LMFDB - Embedded newform 175.2.x.a.108.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			108.5
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0825201 - 1.57458i) q^{2} +(-0.0997864 - 0.0808054i) q^{3} +(-0.483440 + 0.0508115i) q^{4} +(-1.93750 - 1.11629i) q^{5} +(-0.119000 + 0.163789i) q^{6} +(2.63799 + 0.202552i) q^{7} +(-0.373412 - 2.35763i) q^{8} +(-0.620307 - 2.91832i) q^{9} +O(q^{10})$	\(q+(-0.0825201 - 1.57458i) q^{2} +(-0.0997864 - 0.0808054i) q^{3} +(-0.483440 + 0.0508115i) q^{4} +(-1.93750 - 1.11629i) q^{5} +(-0.119000 + 0.163789i) q^{6} +(2.63799 + 0.202552i) q^{7} +(-0.373412 - 2.35763i) q^{8} +(-0.620307 - 2.91832i) q^{9} +(-1.59780 + 3.14286i) q^{10} +(-3.49879 - 0.743691i) q^{11} +(0.0523465 + 0.0339942i) q^{12} +(0.403536 + 0.791984i) q^{13} +(0.101247 - 4.17043i) q^{14} +(0.103134 + 0.267951i) q^{15} +(-4.63242 + 0.984651i) q^{16} +(6.15204 + 2.36155i) q^{17} +(-4.54393 + 1.21754i) q^{18} +(-0.107522 + 1.02301i) q^{19} +(0.993383 + 0.441211i) q^{20} +(-0.246868 - 0.233375i) q^{21} +(-0.882278 + 5.57049i) q^{22} +(2.68721 - 0.140831i) q^{23} +(-0.153248 + 0.265433i) q^{24} +(2.50779 + 4.32562i) q^{25} +(1.21374 - 0.700753i) q^{26} +(-0.348796 + 0.684551i) q^{27} +(-1.28560 + 0.0361186i) q^{28} +(-0.242693 - 0.334038i) q^{29} +(0.413399 - 0.184503i) q^{30} +(1.79233 + 4.02565i) q^{31} +(0.697064 + 2.60148i) q^{32} +(0.289037 + 0.356931i) q^{33} +(3.21077 - 9.88174i) q^{34} +(-4.88499 - 3.33720i) q^{35} +(0.448165 + 1.37931i) q^{36} +(5.67907 - 8.74501i) q^{37} +(1.61967 + 0.0848835i) q^{38} +(0.0237292 - 0.111637i) q^{39} +(-1.90831 + 4.98474i) q^{40} +(-0.884011 - 0.287233i) q^{41} +(-0.347096 + 0.407971i) q^{42} +(3.39602 + 3.39602i) q^{43} +(1.72924 + 0.181751i) q^{44} +(-2.05584 + 6.34667i) q^{45} +(-0.443498 - 4.21960i) q^{46} +(2.43023 + 6.33097i) q^{47} +(0.541817 + 0.276070i) q^{48} +(6.91795 + 1.06866i) q^{49} +(6.60407 - 4.30567i) q^{50} +(-0.423064 - 0.732768i) q^{51} +(-0.235327 - 0.362372i) q^{52} +(-5.17105 + 6.38571i) q^{53} +(1.10666 + 0.492717i) q^{54} +(5.94873 + 5.34656i) q^{55} +(-0.507514 - 6.29504i) q^{56} +(0.0933936 - 0.0933936i) q^{57} +(-0.505941 + 0.409703i) q^{58} +(3.83266 + 4.25660i) q^{59} +(-0.0634739 - 0.124298i) q^{60} +(-3.99440 - 3.59658i) q^{61} +(6.19079 - 3.15437i) q^{62} +(-1.04525 - 7.82412i) q^{63} +(-4.96953 + 1.61470i) q^{64} +(0.102233 - 1.98493i) q^{65} +(0.538165 - 0.484566i) q^{66} +(3.90663 - 10.1771i) q^{67} +(-3.09413 - 0.829071i) q^{68} +(-0.279527 - 0.203088i) q^{69} +(-4.85157 + 7.96717i) q^{70} +(5.23629 - 3.80439i) q^{71} +(-6.64868 + 2.55219i) q^{72} +(-9.62453 + 6.25024i) q^{73} +(-14.2383 - 8.22050i) q^{74} +(0.0992895 - 0.634281i) q^{75} -0.500025i q^{76} +(-9.07913 - 2.67053i) q^{77} +(-0.177739 - 0.0281511i) q^{78} +(-5.43361 + 12.2041i) q^{79} +(10.0745 + 3.26336i) q^{80} +(-8.08660 + 3.60039i) q^{81} +(-0.379321 + 1.41565i) q^{82} +(-10.5884 + 1.67704i) q^{83} +(0.131204 + 0.100279i) q^{84} +(-9.28339 - 11.4430i) q^{85} +(5.06705 - 5.62753i) q^{86} +(-0.00277464 + 0.0529433i) q^{87} +(-0.446858 + 8.52656i) q^{88} +(3.49677 - 3.88355i) q^{89} +(10.1630 + 2.71335i) q^{90} +(0.904105 + 2.17098i) q^{91} +(-1.29195 + 0.204625i) q^{92} +(0.146444 - 0.546535i) q^{93} +(9.76806 - 4.34902i) q^{94} +(1.35029 - 1.86204i) q^{95} +(0.140656 - 0.315919i) q^{96} +(-14.9519 - 2.36815i) q^{97} +(1.11181 - 10.9810i) q^{98} +10.6719i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.0825201	−	1.57458i	−0.0583505	−	1.11339i	−0.858241	−	0.513248i	$-0.828442\pi$
$2$	−0.0825201	−	1.57458i	−0.0583505	−	1.11339i	0.799890	−	0.600147i	$-0.204891\pi$
$3$	−0.0997864	−	0.0808054i	−0.0576117	−	0.0466530i	0.600082	−	0.799938i	$-0.295135\pi$
$3$	−0.0997864	−	0.0808054i	−0.0576117	−	0.0466530i	−0.657694	+	0.753285i	$0.728468\pi$
$4$	−0.483440	+	0.0508115i	−0.241720	+	0.0254058i
$5$	−1.93750	−	1.11629i	−0.866475	−	0.499220i
$5$	−1.93750	−	1.11629i	−0.866475	−	0.499220i
$6$	−0.119000	+	0.163789i	−0.0485815	+	0.0668667i
$7$	2.63799	+	0.202552i	0.997065	+	0.0765574i
$7$	2.63799	+	0.202552i	0.997065	+	0.0765574i
$8$	−0.373412	−	2.35763i	−0.132021	−	0.833549i
$9$	−0.620307	−	2.91832i	−0.206769	−	0.972772i
$10$	−1.59780	+	3.14286i	−0.505269	+	0.993858i
$11$	−3.49879	−	0.743691i	−1.05493	−	0.224231i	−0.352370	−	0.935861i	$-0.614624\pi$
$11$	−3.49879	−	0.743691i	−1.05493	−	0.224231i	−0.702555	+	0.711629i	$0.747958\pi$
$12$	0.0523465	+	0.0339942i	0.0151111	+	0.00981329i
$13$	0.403536	+	0.791984i	0.111921	+	0.219657i	0.940172	−	0.340700i	$-0.110664\pi$
$13$	0.403536	+	0.791984i	0.111921	+	0.219657i	−0.828251	+	0.560357i	$0.810664\pi$
$14$	0.101247	−	4.17043i	0.0270593	−	1.11459i
$15$	0.103134	+	0.267951i	0.0266290	+	0.0691846i
$16$	−4.63242	+	0.984651i	−1.15810	+	0.246163i
$17$	6.15204	+	2.36155i	1.49209	+	0.572759i	0.961484	−	0.274860i	$-0.0886316\pi$
$17$	6.15204	+	2.36155i	1.49209	+	0.572759i	0.530605	+	0.847619i	$0.321965\pi$
$18$	−4.54393	+	1.21754i	−1.07101	+	0.286977i
$19$	−0.107522	+	1.02301i	−0.0246673	+	0.234693i	0.975241	+	0.221145i	$0.0709794\pi$
$19$	−0.107522	+	1.02301i	−0.0246673	+	0.234693i	−0.999908	+	0.0135485i	$0.995687\pi$
$20$	0.993383	+	0.441211i	0.222127	+	0.0986579i
$21$	−0.246868	−	0.233375i	−0.0538710	−	0.0509267i
$22$	−0.882278	+	5.57049i	−0.188102	+	1.18763i
$23$	2.68721	−	0.140831i	0.560322	−	0.0293652i	0.229927	−	0.973208i	$-0.426151\pi$
$23$	2.68721	−	0.140831i	0.560322	−	0.0293652i	0.330395	+	0.943843i	$0.392818\pi$
$24$	−0.153248	+	0.265433i	−0.0312816	+	0.0541813i
$25$	2.50779	+	4.32562i	0.501559	+	0.865123i
$26$	1.21374	−	0.700753i	0.238034	−	0.137429i
$27$	−0.348796	+	0.684551i	−0.0671258	+	0.131742i
$28$	−1.28560	+	0.0361186i	−0.242955	+	0.00682577i
$29$	−0.242693	−	0.334038i	−0.0450669	−	0.0620293i	0.785889	−	0.618368i	$-0.212206\pi$
$29$	−0.242693	−	0.334038i	−0.0450669	−	0.0620293i	−0.830956	+	0.556339i	$0.812206\pi$
$30$	0.413399	−	0.184503i	0.0754759	−	0.0336855i
$31$	1.79233	+	4.02565i	0.321913	+	0.723028i	0.999928	−	0.0120201i	$-0.00382622\pi$
$31$	1.79233	+	4.02565i	0.321913	+	0.723028i	−0.678015	+	0.735048i	$0.737160\pi$
$32$	0.697064	+	2.60148i	0.123225	+	0.459881i
$33$	0.289037	+	0.356931i	0.0503150	+	0.0621338i
$34$	3.21077	−	9.88174i	0.550643	−	1.69470i
$35$	−4.88499	−	3.33720i	−0.825713	−	0.564090i
$36$	0.448165	+	1.37931i	0.0746942	+	0.229885i
$37$	5.67907	−	8.74501i	0.933634	−	1.43767i	0.0347933	−	0.999395i	$-0.488923\pi$
$37$	5.67907	−	8.74501i	0.933634	−	1.43767i	0.898841	−	0.438276i	$-0.144411\pi$
$38$	1.61967	+	0.0848835i	0.262746	+	0.0137699i
$39$	0.0237292	−	0.111637i	0.00379971	−	0.0178762i
$40$	−1.90831	+	4.98474i	−0.301731	+	0.788157i
$41$	−0.884011	−	0.287233i	−0.138059	−	0.0448582i	0.239172	−	0.970977i	$-0.423124\pi$
$41$	−0.884011	−	0.287233i	−0.138059	−	0.0448582i	−0.377232	+	0.926119i	$0.623124\pi$
$42$	−0.347096	+	0.407971i	−0.0535581	+	0.0629512i
$43$	3.39602	+	3.39602i	0.517888	+	0.517888i	0.916932	−	0.399044i	$-0.130658\pi$
$43$	3.39602	+	3.39602i	0.517888	+	0.517888i	−0.399044	+	0.916932i	$0.630658\pi$
$44$	1.72924	+	0.181751i	0.260693	+	0.0273999i
$45$	−2.05584	+	6.34667i	−0.306467	+	0.946106i
$46$	−0.443498	−	4.21960i	−0.0653902	−	0.622146i
$47$	2.43023	+	6.33097i	0.354486	+	0.923467i	0.988646	+	0.150265i	$0.0480127\pi$
$47$	2.43023	+	6.33097i	0.354486	+	0.923467i	−0.634160	+	0.773202i	$0.718654\pi$
$48$	0.541817	+	0.276070i	0.0782046	+	0.0398472i
$49$	6.91795	+	1.06866i	0.988278	+	0.152665i
$50$	6.60407	−	4.30567i	0.933957	−	0.608913i
$51$	−0.423064	−	0.732768i	−0.0592408	−	0.102608i
$52$	−0.235327	−	0.362372i	−0.0326340	−	0.0502520i
$53$	−5.17105	+	6.38571i	−0.710298	+	0.877145i	−0.996717	−	0.0809593i	$-0.974202\pi$
$53$	−5.17105	+	6.38571i	−0.710298	+	0.877145i	0.286419	+	0.958104i	$0.407535\pi$
$54$	1.10666	+	0.492717i	0.150597	+	0.0670503i
$55$	5.94873	+	5.34656i	0.802126	+	0.720931i
$56$	−0.507514	−	6.29504i	−0.0678194	−	0.841209i
$57$	0.0933936	−	0.0933936i	0.0123703	−	0.0123703i
$58$	−0.505941	+	0.409703i	−0.0664334	+	0.0537967i
$59$	3.83266	+	4.25660i	0.498969	+	0.554162i	0.939043	−	0.343800i	$-0.111714\pi$
$59$	3.83266	+	4.25660i	0.498969	+	0.554162i	−0.440073	+	0.897962i	$0.645048\pi$
$60$	−0.0634739	−	0.124298i	−0.00819444	−	0.0160468i
$61$	−3.99440	−	3.59658i	−0.511431	−	0.460494i	0.372554	−	0.928011i	$-0.378482\pi$
$61$	−3.99440	−	3.59658i	−0.511431	−	0.460494i	−0.883984	+	0.467516i	$0.845149\pi$
$62$	6.19079	−	3.15437i	0.786231	−	0.400605i
$63$	−1.04525	−	7.82412i	−0.131689	−	0.985747i
$64$	−4.96953	+	1.61470i	−0.621191	+	0.201837i
$65$	0.102233	−	1.98493i	0.0126805	−	0.246200i
$66$	0.538165	−	0.484566i	0.0662435	−	0.0596459i
$67$	3.90663	−	10.1771i	0.477271	−	1.24333i	−0.457858	−	0.889025i	$-0.651383\pi$
$67$	3.90663	−	10.1771i	0.477271	−	1.24333i	0.935129	−	0.354308i	$-0.115283\pi$
$68$	−3.09413	−	0.829071i	−0.375219	−	0.100540i
$69$	−0.279527	−	0.203088i	−0.0336511	−	0.0244489i
$70$	−4.85157	+	7.96717i	−0.579874	+	0.952259i
$71$	5.23629	−	3.80439i	0.621433	−	0.451498i	−0.231988	−	0.972719i	$-0.574523\pi$
$71$	5.23629	−	3.80439i	0.621433	−	0.451498i	0.853422	+	0.521221i	$0.174523\pi$
$72$	−6.64868	+	2.55219i	−0.783555	+	0.300779i
$73$	−9.62453	+	6.25024i	−1.12647	+	0.731536i	−0.966774	−	0.255631i	$-0.917717\pi$
$73$	−9.62453	+	6.25024i	−1.12647	+	0.731536i	−0.159692	+	0.987167i	$0.551050\pi$
$74$	−14.2383	−	8.22050i	−1.65517	−	0.955614i
$75$	0.0992895	−	0.634281i	0.0114650	−	0.0732405i
$76$		−	0.500025i		−	0.0573567i
$77$	−9.07913	−	2.67053i	−1.03466	−	0.304336i
$78$	−0.177739	−	0.0281511i	−0.0201250	−	0.00318749i
$79$	−5.43361	+	12.2041i	−0.611329	+	1.37307i	0.297028	+	0.954869i	$0.404005\pi$
$79$	−5.43361	+	12.2041i	−0.611329	+	1.37307i	−0.908356	+	0.418198i	$0.862662\pi$
$80$	10.0745	+	3.26336i	1.12636	+	0.364855i
$81$	−8.08660	+	3.60039i	−0.898512	+	0.400043i
$82$	−0.379321	+	1.41565i	−0.0418890	+	0.156332i
$83$	−10.5884	+	1.67704i	−1.16223	+	0.184079i	−0.707607	−	0.706606i	$-0.750225\pi$
$83$	−10.5884	+	1.67704i	−1.16223	+	0.184079i	−0.454621	+	0.890685i	$0.650225\pi$
$84$	0.131204	+	0.100279i	0.0143155	+	0.0109414i
$85$	−9.28339	−	11.4430i	−1.00693	−	1.24116i
$86$	5.06705	−	5.62753i	0.546394	−	0.606832i
$87$	−0.00277464	+	0.0529433i	−0.000297473	+	0.00567612i
$88$	−0.446858	+	8.52656i	−0.0476353	+	0.908935i
$89$	3.49677	−	3.88355i	0.370657	−	0.411656i	−0.528744	−	0.848781i	$-0.677337\pi$
$89$	3.49677	−	3.88355i	0.370657	−	0.411656i	0.899401	+	0.437125i	$0.144003\pi$
$90$	10.1630	+	2.71335i	1.07127	+	0.286013i
$91$	0.904105	+	2.17098i	0.0947759	+	0.227580i
$92$	−1.29195	+	0.204625i	−0.134695	+	0.0213336i
$93$	0.146444	−	0.546535i	0.0151855	−	0.0566731i
$94$	9.76806	−	4.34902i	1.00750	−	0.448567i
$95$	1.35029	−	1.86204i	0.138537	−	0.191042i
$96$	0.140656	−	0.315919i	0.0143556	−	0.0322433i
$97$	−14.9519	−	2.36815i	−1.51813	−	0.240449i	−0.658978	−	0.752163i	$-0.729011\pi$
$97$	−14.9519	−	2.36815i	−1.51813	−	0.240449i	−0.859156	+	0.511714i	$0.829011\pi$
$98$	1.11181	−	10.9810i	0.112310	−	1.10925i
$99$			10.6719i			1.07257i
$100$	−1.43216	−	1.96375i	−0.143216	−	0.196375i
$101$	−16.4574	−	9.50169i	−1.63757	−	0.945453i	−0.981665	−	0.190612i	$-0.938953\pi$
$101$	−16.4574	−	9.50169i	−1.63757	−	0.945453i	−0.655908	−	0.754841i	$-0.727714\pi$
$102$	−1.11889	+	0.726615i	−0.110786	+	0.0719456i
$103$	9.23944	−	3.54669i	0.910389	−	0.349466i	0.142311	−	0.989822i	$-0.454547\pi$
$103$	9.23944	−	3.54669i	0.910389	−	0.349466i	0.768078	+	0.640356i	$0.221213\pi$
$104$	1.71652	−	1.24713i	0.168319	−	0.122291i
$105$	0.217791	+	0.727740i	0.0212542	+	0.0710202i
$106$	10.4815	+	7.61526i	1.01805	+	0.739660i
$107$	11.0384	+	2.95772i	1.06712	+	0.285933i	0.749309	−	0.662221i	$-0.230386\pi$
$107$	11.0384	+	2.95772i	1.06712	+	0.285933i	0.317810	+	0.948155i	$0.397053\pi$
$108$	0.133839	−	0.348662i	0.0128786	−	0.0335500i
$109$	3.36131	−	3.02654i	0.321955	−	0.289890i	−0.492266	−	0.870445i	$-0.663831\pi$
$109$	3.36131	−	3.02654i	0.321955	−	0.289890i	0.814221	+	0.580555i	$0.197164\pi$
$110$	7.92769	−	9.80793i	0.755875	−	0.935149i
$111$	−1.27334	+	0.413733i	−0.120860	+	0.0392698i
$112$	−12.4197	+	1.65919i	−1.17355	+	0.156779i
$113$	−5.01371	+	2.55462i	−0.471651	+	0.240318i	−0.673626	−	0.739073i	$-0.735264\pi$
$113$	−5.01371	+	2.55462i	−0.471651	+	0.240318i	0.201975	+	0.979391i	$0.435264\pi$
$114$	−0.154762	−	0.139349i	−0.0144948	−	0.0130512i
$115$	−5.36367	−	2.72685i	−0.500165	−	0.254280i
$116$	0.134300	+	0.149156i	0.0124695	+	0.0138487i
$117$	2.06094	−	1.66892i	0.190534	−	0.154292i
$118$	6.38607	−	6.38607i	0.587885	−	0.587885i
$119$	15.7507	+	7.47584i	1.44386	+	0.685309i
$120$	0.593218	−	0.343207i	0.0541531	−	0.0313304i
$121$	1.63947	+	0.729937i	0.149042	+	0.0663579i
$122$	−5.33347	+	6.58628i	−0.482869	+	0.596294i
$123$	0.0650023	+	0.100095i	0.00586106	+	0.00902524i
$124$	−1.07103	−	1.85509i	−0.0961818	−	0.166592i
$125$	−0.0302046	−	11.1803i	−0.00270158	−	0.999996i
$126$	−12.2334	+	2.29148i	−1.08984	+	0.204141i
$127$	−8.63797	−	4.40126i	−0.766495	−	0.390549i	0.0266001	−	0.999646i	$-0.491532\pi$
$127$	−8.63797	−	4.40126i	−0.766495	−	0.390549i	−0.793096	+	0.609097i	$0.791532\pi$
$128$	4.88290	+	12.7204i	0.431591	+	1.12433i
$129$	−0.0644597	−	0.613293i	−0.00567536	−	0.0539974i
$130$	−3.13386	+	0.00282213i	−0.274858	+	0.000247517i
$131$	18.0626	+	1.89846i	1.57814	+	0.165869i	0.852695	−	0.522410i	$-0.174967\pi$
$131$	18.0626	+	1.89846i	1.57814	+	0.165869i	0.725446	+	0.688279i	$0.241634\pi$
$132$	−0.157868	−	0.157868i	−0.0137407	−	0.0137407i
$133$	−0.490854	+	2.67689i	−0.0425624	+	0.232116i
$134$	−16.3470	−	5.31147i	−1.41217	−	0.458841i
$135$	1.43995	−	0.936958i	0.123931	−	0.0806405i
$136$	3.27041	−	15.3861i	0.280435	−	1.31934i
$137$	12.2533	+	0.642167i	1.04687	+	0.0548640i	0.568005	−	0.823025i	$-0.307716\pi$
$137$	12.2533	+	0.642167i	1.04687	+	0.0548640i	0.478863	+	0.877889i	$0.341049\pi$
$138$	−0.296711	+	0.456895i	−0.0252578	+	0.0388935i
$139$	1.49559	+	4.60294i	0.126854	+	0.390417i	0.994234	−	0.107229i	$-0.0341979\pi$
$139$	1.49559	+	4.60294i	0.126854	+	0.390417i	−0.867380	+	0.497646i	$0.834198\pi$
$140$	2.53116	+	1.36512i	0.213922	+	0.115374i
$141$	0.269073	−	0.828120i	0.0226600	−	0.0697403i
$142$	−6.42240	−	7.93101i	−0.538956	−	0.665555i
$143$	−0.822897	−	3.07109i	−0.0688141	−	0.256818i
$144$	5.74705	+	12.9081i	0.478920	+	1.07567i
$145$	0.0973336	+	0.918113i	0.00808311	+	0.0762451i
$146$	10.6357	+	14.6388i	0.880218	+	1.21152i
$147$	−0.603963	−	0.665645i	−0.0498140	−	0.0549015i
$148$	−2.30114	+	4.51624i	−0.189153	+	0.371233i
$149$	−8.82683	+	5.09617i	−0.723122	+	0.417495i	−0.815901	−	0.578192i	$-0.803758\pi$
$149$	−8.82683	+	5.09617i	−0.723122	+	0.417495i	0.0927785	+	0.995687i	$0.470425\pi$
$150$	−1.00692	−	0.103998i	−0.0822145	−	0.00849141i
$151$	−0.622057	+	1.07743i	−0.0506223	+	0.0876804i	−0.890226	−	0.455519i	$-0.849454\pi$
$151$	−0.622057	+	1.07743i	−0.0506223	+	0.0876804i	0.839604	+	0.543199i	$0.182787\pi$
$152$	2.45202	−	0.128505i	0.198885	−	0.0104231i
$153$	3.07559	−	19.4185i	0.248646	−	1.56989i
$154$	−3.45575	+	14.5162i	−0.278472	+	1.16975i
$155$	1.02115	−	9.80045i	0.0820205	−	0.787191i
$156$	−0.00579918	+	0.0551755i	−0.000464306	+	0.00441757i
$157$	9.24318	−	2.47670i	0.737686	−	0.197662i	0.129637	−	0.991562i	$-0.458619\pi$
$157$	9.24318	−	2.47670i	0.737686	−	0.197662i	0.608050	+	0.793899i	$0.291952\pi$
$158$	19.6646	+	7.54855i	1.56444	+	0.600530i
$159$	1.03200	−	0.219358i	0.0818429	−	0.0173963i
$160$	1.55344	−	5.81848i	0.122810	−	0.459992i
$161$	7.11735	+	0.172790i	0.560926	+	0.0136177i
$162$	6.33640	+	12.4359i	0.497834	+	0.977055i
$163$	5.76084	+	3.74113i	0.451223	+	0.293028i	0.750174	−	0.661241i	$-0.229970\pi$
$163$	5.76084	+	3.74113i	0.451223	+	0.293028i	−0.298950	+	0.954269i	$0.596636\pi$
$164$	0.441961	+	0.0939417i	0.0345113	+	0.00733561i
$165$	−0.161570	−	1.01420i	−0.0125782	−	0.0789556i
$166$	3.51438	+	16.5339i	0.272769	+	1.28328i
$167$	−0.493915	−	3.11846i	−0.0382203	−	0.241313i	0.961181	−	0.275919i	$-0.0889823\pi$
$167$	−0.493915	−	3.11846i	−0.0382203	−	0.241313i	−0.999401	+	0.0346062i	$0.988982\pi$
$168$	−0.458030	+	0.669168i	−0.0353378	+	0.0516275i
$169$	7.17681	−	9.87803i	0.552062	−	0.759849i
$170$	−17.2517	+	15.5617i	−1.32315	+	1.19353i
$171$	3.05215	−	0.320794i	0.233404	−	0.0245317i
$172$	−1.81433	−	1.46921i	−0.138341	−	0.112026i
$173$	0.203072	+	3.87484i	0.0154393	+	0.294599i	0.995426	+	0.0955359i	$0.0304565\pi$
$173$	0.203072	+	3.87484i	0.0154393	+	0.294599i	−0.979987	+	0.199063i	$0.936210\pi$
$174$	0.0835923			0.00633712
$175$	5.73937	+	11.9189i	0.433855	+	0.900983i
$176$	16.9401			1.27691
$177$	−0.0384909	−	0.734450i	−0.00289315	−	0.0552046i
$178$	−6.40351	−	5.18546i	−0.479963	−	0.388667i
$179$	−18.1903	+	1.91188i	−1.35961	+	0.142901i	−0.756100	−	0.654456i	$-0.772898\pi$
$179$	−18.1903	+	1.91188i	−1.35961	+	0.142901i	−0.603508	+	0.797357i	$0.706231\pi$
$180$	0.671391	−	3.17269i	0.0500426	−	0.236479i
$181$	−11.0244	+	15.1738i	−0.819436	+	1.12786i	0.170362	+	0.985381i	$0.445506\pi$
$181$	−11.0244	+	15.1738i	−0.819436	+	1.12786i	−0.989798	+	0.142475i	$0.954494\pi$
$182$	3.34377	−	1.60273i	0.247857	−	0.118802i
$183$	0.107964	+	0.681658i	0.00798093	+	0.0503896i
$184$	−1.33546	−	6.28287i	−0.0984517	−	0.463179i
$185$	−20.7652	+	10.6039i	−1.52668	+	0.779617i
$186$	−0.872646	−	0.185487i	−0.0639855	−	0.0136005i
$187$	−19.7684	−	12.8378i	−1.44561	−	0.938791i
$188$	−1.49656	−	2.93716i	−0.109148	−	0.214214i
$189$	−1.05878	+	1.73519i	−0.0770146	+	0.126216i
$190$	−3.04336	−	1.97249i	−0.220788	−	0.143099i
$191$	−7.51908	+	1.59823i	−0.544062	+	0.115644i	−0.471740	−	0.881737i	$-0.656374\pi$
$191$	−7.51908	+	1.59823i	−0.544062	+	0.115644i	−0.0723214	+	0.997381i	$0.523041\pi$
$192$	0.626367	+	0.240440i	0.0452042	+	0.0173523i
$193$	13.8743	−	3.71761i	0.998695	−	0.267599i	0.277796	−	0.960640i	$-0.410396\pi$
$193$	13.8743	−	3.71761i	0.998695	−	0.267599i	0.720899	+	0.693041i	$0.243729\pi$
$194$	−2.49500	+	23.7383i	−0.179130	+	1.70431i
$195$	−0.170595	+	0.189808i	−0.0122165	+	0.0135924i
$196$	−3.39871	−	0.165120i	−0.242765	−	0.0117943i
$197$	0.320426	−	2.02309i	0.0228294	−	0.144139i	−0.973641	−	0.228087i	$-0.926753\pi$
$197$	0.320426	−	2.02309i	0.0228294	−	0.144139i	0.996470	+	0.0839479i	$0.0267529\pi$
$198$	16.8037	−	0.880646i	1.19419	−	0.0625848i
$199$	2.93779	−	5.08840i	0.208254	−	0.360707i	−0.742910	−	0.669391i	$-0.766555\pi$
$199$	2.93779	−	5.08840i	0.208254	−	0.360707i	0.951165	+	0.308684i	$0.0998885\pi$
$200$	9.26177	−	7.52769i	0.654906	−	0.532288i
$201$	−1.21219	+	0.699861i	−0.0855016	+	0.0493644i
$202$	−13.6031	+	26.6975i	−0.957109	+	1.87843i
$203$	−0.572560	−	0.930345i	−0.0401859	−	0.0652974i
$204$	0.241759	+	0.332753i	0.0169265	+	0.0232973i
$205$	1.39214	+	1.54333i	0.0972309	+	0.107791i
$206$	−6.34698	−	14.2555i	−0.442215	−	0.993231i
$207$	−2.07789	−	7.75477i	−0.144423	−	0.538994i
$208$	−2.64917	−	3.27146i	−0.183687	−	0.226835i
$209$	1.13700	−	3.49932i	0.0786478	−	0.242053i
$210$	1.12791	−	0.402982i	0.0778333	−	0.0278084i
$211$	5.78925	+	17.8175i	0.398549	+	1.22661i	0.926163	+	0.377123i	$0.123086\pi$
$211$	5.78925	+	17.8175i	0.398549	+	1.22661i	−0.527615	+	0.849484i	$0.676914\pi$
$212$	2.17542	−	3.34986i	0.149409	−	0.230069i
$213$	−0.829926	−	0.0434946i	−0.0568656	−	0.00298020i
$214$	3.74627	−	17.6248i	0.256090	−	1.20481i
$215$	−2.78884	−	10.3707i	−0.190197	−	0.707277i
$216$	1.74416	+	0.566713i	0.118675	+	0.0385599i
$217$	3.91275	+	10.9826i	0.265615	+	0.745551i
$218$	−5.04289	−	5.04289i	−0.341548	−	0.341548i
$219$	1.46545	+	0.154025i	0.0990260	+	0.0104080i
$220$	−3.14752	−	2.28248i	−0.212206	−	0.153885i
$221$	0.612262	+	5.82528i	0.0411852	+	0.391851i
$222$	0.756530	+	1.97083i	0.0507749	+	0.132273i
$223$	−9.90574	−	5.04723i	−0.663338	−	0.337987i	0.0896962	−	0.995969i	$-0.471410\pi$
$223$	−9.90574	−	5.04723i	−0.663338	−	0.337987i	−0.753034	+	0.657982i	$0.771410\pi$
$224$	1.31191	+	7.00386i	0.0876558	+	0.467965i
$225$	11.0679	−	10.0018i	0.737861	−	0.666783i
$226$	4.43617	+	7.68367i	0.295090	+	0.511110i
$227$	10.5062	+	16.1781i	0.697319	+	1.07378i	0.992957	+	0.118477i	$0.0378011\pi$
$227$	10.5062	+	16.1781i	0.697319	+	1.07378i	−0.295638	+	0.955300i	$0.595532\pi$
$228$	−0.0404047	+	0.0498956i	−0.00267587	+	0.00330442i
$229$	−24.8300	−	11.0550i	−1.64081	−	0.730538i	−0.641485	−	0.767136i	$-0.721681\pi$
$229$	−24.8300	−	11.0550i	−1.64081	−	0.730538i	−0.999330	+	0.0365981i	$0.988348\pi$
$230$	−3.85102	+	8.67054i	−0.253929	+	0.571718i
$231$	0.690180	+	1.00013i	0.0454105	+	0.0658034i
$232$	−0.696914	+	0.696914i	−0.0457546	+	0.0457546i
$233$	17.2555	−	13.9732i	1.13045	−	0.915417i	0.133312	−	0.991074i	$-0.457439\pi$
$233$	17.2555	−	13.9732i	1.13045	−	0.915417i	0.997134	+	0.0756570i	$0.0241054\pi$
$234$	−2.79791	−	3.10739i	−0.182905	−	0.203137i
$235$	2.35863	−	14.9791i	0.153860	−	0.977127i
$236$	−2.06914	−	1.86306i	−0.134690	−	0.121275i
$237$	1.52836	−	0.778736i	0.0992774	−	0.0505843i
$238$	10.4715	−	25.4175i	0.678769	−	1.64757i
$239$	−27.7649	+	9.02136i	−1.79596	+	0.583543i	−0.999769	−	0.0215007i	$-0.993156\pi$
$239$	−27.7649	+	9.02136i	−1.79596	+	0.583543i	−0.796192	+	0.605044i	$0.793156\pi$
$240$	−0.741596	−	1.13971i	−0.0478698	−	0.0735679i
$241$	1.39616	−	1.25711i	0.0899346	−	0.0809775i	−0.622937	−	0.782272i	$-0.714061\pi$
$241$	1.39616	−	1.25711i	0.0899346	−	0.0809775i	0.712872	+	0.701294i	$0.247394\pi$
$242$	1.01405	−	2.64170i	0.0651858	−	0.169815i
$243$	3.32420	+	0.890715i	0.213247	+	0.0571394i
$244$	2.11380	+	1.53577i	0.135322	+	0.0983173i
$245$	−12.2106	−	9.79295i	−0.780105	−	0.625649i
$246$	0.152243	−	0.110611i	0.00970666	−	0.00705230i
$247$	−0.853593	+	0.327663i	−0.0543128	+	0.0208487i
$248$	8.82172	−	5.72889i	0.560180	−	0.363785i
$249$	1.19209	+	0.688255i	0.0755458	+	0.0436164i
$250$	−17.6018	+	0.970159i	−1.11323	+	0.0613582i
$251$			16.4158i			1.03616i	0.855333	+	0.518078i	$0.173352\pi$
$251$			16.4158i			1.03616i	−0.855333	+	0.518078i	$0.826648\pi$
$252$	0.902872	+	3.72938i	0.0568756	+	0.234929i
$253$	−9.50673	−	1.50572i	−0.597683	−	0.0946636i
$254$	−6.21732	+	13.9643i	−0.390110	+	0.876200i
$255$	0.00170380	+	1.89200i	0.000106696	+	0.118482i
$256$	10.0792	−	4.48757i	0.629953	−	0.280473i
$257$	−1.66061	+	6.19747i	−0.103586	+	0.386587i	−0.998181	−	0.0602903i	$-0.980797\pi$
$257$	−1.66061	+	6.19747i	−0.103586	+	0.386587i	0.894595	+	0.446878i	$0.147464\pi$
$258$	−0.960357	+	0.152106i	−0.0597892	+	0.00946969i
$259$	16.7526	−	21.9189i	1.04096	−	1.36197i
$260$	0.0514337	+	0.964788i	0.00318978	+	0.0598336i
$261$	−0.824284	+	0.915460i	−0.0510219	+	0.0566656i
$262$	1.49874	−	28.5977i	0.0925925	−	1.76677i
$263$	−0.285445	+	5.44662i	−0.0176013	+	0.335853i	0.975609	+	0.219517i	$0.0704482\pi$
$263$	−0.285445	+	5.44662i	−0.0176013	+	0.335853i	−0.993210	+	0.116336i	$0.962885\pi$
$264$	0.733583	−	0.814726i	0.0451489	−	0.0501429i
$265$	17.1472	−	6.59992i	1.05334	−	0.405430i
$266$	4.25548	+	0.551989i	0.260920	+	0.0338446i
$267$	−0.662742	+	0.104968i	−0.0405592	+	0.00642394i
$268$	−1.37150	+	5.11852i	−0.0837780	+	0.312664i
$269$	11.0790	−	4.93269i	0.675499	−	0.300751i	−0.0401683	−	0.999193i	$-0.512789\pi$
$269$	11.0790	−	4.93269i	0.675499	−	0.300751i	0.715667	+	0.698441i	$0.246123\pi$
$270$	−1.59414	−	2.18999i	−0.0970161	−	0.133279i
$271$	5.77787	−	12.9773i	0.350981	−	0.788315i	−0.648649	−	0.761088i	$-0.724666\pi$
$271$	5.77787	−	12.9773i	0.350981	−	0.788315i	0.999629	−	0.0272272i	$-0.00866777\pi$
$272$	−30.8241	−	4.88206i	−1.86899	−	0.296018i
$273$	0.0852096	−	0.289691i	0.00515712	−	0.0175329i
$274$		−	19.3467i		−	1.16878i
$275$	−5.55733	−	16.9995i	−0.335119	−	1.02511i
$276$	0.145454	+	0.0839777i	0.00875528	+	0.00505486i
$277$	7.89979	−	5.13018i	0.474652	−	0.308243i	−0.285051	−	0.958512i	$-0.592011\pi$
$277$	7.89979	−	5.13018i	0.474652	−	0.308243i	0.759704	+	0.650269i	$0.225344\pi$
$278$	7.12427	−	2.73475i	0.427286	−	0.164020i
$279$	10.6363	−	7.72774i	0.636780	−	0.462648i
$280$	−6.04378	+	12.7631i	−0.361185	+	0.762744i
$281$	−0.976989	−	0.709824i	−0.0582823	−	0.0423446i	0.558263	−	0.829664i	$-0.311468\pi$
$281$	−0.976989	−	0.709824i	−0.0582823	−	0.0423446i	−0.616545	+	0.787320i	$0.711468\pi$
$282$	−1.32614	−	0.355339i	−0.0789707	−	0.0211601i
$283$	1.88714	−	4.91617i	0.112179	−	0.292236i	−0.865985	−	0.500069i	$-0.833308\pi$
$283$	1.88714	−	4.91617i	0.112179	−	0.292236i	0.978164	+	0.207833i	$0.0666412\pi$
$284$	−2.33812	+	2.10526i	−0.138742	+	0.124924i
$285$	−0.285204	+	0.0766956i	−0.0168940	+	0.00454305i
$286$	−4.76777	+	1.54914i	−0.281924	+	0.0916026i
$287$	−2.27383	−	0.936774i	−0.134220	−	0.0552960i
$288$	7.15954	−	3.64797i	0.421880	−	0.214959i
$289$	19.6372	+	17.6814i	1.15513	+	1.04008i
$290$	1.43761	−	0.229022i	0.0844192	−	0.0134486i
$291$	1.30063	+	1.44450i	0.0762446	+	0.0846782i
$292$	4.33530	−	3.51065i	0.253704	−	0.205445i
$293$	−15.0009	+	15.0009i	−0.876365	+	0.876365i	−0.993156	−	0.116792i	$-0.962739\pi$
$293$	−15.0009	+	15.0009i	−0.876365	+	0.876365i	0.116792	+	0.993156i	$0.462739\pi$
$294$	−0.998270	+	1.00592i	−0.0582203	+	0.0586662i
$295$	−2.67417	−	12.5255i	−0.155696	−	0.729263i
$296$	−22.7381	−	10.1237i	−1.32163	−	0.588426i
$297$	1.72946	−	2.13570i	0.100353	−	0.123926i
$298$	8.75271	+	13.4780i	0.507031	+	0.780759i
$299$	1.19592	+	2.07140i	0.0691619	+	0.119792i
$300$	−0.0157717	+	0.311682i	−0.000910579	+	0.0179949i
$301$	8.27078	+	9.64652i	0.476720	+	0.556016i
$302$	1.74784	+	0.890567i	0.100577	+	0.0512464i
$303$	0.874437	+	2.27799i	0.0502351	+	0.130867i
$304$	−0.509215	−	4.84486i	−0.0292055	−	0.277872i
$305$	3.72432	+	11.4273i	0.213254	+	0.654323i
$306$	−30.8297	−	3.24033i	−1.76242	−	0.185237i
$307$	9.86884	+	9.86884i	0.563245	+	0.563245i	0.930228	−	0.366983i	$-0.119609\pi$
$307$	9.86884	+	9.86884i	0.563245	+	0.563245i	−0.366983	+	0.930228i	$0.619609\pi$
$308$	4.52490	+	0.829717i	0.257830	+	0.0472775i
$309$	−1.20856	−	0.392686i	−0.0687527	−	0.0223391i
$310$	−15.5158	−	0.799140i	−0.881240	−	0.0453881i
$311$	−5.16757	+	24.3115i	−0.293026	+	1.37858i	0.547498	+	0.836807i	$0.315580\pi$
$311$	−5.16757	+	24.3115i	−0.293026	+	1.37858i	−0.840525	+	0.541773i	$0.817753\pi$
$312$	−0.272060	−	0.0142581i	−0.0154024	−	0.000807203i
$313$	−15.3864	+	23.6929i	−0.869688	+	1.33920i	0.0701337	+	0.997538i	$0.477657\pi$
$313$	−15.3864	+	23.6929i	−0.869688	+	1.33920i	−0.939822	+	0.341665i	$0.889009\pi$
$314$	−4.66251	−	14.3497i	−0.263121	−	0.809802i
$315$	−6.70881	+	16.3260i	−0.377999	+	0.919867i
$316$	2.00671	−	6.17603i	0.112886	−	0.347429i
$317$	0.00782561	+	0.00966382i	0.000439530	+	0.000542774i	0.777366	−	0.629049i	$-0.216556\pi$
$317$	0.00782561	+	0.00966382i	0.000439530	+	0.000542774i	−0.776926	+	0.629592i	$0.783222\pi$
$318$	−0.430557	−	1.60686i	−0.0241445	−	0.0901084i
$319$	0.600710	+	1.34922i	0.0336333	+	0.0755417i
$320$	11.4309	+	2.41896i	0.639008	+	0.135224i
$321$	−0.862478	−	1.18710i	−0.0481388	−	0.0662574i
$322$	−0.315254	−	11.2211i	−0.0175684	−	0.625326i
$323$	−3.07736	+	6.03965i	−0.171229	+	0.336055i
$324$	3.72644	−	2.15146i	0.207025	−	0.119526i
$325$	−2.41383	+	3.73167i	−0.133895	+	0.206996i
$326$	5.41531	−	9.37960i	0.299926	−	0.519488i
$327$	−0.579974	+	0.0303951i	−0.0320726	+	0.00168085i
$328$	−0.347088	+	2.19143i	−0.0191647	+	0.121001i
$329$	5.12857	+	17.1933i	0.282747	+	0.947895i
$330$	−1.58361	+	0.338097i	−0.0871748	+	0.0186116i
$331$	2.27598	−	21.6545i	0.125099	−	1.19024i	−0.734260	−	0.678869i	$-0.762471\pi$
$331$	2.27598	−	21.6545i	0.125099	−	1.19024i	0.859359	−	0.511372i	$-0.170863\pi$
$332$	5.03364	−	1.34876i	0.276257	−	0.0740228i
$333$	−29.0435	−	11.1487i	−1.59157	−	0.610947i
$334$	−4.86949	+	1.03504i	−0.266447	+	0.0566350i
$335$	−18.9297	+	15.3572i	−1.03424	+	0.839054i
$336$	1.37339	+	0.838014i	0.0749245	+	0.0457174i
$337$	10.8166	+	21.2288i	0.589219	+	1.15641i	0.972528	+	0.232787i	$0.0747844\pi$
$337$	10.8166	+	21.2288i	0.589219	+	1.15641i	−0.383309	+	0.923620i	$0.625216\pi$
$338$	−16.1460	−	10.4853i	−0.878224	−	0.570325i
$339$	0.706727	+	0.150219i	0.0383841	+	0.00815880i
$340$	5.06939	+	5.06027i	0.274926	+	0.274432i
$341$	−3.27717	−	15.4179i	−0.177468	−	0.834923i
$342$	−0.756978	−	4.77937i	−0.0409327	−	0.258439i
$343$	18.0330	+	4.22035i	0.973690	+	0.227877i
$344$	6.73844	−	9.27467i	0.363312	−	0.500057i
$345$	0.314877	+	0.705516i	0.0169524	+	0.0379837i
$346$	6.08448	−	0.639505i	0.327104	−	0.0343800i
$347$	17.6098	+	14.2601i	0.945343	+	0.765524i	0.972209	−	0.234115i	$-0.0752193\pi$
$347$	17.6098	+	14.2601i	0.945343	+	0.765524i	−0.0268657	+	0.999639i	$0.508553\pi$
$348$	−0.00134876	−	0.0257359i	−7.23011e−5	−	0.00137959i
$349$	−10.6290			−0.568958			−0.284479	−	0.958682i	$-0.591821\pi$
$349$	−10.6290			−0.568958			−0.284479	+	0.958682i	$0.591821\pi$
$350$	18.2936	−	10.0206i	0.977833	−	0.535625i
$351$	−0.682905			−0.0364508
$352$	−0.504185	−	9.62043i	−0.0268732	−	0.512771i
$353$	−3.59298	−	2.90954i	−0.191235	−	0.154859i	0.528921	−	0.848671i	$-0.322597\pi$
$353$	−3.59298	−	2.90954i	−0.191235	−	0.154859i	−0.720156	+	0.693812i	$0.755930\pi$
$354$	−1.15327	+	0.121214i	−0.0612957	+	0.00644243i
$355$	−14.3921	+	1.52578i	−0.763853	+	0.0809798i
$356$	−1.49315	+	2.05514i	−0.0791366	+	0.108922i
$357$	−0.967613	−	2.01872i	−0.0512115	−	0.106842i
$358$	4.51147	+	28.4843i	0.238438	+	1.50544i
$359$	0.604866	+	2.84567i	0.0319236	+	0.150189i	0.991223	−	0.132204i	$-0.0422053\pi$
$359$	0.604866	+	2.84567i	0.0319236	+	0.150189i	−0.959299	+	0.282392i	$0.908872\pi$
$360$	15.7308	+	2.47699i	0.829086	+	0.130549i
$361$	17.5498	+	3.73033i	0.923675	+	0.196333i
$362$	24.8020	+	16.1066i	1.30356	+	0.846544i
$363$	−0.104613	−	0.205315i	−0.00549078	−	0.0107763i
$364$	−0.547391	−	1.00360i	−0.0286911	−	0.0526029i
$365$	25.6246	−	1.36607i	1.34125	−	0.0715033i
$366$	1.06441	−	0.226248i	0.0556378	−	0.0118262i
$367$	−28.5231	−	10.9490i	−1.48890	−	0.571533i	−0.528196	−	0.849123i	$-0.677131\pi$
$367$	−28.5231	−	10.9490i	−1.48890	−	0.571533i	−0.960700	+	0.277589i	$0.910465\pi$
$368$	−12.3096	+	3.29835i	−0.641683	+	0.171938i
$369$	−0.289877	+	2.75800i	−0.0150904	+	0.143576i
$370$	18.4103	+	31.8213i	0.957104	+	1.65431i
$371$	−14.9346	+	15.7980i	−0.775365	+	0.820192i
$372$	−0.0430264	+	0.271658i	−0.00223081	+	0.0140848i
$373$	−14.2402	+	0.746297i	−0.737329	+	0.0386418i	−0.417304	−	0.908767i	$-0.637025\pi$
$373$	−14.2402	+	0.746297i	−0.737329	+	0.0386418i	−0.320026	+	0.947409i	$0.603692\pi$
$374$	−18.5828	+	32.1863i	−0.960892	+	1.66431i
$375$	−0.900415	+	1.11808i	−0.0464972	+	0.0577375i
$376$	14.0186	−	8.09365i	0.722955	−	0.417398i
$377$	0.166617	−	0.327005i	0.00858123	−	0.0168416i
$378$	2.81956	+	1.52394i	0.145022	+	0.0783829i
$379$	17.6898	+	24.3480i	0.908666	+	1.25067i	0.967620	+	0.252410i	$0.0812233\pi$
$379$	17.6898	+	24.3480i	0.908666	+	1.25067i	−0.0589546	+	0.998261i	$0.518777\pi$
$380$	−0.558172	+	0.968796i	−0.0286336	+	0.0496982i
$381$	0.506305	+	1.13718i	0.0259388	+	0.0582595i
$382$	3.13701	+	11.7075i	0.160504	+	0.599007i
$383$	−12.7747	−	15.7754i	−0.652756	−	0.806087i	0.338085	−	0.941115i	$-0.390221\pi$
$383$	−12.7747	−	15.7754i	−0.652756	−	0.806087i	−0.990842	+	0.135028i	$0.956887\pi$
$384$	0.540629	−	1.66389i	0.0275889	−	0.0849098i
$385$	14.6097	+	15.3091i	0.744579	+	0.780224i
$386$	−6.99857	−	21.5394i	−0.356218	−	1.09633i
$387$	7.80408	−	12.0172i	0.396704	−	0.610870i
$388$	7.34866	+	0.385127i	0.373072	+	0.0195519i
$389$	−0.551377	+	2.59402i	−0.0279559	+	0.131522i	−0.989912	−	0.141680i	$-0.954750\pi$
$389$	−0.551377	+	2.59402i	−0.0279559	+	0.131522i	0.961957	+	0.273202i	$0.0880829\pi$
$390$	0.312945	+	0.252951i	0.0158466	+	0.0128087i
$391$	16.8644	+	5.47958i	0.852870	+	0.277114i
$392$	−0.0637432	−	16.7090i	−0.00321952	−	0.843933i
$393$	−1.64900	−	1.64900i	−0.0831810	−	0.0831810i
$394$	−3.21195	−	0.337589i	−0.161816	−	0.0170075i
$395$	24.1509	−	17.5799i	1.21516	−	0.884541i
$396$	−0.542256	−	5.15922i	−0.0272494	−	0.259260i
$397$	−4.32531	−	11.2678i	−0.217081	−	0.565516i	0.781190	−	0.624293i	$-0.214613\pi$
$397$	−4.32531	−	11.2678i	−0.217081	−	0.565516i	−0.998271	+	0.0587777i	$0.981280\pi$
$398$	−8.25450	−	4.20588i	−0.413761	−	0.210822i
$399$	0.265288	−	0.227454i	0.0132810	−	0.0113869i
$400$	−15.8764	−	17.5688i	−0.793819	−	0.878438i
$401$	−13.8545	−	23.9967i	−0.691861	−	1.19834i	−0.971227	−	0.238154i	$-0.923458\pi$
$401$	−13.8545	−	23.9967i	−0.691861	−	1.19834i	0.279366	−	0.960185i	$-0.409876\pi$
$402$	1.20202	+	1.85094i	0.0599511	+	0.0923166i
$403$	−2.46498	+	3.04399i	−0.122789	+	0.151632i
$404$	8.43896	+	3.75727i	0.419854	+	0.186931i
$405$	19.6869	+	2.05125i	0.978248	+	0.101927i
$406$	−1.41765	+	0.978312i	−0.0703569	+	0.0485528i
$407$	−26.3735	+	26.3735i	−1.30728	+	1.30728i
$408$	−1.56962	+	1.27105i	−0.0777078	+	0.0629265i
$409$	−2.31404	−	2.57000i	−0.114422	−	0.127078i	0.683213	−	0.730220i	$-0.260582\pi$
$409$	−2.31404	−	2.57000i	−0.114422	−	0.127078i	−0.797634	+	0.603141i	$0.793916\pi$
$410$	2.31521	−	2.31938i	0.114340	−	0.114546i
$411$	−1.17082	−	1.05421i	−0.0577522	−	0.0520004i
$412$	−4.28650	+	2.18408i	−0.211181	+	0.107602i
$413$	9.24831	+	12.0052i	0.455080	+	0.590735i
$414$	−12.0390	+	3.91172i	−0.591686	+	0.192250i
$415$	22.3871	+	8.57047i	1.09894	+	0.420708i
$416$	−1.77904	+	1.60185i	−0.0872245	+	0.0785373i
$417$	0.222704	−	0.580163i	0.0109058	−	0.0284107i
$418$	−5.60377	−	1.50153i	−0.274089	−	0.0734420i
$419$	−2.09086	−	1.51910i	−0.102145	−	0.0742128i	0.535540	−	0.844510i	$-0.320108\pi$
$419$	−2.09086	−	1.51910i	−0.102145	−	0.0742128i	−0.637685	+	0.770297i	$0.720108\pi$
$420$	−0.142266	−	0.340752i	−0.00694189	−	0.0166270i
$421$	2.23083	−	1.62080i	0.108724	−	0.0789928i	−0.532095	−	0.846685i	$-0.678595\pi$
$421$	2.23083	−	1.62080i	0.108724	−	0.0789928i	0.640819	+	0.767692i	$0.278595\pi$
$422$	27.5773	−	10.5859i	1.34244	−	0.515315i
$423$	16.9683	−	11.0193i	0.825026	−	0.535778i
$424$	16.9861	+	9.80692i	0.824917	+	0.476266i
$425$	5.21291	+	32.5336i	0.252863	+	1.57811i
$426$			1.31037i			0.0634877i
$427$	−9.80868	−	10.2968i	−0.474676	−	0.498297i
$428$	−5.48667	−	0.869002i	−0.265208	−	0.0420048i
$429$	−0.166047	+	0.372948i	−0.00801682	+	0.0180061i
$430$	−16.0994	+	5.24703i	−0.776380	+	0.253034i
$431$	9.59014	−	4.26981i	0.461941	−	0.205669i	−0.162552	−	0.986700i	$-0.551972\pi$
$431$	9.59014	−	4.26981i	0.461941	−	0.205669i	0.624493	+	0.781031i	$0.285306\pi$
$432$	0.941726	−	3.51457i	0.0453088	−	0.169095i
$433$	−0.117809	+	0.0186591i	−0.00566154	+	0.000896700i	−0.159265	−	0.987236i	$-0.550912\pi$
$433$	−0.117809	+	0.0186591i	−0.00566154	+	0.000896700i	0.153603	+	0.988133i	$0.450912\pi$
$434$	16.9701	−	7.06722i	0.814593	−	0.339237i
$435$	0.0644759	−	0.0994802i	0.00309138	−	0.00476971i
$436$	−1.47121	+	1.63394i	−0.0704581	+	0.0782516i
$437$	−0.144864	+	2.76417i	−0.00692979	+	0.132228i
$438$	0.121595	−	2.32017i	0.00581004	−	0.110862i
$439$	22.7045	−	25.2159i	1.08362	−	1.20349i	0.105729	−	0.994395i	$-0.466282\pi$
$439$	22.7045	−	25.2159i	1.08362	−	1.20349i	0.977896	−	0.209092i	$-0.0670508\pi$
$440$	10.3839	−	16.0214i	0.495033	−	0.763789i
$441$	−1.17257	−	20.8516i	−0.0558367	−	0.992936i
$442$	9.12184	−	1.44476i	0.433881	−	0.0687201i
$443$	−3.68199	+	13.7414i	−0.174937	+	0.652872i	0.821626	+	0.570027i	$0.193067\pi$
$443$	−3.68199	+	13.7414i	−0.174937	+	0.652872i	−0.996562	+	0.0828450i	$0.973599\pi$
$444$	0.594560	−	0.264715i	0.0282165	−	0.0125628i
$445$	−11.1102	+	3.62097i	−0.526672	+	0.171651i
$446$	−7.12983	+	16.0139i	−0.337607	+	0.758278i
$447$	1.29260	+	0.204727i	0.0611377	+	0.00968326i
$448$	−13.4366	+	3.25296i	−0.634820	+	0.153688i
$449$		−	34.5384i		−	1.62997i	−0.579485	−	0.814983i	$-0.696746\pi$
$449$		−	34.5384i		−	1.62997i	0.579485	−	0.814983i	$-0.303254\pi$
$450$	−16.6619	−	16.6019i	−0.785447	−	0.782623i
$451$	2.87936	+	1.66240i	0.135584	+	0.0782793i
$452$	2.29402	−	1.48976i	0.107902	−	0.0700723i
$453$	0.149135	−	0.0572477i	0.00700699	−	0.00268973i
$454$	24.6067	−	17.8778i	1.15485	−	0.839046i
$455$	0.671742	−	5.21551i	0.0314917	−	0.244507i
$456$	−0.255062	−	0.185313i	−0.0119444	−	0.00867809i
$457$	−11.9839	−	3.21108i	−0.560584	−	0.150208i	−0.0326096	−	0.999468i	$-0.510382\pi$
$457$	−11.9839	−	3.21108i	−0.560584	−	0.150208i	−0.527975	+	0.849260i	$0.677048\pi$
$458$	−15.3580	+	40.0091i	−0.717634	+	1.86950i
$459$	−3.76241	+	3.38769i	−0.175614	+	0.158124i
$460$	2.73157	+	1.04573i	0.127360	+	0.0487574i
$461$	−5.98374	+	1.94423i	−0.278691	+	0.0905520i	−0.445027	−	0.895517i	$-0.646806\pi$
$461$	−5.98374	+	1.94423i	−0.278691	+	0.0905520i	0.166337	+	0.986069i	$0.446806\pi$
$462$	1.51782	−	1.16927i	0.0706154	−	0.0543994i
$463$	−9.49520	+	4.83804i	−0.441279	+	0.224843i	−0.660490	−	0.750834i	$-0.729652\pi$
$463$	−9.49520	+	4.83804i	−0.441279	+	0.224843i	0.219211	+	0.975677i	$0.429652\pi$
$464$	1.45317	+	1.30844i	0.0674615	+	0.0607426i
$465$	−0.893826	+	0.895437i	−0.0414502	+	0.0415249i
$466$	−23.4259	−	26.0171i	−1.08518	−	1.20522i
$467$	−28.4949	+	23.0747i	−1.31859	+	1.06777i	−0.326113	+	0.945331i	$0.605739\pi$
$467$	−28.4949	+	23.0747i	−1.31859	+	1.06777i	−0.992476	+	0.122441i	$0.960928\pi$
$468$	−0.911541	+	0.911541i	−0.0421360	+	0.0421360i
$469$	12.3670	−	26.0558i	0.571056	−	1.20315i
$470$	−23.7804	−	2.47777i	−1.09691	−	0.114291i
$471$	−1.12247	−	0.499758i	−0.0517209	−	0.0230276i
$472$	8.60432	−	10.6255i	0.396046	−	0.489076i
$473$	−9.35637	−	14.4075i	−0.430206	−	0.662460i
$474$	−1.35230	−	2.34225i	−0.0621132	−	0.107583i
$475$	−4.69477	+	2.10039i	−0.215411	+	0.0963724i
$476$	−7.99435	−	2.81380i	−0.366421	−	0.128970i
$477$	21.8432	+	11.1296i	1.00013	+	0.509592i
$478$	16.4960	+	42.9735i	0.754509	+	1.96556i
$479$	−2.02142	−	19.2326i	−0.0923612	−	0.878758i	−0.938380	−	0.345605i	$-0.887674\pi$
$479$	−2.02142	−	19.2326i	−0.0923612	−	0.878758i	0.846019	−	0.533153i	$-0.178993\pi$
$480$	−0.625177	+	0.455079i	−0.0285353	+	0.0207714i
$481$	9.21761	+	0.968810i	0.420287	+	0.0441739i
$482$	−2.09462	−	2.09462i	−0.0954076	−	0.0954076i
$483$	−0.696252	−	0.592363i	−0.0316806	−	0.0269534i
$484$	−0.829672	−	0.269577i	−0.0377124	−	0.0122535i
$485$	26.3257	+	21.2789i	1.19539	+	0.966225i
$486$	1.12819	−	5.30770i	0.0511756	−	0.240762i
$487$	0.438600	+	0.0229860i	0.0198749	+	0.00104160i	0.0622708	−	0.998059i	$-0.480166\pi$
$487$	0.438600	+	0.0229860i	0.0198749	+	0.00104160i	−0.0423959	+	0.999101i	$0.513499\pi$
$488$	−6.98784	+	10.7603i	−0.316325	+	0.487097i
$489$	−0.272549	−	0.838820i	−0.0123251	−	0.0379328i
$490$	−14.4121	+	20.0346i	−0.651074	+	0.905071i
$491$	7.42044	−	22.8378i	0.334880	−	1.03065i	−0.631902	−	0.775049i	$-0.717725\pi$
$491$	7.42044	−	22.8378i	0.334880	−	1.03065i	0.966781	−	0.255605i	$-0.0822747\pi$
$492$	−0.0365107	−	0.0450869i	−0.00164603	−	0.00203268i
$493$	−0.704209	−	2.62814i	−0.0317160	−	0.118366i
$494$	0.586370	+	1.31701i	0.0263820	+	0.0592550i
$495$	11.9129	−	20.6768i	0.535446	−	0.929352i
$496$	−12.2667	−	16.8837i	−0.550791	−	0.758099i
$497$	14.5839	−	8.97530i	0.654175	−	0.402597i
$498$	0.985339	−	1.93384i	0.0441541	−	0.0866573i
$499$	4.58467	−	2.64696i	0.205238	−	0.118494i	−0.393858	−	0.919171i	$-0.628860\pi$
$499$	4.58467	−	2.64696i	0.205238	−	0.118494i	0.599096	+	0.800677i	$0.295527\pi$
$500$	0.582690	+	5.40346i	0.0260587	+	0.241650i
$501$	−0.202702	+	0.351090i	−0.00905606	+	0.0156856i
$502$	25.8479	−	1.35463i	1.15365	−	0.0604603i
$503$	0.292858	−	1.84903i	0.0130579	−	0.0824444i	−0.980299	−	0.197520i	$-0.936711\pi$
$503$	0.292858	−	1.84903i	0.0130579	−	0.0824444i	0.993357	+	0.115076i	$0.0367111\pi$
$504$	−18.0561	+	5.38594i	−0.804282	+	0.239909i
$505$	21.2796	+	36.7807i	0.946928	+	1.63672i
$506$	−1.58637	+	15.0933i	−0.0705229	+	0.670980i
$507$	−1.51435	+	0.405768i	−0.0672545	+	0.0180208i
$508$	4.39957	+	1.68884i	0.195199	+	0.0749300i
$509$	4.91131	−	1.04393i	0.217690	−	0.0462714i	−0.0977755	−	0.995208i	$-0.531173\pi$
$509$	4.91131	−	1.04393i	0.217690	−	0.0462714i	0.315465	+	0.948937i	$0.397839\pi$
$510$	2.97896	−	0.158811i	0.131910	−	0.00703225i
$511$	−26.6554	+	14.5386i	−1.17916	+	0.643150i
$512$	4.47382	+	8.78037i	0.197717	+	0.388041i
$513$	−0.662796	−	0.430425i	−0.0292631	−	0.0190037i
$514$	9.89542	+	2.10334i	0.436468	+	0.0927742i
$515$	−21.8605	−	3.44219i	−0.963290	−	0.151681i
$516$	0.0623247	+	0.293215i	0.00274369	+	0.0129081i
$517$	−3.79459	−	23.9581i	−0.166886	−	1.05368i
$518$	−35.8954	−	24.5696i	−1.57715	−	1.07952i
$519$	0.292844	−	0.403066i	0.0128544	−	0.0176926i
$520$	−4.71791	+	0.500168i	−0.206894	+	0.0219338i
$521$	−18.7192	+	1.96746i	−0.820101	+	0.0861961i	−0.505281	−	0.862955i	$-0.668611\pi$
$521$	−18.7192	+	1.96746i	−0.820101	+	0.0861961i	−0.314821	+	0.949151i	$0.601944\pi$
$522$	1.50948	+	1.22236i	0.0660683	+	0.0535010i
$523$	−0.0908633	−	1.73377i	−0.00397317	−	0.0758127i	0.995923	−	0.0902046i	$-0.0287521\pi$
$523$	−0.0908633	−	1.73377i	−0.00397317	−	0.0758127i	−0.999896	+	0.0143919i	$0.995419\pi$
$524$	−8.82866			−0.385682
$525$	0.390399	−	1.65311i	0.0170384	−	0.0721478i
$526$	8.59967			0.374964
$527$	1.51975	+	28.9986i	0.0662015	+	1.26320i
$528$	−1.69040	−	1.36885i	−0.0735650	−	0.0595718i
$529$	−15.6727	+	1.64727i	−0.681423	+	0.0716205i
$530$	−11.8071	−	26.4550i	−0.512866	−	1.14913i
$531$	10.0447	−	13.8253i	0.435902	−	0.599967i
$532$	0.101281	−	1.31906i	0.00439108	−	0.0571884i
$533$	−0.129247	−	0.816031i	−0.00559830	−	0.0353462i
$534$	0.219970	+	1.03488i	0.00951902	+	0.0447835i
$535$	−18.0851	−	18.0526i	−0.781888	−	0.780481i
$536$	−25.4527	−	5.41013i	−1.09939	−	0.233682i
$537$	1.96964	+	1.27910i	0.0849961	+	0.0551971i
$538$	−8.68114	−	17.0377i	−0.374271	−	0.734547i
$539$	−23.4097	−	8.88383i	−1.00833	−	0.382653i
$540$	−0.648520	+	0.526129i	−0.0279079	+	0.0226410i
$541$	12.8851	−	2.73881i	0.553974	−	0.117751i	0.0775854	−	0.996986i	$-0.475279\pi$
$541$	12.8851	−	2.73881i	0.553974	−	0.117751i	0.476388	+	0.879235i	$0.341946\pi$
$542$	−20.9106	−	8.02681i	−0.898185	−	0.344781i
$543$	2.32621	−	0.623305i	0.0998270	−	0.0267486i
$544$	−1.85515	+	17.6505i	−0.0795388	+	0.756761i
$545$	−9.89102	+	2.11171i	−0.423685	+	0.0904559i
$546$	−0.463172	−	0.110264i	−0.0198219	−	0.00471885i
$547$	4.06079	−	25.6388i	0.173627	−	1.09624i	−0.734828	−	0.678253i	$-0.762737\pi$
$547$	4.06079	−	25.6388i	0.173627	−	1.09624i	0.908455	−	0.417983i	$-0.137263\pi$
$548$	−5.95635	+	0.312159i	−0.254443	+	0.0133348i
$549$	−8.01819	+	13.8879i	−0.342208	+	0.592722i
$550$	−26.3084	+	10.1532i	−1.12179	+	0.432936i
$551$	0.367817	−	0.212359i	0.0156695	−	0.00904682i
$552$	−0.374428	+	0.734857i	−0.0159367	+	0.0312776i
$553$	−16.8057	+	31.0936i	−0.714653	+	1.32223i
$554$	−8.72976	−	12.0155i	−0.370892	−	0.510489i
$555$	2.92893	+	0.619808i	0.124326	+	0.0263094i
$556$	−0.956909	−	2.14925i	−0.0405820	−	0.0911486i
$557$	−3.72592	−	13.9053i	−0.157872	−	0.589188i	−0.998842	−	0.0481059i	$-0.984682\pi$
$557$	−3.72592	−	13.9053i	−0.157872	−	0.589188i	0.840970	−	0.541082i	$-0.181985\pi$
$558$	−13.0456	−	16.1100i	−0.552266	−	0.681991i
$559$	−1.31918	+	4.06001i	−0.0557952	+	0.171720i
$560$	25.9153	+	10.6493i	1.09512	+	0.450015i
$561$	0.935259	+	2.87843i	0.0394867	+	0.121527i
$562$	−1.03705	+	1.59692i	−0.0437454	+	0.0673620i
$563$	41.4901	+	2.17441i	1.74860	+	0.0916403i	0.899590	−	0.436735i	$-0.143865\pi$
$563$	41.4901	+	2.17441i	1.74860	+	0.0916403i	0.849011	+	0.528376i	$0.177199\pi$
$564$	−0.0880023	+	0.414018i	−0.00370556	+	0.0174333i
$565$	12.5658	+	0.647197i	0.528645	+	0.0272278i
$566$	−7.89661	−	2.56577i	−0.331919	−	0.107847i
$567$	−22.0616	+	7.85982i	−0.926501	+	0.330081i
$568$	−10.9246	−	10.9246i	−0.458388	−	0.458388i
$569$	−23.0473	−	2.42237i	−0.966192	−	0.101551i	−0.391728	−	0.920081i	$-0.628123\pi$
$569$	−23.0473	−	2.42237i	−0.966192	−	0.101551i	−0.574463	+	0.818530i	$0.694789\pi$
$570$	0.144298	+	0.442747i	0.00604398	+	0.0185446i
$571$	−0.913150	−	8.68804i	−0.0382141	−	0.363583i	−0.996873	−	0.0790244i	$-0.974820\pi$
$571$	−0.913150	−	8.68804i	−0.0382141	−	0.363583i	0.958659	−	0.284559i	$-0.0918472\pi$
$572$	0.553868	+	1.44287i	0.0231584	+	0.0603296i
$573$	0.879448	+	0.448101i	0.0367395	+	0.0187197i
$574$	−1.28739	+	3.65762i	−0.0537345	+	0.152666i
$575$	7.34815	+	11.2707i	0.306439	+	0.470020i
$576$	7.79483	+	13.5010i	0.324785	+	0.562544i
$577$	7.30287	+	11.2454i	0.304023	+	0.468154i	0.957354	−	0.288919i	$-0.0932957\pi$
$577$	7.30287	+	11.2454i	0.304023	+	0.468154i	−0.653331	+	0.757072i	$0.726629\pi$
$578$	26.2203	−	32.3794i	1.09062	−	1.34681i
$579$	−1.68487	−	0.750152i	−0.0700208	−	0.0311753i
$580$	−0.0937057	−	0.438907i	−0.00389092	−	0.0182246i
$581$	−28.2718	+	2.27931i	−1.17291	+	0.0945615i
$582$	2.16715	−	2.16715i	0.0898313	−	0.0898313i
$583$	22.8414	−	18.4966i	0.945995	−	0.766051i
$584$	18.3297	+	20.3572i	0.758488	+	0.842386i
$585$	−5.85607	+	0.932917i	−0.242119	+	0.0385714i
$586$	24.8580	+	22.3823i	1.02688	+	0.924603i
$587$	−6.86391	+	3.49734i	−0.283304	+	0.144350i	−0.589868	−	0.807499i	$-0.700820\pi$
$587$	−6.86391	+	3.49734i	−0.283304	+	0.144350i	0.306565	+	0.951850i	$0.400820\pi$
$588$	0.325802	+	0.291111i	0.0134359	+	0.0120052i
$589$	−4.31098	+	1.40072i	−0.177631	+	0.0577157i
$590$	−19.5017	+	5.24429i	−0.802872	+	0.215904i
$591$	−0.195451	+	0.175984i	−0.00803976	+	0.00723903i
$592$	−17.6971	+	46.1024i	−0.727345	+	1.89480i
$593$	39.7071	+	10.6395i	1.63057	+	0.436911i	0.954084	−	0.299540i	$-0.0968331\pi$
$593$	39.7071	+	10.6395i	1.63057	+	0.436911i	0.676491	+	0.736451i	$0.263500\pi$
$594$	−3.50555	−	2.54693i	−0.143834	−	0.104502i
$595$	−22.1717	−	32.0667i	−0.908950	−	1.31461i
$596$	4.00830	−	2.91220i	0.164186	−	0.119288i
$597$	−0.704321	+	0.270364i	−0.0288259	+	0.0110652i
$598$	3.16289	−	2.05400i	0.129340	−	0.0839944i
$599$	22.8775	+	13.2083i	0.934750	+	0.539678i	0.888311	−	0.459243i	$-0.151879\pi$
$599$	22.8775	+	13.2083i	0.934750	+	0.539678i	0.0464390	+	0.998921i	$0.485213\pi$
$600$	−1.53248	+	0.00276008i	−0.0625631	+	0.000112680i
$601$		−	9.66655i		−	0.394307i	−0.980373	−	0.197153i	$-0.936830\pi$
$601$		−	9.66655i		−	0.394307i	0.980373	−	0.197153i	$-0.0631697\pi$
$602$	14.5067	−	13.8190i	0.591248	−	0.563221i
$603$	−32.1234	−	5.08784i	−1.30816	−	0.207193i
$604$	0.245981	−	0.552482i	0.0100088	−	0.0224802i
$605$	−2.36164	−	3.24437i	−0.0960143	−	0.131902i
$606$	3.51471	−	1.56485i	0.142775	−	0.0635676i
$607$	7.29707	−	27.2330i	0.296179	−	1.10535i	−0.644098	−	0.764943i	$-0.722767\pi$
$607$	7.29707	−	27.2330i	0.296179	−	1.10535i	0.940277	−	0.340412i	$-0.110566\pi$
$608$	−2.73628	+	0.433384i	−0.110971	+	0.0175760i
$609$	−0.0180432	+	0.139102i	−0.000731149	+	0.00563669i
$610$	17.6858	−	6.80721i	0.716076	−	0.275616i
$611$	−4.03334	+	4.47948i	−0.163171	+	0.181220i
$612$	−0.500177	+	9.54394i	−0.0202184	+	0.385791i
$613$	−0.186043	+	3.54991i	−0.00751421	+	0.143380i	0.992296	+	0.123891i	$0.0395372\pi$
$613$	−0.186043	+	3.54991i	−0.00751421	+	0.143380i	−0.999810	+	0.0194889i	$0.993796\pi$
$614$	14.7249	−	16.3536i	0.594248	−	0.659979i
$615$	−0.0142071	−	0.266495i	−0.000572884	−	0.0107461i
$616$	−2.90588	+	22.4024i	−0.117081	+	0.902620i
$617$	30.7567	−	4.87138i	1.23822	−	0.196114i	0.497222	−	0.867623i	$-0.334354\pi$
$617$	30.7567	−	4.87138i	1.23822	−	0.196114i	0.740996	+	0.671509i	$0.234354\pi$
$618$	−0.518583	+	1.93538i	−0.0208605	+	0.0778523i
$619$	−43.7743	+	19.4896i	−1.75944	+	0.783351i	−0.770060	+	0.637972i	$0.779774\pi$
$619$	−43.7743	+	19.4896i	−1.75944	+	0.783351i	−0.989376	+	0.145379i	$0.953560\pi$
$620$	0.00431336	+	4.78981i	0.000173229	+	0.192363i
$621$	−0.840883	+	1.88865i	−0.0337435	+	0.0757891i
$622$	38.7068	+	6.13055i	1.55200	+	0.245813i
$623$	10.0110	−	9.53649i	0.401084	−	0.382071i
$624$			0.540515i			0.0216379i
$625$	−12.4219	+	21.6955i	−0.496877	+	0.867821i
$626$	38.5760	+	22.2719i	1.54181	+	0.890163i
$627$	−0.396221	+	0.257309i	−0.0158235	+	0.0102759i
$628$	−4.34268	+	1.66700i	−0.173292	+	0.0665204i
$629$	55.5896	−	40.3882i	2.21650	−	1.61038i
$630$	26.2602	+	9.21632i	1.04623	+	0.367187i
$631$	−9.95692	−	7.23413i	−0.396379	−	0.287986i	0.371686	−	0.928359i	$-0.378780\pi$
$631$	−9.95692	−	7.23413i	−0.396379	−	0.287986i	−0.768064	+	0.640373i	$0.778780\pi$
$632$	30.8017	+	8.25329i	1.22523	+	0.328298i
$633$	0.862061	−	2.24574i	0.0342638	−	0.0892603i
$634$	0.0145707	−	0.0131195i	0.000578675	−	0.000521041i
$635$	11.8230	+	18.1699i	0.469180	+	0.721051i
$636$	−0.487764	+	0.158484i	−0.0193411	+	0.00628430i
$637$	1.94528	+	5.91014i	0.0770748	+	0.234168i
$638$	2.07488	−	1.05720i	0.0821451	−	0.0418550i
$639$	−14.3505	−	12.9213i	−0.567698	−	0.511157i
$640$	4.73903	−	30.0965i	0.187327	−	1.18967i
$641$	20.2434	+	22.4826i	0.799568	+	0.888010i	0.995707	−	0.0925658i	$-0.0295069\pi$
$641$	20.2434	+	22.4826i	0.799568	+	0.888010i	−0.196138	+	0.980576i	$0.562840\pi$
$642$	−1.79801	+	1.45600i	−0.0709617	+	0.0574636i
$643$	30.5033	−	30.5033i	1.20293	−	1.20293i	0.229664	−	0.973270i	$-0.426237\pi$
$643$	30.5033	−	30.5033i	1.20293	−	1.20293i	0.973270	−	0.229664i	$-0.0737627\pi$
$644$	−3.44959	+	0.278110i	−0.135933	+	0.0109591i
$645$	−0.559722	+	1.26021i	−0.0220390	+	0.0496207i
$646$	9.76384	+	4.34714i	0.384153	+	0.171036i
$647$	3.68133	−	4.54606i	0.144728	−	0.178724i	−0.699627	−	0.714508i	$-0.746651\pi$
$647$	3.68133	−	4.54606i	0.144728	−	0.178724i	0.844355	+	0.535784i	$0.179984\pi$
$648$	11.5080	+	17.7208i	0.452078	+	0.696139i
$649$	−10.2441	−	17.7433i	−0.402115	−	0.696484i
$650$	6.07500	+	3.49283i	0.238281	+	0.137000i
$651$	0.497018	−	1.41209i	0.0194797	−	0.0553442i
$652$	−2.97511	−	1.51589i	−0.116514	−	0.0593670i
$653$	−11.3188	−	29.4865i	−0.442939	−	1.15390i	−0.955434	−	0.295205i	$-0.904612\pi$
$653$	−11.3188	−	29.4865i	−0.442939	−	1.15390i	0.512495	−	0.858690i	$-0.328721\pi$
$654$	0.0957189	+	0.910705i	0.00374291	+	0.0356114i
$655$	−32.8771	−	23.8414i	−1.28461	−	0.931561i
$656$	4.37793	+	0.460139i	0.170930	+	0.0179654i
$657$	24.2104	+	24.2104i	0.944536	+	0.944536i
$658$	26.6489	−	9.49412i	1.03888	−	0.370119i
$659$	−15.9469	−	5.18146i	−0.621202	−	0.201841i	−0.0185282	−	0.999828i	$-0.505898\pi$
$659$	−15.9469	−	5.18146i	−0.621202	−	0.201841i	−0.602674	+	0.797988i	$0.705898\pi$
$660$	0.129643	+	0.482096i	0.00504634	+	0.0187656i
$661$	−3.02029	+	14.2094i	−0.117476	+	0.552680i	0.879563	+	0.475782i	$0.157835\pi$
$661$	−3.02029	+	14.2094i	−0.117476	+	0.552680i	−0.997039	+	0.0768979i	$0.975498\pi$
$662$	−34.2846	−	1.79678i	−1.33251	−	0.0698337i
$663$	0.409619	−	0.630758i	0.0159083	−	0.0244966i
$664$	7.90768	+	24.3373i	0.306878	+	0.944472i
$665$	3.93922	−	4.63854i	0.152756	−	0.179875i
$666$	−15.1579	+	46.6512i	−0.587356	+	1.80770i
$667$	−0.699210	−	0.863452i	−0.0270735	−	0.0334330i
$668$	0.397232	+	1.48249i	0.0153693	+	0.0573592i
$669$	0.580615	+	1.30408i	0.0224479	+	0.0504187i
$670$	25.7432	+	28.5390i	0.994546	+	1.10256i
$671$	11.3008	+	15.5543i	0.436264	+	0.600466i
$672$	0.435039	−	0.804899i	0.0167820	−	0.0310496i
$673$	−13.3101	+	26.1226i	−0.513068	+	1.00695i	0.478588	+	0.878039i	$0.341149\pi$
$673$	−13.3101	+	26.1226i	−0.513068	+	1.00695i	−0.991656	+	0.128912i	$0.958851\pi$
$674$	32.5338	−	18.7834i	1.25316	−	0.723510i
$675$	−3.83581	+	0.207955i	−0.147641	+	0.00800418i
$676$	−2.96764	+	5.14010i	−0.114140	+	0.197696i
$677$	21.3039	−	1.11649i	0.818776	−	0.0429102i	0.361652	−	0.932313i	$-0.382213\pi$
$677$	21.3039	−	1.11649i	0.818776	−	0.0429102i	0.457124	+	0.889403i	$0.348880\pi$
$678$	0.178213	−	1.12519i	0.00684423	−	0.0432128i
$679$	−38.9632	−	9.27567i	−1.49527	−	0.355967i
$680$	−23.5117	+	26.1598i	−0.901634	+	1.00318i
$681$	0.258904	−	2.46331i	0.00992122	−	0.0943941i
$682$	−24.0062	+	6.43243i	−0.919244	+	0.246311i
$683$	−27.3101	−	10.4833i	−1.04499	−	0.401134i	−0.225510	−	0.974241i	$-0.572405\pi$
$683$	−27.3101	−	10.4833i	−1.04499	−	0.401134i	−0.819481	+	0.573107i	$0.805738\pi$
$684$	−1.45923	+	0.310169i	−0.0557950	+	0.0118596i
$685$	−23.0238	−	14.9224i	−0.879696	−	0.570156i
$686$	5.15718	−	28.7426i	0.196902	−	1.09740i
$687$	1.58439	+	3.10954i	0.0604483	+	0.118636i
$688$	−19.0757	−	12.3879i	−0.727253	−	0.472284i
$689$	−7.14408	−	1.51852i	−0.272168	−	0.0578511i
$690$	1.08491	−	0.554018i	0.0413016	−	0.0210911i
$691$	−3.59164	−	16.8973i	−0.136632	−	0.642804i	−0.992152	−	0.125035i	$-0.960096\pi$
$691$	−3.59164	−	16.8973i	−0.136632	−	0.642804i	0.855520	−	0.517770i	$-0.173238\pi$
$692$	−0.295060	−	1.86293i	−0.0112165	−	0.0708181i
$693$	−2.16161	+	28.1523i	−0.0821129	+	1.06942i
$694$	21.0005	−	28.9047i	0.797168	−	1.09721i
$695$	2.24052	−	10.5877i	0.0849879	−	0.401614i
$696$	0.125857	−	0.0132281i	0.00477059	−	0.000501410i
$697$	−4.76016	−	3.85470i	−0.180304	−	0.146007i
$698$	0.877107	+	16.7362i	0.0331990	+	0.633474i
$699$	−2.85098			−0.107834
$700$	−3.38025	−	5.47043i	−0.127762	−	0.206763i
$701$	−16.6238			−0.627872			−0.313936	−	0.949444i	$-0.601648\pi$
$701$	−16.6238			−0.627872			−0.313936	+	0.949444i	$0.601648\pi$
$702$	0.0563534	+	1.07529i	0.00212692	+	0.0405841i
$703$	8.33556	+	6.75000i	0.314382	+	0.254581i
$704$	18.5882	−	1.95370i	0.700568	−	0.0736327i
$705$	−1.44575	+	1.30412i	−0.0544501	+	0.0491159i
$706$	−4.28480	+	5.89752i	−0.161261	+	0.221956i
$707$	−41.4898	−	28.3988i	−1.56039	−	1.06805i
$708$	0.0559265	+	0.353106i	0.00210185	+	0.0132705i
$709$	−0.152838	−	0.719046i	−0.00573995	−	0.0270043i	0.975184	−	0.221394i	$-0.0710607\pi$
$709$	−0.152838	−	0.719046i	−0.00573995	−	0.0270043i	−0.980924	+	0.194390i	$0.937727\pi$
$710$	3.59009	+	22.5356i	0.134734	+	0.845745i
$711$	38.9859	+	8.28670i	1.46208	+	0.310776i
$712$	−10.4617	−	6.79392i	−0.392070	−	0.254613i
$713$	5.38332	+	10.5654i	0.201607	+	0.395676i
$714$	−3.09879	+	1.69017i	−0.115969	+	0.0632529i
$715$	−1.83387	+	6.86883i	−0.0685828	+	0.256880i
$716$	8.69677	−	1.84856i	0.325014	−	0.0690838i
$717$	3.49953	+	1.34334i	0.130692	+	0.0501681i
$718$	4.43081	−	1.18723i	0.165357	−	0.0443071i
$719$	−2.67423	+	25.4436i	−0.0997318	+	0.948885i	0.824193	+	0.566310i	$0.191629\pi$
$719$	−2.67423	+	25.4436i	−0.0997318	+	0.948885i	−0.923924	+	0.382575i	$0.875037\pi$
$720$	3.27426	−	31.4247i	0.122025	−	1.17113i
$721$	25.0919	−	7.48465i	0.934472	−	0.278743i
$722$	4.42548	−	27.9414i	0.164699	−	1.03987i
$723$	−0.240899	+	0.0126250i	−0.00895912	+	0.000469528i
$724$	4.55862	−	7.89576i	0.169420	−	0.293444i
$725$	0.836297	−	1.88749i	0.0310593	−	0.0700998i
$726$	−0.314652	+	0.181665i	−0.0116778	+	0.00674221i
$727$	0.931344	−	1.82787i	0.0345416	−	0.0677918i	−0.873091	−	0.487558i	$-0.837888\pi$
$727$	0.931344	−	1.82787i	0.0345416	−	0.0677918i	0.907632	+	0.419766i	$0.137888\pi$
$728$	4.78077	−	2.94222i	0.177187	−	0.109046i
$729$	15.3493	+	21.1265i	0.568492	+	0.782463i
$730$	−4.26552	−	40.2352i	−0.157874	−	1.48917i
$731$	12.8726	+	28.9123i	0.476110	+	1.06936i
$732$	−0.0868302	−	0.324055i	−0.00320934	−	0.0119774i
$733$	−7.00513	−	8.65061i	−0.258740	−	0.319518i	0.631178	−	0.775638i	$-0.282572\pi$
$733$	−7.00513	−	8.65061i	−0.258740	−	0.319518i	−0.889918	+	0.456121i	$0.849239\pi$
$734$	−14.8863	+	45.8154i	−0.549464	+	1.69108i
$735$	0.427125	+	1.96388i	0.0157547	+	0.0724389i
$736$	2.23953	+	6.89255i	0.0825500	+	0.254063i
$737$	−21.2371	+	32.7023i	−0.782279	+	1.20460i
$738$	4.36660	+	0.228844i	0.160737	+	0.00842386i
$739$	−4.86660	+	22.8956i	−0.179021	+	0.842227i	0.793346	+	0.608770i	$0.208337\pi$
$739$	−4.86660	+	22.8956i	−0.179021	+	0.842227i	−0.972367	+	0.233456i	$0.924996\pi$
$740$	9.49989	−	6.18147i	0.349223	−	0.227235i
$741$	0.111654	+	0.0362785i	0.00410171	+	0.00133273i
$742$	26.1076	+	22.2120i	0.958440	+	0.815429i
$743$	9.74553	+	9.74553i	0.357529	+	0.357529i	0.862901	−	0.505373i	$-0.168645\pi$
$743$	9.74553	+	9.74553i	0.357529	+	0.357529i	−0.505373	+	0.862901i	$0.668645\pi$
$744$	−1.34321	−	0.141177i	−0.0492446	−	0.00517581i
$745$	22.7908	−	0.0205237i	0.834989	−	0.000751931i
$746$	2.35020	+	22.3607i	0.0860471	+	0.818683i
$747$	11.4622	+	29.8600i	0.419380	+	1.09252i
$748$	10.2092	+	5.20182i	0.373284	+	0.190198i
$749$	28.5199	+	10.0383i	1.04210	+	0.366790i
$750$	1.83481	+	1.32551i	0.0669977	+	0.0484007i
$751$	−12.3488	−	21.3888i	−0.450616	−	0.780490i	0.547808	−	0.836604i	$-0.315462\pi$
$751$	−12.3488	−	21.3888i	−0.450616	−	0.780490i	−0.998424	+	0.0561142i	$0.982129\pi$
$752$	−17.4916	−	26.9348i	−0.637855	−	0.982210i
$753$	1.32649	−	1.63807i	0.0483398	−	0.0596947i
$754$	−0.528644	−	0.235367i	−0.0192521	−	0.00857158i
$755$	2.40796	−	1.39313i	0.0876347	−	0.0507012i
$756$	0.423687	−	0.892656i	0.0154093	−	0.0324656i
$757$	−4.91711	+	4.91711i	−0.178715	+	0.178715i	−0.790796	−	0.612080i	$-0.790333\pi$
$757$	−4.91711	+	4.91711i	−0.178715	+	0.178715i	0.612080	+	0.790796i	$0.290333\pi$
$758$	36.8780	−	29.8632i	1.33947	−	1.08468i
$759$	0.826971	+	0.918445i	0.0300172	+	0.0333374i
$760$	−4.89423	−	2.48819i	−0.177532	−	0.0902560i
$761$	−19.9994	−	18.0075i	−0.724977	−	0.652773i	0.221641	−	0.975128i	$-0.428859\pi$
$761$	−19.9994	−	18.0075i	−0.724977	−	0.652773i	−0.946619	+	0.322356i	$0.895525\pi$
$762$	1.74880	−	0.891057i	0.0633523	−	0.0322796i
$763$	9.48012	−	7.30313i	0.343203	−	0.264391i
$764$	3.55381	−	1.15470i	0.128573	−	0.0417757i
$765$	−27.6356	+	34.1900i	−0.999167	+	1.23614i
$766$	−23.7855	+	21.4165i	−0.859404	+	0.773811i
$767$	−1.82454	+	4.75309i	−0.0658804	+	0.171624i
$768$	−1.36839	−	0.366659i	−0.0493776	−	0.0132307i
$769$	−39.8628	−	28.9620i	−1.43749	−	1.04440i	−0.988560	−	0.150829i	$-0.951806\pi$
$769$	−39.8628	−	28.9620i	−1.43749	−	1.04440i	−0.448929	−	0.893567i	$-0.648194\pi$
$770$	22.8997	−	24.2674i	0.825250	−	0.874537i
$771$	0.666494	−	0.484237i	0.0240032	−	0.0174394i
$772$	−6.51849	+	2.50222i	−0.234606	+	0.0900567i
$773$	29.1185	−	18.9098i	1.04732	−	0.680136i	0.0982355	−	0.995163i	$-0.468680\pi$
$773$	29.1185	−	18.9098i	1.04732	−	0.680136i	0.949083	+	0.315027i	$0.102013\pi$
$774$	−19.5660	−	11.2965i	−0.703287	−	0.406043i
$775$	−12.9186	+	17.8485i	−0.464050	+	0.641135i
$776$			36.1353i			1.29718i
$777$	−3.44285	+	0.833504i	−0.123512	+	0.0299018i
$778$	4.12999	+	0.654126i	0.148067	+	0.0234516i
$779$	0.388891	−	0.873464i	0.0139335	−	0.0312951i
$780$	0.0728277	−	0.100429i	0.00260765	−	0.00359593i
$781$	−21.1500	+	9.41658i	−0.756806	+	0.336952i
$782$	7.23637	−	27.0065i	0.258772	−	0.965750i
$783$	0.313316	−	0.0496244i	0.0111970	−	0.00177343i
$784$	−33.0991	+	1.86129i	−1.18211	+	0.0664747i
$785$	−20.6734	−	5.51946i	−0.737864	−	0.196998i
$786$	−2.46040	+	2.73255i	−0.0877596	+	0.0974669i
$787$	−1.39862	+	26.6873i	−0.0498555	+	0.951300i	0.853149	+	0.521668i	$0.174690\pi$
$787$	−1.39862	+	26.6873i	−0.0498555	+	0.951300i	−0.903004	+	0.429632i	$0.858643\pi$
$788$	−0.0521102	+	0.994322i	−0.00185635	+	0.0354213i
$789$	0.468600	−	0.520433i	0.0166826	−	0.0185279i
$790$	−29.6738	−	36.5767i	−1.05575	−	1.30134i
$791$	−13.7436	+	5.72350i	−0.488665	+	0.203504i
$792$	25.1604	−	3.98502i	0.894036	−	0.141601i
$793$	1.23654	−	4.61485i	0.0439110	−	0.163878i
$794$	−17.3851	+	7.74036i	−0.616975	+	0.274695i
$795$	−2.24437	−	0.727005i	−0.0795994	−	0.0257842i
$796$	−1.16169	+	2.60921i	−0.0411751	+	0.0924809i
$797$	−40.7379	−	6.45225i	−1.44301	−	0.228551i	−0.614675	−	0.788781i	$-0.710713\pi$
$797$	−40.7379	−	6.45225i	−1.44301	−	0.228551i	−0.828337	+	0.560230i	$0.810713\pi$
$798$	−0.380035	−	0.398947i	−0.0134531	−	0.0141226i
$799$			44.6875i			1.58093i
$800$	−9.50491	+	9.53921i	−0.336049	+	0.337262i
$801$	−13.5025	−	7.79568i	−0.477088	−	0.275447i
$802$	−36.6414	+	23.7952i	−1.29385	+	0.840238i
$803$	38.3225	−	14.7106i	1.35237	−	0.519127i
$804$	0.550462	−	0.399934i	0.0194133	−	0.0141046i
$805$	−13.5970	−	8.27981i	−0.479230	−	0.291825i
$806$	4.99641	+	3.63011i	0.175991	+	0.127865i
$807$	−1.50412	−	0.403028i	−0.0529476	−	0.0141873i
$808$	−16.2561	+	42.3485i	−0.571887	+	1.48982i
$809$	−5.13057	+	4.61959i	−0.180381	+	0.162416i	−0.754375	−	0.656444i	$-0.772060\pi$
$809$	−5.13057	+	4.61959i	−0.180381	+	0.162416i	0.573994	+	0.818860i	$0.305393\pi$
$810$	1.60529	−	31.1677i	0.0564041	−	1.09512i
$811$	22.5964	−	7.34202i	0.793467	−	0.257813i	0.115887	−	0.993262i	$-0.463029\pi$
$811$	22.5964	−	7.34202i	0.793467	−	0.257813i	0.677580	+	0.735449i	$0.263029\pi$
$812$	0.324071	+	0.420673i	0.0113726	+	0.0147627i
$813$	−1.62519	+	0.828075i	−0.0569979	+	0.0290419i
$814$	43.7034	+	39.3507i	1.53180	+	1.37924i
$815$	−6.98542	−	13.6792i	−0.244689	−	0.479161i
$816$	2.68133	+	2.97792i	0.0938653	+	0.104248i
$817$	−3.83929	+	3.10900i	−0.134320	+	0.108770i
$818$	−3.85571	+	3.85571i	−0.134812	+	0.134812i
$819$	5.77478	−	3.98514i	0.201787	−	0.139252i
$820$	−0.751432	−	0.675368i	−0.0262411	−	0.0235849i
$821$	6.31990	+	2.81380i	0.220566	+	0.0982023i	0.514045	−	0.857763i	$-0.328146\pi$
$821$	6.31990	+	2.81380i	0.220566	+	0.0982023i	−0.293479	+	0.955966i	$0.594813\pi$
$822$	−1.56332	+	1.93054i	−0.0545270	+	0.0673353i
$823$	−11.9200	−	18.3553i	−0.415507	−	0.639824i	0.567504	−	0.823370i	$-0.307909\pi$
$823$	−11.9200	−	18.3553i	−0.415507	−	0.639824i	−0.983011	+	0.183546i	$0.941242\pi$
$824$	−11.8119	−	20.4588i	−0.411487	−	0.712717i
$825$	−0.819102	+	2.14538i	−0.0285175	+	0.0746924i
$826$	18.1399	−	15.5529i	0.631167	−	0.541153i
$827$	−30.9277	−	15.7585i	−1.07546	−	0.547975i	−0.175739	−	0.984437i	$-0.556232\pi$
$827$	−30.9277	−	15.7585i	−1.07546	−	0.547975i	−0.899723	+	0.436461i	$0.856232\pi$
$828$	1.39856	+	3.64338i	0.0486035	+	0.126616i
$829$	−2.32589	−	22.1294i	−0.0807816	−	0.768585i	−0.957666	−	0.287883i	$-0.907049\pi$
$829$	−2.32589	−	22.1294i	−0.0807816	−	0.768585i	0.876884	−	0.480702i	$-0.159618\pi$
$830$	11.6475	−	35.9574i	0.404290	−	1.24810i
$831$	−1.20284	−	0.126423i	−0.0417260	−	0.00438558i
$832$	−3.28420	−	3.28420i	−0.113859	−	0.113859i
$833$	40.0358	+	22.9115i	1.38716	+	0.793836i
$834$	−0.931888	−	0.302789i	−0.0322686	−	0.0104847i
$835$	−2.52414	+	6.59335i	−0.0873515	+	0.228172i
$836$	−0.371864	+	1.74948i	−0.0128612	+	0.0605071i
$837$	−3.38092	−	0.177187i	−0.116862	−	0.00612446i
$838$	−2.21940	+	3.41758i	−0.0766679	+	0.118058i
$839$	15.5792	+	47.9479i	0.537855	+	1.65535i	0.737399	+	0.675457i	$0.236054\pi$
$839$	15.5792	+	47.9479i	0.537855	+	1.65535i	−0.199544	+	0.979889i	$0.563946\pi$
$840$	1.63442	−	0.785218i	0.0563928	−	0.0270926i
$841$	8.90881	−	27.4185i	0.307200	−	0.945466i
$842$	−2.73616	−	3.37887i	−0.0942942	−	0.116444i
$843$	0.0401326	+	0.149777i	0.00138224	+	0.00515859i
$844$	−3.70409	−	8.31952i	−0.127500	−	0.286370i
$845$	−24.9318	+	11.1273i	−0.857680	+	0.382790i
$846$	−18.7510	−	25.8085i	−0.644673	−	0.887316i
$847$	4.17704	+	2.25764i	0.143525	+	0.0775735i
$848$	17.6668	−	34.6730i	0.606679	−	1.19067i
$849$	−0.585564	+	0.338075i	−0.0200965	+	0.0116027i
$850$	50.7966	−	10.8928i	1.74231	−	0.373620i
$851$	14.0293	−	24.2995i	0.480918	−	0.832975i
$852$	0.403429	−	0.0211428i	0.0138212	−	0.000724341i
$853$	−0.136081	+	0.859182i	−0.00465933	+	0.0294178i	−0.989908	−	0.141708i	$-0.954741\pi$
$853$	−0.136081	+	0.859182i	−0.00465933	+	0.0294178i	0.985249	+	0.171126i	$0.0547405\pi$
$854$	−15.4037	+	16.2942i	−0.527103	+	0.557577i
$855$	−6.27163	−	2.78555i	−0.214485	−	0.0952636i
$856$	2.85135	−	27.1288i	0.0974573	−	0.927244i
$857$	2.01996	−	0.541246i	0.0690004	−	0.0184886i	−0.224154	−	0.974554i	$-0.571962\pi$
$857$	2.01996	−	0.541246i	0.0690004	−	0.0184886i	0.293154	+	0.956065i	$0.405295\pi$
$858$	0.600937	+	0.230678i	0.0205156	+	0.00787522i
$859$	−24.8394	+	5.27978i	−0.847510	+	0.180144i	−0.611143	−	0.791520i	$-0.709290\pi$
$859$	−24.8394	+	5.27978i	−0.847510	+	0.180144i	−0.236367	+	0.971664i	$0.575957\pi$
$860$	1.87519	+	4.87191i	0.0639433	+	0.166131i
$861$	0.151201	+	0.277215i	0.00515291	+	0.00944746i
$862$	−7.51452	−	14.7481i	−0.255946	−	0.502321i
$863$	−33.4896	−	21.7484i	−1.14000	−	0.740323i	−0.170484	−	0.985360i	$-0.554533\pi$
$863$	−33.4896	−	21.7484i	−1.14000	−	0.740323i	−0.969514	+	0.245037i	$0.921200\pi$
$864$	−2.02398	−	0.430210i	−0.0688571	−	0.0146360i
$865$	3.93200	−	7.73419i	0.133692	−	0.262970i
$866$	0.0391018	+	0.183960i	0.00132873	+	0.00625120i
$867$	−0.530772	−	3.35116i	−0.0180260	−	0.113811i
$868$	−2.44962	−	5.11063i	−0.0831457	−	0.173466i
$869$	28.0871	−	38.6586i	0.952790	−	1.31140i
$870$	−0.161960	−	0.0933132i	−0.00549095	−	0.00316361i
$871$	9.63658	−	1.01285i	0.326523	−	0.0343190i
$872$	−8.39061	−	6.79459i	−0.284142	−	0.230094i
$873$	2.36376	+	45.1033i	0.0800013	+	1.52652i
$874$	4.36436			0.147627
$875$	2.18491	−	29.4996i	0.0738635	−	0.997268i
$876$	−0.716283			−0.0242010
$877$	−1.57981	−	30.1445i	−0.0533463	−	1.01791i	−0.885874	−	0.463925i	$-0.846441\pi$
$877$	−1.57981	−	30.1445i	−0.0533463	−	1.01791i	0.832528	−	0.553983i	$-0.186893\pi$
$878$	−41.5779	−	33.6691i	−1.40319	−	1.13628i
$879$	2.70905	−	0.284732i	0.0913739	−	0.00960378i
$880$	−32.8215	−	18.9101i	−1.10641	−	0.637460i
$881$	30.9331	−	42.5757i	1.04216	−	1.43441i	0.146750	−	0.989174i	$-0.453119\pi$
$881$	30.9331	−	42.5757i	1.04216	−	1.43441i	0.895412	−	0.445239i	$-0.146881\pi$
$882$	−32.7358	+	3.56698i	−1.10227	+	0.120107i
$883$	−0.132520	−	0.836696i	−0.00445964	−	0.0281571i	0.985358	−	0.170497i	$-0.0545374\pi$
$883$	−0.132520	−	0.836696i	−0.00445964	−	0.0281571i	−0.989818	+	0.142340i	$0.954537\pi$
$884$	−0.591983	−	2.78506i	−0.0199106	−	0.0936718i
$885$	−0.745282	+	1.46596i	−0.0250524	+	0.0492778i
$886$	21.9407	+	4.66364i	0.737112	+	0.156678i
$887$	−31.3359	−	20.3498i	−1.05216	−	0.683279i	−0.101915	−	0.994793i	$-0.532497\pi$
$887$	−31.3359	−	20.3498i	−1.05216	−	0.683279i	−0.950241	+	0.311514i	$0.899164\pi$
$888$	1.45091	+	2.84757i	0.0486893	+	0.0955581i
$889$	−21.8954	−	13.3601i	−0.734347	−	0.448084i
$890$	6.61831	+	17.1950i	0.221846	+	0.576377i
$891$	30.9709	−	6.58307i	1.03756	−	0.220541i
$892$	5.04529	+	1.93670i	0.168929	+	0.0648456i
$893$	−6.73792	+	1.80542i	−0.225476	+	0.0604161i
$894$	0.215693	−	2.05219i	0.00721387	−	0.0686354i
$895$	37.3779	+	16.6014i	1.24941	+	0.554924i
$896$	10.3045	+	34.5453i	0.344249	+	1.15408i
$897$	0.0480434	−	0.303334i	0.00160412	−	0.0101280i
$898$	−54.3833	+	2.85011i	−1.81479	+	0.0951094i
$899$	0.909733	−	1.57570i	0.0303413	−	0.0525527i
$900$	−4.84246	+	5.39762i	−0.161415	+	0.179921i
$901$	−46.8927	+	27.0735i	−1.56222	+	0.901949i
$902$	2.37997	−	4.67095i	0.0792443	−	0.155526i
$903$	−0.0458202	−	1.63091i	−0.00152480	−	0.0542734i
$904$	7.89502	+	10.8666i	0.262585	+	0.361417i
$905$	38.2980	−	17.0927i	1.27307	−	0.568181i
$906$	−0.102448	−	0.230101i	−0.00340359	−	0.00764459i
$907$	−2.33385	−	8.71004i	−0.0774942	−	0.289212i	0.916293	−	0.400508i	$-0.131166\pi$
$907$	−2.33385	−	8.71004i	−0.0774942	−	0.289212i	−0.993787	+	0.111296i	$0.964500\pi$
$908$	−5.90113	−	7.28729i	−0.195836	−	0.241837i
$909$	−17.5203	+	53.9219i	−0.581111	+	1.78848i
$910$	−8.26766	−	0.627325i	−0.274070	−	0.0207956i
$911$	−12.2855	−	37.8110i	−0.407038	−	1.25273i	−0.919181	−	0.393834i	$-0.871148\pi$
$911$	−12.2855	−	37.8110i	−0.407038	−	1.25273i	0.512143	−	0.858900i	$-0.328852\pi$
$912$	−0.340678	+	0.524598i	−0.0112810	+	0.0173712i
$913$	38.2938	+	2.00689i	1.26734	+	0.0664185i
$914$	−4.06718	+	19.1346i	−0.134530	+	0.632916i
$915$	0.551748	−	1.44123i	0.0182402	−	0.0476456i
$916$	12.5655	+	4.08279i	0.415177	+	0.134899i
$917$	47.2645	+	8.66673i	1.56081	+	0.286201i
$918$	5.64465	+	5.64465i	0.186301	+	0.186301i
$919$	−46.7982	−	4.91868i	−1.54373	−	0.162252i	−0.705950	−	0.708262i	$-0.749480\pi$
$919$	−46.7982	−	4.91868i	−1.54373	−	0.162252i	−0.837779	+	0.546009i	$0.816146\pi$
$920$	−4.42604	+	13.6638i	−0.145922	+	0.450482i
$921$	−0.187320	−	1.78223i	−0.00617241	−	0.0587265i
$922$	3.55513	+	9.26142i	0.117082	+	0.305009i
$923$	5.12605	+	2.61185i	0.168726	+	0.0859701i
$924$	−0.384478	−	0.448431i	−0.0126484	−	0.0147523i
$925$	52.0695	+	2.63482i	1.71203	+	0.0866323i
$926$	8.40142	+	14.5517i	0.276088	+	0.478198i
$927$	−16.0817	−	24.7636i	−0.528191	−	0.813343i
$928$	0.699820	−	0.864206i	0.0229727	−	0.0283689i
$929$	15.6038	+	6.94725i	0.511944	+	0.227932i	0.646416	−	0.762985i	$-0.276267\pi$
$929$	15.6038	+	6.94725i	0.511944	+	0.227932i	−0.134472	+	0.990917i	$0.542934\pi$
$930$	1.48369	+	1.33351i	0.0486522	+	0.0437274i
$931$	−1.83708	+	6.96219i	−0.0602077	+	0.228177i
$932$	−7.63199	+	7.63199i	−0.249994	+	0.249994i
$933$	2.48016	−	2.00839i	0.0811967	−	0.0657518i
$934$	38.6844	+	42.9633i	1.26579	+	1.40580i
$935$	23.9706	+	46.9405i	0.783924	+	1.53512i
$936$	−4.70428	−	4.23575i	−0.153764	−	0.138450i
$937$	8.78861	−	4.47802i	0.287111	−	0.146290i	−0.304504	−	0.952511i	$-0.598491\pi$
$937$	8.78861	−	4.47802i	0.287111	−	0.146290i	0.591615	+	0.806221i	$0.298491\pi$
$938$	−42.0474	−	17.3227i	−1.37290	−	0.565607i
$939$	3.44986	−	1.12093i	0.112582	−	0.0365801i
$940$	−0.379144	+	7.36133i	−0.0123663	+	0.240100i
$941$	32.7443	−	29.4831i	1.06743	−	0.961120i	0.0681009	−	0.997678i	$-0.478306\pi$
$941$	32.7443	−	29.4831i	1.06743	−	0.961120i	0.999332	+	0.0365580i	$0.0116394\pi$
$942$	−0.694281	+	1.80866i	−0.0226209	+	0.0589294i
$943$	−2.41598	−	0.647359i	−0.0786750	−	0.0210809i
$944$	−21.9457	−	15.9445i	−0.714273	−	0.518949i
$945$	3.98835	−	2.18002i	0.129741	−	0.0709160i
$946$	−21.9137	+	15.9212i	−0.712476	+	0.517644i
$947$	−34.1449	+	13.1070i	−1.10956	+	0.425920i	−0.843008	−	0.537900i	$-0.819218\pi$
$947$	−34.1449	+	13.1070i	−1.10956	+	0.425920i	−0.266552	+	0.963821i	$0.585884\pi$
$948$	−0.699299	+	0.454130i	−0.0227122	+	0.0147495i
$949$	−8.83394	−	5.10028i	−0.286762	−	0.165562i
$950$	3.69463	+	7.21896i	0.119870	+	0.234214i
$951$		−	0.00159667i		−	5.17755e-5i
$952$	11.7438	−	39.9258i	0.380618	−	1.29400i
$953$	31.9821	+	5.06547i	1.03600	+	0.164087i	0.651195	−	0.758910i	$-0.274268\pi$
$953$	31.9821	+	5.06547i	1.03600	+	0.164087i	0.384807	+	0.922997i	$0.374268\pi$
$954$	15.7220	−	35.3122i	0.509018	−	1.14327i
$955$	16.3523	+	5.29691i	0.529148	+	0.171404i
$956$	12.9643	−	5.77206i	0.419294	−	0.186682i
$957$	0.0490814	−	0.183174i	0.00158658	−	0.00592118i
$958$	−30.1163	+	4.76996i	−0.973015	+	0.154110i
$959$	32.1939	+	4.17595i	1.03960	+	0.134848i
$960$	−0.945185	−	1.16506i	−0.0305057	−	0.0376021i
$961$	7.74966	−	8.60687i	0.249989	−	0.277641i
$962$	0.764828	−	14.5938i	0.0246590	−	0.470523i
$963$	1.78439	−	34.0481i	0.0575010	−	1.09719i
$964$	−0.611083	+	0.678677i	−0.0196817	+	0.0218587i
$965$	−31.0314	−	8.28489i	−0.998935	−	0.266700i
$966$	−0.875266	+	1.14518i	−0.0281612	+	0.0368457i
$967$	12.7238	−	2.01526i	0.409171	−	0.0648063i	0.0515438	−	0.998671i	$-0.483586\pi$
$967$	12.7238	−	2.01526i	0.409171	−	0.0648063i	0.357627	+	0.933864i	$0.383586\pi$
$968$	1.10873	−	4.13782i	0.0356358	−	0.132995i
$969$	0.795114	−	0.354008i	0.0255428	−	0.0113724i
$970$	31.3329	−	43.2078i	1.00604	−	1.38732i
$971$	−2.92128	+	6.56130i	−0.0937482	+	0.210562i	−0.954333	−	0.298746i	$-0.903432\pi$
$971$	−2.92128	+	6.56130i	−0.0937482	+	0.210562i	0.860585	+	0.509308i	$0.170098\pi$
$972$	−1.65231	−	0.261700i	−0.0529977	−	0.00839402i
$973$	3.01300	+	12.4454i	0.0965925	+	0.398982i
$974$		−	0.692506i		−	0.0221893i
$975$	0.542407	−	0.177319i	0.0173709	−	0.00567877i
$976$	22.0451	+	12.7278i	0.705647	+	0.407405i
$977$	4.52645	−	2.93951i	0.144814	−	0.0940432i	−0.470198	−	0.882561i	$-0.655818\pi$
$977$	4.52645	−	2.93951i	0.144814	−	0.0940432i	0.615012	+	0.788517i	$0.289151\pi$
$978$	−1.29830	+	0.498369i	−0.0415149	+	0.0159361i
$979$	−15.1226	+	10.9872i	−0.483321	+	0.351153i
$980$	6.40067	+	4.11386i	0.204462	+	0.131413i
$981$	−10.9174	−	7.93198i	−0.348567	−	0.253249i
$982$	−36.5721	−	9.79948i	−1.16706	−	0.312714i
$983$	1.06451	−	2.77315i	0.0339527	−	0.0884498i	−0.915556	−	0.402191i	$-0.868249\pi$
$983$	1.06451	−	2.77315i	0.0339527	−	0.0884498i	0.949509	+	0.313741i	$0.101582\pi$
$984$	0.211714	−	0.190628i	0.00674920	−	0.00607700i
$985$	−2.87918	+	3.56204i	−0.0917382	+	0.113496i
$986$	−4.08011	+	1.32571i	−0.129937	+	0.0422191i
$987$	0.877547	−	2.13007i	0.0279326	−	0.0678008i
$988$	0.396011	−	0.201778i	0.0125988	−	0.00641941i
$989$	9.60408	+	8.64755i	0.305392	+	0.274976i
$990$	−33.5402	−	17.0516i	−1.06598	−	0.541935i
$991$	19.6935	+	21.8718i	0.625583	+	0.694780i	0.969742	−	0.244131i	$-0.0785027\pi$
$991$	19.6935	+	21.8718i	0.625583	+	0.694780i	−0.344159	+	0.938911i	$0.611836\pi$
$992$	−9.22327	+	7.46886i	−0.292839	+	0.237136i
$993$	−1.97692	+	1.97692i	−0.0627355	+	0.0627355i
$994$	−15.3358	−	22.2228i	−0.486421	−	0.704863i
$995$	−11.3721	+	6.57934i	−0.360519	+	0.208579i
$996$	−0.611276	−	0.272158i	−0.0193690	−	0.00862364i
$997$	−18.8418	+	23.2676i	−0.596724	+	0.736893i	−0.982616	−	0.185651i	$-0.940561\pi$
$997$	−18.8418	+	23.2676i	−0.596724	+	0.736893i	0.385891	+	0.922544i	$0.373894\pi$
$998$	−4.54617	−	7.00049i	−0.143907	−	0.221597i
$999$	4.00556	+	6.93784i	0.126730	+	0.219503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.5	yes	288
5.2	odd	4		875.2.bb.b.857.14		288
5.3	odd	4		875.2.bb.a.857.5		288
5.4	even	2		875.2.bb.c.143.14		288
7.5	odd	6	inner	175.2.x.a.33.5	✓	288
25.3	odd	20		875.2.bb.c.507.14		288
25.4	even	10		875.2.bb.a.493.14		288
25.21	even	5		875.2.bb.b.493.5		288
25.22	odd	20	inner	175.2.x.a.122.5	yes	288
35.12	even	12		875.2.bb.b.607.5		288
35.19	odd	6		875.2.bb.c.768.14		288
35.33	even	12		875.2.bb.a.607.14		288
175.47	even	60	inner	175.2.x.a.47.5	yes	288
175.54	odd	30		875.2.bb.a.243.5		288
175.96	odd	30		875.2.bb.b.243.14		288
175.103	even	60		875.2.bb.c.257.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.5	✓	288	7.5	odd	6	inner
175.2.x.a.47.5	yes	288	175.47	even	60	inner
175.2.x.a.108.5	yes	288	1.1	even	1	trivial
175.2.x.a.122.5	yes	288	25.22	odd	20	inner
875.2.bb.a.243.5		288	175.54	odd	30
875.2.bb.a.493.14		288	25.4	even	10
875.2.bb.a.607.14		288	35.33	even	12
875.2.bb.a.857.5		288	5.3	odd	4
875.2.bb.b.243.14		288	175.96	odd	30
875.2.bb.b.493.5		288	25.21	even	5
875.2.bb.b.607.5		288	35.12	even	12
875.2.bb.b.857.14		288	5.2	odd	4
875.2.bb.c.143.14		288	5.4	even	2
875.2.bb.c.257.14		288	175.103	even	60
875.2.bb.c.507.14		288	25.3	odd	20
875.2.bb.c.768.14		288	35.19	odd	6

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0825201 - 1.57458i) q^{2} +(-0.0997864 - 0.0808054i) q^{3} +(-0.483440 + 0.0508115i) q^{4} +(-1.93750 - 1.11629i) q^{5} +(-0.119000 + 0.163789i) q^{6} +(2.63799 + 0.202552i) q^{7} +(-0.373412 - 2.35763i) q^{8} +(-0.620307 - 2.91832i) q^{9} +O(q^{10})\)	\(q+(-0.0825201 - 1.57458i) q^{2} +(-0.0997864 - 0.0808054i) q^{3} +(-0.483440 + 0.0508115i) q^{4} +(-1.93750 - 1.11629i) q^{5} +(-0.119000 + 0.163789i) q^{6} +(2.63799 + 0.202552i) q^{7} +(-0.373412 - 2.35763i) q^{8} +(-0.620307 - 2.91832i) q^{9} +(-1.59780 + 3.14286i) q^{10} +(-3.49879 - 0.743691i) q^{11} +(0.0523465 + 0.0339942i) q^{12} +(0.403536 + 0.791984i) q^{13} +(0.101247 - 4.17043i) q^{14} +(0.103134 + 0.267951i) q^{15} +(-4.63242 + 0.984651i) q^{16} +(6.15204 + 2.36155i) q^{17} +(-4.54393 + 1.21754i) q^{18} +(-0.107522 + 1.02301i) q^{19} +(0.993383 + 0.441211i) q^{20} +(-0.246868 - 0.233375i) q^{21} +(-0.882278 + 5.57049i) q^{22} +(2.68721 - 0.140831i) q^{23} +(-0.153248 + 0.265433i) q^{24} +(2.50779 + 4.32562i) q^{25} +(1.21374 - 0.700753i) q^{26} +(-0.348796 + 0.684551i) q^{27} +(-1.28560 + 0.0361186i) q^{28} +(-0.242693 - 0.334038i) q^{29} +(0.413399 - 0.184503i) q^{30} +(1.79233 + 4.02565i) q^{31} +(0.697064 + 2.60148i) q^{32} +(0.289037 + 0.356931i) q^{33} +(3.21077 - 9.88174i) q^{34} +(-4.88499 - 3.33720i) q^{35} +(0.448165 + 1.37931i) q^{36} +(5.67907 - 8.74501i) q^{37} +(1.61967 + 0.0848835i) q^{38} +(0.0237292 - 0.111637i) q^{39} +(-1.90831 + 4.98474i) q^{40} +(-0.884011 - 0.287233i) q^{41} +(-0.347096 + 0.407971i) q^{42} +(3.39602 + 3.39602i) q^{43} +(1.72924 + 0.181751i) q^{44} +(-2.05584 + 6.34667i) q^{45} +(-0.443498 - 4.21960i) q^{46} +(2.43023 + 6.33097i) q^{47} +(0.541817 + 0.276070i) q^{48} +(6.91795 + 1.06866i) q^{49} +(6.60407 - 4.30567i) q^{50} +(-0.423064 - 0.732768i) q^{51} +(-0.235327 - 0.362372i) q^{52} +(-5.17105 + 6.38571i) q^{53} +(1.10666 + 0.492717i) q^{54} +(5.94873 + 5.34656i) q^{55} +(-0.507514 - 6.29504i) q^{56} +(0.0933936 - 0.0933936i) q^{57} +(-0.505941 + 0.409703i) q^{58} +(3.83266 + 4.25660i) q^{59} +(-0.0634739 - 0.124298i) q^{60} +(-3.99440 - 3.59658i) q^{61} +(6.19079 - 3.15437i) q^{62} +(-1.04525 - 7.82412i) q^{63} +(-4.96953 + 1.61470i) q^{64} +(0.102233 - 1.98493i) q^{65} +(0.538165 - 0.484566i) q^{66} +(3.90663 - 10.1771i) q^{67} +(-3.09413 - 0.829071i) q^{68} +(-0.279527 - 0.203088i) q^{69} +(-4.85157 + 7.96717i) q^{70} +(5.23629 - 3.80439i) q^{71} +(-6.64868 + 2.55219i) q^{72} +(-9.62453 + 6.25024i) q^{73} +(-14.2383 - 8.22050i) q^{74} +(0.0992895 - 0.634281i) q^{75} -0.500025i q^{76} +(-9.07913 - 2.67053i) q^{77} +(-0.177739 - 0.0281511i) q^{78} +(-5.43361 + 12.2041i) q^{79} +(10.0745 + 3.26336i) q^{80} +(-8.08660 + 3.60039i) q^{81} +(-0.379321 + 1.41565i) q^{82} +(-10.5884 + 1.67704i) q^{83} +(0.131204 + 0.100279i) q^{84} +(-9.28339 - 11.4430i) q^{85} +(5.06705 - 5.62753i) q^{86} +(-0.00277464 + 0.0529433i) q^{87} +(-0.446858 + 8.52656i) q^{88} +(3.49677 - 3.88355i) q^{89} +(10.1630 + 2.71335i) q^{90} +(0.904105 + 2.17098i) q^{91} +(-1.29195 + 0.204625i) q^{92} +(0.146444 - 0.546535i) q^{93} +(9.76806 - 4.34902i) q^{94} +(1.35029 - 1.86204i) q^{95} +(0.140656 - 0.315919i) q^{96} +(-14.9519 - 2.36815i) q^{97} +(1.11181 - 10.9810i) q^{98} +10.6719i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

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