LMFDB - Embedded newform 287.2.f.a.50.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.f (of order $4$, degree $2$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.3
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99257i q^{2} +(1.04836 + 1.04836i) q^{3} -1.97032 q^{4} -1.71001i q^{5} +(2.08892 - 2.08892i) q^{6} +(-0.707107 - 0.707107i) q^{7} -0.0591377i q^{8} -0.801887i q^{9} +O(q^{10})$	\(q-1.99257i q^{2} +(1.04836 + 1.04836i) q^{3} -1.97032 q^{4} -1.71001i q^{5} +(2.08892 - 2.08892i) q^{6} +(-0.707107 - 0.707107i) q^{7} -0.0591377i q^{8} -0.801887i q^{9} -3.40730 q^{10} +(2.84040 + 2.84040i) q^{11} +(-2.06560 - 2.06560i) q^{12} +(-0.592796 - 0.592796i) q^{13} +(-1.40896 + 1.40896i) q^{14} +(1.79270 - 1.79270i) q^{15} -4.05848 q^{16} +(4.76775 - 4.76775i) q^{17} -1.59781 q^{18} +(-1.80684 + 1.80684i) q^{19} +3.36926i q^{20} -1.48260i q^{21} +(5.65969 - 5.65969i) q^{22} -7.37711 q^{23} +(0.0619976 - 0.0619976i) q^{24} +2.07587 q^{25} +(-1.18119 + 1.18119i) q^{26} +(3.98574 - 3.98574i) q^{27} +(1.39323 + 1.39323i) q^{28} +(6.01291 + 6.01291i) q^{29} +(-3.57208 - 3.57208i) q^{30} -7.24235 q^{31} +7.96851i q^{32} +5.95553i q^{33} +(-9.50005 - 9.50005i) q^{34} +(-1.20916 + 1.20916i) q^{35} +1.57997i q^{36} +8.10162 q^{37} +(3.60024 + 3.60024i) q^{38} -1.24293i q^{39} -0.101126 q^{40} +(-0.359047 + 6.39305i) q^{41} -2.95419 q^{42} +10.4798i q^{43} +(-5.59651 - 5.59651i) q^{44} -1.37123 q^{45} +14.6994i q^{46} +(-4.86475 + 4.86475i) q^{47} +(-4.25474 - 4.25474i) q^{48} +1.00000i q^{49} -4.13632i q^{50} +9.99662 q^{51} +(1.16800 + 1.16800i) q^{52} +(2.81694 + 2.81694i) q^{53} +(-7.94186 - 7.94186i) q^{54} +(4.85711 - 4.85711i) q^{55} +(-0.0418167 + 0.0418167i) q^{56} -3.78843 q^{57} +(11.9811 - 11.9811i) q^{58} +1.07024 q^{59} +(-3.53220 + 3.53220i) q^{60} -3.67573i q^{61} +14.4309i q^{62} +(-0.567020 + 0.567020i) q^{63} +7.76083 q^{64} +(-1.01369 + 1.01369i) q^{65} +11.8668 q^{66} +(5.59350 - 5.59350i) q^{67} +(-9.39399 + 9.39399i) q^{68} +(-7.73386 - 7.73386i) q^{69} +(2.40933 + 2.40933i) q^{70} +(8.63919 + 8.63919i) q^{71} -0.0474218 q^{72} -8.12811i q^{73} -16.1430i q^{74} +(2.17626 + 2.17626i) q^{75} +(3.56005 - 3.56005i) q^{76} -4.01694i q^{77} -2.47661 q^{78} +(-9.11025 - 9.11025i) q^{79} +6.94003i q^{80} +5.95132 q^{81} +(12.7386 + 0.715426i) q^{82} +0.0385714 q^{83} +2.92120i q^{84} +(-8.15288 - 8.15288i) q^{85} +20.8816 q^{86} +12.6074i q^{87} +(0.167975 - 0.167975i) q^{88} +(5.40564 + 5.40564i) q^{89} +2.73227i q^{90} +0.838340i q^{91} +14.5353 q^{92} +(-7.59258 - 7.59258i) q^{93} +(9.69333 + 9.69333i) q^{94} +(3.08970 + 3.08970i) q^{95} +(-8.35386 + 8.35386i) q^{96} +(-3.41803 + 3.41803i) q^{97} +1.99257 q^{98} +(2.27768 - 2.27768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.99257i		−	1.40896i	−0.709725	−	0.704479i	$-0.751181\pi$
$2$		−	1.99257i		−	1.40896i	0.709725	−	0.704479i	$-0.248819\pi$
$3$	1.04836	+	1.04836i	0.605270	+	0.605270i	0.941706	−	0.336436i	$-0.109222\pi$
$3$	1.04836	+	1.04836i	0.605270	+	0.605270i	−0.336436	+	0.941706i	$0.609222\pi$
$4$	−1.97032			−0.985160
$5$		−	1.71001i		−	0.764739i	−0.924010	−	0.382369i	$-0.875108\pi$
$5$		−	1.71001i		−	0.764739i	0.924010	−	0.382369i	$-0.124892\pi$
$6$	2.08892	−	2.08892i	0.852800	−	0.852800i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		−	0.0591377i		−	0.0209083i
$9$		−	0.801887i		−	0.267296i
$10$	−3.40730			−1.07748
$11$	2.84040	+	2.84040i	0.856414	+	0.856414i	0.990914	−	0.134499i	$-0.0429426\pi$
$11$	2.84040	+	2.84040i	0.856414	+	0.856414i	−0.134499	+	0.990914i	$0.542943\pi$
$12$	−2.06560	−	2.06560i	−0.596288	−	0.596288i
$13$	−0.592796	−	0.592796i	−0.164412	−	0.164412i	0.620106	−	0.784518i	$-0.287090\pi$
$13$	−0.592796	−	0.592796i	−0.164412	−	0.164412i	−0.784518	+	0.620106i	$0.787090\pi$
$14$	−1.40896	+	1.40896i	−0.376560	+	0.376560i
$15$	1.79270	−	1.79270i	0.462874	−	0.462874i
$16$	−4.05848			−1.01462
$17$	4.76775	−	4.76775i	1.15635	−	1.15635i	0.171093	−	0.985255i	$-0.445270\pi$
$17$	4.76775	−	4.76775i	1.15635	−	1.15635i	0.985255	−	0.171093i	$-0.0547300\pi$
$18$	−1.59781			−0.376608
$19$	−1.80684	+	1.80684i	−0.414517	+	0.414517i	−0.883309	−	0.468792i	$-0.844689\pi$
$19$	−1.80684	+	1.80684i	−0.414517	+	0.414517i	0.468792	+	0.883309i	$0.344689\pi$
$20$			3.36926i			0.753390i
$21$		−	1.48260i		−	0.323531i
$22$	5.65969	−	5.65969i	1.20665	−	1.20665i
$23$	−7.37711			−1.53823			−0.769117	−	0.639108i	$-0.779304\pi$
$23$	−7.37711			−1.53823			−0.769117	+	0.639108i	$0.779304\pi$
$24$	0.0619976	−	0.0619976i	0.0126552	−	0.0126552i
$25$	2.07587			0.415175
$26$	−1.18119	+	1.18119i	−0.231650	+	0.231650i
$27$	3.98574	−	3.98574i	0.767056	−	0.767056i
$28$	1.39323	+	1.39323i	0.263295	+	0.263295i
$29$	6.01291	+	6.01291i	1.11657	+	1.11657i	0.992241	+	0.124327i	$0.0396773\pi$
$29$	6.01291	+	6.01291i	1.11657	+	1.11657i	0.124327	+	0.992241i	$0.460323\pi$
$30$	−3.57208	−	3.57208i	−0.652169	−	0.652169i
$31$	−7.24235			−1.30076			−0.650382	−	0.759607i	$-0.725391\pi$
$31$	−7.24235			−1.30076			−0.650382	+	0.759607i	$0.725391\pi$
$32$			7.96851i			1.40865i
$33$			5.95553i			1.03672i
$34$	−9.50005	−	9.50005i	−1.62925	−	1.62925i
$35$	−1.20916	+	1.20916i	−0.204385	+	0.204385i
$36$			1.57997i			0.263329i
$37$	8.10162			1.33190			0.665949	−	0.745997i	$-0.268027\pi$
$37$	8.10162			1.33190			0.665949	+	0.745997i	$0.268027\pi$
$38$	3.60024	+	3.60024i	0.584036	+	0.584036i
$39$		−	1.24293i		−	0.199027i
$40$	−0.101126			−0.0159894
$41$	−0.359047	+	6.39305i	−0.0560738	+	0.998427i
$41$	−0.359047	+	6.39305i	−0.0560738	+	0.998427i
$42$	−2.95419			−0.455841
$43$			10.4798i			1.59815i	0.601233	+	0.799074i	$0.294677\pi$
$43$			10.4798i			1.59815i	−0.601233	+	0.799074i	$0.705323\pi$
$44$	−5.59651	−	5.59651i	−0.843705	−	0.843705i
$45$	−1.37123			−0.204411
$46$			14.6994i			2.16730i
$47$	−4.86475	+	4.86475i	−0.709596	+	0.709596i	−0.966450	−	0.256854i	$-0.917314\pi$
$47$	−4.86475	+	4.86475i	−0.709596	+	0.709596i	0.256854	+	0.966450i	$0.417314\pi$
$48$	−4.25474	−	4.25474i	−0.614119	−	0.614119i
$49$			1.00000i			0.142857i
$50$		−	4.13632i		−	0.584964i
$51$	9.99662			1.39981
$52$	1.16800	+	1.16800i	0.161972	+	0.161972i
$53$	2.81694	+	2.81694i	0.386937	+	0.386937i	0.873593	−	0.486656i	$-0.161784\pi$
$53$	2.81694	+	2.81694i	0.386937	+	0.386937i	−0.486656	+	0.873593i	$0.661784\pi$
$54$	−7.94186	−	7.94186i	−1.08075	−	1.08075i
$55$	4.85711	−	4.85711i	0.654933	−	0.654933i
$56$	−0.0418167	+	0.0418167i	−0.00558799	+	0.00558799i
$57$	−3.78843			−0.501789
$58$	11.9811	−	11.9811i	1.57320	−	1.57320i
$59$	1.07024			0.139334			0.0696670	−	0.997570i	$-0.477806\pi$
$59$	1.07024			0.139334			0.0696670	+	0.997570i	$0.477806\pi$
$60$	−3.53220	+	3.53220i	−0.456005	+	0.456005i
$61$		−	3.67573i		−	0.470628i	−0.971919	−	0.235314i	$-0.924388\pi$
$61$		−	3.67573i		−	0.470628i	0.971919	−	0.235314i	$-0.0756119\pi$
$62$			14.4309i			1.83272i
$63$	−0.567020	+	0.567020i	−0.0714378	+	0.0714378i
$64$	7.76083			0.970104
$65$	−1.01369	+	1.01369i	−0.125732	+	0.125732i
$66$	11.8668			1.46070
$67$	5.59350	−	5.59350i	0.683355	−	0.683355i	−0.277400	−	0.960755i	$-0.589473\pi$
$67$	5.59350	−	5.59350i	0.683355	−	0.683355i	0.960755	+	0.277400i	$0.0894726\pi$
$68$	−9.39399	+	9.39399i	−1.13919	+	1.13919i
$69$	−7.73386	−	7.73386i	−0.931047	−	0.931047i
$70$	2.40933	+	2.40933i	0.287970	+	0.287970i
$71$	8.63919	+	8.63919i	1.02528	+	1.02528i	0.999672	+	0.0256115i	$0.00815327\pi$
$71$	8.63919	+	8.63919i	1.02528	+	1.02528i	0.0256115	+	0.999672i	$0.491847\pi$
$72$	−0.0474218			−0.00558871
$73$		−	8.12811i		−	0.951324i	−0.879628	−	0.475662i	$-0.842209\pi$
$73$		−	8.12811i		−	0.951324i	0.879628	−	0.475662i	$-0.157791\pi$
$74$		−	16.1430i		−	1.87659i
$75$	2.17626	+	2.17626i	0.251293	+	0.251293i
$76$	3.56005	−	3.56005i	0.408365	−	0.408365i
$77$		−	4.01694i		−	0.457773i
$78$	−2.47661			−0.280421
$79$	−9.11025	−	9.11025i	−1.02498	−	1.02498i	−0.999680	−	0.0253031i	$-0.991945\pi$
$79$	−9.11025	−	9.11025i	−1.02498	−	1.02498i	−0.0253031	−	0.999680i	$-0.508055\pi$
$80$			6.94003i			0.775919i
$81$	5.95132			0.661257
$82$	12.7386	+	0.715426i	1.40674	+	0.0790055i
$83$	0.0385714			0.00423376			0.00211688	−	0.999998i	$-0.499326\pi$
$83$	0.0385714			0.00423376			0.00211688	+	0.999998i	$0.499326\pi$
$84$			2.92120i			0.318730i
$85$	−8.15288	−	8.15288i	−0.884304	−	0.884304i
$86$	20.8816			2.25172
$87$			12.6074i			1.35165i
$88$	0.167975	−	0.167975i	0.0179062	−	0.0179062i
$89$	5.40564	+	5.40564i	0.572996	+	0.572996i	0.932965	−	0.359968i	$-0.117212\pi$
$89$	5.40564	+	5.40564i	0.572996	+	0.572996i	−0.359968	+	0.932965i	$0.617212\pi$
$90$			2.73227i			0.288007i
$91$			0.838340i			0.0878819i
$92$	14.5353			1.51541
$93$	−7.59258	−	7.59258i	−0.787314	−	0.787314i
$94$	9.69333	+	9.69333i	0.999791	+	0.999791i
$95$	3.08970	+	3.08970i	0.316997	+	0.316997i
$96$	−8.35386	+	8.35386i	−0.852612	+	0.852612i
$97$	−3.41803	+	3.41803i	−0.347048	+	0.347048i	−0.859009	−	0.511961i	$-0.828919\pi$
$97$	−3.41803	+	3.41803i	−0.347048	+	0.347048i	0.511961	+	0.859009i	$0.328919\pi$
$98$	1.99257			0.201280
$99$	2.27768	−	2.27768i	0.228916	−	0.228916i
$100$	−4.09014			−0.409014
$101$	−7.36286	+	7.36286i	−0.732632	+	0.732632i	−0.971140	−	0.238508i	$-0.923342\pi$
$101$	−7.36286	+	7.36286i	−0.732632	+	0.732632i	0.238508	+	0.971140i	$0.423342\pi$
$102$		−	19.9189i		−	1.97227i
$103$			4.00131i			0.394260i	0.980377	+	0.197130i	$0.0631622\pi$
$103$			4.00131i			0.394260i	−0.980377	+	0.197130i	$0.936838\pi$
$104$	−0.0350566	+	0.0350566i	−0.00343758	+	0.00343758i
$105$	−2.53526			−0.247416
$106$	5.61295	−	5.61295i	0.545178	−	0.545178i
$107$	−6.38500			−0.617261			−0.308631	−	0.951182i	$-0.599871\pi$
$107$	−6.38500			−0.617261			−0.308631	+	0.951182i	$0.599871\pi$
$108$	−7.85319	+	7.85319i	−0.755674	+	0.755674i
$109$	−2.49830	+	2.49830i	−0.239293	+	0.239293i	−0.816557	−	0.577264i	$-0.804120\pi$
$109$	−2.49830	+	2.49830i	−0.239293	+	0.239293i	0.577264	+	0.816557i	$0.304120\pi$
$110$	−9.67812	−	9.67812i	−0.922773	−	0.922773i
$111$	8.49340	+	8.49340i	0.806158	+	0.806158i
$112$	2.86978	+	2.86978i	0.271168	+	0.271168i
$113$	1.95873			0.184262			0.0921310	−	0.995747i	$-0.470632\pi$
$113$	1.95873			0.184262			0.0921310	+	0.995747i	$0.470632\pi$
$114$			7.54869i			0.707000i
$115$			12.6149i			1.17635i
$116$	−11.8474	−	11.8474i	−1.10000	−	1.10000i
$117$	−0.475355	+	0.475355i	−0.0439466	+	0.0439466i
$118$		−	2.13253i		−	0.196316i
$119$	−6.74261			−0.618094
$120$	−0.106016	−	0.106016i	−0.00967792	−	0.00967792i
$121$			5.13580i			0.466891i
$122$	−7.32413			−0.663095
$123$	−7.07862	+	6.32580i	−0.638258	+	0.570378i
$124$	14.2697			1.28146
$125$		−	12.0998i		−	1.08224i
$126$	1.12982	+	1.12982i	0.100653	+	0.100653i
$127$	−13.7185			−1.21732			−0.608660	−	0.793431i	$-0.708293\pi$
$127$	−13.7185			−1.21732			−0.608660	+	0.793431i	$0.708293\pi$
$128$			0.473050i			0.0418121i
$129$	−10.9865	+	10.9865i	−0.967312	+	0.967312i
$130$	2.01984	+	2.01984i	0.177151	+	0.177151i
$131$		−	17.8281i		−	1.55765i	−0.627242	−	0.778824i	$-0.715816\pi$
$131$		−	17.8281i		−	1.55765i	0.627242	−	0.778824i	$-0.284184\pi$
$132$		−	11.7343i		−	1.02134i
$133$	2.55525			0.221568
$134$	−11.1454	−	11.1454i	−0.962818	−	0.962818i
$135$	−6.81565	−	6.81565i	−0.586598	−	0.586598i
$136$	−0.281954	−	0.281954i	−0.0241773	−	0.0241773i
$137$	2.76325	−	2.76325i	0.236080	−	0.236080i	−0.579145	−	0.815225i	$-0.696613\pi$
$137$	2.76325	−	2.76325i	0.236080	−	0.236080i	0.815225	+	0.579145i	$0.196613\pi$
$138$	−15.4102	+	15.4102i	−1.31181	+	1.31181i
$139$	−12.1962			−1.03447			−0.517235	−	0.855843i	$-0.673039\pi$
$139$	−12.1962			−1.03447			−0.517235	+	0.855843i	$0.673039\pi$
$140$	2.38243	−	2.38243i	0.201352	−	0.201352i
$141$	−10.2000			−0.858995
$142$	17.2142	−	17.2142i	1.44458	−	1.44458i
$143$		−	3.36756i		−	0.281610i
$144$			3.25444i			0.271203i
$145$	10.2821	−	10.2821i	0.853883	−	0.853883i
$146$	−16.1958			−1.34037
$147$	−1.04836	+	1.04836i	−0.0864672	+	0.0864672i
$148$	−15.9628			−1.31213
$149$	3.30313	−	3.30313i	0.270603	−	0.270603i	−0.558740	−	0.829343i	$-0.688715\pi$
$149$	3.30313	−	3.30313i	0.270603	−	0.270603i	0.829343	+	0.558740i	$0.188715\pi$
$150$	4.33634	−	4.33634i	0.354061	−	0.354061i
$151$	−1.07734	−	1.07734i	−0.0876725	−	0.0876725i	0.661910	−	0.749583i	$-0.269746\pi$
$151$	−1.07734	−	1.07734i	−0.0876725	−	0.0876725i	−0.749583	+	0.661910i	$0.769746\pi$
$152$	0.106852	+	0.106852i	0.00866686	+	0.00866686i
$153$	−3.82319	−	3.82319i	−0.309087	−	0.309087i
$154$	−8.00402			−0.644982
$155$			12.3845i			0.994744i
$156$			2.44896i			0.196074i
$157$	−12.5103	−	12.5103i	−0.998431	−	0.998431i	0.00156749	−	0.999999i	$-0.499501\pi$
$157$	−12.5103	−	12.5103i	−0.998431	−	0.998431i	−0.999999	+	0.00156749i	$0.999501\pi$
$158$	−18.1528	+	18.1528i	−1.44416	+	1.44416i
$159$			5.90634i			0.468403i
$160$	13.6262			1.07725
$161$	5.21640	+	5.21640i	0.411110	+	0.411110i
$162$		−	11.8584i		−	0.931683i
$163$	16.2432			1.27227			0.636134	−	0.771578i	$-0.280532\pi$
$163$	16.2432			1.27227			0.636134	+	0.771578i	$0.280532\pi$
$164$	0.707438	−	12.5964i	0.0552417	−	0.983610i
$165$	10.1840			0.792823
$166$		−	0.0768560i		−	0.00596518i
$167$	−2.76406	−	2.76406i	−0.213889	−	0.213889i	0.592028	−	0.805917i	$-0.298327\pi$
$167$	−2.76406	−	2.76406i	−0.213889	−	0.213889i	−0.805917	+	0.592028i	$0.798327\pi$
$168$	−0.0876778			−0.00676449
$169$		−	12.2972i		−	0.945937i
$170$	−16.2452	+	16.2452i	−1.24595	+	1.24595i
$171$	1.44888	+	1.44888i	0.110798	+	0.110798i
$172$		−	20.6485i		−	1.57443i
$173$			6.73549i			0.512089i	0.966665	+	0.256045i	$0.0824194\pi$
$173$			6.73549i			0.512089i	−0.966665	+	0.256045i	$0.917581\pi$
$174$	25.1210			1.90442
$175$	−1.46786	−	1.46786i	−0.110960	−	0.110960i
$176$	−11.5277	−	11.5277i	−0.868934	−	0.868934i
$177$	1.12200	+	1.12200i	0.0843347	+	0.0843347i
$178$	10.7711	−	10.7711i	0.807327	−	0.807327i
$179$	−2.24734	+	2.24734i	−0.167974	+	0.167974i	−0.786088	−	0.618114i	$-0.787897\pi$
$179$	−2.24734	+	2.24734i	−0.167974	+	0.167974i	0.618114	+	0.786088i	$0.287897\pi$
$180$	2.70177			0.201378
$181$	−1.94277	+	1.94277i	−0.144405	+	0.144405i	−0.775613	−	0.631208i	$-0.782559\pi$
$181$	−1.94277	+	1.94277i	−0.144405	+	0.144405i	0.631208	+	0.775613i	$0.282559\pi$
$182$	1.67045			0.123822
$183$	3.85348	−	3.85348i	0.284857	−	0.284857i
$184$			0.436265i			0.0321619i
$185$		−	13.8538i		−	1.01855i
$186$	−15.1287	+	15.1287i	−1.10929	+	1.10929i
$187$	27.0847			1.98063
$188$	9.58511	−	9.58511i	0.699066	−	0.699066i
$189$	−5.63669			−0.410009
$190$	6.15644	−	6.15644i	0.446635	−	0.446635i
$191$	−3.68711	+	3.68711i	−0.266790	+	0.266790i	−0.827805	−	0.561015i	$-0.810411\pi$
$191$	−3.68711	+	3.68711i	−0.266790	+	0.266790i	0.561015	+	0.827805i	$0.310411\pi$
$192$	8.13614	+	8.13614i	0.587175	+	0.587175i
$193$	−2.01594	−	2.01594i	−0.145111	−	0.145111i	0.630819	−	0.775930i	$-0.282719\pi$
$193$	−2.01594	−	2.01594i	−0.145111	−	0.145111i	−0.775930	+	0.630819i	$0.782719\pi$
$194$	6.81065	+	6.81065i	0.488976	+	0.488976i
$195$	−2.12541			−0.152204
$196$		−	1.97032i		−	0.140737i
$197$			17.8984i			1.27521i	0.770365	+	0.637603i	$0.220074\pi$
$197$			17.8984i			1.27521i	−0.770365	+	0.637603i	$0.779926\pi$
$198$	−4.53843	−	4.53843i	−0.322532	−	0.322532i
$199$	−15.7627	+	15.7627i	−1.11739	+	1.11739i	−0.125263	+	0.992124i	$0.539977\pi$
$199$	−15.7627	+	15.7627i	−1.11739	+	1.11739i	−0.992124	+	0.125263i	$0.960023\pi$
$200$		−	0.122762i		−	0.00868062i
$201$	11.7280			0.827229
$202$	14.6710	+	14.6710i	1.03225	+	1.03225i
$203$		−	8.50353i		−	0.596831i
$204$	−19.6965			−1.37903
$205$	10.9322	+	0.613974i	0.763535	+	0.0428818i
$206$	7.97287			0.555496
$207$			5.91561i			0.411163i
$208$	2.40585	+	2.40585i	0.166816	+	0.166816i
$209$	−10.2643			−0.709996
$210$			5.05168i			0.348599i
$211$	−3.51812	+	3.51812i	−0.242197	+	0.242197i	−0.817759	−	0.575561i	$-0.804784\pi$
$211$	−3.51812	+	3.51812i	−0.242197	+	0.242197i	0.575561	+	0.817759i	$0.304784\pi$
$212$	−5.55028	−	5.55028i	−0.381195	−	0.381195i
$213$			18.1139i			1.24115i
$214$			12.7225i			0.869695i
$215$	17.9205			1.22217
$216$	−0.235708	−	0.235708i	−0.0160379	−	0.0160379i
$217$	5.12111	+	5.12111i	0.347644	+	0.347644i
$218$	4.97802	+	4.97802i	0.337154	+	0.337154i
$219$	8.52118	−	8.52118i	0.575808	−	0.575808i
$220$	−9.57007	+	9.57007i	−0.645214	+	0.645214i
$221$	−5.65260			−0.380235
$222$	16.9237	−	16.9237i	1.13584	−	1.13584i
$223$	18.9379			1.26818			0.634089	−	0.773260i	$-0.281375\pi$
$223$	18.9379			1.26818			0.634089	+	0.773260i	$0.281375\pi$
$224$	5.63459	−	5.63459i	0.376477	−	0.376477i
$225$		−	1.66462i		−	0.110974i
$226$		−	3.90290i		−	0.259617i
$227$	20.9028	−	20.9028i	1.38737	−	1.38737i	0.556560	−	0.830807i	$-0.312121\pi$
$227$	20.9028	−	20.9028i	1.38737	−	1.38737i	0.830807	−	0.556560i	$-0.187879\pi$
$228$	7.46441			0.494343
$229$	−11.5626	+	11.5626i	−0.764076	+	0.764076i	−0.977056	−	0.212981i	$-0.931683\pi$
$229$	−11.5626	+	11.5626i	−0.764076	+	0.764076i	0.212981	+	0.977056i	$0.431683\pi$
$230$	25.1360			1.65742
$231$	4.21119	−	4.21119i	0.277076	−	0.277076i
$232$	0.355590	−	0.355590i	0.0233456	−	0.0233456i
$233$	1.50094	+	1.50094i	0.0983298	+	0.0983298i	0.754560	−	0.656231i	$-0.227850\pi$
$233$	1.50094	+	1.50094i	0.0983298	+	0.0983298i	−0.656231	+	0.754560i	$0.727850\pi$
$234$	0.947177	+	0.947177i	0.0619189	+	0.0619189i
$235$	8.31875	+	8.31875i	0.542656	+	0.542656i
$236$	−2.10872			−0.137266
$237$		−	19.1016i		−	1.24078i
$238$			13.4351i			0.870868i
$239$	−16.5540	−	16.5540i	−1.07079	−	1.07079i	−0.997296	−	0.0734940i	$-0.976585\pi$
$239$	−16.5540	−	16.5540i	−1.07079	−	1.07079i	−0.0734940	−	0.997296i	$-0.523415\pi$
$240$	−7.27564	+	7.27564i	−0.469641	+	0.469641i
$241$		−	11.4183i		−	0.735516i	−0.929922	−	0.367758i	$-0.880126\pi$
$241$		−	11.4183i		−	0.735516i	0.929922	−	0.367758i	$-0.119874\pi$
$242$	10.2334			0.657829
$243$	−5.71811	−	5.71811i	−0.366817	−	0.366817i
$244$			7.24236i			0.463644i
$245$	1.71001			0.109248
$246$	12.6046	+	14.1046i	0.803639	+	0.899278i
$247$	2.14217			0.136303
$248$			0.428296i			0.0271968i
$249$	0.0404366	+	0.0404366i	0.00256257	+	0.00256257i
$250$	−24.1097			−1.52483
$251$			10.2461i			0.646729i	0.946274	+	0.323365i	$0.104814\pi$
$251$			10.2461i			0.646729i	−0.946274	+	0.323365i	$0.895186\pi$
$252$	1.11721	−	1.11721i	0.0703776	−	0.0703776i
$253$	−20.9540	−	20.9540i	−1.31736	−	1.31736i
$254$			27.3350i			1.71515i
$255$		−	17.0943i		−	1.07049i
$256$	16.4642			1.02902
$257$	−15.5713	−	15.5713i	−0.971311	−	0.971311i	0.0282886	−	0.999600i	$-0.490994\pi$
$257$	−15.5713	−	15.5713i	−0.971311	−	0.971311i	−0.999600	+	0.0282886i	$0.990994\pi$
$258$	21.8914	+	21.8914i	1.36290	+	1.36290i
$259$	−5.72871	−	5.72871i	−0.355965	−	0.355965i
$260$	1.99729	−	1.99729i	0.123866	−	0.123866i
$261$	4.82167	−	4.82167i	0.298454	−	0.298454i
$262$	−35.5237			−2.19466
$263$	19.0396	−	19.0396i	1.17403	−	1.17403i	0.192794	−	0.981239i	$-0.438245\pi$
$263$	19.0396	−	19.0396i	1.17403	−	1.17403i	0.981239	−	0.192794i	$-0.0617550\pi$
$264$	0.352196			0.0216762
$265$	4.81700	−	4.81700i	0.295906	−	0.295906i
$266$		−	5.09151i		−	0.312180i
$267$			11.3341i			0.693635i
$268$	−11.0210	+	11.0210i	−0.673214	+	0.673214i
$269$	−15.6959			−0.956998			−0.478499	−	0.878088i	$-0.658819\pi$
$269$	−15.6959			−0.956998			−0.478499	+	0.878088i	$0.658819\pi$
$270$	−13.5806	+	13.5806i	−0.826491	+	0.826491i
$271$	10.1358			0.615706			0.307853	−	0.951434i	$-0.400390\pi$
$271$	10.1358			0.615706			0.307853	+	0.951434i	$0.400390\pi$
$272$	−19.3498	+	19.3498i	−1.17325	+	1.17325i
$273$	−0.878881	+	0.878881i	−0.0531923	+	0.0531923i
$274$	−5.50595	−	5.50595i	−0.332627	−	0.332627i
$275$	5.89632	+	5.89632i	0.355562	+	0.355562i
$276$	15.2382	+	15.2382i	0.917231	+	0.917231i
$277$	−5.96062			−0.358139			−0.179070	−	0.983836i	$-0.557309\pi$
$277$	−5.96062			−0.358139			−0.179070	+	0.983836i	$0.557309\pi$
$278$			24.3018i			1.45753i
$279$			5.80754i			0.347688i
$280$	0.0715068	+	0.0715068i	0.00427335	+	0.00427335i
$281$	−3.56491	+	3.56491i	−0.212665	+	0.212665i	−0.805398	−	0.592734i	$-0.798049\pi$
$281$	−3.56491	+	3.56491i	−0.212665	+	0.212665i	0.592734	+	0.805398i	$0.298049\pi$
$282$			20.3242i			1.21029i
$283$	−9.43270			−0.560716			−0.280358	−	0.959896i	$-0.590453\pi$
$283$	−9.43270			−0.560716			−0.280358	+	0.959896i	$0.590453\pi$
$284$	−17.0220	−	17.0220i	−1.01007	−	1.01007i
$285$			6.47824i			0.383738i
$286$	−6.71009			−0.396776
$287$	4.77445	−	4.26668i	0.281827	−	0.251854i
$288$	6.38984			0.376525
$289$		−	28.4628i		−	1.67428i
$290$	−20.4878	−	20.4878i	−1.20308	−	1.20308i
$291$	−7.16664			−0.420116
$292$			16.0150i			0.937207i
$293$	11.5566	−	11.5566i	0.675142	−	0.675142i	−0.283755	−	0.958897i	$-0.591580\pi$
$293$	11.5566	−	11.5566i	0.675142	−	0.675142i	0.958897	+	0.283755i	$0.0915801\pi$
$294$	2.08892	+	2.08892i	0.121829	+	0.121829i
$295$		−	1.83013i		−	0.106554i
$296$		−	0.479111i		−	0.0278478i
$297$	22.6422			1.31384
$298$	−6.58170	−	6.58170i	−0.381268	−	0.381268i
$299$	4.37312	+	4.37312i	0.252904	+	0.252904i
$300$	−4.28793	−	4.28793i	−0.247564	−	0.247564i
$301$	7.41031	−	7.41031i	0.427123	−	0.427123i
$302$	−2.14667	+	2.14667i	−0.123527	+	0.123527i
$303$	−15.4378			−0.886881
$304$	7.33300	−	7.33300i	0.420577	−	0.420577i
$305$	−6.28552			−0.359908
$306$	−7.61796	+	7.61796i	−0.435490	+	0.435490i
$307$			17.6708i			1.00852i	0.863551	+	0.504262i	$0.168235\pi$
$307$			17.6708i			1.00852i	−0.863551	+	0.504262i	$0.831765\pi$
$308$			7.91466i			0.450980i
$309$	−4.19480	+	4.19480i	−0.238634	+	0.238634i
$310$	24.6769			1.40155
$311$	−4.71217	+	4.71217i	−0.267203	+	0.267203i	−0.827972	−	0.560769i	$-0.810505\pi$
$311$	−4.71217	+	4.71217i	−0.267203	+	0.267203i	0.560769	+	0.827972i	$0.310505\pi$
$312$	−0.0735038			−0.00416133
$313$	−12.8211	+	12.8211i	−0.724690	+	0.724690i	−0.969557	−	0.244866i	$-0.921256\pi$
$313$	−12.8211	+	12.8211i	−0.724690	+	0.724690i	0.244866	+	0.969557i	$0.421256\pi$
$314$	−24.9276	+	24.9276i	−1.40675	+	1.40675i
$315$	0.969608	+	0.969608i	0.0546312	+	0.0546312i
$316$	17.9501	+	17.9501i	1.00977	+	1.00977i
$317$	16.9776	+	16.9776i	0.953555	+	0.953555i	0.998968	−	0.0454129i	$-0.0144603\pi$
$317$	16.9776	+	16.9776i	0.953555	+	0.953555i	−0.0454129	+	0.998968i	$0.514460\pi$
$318$	11.7688			0.659960
$319$			34.1582i			1.91249i
$320$		−	13.2711i		−	0.741876i
$321$	−6.69377	−	6.69377i	−0.373610	−	0.373610i
$322$	10.3940	−	10.3940i	0.579237	−	0.579237i
$323$			17.2291i			0.958651i
$324$	−11.7260			−0.651445
$325$	−1.23057	−	1.23057i	−0.0682597	−	0.0682597i
$326$		−	32.3657i		−	1.79257i
$327$	−5.23822			−0.289674
$328$	0.378070	+	0.0212332i	0.0208754	+	0.00117241i
$329$	6.87979			0.379295
$330$		−	20.2923i		−	1.11705i
$331$	9.67940	+	9.67940i	0.532028	+	0.532028i	0.921175	−	0.389148i	$-0.127230\pi$
$331$	9.67940	+	9.67940i	0.532028	+	0.532028i	−0.389148	+	0.921175i	$0.627230\pi$
$332$	−0.0759979			−0.00417093
$333$		−	6.49658i		−	0.356010i
$334$	−5.50757	+	5.50757i	−0.301361	+	0.301361i
$335$	−9.56493	−	9.56493i	−0.522588	−	0.522588i
$336$			6.01711i			0.328260i
$337$			19.9893i			1.08889i	0.838798	+	0.544443i	$0.183259\pi$
$337$			19.9893i			1.08889i	−0.838798	+	0.544443i	$0.816741\pi$
$338$	−24.5030			−1.33279
$339$	2.05345	+	2.05345i	0.111528	+	0.111528i
$340$	16.0638	+	16.0638i	0.871181	+	0.871181i
$341$	−20.5712	−	20.5712i	−1.11399	−	1.11399i
$342$	2.88699	−	2.88699i	0.156110	−	0.156110i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	0.619749			0.0334146
$345$	−13.2250	+	13.2250i	−0.712008	+	0.712008i
$346$	13.4209			0.721512
$347$	−8.14927	+	8.14927i	−0.437476	+	0.437476i	−0.891162	−	0.453686i	$-0.850109\pi$
$347$	−8.14927	+	8.14927i	−0.437476	+	0.437476i	0.453686	+	0.891162i	$0.350109\pi$
$348$		−	24.8406i		−	1.33159i
$349$		−	33.0530i		−	1.76929i	−0.466268	−	0.884643i	$-0.654402\pi$
$349$		−	33.0530i		−	1.76929i	0.466268	−	0.884643i	$-0.345598\pi$
$350$	−2.92482	+	2.92482i	−0.156338	+	0.156338i
$351$	−4.72546			−0.252227
$352$	−22.6338	+	22.6338i	−1.20639	+	1.20639i
$353$	26.5993			1.41574			0.707870	−	0.706343i	$-0.249656\pi$
$353$	26.5993			1.41574			0.707870	+	0.706343i	$0.249656\pi$
$354$	2.23566	−	2.23566i	0.118824	−	0.118824i
$355$	14.7731	−	14.7731i	0.784074	−	0.784074i
$356$	−10.6508	−	10.6508i	−0.564493	−	0.564493i
$357$	−7.06868	−	7.06868i	−0.374114	−	0.374114i
$358$	4.47798	+	4.47798i	0.236669	+	0.236669i
$359$	26.2971			1.38791			0.693953	−	0.720020i	$-0.255868\pi$
$359$	26.2971			1.38791			0.693953	+	0.720020i	$0.255868\pi$
$360$			0.0810916i			0.00427390i
$361$			12.4707i			0.656352i
$362$	3.87109	+	3.87109i	0.203460	+	0.203460i
$363$	−5.38416	+	5.38416i	−0.282595	+	0.282595i
$364$		−	1.65180i		−	0.0865778i
$365$	−13.8991			−0.727514
$366$	−7.67831	−	7.67831i	−0.401352	−	0.401352i
$367$		−	2.09815i		−	0.109522i	−0.998499	−	0.0547612i	$-0.982560\pi$
$367$		−	2.09815i		−	0.109522i	0.998499	−	0.0547612i	$-0.0174397\pi$
$368$	29.9398			1.56072
$369$	5.12650	+	0.287915i	0.266875	+	0.0149883i
$370$	−27.6047			−1.43510
$371$		−	3.98376i		−	0.206827i
$372$	14.9598	+	14.9598i	0.775630	+	0.775630i
$373$	−16.6588			−0.862559			−0.431279	−	0.902218i	$-0.641938\pi$
$373$	−16.6588			−0.862559			−0.431279	+	0.902218i	$0.641938\pi$
$374$		−	53.9680i		−	2.79062i
$375$	12.6849	−	12.6849i	0.655047	−	0.655047i
$376$	0.287690	+	0.287690i	0.0148365	+	0.0148365i
$377$		−	7.12885i		−	0.367155i
$378$			11.2315i			0.577685i
$379$	−10.7197			−0.550636			−0.275318	−	0.961353i	$-0.588783\pi$
$379$	−10.7197			−0.550636			−0.275318	+	0.961353i	$0.588783\pi$
$380$	−6.08771	−	6.08771i	−0.312293	−	0.312293i
$381$	−14.3819	−	14.3819i	−0.736808	−	0.736808i
$382$	7.34681	+	7.34681i	0.375896	+	0.375896i
$383$	25.1439	−	25.1439i	1.28479	−	1.28479i	0.346887	−	0.937907i	$-0.387239\pi$
$383$	25.1439	−	25.1439i	1.28479	−	1.28479i	0.937907	−	0.346887i	$-0.112761\pi$
$384$	−0.495926	+	0.495926i	−0.0253076	+	0.0253076i
$385$	−6.86900			−0.350076
$386$	−4.01690	+	4.01690i	−0.204455	+	0.204455i
$387$	8.40358			0.427178
$388$	6.73461	−	6.73461i	0.341898	−	0.341898i
$389$			16.9589i			0.859850i	0.902865	+	0.429925i	$0.141460\pi$
$389$			16.9589i			0.859850i	−0.902865	+	0.429925i	$0.858540\pi$
$390$			4.23503i			0.214449i
$391$	−35.1722	+	35.1722i	−1.77873	+	1.77873i
$392$	0.0591377			0.00298691
$393$	18.6903	−	18.6903i	0.942799	−	0.942799i
$394$	35.6637			1.79671
$395$	−15.5786	+	15.5786i	−0.783844	+	0.783844i
$396$	−4.48777	+	4.48777i	−0.225519	+	0.225519i
$397$	2.85558	+	2.85558i	0.143317	+	0.143317i	0.775125	−	0.631808i	$-0.217687\pi$
$397$	2.85558	+	2.85558i	0.143317	+	0.143317i	−0.631808	+	0.775125i	$0.717687\pi$
$398$	31.4082	+	31.4082i	1.57435	+	1.57435i
$399$	2.67882	+	2.67882i	0.134109	+	0.134109i
$400$	−8.42489			−0.421244
$401$		−	2.69537i		−	0.134600i	−0.997733	−	0.0673001i	$-0.978562\pi$
$401$		−	2.69537i		−	0.134600i	0.997733	−	0.0673001i	$-0.0214385\pi$
$402$		−	23.3688i		−	1.16553i
$403$	4.29323	+	4.29323i	0.213861	+	0.213861i
$404$	14.5072	−	14.5072i	0.721760	−	0.721760i
$405$		−	10.1768i		−	0.505689i
$406$	−16.9439			−0.840909
$407$	23.0119	+	23.0119i	1.14066	+	1.14066i
$408$		−	0.591177i		−	0.0292676i
$409$	−29.7521			−1.47115			−0.735574	−	0.677444i	$-0.763087\pi$
$409$	−29.7521			−1.47115			−0.735574	+	0.677444i	$0.763087\pi$
$410$	1.22338	−	21.7831i	0.0604186	−	1.07579i
$411$	5.79375			0.285784
$412$		−	7.88386i		−	0.388410i
$413$	−0.756777	−	0.756777i	−0.0372386	−	0.0372386i
$414$	11.7872			0.579311
$415$		−	0.0659573i		−	0.00323772i
$416$	4.72370	−	4.72370i	0.231599	−	0.231599i
$417$	−12.7860	−	12.7860i	−0.626135	−	0.626135i
$418$			20.4523i			1.00035i
$419$			6.75170i			0.329842i	0.986307	+	0.164921i	$0.0527370\pi$
$419$			6.75170i			0.329842i	−0.986307	+	0.164921i	$0.947263\pi$
$420$	4.99528			0.243745
$421$	−0.0879658	−	0.0879658i	−0.00428719	−	0.00428719i	0.704960	−	0.709247i	$-0.250965\pi$
$421$	−0.0879658	−	0.0879658i	−0.00428719	−	0.00428719i	−0.709247	+	0.704960i	$0.750965\pi$
$422$	7.01008	+	7.01008i	0.341245	+	0.341245i
$423$	3.90098	+	3.90098i	0.189672	+	0.189672i
$424$	0.166588	−	0.166588i	0.00809021	−	0.00809021i
$425$	9.89724	−	9.89724i	0.480087	−	0.480087i
$426$	36.0932			1.74872
$427$	−2.59913	+	2.59913i	−0.125781	+	0.125781i
$428$	12.5805			0.608101
$429$	3.53041	−	3.53041i	0.170450	−	0.170450i
$430$		−	35.7077i		−	1.72198i
$431$		−	36.2041i		−	1.74389i	−0.489604	−	0.871945i	$-0.662859\pi$
$431$		−	36.2041i		−	1.74389i	0.489604	−	0.871945i	$-0.337141\pi$
$432$	−16.1760	+	16.1760i	−0.778270	+	0.778270i
$433$	7.25278			0.348546			0.174273	−	0.984697i	$-0.444242\pi$
$433$	7.25278			0.348546			0.174273	+	0.984697i	$0.444242\pi$
$434$	10.2042	−	10.2042i	0.489815	−	0.489815i
$435$	21.5587			1.03366
$436$	4.92244	−	4.92244i	0.235742	−	0.235742i
$437$	13.3292	−	13.3292i	0.637623	−	0.637623i
$438$	−16.9790	−	16.9790i	−0.811289	−	0.811289i
$439$	−17.0495	−	17.0495i	−0.813728	−	0.813728i	0.171462	−	0.985191i	$-0.445151\pi$
$439$	−17.0495	−	17.0495i	−0.813728	−	0.813728i	−0.985191	+	0.171462i	$0.945151\pi$
$440$	−0.287239	−	0.287239i	−0.0136936	−	0.0136936i
$441$	0.801887			0.0381851
$442$			11.2632i			0.535735i
$443$			0.850459i			0.0404065i	0.999796	+	0.0202033i	$0.00643133\pi$
$443$			0.850459i			0.0404065i	−0.999796	+	0.0202033i	$0.993569\pi$
$444$	−16.7347	−	16.7347i	−0.794195	−	0.794195i
$445$	9.24368	−	9.24368i	0.438192	−	0.438192i
$446$		−	37.7351i		−	1.78681i
$447$	6.92573			0.327576
$448$	−5.48774	−	5.48774i	−0.259271	−	0.259271i
$449$			31.2196i			1.47334i	0.676250	+	0.736672i	$0.263604\pi$
$449$			31.2196i			1.47334i	−0.676250	+	0.736672i	$0.736396\pi$
$450$	−3.31686			−0.156358
$451$	−19.1787	+	17.1390i	−0.903089	+	0.807044i
$452$	−3.85933			−0.181528
$453$		−	2.25887i		−	0.106131i
$454$	−41.6502	−	41.6502i	−1.95474	−	1.95474i
$455$	1.43357			0.0672067
$456$			0.224039i			0.0104916i
$457$	−14.3012	+	14.3012i	−0.668981	+	0.668981i	−0.957480	−	0.288499i	$-0.906844\pi$
$457$	−14.3012	+	14.3012i	−0.668981	+	0.668981i	0.288499	+	0.957480i	$0.406844\pi$
$458$	23.0392	+	23.0392i	1.07655	+	1.07655i
$459$		−	38.0060i		−	1.77397i
$460$		−	24.8554i		−	1.15889i
$461$	−22.9484			−1.06881			−0.534406	−	0.845228i	$-0.679465\pi$
$461$	−22.9484			−1.06881			−0.534406	+	0.845228i	$0.679465\pi$
$462$	−8.39108	−	8.39108i	−0.390389	−	0.390389i
$463$	−2.36368	−	2.36368i	−0.109849	−	0.109849i	0.650046	−	0.759895i	$-0.274750\pi$
$463$	−2.36368	−	2.36368i	−0.109849	−	0.109849i	−0.759895	+	0.650046i	$0.774750\pi$
$464$	−24.4032	−	24.4032i	−1.13289	−	1.13289i
$465$	−12.9834	+	12.9834i	−0.602089	+	0.602089i
$466$	2.99072	−	2.99072i	0.138542	−	0.138542i
$467$	−14.4232			−0.667427			−0.333714	−	0.942674i	$-0.608302\pi$
$467$	−14.4232			−0.667427			−0.333714	+	0.942674i	$0.608302\pi$
$468$	0.936602	−	0.936602i	0.0432945	−	0.0432945i
$469$	−7.91041			−0.365269
$470$	16.5757	−	16.5757i	0.764579	−	0.764579i
$471$		−	26.2306i		−	1.20864i
$472$		−	0.0632918i		−	0.00291324i
$473$	−29.7668	+	29.7668i	−1.36868	+	1.36868i
$474$	−38.0612			−1.74821
$475$	−3.75076	+	3.75076i	−0.172097	+	0.172097i
$476$	13.2851			0.608922
$477$	2.25887	−	2.25887i	0.103427	−	0.103427i
$478$	−32.9850	+	32.9850i	−1.50870	+	1.50870i
$479$	18.7463	+	18.7463i	0.856539	+	0.856539i	0.990929	−	0.134390i	$-0.0429074\pi$
$479$	18.7463	+	18.7463i	0.856539	+	0.856539i	−0.134390	+	0.990929i	$0.542907\pi$
$480$	14.2852	+	14.2852i	0.652026	+	0.652026i
$481$	−4.80261	−	4.80261i	−0.218980	−	0.218980i
$482$	−22.7517			−1.03631
$483$			10.9373i			0.497666i
$484$		−	10.1192i		−	0.459962i
$485$	5.84485	+	5.84485i	0.265401	+	0.265401i
$486$	−11.3937	+	11.3937i	−0.516829	+	0.516829i
$487$			4.25654i			0.192882i	0.995339	+	0.0964412i	$0.0307460\pi$
$487$			4.25654i			0.192882i	−0.995339	+	0.0964412i	$0.969254\pi$
$488$	−0.217374			−0.00984006
$489$	17.0287	+	17.0287i	0.770067	+	0.770067i
$490$		−	3.40730i		−	0.153926i
$491$	20.9573			0.945791			0.472895	−	0.881119i	$-0.343209\pi$
$491$	20.9573			0.945791			0.472895	+	0.881119i	$0.343209\pi$
$492$	13.9472	−	12.4639i	0.628786	−	0.561914i
$493$	57.3360			2.58228
$494$		−	4.26842i		−	0.192045i
$495$	−3.89486	−	3.89486i	−0.175061	−	0.175061i
$496$	29.3929			1.31978
$497$		−	12.2177i		−	0.548037i
$498$	0.0805727	−	0.0805727i	0.00361055	−	0.00361055i
$499$	−25.4040	−	25.4040i	−1.13724	−	1.13724i	−0.988943	−	0.148294i	$-0.952622\pi$
$499$	−25.4040	−	25.4040i	−1.13724	−	1.13724i	−0.148294	−	0.988943i	$-0.547378\pi$
$500$			23.8405i			1.06618i
$501$		−	5.79545i		−	0.258922i
$502$	20.4161			0.911214
$503$	15.6703	+	15.6703i	0.698702	+	0.698702i	0.964131	−	0.265428i	$-0.0855134\pi$
$503$	15.6703	+	15.6703i	0.698702	+	0.698702i	−0.265428	+	0.964131i	$0.585513\pi$
$504$	0.0335322	+	0.0335322i	0.00149364	+	0.00149364i
$505$	12.5905	+	12.5905i	0.560272	+	0.560272i
$506$	−41.7522	+	41.7522i	−1.85611	+	1.85611i
$507$	12.8919	−	12.8919i	0.572548	−	0.572548i
$508$	27.0299			1.19926
$509$	15.2678	−	15.2678i	0.676732	−	0.676732i	−0.282527	−	0.959259i	$-0.591173\pi$
$509$	15.2678	−	15.2678i	0.676732	−	0.676732i	0.959259	+	0.282527i	$0.0911728\pi$
$510$	−34.0615			−1.50827
$511$	−5.74745	+	5.74745i	−0.254252	+	0.254252i
$512$		−	31.8600i		−	1.40803i
$513$			14.4032i			0.635915i
$514$	−31.0269	+	31.0269i	−1.36854	+	1.36854i
$515$	6.84226			0.301506
$516$	21.6470	−	21.6470i	0.952957	−	0.952957i
$517$	−27.6357			−1.21542
$518$	−11.4148	+	11.4148i	−0.501539	+	0.501539i
$519$	−7.06121	+	7.06121i	−0.309953	+	0.309953i
$520$	0.0599471	+	0.0599471i	0.00262885	+	0.00262885i
$521$	2.84545	+	2.84545i	0.124661	+	0.124661i	0.766685	−	0.642024i	$-0.221905\pi$
$521$	2.84545	+	2.84545i	0.124661	+	0.124661i	−0.642024	+	0.766685i	$0.721905\pi$
$522$	−9.60750	−	9.60750i	−0.420509	−	0.420509i
$523$	−23.3325			−1.02026			−0.510129	−	0.860098i	$-0.670402\pi$
$523$	−23.3325			−1.02026			−0.510129	+	0.860098i	$0.670402\pi$
$524$			35.1271i			1.53453i
$525$		−	3.07770i		−	0.134322i
$526$	−37.9377	−	37.9377i	−1.65416	−	1.65416i
$527$	−34.5297	+	34.5297i	−1.50414	+	1.50414i
$528$		−	24.1704i		−	1.05188i
$529$	31.4217			1.36616
$530$	−9.59819	−	9.59819i	−0.416919	−	0.416919i
$531$		−	0.858215i		−	0.0372434i
$532$	−5.03467			−0.218280
$533$	4.00262	−	3.57693i	0.173373	−	0.154934i
$534$	22.5839			0.977302
$535$			10.9184i			0.472044i
$536$	−0.330787	−	0.330787i	−0.0142878	−	0.0142878i
$537$	−4.71204			−0.203340
$538$			31.2752i			1.34837i
$539$	−2.84040	+	2.84040i	−0.122345	+	0.122345i
$540$	13.4290	+	13.4290i	0.577893	+	0.577893i
$541$			11.1045i			0.477421i	0.971091	+	0.238711i	$0.0767247\pi$
$541$			11.1045i			0.477421i	−0.971091	+	0.238711i	$0.923275\pi$
$542$		−	20.1963i		−	0.867503i
$543$	−4.07344			−0.174808
$544$	37.9918	+	37.9918i	1.62889	+	1.62889i
$545$	4.27210	+	4.27210i	0.182997	+	0.182997i
$546$	1.75123	+	1.75123i	0.0749457	+	0.0749457i
$547$	−0.533484	+	0.533484i	−0.0228101	+	0.0228101i	−0.718420	−	0.695610i	$-0.755134\pi$
$547$	−0.533484	+	0.533484i	−0.0228101	+	0.0228101i	0.695610	+	0.718420i	$0.255134\pi$
$548$	−5.44448	+	5.44448i	−0.232577	+	0.232577i
$549$	−2.94752			−0.125797
$550$	11.7488	−	11.7488i	0.500971	−	0.500971i
$551$	−21.7287			−0.925673
$552$	−0.457363	+	0.457363i	−0.0194666	+	0.0194666i
$553$			12.8838i			0.547876i
$554$			11.8769i			0.504603i
$555$	14.5238	−	14.5238i	0.616500	−	0.616500i
$556$	24.0305			1.01912
$557$	−17.9695	+	17.9695i	−0.761390	+	0.761390i	−0.976574	−	0.215183i	$-0.930965\pi$
$557$	−17.9695	+	17.9695i	−0.761390	+	0.761390i	0.215183	+	0.976574i	$0.430965\pi$
$558$	11.5719			0.489878
$559$	6.21236	−	6.21236i	0.262755	−	0.262755i
$560$	4.90734	−	4.90734i	0.207373	−	0.207373i
$561$	28.3944	+	28.3944i	1.19881	+	1.19881i
$562$	7.10332	+	7.10332i	0.299636	+	0.299636i
$563$	−0.216897	−	0.216897i	−0.00914112	−	0.00914112i	0.702521	−	0.711663i	$-0.252057\pi$
$563$	−0.216897	−	0.216897i	−0.00914112	−	0.00914112i	−0.711663	+	0.702521i	$0.752057\pi$
$564$	20.0973			0.846248
$565$		−	3.34945i		−	0.140912i
$566$			18.7953i			0.790025i
$567$	−4.20822	−	4.20822i	−0.176728	−	0.176728i
$568$	0.510902	−	0.510902i	0.0214370	−	0.0214370i
$569$			24.1249i			1.01137i	0.862719	+	0.505684i	$0.168760\pi$
$569$			24.1249i			1.01137i	−0.862719	+	0.505684i	$0.831240\pi$
$570$	12.9083			0.540670
$571$	2.88255	+	2.88255i	0.120631	+	0.120631i	0.764845	−	0.644214i	$-0.222815\pi$
$571$	2.88255	+	2.88255i	0.120631	+	0.120631i	−0.644214	+	0.764845i	$0.722815\pi$
$572$			6.63518i			0.277431i
$573$	−7.73083			−0.322960
$574$	−8.50165	−	9.51342i	−0.354852	−	0.397082i
$575$	−15.3139			−0.638636
$576$		−	6.22331i		−	0.259304i
$577$	27.3416	+	27.3416i	1.13824	+	1.13824i	0.988765	+	0.149480i	$0.0477598\pi$
$577$	27.3416	+	27.3416i	1.13824	+	1.13824i	0.149480	+	0.988765i	$0.452240\pi$
$578$	−56.7140			−2.35899
$579$		−	4.22687i		−	0.175663i
$580$	−20.2591	+	20.2591i	−0.841212	+	0.841212i
$581$	−0.0272741	−	0.0272741i	−0.00113152	−	0.00113152i
$582$			14.2800i			0.591925i
$583$			16.0025i			0.662757i
$584$	−0.480678			−0.0198906
$585$	0.812861	+	0.812861i	0.0336077	+	0.0336077i
$586$	−23.0272	−	23.0272i	−0.951247	−	0.951247i
$587$	17.0601	+	17.0601i	0.704147	+	0.704147i	0.965298	−	0.261151i	$-0.0841021\pi$
$587$	17.0601	+	17.0601i	0.704147	+	0.704147i	−0.261151	+	0.965298i	$0.584102\pi$
$588$	2.06560	−	2.06560i	0.0851841	−	0.0851841i
$589$	13.0857	−	13.0857i	0.539188	−	0.539188i
$590$	−3.64665			−0.150130
$591$	−18.7639	+	18.7639i	−0.771844	+	0.771844i
$592$	−32.8802			−1.35137
$593$	−3.32625	+	3.32625i	−0.136593	+	0.136593i	−0.772097	−	0.635505i	$-0.780792\pi$
$593$	−3.32625	+	3.32625i	−0.136593	+	0.136593i	0.635505	+	0.772097i	$0.280792\pi$
$594$		−	45.1162i		−	1.85114i
$595$			11.5299i			0.472680i
$596$	−6.50822	+	6.50822i	−0.266587	+	0.266587i
$597$	−33.0499			−1.35264
$598$	8.71373	−	8.71373i	0.356331	−	0.356331i
$599$	30.1422			1.23158			0.615788	−	0.787912i	$-0.288838\pi$
$599$	30.1422			1.23158			0.615788	+	0.787912i	$0.288838\pi$
$600$	0.128699	−	0.128699i	0.00525412	−	0.00525412i
$601$	4.55796	−	4.55796i	0.185923	−	0.185923i	−0.608008	−	0.793931i	$-0.708031\pi$
$601$	4.55796	−	4.55796i	0.185923	−	0.185923i	0.793931	+	0.608008i	$0.208031\pi$
$602$	−14.7655	−	14.7655i	−0.601798	−	0.601798i
$603$	−4.48535	−	4.48535i	−0.182658	−	0.182658i
$604$	2.12270	+	2.12270i	0.0863715	+	0.0863715i
$605$	8.78225			0.357049
$606$			30.7609i			1.24958i
$607$		−	10.5388i		−	0.427758i	−0.976860	−	0.213879i	$-0.931390\pi$
$607$		−	10.5388i		−	0.427758i	0.976860	−	0.213879i	$-0.0686099\pi$
$608$	−14.3978	−	14.3978i	−0.583908	−	0.583908i
$609$	8.91476	−	8.91476i	0.361244	−	0.361244i
$610$			12.5243i			0.507095i
$611$	5.76760			0.233332
$612$	7.53292	+	7.53292i	0.304500	+	0.304500i
$613$		−	31.3704i		−	1.26704i	−0.773726	−	0.633520i	$-0.781609\pi$
$613$		−	31.3704i		−	1.26704i	0.773726	−	0.633520i	$-0.218391\pi$
$614$	35.2101			1.42097
$615$	10.8172	+	12.1045i	0.436190	+	0.488100i
$616$	−0.237553			−0.00957127
$617$			20.6791i			0.832509i	0.909248	+	0.416254i	$0.136657\pi$
$617$			20.6791i			0.832509i	−0.909248	+	0.416254i	$0.863343\pi$
$618$	8.35843	+	8.35843i	0.336225	+	0.336225i
$619$	12.2525			0.492469			0.246235	−	0.969210i	$-0.420807\pi$
$619$	12.2525			0.492469			0.246235	+	0.969210i	$0.420807\pi$
$620$		−	24.4014i		−	0.979983i
$621$	−29.4032	+	29.4032i	−1.17991	+	1.17991i
$622$	9.38931	+	9.38931i	0.376477	+	0.376477i
$623$		−	7.64472i		−	0.306279i
$624$			5.04439i			0.201937i
$625$	−10.3114			−0.412455
$626$	25.5469	+	25.5469i	1.02106	+	1.02106i
$627$	−10.7607	−	10.7607i	−0.429739	−	0.429739i
$628$	24.6493	+	24.6493i	0.983615	+	0.983615i
$629$	38.6264	−	38.6264i	1.54014	−	1.54014i
$630$	1.93201	−	1.93201i	0.0769730	−	0.0769730i
$631$	4.34934			0.173145			0.0865723	−	0.996246i	$-0.472409\pi$
$631$	4.34934			0.173145			0.0865723	+	0.996246i	$0.472409\pi$
$632$	−0.538759	+	0.538759i	−0.0214307	+	0.0214307i
$633$	−7.37650			−0.293189
$634$	33.8289	−	33.8289i	1.34352	−	1.34352i
$635$			23.4587i			0.930932i
$636$		−	11.6374i		−	0.461452i
$637$	0.592796	−	0.592796i	0.0234874	−	0.0234874i
$638$	68.0624			2.69462
$639$	6.92765	−	6.92765i	0.274054	−	0.274054i
$640$	0.808919			0.0319753
$641$	−23.2282	+	23.2282i	−0.917458	+	0.917458i	−0.996844	−	0.0793858i	$-0.974704\pi$
$641$	−23.2282	+	23.2282i	−0.917458	+	0.917458i	0.0793858	+	0.996844i	$0.474704\pi$
$642$	−13.3378	+	13.3378i	−0.526401	+	0.526401i
$643$	−27.7644	−	27.7644i	−1.09492	−	1.09492i	−0.994995	−	0.0999256i	$-0.968140\pi$
$643$	−27.7644	−	27.7644i	−1.09492	−	1.09492i	−0.0999256	−	0.994995i	$-0.531860\pi$
$644$	−10.2780	−	10.2780i	−0.405009	−	0.405009i
$645$	18.7871	+	18.7871i	0.739741	+	0.739741i
$646$	34.3301			1.35070
$647$			5.73999i			0.225662i	0.993614	+	0.112831i	$0.0359919\pi$
$647$			5.73999i			0.225662i	−0.993614	+	0.112831i	$0.964008\pi$
$648$		−	0.351947i		−	0.0138258i
$649$	3.03993	+	3.03993i	0.119328	+	0.119328i
$650$	−2.45199	+	2.45199i	−0.0961750	+	0.0961750i
$651$			10.7375i			0.420837i
$652$	−32.0044			−1.25339
$653$	26.7554	+	26.7554i	1.04702	+	1.04702i	0.998839	+	0.0481793i	$0.0153419\pi$
$653$	26.7554	+	26.7554i	1.04702	+	1.04702i	0.0481793	+	0.998839i	$0.484658\pi$
$654$			10.4375i			0.408139i
$655$	−30.4862			−1.19119
$656$	1.45719	−	25.9460i	0.0568935	−	1.01302i
$657$	−6.51783			−0.254285
$658$		−	13.7084i		−	0.534411i
$659$	−27.2723	−	27.2723i	−1.06238	−	1.06238i	−0.997920	−	0.0644589i	$-0.979468\pi$
$659$	−27.2723	−	27.2723i	−1.06238	−	1.06238i	−0.0644589	−	0.997920i	$-0.520532\pi$
$660$	−20.0657			−0.781058
$661$		−	3.44766i		−	0.134098i	−0.997750	−	0.0670492i	$-0.978642\pi$
$661$		−	3.44766i		−	0.134098i	0.997750	−	0.0670492i	$-0.0213585\pi$
$662$	19.2868	−	19.2868i	0.749604	−	0.749604i
$663$	−5.92596	−	5.92596i	−0.230145	−	0.230145i
$664$		−	0.00228102i		−	8.85208e-5i
$665$		−	4.36950i		−	0.169442i
$666$	−12.9449			−0.501603
$667$	−44.3579	−	44.3579i	−1.71754	−	1.71754i
$668$	5.44608	+	5.44608i	0.210715	+	0.210715i
$669$	19.8538	+	19.8538i	0.767590	+	0.767590i
$670$	−19.0588	+	19.0588i	−0.736304	+	0.736304i
$671$	10.4405	−	10.4405i	0.403053	−	0.403053i
$672$	11.8141			0.455740
$673$	3.87996	−	3.87996i	0.149562	−	0.149562i	−0.628361	−	0.777922i	$-0.716274\pi$
$673$	3.87996	−	3.87996i	0.149562	−	0.149562i	0.777922	+	0.628361i	$0.216274\pi$
$674$	39.8300			1.53419
$675$	8.27390	−	8.27390i	0.318463	−	0.318463i
$676$			24.2294i			0.931900i
$677$		−	47.0021i		−	1.80644i	−0.429179	−	0.903219i	$-0.641197\pi$
$677$		−	47.0021i		−	1.80644i	0.429179	−	0.903219i	$-0.358803\pi$
$678$	4.09165	−	4.09165i	0.157139	−	0.157139i
$679$	4.83382			0.185505
$680$	−0.482143	+	0.482143i	−0.0184893	+	0.0184893i
$681$	43.8273			1.67946
$682$	−40.9895	+	40.9895i	−1.56957	+	1.56957i
$683$	4.16404	−	4.16404i	0.159333	−	0.159333i	−0.622938	−	0.782271i	$-0.714061\pi$
$683$	4.16404	−	4.16404i	0.159333	−	0.159333i	0.782271	+	0.622938i	$0.214061\pi$
$684$	−2.85475	−	2.85475i	−0.109154	−	0.109154i
$685$	−4.72517	−	4.72517i	−0.180540	−	0.180540i
$686$	−1.40896	−	1.40896i	−0.0537942	−	0.0537942i
$687$	−24.2434			−0.924945
$688$		−	42.5319i		−	1.62151i
$689$		−	3.33975i		−	0.127234i
$690$	26.3516	+	26.3516i	1.00319	+	1.00319i
$691$	−0.971263	+	0.971263i	−0.0369486	+	0.0369486i	−0.725340	−	0.688391i	$-0.758317\pi$
$691$	−0.971263	+	0.971263i	−0.0369486	+	0.0369486i	0.688391	+	0.725340i	$0.258317\pi$
$692$		−	13.2711i		−	0.504490i
$693$	−3.22113			−0.122361
$694$	16.2380	+	16.2380i	0.616385	+	0.616385i
$695$			20.8556i			0.791100i
$696$	0.745571			0.0282608
$697$	28.7686	+	32.1923i	1.08969	+	1.21937i
$698$	−65.8603			−2.49285
$699$			3.14705i			0.119032i
$700$	2.89216	+	2.89216i	0.109314	+	0.109314i
$701$	−37.1693			−1.40387			−0.701933	−	0.712243i	$-0.747679\pi$
$701$	−37.1693			−1.40387			−0.701933	+	0.712243i	$0.747679\pi$
$702$			9.41580i			0.355377i
$703$	−14.6383	+	14.6383i	−0.552094	+	0.552094i
$704$	22.0439	+	22.0439i	0.830811	+	0.830811i
$705$			17.4421i			0.656907i
$706$		−	53.0009i		−	1.99472i
$707$	10.4127			0.391608
$708$	−2.21070	−	2.21070i	−0.0830832	−	0.0830832i
$709$	−15.5517	−	15.5517i	−0.584057	−	0.584057i	0.351959	−	0.936015i	$-0.385516\pi$
$709$	−15.5517	−	15.5517i	−0.584057	−	0.584057i	−0.936015	+	0.351959i	$0.885516\pi$
$710$	−29.4364	−	29.4364i	−1.10473	−	1.10473i
$711$	−7.30539	+	7.30539i	−0.273973	+	0.273973i
$712$	0.319677	−	0.319677i	0.0119804	−	0.0119804i
$713$	53.4276			2.00088
$714$	−14.0848	+	14.0848i	−0.527111	+	0.527111i
$715$	−5.75856			−0.215358
$716$	4.42799	−	4.42799i	0.165482	−	0.165482i
$717$		−	34.7091i		−	1.29623i
$718$		−	52.3986i		−	1.95550i
$719$	−20.8748	+	20.8748i	−0.778500	+	0.778500i	−0.979576	−	0.201076i	$-0.935556\pi$
$719$	−20.8748	+	20.8748i	−0.778500	+	0.778500i	0.201076	+	0.979576i	$0.435556\pi$
$720$	5.56512			0.207400
$721$	2.82935	−	2.82935i	0.105371	−	0.105371i
$722$	24.8487			0.924772
$723$	11.9704	−	11.9704i	0.445186	−	0.445186i
$724$	3.82788	−	3.82788i	0.142262	−	0.142262i
$725$	12.4820	+	12.4820i	0.463571	+	0.463571i
$726$	10.7283	+	10.7283i	0.398164	+	0.398164i
$727$	3.07500	+	3.07500i	0.114046	+	0.114046i	0.761827	−	0.647781i	$-0.224303\pi$
$727$	3.07500	+	3.07500i	0.114046	+	0.114046i	−0.647781	+	0.761827i	$0.724303\pi$
$728$	0.0495775			0.00183747
$729$		−	29.8432i		−	1.10530i
$730$			27.6950i			1.02504i
$731$	49.9648	+	49.9648i	1.84802	+	1.84802i
$732$	−7.59259	+	7.59259i	−0.280630	+	0.280630i
$733$			34.4621i			1.27289i	0.771323	+	0.636444i	$0.219595\pi$
$733$			34.4621i			1.27289i	−0.771323	+	0.636444i	$0.780405\pi$
$734$	−4.18070			−0.154312
$735$	1.79270	+	1.79270i	0.0661248	+	0.0661248i
$736$		−	58.7846i		−	2.16683i
$737$	31.7756			1.17047
$738$	0.573690	−	10.2149i	0.0211178	−	0.376016i
$739$	−2.54919			−0.0937736			−0.0468868	−	0.998900i	$-0.514930\pi$
$739$	−2.54919			−0.0937736			−0.0468868	+	0.998900i	$0.514930\pi$
$740$			27.2965i			1.00344i
$741$	2.24576	+	2.24576i	0.0825002	+	0.0825002i
$742$	−7.93791			−0.291410
$743$		−	8.18985i		−	0.300456i	−0.988651	−	0.150228i	$-0.951999\pi$
$743$		−	8.18985i		−	0.300456i	0.988651	−	0.150228i	$-0.0480009\pi$
$744$	−0.449008	+	0.449008i	−0.0164614	+	0.0164614i
$745$	−5.64837	−	5.64837i	−0.206940	−	0.206940i
$746$			33.1937i			1.21531i
$747$		−	0.0309299i		−	0.00113166i
$748$	−53.3655			−1.95123
$749$	4.51488	+	4.51488i	0.164970	+	0.164970i
$750$	−25.2756	−	25.2756i	−0.922933	−	0.922933i
$751$	14.6519	+	14.6519i	0.534654	+	0.534654i	0.921954	−	0.387300i	$-0.126592\pi$
$751$	14.6519	+	14.6519i	0.534654	+	0.534654i	−0.387300	+	0.921954i	$0.626592\pi$
$752$	19.7435	−	19.7435i	0.719970	−	0.719970i
$753$	−10.7416	+	10.7416i	−0.391446	+	0.391446i
$754$	−14.2047			−0.517305
$755$	−1.84226	+	1.84226i	−0.0670465	+	0.0670465i
$756$	11.1061			0.403925
$757$	12.6475	−	12.6475i	0.459680	−	0.459680i	−0.438870	−	0.898550i	$-0.644621\pi$
$757$	12.6475	−	12.6475i	0.459680	−	0.459680i	0.898550	+	0.438870i	$0.144621\pi$
$758$			21.3598i			0.775823i
$759$		−	43.9346i		−	1.59472i
$760$	0.182718	−	0.182718i	0.00662788	−	0.00662788i
$761$	−5.93972			−0.215315			−0.107657	−	0.994188i	$-0.534335\pi$
$761$	−5.93972			−0.215315			−0.107657	+	0.994188i	$0.534335\pi$
$762$	−28.6569	+	28.6569i	−1.03813	+	1.03813i
$763$	3.53312			0.127908
$764$	7.26479	−	7.26479i	0.262831	−	0.262831i
$765$	−6.53769	+	6.53769i	−0.236371	+	0.236371i
$766$	−50.1009	−	50.1009i	−1.81022	−	1.81022i
$767$	−0.634437	−	0.634437i	−0.0229082	−	0.0229082i
$768$	17.2604	+	17.2604i	0.622832	+	0.622832i
$769$	−32.3787			−1.16761			−0.583804	−	0.811895i	$-0.698436\pi$
$769$	−32.3787			−1.16761			−0.583804	+	0.811895i	$0.698436\pi$
$770$			13.6869i			0.493243i
$771$		−	32.6486i		−	1.17581i
$772$	3.97206	+	3.97206i	0.142957	+	0.142957i
$773$	9.55377	−	9.55377i	0.343625	−	0.343625i	−0.514103	−	0.857728i	$-0.671875\pi$
$773$	9.55377	−	9.55377i	0.343625	−	0.343625i	0.857728	+	0.514103i	$0.171875\pi$
$774$		−	16.7447i		−	0.601875i
$775$	−15.0342			−0.540044
$776$	0.202134	+	0.202134i	0.00725620	+	0.00725620i
$777$		−	12.0115i		−	0.430910i
$778$	33.7917			1.21149
$779$	−10.9025	−	12.1999i	−0.390621	−	0.437108i
$780$	4.18775			0.149945
$781$			49.0776i			1.75613i
$782$	70.0829	+	70.0829i	2.50616	+	2.50616i
$783$	47.9318			1.71294
$784$		−	4.05848i		−	0.144946i
$785$	−21.3927	+	21.3927i	−0.763539	+	0.763539i
$786$	−37.2416	−	37.2416i	−1.32836	−	1.32836i
$787$			28.1963i			1.00509i	0.864551	+	0.502544i	$0.167603\pi$
$787$			28.1963i			1.00509i	−0.864551	+	0.502544i	$0.832397\pi$
$788$		−	35.2655i		−	1.25628i
$789$	39.9207			1.42122
$790$	31.0414	+	31.0414i	1.10440	+	1.10440i
$791$	−1.38503	−	1.38503i	−0.0492461	−	0.0492461i
$792$	−0.134697	−	0.134697i	−0.00478625	−	0.00478625i
$793$	−2.17896	+	2.17896i	−0.0773770	+	0.0773770i
$794$	5.68993	−	5.68993i	0.201928	−	0.201928i
$795$	10.0999			0.358206
$796$	31.0575	−	31.0575i	1.10080	−	1.10080i
$797$	4.58602			0.162445			0.0812226	−	0.996696i	$-0.474118\pi$
$797$	4.58602			0.162445			0.0812226	+	0.996696i	$0.474118\pi$
$798$	5.33773	−	5.33773i	0.188954	−	0.188954i
$799$			46.3877i			1.64108i
$800$			16.5416i			0.584835i
$801$	4.33471	−	4.33471i	0.153159	−	0.153159i
$802$	−5.37070			−0.189646
$803$	23.0871	−	23.0871i	0.814727	−	0.814727i
$804$	−23.1079			−0.814953
$805$	8.92009	−	8.92009i	0.314392	−	0.314392i
$806$	8.55455	−	8.55455i	0.301321	−	0.301321i
$807$	−16.4550	−	16.4550i	−0.579243	−	0.579243i
$808$	0.435423	+	0.435423i	0.0153181	+	0.0153181i
$809$	−13.4150	−	13.4150i	−0.471648	−	0.471648i	0.430800	−	0.902448i	$-0.358232\pi$
$809$	−13.4150	−	13.4150i	−0.471648	−	0.471648i	−0.902448	+	0.430800i	$0.858232\pi$
$810$	−20.2779			−0.712494
$811$		−	2.74583i		−	0.0964193i	−0.998837	−	0.0482097i	$-0.984648\pi$
$811$		−	2.74583i		−	0.0964193i	0.998837	−	0.0482097i	$-0.0153516\pi$
$812$			16.7547i			0.587974i
$813$	10.6260	+	10.6260i	0.372669	+	0.372669i
$814$	45.8527	−	45.8527i	1.60714	−	1.60714i
$815$		−	27.7761i		−	0.972953i
$816$	−40.5711			−1.42027
$817$	−18.9352	−	18.9352i	−0.662459	−	0.662459i
$818$			59.2831i			2.07278i
$819$	0.672254			0.0234905
$820$	−21.5399	−	1.20972i	−0.752205	−	0.0422454i
$821$	−22.3552			−0.780201			−0.390101	−	0.920772i	$-0.627560\pi$
$821$	−22.3552			−0.780201			−0.390101	+	0.920772i	$0.627560\pi$
$822$		−	11.5444i		−	0.402658i
$823$	−15.5208	−	15.5208i	−0.541023	−	0.541023i	0.382806	−	0.923829i	$-0.374958\pi$
$823$	−15.5208	−	15.5208i	−0.541023	−	0.541023i	−0.923829	+	0.382806i	$0.874958\pi$
$824$	0.236628			0.00824333
$825$			12.3629i			0.430422i
$826$	−1.50793	+	1.50793i	−0.0524675	+	0.0524675i
$827$	−22.5409	−	22.5409i	−0.783823	−	0.783823i	0.196650	−	0.980474i	$-0.436994\pi$
$827$	−22.5409	−	22.5409i	−0.783823	−	0.783823i	−0.980474	+	0.196650i	$0.936994\pi$
$828$		−	11.6556i		−	0.405061i
$829$			7.40122i			0.257055i	0.991706	+	0.128528i	$0.0410251\pi$
$829$			7.40122i			0.257055i	−0.991706	+	0.128528i	$0.958975\pi$
$830$	−0.131424			−0.00456180
$831$	−6.24887	−	6.24887i	−0.216771	−	0.216771i
$832$	−4.60059	−	4.60059i	−0.159497	−	0.159497i
$833$	4.76775	+	4.76775i	0.165193	+	0.165193i
$834$	−25.4770	+	25.4770i	−0.882197	+	0.882197i
$835$	−4.72656	+	4.72656i	−0.163569	+	0.163569i
$836$	20.2239			0.699460
$837$	−28.8661	+	28.8661i	−0.997759	+	0.997759i
$838$	13.4532			0.464734
$839$	2.97066	−	2.97066i	0.102559	−	0.102559i	−0.653966	−	0.756524i	$-0.726896\pi$
$839$	2.97066	−	2.97066i	0.102559	−	0.102559i	0.756524	+	0.653966i	$0.226896\pi$
$840$			0.149930i			0.00517307i
$841$			43.3101i			1.49345i
$842$	−0.175278	+	0.175278i	−0.00604047	+	0.00604047i
$843$	−7.47461			−0.257439
$844$	6.93182	−	6.93182i	0.238603	−	0.238603i
$845$	−21.0283			−0.723395
$846$	7.77295	−	7.77295i	0.267240	−	0.267240i
$847$	3.63156	−	3.63156i	0.124782	−	0.124782i
$848$	−11.4325	−	11.4325i	−0.392594	−	0.392594i
$849$	−9.88886	−	9.88886i	−0.339385	−	0.339385i
$850$	−19.7209	−	19.7209i	−0.676422	−	0.676422i
$851$	−59.7665			−2.04877
$852$		−	35.6903i		−	1.22273i
$853$		−	49.5149i		−	1.69536i	−0.530508	−	0.847680i	$-0.677999\pi$
$853$		−	49.5149i		−	1.69536i	0.530508	−	0.847680i	$-0.322001\pi$
$854$	5.17894	+	5.17894i	0.177220	+	0.177220i
$855$	2.47759	−	2.47759i	0.0847319	−	0.0847319i
$856$			0.377594i			0.0129059i
$857$	−20.7292			−0.708096			−0.354048	−	0.935227i	$-0.615195\pi$
$857$	−20.7292			−0.708096			−0.354048	+	0.935227i	$0.615195\pi$
$858$	−7.03458	−	7.03458i	−0.240157	−	0.240157i
$859$			7.82023i			0.266823i	0.991061	+	0.133411i	$0.0425932\pi$
$859$			7.82023i			0.266823i	−0.991061	+	0.133411i	$0.957407\pi$
$860$	−35.3091			−1.20403
$861$	9.47836	+	0.532325i	0.323022	+	0.0181416i
$862$	−72.1390			−2.45707
$863$		−	34.6637i		−	1.17996i	−0.807416	−	0.589982i	$-0.799135\pi$
$863$		−	34.6637i		−	1.17996i	0.807416	−	0.589982i	$-0.200865\pi$
$864$	31.7604	+	31.7604i	1.08051	+	1.08051i
$865$	11.5177			0.391615
$866$		−	14.4516i		−	0.491087i
$867$	29.8392	−	29.8392i	1.01339	−	1.01339i
$868$	−10.0902	−	10.0902i	−0.342485	−	0.342485i
$869$		−	51.7536i		−	1.75562i
$870$		−	42.9571i		−	1.45638i
$871$	−6.63161			−0.224704
$872$	0.147744	+	0.147744i	0.00500323	+	0.00500323i
$873$	2.74087	+	2.74087i	0.0927644	+	0.0927644i
$874$	−26.5594	−	26.5594i	−0.898384	−	0.898384i
$875$	−8.55585	+	8.55585i	−0.289241	+	0.289241i
$876$	−16.7895	+	16.7895i	−0.567263	+	0.567263i
$877$	18.1318			0.612267			0.306133	−	0.951989i	$-0.400965\pi$
$877$	18.1318			0.612267			0.306133	+	0.951989i	$0.400965\pi$
$878$	−33.9723	+	33.9723i	−1.14651	+	1.14651i
$879$	24.2309			0.817287
$880$	−19.7125	+	19.7125i	−0.664508	+	0.664508i
$881$		−	36.3583i		−	1.22494i	−0.790493	−	0.612471i	$-0.790176\pi$
$881$		−	36.3583i		−	1.22494i	0.790493	−	0.612471i	$-0.209824\pi$
$882$		−	1.59781i		−	0.0538011i
$883$	13.9881	−	13.9881i	0.470738	−	0.470738i	−0.431415	−	0.902153i	$-0.641986\pi$
$883$	13.9881	−	13.9881i	0.470738	−	0.470738i	0.902153	+	0.431415i	$0.141986\pi$
$884$	11.1374			0.374593
$885$	1.91863	−	1.91863i	0.0644940	−	0.0644940i
$886$	1.69460			0.0569310
$887$	36.3912	−	36.3912i	1.22190	−	1.22190i	0.254939	−	0.966957i	$-0.417944\pi$
$887$	36.3912	−	36.3912i	1.22190	−	1.22190i	0.966957	−	0.254939i	$-0.0820555\pi$
$888$	0.502280	−	0.502280i	0.0168554	−	0.0168554i
$889$	9.70045	+	9.70045i	0.325343	+	0.325343i
$890$	−18.4186	−	18.4186i	−0.617394	−	0.617394i
$891$	16.9041	+	16.9041i	0.566310	+	0.566310i
$892$	−37.3138			−1.24936
$893$		−	17.5796i		−	0.588279i
$894$		−	13.8000i		−	0.461540i
$895$	3.84297	+	3.84297i	0.128456	+	0.128456i
$896$	0.334497	−	0.334497i	0.0111747	−	0.0111747i
$897$			9.16920i			0.306151i
$898$	62.2072			2.07588
$899$	−43.5475	−	43.5475i	−1.45239	−	1.45239i
$900$			3.27983i			0.109328i
$901$	26.8610			0.894868
$902$	34.1506	+	38.2148i	1.13709	+	1.27241i
$903$	15.5373			0.517050
$904$		−	0.115835i		−	0.00385261i
$905$	3.32215	+	3.32215i	0.110432	+	0.110432i
$906$	−4.50095			−0.149534
$907$		−	26.8512i		−	0.891581i	−0.895137	−	0.445790i	$-0.852923\pi$
$907$		−	26.8512i		−	0.891581i	0.895137	−	0.445790i	$-0.147077\pi$
$908$	−41.1852	+	41.1852i	−1.36678	+	1.36678i
$909$	5.90418	+	5.90418i	0.195829	+	0.195829i
$910$		−	2.85648i		−	0.0946914i
$911$			13.0593i			0.432674i	0.976319	+	0.216337i	$0.0694110\pi$
$911$			13.0593i			0.432674i	−0.976319	+	0.216337i	$0.930589\pi$
$912$	15.3752			0.509125
$913$	0.109558	+	0.109558i	0.00362585	+	0.00362585i
$914$	28.4960	+	28.4960i	0.942565	+	0.942565i
$915$	−6.58948	−	6.58948i	−0.217841	−	0.217841i
$916$	22.7820	−	22.7820i	0.752737	−	0.752737i
$917$	−12.6064	+	12.6064i	−0.416299	+	0.416299i
$918$	−75.7295			−2.49945
$919$	−15.6928	+	15.6928i	−0.517659	+	0.517659i	−0.916862	−	0.399203i	$-0.869287\pi$
$919$	−15.6928	+	15.6928i	−0.517659	+	0.517659i	0.399203	+	0.916862i	$0.369287\pi$
$920$	0.746017			0.0245955
$921$	−18.5253	+	18.5253i	−0.610429	+	0.610429i
$922$			45.7262i			1.50591i
$923$		−	10.2426i		−	0.337138i
$924$	−8.29740	+	8.29740i	−0.272965	+	0.272965i
$925$	16.8179			0.552970
$926$	−4.70978	+	4.70978i	−0.154773	+	0.154773i
$927$	3.20859			0.105384
$928$	−47.9139	+	47.9139i	−1.57285	+	1.57285i
$929$	−11.1049	+	11.1049i	−0.364341	+	0.364341i	−0.865408	−	0.501067i	$-0.832941\pi$
$929$	−11.1049	+	11.1049i	−0.364341	+	0.364341i	0.501067	+	0.865408i	$0.332941\pi$
$930$	25.8702	+	25.8702i	0.848318	+	0.848318i
$931$	−1.80684	−	1.80684i	−0.0592167	−	0.0592167i
$932$	−2.95733	−	2.95733i	−0.0968706	−	0.0968706i
$933$	−9.88009			−0.323460
$934$			28.7392i			0.940377i
$935$		−	46.3150i		−	1.51466i
$936$	0.0281114	+	0.0281114i	0.000918851	+	0.000918851i
$937$	−15.4087	+	15.4087i	−0.503382	+	0.503382i	−0.912487	−	0.409105i	$-0.865841\pi$
$937$	−15.4087	+	15.4087i	−0.503382	+	0.503382i	0.409105	+	0.912487i	$0.365841\pi$
$938$			15.7620i			0.514648i
$939$	−26.8822			−0.877267
$940$	−16.3906	−	16.3906i	−0.534603	−	0.534603i
$941$			54.9102i			1.79002i	0.446045	+	0.895011i	$0.352832\pi$
$941$			54.9102i			1.79002i	−0.446045	+	0.895011i	$0.647168\pi$
$942$	−52.2662			−1.70292
$943$	2.64873	−	47.1622i	0.0862545	−	1.53581i
$944$	−4.34356			−0.141371
$945$			9.63878i			0.313550i
$946$	59.3122	+	59.3122i	1.92841	+	1.92841i
$947$	−20.5795			−0.668744			−0.334372	−	0.942441i	$-0.608524\pi$
$947$	−20.5795			−0.668744			−0.334372	+	0.942441i	$0.608524\pi$
$948$			37.6363i			1.22237i
$949$	−4.81831	+	4.81831i	−0.156409	+	0.156409i
$950$	7.47365	+	7.47365i	0.242477	+	0.242477i
$951$			35.5972i			1.15432i
$952$			0.398743i			0.0129233i
$953$	40.3680			1.30765			0.653823	−	0.756647i	$-0.273164\pi$
$953$	40.3680			1.30765			0.653823	+	0.756647i	$0.273164\pi$
$954$	−4.50095	−	4.50095i	−0.145724	−	0.145724i
$955$	6.30499	+	6.30499i	0.204025	+	0.204025i
$956$	32.6167	+	32.6167i	1.05490	+	1.05490i
$957$	−35.8100	+	35.8100i	−1.15757	+	1.15757i
$958$	37.3532	−	37.3532i	1.20683	−	1.20683i
$959$	−3.90782			−0.126190
$960$	13.9129	−	13.9129i	0.449036	−	0.449036i
$961$	21.4516			0.691986
$962$	−9.56951	+	9.56951i	−0.308533	+	0.308533i
$963$			5.12005i			0.164991i
$964$			22.4977i			0.724601i
$965$	−3.44728	+	3.44728i	−0.110972	+	0.110972i
$966$	21.7933			0.701189
$967$	12.8355	−	12.8355i	0.412761	−	0.412761i	−0.469938	−	0.882699i	$-0.655724\pi$
$967$	12.8355	−	12.8355i	0.412761	−	0.412761i	0.882699	+	0.469938i	$0.155724\pi$
$968$	0.303719			0.00976191
$969$	−18.0623	+	18.0623i	−0.580243	+	0.580243i
$970$	11.6463	−	11.6463i	0.373939	−	0.373939i
$971$	21.3821	+	21.3821i	0.686185	+	0.686185i	0.961387	−	0.275202i	$-0.0887446\pi$
$971$	21.3821	+	21.3821i	0.686185	+	0.686185i	−0.275202	+	0.961387i	$0.588745\pi$
$972$	11.2665	+	11.2665i	0.361373	+	0.361373i
$973$	8.62404	+	8.62404i	0.276474	+	0.276474i
$974$	8.48145			0.271763
$975$		−	2.58016i		−	0.0826312i
$976$			14.9178i			0.477509i
$977$	−30.9984	−	30.9984i	−0.991726	−	0.991726i	0.00823958	−	0.999966i	$-0.497377\pi$
$977$	−30.9984	−	30.9984i	−0.991726	−	0.991726i	−0.999966	+	0.00823958i	$0.997377\pi$
$978$	33.9309	−	33.9309i	1.08499	−	1.08499i
$979$			30.7084i			0.981444i
$980$	−3.36926			−0.107627
$981$	2.00335	+	2.00335i	0.0639621	+	0.0639621i
$982$		−	41.7589i		−	1.33258i
$983$	−47.7471			−1.52290			−0.761448	−	0.648226i	$-0.775511\pi$
$983$	−47.7471			−1.52290			−0.761448	+	0.648226i	$0.775511\pi$
$984$	0.374093	+	0.418614i	0.0119257	+	0.0133449i
$985$	30.6063			0.975199
$986$		−	114.246i		−	3.63833i
$987$	7.21249	+	7.21249i	0.229576	+	0.229576i
$988$	−4.22076			−0.134280
$989$		−	77.3103i		−	2.45832i
$990$	−7.76076	+	7.76076i	−0.246653	+	0.246653i
$991$	−8.11917	−	8.11917i	−0.257914	−	0.257914i	0.566291	−	0.824205i	$-0.308378\pi$
$991$	−8.11917	−	8.11917i	−0.257914	−	0.257914i	−0.824205	+	0.566291i	$0.808378\pi$
$992$		−	57.7107i		−	1.83232i
$993$			20.2950i			0.644041i
$994$	−24.3445			−0.772161
$995$	26.9543	+	26.9543i	0.854509	+	0.854509i
$996$	−0.0796731	−	0.0796731i	−0.00252454	−	0.00252454i
$997$	−26.7998	−	26.7998i	−0.848759	−	0.848759i	0.141220	−	0.989978i	$-0.454898\pi$
$997$	−26.7998	−	26.7998i	−0.848759	−	0.848759i	−0.989978	+	0.141220i	$0.954898\pi$
$998$	−50.6191	+	50.6191i	−1.60232	+	1.60232i
$999$	32.2910	−	32.2910i	1.02164	−	1.02164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.3	✓	40
41.32	even	4	inner	287.2.f.a.155.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.3	✓	40	1.1	even	1	trivial
287.2.f.a.155.18	yes	40	41.32	even	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.99257i q^{2} +(1.04836 + 1.04836i) q^{3} -1.97032 q^{4} -1.71001i q^{5} +(2.08892 - 2.08892i) q^{6} +(-0.707107 - 0.707107i) q^{7} -0.0591377i q^{8} -0.801887i q^{9} +O(q^{10})\)	\(q-1.99257i q^{2} +(1.04836 + 1.04836i) q^{3} -1.97032 q^{4} -1.71001i q^{5} +(2.08892 - 2.08892i) q^{6} +(-0.707107 - 0.707107i) q^{7} -0.0591377i q^{8} -0.801887i q^{9} -3.40730 q^{10} +(2.84040 + 2.84040i) q^{11} +(-2.06560 - 2.06560i) q^{12} +(-0.592796 - 0.592796i) q^{13} +(-1.40896 + 1.40896i) q^{14} +(1.79270 - 1.79270i) q^{15} -4.05848 q^{16} +(4.76775 - 4.76775i) q^{17} -1.59781 q^{18} +(-1.80684 + 1.80684i) q^{19} +3.36926i q^{20} -1.48260i q^{21} +(5.65969 - 5.65969i) q^{22} -7.37711 q^{23} +(0.0619976 - 0.0619976i) q^{24} +2.07587 q^{25} +(-1.18119 + 1.18119i) q^{26} +(3.98574 - 3.98574i) q^{27} +(1.39323 + 1.39323i) q^{28} +(6.01291 + 6.01291i) q^{29} +(-3.57208 - 3.57208i) q^{30} -7.24235 q^{31} +7.96851i q^{32} +5.95553i q^{33} +(-9.50005 - 9.50005i) q^{34} +(-1.20916 + 1.20916i) q^{35} +1.57997i q^{36} +8.10162 q^{37} +(3.60024 + 3.60024i) q^{38} -1.24293i q^{39} -0.101126 q^{40} +(-0.359047 + 6.39305i) q^{41} -2.95419 q^{42} +10.4798i q^{43} +(-5.59651 - 5.59651i) q^{44} -1.37123 q^{45} +14.6994i q^{46} +(-4.86475 + 4.86475i) q^{47} +(-4.25474 - 4.25474i) q^{48} +1.00000i q^{49} -4.13632i q^{50} +9.99662 q^{51} +(1.16800 + 1.16800i) q^{52} +(2.81694 + 2.81694i) q^{53} +(-7.94186 - 7.94186i) q^{54} +(4.85711 - 4.85711i) q^{55} +(-0.0418167 + 0.0418167i) q^{56} -3.78843 q^{57} +(11.9811 - 11.9811i) q^{58} +1.07024 q^{59} +(-3.53220 + 3.53220i) q^{60} -3.67573i q^{61} +14.4309i q^{62} +(-0.567020 + 0.567020i) q^{63} +7.76083 q^{64} +(-1.01369 + 1.01369i) q^{65} +11.8668 q^{66} +(5.59350 - 5.59350i) q^{67} +(-9.39399 + 9.39399i) q^{68} +(-7.73386 - 7.73386i) q^{69} +(2.40933 + 2.40933i) q^{70} +(8.63919 + 8.63919i) q^{71} -0.0474218 q^{72} -8.12811i q^{73} -16.1430i q^{74} +(2.17626 + 2.17626i) q^{75} +(3.56005 - 3.56005i) q^{76} -4.01694i q^{77} -2.47661 q^{78} +(-9.11025 - 9.11025i) q^{79} +6.94003i q^{80} +5.95132 q^{81} +(12.7386 + 0.715426i) q^{82} +0.0385714 q^{83} +2.92120i q^{84} +(-8.15288 - 8.15288i) q^{85} +20.8816 q^{86} +12.6074i q^{87} +(0.167975 - 0.167975i) q^{88} +(5.40564 + 5.40564i) q^{89} +2.73227i q^{90} +0.838340i q^{91} +14.5353 q^{92} +(-7.59258 - 7.59258i) q^{93} +(9.69333 + 9.69333i) q^{94} +(3.08970 + 3.08970i) q^{95} +(-8.35386 + 8.35386i) q^{96} +(-3.41803 + 3.41803i) q^{97} +1.99257 q^{98} +(2.27768 - 2.27768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Introduction

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