LMFDB - Embedded newform 370.2.ba.a.87.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(17,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("370.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.ba (of order $36$, degree $12$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			87.7
Character	$\chi$	$=$	370.87
Dual form			370.2.ba.a.353.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(0.131617 - 0.187969i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.561282 + 2.16448i) q^{5} +(-0.162258 - 0.162258i) q^{6} +(2.06533 + 0.180693i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.00805 + 2.76960i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(0.131617 - 0.187969i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.561282 + 2.16448i) q^{5} +(-0.162258 - 0.162258i) q^{6} +(2.06533 + 0.180693i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.00805 + 2.76960i) q^{9} +(2.22906 - 0.176897i) q^{10} +(-3.73102 - 2.15411i) q^{11} +(-0.187969 + 0.131617i) q^{12} +(5.88568 + 2.14221i) q^{13} +(0.536588 - 2.00257i) q^{14} +(0.480729 + 0.179379i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.489390 + 1.34459i) q^{17} +(2.90257 - 0.511801i) q^{18} +(2.98063 + 2.08706i) q^{19} +(0.212862 - 2.22591i) q^{20} +(0.305797 - 0.364435i) q^{21} +(-2.76927 + 3.30028i) q^{22} +(-3.67488 - 6.36507i) q^{23} +(0.0969772 + 0.207968i) q^{24} +(-4.36992 + 2.42976i) q^{25} +(3.13170 - 5.42427i) q^{26} +(1.31822 + 0.353216i) q^{27} +(-1.87897 - 0.876179i) q^{28} +(6.26247 - 1.67802i) q^{29} +(0.260131 - 0.442277i) q^{30} +(2.78372 - 2.78372i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.895972 + 0.417799i) q^{33} +(1.40914 - 0.248470i) q^{34} +(0.768126 + 4.57177i) q^{35} -2.94734i q^{36} +(-5.76298 - 1.94628i) q^{37} +(2.57294 - 2.57294i) q^{38} +(1.17733 - 0.824372i) q^{39} +(-2.15513 - 0.596154i) q^{40} +(2.57552 - 7.07618i) q^{41} +(-0.305797 - 0.364435i) q^{42} -4.33577 q^{43} +(2.76927 + 3.30028i) q^{44} +(-5.42893 + 3.73643i) q^{45} +(-6.90651 + 2.51376i) q^{46} +(-2.93566 + 10.9560i) q^{47} +(0.221649 - 0.0593906i) q^{48} +(-2.66073 - 0.469158i) q^{49} +(1.63402 + 4.72546i) q^{50} +(0.317153 + 0.0849808i) q^{51} +(-4.79805 - 4.02604i) q^{52} +(-4.91468 + 0.429979i) q^{53} +(0.576757 - 1.23686i) q^{54} +(2.56836 - 9.28477i) q^{55} +(-1.18915 + 1.69828i) q^{56} +(0.784605 - 0.285573i) q^{57} +(-0.565065 - 6.45872i) q^{58} +(-5.69444 + 0.498199i) q^{59} +(-0.390386 - 0.332980i) q^{60} +(6.74080 - 3.14328i) q^{61} +(-2.25804 - 3.22481i) q^{62} +(1.58151 + 5.90227i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.33324 + 13.9418i) q^{65} +(0.255867 + 0.954910i) q^{66} +(-0.254169 + 2.90517i) q^{67} -1.43088i q^{68} +(-1.68011 - 0.146991i) q^{69} +(4.63570 + 0.0374238i) q^{70} +(-1.06905 - 6.06286i) q^{71} +(-2.90257 - 0.511801i) q^{72} +(9.46672 + 9.46672i) q^{73} +(-2.91745 + 5.33746i) q^{74} +(-0.118437 + 1.14121i) q^{75} +(-2.08706 - 2.98063i) q^{76} +(-7.31655 - 5.12310i) q^{77} +(-0.607408 - 1.30259i) q^{78} +(-0.381511 + 4.36069i) q^{79} +(-0.961332 + 2.01887i) q^{80} +(-6.53350 + 5.48225i) q^{81} +(-6.52145 - 3.76516i) q^{82} +(4.02147 - 8.62408i) q^{83} +(-0.412000 + 0.237868i) q^{84} +(-2.63564 + 1.81397i) q^{85} +(-0.752899 + 4.26990i) q^{86} +(0.508833 - 1.39801i) q^{87} +(3.73102 - 2.15411i) q^{88} +(-0.438640 - 5.01367i) q^{89} +(2.73694 + 5.99528i) q^{90} +(11.7688 + 5.48786i) q^{91} +(1.27627 + 7.23809i) q^{92} +(-0.156867 - 0.889637i) q^{93} +(10.2798 + 4.79356i) q^{94} +(-2.84442 + 7.62294i) q^{95} +(-0.0199994 - 0.228594i) q^{96} +(-16.2633 + 9.38962i) q^{97} +(-0.924061 + 2.53884i) q^{98} +(2.20495 - 12.5049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	0.131617	−	0.187969i	0.0759893	−	0.108524i	−0.779358	−	0.626579i	$-0.784455\pi$
$3$	0.131617	−	0.187969i	0.0759893	−	0.108524i	0.855347	+	0.518055i	$0.173344\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.561282	+	2.16448i	0.251013	+	0.967984i
$5$	0.561282	+	2.16448i	0.251013	+	0.967984i
$6$	−0.162258	−	0.162258i	−0.0662416	−	0.0662416i
$7$	2.06533	+	0.180693i	0.780620	+	0.0682954i	0.470498	−	0.882401i	$-0.344074\pi$
$7$	2.06533	+	0.180693i	0.780620	+	0.0682954i	0.310122	+	0.950697i	$0.399630\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.00805	+	2.76960i	0.336017	+	0.923199i
$10$	2.22906	−	0.176897i	0.704891	−	0.0559399i
$11$	−3.73102	−	2.15411i	−1.12495	−	0.649488i	−0.182287	−	0.983245i	$-0.558350\pi$
$11$	−3.73102	−	2.15411i	−1.12495	−	0.649488i	−0.942659	+	0.333758i	$0.891683\pi$
$12$	−0.187969	+	0.131617i	−0.0542620	+	0.0379946i
$13$	5.88568	+	2.14221i	1.63239	+	0.594142i	0.985685	−	0.168596i	$-0.0539233\pi$
$13$	5.88568	+	2.14221i	1.63239	+	0.594142i	0.646707	+	0.762738i	$0.276145\pi$
$14$	0.536588	−	2.00257i	0.143409	−	0.535210i
$15$	0.480729	+	0.179379i	0.124124	+	0.0463155i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.489390	+	1.34459i	0.118694	+	0.326110i	0.984785	−	0.173777i	$-0.0555971\pi$
$17$	0.489390	+	1.34459i	0.118694	+	0.326110i	−0.866091	+	0.499887i	$0.833375\pi$
$18$	2.90257	−	0.511801i	0.684142	−	0.120633i
$19$	2.98063	+	2.08706i	0.683804	+	0.478805i	0.863128	−	0.504985i	$-0.168502\pi$
$19$	2.98063	+	2.08706i	0.683804	+	0.478805i	−0.179324	+	0.983790i	$0.557391\pi$
$20$	0.212862	−	2.22591i	0.0475974	−	0.497729i
$21$	0.305797	−	0.364435i	0.0667304	−	0.0795262i
$22$	−2.76927	+	3.30028i	−0.590409	+	0.703623i
$23$	−3.67488	−	6.36507i	−0.766265	−	1.32721i	−0.939575	−	0.342342i	$-0.888780\pi$
$23$	−3.67488	−	6.36507i	−0.766265	−	1.32721i	0.173310	−	0.984867i	$-0.444554\pi$
$24$	0.0969772	+	0.207968i	0.0197954	+	0.0424514i
$25$	−4.36992	+	2.42976i	−0.873985	+	0.485953i
$26$	3.13170	−	5.42427i	0.614177	−	1.06379i
$27$	1.31822	+	0.353216i	0.253692	+	0.0679765i
$28$	−1.87897	−	0.876179i	−0.355092	−	0.165582i
$29$	6.26247	−	1.67802i	1.16291	−	0.311601i	0.374784	−	0.927112i	$-0.377717\pi$
$29$	6.26247	−	1.67802i	1.16291	−	0.311601i	0.788128	+	0.615511i	$0.211050\pi$
$30$	0.260131	−	0.442277i	0.0474933	−	0.0807483i
$31$	2.78372	−	2.78372i	0.499970	−	0.499970i	−0.411458	−	0.911429i	$-0.634980\pi$
$31$	2.78372	−	2.78372i	0.499970	−	0.499970i	0.911429	+	0.411458i	$0.134980\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−0.895972	+	0.417799i	−0.155969	+	0.0727294i
$34$	1.40914	−	0.248470i	0.241666	−	0.0426122i
$35$	0.768126	+	4.57177i	0.129837	+	0.772771i
$36$		−	2.94734i		−	0.491224i
$37$	−5.76298	−	1.94628i	−0.947429	−	0.319967i
$37$	−5.76298	−	1.94628i	−0.947429	−	0.319967i
$38$	2.57294	−	2.57294i	0.417385	−	0.417385i
$39$	1.17733	−	0.824372i	0.188523	−	0.132005i
$40$	−2.15513	−	0.596154i	−0.340757	−	0.0942602i
$41$	2.57552	−	7.07618i	0.402229	−	1.10511i	−0.558953	−	0.829199i	$-0.688797\pi$
$41$	2.57552	−	7.07618i	0.402229	−	1.10511i	0.961182	−	0.275915i	$-0.0889808\pi$
$42$	−0.305797	−	0.364435i	−0.0471855	−	0.0562335i
$43$	−4.33577			−0.661199			−0.330599	−	0.943771i	$-0.607251\pi$
$43$	−4.33577			−0.661199			−0.330599	+	0.943771i	$0.607251\pi$
$44$	2.76927	+	3.30028i	0.417483	+	0.497536i
$45$	−5.42893	+	3.73643i	−0.809297	+	0.556994i
$46$	−6.90651	+	2.51376i	−1.01831	+	0.370634i
$47$	−2.93566	+	10.9560i	−0.428210	+	1.59810i	0.328602	+	0.944469i	$0.393423\pi$
$47$	−2.93566	+	10.9560i	−0.428210	+	1.59810i	−0.756812	+	0.653633i	$0.773244\pi$
$48$	0.221649	−	0.0593906i	0.0319922	−	0.00857230i
$49$	−2.66073	−	0.469158i	−0.380104	−	0.0670226i
$50$	1.63402	+	4.72546i	0.231086	+	0.668281i
$51$	0.317153	+	0.0849808i	0.0444103	+	0.0118997i
$52$	−4.79805	−	4.02604i	−0.665369	−	0.558311i
$53$	−4.91468	+	0.429979i	−0.675083	+	0.0590621i	−0.419542	−	0.907736i	$-0.637809\pi$
$53$	−4.91468	+	0.429979i	−0.675083	+	0.0590621i	−0.255541	+	0.966798i	$0.582254\pi$
$54$	0.576757	−	1.23686i	0.0784867	−	0.168315i
$55$	2.56836	−	9.28477i	0.346317	−	1.25196i
$56$	−1.18915	+	1.69828i	−0.158907	+	0.226942i
$57$	0.784605	−	0.285573i	0.103924	−	0.0378251i
$58$	−0.565065	−	6.45872i	−0.0741966	−	0.848071i
$59$	−5.69444	+	0.498199i	−0.741353	+	0.0648600i	−0.451574	−	0.892234i	$-0.649137\pi$
$59$	−5.69444	+	0.498199i	−0.741353	+	0.0648600i	−0.289779	+	0.957094i	$0.593582\pi$
$60$	−0.390386	−	0.332980i	−0.0503986	−	0.0429875i
$61$	6.74080	−	3.14328i	0.863071	−	0.402456i	0.0598991	−	0.998204i	$-0.480922\pi$
$61$	6.74080	−	3.14328i	0.863071	−	0.402456i	0.803171	+	0.595748i	$0.203144\pi$
$62$	−2.25804	−	3.22481i	−0.286771	−	0.409552i
$63$	1.58151	+	5.90227i	0.199251	+	0.743616i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.33324	+	13.9418i	−0.165368	+	1.72927i
$66$	0.255867	+	0.954910i	0.0314951	+	0.117541i
$67$	−0.254169	+	2.90517i	−0.0310517	+	0.354923i	0.964735	+	0.263223i	$0.0847856\pi$
$67$	−0.254169	+	2.90517i	−0.0310517	+	0.354923i	−0.995787	+	0.0916998i	$0.970770\pi$
$68$		−	1.43088i		−	0.173520i
$69$	−1.68011	−	0.146991i	−0.202262	−	0.0176956i
$70$	4.63570	+	0.0374238i	0.554072	+	0.00447300i
$71$	−1.06905	−	6.06286i	−0.126872	−	0.719529i	−0.980178	−	0.198118i	$-0.936517\pi$
$71$	−1.06905	−	6.06286i	−0.126872	−	0.719529i	0.853306	−	0.521411i	$-0.174594\pi$
$72$	−2.90257	−	0.511801i	−0.342071	−	0.0603163i
$73$	9.46672	+	9.46672i	1.10800	+	1.10800i	0.993414	+	0.114582i	$0.0365530\pi$
$73$	9.46672	+	9.46672i	1.10800	+	1.10800i	0.114582	+	0.993414i	$0.463447\pi$
$74$	−2.91745	+	5.33746i	−0.339146	+	0.620467i
$75$	−0.118437	+	1.14121i	−0.0136760	+	0.131775i
$76$	−2.08706	−	2.98063i	−0.239402	−	0.341902i
$77$	−7.31655	−	5.12310i	−0.833798	−	0.583832i
$78$	−0.607408	−	1.30259i	−0.0687754	−	0.147489i
$79$	−0.381511	+	4.36069i	−0.0429233	+	0.490616i	0.944058	+	0.329780i	$0.106975\pi$
$79$	−0.381511	+	4.36069i	−0.0429233	+	0.490616i	−0.986981	+	0.160836i	$0.948581\pi$
$80$	−0.961332	+	2.01887i	−0.107480	+	0.225717i
$81$	−6.53350	+	5.48225i	−0.725944	+	0.609139i
$82$	−6.52145	−	3.76516i	−0.720173	−	0.415792i
$83$	4.02147	−	8.62408i	0.441414	−	0.946615i	−0.552193	−	0.833717i	$-0.686209\pi$
$83$	4.02147	−	8.62408i	0.441414	−	0.946615i	0.993607	−	0.112899i	$-0.0360136\pi$
$84$	−0.412000	+	0.237868i	−0.0449528	+	0.0259535i
$85$	−2.63564	+	1.81397i	−0.285876	+	0.196752i
$86$	−0.752899	+	4.26990i	−0.0811871	+	0.460435i
$87$	0.508833	−	1.39801i	0.0545526	−	0.149882i
$88$	3.73102	−	2.15411i	0.397728	−	0.229629i
$89$	−0.438640	−	5.01367i	−0.0464957	−	0.531448i	−0.983349	−	0.181726i	$-0.941832\pi$
$89$	−0.438640	−	5.01367i	−0.0464957	−	0.531448i	0.936853	−	0.349722i	$-0.113724\pi$
$90$	2.73694	+	5.99528i	0.288499	+	0.631958i
$91$	11.7688	+	5.48786i	1.23370	+	0.575284i
$92$	1.27627	+	7.23809i	0.133060	+	0.754624i
$93$	−0.156867	−	0.889637i	−0.0162664	−	0.0922511i
$94$	10.2798	+	4.79356i	1.06028	+	0.494417i
$95$	−2.84442	+	7.62294i	−0.291832	+	0.782097i
$96$	−0.0199994	−	0.228594i	−0.00204118	−	0.0233308i
$97$	−16.2633	+	9.38962i	−1.65129	+	0.953372i	−0.674745	+	0.738051i	$0.735746\pi$
$97$	−16.2633	+	9.38962i	−1.65129	+	0.953372i	−0.976543	+	0.215321i	$0.930920\pi$
$98$	−0.924061	+	2.53884i	−0.0933443	+	0.256461i
$99$	2.20495	−	12.5049i	0.221606	−	1.25679i
$100$	4.93741	−	0.788630i	0.493741	−	0.0788630i
$101$	6.05046	−	3.49323i	0.602043	−	0.347590i	−0.167802	−	0.985821i	$-0.553667\pi$
$101$	6.05046	−	3.49323i	0.602043	−	0.347590i	0.769845	+	0.638231i	$0.220334\pi$
$102$	0.138763	−	0.297578i	0.0137396	−	0.0294646i
$103$	−7.26711	−	4.19567i	−0.716049	−	0.413411i	0.0972476	−	0.995260i	$-0.468996\pi$
$103$	−7.26711	−	4.19567i	−0.716049	−	0.413411i	−0.813297	+	0.581849i	$0.802329\pi$
$104$	−4.79805	+	4.02604i	−0.470487	+	0.394786i
$105$	0.960450	+	0.457340i	0.0937303	+	0.0446319i
$106$	−0.429979	+	4.91468i	−0.0417632	+	0.477356i
$107$	−2.62274	−	5.62447i	−0.253549	−	0.543739i	0.737795	−	0.675025i	$-0.235867\pi$
$107$	−2.62274	−	5.62447i	−0.253549	−	0.543739i	−0.991345	+	0.131286i	$0.958089\pi$
$108$	−1.11792	−	0.782773i	−0.107572	−	0.0753224i
$109$	−8.13337	−	11.6157i	−0.779036	−	1.11258i	−0.990810	−	0.135260i	$-0.956813\pi$
$109$	−8.13337	−	11.6157i	−0.779036	−	1.11258i	0.211774	−	0.977319i	$-0.432076\pi$
$110$	−8.69773	−	4.14162i	−0.829296	−	0.394888i
$111$	−1.12435	+	0.827097i	−0.106718	+	0.0785046i
$112$	1.46599	+	1.46599i	0.138523	+	0.138523i
$113$	−7.90103	−	1.39316i	−0.743266	−	0.131058i	−0.210824	−	0.977524i	$-0.567615\pi$
$113$	−7.90103	−	1.39316i	−0.743266	−	0.131058i	−0.532443	+	0.846466i	$0.678726\pi$
$114$	−0.144989	−	0.822275i	−0.0135795	−	0.0770131i
$115$	11.7144	−	11.5268i	1.09237	−	1.07488i
$116$	−6.45872	−	0.565065i	−0.599677	−	0.0524649i
$117$			18.4604i			1.70667i
$118$	−0.498199	+	5.69444i	−0.0458630	+	0.524216i
$119$	0.767793	+	2.86544i	0.0703834	+	0.262675i
$120$	−0.395711	+	0.326634i	−0.0361233	+	0.0298175i
$121$	3.78035	+	6.54776i	0.343668	+	0.595251i
$122$	−1.92500	−	7.18421i	−0.174282	−	0.650428i
$123$	−0.991119	−	1.41547i	−0.0893662	−	0.127628i
$124$	−3.56793	+	1.66375i	−0.320409	+	0.149409i
$125$	−7.71193	−	8.09482i	−0.689776	−	0.724023i
$126$	6.08723	−	0.532564i	0.542294	−	0.0474445i
$127$	−1.08910	−	12.4484i	−0.0966417	−	1.10462i	−0.877391	−	0.479776i	$-0.840718\pi$
$127$	−1.08910	−	12.4484i	−0.0966417	−	1.10462i	0.780749	−	0.624844i	$-0.214838\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−0.570662	+	0.814990i	−0.0502440	+	0.0717559i
$130$	13.4985	+	3.73395i	1.18389	+	0.327490i
$131$	1.77154	−	3.79908i	0.154780	−	0.331927i	−0.813592	−	0.581436i	$-0.802491\pi$
$131$	1.77154	−	3.79908i	0.154780	−	0.331927i	0.968373	+	0.249508i	$0.0802690\pi$
$132$	0.984834	−	0.0861618i	0.0857188	−	0.00749942i
$133$	5.77887	+	4.84904i	0.501091	+	0.420465i
$134$	2.81690	+	0.754785i	0.243343	+	0.0652035i
$135$	−0.0246347	+	3.05151i	−0.00212022	+	0.262633i
$136$	−1.40914	−	0.248470i	−0.120833	−	0.0213061i
$137$	−0.128868	+	0.0345302i	−0.0110100	+	0.00295011i	−0.264320	−	0.964435i	$-0.585147\pi$
$137$	−0.128868	+	0.0345302i	−0.0110100	+	0.00295011i	0.253310	+	0.967385i	$0.418481\pi$
$138$	−0.436506	+	1.62906i	−0.0371579	+	0.138675i
$139$	20.2786	−	7.38082i	1.72001	−	0.626033i	0.722171	−	0.691714i	$-0.243144\pi$
$139$	20.2786	−	7.38082i	1.72001	−	0.626033i	0.997841	+	0.0656814i	$0.0209221\pi$
$140$	0.841836	−	4.55878i	0.0711482	−	0.385287i
$141$	1.67301	+	1.99382i	0.140893	+	0.167910i
$142$	−6.15639			−0.516633
$143$	−17.3450	−	20.6710i	−1.45046	−	1.72860i
$144$	−1.00805	+	2.76960i	−0.0840043	+	0.230800i
$145$	7.14706	+	12.6131i	0.593531	+	1.04746i
$146$	10.9668	−	7.67902i	0.907617	−	0.635520i
$147$	−0.438385	+	0.438385i	−0.0361574	+	0.0361574i
$148$	4.74976	+	3.79997i	0.390428	+	0.312355i
$149$		−	4.66525i		−	0.382192i	−0.981571	−	0.191096i	$-0.938796\pi$
$149$		−	4.66525i		−	0.382192i	0.981571	−	0.191096i	$-0.0612042\pi$
$150$	1.10331	+	0.314807i	0.0900845	+	0.0257039i
$151$	−8.02154	+	1.41441i	−0.652783	+	0.115103i	−0.490225	−	0.871596i	$-0.663086\pi$
$151$	−8.02154	+	1.41441i	−0.652783	+	0.115103i	−0.162558	+	0.986699i	$0.551974\pi$
$152$	−3.29776	+	1.53777i	−0.267484	+	0.124730i
$153$	−3.23064	+	2.71082i	−0.261181	+	0.219157i
$154$	−6.31578	+	6.31578i	−0.508940	+	0.508940i
$155$	7.58774	+	4.46284i	0.609462	+	0.358464i
$156$	−1.38828	+	0.371987i	−0.111151	+	0.0297828i
$157$	4.99362	+	2.32856i	0.398534	+	0.185839i	0.611544	−	0.791211i	$-0.290549\pi$
$157$	4.99362	+	2.32856i	0.398534	+	0.185839i	−0.213010	+	0.977050i	$0.568327\pi$
$158$	4.22819	+	1.13294i	0.336377	+	0.0901319i
$159$	−0.566034	+	0.980399i	−0.0448894	+	0.0777507i
$160$	1.82127	+	1.29730i	0.143984	+	0.102561i
$161$	−6.43970	−	13.8100i	−0.507519	−	1.08838i
$162$	4.26444	+	7.38622i	0.335046	+	0.580316i
$163$	4.13971	−	4.93351i	0.324247	−	0.386422i	−0.579155	−	0.815217i	$-0.696617\pi$
$163$	4.13971	−	4.93351i	0.324247	−	0.386422i	0.903402	+	0.428795i	$0.141062\pi$
$164$	−4.84039	+	5.76856i	−0.377971	+	0.450449i
$165$	−1.40721	−	1.70481i	−0.109551	−	0.132719i
$166$	−7.79474	−	5.45793i	−0.604989	−	0.423618i
$167$	9.35575	−	1.64967i	0.723970	−	0.127655i	0.200493	−	0.979695i	$-0.435746\pi$
$167$	9.35575	−	1.64967i	0.723970	−	0.127655i	0.523477	+	0.852040i	$0.324635\pi$
$168$	0.162711	+	0.447046i	0.0125535	+	0.0344903i
$169$	20.0935	+	16.8605i	1.54566	+	1.29696i
$170$	1.32873	+	2.91059i	0.101909	+	0.223232i
$171$	−2.77569	+	10.3590i	−0.212262	+	0.792174i
$172$	4.07429	+	1.48292i	0.310662	+	0.113072i
$173$	−13.5841	+	9.51169i	−1.03278	+	0.723160i	−0.961642	−	0.274306i	$-0.911552\pi$
$173$	−13.5841	+	9.51169i	−1.03278	+	0.723160i	−0.0711374	+	0.997467i	$0.522663\pi$
$174$	−1.28841	−	0.743864i	−0.0976741	−	0.0563922i
$175$	−9.46436	+	4.22865i	−0.715439	+	0.319656i
$176$	−1.47350	−	4.04840i	−0.111069	−	0.305159i
$177$	−0.655841	+	1.13595i	−0.0492960	+	0.0853832i
$178$	−5.01367	−	0.438640i	−0.375791	−	0.0328774i
$179$	−9.83882	−	9.83882i	−0.735388	−	0.735388i	0.236294	−	0.971682i	$-0.424067\pi$
$179$	−9.83882	−	9.83882i	−0.735388	−	0.735388i	−0.971682	+	0.236294i	$0.924067\pi$
$180$	6.37946	−	1.65429i	0.475497	−	0.123304i
$181$	0.249156	+	0.0906854i	0.0185196	+	0.00674059i	0.351263	−	0.936277i	$-0.385752\pi$
$181$	0.249156	+	0.0906854i	0.0185196	+	0.00674059i	−0.332744	+	0.943017i	$0.607974\pi$
$182$	7.44812	−	10.6370i	0.552091	−	0.788468i
$183$	0.296365	−	1.68077i	0.0219079	−	0.124246i
$184$	7.34975			0.541831
$185$	0.978029	−	13.5663i	0.0719061	−	0.997411i
$186$	−0.903362			−0.0662377
$187$	1.07046	−	6.07088i	0.0782798	−	0.443947i
$188$	6.50580	−	9.29125i	0.474484	−	0.677634i
$189$	2.65873	+	0.967700i	0.193395	+	0.0703898i
$190$	7.01320	+	4.12492i	0.508791	+	0.299253i
$191$	6.01636	+	6.01636i	0.435328	+	0.435328i	0.890436	−	0.455108i	$-0.150399\pi$
$191$	6.01636	+	6.01636i	0.435328	+	0.435328i	−0.455108	+	0.890436i	$0.650399\pi$
$192$	−0.228594	−	0.0199994i	−0.0164974	−	0.00144333i
$193$	12.2740	−	21.2592i	0.883502	−	1.53027i	0.0360818	−	0.999349i	$-0.488512\pi$
$193$	12.2740	−	21.2592i	0.883502	−	1.53027i	0.847421	−	0.530922i	$-0.178154\pi$
$194$	6.42288	+	17.6467i	0.461136	+	1.26696i
$195$	2.44515	+	2.08559i	0.175101	+	0.149352i
$196$	2.33981	+	1.35089i	0.167129	+	0.0964919i
$197$	9.88772	−	6.92346i	0.704471	−	0.493276i	−0.165606	−	0.986192i	$-0.552958\pi$
$197$	9.88772	−	6.92346i	0.704471	−	0.493276i	0.870077	+	0.492916i	$0.164069\pi$
$198$	−11.9320	−	4.34290i	−0.847972	−	0.308636i
$199$	−3.20188	+	11.9496i	−0.226975	+	0.847083i	0.754628	+	0.656152i	$0.227817\pi$
$199$	−3.20188	+	11.9496i	−0.226975	+	0.847083i	−0.981604	+	0.190931i	$0.938849\pi$
$200$	0.0807243	−	4.99935i	0.00570807	−	0.353507i
$201$	0.512628	+	0.430146i	0.0361580	+	0.0303402i
$202$	−2.38951	−	6.56513i	−0.168125	−	0.461921i
$203$	13.2373	−	2.33409i	0.929074	−	0.163821i
$204$	−0.268961	−	0.188328i	−0.0188310	−	0.0131856i
$205$	16.7618	+	1.60292i	1.17070	+	0.111953i
$206$	−5.39384	+	6.42813i	−0.375807	+	0.447869i
$207$	13.9242	−	16.5943i	0.967801	−	1.15338i
$208$	3.13170	+	5.42427i	0.217145	+	0.376105i
$209$	−6.62505	−	14.2075i	−0.458265	−	0.982752i
$210$	0.617173	−	0.866442i	0.0425890	−	0.0597902i
$211$	13.5756	−	23.5137i	0.934586	−	1.61875i	0.159215	−	0.987244i	$-0.449104\pi$
$211$	13.5756	−	23.5137i	0.934586	−	1.61875i	0.775371	−	0.631506i	$-0.217563\pi$
$212$	4.76535	+	1.27687i	0.327286	+	0.0876959i
$213$	−1.28033	−	0.597030i	−0.0877270	−	0.0409078i
$214$	−5.99446	+	1.60621i	−0.409773	+	0.109798i
$215$	−2.43359	−	9.38468i	−0.165969	−	0.640030i
$216$	−0.965005	+	0.965005i	−0.0656603	+	0.0656603i
$217$	6.25228	−	5.24629i	0.424433	−	0.356141i
$218$	−12.8515	+	5.99277i	−0.870416	+	0.405882i
$219$	3.02543	−	0.533466i	0.204440	−	0.0360483i
$220$	−5.58905	+	7.84640i	−0.376814	+	0.529004i
$221$			8.96218i			0.602861i
$222$	0.619291	+	1.25089i	0.0415641	+	0.0839543i
$223$	8.31963	−	8.31963i	0.557124	−	0.557124i	−0.371364	−	0.928487i	$-0.621110\pi$
$223$	8.31963	−	8.31963i	0.557124	−	0.557124i	0.928487	+	0.371364i	$0.121110\pi$
$224$	1.69828	−	1.18915i	0.113471	−	0.0794533i
$225$	−11.1346	−	9.65361i	−0.742305	−	0.643574i
$226$	−2.74400	+	7.53907i	−0.182528	+	0.501492i
$227$	4.54066	+	5.41134i	0.301374	+	0.359163i	0.895385	−	0.445294i	$-0.146901\pi$
$227$	4.54066	+	5.41134i	0.301374	+	0.359163i	−0.594011	+	0.804457i	$0.702456\pi$
$228$	−0.834960			−0.0552966
$229$	−10.3151	−	12.2930i	−0.681638	−	0.812345i	0.308679	−	0.951166i	$-0.400113\pi$
$229$	−10.3151	−	12.2930i	−0.681638	−	0.812345i	−0.990317	+	0.138821i	$0.955669\pi$
$230$	−9.31749	−	13.5381i	−0.614377	−	0.892673i
$231$	−1.92597	+	0.700995i	−0.126719	+	0.0461221i
$232$	−1.67802	+	6.26247i	−0.110168	+	0.411152i
$233$	−1.39133	+	0.372806i	−0.0911491	+	0.0244233i	−0.304105	−	0.952638i	$-0.598357\pi$
$233$	−1.39133	+	0.372806i	−0.0911491	+	0.0244233i	0.212956	+	0.977062i	$0.431691\pi$
$234$	18.1800	+	3.20562i	1.18846	+	0.209558i
$235$	−25.3618	−	0.204745i	−1.65442	−	0.0133561i
$236$	5.52142	+	1.47946i	0.359414	+	0.0963047i
$237$	0.769460	+	0.645654i	0.0499818	+	0.0419397i
$238$	2.95523	−	0.258549i	0.191559	−	0.0167593i
$239$	−12.9958	+	27.8695i	−0.840626	+	1.80273i	−0.325785	+	0.945444i	$0.605629\pi$
$239$	−12.9958	+	27.8695i	−0.840626	+	1.80273i	−0.514842	+	0.857285i	$0.672149\pi$
$240$	0.252957	+	0.446419i	0.0163283	+	0.0288162i
$241$	11.6337	−	16.6146i	0.749391	−	1.07024i	−0.245511	−	0.969394i	$-0.578956\pi$
$241$	11.6337	−	16.6146i	0.749391	−	1.07024i	0.994902	−	0.100848i	$-0.0321555\pi$
$242$	7.10473	−	2.58591i	0.456710	−	0.166229i
$243$	0.527403	+	6.02824i	0.0338329	+	0.386712i
$244$	−7.40934	+	0.648234i	−0.474335	+	0.0414989i
$245$	−0.477937	−	6.02242i	−0.0305343	−	0.384758i
$246$	−1.56607	+	0.730269i	−0.0998488	+	0.0465603i
$247$	13.0721	+	18.6689i	0.831759	+	1.18787i
$248$	1.01891	+	3.80263i	0.0647009	+	0.241467i
$249$	−1.09176	−	1.89099i	−0.0691877	−	0.119837i
$250$	−9.31100	+	6.18912i	−0.588880	+	0.391434i
$251$	1.81791	+	6.78452i	0.114745	+	0.428235i	0.999268	−	0.0382626i	$-0.0121823\pi$
$251$	1.81791	+	6.78452i	0.114745	+	0.428235i	−0.884523	+	0.466497i	$0.845516\pi$
$252$	0.532564	−	6.08723i	0.0335484	−	0.383459i
$253$			31.6643i			1.99072i
$254$	−12.4484	−	1.08910i	−0.781084	−	0.0683360i
$255$	−0.00592691	+	0.734168i	−0.000371157	+	0.0459754i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−14.7604	−	2.60266i	−0.920731	−	0.162350i	−0.306859	−	0.951755i	$-0.599278\pi$
$257$	−14.7604	−	2.60266i	−0.920731	−	0.162350i	−0.613872	+	0.789405i	$0.710389\pi$
$258$	0.703514	+	0.703514i	0.0437989	+	0.0437989i
$259$	−11.5508	−	5.06104i	−0.717730	−	0.314478i
$260$	6.02121	−	12.6450i	0.373420	−	0.784210i
$261$	10.9603	+	15.6530i	0.678428	+	0.968896i
$262$	−3.43374	−	2.40433i	−0.212137	−	0.148540i
$263$	8.03568	+	17.2326i	0.495501	+	1.06261i	0.981992	+	0.188921i	$0.0604989\pi$
$263$	8.03568	+	17.2326i	0.495501	+	1.06261i	−0.486491	+	0.873686i	$0.661723\pi$
$264$	0.0861618	−	0.984834i	0.00530289	−	0.0606123i
$265$	−3.68920	−	10.3964i	−0.226626	−	0.638644i
$266$	5.77887	−	4.84904i	0.354325	−	0.297314i
$267$	−1.00015	−	0.577435i	−0.0612080	−	0.0353385i
$268$	1.23247	−	2.64304i	0.0752849	−	0.161449i
$269$	−4.10593	+	2.37056i	−0.250343	+	0.144536i	−0.619921	−	0.784664i	$-0.712835\pi$
$269$	−4.10593	+	2.37056i	−0.250343	+	0.144536i	0.369578	+	0.929200i	$0.379502\pi$
$270$	3.00088	+	0.554150i	0.182628	+	0.0337245i
$271$	−3.88086	+	22.0095i	−0.235746	+	1.33698i	0.605292	+	0.796003i	$0.293056\pi$
$271$	−3.88086	+	22.0095i	−0.235746	+	1.33698i	−0.841038	+	0.540976i	$0.818055\pi$
$272$	−0.489390	+	1.34459i	−0.0296736	+	0.0815276i
$273$	2.58052	−	1.48986i	0.156180	−	0.0901707i
$274$	0.0116278	+	0.132907i	0.000702463	+	0.00802918i
$275$	21.5383	+	0.347777i	1.29881	+	0.0209718i
$276$	1.52852	+	0.712759i	0.0920059	+	0.0429030i
$277$	3.41968	+	19.3940i	0.205469	+	1.16527i	0.896700	+	0.442638i	$0.145957\pi$
$277$	3.41968	+	19.3940i	0.205469	+	1.16527i	−0.691232	+	0.722633i	$0.742932\pi$
$278$	−3.74734	−	21.2522i	−0.224751	−	1.27462i
$279$	10.5159	+	4.90365i	0.629571	+	0.293574i
$280$	−4.34333	−	1.62067i	−0.259564	−	0.0968536i
$281$	1.26999	+	14.5161i	0.0757613	+	0.865955i	0.935062	+	0.354484i	$0.115344\pi$
$281$	1.26999	+	14.5161i	0.0757613	+	0.865955i	−0.859301	+	0.511471i	$0.829101\pi$
$282$	2.25404	−	1.30137i	0.134226	−	0.0774955i
$283$	−10.6892	+	29.3683i	−0.635405	+	1.74576i	0.0302934	+	0.999541i	$0.490356\pi$
$283$	−10.6892	+	29.3683i	−0.635405	+	1.74576i	−0.665699	+	0.746221i	$0.731866\pi$
$284$	−1.06905	+	6.06286i	−0.0634362	+	0.359765i
$285$	1.05850	+	1.53797i	0.0627002	+	0.0911017i
$286$	−23.3689	+	13.4920i	−1.38183	+	0.797801i
$287$	6.59791	−	14.1493i	0.389462	−	0.835204i
$288$	2.55248	+	1.47367i	0.150406	+	0.0868370i
$289$	11.4543	−	9.61134i	0.673785	−	0.565373i
$290$	13.6626	−	4.84823i	0.802295	−	0.284698i
$291$	−0.375574	+	4.29283i	−0.0220165	+	0.251650i
$292$	−5.65800	−	12.1336i	−0.331109	−	0.710066i
$293$	4.27163	+	2.99103i	0.249552	+	0.174738i	0.691659	−	0.722224i	$-0.256880\pi$
$293$	4.27163	+	2.99103i	0.249552	+	0.174738i	−0.442107	+	0.896962i	$0.645769\pi$
$294$	0.355600	+	0.507850i	0.0207390	+	0.0296184i
$295$	−4.27453	−	12.0459i	−0.248873	−	0.701337i
$296$	4.56702	−	4.01775i	0.265453	−	0.233527i
$297$	−4.15745	−	4.15745i	−0.241240	−	0.241240i
$298$	−4.59437	−	0.810111i	−0.266145	−	0.0469285i
$299$	−7.99380	−	45.3351i	−0.462294	−	2.62180i
$300$	0.501611	−	1.03188i	0.0289605	−	0.0595755i
$301$	−8.95478	−	0.783442i	−0.516145	−	0.0451569i
$302$			8.14528i			0.468708i
$303$	0.139725	−	1.59707i	0.00802701	−	0.0917491i
$304$	0.941760	+	3.51470i	0.0540136	+	0.201582i
$305$	10.5871	+	12.8260i	0.606213	+	0.734416i
$306$	2.10865	+	3.65228i	0.120543	+	0.208787i
$307$	2.78496	+	10.3936i	0.158946	+	0.593195i	0.998735	+	0.0502820i	$0.0160120\pi$
$307$	2.78496	+	10.3936i	0.158946	+	0.593195i	−0.839789	+	0.542913i	$0.817321\pi$
$308$	5.12310	+	7.31655i	0.291916	+	0.416899i
$309$	−1.74513	+	0.813768i	−0.0992771	+	0.0462937i
$310$	5.71264	−	6.69750i	0.324456	−	0.380393i
$311$	−16.7107	+	1.46200i	−0.947578	+	0.0829023i	−0.550456	−	0.834864i	$-0.685546\pi$
$311$	−16.7107	+	1.46200i	−0.947578	+	0.0829023i	−0.397121	+	0.917766i	$0.629991\pi$
$312$	0.125265	+	1.43178i	0.00709171	+	0.0810586i
$313$	−10.8384	+	3.94484i	−0.612621	+	0.222976i	−0.629650	−	0.776879i	$-0.716802\pi$
$313$	−10.8384	+	3.94484i	−0.612621	+	0.222976i	0.0170288	+	0.999855i	$0.494579\pi$
$314$	3.16032	−	4.51340i	0.178347	−	0.254706i
$315$	−11.8877	+	6.73598i	−0.669794	+	0.379530i
$316$	1.84995	−	3.96722i	0.104068	−	0.223174i
$317$	1.39825	−	0.122331i	0.0785334	−	0.00687078i	−0.0478213	−	0.998856i	$-0.515228\pi$
$317$	1.39825	−	0.122331i	0.0785334	−	0.00687078i	0.126355	+	0.991985i	$0.459672\pi$
$318$	0.867214	+	0.727679i	0.0486310	+	0.0408062i
$319$	−26.9801	−	7.22929i	−1.51059	−	0.404762i
$320$	1.59385	−	1.56832i	0.0890990	−	0.0876719i
$321$	−1.40242	−	0.247285i	−0.0782757	−	0.0138021i
$322$	−14.7184	+	3.94379i	−0.820225	+	0.219779i
$323$	−1.34755	+	5.02911i	−0.0749794	+	0.279827i
$324$	8.01452	−	2.91705i	0.445251	−	0.162058i
$325$	−30.9250	+	4.93951i	−1.71541	+	0.273995i
$326$	−4.13971	−	4.93351i	−0.229277	−	0.273242i
$327$	−3.25388			−0.179940
$328$	4.84039	+	5.76856i	0.267266	+	0.318515i
$329$	−8.04277	+	22.0973i	−0.443412	+	1.21827i
$330$	−1.92327	+	1.08979i	−0.105872	+	0.0599911i
$331$	12.2332	−	8.56579i	0.672398	−	0.470818i	−0.186843	−	0.982390i	$-0.559825\pi$
$331$	12.2332	−	8.56579i	0.672398	−	0.470818i	0.859241	+	0.511572i	$0.170937\pi$
$332$	−6.72856	+	6.72856i	−0.369277	+	0.369277i
$333$	−0.418957	−	17.9231i	−0.0229587	−	0.982180i
$334$		−	9.50008i		−	0.519821i
$335$	−6.43083	+	1.08048i	−0.351354	+	0.0590327i
$336$	0.468509	−	0.0826107i	0.0255592	−	0.00450678i
$337$	−24.8435	+	11.5847i	−1.35331	+	0.631060i	−0.957809	−	0.287404i	$-0.907208\pi$
$337$	−24.8435	+	11.5847i	−1.35331	+	0.631060i	−0.395504	+	0.918464i	$0.629430\pi$
$338$	20.0935	−	16.8605i	1.09294	−	0.917089i
$339$	−1.30178	+	1.30178i	−0.0707032	+	0.0707032i
$340$	3.09711	−	0.803127i	0.167964	−	0.0435557i
$341$	−16.3825	+	4.38969i	−0.887164	+	0.237715i
$342$	9.71965	+	4.53235i	0.525578	+	0.245081i
$343$	−19.4285	−	5.20585i	−1.04904	−	0.281090i
$344$	2.16789	−	3.75489i	0.116885	−	0.202450i
$345$	−0.624859	−	3.71907i	−0.0336413	−	0.200228i
$346$	7.00833	+	15.0294i	0.376770	+	0.807986i
$347$	−6.55977	−	11.3619i	−0.352147	−	0.609937i	0.634478	−	0.772941i	$-0.281215\pi$
$347$	−6.55977	−	11.3619i	−0.352147	−	0.609937i	−0.986625	+	0.163004i	$0.947882\pi$
$348$	−0.956293	+	1.13967i	−0.0512627	+	0.0610925i
$349$	1.88138	−	2.24214i	0.100708	−	0.120019i	−0.713336	−	0.700822i	$-0.752817\pi$
$349$	1.88138	−	2.24214i	0.100708	−	0.120019i	0.814044	+	0.580803i	$0.197261\pi$
$350$	2.52093	+	10.0549i	0.134750	+	0.537456i
$351$	7.00196	+	4.90283i	0.373737	+	0.261693i
$352$	−4.24276	+	0.748113i	−0.226140	+	0.0398746i
$353$	2.70433	+	7.43009i	0.143937	+	0.395464i	0.990622	−	0.136631i	$-0.0436274\pi$
$353$	2.70433	+	7.43009i	0.143937	+	0.395464i	−0.846685	+	0.532094i	$0.821405\pi$
$354$	1.00481	+	0.843133i	0.0534049	+	0.0448120i
$355$	12.5229	−	5.71690i	0.664646	−	0.303422i
$356$	−1.30259	+	4.86134i	−0.0690372	+	0.257650i
$357$	0.639669	+	0.232820i	0.0338548	+	0.0123222i
$358$	−11.3978	+	7.98085i	−0.602394	+	0.421801i
$359$	−16.6321	−	9.60254i	−0.877808	−	0.506803i	−0.00787285	−	0.999969i	$-0.502506\pi$
$359$	−16.6321	−	9.60254i	−0.877808	−	0.506803i	−0.869935	+	0.493166i	$0.835839\pi$
$360$	−0.521378	−	6.56981i	−0.0274790	−	0.346259i
$361$	−1.97004	−	5.41263i	−0.103686	−	0.284875i
$362$	0.132573	−	0.229624i	0.00696789	−	0.0120687i
$363$	1.72833	+	0.151210i	0.0907140	+	0.00793645i
$364$	−9.18206	−	9.18206i	−0.481271	−	0.481271i
$365$	−15.1770	+	25.8040i	−0.794401	+	1.35064i
$366$	−1.60377	−	0.583726i	−0.0838305	−	0.0305118i
$367$	0.378055	−	0.539918i	0.0197343	−	0.0281835i	−0.809164	−	0.587583i	$-0.800079\pi$
$367$	0.378055	−	0.539918i	0.0197343	−	0.0281835i	0.828898	+	0.559400i	$0.188968\pi$
$368$	1.27627	−	7.23809i	0.0665302	−	0.377312i
$369$	22.1944			1.15540
$370$	−13.1903	−	3.31893i	−0.685732	−	0.172543i
$371$	−10.2281			−0.531017
$372$	−0.156867	+	0.889637i	−0.00813318	+	0.0461256i
$373$	0.724034	−	1.03403i	0.0374890	−	0.0535399i	−0.799970	−	0.600040i	$-0.795151\pi$
$373$	0.724034	−	1.03403i	0.0374890	−	0.0535399i	0.837459	+	0.546500i	$0.184040\pi$
$374$	−5.79277	−	2.10839i	−0.299537	−	0.109022i
$375$	−2.53660	+	0.384185i	−0.130989	+	0.0198393i
$376$	−8.02037	−	8.02037i	−0.413619	−	0.413619i
$377$	40.4536	+	3.53923i	2.08346	+	0.182280i
$378$	1.41468	−	2.45030i	0.0727635	−	0.126030i
$379$	−0.0235274	−	0.0646411i	−0.00120852	−	0.00332039i	0.939087	−	0.343680i	$-0.111673\pi$
$379$	−0.0235274	−	0.0646411i	−0.00120852	−	0.00332039i	−0.940295	+	0.340359i	$0.889451\pi$
$380$	5.28008	−	6.19037i	0.270863	−	0.317559i
$381$	−2.48326	−	1.43371i	−0.127221	−	0.0734513i
$382$	6.96968	−	4.88023i	0.356600	−	0.249694i
$383$	−0.660923	−	0.240556i	−0.0337716	−	0.0122919i	0.325079	−	0.945687i	$-0.394609\pi$
$383$	−0.660923	−	0.240556i	−0.0337716	−	0.0122919i	−0.358851	+	0.933395i	$0.616831\pi$
$384$	−0.0593906	+	0.221649i	−0.00303076	+	0.0113110i
$385$	6.98219	−	18.7120i	0.355845	−	0.953652i
$386$	−18.8049	−	15.7792i	−0.957143	−	0.803138i
$387$	−4.37068	−	12.0083i	−0.222174	−	0.610418i
$388$	18.4939	−	3.26098i	0.938888	−	0.165551i
$389$	25.9389	+	18.1626i	1.31516	+	0.920882i	0.999607	−	0.0280281i	$-0.00892280\pi$
$389$	25.9389	+	18.1626i	1.31516	+	0.920882i	0.315548	+	0.948910i	$0.397812\pi$
$390$	2.47850	−	2.04584i	0.125504	−	0.103595i
$391$	6.75995	−	8.05619i	0.341865	−	0.407419i
$392$	1.73667	−	2.06968i	0.0877149	−	0.104535i
$393$	−0.480944	−	0.833020i	−0.0242604	−	0.0420203i
$394$	−5.10129	−	10.9398i	−0.256999	−	0.551137i
$395$	−9.65275	+	1.62180i	−0.485682	+	0.0816019i
$396$	−6.34889	+	10.9966i	−0.319044	+	0.552600i
$397$	8.22159	+	2.20297i	0.412630	+	0.110564i	0.459161	−	0.888353i	$-0.348150\pi$
$397$	8.22159	+	2.20297i	0.412630	+	0.110564i	−0.0465313	+	0.998917i	$0.514817\pi$
$398$	11.2120	+	5.22826i	0.562009	+	0.262069i
$399$	1.67207	−	0.448029i	0.0837081	−	0.0224295i
$400$	−4.90938	−	0.947626i	−0.245469	−	0.0473813i
$401$	−1.45110	+	1.45110i	−0.0724646	+	0.0724646i	−0.742410	−	0.669946i	$-0.766317\pi$
$401$	−1.45110	+	1.45110i	−0.0724646	+	0.0724646i	0.669946	+	0.742410i	$0.266317\pi$
$402$	0.512628	−	0.430146i	0.0255676	−	0.0214538i
$403$	22.3474	−	10.4207i	1.11320	−	0.519094i
$404$	−6.88032	+	1.21319i	−0.342309	+	0.0603583i
$405$	−15.5334	−	11.0645i	−0.771858	−	0.549800i
$406$		−	13.4415i		−	0.667089i
$407$	17.3093	+	19.6757i	0.857991	+	0.975289i
$408$	−0.232172	+	0.232172i	−0.0114942	+	0.0114942i
$409$	−1.23160	+	0.862377i	−0.0608988	+	0.0426418i	−0.603629	−	0.797265i	$-0.706279\pi$
$409$	−1.23160	+	0.862377i	−0.0608988	+	0.0426418i	0.542731	+	0.839907i	$0.317390\pi$
$410$	4.48923	−	16.2288i	0.221707	−	0.801485i
$411$	−0.0104707	+	0.0287680i	−0.000516481	+	0.00141902i
$412$	5.39384	+	6.42813i	0.265736	+	0.316691i
$413$	−11.8509			−0.583145
$414$	−13.9242	−	16.5943i	−0.684339	−	0.815563i
$415$	20.9238	+	3.86385i	1.02711	+	0.189669i
$416$	5.88568	−	2.14221i	0.288569	−	0.105031i
$417$	1.28165	−	4.78320i	0.0627629	−	0.234234i
$418$	−15.1421	+	4.05730i	−0.740622	+	0.198449i
$419$	17.6930	+	3.11975i	0.864359	+	0.152410i	0.588213	−	0.808706i	$-0.299832\pi$
$419$	17.6930	+	3.11975i	0.864359	+	0.152410i	0.276146	+	0.961116i	$0.410943\pi$
$420$	−0.746108	−	0.758253i	−0.0364063	−	0.0369989i
$421$	17.6057	+	4.71743i	0.858049	+	0.229913i	0.660913	−	0.750463i	$-0.270169\pi$
$421$	17.6057	+	4.71743i	0.858049	+	0.229913i	0.197136	+	0.980376i	$0.436836\pi$
$422$	−20.7991	−	17.4525i	−1.01248	−	0.849575i
$423$	−33.3031	+	2.91364i	−1.61925	+	0.141666i
$424$	2.08497	−	4.47123i	0.101255	−	0.217142i
$425$	−5.40563	−	4.68664i	−0.262211	−	0.227336i
$426$	−0.810287	+	1.15721i	−0.0392585	+	0.0560670i
$427$	14.4899	−	5.27390i	0.701216	−	0.255222i
$428$	0.540882	+	6.18231i	0.0261445	+	0.298833i
$429$	−6.16841	+	0.539666i	−0.297814	+	0.0260553i
$430$	−9.66469	+	0.766987i	−0.466073	+	0.0369874i
$431$	−29.6786	+	13.8394i	−1.42957	+	0.666619i	−0.974613	−	0.223895i	$-0.928123\pi$
$431$	−29.6786	+	13.8394i	−1.42957	+	0.666619i	−0.454956	+	0.890514i	$0.650345\pi$
$432$	0.782773	+	1.11792i	0.0376612	+	0.0537858i
$433$	2.52213	+	9.41272i	0.121206	+	0.452347i	0.999676	−	0.0254506i	$-0.00810204\pi$
$433$	2.52213	+	9.41272i	0.121206	+	0.452347i	−0.878470	+	0.477797i	$0.841435\pi$
$434$	−4.08089	−	7.06831i	−0.195889	−	0.339290i
$435$	3.31155	+	0.316681i	0.158777	+	0.0151837i
$436$	3.67008	+	13.6969i	0.175765	+	0.655964i
$437$	2.33084	−	26.6416i	0.111499	−	1.27444i
$438$		−	3.07211i		−	0.146791i
$439$	−32.7668	−	2.86672i	−1.56387	−	0.136821i	−0.727936	−	0.685645i	$-0.759520\pi$
$439$	−32.7668	−	2.86672i	−1.56387	−	0.136821i	−0.835938	+	0.548823i	$0.815076\pi$
$440$	6.75667	+	6.86665i	0.322112	+	0.327355i
$441$	−1.38277	−	7.84208i	−0.0658462	−	0.373433i
$442$	8.82602	+	1.55627i	0.419811	+	0.0740240i
$443$	12.0449	+	12.0449i	0.572272	+	0.572272i	0.932763	−	0.360491i	$-0.117391\pi$
$443$	12.0449	+	12.0449i	0.572272	+	0.572272i	−0.360491	+	0.932763i	$0.617391\pi$
$444$	1.33943	−	0.392667i	0.0635664	−	0.0186352i
$445$	10.6058	−	3.76351i	0.502762	−	0.178408i
$446$	−6.74855	−	9.63793i	−0.319553	−	0.456369i
$447$	−0.876921	−	0.614027i	−0.0414769	−	0.0290425i
$448$	−0.876179	−	1.87897i	−0.0413956	−	0.0887731i
$449$	−2.65684	+	30.3678i	−0.125384	+	1.43314i	0.629354	+	0.777118i	$0.283319\pi$
$449$	−2.65684	+	30.3678i	−0.125384	+	1.43314i	−0.754738	+	0.656026i	$0.772236\pi$
$450$	−11.4404	+	9.28909i	−0.539308	+	0.437892i
$451$	−24.8522	+	20.8534i	−1.17024	+	0.981951i
$452$	6.94805	+	4.01146i	0.326809	+	0.188683i
$453$	−0.789907	+	1.69396i	−0.0371131	+	0.0795892i
$454$	6.11761	−	3.53200i	0.287114	−	0.165765i
$455$	−5.27276	+	28.5535i	−0.247191	+	1.33861i
$456$	−0.144989	+	0.822275i	−0.00678974	+	0.0385065i
$457$	−5.45141	+	14.9776i	−0.255006	+	0.700624i	0.744451	+	0.667677i	$0.232711\pi$
$457$	−5.45141	+	14.9776i	−0.255006	+	0.700624i	−0.999457	+	0.0329466i	$0.989511\pi$
$458$	−13.8974	+	8.02369i	−0.649385	+	0.374923i
$459$	0.170194	+	1.94532i	0.00794397	+	0.0907999i
$460$	−14.9503	+	6.82507i	−0.697063	+	0.318221i
$461$	−3.65766	−	1.70560i	−0.170354	−	0.0794375i	0.335571	−	0.942015i	$-0.391071\pi$
$461$	−3.65766	−	1.70560i	−0.170354	−	0.0794375i	−0.505925	+	0.862578i	$0.668849\pi$
$462$	0.355905	+	2.01843i	0.0165582	+	0.0939061i
$463$	1.01773	+	5.77181i	0.0472977	+	0.268239i	0.999281	−	0.0379109i	$-0.0120703\pi$
$463$	1.01773	+	5.77181i	0.0472977	+	0.268239i	−0.951983	+	0.306150i	$0.900959\pi$
$464$	5.87595	+	2.74000i	0.272784	+	0.127201i
$465$	1.83755	−	0.838873i	0.0852145	−	0.0389018i
$466$	0.125540	+	1.43493i	0.00581554	+	0.0664719i
$467$	18.7622	−	10.8323i	0.868209	−	0.501261i	0.00145667	−	0.999999i	$-0.499536\pi$
$467$	18.7622	−	10.8323i	0.868209	−	0.501261i	0.866753	+	0.498738i	$0.166203\pi$
$468$	6.31383	−	17.3471i	0.291857	−	0.801871i
$469$	−1.04989	+	5.95420i	−0.0484792	+	0.274939i
$470$	−4.60567	+	24.9410i	−0.212444	+	1.15044i
$471$	1.09494	−	0.632166i	0.0504523	−	0.0291287i
$472$	2.41577	−	5.18063i	0.111195	−	0.238458i
$473$	16.1769	+	9.33971i	0.743813	+	0.429440i
$474$	0.769460	−	0.645654i	0.0353425	−	0.0296559i
$475$	−18.0962	−	1.87807i	−0.830311	−	0.0861715i
$476$	0.258549	−	2.95523i	0.0118506	−	0.135453i
$477$	−6.14512	−	13.1782i	−0.281366	−	0.603390i
$478$	25.1894	+	17.6378i	1.15214	+	0.806735i
$479$	1.52514	+	2.17812i	0.0696853	+	0.0995210i	0.852482	−	0.522757i	$-0.175096\pi$
$479$	1.52514	+	2.17812i	0.0696853	+	0.0995210i	−0.782797	+	0.622278i	$0.786207\pi$
$480$	0.483562	−	0.171594i	0.0220715	−	0.00783217i
$481$	−29.7497	−	23.8007i	−1.35647	−	1.08522i
$482$	−14.3420	−	14.3420i	−0.653262	−	0.653262i
$483$	−3.44342	−	0.607168i	−0.156681	−	0.0276271i
$484$	−1.31290	−	7.44584i	−0.0596774	−	0.338447i
$485$	−29.4519	−	29.9313i	−1.33734	−	1.35911i
$486$	6.02824	+	0.527403i	0.273447	+	0.0239235i
$487$			36.8756i			1.67099i	0.549497	+	0.835496i	$0.314820\pi$
$487$			36.8756i			1.67099i	−0.549497	+	0.835496i	$0.685180\pi$
$488$	−0.648234	+	7.40934i	−0.0293442	+	0.335405i
$489$	−0.382490	−	1.42747i	−0.0172968	−	0.0645525i
$490$	−6.01392	−	0.575106i	−0.271681	−	0.0259806i
$491$	5.07237	+	8.78561i	0.228913	+	0.396489i	0.957486	−	0.288479i	$-0.0931496\pi$
$491$	5.07237	+	8.78561i	0.228913	+	0.396489i	−0.728573	+	0.684968i	$0.759816\pi$
$492$	0.447230	+	1.66909i	0.0201627	+	0.0752482i
$493$	5.32104	+	7.59923i	0.239648	+	0.342252i
$494$	20.6552	−	9.63170i	0.929323	−	0.433350i
$495$	28.3041	−	2.24621i	1.27218	−	0.100959i
$496$	3.92179	−	0.343112i	0.176094	−	0.0154062i
$497$	−1.11241	−	12.7150i	−0.0498986	−	0.570344i
$498$	−2.05184	+	0.746810i	−0.0919453	+	0.0334654i
$499$	23.0157	−	32.8698i	1.03032	−	1.47145i	0.155000	−	0.987915i	$-0.450462\pi$
$499$	23.0157	−	32.8698i	1.03032	−	1.47145i	0.875323	−	0.483539i	$-0.160649\pi$
$500$	4.47825	+	10.2443i	0.200274	+	0.458138i
$501$	0.921291	−	1.97572i	0.0411602	−	0.0882684i
$502$	6.99712	−	0.612169i	0.312297	−	0.0273224i
$503$	8.76311	+	7.35312i	0.390728	+	0.327860i	0.816897	−	0.576784i	$-0.195693\pi$
$503$	8.76311	+	7.35312i	0.390728	+	0.327860i	−0.426169	+	0.904644i	$0.640137\pi$
$504$	−5.90227	−	1.58151i	−0.262908	−	0.0704460i
$505$	10.9570	+	11.1354i	0.487582	+	0.495518i
$506$	31.1833	+	5.49845i	1.38626	+	0.244436i
$507$	5.81390	−	1.55783i	0.258204	−	0.0691857i
$508$	−3.23420	+	12.0702i	−0.143494	+	0.535528i
$509$	10.7106	−	3.89832i	0.474737	−	0.172790i	−0.0935601	−	0.995614i	$-0.529825\pi$
$509$	10.7106	−	3.89832i	0.474737	−	0.172790i	0.568297	+	0.822824i	$0.307603\pi$
$510$	0.721985	+	0.133324i	0.0319700	+	0.00590368i
$511$	17.8413	+	21.2624i	0.789253	+	0.940595i
$512$	1.00000			0.0441942
$513$	3.19195	+	3.80402i	0.140928	+	0.167951i
$514$	−5.12625	+	14.0842i	−0.226109	+	0.621229i
$515$	5.00253	−	18.0844i	0.220438	−	0.796896i
$516$	0.814990	−	0.570662i	0.0358779	−	0.0251220i
$517$	34.5535	−	34.5535i	1.51966	−	1.51966i
$518$	−6.98992	+	10.4964i	−0.307120	+	0.461187i
$519$			3.80529i			0.167034i
$520$	−11.4073	−	8.12552i	−0.500244	−	0.356328i
$521$	−4.78291	+	0.843356i	−0.209543	+	0.0369481i	−0.277434	−	0.960745i	$-0.589484\pi$
$521$	−4.78291	+	0.843356i	−0.209543	+	0.0369481i	0.0678911	+	0.997693i	$0.478373\pi$
$522$	17.3184	−	8.07572i	0.758007	−	0.353465i
$523$	−11.6308	+	9.75940i	−0.508579	+	0.426749i	−0.860629	−	0.509233i	$-0.829929\pi$
$523$	−11.6308	+	9.75940i	−0.508579	+	0.426749i	0.352050	+	0.935981i	$0.385485\pi$
$524$	−2.96407	+	2.96407i	−0.129486	+	0.129486i
$525$	−0.450820	+	2.33557i	−0.0196754	+	0.101933i
$526$	18.3662	−	4.92120i	0.800803	−	0.214574i
$527$	5.10527	+	2.38063i	0.222389	+	0.103702i
$528$	−0.954910	−	0.255867i	−0.0415571	−	0.0111352i
$529$	−15.5094	+	26.8631i	−0.674324	+	1.16796i
$530$	−10.8791	+	1.82784i	−0.472556	+	0.0793964i
$531$	−7.12010	−	15.2691i	−0.308986	−	0.662623i
$532$	−3.77189	−	6.53310i	−0.163532	−	0.283246i
$533$	30.3173	−	36.1308i	1.31319	−	1.56500i
$534$	−0.742337	+	0.884682i	−0.0321241	+	0.0382840i
$535$	10.7020	−	8.83377i	0.462686	−	0.381917i
$536$	−2.38887	−	1.67270i	−0.103183	−	0.0722497i
$537$	−3.14435	+	0.554434i	−0.135689	+	0.0239256i
$538$	1.62156	+	4.45519i	0.0699103	+	0.192077i
$539$	8.91662	+	7.48193i	0.384066	+	0.322270i
$540$	1.06683	−	2.85906i	0.0459090	−	0.123034i
$541$	8.98277	−	33.5242i	0.386200	−	1.44132i	−0.450068	−	0.892994i	$-0.648600\pi$
$541$	8.98277	−	33.5242i	0.386200	−	1.44132i	0.836267	−	0.548322i	$-0.184733\pi$
$542$	21.0012	+	7.64381i	0.902078	+	0.328330i
$543$	0.0498393	−	0.0348978i	0.00213881	−	0.00149761i
$544$	1.23918	+	0.715440i	0.0531293	+	0.0306742i
$545$	20.5767	−	24.1242i	0.881410	−	1.03337i
$546$	−1.01913	−	2.80003i	−0.0436146	−	0.119830i
$547$	−6.52657	+	11.3044i	−0.279056	+	0.483339i	−0.971150	−	0.238468i	$-0.923355\pi$
$547$	−6.52657	+	11.3044i	−0.279056	+	0.483339i	0.692094	+	0.721807i	$0.256688\pi$
$548$	0.132907	+	0.0116278i	0.00567749	+	0.000496716i
$549$	15.5007	+	15.5007i	0.661554	+	0.661554i
$550$	4.08257	−	21.1507i	0.174082	−	0.901867i
$551$	22.1683	+	8.06859i	0.944400	+	0.343734i
$552$	0.967354	−	1.38153i	0.0411733	−	0.0588016i
$553$	−1.57589	+	8.93731i	−0.0670136	+	0.380053i
$554$	19.6932			0.836682
$555$	−2.42131	−	1.96939i	−0.102779	−	0.0835961i
$556$	−21.5801			−0.915199
$557$	−5.24531	+	29.7476i	−0.222251	+	1.26045i	0.645620	+	0.763659i	$0.276599\pi$
$557$	−5.24531	+	29.7476i	−0.222251	+	1.26045i	−0.867871	+	0.496789i	$0.834512\pi$
$558$	6.65522	−	9.50464i	0.281738	−	0.402363i
$559$	−25.5189	−	9.28813i	−1.07934	−	0.392846i
$560$	−2.35026	+	3.99592i	−0.0993166	+	0.168859i
$561$	−1.00025	−	1.00025i	−0.0422304	−	0.0422304i
$562$	14.5161	+	1.26999i	0.612323	+	0.0535713i
$563$	0.196115	−	0.339680i	0.00826524	−	0.0143158i	−0.861863	−	0.507141i	$-0.830702\pi$
$563$	0.196115	−	0.339680i	0.00826524	−	0.0143158i	0.870128	+	0.492825i	$0.164036\pi$
$564$	−0.890190	−	2.44578i	−0.0374838	−	0.102986i
$565$	−1.41923	−	17.8836i	−0.0597076	−	0.752367i
$566$	27.0659	+	15.6265i	1.13767	+	0.656832i
$567$	−14.4844	+	10.1421i	−0.608288	+	0.425928i
$568$	5.78511	+	2.10561i	0.242738	+	0.0883494i
$569$	11.3326	−	42.2940i	0.475089	−	1.77306i	−0.145965	−	0.989290i	$-0.546629\pi$
$569$	11.3326	−	42.2940i	0.475089	−	1.77306i	0.621054	−	0.783768i	$-0.286705\pi$
$570$	1.69842	−	0.775354i	0.0711388	−	0.0324760i
$571$	−4.23851	−	3.55653i	−0.177376	−	0.148836i	0.549777	−	0.835311i	$-0.314713\pi$
$571$	−4.23851	−	3.55653i	−0.177376	−	0.148836i	−0.727153	+	0.686475i	$0.759157\pi$
$572$	9.22910	+	25.3567i	0.385888	+	1.06022i
$573$	1.92274	−	0.339032i	0.0803238	−	0.0141633i
$574$	−12.7886	−	8.95466i	−0.533785	−	0.373760i
$575$	31.5246	+	18.8858i	1.31467	+	0.787593i
$576$	1.89452	−	2.25780i	0.0789382	−	0.0940749i
$577$	11.9901	−	14.2893i	0.499156	−	0.594871i	−0.456366	−	0.889792i	$-0.650849\pi$
$577$	11.9901	−	14.2893i	0.499156	−	0.594871i	0.955521	+	0.294922i	$0.0952936\pi$
$578$	−7.47629	−	12.9493i	−0.310973	−	0.538621i
$579$	−2.38060	−	5.10521i	−0.0989343	−	0.212165i
$580$	−2.40209	−	14.2969i	−0.0997415	−	0.593647i
$581$	9.86396	−	17.0849i	0.409226	−	0.708801i
$582$	4.16240	+	1.11531i	0.172537	+	0.0462311i
$583$	19.2630	+	8.98248i	0.797792	+	0.372016i
$584$	−12.9318	+	3.46506i	−0.535121	+	0.143385i
$585$	−39.9571	+	10.3615i	−1.65202	+	0.428395i
$586$	3.68735	−	3.68735i	0.152323	−	0.152323i
$587$	−31.3284	+	26.2876i	−1.29306	+	1.08501i	−0.301761	+	0.953384i	$0.597575\pi$
$587$	−31.3284	+	26.2876i	−1.29306	+	1.08501i	−0.991300	+	0.131623i	$0.957981\pi$
$588$	0.561884	−	0.262011i	0.0231717	−	0.0108051i
$589$	14.1070	−	2.48745i	0.581270	−	0.102494i
$590$	−12.6051	+	2.11785i	−0.518945	+	0.0871904i
$591$		−	2.76983i		−	0.113936i
$592$	−3.16365	−	5.19531i	−0.130025	−	0.213526i
$593$	−1.46227	+	1.46227i	−0.0600480	+	0.0600480i	−0.736493	−	0.676445i	$-0.763520\pi$
$593$	−1.46227	+	1.46227i	−0.0600480	+	0.0600480i	0.676445	+	0.736493i	$0.263520\pi$
$594$	−4.81622	+	3.37235i	−0.197612	+	0.138369i
$595$	−5.77123	+	3.27019i	−0.236598	+	0.134065i
$596$	−1.59561	+	4.38390i	−0.0653587	+	0.179571i
$597$	1.82473	+	2.17462i	0.0746811	+	0.0890014i
$598$	−46.0345			−1.88249
$599$	26.0471	+	31.0418i	1.06426	+	1.26833i	0.961847	+	0.273589i	$0.0882110\pi$
$599$	26.0471	+	31.0418i	1.06426	+	1.26833i	0.102410	+	0.994742i	$0.467345\pi$
$600$	−0.929097	−	0.673174i	−0.0379302	−	0.0274822i
$601$	23.9503	−	8.71718i	0.976952	−	0.355581i	0.196297	−	0.980544i	$-0.437108\pi$
$601$	23.9503	−	8.71718i	0.976952	−	0.355581i	0.780654	+	0.624963i	$0.214886\pi$
$602$	−2.32652	+	8.68270i	−0.0948219	+	0.353880i
$603$	−8.30237	+	2.22461i	−0.338099	+	0.0905932i
$604$	8.02154	+	1.41441i	0.326392	+	0.0575517i
$605$	−12.0506	+	11.8576i	−0.489928	+	0.482081i
$606$	−1.54854	−	0.414930i	−0.0629052	−	0.0168554i
$607$	2.16439	+	1.81614i	0.0878500	+	0.0737149i	0.685655	−	0.727927i	$-0.259516\pi$
$607$	2.16439	+	1.81614i	0.0878500	+	0.0737149i	−0.597805	+	0.801642i	$0.703960\pi$
$608$	3.62483	−	0.317132i	0.147006	−	0.0128614i
$609$	1.30352	−	2.79540i	0.0528211	−	0.113275i
$610$	14.4696	−	8.19900i	0.585857	−	0.331968i
$611$	−40.7485	+	58.1948i	−1.64851	+	2.35431i
$612$	3.96296	−	1.44240i	0.160193	−	0.0583056i
$613$	0.998612	+	11.4142i	0.0403335	+	0.461014i	0.989326	+	0.145717i	$0.0465488\pi$
$613$	0.998612	+	11.4142i	0.0403335	+	0.461014i	−0.948993	+	0.315298i	$0.897896\pi$
$614$	10.7193	−	0.937819i	0.432596	−	0.0378473i
$615$	2.50745	−	2.93973i	0.101110	−	0.118541i
$616$	8.09501	−	3.77477i	0.326157	−	0.152090i
$617$	0.339887	+	0.485409i	0.0136833	+	0.0195418i	0.825935	−	0.563765i	$-0.190648\pi$
$617$	0.339887	+	0.485409i	0.0136833	+	0.0195418i	−0.812252	+	0.583307i	$0.801759\pi$
$618$	0.498366	+	1.85993i	0.0200472	+	0.0748173i
$619$	5.89864	+	10.2167i	0.237086	+	0.410646i	0.959877	−	0.280421i	$-0.0904742\pi$
$619$	5.89864	+	10.2167i	0.237086	+	0.410646i	−0.722791	+	0.691067i	$0.757141\pi$
$620$	−5.60376	−	6.78886i	−0.225053	−	0.272647i
$621$	−2.59605	−	9.68860i	−0.104176	−	0.388790i
$622$	−1.46200	+	16.7107i	−0.0586208	+	0.670039i
$623$		−	10.4341i		−	0.418035i
$624$	1.43178	+	0.125265i	0.0573171	+	0.00501459i
$625$	13.1925	−	21.2358i	0.527699	−	0.849431i
$626$	2.00285	+	11.3587i	0.0800500	+	0.453986i
$627$	−3.54253	−	0.624644i	−0.141475	−	0.0249459i
$628$	−3.89605	−	3.89605i	−0.155469	−	0.155469i
$629$	−0.203396	−	8.70132i	−0.00810992	−	0.346944i
$630$	4.56938	+	12.8768i	0.182048	+	0.513022i
$631$	5.27971	+	7.54021i	0.210182	+	0.300171i	0.910376	−	0.413781i	$-0.135792\pi$
$631$	5.27971	+	7.54021i	0.210182	+	0.300171i	−0.700194	+	0.713952i	$0.746903\pi$
$632$	−3.58571	−	2.51074i	−0.142632	−	0.0998720i
$633$	−2.63306	−	5.64661i	−0.104655	−	0.224432i
$634$	0.122331	−	1.39825i	0.00485837	−	0.0555315i
$635$	26.3331	−	9.34441i	1.04500	−	0.370822i
$636$	0.867214	−	0.727679i	0.0343873	−	0.0288544i
$637$	−14.6551	−	8.46115i	−0.580658	−	0.335243i
$638$	−11.8045	+	25.3148i	−0.467345	+	1.00222i
$639$	15.7140	−	9.07250i	0.621637	−	0.358903i
$640$	−1.26773	−	1.84197i	−0.0501113	−	0.0728104i
$641$	4.84595	−	27.4827i	0.191403	−	1.08550i	−0.726045	−	0.687648i	$-0.758643\pi$
$641$	4.84595	−	27.4827i	0.191403	−	1.08550i	0.917448	−	0.397855i	$-0.130245\pi$
$642$	−0.487057	+	1.33818i	−0.0192226	+	0.0528136i
$643$	12.5357	−	7.23747i	0.494359	−	0.285418i	−0.232022	−	0.972710i	$-0.574534\pi$
$643$	12.5357	−	7.23747i	0.494359	−	0.285418i	0.726381	+	0.687292i	$0.241201\pi$
$644$	1.32805	+	15.1796i	0.0523324	+	0.598162i
$645$	−2.08433	−	0.777746i	−0.0820704	−	0.0306237i
$646$	4.71870	+	2.20037i	0.185655	+	0.0865723i
$647$	−7.88308	−	44.7072i	−0.309916	−	1.75762i	−0.599412	−	0.800441i	$-0.704599\pi$
$647$	−7.88308	−	44.7072i	−0.309916	−	1.75762i	0.289496	−	0.957179i	$-0.406512\pi$
$648$	−1.48102	−	8.39930i	−0.0581801	−	0.329956i
$649$	22.3193	+	10.4076i	0.876108	+	0.408536i
$650$	−0.505609	+	31.3129i	−0.0198316	+	1.22819i
$651$	−0.163231	−	1.86574i	−0.00639752	−	0.0731240i
$652$	−5.57741	+	3.22012i	−0.218428	+	0.126110i
$653$	−1.61726	+	4.44338i	−0.0632883	+	0.173883i	−0.967306	−	0.253612i	$-0.918381\pi$
$653$	−1.61726	+	4.44338i	−0.0632883	+	0.173883i	0.904018	+	0.427495i	$0.140604\pi$
$654$	−0.565030	+	3.20444i	−0.0220944	+	0.125304i
$655$	9.21736	+	1.70210i	0.360152	+	0.0665067i
$656$	6.52145	−	3.76516i	0.254620	−	0.147005i
$657$	−16.6761	+	35.7620i	−0.650596	+	1.39521i
$658$	20.3650	+	11.7577i	0.793911	+	0.458365i
$659$	16.7323	−	14.0401i	0.651798	−	0.546923i	−0.255818	−	0.966725i	$-0.582345\pi$
$659$	16.7323	−	14.0401i	0.651798	−	0.546923i	0.907616	+	0.419802i	$0.137900\pi$
$660$	0.739265	+	2.08329i	0.0287758	+	0.0810919i
$661$	2.93114	−	33.5031i	0.114008	−	1.30312i	−0.696569	−	0.717489i	$-0.745291\pi$
$661$	2.93114	−	33.5031i	0.114008	−	1.30312i	0.810578	−	0.585631i	$-0.199153\pi$
$662$	−6.31138	−	13.5348i	−0.245299	−	0.526045i
$663$	1.68461	+	1.17958i	0.0654249	+	0.0458110i
$664$	5.45793	+	7.79474i	0.211809	+	0.302494i
$665$	−7.25207	+	15.2299i	−0.281223	+	0.590590i
$666$	−17.7236	−	2.69972i	−0.686774	−	0.104612i
$667$	−33.6946	−	33.6946i	−1.30466	−	1.30466i
$668$	−9.35575	−	1.64967i	−0.361985	−	0.0638277i
$669$	−0.468825	−	2.65884i	−0.0181258	−	0.102797i
$670$	−0.0526418	+	6.52076i	−0.00203373	+	0.251919i
$671$	−31.9210	−	2.79273i	−1.23230	−	0.107812i
$672$		−	0.475736i		−	0.0183519i
$673$	−0.292263	+	3.34058i	−0.0112659	+	0.128770i	−0.999745	−	0.0225886i	$-0.992809\pi$
$673$	−0.292263	+	3.34058i	−0.0112659	+	0.128770i	0.988479	+	0.151358i	$0.0483648\pi$
$674$	7.09470	+	26.4778i	0.273277	+	1.01989i
$675$	−6.61876	+	1.65944i	−0.254756	+	0.0638718i
$676$	−13.1151	−	22.7161i	−0.504428	−	0.873695i
$677$	−3.02759	−	11.2991i	−0.116360	−	0.434261i	0.883025	−	0.469326i	$-0.155503\pi$
$677$	−3.02759	−	11.2991i	−0.116360	−	0.434261i	−0.999385	+	0.0350648i	$0.988836\pi$
$678$	1.05595	+	1.50806i	0.0405537	+	0.0579166i
$679$	−35.2857	+	16.4540i	−1.35414	+	0.631446i
$680$	−0.253119	−	3.18952i	−0.00970667	−	0.122312i
$681$	1.61479	−	0.141276i	0.0618790	−	0.00541371i
$682$	1.47820	+	16.8959i	0.0566032	+	0.646978i
$683$	14.7160	−	5.35619i	0.563093	−	0.204949i	−0.0447615	−	0.998998i	$-0.514253\pi$
$683$	14.7160	−	5.35619i	0.563093	−	0.204949i	0.607854	+	0.794049i	$0.292031\pi$
$684$	6.15129	−	8.78495i	0.235200	−	0.335901i
$685$	−0.147071	−	0.259551i	−0.00561930	−	0.00991695i
$686$	−8.50049	+	18.2294i	−0.324550	+	0.696000i
$687$	−3.66834	+	0.320938i	−0.139956	+	0.0122446i
$688$	−3.32139	−	2.78698i	−0.126627	−	0.106253i
$689$	−29.8473	−	7.99756i	−1.13709	−	0.304683i
$690$	−3.77107	−	0.0304437i	−0.143562	−	0.00115897i
$691$	0.157830	+	0.0278296i	0.00600412	+	0.00105869i	0.176649	−	0.984274i	$-0.443474\pi$
$691$	0.157830	+	0.0278296i	0.00600412	+	0.00105869i	−0.170645	+	0.985333i	$0.554585\pi$
$692$	16.0181	−	4.29203i	0.608915	−	0.163158i
$693$	6.81348	−	25.4282i	0.258823	−	0.965939i
$694$	−12.3283	+	4.48715i	−0.467977	+	0.170330i
$695$	27.3577	+	39.7499i	1.03774	+	1.50780i
$696$	0.956293	+	1.13967i	0.0362482	+	0.0431989i
$697$	10.7750			0.408131
$698$	−1.88138	−	2.24214i	−0.0712114	−	0.0848664i
$699$	−0.113047	+	0.310595i	−0.00427584	+	0.0117478i
$700$	10.3399	−	0.736624i	0.390811	−	0.0278418i
$701$	4.16883	−	2.91905i	0.157455	−	0.110251i	−0.492194	−	0.870486i	$-0.663805\pi$
$701$	4.16883	−	2.91905i	0.157455	−	0.110251i	0.649649	+	0.760235i	$0.274916\pi$
$702$	6.04422	−	6.04422i	0.228124	−	0.228124i
$703$	−13.1153	−	17.8289i	−0.494654	−	0.672428i
$704$			4.30821i			0.162372i
$705$	−3.37654	+	4.74028i	−0.127168	+	0.178529i
$706$	7.78681	−	1.37302i	0.293061	−	0.0516745i
$707$	13.1274	−	6.12139i	0.493706	−	0.230219i
$708$	1.00481	−	0.843133i	0.0377629	−	0.0316869i
$709$	−16.3509	+	16.3509i	−0.614070	+	0.614070i	−0.944004	−	0.329934i	$-0.892974\pi$
$709$	−16.3509	+	16.3509i	−0.614070	+	0.614070i	0.329934	+	0.944004i	$0.392974\pi$
$710$	−3.45547	−	13.3254i	−0.129682	−	0.500092i
$711$	−12.4619	+	3.33917i	−0.467359	+	0.125228i
$712$	4.56129	+	2.12696i	0.170942	+	0.0797114i
$713$	−27.9484	−	7.48875i	−1.04668	−	0.280456i
$714$	0.340361	−	0.589522i	0.0127377	−	0.0220623i
$715$	35.0065	−	49.1452i	1.30917	−	1.83793i
$716$	5.88039	+	12.6105i	0.219760	+	0.471278i
$717$	3.52814	+	6.11091i	0.131761	+	0.228216i
$718$	−12.3448	+	14.7119i	−0.460703	+	0.549045i
$719$	−33.7001	+	40.1622i	−1.25680	+	1.49780i	−0.467231	+	0.884135i	$0.654748\pi$
$719$	−33.7001	+	40.1622i	−1.25680	+	1.49780i	−0.789570	+	0.613661i	$0.789696\pi$
$720$	−6.56053	−	0.627378i	−0.244497	−	0.0233810i
$721$	−14.2508	−	9.97854i	−0.530728	−	0.371620i
$722$	−5.67249	+	1.00021i	−0.211108	+	0.0372241i
$723$	−1.59184	−	4.37354i	−0.0592011	−	0.162654i
$724$	−0.203114	−	0.170433i	−0.00754867	−	0.00633409i
$725$	−23.2893	+	22.5492i	−0.864944	+	0.837455i
$726$	0.449035	−	1.67582i	0.0166652	−	0.0621955i
$727$	−20.2863	−	7.38362i	−0.752378	−	0.273843i	−0.0627721	−	0.998028i	$-0.519994\pi$
$727$	−20.2863	−	7.38362i	−0.752378	−	0.273843i	−0.689606	+	0.724185i	$0.742216\pi$
$728$	−10.6370	+	7.44812i	−0.394234	+	0.276046i
$729$	−20.9561	−	12.0990i	−0.776153	−	0.448112i
$730$	22.7765	+	19.4273i	0.842997	+	0.719035i
$731$	−2.12188	−	5.82982i	−0.0784806	−	0.215624i
$732$	−0.853350	+	1.47804i	−0.0315407	+	0.0546301i
$733$	7.22524	+	0.632126i	0.266870	+	0.0233481i	0.219805	−	0.975544i	$-0.429458\pi$
$733$	7.22524	+	0.632126i	0.266870	+	0.0233481i	0.0470647	+	0.998892i	$0.485013\pi$
$734$	−0.466067	−	0.466067i	−0.0172029	−	0.0172029i
$735$	−1.19493	−	0.702817i	−0.0440757	−	0.0259238i
$736$	−6.90651	−	2.51376i	−0.254577	−	0.0926586i
$737$	7.20636	−	10.2917i	0.265450	−	0.379101i
$738$	3.85402	−	21.8573i	0.141869	−	0.804577i
$739$	−25.1066			−0.923563			−0.461781	−	0.886994i	$-0.652790\pi$
$739$	−25.1066			−0.923563			−0.461781	+	0.886994i	$0.652790\pi$
$740$	−5.55898	+	12.4136i	−0.204352	+	0.456333i
$741$	5.22969			0.192117
$742$	−1.77609	+	10.0727i	−0.0652024	+	0.369781i
$743$	18.0558	−	25.7864i	0.662403	−	0.946010i	−0.337585	−	0.941295i	$-0.609610\pi$
$743$	18.0558	−	25.7864i	0.662403	−	0.946010i	0.999989	−	0.00471522i	$-0.00150091\pi$
$744$	0.848882	+	0.308968i	0.0311215	+	0.0113273i
$745$	10.0978	−	2.61852i	0.369955	−	0.0959351i
$746$	−0.892591	−	0.892591i	−0.0326801	−	0.0326801i
$747$	27.9391	+	2.44435i	1.02224	+	0.0894342i
$748$	−3.08227	+	5.33864i	−0.112699	+	0.195200i
$749$	−4.40051	−	12.0903i	−0.160791	−	0.441770i
$750$	−0.0621267	+	2.56477i	−0.00226855	+	0.0936523i
$751$	17.3471	+	10.0153i	0.633004	+	0.365465i	0.781915	−	0.623386i	$-0.214243\pi$
$751$	17.3471	+	10.0153i	0.633004	+	0.365465i	−0.148911	+	0.988851i	$0.547577\pi$
$752$	−9.29125	+	6.50580i	−0.338817	+	0.237242i
$753$	1.51455	+	0.551250i	0.0551931	+	0.0200887i
$754$	10.5101	−	39.2244i	0.382757	−	1.42847i
$755$	−7.56381	−	16.5685i	−0.275275	−	0.602991i
$756$	−2.16742	−	1.81868i	−0.0788283	−	0.0661448i
$757$	−6.33935	−	17.4172i	−0.230408	−	0.633040i	0.769577	−	0.638554i	$-0.220467\pi$
$757$	−6.33935	−	17.4172i	−0.230408	−	0.633040i	−0.999985	+	0.00551387i	$0.998245\pi$
$758$	−0.0677446	+	0.0119452i	−0.00246059	+	0.000433869i
$759$	5.95191	+	4.16757i	0.216040	+	0.151273i
$760$	−5.17945	−	6.27481i	−0.187878	−	0.227611i
$761$	−2.62769	+	3.13155i	−0.0952536	+	0.113519i	−0.811566	−	0.584261i	$-0.801384\pi$
$761$	−2.62769	+	3.13155i	−0.0952536	+	0.113519i	0.716312	+	0.697780i	$0.245829\pi$
$762$	−1.84315	+	2.19657i	−0.0667701	+	0.0795735i
$763$	−14.6992	−	25.4598i	−0.532147	−	0.921706i
$764$	−3.59581	−	7.71124i	−0.130092	−	0.278983i
$765$	−7.68082	−	5.47110i	−0.277701	−	0.197808i
$766$	−0.351670	+	0.609110i	−0.0127063	+	0.0220080i
$767$	−34.5829	−	9.26646i	−1.24872	−	0.334592i
$768$	0.207968	+	0.0969772i	0.00750441	+	0.00349936i
$769$	9.64827	−	2.58525i	0.347926	−	0.0932264i	−0.0806242	−	0.996745i	$-0.525691\pi$
$769$	9.64827	−	2.58525i	0.347926	−	0.0932264i	0.428550	+	0.903518i	$0.359025\pi$
$770$	−17.2153	−	10.1254i	−0.620396	−	0.364895i
$771$	−2.43195	+	2.43195i	−0.0875845	+	0.0875845i
$772$	−18.8049	+	15.7792i	−0.676802	+	0.567904i
$773$	11.5938	−	5.40630i	0.417002	−	0.194451i	−0.202782	−	0.979224i	$-0.564998\pi$
$773$	11.5938	−	5.40630i	0.417002	−	0.194451i	0.619783	+	0.784773i	$0.287220\pi$
$774$	−12.5849	+	2.21905i	−0.452354	+	0.0797622i
$775$	−5.40086	+	18.9284i	−0.194004	+	0.679929i
$776$		−	18.7792i		−	0.674136i
$777$	−2.47160	+	1.50506i	−0.0886681	+	0.0539939i
$778$	22.3909	−	22.3909i	0.802754	−	0.802754i
$779$	22.4451	−	15.7162i	0.804179	−	0.563093i
$780$	−1.58437	−	2.79610i	−0.0567296	−	0.100117i
$781$	−9.07141	+	24.9235i	−0.324601	+	0.891833i
$782$	−6.75995	−	8.05619i	−0.241735	−	0.288089i
$783$	8.84803			0.316203
$784$	−1.73667	−	2.06968i	−0.0620238	−	0.0739171i
$785$	−2.23729	+	12.1155i	−0.0798523	+	0.432422i
$786$	−0.903879	+	0.328985i	−0.0322403	+	0.0117345i
$787$	−2.75438	+	10.2795i	−0.0981832	+	0.366425i	−0.997483	−	0.0709083i	$-0.977410\pi$
$787$	−2.75438	+	10.2795i	−0.0981832	+	0.366425i	0.899300	+	0.437333i	$0.144077\pi$
$788$	−11.6594	+	3.12412i	−0.415348	+	0.111292i
$789$	4.29682	+	0.757646i	0.152971	+	0.0269729i
$790$	−0.0790158	+	9.78772i	−0.00281126	+	0.348232i
$791$	−16.0665	−	4.30500i	−0.571258	−	0.153068i
$792$	9.72707	+	8.16198i	0.345636	+	0.290023i
$793$	46.4077	−	4.06015i	1.64799	−	0.144180i
$794$	3.59716	−	7.71414i	0.127659	−	0.273765i
$795$	−2.43976	−	0.674887i	−0.0865293	−	0.0239358i
$796$	7.09578	−	10.1338i	0.251503	−	0.359184i
$797$	−27.5091	+	10.0125i	−0.974422	+	0.354661i	−0.779669	−	0.626192i	$-0.784613\pi$
$797$	−27.5091	+	10.0125i	−0.974422	+	0.354661i	−0.194753	+	0.980852i	$0.562391\pi$
$798$	−0.150871	−	1.72446i	−0.00534078	−	0.0610454i
$799$	−16.1680	+	1.41452i	−0.571983	+	0.0500421i
$800$	−1.78573	+	4.67024i	−0.0631352	+	0.165118i
$801$	13.4437	−	6.26890i	0.475010	−	0.221501i
$802$	1.17708	+	1.68104i	0.0415640	+	0.0593595i
$803$	−14.9282	−	55.7129i	−0.526805	−	1.96606i
$804$	−0.334594	−	0.579535i	−0.0118002	−	0.0204386i
$805$	26.2769	−	21.6899i	0.926139	−	0.764468i
$806$	−6.38185	−	23.8174i	−0.224791	−	0.838932i
$807$	−0.0948196	+	1.08379i	−0.00333781	+	0.0381513i
$808$			6.98646i			0.245783i
$809$	−6.76987	−	0.592287i	−0.238016	−	0.0208237i	−0.0324763	−	0.999473i	$-0.510339\pi$
$809$	−6.76987	−	0.592287i	−0.238016	−	0.0208237i	−0.205540	+	0.978649i	$0.565895\pi$
$810$	−13.5938	+	13.3760i	−0.477636	+	0.469986i
$811$	5.84919	+	33.1724i	0.205393	+	1.16484i	0.896820	+	0.442395i	$0.145871\pi$
$811$	5.84919	+	33.1724i	0.205393	+	1.16484i	−0.691427	+	0.722446i	$0.743018\pi$
$812$	−13.2373	−	2.33409i	−0.464537	−	0.0819104i
$813$	3.62631	+	3.62631i	0.127180	+	0.127180i
$814$	22.3825	−	13.6297i	0.784507	−	0.477721i
$815$	13.0020	+	6.19121i	0.455441	+	0.216869i
$816$	0.188328	+	0.268961i	0.00659281	+	0.00941551i
$817$	−12.9233	−	9.04902i	−0.452130	−	0.316585i
$818$	0.635410	+	1.36264i	0.0222166	+	0.0476436i
$819$	−3.33566	+	38.1268i	−0.116557	+	1.33226i
$820$	−15.2027	−	7.23914i	−0.530903	−	0.252802i
$821$	−6.26864	+	5.26002i	−0.218777	+	0.183576i	−0.745589	−	0.666406i	$-0.767832\pi$
$821$	−6.26864	+	5.26002i	−0.218777	+	0.183576i	0.526812	+	0.849982i	$0.323387\pi$
$822$	0.0265127	+	0.0153071i	0.000924738	+	0.000533898i
$823$	−14.6691	+	31.4580i	−0.511333	+	1.09656i	0.465987	+	0.884791i	$0.345699\pi$
$823$	−14.6691	+	31.4580i	−0.511333	+	1.09656i	−0.977320	+	0.211766i	$0.932079\pi$
$824$	7.26711	−	4.19567i	0.253162	−	0.146163i
$825$	2.90018	−	4.00275i	0.100971	−	0.139358i
$826$	−2.05789	+	11.6709i	−0.0716031	+	0.406081i
$827$	2.71397	−	7.45656i	0.0943739	−	0.259290i	−0.883519	−	0.468394i	$-0.844833\pi$
$827$	2.71397	−	7.45656i	0.0943739	−	0.259290i	0.977893	+	0.209104i	$0.0670548\pi$
$828$	−18.7601	+	10.8311i	−0.651957	+	0.376408i
$829$	−1.30887	−	14.9604i	−0.0454588	−	0.519596i	−0.984451	−	0.175658i	$-0.943795\pi$
$829$	−1.30887	−	14.9604i	−0.0454588	−	0.519596i	0.938992	−	0.343938i	$-0.111761\pi$
$830$	7.43853	−	19.9350i	0.258195	−	0.691953i
$831$	4.09555	+	1.90979i	0.142073	+	0.0662498i
$832$	−1.08763	−	6.16825i	−0.0377067	−	0.213846i
$833$	−0.671309	−	3.80718i	−0.0232595	−	0.131911i
$834$	−4.48797	−	2.09278i	−0.155406	−	0.0724669i
$835$	8.82189	+	19.3244i	0.305294	+	0.668748i
$836$	1.36627	+	15.6166i	0.0472535	+	0.540110i
$837$	4.65281	−	2.68630i	0.160825	−	0.0928521i
$838$	6.14471	−	16.8825i	0.212265	−	0.583195i
$839$	−9.99901	+	56.7072i	−0.345204	+	1.95775i	−0.0646639	+	0.997907i	$0.520598\pi$
$839$	−9.99901	+	56.7072i	−0.345204	+	1.95775i	−0.280540	+	0.959842i	$0.590514\pi$
$840$	−0.876293	+	0.603104i	−0.0302350	+	0.0208091i
$841$	11.2881	−	6.51717i	0.389244	−	0.224730i
$842$	7.70296	−	16.5190i	0.265461	−	0.569284i
$843$	2.89572	+	1.67184i	0.0997339	+	0.0575814i
$844$	−20.7991	+	17.4525i	−0.715934	+	0.600740i
$845$	−25.2160	+	52.9555i	−0.867456	+	1.82172i
$846$	−2.91364	+	33.3031i	−0.100173	+	1.14498i
$847$	6.62453	+	14.2063i	0.227621	+	0.488136i
$848$	−4.04125	−	2.82971i	−0.138777	−	0.0971727i
$849$	4.11344	+	5.87460i	0.141173	+	0.201616i
$850$	−5.55412	+	4.50968i	−0.190505	+	0.154681i
$851$	8.79001	+	43.8342i	0.301318	+	1.50262i
$852$	0.998924	+	0.998924i	0.0342226	+	0.0342226i
$853$	19.4346	+	3.42684i	0.665427	+	0.117333i	0.496151	−	0.868236i	$-0.334746\pi$
$853$	19.4346	+	3.42684i	0.665427	+	0.117333i	0.169275	+	0.985569i	$0.445857\pi$
$854$	−2.67763	−	15.1856i	−0.0916266	−	0.519640i
$855$	−23.9798	−	0.193588i	−0.820092	−	0.00662057i
$856$	6.18231	+	0.540882i	0.211307	+	0.0184870i
$857$			32.6218i			1.11434i	0.830398	+	0.557170i	$0.188113\pi$
$857$			32.6218i			1.11434i	−0.830398	+	0.557170i	$0.811887\pi$
$858$	−0.539666	+	6.16841i	−0.0184239	+	0.210586i
$859$	−9.97841	−	37.2399i	−0.340459	−	1.27061i	−0.897828	−	0.440345i	$-0.854856\pi$
$859$	−9.97841	−	37.2399i	−0.340459	−	1.27061i	0.557369	−	0.830265i	$-0.311811\pi$
$860$	−0.922922	+	9.65105i	−0.0314714	+	0.329098i
$861$	−1.79122	−	3.10249i	−0.0610447	−	0.105732i
$862$	8.47548	+	31.6309i	0.288676	+	1.07735i
$863$	−0.463085	−	0.661354i	−0.0157636	−	0.0225128i	0.811193	−	0.584779i	$-0.198819\pi$
$863$	−0.463085	−	0.661354i	−0.0157636	−	0.0225128i	−0.826957	+	0.562266i	$0.809930\pi$
$864$	1.23686	−	0.576757i	0.0420788	−	0.0196217i
$865$	−28.2123	−	24.0637i	−0.959248	−	0.818191i
$866$	9.70769	−	0.849313i	0.329881	−	0.0288608i
$867$	−0.299043	−	3.41808i	−0.0101560	−	0.116084i
$868$	−7.66956	+	2.79149i	−0.260322	+	0.0947494i
$869$	10.8168	−	15.4480i	0.366935	−	0.524038i
$870$	0.886915	−	3.20625i	0.0300692	−	0.108702i
$871$	−7.71944	+	16.5544i	−0.261563	+	0.560924i
$872$	14.1261	−	1.23588i	0.478372	−	0.0418521i
$873$	−42.3997	−	35.5776i	−1.43501	−	1.20412i
$874$	−25.8322	−	6.92170i	−0.873786	−	0.234130i
$875$	−14.4650	−	18.1119i	−0.489006	−	0.612295i
$876$	−3.02543	−	0.533466i	−0.102220	−	0.0180241i
$877$	−10.0447	+	2.69148i	−0.339187	+	0.0908848i	−0.424392	−	0.905479i	$-0.639512\pi$
$877$	−10.0447	+	2.69148i	−0.339187	+	0.0908848i	0.0852051	+	0.996363i	$0.472845\pi$
$878$	−8.51307	+	31.7712i	−0.287302	+	1.07223i
$879$	1.12444	−	0.409263i	0.0379265	−	0.0138041i
$880$	7.93561	−	5.46164i	0.267510	−	0.184112i
$881$	24.4625	+	29.1533i	0.824164	+	0.982200i	0.999998	−	0.00221959i	$-0.000706517\pi$
$881$	24.4625	+	29.1533i	0.824164	+	0.982200i	−0.175834	+	0.984420i	$0.556262\pi$
$882$	−7.96306			−0.268130
$883$	−15.0032	−	17.8802i	−0.504899	−	0.601715i	0.452042	−	0.891997i	$-0.350696\pi$
$883$	−15.0032	−	17.8802i	−0.504899	−	0.601715i	−0.956941	+	0.290281i	$0.906251\pi$
$884$	3.06525	−	8.42169i	0.103095	−	0.283252i
$885$	−2.82685	−	0.781965i	−0.0950235	−	0.0262855i
$886$	13.9535	−	9.77036i	0.468778	−	0.328242i
$887$	−9.46958	+	9.46958i	−0.317957	+	0.317957i	−0.847982	−	0.530025i	$-0.822183\pi$
$887$	−9.46958	+	9.46958i	−0.317957	+	0.317957i	0.530025	+	0.847982i	$0.322183\pi$
$888$	−0.154113	−	1.38726i	−0.00517168	−	0.0465535i
$889$		−	25.9069i		−	0.868889i
$890$	−1.86466	−	11.0982i	−0.0625036	−	0.372012i
$891$	36.1860	−	6.38056i	1.21228	−	0.213757i
$892$	−10.6634	+	4.97241i	−0.357036	+	0.166489i
$893$	−31.6160	+	26.5290i	−1.05799	+	0.887759i
$894$	−0.756974	+	0.756974i	−0.0253170	+	0.0253170i
$895$	15.7735	−	26.8182i	0.527251	−	0.896435i
$896$	−2.00257	+	0.536588i	−0.0669013	+	0.0179261i
$897$	−9.57372	−	4.46430i	−0.319657	−	0.149059i
$898$	29.4451	+	7.88979i	0.982595	+	0.263286i
$899$	12.7618	−	22.1041i	0.425630	−	0.737213i
$900$	7.16135	+	12.8797i	0.238712	+	0.429322i
$901$	−2.98334	−	6.39779i	−0.0993894	−	0.213141i
$902$	16.2211	+	28.0958i	0.540104	+	0.935487i
$903$	−1.32587	+	1.58011i	−0.0441221	+	0.0525827i
$904$	5.15703	−	6.14591i	0.171520	−	0.204410i
$905$	−0.0564397	+	0.590193i	−0.00187612	+	0.0196187i
$906$	1.53106	+	1.07206i	0.0508661	+	0.0356168i
$907$	−41.6949	+	7.35194i	−1.38446	+	0.244117i	−0.815741	−	0.578417i	$-0.803671\pi$
$907$	−41.6949	+	7.35194i	−1.38446	+	0.244117i	−0.568716	+	0.822534i	$0.692560\pi$
$908$	−2.41603	−	6.63799i	−0.0801788	−	0.220290i
$909$	15.7740	+	13.2360i	0.523191	+	0.439009i
$910$	27.2041	+	10.1509i	0.901806	+	0.336500i
$911$	−9.15295	+	34.1593i	−0.303251	+	1.13175i	0.631190	+	0.775628i	$0.282567\pi$
$911$	−9.15295	+	34.1593i	−0.303251	+	1.13175i	−0.934441	+	0.356119i	$0.884100\pi$
$912$	0.784605	+	0.285573i	0.0259809	+	0.00945627i
$913$	−33.5814	+	23.5139i	−1.11138	+	0.778198i
$914$	13.8035	+	7.96943i	0.456578	+	0.263605i
$915$	3.80433	−	0.301911i	0.125767	−	0.00998086i
$916$	5.48853	+	15.0796i	0.181346	+	0.498244i
$917$	4.34528	−	7.52624i	0.143494	−	0.248538i
$918$	1.94532	+	0.170194i	0.0642053	+	0.00561723i
$919$	−16.2599	−	16.2599i	−0.536365	−	0.536365i	0.386095	−	0.922459i	$-0.373824\pi$
$919$	−16.2599	−	16.2599i	−0.536365	−	0.536365i	−0.922459	+	0.386095i	$0.873824\pi$
$920$	4.12529	+	15.9084i	0.136007	+	0.524484i
$921$	2.32023	+	0.844493i	0.0764540	+	0.0278270i
$922$	−2.31483	+	3.30592i	−0.0762349	+	0.108875i
$923$	6.69587	−	37.9741i	0.220397	−	1.24993i
$924$	2.04957			0.0674260
$925$	29.9128	−	5.49758i	0.983527	−	0.180759i
$926$	5.86085			0.192599
$927$	4.29469	−	24.3564i	0.141056	−	0.799969i
$928$	3.71872	−	5.31088i	0.122073	−	0.174338i
$929$	35.5614	+	12.9433i	1.16673	+	0.424656i	0.851498	−	0.524357i	$-0.175694\pi$
$929$	35.5614	+	12.9433i	1.16673	+	0.424656i	0.315235	+	0.949014i	$0.397917\pi$
$930$	−0.507041	−	1.95531i	−0.0166265	−	0.0641170i
$931$	−6.95149	−	6.95149i	−0.227826	−	0.227826i
$932$	1.43493	+	0.125540i	0.0470027	+	0.00411221i
$933$	−1.92461	+	3.33352i	−0.0630088	+	0.109135i
$934$	−7.40976	−	20.3581i	−0.242455	−	0.666139i
$935$	13.7411	−	1.09049i	0.449382	−	0.0356628i
$936$	−15.9872	−	9.23021i	−0.522558	−	0.301699i
$937$	3.49226	−	2.44531i	0.114087	−	0.0798847i	−0.515140	−	0.857106i	$-0.672260\pi$
$937$	3.49226	−	2.44531i	0.114087	−	0.0798847i	0.629228	+	0.777221i	$0.283371\pi$
$938$	5.68143	+	2.06787i	0.185505	+	0.0675184i
$939$	−0.685008	+	2.55649i	−0.0223544	+	0.0834278i
$940$	23.7623	+	8.86665i	0.775040	+	0.289198i
$941$	−6.09588	−	5.11505i	−0.198720	−	0.166746i	0.537998	−	0.842946i	$-0.319181\pi$
$941$	−6.09588	−	5.11505i	−0.198720	−	0.166746i	−0.736718	+	0.676200i	$0.763625\pi$
$942$	−0.432427	−	1.18808i	−0.0140892	−	0.0387098i
$943$	−54.5051	+	9.61073i	−1.77493	+	0.312968i
$944$	−4.68243	−	3.27867i	−0.152400	−	0.106712i
$945$	−0.602265	+	6.29792i	−0.0195917	+	0.204871i
$946$	12.0069	−	14.3093i	0.390378	−	0.465234i
$947$	−3.99255	+	4.75813i	−0.129740	+	0.154619i	−0.827004	−	0.562197i	$-0.809956\pi$
$947$	−3.99255	+	4.75813i	−0.129740	+	0.154619i	0.697263	+	0.716815i	$0.254401\pi$
$948$	−0.502230	−	0.869887i	−0.0163117	−	0.0282526i
$949$	35.4383	+	75.9978i	1.15038	+	2.46699i
$950$	−4.99191	+	17.4952i	−0.161959	+	0.567618i
$951$	0.161039	−	0.278928i	0.00522205	−	0.00904485i
$952$	−2.86544	−	0.767793i	−0.0928695	−	0.0248843i
$953$	46.4594	+	21.6644i	1.50497	+	0.701777i	0.988032	−	0.154248i	$-0.0492955\pi$
$953$	46.4594	+	21.6644i	1.50497	+	0.701777i	0.516934	+	0.856025i	$0.327073\pi$
$954$	−14.0451	+	3.76338i	−0.454728	+	0.121844i
$955$	−9.64539	+	16.3991i	−0.312118	+	0.530664i
$956$	21.7440	−	21.7440i	0.703250	−	0.703250i
$957$	−4.90992	+	4.11992i	−0.158715	+	0.133178i
$958$	2.40987	−	1.12374i	0.0778594	−	0.0363064i
$959$	−0.272395	+	0.0480305i	−0.00879608	+	0.00155099i
$960$	−0.0850177	−	0.506013i	−0.00274393	−	0.0163315i
$961$			15.5018i			0.500059i
$962$	−28.6051	+	25.1648i	−0.922266	+	0.811345i
$963$	12.9337	−	12.9337i	0.416782	−	0.416782i
$964$	−16.6146	+	11.6337i	−0.535121	+	0.374696i
$965$	52.9042	+	14.6344i	1.70305	+	0.471098i
$966$	−1.19589	+	3.28568i	−0.0384771	+	0.105715i
$967$	−16.1778	−	19.2800i	−0.520245	−	0.620003i	0.440394	−	0.897805i	$-0.354839\pi$
$967$	−16.1778	−	19.2800i	−0.520245	−	0.620003i	−0.960639	+	0.277801i	$0.910394\pi$
$968$	−7.56070			−0.243010
$969$	0.767956	+	0.915214i	0.0246703	+	0.0294009i
$970$	−34.5909	+	23.8070i	−1.11065	+	0.764396i
$971$	31.6662	−	11.5256i	1.01622	−	0.369873i	0.220400	−	0.975410i	$-0.429264\pi$
$971$	31.6662	−	11.5256i	1.01622	−	0.369873i	0.795817	+	0.605537i	$0.207042\pi$
$972$	1.56618	−	5.84508i	0.0502354	−	0.187481i
$973$	43.2157	−	11.5796i	1.38543	−	0.371225i
$974$	36.3154	+	6.40338i	1.16362	+	0.205177i
$975$	−3.14179	+	6.46307i	−0.100618	+	0.206984i
$976$	7.18421	+	1.92500i	0.229961	+	0.0616179i
$977$	−33.4695	−	28.0843i	−1.07079	−	0.898496i	−0.0756619	−	0.997134i	$-0.524107\pi$
$977$	−33.4695	−	28.0843i	−1.07079	−	0.898496i	−0.995123	+	0.0986380i	$0.968551\pi$
$978$	−1.47220	+	0.128801i	−0.0470759	+	0.00411860i
$979$	−9.16342	+	19.6510i	−0.292864	+	0.628049i
$980$	−1.61067	+	5.82268i	−0.0514511	+	0.185999i
$981$	23.9719	−	34.2354i	0.765362	−	1.09305i
$982$	9.53294	−	3.46971i	0.304208	−	0.110723i
$983$	1.67460	+	19.1407i	0.0534114	+	0.610495i	0.974982	+	0.222284i	$0.0713512\pi$
$983$	1.67460	+	19.1407i	0.0534114	+	0.610495i	−0.921571	+	0.388211i	$0.873093\pi$
$984$	1.72139	−	0.150602i	0.0548759	−	0.00480102i
$985$	20.5355	+	17.5157i	0.654315	+	0.558098i
$986$	8.40777	−	3.92061i	0.267758	−	0.124858i
$987$	3.09504	+	4.42018i	0.0985163	+	0.140696i
$988$	−5.89862	−	22.0140i	−0.187660	−	0.700358i
$989$	15.9334	+	27.5975i	0.506653	+	0.877549i
$990$	2.70288	−	28.2642i	0.0859031	−	0.898294i
$991$	−10.3866	−	38.7632i	−0.329941	−	1.23136i	−0.909251	−	0.416248i	$-0.863345\pi$
$991$	−10.3866	−	38.7632i	−0.329941	−	1.23136i	0.579310	−	0.815107i	$-0.303322\pi$
$992$	0.343112	−	3.92179i	0.0108938	−	0.124517i
$993$		−	3.42687i		−	0.108748i
$994$	−12.7150	−	1.11241i	−0.403294	−	0.0352836i
$995$	−27.6617	−	0.223312i	−0.876936	−	0.00707947i
$996$	0.379165	+	2.15035i	0.0120143	+	0.0681366i
$997$	−29.6463	−	5.22744i	−0.938907	−	0.165555i	−0.316805	−	0.948491i	$-0.602610\pi$
$997$	−29.6463	−	5.22744i	−0.938907	−	0.165555i	−0.622102	+	0.782936i	$0.713721\pi$
$998$	−28.3738	−	28.3738i	−0.898156	−	0.898156i
$999$	−6.90943	−	4.60121i	−0.218605	−	0.145576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.ba.a.87.7	✓	108
5.3	odd	4		370.2.bd.a.13.7	yes	108
37.20	odd	36		370.2.bd.a.57.7	yes	108
185.168	even	36	inner	370.2.ba.a.353.7	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.ba.a.87.7	✓	108	1.1	even	1	trivial
370.2.ba.a.353.7	yes	108	185.168	even	36	inner
370.2.bd.a.13.7	yes	108	5.3	odd	4
370.2.bd.a.57.7	yes	108	37.20	odd	36

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.131617 - 0.187969i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.561282 + 2.16448i) q^{5} +(-0.162258 - 0.162258i) q^{6} +(2.06533 + 0.180693i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.00805 + 2.76960i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.131617 - 0.187969i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.561282 + 2.16448i) q^{5} +(-0.162258 - 0.162258i) q^{6} +(2.06533 + 0.180693i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.00805 + 2.76960i) q^{9} +(2.22906 - 0.176897i) q^{10} +(-3.73102 - 2.15411i) q^{11} +(-0.187969 + 0.131617i) q^{12} +(5.88568 + 2.14221i) q^{13} +(0.536588 - 2.00257i) q^{14} +(0.480729 + 0.179379i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.489390 + 1.34459i) q^{17} +(2.90257 - 0.511801i) q^{18} +(2.98063 + 2.08706i) q^{19} +(0.212862 - 2.22591i) q^{20} +(0.305797 - 0.364435i) q^{21} +(-2.76927 + 3.30028i) q^{22} +(-3.67488 - 6.36507i) q^{23} +(0.0969772 + 0.207968i) q^{24} +(-4.36992 + 2.42976i) q^{25} +(3.13170 - 5.42427i) q^{26} +(1.31822 + 0.353216i) q^{27} +(-1.87897 - 0.876179i) q^{28} +(6.26247 - 1.67802i) q^{29} +(0.260131 - 0.442277i) q^{30} +(2.78372 - 2.78372i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.895972 + 0.417799i) q^{33} +(1.40914 - 0.248470i) q^{34} +(0.768126 + 4.57177i) q^{35} -2.94734i q^{36} +(-5.76298 - 1.94628i) q^{37} +(2.57294 - 2.57294i) q^{38} +(1.17733 - 0.824372i) q^{39} +(-2.15513 - 0.596154i) q^{40} +(2.57552 - 7.07618i) q^{41} +(-0.305797 - 0.364435i) q^{42} -4.33577 q^{43} +(2.76927 + 3.30028i) q^{44} +(-5.42893 + 3.73643i) q^{45} +(-6.90651 + 2.51376i) q^{46} +(-2.93566 + 10.9560i) q^{47} +(0.221649 - 0.0593906i) q^{48} +(-2.66073 - 0.469158i) q^{49} +(1.63402 + 4.72546i) q^{50} +(0.317153 + 0.0849808i) q^{51} +(-4.79805 - 4.02604i) q^{52} +(-4.91468 + 0.429979i) q^{53} +(0.576757 - 1.23686i) q^{54} +(2.56836 - 9.28477i) q^{55} +(-1.18915 + 1.69828i) q^{56} +(0.784605 - 0.285573i) q^{57} +(-0.565065 - 6.45872i) q^{58} +(-5.69444 + 0.498199i) q^{59} +(-0.390386 - 0.332980i) q^{60} +(6.74080 - 3.14328i) q^{61} +(-2.25804 - 3.22481i) q^{62} +(1.58151 + 5.90227i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.33324 + 13.9418i) q^{65} +(0.255867 + 0.954910i) q^{66} +(-0.254169 + 2.90517i) q^{67} -1.43088i q^{68} +(-1.68011 - 0.146991i) q^{69} +(4.63570 + 0.0374238i) q^{70} +(-1.06905 - 6.06286i) q^{71} +(-2.90257 - 0.511801i) q^{72} +(9.46672 + 9.46672i) q^{73} +(-2.91745 + 5.33746i) q^{74} +(-0.118437 + 1.14121i) q^{75} +(-2.08706 - 2.98063i) q^{76} +(-7.31655 - 5.12310i) q^{77} +(-0.607408 - 1.30259i) q^{78} +(-0.381511 + 4.36069i) q^{79} +(-0.961332 + 2.01887i) q^{80} +(-6.53350 + 5.48225i) q^{81} +(-6.52145 - 3.76516i) q^{82} +(4.02147 - 8.62408i) q^{83} +(-0.412000 + 0.237868i) q^{84} +(-2.63564 + 1.81397i) q^{85} +(-0.752899 + 4.26990i) q^{86} +(0.508833 - 1.39801i) q^{87} +(3.73102 - 2.15411i) q^{88} +(-0.438640 - 5.01367i) q^{89} +(2.73694 + 5.99528i) q^{90} +(11.7688 + 5.48786i) q^{91} +(1.27627 + 7.23809i) q^{92} +(-0.156867 - 0.889637i) q^{93} +(10.2798 + 4.79356i) q^{94} +(-2.84442 + 7.62294i) q^{95} +(-0.0199994 - 0.228594i) q^{96} +(-16.2633 + 9.38962i) q^{97} +(-0.924061 + 2.53884i) q^{98} +(2.20495 - 12.5049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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