LMFDB - Embedded newform 287.3.g.a.132.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(132,287)]

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([2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("287.132");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.g (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			132.12
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66341i q^{2} +(2.47686 - 2.47686i) q^{3} -3.09375 q^{4} +7.32409 q^{5} +(-6.59690 - 6.59690i) q^{6} +(-6.14216 - 3.35766i) q^{7} -2.41372i q^{8} -3.26970i q^{9} +O(q^{10})$	\(q-2.66341i q^{2} +(2.47686 - 2.47686i) q^{3} -3.09375 q^{4} +7.32409 q^{5} +(-6.59690 - 6.59690i) q^{6} +(-6.14216 - 3.35766i) q^{7} -2.41372i q^{8} -3.26970i q^{9} -19.5070i q^{10} +(8.73479 + 8.73479i) q^{11} +(-7.66279 + 7.66279i) q^{12} +(-0.633082 + 0.633082i) q^{13} +(-8.94283 + 16.3591i) q^{14} +(18.1408 - 18.1408i) q^{15} -18.8037 q^{16} +(-5.21316 - 5.21316i) q^{17} -8.70855 q^{18} +(-20.3757 - 20.3757i) q^{19} -22.6589 q^{20} +(-23.5298 + 6.89682i) q^{21} +(23.2643 - 23.2643i) q^{22} +30.6331 q^{23} +(-5.97846 - 5.97846i) q^{24} +28.6423 q^{25} +(1.68616 + 1.68616i) q^{26} +(14.1932 + 14.1932i) q^{27} +(19.0023 + 10.3878i) q^{28} +(20.7022 + 20.7022i) q^{29} +(-48.3163 - 48.3163i) q^{30} -0.808528i q^{31} +40.4271i q^{32} +43.2698 q^{33} +(-13.8848 + 13.8848i) q^{34} +(-44.9857 - 24.5918i) q^{35} +10.1156i q^{36} -44.3759 q^{37} +(-54.2689 + 54.2689i) q^{38} +3.13611i q^{39} -17.6783i q^{40} +(-34.1924 + 22.6248i) q^{41} +(18.3690 + 62.6694i) q^{42} +43.1807i q^{43} +(-27.0232 - 27.0232i) q^{44} -23.9476i q^{45} -81.5885i q^{46} +(29.0146 + 29.0146i) q^{47} +(-46.5742 + 46.5742i) q^{48} +(26.4522 + 41.2466i) q^{49} -76.2861i q^{50} -25.8246 q^{51} +(1.95860 - 1.95860i) q^{52} +(17.2800 + 17.2800i) q^{53} +(37.8022 - 37.8022i) q^{54} +(63.9744 + 63.9744i) q^{55} +(-8.10446 + 14.8255i) q^{56} -100.936 q^{57} +(55.1383 - 55.1383i) q^{58} -31.5623i q^{59} +(-56.1229 + 56.1229i) q^{60} +2.92933 q^{61} -2.15344 q^{62} +(-10.9786 + 20.0830i) q^{63} +32.4590 q^{64} +(-4.63675 + 4.63675i) q^{65} -115.245i q^{66} +(34.5924 - 34.5924i) q^{67} +(16.1282 + 16.1282i) q^{68} +(75.8740 - 75.8740i) q^{69} +(-65.4980 + 119.815i) q^{70} +(8.12779 + 8.12779i) q^{71} -7.89215 q^{72} +28.9361 q^{73} +118.191i q^{74} +(70.9430 - 70.9430i) q^{75} +(63.0374 + 63.0374i) q^{76} +(-24.3220 - 82.9789i) q^{77} +8.35276 q^{78} +(50.8049 + 50.8049i) q^{79} -137.720 q^{80} +99.7364 q^{81} +(60.2590 + 91.0683i) q^{82} -40.1662i q^{83} +(72.7951 - 21.3370i) q^{84} +(-38.1817 - 38.1817i) q^{85} +115.008 q^{86} +102.553 q^{87} +(21.0834 - 21.0834i) q^{88} +(-6.72411 + 6.72411i) q^{89} -63.7822 q^{90} +(6.01416 - 1.76281i) q^{91} -94.7711 q^{92} +(-2.00261 - 2.00261i) q^{93} +(77.2778 - 77.2778i) q^{94} +(-149.234 - 149.234i) q^{95} +(100.132 + 100.132i) q^{96} +(-116.099 - 116.099i) q^{97} +(109.857 - 70.4531i) q^{98} +(28.5602 - 28.5602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) $ 108 * q - 216 * q^4 - 2 * q^7	$ 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) $ 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * 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 $

$2$		−	2.66341i		−	1.33170i	−0.746084	−	0.665852i	$-0.768068\pi$
$2$		−	2.66341i		−	1.33170i	0.746084	−	0.665852i	$-0.231932\pi$
$3$	2.47686	−	2.47686i	0.825621	−	0.825621i	−0.161287	−	0.986908i	$-0.551564\pi$
$3$	2.47686	−	2.47686i	0.825621	−	0.825621i	0.986908	+	0.161287i	$0.0515643\pi$
$4$	−3.09375			−0.773437
$5$	7.32409			1.46482			0.732409	−	0.680865i	$-0.238396\pi$
$5$	7.32409			1.46482			0.732409	+	0.680865i	$0.238396\pi$
$6$	−6.59690	−	6.59690i	−1.09948	−	1.09948i
$7$	−6.14216	−	3.35766i	−0.877451	−	0.479666i
$7$	−6.14216	−	3.35766i	−0.877451	−	0.479666i
$8$		−	2.41372i		−	0.301715i
$9$		−	3.26970i		−	0.363300i
$10$		−	19.5070i		−	1.95070i
$11$	8.73479	+	8.73479i	0.794072	+	0.794072i	0.982153	−	0.188082i	$-0.0602270\pi$
$11$	8.73479	+	8.73479i	0.794072	+	0.794072i	−0.188082	+	0.982153i	$0.560227\pi$
$12$	−7.66279	+	7.66279i	−0.638566	+	0.638566i
$13$	−0.633082	+	0.633082i	−0.0486986	+	0.0486986i	−0.731037	−	0.682338i	$-0.760963\pi$
$13$	−0.633082	+	0.633082i	−0.0486986	+	0.0486986i	0.682338	+	0.731037i	$0.260963\pi$
$14$	−8.94283	+	16.3591i	−0.638773	+	1.16851i
$15$	18.1408	−	18.1408i	1.20938	−	1.20938i
$16$	−18.8037			−1.17523
$17$	−5.21316	−	5.21316i	−0.306657	−	0.306657i	0.536955	−	0.843611i	$-0.319575\pi$
$17$	−5.21316	−	5.21316i	−0.306657	−	0.306657i	−0.843611	+	0.536955i	$0.819575\pi$
$18$	−8.70855			−0.483809
$19$	−20.3757	−	20.3757i	−1.07241	−	1.07241i	−0.997165	−	0.0752423i	$-0.976027\pi$
$19$	−20.3757	−	20.3757i	−1.07241	−	1.07241i	−0.0752423	−	0.997165i	$-0.523973\pi$
$20$	−22.6589			−1.13294
$21$	−23.5298	+	6.89682i	−1.12046	+	0.328420i
$22$	23.2643	−	23.2643i	1.05747	−	1.05747i
$23$	30.6331			1.33187			0.665937	−	0.746008i	$-0.268032\pi$
$23$	30.6331			1.33187			0.665937	+	0.746008i	$0.268032\pi$
$24$	−5.97846	−	5.97846i	−0.249102	−	0.249102i
$25$	28.6423			1.14569
$26$	1.68616	+	1.68616i	0.0648522	+	0.0648522i
$27$	14.1932	+	14.1932i	0.525673	+	0.525673i
$28$	19.0023	+	10.3878i	0.678653	+	0.370991i
$29$	20.7022	+	20.7022i	0.713868	+	0.713868i	0.967342	−	0.253474i	$-0.0815734\pi$
$29$	20.7022	+	20.7022i	0.713868	+	0.713868i	−0.253474	+	0.967342i	$0.581573\pi$
$30$	−48.3163	−	48.3163i	−1.61054	−	1.61054i
$31$		−	0.808528i		−	0.0260816i	−0.999915	−	0.0130408i	$-0.995849\pi$
$31$		−	0.808528i		−	0.0260816i	0.999915	−	0.0130408i	$-0.00415113\pi$
$32$			40.4271i			1.26335i
$33$	43.2698			1.31120
$34$	−13.8848	+	13.8848i	−0.408376	+	0.408376i
$35$	−44.9857	−	24.5918i	−1.28531	−	0.702623i
$36$			10.1156i			0.280990i
$37$	−44.3759			−1.19935			−0.599674	−	0.800244i	$-0.704703\pi$
$37$	−44.3759			−1.19935			−0.599674	+	0.800244i	$0.704703\pi$
$38$	−54.2689	+	54.2689i	−1.42813	+	1.42813i
$39$			3.13611i			0.0804132i
$40$		−	17.6783i		−	0.441958i
$41$	−34.1924	+	22.6248i	−0.833961	+	0.551824i
$41$	−34.1924	+	22.6248i	−0.833961	+	0.551824i
$42$	18.3690	+	62.6694i	0.437358	+	1.49213i
$43$			43.1807i			1.00420i	0.864809	+	0.502101i	$0.167440\pi$
$43$			43.1807i			1.00420i	−0.864809	+	0.502101i	$0.832560\pi$
$44$	−27.0232	−	27.0232i	−0.614164	−	0.614164i
$45$		−	23.9476i		−	0.532169i
$46$		−	81.5885i		−	1.77366i
$47$	29.0146	+	29.0146i	0.617332	+	0.617332i	0.944846	−	0.327514i	$-0.106211\pi$
$47$	29.0146	+	29.0146i	0.617332	+	0.617332i	−0.327514	+	0.944846i	$0.606211\pi$
$48$	−46.5742	+	46.5742i	−0.970297	+	0.970297i
$49$	26.4522	+	41.2466i	0.539841	+	0.841767i
$50$		−	76.2861i		−	1.52572i
$51$	−25.8246			−0.506364
$52$	1.95860	−	1.95860i	0.0376653	−	0.0376653i
$53$	17.2800	+	17.2800i	0.326037	+	0.326037i	0.851077	−	0.525040i	$-0.175950\pi$
$53$	17.2800	+	17.2800i	0.326037	+	0.326037i	−0.525040	+	0.851077i	$0.675950\pi$
$54$	37.8022	−	37.8022i	0.700041	−	0.700041i
$55$	63.9744	+	63.9744i	1.16317	+	1.16317i
$56$	−8.10446	+	14.8255i	−0.144723	+	0.264740i
$57$	−100.936			−1.77080
$58$	55.1383	−	55.1383i	0.950661	−	0.950661i
$59$		−	31.5623i		−	0.534954i	−0.963564	−	0.267477i	$-0.913810\pi$
$59$		−	31.5623i		−	0.534954i	0.963564	−	0.267477i	$-0.0861900\pi$
$60$	−56.1229	+	56.1229i	−0.935382	+	0.935382i
$61$	2.92933			0.0480218			0.0240109	−	0.999712i	$-0.492356\pi$
$61$	2.92933			0.0480218			0.0240109	+	0.999712i	$0.492356\pi$
$62$	−2.15344			−0.0347329
$63$	−10.9786	+	20.0830i	−0.174263	+	0.318778i
$64$	32.4590			0.507172
$65$	−4.63675	+	4.63675i	−0.0713346	+	0.0713346i
$66$		−	115.245i		−	1.74614i
$67$	34.5924	−	34.5924i	0.516304	−	0.516304i	−0.400147	−	0.916451i	$-0.631041\pi$
$67$	34.5924	−	34.5924i	0.516304	−	0.516304i	0.916451	+	0.400147i	$0.131041\pi$
$68$	16.1282	+	16.1282i	0.237179	+	0.237179i
$69$	75.8740	−	75.8740i	1.09962	−	1.09962i
$70$	−65.4980	+	119.815i	−0.935686	+	1.71165i
$71$	8.12779	+	8.12779i	0.114476	+	0.114476i	0.762024	−	0.647548i	$-0.224206\pi$
$71$	8.12779	+	8.12779i	0.114476	+	0.114476i	−0.647548	+	0.762024i	$0.724206\pi$
$72$	−7.89215			−0.109613
$73$	28.9361			0.396385			0.198192	−	0.980163i	$-0.436493\pi$
$73$	28.9361			0.396385			0.198192	+	0.980163i	$0.436493\pi$
$74$			118.191i			1.59718i
$75$	70.9430	−	70.9430i	0.945906	−	0.945906i
$76$	63.0374	+	63.0374i	0.829440	+	0.829440i
$77$	−24.3220	−	82.9789i	−0.315870	−	1.07765i
$78$	8.35276			0.107087
$79$	50.8049	+	50.8049i	0.643099	+	0.643099i	0.951316	−	0.308217i	$-0.0997322\pi$
$79$	50.8049	+	50.8049i	0.643099	+	0.643099i	−0.308217	+	0.951316i	$0.599732\pi$
$80$	−137.720			−1.72150
$81$	99.7364			1.23131
$82$	60.2590	+	91.0683i	0.734866	+	1.11059i
$83$		−	40.1662i		−	0.483930i	−0.970285	−	0.241965i	$-0.922208\pi$
$83$		−	40.1662i		−	0.483930i	0.970285	−	0.241965i	$-0.0777920\pi$
$84$	72.7951	−	21.3370i	0.866608	−	0.254012i
$85$	−38.1817	−	38.1817i	−0.449196	−	0.449196i
$86$	115.008			1.33730
$87$	102.553			1.17877
$88$	21.0834	−	21.0834i	0.239584	−	0.239584i
$89$	−6.72411	+	6.72411i	−0.0755518	+	0.0755518i	−0.743873	−	0.668321i	$-0.767013\pi$
$89$	−6.72411	+	6.72411i	−0.0755518	+	0.0755518i	0.668321	+	0.743873i	$0.267013\pi$
$90$	−63.7822			−0.708691
$91$	6.01416	−	1.76281i	0.0660897	−	0.0193716i
$92$	−94.7711			−1.03012
$93$	−2.00261	−	2.00261i	−0.0215335	−	0.0215335i
$94$	77.2778	−	77.2778i	0.822104	−	0.822104i
$95$	−149.234	−	149.234i	−1.57088	−	1.57088i
$96$	100.132	+	100.132i	1.04305	+	1.04305i
$97$	−116.099	−	116.099i	−1.19690	−	1.19690i	−0.975091	−	0.221804i	$-0.928805\pi$
$97$	−116.099	−	116.099i	−1.19690	−	1.19690i	−0.221804	−	0.975091i	$-0.571195\pi$
$98$	109.857	−	70.4531i	1.12098	−	0.718909i
$99$	28.5602	−	28.5602i	0.288486	−	0.288486i
$100$	−88.6119			−0.886119
$101$	−141.704	−	141.704i	−1.40301	−	1.40301i	−0.790333	−	0.612678i	$-0.790092\pi$
$101$	−141.704	−	141.704i	−1.40301	−	1.40301i	−0.612678	−	0.790333i	$-0.709908\pi$
$102$			68.7814i			0.674328i
$103$	131.284			1.27460			0.637301	−	0.770615i	$-0.280051\pi$
$103$	131.284			1.27460			0.637301	+	0.770615i	$0.280051\pi$
$104$	1.52808	+	1.52808i	0.0146931	+	0.0146931i
$105$	−172.334	+	50.5129i	−1.64128	+	0.481075i
$106$	46.0236	−	46.0236i	0.434185	−	0.434185i
$107$	139.563			1.30433			0.652164	−	0.758078i	$-0.273861\pi$
$107$	139.563			1.30433			0.652164	+	0.758078i	$0.273861\pi$
$108$	−43.9101	−	43.9101i	−0.406575	−	0.406575i
$109$	−125.434	+	125.434i	−1.15077	+	1.15077i	−0.164372	+	0.986398i	$0.552560\pi$
$109$	−125.434	+	125.434i	−1.15077	+	1.15077i	−0.986398	+	0.164372i	$0.947440\pi$
$110$	170.390	−	170.390i	1.54900	−	1.54900i
$111$	−109.913	+	109.913i	−0.990207	+	0.990207i
$112$	115.495	+	63.1365i	1.03121	+	0.563719i
$113$	109.663			0.970470			0.485235	−	0.874384i	$-0.338734\pi$
$113$	109.663			0.970470			0.485235	+	0.874384i	$0.338734\pi$
$114$			268.833i			2.35819i
$115$	224.360			1.95095
$116$	−64.0473	−	64.0473i	−0.552132	−	0.552132i
$117$	2.06999	+	2.06999i	0.0176922	+	0.0176922i
$118$	−84.0633			−0.712401
$119$	14.5160	+	49.5241i	0.121983	+	0.416169i
$120$	−43.7868	−	43.7868i	−0.364890	−	0.364890i
$121$			31.5931i			0.261100i
$122$		−	7.80200i		−	0.0639508i
$123$	−28.6514	+	140.728i	−0.232938	+	1.14413i
$124$			2.50138i			0.0201724i
$125$	26.6762			0.213410
$126$	53.4893	+	29.2404i	0.424518	+	0.232066i
$127$	−53.0812			−0.417963			−0.208981	−	0.977920i	$-0.567015\pi$
$127$	−53.0812			−0.417963			−0.208981	+	0.977920i	$0.567015\pi$
$128$			75.2567i			0.587943i
$129$	106.953	+	106.953i	0.829091	+	0.829091i
$130$	12.3496	+	12.3496i	0.0949966	+	0.0949966i
$131$	50.1588			0.382891			0.191446	−	0.981503i	$-0.438682\pi$
$131$	50.1588			0.382891			0.191446	+	0.981503i	$0.438682\pi$
$132$	−133.866			−1.01413
$133$	56.7362	+	193.566i	0.426588	+	1.45538i
$134$	−92.1336	−	92.1336i	−0.687564	−	0.687564i
$135$	103.952	+	103.952i	0.770015	+	0.770015i
$136$	−12.5831	+	12.5831i	−0.0925230	+	0.0925230i
$137$	−96.1499	+	96.1499i	−0.701824	+	0.701824i	−0.964802	−	0.262978i	$-0.915295\pi$
$137$	−96.1499	+	96.1499i	−0.701824	+	0.701824i	0.262978	+	0.964802i	$0.415295\pi$
$138$	−202.084	−	202.084i	−1.46437	−	1.46437i
$139$		−	141.693i		−	1.01937i	−0.860360	−	0.509687i	$-0.829761\pi$
$139$		−	141.693i		−	1.01937i	0.860360	−	0.509687i	$-0.170239\pi$
$140$	139.174	+	76.0808i	0.994103	+	0.543435i
$141$	143.730			1.01936
$142$	21.6476	−	21.6476i	0.152448	−	0.152448i
$143$	−11.0597			−0.0773404
$144$			61.4826i			0.426962i
$145$	151.624	+	151.624i	1.04569	+	1.04569i
$146$		−	77.0687i		−	0.527868i
$147$	167.681	+	36.6436i	1.14068	+	0.249276i
$148$	137.288			0.927620
$149$	205.771	−	205.771i	1.38101	−	1.38101i	0.538189	−	0.842824i	$-0.319109\pi$
$149$	205.771	−	205.771i	1.38101	−	1.38101i	0.842824	−	0.538189i	$-0.180891\pi$
$150$	−188.950	−	188.950i	−1.25967	−	1.25967i
$151$	−198.905	−	198.905i	−1.31725	−	1.31725i	−0.915944	−	0.401305i	$-0.868557\pi$
$151$	−198.905	−	198.905i	−1.31725	−	1.31725i	−0.401305	−	0.915944i	$-0.631443\pi$
$152$	−49.1814	+	49.1814i	−0.323562	+	0.323562i
$153$	−17.0455	+	17.0455i	−0.111408	+	0.111408i
$154$	−221.007	+	64.7794i	−1.43511	+	0.420646i
$155$		−	5.92173i		−	0.0382047i
$156$		−	9.70235i		−	0.0621945i
$157$	−198.310	+	198.310i	−1.26312	+	1.26312i	−0.313549	+	0.949572i	$0.601518\pi$
$157$	−198.310	+	198.310i	−1.26312	+	1.26312i	−0.949572	+	0.313549i	$0.898482\pi$
$158$	135.314	−	135.314i	0.856418	−	0.856418i
$159$	85.6002			0.538366
$160$			296.092i			1.85057i
$161$	−188.153	−	102.856i	−1.16865	−	0.638855i
$162$		−	265.639i		−	1.63975i
$163$	−87.2170			−0.535073			−0.267537	−	0.963548i	$-0.586210\pi$
$163$	−87.2170			−0.535073			−0.267537	+	0.963548i	$0.586210\pi$
$164$	105.783	−	69.9953i	0.645016	−	0.426801i
$165$	316.911			1.92068
$166$	−106.979			−0.644452
$167$	−30.4113	+	30.4113i	−0.182104	+	0.182104i	−0.792272	−	0.610168i	$-0.791102\pi$
$167$	−30.4113	+	30.4113i	−0.182104	+	0.182104i	0.610168	+	0.792272i	$0.291102\pi$
$168$	16.6470	+	56.7943i	0.0990893	+	0.338061i
$169$			168.198i			0.995257i
$170$	−101.693	+	101.693i	−0.598196	+	0.598196i
$171$	−66.6226	+	66.6226i	−0.389606	+	0.389606i
$172$		−	133.590i		−	0.776687i
$173$	−69.1633			−0.399788			−0.199894	−	0.979818i	$-0.564060\pi$
$173$	−69.1633			−0.399788			−0.199894	+	0.979818i	$0.564060\pi$
$174$		−	273.140i		−	1.56977i
$175$	−175.925	−	96.1710i	−1.00529	−	0.549549i
$176$	−164.247	−	164.247i	−0.933219	−	0.933219i
$177$	−78.1755	−	78.1755i	−0.441669	−	0.441669i
$178$	17.9091	+	17.9091i	0.100613	+	0.100613i
$179$	−36.7757	+	36.7757i	−0.205451	+	0.205451i	−0.802331	−	0.596880i	$-0.796407\pi$
$179$	−36.7757	+	36.7757i	−0.205451	+	0.205451i	0.596880	+	0.802331i	$0.296407\pi$
$180$			74.0878i			0.411599i
$181$	128.059	+	128.059i	0.707508	+	0.707508i	0.966011	−	0.258502i	$-0.0832289\pi$
$181$	128.059	+	128.059i	0.707508	+	0.707508i	−0.258502	+	0.966011i	$0.583229\pi$
$182$	−4.69510	−	16.0182i	−0.0257972	−	0.0880120i
$183$	7.25554	−	7.25554i	0.0396478	−	0.0396478i
$184$		−	73.9398i		−	0.401847i
$185$	−325.013			−1.75683
$186$	−5.33378	+	5.33378i	−0.0286762	+	0.0286762i
$187$		−	91.0717i		−	0.487015i
$188$	−89.7639	−	89.7639i	−0.477467	−	0.477467i
$189$	−39.5208	−	134.832i	−0.209105	−	0.713399i
$190$	−397.470	+	397.470i	−2.09195	+	2.09195i
$191$	84.4157	−	84.4157i	0.441967	−	0.441967i	−0.450706	−	0.892673i	$-0.648828\pi$
$191$	84.4157	−	84.4157i	0.441967	−	0.441967i	0.892673	+	0.450706i	$0.148828\pi$
$192$	80.3966	−	80.3966i	0.418732	−	0.418732i
$193$	85.0416	+	85.0416i	0.440630	+	0.440630i	0.892224	−	0.451594i	$-0.149144\pi$
$193$	85.0416	+	85.0416i	0.440630	+	0.440630i	−0.451594	+	0.892224i	$0.649144\pi$
$194$	−309.219	+	309.219i	−1.59391	+	1.59391i
$195$			22.9692i			0.117791i
$196$	−81.8365	−	127.606i	−0.417533	−	0.651053i
$197$			322.497i			1.63704i	0.574476	+	0.818521i	$0.305206\pi$
$197$			322.497i			1.63704i	−0.574476	+	0.818521i	$0.694794\pi$
$198$	−76.0674	−	76.0674i	−0.384179	−	0.384179i
$199$	−102.216	−	102.216i	−0.513648	−	0.513648i	0.401994	−	0.915642i	$-0.368317\pi$
$199$	−102.216	−	102.216i	−0.513648	−	0.513648i	−0.915642	+	0.401994i	$0.868317\pi$
$200$		−	69.1344i		−	0.345672i
$201$		−	171.361i		−	0.852543i
$202$	−377.416	+	377.416i	−1.86840	+	1.86840i
$203$	−57.6451	−	196.667i	−0.283966	−	0.968802i
$204$	79.8947			0.391641
$205$	−250.428	+	165.706i	−1.22160	+	0.808321i
$206$		−	349.663i		−	1.69739i
$207$		−	100.161i		−	0.483870i
$208$	11.9043	−	11.9043i	0.0572322	−	0.0572322i
$209$		−	355.956i		−	1.70314i
$210$	134.537	+	458.996i	0.640650	+	2.18569i
$211$	−226.392	+	226.392i	−1.07295	+	1.07295i	−0.0758294	+	0.997121i	$0.524160\pi$
$211$	−226.392	+	226.392i	−1.07295	+	1.07295i	−0.997121	+	0.0758294i	$0.975840\pi$
$212$	−53.4598	−	53.4598i	−0.252169	−	0.252169i
$213$	40.2628			0.189027
$214$		−	371.713i		−	1.73698i
$215$			316.259i			1.47097i
$216$	34.2583	−	34.2583i	0.158603	−	0.158603i
$217$	−2.71476	+	4.96611i	−0.0125104	+	0.0228853i
$218$	334.082	+	334.082i	1.53249	+	1.53249i
$219$	71.6708	−	71.6708i	0.327264	−	0.327264i
$220$	−197.921	−	197.921i	−0.899639	−	0.899639i
$221$	6.60072			0.0298675
$222$	292.743	+	292.743i	1.31866	+	1.31866i
$223$		−	3.54814i		−	0.0159109i	−0.999968	−	0.00795547i	$-0.997468\pi$
$223$		−	3.54814i		−	0.0159109i	0.999968	−	0.00795547i	$-0.00253233\pi$
$224$	135.741	−	248.310i	0.605984	−	1.10853i
$225$		−	93.6517i		−	0.416230i
$226$		−	292.078i		−	1.29238i
$227$	129.703	+	129.703i	0.571379	+	0.571379i	0.932514	−	0.361134i	$-0.117610\pi$
$227$	129.703	+	129.703i	0.571379	+	0.571379i	−0.361134	+	0.932514i	$0.617610\pi$
$228$	312.270			1.36961
$229$	199.976	+	199.976i	0.873257	+	0.873257i	0.992826	−	0.119569i	$-0.0381514\pi$
$229$	199.976	+	199.976i	0.873257	+	0.873257i	−0.119569	+	0.992826i	$0.538151\pi$
$230$		−	597.561i		−	2.59809i
$231$	−265.770	−	145.285i	−1.15052	−	0.628940i
$232$	49.9693	−	49.9693i	0.215385	−	0.215385i
$233$	−35.2148	−	35.2148i	−0.151136	−	0.151136i	0.627489	−	0.778625i	$-0.284083\pi$
$233$	−35.2148	−	35.2148i	−0.151136	−	0.151136i	−0.778625	+	0.627489i	$0.784083\pi$
$234$	5.51323	−	5.51323i	0.0235608	−	0.0235608i
$235$	212.506	+	212.506i	0.904279	+	0.904279i
$236$			97.6458i			0.413753i
$237$	251.673			1.06191
$238$	131.903	−	38.6621i	0.554214	−	0.162446i
$239$	−232.023	−	232.023i	−0.970806	−	0.970806i	0.0287802	−	0.999586i	$-0.490838\pi$
$239$	−232.023	−	232.023i	−0.970806	−	0.970806i	−0.999586	+	0.0287802i	$0.990838\pi$
$240$	−341.114	+	341.114i	−1.42131	+	1.42131i
$241$	−332.945			−1.38152			−0.690758	−	0.723086i	$-0.742723\pi$
$241$	−332.945			−1.38152			−0.690758	+	0.723086i	$0.742723\pi$
$242$	84.1453			0.347708
$243$	119.295	−	119.295i	0.490925	−	0.490925i
$244$	−9.06260			−0.0371418
$245$	193.738	+	302.094i	0.790769	+	1.23303i
$246$	374.817	+	76.3104i	1.52365	+	0.310205i
$247$	25.7990			0.104450
$248$	−1.95156			−0.00786920
$249$	−99.4863	−	99.4863i	−0.399543	−	0.399543i
$250$		−	71.0497i		−	0.284199i
$251$	20.7700			0.0827491			0.0413745	−	0.999144i	$-0.486826\pi$
$251$	20.7700			0.0827491			0.0413745	+	0.999144i	$0.486826\pi$
$252$	33.9649	−	62.1318i	0.134781	−	0.246555i
$253$	267.574	+	267.574i	1.05760	+	1.05760i
$254$			141.377i			0.556603i
$255$	−189.141			−0.741731
$256$	330.276			1.29014
$257$	−16.2323	+	16.2323i	−0.0631606	+	0.0631606i	−0.737982	−	0.674821i	$-0.764221\pi$
$257$	−16.2323	+	16.2323i	−0.0631606	+	0.0631606i	0.674821	+	0.737982i	$0.264221\pi$
$258$	284.859	−	284.859i	1.10410	−	1.10410i
$259$	272.564	+	148.999i	1.05237	+	0.575287i
$260$	14.3449	−	14.3449i	0.0551728	−	0.0551728i
$261$	67.6899	−	67.6899i	0.259348	−	0.259348i
$262$		−	133.593i		−	0.509898i
$263$	−95.3791	+	95.3791i	−0.362658	+	0.362658i	−0.864791	−	0.502133i	$-0.832549\pi$
$263$	−95.3791	+	95.3791i	−0.362658	+	0.362658i	0.502133	+	0.864791i	$0.332549\pi$
$264$		−	104.441i		−	0.395610i
$265$	126.560	+	126.560i	0.477585	+	0.477585i
$266$	515.545	−	151.112i	1.93814	−	0.568089i
$267$			33.3094i			0.124754i
$268$	−107.020	+	107.020i	−0.399328	+	0.399328i
$269$		−	263.468i		−	0.979437i	−0.871881	−	0.489718i	$-0.837100\pi$
$269$		−	263.468i		−	0.979437i	0.871881	−	0.489718i	$-0.162900\pi$
$270$	276.867	−	276.867i	1.02543	−	1.02543i
$271$			90.0254i			0.332197i	0.986109	+	0.166098i	$0.0531170\pi$
$271$			90.0254i			0.332197i	−0.986109	+	0.166098i	$0.946883\pi$
$272$	98.0268	+	98.0268i	0.360393	+	0.360393i
$273$	10.5300	−	19.2625i	0.0385715	−	0.0705586i
$274$	256.086	+	256.086i	0.934622	+	0.934622i
$275$	250.184	+	250.184i	0.909760	+	0.909760i
$276$	−234.735	+	234.735i	−0.850489	+	0.850489i
$277$	235.917			0.851685			0.425843	−	0.904797i	$-0.359978\pi$
$277$	235.917			0.851685			0.425843	+	0.904797i	$0.359978\pi$
$278$	−377.387			−1.35751
$279$	−2.64365			−0.00947544
$280$	−59.3578	+	108.583i	−0.211992	+	0.387796i
$281$	−376.454	+	376.454i	−1.33969	+	1.33969i	−0.443339	+	0.896354i	$0.646206\pi$
$281$	−376.454	+	376.454i	−1.33969	+	1.33969i	−0.896354	+	0.443339i	$0.853794\pi$
$282$		−	382.813i		−	1.35749i
$283$		−	20.1086i		−	0.0710552i	−0.999369	−	0.0355276i	$-0.988689\pi$
$283$		−	20.1086i		−	0.0710552i	0.999369	−	0.0355276i	$-0.0113112\pi$
$284$	−25.1453	−	25.1453i	−0.0885399	−	0.0885399i
$285$	−739.263			−2.59391
$286$			29.4564i			0.102995i
$287$	285.981	−	24.1585i	0.996451	−	0.0841759i
$288$	132.185			0.458974
$289$		−	234.646i		−	0.811923i
$290$	403.838	−	403.838i	1.39254	−	1.39254i
$291$	−575.122			−1.97636
$292$	−89.5210			−0.306579
$293$	−384.273	−	384.273i	−1.31151	−	1.31151i	−0.920301	−	0.391212i	$-0.872056\pi$
$293$	−384.273	−	384.273i	−1.31151	−	1.31151i	−0.391212	−	0.920301i	$-0.627944\pi$
$294$	97.5969	−	446.602i	0.331962	−	1.51905i
$295$		−	231.165i		−	0.783610i
$296$			107.111i			0.361862i
$297$			247.949i			0.834844i
$298$	−548.052	−	548.052i	−1.83910	−	1.83910i
$299$	−19.3933	+	19.3933i	−0.0648604	+	0.0648604i
$300$	−219.480	+	219.480i	−0.731599	+	0.731599i
$301$	144.986	−	265.223i	0.481682	−	0.881139i
$302$	−529.765	+	529.765i	−1.75419	+	1.75419i
$303$	−701.963			−2.31671
$304$	383.140	+	383.140i	1.26033	+	1.26033i
$305$	21.4547			0.0703431
$306$	45.3991	+	45.3991i	0.148363	+	0.148363i
$307$	424.957			1.38423			0.692113	−	0.721790i	$-0.256680\pi$
$307$	424.957			1.38423			0.692113	+	0.721790i	$0.256680\pi$
$308$	75.2461	+	256.716i	0.244306	+	0.833493i
$309$	325.173	−	325.173i	1.05234	−	1.05234i
$310$	−15.7720			−0.0508774
$311$	−311.857	−	311.857i	−1.00275	−	1.00275i	−0.999996	−	0.00275862i	$-0.999122\pi$
$311$	−311.857	−	311.857i	−1.00275	−	1.00275i	−0.00275862	−	0.999996i	$-0.500878\pi$
$312$	7.56971			0.0242619
$313$	−122.272	−	122.272i	−0.390645	−	0.390645i	0.484273	−	0.874917i	$-0.339084\pi$
$313$	−122.272	−	122.272i	−0.390645	−	0.390645i	−0.874917	+	0.484273i	$0.839084\pi$
$314$	528.181	+	528.181i	1.68210	+	1.68210i
$315$	−80.4079	+	147.090i	−0.255263	+	0.466952i
$316$	−157.177	−	157.177i	−0.497397	−	0.497397i
$317$	−148.437	−	148.437i	−0.468255	−	0.468255i	0.433094	−	0.901349i	$-0.357422\pi$
$317$	−148.437	−	148.437i	−0.468255	−	0.468255i	−0.901349	+	0.433094i	$0.857422\pi$
$318$		−	227.988i		−	0.716944i
$319$			361.658i			1.13372i
$320$	237.733			0.742915
$321$	345.679	−	345.679i	1.07688	−	1.07688i
$322$	−273.947	+	501.130i	−0.850766	+	1.55630i
$323$			212.444i			0.657722i
$324$	−308.559			−0.952343
$325$	−18.1329	+	18.1329i	−0.0557935	+	0.0557935i
$326$			232.294i			0.712560i
$327$			621.366i			1.90020i
$328$	54.6099	+	82.5309i	0.166494	+	0.251619i
$329$	−80.7911	−	275.634i	−0.245566	−	0.837792i
$330$		−	844.065i		−	2.55777i
$331$	−95.7361	−	95.7361i	−0.289233	−	0.289233i	0.547544	−	0.836777i	$-0.315563\pi$
$331$	−95.7361	−	95.7361i	−0.289233	−	0.289233i	−0.836777	+	0.547544i	$0.815563\pi$
$332$			124.264i			0.374290i
$333$			145.096i			0.435724i
$334$	80.9977	+	80.9977i	0.242508	+	0.242508i
$335$	253.357	−	253.357i	0.756291	−	0.756291i
$336$	442.447	−	129.686i	1.31681	−	0.385970i
$337$		−	294.359i		−	0.873470i	−0.899590	−	0.436735i	$-0.856135\pi$
$337$		−	294.359i		−	0.873470i	0.899590	−	0.436735i	$-0.143865\pi$
$338$	447.981			1.32539
$339$	271.621	−	271.621i	0.801241	−	0.801241i
$340$	118.124	+	118.124i	0.347425	+	0.347425i
$341$	7.06232	−	7.06232i	0.0207106	−	0.0207106i
$342$	177.443	+	177.443i	0.518840	+	0.518840i
$343$	−23.9817	−	342.161i	−0.0699174	−	0.997553i
$344$	104.226			0.302983
$345$	555.708	−	555.708i	1.61075	−	1.61075i
$346$			184.210i			0.532399i
$347$	−131.876	+	131.876i	−0.380046	+	0.380046i	−0.871119	−	0.491073i	$-0.836605\pi$
$347$	−131.876	+	131.876i	−0.380046	+	0.380046i	0.491073	+	0.871119i	$0.336605\pi$
$348$	−317.273			−0.911703
$349$	−554.816			−1.58973			−0.794866	−	0.606785i	$-0.792459\pi$
$349$	−554.816			−1.58973			−0.794866	+	0.606785i	$0.792459\pi$
$350$	−256.143	+	468.561i	−0.731836	+	1.33875i
$351$	−17.9709			−0.0511991
$352$	−353.122	+	353.122i	−1.00319	+	1.00319i
$353$			468.826i			1.32812i	0.747679	+	0.664060i	$0.231168\pi$
$353$			468.826i			1.32812i	−0.747679	+	0.664060i	$0.768832\pi$
$354$	−208.213	+	208.213i	−0.588173	+	0.588173i
$355$	59.5286	+	59.5286i	0.167686	+	0.167686i
$356$	20.8027	−	20.8027i	0.0584345	−	0.0584345i
$357$	158.619	+	86.7102i	0.444310	+	0.242886i
$358$	97.9486	+	97.9486i	0.273600	+	0.273600i
$359$	−43.7182			−0.121778			−0.0608888	−	0.998145i	$-0.519394\pi$
$359$	−43.7182			−0.121778			−0.0608888	+	0.998145i	$0.519394\pi$
$360$	−57.8028			−0.160563
$361$			469.342i			1.30012i
$362$	341.074	−	341.074i	0.942192	−	0.942192i
$363$	78.2518	+	78.2518i	0.215570	+	0.215570i
$364$	−18.6063	+	5.45370i	−0.0511162	+	0.0149827i
$365$	211.931			0.580632
$366$	−19.3245	−	19.3245i	−0.0527991	−	0.0527991i
$367$	−296.082			−0.806763			−0.403381	−	0.915032i	$-0.632165\pi$
$367$	−296.082			−0.806763			−0.403381	+	0.915032i	$0.632165\pi$
$368$	−576.016			−1.56526
$369$	73.9763	+	111.799i	0.200478	+	0.302978i
$370$			865.642i			2.33957i
$371$	−48.1160	−	164.156i	−0.129693	−	0.442470i
$372$	6.19558	+	6.19558i	0.0166548	+	0.0166548i
$373$	286.894			0.769152			0.384576	−	0.923093i	$-0.374348\pi$
$373$	286.894			0.769152			0.384576	+	0.923093i	$0.374348\pi$
$374$	−242.561			−0.648560
$375$	66.0734	−	66.0734i	0.176196	−	0.176196i
$376$	70.0332	−	70.0332i	0.186258	−	0.186258i
$377$	−26.2123			−0.0695287
$378$	−359.114	+	105.260i	−0.950037	+	0.278466i
$379$	529.311			1.39660			0.698299	−	0.715806i	$-0.253941\pi$
$379$	529.311			1.39660			0.698299	+	0.715806i	$0.253941\pi$
$380$	461.691	+	461.691i	1.21498	+	1.21498i
$381$	−131.475	+	131.475i	−0.345079	+	0.345079i
$382$	−224.833	−	224.833i	−0.588569	−	0.588569i
$383$	448.922	+	448.922i	1.17212	+	1.17212i	0.981703	+	0.190416i	$0.0609837\pi$
$383$	448.922	+	448.922i	1.17212	+	1.17212i	0.190416	+	0.981703i	$0.439016\pi$
$384$	186.401	+	186.401i	0.485418	+	0.485418i
$385$	−178.136	−	607.745i	−0.462692	−	1.57856i
$386$	226.500	−	226.500i	0.586789	−	0.586789i
$387$	141.188			0.364827
$388$	359.181	+	359.181i	0.925723	+	0.925723i
$389$		−	248.352i		−	0.638438i	−0.947681	−	0.319219i	$-0.896579\pi$
$389$		−	248.352i		−	0.638438i	0.947681	−	0.319219i	$-0.103421\pi$
$390$	61.1763			0.156862
$391$	−159.695	−	159.695i	−0.408428	−	0.408428i
$392$	99.5578	−	63.8483i	0.253974	−	0.162878i
$393$	124.236	−	124.236i	0.316123	−	0.316123i
$394$	858.943			2.18006
$395$	372.099	+	372.099i	0.942023	+	0.942023i
$396$	−88.3579	+	88.3579i	−0.223126	+	0.223126i
$397$	−72.0912	+	72.0912i	−0.181590	+	0.181590i	−0.792048	−	0.610458i	$-0.790985\pi$
$397$	−72.0912	+	72.0912i	−0.181590	+	0.181590i	0.610458	+	0.792048i	$0.290985\pi$
$398$	−272.243	+	272.243i	−0.684028	+	0.684028i
$399$	619.964	+	338.908i	1.55379	+	0.849395i
$400$	−538.581			−1.34645
$401$		−	160.422i		−	0.400055i	−0.979790	−	0.200027i	$-0.935897\pi$
$401$		−	160.422i		−	0.400055i	0.979790	−	0.200027i	$-0.0641031\pi$
$402$	−456.405			−1.13533
$403$	0.511865	+	0.511865i	0.00127014	+	0.00127014i
$404$	438.397	+	438.397i	1.08514	+	1.08514i
$405$	730.478			1.80365
$406$	−523.804	+	153.532i	−1.29016	+	0.378159i
$407$	−387.614	−	387.614i	−0.952369	−	0.952369i
$408$			62.3333i			0.152778i
$409$			480.408i			1.17459i	0.809372	+	0.587296i	$0.199808\pi$
$409$			480.408i			1.17459i	−0.809372	+	0.587296i	$0.800192\pi$
$410$	441.342	+	666.992i	1.07644	+	1.62681i
$411$			476.300i			1.15888i
$412$	−406.160			−0.985824
$413$	−105.975	+	193.861i	−0.256599	+	0.469396i
$414$	−266.770			−0.644372
$415$		−	294.181i		−	0.708870i
$416$	−25.5937	−	25.5937i	−0.0615232	−	0.0615232i
$417$	−350.954	−	350.954i	−0.841617	−	0.841617i
$418$	−948.056			−2.26808
$419$	371.958			0.887727			0.443864	−	0.896094i	$-0.353607\pi$
$419$	371.958			0.887727			0.443864	+	0.896094i	$0.353607\pi$
$420$	533.158	−	156.274i	1.26942	−	0.372081i
$421$	−293.584	−	293.584i	−0.697348	−	0.697348i	0.266490	−	0.963838i	$-0.414136\pi$
$421$	−293.584	−	293.584i	−0.697348	−	0.697348i	−0.963838	+	0.266490i	$0.914136\pi$
$422$	602.976	+	602.976i	1.42885	+	1.42885i
$423$	94.8691	−	94.8691i	0.224277	−	0.224277i
$424$	41.7090	−	41.7090i	0.0983703	−	0.0983703i
$425$	−149.317	−	149.317i	−0.351334	−	0.351334i
$426$		−	107.236i		−	0.251729i
$427$	−17.9924	−	9.83569i	−0.0421368	−	0.0230344i
$428$	−431.773			−1.00881
$429$	−27.3933	+	27.3933i	−0.0638538	+	0.0638538i
$430$	842.328			1.95890
$431$		−	129.458i		−	0.300367i	−0.988658	−	0.150184i	$-0.952013\pi$
$431$		−	129.458i		−	0.300367i	0.988658	−	0.150184i	$-0.0479865\pi$
$432$	−266.884	−	266.884i	−0.617788	−	0.617788i
$433$		−	537.777i		−	1.24198i	−0.783819	−	0.620989i	$-0.786731\pi$
$433$		−	537.777i		−	1.24198i	0.783819	−	0.620989i	$-0.213269\pi$
$434$	13.2268	+	7.23053i	0.0304764	+	0.0166602i
$435$	751.106			1.72668
$436$	388.061	−	388.061i	0.890048	−	0.890048i
$437$	−624.172	−	624.172i	−1.42831	−	1.42831i
$438$	−190.889	−	190.889i	−0.435819	−	0.435819i
$439$	583.478	−	583.478i	1.32911	−	1.32911i	0.422956	−	0.906150i	$-0.360992\pi$
$439$	583.478	−	583.478i	1.32911	−	1.32911i	0.906150	−	0.422956i	$-0.139008\pi$
$440$	154.416	−	154.416i	0.350946	−	0.350946i
$441$	134.864	−	86.4909i	0.305814	−	0.196124i
$442$		−	17.5804i		−	0.0397747i
$443$			362.650i			0.818623i	0.912395	+	0.409311i	$0.134231\pi$
$443$			362.650i			0.818623i	−0.912395	+	0.409311i	$0.865769\pi$
$444$	340.043	−	340.043i	0.765863	−	0.765863i
$445$	−49.2480	+	49.2480i	−0.110670	+	0.110670i
$446$	−9.45015			−0.0211887
$447$		−	1019.33i		−	2.28039i
$448$	−199.369	−	108.986i	−0.445019	−	0.243273i
$449$			591.381i			1.31711i	0.752534	+	0.658553i	$0.228831\pi$
$449$			591.381i			1.31711i	−0.752534	+	0.658553i	$0.771169\pi$
$450$	−249.433			−0.554295
$451$	−496.286	−	101.041i	−1.10041	−	0.224037i
$452$	−339.270			−0.750598
$453$	−985.319			−2.17510
$454$	345.452	−	345.452i	0.760908	−	0.760908i
$455$	44.0483	−	12.9110i	0.0968094	−	0.0283758i
$456$			243.631i			0.534279i
$457$	−394.870	+	394.870i	−0.864047	+	0.864047i	−0.991805	−	0.127758i	$-0.959222\pi$
$457$	−394.870	+	394.870i	−0.864047	+	0.864047i	0.127758	+	0.991805i	$0.459222\pi$
$458$	532.617	−	532.617i	1.16292	−	1.16292i
$459$		−	147.983i		−	0.322402i
$460$	−694.112			−1.50894
$461$			84.4715i			0.183235i	0.995794	+	0.0916177i	$0.0292038\pi$
$461$			84.4715i			0.183235i	−0.995794	+	0.0916177i	$0.970796\pi$
$462$	−386.954	+	707.853i	−0.837563	+	1.53215i
$463$	−181.252	−	181.252i	−0.391473	−	0.391473i	0.483739	−	0.875212i	$-0.339278\pi$
$463$	−181.252	−	181.252i	−0.391473	−	0.391473i	−0.875212	+	0.483739i	$0.839278\pi$
$464$	−389.278	−	389.278i	−0.838960	−	0.838960i
$465$	−14.6673	−	14.6673i	−0.0315426	−	0.0315426i
$466$	−93.7914	+	93.7914i	−0.201269	+	0.201269i
$467$			737.974i			1.58024i	0.612949	+	0.790122i	$0.289983\pi$
$467$			737.974i			1.58024i	−0.612949	+	0.790122i	$0.710017\pi$
$468$	−6.40402	−	6.40402i	−0.0136838	−	0.0136838i
$469$	−328.621	+	96.3223i	−0.700685	+	0.205378i
$470$	565.989	−	565.989i	1.20423	−	1.20423i
$471$			982.373i			2.08572i
$472$	−76.1826			−0.161404
$473$	−377.174	+	377.174i	−0.797409	+	0.797409i
$474$		−	670.309i		−	1.41415i
$475$	−583.607	−	583.607i	−1.22865	−	1.22865i
$476$	−44.9089	−	153.215i	−0.0943465	−	0.321880i
$477$	56.5003	−	56.5003i	0.118449	−	0.118449i
$478$	−617.971	+	617.971i	−1.29283	+	1.29283i
$479$	−299.119	+	299.119i	−0.624467	+	0.624467i	−0.946670	−	0.322204i	$-0.895576\pi$
$479$	−299.119	+	299.119i	−0.624467	+	0.624467i	0.322204	+	0.946670i	$0.395576\pi$
$480$	733.378	+	733.378i	1.52787	+	1.52787i
$481$	28.0936	−	28.0936i	0.0584066	−	0.0584066i
$482$			886.770i			1.83977i
$483$	−720.790	+	211.271i	−1.49232	+	0.437414i
$484$		−	97.7410i		−	0.201944i
$485$	−850.318	−	850.318i	−1.75323	−	1.75323i
$486$	−317.731	−	317.731i	−0.653768	−	0.653768i
$487$		−	251.214i		−	0.515839i	−0.966166	−	0.257920i	$-0.916963\pi$
$487$		−	251.214i		−	0.515839i	0.966166	−	0.257920i	$-0.0830370\pi$
$488$		−	7.07058i		−	0.0144889i
$489$	−216.024	+	216.024i	−0.441768	+	0.441768i
$490$	804.599	−	516.004i	1.64204	−	1.05307i
$491$	−174.070			−0.354520			−0.177260	−	0.984164i	$-0.556723\pi$
$491$	−174.070			−0.354520			−0.177260	+	0.984164i	$0.556723\pi$
$492$	88.6402	−	435.378i	0.180163	−	0.884914i
$493$		−	215.847i		−	0.437824i
$494$		−	68.7134i		−	0.139096i
$495$	209.177	−	209.177i	0.422580	−	0.422580i
$496$			15.2033i			0.0306519i
$497$	−22.6318	−	77.2125i	−0.0455368	−	0.155357i
$498$	−264.973	+	264.973i	−0.532073	+	0.532073i
$499$	433.306	+	433.306i	0.868349	+	0.868349i	0.992290	−	0.123940i	$-0.0395531\pi$
$499$	433.306	+	433.306i	0.868349	+	0.868349i	−0.123940	+	0.992290i	$0.539553\pi$
$500$	−82.5295			−0.165059
$501$			150.649i			0.300697i
$502$		−	55.3190i		−	0.110197i
$503$	644.477	−	644.477i	1.28127	−	1.28127i	0.341318	−	0.939948i	$-0.389127\pi$
$503$	644.477	−	644.477i	1.28127	−	1.28127i	0.939948	−	0.341318i	$-0.110873\pi$
$504$	48.4748	+	26.4992i	0.0961802	+	0.0525777i
$505$	−1037.85	−	1037.85i	−2.05515	−	2.05515i
$506$	712.658	−	712.658i	1.40842	−	1.40842i
$507$	416.604	+	416.604i	0.821705	+	0.821705i
$508$	164.220			0.323268
$509$	−499.587	−	499.587i	−0.981507	−	0.981507i	0.0183251	−	0.999832i	$-0.494167\pi$
$509$	−499.587	−	499.587i	−0.981507	−	0.981507i	−0.999832	+	0.0183251i	$0.994167\pi$
$510$			503.761i			0.987767i
$511$	−177.730	−	97.1576i	−0.347808	−	0.190132i
$512$		−	578.632i		−	1.13014i
$513$		−	578.393i		−	1.12747i
$514$	43.2332	+	43.2332i	0.0841113	+	0.0841113i
$515$	961.536			1.86706
$516$	−330.885	−	330.885i	−0.641249	−	0.641249i
$517$			506.873i			0.980412i
$518$	396.846	−	725.949i	0.766112	−	1.40145i
$519$	−171.308	+	171.308i	−0.330073	+	0.330073i
$520$	11.1918	+	11.1918i	0.0215227	+	0.0215227i
$521$	66.2116	−	66.2116i	0.127086	−	0.127086i	−0.640703	−	0.767789i	$-0.721357\pi$
$521$	66.2116	−	66.2116i	0.127086	−	0.127086i	0.767789	+	0.640703i	$0.221357\pi$
$522$	−180.286	−	180.286i	−0.345375	−	0.345375i
$523$		−	566.123i		−	1.08245i	−0.840877	−	0.541227i	$-0.817960\pi$
$523$		−	566.123i		−	1.08245i	0.840877	−	0.541227i	$-0.182040\pi$
$524$	−155.178			−0.296142
$525$	−673.945	+	197.540i	−1.28371	+	0.376268i
$526$	254.034	+	254.034i	0.482953	+	0.482953i
$527$	−4.21499	+	4.21499i	−0.00799808	+	0.00799808i
$528$	−813.632			−1.54097
$529$	409.388			0.773890
$530$	337.081	−	337.081i	0.636001	−	0.636001i
$531$	−103.199			−0.194349
$532$	−175.527	−	598.844i	−0.329939	−	1.12565i
$533$	7.32325	−	35.9699i	0.0137397	−	0.0674858i
$534$	88.7165			0.166136
$535$	1022.17			1.91060
$536$	−83.4963	−	83.4963i	−0.155777	−	0.155777i
$537$			182.177i			0.339249i
$538$	−701.724			−1.30432
$539$	−129.226	+	591.335i	−0.239751	+	1.09710i
$540$	−321.601	−	321.601i	−0.595558	−	0.595558i
$541$		−	495.664i		−	0.916200i	−0.888901	−	0.458100i	$-0.848530\pi$
$541$		−	495.664i		−	0.916200i	0.888901	−	0.458100i	$-0.151470\pi$
$542$	239.774			0.442388
$543$	634.369			1.16827
$544$	210.753	−	210.753i	0.387414	−	0.387414i
$545$	−918.690	+	918.690i	−1.68567	+	1.68567i
$546$	−51.3039	−	28.0457i	−0.0939633	−	0.0513658i
$547$	284.270	−	284.270i	0.519689	−	0.519689i	−0.397788	−	0.917477i	$-0.630222\pi$
$547$	284.270	−	284.270i	0.519689	−	0.519689i	0.917477	+	0.397788i	$0.130222\pi$
$548$	297.463	−	297.463i	0.542816	−	0.542816i
$549$		−	9.57803i		−	0.0174463i
$550$	666.343	−	666.343i	1.21153	−	1.21153i
$551$		−	843.644i		−	1.53111i
$552$	−183.139	−	183.139i	−0.331773	−	0.331773i
$553$	−141.466	−	482.637i	−0.255815	−	0.872761i
$554$		−	628.343i		−	1.13419i
$555$	−805.013	+	805.013i	−1.45047	+	1.45047i
$556$			438.362i			0.788422i
$557$	300.789	−	300.789i	0.540016	−	0.540016i	−0.383517	−	0.923534i	$-0.625287\pi$
$557$	300.789	−	300.789i	0.540016	−	0.540016i	0.923534	+	0.383517i	$0.125287\pi$
$558$			7.04111i			0.0126185i
$559$	−27.3369	−	27.3369i	−0.0489033	−	0.0489033i
$560$	845.898	+	462.417i	1.51053	+	0.825745i
$561$	−225.572	−	225.572i	−0.402090	−	0.402090i
$562$	1002.65	+	1002.65i	1.78408	+	1.78408i
$563$	−305.083	+	305.083i	−0.541888	+	0.541888i	−0.924082	−	0.382194i	$-0.875169\pi$
$563$	−305.083	+	305.083i	−0.541888	+	0.541888i	0.382194	+	0.924082i	$0.375169\pi$
$564$	−444.666			−0.788414
$565$	803.183			1.42156
$566$	−53.5575			−0.0946245
$567$	−612.597	−	334.881i	−1.08042	−	0.590619i
$568$	19.6182	−	19.6182i	0.0345391	−	0.0345391i
$569$			104.025i			0.182821i	0.995813	+	0.0914107i	$0.0291376\pi$
$569$			104.025i			0.182821i	−0.995813	+	0.0914107i	$0.970862\pi$
$570$			1968.96i			3.45432i
$571$	522.533	+	522.533i	0.915120	+	0.915120i	0.996669	−	0.0815494i	$-0.0259868\pi$
$571$	522.533	+	522.533i	0.915120	+	0.915120i	−0.0815494	+	0.996669i	$0.525987\pi$
$572$	34.2158			0.0598179
$573$		−	418.172i		−	0.729794i
$574$	−64.3439	−	761.685i	−0.112097	−	1.32698i
$575$	877.402			1.52592
$576$		−	106.131i		−	0.184256i
$577$	496.297	−	496.297i	0.860134	−	0.860134i	−0.131219	−	0.991353i	$-0.541889\pi$
$577$	496.297	−	496.297i	0.860134	−	0.860134i	0.991353	+	0.131219i	$0.0418891\pi$
$578$	−624.958			−1.08124
$579$	421.273			0.727587
$580$	−469.088	−	469.088i	−0.808772	−	0.808772i
$581$	−134.865	+	246.707i	−0.232125	+	0.424625i
$582$			1531.79i			2.63193i
$583$			301.874i			0.517793i
$584$		−	69.8437i		−	0.119595i
$585$	15.1608	+	15.1608i	0.0259159	+	0.0259159i
$586$	−1023.48	+	1023.48i	−1.74655	+	1.74655i
$587$	−9.61238	+	9.61238i	−0.0163754	+	0.0163754i	−0.715247	−	0.698872i	$-0.753686\pi$
$587$	−9.61238	+	9.61238i	−0.0163754	+	0.0163754i	0.698872	+	0.715247i	$0.253686\pi$
$588$	−518.762	−	113.366i	−0.882248	−	0.192799i
$589$	−16.4744	+	16.4744i	−0.0279701	+	0.0279701i
$590$	−615.687			−1.04354
$591$	798.782	+	798.782i	1.35158	+	1.35158i
$592$	834.432			1.40951
$593$	419.930	+	419.930i	0.708145	+	0.708145i	0.966145	−	0.258000i	$-0.0830634\pi$
$593$	419.930	+	419.930i	0.708145	+	0.708145i	−0.258000	+	0.966145i	$0.583063\pi$
$594$	660.388			1.11177
$595$	106.317	+	362.719i	0.178684	+	0.609611i
$596$	−636.603	+	636.603i	−1.06813	+	1.06813i
$597$	−506.350			−0.848158
$598$	51.6522	+	51.6522i	0.0863749	+	0.0863749i
$599$	−162.209			−0.270799			−0.135399	−	0.990791i	$-0.543232\pi$
$599$	−162.209			−0.270799			−0.135399	+	0.990791i	$0.543232\pi$
$600$	−171.237	−	171.237i	−0.285394	−	0.285394i
$601$	−38.1221	−	38.1221i	−0.0634311	−	0.0634311i	0.674680	−	0.738111i	$-0.264282\pi$
$601$	−38.1221	−	38.1221i	−0.0634311	−	0.0634311i	−0.738111	+	0.674680i	$0.764282\pi$
$602$	−706.397	−	386.158i	−1.17342	−	0.641458i
$603$	−113.107	−	113.107i	−0.187573	−	0.187573i
$604$	615.361	+	615.361i	1.01881	+	1.01881i
$605$			231.391i			0.382464i
$606$			1869.62i			3.08517i
$607$	−302.918			−0.499042			−0.249521	−	0.968369i	$-0.580273\pi$
$607$	−302.918			−0.499042			−0.249521	+	0.968369i	$0.580273\pi$
$608$	823.732	−	823.732i	1.35482	−	1.35482i
$609$	−629.896	−	344.338i	−1.03431	−	0.565415i
$610$		−	57.1425i		−	0.0936763i
$611$	−36.7372			−0.0601264
$612$	52.7344	−	52.7344i	0.0861674	−	0.0861674i
$613$		−	230.401i		−	0.375858i	−0.982183	−	0.187929i	$-0.939823\pi$
$613$		−	230.401i		−	0.375858i	0.982183	−	0.187929i	$-0.0601775\pi$
$614$		−	1131.83i		−	1.84338i
$615$	−209.845	+	1030.71i	−0.341212	+	1.67595i
$616$	−200.288	+	58.7065i	−0.325143	+	0.0953028i
$617$			44.8380i			0.0726710i	0.999340	+	0.0363355i	$0.0115685\pi$
$617$			44.8380i			0.0726710i	−0.999340	+	0.0363355i	$0.988432\pi$
$618$	−866.068	−	866.068i	−1.40140	−	1.40140i
$619$		−	10.6088i		−	0.0171386i	−0.999963	−	0.00856932i	$-0.997272\pi$
$619$		−	10.6088i		−	0.0171386i	0.999963	−	0.00856932i	$-0.00272773\pi$
$620$			18.3203i			0.0295489i
$621$	434.781	+	434.781i	0.700130	+	0.700130i
$622$	−830.602	+	830.602i	−1.33537	+	1.33537i
$623$	63.8778	−	18.7233i	0.102533	−	0.0300534i
$624$		−	58.9706i		−	0.0945042i
$625$	−520.677			−0.833084
$626$	−325.660	+	325.660i	−0.520223	+	0.520223i
$627$	−881.654	−	881.654i	−1.40615	−	1.40615i
$628$	613.521	−	613.521i	0.976944	−	0.976944i
$629$	231.339	+	231.339i	0.367788	+	0.367788i
$630$	391.760	+	214.159i	0.621842	+	0.339935i
$631$	−906.441			−1.43652			−0.718258	−	0.695777i	$-0.755060\pi$
$631$	−906.441			−1.43652			−0.718258	+	0.695777i	$0.755060\pi$
$632$	122.629	−	122.629i	0.194033	−	0.194033i
$633$			1121.49i			1.77170i
$634$	−395.348	+	395.348i	−0.623577	+	0.623577i
$635$	−388.772			−0.612239
$636$	−264.825			−0.416392
$637$	−42.8589	−	9.36604i	−0.0672824	−	0.0147034i
$638$	963.243			1.50979
$639$	26.5755	−	26.5755i	0.0415891	−	0.0415891i
$640$			551.187i			0.861229i
$641$	−229.143	+	229.143i	−0.357477	+	0.357477i	−0.862882	−	0.505405i	$-0.831343\pi$
$641$	−229.143	+	229.143i	−0.357477	+	0.357477i	0.505405	+	0.862882i	$0.331343\pi$
$642$	−920.683	−	920.683i	−1.43409	−	1.43409i
$643$	−646.007	+	646.007i	−1.00468	+	1.00468i	−0.00468817	+	0.999989i	$0.501492\pi$
$643$	−646.007	+	646.007i	−1.00468	+	1.00468i	−0.999989	+	0.00468817i	$0.998508\pi$
$644$	582.099	+	318.209i	0.903881	+	0.494114i
$645$	783.331	+	783.331i	1.21447	+	1.21447i
$646$	565.826			0.875891
$647$	−728.809			−1.12644			−0.563222	−	0.826306i	$-0.690438\pi$
$647$	−728.809			−1.12644			−0.563222	+	0.826306i	$0.690438\pi$
$648$		−	240.736i		−	0.371506i
$649$	275.690	−	275.690i	0.424792	−	0.424792i
$650$	48.2953	+	48.2953i	0.0743005	+	0.0743005i
$651$	5.57627	+	19.0245i	0.00856570	+	0.0292235i
$652$	269.827			0.413845
$653$	−427.457	−	427.457i	−0.654605	−	0.654605i	0.299493	−	0.954098i	$-0.403182\pi$
$653$	−427.457	−	427.457i	−0.654605	−	0.654605i	−0.954098	+	0.299493i	$0.903182\pi$
$654$	1654.95			2.53051
$655$	367.367			0.560866
$656$	642.944	−	425.430i	0.980098	−	0.648521i
$657$		−	94.6124i		−	0.144007i
$658$	−734.125	+	215.180i	−1.11569	+	0.327021i
$659$	−339.090	−	339.090i	−0.514552	−	0.514552i	0.401365	−	0.915918i	$-0.368536\pi$
$659$	−339.090	−	339.090i	−0.514552	−	0.514552i	−0.915918	+	0.401365i	$0.868536\pi$
$660$	−980.444			−1.48552
$661$	923.313			1.39684			0.698421	−	0.715687i	$-0.253886\pi$
$661$	923.313			1.39684			0.698421	+	0.715687i	$0.253886\pi$
$662$	−254.984	+	254.984i	−0.385173	+	0.385173i
$663$	16.3491	−	16.3491i	0.0246592	−	0.0246592i
$664$	−96.9501			−0.146009
$665$	415.541	+	1417.69i	0.624874	+	2.13187i
$666$	386.450			0.580255
$667$	634.172	+	634.172i	0.950782	+	0.950782i
$668$	94.0849	−	94.0849i	0.140846	−	0.140846i
$669$	−8.78826	−	8.78826i	−0.0131364	−	0.0131364i
$670$	−674.795	−	674.795i	−1.00716	−	1.00716i
$671$	25.5871	+	25.5871i	0.0381327	+	0.0381327i
$672$	−278.818	−	951.240i	−0.414908	−	1.41554i
$673$	658.488	−	658.488i	0.978436	−	0.978436i	−0.0213359	−	0.999772i	$-0.506792\pi$
$673$	658.488	−	658.488i	0.978436	−	0.978436i	0.999772	+	0.0213359i	$0.00679194\pi$
$674$	−784.000			−1.16320
$675$	406.524	+	406.524i	0.602258	+	0.602258i
$676$		−	520.363i		−	0.769768i
$677$	454.783			0.671762			0.335881	−	0.941904i	$-0.390966\pi$
$677$	454.783			0.671762			0.335881	+	0.941904i	$0.390966\pi$
$678$	−723.437	−	723.437i	−1.06702	−	1.06702i
$679$	323.277	+	1102.92i	0.476107	+	1.62433i
$680$	−92.1599	+	92.1599i	−0.135529	+	0.135529i
$681$	642.514			0.943486
$682$	−18.8099	−	18.8099i	−0.0275804	−	0.0275804i
$683$	177.819	−	177.819i	0.260349	−	0.260349i	−0.564846	−	0.825196i	$-0.691065\pi$
$683$	177.819	−	177.819i	0.260349	−	0.260349i	0.825196	+	0.564846i	$0.191065\pi$
$684$	206.114	−	206.114i	0.301336	−	0.301336i
$685$	−704.210	+	704.210i	−1.02804	+	1.02804i
$686$	−911.314	+	63.8730i	−1.32845	+	0.0931093i
$687$	990.625			1.44196
$688$		−	811.958i		−	1.18017i
$689$	−21.8793			−0.0317551
$690$	−1480.08	−	1480.08i	−2.14504	−	2.14504i
$691$	−380.430	−	380.430i	−0.550550	−	0.550550i	0.376050	−	0.926600i	$-0.377282\pi$
$691$	−380.430	−	380.430i	−0.550550	−	0.550550i	−0.926600	+	0.376050i	$0.877282\pi$
$692$	213.974			0.309210
$693$	−271.316	+	79.5257i	−0.391510	+	0.114756i
$694$	351.240	+	351.240i	0.506109	+	0.506109i
$695$		−	1037.77i		−	1.49320i
$696$		−	247.534i		−	0.355652i
$697$	296.197	+	60.3038i	0.424960	+	0.0865191i
$698$			1477.70i			2.11705i
$699$	−174.444			−0.249563
$700$	544.268	+	297.529i	0.777526	+	0.425041i
$701$	108.583			0.154897			0.0774487	−	0.996996i	$-0.475323\pi$
$701$	108.583			0.154897			0.0774487	+	0.996996i	$0.475323\pi$
$702$			47.8638i			0.0681820i
$703$	904.192	+	904.192i	1.28619	+	1.28619i
$704$	283.523	+	283.523i	0.402731	+	0.402731i
$705$	1052.69			1.49318
$706$	1248.68			1.76866
$707$	394.575	+	1346.16i	0.558097	+	1.90405i
$708$	241.855	+	241.855i	0.341603	+	0.341603i
$709$	−613.384	−	613.384i	−0.865140	−	0.865140i	0.126789	−	0.991930i	$-0.459533\pi$
$709$	−613.384	−	613.384i	−0.865140	−	0.865140i	−0.991930	+	0.126789i	$0.959533\pi$
$710$	158.549	−	158.549i	0.223309	−	0.223309i
$711$	166.117	−	166.117i	0.233638	−	0.233638i
$712$	16.2301	+	16.2301i	0.0227951	+	0.0227951i
$713$		−	24.7677i		−	0.0347374i
$714$	230.945	−	422.466i	0.323452	−	0.591690i
$715$	−81.0020			−0.113290
$716$	113.775	−	113.775i	0.158903	−	0.158903i
$717$	−1149.38			−1.60304
$718$			116.439i			0.162172i
$719$	309.079	+	309.079i	0.429873	+	0.429873i	0.888585	−	0.458712i	$-0.151689\pi$
$719$	309.079	+	309.079i	0.429873	+	0.429873i	−0.458712	+	0.888585i	$0.651689\pi$
$720$			450.304i			0.625422i
$721$	−806.367	−	440.807i	−1.11840	−	0.611383i
$722$	1250.05			1.73137
$723$	−824.660	+	824.660i	−1.14061	+	1.14061i
$724$	−396.182	−	396.182i	−0.547213	−	0.547213i
$725$	592.957	+	592.957i	0.817871	+	0.817871i
$726$	208.416	−	208.416i	0.287075	−	0.287075i
$727$	605.068	−	605.068i	0.832281	−	0.832281i	−0.155548	−	0.987828i	$-0.549714\pi$
$727$	605.068	−	605.068i	0.832281	−	0.832281i	0.987828	+	0.155548i	$0.0497142\pi$
$728$	−4.25494	−	14.5165i	−0.00584470	−	0.0199403i
$729$			306.673i			0.420677i
$730$		−	564.458i		−	0.773230i
$731$	225.108	−	225.108i	0.307945	−	0.307945i
$732$	−22.4468	+	22.4468i	−0.0306651	+	0.0306651i
$733$	321.139			0.438116			0.219058	−	0.975712i	$-0.429702\pi$
$733$	321.139			0.438116			0.219058	+	0.975712i	$0.429702\pi$
$734$			788.587i			1.07437i
$735$	1228.11	+	268.381i	1.67089	+	0.365144i
$736$			1238.41i			1.68262i
$737$	604.314			0.819965
$738$	297.766	−	197.029i	0.403477	−	0.266977i
$739$	−515.087			−0.697005			−0.348503	−	0.937308i	$-0.613310\pi$
$739$	−515.087			−0.697005			−0.348503	+	0.937308i	$0.613310\pi$
$740$	1005.51			1.35879
$741$	63.9007	−	63.9007i	0.0862357	−	0.0862357i
$742$	−437.216	+	128.153i	−0.589240	+	0.172712i
$743$			482.268i			0.649083i	0.945872	+	0.324541i	$0.105210\pi$
$743$			482.268i			0.649083i	−0.945872	+	0.324541i	$0.894790\pi$
$744$	−4.83375	+	4.83375i	−0.00649698	+	0.00649698i
$745$	1507.08	−	1507.08i	2.02293	−	2.02293i
$746$		−	764.115i		−	1.02428i
$747$	−131.332			−0.175812
$748$			281.753i			0.376675i
$749$	−857.218	−	468.605i	−1.14448	−	0.625641i
$750$	−175.980	−	175.980i	−0.234641	−	0.234641i
$751$	721.759	+	721.759i	0.961063	+	0.961063i	0.999270	−	0.0382064i	$-0.0121644\pi$
$751$	721.759	+	721.759i	0.961063	+	0.961063i	−0.0382064	+	0.999270i	$0.512164\pi$
$752$	−545.582	−	545.582i	−0.725509	−	0.725509i
$753$	51.4445	−	51.4445i	0.0683194	−	0.0683194i
$754$			69.8141i			0.0925917i
$755$	−1456.80	−	1456.80i	−1.92953	−	1.92953i
$756$	122.267	+	417.138i	0.161729	+	0.551769i
$757$	−731.668	+	731.668i	−0.966536	+	0.966536i	−0.999458	−	0.0329221i	$-0.989519\pi$
$757$	−731.668	+	731.668i	−0.966536	+	0.966536i	0.0329221	+	0.999458i	$0.489519\pi$
$758$		−	1409.77i		−	1.85986i
$759$	1325.49			1.74636
$760$	−360.209	+	360.209i	−0.473959	+	0.473959i
$761$		−	485.743i		−	0.638296i	−0.947705	−	0.319148i	$-0.896603\pi$
$761$		−	485.743i		−	0.638296i	0.947705	−	0.319148i	$-0.103397\pi$
$762$	350.172	+	350.172i	0.459543	+	0.459543i
$763$	1191.60	−	349.271i	1.56173	−	0.457760i
$764$	−261.161	+	261.161i	−0.341834	+	0.341834i
$765$	−124.843	+	124.843i	−0.163193	+	0.163193i
$766$	1195.66	−	1195.66i	1.56092	−	1.56092i
$767$	19.9815	+	19.9815i	0.0260515	+	0.0260515i
$768$	818.047	−	818.047i	1.06517	−	1.06517i
$769$			992.519i			1.29066i	0.763903	+	0.645331i	$0.223281\pi$
$769$			992.519i			1.29066i	−0.763903	+	0.645331i	$0.776719\pi$
$770$	−1618.67	+	474.450i	−2.10217	+	0.616169i
$771$			80.4103i			0.104293i
$772$	−263.097	−	263.097i	−0.340799	−	0.340799i
$773$	−918.853	−	918.853i	−1.18868	−	1.18868i	−0.977432	−	0.211252i	$-0.932246\pi$
$773$	−918.853	−	918.853i	−1.18868	−	1.18868i	−0.211252	−	0.977432i	$-0.567754\pi$
$774$		−	376.042i		−	0.485842i
$775$		−	23.1581i		−	0.0298814i
$776$	−280.230	+	280.230i	−0.361122	+	0.361122i
$777$	1044.15	−	306.052i	1.34383	−	0.393890i
$778$	−661.464			−0.850211
$779$	1157.69	+	235.699i	1.48613	+	0.302566i
$780$		−	71.0608i		−	0.0911036i
$781$			141.989i			0.181804i
$782$	−425.334	+	425.334i	−0.543905	+	0.543905i
$783$			587.658i			0.750522i
$784$	−497.400	−	775.589i	−0.634439	−	0.989272i
$785$	−1452.44	+	1452.44i	−1.85024	+	1.85024i
$786$	−330.892	−	330.892i	−0.420982	−	0.420982i
$787$	−837.925			−1.06471			−0.532354	−	0.846522i	$-0.678693\pi$
$787$	−837.925			−1.06471			−0.532354	+	0.846522i	$0.678693\pi$
$788$		−	997.726i		−	1.26615i
$789$			472.482i			0.598836i
$790$	991.052	−	991.052i	1.25450	−	1.25450i
$791$	−673.568	−	368.212i	−0.851540	−	0.465502i
$792$	−68.9363	−	68.9363i	−0.0870408	−	0.0870408i
$793$	−1.85450	+	1.85450i	−0.00233859	+	0.00233859i
$794$	192.008	+	192.008i	0.241824	+	0.241824i
$795$	626.943			0.788608
$796$	316.231	+	316.231i	0.397275	+	0.397275i
$797$		−	802.284i		−	1.00663i	−0.864103	−	0.503315i	$-0.832114\pi$
$797$		−	802.284i		−	1.00663i	0.864103	−	0.503315i	$-0.167886\pi$
$798$	902.652	−	1651.22i	1.13114	−	2.06920i
$799$		−	302.516i		−	0.378618i
$800$			1157.92i			1.44740i
$801$	21.9858	+	21.9858i	0.0274480	+	0.0274480i
$802$	−427.269			−0.532755
$803$	252.751	+	252.751i	0.314758	+	0.314758i
$804$			530.148i			0.659388i
$805$	−1378.05	−	753.324i	−1.71187	−	0.935806i
$806$	1.36330	−	1.36330i	0.00169144	−	0.00169144i
$807$	−652.575	−	652.575i	−0.808644	−	0.808644i
$808$	−342.034	+	342.034i	−0.423310	+	0.423310i
$809$	452.842	+	452.842i	0.559755	+	0.559755i	0.929238	−	0.369482i	$-0.120465\pi$
$809$	452.842	+	452.842i	0.559755	+	0.559755i	−0.369482	+	0.929238i	$0.620465\pi$
$810$		−	1945.56i		−	2.40193i
$811$	960.125			1.18388			0.591939	−	0.805983i	$-0.298363\pi$
$811$	960.125			1.18388			0.591939	+	0.805983i	$0.298363\pi$
$812$	178.339	+	608.437i	0.219630	+	0.749307i
$813$	222.980	+	222.980i	0.274269	+	0.274269i
$814$	−1032.37	+	1032.37i	−1.26827	+	1.26827i
$815$	−638.785			−0.783785
$816$	485.598			0.595096
$817$	879.839	−	879.839i	1.07691	−	1.07691i
$818$	1279.52			1.56421
$819$	−5.76388	−	19.6645i	−0.00703770	−	0.0240104i
$820$	774.761	−	512.652i	0.944831	−	0.625185i
$821$	1395.25			1.69945			0.849726	−	0.527225i	$-0.176768\pi$
$821$	1395.25			1.69945			0.849726	+	0.527225i	$0.176768\pi$
$822$	1268.58			1.54329
$823$	−795.266	−	795.266i	−0.966302	−	0.966302i	0.0331487	−	0.999450i	$-0.489447\pi$
$823$	−795.266	−	795.266i	−0.966302	−	0.966302i	−0.999450	+	0.0331487i	$0.989447\pi$
$824$		−	316.883i		−	0.384567i
$825$	1239.34			1.50223
$826$	516.330	+	282.256i	0.625097	+	0.341714i
$827$	−744.690	−	744.690i	−0.900472	−	0.900472i	0.0950050	−	0.995477i	$-0.469713\pi$
$827$	−744.690	−	744.690i	−0.900472	−	0.900472i	−0.995477	+	0.0950050i	$0.969713\pi$
$828$			309.873i			0.374243i
$829$	−143.911			−0.173596			−0.0867980	−	0.996226i	$-0.527663\pi$
$829$	−143.911			−0.173596			−0.0867980	+	0.996226i	$0.527663\pi$
$830$	−783.524			−0.944005
$831$	584.334	−	584.334i	0.703169	−	0.703169i
$832$	−20.5492	+	20.5492i	−0.0246986	+	0.0246986i
$833$	77.1254	−	352.925i	0.0925875	−	0.423679i
$834$	−934.735	+	934.735i	−1.12079	+	1.12079i
$835$	−222.735	+	222.735i	−0.266748	+	0.266748i
$836$			1101.24i			1.31727i
$837$	11.4756	−	11.4756i	0.0137104	−	0.0137104i
$838$		−	990.676i		−	1.18219i
$839$	666.154	+	666.154i	0.793986	+	0.793986i	0.982140	−	0.188154i	$-0.0602504\pi$
$839$	666.154	+	666.154i	0.793986	+	0.793986i	−0.188154	+	0.982140i	$0.560250\pi$
$840$	121.924	+	415.966i	0.145148	+	0.495198i
$841$			16.1591i			0.0192141i
$842$	−781.933	+	781.933i	−0.928662	+	0.928662i
$843$			1864.85i			2.21216i
$844$	700.401	−	700.401i	0.829859	−	0.829859i
$845$			1231.90i			1.45787i
$846$	−252.675	−	252.675i	−0.298671	−	0.298671i
$847$	106.079	−	194.050i	0.125241	−	0.229102i
$848$	−324.927	−	324.927i	−0.383169	−	0.383169i
$849$	−49.8063	−	49.8063i	−0.0586647	−	0.0586647i
$850$	−397.692	+	397.692i	−0.467872	+	0.467872i
$851$	−1359.37			−1.59738
$852$	−124.563			−0.146201
$853$	898.941			1.05386			0.526929	−	0.849909i	$-0.323343\pi$
$853$	898.941			1.05386			0.526929	+	0.849909i	$0.323343\pi$
$854$	−26.1965	+	47.9211i	−0.0306750	+	0.0561137i
$855$	−487.950	+	487.950i	−0.570702	+	0.570702i
$856$		−	336.866i		−	0.393535i
$857$			440.606i			0.514126i	0.966395	+	0.257063i	$0.0827548\pi$
$857$			440.606i			0.514126i	−0.966395	+	0.257063i	$0.917245\pi$
$858$	72.9596	+	72.9596i	0.0850344	+	0.0850344i
$859$	727.686			0.847132			0.423566	−	0.905865i	$-0.360778\pi$
$859$	727.686			0.847132			0.423566	+	0.905865i	$0.360778\pi$
$860$		−	978.426i		−	1.13770i
$861$	648.500	−	768.174i	0.753193	−	0.892188i
$862$	−344.801			−0.400001
$863$			345.026i			0.399799i	0.979816	+	0.199899i	$0.0640616\pi$
$863$			345.026i			0.399799i	−0.979816	+	0.199899i	$0.935938\pi$
$864$	−573.788	+	573.788i	−0.664107	+	0.664107i
$865$	−506.558			−0.585616
$866$	−1432.32			−1.65395
$867$	−581.186	−	581.186i	−0.670341	−	0.670341i
$868$	8.39879	−	15.3639i	0.00967603	−	0.0177003i
$869$			887.539i			1.02133i
$870$		−	2000.50i		−	2.29943i
$871$			43.7996i			0.0502866i
$872$	302.763	+	302.763i	0.347205	+	0.347205i
$873$	−379.609	+	379.609i	−0.434832	+	0.434832i
$874$	−1662.43	+	1662.43i	−1.90209	+	1.90209i
$875$	−163.850	−	89.5698i	−0.187257	−	0.102365i
$876$	−221.731	+	221.731i	−0.253118	+	0.253118i
$877$	1313.07			1.49723			0.748614	−	0.663006i	$-0.230720\pi$
$877$	1313.07			1.49723			0.748614	+	0.663006i	$0.230720\pi$
$878$	−1554.04	−	1554.04i	−1.76998	−	1.76998i
$879$	−1903.58			−2.16562
$880$	−1202.96	−	1202.96i	−1.36700	−	1.36700i
$881$	−858.677			−0.974661			−0.487331	−	0.873217i	$-0.662029\pi$
$881$	−858.677			−0.974661			−0.487331	+	0.873217i	$0.662029\pi$
$882$	−230.361	−	359.198i	−0.261180	−	0.407254i
$883$	294.432	−	294.432i	0.333445	−	0.333445i	−0.520448	−	0.853893i	$-0.674235\pi$
$883$	294.432	−	294.432i	0.333445	−	0.333445i	0.853893	+	0.520448i	$0.174235\pi$
$884$	−20.4209			−0.0231006
$885$	−572.564	−	572.564i	−0.646965	−	0.646965i
$886$	965.885			1.09016
$887$	280.842	+	280.842i	0.316620	+	0.316620i	0.847467	−	0.530848i	$-0.178126\pi$
$887$	280.842	+	280.842i	0.316620	+	0.316620i	−0.530848	+	0.847467i	$0.678126\pi$
$888$	265.299	+	265.299i	0.298761	+	0.298761i
$889$	326.033	+	178.229i	0.366742	+	0.200482i
$890$	131.167	+	131.167i	0.147379	+	0.147379i
$891$	871.176	+	871.176i	0.977751	+	0.977751i
$892$			10.9771i			0.0123061i
$893$		−	1182.39i		−	1.32406i
$894$	−2714.90			−3.03680
$895$	−269.348	+	269.348i	−0.300948	+	0.300948i
$896$	252.687	−	462.239i	0.282016	−	0.515891i
$897$			96.0689i			0.107100i
$898$	1575.09			1.75400
$899$	16.7383	−	16.7383i	0.0186188	−	0.0186188i
$900$			289.735i			0.321927i
$901$		−	180.166i		−	0.199963i
$902$	−269.113	+	1321.81i	−0.298351	+	1.46542i
$903$	−297.809	−	1016.03i	−0.329800	−	1.12517i
$904$		−	264.696i		−	0.292806i
$905$	937.916	+	937.916i	1.03637	+	1.03637i
$906$			2624.31i			2.89659i
$907$			42.2615i			0.0465948i	0.999729	+	0.0232974i	$0.00741646\pi$
$907$			42.2615i			0.0465948i	−0.999729	+	0.0232974i	$0.992584\pi$
$908$	−401.269	−	401.269i	−0.441926	−	0.441926i
$909$	−463.330	+	463.330i	−0.509714	+	0.509714i
$910$	−34.3873	−	117.319i	−0.0377882	−	0.128921i
$911$		−	1364.86i		−	1.49820i	−0.662459	−	0.749098i	$-0.730487\pi$
$911$		−	1364.86i		−	1.49820i	0.662459	−	0.749098i	$-0.269513\pi$
$912$	1897.97			2.08111
$913$	350.844	−	350.844i	0.384276	−	0.384276i
$914$	1051.70	+	1051.70i	1.15066	+	1.15066i
$915$	53.1402	−	53.1402i	0.0580768	−	0.0580768i
$916$	−618.674	−	618.674i	−0.675409	−	0.675409i
$917$	−308.083	−	168.416i	−0.335968	−	0.183660i
$918$	−394.138			−0.429344
$919$	−911.889	+	911.889i	−0.992262	+	0.992262i	−0.999970	−	0.00770795i	$-0.997546\pi$
$919$	−911.889	+	911.889i	−0.992262	+	0.992262i	0.00770795	+	0.999970i	$0.497546\pi$
$920$		−	541.542i		−	0.588632i
$921$	1052.56	−	1052.56i	1.14285	−	1.14285i
$922$	224.982			0.244015
$923$	−10.2911			−0.0111496
$924$	822.224	+	449.476i	0.889853	+	0.486446i
$925$	−1271.03			−1.37408
$926$	−482.748	+	482.748i	−0.521326	+	0.521326i
$927$		−	429.260i		−	0.463063i
$928$	−836.928	+	836.928i	−0.901863	+	0.901863i
$929$	280.424	+	280.424i	0.301856	+	0.301856i	0.841740	−	0.539884i	$-0.181532\pi$
$929$	280.424	+	280.424i	0.301856	+	0.301856i	−0.539884	+	0.841740i	$0.681532\pi$
$930$	−39.0651	+	39.0651i	−0.0420054	+	0.0420054i
$931$	301.446	−	1379.41i	0.323787	−	1.48165i
$932$	108.946	+	108.946i	0.116894	+	0.116894i
$933$	−1544.85			−1.65579
$934$	1965.53			2.10442
$935$		−	667.017i		−	0.713388i
$936$	4.99638	−	4.99638i	0.00533801	−	0.00533801i
$937$	−45.3450	−	45.3450i	−0.0483938	−	0.0483938i	0.682496	−	0.730890i	$-0.260895\pi$
$937$	−45.3450	−	45.3450i	−0.0483938	−	0.0483938i	−0.730890	+	0.682496i	$0.760895\pi$
$938$	256.546	+	875.253i	0.273503	+	0.933105i
$939$	−605.701			−0.645049
$940$	−657.438	−	657.438i	−0.699403	−	0.699403i
$941$	−1300.01			−1.38152			−0.690762	−	0.723082i	$-0.742725\pi$
$941$	−1300.01			−1.38152			−0.690762	+	0.723082i	$0.742725\pi$
$942$	2616.46			2.77756
$943$	−1047.42	+	693.067i	−1.11073	+	0.734960i
$944$			593.488i			0.628695i
$945$	−289.454	−	987.525i	−0.306300	−	1.04500i
$946$	1004.57	+	1004.57i	1.06191	+	1.06191i
$947$	−3.29382			−0.00347816			−0.00173908	−	0.999998i	$-0.500554\pi$
$947$	−3.29382			−0.00347816			−0.00173908	+	0.999998i	$0.500554\pi$
$948$	−778.614			−0.821323
$949$	−18.3189	+	18.3189i	−0.0193034	+	0.0193034i
$950$	−1554.39	+	1554.39i	−1.63619	+	1.63619i
$951$	−735.315			−0.773202
$952$	119.537	−	35.0377i	0.125564	−	0.0368043i
$953$	1030.15			1.08096			0.540479	−	0.841357i	$-0.318243\pi$
$953$	1030.15			1.08096			0.540479	+	0.841357i	$0.318243\pi$
$954$	−150.483	−	150.483i	−0.157739	−	0.157739i
$955$	618.268	−	618.268i	0.647401	−	0.647401i
$956$	717.819	+	717.819i	0.750857	+	0.750857i
$957$	895.778	+	895.778i	0.936027	+	0.936027i
$958$	796.677	+	796.677i	0.831605	+	0.831605i
$959$	913.406	−	267.729i	0.952457	−	0.279175i
$960$	588.832	−	588.832i	0.613366	−	0.613366i
$961$	960.346			0.999320
$962$	−74.8247	−	74.8247i	−0.0777803	−	0.0777803i
$963$		−	456.330i		−	0.473863i
$964$	1030.05			1.06852
$965$	622.852	+	622.852i	0.645442	+	0.645442i
$966$	562.701	+	1919.76i	0.582506	+	1.98733i
$967$	418.419	−	418.419i	0.432698	−	0.432698i	−0.456847	−	0.889545i	$-0.651021\pi$
$967$	418.419	−	418.419i	0.432698	−	0.432698i	0.889545	+	0.456847i	$0.151021\pi$
$968$	76.2569			0.0787778
$969$	526.195	+	526.195i	0.543029	+	0.543029i
$970$	−2264.75	+	2264.75i	−2.33479	+	2.33479i
$971$	−210.595	+	210.595i	−0.216885	+	0.216885i	−0.807184	−	0.590299i	$-0.799010\pi$
$971$	−210.595	+	210.595i	−0.216885	+	0.216885i	0.590299	+	0.807184i	$0.299010\pi$
$972$	−369.068	+	369.068i	−0.379700	+	0.379700i
$973$	−475.757	+	870.301i	−0.488959	+	0.894451i
$974$	−669.085			−0.686946
$975$			89.8254i			0.0921286i
$976$	−55.0823			−0.0564367
$977$	−491.707	−	491.707i	−0.503282	−	0.503282i	0.409174	−	0.912456i	$-0.365817\pi$
$977$	−491.707	−	491.707i	−0.503282	−	0.503282i	−0.912456	+	0.409174i	$0.865817\pi$
$978$	575.362	+	575.362i	0.588304	+	0.588304i
$979$	−117.467			−0.119987
$980$	−599.378	−	934.601i	−0.611610	−	0.953675i
$981$	410.132	+	410.132i	0.418075	+	0.418075i
$982$			463.618i			0.472116i
$983$			459.116i			0.467056i	0.972350	+	0.233528i	$0.0750271\pi$
$983$			459.116i			0.467056i	−0.972350	+	0.233528i	$0.924973\pi$
$984$	339.679	+	69.1565i	0.345202	+	0.0702810i
$985$			2362.00i			2.39797i
$986$	−574.890			−0.583053
$987$	−882.815	−	482.598i	−0.894443	−	0.488955i
$988$	−79.8157			−0.0807851
$989$			1322.76i			1.33747i
$990$	−557.124	−	557.124i	−0.562752	−	0.562752i
$991$	−254.634	−	254.634i	−0.256947	−	0.256947i	0.566864	−	0.823811i	$-0.308156\pi$
$991$	−254.634	−	254.634i	−0.256947	−	0.256947i	−0.823811	+	0.566864i	$0.808156\pi$
$992$	32.6864			0.0329501
$993$	−474.250			−0.477593
$994$	−205.649	+	60.2778i	−0.206890	+	0.0606416i
$995$	−748.639	−	748.639i	−0.752401	−	0.752401i
$996$	307.785	+	307.785i	0.309021	+	0.309021i
$997$	945.983	−	945.983i	0.948829	−	0.948829i	−0.0499237	−	0.998753i	$-0.515898\pi$
$997$	945.983	−	945.983i	0.948829	−	0.948829i	0.998753	+	0.0499237i	$0.0158978\pi$
$998$	1154.07	−	1154.07i	1.15638	−	1.15638i
$999$	−629.834	−	629.834i	−0.630465	−	0.630465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.12	yes	108
7.6	odd	2	inner	287.3.g.a.132.11	✓	108
41.32	even	4	inner	287.3.g.a.237.43	yes	108
287.237	odd	4	inner	287.3.g.a.237.44	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.11	✓	108	7.6	odd	2	inner
287.3.g.a.132.12	yes	108	1.1	even	1	trivial
287.3.g.a.237.43	yes	108	41.32	even	4	inner
287.3.g.a.237.44	yes	108	287.237	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.66341i q^{2} +(2.47686 - 2.47686i) q^{3} -3.09375 q^{4} +7.32409 q^{5} +(-6.59690 - 6.59690i) q^{6} +(-6.14216 - 3.35766i) q^{7} -2.41372i q^{8} -3.26970i q^{9} +O(q^{10})\)	\(q-2.66341i q^{2} +(2.47686 - 2.47686i) q^{3} -3.09375 q^{4} +7.32409 q^{5} +(-6.59690 - 6.59690i) q^{6} +(-6.14216 - 3.35766i) q^{7} -2.41372i q^{8} -3.26970i q^{9} -19.5070i q^{10} +(8.73479 + 8.73479i) q^{11} +(-7.66279 + 7.66279i) q^{12} +(-0.633082 + 0.633082i) q^{13} +(-8.94283 + 16.3591i) q^{14} +(18.1408 - 18.1408i) q^{15} -18.8037 q^{16} +(-5.21316 - 5.21316i) q^{17} -8.70855 q^{18} +(-20.3757 - 20.3757i) q^{19} -22.6589 q^{20} +(-23.5298 + 6.89682i) q^{21} +(23.2643 - 23.2643i) q^{22} +30.6331 q^{23} +(-5.97846 - 5.97846i) q^{24} +28.6423 q^{25} +(1.68616 + 1.68616i) q^{26} +(14.1932 + 14.1932i) q^{27} +(19.0023 + 10.3878i) q^{28} +(20.7022 + 20.7022i) q^{29} +(-48.3163 - 48.3163i) q^{30} -0.808528i q^{31} +40.4271i q^{32} +43.2698 q^{33} +(-13.8848 + 13.8848i) q^{34} +(-44.9857 - 24.5918i) q^{35} +10.1156i q^{36} -44.3759 q^{37} +(-54.2689 + 54.2689i) q^{38} +3.13611i q^{39} -17.6783i q^{40} +(-34.1924 + 22.6248i) q^{41} +(18.3690 + 62.6694i) q^{42} +43.1807i q^{43} +(-27.0232 - 27.0232i) q^{44} -23.9476i q^{45} -81.5885i q^{46} +(29.0146 + 29.0146i) q^{47} +(-46.5742 + 46.5742i) q^{48} +(26.4522 + 41.2466i) q^{49} -76.2861i q^{50} -25.8246 q^{51} +(1.95860 - 1.95860i) q^{52} +(17.2800 + 17.2800i) q^{53} +(37.8022 - 37.8022i) q^{54} +(63.9744 + 63.9744i) q^{55} +(-8.10446 + 14.8255i) q^{56} -100.936 q^{57} +(55.1383 - 55.1383i) q^{58} -31.5623i q^{59} +(-56.1229 + 56.1229i) q^{60} +2.92933 q^{61} -2.15344 q^{62} +(-10.9786 + 20.0830i) q^{63} +32.4590 q^{64} +(-4.63675 + 4.63675i) q^{65} -115.245i q^{66} +(34.5924 - 34.5924i) q^{67} +(16.1282 + 16.1282i) q^{68} +(75.8740 - 75.8740i) q^{69} +(-65.4980 + 119.815i) q^{70} +(8.12779 + 8.12779i) q^{71} -7.89215 q^{72} +28.9361 q^{73} +118.191i q^{74} +(70.9430 - 70.9430i) q^{75} +(63.0374 + 63.0374i) q^{76} +(-24.3220 - 82.9789i) q^{77} +8.35276 q^{78} +(50.8049 + 50.8049i) q^{79} -137.720 q^{80} +99.7364 q^{81} +(60.2590 + 91.0683i) q^{82} -40.1662i q^{83} +(72.7951 - 21.3370i) q^{84} +(-38.1817 - 38.1817i) q^{85} +115.008 q^{86} +102.553 q^{87} +(21.0834 - 21.0834i) q^{88} +(-6.72411 + 6.72411i) q^{89} -63.7822 q^{90} +(6.01416 - 1.76281i) q^{91} -94.7711 q^{92} +(-2.00261 - 2.00261i) q^{93} +(77.2778 - 77.2778i) q^{94} +(-149.234 - 149.234i) q^{95} +(100.132 + 100.132i) q^{96} +(-116.099 - 116.099i) q^{97} +(109.857 - 70.4531i) q^{98} +(28.5602 - 28.5602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) 108 * q - 216 * q^4 - 2 * q^7	\( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Introduction

L-functions

Modular forms

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