LMFDB - Embedded newform 525.2.bs.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 3, 20]))

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

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

chi := DirichletCharacter("525.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bs (of order $60$, degree $16$, 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:	$1216$
Relative dimension:	$76$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	525.2
Dual form			525.2.bs.a.263.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02020 - 1.63593i) q^{2} +(-1.04782 - 1.37916i) q^{3} +(0.989132 + 4.65350i) q^{4} +(-1.01425 + 1.99281i) q^{5} +(-0.139395 + 4.50033i) q^{6} +(-2.56962 + 0.630106i) q^{7} +(3.25423 - 6.38679i) q^{8} +(-0.804150 + 2.89022i) q^{9} +O(q^{10})$	\(q+(-2.02020 - 1.63593i) q^{2} +(-1.04782 - 1.37916i) q^{3} +(0.989132 + 4.65350i) q^{4} +(-1.01425 + 1.99281i) q^{5} +(-0.139395 + 4.50033i) q^{6} +(-2.56962 + 0.630106i) q^{7} +(3.25423 - 6.38679i) q^{8} +(-0.804150 + 2.89022i) q^{9} +(5.30908 - 2.36665i) q^{10} +(-1.39099 + 3.12422i) q^{11} +(5.38148 - 6.24020i) q^{12} +(-4.52425 + 0.716571i) q^{13} +(6.22196 + 2.93077i) q^{14} +(3.81115 - 0.689301i) q^{15} +(-8.33019 + 3.70884i) q^{16} +(0.0699189 + 1.33413i) q^{17} +(6.35272 - 4.52328i) q^{18} +(1.47040 - 6.91769i) q^{19} +(-10.2768 - 2.74865i) q^{20} +(3.56152 + 2.88368i) q^{21} +(7.92107 - 4.03599i) q^{22} +(4.92221 - 6.07843i) q^{23} +(-12.2182 + 2.20410i) q^{24} +(-2.94260 - 4.04241i) q^{25} +(10.3122 + 5.95372i) q^{26} +(4.82866 - 1.91937i) q^{27} +(-5.47390 - 11.3345i) q^{28} +(1.03738 - 3.19273i) q^{29} +(-8.82693 - 4.84223i) q^{30} +(1.53752 - 1.70759i) q^{31} +(9.04842 + 2.42452i) q^{32} +(5.76629 - 1.35522i) q^{33} +(2.04129 - 2.80960i) q^{34} +(1.35055 - 5.75986i) q^{35} +(-14.2450 - 0.883307i) q^{36} +(4.47894 + 1.71930i) q^{37} +(-14.2873 + 11.5697i) q^{38} +(5.72886 + 5.48882i) q^{39} +(9.42708 + 12.9629i) q^{40} +(-0.977598 + 1.34555i) q^{41} +(-2.47749 - 11.6520i) q^{42} +(-4.39698 + 4.39698i) q^{43} +(-15.9144 - 3.38272i) q^{44} +(-4.94405 - 4.53391i) q^{45} +(-19.8877 + 4.22726i) q^{46} +(-2.01654 - 0.105683i) q^{47} +(13.8436 + 7.60245i) q^{48} +(6.20593 - 3.23827i) q^{49} +(-0.668432 + 12.9804i) q^{50} +(1.76672 - 1.49436i) q^{51} +(-7.80965 - 20.3448i) q^{52} +(7.73114 + 5.02066i) q^{53} +(-12.8948 - 4.02182i) q^{54} +(-4.81517 - 5.94071i) q^{55} +(-4.33780 + 18.4622i) q^{56} +(-11.0813 + 5.22058i) q^{57} +(-7.31880 + 4.75288i) q^{58} +(-0.165575 + 1.57534i) q^{59} +(6.97739 + 17.0534i) q^{60} +(0.252752 + 2.40477i) q^{61} +(-5.89960 + 0.934404i) q^{62} +(0.245221 - 7.93346i) q^{63} +(-3.59381 - 4.94646i) q^{64} +(3.16072 - 9.74276i) q^{65} +(-13.8661 - 6.69542i) q^{66} +(5.74876 - 0.301280i) q^{67} +(-6.13922 + 1.64500i) q^{68} +(-13.5407 - 0.419413i) q^{69} +(-12.1511 + 9.42667i) q^{70} +(2.90272 + 0.943152i) q^{71} +(15.8423 + 14.5414i) q^{72} +(-5.14589 + 1.97532i) q^{73} +(-6.23570 - 10.8006i) q^{74} +(-2.49180 + 8.29403i) q^{75} +33.6459 q^{76} +(1.60574 - 8.90453i) q^{77} +(-2.59415 - 20.4605i) q^{78} +(7.64132 - 6.88028i) q^{79} +(1.05785 - 20.3622i) q^{80} +(-7.70669 - 4.64833i) q^{81} +(4.17616 - 1.11900i) q^{82} +(2.79845 - 5.49226i) q^{83} +(-9.89639 + 19.4259i) q^{84} +(-2.72959 - 1.21380i) q^{85} +(16.0759 - 1.68965i) q^{86} +(-5.49027 + 1.91470i) q^{87} +(15.4271 + 19.0509i) q^{88} +(-1.80804 - 17.2023i) q^{89} +(2.57083 + 17.2475i) q^{90} +(11.1741 - 4.69207i) q^{91} +(33.1547 + 16.8932i) q^{92} +(-3.96608 - 0.331238i) q^{93} +(3.90093 + 3.51241i) q^{94} +(12.2943 + 9.94648i) q^{95} +(-6.13732 - 15.0196i) q^{96} +(-0.498143 + 0.253817i) q^{97} +(-17.8348 - 3.61050i) q^{98} +(-7.91109 - 6.53260i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.02020	−	1.63593i	−1.42850	−	1.15677i	−0.962266	−	0.272112i	$-0.912278\pi$
$2$	−2.02020	−	1.63593i	−1.42850	−	1.15677i	−0.466232	−	0.884663i	$-0.654389\pi$
$3$	−1.04782	−	1.37916i	−0.604959	−	0.796257i
$3$	−1.04782	−	1.37916i	−0.604959	−	0.796257i
$4$	0.989132	+	4.65350i	0.494566	+	2.32675i
$5$	−1.01425	+	1.99281i	−0.453585	+	0.891213i
$5$	−1.01425	+	1.99281i	−0.453585	+	0.891213i
$6$	−0.139395	+	4.50033i	−0.0569076	+	1.83725i
$7$	−2.56962	+	0.630106i	−0.971227	+	0.238158i
$7$	−2.56962	+	0.630106i	−0.971227	+	0.238158i
$8$	3.25423	−	6.38679i	1.15054	−	2.25807i
$9$	−0.804150	+	2.89022i	−0.268050	+	0.963405i
$10$	5.30908	−	2.36665i	1.67888	−	0.748400i
$11$	−1.39099	+	3.12422i	−0.419400	+	0.941987i	0.573071	+	0.819506i	$0.305752\pi$
$11$	−1.39099	+	3.12422i	−0.419400	+	0.941987i	−0.992471	+	0.122481i	$0.960915\pi$
$12$	5.38148	−	6.24020i	1.55350	−	1.80139i
$13$	−4.52425	+	0.716571i	−1.25480	+	0.198741i	−0.748220	−	0.663451i	$-0.769091\pi$
$13$	−4.52425	+	0.716571i	−1.25480	+	0.198741i	−0.506582	+	0.862192i	$0.669091\pi$
$14$	6.22196	+	2.93077i	1.66289	+	0.783282i
$15$	3.81115	−	0.689301i	0.984035	−	0.177977i
$16$	−8.33019	+	3.70884i	−2.08255	+	0.927210i
$17$	0.0699189	+	1.33413i	0.0169578	+	0.323574i	0.993916	+	0.110143i	$0.0351308\pi$
$17$	0.0699189	+	1.33413i	0.0169578	+	0.323574i	−0.976958	+	0.213432i	$0.931536\pi$
$18$	6.35272	−	4.52328i	1.49735	−	1.06615i
$19$	1.47040	−	6.91769i	0.337333	−	1.58703i	−0.403268	−	0.915082i	$-0.632126\pi$
$19$	1.47040	−	6.91769i	0.337333	−	1.58703i	0.740601	−	0.671945i	$-0.234541\pi$
$20$	−10.2768	−	2.74865i	−2.29796	−	0.614616i
$21$	3.56152	+	2.88368i	0.777187	+	0.629270i
$22$	7.92107	−	4.03599i	1.68878	−	0.860475i
$23$	4.92221	−	6.07843i	1.02635	−	1.26744i	0.0633370	−	0.997992i	$-0.479826\pi$
$23$	4.92221	−	6.07843i	1.02635	−	1.26744i	0.963015	−	0.269447i	$-0.0868410\pi$
$24$	−12.2182	+	2.20410i	−2.49404	+	0.449911i
$25$	−2.94260	−	4.04241i	−0.588521	−	0.808482i
$26$	10.3122	+	5.95372i	2.02238	+	1.16762i
$27$	4.82866	−	1.91937i	0.929277	−	0.369384i
$28$	−5.47390	−	11.3345i	−1.03447	−	2.14202i
$29$	1.03738	−	3.19273i	0.192637	−	0.592876i	−0.807359	−	0.590061i	$-0.799104\pi$
$29$	1.03738	−	3.19273i	0.192637	−	0.592876i	0.999996	−	0.00281536i	$-0.000896158\pi$
$30$	−8.82693	−	4.84223i	−1.61157	−	0.884067i
$31$	1.53752	−	1.70759i	0.276147	−	0.306693i	−0.589078	−	0.808076i	$-0.700509\pi$
$31$	1.53752	−	1.70759i	0.276147	−	0.306693i	0.865225	+	0.501384i	$0.167176\pi$
$32$	9.04842	+	2.42452i	1.59955	+	0.428598i
$33$	5.76629	−	1.35522i	1.00378	−	0.235913i
$34$	2.04129	−	2.80960i	0.350078	−	0.481842i
$35$	1.35055	−	5.75986i	0.228285	−	0.973594i
$36$	−14.2450	−	0.883307i	−2.37417	−	0.147218i
$37$	4.47894	+	1.71930i	0.736333	+	0.282652i	0.697491	−	0.716593i	$-0.254300\pi$
$37$	4.47894	+	1.71930i	0.736333	+	0.282652i	0.0388423	+	0.999245i	$0.487633\pi$
$38$	−14.2873	+	11.5697i	−2.31771	+	1.87685i
$39$	5.72886	+	5.48882i	0.917352	+	0.878914i
$40$	9.42708	+	12.9629i	1.49055	+	2.04961i
$41$	−0.977598	+	1.34555i	−0.152675	+	0.210139i	−0.878503	−	0.477737i	$-0.841457\pi$
$41$	−0.977598	+	1.34555i	−0.152675	+	0.210139i	0.725828	+	0.687877i	$0.241457\pi$
$42$	−2.47749	−	11.6520i	−0.382285	−	1.79794i
$43$	−4.39698	+	4.39698i	−0.670533	+	0.670533i	−0.957839	−	0.287306i	$-0.907240\pi$
$43$	−4.39698	+	4.39698i	−0.670533	+	0.670533i	0.287306	+	0.957839i	$0.407240\pi$
$44$	−15.9144	−	3.38272i	−2.39919	−	0.509963i
$45$	−4.94405	−	4.53391i	−0.737016	−	0.675876i
$46$	−19.8877	+	4.22726i	−2.93228	+	0.623276i
$47$	−2.01654	−	0.105683i	−0.294143	−	0.0154154i	−0.0953062	−	0.995448i	$-0.530383\pi$
$47$	−2.01654	−	0.105683i	−0.294143	−	0.0154154i	−0.198837	+	0.980033i	$0.563716\pi$
$48$	13.8436	+	7.60245i	1.99815	+	1.09732i
$49$	6.20593	−	3.23827i	0.886562	−	0.462610i
$50$	−0.668432	+	12.9804i	−0.0945305	+	1.83570i
$51$	1.76672	−	1.49436i	0.247390	−	0.209252i
$52$	−7.80965	−	20.3448i	−1.08300	−	2.82132i
$53$	7.73114	+	5.02066i	1.06195	+	0.689641i	0.952558	−	0.304357i	$-0.0984416\pi$
$53$	7.73114	+	5.02066i	1.06195	+	0.689641i	0.109396	+	0.993998i	$0.465108\pi$
$54$	−12.8948	−	4.02182i	−1.75476	−	0.547300i
$55$	−4.81517	−	5.94071i	−0.649277	−	0.801046i
$56$	−4.33780	+	18.4622i	−0.579663	+	2.46711i
$57$	−11.0813	+	5.22058i	−1.46775	+	0.691482i
$58$	−7.31880	+	4.75288i	−0.961005	+	0.624084i
$59$	−0.165575	+	1.57534i	−0.0215561	+	0.205092i	−0.999999	−	0.00142511i	$-0.999546\pi$
$59$	−0.165575	+	1.57534i	−0.0215561	+	0.205092i	0.978443	+	0.206518i	$0.0662130\pi$
$60$	6.97739	+	17.0534i	0.900778	+	2.20158i
$61$	0.252752	+	2.40477i	0.0323615	+	0.307899i	0.998715	+	0.0506812i	$0.0161392\pi$
$61$	0.252752	+	2.40477i	0.0323615	+	0.307899i	−0.966353	+	0.257218i	$0.917194\pi$
$62$	−5.89960	+	0.934404i	−0.749250	+	0.118669i
$63$	0.245221	−	7.93346i	0.0308950	−	0.999523i
$64$	−3.59381	−	4.94646i	−0.449227	−	0.618308i
$65$	3.16072	−	9.74276i	0.392039	−	1.20844i
$66$	−13.8661	−	6.69542i	−1.70680	−	0.824149i
$67$	5.74876	−	0.301280i	0.702323	−	0.0368072i	0.302168	−	0.953255i	$-0.402290\pi$
$67$	5.74876	−	0.301280i	0.702323	−	0.0368072i	0.400155	+	0.916447i	$0.368956\pi$
$68$	−6.13922	+	1.64500i	−0.744490	+	0.199486i
$69$	−13.5407	−	0.419413i	−1.63011	−	0.0504914i
$70$	−12.1511	+	9.42667i	−1.45233	+	1.12670i
$71$	2.90272	+	0.943152i	0.344490	+	0.111932i	0.476152	−	0.879363i	$-0.342031\pi$
$71$	2.90272	+	0.943152i	0.344490	+	0.111932i	−0.131662	+	0.991295i	$0.542031\pi$
$72$	15.8423	+	14.5414i	1.86703	+	1.71372i
$73$	−5.14589	+	1.97532i	−0.602281	+	0.231194i	−0.640353	−	0.768081i	$-0.721212\pi$
$73$	−5.14589	+	1.97532i	−0.602281	+	0.231194i	0.0380717	+	0.999275i	$0.487878\pi$
$74$	−6.23570	−	10.8006i	−0.724886	−	1.25554i
$75$	−2.49180	+	8.29403i	−0.287728	+	0.957712i
$76$	33.6459			3.85945
$77$	1.60574	−	8.90453i	0.182991	−	1.01477i
$78$	−2.59415	−	20.4605i	−0.293730	−	2.31670i
$79$	7.64132	−	6.88028i	0.859716	−	0.774092i	−0.115973	−	0.993252i	$-0.536999\pi$
$79$	7.64132	−	6.88028i	0.859716	−	0.774092i	0.975689	+	0.219161i	$0.0703319\pi$
$80$	1.05785	−	20.3622i	0.118271	−	2.27656i
$81$	−7.70669	−	4.64833i	−0.856298	−	0.516481i
$82$	4.17616	−	1.11900i	0.461180	−	0.123573i
$83$	2.79845	−	5.49226i	0.307170	−	0.602854i	−0.684887	−	0.728650i	$-0.740148\pi$
$83$	2.79845	−	5.49226i	0.307170	−	0.602854i	0.992056	+	0.125795i	$0.0401483\pi$
$84$	−9.89639	+	19.4259i	−1.07978	+	2.11954i
$85$	−2.72959	−	1.21380i	−0.296066	−	0.131656i
$86$	16.0759	−	1.68965i	1.73351	−	0.182199i
$87$	−5.49027	+	1.91470i	−0.588619	+	0.205277i
$88$	15.4271	+	19.0509i	1.64454	+	2.03083i
$89$	−1.80804	−	17.2023i	−0.191652	−	1.82344i	−0.493112	−	0.869966i	$-0.664141\pi$
$89$	−1.80804	−	17.2023i	−0.191652	−	1.82344i	0.301460	−	0.953479i	$-0.402526\pi$
$90$	2.57083	+	17.2475i	0.270989	+	1.81805i
$91$	11.1741	−	4.69207i	1.17136	−	0.491863i
$92$	33.1547	+	16.8932i	3.45661	+	1.76123i
$93$	−3.96608	−	0.331238i	−0.411264	−	0.0343478i
$94$	3.90093	+	3.51241i	0.402350	+	0.362278i
$95$	12.2943	+	9.94648i	1.26137	+	1.02049i
$96$	−6.13732	−	15.0196i	−0.626387	−	1.53294i
$97$	−0.498143	+	0.253817i	−0.0505788	+	0.0257712i	−0.479097	−	0.877762i	$-0.659036\pi$
$97$	−0.498143	+	0.253817i	−0.0505788	+	0.0257712i	0.428518	+	0.903533i	$0.359036\pi$
$98$	−17.8348	−	3.61050i	−1.80159	−	0.364715i
$99$	−7.91109	−	6.53260i	−0.795095	−	0.656551i
$100$	15.9007	−	17.6919i	1.59007	−	1.76919i
$101$	−1.69885	+	0.980833i	−0.169042	+	0.0975965i	−0.582134	−	0.813093i	$-0.697782\pi$
$101$	−1.69885	+	0.980833i	−0.169042	+	0.0975965i	0.413092	+	0.910689i	$0.364449\pi$
$102$	−6.01378	+	0.128687i	−0.595453	+	0.0127419i
$103$	12.1046	+	0.634378i	1.19271	+	0.0625071i	0.638333	−	0.769761i	$-0.279624\pi$
$103$	12.1046	+	0.634378i	1.19271	+	0.0625071i	0.554374	+	0.832268i	$0.312958\pi$
$104$	−10.1464	+	31.2273i	−0.994934	+	3.06209i
$105$	−9.35889	+	4.17267i	−0.913334	+	0.407211i
$106$	−7.40503	−	22.7903i	−0.719240	−	2.21359i
$107$	4.43364	+	16.5466i	0.428616	+	1.59962i	0.755898	+	0.654690i	$0.227201\pi$
$107$	4.43364	+	16.5466i	0.428616	+	1.59962i	−0.327282	+	0.944927i	$0.606133\pi$
$108$	13.7080	+	20.5717i	1.31905	+	1.97951i
$109$	−7.06449	−	0.742507i	−0.676655	−	0.0711193i	−0.240033	−	0.970765i	$-0.577158\pi$
$109$	−7.06449	−	0.742507i	−0.676655	−	0.0711193i	−0.436621	+	0.899645i	$0.643825\pi$
$110$	0.00904184	+	19.8787i	0.000862105	+	1.89536i
$111$	−2.32193	−	7.97869i	−0.220388	−	0.757303i
$112$	19.0685	−	14.7792i	1.80180	−	1.39651i
$113$	−1.13831	−	7.18699i	−0.107083	−	0.676095i	−0.981578	−	0.191061i	$-0.938807\pi$
$113$	−1.13831	−	7.18699i	−0.107083	−	0.676095i	0.874495	−	0.485034i	$-0.161193\pi$
$114$	30.9269	+	7.58157i	2.89657	+	0.710079i
$115$	7.12082	+	15.9741i	0.664020	+	1.48959i
$116$	15.8835	+	1.66942i	1.47475	+	0.155002i
$117$	1.56713	−	13.6523i	0.144881	−	1.26215i
$118$	2.91164	−	2.91164i	0.268038	−	0.268038i
$119$	−1.02031	−	3.38416i	−0.0935316	−	0.310225i
$120$	7.99994	−	26.5842i	0.730292	−	2.42679i
$121$	−0.465440	−	0.516923i	−0.0423127	−	0.0469930i
$122$	3.42342	−	5.27160i	0.309942	−	0.477269i
$123$	2.88007	−	0.0616299i	0.259687	−	0.00555698i
$124$	9.46709	+	5.46583i	0.850170	+	0.490846i
$125$	11.0403	−	1.76406i	0.987474	−	0.157782i
$126$	−13.4740	+	15.6260i	−1.20036	+	1.39208i
$127$	−8.72361	−	1.38168i	−0.774095	−	0.122605i	−0.243125	−	0.969995i	$-0.578173\pi$
$127$	−8.72361	−	1.38168i	−0.774095	−	0.122605i	−0.530970	+	0.847390i	$0.678173\pi$
$128$	0.148707	−	2.83749i	0.0131439	−	0.250801i
$129$	10.6714	+	1.45689i	0.939561	+	0.128272i
$130$	−22.3237	+	14.5116i	−1.95792	+	1.27275i
$131$	−0.332687	+	1.56517i	−0.0290670	+	0.136750i	−0.990288	−	0.139028i	$-0.955602\pi$
$131$	−0.332687	+	1.56517i	−0.0290670	+	0.136750i	0.961221	+	0.275778i	$0.0889354\pi$
$132$	12.0101	+	25.4930i	1.04535	+	2.21888i
$133$	0.580500	+	18.7024i	0.0503357	+	1.62170i
$134$	−12.1065	−	8.79591i	−1.04584	−	0.759851i
$135$	−1.07251	+	11.5693i	−0.0923068	+	0.995731i
$136$	8.74835	+	3.89502i	0.750165	+	0.333995i
$137$	−9.42642	−	11.6407i	−0.805353	−	0.994528i	−0.999907	−	0.0136365i	$-0.995659\pi$
$137$	−9.42642	−	11.6407i	−0.805353	−	0.994528i	0.194554	−	0.980892i	$-0.437674\pi$
$138$	26.6688	+	22.9989i	2.27020	+	1.95779i
$139$	−8.90929	−	12.2626i	−0.755676	−	1.04010i	−0.997561	−	0.0697937i	$-0.977766\pi$
$139$	−8.90929	−	12.2626i	−0.755676	−	1.04010i	0.241886	−	0.970305i	$-0.422234\pi$
$140$	28.1394	+	0.587527i	2.37821	+	0.0496551i
$141$	1.96722	+	2.89187i	0.165670	+	0.243539i
$142$	−4.32115	−	6.65399i	−0.362623	−	0.558391i
$143$	4.05447	−	15.1315i	0.339052	−	1.26536i
$144$	−4.02063	−	27.0585i	−0.335052	−	2.25488i
$145$	5.31036	+	5.30553i	0.441001	+	0.440600i
$146$	13.6272	+	4.42775i	1.12780	+	0.366443i
$147$	−10.9688	−	5.16584i	−0.904690	−	0.426071i
$148$	−3.57052	+	22.5434i	−0.293495	+	1.85305i
$149$	1.95806	−	3.39147i	0.160411	−	0.277840i	−0.774605	−	0.632445i	$-0.782051\pi$
$149$	1.95806	−	3.39147i	0.160411	−	0.277840i	0.935016	+	0.354605i	$0.115385\pi$
$150$	18.6024	−	12.6792i	1.51888	−	1.03525i
$151$	11.5152	+	19.9449i	0.937095	+	1.62310i	0.770855	+	0.637011i	$0.219829\pi$
$151$	11.5152	+	19.9449i	0.937095	+	1.62310i	0.166240	+	0.986085i	$0.446837\pi$
$152$	−39.3968	−	31.9029i	−3.19550	−	2.58767i
$153$	−3.91215	−	0.870761i	−0.316279	−	0.0703969i
$154$	−17.8111	+	15.3621i	−1.43526	+	1.23791i
$155$	1.84348	+	4.79591i	0.148072	+	0.385217i
$156$	−19.8756	+	32.0884i	−1.59132	+	2.56913i
$157$	2.21990	−	8.28477i	0.177167	−	0.661196i	−0.819005	−	0.573786i	$-0.805474\pi$
$157$	2.21990	−	8.28477i	0.177167	−	0.661196i	0.996172	−	0.0874104i	$-0.0278592\pi$
$158$	−26.6926	+	1.39890i	−2.12355	+	0.111291i
$159$	−1.17656	−	15.9232i	−0.0933070	−	1.26279i
$160$	−14.0089	+	15.5727i	−1.10750	+	1.23113i
$161$	−8.81818	+	18.7208i	−0.694970	+	1.47540i
$162$	7.96472	+	21.9981i	0.625768	+	1.72834i
$163$	3.33314	−	8.68314i	0.261072	−	0.680116i	−0.738908	−	0.673806i	$-0.764658\pi$
$163$	3.33314	−	8.68314i	0.261072	−	0.680116i	0.999980	−	0.00630956i	$-0.00200841\pi$
$164$	−7.22849	−	3.21833i	−0.564450	−	0.251309i
$165$	−3.14775	+	12.8657i	−0.245052	+	1.00159i
$166$	−14.6384	+	6.51742i	−1.13616	+	0.505850i
$167$	−2.55662	−	1.30266i	−0.197837	−	0.100803i	0.352265	−	0.935900i	$-0.385411\pi$
$167$	−2.55662	−	1.30266i	−0.197837	−	0.100803i	−0.550103	+	0.835097i	$0.685411\pi$
$168$	30.0074	−	13.3625i	2.31512	−	1.03094i
$169$	7.59164	−	2.46667i	0.583972	−	0.189744i
$170$	3.52862	+	6.91753i	0.270633	+	0.530551i
$171$	18.8112	+	9.81263i	1.43853	+	0.750391i
$172$	−24.8105	−	16.1122i	−1.89179	−	1.22854i
$173$	0.985770	−	1.21733i	0.0749467	−	0.0925515i	−0.738294	−	0.674479i	$-0.764368\pi$
$173$	0.985770	−	1.21733i	0.0749467	−	0.0925515i	0.813240	+	0.581928i	$0.197701\pi$
$174$	14.2238	+	5.11361i	1.07830	+	0.387662i
$175$	10.1085	+	8.53332i	0.764133	+	0.645058i
$176$		−	31.1843i		−	2.35060i
$177$	2.34614	−	1.42232i	0.176347	−	0.106908i
$178$	−24.4892	+	37.7100i	−1.83554	+	2.82648i
$179$	17.8886	−	3.80235i	1.33706	−	0.284201i	0.516758	−	0.856132i	$-0.327139\pi$
$179$	17.8886	−	3.80235i	1.33706	−	0.284201i	0.820302	+	0.571931i	$0.193805\pi$
$180$	16.2082	−	27.4918i	1.20809	−	2.04912i
$181$	−1.45864	−	4.48922i	−0.108420	−	0.333681i	0.882098	−	0.471066i	$-0.156131\pi$
$181$	−1.45864	−	4.48922i	−0.108420	−	0.333681i	−0.990518	+	0.137384i	$0.956131\pi$
$182$	−30.2498	−	8.80108i	−2.24227	−	0.652380i
$183$	3.05172	−	2.86835i	0.225590	−	0.212035i
$184$	−22.8036	−	51.2177i	−1.68110	−	3.77582i
$185$	−7.96901	+	7.18189i	−0.585893	+	0.528023i
$186$	7.47040	+	7.15739i	0.547756	+	0.524805i
$187$	−4.26537	−	1.63732i	−0.311915	−	0.119733i
$188$	−1.50283	−	9.48852i	−0.109605	−	0.692021i
$189$	−11.1984	+	7.97464i	−0.814567	+	0.580070i
$190$	−8.56526	−	40.2065i	−0.621390	−	2.91688i
$191$	−5.45849	−	12.2600i	−0.394963	−	0.887101i	−0.996123	−	0.0879722i	$-0.971961\pi$
$191$	−5.45849	−	12.2600i	−0.394963	−	0.887101i	0.601160	−	0.799128i	$-0.294705\pi$
$192$	−3.05628	+	10.1394i	−0.220568	+	0.731751i
$193$	−7.11843	−	1.90738i	−0.512396	−	0.137296i	−0.00664900	−	0.999978i	$-0.502116\pi$
$193$	−7.11843	−	1.90738i	−0.512396	−	0.137296i	−0.505747	+	0.862682i	$0.668783\pi$
$194$	1.42157	+	0.302165i	0.102063	+	0.0216942i
$195$	−16.7487	+	5.84953i	−1.19940	+	0.418894i
$196$	21.2078	+	25.6762i	1.51484	+	1.83402i
$197$	3.03398	+	5.95453i	0.216162	+	0.424243i	0.973470	−	0.228816i	$-0.0734855\pi$
$197$	3.03398	+	5.95453i	0.216162	+	0.424243i	−0.757307	+	0.653059i	$0.773485\pi$
$198$	5.29514	+	26.1391i	0.376309	+	1.85763i
$199$	11.9553	−	6.90241i	0.847490	−	0.489299i	−0.0123131	−	0.999924i	$-0.503919\pi$
$199$	11.9553	−	6.90241i	0.847490	−	0.489299i	0.859803	+	0.510626i	$0.170586\pi$
$200$	−35.3939	+	5.63886i	−2.50273	+	0.398727i
$201$	−6.43918	−	7.61276i	−0.454185	−	0.536963i
$202$	5.03659	+	0.797718i	0.354373	+	0.0561272i
$203$	−0.653922	+	8.85779i	−0.0458963	+	0.621695i
$204$	8.70151	+	6.74329i	0.609228	+	0.472125i
$205$	−1.68990	−	3.31289i	−0.118028	−	0.231382i
$206$	−23.4160	−	21.0839i	−1.63147	−	1.46898i
$207$	13.6098	+	19.1142i	0.945944	+	1.32853i
$208$	35.0302	−	22.7489i	2.42891	−	1.57735i
$209$	19.5671	+	14.2163i	1.35348	+	0.983362i
$210$	25.7330	+	6.88082i	1.77575	+	0.474822i
$211$	0.418515	−	0.304069i	0.0288118	−	0.0209330i	−0.573286	−	0.819355i	$-0.694332\pi$
$211$	0.418515	−	0.304069i	0.0288118	−	0.0209330i	0.602098	+	0.798422i	$0.294332\pi$
$212$	−15.7165	+	40.9430i	−1.07942	+	2.81198i
$213$	−1.74077	−	4.99156i	−0.119276	−	0.342016i
$214$	18.1121	−	40.6805i	1.23812	−	2.78086i
$215$	−4.30273	−	13.2220i	−0.293444	−	0.901732i
$216$	3.45496	−	37.0857i	0.235080	−	2.52337i
$217$	−2.87489	+	5.35667i	−0.195160	+	0.363634i
$218$	13.0570	+	13.0570i	0.884331	+	0.884331i
$219$	8.11624	+	5.02721i	0.548445	+	0.339708i
$220$	22.8823	−	28.2836i	1.54272	−	1.90688i
$221$	−1.27233	−	5.98584i	−0.0855862	−	0.402651i
$222$	−8.36178	+	19.9170i	−0.561206	+	1.33674i
$223$	4.32721	−	27.3209i	0.289771	−	1.82955i	−0.227565	−	0.973763i	$-0.573076\pi$
$223$	4.32721	−	27.3209i	0.289771	−	1.82955i	0.517336	−	0.855782i	$-0.326924\pi$
$224$	−24.7787	−	0.528635i	−1.65560	−	0.0353209i
$225$	14.0497	−	5.25406i	0.936649	−	0.350271i
$226$	−9.45778	+	16.3814i	−0.629122	+	1.08967i
$227$	−9.45139	+	3.62805i	−0.627311	+	0.240802i	−0.651192	−	0.758913i	$-0.725731\pi$
$227$	−9.45139	+	3.62805i	−0.627311	+	0.240802i	0.0238816	+	0.999715i	$0.492398\pi$
$228$	−35.2548	−	46.4030i	−2.33481	−	3.07311i
$229$	−20.5980	+	18.5465i	−1.36115	+	1.22559i	−0.411841	+	0.911256i	$0.635114\pi$
$229$	−20.5980	+	18.5465i	−1.36115	+	1.22559i	−0.949313	+	0.314332i	$0.898219\pi$
$230$	11.7469	−	43.9200i	0.774568	−	2.89600i
$231$	−13.9633	+	7.11578i	−0.918716	+	0.468184i
$232$	−17.0154	−	17.0154i	−1.11712	−	1.11712i
$233$	6.32478	+	9.73931i	0.414350	+	0.638043i	0.982800	−	0.184675i	$-0.0591232\pi$
$233$	6.32478	+	9.73931i	0.414350	+	0.638043i	−0.568450	+	0.822718i	$0.692457\pi$
$234$	−25.5001	+	25.0166i	−1.66699	+	1.63539i
$235$	2.25588	−	3.91140i	0.147157	−	0.255152i
$236$	−7.49464	+	0.787719i	−0.487860	+	0.0512761i
$237$	−17.4957	−	3.32930i	−1.13647	−	0.216261i
$238$	−3.47501	+	8.50583i	−0.225251	+	0.551351i
$239$	9.24542	−	6.71719i	0.598036	−	0.434499i	−0.247145	−	0.968978i	$-0.579492\pi$
$239$	9.24542	−	6.71719i	0.598036	−	0.434499i	0.845181	+	0.534480i	$0.179492\pi$
$240$	−29.1911	+	19.8770i	−1.88428	+	1.28305i
$241$	−0.810608	+	7.71242i	−0.0522159	+	0.496801i	0.936893	+	0.349616i	$0.113688\pi$
$241$	−0.810608	+	7.71242i	−0.0522159	+	0.496801i	−0.989109	+	0.147185i	$0.952979\pi$
$242$	0.0946335	+	1.80571i	0.00608327	+	0.116076i
$243$	1.66443	+	15.4993i	0.106773	+	0.994283i
$244$	−10.9406	+	3.55482i	−0.700400	+	0.227574i
$245$	0.158913	+	15.6517i	0.0101526	+	0.999948i
$246$	−5.91914	−	4.58708i	−0.377391	−	0.292461i
$247$	−1.69544	+	32.3510i	−0.107879	+	2.05845i
$248$	−5.90257	−	15.3767i	−0.374814	−	0.976423i
$249$	−10.5070	+	1.89540i	−0.665852	+	0.120116i
$250$	−25.1895	−	14.4974i	−1.59312	−	0.916893i
$251$			16.3603i			1.03265i	0.856392	+	0.516325i	$0.172700\pi$
$251$			16.3603i			1.03265i	−0.856392	+	0.516325i	$0.827300\pi$
$252$	37.1609	−	6.70611i	2.34092	−	0.422445i
$253$	12.1436	+	23.8331i	0.763460	+	1.49837i
$254$	15.3631	+	17.0625i	0.963967	+	1.07059i
$255$	1.18609	+	5.03638i	0.0742758	+	0.315390i
$256$	−13.1247	+	14.5764i	−0.820293	+	0.911028i
$257$	−1.50951	−	5.63356i	−0.0941605	−	0.351412i	0.902730	−	0.430207i	$-0.141559\pi$
$257$	−1.50951	−	5.63356i	−0.0941605	−	0.351412i	−0.996891	+	0.0787950i	$0.974893\pi$
$258$	−19.1749	−	20.4008i	−1.19378	−	1.27010i
$259$	−12.5925	−	1.59576i	−0.782462	−	0.0991557i
$260$	48.4643	+	5.07152i	3.00563	+	0.314522i
$261$	8.39348	+	5.56570i	0.519543	+	0.344508i
$262$	3.23260	−	2.61771i	0.199711	−	0.161723i
$263$	3.32257	−	2.69057i	0.204879	−	0.165907i	−0.521390	−	0.853319i	$-0.674586\pi$
$263$	3.32257	−	2.69057i	0.204879	−	0.165907i	0.726268	+	0.687411i	$0.241253\pi$
$264$	10.1094	−	41.2383i	0.622188	−	2.53804i
$265$	−17.8465	+	10.3145i	−1.09630	+	0.633616i
$266$	29.4230	−	38.7322i	1.80404	−	2.37482i
$267$	−21.8302	+	20.5185i	−1.33599	+	1.25571i
$268$	7.08829	+	26.4539i	0.432986	+	1.61593i
$269$	14.1049	−	15.6650i	0.859989	−	0.955114i	−0.139394	−	0.990237i	$-0.544516\pi$
$269$	14.1049	−	15.6650i	0.859989	−	0.955114i	0.999383	+	0.0351227i	$0.0111822\pi$
$270$	21.0933	−	21.6179i	1.28370	−	1.31562i
$271$	−13.6492	−	15.1590i	−0.829131	−	0.920843i	0.168767	−	0.985656i	$-0.446022\pi$
$271$	−13.6492	−	15.1590i	−0.829131	−	0.920843i	−0.997897	+	0.0648130i	$0.979355\pi$
$272$	−5.53052	−	10.8543i	−0.335337	−	0.658136i
$273$	−18.1796	−	10.4944i	−1.10028	−	0.635150i
$274$			38.9374i			2.35229i
$275$	16.7225	−	3.57038i	1.00840	−	0.215302i
$276$	−11.4418	−	63.4265i	−0.688715	−	3.81783i
$277$	0.130720	+	0.340537i	0.00785420	+	0.0204609i	0.937451	−	0.348116i	$-0.113178\pi$
$277$	0.130720	+	0.340537i	0.00785420	+	0.0204609i	−0.929597	+	0.368577i	$0.879845\pi$
$278$	−2.06213	+	39.3478i	−0.123678	+	2.35992i
$279$	3.69891	+	5.81693i	0.221448	+	0.348251i
$280$	−32.3920	−	27.3696i	−1.93579	−	1.63565i
$281$	−17.1389	+	5.56877i	−1.02242	+	0.332205i	−0.771790	−	0.635878i	$-0.780638\pi$
$281$	−17.1389	+	5.56877i	−1.02242	+	0.332205i	−0.250632	+	0.968083i	$0.580638\pi$
$282$	0.756701	−	9.06037i	0.0450609	−	0.539537i
$283$	−1.65655	−	31.6089i	−0.0984718	−	1.87895i	−0.387828	−	0.921732i	$-0.626775\pi$
$283$	−1.65655	−	31.6089i	−0.0984718	−	1.87895i	0.289356	−	0.957222i	$-0.406559\pi$
$284$	−1.51778	+	14.4407i	−0.0900637	+	0.856899i
$285$	0.835547	−	27.3779i	0.0494935	−	1.62173i
$286$	−32.9448	+	23.9358i	−1.94807	+	1.41535i
$287$	1.66422	−	4.07354i	0.0982359	−	0.240454i
$288$	−14.2837	+	24.2022i	−0.841673	+	1.42613i
$289$	15.1319	−	1.59042i	0.890109	−	0.0935542i
$290$	−2.04853	−	19.4056i	−0.120294	−	1.13954i
$291$	0.872017	+	0.421064i	0.0511185	+	0.0246832i
$292$	−14.2821	−	21.9926i	−0.835799	−	1.28702i
$293$	−16.0212	−	16.0212i	−0.935967	−	0.935967i	0.0621030	−	0.998070i	$-0.480219\pi$
$293$	−16.0212	−	16.0212i	−0.935967	−	0.935967i	−0.998070	+	0.0621030i	$0.980219\pi$
$294$	13.7082	+	28.3801i	0.799479	+	1.65516i
$295$	−2.97143	−	1.92775i	−0.173003	−	0.112238i
$296$	25.5563	−	23.0110i	1.48543	−	1.33749i
$297$	−0.720089	+	17.7556i	−0.0417838	+	1.03029i
$298$	−9.50387	+	3.64819i	−0.550544	+	0.211334i
$299$	−17.9137	+	31.0274i	−1.03598	+	1.79436i
$300$	−41.0610	−	3.39171i	−2.37066	−	0.195820i
$301$	8.52802	−	14.0691i	0.491547	−	0.810932i
$302$	9.36540	−	59.1308i	0.538918	−	3.40260i
$303$	3.13281	+	1.31525i	0.179975	+	0.0755591i
$304$	13.4079	+	63.0792i	0.768995	+	3.61784i
$305$	−5.04861	−	1.93535i	−0.289083	−	0.110818i
$306$	6.47883	+	8.15910i	0.370370	+	0.466425i
$307$	1.97583	+	1.97583i	0.112766	+	0.112766i	0.761238	−	0.648472i	$-0.224592\pi$
$307$	1.97583	+	1.97583i	0.112766	+	0.112766i	−0.648472	+	0.761238i	$0.724592\pi$
$308$	43.0255	−	1.33546i	2.45161	−	0.0760951i
$309$	−11.8086	−	17.3589i	−0.671767	−	0.987515i
$310$	4.12156	−	12.7045i	0.234089	−	0.721568i
$311$	8.67261	−	19.4790i	0.491779	−	1.10455i	−0.481817	−	0.876272i	$-0.660023\pi$
$311$	8.67261	−	19.4790i	0.491779	−	1.10455i	0.973595	−	0.228281i	$-0.0733105\pi$
$312$	53.6989	−	18.7271i	3.04010	−	1.06022i
$313$	−0.845795	+	2.20337i	−0.0478072	+	0.124542i	−0.955405	−	0.295299i	$-0.904581\pi$
$313$	−0.845795	+	2.20337i	−0.0478072	+	0.124542i	0.907598	+	0.419841i	$0.137914\pi$
$314$	−18.0379	+	13.1053i	−1.01794	+	0.739575i
$315$	15.5612	+	8.53518i	0.876774	+	0.480903i
$316$	39.5757	+	28.7534i	2.22630	+	1.61751i
$317$	4.15779	−	2.70010i	0.233525	−	0.151653i	−0.422573	−	0.906329i	$-0.638873\pi$
$317$	4.15779	−	2.70010i	0.233525	−	0.151653i	0.656097	+	0.754676i	$0.272206\pi$
$318$	−23.6723	+	34.0928i	−1.32748	+	1.91183i
$319$	8.53181	+	7.68207i	0.477689	+	0.430114i
$320$	13.5024	−	2.14486i	0.754806	−	0.119902i
$321$	18.1747	−	23.4525i	1.01441	−	1.30899i
$322$	48.4403	−	23.3938i	2.69947	−	1.30369i
$323$	9.33192	+	1.47803i	0.519242	+	0.0822398i
$324$	14.0081	−	40.4609i	0.778227	−	2.24783i
$325$	16.2098	+	16.1803i	0.899156	+	0.897521i
$326$	−20.9386	+	12.0889i	−1.15968	+	0.669542i
$327$	6.37827	+	10.5210i	0.352719	+	0.581815i
$328$	5.41240	+	10.6224i	0.298850	+	0.586526i
$329$	5.24835	−	0.999071i	0.289351	−	0.0550806i
$330$	27.4064	−	20.8417i	1.50867	−	1.14730i
$331$	−2.13711	−	0.454256i	−0.117466	−	0.0249682i	0.148804	−	0.988867i	$-0.452458\pi$
$331$	−2.13711	−	0.454256i	−0.117466	−	0.0249682i	−0.266270	+	0.963899i	$0.585791\pi$
$332$	28.3263	+	7.59001i	1.55461	+	0.416556i
$333$	−8.57090	+	11.5625i	−0.469682	+	0.633623i
$334$	3.03383	+	6.81409i	0.166004	+	0.372850i
$335$	−5.23027	+	11.7618i	−0.285760	+	0.642615i
$336$	−40.3632	−	10.8125i	−2.20199	−	0.589870i
$337$	−0.330409	−	2.08612i	−0.0179985	−	0.113638i	0.977053	−	0.212995i	$-0.0683217\pi$
$337$	−0.330409	−	2.08612i	−0.0179985	−	0.113638i	−0.995052	+	0.0993562i	$0.968322\pi$
$338$	−19.3719	−	7.43619i	−1.05369	−	0.404475i
$339$	−8.71925	+	9.10058i	−0.473565	+	0.494275i
$340$	2.94851	−	13.9028i	0.159906	−	0.753983i
$341$	3.19621	+	7.17880i	0.173084	+	0.388754i
$342$	−21.9496	−	50.5972i	−1.18690	−	2.73598i
$343$	−13.9065	+	12.2315i	−0.750878	+	0.660440i
$344$	13.7738	+	42.3914i	0.742633	+	2.28559i
$345$	14.5694	−	26.5587i	0.784391	−	1.42987i
$346$	−3.98291	+	0.846593i	−0.214122	+	0.0455131i
$347$	2.47003	−	3.80351i	0.132598	−	0.204183i	−0.766135	−	0.642680i	$-0.777822\pi$
$347$	2.47003	−	3.80351i	0.132598	−	0.204183i	0.898733	+	0.438497i	$0.144489\pi$
$348$	−14.3406	−	23.6551i	−0.768739	−	1.26805i
$349$		−	25.0668i		−	1.34180i	−0.741550	−	0.670898i	$-0.765909\pi$
$349$		−	25.0668i		−	1.34180i	0.741550	−	0.670898i	$-0.234091\pi$
$350$	−6.46138	−	33.7758i	−0.345375	−	1.80539i
$351$	−20.4707	+	12.1438i	−1.09265	+	0.648189i
$352$	−20.1610	+	24.8967i	−1.07458	+	1.32700i
$353$	−1.34662	−	0.874503i	−0.0716732	−	0.0465451i	0.508305	−	0.861177i	$-0.330272\pi$
$353$	−1.34662	−	0.874503i	−0.0716732	−	0.0465451i	−0.579978	+	0.814632i	$0.696939\pi$
$354$	−7.06649	−	0.964738i	−0.375580	−	0.0512753i
$355$	−4.82360	+	4.82799i	−0.256010	+	0.256243i
$356$	78.2627	−	25.4291i	4.14792	−	1.34774i
$357$	−3.59819	+	4.95315i	−0.190436	+	0.262149i
$358$	−42.3590	−	21.5830i	−2.23874	−	1.14070i
$359$	−11.6425	+	5.18356i	−0.614466	+	0.273578i	−0.690278	−	0.723544i	$-0.742512\pi$
$359$	−11.6425	+	5.18356i	−0.614466	+	0.273578i	0.0758122	+	0.997122i	$0.475845\pi$
$360$	−45.0462	+	16.8222i	−2.37414	+	0.886608i
$361$	−28.3350	−	12.6156i	−1.49132	−	0.663976i
$362$	−4.39730	+	11.4554i	−0.231117	+	0.602080i
$363$	−0.225222	+	1.18356i	−0.0118211	+	0.0621206i
$364$	32.8872	+	47.3576i	1.72376	+	2.48222i
$365$	1.28276	−	12.2583i	0.0671426	−	0.641627i
$366$	−10.8575	+	0.802254i	−0.567530	+	0.0419345i
$367$	−3.14113	+	0.164620i	−0.163966	+	0.00859308i	−0.134142	−	0.990962i	$-0.542828\pi$
$367$	−3.14113	+	0.164620i	−0.163966	+	0.00859308i	−0.0298236	+	0.999555i	$0.509495\pi$
$368$	−18.4591	+	68.8902i	−0.962245	+	3.59115i
$369$	−3.10279	−	3.90749i	−0.161525	−	0.203416i
$370$	27.8480	−	1.47216i	1.44775	−	0.0765337i
$371$	−23.0297	−	8.02978i	−1.19564	−	0.416885i
$372$	−2.38156	−	18.7838i	−0.123478	−	0.973895i
$373$	8.94328	+	7.24213i	0.463066	+	0.374983i	0.832275	−	0.554363i	$-0.187038\pi$
$373$	8.94328	+	7.24213i	0.463066	+	0.374983i	−0.369209	+	0.929346i	$0.620371\pi$
$374$	5.93837	+	10.2856i	0.307066	+	0.531853i
$375$	−14.0011	−	13.3779i	−0.723016	−	0.690831i
$376$	−7.23727	+	12.5353i	−0.373234	+	0.646460i
$377$	−2.40556	+	15.1881i	−0.123893	+	0.782227i
$378$	35.6690	+	2.20946i	1.83462	+	0.113642i
$379$	7.36079	+	2.39166i	0.378098	+	0.122852i	0.491900	−	0.870652i	$-0.336303\pi$
$379$	7.36079	+	2.39166i	0.378098	+	0.122852i	−0.113801	+	0.993504i	$0.536303\pi$
$380$	−34.1253	+	67.0500i	−1.75059	+	3.43959i
$381$	7.23521	+	13.4790i	0.370671	+	0.690550i
$382$	−9.02916	+	33.6973i	−0.461972	+	1.72410i
$383$	−3.37627	−	5.19899i	−0.172519	−	0.265656i	0.741826	−	0.670593i	$-0.233960\pi$
$383$	−3.37627	−	5.19899i	−0.172519	−	0.265656i	−0.914345	+	0.404937i	$0.867294\pi$
$384$	−4.06917	+	2.76809i	−0.207654	+	0.141258i
$385$	16.1165	+	12.2313i	0.821371	+	0.623366i
$386$	11.2603	+	15.4985i	0.573136	+	0.788854i
$387$	−9.17239	−	16.2440i	−0.466259	−	0.825731i
$388$	−1.67387	−	2.06705i	−0.0849776	−	0.104939i
$389$	11.2315	+	5.00059i	0.569461	+	0.253540i	0.671207	−	0.741270i	$-0.265776\pi$
$389$	11.2315	+	5.00059i	0.569461	+	0.253540i	−0.101746	+	0.994810i	$0.532443\pi$
$390$	43.4051	+	15.5824i	2.19790	+	0.789043i
$391$	8.45358	+	6.14188i	0.427516	+	0.310608i
$392$	−0.486598	−	50.1741i	−0.0245769	−	2.53417i
$393$	2.50721	−	1.18119i	0.126472	−	0.0595831i
$394$	3.61191	−	16.9927i	0.181966	−	0.856081i
$395$	5.96091	+	22.2060i	0.299926	+	1.11731i
$396$	22.5744	−	43.2759i	1.13440	−	2.17470i
$397$	−1.63550	+	31.2073i	−0.0820836	+	1.56625i	0.578617	+	0.815599i	$0.303593\pi$
$397$	−1.63550	+	31.2073i	−0.0820836	+	1.56625i	−0.660701	+	0.750649i	$0.729741\pi$
$398$	−35.4440	−	5.61377i	−1.77665	−	0.281393i
$399$	25.1853	−	20.3973i	1.26084	−	1.02114i
$400$	39.5051	+	22.7604i	1.97526	+	1.13802i
$401$	−30.0507	−	17.3498i	−1.50066	−	0.866407i	−1.00000		0.000764393i	$-0.999757\pi$
$401$	−30.0507	−	17.3498i	−1.50066	−	0.866407i	−0.500662	−	0.865643i	$-0.666910\pi$
$402$	0.554513	+	25.9133i	0.0276566	+	1.29244i
$403$	−5.73253	+	8.82732i	−0.285558	+	0.439720i
$404$	−6.24470	−	6.93544i	−0.310685	−	0.345051i
$405$	17.0797	−	10.6434i	0.848699	−	0.528876i
$406$	15.8117	−	16.8247i	0.784723	−	0.834998i
$407$	−11.6016	+	11.6016i	−0.575072	+	0.575072i
$408$	−3.79485	−	16.1466i	−0.187873	−	0.799377i
$409$	−8.55038	−	0.898682i	−0.422789	−	0.0444369i	−0.109255	−	0.994014i	$-0.534846\pi$
$409$	−8.55038	−	0.898682i	−0.422789	−	0.0444369i	−0.313534	+	0.949577i	$0.601513\pi$
$410$	−2.00571	+	9.45725i	−0.0990547	+	0.467060i
$411$	−6.17711	+	25.1978i	−0.304695	+	1.24292i
$412$	9.02102	+	56.9565i	0.444434	+	2.80604i
$413$	−0.567167	−	4.15237i	−0.0279085	−	0.204325i
$414$	3.77500	−	60.8791i	0.185531	−	2.99204i
$415$	8.10673	+	11.1473i	0.397944	+	0.547199i
$416$	−42.6747	−	4.48529i	−2.09230	−	0.219909i
$417$	−7.57671	+	25.1363i	−0.371033	+	1.23093i
$418$	−16.2726	−	60.7300i	−0.795917	−	2.97040i
$419$	11.5239	+	35.4670i	0.562980	+	1.73267i	0.673878	+	0.738843i	$0.264627\pi$
$419$	11.5239	+	35.4670i	0.562980	+	1.73267i	−0.110897	+	0.993832i	$0.535373\pi$
$420$	−28.6747	−	39.4243i	−1.39918	−	1.92371i
$421$	2.72792	−	8.39567i	0.132951	−	0.409180i	−0.862315	−	0.506372i	$-0.830986\pi$
$421$	2.72792	−	8.39567i	0.132951	−	0.409180i	0.995266	+	0.0971924i	$0.0309862\pi$
$422$	−1.34292	−	0.0703794i	−0.0653723	−	0.00342602i
$423$	1.92705	−	5.74326i	0.0936963	−	0.279247i
$424$	57.2248	−	33.0388i	2.77908	−	1.60450i
$425$	5.18736	−	4.20846i	0.251624	−	0.204140i
$426$	−4.64912	+	12.9317i	−0.225250	+	0.626545i
$427$	−2.16474	−	6.02010i	−0.104759	−	0.291333i
$428$	−72.6140	+	36.9987i	−3.50993	+	1.78840i
$429$	−25.1171	+	10.2633i	−1.21266	+	0.495517i
$430$	−12.9378	+	33.7500i	−0.623916	+	1.62757i
$431$	10.9587	+	9.86729i	0.527864	+	0.475291i	0.889440	−	0.457052i	$-0.151095\pi$
$431$	10.9587	+	9.86729i	0.527864	+	0.475291i	−0.361576	+	0.932343i	$0.617761\pi$
$432$	−33.1051	+	33.8975i	−1.59277	+	1.63089i
$433$	5.21524	+	2.65730i	0.250628	+	0.127701i	0.574792	−	0.818299i	$-0.305083\pi$
$433$	5.21524	+	2.65730i	0.250628	+	0.127701i	−0.324164	+	0.946001i	$0.605083\pi$
$434$	14.5710	−	6.11844i	0.699429	−	0.293694i
$435$	1.75287	−	12.8831i	0.0840434	−	0.617695i
$436$	−3.53245	−	33.6090i	−0.169174	−	1.60958i
$437$	−34.8110	−	42.9881i	−1.66524	−	2.05640i
$438$	−8.17229	−	23.4336i	−0.390487	−	1.11970i
$439$	21.3543	−	2.24443i	1.01918	−	0.107121i	0.419829	−	0.907603i	$-0.362090\pi$
$439$	21.3543	−	2.24443i	1.01918	−	0.107121i	0.599356	+	0.800483i	$0.295423\pi$
$440$	−53.6118	+	11.4210i	−2.55584	+	0.544476i
$441$	4.36879	+	20.5405i	0.208038	+	0.978121i
$442$	−7.22204	+	14.1740i	−0.343517	+	0.674191i
$443$	18.0811	−	4.84481i	0.859058	−	0.230184i	0.197708	−	0.980261i	$-0.436650\pi$
$443$	18.0811	−	4.84481i	0.859058	−	0.230184i	0.661350	+	0.750077i	$0.269984\pi$
$444$	34.8321	−	18.6971i	1.65306	−	0.887324i
$445$	36.1149	+	13.8443i	1.71201	+	0.656285i
$446$	−53.4369	+	48.1148i	−2.53031	+	2.27830i
$447$	−6.72906	+	0.853165i	−0.318274	+	0.0403533i
$448$	12.3515	+	10.4461i	0.583556	+	0.493530i
$449$	11.9969			0.566168			0.283084	−	0.959095i	$-0.408642\pi$
$449$	11.9969			0.566168			0.283084	+	0.959095i	$0.408642\pi$
$450$	−36.9785	−	12.3701i	−1.74318	−	0.583131i
$451$	−2.84396	−	4.92588i	−0.133917	−	0.231950i
$452$	32.3187	−	12.4060i	1.52015	−	0.583529i
$453$	15.4413	−	36.7800i	0.725498	−	1.72807i
$454$	25.0289	+	8.13239i	1.17467	+	0.381672i
$455$	−1.98288	+	27.0268i	−0.0929590	+	1.26704i
$456$	−2.71839	+	87.7628i	−0.127300	+	4.10987i
$457$	25.2701	−	6.77111i	1.18209	−	0.316739i	0.386333	−	0.922359i	$-0.373742\pi$
$457$	25.2701	−	6.77111i	1.18209	−	0.316739i	0.795754	+	0.605620i	$0.207075\pi$
$458$	71.9528	−	3.77089i	3.36213	−	0.176202i
$459$	2.89831	+	6.30787i	0.135282	+	0.294426i
$460$	−67.2919	+	48.9372i	−3.13750	+	2.28171i
$461$	16.6252	+	22.8826i	0.774311	+	1.06575i	0.995887	+	0.0906041i	$0.0288798\pi$
$461$	16.6252	+	22.8826i	0.774311	+	1.06575i	−0.221576	+	0.975143i	$0.571120\pi$
$462$	39.8495	+	8.46759i	1.85397	+	0.393948i
$463$	34.9920	−	5.54218i	1.62621	−	0.257567i	0.724301	−	0.689484i	$-0.242163\pi$
$463$	34.9920	−	5.54218i	1.62621	−	0.257567i	0.901913	+	0.431917i	$0.142163\pi$
$464$	3.19975	+	30.4436i	0.148545	+	1.41331i
$465$	4.68268	−	7.56770i	0.217154	−	0.350944i
$466$	3.15546	−	30.0222i	0.146174	−	1.39075i
$467$	4.09180	−	2.65725i	0.189346	−	0.122963i	−0.446485	−	0.894791i	$-0.647324\pi$
$467$	4.09180	−	2.65725i	0.189346	−	0.122963i	0.635831	+	0.771829i	$0.280658\pi$
$468$	65.0810	−	6.21127i	3.00837	−	0.287116i
$469$	−14.5823	+	4.39650i	−0.673349	+	0.203012i
$470$	−10.9561	+	4.21137i	−0.505367	+	0.194256i
$471$	−13.7520	+	5.61935i	−0.633661	+	0.258926i
$472$	9.52257	+	6.18403i	0.438312	+	0.284643i
$473$	−7.62096	−	19.8533i	−0.350412	−	0.912855i
$474$	29.8984	+	35.3475i	1.37328	+	1.62357i
$475$	−32.2909	+	14.4121i	−1.48161	+	0.661271i
$476$	14.7390	−	8.09539i	0.675560	−	0.371052i
$477$	−20.7278	+	18.3073i	−0.949061	+	0.838234i
$478$	−29.6664	−	1.55475i	−1.35691	−	0.0711126i
$479$	−15.5537	+	3.30604i	−0.710666	+	0.151057i	−0.549041	−	0.835796i	$-0.685007\pi$
$479$	−15.5537	+	3.30604i	−0.710666	+	0.151057i	−0.161625	+	0.986852i	$0.551674\pi$
$480$	36.1561	+	3.00311i	1.65029	+	0.137073i
$481$	−21.4959	−	4.56909i	−0.980127	−	0.208332i
$482$	14.2545	−	14.2545i	0.649277	−	0.649277i
$483$	35.0588	−	7.45433i	1.59523	−	0.339184i
$484$	1.94512	−	2.67723i	0.0884146	−	0.121692i
$485$	−0.000568626	−	1.25014i	−2.58200e−5	−	0.0567659i
$486$	21.9933	−	34.0347i	0.997636	−	1.54384i
$487$	29.1568	−	23.6107i	1.32122	−	1.06990i	0.329143	−	0.944280i	$-0.393240\pi$
$487$	29.1568	−	23.6107i	1.32122	−	1.06990i	0.992078	−	0.125623i	$-0.0400930\pi$
$488$	16.1813	+	6.21141i	0.732492	+	0.281177i
$489$	−15.4679	+	4.50143i	−0.699485	+	0.203562i
$490$	25.2839	−	31.8795i	1.14221	−	1.44017i
$491$	−10.1327	+	13.9464i	−0.457281	+	0.629393i	−0.973942	−	0.226797i	$-0.927175\pi$
$491$	−10.1327	+	13.9464i	−0.457281	+	0.629393i	0.516661	+	0.856190i	$0.327175\pi$
$492$	3.13556	+	13.3414i	0.141362	+	0.601479i
$493$	4.33206	+	1.16077i	0.195106	+	0.0522786i
$494$	56.3490	−	62.5819i	2.53526	−	2.81569i
$495$	21.0421	−	9.13966i	0.945770	−	0.410797i
$496$	−6.47467	+	19.9270i	−0.290721	+	0.894748i
$497$	−8.05319	−	0.594523i	−0.361235	−	0.0266680i
$498$	24.3269	+	13.3595i	1.09011	+	0.598655i
$499$	−4.32051	−	2.49445i	−0.193413	−	0.111667i	0.400167	−	0.916442i	$-0.368952\pi$
$499$	−4.32051	−	2.49445i	−0.193413	−	0.111667i	−0.593579	+	0.804776i	$0.702286\pi$
$500$	19.1294	+	49.6311i	0.855491	+	2.21957i
$501$	0.882299	+	4.89094i	0.0394182	+	0.218511i
$502$	26.7642	−	33.0510i	1.19454	−	1.47514i
$503$	5.94631	−	3.02980i	0.265133	−	0.135092i	−0.316371	−	0.948636i	$-0.602464\pi$
$503$	5.94631	−	3.02980i	0.265133	−	0.135092i	0.581504	+	0.813544i	$0.302464\pi$
$504$	−49.8714	−	27.3835i	−2.22145	−	1.21976i
$505$	−0.231560	−	4.38030i	−0.0103043	−	0.194921i
$506$	14.4567	−	68.0136i	0.642680	−	3.02357i
$507$	−11.3566	−	7.88544i	−0.504364	−	0.350205i
$508$	−2.19914	−	41.9620i	−0.0975709	−	1.86176i
$509$	−6.23076	+	2.77411i	−0.276174	+	0.122960i	−0.540150	−	0.841569i	$-0.681633\pi$
$509$	−6.23076	+	2.77411i	−0.276174	+	0.122960i	0.263976	+	0.964529i	$0.414966\pi$
$510$	5.84301	−	12.1149i	0.258733	−	0.536455i
$511$	11.9783	−	8.31829i	0.529891	−	0.367980i
$512$	44.7477	−	7.08734i	1.97759	−	0.313219i
$513$	−6.17756	−	36.2255i	−0.272746	−	1.59939i
$514$	−6.16658	+	13.8504i	−0.271996	+	0.610913i
$515$	−13.5413	+	23.4789i	−0.596701	+	1.03460i
$516$	3.77577	+	51.1003i	0.166219	+	2.24956i
$517$	3.13517	−	6.15311i	0.137885	−	0.270614i
$518$	22.8289	+	23.8242i	1.00304	+	1.04678i
$519$	−2.71179	−	0.0839958i	−0.119034	−	0.00368701i
$520$	−51.9393	−	51.8920i	−2.27769	−	2.27562i
$521$	−1.40892	−	6.62843i	−0.0617257	−	0.290397i	0.936448	−	0.350807i	$-0.114093\pi$
$521$	−1.40892	−	6.62843i	−0.0617257	−	0.290397i	−0.998174	+	0.0604099i	$0.980759\pi$
$522$	−7.85144	−	24.9749i	−0.343648	−	1.09312i
$523$	−24.1081	−	19.5224i	−1.05417	−	0.853653i	−0.0646337	−	0.997909i	$-0.520588\pi$
$523$	−24.1081	−	19.5224i	−1.05417	−	0.853653i	−0.989540	+	0.144256i	$0.953921\pi$
$524$	−7.61260			−0.332558
$525$	1.17688	−	22.8826i	0.0513631	−	0.998680i
$526$	−11.1138			−0.484586
$527$	2.38565	+	1.93186i	0.103921	+	0.0841533i
$528$	−43.0080	+	32.6755i	−1.87169	+	1.42202i
$529$	−7.93712	−	37.3412i	−0.345092	−	1.62353i
$530$	52.9274	+	8.35820i	2.29902	+	0.363057i
$531$	−4.41994	−	1.74536i	−0.191809	−	0.0757422i
$532$	−86.4573	+	21.2005i	−3.74840	+	0.919157i
$533$	3.45872	−	6.78812i	0.149814	−	0.294026i
$534$	77.6682	−	5.73886i	3.36103	−	0.248345i
$535$	−37.4710	−	7.94690i	−1.62001	−	0.343574i
$536$	16.7836	−	37.6966i	0.724941	−	1.62824i
$537$	−23.9881	−	20.6871i	−1.03516	−	0.892713i
$538$	−54.1215	+	8.57200i	−2.33334	+	0.369565i
$539$	1.48466	+	23.8931i	0.0639488	+	1.02915i
$540$	−54.8988	+	6.45270i	−2.36247	+	0.277680i
$541$	33.6303	−	14.9732i	1.44588	−	0.643747i	0.474280	−	0.880374i	$-0.342709\pi$
$541$	33.6303	−	14.9732i	1.44588	−	0.643747i	0.971601	+	0.236627i	$0.0760419\pi$
$542$	2.77516	+	52.9533i	0.119204	+	2.27454i
$543$	−4.66296	+	6.71559i	−0.200107	+	0.288193i
$544$	−2.60197	+	12.2413i	−0.111559	+	0.524842i
$545$	8.64481	−	13.3251i	0.370303	−	0.570785i
$546$	19.5583	+	50.9412i	0.837017	+	2.18008i
$547$	8.01125	−	4.08194i	0.342536	−	0.174531i	−0.274256	−	0.961657i	$-0.588432\pi$
$547$	8.01125	−	4.08194i	0.342536	−	0.174531i	0.616793	+	0.787126i	$0.288432\pi$
$548$	44.8458	−	55.3800i	1.91572	−	2.36572i
$549$	−7.15356	−	1.20329i	−0.305306	−	0.0513552i
$550$	−39.6237	−	20.1439i	−1.68956	−	0.858938i
$551$	−20.5610	−	11.8709i	−0.875927	−	0.505717i
$552$	−46.7432	+	85.1167i	−1.98952	+	3.62281i
$553$	−15.3000	+	22.4946i	−0.650623	+	0.956566i
$554$	0.293013	−	0.901802i	0.0124489	−	0.0383139i
$555$	18.2550	+	3.46519i	0.774883	+	0.147089i
$556$	48.2515	−	53.5887i	2.04632	−	2.27267i
$557$	29.7850	+	7.98086i	1.26203	+	0.338160i	0.826972	−	0.562243i	$-0.190061\pi$
$557$	29.7850	+	7.98086i	1.26203	+	0.338160i	0.435057	+	0.900403i	$0.356728\pi$
$558$	2.04353	−	17.8025i	0.0865095	−	0.753640i
$559$	16.7423	−	23.0438i	0.708123	−	0.974648i
$560$	10.1121	+	52.9897i	0.427312	+	2.23923i
$561$	2.21121	+	7.59824i	0.0933575	+	0.320798i
$562$	43.7341	+	16.7880i	1.84481	+	0.708157i
$563$	−2.96881	+	2.40409i	−0.125120	+	0.101320i	−0.689838	−	0.723964i	$-0.742318\pi$
$563$	−2.96881	+	2.40409i	−0.125120	+	0.101320i	0.564718	+	0.825284i	$0.308985\pi$
$564$	−11.5115	+	12.0149i	−0.484720	+	0.505918i
$565$	15.4769	+	5.02095i	0.651116	+	0.211233i
$566$	−48.3632	+	66.5663i	−2.03286	+	2.79799i
$567$	22.7322	+	7.08844i	0.954664	+	0.297686i
$568$	15.4698	−	15.4698i	0.649100	−	0.649100i
$569$	−35.3737	−	7.51891i	−1.48294	−	0.315209i	−0.605868	−	0.795565i	$-0.707174\pi$
$569$	−35.3737	−	7.51891i	−1.48294	−	0.315209i	−0.877074	+	0.480356i	$0.840508\pi$
$570$	−46.4762	+	53.9420i	−1.94667	+	2.25938i
$571$	20.4327	−	4.34310i	0.855081	−	0.181753i	0.240541	−	0.970639i	$-0.422675\pi$
$571$	20.4327	−	4.34310i	0.855081	−	0.181753i	0.614540	+	0.788886i	$0.289342\pi$
$572$	74.4248	+	3.90044i	3.11186	+	0.163086i
$573$	−11.1889	+	20.3744i	−0.467424	+	0.851151i
$574$	−10.0261	+	5.50683i	−0.418480	+	0.229851i
$575$	−39.0556	−	2.01119i	−1.62873	−	0.0838725i
$576$	17.1863	−	6.40920i	0.716096	−	0.267050i
$577$	−1.80058	−	4.69066i	−0.0749589	−	0.195275i	0.890981	−	0.454040i	$-0.150018\pi$
$577$	−1.80058	−	4.69066i	−0.0749589	−	0.195275i	−0.965940	+	0.258765i	$0.916684\pi$
$578$	−33.1712	−	21.5416i	−1.37974	−	0.896013i
$579$	4.82826	+	11.8160i	0.200656	+	0.491057i
$580$	−19.4366	+	29.9596i	−0.807063	+	1.24401i
$581$	−3.73025	+	15.8764i	−0.154757	+	0.658663i
$582$	−1.07282	−	2.27719i	−0.0444698	−	0.0943925i
$583$	−26.4396	+	17.1701i	−1.09502	+	0.711112i
$584$	−4.12995	+	39.2939i	−0.170899	+	1.62599i
$585$	25.6170	+	16.9698i	1.05913	+	0.701615i
$586$	6.15652	+	58.5754i	0.254324	+	2.41973i
$587$	1.14627	−	0.181552i	0.0473117	−	0.00749343i	−0.132734	−	0.991152i	$-0.542376\pi$
$587$	1.14627	−	0.181552i	0.0473117	−	0.00749343i	0.180045	+	0.983658i	$0.442376\pi$
$588$	13.1897	−	56.1529i	0.543932	−	2.31571i
$589$	−9.55182	−	13.1469i	−0.393576	−	0.541711i
$590$	2.84923	+	8.75548i	0.117301	+	0.360458i
$591$	5.03316	−	10.4236i	0.207037	−	0.428770i
$592$	−43.6871	+	2.28954i	−1.79553	+	0.0940996i
$593$	−18.7496	+	5.02395i	−0.769955	+	0.206309i	−0.622352	−	0.782738i	$-0.713823\pi$
$593$	−18.7496	+	5.02395i	−0.769955	+	0.206309i	−0.147604	+	0.989047i	$0.547156\pi$
$594$	30.5016	−	34.6919i	1.25150	−	1.42343i
$595$	7.77884	+	1.39909i	0.318901	+	0.0573571i
$596$	17.7190	+	5.75725i	0.725798	+	0.235826i
$597$	−22.0465	−	9.25579i	−0.902304	−	0.378814i
$598$	86.9479	−	33.3762i	3.55556	−	1.36485i
$599$	9.19934	+	15.9337i	0.375875	+	0.651034i	0.990458	−	0.137818i	$-0.0440090\pi$
$599$	9.19934	+	15.9337i	0.375875	+	0.651034i	−0.614583	+	0.788852i	$0.710676\pi$
$600$	44.8633	+	42.9053i	1.83154	+	1.75160i
$601$	28.1789			1.14944			0.574720	−	0.818350i	$-0.305111\pi$
$601$	28.1789			1.14944			0.574720	+	0.818350i	$0.305111\pi$
$602$	−40.2444	+	14.4713i	−1.64024	+	0.589805i
$603$	−3.75210	+	16.8574i	−0.152797	+	0.686488i
$604$	−81.4237	+	73.3142i	−3.31308	+	2.98311i
$605$	1.50220	−	0.403246i	0.0610732	−	0.0163943i
$606$	−4.17726	−	7.78212i	−0.169690	−	0.316127i
$607$	15.4652	−	4.14388i	0.627712	−	0.168195i	0.0690806	−	0.997611i	$-0.477993\pi$
$607$	15.4652	−	4.14388i	0.627712	−	0.168195i	0.558631	+	0.829416i	$0.311327\pi$
$608$	30.0769	−	59.0292i	1.21978	−	2.39395i
$609$	12.9015	−	8.37950i	0.522794	−	0.339554i
$610$	7.03312	+	12.1689i	0.284763	+	0.492706i
$611$	9.19907	−	0.966862i	0.372155	−	0.0391150i
$612$	0.182451	−	19.0665i	0.00737516	−	0.770718i
$613$	19.9765	+	24.6689i	0.806842	+	0.996367i	0.999885	+	0.0151770i	$0.00483116\pi$
$613$	19.9765	+	24.6689i	0.806842	+	0.996367i	−0.193042	+	0.981190i	$0.561836\pi$
$614$	−0.759260	−	7.22387i	−0.0306412	−	0.291532i
$615$	−2.79829	+	5.80195i	−0.112838	+	0.233957i
$616$	−51.6459	−	39.2329i	−2.08087	−	1.58074i
$617$	−19.9935	−	10.1872i	−0.804909	−	0.410122i	0.00258567	−	0.999997i	$-0.499177\pi$
$617$	−19.9935	−	10.1872i	−0.804909	−	0.410122i	−0.807494	+	0.589875i	$0.799177\pi$
$618$	−4.54223	+	54.3865i	−0.182715	+	2.18774i
$619$	−24.6938	−	22.2344i	−0.992528	−	0.893676i	0.00180381	−	0.999998i	$-0.499426\pi$
$619$	−24.6938	−	22.2344i	−0.992528	−	0.893676i	−0.994332	+	0.106322i	$0.966092\pi$
$620$	−20.4943	+	13.3224i	−0.823073	+	0.535042i
$621$	12.1009	−	38.7982i	0.485594	−	1.55692i
$622$	−49.3866	+	25.1637i	−1.98022	+	1.00897i
$623$	15.4853	+	43.0643i	0.620405	+	1.72533i
$624$	−68.0797	−	24.4755i	−2.72537	−	0.979803i
$625$	−7.68215	+	23.7904i	−0.307286	+	0.951617i
$626$	5.31323	−	3.06759i	0.212359	−	0.122606i
$627$	−0.896225	−	41.8822i	−0.0357918	−	1.67261i
$628$	40.7489	+	2.13556i	1.62606	+	0.0852182i
$629$	−1.98062	+	6.09571i	−0.0789723	+	0.243052i
$630$	−17.4738	−	42.6997i	−0.696173	−	1.70120i
$631$	−12.5999	−	38.7785i	−0.501594	−	1.54375i	−0.806422	−	0.591340i	$-0.798599\pi$
$631$	−12.5999	−	38.7785i	−0.501594	−	1.54375i	0.304828	−	0.952407i	$-0.401401\pi$
$632$	−19.0762	−	71.1935i	−0.758812	−	2.83193i
$633$	−0.857888	−	0.258589i	−0.0340980	−	0.0102780i
$634$	−12.8167	−	1.34709i	−0.509017	−	0.0534998i
$635$	11.6013	−	15.9832i	0.460385	−	0.634272i
$636$	72.9349	−	21.2253i	2.89206	−	0.841637i
$637$	−25.7568	+	19.0977i	−1.02052	+	0.756680i
$638$	−4.66866	−	29.4767i	−0.184834	−	1.16700i
$639$	−5.06013	+	7.63106i	−0.200176	+	0.301880i
$640$	5.50377	+	3.17426i	0.217555	+	0.125474i
$641$	−30.6978	−	3.22647i	−1.21249	−	0.127438i	−0.523384	−	0.852097i	$-0.675331\pi$
$641$	−30.6978	−	3.22647i	−1.21249	−	0.127438i	−0.689108	+	0.724659i	$0.741997\pi$
$642$	−75.0830	+	17.6463i	−2.96329	+	0.696445i
$643$	−10.2754	+	10.2754i	−0.405222	+	0.405222i	−0.880068	−	0.474847i	$-0.842503\pi$
$643$	−10.2754	+	10.2754i	−0.405222	+	0.405222i	0.474847	+	0.880068i	$0.342503\pi$
$644$	−95.8395	−	22.5181i	−3.77661	−	0.887337i
$645$	−13.7267	+	19.7884i	−0.540488	+	0.779167i
$646$	−16.4344	−	18.2522i	−0.646603	−	0.718125i
$647$	7.12612	−	10.9733i	0.280157	−	0.431403i	−0.670379	−	0.742019i	$-0.733868\pi$
$647$	7.12612	−	10.9733i	0.280157	−	0.431403i	0.950536	+	0.310615i	$0.100535\pi$
$648$	−54.7672	+	34.0942i	−2.15146	+	1.33935i
$649$	−4.69140	−	2.70858i	−0.184154	−	0.106321i
$650$	−6.27720	−	59.2054i	−0.246212	−	2.32223i
$651$	10.4001	−	1.64789i	0.407610	−	0.0645861i
$652$	43.7039	+	6.92202i	1.71158	+	0.271087i
$653$	0.848821	−	16.1965i	0.0332169	−	0.633817i	−0.930403	−	0.366539i	$-0.880543\pi$
$653$	0.848821	−	16.1965i	0.0332169	−	0.633817i	0.963620	−	0.267278i	$-0.0861241\pi$
$654$	4.32628	−	31.6890i	0.169171	−	1.23914i
$655$	−2.78167	−	2.25045i	−0.108689	−	0.0879325i
$656$	3.15316	−	14.8344i	0.123110	−	0.579187i
$657$	−1.57104	−	16.4612i	−0.0612921	−	0.642212i
$658$	−12.2371	−	6.56759i	−0.477053	−	0.256031i
$659$	−38.9699	−	28.3133i	−1.51805	−	1.10293i	−0.962443	−	0.271483i	$-0.912486\pi$
$659$	−38.9699	−	28.3133i	−1.51805	−	1.10293i	−0.555607	−	0.831445i	$-0.687514\pi$
$660$	−62.9840	−	1.92221i	−2.45165	−	0.0748219i
$661$	−16.7350	−	7.45092i	−0.650918	−	0.289807i	0.0545907	−	0.998509i	$-0.482615\pi$
$661$	−16.7350	−	7.45092i	−0.650918	−	0.289807i	−0.705508	+	0.708702i	$0.749281\pi$
$662$	3.57425	+	4.41384i	0.138917	+	0.171549i
$663$	−6.92225	+	8.02683i	−0.268838	+	0.311736i
$664$	−25.9711	−	35.7462i	−1.00787	−	1.38722i
$665$	−37.8591	−	17.8120i	−1.46811	−	0.690720i
$666$	36.2304	−	9.33726i	1.40390	−	0.361812i
$667$	−14.3006	−	22.0210i	−0.553721	−	0.852655i
$668$	3.53311	−	13.1858i	0.136700	−	0.510172i
$669$	−42.2140	+	22.6595i	−1.63209	+	0.876067i
$670$	29.8076	−	15.2048i	1.15157	−	0.587413i
$671$	−7.86460	−	2.55536i	−0.303610	−	0.0986488i
$672$	25.2346	+	34.7277i	0.973445	+	1.33965i
$673$	−0.951273	+	6.00610i	−0.0366689	+	0.231518i	−0.999216	−	0.0395972i	$-0.987393\pi$
$673$	−0.951273	+	6.00610i	−0.0366689	+	0.231518i	0.962547	+	0.271115i	$0.0873925\pi$
$674$	−2.74525	+	4.75491i	−0.105743	+	0.183152i
$675$	−21.9677	−	13.8715i	−0.845539	−	0.533914i
$676$	18.9878	+	32.8878i	0.730300	+	1.26492i
$677$	12.4653	+	10.0942i	0.479080	+	0.387951i	0.838220	−	0.545332i	$-0.183597\pi$
$677$	12.4653	+	10.0942i	0.479080	+	0.387951i	−0.359140	+	0.933284i	$0.616930\pi$
$678$	32.5025	−	4.12093i	1.24825	−	0.158263i
$679$	1.12011	−	0.966096i	0.0429858	−	0.0370754i
$680$	−16.6350	+	13.4833i	−0.637924	+	0.517061i
$681$	14.9070	+	9.23341i	0.571237	+	0.353825i
$682$	5.28701	−	19.7314i	0.202450	−	0.755553i
$683$	−22.6201	+	1.18547i	−0.865534	+	0.0453607i	−0.479933	−	0.877305i	$-0.659339\pi$
$683$	−22.6201	+	1.18547i	−0.865534	+	0.0453607i	−0.385601	+	0.922666i	$0.626006\pi$
$684$	−27.0563	+	97.2439i	−1.03453	+	3.71821i
$685$	32.7584	−	6.97858i	1.25163	−	0.266638i
$686$	48.1037	−	1.96019i	1.83661	−	0.0748405i
$687$	47.1615	+	8.97448i	1.79932	+	0.342398i
$688$	20.3200	−	52.9354i	0.774692	−	2.01814i
$689$	−38.5753	−	17.1748i	−1.46960	−	0.654309i
$690$	−72.8812	+	29.8193i	−2.77454	+	1.13520i
$691$	21.1811	−	9.43042i	0.805766	−	0.358750i	0.0378362	−	0.999284i	$-0.487954\pi$
$691$	21.1811	−	9.43042i	0.805766	−	0.358750i	0.767930	+	0.640534i	$0.221287\pi$
$692$	6.63988	+	3.38319i	0.252410	+	0.128610i
$693$	24.4448	+	11.8015i	0.928580	+	0.448302i
$694$	−11.2122	+	3.64307i	−0.425609	+	0.138289i
$695$	33.4732	−	5.31725i	1.26971	−	0.201695i
$696$	−5.63786	+	41.2961i	−0.213703	+	1.56532i
$697$	−1.86349	−	1.21017i	−0.0705848	−	0.0458383i
$698$	−41.0075	+	50.6400i	−1.55216	+	1.91675i
$699$	6.80481	−	18.9279i	0.257382	−	0.715919i
$700$	−29.7111	+	55.4807i	−1.12298	+	2.09697i
$701$		−	27.6327i		−	1.04367i	−0.853046	−	0.521836i	$-0.825247\pi$
$701$		−	27.6327i		−	1.04367i	0.853046	−	0.521836i	$-0.174753\pi$
$702$	61.2213	+	8.95566i	2.31065	+	0.338010i
$703$	18.4795	−	28.4559i	0.696966	−	1.07323i
$704$	20.4528	−	4.34737i	0.770843	−	0.163848i
$705$	−7.75819	+	0.987233i	−0.292190	+	0.0371813i
$706$	1.28981	+	3.96964i	0.0485428	+	0.149399i
$707$	3.74738	−	3.59083i	0.140935	−	0.135047i
$708$	8.93942	+	9.51091i	0.335964	+	0.357442i
$709$	10.9144	+	24.5141i	0.409898	+	0.920646i	0.994042	+	0.108996i	$0.0347635\pi$
$709$	10.9144	+	24.5141i	0.409898	+	0.920646i	−0.584144	+	0.811650i	$0.698570\pi$
$710$	17.6429	−	1.86246i	0.662126	−	0.0698967i
$711$	13.7407	+	27.6178i	0.515317	+	1.03575i
$712$	−115.752	−	44.4328i	−4.33797	−	1.66519i
$713$	−2.81146	−	17.7508i	−0.105290	−	0.664774i
$714$	15.3721	−	4.11999i	0.575285	−	0.154187i
$715$	26.0420	+	23.4269i	0.973915	+	0.876115i
$716$	35.3885	+	79.4838i	1.32253	+	2.97045i
$717$	−18.9516	−	5.71248i	−0.707760	−	0.213337i
$718$	32.0000	+	8.57438i	1.19423	+	0.319993i
$719$	−7.62338	−	1.62040i	−0.284304	−	0.0604307i	0.0635524	−	0.997979i	$-0.479757\pi$
$719$	−7.62338	−	1.62040i	−0.284304	−	0.0604307i	−0.347856	+	0.937548i	$0.613090\pi$
$720$	58.0005	+	19.4317i	2.16155	+	0.724176i
$721$	−31.5041	+	5.99710i	−1.17327	+	0.223344i
$722$	36.6043	+	71.8399i	1.36227	+	2.67360i
$723$	11.4860	−	6.96327i	0.427169	−	0.258967i
$724$	19.4478	−	11.2282i	0.722773	−	0.417293i
$725$	−15.9589	+	5.20143i	−0.592700	+	0.193176i
$726$	2.39120	−	2.02258i	0.0887459	−	0.0750648i
$727$	10.0679	+	1.59460i	0.373397	+	0.0591403i	0.340313	−	0.940312i	$-0.389467\pi$
$727$	10.0679	+	1.59460i	0.373397	+	0.0591403i	0.0330844	+	0.999453i	$0.489467\pi$
$728$	6.39585	−	86.6358i	0.237046	−	3.21093i
$729$	19.6320	−	18.5360i	0.727111	−	0.686519i
$730$	−22.6450	+	22.6656i	−0.838131	+	0.838893i
$731$	−6.17358	−	5.55872i	−0.228338	−	0.205597i
$732$	16.3664	+	11.3640i	0.604921	+	0.420026i
$733$	−16.5495	+	10.7474i	−0.611271	+	0.396964i	−0.812820	−	0.582514i	$-0.802069\pi$
$733$	−16.5495	+	10.7474i	−0.611271	+	0.396964i	0.201549	+	0.979478i	$0.435402\pi$
$734$	6.61502	+	4.80609i	0.244165	+	0.177396i
$735$	21.4196	−	16.6193i	0.790074	−	0.613012i
$736$	59.2755	−	43.0662i	2.18492	−	1.58744i
$737$	−7.05522	+	18.3795i	−0.259882	+	0.677016i
$738$	−0.124111	+	12.9699i	−0.00456860	+	0.477427i
$739$	−15.4607	+	34.7254i	−0.568732	+	1.27739i	0.368805	+	0.929507i	$0.379767\pi$
$739$	−15.4607	+	34.7254i	−0.568732	+	1.27739i	−0.937537	+	0.347886i	$0.886900\pi$
$740$	−41.3033	−	29.9799i	−1.51834	−	1.10208i
$741$	46.3937	−	31.5597i	1.70431	−	1.15938i
$742$	33.3884	+	53.8966i	1.22573	+	1.97861i
$743$	5.26371	+	5.26371i	0.193107	+	0.193107i	0.797037	−	0.603930i	$-0.206400\pi$
$743$	5.26371	+	5.26371i	0.193107	+	0.193107i	−0.603930	+	0.797037i	$0.706400\pi$
$744$	−15.0221	+	24.2526i	−0.550737	+	0.889144i
$745$	4.77260	+	7.34184i	0.174854	+	0.268984i
$746$	−6.21964	−	29.2611i	−0.227717	−	1.07132i
$747$	13.6234	+	12.5047i	0.498456	+	0.457524i
$748$	3.40027	−	21.4685i	0.124326	−	0.784964i
$749$	−21.8189	−	39.7248i	−0.797244	−	1.45151i
$750$	6.39988	+	49.9309i	0.233691	+	1.82322i
$751$	14.8415	−	25.7062i	0.541574	−	0.938034i	−0.457240	−	0.889344i	$-0.651162\pi$
$751$	14.8415	−	25.7062i	0.541574	−	0.938034i	0.998814	−	0.0486908i	$-0.0155049\pi$
$752$	17.1901	−	6.59868i	0.626860	−	0.240629i
$753$	22.5634	−	17.1426i	0.822255	−	0.624711i
$754$	29.7063	−	26.7477i	1.08184	−	0.974093i
$755$	−51.4258	+	2.71857i	−1.87158	+	0.0989388i
$756$	−48.1867	−	44.2240i	−1.75253	−	1.60841i
$757$	−0.696855	−	0.696855i	−0.0253276	−	0.0253276i	0.694330	−	0.719657i	$-0.255701\pi$
$757$	−0.696855	−	0.696855i	−0.0253276	−	0.0253276i	−0.719657	+	0.694330i	$0.755701\pi$
$758$	−10.9577	−	16.8733i	−0.398001	−	0.612868i
$759$	20.1453	−	41.7207i	0.731229	−	1.51436i
$760$	103.535	−	46.1530i	3.75559	−	1.67415i
$761$	47.0438	−	4.94450i	1.70534	−	0.179238i	0.798866	−	0.601509i	$-0.205433\pi$
$761$	47.0438	−	4.94450i	1.70534	−	0.179238i	0.906470	+	0.422271i	$0.138767\pi$
$762$	7.43406	−	39.0665i	0.269308	−	1.41523i
$763$	18.6209	−	2.54341i	0.674123	−	0.0920776i
$764$	51.6526	−	37.5278i	1.86873	−	1.35771i
$765$	5.70315	−	6.91302i	0.206198	−	0.249941i
$766$	−1.68444	+	16.0263i	−0.0608611	+	0.579055i
$767$	−0.379742	−	7.24590i	−0.0137117	−	0.261634i
$768$	33.8555	+	2.82753i	1.22166	+	0.102030i
$769$	−15.4954	+	5.03475i	−0.558777	+	0.181558i	−0.574771	−	0.818314i	$-0.694909\pi$
$769$	−15.4954	+	5.03475i	−0.558777	+	0.181558i	0.0159938	+	0.999872i	$0.494909\pi$
$770$	−12.5489	−	51.0751i	−0.452231	−	1.84062i
$771$	−6.18788	+	7.98480i	−0.222851	+	0.287566i
$772$	1.83492	−	35.0123i	0.0660401	−	1.26012i
$773$	18.9736	+	49.4280i	0.682433	+	1.77780i	0.626575	+	0.779361i	$0.284456\pi$
$773$	18.9736	+	49.4280i	0.682433	+	1.77780i	0.0558584	+	0.998439i	$0.482210\pi$
$774$	−8.04400	+	47.8216i	−0.289136	+	1.71891i
$775$	−11.4271	−	1.19053i	−0.410474	−	0.0427650i
$776$			4.00751i			0.143861i
$777$	10.9939	+	19.0392i	0.394404	+	0.683026i
$778$	−14.5093	−	28.4761i	−0.520184	−	1.02092i
$779$	7.87063	+	8.74122i	0.281994	+	0.313187i
$780$	−43.7874	−	72.1540i	−1.56784	−	2.58353i
$781$	−6.98427	+	7.75682i	−0.249917	+	0.277561i
$782$	−7.03025	−	26.2373i	−0.251401	−	0.938242i
$783$	−1.11888	−	17.4078i	−0.0399855	−	0.622103i
$784$	−39.6864	+	49.9922i	−1.41737	+	1.78544i
$785$	14.2585	+	12.8266i	0.508906	+	0.457802i
$786$	−6.99741	−	1.71538i	−0.249589	−	0.0611855i
$787$	−7.46888	+	6.04818i	−0.266237	+	0.215594i	−0.753138	−	0.657863i	$-0.771461\pi$
$787$	−7.46888	+	6.04818i	−0.266237	+	0.215594i	0.486901	+	0.873457i	$0.338127\pi$
$788$	−24.7084	+	20.0085i	−0.880200	+	0.712772i
$789$	−7.19217	−	1.76312i	−0.256048	−	0.0627688i
$790$	24.2852	−	54.6122i	0.864028	−	1.94302i
$791$	7.45359	+	17.7506i	0.265019	+	0.631139i
$792$	−67.4669	+	29.2679i	−2.39733	+	1.03999i
$793$	−2.86670	−	10.6987i	−0.101800	−	0.379921i
$794$	54.3569	−	60.3694i	1.92905	−	2.14243i
$795$	32.9253	+	13.8054i	1.16774	+	0.489628i
$796$	43.9458	+	48.8067i	1.55762	+	1.72991i
$797$	0.469818	+	0.922070i	0.0166418	+	0.0326614i	0.899178	−	0.437584i	$-0.144166\pi$
$797$	0.469818	+	0.922070i	0.0166418	+	0.0326614i	−0.882536	+	0.470245i	$0.844166\pi$
$798$	−84.2477	+	0.00543315i	−2.98234	+	0.000192332i
$799$		−	2.69772i		−	0.0954386i
$800$	−16.8250	−	43.7118i	−0.594855	−	1.54545i
$801$	51.1724	+	8.60764i	1.80809	+	0.304136i
$802$	32.3255	+	84.2108i	1.14145	+	2.97359i
$803$	0.986552	−	18.8245i	0.0348147	−	0.664304i
$804$	29.0568	−	37.4948i	1.02475	−	1.32234i
$805$	−28.3632	−	36.5605i	−0.999671	−	1.28859i
$806$	26.0217	−	8.45496i	0.916575	−	0.297813i
$807$	−36.3839	−	3.03870i	−1.28077	−	0.106967i
$808$	0.735913	+	14.0421i	0.0258893	+	0.493998i
$809$	0.631687	−	6.01010i	0.0222089	−	0.211304i	−0.977790	−	0.209589i	$-0.932787\pi$
$809$	0.631687	−	6.01010i	0.0222089	−	0.211304i	0.999999	−	0.00171492i	$-0.000545877\pi$
$810$	−51.9164	−	6.43934i	−1.82415	−	0.226255i
$811$	−23.1113	+	16.7914i	−0.811549	+	0.589625i	−0.914279	−	0.405085i	$-0.867242\pi$
$811$	−23.1113	+	16.7914i	−0.811549	+	0.589625i	0.102731	+	0.994709i	$0.467242\pi$
$812$	−41.8665	+	5.71850i	−1.46923	+	0.200680i
$813$	−6.60472	+	34.7083i	−0.231638	+	1.21727i
$814$	42.4171	−	4.45822i	1.48672	−	0.156260i
$815$	13.9232	+	15.4492i	0.487710	+	0.541161i
$816$	−9.17474	+	19.0008i	−0.321180	+	0.665159i
$817$	23.9516	+	36.8823i	0.837961	+	1.29035i
$818$	15.8033	+	15.8033i	0.552550	+	0.552550i
$819$	4.57545	+	36.0687i	0.159879	+	1.26034i
$820$	13.7450	−	11.1408i	0.479996	−	0.389055i
$821$	3.39043	−	3.05276i	0.118327	−	0.106542i	−0.607843	−	0.794057i	$-0.707965\pi$
$821$	3.39043	−	3.05276i	0.118327	−	0.106542i	0.726170	+	0.687515i	$0.241298\pi$
$822$	53.7008	−	40.7993i	1.87303	−	1.42304i
$823$	−38.4981	+	14.7781i	−1.34196	+	0.515131i	−0.920155	−	0.391555i	$-0.871937\pi$
$823$	−38.4981	+	14.7781i	−1.34196	+	0.515131i	−0.421806	+	0.906686i	$0.638604\pi$
$824$	43.4430	−	75.2454i	1.51341	−	2.62130i
$825$	−22.4463	−	19.3218i	−0.781479	−	0.672700i
$826$	−5.64718	+	9.31647i	−0.196491	+	0.324161i
$827$	−1.19492	+	7.54443i	−0.0415515	+	0.262346i	−0.999715	−	0.0238759i	$-0.992399\pi$
$827$	−1.19492	+	7.54443i	−0.0415515	+	0.262346i	0.958163	+	0.286222i	$0.0923993\pi$
$828$	−75.4862	+	82.2395i	−2.62333	+	2.85802i
$829$	−2.07696	−	9.77133i	−0.0721358	−	0.339372i	0.927249	−	0.374446i	$-0.122167\pi$
$829$	−2.07696	−	9.77133i	−0.0721358	−	0.339372i	−0.999385	+	0.0350731i	$0.988834\pi$
$830$	1.85892	−	35.7818i	0.0645242	−	1.24200i
$831$	0.332684	−	0.537105i	0.0115407	−	0.0186320i
$832$	19.8038	+	19.8038i	0.686574	+	0.686574i
$833$	4.75419	+	8.05312i	0.164723	+	0.279024i
$834$	56.4275	−	38.3854i	1.95393	−	1.32918i
$835$	5.18901	−	3.77365i	0.179573	−	0.130592i
$836$	−46.8011	+	105.117i	−1.61865	+	3.63555i
$837$	4.14667	−	11.1965i	0.143330	−	0.387007i
$838$	34.7407	−	90.5027i	1.20010	−	3.12636i
$839$	35.1491	−	25.5373i	1.21348	−	0.881647i	0.217941	−	0.975962i	$-0.430066\pi$
$839$	35.1491	−	25.5373i	1.21348	−	0.881647i	0.995542	+	0.0943149i	$0.0300660\pi$
$840$	−3.80602	+	73.3521i	−0.131320	+	2.53089i
$841$	14.3441	+	10.4216i	0.494624	+	0.359365i
$842$	−19.2456	+	12.4983i	−0.663248	+	0.430718i
$843$	25.6387	+	17.8022i	0.883043	+	0.613140i
$844$	1.82895	+	1.64680i	0.0629552	+	0.0566851i
$845$	−2.78418	+	17.6305i	−0.0957788	+	0.606509i
$846$	−13.2886	+	8.45002i	−0.456870	+	0.290518i
$847$	1.52172	+	1.03502i	0.0522870	+	0.0355638i
$848$	−83.0228	−	13.1495i	−2.85101	−	0.451556i
$849$	−41.8579	+	35.4050i	−1.43656	+	1.21510i
$850$	−17.3642	+	0.0157963i	−0.595589	+	0.000541808i
$851$	32.4970	−	18.7621i	1.11398	−	0.643158i
$852$	21.5064	−	13.0380i	0.736797	−	0.446675i
$853$	3.70577	+	7.27298i	0.126883	+	0.249022i	0.945705	−	0.325025i	$-0.105373\pi$
$853$	3.70577	+	7.27298i	0.126883	+	0.249022i	−0.818822	+	0.574047i	$0.805373\pi$
$854$	−5.47523	+	15.7032i	−0.187359	+	0.537351i
$855$	−38.6339	+	27.5347i	−1.32125	+	0.941668i
$856$	120.107	+	25.5296i	4.10519	+	0.872585i
$857$	32.2040	+	8.62905i	1.10007	+	0.294763i	0.762793	−	0.646643i	$-0.223828\pi$
$857$	32.2040	+	8.62905i	1.10007	+	0.294763i	0.337276	+	0.941406i	$0.390494\pi$
$858$	67.5315	+	20.3557i	2.30549	+	0.694932i
$859$	−10.1209	−	22.7320i	−0.345322	−	0.775607i	−0.999809	−	0.0195333i	$-0.993782\pi$
$859$	−10.1209	−	22.7320i	−0.345322	−	0.775607i	0.654487	−	0.756073i	$-0.272885\pi$
$860$	57.2725	−	33.1011i	1.95298	−	1.12874i
$861$	−7.36186	+	1.97311i	−0.250892	+	0.0672435i
$862$	−5.99669	−	37.8616i	−0.204248	−	1.28957i
$863$	23.4264	+	8.99253i	0.797442	+	0.306109i	0.722761	−	0.691098i	$-0.242873\pi$
$863$	23.4264	+	8.99253i	0.797442	+	0.306109i	0.0746813	+	0.997207i	$0.476206\pi$
$864$	48.3453	−	5.66012i	1.64474	−	0.192561i
$865$	1.42609	+	3.19912i	0.0484884	+	0.108773i
$866$	−6.18868	−	13.9000i	−0.210300	−	0.472341i
$867$	−18.0489	−	19.2027i	−0.612972	−	0.652159i
$868$	−27.7709	−	8.07986i	−0.942606	−	0.274248i
$869$	10.8665	+	33.4436i	0.368620	+	1.13449i
$870$	−24.6169	+	23.1588i	−0.834590	+	0.785157i
$871$	−25.7930	+	5.48246i	−0.873961	+	0.185766i
$872$	−27.7317	+	42.7031i	−0.939114	+	1.44611i
$873$	−0.333003	−	1.64385i	−0.0112704	−	0.0556358i
$874$			143.793i			4.86386i
$875$	−27.2579	+	11.4895i	−0.921484	+	0.388417i
$876$	−15.3661	+	42.7415i	−0.519172	+	1.44410i
$877$	19.0908	−	23.5751i	0.644649	−	0.796076i	−0.345149	−	0.938548i	$-0.612172\pi$
$877$	19.0908	−	23.5751i	0.644649	−	0.796076i	0.989799	+	0.142472i	$0.0455051\pi$
$878$	−46.8116	−	30.3998i	−1.57982	−	1.02594i
$879$	−5.30842	+	38.8830i	−0.179049	+	1.31149i
$880$	62.1445	+	31.6286i	2.09489	+	1.06620i
$881$	1.42291	−	0.462332i	0.0479391	−	0.0155764i	−0.284949	−	0.958543i	$-0.591977\pi$
$881$	1.42291	−	0.462332i	0.0479391	−	0.0155764i	0.332888	+	0.942966i	$0.391977\pi$
$882$	24.7770	−	48.6430i	0.834284	−	1.63790i
$883$	−23.3136	−	11.8789i	−0.784566	−	0.399756i	0.0153395	−	0.999882i	$-0.495117\pi$
$883$	−23.3136	−	11.8789i	−0.784566	−	0.399756i	−0.799905	+	0.600126i	$0.795117\pi$
$884$	26.5966	−	11.8416i	0.894542	−	0.398276i
$885$	0.454854	+	6.11801i	0.0152897	+	0.205655i
$886$	−44.4532	−	19.7918i	−1.49343	−	0.664919i
$887$	3.91286	−	10.1933i	0.131381	−	0.342259i	−0.852072	−	0.523425i	$-0.824654\pi$
$887$	3.91286	−	10.1933i	0.131381	−	0.342259i	0.983452	+	0.181166i	$0.0579872\pi$
$888$	−58.5143	−	11.1348i	−1.96361	−	0.373660i
$889$	23.2870	−	1.94639i	0.781021	−	0.0652798i
$890$	−50.3109	−	87.0496i	−1.68643	−	2.91791i
$891$	25.2423	−	17.6116i	0.845650	−	0.590010i
$892$	131.418	−	6.88734i	4.40021	−	0.230605i
$893$	−3.69620	+	13.7944i	−0.123689	+	0.461613i
$894$	14.9898	+	9.28468i	0.501333	+	0.310526i
$895$	−10.5661	+	39.5052i	−0.353187	+	1.32051i
$896$	1.40580	+	7.38499i	0.0469645	+	0.246715i
$897$	61.5620	−	7.80534i	2.05550	−	0.260613i
$898$	−24.2361	−	19.6260i	−0.808770	−	0.654929i
$899$	−3.85689	−	6.68033i	−0.128634	−	0.222801i
$900$	38.3468	+	60.1835i	1.27823	+	2.00612i
$901$	−6.15767	+	10.6654i	−0.205142	+	0.355316i
$902$	−2.31301	+	14.6038i	−0.0770147	+	0.486252i
$903$	−28.3394	+	2.98044i	−0.943076	+	0.0991827i
$904$	−49.6061	−	16.1180i	−1.64987	−	0.536077i
$905$	10.4256	+	1.64639i	0.346559	+	0.0547279i
$906$	−91.3639	+	49.0420i	−3.03536	+	1.62931i
$907$	−11.6017	+	43.2982i	−0.385229	+	1.43769i	0.452577	+	0.891725i	$0.350505\pi$
$907$	−11.6017	+	43.2982i	−0.385229	+	1.43769i	−0.837806	+	0.545968i	$0.816162\pi$
$908$	−26.2318	−	40.3934i	−0.870533	−	1.34050i
$909$	−1.46869	−	5.69878i	−0.0487132	−	0.189017i
$910$	48.2197	−	51.3558i	1.59847	−	1.70243i
$911$	−31.8932	−	43.8972i	−1.05667	−	1.45438i	−0.882882	−	0.469595i	$-0.844400\pi$
$911$	−31.8932	−	43.8972i	−1.05667	−	1.45438i	−0.173786	−	0.984783i	$-0.555600\pi$
$912$	72.9471	−	84.5872i	2.41552	−	2.80096i
$913$	13.2664	+	16.3826i	0.439054	+	0.542186i
$914$	−62.1278	−	27.6611i	−2.05500	−	0.914946i
$915$	2.62089	+	8.99072i	0.0866438	+	0.297224i
$916$	−106.680	−	77.5078i	−3.52482	−	2.56093i
$917$	−0.131342	−	4.23153i	−0.00433729	−	0.139737i
$918$	4.46404	−	17.4846i	0.147335	−	0.577078i
$919$	−6.14549	+	28.9123i	−0.202721	+	0.953728i	0.752673	+	0.658394i	$0.228764\pi$
$919$	−6.14549	+	28.9123i	−0.202721	+	0.953728i	−0.955394	+	0.295334i	$0.904569\pi$
$920$	125.196	+	6.50413i	4.12758	+	0.214435i
$921$	0.654667	−	4.79529i	0.0215720	−	0.158010i
$922$	3.84803	−	73.4249i	0.126728	−	2.41812i
$923$	−13.8085	−	2.18705i	−0.454512	−	0.0719876i
$924$	−46.9248	−	57.9397i	−1.54371	−	1.90608i
$925$	−6.22962	−	23.1650i	−0.204829	−	0.761659i
$926$	−79.7574	−	46.0479i	−2.62099	−	1.51323i
$927$	−11.5674	+	34.4749i	−0.379925	+	1.13230i
$928$	17.1275	−	26.3741i	0.562238	−	0.865771i
$929$	−20.9685	−	23.2879i	−0.687955	−	0.764052i	0.293455	−	0.955973i	$-0.405195\pi$
$929$	−20.9685	−	23.2879i	−0.687955	−	0.764052i	−0.981410	+	0.191921i	$0.938528\pi$
$930$	−21.8402	+	7.62775i	−0.716167	+	0.250124i
$931$	−13.2761	−	47.6923i	−0.435108	−	1.56305i
$932$	−39.0658	+	39.0658i	−1.27964	+	1.27964i
$933$	−35.9519	+	8.44958i	−1.17701	+	0.276627i
$934$	−12.6133	−	1.32571i	−0.412720	−	0.0433786i
$935$	7.58902	−	6.83944i	0.248188	−	0.223674i
$936$	−82.0945	−	54.4366i	−2.68334	−	1.77932i
$937$	−4.50465	−	28.4413i	−0.147161	−	0.929135i	−0.945191	−	0.326518i	$-0.894125\pi$
$937$	−4.50465	−	28.4413i	−0.147161	−	0.929135i	0.798030	−	0.602617i	$-0.205875\pi$
$938$	36.6516	+	14.9738i	1.19672	+	0.488911i
$939$	3.92504	−	1.14225i	0.128089	−	0.0372759i
$940$	20.4331	+	6.62884i	0.666454	+	0.216209i
$941$	28.4275	+	2.98785i	0.926711	+	0.0974013i	0.555846	−	0.831285i	$-0.312394\pi$
$941$	28.4275	+	2.98785i	0.926711	+	0.0974013i	0.370865	+	0.928687i	$0.379061\pi$
$942$	36.9747	+	11.1451i	1.20470	+	0.363127i
$943$	3.36687	+	12.5653i	0.109640	+	0.409184i
$944$	−4.46343	−	13.7370i	−0.145272	−	0.447102i
$945$	−4.53397	−	30.4047i	−0.147490	−	0.989064i
$946$	−17.0826	+	52.5749i	−0.555404	+	1.70936i
$947$	−50.3979	−	2.64124i	−1.63771	−	0.0858288i	−0.788899	−	0.614523i	$-0.789349\pi$
$947$	−50.3979	−	2.64124i	−1.63771	−	0.0858288i	−0.848813	+	0.528694i	$0.822682\pi$
$948$	−1.81268	−	84.7094i	−0.0588730	−	2.75123i
$949$	21.8658	−	12.6243i	0.709795	−	0.409801i
$950$	88.8113	+	23.7103i	2.88142	+	0.769265i
$951$	−8.08047	−	2.90503i	−0.262027	−	0.0942019i
$952$	−24.9342	−	4.49634i	−0.808123	−	0.145727i
$953$	38.3479	−	19.5392i	1.24221	−	0.632938i	0.295598	−	0.955312i	$-0.404481\pi$
$953$	38.3479	−	19.5392i	1.24221	−	0.632938i	0.946612	+	0.322375i	$0.104481\pi$
$954$	71.8237	−	3.07528i	2.32538	−	0.0995659i
$955$	29.9681	+	1.55689i	0.969745	+	0.0503799i
$956$	40.4034	+	36.3794i	1.30674	+	1.17659i
$957$	1.65500	−	19.8161i	0.0534984	−	0.640564i
$958$	36.8300	+	18.7658i	1.18992	+	0.606296i
$959$	31.5572	+	23.9725i	1.01903	+	0.774111i
$960$	−17.1062	−	16.3745i	−0.552099	−	0.528484i
$961$	2.68849	+	25.5793i	0.0867254	+	0.825137i
$962$	35.9513	+	44.3961i	1.15912	+	1.43139i
$963$	−51.3884	−	0.491747i	−1.65597	−	0.0158463i
$964$	−36.6916	+	3.85644i	−1.18176	+	0.124208i
$965$	11.0209	−	12.2512i	0.354775	−	0.394379i
$966$	−83.0205	−	42.2943i	−2.67114	−	1.36080i
$967$	4.64829	−	9.12279i	0.149479	−	0.293369i	−0.804110	−	0.594481i	$-0.797358\pi$
$967$	4.64829	−	9.12279i	0.149479	−	0.293369i	0.953589	+	0.301112i	$0.0973577\pi$
$968$	−4.81613	+	1.29048i	−0.154796	+	0.0414775i
$969$	−7.73973	−	14.4189i	−0.248636	−	0.463202i
$970$	−2.04399	+	2.52646i	−0.0656284	+	0.0811198i
$971$	−26.3145	+	23.6937i	−0.844473	+	0.760367i	−0.972869	−	0.231356i	$-0.925684\pi$
$971$	−26.3145	+	23.6937i	−0.844473	+	0.760367i	0.128396	+	0.991723i	$0.459017\pi$
$972$	−70.4799	+	23.0763i	−2.26064	+	0.740174i
$973$	30.6202	+	25.8964i	0.981640	+	0.830201i
$974$	−97.5279			−3.12500
$975$	5.33027	−	39.3098i	0.170705	−	1.25892i
$976$	−11.0244	−	19.0948i	−0.352882	−	0.611209i
$977$	12.0924	−	4.64182i	0.386869	−	0.148505i	−0.157157	−	0.987574i	$-0.550233\pi$
$977$	12.0924	−	4.64182i	0.386869	−	0.148505i	0.544026	+	0.839069i	$0.316899\pi$
$978$	38.6123	+	16.2106i	1.23469	+	0.518359i
$979$	56.2588	+	18.2796i	1.79804	+	0.584219i
$980$	−72.6779	+	16.2211i	−2.32161	+	0.518163i
$981$	7.82691	−	19.8208i	0.249894	−	0.632829i
$982$	43.2853	−	11.5983i	1.38129	−	0.370115i
$983$	−49.3885	+	2.58834i	−1.57525	+	0.0825553i	−0.819799	−	0.572651i	$-0.805915\pi$
$983$	−49.3885	+	2.58834i	−1.57525	+	0.0825553i	−0.755450	+	0.655206i	$0.772582\pi$
$984$	8.97879	−	18.5950i	0.286234	−	0.592785i
$985$	−14.9435	+	0.00679705i	−0.476139	+	0.000216572i
$986$	−6.85269	−	9.43192i	−0.218234	−	0.300374i
$987$	−6.87720	−	6.19145i	−0.218904	−	0.197076i
$988$	−152.223	+	24.1097i	−4.84284	+	0.767031i
$989$	5.08385	+	48.3696i	0.161657	+	1.53806i
$990$	−57.4610	−	15.9593i	−1.82623	−	0.507220i
$991$	0.900679	−	8.56939i	0.0286110	−	0.272216i	−0.970859	−	0.239653i	$-0.922966\pi$
$991$	0.900679	−	8.56939i	0.0286110	−	0.272216i	0.999470	−	0.0325629i	$-0.0103669\pi$
$992$	18.0522	−	11.7233i	0.573159	−	0.372214i
$993$	1.61281	+	3.42338i	0.0511810	+	0.108638i
$994$	15.2965	+	14.3755i	0.485174	+	0.455962i
$995$	1.62955	+	30.8255i	0.0516603	+	0.977233i
$996$	−19.2130	−	47.0194i	−0.608788	−	1.48987i
$997$	36.2338	+	23.5305i	1.14753	+	0.745218i	0.971001	−	0.239077i	$-0.0768448\pi$
$997$	36.2338	+	23.5305i	1.14753	+	0.745218i	0.176534	+	0.984295i	$0.443511\pi$
$998$	4.64756	+	12.1073i	0.147116	+	0.383250i
$999$	24.9273	−	0.294818i	0.788665	−	0.00932763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bs.a.2.4	✓	1216
3.2	odd	2	inner	525.2.bs.a.2.73	yes	1216
7.4	even	3	inner	525.2.bs.a.452.73	yes	1216
21.11	odd	6	inner	525.2.bs.a.452.4	yes	1216
25.13	odd	20	inner	525.2.bs.a.338.4	yes	1216
75.38	even	20	inner	525.2.bs.a.338.73	yes	1216
175.88	odd	60	inner	525.2.bs.a.263.73	yes	1216
525.263	even	60	inner	525.2.bs.a.263.4	yes	1216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bs.a.2.4	✓	1216	1.1	even	1	trivial
525.2.bs.a.2.73	yes	1216	3.2	odd	2	inner
525.2.bs.a.263.4	yes	1216	525.263	even	60	inner
525.2.bs.a.263.73	yes	1216	175.88	odd	60	inner
525.2.bs.a.338.4	yes	1216	25.13	odd	20	inner
525.2.bs.a.338.73	yes	1216	75.38	even	20	inner
525.2.bs.a.452.4	yes	1216	21.11	odd	6	inner
525.2.bs.a.452.73	yes	1216	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02020 - 1.63593i) q^{2} +(-1.04782 - 1.37916i) q^{3} +(0.989132 + 4.65350i) q^{4} +(-1.01425 + 1.99281i) q^{5} +(-0.139395 + 4.50033i) q^{6} +(-2.56962 + 0.630106i) q^{7} +(3.25423 - 6.38679i) q^{8} +(-0.804150 + 2.89022i) q^{9} +O(q^{10})\)	\(q+(-2.02020 - 1.63593i) q^{2} +(-1.04782 - 1.37916i) q^{3} +(0.989132 + 4.65350i) q^{4} +(-1.01425 + 1.99281i) q^{5} +(-0.139395 + 4.50033i) q^{6} +(-2.56962 + 0.630106i) q^{7} +(3.25423 - 6.38679i) q^{8} +(-0.804150 + 2.89022i) q^{9} +(5.30908 - 2.36665i) q^{10} +(-1.39099 + 3.12422i) q^{11} +(5.38148 - 6.24020i) q^{12} +(-4.52425 + 0.716571i) q^{13} +(6.22196 + 2.93077i) q^{14} +(3.81115 - 0.689301i) q^{15} +(-8.33019 + 3.70884i) q^{16} +(0.0699189 + 1.33413i) q^{17} +(6.35272 - 4.52328i) q^{18} +(1.47040 - 6.91769i) q^{19} +(-10.2768 - 2.74865i) q^{20} +(3.56152 + 2.88368i) q^{21} +(7.92107 - 4.03599i) q^{22} +(4.92221 - 6.07843i) q^{23} +(-12.2182 + 2.20410i) q^{24} +(-2.94260 - 4.04241i) q^{25} +(10.3122 + 5.95372i) q^{26} +(4.82866 - 1.91937i) q^{27} +(-5.47390 - 11.3345i) q^{28} +(1.03738 - 3.19273i) q^{29} +(-8.82693 - 4.84223i) q^{30} +(1.53752 - 1.70759i) q^{31} +(9.04842 + 2.42452i) q^{32} +(5.76629 - 1.35522i) q^{33} +(2.04129 - 2.80960i) q^{34} +(1.35055 - 5.75986i) q^{35} +(-14.2450 - 0.883307i) q^{36} +(4.47894 + 1.71930i) q^{37} +(-14.2873 + 11.5697i) q^{38} +(5.72886 + 5.48882i) q^{39} +(9.42708 + 12.9629i) q^{40} +(-0.977598 + 1.34555i) q^{41} +(-2.47749 - 11.6520i) q^{42} +(-4.39698 + 4.39698i) q^{43} +(-15.9144 - 3.38272i) q^{44} +(-4.94405 - 4.53391i) q^{45} +(-19.8877 + 4.22726i) q^{46} +(-2.01654 - 0.105683i) q^{47} +(13.8436 + 7.60245i) q^{48} +(6.20593 - 3.23827i) q^{49} +(-0.668432 + 12.9804i) q^{50} +(1.76672 - 1.49436i) q^{51} +(-7.80965 - 20.3448i) q^{52} +(7.73114 + 5.02066i) q^{53} +(-12.8948 - 4.02182i) q^{54} +(-4.81517 - 5.94071i) q^{55} +(-4.33780 + 18.4622i) q^{56} +(-11.0813 + 5.22058i) q^{57} +(-7.31880 + 4.75288i) q^{58} +(-0.165575 + 1.57534i) q^{59} +(6.97739 + 17.0534i) q^{60} +(0.252752 + 2.40477i) q^{61} +(-5.89960 + 0.934404i) q^{62} +(0.245221 - 7.93346i) q^{63} +(-3.59381 - 4.94646i) q^{64} +(3.16072 - 9.74276i) q^{65} +(-13.8661 - 6.69542i) q^{66} +(5.74876 - 0.301280i) q^{67} +(-6.13922 + 1.64500i) q^{68} +(-13.5407 - 0.419413i) q^{69} +(-12.1511 + 9.42667i) q^{70} +(2.90272 + 0.943152i) q^{71} +(15.8423 + 14.5414i) q^{72} +(-5.14589 + 1.97532i) q^{73} +(-6.23570 - 10.8006i) q^{74} +(-2.49180 + 8.29403i) q^{75} +33.6459 q^{76} +(1.60574 - 8.90453i) q^{77} +(-2.59415 - 20.4605i) q^{78} +(7.64132 - 6.88028i) q^{79} +(1.05785 - 20.3622i) q^{80} +(-7.70669 - 4.64833i) q^{81} +(4.17616 - 1.11900i) q^{82} +(2.79845 - 5.49226i) q^{83} +(-9.89639 + 19.4259i) q^{84} +(-2.72959 - 1.21380i) q^{85} +(16.0759 - 1.68965i) q^{86} +(-5.49027 + 1.91470i) q^{87} +(15.4271 + 19.0509i) q^{88} +(-1.80804 - 17.2023i) q^{89} +(2.57083 + 17.2475i) q^{90} +(11.1741 - 4.69207i) q^{91} +(33.1547 + 16.8932i) q^{92} +(-3.96608 - 0.331238i) q^{93} +(3.90093 + 3.51241i) q^{94} +(12.2943 + 9.94648i) q^{95} +(-6.13732 - 15.0196i) q^{96} +(-0.498143 + 0.253817i) q^{97} +(-17.8348 - 3.61050i) q^{98} +(-7.91109 - 6.53260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

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