LMFDB - Embedded newform 525.2.bg.b.16.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			16.19
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.b.361.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.34261 - 1.04299i) q^{2} +(0.669131 - 0.743145i) q^{3} +(3.06170 - 3.40036i) q^{4} +(-1.80799 - 1.31574i) q^{5} +(0.792412 - 2.43879i) q^{6} +(-2.61898 - 0.375455i) q^{7} +(2.04097 - 6.28145i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(2.34261 - 1.04299i) q^{2} +(0.669131 - 0.743145i) q^{3} +(3.06170 - 3.40036i) q^{4} +(-1.80799 - 1.31574i) q^{5} +(0.792412 - 2.43879i) q^{6} +(-2.61898 - 0.375455i) q^{7} +(2.04097 - 6.28145i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-5.60772 - 1.19654i) q^{10} +(-0.599625 + 5.70505i) q^{11} +(-0.478284 - 4.55057i) q^{12} +(3.79450 - 2.75687i) q^{13} +(-6.52682 + 1.85203i) q^{14} +(-2.18757 + 0.463193i) q^{15} +(-0.813773 - 7.74253i) q^{16} +(5.12631 - 1.08963i) q^{17} +(-1.28215 - 2.22075i) q^{18} +(-0.754708 - 0.838188i) q^{19} +(-10.0095 + 2.11940i) q^{20} +(-2.03145 + 1.69505i) q^{21} +(4.54566 + 13.9901i) q^{22} +(4.43301 - 1.97370i) q^{23} +(-3.30235 - 5.71985i) q^{24} +(1.53764 + 4.75769i) q^{25} +(6.01362 - 10.4159i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-9.29520 + 7.75593i) q^{28} +(1.62117 + 4.98944i) q^{29} +(-4.64150 + 3.36670i) q^{30} +(-6.68416 + 1.42076i) q^{31} +(-3.37707 - 5.84925i) q^{32} +(3.83845 + 4.26303i) q^{33} +(10.8724 - 7.89929i) q^{34} +(4.24107 + 4.12472i) q^{35} +(-3.70177 - 2.68949i) q^{36} +(0.410428 + 3.90496i) q^{37} +(-2.64221 - 1.17639i) q^{38} +(0.490266 - 4.66457i) q^{39} +(-11.9548 + 8.67140i) q^{40} +(4.80509 - 3.49110i) q^{41} +(-2.99097 + 6.08963i) q^{42} -1.92816 q^{43} +(17.5634 + 19.5061i) q^{44} +(-1.11955 + 1.93562i) q^{45} +(8.32622 - 9.24721i) q^{46} +(-5.31131 - 1.12895i) q^{47} +(-6.29834 - 4.57602i) q^{48} +(6.71807 + 1.96662i) q^{49} +(8.56434 + 9.54165i) q^{50} +(2.62042 - 4.53869i) q^{51} +(2.24328 - 21.3434i) q^{52} +(4.67689 - 5.19421i) q^{53} +(-2.50826 - 0.533148i) q^{54} +(8.59050 - 9.52571i) q^{55} +(-7.70365 + 15.6847i) q^{56} -1.12789 q^{57} +(9.00171 + 9.99741i) q^{58} +(-2.68562 - 1.19572i) q^{59} +(-5.12265 + 8.85668i) q^{60} +(-9.64675 + 4.29501i) q^{61} +(-14.1765 + 10.2998i) q^{62} +(-0.0996411 + 2.64387i) q^{63} +(-1.41518 - 1.02819i) q^{64} +(-10.4877 - 0.00820591i) q^{65} +(13.4383 + 5.98312i) q^{66} +(-14.8125 + 3.14850i) q^{67} +(11.9901 - 20.7674i) q^{68} +(1.49951 - 4.61503i) q^{69} +(14.2372 + 5.23916i) q^{70} +(-3.32528 - 10.2341i) q^{71} +(-6.46038 - 1.37320i) q^{72} +(-1.60778 + 15.2970i) q^{73} +(5.03432 + 8.71970i) q^{74} +(4.56454 + 2.04083i) q^{75} -5.16083 q^{76} +(3.71240 - 14.7163i) q^{77} +(-3.71662 - 11.4386i) q^{78} +(0.210018 + 0.0446407i) q^{79} +(-8.71589 + 15.0691i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(7.61522 - 13.1900i) q^{82} +(-0.715960 + 2.20350i) q^{83} +(-0.455922 + 12.0974i) q^{84} +(-10.7020 - 4.77486i) q^{85} +(-4.51693 + 2.01107i) q^{86} +(4.79265 + 2.13382i) q^{87} +(34.6122 + 15.4103i) q^{88} +(-2.40937 + 1.07272i) q^{89} +(-0.603823 + 5.70207i) q^{90} +(-10.9728 + 5.79550i) q^{91} +(6.86123 - 21.1167i) q^{92} +(-3.41674 + 5.91797i) q^{93} +(-13.6198 + 2.89498i) q^{94} +(0.261663 + 2.50844i) q^{95} +(-6.60654 - 1.40426i) q^{96} +(1.50803 + 4.64123i) q^{97} +(17.7889 - 2.39990i) q^{98} +5.73648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.34261	−	1.04299i	1.65647	−	0.737509i	0.656612	−	0.754229i	$-0.271989\pi$
$2$	2.34261	−	1.04299i	1.65647	−	0.737509i	0.999860	+	0.0167199i	$0.00532236\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	3.06170	−	3.40036i	1.53085	−	1.70018i
$5$	−1.80799	−	1.31574i	−0.808557	−	0.588418i
$5$	−1.80799	−	1.31574i	−0.808557	−	0.588418i
$6$	0.792412	−	2.43879i	0.323501	−	0.995634i
$7$	−2.61898	−	0.375455i	−0.989880	−	0.141909i
$7$	−2.61898	−	0.375455i	−0.989880	−	0.141909i
$8$	2.04097	−	6.28145i	0.721591	−	2.22083i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−5.60772	−	1.19654i	−1.77332	−	0.378380i
$11$	−0.599625	+	5.70505i	−0.180794	+	1.72014i	0.408958	+	0.912553i	$0.365892\pi$
$11$	−0.599625	+	5.70505i	−0.180794	+	1.72014i	−0.589752	+	0.807585i	$0.700774\pi$
$12$	−0.478284	−	4.55057i	−0.138069	−	1.31364i
$13$	3.79450	−	2.75687i	1.05240	−	0.764617i	0.0797367	−	0.996816i	$-0.474592\pi$
$13$	3.79450	−	2.75687i	1.05240	−	0.764617i	0.972668	+	0.232199i	$0.0745921\pi$
$14$	−6.52682	+	1.85203i	−1.74437	+	0.494977i
$15$	−2.18757	+	0.463193i	−0.564828	+	0.119596i
$16$	−0.813773	−	7.74253i	−0.203443	−	1.93563i
$17$	5.12631	−	1.08963i	1.24331	−	0.264274i	0.461135	−	0.887330i	$-0.347442\pi$
$17$	5.12631	−	1.08963i	1.24331	−	0.264274i	0.782177	+	0.623056i	$0.214109\pi$
$18$	−1.28215	−	2.22075i	−0.302206	−	0.523436i
$19$	−0.754708	−	0.838188i	−0.173142	−	0.192294i	0.650328	−	0.759654i	$-0.274631\pi$
$19$	−0.754708	−	0.838188i	−0.173142	−	0.192294i	−0.823470	+	0.567360i	$0.807965\pi$
$20$	−10.0095	+	2.11940i	−2.23820	+	0.473913i
$21$	−2.03145	+	1.69505i	−0.443300	+	0.369890i
$22$	4.54566	+	13.9901i	0.969137	+	2.98270i
$23$	4.43301	−	1.97370i	0.924346	−	0.411545i	0.111328	−	0.993784i	$-0.464490\pi$
$23$	4.43301	−	1.97370i	0.924346	−	0.411545i	0.813018	+	0.582238i	$0.197823\pi$
$24$	−3.30235	−	5.71985i	−0.674090	−	1.16756i
$25$	1.53764	+	4.75769i	0.307528	+	0.951539i
$26$	6.01362	−	10.4159i	1.17937	−	2.04272i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−9.29520	+	7.75593i	−1.75663	+	1.46573i
$29$	1.62117	+	4.98944i	0.301043	+	0.926515i	0.981124	+	0.193378i	$0.0619445\pi$
$29$	1.62117	+	4.98944i	0.301043	+	0.926515i	−0.680081	+	0.733137i	$0.738056\pi$
$30$	−4.64150	+	3.36670i	−0.847418	+	0.614673i
$31$	−6.68416	+	1.42076i	−1.20051	+	0.255176i	−0.764415	−	0.644724i	$-0.776972\pi$
$31$	−6.68416	+	1.42076i	−1.20051	+	0.255176i	−0.436095	+	0.899901i	$0.643639\pi$
$32$	−3.37707	−	5.84925i	−0.596986	−	1.03401i
$33$	3.83845	+	4.26303i	0.668189	+	0.742099i
$34$	10.8724	−	7.89929i	1.86461	−	1.35472i
$35$	4.24107	+	4.12472i	0.716872	+	0.697204i
$36$	−3.70177	−	2.68949i	−0.616961	−	0.448249i
$37$	0.410428	+	3.90496i	0.0674739	+	0.641971i	0.975035	+	0.222051i	$0.0712752\pi$
$37$	0.410428	+	3.90496i	0.0674739	+	0.641971i	−0.907561	+	0.419920i	$0.862058\pi$
$38$	−2.64221	−	1.17639i	−0.428623	−	0.190835i
$39$	0.490266	−	4.66457i	0.0785053	−	0.746928i
$40$	−11.9548	+	8.67140i	−1.89022	+	1.37107i
$41$	4.80509	−	3.49110i	0.750429	−	0.545218i	−0.145531	−	0.989354i	$-0.546489\pi$
$41$	4.80509	−	3.49110i	0.750429	−	0.545218i	0.895960	+	0.444135i	$0.146489\pi$
$42$	−2.99097	+	6.08963i	−0.461516	+	0.939650i
$43$	−1.92816			−0.294042			−0.147021	−	0.989133i	$-0.546969\pi$
$43$	−1.92816			−0.294042			−0.147021	+	0.989133i	$0.546969\pi$
$44$	17.5634	+	19.5061i	2.64778	+	2.94065i
$45$	−1.11955	+	1.93562i	−0.166892	+	0.288545i
$46$	8.32622	−	9.24721i	1.22763	−	1.36343i
$47$	−5.31131	−	1.12895i	−0.774734	−	0.164675i	−0.196454	−	0.980513i	$-0.562943\pi$
$47$	−5.31131	−	1.12895i	−0.774734	−	0.164675i	−0.578280	+	0.815838i	$0.696276\pi$
$48$	−6.29834	−	4.57602i	−0.909088	−	0.660491i
$49$	6.71807	+	1.96662i	0.959724	+	0.280945i
$50$	8.56434	+	9.54165i	1.21118	+	1.34939i
$51$	2.62042	−	4.53869i	0.366932	−	0.635544i
$52$	2.24328	−	21.3434i	0.311087	−	2.95979i
$53$	4.67689	−	5.19421i	0.642420	−	0.713480i	−0.330711	−	0.943732i	$-0.607288\pi$
$53$	4.67689	−	5.19421i	0.642420	−	0.713480i	0.973131	+	0.230252i	$0.0739551\pi$
$54$	−2.50826	−	0.533148i	−0.341332	−	0.0725523i
$55$	8.59050	−	9.52571i	1.15834	−	1.28445i
$56$	−7.70365	+	15.6847i	−1.02944	+	2.09595i
$57$	−1.12789			−0.149393
$58$	9.00171	+	9.99741i	1.18198	+	1.31272i
$59$	−2.68562	−	1.19572i	−0.349638	−	0.155669i	0.224401	−	0.974497i	$-0.427958\pi$
$59$	−2.68562	−	1.19572i	−0.349638	−	0.155669i	−0.574039	+	0.818828i	$0.694624\pi$
$60$	−5.12265	+	8.85668i	−0.661331	+	1.14339i
$61$	−9.64675	+	4.29501i	−1.23514	+	0.549920i	−0.917289	−	0.398221i	$-0.869628\pi$
$61$	−9.64675	+	4.29501i	−1.23514	+	0.549920i	−0.317851	+	0.948141i	$0.602961\pi$
$62$	−14.1765	+	10.2998i	−1.80042	+	1.30808i
$63$	−0.0996411	+	2.64387i	−0.0125536	+	0.333097i
$64$	−1.41518	−	1.02819i	−0.176897	−	0.128523i
$65$	−10.4877	−	0.00820591i	−1.30084	−	0.00101782i
$66$	13.4383	+	5.98312i	1.65414	+	0.736471i
$67$	−14.8125	+	3.14850i	−1.80964	+	0.384650i	−0.983801	−	0.179263i	$-0.942629\pi$
$67$	−14.8125	+	3.14850i	−1.80964	+	0.384650i	−0.825834	+	0.563913i	$0.809295\pi$
$68$	11.9901	−	20.7674i	1.45401	−	2.51842i
$69$	1.49951	−	4.61503i	0.180520	−	0.555584i
$70$	14.2372	+	5.23916i	1.70167	+	0.626200i
$71$	−3.32528	−	10.2341i	−0.394638	−	1.21457i	−0.929243	−	0.369468i	$-0.879540\pi$
$71$	−3.32528	−	10.2341i	−0.394638	−	1.21457i	0.534606	−	0.845102i	$-0.320460\pi$
$72$	−6.46038	−	1.37320i	−0.761363	−	0.161833i
$73$	−1.60778	+	15.2970i	−0.188176	+	1.79038i	0.339170	+	0.940725i	$0.389854\pi$
$73$	−1.60778	+	15.2970i	−0.188176	+	1.79038i	−0.527346	+	0.849651i	$0.676813\pi$
$74$	5.03432	+	8.71970i	0.585228	+	1.01364i
$75$	4.56454	+	2.04083i	0.527068	+	0.235655i
$76$	−5.16083			−0.591988
$77$	3.71240	−	14.7163i	0.423067	−	1.67707i
$78$	−3.71662	−	11.4386i	−0.420824	−	1.29516i
$79$	0.210018	+	0.0446407i	0.0236289	+	0.00502247i	0.219711	−	0.975565i	$-0.429489\pi$
$79$	0.210018	+	0.0446407i	0.0236289	+	0.00502247i	−0.196082	+	0.980587i	$0.562822\pi$
$80$	−8.71589	+	15.0691i	−0.974466	+	1.68478i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	7.61522	−	13.1900i	0.840961	−	1.45659i
$83$	−0.715960	+	2.20350i	−0.0785868	+	0.241865i	−0.982630	−	0.185576i	$-0.940585\pi$
$83$	−0.715960	+	2.20350i	−0.0785868	+	0.241865i	0.904043	+	0.427441i	$0.140585\pi$
$84$	−0.455922	+	12.0974i	−0.0497451	+	1.31994i
$85$	−10.7020	−	4.77486i	−1.16079	−	0.517907i
$86$	−4.51693	+	2.01107i	−0.487073	+	0.216859i
$87$	4.79265	+	2.13382i	0.513826	+	0.228770i
$88$	34.6122	+	15.4103i	3.68967	+	1.64275i
$89$	−2.40937	+	1.07272i	−0.255393	+	0.113708i	−0.530440	−	0.847722i	$-0.677973\pi$
$89$	−2.40937	+	1.07272i	−0.255393	+	0.113708i	0.275047	+	0.961431i	$0.411307\pi$
$90$	−0.603823	+	5.70207i	−0.0636485	+	0.601051i
$91$	−10.9728	+	5.79550i	−1.15026	+	0.607533i
$92$	6.86123	−	21.1167i	0.715333	−	2.20157i
$93$	−3.41674	+	5.91797i	−0.354300	+	0.613665i
$94$	−13.6198	+	2.89498i	−1.40477	+	0.298594i
$95$	0.261663	+	2.50844i	0.0268461	+	0.257360i
$96$	−6.60654	−	1.40426i	−0.674277	−	0.143322i
$97$	1.50803	+	4.64123i	0.153117	+	0.471245i	0.997965	−	0.0637607i	$-0.0203094\pi$
$97$	1.50803	+	4.64123i	0.153117	+	0.471245i	−0.844848	+	0.535006i	$0.820309\pi$
$98$	17.7889	−	2.39990i	1.79696	−	0.242427i
$99$	5.73648			0.576538
$100$	20.8857	+	9.33809i	2.08857	+	0.933809i
$101$	−4.22003	−	7.30931i	−0.419909	−	0.727304i	0.576021	−	0.817435i	$-0.304605\pi$
$101$	−4.22003	−	7.30931i	−0.419909	−	0.727304i	−0.995930	+	0.0901312i	$0.971271\pi$
$102$	1.40477	−	13.3655i	0.139093	−	1.32338i
$103$	3.25563	+	0.692006i	0.320787	+	0.0681854i	0.365491	−	0.930815i	$-0.380901\pi$
$103$	3.25563	+	0.692006i	0.320787	+	0.0681854i	−0.0447039	+	0.999000i	$0.514234\pi$
$104$	−9.57267	−	29.4616i	−0.938677	−	2.88895i
$105$	5.90309	−	0.391758i	0.576083	−	0.0382316i
$106$	5.53857	−	17.0460i	0.537953	−	1.65565i
$107$	−2.21663	+	3.83931i	−0.214290	+	0.371160i	−0.953053	−	0.302805i	$-0.902077\pi$
$107$	−2.21663	+	3.83931i	−0.214290	+	0.371160i	0.738763	+	0.673965i	$0.235410\pi$
$108$	−4.47565	+	0.951328i	−0.430669	+	0.0915416i
$109$	7.21500	+	3.21233i	0.691072	+	0.307685i	0.722056	−	0.691835i	$-0.243197\pi$
$109$	7.21500	+	3.21233i	0.691072	+	0.307685i	−0.0309839	+	0.999520i	$0.509864\pi$
$110$	10.1889	−	31.2748i	0.971471	−	2.98194i
$111$	3.17658	+	2.30792i	0.301508	+	0.219058i
$112$	−0.775724	+	20.5830i	−0.0732990	+	1.94491i
$113$	−2.23757	+	1.62569i	−0.210493	+	0.152932i	−0.688037	−	0.725676i	$-0.741527\pi$
$113$	−2.23757	+	1.62569i	−0.210493	+	0.152932i	0.477544	+	0.878608i	$0.341527\pi$
$114$	−2.64221	+	1.17639i	−0.247466	+	0.110179i
$115$	−10.6117	−	2.26427i	−0.989547	−	0.211144i
$116$	21.9294	+	9.76360i	2.03609	+	0.906528i
$117$	−3.13840	−	3.48554i	−0.290145	−	0.322239i
$118$	−7.53848			−0.693973
$119$	−13.8348	+	0.929016i	−1.26823	+	0.0851627i
$120$	−1.55523	+	14.6865i	−0.141972	+	1.34068i
$121$	−21.4285	−	4.55476i	−1.94804	−	0.414069i
$122$	−18.1189	+	20.1230i	−1.64040	+	1.82185i
$123$	0.620838	−	5.90688i	0.0559791	−	0.532605i
$124$	−15.6338	+	27.0785i	−1.40395	+	2.43172i
$125$	3.47986	−	10.6250i	0.311249	−	0.950329i
$126$	2.52413	+	6.29748i	0.224867	+	0.561024i
$127$	2.44016	+	1.77288i	0.216529	+	0.157318i	0.690763	−	0.723081i	$-0.257275\pi$
$127$	2.44016	+	1.77288i	0.216529	+	0.157318i	−0.474234	+	0.880399i	$0.657275\pi$
$128$	8.82548	+	1.87591i	0.780069	+	0.165809i
$129$	−1.29019	+	1.43291i	−0.113595	+	0.126160i
$130$	−24.5772	+	10.9194i	−2.15556	+	0.957698i
$131$	6.43269	+	7.14422i	0.562027	+	0.624194i	0.955446	−	0.295165i	$-0.0953747\pi$
$131$	6.43269	+	7.14422i	0.562027	+	0.624194i	−0.393420	+	0.919359i	$0.628708\pi$
$132$	26.2480			2.28460
$133$	1.66186	+	2.47855i	0.144102	+	0.214918i
$134$	−31.4160	+	22.8251i	−2.71393	+	1.97178i
$135$	0.689319	+	2.12717i	0.0593271	+	0.183077i
$136$	3.61817	−	34.4246i	0.310255	−	2.95188i
$137$	6.42259	+	2.85952i	0.548719	+	0.244305i	0.662320	−	0.749221i	$-0.269572\pi$
$137$	6.42259	+	2.85952i	0.548719	+	0.244305i	−0.113601	+	0.993526i	$0.536239\pi$
$138$	−1.30068	−	12.3752i	−0.110722	−	1.05345i
$139$	5.91985	+	4.30102i	0.502115	+	0.364808i	0.809824	−	0.586673i	$-0.199562\pi$
$139$	5.91985	+	4.30102i	0.502115	+	0.364808i	−0.307709	+	0.951480i	$0.599562\pi$
$140$	27.0104	−	1.79254i	2.28280	−	0.151497i
$141$	−4.39293	+	3.19165i	−0.369952	+	0.268786i
$142$	−18.4640	−	20.5063i	−1.54946	−	1.72085i
$143$	13.4528	+	23.3009i	1.12498	+	1.94852i
$144$	−7.61506	+	1.61863i	−0.634588	+	0.134886i
$145$	3.63377	−	11.1539i	0.301768	−	0.926279i
$146$	12.1883	+	37.5117i	1.00871	+	3.10449i
$147$	5.95675	−	3.67657i	0.491304	−	0.303239i
$148$	14.5349	+	10.5602i	1.19476	+	0.868044i
$149$	−0.515278	+	0.892488i	−0.0422132	+	0.0731154i	−0.886360	−	0.462997i	$-0.846774\pi$
$149$	−0.515278	+	0.892488i	−0.0422132	+	0.0731154i	0.844147	+	0.536112i	$0.180108\pi$
$150$	12.8215	+	0.0200638i	1.04687	+	0.00163820i
$151$	−6.87975	−	11.9161i	−0.559866	−	0.969717i	−0.997507	−	0.0705669i	$-0.977519\pi$
$151$	−6.87975	−	11.9161i	−0.559866	−	0.969717i	0.437641	−	0.899150i	$-0.355814\pi$
$152$	−6.80537	+	3.02995i	−0.551989	+	0.245761i
$153$	−1.61951	−	4.98433i	−0.130929	−	0.402959i
$154$	−6.65231	−	38.3464i	−0.536058	−	3.09004i
$155$	13.9542	+	6.22591i	1.12083	+	0.500077i
$156$	−14.3602	−	15.9486i	−1.14973	−	1.27691i
$157$	−2.04167	−	3.53628i	−0.162943	−	0.282226i	0.772980	−	0.634431i	$-0.218765\pi$
$157$	−2.04167	−	3.53628i	−0.162943	−	0.282226i	−0.935923	+	0.352205i	$0.885432\pi$
$158$	0.538549	−	0.114472i	0.0428447	−	0.00910692i
$159$	−0.730602	−	6.95121i	−0.0579405	−	0.551267i
$160$	−1.59041	+	15.0187i	−0.125733	+	1.18733i
$161$	−12.3510	+	3.50468i	−0.973393	+	0.276208i
$162$	−2.07456	+	1.50726i	−0.162993	+	0.118421i
$163$	−0.577024	−	5.49002i	−0.0451960	−	0.430012i	−0.993601	−	0.112949i	$-0.963970\pi$
$163$	−0.577024	−	5.49002i	−0.0451960	−	0.430012i	0.948405	−	0.317062i	$-0.102696\pi$
$164$	2.84073	−	27.0277i	0.221824	−	2.11051i
$165$	−1.33082	−	12.7579i	−0.103604	−	0.993204i
$166$	0.621026	+	5.90867i	0.0482010	+	0.458602i
$167$	1.35100	−	4.15796i	0.104544	−	0.321753i	−0.885079	−	0.465440i	$-0.845896\pi$
$167$	1.35100	−	4.15796i	0.104544	−	0.321753i	0.989623	+	0.143688i	$0.0458960\pi$
$168$	6.50124	+	16.2200i	0.501581	+	1.25140i
$169$	2.78070	−	8.55812i	0.213900	−	0.658317i
$170$	−30.0507	−	0.0235125i	−2.30478	−	0.00180333i
$171$	−0.754708	+	0.838188i	−0.0577140	+	0.0640979i
$172$	−5.90346	+	6.55646i	−0.450135	+	0.499925i
$173$	4.09759	−	1.82436i	0.311534	−	0.138704i	−0.245014	−	0.969520i	$-0.578792\pi$
$173$	4.09759	−	1.82436i	0.311534	−	0.138704i	0.556547	+	0.830816i	$0.312126\pi$
$174$	13.4528			1.01986
$175$	−2.24074	−	13.0376i	−0.169384	−	0.985550i
$176$	44.6595			3.36634
$177$	−2.68562	+	1.19572i	−0.201864	+	0.0898755i
$178$	−4.52537	+	5.02593i	−0.339191	+	0.376709i
$179$	17.3818	−	19.3044i	1.29918	−	1.44288i	0.471299	−	0.881974i	$-0.343785\pi$
$179$	17.3818	−	19.3044i	1.29918	−	1.44288i	0.827878	−	0.560908i	$-0.189548\pi$
$180$	3.15407	+	9.73314i	0.235091	+	0.725466i
$181$	−3.00350	+	9.24381i	−0.223248	+	0.687087i	0.775217	+	0.631696i	$0.217641\pi$
$181$	−3.00350	+	9.24381i	−0.223248	+	0.687087i	−0.998465	+	0.0553915i	$0.982359\pi$
$182$	−19.6602	+	25.0211i	−1.45731	+	1.85469i
$183$	−3.26312	+	10.0429i	−0.241217	+	0.742389i
$184$	−3.35009	−	31.8740i	−0.246972	−	2.34978i
$185$	4.39587	−	7.60014i	0.323191	−	0.558773i
$186$	−1.83166	+	17.4271i	−0.134304	+	1.27782i
$187$	3.14254	+	29.8992i	0.229805	+	2.18645i
$188$	−20.1005	+	14.6038i	−1.46598	+	1.06510i
$189$	1.89811	+	1.84315i	0.138067	+	0.134069i
$190$	3.22926	+	5.60336i	0.234275	+	0.406511i
$191$	2.41904	+	23.0157i	0.175036	+	1.66536i	0.631321	+	0.775522i	$0.282513\pi$
$191$	2.41904	+	23.0157i	0.175036	+	1.66536i	−0.456285	+	0.889834i	$0.650820\pi$
$192$	−1.71103	+	0.363691i	−0.123483	+	0.0262471i
$193$	−10.3542	−	17.9341i	−0.745315	−	1.29092i	−0.950048	−	0.312105i	$-0.898966\pi$
$193$	−10.3542	−	17.9341i	−0.745315	−	1.29092i	0.204733	−	0.978818i	$-0.434367\pi$
$194$	8.37348	+	9.29970i	0.601181	+	0.667679i
$195$	−7.02376	+	7.78842i	−0.502982	+	0.557740i
$196$	27.2559	−	16.8227i	1.94685	−	1.20162i
$197$	−0.538261	−	1.65660i	−0.0383495	−	0.118028i	0.930049	−	0.367435i	$-0.119764\pi$
$197$	−0.538261	−	1.65660i	−0.0383495	−	0.118028i	−0.968399	+	0.249408i	$0.919764\pi$
$198$	13.4383	−	5.98312i	0.955019	−	0.425202i
$199$	−11.3931	−	19.7335i	−0.807638	−	1.39887i	−0.914495	−	0.404596i	$-0.867412\pi$
$199$	−11.3931	−	19.7335i	−0.807638	−	1.39887i	0.106857	−	0.994274i	$-0.465921\pi$
$200$	33.0235	+	0.0516771i	2.33511	+	0.00365412i
$201$	−7.57171	+	13.1146i	−0.534067	+	0.925032i
$202$	−17.5095	−	12.7214i	−1.23196	−	0.895072i
$203$	−2.37248	−	13.6759i	−0.166516	−	0.959859i
$204$	−7.41027	−	22.8065i	−0.518823	−	1.59677i
$205$	−13.2809	−	0.0103914i	−0.927580	−	0.000725766i
$206$	8.34842	−	1.77451i	0.581662	−	0.123636i
$207$	−2.42627	−	4.20241i	−0.168637	−	0.292088i
$208$	−24.4330	−	27.1356i	−1.69412	−	1.88151i
$209$	5.23445	−	3.80305i	0.362075	−	0.263063i
$210$	13.4200	−	7.07463i	0.926069	−	0.488196i
$211$	4.15269	+	3.01710i	0.285883	+	0.207706i	0.721479	−	0.692436i	$-0.243463\pi$
$211$	4.15269	+	3.01710i	0.285883	+	0.207706i	−0.435597	+	0.900142i	$0.643463\pi$
$212$	−3.34297	−	31.8062i	−0.229596	−	2.18446i
$213$	−9.83050	−	4.37682i	−0.673575	−	0.299895i
$214$	−1.18830	+	11.3059i	−0.0812306	+	0.772857i
$215$	3.48610	+	2.53697i	0.237750	+	0.173020i
$216$	−5.34332	+	3.88215i	−0.363567	+	0.264147i
$217$	18.0391	−	1.21134i	1.22457	−	0.0822309i
$218$	20.2523			1.37166
$219$	10.2921	+	11.4305i	0.695473	+	0.772401i
$220$	−6.08935	−	58.3757i	−0.410544	−	3.93569i
$221$	16.4478	−	18.2671i	1.10640	−	1.22878i
$222$	9.84862	+	2.09339i	0.660996	+	0.140499i
$223$	−6.73648	−	4.89434i	−0.451108	−	0.327749i	0.338925	−	0.940813i	$-0.389937\pi$
$223$	−6.73648	−	4.89434i	−0.451108	−	0.327749i	−0.790033	+	0.613064i	$0.789937\pi$
$224$	6.64832	+	16.5870i	0.444210	+	1.10826i
$225$	4.57090	−	2.02653i	0.304727	−	0.135102i
$226$	−3.54616	+	6.14214i	−0.235887	+	0.408569i
$227$	−1.36015	+	12.9409i	−0.0902761	+	0.858919i	0.851878	+	0.523740i	$0.175464\pi$
$227$	−1.36015	+	12.9409i	−0.0902761	+	0.858919i	−0.942154	+	0.335179i	$0.891203\pi$
$228$	−3.45327	+	3.83525i	−0.228698	+	0.253995i
$229$	−9.68366	−	2.05833i	−0.639914	−	0.136018i	−0.123483	−	0.992347i	$-0.539406\pi$
$229$	−9.68366	−	2.05833i	−0.639914	−	0.136018i	−0.516431	+	0.856329i	$0.672740\pi$
$230$	−27.2207	+	5.76367i	−1.79488	+	0.380045i
$231$	−8.45224	−	12.6059i	−0.556116	−	0.829411i
$232$	34.6496			2.27486
$233$	0.454970	+	0.505296i	0.0298061	+	0.0331030i	0.757864	−	0.652413i	$-0.226243\pi$
$233$	0.454970	+	0.505296i	0.0298061	+	0.0331030i	−0.728057	+	0.685516i	$0.759577\pi$
$234$	−10.9874	−	4.89192i	−0.718271	−	0.319795i
$235$	8.11737	+	9.02945i	0.529519	+	0.589016i
$236$	−12.2884	+	5.47116i	−0.799909	+	0.356142i
$237$	0.173704	−	0.126203i	0.0112833	−	0.00819779i
$238$	−31.4405	+	16.6059i	−2.03798	+	1.07640i
$239$	8.45601	+	6.14365i	0.546974	+	0.397400i	0.826669	−	0.562689i	$-0.190233\pi$
$239$	8.45601	+	6.14365i	0.546974	+	0.397400i	−0.279694	+	0.960089i	$0.590233\pi$
$240$	5.36647	+	16.5604i	0.346404	+	1.06897i
$241$	12.3702	+	5.50755i	0.796832	+	0.354773i	0.764434	−	0.644702i	$-0.223019\pi$
$241$	12.3702	+	5.50755i	0.796832	+	0.354773i	0.0323987	+	0.999475i	$0.489685\pi$
$242$	−54.9490	+	11.6798i	−3.53225	+	0.750804i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−14.9309	+	45.9525i	−0.955851	+	2.94181i
$245$	−9.55862	−	12.3949i	−0.610678	−	0.791879i
$246$	−4.70647	−	14.4850i	−0.300073	−	0.923531i
$247$	−5.17451	−	1.09988i	−0.329246	−	0.0699835i
$248$	−4.71770	+	44.8859i	−0.299574	+	2.85026i
$249$	1.15845	+	2.00649i	0.0734136	+	0.127156i
$250$	−2.92987	−	28.5197i	−0.185301	−	1.80374i
$251$	−12.0755			−0.762196			−0.381098	−	0.924535i	$-0.624454\pi$
$251$	−12.0755			−0.762196			−0.381098	+	0.924535i	$0.624454\pi$
$252$	8.68506	+	8.43356i	0.547107	+	0.531265i
$253$	8.60193	+	26.4740i	0.540799	+	1.66441i
$254$	7.56545	+	1.60809i	0.474698	+	0.100900i
$255$	−10.7094	+	4.75811i	−0.670651	+	0.297965i
$256$	26.0532	−	5.53779i	1.62833	−	0.346112i
$257$	1.93903	−	3.35851i	0.120954	−	0.209498i	−0.799190	−	0.601078i	$-0.794738\pi$
$257$	1.93903	−	3.35851i	0.120954	−	0.209498i	0.920144	+	0.391580i	$0.128071\pi$
$258$	−1.52790	+	4.70240i	−0.0951230	+	0.292758i
$259$	0.391238	−	10.3811i	0.0243103	−	0.645049i
$260$	−32.1382	+	35.6370i	−1.99313	+	2.21011i
$261$	4.79265	−	2.13382i	0.296657	−	0.132080i
$262$	22.5206	+	10.0268i	1.39133	+	0.619460i
$263$	0.559072	+	0.248915i	0.0344739	+	0.0153488i	0.423901	−	0.905708i	$-0.360660\pi$
$263$	0.559072	+	0.248915i	0.0344739	+	0.0153488i	−0.389427	+	0.921057i	$0.627327\pi$
$264$	34.6122	−	15.4103i	2.13023	−	0.948441i
$265$	−15.2900	+	3.23749i	−0.939258	+	0.198877i
$266$	6.47820	+	4.07296i	0.397204	+	0.249729i
$267$	−0.814998	+	2.50831i	−0.0498771	+	0.153506i
$268$	−34.6454	+	60.0076i	−2.11631	+	3.66555i
$269$	−21.3120	+	4.53001i	−1.29942	+	0.276200i	−0.805130	−	0.593099i	$-0.797904\pi$
$269$	−21.3120	+	4.53001i	−1.29942	+	0.276200i	−0.494288	+	0.869298i	$0.664571\pi$
$270$	3.83343	+	4.26416i	0.233295	+	0.259508i
$271$	−20.9163	−	4.44589i	−1.27057	−	0.270069i	−0.477194	−	0.878798i	$-0.658346\pi$
$271$	−20.9163	−	4.44589i	−1.27057	−	0.270069i	−0.793378	+	0.608729i	$0.791680\pi$
$272$	−12.6082	−	38.8039i	−0.764482	−	2.35283i
$273$	−3.03533	+	12.0323i	−0.183707	+	0.728229i
$274$	18.0281			1.08912
$275$	−28.0649	+	5.91949i	−1.69238	+	0.356959i
$276$	−11.1017	−	19.2287i	−0.668244	−	1.15743i
$277$	2.32140	−	22.0867i	0.139480	−	1.32706i	−0.671072	−	0.741392i	$-0.734166\pi$
$277$	2.32140	−	22.0867i	0.139480	−	1.32706i	0.810552	−	0.585667i	$-0.199167\pi$
$278$	18.3538	+	3.90122i	1.10079	+	0.233980i
$279$	2.11166	+	6.49903i	0.126422	+	0.389087i
$280$	34.5651	−	18.2217i	2.06566	−	1.08895i
$281$	1.40248	−	4.31638i	0.0836647	−	0.257493i	−0.900469	−	0.434919i	$-0.856777\pi$
$281$	1.40248	−	4.31638i	0.0836647	−	0.257493i	0.984134	+	0.177426i	$0.0567769\pi$
$282$	−6.96203	+	12.0586i	−0.414583	+	0.718079i
$283$	−3.84913	+	0.818157i	−0.228807	+	0.0486344i	−0.320888	−	0.947117i	$-0.603981\pi$
$283$	−3.84913	+	0.818157i	−0.228807	+	0.0486344i	0.0920813	+	0.995751i	$0.470648\pi$
$284$	−44.9808	−	20.0267i	−2.66912	−	1.18837i
$285$	2.03922	+	1.48402i	0.120793	+	0.0879056i
$286$	55.8173	+	40.5536i	3.30055	+	2.39799i
$287$	−13.8952	+	7.33901i	−0.820205	+	0.433208i
$288$	−5.46421	+	3.96998i	−0.321981	+	0.233933i
$289$	9.56147	−	4.25704i	0.562439	−	0.250414i
$290$	−3.12096	−	29.9191i	−0.183269	−	1.75691i
$291$	4.45817	+	1.98490i	0.261343	+	0.116357i
$292$	47.0927	+	52.3018i	2.75589	+	3.06073i
$293$	12.6550			0.739313			0.369656	−	0.929169i	$-0.379475\pi$
$293$	12.6550			0.739313			0.369656	+	0.929169i	$0.379475\pi$
$294$	10.1197	−	14.8256i	0.590190	−	0.864647i
$295$	3.28232	+	5.69543i	0.191104	+	0.331601i
$296$	25.3665	+	5.39181i	1.47440	+	0.313393i
$297$	3.83845	−	4.26303i	0.222730	−	0.247366i
$298$	−0.276233	+	2.62818i	−0.0160017	+	0.152246i
$299$	11.3798	−	19.7104i	0.658112	−	1.13988i
$300$	20.9148	−	9.27268i	1.20752	−	0.535358i
$301$	5.04982	+	0.723940i	0.291067	+	0.0417272i
$302$	−28.5450	−	20.7391i	−1.64258	−	1.19340i
$303$	−8.25563	−	1.75479i	−0.474274	−	0.100810i
$304$	−5.87554	+	6.52545i	−0.336985	+	0.374260i
$305$	23.0923	+	4.92732i	1.32226	+	0.282137i
$306$	−8.99249	−	9.98718i	−0.514067	−	0.570929i
$307$	−15.9584			−0.910793			−0.455397	−	0.890289i	$-0.650503\pi$
$307$	−15.9584			−0.910793			−0.455397	+	0.890289i	$0.650503\pi$
$308$	−38.6744	−	57.6803i	−2.20368	−	3.28664i
$309$	2.69270	−	1.95636i	0.153183	−	0.111294i
$310$	39.1829	+	0.0306578i	2.22544	+	0.00174125i
$311$	3.03784	−	28.9031i	0.172260	−	1.63895i	−0.477374	−	0.878700i	$-0.658411\pi$
$311$	3.03784	−	28.9031i	0.172260	−	1.63895i	0.649635	−	0.760247i	$-0.274922\pi$
$312$	−28.2996	−	12.5998i	−1.60215	−	0.713324i
$313$	−0.289381	−	2.75328i	−0.0163568	−	0.155625i	0.983295	−	0.182020i	$-0.0582637\pi$
$313$	−0.289381	−	2.75328i	−0.0163568	−	0.155625i	−0.999652	+	0.0263958i	$0.991597\pi$
$314$	−8.47115	−	6.15465i	−0.478055	−	0.347327i
$315$	3.65881	−	4.64899i	0.206151	−	0.261941i
$316$	0.794806	−	0.577461i	0.0447113	−	0.0324847i
$317$	16.2564	+	18.0546i	0.913051	+	1.01405i	0.999841	+	0.0178190i	$0.00567225\pi$
$317$	16.2564	+	18.0546i	0.913051	+	1.01405i	−0.0867905	+	0.996227i	$0.527661\pi$
$318$	−8.96159	−	15.5219i	−0.502541	−	0.870427i
$319$	−29.4371	+	6.25705i	−1.64816	+	0.350327i
$320$	1.20580	+	3.72096i	0.0674060	+	0.208008i
$321$	1.36995	+	4.21628i	0.0764632	+	0.235330i
$322$	−25.2781	+	21.0921i	−1.40869	+	1.17542i
$323$	−4.78218	−	3.47446i	−0.266088	−	0.193324i
$324$	−2.28782	+	3.96262i	−0.127101	+	0.220145i
$325$	18.9509	+	13.8140i	1.05121	+	0.766263i
$326$	−7.07780	−	12.2591i	−0.392003	−	0.678970i
$327$	7.21500	−	3.21233i	0.398990	−	0.177642i
$328$	−12.1221	−	37.3081i	−0.669334	−	2.06000i
$329$	13.4863	+	4.95086i	0.743525	+	0.272950i
$330$	−16.4240	−	28.4988i	−0.904114	−	1.56880i
$331$	−13.3530	−	14.8300i	−0.733947	−	0.815130i	0.254440	−	0.967088i	$-0.418109\pi$
$331$	−13.3530	−	14.8300i	−0.733947	−	0.815130i	−0.988387	+	0.151958i	$0.951442\pi$
$332$	5.30064	+	9.18097i	0.290910	+	0.503871i
$333$	3.84067	−	0.816359i	0.210467	−	0.0447362i
$334$	−1.17186	−	11.1495i	−0.0641216	−	0.610076i
$335$	30.9234	+	13.7970i	1.68953	+	0.753811i
$336$	14.7771	+	14.3492i	0.806158	+	0.782814i
$337$	−11.1739	+	8.11831i	−0.608681	+	0.442233i	−0.848950	−	0.528474i	$-0.822764\pi$
$337$	−11.1739	+	8.11831i	−0.608681	+	0.442233i	0.240269	+	0.970706i	$0.422764\pi$
$338$	−2.41199	−	22.9486i	−0.131195	−	1.24824i
$339$	−0.289104	+	2.75064i	−0.0157020	+	0.149394i
$340$	−49.0025	+	21.7714i	−2.65753	+	1.18072i
$341$	−4.09753	−	38.9854i	−0.221894	−	2.11118i
$342$	−0.893757	+	2.75070i	−0.0483288	+	0.148741i
$343$	−16.8561	−	7.67286i	−0.910143	−	0.414295i
$344$	−3.93532	+	12.1117i	−0.212178	+	0.653018i
$345$	−8.78330	+	6.37095i	−0.472877	+	0.343000i
$346$	7.69623	−	8.54753i	0.413752	−	0.459518i
$347$	−8.51732	+	9.45944i	−0.457234	+	0.507809i	−0.927041	−	0.374959i	$-0.877657\pi$
$347$	−8.51732	+	9.45944i	−0.457234	+	0.507809i	0.469808	+	0.882769i	$0.344323\pi$
$348$	21.9294	−	9.76360i	1.17554	−	0.523384i
$349$	31.0346			1.66124			0.830621	−	0.556838i	$-0.187986\pi$
$349$	31.0346			1.66124			0.830621	+	0.556838i	$0.187986\pi$
$350$	−18.8473	−	28.2049i	−1.00743	−	1.50761i
$351$	−4.69026			−0.250348
$352$	35.3952	−	15.7590i	1.88657	−	0.839956i
$353$	−0.432677	+	0.480536i	−0.0230291	+	0.0255764i	−0.754549	−	0.656243i	$-0.772144\pi$
$353$	−0.432677	+	0.480536i	−0.0230291	+	0.0255764i	0.731520	+	0.681820i	$0.238811\pi$
$354$	−5.04422	+	5.60218i	−0.268098	+	0.297752i
$355$	−7.45345	+	22.8784i	−0.395588	+	1.21426i
$356$	−3.72913	+	11.4771i	−0.197644	+	0.608285i
$357$	−8.56688	+	10.9029i	−0.453408	+	0.577042i
$358$	20.5843	−	63.3518i	1.08791	−	3.34825i
$359$	1.22444	+	11.6498i	0.0646236	+	0.614853i	0.978125	+	0.208017i	$0.0667011\pi$
$359$	1.22444	+	11.6498i	0.0646236	+	0.614853i	−0.913501	+	0.406835i	$0.866632\pi$
$360$	9.87352	+	10.9829i	0.520380	+	0.578851i
$361$	1.85307	−	17.6307i	0.0975298	−	0.927934i
$362$	2.60524	+	24.7872i	0.136929	+	1.30279i
$363$	−17.7233	+	12.8767i	−0.930231	+	0.675852i
$364$	−13.8886	+	55.0555i	−0.727959	+	2.88569i
$365$	23.0337	−	25.5413i	1.20564	−	1.33689i
$366$	2.83044	+	26.9299i	0.147950	+	1.40765i
$367$	23.4416	−	4.98267i	1.22364	−	0.260093i	0.449602	−	0.893229i	$-0.351566\pi$
$367$	23.4416	−	4.98267i	1.22364	−	0.260093i	0.774041	+	0.633136i	$0.218233\pi$
$368$	−18.8889	−	32.7166i	−0.984653	−	1.70547i
$369$	−3.97424	−	4.41385i	−0.206891	−	0.229776i
$370$	2.37089	−	22.3890i	0.123257	−	1.16395i
$371$	−14.1989	+	11.8476i	−0.737168	+	0.615094i
$372$	9.66221	+	29.7372i	0.500962	+	1.54180i
$373$	6.47457	−	2.88266i	0.335241	−	0.149259i	−0.232211	−	0.972665i	$-0.574596\pi$
$373$	6.47457	−	2.88266i	0.335241	−	0.149259i	0.567452	+	0.823407i	$0.307929\pi$
$374$	38.5465	+	66.7644i	1.99319	+	3.45231i
$375$	−5.56743	−	9.69555i	−0.287501	−	0.500676i
$376$	−17.9317	+	31.0586i	−0.924755	+	1.60172i
$377$	19.9067	+	14.4631i	1.02525	+	0.744886i
$378$	6.36891	+	2.33804i	0.327581	+	0.120256i
$379$	−6.74583	−	20.7615i	−0.346510	−	1.06645i	−0.960771	−	0.277344i	$-0.910546\pi$
$379$	−6.74583	−	20.7615i	−0.346510	−	1.06645i	0.614261	−	0.789103i	$-0.289454\pi$
$380$	9.33072	+	6.79033i	0.478656	+	0.348336i
$381$	2.95030	−	0.627105i	0.151148	−	0.0321275i
$382$	29.6721	+	51.3936i	1.51816	+	2.62952i
$383$	−12.3595	−	13.7267i	−0.631543	−	0.701399i	0.339419	−	0.940635i	$-0.389770\pi$
$383$	−12.3595	−	13.7267i	−0.631543	−	0.701399i	−0.970961	+	0.239236i	$0.923103\pi$
$384$	7.29947	−	5.30338i	0.372500	−	0.270637i
$385$	−26.0748	+	21.7223i	−1.32889	+	1.10707i
$386$	−42.9610	−	31.2130i	−2.18666	−	1.58870i
$387$	0.201548	+	1.91760i	0.0102453	+	0.0974772i
$388$	20.3990	+	9.08221i	1.03560	+	0.461079i
$389$	3.52574	−	33.5451i	0.178762	−	1.70081i	−0.426262	−	0.904600i	$-0.640170\pi$
$389$	3.52574	−	33.5451i	0.178762	−	1.70081i	0.605024	−	0.796207i	$-0.293163\pi$
$390$	−8.33063	+	25.5709i	−0.421838	+	1.29483i
$391$	20.5744	−	14.9481i	1.04049	−	0.755960i
$392$	26.0646	−	38.1854i	1.31646	−	1.92865i
$393$	9.61350			0.484937
$394$	−2.98876	−	3.31935i	−0.150571	−	0.167226i
$395$	−0.320974	−	0.357039i	−0.0161500	−	0.0179646i
$396$	17.5634	−	19.5061i	0.882592	−	0.980218i
$397$	−16.0050	−	3.40197i	−0.803269	−	0.170740i	−0.212058	−	0.977257i	$-0.568017\pi$
$397$	−16.0050	−	3.40197i	−0.803269	−	0.170740i	−0.591211	+	0.806517i	$0.701350\pi$
$398$	−47.2716	−	34.3448i	−2.36951	−	1.72155i
$399$	2.95393	+	0.423474i	0.147881	+	0.0212002i
$400$	35.5853	−	15.7769i	1.77927	−	0.788846i
$401$	9.65743	−	16.7272i	0.482269	−	0.835314i	−0.517524	−	0.855669i	$-0.673146\pi$
$401$	9.65743	−	16.7272i	0.482269	−	0.835314i	0.999793	+	0.0203543i	$0.00647943\pi$
$402$	−4.05908	+	38.6196i	−0.202449	+	1.92617i
$403$	−21.4462	+	23.8184i	−1.06831	+	1.18648i
$404$	−37.7748	−	8.02928i	−1.87937	−	0.399471i
$405$	2.04204	+	0.911089i	0.101470	+	0.0452724i
$406$	−19.8217	−	29.5627i	−0.983733	−	1.46717i
$407$	−22.5241			−1.11648
$408$	−23.1614	−	25.7233i	−1.14666	−	1.27350i
$409$	−15.1655	−	6.75211i	−0.749885	−	0.333870i	−0.00404189	−	0.999992i	$-0.501287\pi$
$409$	−15.1655	−	6.75211i	−0.749885	−	0.333870i	−0.745843	+	0.666121i	$0.767953\pi$
$410$	−31.1228	+	13.8276i	−1.53705	+	0.682897i
$411$	6.42259	−	2.85952i	0.316803	−	0.141050i
$412$	12.3208	−	8.95161i	0.607004	−	0.441014i
$413$	6.58464	+	4.13988i	0.324009	+	0.203710i
$414$	−10.0669	−	7.31402i	−0.494760	−	0.359464i
$415$	4.19368	−	3.04188i	0.205860	−	0.149320i
$416$	−28.9399	−	12.8849i	−1.41889	−	0.631732i
$417$	7.15743	−	1.52136i	0.350501	−	0.0745013i
$418$	8.29569	−	14.3686i	0.405755	−	0.702789i
$419$	2.24299	−	6.90320i	0.109577	−	0.337243i	−0.881200	−	0.472743i	$-0.843264\pi$
$419$	2.24299	−	6.90320i	0.109577	−	0.337243i	0.990777	+	0.135500i	$0.0432639\pi$
$420$	16.7414	−	21.2721i	0.816896	−	1.03797i
$421$	8.91265	+	27.4303i	0.434376	+	1.33687i	0.893725	+	0.448616i	$0.148083\pi$
$421$	8.91265	+	27.4303i	0.434376	+	1.33687i	−0.459349	+	0.888256i	$0.651917\pi$
$422$	12.8749	+	2.73665i	0.626742	+	0.133218i
$423$	−0.567586	+	5.40022i	−0.0275970	+	0.262568i
$424$	−23.0818	−	39.9789i	−1.12095	−	1.94155i
$425$	13.0666	+	22.7139i	0.633821	+	1.10179i
$426$	−27.5940			−1.33693
$427$	26.8772	−	7.62660i	1.30068	−	0.369077i
$428$	6.26840	+	19.2922i	0.302995	+	0.932522i
$429$	26.3176	+	5.59398i	1.27063	+	0.270080i
$430$	10.8126	+	2.30713i	0.521430	+	0.111260i
$431$	−32.0634	+	6.81528i	−1.54444	+	0.328281i	−0.899833	−	0.436234i	$-0.856312\pi$
$431$	−32.0634	+	6.81528i	−1.54444	+	0.328281i	−0.644606	+	0.764515i	$0.722979\pi$
$432$	−3.89259	+	6.74217i	−0.187282	+	0.324383i
$433$	−4.49497	+	13.8341i	−0.216015	+	0.664825i	0.783065	+	0.621939i	$0.213655\pi$
$433$	−4.49497	+	13.8341i	−0.216015	+	0.664825i	−0.999080	+	0.0428853i	$0.986345\pi$
$434$	40.9950	−	21.6524i	1.96782	−	1.03935i
$435$	−5.85748	−	10.1638i	−0.280845	−	0.487318i
$436$	33.0132	−	14.6984i	1.58105	−	0.703927i
$437$	−4.99996	−	2.22613i	−0.239181	−	0.106490i
$438$	36.0322	+	16.0426i	1.72168	+	0.766543i
$439$	27.4831	−	12.2363i	1.31170	−	0.584004i	0.372706	−	0.927950i	$-0.378430\pi$
$439$	27.4831	−	12.2363i	1.31170	−	0.584004i	0.938990	+	0.343945i	$0.111763\pi$
$440$	−42.3024	−	73.4025i	−2.01669	−	3.49932i
$441$	1.25361	−	6.88683i	0.0596959	−	0.327944i
$442$	19.4782	−	59.9477i	0.926483	−	2.85142i
$443$	2.87932	−	4.98713i	0.136801	−	0.236946i	−0.789483	−	0.613772i	$-0.789651\pi$
$443$	2.87932	−	4.98713i	0.136801	−	0.236946i	0.926284	+	0.376827i	$0.122985\pi$
$444$	17.5735	−	3.73536i	0.834001	−	0.177272i
$445$	5.76755	+	1.23065i	0.273408	+	0.0583383i
$446$	−20.8857	−	4.43939i	−0.988966	−	0.210211i
$447$	0.318459	+	0.980117i	0.0150626	+	0.0463579i
$448$	3.32028	+	3.22413i	0.156868	+	0.152326i
$449$	−6.81024			−0.321395			−0.160698	−	0.987004i	$-0.551374\pi$
$449$	−6.81024			−0.321395			−0.160698	+	0.987004i	$0.551374\pi$
$450$	8.59416	−	9.51480i	0.405133	−	0.448532i
$451$	17.0357	+	29.5066i	0.802178	+	1.38941i
$452$	−1.32284	+	12.5859i	−0.0622210	+	0.591993i
$453$	−13.4588	−	2.86076i	−0.632351	−	0.134410i
$454$	10.3110	+	31.7341i	0.483921	+	1.48936i
$455$	27.4640	+	3.95917i	1.28753	+	0.185609i
$456$	−2.30199	+	7.08481i	−0.107801	+	0.331777i
$457$	15.2180	−	26.3584i	0.711869	−	1.23299i	−0.252286	−	0.967653i	$-0.581182\pi$
$457$	15.2180	−	26.3584i	0.711869	−	1.23299i	0.964155	−	0.265341i	$-0.0854844\pi$
$458$	−24.8318	+	5.27817i	−1.16031	+	0.246632i
$459$	−4.78774	−	2.13164i	−0.223473	−	0.0994964i
$460$	−40.1892	+	29.1511i	−1.87383	+	1.35918i
$461$	−8.46828	−	6.15257i	−0.394407	−	0.286554i	0.372852	−	0.927891i	$-0.378380\pi$
$461$	−8.46828	−	6.15257i	−0.394407	−	0.286554i	−0.767259	+	0.641337i	$0.778380\pi$
$462$	−32.9482	−	20.7151i	−1.53289	−	0.963755i
$463$	30.8990	−	22.4494i	1.43600	−	1.04331i	0.447138	−	0.894465i	$-0.352443\pi$
$463$	30.8990	−	22.4494i	1.43600	−	1.04331i	0.988860	−	0.148848i	$-0.0475566\pi$
$464$	37.3116	−	16.6122i	1.73215	−	0.771202i
$465$	13.9640	−	6.20407i	0.647563	−	0.287707i
$466$	1.59284	+	0.709176i	0.0737867	+	0.0328520i
$467$	18.6623	+	20.7266i	0.863589	+	0.959113i	0.999500	−	0.0316078i	$-0.0100628\pi$
$467$	18.6623	+	20.7266i	0.863589	+	0.959113i	−0.135911	+	0.990721i	$0.543396\pi$
$468$	−21.4609			−0.992032
$469$	39.9757	−	2.68440i	1.84591	−	0.123954i
$470$	28.4335	+	12.6861i	1.31154	+	0.585164i
$471$	−3.99411	−	0.848975i	−0.184039	−	0.0391187i
$472$	−12.9921	+	14.4292i	−0.598010	+	0.664157i
$473$	1.15618	−	11.0003i	0.0531610	−	0.505793i
$474$	0.275290	−	0.476817i	0.0126445	−	0.0219009i
$475$	2.82737	−	4.87950i	0.129729	−	0.223887i
$476$	−39.1990	+	49.8876i	−1.79668	+	2.28660i
$477$	−5.65463	−	4.10833i	−0.258908	−	0.188107i
$478$	26.2169	+	5.57257i	1.19913	+	0.254884i
$479$	−3.54812	+	3.94059i	−0.162118	+	0.180050i	−0.818731	−	0.574178i	$-0.805322\pi$
$479$	−3.54812	+	3.94059i	−0.162118	+	0.180050i	0.656613	+	0.754228i	$0.271989\pi$
$480$	10.0969	+	11.2314i	0.460858	+	0.512641i
$481$	12.3228	+	13.6859i	0.561872	+	0.624022i
$482$	34.7228			1.58158
$483$	−5.65993	+	11.5237i	−0.257536	+	0.524344i
$484$	−81.0953	+	58.9192i	−3.68615	+	2.67814i
$485$	3.38017	−	10.3755i	0.153485	−	0.471125i
$486$	−0.268042	+	2.55025i	−0.0121586	+	0.115682i
$487$	7.46363	+	3.32302i	0.338210	+	0.150581i	0.568812	−	0.822467i	$-0.307403\pi$
$487$	7.46363	+	3.32302i	0.338210	+	0.150581i	−0.230603	+	0.973048i	$0.574070\pi$
$488$	7.29020	+	69.3616i	0.330012	+	3.13985i
$489$	−4.46599	−	3.24473i	−0.201959	−	0.146732i
$490$	−35.3199	−	19.0667i	−1.59559	−	0.861345i
$491$	−7.51748	+	5.46177i	−0.339259	+	0.246486i	−0.744349	−	0.667791i	$-0.767240\pi$
$491$	−7.51748	+	5.46177i	−0.339259	+	0.246486i	0.405090	+	0.914277i	$0.367240\pi$
$492$	−18.1847	−	20.1962i	−0.819830	−	0.910513i
$493$	13.7472	+	23.8109i	0.619145	+	1.07239i
$494$	−13.2690	+	2.82041i	−0.597001	+	0.126896i
$495$	−10.3715	−	7.54773i	−0.466163	−	0.339245i
$496$	16.4397	+	50.5961i	0.738164	+	2.27183i
$497$	4.86635	+	28.0515i	0.218286	+	1.25828i
$498$	4.80654	+	3.49216i	0.215386	+	0.156487i
$499$	−14.6153	+	25.3144i	−0.654270	+	1.13323i	0.327807	+	0.944745i	$0.393691\pi$
$499$	−14.6153	+	25.3144i	−0.654270	+	1.13323i	−0.982076	+	0.188483i	$0.939643\pi$
$500$	−25.4745	−	44.3633i	−1.13926	−	1.98399i
$501$	−2.18597	−	3.78621i	−0.0976619	−	0.169155i
$502$	−28.2880	+	12.5946i	−1.26256	+	0.562127i
$503$	11.1758	+	34.3955i	0.498304	+	1.53362i	0.811744	+	0.584013i	$0.198518\pi$
$503$	11.1758	+	34.3955i	0.498304	+	1.53362i	−0.313440	+	0.949608i	$0.601482\pi$
$504$	16.4040	+	6.02195i	0.730692	+	0.268239i
$505$	−1.98741	+	18.7676i	−0.0884384	+	0.835149i
$506$	47.7632	+	53.0464i	2.12333	+	2.35820i
$507$	−4.49927	−	7.79296i	−0.199820	−	0.346098i
$508$	13.4995	−	2.86940i	0.598943	−	0.127309i
$509$	2.87737	+	27.3764i	0.127537	+	1.21344i	0.851783	+	0.523895i	$0.175522\pi$
$509$	2.87737	+	27.3764i	0.127537	+	1.21344i	−0.724245	+	0.689542i	$0.757812\pi$
$510$	−20.1253	+	22.3163i	−0.891163	+	0.988181i
$511$	9.95406	−	39.4588i	0.440342	−	1.74555i
$512$	40.6576	−	29.5395i	1.79683	−	1.30547i
$513$	0.117897	+	1.12171i	0.00520528	+	0.0495249i
$514$	1.03949	−	9.89006i	0.0458498	−	0.436232i
$515$	−4.97564	−	5.53471i	−0.219253	−	0.243889i
$516$	0.922211	+	8.77425i	0.0405981	+	0.386265i
$517$	9.62553	−	29.6243i	0.423330	−	1.30288i
$518$	−9.91091	−	24.7268i	−0.435460	−	1.08644i
$519$	1.38606	−	4.26584i	0.0608411	−	0.187250i
$520$	−21.4567	+	65.8615i	−0.940937	+	2.88822i
$521$	−25.1248	+	27.9039i	−1.10074	+	1.22249i	−0.127709	+	0.991812i	$0.540762\pi$
$521$	−25.1248	+	27.9039i	−1.10074	+	1.22249i	−0.973029	+	0.230682i	$0.925904\pi$
$522$	9.00171	−	9.99741i	0.393994	−	0.437575i
$523$	14.0161	−	6.24035i	0.612879	−	0.272871i	−0.0767314	−	0.997052i	$-0.524448\pi$
$523$	14.0161	−	6.24035i	0.612879	−	0.272871i	0.689611	+	0.724180i	$0.257782\pi$
$524$	43.9879			1.92162
$525$	−11.1882	−	7.05866i	−0.488292	−	0.308065i
$526$	1.56930			0.0684249
$527$	−32.7170	+	14.5665i	−1.42517	+	0.634528i
$528$	29.8831	−	33.1885i	1.30049	−	1.44434i
$529$	0.366049	−	0.406539i	0.0159152	−	0.0176756i
$530$	−32.4418	+	23.5316i	−1.40918	+	1.02215i
$531$	−0.908442	+	2.79590i	−0.0394230	+	0.121332i
$532$	13.5161	+	1.93766i	0.585997	+	0.0840083i
$533$	8.60841	−	26.4940i	0.372872	−	1.14758i
$534$	0.706932	+	6.72601i	0.0305919	+	0.291063i
$535$	9.05919	−	4.02492i	0.391663	−	0.174012i
$536$	−10.4547	+	99.4700i	−0.451575	+	4.29645i
$537$	−2.71530	−	25.8344i	−0.117174	−	1.11484i
$538$	−45.2009	+	32.8404i	−1.94875	+	1.41585i
$539$	−15.2480	+	37.1477i	−0.656777	+	1.60006i
$540$	9.34362	+	4.16881i	0.402086	+	0.179397i
$541$	2.69578	+	25.6486i	0.115900	+	1.10272i	0.885644	+	0.464365i	$0.153718\pi$
$541$	2.69578	+	25.6486i	0.115900	+	1.10272i	−0.769743	+	0.638354i	$0.779616\pi$
$542$	−53.6356	+	11.4006i	−2.30385	+	0.489698i
$543$	4.85976	+	8.41735i	0.208552	+	0.361223i
$544$	−23.6854	−	26.3053i	−1.01550	−	1.12783i
$545$	−8.81804	−	15.3009i	−0.377723	−	0.655420i
$546$	5.43906	+	31.3528i	0.232770	+	1.34178i
$547$	11.8273	+	36.4005i	0.505697	+	1.55637i	0.799596	+	0.600538i	$0.205047\pi$
$547$	11.8273	+	36.4005i	0.505697	+	1.55637i	−0.293899	+	0.955836i	$0.594953\pi$
$548$	29.3874	−	13.0841i	1.25537	−	0.558927i
$549$	5.27984	+	9.14496i	0.225338	+	0.390297i
$550$	−59.5710	+	43.1386i	−2.54012	+	1.83944i
$551$	2.95858	−	5.12441i	0.126040	−	0.218307i
$552$	−25.9286	−	18.8383i	−1.10360	−	0.801809i
$553$	−0.533271	−	0.195765i	−0.0226770	−	0.00832479i
$554$	−17.5982	−	54.1615i	−0.747674	−	2.30110i
$555$	−2.70659	−	8.35225i	−0.114888	−	0.354533i
$556$	32.7498	−	6.96119i	1.38890	−	0.295220i
$557$	−2.44746	−	4.23913i	−0.103702	−	0.179618i	0.809505	−	0.587113i	$-0.199736\pi$
$557$	−2.44746	−	4.23913i	−0.103702	−	0.179618i	−0.913207	+	0.407495i	$0.866402\pi$
$558$	11.7253	+	13.0222i	0.496369	+	0.551274i
$559$	−7.31642	+	5.31569i	−0.309452	+	0.224830i
$560$	28.4845	−	36.1932i	1.20369	−	1.52944i
$561$	24.3222	+	17.6711i	1.02689	+	0.746076i
$562$	−1.21651	−	11.5743i	−0.0513155	−	0.488234i
$563$	19.9727	+	8.89240i	0.841747	+	0.374770i	0.781874	−	0.623436i	$-0.214264\pi$
$563$	19.9727	+	8.89240i	0.841747	+	0.374770i	0.0598729	+	0.998206i	$0.480930\pi$
$564$	−2.59707	+	24.7094i	−0.109356	+	1.04046i
$565$	6.18450	+	0.00483893i	0.260184	+	0.000203575i
$566$	−8.16365	+	5.93124i	−0.343144	+	0.249309i
$567$	2.63981	−	0.177265i	0.110861	−	0.00744442i
$568$	−71.0721			−2.98212
$569$	−8.74577	−	9.71317i	−0.366642	−	0.407197i	0.531390	−	0.847127i	$-0.321670\pi$
$569$	−8.74577	−	9.71317i	−0.366642	−	0.407197i	−0.898032	+	0.439930i	$0.855003\pi$
$570$	6.32491	+	1.34957i	0.264921	+	0.0565274i
$571$	−24.8064	+	27.5503i	−1.03811	+	1.15294i	−0.0500735	+	0.998746i	$0.515946\pi$
$571$	−24.8064	+	27.5503i	−1.03811	+	1.15294i	−0.988040	+	0.154197i	$0.950721\pi$
$572$	120.420	+	25.5960i	5.03501	+	1.07022i
$573$	18.7226	+	13.6028i	0.782149	+	0.568265i
$574$	−24.8963	+	31.6850i	−1.03915	+	1.32251i
$575$	16.2066	+	18.0560i	0.675864	+	0.752989i
$576$	−0.874628	+	1.51490i	−0.0364428	+	0.0631209i
$577$	−1.38491	+	13.1766i	−0.0576546	+	0.548547i	0.927127	+	0.374748i	$0.122271\pi$
$577$	−1.38491	+	13.1766i	−0.0576546	+	0.548547i	−0.984781	+	0.173799i	$0.944396\pi$
$578$	17.9587	−	19.9451i	0.746982	−	0.829608i
$579$	−20.2560	−	4.30554i	−0.841809	−	0.178932i
$580$	−26.8017	−	46.5059i	−1.11288	−	1.93105i
$581$	2.70240	−	5.50210i	0.112114	−	0.228265i
$582$	12.5140			0.518721
$583$	26.8289	+	29.7965i	1.11114	+	1.23404i
$584$	92.8058	+	41.3198i	3.84033	+	1.70983i
$585$	1.08811	+	10.4311i	0.0449876	+	0.431275i
$586$	29.6457	−	13.1991i	1.22465	−	0.545250i
$587$	2.31513	−	1.68204i	0.0955557	−	0.0694253i	−0.538982	−	0.842318i	$-0.681191\pi$
$587$	2.31513	−	1.68204i	0.0955557	−	0.0694253i	0.634537	+	0.772892i	$0.281191\pi$
$588$	5.73609	−	31.5116i	0.236552	−	1.29952i
$589$	6.23545	+	4.53032i	0.256927	+	0.186669i
$590$	13.6295	+	9.91870i	0.561117	+	0.408346i
$591$	−1.59126	−	0.708474i	−0.0654557	−	0.0291427i
$592$	29.9003	−	6.35550i	1.22889	−	0.261209i
$593$	−15.3880	+	26.6527i	−0.631908	+	1.09450i	0.355254	+	0.934770i	$0.384394\pi$
$593$	−15.3880	+	26.6527i	−0.631908	+	1.09450i	−0.987161	+	0.159726i	$0.948939\pi$
$594$	4.54566	−	13.9901i	0.186511	−	0.574020i
$595$	26.2355	+	16.5234i	1.07555	+	0.677392i
$596$	1.45715	+	4.48466i	0.0596874	+	0.183699i
$597$	−22.2883	−	4.73753i	−0.912201	−	0.193894i
$598$	6.10055	−	58.0428i	0.249470	−	2.37355i
$599$	−13.7342	−	23.7883i	−0.561163	−	0.971963i	−0.997395	−	0.0721291i	$-0.977021\pi$
$599$	−13.7342	−	23.7883i	−0.561163	−	0.971963i	0.436232	−	0.899834i	$-0.356313\pi$
$600$	22.1354	−	24.5067i	0.903675	−	1.00048i
$601$	−14.4776			−0.590554			−0.295277	−	0.955412i	$-0.595412\pi$
$601$	−14.4776			−0.590554			−0.295277	+	0.955412i	$0.595412\pi$
$602$	12.5848	−	3.57103i	0.512918	−	0.145544i
$603$	4.67958	+	14.4023i	0.190567	+	0.586505i
$604$	−61.5827	−	13.0898i	−2.50576	−	0.532617i
$605$	32.7495	+	36.4293i	1.33146	+	1.48106i
$606$	−21.1699	+	4.49981i	−0.859969	+	0.182792i
$607$	2.62875	−	4.55312i	0.106698	−	0.184806i	−0.807733	−	0.589549i	$-0.799306\pi$
$607$	2.62875	−	4.55312i	0.106698	−	0.184806i	0.914430	+	0.404743i	$0.132639\pi$
$608$	−2.35407	+	7.24509i	−0.0954703	+	0.293827i
$609$	−11.7507	−	7.38786i	−0.476161	−	0.299371i
$610$	59.2354	−	12.5424i	2.39837	−	0.507829i
$611$	−23.2661	+	10.3587i	−0.941247	+	0.419070i
$612$	−21.9070	−	9.75361i	−0.885536	−	0.394266i
$613$	−14.8199	−	6.59827i	−0.598572	−	0.266501i	0.0850042	−	0.996381i	$-0.472910\pi$
$613$	−14.8199	−	6.59827i	−0.598572	−	0.266501i	−0.683576	+	0.729879i	$0.739576\pi$
$614$	−37.3842	+	16.6445i	−1.50870	+	0.671718i
$615$	−8.89440	+	9.86270i	−0.358657	+	0.397703i
$616$	−84.8626	−	53.3546i	−3.41921	−	2.14972i
$617$	6.72687	−	20.7032i	0.270813	−	0.833478i	−0.719483	−	0.694510i	$-0.755621\pi$
$617$	6.72687	−	20.7032i	0.270813	−	0.833478i	0.990297	−	0.138968i	$-0.0443786\pi$
$618$	4.26746	−	7.39147i	0.171663	−	0.297328i
$619$	−2.91777	+	0.620190i	−0.117275	+	0.0249276i	−0.266175	−	0.963925i	$-0.585760\pi$
$619$	−2.91777	+	0.620190i	−0.117275	+	0.0249276i	0.148900	+	0.988852i	$0.452427\pi$
$620$	63.8940	−	28.3876i	2.56605	−	1.14007i
$621$	−4.74649	−	1.00890i	−0.190470	−	0.0404857i
$622$	−23.0294	−	70.8771i	−0.923393	−	2.84191i
$623$	6.71285	−	1.90482i	0.268945	−	0.0763151i
$624$	−36.5145			−1.46175
$625$	−20.2713	+	14.6313i	−0.810853	+	0.585250i
$626$	−3.54956	−	6.14802i	−0.141869	−	0.245724i
$627$	0.676313	−	6.43469i	0.0270094	−	0.256977i
$628$	−18.2756	−	3.88460i	−0.729277	−	0.155013i
$629$	6.35894	+	19.5708i	0.253548	+	0.780339i
$630$	3.72227	−	14.7069i	0.148299	−	0.585936i
$631$	−13.7827	+	42.4189i	−0.548681	+	1.68867i	0.163391	+	0.986561i	$0.447757\pi$
$631$	−13.7827	+	42.4189i	−0.548681	+	1.68867i	−0.712072	+	0.702106i	$0.752243\pi$
$632$	0.709048	−	1.22811i	0.0282044	−	0.0488515i
$633$	5.02083	−	1.06721i	0.199560	−	0.0424178i
$634$	56.9132	+	25.3394i	2.26031	+	1.00636i
$635$	−2.07913	−	6.41598i	−0.0825077	−	0.254610i
$636$	−25.8735	−	18.7982i	−1.02595	−	0.745398i
$637$	30.9134	−	11.0585i	1.22483	−	0.438153i
$638$	−62.4334	+	45.3605i	−2.47176	+	1.79584i
$639$	−9.83050	+	4.37682i	−0.388889	+	0.173144i
$640$	−13.4881	−	15.0037i	−0.533165	−	0.593073i
$641$	6.49197	+	2.89041i	0.256417	+	0.114164i	0.530920	−	0.847422i	$-0.321846\pi$
$641$	6.49197	+	2.89041i	0.256417	+	0.114164i	−0.274502	+	0.961586i	$0.588513\pi$
$642$	7.60681	+	8.44822i	0.300217	+	0.333425i
$643$	22.9732			0.905974			0.452987	−	0.891517i	$-0.350358\pi$
$643$	22.9732			0.905974			0.452987	+	0.891517i	$0.350358\pi$
$644$	−25.8978	+	52.7281i	−1.02052	+	2.07778i
$645$	4.21799	−	0.893113i	0.166083	−	0.0351663i
$646$	−14.8266	−	3.15149i	−0.583345	−	0.123994i
$647$	20.2717	−	22.5140i	0.796963	−	0.885117i	−0.198516	−	0.980098i	$-0.563612\pi$
$647$	20.2717	−	22.5140i	0.796963	−	0.885117i	0.995479	+	0.0949804i	$0.0302788\pi$
$648$	−0.690380	+	6.56853i	−0.0271207	+	0.258036i
$649$	8.43199	−	14.6046i	0.330984	−	0.573282i
$650$	58.8024	+	12.5950i	2.30642	+	0.494018i
$651$	11.1703	−	14.2162i	0.437799	−	0.557176i
$652$	−20.4347	−	14.8467i	−0.800286	−	0.581442i
$653$	0.236538	+	0.0502777i	0.00925645	+	0.00196752i	0.212538	−	0.977153i	$-0.431827\pi$
$653$	0.236538	+	0.0502777i	0.00925645	+	0.00196752i	−0.203281	+	0.979120i	$0.565161\pi$
$654$	13.5515	−	15.0504i	0.529904	−	0.588518i
$655$	−2.23026	−	21.3804i	−0.0871436	−	0.835403i
$656$	−30.9402	−	34.3626i	−1.20801	−	1.34163i
$657$	15.3812			0.600079
$658$	36.7568	−	2.46825i	1.43293	−	0.0962223i
$659$	−11.3589	+	8.25275i	−0.442481	+	0.321481i	−0.786620	−	0.617437i	$-0.788171\pi$
$659$	−11.3589	+	8.25275i	−0.442481	+	0.321481i	0.344139	+	0.938919i	$0.388171\pi$
$660$	−47.4561	−	34.5357i	−1.84723	−	1.34430i
$661$	0.205753	−	1.95760i	0.00800285	−	0.0761420i	−0.989792	−	0.142523i	$-0.954479\pi$
$661$	0.205753	−	1.95760i	0.00800285	−	0.0761420i	0.997794	+	0.0663808i	$0.0211452\pi$
$662$	−46.7484	−	20.8137i	−1.81693	−	0.808948i
$663$	−2.56940	−	24.4462i	−0.0997872	−	0.949412i
$664$	12.3799	+	8.99454i	0.480434	+	0.349056i
$665$	0.256517	−	6.66778i	0.00994729	−	0.258565i
$666$	8.14570	−	5.91820i	0.315640	−	0.229326i
$667$	17.0343	+	18.9185i	0.659571	+	0.732528i
$668$	−10.0022	−	17.3243i	−0.386997	−	0.670298i
$669$	−8.14479	+	1.73123i	−0.314896	+	0.0669332i
$670$	86.8316	+	0.0679396i	3.35460	+	0.00262473i
$671$	−18.7188	−	57.6106i	−0.722632	−	2.22403i
$672$	16.7751	+	6.15819i	0.647114	+	0.237557i
$673$	−3.44271	−	2.50127i	−0.132707	−	0.0964170i	0.519452	−	0.854500i	$-0.326136\pi$
$673$	−3.44271	−	2.50127i	−0.132707	−	0.0964170i	−0.652158	+	0.758083i	$0.726136\pi$
$674$	−17.7087	+	30.6723i	−0.682113	+	1.18145i
$675$	1.55252	−	4.75286i	0.0597567	−	0.182938i
$676$	−20.5870	−	35.6578i	−0.791809	−	1.37145i
$677$	−20.4383	+	9.09973i	−0.785509	+	0.349731i	−0.759983	−	0.649943i	$-0.774793\pi$
$677$	−20.4383	+	9.09973i	−0.785509	+	0.349731i	−0.0255258	+	0.999674i	$0.508126\pi$
$678$	2.19165	+	6.74520i	0.0841698	+	0.259048i
$679$	−2.20691	−	12.7215i	−0.0846934	−	0.488205i
$680$	−51.8355	+	57.4786i	−1.98780	+	2.20420i
$681$	8.70687	+	9.66995i	0.333648	+	0.370553i
$682$	−50.2605	−	87.0537i	−1.92457	−	3.33346i
$683$	44.9149	−	9.54695i	1.71862	−	0.365304i	0.759985	−	0.649941i	$-0.225206\pi$
$683$	44.9149	−	9.54695i	1.71862	−	0.365304i	0.958635	+	0.284637i	$0.0918730\pi$
$684$	0.539454	+	5.13256i	0.0206265	+	0.196248i
$685$	−7.84957	−	13.6205i	−0.299917	−	0.520411i
$686$	−47.4899	−	0.393670i	−1.81317	−	0.0150304i
$687$	−8.00927	+	5.81907i	−0.305573	+	0.222012i
$688$	1.56909	+	14.9289i	0.0598209	+	0.569158i
$689$	3.42671	−	32.6030i	0.130547	−	1.24208i
$690$	−13.9309	+	24.0855i	−0.530342	+	0.916921i
$691$	2.35885	+	22.4430i	0.0897349	+	0.853771i	0.943112	+	0.332476i	$0.107884\pi$
$691$	2.35885	+	22.4430i	0.0897349	+	0.853771i	−0.853377	+	0.521295i	$0.825449\pi$
$692$	6.34209	−	19.5189i	0.241090	−	0.741999i
$693$	−15.0237	−	2.15379i	−0.570703	−	0.0818158i
$694$	−10.0866	+	31.0433i	−0.382881	+	1.17839i
$695$	−5.04398	−	15.5652i	−0.191329	−	0.590421i
$696$	23.1851	−	25.7497i	0.878830	−	0.976040i
$697$	20.8283	−	23.1322i	0.788930	−	0.876196i
$698$	72.7017	−	32.3689i	2.75180	−	1.22518i
$699$	0.679942			0.0257178
$700$	−51.1930	−	32.2979i	−1.93492	−	1.22074i
$701$	41.6724			1.57395			0.786973	−	0.616988i	$-0.211647\pi$
$701$	41.6724			1.57395			0.786973	+	0.616988i	$0.211647\pi$
$702$	−10.9874	+	4.89192i	−0.414694	+	0.184634i
$703$	2.96334	−	3.29112i	0.111764	−	0.124127i
$704$	6.71444	−	7.45714i	0.253060	−	0.281052i
$705$	12.1418	+	0.00950007i	0.457285	+	0.000357793i
$706$	−0.512394	+	1.57699i	−0.0192842	+	0.0593507i
$707$	8.30784	+	20.7273i	0.312449	+	0.779532i
$708$	−4.15670	+	12.7930i	−0.156218	+	0.480791i
$709$	−3.67566	−	34.9716i	−0.138042	−	1.31338i	−0.815901	−	0.578192i	$-0.803758\pi$
$709$	−3.67566	−	34.9716i	−0.138042	−	1.31338i	0.677858	−	0.735193i	$-0.262908\pi$
$710$	6.40160	+	61.3690i	0.240248	+	2.30314i
$711$	0.0224433	−	0.213534i	0.000841689	−	0.00800814i
$712$	1.82080	+	17.3238i	0.0682374	+	0.649235i
$713$	−26.8268	+	19.4908i	−1.00467	+	0.729936i
$714$	−8.69718	+	34.4764i	−0.325484	+	1.29025i
$715$	6.33553	−	59.8282i	0.236935	−	2.23745i
$716$	−12.4242	−	118.209i	−0.464316	−	4.41767i
$717$	10.2238	−	2.17314i	0.381815	−	0.0811573i
$718$	15.0191	+	26.0138i	0.560507	+	0.970826i
$719$	14.3634	+	15.9521i	0.535663	+	0.594914i	0.948848	−	0.315733i	$-0.102250\pi$
$719$	14.3634	+	15.9521i	0.535663	+	0.594914i	−0.413185	+	0.910647i	$0.635584\pi$
$720$	15.8976	+	7.09299i	0.592470	+	0.264340i
$721$	−8.26661	−	3.03469i	−0.307864	−	0.113018i
$722$	−14.0478	−	43.2346i	−0.522804	−	1.60903i
$723$	12.3702	−	5.50755i	0.460051	−	0.204828i
$724$	22.2365	+	38.5147i	0.826413	+	1.43139i
$725$	−21.2454	+	15.3850i	−0.789036	+	0.571384i
$726$	−28.0883	+	48.6503i	−1.04245	+	1.80558i
$727$	−2.75578	−	2.00219i	−0.102206	−	0.0742572i	0.535508	−	0.844530i	$-0.320120\pi$
$727$	−2.75578	−	2.00219i	−0.102206	−	0.0742572i	−0.637715	+	0.770273i	$0.720120\pi$
$728$	14.0090	+	80.7534i	0.519210	+	2.99292i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	27.3195	−	83.8573i	1.01114	−	3.10370i
$731$	−9.88437	+	2.10099i	−0.365586	+	0.0777078i
$732$	24.1586	+	41.8440i	0.892929	+	1.54660i
$733$	−7.39967	−	8.21817i	−0.273313	−	0.303545i	0.590825	−	0.806800i	$-0.298802\pi$
$733$	−7.39967	−	8.21817i	−0.273313	−	0.303545i	−0.864138	+	0.503255i	$0.832136\pi$
$734$	49.7176	−	36.1219i	1.83511	−	1.33328i
$735$	−15.6071	−	1.19035i	−0.575678	−	0.0439065i
$736$	−26.5152	−	19.2644i	−0.977364	−	0.710097i
$737$	−9.08038	−	86.3940i	−0.334480	−	3.18237i
$738$	−13.9137	−	6.19478i	−0.512170	−	0.228033i
$739$	1.27369	−	12.1183i	0.0468534	−	0.445780i	−0.945797	−	0.324760i	$-0.894717\pi$
$739$	1.27369	−	12.1183i	0.0468534	−	0.445780i	0.992650	−	0.121021i	$-0.0386168\pi$
$740$	−12.3844	−	38.2169i	−0.455258	−	1.40488i
$741$	−4.27979	+	3.10945i	−0.157222	+	0.114229i
$742$	−20.9054	+	42.5635i	−0.767461	+	1.56255i
$743$	−4.30386			−0.157893			−0.0789467	−	0.996879i	$-0.525156\pi$
$743$	−4.30386			−0.157893			−0.0789467	+	0.996879i	$0.525156\pi$
$744$	30.2000	+	33.5405i	1.10719	+	1.22965i
$745$	2.10590	−	0.935634i	0.0771542	−	0.0342790i
$746$	12.1608	−	13.5059i	0.445237	−	0.494486i
$747$	2.26627	+	0.481710i	0.0829183	+	0.0176248i
$748$	111.290	+	80.8567i	4.06915	+	2.95641i
$749$	7.24679	−	9.22282i	0.264792	−	0.336995i
$750$	−23.1547	−	16.9061i	−0.845490	−	0.617322i
$751$	−1.93279	+	3.34770i	−0.0705286	+	0.122159i	−0.899133	−	0.437675i	$-0.855802\pi$
$751$	−1.93279	+	3.34770i	−0.0705286	+	0.122159i	0.828604	+	0.559834i	$0.189135\pi$
$752$	−4.41876	+	42.0417i	−0.161136	+	1.53310i
$753$	−8.08006	+	8.97382i	−0.294454	+	0.327024i
$754$	61.7185	+	13.1187i	2.24766	+	0.477754i
$755$	−3.23999	+	30.5961i	−0.117915	+	1.11351i
$756$	12.0788	−	0.811100i	0.439302	−	0.0294994i
$757$	−20.7006			−0.752375			−0.376187	−	0.926544i	$-0.622765\pi$
$757$	−20.7006			−0.752375			−0.376187	+	0.926544i	$0.622765\pi$
$758$	−37.4570	−	41.6002i	−1.36050	−	1.51099i
$759$	25.4298	+	11.3221i	0.923045	+	0.410966i
$760$	16.2907	+	3.47601i	0.590925	+	0.126088i
$761$	10.1124	−	4.50235i	0.366576	−	0.163210i	−0.215178	−	0.976575i	$-0.569033\pi$
$761$	10.1124	−	4.50235i	0.366576	−	0.163210i	0.581754	+	0.813365i	$0.302367\pi$
$762$	6.25731	−	4.54620i	0.226678	−	0.164692i
$763$	−17.6898	−	11.1219i	−0.640415	−	0.402640i
$764$	85.6680	+	62.2414i	3.09936	+	2.25182i
$765$	−3.63005	+	11.1425i	−0.131245	+	0.402857i
$766$	−43.2703	−	19.2652i	−1.56342	−	0.696080i
$767$	−13.4870	+	2.86675i	−0.486988	+	0.103512i
$768$	13.3176	−	23.0668i	0.480559	−	0.832352i
$769$	11.9733	−	36.8499i	0.431767	−	1.32884i	−0.464597	−	0.885522i	$-0.653801\pi$
$769$	11.9733	−	36.8499i	0.431767	−	1.32884i	0.896364	−	0.443320i	$-0.146199\pi$
$770$	−38.4267	+	78.0826i	−1.38480	+	2.81390i
$771$	−1.19839	−	3.68826i	−0.0431589	−	0.132830i
$772$	−92.6839	−	19.7006i	−3.33577	−	0.709039i
$773$	−1.26767	+	12.0611i	−0.0455949	+	0.433807i	0.947783	+	0.318915i	$0.103319\pi$
$773$	−1.26767	+	12.0611i	−0.0455949	+	0.433807i	−0.993378	+	0.114891i	$0.963348\pi$
$774$	2.47220	+	4.28197i	0.0888613	+	0.153912i
$775$	−17.0374	−	29.6166i	−0.612001	−	1.06386i
$776$	32.2315			1.15704
$777$	−7.45286	−	7.23705i	−0.267370	−	0.259628i
$778$	−26.7280	−	82.2604i	−0.958246	−	2.94918i
$779$	−6.55264	−	1.39281i	−0.234773	−	0.0499025i
$780$	4.97878	+	47.7291i	0.178269	+	1.70898i
$781$	60.3803	−	12.8342i	2.16058	−	0.459245i
$782$	32.6068	−	56.4766i	1.16602	−	2.01960i
$783$	1.62117	−	4.98944i	0.0579357	−	0.178308i
$784$	9.75962	−	53.6152i	0.348558	−	1.91483i
$785$	−0.961516	+	9.07987i	−0.0343180	+	0.324074i
$786$	22.5206	−	10.0268i	0.803285	−	0.357645i
$787$	−17.2152	−	7.66469i	−0.613654	−	0.273217i	0.0762823	−	0.997086i	$-0.475695\pi$
$787$	−17.2152	−	7.66469i	−0.613654	−	0.273217i	−0.689937	+	0.723870i	$0.742362\pi$
$788$	−7.28102	−	3.24172i	−0.259376	−	0.115482i
$789$	0.559072	−	0.248915i	0.0199035	−	0.00886161i
$790$	−1.12431	−	0.501628i	−0.0400010	−	0.0178471i
$791$	6.47053	−	3.41754i	0.230065	−	0.121514i
$792$	11.7080	−	36.0334i	0.416024	−	1.28039i
$793$	−24.7638	+	42.8922i	−0.879390	+	1.52315i
$794$	−41.0417	+	8.72368i	−1.45651	+	0.309592i
$795$	−7.82509	+	13.5290i	−0.277527	+	0.479824i
$796$	−101.983	−	21.6772i	−3.61471	−	0.768329i
$797$	12.1320	+	37.3383i	0.429736	+	1.32259i	0.898386	+	0.439207i	$0.144740\pi$
$797$	12.1320	+	37.3383i	0.429736	+	1.32259i	−0.468650	+	0.883384i	$0.655260\pi$
$798$	7.36156	−	2.08890i	0.260597	−	0.0739462i
$799$	−28.4575			−1.00676
$800$	22.6362	−	25.0611i	0.800311	−	0.886043i
$801$	1.31869	+	2.28405i	0.0465938	+	0.0807028i
$802$	5.17720	−	49.2578i	0.182813	−	1.73935i
$803$	−86.3060	−	18.3449i	−3.04567	−	0.647378i
$804$	21.4120	+	65.8995i	0.755144	+	2.32410i
$805$	26.9417	+	9.91428i	0.949569	+	0.349433i
$806$	−25.3975	+	78.1654i	−0.894588	+	2.75326i
$807$	−10.8941	+	18.8691i	−0.383490	+	0.664224i
$808$	−54.5260	+	11.5899i	−1.91822	+	0.407730i
$809$	−26.7205	−	11.8967i	−0.939441	−	0.418266i	−0.120868	−	0.992669i	$-0.538568\pi$
$809$	−26.7205	−	11.8967i	−0.939441	−	0.418266i	−0.818573	+	0.574402i	$0.805234\pi$
$810$	5.73395	+	0.00448641i	0.201470	+	0.000157636i
$811$	−17.0315	−	12.3741i	−0.598057	−	0.434514i	0.247132	−	0.968982i	$-0.420512\pi$
$811$	−17.0315	−	12.3741i	−0.598057	−	0.434514i	−0.845189	+	0.534468i	$0.820512\pi$
$812$	−53.7668	−	33.8041i	−1.88684	−	1.18629i
$813$	−17.2997	+	12.5689i	−0.606725	+	0.440812i
$814$	−52.7651	+	23.4925i	−1.84941	+	0.823412i
$815$	−6.18020	+	10.6851i	−0.216483	+	0.374283i
$816$	−37.2734	−	16.5952i	−1.30483	−	0.580948i
$817$	1.45520	+	1.61617i	0.0509111	+	0.0565425i
$818$	−42.5692			−1.48840
$819$	6.91072	+	10.3069i	0.241480	+	0.360151i
$820$	−40.6975	+	45.1281i	−1.42122	+	1.57594i
$821$	50.8113	+	10.8003i	1.77333	+	0.376932i	0.974457	−	0.224572i	$-0.0720984\pi$
$821$	50.8113	+	10.8003i	1.77333	+	0.376932i	0.798870	+	0.601504i	$0.205432\pi$
$822$	12.0631	−	13.3975i	0.420750	−	0.467290i
$823$	1.17798	−	11.2077i	0.0410618	−	0.390677i	−0.954619	−	0.297831i	$-0.903737\pi$
$823$	1.17798	−	11.2077i	0.0410618	−	0.390677i	0.995680	−	0.0928462i	$-0.0295965\pi$
$824$	10.9914	−	19.0377i	0.382905	−	0.663211i
$825$	−14.3800	+	24.8172i	−0.500649	+	0.864024i
$826$	19.7431	+	2.83036i	0.686950	+	0.0984809i
$827$	36.7303	+	26.6861i	1.27724	+	0.927968i	0.999466	−	0.0326790i	$-0.0104039\pi$
$827$	36.7303	+	26.6861i	1.27724	+	0.927968i	0.277772	+	0.960647i	$0.410404\pi$
$828$	−21.7182	−	4.61635i	−0.754760	−	0.160429i
$829$	−16.6800	+	18.5250i	−0.579321	+	0.643401i	−0.959566	−	0.281485i	$-0.909173\pi$
$829$	−16.6800	+	18.5250i	−0.579321	+	0.643401i	0.380245	+	0.924886i	$0.375840\pi$
$830$	6.65148	−	11.4999i	0.230876	−	0.399168i
$831$	−14.8603	−	16.5040i	−0.515497	−	0.572517i
$832$	−8.20447			−0.284439
$833$	36.5818	+	2.76128i	1.26748	+	0.0956725i
$834$	15.1803	−	11.0291i	0.525650	−	0.381907i
$835$	−7.91340	+	5.73997i	−0.273855	+	0.198640i
$836$	3.09457	−	29.4428i	0.107028	−	1.01830i
$837$	6.24270	+	2.77943i	0.215779	+	0.0960711i
$838$	−1.94557	−	18.5109i	−0.0672087	−	0.639448i
$839$	5.96730	+	4.33550i	0.206014	+	0.149678i	0.686008	−	0.727594i	$-0.259361\pi$
$839$	5.96730	+	4.33550i	0.206014	+	0.149678i	−0.479994	+	0.877272i	$0.659361\pi$
$840$	9.58722	−	37.8796i	0.330790	−	1.30697i
$841$	1.19520	−	0.868363i	0.0412138	−	0.0299436i
$842$	49.4885	+	54.9625i	1.70549	+	1.89413i
$843$	−2.26925	−	3.93046i	−0.0781573	−	0.135372i
$844$	22.9735	−	4.88317i	0.790781	−	0.168086i
$845$	−16.2878	+	11.8143i	−0.560316	+	0.406424i
$846$	4.30277	+	13.2426i	0.147932	+	0.455289i
$847$	54.4105	+	19.9742i	1.86957	+	0.686323i
$848$	−44.0223	−	31.9841i	−1.51173	−	1.09834i
$849$	−1.96756	+	3.40791i	−0.0675265	+	0.116959i
$850$	54.3003	+	39.5815i	1.86249	+	1.35763i
$851$	9.52665	+	16.5006i	0.326569	+	0.565635i
$852$	−44.9808	+	20.0267i	−1.54102	+	0.686105i
$853$	−15.2263	−	46.8617i	−0.521338	−	1.60451i	−0.771446	−	0.636295i	$-0.780466\pi$
$853$	−15.2263	−	46.8617i	−0.521338	−	1.60451i	0.250108	−	0.968218i	$-0.419534\pi$
$854$	55.0081	−	45.8989i	1.88234	−	1.57063i
$855$	2.46734	−	0.522433i	0.0843814	−	0.0178668i
$856$	19.5924	+	21.7596i	0.669654	+	0.743726i
$857$	−15.1629	−	26.2630i	−0.517956	−	0.897127i	−0.999782	−	0.0208600i	$-0.993360\pi$
$857$	−15.1629	−	26.2630i	−0.517956	−	0.897127i	0.481826	−	0.876267i	$-0.339974\pi$
$858$	67.4863	−	14.3447i	2.30394	−	0.489718i
$859$	4.52286	+	43.0321i	0.154318	+	1.46824i	0.748087	+	0.663601i	$0.230973\pi$
$859$	4.52286	+	43.0321i	0.154318	+	1.46824i	−0.593769	+	0.804635i	$0.702361\pi$
$860$	19.3000	−	4.08656i	0.658124	−	0.139351i
$861$	−3.84373	+	15.2369i	−0.130994	+	0.519271i
$862$	−68.0035	+	49.4075i	−2.31621	+	1.68283i
$863$	−2.20063	−	20.9376i	−0.0749105	−	0.712725i	−0.965938	−	0.258775i	$-0.916681\pi$
$863$	−2.20063	−	20.9376i	−0.0749105	−	0.712725i	0.891027	−	0.453950i	$-0.149986\pi$
$864$	−0.705999	+	6.71713i	−0.0240186	+	0.228521i
$865$	−9.80879	−	2.09294i	−0.333509	−	0.0711623i
$866$	3.89896	+	37.0961i	0.132492	+	1.26058i
$867$	3.23427	−	9.95407i	0.109842	−	0.338058i
$868$	51.1112	−	65.0481i	1.73483	−	2.20788i
$869$	−0.380610	+	1.17140i	−0.0129113	+	0.0397369i
$870$	−24.3226	−	17.7005i	−0.824613	−	0.600103i
$871$	−47.5261	+	52.7831i	−1.61036	+	1.78849i
$872$	34.9036	−	38.7644i	1.18199	−	1.31273i
$873$	4.45817	−	1.98490i	0.150886	−	0.0671789i
$874$	−14.0348			−0.474733
$875$	−13.1029	+	26.5201i	−0.442959	+	0.896542i
$876$	70.3790			2.37789
$877$	13.5769	−	6.04485i	0.458461	−	0.204120i	−0.164493	−	0.986378i	$-0.552599\pi$
$877$	13.5769	−	6.04485i	0.458461	−	0.204120i	0.622954	+	0.782258i	$0.285932\pi$
$878$	51.6196	−	57.3294i	1.74208	−	1.93477i
$879$	8.46784	−	9.40449i	0.285613	−	0.317206i
$880$	−80.7439	−	58.7604i	−2.72188	−	1.98081i
$881$	6.82078	−	20.9922i	0.229798	−	0.707245i	−0.767971	−	0.640484i	$-0.778734\pi$
$881$	6.82078	−	20.9922i	0.229798	−	0.707245i	0.997769	−	0.0667605i	$-0.0212664\pi$
$882$	−4.24621	−	17.4406i	−0.142977	−	0.587257i
$883$	−13.4075	+	41.2641i	−0.451199	+	1.38865i	0.424342	+	0.905502i	$0.360506\pi$
$883$	−13.4075	+	41.2641i	−0.451199	+	1.38865i	−0.875540	+	0.483145i	$0.839494\pi$
$884$	−11.7566	−	111.857i	−0.395419	−	3.76216i
$885$	6.42883	+	1.37175i	0.216103	+	0.0461108i
$886$	1.54356	−	14.6860i	0.0518569	−	0.493385i
$887$	0.392500	+	3.73438i	0.0131788	+	0.125388i	0.999133	−	0.0416264i	$-0.0132539\pi$
$887$	0.392500	+	3.73438i	0.0131788	+	0.125388i	−0.985954	+	0.167015i	$0.946587\pi$
$888$	20.9804	−	15.2431i	0.704055	−	0.511526i
$889$	−5.72509	−	5.55931i	−0.192013	−	0.186453i
$890$	14.7946	−	3.13260i	0.495918	−	0.105005i
$891$	−0.599625	−	5.70505i	−0.0200882	−	0.191126i
$892$	−37.2676	+	7.92148i	−1.24781	+	0.265231i
$893$	3.06221	+	5.30391i	0.102473	+	0.177488i
$894$	1.76828	+	1.96388i	0.0591402	+	0.0656818i
$895$	−56.8258	+	12.0322i	−1.89948	+	0.402193i
$896$	−22.4094	−	8.22654i	−0.748645	−	0.274829i
$897$	−7.03311	−	21.6457i	−0.234829	−	0.722729i
$898$	−15.9537	+	7.10305i	−0.532382	+	0.237032i
$899$	−17.9249	−	31.0469i	−0.597830	−	1.03547i
$900$	7.10379	−	21.7474i	0.236793	−	0.724912i
$901$	18.3154	−	31.7232i	0.610175	−	1.05685i
$902$	70.6831	+	51.3543i	2.35349	+	1.70991i
$903$	3.91698	−	3.26833i	0.130349	−	0.108763i
$904$	5.64489	+	17.3732i	0.187746	+	0.577824i
$905$	17.5928	−	12.7609i	0.584803	−	0.424186i
$906$	−34.5125	+	7.33585i	−1.14660	+	0.243717i
$907$	−4.93687	−	8.55091i	−0.163926	−	0.283928i	0.772347	−	0.635200i	$-0.219083\pi$
$907$	−4.93687	−	8.55091i	−0.163926	−	0.283928i	−0.936273	+	0.351272i	$0.885749\pi$
$908$	39.8395	+	44.2462i	1.32212	+	1.46836i
$909$	−6.82816	+	4.96095i	−0.226476	+	0.164544i
$910$	68.4668	−	19.3701i	2.26965	−	0.642112i
$911$	−14.8318	−	10.7759i	−0.491400	−	0.357023i	0.314323	−	0.949316i	$-0.398223\pi$
$911$	−14.8318	−	10.7759i	−0.491400	−	0.357023i	−0.805722	+	0.592294i	$0.798223\pi$
$912$	0.917850	+	8.73276i	0.0303930	+	0.289170i
$913$	−12.1418	−	5.40586i	−0.401834	−	0.178908i
$914$	8.15815	−	77.6196i	0.269848	−	2.56743i
$915$	19.1135	−	13.8639i	0.631873	−	0.458328i
$916$	−36.6475	+	26.6260i	−1.21087	+	0.879747i
$917$	−14.1647	−	21.1257i	−0.467760	−	0.697633i
$918$	−13.4391			−0.443555
$919$	9.02546	+	10.0238i	0.297722	+	0.330654i	0.873383	−	0.487035i	$-0.161922\pi$
$919$	9.02546	+	10.0238i	0.297722	+	0.330654i	−0.575660	+	0.817689i	$0.695255\pi$
$920$	−35.8810	+	62.0356i	−1.18296	+	2.04525i
$921$	−10.6782	+	11.8594i	−0.351860	+	0.390780i
$922$	−26.2549	−	5.58066i	−0.864660	−	0.183789i
$923$	−40.8319	−	29.6661i	−1.34400	−	0.976473i
$924$	−68.7430	−	9.85497i	−2.26148	−	0.324205i
$925$	−17.9475	+	7.95712i	−0.590110	+	0.261628i
$926$	48.9695	−	84.8176i	1.60924	−	2.78728i
$927$	0.347909	−	3.31013i	0.0114268	−	0.108719i
$928$	23.7097	−	26.3323i	0.778308	−	0.864399i
$929$	−15.8392	−	3.36672i	−0.519666	−	0.110458i	−0.0593911	−	0.998235i	$-0.518916\pi$
$929$	−15.8392	−	3.36672i	−0.519666	−	0.110458i	−0.460275	+	0.887776i	$0.652249\pi$
$930$	26.2412	−	29.0980i	0.860484	−	0.954162i
$931$	−3.42178	−	7.11523i	−0.112144	−	0.233192i
$932$	3.11117			0.101910
$933$	−19.4465	−	21.5975i	−0.636650	−	0.707071i
$934$	65.3362	+	29.0896i	2.13787	+	0.951839i
$935$	33.6580	−	58.1922i	1.10074	−	1.90309i
$936$	−28.2996	+	12.5998i	−0.925002	+	0.411838i
$937$	17.5327	−	12.7383i	0.572770	−	0.416142i	−0.263340	−	0.964703i	$-0.584824\pi$
$937$	17.5327	−	12.7383i	0.572770	−	0.416142i	0.836110	+	0.548561i	$0.184824\pi$
$938$	90.8475	−	47.9829i	2.96628	−	1.56670i
$939$	−2.23972	−	1.62725i	−0.0730905	−	0.0531033i
$940$	55.5563	+	0.0434689i	1.81205	+	0.00141780i
$941$	−4.75677	−	2.11785i	−0.155066	−	0.0690400i	0.327736	−	0.944769i	$-0.393714\pi$
$941$	−4.75677	−	2.11785i	−0.155066	−	0.0690400i	−0.482802	+	0.875729i	$0.660381\pi$
$942$	−10.2421	+	2.17703i	−0.333706	+	0.0709314i
$943$	14.4106	−	24.9599i	0.469274	−	0.812806i
$944$	−7.07238	+	21.7666i	−0.230186	+	0.708441i
$945$	−1.00665	−	5.82981i	−0.0327464	−	0.189644i
$946$	−8.76477	−	26.9752i	−0.284967	−	0.877039i
$947$	0.400168	+	0.0850583i	0.0130037	+	0.00276402i	0.214409	−	0.976744i	$-0.431217\pi$
$947$	0.400168	+	0.0850583i	0.0130037	+	0.00276402i	−0.201405	+	0.979508i	$0.564551\pi$
$948$	0.102692	−	0.977053i	0.00333529	−	0.0317332i
$949$	36.0710	+	62.4768i	1.17091	+	2.02808i
$950$	1.53412	−	14.3797i	0.0497734	−	0.466539i
$951$	24.2948			0.787813
$952$	−22.4008	+	88.7986i	−0.726013	+	2.87798i
$953$	−12.7378	−	39.2029i	−0.412618	−	1.26991i	−0.914364	−	0.404893i	$-0.867309\pi$
$953$	−12.7378	−	39.2029i	−0.412618	−	1.26991i	0.501746	−	0.865015i	$-0.332691\pi$
$954$	−17.5315	−	3.72644i	−0.567604	−	0.120648i
$955$	25.9091	−	44.7949i	0.838399	−	1.44953i
$956$	46.7804	−	9.94348i	1.51299	−	0.321595i
$957$	−15.0474	+	26.0628i	−0.486412	+	0.842491i
$958$	−4.20183	+	12.9319i	−0.135755	+	0.417811i
$959$	−15.7470	−	9.90041i	−0.508497	−	0.319701i
$960$	3.57205	+	1.59373i	0.115287	+	0.0514374i
$961$	14.3395	−	6.38436i	0.462564	−	0.205947i
$962$	43.1418	+	19.2080i	1.39095	+	0.619289i
$963$	4.04998	+	1.80317i	0.130509	+	0.0581063i
$964$	56.6014	−	25.2006i	1.82301	−	0.811655i
$965$	−4.87628	+	46.0481i	−0.156973	+	1.48234i
$966$	−1.23987	+	32.8986i	−0.0398921	+	1.05850i
$967$	5.60426	−	17.2481i	0.180221	−	0.554662i	−0.819613	−	0.572918i	$-0.805811\pi$
$967$	5.60426	−	17.2481i	0.180221	−	0.554662i	0.999833	+	0.0182557i	$0.00581129\pi$
$968$	−72.3453	+	125.306i	−2.32526	+	4.02748i
$969$	−5.78193	+	1.22899i	−0.185742	+	0.0394808i
$970$	−2.90315	−	27.8311i	−0.0932146	−	0.893603i
$971$	−30.3110	−	6.44280i	−0.972725	−	0.206759i	−0.305974	−	0.952040i	$-0.598982\pi$
$971$	−30.3110	−	6.44280i	−0.972725	−	0.206759i	−0.666751	+	0.745281i	$0.732316\pi$
$972$	1.41395	+	4.35169i	0.0453525	+	0.139581i
$973$	−13.8891	−	13.4869i	−0.445264	−	0.432370i
$974$	20.9502			0.671289
$975$	22.9464	−	4.83990i	0.734874	−	0.155001i
$976$	41.1045	+	71.1951i	1.31572	+	2.27890i
$977$	−5.10100	+	48.5328i	−0.163195	+	1.55270i	0.539976	+	0.841680i	$0.318433\pi$
$977$	−5.10100	+	48.5328i	−0.163195	+	1.55270i	−0.703172	+	0.711020i	$0.748233\pi$
$978$	−13.8463	−	2.94312i	−0.442755	−	0.0941105i
$979$	−4.67522	−	14.3888i	−0.149421	−	0.459869i
$980$	−71.4127	−	5.44659i	−2.28119	−	0.173985i
$981$	2.44056	−	7.51126i	0.0779209	−	0.239816i
$982$	−11.9139	+	20.6355i	−0.380188	+	0.658504i
$983$	4.36992	−	0.928855i	0.139379	−	0.0296259i	−0.137694	−	0.990475i	$-0.543969\pi$
$983$	4.36992	−	0.928855i	0.139379	−	0.0296259i	0.277073	+	0.960849i	$0.410636\pi$
$984$	−35.8367	−	15.9555i	−1.14243	−	0.508643i
$985$	−1.20649	+	3.70332i	−0.0384419	+	0.117998i
$986$	57.0390	+	41.4413i	1.81649	+	1.31976i
$987$	12.7033	−	6.70951i	0.404351	−	0.213566i
$988$	−19.5828	+	14.2277i	−0.623011	+	0.452644i
$989$	−8.54757	+	3.80562i	−0.271797	+	0.121012i
$990$	−32.1685	−	6.86394i	−1.02238	−	0.218150i
$991$	9.60087	+	4.27458i	0.304982	+	0.135787i	0.553521	−	0.832835i	$-0.313284\pi$
$991$	9.60087	+	4.27458i	0.304982	+	0.135787i	−0.248539	+	0.968622i	$0.579951\pi$
$992$	30.8832	+	34.2993i	0.980543	+	1.08900i
$993$	−19.9557			−0.633276
$994$	40.6575	+	60.6380i	1.28958	+	1.92332i
$995$	−5.36555	+	50.6684i	−0.170099	+	1.60630i
$996$	10.3696	+	2.20413i	0.328574	+	0.0698405i
$997$	−24.5810	+	27.2999i	−0.778487	+	0.864598i	−0.993712	−	0.111967i	$-0.964285\pi$
$997$	−24.5810	+	27.2999i	−0.778487	+	0.864598i	0.215225	+	0.976565i	$0.430952\pi$
$998$	−7.83503	+	74.5453i	−0.248013	+	2.35969i
$999$	1.96323	−	3.40042i	0.0621140	−	0.107585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.b.16.19	✓	160
7.4	even	3	inner	525.2.bg.b.466.2	yes	160
25.11	even	5	inner	525.2.bg.b.436.2	yes	160
175.11	even	15	inner	525.2.bg.b.361.19	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.b.16.19	✓	160	1.1	even	1	trivial
525.2.bg.b.361.19	yes	160	175.11	even	15	inner
525.2.bg.b.436.2	yes	160	25.11	even	5	inner
525.2.bg.b.466.2	yes	160	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.34261 - 1.04299i) q^{2} +(0.669131 - 0.743145i) q^{3} +(3.06170 - 3.40036i) q^{4} +(-1.80799 - 1.31574i) q^{5} +(0.792412 - 2.43879i) q^{6} +(-2.61898 - 0.375455i) q^{7} +(2.04097 - 6.28145i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(2.34261 - 1.04299i) q^{2} +(0.669131 - 0.743145i) q^{3} +(3.06170 - 3.40036i) q^{4} +(-1.80799 - 1.31574i) q^{5} +(0.792412 - 2.43879i) q^{6} +(-2.61898 - 0.375455i) q^{7} +(2.04097 - 6.28145i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-5.60772 - 1.19654i) q^{10} +(-0.599625 + 5.70505i) q^{11} +(-0.478284 - 4.55057i) q^{12} +(3.79450 - 2.75687i) q^{13} +(-6.52682 + 1.85203i) q^{14} +(-2.18757 + 0.463193i) q^{15} +(-0.813773 - 7.74253i) q^{16} +(5.12631 - 1.08963i) q^{17} +(-1.28215 - 2.22075i) q^{18} +(-0.754708 - 0.838188i) q^{19} +(-10.0095 + 2.11940i) q^{20} +(-2.03145 + 1.69505i) q^{21} +(4.54566 + 13.9901i) q^{22} +(4.43301 - 1.97370i) q^{23} +(-3.30235 - 5.71985i) q^{24} +(1.53764 + 4.75769i) q^{25} +(6.01362 - 10.4159i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-9.29520 + 7.75593i) q^{28} +(1.62117 + 4.98944i) q^{29} +(-4.64150 + 3.36670i) q^{30} +(-6.68416 + 1.42076i) q^{31} +(-3.37707 - 5.84925i) q^{32} +(3.83845 + 4.26303i) q^{33} +(10.8724 - 7.89929i) q^{34} +(4.24107 + 4.12472i) q^{35} +(-3.70177 - 2.68949i) q^{36} +(0.410428 + 3.90496i) q^{37} +(-2.64221 - 1.17639i) q^{38} +(0.490266 - 4.66457i) q^{39} +(-11.9548 + 8.67140i) q^{40} +(4.80509 - 3.49110i) q^{41} +(-2.99097 + 6.08963i) q^{42} -1.92816 q^{43} +(17.5634 + 19.5061i) q^{44} +(-1.11955 + 1.93562i) q^{45} +(8.32622 - 9.24721i) q^{46} +(-5.31131 - 1.12895i) q^{47} +(-6.29834 - 4.57602i) q^{48} +(6.71807 + 1.96662i) q^{49} +(8.56434 + 9.54165i) q^{50} +(2.62042 - 4.53869i) q^{51} +(2.24328 - 21.3434i) q^{52} +(4.67689 - 5.19421i) q^{53} +(-2.50826 - 0.533148i) q^{54} +(8.59050 - 9.52571i) q^{55} +(-7.70365 + 15.6847i) q^{56} -1.12789 q^{57} +(9.00171 + 9.99741i) q^{58} +(-2.68562 - 1.19572i) q^{59} +(-5.12265 + 8.85668i) q^{60} +(-9.64675 + 4.29501i) q^{61} +(-14.1765 + 10.2998i) q^{62} +(-0.0996411 + 2.64387i) q^{63} +(-1.41518 - 1.02819i) q^{64} +(-10.4877 - 0.00820591i) q^{65} +(13.4383 + 5.98312i) q^{66} +(-14.8125 + 3.14850i) q^{67} +(11.9901 - 20.7674i) q^{68} +(1.49951 - 4.61503i) q^{69} +(14.2372 + 5.23916i) q^{70} +(-3.32528 - 10.2341i) q^{71} +(-6.46038 - 1.37320i) q^{72} +(-1.60778 + 15.2970i) q^{73} +(5.03432 + 8.71970i) q^{74} +(4.56454 + 2.04083i) q^{75} -5.16083 q^{76} +(3.71240 - 14.7163i) q^{77} +(-3.71662 - 11.4386i) q^{78} +(0.210018 + 0.0446407i) q^{79} +(-8.71589 + 15.0691i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(7.61522 - 13.1900i) q^{82} +(-0.715960 + 2.20350i) q^{83} +(-0.455922 + 12.0974i) q^{84} +(-10.7020 - 4.77486i) q^{85} +(-4.51693 + 2.01107i) q^{86} +(4.79265 + 2.13382i) q^{87} +(34.6122 + 15.4103i) q^{88} +(-2.40937 + 1.07272i) q^{89} +(-0.603823 + 5.70207i) q^{90} +(-10.9728 + 5.79550i) q^{91} +(6.86123 - 21.1167i) q^{92} +(-3.41674 + 5.91797i) q^{93} +(-13.6198 + 2.89498i) q^{94} +(0.261663 + 2.50844i) q^{95} +(-6.60654 - 1.40426i) q^{96} +(1.50803 + 4.64123i) q^{97} +(17.7889 - 2.39990i) q^{98} +5.73648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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