LMFDB - Embedded newform 1050.3.p.b.901.2

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			901.2
Root			$-1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.b.451.2

$q$-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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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	−0.997480	−	0.0709528i	$-0.977396\pi$
$11$	−6.16205	−	10.6730i	−0.560187	−	0.970272i	0.437293	−	0.899319i	$-0.355937\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$			7.26007i			0.558467i	0.960223	+	0.279233i	$0.0900803\pi$
$13$			7.26007i			0.558467i	−0.960223	+	0.279233i	$0.909920\pi$
$14$	−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	−0.717628	−	0.696426i	$-0.754772\pi$
$17$	−8.04643	+	4.64561i	−0.473319	+	0.273271i	0.244309	+	0.969697i	$0.421439\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	5.26235	+	3.03822i	0.276966	+	0.159906i	0.632049	−	0.774928i	$-0.282214\pi$
$19$	5.26235	+	3.03822i	0.276966	+	0.159906i	−0.355083	+	0.934835i	$0.615547\pi$
$20$		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	−0.889448	−	0.457036i	$-0.848911\pi$
$23$	−1.12514	+	1.94880i	−0.0489192	+	0.0847306i	0.840529	+	0.541767i	$0.182244\pi$
$24$	−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	−0.516924	−	0.856031i	$-0.672923\pi$
$31$	−1.05527	+	0.609262i	−0.0340411	+	0.0196536i	0.482883	+	0.875685i	$0.339590\pi$
$32$	−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	−0.525775	−	0.850623i	$-0.676225\pi$
$37$	17.5296	−	30.3622i	0.473774	−	0.820600i	0.999549	+	0.0300231i	$0.00955808\pi$
$38$	−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	$-0.750558\pi$
$41$		−	57.8811i		−	1.41173i	0.708345	−	0.705867i	$-0.249442\pi$
$42$	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	−0.128747	−	0.991677i	$-0.541096\pi$
$47$	−49.4411	−	28.5448i	−1.05194	−	0.607337i	−0.923191	+	0.384340i	$0.874429\pi$
$48$		−	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	0.926425	−	0.376480i	$-0.122866\pi$
$53$	7.27009	+	12.5922i	0.137172	+	0.237588i	−0.789253	+	0.614068i	$0.789532\pi$
$54$	−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	−0.0111375	−	0.999938i	$-0.503545\pi$
$59$	50.1067	−	28.9291i	0.849266	−	0.490324i	0.860403	+	0.509614i	$0.170212\pi$
$60$		0			0
$61$	−5.07658	−	2.93096i	−0.0832226	−	0.0480486i	0.457811	−	0.889049i	$-0.348634\pi$
$61$	−5.07658	−	2.93096i	−0.0832226	−	0.0480486i	−0.541034	+	0.841001i	$0.681967\pi$
$62$		−	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	0.989439	−	0.144953i	$-0.0463032\pi$
$67$	24.7355	+	42.8431i	0.369186	+	0.639449i	−0.620252	+	0.784402i	$0.712970\pi$
$68$	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	−0.901186	−	0.433433i	$-0.857302\pi$
$73$	−71.2783	+	41.1525i	−0.976415	+	0.563733i	−0.0752290	+	0.997166i	$0.523969\pi$
$74$	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	0.258964	+	0.965887i	$0.416619\pi$
$79$	−55.8530	+	96.7403i	−0.707001	+	1.22456i	−0.965965	+	0.258674i	$0.916714\pi$
$80$		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	$0.186116\pi$
$83$			91.6237i			1.10390i	−0.833877	+	0.551950i	$0.813884\pi$
$84$	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	0.969809	−	0.243864i	$-0.0784151\pi$
$89$	110.673	+	63.8973i	1.24352	+	0.717947i	0.273712	+	0.961812i	$0.411748\pi$
$90$		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	$0.102585\pi$
$97$			61.4455i			0.633459i	−0.948516	+	0.316729i	$0.897415\pi$
$98$	−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	−0.209348	−	0.977841i	$-0.567134\pi$
$101$	53.8141	−	31.0696i	0.532813	−	0.307620i	0.742161	+	0.670221i	$0.233801\pi$
$102$	11.3794	+	19.7096i	0.111562	+	0.193232i
$103$	154.102	+	88.9709i	1.49614	+	0.863795i	0.999990	−	0.00444312i	$-0.00141429\pi$
$103$	154.102	+	88.9709i	1.49614	+	0.863795i	0.496147	+	0.868238i	$0.334748\pi$
$104$			20.5346i			0.197448i
$105$		0			0
$106$	−20.5629			−0.193990
$107$	42.4855	−	73.5871i	0.397061	−	0.687730i	−0.596301	−	0.802761i	$-0.703363\pi$
$107$	42.4855	−	73.5871i	0.397061	−	0.687730i	0.993362	+	0.115031i	$0.0366968\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	86.4291	+	149.700i	0.792928	+	1.37339i	0.924147	+	0.382037i	$0.124777\pi$
$109$	86.4291	+	149.700i	0.792928	+	1.37339i	−0.131219	+	0.991353i	$0.541889\pi$
$110$		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	−0.237368	−	0.971420i	$-0.576285\pi$
$131$	−156.850	−	90.5572i	−1.19733	−	0.691276i	−0.959958	+	0.280143i	$0.909618\pi$
$132$		−	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	0.868322	−	0.496002i	$-0.165199\pi$
$137$	0.631666	+	1.09408i	0.00461070	+	0.00798597i	−0.863711	+	0.503988i	$0.831866\pi$
$138$	4.77358	+	2.75603i	0.0345911	+	0.0199712i
$139$		−	12.1327i		−	0.0872857i	−0.999047	−	0.0436428i	$-0.986104\pi$
$139$		−	12.1327i		−	0.0872857i	0.999047	−	0.0436428i	$-0.0138964\pi$
$140$		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	−0.283453	+	0.958986i	$0.591480\pi$
$149$	−144.863	+	250.910i	−0.972233	+	1.68396i	−0.688780	+	0.724971i	$0.741853\pi$
$150$		0			0
$151$	−58.6516	−	101.588i	−0.388421	−	0.672765i	0.603816	−	0.797124i	$-0.293646\pi$
$151$	−58.6516	−	101.588i	−0.388421	−	0.672765i	−0.992237	+	0.124358i	$0.960313\pi$
$152$	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	−0.912218	−	0.409705i	$-0.865632\pi$
$157$	−159.121	+	91.8687i	−1.01351	+	0.585151i	−0.101294	+	0.994857i	$0.532298\pi$
$158$	−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	−0.617096	−	0.786888i	$-0.711691\pi$
$163$	60.7854	−	105.283i	0.372917	−	0.645911i	0.990013	+	0.140977i	$0.0450244\pi$
$164$	−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	$0.0914608\pi$
$167$			94.6539i			0.566790i	−0.959003	+	0.283395i	$0.908539\pi$
$168$	−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	0.981258	−	0.192699i	$-0.0617240\pi$
$173$	225.766	+	130.346i	1.30501	+	0.753445i	0.323747	+	0.946144i	$0.395057\pi$
$174$		−	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	−0.875504	−	0.483212i	$-0.839470\pi$
$179$	−153.264	−	265.462i	−0.856225	−	1.48303i	0.0192782	−	0.999814i	$-0.493863\pi$
$180$		0			0
$181$			314.885i			1.73970i	0.493318	+	0.869849i	$0.335784\pi$
$181$			314.885i			1.73970i	−0.493318	+	0.869849i	$0.664216\pi$
$182$	−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	−0.722377	−	0.691500i	$-0.756950\pi$
$191$	45.3946	−	78.6257i	0.237668	−	0.411653i	0.960045	+	0.279847i	$0.0902837\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	−114.828	−	198.887i	−0.594961	−	1.03050i	−0.993552	−	0.113374i	$-0.963834\pi$
$193$	−114.828	−	198.887i	−0.594961	−	1.03050i	0.398591	−	0.917129i	$-0.369499\pi$
$194$	−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	−0.475772	−	0.879569i	$-0.657831\pi$
$199$	9.56623	−	5.52307i	0.0480715	−	0.0277541i	0.523843	+	0.851815i	$0.324498\pi$
$200$		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	$-0.756776\pi$
$223$		−	308.586i		−	1.38379i	0.721997	−	0.691896i	$-0.243224\pi$
$224$	−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	−0.679175	−	0.733976i	$-0.737662\pi$
$227$	−86.9683	+	50.2112i	−0.383120	+	0.221195i	0.296055	+	0.955171i	$0.404329\pi$
$228$	10.5247	+	18.2293i	0.0461610	+	0.0799532i
$229$	277.125	+	159.998i	1.21015	+	0.698682i	0.962793	−	0.270241i	$-0.0871034\pi$
$229$	277.125	+	159.998i	1.21015	+	0.698682i	0.247361	+	0.968923i	$0.420437\pi$
$230$		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	−0.311829	−	0.950138i	$-0.600942\pi$
$233$	155.395	−	269.151i	0.666929	−	1.15516i	0.978758	−	0.205017i	$-0.0657251\pi$
$234$	−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	0.394665	−	0.918825i	$-0.370861\pi$
$241$	334.441	−	193.090i	1.38772	−	0.801202i	0.993058	+	0.117623i	$0.0375274\pi$
$242$	−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	$0.0634289\pi$
$251$			99.3717i			0.395903i	−0.980212	+	0.197952i	$0.936571\pi$
$252$	−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	0.463997	−	0.885837i	$-0.346415\pi$
$257$	−18.2886	−	10.5589i	−0.0711617	−	0.0410852i	−0.535159	+	0.844752i	$0.679748\pi$
$258$		−	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	−0.959622	−	0.281292i	$-0.909237\pi$
$263$	−190.259	−	329.538i	−0.723417	−	1.25299i	0.236205	−	0.971703i	$-0.424096\pi$
$264$	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	−0.472728	−	0.881209i	$-0.656731\pi$
$269$	14.5415	−	8.39551i	0.0540574	−	0.0312101i	0.526785	+	0.849998i	$0.323397\pi$
$270$		0			0
$271$	320.146	+	184.836i	1.18135	+	0.682052i	0.956326	−	0.292301i	$-0.0944209\pi$
$271$	320.146	+	184.836i	1.18135	+	0.682052i	0.225023	+	0.974353i	$0.427754\pi$
$272$		−	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	0.854682	+	0.519152i	$0.173752\pi$
$277$	242.912	+	420.736i	0.876940	+	1.51890i	0.0222577	+	0.999752i	$0.492915\pi$
$278$	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	−0.853091	−	0.521762i	$-0.825275\pi$
$283$	−234.261	+	135.251i	−0.827778	+	0.477918i	0.0253131	+	0.999680i	$0.491942\pi$
$284$	−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	$-0.994768\pi$
$293$		−	9.63230i		−	0.0328747i	0.999865	−	0.0164374i	$-0.00523241\pi$
$294$	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	$-0.976109\pi$
$307$		−	46.0412i		−	0.149971i	0.997185	−	0.0749857i	$-0.0238911\pi$
$308$	−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	−0.964049	−	0.265724i	$-0.914389\pi$
$311$	−378.160	+	218.331i	−1.21595	+	0.702029i	−0.251901	+	0.967753i	$0.581056\pi$
$312$	−17.7835	−	30.8019i	−0.0569983	−	0.0987239i
$313$	−248.135	−	143.261i	−0.792764	−	0.457703i	0.0481706	−	0.998839i	$-0.484661\pi$
$313$	−248.135	−	143.261i	−0.792764	−	0.457703i	−0.840935	+	0.541137i	$0.817994\pi$
$314$		−	259.844i		−	0.827529i
$315$		0			0
$316$	223.412			0.707001
$317$	−0.684418	+	1.18545i	−0.00215905	+	0.00373958i	−0.867103	−	0.498129i	$-0.834021\pi$
$317$	−0.684418	+	1.18545i	−0.00215905	+	0.00373958i	0.864944	+	0.501869i	$0.167354\pi$
$318$	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	−0.415354	−	0.909660i	$-0.636342\pi$
$331$	192.017	−	332.583i	0.580111	−	1.00478i	0.995466	−	0.0951223i	$-0.0303242\pi$
$332$	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	0.627345	−	0.778741i	$-0.284142\pi$
$347$	−125.176	−	216.811i	−0.360737	−	0.624815i	−0.988082	+	0.153926i	$0.950808\pi$
$348$	126.637	+	73.1137i	0.363898	+	0.210097i
$349$		−	195.188i		−	0.559277i	−0.960105	−	0.279639i	$-0.909785\pi$
$349$		−	195.188i		−	0.559277i	0.960105	−	0.279639i	$-0.0902147\pi$
$350$		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	−0.664184	−	0.747569i	$-0.731221\pi$
$353$	−123.148	+	71.0997i	−0.348862	+	0.201416i	0.315322	+	0.948985i	$0.397887\pi$
$354$	−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	0.107812	−	0.994171i	$-0.465616\pi$
$359$	328.443	−	568.880i	0.914884	−	1.58462i	0.807072	−	0.590453i	$-0.201051\pi$
$360$		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	0.247950	−	0.968773i	$-0.420243\pi$
$367$	444.403	−	256.576i	1.21091	−	0.699117i	0.962957	+	0.269655i	$0.0869098\pi$
$368$	−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	0.0352027	+	0.999380i	$0.488792\pi$
$373$	−316.262	+	547.782i	−0.847887	+	1.46858i	−0.883090	+	0.469204i	$0.844541\pi$
$374$	−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	0.290276	−	0.956943i	$-0.406253\pi$
$383$	−150.642	−	86.9735i	−0.393322	−	0.227085i	−0.683599	+	0.729858i	$0.739586\pi$
$384$		−	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	0.711949	−	0.702231i	$-0.247813\pi$
$389$	−98.0961	−	169.907i	−0.252175	−	0.436780i	−0.964124	+	0.265451i	$0.914479\pi$
$390$		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	0.867260	−	0.497855i	$-0.165879\pi$
$397$	345.285	+	199.350i	0.869736	+	0.502142i	0.00247542	+	0.999997i	$0.499212\pi$
$398$			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	−0.997123	−	0.0758008i	$-0.975849\pi$
$401$	−173.599	+	300.683i	−0.432916	+	0.749833i	0.564207	+	0.825633i	$0.309182\pi$
$402$	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	−0.0964252	−	0.995340i	$-0.530741\pi$
$409$	293.397	−	169.393i	0.717352	−	0.414163i	0.813777	+	0.581177i	$0.197408\pi$
$410$		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	$-0.854643\pi$
$419$		−	369.514i		−	0.881894i	0.897533	−	0.440947i	$-0.145357\pi$
$420$		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	0.982824	−	0.184546i	$-0.0590814\pi$
$431$	142.916	+	247.537i	0.331591	+	0.574332i	−0.651233	+	0.758878i	$0.725748\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$		−	643.490i		−	1.48612i	−0.669224	−	0.743060i	$-0.733374\pi$
$433$		−	643.490i		−	1.48612i	0.669224	−	0.743060i	$-0.266626\pi$
$434$	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	0.942752	−	0.333494i	$-0.108228\pi$
$439$	494.013	+	285.218i	1.12531	+	0.649700i	0.182562	+	0.983194i	$0.441561\pi$
$440$		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	−0.900873	−	0.434084i	$-0.857072\pi$
$443$	−33.0074	+	57.1705i	−0.0745089	+	0.129053i	0.826364	+	0.563137i	$0.190406\pi$
$444$	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	−0.819551	−	0.573007i	$-0.805777\pi$
$457$	39.5136	−	68.4395i	0.0864629	−	0.149758i	0.906014	+	0.423248i	$0.139110\pi$
$458$	−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	$0.00330854\pi$
$461$			9.58316i			0.0207878i	−0.999946	+	0.0103939i	$0.996691\pi$
$462$	−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	−0.296058	−	0.955170i	$-0.595672\pi$
$467$	−593.692	−	342.768i	−1.27129	−	0.733979i	−0.975230	+	0.221191i	$0.929006\pi$
$468$		−	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	−0.945787	−	0.324787i	$-0.894707\pi$
$479$	−544.818	+	314.551i	−1.13741	+	0.656682i	−0.191619	+	0.981469i	$0.561374\pi$
$480$		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	−0.999902	−	0.0140085i	$-0.995541\pi$
$487$	−249.384	−	431.946i	−0.512083	−	0.886953i	0.487819	−	0.872945i	$-0.337793\pi$
$488$	−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	−0.883642	−	0.468164i	$-0.844916\pi$
$499$	−18.1531	+	31.4421i	−0.0363790	+	0.0630102i	0.847263	+	0.531174i	$0.178249\pi$
$500$		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	$-0.782582\pi$
$503$		−	634.940i		−	1.26231i	0.775658	−	0.631153i	$-0.217418\pi$
$504$	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	0.903480	−	0.428631i	$-0.141004\pi$
$509$	500.864	+	289.174i	0.984015	+	0.568121i	0.0805350	+	0.996752i	$0.474337\pi$
$510$		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	−0.924748	−	0.380579i	$-0.875725\pi$
$521$	−550.974	+	318.105i	−1.05753	+	0.610566i	−0.132783	+	0.991145i	$0.542391\pi$
$522$	89.5456	+	155.098i	0.171543	+	0.297122i
$523$	−392.868	−	226.823i	−0.751182	−	0.433695i	0.0749389	−	0.997188i	$-0.476124\pi$
$523$	−392.868	−	226.823i	−0.751182	−	0.433695i	−0.826121	+	0.563493i	$0.809457\pi$
$524$			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	−0.466632	−	0.884451i	$-0.654533\pi$
$541$	288.159	−	499.106i	0.532641	−	0.922562i	0.999274	−	0.0381102i	$-0.0121338\pi$
$542$	−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	0.910722	−	0.413019i	$-0.135526\pi$
$557$	54.4056	+	94.2333i	0.0976762	+	0.169180i	−0.813046	+	0.582199i	$0.802192\pi$
$558$	−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	−0.885645	−	0.464364i	$-0.846283\pi$
$563$	−521.516	+	301.097i	−0.926316	+	0.534809i	−0.0406717	+	0.999173i	$0.512950\pi$
$564$	−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	−0.861806	−	0.507238i	$-0.830667\pi$
$569$	4.76685	−	8.25642i	0.00837759	−	0.0145104i	0.870184	+	0.492727i	$0.164000\pi$
$570$		0			0
$571$	−491.103	−	850.615i	−0.860075	−	1.48969i	−0.871856	−	0.489762i	$-0.837084\pi$
$571$	−491.103	−	850.615i	−0.860075	−	1.48969i	0.0117813	−	0.999931i	$-0.496250\pi$
$572$	−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	−0.0520155	−	0.998646i	$-0.516565\pi$
$577$	454.001	−	262.117i	0.786830	−	0.454276i	0.838845	+	0.544370i	$0.183231\pi$
$578$	−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	$0.187201\pi$
$587$			651.322i			1.10958i	−0.831991	+	0.554789i	$0.812799\pi$
$588$	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	0.917040	−	0.398796i	$-0.130572\pi$
$593$	610.904	+	352.706i	1.03019	+	0.594782i	0.113152	+	0.993578i	$0.463905\pi$
$594$			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	0.999988	−	0.00498610i	$-0.00158713\pi$
$599$	296.910	+	514.263i	0.495676	+	0.858535i	−0.504312	+	0.863522i	$0.668254\pi$
$600$		0			0
$601$		−	12.1644i		−	0.0202403i	−0.999949	−	0.0101202i	$-0.996779\pi$
$601$		−	12.1644i		−	0.0202403i	0.999949	−	0.0101202i	$-0.00322140\pi$
$602$	−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	−0.201700	−	0.979447i	$-0.564647\pi$
$607$	−698.521	−	403.291i	−1.15078	−	0.664401i	−0.949076	+	0.315047i	$0.897980\pi$
$608$		−	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	−0.983595	−	0.180392i	$-0.942263\pi$
$613$	−397.237	−	688.035i	−0.648021	−	1.12241i	0.335574	−	0.942014i	$-0.391070\pi$
$614$	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	−0.729531	−	0.683948i	$-0.760261\pi$
$619$	−310.725	+	179.397i	−0.501979	+	0.289818i	0.227551	+	0.973766i	$0.426928\pi$
$620$		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	−0.962117	−	0.272637i	$-0.912104\pi$
$641$	−459.706	−	796.233i	−0.717169	−	1.24217i	0.244947	−	0.969536i	$-0.421229\pi$
$642$	−180.251	−	104.068i	−0.280765	−	0.162099i
$643$			835.879i			1.29997i	0.759948	+	0.649984i	$0.225224\pi$
$643$			835.879i			1.29997i	−0.759948	+	0.649984i	$0.774776\pi$
$644$	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	−0.0680932	−	0.997679i	$-0.521692\pi$
$647$	492.933	−	284.595i	0.761876	−	0.439869i	0.829969	+	0.557810i	$0.188358\pi$
$648$	−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	−0.675825	−	0.737062i	$-0.736213\pi$
$653$	196.162	−	339.763i	0.300402	−	0.520311i	0.976227	+	0.216751i	$0.0695460\pi$
$654$	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	−0.680865	−	0.732409i	$-0.738396\pi$
$661$	−255.815	+	147.695i	−0.387013	+	0.223442i	0.293852	+	0.955851i	$0.405063\pi$
$662$	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	0.908181	−	0.418577i	$-0.137471\pi$
$677$	676.847	+	390.778i	0.999774	+	0.577220i	0.0915926	+	0.995797i	$0.470804\pi$
$678$		−	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	0.900849	−	0.434133i	$-0.142945\pi$
$683$	50.8525	+	88.0791i	0.0744546	+	0.128959i	−0.826394	+	0.563092i	$0.809612\pi$
$684$	−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	0.883157	−	0.469078i	$-0.155414\pi$
$691$	634.684	+	366.435i	0.918501	+	0.530297i	0.0353446	+	0.999375i	$0.488747\pi$
$692$		−	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	0.232964	+	0.972485i	$0.425158\pi$
$709$	−514.532	+	891.196i	−0.725715	+	1.25698i	−0.958679	+	0.284490i	$0.908176\pi$
$710$		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	0.402028	−	0.915628i	$-0.368306\pi$
$719$	−136.549	−	78.8367i	−0.189915	−	0.109648i	−0.591943	+	0.805980i	$0.701639\pi$
$720$		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	$-0.997040\pi$
$727$		−	13.5224i		−	0.0186003i	0.999957	−	0.00930013i	$-0.00296037\pi$
$728$	−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	0.248529	−	0.968624i	$-0.420053\pi$
$733$	−341.622	−	197.235i	−0.466060	−	0.269080i	−0.714589	+	0.699545i	$0.753386\pi$
$734$			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	−0.984789	−	0.173753i	$-0.944411\pi$
$739$	−475.080	−	822.863i	−0.642869	−	1.11348i	0.341920	−	0.939729i	$-0.388923\pi$
$740$		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	−0.575395	−	0.817876i	$-0.695151\pi$
$751$	315.874	−	547.109i	0.420604	−	0.728508i	0.995999	+	0.0893683i	$0.0284848\pi$
$752$	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	−0.310653	−	0.950523i	$-0.600548\pi$
$761$	−981.049	−	566.409i	−1.28916	−	0.744295i	−0.978504	+	0.206228i	$0.933881\pi$
$762$		−	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	$0.00861944\pi$
$769$			41.6421i			0.0541510i	−0.999633	+	0.0270755i	$0.991381\pi$
$770$		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	−0.997926	−	0.0643767i	$-0.979494\pi$
$773$	−1114.00	+	643.167i	−1.44114	+	0.832041i	−0.443211	+	0.896417i	$0.646161\pi$
$774$	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	0.162034	−	0.986785i	$-0.448195\pi$
$787$	863.836	−	498.736i	1.09763	−	0.633718i	0.935598	+	0.353067i	$0.114861\pi$
$788$	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	$0.208631\pi$
$797$			971.547i			1.21901i	−0.792784	+	0.609503i	$0.791369\pi$
$798$	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	0.915565	+	0.402170i	$0.131744\pi$
$809$	652.112	+	1129.49i	0.806072	+	1.39616i	−0.109493	+	0.993988i	$0.534923\pi$
$810$		0			0
$811$			210.763i			0.259880i	0.991522	+	0.129940i	$0.0414785\pi$
$811$			210.763i			0.259880i	−0.991522	+	0.129940i	$0.958521\pi$
$812$	−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	−0.556548	−	0.830816i	$-0.687874\pi$
$821$	362.253	−	627.440i	0.441234	−	0.764239i	0.997781	+	0.0665766i	$0.0212077\pi$
$822$	2.67993	−	1.54726i	0.00326026	−	0.00188231i
$823$	−223.018	−	386.279i	−0.270982	−	0.469355i	0.698131	−	0.715970i	$-0.254015\pi$
$823$	−223.018	−	386.279i	−0.270982	−	0.469355i	−0.969114	+	0.246615i	$0.920682\pi$
$824$	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	−0.701683	−	0.712489i	$-0.747568\pi$
$829$	−361.023	+	208.437i	−0.435492	+	0.251431i	0.266192	+	0.963920i	$0.414235\pi$
$830$		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	$0.0686763\pi$
$839$			359.231i			0.428166i	−0.976815	+	0.214083i	$0.931324\pi$
$840$		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	$0.196826\pi$
$853$			988.948i			1.15938i	−0.814838	+	0.579688i	$0.803174\pi$
$854$	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	−0.671317	−	0.741170i	$-0.734271\pi$
$857$	−312.893	+	180.649i	−0.365103	+	0.210792i	0.306214	+	0.951963i	$0.400938\pi$
$858$	−109.583	−	189.803i	−0.127719	−	0.221215i
$859$	−608.464	−	351.297i	−0.708339	−	0.408960i	0.102106	−	0.994773i	$-0.467442\pi$
$859$	−608.464	−	351.297i	−0.708339	−	0.408960i	−0.810446	+	0.585814i	$0.800775\pi$
$860$		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	−0.347005	−	0.937863i	$-0.612801\pi$
$863$	551.208	−	954.720i	0.638711	−	1.10628i	0.985716	−	0.168417i	$-0.0538655\pi$
$864$	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	−0.610280	−	0.792186i	$-0.708943\pi$
$877$	334.061	−	578.610i	0.380913	−	0.659761i	0.991193	+	0.132425i	$0.0422764\pi$
$878$	−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	$-0.997221\pi$
$881$		−	15.3854i		−	0.0174636i	0.999962	−	0.00873178i	$-0.00277945\pi$
$882$	−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	0.485064	−	0.874478i	$-0.338796\pi$
$887$	−26.3653	−	15.2220i	−0.0297241	−	0.0171612i	−0.514788	+	0.857317i	$0.672130\pi$
$888$			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	0.610733	−	0.791836i	$-0.290875\pi$
$907$	−345.008	−	597.571i	−0.380384	−	0.658844i	−0.991117	+	0.132993i	$0.957541\pi$
$908$	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	−0.974467	−	0.224532i	$-0.927915\pi$
$919$	−269.068	+	466.039i	−0.292783	+	0.507115i	0.681684	+	0.731647i	$0.261248\pi$
$920$		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	0.0245611	−	0.999698i	$-0.492181\pi$
$929$	−770.069	−	444.600i	−0.828922	−	0.478579i	−0.853484	+	0.521120i	$0.825515\pi$
$930$		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	$-0.821363\pi$
$937$		−	997.355i		−	1.06441i	0.846615	−	0.532206i	$-0.178637\pi$
$938$	−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	−0.913882	−	0.405981i	$-0.866930\pi$
$941$	−959.098	+	553.735i	−1.01923	+	0.588454i	−0.105351	+	0.994435i	$0.533597\pi$
$942$	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	−0.668171	−	0.744008i	$-0.732923\pi$
$947$	293.801	−	508.878i	0.310244	−	0.537358i	0.978415	+	0.206650i	$0.0662560\pi$
$948$	−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	0.742024	−	0.670374i	$-0.233866\pi$
$971$	517.033	+	298.509i	0.532475	+	0.307425i	−0.209549	+	0.977798i	$0.567199\pi$
$972$		−	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	0.806835	−	0.590777i	$-0.201179\pi$
$977$	−105.721	−	183.114i	−0.108210	−	0.187425i	−0.915045	+	0.403351i	$0.867845\pi$
$978$	−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	−0.215577	−	0.976487i	$-0.569163\pi$
$983$	513.418	−	296.422i	0.522297	−	0.301548i	0.737874	+	0.674939i	$0.235830\pi$
$984$	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	0.945812	−	0.324714i	$-0.105268\pi$
$991$	189.970	+	329.038i	0.191696	+	0.332027i	−0.754117	+	0.656740i	$0.771935\pi$
$992$	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	−0.587052	−	0.809549i	$-0.699712\pi$
$997$	−178.950	+	103.317i	−0.179489	+	0.103628i	0.407564	+	0.913177i	$0.366378\pi$
$998$	−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.901.2		8
5.2	odd	4		1050.3.q.c.649.4		16
5.3	odd	4		1050.3.q.c.649.5		16
5.4	even	2		210.3.o.a.61.3	yes	8
7.3	odd	6	inner	1050.3.p.b.451.2		8
15.14	odd	2		630.3.v.b.271.2		8
35.3	even	12		1050.3.q.c.199.4		16
35.9	even	6		1470.3.f.a.391.4		8
35.17	even	12		1050.3.q.c.199.5		16
35.19	odd	6		1470.3.f.a.391.1		8
35.24	odd	6		210.3.o.a.31.3	✓	8
105.59	even	6		630.3.v.b.451.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.3	✓	8	35.24	odd	6
210.3.o.a.61.3	yes	8	5.4	even	2
630.3.v.b.271.2		8	15.14	odd	2
630.3.v.b.451.2		8	105.59	even	6
1050.3.p.b.451.2		8	7.3	odd	6	inner
1050.3.p.b.901.2		8	1.1	even	1	trivial
1050.3.q.c.199.4		16	35.3	even	12
1050.3.q.c.199.5		16	35.17	even	12
1050.3.q.c.649.4		16	5.2	odd	4
1050.3.q.c.649.5		16	5.3	odd	4
1470.3.f.a.391.1		8	35.19	odd	6
1470.3.f.a.391.4		8	35.9	even	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

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