LMFDB - Embedded newform 287.3.g.a.132.6

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			132.6
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.39532i q^{2} +(3.29534 - 3.29534i) q^{3} -7.52821 q^{4} -3.85237 q^{5} +(-11.1888 - 11.1888i) q^{6} +(-5.99443 + 3.61480i) q^{7} +11.9794i q^{8} -12.7186i q^{9} +O(q^{10})$	\(q-3.39532i q^{2} +(3.29534 - 3.29534i) q^{3} -7.52821 q^{4} -3.85237 q^{5} +(-11.1888 - 11.1888i) q^{6} +(-5.99443 + 3.61480i) q^{7} +11.9794i q^{8} -12.7186i q^{9} +13.0800i q^{10} +(-4.80013 - 4.80013i) q^{11} +(-24.8081 + 24.8081i) q^{12} +(10.4138 - 10.4138i) q^{13} +(12.2734 + 20.3530i) q^{14} +(-12.6949 + 12.6949i) q^{15} +10.5611 q^{16} +(4.31179 + 4.31179i) q^{17} -43.1837 q^{18} +(6.45808 + 6.45808i) q^{19} +29.0015 q^{20} +(-7.84170 + 31.6657i) q^{21} +(-16.2980 + 16.2980i) q^{22} +10.4426 q^{23} +(39.4763 + 39.4763i) q^{24} -10.1592 q^{25} +(-35.3584 - 35.3584i) q^{26} +(-12.2540 - 12.2540i) q^{27} +(45.1274 - 27.2130i) q^{28} +(-17.4031 - 17.4031i) q^{29} +(43.1032 + 43.1032i) q^{30} -39.1124i q^{31} +12.0592i q^{32} -31.6362 q^{33} +(14.6399 - 14.6399i) q^{34} +(23.0928 - 13.9256i) q^{35} +95.7483i q^{36} -71.6854 q^{37} +(21.9273 - 21.9273i) q^{38} -68.6344i q^{39} -46.1491i q^{40} +(27.5888 - 30.3291i) q^{41} +(107.515 + 26.6251i) q^{42} -37.9080i q^{43} +(36.1364 + 36.1364i) q^{44} +48.9967i q^{45} -35.4560i q^{46} +(18.4611 + 18.4611i) q^{47} +(34.8026 - 34.8026i) q^{48} +(22.8664 - 43.3374i) q^{49} +34.4939i q^{50} +28.4177 q^{51} +(-78.3976 + 78.3976i) q^{52} +(-18.6776 - 18.6776i) q^{53} +(-41.6064 + 41.6064i) q^{54} +(18.4919 + 18.4919i) q^{55} +(-43.3032 - 71.8098i) q^{56} +42.5632 q^{57} +(-59.0890 + 59.0890i) q^{58} +48.9655i q^{59} +(95.5698 - 95.5698i) q^{60} -2.80691 q^{61} -132.799 q^{62} +(45.9752 + 76.2407i) q^{63} +83.1895 q^{64} +(-40.1180 + 40.1180i) q^{65} +107.415i q^{66} +(40.4702 - 40.4702i) q^{67} +(-32.4601 - 32.4601i) q^{68} +(34.4120 - 34.4120i) q^{69} +(-47.2817 - 78.4074i) q^{70} +(51.9908 + 51.9908i) q^{71} +152.361 q^{72} +21.4373 q^{73} +243.395i q^{74} +(-33.4782 + 33.4782i) q^{75} +(-48.6178 - 48.6178i) q^{76} +(46.1256 + 11.4225i) q^{77} -233.036 q^{78} +(-76.6677 - 76.6677i) q^{79} -40.6854 q^{80} +33.7047 q^{81} +(-102.977 - 93.6729i) q^{82} -135.452i q^{83} +(59.0340 - 238.386i) q^{84} +(-16.6106 - 16.6106i) q^{85} -128.710 q^{86} -114.698 q^{87} +(57.5028 - 57.5028i) q^{88} +(-1.82467 + 1.82467i) q^{89} +166.360 q^{90} +(-24.7811 + 100.069i) q^{91} -78.6142 q^{92} +(-128.889 - 128.889i) q^{93} +(62.6815 - 62.6815i) q^{94} +(-24.8789 - 24.8789i) q^{95} +(39.7393 + 39.7393i) q^{96} +(-11.3772 - 11.3772i) q^{97} +(-147.144 - 77.6388i) q^{98} +(-61.0509 + 61.0509i) 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 $

$2$		−	3.39532i		−	1.69766i	−0.528665	−	0.848831i	$-0.677307\pi$
$2$		−	3.39532i		−	1.69766i	0.528665	−	0.848831i	$-0.322693\pi$
$3$	3.29534	−	3.29534i	1.09845	−	1.09845i	0.103856	−	0.994592i	$-0.466882\pi$
$3$	3.29534	−	3.29534i	1.09845	−	1.09845i	0.994592	−	0.103856i	$-0.0331181\pi$
$4$	−7.52821			−1.88205
$5$	−3.85237			−0.770474			−0.385237	−	0.922818i	$-0.625880\pi$
$5$	−3.85237			−0.770474			−0.385237	+	0.922818i	$0.625880\pi$
$6$	−11.1888	−	11.1888i	−1.86479	−	1.86479i
$7$	−5.99443	+	3.61480i	−0.856347	+	0.516400i
$7$	−5.99443	+	3.61480i	−0.856347	+	0.516400i
$8$			11.9794i			1.49743i
$9$		−	12.7186i		−	1.41318i
$10$			13.0800i			1.30800i
$11$	−4.80013	−	4.80013i	−0.436375	−	0.436375i	0.454415	−	0.890790i	$-0.349848\pi$
$11$	−4.80013	−	4.80013i	−0.436375	−	0.436375i	−0.890790	+	0.454415i	$0.849848\pi$
$12$	−24.8081	+	24.8081i	−2.06734	+	2.06734i
$13$	10.4138	−	10.4138i	0.801065	−	0.801065i	−0.182197	−	0.983262i	$-0.558321\pi$
$13$	10.4138	−	10.4138i	0.801065	−	0.801065i	0.983262	+	0.182197i	$0.0583209\pi$
$14$	12.2734	+	20.3530i	0.876673	+	1.45379i
$15$	−12.6949	+	12.6949i	−0.846326	+	0.846326i
$16$	10.5611			0.660071
$17$	4.31179	+	4.31179i	0.253635	+	0.253635i	0.822459	−	0.568824i	$-0.192602\pi$
$17$	4.31179	+	4.31179i	0.253635	+	0.253635i	−0.568824	+	0.822459i	$0.692602\pi$
$18$	−43.1837			−2.39910
$19$	6.45808	+	6.45808i	0.339899	+	0.339899i	0.856329	−	0.516430i	$-0.172739\pi$
$19$	6.45808	+	6.45808i	0.339899	+	0.339899i	−0.516430	+	0.856329i	$0.672739\pi$
$20$	29.0015			1.45007
$21$	−7.84170	+	31.6657i	−0.373414	+	1.50789i
$22$	−16.2980	+	16.2980i	−0.740818	+	0.740818i
$23$	10.4426			0.454027			0.227013	−	0.973892i	$-0.427104\pi$
$23$	10.4426			0.454027			0.227013	+	0.973892i	$0.427104\pi$
$24$	39.4763	+	39.4763i	1.64485	+	1.64485i
$25$	−10.1592			−0.406370
$26$	−35.3584	−	35.3584i	−1.35994	−	1.35994i
$27$	−12.2540	−	12.2540i	−0.453854	−	0.453854i
$28$	45.1274	−	27.2130i	1.61169	−	0.971893i
$29$	−17.4031	−	17.4031i	−0.600106	−	0.600106i	0.340235	−	0.940341i	$-0.389494\pi$
$29$	−17.4031	−	17.4031i	−0.600106	−	0.600106i	−0.940341	+	0.340235i	$0.889494\pi$
$30$	43.1032	+	43.1032i	1.43677	+	1.43677i
$31$		−	39.1124i		−	1.26169i	−0.775909	−	0.630845i	$-0.782708\pi$
$31$		−	39.1124i		−	1.26169i	0.775909	−	0.630845i	$-0.217292\pi$
$32$			12.0592i			0.376850i
$33$	−31.6362			−0.958672
$34$	14.6399	−	14.6399i	0.430586	−	0.430586i
$35$	23.0928	−	13.9256i	0.659793	−	0.397873i
$36$			95.7483i			2.65967i
$37$	−71.6854			−1.93744			−0.968722	−	0.248150i	$-0.920177\pi$
$37$	−71.6854			−1.93744			−0.968722	+	0.248150i	$0.920177\pi$
$38$	21.9273	−	21.9273i	0.577033	−	0.577033i
$39$		−	68.6344i		−	1.75986i
$40$		−	46.1491i		−	1.15373i
$41$	27.5888	−	30.3291i	0.672898	−	0.739735i
$41$	27.5888	−	30.3291i	0.672898	−	0.739735i
$42$	107.515	+	26.6251i	2.55989	+	0.633931i
$43$		−	37.9080i		−	0.881582i	−0.897610	−	0.440791i	$-0.854698\pi$
$43$		−	37.9080i		−	0.881582i	0.897610	−	0.440791i	$-0.145302\pi$
$44$	36.1364	+	36.1364i	0.821282	+	0.821282i
$45$			48.9967i			1.08882i
$46$		−	35.4560i		−	0.770783i
$47$	18.4611	+	18.4611i	0.392790	+	0.392790i	0.875681	−	0.482890i	$-0.160413\pi$
$47$	18.4611	+	18.4611i	0.392790	+	0.392790i	−0.482890	+	0.875681i	$0.660413\pi$
$48$	34.8026	−	34.8026i	0.725054	−	0.725054i
$49$	22.8664	−	43.3374i	0.466661	−	0.884436i
$50$			34.4939i			0.689879i
$51$	28.4177			0.557210
$52$	−78.3976	+	78.3976i	−1.50765	+	1.50765i
$53$	−18.6776	−	18.6776i	−0.352408	−	0.352408i	0.508597	−	0.861005i	$-0.330164\pi$
$53$	−18.6776	−	18.6776i	−0.352408	−	0.352408i	−0.861005	+	0.508597i	$0.830164\pi$
$54$	−41.6064	+	41.6064i	−0.770489	+	0.770489i
$55$	18.4919	+	18.4919i	0.336216	+	0.336216i
$56$	−43.3032	−	71.8098i	−0.773272	−	1.28232i
$57$	42.5632			0.746723
$58$	−59.0890	+	59.0890i	−1.01878	+	1.01878i
$59$			48.9655i			0.829923i	0.909839	+	0.414962i	$0.136205\pi$
$59$			48.9655i			0.829923i	−0.909839	+	0.414962i	$0.863795\pi$
$60$	95.5698	−	95.5698i	1.59283	−	1.59283i
$61$	−2.80691			−0.0460148			−0.0230074	−	0.999735i	$-0.507324\pi$
$61$	−2.80691			−0.0460148			−0.0230074	+	0.999735i	$0.507324\pi$
$62$	−132.799			−2.14192
$63$	45.9752	+	76.2407i	0.729765	+	1.21017i
$64$	83.1895			1.29984
$65$	−40.1180	+	40.1180i	−0.617200	+	0.617200i
$66$			107.415i			1.62750i
$67$	40.4702	−	40.4702i	0.604033	−	0.604033i	−0.337347	−	0.941380i	$-0.609530\pi$
$67$	40.4702	−	40.4702i	0.604033	−	0.604033i	0.941380	+	0.337347i	$0.109530\pi$
$68$	−32.4601	−	32.4601i	−0.477354	−	0.477354i
$69$	34.4120	−	34.4120i	0.498725	−	0.498725i
$70$	−47.2817	−	78.4074i	−0.675453	−	1.12011i
$71$	51.9908	+	51.9908i	0.732264	+	0.732264i	0.971068	−	0.238804i	$-0.0767553\pi$
$71$	51.9908	+	51.9908i	0.732264	+	0.732264i	−0.238804	+	0.971068i	$0.576755\pi$
$72$	152.361			2.11613
$73$	21.4373			0.293662			0.146831	−	0.989162i	$-0.453093\pi$
$73$	21.4373			0.293662			0.146831	+	0.989162i	$0.453093\pi$
$74$			243.395i			3.28912i
$75$	−33.4782	+	33.4782i	−0.446376	+	0.446376i
$76$	−48.6178	−	48.6178i	−0.639708	−	0.639708i
$77$	46.1256	+	11.4225i	0.599033	+	0.148345i
$78$	−233.036			−2.98764
$79$	−76.6677	−	76.6677i	−0.970477	−	0.970477i	0.0290993	−	0.999577i	$-0.490736\pi$
$79$	−76.6677	−	76.6677i	−0.970477	−	0.970477i	−0.999577	+	0.0290993i	$0.990736\pi$
$80$	−40.6854			−0.508568
$81$	33.7047			0.416108
$82$	−102.977	−	93.6729i	−1.25582	−	1.14235i
$83$		−	135.452i		−	1.63195i	−0.578089	−	0.815974i	$-0.696201\pi$
$83$		−	135.452i		−	1.63195i	0.578089	−	0.815974i	$-0.303799\pi$
$84$	59.0340	−	238.386i	0.702785	−	2.83793i
$85$	−16.6106	−	16.6106i	−0.195419	−	0.195419i
$86$	−128.710			−1.49663
$87$	−114.698			−1.31837
$88$	57.5028	−	57.5028i	0.653441	−	0.653441i
$89$	−1.82467	+	1.82467i	−0.0205019	+	0.0205019i	−0.717283	−	0.696782i	$-0.754615\pi$
$89$	−1.82467	+	1.82467i	−0.0205019	+	0.0205019i	0.696782	+	0.717283i	$0.254615\pi$
$90$	166.360			1.84844
$91$	−24.7811	+	100.069i	−0.272320	+	1.09966i
$92$	−78.6142			−0.854502
$93$	−128.889	−	128.889i	−1.38590	−	1.38590i
$94$	62.6815	−	62.6815i	0.666825	−	0.666825i
$95$	−24.8789	−	24.8789i	−0.261883	−	0.261883i
$96$	39.7393	+	39.7393i	0.413951	+	0.413951i
$97$	−11.3772	−	11.3772i	−0.117290	−	0.117290i	0.646025	−	0.763316i	$-0.276430\pi$
$97$	−11.3772	−	11.3772i	−0.117290	−	0.117290i	−0.763316	+	0.646025i	$0.776430\pi$
$98$	−147.144	−	77.6388i	−1.50147	−	0.792233i
$99$	−61.0509	+	61.0509i	−0.616676	+	0.616676i
$100$	76.4810			0.764810
$101$	93.8797	+	93.8797i	0.929502	+	0.929502i	0.997674	−	0.0681719i	$-0.0217166\pi$
$101$	93.8797	+	93.8797i	0.929502	+	0.929502i	−0.0681719	+	0.997674i	$0.521717\pi$
$102$		−	96.4872i		−	0.945953i
$103$	−165.124			−1.60315			−0.801573	−	0.597896i	$-0.796003\pi$
$103$	−165.124			−1.60315			−0.801573	+	0.597896i	$0.796003\pi$
$104$	124.752	+	124.752i	1.19954	+	1.19954i
$105$	30.2091	−	121.988i	0.287706	−	1.16179i
$106$	−63.4166	+	63.4166i	−0.598270	+	0.598270i
$107$	−5.76942			−0.0539198			−0.0269599	−	0.999637i	$-0.508583\pi$
$107$	−5.76942			−0.0539198			−0.0269599	+	0.999637i	$0.508583\pi$
$108$	92.2511	+	92.2511i	0.854176	+	0.854176i
$109$	95.5118	−	95.5118i	0.876255	−	0.876255i	−0.116890	−	0.993145i	$-0.537292\pi$
$109$	95.5118	−	95.5118i	0.876255	−	0.876255i	0.993145	+	0.116890i	$0.0372924\pi$
$110$	62.7859	−	62.7859i	0.570781	−	0.570781i
$111$	−236.228	+	236.228i	−2.12818	+	2.12818i
$112$	−63.3080	+	38.1764i	−0.565250	+	0.340861i
$113$	207.322			1.83470			0.917352	−	0.398077i	$-0.130322\pi$
$113$	207.322			1.83470			0.917352	+	0.398077i	$0.130322\pi$
$114$		−	144.516i		−	1.26768i
$115$	−40.2288			−0.349816
$116$	131.014	+	131.014i	1.12943	+	1.12943i
$117$	−132.449	−	132.449i	−1.13205	−	1.13205i
$118$	166.254			1.40893
$119$	−41.4330	−	10.2605i	−0.348177	−	0.0862224i
$120$	−152.077	−	152.077i	−1.26731	−	1.26731i
$121$		−	74.9175i		−	0.619153i
$122$			9.53035i			0.0781176i
$123$	−9.03033	−	190.860i	−0.0734173	−	1.55170i
$124$			294.446i			2.37457i
$125$	135.446			1.08357
$126$	258.862	−	156.101i	2.05446	−	1.23889i
$127$	162.121			1.27655			0.638273	−	0.769810i	$-0.279649\pi$
$127$	162.121			1.27655			0.638273	+	0.769810i	$0.279649\pi$
$128$		−	234.218i		−	1.82983i
$129$	−124.920	−	124.920i	−0.968372	−	0.968372i
$130$	136.213	+	136.213i	1.04780	+	1.04780i
$131$	101.965			0.778362			0.389181	−	0.921161i	$-0.372758\pi$
$131$	101.965			0.778362			0.389181	+	0.921161i	$0.372758\pi$
$132$	238.164			1.80427
$133$	−62.0572	−	15.3678i	−0.466595	−	0.115548i
$134$	−137.409	−	137.409i	−1.02544	−	1.02544i
$135$	47.2071	+	47.2071i	0.349682	+	0.349682i
$136$	−51.6528	+	51.6528i	−0.379800	+	0.379800i
$137$	−164.126	+	164.126i	−1.19800	+	1.19800i	−0.223240	+	0.974763i	$0.571663\pi$
$137$	−164.126	+	164.126i	−1.19800	+	1.19800i	−0.974763	+	0.223240i	$0.928337\pi$
$138$	−116.840	−	116.840i	−0.846665	−	0.846665i
$139$			109.446i			0.787380i	0.919243	+	0.393690i	$0.128802\pi$
$139$			109.446i			0.787380i	−0.919243	+	0.393690i	$0.871198\pi$
$140$	−173.847	+	104.835i	−1.24177	+	0.748818i
$141$	121.672			0.862920
$142$	176.525	−	176.525i	1.24314	−	1.24314i
$143$	−99.9756			−0.699130
$144$		−	134.323i		−	0.932797i
$145$	67.0431	+	67.0431i	0.462366	+	0.462366i
$146$		−	72.7866i		−	0.498538i
$147$	−67.4589	−	218.164i	−0.458904	−	1.48411i
$148$	539.663			3.64637
$149$	−147.922	+	147.922i	−0.992765	+	0.992765i	−0.999974	−	0.00720920i	$-0.997705\pi$
$149$	−147.922	+	147.922i	−0.992765	+	0.992765i	0.00720920	+	0.999974i	$0.497705\pi$
$150$	113.669	+	113.669i	0.757796	+	0.757796i
$151$	−20.6936	−	20.6936i	−0.137044	−	0.137044i	0.635257	−	0.772301i	$-0.280894\pi$
$151$	−20.6936	−	20.6936i	−0.137044	−	0.137044i	−0.772301	+	0.635257i	$0.780894\pi$
$152$	−77.3640	+	77.3640i	−0.508974	+	0.508974i
$153$	54.8399	−	54.8399i	0.358431	−	0.358431i
$154$	38.7832	−	156.611i	0.251839	−	1.01696i
$155$			150.675i			0.972099i
$156$			516.694i			3.31214i
$157$	147.505	−	147.505i	0.939523	−	0.939523i	−0.0587500	−	0.998273i	$-0.518711\pi$
$157$	147.505	−	147.505i	0.939523	−	0.939523i	0.998273	+	0.0587500i	$0.0187115\pi$
$158$	−260.312	+	260.312i	−1.64754	+	1.64754i
$159$	−123.099			−0.774205
$160$		−	46.4565i		−	0.290353i
$161$	−62.5975	+	37.7480i	−0.388804	+	0.234459i
$162$		−	114.438i		−	0.706410i
$163$	38.0580			0.233485			0.116742	−	0.993162i	$-0.462755\pi$
$163$	38.0580			0.233485			0.116742	+	0.993162i	$0.462755\pi$
$164$	−207.694	+	228.324i	−1.26643	+	1.39222i
$165$	121.874			0.738632
$166$	−459.902			−2.77049
$167$	−119.062	+	119.062i	−0.712946	+	0.712946i	−0.967150	−	0.254205i	$-0.918186\pi$
$167$	−119.062	+	119.062i	−0.712946	+	0.712946i	0.254205	+	0.967150i	$0.418186\pi$
$168$	−379.337	−	93.9390i	−2.25796	−	0.559161i
$169$		−	47.8962i		−	0.283410i
$170$	−56.3984	+	56.3984i	−0.331755	+	0.331755i
$171$	82.1377	−	82.1377i	0.480337	−	0.480337i
$172$			285.380i			1.65918i
$173$	−171.362			−0.990530			−0.495265	−	0.868742i	$-0.664929\pi$
$173$	−171.362			−0.990530			−0.495265	+	0.868742i	$0.664929\pi$
$174$			389.438i			2.23815i
$175$	60.8989	−	36.7237i	0.347994	−	0.209850i
$176$	−50.6948	−	50.6948i	−0.288039	−	0.288039i
$177$	161.358	+	161.358i	0.911628	+	0.911628i
$178$	6.19535	+	6.19535i	0.0348053	+	0.0348053i
$179$	200.065	−	200.065i	1.11768	−	1.11768i	0.125601	−	0.992081i	$-0.459914\pi$
$179$	200.065	−	200.065i	1.11768	−	1.11768i	0.992081	−	0.125601i	$-0.0400859\pi$
$180$		−	368.858i		−	2.04921i
$181$	230.989	+	230.989i	1.27618	+	1.27618i	0.942788	+	0.333393i	$0.108194\pi$
$181$	230.989	+	230.989i	1.27618	+	1.27618i	0.333393	+	0.942788i	$0.391806\pi$
$182$	339.767	+	84.1397i	1.86685	+	0.462306i
$183$	−9.24972	+	9.24972i	−0.0505449	+	0.0505449i
$184$			125.096i			0.679872i
$185$	276.159			1.49275
$186$	−437.619	+	437.619i	−2.35279	+	2.35279i
$187$		−	41.3943i		−	0.221360i
$188$	−138.979	−	138.979i	−0.739252	−	0.739252i
$189$	117.752	+	29.1601i	0.623026	+	0.154286i
$190$	−84.4719	+	84.4719i	−0.444589	+	0.444589i
$191$	−143.701	+	143.701i	−0.752359	+	0.752359i	−0.974919	−	0.222560i	$-0.928559\pi$
$191$	−143.701	+	143.701i	−0.752359	+	0.752359i	0.222560	+	0.974919i	$0.428559\pi$
$192$	274.138	−	274.138i	1.42780	−	1.42780i
$193$	183.395	+	183.395i	0.950232	+	0.950232i	0.998819	−	0.0485871i	$-0.0154718\pi$
$193$	183.395	+	183.395i	0.950232	+	0.950232i	−0.0485871	+	0.998819i	$0.515472\pi$
$194$	−38.6291	+	38.6291i	−0.199119	+	0.199119i
$195$			264.405i			1.35592i
$196$	−172.143	+	326.253i	−0.878282	+	1.66456i
$197$		−	176.115i		−	0.893986i	−0.894537	−	0.446993i	$-0.852495\pi$
$197$		−	176.115i		−	0.893986i	0.894537	−	0.446993i	$-0.147505\pi$
$198$	207.287	+	207.287i	1.04691	+	1.04691i
$199$	−128.769	−	128.769i	−0.647081	−	0.647081i	0.305205	−	0.952287i	$-0.401275\pi$
$199$	−128.769	−	128.769i	−0.647081	−	0.647081i	−0.952287	+	0.305205i	$0.901275\pi$
$200$		−	121.702i		−	0.608510i
$201$		−	266.727i		−	1.32700i
$202$	318.752	−	318.752i	1.57798	−	1.57798i
$203$	167.230	+	41.4129i	0.823794	+	0.204004i
$204$	−213.934			−1.04870
$205$	−106.282	+	116.839i	−0.518450	+	0.569947i
$206$			560.650i			2.72160i
$207$		−	132.815i		−	0.641620i
$208$	109.982	−	109.982i	0.528760	−	0.528760i
$209$		−	61.9992i		−	0.296647i
$210$	−414.189	−	102.570i	−1.97233	−	0.488427i
$211$	131.762	−	131.762i	0.624465	−	0.624465i	−0.322205	−	0.946670i	$-0.604424\pi$
$211$	131.762	−	131.762i	0.624465	−	0.624465i	0.946670	+	0.322205i	$0.104424\pi$
$212$	140.609	+	140.609i	0.663251	+	0.663251i
$213$	342.655			1.60871
$214$			19.5890i			0.0915375i
$215$			146.036i			0.679236i
$216$	146.796	−	146.796i	0.679613	−	0.679613i
$217$	141.384	+	234.456i	0.651537	+	1.08044i
$218$	−324.293	−	324.293i	−1.48758	−	1.48758i
$219$	70.6433	−	70.6433i	0.322572	−	0.322572i
$220$	−139.211	−	139.211i	−0.632776	−	0.632776i
$221$	89.8047			0.406356
$222$	802.070	+	802.070i	3.61293	+	3.61293i
$223$		−	117.058i		−	0.524925i	−0.964942	−	0.262463i	$-0.915465\pi$
$223$		−	117.058i		−	0.524925i	0.964942	−	0.262463i	$-0.0845346\pi$
$224$	−43.5917	−	72.2881i	−0.194606	−	0.322715i
$225$			129.211i			0.574273i
$226$		−	703.923i		−	3.11470i
$227$	155.936	+	155.936i	0.686944	+	0.686944i	0.961555	−	0.274611i	$-0.0885491\pi$
$227$	155.936	+	155.936i	0.686944	+	0.686944i	−0.274611	+	0.961555i	$0.588549\pi$
$228$	−320.425			−1.40537
$229$	249.312	+	249.312i	1.08870	+	1.08870i	0.995663	+	0.0930357i	$0.0296571\pi$
$229$	249.312	+	249.312i	1.08870	+	1.08870i	0.0930357	+	0.995663i	$0.470343\pi$
$230$			136.590i			0.593868i
$231$	189.641	−	114.358i	0.820956	−	0.495058i
$232$	208.479	−	208.479i	0.898615	−	0.898615i
$233$	73.9906	+	73.9906i	0.317556	+	0.317556i	0.847828	−	0.530271i	$-0.177910\pi$
$233$	73.9906	+	73.9906i	0.317556	+	0.317556i	−0.530271	+	0.847828i	$0.677910\pi$
$234$	−449.708	+	449.708i	−1.92183	+	1.92183i
$235$	−71.1192	−	71.1192i	−0.302635	−	0.302635i
$236$		−	368.623i		−	1.56196i
$237$	−505.293			−2.13204
$238$	−34.8376	+	140.678i	−0.146376	+	0.591086i
$239$	−102.295	−	102.295i	−0.428013	−	0.428013i	0.459938	−	0.887951i	$-0.347872\pi$
$239$	−102.295	−	102.295i	−0.428013	−	0.428013i	−0.887951	+	0.459938i	$0.847872\pi$
$240$	−134.072	+	134.072i	−0.558635	+	0.558635i
$241$	−145.163			−0.602337			−0.301168	−	0.953571i	$-0.597377\pi$
$241$	−145.163			−0.602337			−0.301168	+	0.953571i	$0.597377\pi$
$242$	−254.369			−1.05111
$243$	221.355	−	221.355i	0.910926	−	0.910926i
$244$	21.1310			0.0866024
$245$	−88.0898	+	166.952i	−0.359550	+	0.681435i
$246$	−648.030	+	30.6609i	−2.63427	+	0.124638i
$247$	134.507			0.544562
$248$	468.544			1.88929
$249$	−446.360	−	446.360i	−1.79261	−	1.79261i
$250$		−	459.884i		−	1.83954i
$251$	−204.433			−0.814472			−0.407236	−	0.913323i	$-0.633507\pi$
$251$	−204.433			−0.814472			−0.407236	+	0.913323i	$0.633507\pi$
$252$	−346.111	−	573.956i	−1.37346	−	2.27760i
$253$	−50.1259	−	50.1259i	−0.198126	−	0.198126i
$254$		−	550.454i		−	2.16714i
$255$	−109.475			−0.429315
$256$	−462.488			−1.80660
$257$	266.034	−	266.034i	1.03515	−	1.03515i	0.0357937	−	0.999359i	$-0.488604\pi$
$257$	266.034	−	266.034i	1.03515	−	1.03515i	0.999359	−	0.0357937i	$-0.0113959\pi$
$258$	−424.144	+	424.144i	−1.64397	+	1.64397i
$259$	429.713	−	259.129i	1.65912	−	1.00050i
$260$	302.017	−	302.017i	1.16160	−	1.16160i
$261$	−221.343	+	221.343i	−0.848056	+	0.848056i
$262$		−	346.205i		−	1.32139i
$263$	−78.5274	+	78.5274i	−0.298583	+	0.298583i	−0.840459	−	0.541876i	$-0.817714\pi$
$263$	−78.5274	+	78.5274i	−0.298583	+	0.298583i	0.541876	+	0.840459i	$0.317714\pi$
$264$		−	378.983i		−	1.43554i
$265$	71.9532	+	71.9532i	0.271521	+	0.271521i
$266$	−52.1787	+	210.704i	−0.196161	+	0.792121i
$267$			12.0258i			0.0450406i
$268$	−304.668	+	304.668i	−1.13682	+	1.13682i
$269$		−	272.034i		−	1.01128i	−0.862744	−	0.505640i	$-0.831256\pi$
$269$		−	272.034i		−	1.01128i	0.862744	−	0.505640i	$-0.168744\pi$
$270$	160.283	−	160.283i	0.593642	−	0.593642i
$271$			34.8968i			0.128771i	0.997925	+	0.0643853i	$0.0205087\pi$
$271$			34.8968i			0.128771i	−0.997925	+	0.0643853i	$0.979491\pi$
$272$	45.5374	+	45.5374i	0.167417	+	0.167417i
$273$	248.100	+	411.424i	0.908790	+	1.50705i
$274$	557.262	+	557.262i	2.03380	+	2.03380i
$275$	48.7657	+	48.7657i	0.177330	+	0.177330i
$276$	−259.061	+	259.061i	−0.938626	+	0.938626i
$277$	−152.656			−0.551103			−0.275552	−	0.961286i	$-0.588861\pi$
$277$	−152.656			−0.551103			−0.275552	+	0.961286i	$0.588861\pi$
$278$	371.604			1.33670
$279$	−497.454			−1.78299
$280$	166.820	+	276.638i	0.595786	+	0.987992i
$281$	−82.3306	+	82.3306i	−0.292992	+	0.292992i	−0.838261	−	0.545269i	$-0.816427\pi$
$281$	−82.3306	+	82.3306i	−0.292992	+	0.292992i	0.545269	+	0.838261i	$0.316427\pi$
$282$		−	413.115i		−	1.46495i
$283$			47.0966i			0.166419i	0.996532	+	0.0832095i	$0.0265171\pi$
$283$			47.0966i			0.166419i	−0.996532	+	0.0832095i	$0.973483\pi$
$284$	−391.397	−	391.397i	−1.37816	−	1.37816i
$285$	−163.969			−0.575330
$286$			339.449i			1.18689i
$287$	−55.7454	+	281.534i	−0.194235	+	0.980955i
$288$	153.376			0.532556
$289$		−	251.817i		−	0.871339i
$290$	227.633	−	227.633i	0.784941	−	0.784941i
$291$	−74.9833			−0.257675
$292$	−161.385			−0.552687
$293$	−48.1913	−	48.1913i	−0.164476	−	0.164476i	0.620071	−	0.784546i	$-0.287104\pi$
$293$	−48.1913	−	48.1913i	−0.164476	−	0.164476i	−0.784546	+	0.620071i	$0.787104\pi$
$294$	−740.738	+	229.045i	−2.51952	+	0.779063i
$295$		−	188.633i		−	0.639434i
$296$		−	858.749i		−	2.90118i
$297$			117.642i			0.396101i
$298$	502.243	+	502.243i	1.68538	+	1.68538i
$299$	108.748	−	108.748i	0.363705	−	0.363705i
$300$	252.031	−	252.031i	0.840104	−	0.840104i
$301$	137.030	+	227.237i	0.455249	+	0.754940i
$302$	−70.2615	+	70.2615i	−0.232654	+	0.232654i
$303$	618.732			2.04202
$304$	68.2047	+	68.2047i	0.224357	+	0.224357i
$305$	10.8132			0.0354532
$306$	−186.199	−	186.199i	−0.608494	−	0.608494i
$307$	10.6699			0.0347555			0.0173778	−	0.999849i	$-0.494468\pi$
$307$	10.6699			0.0347555			0.0173778	+	0.999849i	$0.494468\pi$
$308$	−347.243	−	85.9912i	−1.12741	−	0.279192i
$309$	−544.141	+	544.141i	−1.76097	+	1.76097i
$310$	511.591			1.65029
$311$	148.706	+	148.706i	0.478153	+	0.478153i	0.904541	−	0.426387i	$-0.140214\pi$
$311$	148.706	+	148.706i	0.478153	+	0.478153i	−0.426387	+	0.904541i	$0.640214\pi$
$312$	822.200			2.63526
$313$	181.927	+	181.927i	0.581238	+	0.581238i	0.935243	−	0.354006i	$-0.115181\pi$
$313$	181.927	+	181.927i	0.581238	+	0.581238i	−0.354006	+	0.935243i	$0.615181\pi$
$314$	−500.827	−	500.827i	−1.59499	−	1.59499i
$315$	−177.113	−	293.707i	−0.562265	−	0.932405i
$316$	577.171	+	577.171i	1.82649	+	1.82649i
$317$	154.294	+	154.294i	0.486733	+	0.486733i	0.907274	−	0.420541i	$-0.138160\pi$
$317$	154.294	+	154.294i	0.486733	+	0.486733i	−0.420541	+	0.907274i	$0.638160\pi$
$318$			417.959i			1.31434i
$319$			167.074i			0.523743i
$320$	−320.477			−1.00149
$321$	−19.0122	+	19.0122i	−0.0592281	+	0.0592281i
$322$	128.167	+	212.539i	0.398033	+	0.660058i
$323$			55.6918i			0.172420i
$324$	−253.736			−0.783137
$325$	−105.797	+	105.797i	−0.325529	+	0.325529i
$326$		−	129.219i		−	0.396378i
$327$		−	629.489i		−	1.92504i
$328$	363.326	+	330.498i	1.10770	+	1.00762i
$329$	−177.397	−	43.9307i	−0.539202	−	0.133528i
$330$		−	413.802i		−	1.25395i
$331$	−433.399	−	433.399i	−1.30936	−	1.30936i	−0.921874	−	0.387489i	$-0.873343\pi$
$331$	−433.399	−	433.399i	−1.30936	−	1.30936i	−0.387489	−	0.921874i	$-0.626657\pi$
$332$			1019.71i			3.07141i
$333$			911.737i			2.73795i
$334$	404.254	+	404.254i	1.21034	+	1.21034i
$335$	−155.906	+	155.906i	−0.465392	+	0.465392i
$336$	−82.8172	+	334.426i	−0.246480	+	0.995316i
$337$		−	328.114i		−	0.973633i	−0.873504	−	0.486817i	$-0.838158\pi$
$337$		−	328.114i		−	0.973633i	0.873504	−	0.486817i	$-0.161842\pi$
$338$	−162.623			−0.481134
$339$	683.196	−	683.196i	2.01533	−	2.01533i
$340$	125.048	+	125.048i	0.367789	+	0.367789i
$341$	−187.745	+	187.745i	−0.550570	+	0.550570i
$342$	−278.884	−	278.884i	−0.815450	−	0.815450i
$343$	19.5849	+	342.440i	0.0570989	+	0.998369i
$344$	454.116			1.32010
$345$	−132.568	+	132.568i	−0.384254	+	0.384254i
$346$			581.828i			1.68158i
$347$	110.611	−	110.611i	0.318764	−	0.318764i	−0.529528	−	0.848292i	$-0.677631\pi$
$347$	110.611	−	110.611i	0.318764	−	0.318764i	0.848292	+	0.529528i	$0.177631\pi$
$348$	863.473			2.48124
$349$	−527.539			−1.51157			−0.755786	−	0.654818i	$-0.772745\pi$
$349$	−527.539			−1.51157			−0.755786	+	0.654818i	$0.772745\pi$
$350$	−124.689	−	206.771i	−0.356254	−	0.590776i
$351$	−255.223			−0.727132
$352$	57.8858	−	57.8858i	0.164448	−	0.164448i
$353$		−	161.096i		−	0.456362i	−0.973619	−	0.228181i	$-0.926722\pi$
$353$		−	161.096i		−	0.456362i	0.973619	−	0.228181i	$-0.0732778\pi$
$354$	547.863	−	547.863i	1.54764	−	1.54764i
$355$	−200.288	−	200.288i	−0.564190	−	0.564190i
$356$	13.7365	−	13.7365i	0.0385857	−	0.0385857i
$357$	−170.348	+	102.724i	−0.477165	+	0.287743i
$358$	−679.285	−	679.285i	−1.89744	−	1.89744i
$359$	−16.2806			−0.0453500			−0.0226750	−	0.999743i	$-0.507218\pi$
$359$	−16.2806			−0.0453500			−0.0226750	+	0.999743i	$0.507218\pi$
$360$	−586.952			−1.63042
$361$		−	277.586i		−	0.768937i
$362$	784.281	−	784.281i	2.16652	−	2.16652i
$363$	−246.879	−	246.879i	−0.680107	−	0.680107i
$364$	186.557	−	753.341i	0.512520	−	2.06962i
$365$	−82.5845			−0.226259
$366$	31.4058	+	31.4058i	0.0858081	+	0.0858081i
$367$	−527.594			−1.43759			−0.718793	−	0.695224i	$-0.755305\pi$
$367$	−527.594			−1.43759			−0.718793	+	0.695224i	$0.755305\pi$
$368$	110.286			0.299690
$369$	−385.744	−	350.891i	−1.04538	−	0.950924i
$370$		−	937.648i		−	2.53418i
$371$	179.478	+	44.4459i	0.483768	+	0.119800i
$372$	970.302	+	970.302i	2.60834	+	2.60834i
$373$	701.781			1.88145			0.940725	−	0.339169i	$-0.110146\pi$
$373$	701.781			1.88145			0.940725	+	0.339169i	$0.110146\pi$
$374$	−140.547			−0.375794
$375$	446.343	−	446.343i	1.19025	−	1.19025i
$376$	−221.154	+	221.154i	−0.588175	+	0.588175i
$377$	−362.466			−0.961448
$378$	99.0079	−	399.806i	0.261926	−	1.05769i
$379$	−410.024			−1.08186			−0.540929	−	0.841068i	$-0.681927\pi$
$379$	−410.024			−1.08186			−0.540929	+	0.841068i	$0.681927\pi$
$380$	187.294	+	187.294i	0.492878	+	0.492878i
$381$	534.246	−	534.246i	1.40222	−	1.40222i
$382$	487.910	+	487.910i	1.27725	+	1.27725i
$383$	97.4478	+	97.4478i	0.254433	+	0.254433i	0.822785	−	0.568352i	$-0.192419\pi$
$383$	97.4478	+	97.4478i	0.254433	+	0.254433i	−0.568352	+	0.822785i	$0.692419\pi$
$384$	−771.830	−	771.830i	−2.00997	−	2.00997i
$385$	−177.693	−	44.0038i	−0.461540	−	0.114296i
$386$	622.684	−	622.684i	1.61317	−	1.61317i
$387$	−482.137			−1.24583
$388$	85.6497	+	85.6497i	0.220747	+	0.220747i
$389$			5.00706i			0.0128716i	0.999979	+	0.00643581i	$0.00204860\pi$
$389$			5.00706i			0.0128716i	−0.999979	+	0.00643581i	$0.997951\pi$
$390$	897.740			2.30190
$391$	45.0264	+	45.0264i	0.115157	+	0.115157i
$392$	519.157	+	273.926i	1.32438	+	0.698792i
$393$	336.011	−	336.011i	0.854990	−	0.854990i
$394$	−597.968			−1.51769
$395$	295.352	+	295.352i	0.747727	+	0.747727i
$396$	459.604	−	459.604i	1.16062	−	1.16062i
$397$	−311.528	+	311.528i	−0.784705	+	0.784705i	−0.980621	−	0.195915i	$-0.937232\pi$
$397$	−311.528	+	311.528i	−0.784705	+	0.784705i	0.195915	+	0.980621i	$0.437232\pi$
$398$	−437.213	+	437.213i	−1.09852	+	1.09852i
$399$	−255.142	+	153.858i	−0.639454	+	0.385608i
$400$	−107.293			−0.268233
$401$			565.255i			1.40961i	0.709399	+	0.704807i	$0.248966\pi$
$401$			565.255i			1.40961i	−0.709399	+	0.704807i	$0.751034\pi$
$402$	−905.623			−2.25279
$403$	−407.310	−	407.310i	−1.01070	−	1.01070i
$404$	−706.746	−	706.746i	−1.74937	−	1.74937i
$405$	−129.843			−0.320600
$406$	140.610	−	567.800i	0.346330	−	1.39852i
$407$	344.099	+	344.099i	0.845453	+	0.845453i
$408$			340.427i			0.834381i
$409$			507.874i			1.24175i	0.783911	+	0.620873i	$0.213222\pi$
$409$			507.874i			1.24175i	−0.783911	+	0.620873i	$0.786778\pi$
$410$	396.706	+	360.863i	0.967576	+	0.880153i
$411$			1081.71i			2.63189i
$412$	1243.09			3.01721
$413$	−177.001	−	293.520i	−0.428573	−	0.710703i
$414$	−450.951			−1.08925
$415$			521.810i			1.25737i
$416$	125.583	+	125.583i	0.301882	+	0.301882i
$417$	360.662	+	360.662i	0.864896	+	0.864896i
$418$	−210.507			−0.503606
$419$	791.858			1.88988			0.944938	−	0.327248i	$-0.106121\pi$
$419$	791.858			1.88988			0.944938	+	0.327248i	$0.106121\pi$
$420$	−227.421	+	918.352i	−0.541478	+	2.18655i
$421$	185.574	+	185.574i	0.440793	+	0.440793i	0.892279	−	0.451485i	$-0.149106\pi$
$421$	185.574	+	185.574i	0.440793	+	0.440793i	−0.451485	+	0.892279i	$0.649106\pi$
$422$	−447.375	−	447.375i	−1.06013	−	1.06013i
$423$	234.800	−	234.800i	0.555082	−	0.555082i
$424$	223.747	−	223.747i	0.527706	−	0.527706i
$425$	−43.8046	−	43.8046i	−0.103070	−	0.103070i
$426$		−	1163.42i		−	2.73104i
$427$	16.8258	−	10.1464i	0.0394047	−	0.0237621i
$428$	43.4334			0.101480
$429$	−329.454	+	329.454i	−0.767958	+	0.767958i
$430$	495.838			1.15311
$431$			66.6466i			0.154633i	0.997007	+	0.0773163i	$0.0246351\pi$
$431$			66.6466i			0.154633i	−0.997007	+	0.0773163i	$0.975365\pi$
$432$	−129.417	−	129.417i	−0.299576	−	0.299576i
$433$			19.7822i			0.0456863i	0.999739	+	0.0228432i	$0.00727184\pi$
$433$			19.7822i			0.0456863i	−0.999739	+	0.0228432i	$0.992728\pi$
$434$	796.055	−	480.043i	1.83423	−	1.10609i
$435$	441.860			1.01577
$436$	−719.033	+	719.033i	−1.64916	+	1.64916i
$437$	67.4392	+	67.4392i	0.154323	+	0.154323i
$438$	−239.857	−	239.857i	−0.547619	−	0.547619i
$439$	214.442	−	214.442i	0.488478	−	0.488478i	−0.419347	−	0.907826i	$-0.637741\pi$
$439$	214.442	−	214.442i	0.488478	−	0.488478i	0.907826	+	0.419347i	$0.137741\pi$
$440$	−221.522	+	221.522i	−0.503459	+	0.503459i
$441$	−551.190	−	290.829i	−1.24986	−	0.659475i
$442$		−	304.916i		−	0.689855i
$443$		−	287.358i		−	0.648664i	−0.945943	−	0.324332i	$-0.894860\pi$
$443$		−	287.358i		−	0.648664i	0.945943	−	0.324332i	$-0.105140\pi$
$444$	1778.38	−	1778.38i	4.00535	−	4.00535i
$445$	7.02931	−	7.02931i	0.0157962	−	0.0157962i
$446$	−397.451			−0.891145
$447$			974.908i			2.18100i
$448$	−498.674	+	300.713i	−1.11311	+	0.671235i
$449$			53.1821i			0.118446i	0.998245	+	0.0592228i	$0.0188623\pi$
$449$			53.1821i			0.118446i	−0.998245	+	0.0592228i	$0.981138\pi$
$450$	438.714			0.974920
$451$	−278.014	+	13.1539i	−0.616439	+	0.0291662i
$452$	−1560.76			−3.45301
$453$	−136.385			−0.301071
$454$	529.454	−	529.454i	1.16620	−	1.16620i
$455$	95.4659	−	385.503i	0.209815	−	0.847259i
$456$			509.882i			1.11816i
$457$	−360.746	+	360.746i	−0.789377	+	0.789377i	−0.981392	−	0.192015i	$-0.938498\pi$
$457$	−360.746	+	360.746i	−0.789377	+	0.789377i	0.192015	+	0.981392i	$0.438498\pi$
$458$	846.494	−	846.494i	1.84824	−	1.84824i
$459$		−	105.674i		−	0.230226i
$460$	302.851			0.658372
$461$			625.824i			1.35754i	0.734353	+	0.678768i	$0.237486\pi$
$461$			625.824i			1.35754i	−0.734353	+	0.678768i	$0.762514\pi$
$462$	−388.284	−	643.892i	−0.840441	−	1.39370i
$463$	−628.245	−	628.245i	−1.35690	−	1.35690i	−0.877712	−	0.479189i	$-0.840931\pi$
$463$	−628.245	−	628.245i	−1.35690	−	1.35690i	−0.479189	−	0.877712i	$-0.659069\pi$
$464$	−183.796	−	183.796i	−0.396113	−	0.396113i
$465$	496.527	+	496.527i	1.06780	+	1.06780i
$466$	251.222	−	251.222i	0.539103	−	0.539103i
$467$		−	183.080i		−	0.392034i	−0.980601	−	0.196017i	$-0.937199\pi$
$467$		−	183.080i		−	0.392034i	0.980601	−	0.196017i	$-0.0628007\pi$
$468$	997.107	+	997.107i	2.13057	+	2.13057i
$469$	−96.3041	+	388.888i	−0.205339	+	0.829185i
$470$	−241.472	+	241.472i	−0.513771	+	0.513771i
$471$		−	972.160i		−	2.06403i
$472$	−586.578			−1.24275
$473$	−181.963	+	181.963i	−0.384701	+	0.384701i
$474$			1715.63i			3.61948i
$475$	−65.6092	−	65.6092i	−0.138125	−	0.138125i
$476$	311.917	+	77.2430i	0.655287	+	0.162275i
$477$	−237.553	+	237.553i	−0.498015	+	0.498015i
$478$	−347.325	+	347.325i	−0.726621	+	0.726621i
$479$	−280.418	+	280.418i	−0.585424	+	0.585424i	−0.936389	−	0.350965i	$-0.885854\pi$
$479$	−280.418	+	280.418i	−0.585424	+	0.585424i	0.350965	+	0.936389i	$0.385854\pi$
$480$	−153.090	−	153.090i	−0.318938	−	0.318938i
$481$	−746.520	+	746.520i	−1.55202	+	1.55202i
$482$			492.876i			1.02256i
$483$	−81.8878	+	330.673i	−0.169540	+	0.684623i
$484$			563.995i			1.16528i
$485$	43.8290	+	43.8290i	0.0903691	+	0.0903691i
$486$	−751.572	−	751.572i	−1.54644	−	1.54644i
$487$		−	266.862i		−	0.547971i	−0.961734	−	0.273985i	$-0.911658\pi$
$487$		−	266.862i		−	0.547971i	0.961734	−	0.273985i	$-0.0883420\pi$
$488$		−	33.6251i		−	0.0689039i
$489$	125.414	−	125.414i	0.256471	−	0.256471i
$490$	566.854	+	299.093i	1.15685	+	0.610395i
$491$	−357.186			−0.727467			−0.363734	−	0.931503i	$-0.618498\pi$
$491$	−357.186			−0.727467			−0.363734	+	0.931503i	$0.618498\pi$
$492$	67.9822	+	1436.83i	0.138175	+	2.92039i
$493$		−	150.077i		−	0.304416i
$494$		−	456.694i		−	0.924482i
$495$	235.191	−	235.191i	0.475133	−	0.475133i
$496$		−	413.071i		−	0.832805i
$497$	−499.591	−	123.719i	−1.00521	−	0.248931i
$498$	−1515.54	+	1515.54i	−3.04325	+	3.04325i
$499$	692.859	+	692.859i	1.38849	+	1.38849i	0.828489	+	0.560005i	$0.189201\pi$
$499$	692.859	+	692.859i	1.38849	+	1.38849i	0.560005	+	0.828489i	$0.310799\pi$
$500$	−1019.67			−2.03934
$501$			784.700i			1.56627i
$502$			694.114i			1.38270i
$503$	−154.240	+	154.240i	−0.306641	+	0.306641i	−0.843605	−	0.536964i	$-0.819571\pi$
$503$	−154.240	+	154.240i	−0.306641	+	0.306641i	0.536964	+	0.843605i	$0.319571\pi$
$504$	−913.320	+	550.756i	−1.81214	+	1.09277i
$505$	−361.659	−	361.659i	−0.716157	−	0.716157i
$506$	−170.194	+	170.194i	−0.336351	+	0.336351i
$507$	−157.835	−	157.835i	−0.311311	−	0.311311i
$508$	−1220.48			−2.40253
$509$	61.1228	+	61.1228i	0.120084	+	0.120084i	0.764595	−	0.644511i	$-0.222939\pi$
$509$	61.1228	+	61.1228i	0.120084	+	0.120084i	−0.644511	+	0.764595i	$0.722939\pi$
$510$			371.704i			0.728832i
$511$	−128.505	+	77.4917i	−0.251477	+	0.151647i
$512$			633.424i			1.23716i
$513$		−	158.275i		−	0.308529i
$514$	−903.272	−	903.272i	−1.75734	−	1.75734i
$515$	636.119			1.23518
$516$	940.424	+	940.424i	1.82253	+	1.82253i
$517$		−	177.232i		−	0.342808i
$518$	−879.825	−	1459.01i	−1.69850	−	2.81663i
$519$	−564.696	+	564.696i	−1.08805	+	1.08805i
$520$	−480.590	−	480.590i	−0.924211	−	0.924211i
$521$	−269.700	+	269.700i	−0.517658	+	0.517658i	−0.916862	−	0.399204i	$-0.869286\pi$
$521$	−269.700	+	269.700i	−0.517658	+	0.517658i	0.399204	+	0.916862i	$0.369286\pi$
$522$	751.529	+	751.529i	1.43971	+	1.43971i
$523$		−	665.529i		−	1.27252i	−0.771474	−	0.636261i	$-0.780480\pi$
$523$		−	665.529i		−	1.27252i	0.771474	−	0.636261i	$-0.219520\pi$
$524$	−767.617			−1.46492
$525$	79.6658	−	321.700i	0.151744	−	0.612762i
$526$	266.626	+	266.626i	0.506893	+	0.506893i
$527$	168.645	−	168.645i	0.320009	−	0.320009i
$528$	−334.114			−0.632792
$529$	−419.952			−0.793860
$530$	244.304	−	244.304i	0.460951	−	0.460951i
$531$	622.772			1.17283
$532$	467.180	+	115.692i	0.878157	+	0.217467i
$533$	−28.5374	−	603.149i	−0.0535410	−	1.13161i
$534$	40.8316			0.0764637
$535$	22.2259			0.0415438
$536$	484.810	+	484.810i	0.904496	+	0.904496i
$537$		−	1318.57i		−	2.45543i
$538$	−923.645			−1.71681
$539$	−317.787	+	98.2633i	−0.589586	+	0.182307i
$540$	−355.385	−	355.385i	−0.658121	−	0.658121i
$541$			317.046i			0.586038i	0.956107	+	0.293019i	$0.0946599\pi$
$541$			317.046i			0.586038i	−0.956107	+	0.293019i	$0.905340\pi$
$542$	118.486			0.218609
$543$	1522.38			2.80364
$544$	−51.9968	+	51.9968i	−0.0955824	+	0.0955824i
$545$	−367.947	+	367.947i	−0.675132	+	0.675132i
$546$	1396.92	−	842.379i	2.55846	−	1.54282i
$547$	−0.493346	+	0.493346i	−0.000901912	+	0.000901912i	−0.707558	−	0.706656i	$-0.750203\pi$
$547$	−0.493346	+	0.493346i	−0.000901912	+	0.000901912i	0.706656	+	0.707558i	$0.250203\pi$
$548$	1235.58	−	1235.58i	2.25471	−	2.25471i
$549$			35.6999i			0.0650271i
$550$	165.575	−	165.575i	0.301046	−	0.301046i
$551$		−	224.781i		−	0.407951i
$552$	412.236	+	412.236i	0.746804	+	0.746804i
$553$	736.718	+	182.441i	1.33222	+	0.329911i
$554$			518.315i			0.935587i
$555$	910.038	−	910.038i	1.63971	−	1.63971i
$556$		−	823.931i		−	1.48189i
$557$	110.692	−	110.692i	0.198729	−	0.198729i	−0.600726	−	0.799455i	$-0.705122\pi$
$557$	110.692	−	110.692i	0.198729	−	0.198729i	0.799455	+	0.600726i	$0.205122\pi$
$558$			1689.02i			3.02691i
$559$	−394.768	−	394.768i	−0.706204	−	0.706204i
$560$	243.886	−	147.070i	0.435510	−	0.262624i
$561$	−136.409	−	136.409i	−0.243153	−	0.243153i
$562$	279.539	+	279.539i	0.497400	+	0.497400i
$563$	−152.143	+	152.143i	−0.270236	+	0.270236i	−0.829195	−	0.558959i	$-0.811201\pi$
$563$	−152.143	+	152.143i	−0.270236	+	0.270236i	0.558959	+	0.829195i	$0.311201\pi$
$564$	−915.970			−1.62406
$565$	−798.679			−1.41359
$566$	159.908			0.282523
$567$	−202.041	+	121.836i	−0.356333	+	0.214878i
$568$	−622.819	+	622.819i	−1.09651	+	1.09651i
$569$			240.697i			0.423018i	0.977376	+	0.211509i	$0.0678378\pi$
$569$			240.697i			0.423018i	−0.977376	+	0.211509i	$0.932162\pi$
$570$			556.728i			0.976716i
$571$	−606.950	−	606.950i	−1.06296	−	1.06296i	−0.997880	−	0.0650802i	$-0.979270\pi$
$571$	−606.950	−	606.950i	−1.06296	−	1.06296i	−0.0650802	−	0.997880i	$-0.520730\pi$
$572$	752.638			1.31580
$573$			947.085i			1.65285i
$574$	955.899	+	189.274i	1.66533	+	0.329745i
$575$	−106.089			−0.184503
$576$		−	1058.05i		−	1.83690i
$577$	290.329	−	290.329i	0.503171	−	0.503171i	−0.409251	−	0.912422i	$-0.634210\pi$
$577$	290.329	−	290.329i	0.503171	−	0.503171i	0.912422	+	0.409251i	$0.134210\pi$
$578$	−854.999			−1.47924
$579$	1208.70			2.08756
$580$	−504.715	−	504.715i	−0.870197	−	0.870197i
$581$	489.631	+	811.956i	0.842739	+	1.39751i
$582$			254.593i			0.437444i
$583$			179.310i			0.307565i
$584$			256.807i			0.439737i
$585$	510.244	+	510.244i	0.872212	+	0.872212i
$586$	−163.625	+	163.625i	−0.279224	+	0.279224i
$587$	508.397	−	508.397i	0.866094	−	0.866094i	−0.125943	−	0.992037i	$-0.540196\pi$
$587$	508.397	−	508.397i	0.866094	−	0.866094i	0.992037	+	0.125943i	$0.0401958\pi$
$588$	507.845	+	1642.39i	0.863682	+	2.79318i
$589$	252.591	−	252.591i	0.428847	−	0.428847i
$590$	−640.470			−1.08554
$591$	−580.360	−	580.360i	−0.981997	−	0.981997i
$592$	−757.079			−1.27885
$593$	−593.410	−	593.410i	−1.00069	−	1.00069i	−1.00000		0.000692334i	$-0.999780\pi$
$593$	−593.410	−	593.410i	−1.00069	−	1.00069i	−0.000692334	−	1.00000i	$-0.500220\pi$
$594$	399.433			0.672445
$595$	159.615	+	39.5271i	0.268261	+	0.0664321i
$596$	1113.59	−	1113.59i	1.86844	−	1.86844i
$597$	−848.677			−1.42157
$598$	−369.234	−	369.234i	−0.617447	−	0.617447i
$599$	−880.555			−1.47004			−0.735021	−	0.678044i	$-0.762828\pi$
$599$	−880.555			−1.47004			−0.735021	+	0.678044i	$0.762828\pi$
$600$	−401.050	−	401.050i	−0.668416	−	0.668416i
$601$	592.822	+	592.822i	0.986393	+	0.986393i	0.999909	−	0.0135154i	$-0.00430220\pi$
$601$	592.822	+	592.822i	0.986393	+	0.986393i	−0.0135154	+	0.999909i	$0.504302\pi$
$602$	771.543	−	465.261i	1.28163	−	0.772859i
$603$	−514.724	−	514.724i	−0.853606	−	0.853606i
$604$	155.786	+	155.786i	0.257924	+	0.257924i
$605$			288.610i			0.477041i
$606$		−	2100.79i		−	3.46666i
$607$	−317.085			−0.522380			−0.261190	−	0.965287i	$-0.584115\pi$
$607$	−317.085			−0.522380			−0.261190	+	0.965287i	$0.584115\pi$
$608$	−77.8793	+	77.8793i	−0.128091	+	0.128091i
$609$	687.551	−	414.612i	1.12898	−	0.680807i
$610$		−	36.7144i		−	0.0601876i
$611$	384.503			0.629301
$612$	−412.847	+	412.847i	−0.674586	+	0.674586i
$613$			1014.86i			1.65557i	0.561046	+	0.827785i	$0.310399\pi$
$613$			1014.86i			1.65557i	−0.561046	+	0.827785i	$0.689601\pi$
$614$		−	36.2279i		−	0.0590031i
$615$	34.7882	+	735.262i	0.0565661	+	1.19555i
$616$	−136.835	+	552.558i	−0.222135	+	0.897009i
$617$			873.917i			1.41640i	0.706014	+	0.708198i	$0.250492\pi$
$617$			873.917i			1.41640i	−0.706014	+	0.708198i	$0.749508\pi$
$618$	1847.53	+	1847.53i	2.98954	+	2.98954i
$619$		−	99.9022i		−	0.161393i	−0.996739	−	0.0806964i	$-0.974286\pi$
$619$		−	99.9022i		−	0.161393i	0.996739	−	0.0806964i	$-0.0257144\pi$
$620$		−	1134.32i		−	1.82954i
$621$	−127.964	−	127.964i	−0.206062	−	0.206062i
$622$	504.904	−	504.904i	0.811742	−	0.811742i
$623$	4.34204	−	17.5337i	0.00696957	−	0.0281440i
$624$		−	724.857i		−	1.16163i
$625$	−267.808			−0.428493
$626$	617.702	−	617.702i	0.986745	−	0.986745i
$627$	−204.309	−	204.309i	−0.325851	−	0.325851i
$628$	−1110.45	+	1110.45i	−1.76823	+	1.76823i
$629$	−309.093	−	309.093i	−0.491403	−	0.491403i
$630$	−997.231	+	601.357i	−1.58291	+	0.954535i
$631$	166.443			0.263776			0.131888	−	0.991265i	$-0.457896\pi$
$631$	166.443			0.263776			0.131888	+	0.991265i	$0.457896\pi$
$632$	918.435	−	918.435i	1.45322	−	1.45322i
$633$		−	868.403i		−	1.37188i
$634$	523.879	−	523.879i	0.826307	−	0.826307i
$635$	−624.551			−0.983546
$636$	926.712			1.45709
$637$	−213.181	−	689.436i	−0.334665	−	1.08232i
$638$	567.270			0.889138
$639$	661.249	−	661.249i	1.03482	−	1.03482i
$640$			902.295i			1.40984i
$641$	531.296	−	531.296i	0.828854	−	0.828854i	−0.158504	−	0.987358i	$-0.550667\pi$
$641$	531.296	−	531.296i	0.828854	−	0.828854i	0.987358	+	0.158504i	$0.0506671\pi$
$642$	64.5526	+	64.5526i	0.100549	+	0.100549i
$643$	−41.8360	+	41.8360i	−0.0650637	+	0.0650637i	−0.738890	−	0.673826i	$-0.764650\pi$
$643$	−41.8360	+	41.8360i	−0.0650637	+	0.0650637i	0.673826	+	0.738890i	$0.264650\pi$
$644$	471.247	−	284.175i	0.731751	−	0.441265i
$645$	481.238	+	481.238i	0.746105	+	0.746105i
$646$	189.092			0.292711
$647$	927.485			1.43352			0.716758	−	0.697322i	$-0.245625\pi$
$647$	927.485			1.43352			0.716758	+	0.697322i	$0.245625\pi$
$648$			403.763i			0.623091i
$649$	235.041	−	235.041i	0.362158	−	0.362158i
$650$	359.214	+	359.214i	0.552637	+	0.552637i
$651$	1238.52	+	306.707i	1.90249	+	0.471133i
$652$	−286.509			−0.439431
$653$	590.152	+	590.152i	0.903756	+	0.903756i	0.995759	−	0.0920030i	$-0.0293270\pi$
$653$	590.152	+	590.152i	0.903756	+	0.903756i	−0.0920030	+	0.995759i	$0.529327\pi$
$654$	−2137.32			−3.26807
$655$	−392.808			−0.599707
$656$	291.369	−	320.310i	0.444161	−	0.488278i
$657$		−	272.652i		−	0.414996i
$658$	−149.159	+	602.322i	−0.226685	+	0.915382i
$659$	−113.127	−	113.127i	−0.171665	−	0.171665i	0.616046	−	0.787710i	$-0.288734\pi$
$659$	−113.127	−	113.127i	−0.171665	−	0.171665i	−0.787710	+	0.616046i	$0.788734\pi$
$660$	−917.495			−1.39014
$661$	−171.283			−0.259128			−0.129564	−	0.991571i	$-0.541358\pi$
$661$	−171.283			−0.259128			−0.129564	+	0.991571i	$0.541358\pi$
$662$	−1471.53	+	1471.53i	−2.22285	+	2.22285i
$663$	295.937	−	295.937i	0.446361	−	0.446361i
$664$	1622.63			2.44372
$665$	239.067	+	59.2026i	0.359500	+	0.0890264i
$666$	3095.64			4.64811
$667$	−181.734	−	181.734i	−0.272464	−	0.272464i
$668$	896.324	−	896.324i	1.34180	−	1.34180i
$669$	−385.747	−	385.747i	−0.576603	−	0.576603i
$670$	529.352	+	529.352i	0.790078	+	0.790078i
$671$	13.4735	+	13.4735i	0.0200797	+	0.0200797i
$672$	−381.864	−	94.5647i	−0.568250	−	0.140721i
$673$	−47.5762	+	47.5762i	−0.0706927	+	0.0706927i	−0.741569	−	0.670876i	$-0.765918\pi$
$673$	−47.5762	+	47.5762i	−0.0706927	+	0.0706927i	0.670876	+	0.741569i	$0.265918\pi$
$674$	−1114.05			−1.65290
$675$	124.492	+	124.492i	0.184432	+	0.184432i
$676$			360.573i			0.533392i
$677$	1336.82			1.97462			0.987312	−	0.158793i	$-0.0507602\pi$
$677$	1336.82			1.97462			0.987312	+	0.158793i	$0.0507602\pi$
$678$	−2319.67	−	2319.67i	−3.42134	−	3.42134i
$679$	109.326	+	27.0734i	0.161010	+	0.0398725i
$680$	198.986	−	198.986i	0.292626	−	0.292626i
$681$	1027.73			1.50915
$682$	637.453	+	637.453i	0.934682	+	0.934682i
$683$	114.935	−	114.935i	0.168280	−	0.168280i	−0.617943	−	0.786223i	$-0.712034\pi$
$683$	114.935	−	114.935i	0.168280	−	0.168280i	0.786223	+	0.617943i	$0.212034\pi$
$684$	−618.350	+	618.350i	−0.904020	+	0.904020i
$685$	632.276	−	632.276i	0.923030	−	0.923030i
$686$	1162.70	−	66.4971i	1.69489	−	0.0969346i
$687$	1643.14			2.39176
$688$		−	400.352i		−	0.581907i
$689$	−389.012			−0.564604
$690$	450.110	+	450.110i	0.652334	+	0.652334i
$691$	−242.900	−	242.900i	−0.351519	−	0.351519i	0.509155	−	0.860675i	$-0.329958\pi$
$691$	−242.900	−	242.900i	−0.351519	−	0.351519i	−0.860675	+	0.509155i	$0.829958\pi$
$692$	1290.05			1.86423
$693$	145.278	−	586.652i	0.209637	−	0.846540i
$694$	−375.560	−	375.560i	−0.541153	−	0.541153i
$695$		−	421.626i		−	0.606656i
$696$		−	1374.02i		−	1.97416i
$697$	249.730	−	11.8157i	0.358293	−	0.0169523i
$698$			1791.16i			2.56614i
$699$	487.649			0.697639
$700$	−458.460	+	276.464i	−0.654943	+	0.394948i
$701$	805.253			1.14872			0.574361	−	0.818602i	$-0.305251\pi$
$701$	805.253			1.14872			0.574361	+	0.818602i	$0.305251\pi$
$702$			866.566i			1.23442i
$703$	−462.950	−	462.950i	−0.658535	−	0.658535i
$704$	−399.320	−	399.320i	−0.567216	−	0.567216i
$705$	−468.724			−0.664857
$706$	−546.972			−0.774748
$707$	−902.112	−	223.399i	−1.27597	−	0.315981i
$708$	−1214.74	−	1214.74i	−1.71573	−	1.71573i
$709$	−334.535	−	334.535i	−0.471841	−	0.471841i	0.430669	−	0.902510i	$-0.358278\pi$
$709$	−334.535	−	334.535i	−0.471841	−	0.471841i	−0.902510	+	0.430669i	$0.858278\pi$
$710$	−680.041	+	680.041i	−0.957804	+	0.957804i
$711$	−975.105	+	975.105i	−1.37146	+	1.37146i
$712$	−21.8585	−	21.8585i	−0.0307002	−	0.0307002i
$713$		−	408.435i		−	0.572841i
$714$	348.782	+	578.386i	0.488491	+	0.810064i
$715$	385.143			0.538661
$716$	−1506.13	+	1506.13i	−2.10354	+	2.10354i
$717$	−674.195			−0.940300
$718$			55.2780i			0.0769889i
$719$	378.582	+	378.582i	0.526539	+	0.526539i	0.919539	−	0.393000i	$-0.128563\pi$
$719$	378.582	+	378.582i	0.526539	+	0.526539i	−0.393000	+	0.919539i	$0.628563\pi$
$720$			517.461i			0.718696i
$721$	989.825	−	596.891i	1.37285	−	0.827865i
$722$	−942.495			−1.30540
$723$	−478.362	+	478.362i	−0.661635	+	0.661635i
$724$	−1738.93	−	1738.93i	−2.40184	−	2.40184i
$725$	176.802	+	176.802i	0.243865	+	0.243865i
$726$	−838.234	+	838.234i	−1.15459	+	1.15459i
$727$	41.6129	−	41.6129i	0.0572393	−	0.0572393i	−0.677908	−	0.735147i	$-0.737113\pi$
$727$	41.6129	−	41.6129i	0.0572393	−	0.0572393i	0.735147	+	0.677908i	$0.237113\pi$
$728$	−1198.77	−	296.863i	−1.64666	−	0.407779i
$729$		−	1155.54i		−	1.58510i
$730$			280.401i			0.384111i
$731$	163.452	−	163.452i	0.223600	−	0.223600i
$732$	69.6339	−	69.6339i	0.0951282	−	0.0951282i
$733$	341.272			0.465582			0.232791	−	0.972527i	$-0.425214\pi$
$733$	341.272			0.465582			0.232791	+	0.972527i	$0.425214\pi$
$734$			1791.35i			2.44054i
$735$	259.876	+	840.449i	0.353573	+	1.14347i
$736$			125.930i			0.171100i
$737$	−388.525			−0.527171
$738$	−1191.39	+	1309.73i	−1.61435	+	1.77470i
$739$	829.355			1.12227			0.561133	−	0.827726i	$-0.310366\pi$
$739$	829.355			1.12227			0.561133	+	0.827726i	$0.310366\pi$
$740$	−2078.98			−2.80943
$741$	443.246	−	443.246i	0.598173	−	0.598173i
$742$	150.908	−	609.385i	0.203380	−	0.821274i
$743$			277.245i			0.373143i	0.982441	+	0.186571i	$0.0597376\pi$
$743$			277.245i			0.373143i	−0.982441	+	0.186571i	$0.940262\pi$
$744$	1544.01	−	1544.01i	2.07529	−	2.07529i
$745$	569.850	−	569.850i	0.764899	−	0.764899i
$746$		−	2382.77i		−	3.19407i
$747$	−1722.75			−2.30623
$748$			311.625i			0.416612i
$749$	34.5844	−	20.8553i	0.0461741	−	0.0278442i
$750$	−1515.48	−	1515.48i	−2.02064	−	2.02064i
$751$	−543.282	−	543.282i	−0.723412	−	0.723412i	0.245887	−	0.969299i	$-0.420921\pi$
$751$	−543.282	−	543.282i	−0.723412	−	0.723412i	−0.969299	+	0.245887i	$0.920921\pi$
$752$	194.971	+	194.971i	0.259270	+	0.259270i
$753$	−673.676	+	673.676i	−0.894656	+	0.894656i
$754$			1230.69i			1.63221i
$755$	79.7194	+	79.7194i	0.105589	+	0.105589i
$756$	−886.462	−	219.523i	−1.17257	−	0.290375i
$757$	166.026	−	166.026i	0.219321	−	0.219321i	−0.588891	−	0.808212i	$-0.700435\pi$
$757$	166.026	−	166.026i	0.219321	−	0.219321i	0.808212	+	0.588891i	$0.200435\pi$
$758$			1392.16i			1.83663i
$759$	−330.364			−0.435262
$760$	298.035	−	298.035i	0.392151	−	0.392151i
$761$		−	243.955i		−	0.320571i	−0.987071	−	0.160286i	$-0.948758\pi$
$761$		−	243.955i		−	0.320571i	0.987071	−	0.160286i	$-0.0512415\pi$
$762$	−1813.94	−	1813.94i	−2.38049	−	2.38049i
$763$	−227.283	+	917.795i	−0.297880	+	1.20288i
$764$	1081.81	−	1081.81i	1.41598	−	1.41598i
$765$	−211.264	+	211.264i	−0.276162	+	0.276162i
$766$	330.867	−	330.867i	0.431941	−	0.431941i
$767$	509.919	+	509.919i	0.664822	+	0.664822i
$768$	−1524.06	+	1524.06i	−1.98445	+	1.98445i
$769$			301.946i			0.392648i	0.980539	+	0.196324i	$0.0629004\pi$
$769$			301.946i			0.392648i	−0.980539	+	0.196324i	$0.937100\pi$
$770$	−149.407	+	603.324i	−0.194035	+	0.783538i
$771$		−	1753.35i		−	2.27412i
$772$	−1380.63	−	1380.63i	−1.78839	−	1.78839i
$773$	−624.704	−	624.704i	−0.808156	−	0.808156i	0.176199	−	0.984355i	$-0.443620\pi$
$773$	−624.704	−	624.704i	−0.808156	−	0.808156i	−0.984355	+	0.176199i	$0.943620\pi$
$774$			1637.01i			2.11500i
$775$			397.352i			0.512713i
$776$	136.292	−	136.292i	0.175634	−	0.175634i
$777$	562.135	−	2269.97i	0.723469	−	2.92146i
$778$	17.0006			0.0218517
$779$	374.039	−	17.6973i	0.480152	−	0.0227179i
$780$		−	1990.50i		−	2.55192i
$781$		−	499.125i		−	0.639084i
$782$	152.879	−	152.879i	0.195498	−	0.195498i
$783$			426.516i			0.544720i
$784$	241.495	−	457.692i	0.308030	−	0.583791i
$785$	−568.244	+	568.244i	−0.723878	+	0.723878i
$786$	−1140.87	−	1140.87i	−1.45148	−	1.45148i
$787$	123.638			0.157100			0.0785500	−	0.996910i	$-0.474971\pi$
$787$	123.638			0.157100			0.0785500	+	0.996910i	$0.474971\pi$
$788$			1325.83i			1.68253i
$789$			517.549i			0.655956i
$790$	1002.82	−	1002.82i	1.26939	−	1.26939i
$791$	−1242.77	+	749.426i	−1.57114	+	0.947442i
$792$	−731.354	−	731.354i	−0.923427	−	0.923427i
$793$	−29.2307	+	29.2307i	−0.0368609	+	0.0368609i
$794$	1057.74	+	1057.74i	1.33216	+	1.33216i
$795$	474.221			0.596505
$796$	969.402	+	969.402i	1.21784	+	1.21784i
$797$			937.152i			1.17585i	0.808916	+	0.587925i	$0.200055\pi$
$797$			937.152i			1.17585i	−0.808916	+	0.587925i	$0.799945\pi$
$798$	522.396	+	866.290i	0.654631	+	1.08558i
$799$			159.201i			0.199251i
$800$		−	122.513i		−	0.153141i
$801$	23.2073	+	23.2073i	0.0289729	+	0.0289729i
$802$	1919.22			2.39305
$803$	−102.902	−	102.902i	−0.128147	−	0.128147i
$804$			2007.98i			2.49748i
$805$	241.149	−	145.419i	0.299564	−	0.180645i
$806$	−1382.95	+	1382.95i	−1.71582	+	1.71582i
$807$	−896.447	−	896.447i	−1.11084	−	1.11084i
$808$	−1124.62	+	1124.62i	−1.39186	+	1.39186i
$809$	224.923	+	224.923i	0.278026	+	0.278026i	0.832320	−	0.554295i	$-0.187012\pi$
$809$	224.923	+	224.923i	0.278026	+	0.278026i	−0.554295	+	0.832320i	$0.687012\pi$
$810$			440.859i			0.544271i
$811$	63.6350			0.0784649			0.0392324	−	0.999230i	$-0.487509\pi$
$811$	63.6350			0.0784649			0.0392324	+	0.999230i	$0.487509\pi$
$812$	−1258.94	−	311.765i	−1.55042	−	0.383947i
$813$	114.997	+	114.997i	0.141448	+	0.141448i
$814$	1168.33	−	1168.33i	1.43529	−	1.43529i
$815$	−146.614			−0.179894
$816$	300.123			0.367798
$817$	244.813	−	244.813i	0.299649	−	0.299649i
$818$	1724.40			2.10806
$819$	1272.74	+	315.180i	1.55401	+	0.384836i
$820$	800.116	−	879.589i	0.975751	−	1.07267i
$821$	−1027.58			−1.25161			−0.625807	−	0.779978i	$-0.715230\pi$
$821$	−1027.58			−1.25161			−0.625807	+	0.779978i	$0.715230\pi$
$822$	3672.74			4.46806
$823$	−693.947	−	693.947i	−0.843192	−	0.843192i	0.146080	−	0.989273i	$-0.453334\pi$
$823$	−693.947	−	693.947i	−0.843192	−	0.843192i	−0.989273	+	0.146080i	$0.953334\pi$
$824$		−	1978.09i		−	2.40060i
$825$	321.400			0.389575
$826$	−996.596	+	600.974i	−1.20653	+	0.727571i
$827$	1022.10	+	1022.10i	1.23591	+	1.23591i	0.961656	+	0.274258i	$0.0884321\pi$
$827$	1022.10	+	1022.10i	1.23591	+	1.23591i	0.274258	+	0.961656i	$0.411568\pi$
$828$			999.862i			1.20756i
$829$	688.274			0.830246			0.415123	−	0.909765i	$-0.363738\pi$
$829$	688.274			0.830246			0.415123	+	0.909765i	$0.363738\pi$
$830$	1771.71			2.13459
$831$	−503.053	+	503.053i	−0.605358	+	0.605358i
$832$	866.322	−	866.322i	1.04125	−	1.04125i
$833$	285.457	−	88.2666i	0.342685	−	0.105962i
$834$	1224.56	−	1224.56i	1.46830	−	1.46830i
$835$	458.671	−	458.671i	0.549306	−	0.549306i
$836$			466.743i			0.558306i
$837$	−479.285	+	479.285i	−0.572622	+	0.572622i
$838$		−	2688.61i		−	3.20837i
$839$	−163.569	−	163.569i	−0.194957	−	0.194957i	0.602877	−	0.797834i	$-0.294021\pi$
$839$	−163.569	−	163.569i	−0.194957	−	0.194957i	−0.797834	+	0.602877i	$0.794021\pi$
$840$	1461.35	+	361.888i	1.73970	+	0.430819i
$841$		−	235.266i		−	0.279746i
$842$	630.084	−	630.084i	0.748318	−	0.748318i
$843$			542.616i			0.643672i
$844$	−991.933	+	991.933i	−1.17528	+	1.17528i
$845$			184.514i			0.218360i
$846$	−797.221	−	797.221i	−0.942342	−	0.942342i
$847$	270.812	+	449.088i	0.319731	+	0.530210i
$848$	−197.257	−	197.257i	−0.232615	−	0.232615i
$849$	155.199	+	155.199i	0.182803	+	0.182803i
$850$	−148.731	+	148.731i	−0.174977	+	0.174977i
$851$	−748.583			−0.879651
$852$	−2579.58			−3.02767
$853$	1256.83			1.47343			0.736714	−	0.676205i	$-0.236377\pi$
$853$	1256.83			1.47343			0.736714	+	0.676205i	$0.236377\pi$
$854$	−34.4503	−	57.1290i	−0.0403400	−	0.0668958i
$855$	−316.425	+	316.425i	−0.370087	+	0.370087i
$856$		−	69.1143i		−	0.0807410i
$857$			1229.01i			1.43408i	0.697031	+	0.717041i	$0.254504\pi$
$857$			1229.01i			1.43408i	−0.697031	+	0.717041i	$0.745496\pi$
$858$	1118.60	+	1118.60i	1.30373	+	1.30373i
$859$	−1034.91			−1.20479			−0.602393	−	0.798200i	$-0.705786\pi$
$859$	−1034.91			−1.20479			−0.602393	+	0.798200i	$0.705786\pi$
$860$		−	1099.39i		−	1.27836i
$861$	744.052	+	1111.45i	0.864171	+	1.29089i
$862$	226.287			0.262514
$863$		−	293.947i		−	0.340611i	−0.985391	−	0.170306i	$-0.945525\pi$
$863$		−	293.947i		−	0.340611i	0.985391	−	0.170306i	$-0.0544755\pi$
$864$	147.774	−	147.774i	0.171035	−	0.171035i
$865$	660.148			0.763177
$866$	67.1669			0.0775599
$867$	−829.823	−	829.823i	−0.957120	−	0.957120i
$868$	−1064.37	−	1765.04i	−1.22623	−	2.03345i
$869$			736.030i			0.846985i
$870$		−	1500.26i		−	1.72443i
$871$		−	842.901i		−	0.967740i
$872$	1144.18	+	1144.18i	1.31213	+	1.31213i
$873$	−144.701	+	144.701i	−0.165752	+	0.165752i
$874$	228.978	−	228.978i	0.261988	−	0.261988i
$875$	−811.924	+	489.612i	−0.927913	+	0.559557i
$876$	−531.818	+	531.818i	−0.607098	+	0.607098i
$877$	−953.826			−1.08760			−0.543800	−	0.839215i	$-0.683015\pi$
$877$	−953.826			−1.08760			−0.543800	+	0.839215i	$0.683015\pi$
$878$	−728.100	−	728.100i	−0.829271	−	0.829271i
$879$	−317.614			−0.361336
$880$	195.295	+	195.295i	0.221926	+	0.221926i
$881$	−1096.00			−1.24405			−0.622023	−	0.782999i	$-0.713689\pi$
$881$	−1096.00			−1.24405			−0.622023	+	0.782999i	$0.713689\pi$
$882$	−987.457	+	1871.47i	−1.11957	+	2.12185i
$883$	−441.503	+	441.503i	−0.500004	+	0.500004i	−0.911439	−	0.411435i	$-0.865028\pi$
$883$	−441.503	+	441.503i	−0.500004	+	0.500004i	0.411435	+	0.911439i	$0.365028\pi$
$884$	−676.069			−0.764784
$885$	−621.611	−	621.611i	−0.702385	−	0.702385i
$886$	−975.674			−1.10121
$887$	−950.144	−	950.144i	−1.07119	−	1.07119i	−0.997264	−	0.0739246i	$-0.976448\pi$
$887$	−950.144	−	950.144i	−1.07119	−	1.07119i	−0.0739246	−	0.997264i	$-0.523552\pi$
$888$	−2829.88	−	2829.88i	−3.18680	−	3.18680i
$889$	−971.825	+	586.037i	−1.09317	+	0.659209i
$890$	−23.8668	−	23.8668i	−0.0268166	−	0.0268166i
$891$	−161.787	−	161.787i	−0.181579	−	0.181579i
$892$			881.240i			0.987937i
$893$			238.447i			0.267018i
$894$	3310.13			3.70260
$895$	−770.724	+	770.724i	−0.861145	+	0.861145i
$896$	846.652	+	1404.00i	0.944925	+	1.56697i
$897$		−	716.722i		−	0.799022i
$898$	180.570			0.201081
$899$	−680.676	+	680.676i	−0.757148	+	0.757148i
$900$		−	972.731i		−	1.08081i
$901$		−	161.068i		−	0.178766i
$902$	44.6619	+	943.946i	0.0495143	+	1.04650i
$903$	1200.39	+	297.263i	1.32933	+	0.329195i
$904$			2483.59i			2.74734i
$905$	−889.854	−	889.854i	−0.983264	−	0.983264i
$906$			463.071i			0.511116i
$907$		−	145.976i		−	0.160944i	−0.996757	−	0.0804719i	$-0.974357\pi$
$907$		−	145.976i		−	0.160944i	0.996757	−	0.0804719i	$-0.0256427\pi$
$908$	−1173.92	−	1173.92i	−1.29287	−	1.29287i
$909$	1194.02	−	1194.02i	1.31355	−	1.31355i
$910$	−1308.91	−	324.137i	−1.43836	−	0.356195i
$911$			1384.89i			1.52018i	0.649817	+	0.760091i	$0.274846\pi$
$911$			1384.89i			1.52018i	−0.649817	+	0.760091i	$0.725154\pi$
$912$	449.516			0.492890
$913$	−650.186	+	650.186i	−0.712142	+	0.712142i
$914$	1224.85	+	1224.85i	1.34010	+	1.34010i
$915$	35.6333	−	35.6333i	0.0389435	−	0.0389435i
$916$	−1876.87	−	1876.87i	−2.04899	−	2.04899i
$917$	−611.224	+	368.585i	−0.666548	+	0.401946i
$918$	−358.797			−0.390846
$919$	737.733	−	737.733i	0.802756	−	0.802756i	−0.180769	−	0.983526i	$-0.557859\pi$
$919$	737.733	−	737.733i	0.802756	−	0.802756i	0.983526	+	0.180769i	$0.0578587\pi$
$920$		−	481.918i		−	0.523824i
$921$	35.1612	−	35.1612i	0.0381772	−	0.0381772i
$922$	2124.87			2.30464
$923$	1082.85			1.17318
$924$	−1427.66	+	860.915i	−1.54508	+	0.931726i
$925$	728.270			0.787319
$926$	−2133.09	+	2133.09i	−2.30356	+	2.30356i
$927$			2100.15i			2.26553i
$928$	209.867	−	209.867i	0.226150	−	0.226150i
$929$	872.983	+	872.983i	0.939702	+	0.939702i	0.998283	−	0.0585807i	$-0.0186575\pi$
$929$	872.983	+	872.983i	0.939702	+	0.939702i	−0.0585807	+	0.998283i	$0.518658\pi$
$930$	1685.87	−	1685.87i	1.81276	−	1.81276i
$931$	427.549	−	132.203i	0.459237	−	0.142001i
$932$	−557.017	−	557.017i	−0.597658	−	0.597658i
$933$	980.073			1.05045
$934$	−621.614			−0.665540
$935$			159.466i			0.170552i
$936$	1586.67	−	1586.67i	1.69516	−	1.69516i
$937$	−202.627	−	202.627i	−0.216251	−	0.216251i	0.590665	−	0.806917i	$-0.298865\pi$
$937$	−202.627	−	202.627i	−0.216251	−	0.216251i	−0.806917	+	0.590665i	$0.798865\pi$
$938$	1320.40	+	326.983i	1.40768	+	0.348596i
$939$	1199.03			1.27692
$940$	535.400	+	535.400i	0.569575	+	0.569575i
$941$	956.809			1.01680			0.508400	−	0.861121i	$-0.330237\pi$
$941$	956.809			1.01680			0.508400	+	0.861121i	$0.330237\pi$
$942$	−3300.80			−3.50403
$943$	288.099	−	316.715i	0.305514	−	0.335859i
$944$			517.131i			0.547808i
$945$	−453.624	−	112.335i	−0.480026	−	0.118873i
$946$	617.824	+	617.824i	0.653091	+	0.653091i
$947$	402.883			0.425431			0.212715	−	0.977114i	$-0.431769\pi$
$947$	402.883			0.425431			0.212715	+	0.977114i	$0.431769\pi$
$948$	3803.95			4.01261
$949$	223.245	−	223.245i	0.235242	−	0.235242i
$950$	−222.765	+	222.765i	−0.234489	+	0.234489i
$951$	1016.91			1.06930
$952$	122.914	−	496.344i	0.129112	−	0.521369i
$953$	−474.815			−0.498232			−0.249116	−	0.968474i	$-0.580140\pi$
$953$	−474.815			−0.498232			−0.249116	+	0.968474i	$0.580140\pi$
$954$	806.570	+	806.570i	0.845462	+	0.845462i
$955$	553.587	−	553.587i	0.579673	−	0.579673i
$956$	770.099	+	770.099i	0.805543	+	0.805543i
$957$	550.567	+	550.567i	0.575305	+	0.575305i
$958$	952.110	+	952.110i	0.993852	+	0.993852i
$959$	390.560	−	1577.13i	0.407258	−	1.64456i
$960$	−1056.08	+	1056.08i	−1.10008	+	1.10008i
$961$	−568.779			−0.591861
$962$	2534.68	+	2534.68i	2.63480	+	2.63480i
$963$			73.3789i			0.0761982i
$964$	1092.82			1.13363
$965$	−706.504	−	706.504i	−0.732129	−	0.732129i
$966$	1122.74	+	278.035i	1.16226	+	0.287821i
$967$	−224.702	+	224.702i	−0.232370	+	0.232370i	−0.813681	−	0.581311i	$-0.802540\pi$
$967$	−224.702	+	224.702i	−0.232370	+	0.232370i	0.581311	+	0.813681i	$0.302540\pi$
$968$	897.468			0.927137
$969$	183.524	+	183.524i	0.189395	+	0.189395i
$970$	148.814	−	148.814i	0.153416	−	0.153416i
$971$	179.204	−	179.204i	0.184556	−	0.184556i	−0.608782	−	0.793338i	$-0.708342\pi$
$971$	179.204	−	179.204i	0.184556	−	0.184556i	0.793338	+	0.608782i	$0.208342\pi$
$972$	−1666.41	+	1666.41i	−1.71441	+	1.71441i
$973$	−395.625	−	656.065i	−0.406603	−	0.674271i
$974$	−906.081			−0.930268
$975$			697.274i			0.715153i
$976$	−29.6441			−0.0303731
$977$	−1173.69	−	1173.69i	−1.20133	−	1.20133i	−0.973764	−	0.227561i	$-0.926925\pi$
$977$	−1173.69	−	1173.69i	−1.20133	−	1.20133i	−0.227561	−	0.973764i	$-0.573075\pi$
$978$	−425.822	−	425.822i	−0.435401	−	0.435401i
$979$	17.5173			0.0178931
$980$	663.159	−	1256.85i	0.676693	−	1.28250i
$981$	−1214.78	−	1214.78i	−1.23830	−	1.23830i
$982$			1212.76i			1.23499i
$983$		−	1764.76i		−	1.79528i	−0.440731	−	0.897639i	$-0.645281\pi$
$983$		−	1764.76i		−	1.79528i	0.440731	−	0.897639i	$-0.354719\pi$
$984$	2286.39	−	108.178i	2.32356	−	0.109937i
$985$			678.461i			0.688793i
$986$	−509.560			−0.516795
$987$	−729.352	+	439.819i	−0.738959	+	0.445612i
$988$	−1012.60			−1.02489
$989$		−	395.859i		−	0.400262i
$990$	−798.548	−	798.548i	−0.806614	−	0.806614i
$991$	−218.869	−	218.869i	−0.220857	−	0.220857i	0.588002	−	0.808859i	$-0.299915\pi$
$991$	−218.869	−	218.869i	−0.220857	−	0.220857i	−0.808859	+	0.588002i	$0.799915\pi$
$992$	471.665			0.475468
$993$	−2856.40			−2.87654
$994$	−420.065	+	1696.27i	−0.422600	+	1.70651i
$995$	496.066	+	496.066i	0.498559	+	0.498559i
$996$	3360.29	+	3360.29i	3.37379	+	3.37379i
$997$	−1240.54	+	1240.54i	−1.24427	+	1.24427i	−0.286056	+	0.958213i	$0.592344\pi$
$997$	−1240.54	+	1240.54i	−1.24427	+	1.24427i	−0.958213	+	0.286056i	$0.907656\pi$
$998$	2352.48	−	2352.48i	2.35719	−	2.35719i
$999$	878.436	+	878.436i	0.879315	+	0.879315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.6	yes	108
7.6	odd	2	inner	287.3.g.a.132.5	✓	108
41.32	even	4	inner	287.3.g.a.237.49	yes	108
287.237	odd	4	inner	287.3.g.a.237.50	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.5	✓	108	7.6	odd	2	inner
287.3.g.a.132.6	yes	108	1.1	even	1	trivial
287.3.g.a.237.49	yes	108	41.32	even	4	inner
287.3.g.a.237.50	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)

\(f(q)\)	\(=\)	\(q-3.39532i q^{2} +(3.29534 - 3.29534i) q^{3} -7.52821 q^{4} -3.85237 q^{5} +(-11.1888 - 11.1888i) q^{6} +(-5.99443 + 3.61480i) q^{7} +11.9794i q^{8} -12.7186i q^{9} +O(q^{10})\)	\(q-3.39532i q^{2} +(3.29534 - 3.29534i) q^{3} -7.52821 q^{4} -3.85237 q^{5} +(-11.1888 - 11.1888i) q^{6} +(-5.99443 + 3.61480i) q^{7} +11.9794i q^{8} -12.7186i q^{9} +13.0800i q^{10} +(-4.80013 - 4.80013i) q^{11} +(-24.8081 + 24.8081i) q^{12} +(10.4138 - 10.4138i) q^{13} +(12.2734 + 20.3530i) q^{14} +(-12.6949 + 12.6949i) q^{15} +10.5611 q^{16} +(4.31179 + 4.31179i) q^{17} -43.1837 q^{18} +(6.45808 + 6.45808i) q^{19} +29.0015 q^{20} +(-7.84170 + 31.6657i) q^{21} +(-16.2980 + 16.2980i) q^{22} +10.4426 q^{23} +(39.4763 + 39.4763i) q^{24} -10.1592 q^{25} +(-35.3584 - 35.3584i) q^{26} +(-12.2540 - 12.2540i) q^{27} +(45.1274 - 27.2130i) q^{28} +(-17.4031 - 17.4031i) q^{29} +(43.1032 + 43.1032i) q^{30} -39.1124i q^{31} +12.0592i q^{32} -31.6362 q^{33} +(14.6399 - 14.6399i) q^{34} +(23.0928 - 13.9256i) q^{35} +95.7483i q^{36} -71.6854 q^{37} +(21.9273 - 21.9273i) q^{38} -68.6344i q^{39} -46.1491i q^{40} +(27.5888 - 30.3291i) q^{41} +(107.515 + 26.6251i) q^{42} -37.9080i q^{43} +(36.1364 + 36.1364i) q^{44} +48.9967i q^{45} -35.4560i q^{46} +(18.4611 + 18.4611i) q^{47} +(34.8026 - 34.8026i) q^{48} +(22.8664 - 43.3374i) q^{49} +34.4939i q^{50} +28.4177 q^{51} +(-78.3976 + 78.3976i) q^{52} +(-18.6776 - 18.6776i) q^{53} +(-41.6064 + 41.6064i) q^{54} +(18.4919 + 18.4919i) q^{55} +(-43.3032 - 71.8098i) q^{56} +42.5632 q^{57} +(-59.0890 + 59.0890i) q^{58} +48.9655i q^{59} +(95.5698 - 95.5698i) q^{60} -2.80691 q^{61} -132.799 q^{62} +(45.9752 + 76.2407i) q^{63} +83.1895 q^{64} +(-40.1180 + 40.1180i) q^{65} +107.415i q^{66} +(40.4702 - 40.4702i) q^{67} +(-32.4601 - 32.4601i) q^{68} +(34.4120 - 34.4120i) q^{69} +(-47.2817 - 78.4074i) q^{70} +(51.9908 + 51.9908i) q^{71} +152.361 q^{72} +21.4373 q^{73} +243.395i q^{74} +(-33.4782 + 33.4782i) q^{75} +(-48.6178 - 48.6178i) q^{76} +(46.1256 + 11.4225i) q^{77} -233.036 q^{78} +(-76.6677 - 76.6677i) q^{79} -40.6854 q^{80} +33.7047 q^{81} +(-102.977 - 93.6729i) q^{82} -135.452i q^{83} +(59.0340 - 238.386i) q^{84} +(-16.6106 - 16.6106i) q^{85} -128.710 q^{86} -114.698 q^{87} +(57.5028 - 57.5028i) q^{88} +(-1.82467 + 1.82467i) q^{89} +166.360 q^{90} +(-24.7811 + 100.069i) q^{91} -78.6142 q^{92} +(-128.889 - 128.889i) q^{93} +(62.6815 - 62.6815i) q^{94} +(-24.8789 - 24.8789i) q^{95} +(39.7393 + 39.7393i) q^{96} +(-11.3772 - 11.3772i) q^{97} +(-147.144 - 77.6388i) q^{98} +(-61.0509 + 61.0509i) 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

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