LMFDB - Embedded newform 460.2.w.a.167.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.12
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28216 + 0.596717i) q^{2} +(-0.914180 - 1.67420i) q^{3} +(1.28786 - 1.53017i) q^{4} +(1.12269 - 1.93379i) q^{5} +(2.17114 + 1.60108i) q^{6} +(-0.498606 - 0.666060i) q^{7} +(-0.738158 + 2.73041i) q^{8} +(-0.345283 + 0.537271i) q^{9} +O(q^{10})$	\(q+(-1.28216 + 0.596717i) q^{2} +(-0.914180 - 1.67420i) q^{3} +(1.28786 - 1.53017i) q^{4} +(1.12269 - 1.93379i) q^{5} +(2.17114 + 1.60108i) q^{6} +(-0.498606 - 0.666060i) q^{7} +(-0.738158 + 2.73041i) q^{8} +(-0.345283 + 0.537271i) q^{9} +(-0.285542 + 3.14936i) q^{10} +(5.53313 - 2.52690i) q^{11} +(-3.73914 - 0.757274i) q^{12} +(4.48251 + 3.35557i) q^{13} +(1.03674 + 0.556467i) q^{14} +(-4.26389 - 0.111772i) q^{15} +(-0.682845 - 3.94128i) q^{16} +(1.70676 - 0.122070i) q^{17} +(0.122109 - 0.894903i) q^{18} +(-2.71712 - 3.13572i) q^{19} +(-1.51317 - 4.20836i) q^{20} +(-0.659299 + 1.44366i) q^{21} +(-5.58651 + 6.54160i) q^{22} +(-4.06898 + 2.53839i) q^{23} +(5.24604 - 1.26026i) q^{24} +(-2.47912 - 4.34212i) q^{25} +(-7.74962 - 1.62758i) q^{26} +(-4.49285 - 0.321335i) q^{27} +(-1.66132 - 0.0948378i) q^{28} +(4.36657 + 3.78365i) q^{29} +(5.53368 - 2.40103i) q^{30} +(-1.04849 - 3.57083i) q^{31} +(3.22735 + 4.64588i) q^{32} +(-9.28880 - 6.95351i) q^{33} +(-2.11549 + 1.17496i) q^{34} +(-1.84780 + 0.216421i) q^{35} +(0.377441 + 1.22027i) q^{36} +(-0.270108 - 1.24167i) q^{37} +(5.35491 + 2.39914i) q^{38} +(1.52005 - 10.5722i) q^{39} +(4.45132 + 4.49286i) q^{40} +(-2.91347 + 1.87237i) q^{41} +(-0.0161330 - 2.24442i) q^{42} +(-0.345846 - 0.633370i) q^{43} +(3.25930 - 11.7209i) q^{44} +(0.651325 + 1.27090i) q^{45} +(3.70237 - 5.68265i) q^{46} +(2.59286 - 2.59286i) q^{47} +(-5.97424 + 4.74626i) q^{48} +(1.77710 - 6.05225i) q^{49} +(5.76964 + 4.08794i) q^{50} +(-1.76465 - 2.74585i) q^{51} +(10.9074 - 2.53752i) q^{52} +(-1.76383 - 2.35620i) q^{53} +(5.95229 - 2.26896i) q^{54} +(1.32551 - 13.5369i) q^{55} +(2.18666 - 0.869740i) q^{56} +(-2.76588 + 7.41560i) q^{57} +(-7.85640 - 2.24563i) q^{58} +(1.91686 + 13.3321i) q^{59} +(-5.66232 + 6.38054i) q^{60} +(-11.0538 + 3.24570i) q^{61} +(3.47511 + 3.95272i) q^{62} +(0.530015 - 0.0379074i) q^{63} +(-6.91024 - 4.03094i) q^{64} +(11.5215 - 4.90099i) q^{65} +(16.0590 + 3.37271i) q^{66} +(-4.03801 - 10.8263i) q^{67} +(2.01127 - 2.76884i) q^{68} +(7.96954 + 4.49171i) q^{69} +(2.24003 - 1.38010i) q^{70} +(6.29845 + 2.87641i) q^{71} +(-1.21210 - 1.33936i) q^{72} +(2.64676 + 0.189300i) q^{73} +(1.08724 + 1.43083i) q^{74} +(-5.00319 + 8.12001i) q^{75} +(-8.29745 + 0.119291i) q^{76} +(-4.44192 - 2.42547i) q^{77} +(4.35966 + 14.4623i) q^{78} +(1.84232 + 12.8136i) q^{79} +(-8.38826 - 3.10437i) q^{80} +(4.36522 + 9.55849i) q^{81} +(2.61825 - 4.13919i) q^{82} +(1.54925 + 7.12178i) q^{83} +(1.35997 + 2.86807i) q^{84} +(1.68011 - 3.43756i) q^{85} +(0.821372 + 0.605708i) q^{86} +(2.34274 - 10.7694i) q^{87} +(2.81513 + 16.9730i) q^{88} +(-2.81622 + 9.59117i) q^{89} +(-1.59347 - 1.24084i) q^{90} -4.65873i q^{91} +(-1.35609 + 9.49532i) q^{92} +(-5.01976 + 5.01976i) q^{93} +(-1.77725 + 4.87165i) q^{94} +(-9.11433 + 1.73389i) q^{95} +(4.82774 - 9.65038i) q^{96} +(-2.89037 - 0.628762i) q^{97} +(1.33296 + 8.82036i) q^{98} +(-0.552869 + 3.84529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−1.28216	+	0.596717i	−0.906623	+	0.421943i
$2$	−1.28216	+	0.596717i	−0.906623	+	0.421943i
$3$	−0.914180	−	1.67420i	−0.527802	−	0.966597i	−0.996528	−	0.0832538i	$-0.973469\pi$
$3$	−0.914180	−	1.67420i	−0.527802	−	0.966597i	0.468726	−	0.883343i	$-0.344713\pi$
$4$	1.28786	−	1.53017i	0.643929	−	0.765085i
$5$	1.12269	−	1.93379i	0.502084	−	0.864819i
$5$	1.12269	−	1.93379i	0.502084	−	0.864819i
$6$	2.17114	+	1.60108i	0.886366	+	0.653637i
$7$	−0.498606	−	0.666060i	−0.188455	−	0.251747i	0.696356	−	0.717697i	$-0.254804\pi$
$7$	−0.498606	−	0.666060i	−0.188455	−	0.251747i	−0.884811	+	0.465950i	$0.845713\pi$
$8$	−0.738158	+	2.73041i	−0.260978	+	0.965345i
$9$	−0.345283	+	0.537271i	−0.115094	+	0.179090i
$10$	−0.285542	+	3.14936i	−0.0902964	+	0.995915i
$11$	5.53313	−	2.52690i	1.66830	−	0.761888i	0.668467	−	0.743742i	$-0.266951\pi$
$11$	5.53313	−	2.52690i	1.66830	−	0.761888i	0.999835	−	0.0181465i	$-0.00577651\pi$
$12$	−3.73914	−	0.757274i	−1.07940	−	0.218606i
$13$	4.48251	+	3.35557i	1.24323	+	0.930667i	0.999235	−	0.0391104i	$-0.0124524\pi$
$13$	4.48251	+	3.35557i	1.24323	+	0.930667i	0.243991	+	0.969778i	$0.421543\pi$
$14$	1.03674	+	0.556467i	0.277081	+	0.148722i
$15$	−4.26389	−	0.111772i	−1.10093	−	0.0288595i
$16$	−0.682845	−	3.94128i	−0.170711	−	0.985321i
$17$	1.70676	−	0.122070i	0.413949	−	0.0296062i	0.137188	−	0.990545i	$-0.456193\pi$
$17$	1.70676	−	0.122070i	0.413949	−	0.0296062i	0.276761	+	0.960939i	$0.410739\pi$
$18$	0.122109	−	0.894903i	0.0287813	−	0.210931i
$19$	−2.71712	−	3.13572i	−0.623350	−	0.719384i	0.352990	−	0.935627i	$-0.385165\pi$
$19$	−2.71712	−	3.13572i	−0.623350	−	0.719384i	−0.976339	+	0.216243i	$0.930620\pi$
$20$	−1.51317	−	4.20836i	−0.338354	−	0.941019i
$21$	−0.659299	+	1.44366i	−0.143871	+	0.315033i
$22$	−5.58651	+	6.54160i	−1.19105	+	1.39467i
$23$	−4.06898	+	2.53839i	−0.848440	+	0.529291i
$23$	−4.06898	+	2.53839i	−0.848440	+	0.529291i
$24$	5.24604	−	1.26026i	1.07084	−	0.257250i
$25$	−2.47912	−	4.34212i	−0.495824	−	0.868423i
$26$	−7.74962	−	1.62758i	−1.51982	−	0.319194i
$27$	−4.49285	−	0.321335i	−0.864649	−	0.0618409i
$28$	−1.66132	−	0.0948378i	−0.313960	−	0.0179227i
$29$	4.36657	+	3.78365i	0.810851	+	0.702606i	0.958081	−	0.286496i	$-0.0924905\pi$
$29$	4.36657	+	3.78365i	0.810851	+	0.702606i	−0.147230	+	0.989102i	$0.547036\pi$
$30$	5.53368	−	2.40103i	1.01031	−	0.438366i
$31$	−1.04849	−	3.57083i	−0.188314	−	0.641340i	−0.998479	−	0.0551373i	$-0.982440\pi$
$31$	−1.04849	−	3.57083i	−0.188314	−	0.641340i	0.810164	−	0.586203i	$-0.199378\pi$
$32$	3.22735	+	4.64588i	0.570520	+	0.821284i
$33$	−9.28880	−	6.95351i	−1.61697	−	1.21045i
$34$	−2.11549	+	1.17496i	−0.362804	+	0.201505i
$35$	−1.84780	+	0.216421i	−0.312336	+	0.0365818i
$36$	0.377441	+	1.22027i	0.0629068	+	0.203379i
$37$	−0.270108	−	1.24167i	−0.0444055	−	0.204129i	0.949599	−	0.313467i	$-0.101490\pi$
$37$	−0.270108	−	1.24167i	−0.0444055	−	0.204129i	−0.994005	+	0.109338i	$0.965127\pi$
$38$	5.35491	+	2.39914i	0.868681	+	0.389192i
$39$	1.52005	−	10.5722i	0.243403	−	1.69291i
$40$	4.45132	+	4.49286i	0.703815	+	0.710383i
$41$	−2.91347	+	1.87237i	−0.455007	+	0.292415i	−0.747999	−	0.663700i	$-0.768985\pi$
$41$	−2.91347	+	1.87237i	−0.455007	+	0.292415i	0.292992	+	0.956115i	$0.405349\pi$
$42$	−0.0161330	−	2.24442i	−0.00248938	−	0.346321i
$43$	−0.345846	−	0.633370i	−0.0527411	−	0.0965880i	0.849979	−	0.526817i	$-0.176615\pi$
$43$	−0.345846	−	0.633370i	−0.0527411	−	0.0965880i	−0.902720	+	0.430229i	$0.858433\pi$
$44$	3.25930	−	11.7209i	0.491359	−	1.76700i
$45$	0.651325	+	1.27090i	0.0970938	+	0.189454i
$46$	3.70237	−	5.68265i	0.545884	−	0.837860i
$47$	2.59286	−	2.59286i	0.378207	−	0.378207i	−0.492248	−	0.870455i	$-0.663825\pi$
$47$	2.59286	−	2.59286i	0.378207	−	0.378207i	0.870455	+	0.492248i	$0.163825\pi$
$48$	−5.97424	+	4.74626i	−0.862307	+	0.685063i
$49$	1.77710	−	6.05225i	0.253871	−	0.864607i
$50$	5.76964	+	4.08794i	0.815950	+	0.578123i
$51$	−1.76465	−	2.74585i	−0.247101	−	0.384496i
$52$	10.9074	−	2.53752i	1.51259	−	0.351890i
$53$	−1.76383	−	2.35620i	−0.242280	−	0.323649i	0.662875	−	0.748730i	$-0.269336\pi$
$53$	−1.76383	−	2.35620i	−0.242280	−	0.323649i	−0.905155	+	0.425082i	$0.860245\pi$
$54$	5.95229	−	2.26896i	0.810004	−	0.308766i
$55$	1.32551	−	13.5369i	0.178732	−	1.82531i
$56$	2.18666	−	0.869740i	0.292205	−	0.116224i
$57$	−2.76588	+	7.41560i	−0.366349	+	0.982220i
$58$	−7.85640	−	2.24563i	−1.03160	−	0.294866i
$59$	1.91686	+	13.3321i	0.249554	+	1.73569i	0.600796	+	0.799402i	$0.294850\pi$
$59$	1.91686	+	13.3321i	0.249554	+	1.73569i	−0.351242	+	0.936285i	$0.614240\pi$
$60$	−5.66232	+	6.38054i	−0.731002	+	0.823724i
$61$	−11.0538	+	3.24570i	−1.41530	+	0.415570i	−0.897910	−	0.440180i	$-0.854915\pi$
$61$	−11.0538	+	3.24570i	−1.41530	+	0.415570i	−0.517391	+	0.855749i	$0.673097\pi$
$62$	3.47511	+	3.95272i	0.441339	+	0.501996i
$63$	0.530015	−	0.0379074i	0.0667756	−	0.00477589i
$64$	−6.91024	−	4.03094i	−0.863781	−	0.503868i
$65$	11.5215	−	4.90099i	1.42906	−	0.607893i
$66$	16.0590	+	3.37271i	1.97672	+	0.415152i
$67$	−4.03801	−	10.8263i	−0.493321	−	1.32265i	−0.910383	−	0.413767i	$-0.864213\pi$
$67$	−4.03801	−	10.8263i	−0.493321	−	1.32265i	0.417062	−	0.908878i	$-0.363060\pi$
$68$	2.01127	−	2.76884i	0.243903	−	0.335771i
$69$	7.96954	+	4.49171i	0.959420	+	0.540739i
$70$	2.24003	−	1.38010i	0.267735	−	0.164954i
$71$	6.29845	+	2.87641i	0.747488	+	0.341367i	0.752475	−	0.658621i	$-0.228860\pi$
$71$	6.29845	+	2.87641i	0.747488	+	0.341367i	−0.00498639	+	0.999988i	$0.501587\pi$
$72$	−1.21210	−	1.33936i	−0.142847	−	0.157845i
$73$	2.64676	+	0.189300i	0.309780	+	0.0221559i	0.225364	−	0.974275i	$-0.427643\pi$
$73$	2.64676	+	0.189300i	0.309780	+	0.0221559i	0.0844161	+	0.996431i	$0.473098\pi$
$74$	1.08724	+	1.43083i	0.126390	+	0.166331i
$75$	−5.00319	+	8.12001i	−0.577718	+	0.937618i
$76$	−8.29745	+	0.119291i	−0.951783	+	0.0136836i
$77$	−4.44192	−	2.42547i	−0.506204	−	0.276408i
$78$	4.35966	+	14.4623i	0.493635	+	1.63753i
$79$	1.84232	+	12.8136i	0.207277	+	1.44164i	0.781991	+	0.623290i	$0.214204\pi$
$79$	1.84232	+	12.8136i	0.207277	+	1.44164i	−0.574714	+	0.818355i	$0.694887\pi$
$80$	−8.38826	−	3.10437i	−0.937836	−	0.347079i
$81$	4.36522	+	9.55849i	0.485024	+	1.06205i
$82$	2.61825	−	4.13919i	0.289137	−	0.457097i
$83$	1.54925	+	7.12178i	0.170052	+	0.781717i	0.980596	+	0.196039i	$0.0628080\pi$
$83$	1.54925	+	7.12178i	0.170052	+	0.781717i	−0.810544	+	0.585678i	$0.800828\pi$
$84$	1.35997	+	2.86807i	0.148385	+	0.312932i
$85$	1.68011	−	3.43756i	0.182233	−	0.372856i
$86$	0.821372	+	0.605708i	0.0885708	+	0.0653152i
$87$	2.34274	−	10.7694i	0.251169	−	1.15460i
$88$	2.81513	+	16.9730i	0.300094	+	1.80932i
$89$	−2.81622	+	9.59117i	−0.298519	+	1.01666i	0.664513	+	0.747276i	$0.268639\pi$
$89$	−2.81622	+	9.59117i	−0.298519	+	1.01666i	−0.963032	+	0.269386i	$0.913179\pi$
$90$	−1.59347	−	1.24084i	−0.167966	−	0.130795i
$91$		−	4.65873i		−	0.488367i
$92$	−1.35609	+	9.49532i	−0.141382	+	0.989955i
$93$	−5.01976	+	5.01976i	−0.520525	+	0.520525i
$94$	−1.77725	+	4.87165i	−0.183309	+	0.502473i
$95$	−9.11433	+	1.73389i	−0.935110	+	0.177894i
$96$	4.82774	−	9.65038i	0.492729	−	0.984938i
$97$	−2.89037	−	0.628762i	−0.293473	−	0.0638411i	0.0634184	−	0.997987i	$-0.479800\pi$
$97$	−2.89037	−	0.628762i	−0.293473	−	0.0638411i	−0.356891	+	0.934146i	$0.616163\pi$
$98$	1.33296	+	8.82036i	0.134649	+	0.890991i
$99$	−0.552869	+	3.84529i	−0.0555654	+	0.386466i
$100$	−9.83693	−	1.79855i	−0.983693	−	0.179855i
$101$	−0.636169	−	0.408841i	−0.0633012	−	0.0406812i	0.508607	−	0.860999i	$-0.330160\pi$
$101$	−0.636169	−	0.408841i	−0.0633012	−	0.0406812i	−0.571909	+	0.820317i	$0.693797\pi$
$102$	3.90106	+	2.46762i	0.386262	+	0.244331i
$103$	−2.05320	+	5.50483i	−0.202307	+	0.542407i	−0.997994	−	0.0633008i	$-0.979837\pi$
$103$	−2.05320	+	5.50483i	−0.202307	+	0.542407i	0.795687	+	0.605708i	$0.207110\pi$
$104$	−12.4709	+	9.76215i	−1.22287	+	0.957257i
$105$	2.05156	+	2.89574i	0.200211	+	0.282595i
$106$	3.66749	+	1.96851i	0.356218	+	0.191199i
$107$	−1.24103	+	2.27277i	−0.119974	+	0.219717i	−0.930764	−	0.365621i	$-0.880856\pi$
$107$	−1.24103	+	2.27277i	−0.119974	+	0.219717i	0.810789	+	0.585338i	$0.199038\pi$
$108$	−6.27785	+	6.46099i	−0.604086	+	0.621709i
$109$	−8.53164	−	7.39271i	−0.817183	−	0.708093i	0.142311	−	0.989822i	$-0.454547\pi$
$109$	−8.53164	−	7.39271i	−0.817183	−	0.708093i	−0.959494	+	0.281729i	$0.909092\pi$
$110$	6.37816	+	18.1474i	0.608134	+	1.73028i
$111$	−1.83186	+	1.58732i	−0.173873	+	0.150662i
$112$	−2.28466	+	2.41996i	−0.215880	+	0.228665i
$113$	−3.46480	−	9.28949i	−0.325941	−	0.873881i	−0.991800	−	0.127803i	$-0.959207\pi$
$113$	−3.46480	−	9.28949i	−0.325941	−	0.873881i	0.665859	−	0.746078i	$-0.268065\pi$
$114$	−0.878725	−	11.1584i	−0.0823001	−	1.04508i
$115$	0.340516	+	10.7184i	0.0317533	+	0.999496i
$116$	11.4131	−	1.80879i	1.05968	−	0.167942i
$117$	−3.35059	+	1.24970i	−0.309762	+	0.115535i
$118$	−10.4132	−	15.9500i	−0.958612	−	1.46832i
$119$	−0.932305	−	1.07594i	−0.0854643	−	0.0986310i
$120$	3.45261	−	11.5597i	0.315179	−	1.05525i
$121$	17.0269	−	19.6501i	1.54790	−	1.78637i
$122$	12.2360	−	10.7575i	1.10780	−	0.973940i
$123$	5.79815	+	3.16603i	0.522801	+	0.285471i
$124$	−6.81429	−	2.99435i	−0.611941	−	0.268901i
$125$	−11.1800	−	0.0807560i	−0.999974	−	0.00722304i
$126$	−0.656943	+	0.364872i	−0.0585251	+	0.0325054i
$127$	10.3032	+	3.84291i	0.914265	+	0.341003i	0.762181	−	0.647364i	$-0.224129\pi$
$127$	10.3032	+	3.84291i	0.914265	+	0.341003i	0.152084	+	0.988368i	$0.451401\pi$
$128$	11.2654	+	1.04485i	0.995726	+	0.0923523i
$129$	−0.744220	+	1.15803i	−0.0655249	+	0.101959i
$130$	−11.8478	+	13.1589i	−1.03912	+	1.15411i
$131$	20.0574	+	2.88382i	1.75242	+	0.251961i	0.942412	−	0.334453i	$-0.108552\pi$
$131$	20.0574	+	2.88382i	1.75242	+	0.251961i	0.810012	+	0.586414i	$0.199461\pi$
$132$	−22.6027	+	5.25832i	−1.96731	+	0.457678i
$133$	−0.733806	+	3.37325i	−0.0636291	+	0.292498i
$134$	11.6376	+	11.4715i	1.00534	+	0.990987i
$135$	−5.66549	+	8.32749i	−0.487607	+	0.716716i
$136$	−0.926557	+	4.75025i	−0.0794516	+	0.407330i
$137$	−7.74538	−	7.74538i	−0.661733	−	0.661733i	0.294055	−	0.955788i	$-0.404995\pi$
$137$	−7.74538	−	7.74538i	−0.661733	−	0.661733i	−0.955788	+	0.294055i	$0.904995\pi$
$138$	−12.8985	−	1.00353i	−1.09799	−	0.0854259i
$139$	−6.61738			−0.561279			−0.280639	−	0.959813i	$-0.590546\pi$
$139$	−6.61738			−0.561279			−0.280639	+	0.959813i	$0.590546\pi$
$140$	−2.04855	+	3.10617i	−0.173134	+	0.262520i
$141$	−6.71129	−	1.97061i	−0.565192	−	0.165955i
$142$	−9.79201	+	0.0703855i	−0.821727	+	0.00590662i
$143$	33.2815	+	7.23995i	2.78314	+	0.605435i
$144$	2.35331	+	0.993987i	0.196110	+	0.0828322i
$145$	12.2191	−	4.19616i	1.01474	−	0.348472i
$146$	−3.50652	+	1.33665i	−0.290202	+	0.110622i
$147$	−11.7572	+	2.55763i	−0.969720	+	0.210950i
$148$	−2.24782	−	1.18578i	−0.184770	−	0.0974703i
$149$	8.61175	−	3.93285i	0.705502	−	0.322192i	−0.0301559	−	0.999545i	$-0.509600\pi$
$149$	8.61175	−	3.93285i	0.705502	−	0.322192i	0.735658	+	0.677353i	$0.236873\pi$
$150$	1.56953	−	13.3966i	0.128152	−	1.09383i
$151$	−2.17857	+	0.313231i	−0.177289	+	0.0254903i	−0.230388	−	0.973099i	$-0.573999\pi$
$151$	−2.17857	+	0.313231i	−0.177289	+	0.0254903i	0.0530984	+	0.998589i	$0.483090\pi$
$152$	10.5675	−	5.10418i	0.857134	−	0.414004i
$153$	−0.523730	+	0.959140i	−0.0423411	+	0.0775419i
$154$	7.14256	+	0.459269i	0.575564	+	0.0370089i
$155$	−8.08239	−	1.98138i	−0.649193	−	0.159148i
$156$	−14.2197	−	15.9414i	−1.13848	−	1.27634i
$157$	−1.09350	+	15.2891i	−0.0872707	+	1.22020i	0.745469	+	0.666540i	$0.232225\pi$
$157$	−1.09350	+	15.2891i	−0.0872707	+	1.22020i	−0.832740	+	0.553664i	$0.813229\pi$
$158$	−10.0082	−	15.3297i	−0.796213	−	1.21957i
$159$	−2.33228	+	5.10698i	−0.184962	+	0.405010i
$160$	12.6075	−	1.02512i	0.996711	−	0.0810429i
$161$	3.71954	+	1.44452i	0.293141	+	0.113844i
$162$	−11.3006	−	9.65070i	−0.887860	−	0.758230i
$163$	−11.5166	+	4.29548i	−0.902051	+	0.336448i	−0.757336	−	0.653026i	$-0.773499\pi$
$163$	−11.5166	+	4.29548i	−0.902051	+	0.336448i	−0.144715	+	0.989473i	$0.546227\pi$
$164$	−0.887083	+	6.86945i	−0.0692695	+	0.536414i
$165$	−23.8751	+	10.1560i	−1.85868	+	0.790641i
$166$	−6.23607	−	8.20679i	−0.484013	−	0.636970i
$167$	−0.635925	−	8.89139i	−0.0492093	−	0.688037i	−0.960854	−	0.277056i	$-0.910641\pi$
$167$	−0.635925	−	8.89139i	−0.0492093	−	0.688037i	0.911644	−	0.410980i	$-0.134813\pi$
$168$	−3.45512	−	2.86580i	−0.266568	−	0.221102i
$169$	5.17057	+	17.6094i	0.397736	+	1.35457i
$170$	−0.102910	+	5.41005i	−0.00789283	+	0.414932i
$171$	2.62291	−	0.377117i	0.200579	−	0.0288389i
$172$	−1.41457	−	0.286487i	−0.107860	−	0.0218444i
$173$	20.4223	+	7.61711i	1.55268	+	0.579118i	0.971993	−	0.235012i	$-0.0755128\pi$
$173$	20.4223	+	7.61711i	1.55268	+	0.579118i	0.580683	+	0.814130i	$0.302786\pi$
$174$	3.42253	+	15.2061i	0.259461	+	1.15277i
$175$	−1.65600	+	3.81625i	−0.125182	+	0.288481i
$176$	−13.7375	−	20.0822i	−1.03550	−	1.51375i
$177$	20.5681	−	15.3971i	1.54600	−	1.15732i
$178$	−2.11237	−	13.9779i	−0.158329	−	1.04769i
$179$	−5.07634	+	3.26236i	−0.379423	+	0.243841i	−0.716426	−	0.697663i	$-0.754223\pi$
$179$	−5.07634	+	3.26236i	−0.379423	+	0.243841i	0.337003	+	0.941504i	$0.390587\pi$
$180$	2.78350	+	0.640097i	0.207470	+	0.0477100i
$181$	11.3859	+	3.34320i	0.846307	+	0.248498i	0.676008	−	0.736894i	$-0.263708\pi$
$181$	11.3859	+	3.34320i	0.846307	+	0.248498i	0.170299	+	0.985392i	$0.445527\pi$
$182$	2.77994	+	5.97323i	0.206063	+	0.442765i
$183$	15.5391	+	15.5391i	1.14869	+	1.14869i
$184$	−3.92730	−	12.9837i	−0.289524	−	0.957171i
$185$	−2.70437	−	0.871677i	−0.198830	−	0.0640870i
$186$	3.44075	−	9.43150i	0.252288	−	0.691551i
$187$	9.13526	−	4.98823i	0.668036	−	0.364775i
$188$	−0.628283	−	7.30674i	−0.0458222	−	0.532899i
$189$	2.02613	+	3.15273i	0.147380	+	0.229327i
$190$	10.6514	−	7.66180i	0.772731	−	0.555845i
$191$	4.56862	+	0.656868i	0.330573	+	0.0475293i	0.305603	−	0.952159i	$-0.401142\pi$
$191$	4.56862	+	0.656868i	0.330573	+	0.0475293i	0.0249701	+	0.999688i	$0.492051\pi$
$192$	−0.431383	+	15.2541i	−0.0311324	+	1.10087i
$193$	17.8930	−	3.89239i	1.28797	−	0.280180i	0.484113	−	0.875005i	$-0.339142\pi$
$193$	17.8930	−	3.89239i	1.28797	−	0.280180i	0.803855	+	0.594825i	$0.202779\pi$
$194$	4.08111	−	0.918562i	0.293006	−	0.0659489i
$195$	−18.7379	−	14.8088i	−1.34185	−	1.06048i
$196$	−6.97232	−	10.5137i	−0.498023	−	0.750979i
$197$	2.13245	−	2.84862i	0.151931	−	0.202955i	−0.718118	−	0.695921i	$-0.754996\pi$
$197$	2.13245	−	2.84862i	0.151931	−	0.202955i	0.870049	+	0.492966i	$0.164087\pi$
$198$	−1.58568	−	5.26017i	−0.112690	−	0.373824i
$199$	24.7254	−	7.26003i	1.75274	−	0.514650i	0.761663	−	0.647973i	$-0.224383\pi$
$199$	24.7254	−	7.26003i	1.75274	−	0.514650i	0.991073	+	0.133324i	$0.0425649\pi$
$200$	13.6857	−	3.56384i	0.967727	−	0.252001i
$201$	−14.4339	+	16.6576i	−1.01809	+	1.17494i
$202$	1.05963	+	0.144586i	0.0745554	+	0.0101730i
$203$	0.342941	−	4.79495i	0.0240698	−	0.336539i
$204$	−6.47424	−	0.836048i	−0.453288	−	0.0585351i
$205$	0.349851	+	7.73614i	0.0244347	+	0.540316i
$206$	−0.652305	−	8.28324i	−0.0454482	−	0.577121i
$207$	0.0411443	−	3.06261i	0.00285973	−	0.212866i
$208$	10.1644	−	19.9582i	0.704773	−	1.38385i
$209$	−22.9578	−	10.4845i	−1.58803	−	0.725227i
$210$	−4.35835	−	2.48859i	−0.300755	−	0.171729i
$211$	−20.3507	+	17.6340i	−1.40100	+	1.21397i	−0.454714	+	0.890637i	$0.650259\pi$
$211$	−20.3507	+	17.6340i	−1.40100	+	1.21397i	−0.946285	+	0.323335i	$0.895196\pi$
$212$	−5.87695	−	0.335490i	−0.403630	−	0.0230416i
$213$	−0.942251	−	13.1744i	−0.0645620	−	0.902694i
$214$	0.234991	−	3.65459i	0.0160637	−	0.249823i
$215$	−1.61309	−	0.0422849i	−0.110012	−	0.00288381i
$216$	4.19381	−	12.0301i	0.285353	−	0.818545i
$217$	−1.85560	+	2.47880i	−0.125967	+	0.168272i
$218$	15.3503	+	4.38764i	1.03965	+	0.297169i
$219$	−2.10269	−	4.60425i	−0.142087	−	0.311126i
$220$	−19.0067	−	19.4618i	−1.28143	−	1.31212i
$221$	8.06018	+	5.17996i	0.542186	+	0.348442i
$222$	1.40156	−	3.12830i	0.0940665	−	0.209958i
$223$	10.4358	−	7.81213i	0.698832	−	0.523139i	−0.189764	−	0.981830i	$-0.560772\pi$
$223$	10.4358	−	7.81213i	0.698832	−	0.523139i	0.888596	+	0.458691i	$0.151681\pi$
$224$	1.48526	−	4.46607i	0.0992382	−	0.298402i
$225$	3.18889	+	0.167300i	0.212593	+	0.0111533i
$226$	9.98561	+	9.84308i	0.664233	+	0.654752i
$227$	−9.93311	+	5.42389i	−0.659284	+	0.359996i	−0.773804	−	0.633425i	$-0.781649\pi$
$227$	−9.93311	+	5.42389i	−0.659284	+	0.359996i	0.114521	+	0.993421i	$0.463467\pi$
$228$	7.78508	+	13.7825i	0.515579	+	0.912768i
$229$		−	12.6769i		−	0.837715i	−0.908052	−	0.418857i	$-0.862431\pi$
$229$		−	12.6769i		−	0.837715i	0.908052	−	0.418857i	$-0.137569\pi$
$230$	−6.83244	−	13.5395i	−0.450518	−	0.892767i
$231$			9.65396i			0.635184i
$232$	−13.5541	+	9.12957i	−0.889872	+	0.599386i
$233$	0.642572	−	0.350871i	0.0420963	−	0.0229863i	−0.458063	−	0.888920i	$-0.651457\pi$
$233$	0.642572	−	0.350871i	0.0420963	−	0.0229863i	0.500159	+	0.865933i	$0.333275\pi$
$234$	3.55026	−	3.60167i	0.232088	−	0.235449i
$235$	−2.10307	−	7.92503i	−0.137189	−	0.516972i
$236$	22.8690	+	14.2367i	1.48864	+	0.926729i
$237$	19.7683	−	14.7984i	1.28409	−	0.961257i
$238$	1.83739	+	0.823199i	0.119100	+	0.0533601i
$239$	−8.90913	−	5.72555i	−0.576284	−	0.370355i	0.219797	−	0.975546i	$-0.429461\pi$
$239$	−8.90913	−	5.72555i	−0.576284	−	0.370355i	−0.796081	+	0.605190i	$0.793097\pi$
$240$	2.47105	+	16.8815i	0.159506	+	1.08970i
$241$	−5.54561	−	12.1432i	−0.357224	−	0.782212i	−0.999871	−	0.0160493i	$-0.994891\pi$
$241$	−5.54561	−	12.1432i	−0.357224	−	0.782212i	0.642647	−	0.766162i	$-0.277836\pi$
$242$	−10.1056	+	35.3547i	−0.649614	+	2.27269i
$243$	3.91416	−	5.22871i	0.251094	−	0.335422i
$244$	−9.26931	+	21.0943i	−0.593407	+	1.35042i
$245$	−9.70866	−	10.2314i	−0.620264	−	0.653658i
$246$	−9.32336	−	0.599495i	−0.594436	−	0.0382224i
$247$	−1.65739	−	23.1734i	−0.105457	−	1.47449i
$248$	10.5238	−	0.226968i	0.668260	−	0.0144125i
$249$	10.5070	−	9.10434i	0.665852	−	0.576964i
$250$	14.3828	−	6.56778i	0.909647	−	0.415383i
$251$	22.3598	+	10.2114i	1.41134	+	0.644537i	0.967800	−	0.251719i	$-0.0809958\pi$
$251$	22.3598	+	10.2114i	1.41134	+	0.644537i	0.443538	+	0.896255i	$0.353723\pi$
$252$	0.624579	−	0.859833i	0.0393448	−	0.0541644i
$253$	−16.0999	+	24.3271i	−1.01219	+	1.52943i
$254$	−15.5035	+	1.22090i	−0.972777	+	0.0766062i
$255$	−7.29107	+	0.329724i	−0.456585	+	0.0206481i
$256$	−15.0674	+	5.38257i	−0.941715	+	0.336411i
$257$	0.0302884	−	0.423487i	0.00188934	−	0.0264164i	−0.996420	−	0.0845411i	$-0.973058\pi$
$257$	0.0302884	−	0.423487i	0.00188934	−	0.0264164i	0.998309	+	0.0581247i	$0.0185121\pi$
$258$	0.263192	−	1.92886i	0.0163856	−	0.120086i
$259$	−0.692346	+	0.799010i	−0.0430203	+	0.0496481i
$260$	7.33866	−	23.9416i	0.455125	−	1.48479i
$261$	−3.54055	+	1.03960i	−0.219155	+	0.0643496i
$262$	−27.4376	+	8.27108i	−1.69510	+	0.510989i
$263$	10.0739	−	13.4571i	0.621182	−	0.829803i	−0.374042	−	0.927412i	$-0.622029\pi$
$263$	10.0739	−	13.4571i	0.621182	−	0.829803i	0.995225	+	0.0976090i	$0.0311195\pi$
$264$	25.8425	−	20.2294i	1.59050	−	1.24503i
$265$	−6.53664	+	0.765592i	−0.401543	+	0.0470300i
$266$	−1.07202	−	4.76292i	−0.0657298	−	0.292033i
$267$	18.6320	−	4.05315i	1.14026	−	0.248049i
$268$	−21.7665	−	7.76392i	−1.32960	−	0.474257i
$269$	−10.8538	−	1.56054i	−0.661769	−	0.0951479i	−0.196757	−	0.980452i	$-0.563041\pi$
$269$	−10.8538	−	1.56054i	−0.661769	−	0.0951479i	−0.465012	+	0.885304i	$0.653950\pi$
$270$	2.29490	−	14.0578i	0.139663	−	0.855533i
$271$	9.25895	+	14.4072i	0.562441	+	0.875175i	0.999708	−	0.0241563i	$-0.00768992\pi$
$271$	9.25895	+	14.4072i	0.562441	+	0.875175i	−0.437267	+	0.899332i	$0.644054\pi$
$272$	−1.64656	−	6.64346i	−0.0998374	−	0.402819i
$273$	−7.79962	+	4.25892i	−0.472055	+	0.257761i
$274$	14.5526	+	5.30900i	0.879155	+	0.320729i
$275$	−24.6894	−	17.7610i	−1.48883	−	1.07103i
$276$	17.1367	−	6.41007i	1.03151	−	0.385841i
$277$	−5.98761	−	5.98761i	−0.359761	−	0.359761i	0.503964	−	0.863725i	$-0.331874\pi$
$277$	−5.98761	−	5.98761i	−0.359761	−	0.359761i	−0.863725	+	0.503964i	$0.831874\pi$
$278$	8.48453	−	3.94870i	0.508868	−	0.236827i
$279$	2.28053	+	0.669624i	0.136532	+	0.0400894i
$280$	0.773055	−	5.20501i	0.0461989	−	0.311059i
$281$	4.84024	−	3.11063i	0.288744	−	0.185565i	−0.388248	−	0.921555i	$-0.626920\pi$
$281$	4.84024	−	3.11063i	0.288744	−	0.185565i	0.676992	+	0.735990i	$0.263283\pi$
$282$	9.78082	−	1.47810i	0.582440	−	0.0880198i
$283$	15.4151	−	11.5396i	0.916332	−	0.685958i	−0.0332594	−	0.999447i	$-0.510589\pi$
$283$	15.4151	−	11.5396i	0.916332	−	0.685958i	0.949592	+	0.313489i	$0.101498\pi$
$284$	12.5129	−	5.93330i	0.742504	−	0.352077i
$285$	11.2350	+	13.6741i	0.665505	+	0.809982i
$286$	−46.9924	+	10.5769i	−2.77872	+	0.625424i
$287$	2.69978	+	1.00697i	0.159363	+	0.0594394i
$288$	−3.61045	+	0.129814i	−0.212748	+	0.00764938i
$289$	−13.9288	+	2.00267i	−0.819344	+	0.117804i
$290$	−13.1629	+	12.6715i	−0.772953	+	0.744096i
$291$	1.58965	+	5.41385i	0.0931870	+	0.317366i
$292$	3.69831	−	3.80620i	0.216427	−	0.222741i
$293$	0.961373	+	13.4417i	0.0561640	+	0.785275i	0.945004	+	0.327058i	$0.106057\pi$
$293$	0.961373	+	13.4417i	0.0561640	+	0.785275i	−0.888840	+	0.458217i	$0.848488\pi$
$294$	13.5485	−	10.2950i	0.790162	−	0.600418i
$295$	27.9335	+	11.2610i	1.62635	+	0.655641i
$296$	3.58964	+	0.179041i	0.208643	+	0.0104066i
$297$	−25.6715	+	9.57498i	−1.48961	+	0.555597i
$298$	−8.69482	+	10.1813i	−0.503678	+	0.589788i
$299$	−26.7570	−	2.27535i	−1.54740	−	0.131587i
$300$	5.98160	+	18.1131i	0.345348	+	1.04576i
$301$	−0.249421	+	0.546156i	−0.0143764	+	0.0314799i
$302$	2.60636	−	1.70160i	0.149979	−	0.0979160i
$303$	−0.102907	+	1.43883i	−0.00591184	+	0.0826584i
$304$	−10.5034	+	12.8501i	−0.602411	+	0.737006i
$305$	−6.13356	+	25.0198i	−0.351207	+	1.43263i
$306$	0.0991696	−	1.54229i	0.00566915	−	0.0881667i
$307$	−0.111632	+	0.204439i	−0.00637119	+	0.0116680i	−0.880845	−	0.473404i	$-0.843025\pi$
$307$	−0.111632	+	0.204439i	−0.00637119	+	0.0116680i	0.874474	+	0.485072i	$0.161207\pi$
$308$	−9.43194	+	3.67323i	−0.537435	+	0.209302i
$309$	11.0932	−	1.59495i	0.631067	−	0.0907338i
$310$	11.5452	−	2.28245i	0.655724	−	0.129634i
$311$	−19.6931	+	8.99353i	−1.11669	+	0.509976i	−0.886295	−	0.463121i	$-0.846730\pi$
$311$	−19.6931	+	8.99353i	−1.11669	+	0.509976i	−0.230397	+	0.973097i	$0.574002\pi$
$312$	27.7444	+	11.9543i	1.57072	+	0.676780i
$313$	1.40743	−	0.306168i	0.0795528	−	0.0173056i	−0.172613	−	0.984990i	$-0.555221\pi$
$313$	1.40743	−	0.306168i	0.0795528	−	0.0173056i	0.252165	+	0.967684i	$0.418857\pi$
$314$	−7.72123	−	20.2556i	−0.435734	−	1.14309i
$315$	0.521739	−	1.06750i	0.0293967	−	0.0601467i
$316$	21.9797	+	13.6831i	1.23645	+	0.769732i
$317$	22.4163	+	4.87636i	1.25902	+	0.273884i	0.792088	−	0.610408i	$-0.208994\pi$
$317$	22.4163	+	4.87636i	1.25902	+	0.273884i	0.466936	+	0.884291i	$0.345358\pi$
$318$	−0.0570708	−	7.93967i	−0.00320037	−	0.445235i
$319$	33.7217	+	9.90158i	1.88805	+	0.554382i
$320$	−15.5531	+	8.83748i	−0.869445	+	0.494030i
$321$	4.93958			0.275700
$322$	−5.63100	+	0.367404i	−0.313804	+	0.0204746i
$323$	−5.02024	−	5.02024i	−0.279333	−	0.279333i
$324$	20.2479	+	5.63045i	1.12488	+	0.312803i
$325$	3.45757	−	27.7824i	0.191792	−	1.54109i
$326$	12.2029	−	12.3796i	0.675858	−	0.685645i
$327$	−4.57738	+	21.0419i	−0.253130	+	1.16362i
$328$	−2.96174	−	9.33705i	−0.163535	−	0.515553i
$329$	−3.01981	−	0.434183i	−0.166488	−	0.0239373i
$330$	24.5514	−	27.2682i	1.35151	−	1.50107i
$331$	9.26362	−	14.4145i	0.509175	−	0.792291i	−0.487556	−	0.873092i	$-0.662111\pi$
$331$	9.26362	−	14.4145i	0.509175	−	0.792291i	0.996730	+	0.0808008i	$0.0257478\pi$
$332$	12.8928	+	6.80123i	0.707582	+	0.373266i
$333$	0.760375	+	0.283605i	0.0416683	+	0.0155415i
$334$	6.12100	+	11.0207i	0.334926	+	0.603026i
$335$	−25.4693	−	4.34596i	−1.39154	−	0.237445i
$336$	6.14008	+	1.61269i	0.334969	+	0.0879792i
$337$	−20.5565	−	11.2247i	−1.11978	−	0.611449i	−0.190823	−	0.981624i	$-0.561116\pi$
$337$	−20.5565	−	11.2247i	−1.11978	−	0.611449i	−0.928962	+	0.370176i	$0.879297\pi$
$338$	−17.1373	−	19.4926i	−0.932146	−	1.06026i
$339$	−12.3850	+	14.2930i	−0.672659	+	0.776290i
$340$	−3.09632	−	6.99794i	−0.167922	−	0.379517i
$341$	−14.8246	−	17.1085i	−0.802795	−	0.926475i
$342$	−3.13795	+	2.04866i	−0.169681	+	0.110779i
$343$	−10.3741	+	3.86934i	−0.560149	+	0.208925i
$344$	1.98465	−	0.476774i	0.107005	−	0.0257059i
$345$	17.6334	−	10.3686i	0.949350	−	0.558228i
$346$	−30.7298	+	2.41997i	−1.65205	+	0.130098i
$347$	−0.422852	−	1.13371i	−0.0226999	−	0.0608607i	0.925106	−	0.379710i	$-0.123976\pi$
$347$	−0.422852	−	1.13371i	−0.0226999	−	0.0608607i	−0.947805	+	0.318849i	$0.896704\pi$
$348$	−13.4619	−	17.4543i	−0.721635	−	0.935648i
$349$	−23.5138	+	20.3748i	−1.25866	+	1.09064i	−0.266744	+	0.963768i	$0.585948\pi$
$349$	−23.5138	+	20.3748i	−1.25866	+	1.09064i	−0.991919	+	0.126870i	$0.959507\pi$
$350$	−0.153961	−	5.88120i	−0.00822954	−	0.314363i
$351$	−19.0610	−	16.5164i	−1.01740	−	0.881583i
$352$	29.5970	+	17.5511i	1.57753	+	0.935478i
$353$	−12.0905	+	22.1421i	−0.643512	+	1.17850i	0.328707	+	0.944432i	$0.393387\pi$
$353$	−12.0905	+	22.1421i	−0.643512	+	1.17850i	−0.972219	+	0.234073i	$0.924795\pi$
$354$	−17.1839	+	32.0149i	−0.913313	+	1.70157i
$355$	12.6336	−	8.95058i	0.670522	−	0.475048i
$356$	11.0492	+	16.6614i	0.585609	+	0.883051i
$357$	−0.949035	+	2.54446i	−0.0502283	+	0.134667i
$358$	4.56196	−	7.21200i	0.241107	−	0.381166i
$359$	−10.2722	−	6.60154i	−0.542146	−	0.348416i	0.240732	−	0.970592i	$-0.422613\pi$
$359$	−10.2722	−	6.60154i	−0.542146	−	0.348416i	−0.782878	+	0.622176i	$0.786249\pi$
$360$	−3.95085	+	0.840259i	−0.208228	+	0.0442855i
$361$	0.253965	−	1.76636i	0.0133666	−	0.0929664i
$362$	−16.5935	+	2.50765i	−0.872133	+	0.131799i
$363$	−48.4637	−	10.5426i	−2.54368	−	0.553345i
$364$	−7.12865	−	5.99978i	−0.373643	−	0.314474i
$365$	3.33757	−	4.90576i	0.174696	−	0.256779i
$366$	−29.1961	−	10.6512i	−1.52611	−	0.556746i
$367$	−0.693636	+	0.693636i	−0.0362075	+	0.0362075i	−0.724979	−	0.688771i	$-0.758150\pi$
$367$	−0.693636	+	0.693636i	−0.0362075	+	0.0362075i	0.688771	+	0.724979i	$0.258150\pi$
$368$	12.7830	+	14.3037i	0.666360	+	0.745630i
$369$		−	2.21182i		−	0.115143i
$370$	3.98758	−	0.496119i	0.207304	−	0.0257920i
$371$	−0.689914	+	2.34963i	−0.0358185	+	0.121987i
$372$	1.21635	+	14.1458i	0.0630650	+	0.733427i
$373$	1.78416	−	8.20165i	0.0923803	−	0.424665i	−0.907608	−	0.419819i	$-0.862094\pi$
$373$	1.78416	−	8.20165i	0.0923803	−	0.424665i	0.999988	−	0.00484652i	$-0.00154270\pi$
$374$	−8.73628	+	11.8469i	−0.451742	+	0.612586i
$375$	10.0854	+	18.7914i	0.520806	+	0.970384i
$376$	5.16561	+	8.99349i	0.266396	+	0.463804i
$377$	6.87690	+	31.6126i	0.354178	+	1.62813i
$378$	−4.47911	−	2.83326i	−0.230380	−	0.145727i
$379$	6.30610	+	13.8084i	0.323922	+	0.709291i	0.999611	−	0.0278962i	$-0.00888079\pi$
$379$	6.30610	+	13.8084i	0.323922	+	0.709291i	−0.675688	+	0.737187i	$0.736154\pi$
$380$	−9.08481	+	16.1795i	−0.466041	+	0.829990i
$381$	−2.98523	−	20.7628i	−0.152938	−	1.06371i
$382$	−6.24965	+	1.88396i	−0.319760	+	0.0963919i
$383$	27.4206	+	14.9728i	1.40113	+	0.765075i	0.989260	−	0.146168i	$-0.0466941\pi$
$383$	27.4206	+	14.9728i	1.40113	+	0.765075i	0.411870	+	0.911243i	$0.364876\pi$
$384$	−8.54929	−	19.8156i	−0.436279	−	1.01121i
$385$	−9.67727	+	5.86670i	−0.493199	+	0.298994i
$386$	−20.6190	+	15.6677i	−1.04948	+	0.797466i
$387$	0.459707	+	0.0328789i	0.0233682	+	0.00167133i
$388$	−4.68450	+	3.61301i	−0.237820	+	0.183423i
$389$	3.25542	+	1.48670i	0.165057	+	0.0753788i	0.496230	−	0.868191i	$-0.334717\pi$
$389$	3.25542	+	1.48670i	0.165057	+	0.0753788i	−0.331173	+	0.943570i	$0.607445\pi$
$390$	32.8616	+	7.80600i	1.66401	+	0.395272i
$391$	−6.63489	+	4.82912i	−0.335541	+	0.244219i
$392$	15.2133	+	9.31972i	0.768389	+	0.470717i
$393$	−13.5080	−	36.2164i	−0.681389	−	1.82687i
$394$	−1.03432	+	4.92484i	−0.0521081	+	0.248110i
$395$	26.8473	+	10.8231i	1.35083	+	0.544569i
$396$	5.17193	+	5.79817i	0.259899	+	0.291369i
$397$	19.5702	−	1.39969i	0.982201	−	0.0702484i	0.429007	−	0.903301i	$-0.358864\pi$
$397$	19.5702	−	1.39969i	0.982201	−	0.0702484i	0.553194	+	0.833053i	$0.313409\pi$
$398$	−27.3697	+	24.0626i	−1.37192	+	1.20615i
$399$	6.31831	−	1.85522i	0.316311	−	0.0928774i
$400$	−15.4207	+	12.7359i	−0.771033	+	0.636795i
$401$	−0.353390	−	2.45788i	−0.0176474	−	0.122741i	0.979093	−	0.203411i	$-0.0652029\pi$
$401$	−0.353390	−	2.45788i	−0.0176474	−	0.122741i	−0.996741	+	0.0806707i	$0.974294\pi$
$402$	8.56667	−	29.9707i	0.427266	−	1.49480i
$403$	7.28229	−	19.5246i	0.362757	−	0.972589i
$404$	−1.44489	+	0.446918i	−0.0718861	+	0.0222350i
$405$	23.3850	+	2.28982i	1.16201	+	0.113782i
$406$	2.42152	+	6.35252i	0.120178	+	0.315270i
$407$	−4.63210	−	6.18777i	−0.229605	−	0.306716i
$408$	8.79988	−	2.79134i	0.435659	−	0.138192i
$409$	0.198598	+	0.309025i	0.00982005	+	0.0152803i	0.846129	−	0.532978i	$-0.178927\pi$
$409$	0.198598	+	0.309025i	0.00982005	+	0.0152803i	−0.836309	+	0.548259i	$0.815291\pi$
$410$	−5.06485	−	9.71019i	−0.250135	−	0.479552i
$411$	−5.88661	+	20.0480i	−0.290365	+	0.988893i
$412$	5.77911	+	10.2312i	0.284716	+	0.504054i
$413$	7.92419	−	7.92419i	0.389924	−	0.389924i
$414$	1.77476	+	3.95130i	0.0872246	+	0.194196i
$415$	15.5114	+	4.99965i	0.761424	+	0.245423i
$416$	−1.12296	+	31.6548i	−0.0550574	+	1.55201i
$417$	6.04948	+	11.0788i	0.296244	+	0.542531i
$418$	35.6918	−	0.256555i	1.74574	−	0.0125485i
$419$	−13.3286	+	8.56578i	−0.651145	+	0.418466i	−0.824085	−	0.566467i	$-0.808310\pi$
$419$	−13.3286	+	8.56578i	−0.651145	+	0.418466i	0.172939	+	0.984932i	$0.444674\pi$
$420$	7.07309	+	0.590067i	0.345131	+	0.0287923i
$421$	−2.78113	+	19.3432i	−0.135544	+	0.942728i	0.802609	+	0.596506i	$0.203445\pi$
$421$	−2.78113	+	19.3432i	−0.135544	+	0.942728i	−0.938153	+	0.346222i	$0.887464\pi$
$422$	15.5703	−	34.7531i	0.757950	−	1.69176i
$423$	0.497797	+	2.28834i	0.0242037	+	0.111263i
$424$	7.73537	−	3.07672i	0.375663	−	0.149419i
$425$	−4.76130	−	7.10831i	−0.230957	−	0.344804i
$426$	9.06949	+	16.3294i	0.439418	+	0.791161i
$427$	7.67335	+	5.74420i	0.371339	+	0.277981i
$428$	1.87946	+	4.82598i	0.0908471	+	0.233273i
$429$	−18.3042	−	62.3384i	−0.883735	−	3.00973i
$430$	2.09346	−	0.908340i	0.100956	−	0.0438041i
$431$	2.53346	+	2.19526i	0.122033	+	0.105742i	0.713739	−	0.700412i	$-0.247000\pi$
$431$	2.53346	+	2.19526i	0.122033	+	0.105742i	−0.591707	+	0.806153i	$0.701546\pi$
$432$	1.80145	+	17.9270i	0.0866721	+	0.862514i
$433$	−5.21424	−	0.372930i	−0.250580	−	0.0179219i	−0.0545160	−	0.998513i	$-0.517362\pi$
$433$	−5.21424	−	0.372930i	−0.250580	−	0.0179219i	−0.196064	+	0.980591i	$0.562816\pi$
$434$	0.900037	−	4.28548i	0.0432031	−	0.205709i
$435$	−18.1957	−	16.6211i	−0.872415	−	0.796923i
$436$	−22.2996	+	3.53411i	−1.06796	+	0.169253i
$437$	19.0156	+	5.86206i	0.909638	+	0.280421i
$438$	5.44341	+	4.64866i	0.260096	+	0.222122i
$439$	−2.95136	+	6.46257i	−0.140861	+	0.308442i	−0.966894	−	0.255180i	$-0.917865\pi$
$439$	−2.95136	+	6.46257i	−0.140861	+	0.308442i	0.826033	+	0.563622i	$0.190592\pi$
$440$	35.9827	+	13.6115i	1.71541	+	0.648905i
$441$	2.63810	+	3.04453i	0.125624	+	0.144977i
$442$	−13.4254	−	1.83188i	−0.638581	−	0.0871338i
$443$	−15.6482	+	1.11918i	−0.743469	+	0.0531740i	−0.437935	−	0.899007i	$-0.644290\pi$
$443$	−15.6482	+	1.11918i	−0.743469	+	0.0531740i	−0.305535	+	0.952181i	$0.598835\pi$
$444$	0.0696890	+	4.84731i	0.00330730	+	0.230043i
$445$	15.3856	+	16.2139i	0.729348	+	0.768615i
$446$	−8.71869	+	16.2436i	−0.412842	+	0.769156i
$447$	−14.4571	−	10.8224i	−0.683795	−	0.511883i
$448$	0.760640	+	6.61249i	0.0359369	+	0.312411i
$449$	29.2985	−	13.3802i	1.38268	−	0.631450i	0.421365	−	0.906891i	$-0.361551\pi$
$449$	29.2985	−	13.3802i	1.38268	−	0.631450i	0.961318	+	0.275442i	$0.0888240\pi$
$450$	−4.18850	+	1.68836i	−0.197448	+	0.0795901i
$451$	−11.3893	+	17.7221i	−0.536302	+	0.834501i
$452$	−18.6767	−	6.66180i	−0.878477	−	0.313345i
$453$	2.51601	+	3.36100i	0.118213	+	0.157913i
$454$	9.49929	−	12.8815i	0.445824	−	0.604560i
$455$	−9.00902	−	5.23032i	−0.422349	−	0.245201i
$456$	−18.2060	−	13.0259i	−0.852572	−	0.609991i
$457$	12.3872	+	22.6855i	0.579451	+	1.06118i	0.988862	+	0.148835i	$0.0475522\pi$
$457$	12.3872	+	22.6855i	0.579451	+	1.06118i	−0.409412	+	0.912350i	$0.634266\pi$
$458$	7.56454	+	16.2538i	0.353468	+	0.759491i
$459$	−7.70743			−0.359752
$460$	16.8395	+	13.2827i	0.785146	+	0.619310i
$461$	16.2214			0.755506			0.377753	−	0.925907i	$-0.376697\pi$
$461$	16.2214			0.755506			0.377753	+	0.925907i	$0.376697\pi$
$462$	−5.76068	−	12.3779i	−0.268011	−	0.575872i
$463$	−1.36133	−	2.49309i	−0.0632664	−	0.115864i	0.844132	−	0.536136i	$-0.180116\pi$
$463$	−1.36133	−	2.49309i	−0.0632664	−	0.115864i	−0.907398	+	0.420272i	$0.861935\pi$
$464$	11.9308	−	19.7935i	0.553872	−	0.918891i
$465$	4.07153	+	15.3428i	0.188813	+	0.711507i
$466$	−0.614508	+	0.833306i	−0.0284666	+	0.0386021i
$467$	−9.49473	−	12.6835i	−0.439364	−	0.586921i	0.525132	−	0.851021i	$-0.324016\pi$
$467$	−9.49473	−	12.6835i	−0.439364	−	0.586921i	−0.964495	+	0.264100i	$0.914925\pi$
$468$	−2.40282	+	6.73641i	−0.111070	+	0.311391i
$469$	−5.19760	+	8.08762i	−0.240003	+	0.373452i
$470$	7.42547	+	8.90621i	0.342511	+	0.410813i
$471$	26.5966	−	12.1463i	1.22551	−	0.559671i
$472$	−37.8169	−	4.60736i	−1.74066	−	0.212071i
$473$	−3.51407	−	2.63060i	−0.161577	−	0.120955i
$474$	−16.5156	+	30.7699i	−0.758588	+	1.41331i
$475$	−6.87960	+	19.5719i	−0.315658	+	0.898019i
$476$	−2.84704	+	0.0409316i	−0.130494	+	0.00187609i
$477$	1.87494	−	0.134098i	0.0858475	−	0.00613994i
$478$	14.8394	+	2.02483i	0.678741	+	0.0926136i
$479$	−9.76541	−	11.2699i	−0.446193	−	0.514934i	0.487444	−	0.873154i	$-0.337929\pi$
$479$	−9.76541	−	11.2699i	−0.446193	−	0.514934i	−0.933637	+	0.358220i	$0.883384\pi$
$480$	−13.2418	−	20.1703i	−0.604402	−	0.920643i
$481$	2.95573	−	6.47215i	0.134770	−	0.295105i
$482$	14.3564	+	12.2603i	0.653916	+	0.558443i
$483$	−0.981911	−	7.54779i	−0.0446785	−	0.343436i
$484$	−8.13976	−	51.3605i	−0.369989	−	2.33457i
$485$	−4.46090	+	4.88348i	−0.202559	+	0.221747i
$486$	−1.89852	+	9.03968i	−0.0861184	+	0.410048i
$487$	42.0772	+	3.00942i	1.90670	+	0.136370i	0.974328	−	0.225135i	$-0.0722823\pi$
$487$	42.0772	+	3.00942i	1.90670	+	0.136370i	0.932370	+	0.361505i	$0.117737\pi$
$488$	−0.702600	−	32.5773i	−0.0318052	−	1.47471i
$489$	17.7197	+	15.3542i	0.801314	+	0.694343i
$490$	18.5533	+	7.32490i	0.838151	+	0.330905i
$491$	−9.59074	−	32.6631i	−0.432824	−	1.47406i	−0.830750	−	0.556646i	$-0.812088\pi$
$491$	−9.59074	−	32.6631i	−0.432824	−	1.47406i	0.397926	−	0.917417i	$-0.369730\pi$
$492$	12.3118	−	4.79476i	0.555057	−	0.216165i
$493$	7.91454	+	5.92475i	0.356453	+	0.266837i
$494$	15.9530	+	28.7229i	0.717759	+	1.29231i
$495$	6.81530	+	5.38622i	0.306325	+	0.242092i
$496$	−13.3577	+	6.57072i	−0.599779	+	0.295034i
$497$	−1.22459	−	5.62934i	−0.0549302	−	0.252510i
$498$	−8.03888	+	17.9429i	−0.360231	+	0.804040i
$499$	−3.15834	+	21.9667i	−0.141387	+	0.983366i	0.788372	+	0.615198i	$0.210924\pi$
$499$	−3.15834	+	21.9667i	−0.141387	+	0.983366i	−0.929759	+	0.368168i	$0.879985\pi$
$500$	−14.5219	+	17.0034i	−0.649438	+	0.760414i
$501$	−14.3046	+	9.19299i	−0.639081	+	0.410713i
$502$	−34.7621	+	0.249872i	−1.55151	+	0.0111523i
$503$	−4.62955	−	8.47840i	−0.206422	−	0.378033i	0.753873	−	0.657020i	$-0.228183\pi$
$503$	−4.62955	−	8.47840i	−0.206422	−	0.378033i	−0.960295	+	0.278987i	$0.910001\pi$
$504$	−0.287732	+	1.47514i	−0.0128166	+	0.0657079i
$505$	−1.50484	+	0.771217i	−0.0669644	+	0.0343187i
$506$	6.12623	−	40.7983i	0.272344	−	1.81371i
$507$	24.7547	−	24.7547i	1.09939	−	1.09939i
$508$	19.1494	−	10.8166i	0.849618	−	0.479909i
$509$	−8.77225	+	29.8755i	−0.388823	+	1.32421i	0.500026	+	0.866010i	$0.333324\pi$
$509$	−8.77225	+	29.8755i	−0.388823	+	1.32421i	−0.888849	+	0.458200i	$0.848494\pi$
$510$	9.15156	−	4.77347i	0.405238	−	0.211373i
$511$	−1.19361	−	1.85729i	−0.0528020	−	0.0821615i
$512$	16.1070	−	15.8923i	0.711834	−	0.702347i
$513$	11.2000	+	14.9614i	0.494491	+	0.660563i
$514$	0.213867	+	0.561050i	0.00943328	+	0.0247469i
$515$	8.34010	+	10.1507i	0.367509	+	0.447293i
$516$	0.813532	+	2.63016i	0.0358138	+	0.115786i
$517$	7.79474	−	20.8985i	0.342812	−	0.919115i
$518$	0.410914	−	1.43759i	0.0180545	−	0.0631642i
$519$	−5.91709	−	41.1543i	−0.259731	−	1.80647i
$520$	4.87702	+	35.0760i	0.213872	+	1.53818i
$521$	25.8214	−	7.58185i	1.13126	−	0.332167i	0.338055	−	0.941126i	$-0.390231\pi$
$521$	25.8214	−	7.58185i	1.13126	−	0.332167i	0.793201	+	0.608959i	$0.208413\pi$
$522$	3.91920	−	3.44564i	0.171539	−	0.150811i
$523$	−33.8447	+	2.42062i	−1.47992	+	0.105846i	−0.787799	−	0.615932i	$-0.788780\pi$
$523$	−33.8447	+	2.42062i	−1.47992	+	0.105846i	−0.692125	+	0.721778i	$0.743325\pi$
$524$	30.2438	−	26.9773i	1.32121	−	1.17851i
$525$	7.90303	−	0.716262i	0.344916	−	0.0312602i
$526$	−4.88621	+	23.2654i	−0.213049	+	1.01442i
$527$	−2.22541	−	5.96655i	−0.0969403	−	0.259907i
$528$	−21.0629	+	41.3580i	−0.916647	+	1.79987i
$529$	10.1131	−	20.6573i	0.439701	−	0.898144i
$530$	7.92416	−	4.88213i	0.344204	−	0.212066i
$531$	−7.82480	−	3.57347i	−0.339567	−	0.155075i
$532$	4.21661	+	5.46712i	0.182813	+	0.237030i
$533$	−19.3425	−	1.38340i	−0.837818	−	0.0599219i
$534$	−21.4706	+	16.3148i	−0.929125	+	0.706012i
$535$	3.00178	+	4.95151i	0.129778	+	0.214072i
$536$	32.5409	−	3.03387i	1.40555	−	0.131043i
$537$	10.1025	+	5.51639i	0.435956	+	0.238050i
$538$	14.8475	−	4.47579i	0.640121	−	0.192965i
$539$	−5.46048	−	37.9784i	−0.235199	−	1.63585i
$540$	5.44613	+	19.3938i	0.234364	+	0.834575i
$541$	6.29681	+	13.7881i	0.270721	+	0.592797i	0.995348	−	0.0963447i	$-0.0307151\pi$
$541$	6.29681	+	13.7881i	0.270721	+	0.592797i	−0.724627	+	0.689141i	$0.757988\pi$
$542$	−20.4685	−	12.9473i	−0.879196	−	0.556136i
$543$	−4.81159	−	22.1185i	−0.206485	−	0.949196i
$544$	6.07542	+	7.53543i	0.260481	+	0.323079i
$545$	−23.8744	+	8.19869i	−1.02267	+	0.351193i
$546$	7.45898	−	10.1148i	0.319215	−	0.432872i
$547$	−0.131453	+	0.604279i	−0.00562052	+	0.0258371i	−0.979872	−	0.199628i	$-0.936027\pi$
$547$	−0.131453	+	0.604279i	−0.00562052	+	0.0258371i	0.974251	+	0.225465i	$0.0723902\pi$
$548$	−21.8267	+	1.87681i	−0.932391	+	0.0801732i
$549$	2.07289	−	7.05960i	0.0884686	−	0.301297i
$550$	42.2540	+	8.03986i	1.80172	+	0.342821i
$551$		−	23.9730i		−	1.02128i
$552$	−18.1470	+	18.4445i	−0.772387	+	0.785050i
$553$	7.61604	−	7.61604i	0.323867	−	0.323867i
$554$	11.2500	+	4.10415i	0.477965	+	0.174369i
$555$	1.01293	+	5.32452i	0.0429964	+	0.226013i
$556$	−8.52224	+	10.1257i	−0.361424	+	0.429426i
$557$	−3.39395	−	0.738308i	−0.143806	−	0.0312831i	0.140086	−	0.990139i	$-0.455262\pi$
$557$	−3.39395	−	0.738308i	−0.143806	−	0.0312831i	−0.283892	+	0.958856i	$0.591626\pi$
$558$	−3.32358	+	0.502267i	−0.140698	+	0.0212627i
$559$	0.575056	−	3.99960i	0.0243223	−	0.169165i
$560$	2.11474	+	7.13494i	0.0893640	+	0.301506i
$561$	−16.7025	−	10.7341i	−0.705182	−	0.453193i
$562$	−4.34978	+	6.87657i	−0.183484	+	0.290071i
$563$	−12.6155	+	33.8236i	−0.531681	+	1.42549i	0.342327	+	0.939581i	$0.388785\pi$
$563$	−12.6155	+	33.8236i	−0.531681	+	1.42549i	−0.874008	+	0.485912i	$0.838488\pi$
$564$	−11.6586	+	7.73155i	−0.490914	+	0.325557i
$565$	−21.8539	−	3.72904i	−0.919399	−	0.156882i
$566$	−12.8787	+	23.9940i	−0.541333	+	1.00854i
$567$	4.19000	−	7.67342i	0.175964	−	0.322253i
$568$	−12.5030	+	15.0741i	−0.524615	+	0.632495i
$569$	−5.16040	−	4.47151i	−0.216335	−	0.187455i	0.539951	−	0.841696i	$-0.318443\pi$
$569$	−5.16040	−	4.47151i	−0.216335	−	0.187455i	−0.756286	+	0.654241i	$0.772988\pi$
$570$	−22.5646	−	10.8282i	−0.945128	−	0.453544i
$571$	5.07550	−	4.39795i	0.212403	−	0.184048i	−0.542161	−	0.840275i	$-0.682394\pi$
$571$	5.07550	−	4.39795i	0.212403	−	0.184048i	0.754564	+	0.656226i	$0.227848\pi$
$572$	53.9402	−	41.6024i	2.25535	−	1.73948i
$573$	−3.07681	−	8.24925i	−0.128536	−	0.344617i
$574$	−4.06242	+	0.319916i	−0.169562	+	0.0133530i
$575$	21.1095	+	11.3750i	0.880326	+	0.474370i
$576$	4.55170	−	2.32086i	0.189654	−	0.0967024i
$577$	−39.7424	+	14.8231i	−1.65450	+	0.617096i	−0.991332	−	0.131377i	$-0.958060\pi$
$577$	−39.7424	+	14.8231i	−1.65450	+	0.617096i	−0.663165	+	0.748473i	$0.730787\pi$
$578$	16.6640	−	10.8793i	0.693129	−	0.452520i
$579$	−22.8741	−	26.3981i	−0.950614	−	1.09707i
$580$	9.31564	−	24.1014i	0.386811	−	1.00076i
$581$	3.97107	−	4.58286i	0.164748	−	0.190129i
$582$	−5.26872	−	5.99284i	−0.218395	−	0.248411i
$583$	−15.7134	−	8.58015i	−0.650781	−	0.355353i
$584$	−2.47059	+	7.08700i	−0.102234	+	0.293262i
$585$	−1.34501	+	7.88238i	−0.0556094	+	0.325896i
$586$	−9.25355	−	16.6608i	−0.382261	−	0.688250i
$587$	−11.0564	−	4.12384i	−0.456348	−	0.170209i	0.110769	−	0.993846i	$-0.464669\pi$
$587$	−11.0564	−	4.12384i	−0.456348	−	0.170209i	−0.567117	+	0.823637i	$0.691941\pi$
$588$	−11.2280	+	21.2844i	−0.463036	+	0.877756i
$589$	−8.34826	+	12.9901i	−0.343984	+	0.535249i
$590$	−42.5348	+	2.23002i	−1.75113	+	0.0918084i
$591$	−6.71858	−	0.965986i	−0.276365	−	0.0397353i
$592$	−4.70932	+	1.91244i	−0.193552	+	0.0786007i
$593$	−3.63191	+	16.6956i	−0.149145	+	0.685607i	0.840470	+	0.541859i	$0.182279\pi$
$593$	−3.63191	+	16.6956i	−0.149145	+	0.685607i	−0.989614	+	0.143748i	$0.954084\pi$
$594$	27.2014	−	27.5953i	1.11609	−	1.13225i
$595$	−3.12733	+	0.594938i	−0.128208	+	0.0243901i
$596$	5.07277	−	18.2424i	0.207789	−	0.747238i
$597$	−34.7582	−	34.7582i	−1.42256	−	1.42256i
$598$	35.6644	−	13.0490i	1.45843	−	0.533613i
$599$	−17.4831			−0.714339			−0.357170	−	0.934040i	$-0.616258\pi$
$599$	−17.4831			−0.714339			−0.357170	+	0.934040i	$0.616258\pi$
$600$	−18.4778	−	19.6546i	−0.754352	−	0.802395i
$601$	−34.0587	−	10.0005i	−1.38928	−	0.407931i	−0.500294	−	0.865856i	$-0.666775\pi$
$601$	−34.0587	−	10.0005i	−1.38928	−	0.407931i	−0.888991	+	0.457925i	$0.848593\pi$
$602$	−0.00610333	−	0.849093i	−0.000248753	−	0.0346064i
$603$	7.21093	+	1.56864i	0.293652	+	0.0638800i
$604$	−2.32639	+	3.73698i	−0.0946594	+	0.152055i
$605$	−18.8832	−	54.9875i	−0.767712	−	2.23556i
$606$	−0.726629	−	1.90621i	−0.0295173	−	0.0774344i
$607$	26.5632	−	5.77847i	1.07817	−	0.234541i	0.361794	−	0.932258i	$-0.382164\pi$
$607$	26.5632	−	5.77847i	1.07817	−	0.234541i	0.716373	+	0.697717i	$0.245801\pi$
$608$	5.79912	−	22.7435i	0.235185	−	0.922369i
$609$	−8.34119	+	3.80929i	−0.338002	+	0.154360i
$610$	−7.06554	−	35.7393i	−0.286076	−	1.44704i
$611$	20.3230	−	2.92201i	0.822181	−	0.118212i
$612$	0.793158	+	2.03663i	0.0320615	+	0.0823260i
$613$	13.7309	−	25.1463i	0.554587	−	1.01565i	−0.438552	−	0.898706i	$-0.644508\pi$
$613$	13.7309	−	25.1463i	0.554587	−	1.01565i	0.993138	−	0.116944i	$-0.0373098\pi$
$614$	0.0211378	−	0.328736i	0.000853054	−	0.0132667i
$615$	12.6320	−	7.65795i	0.509371	−	0.308798i
$616$	9.90136	−	10.3379i	0.398937	−	0.416524i
$617$	2.13252	−	29.8165i	0.0858520	−	1.20037i	−0.753748	−	0.657163i	$-0.771756\pi$
$617$	2.13252	−	29.8165i	0.0858520	−	1.20037i	0.839600	−	0.543204i	$-0.182789\pi$
$618$	−13.2714	+	8.66446i	−0.533855	+	0.348536i
$619$	−5.15493	+	11.2877i	−0.207194	+	0.453692i	−0.984489	−	0.175444i	$-0.943864\pi$
$619$	−5.15493	+	11.2877i	−0.207194	+	0.453692i	0.777295	+	0.629136i	$0.216591\pi$
$620$	−13.4408	+	9.81569i	−0.539796	+	0.394208i
$621$	19.0970	−	10.0971i	0.766335	−	0.405183i
$622$	19.8830	−	23.2823i	0.797238	−	0.933536i
$623$	7.79248	−	2.90645i	0.312199	−	0.116444i
$624$	−42.7060	+	1.22821i	−1.70961	+	0.0491678i
$625$	−12.7079	+	21.5292i	−0.508317	+	0.861170i
$626$	−1.62185	+	1.23239i	−0.0648224	+	0.0492564i
$627$	3.43450	+	48.0206i	0.137161	+	1.91776i
$628$	21.9867	+	21.3634i	0.877364	+	0.852494i
$629$	−0.612578	−	2.08625i	−0.0244251	−	0.0831842i
$630$	−0.0319576	+	1.68003i	−0.00127322	+	0.0669341i
$631$	14.9677	−	2.15203i	0.595854	−	0.0856709i	0.162212	−	0.986756i	$-0.448137\pi$
$631$	14.9677	−	2.15203i	0.595854	−	0.0856709i	0.433642	+	0.901085i	$0.357228\pi$
$632$	−36.3463	−	4.42819i	−1.44578	−	0.176144i
$633$	48.1269	+	17.9504i	1.91287	+	0.713465i
$634$	−31.6510	+	7.12390i	−1.25702	+	0.282926i
$635$	18.9988	−	15.6099i	0.753944	−	0.619462i
$636$	4.81091	+	10.1459i	0.190765	+	0.402309i
$637$	28.2746	−	21.1661i	1.12028	−	0.838632i
$638$	−49.1450	+	7.42691i	−1.94567	+	0.294034i
$639$	−3.72016	+	2.39080i	−0.147167	+	0.0945786i
$640$	14.6681	−	20.6118i	0.579806	−	0.814755i
$641$	−33.4333	−	9.81691i	−1.32054	−	0.387745i	−0.455851	−	0.890056i	$-0.650665\pi$
$641$	−33.4333	−	9.81691i	−1.32054	−	0.387745i	−0.864687	+	0.502311i	$0.832483\pi$
$642$	−6.33332	+	2.94753i	−0.249956	+	0.116330i
$643$	−3.76654	−	3.76654i	−0.148538	−	0.148538i	0.628927	−	0.777465i	$-0.283495\pi$
$643$	−3.76654	−	3.76654i	−0.148538	−	0.148538i	−0.777465	+	0.628927i	$0.783495\pi$
$644$	7.00060	−	3.83119i	0.275862	−	0.150970i
$645$	1.40386	+	2.73928i	0.0552769	+	0.107859i
$646$	9.43240	+	3.44108i	0.371113	+	0.135387i
$647$	0.302048	−	0.164930i	0.0118747	−	0.00648409i	−0.473301	−	0.880901i	$-0.656938\pi$
$647$	0.302048	−	0.164930i	0.0118747	−	0.00648409i	0.485175	+	0.874417i	$0.338756\pi$
$648$	−29.3208	+	4.86314i	−1.15183	+	0.191042i
$649$	44.2950	+	68.9244i	1.73873	+	2.70552i
$650$	12.1451	+	37.6847i	0.476370	+	1.47811i
$651$	5.84634	+	0.840577i	0.229136	+	0.0329448i
$652$	−8.25896	+	23.1544i	−0.323446	+	0.906795i
$653$	−9.67464	+	2.10459i	−0.378598	+	0.0823590i	−0.397837	−	0.917456i	$-0.630239\pi$
$653$	−9.67464	+	2.10459i	−0.378598	+	0.0823590i	0.0192393	+	0.999815i	$0.493876\pi$
$654$	−6.68713	−	29.7104i	−0.261487	−	1.16177i
$655$	28.0950	−	35.5493i	1.09776	−	1.38902i
$656$	9.36899	+	10.2043i	0.365798	+	0.398409i
$657$	−1.01559	+	1.35667i	−0.0396218	+	0.0529286i
$658$	4.13096	−	1.24528i	0.161042	−	0.0485461i
$659$	−4.38579	+	1.28778i	−0.170846	+	0.0501649i	−0.366037	−	0.930600i	$-0.619286\pi$
$659$	−4.38579	+	1.28778i	−0.170846	+	0.0501649i	0.195191	+	0.980765i	$0.437467\pi$
$660$	−15.2074	+	49.6125i	−0.591947	+	1.93116i
$661$	−2.81666	+	3.25060i	−0.109555	+	0.126434i	−0.807879	−	0.589349i	$-0.799384\pi$
$661$	−2.81666	+	3.25060i	−0.109555	+	0.126434i	0.698323	+	0.715782i	$0.253930\pi$
$662$	−3.27606	+	24.0094i	−0.127328	+	0.933151i
$663$	1.30382	−	18.2297i	0.0506360	−	0.707984i
$664$	−20.5890	−	1.02692i	−0.799006	−	0.0398523i
$665$	5.69934	+	5.20616i	0.221011	+	0.201886i
$666$	−1.14415	+	0.0901020i	−0.0443350	+	0.00349138i
$667$	−27.3718	−	4.31153i	−1.05984	−	0.166943i
$668$	−14.4243	−	10.4778i	−0.558094	−	0.405397i
$669$	−22.6192	−	10.3299i	−0.874509	−	0.399375i
$670$	35.2490	−	9.62577i	1.36179	−	0.371876i
$671$	−52.9609	+	45.8908i	−2.04453	+	1.77160i
$672$	−8.83487	+	1.59617i	−0.340813	+	0.0615737i
$673$	1.54163	+	21.5548i	0.0594255	+	0.830878i	0.936532	+	0.350582i	$0.114016\pi$
$673$	1.54163	+	21.5548i	0.0594255	+	0.830878i	−0.877107	+	0.480296i	$0.840529\pi$
$674$	33.0547	+	2.12542i	1.27322	+	0.0818683i
$675$	9.74304	+	20.3051i	0.375010	+	0.781544i
$676$	33.6043	+	14.7665i	1.29247	+	0.567942i
$677$	−19.3559	+	25.8564i	−0.743906	+	0.993742i	0.255729	+	0.966748i	$0.417684\pi$
$677$	−19.3559	+	25.8564i	−0.743906	+	0.993742i	−0.999636	+	0.0269939i	$0.991407\pi$
$678$	7.35060	−	25.7162i	0.282298	−	0.987626i
$679$	1.02236	+	2.23867i	0.0392347	+	0.0859121i
$680$	8.14576	+	7.12484i	0.312376	+	0.273225i
$681$	18.1613	+	11.6716i	0.695942	+	0.447255i
$682$	29.2163	+	13.0897i	1.11875	+	0.501230i
$683$	3.05730	−	2.28866i	0.116984	−	0.0875733i	−0.539184	−	0.842188i	$-0.681267\pi$
$683$	3.05730	−	2.28866i	0.116984	−	0.0875733i	0.656168	+	0.754615i	$0.272176\pi$
$684$	2.80088	−	4.49917i	0.107094	−	0.172030i
$685$	−23.6737	+	6.28229i	−0.904524	+	0.240034i
$686$	10.9923	−	11.1515i	0.419689	−	0.425767i
$687$	−21.2237	+	11.5890i	−0.809733	+	0.442148i
$688$	−2.26013	+	1.79557i	−0.0861667	+	0.0684555i
$689$		−	16.4803i		−	0.627851i
$690$	−16.4217	+	23.8164i	−0.625162	+	0.906674i
$691$			50.2533i			1.91172i	0.293815	+	0.955862i	$0.405075\pi$
$691$			50.2533i			1.91172i	−0.293815	+	0.955862i	$0.594925\pi$
$692$	37.9564	−	21.4398i	1.44289	−	0.815018i
$693$	2.83686	−	1.54904i	0.107763	−	0.0588432i
$694$	1.21867	+	1.20127i	0.0462599	+	0.0455996i
$695$	−7.42929	+	12.7966i	−0.281809	+	0.485405i
$696$	27.6756	+	14.3462i	1.04904	+	0.543791i
$697$	−4.74402	+	3.55133i	−0.179693	+	0.134516i
$698$	17.9904	−	40.1548i	0.680946	−	1.51988i
$699$	−1.17485	−	0.755032i	−0.0444370	−	0.0285580i
$700$	3.70681	+	7.44875i	0.140104	+	0.281536i
$701$	18.2770	+	40.0211i	0.690314	+	1.51158i	0.851333	+	0.524625i	$0.175795\pi$
$701$	18.2770	+	40.0211i	0.690314	+	1.51158i	−0.161019	+	0.986951i	$0.551478\pi$
$702$	34.2949	+	9.80268i	1.29438	+	0.369978i
$703$	−3.15960	+	4.22074i	−0.119167	+	0.159188i
$704$	−48.4211	−	4.84228i	−1.82494	−	0.182500i
$705$	−11.3455	+	10.7659i	−0.427295	+	0.405465i
$706$	2.28937	−	35.6043i	0.0861614	−	1.33998i
$707$	0.0448852	+	0.627577i	0.00168808	+	0.0236025i
$708$	2.92862	−	51.3020i	0.110064	−	1.92805i
$709$	17.5313	−	15.1910i	0.658403	−	0.570509i	−0.260267	−	0.965537i	$-0.583810\pi$
$709$	17.5313	−	15.1910i	0.658403	−	0.570509i	0.918669	+	0.395028i	$0.129265\pi$
$710$	−10.8573	+	19.0147i	−0.407468	+	0.713611i
$711$	−7.52051	−	3.43450i	−0.282041	−	0.128804i
$712$	−24.1090	−	14.7692i	−0.903523	−	0.553501i
$713$	13.3305	+	11.8681i	0.499229	+	0.444466i
$714$	−0.301510	−	3.82871i	−0.0112837	−	0.143286i
$715$	51.3655	−	56.2314i	1.92096	−	2.10293i
$716$	−1.54563	+	11.9691i	−0.0577628	+	0.447307i
$717$	−1.44114	+	20.1498i	−0.0538205	+	0.752509i
$718$	17.1098	+	2.33462i	0.638533	+	0.0871273i
$719$	9.10642	−	10.5094i	0.339612	−	0.391933i	−0.560094	−	0.828429i	$-0.689235\pi$
$719$	9.10642	−	10.5094i	0.339612	−	0.391933i	0.899706	+	0.436496i	$0.143781\pi$
$720$	4.56422	−	3.43488i	0.170098	−	0.128011i
$721$	4.69028	−	1.37719i	0.174675	−	0.0512893i
$722$	0.728396	+	2.41630i	0.0271081	+	0.0899254i
$723$	−15.2604	+	20.3855i	−0.567540	+	0.758145i
$724$	19.7791	−	13.1168i	0.735084	−	0.487482i
$725$	5.60381	−	28.3403i	0.208120	−	1.05253i
$726$	68.4291	−	15.4018i	2.53964	−	0.571614i
$727$	−37.3610	+	8.12739i	−1.38564	+	0.301428i	−0.842719	−	0.538354i	$-0.819046\pi$
$727$	−37.3610	+	8.12739i	−1.38564	+	0.301428i	−0.542924	+	0.839782i	$0.682683\pi$
$728$	12.7202	+	3.43888i	0.471443	+	0.127453i
$729$	18.8713	+	2.71328i	0.698935	+	0.100492i
$730$	−1.35194	+	8.28155i	−0.0500374	+	0.306514i
$731$	−0.667591	−	1.03879i	−0.0246917	−	0.0384211i
$732$	43.7898	−	3.76534i	1.61852	−	0.139171i
$733$	−18.7146	+	10.2189i	−0.691239	+	0.377445i	−0.786146	−	0.618041i	$-0.787927\pi$
$733$	−18.7146	+	10.2189i	−0.691239	+	0.377445i	0.0949067	+	0.995486i	$0.469745\pi$
$734$	0.475446	−	1.30325i	0.0175490	−	0.0481040i
$735$	−8.25384	+	25.6075i	−0.304447	+	0.944547i
$736$	−24.9251	−	10.7117i	−0.918750	−	0.394839i
$737$	−49.6998	−	49.6998i	−1.83072	−	1.83072i
$738$	1.31983	+	2.83590i	0.0485836	+	0.104391i
$739$	20.2967	+	5.95965i	0.746626	+	0.219229i	0.632847	−	0.774277i	$-0.281886\pi$
$739$	20.2967	+	5.95965i	0.746626	+	0.219229i	0.113779	+	0.993506i	$0.463704\pi$
$740$	−4.81666	+	3.01556i	−0.177064	+	0.110854i
$741$	−37.2816	+	23.9594i	−1.36957	+	0.880172i
$742$	−0.517486	−	3.42428i	−0.0189975	−	0.125709i
$743$	−2.40557	+	1.80079i	−0.0882520	+	0.0660646i	−0.642493	−	0.766292i	$-0.722100\pi$
$743$	−2.40557	+	1.80079i	−0.0882520	+	0.0660646i	0.554241	+	0.832356i	$0.313009\pi$
$744$	−10.0006	−	17.4114i	−0.366640	−	0.638332i
$745$	2.06302	−	21.0687i	0.0755833	−	0.771899i
$746$	2.60649	+	11.5804i	0.0954303	+	0.423990i
$747$	−4.36126	−	1.62667i	−0.159570	−	0.0595166i
$748$	4.13207	−	20.4026i	0.151084	−	0.745994i
$749$	2.13258	−	0.306619i	0.0779229	−	0.0112036i
$750$	−24.1442	−	18.0754i	−0.881621	−	0.660022i
$751$	−12.0908	−	41.1775i	−0.441200	−	1.50259i	−0.817411	−	0.576055i	$-0.804591\pi$
$751$	−12.0908	−	41.1775i	−0.441200	−	1.50259i	0.376211	−	0.926534i	$-0.377227\pi$
$752$	−11.9897	−	8.44867i	−0.437219	−	0.308091i
$753$	−3.34504	−	46.7697i	−0.121900	−	1.70438i
$754$	−27.6810	−	36.4288i	−1.00808	−	1.32666i
$755$	−1.84014	+	4.56456i	−0.0669695	+	0.166121i
$756$	7.43358	+	0.959932i	0.270357	+	0.0349124i
$757$	12.6741	−	4.72720i	0.460649	−	0.171813i	−0.108416	−	0.994106i	$-0.534578\pi$
$757$	12.6741	−	4.72720i	0.460649	−	0.171813i	0.569065	+	0.822292i	$0.307305\pi$
$758$	−16.3251	−	13.9416i	−0.592956	−	0.506383i
$759$	55.4466	+	4.71504i	2.01259	+	0.171145i
$760$	1.99358	−	26.1657i	0.0723148	−	0.949130i
$761$	−11.0267	+	24.1452i	−0.399719	+	0.875263i	0.597579	+	0.801810i	$0.296129\pi$
$761$	−11.0267	+	24.1452i	−0.399719	+	0.875263i	−0.997299	+	0.0734533i	$0.976598\pi$
$762$	16.2170	+	24.8398i	0.587481	+	0.899851i
$763$	−0.670057	+	9.36863i	−0.0242577	+	0.339167i
$764$	6.88885	−	6.14481i	0.249230	−	0.222311i
$765$	1.26679	+	2.08961i	0.0458009	+	0.0755499i
$766$	−44.0921	−	2.83514i	−1.59311	−	0.102438i
$767$	−36.1443	+	66.1933i	−1.30509	+	2.39010i
$768$	22.7858	+	20.3052i	0.822213	+	0.732701i
$769$	34.2399	−	4.92295i	1.23472	−	0.177526i	0.506120	−	0.862463i	$-0.331079\pi$
$769$	34.2399	−	4.92295i	1.23472	−	0.177526i	0.728602	+	0.684937i	$0.240170\pi$
$770$	8.90703	−	13.2966i	0.320987	−	0.479177i
$771$	−0.736688	+	0.336434i	−0.0265312	+	0.0121164i
$772$	17.0877	−	32.3922i	0.614998	−	1.16582i
$773$	23.3803	−	5.08608i	0.840932	−	0.182934i	0.228586	−	0.973524i	$-0.426590\pi$
$773$	23.3803	−	5.08608i	0.840932	−	0.182934i	0.612346	+	0.790590i	$0.290226\pi$
$774$	−0.609036	+	0.232159i	−0.0218913	+	0.00834478i
$775$	−12.9056	+	13.4052i	−0.463584	+	0.481528i
$776$	3.85033	−	7.42777i	0.138219	−	0.266641i
$777$	1.97063	+	0.428684i	0.0706959	+	0.0153789i
$778$	−5.06111	+	0.0363795i	−0.181449	+	0.00130427i
$779$	13.7875	+	4.04836i	0.493987	+	0.145048i
$780$	−46.7918	+	9.60056i	−1.67541	+	0.343755i
$781$	42.1185			1.50712
$782$	5.62536	−	10.1508i	0.201163	−	0.362993i
$783$	−18.4025	−	18.4025i	−0.657652	−	0.657652i
$784$	−25.0671	−	2.87131i	−0.895254	−	0.102547i
$785$	28.3383	+	19.2796i	1.01144	+	0.688118i
$786$	38.9303	+	38.3746i	1.38860	+	1.36878i
$787$	4.33490	−	19.9272i	0.154523	−	0.710329i	−0.833054	−	0.553192i	$-0.813410\pi$
$787$	4.33490	−	19.9272i	0.154523	−	0.710329i	0.987577	−	0.157138i	$-0.0502266\pi$
$788$	−1.61258	−	6.93162i	−0.0574458	−	0.246929i
$789$	−31.7392	−	4.56341i	−1.12995	−	0.162462i
$790$	−40.8808	+	2.14330i	−1.45447	+	0.0762552i
$791$	−4.45978	+	6.93956i	−0.158572	+	0.246742i
$792$	−10.0911	−	4.34799i	−0.358572	−	0.154499i
$793$	−60.4402	−	22.5430i	−2.14629	−	0.800527i
$794$	−24.2569	+	13.4725i	−0.860844	+	0.478121i
$795$	7.25742	+	10.2437i	0.257394	+	0.363308i
$796$	20.7337	−	47.1839i	0.734886	−	1.67239i
$797$	−3.39564	−	1.85416i	−0.120280	−	0.0656778i	0.417983	−	0.908455i	$-0.362737\pi$
$797$	−3.39564	−	1.85416i	−0.120280	−	0.0656778i	−0.538263	+	0.842777i	$0.680919\pi$
$798$	−6.99403	+	6.14894i	−0.247586	+	0.217670i
$799$	4.10887	−	4.74188i	0.145361	−	0.167756i
$800$	12.1720	−	25.5312i	0.430345	−	0.902665i
$801$	−4.18067	−	4.82475i	−0.147717	−	0.170474i
$802$	1.91976	+	2.94052i	0.0677891	+	0.103833i
$803$	15.1232	−	5.64067i	0.533687	−	0.199055i
$804$	6.90018	+	43.5390i	0.243350	+	1.53550i
$805$	6.96931	−	5.57106i	0.245636	−	0.196354i
$806$	2.31360	+	29.3791i	0.0814931	+	1.03483i
$807$	7.30968	+	19.5980i	0.257313	+	0.689883i
$808$	1.58590	−	1.43521i	0.0557916	−	0.0504906i
$809$	−2.92053	+	2.53066i	−0.102680	+	0.0889731i	−0.704688	−	0.709517i	$-0.748913\pi$
$809$	−2.92053	+	2.53066i	−0.102680	+	0.0889731i	0.602008	+	0.798490i	$0.294368\pi$
$810$	−31.3496	+	11.0183i	−1.10151	+	0.387143i
$811$	−6.94006	−	6.01360i	−0.243699	−	0.211166i	0.524444	−	0.851445i	$-0.324273\pi$
$811$	−6.94006	−	6.01360i	−0.243699	−	0.211166i	−0.768142	+	0.640279i	$0.778819\pi$
$812$	−6.89543	−	6.69997i	−0.241982	−	0.235123i
$813$	15.6561	−	28.6721i	0.549085	−	1.00557i
$814$	9.63144	+	5.16964i	0.337582	+	0.181196i
$815$	−4.62306	+	27.0933i	−0.161939	+	0.949036i
$816$	−9.61720	+	8.82998i	−0.336669	+	0.309111i
$817$	−1.04637	+	2.80542i	−0.0366077	+	0.0981492i
$818$	−0.439035	−	0.277712i	−0.0153505	−	0.00970997i
$819$	2.50300	+	1.60858i	0.0874619	+	0.0562084i
$820$	12.2882	+	9.42772i	0.429122	+	0.329230i
$821$	−4.93142	+	34.2988i	−0.172108	+	1.19703i	0.702314	+	0.711868i	$0.252150\pi$
$821$	−4.93142	+	34.2988i	−0.172108	+	1.19703i	−0.874421	+	0.485167i	$0.838759\pi$
$822$	−4.41539	−	29.2173i	−0.154004	−	1.01907i
$823$	49.9218	+	10.8598i	1.74016	+	0.378549i	0.966824	−	0.255443i	$-0.0822214\pi$
$823$	49.9218	+	10.8598i	1.74016	+	0.378549i	0.773339	+	0.633993i	$0.218585\pi$
$824$	−13.5148	−	9.66949i	−0.470812	−	0.336853i
$825$	−7.16489	+	57.5716i	−0.249449	+	2.00439i
$826$	−5.43157	+	14.8886i	−0.188988	+	0.518040i
$827$	29.3094	−	29.3094i	1.01919	−	1.01919i	0.0193756	−	0.999812i	$-0.493832\pi$
$827$	29.3094	−	29.3094i	1.01919	−	1.01919i	0.999812	−	0.0193756i	$-0.00616782\pi$
$828$	−4.63333	−	4.00716i	−0.161019	−	0.139259i
$829$			19.0962i			0.663239i	0.943413	+	0.331620i	$0.107595\pi$
$829$			19.0962i			0.663239i	−0.943413	+	0.331620i	$0.892405\pi$
$830$	−22.8714	+	2.84557i	−0.793879	+	0.0987713i
$831$	−4.55068	+	15.4982i	−0.157861	+	0.537626i
$832$	−17.4492	−	41.2566i	−0.604941	−	1.43031i
$833$	2.29428	−	10.5466i	0.0794922	−	0.365420i
$834$	−14.3673	−	10.5949i	−0.497498	−	0.366872i
$835$	−17.9081	−	8.75256i	−0.619734	−	0.302895i
$836$	−45.6095	+	21.6269i	−1.57744	+	0.747980i
$837$	3.56328	+	16.3801i	0.123165	+	0.566180i
$838$	11.9780	−	18.9361i	0.413774	−	0.654136i
$839$	−3.13388	−	6.86224i	−0.108194	−	0.236911i	0.847789	−	0.530333i	$-0.177933\pi$
$839$	−3.13388	−	6.86224i	−0.108194	−	0.236911i	−0.955983	+	0.293422i	$0.905206\pi$
$840$	−9.42092	+	3.46407i	−0.325052	+	0.119522i
$841$	0.623754	+	4.33831i	0.0215088	+	0.149597i
$842$	−7.97655	−	26.4605i	−0.274890	−	0.911890i
$843$	−9.63265	−	5.25982i	−0.331766	−	0.181158i
$844$	0.774195	+	53.8501i	0.0266489	+	1.85360i
$845$	39.8578	+	9.77108i	1.37115	+	0.336135i
$846$	−2.00374	−	2.63697i	−0.0688902	−	0.0906607i
$847$	−21.5778	−	1.54328i	−0.741423	−	0.0530276i
$848$	−8.08203	+	8.56067i	−0.277538	+	0.293974i
$849$	−33.4117	−	15.2586i	−1.14669	−	0.523674i
$850$	10.3464	+	6.27283i	0.354878	+	0.215156i
$851$	4.25090	+	4.36667i	0.145719	+	0.149687i
$852$	−21.3725	−	15.5249i	−0.732211	−	0.531875i
$853$	−16.0470	−	43.0237i	−0.549439	−	1.47310i	−0.853828	−	0.520555i	$-0.825725\pi$
$853$	−16.0470	−	43.0237i	−0.549439	−	1.47310i	0.304390	−	0.952548i	$-0.401548\pi$
$854$	−13.2661	−	2.78615i	−0.453957	−	0.0953401i
$855$	2.21545	−	5.49555i	0.0757669	−	0.187944i
$856$	−5.28951	−	5.06617i	−0.180792	−	0.173158i
$857$	6.92129	−	0.495021i	0.236427	−	0.0169096i	0.0473770	−	0.998877i	$-0.484914\pi$
$857$	6.92129	−	0.495021i	0.236427	−	0.0169096i	0.189050	+	0.981967i	$0.439459\pi$
$858$	60.6673	+	69.0052i	2.07115	+	2.35580i
$859$	2.52440	−	0.741229i	0.0861313	−	0.0252904i	−0.238383	−	0.971171i	$-0.576617\pi$
$859$	2.52440	−	0.741229i	0.0861313	−	0.0252904i	0.324514	+	0.945881i	$0.394799\pi$
$860$	−2.14213	+	2.41384i	−0.0730460	+	0.0823113i
$861$	−0.782228	−	5.44051i	−0.0266582	−	0.185412i
$862$	−4.55824	−	1.30291i	−0.155254	−	0.0443772i
$863$	−8.25553	+	22.1339i	−0.281022	+	0.753448i	0.717367	+	0.696696i	$0.245347\pi$
$863$	−8.25553	+	22.1339i	−0.281022	+	0.753448i	−0.998388	+	0.0567522i	$0.981926\pi$
$864$	−13.0071	−	21.9103i	−0.442510	−	0.745404i
$865$	37.6579	−	30.9408i	1.28041	−	1.05202i
$866$	6.90801	−	2.63327i	0.234744	−	0.0894821i
$867$	16.0863	+	21.4888i	0.546320	+	0.729798i
$868$	1.40323	+	6.03172i	0.0476286	+	0.204730i
$869$	42.5725	+	66.2441i	1.44417	+	2.24718i
$870$	33.2478	+	10.4533i	1.12721	+	0.354399i
$871$	18.2280	−	62.0789i	0.617633	−	2.10346i
$872$	26.4828	−	17.8379i	0.896821	−	0.604066i
$873$	1.33581	−	1.33581i	0.0452104	−	0.0452104i
$874$	−27.8790	+	3.83082i	−0.943020	+	0.129580i
$875$	5.52065	+	7.48685i	0.186632	+	0.253102i
$876$	−9.75325	−	2.71214i	−0.329532	−	0.0916348i
$877$	8.05763	+	14.7565i	0.272087	+	0.498290i	0.977618	−	0.210389i	$-0.0674732\pi$
$877$	8.05763	+	14.7565i	0.272087	+	0.498290i	−0.705531	+	0.708679i	$0.749291\pi$
$878$	−0.0722196	−	10.0472i	−0.00243729	−	0.339075i
$879$	21.6252	−	13.8977i	0.729401	−	0.468758i
$880$	−54.2578	+	4.01936i	−1.82903	+	0.135493i
$881$	7.96303	−	55.3841i	0.268281	−	1.86594i	−0.196490	−	0.980506i	$-0.562954\pi$
$881$	7.96303	−	55.3841i	0.268281	−	1.86594i	0.464771	−	0.885431i	$-0.346137\pi$
$882$	−5.19918	−	2.32937i	−0.175065	−	0.0784338i
$883$	−3.16942	−	14.5696i	−0.106660	−	0.490306i	−0.999224	−	0.0393862i	$-0.987460\pi$
$883$	−3.16942	−	14.5696i	−0.106660	−	0.490306i	0.892565	−	0.450920i	$-0.148904\pi$
$884$	18.3066	−	5.66239i	0.615717	−	0.190447i
$885$	−6.68314	−	57.0608i	−0.224651	−	1.91808i
$886$	19.3957	−	10.7725i	0.651610	−	0.361910i
$887$	4.10697	+	3.07444i	0.137899	+	0.103230i	0.666000	−	0.745952i	$-0.268005\pi$
$887$	4.10697	+	3.07444i	0.137899	+	0.103230i	−0.528101	+	0.849181i	$0.677096\pi$
$888$	−2.98182	−	6.17343i	−0.100063	−	0.207167i
$889$	−2.57765	−	8.77867i	−0.0864517	−	0.294427i
$890$	−29.4019	−	11.6080i	−0.985554	−	0.389101i
$891$	48.3067	+	41.8580i	1.61833	+	1.40229i
$892$	1.48591	−	26.0294i	0.0497520	−	0.871530i
$893$	−15.1756	−	1.08538i	−0.507831	−	0.0363208i
$894$	24.9941	+	5.24928i	0.835929	+	0.175562i
$895$	0.609571	+	13.4792i	0.0203757	+	0.450561i
$896$	−4.92104	−	8.02437i	−0.164401	−	0.268075i
$897$	20.6513	+	46.8765i	0.689528	+	1.56516i
$898$	−29.5811	+	34.6384i	−0.987135	+	1.15590i
$899$	8.93248	−	19.5594i	0.297915	−	0.652342i
$900$	4.36284	−	4.66409i	0.145428	−	0.155470i
$901$	−3.29805	−	3.80615i	−0.109874	−	0.126801i
$902$	4.02781	−	29.5187i	0.134111	−	0.982866i
$903$	1.14239	−	0.0817052i	0.0380163	−	0.00271898i
$904$	27.9217	−	2.60320i	0.928660	−	0.0865812i
$905$	19.2479	−	18.2646i	0.639823	−	0.607136i
$906$	−5.23149	−	2.80798i	−0.173805	−	0.0932890i
$907$	14.0842	+	10.5433i	0.467658	+	0.350084i	0.806973	−	0.590589i	$-0.201104\pi$
$907$	14.0842	+	10.5433i	0.467658	+	0.350084i	−0.339315	+	0.940673i	$0.610195\pi$
$908$	−4.49296	+	22.1845i	−0.149104	+	0.736220i
$909$	0.439317	−	0.200629i	0.0145712	−	0.00665446i
$910$	14.6720	+	1.33026i	0.486372	+	0.0440978i
$911$	−2.75970	+	4.29417i	−0.0914328	+	0.142272i	−0.883957	−	0.467568i	$-0.845130\pi$
$911$	−2.75970	+	4.29417i	−0.0914328	+	0.142272i	0.792524	+	0.609841i	$0.208767\pi$
$912$	31.1157	+	5.83740i	1.03034	+	0.193296i
$913$	26.5682	+	35.4910i	0.879280	+	1.17458i
$914$	−29.4192	−	21.6948i	−0.973102	−	0.717599i
$915$	47.4952	−	12.6038i	1.57014	−	0.416669i
$916$	−19.3979	−	16.3261i	−0.640923	−	0.539429i
$917$	−8.07995	−	14.7973i	−0.266823	−	0.488651i
$918$	9.88214	−	4.59915i	0.326159	−	0.151795i
$919$	50.2776			1.65850			0.829252	−	0.558874i	$-0.188767\pi$
$919$	50.2776			1.65850			0.829252	+	0.558874i	$0.188767\pi$
$920$	−29.5169	−	6.98213i	−0.973145	−	0.230194i
$921$	0.444323			0.0146410
$922$	−20.7984	+	9.67958i	−0.684958	+	0.318780i
$923$	18.5809	+	34.0284i	0.611598	+	1.12006i
$924$	14.7722	+	12.4329i	0.485970	+	0.409013i
$925$	−4.72183	+	4.25108i	−0.155253	+	0.139775i
$926$	3.23311	+	2.38421i	0.106247	+	0.0783499i
$927$	−2.24865	−	3.00385i	−0.0738555	−	0.0986594i
$928$	−3.48598	+	32.4977i	−0.114433	+	1.06679i
$929$	−14.2875	+	22.2318i	−0.468758	+	0.729401i	−0.992469	−	0.122494i	$-0.960911\pi$
$929$	−14.2875	+	22.2318i	−0.468758	+	0.729401i	0.523711	+	0.851896i	$0.324547\pi$
$930$	−14.3757	−	17.2424i	−0.471397	−	0.565400i
$931$	−23.8068	+	10.8722i	−0.780235	+	0.356321i
$932$	0.290649	−	1.43512i	0.00952053	−	0.0470088i
$933$	33.0599	+	24.7484i	1.08233	+	0.810225i
$934$	19.7422	+	10.5966i	0.645984	+	0.346730i
$935$	0.609886	−	23.2660i	0.0199454	−	0.760878i
$936$	−0.938938	−	10.0709i	−0.0306902	−	0.329179i
$937$	−44.0100	+	3.14766i	−1.43775	+	0.102830i	−0.768328	−	0.640057i	$-0.778911\pi$
$937$	−44.0100	+	3.14766i	−1.43775	+	0.102830i	−0.669418	+	0.742886i	$0.733456\pi$
$938$	1.83812	−	13.4711i	0.0600168	−	0.439847i
$939$	−1.79923	−	2.07642i	−0.0587157	−	0.0677615i
$940$	−14.8351	−	6.98826i	−0.483868	−	0.227932i
$941$	−2.91806	+	6.38965i	−0.0951259	+	0.208297i	−0.951213	−	0.308535i	$-0.900161\pi$
$941$	−2.91806	+	6.38965i	−0.0951259	+	0.208297i	0.856087	+	0.516831i	$0.172889\pi$
$942$	−26.8532	+	31.4441i	−0.874924	+	1.02450i
$943$	7.10201	−	15.0142i	0.231273	−	0.488928i
$944$	51.2366	−	16.6586i	1.66761	−	0.542192i
$945$	8.37145	−	0.378582i	0.272323	−	0.0123153i
$946$	6.07532	+	1.27594i	0.197526	+	0.0414844i
$947$	−4.38281	−	0.313465i	−0.142422	−	0.0101862i	−5.39270e−5	−	1.00000i	$-0.500017\pi$
$947$	−4.38281	−	0.313465i	−0.142422	−	0.0101862i	−0.142368	+	0.989814i	$0.545472\pi$
$948$	2.81473	−	49.3070i	0.0914183	−	1.60142i
$949$	11.2289	+	9.72992i	0.364506	+	0.315847i
$950$	−2.85813	−	29.1994i	−0.0927299	−	0.947354i
$951$	−12.3285	−	41.9871i	−0.399780	−	1.36152i
$952$	3.62594	−	1.75136i	0.117517	−	0.0567619i
$953$	−24.9340	−	18.6654i	−0.807692	−	0.604631i	0.113589	−	0.993528i	$-0.463765\pi$
$953$	−24.9340	−	18.6654i	−0.807692	−	0.604631i	−0.921281	+	0.388897i	$0.872856\pi$
$954$	−2.32395	+	1.29074i	−0.0752406	+	0.0417893i
$955$	6.39940	−	8.09730i	0.207080	−	0.262023i
$956$	−20.2348	+	6.25880i	−0.654439	+	0.202424i
$957$	−14.2505	−	65.5085i	−0.460654	−	2.11759i
$958$	19.2457	+	8.62259i	0.621801	+	0.278583i
$959$	−1.29699	+	9.02078i	−0.0418821	+	0.291296i
$960$	29.0140	+	17.9599i	0.936423	+	0.579653i
$961$	14.4274	−	9.27190i	0.465399	−	0.299094i
$962$	0.0723266	+	10.0621i	0.00233190	+	0.324414i
$963$	−0.792588	−	1.45152i	−0.0255408	−	0.0467745i
$964$	−25.7231	−	7.15297i	−0.828486	−	0.230382i
$965$	12.5613	−	38.9714i	0.404363	−	1.25453i
$966$	5.76286	+	9.09153i	0.185417	+	0.292515i
$967$	−19.1346	+	19.1346i	−0.615327	+	0.615327i	−0.944329	−	0.329002i	$-0.893288\pi$
$967$	−19.1346	+	19.1346i	−0.615327	+	0.615327i	0.329002	+	0.944329i	$0.393288\pi$
$968$	41.0842	+	60.9952i	1.32049	+	1.96046i
$969$	−3.81546	+	12.9943i	−0.122570	+	0.417436i
$970$	2.80552	−	8.92329i	0.0900799	−	0.286509i
$971$	−23.6631	−	36.8206i	−0.759386	−	1.18163i	−0.978564	−	0.205943i	$-0.933974\pi$
$971$	−23.6631	−	36.8206i	−0.759386	−	1.18163i	0.219178	−	0.975685i	$-0.429663\pi$
$972$	−2.95993	−	12.7232i	−0.0949399	−	0.408096i
$973$	3.29947	+	4.40757i	0.105776	+	0.141300i
$974$	−55.7453	+	21.2496i	−1.78620	+	0.680881i
$975$	−49.6741	+	19.6095i	−1.59084	+	0.628007i
$976$	20.3403	+	41.3501i	0.651077	+	1.32358i
$977$	−15.1611	+	40.6486i	−0.485048	+	1.30046i	0.432068	+	0.901841i	$0.357784\pi$
$977$	−15.1611	+	40.6486i	−0.485048	+	1.30046i	−0.917115	+	0.398622i	$0.869489\pi$
$978$	−31.8816	−	9.11289i	−1.01946	−	0.291398i
$979$	8.65338	+	60.1856i	0.276563	+	1.92354i
$980$	−28.1591	+	1.67937i	−0.899510	+	0.0536455i
$981$	6.91772	−	2.03123i	0.220866	−	0.0648521i
$982$	31.7874	+	36.1562i	1.01438	+	1.15379i
$983$	3.82592	−	0.273635i	0.122028	−	0.00872761i	−0.0101916	−	0.999948i	$-0.503244\pi$
$983$	3.82592	−	0.273635i	0.122028	−	0.00872761i	0.132220	+	0.991220i	$0.457790\pi$
$984$	−12.9245	+	13.4943i	−0.412018	+	0.430182i
$985$	−3.11455	−	7.32183i	−0.0992379	−	0.233293i
$986$	−13.6831	−	2.87372i	−0.435758	−	0.0915180i
$987$	2.03374	+	5.45268i	0.0647347	+	0.173561i
$988$	−37.5937	−	27.3079i	−1.19602	−	0.868781i
$989$	3.01498	+	1.69927i	0.0958708	+	0.0540338i
$990$	−11.9523	−	2.83918i	−0.379870	−	0.0902349i
$991$	−20.3770	−	9.30585i	−0.647296	−	0.295610i	0.0645831	−	0.997912i	$-0.479428\pi$
$991$	−20.3770	−	9.30585i	−0.647296	−	0.295610i	−0.711879	+	0.702302i	$0.752156\pi$
$992$	13.2058	−	16.3955i	0.419285	−	0.520557i
$993$	−32.6013	−	2.33169i	−1.03457	−	0.0739939i
$994$	4.92923	+	6.48697i	0.156346	+	0.205754i
$995$	13.7196	−	55.9646i	0.434941	−	1.77420i
$996$	−0.399713	−	27.8025i	−0.0126654	−	0.880957i
$997$	23.4615	+	12.8110i	0.743034	+	0.405727i	0.805713	−	0.592307i	$-0.201783\pi$
$997$	23.4615	+	12.8110i	0.743034	+	0.405727i	−0.0626790	+	0.998034i	$0.519964\pi$
$998$	−9.05844	−	30.0495i	−0.286740	−	0.951199i
$999$	0.814563	+	5.66541i	0.0257716	+	0.179246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.12	yes	1360
4.3	odd	2	inner	460.2.w.a.167.6	yes	1360
5.3	odd	4	inner	460.2.w.a.443.44	yes	1360
20.3	even	4	inner	460.2.w.a.443.41	yes	1360
23.4	even	11	inner	460.2.w.a.27.41	✓	1360
92.27	odd	22	inner	460.2.w.a.27.44	yes	1360
115.73	odd	44	inner	460.2.w.a.303.6	yes	1360
460.303	even	44	inner	460.2.w.a.303.12	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.41	✓	1360	23.4	even	11	inner
460.2.w.a.27.44	yes	1360	92.27	odd	22	inner
460.2.w.a.167.6	yes	1360	4.3	odd	2	inner
460.2.w.a.167.12	yes	1360	1.1	even	1	trivial
460.2.w.a.303.6	yes	1360	115.73	odd	44	inner
460.2.w.a.303.12	yes	1360	460.303	even	44	inner
460.2.w.a.443.41	yes	1360	20.3	even	4	inner
460.2.w.a.443.44	yes	1360	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28216 + 0.596717i) q^{2} +(-0.914180 - 1.67420i) q^{3} +(1.28786 - 1.53017i) q^{4} +(1.12269 - 1.93379i) q^{5} +(2.17114 + 1.60108i) q^{6} +(-0.498606 - 0.666060i) q^{7} +(-0.738158 + 2.73041i) q^{8} +(-0.345283 + 0.537271i) q^{9} +O(q^{10})\)	\(q+(-1.28216 + 0.596717i) q^{2} +(-0.914180 - 1.67420i) q^{3} +(1.28786 - 1.53017i) q^{4} +(1.12269 - 1.93379i) q^{5} +(2.17114 + 1.60108i) q^{6} +(-0.498606 - 0.666060i) q^{7} +(-0.738158 + 2.73041i) q^{8} +(-0.345283 + 0.537271i) q^{9} +(-0.285542 + 3.14936i) q^{10} +(5.53313 - 2.52690i) q^{11} +(-3.73914 - 0.757274i) q^{12} +(4.48251 + 3.35557i) q^{13} +(1.03674 + 0.556467i) q^{14} +(-4.26389 - 0.111772i) q^{15} +(-0.682845 - 3.94128i) q^{16} +(1.70676 - 0.122070i) q^{17} +(0.122109 - 0.894903i) q^{18} +(-2.71712 - 3.13572i) q^{19} +(-1.51317 - 4.20836i) q^{20} +(-0.659299 + 1.44366i) q^{21} +(-5.58651 + 6.54160i) q^{22} +(-4.06898 + 2.53839i) q^{23} +(5.24604 - 1.26026i) q^{24} +(-2.47912 - 4.34212i) q^{25} +(-7.74962 - 1.62758i) q^{26} +(-4.49285 - 0.321335i) q^{27} +(-1.66132 - 0.0948378i) q^{28} +(4.36657 + 3.78365i) q^{29} +(5.53368 - 2.40103i) q^{30} +(-1.04849 - 3.57083i) q^{31} +(3.22735 + 4.64588i) q^{32} +(-9.28880 - 6.95351i) q^{33} +(-2.11549 + 1.17496i) q^{34} +(-1.84780 + 0.216421i) q^{35} +(0.377441 + 1.22027i) q^{36} +(-0.270108 - 1.24167i) q^{37} +(5.35491 + 2.39914i) q^{38} +(1.52005 - 10.5722i) q^{39} +(4.45132 + 4.49286i) q^{40} +(-2.91347 + 1.87237i) q^{41} +(-0.0161330 - 2.24442i) q^{42} +(-0.345846 - 0.633370i) q^{43} +(3.25930 - 11.7209i) q^{44} +(0.651325 + 1.27090i) q^{45} +(3.70237 - 5.68265i) q^{46} +(2.59286 - 2.59286i) q^{47} +(-5.97424 + 4.74626i) q^{48} +(1.77710 - 6.05225i) q^{49} +(5.76964 + 4.08794i) q^{50} +(-1.76465 - 2.74585i) q^{51} +(10.9074 - 2.53752i) q^{52} +(-1.76383 - 2.35620i) q^{53} +(5.95229 - 2.26896i) q^{54} +(1.32551 - 13.5369i) q^{55} +(2.18666 - 0.869740i) q^{56} +(-2.76588 + 7.41560i) q^{57} +(-7.85640 - 2.24563i) q^{58} +(1.91686 + 13.3321i) q^{59} +(-5.66232 + 6.38054i) q^{60} +(-11.0538 + 3.24570i) q^{61} +(3.47511 + 3.95272i) q^{62} +(0.530015 - 0.0379074i) q^{63} +(-6.91024 - 4.03094i) q^{64} +(11.5215 - 4.90099i) q^{65} +(16.0590 + 3.37271i) q^{66} +(-4.03801 - 10.8263i) q^{67} +(2.01127 - 2.76884i) q^{68} +(7.96954 + 4.49171i) q^{69} +(2.24003 - 1.38010i) q^{70} +(6.29845 + 2.87641i) q^{71} +(-1.21210 - 1.33936i) q^{72} +(2.64676 + 0.189300i) q^{73} +(1.08724 + 1.43083i) q^{74} +(-5.00319 + 8.12001i) q^{75} +(-8.29745 + 0.119291i) q^{76} +(-4.44192 - 2.42547i) q^{77} +(4.35966 + 14.4623i) q^{78} +(1.84232 + 12.8136i) q^{79} +(-8.38826 - 3.10437i) q^{80} +(4.36522 + 9.55849i) q^{81} +(2.61825 - 4.13919i) q^{82} +(1.54925 + 7.12178i) q^{83} +(1.35997 + 2.86807i) q^{84} +(1.68011 - 3.43756i) q^{85} +(0.821372 + 0.605708i) q^{86} +(2.34274 - 10.7694i) q^{87} +(2.81513 + 16.9730i) q^{88} +(-2.81622 + 9.59117i) q^{89} +(-1.59347 - 1.24084i) q^{90} -4.65873i q^{91} +(-1.35609 + 9.49532i) q^{92} +(-5.01976 + 5.01976i) q^{93} +(-1.77725 + 4.87165i) q^{94} +(-9.11433 + 1.73389i) q^{95} +(4.82774 - 9.65038i) q^{96} +(-2.89037 - 0.628762i) q^{97} +(1.33296 + 8.82036i) q^{98} +(-0.552869 + 3.84529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

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