LMFDB - Embedded newform 125.2.g.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	125.71
Dual form			125.2.g.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32504 + 1.60169i) q^{2} +(-2.43590 - 0.307726i) q^{3} +(-0.434938 - 2.28002i) q^{4} +(0.883071 - 2.05431i) q^{5} +(3.72054 - 3.49382i) q^{6} +(0.629574 + 0.457412i) q^{7} +(0.584987 + 0.321599i) q^{8} +(2.93319 + 0.753115i) q^{9} +O(q^{10})$	\(q+(-1.32504 + 1.60169i) q^{2} +(-2.43590 - 0.307726i) q^{3} +(-0.434938 - 2.28002i) q^{4} +(0.883071 - 2.05431i) q^{5} +(3.72054 - 3.49382i) q^{6} +(0.629574 + 0.457412i) q^{7} +(0.584987 + 0.321599i) q^{8} +(2.93319 + 0.753115i) q^{9} +(2.12027 + 4.13644i) q^{10} +(2.06052 - 2.49074i) q^{11} +(0.357844 + 5.68776i) q^{12} +(3.07406 + 0.789285i) q^{13} +(-1.56684 + 0.402296i) q^{14} +(-2.78324 + 4.73236i) q^{15} +(3.02605 - 1.19810i) q^{16} +(1.16451 - 6.10458i) q^{17} +(-5.09284 + 3.70016i) q^{18} +(-4.38516 + 0.553975i) q^{19} +(-5.06795 - 1.11993i) q^{20} +(-1.39282 - 1.30795i) q^{21} +(1.25914 + 6.60063i) q^{22} +(-2.87542 - 4.53094i) q^{23} +(-1.32601 - 0.963402i) q^{24} +(-3.44037 - 3.62820i) q^{25} +(-5.33743 + 3.87787i) q^{26} +(-0.0646699 - 0.0256046i) q^{27} +(0.769085 - 1.63439i) q^{28} +(2.56070 - 5.44177i) q^{29} +(-3.89189 - 10.7284i) q^{30} +(0.00238475 - 0.0125013i) q^{31} +(-2.50321 + 7.70409i) q^{32} +(-5.78569 + 5.43313i) q^{33} +(8.23465 + 9.95398i) q^{34} +(1.49562 - 0.889412i) q^{35} +(0.441365 - 7.01530i) q^{36} +(6.84347 - 2.70952i) q^{37} +(4.92320 - 7.75772i) q^{38} +(-7.24524 - 2.86859i) q^{39} +(1.17725 - 0.917750i) q^{40} +(-6.20373 + 9.77552i) q^{41} +(3.94047 - 0.497797i) q^{42} +(1.76593 + 5.43498i) q^{43} +(-6.57514 - 3.61471i) q^{44} +(4.13734 - 5.36062i) q^{45} +(11.0672 + 1.39811i) q^{46} +(-5.86131 + 3.22228i) q^{47} +(-7.73985 + 1.98725i) q^{48} +(-1.97598 - 6.08145i) q^{49} +(10.3699 - 0.702923i) q^{50} +(-4.71518 + 14.5118i) q^{51} +(0.462563 - 7.35223i) q^{52} +(1.75608 + 1.64907i) q^{53} +(0.126701 - 0.0696543i) q^{54} +(-3.29716 - 6.43244i) q^{55} +(0.221189 + 0.470051i) q^{56} +10.8523 q^{57} +(5.32302 + 11.3120i) q^{58} +(0.0986283 + 1.56765i) q^{59} +(12.0004 + 4.28758i) q^{60} +(7.16121 + 11.2843i) q^{61} +(0.0168634 + 0.0203843i) q^{62} +(1.50217 + 1.81582i) q^{63} +(-5.53494 - 8.72167i) q^{64} +(4.33605 - 5.61808i) q^{65} +(-1.03595 - 16.4660i) q^{66} +(-3.96761 - 8.43161i) q^{67} -14.4251 q^{68} +(5.60996 + 11.9218i) q^{69} +(-0.557190 + 3.57403i) q^{70} +(4.47304 - 2.45907i) q^{71} +(1.47368 + 1.38387i) q^{72} +(0.634423 - 10.0839i) q^{73} +(-4.72802 + 14.5513i) q^{74} +(7.26393 + 9.89665i) q^{75} +(3.17035 + 9.75733i) q^{76} +(2.43654 - 0.625598i) q^{77} +(14.1948 - 7.80366i) q^{78} +(1.81498 + 0.229286i) q^{79} +(0.210953 - 7.27444i) q^{80} +(-7.81158 - 4.29445i) q^{81} +(-7.43721 - 22.8894i) q^{82} +(3.86348 - 0.488071i) q^{83} +(-2.37636 + 3.74455i) q^{84} +(-11.5124 - 7.78305i) q^{85} +(-11.0451 - 4.37306i) q^{86} +(-7.91220 + 12.4676i) q^{87} +(2.00640 - 0.794389i) q^{88} +(0.254721 - 4.04868i) q^{89} +(3.10394 + 13.7298i) q^{90} +(1.57432 + 1.90303i) q^{91} +(-9.08002 + 8.52670i) q^{92} +(-0.00965601 + 0.0297182i) q^{93} +(2.60534 - 13.6576i) q^{94} +(-2.73437 + 9.49768i) q^{95} +(8.46833 - 17.9961i) q^{96} +(-0.777570 + 1.65242i) q^{97} +(12.3589 + 4.89322i) q^{98} +(7.91970 - 5.75400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{18}{25}\right)$

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 $

$2$	−1.32504	+	1.60169i	−0.936941	+	1.13257i	0.0540360	+	0.998539i	$0.482791\pi$
$2$	−1.32504	+	1.60169i	−0.936941	+	1.13257i	−0.990977	+	0.134029i	$0.957209\pi$
$3$	−2.43590	−	0.307726i	−1.40637	−	0.177666i	−0.614771	−	0.788706i	$-0.710751\pi$
$3$	−2.43590	−	0.307726i	−1.40637	−	0.177666i	−0.791600	+	0.611040i	$0.790751\pi$
$4$	−0.434938	−	2.28002i	−0.217469	−	1.14001i
$5$	0.883071	−	2.05431i	0.394921	−	0.918715i
$5$	0.883071	−	2.05431i	0.394921	−	0.918715i
$6$	3.72054	−	3.49382i	1.51891	−	1.42635i
$7$	0.629574	+	0.457412i	0.237956	+	0.172885i	0.700372	−	0.713778i	$-0.253017\pi$
$7$	0.629574	+	0.457412i	0.237956	+	0.172885i	−0.462416	+	0.886663i	$0.653017\pi$
$8$	0.584987	+	0.321599i	0.206824	+	0.113703i
$9$	2.93319	+	0.753115i	0.977729	+	0.251038i
$10$	2.12027	+	4.13644i	0.670489	+	1.30806i
$11$	2.06052	−	2.49074i	0.621270	−	0.750986i	−0.362192	−	0.932104i	$-0.617971\pi$
$11$	2.06052	−	2.49074i	0.621270	−	0.750986i	0.983461	+	0.181118i	$0.0579715\pi$
$12$	0.357844	+	5.68776i	0.103301	+	1.64192i
$13$	3.07406	+	0.789285i	0.852592	+	0.218908i	0.649604	−	0.760273i	$-0.274935\pi$
$13$	3.07406	+	0.789285i	0.852592	+	0.218908i	0.202988	+	0.979181i	$0.434935\pi$
$14$	−1.56684	+	0.402296i	−0.418756	+	0.107518i
$15$	−2.78324	+	4.73236i	−0.718630	+	1.22189i
$16$	3.02605	−	1.19810i	0.756512	−	0.299524i
$17$	1.16451	−	6.10458i	0.282436	−	1.48058i	−0.504429	−	0.863453i	$-0.668297\pi$
$17$	1.16451	−	6.10458i	0.282436	−	1.48058i	0.786864	−	0.617126i	$-0.211703\pi$
$18$	−5.09284	+	3.70016i	−1.20039	+	0.872137i
$19$	−4.38516	+	0.553975i	−1.00603	+	0.127091i	−0.611042	−	0.791598i	$-0.709250\pi$
$19$	−4.38516	+	0.553975i	−1.00603	+	0.127091i	−0.394983	+	0.918688i	$0.629250\pi$
$20$	−5.06795	−	1.11993i	−1.13323	−	0.250423i
$21$	−1.39282	−	1.30795i	−0.303939	−	0.285418i
$22$	1.25914	+	6.60063i	0.268449	+	1.40726i
$23$	−2.87542	−	4.53094i	−0.599567	−	0.944766i	−0.999600	−	0.0282655i	$-0.991002\pi$
$23$	−2.87542	−	4.53094i	−0.599567	−	0.944766i	0.400034	−	0.916500i	$-0.368998\pi$
$24$	−1.32601	−	0.963402i	−0.270670	−	0.196654i
$25$	−3.44037	−	3.62820i	−0.688074	−	0.725640i
$26$	−5.33743	+	3.87787i	−1.04676	+	0.760513i
$27$	−0.0646699	−	0.0256046i	−0.0124457	−	0.00492761i
$28$	0.769085	−	1.63439i	0.145343	−	0.308870i
$29$	2.56070	−	5.44177i	0.475510	−	1.01051i	−0.512864	−	0.858470i	$-0.671416\pi$
$29$	2.56070	−	5.44177i	0.475510	−	1.01051i	0.988374	−	0.152041i	$-0.0485845\pi$
$30$	−3.89189	−	10.7284i	−0.710558	−	1.95874i
$31$	0.00238475	−	0.0125013i	0.000428314	−	0.00224530i	−0.982072	−	0.188504i	$-0.939636\pi$
$31$	0.00238475	−	0.0125013i	0.000428314	−	0.00224530i	0.982501	+	0.186259i	$0.0596362\pi$
$32$	−2.50321	+	7.70409i	−0.442509	+	1.36190i
$33$	−5.78569	+	5.43313i	−1.00716	+	0.945786i
$34$	8.23465	+	9.95398i	1.41223	+	1.70709i
$35$	1.49562	−	0.889412i	0.252807	−	0.150338i
$36$	0.441365	−	7.01530i	0.0735608	−	1.16922i
$37$	6.84347	−	2.70952i	1.12506	−	0.445443i	0.269424	−	0.963022i	$-0.413167\pi$
$37$	6.84347	−	2.70952i	1.12506	−	0.445443i	0.855635	+	0.517579i	$0.173167\pi$
$38$	4.92320	−	7.75772i	0.798648	−	1.25847i
$39$	−7.24524	−	2.86859i	−1.16017	−	0.459343i
$40$	1.17725	−	0.917750i	0.186140	−	0.145109i
$41$	−6.20373	+	9.77552i	−0.968861	+	1.52668i	−0.123596	+	0.992333i	$0.539443\pi$
$41$	−6.20373	+	9.77552i	−0.968861	+	1.52668i	−0.845265	+	0.534347i	$0.820557\pi$
$42$	3.94047	−	0.497797i	0.608028	−	0.0768118i
$43$	1.76593	+	5.43498i	0.269302	+	0.828827i	0.990671	+	0.136276i	$0.0435134\pi$
$43$	1.76593	+	5.43498i	0.269302	+	0.828827i	−0.721369	+	0.692551i	$0.756487\pi$
$44$	−6.57514	−	3.61471i	−0.991240	−	0.544939i
$45$	4.13734	−	5.36062i	0.616759	−	0.799114i
$46$	11.0672	+	1.39811i	1.63177	+	0.206141i
$47$	−5.86131	+	3.22228i	−0.854959	+	0.470018i	−0.848024	−	0.529958i	$-0.822208\pi$
$47$	−5.86131	+	3.22228i	−0.854959	+	0.470018i	−0.00693559	+	0.999976i	$0.502208\pi$
$48$	−7.73985	+	1.98725i	−1.11715	+	0.286836i
$49$	−1.97598	−	6.08145i	−0.282283	−	0.868778i
$50$	10.3699	−	0.702923i	1.46652	−	0.0994084i
$51$	−4.71518	+	14.5118i	−0.660258	+	2.03206i
$52$	0.462563	−	7.35223i	0.0641459	−	1.01957i
$53$	1.75608	+	1.64907i	0.241217	+	0.226518i	0.795721	−	0.605663i	$-0.207092\pi$
$53$	1.75608	+	1.64907i	0.241217	+	0.226518i	−0.554504	+	0.832181i	$0.687092\pi$
$54$	0.126701	−	0.0696543i	0.0172418	−	0.00947875i
$55$	−3.29716	−	6.43244i	−0.444589	−	0.867350i
$56$	0.221189	+	0.470051i	0.0295576	+	0.0628132i
$57$	10.8523			1.43742
$58$	5.32302	+	11.3120i	0.698946	+	1.48534i
$59$	0.0986283	+	1.56765i	0.0128403	+	0.204091i	0.999216	+	0.0395840i	$0.0126033\pi$
$59$	0.0986283	+	1.56765i	0.0128403	+	0.204091i	−0.986376	+	0.164507i	$0.947397\pi$
$60$	12.0004	+	4.28758i	1.54925	+	0.553524i
$61$	7.16121	+	11.2843i	0.916899	+	1.44480i	0.895516	+	0.445030i	$0.146807\pi$
$61$	7.16121	+	11.2843i	0.916899	+	1.44480i	0.0213827	+	0.999771i	$0.493193\pi$
$62$	0.0168634	+	0.0203843i	0.00214165	+	0.00258881i
$63$	1.50217	+	1.81582i	0.189256	+	0.228771i
$64$	−5.53494	−	8.72167i	−0.691868	−	1.09021i
$65$	4.33605	−	5.61808i	0.537821	−	0.696837i
$66$	−1.03595	−	16.4660i	−0.127517	−	2.02682i
$67$	−3.96761	−	8.43161i	−0.484721	−	1.03009i	−0.986298	−	0.164972i	$-0.947247\pi$
$67$	−3.96761	−	8.43161i	−0.484721	−	1.03009i	0.501577	−	0.865113i	$-0.332753\pi$
$68$	−14.4251			−1.74930
$69$	5.60996	+	11.9218i	0.675360	+	1.43521i
$70$	−0.557190	+	3.57403i	−0.0665970	+	0.427178i
$71$	4.47304	−	2.45907i	0.530852	−	0.291838i	−0.193697	−	0.981061i	$-0.562048\pi$
$71$	4.47304	−	2.45907i	0.530852	−	0.291838i	0.724549	+	0.689223i	$0.242048\pi$
$72$	1.47368	+	1.38387i	0.173674	+	0.163091i
$73$	0.634423	−	10.0839i	0.0742536	−	1.18023i	−0.767748	−	0.640752i	$-0.778623\pi$
$73$	0.634423	−	10.0839i	0.0742536	−	1.18023i	0.842001	−	0.539476i	$-0.181377\pi$
$74$	−4.72802	+	14.5513i	−0.549621	+	1.69156i
$75$	7.26393	+	9.89665i	0.838766	+	1.14277i
$76$	3.17035	+	9.75733i	0.363664	+	1.11924i
$77$	2.43654	−	0.625598i	0.277670	−	0.0712935i
$78$	14.1948	−	7.80366i	1.60725	−	0.883591i
$79$	1.81498	+	0.229286i	0.204201	+	0.0257966i	0.226769	−	0.973949i	$-0.427184\pi$
$79$	1.81498	+	0.229286i	0.204201	+	0.0257966i	−0.0225670	+	0.999745i	$0.507184\pi$
$80$	0.210953	−	7.27444i	0.0235852	−	0.813307i
$81$	−7.81158	−	4.29445i	−0.867954	−	0.477162i
$82$	−7.43721	−	22.8894i	−0.821303	−	2.52771i
$83$	3.86348	−	0.488071i	0.424072	−	0.0535727i	0.0895985	−	0.995978i	$-0.471442\pi$
$83$	3.86348	−	0.488071i	0.424072	−	0.0535727i	0.334473	+	0.942405i	$0.391442\pi$
$84$	−2.37636	+	3.74455i	−0.259282	+	0.408564i
$85$	−11.5124	−	7.78305i	−1.24869	−	0.844190i
$86$	−11.0451	−	4.37306i	−1.19102	−	0.471560i
$87$	−7.91220	+	12.4676i	−0.848277	+	1.33667i
$88$	2.00640	−	0.794389i	0.213883	−	0.0846821i
$89$	0.254721	−	4.04868i	0.0270004	−	0.429159i	−0.961186	−	0.275902i	$-0.911024\pi$
$89$	0.254721	−	4.04868i	0.0270004	−	0.429159i	0.988186	−	0.153257i	$-0.0489764\pi$
$90$	3.10394	+	13.7298i	0.327184	+	1.44724i
$91$	1.57432	+	1.90303i	0.165034	+	0.199491i
$92$	−9.08002	+	8.52670i	−0.946657	+	0.888970i
$93$	−0.00965601	+	0.0297182i	−0.00100128	+	0.00308163i
$94$	2.60534	−	13.6576i	0.268720	−	1.40868i
$95$	−2.73437	+	9.49768i	−0.280541	+	0.974441i
$96$	8.46833	−	17.9961i	0.864296	−	1.83672i
$97$	−0.777570	+	1.65242i	−0.0789502	+	0.167778i	−0.940405	−	0.340057i	$-0.889554\pi$
$97$	−0.777570	+	1.65242i	−0.0789502	+	0.167778i	0.861455	+	0.507834i	$0.169554\pi$
$98$	12.3589	+	4.89322i	1.24843	+	0.494289i
$99$	7.91970	−	5.75400i	0.795960	−	0.578299i
$100$	−6.77604	+	9.42217i	−0.677604	+	0.942217i
$101$	−0.242135	−	0.175921i	−0.0240933	−	0.0175048i	0.575673	−	0.817680i	$-0.304740\pi$
$101$	−0.242135	−	0.175921i	−0.0240933	−	0.0175048i	−0.599767	+	0.800175i	$0.704740\pi$
$102$	−16.9957	−	26.7810i	−1.68283	−	2.65171i
$103$	2.99809	+	15.7165i	0.295411	+	1.54860i	0.752148	+	0.658995i	$0.229018\pi$
$103$	2.99809	+	15.7165i	0.295411	+	1.54860i	−0.456737	+	0.889602i	$0.650982\pi$
$104$	1.54445	+	1.45034i	0.151446	+	0.142217i
$105$	−3.91689	+	1.70628i	−0.382250	+	0.166516i
$106$	−4.96818	+	0.627627i	−0.482552	+	0.0609605i
$107$	15.0619	−	10.9431i	1.45609	−	1.05791i	0.471726	−	0.881745i	$-0.343631\pi$
$107$	15.0619	−	10.9431i	1.45609	−	1.05791i	0.984361	−	0.176163i	$-0.0563687\pi$
$108$	−0.0302518	+	0.158585i	−0.00291098	+	0.0152599i
$109$	−4.84439	+	1.91803i	−0.464008	+	0.183714i	−0.588484	−	0.808509i	$-0.700275\pi$
$109$	−4.84439	+	1.91803i	−0.464008	+	0.183714i	0.124476	+	0.992223i	$0.460275\pi$
$110$	14.6717	+	3.24217i	1.39889	+	0.309129i
$111$	−17.5038	+	4.49422i	−1.66139	+	0.426573i
$112$	2.45314	+	0.629860i	0.231800	+	0.0595162i
$113$	0.619002	+	9.83875i	0.0582308	+	0.925552i	0.913364	+	0.407144i	$0.133475\pi$
$113$	0.619002	+	9.83875i	0.0582308	+	0.925552i	−0.855133	+	0.518408i	$0.826525\pi$
$114$	−14.3797	+	17.3821i	−1.34678	+	1.62798i
$115$	−11.8471	+	1.90586i	−1.10475	+	0.177723i
$116$	−13.5211	−	3.47163i	−1.25540	−	0.322333i
$117$	8.42238	+	4.63024i	0.778649	+	0.428066i
$118$	−2.64158	−	1.91922i	−0.243177	−	0.176679i
$119$	3.52546	−	3.31062i	0.323178	−	0.303484i
$120$	−3.15008	+	1.87328i	−0.287562	+	0.171006i
$121$	0.103150	+	0.540733i	0.00937731	+	0.0491576i
$122$	−27.5628	−	3.48199i	−2.49542	−	0.315244i
$123$	18.1199	−	21.9032i	1.63382	−	1.97494i
$124$	−0.0295405			−0.00265282
$125$	−10.4915	+	3.86363i	−0.938392	+	0.345573i
$126$	−4.89881			−0.436421
$127$	−4.40137	+	5.32035i	−0.390559	+	0.472104i	−0.928744	−	0.370722i	$-0.879110\pi$
$127$	−4.40137	+	5.32035i	−0.390559	+	0.472104i	0.538185	+	0.842827i	$0.319110\pi$
$128$	5.23007	+	0.660711i	0.462277	+	0.0583992i
$129$	−2.62916	−	13.7825i	−0.231484	−	1.21348i
$130$	3.25302	+	14.3892i	0.285308	+	1.26201i
$131$	−4.45323	+	4.18186i	−0.389080	+	0.365371i	−0.854260	−	0.519845i	$-0.825990\pi$
$131$	−4.45323	+	4.18186i	−0.389080	+	0.365371i	0.465180	+	0.885216i	$0.345990\pi$
$132$	14.9041	+	10.8284i	1.29723	+	0.942495i
$133$	−3.01418	−	1.65706i	−0.261362	−	0.143685i
$134$	18.7621	+	4.81728i	1.62080	+	0.416150i
$135$	−0.109708	+	0.110241i	−0.00944216	+	0.00948806i
$136$	2.64446	−	3.19660i	0.226760	−	0.274106i
$137$	0.846660	+	13.4573i	0.0723351	+	1.14973i	0.852002	+	0.523539i	$0.175388\pi$
$137$	0.846660	+	13.4573i	0.0723351	+	1.14973i	−0.779667	+	0.626195i	$0.784612\pi$
$138$	−26.5284	−	6.81134i	−2.25825	−	0.579820i
$139$	5.66146	−	1.45362i	0.480199	−	0.123294i	−0.000828731	−	1.00000i	$-0.500264\pi$
$139$	5.66146	−	1.45362i	0.480199	−	0.123294i	0.481027	+	0.876706i	$0.340264\pi$
$140$	−2.67838	−	3.02322i	−0.226365	−	0.255509i
$141$	15.2692	−	6.04549i	1.28590	−	0.509122i
$142$	−1.98825	+	10.4228i	−0.166850	+	0.874661i
$143$	8.30007	−	6.03035i	0.694086	−	0.504283i
$144$	9.77827	−	1.23528i	0.814856	−	0.102940i
$145$	−8.91779	−	10.0659i	−0.740582	−	0.835930i
$146$	15.3106	+	14.3776i	1.26712	+	1.18990i
$147$	2.94188	+	15.4219i	0.242642	+	1.27198i
$148$	−9.15426	−	14.4248i	−0.752475	−	1.18571i
$149$	14.9590	+	10.8683i	1.22549	+	0.890370i	0.996544	−	0.0830697i	$-0.0264724\pi$
$149$	14.9590	+	10.8683i	1.22549	+	0.890370i	0.228945	+	0.973439i	$0.426472\pi$
$150$	−25.4763	−	1.47883i	−2.08013	−	0.120746i
$151$	16.0977	−	11.6956i	1.31001	−	0.951778i	0.310010	−	0.950733i	$-0.399668\pi$
$151$	16.0977	−	11.6956i	1.31001	−	0.951778i	0.999999	−	0.00104421i	$-0.000332383\pi$
$152$	−2.74342	−	1.08620i	−0.222521	−	0.0881023i
$153$	8.01318	−	17.0289i	0.647828	−	1.37670i
$154$	−2.22649	+	4.73153i	−0.179416	+	0.381278i
$155$	−0.0235757	−	0.0159386i	−0.00189364	−	0.00128022i
$156$	−3.38923	+	17.7670i	−0.271356	+	1.42250i
$157$	−0.416703	+	1.28248i	−0.0332566	+	0.102353i	−0.966307	−	0.257393i	$-0.917137\pi$
$157$	−0.416703	+	1.28248i	−0.0332566	+	0.102353i	0.933050	+	0.359746i	$0.117137\pi$
$158$	−2.77216	+	2.60323i	−0.220541	+	0.207102i
$159$	−3.77019	−	4.55738i	−0.298996	−	0.361424i
$160$	13.6161	+	11.9456i	1.07644	+	0.944385i
$161$	0.262216	−	4.16781i	0.0206656	−	0.328470i
$162$	17.2290	−	6.82145i	1.35364	−	0.535944i
$163$	−2.34847	+	3.70060i	−0.183947	+	0.289854i	−0.923770	−	0.382947i	$-0.874909\pi$
$163$	−2.34847	+	3.70060i	−0.183947	+	0.289854i	0.739823	+	0.672801i	$0.234909\pi$
$164$	24.9867	+	9.89292i	1.95113	+	0.772507i
$165$	6.05215	+	16.6834i	0.471159	+	1.29880i
$166$	−4.33750	+	6.83481i	−0.336656	+	0.530484i
$167$	−5.54292	+	0.700234i	−0.428924	+	0.0541857i	−0.336832	−	0.941565i	$-0.609355\pi$
$167$	−5.54292	+	0.700234i	−0.428924	+	0.0541857i	−0.0920922	+	0.995750i	$0.529355\pi$
$168$	−0.394149	−	1.21306i	−0.0304092	−	0.0935900i
$169$	−2.56510	−	1.41017i	−0.197315	−	0.108475i
$170$	27.7203	−	8.12644i	2.12605	−	0.623270i
$171$	−13.2797	−	1.67762i	−1.01553	−	0.128291i
$172$	11.6238	−	6.39025i	0.886308	−	0.487252i
$173$	−13.9786	+	3.58908i	−1.06277	+	0.272873i	−0.739308	−	0.673368i	$-0.764847\pi$
$173$	−13.9786	+	3.58908i	−1.06277	+	0.272873i	−0.323463	+	0.946241i	$0.604847\pi$
$174$	−9.48537	−	29.1930i	−0.719084	−	2.21311i
$175$	−0.506385	−	3.85789i	−0.0382791	−	0.291629i
$176$	3.25108	−	10.0058i	0.245059	−	0.754215i
$177$	0.242159	−	3.84900i	0.0182018	−	0.289309i
$178$	6.14722	+	5.77263i	0.460754	+	0.432677i
$179$	−1.34083	+	0.737128i	−0.100218	+	0.0550956i	−0.531075	−	0.847325i	$-0.678212\pi$
$179$	−1.34083	+	0.737128i	−0.100218	+	0.0550956i	0.430856	+	0.902421i	$0.358212\pi$
$180$	−14.0218	−	7.10170i	−1.04513	−	0.529330i
$181$	−1.67103	−	3.55112i	−0.124207	−	0.263952i	0.833047	−	0.553202i	$-0.186594\pi$
$181$	−1.67103	−	3.55112i	−0.124207	−	0.263952i	−0.957254	+	0.289250i	$0.906594\pi$
$182$	−5.13409			−0.380564
$183$	−13.9716	−	29.6911i	−1.03281	−	2.19483i
$184$	−0.224937	−	3.57527i	−0.0165826	−	0.263573i
$185$	0.477074	−	16.4513i	0.0350752	−	1.20952i
$186$	−0.0348048	−	0.0548436i	−0.00255201	−	0.00402133i
$187$	−12.8054	−	15.4791i	−0.936426	−	1.13194i
$188$	9.89618	+	11.9624i	0.721753	+	0.872450i
$189$	−0.0290026	−	0.0457008i	−0.00210963	−	0.00332424i
$190$	−11.5892	−	16.9644i	−0.840770	−	1.23073i
$191$	−1.05847	−	16.8239i	−0.0765880	−	1.21733i	−0.829232	−	0.558904i	$-0.811222\pi$
$191$	−1.05847	−	16.8239i	−0.0765880	−	1.21733i	0.752644	−	0.658428i	$-0.228778\pi$
$192$	10.7987	+	22.9484i	0.779329	+	1.65616i
$193$	−6.29614			−0.453206			−0.226603	−	0.973987i	$-0.572762\pi$
$193$	−6.29614			−0.453206			−0.226603	+	0.973987i	$0.572762\pi$
$194$	−1.61636	−	3.43494i	−0.116048	−	0.246614i
$195$	−12.2910	+	12.3508i	−0.880180	+	0.884459i
$196$	−13.0064	+	7.15034i	−0.929030	+	0.510738i
$197$	7.66463	+	7.19757i	0.546082	+	0.512805i	0.907756	−	0.419499i	$-0.137794\pi$
$197$	7.66463	+	7.19757i	0.546082	+	0.512805i	−0.361673	+	0.932305i	$0.617794\pi$
$198$	−1.27775	+	20.3092i	−0.0908054	+	1.44331i
$199$	2.95165	−	9.08423i	0.209237	−	0.643964i	−0.790276	−	0.612751i	$-0.790063\pi$
$199$	2.95165	−	9.08423i	0.209237	−	0.643964i	0.999513	−	0.0312133i	$-0.00993711\pi$
$200$	−0.845746	−	3.22887i	−0.0598033	−	0.228316i
$201$	7.07010	+	21.7595i	0.498687	+	1.53480i
$202$	0.602610	−	0.154724i	0.0423995	−	0.0108863i
$203$	4.10128	−	2.25470i	0.287853	−	0.158249i
$204$	35.1381	+	4.43898i	2.46016	+	0.310791i
$205$	14.6036	+	21.3769i	1.01996	+	1.49303i
$206$	−29.1456	−	16.0229i	−2.03067	−	1.11637i
$207$	−5.02183	−	15.4556i	−0.349042	−	1.07424i
$208$	10.2479	−	1.29461i	0.710564	−	0.0897651i
$209$	−7.65590	+	12.0638i	−0.529570	+	0.834468i
$210$	2.45709	−	8.53454i	0.169555	−	0.588939i
$211$	6.24127	+	2.47110i	0.429667	+	0.170117i	0.572996	−	0.819558i	$-0.305781\pi$
$211$	6.24127	+	2.47110i	0.429667	+	0.170117i	−0.143329	+	0.989675i	$0.545781\pi$
$212$	2.99614	−	4.72116i	0.205776	−	0.324250i
$213$	−11.6526	+	4.61360i	−0.798424	+	0.316118i
$214$	−2.43005	+	38.6245i	−0.166115	+	2.64032i
$215$	12.7246	+	1.17170i	0.867809	+	0.0799095i
$216$	−0.0295966	−	0.0357762i	−0.00201380	−	0.00243426i
$217$	0.00721963	−	0.00677968i	0.000490100	−	0.000460235i
$218$	3.34689	−	10.3007i	0.226680	−	0.697650i
$219$	−4.64847	+	24.3681i	−0.314114	+	1.64665i
$220$	−13.2321	+	10.3153i	−0.892105	+	0.695459i
$221$	8.39804	−	17.8467i	0.564913	−	1.20050i
$222$	15.9948	−	33.9908i	1.07350	−	2.28131i
$223$	−5.10599	−	2.02160i	−0.341922	−	0.135377i	0.190887	−	0.981612i	$-0.438864\pi$
$223$	−5.10599	−	2.02160i	−0.341922	−	0.135377i	−0.532809	+	0.846235i	$0.678864\pi$
$224$	−5.09990	+	3.70529i	−0.340751	+	0.247570i
$225$	−7.35881	−	13.2332i	−0.490587	−	0.882213i
$226$	−16.5789	−	12.0452i	−1.10281	−	0.801238i
$227$	9.66561	+	15.2306i	0.641529	+	1.01089i	0.997090	+	0.0762352i	$0.0242900\pi$
$227$	9.66561	+	15.2306i	0.641529	+	1.01089i	−0.355561	+	0.934653i	$0.615710\pi$
$228$	−4.72008	−	24.7435i	−0.312595	−	1.63868i
$229$	11.3947	+	10.7003i	0.752984	+	0.707099i	0.962672	−	0.270669i	$-0.0872450\pi$
$229$	11.3947	+	10.7003i	0.752984	+	0.707099i	−0.209688	+	0.977768i	$0.567245\pi$
$230$	12.6453	−	21.5008i	0.833805	−	1.41772i
$231$	−6.12770	+	0.774108i	−0.403173	+	0.0509326i
$232$	3.24805	−	2.35984i	0.213245	−	0.154931i
$233$	−3.53056	+	18.5079i	−0.231295	+	1.21249i	0.657240	+	0.753681i	$0.271724\pi$
$233$	−3.53056	+	18.5079i	−0.231295	+	1.21249i	−0.888535	+	0.458809i	$0.848276\pi$
$234$	−18.5762	+	7.35483i	−1.21436	+	0.480800i
$235$	1.44361	+	14.8864i	0.0941708	+	0.971084i
$236$	3.53139	−	0.906706i	0.229874	−	0.0590215i
$237$	−4.35057	−	1.11704i	−0.282600	−	0.0725593i
$238$	0.631247	+	10.0334i	0.0409177	+	0.650368i
$239$	−4.44545	+	5.37363i	−0.287552	+	0.347591i	−0.894433	−	0.447202i	$-0.852421\pi$
$239$	−4.44545	+	5.37363i	−0.287552	+	0.347591i	0.606881	+	0.794793i	$0.292421\pi$
$240$	−2.75240	+	17.6549i	−0.177666	+	1.13962i
$241$	18.6366	+	4.78508i	1.20049	+	0.308234i	0.795424	−	0.606053i	$-0.207248\pi$
$241$	18.6366	+	4.78508i	1.20049	+	0.308234i	0.405068	+	0.914287i	$0.367248\pi$
$242$	−1.00277	−	0.551275i	−0.0644603	−	0.0354373i
$243$	17.8756	+	12.9874i	1.14672	+	0.833140i
$244$	22.6137	−	21.2357i	1.44769	−	1.35947i
$245$	−14.2381	−	1.31107i	−0.909639	−	0.0837612i
$246$	11.0727	+	58.0450i	0.705968	+	3.70081i
$247$	−13.9175	−	1.75819i	−0.885550	−	0.111871i
$248$	0.00541547	−	0.00654617i	0.000343882	−	0.000415682i
$249$	−9.56126			−0.605920
$250$	7.71331	−	21.9237i	0.487833	−	1.38657i
$251$	−9.68217			−0.611133			−0.305567	−	0.952171i	$-0.598846\pi$
$251$	−9.68217			−0.611133			−0.305567	+	0.952171i	$0.598846\pi$
$252$	3.48675	−	4.21476i	0.219645	−	0.265505i
$253$	−17.2102	−	2.17416i	−1.08200	−	0.136688i
$254$	−2.68958	−	14.0993i	−0.168760	−	0.884668i
$255$	25.6480	+	22.5014i	1.60614	+	1.40909i
$256$	7.07181	−	6.64087i	0.441988	−	0.415054i
$257$	−0.998633	−	0.725549i	−0.0622930	−	0.0452585i	0.556203	−	0.831046i	$-0.312258\pi$
$257$	−0.998633	−	0.725549i	−0.0622930	−	0.0452585i	−0.618496	+	0.785788i	$0.712258\pi$
$258$	25.5591	+	14.0512i	1.59124	+	0.874792i
$259$	5.54784	+	1.42444i	0.344726	+	0.0885105i
$260$	−14.6953	−	7.44278i	−0.911362	−	0.461582i
$261$	11.6093	−	14.0332i	0.718597	−	0.868634i
$262$	−0.797368	−	12.6738i	−0.0492616	−	0.782990i
$263$	9.86257	+	2.53228i	0.608152	+	0.156147i	0.540193	−	0.841541i	$-0.318351\pi$
$263$	9.86257	+	2.53228i	0.608152	+	0.156147i	0.0679590	+	0.997688i	$0.478351\pi$
$264$	−5.13185	+	1.31763i	−0.315843	+	0.0810948i
$265$	4.93845	−	2.15129i	0.303367	−	0.132153i
$266$	6.64799	−	2.63213i	0.407614	−	0.161386i
$267$	−1.86636	+	9.78381i	−0.114219	+	0.598759i
$268$	−17.4986	+	12.7135i	−1.06890	+	0.776599i
$269$	−31.8523	+	4.02388i	−1.94207	+	0.245340i	−0.996734	−	0.0807606i	$-0.974265\pi$
$269$	−31.8523	+	4.02388i	−1.94207	+	0.245340i	−0.945335	+	0.326101i	$0.894265\pi$
$270$	−0.0312058	−	0.321792i	−0.00189912	−	0.0195836i
$271$	−5.44124	−	5.10966i	−0.330532	−	0.310390i	0.501457	−	0.865183i	$-0.332798\pi$
$271$	−5.44124	−	5.10966i	−0.330532	−	0.310390i	−0.831989	+	0.554793i	$0.812798\pi$
$272$	−3.79001	−	19.8680i	−0.229803	−	1.20467i
$273$	−3.24928	−	5.12005i	−0.196656	−	0.309880i
$274$	−22.6763	−	16.4753i	−1.36992	−	0.995308i
$275$	−16.1259	+	1.09309i	−0.972425	+	0.0659160i
$276$	24.7420	−	17.9761i	1.48929	−	1.08203i
$277$	0.978065	+	0.387243i	0.0587662	+	0.0232672i	0.397324	−	0.917678i	$-0.369939\pi$
$277$	0.978065	+	0.387243i	0.0587662	+	0.0232672i	−0.338558	+	0.940946i	$0.609939\pi$
$278$	−5.17339	+	10.9940i	−0.310279	+	0.659377i
$279$	0.0164098	−	0.0348727i	0.000982432	−	0.00208777i
$280$	1.16096	−	0.0393027i	0.0693803	−	0.00234878i
$281$	0.975796	−	5.11530i	0.0582111	−	0.305153i	−0.941260	−	0.337684i	$-0.890357\pi$
$281$	0.975796	−	5.11530i	0.0582111	−	0.305153i	0.999471	+	0.0325303i	$0.0103566\pi$
$282$	−10.5492	+	32.4670i	−0.628194	+	1.93338i
$283$	22.9620	−	21.5628i	1.36495	−	1.28177i	0.441914	−	0.897058i	$-0.354300\pi$
$283$	22.9620	−	21.5628i	1.36495	−	1.28177i	0.923035	−	0.384715i	$-0.125700\pi$
$284$	−7.55224	−	9.12908i	−0.448143	−	0.541712i
$285$	9.58336	−	22.2940i	0.567669	−	1.32058i
$286$	−1.33911	+	21.2846i	−0.0791834	+	1.25858i
$287$	−8.37715	+	3.31675i	−0.494487	+	0.195781i
$288$	−13.1445	+	20.7123i	−0.774544	+	1.22049i
$289$	−20.1037	−	7.95960i	−1.18257	−	0.468212i
$290$	27.9389	−	0.945836i	1.64063	−	0.0555414i
$291$	2.40258	−	3.78586i	0.140842	−	0.221931i
$292$	−23.2674	+	2.93936i	−1.36162	+	0.172013i
$293$	−0.700027	−	2.15446i	−0.0408960	−	0.125865i	0.928524	−	0.371272i	$-0.121078\pi$
$293$	−0.700027	−	2.15446i	−0.0408960	−	0.125865i	−0.969420	+	0.245407i	$0.921078\pi$
$294$	−28.5992	−	15.7226i	−1.66794	−	0.916958i
$295$	3.30754	+	1.18173i	0.192572	+	0.0688032i
$296$	4.87472	+	0.615821i	0.283338	+	0.0357939i
$297$	−0.197028	+	0.108317i	−0.0114327	+	0.00628519i
$298$	−37.2289	+	9.55877i	−2.15662	+	0.553725i
$299$	−5.26302	−	16.1979i	−0.304368	−	0.936750i
$300$	19.4052	−	20.8663i	1.12036	−	1.20472i
$301$	−1.37424	+	4.22948i	−0.0792100	+	0.243783i
$302$	−2.59716	+	41.2806i	−0.149450	+	2.37543i
$303$	0.535682	+	0.503039i	0.0307741	+	0.0288988i
$304$	−12.6060	+	6.93020i	−0.723003	+	0.397474i
$305$	29.5052	−	4.74653i	1.68946	−	0.271786i
$306$	16.6573	+	35.3985i	0.952234	+	2.02360i
$307$	−18.9044			−1.07893			−0.539466	−	0.842008i	$-0.681374\pi$
$307$	−18.9044			−1.07893			−0.539466	+	0.842008i	$0.681374\pi$
$308$	−2.48612	−	5.28328i	−0.141660	−	0.301043i
$309$	−2.46667	−	39.2066i	−0.140324	−	2.23038i
$310$	0.0567672	−	0.0166418i	0.00322416	−	0.000945190i
$311$	−7.84921	−	12.3684i	−0.445088	−	0.701346i	0.545517	−	0.838100i	$-0.316333\pi$
$311$	−7.84921	−	12.3684i	−0.445088	−	0.701346i	−0.990605	+	0.136753i	$0.956333\pi$
$312$	−3.31584	−	4.00816i	−0.187722	−	0.226917i
$313$	5.44984	+	6.58773i	0.308043	+	0.372360i	0.901703	−	0.432356i	$-0.142318\pi$
$313$	5.44984	+	6.58773i	0.308043	+	0.372360i	−0.593660	+	0.804716i	$0.702318\pi$
$314$	−1.50199	−	2.36676i	−0.0847624	−	0.133564i
$315$	5.05677	−	1.48244i	0.284917	−	0.0835258i
$316$	−0.266628	−	4.23793i	−0.0149990	−	0.238402i
$317$	2.63436	+	5.59830i	0.147960	+	0.314432i	0.965044	−	0.262087i	$-0.0844108\pi$
$317$	2.63436	+	5.59830i	0.147960	+	0.314432i	−0.817084	+	0.576519i	$0.804411\pi$
$318$	12.2952			0.689478
$319$	−8.27765	−	17.5909i	−0.463459	−	0.984901i
$320$	−22.8048	+	3.66863i	−1.27482	+	0.205082i
$321$	−40.0568	+	22.0214i	−2.23575	+	1.22911i
$322$	6.32811	+	5.94249i	0.352652	+	0.331162i
$323$	−1.72479	+	27.4147i	−0.0959697	+	1.52540i
$324$	−6.39391	+	19.6784i	−0.355217	+	1.09325i
$325$	−7.71223	−	13.8688i	−0.427798	−	0.769300i
$326$	−2.81542	−	8.66496i	−0.155932	−	0.479908i
$327$	12.3907	−	3.18139i	0.685207	−	0.175931i
$328$	−6.77291	+	3.72344i	−0.373971	+	0.205592i
$329$	−5.16403	−	0.652369i	−0.284702	−	0.0359663i
$330$	−34.7410	−	12.4125i	−1.91243	−	0.683284i
$331$	16.2091	+	8.91105i	0.890935	+	0.489796i	0.860331	−	0.509736i	$-0.170257\pi$
$331$	16.2091	+	8.91105i	0.890935	+	0.489796i	0.0306039	+	0.999532i	$0.490257\pi$
$332$	−2.79319	−	8.59654i	−0.153296	−	0.471796i
$333$	22.1138	−	2.79362i	1.21183	−	0.153089i
$334$	6.22301	−	9.80589i	0.340508	−	0.536555i
$335$	−20.8248	+	0.704997i	−1.13778	+	0.0385181i
$336$	−5.78180	−	2.28918i	−0.315423	−	0.124885i
$337$	7.00020	−	11.0306i	0.381325	−	0.600873i	−0.598405	−	0.801194i	$-0.704199\pi$
$337$	7.00020	−	11.0306i	0.381325	−	0.600873i	0.979730	+	0.200321i	$0.0641986\pi$
$338$	5.65751	−	2.23997i	0.307728	−	0.121838i
$339$	1.51981	−	24.1568i	0.0825450	−	1.31201i
$340$	−12.7384	+	29.6336i	−0.690835	+	1.60711i
$341$	−0.0262237	−	0.0316990i	−0.00142009	−	0.00171660i
$342$	20.2831	−	19.0471i	1.09679	−	1.02995i
$343$	3.22103	−	9.91331i	0.173919	−	0.535269i
$344$	−0.714840	+	3.74732i	−0.0385416	+	0.202042i
$345$	29.4450	−	0.996823i	1.58527	−	0.0536671i
$346$	12.7735	−	27.1450i	0.686706	−	1.45933i
$347$	−0.670629	+	1.42516i	−0.0360013	+	0.0765066i	−0.922019	−	0.387145i	$-0.873461\pi$
$347$	−0.670629	+	1.42516i	−0.0360013	+	0.0765066i	0.886017	+	0.463652i	$0.153461\pi$
$348$	31.8678	+	12.6174i	1.70829	+	0.676361i
$349$	7.85282	−	5.70541i	0.420352	−	0.305404i	−0.357427	−	0.933941i	$-0.616346\pi$
$349$	7.85282	−	5.70541i	0.420352	−	0.305404i	0.777779	+	0.628537i	$0.216346\pi$
$350$	6.85013	+	4.30076i	0.366155	+	0.229886i
$351$	−0.178590	−	0.129753i	−0.00953243	−	0.00692572i
$352$	14.0310	+	22.1093i	0.747853	+	1.17843i
$353$	5.97101	+	31.3011i	0.317805	+	1.66599i	0.679486	+	0.733689i	$0.262203\pi$
$353$	5.97101	+	31.3011i	0.317805	+	1.66599i	−0.361681	+	0.932302i	$0.617797\pi$
$354$	5.84405	+	5.48792i	0.310608	+	0.291680i
$355$	−1.10169	−	11.3605i	−0.0584715	−	0.602954i
$356$	−9.34187	+	1.18015i	−0.495118	+	0.0625480i
$357$	−9.60644	+	6.97949i	−0.508427	+	0.369394i
$358$	0.595996	−	3.12432i	0.0314994	−	0.165126i
$359$	14.9378	−	5.91429i	0.788386	−	0.312144i	0.0607906	−	0.998151i	$-0.480638\pi$
$359$	14.9378	−	5.91429i	0.788386	−	0.312144i	0.727596	+	0.686006i	$0.240638\pi$
$360$	4.14427	−	1.80533i	0.218422	−	0.0951491i
$361$	0.519683	−	0.133432i	0.0273517	−	0.00702273i
$362$	7.90197	+	2.02888i	0.415318	+	0.106636i
$363$	−0.0848667	−	1.34892i	−0.00445434	−	0.0707998i
$364$	3.65421	−	4.41719i	0.191533	−	0.231523i
$365$	−20.1551	−	10.2081i	−1.05497	−	0.534315i
$366$	66.0688	+	16.9636i	3.45347	+	0.886700i
$367$	5.34033	+	2.93587i	0.278763	+	0.153251i	0.615002	−	0.788525i	$-0.289155\pi$
$367$	5.34033	+	2.93587i	0.278763	+	0.153251i	−0.336239	+	0.941777i	$0.609155\pi$
$368$	−14.1297	−	10.2658i	−0.736559	−	0.535142i
$369$	−25.5588	+	24.0013i	−1.33054	+	1.24946i
$370$	25.7178	+	22.5627i	1.33700	+	1.17298i
$371$	0.351279	+	1.84147i	0.0182375	+	0.0956042i
$372$	0.0719579	+	0.00909039i	0.00373084	+	0.000471315i
$373$	15.2917	−	18.4846i	0.791777	−	0.957094i	−0.208002	−	0.978128i	$-0.566696\pi$
$373$	15.2917	−	18.4846i	0.791777	−	0.957094i	0.999779	+	0.0210347i	$0.00669604\pi$
$374$	41.7604			2.15938
$375$	26.7453	−	6.18291i	1.38112	−	0.319284i
$376$	−4.46507			−0.230269
$377$	12.1669	−	14.7072i	0.626625	−	0.757460i
$378$	0.111628	+	0.0141019i	0.00574153	+	0.000725324i
$379$	5.07836	+	26.6217i	0.260858	+	1.36746i	0.835694	+	0.549196i	$0.185066\pi$
$379$	5.07836	+	26.6217i	0.260858	+	1.36746i	−0.574836	+	0.818269i	$0.694934\pi$
$380$	22.8442	+	2.10354i	1.17188	+	0.107909i
$381$	12.3585	−	11.6054i	0.633147	−	0.594565i
$382$	28.3492	+	20.5969i	1.45047	+	1.05383i
$383$	−17.4647	−	9.60131i	−0.892405	−	0.490604i	−0.0315779	−	0.999501i	$-0.510053\pi$
$383$	−17.4647	−	9.60131i	−0.892405	−	0.490604i	−0.860827	+	0.508897i	$0.830053\pi$
$384$	−12.5366	−	3.21886i	−0.639757	−	0.164262i
$385$	0.866468	−	5.55786i	0.0441593	−	0.283255i
$386$	8.34261	−	10.0845i	0.424628	−	0.513287i
$387$	1.08665	+	17.2718i	0.0552374	+	0.877974i
$388$	4.10575	+	1.05418i	0.208438	+	0.0535178i
$389$	28.8080	−	7.39663i	1.46062	−	0.375024i	0.566953	−	0.823750i	$-0.308122\pi$
$389$	28.8080	−	7.39663i	1.46062	−	0.375024i	0.893669	+	0.448726i	$0.148122\pi$
$390$	−3.49611	−	36.0517i	−0.177032	−	1.82555i
$391$	−31.0080	+	12.2769i	−1.56814	+	0.620870i
$392$	0.799866	−	4.19304i	0.0403993	−	0.211781i
$393$	12.1345	−	8.81623i	0.612105	−	0.444720i
$394$	−21.6842	+	2.73935i	−1.09243	+	0.138007i
$395$	2.07378	−	3.52606i	0.104343	−	0.177415i
$396$	−16.5638	−	15.5545i	−0.832364	−	0.781642i
$397$	2.56108	+	13.4257i	0.128537	+	0.673815i	0.986972	+	0.160892i	$0.0514372\pi$
$397$	2.56108	+	13.4257i	0.128537	+	0.673815i	−0.858435	+	0.512922i	$0.828563\pi$
$398$	10.6391	+	16.7646i	0.533291	+	0.840331i
$399$	6.83233	+	4.96398i	0.342044	+	0.248510i
$400$	−14.7577	−	6.85721i	−0.737883	−	0.342860i
$401$	10.6129	−	7.71074i	0.529984	−	0.385056i	−0.290368	−	0.956915i	$-0.593778\pi$
$401$	10.6129	−	7.71074i	0.529984	−	0.385056i	0.820352	+	0.571859i	$0.193778\pi$
$402$	−44.2202	−	17.5080i	−2.20550	−	0.873221i
$403$	0.0171980	−	0.0365476i	0.000856692	−	0.00182056i
$404$	−0.295791	+	0.628589i	−0.0147162	+	0.0312735i
$405$	−15.7203	+	12.2551i	−0.781149	+	0.608961i
$406$	−1.82301	+	9.55654i	−0.0904743	+	0.474283i
$407$	7.35239	−	22.6283i	0.364444	−	1.12164i
$408$	−7.42532	+	6.97284i	−0.367608	+	0.345207i
$409$	7.71814	+	9.32962i	0.381637	+	0.461320i	0.925997	−	0.377532i	$-0.123227\pi$
$409$	7.71814	+	9.32962i	0.381637	+	0.461320i	−0.544359	+	0.838852i	$0.683227\pi$
$410$	−53.5895	−	4.93462i	−2.64659	−	0.243703i
$411$	2.07878	−	33.0412i	0.102538	−	1.62980i
$412$	34.5301	−	13.6714i	1.70118	−	0.673543i
$413$	−0.654969	+	1.03207i	−0.0322289	+	0.0507846i
$414$	31.4093	+	12.4358i	1.54368	+	0.611186i
$415$	2.40908	−	8.36778i	0.118257	−	0.410758i
$416$	−13.7758	+	21.7071i	−0.675412	+	1.06428i
$417$	−14.2381	+	1.79869i	−0.697242	+	0.0880822i
$418$	−9.17811	−	28.2473i	−0.448916	−	1.38162i
$419$	9.95753	+	5.47420i	0.486457	+	0.267432i	0.706053	−	0.708159i	$-0.250474\pi$
$419$	9.95753	+	5.47420i	0.486457	+	0.267432i	−0.219596	+	0.975591i	$0.570474\pi$
$420$	5.59396	+	8.18848i	0.272957	+	0.399557i
$421$	−23.6601	−	2.98896i	−1.15312	−	0.145673i	−0.474564	−	0.880221i	$-0.657394\pi$
$421$	−23.6601	−	2.98896i	−1.15312	−	0.145673i	−0.678557	+	0.734548i	$0.737394\pi$
$422$	−12.2278	+	6.72231i	−0.595242	+	0.327237i
$423$	−19.6191	+	5.03732i	−0.953911	+	0.244923i
$424$	0.496946	+	1.52944i	0.0241338	+	0.0742763i
$425$	−26.1550	+	16.7770i	−1.26870	+	0.813802i
$426$	8.05056	−	24.7771i	0.390051	−	1.20045i
$427$	−0.653047	+	10.3799i	−0.0316032	+	0.502318i
$428$	−31.5015	−	29.5819i	−1.52268	−	1.42989i
$429$	−22.0739	+	12.1352i	−1.06574	+	0.585894i
$430$	−18.7372	+	18.8283i	−0.903589	+	0.907982i
$431$	9.96374	+	21.1740i	0.479937	+	1.01992i	0.987400	+	0.158244i	$0.0505833\pi$
$431$	9.96374	+	21.1740i	0.479937	+	1.01992i	−0.507463	+	0.861673i	$0.669417\pi$
$432$	−0.226371			−0.0108913
$433$	11.0497	+	23.4818i	0.531014	+	1.12846i	0.972865	+	0.231373i	$0.0743219\pi$
$433$	11.0497	+	23.4818i	0.531014	+	1.12846i	−0.441851	+	0.897088i	$0.645678\pi$
$434$	0.00129270	+	0.0205469i	6.20518e−5	+	0.000986285i
$435$	18.6253	+	27.2639i	0.893016	+	1.30720i
$436$	6.48016	+	10.2111i	0.310343	+	0.489023i
$437$	15.1192	+	18.2760i	0.723250	+	0.874259i
$438$	−32.8709	−	39.7340i	−1.57063	−	1.89857i
$439$	2.11965	+	3.34003i	0.101165	+	0.159411i	0.891140	−	0.453728i	$-0.149906\pi$
$439$	2.11965	+	3.34003i	0.101165	+	0.159411i	−0.789975	+	0.613139i	$0.789906\pi$
$440$	0.139871	−	4.82326i	0.00666807	−	0.229940i
$441$	−1.21590	−	19.3262i	−0.0579000	−	0.920294i
$442$	17.4573	+	37.0986i	0.830359	+	1.76460i
$443$	11.5842			0.550383			0.275191	−	0.961389i	$-0.411259\pi$
$443$	11.5842			0.550383			0.275191	+	0.961389i	$0.411259\pi$
$444$	17.8600	+	37.9545i	0.847599	+	1.80124i
$445$	−8.09230	−	4.09855i	−0.383612	−	0.194290i
$446$	10.0036	−	5.49953i	0.473684	−	0.260410i
$447$	−33.0942	−	31.0775i	−1.56530	−	1.46992i
$448$	0.504745	−	8.02269i	0.0238469	−	0.379036i
$449$	−7.65420	+	23.5572i	−0.361224	+	1.11173i	0.591088	+	0.806607i	$0.298698\pi$
$449$	−7.65420	+	23.5572i	−0.361224	+	1.11173i	−0.952312	+	0.305126i	$0.901302\pi$
$450$	30.9462	+	5.74790i	1.45882	+	0.270959i
$451$	11.5654	+	35.5945i	0.544592	+	1.67608i
$452$	22.1634	−	5.69059i	1.04248	−	0.267663i
$453$	−42.8114	+	23.5358i	−2.01146	+	1.10581i
$454$	−37.2020	−	4.69970i	−1.74597	−	0.220568i
$455$	5.29964	−	1.55363i	0.248451	−	0.0728355i
$456$	6.34846	+	3.49010i	0.297294	+	0.163439i
$457$	−4.80474	−	14.7875i	−0.224756	−	0.691729i	−0.998316	−	0.0580056i	$-0.981526\pi$
$457$	−4.80474	−	14.7875i	−0.224756	−	0.691729i	0.773560	−	0.633723i	$-0.218474\pi$
$458$	−32.2371	+	4.07249i	−1.50634	+	0.190295i
$459$	−0.231615	+	0.364966i	−0.0108108	+	0.0170352i
$460$	9.49819	+	26.1828i	0.442855	+	1.22078i
$461$	−17.1720	−	6.79886i	−0.799778	−	0.316654i	−0.0675514	−	0.997716i	$-0.521519\pi$
$461$	−17.1720	−	6.79886i	−0.799778	−	0.316654i	−0.732226	+	0.681061i	$0.761519\pi$
$462$	6.87953	−	10.8404i	0.320065	−	0.504341i
$463$	−8.09227	+	3.20396i	−0.376080	+	0.148900i	−0.548557	−	0.836113i	$-0.684823\pi$
$463$	−8.09227	+	3.20396i	−0.376080	+	0.148900i	0.172478	+	0.985013i	$0.444823\pi$
$464$	1.22904	−	19.5350i	0.0570567	−	0.906890i
$465$	0.0525233	+	0.0460797i	0.00243571	+	0.00213689i
$466$	−24.9658	−	30.1784i	−1.15652	−	1.39799i
$467$	28.2318	−	26.5114i	1.30641	−	1.22680i	0.349325	−	0.937002i	$-0.386411\pi$
$467$	28.2318	−	26.5114i	1.30641	−	1.22680i	0.957087	−	0.289801i	$-0.0935891\pi$
$468$	6.89385	−	21.2171i	0.318668	−	0.980761i
$469$	1.35881	−	7.12315i	0.0627442	−	0.328917i
$470$	−25.7563	−	17.4128i	−1.18805	−	0.803194i
$471$	1.40970	−	2.99577i	0.0649557	−	0.138038i
$472$	−0.446460	+	0.948775i	−0.0205500	+	0.0436709i
$473$	17.1759	+	6.80041i	0.789747	+	0.312683i
$474$	7.55380	−	5.48816i	0.346958	−	0.252080i
$475$	17.0965	+	14.0044i	0.784442	+	0.642565i
$476$	−9.08166	−	6.59821i	−0.416257	−	0.302428i
$477$	3.90898	+	6.15957i	0.178980	+	0.282028i
$478$	−2.71652	−	14.2405i	−0.124251	−	0.651345i
$479$	16.1778	+	15.1920i	0.739184	+	0.694140i	0.959632	−	0.281259i	$-0.0907519\pi$
$479$	16.1778	+	15.1920i	0.739184	+	0.694140i	−0.220448	+	0.975399i	$0.570752\pi$
$480$	−29.4915	−	33.2884i	−1.34610	−	1.51940i
$481$	23.1758	−	2.92779i	1.05673	−	0.133496i
$482$	−32.3584	+	23.5098i	−1.47389	+	1.07084i
$483$	−1.92128	+	10.0717i	−0.0874213	+	0.458278i
$484$	1.18802	−	0.470371i	0.0540009	−	0.0213805i
$485$	2.70793	+	3.05657i	0.122961	+	0.138792i
$486$	−44.4875	+	11.4225i	−2.01799	+	0.518133i
$487$	−11.8909	−	3.05307i	−0.538830	−	0.138348i	−0.0305390	−	0.999534i	$-0.509722\pi$
$487$	−11.8909	−	3.05307i	−0.538830	−	0.138348i	−0.508291	+	0.861186i	$0.669722\pi$
$488$	0.560204	+	8.90419i	0.0253592	+	0.403074i
$489$	6.85943	−	8.29163i	0.310194	−	0.374960i
$490$	20.9659	−	21.0678i	0.947144	−	0.951748i
$491$	−1.41728	−	0.363896i	−0.0639611	−	0.0164224i	0.216574	−	0.976266i	$-0.430512\pi$
$491$	−1.41728	−	0.363896i	−0.0639611	−	0.0164224i	−0.280535	+	0.959844i	$0.590512\pi$
$492$	−57.8208	−	31.7873i	−2.60676	−	1.43308i
$493$	−30.2378	−	21.9690i	−1.36184	−	0.989435i
$494$	21.2573	−	19.9619i	0.956410	−	0.898129i
$495$	−4.82684	−	21.3507i	−0.216950	−	0.959643i
$496$	−0.00776140	−	0.0406867i	−0.000348497	−	0.00182689i
$497$	3.94091	+	0.497853i	0.176774	+	0.0223318i
$498$	12.6690	−	15.3142i	0.567712	−	0.686245i
$499$	11.5060			0.515081			0.257540	−	0.966268i	$-0.417088\pi$
$499$	11.5060			0.515081			0.257540	+	0.966268i	$0.417088\pi$
$500$	13.3723	+	22.2405i	0.598029	+	0.994626i
$501$	13.7175			0.612853
$502$	12.8292	−	15.5079i	0.572596	−	0.692150i
$503$	7.00757	+	0.885262i	0.312452	+	0.0394719i	0.279996	−	0.960001i	$-0.409667\pi$
$503$	7.00757	+	0.885262i	0.312452	+	0.0394719i	0.0324565	+	0.999473i	$0.489667\pi$
$504$	0.294787	+	1.54533i	0.0131309	+	0.0688344i
$505$	−0.575219	+	0.342069i	−0.0255969	+	0.0152219i
$506$	26.2865	−	24.6847i	1.16858	−	1.09737i
$507$	5.81438	+	4.22440i	0.258226	+	0.187612i
$508$	14.0448	+	7.72122i	0.623139	+	0.342574i
$509$	−10.1123	−	2.59639i	−0.448219	−	0.115083i	0.0178318	−	0.999841i	$-0.494324\pi$
$509$	−10.1123	−	2.59639i	−0.448219	−	0.115083i	−0.466051	+	0.884758i	$0.654324\pi$
$510$	−70.0248	+	11.2650i	−3.10075	+	0.498821i
$511$	5.01190	−	6.05835i	0.221713	−	0.268005i
$512$	1.92825	+	30.6487i	0.0852176	+	1.35449i
$513$	0.297772	+	0.0764550i	0.0131470	+	0.00337557i
$514$	2.48533	−	0.638125i	0.109623	−	0.0281465i
$515$	34.9341	+	7.71981i	1.53938	+	0.340176i
$516$	−30.2810	+	11.9891i	−1.33305	+	0.527790i
$517$	−4.05147	+	21.2386i	−0.178183	+	0.934071i
$518$	−9.63260	+	6.99849i	−0.423232	+	0.307496i
$519$	35.1549	−	4.44110i	1.54313	−	0.194943i
$520$	4.34331	−	1.89203i	0.190467	−	0.0829712i
$521$	−4.42096	−	4.15155i	−0.193686	−	0.181883i	0.581637	−	0.813449i	$-0.302413\pi$
$521$	−4.42096	−	4.15155i	−0.193686	−	0.181883i	−0.775322	+	0.631566i	$0.782413\pi$
$522$	7.09419	+	37.1890i	0.310504	+	1.62772i
$523$	−14.1536	−	22.3024i	−0.618892	−	0.975217i	−0.998741	−	0.0501689i	$-0.984024\pi$
$523$	−14.1536	−	22.3024i	−0.618892	−	0.975217i	0.379849	−	0.925049i	$-0.375976\pi$
$524$	11.4716	+	8.33461i	0.501140	+	0.364099i
$525$	0.0463312	+	9.55327i	0.00202206	+	0.416939i
$526$	−17.1242	+	12.4414i	−0.746650	+	0.542473i
$527$	−0.0735382	−	0.0291158i	−0.00320338	−	0.00126831i
$528$	−10.9984	+	23.3727i	−0.478642	+	1.01717i
$529$	−2.46843	+	5.24568i	−0.107323	+	0.228073i
$530$	−3.09792	+	10.7604i	−0.134565	+	0.467403i
$531$	−0.891326	+	4.67249i	−0.0386803	+	0.202769i
$532$	−2.46715	+	7.59311i	−0.106965	+	0.329203i
$533$	−26.7863	+	25.1541i	−1.16025	+	1.08954i
$534$	−13.1977	−	15.9532i	−0.571119	−	0.690364i
$535$	−9.17979	−	40.6053i	−0.396877	−	1.75552i
$536$	0.390597	−	6.20837i	0.0168712	−	0.268161i
$537$	3.49297	−	1.38297i	0.150733	−	0.0596794i
$538$	35.7604	−	56.3494i	1.54174	−	2.42939i
$539$	−19.2188	−	7.60928i	−0.827814	−	0.327755i
$540$	0.299069	+	0.202189i	0.0128699	+	0.00870081i
$541$	17.3707	−	27.3719i	0.746826	−	1.17681i	−0.232120	−	0.972687i	$-0.574566\pi$
$541$	17.3707	−	27.3719i	0.746826	−	1.17681i	0.978946	−	0.204122i	$-0.0654338\pi$
$542$	15.3939	−	1.94471i	0.661226	−	0.0835323i
$543$	2.97769	+	9.16440i	0.127785	+	0.393282i
$544$	44.1153	+	24.2526i	1.89143	+	1.03982i
$545$	−0.337714	+	11.6456i	−0.0144661	+	0.498844i
$546$	12.5062	+	1.57990i	0.535214	+	0.0676133i
$547$	17.4221	−	9.57786i	0.744913	−	0.409520i	−0.0636167	−	0.997974i	$-0.520264\pi$
$547$	17.4221	−	9.57786i	0.744913	−	0.409520i	0.808530	+	0.588455i	$0.200264\pi$
$548$	30.3147	−	7.78349i	1.29498	−	0.332494i
$549$	12.5068	+	38.4921i	0.533778	+	1.64280i
$550$	19.6165	−	27.2770i	0.836451	−	1.16310i
$551$	−8.21449	+	25.2816i	−0.349949	+	1.07703i
$552$	−0.552281	+	8.77825i	−0.0235066	+	0.373627i
$553$	1.03779	+	0.974547i	0.0441312	+	0.0414420i
$554$	−1.91622	+	1.05345i	−0.0814122	+	0.0447567i
$555$	−6.22461	+	39.9270i	−0.264220	+	1.69481i
$556$	−5.77666	−	12.2760i	−0.244985	−	0.520619i
$557$	−40.9886			−1.73674			−0.868372	−	0.495913i	$-0.834833\pi$
$557$	−40.9886			−1.73674			−0.868372	+	0.495913i	$0.834833\pi$
$558$	0.0341117	+	0.0724911i	0.00144406	+	0.00306879i
$559$	1.13884	+	18.1013i	0.0481677	+	0.765604i
$560$	3.46023	−	4.48330i	0.146221	−	0.189454i
$561$	26.4295	+	41.6462i	1.11585	+	1.75830i
$562$	6.90018	+	8.34088i	0.291067	+	0.351839i
$563$	−5.60788	−	6.77876i	−0.236344	−	0.285691i	0.638984	−	0.769220i	$-0.279355\pi$
$563$	−5.60788	−	6.77876i	−0.236344	−	0.285691i	−0.875328	+	0.483529i	$0.839355\pi$
$564$	−20.4250	−	32.1847i	−0.860048	−	1.35522i
$565$	20.7585	+	7.41670i	0.873315	+	0.312023i
$566$	4.11144	+	65.3495i	0.172817	+	2.74684i
$567$	−2.95363	−	6.27679i	−0.124041	−	0.263600i
$568$	3.40751			0.142976
$569$	−3.85270	−	8.18740i	−0.161513	−	0.343234i	0.807646	−	0.589667i	$-0.200741\pi$
$569$	−3.85270	−	8.18740i	−0.161513	−	0.343234i	−0.969160	+	0.246434i	$0.920741\pi$
$570$	23.0098	+	44.8899i	0.963776	+	1.88023i
$571$	−13.3539	+	7.34135i	−0.558842	+	0.307226i	−0.736028	−	0.676951i	$-0.763301\pi$
$571$	−13.3539	+	7.34135i	−0.558842	+	0.307226i	0.177186	+	0.984177i	$0.443301\pi$
$572$	−17.3594	−	16.3015i	−0.725831	−	0.681601i
$573$	−2.59882	+	41.3071i	−0.108567	+	1.72563i
$574$	5.78761	−	17.8124i	0.241570	−	0.743476i
$575$	−6.54664	+	26.0207i	−0.273014	+	1.08514i
$576$	−9.66661	−	29.7508i	−0.402775	−	1.23961i
$577$	0.186241	−	0.0478187i	0.00775333	−	0.00199072i	−0.244811	−	0.969571i	$-0.578726\pi$
$577$	0.186241	−	0.0478187i	0.00775333	−	0.00199072i	0.252565	+	0.967580i	$0.418726\pi$
$578$	39.3869	−	21.6531i	1.63828	−	0.900652i
$579$	15.3368	+	1.93749i	0.637376	+	0.0805193i
$580$	−19.0719	+	24.7108i	−0.791917	+	1.02606i
$581$	2.65559	+	1.45992i	0.110173	+	0.0605679i
$582$	2.88028	+	8.86459i	0.119391	+	0.367449i
$583$	7.72585	−	0.976002i	0.319972	−	0.0404219i
$584$	3.61410	−	5.69491i	0.149552	−	0.235657i
$585$	16.9495	−	13.2133i	0.700776	−	0.546304i
$586$	4.37835	+	1.73351i	0.180868	+	0.0716107i
$587$	8.16964	−	12.8733i	0.337197	−	0.531338i	−0.632844	−	0.774280i	$-0.718112\pi$
$587$	8.16964	−	12.8733i	0.337197	−	0.531338i	0.970041	+	0.242942i	$0.0781125\pi$
$588$	33.8827	−	13.4151i	1.39730	−	0.553230i
$589$	−0.00353212	+	0.0561414i	−0.000145538	+	0.00231327i
$590$	−6.27538	+	3.73182i	−0.258353	+	0.153636i
$591$	−16.4554	−	19.8912i	−0.676886	−	0.818215i
$592$	17.4624	−	16.3983i	0.717700	−	0.673965i
$593$	−14.0758	+	43.3208i	−0.578023	+	1.77897i	0.0476219	+	0.998865i	$0.484836\pi$
$593$	−14.0758	+	43.3208i	−0.578023	+	1.77897i	−0.625645	+	0.780108i	$0.715164\pi$
$594$	0.0875784	−	0.459102i	0.00359339	−	0.0188372i
$595$	−3.68782	−	10.1659i	−0.151186	−	0.416761i
$596$	18.2739	−	38.8339i	0.748526	−	1.59070i
$597$	−9.98539	+	21.2200i	−0.408675	+	0.868478i
$598$	32.9178	+	13.0331i	1.34611	+	0.532962i
$599$	−16.4139	+	11.9254i	−0.670653	+	0.487258i	−0.870244	−	0.492621i	$-0.836039\pi$
$599$	−16.4139	+	11.9254i	−0.670653	+	0.487258i	0.199590	+	0.979879i	$0.436039\pi$
$600$	1.06655	+	8.12549i	0.0435416	+	0.331722i
$601$	−5.83295	−	4.23788i	−0.237931	−	0.172867i	0.462430	−	0.886656i	$-0.346978\pi$
$601$	−5.83295	−	4.23788i	−0.237931	−	0.172867i	−0.700361	+	0.713789i	$0.746978\pi$
$602$	−4.95341	−	7.80533i	−0.201886	−	0.318121i
$603$	−5.28779	−	27.7196i	−0.215335	−	1.12883i
$604$	−33.6678	−	31.6162i	−1.36992	−	1.28644i
$605$	1.20192	+	0.265603i	0.0488651	+	0.0107983i
$606$	−1.51551	+	0.191454i	−0.0615635	+	0.00777728i
$607$	2.44524	−	1.77657i	0.0992490	−	0.0721087i	−0.537054	−	0.843548i	$-0.680463\pi$
$607$	2.44524	−	1.77657i	0.0992490	−	0.0721087i	0.636303	+	0.771439i	$0.280463\pi$
$608$	6.70911	−	35.1704i	0.272090	−	1.42635i
$609$	−10.6842	+	4.23016i	−0.432944	+	0.171415i
$610$	−31.4929	+	53.5476i	−1.27511	+	2.16808i
$611$	−20.5613	+	5.27925i	−0.831822	+	0.213576i
$612$	−42.3115	−	10.8637i	−1.71034	−	0.439141i
$613$	−1.51718	−	24.1150i	−0.0612785	−	0.973994i	−0.901783	−	0.432189i	$-0.857741\pi$
$613$	−1.51718	−	24.1150i	−0.0612785	−	0.973994i	0.840504	−	0.541805i	$-0.182259\pi$
$614$	25.0490	−	30.2790i	1.01090	−	1.22196i
$615$	−28.9948	−	56.5659i	−1.16918	−	2.28096i
$616$	1.62654	+	0.417624i	0.0655351	+	0.0168265i
$617$	−29.2112	−	16.0590i	−1.17600	−	0.646511i	−0.230798	−	0.973002i	$-0.574134\pi$
$617$	−29.2112	−	16.0590i	−1.17600	−	0.646511i	−0.945200	+	0.326491i	$0.894134\pi$
$618$	66.0653	+	47.9993i	2.65754	+	1.93081i
$619$	−8.36904	+	7.85905i	−0.336380	+	0.315882i	−0.834268	−	0.551360i	$-0.814109\pi$
$619$	−8.36904	+	7.85905i	−0.336380	+	0.315882i	0.497888	+	0.867242i	$0.334109\pi$
$620$	−0.0260864	+	0.0606853i	−0.00104765	+	0.00243718i
$621$	0.0699402	+	0.366639i	0.00280660	+	0.0147127i
$622$	30.2108	+	3.81651i	1.21134	+	0.153028i
$623$	2.01228	−	2.43243i	0.0806203	−	0.0974532i
$624$	−25.3613			−1.01526
$625$	−1.32768	+	24.9647i	−0.0531074	+	0.998589i
$626$	−17.7727			−0.710342
$627$	22.3614	−	27.0303i	0.893028	−	1.07949i
$628$	3.10533	+	0.392294i	0.123916	+	0.0156542i
$629$	−8.57120	−	44.9318i	−0.341756	−	1.79155i
$630$	−4.32600	+	10.0637i	−0.172352	+	0.400947i
$631$	14.7988	−	13.8970i	0.589130	−	0.553230i	−0.331605	−	0.943418i	$-0.607590\pi$
$631$	14.7988	−	13.8970i	0.589130	−	0.553230i	0.920735	+	0.390188i	$0.127590\pi$
$632$	0.988004	+	0.717827i	0.0393007	+	0.0285536i
$633$	−14.4427	−	7.93996i	−0.574047	−	0.315585i
$634$	−12.4574	−	3.19851i	−0.494745	−	0.127029i
$635$	7.04291	+	13.7400i	0.279489	+	0.545256i
$636$	−8.75113	+	10.5783i	−0.347005	+	0.419457i
$637$	−1.27430	−	20.2544i	−0.0504895	−	0.802507i
$638$	39.1434	+	10.0503i	1.54970	+	0.397896i
$639$	14.9722	−	3.84421i	0.592292	−	0.152075i
$640$	5.97582	−	10.1607i	0.236215	−	0.401638i
$641$	−16.1026	+	6.37546i	−0.636014	+	0.251816i	−0.663930	−	0.747795i	$-0.731113\pi$
$641$	−16.1026	+	6.37546i	−0.636014	+	0.251816i	0.0279163	+	0.999610i	$0.491113\pi$
$642$	17.8051	−	93.3378i	0.702713	−	3.68375i
$643$	27.8652	−	20.2453i	1.09890	−	0.798395i	0.118018	−	0.993012i	$-0.462346\pi$
$643$	27.8652	−	20.2453i	1.09890	−	0.798395i	0.980879	+	0.194616i	$0.0623461\pi$
$644$	−9.61676	+	1.21488i	−0.378953	+	0.0478729i
$645$	−30.6353	−	6.76985i	−1.20626	−	0.266562i
$646$	−41.6245	−	39.0880i	−1.63770	−	1.53790i
$647$	−7.64256	−	40.0637i	−0.300460	−	1.57507i	−0.737324	−	0.675539i	$-0.763911\pi$
$647$	−7.64256	−	40.0637i	−0.300460	−	1.57507i	0.436864	−	0.899528i	$-0.356089\pi$
$648$	−3.18858	−	5.02440i	−0.125259	−	0.197377i
$649$	4.10784	+	2.98452i	0.161247	+	0.117153i
$650$	32.4325	+	6.02396i	1.27211	+	0.236279i
$651$	−0.0196726	+	0.0142930i	−0.000771030	+	0.000560186i
$652$	9.45890	+	3.74505i	0.370439	+	0.146667i
$653$	18.2985	−	38.8863i	0.716075	−	1.52174i	−0.131646	−	0.991297i	$-0.542026\pi$
$653$	18.2985	−	38.8863i	0.716075	−	1.52174i	0.847722	−	0.530441i	$-0.177974\pi$
$654$	−11.3225	+	24.0615i	−0.442745	+	0.940880i
$655$	4.65831	+	12.8412i	0.182015	+	0.501746i
$656$	−7.06077	+	37.0139i	−0.275677	+	1.44515i
$657$	9.45519	−	29.1001i	0.368882	−	1.13530i
$658$	7.88742	−	7.40678i	0.307484	−	0.288746i
$659$	22.5002	+	27.1981i	0.876485	+	1.05949i	0.997762	+	0.0668697i	$0.0213012\pi$
$659$	22.5002	+	27.1981i	0.876485	+	1.05949i	−0.121277	+	0.992619i	$0.538699\pi$
$660$	35.4063	−	21.0553i	1.37819	−	0.819576i
$661$	−0.409348	+	6.50640i	−0.0159218	+	0.253070i	0.982012	+	0.188819i	$0.0604658\pi$
$661$	−0.409348	+	6.50640i	−0.0159218	+	0.253070i	−0.997934	+	0.0642510i	$0.979534\pi$
$662$	−35.7504	+	14.1546i	−1.38948	+	0.550134i
$663$	−25.9487	+	40.8887i	−1.00777	+	1.58798i
$664$	2.41705	+	0.956977i	0.0937997	+	0.0371379i
$665$	−6.06584	+	4.72875i	−0.235223	+	0.183373i
$666$	−24.8270	+	39.1211i	−0.962027	+	1.51591i
$667$	−32.0194	+	4.04499i	−1.23980	+	0.156623i
$668$	4.00738	+	12.3334i	0.155050	+	0.477195i
$669$	11.8156	+	6.49568i	0.456818	+	0.251138i
$670$	26.4644	−	34.2891i	1.02241	−	1.32470i
$671$	42.8619	+	5.41472i	1.65467	+	0.209033i
$672$	13.5631	−	7.45637i	0.523207	−	0.287636i
$673$	24.5764	−	6.31015i	0.947351	−	0.243238i	0.256753	−	0.966477i	$-0.417347\pi$
$673$	24.5764	−	6.31015i	0.947351	−	0.243238i	0.690598	+	0.723239i	$0.257347\pi$
$674$	8.39204	+	25.8280i	0.323249	+	0.994859i
$675$	0.129590	+	0.322725i	0.00498791	+	0.0124217i
$676$	−2.09957	+	6.46182i	−0.0807528	+	0.248532i
$677$	−1.93666	+	30.7824i	−0.0744320	+	1.18306i	0.766617	+	0.642105i	$0.221939\pi$
$677$	−1.93666	+	30.7824i	−0.0744320	+	1.18306i	−0.841049	+	0.540959i	$0.818061\pi$
$678$	36.6779	+	34.4428i	1.40861	+	1.32277i
$679$	−1.24537	+	0.684650i	−0.0477931	+	0.0262745i
$680$	−4.23156	−	8.25535i	−0.162273	−	0.316578i
$681$	−18.8577	−	40.0746i	−0.722627	−	1.53566i
$682$	0.0855193			0.00327470
$683$	0.266017	+	0.565314i	0.0101788	+	0.0216312i	0.909852	−	0.414933i	$-0.136195\pi$
$683$	0.266017	+	0.565314i	0.0101788	+	0.0216312i	−0.899673	+	0.436564i	$0.856195\pi$
$684$	1.95084	+	31.0077i	0.0745923	+	1.18561i
$685$	28.3931	+	10.1444i	1.08484	+	0.387599i
$686$	11.6101	+	18.2946i	0.443276	+	0.698491i
$687$	−24.4637	−	29.5715i	−0.933347	−	1.12822i
$688$	11.8554	+	14.3308i	0.451984	+	0.546355i
$689$	4.09672	+	6.45540i	0.156073	+	0.245931i
$690$	−37.4191	+	48.4827i	−1.42452	+	1.84570i
$691$	2.07242	+	32.9402i	0.0788386	+	1.25310i	0.816266	+	0.577676i	$0.196040\pi$
$691$	2.07242	+	32.9402i	0.0788386	+	1.25310i	−0.737427	+	0.675427i	$0.763960\pi$
$692$	14.2630	+	30.3104i	0.542198	+	1.15223i
$693$	7.61798			0.289383
$694$	−1.39406	−	2.96253i	−0.0529178	−	0.112456i
$695$	2.01329	−	12.9140i	0.0763686	−	0.489857i
$696$	−8.63812	+	4.74885i	−0.327427	+	0.180005i
$697$	52.4512	+	49.2549i	1.98673	+	1.86566i
$698$	−1.26696	+	20.1377i	−0.0479550	+	0.762222i
$699$	14.2955	−	43.9969i	0.540705	−	1.66412i
$700$	−8.57583	+	2.83251i	−0.324136	+	0.107059i
$701$	−7.08536	−	21.8065i	−0.267610	−	0.823620i	−0.991081	−	0.133264i	$-0.957454\pi$
$701$	−7.08536	−	21.8065i	−0.267610	−	0.823620i	0.723470	−	0.690356i	$-0.242546\pi$
$702$	0.444463	−	0.114119i	0.0167752	−	0.00430713i
$703$	−28.5087	+	15.6728i	−1.07523	+	0.591111i
$704$	−33.1283	−	4.18507i	−1.24857	−	0.157731i
$705$	1.06445	−	36.7062i	0.0400895	−	1.38243i
$706$	−58.0466	−	31.9114i	−2.18461	−	1.20100i
$707$	−0.0719733	−	0.221511i	−0.00270683	−	0.00833078i
$708$	−8.88114	+	1.12195i	−0.333774	+	0.0421654i
$709$	−3.41258	+	5.37737i	−0.128162	+	0.201951i	−0.902349	−	0.431005i	$-0.858159\pi$
$709$	−3.41258	+	5.37737i	−0.128162	+	0.201951i	0.774187	+	0.632957i	$0.218159\pi$
$710$	19.6559	+	13.2885i	0.737671	+	0.498710i
$711$	5.15101	+	2.03943i	0.193178	+	0.0764845i
$712$	1.45106	−	2.28651i	0.0543808	−	0.0856905i
$713$	−0.0634998	+	0.0251414i	−0.00237809	+	0.000941551i
$714$	1.54988	−	24.6346i	0.0580028	−	0.921928i
$715$	−5.05866	−	22.3761i	−0.189183	−	0.836820i
$716$	2.26385	+	2.73652i	0.0846040	+	0.102269i
$717$	12.4823	−	11.7217i	0.466160	−	0.437753i
$718$	−10.3202	+	31.7624i	−0.385147	+	1.18536i
$719$	−2.48139	+	13.0079i	−0.0925403	+	0.485113i	0.905599	+	0.424135i	$0.139422\pi$
$719$	−2.48139	+	13.0079i	−0.0925403	+	0.485113i	−0.998139	+	0.0609778i	$0.980578\pi$
$720$	6.09725	−	21.1784i	0.227231	−	0.789273i
$721$	−5.30141	+	11.2661i	−0.197435	+	0.419571i
$722$	−0.474881	+	1.00917i	−0.0176732	+	0.0375576i
$723$	−43.9246	−	17.3910i	−1.63357	−	0.646778i
$724$	−7.36984	+	5.35450i	−0.273898	+	0.198998i
$725$	−28.5536	+	9.43096i	−1.06045	+	0.350257i
$726$	2.27300	+	1.65143i	0.0843590	+	0.0612904i
$727$	−15.0569	−	23.7258i	−0.558429	−	0.879943i	0.441421	−	0.897300i	$-0.354475\pi$
$727$	−15.0569	−	23.7258i	−0.558429	−	0.879943i	−0.999849	+	0.0173574i	$0.994475\pi$
$728$	0.308945	+	1.61955i	0.0114503	+	0.0600244i
$729$	−20.0521	−	18.8302i	−0.742670	−	0.697414i
$730$	43.0565	−	18.7563i	1.59359	−	0.694201i
$731$	35.2348	−	4.45119i	1.30321	−	0.164633i
$732$	−61.6196	+	44.7693i	−2.27753	+	1.65472i
$733$	2.97459	−	15.5934i	0.109869	−	0.575954i	−0.884191	−	0.467125i	$-0.845290\pi$
$733$	2.97459	−	15.5934i	0.109869	−	0.575954i	0.994060	−	0.108829i	$-0.0347102\pi$
$734$	−11.7785	+	4.66343i	−0.434752	+	0.172130i
$735$	34.2792	+	7.57508i	1.26441	+	0.279411i
$736$	42.1045	−	10.8106i	1.55199	−	0.398484i
$737$	−29.1763	−	7.49120i	−1.07472	−	0.275942i
$738$	−4.57641	−	72.7400i	−0.168460	−	2.67759i
$739$	−32.8772	+	39.7417i	−1.20941	+	1.46192i	−0.361009	+	0.932562i	$0.617568\pi$
$739$	−32.8772	+	39.7417i	−1.20941	+	1.46192i	−0.848398	+	0.529360i	$0.822432\pi$
$740$	−37.7169	+	6.06755i	−1.38650	+	0.223048i
$741$	33.3607	+	8.56557i	1.22554	+	0.314664i
$742$	−3.41492	−	1.87737i	−0.125366	−	0.0689204i
$743$	−18.2825	−	13.2830i	−0.670720	−	0.487307i	0.199546	−	0.979888i	$-0.436053\pi$
$743$	−18.2825	−	13.2830i	−0.670720	−	0.487307i	−0.870266	+	0.492582i	$0.836053\pi$
$744$	−0.0152060	+	0.0142794i	−0.000557479	+	0.000523507i
$745$	35.5368	−	21.1329i	1.30197	−	0.774249i
$746$	9.34446	+	48.9854i	0.342125	+	1.79348i
$747$	11.6999	+	1.47804i	0.428076	+	0.0540786i
$748$	−29.7232	+	35.9291i	−1.08679	+	1.31370i
$749$	14.4881			0.529382
$750$	−25.5354	+	51.0304i	−0.932421	+	1.86337i
$751$	−44.1937			−1.61265			−0.806326	−	0.591471i	$-0.798547\pi$
$751$	−44.1937			−1.61265			−0.806326	+	0.591471i	$0.798547\pi$
$752$	−13.8760	+	16.7732i	−0.506005	+	0.611655i
$753$	23.5849	+	2.97946i	0.859480	+	0.108578i
$754$	7.43490	+	38.9751i	0.270763	+	1.41939i
$755$	−9.81108	−	43.3977i	−0.357062	−	1.57940i
$756$	−0.0915846	+	0.0860037i	−0.00333090	+	0.00312792i
$757$	4.17190	+	3.03106i	0.151630	+	0.110166i	0.661014	−	0.750374i	$-0.270126\pi$
$757$	4.17190	+	3.03106i	0.151630	+	0.110166i	−0.509383	+	0.860540i	$0.670126\pi$
$758$	−49.3688	−	27.1407i	−1.79315	−	0.985795i
$759$	41.2535	+	10.5921i	1.49741	+	0.384468i
$760$	−4.65402	+	4.67665i	−0.168819	+	0.169640i
$761$	10.8259	−	13.0862i	0.392437	−	0.474375i	−0.536879	−	0.843659i	$-0.680397\pi$
$761$	10.8259	−	13.0862i	0.392437	−	0.474375i	0.929317	+	0.369284i	$0.120397\pi$
$762$	2.21285	+	35.1722i	0.0801630	+	1.27415i
$763$	−3.92723	−	1.00834i	−0.142175	−	0.0365044i
$764$	−37.8984	+	9.73067i	−1.37112	+	0.352043i
$765$	−27.9064	−	31.4993i	−1.00896	−	1.13886i
$766$	38.5197	−	15.2510i	1.39177	−	0.551042i
$767$	−0.934134	+	4.89690i	−0.0337296	+	0.176817i
$768$	−19.2698	+	14.0004i	−0.695340	+	0.505194i
$769$	15.4047	−	1.94606i	0.555507	−	0.0701768i	0.157432	−	0.987530i	$-0.449679\pi$
$769$	15.4047	−	1.94606i	0.555507	−	0.0701768i	0.398075	+	0.917353i	$0.369679\pi$
$770$	7.75388	+	8.75217i	0.279430	+	0.315406i
$771$	2.20930	+	2.07468i	0.0795662	+	0.0747176i
$772$	2.73843	+	14.3554i	0.0985583	+	0.516661i
$773$	−4.48315	−	7.06432i	−0.161248	−	0.254086i	0.754091	−	0.656769i	$-0.228078\pi$
$773$	−4.48315	−	7.06432i	−0.161248	−	0.254086i	−0.915339	+	0.402683i	$0.868078\pi$
$774$	−29.1039	−	21.1452i	−1.04612	−	0.760050i
$775$	−0.0535617	+	0.0343568i	−0.00192399	+	0.00123413i
$776$	−0.986286	+	0.716579i	−0.0354056	+	0.0257237i
$777$	−13.0757	−	5.17702i	−0.469087	−	0.185725i
$778$	−26.3245	+	55.9423i	−0.943777	+	2.00563i
$779$	21.7890	−	46.3040i	0.780672	−	1.65901i
$780$	33.5059	+	22.6520i	1.19971	+	0.811073i
$781$	3.09187	−	16.2081i	0.110636	−	0.579972i
$782$	21.4228	−	65.9326i	0.766077	−	2.35774i
$783$	−0.304935	+	0.286353i	−0.0108975	+	0.0102334i
$784$	−13.2656	−	16.0353i	−0.473770	−	0.572690i
$785$	2.26663	+	1.98856i	0.0808997	+	0.0709747i
$786$	−1.95775	+	31.1176i	−0.0698307	+	1.10993i
$787$	−47.9028	+	18.9661i	−1.70755	+	0.676067i	−0.999546	−	0.0301394i	$-0.990405\pi$
$787$	−47.9028	+	18.9661i	−1.70755	+	0.676067i	−0.708006	+	0.706207i	$0.750405\pi$
$788$	13.0770	−	20.6060i	0.465848	−	0.734060i
$789$	−23.2450	−	9.20336i	−0.827545	−	0.327648i
$790$	2.89983	+	7.99371i	0.103171	+	0.284404i
$791$	−4.11066	+	6.47736i	−0.146158	+	0.230308i
$792$	6.48341	−	0.819045i	0.230378	−	0.0291035i
$793$	13.1075	+	40.3407i	0.465461	+	1.43254i
$794$	−24.8973	−	13.6874i	−0.883572	−	0.485748i
$795$	−12.6916	+	3.72065i	−0.450125	+	0.131958i
$796$	−21.9961	−	2.77875i	−0.779629	−	0.0984901i
$797$	13.9758	−	7.68325i	0.495047	−	0.272155i	−0.214612	−	0.976699i	$-0.568849\pi$
$797$	13.9758	−	7.68325i	0.495047	−	0.272155i	0.709660	+	0.704545i	$0.248849\pi$
$798$	−17.0038	+	4.36585i	−0.601930	+	0.154549i
$799$	12.8451	+	39.5332i	0.454428	+	1.39859i
$800$	36.5640	−	17.4228i	1.29273	−	0.615988i
$801$	3.79626	−	11.6837i	0.134134	−	0.412823i
$802$	−1.71226	+	27.2156i	−0.0604621	+	0.961018i
$803$	−23.8090	−	22.3582i	−0.840203	−	0.789003i
$804$	46.5372	−	25.5840i	1.64124	−	0.902280i
$805$	−8.33042	−	4.21915i	−0.293609	−	0.148705i
$806$	0.0357500	+	0.0759727i	0.00125924	+	0.00267602i
$807$	78.8274			2.77486
$808$	−0.0850697	−	0.180782i	−0.00299274	−	0.00635990i
$809$	−2.33909	−	37.1787i	−0.0822379	−	1.30713i	−0.795379	−	0.606113i	$-0.792728\pi$
$809$	−2.33909	−	37.1787i	−0.0822379	−	1.30713i	0.713141	−	0.701021i	$-0.247272\pi$
$810$	1.20108	−	41.4176i	0.0422015	−	1.45526i
$811$	15.9114	+	25.0723i	0.558723	+	0.880407i	0.999855	−	0.0170354i	$-0.00542281\pi$
$811$	15.9114	+	25.0723i	0.558723	+	0.880407i	−0.441132	+	0.897442i	$0.645423\pi$
$812$	−6.92456	−	8.37036i	−0.243005	−	0.293742i
$813$	11.6820	+	14.1211i	0.409704	+	0.495247i
$814$	26.5014	+	41.7596i	0.928875	+	1.46367i
$815$	5.52831	+	8.09239i	0.193648	+	0.283464i
$816$	3.11822	+	49.5627i	0.109160	+	1.73504i
$817$	−10.7547	−	22.8550i	−0.376261	−	0.799595i
$818$	−25.1700			−0.880048
$819$	3.18458	+	6.76758i	0.111278	+	0.236478i
$820$	42.3881	−	42.5942i	1.48026	−	1.48745i
$821$	−22.3092	+	12.2646i	−0.778598	+	0.428038i	−0.820903	−	0.571067i	$-0.806530\pi$
$821$	−22.3092	+	12.2646i	−0.778598	+	0.428038i	0.0423058	+	0.999105i	$0.486530\pi$
$822$	50.1674	+	47.1103i	1.74979	+	1.64316i
$823$	0.607457	−	9.65525i	0.0211746	−	0.336561i	−0.973150	−	0.230172i	$-0.926071\pi$
$823$	0.607457	−	9.65525i	0.0211746	−	0.336561i	0.994325	−	0.106389i	$-0.0339289\pi$
$824$	−3.30059	+	10.1582i	−0.114981	+	0.353876i
$825$	39.6174	+	2.29968i	1.37930	+	0.0800646i
$826$	−0.785195	−	2.41658i	−0.0273204	−	0.0840836i
$827$	41.0839	−	10.5485i	1.42863	−	0.366809i	0.546356	−	0.837553i	$-0.316014\pi$
$827$	41.0839	−	10.5485i	1.42863	−	0.366809i	0.882270	+	0.470744i	$0.156014\pi$
$828$	−33.0550	+	18.1721i	−1.14874	+	0.631525i
$829$	0.209963	+	0.0265245i	0.00729232	+	0.000921234i	0.128979	−	0.991647i	$-0.458830\pi$
$829$	0.209963	+	0.0265245i	0.00729232	+	0.000921234i	−0.121686	+	0.992569i	$0.538830\pi$
$830$	10.2105	+	14.9462i	0.354411	+	0.518790i
$831$	−2.26331	−	1.24426i	−0.0785133	−	0.0431630i
$832$	−10.1309	−	31.1796i	−0.351225	−	1.08096i
$833$	−39.4258	+	4.98063i	−1.36602	+	0.172569i
$834$	15.9850	−	25.1884i	0.553516	−	0.872202i
$835$	−3.45630	+	12.0052i	−0.119610	+	0.415458i
$836$	30.8355	+	12.2086i	1.06647	+	0.422245i
$837$	−0.000474313	0	0.000747398i	−1.63947e−5	0	2.58339e-5i
$838$	−21.9621	+	8.69540i	−0.758667	+	0.300377i
$839$	−2.96801	+	47.1751i	−0.102467	+	1.62867i	0.525758	+	0.850634i	$0.323782\pi$
$839$	−2.96801	+	47.1751i	−0.102467	+	1.62867i	−0.628225	+	0.778032i	$0.716218\pi$
$840$	−2.84007	−	0.261519i	−0.0979918	−	0.00902326i
$841$	−4.57033	−	5.52458i	−0.157597	−	0.190503i
$842$	36.1378	−	33.9357i	1.24539	−	1.16950i
$843$	−3.95106	+	12.1601i	−0.136082	+	0.418817i
$844$	2.91959	−	15.3050i	0.100496	−	0.526821i
$845$	−5.16210	+	4.02422i	−0.177581	+	0.138437i
$846$	17.9277	−	38.0983i	0.616368	−	1.30985i
$847$	−0.182397	+	0.387614i	−0.00626724	+	0.0133186i
$848$	7.28974	+	2.88621i	0.250331	+	0.0991129i
$849$	−62.5687	+	45.4588i	−2.14735	+	1.56014i
$850$	7.78479	−	64.1224i	0.267016	−	2.19938i
$851$	−31.9545	−	23.2163i	−1.09539	−	0.795845i
$852$	15.5873	+	24.5616i	0.534011	+	0.841467i
$853$	−0.736574	−	3.86126i	−0.0252198	−	0.132207i	0.967451	−	0.253060i	$-0.0814370\pi$
$853$	−0.736574	−	3.86126i	−0.0252198	−	0.132207i	−0.992670	+	0.120853i	$0.961437\pi$
$854$	−15.7601	−	14.7997i	−0.539299	−	0.506435i
$855$	−15.1733	+	25.7992i	−0.518915	+	0.882313i
$856$	12.3303	−	1.55768i	0.421441	−	0.0532404i
$857$	−24.1520	+	17.5475i	−0.825017	+	0.599410i	−0.918145	−	0.396244i	$-0.870313\pi$
$857$	−24.1520	+	17.5475i	−0.825017	+	0.599410i	0.0931279	+	0.995654i	$0.470313\pi$
$858$	9.81178	−	51.4351i	0.334969	−	1.75597i
$859$	35.8707	−	14.2022i	1.22389	−	0.484574i	0.334796	−	0.942291i	$-0.391333\pi$
$859$	35.8707	−	14.2022i	1.22389	−	0.484574i	0.889098	+	0.457717i	$0.151333\pi$
$860$	−2.86289	−	29.5220i	−0.0976238	−	1.00669i
$861$	21.4266	−	5.50141i	0.730216	−	0.187488i
$862$	−47.1166	−	12.0975i	−1.60480	−	0.412042i
$863$	0.368155	+	5.85166i	0.0125322	+	0.199193i	0.999311	+	0.0371194i	$0.0118182\pi$
$863$	0.368155	+	5.85166i	0.0125322	+	0.199193i	−0.986779	+	0.162074i	$0.948182\pi$
$864$	0.359143	−	0.434129i	0.0122183	−	0.0147694i
$865$	−4.97097	+	31.8857i	−0.169018	+	1.08415i
$866$	−52.2518	−	13.4160i	−1.77559	−	0.455893i
$867$	46.5212	+	25.5753i	1.57994	+	0.868582i
$868$	−0.0185979	−	0.0135122i	−0.000631255	−	0.000458633i
$869$	4.31090	−	4.04820i	0.146237	−	0.137326i
$870$	−68.3476	−	6.29357i	−2.31720	−	0.213372i
$871$	−5.54175	−	29.0509i	−0.187775	−	0.984351i
$872$	−3.45074	−	0.435930i	−0.116857	−	0.0147625i
$873$	−3.52522	+	4.26126i	−0.119311	+	0.144222i
$874$	−49.3060			−1.66780
$875$	−8.37247	−	2.36652i	−0.283041	−	0.0800029i
$876$	57.5817			1.94551
$877$	3.40800	−	4.11957i	0.115080	−	0.139108i	−0.709828	−	0.704376i	$-0.751227\pi$
$877$	3.40800	−	4.11957i	0.115080	−	0.139108i	0.824908	+	0.565268i	$0.191227\pi$
$878$	−8.15831	−	1.03063i	−0.275330	−	0.0347822i
$879$	1.04222	+	5.46348i	0.0351531	+	0.184279i
$880$	−17.6841	−	15.5145i	−0.596129	−	0.522995i
$881$	−10.9723	+	10.3037i	−0.369666	+	0.347139i	−0.847010	−	0.531577i	$-0.821600\pi$
$881$	−10.9723	+	10.3037i	−0.369666	+	0.347139i	0.477344	+	0.878717i	$0.341600\pi$
$882$	32.5657	+	23.6604i	1.09654	+	0.796686i
$883$	−36.0582	−	19.8232i	−1.21345	−	0.667102i	−0.259121	−	0.965845i	$-0.583433\pi$
$883$	−36.0582	−	19.8232i	−1.21345	−	0.667102i	−0.954334	+	0.298743i	$0.903433\pi$
$884$	−44.3436	−	11.3855i	−1.49144	−	0.382936i
$885$	−7.69319	−	3.89641i	−0.258604	−	0.130976i
$886$	−15.3495	+	18.5544i	−0.515676	+	0.623346i
$887$	−0.231751	−	3.68358i	−0.00778145	−	0.123683i	0.992218	−	0.124511i	$-0.0397363\pi$
$887$	−0.231751	−	3.68358i	−0.00778145	−	0.123683i	−1.00000		0.000828554i	$0.999736\pi$
$888$	−11.6849	−	3.00016i	−0.392118	−	0.100679i
$889$	−5.20458	+	1.33631i	−0.174556	+	0.0448184i
$890$	17.2872	−	7.53066i	0.579468	−	0.252428i
$891$	−26.7923	+	10.6078i	−0.897575	+	0.355375i
$892$	−2.38852	+	12.5211i	−0.0799735	+	0.419236i
$893$	23.9177	−	17.3772i	0.800376	−	0.581507i
$894$	93.6277	−	11.8279i	3.13138	−	0.395585i
$895$	0.330240	+	3.40542i	0.0110387	+	0.113831i
$896$	2.99049	+	2.80826i	0.0999054	+	0.0938174i
$897$	7.83569	+	41.0761i	0.261626	+	1.37149i
$898$	−27.5893	−	43.4738i	−0.920667	−	1.45074i
$899$	−0.0619226	−	0.0449894i	−0.00206523	−	0.00150048i
$900$	−26.9714	+	22.5339i	−0.899046	+	0.751129i
$901$	12.1119	−	8.79980i	0.403505	−	0.293164i
$902$	−72.3360	−	28.6398i	−2.40853	−	0.953603i
$903$	4.64905	−	9.87973i	0.154711	−	0.328777i
$904$	−2.80203	+	5.95462i	−0.0931941	+	0.198048i
$905$	−8.77073	+	0.296922i	−0.291549	+	0.00987001i
$906$	19.0296	−	99.7565i	0.632215	−	3.31419i
$907$	−17.0598	+	52.5047i	−0.566462	+	1.74339i	0.0971061	+	0.995274i	$0.469041\pi$
$907$	−17.0598	+	52.5047i	−0.566462	+	1.74339i	−0.663568	+	0.748116i	$0.730959\pi$
$908$	30.5221	−	28.6622i	1.01291	−	0.951188i
$909$	−0.577739	−	0.698366i	−0.0191624	−	0.0231633i
$910$	−4.53377	+	10.5470i	−0.150293	+	0.349630i
$911$	−0.324565	+	5.15882i	−0.0107533	+	0.170919i	0.988984	+	0.148020i	$0.0472899\pi$
$911$	−0.324565	+	5.15882i	−0.0107533	+	0.170919i	−0.999738	+	0.0228998i	$0.992710\pi$
$912$	32.8396	−	13.0021i	1.08743	−	0.430543i
$913$	6.74511	−	10.6286i	0.223231	−	0.351755i
$914$	30.0514	+	11.8982i	0.994013	+	0.393558i
$915$	−73.3325	+	2.48258i	−2.42430	+	0.0820715i
$916$	19.4411	−	30.6342i	0.642351	−	1.01218i
$917$	−4.71647	+	0.595828i	−0.155751	+	0.0196760i
$918$	−0.277666	−	0.854568i	−0.00916435	−	0.0282050i
$919$	34.5276	+	18.9817i	1.13896	+	0.626148i	0.935637	−	0.352964i	$-0.114826\pi$
$919$	34.5276	+	18.9817i	1.13896	+	0.626148i	0.203322	+	0.979112i	$0.434826\pi$
$920$	−7.54336	−	2.69513i	−0.248697	−	0.0888558i
$921$	46.0493	+	5.81738i	1.51738	+	0.191689i
$922$	33.6431	−	18.4955i	1.10798	−	0.609116i
$923$	15.6913	−	4.02884i	0.516485	−	0.132611i
$924$	4.43015	+	13.6346i	0.145741	+	0.448546i
$925$	−33.3748	−	15.5077i	−1.09736	−	0.509891i
$926$	5.59079	−	17.2067i	0.183725	−	0.565447i
$927$	−3.04239	+	48.3575i	−0.0999253	+	1.58827i
$928$	35.5139	+	33.3498i	1.16580	+	1.09476i
$929$	23.2303	−	12.7709i	0.762160	−	0.419001i	−0.0527356	−	0.998609i	$-0.516794\pi$
$929$	23.2303	−	12.7709i	0.762160	−	0.419001i	0.814896	+	0.579607i	$0.196794\pi$
$930$	−0.143401	+	0.0230690i	−0.00470230	+	0.000756463i
$931$	12.0340	+	25.5735i	0.394397	+	0.838137i
$932$	43.7339			1.43255
$933$	15.3139	+	32.5436i	0.501353	+	1.06543i
$934$	5.05502	+	80.3472i	0.165405	+	2.62904i
$935$	−43.1070	+	12.6372i	−1.40975	+	0.413279i
$936$	3.43790	+	5.41727i	0.112371	+	0.177069i
$937$	−0.315613	−	0.381511i	−0.0103106	−	0.0124634i	0.765333	−	0.643635i	$-0.222574\pi$
$937$	−0.315613	−	0.381511i	−0.0103106	−	0.0124634i	−0.775643	+	0.631171i	$0.782574\pi$
$938$	9.60862	+	11.6148i	0.313733	+	0.379238i
$939$	−11.2481	−	17.7241i	−0.367067	−	0.578405i
$940$	33.3136	−	9.76614i	1.08657	−	0.318536i
$941$	−3.61488	−	57.4569i	−0.117842	−	1.87304i	−0.403863	−	0.914820i	$-0.632333\pi$
$941$	−3.61488	−	57.4569i	−0.117842	−	1.87304i	0.286021	−	0.958223i	$-0.407667\pi$
$942$	2.93040	+	6.22742i	0.0954776	+	0.202900i
$943$	62.1306			2.02325
$944$	2.17665	+	4.62562i	0.0708440	+	0.150551i
$945$	−0.119495	+	0.0192233i	−0.00388717	+	0.000625333i
$946$	−33.6508	+	18.4997i	−1.09408	+	0.601476i
$947$	−22.0805	−	20.7350i	−0.717519	−	0.673796i	0.237147	−	0.971474i	$-0.423788\pi$
$947$	−22.0805	−	20.7350i	−0.717519	−	0.673796i	−0.954666	+	0.297678i	$0.903788\pi$
$948$	−0.654642	+	10.4052i	−0.0212618	+	0.337946i
$949$	9.90931	−	30.4977i	0.321670	−	0.989998i
$950$	−45.0842	+	8.82708i	−1.46272	+	0.286388i
$951$	−4.69430	−	14.4476i	−0.152223	−	0.468495i
$952$	3.12704	−	0.802888i	0.101348	−	0.0260217i
$953$	34.9205	−	19.1977i	1.13118	−	0.621874i	0.197619	−	0.980279i	$-0.436679\pi$
$953$	34.9205	−	19.1977i	1.13118	−	0.621874i	0.933566	+	0.358405i	$0.116679\pi$
$954$	−15.0453	−	1.90066i	−0.487109	−	0.0615362i
$955$	−35.4961	−	12.6822i	−1.14863	−	0.410388i
$956$	14.1855	+	7.79854i	0.458792	+	0.252223i
$957$	14.7504	+	45.3970i	0.476812	+	1.46748i
$958$	−45.7691	+	5.78198i	−1.47873	+	0.186807i
$959$	−5.62249	+	8.85962i	−0.181560	+	0.286092i
$960$	56.6792	−	1.91880i	1.82931	−	0.0619290i
$961$	28.8229	+	11.4118i	0.929772	+	0.368123i
$962$	−26.0194	+	41.0000i	−0.838899	+	1.32189i
$963$	52.4207	−	20.7548i	1.68923	−	0.668815i
$964$	2.80431	−	44.5732i	0.0903207	−	1.43561i
$965$	−5.55994	+	12.9342i	−0.178981	+	0.416367i
$966$	−13.5860	−	16.4227i	−0.437123	−	0.528390i
$967$	−36.8089	+	34.5659i	−1.18369	+	1.11156i	−0.192208	+	0.981354i	$0.561565\pi$
$967$	−36.8089	+	34.5659i	−1.18369	+	1.11156i	−0.991487	+	0.130209i	$0.958435\pi$
$968$	−0.113558	+	0.349495i	−0.00364989	+	0.0112332i
$969$	12.6376	−	66.2489i	0.405980	−	2.12822i
$970$	−8.48379	+	0.287208i	−0.272398	+	0.00922169i
$971$	8.63645	−	18.3534i	0.277157	−	0.588988i	−0.716983	−	0.697091i	$-0.754477\pi$
$971$	8.63645	−	18.3534i	0.277157	−	0.588988i	0.994140	+	0.108103i	$0.0344775\pi$
$972$	21.8367	−	46.4054i	0.700414	−	1.48845i
$973$	4.22921	+	1.67446i	0.135582	+	0.0536808i
$974$	20.6460	−	15.0002i	0.661540	−	0.480637i
$975$	14.5185	+	36.1562i	0.464964	+	1.15793i
$976$	35.1898	+	25.5669i	1.12640	+	0.818375i
$977$	11.0930	+	17.4798i	0.354897	+	0.559228i	0.974133	−	0.225977i	$-0.0725575\pi$
$977$	11.0930	+	17.4798i	0.354897	+	0.559228i	−0.619236	+	0.785205i	$0.712558\pi$
$978$	4.19165	+	21.9734i	0.134034	+	0.702632i
$979$	−9.55934	−	8.97682i	−0.305518	−	0.286900i
$980$	3.20342	+	33.0334i	0.102329	+	1.05521i
$981$	−15.6540	+	1.97756i	−0.499793	+	0.0631386i
$982$	2.46080	−	1.78788i	0.0785273	−	0.0570534i
$983$	−9.32449	+	48.8807i	−0.297405	+	1.55905i	0.448983	+	0.893540i	$0.351786\pi$
$983$	−9.32449	+	48.8807i	−0.297405	+	1.55905i	−0.746388	+	0.665511i	$0.768214\pi$
$984$	17.6440	−	6.98574i	0.562469	−	0.222697i
$985$	21.5544	−	9.38956i	0.686782	−	0.299176i
$986$	75.2537	−	19.3219i	2.39657	−	0.615333i
$987$	12.3783	+	3.17822i	0.394007	+	0.101164i
$988$	2.04454	+	32.4970i	0.0650453	+	1.03387i
$989$	19.5478	−	23.6292i	0.621583	−	0.751365i
$990$	40.5930	+	20.5593i	1.29013	+	0.653418i
$991$	−50.6629	−	13.0080i	−1.60936	−	0.413214i	−0.666260	−	0.745720i	$-0.732106\pi$
$991$	−50.6629	−	13.0080i	−1.60936	−	0.413214i	−0.943101	+	0.332506i	$0.892106\pi$
$992$	0.0903417	+	0.0496658i	0.00286835	+	0.00157689i
$993$	−36.7418	−	26.6944i	−1.16596	−	0.847123i
$994$	−6.01926	+	5.65246i	−0.190919	+	0.179285i
$995$	−16.0553	−	14.0856i	−0.508988	−	0.446544i
$996$	4.15855	+	21.7999i	0.131769	+	0.690756i
$997$	−39.9545	−	5.04743i	−1.26537	−	0.159854i	−0.536145	−	0.844126i	$-0.680120\pi$
$997$	−39.9545	−	5.04743i	−1.26537	−	0.159854i	−0.729226	+	0.684272i	$0.760120\pi$
$998$	−15.2459	+	18.4291i	−0.482600	+	0.583364i
$999$	−0.511943			−0.0161972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.71.2	✓	220
5.2	odd	4		625.2.h.b.24.4		440
5.3	odd	4		625.2.h.b.24.19		440
5.4	even	2		625.2.g.a.601.10		220
125.8	odd	100		625.2.h.b.599.4		440
125.44	even	50		625.2.g.a.26.10		220
125.81	even	25	inner	125.2.g.a.81.2	yes	220
125.117	odd	100		625.2.h.b.599.19		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.71.2	✓	220	1.1	even	1	trivial
125.2.g.a.81.2	yes	220	125.81	even	25	inner
625.2.g.a.26.10		220	125.44	even	50
625.2.g.a.601.10		220	5.4	even	2
625.2.h.b.24.4		440	5.2	odd	4
625.2.h.b.24.19		440	5.3	odd	4
625.2.h.b.599.4		440	125.8	odd	100
625.2.h.b.599.19		440	125.117	odd	100

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32504 + 1.60169i) q^{2} +(-2.43590 - 0.307726i) q^{3} +(-0.434938 - 2.28002i) q^{4} +(0.883071 - 2.05431i) q^{5} +(3.72054 - 3.49382i) q^{6} +(0.629574 + 0.457412i) q^{7} +(0.584987 + 0.321599i) q^{8} +(2.93319 + 0.753115i) q^{9} +O(q^{10})\)	\(q+(-1.32504 + 1.60169i) q^{2} +(-2.43590 - 0.307726i) q^{3} +(-0.434938 - 2.28002i) q^{4} +(0.883071 - 2.05431i) q^{5} +(3.72054 - 3.49382i) q^{6} +(0.629574 + 0.457412i) q^{7} +(0.584987 + 0.321599i) q^{8} +(2.93319 + 0.753115i) q^{9} +(2.12027 + 4.13644i) q^{10} +(2.06052 - 2.49074i) q^{11} +(0.357844 + 5.68776i) q^{12} +(3.07406 + 0.789285i) q^{13} +(-1.56684 + 0.402296i) q^{14} +(-2.78324 + 4.73236i) q^{15} +(3.02605 - 1.19810i) q^{16} +(1.16451 - 6.10458i) q^{17} +(-5.09284 + 3.70016i) q^{18} +(-4.38516 + 0.553975i) q^{19} +(-5.06795 - 1.11993i) q^{20} +(-1.39282 - 1.30795i) q^{21} +(1.25914 + 6.60063i) q^{22} +(-2.87542 - 4.53094i) q^{23} +(-1.32601 - 0.963402i) q^{24} +(-3.44037 - 3.62820i) q^{25} +(-5.33743 + 3.87787i) q^{26} +(-0.0646699 - 0.0256046i) q^{27} +(0.769085 - 1.63439i) q^{28} +(2.56070 - 5.44177i) q^{29} +(-3.89189 - 10.7284i) q^{30} +(0.00238475 - 0.0125013i) q^{31} +(-2.50321 + 7.70409i) q^{32} +(-5.78569 + 5.43313i) q^{33} +(8.23465 + 9.95398i) q^{34} +(1.49562 - 0.889412i) q^{35} +(0.441365 - 7.01530i) q^{36} +(6.84347 - 2.70952i) q^{37} +(4.92320 - 7.75772i) q^{38} +(-7.24524 - 2.86859i) q^{39} +(1.17725 - 0.917750i) q^{40} +(-6.20373 + 9.77552i) q^{41} +(3.94047 - 0.497797i) q^{42} +(1.76593 + 5.43498i) q^{43} +(-6.57514 - 3.61471i) q^{44} +(4.13734 - 5.36062i) q^{45} +(11.0672 + 1.39811i) q^{46} +(-5.86131 + 3.22228i) q^{47} +(-7.73985 + 1.98725i) q^{48} +(-1.97598 - 6.08145i) q^{49} +(10.3699 - 0.702923i) q^{50} +(-4.71518 + 14.5118i) q^{51} +(0.462563 - 7.35223i) q^{52} +(1.75608 + 1.64907i) q^{53} +(0.126701 - 0.0696543i) q^{54} +(-3.29716 - 6.43244i) q^{55} +(0.221189 + 0.470051i) q^{56} +10.8523 q^{57} +(5.32302 + 11.3120i) q^{58} +(0.0986283 + 1.56765i) q^{59} +(12.0004 + 4.28758i) q^{60} +(7.16121 + 11.2843i) q^{61} +(0.0168634 + 0.0203843i) q^{62} +(1.50217 + 1.81582i) q^{63} +(-5.53494 - 8.72167i) q^{64} +(4.33605 - 5.61808i) q^{65} +(-1.03595 - 16.4660i) q^{66} +(-3.96761 - 8.43161i) q^{67} -14.4251 q^{68} +(5.60996 + 11.9218i) q^{69} +(-0.557190 + 3.57403i) q^{70} +(4.47304 - 2.45907i) q^{71} +(1.47368 + 1.38387i) q^{72} +(0.634423 - 10.0839i) q^{73} +(-4.72802 + 14.5513i) q^{74} +(7.26393 + 9.89665i) q^{75} +(3.17035 + 9.75733i) q^{76} +(2.43654 - 0.625598i) q^{77} +(14.1948 - 7.80366i) q^{78} +(1.81498 + 0.229286i) q^{79} +(0.210953 - 7.27444i) q^{80} +(-7.81158 - 4.29445i) q^{81} +(-7.43721 - 22.8894i) q^{82} +(3.86348 - 0.488071i) q^{83} +(-2.37636 + 3.74455i) q^{84} +(-11.5124 - 7.78305i) q^{85} +(-11.0451 - 4.37306i) q^{86} +(-7.91220 + 12.4676i) q^{87} +(2.00640 - 0.794389i) q^{88} +(0.254721 - 4.04868i) q^{89} +(3.10394 + 13.7298i) q^{90} +(1.57432 + 1.90303i) q^{91} +(-9.08002 + 8.52670i) q^{92} +(-0.00965601 + 0.0297182i) q^{93} +(2.60534 - 13.6576i) q^{94} +(-2.73437 + 9.49768i) q^{95} +(8.46833 - 17.9961i) q^{96} +(-0.777570 + 1.65242i) q^{97} +(12.3589 + 4.89322i) q^{98} +(7.91970 - 5.75400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

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