LMFDB - Embedded newform 287.2.f.a.50.12

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			50.12
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.710667i q^{2} +(0.708215 + 0.708215i) q^{3} +1.49495 q^{4} +3.05444i q^{5} +(-0.503305 + 0.503305i) q^{6} +(0.707107 + 0.707107i) q^{7} +2.48375i q^{8} -1.99686i q^{9} +O(q^{10})$	\(q+0.710667i q^{2} +(0.708215 + 0.708215i) q^{3} +1.49495 q^{4} +3.05444i q^{5} +(-0.503305 + 0.503305i) q^{6} +(0.707107 + 0.707107i) q^{7} +2.48375i q^{8} -1.99686i q^{9} -2.17069 q^{10} +(-0.816593 - 0.816593i) q^{11} +(1.05875 + 1.05875i) q^{12} +(-4.51582 - 4.51582i) q^{13} +(-0.502517 + 0.502517i) q^{14} +(-2.16320 + 2.16320i) q^{15} +1.22479 q^{16} +(0.540691 - 0.540691i) q^{17} +1.41910 q^{18} +(-0.910890 + 0.910890i) q^{19} +4.56625i q^{20} +1.00157i q^{21} +(0.580326 - 0.580326i) q^{22} +7.35877 q^{23} +(-1.75903 + 1.75903i) q^{24} -4.32962 q^{25} +(3.20924 - 3.20924i) q^{26} +(3.53885 - 3.53885i) q^{27} +(1.05709 + 1.05709i) q^{28} +(-0.167843 - 0.167843i) q^{29} +(-1.53731 - 1.53731i) q^{30} -7.78826 q^{31} +5.83791i q^{32} -1.15665i q^{33} +(0.384251 + 0.384251i) q^{34} +(-2.15982 + 2.15982i) q^{35} -2.98522i q^{36} +4.77359 q^{37} +(-0.647339 - 0.647339i) q^{38} -6.39633i q^{39} -7.58646 q^{40} +(2.89389 + 5.71187i) q^{41} -0.711780 q^{42} -3.37868i q^{43} +(-1.22077 - 1.22077i) q^{44} +6.09931 q^{45} +5.22963i q^{46} +(0.556419 - 0.556419i) q^{47} +(0.867414 + 0.867414i) q^{48} +1.00000i q^{49} -3.07692i q^{50} +0.765850 q^{51} +(-6.75093 - 6.75093i) q^{52} +(-3.52167 - 3.52167i) q^{53} +(2.51494 + 2.51494i) q^{54} +(2.49424 - 2.49424i) q^{55} +(-1.75627 + 1.75627i) q^{56} -1.29021 q^{57} +(0.119281 - 0.119281i) q^{58} +1.06581 q^{59} +(-3.23388 + 3.23388i) q^{60} +2.75192i q^{61} -5.53486i q^{62} +(1.41200 - 1.41200i) q^{63} -1.69923 q^{64} +(13.7933 - 13.7933i) q^{65} +0.821990 q^{66} +(4.63995 - 4.63995i) q^{67} +(0.808307 - 0.808307i) q^{68} +(5.21159 + 5.21159i) q^{69} +(-1.53491 - 1.53491i) q^{70} +(-9.33534 - 9.33534i) q^{71} +4.95970 q^{72} -3.22817i q^{73} +3.39243i q^{74} +(-3.06630 - 3.06630i) q^{75} +(-1.36174 + 1.36174i) q^{76} -1.15484i q^{77} +4.54566 q^{78} +(-6.84941 - 6.84941i) q^{79} +3.74105i q^{80} -0.978058 q^{81} +(-4.05923 + 2.05659i) q^{82} +4.02107 q^{83} +1.49730i q^{84} +(1.65151 + 1.65151i) q^{85} +2.40111 q^{86} -0.237738i q^{87} +(2.02821 - 2.02821i) q^{88} +(4.95019 + 4.95019i) q^{89} +4.33457i q^{90} -6.38633i q^{91} +11.0010 q^{92} +(-5.51576 - 5.51576i) q^{93} +(0.395429 + 0.395429i) q^{94} +(-2.78226 - 2.78226i) q^{95} +(-4.13449 + 4.13449i) q^{96} +(11.3870 - 11.3870i) q^{97} -0.710667 q^{98} +(-1.63063 + 1.63063i) 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 $

$2$			0.710667i			0.502517i	0.967920	+	0.251259i	$0.0808445\pi$
$2$			0.710667i			0.502517i	−0.967920	+	0.251259i	$0.919156\pi$
$3$	0.708215	+	0.708215i	0.408888	+	0.408888i	0.881351	−	0.472463i	$-0.156635\pi$
$3$	0.708215	+	0.708215i	0.408888	+	0.408888i	−0.472463	+	0.881351i	$0.656635\pi$
$4$	1.49495			0.747476
$5$			3.05444i			1.36599i	0.730424	+	0.682994i	$0.239323\pi$
$5$			3.05444i			1.36599i	−0.730424	+	0.682994i	$0.760677\pi$
$6$	−0.503305	+	0.503305i	−0.205473	+	0.205473i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$			2.48375i			0.878137i
$9$		−	1.99686i		−	0.665621i
$10$	−2.17069			−0.686433
$11$	−0.816593	−	0.816593i	−0.246212	−	0.246212i	0.573202	−	0.819414i	$-0.305701\pi$
$11$	−0.816593	−	0.816593i	−0.246212	−	0.246212i	−0.819414	+	0.573202i	$0.805701\pi$
$12$	1.05875	+	1.05875i	0.305634	+	0.305634i
$13$	−4.51582	−	4.51582i	−1.25246	−	1.25246i	−0.954613	−	0.297849i	$-0.903731\pi$
$13$	−4.51582	−	4.51582i	−1.25246	−	1.25246i	−0.297849	−	0.954613i	$-0.596269\pi$
$14$	−0.502517	+	0.502517i	−0.134303	+	0.134303i
$15$	−2.16320	+	2.16320i	−0.558536	+	0.558536i
$16$	1.22479			0.306198
$17$	0.540691	−	0.540691i	0.131137	−	0.131137i	−0.638492	−	0.769629i	$-0.720441\pi$
$17$	0.540691	−	0.540691i	0.131137	−	0.131137i	0.769629	+	0.638492i	$0.220441\pi$
$18$	1.41910			0.334486
$19$	−0.910890	+	0.910890i	−0.208973	+	0.208973i	−0.803831	−	0.594858i	$-0.797208\pi$
$19$	−0.910890	+	0.910890i	−0.208973	+	0.208973i	0.594858	+	0.803831i	$0.297208\pi$
$20$			4.56625i			1.02104i
$21$			1.00157i			0.218560i
$22$	0.580326	−	0.580326i	0.123726	−	0.123726i
$23$	7.35877			1.53441			0.767204	−	0.641403i	$-0.221647\pi$
$23$	7.35877			1.53441			0.767204	+	0.641403i	$0.221647\pi$
$24$	−1.75903	+	1.75903i	−0.359060	+	0.359060i
$25$	−4.32962			−0.865924
$26$	3.20924	−	3.20924i	0.629384	−	0.629384i
$27$	3.53885	−	3.53885i	0.681052	−	0.681052i
$28$	1.05709	+	1.05709i	0.199771	+	0.199771i
$29$	−0.167843	−	0.167843i	−0.0311677	−	0.0311677i	0.691351	−	0.722519i	$-0.257016\pi$
$29$	−0.167843	−	0.167843i	−0.0311677	−	0.0311677i	−0.722519	+	0.691351i	$0.757016\pi$
$30$	−1.53731	−	1.53731i	−0.280674	−	0.280674i
$31$	−7.78826			−1.39881			−0.699406	−	0.714724i	$-0.746552\pi$
$31$	−7.78826			−1.39881			−0.699406	+	0.714724i	$0.746552\pi$
$32$			5.83791i			1.03201i
$33$		−	1.15665i		−	0.201346i
$34$	0.384251	+	0.384251i	0.0658985	+	0.0658985i
$35$	−2.15982	+	2.15982i	−0.365076	+	0.365076i
$36$		−	2.98522i		−	0.497536i
$37$	4.77359			0.784773			0.392386	−	0.919801i	$-0.371650\pi$
$37$	4.77359			0.784773			0.392386	+	0.919801i	$0.371650\pi$
$38$	−0.647339	−	0.647339i	−0.105012	−	0.105012i
$39$		−	6.39633i		−	1.02423i
$40$	−7.58646			−1.19952
$41$	2.89389	+	5.71187i	0.451949	+	0.892044i
$41$	2.89389	+	5.71187i	0.451949	+	0.892044i
$42$	−0.711780			−0.109830
$43$		−	3.37868i		−	0.515243i	−0.966246	−	0.257622i	$-0.917061\pi$
$43$		−	3.37868i		−	0.515243i	0.966246	−	0.257622i	$-0.0829388\pi$
$44$	−1.22077	−	1.22077i	−0.184038	−	0.184038i
$45$	6.09931			0.909231
$46$			5.22963i			0.771067i
$47$	0.556419	−	0.556419i	0.0811621	−	0.0811621i	−0.665360	−	0.746522i	$-0.731722\pi$
$47$	0.556419	−	0.556419i	0.0811621	−	0.0811621i	0.746522	+	0.665360i	$0.231722\pi$
$48$	0.867414	+	0.867414i	0.125200	+	0.125200i
$49$			1.00000i			0.142857i
$50$		−	3.07692i		−	0.435142i
$51$	0.765850			0.107241
$52$	−6.75093	−	6.75093i	−0.936186	−	0.936186i
$53$	−3.52167	−	3.52167i	−0.483739	−	0.483739i	0.422585	−	0.906323i	$-0.361123\pi$
$53$	−3.52167	−	3.52167i	−0.483739	−	0.483739i	−0.906323	+	0.422585i	$0.861123\pi$
$54$	2.51494	+	2.51494i	0.342241	+	0.342241i
$55$	2.49424	−	2.49424i	0.336323	−	0.336323i
$56$	−1.75627	+	1.75627i	−0.234692	+	0.234692i
$57$	−1.29021			−0.170893
$58$	0.119281	−	0.119281i	0.0156623	−	0.0156623i
$59$	1.06581			0.138757			0.0693785	−	0.997590i	$-0.477898\pi$
$59$	1.06581			0.138757			0.0693785	+	0.997590i	$0.477898\pi$
$60$	−3.23388	+	3.23388i	−0.417493	+	0.417493i
$61$			2.75192i			0.352348i	0.984359	+	0.176174i	$0.0563721\pi$
$61$			2.75192i			0.352348i	−0.984359	+	0.176174i	$0.943628\pi$
$62$		−	5.53486i		−	0.702927i
$63$	1.41200	−	1.41200i	0.177895	−	0.177895i
$64$	−1.69923			−0.212403
$65$	13.7933	−	13.7933i	1.71085	−	1.71085i
$66$	0.821990			0.101180
$67$	4.63995	−	4.63995i	0.566860	−	0.566860i	−0.364388	−	0.931247i	$-0.618722\pi$
$67$	4.63995	−	4.63995i	0.566860	−	0.566860i	0.931247	+	0.364388i	$0.118722\pi$
$68$	0.808307	−	0.808307i	0.0980217	−	0.0980217i
$69$	5.21159	+	5.21159i	0.627401	+	0.627401i
$70$	−1.53491	−	1.53491i	−0.183457	−	0.183457i
$71$	−9.33534	−	9.33534i	−1.10790	−	1.10790i	−0.993426	−	0.114475i	$-0.963481\pi$
$71$	−9.33534	−	9.33534i	−1.10790	−	1.10790i	−0.114475	−	0.993426i	$-0.536519\pi$
$72$	4.95970			0.584507
$73$		−	3.22817i		−	0.377829i	−0.981994	−	0.188915i	$-0.939503\pi$
$73$		−	3.22817i		−	0.377829i	0.981994	−	0.188915i	$-0.0604969\pi$
$74$			3.39243i			0.394362i
$75$	−3.06630	−	3.06630i	−0.354066	−	0.354066i
$76$	−1.36174	+	1.36174i	−0.156202	+	0.156202i
$77$		−	1.15484i		−	0.131606i
$78$	4.54566			0.514695
$79$	−6.84941	−	6.84941i	−0.770619	−	0.770619i	0.207596	−	0.978215i	$-0.433436\pi$
$79$	−6.84941	−	6.84941i	−0.770619	−	0.770619i	−0.978215	+	0.207596i	$0.933436\pi$
$80$			3.74105i			0.418262i
$81$	−0.978058			−0.108673
$82$	−4.05923	+	2.05659i	−0.448267	+	0.227112i
$83$	4.02107			0.441370			0.220685	−	0.975345i	$-0.429171\pi$
$83$	4.02107			0.441370			0.220685	+	0.975345i	$0.429171\pi$
$84$			1.49730i			0.163368i
$85$	1.65151	+	1.65151i	0.179131	+	0.179131i
$86$	2.40111			0.258919
$87$		−	0.237738i		−	0.0254882i
$88$	2.02821	−	2.02821i	0.216208	−	0.216208i
$89$	4.95019	+	4.95019i	0.524719	+	0.524719i	0.918993	−	0.394274i	$-0.129004\pi$
$89$	4.95019	+	4.95019i	0.524719	+	0.524719i	−0.394274	+	0.918993i	$0.629004\pi$
$90$			4.33457i			0.456904i
$91$		−	6.38633i		−	0.669469i
$92$	11.0010			1.14693
$93$	−5.51576	−	5.51576i	−0.571958	−	0.571958i
$94$	0.395429	+	0.395429i	0.0407853	+	0.0407853i
$95$	−2.78226	−	2.78226i	−0.285454	−	0.285454i
$96$	−4.13449	+	4.13449i	−0.421975	+	0.421975i
$97$	11.3870	−	11.3870i	1.15618	−	1.15618i	0.170886	−	0.985291i	$-0.445337\pi$
$97$	11.3870	−	11.3870i	1.15618	−	1.15618i	0.985291	−	0.170886i	$-0.0546629\pi$
$98$	−0.710667			−0.0717882
$99$	−1.63063	+	1.63063i	−0.163884	+	0.163884i
$100$	−6.47258			−0.647258
$101$	−13.4403	+	13.4403i	−1.33736	+	1.33736i	−0.438750	+	0.898609i	$0.644579\pi$
$101$	−13.4403	+	13.4403i	−1.33736	+	1.33736i	−0.898609	+	0.438750i	$0.855421\pi$
$102$			0.544264i			0.0538902i
$103$			11.0541i			1.08920i	0.838697	+	0.544598i	$0.183318\pi$
$103$			11.0541i			1.08920i	−0.838697	+	0.544598i	$0.816682\pi$
$104$	11.2161	−	11.2161i	1.09983	−	1.09983i
$105$	−3.05923			−0.298550
$106$	2.50273	−	2.50273i	0.243087	−	0.243087i
$107$	−4.69841			−0.454212			−0.227106	−	0.973870i	$-0.572926\pi$
$107$	−4.69841			−0.454212			−0.227106	+	0.973870i	$0.572926\pi$
$108$	5.29042	−	5.29042i	0.509071	−	0.509071i
$109$	−10.8294	+	10.8294i	−1.03727	+	1.03727i	−0.0379922	+	0.999278i	$0.512096\pi$
$109$	−10.8294	+	10.8294i	−1.03727	+	1.03727i	−0.999278	+	0.0379922i	$0.987904\pi$
$110$	1.77257	+	1.77257i	0.169008	+	0.169008i
$111$	3.38072	+	3.38072i	0.320884	+	0.320884i
$112$	0.866057	+	0.866057i	0.0818347	+	0.0818347i
$113$	−0.331874			−0.0312201			−0.0156101	−	0.999878i	$-0.504969\pi$
$113$	−0.331874			−0.0312201			−0.0156101	+	0.999878i	$0.504969\pi$
$114$		−	0.916910i		−	0.0858765i
$115$			22.4769i			2.09598i
$116$	−0.250918	−	0.250918i	−0.0232971	−	0.0232971i
$117$	−9.01747	+	9.01747i	−0.833665	+	0.833665i
$118$			0.757437i			0.0697277i
$119$	0.764652			0.0700956
$120$	−5.37284	−	5.37284i	−0.490471	−	0.490471i
$121$		−	9.66635i		−	0.878759i
$122$	−1.95570			−0.177061
$123$	−1.99573	+	6.09472i	−0.179949	+	0.549542i
$124$	−11.6431			−1.04558
$125$			2.04764i			0.183146i
$126$	1.00346	+	1.00346i	0.0893952	+	0.0893952i
$127$	2.18926			0.194266			0.0971328	−	0.995271i	$-0.469033\pi$
$127$	2.18926			0.194266			0.0971328	+	0.995271i	$0.469033\pi$
$128$			10.4682i			0.925270i
$129$	2.39283	−	2.39283i	0.210677	−	0.210677i
$130$	9.80244	+	9.80244i	0.859731	+	0.859731i
$131$		−	21.4230i		−	1.87173i	−0.352355	−	0.935866i	$-0.614619\pi$
$131$		−	21.4230i		−	1.87173i	0.352355	−	0.935866i	$-0.385381\pi$
$132$		−	1.72913i		−	0.150502i
$133$	−1.28819			−0.111701
$134$	3.29745	+	3.29745i	0.284857	+	0.284857i
$135$	10.8092	+	10.8092i	0.930310	+	0.930310i
$136$	1.34294	+	1.34294i	0.115156	+	0.115156i
$137$	−11.4219	+	11.4219i	−0.975836	+	0.975836i	−0.999715	−	0.0238786i	$-0.992398\pi$
$137$	−11.4219	+	11.4219i	−0.975836	+	0.975836i	0.0238786	+	0.999715i	$0.492398\pi$
$138$	−3.70370	+	3.70370i	−0.315280	+	0.315280i
$139$	−16.5423			−1.40310			−0.701550	−	0.712620i	$-0.747508\pi$
$139$	−16.5423			−1.40310			−0.701550	+	0.712620i	$0.747508\pi$
$140$	−3.22883	+	3.22883i	−0.272886	+	0.272886i
$141$	0.788129			0.0663724
$142$	6.63432	−	6.63432i	0.556740	−	0.556740i
$143$			7.37517i			0.616743i
$144$		−	2.44574i		−	0.203812i
$145$	0.512668	−	0.512668i	0.0425747	−	0.0425747i
$146$	2.29416			0.189866
$147$	−0.708215	+	0.708215i	−0.0584126	+	0.0584126i
$148$	7.13628			0.586599
$149$	−7.76248	+	7.76248i	−0.635927	+	0.635927i	−0.949548	−	0.313621i	$-0.898458\pi$
$149$	−7.76248	+	7.76248i	−0.635927	+	0.635927i	0.313621	+	0.949548i	$0.398458\pi$
$150$	2.17912	−	2.17912i	0.177924	−	0.177924i
$151$	5.18758	+	5.18758i	0.422159	+	0.422159i	0.885946	−	0.463787i	$-0.153510\pi$
$151$	5.18758	+	5.18758i	0.422159	+	0.422159i	−0.463787	+	0.885946i	$0.653510\pi$
$152$	−2.26242	−	2.26242i	−0.183506	−	0.183506i
$153$	−1.07969	−	1.07969i	−0.0872875	−	0.0872875i
$154$	0.820704			0.0661342
$155$		−	23.7888i		−	1.91076i
$156$		−	9.56222i		−	0.765590i
$157$	−0.585935	−	0.585935i	−0.0467627	−	0.0467627i	0.683339	−	0.730101i	$-0.260527\pi$
$157$	−0.585935	−	0.585935i	−0.0467627	−	0.0467627i	−0.730101	+	0.683339i	$0.760527\pi$
$158$	4.86765	−	4.86765i	0.387249	−	0.387249i
$159$		−	4.98820i		−	0.395590i
$160$	−17.8316			−1.40971
$161$	5.20343	+	5.20343i	0.410088	+	0.410088i
$162$		−	0.695073i		−	0.0546101i
$163$	19.1917			1.50321			0.751605	−	0.659613i	$-0.229280\pi$
$163$	19.1917			1.50321			0.751605	+	0.659613i	$0.229280\pi$
$164$	4.32622	+	8.53897i	0.337821	+	0.666782i
$165$	3.53291			0.275037
$166$			2.85764i			0.221796i
$167$	−5.47253	−	5.47253i	−0.423477	−	0.423477i	0.462922	−	0.886399i	$-0.346801\pi$
$167$	−5.47253	−	5.47253i	−0.423477	−	0.423477i	−0.886399	+	0.462922i	$0.846801\pi$
$168$	−2.48764			−0.191925
$169$			27.7852i			2.13732i
$170$	−1.17367	+	1.17367i	−0.0900166	+	0.0900166i
$171$	1.81892	+	1.81892i	0.139097	+	0.139097i
$172$		−	5.05096i		−	0.385132i
$173$			5.64590i			0.429250i	0.976697	+	0.214625i	$0.0688529\pi$
$173$			5.64590i			0.429250i	−0.976697	+	0.214625i	$0.931147\pi$
$174$	0.168953			0.0128083
$175$	−3.06150	−	3.06150i	−0.231428	−	0.231428i
$176$	−1.00016	−	1.00016i	−0.0753895	−	0.0753895i
$177$	0.754824	+	0.754824i	0.0567360	+	0.0567360i
$178$	−3.51793	+	3.51793i	−0.263680	+	0.263680i
$179$	−3.70668	+	3.70668i	−0.277050	+	0.277050i	−0.831930	−	0.554880i	$-0.812764\pi$
$179$	−3.70668	+	3.70668i	−0.277050	+	0.277050i	0.554880	+	0.831930i	$0.312764\pi$
$180$	9.11818			0.679629
$181$	0.939298	−	0.939298i	0.0698175	−	0.0698175i	−0.671336	−	0.741153i	$-0.734279\pi$
$181$	0.939298	−	0.939298i	0.0698175	−	0.0698175i	0.741153	+	0.671336i	$0.234279\pi$
$182$	4.53855			0.336420
$183$	−1.94895	+	1.94895i	−0.144071	+	0.144071i
$184$			18.2773i			1.34742i
$185$			14.5806i			1.07199i
$186$	3.91987	−	3.91987i	0.287419	−	0.287419i
$187$	−0.883049			−0.0645749
$188$	0.831821	−	0.831821i	0.0606668	−	0.0606668i
$189$	5.00469			0.364038
$190$	1.97726	−	1.97726i	0.143446	−	0.143446i
$191$	13.8897	−	13.8897i	1.00502	−	1.00502i	0.00503754	−	0.999987i	$-0.498396\pi$
$191$	13.8897	−	13.8897i	1.00502	−	1.00502i	0.999987	−	0.00503754i	$-0.00160351\pi$
$192$	−1.20342	−	1.20342i	−0.0868492	−	0.0868492i
$193$	−10.3453	−	10.3453i	−0.744668	−	0.744668i	0.228805	−	0.973472i	$-0.426518\pi$
$193$	−10.3453	−	10.3453i	−0.744668	−	0.744668i	−0.973472	+	0.228805i	$0.926518\pi$
$194$	8.09237	+	8.09237i	0.580999	+	0.580999i
$195$	19.5372			1.39909
$196$			1.49495i			0.106782i
$197$			21.4752i			1.53005i	0.644003	+	0.765023i	$0.277272\pi$
$197$			21.4752i			1.53005i	−0.644003	+	0.765023i	$0.722728\pi$
$198$	−1.15883	−	1.15883i	−0.0823545	−	0.0823545i
$199$	7.57207	−	7.57207i	0.536770	−	0.536770i	−0.385809	−	0.922579i	$-0.626078\pi$
$199$	7.57207	−	7.57207i	0.536770	−	0.536770i	0.922579	+	0.385809i	$0.126078\pi$
$200$		−	10.7537i		−	0.760400i
$201$	6.57216			0.463564
$202$	−9.55157	−	9.55157i	−0.672046	−	0.672046i
$203$		−	0.237366i		−	0.0166598i
$204$	1.14491			0.0801598
$205$	−17.4466	+	8.83921i	−1.21852	+	0.617357i
$206$	−7.85581			−0.547340
$207$		−	14.6945i		−	1.02134i
$208$	−5.53093	−	5.53093i	−0.383501	−	0.383501i
$209$	1.48765			0.102903
$210$		−	2.17409i		−	0.150027i
$211$	−2.57205	+	2.57205i	−0.177067	+	0.177067i	−0.790076	−	0.613009i	$-0.789959\pi$
$211$	−2.57205	+	2.57205i	−0.177067	+	0.177067i	0.613009	+	0.790076i	$0.289959\pi$
$212$	−5.26473	−	5.26473i	−0.361583	−	0.361583i
$213$		−	13.2229i		−	0.906015i
$214$		−	3.33900i		−	0.228249i
$215$	10.3200			0.703817
$216$	8.78961	+	8.78961i	0.598057	+	0.598057i
$217$	−5.50713	−	5.50713i	−0.373848	−	0.373848i
$218$	−7.69611	−	7.69611i	−0.521246	−	0.521246i
$219$	2.28624	−	2.28624i	0.154490	−	0.154490i
$220$	3.72877	−	3.72877i	0.251393	−	0.251393i
$221$	−4.88332			−0.328488
$222$	−2.40257	+	2.40257i	−0.161250	+	0.161250i
$223$	−22.9758			−1.53857			−0.769286	−	0.638905i	$-0.779388\pi$
$223$	−22.9758			−1.53857			−0.769286	+	0.638905i	$0.779388\pi$
$224$	−4.12803	+	4.12803i	−0.275815	+	0.275815i
$225$			8.64566i			0.576378i
$226$		−	0.235852i		−	0.0156886i
$227$	−6.06681	+	6.06681i	−0.402669	+	0.402669i	−0.879172	−	0.476504i	$-0.841904\pi$
$227$	−6.06681	+	6.06681i	−0.402669	+	0.402669i	0.476504	+	0.879172i	$0.341904\pi$
$228$	−1.92881			−0.127738
$229$	−8.78131	+	8.78131i	−0.580285	+	0.580285i	−0.934982	−	0.354696i	$-0.884584\pi$
$229$	−8.78131	+	8.78131i	−0.580285	+	0.580285i	0.354696	+	0.934982i	$0.384584\pi$
$230$	−15.9736			−1.05327
$231$	0.817873	−	0.817873i	0.0538121	−	0.0538121i
$232$	0.416880	−	0.416880i	0.0273695	−	0.0273695i
$233$	−0.834351	−	0.834351i	−0.0546602	−	0.0546602i	0.679248	−	0.733909i	$-0.262306\pi$
$233$	−0.834351	−	0.834351i	−0.0546602	−	0.0546602i	−0.733909	+	0.679248i	$0.762306\pi$
$234$	−6.40842	−	6.40842i	−0.418931	−	0.418931i
$235$	1.69955	+	1.69955i	0.110866	+	0.110866i
$236$	1.59334			0.103718
$237$		−	9.70170i		−	0.630193i
$238$			0.543413i			0.0352242i
$239$	20.8470	+	20.8470i	1.34848	+	1.34848i	0.887316	+	0.461162i	$0.152567\pi$
$239$	20.8470	+	20.8470i	1.34848	+	1.34848i	0.461162	+	0.887316i	$0.347433\pi$
$240$	−2.64947	+	2.64947i	−0.171022	+	0.171022i
$241$		−	25.0690i		−	1.61484i	−0.589979	−	0.807419i	$-0.700864\pi$
$241$		−	25.0690i		−	1.61484i	0.589979	−	0.807419i	$-0.299136\pi$
$242$	6.86955			0.441592
$243$	−11.3092	−	11.3092i	−0.725488	−	0.725488i
$244$			4.11400i			0.263372i
$245$	−3.05444			−0.195141
$246$	−4.33131	−	1.41830i	−0.276155	−	0.0904276i
$247$	8.22682			0.523460
$248$		−	19.3441i		−	1.22835i
$249$	2.84778	+	2.84778i	0.180471	+	0.180471i
$250$	−1.45519			−0.0920341
$251$		−	6.30213i		−	0.397787i	−0.980021	−	0.198893i	$-0.936265\pi$
$251$		−	6.30213i		−	0.397787i	0.980021	−	0.198893i	$-0.0637348\pi$
$252$	2.11087	−	2.11087i	0.132972	−	0.132972i
$253$	−6.00912	−	6.00912i	−0.377790	−	0.377790i
$254$			1.55584i			0.0976218i
$255$			2.33925i			0.146489i
$256$	−10.8379			−0.677368
$257$	15.3084	+	15.3084i	0.954915	+	0.954915i	0.999027	−	0.0441119i	$-0.0140458\pi$
$257$	15.3084	+	15.3084i	0.954915	+	0.954915i	−0.0441119	+	0.999027i	$0.514046\pi$
$258$	1.70050	+	1.70050i	0.105869	+	0.105869i
$259$	3.37543	+	3.37543i	0.209739	+	0.209739i
$260$	20.6203	−	20.6203i	1.27882	−	1.27882i
$261$	−0.335160	+	0.335160i	−0.0207459	+	0.0207459i
$262$	15.2246			0.940578
$263$	14.8722	−	14.8722i	0.917060	−	0.917060i	−0.0797544	−	0.996815i	$-0.525414\pi$
$263$	14.8722	−	14.8722i	0.917060	−	0.917060i	0.996815	+	0.0797544i	$0.0254136\pi$
$264$	2.87282			0.176810
$265$	10.7567	−	10.7567i	0.660781	−	0.660781i
$266$		−	0.915476i		−	0.0561314i
$267$			7.01159i			0.429102i
$268$	6.93650	−	6.93650i	0.423714	−	0.423714i
$269$	−7.43290			−0.453192			−0.226596	−	0.973989i	$-0.572760\pi$
$269$	−7.43290			−0.453192			−0.226596	+	0.973989i	$0.572760\pi$
$270$	−7.68175	+	7.68175i	−0.467497	+	0.467497i
$271$	7.84615			0.476620			0.238310	−	0.971189i	$-0.423407\pi$
$271$	7.84615			0.476620			0.238310	+	0.971189i	$0.423407\pi$
$272$	0.662233	−	0.662233i	0.0401538	−	0.0401538i
$273$	4.52289	−	4.52289i	0.273738	−	0.273738i
$274$	−8.11714	−	8.11714i	−0.490375	−	0.490375i
$275$	3.53554	+	3.53554i	0.213201	+	0.213201i
$276$	7.79108	+	7.79108i	0.468968	+	0.468968i
$277$	32.9500			1.97977			0.989885	−	0.141870i	$-0.0453114\pi$
$277$	32.9500			1.97977			0.989885	+	0.141870i	$0.0453114\pi$
$278$		−	11.7561i		−	0.705082i
$279$			15.5521i			0.931080i
$280$	−5.36444	−	5.36444i	−0.320587	−	0.320587i
$281$	2.41851	−	2.41851i	0.144276	−	0.144276i	−0.631279	−	0.775556i	$-0.717470\pi$
$281$	2.41851	−	2.41851i	0.144276	−	0.144276i	0.775556	+	0.631279i	$0.217470\pi$
$282$			0.560097i			0.0333533i
$283$	−15.5435			−0.923966			−0.461983	−	0.886889i	$-0.652862\pi$
$283$	−15.5435			−0.923966			−0.461983	+	0.886889i	$0.652862\pi$
$284$	−13.9559	−	13.9559i	−0.828130	−	0.828130i
$285$		−	3.94088i		−	0.233437i
$286$	−5.24129			−0.309924
$287$	−1.99261	+	6.08519i	−0.117620	+	0.359197i
$288$	11.6575			0.686926
$289$			16.4153i			0.965606i
$290$	0.364336	+	0.364336i	0.0213945	+	0.0213945i
$291$	16.1289			0.945493
$292$		−	4.82597i		−	0.282418i
$293$	−2.86404	+	2.86404i	−0.167319	+	0.167319i	−0.785800	−	0.618481i	$-0.787748\pi$
$293$	−2.86404	+	2.86404i	−0.167319	+	0.167319i	0.618481	+	0.785800i	$0.287748\pi$
$294$	−0.503305	−	0.503305i	−0.0293533	−	0.0293533i
$295$			3.25546i			0.189540i
$296$			11.8564i			0.689138i
$297$	−5.77961			−0.335367
$298$	−5.51654	−	5.51654i	−0.319564	−	0.319564i
$299$	−33.2308	−	33.2308i	−1.92179	−	1.92179i
$300$	−4.58398	−	4.58398i	−0.264656	−	0.264656i
$301$	2.38909	−	2.38909i	0.137705	−	0.137705i
$302$	−3.68664	+	3.68664i	−0.212142	+	0.212142i
$303$	−19.0372			−1.09366
$304$	−1.11565	+	1.11565i	−0.0639869	+	0.0639869i
$305$	−8.40560			−0.481303
$306$	0.767297	−	0.767297i	0.0438634	−	0.0438634i
$307$		−	4.34253i		−	0.247841i	−0.992292	−	0.123921i	$-0.960453\pi$
$307$		−	4.34253i		−	0.247841i	0.992292	−	0.123921i	$-0.0395468\pi$
$308$		−	1.72643i		−	0.0983723i
$309$	−7.82870	+	7.82870i	−0.445359	+	0.445359i
$310$	16.9059			0.960191
$311$	0.993600	−	0.993600i	0.0563419	−	0.0563419i	−0.678374	−	0.734716i	$-0.737315\pi$
$311$	0.993600	−	0.993600i	0.0563419	−	0.0563419i	0.734716	+	0.678374i	$0.237315\pi$
$312$	15.8869			0.899417
$313$	19.6342	−	19.6342i	1.10979	−	1.10979i	0.116616	−	0.993177i	$-0.462795\pi$
$313$	19.6342	−	19.6342i	1.10979	−	1.10979i	0.993177	−	0.116616i	$-0.0372045\pi$
$314$	0.416404	−	0.416404i	0.0234991	−	0.0234991i
$315$	4.31286	+	4.31286i	0.243002	+	0.243002i
$316$	−10.2395	−	10.2395i	−0.576019	−	0.576019i
$317$	−14.4078	−	14.4078i	−0.809224	−	0.809224i	0.175293	−	0.984516i	$-0.443913\pi$
$317$	−14.4078	−	14.4078i	−0.809224	−	0.809224i	−0.984516	+	0.175293i	$0.943913\pi$
$318$	3.54495			0.198791
$319$			0.274119i			0.0153477i
$320$		−	5.19019i		−	0.290141i
$321$	−3.32748	−	3.32748i	−0.185722	−	0.185722i
$322$	−3.69791	+	3.69791i	−0.206076	+	0.206076i
$323$			0.985020i			0.0548080i
$324$	−1.46215			−0.0812306
$325$	19.5518	+	19.5518i	1.08454	+	1.08454i
$326$			13.6389i			0.755389i
$327$	−15.3391			−0.848255
$328$	−14.1868	+	7.18768i	−0.783337	+	0.396873i
$329$	0.786896			0.0433830
$330$			2.51072i			0.138211i
$331$	−18.7292	−	18.7292i	−1.02945	−	1.02945i	−0.999553	−	0.0298997i	$-0.990481\pi$
$331$	−18.7292	−	18.7292i	−1.02945	−	1.02945i	−0.0298997	−	0.999553i	$-0.509519\pi$
$332$	6.01131			0.329914
$333$		−	9.53220i		−	0.522361i
$334$	3.88915	−	3.88915i	0.212805	−	0.212805i
$335$	14.1724	+	14.1724i	0.774324	+	0.774324i
$336$			1.22671i			0.0669225i
$337$			27.5741i			1.50206i	0.660271	+	0.751028i	$0.270442\pi$
$337$			27.5741i			1.50206i	−0.660271	+	0.751028i	$0.729558\pi$
$338$	−19.7460			−1.07404
$339$	−0.235038	−	0.235038i	−0.0127655	−	0.0127655i
$340$	2.46893	+	2.46893i	0.133896	+	0.133896i
$341$	6.35984	+	6.35984i	0.344405	+	0.344405i
$342$	−1.29265	+	1.29265i	−0.0698984	+	0.0698984i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	8.39178			0.452454
$345$	−15.9185	+	15.9185i	−0.857023	+	0.857023i
$346$	−4.01235			−0.215705
$347$	−21.6977	+	21.6977i	−1.16480	+	1.16480i	−0.181382	+	0.983413i	$0.558057\pi$
$347$	−21.6977	+	21.6977i	−1.16480	+	1.16480i	−0.983413	+	0.181382i	$0.941943\pi$
$348$		−	0.355407i		−	0.0190518i
$349$			21.9763i			1.17637i	0.808728	+	0.588183i	$0.200156\pi$
$349$			21.9763i			1.17637i	−0.808728	+	0.588183i	$0.799844\pi$
$350$	2.17571	−	2.17571i	0.116297	−	0.116297i
$351$	−31.9616			−1.70598
$352$	4.76720	−	4.76720i	0.254093	−	0.254093i
$353$	−9.46613			−0.503831			−0.251916	−	0.967749i	$-0.581061\pi$
$353$	−9.46613			−0.503831			−0.251916	+	0.967749i	$0.581061\pi$
$354$	−0.536428	+	0.536428i	−0.0285108	+	0.0285108i
$355$	28.5143	−	28.5143i	1.51338	−	1.51338i
$356$	7.40029	+	7.40029i	0.392215	+	0.392215i
$357$	0.541538	+	0.541538i	0.0286612	+	0.0286612i
$358$	−2.63421	−	2.63421i	−0.139223	−	0.139223i
$359$	5.60067			0.295592			0.147796	−	0.989018i	$-0.452782\pi$
$359$	5.60067			0.295592			0.147796	+	0.989018i	$0.452782\pi$
$360$			15.1491i			0.798429i
$361$			17.3406i			0.912661i
$362$	0.667528	+	0.667528i	0.0350845	+	0.0350845i
$363$	6.84585	−	6.84585i	0.359314	−	0.359314i
$364$		−	9.54726i		−	0.500412i
$365$	9.86027			0.516110
$366$	−1.38506	−	1.38506i	−0.0723981	−	0.0723981i
$367$		−	20.5237i		−	1.07133i	−0.844431	−	0.535665i	$-0.820061\pi$
$367$		−	20.5237i		−	1.07133i	0.844431	−	0.535665i	$-0.179939\pi$
$368$	9.01294			0.469832
$369$	11.4058	−	5.77870i	0.593763	−	0.300827i
$370$	−10.3620			−0.538693
$371$		−	4.98040i		−	0.258569i
$372$	−8.24580	−	8.24580i	−0.427525	−	0.427525i
$373$	−29.4638			−1.52558			−0.762790	−	0.646646i	$-0.776171\pi$
$373$	−29.4638			−1.52558			−0.762790	+	0.646646i	$0.776171\pi$
$374$		−	0.627553i		−	0.0324500i
$375$	−1.45017	+	1.45017i	−0.0748862	+	0.0748862i
$376$	1.38200	+	1.38200i	0.0712714	+	0.0712714i
$377$			1.51590i			0.0780727i
$378$			3.55667i			0.182935i
$379$	−21.9096			−1.12542			−0.562710	−	0.826654i	$-0.690241\pi$
$379$	−21.9096			−1.12542			−0.562710	+	0.826654i	$0.690241\pi$
$380$	−4.15935	−	4.15935i	−0.213370	−	0.213370i
$381$	1.55047	+	1.55047i	0.0794329	+	0.0794329i
$382$	9.87096	+	9.87096i	0.505042	+	0.505042i
$383$	2.43934	−	2.43934i	0.124644	−	0.124644i	−0.642033	−	0.766677i	$-0.721909\pi$
$383$	2.43934	−	2.43934i	0.124644	−	0.124644i	0.766677	+	0.642033i	$0.221909\pi$
$384$	−7.41376	+	7.41376i	−0.378332	+	0.378332i
$385$	3.52738			0.179772
$386$	7.35203	−	7.35203i	0.374208	−	0.374208i
$387$	−6.74676			−0.342957
$388$	17.0231	−	17.0231i	0.864215	−	0.864215i
$389$		−	3.03429i		−	0.153845i	−0.997037	−	0.0769223i	$-0.975491\pi$
$389$		−	3.03429i		−	0.153845i	0.997037	−	0.0769223i	$-0.0245093\pi$
$390$			13.8845i			0.703067i
$391$	3.97882	−	3.97882i	0.201217	−	0.201217i
$392$	−2.48375			−0.125448
$393$	15.1721	−	15.1721i	0.765329	−	0.765329i
$394$	−15.2617			−0.768874
$395$	20.9211	−	20.9211i	1.05266	−	1.05266i
$396$	−2.43771	+	2.43771i	−0.122499	+	0.122499i
$397$	20.7455	+	20.7455i	1.04119	+	1.04119i	0.999115	+	0.0420719i	$0.0133958\pi$
$397$	20.7455	+	20.7455i	1.04119	+	1.04119i	0.0420719	+	0.999115i	$0.486604\pi$
$398$	5.38121	+	5.38121i	0.269736	+	0.269736i
$399$	−0.912317	−	0.912317i	−0.0456730	−	0.0456730i
$400$	−5.30288			−0.265144
$401$			20.3314i			1.01530i	0.861563	+	0.507650i	$0.169486\pi$
$401$			20.3314i			1.01530i	−0.861563	+	0.507650i	$0.830514\pi$
$402$			4.67061i			0.232949i
$403$	35.1703	+	35.1703i	1.75196	+	1.75196i
$404$	−20.0926	+	20.0926i	−0.999644	+	0.999644i
$405$		−	2.98742i		−	0.148446i
$406$	0.168688			0.00837186
$407$	−3.89808	−	3.89808i	−0.193221	−	0.193221i
$408$			1.90218i			0.0941719i
$409$	12.8124			0.633530			0.316765	−	0.948504i	$-0.397403\pi$
$409$	12.8124			0.633530			0.316765	+	0.948504i	$0.397403\pi$
$410$	−6.28173	−	12.3987i	−0.310233	−	0.612328i
$411$	−16.1783			−0.798015
$412$			16.5254i			0.814149i
$413$	0.753643	+	0.753643i	0.0370843	+	0.0370843i
$414$	10.4429			0.513239
$415$			12.2821i			0.602906i
$416$	26.3629	−	26.3629i	1.29255	−	1.29255i
$417$	−11.7155	−	11.7155i	−0.573711	−	0.573711i
$418$			1.05723i			0.0517106i
$419$			37.7334i			1.84340i	0.387905	+	0.921699i	$0.373199\pi$
$419$			37.7334i			1.84340i	−0.387905	+	0.921699i	$0.626801\pi$
$420$	−4.57340			−0.223159
$421$	−3.01804	−	3.01804i	−0.147090	−	0.147090i	0.629727	−	0.776817i	$-0.283167\pi$
$421$	−3.01804	−	3.01804i	−0.147090	−	0.147090i	−0.776817	+	0.629727i	$0.783167\pi$
$422$	−1.82787	−	1.82787i	−0.0889793	−	0.0889793i
$423$	−1.11109	−	1.11109i	−0.0540232	−	0.0540232i
$424$	8.74694	−	8.74694i	0.424789	−	0.424789i
$425$	−2.34099	+	2.34099i	−0.113555	+	0.113555i
$426$	9.39704			0.455288
$427$	−1.94590	+	1.94590i	−0.0941689	+	0.0941689i
$428$	−7.02390			−0.339513
$429$	−5.22320	+	5.22320i	−0.252179	+	0.252179i
$430$			7.33406i			0.353680i
$431$		−	23.4255i		−	1.12837i	−0.825650	−	0.564183i	$-0.809191\pi$
$431$		−	23.4255i		−	1.12837i	0.825650	−	0.564183i	$-0.190809\pi$
$432$	4.33435	−	4.33435i	0.208537	−	0.208537i
$433$	23.3401			1.12165			0.560826	−	0.827933i	$-0.310483\pi$
$433$	23.3401			1.12165			0.560826	+	0.827933i	$0.310483\pi$
$434$	3.91373	−	3.91373i	0.187865	−	0.187865i
$435$	0.726157			0.0348166
$436$	−16.1895	+	16.1895i	−0.775335	+	0.775335i
$437$	−6.70303	+	6.70303i	−0.320649	+	0.320649i
$438$	1.62475	+	1.62475i	0.0776338	+	0.0776338i
$439$	22.0363	+	22.0363i	1.05174	+	1.05174i	0.998586	+	0.0531508i	$0.0169264\pi$
$439$	22.0363	+	22.0363i	1.05174	+	1.05174i	0.0531508	+	0.998586i	$0.483074\pi$
$440$	6.19505	+	6.19505i	0.295338	+	0.295338i
$441$	1.99686			0.0950888
$442$		−	3.47041i		−	0.165071i
$443$		−	15.8621i		−	0.753630i	−0.926289	−	0.376815i	$-0.877019\pi$
$443$		−	15.8621i		−	0.753630i	0.926289	−	0.376815i	$-0.122981\pi$
$444$	5.05402	+	5.05402i	0.239853	+	0.239853i
$445$	−15.1201	+	15.1201i	−0.716760	+	0.716760i
$446$		−	16.3281i		−	0.773158i
$447$	−10.9950			−0.520046
$448$	−1.20154	−	1.20154i	−0.0567672	−	0.0567672i
$449$			39.9684i			1.88623i	0.332473	+	0.943113i	$0.392117\pi$
$449$			39.9684i			1.88623i	−0.332473	+	0.943113i	$0.607883\pi$
$450$	−6.14418			−0.289640
$451$	2.30114	−	7.02740i	0.108357	−	0.330907i
$452$	−0.496137			−0.0233363
$453$			7.34784i			0.345231i
$454$	−4.31148	−	4.31148i	−0.202348	−	0.202348i
$455$	19.5067			0.914487
$456$		−	3.20456i		−	0.150067i
$457$	23.5551	−	23.5551i	1.10186	−	1.10186i	0.107675	−	0.994186i	$-0.465660\pi$
$457$	23.5551	−	23.5551i	1.10186	−	1.10186i	0.994186	−	0.107675i	$-0.0343405\pi$
$458$	−6.24058	−	6.24058i	−0.291603	−	0.291603i
$459$		−	3.82685i		−	0.178622i
$460$			33.6020i			1.56670i
$461$	−2.21443			−0.103136			−0.0515682	−	0.998669i	$-0.516422\pi$
$461$	−2.21443			−0.103136			−0.0515682	+	0.998669i	$0.516422\pi$
$462$	0.581235	+	0.581235i	0.0270415	+	0.0270415i
$463$	18.7504	+	18.7504i	0.871407	+	0.871407i	0.992626	−	0.121219i	$-0.0386802\pi$
$463$	18.7504	+	18.7504i	0.871407	+	0.871407i	−0.121219	+	0.992626i	$0.538680\pi$
$464$	−0.205573	−	0.205573i	−0.00954348	−	0.00954348i
$465$	16.8476	−	16.8476i	0.781287	−	0.781287i
$466$	0.592946	−	0.592946i	0.0274677	−	0.0274677i
$467$	−12.5721			−0.581768			−0.290884	−	0.956758i	$-0.593949\pi$
$467$	−12.5721			−0.581768			−0.290884	+	0.956758i	$0.593949\pi$
$468$	−13.4807	+	13.4807i	−0.623145	+	0.623145i
$469$	6.56187			0.302999
$470$	−1.20781	+	1.20781i	−0.0557123	+	0.0557123i
$471$		−	0.829936i		−	0.0382414i
$472$			2.64721i			0.121848i
$473$	−2.75900	+	2.75900i	−0.126859	+	0.126859i
$474$	6.89468			0.316683
$475$	3.94381	−	3.94381i	0.180954	−	0.180954i
$476$	1.14312			0.0523948
$477$	−7.03230	+	7.03230i	−0.321987	+	0.321987i
$478$	−14.8152	+	14.8152i	−0.677633	+	0.677633i
$479$	−8.12217	−	8.12217i	−0.371112	−	0.371112i	0.496770	−	0.867882i	$-0.334519\pi$
$479$	−8.12217	−	8.12217i	−0.371112	−	0.371112i	−0.867882	+	0.496770i	$0.834519\pi$
$480$	−12.6286	−	12.6286i	−0.576413	−	0.576413i
$481$	−21.5566	−	21.5566i	−0.982898	−	0.982898i
$482$	17.8157			0.811484
$483$			7.37030i			0.335360i
$484$		−	14.4507i		−	0.656852i
$485$	34.7810	+	34.7810i	1.57932	+	1.57932i
$486$	8.03709	−	8.03709i	0.364570	−	0.364570i
$487$		−	10.5768i		−	0.479282i	−0.970862	−	0.239641i	$-0.922970\pi$
$487$		−	10.5768i		−	0.479282i	0.970862	−	0.239641i	$-0.0770297\pi$
$488$	−6.83508			−0.309410
$489$	13.5918	+	13.5918i	0.614645	+	0.614645i
$490$		−	2.17069i		−	0.0980618i
$491$	−37.6499			−1.69912			−0.849558	−	0.527496i	$-0.823131\pi$
$491$	−37.6499			−1.69912			−0.849558	+	0.527496i	$0.823131\pi$
$492$	−2.98353	+	9.11132i	−0.134508	+	0.410770i
$493$	−0.181503			−0.00817447
$494$			5.84653i			0.263048i
$495$	−4.98065	−	4.98065i	−0.223864	−	0.223864i
$496$	−9.53898			−0.428313
$497$		−	13.2022i		−	0.592198i
$498$	−2.02382	+	2.02382i	−0.0906897	+	0.0906897i
$499$	1.92115	+	1.92115i	0.0860024	+	0.0860024i	0.748799	−	0.662797i	$-0.230631\pi$
$499$	1.92115	+	1.92115i	0.0860024	+	0.0860024i	−0.662797	+	0.748799i	$0.730631\pi$
$500$			3.06112i			0.136897i
$501$		−	7.75145i		−	0.346309i
$502$	4.47871			0.199895
$503$	−13.4311	−	13.4311i	−0.598864	−	0.598864i	0.341146	−	0.940010i	$-0.389185\pi$
$503$	−13.4311	−	13.4311i	−0.598864	−	0.598864i	−0.940010	+	0.341146i	$0.889185\pi$
$504$	3.50704	+	3.50704i	0.156216	+	0.156216i
$505$	−41.0526	−	41.0526i	−1.82682	−	1.82682i
$506$	4.27048	−	4.27048i	0.189846	−	0.189846i
$507$	−19.6779	+	19.6779i	−0.873925	+	0.873925i
$508$	3.27284			0.145209
$509$	9.96636	−	9.96636i	0.441751	−	0.441751i	−0.450849	−	0.892600i	$-0.648879\pi$
$509$	9.96636	−	9.96636i	0.441751	−	0.441751i	0.892600	+	0.450849i	$0.148879\pi$
$510$	−1.66242			−0.0736134
$511$	2.28266	−	2.28266i	0.100979	−	0.100979i
$512$			13.2344i			0.584881i
$513$			6.44701i			0.284642i
$514$	−10.8792	+	10.8792i	−0.479861	+	0.479861i
$515$	−33.7642			−1.48783
$516$	3.57717	−	3.57717i	0.157476	−	0.157476i
$517$	−0.908736			−0.0399662
$518$	−2.39881	+	2.39881i	−0.105398	+	0.105398i
$519$	−3.99851	+	3.99851i	−0.175515	+	0.175515i
$520$	34.2591	+	34.2591i	1.50236	+	1.50236i
$521$	−12.8052	−	12.8052i	−0.561007	−	0.561007i	0.368587	−	0.929593i	$-0.379842\pi$
$521$	−12.8052	−	12.8052i	−0.561007	−	0.561007i	−0.929593	+	0.368587i	$0.879842\pi$
$522$	−0.238187	−	0.238187i	−0.0104252	−	0.0104252i
$523$	33.8033			1.47812			0.739058	−	0.673641i	$-0.235271\pi$
$523$	33.8033			1.47812			0.739058	+	0.673641i	$0.235271\pi$
$524$		−	32.0263i		−	1.39908i
$525$		−	4.33640i		−	0.189256i
$526$	10.5692	+	10.5692i	0.460839	+	0.460839i
$527$	−4.21104	+	4.21104i	−0.183436	+	0.183436i
$528$		−	1.41665i		−	0.0616517i
$529$	31.1514			1.35441
$530$	7.64446	+	7.64446i	0.332054	+	0.332054i
$531$		−	2.12828i		−	0.0923596i
$532$	−1.92579			−0.0834935
$533$	12.7255	−	38.8620i	0.551202	−	1.68330i
$534$	−4.98290			−0.215631
$535$		−	14.3510i		−	0.620449i
$536$	11.5244	+	11.5244i	0.497780	+	0.497780i
$537$	−5.25025			−0.226565
$538$		−	5.28231i		−	0.227737i
$539$	0.816593	−	0.816593i	0.0351732	−	0.0351732i
$540$	16.1593	+	16.1593i	0.695385	+	0.695385i
$541$			21.0929i			0.906854i	0.891294	+	0.453427i	$0.149799\pi$
$541$			21.0929i			0.906854i	−0.891294	+	0.453427i	$0.850201\pi$
$542$			5.57600i			0.239510i
$543$	1.33045			0.0570951
$544$	3.15651	+	3.15651i	0.135334	+	0.135334i
$545$	−33.0778	−	33.0778i	−1.41690	−	1.41690i
$546$	3.21427	+	3.21427i	0.137558	+	0.137558i
$547$	12.0413	−	12.0413i	0.514849	−	0.514849i	−0.401159	−	0.916008i	$-0.631393\pi$
$547$	12.0413	−	12.0413i	0.514849	−	0.514849i	0.916008	+	0.401159i	$0.131393\pi$
$548$	−17.0752	+	17.0752i	−0.729415	+	0.729415i
$549$	5.49522			0.234530
$550$	−2.51259	+	2.51259i	−0.107137	+	0.107137i
$551$	0.305774			0.0130264
$552$	−12.9443	+	12.9443i	−0.550944	+	0.550944i
$553$		−	9.68653i		−	0.411913i
$554$			23.4164i			0.994869i
$555$	−10.3262	+	10.3262i	−0.438324	+	0.438324i
$556$	−24.7300			−1.04878
$557$	−9.26103	+	9.26103i	−0.392402	+	0.392402i	−0.875543	−	0.483140i	$-0.839496\pi$
$557$	−9.26103	+	9.26103i	−0.392402	+	0.392402i	0.483140	+	0.875543i	$0.339496\pi$
$558$	−11.0524			−0.467884
$559$	−15.2575	+	15.2575i	−0.645323	+	0.645323i
$560$	−2.64532	+	2.64532i	−0.111785	+	0.111785i
$561$	−0.625388	−	0.625388i	−0.0264039	−	0.0264039i
$562$	1.71875	+	1.71875i	0.0725013	+	0.0725013i
$563$	3.40074	+	3.40074i	0.143324	+	0.143324i	0.775128	−	0.631804i	$-0.217685\pi$
$563$	3.40074	+	3.40074i	0.143324	+	0.143324i	−0.631804	+	0.775128i	$0.717685\pi$
$564$	1.17822			0.0496118
$565$		−	1.01369i		−	0.0426463i
$566$		−	11.0463i		−	0.464309i
$567$	−0.691592	−	0.691592i	−0.0290441	−	0.0290441i
$568$	23.1866	−	23.1866i	0.972889	−	0.972889i
$569$		−	31.9201i		−	1.33816i	−0.743191	−	0.669079i	$-0.766689\pi$
$569$		−	31.9201i		−	1.33816i	0.743191	−	0.669079i	$-0.233311\pi$
$570$	2.80065			0.117306
$571$	−2.50181	−	2.50181i	−0.104697	−	0.104697i	0.652818	−	0.757515i	$-0.273587\pi$
$571$	−2.50181	−	2.50181i	−0.104697	−	0.104697i	−0.757515	+	0.652818i	$0.773587\pi$
$572$			11.0255i			0.461001i
$573$	19.6738			0.821885
$574$	−4.32454	−	1.41608i	−0.180503	−	0.0591062i
$575$	−31.8607			−1.32868
$576$			3.39313i			0.141380i
$577$	−26.7883	−	26.7883i	−1.11521	−	1.11521i	−0.992434	−	0.122777i	$-0.960820\pi$
$577$	−26.7883	−	26.7883i	−1.11521	−	1.11521i	−0.122777	−	0.992434i	$-0.539180\pi$
$578$	−11.6658			−0.485234
$579$		−	14.6533i		−	0.608971i
$580$	0.766414	−	0.766414i	0.0318236	−	0.0318236i
$581$	2.84333	+	2.84333i	0.117961	+	0.117961i
$582$			11.4623i			0.475127i
$583$			5.75155i			0.238205i
$584$	8.01796			0.331786
$585$	−27.5433	−	27.5433i	−1.13878	−	1.13878i
$586$	−2.03538	−	2.03538i	−0.0840806	−	0.0840806i
$587$	15.0176	+	15.0176i	0.619843	+	0.619843i	0.945491	−	0.325648i	$-0.105583\pi$
$587$	15.0176	+	15.0176i	0.619843	+	0.619843i	−0.325648	+	0.945491i	$0.605583\pi$
$588$	−1.05875	+	1.05875i	−0.0436620	+	0.0436620i
$589$	7.09425	−	7.09425i	0.292313	−	0.292313i
$590$	−2.31355			−0.0952473
$591$	−15.2091	+	15.2091i	−0.625617	+	0.625617i
$592$	5.84664			0.240295
$593$	−21.3334	+	21.3334i	−0.876060	+	0.876060i	−0.993124	−	0.117065i	$-0.962652\pi$
$593$	−21.3334	+	21.3334i	−0.876060	+	0.876060i	0.117065	+	0.993124i	$0.462652\pi$
$594$		−	4.10737i		−	0.168528i
$595$			2.33559i			0.0957497i
$596$	−11.6045	+	11.6045i	−0.475341	+	0.475341i
$597$	10.7253			0.438957
$598$	23.6160	−	23.6160i	0.965732	−	0.965732i
$599$	−12.9952			−0.530968			−0.265484	−	0.964115i	$-0.585532\pi$
$599$	−12.9952			−0.530968			−0.265484	+	0.964115i	$0.585532\pi$
$600$	7.61591	−	7.61591i	0.310918	−	0.310918i
$601$	32.1733	−	32.1733i	1.31238	−	1.31238i	0.392715	−	0.919660i	$-0.371536\pi$
$601$	32.1733	−	32.1733i	1.31238	−	1.31238i	0.919660	−	0.392715i	$-0.128464\pi$
$602$	1.69784	+	1.69784i	0.0691989	+	0.0691989i
$603$	−9.26534	−	9.26534i	−0.377314	−	0.377314i
$604$	7.75518	+	7.75518i	0.315554	+	0.315554i
$605$	29.5253			1.20037
$606$		−	13.5291i		−	0.549583i
$607$		−	37.6108i		−	1.52657i	−0.646060	−	0.763287i	$-0.723584\pi$
$607$		−	37.6108i		−	1.52657i	0.646060	−	0.763287i	$-0.276416\pi$
$608$	−5.31769	−	5.31769i	−0.215661	−	0.215661i
$609$	0.168106	−	0.168106i	0.00681201	−	0.00681201i
$610$		−	5.97358i		−	0.241863i
$611$	−5.02537			−0.203305
$612$	−1.61408	−	1.61408i	−0.0652453	−	0.0652453i
$613$		−	14.9861i		−	0.605283i	−0.953104	−	0.302641i	$-0.902132\pi$
$613$		−	14.9861i		−	0.605283i	0.953104	−	0.302641i	$-0.0978685\pi$
$614$	3.08609			0.124545
$615$	−18.6160	−	6.09586i	−0.750669	−	0.245809i
$616$	2.86832			0.115568
$617$		−	38.8014i		−	1.56208i	−0.624478	−	0.781042i	$-0.714688\pi$
$617$		−	38.8014i		−	1.56208i	0.624478	−	0.781042i	$-0.285312\pi$
$618$	−5.56360	−	5.56360i	−0.223801	−	0.223801i
$619$	22.6130			0.908895			0.454447	−	0.890774i	$-0.349837\pi$
$619$	22.6130			0.908895			0.454447	+	0.890774i	$0.349837\pi$
$620$		−	35.5631i		−	1.42825i
$621$	26.0416	−	26.0416i	1.04501	−	1.04501i
$622$	0.706118	+	0.706118i	0.0283128	+	0.0283128i
$623$			7.00062i			0.280474i
$624$		−	7.83417i		−	0.313618i
$625$	−27.9025			−1.11610
$626$	13.9534	+	13.9534i	0.557690	+	0.557690i
$627$	1.05358	+	1.05358i	0.0420758	+	0.0420758i
$628$	−0.875945	−	0.875945i	−0.0349540	−	0.0349540i
$629$	2.58103	−	2.58103i	0.102913	−	0.102913i
$630$	−3.06501	+	3.06501i	−0.122113	+	0.122113i
$631$	34.8165			1.38602			0.693011	−	0.720927i	$-0.256284\pi$
$631$	34.8165			1.38602			0.693011	+	0.720927i	$0.256284\pi$
$632$	17.0122	−	17.0122i	0.676709	−	0.676709i
$633$	−3.64313			−0.144801
$634$	10.2392	−	10.2392i	0.406649	−	0.406649i
$635$			6.68698i			0.265365i
$636$		−	7.45712i		−	0.295694i
$637$	4.51582	−	4.51582i	0.178923	−	0.178923i
$638$	−0.194807			−0.00771250
$639$	−18.6414	+	18.6414i	−0.737443	+	0.737443i
$640$	−31.9746			−1.26391
$641$	−17.0293	+	17.0293i	−0.672617	+	0.672617i	−0.958319	−	0.285702i	$-0.907773\pi$
$641$	−17.0293	+	17.0293i	−0.672617	+	0.672617i	0.285702	+	0.958319i	$0.407773\pi$
$642$	2.36473	−	2.36473i	0.0933284	−	0.0933284i
$643$	−8.99740	−	8.99740i	−0.354823	−	0.354823i	0.507078	−	0.861900i	$-0.330726\pi$
$643$	−8.99740	−	8.99740i	−0.354823	−	0.354823i	−0.861900	+	0.507078i	$0.830726\pi$
$644$	7.77889	+	7.77889i	0.306531	+	0.306531i
$645$	7.30876	+	7.30876i	0.287782	+	0.287782i
$646$	−0.700021			−0.0275420
$647$			1.35102i			0.0531141i	0.999647	+	0.0265571i	$0.00845437\pi$
$647$			1.35102i			0.0531141i	−0.999647	+	0.0265571i	$0.991546\pi$
$648$		−	2.42925i		−	0.0954299i
$649$	−0.870335	−	0.870335i	−0.0341636	−	0.0341636i
$650$	−13.8948	+	13.8948i	−0.544999	+	0.544999i
$651$		−	7.80046i		−	0.305724i
$652$	28.6907			1.12361
$653$	24.7668	+	24.7668i	0.969199	+	0.969199i	0.999540	−	0.0303408i	$-0.00965925\pi$
$653$	24.7668	+	24.7668i	0.969199	+	0.969199i	−0.0303408	+	0.999540i	$0.509659\pi$
$654$		−	10.9010i		−	0.426262i
$655$	65.4352			2.55677
$656$	3.54440	+	6.99584i	0.138386	+	0.273142i
$657$	−6.44622			−0.251491
$658$			0.559220i			0.0218007i
$659$	7.69583	+	7.69583i	0.299787	+	0.299787i	0.840930	−	0.541143i	$-0.182008\pi$
$659$	7.69583	+	7.69583i	0.299787	+	0.299787i	−0.541143	+	0.840930i	$0.682008\pi$
$660$	5.28154			0.205583
$661$			19.9077i			0.774322i	0.922012	+	0.387161i	$0.126544\pi$
$661$			19.9077i			0.774322i	−0.922012	+	0.387161i	$0.873456\pi$
$662$	13.3103	−	13.3103i	0.517318	−	0.517318i
$663$	−3.45844	−	3.45844i	−0.134315	−	0.134315i
$664$			9.98732i			0.387583i
$665$		−	3.93471i		−	0.152582i
$666$	6.77422			0.262496
$667$	−1.23512	−	1.23512i	−0.0478240	−	0.0478240i
$668$	−8.18118	−	8.18118i	−0.316539	−	0.316539i
$669$	−16.2718	−	16.2718i	−0.629103	−	0.629103i
$670$	−10.0719	+	10.0719i	−0.389111	+	0.389111i
$671$	2.24720	−	2.24720i	0.0867523	−	0.0867523i
$672$	−5.84706			−0.225555
$673$	10.2659	−	10.2659i	0.395721	−	0.395721i	−0.480999	−	0.876721i	$-0.659726\pi$
$673$	10.2659	−	10.2659i	0.395721	−	0.395721i	0.876721	+	0.480999i	$0.159726\pi$
$674$	−19.5960			−0.754809
$675$	−15.3219	+	15.3219i	−0.589740	+	0.589740i
$676$			41.5376i			1.59760i
$677$			1.97394i			0.0758646i	0.999280	+	0.0379323i	$0.0120771\pi$
$677$			1.97394i			0.0758646i	−0.999280	+	0.0379323i	$0.987923\pi$
$678$	0.167034	−	0.167034i	0.00641490	−	0.00641490i
$679$	16.1037			0.618002
$680$	−4.10193	+	4.10193i	−0.157302	+	0.157302i
$681$	−8.59321			−0.329293
$682$	−4.51973	+	4.51973i	−0.173069	+	0.173069i
$683$	17.2095	−	17.2095i	0.658503	−	0.658503i	−0.296523	−	0.955026i	$-0.595827\pi$
$683$	17.2095	−	17.2095i	0.658503	−	0.658503i	0.955026	+	0.296523i	$0.0958270\pi$
$684$	2.71921	+	2.71921i	0.103971	+	0.103971i
$685$	−34.8875	−	34.8875i	−1.33298	−	1.33298i
$686$	−0.502517	−	0.502517i	−0.0191862	−	0.0191862i
$687$	−12.4381			−0.474543
$688$		−	4.13817i		−	0.157766i
$689$			31.8064i			1.21173i
$690$	−11.3127	−	11.3127i	−0.430669	−	0.430669i
$691$	28.5820	−	28.5820i	1.08731	−	1.08731i	0.0915045	−	0.995805i	$-0.470832\pi$
$691$	28.5820	−	28.5820i	1.08731	−	1.08731i	0.995805	−	0.0915045i	$-0.0291676\pi$
$692$			8.44035i			0.320854i
$693$	−2.30605			−0.0875997
$694$	−15.4199	−	15.4199i	−0.585330	−	0.585330i
$695$		−	50.5275i		−	1.91662i
$696$	0.590481			0.0223821
$697$	4.65305	+	1.52366i	0.176247	+	0.0577126i
$698$	−15.6178			−0.591144
$699$		−	1.18180i		−	0.0446998i
$700$	−4.57680	−	4.57680i	−0.172987	−	0.172987i
$701$	17.9766			0.678967			0.339484	−	0.940612i	$-0.389748\pi$
$701$	17.9766			0.678967			0.339484	+	0.940612i	$0.389748\pi$
$702$		−	22.7141i		−	0.857287i
$703$	−4.34821	+	4.34821i	−0.163996	+	0.163996i
$704$	1.38758	+	1.38758i	0.0522963	+	0.0522963i
$705$			2.40729i			0.0906639i
$706$		−	6.72726i		−	0.253184i
$707$	−19.0074			−0.714849
$708$	1.12843	+	1.12843i	0.0424088	+	0.0424088i
$709$	4.78751	+	4.78751i	0.179799	+	0.179799i	0.791268	−	0.611469i	$-0.209421\pi$
$709$	4.78751	+	4.78751i	0.179799	+	0.179799i	−0.611469	+	0.791268i	$0.709421\pi$
$710$	20.2641	+	20.2641i	0.760500	+	0.760500i
$711$	−13.6773	+	13.6773i	−0.512940	+	0.512940i
$712$	−12.2950	+	12.2950i	−0.460775	+	0.460775i
$713$	−57.3120			−2.14635
$714$	−0.384853	+	0.384853i	−0.0144028	+	0.0144028i
$715$	−22.5270			−0.842463
$716$	−5.54131	+	5.54131i	−0.207089	+	0.207089i
$717$			29.5283i			1.10275i
$718$			3.98021i			0.148540i
$719$	−1.21457	+	1.21457i	−0.0452958	+	0.0452958i	−0.729392	−	0.684096i	$-0.760197\pi$
$719$	−1.21457	+	1.21457i	−0.0452958	+	0.0452958i	0.684096	+	0.729392i	$0.260197\pi$
$720$	7.47037			0.278404
$721$	−7.81646	+	7.81646i	−0.291100	+	0.291100i
$722$	−12.3234			−0.458628
$723$	17.7542	−	17.7542i	0.660288	−	0.660288i
$724$	1.40421	−	1.40421i	0.0521869	−	0.0521869i
$725$	0.726698	+	0.726698i	0.0269889	+	0.0269889i
$726$	4.86512	+	4.86512i	0.180561	+	0.180561i
$727$	21.0605	+	21.0605i	0.781090	+	0.781090i	0.980015	−	0.198925i	$-0.0637450\pi$
$727$	21.0605	+	21.0605i	0.781090	+	0.781090i	−0.198925	+	0.980015i	$0.563745\pi$
$728$	15.8620			0.587886
$729$		−	13.0846i		−	0.484613i
$730$			7.00737i			0.259354i
$731$	−1.82682	−	1.82682i	−0.0675674	−	0.0675674i
$732$	−2.91359	+	2.91359i	−0.107690	+	0.107690i
$733$			43.3590i			1.60150i	0.598997	+	0.800751i	$0.295566\pi$
$733$			43.3590i			1.60150i	−0.598997	+	0.800751i	$0.704434\pi$
$734$	14.5855			0.538361
$735$	−2.16320	−	2.16320i	−0.0797909	−	0.0797909i
$736$			42.9598i			1.58352i
$737$	−7.57790			−0.279135
$738$	4.10673	+	8.10574i	0.151171	+	0.298376i
$739$	11.8805			0.437031			0.218516	−	0.975833i	$-0.429879\pi$
$739$	11.8805			0.437031			0.218516	+	0.975833i	$0.429879\pi$
$740$			21.7974i			0.801287i
$741$	5.82636	+	5.82636i	0.214037	+	0.214037i
$742$	3.53940			0.129935
$743$			25.0523i			0.919079i	0.888157	+	0.459539i	$0.151985\pi$
$743$			25.0523i			0.919079i	−0.888157	+	0.459539i	$0.848015\pi$
$744$	13.6997	−	13.6997i	0.502257	−	0.502257i
$745$	−23.7101	−	23.7101i	−0.868669	−	0.868669i
$746$		−	20.9390i		−	0.766630i
$747$		−	8.02953i		−	0.293785i
$748$	−1.32012			−0.0482682
$749$	−3.32228	−	3.32228i	−0.121393	−	0.121393i
$750$	−1.03058	−	1.03058i	−0.0376316	−	0.0376316i
$751$	29.1301	+	29.1301i	1.06297	+	1.06297i	0.997879	+	0.0650939i	$0.0207347\pi$
$751$	29.1301	+	29.1301i	1.06297	+	1.06297i	0.0650939	+	0.997879i	$0.479265\pi$
$752$	0.681497	−	0.681497i	0.0248516	−	0.0248516i
$753$	4.46326	−	4.46326i	0.162650	−	0.162650i
$754$	−1.07730			−0.0392329
$755$	−15.8452	+	15.8452i	−0.576664	+	0.576664i
$756$	7.48178			0.272110
$757$	−31.7859	+	31.7859i	−1.15528	+	1.15528i	−0.169799	+	0.985479i	$0.554312\pi$
$757$	−31.7859	+	31.7859i	−1.15528	+	1.15528i	−0.985479	+	0.169799i	$0.945688\pi$
$758$		−	15.5704i		−	0.565543i
$759$		−	8.51149i		−	0.308948i
$760$	6.91043	−	6.91043i	0.250668	−	0.250668i
$761$	9.81488			0.355789			0.177895	−	0.984050i	$-0.443071\pi$
$761$	9.81488			0.355789			0.177895	+	0.984050i	$0.443071\pi$
$762$	−1.10187	+	1.10187i	−0.0399164	+	0.0399164i
$763$	−15.3151			−0.554444
$764$	20.7645	−	20.7645i	0.751232	−	0.751232i
$765$	3.29784	−	3.29784i	0.119234	−	0.119234i
$766$	1.73355	+	1.73355i	0.0626359	+	0.0626359i
$767$	−4.81301	−	4.81301i	−0.173788	−	0.173788i
$768$	−7.67555	−	7.67555i	−0.276967	−	0.276967i
$769$	16.6127			0.599070			0.299535	−	0.954085i	$-0.403169\pi$
$769$	16.6127			0.599070			0.299535	+	0.954085i	$0.403169\pi$
$770$			2.50679i			0.0903386i
$771$			21.6833i			0.780906i
$772$	−15.4657	−	15.4657i	−0.556622	−	0.556622i
$773$	27.6692	−	27.6692i	0.995192	−	0.995192i	−0.00479668	−	0.999988i	$-0.501527\pi$
$773$	27.6692	−	27.6692i	0.995192	−	0.995192i	0.999988	+	0.00479668i	$0.00152684\pi$
$774$		−	4.79470i		−	0.172342i
$775$	33.7202			1.21127
$776$	28.2825	+	28.2825i	1.01528	+	1.01528i
$777$			4.78106i			0.171520i
$778$	2.15637			0.0773095
$779$	−7.83890	−	2.56687i	−0.280858	−	0.0919677i
$780$	29.2072			1.04579
$781$			15.2464i			0.545558i
$782$	2.82761	+	2.82761i	0.101115	+	0.101115i
$783$	−1.18794			−0.0424537
$784$			1.22479i			0.0437425i
$785$	1.78971	−	1.78971i	0.0638773	−	0.0638773i
$786$	10.7823	+	10.7823i	0.384591	+	0.384591i
$787$			16.2265i			0.578414i	0.957267	+	0.289207i	$0.0933915\pi$
$787$			16.2265i			0.578414i	−0.957267	+	0.289207i	$0.906608\pi$
$788$			32.1044i			1.14367i
$789$	21.0654			0.749950
$790$	14.8679	+	14.8679i	0.528978	+	0.528978i
$791$	−0.234671	−	0.234671i	−0.00834393	−	0.00834393i
$792$	−4.05006	−	4.05006i	−0.143913	−	0.143913i
$793$	12.4272	−	12.4272i	0.441302	−	0.441302i
$794$	−14.7431	+	14.7431i	−0.523214	+	0.523214i
$795$	15.2362			0.540371
$796$	11.3199	−	11.3199i	0.401223	−	0.401223i
$797$	38.1120			1.35000			0.674998	−	0.737819i	$-0.264144\pi$
$797$	38.1120			1.35000			0.674998	+	0.737819i	$0.264144\pi$
$798$	0.648353	−	0.648353i	0.0229515	−	0.0229515i
$799$		−	0.601702i		−	0.0212867i
$800$		−	25.2759i		−	0.893639i
$801$	9.88485	−	9.88485i	0.349264	−	0.349264i
$802$	−14.4488			−0.510206
$803$	−2.63610	+	2.63610i	−0.0930261	+	0.0930261i
$804$	9.82506			0.346503
$805$	−15.8936	+	15.8936i	−0.560175	+	0.560175i
$806$	−24.9944	+	24.9944i	−0.880390	+	0.880390i
$807$	−5.26409	−	5.26409i	−0.185305	−	0.185305i
$808$	−33.3823	−	33.3823i	−1.17438	−	1.17438i
$809$	7.01453	+	7.01453i	0.246618	+	0.246618i	0.819581	−	0.572963i	$-0.194206\pi$
$809$	7.01453	+	7.01453i	0.246618	+	0.246618i	−0.572963	+	0.819581i	$0.694206\pi$
$810$	2.12306			0.0745968
$811$		−	34.2813i		−	1.20378i	−0.798579	−	0.601890i	$-0.794415\pi$
$811$		−	34.2813i		−	1.20378i	0.798579	−	0.601890i	$-0.205585\pi$
$812$		−	0.354851i		−	0.0124528i
$813$	5.55676	+	5.55676i	0.194884	+	0.194884i
$814$	2.77023	−	2.77023i	0.0970966	−	0.0970966i
$815$			58.6200i			2.05337i
$816$	0.938006			0.0328368
$817$	3.07760	+	3.07760i	0.107672	+	0.107672i
$818$			9.10531i			0.318360i
$819$	−12.7526			−0.445613
$820$	−26.0818	+	13.2142i	−0.910816	+	0.461460i
$821$	−4.60780			−0.160813			−0.0804066	−	0.996762i	$-0.525622\pi$
$821$	−4.60780			−0.160813			−0.0804066	+	0.996762i	$0.525622\pi$
$822$		−	11.4974i		−	0.401016i
$823$	4.07777	+	4.07777i	0.142142	+	0.142142i	0.774597	−	0.632455i	$-0.217953\pi$
$823$	4.07777	+	4.07777i	0.142142	+	0.142142i	−0.632455	+	0.774597i	$0.717953\pi$
$824$	−27.4557			−0.956464
$825$			5.00784i			0.174351i
$826$	−0.535589	+	0.535589i	−0.0186355	+	0.0186355i
$827$	8.20984	+	8.20984i	0.285484	+	0.285484i	0.835291	−	0.549807i	$-0.185299\pi$
$827$	8.20984	+	8.20984i	0.285484	+	0.285484i	−0.549807	+	0.835291i	$0.685299\pi$
$828$		−	21.9675i		−	0.763424i
$829$			3.68036i			0.127824i	0.997956	+	0.0639120i	$0.0203577\pi$
$829$			3.68036i			0.127824i	−0.997956	+	0.0639120i	$0.979642\pi$
$830$	−8.72850			−0.302971
$831$	23.3356	+	23.3356i	0.809504	+	0.809504i
$832$	7.67340	+	7.67340i	0.266027	+	0.266027i
$833$	0.540691	+	0.540691i	0.0187338	+	0.0187338i
$834$	8.32582	−	8.32582i	0.288299	−	0.288299i
$835$	16.7155	−	16.7155i	0.578465	−	0.578465i
$836$	2.22397			0.0769177
$837$	−27.5615	+	27.5615i	−0.952665	+	0.952665i
$838$	−26.8159			−0.926339
$839$	−11.2335	+	11.2335i	−0.387823	+	0.387823i	−0.873910	−	0.486087i	$-0.838424\pi$
$839$	−11.2335	+	11.2335i	−0.387823	+	0.387823i	0.486087	+	0.873910i	$0.338424\pi$
$840$		−	7.59835i		−	0.262168i
$841$		−	28.9437i		−	0.998057i
$842$	2.14482	−	2.14482i	0.0739154	−	0.0739154i
$843$	3.42565			0.117986
$844$	−3.84509	+	3.84509i	−0.132354	+	0.132354i
$845$	−84.8683			−2.91956
$846$	0.789617	−	0.789617i	0.0271476	−	0.0271476i
$847$	6.83514	−	6.83514i	0.234858	−	0.234858i
$848$	−4.31331	−	4.31331i	−0.148120	−	0.148120i
$849$	−11.0081	−	11.0081i	−0.377798	−	0.377798i
$850$	−1.66366	−	1.66366i	−0.0570631	−	0.0570631i
$851$	35.1277			1.20416
$852$		−	19.7675i		−	0.677225i
$853$		−	11.4616i		−	0.392438i	−0.980560	−	0.196219i	$-0.937134\pi$
$853$		−	11.4616i		−	0.392438i	0.980560	−	0.196219i	$-0.0628664\pi$
$854$	−1.38289	−	1.38289i	−0.0473215	−	0.0473215i
$855$	−5.55580	+	5.55580i	−0.190004	+	0.190004i
$856$		−	11.6697i		−	0.398861i
$857$	8.11450			0.277186			0.138593	−	0.990349i	$-0.455742\pi$
$857$	8.11450			0.277186			0.138593	+	0.990349i	$0.455742\pi$
$858$	−3.71196	−	3.71196i	−0.126724	−	0.126724i
$859$			17.1782i			0.586112i	0.956095	+	0.293056i	$0.0946723\pi$
$859$			17.1782i			0.586112i	−0.956095	+	0.293056i	$0.905328\pi$
$860$	15.4279			0.526086
$861$	−5.72082	+	2.89842i	−0.194965	+	0.0987779i
$862$	16.6477			0.567023
$863$			23.7047i			0.806918i	0.914998	+	0.403459i	$0.132192\pi$
$863$			23.7047i			0.806918i	−0.914998	+	0.403459i	$0.867808\pi$
$864$	20.6595	+	20.6595i	0.702851	+	0.702851i
$865$	−17.2451			−0.586350
$866$			16.5870i			0.563650i
$867$	−11.6256	+	11.6256i	−0.394825	+	0.394825i
$868$	−8.23290	−	8.23290i	−0.279443	−	0.279443i
$869$			11.1864i			0.379471i
$870$			0.516056i			0.0174959i
$871$	−41.9063			−1.41994
$872$	−26.8975	−	26.8975i	−0.910865	−	0.910865i
$873$	−22.7383	−	22.7383i	−0.769576	−	0.769576i
$874$	−4.76362	−	4.76362i	−0.161132	−	0.161132i
$875$	−1.44790	+	1.44790i	−0.0489479	+	0.0489479i
$876$	3.41782	−	3.41782i	0.115477	−	0.115477i
$877$	18.9099			0.638541			0.319271	−	0.947664i	$-0.396562\pi$
$877$	18.9099			0.638541			0.319271	+	0.947664i	$0.396562\pi$
$878$	−15.6605	+	15.6605i	−0.528516	+	0.528516i
$879$	−4.05671			−0.136829
$880$	3.05492	−	3.05492i	0.102981	−	0.102981i
$881$		−	46.8575i		−	1.57867i	−0.613964	−	0.789334i	$-0.710426\pi$
$881$		−	46.8575i		−	1.57867i	0.613964	−	0.789334i	$-0.289574\pi$
$882$			1.41910i			0.0477837i
$883$	31.9349	−	31.9349i	1.07470	−	1.07470i	0.0777213	−	0.996975i	$-0.475236\pi$
$883$	31.9349	−	31.9349i	1.07470	−	1.07470i	0.996975	−	0.0777213i	$-0.0247644\pi$
$884$	−7.30034			−0.245537
$885$	−2.30557	+	2.30557i	−0.0775007	+	0.0775007i
$886$	11.2726			0.378712
$887$	−14.6121	+	14.6121i	−0.490626	+	0.490626i	−0.908504	−	0.417877i	$-0.862774\pi$
$887$	−14.6121	+	14.6121i	−0.490626	+	0.490626i	0.417877	+	0.908504i	$0.362774\pi$
$888$	−8.39686	+	8.39686i	−0.281780	+	0.281780i
$889$	1.54804	+	1.54804i	0.0519197	+	0.0519197i
$890$	−10.7453	−	10.7453i	−0.360184	−	0.360184i
$891$	0.798676	+	0.798676i	0.0267566	+	0.0267566i
$892$	−34.3477			−1.15005
$893$			1.01367i			0.0339213i
$894$		−	7.81378i		−	0.261332i
$895$	−11.3218	−	11.3218i	−0.378447	−	0.378447i
$896$	−7.40216	+	7.40216i	−0.247289	+	0.247289i
$897$		−	47.0691i		−	1.57159i
$898$	−28.4042			−0.947861
$899$	1.30721	+	1.30721i	0.0435978	+	0.0435978i
$900$			12.9249i			0.430829i
$901$	−3.80827			−0.126872
$902$	4.99414	+	1.63535i	0.166287	+	0.0544511i
$903$	3.38397			0.112611
$904$		−	0.824292i		−	0.0274155i
$905$	2.86903	+	2.86903i	0.0953699	+	0.0953699i
$906$	−5.22186			−0.173485
$907$			40.7867i			1.35430i	0.735844	+	0.677151i	$0.236785\pi$
$907$			40.7867i			1.35430i	−0.735844	+	0.677151i	$0.763215\pi$
$908$	−9.06960	+	9.06960i	−0.300985	+	0.300985i
$909$	26.8384	+	26.8384i	0.890175	+	0.890175i
$910$			13.8627i			0.459545i
$911$			13.4531i			0.445721i	0.974850	+	0.222860i	$0.0715394\pi$
$911$			13.4531i			0.445721i	−0.974850	+	0.222860i	$0.928461\pi$
$912$	−1.58024			−0.0523269
$913$	−3.28358	−	3.28358i	−0.108671	−	0.108671i
$914$	16.7398	+	16.7398i	0.553704	+	0.553704i
$915$	−5.95297	−	5.95297i	−0.196799	−	0.196799i
$916$	−13.1276	+	13.1276i	−0.433749	+	0.433749i
$917$	15.1483	−	15.1483i	0.500242	−	0.500242i
$918$	2.71961			0.0897607
$919$	2.27820	−	2.27820i	0.0751510	−	0.0751510i	−0.668532	−	0.743683i	$-0.733077\pi$
$919$	2.27820	−	2.27820i	0.0751510	−	0.0751510i	0.743683	+	0.668532i	$0.233077\pi$
$920$	−55.8270			−1.84056
$921$	3.07544	−	3.07544i	0.101339	−	0.101339i
$922$		−	1.57372i		−	0.0518278i
$923$			84.3134i			2.77521i
$924$	1.22268	−	1.22268i	0.0402233	−	0.0402233i
$925$	−20.6678			−0.679553
$926$	−13.3253	+	13.3253i	−0.437897	+	0.437897i
$927$	22.0736			0.724992
$928$	0.979854	−	0.979854i	0.0321653	−	0.0321653i
$929$	10.6978	−	10.6978i	0.350983	−	0.350983i	−0.509492	−	0.860475i	$-0.670167\pi$
$929$	10.6978	−	10.6978i	0.350983	−	0.350983i	0.860475	+	0.509492i	$0.170167\pi$
$930$	11.9730	+	11.9730i	0.392610	+	0.392610i
$931$	−0.910890	−	0.910890i	−0.0298532	−	0.0298532i
$932$	−1.24732	−	1.24732i	−0.0408572	−	0.0408572i
$933$	1.40736			0.0460750
$934$		−	8.93458i		−	0.292348i
$935$		−	2.69722i		−	0.0882086i
$936$	−22.3971	−	22.3971i	−0.732072	−	0.732072i
$937$	0.760139	−	0.760139i	0.0248326	−	0.0248326i	−0.694581	−	0.719414i	$-0.744410\pi$
$937$	0.760139	−	0.760139i	0.0248326	−	0.0248326i	0.719414	+	0.694581i	$0.244410\pi$
$938$			4.66331i			0.152262i
$939$	27.8105			0.907562
$940$	2.54075	+	2.54075i	0.0828701	+	0.0828701i
$941$			12.2163i			0.398239i	0.979975	+	0.199119i	$0.0638082\pi$
$941$			12.2163i			0.398239i	−0.979975	+	0.199119i	$0.936192\pi$
$942$	0.589808			0.0192170
$943$	21.2954	+	42.0323i	0.693475	+	1.36876i
$944$	1.30540			0.0424870
$945$			15.2865i			0.497271i
$946$	−1.96073	−	1.96073i	−0.0637489	−	0.0637489i
$947$	30.2465			0.982879			0.491439	−	0.870912i	$-0.336471\pi$
$947$	30.2465			0.982879			0.491439	+	0.870912i	$0.336471\pi$
$948$		−	14.5036i		−	0.471055i
$949$	−14.5778	+	14.5778i	−0.473217	+	0.473217i
$950$	2.80273	+	2.80273i	0.0909327	+	0.0909327i
$951$		−	20.4077i		−	0.661764i
$952$			1.89920i			0.0615535i
$953$	5.19643			0.168329			0.0841645	−	0.996452i	$-0.473178\pi$
$953$	5.19643			0.168329			0.0841645	+	0.996452i	$0.473178\pi$
$954$	−4.99762	−	4.99762i	−0.161804	−	0.161804i
$955$	42.4254	+	42.4254i	1.37285	+	1.37285i
$956$	31.1652	+	31.1652i	1.00796	+	1.00796i
$957$	−0.194135	+	0.194135i	−0.00627550	+	0.00627550i
$958$	5.77216	−	5.77216i	0.186490	−	0.186490i
$959$	−16.1530			−0.521606
$960$	3.67577	−	3.67577i	0.118635	−	0.118635i
$961$	29.6570			0.956677
$962$	15.3196	−	15.3196i	0.493923	−	0.493923i
$963$			9.38208i			0.302333i
$964$		−	37.4770i		−	1.20705i
$965$	31.5990	−	31.5990i	1.01721	−	1.01721i
$966$	−5.23782			−0.168524
$967$	−7.46963	+	7.46963i	−0.240207	+	0.240207i	−0.816936	−	0.576729i	$-0.804329\pi$
$967$	−7.46963	+	7.46963i	−0.240207	+	0.240207i	0.576729	+	0.816936i	$0.304329\pi$
$968$	24.0088			0.771671
$969$	−0.697606	+	0.697606i	−0.0224103	+	0.0224103i
$970$	−24.7177	+	24.7177i	−0.793637	+	0.793637i
$971$	0.980515	+	0.980515i	0.0314662	+	0.0314662i	0.722665	−	0.691199i	$-0.242917\pi$
$971$	0.980515	+	0.980515i	0.0314662	+	0.0314662i	−0.691199	+	0.722665i	$0.742917\pi$
$972$	−16.9068	−	16.9068i	−0.542285	−	0.542285i
$973$	−11.6972	−	11.6972i	−0.374994	−	0.374994i
$974$	7.51660			0.240847
$975$			27.6937i			0.886908i
$976$			3.37053i			0.107888i
$977$	12.4278	+	12.4278i	0.397601	+	0.397601i	0.877386	−	0.479785i	$-0.159285\pi$
$977$	12.4278	+	12.4278i	0.397601	+	0.397601i	−0.479785	+	0.877386i	$0.659285\pi$
$978$	−9.65927	+	9.65927i	−0.308870	+	0.308870i
$979$		−	8.08458i		−	0.258384i
$980$	−4.56625			−0.145863
$981$	21.6249	+	21.6249i	0.690429	+	0.690429i
$982$		−	26.7565i		−	0.853835i
$983$	33.5929			1.07145			0.535724	−	0.844393i	$-0.320039\pi$
$983$	33.5929			1.07145			0.535724	+	0.844393i	$0.320039\pi$
$984$	−15.1377	−	4.95690i	−0.482574	−	0.158020i
$985$	−65.5948			−2.09002
$986$		−	0.128988i		−	0.00410781i
$987$	0.557291	+	0.557291i	0.0177388	+	0.0177388i
$988$	12.2987			0.391274
$989$		−	24.8629i		−	0.790594i
$990$	3.53958	−	3.53958i	0.112495	−	0.112495i
$991$	−8.44631	−	8.44631i	−0.268306	−	0.268306i	0.560111	−	0.828417i	$-0.310758\pi$
$991$	−8.44631	−	8.44631i	−0.268306	−	0.268306i	−0.828417	+	0.560111i	$0.810758\pi$
$992$		−	45.4672i		−	1.44358i
$993$		−	26.5287i		−	0.841861i
$994$	9.38234			0.297590
$995$	23.1284	+	23.1284i	0.733221	+	0.733221i
$996$	4.25730	+	4.25730i	0.134898	+	0.134898i
$997$	−24.4373	−	24.4373i	−0.773938	−	0.773938i	0.204854	−	0.978793i	$-0.434328\pi$
$997$	−24.4373	−	24.4373i	−0.773938	−	0.773938i	−0.978793	+	0.204854i	$0.934328\pi$
$998$	−1.36530	+	1.36530i	−0.0432177	+	0.0432177i
$999$	16.8930	−	16.8930i	0.534471	−	0.534471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.12	✓	40
41.32	even	4	inner	287.2.f.a.155.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.12	✓	40	1.1	even	1	trivial
287.2.f.a.155.9	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)

\(f(q)\)	\(=\)	\(q+0.710667i q^{2} +(0.708215 + 0.708215i) q^{3} +1.49495 q^{4} +3.05444i q^{5} +(-0.503305 + 0.503305i) q^{6} +(0.707107 + 0.707107i) q^{7} +2.48375i q^{8} -1.99686i q^{9} +O(q^{10})\)	\(q+0.710667i q^{2} +(0.708215 + 0.708215i) q^{3} +1.49495 q^{4} +3.05444i q^{5} +(-0.503305 + 0.503305i) q^{6} +(0.707107 + 0.707107i) q^{7} +2.48375i q^{8} -1.99686i q^{9} -2.17069 q^{10} +(-0.816593 - 0.816593i) q^{11} +(1.05875 + 1.05875i) q^{12} +(-4.51582 - 4.51582i) q^{13} +(-0.502517 + 0.502517i) q^{14} +(-2.16320 + 2.16320i) q^{15} +1.22479 q^{16} +(0.540691 - 0.540691i) q^{17} +1.41910 q^{18} +(-0.910890 + 0.910890i) q^{19} +4.56625i q^{20} +1.00157i q^{21} +(0.580326 - 0.580326i) q^{22} +7.35877 q^{23} +(-1.75903 + 1.75903i) q^{24} -4.32962 q^{25} +(3.20924 - 3.20924i) q^{26} +(3.53885 - 3.53885i) q^{27} +(1.05709 + 1.05709i) q^{28} +(-0.167843 - 0.167843i) q^{29} +(-1.53731 - 1.53731i) q^{30} -7.78826 q^{31} +5.83791i q^{32} -1.15665i q^{33} +(0.384251 + 0.384251i) q^{34} +(-2.15982 + 2.15982i) q^{35} -2.98522i q^{36} +4.77359 q^{37} +(-0.647339 - 0.647339i) q^{38} -6.39633i q^{39} -7.58646 q^{40} +(2.89389 + 5.71187i) q^{41} -0.711780 q^{42} -3.37868i q^{43} +(-1.22077 - 1.22077i) q^{44} +6.09931 q^{45} +5.22963i q^{46} +(0.556419 - 0.556419i) q^{47} +(0.867414 + 0.867414i) q^{48} +1.00000i q^{49} -3.07692i q^{50} +0.765850 q^{51} +(-6.75093 - 6.75093i) q^{52} +(-3.52167 - 3.52167i) q^{53} +(2.51494 + 2.51494i) q^{54} +(2.49424 - 2.49424i) q^{55} +(-1.75627 + 1.75627i) q^{56} -1.29021 q^{57} +(0.119281 - 0.119281i) q^{58} +1.06581 q^{59} +(-3.23388 + 3.23388i) q^{60} +2.75192i q^{61} -5.53486i q^{62} +(1.41200 - 1.41200i) q^{63} -1.69923 q^{64} +(13.7933 - 13.7933i) q^{65} +0.821990 q^{66} +(4.63995 - 4.63995i) q^{67} +(0.808307 - 0.808307i) q^{68} +(5.21159 + 5.21159i) q^{69} +(-1.53491 - 1.53491i) q^{70} +(-9.33534 - 9.33534i) q^{71} +4.95970 q^{72} -3.22817i q^{73} +3.39243i q^{74} +(-3.06630 - 3.06630i) q^{75} +(-1.36174 + 1.36174i) q^{76} -1.15484i q^{77} +4.54566 q^{78} +(-6.84941 - 6.84941i) q^{79} +3.74105i q^{80} -0.978058 q^{81} +(-4.05923 + 2.05659i) q^{82} +4.02107 q^{83} +1.49730i q^{84} +(1.65151 + 1.65151i) q^{85} +2.40111 q^{86} -0.237738i q^{87} +(2.02821 - 2.02821i) q^{88} +(4.95019 + 4.95019i) q^{89} +4.33457i q^{90} -6.38633i q^{91} +11.0010 q^{92} +(-5.51576 - 5.51576i) q^{93} +(0.395429 + 0.395429i) q^{94} +(-2.78226 - 2.78226i) q^{95} +(-4.13449 + 4.13449i) q^{96} +(11.3870 - 11.3870i) q^{97} -0.710667 q^{98} +(-1.63063 + 1.63063i) 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

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