LMFDB - Embedded newform 1050.3.p.b.451.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,3,Mod(451,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.451"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-12,-8,0,0,0,0,12,0,-4,24,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.2
Root			$-1.01575 + 1.40294i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.b.901.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(6.51658 - 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.16205 + 10.6730i) q^{11} +(3.00000 - 1.73205i) q^{12} -7.26007i q^{13} +(-7.73861 - 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-8.04643 - 4.64561i) q^{17} +(2.12132 - 3.67423i) q^{18} +(5.26235 - 3.03822i) q^{19} +(-11.9886 - 1.80922i) q^{21} +17.4289 q^{22} +(-1.12514 - 1.94880i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-8.89173 + 5.13364i) q^{26} -5.19615i q^{27} +(-2.08911 + 13.8433i) q^{28} +42.2122 q^{29} +(-1.05527 - 0.609262i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(18.4862 - 10.6730i) q^{33} +13.1398i q^{34} -6.00000 q^{36} +(17.5296 + 30.3622i) q^{37} +(-7.44209 - 4.29669i) q^{38} +(-6.28740 + 10.8901i) q^{39} +57.8811i q^{41} +(6.26139 + 15.9623i) q^{42} +34.0190 q^{43} +(-12.3241 - 21.3460i) q^{44} +(-1.59119 + 2.75603i) q^{46} +(-49.4411 + 28.5448i) q^{47} +6.92820i q^{48} +(35.9317 - 33.3154i) q^{49} +(8.04643 + 13.9368i) q^{51} +(12.5748 + 7.26007i) q^{52} +(7.27009 - 12.5922i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(18.4317 - 7.23003i) q^{56} -10.5247 q^{57} +(-29.8485 - 51.6992i) q^{58} +(50.1067 + 28.9291i) q^{59} +(-5.07658 + 2.93096i) q^{61} +1.72325i q^{62} +(16.4161 + 13.0963i) q^{63} +8.00000 q^{64} +(-26.1434 - 15.0939i) q^{66} +(24.7355 - 42.8431i) q^{67} +(16.0929 - 9.29122i) q^{68} +3.89761i q^{69} +101.986 q^{71} +(4.24264 + 7.34847i) q^{72} +(-71.2783 - 41.1525i) q^{73} +(24.7906 - 42.9387i) q^{74} +12.1529i q^{76} +(-12.8732 + 85.3029i) q^{77} +17.7835 q^{78} +(-55.8530 - 96.7403i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(70.8895 - 40.9281i) q^{82} -91.6237i q^{83} +(15.1223 - 18.9557i) q^{84} +(-24.0551 - 41.6646i) q^{86} +(-63.3183 - 36.5568i) q^{87} +(-17.4289 + 30.1878i) q^{88} +(110.673 - 63.8973i) q^{89} +(-18.5582 - 47.3108i) q^{91} +4.50057 q^{92} +(1.05527 + 1.82779i) q^{93} +(69.9203 + 40.3685i) q^{94} +(8.48528 - 4.89898i) q^{96} -61.4455i q^{97} +(-66.2104 - 20.4496i) q^{98} -36.9723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} + 48 q^{22} - 12 q^{23} - 96 q^{26} + 72 q^{29} - 132 q^{31} + 12 q^{33} - 48 q^{36} + 96 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 + 48 * q^22 - 12 * q^23 - 96 * q^26 + 72 * q^29 - 132 * q^31 + 12 * q^33 - 48 * q^36 + 96 * q^37 + 168 * q^38 + 24 * q^39 + 72 * q^42 + 112 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 84 * q^51 - 48 * q^52 - 32 * q^53 + 16 * q^56 - 216 * q^57 - 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 - 72 * q^66 + 120 * q^67 + 168 * q^68 + 8 * q^71 - 24 * q^73 - 16 * q^74 + 216 * q^77 + 192 * q^78 + 12 * q^79 - 36 * q^81 - 24 * q^82 - 40 * q^86 - 108 * q^87 - 48 * q^88 + 492 * q^89 - 308 * q^91 + 48 * q^92 + 132 * q^93 + 480 * q^94 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	6.51658	−	2.55620i	0.930940	−	0.365172i
$7$	6.51658	−	2.55620i	0.930940	−	0.365172i
$8$	2.82843			0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−6.16205	+	10.6730i	−0.560187	+	0.970272i	0.437293	+	0.899319i	$0.355937\pi$
$11$	−6.16205	+	10.6730i	−0.560187	+	0.970272i	−0.997480	+	0.0709528i	$0.977396\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$		−	7.26007i		−	0.558467i	−0.960223	−	0.279233i	$-0.909920\pi$
$13$		−	7.26007i		−	0.558467i	0.960223	−	0.279233i	$-0.0900803\pi$
$14$	−7.73861	−	6.17364i	−0.552758	−	0.440975i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−8.04643	−	4.64561i	−0.473319	−	0.273271i	0.244309	−	0.969697i	$-0.421439\pi$
$17$	−8.04643	−	4.64561i	−0.473319	−	0.273271i	−0.717628	+	0.696426i	$0.754772\pi$
$18$	2.12132	−	3.67423i	0.117851	−	0.204124i
$19$	5.26235	−	3.03822i	0.276966	−	0.159906i	−0.355083	−	0.934835i	$-0.615547\pi$
$19$	5.26235	−	3.03822i	0.276966	−	0.159906i	0.632049	+	0.774928i	$0.282214\pi$
$20$		0			0
$21$	−11.9886	−	1.80922i	−0.570886	−	0.0861535i
$22$	17.4289			0.792224
$23$	−1.12514	−	1.94880i	−0.0489192	−	0.0847306i	0.840529	−	0.541767i	$-0.182244\pi$
$23$	−1.12514	−	1.94880i	−0.0489192	−	0.0847306i	−0.889448	+	0.457036i	$0.848911\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−8.89173	+	5.13364i	−0.341990	+	0.197448i
$27$		−	5.19615i		−	0.192450i
$28$	−2.08911	+	13.8433i	−0.0746112	+	0.494402i
$29$	42.2122			1.45559			0.727797	−	0.685793i	$-0.240544\pi$
$29$	42.2122			1.45559			0.727797	+	0.685793i	$0.240544\pi$
$30$		0			0
$31$	−1.05527	−	0.609262i	−0.0340411	−	0.0196536i	0.482883	−	0.875685i	$-0.339590\pi$
$31$	−1.05527	−	0.609262i	−0.0340411	−	0.0196536i	−0.516924	+	0.856031i	$0.672923\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	18.4862	−	10.6730i	0.560187	−	0.323424i
$34$			13.1398i			0.386464i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	17.5296	+	30.3622i	0.473774	+	0.820600i	0.999549	−	0.0300231i	$-0.00955808\pi$
$37$	17.5296	+	30.3622i	0.473774	+	0.820600i	−0.525775	+	0.850623i	$0.676225\pi$
$38$	−7.44209	−	4.29669i	−0.195845	−	0.113071i
$39$	−6.28740	+	10.8901i	−0.161215	+	0.279233i
$40$		0			0
$41$			57.8811i			1.41173i	0.708345	+	0.705867i	$0.249442\pi$
$41$			57.8811i			1.41173i	−0.708345	+	0.705867i	$0.750558\pi$
$42$	6.26139	+	15.9623i	0.149081	+	0.380055i
$43$	34.0190			0.791140			0.395570	−	0.918436i	$-0.370547\pi$
$43$	34.0190			0.791140			0.395570	+	0.918436i	$0.370547\pi$
$44$	−12.3241	−	21.3460i	−0.280093	−	0.485136i
$45$		0			0
$46$	−1.59119	+	2.75603i	−0.0345911	+	0.0599136i
$47$	−49.4411	+	28.5448i	−1.05194	+	0.607337i	−0.923191	−	0.384340i	$-0.874429\pi$
$47$	−49.4411	+	28.5448i	−1.05194	+	0.607337i	−0.128747	+	0.991677i	$0.541096\pi$
$48$			6.92820i			0.144338i
$49$	35.9317	−	33.3154i	0.733300	−	0.679906i
$50$		0			0
$51$	8.04643	+	13.9368i	0.157773	+	0.273271i
$52$	12.5748	+	7.26007i	0.241823	+	0.139617i
$53$	7.27009	−	12.5922i	0.137172	−	0.237588i	−0.789253	−	0.614068i	$-0.789532\pi$
$53$	7.27009	−	12.5922i	0.137172	−	0.237588i	0.926425	+	0.376480i	$0.122866\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	18.4317	−	7.23003i	0.329137	−	0.129108i
$57$	−10.5247			−0.184644
$58$	−29.8485	−	51.6992i	−0.514630	−	0.891365i
$59$	50.1067	+	28.9291i	0.849266	+	0.490324i	0.860403	−	0.509614i	$-0.170212\pi$
$59$	50.1067	+	28.9291i	0.849266	+	0.490324i	−0.0111375	+	0.999938i	$0.503545\pi$
$60$		0			0
$61$	−5.07658	+	2.93096i	−0.0832226	+	0.0480486i	−0.541034	−	0.841001i	$-0.681967\pi$
$61$	−5.07658	+	2.93096i	−0.0832226	+	0.0480486i	0.457811	+	0.889049i	$0.348634\pi$
$62$			1.72325i			0.0277944i
$63$	16.4161	+	13.0963i	0.260573	+	0.207877i
$64$	8.00000			0.125000
$65$		0			0
$66$	−26.1434	−	15.0939i	−0.396112	−	0.228695i
$67$	24.7355	−	42.8431i	0.369186	−	0.639449i	−0.620252	−	0.784402i	$-0.712970\pi$
$67$	24.7355	−	42.8431i	0.369186	−	0.639449i	0.989439	+	0.144953i	$0.0463032\pi$
$68$	16.0929	−	9.29122i	0.236660	−	0.136636i
$69$			3.89761i			0.0564871i
$70$		0			0
$71$	101.986			1.43643			0.718214	−	0.695822i	$-0.244960\pi$
$71$	101.986			1.43643			0.718214	+	0.695822i	$0.244960\pi$
$72$	4.24264	+	7.34847i	0.0589256	+	0.102062i
$73$	−71.2783	−	41.1525i	−0.976415	−	0.563733i	−0.0752290	−	0.997166i	$-0.523969\pi$
$73$	−71.2783	−	41.1525i	−0.976415	−	0.563733i	−0.901186	+	0.433433i	$0.857302\pi$
$74$	24.7906	−	42.9387i	0.335009	−	0.580252i
$75$		0			0
$76$			12.1529i			0.159906i
$77$	−12.8732	+	85.3029i	−0.167185	+	1.10783i
$78$	17.7835			0.227993
$79$	−55.8530	−	96.7403i	−0.707001	−	1.22456i	−0.965965	−	0.258674i	$-0.916714\pi$
$79$	−55.8530	−	96.7403i	−0.707001	−	1.22456i	0.258964	−	0.965887i	$-0.416619\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	70.8895	−	40.9281i	0.864507	−	0.499123i
$83$		−	91.6237i		−	1.10390i	−0.833877	−	0.551950i	$-0.813884\pi$
$83$		−	91.6237i		−	1.10390i	0.833877	−	0.551950i	$-0.186116\pi$
$84$	15.1223	−	18.9557i	0.180027	−	0.225663i
$85$		0			0
$86$	−24.0551	−	41.6646i	−0.279710	−	0.484472i
$87$	−63.3183	−	36.5568i	−0.727797	−	0.420194i
$88$	−17.4289	+	30.1878i	−0.198056	+	0.343043i
$89$	110.673	−	63.8973i	1.24352	−	0.717947i	0.273712	−	0.961812i	$-0.411748\pi$
$89$	110.673	−	63.8973i	1.24352	−	0.717947i	0.969809	+	0.243864i	$0.0784151\pi$
$90$		0			0
$91$	−18.5582	−	47.3108i	−0.203936	−	0.519899i
$92$	4.50057			0.0489192
$93$	1.05527	+	1.82779i	0.0113470	+	0.0196536i
$94$	69.9203	+	40.3685i	0.743833	+	0.429452i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$		−	61.4455i		−	0.633459i	−0.948516	−	0.316729i	$-0.897415\pi$
$97$		−	61.4455i		−	0.633459i	0.948516	−	0.316729i	$-0.102585\pi$
$98$	−66.2104	−	20.4496i	−0.675616	−	0.208669i
$99$	−36.9723			−0.373458
$100$		0			0
$101$	53.8141	+	31.0696i	0.532813	+	0.307620i	0.742161	−	0.670221i	$-0.233801\pi$
$101$	53.8141	+	31.0696i	0.532813	+	0.307620i	−0.209348	+	0.977841i	$0.567134\pi$
$102$	11.3794	−	19.7096i	0.111562	−	0.193232i
$103$	154.102	−	88.9709i	1.49614	−	0.863795i	0.496147	−	0.868238i	$-0.334748\pi$
$103$	154.102	−	88.9709i	1.49614	−	0.863795i	0.999990	+	0.00444312i	$0.00141429\pi$
$104$		−	20.5346i		−	0.197448i
$105$		0			0
$106$	−20.5629			−0.193990
$107$	42.4855	+	73.5871i	0.397061	+	0.687730i	0.993362	−	0.115031i	$-0.0366968\pi$
$107$	42.4855	+	73.5871i	0.397061	+	0.687730i	−0.596301	+	0.802761i	$0.703363\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	86.4291	−	149.700i	0.792928	−	1.37339i	−0.131219	−	0.991353i	$-0.541889\pi$
$109$	86.4291	−	149.700i	0.792928	−	1.37339i	0.924147	−	0.382037i	$-0.124777\pi$
$110$		0			0
$111$		−	60.7244i		−	0.547067i
$112$	−21.8881	−	17.4617i	−0.195429	−	0.155908i
$113$	82.0616			0.726209			0.363105	−	0.931748i	$-0.381717\pi$
$113$	82.0616			0.726209			0.363105	+	0.931748i	$0.381717\pi$
$114$	7.44209	+	12.8901i	0.0652815	+	0.113071i
$115$		0			0
$116$	−42.2122	+	73.1137i	−0.363898	+	0.630290i
$117$	18.8622	−	10.8901i	0.161215	−	0.0930778i
$118$		−	81.8238i		−	0.693422i
$119$	−64.3103	−	9.70520i	−0.540423	−	0.0815563i
$120$		0			0
$121$	−15.4418	−	26.7460i	−0.127618	−	0.221042i
$122$	7.17937	+	4.14501i	0.0588473	+	0.0339755i
$123$	50.1265	−	86.8216i	0.407532	−	0.705867i
$124$	2.11055	−	1.21852i	0.0170205	−	0.00982681i
$125$		0			0
$126$	4.43168	−	29.3660i	0.0351720	−	0.233063i
$127$	193.480			1.52346			0.761732	−	0.647892i	$-0.224349\pi$
$127$	193.480			1.52346			0.761732	+	0.647892i	$0.224349\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	−51.0285	−	29.4613i	−0.395570	−	0.228382i
$130$		0			0
$131$	−156.850	+	90.5572i	−1.19733	+	0.691276i	−0.959958	−	0.280143i	$-0.909618\pi$
$131$	−156.850	+	90.5572i	−1.19733	+	0.691276i	−0.237368	+	0.971420i	$0.576285\pi$
$132$			42.6920i			0.323424i
$133$	26.5263	−	33.2504i	0.199446	−	0.250003i
$134$	−69.9625			−0.522108
$135$		0			0
$136$	−22.7587	−	13.1398i	−0.167344	−	0.0966159i
$137$	0.631666	−	1.09408i	0.00461070	−	0.00798597i	−0.863711	−	0.503988i	$-0.831866\pi$
$137$	0.631666	−	1.09408i	0.00461070	−	0.00798597i	0.868322	+	0.496002i	$0.165199\pi$
$138$	4.77358	−	2.75603i	0.0345911	−	0.0199712i
$139$			12.1327i			0.0872857i	0.999047	+	0.0436428i	$0.0138964\pi$
$139$			12.1327i			0.0872857i	−0.999047	+	0.0436428i	$0.986104\pi$
$140$		0			0
$141$	98.8822			0.701292
$142$	−72.1153	−	124.907i	−0.507854	−	0.879629i
$143$	77.4866	+	44.7369i	0.541865	+	0.312846i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$			116.397i			0.797239i
$147$	−82.7495	+	18.8553i	−0.562922	+	0.128268i
$148$	−70.1185			−0.473774
$149$	−144.863	−	250.910i	−0.972233	−	1.68396i	−0.688780	−	0.724971i	$-0.741853\pi$
$149$	−144.863	−	250.910i	−0.972233	−	1.68396i	−0.283453	−	0.958986i	$-0.591480\pi$
$150$		0			0
$151$	−58.6516	+	101.588i	−0.388421	+	0.672765i	−0.992237	−	0.124358i	$-0.960313\pi$
$151$	−58.6516	+	101.588i	−0.388421	+	0.672765i	0.603816	+	0.797124i	$0.293646\pi$
$152$	14.8842	−	8.59339i	0.0979223	−	0.0565354i
$153$		−	27.8737i		−	0.182181i
$154$	113.577	−	44.5518i	0.737513	−	0.289298i
$155$		0			0
$156$	−12.5748	−	21.7802i	−0.0806077	−	0.139617i
$157$	−159.121	−	91.8687i	−1.01351	−	0.585151i	−0.101294	−	0.994857i	$-0.532298\pi$
$157$	−159.121	−	91.8687i	−1.01351	−	0.585151i	−0.912218	+	0.409705i	$0.865632\pi$
$158$	−78.9881	+	136.811i	−0.499925	+	0.865895i
$159$	−21.8103	+	12.5922i	−0.137172	+	0.0791960i
$160$		0			0
$161$	−12.3136	−	9.82345i	−0.0764821	−	0.0610152i
$162$	12.7279			0.0785674
$163$	60.7854	+	105.283i	0.372917	+	0.645911i	0.990013	−	0.140977i	$-0.0450244\pi$
$163$	60.7854	+	105.283i	0.372917	+	0.645911i	−0.617096	+	0.786888i	$0.711691\pi$
$164$	−100.253	−	57.8811i	−0.611298	−	0.352933i
$165$		0			0
$166$	−112.216	+	64.7878i	−0.675998	+	0.390288i
$167$		−	94.6539i		−	0.566790i	−0.959003	−	0.283395i	$-0.908539\pi$
$167$		−	94.6539i		−	0.566790i	0.959003	−	0.283395i	$-0.0914608\pi$
$168$	−33.9089	−	5.11726i	−0.201839	−	0.0304599i
$169$	116.291			0.688115
$170$		0			0
$171$	15.7871	+	9.11466i	0.0923220	+	0.0533021i
$172$	−34.0190	+	58.9227i	−0.197785	+	0.342574i
$173$	225.766	−	130.346i	1.30501	−	0.753445i	0.323747	−	0.946144i	$-0.395057\pi$
$173$	225.766	−	130.346i	1.30501	−	0.753445i	0.981258	+	0.192699i	$0.0617240\pi$
$174$			103.398i			0.594244i
$175$		0			0
$176$	49.2964			0.280093
$177$	−50.1067	−	86.7873i	−0.283089	−	0.490324i
$178$	−156.516	−	90.3645i	−0.879302	−	0.507666i
$179$	−153.264	+	265.462i	−0.856225	+	1.48303i	0.0192782	+	0.999814i	$0.493863\pi$
$179$	−153.264	+	265.462i	−0.856225	+	1.48303i	−0.875504	+	0.483212i	$0.839470\pi$
$180$		0			0
$181$		−	314.885i		−	1.73970i	−0.493318	−	0.869849i	$-0.664216\pi$
$181$		−	314.885i		−	1.73970i	0.493318	−	0.869849i	$-0.335784\pi$
$182$	−44.8211	+	56.1828i	−0.246270	+	0.308697i
$183$	10.1532			0.0554817
$184$	−3.18238	−	5.51205i	−0.0172956	−	0.0299568i
$185$		0			0
$186$	1.49238	−	2.58488i	0.00802356	−	0.0138972i
$187$	99.1651	−	57.2530i	0.530295	−	0.306166i
$188$		−	114.179i		−	0.607337i
$189$	−13.2824	−	33.8612i	−0.0702773	−	0.179160i
$190$		0			0
$191$	45.3946	+	78.6257i	0.237668	+	0.411653i	0.960045	−	0.279847i	$-0.0902837\pi$
$191$	45.3946	+	78.6257i	0.237668	+	0.411653i	−0.722377	+	0.691500i	$0.756950\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	−114.828	+	198.887i	−0.594961	+	1.03050i	0.398591	+	0.917129i	$0.369499\pi$
$193$	−114.828	+	198.887i	−0.594961	+	1.03050i	−0.993552	+	0.113374i	$0.963834\pi$
$194$	−75.2551	+	43.4485i	−0.387913	+	0.223962i
$195$		0			0
$196$	21.7723	+	95.5509i	0.111083	+	0.487504i
$197$	−227.989			−1.15730			−0.578652	−	0.815574i	$-0.696421\pi$
$197$	−227.989			−1.15730			−0.578652	+	0.815574i	$0.696421\pi$
$198$	26.1434	+	45.2817i	0.132037	+	0.228695i
$199$	9.56623	+	5.52307i	0.0480715	+	0.0277541i	0.523843	−	0.851815i	$-0.324498\pi$
$199$	9.56623	+	5.52307i	0.0480715	+	0.0277541i	−0.475772	+	0.879569i	$0.657831\pi$
$200$		0			0
$201$	−74.2064	+	42.8431i	−0.369186	+	0.213150i
$202$		−	87.8781i		−	0.435040i
$203$	275.079	−	107.903i	1.35507	−	0.531541i
$204$	−32.1857			−0.157773
$205$		0			0
$206$	−217.933	−	125.824i	−1.05793	−	0.610796i
$207$	3.37543	−	5.84641i	0.0163064	−	0.0282435i
$208$	−25.1496	+	14.5201i	−0.120912	+	0.0698083i
$209$			74.8867i			0.358310i
$210$		0			0
$211$	151.187			0.716526			0.358263	−	0.933621i	$-0.383369\pi$
$211$	151.187			0.716526			0.358263	+	0.933621i	$0.383369\pi$
$212$	14.5402	+	25.1843i	0.0685858	+	0.118794i
$213$	−152.980	−	88.3228i	−0.718214	−	0.414661i
$214$	60.0836	−	104.068i	0.280765	−	0.486298i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−8.43417	−	1.27282i	−0.0388671	−	0.00586552i
$218$	−244.458			−1.12137
$219$	71.2783	+	123.458i	0.325472	+	0.563733i
$220$		0			0
$221$	−33.7274	+	58.4176i	−0.152613	+	0.264333i
$222$	−74.3719	+	42.9387i	−0.335009	+	0.193417i
$223$			308.586i			1.38379i	0.721997	+	0.691896i	$0.243224\pi$
$223$			308.586i			1.38379i	−0.721997	+	0.691896i	$0.756776\pi$
$224$	−5.90890	+	39.1546i	−0.0263790	+	0.174797i
$225$		0			0
$226$	−58.0263	−	100.505i	−0.256754	−	0.444710i
$227$	−86.9683	−	50.2112i	−0.383120	−	0.221195i	0.296055	−	0.955171i	$-0.404329\pi$
$227$	−86.9683	−	50.2112i	−0.383120	−	0.221195i	−0.679175	+	0.733976i	$0.737662\pi$
$228$	10.5247	−	18.2293i	0.0461610	−	0.0799532i
$229$	277.125	−	159.998i	1.21015	−	0.698682i	0.247361	−	0.968923i	$-0.420437\pi$
$229$	277.125	−	159.998i	1.21015	−	0.698682i	0.962793	+	0.270241i	$0.0871034\pi$
$230$		0			0
$231$	93.1843	−	116.806i	0.403395	−	0.505653i
$232$	119.394			0.514630
$233$	155.395	+	269.151i	0.666929	+	1.15516i	0.978758	+	0.205017i	$0.0657251\pi$
$233$	155.395	+	269.151i	0.666929	+	1.15516i	−0.311829	+	0.950138i	$0.600942\pi$
$234$	−26.6752	−	15.4009i	−0.113997	−	0.0658159i
$235$		0			0
$236$	−100.213	+	57.8582i	−0.424633	+	0.245162i
$237$			193.481i			0.816374i
$238$	33.5879	+	85.6264i	0.141126	+	0.359775i
$239$	136.263			0.570139			0.285069	−	0.958507i	$-0.407983\pi$
$239$	136.263			0.570139			0.285069	+	0.958507i	$0.407983\pi$
$240$		0			0
$241$	334.441	+	193.090i	1.38772	+	0.801202i	0.993058	−	0.117623i	$-0.0375274\pi$
$241$	334.441	+	193.090i	1.38772	+	0.801202i	0.394665	+	0.918825i	$0.370861\pi$
$242$	−21.8380	+	37.8246i	−0.0902398	+	0.156300i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	11.7239i		−	0.0480486i
$245$		0			0
$246$	−141.779			−0.576338
$247$	−22.0577	−	38.2050i	−0.0893024	−	0.154676i
$248$	−2.98476	−	1.72325i	−0.0120353	−	0.00694860i
$249$	−79.3485	+	137.436i	−0.318669	+	0.551950i
$250$		0			0
$251$		−	99.3717i		−	0.395903i	−0.980212	−	0.197952i	$-0.936571\pi$
$251$		−	99.3717i		−	0.395903i	0.980212	−	0.197952i	$-0.0634289\pi$
$252$	−39.0995	+	15.3372i	−0.155157	+	0.0608619i
$253$	27.7328			0.109616
$254$	−136.811	−	236.964i	−0.538626	−	0.932928i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−18.2886	+	10.5589i	−0.0711617	+	0.0410852i	−0.535159	−	0.844752i	$-0.679748\pi$
$257$	−18.2886	+	10.5589i	−0.0711617	+	0.0410852i	0.463997	+	0.885837i	$0.346415\pi$
$258$			83.3292i			0.322982i
$259$	191.845	+	153.049i	0.740715	+	0.590921i
$260$		0			0
$261$	63.3183	+	109.671i	0.242599	+	0.420194i
$262$	221.819	+	128.067i	0.846637	+	0.488806i
$263$	−190.259	+	329.538i	−0.723417	+	1.25299i	0.236205	+	0.971703i	$0.424096\pi$
$263$	−190.259	+	329.538i	−0.723417	+	1.25299i	−0.959622	+	0.281292i	$0.909237\pi$
$264$	52.2868	−	30.1878i	0.198056	−	0.114348i
$265$		0			0
$266$	−59.4802	−	8.97628i	−0.223610	−	0.0337454i
$267$	−221.347			−0.829014
$268$	49.4709	+	85.6862i	0.184593	+	0.319725i
$269$	14.5415	+	8.39551i	0.0540574	+	0.0312101i	0.526785	−	0.849998i	$-0.323397\pi$
$269$	14.5415	+	8.39551i	0.0540574	+	0.0312101i	−0.472728	+	0.881209i	$0.656731\pi$
$270$		0			0
$271$	320.146	−	184.836i	1.18135	−	0.682052i	0.225023	−	0.974353i	$-0.427754\pi$
$271$	320.146	−	184.836i	1.18135	−	0.682052i	0.956326	+	0.292301i	$0.0944209\pi$
$272$			37.1649i			0.136636i
$273$	−13.1351	+	87.0381i	−0.0481139	+	0.318821i
$274$	−1.78662			−0.00652051
$275$		0			0
$276$	−6.75086	−	3.89761i	−0.0244596	−	0.0141218i
$277$	242.912	−	420.736i	0.876940	−	1.51890i	0.0222577	−	0.999752i	$-0.492915\pi$
$277$	242.912	−	420.736i	0.876940	−	1.51890i	0.854682	−	0.519152i	$-0.173752\pi$
$278$	14.8595	−	8.57912i	0.0534513	−	0.0308601i
$279$		−	3.65557i		−	0.0131024i
$280$		0			0
$281$	360.234			1.28197			0.640986	−	0.767553i	$-0.278526\pi$
$281$	360.234			1.28197			0.640986	+	0.767553i	$0.278526\pi$
$282$	−69.9203	−	121.106i	−0.247944	−	0.429452i
$283$	−234.261	−	135.251i	−0.827778	−	0.477918i	0.0253131	−	0.999680i	$-0.491942\pi$
$283$	−234.261	−	135.251i	−0.827778	−	0.477918i	−0.853091	+	0.521762i	$0.825275\pi$
$284$	−101.986	+	176.646i	−0.359107	+	0.621992i
$285$		0			0
$286$		−	126.535i		−	0.442431i
$287$	147.956	+	377.187i	0.515525	+	1.31424i
$288$	−16.9706			−0.0589256
$289$	−101.337	−	175.520i	−0.350646	−	0.607336i
$290$		0			0
$291$	−53.2134	+	92.1683i	−0.182864	+	0.316729i
$292$	142.557	−	82.3051i	0.488207	−	0.281867i
$293$			9.63230i			0.0328747i	0.999865	+	0.0164374i	$0.00523241\pi$
$293$			9.63230i			0.0328747i	−0.999865	+	0.0164374i	$0.994768\pi$
$294$	81.6057	+	88.0143i	0.277570	+	0.299368i
$295$		0			0
$296$	49.5813	+	85.8773i	0.167504	+	0.290126i
$297$	55.4585	+	32.0190i	0.186729	+	0.107808i
$298$	−204.867	+	354.840i	−0.687472	+	1.19074i
$299$	−14.1484	+	8.16861i	−0.0473192	+	0.0273198i
$300$		0			0
$301$	221.688	−	86.9594i	0.736504	−	0.288902i
$302$	165.892			0.549310
$303$	−53.8141	−	93.2088i	−0.177604	−	0.307620i
$304$	−21.0494	−	12.1529i	−0.0692415	−	0.0399766i
$305$		0			0
$306$	−34.1381	+	19.7096i	−0.111562	+	0.0644106i
$307$			46.0412i			0.149971i	0.997185	+	0.0749857i	$0.0238911\pi$
$307$			46.0412i			0.149971i	−0.997185	+	0.0749857i	$0.976109\pi$
$308$	−134.876	−	107.600i	−0.437908	−	0.349350i
$309$	−308.204			−0.997425
$310$		0			0
$311$	−378.160	−	218.331i	−1.21595	−	0.702029i	−0.251901	−	0.967753i	$-0.581056\pi$
$311$	−378.160	−	218.331i	−1.21595	−	0.702029i	−0.964049	+	0.265724i	$0.914389\pi$
$312$	−17.7835	+	30.8019i	−0.0569983	+	0.0987239i
$313$	−248.135	+	143.261i	−0.792764	+	0.457703i	−0.840935	−	0.541137i	$-0.817994\pi$
$313$	−248.135	+	143.261i	−0.792764	+	0.457703i	0.0481706	+	0.998839i	$0.484661\pi$
$314$			259.844i			0.827529i
$315$		0			0
$316$	223.412			0.707001
$317$	−0.684418	−	1.18545i	−0.00215905	−	0.00373958i	0.864944	−	0.501869i	$-0.167354\pi$
$317$	−0.684418	−	1.18545i	−0.00215905	−	0.00373958i	−0.867103	+	0.498129i	$0.834021\pi$
$318$	30.8444	+	17.8080i	0.0969949	+	0.0560001i
$319$	−260.114	+	450.531i	−0.815404	+	1.41232i
$320$		0			0
$321$		−	147.174i		−	0.458487i
$322$	−3.32418	+	22.0273i	−0.0103235	+	0.0684077i
$323$	−56.4575			−0.174791
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	85.9636	−	148.893i	0.263692	−	0.456728i
$327$	−259.287	+	149.700i	−0.792928	+	0.457797i
$328$			163.712i			0.499123i
$329$	−249.221	+	312.396i	−0.757510	+	0.949533i
$330$		0			0
$331$	192.017	+	332.583i	0.580111	+	1.00478i	0.995466	+	0.0951223i	$0.0303242\pi$
$331$	192.017	+	332.583i	0.580111	+	1.00478i	−0.415354	+	0.909660i	$0.636342\pi$
$332$	158.697	+	91.6237i	0.478003	+	0.275975i
$333$	−52.5889	+	91.0866i	−0.157925	+	0.273533i
$334$	−115.927	+	66.9304i	−0.347087	+	0.200391i
$335$		0			0
$336$	17.7099	+	45.1482i	0.0527080	+	0.134370i
$337$	141.948			0.421211			0.210606	−	0.977571i	$-0.432456\pi$
$337$	141.948			0.421211			0.210606	+	0.977571i	$0.432456\pi$
$338$	−82.2305	−	142.427i	−0.243285	−	0.421383i
$339$	−123.092	−	71.0675i	−0.363105	−	0.209639i
$340$		0			0
$341$	13.0053	−	7.50861i	0.0381387	−	0.0220194i
$342$		−	25.7802i		−	0.0753806i
$343$	148.991	−	308.951i	0.434376	−	0.900732i
$344$	96.2203			0.279710
$345$		0			0
$346$	−319.281	−	184.337i	−0.922778	−	0.532766i
$347$	−125.176	+	216.811i	−0.360737	+	0.624815i	−0.988082	−	0.153926i	$-0.950808\pi$
$347$	−125.176	+	216.811i	−0.360737	+	0.624815i	0.627345	+	0.778741i	$0.284142\pi$
$348$	126.637	−	73.1137i	0.363898	−	0.210097i
$349$			195.188i			0.559277i	0.960105	+	0.279639i	$0.0902147\pi$
$349$			195.188i			0.559277i	−0.960105	+	0.279639i	$0.909785\pi$
$350$		0			0
$351$	−37.7244			−0.107477
$352$	−34.8578	−	60.3756i	−0.0990280	−	0.171521i
$353$	−123.148	−	71.0997i	−0.348862	−	0.201416i	0.315322	−	0.948985i	$-0.397887\pi$
$353$	−123.148	−	71.0997i	−0.348862	−	0.201416i	−0.664184	+	0.747569i	$0.731221\pi$
$354$	−70.8615	+	122.736i	−0.200174	+	0.346711i
$355$		0			0
$356$			255.589i			0.717947i
$357$	88.0605	+	70.2522i	0.246668	+	0.196785i
$358$	433.497			1.21089
$359$	328.443	+	568.880i	0.914884	+	1.58462i	0.807072	+	0.590453i	$0.201051\pi$
$359$	328.443	+	568.880i	0.914884	+	1.58462i	0.107812	+	0.994171i	$0.465616\pi$
$360$		0			0
$361$	−162.038	+	280.659i	−0.448860	+	0.777448i
$362$	−385.654	+	222.658i	−1.06534	+	0.615076i
$363$			53.4921i			0.147361i
$364$	100.503	+	15.1671i	0.276107	+	0.0416678i
$365$		0			0
$366$	−7.17937	−	12.4350i	−0.0196158	−	0.0339755i
$367$	444.403	+	256.576i	1.21091	+	0.699117i	0.962957	−	0.269655i	$-0.0869098\pi$
$367$	444.403	+	256.576i	1.21091	+	0.699117i	0.247950	+	0.968773i	$0.420243\pi$
$368$	−4.50057	+	7.79522i	−0.0122298	+	0.0211827i
$369$	−150.379	+	86.8216i	−0.407532	+	0.235289i
$370$		0			0
$371$	15.1880	−	100.642i	0.0409381	−	0.271271i
$372$	−4.22109			−0.0113470
$373$	−316.262	−	547.782i	−0.847887	−	1.46858i	−0.883090	−	0.469204i	$-0.844541\pi$
$373$	−316.262	−	547.782i	−0.847887	−	1.46858i	0.0352027	−	0.999380i	$-0.488792\pi$
$374$	−140.241	−	80.9679i	−0.374975	−	0.216492i
$375$		0			0
$376$	−139.841	+	80.7370i	−0.371916	+	0.214726i
$377$		−	306.463i		−	0.812900i
$378$	−32.0792	+	40.2110i	−0.0848656	+	0.106378i
$379$	−617.180			−1.62844			−0.814222	−	0.580553i	$-0.802836\pi$
$379$	−617.180			−1.62844			−0.814222	+	0.580553i	$0.802836\pi$
$380$		0			0
$381$	−290.220	−	167.559i	−0.761732	−	0.439786i
$382$	64.1976	−	111.193i	0.168057	−	0.291082i
$383$	−150.642	+	86.9735i	−0.393322	+	0.227085i	−0.683599	−	0.729858i	$-0.739586\pi$
$383$	−150.642	+	86.9735i	−0.393322	+	0.227085i	0.290276	+	0.956943i	$0.406253\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	324.781			0.841402
$387$	51.0285	+	88.3840i	0.131857	+	0.228382i
$388$	106.427	+	61.4455i	0.274296	+	0.158365i
$389$	−98.0961	+	169.907i	−0.252175	+	0.436780i	−0.964124	−	0.265451i	$-0.914479\pi$
$389$	−98.0961	+	169.907i	−0.252175	+	0.436780i	0.711949	+	0.702231i	$0.247813\pi$
$390$		0			0
$391$			20.9079i			0.0534729i
$392$	101.630	−	94.2301i	0.259261	−	0.240383i
$393$	313.699			0.798217
$394$	161.213	+	279.228i	0.409169	+	0.708702i
$395$		0			0
$396$	36.9723	−	64.0379i	0.0933645	−	0.161712i
$397$	345.285	−	199.350i	0.869736	−	0.502142i	0.00247542	−	0.999997i	$-0.499212\pi$
$397$	345.285	−	199.350i	0.869736	−	0.502142i	0.867260	+	0.497855i	$0.165879\pi$
$398$		−	15.6216i		−	0.0392502i
$399$	−68.5851	+	26.9033i	−0.171893	+	0.0674267i
$400$		0			0
$401$	−173.599	−	300.683i	−0.432916	−	0.749833i	0.564207	−	0.825633i	$-0.309182\pi$
$401$	−173.599	−	300.683i	−0.432916	−	0.749833i	−0.997123	+	0.0758008i	$0.975849\pi$
$402$	104.944	+	60.5893i	0.261054	+	0.150720i
$403$	−4.42328	+	7.66135i	−0.0109759	+	0.0190108i
$404$	−107.628	+	62.1392i	−0.266407	+	0.153810i
$405$		0			0
$406$	−326.664	−	260.603i	−0.804591	−	0.641880i
$407$	−432.074			−1.06161
$408$	22.7587	+	39.4193i	0.0557812	+	0.0966159i
$409$	293.397	+	169.393i	0.717352	+	0.414163i	0.813777	−	0.581177i	$-0.197408\pi$
$409$	293.397	+	169.393i	0.717352	+	0.414163i	−0.0964252	+	0.995340i	$0.530741\pi$
$410$		0			0
$411$	−1.89500	+	1.09408i	−0.00461070	+	0.00266199i
$412$			355.884i			0.863795i
$413$	400.473	+	60.4361i	0.969668	+	0.146334i
$414$	−9.54715			−0.0230608
$415$		0			0
$416$	35.5669	+	20.5346i	0.0854974	+	0.0493619i
$417$	10.5072	−	18.1991i	0.0251972	−	0.0436428i
$418$	91.7171	−	52.9529i	0.219419	−	0.126682i
$419$			369.514i			0.881894i	0.897533	+	0.440947i	$0.145357\pi$
$419$			369.514i			0.881894i	−0.897533	+	0.440947i	$0.854643\pi$
$420$		0			0
$421$	−217.571			−0.516797			−0.258398	−	0.966038i	$-0.583195\pi$
$421$	−217.571			−0.516797			−0.258398	+	0.966038i	$0.583195\pi$
$422$	−106.905	−	185.166i	−0.253330	−	0.438781i
$423$	−148.323	−	85.6345i	−0.350646	−	0.202446i
$424$	20.5629	−	35.6160i	0.0484975	−	0.0840001i
$425$		0			0
$426$			249.815i			0.586420i
$427$	−25.5898	+	32.0766i	−0.0599293	+	0.0751209i
$428$	−169.942			−0.397061
$429$	−77.4866	−	134.211i	−0.180622	−	0.312846i
$430$		0			0
$431$	142.916	−	247.537i	0.331591	−	0.574332i	−0.651233	−	0.758878i	$-0.725748\pi$
$431$	142.916	−	247.537i	0.331591	−	0.574332i	0.982824	+	0.184546i	$0.0590814\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$			643.490i			1.48612i	0.669224	+	0.743060i	$0.266626\pi$
$433$			643.490i			1.48612i	−0.669224	+	0.743060i	$0.733374\pi$
$434$	4.40498	+	11.2297i	0.0101497	+	0.0258749i
$435$		0			0
$436$	172.858	+	299.399i	0.396464	+	0.686695i
$437$	−11.8418	−	6.83686i	−0.0270979	−	0.0156450i
$438$	100.803	−	174.595i	0.230143	−	0.398620i
$439$	494.013	−	285.218i	1.12531	−	0.649700i	0.182562	−	0.983194i	$-0.441561\pi$
$439$	494.013	−	285.218i	1.12531	−	0.649700i	0.942752	+	0.333494i	$0.108228\pi$
$440$		0			0
$441$	140.453	+	43.3802i	0.318488	+	0.0983677i
$442$	95.3956			0.215827
$443$	−33.0074	−	57.1705i	−0.0745089	−	0.129053i	0.826364	−	0.563137i	$-0.190406\pi$
$443$	−33.0074	−	57.1705i	−0.0745089	−	0.129053i	−0.900873	+	0.434084i	$0.857072\pi$
$444$	105.178	+	60.7244i	0.236887	+	0.136767i
$445$		0			0
$446$	377.939	−	218.203i	0.847396	−	0.489244i
$447$			501.819i			1.12264i
$448$	52.1327	−	20.4496i	0.116368	−	0.0456464i
$449$	515.072			1.14715			0.573577	−	0.819152i	$-0.305555\pi$
$449$	515.072			1.14715			0.573577	+	0.819152i	$0.305555\pi$
$450$		0			0
$451$	−617.764	−	356.666i	−1.36977	−	0.790834i
$452$	−82.0616	+	142.135i	−0.181552	+	0.314458i
$453$	175.955	−	101.588i	0.388421	−	0.224255i
$454$			142.019i			0.312816i
$455$		0			0
$456$	−29.7684			−0.0652815
$457$	39.5136	+	68.4395i	0.0864629	+	0.149758i	0.906014	−	0.423248i	$-0.139110\pi$
$457$	39.5136	+	68.4395i	0.0864629	+	0.149758i	−0.819551	+	0.573007i	$0.805777\pi$
$458$	−391.914	−	226.272i	−0.855708	−	0.494043i
$459$	−24.1393	+	41.8105i	−0.0525910	+	0.0910904i
$460$		0			0
$461$		−	9.58316i		−	0.0207878i	−0.999946	−	0.0103939i	$-0.996691\pi$
$461$		−	9.58316i		−	0.0207878i	0.999946	−	0.0103939i	$-0.00330854\pi$
$462$	−208.948	−	31.5328i	−0.452269	−	0.0682529i
$463$	232.103			0.501303			0.250652	−	0.968077i	$-0.419355\pi$
$463$	232.103			0.501303			0.250652	+	0.968077i	$0.419355\pi$
$464$	−84.4244	−	146.227i	−0.181949	−	0.315145i
$465$		0			0
$466$	219.761	−	380.637i	0.471590	−	0.816818i
$467$	−593.692	+	342.768i	−1.27129	+	0.733979i	−0.975230	−	0.221191i	$-0.929006\pi$
$467$	−593.692	+	342.768i	−1.27129	+	0.733979i	−0.296058	+	0.955170i	$0.595672\pi$
$468$			43.5604i			0.0930778i
$469$	51.6752	−	342.419i	0.110182	−	0.730105i
$470$		0			0
$471$	159.121	+	275.606i	0.337837	+	0.585151i
$472$	141.723	+	81.8238i	0.300261	+	0.173356i
$473$	−209.627	+	363.085i	−0.443186	+	0.767621i
$474$	236.964	−	136.811i	0.499925	−	0.288632i
$475$		0			0
$476$	81.1202	−	101.684i	0.170421	−	0.213621i
$477$	43.6206			0.0914477
$478$	−96.3526	−	166.888i	−0.201575	−	0.349137i
$479$	−544.818	−	314.551i	−1.13741	−	0.656682i	−0.191619	−	0.981469i	$-0.561374\pi$
$479$	−544.818	−	314.551i	−1.13741	−	0.656682i	−0.945787	+	0.324787i	$0.894707\pi$
$480$		0			0
$481$	220.432	−	127.266i	0.458278	−	0.264587i
$482$		−	546.140i		−	1.13307i
$483$	9.96307	+	25.3991i	0.0206275	+	0.0525861i
$484$	61.7673			0.127618
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−249.384	+	431.946i	−0.512083	+	0.886953i	0.487819	+	0.872945i	$0.337793\pi$
$487$	−249.384	+	431.946i	−0.512083	+	0.886953i	−0.999902	+	0.0140085i	$0.995541\pi$
$488$	−14.3587	+	8.29002i	−0.0294236	+	0.0169877i
$489$		−	210.567i		−	0.430607i
$490$		0			0
$491$	166.583			0.339274			0.169637	−	0.985507i	$-0.445741\pi$
$491$	166.583			0.339274			0.169637	+	0.985507i	$0.445741\pi$
$492$	100.253	+	173.643i	0.203766	+	0.352933i
$493$	−339.658	−	196.101i	−0.688961	−	0.397772i
$494$	−31.1943	+	54.0301i	−0.0631463	+	0.109373i
$495$		0			0
$496$			4.87410i			0.00982681i
$497$	664.603	−	260.698i	1.33723	−	0.524543i
$498$	224.431			0.450665
$499$	−18.1531	−	31.4421i	−0.0363790	−	0.0630102i	0.847263	−	0.531174i	$-0.178249\pi$
$499$	−18.1531	−	31.4421i	−0.0363790	−	0.0630102i	−0.883642	+	0.468164i	$0.844916\pi$
$500$		0			0
$501$	−81.9727	+	141.981i	−0.163618	+	0.283395i
$502$	−121.705	+	70.2664i	−0.242440	+	0.139973i
$503$			634.940i			1.26231i	0.775658	+	0.631153i	$0.217418\pi$
$503$			634.940i			1.26231i	−0.775658	+	0.631153i	$0.782582\pi$
$504$	46.4317	+	37.0419i	0.0921263	+	0.0734958i
$505$		0			0
$506$	−19.6100	−	33.9656i	−0.0387550	−	0.0671256i
$507$	−174.437	−	100.711i	−0.344057	−	0.198642i
$508$	−193.480	+	335.117i	−0.380866	+	0.659680i
$509$	500.864	−	289.174i	0.984015	−	0.568121i	0.0805350	−	0.996752i	$-0.474337\pi$
$509$	500.864	−	289.174i	0.984015	−	0.568121i	0.903480	+	0.428631i	$0.141004\pi$
$510$		0			0
$511$	−569.685	−	85.9723i	−1.11484	−	0.168243i
$512$	22.6274			0.0441942
$513$	−15.7871	−	27.3440i	−0.0307740	−	0.0533021i
$514$	25.8639	+	14.9325i	0.0503189	+	0.0290516i
$515$		0			0
$516$	102.057	−	58.9227i	0.197785	−	0.114191i
$517$		−	703.579i		−	1.36089i
$518$	51.7904	−	343.183i	0.0999815	−	0.662516i
$519$	−451.532			−0.870003
$520$		0			0
$521$	−550.974	−	318.105i	−1.05753	−	0.610566i	−0.132783	−	0.991145i	$-0.542391\pi$
$521$	−550.974	−	318.105i	−1.05753	−	0.610566i	−0.924748	+	0.380579i	$0.875725\pi$
$522$	89.5456	−	155.098i	0.171543	−	0.297122i
$523$	−392.868	+	226.823i	−0.751182	+	0.433695i	−0.826121	−	0.563493i	$-0.809457\pi$
$523$	−392.868	+	226.823i	−0.751182	+	0.433695i	0.0749389	+	0.997188i	$0.476124\pi$
$524$		−	362.229i		−	0.691276i
$525$		0			0
$526$	538.133			1.02307
$527$	5.66079	+	9.80477i	0.0107415	+	0.0186049i
$528$	−73.9447	−	42.6920i	−0.140047	−	0.0808560i
$529$	261.968	−	453.742i	0.495214	−	0.857735i
$530$		0			0
$531$			173.575i			0.326882i
$532$	31.0652	+	79.1953i	0.0583933	+	0.148863i
$533$	420.220			0.788406
$534$	156.516	+	271.093i	0.293101	+	0.507666i
$535$		0			0
$536$	69.9625	−	121.179i	0.130527	−	0.226079i
$537$	459.793	−	265.462i	0.856225	−	0.494342i
$538$		−	23.7461i		−	0.0441377i
$539$	134.162	+	588.790i	0.248909	+	1.09237i
$540$		0			0
$541$	288.159	+	499.106i	0.532641	+	0.922562i	0.999274	+	0.0381102i	$0.0121338\pi$
$541$	288.159	+	499.106i	0.532641	+	0.922562i	−0.466632	+	0.884451i	$0.654533\pi$
$542$	−452.754	−	261.398i	−0.835340	−	0.482284i
$543$	−272.699	+	472.328i	−0.502208	+	0.869849i
$544$	45.5175	−	26.2795i	0.0836718	−	0.0483080i
$545$		0			0
$546$	115.887	−	45.4581i	0.212248	−	0.0832566i
$547$	−481.306			−0.879901			−0.439950	−	0.898022i	$-0.645004\pi$
$547$	−481.306			−0.879901			−0.439950	+	0.898022i	$0.645004\pi$
$548$	1.26333	+	2.18815i	0.00230535	+	0.00399298i
$549$	−15.2297	−	8.79289i	−0.0277409	−	0.0160162i
$550$		0			0
$551$	222.136	−	128.250i	0.403150	−	0.232759i
$552$			11.0241i			0.0199712i
$553$	−611.259	−	487.645i	−1.10535	−	0.881817i
$554$	−687.060			−1.24018
$555$		0			0
$556$	−21.0145	−	12.1327i	−0.0377958	−	0.0218214i
$557$	54.4056	−	94.2333i	0.0976762	−	0.169180i	−0.813046	−	0.582199i	$-0.802192\pi$
$557$	54.4056	−	94.2333i	0.0976762	−	0.169180i	0.910722	+	0.413019i	$0.135526\pi$
$558$	−4.47714	+	2.58488i	−0.00802356	+	0.00463240i
$559$		−	246.980i		−	0.441825i
$560$		0			0
$561$	−198.330			−0.353530
$562$	−254.724	−	441.195i	−0.453245	−	0.785044i
$563$	−521.516	−	301.097i	−0.926316	−	0.534809i	−0.0406717	−	0.999173i	$-0.512950\pi$
$563$	−521.516	−	301.097i	−0.926316	−	0.534809i	−0.885645	+	0.464364i	$0.846283\pi$
$564$	−98.8822	+	171.269i	−0.175323	+	0.303669i
$565$		0			0
$566$			382.547i			0.675878i
$567$	−9.40101	+	62.2946i	−0.0165803	+	0.109867i
$568$	288.461			0.507854
$569$	4.76685	+	8.25642i	0.00837759	+	0.0145104i	0.870184	−	0.492727i	$-0.164000\pi$
$569$	4.76685	+	8.25642i	0.00837759	+	0.0145104i	−0.861806	+	0.507238i	$0.830667\pi$
$570$		0			0
$571$	−491.103	+	850.615i	−0.860075	+	1.48969i	0.0117813	+	0.999931i	$0.496250\pi$
$571$	−491.103	+	850.615i	−0.860075	+	1.48969i	−0.871856	+	0.489762i	$0.837084\pi$
$572$	−154.973	+	89.4739i	−0.270932	+	0.156423i
$573$		−	157.251i		−	0.274435i
$574$	357.337	−	447.919i	0.622538	−	0.780347i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	454.001	+	262.117i	0.786830	+	0.454276i	0.838845	−	0.544370i	$-0.183231\pi$
$577$	454.001	+	262.117i	0.786830	+	0.454276i	−0.0520155	+	0.998646i	$0.516565\pi$
$578$	−143.312	+	248.223i	−0.247944	+	0.429452i
$579$	344.483	−	198.887i	0.594961	−	0.343501i
$580$		0			0
$581$	−234.209	−	597.073i	−0.403113	−	1.02767i
$582$	150.510			0.258608
$583$	89.5974	+	155.187i	0.153683	+	0.266187i
$584$	−201.605	−	116.397i	−0.345215	−	0.199310i
$585$		0			0
$586$	11.7971	−	6.81106i	0.0201316	−	0.0116230i
$587$		−	651.322i		−	1.10958i	−0.831991	−	0.554789i	$-0.812799\pi$
$587$		−	651.322i		−	1.10958i	0.831991	−	0.554789i	$-0.187201\pi$
$588$	50.0911	−	162.182i	0.0851889	−	0.275819i
$589$	−7.40429			−0.0125710
$590$		0			0
$591$	341.984	+	197.444i	0.578652	+	0.334085i
$592$	70.1185	−	121.449i	0.118443	−	0.205150i
$593$	610.904	−	352.706i	1.03019	−	0.594782i	0.113152	−	0.993578i	$-0.463905\pi$
$593$	610.904	−	352.706i	1.03019	−	0.594782i	0.917040	+	0.398796i	$0.130572\pi$
$594$		−	90.5633i		−	0.152464i
$595$		0			0
$596$	579.451			0.972233
$597$	−9.56623	−	16.5692i	−0.0160238	−	0.0277541i
$598$	20.0089	+	11.5522i	0.0334597	+	0.0193180i
$599$	296.910	−	514.263i	0.495676	−	0.858535i	−0.504312	−	0.863522i	$-0.668254\pi$
$599$	296.910	−	514.263i	0.495676	−	0.858535i	0.999988	+	0.00498610i	$0.00158713\pi$
$600$		0			0
$601$			12.1644i			0.0202403i	0.999949	+	0.0101202i	$0.00322140\pi$
$601$			12.1644i			0.0202403i	−0.999949	+	0.0101202i	$0.996779\pi$
$602$	−263.260	−	210.021i	−0.437309	−	0.348873i
$603$	148.413			0.246124
$604$	−117.303	−	203.175i	−0.194211	−	0.336383i
$605$		0			0
$606$	−76.1047	+	131.817i	−0.125585	+	0.217520i
$607$	−698.521	+	403.291i	−1.15078	+	0.664401i	−0.949076	−	0.315047i	$-0.897980\pi$
$607$	−698.521	+	403.291i	−1.15078	+	0.664401i	−0.201700	+	0.979447i	$0.564647\pi$
$608$			34.3736i			0.0565354i
$609$	−506.066	−	76.3714i	−0.830978	−	0.125405i
$610$		0			0
$611$	207.237	+	358.946i	0.339178	+	0.587473i
$612$	48.2786	+	27.8737i	0.0788866	+	0.0455452i
$613$	−397.237	+	688.035i	−0.648021	+	1.12241i	0.335574	+	0.942014i	$0.391070\pi$
$613$	−397.237	+	688.035i	−0.648021	+	1.12241i	−0.983595	+	0.180392i	$0.942263\pi$
$614$	56.3887	−	32.5560i	0.0918383	−	0.0530229i
$615$		0			0
$616$	−36.4110	+	241.273i	−0.0591087	+	0.391677i
$617$	−108.982			−0.176633			−0.0883164	−	0.996092i	$-0.528149\pi$
$617$	−108.982			−0.176633			−0.0883164	+	0.996092i	$0.528149\pi$
$618$	217.933	+	377.472i	0.352643	+	0.610796i
$619$	−310.725	−	179.397i	−0.501979	−	0.289818i	0.227551	−	0.973766i	$-0.426928\pi$
$619$	−310.725	−	179.397i	−0.501979	−	0.289818i	−0.729531	+	0.683948i	$0.760261\pi$
$620$		0			0
$621$	−10.1263	+	5.84641i	−0.0163064	+	0.00941451i
$622$			617.533i			0.992819i
$623$	557.878	−	699.296i	0.895470	−	1.12246i
$624$	50.2992			0.0806077
$625$		0			0
$626$	350.916	+	202.602i	0.560569	+	0.323645i
$627$	64.8538	−	112.330i	0.103435	−	0.179155i
$628$	318.243	−	183.737i	0.506756	−	0.292576i
$629$		−	325.743i		−	0.517875i
$630$		0			0
$631$	−612.351			−0.970446			−0.485223	−	0.874391i	$-0.661262\pi$
$631$	−612.351			−0.970446			−0.485223	+	0.874391i	$0.661262\pi$
$632$	−157.976	−	273.623i	−0.249962	−	0.432948i
$633$	−226.781	−	130.932i	−0.358263	−	0.206843i
$634$	−0.967913	+	1.67647i	−0.00152668	+	0.00264428i
$635$		0			0
$636$		−	50.3687i		−	0.0791960i
$637$	−241.872	−	260.866i	−0.379705	−	0.409523i
$638$	735.713			1.15316
$639$	152.980	+	264.969i	0.239405	+	0.414661i
$640$		0			0
$641$	−459.706	+	796.233i	−0.717169	+	1.24217i	0.244947	+	0.969536i	$0.421229\pi$
$641$	−459.706	+	796.233i	−0.717169	+	1.24217i	−0.962117	+	0.272637i	$0.912104\pi$
$642$	−180.251	+	104.068i	−0.280765	+	0.162099i
$643$		−	835.879i		−	1.29997i	−0.759948	−	0.649984i	$-0.774776\pi$
$643$		−	835.879i		−	1.29997i	0.759948	−	0.649984i	$-0.225224\pi$
$644$	29.3283	−	11.5044i	0.0455409	−	0.0178639i
$645$		0			0
$646$	39.9215	+	69.1461i	0.0617980	+	0.107037i
$647$	492.933	+	284.595i	0.761876	+	0.439869i	0.829969	−	0.557810i	$-0.188358\pi$
$647$	492.933	+	284.595i	0.761876	+	0.439869i	−0.0680932	+	0.997679i	$0.521692\pi$
$648$	−12.7279	+	22.0454i	−0.0196419	+	0.0340207i
$649$	−617.520	+	356.525i	−0.951495	+	0.549346i
$650$		0			0
$651$	11.5490	+	9.21343i	0.0177403	+	0.0141527i
$652$	−243.142			−0.372917
$653$	196.162	+	339.763i	0.300402	+	0.520311i	0.976227	−	0.216751i	$-0.0695460\pi$
$653$	196.162	+	339.763i	0.300402	+	0.520311i	−0.675825	+	0.737062i	$0.736213\pi$
$654$	366.688	+	211.707i	0.560684	+	0.323711i
$655$		0			0
$656$	200.506	−	115.762i	0.305649	−	0.176467i
$657$		−	246.915i		−	0.375822i
$658$	558.831	+	84.3343i	0.849288	+	0.128168i
$659$	505.063			0.766408			0.383204	−	0.923664i	$-0.374821\pi$
$659$	505.063			0.766408			0.383204	+	0.923664i	$0.374821\pi$
$660$		0			0
$661$	−255.815	−	147.695i	−0.387013	−	0.223442i	0.293852	−	0.955851i	$-0.405063\pi$
$661$	−255.815	−	147.695i	−0.387013	−	0.223442i	−0.680865	+	0.732409i	$0.738396\pi$
$662$	271.553	−	470.343i	0.410201	−	0.710488i
$663$	101.182	−	58.4176i	0.152613	−	0.0881110i
$664$		−	259.151i		−	0.390288i
$665$		0			0
$666$	148.744			0.223339
$667$	−47.4948	−	82.2633i	−0.0712065	−	0.123333i
$668$	163.945	+	94.6539i	0.245427	+	0.141698i
$669$	267.243	−	462.878i	0.399466	−	0.691896i
$670$		0			0
$671$		−	72.2430i		−	0.107665i
$672$	42.7723	−	53.6147i	0.0636492	−	0.0797838i
$673$	624.569			0.928038			0.464019	−	0.885825i	$-0.346407\pi$
$673$	624.569			0.928038			0.464019	+	0.885825i	$0.346407\pi$
$674$	−100.373	−	173.850i	−0.148921	−	0.257938i
$675$		0			0
$676$	−116.291	+	201.423i	−0.172029	+	0.297963i
$677$	676.847	−	390.778i	0.999774	−	0.577220i	0.0915926	−	0.995797i	$-0.470804\pi$
$677$	676.847	−	390.778i	0.999774	−	0.577220i	0.908181	+	0.418577i	$0.137471\pi$
$678$			201.009i			0.296474i
$679$	−157.067	−	400.415i	−0.231321	−	0.589712i
$680$		0			0
$681$	86.9683	+	150.634i	0.127707	+	0.221195i
$682$	−18.3923	−	10.6188i	−0.0269681	−	0.0155701i
$683$	50.8525	−	88.0791i	0.0744546	−	0.128959i	−0.826394	−	0.563092i	$-0.809612\pi$
$683$	50.8525	−	88.0791i	0.0744546	−	0.128959i	0.900849	+	0.434133i	$0.142945\pi$
$684$	−31.5741	+	18.2293i	−0.0461610	+	0.0266511i
$685$		0			0
$686$	−483.739	+	35.9855i	−0.705158	+	0.0524570i
$687$	−554.250			−0.806769
$688$	−68.0380	−	117.845i	−0.0988925	−	0.171287i
$689$	−91.4200	−	52.7814i	−0.132685	−	0.0766057i
$690$		0			0
$691$	634.684	−	366.435i	0.918501	−	0.530297i	0.0353446	−	0.999375i	$-0.488747\pi$
$691$	634.684	−	366.435i	0.918501	−	0.530297i	0.883157	+	0.469078i	$0.155414\pi$
$692$			521.384i			0.753445i
$693$	−240.933	+	94.5087i	−0.347667	+	0.136376i
$694$	354.051			0.510160
$695$		0			0
$696$	−179.091	−	103.398i	−0.257315	−	0.148561i
$697$	268.893	−	465.736i	0.385786	−	0.668201i
$698$	239.055	−	138.019i	0.342486	−	0.197734i
$699$		−	538.303i		−	0.770104i
$700$		0			0
$701$	−795.928			−1.13542			−0.567709	−	0.823229i	$-0.692170\pi$
$701$	−795.928			−1.13542			−0.567709	+	0.823229i	$0.692170\pi$
$702$	26.6752	+	46.2028i	0.0379988	+	0.0658159i
$703$	184.494	+	106.518i	0.262438	+	0.151519i
$704$	−49.2964	+	85.3839i	−0.0700233	+	0.121284i
$705$		0			0
$706$			201.100i			0.284845i
$707$	430.104	+	64.9079i	0.608351	+	0.0918075i
$708$	200.427			0.283089
$709$	−514.532	−	891.196i	−0.725715	−	1.25698i	−0.958679	−	0.284490i	$-0.908176\pi$
$709$	−514.532	−	891.196i	−0.725715	−	1.25698i	0.232964	−	0.972485i	$-0.425158\pi$
$710$		0			0
$711$	167.559	−	290.221i	0.235667	−	0.408187i
$712$	313.032	−	180.729i	0.439651	−	0.253833i
$713$			2.74203i			0.00384576i
$714$	23.7728	−	157.527i	0.0332952	−	0.220627i
$715$		0			0
$716$	−306.529	−	530.923i	−0.428113	−	0.741513i
$717$	−204.395	−	118.007i	−0.285069	−	0.164585i
$718$	464.489	−	804.518i	0.646920	−	1.12050i
$719$	−136.549	+	78.8367i	−0.189915	+	0.109648i	−0.591943	−	0.805980i	$-0.701639\pi$
$719$	−136.549	+	78.8367i	−0.189915	+	0.109648i	0.402028	+	0.915628i	$0.368306\pi$
$720$		0			0
$721$	776.792	−	973.702i	1.07738	−	1.35049i
$722$	458.314			0.634784
$723$	−334.441	−	579.269i	−0.462574	−	0.801202i
$724$	545.397	+	314.885i	0.753311	+	0.434925i
$725$		0			0
$726$	65.5141	−	37.8246i	0.0902398	−	0.0521000i
$727$			13.5224i			0.0186003i	0.999957	+	0.00930013i	$0.00296037\pi$
$727$			13.5224i			0.0186003i	−0.999957	+	0.00930013i	$0.997040\pi$
$728$	−52.4905	−	133.815i	−0.0721023	−	0.183812i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−273.732	−	158.039i	−0.374462	−	0.216196i
$732$	−10.1532	+	17.5858i	−0.0138704	+	0.0240243i
$733$	−341.622	+	197.235i	−0.466060	+	0.269080i	−0.714589	−	0.699545i	$-0.753386\pi$
$733$	−341.622	+	197.235i	−0.466060	+	0.269080i	0.248529	+	0.968624i	$0.420053\pi$
$734$		−	725.707i		−	0.988701i
$735$		0			0
$736$	12.7295			0.0172956
$737$	304.843	+	528.003i	0.413626	+	0.716422i
$738$	212.669	+	122.784i	0.288169	+	0.166374i
$739$	−475.080	+	822.863i	−0.642869	+	1.11348i	0.341920	+	0.939729i	$0.388923\pi$
$739$	−475.080	+	822.863i	−0.642869	+	1.11348i	−0.984789	+	0.173753i	$0.944411\pi$
$740$		0			0
$741$			76.4101i			0.103118i
$742$	−134.000	+	52.5630i	−0.180593	+	0.0708396i
$743$	−425.883			−0.573194			−0.286597	−	0.958051i	$-0.592524\pi$
$743$	−425.883			−0.573194			−0.286597	+	0.958051i	$0.592524\pi$
$744$	2.98476	+	5.16976i	0.00401178	+	0.00694860i
$745$		0			0
$746$	−447.262	+	774.680i	−0.599547	+	1.03845i
$747$	238.045	−	137.436i	0.318669	−	0.183983i
$748$			229.012i			0.306166i
$749$	464.964	+	370.935i	0.620779	+	0.495240i
$750$		0			0
$751$	315.874	+	547.109i	0.420604	+	0.728508i	0.995999	−	0.0893683i	$-0.0284848\pi$
$751$	315.874	+	547.109i	0.420604	+	0.728508i	−0.575395	+	0.817876i	$0.695151\pi$
$752$	197.764	+	114.179i	0.262985	+	0.151834i
$753$	−86.0584	+	149.058i	−0.114287	+	0.197952i
$754$	−375.340	+	216.702i	−0.497798	+	0.287404i
$755$		0			0
$756$	71.9316	+	10.8553i	0.0951477	+	0.0143589i
$757$	−882.903			−1.16632			−0.583159	−	0.812358i	$-0.698184\pi$
$757$	−882.903			−1.16632			−0.583159	+	0.812358i	$0.698184\pi$
$758$	436.412	+	755.889i	0.575742	+	0.997214i
$759$	−41.5991	−	24.0173i	−0.0548078	−	0.0316433i
$760$		0			0
$761$	−981.049	+	566.409i	−1.28916	+	0.744295i	−0.978504	−	0.206228i	$-0.933881\pi$
$761$	−981.049	+	566.409i	−1.28916	+	0.744295i	−0.310653	+	0.950523i	$0.600548\pi$
$762$			473.927i			0.621952i
$763$	180.560	−	1196.46i	0.236645	−	1.56810i
$764$	−181.578			−0.237668
$765$		0			0
$766$	213.041	+	122.999i	0.278121	+	0.160573i
$767$	210.027	−	363.778i	0.273829	−	0.474287i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$		−	41.6421i		−	0.0541510i	−0.999633	−	0.0270755i	$-0.991381\pi$
$769$		−	41.6421i		−	0.0541510i	0.999633	−	0.0270755i	$-0.00861944\pi$
$770$		0			0
$771$	36.5771			0.0474411
$772$	−229.655	−	397.774i	−0.297481	−	0.515252i
$773$	−1114.00	−	643.167i	−1.44114	−	0.832041i	−0.443211	−	0.896417i	$-0.646161\pi$
$773$	−1114.00	−	643.167i	−1.44114	−	0.832041i	−0.997926	+	0.0643767i	$0.979494\pi$
$774$	72.1652	−	124.994i	0.0932367	−	0.161491i
$775$		0			0
$776$		−	173.794i		−	0.223962i
$777$	−155.224	−	395.716i	−0.199773	−	0.509287i
$778$	277.458			0.356629
$779$	175.855	+	304.591i	0.225745	+	0.391002i
$780$		0			0
$781$	−628.446	+	1088.50i	−0.804668	+	1.39373i
$782$	25.6068	−	14.7841i	0.0327453	−	0.0189055i
$783$		−	219.341i		−	0.280129i
$784$	−187.271	−	57.8402i	−0.238866	−	0.0737758i
$785$		0			0
$786$	−221.819	−	384.202i	−0.282212	−	0.488806i
$787$	863.836	+	498.736i	1.09763	+	0.633718i	0.935598	−	0.353067i	$-0.114861\pi$
$787$	863.836	+	498.736i	1.09763	+	0.633718i	0.162034	+	0.986785i	$0.448195\pi$
$788$	227.989	−	394.889i	0.289326	−	0.501128i
$789$	570.776	−	329.538i	0.723417	−	0.417665i
$790$		0			0
$791$	534.761	−	209.766i	0.676057	−	0.265191i
$792$	−104.574			−0.132037
$793$	21.2790	+	36.8563i	0.0268335	+	0.0464770i
$794$	−488.307	−	281.924i	−0.614996	−	0.355068i
$795$		0			0
$796$	−19.1325	+	11.0461i	−0.0240358	+	0.0138771i
$797$		−	971.547i		−	1.21901i	−0.792784	−	0.609503i	$-0.791369\pi$
$797$		−	971.547i		−	1.21901i	0.792784	−	0.609503i	$-0.208631\pi$
$798$	81.4466	+	64.9758i	0.102063	+	0.0814233i
$799$	530.433			0.663871
$800$		0			0
$801$	332.020	+	191.692i	0.414507	+	0.239316i
$802$	−245.507	+	425.230i	−0.306118	+	0.530212i
$803$	878.441	−	507.168i	1.09395	−	0.631592i
$804$		−	171.372i		−	0.213150i
$805$		0			0
$806$	12.5109			0.0155223
$807$	−14.5415	−	25.1865i	−0.0180191	−	0.0312101i
$808$	152.209	+	87.8781i	0.188378	+	0.108760i
$809$	652.112	−	1129.49i	0.806072	−	1.39616i	−0.109493	−	0.993988i	$-0.534923\pi$
$809$	652.112	−	1129.49i	0.806072	−	1.39616i	0.915565	−	0.402170i	$-0.131744\pi$
$810$		0			0
$811$		−	210.763i		−	0.259880i	−0.991522	−	0.129940i	$-0.958521\pi$
$811$		−	210.763i		−	0.259880i	0.991522	−	0.129940i	$-0.0414785\pi$
$812$	−88.1861	+	584.354i	−0.108604	+	0.719648i
$813$	−640.291			−0.787566
$814$	305.523	+	529.181i	0.375335	+	0.650099i
$815$		0			0
$816$	32.1857	−	55.7473i	0.0394433	−	0.0683178i
$817$	179.020	−	103.357i	0.219119	−	0.126508i
$818$		−	479.115i		−	0.585716i
$819$	95.0798	−	119.182i	0.116093	−	0.145521i
$820$		0			0
$821$	362.253	+	627.440i	0.441234	+	0.764239i	0.997781	−	0.0665766i	$-0.0212077\pi$
$821$	362.253	+	627.440i	0.441234	+	0.764239i	−0.556548	+	0.830816i	$0.687874\pi$
$822$	2.67993	+	1.54726i	0.00326026	+	0.00188231i
$823$	−223.018	+	386.279i	−0.270982	+	0.469355i	−0.969114	−	0.246615i	$-0.920682\pi$
$823$	−223.018	+	386.279i	−0.270982	+	0.469355i	0.698131	+	0.715970i	$0.254015\pi$
$824$	435.867	−	251.648i	0.528964	−	0.305398i
$825$		0			0
$826$	−209.158	−	533.212i	−0.253218	−	0.645535i
$827$	702.737			0.849743			0.424871	−	0.905254i	$-0.360319\pi$
$827$	702.737			0.849743			0.424871	+	0.905254i	$0.360319\pi$
$828$	6.75086	+	11.6928i	0.00815321	+	0.0141218i
$829$	−361.023	−	208.437i	−0.435492	−	0.251431i	0.266192	−	0.963920i	$-0.414235\pi$
$829$	−361.023	−	208.437i	−0.435492	−	0.251431i	−0.701683	+	0.712489i	$0.747568\pi$
$830$		0			0
$831$	−728.737	+	420.736i	−0.876940	+	0.506301i
$832$		−	58.0805i		−	0.0698083i
$833$	−443.892	+	101.145i	−0.532883	+	0.121423i
$834$	−29.7189			−0.0356342
$835$		0			0
$836$	−129.708	−	74.8867i	−0.155153	−	0.0895774i
$837$	−3.16582	+	5.48336i	−0.00378234	+	0.00655121i
$838$	452.560	−	261.286i	0.540047	−	0.311797i
$839$		−	359.231i		−	0.428166i	−0.976815	−	0.214083i	$-0.931324\pi$
$839$		−	359.231i		−	0.428166i	0.976815	−	0.214083i	$-0.0686763\pi$
$840$		0			0
$841$	940.871			1.11875
$842$	153.846	+	266.469i	0.182715	+	0.316472i
$843$	−540.351	−	311.972i	−0.640986	−	0.370073i
$844$	−151.187	+	261.864i	−0.179132	+	0.310265i
$845$		0			0
$846$			242.211i			0.286301i
$847$	−168.996	−	134.820i	−0.199523	−	0.159174i
$848$	−58.1607			−0.0685858
$849$	234.261	+	405.752i	0.275926	+	0.477918i
$850$		0			0
$851$	39.4467	−	68.3236i	0.0463533	−	0.0802863i
$852$	305.959	−	176.646i	0.359107	−	0.207331i
$853$		−	988.948i		−	1.15938i	−0.814838	−	0.579688i	$-0.803174\pi$
$853$		−	988.948i		−	1.15938i	0.814838	−	0.579688i	$-0.196826\pi$
$854$	57.3804	+	8.65939i	0.0671902	+	0.0101398i
$855$		0			0
$856$	120.167	+	208.136i	0.140382	+	0.243149i
$857$	−312.893	−	180.649i	−0.365103	−	0.210792i	0.306214	−	0.951963i	$-0.400938\pi$
$857$	−312.893	−	180.649i	−0.365103	−	0.210792i	−0.671317	+	0.741170i	$0.734271\pi$
$858$	−109.583	+	189.803i	−0.127719	+	0.221215i
$859$	−608.464	+	351.297i	−0.708339	+	0.408960i	−0.810446	−	0.585814i	$-0.800775\pi$
$859$	−608.464	+	351.297i	−0.708339	+	0.408960i	0.102106	+	0.994773i	$0.467442\pi$
$860$		0			0
$861$	104.720	−	693.913i	0.121626	−	0.805939i
$862$	−404.226			−0.468940
$863$	551.208	+	954.720i	0.638711	+	1.10628i	0.985716	+	0.168417i	$0.0538655\pi$
$863$	551.208	+	954.720i	0.638711	+	1.10628i	−0.347005	+	0.937863i	$0.612801\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	788.111	−	455.016i	0.910059	−	0.525423i
$867$			351.040i			0.404891i
$868$	10.6388	−	13.3356i	0.0122566	−	0.0153636i
$869$	1376.68			1.58421
$870$		0			0
$871$	−311.044	−	179.581i	−0.357111	−	0.206178i
$872$	244.458	−	423.414i	0.280342	−	0.485567i
$873$	159.640	−	92.1683i	0.182864	−	0.105576i
$874$			19.3376i			0.0221254i
$875$		0			0
$876$	−285.113			−0.325472
$877$	334.061	+	578.610i	0.380913	+	0.659761i	0.991193	−	0.132425i	$-0.0422764\pi$
$877$	334.061	+	578.610i	0.380913	+	0.659761i	−0.610280	+	0.792186i	$0.708943\pi$
$878$	−698.640	−	403.360i	−0.795717	−	0.459408i
$879$	8.34182	−	14.4484i	0.00949012	−	0.0164374i
$880$		0			0
$881$			15.3854i			0.0174636i	0.999962	+	0.00873178i	$0.00277945\pi$
$881$			15.3854i			0.0174636i	−0.999962	+	0.00873178i	$0.997221\pi$
$882$	−46.1859	−	202.694i	−0.0523650	−	0.229812i
$883$	−51.0884			−0.0578577			−0.0289289	−	0.999581i	$-0.509210\pi$
$883$	−51.0884			−0.0578577			−0.0289289	+	0.999581i	$0.509210\pi$
$884$	−67.4549	−	116.835i	−0.0763064	−	0.132167i
$885$		0			0
$886$	−46.6796	+	80.8514i	−0.0526857	+	0.0912543i
$887$	−26.3653	+	15.2220i	−0.0297241	+	0.0171612i	−0.514788	−	0.857317i	$-0.672130\pi$
$887$	−26.3653	+	15.2220i	−0.0297241	+	0.0171612i	0.485064	+	0.874478i	$0.338796\pi$
$888$		−	171.755i		−	0.193417i
$889$	1260.83	−	494.574i	1.41825	−	0.556326i
$890$		0			0
$891$	−55.4585	−	96.0569i	−0.0622430	−	0.107808i
$892$	−534.486	−	308.586i	−0.599200	−	0.345948i
$893$	−173.451	+	300.426i	−0.194234	+	0.336423i
$894$	614.600	−	354.840i	0.687472	−	0.396912i
$895$		0			0
$896$	−61.9089	−	49.3891i	−0.0690948	−	0.0551218i
$897$	28.2969			0.0315462
$898$	−364.211	−	630.832i	−0.405580	−	0.702485i
$899$	−44.5454	−	25.7183i	−0.0495500	−	0.0286077i
$900$		0			0
$901$	−116.997	+	67.5480i	−0.129852	+	0.0749700i
$902$			1008.80i			1.11841i
$903$	−407.841	−	61.5480i	−0.451651	−	0.0681595i
$904$	232.105			0.256754
$905$		0			0
$906$	−248.838	−	143.666i	−0.274655	−	0.158572i
$907$	−345.008	+	597.571i	−0.380384	+	0.658844i	−0.991117	−	0.132993i	$-0.957541\pi$
$907$	−345.008	+	597.571i	−0.380384	+	0.658844i	0.610733	+	0.791836i	$0.290875\pi$
$908$	173.937	−	100.422i	0.191560	−	0.110597i
$909$			186.418i			0.205080i
$910$		0			0
$911$	−264.542			−0.290386			−0.145193	−	0.989403i	$-0.546380\pi$
$911$	−264.542			−0.290386			−0.145193	+	0.989403i	$0.546380\pi$
$912$	21.0494	+	36.4587i	0.0230805	+	0.0399766i
$913$	977.899	+	564.590i	1.07108	+	0.618390i
$914$	55.8806	−	96.7881i	0.0611385	−	0.105895i
$915$		0			0
$916$			639.993i			0.698682i
$917$	−790.641	+	991.063i	−0.862204	+	1.08077i
$918$	68.2762			0.0743750
$919$	−269.068	−	466.039i	−0.292783	−	0.507115i	0.681684	−	0.731647i	$-0.261248\pi$
$919$	−269.068	−	466.039i	−0.292783	−	0.507115i	−0.974467	+	0.224532i	$0.927915\pi$
$920$		0			0
$921$	39.8729	−	69.0618i	0.0432930	−	0.0749857i
$922$	−11.7369	+	6.77632i	−0.0127299	+	0.00734959i
$923$		−	740.428i		−	0.802198i
$924$	109.129	+	278.206i	0.118105	+	0.301088i
$925$		0			0
$926$	−164.122	−	284.267i	−0.177237	−	0.306984i
$927$	462.306	+	266.913i	0.498712	+	0.287932i
$928$	−119.394	+	206.797i	−0.128658	+	0.222841i
$929$	−770.069	+	444.600i	−0.828922	+	0.478579i	−0.853484	−	0.521120i	$-0.825515\pi$
$929$	−770.069	+	444.600i	−0.828922	+	0.478579i	0.0245611	+	0.999698i	$0.492181\pi$
$930$		0			0
$931$	87.8657	−	284.486i	0.0943778	−	0.305570i
$932$	−621.578			−0.666929
$933$	378.160	+	654.993i	0.405317	+	0.702029i
$934$	839.607	+	484.747i	0.898937	+	0.519001i
$935$		0			0
$936$	53.3504	−	30.8019i	0.0569983	−	0.0329080i
$937$			997.355i			1.06441i	0.846615	+	0.532206i	$0.178637\pi$
$937$			997.355i			1.06441i	−0.846615	+	0.532206i	$0.821363\pi$
$938$	−455.916	+	178.838i	−0.486051	+	0.190659i
$939$	496.270			0.528509
$940$		0			0
$941$	−959.098	−	553.735i	−1.01923	−	0.588454i	−0.105351	−	0.994435i	$-0.533597\pi$
$941$	−959.098	−	553.735i	−1.01923	−	0.588454i	−0.913882	+	0.405981i	$0.866930\pi$
$942$	225.032	−	389.766i	0.238887	−	0.413764i
$943$	112.799	−	65.1245i	0.119617	−	0.0690609i
$944$		−	231.433i		−	0.245162i
$945$		0			0
$946$	592.915			0.626760
$947$	293.801	+	508.878i	0.310244	+	0.537358i	0.978415	−	0.206650i	$-0.0662560\pi$
$947$	293.801	+	508.878i	0.310244	+	0.537358i	−0.668171	+	0.744008i	$0.732923\pi$
$948$	−335.118	−	193.481i	−0.353500	−	0.204093i
$949$	−298.770	+	517.485i	−0.314826	+	0.545295i
$950$		0			0
$951$			2.37089i			0.00249305i
$952$	−181.897	−	27.4504i	−0.191068	−	0.0288345i
$953$	−441.771			−0.463558			−0.231779	−	0.972768i	$-0.574455\pi$
$953$	−441.771			−0.463558			−0.231779	+	0.972768i	$0.574455\pi$
$954$	−30.8444	−	53.4241i	−0.0323316	−	0.0560001i
$955$		0			0
$956$	−136.263	+	236.015i	−0.142535	+	0.246877i
$957$	780.342	−	450.531i	0.815404	−	0.470774i
$958$			889.684i			0.928688i
$959$	1.31962	−	8.74431i	0.00137604	−	0.00911815i
$960$		0			0
$961$	−479.758	−	830.965i	−0.499227	−	0.864687i
$962$	−311.738	−	179.982i	−0.324051	−	0.187091i
$963$	−127.457	+	220.761i	−0.132354	+	0.229243i
$964$	−668.883	+	386.179i	−0.693862	+	0.400601i
$965$		0			0
$966$	24.0624	−	30.1621i	0.0249094	−	0.0312237i
$967$	−1581.63			−1.63561			−0.817804	−	0.575497i	$-0.804809\pi$
$967$	−1581.63			−1.63561			−0.817804	+	0.575497i	$0.804809\pi$
$968$	−43.6761	−	75.6492i	−0.0451199	−	0.0781500i
$969$	84.6863	+	48.8937i	0.0873956	+	0.0504579i
$970$		0			0
$971$	517.033	−	298.509i	0.532475	−	0.307425i	−0.209549	−	0.977798i	$-0.567199\pi$
$971$	517.033	−	298.509i	0.532475	−	0.307425i	0.742024	+	0.670374i	$0.233866\pi$
$972$			31.1769i			0.0320750i
$973$	31.0136	+	79.0638i	0.0318742	+	0.0812577i
$974$	705.365			0.724194
$975$		0			0
$976$	20.3063	+	11.7239i	0.0208056	+	0.0120121i
$977$	−105.721	+	183.114i	−0.108210	+	0.187425i	−0.915045	−	0.403351i	$-0.867845\pi$
$977$	−105.721	+	183.114i	−0.108210	+	0.187425i	0.806835	+	0.590777i	$0.201179\pi$
$978$	−257.891	+	148.893i	−0.263692	+	0.152243i
$979$			1574.96i			1.60874i
$980$		0			0
$981$	518.575			0.528618
$982$	−117.792	−	204.022i	−0.119951	−	0.207762i
$983$	513.418	+	296.422i	0.522297	+	0.301548i	0.737874	−	0.674939i	$-0.235830\pi$
$983$	513.418	+	296.422i	0.522297	+	0.301548i	−0.215577	+	0.976487i	$0.569163\pi$
$984$	141.779	−	245.569i	0.144084	−	0.249562i
$985$		0			0
$986$			554.659i			0.562534i
$987$	644.374	−	252.763i	0.652861	−	0.256092i
$988$	88.2308			0.0893024
$989$	−38.2762	−	66.2964i	−0.0387020	−	0.0670338i
$990$		0			0
$991$	189.970	−	329.038i	0.191696	−	0.332027i	−0.754117	−	0.656740i	$-0.771935\pi$
$991$	189.970	−	329.038i	0.191696	−	0.332027i	0.945812	+	0.324714i	$0.105268\pi$
$992$	5.96953	−	3.44651i	0.00601767	−	0.00347430i
$993$		−	665.166i		−	0.669855i
$994$	−789.233	−	629.628i	−0.793997	−	0.633428i
$995$		0			0
$996$	−158.697	−	274.871i	−0.159334	−	0.275975i
$997$	−178.950	−	103.317i	−0.179489	−	0.103628i	0.407564	−	0.913177i	$-0.366378\pi$
$997$	−178.950	−	103.317i	−0.179489	−	0.103628i	−0.587052	+	0.809549i	$0.699712\pi$
$998$	−25.6724	+	44.4658i	−0.0257238	+	0.0445550i
$999$	157.767	−	91.0866i	0.157925	−	0.0911778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.b.451.2		8
5.2	odd	4		1050.3.q.c.199.5		16
5.3	odd	4		1050.3.q.c.199.4		16
5.4	even	2		210.3.o.a.31.3	✓	8
7.5	odd	6	inner	1050.3.p.b.901.2		8
15.14	odd	2		630.3.v.b.451.2		8
35.4	even	6		1470.3.f.a.391.1		8
35.12	even	12		1050.3.q.c.649.4		16
35.19	odd	6		210.3.o.a.61.3	yes	8
35.24	odd	6		1470.3.f.a.391.4		8
35.33	even	12		1050.3.q.c.649.5		16
105.89	even	6		630.3.v.b.271.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.3	✓	8	5.4	even	2
210.3.o.a.61.3	yes	8	35.19	odd	6
630.3.v.b.271.2		8	105.89	even	6
630.3.v.b.451.2		8	15.14	odd	2
1050.3.p.b.451.2		8	1.1	even	1	trivial
1050.3.p.b.901.2		8	7.5	odd	6	inner
1050.3.q.c.199.4		16	5.3	odd	4
1050.3.q.c.199.5		16	5.2	odd	4
1050.3.q.c.649.4		16	35.12	even	12
1050.3.q.c.649.5		16	35.33	even	12
1470.3.f.a.391.1		8	35.4	even	6
1470.3.f.a.391.4		8	35.24	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(6.51658 - 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.16205 + 10.6730i) q^{11} +(3.00000 - 1.73205i) q^{12} -7.26007i q^{13} +(-7.73861 - 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-8.04643 - 4.64561i) q^{17} +(2.12132 - 3.67423i) q^{18} +(5.26235 - 3.03822i) q^{19} +(-11.9886 - 1.80922i) q^{21} +17.4289 q^{22} +(-1.12514 - 1.94880i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-8.89173 + 5.13364i) q^{26} -5.19615i q^{27} +(-2.08911 + 13.8433i) q^{28} +42.2122 q^{29} +(-1.05527 - 0.609262i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(18.4862 - 10.6730i) q^{33} +13.1398i q^{34} -6.00000 q^{36} +(17.5296 + 30.3622i) q^{37} +(-7.44209 - 4.29669i) q^{38} +(-6.28740 + 10.8901i) q^{39} +57.8811i q^{41} +(6.26139 + 15.9623i) q^{42} +34.0190 q^{43} +(-12.3241 - 21.3460i) q^{44} +(-1.59119 + 2.75603i) q^{46} +(-49.4411 + 28.5448i) q^{47} +6.92820i q^{48} +(35.9317 - 33.3154i) q^{49} +(8.04643 + 13.9368i) q^{51} +(12.5748 + 7.26007i) q^{52} +(7.27009 - 12.5922i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(18.4317 - 7.23003i) q^{56} -10.5247 q^{57} +(-29.8485 - 51.6992i) q^{58} +(50.1067 + 28.9291i) q^{59} +(-5.07658 + 2.93096i) q^{61} +1.72325i q^{62} +(16.4161 + 13.0963i) q^{63} +8.00000 q^{64} +(-26.1434 - 15.0939i) q^{66} +(24.7355 - 42.8431i) q^{67} +(16.0929 - 9.29122i) q^{68} +3.89761i q^{69} +101.986 q^{71} +(4.24264 + 7.34847i) q^{72} +(-71.2783 - 41.1525i) q^{73} +(24.7906 - 42.9387i) q^{74} +12.1529i q^{76} +(-12.8732 + 85.3029i) q^{77} +17.7835 q^{78} +(-55.8530 - 96.7403i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(70.8895 - 40.9281i) q^{82} -91.6237i q^{83} +(15.1223 - 18.9557i) q^{84} +(-24.0551 - 41.6646i) q^{86} +(-63.3183 - 36.5568i) q^{87} +(-17.4289 + 30.1878i) q^{88} +(110.673 - 63.8973i) q^{89} +(-18.5582 - 47.3108i) q^{91} +4.50057 q^{92} +(1.05527 + 1.82779i) q^{93} +(69.9203 + 40.3685i) q^{94} +(8.48528 - 4.89898i) q^{96} -61.4455i q^{97} +(-66.2104 - 20.4496i) q^{98} -36.9723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} + 48 q^{22} - 12 q^{23} - 96 q^{26} + 72 q^{29} - 132 q^{31} + 12 q^{33} - 48 q^{36} + 96 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 + 48 * q^22 - 12 * q^23 - 96 * q^26 + 72 * q^29 - 132 * q^31 + 12 * q^33 - 48 * q^36 + 96 * q^37 + 168 * q^38 + 24 * q^39 + 72 * q^42 + 112 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 84 * q^51 - 48 * q^52 - 32 * q^53 + 16 * q^56 - 216 * q^57 - 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 - 72 * q^66 + 120 * q^67 + 168 * q^68 + 8 * q^71 - 24 * q^73 - 16 * q^74 + 216 * q^77 + 192 * q^78 + 12 * q^79 - 36 * q^81 - 24 * q^82 - 40 * q^86 - 108 * q^87 - 48 * q^88 + 492 * q^89 - 308 * q^91 + 48 * q^92 + 132 * q^93 + 480 * q^94 - 24 * q^99

Introduction

L-functions

Modular forms

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