LMFDB - Embedded newform 507.2.q.b.490.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			490.6
Character	$\chi$	$=$	507.490
Dual form			507.2.q.b.328.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.284984 - 1.39594i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-0.0274838 + 0.0117098i) q^{4} +(4.22141 - 1.04049i) q^{5} +(-0.0573684 - 1.42358i) q^{6} +(-1.74204 + 3.67128i) q^{7} +(-1.59451 - 2.31004i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(-0.284984 - 1.39594i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-0.0274838 + 0.0117098i) q^{4} +(4.22141 - 1.04049i) q^{5} +(-0.0573684 - 1.42358i) q^{6} +(-1.74204 + 3.67128i) q^{7} +(-1.59451 - 2.31004i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-2.65549 - 5.59634i) q^{10} +(1.76063 - 0.587783i) q^{11} +(-0.0290063 + 0.00714941i) q^{12} +(-2.68518 - 2.40620i) q^{13} +(5.62135 + 1.38554i) q^{14} +(4.33365 - 0.349849i) q^{15} +(-2.81167 + 2.92726i) q^{16} +(1.16844 - 2.46243i) q^{17} +(0.171733 - 1.41435i) q^{18} +(0.447772 + 0.775563i) q^{19} +(-0.103837 + 0.0780282i) q^{20} +(-2.30840 + 3.34429i) q^{21} +(-1.32226 - 2.29023i) q^{22} +(-3.66314 + 6.34474i) q^{23} +(-1.20330 - 2.53590i) q^{24} +(12.3105 - 6.46102i) q^{25} +(-2.59369 + 4.43409i) q^{26} +(0.885456 + 0.464723i) q^{27} +(0.00488821 - 0.121300i) q^{28} +(0.453246 + 2.22015i) q^{29} +(-1.72339 - 5.94984i) q^{30} +(3.88053 + 2.03666i) q^{31} +(0.142821 + 0.0903145i) q^{32} +(1.83211 - 0.297747i) q^{33} +(-3.77040 - 0.929319i) q^{34} +(-3.53397 + 17.3106i) q^{35} +(-0.0297775 + 0.00240389i) q^{36} +(-2.16724 + 1.37048i) q^{37} +(0.955035 - 0.846087i) q^{38} +(-2.26443 - 2.80577i) q^{39} +(-9.13464 - 8.09258i) q^{40} +(-3.95069 - 0.642050i) q^{41} +(5.32630 + 2.26932i) q^{42} +(-8.25003 - 5.21700i) q^{43} +(-0.0415059 + 0.0367710i) q^{44} +(4.33365 + 0.349849i) q^{45} +(9.90083 + 3.30538i) q^{46} +(-1.18734 - 9.77863i) q^{47} +(-3.24482 + 2.43833i) q^{48} +(-6.01644 - 7.36881i) q^{49} +(-12.5275 - 15.3434i) q^{50} +(1.54831 - 2.24311i) q^{51} +(0.101975 + 0.0346887i) q^{52} +(4.46734 + 6.47206i) q^{53} +(0.396387 - 1.36849i) q^{54} +(6.82075 - 4.31318i) q^{55} +(11.2585 - 1.82968i) q^{56} +(0.317564 + 0.837347i) q^{57} +(2.97003 - 1.26541i) q^{58} +(3.42532 + 3.56614i) q^{59} +(-0.115009 + 0.0603612i) q^{60} +(-0.751249 - 0.0606471i) q^{61} +(1.73717 - 5.99741i) q^{62} +(-2.81497 + 2.93069i) q^{63} +(-2.79321 + 7.36508i) q^{64} +(-13.8389 - 7.36368i) q^{65} +(-0.937762 - 2.47267i) q^{66} +(-9.51783 - 4.05517i) q^{67} +(-0.00327866 + 0.0813590i) q^{68} +(-4.63347 + 5.67497i) q^{69} +25.1717 q^{70} +(-8.82117 + 10.8040i) q^{71} +(-0.780931 - 2.69609i) q^{72} +(-3.47533 - 3.07887i) q^{73} +(2.53074 + 2.63478i) q^{74} +(13.1875 - 4.40262i) q^{75} +(-0.0213881 - 0.0160721i) q^{76} +(-0.909170 + 7.48769i) q^{77} +(-3.27138 + 3.96061i) q^{78} +(1.50705 + 12.4117i) q^{79} +(-8.82345 + 15.2827i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.229618 + 5.69792i) q^{82} +(2.59004 - 6.82937i) q^{83} +(0.0242827 - 0.118945i) q^{84} +(2.37034 - 11.6107i) q^{85} +(-4.93151 + 13.0033i) q^{86} +(0.0912402 + 2.26410i) q^{87} +(-4.16513 - 3.12990i) q^{88} +(-0.211443 + 0.366230i) q^{89} +(-0.746653 - 6.14924i) q^{90} +(13.5115 - 5.66634i) q^{91} +(0.0263816 - 0.217272i) q^{92} +(3.50357 + 2.63276i) q^{93} +(-13.3120 + 4.44421i) q^{94} +(2.69719 + 2.80807i) q^{95} +(0.126484 + 0.112055i) q^{96} +(-3.05097 - 10.5332i) q^{97} +(-8.57185 + 10.4986i) q^{98} +1.85615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{17}{39}\right)$

Coefficient data

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

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

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

$2$	−0.284984	−	1.39594i	−0.201514	−	0.987081i	−0.947166	−	0.320745i	$-0.896067\pi$
$2$	−0.284984	−	1.39594i	−0.201514	−	0.987081i	0.745651	−	0.666336i	$-0.232138\pi$
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$4$	−0.0274838	+	0.0117098i	−0.0137419	+	0.00585488i
$5$	4.22141	−	1.04049i	1.88787	−	0.465319i	0.887888	−	0.460060i	$-0.152172\pi$
$5$	4.22141	−	1.04049i	1.88787	−	0.465319i	0.999986	−	0.00525922i	$-0.00167407\pi$
$6$	−0.0573684	−	1.42358i	−0.0234205	−	0.581175i
$7$	−1.74204	+	3.67128i	−0.658430	+	1.38761i	0.249452	+	0.968387i	$0.419749\pi$
$7$	−1.74204	+	3.67128i	−0.658430	+	1.38761i	−0.907882	+	0.419225i	$0.862302\pi$
$8$	−1.59451	−	2.31004i	−0.563743	−	0.816723i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	−2.65549	−	5.59634i	−0.839741	−	1.76972i
$11$	1.76063	−	0.587783i	0.530849	−	0.177223i	−0.0385930	−	0.999255i	$-0.512288\pi$
$11$	1.76063	−	0.587783i	0.530849	−	0.177223i	0.569442	+	0.822032i	$0.307159\pi$
$12$	−0.0290063	+	0.00714941i	−0.00837339	+	0.00206386i
$13$	−2.68518	−	2.40620i	−0.744735	−	0.667360i
$13$	−2.68518	−	2.40620i	−0.744735	−	0.667360i
$14$	5.62135	+	1.38554i	1.50237	+	0.370301i
$15$	4.33365	−	0.349849i	1.11894	−	0.0903306i
$16$	−2.81167	+	2.92726i	−0.702917	+	0.731814i
$17$	1.16844	−	2.46243i	0.283388	−	0.597227i	−0.710980	−	0.703212i	$-0.751748\pi$
$17$	1.16844	−	2.46243i	0.283388	−	0.597227i	0.994368	+	0.105985i	$0.0337997\pi$
$18$	0.171733	−	1.41435i	0.0404779	−	0.333365i
$19$	0.447772	+	0.775563i	0.102726	+	0.177926i	0.912807	−	0.408392i	$-0.133910\pi$
$19$	0.447772	+	0.775563i	0.102726	+	0.177926i	−0.810081	+	0.586318i	$0.800577\pi$
$20$	−0.103837	+	0.0780282i	−0.0232186	+	0.0174476i
$21$	−2.30840	+	3.34429i	−0.503734	+	0.729784i
$22$	−1.32226	−	2.29023i	−0.281907	−	0.488278i
$23$	−3.66314	+	6.34474i	−0.763817	+	1.32297i	0.177053	+	0.984201i	$0.443343\pi$
$23$	−3.66314	+	6.34474i	−0.763817	+	1.32297i	−0.940870	+	0.338768i	$0.889990\pi$
$24$	−1.20330	−	2.53590i	−0.245623	−	0.517639i
$25$	12.3105	−	6.46102i	2.46209	−	1.29220i
$26$	−2.59369	+	4.43409i	−0.508664	+	0.869597i
$27$	0.885456	+	0.464723i	0.170406	+	0.0894360i
$28$	0.00488821	−	0.121300i	0.000923784	−	0.0229235i
$29$	0.453246	+	2.22015i	0.0841657	+	0.412271i	0.999944	+	0.0105866i	$0.00336988\pi$
$29$	0.453246	+	2.22015i	0.0841657	+	0.412271i	−0.915778	+	0.401684i	$0.868425\pi$
$30$	−1.72339	−	5.94984i	−0.314647	−	1.08629i
$31$	3.88053	+	2.03666i	0.696963	+	0.365794i	0.775701	−	0.631101i	$-0.217397\pi$
$31$	3.88053	+	2.03666i	0.696963	+	0.365794i	−0.0787377	+	0.996895i	$0.525089\pi$
$32$	0.142821	+	0.0903145i	0.0252474	+	0.0159655i
$33$	1.83211	−	0.297747i	0.318930	−	0.0518312i
$34$	−3.77040	−	0.929319i	−0.646618	−	0.159377i
$35$	−3.53397	+	17.3106i	−0.597351	+	2.92602i
$36$	−0.0297775	+	0.00240389i	−0.00496292	+	0.000400648i
$37$	−2.16724	+	1.37048i	−0.356292	+	0.225305i	−0.700605	−	0.713550i	$-0.747086\pi$
$37$	−2.16724	+	1.37048i	−0.356292	+	0.225305i	0.344313	+	0.938855i	$0.388112\pi$
$38$	0.955035	−	0.846087i	0.154927	−	0.137253i
$39$	−2.26443	−	2.80577i	−0.362599	−	0.449283i
$40$	−9.13464	−	8.09258i	−1.44431	−	1.27955i
$41$	−3.95069	−	0.642050i	−0.616994	−	0.100271i	−0.156122	−	0.987738i	$-0.549899\pi$
$41$	−3.95069	−	0.642050i	−0.616994	−	0.100271i	−0.460872	+	0.887466i	$0.652463\pi$
$42$	5.32630	+	2.26932i	0.821866	+	0.350164i
$43$	−8.25003	−	5.21700i	−1.25812	−	0.795585i	−0.272107	−	0.962267i	$-0.587720\pi$
$43$	−8.25003	−	5.21700i	−1.25812	−	0.795585i	−0.986011	+	0.166682i	$0.946695\pi$
$44$	−0.0415059	+	0.0367710i	−0.00625725	+	0.00554344i
$45$	4.33365	+	0.349849i	0.646023	+	0.0521524i
$46$	9.90083	+	3.30538i	1.45980	+	0.487352i
$47$	−1.18734	−	9.77863i	−0.173191	−	1.42636i	−0.777136	−	0.629333i	$-0.783328\pi$
$47$	−1.18734	−	9.77863i	−0.173191	−	1.42636i	0.603945	−	0.797026i	$-0.293595\pi$
$48$	−3.24482	+	2.43833i	−0.468350	+	0.351942i
$49$	−6.01644	−	7.36881i	−0.859492	−	1.05269i
$50$	−12.5275	−	15.3434i	−1.77166	−	2.16989i
$51$	1.54831	−	2.24311i	0.216806	−	0.314098i
$52$	0.101975	+	0.0346887i	0.0141414	+	0.00481046i
$53$	4.46734	+	6.47206i	0.613637	+	0.889006i	0.999436	−	0.0335763i	$-0.0106897\pi$
$53$	4.46734	+	6.47206i	0.613637	+	0.889006i	−0.385799	+	0.922583i	$0.626074\pi$
$54$	0.396387	−	1.36849i	0.0539414	−	0.186227i
$55$	6.82075	−	4.31318i	0.919710	−	0.581590i
$56$	11.2585	−	1.82968i	1.50448	−	0.244502i
$57$	0.317564	+	0.837347i	0.0420624	+	0.110909i
$58$	2.97003	−	1.26541i	0.389984	−	0.166157i
$59$	3.42532	+	3.56614i	0.445939	+	0.464271i	0.905791	−	0.423724i	$-0.139277\pi$
$59$	3.42532	+	3.56614i	0.445939	+	0.464271i	−0.459853	+	0.887995i	$0.652098\pi$
$60$	−0.115009	+	0.0603612i	−0.0148476	+	0.00779260i
$61$	−0.751249	−	0.0606471i	−0.0961876	−	0.00776507i	0.0322790	−	0.999479i	$-0.489723\pi$
$61$	−0.751249	−	0.0606471i	−0.0961876	−	0.00776507i	−0.128467	+	0.991714i	$0.541006\pi$
$62$	1.73717	−	5.99741i	0.220621	−	0.761672i
$63$	−2.81497	+	2.93069i	−0.354652	+	0.369232i
$64$	−2.79321	+	7.36508i	−0.349151	+	0.920636i
$65$	−13.8389	−	7.36368i	−1.71650	−	0.913352i
$66$	−0.937762	−	2.47267i	−0.115430	−	0.304365i
$67$	−9.51783	−	4.05517i	−1.16279	−	0.495418i	−0.277621	−	0.960691i	$-0.589546\pi$
$67$	−9.51783	−	4.05517i	−1.16279	−	0.495418i	−0.885167	+	0.465273i	$0.845956\pi$
$68$	−0.00327866	+	0.0813590i	−0.000397596	+	0.00986623i
$69$	−4.63347	+	5.67497i	−0.557804	+	0.683186i
$70$	25.1717			3.00859
$71$	−8.82117	+	10.8040i	−1.04688	+	1.28220i	−0.0886919	+	0.996059i	$0.528269\pi$
$71$	−8.82117	+	10.8040i	−1.04688	+	1.28220i	−0.958189	+	0.286137i	$0.907629\pi$
$72$	−0.780931	−	2.69609i	−0.0920336	−	0.317737i
$73$	−3.47533	−	3.07887i	−0.406757	−	0.360355i	0.434797	−	0.900528i	$-0.356820\pi$
$73$	−3.47533	−	3.07887i	−0.406757	−	0.360355i	−0.841554	+	0.540174i	$0.818359\pi$
$74$	2.53074	+	2.63478i	0.294192	+	0.306287i
$75$	13.1875	−	4.40262i	1.52276	−	0.508371i
$76$	−0.0213881	−	0.0160721i	−0.00245339	−	0.00184360i
$77$	−0.909170	+	7.48769i	−0.103610	+	0.853302i
$78$	−3.27138	+	3.96061i	−0.370411	+	0.448451i
$79$	1.50705	+	12.4117i	0.169557	+	1.39642i	0.790449	+	0.612528i	$0.209848\pi$
$79$	1.50705	+	12.4117i	0.169557	+	1.39642i	−0.620892	+	0.783896i	$0.713229\pi$
$80$	−8.82345	+	15.2827i	−0.986492	+	1.70865i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	0.229618	+	5.69792i	0.0253571	+	0.629230i
$83$	2.59004	−	6.82937i	0.284294	−	0.749621i	−0.714458	−	0.699678i	$-0.753327\pi$
$83$	2.59004	−	6.82937i	0.284294	−	0.749621i	0.998752	−	0.0499431i	$-0.0159040\pi$
$84$	0.0242827	−	0.118945i	0.00264946	−	0.0129779i
$85$	2.37034	−	11.6107i	0.257099	−	1.25935i
$86$	−4.93151	+	13.0033i	−0.531779	+	1.40219i
$87$	0.0912402	+	2.26410i	0.00978197	+	0.242737i
$88$	−4.16513	−	3.12990i	−0.444005	−	0.333648i
$89$	−0.211443	+	0.366230i	−0.0224129	+	0.0388203i	−0.877014	−	0.480464i	$-0.840468\pi$
$89$	−0.211443	+	0.366230i	−0.0224129	+	0.0388203i	0.854601	+	0.519285i	$0.173802\pi$
$90$	−0.746653	−	6.14924i	−0.0787041	−	0.648187i
$91$	13.5115	−	5.66634i	1.41639	−	0.593994i
$92$	0.0263816	−	0.217272i	0.00275047	−	0.0226522i
$93$	3.50357	+	2.63276i	0.363303	+	0.273005i
$94$	−13.3120	+	4.44421i	−1.37303	+	0.458385i
$95$	2.69719	+	2.80807i	0.276726	+	0.288102i
$96$	0.126484	+	0.112055i	0.0129092	+	0.0114366i
$97$	−3.05097	−	10.5332i	−0.309779	−	1.06948i	−0.952792	−	0.303625i	$-0.901803\pi$
$97$	−3.05097	−	10.5332i	−0.309779	−	1.06948i	0.643013	−	0.765855i	$-0.277684\pi$
$98$	−8.57185	+	10.4986i	−0.865887	+	1.06052i
$99$	1.85615			0.186550
$100$	−0.262681	+	0.321726i	−0.0262681	+	0.0321726i
$101$	0.103186	−	2.56054i	0.0102674	−	0.254783i	−0.985901	−	0.167329i	$-0.946486\pi$
$101$	0.103186	−	2.56054i	0.0102674	−	0.254783i	0.996169	−	0.0874541i	$-0.0278731\pi$
$102$	−3.57250	−	1.52210i	−0.353730	−	0.150710i
$103$	2.88856	+	7.61652i	0.284619	+	0.750478i	0.998727	+	0.0504425i	$0.0160632\pi$
$103$	2.88856	+	7.61652i	0.284619	+	0.750478i	−0.714108	+	0.700035i	$0.753168\pi$
$104$	−1.27688	+	10.0396i	−0.125209	+	0.984462i
$105$	−6.26502	+	16.5195i	−0.611403	+	1.61214i
$106$	7.76152	−	8.08059i	0.753865	−	0.784857i
$107$	−4.20531	+	14.5184i	−0.406542	+	1.40355i	0.452556	+	0.891736i	$0.350512\pi$
$107$	−4.20531	+	14.5184i	−0.406542	+	1.40355i	−0.859098	+	0.511811i	$0.828975\pi$
$108$	−0.0297775	−	0.00240389i	−0.00286534	−	0.000231314i
$109$	−5.91331	+	3.10354i	−0.566392	+	0.297265i	−0.723509	−	0.690315i	$-0.757472\pi$
$109$	−5.91331	+	3.10354i	−0.566392	+	0.297265i	0.157118	+	0.987580i	$0.449780\pi$
$110$	−7.96477	−	8.29220i	−0.759411	−	0.790630i
$111$	−2.35901	+	1.00508i	−0.223908	+	0.0953982i
$112$	−5.84872	−	15.4218i	−0.552653	−	1.45723i
$113$	1.96482	−	0.319314i	0.184835	−	0.0300386i	−0.0672893	−	0.997734i	$-0.521435\pi$
$113$	1.96482	−	0.319314i	0.184835	−	0.0300386i	0.252124	+	0.967695i	$0.418871\pi$
$114$	1.07839	−	0.681932i	0.101000	−	0.0638688i
$115$	−8.86201	+	30.5952i	−0.826387	+	2.85302i
$116$	−0.0384543	−	0.0557107i	−0.00357039	−	0.00517261i
$117$	−1.78503	−	3.13268i	−0.165026	−	0.289616i
$118$	4.00196	−	5.79785i	0.368411	−	0.533735i
$119$	7.00479	+	8.57931i	0.642128	+	0.786464i
$120$	−7.71821	−	9.45309i	−0.704573	−	0.862945i
$121$	−6.03955	+	4.53843i	−0.549050	+	0.412585i
$122$	0.129434	+	1.06599i	0.0117184	+	0.0965097i
$123$	−3.79654	−	1.26747i	−0.342322	−	0.114284i
$124$	−0.130500	−	0.0105351i	−0.0117193	−	0.000946078i
$125$	28.9732	−	25.6680i	2.59144	−	2.29582i
$126$	4.89330	+	3.09434i	0.435930	+	0.275665i
$127$	11.4317	+	4.87061i	1.01440	+	0.432197i	0.834217	−	0.551436i	$-0.185920\pi$
$127$	11.4317	+	4.87061i	1.01440	+	0.432197i	0.180186	+	0.983633i	$0.442330\pi$
$128$	11.4108	+	1.85444i	1.00859	+	0.163911i
$129$	−7.30633	−	6.47284i	−0.643286	−	0.569902i
$130$	−6.33542	+	21.4168i	−0.555653	+	1.87838i
$131$	7.49788	−	6.64254i	0.655093	−	0.580362i	−0.268714	−	0.963220i	$-0.586599\pi$
$131$	7.49788	−	6.64254i	0.655093	−	0.580362i	0.923807	+	0.382858i	$0.125060\pi$
$132$	−0.0468669	+	0.0296368i	−0.00407924	+	0.00257956i
$133$	−3.62734	+	0.292829i	−0.314531	+	0.0253915i
$134$	−2.94836	+	14.4420i	−0.254699	+	1.24760i
$135$	4.22141	+	1.04049i	0.363322	+	0.0895507i
$136$	−7.55139	+	1.22722i	−0.647527	+	0.105233i
$137$	18.0337	+	11.4038i	1.54072	+	0.974294i	0.990228	+	0.139455i	$0.0445351\pi$
$137$	18.0337	+	11.4038i	1.54072	+	0.974294i	0.550494	+	0.834839i	$0.314439\pi$
$138$	9.24240	+	4.85078i	0.786765	+	0.412926i
$139$	2.09515	+	7.23331i	0.177709	+	0.613521i	0.999070	+	0.0431132i	$0.0137276\pi$
$139$	2.09515	+	7.23331i	0.177709	+	0.613521i	−0.821362	+	0.570408i	$0.806785\pi$
$140$	−0.105575	−	0.517142i	−0.00892274	−	0.0437065i
$141$	0.396637	−	9.84246i	0.0334029	−	0.828884i
$142$	17.5956	+	9.23490i	1.47659	+	0.774976i
$143$	−6.14193	−	2.65811i	−0.513614	−	0.222283i
$144$	−3.59394	+	1.88624i	−0.299495	+	0.157187i
$145$	4.22337	+	8.90056i	0.350732	+	0.739151i
$146$	−3.30752	+	5.72879i	−0.273732	+	0.474118i
$147$	−4.75649	−	8.23849i	−0.392309	−	0.679499i
$148$	0.0435160	−	0.0630438i	0.00357699	−	0.00518217i
$149$	5.84006	−	4.38852i	0.478436	−	0.359521i	−0.333999	−	0.942574i	$-0.608398\pi$
$149$	5.84006	−	4.38852i	0.478436	−	0.359521i	0.812435	+	0.583052i	$0.198142\pi$
$150$	−9.90402	−	17.1543i	−0.808660	−	1.40064i
$151$	2.47570	−	20.3892i	0.201469	−	1.65925i	−0.444421	−	0.895818i	$-0.646590\pi$
$151$	2.47570	−	20.3892i	0.201469	−	1.65925i	0.645890	−	0.763430i	$-0.276486\pi$
$152$	1.07761	−	2.27101i	0.0874056	−	0.184203i
$153$	1.88808	−	1.96570i	0.152642	−	0.158917i
$154$	10.7115	−	0.864721i	0.863157	−	0.0696812i
$155$	18.5004	+	4.55994i	1.48599	+	0.366264i
$156$	0.0950900	+	0.0505975i	0.00761330	+	0.00405104i
$157$	−8.00179	+	1.97226i	−0.638612	+	0.157404i	−0.545311	−	0.838234i	$-0.683588\pi$
$157$	−8.00179	+	1.97226i	−0.638612	+	0.157404i	−0.0933016	+	0.995638i	$0.529742\pi$
$158$	16.8965	−	5.64089i	1.34422	−	0.448765i
$159$	3.37130	+	7.10487i	0.267362	+	0.563453i
$160$	0.696878	+	0.232652i	0.0550930	+	0.0183927i
$161$	−16.9119	−	24.5012i	−1.33285	−	1.93096i
$162$	0.610774	−	1.28718i	0.0479869	−	0.101130i
$163$	−0.872885	−	21.6604i	−0.0683697	−	1.69658i	−0.562187	−	0.827010i	$-0.690040\pi$
$163$	−0.872885	−	21.6604i	−0.0683697	−	1.69658i	0.493818	−	0.869566i	$-0.335601\pi$
$164$	0.116098	−	0.0286157i	0.00906575	−	0.00223451i
$165$	7.42431	−	3.16320i	0.577982	−	0.246255i
$166$	−10.2715	−	1.66929i	−0.797226	−	0.129562i
$167$	1.65189	+	8.09147i	0.127827	+	0.626137i	0.992341	+	0.123528i	$0.0394210\pi$
$167$	1.65189	+	8.09147i	0.127827	+	0.626137i	−0.864514	+	0.502608i	$0.832374\pi$
$168$	11.4062			0.880008
$169$	1.42040	+	12.9222i	0.109261	+	0.994013i
$170$	−16.8834			−1.29489
$171$	0.179132	+	0.877445i	0.0136985	+	0.0670999i
$172$	0.287832	+	0.0467773i	0.0219470	+	0.00356673i
$173$	0.118729	−	0.0505858i	0.00902681	−	0.00384596i	−0.387448	−	0.921891i	$-0.626643\pi$
$173$	0.118729	−	0.0505858i	0.00902681	−	0.00384596i	0.396475	+	0.918045i	$0.370233\pi$
$174$	3.13456	−	0.772599i	0.237630	−	0.0585705i
$175$	2.27488	+	56.4505i	0.171964	+	4.26725i
$176$	−3.22970	+	6.80646i	−0.243448	+	0.513056i
$177$	2.80892	+	4.06942i	0.211131	+	0.305876i
$178$	0.571494	+	0.190793i	0.0428353	+	0.0143005i
$179$	−5.05242	−	10.6478i	−0.377636	−	0.795851i	−0.999915	−	0.0130551i	$-0.995844\pi$
$179$	−5.05242	−	10.6478i	−0.377636	−	0.795851i	0.622279	−	0.782796i	$-0.286207\pi$
$180$	−0.123202	+	0.0411309i	−0.00918293	+	0.00306571i
$181$	1.76002	−	0.433807i	0.130822	−	0.0322446i	−0.173361	−	0.984858i	$-0.555463\pi$
$181$	1.76002	−	0.433807i	0.130822	−	0.0322446i	0.304183	+	0.952614i	$0.401617\pi$
$182$	−11.7605	−	17.2465i	−0.871743	−	1.27840i
$183$	−0.731792	−	0.180371i	−0.0540956	−	0.0133334i
$184$	20.4975	−	1.65473i	1.51110	−	0.121988i
$185$	−7.72285	+	8.04034i	−0.567795	+	0.591138i
$186$	2.67673	−	5.64108i	0.196267	−	0.413624i
$187$	0.609806	−	5.02220i	0.0445934	−	0.367260i
$188$	0.147138	+	0.254850i	0.0107311	+	0.0185869i
$189$	−3.24863	+	2.44119i	−0.236303	+	0.177570i
$190$	3.15126	−	4.56538i	0.228616	−	0.331208i
$191$	−4.40811	−	7.63507i	−0.318960	−	0.552454i	0.661312	−	0.750111i	$-0.270000\pi$
$191$	−4.40811	−	7.63507i	−0.318960	−	0.552454i	−0.980271	+	0.197657i	$0.936667\pi$
$192$	−3.93848	+	6.82165i	−0.284235	+	0.492310i
$193$	−0.305377	−	0.643568i	−0.0219815	−	0.0463250i	0.892163	−	0.451714i	$-0.149187\pi$
$193$	−0.305377	−	0.643568i	−0.0219815	−	0.0463250i	−0.914144	+	0.405389i	$0.867136\pi$
$194$	−13.8342	+	7.26076i	−0.993239	+	0.521292i
$195$	−12.4785	−	9.48823i	−0.893601	−	0.679467i
$196$	0.251642	+	0.132072i	0.0179744	+	0.00943370i
$197$	0.725788	−	18.0102i	0.0517102	−	1.28318i	−0.740137	−	0.672456i	$-0.765239\pi$
$197$	0.725788	−	18.0102i	0.0517102	−	1.28318i	0.791847	−	0.610720i	$-0.209120\pi$
$198$	−0.528973	−	2.59108i	−0.0375925	−	0.184140i
$199$	3.83049	+	13.2244i	0.271536	+	0.937451i	0.974154	+	0.225884i	$0.0725270\pi$
$199$	3.83049	+	13.2244i	0.271536	+	0.937451i	−0.702618	+	0.711567i	$0.747986\pi$
$200$	−34.5543	−	18.1355i	−2.44336	−	1.28237i
$201$	−8.74408	−	5.52942i	−0.616760	−	0.390015i
$202$	−3.60377	+	0.585670i	−0.253560	+	0.0412076i
$203$	−8.94034	−	2.20360i	−0.627489	−	0.154662i
$204$	−0.0162871	+	0.0797795i	−0.00114033	+	0.00558568i
$205$	−17.3455	+	1.40028i	−1.21147	+	0.0977996i
$206$	9.80903	−	6.20286i	0.683428	−	0.432174i
$207$	−5.48379	+	4.85822i	−0.381150	+	0.337669i
$208$	14.5934	−	1.09478i	1.01187	−	0.0759092i
$209$	1.24422	+	1.10228i	0.0860646	+	0.0762466i
$210$	24.8457	+	4.03782i	1.71452	+	0.278636i
$211$	5.81917	+	2.47932i	0.400608	+	0.170683i	0.582867	−	0.812567i	$-0.301931\pi$
$211$	5.81917	+	2.47932i	0.400608	+	0.170683i	−0.182259	+	0.983251i	$0.558341\pi$
$212$	−0.198566	−	0.125565i	−0.0136376	−	0.00862387i
$213$	−10.4400	+	9.24905i	−0.715338	+	0.633735i
$214$	21.4653	+	1.73286i	1.46734	+	0.118456i
$215$	−40.2550	−	13.4391i	−2.74537	−	0.916539i
$216$	−0.338336	−	2.78644i	−0.0230208	−	0.189594i
$217$	−14.2372	+	10.6985i	−0.966482	+	0.726264i
$218$	6.01757	+	7.37018i	0.407561	+	0.499172i
$219$	−2.93644	−	3.59649i	−0.198426	−	0.243028i
$220$	−0.136954	+	0.198412i	−0.00923344	+	0.0133769i
$221$	−9.06256	+	3.80057i	−0.609614	+	0.255654i
$222$	2.07532	+	3.00662i	0.139286	+	0.201791i
$223$	−2.94873	+	10.1802i	−0.197462	+	0.681716i	0.799273	+	0.600968i	$0.205218\pi$
$223$	−2.94873	+	10.1802i	−0.197462	+	0.681716i	−0.996735	+	0.0807481i	$0.974269\pi$
$224$	−0.580370	+	0.367004i	−0.0387776	+	0.0245215i
$225$	13.7229	−	2.23019i	0.914861	−	0.148679i
$226$	−1.00569	−	2.65178i	−0.0668973	−	0.176394i
$227$	−0.486553	+	0.207301i	−0.0322936	+	0.0137590i	−0.408053	−	0.912958i	$-0.633792\pi$
$227$	−0.486553	+	0.207301i	−0.0322936	+	0.0137590i	0.375759	+	0.926717i	$0.377382\pi$
$228$	−0.0185330	−	0.0192949i	−0.00122738	−	0.00127784i
$229$	−5.60023	+	2.93923i	−0.370073	+	0.194230i	−0.639499	−	0.768792i	$-0.720858\pi$
$229$	−5.60023	+	2.93923i	−0.370073	+	0.194230i	0.269426	+	0.963021i	$0.413166\pi$
$230$	45.2347	+	3.65172i	2.98269	+	0.240788i
$231$	−2.09851	+	7.24489i	−0.138072	+	0.476678i
$232$	4.40593	−	4.58705i	0.289263	−	0.301155i
$233$	−10.5295	+	27.7640i	−0.689811	+	1.81888i	−0.127711	+	0.991811i	$0.540763\pi$
$233$	−10.5295	+	27.7640i	−0.689811	+	1.81888i	−0.562099	+	0.827070i	$0.690006\pi$
$234$	−3.86434	+	3.38456i	−0.252620	+	0.221256i
$235$	−15.1868	−	40.0442i	−0.990676	−	2.61220i
$236$	−0.135899	−	0.0579014i	−0.00884630	−	0.00376906i
$237$	−0.503439	+	12.4927i	−0.0327019	+	0.811489i
$238$	9.97998	−	12.2233i	0.646906	−	0.792316i
$239$	18.0120			1.16510			0.582548	−	0.812796i	$-0.302056\pi$
$239$	18.0120			1.16510			0.582548	+	0.812796i	$0.302056\pi$
$240$	−11.1607	+	13.6694i	−0.720420	+	0.882355i
$241$	−3.96173	−	13.6775i	−0.255198	−	0.881045i	−0.981142	−	0.193291i	$-0.938084\pi$
$241$	−3.96173	−	13.6775i	−0.255198	−	0.881045i	0.725944	−	0.687754i	$-0.241403\pi$
$242$	8.05657	+	7.13750i	0.517896	+	0.458816i
$243$	0.692724	+	0.721202i	0.0444383	+	0.0462652i
$244$	0.0213574	−	0.00713013i	0.00136726	−	0.000456460i
$245$	−33.0650	−	24.8468i	−2.11245	−	1.58740i
$246$	−0.687365	+	5.66096i	−0.0438248	+	0.360930i
$247$	0.663812	−	3.15996i	0.0422374	−	0.201063i
$248$	−1.48276	−	12.2116i	−0.0941554	−	0.775440i
$249$	3.65201	−	6.32546i	0.231437	−	0.400860i
$250$	−44.0880	−	33.1300i	−2.78837	−	2.09533i
$251$	−0.537326	−	13.3336i	−0.0339157	−	0.841610i	−0.923215	−	0.384284i	$-0.874448\pi$
$251$	−0.537326	−	13.3336i	−0.0339157	−	0.841610i	0.889299	−	0.457326i	$-0.151193\pi$
$252$	0.0430483	−	0.113509i	0.00271179	−	0.00715040i
$253$	−2.72008	+	13.3238i	−0.171010	+	0.837663i
$254$	3.54124	−	17.3461i	0.222197	−	1.08839i
$255$	4.20212	−	11.0801i	0.263147	−	0.693862i
$256$	−0.0288637	−	0.716244i	−0.00180398	−	0.0447653i
$257$	1.49457	+	1.12309i	0.0932285	+	0.0700567i	0.646334	−	0.763054i	$-0.276301\pi$
$257$	1.49457	+	1.12309i	0.0932285	+	0.0700567i	−0.553106	+	0.833111i	$0.686558\pi$
$258$	−6.95353	+	12.0439i	−0.432908	+	0.749819i
$259$	−1.25598	−	10.3440i	−0.0780431	−	0.642743i
$260$	0.466572	+	0.0403320i	0.0289356	+	0.00250129i
$261$	−0.273129	+	2.24942i	−0.0169062	+	0.139235i
$262$	−11.4094	−	8.57360i	−0.704874	−	0.529679i
$263$	25.7756	−	8.60517i	1.58939	−	0.530618i	0.621810	−	0.783168i	$-0.286398\pi$
$263$	25.7756	−	8.60517i	1.58939	−	0.530618i	0.967584	+	0.252550i	$0.0812693\pi$
$264$	−3.60913	−	3.75750i	−0.222126	−	0.231258i
$265$	25.5926	+	22.6731i	1.57214	+	1.39280i
$266$	1.44251	+	4.98012i	0.0884458	+	0.305350i
$267$	−0.267452	+	0.327569i	−0.0163678	+	0.0200469i
$268$	0.309071			0.0188795
$269$	5.44461	−	6.66843i	0.331963	−	0.406581i	−0.581471	−	0.813567i	$-0.697523\pi$
$269$	5.44461	−	6.66843i	0.331963	−	0.406581i	0.913435	+	0.406986i	$0.133420\pi$
$270$	0.249423	−	6.18938i	0.0151794	−	0.376674i
$271$	−12.5284	−	5.33785i	−0.761045	−	0.324251i	−0.0236568	−	0.999720i	$-0.507531\pi$
$271$	−12.5284	−	5.33785i	−0.761045	−	0.324251i	−0.737388	+	0.675469i	$0.763941\pi$
$272$	3.92290	+	10.3438i	0.237861	+	0.627188i
$273$	14.2455	−	3.42556i	0.862177	−	0.207324i
$274$	10.7798	−	28.4239i	0.651230	−	1.71715i
$275$	17.8764	−	18.6113i	1.07799	−	1.12231i
$276$	0.0608928	−	0.210226i	0.00366532	−	0.0126541i
$277$	−23.7092	−	1.91401i	−1.42455	−	0.115002i	−0.655985	−	0.754774i	$-0.727747\pi$
$277$	−23.7092	−	1.91401i	−1.42455	−	0.115002i	−0.768565	+	0.639772i	$0.779029\pi$
$278$	9.50020	−	4.98609i	0.569784	−	0.299046i
$279$	3.03588	+	3.16068i	0.181753	+	0.189225i
$280$	45.6230	−	19.4382i	2.72650	−	1.16165i
$281$	3.54651	+	9.35139i	0.211567	+	0.557857i	0.998226	−	0.0595304i	$-0.0189603\pi$
$281$	3.54651	+	9.35139i	0.211567	+	0.557857i	−0.786659	+	0.617387i	$0.788191\pi$
$282$	−13.8526	+	2.25126i	−0.824907	+	0.134061i
$283$	8.53918	−	5.39985i	0.507601	−	0.320988i	−0.255999	−	0.966677i	$-0.582404\pi$
$283$	8.53918	−	5.39985i	0.507601	−	0.320988i	0.763600	+	0.645689i	$0.223430\pi$
$284$	0.115928	−	0.400228i	0.00687903	−	0.0237492i
$285$	2.21182	+	3.20437i	0.131017	+	0.189810i
$286$	−1.96023	+	9.33130i	−0.115911	+	0.551771i
$287$	9.23941	−	13.3856i	0.545385	−	0.790127i
$288$	0.106871	+	0.130893i	0.00629745	+	0.00771297i
$289$	6.05326	+	7.41390i	0.356074	+	0.436112i
$290$	11.2211	−	8.43210i	0.658925	−	0.495150i
$291$	−1.32182	−	10.8862i	−0.0774865	−	0.638159i
$292$	0.131568	+	0.0439239i	0.00769945	+	0.00257045i
$293$	−11.0597	−	0.892832i	−0.646115	−	0.0521598i	−0.246934	−	0.969032i	$-0.579423\pi$
$293$	−11.0597	−	0.892832i	−0.646115	−	0.0521598i	−0.399180	+	0.916872i	$0.630705\pi$
$294$	−10.1449	+	8.98763i	−0.591665	+	0.524169i
$295$	18.1702	+	11.4901i	1.05791	+	0.668982i
$296$	6.62154	+	2.82117i	0.384869	+	0.163977i
$297$	1.83211	+	0.297747i	0.106310	+	0.0172771i
$298$	−7.79044	−	6.90173i	−0.451288	−	0.399807i
$299$	25.1029	−	8.22253i	1.45174	−	0.475521i
$300$	−0.310888	+	0.275423i	−0.0179491	+	0.0159015i
$301$	33.5250	−	21.1999i	1.93235	−	1.22194i
$302$	−29.1677	+	2.35466i	−1.67841	+	0.135495i
$303$	0.512589	−	2.51083i	0.0294475	−	0.144243i
$304$	−3.52926	−	0.869884i	−0.202417	−	0.0498913i
$305$	−3.23444	+	0.525647i	−0.185203	+	0.0300985i
$306$	−3.28207	−	2.07546i	−0.187624	−	0.118646i
$307$	−15.4032	−	8.08420i	−0.879105	−	0.461390i	−0.0361327	−	0.999347i	$-0.511504\pi$
$307$	−15.4032	−	8.08420i	−0.879105	−	0.461390i	−0.842972	+	0.537957i	$0.819196\pi$
$308$	−0.0626916	−	0.216436i	−0.00357218	−	0.0123326i
$309$	1.62938	+	7.98124i	0.0926923	+	0.454037i
$310$	1.09310	−	27.1251i	0.0620840	−	1.54060i
$311$	−10.8876	−	5.71426i	−0.617380	−	0.324026i	0.126878	−	0.991918i	$-0.459504\pi$
$311$	−10.8876	−	5.71426i	−0.617380	−	0.324026i	−0.744258	+	0.667892i	$0.767197\pi$
$312$	−2.87081	+	9.70475i	−0.162528	+	0.549423i
$313$	9.21247	−	4.83508i	0.520719	−	0.273295i	−0.183819	−	0.982960i	$-0.558846\pi$
$313$	9.21247	−	4.83508i	0.520719	−	0.273295i	0.704539	+	0.709665i	$0.251154\pi$
$314$	5.03355	+	10.6080i	0.284060	+	0.598643i
$315$	−8.83380	+	15.3006i	−0.497728	+	0.862091i
$316$	−0.186757	−	0.323473i	−0.0105059	−	0.0181968i
$317$	13.7283	−	19.8889i	0.771061	−	1.11707i	−0.218902	−	0.975747i	$-0.570248\pi$
$317$	13.7283	−	19.8889i	0.771061	−	1.11707i	0.989963	−	0.141327i	$-0.0451370\pi$
$318$	8.95723	−	6.73092i	0.502296	−	0.377451i
$319$	2.10296	+	3.64244i	0.117743	+	0.203937i
$320$	−4.12803	+	33.9974i	−0.230764	+	1.90051i
$321$	−6.47977	+	13.6558i	−0.361665	+	0.762193i
$322$	−29.3826	+	30.5906i	−1.63743	+	1.70475i
$323$	2.43296	−	0.196409i	0.135374	−	0.0109285i
$324$	−0.0290063	−	0.00714941i	−0.00161146	−	0.000397189i
$325$	−48.6023	−	12.2724i	−2.69597	−	0.680750i
$326$	−29.9880	+	7.39137i	−1.66088	+	0.409370i
$327$	−6.33457	+	2.11479i	−0.350303	+	0.116948i
$328$	4.81624	+	10.1500i	0.265932	+	0.560441i
$329$	37.9684	+	12.6757i	2.09327	+	0.698835i
$330$	−6.53146	−	9.46246i	−0.359545	−	0.520891i
$331$	−0.767037	+	1.61650i	−0.0421602	+	0.0888507i	−0.923438	−	0.383749i	$-0.874633\pi$
$331$	−0.767037	+	1.61650i	−0.0421602	+	0.0888507i	0.881277	+	0.472599i	$0.156684\pi$
$332$	0.00878615	+	0.218026i	0.000482202	+	0.0119657i
$333$	−2.48969	+	0.613654i	−0.136434	+	0.0336280i
$334$	10.8245	−	4.61188i	0.592289	−	0.252351i
$335$	−44.3981	−	7.21539i	−2.42573	−	0.394219i
$336$	−3.29915	−	16.1603i	−0.179983	−	0.881617i
$337$	−22.9545			−1.25041			−0.625205	−	0.780461i	$-0.714985\pi$
$337$	−22.9545			−1.25041			−0.625205	+	0.780461i	$0.714985\pi$
$338$	17.6338	−	5.66541i	0.959154	−	0.308157i
$339$	1.99060			0.108114
$340$	0.0708123	+	0.346862i	0.00384034	+	0.0188112i
$341$	8.02927	+	1.30488i	0.434809	+	0.0706634i
$342$	1.17381	−	0.500115i	0.0634726	−	0.0270431i
$343$	9.91508	−	2.44385i	0.535364	−	0.131955i
$344$	1.10323	+	27.3765i	0.0594824	+	1.47604i
$345$	−13.6551	+	28.7774i	−0.735164	+	1.54933i
$346$	−0.104451	−	0.151323i	−0.00561531	−	0.00813518i
$347$	−3.61858	−	1.20806i	−0.194255	−	0.0648520i	0.217876	−	0.975977i	$-0.430087\pi$
$347$	−3.61858	−	1.20806i	−0.194255	−	0.0648520i	−0.412131	+	0.911125i	$0.635215\pi$
$348$	−0.0290197	−	0.0611577i	−0.00155562	−	0.00327840i
$349$	33.1661	−	11.0725i	1.77534	−	0.592696i	0.776063	−	0.630655i	$-0.217214\pi$
$349$	33.1661	−	11.0725i	1.77534	−	0.592696i	0.999279	+	0.0379586i	$0.0120855\pi$
$350$	78.1533	−	19.2631i	4.17747	−	1.02965i
$351$	−1.25939	−	3.37845i	−0.0672214	−	0.180328i
$352$	0.304540	+	0.0750623i	0.0162320	+	0.00400083i
$353$	21.4431	−	1.73106i	1.14130	−	0.0921352i	0.504675	−	0.863309i	$-0.331612\pi$
$353$	21.4431	−	1.73106i	1.14130	−	0.0921352i	0.636624	+	0.771174i	$0.280330\pi$
$354$	4.88018	−	5.08081i	0.259379	−	0.270042i
$355$	−25.9965	+	54.7864i	−1.37975	+	2.90776i
$356$	0.00152279	−	0.0125413i	8.07079e−5	−	0.000664689i
$357$	5.53786	+	9.59186i	0.293095	+	0.507655i
$358$	−13.4238	+	10.0873i	−0.709470	+	0.533132i
$359$	12.0050	−	17.3922i	0.633600	−	0.917928i	−0.366321	−	0.930488i	$-0.619383\pi$
$359$	12.0050	−	17.3922i	0.633600	−	0.917928i	0.999921	+	0.0125606i	$0.00399828\pi$
$360$	−6.10188	−	10.5688i	−0.321597	−	0.557022i
$361$	9.09900	−	15.7599i	0.478895	−	0.829470i
$362$	−1.10715	−	2.33327i	−0.0581905	−	0.122634i
$363$	−6.68936	+	3.51085i	−0.351100	+	0.184272i
$364$	−0.304997	+	0.313949i	−0.0159862	+	0.0164554i
$365$	−17.8743	−	9.38117i	−0.935585	−	0.491033i
$366$	−0.0432381	+	1.07294i	−0.00226009	+	0.0560837i
$367$	−5.67289	−	27.7877i	−0.296122	−	1.45050i	−0.806848	−	0.590760i	$-0.798828\pi$
$367$	−5.67289	−	27.7877i	−0.296122	−	1.45050i	0.510725	−	0.859744i	$-0.329377\pi$
$368$	−8.27315	−	28.5622i	−0.431268	−	1.48891i
$369$	−3.54406	−	1.86006i	−0.184496	−	0.0968311i
$370$	13.4247	+	8.48930i	0.697919	+	0.441338i
$371$	−31.5430	+	5.12624i	−1.63763	+	0.266141i
$372$	−0.127121	−	0.0313324i	−0.00659089	−	0.00162451i
$373$	−1.32451	+	6.48786i	−0.0685803	+	0.335928i	−0.999576	−	0.0291004i	$-0.990736\pi$
$373$	−1.32451	+	6.48786i	−0.0685803	+	0.335928i	0.930996	+	0.365029i	$0.118941\pi$
$374$	−7.18450	+	0.579993i	−0.371502	+	0.0299907i
$375$	32.7155	−	20.6880i	1.68942	−	1.06832i
$376$	−20.6958	+	18.3349i	−1.06730	+	0.945550i
$377$	4.12507	−	7.05209i	0.212452	−	0.363201i
$378$	4.33357	+	3.83920i	0.222895	+	0.197467i
$379$	4.10346	+	0.666878i	0.210781	+	0.0342552i	0.264885	−	0.964280i	$-0.414666\pi$
$379$	4.10346	+	0.666878i	0.210781	+	0.0342552i	−0.0541039	+	0.998535i	$0.517230\pi$
$380$	−0.107011	−	0.0455931i	−0.00548955	−	0.00233888i
$381$	10.5024	+	6.64132i	0.538055	+	0.340245i
$382$	−9.40189	+	8.32935i	−0.481042	+	0.426166i
$383$	10.8905	+	0.879170i	0.556477	+	0.0449235i	0.355507	−	0.934674i	$-0.384308\pi$
$383$	10.8905	+	0.879170i	0.556477	+	0.0449235i	0.200971	+	0.979597i	$0.435590\pi$
$384$	10.9656	+	3.66086i	0.559586	+	0.186817i
$385$	3.95285	+	32.5546i	0.201456	+	1.65914i
$386$	−0.811357	+	0.609695i	−0.0412970	+	0.0310327i
$387$	−6.17339	−	7.56104i	−0.313811	−	0.384349i
$388$	0.207193	+	0.253765i	0.0105186	+	0.0128830i
$389$	−1.70212	+	2.46594i	−0.0863007	+	0.125028i	−0.863756	−	0.503909i	$-0.831895\pi$
$389$	−1.70212	+	2.46594i	−0.0863007	+	0.125028i	0.777456	+	0.628938i	$0.216510\pi$
$390$	−9.68888	+	20.1232i	−0.490616	+	1.01898i
$391$	11.3433	+	16.4336i	0.573656	+	0.831085i
$392$	−7.42899	+	25.6478i	−0.375221	+	1.29541i
$393$	8.46632	−	5.35378i	0.427070	−	0.270062i
$394$	−25.3481	+	4.11947i	−1.27702	+	0.207536i
$395$	19.2761	+	50.8268i	0.969885	+	2.55738i
$396$	−0.0510141	+	0.0217351i	−0.00256355	+	0.00109223i
$397$	7.16388	+	7.45839i	0.359545	+	0.374326i	0.876266	−	0.481828i	$-0.160027\pi$
$397$	7.16388	+	7.45839i	0.359545	+	0.374326i	−0.516721	+	0.856154i	$0.672848\pi$
$398$	17.3689	−	9.11588i	0.870622	−	0.456938i
$399$	−3.62734	−	0.292829i	−0.181594	−	0.0146598i
$400$	−15.6998	+	54.2021i	−0.784992	+	2.71011i
$401$	−3.31909	+	3.45554i	−0.165747	+	0.172561i	−0.798897	−	0.601469i	$-0.794583\pi$
$401$	−3.31909	+	3.45554i	−0.165747	+	0.172561i	0.633149	+	0.774030i	$0.281762\pi$
$402$	−5.22684	+	13.7820i	−0.260691	+	0.687386i
$403$	−5.51931	−	14.8061i	−0.274936	−	0.737545i
$404$	0.0271473	+	0.0715816i	0.00135063	+	0.00356132i
$405$	3.99984	+	1.70417i	0.198754	+	0.0846811i
$406$	−0.528243	+	13.1082i	−0.0262162	+	0.650549i
$407$	−3.01015	+	3.68677i	−0.149208	+	0.182746i
$408$	−7.65047			−0.378754
$409$	−18.4617	+	22.6115i	−0.912874	+	1.11807i	0.0797474	+	0.996815i	$0.474589\pi$
$409$	−18.4617	+	22.6115i	−0.912874	+	1.11807i	−0.992622	+	0.121253i	$0.961309\pi$
$410$	6.89791	+	23.8144i	0.340664	+	1.17611i
$411$	15.9709	+	14.1490i	0.787785	+	0.697916i
$412$	−0.168576	−	0.175507i	−0.00830516	−	0.00864659i
$413$	−19.0593	+	6.36294i	−0.937848	+	0.313100i
$414$	8.34459	+	6.27055i	0.410114	+	0.308181i
$415$	3.82777	−	31.5245i	0.187898	−	1.54748i
$416$	−0.166185	−	0.586167i	−0.00814791	−	0.0287392i
$417$	0.907717	+	7.47572i	0.0444511	+	0.366088i
$418$	1.18414	−	2.05100i	0.0579183	−	0.100318i
$419$	11.2592	+	8.46072i	0.550047	+	0.413333i	0.839098	−	0.543980i	$-0.183083\pi$
$419$	11.2592	+	8.46072i	0.550047	+	0.413333i	−0.289051	+	0.957314i	$0.593340\pi$
$420$	−0.0212527	−	0.527381i	−0.00103703	−	0.0257335i
$421$	10.8900	−	28.7146i	0.530747	−	1.39946i	−0.354812	−	0.934938i	$-0.615455\pi$
$421$	10.8900	−	28.7146i	0.530747	−	1.39946i	0.885559	−	0.464527i	$-0.153776\pi$
$422$	1.80262	−	8.82980i	0.0877500	−	0.429828i
$423$	1.97034	−	9.65138i	0.0958013	−	0.469266i
$424$	7.82753	−	20.6395i	0.380138	−	1.00234i
$425$	−1.52582	−	37.8629i	−0.0740133	−	1.83662i
$426$	15.8864	+	11.9378i	0.769698	+	0.578391i
$427$	1.53136	−	2.65239i	0.0741077	−	0.128358i
$428$	−0.0544291	−	0.448264i	−0.00263093	−	0.0216677i
$429$	−5.63600	−	3.60893i	−0.272109	−	0.174241i
$430$	−7.28819	+	60.0236i	−0.351468	+	2.89460i
$431$	−12.8738	−	9.67404i	−0.620110	−	0.465982i	0.243666	−	0.969859i	$-0.421650\pi$
$431$	−12.8738	−	9.67404i	−0.620110	−	0.465982i	−0.863775	+	0.503877i	$0.831906\pi$
$432$	−3.84997	+	1.28531i	−0.185232	+	0.0618395i
$433$	−9.30491	−	9.68744i	−0.447165	−	0.465549i	0.459022	−	0.888425i	$-0.348200\pi$
$433$	−9.30491	−	9.68744i	−0.447165	−	0.465549i	−0.906187	+	0.422876i	$0.861020\pi$
$434$	18.9919	+	16.8254i	0.911642	+	0.807644i
$435$	2.74093	+	9.46278i	0.131417	+	0.453705i
$436$	0.126178	−	0.154541i	0.00604285	−	0.00740115i
$437$	−6.56099			−0.313855
$438$	−4.18365	+	5.12404i	−0.199903	+	0.244836i
$439$	0.00827921	−	0.205447i	0.000395145	−	0.00980543i	−0.998979	−	0.0451682i	$-0.985618\pi$
$439$	0.00827921	−	0.205447i	0.000395145	−	0.00980543i	0.999375	+	0.0353627i	$0.0112587\pi$
$440$	−20.8394	−	8.87883i	−0.993478	−	0.423281i
$441$	−3.37335	−	8.89480i	−0.160636	−	0.423562i
$442$	7.88807	+	11.5677i	0.375197	+	0.550221i
$443$	−2.67438	+	7.05177i	−0.127064	+	0.335039i	−0.983419	−	0.181347i	$-0.941954\pi$
$443$	−2.67438	+	7.05177i	−0.127064	+	0.335039i	0.856355	+	0.516387i	$0.172723\pi$
$444$	0.0530654	−	0.0552470i	0.00251837	−	0.00262190i
$445$	−0.511531	+	1.76601i	−0.0242489	+	0.0837169i
$446$	15.0513	+	1.21507i	0.712701	+	0.0575351i
$447$	6.46840	−	3.39488i	0.305945	−	0.160572i
$448$	−22.1734	−	23.0849i	−1.04759	−	1.09066i
$449$	−1.15205	+	0.490845i	−0.0543688	+	0.0231644i	−0.418980	−	0.907996i	$-0.637612\pi$
$449$	−1.15205	+	0.490845i	−0.0543688	+	0.0231644i	0.364611	+	0.931160i	$0.381202\pi$
$450$	−7.02403	−	18.5208i	−0.331116	−	0.873081i
$451$	−7.33308	+	1.19174i	−0.345301	+	0.0561169i
$452$	−0.0502616	+	0.0317835i	−0.00236411	+	0.00149497i
$453$	5.71429	−	19.7280i	0.268481	−	0.926903i
$454$	0.428040	+	0.620123i	0.0200889	+	0.0291038i
$455$	51.1420	−	37.9785i	2.39757	−	1.78046i
$456$	1.42795	−	2.06874i	0.0668699	−	0.0968777i
$457$	12.2395	+	14.9907i	0.572541	+	0.701235i	0.976980	−	0.213329i	$-0.0684308\pi$
$457$	12.2395	+	14.9907i	0.572541	+	0.701235i	−0.404439	+	0.914565i	$0.632533\pi$
$458$	5.69897	+	6.97997i	0.266295	+	0.326153i
$459$	2.17895	−	1.63737i	0.101705	−	0.0764260i
$460$	−0.114701	−	0.944645i	−0.00534795	−	0.0440443i
$461$	−28.2372	−	9.42696i	−1.31514	−	0.439057i	−0.429346	−	0.903140i	$-0.641256\pi$
$461$	−28.2372	−	9.42696i	−1.31514	−	0.439057i	−0.885792	+	0.464083i	$0.846384\pi$
$462$	10.7115	+	0.864721i	0.498344	+	0.0402305i
$463$	−23.2706	+	20.6159i	−1.08147	+	0.958103i	−0.999258	−	0.0385120i	$-0.987738\pi$
$463$	−23.2706	+	20.6159i	−1.08147	+	0.958103i	−0.0822160	+	0.996615i	$0.526200\pi$
$464$	−7.77331	−	4.91555i	−0.360867	−	0.228199i
$465$	17.5294	+	7.46857i	0.812905	+	0.346347i
$466$	41.7577	+	6.78629i	1.93439	+	0.314369i
$467$	6.37967	+	5.65190i	0.295216	+	0.261539i	0.797709	−	0.603043i	$-0.206045\pi$
$467$	6.37967	+	5.65190i	0.295216	+	0.261539i	−0.502493	+	0.864581i	$0.667584\pi$
$468$	0.0857422	+	0.0651958i	0.00396344	+	0.00301368i
$469$	31.4681	−	27.8783i	1.45306	−	1.28730i
$470$	−51.5715	+	32.6118i	−2.37882	+	1.50427i
$471$	−8.21454	+	0.663146i	−0.378506	+	0.0305562i
$472$	2.77623	−	13.5989i	0.127786	−	0.625938i
$473$	−17.5917	−	4.33596i	−0.808866	−	0.199368i
$474$	17.5826	−	2.85745i	0.807595	−	0.131247i
$475$	10.5232	+	6.65447i	0.482838	+	0.305328i
$476$	−0.292980	−	0.153768i	−0.0134287	−	0.00704793i
$477$	2.18794	+	7.55365i	0.100179	+	0.345858i
$478$	−5.13312	−	25.1437i	−0.234783	−	1.15005i
$479$	−1.19495	+	29.6523i	−0.0545984	+	1.35485i	0.707191	+	0.707022i	$0.249962\pi$
$479$	−1.19495	+	29.6523i	−0.0545984	+	1.35485i	−0.761790	+	0.647824i	$0.775679\pi$
$480$	0.650533	+	0.341426i	0.0296926	+	0.0155839i
$481$	9.11708	+	1.53483i	0.415703	+	0.0699821i
$482$	−17.9640	+	9.42822i	−0.818237	+	0.429444i
$483$	−12.7627	−	26.8968i	−0.580722	−	1.22385i
$484$	0.112846	−	0.195455i	0.00512937	−	0.00888432i
$485$	−23.8390	−	41.2904i	−1.08247	−	1.87490i
$486$	0.809343	−	1.17254i	0.0367125	−	0.0531873i
$487$	12.1927	−	9.16225i	0.552506	−	0.415181i	−0.287482	−	0.957786i	$-0.592818\pi$
$487$	12.1927	−	9.16225i	0.552506	−	0.415181i	0.839988	+	0.542605i	$0.182562\pi$
$488$	1.05777	+	1.83212i	0.0478832	+	0.0829361i
$489$	2.61300	−	21.5200i	0.118164	−	0.973166i
$490$	−25.2617	+	53.2379i	−1.14121	+	2.40504i
$491$	12.5304	−	13.0455i	0.565489	−	0.588736i	−0.375648	−	0.926763i	$-0.622580\pi$
$491$	12.5304	−	13.0455i	0.565489	−	0.588736i	0.941137	+	0.338026i	$0.109759\pi$
$492$	0.119185	−	0.00962162i	0.00537328	−	0.000433776i
$493$	5.99654	+	1.47801i	0.270071	+	0.0665664i
$494$	−4.60030	−	0.0261082i	−0.206977	−	0.00117466i
$495$	7.83558	−	1.93130i	0.352183	−	0.0868054i
$496$	−16.8726	+	5.63289i	−0.757601	+	0.252924i
$497$	−24.2975	−	51.2060i	−1.08989	−	2.29690i
$498$	−9.87076	−	3.29534i	−0.442319	−	0.147668i
$499$	−5.39589	−	7.81730i	−0.241553	−	0.349950i	0.683391	−	0.730052i	$-0.260504\pi$
$499$	−5.39589	−	7.81730i	−0.241553	−	0.349950i	−0.924945	+	0.380102i	$0.875889\pi$
$500$	−0.495728	+	1.04472i	−0.0221696	+	0.0467215i
$501$	0.332531	+	8.25167i	0.0148564	+	0.368657i
$502$	−18.4598	+	4.54994i	−0.823903	+	0.203074i
$503$	2.12203	−	0.904112i	0.0946166	−	0.0403124i	−0.344140	−	0.938918i	$-0.611829\pi$
$503$	2.12203	−	0.904112i	0.0946166	−	0.0403124i	0.438756	+	0.898606i	$0.355419\pi$
$504$	11.2585	+	1.82968i	0.501494	+	0.0815006i
$505$	−2.22861	−	10.9165i	−0.0991718	−	0.485776i
$506$	19.3745			0.861302
$507$	−0.670858	+	12.9827i	−0.0297938	+	0.576581i
$508$	−0.371222			−0.0164703
$509$	−4.55804	−	22.3268i	−0.202032	−	0.989616i	−0.946684	−	0.322164i	$-0.895590\pi$
$509$	−4.55804	−	22.3268i	−0.202032	−	0.989616i	0.744652	−	0.667452i	$-0.232615\pi$
$510$	−16.6647	−	2.70828i	−0.737926	−	0.119925i
$511$	17.3576	−	7.39537i	0.767854	−	0.327152i
$512$	21.4576	−	5.28883i	0.948303	−	0.233736i
$513$	0.0360599	+	0.894817i	0.00159208	+	0.0395071i
$514$	1.14185	−	2.40640i	0.0503648	−	0.106142i
$515$	20.1187	+	29.1470i	0.886536	+	1.28437i
$516$	0.276601	+	0.0923430i	0.0121767	+	0.00406517i
$517$	−7.83818	−	16.5186i	−0.344723	−	0.726488i
$518$	−14.0817	+	4.70115i	−0.618713	+	0.206557i
$519$	0.125306	−	0.0308852i	0.00550033	−	0.00135571i
$520$	5.05578	+	43.7098i	0.221711	+	1.91680i
$521$	23.9358	+	5.89965i	1.04865	+	0.258468i	0.725745	−	0.687964i	$-0.241495\pi$
$521$	23.9358	+	5.89965i	1.04865	+	0.258468i	0.322903	+	0.946432i	$0.395341\pi$
$522$	3.21790	−	0.259776i	0.140844	−	0.0113701i
$523$	−5.01037	+	5.21635i	−0.219088	+	0.228095i	−0.821672	−	0.569961i	$-0.806958\pi$
$523$	−5.01037	+	5.21635i	−0.219088	+	0.228095i	0.602584	+	0.798056i	$0.294138\pi$
$524$	−0.128288	+	0.270361i	−0.00560428	+	0.0118108i
$525$	−6.80987	+	56.0844i	−0.297207	+	2.44772i
$526$	−19.3580	−	33.5290i	−0.844048	−	1.46193i
$527$	9.54927	−	7.17581i	0.415973	−	0.312583i
$528$	−4.27971	+	6.20024i	−0.186251	+	0.269831i
$529$	−15.3371	−	26.5647i	−0.666832	−	1.15499i
$530$	24.3568	−	42.1873i	1.05799	−	1.83250i
$531$	2.11976	+	4.46730i	0.0919898	+	0.193864i
$532$	0.0962643	−	0.0505234i	0.00417359	−	0.00219047i
$533$	9.06342	+	11.2302i	0.392580	+	0.486433i
$534$	0.533488	+	0.279996i	0.0230863	+	0.0121166i
$535$	−2.64616	+	65.6638i	−0.114403	+	2.83889i
$536$	5.80864	+	28.4526i	0.250895	+	1.22896i
$537$	−3.27898	−	11.3203i	−0.141498	−	0.488509i
$538$	−10.8604	−	5.69997i	−0.468224	−	0.245743i
$539$	−14.9240	−	9.43735i	−0.642821	−	0.406495i
$540$	−0.128204	+	0.0208352i	−0.00551704	+	0.000896606i
$541$	11.8839	+	2.92911i	0.510928	+	0.125932i	0.486347	−	0.873766i	$-0.338329\pi$
$541$	11.8839	+	2.92911i	0.510928	+	0.125932i	0.0245802	+	0.999698i	$0.492175\pi$
$542$	−3.88094	+	19.0101i	−0.166701	+	0.816554i
$543$	1.80682	−	0.145862i	0.0775381	−	0.00625952i
$544$	0.389270	−	0.246160i	0.0166898	−	0.0105540i
$545$	−21.7333	+	19.2540i	−0.930953	+	0.824753i
$546$	−8.84163	−	18.9097i	−0.378387	−	0.809260i
$547$	−17.4087	−	15.4228i	−0.744342	−	0.659430i	0.203172	−	0.979143i	$-0.434875\pi$
$547$	−17.4087	−	15.4228i	−0.744342	−	0.659430i	−0.947514	+	0.319713i	$0.896413\pi$
$548$	−0.629171	−	0.102250i	−0.0268768	−	0.00436791i
$549$	−0.693382	−	0.295423i	−0.0295928	−	0.0126083i
$550$	−31.0749	−	19.6505i	−1.32504	−	0.837902i
$551$	−1.51891	+	1.34564i	−0.0647078	+	0.0573261i
$552$	20.4975	+	1.65473i	0.872432	+	0.0704300i
$553$	−48.1921	−	16.0889i	−2.04934	−	0.684169i
$554$	4.08491	+	33.6422i	0.173551	+	1.42932i
$555$	−8.91260	+	6.69739i	−0.378319	+	0.284288i
$556$	−0.142283	−	0.174265i	−0.00603414	−	0.00739049i
$557$	−10.2005	−	12.4933i	−0.432207	−	0.529357i	0.511879	−	0.859058i	$-0.328950\pi$
$557$	−10.2005	−	12.4933i	−0.432207	−	0.529357i	−0.944086	+	0.329700i	$0.893052\pi$
$558$	3.54696	−	5.13866i	0.150155	−	0.217537i
$559$	9.59967	+	33.8598i	0.406023	+	1.43212i
$560$	−40.7361	−	59.0164i	−1.72141	−	2.49390i
$561$	1.40753	−	4.85935i	0.0594259	−	0.205162i
$562$	12.0433	−	7.61573i	0.508016	−	0.321250i
$563$	−13.3583	+	2.17093i	−0.562985	+	0.0914939i	−0.435242	−	0.900313i	$-0.643337\pi$
$563$	−13.3583	+	2.17093i	−0.562985	+	0.0914939i	−0.127742	+	0.991807i	$0.540773\pi$
$564$	0.104352	+	0.275153i	0.00439400	+	0.0115860i
$565$	7.96208	−	3.39232i	0.334967	−	0.142716i
$566$	−9.97141	−	10.3813i	−0.419130	−	0.436360i
$567$	−3.59815	+	1.88846i	−0.151108	+	0.0793077i
$568$	39.0231	+	3.15027i	1.63737	+	0.132182i
$569$	−2.56903	+	8.86931i	−0.107699	+	0.371821i	−0.996204	−	0.0870460i	$-0.972257\pi$
$569$	−2.56903	+	8.86931i	−0.107699	+	0.371821i	0.888505	+	0.458867i	$0.151744\pi$
$570$	3.84279	−	4.00077i	0.160957	−	0.167574i
$571$	12.2186	−	32.2177i	0.511331	−	1.34827i	−0.392253	−	0.919857i	$-0.628304\pi$
$571$	12.2186	−	32.2177i	0.511331	−	1.34827i	0.903584	−	0.428411i	$-0.140926\pi$
$572$	0.199929	+	0.00113467i	0.00835947	+	4.74428e-5i
$573$	−3.12627	−	8.24331i	−0.130602	−	0.344369i
$574$	−21.3186	−	9.08302i	−0.889822	−	0.379118i
$575$	−4.10136	+	101.774i	−0.171039	+	4.24428i
$576$	−4.98175	+	6.10153i	−0.207573	+	0.254230i
$577$	−44.2525			−1.84226			−0.921128	−	0.389260i	$-0.872731\pi$
$577$	−44.2525			−1.84226			−0.921128	+	0.389260i	$0.872731\pi$
$578$	8.62430	−	10.5629i	0.358724	−	0.439357i
$579$	−0.198187	−	0.684220i	−0.00823635	−	0.0284352i
$580$	−0.220298	−	0.195167i	−0.00914736	−	0.00810386i
$581$	20.5606	+	21.4058i	0.852996	+	0.888063i
$582$	−14.8198	+	4.94757i	−0.614300	+	0.205083i
$583$	11.6695	+	8.76906i	0.483301	+	0.363177i
$584$	−1.57089	+	12.9374i	−0.0650039	+	0.535355i
$585$	−10.7948	−	11.3670i	−0.446312	−	0.469970i
$586$	1.90550	+	15.6932i	0.0787153	+	0.648279i
$587$	14.8470	−	25.7157i	0.612800	−	1.06140i	−0.377966	−	0.925820i	$-0.623376\pi$
$587$	14.8470	−	25.7157i	0.612800	−	1.06140i	0.990766	−	0.135582i	$-0.0432904\pi$
$588$	0.227197	+	0.170728i	0.00936946	+	0.00704069i
$589$	0.158033	+	3.92155i	0.00651164	+	0.161585i
$590$	10.8614	−	28.6391i	0.447156	−	1.17905i
$591$	3.60543	−	17.6606i	0.148308	−	0.726459i
$592$	2.08181	−	10.1974i	0.0855620	−	0.419110i
$593$	−8.29187	+	21.8639i	−0.340506	+	0.897841i	0.649945	+	0.759981i	$0.274792\pi$
$593$	−8.29187	+	21.8639i	−0.340506	+	0.897841i	−0.990452	+	0.137860i	$0.955977\pi$
$594$	−0.106484	−	2.64238i	−0.00436910	−	0.108418i
$595$	38.4968	+	28.9284i	1.57821	+	1.18595i
$596$	−0.109119	+	0.188999i	−0.00446967	+	0.00774169i
$597$	1.65954	+	13.6676i	0.0679206	+	0.559377i
$598$	−18.6321	−	32.6989i	−0.761924	−	1.33716i
$599$	−4.66260	+	38.4000i	−0.190509	+	1.56898i	0.513060	+	0.858353i	$0.328512\pi$
$599$	−4.66260	+	38.4000i	−0.190509	+	1.56898i	−0.703569	+	0.710627i	$0.748411\pi$
$600$	−31.1977	−	23.4436i	−1.27364	−	0.957080i
$601$	20.4255	−	6.81905i	0.833175	−	0.278155i	0.132095	−	0.991237i	$-0.457830\pi$
$601$	20.4255	−	6.81905i	0.833175	−	0.278155i	0.701080	+	0.713082i	$0.252701\pi$
$602$	−39.1479	−	40.7573i	−1.59555	−	1.66114i
$603$	−7.74387	−	6.86047i	−0.315355	−	0.279380i
$604$	0.170711	+	0.589362i	0.00694613	+	0.0239808i
$605$	−20.7733	+	25.4427i	−0.844555	+	1.03439i
$606$	−3.65105			−0.148314
$607$	−5.93463	+	7.26860i	−0.240879	+	0.295024i	−0.880869	−	0.473360i	$-0.843041\pi$
$607$	−5.93463	+	7.26860i	−0.240879	+	0.295024i	0.639990	+	0.768383i	$0.278939\pi$
$608$	−0.00609343	+	0.151207i	−0.000247121	+	0.00613225i
$609$	−8.47109	−	3.60919i	−0.343266	−	0.146252i
$610$	1.65554	+	4.36529i	0.0670307	+	0.176745i
$611$	−20.3411	+	29.1144i	−0.822913	+	1.17784i
$612$	−0.0288737	+	0.0761338i	−0.00116715	+	0.00307753i
$613$	0.0404838	−	0.0421482i	0.00163513	−	0.00170235i	−0.720384	−	0.693575i	$-0.756035\pi$
$613$	0.0404838	−	0.0421482i	0.00163513	−	0.00170235i	0.722020	+	0.691873i	$0.243214\pi$
$614$	−6.89544	+	23.8058i	−0.278277	+	0.960724i
$615$	−17.3455	−	1.40028i	−0.699440	−	0.0564646i
$616$	18.7466	−	9.83895i	0.755320	−	0.396423i
$617$	0.874393	+	0.910340i	0.0352017	+	0.0366489i	0.738570	−	0.674176i	$-0.235501\pi$
$617$	0.874393	+	0.910340i	0.0352017	+	0.0366489i	−0.703369	+	0.710825i	$0.748322\pi$
$618$	10.6770	−	4.54905i	0.429493	−	0.182990i
$619$	−4.07338	−	10.7406i	−0.163723	−	0.431702i	0.827899	−	0.560877i	$-0.189536\pi$
$619$	−4.07338	−	10.7406i	−0.163723	−	0.431702i	−0.991622	+	0.129176i	$0.958767\pi$
$620$	−0.561858	+	0.0913108i	−0.0225648	+	0.00366713i
$621$	−6.19209	+	3.91564i	−0.248480	+	0.157129i
$622$	−4.87399	+	16.8270i	−0.195429	+	0.674700i
$623$	−0.976188	−	1.41425i	−0.0391101	−	0.0566608i
$624$	14.5800	+	1.26035i	0.583669	+	0.0504542i
$625$	56.1119	−	81.2921i	2.24448	−	3.25168i
$626$	−9.37490	−	11.4822i	−0.374696	−	0.458920i
$627$	1.05129	+	1.28760i	0.0419845	+	0.0514217i
$628$	0.196825	−	0.147904i	0.00785417	−	0.00590202i
$629$	0.842424	+	6.93799i	0.0335897	+	0.276636i
$630$	23.8763	+	7.97107i	0.951253	+	0.317575i
$631$	−27.0655	−	2.18495i	−1.07746	−	0.0869815i	−0.471029	−	0.882118i	$-0.656117\pi$
$631$	−27.0655	−	2.18495i	−1.07746	−	0.0869815i	−0.606431	+	0.795136i	$0.707399\pi$
$632$	26.2685	−	23.2719i	1.04491	−	0.925706i
$633$	5.34611	+	3.38067i	0.212489	+	0.134370i
$634$	−31.6762	−	13.4960i	−1.25802	−	0.535993i
$635$	53.3259	+	8.66631i	2.11618	+	0.343912i
$636$	−0.175852	−	0.155792i	−0.00697300	−	0.00617754i
$637$	−1.57558	+	34.2634i	−0.0624268	+	1.35756i
$638$	4.48533	−	3.97365i	0.177576	−	0.157318i
$639$	−11.7885	+	7.45458i	−0.466345	+	0.294899i
$640$	50.0994	−	4.04445i	1.98035	−	0.159871i
$641$	5.66638	−	27.7558i	0.223809	−	1.09629i	−0.700209	−	0.713937i	$-0.746910\pi$
$641$	5.66638	−	27.7558i	0.223809	−	1.09629i	0.924018	−	0.382349i	$-0.124885\pi$
$642$	20.9094	+	5.15370i	0.825227	+	0.203400i
$643$	13.3346	−	2.16709i	0.525866	−	0.0854615i	0.108318	−	0.994116i	$-0.465454\pi$
$643$	13.3346	−	2.16709i	0.525866	−	0.0854615i	0.417548	+	0.908655i	$0.362889\pi$
$644$	0.751708	+	0.475351i	0.0296214	+	0.0187315i
$645$	−37.5779	−	19.7224i	−1.47963	−	0.776569i
$646$	−0.967531	−	3.34030i	−0.0380670	−	0.131422i
$647$	−0.510036	−	2.49832i	−0.0200516	−	0.0982191i	0.968533	−	0.248884i	$-0.0800637\pi$
$647$	−0.510036	−	2.49832i	−0.0200516	−	0.0982191i	−0.988585	+	0.150665i	$0.951859\pi$
$648$	0.113023	−	2.80463i	0.00443996	−	0.110176i
$649$	8.12683	+	4.26529i	0.319006	+	0.167427i
$650$	−3.28069	+	71.3435i	−0.128679	+	2.79832i
$651$	−15.7690	+	8.27619i	−0.618035	+	0.324370i
$652$	0.277629	+	0.585090i	0.0108728	+	0.0229139i
$653$	13.1940	−	22.8526i	0.516320	−	0.894292i	−0.483501	−	0.875344i	$-0.660635\pi$
$653$	13.1940	−	22.8526i	0.516320	−	0.894292i	0.999820	−	0.0189481i	$-0.00603174\pi$
$654$	4.75738	+	8.24002i	0.186028	+	0.322210i
$655$	24.7402	−	35.8424i	0.966679	−	1.40048i
$656$	12.9875	−	9.75946i	0.507076	−	0.381043i
$657$	−2.32150	−	4.02095i	−0.0905702	−	0.156872i
$658$	6.87421	−	56.6142i	0.267984	−	2.20705i
$659$	−11.4448	+	24.1194i	−0.445826	+	0.939558i	0.548793	+	0.835958i	$0.315087\pi$
$659$	−11.4448	+	24.1194i	−0.445826	+	0.939558i	−0.994619	+	0.103600i	$0.966964\pi$
$660$	−0.167008	+	0.173874i	−0.00650078	+	0.00676803i
$661$	−15.3267	+	1.23730i	−0.596138	+	0.0481253i	−0.374854	−	0.927084i	$-0.622307\pi$
$661$	−15.3267	+	1.23730i	−0.596138	+	0.0481253i	−0.221285	+	0.975209i	$0.571025\pi$
$662$	2.47513	+	0.610065i	0.0961987	+	0.0237109i
$663$	−9.55486	+	2.29762i	−0.371080	+	0.0892322i
$664$	−19.9060	+	4.90638i	−0.772502	+	0.190405i
$665$	−15.0078	+	5.01035i	−0.581979	+	0.194293i
$666$	1.56615	+	3.30059i	0.0606870	+	0.127895i
$667$	−15.7465	−	5.25697i	−0.609709	−	0.203551i
$668$	−0.140149	−	0.203041i	−0.00542254	−	0.00785590i
$669$	−4.54356	+	9.57535i	−0.175664	+	0.370205i
$670$	2.58046	+	64.0335i	0.0996919	+	2.47383i
$671$	−1.35832	+	0.334795i	−0.0524372	+	0.0129246i
$672$	−0.631726	+	0.269153i	−0.0243694	+	0.0103828i
$673$	12.9181	+	2.09939i	0.497956	+	0.0809257i	0.404202	−	0.914670i	$-0.367549\pi$
$673$	12.9181	+	2.09939i	0.497956	+	0.0809257i	0.0937537	+	0.995595i	$0.470113\pi$
$674$	6.54166	+	32.0432i	0.251975	+	1.23426i
$675$	13.9030			0.535125
$676$	−0.190353	−	0.338518i	−0.00732129	−	0.0130199i
$677$	51.6546			1.98525			0.992623	−	0.121240i	$-0.0386871\pi$
$677$	51.6546			1.98525			0.992623	+	0.121240i	$0.0386871\pi$
$678$	−0.567288	−	2.77876i	−0.0217866	−	0.106718i
$679$	43.9851	+	7.14827i	1.68799	+	0.274325i
$680$	−30.6007	+	13.0377i	−1.17348	+	0.499974i
$681$	−0.513505	+	0.126568i	−0.0196776	+	0.00485008i
$682$	−0.466669	−	11.5803i	−0.0178697	−	0.443432i
$683$	−1.84975	+	3.89827i	−0.0707787	+	0.149163i	−0.935756	−	0.352648i	$-0.885281\pi$
$683$	−1.84975	+	3.89827i	−0.0707787	+	0.149163i	0.864977	+	0.501811i	$0.167333\pi$
$684$	−0.0151979	−	0.0220179i	−0.000581106	−	0.000841877i
$685$	87.9932	+	29.3765i	3.36205	+	1.12242i
$686$	−6.23711	−	13.1444i	−0.238134	−	0.501857i
$687$	−5.99919	+	2.00282i	−0.228883	+	0.0764125i
$688$	38.4678	−	9.48147i	1.46657	−	0.361478i
$689$	3.57746	−	28.1280i	0.136290	−	1.07159i
$690$	44.0632	+	10.8606i	1.67746	+	0.413456i
$691$	−28.9212	+	2.33476i	−1.10021	+	0.0888184i	−0.617209	−	0.786799i	$-0.711737\pi$
$691$	−28.9212	+	2.33476i	−1.10021	+	0.0888184i	−0.483005	+	0.875618i	$0.660455\pi$
$692$	−0.00267078	+	0.00278058i	−0.000101528	+	0.000105702i
$693$	−3.23349	+	6.81444i	−0.122830	+	0.258859i
$694$	−0.655145	+	5.39561i	−0.0248690	+	0.204814i
$695$	16.3707	+	28.3548i	0.620974	+	1.07556i
$696$	5.08468	−	3.82089i	0.192734	−	0.144831i
$697$	−6.19714	+	8.97810i	−0.234733	+	0.340070i
$698$	−24.9084	−	43.1426i	−0.942796	−	1.63297i
$699$	−14.8468	+	25.7154i	−0.561558	+	0.972647i
$700$	−0.723543	−	1.52484i	−0.0273474	−	0.0576334i
$701$	12.2966	−	6.45374i	0.464435	−	0.243754i	−0.216239	−	0.976340i	$-0.569379\pi$
$701$	12.2966	−	6.45374i	0.464435	−	0.243754i	0.680674	+	0.732586i	$0.261687\pi$
$702$	−4.35722	+	2.72085i	−0.164453	+	0.102692i
$703$	−2.03332	−	1.06717i	−0.0766881	−	0.0402490i
$704$	−0.588721	+	14.6090i	−0.0221883	+	0.550596i
$705$	−8.56656	−	41.9618i	−0.322635	−	1.58037i
$706$	−8.52740	−	29.4400i	−0.320933	−	1.10799i
$707$	9.22068	+	4.83939i	0.346780	+	0.182004i
$708$	−0.124852	−	0.0789514i	−0.00469221	−	0.00296717i
$709$	11.7393	−	1.90782i	0.440878	−	0.0716496i	0.0640791	−	0.997945i	$-0.479589\pi$
$709$	11.7393	−	1.90782i	0.440878	−	0.0716496i	0.376799	+	0.926295i	$0.377025\pi$
$710$	83.8872	+	20.6763i	3.14823	+	0.775970i
$711$	−2.50089	+	12.2502i	−0.0937908	+	0.459418i
$712$	1.18315	−	0.0955139i	0.0443405	−	0.00357954i
$713$	−27.1369	+	17.1604i	−1.01629	+	0.642661i
$714$	11.8115	−	10.4641i	0.442034	−	0.391608i
$715$	−28.6933	−	4.83042i	−1.07307	−	0.180648i
$716$	0.263542	+	0.233478i	0.00984904	+	0.00872549i
$717$	17.7787	+	2.88932i	0.663958	+	0.107904i
$718$	−27.6998	−	11.8018i	−1.03375	−	0.440439i
$719$	13.9534	+	8.82360i	0.520374	+	0.329065i	0.768698	−	0.639612i	$-0.220905\pi$
$719$	13.9534	+	8.82360i	0.520374	+	0.329065i	−0.248323	+	0.968677i	$0.579879\pi$
$720$	−13.2089	+	11.7021i	−0.492266	+	0.436110i
$721$	−32.9943	−	2.66358i	−1.22877	−	0.0991969i
$722$	−24.5930	−	8.21037i	−0.915258	−	0.305558i
$723$	−1.71641	−	14.1359i	−0.0638339	−	0.525719i
$724$	−0.0432924	+	0.0325321i	−0.00160895	+	0.00120905i
$725$	19.9241	+	24.4026i	0.739962	+	0.906288i
$726$	6.80730	+	8.33743i	0.252643	+	0.309431i
$727$	11.2797	−	16.3415i	0.418343	−	0.606074i	−0.555990	−	0.831189i	$-0.687661\pi$
$727$	11.2797	−	16.3415i	0.418343	−	0.606074i	0.974332	+	0.225115i	$0.0722759\pi$
$728$	−34.6337	−	22.1772i	−1.28361	−	0.821941i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	−8.00169	+	27.6250i	−0.296156	+	1.02245i
$731$	−22.4861	+	14.2194i	−0.831680	+	0.525922i
$732$	0.0222245	−	0.00361184i	0.000821443	−	0.000133497i
$733$	7.96441	+	21.0004i	0.294172	+	0.775668i	0.997874	+	0.0651728i	$0.0207598\pi$
$733$	7.96441	+	21.0004i	0.294172	+	0.775668i	−0.703702	+	0.710495i	$0.748471\pi$
$734$	−37.1733	+	15.8381i	−1.37209	+	0.584594i
$735$	−28.6512	−	29.8290i	−1.05681	−	1.10026i
$736$	−1.09619	+	0.575327i	−0.0404063	+	0.0212068i
$737$	−19.1409	−	1.54521i	−0.705064	−	0.0569187i
$738$	−1.58655	+	5.47739i	−0.0584016	+	0.201626i
$739$	8.27415	−	8.61430i	0.304370	−	0.316882i	−0.551398	−	0.834242i	$-0.685906\pi$
$739$	8.27415	−	8.61430i	0.304370	−	0.316882i	0.855768	+	0.517360i	$0.173085\pi$
$740$	0.118103	−	0.311412i	0.00434155	−	0.0114477i
$741$	1.16211	−	3.01255i	0.0426911	−	0.110669i
$742$	16.1452	+	42.5714i	0.592709	+	1.56285i
$743$	−21.5946	−	9.20059i	−0.792228	−	0.337537i	−0.0423414	−	0.999103i	$-0.513482\pi$
$743$	−21.5946	−	9.20059i	−0.792228	−	0.337537i	−0.749887	+	0.661566i	$0.769892\pi$
$744$	0.495325	−	12.2914i	0.0181595	−	0.450623i
$745$	20.0871	−	24.6022i	0.735935	−	0.901356i
$746$	9.43414			0.345409
$747$	4.61939	−	5.65773i	0.169015	−	0.207005i
$748$	0.0420490	+	0.145170i	0.00153746	+	0.00530794i
$749$	−45.9753	−	40.7305i	−1.67990	−	1.48826i
$750$	−38.2027	−	39.7732i	−1.39496	−	1.45231i
$751$	3.63018	−	1.21193i	0.132467	−	0.0442240i	−0.249662	−	0.968333i	$-0.580319\pi$
$751$	3.63018	−	1.21193i	0.132467	−	0.0442240i	0.382129	+	0.924109i	$0.375191\pi$
$752$	31.9630	+	24.0186i	1.16557	+	0.875868i
$753$	1.60849	−	13.2471i	0.0586168	−	0.482752i
$754$	−11.0199	−	3.74863i	−0.401321	−	0.136517i
$755$	−10.7637	−	88.6471i	−0.391732	−	3.22620i
$756$	0.0606990	−	0.105134i	0.00220760	−	0.00382368i
$757$	15.4365	+	11.5998i	0.561050	+	0.421602i	0.843068	−	0.537807i	$-0.180747\pi$
$757$	15.4365	+	11.5998i	0.561050	+	0.421602i	−0.282018	+	0.959409i	$0.591004\pi$
$758$	−0.238497	−	5.91825i	−0.00866262	−	0.214961i
$759$	−4.82215	+	12.7150i	−0.175033	+	0.461524i
$760$	2.18608	−	10.7081i	0.0792974	−	0.388424i
$761$	9.26853	−	45.4003i	0.335984	−	1.64576i	−0.363853	−	0.931456i	$-0.618539\pi$
$761$	9.26853	−	45.4003i	0.335984	−	1.64576i	0.699837	−	0.714302i	$-0.253256\pi$
$762$	6.27789	−	16.5534i	0.227424	−	0.599668i
$763$	−1.09273	−	27.1159i	−0.0395596	−	0.981661i
$764$	0.210556	+	0.158223i	0.00761767	+	0.00572431i
$765$	5.92508	−	10.2625i	0.214222	−	0.371043i
$766$	−1.87634	−	15.4530i	−0.0677949	−	0.558341i
$767$	−0.616767	−	17.8177i	−0.0222702	−	0.643361i
$768$	0.0864038	−	0.711599i	0.00311783	−	0.0256776i
$769$	27.4535	+	20.6299i	0.989997	+	0.743934i	0.966731	−	0.255795i	$-0.0823372\pi$
$769$	27.4535	+	20.6299i	0.989997	+	0.743934i	0.0232659	+	0.999729i	$0.492594\pi$
$770$	44.3179	−	14.7955i	1.59711	−	0.533193i
$771$	1.29506	+	1.34830i	0.0466403	+	0.0485577i
$772$	0.0159289	+	0.0141118i	0.000573295	+	0.000507895i
$773$	−12.8816	−	44.4723i	−0.463317	−	1.59956i	−0.763588	−	0.645704i	$-0.776564\pi$
$773$	−12.8816	−	44.4723i	−0.463317	−	1.59956i	0.300271	−	0.953854i	$-0.402923\pi$
$774$	−8.79546	+	10.7725i	−0.316146	+	0.387209i
$775$	60.9299			2.18867
$776$	−19.4673	+	23.8431i	−0.698834	+	0.855916i
$777$	0.419569	−	10.4115i	0.0150519	−	0.373510i
$778$	3.92739	+	1.67330i	0.140804	+	0.0599909i
$779$	−1.27106	−	3.35150i	−0.0455403	−	0.120080i
$780$	0.454060	+	0.114653i	0.0162580	+	0.00410524i
$781$	−9.18039	+	24.2067i	−0.328500	+	0.866184i
$782$	19.7078	−	20.5180i	0.704748	−	0.733721i
$783$	−0.630424	+	2.17648i	−0.0225295	+	0.0777809i
$784$	38.4866	+	3.10696i	1.37452	+	0.110963i
$785$	−31.7268	+	16.6515i	−1.13238	+	0.594317i
$786$	−9.88634	−	10.2928i	−0.352634	−	0.367131i
$787$	7.28199	−	3.10257i	0.259575	−	0.110595i	−0.258259	−	0.966076i	$-0.583149\pi$
$787$	7.28199	−	3.10257i	0.259575	−	0.110595i	0.517834	+	0.855481i	$0.326739\pi$
$788$	0.190948	+	0.503489i	0.00680224	+	0.0179360i
$789$	26.8222	−	4.35903i	0.954896	−	0.155186i
$790$	65.4580	−	41.3932i	2.32889	−	1.47270i
$791$	−2.25051	+	7.76965i	−0.0800188	+	0.276257i
$792$	−2.95964	−	4.28778i	−0.105166	−	0.152360i
$793$	1.87131	+	1.97050i	0.0664522	+	0.0699747i
$794$	8.36990	−	12.1259i	0.297037	−	0.430332i
$795$	21.6242	+	26.4848i	0.766930	+	0.939319i
$796$	−0.260131	−	0.318602i	−0.00922008	−	0.0112926i
$797$	−3.64152	+	2.73642i	−0.128989	+	0.0969290i	−0.663279	−	0.748372i	$-0.730836\pi$
$797$	−3.64152	+	2.73642i	−0.128989	+	0.0969290i	0.534290	+	0.845302i	$0.320579\pi$
$798$	0.624961	+	5.14702i	0.0221234	+	0.182203i
$799$	−25.4665	−	8.50197i	−0.900940	−	0.300778i
$800$	2.34172	+	0.189043i	0.0827921	+	0.00668367i
$801$	−0.316534	+	0.280425i	−0.0111842	+	0.00990833i
$802$	5.76962	+	3.64849i	0.203733	+	0.128833i
$803$	−7.92847	−	3.37800i	−0.279790	−	0.119207i
$804$	0.305069	+	0.0495785i	0.0107590	+	0.00174850i
$805$	−96.8855	−	85.8330i	−3.41476	−	3.02522i
$806$	−19.0956	+	11.9242i	−0.672613	+	0.420010i
$807$	6.44379	−	5.70870i	0.226832	−	0.200956i
$808$	−6.07948	+	3.84443i	−0.213875	+	0.135247i
$809$	−25.4724	+	2.05634i	−0.895560	+	0.0722971i	−0.519670	−	0.854367i	$-0.673945\pi$
$809$	−25.4724	+	2.05634i	−0.895560	+	0.0722971i	−0.375890	+	0.926664i	$0.622663\pi$
$810$	1.23904	−	6.06922i	0.0435354	−	0.213251i
$811$	21.8697	+	5.39039i	0.767948	+	0.189282i	0.603781	−	0.797150i	$-0.293660\pi$
$811$	21.8697	+	5.39039i	0.767948	+	0.189282i	0.164167	+	0.986433i	$0.447506\pi$
$812$	0.271518	−	0.0441260i	0.00952842	−	0.00154852i
$813$	−11.5099	−	7.27842i	−0.403670	−	0.255265i
$814$	6.00437	+	3.15133i	0.210453	+	0.110454i
$815$	−26.2222	−	90.5294i	−0.918522	−	3.17111i
$816$	2.21283	+	10.8392i	0.0774647	+	0.379447i
$817$	0.351986	−	8.73444i	0.0123144	−	0.305579i
$818$	36.8257	+	19.3276i	1.28758	+	0.675775i
$819$	14.6105	−	1.09606i	0.510533	−	0.0382995i
$820$	0.460325	−	0.241597i	0.0160752	−	0.00843694i
$821$	4.73290	+	9.97437i	0.165179	+	0.348108i	0.969115	−	0.246608i	$-0.0793159\pi$
$821$	4.73290	+	9.97437i	0.165179	+	0.348108i	−0.803936	+	0.594716i	$0.797265\pi$
$822$	15.1997	−	26.3266i	0.530150	−	0.918247i
$823$	3.70412	+	6.41573i	0.129118	+	0.223638i	0.923335	−	0.383996i	$-0.125452\pi$
$823$	3.70412	+	6.41573i	0.129118	+	0.223638i	−0.794217	+	0.607634i	$0.792119\pi$
$824$	12.9886	−	18.8173i	0.452481	−	0.655531i
$825$	20.6304	−	15.5027i	0.718258	−	0.539736i
$826$	14.3139	+	24.7924i	0.498045	+	0.862638i
$827$	2.24400	−	18.4810i	0.0780314	−	0.642646i	−0.900251	−	0.435371i	$-0.856617\pi$
$827$	2.24400	−	18.4810i	0.0780314	−	0.642646i	0.978283	−	0.207275i	$-0.0664596\pi$
$828$	0.0938270	−	0.197736i	0.00326071	−	0.00687181i
$829$	−23.9104	+	24.8934i	−0.830444	+	0.864584i	−0.992506	−	0.122197i	$-0.961006\pi$
$829$	−23.9104	+	24.8934i	−0.830444	+	0.864584i	0.162062	+	0.986781i	$0.448186\pi$
$830$	−45.0973	+	3.64063i	−1.56535	+	0.126368i
$831$	−23.0952	−	5.69245i	−0.801163	−	0.197469i
$832$	25.2221	−	13.0556i	0.874420	−	0.452620i
$833$	−25.1750	+	6.20508i	−0.872262	+	0.214993i
$834$	10.1770	−	3.39758i	0.352401	−	0.117649i
$835$	15.3923	+	32.4387i	0.532674	+	1.12259i
$836$	−0.0471034	−	0.0157254i	−0.00162911	−	0.000543876i
$837$	2.48955	+	3.60674i	0.0860515	+	0.124667i
$838$	8.60201	−	18.1284i	0.297151	−	0.626233i
$839$	1.26555	+	31.4043i	0.0436916	+	1.08420i	0.861196	+	0.508273i	$0.169716\pi$
$839$	1.26555	+	31.4043i	0.0436916	+	1.08420i	−0.817504	+	0.575922i	$0.804643\pi$
$840$	48.1503	−	11.8680i	1.66134	−	0.409485i
$841$	21.9558	−	9.35449i	0.757096	−	0.322569i
$842$	−43.1874	−	7.01864i	−1.48834	−	0.241878i
$843$	2.00052	+	9.79919i	0.0689015	+	0.337502i
$844$	−0.188965			−0.00650445
$845$	19.4414	+	53.0719i	0.668805	+	1.82573i
$846$	−14.0343			−0.482509
$847$	−6.14068	−	30.0790i	−0.210996	−	1.03353i
$848$	−31.5061	−	5.12024i	−1.08192	−	0.175830i
$849$	9.29480	−	3.96014i	0.318997	−	0.135912i
$850$	−52.4197	+	12.9203i	−1.79798	+	0.443162i
$851$	−0.756438	−	18.7708i	−0.0259304	−	0.643455i
$852$	0.178627	−	0.376449i	0.00611967	−	0.0128969i
$853$	13.0905	+	18.9649i	0.448210	+	0.649344i	0.980339	−	0.197319i	$-0.0632234\pi$
$853$	13.0905	+	18.9649i	0.448210	+	0.649344i	−0.532129	+	0.846663i	$0.678608\pi$
$854$	−4.13901	−	1.38180i	−0.141634	−	0.0472843i
$855$	1.66916	+	3.51767i	0.0570840	+	0.120302i
$856$	40.2435	−	13.4353i	1.37549	−	0.459208i
$857$	−2.87711	+	0.709143i	−0.0982801	+	0.0242239i	−0.288149	−	0.957586i	$-0.593040\pi$
$857$	−2.87711	+	0.709143i	−0.0982801	+	0.0242239i	0.189869	+	0.981809i	$0.439194\pi$
$858$	−3.43169	+	8.89602i	−0.117156	+	0.303705i
$859$	−38.1230	−	9.39647i	−1.30074	−	0.320603i	−0.472675	−	0.881237i	$-0.656712\pi$
$859$	−38.1230	−	9.39647i	−1.30074	−	0.320603i	−0.828064	+	0.560633i	$0.810558\pi$
$860$	1.26373	−	0.102019i	0.0430928	−	0.00347881i
$861$	11.2670	−	11.7302i	0.383977	−	0.399763i
$862$	−9.83558	+	20.7281i	−0.335001	+	0.706000i
$863$	−4.48748	+	36.9577i	−0.152755	+	1.25805i	0.691604	+	0.722277i	$0.256904\pi$
$863$	−4.48748	+	36.9577i	−0.152755	+	1.25805i	−0.844359	+	0.535778i	$0.820019\pi$
$864$	0.0844905	+	0.146342i	0.00287442	+	0.00497865i
$865$	0.448571	−	0.337079i	0.0152519	−	0.0114610i
$866$	−10.8714	+	15.7499i	−0.369424	+	0.535203i
$867$	4.78560	+	8.28890i	0.162527	+	0.281506i
$868$	0.266014	−	0.460751i	0.00902912	−	0.0156389i
$869$	9.94874	+	20.9665i	0.337488	+	0.711241i
$870$	12.4284	−	6.52292i	0.421362	−	0.221148i
$871$	15.7996	+	33.7907i	0.535348	+	1.14495i
$872$	16.5981	+	8.71136i	0.562083	+	0.295004i
$873$	0.441561	−	10.9572i	0.0149446	−	0.370846i
$874$	1.86978	+	9.15877i	0.0632462	+	0.309800i
$875$	43.7619	+	151.084i	1.47942	+	5.10756i
$876$	0.122819	+	0.0644601i	0.00414965	+	0.00217791i
$877$	23.6023	+	14.9252i	0.796994	+	0.503989i	0.869828	−	0.493355i	$-0.164230\pi$
$877$	23.6023	+	14.9252i	0.796994	+	0.503989i	−0.0728335	+	0.997344i	$0.523204\pi$
$878$	−0.289151	+	0.0469916i	−0.00975838	+	0.00158589i
$879$	−10.7733	−	2.65537i	−0.363373	−	0.0895634i
$880$	−6.55190	+	32.0933i	−0.220865	+	1.08187i
$881$	7.00382	−	0.565407i	0.235965	−	0.0190490i	0.0380814	−	0.999275i	$-0.487875\pi$
$881$	7.00382	−	0.565407i	0.235965	−	0.0190490i	0.197883	+	0.980226i	$0.436593\pi$
$882$	−11.4553	+	7.24388i	−0.385719	+	0.243914i
$883$	−16.2569	+	14.4023i	−0.547087	+	0.484677i	−0.890799	−	0.454399i	$-0.849854\pi$
$883$	−16.2569	+	14.4023i	−0.547087	+	0.484677i	0.343712	+	0.939075i	$0.388316\pi$
$884$	0.204570	−	0.210575i	0.00688043	−	0.00708239i
$885$	16.0918	+	14.2561i	0.540919	+	0.479212i
$886$	10.6060	+	1.72365i	0.356316	+	0.0579070i
$887$	19.6054	+	8.35306i	0.658283	+	0.280468i	0.695164	−	0.718851i	$-0.255332\pi$
$887$	19.6054	+	8.35306i	0.658283	+	0.280468i	−0.0368805	+	0.999320i	$0.511742\pi$
$888$	6.08324	+	3.84681i	0.204140	+	0.129091i
$889$	−37.7960	+	33.4843i	−1.26764	+	1.12303i
$890$	2.61103	+	0.210784i	0.0875219	+	0.00706550i
$891$	1.76063	+	0.587783i	0.0589832	+	0.0196915i
$892$	−0.0381653	−	0.314319i	−0.00127787	−	0.0105242i
$893$	7.05228	−	5.29945i	0.235996	−	0.177339i
$894$	−6.58244	−	8.06203i	−0.220150	−	0.269635i
$895$	−32.4072	−	39.6916i	−1.08325	−	1.32674i
$896$	−26.6864	+	38.6619i	−0.891529	+	1.29160i
$897$	26.0968	−	4.08926i	0.871347	−	0.136537i
$898$	1.01351	+	1.46832i	0.0338212	+	0.0489985i
$899$	−2.76284	+	9.53844i	−0.0921460	+	0.318125i
$900$	−0.351043	+	0.221986i	−0.0117014	+	0.00739954i
$901$	21.1568	−	3.43832i	0.704835	−	0.114547i
$902$	3.75341	+	9.89693i	0.124975	+	0.329532i
$903$	36.4915	−	15.5476i	1.21436	−	0.517391i
$904$	−3.87055	−	4.02967i	−0.128732	−	0.134025i
$905$	6.97842	−	3.66256i	0.231971	−	0.121748i
$906$	−29.1677	−	2.35466i	−0.969032	−	0.0782283i
$907$	−0.0756590	+	0.261205i	−0.00251222	+	0.00867318i	−0.961764	−	0.273878i	$-0.911694\pi$
$907$	−0.0756590	+	0.261205i	−0.00251222	+	0.00867318i	0.959252	+	0.282551i	$0.0911807\pi$
$908$	0.0109449	−	0.0113948i	0.000363219	−	0.000378151i
$909$	0.908716	−	2.39609i	0.0301402	−	0.0794732i
$910$	−67.5905	−	60.5681i	−2.24060	−	2.00781i
$911$	−9.52382	−	25.1122i	−0.315538	−	0.832006i	−0.995144	−	0.0984284i	$-0.968618\pi$
$911$	−9.52382	−	25.1122i	−0.315538	−	0.832006i	0.679606	−	0.733577i	$-0.262151\pi$
$912$	−3.34402	−	1.42475i	−0.110731	−	0.0471782i
$913$	0.545900	−	13.5464i	0.0180666	−	0.448319i
$914$	17.4381	−	21.3578i	0.576801	−	0.706453i
$915$	−3.27687			−0.108330
$916$	0.119498	−	0.146358i	0.00394832	−	0.00483582i
$917$	11.3250	+	39.0984i	0.373984	+	1.29114i
$918$	−2.90664	−	2.57506i	−0.0959336	−	0.0849897i
$919$	16.2203	+	16.8871i	0.535058	+	0.557055i	0.932778	−	0.360452i	$-0.117378\pi$
$919$	16.2203	+	16.8871i	0.535058	+	0.557055i	−0.397719	+	0.917507i	$0.630198\pi$
$920$	84.8067	−	28.3126i	2.79600	−	0.933440i
$921$	−13.9069	−	10.4504i	−0.458248	−	0.344351i
$922$	−5.11236	+	42.1041i	−0.168367	+	1.38662i
$923$	49.6830	−	7.78512i	1.63534	−	0.256250i
$924$	−0.0271609	−	0.223690i	−0.000893528	−	0.00735886i
$925$	−17.8250	+	30.8738i	−0.586082	+	1.01512i
$926$	35.4104	+	26.6092i	1.16366	+	0.874432i
$927$	0.328001	+	8.13926i	0.0107730	+	0.267328i
$928$	−0.135778	+	0.358018i	−0.00445714	+	0.0117525i
$929$	4.79669	−	23.4957i	0.157374	−	0.770870i	−0.822107	−	0.569333i	$-0.807201\pi$
$929$	4.79669	−	23.4957i	0.157374	−	0.770870i	0.979481	−	0.201536i	$-0.0645934\pi$
$930$	5.43011	−	26.5984i	0.178060	−	0.872197i
$931$	3.02098	−	7.96567i	0.0990087	−	0.261064i
$932$	−0.0357190	−	0.886359i	−0.00117002	−	0.0290337i
$933$	−9.82999	−	7.38676i	−0.321820	−	0.241832i
$934$	6.07163	−	10.5164i	0.198670	−	0.344106i
$935$	−2.65129	−	21.8353i	−0.0867063	−	0.714091i
$936$	−4.39039	+	9.11856i	−0.143504	+	0.298050i
$937$	0.0191154	−	0.157430i	0.000624474	−	0.00514301i	−0.992393	−	0.123108i	$-0.960714\pi$
$937$	0.0191154	−	0.157430i	0.000624474	−	0.00514301i	0.993018	+	0.117965i	$0.0376370\pi$
$938$	−47.8845	−	35.9828i	−1.56348	−	1.17488i
$939$	9.86877	−	3.29468i	0.322055	−	0.107518i
$940$	0.886299	+	0.922734i	0.0289079	+	0.0300963i
$941$	4.22496	+	3.74299i	0.137730	+	0.122018i	0.729175	−	0.684327i	$-0.239904\pi$
$941$	4.22496	+	3.74299i	0.137730	+	0.122018i	−0.591445	+	0.806345i	$0.701442\pi$
$942$	3.26673	+	11.2780i	0.106436	+	0.367459i
$943$	18.5456	−	22.7142i	0.603926	−	0.739675i
$944$	−20.0699			−0.653219
$945$	−11.1738	+	13.6854i	−0.363484	+	0.445187i
$946$	−1.03941	+	25.7927i	−0.0337941	+	0.838592i
$947$	−18.6862	−	7.96146i	−0.607221	−	0.258713i	0.0663959	−	0.997793i	$-0.478850\pi$
$947$	−18.6862	−	7.96146i	−0.607221	−	0.258713i	−0.673617	+	0.739081i	$0.735260\pi$
$948$	−0.132450	−	0.349243i	−0.00430178	−	0.0113429i
$949$	1.92350	+	16.6297i	0.0624396	+	0.539822i
$950$	6.29032	−	16.5862i	0.204085	−	0.538128i
$951$	16.7410	−	17.4292i	0.542863	−	0.565181i
$952$	8.64938	−	29.8611i	0.280328	−	0.967805i
$953$	−17.8660	−	1.44229i	−0.578736	−	0.0467204i	−0.212367	−	0.977190i	$-0.568117\pi$
$953$	−17.8660	−	1.44229i	−0.578736	−	0.0467204i	−0.366369	+	0.930470i	$0.619399\pi$
$954$	9.92095	−	5.20691i	0.321203	−	0.168580i
$955$	−26.5526	−	27.6442i	−0.859223	−	0.894546i
$956$	−0.495037	+	0.210916i	−0.0160106	+	0.00682150i
$957$	1.49144	+	3.93261i	0.0482114	+	0.127123i
$958$	41.7334	−	6.78234i	1.34835	−	0.219127i
$959$	−73.2820	+	46.3408i	−2.36640	+	1.49642i
$960$	−9.52813	+	32.8949i	−0.307519	+	1.06168i
$961$	−6.69950	−	9.70590i	−0.216113	−	0.313094i
$962$	−0.455688	−	13.1643i	−0.0146920	−	0.424435i
$963$	−8.58640	+	12.4395i	−0.276693	+	0.400859i
$964$	0.269044	+	0.329519i	0.00866531	+	0.0106131i
$965$	−1.95874	−	2.39903i	−0.0630542	−	0.0772274i
$966$	−33.9092	+	25.4811i	−1.09101	+	0.819842i
$967$	4.12396	+	33.9638i	0.132618	+	1.09220i	0.895310	+	0.445443i	$0.146954\pi$
$967$	4.12396	+	33.9638i	0.132618	+	1.09220i	−0.762693	+	0.646761i	$0.776123\pi$
$968$	20.1141	+	6.71506i	0.646491	+	0.215830i
$969$	2.43296	+	0.196409i	0.0781580	+	0.00630957i
$970$	−50.8453	+	45.0450i	−1.63254	+	1.44631i
$971$	−15.4787	−	9.78813i	−0.496735	−	0.314116i	0.262501	−	0.964932i	$-0.415453\pi$
$971$	−15.4787	−	9.78813i	−0.496735	−	0.314116i	−0.759236	+	0.650816i	$0.774427\pi$
$972$	−0.0274838	−	0.0117098i	−0.000881544	−	0.000375591i
$973$	−30.2053	−	4.90884i	−0.968338	−	0.157370i
$974$	−16.2647	−	14.4093i	−0.521155	−	0.461703i
$975$	−46.0043	−	19.9098i	−1.47332	−	0.637625i
$976$	2.28979	−	2.02858i	0.0732945	−	0.0649333i
$977$	−43.5978	+	27.5696i	−1.39482	+	0.882029i	−0.999336	−	0.0364447i	$-0.988397\pi$
$977$	−43.5978	+	27.5696i	−1.39482	+	0.882029i	−0.395482	+	0.918474i	$0.629422\pi$
$978$	−30.7853	+	2.48525i	−0.984405	+	0.0794694i
$979$	−0.157008	+	0.769076i	−0.00501800	+	0.0245798i
$980$	1.19970	+	0.295700i	0.0383231	+	0.00944580i
$981$	−6.59178	+	1.07127i	−0.210459	+	0.0342030i
$982$	−21.7818	−	13.7740i	−0.695085	−	0.439545i
$983$	31.6581	+	16.6155i	1.00974	+	0.529951i	0.886648	−	0.462445i	$-0.153028\pi$
$983$	31.6581	+	16.6155i	1.00974	+	0.529951i	0.123089	+	0.992396i	$0.460720\pi$
$984$	3.12570	+	10.7912i	0.0996435	+	0.344009i
$985$	−15.6755	−	76.7838i	−0.499464	−	2.44654i
$986$	0.354307	−	8.79204i	0.0112834	−	0.279996i
$987$	35.4434	+	18.6021i	1.12818	+	0.592113i
$988$	0.0187582	+	0.0946207i	0.000596778	+	0.00301029i
$989$	63.3215	−	33.2337i	2.01351	−	1.05677i
$990$	−4.92900	−	10.3876i	−0.156654	−	0.330141i
$991$	13.1655	−	22.8033i	0.418215	−	0.724370i	−0.577545	−	0.816359i	$-0.695989\pi$
$991$	13.1655	−	22.8033i	0.418215	−	0.724370i	0.995760	+	0.0919888i	$0.0293224\pi$
$992$	0.370281	+	0.641345i	0.0117564	+	0.0203627i
$993$	−1.01641	+	1.47252i	−0.0322547	+	0.0467291i
$994$	−64.5562	+	48.5109i	−2.04760	+	1.53867i
$995$	29.9298	+	51.8400i	0.948840	+	1.64344i
$996$	−0.0263015	+	0.216612i	−0.000833394	+	0.00686361i
$997$	9.78713	−	20.6259i	0.309961	−	0.653230i	−0.687364	−	0.726313i	$-0.741232\pi$
$997$	9.78713	−	20.6259i	0.309961	−	0.653230i	0.997326	+	0.0730829i	$0.0232838\pi$
$998$	−9.37477	+	9.76017i	−0.296753	+	0.308953i
$999$	−2.55589	+	0.206333i	−0.0808647	+	0.00652807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.490.6	yes	384
169.159	even	39	inner	507.2.q.b.328.6	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.328.6	✓	384	169.159	even	39	inner
507.2.q.b.490.6	yes	384	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.284984 - 1.39594i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-0.0274838 + 0.0117098i) q^{4} +(4.22141 - 1.04049i) q^{5} +(-0.0573684 - 1.42358i) q^{6} +(-1.74204 + 3.67128i) q^{7} +(-1.59451 - 2.31004i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(-0.284984 - 1.39594i) q^{2} +(0.987050 + 0.160411i) q^{3} +(-0.0274838 + 0.0117098i) q^{4} +(4.22141 - 1.04049i) q^{5} +(-0.0573684 - 1.42358i) q^{6} +(-1.74204 + 3.67128i) q^{7} +(-1.59451 - 2.31004i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-2.65549 - 5.59634i) q^{10} +(1.76063 - 0.587783i) q^{11} +(-0.0290063 + 0.00714941i) q^{12} +(-2.68518 - 2.40620i) q^{13} +(5.62135 + 1.38554i) q^{14} +(4.33365 - 0.349849i) q^{15} +(-2.81167 + 2.92726i) q^{16} +(1.16844 - 2.46243i) q^{17} +(0.171733 - 1.41435i) q^{18} +(0.447772 + 0.775563i) q^{19} +(-0.103837 + 0.0780282i) q^{20} +(-2.30840 + 3.34429i) q^{21} +(-1.32226 - 2.29023i) q^{22} +(-3.66314 + 6.34474i) q^{23} +(-1.20330 - 2.53590i) q^{24} +(12.3105 - 6.46102i) q^{25} +(-2.59369 + 4.43409i) q^{26} +(0.885456 + 0.464723i) q^{27} +(0.00488821 - 0.121300i) q^{28} +(0.453246 + 2.22015i) q^{29} +(-1.72339 - 5.94984i) q^{30} +(3.88053 + 2.03666i) q^{31} +(0.142821 + 0.0903145i) q^{32} +(1.83211 - 0.297747i) q^{33} +(-3.77040 - 0.929319i) q^{34} +(-3.53397 + 17.3106i) q^{35} +(-0.0297775 + 0.00240389i) q^{36} +(-2.16724 + 1.37048i) q^{37} +(0.955035 - 0.846087i) q^{38} +(-2.26443 - 2.80577i) q^{39} +(-9.13464 - 8.09258i) q^{40} +(-3.95069 - 0.642050i) q^{41} +(5.32630 + 2.26932i) q^{42} +(-8.25003 - 5.21700i) q^{43} +(-0.0415059 + 0.0367710i) q^{44} +(4.33365 + 0.349849i) q^{45} +(9.90083 + 3.30538i) q^{46} +(-1.18734 - 9.77863i) q^{47} +(-3.24482 + 2.43833i) q^{48} +(-6.01644 - 7.36881i) q^{49} +(-12.5275 - 15.3434i) q^{50} +(1.54831 - 2.24311i) q^{51} +(0.101975 + 0.0346887i) q^{52} +(4.46734 + 6.47206i) q^{53} +(0.396387 - 1.36849i) q^{54} +(6.82075 - 4.31318i) q^{55} +(11.2585 - 1.82968i) q^{56} +(0.317564 + 0.837347i) q^{57} +(2.97003 - 1.26541i) q^{58} +(3.42532 + 3.56614i) q^{59} +(-0.115009 + 0.0603612i) q^{60} +(-0.751249 - 0.0606471i) q^{61} +(1.73717 - 5.99741i) q^{62} +(-2.81497 + 2.93069i) q^{63} +(-2.79321 + 7.36508i) q^{64} +(-13.8389 - 7.36368i) q^{65} +(-0.937762 - 2.47267i) q^{66} +(-9.51783 - 4.05517i) q^{67} +(-0.00327866 + 0.0813590i) q^{68} +(-4.63347 + 5.67497i) q^{69} +25.1717 q^{70} +(-8.82117 + 10.8040i) q^{71} +(-0.780931 - 2.69609i) q^{72} +(-3.47533 - 3.07887i) q^{73} +(2.53074 + 2.63478i) q^{74} +(13.1875 - 4.40262i) q^{75} +(-0.0213881 - 0.0160721i) q^{76} +(-0.909170 + 7.48769i) q^{77} +(-3.27138 + 3.96061i) q^{78} +(1.50705 + 12.4117i) q^{79} +(-8.82345 + 15.2827i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.229618 + 5.69792i) q^{82} +(2.59004 - 6.82937i) q^{83} +(0.0242827 - 0.118945i) q^{84} +(2.37034 - 11.6107i) q^{85} +(-4.93151 + 13.0033i) q^{86} +(0.0912402 + 2.26410i) q^{87} +(-4.16513 - 3.12990i) q^{88} +(-0.211443 + 0.366230i) q^{89} +(-0.746653 - 6.14924i) q^{90} +(13.5115 - 5.66634i) q^{91} +(0.0263816 - 0.217272i) q^{92} +(3.50357 + 2.63276i) q^{93} +(-13.3120 + 4.44421i) q^{94} +(2.69719 + 2.80807i) q^{95} +(0.126484 + 0.112055i) q^{96} +(-3.05097 - 10.5332i) q^{97} +(-8.57185 + 10.4986i) q^{98} +1.85615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

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