LMFDB - Embedded newform 287.2.f.a.50.17

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			50.17
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30053i q^{2} +(1.78480 + 1.78480i) q^{3} -3.29242 q^{4} -0.414800i q^{5} +(-4.10598 + 4.10598i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.97325i q^{8} +3.37102i q^{9} +O(q^{10})$	\(q+2.30053i q^{2} +(1.78480 + 1.78480i) q^{3} -3.29242 q^{4} -0.414800i q^{5} +(-4.10598 + 4.10598i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.97325i q^{8} +3.37102i q^{9} +0.954258 q^{10} +(-0.962406 - 0.962406i) q^{11} +(-5.87631 - 5.87631i) q^{12} +(-0.368555 - 0.368555i) q^{13} +(-1.62672 + 1.62672i) q^{14} +(0.740335 - 0.740335i) q^{15} +0.255198 q^{16} +(1.81421 - 1.81421i) q^{17} -7.75511 q^{18} +(-0.568761 + 0.568761i) q^{19} +1.36570i q^{20} +2.52409i q^{21} +(2.21404 - 2.21404i) q^{22} +0.152624 q^{23} +(5.30666 - 5.30666i) q^{24} +4.82794 q^{25} +(0.847872 - 0.847872i) q^{26} +(-0.662189 + 0.662189i) q^{27} +(-2.32809 - 2.32809i) q^{28} +(-0.674317 - 0.674317i) q^{29} +(1.70316 + 1.70316i) q^{30} +6.16619 q^{31} -5.35941i q^{32} -3.43540i q^{33} +(4.17364 + 4.17364i) q^{34} +(0.293308 - 0.293308i) q^{35} -11.0988i q^{36} -0.457569 q^{37} +(-1.30845 - 1.30845i) q^{38} -1.31559i q^{39} -1.23330 q^{40} +(5.93700 - 2.39833i) q^{41} -5.80673 q^{42} +0.616219i q^{43} +(3.16865 + 3.16865i) q^{44} +1.39830 q^{45} +0.351116i q^{46} +(-8.26999 + 8.26999i) q^{47} +(0.455478 + 0.455478i) q^{48} +1.00000i q^{49} +11.1068i q^{50} +6.47601 q^{51} +(1.21344 + 1.21344i) q^{52} +(-8.08276 - 8.08276i) q^{53} +(-1.52338 - 1.52338i) q^{54} +(-0.399206 + 0.399206i) q^{55} +(2.10241 - 2.10241i) q^{56} -2.03025 q^{57} +(1.55128 - 1.55128i) q^{58} -12.7593 q^{59} +(-2.43749 + 2.43749i) q^{60} +8.78654i q^{61} +14.1855i q^{62} +(-2.38367 + 2.38367i) q^{63} +12.8399 q^{64} +(-0.152877 + 0.152877i) q^{65} +7.90323 q^{66} +(5.61813 - 5.61813i) q^{67} +(-5.97315 + 5.97315i) q^{68} +(0.272404 + 0.272404i) q^{69} +(0.674763 + 0.674763i) q^{70} +(6.77721 + 6.77721i) q^{71} +10.0229 q^{72} -10.6861i q^{73} -1.05265i q^{74} +(8.61690 + 8.61690i) q^{75} +(1.87260 - 1.87260i) q^{76} -1.36105i q^{77} +3.02656 q^{78} +(4.59225 + 4.59225i) q^{79} -0.105856i q^{80} +7.74930 q^{81} +(5.51742 + 13.6582i) q^{82} -11.3897 q^{83} -8.31036i q^{84} +(-0.752535 - 0.752535i) q^{85} -1.41763 q^{86} -2.40704i q^{87} +(-2.86147 + 2.86147i) q^{88} +(-6.56072 - 6.56072i) q^{89} +3.21682i q^{90} -0.521216i q^{91} -0.502504 q^{92} +(11.0054 + 11.0054i) q^{93} +(-19.0253 - 19.0253i) q^{94} +(0.235922 + 0.235922i) q^{95} +(9.56547 - 9.56547i) q^{96} +(-4.30605 + 4.30605i) q^{97} -2.30053 q^{98} +(3.24429 - 3.24429i) 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 $

$2$			2.30053i			1.62672i	0.581762	+	0.813359i	$0.302363\pi$
$2$			2.30053i			1.62672i	−0.581762	+	0.813359i	$0.697637\pi$
$3$	1.78480	+	1.78480i	1.03045	+	1.03045i	0.999521	+	0.0309328i	$0.00984778\pi$
$3$	1.78480	+	1.78480i	1.03045	+	1.03045i	0.0309328	+	0.999521i	$0.490152\pi$
$4$	−3.29242			−1.64621
$5$		−	0.414800i		−	0.185504i	−0.995689	−	0.0927521i	$-0.970434\pi$
$5$		−	0.414800i		−	0.185504i	0.995689	−	0.0927521i	$-0.0295664\pi$
$6$	−4.10598	+	4.10598i	−1.67626	+	1.67626i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		−	2.97325i		−	1.05120i
$9$			3.37102i			1.12367i
$10$	0.954258			0.301763
$11$	−0.962406	−	0.962406i	−0.290176	−	0.290176i	0.546974	−	0.837150i	$-0.315780\pi$
$11$	−0.962406	−	0.962406i	−0.290176	−	0.290176i	−0.837150	+	0.546974i	$0.815780\pi$
$12$	−5.87631	−	5.87631i	−1.69635	−	1.69635i
$13$	−0.368555	−	0.368555i	−0.102219	−	0.102219i	0.654148	−	0.756367i	$-0.273027\pi$
$13$	−0.368555	−	0.368555i	−0.102219	−	0.102219i	−0.756367	+	0.654148i	$0.773027\pi$
$14$	−1.62672	+	1.62672i	−0.434759	+	0.434759i
$15$	0.740335	−	0.740335i	0.191154	−	0.191154i
$16$	0.255198			0.0637996
$17$	1.81421	−	1.81421i	0.440011	−	0.440011i	−0.452005	−	0.892016i	$-0.649291\pi$
$17$	1.81421	−	1.81421i	0.440011	−	0.440011i	0.892016	+	0.452005i	$0.149291\pi$
$18$	−7.75511			−1.82790
$19$	−0.568761	+	0.568761i	−0.130483	+	0.130483i	−0.769332	−	0.638849i	$-0.779411\pi$
$19$	−0.568761	+	0.568761i	−0.130483	+	0.130483i	0.638849	+	0.769332i	$0.279411\pi$
$20$			1.36570i			0.305379i
$21$			2.52409i			0.550801i
$22$	2.21404	−	2.21404i	0.472035	−	0.472035i
$23$	0.152624			0.0318244			0.0159122	−	0.999873i	$-0.494935\pi$
$23$	0.152624			0.0318244			0.0159122	+	0.999873i	$0.494935\pi$
$24$	5.30666	−	5.30666i	1.08322	−	1.08322i
$25$	4.82794			0.965588
$26$	0.847872	−	0.847872i	0.166281	−	0.166281i
$27$	−0.662189	+	0.662189i	−0.127438	+	0.127438i
$28$	−2.32809	−	2.32809i	−0.439968	−	0.439968i
$29$	−0.674317	−	0.674317i	−0.125218	−	0.125218i	0.641721	−	0.766938i	$-0.278221\pi$
$29$	−0.674317	−	0.674317i	−0.125218	−	0.125218i	−0.766938	+	0.641721i	$0.778221\pi$
$30$	1.70316	+	1.70316i	0.310953	+	0.310953i
$31$	6.16619			1.10748			0.553740	−	0.832689i	$-0.313200\pi$
$31$	6.16619			1.10748			0.553740	+	0.832689i	$0.313200\pi$
$32$		−	5.35941i		−	0.947419i
$33$		−	3.43540i		−	0.598027i
$34$	4.17364	+	4.17364i	0.715774	+	0.715774i
$35$	0.293308	−	0.293308i	0.0495781	−	0.0495781i
$36$		−	11.0988i		−	1.84980i
$37$	−0.457569			−0.0752239			−0.0376120	−	0.999292i	$-0.511975\pi$
$37$	−0.457569			−0.0752239			−0.0376120	+	0.999292i	$0.511975\pi$
$38$	−1.30845	−	1.30845i	−0.212259	−	0.212259i
$39$		−	1.31559i		−	0.210664i
$40$	−1.23330			−0.195003
$41$	5.93700	−	2.39833i	0.927204	−	0.374556i
$41$	5.93700	−	2.39833i	0.927204	−	0.374556i
$42$	−5.80673			−0.895998
$43$			0.616219i			0.0939725i	0.998896	+	0.0469863i	$0.0149617\pi$
$43$			0.616219i			0.0939725i	−0.998896	+	0.0469863i	$0.985038\pi$
$44$	3.16865	+	3.16865i	0.477691	+	0.477691i
$45$	1.39830			0.208446
$46$			0.351116i			0.0517693i
$47$	−8.26999	+	8.26999i	−1.20630	+	1.20630i	−0.234085	+	0.972216i	$0.575210\pi$
$47$	−8.26999	+	8.26999i	−1.20630	+	1.20630i	−0.972216	+	0.234085i	$0.924790\pi$
$48$	0.455478	+	0.455478i	0.0657425	+	0.0657425i
$49$			1.00000i			0.142857i
$50$			11.1068i			1.57074i
$51$	6.47601			0.906823
$52$	1.21344	+	1.21344i	0.168274	+	0.168274i
$53$	−8.08276	−	8.08276i	−1.11025	−	1.11025i	−0.993116	−	0.117137i	$-0.962628\pi$
$53$	−8.08276	−	8.08276i	−1.11025	−	1.11025i	−0.117137	−	0.993116i	$-0.537372\pi$
$54$	−1.52338	−	1.52338i	−0.207306	−	0.207306i
$55$	−0.399206	+	0.399206i	−0.0538289	+	0.0538289i
$56$	2.10241	−	2.10241i	0.280946	−	0.280946i
$57$	−2.03025			−0.268913
$58$	1.55128	−	1.55128i	0.203694	−	0.203694i
$59$	−12.7593			−1.66112			−0.830561	−	0.556928i	$-0.811980\pi$
$59$	−12.7593			−1.66112			−0.830561	+	0.556928i	$0.811980\pi$
$60$	−2.43749	+	2.43749i	−0.314679	+	0.314679i
$61$			8.78654i			1.12500i	0.826797	+	0.562501i	$0.190161\pi$
$61$			8.78654i			1.12500i	−0.826797	+	0.562501i	$0.809839\pi$
$62$			14.1855i			1.80156i
$63$	−2.38367	+	2.38367i	−0.300314	+	0.300314i
$64$	12.8399			1.60498
$65$	−0.152877	+	0.152877i	−0.0189620	+	0.0189620i
$66$	7.90323			0.972821
$67$	5.61813	−	5.61813i	0.686364	−	0.686364i	−0.275063	−	0.961426i	$-0.588699\pi$
$67$	5.61813	−	5.61813i	0.686364	−	0.686364i	0.961426	+	0.275063i	$0.0886986\pi$
$68$	−5.97315	+	5.97315i	−0.724351	+	0.724351i
$69$	0.272404	+	0.272404i	0.0327936	+	0.0327936i
$70$	0.674763	+	0.674763i	0.0806496	+	0.0806496i
$71$	6.77721	+	6.77721i	0.804307	+	0.804307i	0.983765	−	0.179459i	$-0.0574347\pi$
$71$	6.77721	+	6.77721i	0.804307	+	0.804307i	−0.179459	+	0.983765i	$0.557435\pi$
$72$	10.0229			1.18121
$73$		−	10.6861i		−	1.25071i	−0.780340	−	0.625356i	$-0.784954\pi$
$73$		−	10.6861i		−	1.25071i	0.780340	−	0.625356i	$-0.215046\pi$
$74$		−	1.05265i		−	0.122368i
$75$	8.61690	+	8.61690i	0.994994	+	0.994994i
$76$	1.87260	−	1.87260i	0.214802	−	0.214802i
$77$		−	1.36105i		−	0.155106i
$78$	3.02656			0.342691
$79$	4.59225	+	4.59225i	0.516669	+	0.516669i	0.916562	−	0.399893i	$-0.130953\pi$
$79$	4.59225	+	4.59225i	0.516669	+	0.516669i	−0.399893	+	0.916562i	$0.630953\pi$
$80$		−	0.105856i		−	0.0118351i
$81$	7.74930			0.861033
$82$	5.51742	+	13.6582i	0.609297	+	1.50830i
$83$	−11.3897			−1.25018			−0.625091	−	0.780552i	$-0.714938\pi$
$83$	−11.3897			−1.25018			−0.625091	+	0.780552i	$0.714938\pi$
$84$		−	8.31036i		−	0.906735i
$85$	−0.752535	−	0.752535i	−0.0816239	−	0.0816239i
$86$	−1.41763			−0.152867
$87$		−	2.40704i		−	0.258062i
$88$	−2.86147	+	2.86147i	−0.305034	+	0.305034i
$89$	−6.56072	−	6.56072i	−0.695435	−	0.695435i	0.267987	−	0.963422i	$-0.413642\pi$
$89$	−6.56072	−	6.56072i	−0.695435	−	0.695435i	−0.963422	+	0.267987i	$0.913642\pi$
$90$			3.21682i			0.339083i
$91$		−	0.521216i		−	0.0546383i
$92$	−0.502504			−0.0523896
$93$	11.0054	+	11.0054i	1.14121	+	1.14121i
$94$	−19.0253	−	19.0253i	−1.96231	−	1.96231i
$95$	0.235922	+	0.235922i	0.0242051	+	0.0242051i
$96$	9.56547	−	9.56547i	0.976272	−	0.976272i
$97$	−4.30605	+	4.30605i	−0.437213	+	0.437213i	−0.891073	−	0.453860i	$-0.850047\pi$
$97$	−4.30605	+	4.30605i	−0.437213	+	0.437213i	0.453860	+	0.891073i	$0.350047\pi$
$98$	−2.30053			−0.232388
$99$	3.24429	−	3.24429i	0.326063	−	0.326063i
$100$	−15.8956			−1.58956
$101$	−1.04635	+	1.04635i	−0.104116	+	0.104116i	−0.757246	−	0.653130i	$-0.773455\pi$
$101$	−1.04635	+	1.04635i	−0.104116	+	0.104116i	0.653130	+	0.757246i	$0.273455\pi$
$102$			14.8982i			1.47514i
$103$			4.02901i			0.396991i	0.980102	+	0.198495i	$0.0636055\pi$
$103$			4.02901i			0.396991i	−0.980102	+	0.198495i	$0.936395\pi$
$104$	−1.09581	+	1.09581i	−0.107453	+	0.107453i
$105$	1.04699			0.102176
$106$	18.5946	−	18.5946i	1.80607	−	1.80607i
$107$	12.5212			1.21047			0.605237	−	0.796045i	$-0.293078\pi$
$107$	12.5212			1.21047			0.605237	+	0.796045i	$0.293078\pi$
$108$	2.18020	−	2.18020i	0.209790	−	0.209790i
$109$	12.6620	−	12.6620i	1.21280	−	1.21280i	0.242701	−	0.970101i	$-0.421967\pi$
$109$	12.6620	−	12.6620i	1.21280	−	1.21280i	0.970101	−	0.242701i	$-0.0780335\pi$
$110$	−0.918384	−	0.918384i	−0.0875645	−	0.0875645i
$111$	−0.816669	−	0.816669i	−0.0775148	−	0.0775148i
$112$	0.180452	+	0.180452i	0.0170512	+	0.0170512i
$113$	−12.5582			−1.18138			−0.590688	−	0.806900i	$-0.701144\pi$
$113$	−12.5582			−1.18138			−0.590688	+	0.806900i	$0.701144\pi$
$114$		−	4.67064i		−	0.437445i
$115$		−	0.0633086i		−	0.00590355i
$116$	2.22014	+	2.22014i	0.206134	+	0.206134i
$117$	1.24241	−	1.24241i	0.114860	−	0.114860i
$118$		−	29.3532i		−	2.70218i
$119$	2.56568			0.235196
$120$	−2.20120	−	2.20120i	−0.200941	−	0.200941i
$121$		−	9.14755i		−	0.831595i
$122$	−20.2137			−1.83006
$123$	14.8769	+	6.31582i	1.34140	+	0.569478i
$124$	−20.3017			−1.82315
$125$		−	4.07663i		−	0.364625i
$126$	−5.48369	−	5.48369i	−0.488526	−	0.488526i
$127$	−7.27019			−0.645125			−0.322562	−	0.946548i	$-0.604544\pi$
$127$	−7.27019			−0.645125			−0.322562	+	0.946548i	$0.604544\pi$
$128$			18.8196i			1.66344i
$129$	−1.09983	+	1.09983i	−0.0968344	+	0.0968344i
$130$	−0.351697	−	0.351697i	−0.0308459	−	0.0308459i
$131$		−	9.00671i		−	0.786920i	−0.919342	−	0.393460i	$-0.871278\pi$
$131$		−	9.00671i		−	0.786920i	0.919342	−	0.393460i	$-0.128722\pi$
$132$			11.3108i			0.984478i
$133$	−0.804349			−0.0697459
$134$	12.9247	+	12.9247i	1.11652	+	1.11652i
$135$	0.274676	+	0.274676i	0.0236403	+	0.0236403i
$136$	−5.39411	−	5.39411i	−0.462541	−	0.462541i
$137$	1.52937	−	1.52937i	0.130663	−	0.130663i	−0.638751	−	0.769414i	$-0.720548\pi$
$137$	1.52937	−	1.52937i	0.130663	−	0.130663i	0.769414	+	0.638751i	$0.220548\pi$
$138$	−0.626672	+	0.626672i	−0.0533459	+	0.0533459i
$139$	−6.43846			−0.546103			−0.273052	−	0.961999i	$-0.588033\pi$
$139$	−6.43846			−0.546103			−0.273052	+	0.961999i	$0.588033\pi$
$140$	−0.965693	+	0.965693i	−0.0816160	+	0.0816160i
$141$	−29.5205			−2.48608
$142$	−15.5911	+	15.5911i	−1.30838	+	1.30838i
$143$			0.709400i			0.0593230i
$144$			0.860278i			0.0716898i
$145$	−0.279707	+	0.279707i	−0.0232284	+	0.0232284i
$146$	24.5836			2.03455
$147$	−1.78480	+	1.78480i	−0.147208	+	0.147208i
$148$	1.50651			0.123834
$149$	−15.7391	+	15.7391i	−1.28940	+	1.28940i	−0.354241	+	0.935154i	$0.615261\pi$
$149$	−15.7391	+	15.7391i	−1.28940	+	1.28940i	−0.935154	+	0.354241i	$0.884739\pi$
$150$	−19.8234	+	19.8234i	−1.61858	+	1.61858i
$151$	−0.0896754	−	0.0896754i	−0.00729768	−	0.00729768i	0.703449	−	0.710746i	$-0.251643\pi$
$151$	−0.0896754	−	0.0896754i	−0.00729768	−	0.00729768i	−0.710746	+	0.703449i	$0.751643\pi$
$152$	1.69107	+	1.69107i	0.137164	+	0.137164i
$153$	6.11574	+	6.11574i	0.494428	+	0.494428i
$154$	3.13113			0.252313
$155$		−	2.55774i		−	0.205442i
$156$			4.33149i			0.346797i
$157$	−5.60626	−	5.60626i	−0.447429	−	0.447429i	0.447070	−	0.894499i	$-0.352467\pi$
$157$	−5.60626	−	5.60626i	−0.447429	−	0.447429i	−0.894499	+	0.447070i	$0.852467\pi$
$158$	−10.5646	+	10.5646i	−0.840475	+	0.840475i
$159$		−	28.8522i		−	2.28813i
$160$	−2.22308			−0.175750
$161$	0.107922	+	0.107922i	0.00850542	+	0.00850542i
$162$			17.8275i			1.40066i
$163$	0.238660			0.0186933			0.00934666	−	0.999956i	$-0.497025\pi$
$163$	0.238660			0.0186933			0.00934666	+	0.999956i	$0.497025\pi$
$164$	−19.5471	+	7.89632i	−1.52637	+	0.616599i
$165$	−1.42501			−0.110936
$166$		−	26.2023i		−	2.03369i
$167$	1.43126	+	1.43126i	0.110754	+	0.110754i	0.760312	−	0.649558i	$-0.225046\pi$
$167$	1.43126	+	1.43126i	0.110754	+	0.110754i	−0.649558	+	0.760312i	$0.725046\pi$
$168$	7.50474			0.579004
$169$		−	12.7283i		−	0.979103i
$170$	1.73123	−	1.73123i	0.132779	−	0.132779i
$171$	−1.91730	−	1.91730i	−0.146620	−	0.146620i
$172$		−	2.02885i		−	0.154699i
$173$		−	13.3689i		−	1.01642i	−0.861233	−	0.508211i	$-0.830307\pi$
$173$		−	13.3689i		−	1.01642i	0.861233	−	0.508211i	$-0.169693\pi$
$174$	5.53746			0.419794
$175$	3.41387	+	3.41387i	0.258064	+	0.258064i
$176$	−0.245604	−	0.245604i	−0.0185131	−	0.0185131i
$177$	−22.7728	−	22.7728i	−1.71171	−	1.71171i
$178$	15.0931	−	15.0931i	1.13128	−	1.13128i
$179$	10.8183	−	10.8183i	0.808598	−	0.808598i	−0.175824	−	0.984422i	$-0.556259\pi$
$179$	10.8183	−	10.8183i	0.808598	−	0.808598i	0.984422	+	0.175824i	$0.0562589\pi$
$180$	−4.60378			−0.343146
$181$	−0.255371	+	0.255371i	−0.0189816	+	0.0189816i	−0.716534	−	0.697552i	$-0.754272\pi$
$181$	−0.255371	+	0.255371i	−0.0189816	+	0.0189816i	0.697552	+	0.716534i	$0.254272\pi$
$182$	1.19907			0.0888811
$183$	−15.6822	+	15.6822i	−1.15926	+	1.15926i
$184$		−	0.453790i		−	0.0334539i
$185$			0.189800i			0.0139544i
$186$	−25.3182	+	25.3182i	−1.85642	+	1.85642i
$187$	−3.49202			−0.255362
$188$	27.2283	−	27.2283i	1.98583	−	1.98583i
$189$	−0.936476			−0.0681186
$190$	−0.542745	+	0.542745i	−0.0393749	+	0.0393749i
$191$	14.5696	−	14.5696i	1.05422	−	1.05422i	0.0557786	−	0.998443i	$-0.482236\pi$
$191$	14.5696	−	14.5696i	1.05422	−	1.05422i	0.998443	−	0.0557786i	$-0.0177641\pi$
$192$	22.9166	+	22.9166i	1.65386	+	1.65386i
$193$	−0.917708	−	0.917708i	−0.0660580	−	0.0660580i	0.673306	−	0.739364i	$-0.264874\pi$
$193$	−0.917708	−	0.917708i	−0.0660580	−	0.0660580i	−0.739364	+	0.673306i	$0.764874\pi$
$194$	−9.90619	−	9.90619i	−0.711223	−	0.711223i
$195$	−0.545709			−0.0390790
$196$		−	3.29242i		−	0.235173i
$197$			7.42262i			0.528840i	0.964408	+	0.264420i	$0.0851805\pi$
$197$			7.42262i			0.528840i	−0.964408	+	0.264420i	$0.914820\pi$
$198$	7.46357	+	7.46357i	0.530412	+	0.530412i
$199$	−18.3159	+	18.3159i	−1.29838	+	1.29838i	−0.368914	+	0.929464i	$0.620270\pi$
$199$	−18.3159	+	18.3159i	−1.29838	+	1.29838i	−0.929464	+	0.368914i	$0.879730\pi$
$200$		−	14.3547i		−	1.01503i
$201$	20.0545			1.41453
$202$	−2.40715	−	2.40715i	−0.169367	−	0.169367i
$203$		−	0.953628i		−	0.0669316i
$204$	−21.3218			−1.49282
$205$	−0.994827	−	2.46267i	−0.0694818	−	0.172000i
$206$	−9.26885			−0.645792
$207$			0.514499i			0.0357601i
$208$	−0.0940547	−	0.0940547i	−0.00652152	−	0.00652152i
$209$	1.09476			0.0757260
$210$			2.40863i			0.166211i
$211$	17.8014	−	17.8014i	1.22550	−	1.22550i	0.259848	−	0.965650i	$-0.416328\pi$
$211$	17.8014	−	17.8014i	1.22550	−	1.22550i	0.965650	−	0.259848i	$-0.0836725\pi$
$212$	26.6119	+	26.6119i	1.82771	+	1.82771i
$213$			24.1919i			1.65760i
$214$			28.8054i			1.96910i
$215$	0.255608			0.0174323
$216$	1.96885	+	1.96885i	0.133963	+	0.133963i
$217$	4.36015	+	4.36015i	0.295987	+	0.295987i
$218$	29.1293	+	29.1293i	1.97289	+	1.97289i
$219$	19.0725	−	19.0725i	1.28880	−	1.28880i
$220$	1.31435	−	1.31435i	0.0886138	−	0.0886138i
$221$	−1.33728			−0.0899549
$222$	1.87877	−	1.87877i	0.126095	−	0.126095i
$223$	−0.603746			−0.0404298			−0.0202149	−	0.999796i	$-0.506435\pi$
$223$	−0.603746			−0.0404298			−0.0202149	+	0.999796i	$0.506435\pi$
$224$	3.78968	−	3.78968i	0.253208	−	0.253208i
$225$			16.2751i			1.08500i
$226$		−	28.8905i		−	1.92177i
$227$	0.990768	−	0.990768i	0.0657596	−	0.0657596i	−0.673462	−	0.739222i	$-0.735194\pi$
$227$	0.990768	−	0.990768i	0.0657596	−	0.0657596i	0.739222	+	0.673462i	$0.235194\pi$
$228$	6.68443			0.442687
$229$	−11.8413	+	11.8413i	−0.782495	+	0.782495i	−0.980251	−	0.197756i	$-0.936635\pi$
$229$	−11.8413	+	11.8413i	−0.782495	+	0.782495i	0.197756	+	0.980251i	$0.436635\pi$
$230$	0.145643			0.00960342
$231$	2.42920	−	2.42920i	0.159829	−	0.159829i
$232$	−2.00491	+	2.00491i	−0.131629	+	0.131629i
$233$	15.9553	+	15.9553i	1.04527	+	1.04527i	0.998926	+	0.0463406i	$0.0147560\pi$
$233$	15.9553	+	15.9553i	1.04527	+	1.04527i	0.0463406	+	0.998926i	$0.485244\pi$
$234$	2.85819	+	2.85819i	0.186846	+	0.186846i
$235$	3.43039	+	3.43039i	0.223774	+	0.223774i
$236$	42.0091			2.73456
$237$			16.3925i			1.06481i
$238$			5.90242i			0.382597i
$239$	−13.4352	−	13.4352i	−0.869054	−	0.869054i	0.123314	−	0.992368i	$-0.460648\pi$
$239$	−13.4352	−	13.4352i	−0.869054	−	0.869054i	−0.992368	+	0.123314i	$0.960648\pi$
$240$	0.188932	−	0.188932i	0.0121955	−	0.0121955i
$241$			20.0195i			1.28957i	0.764364	+	0.644785i	$0.223053\pi$
$241$			20.0195i			1.28957i	−0.764364	+	0.644785i	$0.776947\pi$
$242$	21.0442			1.35277
$243$	15.8175	+	15.8175i	1.01469	+	1.01469i
$244$		−	28.9290i		−	1.85199i
$245$	0.414800			0.0265006
$246$	−14.5297	+	34.2247i	−0.926381	+	2.18209i
$247$	0.419240			0.0266756
$248$		−	18.3336i		−	1.16419i
$249$	−20.3283	−	20.3283i	−1.28826	−	1.28826i
$250$	9.37839			0.593142
$251$			14.6579i			0.925196i	0.886568	+	0.462598i	$0.153083\pi$
$251$			14.6579i			0.925196i	−0.886568	+	0.462598i	$0.846917\pi$
$252$	7.84804	−	7.84804i	0.494380	−	0.494380i
$253$	−0.146887	−	0.146887i	−0.00923468	−	0.00923468i
$254$		−	16.7253i		−	1.04944i
$255$		−	2.68625i		−	0.168219i
$256$	−17.6153			−1.10096
$257$	−15.7154	−	15.7154i	−0.980301	−	0.980301i	0.0195087	−	0.999810i	$-0.493790\pi$
$257$	−15.7154	−	15.7154i	−0.980301	−	0.980301i	−0.999810	+	0.0195087i	$0.993790\pi$
$258$	−2.53018	−	2.53018i	−0.157522	−	0.157522i
$259$	−0.323550	−	0.323550i	−0.0201044	−	0.0201044i
$260$	0.503335	−	0.503335i	0.0312155	−	0.0312155i
$261$	2.27313	−	2.27313i	0.140703	−	0.140703i
$262$	20.7202			1.28010
$263$	−6.16397	+	6.16397i	−0.380087	+	0.380087i	−0.871133	−	0.491047i	$-0.836614\pi$
$263$	−6.16397	+	6.16397i	−0.380087	+	0.380087i	0.491047	+	0.871133i	$0.336614\pi$
$264$	−10.2143			−0.628648
$265$	−3.35273	+	3.35273i	−0.205957	+	0.205957i
$266$		−	1.85043i		−	0.113457i
$267$		−	23.4191i		−	1.43323i
$268$	−18.4972	+	18.4972i	−1.12990	+	1.12990i
$269$	−13.3500			−0.813965			−0.406983	−	0.913436i	$-0.633419\pi$
$269$	−13.3500			−0.813965			−0.406983	+	0.913436i	$0.633419\pi$
$270$	−0.631899	+	0.631899i	−0.0384562	+	0.0384562i
$271$	8.90217			0.540768			0.270384	−	0.962753i	$-0.412849\pi$
$271$	8.90217			0.540768			0.270384	+	0.962753i	$0.412849\pi$
$272$	0.462984	−	0.462984i	0.0280725	−	0.0280725i
$273$	0.930266	−	0.930266i	0.0563023	−	0.0563023i
$274$	3.51836	+	3.51836i	0.212552	+	0.212552i
$275$	−4.64644	−	4.64644i	−0.280191	−	0.280191i
$276$	−0.896868	−	0.896868i	−0.0539851	−	0.0539851i
$277$	3.11361			0.187079			0.0935394	−	0.995616i	$-0.470182\pi$
$277$	3.11361			0.187079			0.0935394	+	0.995616i	$0.470182\pi$
$278$		−	14.8119i		−	0.888356i
$279$			20.7863i			1.24444i
$280$	−0.872078	−	0.872078i	−0.0521166	−	0.0521166i
$281$	−19.1049	+	19.1049i	−1.13970	+	1.13970i	−0.151200	+	0.988503i	$0.548314\pi$
$281$	−19.1049	+	19.1049i	−1.13970	+	1.13970i	−0.988503	+	0.151200i	$0.951686\pi$
$282$		−	67.9128i		−	4.04415i
$283$	21.4159			1.27304			0.636522	−	0.771259i	$-0.280372\pi$
$283$	21.4159			1.27304			0.636522	+	0.771259i	$0.280372\pi$
$284$	−22.3134	−	22.3134i	−1.32406	−	1.32406i
$285$			0.842147i			0.0498845i
$286$	−1.63199			−0.0965018
$287$	5.89397	+	2.50222i	0.347910	+	0.147701i
$288$	18.0667			1.06459
$289$			10.4173i			0.612780i
$290$	−0.643473	−	0.643473i	−0.0377860	−	0.0377860i
$291$	−15.3709			−0.901057
$292$			35.1831i			2.05893i
$293$	−2.85445	+	2.85445i	−0.166759	+	0.166759i	−0.785553	−	0.618794i	$-0.787621\pi$
$293$	−2.85445	+	2.85445i	−0.166759	+	0.166759i	0.618794	+	0.785553i	$0.287621\pi$
$294$	−4.10598	−	4.10598i	−0.239465	−	0.239465i
$295$			5.29257i			0.308145i
$296$			1.36047i			0.0790756i
$297$	1.27459			0.0739591
$298$	−36.2082	−	36.2082i	−2.09748	−	2.09748i
$299$	−0.0562505	−	0.0562505i	−0.00325305	−	0.00325305i
$300$	−28.3705	−	28.3705i	−1.63797	−	1.63797i
$301$	−0.435733	+	0.435733i	−0.0251152	+	0.0251152i
$302$	0.206301	−	0.206301i	0.0118713	−	0.0118713i
$303$	−3.73504			−0.214573
$304$	−0.145147	+	0.145147i	−0.00832474	+	0.00832474i
$305$	3.64466			0.208692
$306$	−14.0694	+	14.0694i	−0.804295	+	0.804295i
$307$			5.73269i			0.327182i	0.986528	+	0.163591i	$0.0523078\pi$
$307$			5.73269i			0.327182i	−0.986528	+	0.163591i	$0.947692\pi$
$308$			4.48114i			0.255337i
$309$	−7.19098	+	7.19098i	−0.409081	+	0.409081i
$310$	5.88414			0.334197
$311$	−5.29381	+	5.29381i	−0.300184	+	0.300184i	−0.841086	−	0.540901i	$-0.818083\pi$
$311$	−5.29381	+	5.29381i	−0.300184	+	0.300184i	0.540901	+	0.841086i	$0.318083\pi$
$312$	−3.91159			−0.221450
$313$	−14.4981	+	14.4981i	−0.819479	+	0.819479i	−0.986032	−	0.166553i	$-0.946736\pi$
$313$	−14.4981	+	14.4981i	−0.819479	+	0.819479i	0.166553	+	0.986032i	$0.446736\pi$
$314$	12.8974	−	12.8974i	0.727840	−	0.727840i
$315$	0.988746	+	0.988746i	0.0557095	+	0.0557095i
$316$	−15.1196	−	15.1196i	−0.850546	−	0.850546i
$317$	−18.5369	−	18.5369i	−1.04113	−	1.04113i	−0.999117	−	0.0420164i	$-0.986622\pi$
$317$	−18.5369	−	18.5369i	−1.04113	−	1.04113i	−0.0420164	−	0.999117i	$-0.513378\pi$
$318$	66.3753			3.72214
$319$			1.29793i			0.0726703i
$320$		−	5.32598i		−	0.297731i
$321$	22.3479	+	22.3479i	1.24734	+	1.24734i
$322$	−0.248277	+	0.248277i	−0.0138359	+	0.0138359i
$323$			2.06371i			0.114828i
$324$	−25.5140			−1.41744
$325$	−1.77936	−	1.77936i	−0.0987013	−	0.0987013i
$326$			0.549045i			0.0304088i
$327$	45.1984			2.49947
$328$	−7.13084	−	17.6522i	−0.393735	−	0.974680i
$329$	−11.6955			−0.644795
$330$		−	3.27826i		−	0.180462i
$331$	6.29221	+	6.29221i	0.345851	+	0.345851i	0.858562	−	0.512710i	$-0.171359\pi$
$331$	6.29221	+	6.29221i	0.345851	+	0.345851i	−0.512710	+	0.858562i	$0.671359\pi$
$332$	37.4997			2.05806
$333$		−	1.54247i		−	0.0845270i
$334$	−3.29265	+	3.29265i	−0.180166	+	0.180166i
$335$	−2.33040	−	2.33040i	−0.127323	−	0.127323i
$336$			0.644143i			0.0351409i
$337$		−	3.43436i		−	0.187081i	−0.995615	−	0.0935407i	$-0.970181\pi$
$337$		−	3.43436i		−	0.187081i	0.995615	−	0.0935407i	$-0.0298185\pi$
$338$	29.2819			1.59272
$339$	−22.4139	−	22.4139i	−1.21735	−	1.21735i
$340$	2.47766	+	2.47766i	0.134370	+	0.134370i
$341$	−5.93438	−	5.93438i	−0.321365	−	0.321365i
$342$	4.41080	−	4.41080i	0.238509	−	0.238509i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	1.83217			0.0987842
$345$	0.112993	−	0.112993i	0.00608334	−	0.00608334i
$346$	30.7556			1.65343
$347$	7.39594	−	7.39594i	0.397035	−	0.397035i	−0.480151	−	0.877186i	$-0.659418\pi$
$347$	7.39594	−	7.39594i	0.397035	−	0.397035i	0.877186	+	0.480151i	$0.159418\pi$
$348$			7.92499i			0.424824i
$349$			19.1468i			1.02491i	0.858715	+	0.512453i	$0.171263\pi$
$349$			19.1468i			1.02491i	−0.858715	+	0.512453i	$0.828737\pi$
$350$	−7.85370	+	7.85370i	−0.419798	+	0.419798i
$351$	0.488106			0.0260532
$352$	−5.15793	+	5.15793i	−0.274919	+	0.274919i
$353$	19.6653			1.04668			0.523339	−	0.852124i	$-0.324686\pi$
$353$	19.6653			1.04668			0.523339	+	0.852124i	$0.324686\pi$
$354$	52.3895	−	52.3895i	2.78447	−	2.78447i
$355$	2.81119	−	2.81119i	0.149202	−	0.149202i
$356$	21.6007	+	21.6007i	1.14483	+	1.14483i
$357$	4.57923	+	4.57923i	0.242359	+	0.242359i
$358$	24.8878	+	24.8878i	1.31536	+	1.31536i
$359$	11.3442			0.598726			0.299363	−	0.954139i	$-0.403226\pi$
$359$	11.3442			0.598726			0.299363	+	0.954139i	$0.403226\pi$
$360$		−	4.15749i		−	0.219119i
$361$			18.3530i			0.965949i
$362$	−0.587488	−	0.587488i	−0.0308777	−	0.0308777i
$363$	16.3265	−	16.3265i	0.856921	−	0.856921i
$364$			1.71606i			0.0899462i
$365$	−4.43259			−0.232012
$366$	−36.0773	−	36.0773i	−1.88579	−	1.88579i
$367$			14.3771i			0.750476i	0.926928	+	0.375238i	$0.122439\pi$
$367$			14.3771i			0.750476i	−0.926928	+	0.375238i	$0.877561\pi$
$368$	0.0389495			0.00203038
$369$	8.08481	+	20.0137i	0.420878	+	1.04187i
$370$	−0.436639			−0.0226998
$371$		−	11.4308i		−	0.593455i
$372$	−36.2345	−	36.2345i	−1.87867	−	1.87867i
$373$	−35.0171			−1.81312			−0.906559	−	0.422079i	$-0.861300\pi$
$373$	−35.0171			−1.81312			−0.906559	+	0.422079i	$0.861300\pi$
$374$		−	8.03348i		−	0.415401i
$375$	7.27597	−	7.27597i	0.375729	−	0.375729i
$376$	24.5887	+	24.5887i	1.26807	+	1.26807i
$377$			0.497046i			0.0255992i
$378$		−	2.15439i		−	0.110810i
$379$	−18.9654			−0.974185			−0.487092	−	0.873350i	$-0.661942\pi$
$379$	−18.9654			−0.974185			−0.487092	+	0.873350i	$0.661942\pi$
$380$	−0.776755	−	0.776755i	−0.0398467	−	0.0398467i
$381$	−12.9758	−	12.9758i	−0.664771	−	0.664771i
$382$	33.5178	+	33.5178i	1.71492	+	1.71492i
$383$	−23.2387	+	23.2387i	−1.18744	+	1.18744i	−0.209670	+	0.977772i	$0.567239\pi$
$383$	−23.2387	+	23.2387i	−1.18744	+	1.18744i	−0.977772	+	0.209670i	$0.932761\pi$
$384$	−33.5892	+	33.5892i	−1.71409	+	1.71409i
$385$	−0.564563			−0.0287728
$386$	2.11121	−	2.11121i	0.107458	−	0.107458i
$387$	−2.07728			−0.105594
$388$	14.1773	−	14.1773i	0.719746	−	0.719746i
$389$			12.5261i			0.635099i	0.948242	+	0.317549i	$0.102860\pi$
$389$			12.5261i			0.635099i	−0.948242	+	0.317549i	$0.897140\pi$
$390$		−	1.25542i		−	0.0635705i
$391$	0.276893	−	0.276893i	0.0140031	−	0.0140031i
$392$	2.97325			0.150172
$393$	16.0752	−	16.0752i	0.810885	−	0.810885i
$394$	−17.0759			−0.860273
$395$	1.90487	−	1.90487i	0.0958443	−	0.0958443i
$396$	−10.6816	+	10.6816i	−0.536768	+	0.536768i
$397$	−22.8355	−	22.8355i	−1.14608	−	1.14608i	−0.987317	−	0.158762i	$-0.949250\pi$
$397$	−22.8355	−	22.8355i	−1.14608	−	1.14608i	−0.158762	−	0.987317i	$-0.550750\pi$
$398$	−42.1361	−	42.1361i	−2.11209	−	2.11209i
$399$	−1.43560	−	1.43560i	−0.0718700	−	0.0718700i
$400$	1.23208			0.0616041
$401$			19.8409i			0.990807i	0.868663	+	0.495404i	$0.164980\pi$
$401$			19.8409i			0.990807i	−0.868663	+	0.495404i	$0.835020\pi$
$402$			46.1358i			2.30105i
$403$	−2.27258	−	2.27258i	−0.113205	−	0.113205i
$404$	3.44502	−	3.44502i	0.171396	−	0.171396i
$405$		−	3.21441i		−	0.159725i
$406$	2.19385			0.108879
$407$	0.440367	+	0.440367i	0.0218282	+	0.0218282i
$408$		−	19.2548i		−	0.953255i
$409$	7.90213			0.390735			0.195368	−	0.980730i	$-0.437410\pi$
$409$	7.90213			0.390735			0.195368	+	0.980730i	$0.437410\pi$
$410$	5.66544	−	2.28863i	0.279796	−	0.113027i
$411$	5.45925			0.269285
$412$		−	13.2652i		−	0.653530i
$413$	−9.02220	−	9.02220i	−0.443954	−	0.443954i
$414$	−1.18362			−0.0581717
$415$			4.72445i			0.231914i
$416$	−1.97524	+	1.97524i	−0.0968441	+	0.0968441i
$417$	−11.4914	−	11.4914i	−0.562734	−	0.562734i
$418$			2.51852i			0.123185i
$419$			3.64209i			0.177928i	0.996035	+	0.0889639i	$0.0283556\pi$
$419$			3.64209i			0.177928i	−0.996035	+	0.0889639i	$0.971644\pi$
$420$	−3.44714			−0.168203
$421$	−15.2548	−	15.2548i	−0.743475	−	0.743475i	0.229770	−	0.973245i	$-0.426203\pi$
$421$	−15.2548	−	15.2548i	−0.743475	−	0.743475i	−0.973245	+	0.229770i	$0.926203\pi$
$422$	40.9525	+	40.9525i	1.99354	+	1.99354i
$423$	−27.8783	−	27.8783i	−1.35549	−	1.35549i
$424$	−24.0321	+	24.0321i	−1.16710	+	1.16710i
$425$	8.75891	−	8.75891i	0.424870	−	0.424870i
$426$	−55.6541			−2.69645
$427$	−6.21302	+	6.21302i	−0.300669	+	0.300669i
$428$	−41.2252			−1.99270
$429$	−1.26614	+	1.26614i	−0.0611296	+	0.0611296i
$430$			0.588032i			0.0283574i
$431$			8.94140i			0.430692i	0.976538	+	0.215346i	$0.0690879\pi$
$431$			8.94140i			0.430692i	−0.976538	+	0.215346i	$0.930912\pi$
$432$	−0.168989	+	0.168989i	−0.00813051	+	0.00813051i
$433$	15.0058			0.721131			0.360566	−	0.932734i	$-0.382584\pi$
$433$	15.0058			0.721131			0.360566	+	0.932734i	$0.382584\pi$
$434$	−10.0307	+	10.0307i	−0.481487	+	0.481487i
$435$	−0.998441			−0.0478716
$436$	−41.6887	+	41.6887i	−1.99653	+	1.99653i
$437$	−0.0868067	+	0.0868067i	−0.00415253	+	0.00415253i
$438$	43.8768	+	43.8768i	2.09652	+	2.09652i
$439$	24.1243	+	24.1243i	1.15139	+	1.15139i	0.986274	+	0.165116i	$0.0527997\pi$
$439$	24.1243	+	24.1243i	1.15139	+	1.15139i	0.165116	+	0.986274i	$0.447200\pi$
$440$	1.18694	+	1.18694i	0.0565851	+	0.0565851i
$441$	−3.37102			−0.160525
$442$		−	3.07644i		−	0.146331i
$443$			27.1551i			1.29018i	0.764107	+	0.645090i	$0.223180\pi$
$443$			27.1551i			1.29018i	−0.764107	+	0.645090i	$0.776820\pi$
$444$	2.68882	+	2.68882i	0.127606	+	0.127606i
$445$	−2.72139	+	2.72139i	−0.129006	+	0.129006i
$446$		−	1.38893i		−	0.0657679i
$447$	−56.1822			−2.65733
$448$	9.07915	+	9.07915i	0.428950	+	0.428950i
$449$		−	23.5581i		−	1.11177i	−0.831258	−	0.555887i	$-0.812379\pi$
$449$		−	23.5581i		−	1.11177i	0.831258	−	0.555887i	$-0.187621\pi$
$450$	−37.4412			−1.76500
$451$	−8.02198	−	3.40564i	−0.377740	−	0.160365i
$452$	41.3469			1.94479
$453$		−	0.320105i		−	0.0150399i
$454$	2.27929	+	2.27929i	0.106972	+	0.106972i
$455$	−0.216200			−0.0101356
$456$			6.03644i			0.282682i
$457$	7.02564	−	7.02564i	0.328646	−	0.328646i	−0.523426	−	0.852071i	$-0.675346\pi$
$457$	7.02564	−	7.02564i	0.328646	−	0.328646i	0.852071	+	0.523426i	$0.175346\pi$
$458$	−27.2412	−	27.2412i	−1.27290	−	1.27290i
$459$			2.40270i			0.112149i
$460$			0.208439i			0.00971850i
$461$	17.5293			0.816422			0.408211	−	0.912888i	$-0.366153\pi$
$461$	17.5293			0.816422			0.408211	+	0.912888i	$0.366153\pi$
$462$	5.58843	+	5.58843i	0.259997	+	0.259997i
$463$	−0.757206	−	0.757206i	−0.0351904	−	0.0351904i	0.689293	−	0.724483i	$-0.257921\pi$
$463$	−0.757206	−	0.757206i	−0.0351904	−	0.0351904i	−0.724483	+	0.689293i	$0.757921\pi$
$464$	−0.172085	−	0.172085i	−0.00798883	−	0.00798883i
$465$	4.56504	−	4.56504i	0.211699	−	0.211699i
$466$	−36.7056	+	36.7056i	−1.70035	+	1.70035i
$467$	2.33826			0.108202			0.0541010	−	0.998535i	$-0.482771\pi$
$467$	2.33826			0.108202			0.0541010	+	0.998535i	$0.482771\pi$
$468$	−4.09053	+	4.09053i	−0.189085	+	0.189085i
$469$	7.94523			0.366877
$470$	−7.89170	+	7.89170i	−0.364017	+	0.364017i
$471$		−	20.0121i		−	0.922110i
$472$			37.9367i			1.74618i
$473$	0.593053	−	0.593053i	0.0272686	−	0.0272686i
$474$	−37.7114			−1.73214
$475$	−2.74594	+	2.74594i	−0.125993	+	0.125993i
$476$	−8.44731			−0.387182
$477$	27.2471	−	27.2471i	1.24756	−	1.24756i
$478$	30.9081	−	30.9081i	1.41371	−	1.41371i
$479$	11.7868	+	11.7868i	0.538554	+	0.538554i	0.923104	−	0.384550i	$-0.125643\pi$
$479$	11.7868	+	11.7868i	0.538554	+	0.538554i	−0.384550	+	0.923104i	$0.625643\pi$
$480$	−3.96776	−	3.96776i	−0.181103	−	0.181103i
$481$	0.168640	+	0.168640i	0.00768930	+	0.00768930i
$482$	−46.0554			−2.09777
$483$			0.385237i			0.0175289i
$484$			30.1176i			1.36898i
$485$	1.78615	+	1.78615i	0.0811049	+	0.0811049i
$486$	−36.3886	+	36.3886i	−1.65062	+	1.65062i
$487$			33.6227i			1.52359i	0.647818	+	0.761795i	$0.275682\pi$
$487$			33.6227i			1.52359i	−0.647818	+	0.761795i	$0.724318\pi$
$488$	26.1246			1.18260
$489$	0.425961	+	0.425961i	0.0192626	+	0.0192626i
$490$			0.954258i			0.0431090i
$491$	29.2410			1.31963			0.659814	−	0.751429i	$-0.270635\pi$
$491$	29.2410			1.31963			0.659814	+	0.751429i	$0.270635\pi$
$492$	−48.9810	−	20.7943i	−2.20823	−	0.937482i
$493$	−2.44671			−0.110194
$494$			0.964472i			0.0433937i
$495$	−1.34573	−	1.34573i	−0.0604861	−	0.0604861i
$496$	1.57360			0.0706568
$497$			9.58442i			0.429920i
$498$	46.7659	−	46.7659i	2.09563	−	2.09563i
$499$	27.3919	+	27.3919i	1.22623	+	1.22623i	0.965380	+	0.260848i	$0.0840022\pi$
$499$	27.3919	+	27.3919i	1.22623	+	1.22623i	0.260848	+	0.965380i	$0.415998\pi$
$500$			13.4220i			0.600249i
$501$			5.10902i			0.228254i
$502$	−33.7208			−1.50503
$503$	−17.2246	−	17.2246i	−0.768006	−	0.768006i	0.209749	−	0.977755i	$-0.432735\pi$
$503$	−17.2246	−	17.2246i	−0.768006	−	0.768006i	−0.977755	+	0.209749i	$0.932735\pi$
$504$	7.08724	+	7.08724i	0.315691	+	0.315691i
$505$	0.434025	+	0.434025i	0.0193139	+	0.0193139i
$506$	0.337916	−	0.337916i	0.0150222	−	0.0150222i
$507$	22.7175	−	22.7175i	1.00892	−	1.00892i
$508$	23.9365			1.06201
$509$	7.17388	−	7.17388i	0.317977	−	0.317977i	−0.530013	−	0.847990i	$-0.677813\pi$
$509$	7.17388	−	7.17388i	0.317977	−	0.317977i	0.847990	+	0.530013i	$0.177813\pi$
$510$	6.17979			0.273646
$511$	7.55620	−	7.55620i	0.334267	−	0.334267i
$512$		−	2.88525i		−	0.127511i
$513$		−	0.753254i		−	0.0332570i
$514$	36.1537	−	36.1537i	1.59467	−	1.59467i
$515$	1.67124			0.0736434
$516$	3.62110	−	3.62110i	0.159410	−	0.159410i
$517$	15.9182			0.700080
$518$	0.744336	−	0.744336i	0.0327042	−	0.0327042i
$519$	23.8609	−	23.8609i	1.04738	−	1.04738i
$520$	0.454541	+	0.454541i	0.0199329	+	0.0199329i
$521$	−2.71458	−	2.71458i	−0.118928	−	0.118928i	0.645138	−	0.764066i	$-0.276800\pi$
$521$	−2.71458	−	2.71458i	−0.118928	−	0.118928i	−0.764066	+	0.645138i	$0.776800\pi$
$522$	5.22940	+	5.22940i	0.228885	+	0.228885i
$523$	19.5260			0.853813			0.426907	−	0.904296i	$-0.359603\pi$
$523$	19.5260			0.853813			0.426907	+	0.904296i	$0.359603\pi$
$524$			29.6539i			1.29544i
$525$			12.1861i			0.531847i
$526$	−14.1804	−	14.1804i	−0.618294	−	0.618294i
$527$	11.1868	−	11.1868i	0.487304	−	0.487304i
$528$		−	0.876709i		−	0.0381539i
$529$	−22.9767			−0.998987
$530$	−7.71304	−	7.71304i	−0.335033	−	0.335033i
$531$		−	43.0119i		−	1.86656i
$532$	2.64826			0.114817
$533$	−3.07203	−	1.30420i	−0.133065	−	0.0564911i
$534$	53.8764			2.33146
$535$		−	5.19381i		−	0.224548i
$536$	−16.7041	−	16.7041i	−0.721507	−	0.721507i
$537$	38.6170			1.66645
$538$		−	30.7121i		−	1.32409i
$539$	0.962406	−	0.962406i	0.0414538	−	0.0414538i
$540$	−0.904349	−	0.904349i	−0.0389170	−	0.0389170i
$541$		−	21.2043i		−	0.911646i	−0.890070	−	0.455823i	$-0.849345\pi$
$541$		−	21.2043i		−	0.911646i	0.890070	−	0.455823i	$-0.150655\pi$
$542$			20.4797i			0.879677i
$543$	−0.911573			−0.0391193
$544$	−9.72311	−	9.72311i	−0.416875	−	0.416875i
$545$	−5.25221	−	5.25221i	−0.224980	−	0.224980i
$546$	2.14010	+	2.14010i	0.0915879	+	0.0915879i
$547$	16.9151	−	16.9151i	0.723235	−	0.723235i	−0.246027	−	0.969263i	$-0.579125\pi$
$547$	16.9151	−	16.9151i	0.723235	−	0.723235i	0.969263	+	0.246027i	$0.0791253\pi$
$548$	−5.03534	+	5.03534i	−0.215099	+	0.215099i
$549$	−29.6196			−1.26413
$550$	10.6893	−	10.6893i	0.455791	−	0.455791i
$551$	0.767050			0.0326774
$552$	0.809925	−	0.809925i	0.0344727	−	0.0344727i
$553$			6.49443i			0.276171i
$554$			7.16295i			0.304325i
$555$	−0.338754	+	0.338754i	−0.0143793	+	0.0143793i
$556$	21.1981			0.899001
$557$	1.36364	−	1.36364i	0.0577795	−	0.0577795i	−0.677627	−	0.735406i	$-0.736991\pi$
$557$	1.36364	−	1.36364i	0.0577795	−	0.0577795i	0.735406	+	0.677627i	$0.236991\pi$
$558$	−47.8195			−2.02436
$559$	0.227111	−	0.227111i	0.00960577	−	0.00960577i
$560$	0.0748517	−	0.0748517i	0.00316306	−	0.00316306i
$561$	−6.23255	−	6.23255i	−0.263138	−	0.263138i
$562$	−43.9513	−	43.9513i	−1.85398	−	1.85398i
$563$	−5.04042	−	5.04042i	−0.212429	−	0.212429i	0.592870	−	0.805298i	$-0.297995\pi$
$563$	−5.04042	−	5.04042i	−0.212429	−	0.212429i	−0.805298	+	0.592870i	$0.797995\pi$
$564$	97.1940			4.09261
$565$			5.20914i			0.219150i
$566$			49.2679i			2.07088i
$567$	5.47958	+	5.47958i	0.230121	+	0.230121i
$568$	20.1503	−	20.1503i	0.845490	−	0.845490i
$569$		−	13.0904i		−	0.548777i	−0.961619	−	0.274388i	$-0.911525\pi$
$569$		−	13.0904i		−	0.548777i	0.961619	−	0.274388i	$-0.0884754\pi$
$570$	−1.93738			−0.0811480
$571$	−12.3572	−	12.3572i	−0.517134	−	0.517134i	0.399569	−	0.916703i	$-0.369160\pi$
$571$	−12.3572	−	12.3572i	−0.517134	−	0.517134i	−0.916703	+	0.399569i	$0.869160\pi$
$572$		−	2.33564i		−	0.0976582i
$573$	52.0077			2.17265
$574$	−5.75642	+	13.5592i	−0.240268	+	0.565952i
$575$	0.736861			0.0307292
$576$			43.2834i			1.80347i
$577$	12.8281	+	12.8281i	0.534039	+	0.534039i	0.921772	−	0.387733i	$-0.126742\pi$
$577$	12.8281	+	12.8281i	0.534039	+	0.534039i	−0.387733	+	0.921772i	$0.626742\pi$
$578$	−23.9652			−0.996821
$579$		−	3.27585i		−	0.136140i
$580$	0.920913	−	0.920913i	0.0382388	−	0.0382388i
$581$	−8.05374	−	8.05374i	−0.334125	−	0.334125i
$582$		−	35.3611i		−	1.46577i
$583$			15.5578i			0.644338i
$584$	−31.7724			−1.31475
$585$	−0.515350	−	0.515350i	−0.0213071	−	0.0213071i
$586$	−6.56673	−	6.56673i	−0.271269	−	0.271269i
$587$	−22.8602	−	22.8602i	−0.943541	−	0.943541i	0.0549486	−	0.998489i	$-0.482500\pi$
$587$	−22.8602	−	22.8602i	−0.943541	−	0.943541i	−0.998489	+	0.0549486i	$0.982500\pi$
$588$	5.87631	−	5.87631i	0.242335	−	0.242335i
$589$	−3.50709	+	3.50709i	−0.144507	+	0.144507i
$590$	−12.1757			−0.501265
$591$	−13.2479	+	13.2479i	−0.544945	+	0.544945i
$592$	−0.116771			−0.00479925
$593$	−7.12465	+	7.12465i	−0.292574	+	0.292574i	−0.838096	−	0.545522i	$-0.816331\pi$
$593$	−7.12465	+	7.12465i	−0.292574	+	0.292574i	0.545522	+	0.838096i	$0.316331\pi$
$594$			2.93222i			0.120311i
$595$		−	1.06425i		−	0.0436298i
$596$	51.8197	−	51.8197i	2.12262	−	2.12262i
$597$	−65.3803			−2.67584
$598$	0.129406	−	0.129406i	0.00529180	−	0.00529180i
$599$	8.70191			0.355550			0.177775	−	0.984071i	$-0.443110\pi$
$599$	8.70191			0.355550			0.177775	+	0.984071i	$0.443110\pi$
$600$	25.6202	−	25.6202i	1.04594	−	1.04594i
$601$	34.0771	−	34.0771i	1.39004	−	1.39004i	0.564824	−	0.825211i	$-0.308944\pi$
$601$	34.0771	−	34.0771i	1.39004	−	1.39004i	0.825211	−	0.564824i	$-0.191056\pi$
$602$	−1.00241	−	1.00241i	−0.0408554	−	0.0408554i
$603$	18.9388	+	18.9388i	0.771247	+	0.771247i
$604$	0.295249	+	0.295249i	0.0120135	+	0.0120135i
$605$	−3.79440			−0.154264
$606$		−	8.59257i		−	0.349049i
$607$			14.4020i			0.584557i	0.956333	+	0.292279i	$0.0944135\pi$
$607$			14.4020i			0.584557i	−0.956333	+	0.292279i	$0.905587\pi$
$608$	3.04822	+	3.04822i	0.123622	+	0.123622i
$609$	1.70203	−	1.70203i	0.0689699	−	0.0689699i
$610$			8.38463i			0.339484i
$611$	6.09590			0.246614
$612$	−20.1356	−	20.1356i	−0.813933	−	0.813933i
$613$		−	23.5630i		−	0.951701i	−0.879526	−	0.475850i	$-0.842140\pi$
$613$		−	23.5630i		−	0.951701i	0.879526	−	0.475850i	$-0.157860\pi$
$614$	−13.1882			−0.532233
$615$	2.61980	−	6.17094i	0.105641	−	0.248836i
$616$	−4.04674			−0.163048
$617$			9.92852i			0.399707i	0.979826	+	0.199854i	$0.0640467\pi$
$617$			9.92852i			0.399707i	−0.979826	+	0.199854i	$0.935953\pi$
$618$	−16.5430	−	16.5430i	−0.665459	−	0.665459i
$619$	14.5453			0.584627			0.292313	−	0.956323i	$-0.405575\pi$
$619$	14.5453			0.584627			0.292313	+	0.956323i	$0.405575\pi$
$620$			8.42115i			0.338201i
$621$	−0.101066	+	0.101066i	−0.00405564	+	0.00405564i
$622$	−12.1786	−	12.1786i	−0.488315	−	0.488315i
$623$		−	9.27826i		−	0.371726i
$624$		−	0.335738i		−	0.0134403i
$625$	22.4487			0.897949
$626$	−33.3532	−	33.3532i	−1.33306	−	1.33306i
$627$	1.95392	+	1.95392i	0.0780322	+	0.0780322i
$628$	18.4582	+	18.4582i	0.736562	+	0.736562i
$629$	−0.830128	+	0.830128i	−0.0330994	+	0.0330994i
$630$	−2.27464	+	2.27464i	−0.0906236	+	0.0906236i
$631$	5.22697			0.208082			0.104041	−	0.994573i	$-0.466823\pi$
$631$	5.22697			0.208082			0.104041	+	0.994573i	$0.466823\pi$
$632$	13.6539	−	13.6539i	0.543124	−	0.543124i
$633$	63.5438			2.52564
$634$	42.6445	−	42.6445i	1.69363	−	1.69363i
$635$			3.01567i			0.119673i
$636$			94.9936i			3.76674i
$637$	0.368555	−	0.368555i	0.0146027	−	0.0146027i
$638$	−2.98593			−0.118214
$639$	−22.8461	+	22.8461i	−0.903777	+	0.903777i
$640$	7.80638			0.308574
$641$	16.7993	−	16.7993i	0.663533	−	0.663533i	−0.292678	−	0.956211i	$-0.594546\pi$
$641$	16.7993	−	16.7993i	0.663533	−	0.663533i	0.956211	+	0.292678i	$0.0945465\pi$
$642$	−51.4119	+	51.4119i	−2.02907	+	2.02907i
$643$	−18.2035	−	18.2035i	−0.717876	−	0.717876i	0.250294	−	0.968170i	$-0.419473\pi$
$643$	−18.2035	−	18.2035i	−0.717876	−	0.717876i	−0.968170	+	0.250294i	$0.919473\pi$
$644$	−0.355324	−	0.355324i	−0.0140017	−	0.0140017i
$645$	0.456208	+	0.456208i	0.0179632	+	0.0179632i
$646$	−4.74761			−0.186792
$647$		−	46.2647i		−	1.81885i	−0.415864	−	0.909427i	$-0.636521\pi$
$647$		−	46.2647i		−	1.81885i	0.415864	−	0.909427i	$-0.363479\pi$
$648$		−	23.0406i		−	0.905121i
$649$	12.2796	+	12.2796i	0.482018	+	0.482018i
$650$	4.09347	−	4.09347i	0.160559	−	0.160559i
$651$			15.5640i			0.610001i
$652$	−0.785771			−0.0307732
$653$	−0.598726	−	0.598726i	−0.0234300	−	0.0234300i	0.695295	−	0.718725i	$-0.255274\pi$
$653$	−0.598726	−	0.598726i	−0.0234300	−	0.0234300i	−0.718725	+	0.695295i	$0.755274\pi$
$654$			103.980i			4.06594i
$655$	−3.73598			−0.145977
$656$	1.51511	−	0.612050i	0.0591552	−	0.0238965i
$657$	36.0230			1.40539
$658$		−	26.9059i		−	1.04890i
$659$	−10.5182	−	10.5182i	−0.409732	−	0.409732i	0.471913	−	0.881645i	$-0.343564\pi$
$659$	−10.5182	−	10.5182i	−0.409732	−	0.409732i	−0.881645	+	0.471913i	$0.843564\pi$
$660$	4.69172			0.182625
$661$		−	10.0247i		−	0.389917i	−0.980811	−	0.194959i	$-0.937543\pi$
$661$		−	10.0247i		−	0.389917i	0.980811	−	0.194959i	$-0.0624573\pi$
$662$	−14.4754	+	14.4754i	−0.562602	+	0.562602i
$663$	−2.38677	−	2.38677i	−0.0926944	−	0.0926944i
$664$			33.8645i			1.31420i
$665$			0.333644i			0.0129382i
$666$	3.54850			0.137502
$667$	−0.102917	−	0.102917i	−0.00398497	−	0.00398497i
$668$	−4.71231	−	4.71231i	−0.182325	−	0.182325i
$669$	−1.07757	−	1.07757i	−0.0416611	−	0.0416611i
$670$	5.36115	−	5.36115i	0.207119	−	0.207119i
$671$	8.45622	−	8.45622i	0.326449	−	0.326449i
$672$	13.5276			0.521839
$673$	−4.13812	+	4.13812i	−0.159513	+	0.159513i	−0.782351	−	0.622838i	$-0.785980\pi$
$673$	−4.13812	+	4.13812i	−0.159513	+	0.159513i	0.622838	+	0.782351i	$0.285980\pi$
$674$	7.90083			0.304329
$675$	−3.19701	+	3.19701i	−0.123053	+	0.123053i
$676$			41.9070i			1.61181i
$677$			42.2247i			1.62283i	0.584472	+	0.811414i	$0.301302\pi$
$677$			42.2247i			1.62283i	−0.584472	+	0.811414i	$0.698698\pi$
$678$	51.5637	−	51.5637i	1.98029	−	1.98029i
$679$	−6.08968			−0.233700
$680$	−2.23748	+	2.23748i	−0.0858033	+	0.0858033i
$681$	3.53664			0.135525
$682$	13.6522	−	13.6522i	0.522770	−	0.522770i
$683$	−11.1217	+	11.1217i	−0.425560	+	0.425560i	−0.887113	−	0.461552i	$-0.847293\pi$
$683$	−11.1217	+	11.1217i	−0.425560	+	0.425560i	0.461552	+	0.887113i	$0.347293\pi$
$684$	6.31257	+	6.31257i	0.241367	+	0.241367i
$685$	−0.634384	−	0.634384i	−0.0242386	−	0.0242386i
$686$	−1.62672	−	1.62672i	−0.0621084	−	0.0621084i
$687$	−42.2687			−1.61265
$688$			0.157258i			0.00599541i
$689$			5.95789i			0.226978i
$690$	0.259944	+	0.259944i	0.00989588	+	0.00989588i
$691$	−20.3838	+	20.3838i	−0.775436	+	0.775436i	−0.979051	−	0.203615i	$-0.934731\pi$
$691$	−20.3838	+	20.3838i	−0.775436	+	0.775436i	0.203615	+	0.979051i	$0.434731\pi$
$692$			44.0162i			1.67325i
$693$	4.58811			0.174288
$694$	17.0146	+	17.0146i	0.645864	+	0.645864i
$695$			2.67067i			0.101304i
$696$	−7.15674			−0.271275
$697$	6.41990	−	15.1221i	0.243171	−	0.572789i
$698$	−44.0478			−1.66723
$699$			56.9540i			2.15420i
$700$	−11.2399	−	11.2399i	−0.424828	−	0.424828i
$701$	43.4536			1.64122			0.820611	−	0.571488i	$-0.193633\pi$
$701$	43.4536			1.64122			0.820611	+	0.571488i	$0.193633\pi$
$702$			1.12290i			0.0423812i
$703$	0.260247	−	0.260247i	0.00981542	−	0.00981542i
$704$	−12.3572	−	12.3572i	−0.465728	−	0.465728i
$705$			12.2451i			0.461178i
$706$			45.2406i			1.70265i
$707$	−1.47976			−0.0556521
$708$	74.9777	+	74.9777i	2.81784	+	2.81784i
$709$	6.05281	+	6.05281i	0.227318	+	0.227318i	0.811571	−	0.584253i	$-0.198613\pi$
$709$	6.05281	+	6.05281i	0.227318	+	0.227318i	−0.584253	+	0.811571i	$0.698613\pi$
$710$	6.46721	+	6.46721i	0.242710	+	0.242710i
$711$	−15.4806	+	15.4806i	−0.580566	+	0.580566i
$712$	−19.5067	+	19.5067i	−0.731044	+	0.731044i
$713$	0.941111			0.0352449
$714$	−10.5346	+	10.5346i	−0.394249	+	0.394249i
$715$	0.294259			0.0110047
$716$	−35.6184	+	35.6184i	−1.33112	+	1.33112i
$717$		−	47.9584i		−	1.79104i
$718$			26.0977i			0.973959i
$719$	22.9632	−	22.9632i	0.856384	−	0.856384i	−0.134526	−	0.990910i	$-0.542951\pi$
$719$	22.9632	−	22.9632i	0.856384	−	0.856384i	0.990910	+	0.134526i	$0.0429511\pi$
$720$	0.356843			0.0132988
$721$	−2.84894	+	2.84894i	−0.106100	+	0.106100i
$722$	−42.2216			−1.57133
$723$	−35.7308	+	35.7308i	−1.32884	+	1.32884i
$724$	0.840790	−	0.840790i	0.0312477	−	0.0312477i
$725$	−3.25556	−	3.25556i	−0.120909	−	0.120909i
$726$	37.5596	+	37.5596i	1.39397	+	1.39397i
$727$	2.13181	+	2.13181i	0.0790644	+	0.0790644i	0.745533	−	0.666469i	$-0.232195\pi$
$727$	2.13181	+	2.13181i	0.0790644	+	0.0790644i	−0.666469	+	0.745533i	$0.732195\pi$
$728$	−1.54971			−0.0574359
$729$			33.2143i			1.23016i
$730$		−	10.1973i		−	0.377418i
$731$	1.11795	+	1.11795i	0.0413490	+	0.0413490i
$732$	51.6324	−	51.6324i	1.90839	−	1.90839i
$733$		−	13.1031i		−	0.483975i	−0.970279	−	0.241988i	$-0.922201\pi$
$733$		−	13.1031i		−	0.483975i	0.970279	−	0.241988i	$-0.0777993\pi$
$734$	−33.0748			−1.22081
$735$	0.740335	+	0.740335i	0.0273077	+	0.0273077i
$736$		−	0.817976i		−	0.0301510i
$737$	−10.8138			−0.398333
$738$	−46.0421	+	18.5993i	−1.69483	+	0.684650i
$739$	−22.0862			−0.812453			−0.406226	−	0.913773i	$-0.633156\pi$
$739$	−22.0862			−0.812453			−0.406226	+	0.913773i	$0.633156\pi$
$740$		−	0.624901i		−	0.0229718i
$741$	0.748259	+	0.748259i	0.0274880	+	0.0274880i
$742$	26.2967			0.965384
$743$			47.5896i			1.74589i	0.487815	+	0.872947i	$0.337794\pi$
$743$			47.5896i			1.74589i	−0.487815	+	0.872947i	$0.662206\pi$
$744$	32.7218	−	32.7218i	1.19964	−	1.19964i
$745$	6.52857	+	6.52857i	0.239188	+	0.239188i
$746$		−	80.5578i		−	2.94943i
$747$		−	38.3949i		−	1.40480i
$748$	11.4972			0.420379
$749$	8.85386	+	8.85386i	0.323513	+	0.323513i
$750$	16.7386	+	16.7386i	0.611205	+	0.611205i
$751$	−10.0749	−	10.0749i	−0.367640	−	0.367640i	0.498976	−	0.866616i	$-0.333710\pi$
$751$	−10.0749	−	10.0749i	−0.367640	−	0.367640i	−0.866616	+	0.498976i	$0.833710\pi$
$752$	−2.11049	+	2.11049i	−0.0769615	+	0.0769615i
$753$	−26.1614	+	26.1614i	−0.953373	+	0.953373i
$754$	−1.14347			−0.0416427
$755$	−0.0371974	+	0.0371974i	−0.00135375	+	0.00135375i
$756$	3.08327			0.112138
$757$	−9.61528	+	9.61528i	−0.349473	+	0.349473i	−0.859913	−	0.510440i	$-0.829483\pi$
$757$	−9.61528	+	9.61528i	−0.349473	+	0.349473i	0.510440	+	0.859913i	$0.329483\pi$
$758$		−	43.6303i		−	1.58472i
$759$		−	0.524326i		−	0.0190318i
$760$	0.701455	−	0.701455i	0.0254445	−	0.0254445i
$761$	−15.4413			−0.559747			−0.279873	−	0.960037i	$-0.590292\pi$
$761$	−15.4413			−0.559747			−0.279873	+	0.960037i	$0.590292\pi$
$762$	29.8512	−	29.8512i	1.08140	−	1.08140i
$763$	17.9068			0.648270
$764$	−47.9694	+	47.9694i	−1.73547	+	1.73547i
$765$	2.53681	−	2.53681i	0.0917185	−	0.0917185i
$766$	−53.4612	−	53.4612i	−1.93163	−	1.93163i
$767$	4.70252	+	4.70252i	0.169798	+	0.169798i
$768$	−31.4398	−	31.4398i	−1.13449	−	1.13449i
$769$	−8.77903			−0.316580			−0.158290	−	0.987393i	$-0.550598\pi$
$769$	−8.77903			−0.316580			−0.158290	+	0.987393i	$0.550598\pi$
$770$		−	1.29879i		−	0.0468052i
$771$		−	56.0977i		−	2.02031i
$772$	3.02148	+	3.02148i	0.108745	+	0.108745i
$773$	−25.6034	+	25.6034i	−0.920891	+	0.920891i	−0.997092	−	0.0762017i	$-0.975721\pi$
$773$	−25.6034	+	25.6034i	−0.920891	+	0.920891i	0.0762017	+	0.997092i	$0.475721\pi$
$774$		−	4.77885i		−	0.171772i
$775$	29.7700			1.06937
$776$	12.8030	+	12.8030i	0.459600	+	0.459600i
$777$		−	1.15494i		−	0.0414334i
$778$	−28.8166			−1.03313
$779$	−2.01266	+	4.74081i	−0.0721110	+	0.169857i
$780$	1.79670			0.0643323
$781$		−	13.0449i		−	0.466781i
$782$	0.636999	+	0.636999i	0.0227791	+	0.0227791i
$783$	0.893050			0.0319150
$784$			0.255198i			0.00911423i
$785$	−2.32548	+	2.32548i	−0.0829999	+	0.0829999i
$786$	36.9813	+	36.9813i	1.31908	+	1.31908i
$787$			14.6320i			0.521576i	0.965396	+	0.260788i	$0.0839823\pi$
$787$			14.6320i			0.521576i	−0.965396	+	0.260788i	$0.916018\pi$
$788$		−	24.4384i		−	0.870582i
$789$	−22.0029			−0.783324
$790$	4.38220	+	4.38220i	0.155912	+	0.155912i
$791$	−8.87999	−	8.87999i	−0.315736	−	0.315736i
$792$	−9.64608	−	9.64608i	−0.342758	−	0.342758i
$793$	3.23833	−	3.23833i	0.114996	−	0.114996i
$794$	52.5336	−	52.5336i	1.86435	−	1.86435i
$795$	−11.9679			−0.424458
$796$	60.3036	−	60.3036i	2.13740	−	2.13740i
$797$	8.67363			0.307236			0.153618	−	0.988130i	$-0.450908\pi$
$797$	8.67363			0.307236			0.153618	+	0.988130i	$0.450908\pi$
$798$	3.30264	−	3.30264i	0.116912	−	0.116912i
$799$			30.0070i			1.06157i
$800$		−	25.8749i		−	0.914817i
$801$	22.1163	−	22.1163i	0.781441	−	0.781441i
$802$	−45.6445			−1.61176
$803$	−10.2844	+	10.2844i	−0.362927	+	0.362927i
$804$	−66.0277			−2.32862
$805$	0.0447659	−	0.0447659i	0.00157779	−	0.00157779i
$806$	5.22814	−	5.22814i	0.184153	−	0.184153i
$807$	−23.8271	−	23.8271i	−0.838754	−	0.838754i
$808$	3.11106	+	3.11106i	0.109447	+	0.109447i
$809$	−32.7418	−	32.7418i	−1.15114	−	1.15114i	−0.986324	−	0.164815i	$-0.947297\pi$
$809$	−32.7418	−	32.7418i	−1.15114	−	1.15114i	−0.164815	−	0.986324i	$-0.552703\pi$
$810$	7.39483			0.259828
$811$		−	0.242920i		−	0.00853008i	−0.999991	−	0.00426504i	$-0.998642\pi$
$811$		−	0.242920i		−	0.00853008i	0.999991	−	0.00426504i	$-0.00135761\pi$
$812$			3.13975i			0.110184i
$813$	15.8886	+	15.8886i	0.557237	+	0.557237i
$814$	−1.01308	+	1.01308i	−0.0355083	+	0.0355083i
$815$		−	0.0989964i		−	0.00346769i
$816$	1.65267			0.0578549
$817$	−0.350481	−	0.350481i	−0.0122618	−	0.0122618i
$818$			18.1791i			0.635616i
$819$	1.75703			0.0613955
$820$	3.27539	+	8.10815i	0.114382	+	0.283149i
$821$	17.2276			0.601246			0.300623	−	0.953743i	$-0.402805\pi$
$821$	17.2276			0.601246			0.300623	+	0.953743i	$0.402805\pi$
$822$			12.5591i			0.438051i
$823$	−1.20419	−	1.20419i	−0.0419753	−	0.0419753i	0.685808	−	0.727783i	$-0.259449\pi$
$823$	−1.20419	−	1.20419i	−0.0419753	−	0.0419753i	−0.727783	+	0.685808i	$0.759449\pi$
$824$	11.9793			0.417318
$825$		−	16.5859i		−	0.577448i
$826$	20.7558	−	20.7558i	0.722187	−	0.722187i
$827$	10.6519	+	10.6519i	0.370402	+	0.370402i	0.867624	−	0.497222i	$-0.165646\pi$
$827$	10.6519	+	10.6519i	0.370402	+	0.370402i	−0.497222	+	0.867624i	$0.665646\pi$
$828$		−	1.69395i		−	0.0588687i
$829$			48.7818i			1.69426i	0.531385	+	0.847131i	$0.321672\pi$
$829$			48.7818i			1.69426i	−0.531385	+	0.847131i	$0.678328\pi$
$830$	−10.8687			−0.377259
$831$	5.55717	+	5.55717i	0.192776	+	0.192776i
$832$	−4.73220	−	4.73220i	−0.164060	−	0.164060i
$833$	1.81421	+	1.81421i	0.0628587	+	0.0628587i
$834$	26.4362	−	26.4362i	0.915410	−	0.915410i
$835$	0.593687	−	0.593687i	0.0205454	−	0.0205454i
$836$	−3.60440			−0.124661
$837$	−4.08318	+	4.08318i	−0.141135	+	0.141135i
$838$	−8.37873			−0.289438
$839$	−15.3446	+	15.3446i	−0.529756	+	0.529756i	−0.920500	−	0.390743i	$-0.872218\pi$
$839$	−15.3446	+	15.3446i	−0.529756	+	0.529756i	0.390743	+	0.920500i	$0.372218\pi$
$840$		−	3.11297i		−	0.107408i
$841$		−	28.0906i		−	0.968641i
$842$	35.0941	−	35.0941i	1.20942	−	1.20942i
$843$	−68.1968			−2.34882
$844$	−58.6097	+	58.6097i	−2.01743	+	2.01743i
$845$	−5.27971			−0.181628
$846$	64.1347	−	64.1347i	2.20499	−	2.20499i
$847$	6.46829	−	6.46829i	0.222253	−	0.222253i
$848$	−2.06271	−	2.06271i	−0.0708336	−	0.0708336i
$849$	38.2231	+	38.2231i	1.31181	+	1.31181i
$850$	20.1501	+	20.1501i	0.691143	+	0.691143i
$851$	−0.0698362			−0.00239395
$852$		−	79.6500i		−	2.72876i
$853$		−	21.0013i		−	0.719071i	−0.933131	−	0.359536i	$-0.882935\pi$
$853$		−	21.0013i		−	0.719071i	0.933131	−	0.359536i	$-0.117065\pi$
$854$	−14.2932	−	14.2932i	−0.489104	−	0.489104i
$855$	−0.795297	+	0.795297i	−0.0271986	+	0.0271986i
$856$		−	37.2288i		−	1.27245i
$857$	56.0866			1.91588			0.957942	−	0.286963i	$-0.0926458\pi$
$857$	56.0866			1.91588			0.957942	+	0.286963i	$0.0926458\pi$
$858$	−2.91278	−	2.91278i	−0.0994407	−	0.0994407i
$859$			45.8687i			1.56502i	0.622637	+	0.782510i	$0.286061\pi$
$859$			45.8687i			1.56502i	−0.622637	+	0.782510i	$0.713939\pi$
$860$	−0.841568			−0.0286972
$861$	6.05360	+	14.9855i	0.206306	+	0.510705i
$862$	−20.5699			−0.700614
$863$			55.1007i			1.87565i	0.347109	+	0.937825i	$0.387163\pi$
$863$			55.1007i			1.87565i	−0.347109	+	0.937825i	$0.612837\pi$
$864$	3.54894	+	3.54894i	0.120737	+	0.120737i
$865$	−5.54544			−0.188551
$866$			34.5212i			1.17308i
$867$	−18.5927	+	18.5927i	−0.631442	+	0.631442i
$868$	−14.3555	−	14.3555i	−0.487256	−	0.487256i
$869$		−	8.83923i		−	0.299850i
$870$		−	2.29694i		−	0.0778735i
$871$	−4.14118			−0.140319
$872$	−37.6474	−	37.6474i	−1.27490	−	1.27490i
$873$	−14.5158	−	14.5158i	−0.491284	−	0.491284i
$874$	−0.199701	−	0.199701i	−0.00675499	−	0.00675499i
$875$	2.88261	−	2.88261i	0.0974501	−	0.0974501i
$876$	−62.7948	+	62.7948i	−2.12164	+	2.12164i
$877$	38.6959			1.30667			0.653334	−	0.757069i	$-0.273370\pi$
$877$	38.6959			1.30667			0.653334	+	0.757069i	$0.273370\pi$
$878$	−55.4986	+	55.4986i	−1.87299	+	1.87299i
$879$	−10.1892			−0.343674
$880$	−0.101877	+	0.101877i	−0.00343426	+	0.00343426i
$881$			13.8118i			0.465331i	0.972557	+	0.232666i	$0.0747448\pi$
$881$			13.8118i			0.465331i	−0.972557	+	0.232666i	$0.925255\pi$
$882$		−	7.75511i		−	0.261128i
$883$	−27.0737	+	27.0737i	−0.911101	+	0.911101i	−0.996359	−	0.0852576i	$-0.972829\pi$
$883$	−27.0737	+	27.0737i	−0.911101	+	0.911101i	0.0852576	+	0.996359i	$0.472829\pi$
$884$	4.40288			0.148085
$885$	−9.44617	+	9.44617i	−0.317529	+	0.317529i
$886$	−62.4711			−2.09876
$887$	10.4654	−	10.4654i	0.351394	−	0.351394i	−0.509234	−	0.860628i	$-0.670071\pi$
$887$	10.4654	−	10.4654i	0.351394	−	0.351394i	0.860628	+	0.509234i	$0.170071\pi$
$888$	−2.42816	+	2.42816i	−0.0814838	+	0.0814838i
$889$	−5.14080	−	5.14080i	−0.172417	−	0.172417i
$890$	−6.26063	−	6.26063i	−0.209857	−	0.209857i
$891$	−7.45797	−	7.45797i	−0.249851	−	0.249851i
$892$	1.98779			0.0665560
$893$		−	9.40729i		−	0.314803i
$894$		−	129.249i		−	4.32272i
$895$	−4.48743	−	4.48743i	−0.149998	−	0.149998i
$896$	−13.3075	+	13.3075i	−0.444572	+	0.444572i
$897$		−	0.200792i		−	0.00670424i
$898$	54.1960			1.80854
$899$	−4.15797	−	4.15797i	−0.138676	−	0.138676i
$900$		−	53.5844i		−	1.78615i
$901$	−29.3277			−0.977047
$902$	7.83476	−	18.4548i	0.260869	−	0.614476i
$903$	−1.55539			−0.0517602
$904$			37.3387i			1.24187i
$905$	0.105928	+	0.105928i	0.00352117	+	0.00352117i
$906$	0.736411			0.0244656
$907$			51.7518i			1.71839i	0.511648	+	0.859195i	$0.329035\pi$
$907$			51.7518i			1.71839i	−0.511648	+	0.859195i	$0.670965\pi$
$908$	−3.26203	+	3.26203i	−0.108254	+	0.108254i
$909$	−3.52726	−	3.52726i	−0.116992	−	0.116992i
$910$		−	0.497375i		−	0.0164878i
$911$		−	28.0756i		−	0.930185i	−0.885262	−	0.465093i	$-0.846021\pi$
$911$		−	28.0756i		−	0.930185i	0.885262	−	0.465093i	$-0.153979\pi$
$912$	−0.518116			−0.0171565
$913$	10.9615	+	10.9615i	0.362773	+	0.362773i
$914$	16.1627	+	16.1627i	0.534614	+	0.534614i
$915$	6.50498	+	6.50498i	0.215048	+	0.215048i
$916$	38.9866	−	38.9866i	1.28815	−	1.28815i
$917$	6.36871	−	6.36871i	0.210313	−	0.210313i
$918$	−5.52748			−0.182434
$919$	24.9829	−	24.9829i	0.824109	−	0.824109i	−0.162585	−	0.986695i	$-0.551983\pi$
$919$	24.9829	−	24.9829i	0.824109	−	0.824109i	0.986695	+	0.162585i	$0.0519832\pi$
$920$	−0.188232			−0.00620583
$921$	−10.2317	+	10.2317i	−0.337146	+	0.337146i
$922$			40.3267i			1.32809i
$923$		−	4.99555i		−	0.164431i
$924$	−7.99794	+	7.99794i	−0.263113	+	0.263113i
$925$	−2.20912			−0.0726353
$926$	1.74197	−	1.74197i	0.0572448	−	0.0572448i
$927$	−13.5819			−0.446087
$928$	−3.61394	+	3.61394i	−0.118633	+	0.118633i
$929$	23.4237	−	23.4237i	0.768505	−	0.768505i	−0.209338	−	0.977843i	$-0.567131\pi$
$929$	23.4237	−	23.4237i	0.768505	−	0.768505i	0.977843	+	0.209338i	$0.0671309\pi$
$930$	10.5020	+	10.5020i	0.344374	+	0.344374i
$931$	−0.568761	−	0.568761i	−0.0186404	−	0.0186404i
$932$	−52.5316	−	52.5316i	−1.72073	−	1.72073i
$933$	−18.8968			−0.618653
$934$			5.37924i			0.176014i
$935$			1.44849i			0.0473707i
$936$	−3.69399	−	3.69399i	−0.120742	−	0.120742i
$937$	40.2808	−	40.2808i	1.31592	−	1.31592i	0.398938	−	0.916978i	$-0.369379\pi$
$937$	40.2808	−	40.2808i	1.31592	−	1.31592i	0.916978	−	0.398938i	$-0.130621\pi$
$938$			18.2782i			0.596805i
$939$	−51.7523			−1.68887
$940$	−11.2943	−	11.2943i	−0.368379	−	0.368379i
$941$			9.80268i			0.319558i	0.987153	+	0.159779i	$0.0510782\pi$
$941$			9.80268i			0.319558i	−0.987153	+	0.159779i	$0.948922\pi$
$942$	46.0384			1.50001
$943$	0.906131	−	0.366044i	0.0295077	−	0.0119200i
$944$	−3.25616			−0.105979
$945$			0.388450i			0.0126363i
$946$	1.36433	+	1.36433i	0.0443583	+	0.0443583i
$947$	−12.1333			−0.394279			−0.197139	−	0.980375i	$-0.563165\pi$
$947$	−12.1333			−0.394279			−0.197139	+	0.980375i	$0.563165\pi$
$948$		−	53.9710i		−	1.75290i
$949$	−3.93841	+	3.93841i	−0.127846	+	0.127846i
$950$	−6.31712	−	6.31712i	−0.204954	−	0.204954i
$951$		−	66.1691i		−	2.14568i
$952$		−	7.62842i		−	0.247239i
$953$	36.7495			1.19043			0.595216	−	0.803566i	$-0.297066\pi$
$953$	36.7495			1.19043			0.595216	+	0.803566i	$0.297066\pi$
$954$	62.6827	+	62.6827i	2.02943	+	2.02943i
$955$	−6.04348	−	6.04348i	−0.195563	−	0.195563i
$956$	44.2345	+	44.2345i	1.43065	+	1.43065i
$957$	−2.31655	+	2.31655i	−0.0748834	+	0.0748834i
$958$	−27.1159	+	27.1159i	−0.876076	+	0.876076i
$959$	2.16286			0.0698424
$960$	9.50580	−	9.50580i	0.306798	−	0.306798i
$961$	7.02190			0.226513
$962$	−0.387960	+	0.387960i	−0.0125083	+	0.0125083i
$963$			42.2093i			1.36018i
$964$		−	65.9126i		−	2.12290i
$965$	−0.380665	+	0.380665i	−0.0122540	+	0.0122540i
$966$	−0.886248			−0.0285146
$967$	−31.6168	+	31.6168i	−1.01673	+	1.01673i	−0.0168693	+	0.999858i	$0.505370\pi$
$967$	−31.6168	+	31.6168i	−1.01673	+	1.01673i	−0.999858	+	0.0168693i	$0.994630\pi$
$968$	−27.1980			−0.874176
$969$	−3.68330	+	3.68330i	−0.118325	+	0.118325i
$970$	−4.10909	+	4.10909i	−0.131935	+	0.131935i
$971$	−22.8575	−	22.8575i	−0.733532	−	0.733532i	0.237786	−	0.971318i	$-0.423578\pi$
$971$	−22.8575	−	22.8575i	−0.733532	−	0.733532i	−0.971318	+	0.237786i	$0.923578\pi$
$972$	−52.0779	−	52.0779i	−1.67040	−	1.67040i
$973$	−4.55268	−	4.55268i	−0.145952	−	0.145952i
$974$	−77.3500			−2.47845
$975$		−	6.35161i		−	0.203414i
$976$			2.24231i			0.0717746i
$977$	1.55379	+	1.55379i	0.0497102	+	0.0497102i	0.731525	−	0.681815i	$-0.238809\pi$
$977$	1.55379	+	1.55379i	0.0497102	+	0.0497102i	−0.681815	+	0.731525i	$0.738809\pi$
$978$	−0.979934	+	0.979934i	−0.0313348	+	0.0313348i
$979$			12.6282i			0.403598i
$980$	−1.36570			−0.0436256
$981$	42.6839	+	42.6839i	1.36279	+	1.36279i
$982$			67.2697i			2.14666i
$983$	25.0325			0.798414			0.399207	−	0.916861i	$-0.369286\pi$
$983$	25.0325			0.798414			0.399207	+	0.916861i	$0.369286\pi$
$984$	18.7785	−	44.2327i	0.598637	−	1.41009i
$985$	3.07890			0.0981020
$986$		−	5.62872i		−	0.179255i
$987$	−20.8742	−	20.8742i	−0.664432	−	0.664432i
$988$	−1.38031			−0.0439137
$989$			0.0940500i			0.00299062i
$990$	3.09589	−	3.09589i	0.0983937	−	0.0983937i
$991$	33.6337	+	33.6337i	1.06841	+	1.06841i	0.997481	+	0.0709287i	$0.0225963\pi$
$991$	33.6337	+	33.6337i	1.06841	+	1.06841i	0.0709287	+	0.997481i	$0.477404\pi$
$992$		−	33.0471i		−	1.04925i
$993$			22.4607i			0.712768i
$994$	−22.0492			−0.699359
$995$	7.59742	+	7.59742i	0.240854	+	0.240854i
$996$	66.9295	+	66.9295i	2.12074	+	2.12074i
$997$	−25.1352	−	25.1352i	−0.796041	−	0.796041i	0.186428	−	0.982469i	$-0.440309\pi$
$997$	−25.1352	−	25.1352i	−0.796041	−	0.796041i	−0.982469	+	0.186428i	$0.940309\pi$
$998$	−63.0157	+	63.0157i	−1.99473	+	1.99473i
$999$	0.302997	−	0.302997i	0.00958640	−	0.00958640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.17	✓	40
41.32	even	4	inner	287.2.f.a.155.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.17	✓	40	1.1	even	1	trivial
287.2.f.a.155.4	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)

\(f(q)\)	\(=\)	\(q+2.30053i q^{2} +(1.78480 + 1.78480i) q^{3} -3.29242 q^{4} -0.414800i q^{5} +(-4.10598 + 4.10598i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.97325i q^{8} +3.37102i q^{9} +O(q^{10})\)	\(q+2.30053i q^{2} +(1.78480 + 1.78480i) q^{3} -3.29242 q^{4} -0.414800i q^{5} +(-4.10598 + 4.10598i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.97325i q^{8} +3.37102i q^{9} +0.954258 q^{10} +(-0.962406 - 0.962406i) q^{11} +(-5.87631 - 5.87631i) q^{12} +(-0.368555 - 0.368555i) q^{13} +(-1.62672 + 1.62672i) q^{14} +(0.740335 - 0.740335i) q^{15} +0.255198 q^{16} +(1.81421 - 1.81421i) q^{17} -7.75511 q^{18} +(-0.568761 + 0.568761i) q^{19} +1.36570i q^{20} +2.52409i q^{21} +(2.21404 - 2.21404i) q^{22} +0.152624 q^{23} +(5.30666 - 5.30666i) q^{24} +4.82794 q^{25} +(0.847872 - 0.847872i) q^{26} +(-0.662189 + 0.662189i) q^{27} +(-2.32809 - 2.32809i) q^{28} +(-0.674317 - 0.674317i) q^{29} +(1.70316 + 1.70316i) q^{30} +6.16619 q^{31} -5.35941i q^{32} -3.43540i q^{33} +(4.17364 + 4.17364i) q^{34} +(0.293308 - 0.293308i) q^{35} -11.0988i q^{36} -0.457569 q^{37} +(-1.30845 - 1.30845i) q^{38} -1.31559i q^{39} -1.23330 q^{40} +(5.93700 - 2.39833i) q^{41} -5.80673 q^{42} +0.616219i q^{43} +(3.16865 + 3.16865i) q^{44} +1.39830 q^{45} +0.351116i q^{46} +(-8.26999 + 8.26999i) q^{47} +(0.455478 + 0.455478i) q^{48} +1.00000i q^{49} +11.1068i q^{50} +6.47601 q^{51} +(1.21344 + 1.21344i) q^{52} +(-8.08276 - 8.08276i) q^{53} +(-1.52338 - 1.52338i) q^{54} +(-0.399206 + 0.399206i) q^{55} +(2.10241 - 2.10241i) q^{56} -2.03025 q^{57} +(1.55128 - 1.55128i) q^{58} -12.7593 q^{59} +(-2.43749 + 2.43749i) q^{60} +8.78654i q^{61} +14.1855i q^{62} +(-2.38367 + 2.38367i) q^{63} +12.8399 q^{64} +(-0.152877 + 0.152877i) q^{65} +7.90323 q^{66} +(5.61813 - 5.61813i) q^{67} +(-5.97315 + 5.97315i) q^{68} +(0.272404 + 0.272404i) q^{69} +(0.674763 + 0.674763i) q^{70} +(6.77721 + 6.77721i) q^{71} +10.0229 q^{72} -10.6861i q^{73} -1.05265i q^{74} +(8.61690 + 8.61690i) q^{75} +(1.87260 - 1.87260i) q^{76} -1.36105i q^{77} +3.02656 q^{78} +(4.59225 + 4.59225i) q^{79} -0.105856i q^{80} +7.74930 q^{81} +(5.51742 + 13.6582i) q^{82} -11.3897 q^{83} -8.31036i q^{84} +(-0.752535 - 0.752535i) q^{85} -1.41763 q^{86} -2.40704i q^{87} +(-2.86147 + 2.86147i) q^{88} +(-6.56072 - 6.56072i) q^{89} +3.21682i q^{90} -0.521216i q^{91} -0.502504 q^{92} +(11.0054 + 11.0054i) q^{93} +(-19.0253 - 19.0253i) q^{94} +(0.235922 + 0.235922i) q^{95} +(9.56547 - 9.56547i) q^{96} +(-4.30605 + 4.30605i) q^{97} -2.30053 q^{98} +(3.24429 - 3.24429i) 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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