−	2.88360i
$783$	−0.398872	+	0.549000i	−0.0142545	+	0.0196197i
$784$	−2.89329	+	8.90464i	−0.103332	+	0.318023i
$785$	29.8755	+	32.5336i	1.06630	+	1.16117i
$786$	7.12968	+	21.9429i	0.254307	+	0.782677i
$787$	−9.59150	−	3.11647i	−0.341900	−	0.111090i	0.133034	−	0.991111i	$-0.457528\pi$
$787$	−9.59150	−	3.11647i	−0.341900	−	0.111090i	−0.474934	+	0.880021i	$0.657528\pi$
$788$	−11.0139	−	3.57863i	−0.392354	−	0.127483i
$789$	8.48431	+	26.1120i	0.302049	+	0.929612i
$790$	7.09180	+	61.6588i	0.252315	+	2.19372i
$791$	1.69061	−	5.20317i	0.0601113	−	0.185004i
$792$	25.8841	−	35.6264i	0.919751	−	1.26593i
$793$			1.41224i			0.0501502i
$794$	8.08129	+	5.87140i	0.286794	+	0.208368i
$795$	−11.5470	−	25.2661i	−0.409529	−	0.896095i
$796$	−64.4694	+	46.8398i	−2.28506	+	1.66019i
$797$	−10.7709	−	14.8249i	−0.381525	−	0.525124i	0.574463	−	0.818531i	$-0.305211\pi$
$797$	−10.7709	−	14.8249i	−0.381525	−	0.525124i	−0.955988	+	0.293406i	$0.905211\pi$
$798$	13.1579	−	4.27526i	0.465784	−	0.151342i
$799$	51.4271			1.81936
$800$	49.1117	+	4.19111i	1.73636	+	0.148178i
$801$	16.1976			0.572314
$802$	−61.2975	+	19.9168i	−2.16449	+	0.703286i
$803$	−50.0931	−	68.9473i	−1.76775	−	2.43310i
$804$	−21.0996	+	15.3297i	−0.744124	+	0.540638i
$805$	−8.21476	−	4.63612i	−0.289532	−	0.163402i
$806$	1.22322	+	0.888722i	0.0430861	+	0.0313039i
$807$			16.3228i			0.574590i
$808$	−12.0960	+	16.6487i	−0.425536	+	0.585701i
$809$	10.1731	−	31.3096i	0.357667	−	1.10079i	−0.596780	−	0.802405i	$-0.703554\pi$
$809$	10.1731	−	31.3096i	0.357667	−	1.10079i	0.954447	−	0.298381i	$-0.0964465\pi$
$810$	5.29939	−	2.42191i	0.186202	−	0.0850971i
$811$	−5.58860	−	17.2000i	−0.196242	−	0.603972i	−0.999960	−	0.00896087i	$-0.997148\pi$
$811$	−5.58860	−	17.2000i	−0.196242	−	0.603972i	0.803717	−	0.595011i	$-0.202852\pi$
$812$	3.09131	+	1.00443i	0.108484	+	0.0352485i
$813$	−16.3423	−	5.30993i	−0.573149	−	0.186227i
$814$	−30.3001	−	93.2540i	−1.06202	−	3.26855i
$815$	26.7402	−	12.2207i	0.936670	−	0.428073i
$816$	21.2251	−	65.3241i	0.743026	−	2.28680i
$817$	−17.7248	+	24.3961i	−0.620113	+	0.853512i
$818$		−	15.5533i		−	0.543809i
$819$	0.722962	+	0.525263i	0.0252623	+	0.0183542i
$820$	11.1984	+	6.31996i	0.391064	+	0.220703i
$821$	−6.65869	+	4.83782i	−0.232390	+	0.168841i	−0.697886	−	0.716209i	$-0.745876\pi$
$821$	−6.65869	+	4.83782i	−0.232390	+	0.168841i	0.465496	+	0.885050i	$0.345876\pi$
$822$	11.7071	+	16.1135i	0.408333	+	0.562022i
$823$	−1.75546	+	0.570385i	−0.0611916	+	0.0198824i	−0.339453	−	0.940623i	$-0.610242\pi$
$823$	−1.75546	+	0.570385i	−0.0611916	+	0.0198824i	0.278261	+	0.960505i	$0.410242\pi$
$824$	−42.2071			−1.47036
$825$	−22.9012	−	19.8221i	−0.797319	−	0.690116i
$826$	9.42013			0.327768
$827$	14.8922	−	4.83876i	0.517851	−	0.168260i	−0.0384186	−	0.999262i	$-0.512232\pi$
$827$	14.8922	−	4.83876i	0.517851	−	0.168260i	0.556270	+	0.831002i	$0.312232\pi$
$828$	11.8766	+	16.3467i	0.412739	+	0.568087i
$829$	−36.9045	+	26.8127i	−1.28175	+	0.931244i	−0.999604	−	0.0281290i	$-0.991045\pi$
$829$	−36.9045	+	26.8127i	−1.28175	+	0.931244i	−0.282142	+	0.959373i	$0.591045\pi$
$830$	−0.422126	−	0.923658i	−0.0146522	−	0.0320607i
$831$	−12.3318	−	8.95955i	−0.427784	−	0.310803i
$832$		−	6.22111i		−	0.215678i
$833$	4.31197	−	5.93491i	0.149401	−	0.205633i
$834$	11.5005	−	35.3950i	0.398231	−	1.22563i
$835$	1.59426	+	13.8611i	0.0551715	+	0.479682i
$836$	47.6057	+	146.515i	1.64648	+	5.06733i
$837$	−0.617541	−	0.200651i	−0.0213453	−	0.00693552i
$838$	−59.5439	−	19.3470i	−2.05691	−	0.668330i
$839$	−1.41208	−	4.34593i	−0.0487503	−	0.150038i	0.923718	−	0.383073i	$-0.125134\pi$
$839$	−1.41208	−	4.34593i	−0.0487503	−	0.150038i	−0.972468	+	0.233035i	$0.925134\pi$
$840$	−10.9947	−	11.9729i	−0.379353	−	0.413105i
$841$	−8.81919	+	27.1427i	−0.304110	+	0.935954i
$842$	48.5075	−	66.7648i	1.67168	−	2.30087i
$843$		−	24.3846i		−	0.839850i
$844$	17.2685	+	12.5463i	0.594405	+	0.431861i
$845$	−27.1045	+	3.11748i	−0.932424	+	0.107244i
$846$	−14.7782	+	10.7370i	−0.508086	+	0.369146i
$847$	15.1033	+	20.7879i	0.518955	+	0.714281i
$848$	110.626	−	35.9446i	3.79892	−	1.23434i
$849$	−23.8812			−0.819601
$850$	−88.0592	−	37.1573i	−3.02041	−	1.27449i
$851$	26.2046			0.898282
$852$	−24.3515	+	7.91227i	−0.834267	+	0.271070i
$853$	−22.2769	−	30.6616i	−0.762748	−	1.04983i	−0.996981	−	0.0776521i	$-0.975258\pi$
$853$	−22.2769	−	30.6616i	−0.762748	−	1.04983i	0.234232	−	0.972181i	$-0.424742\pi$
$854$	−3.33149	+	2.42047i	−0.114001	+	0.0828269i
$855$	−2.35454	+	11.6365i	−0.0805236	+	0.397959i
$856$	105.094	+	76.3554i	3.59205	+	2.60978i
$857$		−	48.7889i		−	1.66660i	−0.552824	−	0.833298i	$-0.686450\pi$
$857$		−	48.7889i		−	1.66660i	0.552824	−	0.833298i	$-0.313550\pi$
$858$	−8.29108	+	11.4117i	−0.283053	+	0.389589i
$859$	7.30389	−	22.4791i	0.249206	−	0.766976i	−0.745711	−	0.666270i	$-0.767890\pi$
$859$	7.30389	−	22.4791i	0.249206	−	0.766976i	0.994916	−	0.100706i	$-0.0321102\pi$
$860$	59.6219	+	12.0640i	2.03309	+	0.411378i
$861$	−0.370998	−	1.14182i	−0.0126436	−	0.0389130i
$862$	−16.1093	−	5.23424i	−0.548686	−	0.178279i
$863$	40.8820	+	13.2834i	1.39164	+	0.452171i	0.906478	−	0.422253i	$-0.138760\pi$
$863$	40.8820	+	13.2834i	1.39164	+	0.452171i	0.485162	+	0.874424i	$0.338760\pi$
$864$	3.04630	+	9.37555i	0.103637	+	0.318963i
$865$	24.0546	−	42.6224i	0.817881	−	1.44921i
$866$	3.46059	−	10.6506i	0.117596	−	0.361922i
$867$	−21.6401	+	29.7850i	−0.734935	+	1.01155i
$868$			3.11014i			0.105565i
$869$	52.2032	+	37.9278i	1.77087	+	1.28661i
$870$	−2.91230	+	2.67435i	−0.0987361	+	0.0906690i
$871$	3.93650	−	2.86003i	0.133383	−	0.0969085i
$872$	−41.3379	−	56.8967i	−1.39988	−	1.92677i
$873$	−5.17724	+	1.68219i	−0.175223	+	0.0569334i
$874$	−58.3621			−1.97413
$875$	−8.84812	+	6.83452i	−0.299121	+	0.231049i
$876$	67.3869			2.27679
$877$	−1.98987	+	0.646548i	−0.0671932	+	0.0218324i	−0.342421	−	0.939547i	$-0.611247\pi$
$877$	−1.98987	+	0.646548i	−0.0671932	+	0.0218324i	0.275228	+	0.961379i	$0.411247\pi$
$878$	20.2120	+	27.8194i	0.682122	+	0.938860i
$879$	−11.6215	+	8.44348i	−0.391982	+	0.284792i
$880$	93.4127	−	85.7805i	3.14894	−	2.89166i
$881$	35.0566	+	25.4701i	1.18109	+	0.858110i	0.992294	−	0.123907i	$-0.0395425\pi$
$881$	35.0566	+	25.4701i	1.18109	+	0.858110i	0.188793	+	0.982017i	$0.439542\pi$
$882$			2.60573i			0.0877396i
$883$	25.4034	−	34.9647i	0.854892	−	1.17666i	−0.127872	−	0.991791i	$-0.540815\pi$
$883$	25.4034	−	34.9647i	0.854892	−	1.17666i	0.982764	−	0.184867i	$-0.0591853\pi$
$884$	−9.70327	+	29.8636i	−0.326356	+	1.00442i
$885$	−3.97311	+	7.03997i	−0.133555	+	0.236646i
$886$	0.0695761	+	0.214133i	0.00233745	+	0.00719395i
$887$	−33.2062	−	10.7893i	−1.11495	−	0.362270i	−0.307114	−	0.951673i	$-0.599363\pi$
$887$	−33.2062	−	10.7893i	−1.11495	−	0.362270i	−0.807840	+	0.589402i	$0.799363\pi$
$888$	42.9479	+	13.9546i	1.44124	+	0.468286i
$889$	−4.86592	−	14.9758i	−0.163198	−	0.502271i
$890$	92.5022	+	18.7170i	3.10068	+	0.627395i
$891$	1.87192	−	5.76118i	0.0627117	−	0.193007i
$892$	18.0688	−	24.8696i	0.604989	−	0.832696i
$893$		−	37.2208i		−	1.24555i
$894$	−35.5758	−	25.8473i	−1.18983	−	0.864463i
$895$	−5.64979	+	27.9221i	−0.188852	+	0.933333i
$896$	−1.27498	+	0.926329i	−0.0425942	+	0.0309465i
$897$	−2.21578	−	3.04977i	−0.0739829	−	0.101829i
$898$	18.0619	−	5.86865i	0.602732	−	0.195840i
$899$	0.440630			0.0146958
$900$	23.3238	−	5.43719i	0.777461	−	0.181240i
$901$	−91.1377			−3.03624
$902$	18.0232	−	5.85608i	0.600105	−	0.194986i
$903$	−3.33835	−	4.59484i	−0.111093	−	0.152907i
$904$	−32.1758	+	23.3771i	−1.07015	+	0.777509i
$905$	2.55651	−	0.294042i	0.0849814	−	0.00977429i
$906$	7.06135	+	5.13037i	0.234598	+	0.170445i
$907$			6.72803i			0.223401i	0.993742	+	0.111700i	$0.0356297\pi$
$907$			6.72803i			0.223401i	−0.993742	+	0.111700i	$0.964370\pi$
$908$	−37.7985	+	52.0252i	−1.25439	+	1.72652i
$909$	−0.874776	+	2.69228i	−0.0290145	+	0.0892974i
$910$	3.52177	+	3.83511i	0.116746	+	0.127133i
$911$	−15.5445	−	47.8411i	−0.515012	−	1.58505i	−0.783260	−	0.621695i	$-0.786444\pi$
$911$	−15.5445	−	47.8411i	−0.515012	−	1.58505i	0.268247	−	0.963350i	$-0.413556\pi$
$912$	−47.2788	−	15.3618i	−1.56556	−	0.508680i
$913$	−1.00415	−	0.326267i	−0.0332324	−	0.0107978i
$914$	−3.20063	−	9.85054i	−0.105868	−	0.325827i
$915$	−0.403779	−	3.51061i	−0.0133485	−	0.116057i
$916$	9.77918	−	30.0972i	0.323113	−	0.994440i
$917$	5.20447	−	7.16334i	0.171867	−	0.236554i
$918$		−	19.1155i		−	0.630907i
$919$	30.4232	+	22.1037i	1.00357	+	0.729135i	0.962850	−	0.270036i	$-0.0870356\pi$
$919$	30.4232	+	22.1037i	1.00357	+	0.729135i	0.0407177	+	0.999171i	$0.487036\pi$
$920$	28.5028	+	62.3673i	0.939710	+	2.05619i
$921$	−3.63055	+	2.63775i	−0.119631	+	0.0869169i
$922$	41.6282	+	57.2963i	1.37095	+	1.88695i
$923$	4.54320	−	1.47617i	0.149541	−	0.0485889i
$924$	−29.0152			−0.954531
$925$	12.0749	−	28.6164i	0.397021	−	0.940901i
$926$	−43.1682			−1.41860
$927$	−5.52183	+	1.79415i	−0.181361	+	0.0589277i
$928$	−3.93209	−	5.41206i	−0.129077	−	0.177660i
$929$	13.8499	−	10.0626i	0.454401	−	0.330142i	−0.336930	−	0.941530i	$-0.609388\pi$
$929$	13.8499	−	10.0626i	0.454401	−	0.330142i	0.791331	+	0.611388i	$0.209388\pi$
$930$	−3.29483	−	1.85949i	−0.108042	−	0.0609749i
$931$	−4.29544	−	3.12082i	−0.140777	−	0.102281i
$932$			97.6213i			3.19769i
$933$	−3.71488	+	5.11309i	−0.121620	+	0.167395i
$934$	−8.40227	+	25.8595i	−0.274931	+	0.846150i
$935$	−90.3771	+	41.3037i	−2.95565	+	1.35078i
$936$	−2.00747	−	6.17836i	−0.0656163	−	0.201946i
$937$	26.0199	+	8.45437i	0.850032	+	0.276192i	0.701460	−	0.712709i	$-0.252532\pi$
$937$	26.0199	+	8.45437i	0.850032	+	0.276192i	0.148573	+	0.988901i	$0.452532\pi$
$938$	13.4937	+	4.38436i	0.440584	+	0.143155i
$939$	9.42542	+	29.0084i	0.307587	+	0.946655i
$940$	−68.2893	+	31.2093i	−2.22735	+	1.01793i
$941$	7.69346	−	23.6780i	0.250800	−	0.771882i	−0.743829	−	0.668370i	$-0.766992\pi$
$941$	7.69346	−	23.6780i	0.250800	−	0.771882i	0.994628	−	0.103511i	$-0.0330078\pi$
$942$	−30.2545	+	41.6417i	−0.985744	+	1.35676i
$943$			5.06455i			0.164924i
$944$	−27.3839	−	19.8955i	−0.891269	−	0.647545i
$945$	−1.94735	−	1.09901i	−0.0633473	−	0.0357510i
$946$	72.5280	−	52.6947i	2.35809	−	1.71325i
$947$	14.4806	+	19.9308i	0.470555	+	0.647664i	0.976656	−	0.214811i	$-0.0689134\pi$
$947$	14.4806	+	19.9308i	0.470555	+	0.647664i	−0.506100	+	0.862475i	$0.668913\pi$
$948$	−48.5246	+	15.7666i	−1.57600	+	0.512075i
$949$	−12.5722			−0.408112
$950$	−26.8929	+	63.7336i	−0.872521	+	2.06779i
$951$	31.5553			1.02325
$952$	−50.7192	+	16.4797i	−1.64382	+	0.534109i
$953$	−27.5910	−	37.9757i	−0.893760	−	1.23015i	−0.972416	−	0.233253i	$-0.925063\pi$
$953$	−27.5910	−	37.9757i	−0.893760	−	1.23015i	0.0786563	−	0.996902i	$-0.474937\pi$
$954$	26.1896	−	19.0278i	0.847919	−	0.616049i
$955$	−3.33632	−	7.30024i	−0.107961	−	0.236230i
$956$	24.4493	+	17.7635i	0.790747	+	0.574511i
$957$			4.11074i			0.132881i
$958$	34.0261	−	46.8329i	1.09933	−	1.51310i
$959$	2.36202	−	7.26956i	0.0762737	−	0.234746i
$960$	1.77870	+	15.4647i	0.0574073	+	0.499121i
$961$	−9.44924	−	29.0818i	−0.304814	−	0.938122i
$962$	−13.7569	−	4.46988i	−0.443540	−	0.144115i
$963$	16.9949	+	5.52198i	0.547653	+	0.177943i
$964$	25.3113	+	77.9001i	0.815221	+	2.50899i
$965$	−5.10732	−	5.56173i	−0.164410	−	0.179038i
$966$	3.39675	−	10.4541i	0.109289	−	0.336356i
$967$	−3.76006	+	5.17528i	−0.120916	+	0.166426i	−0.865184	−	0.501455i	$-0.832798\pi$
$967$	−3.76006	+	5.17528i	−0.120916	+	0.166426i	0.744268	+	0.667881i	$0.232798\pi$
$968$		−	186.794i		−	6.00378i
$969$	31.5112	+	22.8942i	1.01228	+	0.735468i
$970$	−31.5103	+	3.62422i	−1.01174	+	0.116367i
$971$	−34.4116	+	25.0015i	−1.10432	+	0.802335i	−0.981760	−	0.190126i	$-0.939110\pi$
$971$	−34.4116	+	25.0015i	−1.10432	+	0.802335i	−0.122560	+	0.992461i	$0.539110\pi$
$972$	2.81540	+	3.87506i	0.0903039	+	0.124293i
$973$	−13.5835	+	4.41355i	−0.435467	+	0.141492i
$974$	−45.8603			−1.46946
$975$	−4.35148	+	1.01441i	−0.139359	+	0.0324870i
$976$	14.7966			0.473627
$977$	−51.5650	+	16.7545i	−1.64971	+	0.536024i	−0.978678	−	0.205402i	$-0.934150\pi$
$977$	−51.5650	+	16.7545i	−1.64971	+	0.536024i	−0.671034	+	0.741426i	$0.734150\pi$
$978$	20.1380	+	27.7176i	0.643944	+	0.886313i
$979$	79.3804	−	57.6732i	2.53701	−	1.84324i
$980$	−2.12411	+	10.4977i	−0.0678522	+	0.335336i
$981$	−7.82669	−	5.68642i	−0.249887	−	0.181554i
$982$		−	52.9952i		−	1.69114i
$983$	5.39070	−	7.41966i	0.171937	−	0.236651i	−0.714349	−	0.699790i	$-0.753277\pi$
$983$	5.39070	−	7.41966i	0.171937	−	0.236651i	0.886286	+	0.463139i	$0.153277\pi$
$984$	−2.69700	+	8.30052i	−0.0859773	+	0.264611i
$985$	−5.29890	−	1.07218i	−0.168837	−	0.0341626i
$986$	4.00852	+	12.3369i	0.127657	+	0.392888i
$987$	6.66717	+	2.16629i	0.212218	+	0.0689539i
$988$	21.6140	+	7.02282i	0.687633	+	0.223426i
$989$	7.40366	+	22.7861i	0.235423	+	0.724557i
$990$	17.3476	−	30.7382i	0.551342	−	0.976924i
$991$	8.81731	−	27.1369i	0.280091	−	0.862031i	−0.707736	−	0.706477i	$-0.750284\pi$
$991$	8.81731	−	27.1369i	0.280091	−	0.862031i	0.987827	−	0.155555i	$-0.0497165\pi$
$992$	3.76243	−	5.17854i	0.119457	−	0.164419i
$993$		−	6.42631i		−	0.203933i
$994$	11.2690	+	8.18740i	0.357431	+	0.259689i
$995$	−27.4010	+	25.1622i	−0.868669	+	0.797696i
$996$	0.675404	−	0.490710i	0.0214010	−	0.0155487i
$997$	20.4253	+	28.1130i	0.646875	+	0.890348i	0.998959	−	0.0456210i	$-0.0145267\pi$
$997$	20.4253	+	28.1130i	0.646875	+	0.890348i	−0.352083	+	0.935969i	$0.614527\pi$
$998$	62.6493	−	20.3560i	1.98313	−	0.644357i
$999$	6.21193			0.196537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.169.2	✓	72
25.4	even	10	inner	525.2.z.b.379.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.169.2	✓	72	1.1	even	1	trivial
525.2.z.b.379.2	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)

\(f(q)\)	\(=\)	\(q+(-2.47820 + 0.805216i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.87506 - 2.81540i) q^{4} +(1.64699 - 1.51242i) q^{5} +(2.10808 + 1.53161i) q^{6} -1.00000i q^{7} +(-4.27295 + 5.88121i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-2.47820 + 0.805216i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.87506 - 2.81540i) q^{4} +(1.64699 - 1.51242i) q^{5} +(2.10808 + 1.53161i) q^{6} -1.00000i q^{7} +(-4.27295 + 5.88121i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-2.86374 + 5.07427i) q^{10} +(1.87192 + 5.76118i) q^{11} +(-4.55541 - 1.48014i) q^{12} +(0.849893 + 0.276147i) q^{13} +(0.805216 + 2.47820i) q^{14} +(-2.19165 - 0.443462i) q^{15} +(2.89329 - 8.90464i) q^{16} +(-4.31197 + 5.93491i) q^{17} -2.60573i q^{18} +(4.29544 + 3.12082i) q^{19} +(2.12411 - 10.4977i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-9.27798 - 12.7700i) q^{22} +(4.01197 - 1.30357i) q^{23} +7.26958 q^{24} +(0.425146 - 4.98189i) q^{25} -2.32856 q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.81540 - 3.87506i) q^{28} +(-0.549000 + 0.398872i) q^{29} +(5.78843 - 0.665767i) q^{30} +(-0.525312 - 0.381661i) q^{31} +9.85803i q^{32} +(3.56060 - 4.90075i) q^{33} +(5.90703 - 18.1800i) q^{34} +(-1.51242 - 1.64699i) q^{35} +(1.48014 + 4.55541i) q^{36} +(5.90789 + 1.91959i) q^{37} +(-13.1579 - 4.27526i) q^{38} +(-0.276147 - 0.849893i) q^{39} +(1.85738 + 16.1488i) q^{40} +(-0.370998 + 1.14182i) q^{41} +(1.53161 - 2.10808i) q^{42} +5.67954i q^{43} +(23.4738 + 17.0547i) q^{44} +(0.929453 + 2.03374i) q^{45} +(-8.89280 + 6.46100i) q^{46} +(-4.12054 - 5.67143i) q^{47} +(-8.90464 + 2.89329i) q^{48} -1.00000 q^{49} +(2.95790 + 12.6885i) q^{50} +7.33596 q^{51} +(4.07085 - 1.32270i) q^{52} +(7.30230 + 10.0508i) q^{53} +(-2.10808 + 1.53161i) q^{54} +(11.7964 + 6.65746i) q^{55} +(5.88121 + 4.27295i) q^{56} -5.30946i q^{57} +(1.03935 - 1.43055i) q^{58} +(1.11715 - 3.43822i) q^{59} +(-9.74131 + 4.45193i) q^{60} +(0.488353 + 1.50300i) q^{61} +(1.60915 + 0.522843i) q^{62} +(0.951057 + 0.309017i) q^{63} +(-2.15126 - 6.62089i) q^{64} +(1.81742 - 0.830587i) q^{65} +(-4.87772 + 15.0121i) q^{66} +(3.20047 - 4.40506i) q^{67} +35.1381i q^{68} +(-3.41278 - 2.47953i) q^{69} +(5.07427 + 2.86374i) q^{70} +(4.32469 - 3.14207i) q^{71} +(-4.27295 - 5.88121i) q^{72} +(-13.3801 + 4.34747i) q^{73} -16.1866 q^{74} +(-4.28033 + 2.58433i) q^{75} +25.4315 q^{76} +(5.76118 - 1.87192i) q^{77} +(1.36869 + 1.88385i) q^{78} +(8.61771 - 6.26113i) q^{79} +(-8.70237 - 19.0417i) q^{80} +(-0.809017 - 0.587785i) q^{81} -3.12838i q^{82} +(-0.102448 + 0.141008i) q^{83} +(-1.48014 + 4.55541i) q^{84} +(1.87434 + 16.2963i) q^{85} +(-4.57325 - 14.0750i) q^{86} +(0.645388 + 0.209699i) q^{87} +(-41.8813 - 13.6081i) q^{88} +(-5.00533 - 15.4048i) q^{89} +(-3.94097 - 4.29161i) q^{90} +(0.276147 - 0.849893i) q^{91} +(11.8766 - 16.3467i) q^{92} +0.649321i q^{93} +(14.7782 + 10.7370i) q^{94} +(11.7945 - 1.35657i) q^{95} +(7.97532 - 5.79441i) q^{96} +(3.19971 + 4.40403i) q^{97} +(2.47820 - 0.805216i) q^{98} -6.05766 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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