LMFDB - Embedded newform 225.2.w.a.92.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			92.9
Character	$\chi$	$=$	225.92
Dual form			225.2.w.a.203.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.931189 + 0.604721i) q^{2} +(-1.50571 + 0.856055i) q^{3} +(-0.312048 + 0.700871i) q^{4} +(-0.791939 + 2.09113i) q^{5} +(0.884429 - 1.70769i) q^{6} +(-1.61323 + 0.432263i) q^{7} +(-0.480639 - 3.03464i) q^{8} +(1.53434 - 2.57794i) q^{9} +O(q^{10})$	\(q+(-0.931189 + 0.604721i) q^{2} +(-1.50571 + 0.856055i) q^{3} +(-0.312048 + 0.700871i) q^{4} +(-0.791939 + 2.09113i) q^{5} +(0.884429 - 1.70769i) q^{6} +(-1.61323 + 0.432263i) q^{7} +(-0.480639 - 3.03464i) q^{8} +(1.53434 - 2.57794i) q^{9} +(-0.527107 - 2.42614i) q^{10} +(-0.779470 + 3.66712i) q^{11} +(-0.130129 - 1.32244i) q^{12} +(2.40822 - 3.70833i) q^{13} +(1.24082 - 1.37807i) q^{14} +(-0.597691 - 3.82659i) q^{15} +(1.25596 + 1.39489i) q^{16} +(-3.25758 + 0.515949i) q^{17} +(0.130177 + 3.32840i) q^{18} +(3.02825 - 4.16803i) q^{19} +(-1.21849 - 1.20758i) q^{20} +(2.05901 - 2.03187i) q^{21} +(-1.49175 - 3.88614i) q^{22} +(-8.37554 + 0.438943i) q^{23} +(3.32152 + 4.15784i) q^{24} +(-3.74566 - 3.31210i) q^{25} +4.90946i q^{26} +(-0.103414 + 5.19512i) q^{27} +(0.200443 - 1.26555i) q^{28} +(-0.272754 - 2.59508i) q^{29} +(2.87058 + 3.20184i) q^{30} +(-0.701245 + 6.67190i) q^{31} +(3.92249 + 1.05103i) q^{32} +(-1.96560 - 6.18890i) q^{33} +(2.72141 - 2.45037i) q^{34} +(0.373659 - 3.71579i) q^{35} +(1.32802 + 1.87982i) q^{36} +(-3.84275 + 1.95798i) q^{37} +(-0.299378 + 5.71248i) q^{38} +(-0.451550 + 7.64525i) q^{39} +(6.72646 + 1.39817i) q^{40} +(-0.193387 - 0.909813i) q^{41} +(-0.688615 + 3.13719i) q^{42} +(0.0200930 + 0.0749881i) q^{43} +(-2.32694 - 1.69062i) q^{44} +(4.17572 + 5.25008i) q^{45} +(7.53377 - 5.47361i) q^{46} +(6.11611 + 4.95273i) q^{47} +(-3.08522 - 1.02513i) q^{48} +(-3.64653 + 2.10532i) q^{49} +(5.49082 + 0.819107i) q^{50} +(4.46329 - 3.56553i) q^{51} +(1.84758 + 2.84503i) q^{52} +(5.18817 + 0.821726i) q^{53} +(-3.04530 - 4.90018i) q^{54} +(-7.05114 - 4.53411i) q^{55} +(2.08714 + 4.68779i) q^{56} +(-0.991615 + 8.86821i) q^{57} +(1.82329 + 2.25157i) q^{58} +(-12.9738 + 2.75767i) q^{59} +(2.86845 + 0.775174i) q^{60} +(-6.00470 - 1.27634i) q^{61} +(-3.38165 - 6.63686i) q^{62} +(-1.36089 + 4.82205i) q^{63} +(-7.85844 + 2.55336i) q^{64} +(5.84745 + 7.97267i) q^{65} +(5.57290 + 4.57440i) q^{66} +(-5.56072 + 4.50298i) q^{67} +(0.654905 - 2.44414i) q^{68} +(12.2354 - 7.83084i) q^{69} +(1.89907 + 3.68607i) q^{70} +(-1.43840 - 1.97978i) q^{71} +(-8.56059 - 3.41711i) q^{72} +(-3.82539 - 1.94914i) q^{73} +(2.39430 - 4.14704i) q^{74} +(8.47523 + 1.78057i) q^{75} +(1.97629 + 3.42304i) q^{76} +(-0.327697 - 6.25283i) q^{77} +(-4.20276 - 7.39223i) q^{78} +(14.1827 - 1.49066i) q^{79} +(-3.91155 + 1.52172i) q^{80} +(-4.29160 - 7.91089i) q^{81} +(0.730263 + 0.730263i) q^{82} +(-8.90845 - 3.41963i) q^{83} +(0.781570 + 2.07714i) q^{84} +(1.50088 - 7.22062i) q^{85} +(-0.0640573 - 0.0576774i) q^{86} +(2.63222 + 3.67395i) q^{87} +(11.5030 + 0.602848i) q^{88} +(-1.18673 - 3.65238i) q^{89} +(-7.06322 - 2.36368i) q^{90} +(-2.28203 + 7.02336i) q^{91} +(2.30593 - 6.00714i) q^{92} +(-4.65564 - 10.6463i) q^{93} +(-8.69027 - 0.913384i) q^{94} +(6.31772 + 9.63331i) q^{95} +(-6.80587 + 1.77532i) q^{96} +(-6.55830 + 8.09883i) q^{97} +(2.12247 - 4.16559i) q^{98} +(8.25766 + 7.63604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.931189	+	0.604721i	−0.658450	+	0.427603i	−0.830145	−	0.557548i	$-0.811742\pi$
$2$	−0.931189	+	0.604721i	−0.658450	+	0.427603i	0.171695	+	0.985150i	$0.445076\pi$
$3$	−1.50571	+	0.856055i	−0.869324	+	0.494243i
$3$	−1.50571	+	0.856055i	−0.869324	+	0.494243i
$4$	−0.312048	+	0.700871i	−0.156024	+	0.350435i
$5$	−0.791939	+	2.09113i	−0.354166	+	0.935183i
$5$	−0.791939	+	2.09113i	−0.354166	+	0.935183i
$6$	0.884429	−	1.70769i	0.361067	−	0.697160i
$7$	−1.61323	+	0.432263i	−0.609742	+	0.163380i	−0.550460	−	0.834861i	$-0.685548\pi$
$7$	−1.61323	+	0.432263i	−0.609742	+	0.163380i	−0.0592819	+	0.998241i	$0.518881\pi$
$8$	−0.480639	−	3.03464i	−0.169932	−	1.07291i
$9$	1.53434	−	2.57794i	0.511447	−	0.859315i
$10$	−0.527107	−	2.42614i	−0.166686	−	0.767213i
$11$	−0.779470	+	3.66712i	−0.235019	+	1.10568i	0.689424	+	0.724358i	$0.257864\pi$
$11$	−0.779470	+	3.66712i	−0.235019	+	1.10568i	−0.924443	+	0.381320i	$0.875470\pi$
$12$	−0.130129	−	1.32244i	−0.0375651	−	0.381756i
$13$	2.40822	−	3.70833i	0.667919	−	1.02851i	−0.328545	−	0.944488i	$-0.606558\pi$
$13$	2.40822	−	3.70833i	0.667919	−	1.02851i	0.996464	−	0.0840174i	$-0.0267751\pi$
$14$	1.24082	−	1.37807i	0.331623	−	0.368305i
$15$	−0.597691	−	3.82659i	−0.154323	−	0.988020i
$16$	1.25596	+	1.39489i	0.313991	+	0.348722i
$17$	−3.25758	+	0.515949i	−0.790078	+	0.125136i	−0.538416	−	0.842679i	$-0.680977\pi$
$17$	−3.25758	+	0.515949i	−0.790078	+	0.125136i	−0.251662	+	0.967815i	$0.580977\pi$
$18$	0.130177	+	3.32840i	0.0306830	+	0.784512i
$19$	3.02825	−	4.16803i	0.694729	−	0.956212i	−0.305263	−	0.952268i	$-0.598744\pi$
$19$	3.02825	−	4.16803i	0.694729	−	0.956212i	0.999992	−	0.00394446i	$-0.00125556\pi$
$20$	−1.21849	−	1.20758i	−0.272463	−	0.270023i
$21$	2.05901	−	2.03187i	0.449314	−	0.443391i
$22$	−1.49175	−	3.88614i	−0.318042	−	0.828529i
$23$	−8.37554	+	0.438943i	−1.74642	+	0.0915260i	−0.898603	−	0.438763i	$-0.855417\pi$
$23$	−8.37554	+	0.438943i	−1.74642	+	0.0915260i	−0.847817	+	0.530289i	$0.822084\pi$
$24$	3.32152	+	4.15784i	0.678003	+	0.848715i
$25$	−3.74566	−	3.31210i	−0.749133	−	0.662420i
$26$			4.90946i			0.962824i
$27$	−0.103414	+	5.19512i	−0.0199021	+	0.999802i
$28$	0.200443	−	1.26555i	0.0378802	−	0.239166i
$29$	−0.272754	−	2.59508i	−0.0506491	−	0.481894i	−0.990217	−	0.139533i	$-0.955440\pi$
$29$	−0.272754	−	2.59508i	−0.0506491	−	0.481894i	0.939568	−	0.342361i	$-0.111227\pi$
$30$	2.87058	+	3.20184i	0.524094	+	0.584573i
$31$	−0.701245	+	6.67190i	−0.125947	+	1.19831i	0.730807	+	0.682584i	$0.239144\pi$
$31$	−0.701245	+	6.67190i	−0.125947	+	1.19831i	−0.856754	+	0.515725i	$0.827523\pi$
$32$	3.92249	+	1.05103i	0.693404	+	0.185797i
$33$	−1.96560	−	6.18890i	−0.342166	−	1.07735i
$34$	2.72141	−	2.45037i	0.466719	−	0.420235i
$35$	0.373659	−	3.71579i	0.0631599	−	0.628084i
$36$	1.32802	+	1.87982i	0.221336	+	0.313303i
$37$	−3.84275	+	1.95798i	−0.631744	+	0.321890i	−0.740377	−	0.672192i	$-0.765353\pi$
$37$	−3.84275	+	1.95798i	−0.631744	+	0.321890i	0.108632	+	0.994082i	$0.465353\pi$
$38$	−0.299378	+	5.71248i	−0.0485656	+	0.926686i
$39$	−0.451550	+	7.64525i	−0.0723059	+	1.22422i
$40$	6.72646	+	1.39817i	1.06355	+	0.221070i
$41$	−0.193387	−	0.909813i	−0.0302019	−	0.142089i	0.960463	−	0.278407i	$-0.0898064\pi$
$41$	−0.193387	−	0.909813i	−0.0302019	−	0.142089i	−0.990665	+	0.136318i	$0.956473\pi$
$42$	−0.688615	+	3.13719i	−0.106256	+	0.484079i
$43$	0.0200930	+	0.0749881i	0.00306415	+	0.0114356i	0.967441	−	0.253097i	$-0.0814491\pi$
$43$	0.0200930	+	0.0749881i	0.00306415	+	0.0114356i	−0.964377	+	0.264532i	$0.914782\pi$
$44$	−2.32694	−	1.69062i	−0.350800	−	0.254871i
$45$	4.17572	+	5.25008i	0.622479	+	0.782636i
$46$	7.53377	−	5.47361i	1.11079	−	0.807039i
$47$	6.11611	+	4.95273i	0.892126	+	0.722429i	0.961396	−	0.275169i	$-0.0887337\pi$
$47$	6.11611	+	4.95273i	0.892126	+	0.722429i	−0.0692702	+	0.997598i	$0.522067\pi$
$48$	−3.08522	−	1.02513i	−0.445314	−	0.147965i
$49$	−3.64653	+	2.10532i	−0.520933	+	0.300761i
$50$	5.49082	+	0.819107i	0.776519	+	0.115839i
$51$	4.46329	−	3.56553i	0.624986	−	0.499275i
$52$	1.84758	+	2.84503i	0.256213	+	0.394534i
$53$	5.18817	+	0.821726i	0.712650	+	0.112873i	0.502225	−	0.864737i	$-0.332515\pi$
$53$	5.18817	+	0.821726i	0.712650	+	0.112873i	0.210425	+	0.977610i	$0.432515\pi$
$54$	−3.04530	−	4.90018i	−0.414413	−	0.666830i
$55$	−7.05114	−	4.53411i	−0.950775	−	0.611379i
$56$	2.08714	+	4.68779i	0.278906	+	0.626433i
$57$	−0.991615	+	8.86821i	−0.131343	+	1.17462i
$58$	1.82329	+	2.25157i	0.239409	+	0.295646i
$59$	−12.9738	+	2.75767i	−1.68905	+	0.359018i	−0.949423	−	0.314000i	$-0.898331\pi$
$59$	−12.9738	+	2.75767i	−1.68905	+	0.359018i	−0.739626	+	0.673018i	$0.764997\pi$
$60$	2.86845	+	0.775174i	0.370315	+	0.100075i
$61$	−6.00470	−	1.27634i	−0.768823	−	0.163418i	−0.193229	−	0.981154i	$-0.561896\pi$
$61$	−6.00470	−	1.27634i	−0.768823	−	0.163418i	−0.575594	+	0.817735i	$0.695229\pi$
$62$	−3.38165	−	6.63686i	−0.429470	−	0.842882i
$63$	−1.36089	+	4.82205i	−0.171456	+	0.607521i
$64$	−7.85844	+	2.55336i	−0.982305	+	0.319170i
$65$	5.84745	+	7.97267i	0.725286	+	0.988888i
$66$	5.57290	+	4.57440i	0.685977	+	0.563069i
$67$	−5.56072	+	4.50298i	−0.679350	+	0.550127i	−0.905700	−	0.423919i	$-0.860654\pi$
$67$	−5.56072	+	4.50298i	−0.679350	+	0.550127i	0.226350	+	0.974046i	$0.427321\pi$
$68$	0.654905	−	2.44414i	0.0794189	−	0.296396i
$69$	12.2354	−	7.83084i	1.47297	−	0.942722i
$70$	1.89907	+	3.68607i	0.226983	+	0.440569i
$71$	−1.43840	−	1.97978i	−0.170706	−	0.234957i	0.715089	−	0.699034i	$-0.246386\pi$
$71$	−1.43840	−	1.97978i	−0.170706	−	0.234957i	−0.885795	+	0.464077i	$0.846386\pi$
$72$	−8.56059	−	3.41711i	−1.00888	−	0.402710i
$73$	−3.82539	−	1.94914i	−0.447729	−	0.228129i	0.215563	−	0.976490i	$-0.430841\pi$
$73$	−3.82539	−	1.94914i	−0.447729	−	0.228129i	−0.663292	+	0.748361i	$0.730841\pi$
$74$	2.39430	−	4.14704i	0.278331	−	0.482084i
$75$	8.47523	+	1.78057i	0.978635	+	0.205603i
$76$	1.97629	+	3.42304i	0.226696	+	0.392650i
$77$	−0.327697	−	6.25283i	−0.0373445	−	0.712576i
$78$	−4.20276	−	7.39223i	−0.475869	−	0.837006i
$79$	14.1827	−	1.49066i	1.59568	−	0.167712i	0.735433	−	0.677598i	$-0.236979\pi$
$79$	14.1827	−	1.49066i	1.59568	−	0.167712i	0.860242	+	0.509885i	$0.170312\pi$
$80$	−3.91155	+	1.52172i	−0.437324	+	0.170133i
$81$	−4.29160	−	7.91089i	−0.476844	−	0.878988i
$82$	0.730263	+	0.730263i	0.0806440	+	0.0806440i
$83$	−8.90845	−	3.41963i	−0.977830	−	0.375354i	−0.183620	−	0.982997i	$-0.558782\pi$
$83$	−8.90845	−	3.41963i	−0.977830	−	0.375354i	−0.794210	+	0.607644i	$0.792115\pi$
$84$	0.781570	+	2.07714i	0.0852763	+	0.226635i
$85$	1.50088	−	7.22062i	0.162794	−	0.783186i
$86$	−0.0640573	−	0.0576774i	−0.00690747	−	0.00621952i
$87$	2.63222	+	3.67395i	0.282204	+	0.393889i
$88$	11.5030	+	0.602848i	1.22623	+	0.0642638i
$89$	−1.18673	−	3.65238i	−0.125793	−	0.387151i	0.868252	−	0.496124i	$-0.165244\pi$
$89$	−1.18673	−	3.65238i	−0.125793	−	0.387151i	−0.994045	+	0.108973i	$0.965244\pi$
$90$	−7.06322	−	2.36368i	−0.744529	−	0.249153i
$91$	−2.28203	+	7.02336i	−0.239221	+	0.736248i
$92$	2.30593	−	6.00714i	0.240409	−	0.626288i
$93$	−4.65564	−	10.6463i	−0.482767	−	1.10397i
$94$	−8.69027	−	0.913384i	−0.896333	−	0.0942084i
$95$	6.31772	+	9.63331i	0.648184	+	0.988356i
$96$	−6.80587	+	1.77532i	−0.694621	+	0.181193i
$97$	−6.55830	+	8.09883i	−0.665894	+	0.822311i	−0.992422	−	0.122876i	$-0.960788\pi$
$97$	−6.55830	+	8.09883i	−0.665894	+	0.822311i	0.326527	+	0.945188i	$0.394121\pi$
$98$	2.12247	−	4.16559i	0.214402	−	0.420788i
$99$	8.25766	+	7.63604i	0.829926	+	0.767451i
$100$	3.49018	−	1.59169i	0.349018	−	0.159169i
$101$	−3.17481	−	1.83298i	−0.315905	−	0.182388i	0.333661	−	0.942693i	$-0.391716\pi$
$101$	−3.17481	−	1.83298i	−0.315905	−	0.182388i	−0.649566	+	0.760305i	$0.725049\pi$
$102$	−2.00001	+	6.01923i	−0.198031	+	0.595993i
$103$	−5.26128	+	2.01962i	−0.518409	+	0.198999i	−0.603483	−	0.797376i	$-0.706221\pi$
$103$	−5.26128	+	2.01962i	−0.518409	+	0.198999i	0.0850737	+	0.996375i	$0.472887\pi$
$104$	−12.4109	−	5.52570i	−1.21699	−	0.541839i
$105$	2.61830	+	5.91479i	0.255520	+	0.577225i
$106$	−5.32808	+	2.37222i	−0.517509	+	0.230410i
$107$	8.02278	−	8.02278i	0.775591	−	0.775591i	−0.203486	−	0.979078i	$-0.565227\pi$
$107$	8.02278	−	8.02278i	0.775591	−	0.775591i	0.979078	+	0.203486i	$0.0652273\pi$
$108$	−3.60884	−	1.69361i	−0.347261	−	0.162967i
$109$	−4.76665	−	1.54878i	−0.456563	−	0.148346i	0.0717017	−	0.997426i	$-0.477157\pi$
$109$	−4.76665	−	1.54878i	−0.456563	−	0.148346i	−0.528264	+	0.849080i	$0.677157\pi$
$110$	9.30782	−	0.0418583i	0.887465	−	0.00399103i
$111$	4.10994	−	6.23776i	0.390098	−	0.592062i
$112$	−2.62911	−	1.70737i	−0.248428	−	0.161331i
$113$	8.53824	+	5.54480i	0.803210	+	0.521611i	0.879739	−	0.475457i	$-0.157717\pi$
$113$	8.53824	+	5.54480i	0.803210	+	0.521611i	−0.0765290	+	0.997067i	$0.524384\pi$
$114$	−4.43942	−	8.85763i	−0.415789	−	0.829593i
$115$	5.71503	−	17.8620i	0.532929	−	1.66564i
$116$	1.90393	+	0.618624i	0.176775	+	0.0574378i
$117$	−5.86484	−	11.8981i	−0.542205	−	1.09998i
$118$	10.4135	−	10.4135i	0.958637	−	0.958637i
$119$	5.03218	−	2.24047i	0.461299	−	0.205384i
$120$	−11.3250	+	3.65298i	−1.03383	+	0.333470i
$121$	−2.79119	−	1.24272i	−0.253744	−	0.112974i
$122$	6.36334	−	2.44266i	0.576110	−	0.221148i
$123$	1.07003	+	1.20437i	0.0964817	+	0.108594i
$124$	−4.45732	−	2.57343i	−0.400279	−	0.231101i
$125$	9.89237	−	5.20970i	0.884801	−	0.465970i
$126$	−1.64875	−	5.31320i	−0.146882	−	0.473337i
$127$	−7.28687	+	14.3013i	−0.646606	+	1.26903i	0.302221	+	0.953238i	$0.402272\pi$
$127$	−7.28687	+	14.3013i	−0.646606	+	1.26903i	−0.948827	+	0.315797i	$0.897728\pi$
$128$	0.662462	−	0.818073i	0.0585539	−	0.0723081i
$129$	−0.0944482	−	0.0957098i	−0.00831570	−	0.00842678i
$130$	−10.2663	−	3.88799i	−0.900416	−	0.340999i
$131$	−21.1645	−	2.22448i	−1.84915	−	0.194354i	−0.886069	−	0.463554i	$-0.846574\pi$
$131$	−21.1645	−	2.22448i	−1.84915	−	0.194354i	−0.963084	+	0.269200i	$0.913241\pi$
$132$	4.95098	+	0.553602i	0.430927	+	0.0481849i
$133$	−3.08357	+	8.03298i	−0.267380	+	0.696548i
$134$	2.45503	−	7.55582i	0.212083	−	0.652723i
$135$	−10.7818	−	4.33047i	−0.927949	−	0.372708i
$136$	3.13144	+	9.63757i	0.268519	+	0.826415i
$137$	18.9372	+	0.992457i	1.61791	+	0.0847913i	0.839644	−	0.543137i	$-0.182764\pi$
$137$	18.9372	+	0.992457i	1.61791	+	0.0847913i	0.778271	+	0.627929i	$0.216097\pi$
$138$	−6.65799	+	14.6910i	−0.566766	+	1.25058i
$139$	−0.144805	−	0.130383i	−0.0122822	−	0.0110589i	0.662967	−	0.748649i	$-0.269297\pi$
$139$	−0.144805	−	0.130383i	−0.0122822	−	0.0110589i	−0.675249	+	0.737590i	$0.735964\pi$
$140$	2.48769	+	1.42139i	0.210248	+	0.120130i
$141$	−13.4489	−	2.22166i	−1.13260	−	0.187097i
$142$	2.53664	+	0.973723i	0.212870	+	0.0817130i
$143$	11.7218	+	11.7218i	0.980222	+	0.980222i
$144$	5.52303	−	1.09757i	0.460252	−	0.0914642i
$145$	5.64266	+	1.48478i	0.468597	+	0.123304i
$146$	4.74085	−	0.498283i	0.392356	−	0.0412382i
$147$	3.68835	−	6.29164i	0.304210	−	0.518926i
$148$	−0.173169	−	3.30426i	−0.0142344	−	0.271608i
$149$	2.88923	+	5.00429i	0.236695	+	0.409967i	0.959764	−	0.280808i	$-0.0906026\pi$
$149$	2.88923	+	5.00429i	0.236695	+	0.409967i	−0.723069	+	0.690776i	$0.757269\pi$
$150$	−8.96880	+	3.46710i	−0.732299	+	0.283088i
$151$	−3.28301	+	5.68634i	−0.267167	+	0.462748i	−0.968129	−	0.250451i	$-0.919421\pi$
$151$	−3.28301	+	5.68634i	−0.267167	+	0.462748i	0.700962	+	0.713199i	$0.252754\pi$
$152$	−14.1040	−	7.18633i	−1.14398	−	0.582888i
$153$	−3.66814	+	9.18949i	−0.296552	+	0.742926i
$154$	4.08637	+	5.62440i	0.329289	+	0.453227i
$155$	−13.3965	−	6.75013i	−1.07603	−	0.542184i
$156$	−5.21742	−	2.70216i	−0.417728	−	0.216346i
$157$	3.32819	−	12.4210i	0.265619	−	0.991302i	−0.696252	−	0.717797i	$-0.745150\pi$
$157$	3.32819	−	12.4210i	0.265619	−	0.991302i	0.961871	−	0.273505i	$-0.0881829\pi$
$158$	−12.3053	+	9.96465i	−0.978959	+	0.792745i
$159$	−8.51534	+	3.20408i	−0.675310	+	0.254100i
$160$	−5.30421	+	7.37009i	−0.419334	+	0.582656i
$161$	13.3219	−	4.32855i	1.04991	−	0.341137i
$162$	8.78017	+	4.77132i	0.689836	+	0.374870i
$163$	5.51985	+	10.8333i	0.432348	+	0.848530i	0.999686	+	0.0250456i	$0.00797310\pi$
$163$	5.51985	+	10.8333i	0.432348	+	0.848530i	−0.567339	+	0.823485i	$0.692027\pi$
$164$	0.698007	+	0.148366i	0.0545052	+	0.0115854i
$165$	14.4984	+	0.790908i	1.12870	+	0.0615721i
$166$	10.3634	−	2.20280i	0.804354	−	0.170971i
$167$	1.90185	+	2.34859i	0.147170	+	0.181740i	0.845400	−	0.534134i	$-0.179362\pi$
$167$	1.90185	+	2.34859i	0.147170	+	0.181740i	−0.698230	+	0.715873i	$0.746029\pi$
$168$	−7.15564	−	5.27176i	−0.552070	−	0.406725i
$169$	−2.66462	−	5.98484i	−0.204971	−	0.460372i
$170$	2.96886	+	7.63138i	0.227701	+	0.585300i
$171$	−6.09859	−	14.2019i	−0.466371	−	1.08604i
$172$	−0.0588269	−	0.00931727i	−0.00448551	−	0.000710435i
$173$	−3.38316	−	5.20961i	−0.257217	−	0.396079i	0.686345	−	0.727276i	$-0.259214\pi$
$173$	−3.38316	−	5.20961i	−0.257217	−	0.396079i	−0.943562	+	0.331197i	$0.892547\pi$
$174$	−4.67281	−	1.82939i	−0.354245	−	0.138685i
$175$	7.47430	+	3.72405i	0.565004	+	0.281512i
$176$	−6.09421	+	3.51850i	−0.459369	+	0.265217i
$177$	17.1741	−	15.2586i	1.29089	−	1.14690i
$178$	3.31374	+	2.68341i	0.248375	+	0.201130i
$179$	−3.14993	+	2.28856i	−0.235437	+	0.171055i	−0.699248	−	0.714879i	$-0.746482\pi$
$179$	−3.14993	+	2.28856i	−0.235437	+	0.171055i	0.463811	+	0.885934i	$0.346482\pi$
$180$	−4.98265	+	1.28836i	−0.371385	+	0.0960288i
$181$	17.1760	+	12.4791i	1.27668	+	0.927562i	0.999447	−	0.0332408i	$-0.0105828\pi$
$181$	17.1760	+	12.4791i	1.27668	+	0.927562i	0.277232	+	0.960803i	$0.410583\pi$
$182$	−2.12218	−	7.92007i	−0.157306	−	0.587074i
$183$	10.1340	−	3.21855i	0.749125	−	0.237922i
$184$	5.35765	+	25.2057i	0.394971	+	1.85819i
$185$	−1.05117	−	9.58630i	−0.0772834	−	0.704799i
$186$	10.7733	+	7.09833i	0.789937	+	0.520475i
$187$	0.647136	−	12.3481i	0.0473232	−	0.902981i
$188$	−5.37974	+	2.74111i	−0.392358	+	0.199916i
$189$	−2.07883	−	8.42561i	−0.151212	−	0.612873i
$190$	−11.7085	−	5.14997i	−0.849421	−	0.373618i
$191$	−7.87691	+	7.09240i	−0.569953	+	0.513188i	−0.902953	−	0.429739i	$-0.858606\pi$
$191$	−7.87691	+	7.09240i	−0.569953	+	0.513188i	0.333000	+	0.942927i	$0.391939\pi$
$192$	9.64673	−	10.5719i	0.696193	−	0.762960i
$193$	21.3360	+	5.71695i	1.53580	+	0.411515i	0.924905	−	0.380199i	$-0.124144\pi$
$193$	21.3360	+	5.71695i	1.53580	+	0.411515i	0.610892	+	0.791714i	$0.290811\pi$
$194$	1.20949	−	11.5075i	0.0868360	−	0.826189i
$195$	−15.6296	−	6.99882i	−1.11926	−	0.501196i
$196$	−0.337669	−	3.21271i	−0.0241192	−	0.229479i
$197$	−2.04364	+	12.9030i	−0.145603	+	0.919303i	0.801412	+	0.598113i	$0.204083\pi$
$197$	−2.04364	+	12.9030i	−0.145603	+	0.919303i	−0.947015	+	0.321190i	$0.895917\pi$
$198$	−12.3071	−	2.11702i	−0.874629	−	0.150450i
$199$			24.7980i			1.75788i	0.476929	+	0.878942i	$0.341750\pi$
$199$			24.7980i			1.75788i	−0.476929	+	0.878942i	$0.658250\pi$
$200$	−8.25070	+	12.9587i	−0.583413	+	0.916316i
$201$	4.51805	−	11.5405i	0.318678	−	0.814003i
$202$	4.06479	−	0.213027i	0.285997	−	0.0149885i
$203$	1.56177	+	4.06855i	0.109615	+	0.285556i
$204$	1.10622	+	4.24081i	0.0774508	+	0.296916i
$205$	2.05569	+	0.316119i	0.143576	+	0.0220787i
$206$	3.67794	−	5.06225i	0.256254	−	0.352704i
$207$	−11.7194	+	22.2652i	−0.814551	+	1.54754i
$208$	8.19735	−	1.29833i	0.568384	−	0.0900231i
$209$	12.9242	+	14.3538i	0.893988	+	0.992875i
$210$	−6.01493	−	3.92445i	−0.415070	−	0.270813i
$211$	3.21404	−	3.56956i	0.221264	−	0.245738i	−0.622285	−	0.782791i	$-0.713796\pi$
$211$	3.21404	−	3.56956i	0.221264	−	0.245738i	0.843549	+	0.537052i	$0.180462\pi$
$212$	−2.19488	+	3.37982i	−0.150745	+	0.232127i
$213$	3.86061	+	1.74964i	0.264525	+	0.119883i
$214$	−2.61918	+	12.3223i	−0.179043	+	0.842333i
$215$	−0.172722	−	0.0173689i	−0.0117796	−	0.00118455i
$216$	15.8150	−	2.18316i	1.07608	−	0.148545i
$217$	−1.75275	−	11.0664i	−0.118984	−	0.751237i
$218$	5.37524	−	1.44029i	0.364057	−	0.0975488i
$219$	7.42851	−	0.339909i	0.501972	−	0.0229689i
$220$	5.37812	−	3.52708i	0.362593	−	0.237795i
$221$	−5.93164	+	13.3227i	−0.399005	+	0.896181i
$222$	−0.0550264	+	8.29390i	−0.00369313	+	0.556650i
$223$	−3.83871	+	2.49289i	−0.257059	+	0.166936i	−0.666735	−	0.745295i	$-0.732309\pi$
$223$	−3.83871	+	2.49289i	−0.257059	+	0.166936i	0.409675	+	0.912231i	$0.365642\pi$
$224$	−6.78218			−0.453153
$225$	−14.2855	+	4.57423i	−0.952369	+	0.304949i
$226$	−11.3038			−0.751916
$227$	8.37329	−	5.43768i	0.555755	−	0.360911i	−0.235998	−	0.971754i	$-0.575836\pi$
$227$	8.37329	−	5.43768i	0.555755	−	0.360911i	0.791752	+	0.610842i	$0.209169\pi$
$228$	−5.90604	−	3.46230i	−0.391137	−	0.229296i
$229$	−1.20069	+	2.69679i	−0.0793438	+	0.178209i	−0.948861	−	0.315693i	$-0.897763\pi$
$229$	−1.20069	+	2.69679i	−0.0793438	+	0.178209i	0.869518	+	0.493902i	$0.164430\pi$
$230$	5.47974	+	20.0889i	0.361324	+	1.32462i
$231$	5.84618	+	9.13444i	0.384650	+	0.601002i
$232$	−7.74403	+	2.07501i	−0.508421	+	0.136231i
$233$	2.33837	+	14.7639i	0.153192	+	0.967214i	0.937788	+	0.347208i	$0.112870\pi$
$233$	2.33837	+	14.7639i	0.153192	+	0.967214i	−0.784597	+	0.620006i	$0.787130\pi$
$234$	12.6563	+	7.53278i	0.827369	+	0.492433i
$235$	−15.2004	+	8.86733i	−0.991564	+	0.578441i
$236$	2.11568	−	9.95350i	0.137719	−	0.647918i
$237$	−20.0789	+	14.3856i	−1.30427	+	0.934448i
$238$	−3.33105	+	5.12937i	−0.215920	+	0.332488i
$239$	7.37828	−	8.19441i	0.477261	−	0.530052i	−0.455650	−	0.890159i	$-0.650593\pi$
$239$	7.37828	−	8.19441i	0.477261	−	0.530052i	0.932911	+	0.360107i	$0.117260\pi$
$240$	4.58699	−	5.63977i	0.296089	−	0.364045i
$241$	−4.98626	−	5.53780i	−0.321193	−	0.356721i	0.560827	−	0.827933i	$-0.310483\pi$
$241$	−4.98626	−	5.53780i	−0.321193	−	0.356721i	−0.882020	+	0.471212i	$0.843817\pi$
$242$	3.35062	−	0.530686i	0.215386	−	0.0341138i
$243$	13.2341	+	8.23768i	0.848966	+	0.528448i
$244$	2.76830	−	3.81024i	0.177222	−	0.243926i
$245$	−1.51468	−	9.29266i	−0.0967695	−	0.593686i
$246$	−1.72471	−	0.474421i	−0.109964	−	0.0302480i
$247$	−8.16375	−	21.2673i	−0.519447	−	1.35321i
$248$	20.5838	−	1.07875i	1.30708	−	0.0685009i
$249$	16.3410	−	2.47714i	1.03557	−	0.156982i
$250$	−6.06126	+	10.8333i	−0.383347	+	0.685161i
$251$		−	4.78470i		−	0.302008i	−0.988533	−	0.151004i	$-0.951749\pi$
$251$		−	4.78470i		−	0.302008i	0.988533	−	0.151004i	$-0.0482506\pi$
$252$	−2.95497	−	2.45852i	−0.186146	−	0.154872i
$253$	4.91882	−	31.0562i	0.309244	−	1.95249i
$254$	−1.86284	−	17.7237i	−0.116885	−	1.11209i
$255$	3.92135	+	12.1570i	0.245564	+	0.761302i
$256$	1.60523	−	15.2728i	0.100327	−	0.954549i
$257$	−6.19434	−	1.65977i	−0.386392	−	0.103534i	0.0603931	−	0.998175i	$-0.480765\pi$
$257$	−6.19434	−	1.65977i	−0.386392	−	0.103534i	−0.446785	+	0.894641i	$0.647431\pi$
$258$	0.145827	+	0.0320091i	0.00907879	+	0.00199280i
$259$	5.35287	−	4.81974i	0.332611	−	0.299484i
$260$	−7.41250	+	1.61045i	−0.459703	+	0.0998758i
$261$	−7.10847	−	3.27859i	−0.440003	−	0.202940i
$262$	21.0534	−	10.7272i	1.30068	−	0.662730i
$263$	−0.558210	+	10.6513i	−0.0344207	+	0.656787i	0.925880	+	0.377819i	$0.123326\pi$
$263$	−0.558210	+	10.6513i	−0.0344207	+	0.656787i	−0.960300	+	0.278968i	$0.910008\pi$
$264$	−17.8363	+	8.93950i	−1.09775	+	0.550188i
$265$	−5.82705	+	10.1984i	−0.357953	+	0.626482i
$266$	−1.98633	−	9.34493i	−0.121789	−	0.572974i
$267$	4.91351	+	4.48352i	0.300702	+	0.274387i
$268$	−1.42080	−	5.30249i	−0.0867891	−	0.323901i
$269$	−9.04255	−	6.56980i	−0.551334	−	0.400568i	0.276943	−	0.960886i	$-0.410679\pi$
$269$	−9.04255	−	6.56980i	−0.551334	−	0.400568i	−0.828277	+	0.560319i	$0.810679\pi$
$270$	12.6586	−	2.48749i	0.770379	−	0.151384i
$271$	7.07290	−	5.13876i	0.429648	−	0.312158i	−0.351860	−	0.936053i	$-0.614451\pi$
$271$	7.07290	−	5.13876i	0.429648	−	0.312158i	0.781508	+	0.623895i	$0.214451\pi$
$272$	−4.81109	−	3.89594i	−0.291715	−	0.236226i
$273$	−2.57630	−	12.5287i	−0.155925	−	0.758271i
$274$	−18.2343	+	10.5276i	−1.10157	+	0.635994i
$275$	15.0655	−	11.1541i	0.908483	−	0.672619i
$276$	1.67038	+	11.0190i	0.100545	+	0.663267i
$277$	9.77953	+	15.0592i	0.587595	+	0.904817i	0.999981	−	0.00619247i	$-0.00197114\pi$
$277$	9.77953	+	15.0592i	0.587595	+	0.904817i	−0.412386	+	0.911009i	$0.635304\pi$
$278$	0.213686	+	0.0338446i	0.0128161	+	0.00202986i
$279$	16.1238	+	12.0447i	0.965309	+	0.721100i
$280$	−11.4557	+	0.652038i	−0.684608	+	0.0389667i
$281$	−0.669176	−	1.50299i	−0.0399197	−	0.0896610i	0.892485	−	0.451077i	$-0.148960\pi$
$281$	−0.669176	−	1.50299i	−0.0399197	−	0.0896610i	−0.932405	+	0.361416i	$0.882293\pi$
$282$	13.8670	−	6.06405i	0.825765	−	0.361109i
$283$	−12.0153	−	14.8377i	−0.714237	−	0.882009i	0.282781	−	0.959185i	$-0.408743\pi$
$283$	−12.0153	−	14.8377i	−0.714237	−	0.882009i	−0.997018	+	0.0771754i	$0.975410\pi$
$284$	1.83642	−	0.390343i	0.108971	−	0.0231626i
$285$	−17.7593	−	9.09668i	−1.05197	−	0.538841i
$286$	−18.0036	−	3.82678i	−1.06457	−	0.226282i
$287$	0.705255	+	1.38414i	0.0416299	+	0.0817032i
$288$	8.72792	−	8.49932i	0.514298	−	0.500827i
$289$	−5.82237	+	1.89180i	−0.342492	+	0.111282i
$290$	−6.15226	+	2.02962i	−0.361273	+	0.119184i
$291$	2.94188	−	17.8088i	0.172456	−	1.04397i
$292$	2.55980	−	2.07288i	0.149801	−	0.121306i
$293$	5.13946	−	19.1807i	0.300250	−	1.12055i	−0.636707	−	0.771106i	$-0.719704\pi$
$293$	5.13946	−	19.1807i	0.300250	−	1.12055i	0.936957	−	0.349443i	$-0.113629\pi$
$294$	0.370137	+	8.08914i	0.0215868	+	0.471768i
$295$	4.50783	−	29.3139i	0.262456	−	1.70672i
$296$	7.78874	+	10.7203i	0.452711	+	0.623103i
$297$	−18.9705	−	4.42868i	−1.10078	−	0.256978i
$298$	−5.71662	−	2.91276i	−0.331155	−	0.168732i
$299$	−18.5424	+	32.1163i	−1.07233	+	1.85734i
$300$	−3.89263	+	5.38442i	−0.224741	+	0.310870i
$301$	−0.0648291	−	0.112287i	−0.00373669	−	0.00647213i
$302$	−0.381548	−	7.28036i	−0.0219556	−	0.418938i
$303$	6.34948	+	0.0421260i	0.364768	+	0.00242008i
$304$	9.61732	−	1.01082i	0.551591	−	0.0579746i
$305$	7.42435	−	11.5458i	0.425117	−	0.661113i
$306$	−2.14135	−	10.7754i	−0.122413	−	0.615986i
$307$	6.27906	+	6.27906i	0.358365	+	0.358365i	0.863210	−	0.504845i	$-0.168450\pi$
$307$	6.27906	+	6.27906i	0.358365	+	0.358365i	−0.504845	+	0.863210i	$0.668450\pi$
$308$	4.48468	+	1.72151i	0.255538	+	0.0980920i
$309$	6.19307	−	7.54490i	0.352311	−	0.429214i
$310$	16.5566	−	1.81548i	0.940352	−	0.103113i
$311$	−5.79805	−	5.22059i	−0.328777	−	0.296032i	0.488166	−	0.872751i	$-0.337666\pi$
$311$	−5.79805	−	5.22059i	−0.328777	−	0.296032i	−0.816943	+	0.576719i	$0.804333\pi$
$312$	23.4176	−	2.30431i	1.32576	−	0.130456i
$313$	−21.3293	−	1.11782i	−1.20560	−	0.0631829i	−0.561075	−	0.827765i	$-0.689612\pi$
$313$	−21.3293	−	1.11782i	−1.20560	−	0.0631829i	−0.644526	+	0.764582i	$0.722945\pi$
$314$	4.41205	+	13.5789i	0.248987	+	0.766302i
$315$	−9.00579	−	6.66457i	−0.507419	−	0.375506i
$316$	−3.38091	+	10.4054i	−0.190191	+	0.585348i
$317$	−7.43181	+	19.3605i	−0.417412	+	1.08740i	0.550217	+	0.835021i	$0.314545\pi$
$317$	−7.43181	+	19.3605i	−0.417412	+	1.08740i	−0.967630	+	0.252375i	$0.918788\pi$
$318$	5.99182	−	8.13301i	0.336004	−	0.456076i
$319$	9.72907	+	1.02257i	0.544723	+	0.0572527i
$320$	0.883990	−	18.4551i	0.0494165	−	1.03167i
$321$	−5.21206	+	18.9479i	−0.290909	+	1.05757i
$322$	−9.78764	+	12.0867i	−0.545444	+	0.673567i
$323$	−7.71427	+	15.1401i	−0.429233	+	0.842418i
$324$	6.88370	−	0.539280i	0.382428	−	0.0299600i
$325$	−21.3027	+	5.91391i	−1.18166	+	0.328045i
$326$	−11.6912	−	6.74989i	−0.647513	−	0.373842i
$327$	8.50305	−	1.74850i	0.470220	−	0.0966923i
$328$	−2.66800	+	1.02415i	−0.147316	+	0.0565492i
$329$	−12.0075	−	5.34610i	−0.661997	−	0.294740i
$330$	−13.9791	+	8.03103i	−0.769522	+	0.442093i
$331$	17.6820	−	7.87252i	0.971889	−	0.432713i	0.141525	−	0.989935i	$-0.454799\pi$
$331$	17.6820	−	7.87252i	0.971889	−	0.432713i	0.830364	+	0.557222i	$0.188133\pi$
$332$	5.17659	−	5.17659i	0.284102	−	0.284102i
$333$	−0.848526	+	12.9106i	−0.0464990	+	0.707497i
$334$	−3.19123	−	1.03689i	−0.174616	−	0.0567363i
$335$	−5.01258	−	15.1943i	−0.273866	−	0.830153i
$336$	5.42029	+	0.320138i	0.295701	+	0.0174649i
$337$	−27.7748	−	18.0372i	−1.51299	−	0.982547i	−0.991616	−	0.129219i	$-0.958753\pi$
$337$	−27.7748	−	18.0372i	−1.51299	−	0.982547i	−0.521374	−	0.853328i	$-0.674580\pi$
$338$	6.10043	+	3.96167i	0.331820	+	0.215486i
$339$	−17.6028	−	1.03967i	−0.956052	−	0.0564672i
$340$	4.59237	+	3.30510i	0.249056	+	0.179244i
$341$	−23.9201	−	7.77210i	−1.29534	−	0.420883i
$342$	14.2671	+	9.53667i	0.771477	+	0.515684i
$343$	13.2394	−	13.2394i	0.714859	−	0.714859i
$344$	0.217904	−	0.0970172i	0.0117486	−	0.00523082i
$345$	6.68563	+	31.7874i	0.359942	+	1.71137i
$346$	6.30072	+	2.80526i	0.338729	+	0.150812i
$347$	16.6585	−	6.39461i	0.894276	−	0.343280i	0.132548	−	0.991177i	$-0.457684\pi$
$347$	16.6585	−	6.39461i	0.894276	−	0.343280i	0.761729	+	0.647896i	$0.224351\pi$
$348$	−3.39634	+	0.698397i	−0.182063	+	0.0374380i
$349$	−5.46022	−	3.15246i	−0.292279	−	0.168747i	0.346690	−	0.937980i	$-0.387305\pi$
$349$	−5.46022	−	3.15246i	−0.292279	−	0.168747i	−0.638969	+	0.769232i	$0.720639\pi$
$350$	−9.21200	+	1.05207i	−0.492402	+	0.0562356i
$351$	19.0162	+	12.8945i	1.01501	+	0.688257i
$352$	−6.91170	+	13.5650i	−0.368395	+	0.723016i
$353$	−13.1376	+	16.2236i	−0.699244	+	0.863495i	−0.995803	−	0.0915196i	$-0.970828\pi$
$353$	−13.1376	+	16.2236i	−0.699244	+	0.863495i	0.296559	+	0.955015i	$0.404161\pi$
$354$	−6.76519	+	24.5942i	−0.359566	+	1.30717i
$355$	5.27911	−	1.44001i	0.280186	−	0.0764277i
$356$	2.93016	+	0.307972i	0.155298	+	0.0163225i
$357$	−5.65905	+	7.68133i	−0.299509	+	0.406539i
$358$	1.54924	−	4.03591i	0.0818800	−	0.213305i
$359$	3.17878	−	9.78329i	0.167770	−	0.516342i	−0.831460	−	0.555585i	$-0.812494\pi$
$359$	3.17878	−	9.78329i	0.167770	−	0.516342i	0.999230	+	0.0392425i	$0.0124945\pi$
$360$	13.9251	−	15.1952i	0.733917	−	0.800857i
$361$	−2.33086	−	7.17365i	−0.122677	−	0.377561i
$362$	−23.5404	−	1.23370i	−1.23726	−	0.0648419i
$363$	5.26656	−	0.518235i	0.276423	−	0.0272003i
$364$	−4.21037	−	3.79103i	−0.220683	−	0.198704i
$365$	7.10538	−	6.45581i	0.371913	−	0.337912i
$366$	−7.49032	+	9.12531i	−0.391525	+	0.476988i
$367$	−15.2103	−	5.83869i	−0.793972	−	0.304777i	−0.0726325	−	0.997359i	$-0.523140\pi$
$367$	−15.2103	−	5.83869i	−0.793972	−	0.304777i	−0.721340	+	0.692581i	$0.756473\pi$
$368$	−11.1317	−	11.1317i	−0.580277	−	0.580277i
$369$	−2.64217	−	0.897423i	−0.137546	−	0.0467180i
$370$	6.77588	+	8.29100i	0.352261	+	0.431028i
$371$	−8.72490	+	0.917023i	−0.452974	+	0.0476095i
$372$	8.91444	+	0.0591434i	0.462192	+	0.00306644i
$373$	1.35770	+	25.9064i	0.0702989	+	1.34138i	0.775037	+	0.631915i	$0.217731\pi$
$373$	1.35770	+	25.9064i	0.0702989	+	1.34138i	−0.704738	+	0.709467i	$0.748936\pi$
$374$	6.86454	+	11.8897i	0.354957	+	0.614804i
$375$	−10.4353	+	16.3127i	−0.538876	+	0.842385i
$376$	12.0901	−	20.9406i	0.623498	−	1.07993i
$377$	−10.2803	−	5.23806i	−0.529461	−	0.269774i
$378$	7.03093	+	6.58873i	0.361632	+	0.338888i
$379$	−22.5461	−	31.0320i	−1.15811	−	1.59401i	−0.717957	−	0.696088i	$-0.754922\pi$
$379$	−22.5461	−	31.0320i	−1.15811	−	1.59401i	−0.440158	−	0.897920i	$-0.645078\pi$
$380$	−8.72313	+	1.42185i	−0.447487	+	0.0729394i
$381$	−1.27075	−	27.7716i	−0.0651027	−	1.42278i
$382$	3.04597	−	11.3677i	0.155845	−	0.581622i
$383$	0.297825	−	0.241174i	0.0152181	−	0.0123234i	−0.621681	−	0.783270i	$-0.713550\pi$
$383$	0.297825	−	0.241174i	0.0152181	−	0.0123234i	0.636899	+	0.770947i	$0.280217\pi$
$384$	−0.297163	+	1.79889i	−0.0151645	+	0.0917990i
$385$	13.3350	+	4.26660i	0.679615	+	0.217446i
$386$	−23.3250	+	7.57875i	−1.18721	+	0.385748i
$387$	0.224145	+	0.0632586i	0.0113939	+	0.00321562i
$388$	−3.62973	−	7.12374i	−0.184272	−	0.361653i
$389$	27.9174	+	5.93402i	1.41547	+	0.300867i	0.851250	−	0.524760i	$-0.175845\pi$
$389$	27.9174	+	5.93402i	1.41547	+	0.300867i	0.564217	+	0.825627i	$0.309178\pi$
$390$	18.7865	−	2.93434i	0.951290	−	0.148586i
$391$	27.0575	−	5.75124i	1.36836	−	0.290853i
$392$	8.14156	+	10.0540i	0.411211	+	0.507803i
$393$	33.7720	−	14.7686i	1.70357	−	0.744975i
$394$	−5.89972	−	13.2510i	−0.297224	−	0.667575i
$395$	−8.11465	+	30.8383i	−0.408292	+	1.55165i
$396$	−7.92866	+	3.40474i	−0.398430	+	0.171095i
$397$	19.4264	+	3.07684i	0.974984	+	0.154422i	0.623544	−	0.781788i	$-0.285692\pi$
$397$	19.4264	+	3.07684i	0.974984	+	0.154422i	0.351440	+	0.936210i	$0.385692\pi$
$398$	−14.9959	−	23.0916i	−0.751676	−	1.15748i
$399$	−2.23370	−	14.7351i	−0.111825	−	0.737676i
$400$	−0.0844095	−	9.38467i	−0.00422048	−	0.469233i
$401$	10.1526	−	5.86160i	0.506996	−	0.292715i	−0.224602	−	0.974451i	$-0.572108\pi$
$401$	10.1526	−	5.86160i	0.506996	−	0.292715i	0.731598	+	0.681736i	$0.238775\pi$
$402$	2.77162	+	13.4785i	0.138236	+	0.672248i
$403$	23.0529	+	18.6678i	1.14834	+	0.929911i
$404$	2.27537	−	1.65315i	0.113204	−	0.0822475i
$405$	19.9414	−	2.70935i	0.990896	−	0.134629i
$406$	−3.91464	−	2.84415i	−0.194280	−	0.141153i
$407$	−4.18483	−	15.6180i	−0.207435	−	0.774156i
$408$	−12.9653	−	11.8307i	−0.641880	−	0.585709i
$409$	−0.542961	−	2.55443i	−0.0268477	−	0.126309i	0.962683	−	0.270632i	$-0.0872327\pi$
$409$	−0.542961	−	2.55443i	−0.0268477	−	0.126309i	−0.989531	+	0.144324i	$0.953899\pi$
$410$	−2.10540	+	0.948752i	−0.103978	+	0.0468555i
$411$	−29.3636	+	14.7169i	−1.44840	+	0.725933i
$412$	0.226281	−	4.31769i	0.0111480	−	0.212717i
$413$	19.7377	−	10.0569i	0.971228	−	0.494865i
$414$	−2.55128	−	27.8200i	−0.125389	−	1.36728i
$415$	14.2059	−	15.9206i	0.697338	−	0.781512i
$416$	13.3438	−	12.0148i	0.654231	−	0.589073i
$417$	0.329650	+	0.0723583i	0.0161430	+	0.00354340i
$418$	−20.7150	−	5.55056i	−1.01320	−	0.271487i
$419$	−3.09223	+	29.4206i	−0.151065	+	1.43729i	0.611943	+	0.790901i	$0.290388\pi$
$419$	−3.09223	+	29.4206i	−0.151065	+	1.43729i	−0.763009	+	0.646388i	$0.776279\pi$
$420$	−4.96254	−	0.0106069i	−0.242147	−	0.000517562i
$421$	1.52125	+	14.4738i	0.0741414	+	0.705408i	0.966949	+	0.254970i	$0.0820655\pi$
$421$	1.52125	+	14.4738i	0.0741414	+	0.705408i	−0.892808	+	0.450438i	$0.851268\pi$
$422$	−0.834295	+	5.26753i	−0.0406129	+	0.256419i
$423$	22.1520	−	8.16782i	1.07707	−	0.397133i
$424$		−	16.1392i		−	0.783787i
$425$	13.9107	+	8.85684i	0.674766	+	0.429620i
$426$	−4.65300	+	0.705352i	−0.225439	+	0.0341744i
$427$	10.2387	−	0.536585i	0.495483	−	0.0259672i
$428$	3.11944	+	8.12642i	0.150784	+	0.392805i
$429$	−27.6841	−	7.61513i	−1.33660	−	0.367662i
$430$	0.171341	−	0.0882752i	0.00826278	−	0.00425701i
$431$	0.00627509	−	0.00863692i	0.000302261	−	0.000416026i	−0.808866	−	0.587993i	$-0.799918\pi$
$431$	0.00627509	−	0.00863692i	0.000302261	−	0.000416026i	0.809168	+	0.587577i	$0.199918\pi$
$432$	−7.37651	+	6.38064i	−0.354902	+	0.306989i
$433$	−19.8062	+	3.13699i	−0.951825	+	0.150754i	−0.612989	−	0.790091i	$-0.710033\pi$
$433$	−19.8062	+	3.13699i	−0.951825	+	0.150754i	−0.338836	+	0.940846i	$0.610033\pi$
$434$	8.32423	+	9.24500i	0.399576	+	0.443774i
$435$	−9.76728	+	2.59477i	−0.468305	+	0.124410i
$436$	2.57292	−	2.85752i	0.123220	−	0.136850i
$437$	−23.5337	+	36.2388i	−1.12577	+	1.73353i
$438$	−6.71180	+	4.80870i	−0.320702	+	0.229769i
$439$	−8.12192	+	38.2106i	−0.387638	+	1.82369i	0.160170	+	0.987089i	$0.448796\pi$
$439$	−8.12192	+	38.2106i	−0.387638	+	1.82369i	−0.547808	+	0.836604i	$0.684538\pi$
$440$	−10.3703	+	23.5769i	−0.494386	+	1.12399i
$441$	−0.167608	+	12.6308i	−0.00798131	+	0.601468i
$442$	−2.53303	−	15.9929i	−0.120484	−	0.760706i
$443$	−4.44943	+	1.19222i	−0.211399	+	0.0566441i	−0.362964	−	0.931803i	$-0.618235\pi$
$443$	−4.44943	+	1.19222i	−0.211399	+	0.0566441i	0.151565	+	0.988447i	$0.451569\pi$
$444$	3.08937	+	4.82702i	0.146615	+	0.229080i
$445$	8.57742	+	0.410853i	0.406609	+	0.0194763i
$446$	2.06707	−	4.64271i	0.0978784	−	0.219839i
$447$	−8.63429	−	5.06168i	−0.408388	−	0.239409i
$448$	11.5737	−	7.51606i	0.546807	−	0.355100i
$449$	−11.5715			−0.546092			−0.273046	−	0.962001i	$-0.588031\pi$
$449$	−11.5715			−0.546092			−0.273046	+	0.962001i	$0.588031\pi$
$450$	10.5364	−	12.8982i	0.496691	−	0.608029i
$451$	3.48713			0.164203
$452$	−6.55053	+	4.25396i	−0.308111	+	0.200090i
$453$	0.0754511	−	11.3724i	0.00354500	−	0.534323i
$454$	−4.50884	+	10.1270i	−0.211610	+	0.475284i
$455$	−12.8795	−	10.3341i	−0.603802	−	0.484470i
$456$	27.3884	−	1.25322i	1.28258	−	0.0586874i
$457$	−19.2345	+	5.15386i	−0.899750	+	0.241087i	−0.678909	−	0.734223i	$-0.737547\pi$
$457$	−19.2345	+	5.15386i	−0.899750	+	0.241087i	−0.220841	+	0.975310i	$0.570880\pi$
$458$	−0.512739	−	3.23731i	−0.0239587	−	0.151270i
$459$	−2.34354	−	16.9769i	−0.109387	−	0.792412i
$460$	10.7356	+	9.57928i	0.500549	+	0.446636i
$461$	3.44925	−	16.2274i	0.160648	−	0.755788i	−0.821879	−	0.569663i	$-0.807074\pi$
$461$	3.44925	−	16.2274i	0.160648	−	0.755788i	0.982526	−	0.186125i	$-0.0595929\pi$
$462$	−10.9677	−	4.97058i	−0.510263	−	0.231252i
$463$	−14.9155	+	22.9679i	−0.693182	+	1.06741i	0.300347	+	0.953830i	$0.402898\pi$
$463$	−14.9155	+	22.9679i	−0.693182	+	1.06741i	−0.993529	+	0.113577i	$0.963769\pi$
$464$	3.27728	−	3.63979i	0.152144	−	0.168973i
$465$	25.9497	−	1.30436i	1.20339	−	0.0604881i
$466$	−11.1055	−	12.3339i	−0.514452	−	0.571357i
$467$	11.5224	−	1.82497i	0.533195	−	0.0844498i	0.115969	−	0.993253i	$-0.463003\pi$
$467$	11.5224	−	1.82497i	0.533195	−	0.0844498i	0.417225	+	0.908803i	$0.363003\pi$
$468$	10.1691	−	0.397724i	0.470069	−	0.0183848i
$469$	7.02423	−	9.66802i	0.324349	−	0.446428i
$470$	8.79217	−	17.4492i	0.405553	−	0.804870i
$471$	5.62174	+	21.5515i	0.259036	+	0.993042i
$472$	14.6043	+	38.0454i	0.672216	+	1.75118i
$473$	−0.290652	+	0.0152324i	−0.0133642	+	0.000700388i
$474$	9.99799	−	25.5379i	0.459223	−	1.17300i
$475$	−25.1478	+	5.58218i	−1.15386	+	0.256128i
$476$			4.22604i			0.193700i
$477$	10.0788	−	12.1140i	0.461476	−	0.554662i
$478$	−1.91524	+	12.0923i	−0.0876010	+	0.553091i
$479$	−2.77622	−	26.4140i	−0.126849	−	1.20689i	−0.853950	−	0.520356i	$-0.825799\pi$
$479$	−2.77622	−	26.4140i	−0.126849	−	1.20689i	0.727101	−	0.686531i	$-0.240867\pi$
$480$	1.67741	−	15.6379i	0.0765631	−	0.713770i
$481$	−1.99335	+	18.9654i	−0.0908888	+	0.864749i
$482$	7.99197	+	2.14144i	0.364024	+	0.0975401i
$483$	−16.3535	+	17.9218i	−0.744109	+	0.815471i
$484$	1.74197	−	1.56848i	0.0791804	−	0.0712943i
$485$	−11.7419	−	20.1280i	−0.533174	−	0.913968i
$486$	−17.3049	+	0.332080i	−0.784967	+	0.0150635i
$487$	32.1874	−	16.4003i	1.45855	−	0.743169i	0.468446	−	0.883492i	$-0.344814\pi$
$487$	32.1874	−	16.4003i	1.45855	−	0.743169i	0.990106	+	0.140322i	$0.0448139\pi$
$488$	−0.987129	+	18.8356i	−0.0446853	+	0.852645i
$489$	−17.5852	−	11.5866i	−0.795231	−	0.523962i
$490$	7.02993	+	7.73727i	0.317580	+	0.349534i
$491$	−2.00041	−	9.41120i	−0.0902773	−	0.424721i	−0.999956	−	0.00940801i	$-0.997005\pi$
$491$	−2.00041	−	9.41120i	−0.0902773	−	0.424721i	0.909678	−	0.415313i	$-0.136328\pi$
$492$	−1.17801	+	0.374136i	−0.0531087	+	0.0168673i
$493$	2.22745	+	8.31294i	0.100319	+	0.374396i
$494$	20.4628	+	14.8671i	0.920664	+	0.668902i
$495$	−22.5075	+	11.2206i	−1.01164	+	0.504327i
$496$	−10.1873	+	7.40151i	−0.457423	+	0.332338i
$497$	3.17624	+	2.57207i	0.142474	+	0.115373i
$498$	−13.7186	+	12.1884i	−0.614743	+	0.546176i
$499$	26.2567	−	15.1593i	1.17541	−	0.678623i	0.220461	−	0.975396i	$-0.429244\pi$
$499$	26.2567	−	15.1593i	1.17541	−	0.678623i	0.954948	+	0.296773i	$0.0959103\pi$
$500$	0.564433	+	8.55895i	0.0252422	+	0.382768i
$501$	−4.87417	−	1.90822i	−0.217762	−	0.0852528i
$502$	2.89341	+	4.45546i	0.129139	+	0.198857i
$503$	−3.00977	−	0.476701i	−0.134199	−	0.0212550i	0.0889735	−	0.996034i	$-0.471641\pi$
$503$	−3.00977	−	0.476701i	−0.134199	−	0.0212550i	−0.223173	+	0.974779i	$0.571641\pi$
$504$	15.2873	+	1.81214i	0.680949	+	0.0807192i
$505$	6.34725	−	5.18734i	0.282449	−	0.230833i
$506$	14.2000	+	31.8938i	0.631268	+	1.41785i
$507$	9.13551	+	6.73039i	0.405722	+	0.298907i
$508$	−7.74951	−	9.56985i	−0.343829	−	0.424593i
$509$	31.7026	−	6.73860i	1.40519	−	0.298683i	0.557944	−	0.829878i	$-0.311590\pi$
$509$	31.7026	−	6.73860i	1.40519	−	0.298683i	0.847249	+	0.531195i	$0.178257\pi$
$510$	−11.0031	−	8.94916i	−0.487226	−	0.396275i
$511$	7.01377	+	1.49082i	0.310271	+	0.0659501i
$512$	8.69680	+	17.0684i	0.384348	+	0.754325i
$513$	21.3403	+	16.1632i	0.942197	+	0.713622i
$514$	6.77180	−	2.20029i	0.298691	−	0.0970507i
$515$	−0.0566701	−	12.6014i	−0.00249718	−	0.555286i
$516$	0.0965526	−	0.0363299i	0.00425049	−	0.00159934i
$517$	−22.9296	+	18.5680i	−1.00844	+	0.816619i
$518$	−2.06993	+	7.72508i	−0.0909475	+	0.339421i
$519$	9.55377	+	4.94800i	0.419364	+	0.217193i
$520$	21.3837	−	21.5769i	0.937735	−	0.946208i
$521$	16.6489	+	22.9152i	0.729401	+	1.00393i	0.999159	+	0.0410057i	$0.0130562\pi$
$521$	16.6489	+	22.9152i	0.729401	+	1.00393i	−0.269758	+	0.962928i	$0.586944\pi$
$522$	8.60197	−	1.24565i	0.376498	−	0.0545208i
$523$	−10.1771	−	5.18550i	−0.445014	−	0.226746i	0.217100	−	0.976149i	$-0.430340\pi$
$523$	−10.1771	−	5.18550i	−0.445014	−	0.226746i	−0.662114	+	0.749404i	$0.730340\pi$
$524$	8.16342	−	14.1394i	0.356620	−	0.617685i
$525$	−14.4421	+	0.791058i	−0.630307	+	0.0345246i
$526$	−5.92126	−	10.2559i	−0.258179	−	0.447180i
$527$	−1.15800	−	22.0960i	−0.0504434	−	0.962518i
$528$	6.16411	−	10.5148i	0.268258	−	0.457599i
$529$	47.0829	−	4.94862i	2.04708	−	0.215157i
$530$	−0.741098	−	13.0204i	−0.0321912	−	0.565569i
$531$	−12.7971	+	37.6770i	−0.555349	+	1.63504i
$532$	−4.66786	−	4.66786i	−0.202377	−	0.202377i
$533$	−3.83960	−	1.47389i	−0.166312	−	0.0638411i
$534$	−7.28669	−	1.20371i	−0.315326	−	0.0520895i
$535$	10.4231	+	23.1302i	0.450632	+	1.00001i
$536$	16.3376	+	14.7105i	0.705678	+	0.635395i
$537$	2.78376	−	6.14243i	0.120128	−	0.265065i
$538$	12.3932	+	0.649501i	0.534310	+	0.0280020i
$539$	−4.87812	−	15.0133i	−0.210115	−	0.646668i
$540$	6.39954	−	6.20533i	0.275392	−	0.267035i
$541$	−8.73366	+	26.8794i	−0.375489	+	1.15564i	0.567658	+	0.823264i	$0.307849\pi$
$541$	−8.73366	+	26.8794i	−0.375489	+	1.15564i	−0.943148	+	0.332373i	$0.892151\pi$
$542$	−3.47869	+	9.06230i	−0.149423	+	0.389259i
$543$	−36.5448	−	4.08633i	−1.56829	−	0.175361i
$544$	−13.3201	−	1.40000i	−0.571093	−	0.0600243i
$545$	7.01360	−	8.74116i	0.300430	−	0.374430i
$546$	9.97540	+	10.1086i	0.426908	+	0.432610i
$547$	19.3245	−	23.8638i	0.826258	−	1.02034i	−0.173114	−	0.984902i	$-0.555383\pi$
$547$	19.3245	−	23.8638i	0.826258	−	1.02034i	0.999372	−	0.0354415i	$-0.0112837\pi$
$548$	−6.60490	+	12.9628i	−0.282147	+	0.553745i
$549$	−12.5036	+	13.5215i	−0.533640	+	0.577081i
$550$	−7.28369	+	19.4970i	−0.310578	+	0.831356i
$551$	−11.6423	−	6.72171i	−0.495981	−	0.286355i
$552$	−29.6446	−	33.3662i	−1.26176	−	1.42016i
$553$	−22.2355	+	8.53541i	−0.945550	+	0.362963i
$554$	−18.2132	−	8.10903i	−0.773804	−	0.344520i
$555$	9.78915	+	13.5344i	0.415526	+	0.574501i
$556$	0.136568	−	0.0608039i	0.00579176	−	0.00257866i
$557$	−17.2077	+	17.2077i	−0.729113	+	0.729113i	−0.970443	−	0.241330i	$-0.922416\pi$
$557$	−17.2077	+	17.2077i	−0.729113	+	0.729113i	0.241330	+	0.970443i	$0.422416\pi$
$558$	−22.2981	−	1.46550i	−0.943952	−	0.0620395i
$559$	0.326469	+	0.106076i	0.0138082	+	0.00448654i
$560$	5.65243	−	4.14569i	0.238859	−	0.175187i
$561$	9.59623	+	19.1466i	0.405153	+	0.808372i
$562$	1.53202	+	0.994906i	0.0646244	+	0.0419676i
$563$	−29.0990	−	18.8971i	−1.22638	−	0.796418i	−0.241622	−	0.970370i	$-0.577679\pi$
$563$	−29.0990	−	18.8971i	−1.22638	−	0.796418i	−0.984754	+	0.173953i	$0.944346\pi$
$564$	5.75380	−	8.73268i	0.242279	−	0.367712i
$565$	−18.3567	+	13.4634i	−0.772271	+	0.566411i
$566$	20.1612	+	6.55078i	0.847439	+	0.275350i
$567$	10.3429	+	10.9070i	0.434361	+	0.458049i
$568$	−5.31657	+	5.31657i	−0.223078	+	0.223078i
$569$	−21.0647	+	9.37860i	−0.883077	+	0.393171i	−0.797613	−	0.603170i	$-0.793904\pi$
$569$	−21.0647	+	9.37860i	−0.883077	+	0.393171i	−0.0854643	+	0.996341i	$0.527237\pi$
$570$	22.0382	−	2.26870i	0.923080	−	0.0950253i
$571$	−19.1971	−	8.54709i	−0.803372	−	0.357684i	−0.0363779	−	0.999338i	$-0.511582\pi$
$571$	−19.1971	−	8.54709i	−0.803372	−	0.357684i	−0.766995	+	0.641654i	$0.778249\pi$
$572$	−11.8732	+	4.55769i	−0.496443	+	0.190566i
$573$	5.78888	−	17.4222i	0.241834	−	0.727822i
$574$	−1.49374	−	0.862414i	−0.0623477	−	0.0359965i
$575$	32.8258	+	26.0965i	1.36893	+	1.08830i
$576$	−5.47510	+	24.1763i	−0.228129	+	1.00735i
$577$	0.198295	−	0.389176i	0.00825514	−	0.0162016i	−0.886842	−	0.462073i	$-0.847106\pi$
$577$	0.198295	−	0.389176i	0.00825514	−	0.0162016i	0.895097	+	0.445871i	$0.147106\pi$
$578$	4.27771	−	5.28254i	0.177929	−	0.219725i
$579$	−37.0199	+	9.65666i	−1.53849	+	0.401317i
$580$	−2.80142	+	3.49145i	−0.116323	+	0.144975i
$581$	15.8495	+	1.66585i	0.657549	+	0.0691112i
$582$	8.02990	+	18.3623i	0.332850	+	0.761144i
$583$	−7.05739	+	18.3851i	−0.292287	+	0.761434i
$584$	−4.07629	+	12.5455i	−0.168678	+	0.519137i
$585$	29.5251	−	2.84160i	1.22071	−	0.117485i
$586$	6.81318	+	20.9688i	0.281450	+	0.866213i
$587$	6.37555	+	0.334128i	0.263147	+	0.0137910i	0.183453	−	0.983028i	$-0.441272\pi$
$587$	6.37555	+	0.334128i	0.263147	+	0.0137910i	0.0796938	+	0.996819i	$0.474606\pi$
$588$	3.25869	+	4.54835i	0.134386	+	0.187571i
$589$	25.6852	+	23.1270i	1.05834	+	0.952932i
$590$	13.5291	+	30.0228i	0.556984	+	1.23602i
$591$	−7.96857	−	21.1777i	−0.327783	−	0.871135i
$592$	−7.55752	−	2.90106i	−0.310612	−	0.119233i
$593$	−7.94158	−	7.94158i	−0.326122	−	0.326122i	0.524988	−	0.851110i	$-0.324070\pi$
$593$	−7.94158	−	7.94158i	−0.326122	−	0.326122i	−0.851110	+	0.524988i	$0.824070\pi$
$594$	20.3433	−	7.34795i	0.834694	−	0.301490i
$595$	0.699940	+	12.2973i	0.0286947	+	0.504139i
$596$	−4.40894	+	0.463398i	−0.180597	+	0.0189815i
$597$	−21.2284	−	37.3387i	−0.868822	−	1.52817i
$598$	−2.15497	−	41.1193i	−0.0881234	−	1.68150i
$599$	6.24649	+	10.8192i	0.255225	+	0.442062i	0.964957	−	0.262410i	$-0.0845172\pi$
$599$	6.24649	+	10.8192i	0.255225	+	0.442062i	−0.709732	+	0.704472i	$0.751184\pi$
$600$	1.32987	−	26.5751i	0.0542916	−	1.08492i
$601$	−18.9462	+	32.8158i	−0.772831	+	1.33858i	0.163174	+	0.986597i	$0.447827\pi$
$601$	−18.9462	+	32.8158i	−0.772831	+	1.33858i	−0.936005	+	0.351986i	$0.885507\pi$
$602$	0.128271	+	0.0653572i	0.00522792	+	0.00266376i
$603$	3.07640	+	21.2443i	0.125281	+	0.865136i
$604$	−2.96093	−	4.07537i	−0.120479	−	0.165825i
$605$	4.80914	−	4.85259i	0.195519	−	0.197286i
$606$	−5.93804	+	3.80044i	−0.241216	+	0.154382i
$607$	5.75085	−	21.4624i	0.233420	−	0.871134i	−0.745435	−	0.666578i	$-0.767758\pi$
$607$	5.75085	−	21.4624i	0.233420	−	0.871134i	0.978855	−	0.204556i	$-0.0655750\pi$
$608$	16.2590	−	13.1663i	0.659389	−	0.533963i
$609$	−5.83448	−	4.78911i	−0.236425	−	0.194064i
$610$	0.0685406	+	15.2410i	0.00277513	+	0.617091i
$611$	33.0953	−	10.7533i	1.33889	−	0.435032i
$612$	−5.29601	−	5.43845i	−0.214079	−	0.219836i
$613$	4.41071	+	8.65650i	0.178147	+	0.349633i	0.962762	−	0.270350i	$-0.0871395\pi$
$613$	4.41071	+	8.65650i	0.178147	+	0.349633i	−0.784615	+	0.619983i	$0.787139\pi$
$614$	−9.64408	−	2.04991i	−0.389203	−	0.0827277i
$615$	−3.36589	+	1.28380i	−0.135726	+	0.0517677i
$616$	−18.8176	+	3.99980i	−0.758181	+	0.161156i
$617$	−1.79559	−	2.21736i	−0.0722876	−	0.0892677i	0.739719	−	0.672915i	$-0.234958\pi$
$617$	−1.79559	−	2.21736i	−0.0722876	−	0.0892677i	−0.812007	+	0.583648i	$0.801625\pi$
$618$	−1.20436	+	10.7708i	−0.0484464	+	0.433266i
$619$	−10.9930	−	24.6906i	−0.441845	−	0.992401i	−0.987963	−	0.154692i	$-0.950561\pi$
$619$	−10.9930	−	24.6906i	−0.441845	−	0.992401i	0.546117	−	0.837709i	$-0.316105\pi$
$620$	8.91131	−	7.28284i	0.357887	−	0.292486i
$621$	−1.41421	−	43.5573i	−0.0567505	−	1.74790i
$622$	8.55608	+	1.35515i	0.343068	+	0.0543366i
$623$	3.49325	+	5.37913i	0.139954	+	0.215510i
$624$	−11.2314	+	8.97229i	−0.449616	+	0.359179i
$625$	3.06001	+	24.8120i	0.122400	+	0.992481i
$626$	20.5375	−	11.8574i	0.820845	−	0.473915i
$627$	−31.7479	−	10.5489i	−1.26789	−	0.421282i
$628$	7.66695	+	6.20857i	0.305944	+	0.247749i
$629$	11.5078	−	8.36093i	0.458847	−	0.333372i
$630$	12.4163	+	0.759977i	0.494677	+	0.0302782i
$631$	−7.84281	−	5.69814i	−0.312217	−	0.226839i	0.420630	−	0.907232i	$-0.361809\pi$
$631$	−7.84281	−	5.69814i	−0.312217	−	0.226839i	−0.732847	+	0.680393i	$0.761809\pi$
$632$	−11.3404	−	42.3228i	−0.451095	−	1.68351i
$633$	−1.78369	+	8.12612i	−0.0708953	+	0.322984i
$634$	−4.78731	−	22.5225i	−0.190128	−	0.894483i
$635$	−24.1351	−	26.5636i	−0.957774	−	1.05414i
$636$	0.411549	−	6.96798i	0.0163190	−	0.276298i
$637$	−0.974398	+	18.5926i	−0.0386070	+	0.736666i
$638$	−9.67797	+	4.93117i	−0.383155	+	0.195227i
$639$	−7.31076	+	0.670445i	−0.289209	+	0.0265224i
$640$	1.18607	+	2.03316i	0.0468835	+	0.0803677i
$641$	−27.1226	+	24.4213i	−1.07128	+	0.964584i	−0.999461	−	0.0328339i	$-0.989547\pi$
$641$	−27.1226	+	24.4213i	−1.07128	+	0.964584i	−0.0718181	+	0.997418i	$0.522880\pi$
$642$	−6.60481	−	20.7960i	−0.260671	−	0.820751i
$643$	−20.9917	−	5.62471i	−0.827832	−	0.221817i	−0.180064	−	0.983655i	$-0.557631\pi$
$643$	−20.9917	−	5.62471i	−0.827832	−	0.221817i	−0.647767	+	0.761838i	$0.724297\pi$
$644$	−1.12332	+	10.6876i	−0.0442649	+	0.421152i
$645$	0.274939	−	0.121707i	0.0108257	−	0.00479222i
$646$	−1.97210	−	18.7633i	−0.0775913	−	0.738232i
$647$	−0.880550	+	5.55957i	−0.0346180	+	0.218569i	−0.998933	−	0.0461893i	$-0.985292\pi$
$647$	−0.880550	+	5.55957i	−0.0346180	+	0.218569i	0.964315	+	0.264759i	$0.0852923\pi$
$648$	−21.9440	+	16.8257i	−0.862041	+	0.660977i
$649$		−	49.7261i		−	1.95192i
$650$	16.2606	−	18.3892i	0.637793	−	0.721283i
$651$	12.1126	+	15.1624i	0.474730	+	0.594261i
$652$	−9.31521	+	0.488189i	−0.364812	+	0.0191190i
$653$	−9.62544	−	25.0751i	−0.376673	−	0.981266i	−0.982598	−	0.185745i	$-0.940530\pi$
$653$	−9.62544	−	25.0751i	−0.376673	−	0.981266i	0.605925	−	0.795522i	$-0.292803\pi$
$654$	−6.86060	+	6.77016i	−0.268271	+	0.264734i
$655$	21.4127	−	42.4961i	0.836663	−	1.66046i
$656$	1.02620	−	1.41245i	0.0400664	−	0.0551467i
$657$	−10.8942	+	6.87102i	−0.425024	+	0.268064i
$658$	14.4142	−	2.28298i	0.561924	−	0.0890000i
$659$	−20.6673	−	22.9533i	−0.805083	−	0.894135i	0.191087	−	0.981573i	$-0.438799\pi$
$659$	−20.6673	−	22.9533i	−0.805083	−	0.894135i	−0.996170	+	0.0874381i	$0.972132\pi$
$660$	−5.07853	+	9.91473i	−0.197681	+	0.385930i
$661$	21.6685	−	24.0653i	0.842807	−	0.936032i	−0.155853	−	0.987780i	$-0.549813\pi$
$661$	21.6685	−	24.0653i	0.842807	−	0.936032i	0.998660	+	0.0517485i	$0.0164794\pi$
$662$	−11.7046	+	18.0235i	−0.454911	+	0.700502i
$663$	−2.47360	−	25.1379i	−0.0960667	−	0.976277i
$664$	−6.09560	+	28.6775i	−0.236555	+	1.11290i
$665$	−14.3560	−	12.8098i	−0.556703	−	0.496742i
$666$	−7.01718	−	12.5353i	−0.271910	−	0.485735i
$667$	3.42355	+	21.6155i	0.132561	+	0.836954i
$668$	−2.23953	+	0.600080i	−0.0866500	+	0.0232178i
$669$	3.64595	−	7.03973i	0.140961	−	0.272172i
$670$	13.8560	+	11.1175i	0.535303	+	0.429508i
$671$	9.36097	−	21.0251i	0.361376	−	0.811665i
$672$	10.2120	−	5.80591i	0.393937	−	0.223968i
$673$	−5.72667	+	3.71895i	−0.220747	+	0.143355i	−0.650275	−	0.759699i	$-0.725346\pi$
$673$	−5.72667	+	3.71895i	−0.220747	+	0.143355i	0.429528	+	0.903053i	$0.358680\pi$
$674$	36.7711			1.41637
$675$	17.5941	−	19.1167i	0.677198	−	0.735801i
$676$	5.02609			0.193311
$677$	13.8040	−	8.96445i	0.530532	−	0.344532i	−0.251412	−	0.967880i	$-0.580895\pi$
$677$	13.8040	−	8.96445i	0.530532	−	0.344532i	0.781944	+	0.623348i	$0.214228\pi$
$678$	17.0202	−	9.67665i	0.653658	−	0.371630i
$679$	7.07920	−	15.9001i	0.271675	−	0.610192i
$680$	−22.6333	−	1.08412i	−0.867949	−	0.0415742i
$681$	−7.95282	+	15.3556i	−0.304753	+	0.588427i
$682$	26.9740	−	7.22767i	1.03289	−	0.276762i
$683$	−6.26704	−	39.5686i	−0.239802	−	1.51405i	−0.754284	−	0.656548i	$-0.772016\pi$
$683$	−6.26704	−	39.5686i	−0.239802	−	1.51405i	0.514483	−	0.857501i	$-0.327984\pi$
$684$	11.8567	+	0.157335i	0.453353	+	0.00601586i
$685$	−17.0725	+	38.8142i	−0.652306	+	1.48302i
$686$	−4.32223	+	20.3345i	−0.165023	+	0.776374i
$687$	−0.500709	−	5.08845i	−0.0191032	−	0.194137i
$688$	−0.0793640	+	0.122210i	−0.00302572	+	0.00465921i
$689$	15.5415	−	17.2606i	0.592083	−	0.657575i
$690$	−25.4481	−	25.5571i	−0.968792	−	0.972942i
$691$	−3.69856	−	4.10767i	−0.140700	−	0.156263i	0.668676	−	0.743554i	$-0.266861\pi$
$691$	−3.69856	−	4.10767i	−0.140700	−	0.156263i	−0.809376	+	0.587291i	$0.800195\pi$
$692$	4.70697	−	0.745510i	0.178932	−	0.0283401i
$693$	−16.6222	−	8.74919i	−0.631427	−	0.332354i
$694$	−11.6453	+	16.0284i	−0.442049	+	0.608428i
$695$	0.387325	−	0.199551i	0.0146921	−	0.00756940i
$696$	9.88396	−	9.75368i	0.374651	−	0.369712i
$697$	1.09939	+	2.86401i	0.0416423	+	0.108482i
$698$	6.99085	−	0.366375i	0.264608	−	0.0138675i
$699$	−16.1596	−	20.2284i	−0.611212	−	0.765108i
$700$	−4.94242	+	4.07644i	−0.186806	+	0.154075i
$701$		−	1.29676i		−	0.0489781i	−0.999700	−	0.0244890i	$-0.992204\pi$
$701$		−	1.29676i		−	0.0489781i	0.999700	−	0.0244890i	$-0.00779588\pi$
$702$	−25.5052	−	0.507708i	−0.962633	−	0.0191622i
$703$	−3.47590	+	21.9460i	−0.131096	+	0.827708i
$704$	−3.23806	−	30.8081i	−0.122039	−	1.16112i
$705$	15.2965	−	26.3640i	0.576099	−	0.992926i
$706$	2.42285	−	23.0518i	0.0911850	−	0.867567i
$707$	5.91401	+	1.58465i	0.222419	+	0.0595971i
$708$	5.33513	+	16.7983i	0.200507	+	0.631317i
$709$	26.3586	−	23.7334i	0.989919	−	0.891327i	−0.00415976	−	0.999991i	$-0.501324\pi$
$709$	26.3586	−	23.7334i	0.989919	−	0.891327i	0.994078	+	0.108665i	$0.0346574\pi$
$710$	−4.04504	+	4.53331i	−0.151808	+	0.170132i
$711$	17.9182	−	38.8493i	0.671985	−	1.45696i
$712$	−10.5133	+	5.35677i	−0.394001	+	0.200753i
$713$	2.94472	−	56.1885i	0.110281	−	2.10428i
$714$	0.624585	−	10.5749i	0.0233745	−	0.395756i
$715$	−33.7946	+	15.2288i	−1.26385	+	0.569525i
$716$	−0.621055	−	2.92183i	−0.0232099	−	0.109194i
$717$	−4.09470	+	18.6546i	−0.152919	+	0.696670i
$718$	2.95611	+	11.0324i	0.110321	+	0.411724i
$719$	6.90482	+	5.01665i	0.257507	+	0.187089i	0.709047	−	0.705161i	$-0.249125\pi$
$719$	6.90482	+	5.01665i	0.257507	+	0.187089i	−0.451541	+	0.892251i	$0.649125\pi$
$720$	−2.07874	+	12.4186i	−0.0774699	+	0.462813i
$721$	7.61463	−	5.53235i	0.283584	−	0.206035i
$722$	6.50853	+	5.27051i	0.242223	+	0.196148i
$723$	12.2485	+	4.06983i	0.455528	+	0.151358i
$724$	−14.1059	+	8.14407i	−0.524243	+	0.302672i
$725$	−7.57352	+	10.6237i	−0.281273	+	0.394554i
$726$	−4.59078	+	3.66738i	−0.170380	+	0.136109i
$727$	21.9830	+	33.8508i	0.815303	+	1.25546i	0.963822	+	0.266547i	$0.0858829\pi$
$727$	21.9830	+	33.8508i	0.815303	+	1.25546i	−0.148518	+	0.988910i	$0.547450\pi$
$728$	22.4102	+	3.54942i	0.830576	+	0.131550i
$729$	−26.9786	−	1.07450i	−0.999208	−	0.0397963i
$730$	−2.71249	+	10.3084i	−0.100394	+	0.381529i
$731$	−0.104144	−	0.233912i	−0.00385192	−	0.00865156i
$732$	−0.906493	+	8.10695i	−0.0335049	+	0.299641i
$733$	−15.5121	−	19.1559i	−0.572954	−	0.707540i	0.405479	−	0.914105i	$-0.367105\pi$
$733$	−15.5121	−	19.1559i	−0.572954	−	0.707540i	−0.978433	+	0.206565i	$0.933772\pi$
$734$	17.6945	−	3.76108i	0.653115	−	0.138824i
$735$	10.2357	+	12.6954i	0.377550	+	0.468278i
$736$	−33.3143	−	7.08117i	−1.22798	−	0.261015i
$737$	−12.1786	−	23.9018i	−0.448603	−	0.880433i
$738$	3.00305	−	0.762105i	0.110544	−	0.0280535i
$739$	−34.6400	+	11.2552i	−1.27425	+	0.414030i	−0.866553	−	0.499086i	$-0.833669\pi$
$739$	−34.6400	+	11.2552i	−1.27425	+	0.414030i	−0.407700	+	0.913116i	$0.633669\pi$
$740$	7.04677	+	2.25465i	0.259044	+	0.0828826i
$741$	30.4982	+	25.0338i	1.12038	+	0.919640i
$742$	7.56999	−	6.13005i	0.277903	−	0.225041i
$743$	−2.04974	+	7.64975i	−0.0751978	+	0.280642i	−0.993278	−	0.115752i	$-0.963072\pi$
$743$	−2.04974	+	7.64975i	−0.0751978	+	0.280642i	0.918080	+	0.396395i	$0.129739\pi$
$744$	−30.0699	+	19.2452i	−1.10242	+	0.705563i
$745$	−12.7527	+	2.07866i	−0.467223	+	0.0761563i
$746$	−16.9304	−	23.3027i	−0.619867	−	0.853174i
$747$	−22.4842	+	17.7186i	−0.822655	+	0.648290i
$748$	8.45247	+	4.30675i	0.309053	+	0.157470i
$749$	−9.47461	+	16.4105i	−0.346195	+	0.599627i
$750$	−0.147428	−	21.5007i	−0.00538330	−	0.785093i
$751$	2.11076	+	3.65594i	0.0770227	+	0.133407i	0.901964	−	0.431811i	$-0.142125\pi$
$751$	2.11076	+	3.65594i	0.0770227	+	0.133407i	−0.824941	+	0.565218i	$0.808792\pi$
$752$	0.773106	+	14.7517i	0.0281923	+	0.537941i
$753$	4.09596	+	7.20438i	0.149265	+	0.262542i
$754$	12.7404	−	1.33907i	0.463979	−	0.0487662i
$755$	−9.29094	−	11.3684i	−0.338132	−	0.413740i
$756$	6.55396	+	1.17220i	0.238365	+	0.0426327i
$757$	4.27864	+	4.27864i	0.155510	+	0.155510i	0.780574	−	0.625064i	$-0.214927\pi$
$757$	4.27864	+	4.27864i	0.155510	+	0.155510i	−0.625064	+	0.780574i	$0.714927\pi$
$758$	39.7604	+	15.2626i	1.44416	+	0.554362i
$759$	19.1795	+	50.9725i	0.696172	+	1.85019i
$760$	26.1971	−	23.8021i	0.950267	−	0.863394i
$761$	23.5761	+	21.2280i	0.854633	+	0.769515i	0.974763	−	0.223243i	$-0.0716643\pi$
$761$	23.5761	+	21.2280i	0.854633	+	0.769515i	−0.120129	+	0.992758i	$0.538331\pi$
$762$	17.9774	+	25.0922i	0.651252	+	0.908993i
$763$	8.35917	+	0.438086i	0.302622	+	0.0158598i
$764$	−2.51289	−	7.73387i	−0.0909130	−	0.279801i
$765$	−16.3115	−	14.9481i	−0.589743	−	0.540449i
$766$	−0.131488	+	0.404680i	−0.00475087	+	0.0146217i
$767$	−21.0174	+	54.7523i	−0.758896	+	1.97699i
$768$	10.6573	+	24.3706i	0.384563	+	0.879398i
$769$	6.24786	+	0.656677i	0.225304	+	0.0236804i	0.216508	−	0.976281i	$-0.430533\pi$
$769$	6.24786	+	0.656677i	0.225304	+	0.0236804i	0.00879616	+	0.999961i	$0.497200\pi$
$770$	−14.9975	+	4.09095i	−0.540473	+	0.147428i
$771$	10.7477	−	2.80356i	0.387071	−	0.100968i
$772$	−10.6647	+	13.1698i	−0.383831	+	0.473991i
$773$	11.9269	−	23.4079i	0.428982	−	0.841924i	−0.570801	−	0.821088i	$-0.693367\pi$
$773$	11.9269	−	23.4079i	0.428982	−	0.841924i	0.999783	−	0.0208358i	$-0.00663272\pi$
$774$	−0.246975	+	0.0766393i	−0.00887733	+	0.00275474i
$775$	24.7246	−	22.6681i	0.888134	−	0.814262i
$776$	27.7292	+	16.0094i	0.995420	+	0.574706i
$777$	−3.93391	+	11.8395i	−0.141128	+	0.424739i
$778$	−29.5848	+	11.3565i	−1.06067	+	0.407152i
$779$	−4.37775	−	1.94910i	−0.156849	−	0.0698338i
$780$	9.78246	−	8.77038i	0.350268	−	0.314030i
$781$	8.38128	−	3.73159i	0.299906	−	0.133527i
$782$	−21.7177	+	21.7177i	−0.776624	+	0.776624i
$783$	13.5100	−	1.14862i	0.482807	−	0.0410484i
$784$	−7.51661	−	2.44229i	−0.268450	−	0.0872248i
$785$	23.3382	+	16.7963i	0.832975	+	0.599487i
$786$	−22.5172	+	34.1749i	−0.803163	+	1.21898i
$787$	5.24362	+	3.40525i	0.186915	+	0.121384i	0.634704	−	0.772755i	$-0.281122\pi$
$787$	5.24362	+	3.40525i	0.186915	+	0.121384i	−0.447789	+	0.894139i	$0.647789\pi$
$788$	−8.40564	−	5.45869i	−0.299439	−	0.194458i
$789$	−8.27758	−	16.5156i	−0.294690	−	0.587972i
$790$	−11.0923	−	33.6234i	−0.394648	−	1.19627i
$791$	−16.1709	−	5.25425i	−0.574972	−	0.186820i
$792$	19.2037	−	28.7292i	0.682372	−	1.02085i
$793$	−19.1937	+	19.1937i	−0.681589	+	0.681589i
$794$	−19.9503	+	8.88245i	−0.708010	+	0.315226i
$795$	0.0434832	−	20.3441i	0.00154219	−	0.721532i
$796$	−17.3802	−	7.73816i	−0.616025	−	0.274272i
$797$	27.4488	−	10.5366i	0.972285	−	0.373225i	0.180196	−	0.983631i	$-0.442327\pi$
$797$	27.4488	−	10.5366i	0.972285	−	0.373225i	0.792089	+	0.610405i	$0.208993\pi$
$798$	10.9906	+	12.3704i	0.389063	+	0.437907i
$799$	−22.4790	−	12.9783i	−0.795251	−	0.459138i
$800$	−11.2112	−	16.9285i	−0.396376	−	0.598511i
$801$	−11.2365	−	2.54467i	−0.397021	−	0.0899114i
$802$	−5.90935	+	11.5978i	−0.208666	+	0.409531i
$803$	10.1295	−	12.5089i	0.357462	−	0.441429i
$804$	6.67854	+	6.76775i	0.235534	+	0.238680i
$805$	−1.49857	+	31.2858i	−0.0528176	+	1.10268i
$806$	−32.7554	−	3.44273i	−1.15376	−	0.121265i
$807$	19.2396	+	2.15131i	0.677266	+	0.0757297i
$808$	−4.03648	+	10.5154i	−0.142003	+	0.369930i
$809$	−13.9751	+	43.0109i	−0.491338	+	1.51218i	0.331248	+	0.943544i	$0.392530\pi$
$809$	−13.9751	+	43.0109i	−0.491338	+	1.51218i	−0.822586	+	0.568640i	$0.807470\pi$
$810$	−16.9308	+	14.5819i	−0.594888	+	0.512356i
$811$	−5.39556	−	16.6058i	−0.189464	−	0.583109i	0.810533	−	0.585693i	$-0.199178\pi$
$811$	−5.39556	−	16.6058i	−0.189464	−	0.583109i	−0.999997	+	0.00258383i	$0.999178\pi$
$812$	−3.33887	−	0.174983i	−0.117172	−	0.00614070i
$813$	−6.25069	+	13.7923i	−0.219221	+	0.483717i
$814$	13.3414	+	12.0127i	0.467616	+	0.421044i
$815$	−27.0253	+	2.96341i	−0.946654	+	0.103804i
$816$	10.5793	+	1.74762i	0.370348	+	0.0611788i
$817$	0.373400	+	0.143335i	0.0130636	+	0.00501465i
$818$	2.05032	+	2.05032i	0.0716878	+	0.0716878i
$819$	14.6044	+	16.6592i	0.510320	+	0.582118i
$820$	−0.863032	+	1.34213i	−0.0301384	+	0.0468691i
$821$	52.2778	−	5.49462i	1.82451	−	0.191764i	0.870627	−	0.491944i	$-0.163713\pi$
$821$	52.2778	−	5.49462i	1.82451	−	0.191764i	0.953883	+	0.300180i	$0.0970468\pi$
$822$	18.4434	−	31.4610i	0.643288	−	1.09733i
$823$	−0.170779	−	3.25866i	−0.00595299	−	0.113590i	−0.999990	−	0.00454364i	$-0.998554\pi$
$823$	−0.170779	−	3.25866i	−0.00595299	−	0.113590i	0.994037	−	0.109046i	$-0.0347796\pi$
$824$	8.65758	+	14.9954i	0.301601	+	0.522388i
$825$	−13.1358	+	29.6918i	−0.457329	+	1.03374i
$826$	−12.2979	+	21.3006i	−0.427900	+	0.741144i
$827$	28.2553	+	14.3968i	0.982531	+	0.500625i	0.870015	−	0.493025i	$-0.164109\pi$
$827$	28.2553	+	14.3968i	0.982531	+	0.500625i	0.112516	+	0.993650i	$0.464109\pi$
$828$	−11.9480	−	15.1615i	−0.415222	−	0.526900i
$829$	27.6695	+	38.0838i	0.961003	+	1.32271i	0.946463	+	0.322812i	$0.104628\pi$
$829$	27.6695	+	38.0838i	0.961003	+	1.32271i	0.0145395	+	0.999894i	$0.495372\pi$
$830$	−3.60081	+	23.4157i	−0.124986	+	0.812770i
$831$	−27.6166	−	14.3029i	−0.958010	−	0.496164i
$832$	−9.45612	+	35.2907i	−0.327832	+	1.22349i
$833$	10.7926	−	8.73968i	0.373942	−	0.302812i
$834$	−0.350723	+	0.131967i	−0.0121445	+	0.00456964i
$835$	−6.41737	+	2.11708i	−0.222082	+	0.0732647i
$836$	−14.0932	+	4.57914i	−0.487422	+	0.158373i
$837$	−34.5888	−	4.33302i	−1.19556	−	0.149771i
$838$	−14.9118	−	29.2661i	−0.515120	−	1.01098i
$839$	22.4841	+	4.77915i	0.776239	+	0.164995i	0.578964	−	0.815353i	$-0.303457\pi$
$839$	22.4841	+	4.77915i	0.776239	+	0.164995i	0.197275	+	0.980348i	$0.436791\pi$
$840$	16.6908	−	10.7885i	0.575887	−	0.372238i
$841$	21.7062	−	4.61380i	0.748491	−	0.159097i
$842$	−10.1692	−	12.5579i	−0.350453	−	0.432773i
$843$	2.29423	+	1.69022i	0.0790175	+	0.0582144i
$844$	1.49886	+	3.36650i	0.0515930	+	0.115880i
$845$	14.6253	−	0.832448i	0.503126	−	0.0286371i
$846$	−15.6885	+	21.0016i	−0.539381	+	0.722050i
$847$	5.04000	+	0.798257i	0.173176	+	0.0274284i
$848$	5.36994	+	8.26898i	0.184405	+	0.283958i
$849$	30.7935	+	12.0555i	1.05683	+	0.413744i
$850$	−18.3094	+	0.164682i	−0.628006	+	0.00564855i
$851$	31.3257	−	18.0859i	1.07383	−	0.619976i
$852$	−2.43097	+	2.15982i	−0.0832835	+	0.0739942i
$853$	−30.5941	−	24.7746i	−1.04752	−	0.848266i	−0.0588350	−	0.998268i	$-0.518739\pi$
$853$	−30.5941	−	24.7746i	−1.04752	−	0.848266i	−0.988686	+	0.150002i	$0.952072\pi$
$854$	−9.20964	+	6.69120i	−0.315148	+	0.228968i
$855$	34.5277	−	1.50595i	1.18082	−	0.0515023i
$856$	−28.2023	−	20.4902i	−0.963935	−	0.700339i
$857$	−2.91380	−	10.8745i	−0.0995335	−	0.371464i	0.898134	−	0.439721i	$-0.144923\pi$
$857$	−2.91380	−	10.8745i	−0.0995335	−	0.371464i	−0.997668	+	0.0682572i	$0.978256\pi$
$858$	30.3841	−	9.65001i	1.03730	−	0.329446i
$859$	3.25065	+	15.2931i	0.110911	+	0.521795i	0.998167	+	0.0605178i	$0.0192752\pi$
$859$	3.25065	+	15.2931i	0.110911	+	0.521795i	−0.887256	+	0.461277i	$0.847391\pi$
$860$	0.0660710	−	0.115636i	0.00225300	−	0.00394316i
$861$	−2.24681	−	1.48038i	−0.0765711	−	0.0504512i
$862$	−0.000620366		0.0118373i	−2.11298e−5		0.000403180i
$863$	−17.1143	+	8.72017i	−0.582577	+	0.296838i	−0.720333	−	0.693628i	$-0.756011\pi$
$863$	−17.1143	+	8.72017i	−0.582577	+	0.296838i	0.137756	+	0.990466i	$0.456011\pi$
$864$	−5.86586	+	20.2691i	−0.199560	+	0.689569i
$865$	13.5732	−	2.94894i	0.461504	−	0.100267i
$866$	16.5463	−	14.8984i	0.562266	−	0.506267i
$867$	7.14733	−	7.83278i	0.242736	−	0.266015i
$868$	8.30306	+	2.22480i	0.281824	+	0.0755146i
$869$	−5.58855	+	53.1715i	−0.189578	+	1.80372i
$870$	7.52607	−	8.32270i	0.255158	−	0.282166i
$871$	3.30712	+	31.4652i	0.112058	+	1.06616i
$872$	−2.40894	+	15.2095i	−0.0815771	+	0.515058i
$873$	10.8157	+	29.3333i	0.366055	+	0.992782i
$874$		−	47.9765i		−	1.62283i
$875$	−13.7067	+	12.6805i	−0.463370	+	0.428680i
$876$	−2.07982	+	5.31249i	−0.0702706	+	0.179493i
$877$	27.1492	−	1.42283i	0.916763	−	0.0480455i	0.411885	−	0.911236i	$-0.364871\pi$
$877$	27.1492	−	1.42283i	0.916763	−	0.0480455i	0.504878	+	0.863190i	$0.331537\pi$
$878$	−15.5437	−	40.4928i	−0.524576	−	1.36657i
$879$	8.68119	+	33.2803i	0.292809	+	1.12252i
$880$	−2.53139	−	15.5302i	−0.0853332	−	0.523524i
$881$	2.20100	−	3.02941i	0.0741534	−	0.102063i	−0.770329	−	0.637646i	$-0.779908\pi$
$881$	2.20100	−	3.02941i	0.0741534	−	0.102063i	0.844483	+	0.535583i	$0.179908\pi$
$882$	−7.48206	−	11.8631i	−0.251934	−	0.399450i
$883$	53.5913	−	8.48802i	1.80349	−	0.285645i	0.837921	−	0.545792i	$-0.183771\pi$
$883$	53.5913	−	8.48802i	1.80349	−	0.285645i	0.965569	+	0.260147i	$0.0837710\pi$
$884$	−7.48652	−	8.31463i	−0.251799	−	0.279651i
$885$	18.3068	+	47.9972i	0.615377	+	1.61341i
$886$	3.42230	−	3.80085i	0.114974	−	0.127692i
$887$	−19.0981	+	29.4085i	−0.641251	+	0.987440i	0.357319	+	0.933982i	$0.383691\pi$
$887$	−19.0981	+	29.4085i	−0.641251	+	0.987440i	−0.998570	+	0.0534577i	$0.982976\pi$
$888$	−20.9047	−	9.47407i	−0.701517	−	0.317929i
$889$	5.57346	−	26.2211i	0.186928	−	0.879427i
$890$	−8.23565	+	4.80437i	−0.276060	+	0.161043i
$891$	32.3553	−	9.57150i	1.08395	−	0.320657i
$892$	−0.549332	−	3.46834i	−0.0183930	−	0.116129i
$893$	39.1642	−	10.4940i	1.31058	−	0.351169i
$894$	11.1011	−	0.507955i	0.371275	−	0.0169886i
$895$	−2.29113	−	8.39932i	−0.0765839	−	0.280758i
$896$	−0.715079	+	1.60609i	−0.0238891	+	0.0536558i
$897$	0.426146	−	64.2312i	0.0142286	−	2.14462i
$898$	10.7752	−	6.99752i	0.359574	−	0.233510i
$899$	17.5054			0.583837
$900$	1.25182	−	11.4397i	0.0417275	−	0.381323i
$901$	−17.3248			−0.577174
$902$	−3.24718	+	2.10874i	−0.108119	+	0.0702135i
$903$	0.193738	+	0.113575i	0.00644720	+	0.00377954i
$904$	12.7226	−	28.5755i	0.423149	−	0.950408i
$905$	−39.6977	+	26.0346i	−1.31960	+	0.865418i
$906$	6.80689	+	10.6355i	0.226144	+	0.353341i
$907$	−21.6498	+	5.80104i	−0.718869	+	0.192620i	−0.599667	−	0.800250i	$-0.704700\pi$
$907$	−21.6498	+	5.80104i	−0.718869	+	0.192620i	−0.119202	+	0.992870i	$0.538034\pi$
$908$	1.19824	+	7.56541i	0.0397651	+	0.251067i
$909$	−9.59655	+	5.37207i	−0.318297	+	0.178180i
$910$	18.2425	+	1.83446i	0.604734	+	0.0608118i
$911$	5.17010	−	24.3234i	0.171293	−	0.805870i	−0.805654	−	0.592387i	$-0.798186\pi$
$911$	5.17010	−	24.3234i	0.171293	−	0.805870i	0.976947	−	0.213484i	$-0.0684810\pi$
$912$	−13.6156	+	9.75496i	−0.450858	+	0.323019i
$913$	19.4841	−	30.0029i	0.644829	−	0.992950i
$914$	14.7943	−	16.4307i	0.489351	−	0.543479i
$915$	−1.29507	+	23.7404i	−0.0428136	+	0.784832i
$916$	−1.51543	−	1.68306i	−0.0500713	−	0.0556098i
$917$	35.1047	−	5.56004i	1.15926	−	0.183609i
$918$	12.4486	+	14.3915i	0.410863	+	0.474990i
$919$	7.35810	−	10.1276i	0.242721	−	0.334077i	−0.670224	−	0.742159i	$-0.733802\pi$
$919$	7.35810	−	10.1276i	0.242721	−	0.334077i	0.912946	+	0.408081i	$0.133802\pi$
$920$	−56.9515	−	8.75787i	−1.87763	−	0.288738i
$921$	−14.8297	−	4.07924i	−0.488655	−	0.134416i
$922$	6.60118	+	17.1967i	0.217398	+	0.566342i
$923$	−10.8057	+	0.566301i	−0.355673	+	0.0186400i
$924$	−8.22635	+	1.24704i	−0.270627	+	0.0410245i
$925$	20.8787	+	5.39363i	0.686487	+	0.177342i
$926$		−	30.4072i		−	0.999241i
$927$	−2.86614	+	16.6621i	−0.0941362	+	0.547254i
$928$	1.65763	−	10.4658i	0.0544142	−	0.343558i
$929$	3.78586	+	36.0200i	0.124210	+	1.18178i	0.862057	+	0.506811i	$0.169176\pi$
$929$	3.78586	+	36.0200i	0.124210	+	1.18178i	−0.737847	+	0.674968i	$0.764158\pi$
$930$	−23.3753	+	16.9070i	−0.766508	+	0.554401i
$931$	−2.26755	+	21.5743i	−0.0743160	+	0.707070i
$932$	−11.0773	−	2.96814i	−0.362848	−	0.0972247i
$933$	13.1993	+	2.89726i	0.432126	+	0.0948519i
$934$	−9.62597	+	8.66726i	−0.314971	+	0.283601i
$935$	25.3090	+	11.1322i	0.827692	+	0.364061i
$936$	−33.2875	+	23.5164i	−1.08804	+	0.768656i
$937$	19.6398	−	10.0070i	0.641603	−	0.326913i	−0.102742	−	0.994708i	$-0.532762\pi$
$937$	19.6398	−	10.0070i	0.641603	−	0.326913i	0.744345	+	0.667795i	$0.232762\pi$
$938$	−0.694427	+	13.2505i	−0.0226739	+	0.432643i
$939$	33.0726	−	16.5759i	1.07928	−	0.540934i
$940$	−1.47160	−	13.4205i	−0.0479984	−	0.437730i
$941$	9.77017	+	45.9651i	0.318499	+	1.49842i	0.788104	+	0.615542i	$0.211063\pi$
$941$	9.77017	+	45.9651i	0.318499	+	1.49842i	−0.469606	+	0.882876i	$0.655604\pi$
$942$	−18.2676	−	16.6690i	−0.595190	−	0.543104i
$943$	2.01907	+	7.53529i	0.0657501	+	0.245383i
$944$	−20.1413	−	14.6335i	−0.655544	−	0.476281i
$945$	19.2654	+	2.32547i	0.626703	+	0.0756475i
$946$	0.261441	−	0.189948i	0.00850017	−	0.00617574i
$947$	10.4146	+	8.43358i	0.338429	+	0.274055i	0.783436	−	0.621473i	$-0.213465\pi$
$947$	10.4146	+	8.43358i	0.338429	+	0.274055i	−0.445007	+	0.895527i	$0.646799\pi$
$948$	−3.81689	−	18.5618i	−0.123967	−	0.602858i
$949$	−16.4404	+	9.49188i	−0.533679	+	0.308120i
$950$	20.0417	−	20.4055i	0.650237	−	0.662040i
$951$	−5.38350	−	35.5134i	−0.174572	−	1.15160i
$952$	−9.21768	−	14.1940i	−0.298747	−	0.460030i
$953$	−33.6046	−	5.32244i	−1.08856	−	0.172411i	−0.413740	−	0.910395i	$-0.635778\pi$
$953$	−33.6046	−	5.32244i	−1.08856	−	0.172411i	−0.674818	+	0.737984i	$0.735778\pi$
$954$	−2.05965	+	17.3753i	−0.0666838	+	0.562546i
$955$	−8.59311	−	22.0884i	−0.278067	−	0.714764i
$956$	3.44084	+	7.72826i	0.111285	+	0.249950i
$957$	−15.5246	+	6.78893i	−0.501838	+	0.219455i
$958$	18.5583	+	22.9176i	0.599591	+	0.740434i
$959$	−30.9790	+	6.58479i	−1.00036	+	0.212634i
$960$	14.4676	+	28.5449i	0.466939	+	0.921282i
$961$	−13.6999	−	2.91201i	−0.441933	−	0.0939358i
$962$	−9.61262	−	18.8658i	−0.309923	−	0.608259i
$963$	−8.37261	−	32.9920i	−0.269803	−	1.06315i
$964$	5.43723	−	1.76666i	0.175121	−	0.0569004i
$965$	−28.8517	+	40.0888i	−0.928769	+	1.29051i
$966$	4.39047	−	26.5779i	0.141261	−	0.855130i
$967$	30.7251	−	24.8807i	0.988052	−	0.800109i	0.00822720	−	0.999966i	$-0.497381\pi$
$967$	30.7251	−	24.8807i	0.988052	−	0.800109i	0.979825	+	0.199857i	$0.0640478\pi$
$968$	−2.42964	+	9.06754i	−0.0780916	+	0.291442i
$969$	−1.34529	−	29.4005i	−0.0432169	−	0.944480i
$970$	23.1058	+	11.6424i	0.741883	+	0.373816i
$971$	−34.4738	−	47.4491i	−1.10632	−	1.52272i	−0.826733	−	0.562594i	$-0.809803\pi$
$971$	−34.4738	−	47.4491i	−1.10632	−	1.52272i	−0.279584	−	0.960121i	$-0.590197\pi$
$972$	−9.90321	+	6.70482i	−0.317646	+	0.215057i
$973$	0.289963	+	0.147744i	0.00929579	+	0.00473644i
$974$	−20.0550	+	34.7362i	−0.642603	+	1.11302i
$975$	27.0132	−	27.1409i	0.865113	−	0.869206i
$976$	−5.76134	−	9.97893i	−0.184416	−	0.319418i
$977$	−0.770754	−	14.7069i	−0.0246586	−	0.470514i	−0.982852	−	0.184394i	$-0.940968\pi$
$977$	−0.770754	−	14.7069i	−0.0246586	−	0.470514i	0.958194	−	0.286120i	$-0.0923657\pi$
$978$	23.3818	+	0.155128i	0.747667	+	0.00496045i
$979$	14.3187	−	1.50496i	0.457628	−	0.0480987i
$980$	6.98561	+	1.83816i	0.223147	+	0.0587178i
$981$	−11.3063	+	9.91182i	−0.360984	+	0.316460i
$982$	7.55391	+	7.55391i	0.241055	+	0.241055i
$983$	−15.8049	−	6.06693i	−0.504098	−	0.193505i	0.0930114	−	0.995665i	$-0.470351\pi$
$983$	−15.8049	−	6.06693i	−0.504098	−	0.193505i	−0.597109	+	0.802160i	$0.703684\pi$
$984$	3.14052	−	3.82603i	0.100116	−	0.121969i
$985$	−25.3635	−	14.4919i	−0.808148	−	0.461751i
$986$	−7.10119	−	6.39394i	−0.226148	−	0.203624i
$987$	22.6565	−	2.22942i	0.721163	−	0.0709632i
$988$	17.4531	+	0.914679i	0.555257	+	0.0290998i
$989$	−0.201205	−	0.619246i	−0.00639795	−	0.0196909i
$990$	14.1735	−	24.0593i	0.450462	−	0.764653i
$991$	2.00469	−	6.16981i	0.0636812	−	0.195990i	−0.914154	−	0.405367i	$-0.867144\pi$
$991$	2.00469	−	6.16981i	0.0636812	−	0.195990i	0.977835	+	0.209377i	$0.0671436\pi$
$992$	−9.76297	+	25.4334i	−0.309975	+	0.807511i
$993$	−19.8847	+	26.9905i	−0.631021	+	0.856517i
$994$	−4.51307	−	0.474343i	−0.143146	−	0.0150452i
$995$	−51.8559	−	19.6385i	−1.64394	−	0.622582i
$996$	−3.36301	+	12.2259i	−0.106561	+	0.387392i
$997$	−21.2780	+	26.2762i	−0.673882	+	0.832176i	−0.993315	−	0.115433i	$-0.963174\pi$
$997$	−21.2780	+	26.2762i	−0.673882	+	0.832176i	0.319433	+	0.947609i	$0.396508\pi$
$998$	−15.2828	+	29.9941i	−0.483768	+	0.949448i
$999$	−9.77455	−	20.1660i	−0.309253	−	0.638026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.92.9	✓	448
3.2	odd	2		675.2.bd.a.467.20		448
9.4	even	3		675.2.bd.a.17.9		448
9.5	odd	6	inner	225.2.w.a.167.20	yes	448
25.3	odd	20	inner	225.2.w.a.128.20	yes	448
75.53	even	20		675.2.bd.a.278.9		448
225.103	odd	60		675.2.bd.a.503.20		448
225.203	even	60	inner	225.2.w.a.203.9	yes	448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.92.9	✓	448	1.1	even	1	trivial
225.2.w.a.128.20	yes	448	25.3	odd	20	inner
225.2.w.a.167.20	yes	448	9.5	odd	6	inner
225.2.w.a.203.9	yes	448	225.203	even	60	inner
675.2.bd.a.17.9		448	9.4	even	3
675.2.bd.a.278.9		448	75.53	even	20
675.2.bd.a.467.20		448	3.2	odd	2
675.2.bd.a.503.20		448	225.103	odd	60

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.931189 + 0.604721i) q^{2} +(-1.50571 + 0.856055i) q^{3} +(-0.312048 + 0.700871i) q^{4} +(-0.791939 + 2.09113i) q^{5} +(0.884429 - 1.70769i) q^{6} +(-1.61323 + 0.432263i) q^{7} +(-0.480639 - 3.03464i) q^{8} +(1.53434 - 2.57794i) q^{9} +O(q^{10})\)	\(q+(-0.931189 + 0.604721i) q^{2} +(-1.50571 + 0.856055i) q^{3} +(-0.312048 + 0.700871i) q^{4} +(-0.791939 + 2.09113i) q^{5} +(0.884429 - 1.70769i) q^{6} +(-1.61323 + 0.432263i) q^{7} +(-0.480639 - 3.03464i) q^{8} +(1.53434 - 2.57794i) q^{9} +(-0.527107 - 2.42614i) q^{10} +(-0.779470 + 3.66712i) q^{11} +(-0.130129 - 1.32244i) q^{12} +(2.40822 - 3.70833i) q^{13} +(1.24082 - 1.37807i) q^{14} +(-0.597691 - 3.82659i) q^{15} +(1.25596 + 1.39489i) q^{16} +(-3.25758 + 0.515949i) q^{17} +(0.130177 + 3.32840i) q^{18} +(3.02825 - 4.16803i) q^{19} +(-1.21849 - 1.20758i) q^{20} +(2.05901 - 2.03187i) q^{21} +(-1.49175 - 3.88614i) q^{22} +(-8.37554 + 0.438943i) q^{23} +(3.32152 + 4.15784i) q^{24} +(-3.74566 - 3.31210i) q^{25} +4.90946i q^{26} +(-0.103414 + 5.19512i) q^{27} +(0.200443 - 1.26555i) q^{28} +(-0.272754 - 2.59508i) q^{29} +(2.87058 + 3.20184i) q^{30} +(-0.701245 + 6.67190i) q^{31} +(3.92249 + 1.05103i) q^{32} +(-1.96560 - 6.18890i) q^{33} +(2.72141 - 2.45037i) q^{34} +(0.373659 - 3.71579i) q^{35} +(1.32802 + 1.87982i) q^{36} +(-3.84275 + 1.95798i) q^{37} +(-0.299378 + 5.71248i) q^{38} +(-0.451550 + 7.64525i) q^{39} +(6.72646 + 1.39817i) q^{40} +(-0.193387 - 0.909813i) q^{41} +(-0.688615 + 3.13719i) q^{42} +(0.0200930 + 0.0749881i) q^{43} +(-2.32694 - 1.69062i) q^{44} +(4.17572 + 5.25008i) q^{45} +(7.53377 - 5.47361i) q^{46} +(6.11611 + 4.95273i) q^{47} +(-3.08522 - 1.02513i) q^{48} +(-3.64653 + 2.10532i) q^{49} +(5.49082 + 0.819107i) q^{50} +(4.46329 - 3.56553i) q^{51} +(1.84758 + 2.84503i) q^{52} +(5.18817 + 0.821726i) q^{53} +(-3.04530 - 4.90018i) q^{54} +(-7.05114 - 4.53411i) q^{55} +(2.08714 + 4.68779i) q^{56} +(-0.991615 + 8.86821i) q^{57} +(1.82329 + 2.25157i) q^{58} +(-12.9738 + 2.75767i) q^{59} +(2.86845 + 0.775174i) q^{60} +(-6.00470 - 1.27634i) q^{61} +(-3.38165 - 6.63686i) q^{62} +(-1.36089 + 4.82205i) q^{63} +(-7.85844 + 2.55336i) q^{64} +(5.84745 + 7.97267i) q^{65} +(5.57290 + 4.57440i) q^{66} +(-5.56072 + 4.50298i) q^{67} +(0.654905 - 2.44414i) q^{68} +(12.2354 - 7.83084i) q^{69} +(1.89907 + 3.68607i) q^{70} +(-1.43840 - 1.97978i) q^{71} +(-8.56059 - 3.41711i) q^{72} +(-3.82539 - 1.94914i) q^{73} +(2.39430 - 4.14704i) q^{74} +(8.47523 + 1.78057i) q^{75} +(1.97629 + 3.42304i) q^{76} +(-0.327697 - 6.25283i) q^{77} +(-4.20276 - 7.39223i) q^{78} +(14.1827 - 1.49066i) q^{79} +(-3.91155 + 1.52172i) q^{80} +(-4.29160 - 7.91089i) q^{81} +(0.730263 + 0.730263i) q^{82} +(-8.90845 - 3.41963i) q^{83} +(0.781570 + 2.07714i) q^{84} +(1.50088 - 7.22062i) q^{85} +(-0.0640573 - 0.0576774i) q^{86} +(2.63222 + 3.67395i) q^{87} +(11.5030 + 0.602848i) q^{88} +(-1.18673 - 3.65238i) q^{89} +(-7.06322 - 2.36368i) q^{90} +(-2.28203 + 7.02336i) q^{91} +(2.30593 - 6.00714i) q^{92} +(-4.65564 - 10.6463i) q^{93} +(-8.69027 - 0.913384i) q^{94} +(6.31772 + 9.63331i) q^{95} +(-6.80587 + 1.77532i) q^{96} +(-6.55830 + 8.09883i) q^{97} +(2.12247 - 4.16559i) q^{98} +(8.25766 + 7.63604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

Varieties

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