LMFDB - Embedded newform 1050.3.q.c.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$0.159959 - 0.596975i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.c.649.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.55620 - 6.51658i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.55620 - 6.51658i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-6.16205 + 10.6730i) q^{11} +(-1.73205 - 3.00000i) q^{12} +7.26007 q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.64561 + 8.04643i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-5.26235 + 3.03822i) q^{19} +(-11.9886 - 1.80922i) q^{21} -17.4289i q^{22} +(1.94880 - 1.12514i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-8.89173 + 5.13364i) q^{26} -5.19615 q^{27} +(-13.8433 - 2.08911i) q^{28} -42.2122 q^{29} +(-1.05527 - 0.609262i) q^{31} +(4.89898 + 2.82843i) q^{32} +(10.6730 + 18.4862i) q^{33} -13.1398i q^{34} -6.00000 q^{36} +(30.3622 - 17.5296i) q^{37} +(4.29669 - 7.44209i) q^{38} +(6.28740 - 10.8901i) q^{39} +57.8811i q^{41} +(15.9623 - 6.26139i) q^{42} +34.0190i q^{43} +(12.3241 + 21.3460i) q^{44} +(-1.59119 + 2.75603i) q^{46} +(28.5448 + 49.4411i) q^{47} -6.92820 q^{48} +(-35.9317 + 33.3154i) q^{49} +(8.04643 + 13.9368i) q^{51} +(7.26007 - 12.5748i) q^{52} +(12.5922 + 7.27009i) q^{53} +(6.36396 - 3.67423i) q^{54} +(18.4317 - 7.23003i) q^{56} +10.5247i q^{57} +(51.6992 - 29.8485i) q^{58} +(-50.1067 - 28.9291i) q^{59} +(-5.07658 + 2.93096i) q^{61} +1.72325 q^{62} +(-13.0963 + 16.4161i) q^{63} -8.00000 q^{64} +(-26.1434 - 15.0939i) q^{66} +(-42.8431 - 24.7355i) q^{67} +(9.29122 + 16.0929i) q^{68} -3.89761i q^{69} +101.986 q^{71} +(7.34847 - 4.24264i) q^{72} +(41.1525 - 71.2783i) q^{73} +(-24.7906 + 42.9387i) q^{74} +12.1529i q^{76} +(85.3029 + 12.8732i) q^{77} +17.7835i q^{78} +(55.8530 + 96.7403i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-40.9281 - 70.8895i) q^{82} +91.6237 q^{83} +(-15.1223 + 18.9557i) q^{84} +(-24.0551 - 41.6646i) q^{86} +(-36.5568 + 63.3183i) q^{87} +(-30.1878 - 17.4289i) q^{88} +(-110.673 + 63.8973i) q^{89} +(-18.5582 - 47.3108i) q^{91} -4.50057i q^{92} +(-1.82779 + 1.05527i) q^{93} +(-69.9203 - 40.3685i) q^{94} +(8.48528 - 4.89898i) q^{96} -61.4455 q^{97} +(20.4496 - 66.2104i) q^{98} +36.9723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^9	$ 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 80 q^{14} - 32 q^{16} - 216 q^{19} - 192 q^{26} - 144 q^{29} - 264 q^{31} - 96 q^{36} - 48 q^{39} + 16 q^{44} + 16 q^{46} - 312 q^{49} + 168 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 128 q^{64} - 144 q^{66} + 16 q^{71} + 32 q^{74} - 24 q^{79} - 72 q^{81} - 80 q^{86} - 984 q^{89} - 616 q^{91} - 960 q^{94} + 48 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 80 * q^14 - 32 * q^16 - 216 * q^19 - 192 * q^26 - 144 * q^29 - 264 * q^31 - 96 * q^36 - 48 * q^39 + 16 * q^44 + 16 * q^46 - 312 * q^49 + 168 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 128 * q^64 - 144 * q^66 + 16 * q^71 + 32 * q^74 - 24 * q^79 - 72 * q^81 - 80 * q^86 - 984 * q^89 - 616 * q^91 - 960 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−2.55620	−	6.51658i	−0.365172	−	0.930940i
$7$	−2.55620	−	6.51658i	−0.365172	−	0.930940i
$8$			2.82843i			0.353553i
$9$	−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	$0.977396\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	7.26007			0.558467			0.279233	−	0.960223i	$-0.409920\pi$
$13$	7.26007			0.558467			0.279233	+	0.960223i	$0.409920\pi$
$14$	7.73861	+	6.17364i	0.552758	+	0.440975i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−4.64561	+	8.04643i	−0.273271	+	0.473319i	−0.969697	−	0.244309i	$-0.921439\pi$
$17$	−4.64561	+	8.04643i	−0.273271	+	0.473319i	0.696426	+	0.717628i	$0.254772\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	−5.26235	+	3.03822i	−0.276966	+	0.159906i	−0.632049	−	0.774928i	$-0.717786\pi$
$19$	−5.26235	+	3.03822i	−0.276966	+	0.159906i	0.355083	+	0.934835i	$0.384453\pi$
$20$		0			0
$21$	−11.9886	−	1.80922i	−0.570886	−	0.0861535i
$22$		−	17.4289i		−	0.792224i
$23$	1.94880	−	1.12514i	0.0847306	−	0.0489192i	−0.457036	−	0.889448i	$-0.651089\pi$
$23$	1.94880	−	1.12514i	0.0847306	−	0.0489192i	0.541767	+	0.840529i	$0.317756\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	−8.89173	+	5.13364i	−0.341990	+	0.197448i
$27$	−5.19615			−0.192450
$28$	−13.8433	−	2.08911i	−0.494402	−	0.0746112i
$29$	−42.2122			−1.45559			−0.727797	−	0.685793i	$-0.759456\pi$
$29$	−42.2122			−1.45559			−0.727797	+	0.685793i	$0.759456\pi$
$30$		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	$0.672923\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	10.6730	+	18.4862i	0.323424	+	0.560187i
$34$		−	13.1398i		−	0.386464i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	30.3622	−	17.5296i	0.820600	−	0.473774i	−0.0300231	−	0.999549i	$-0.509558\pi$
$37$	30.3622	−	17.5296i	0.820600	−	0.473774i	0.850623	+	0.525775i	$0.176225\pi$
$38$	4.29669	−	7.44209i	0.113071	−	0.195845i
$39$	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	$0.750558\pi$
$42$	15.9623	−	6.26139i	0.380055	−	0.149081i
$43$			34.0190i			0.791140i	0.918436	+	0.395570i	$0.129453\pi$
$43$			34.0190i			0.791140i	−0.918436	+	0.395570i	$0.870547\pi$
$44$	12.3241	+	21.3460i	0.280093	+	0.485136i
$45$		0			0
$46$	−1.59119	+	2.75603i	−0.0345911	+	0.0599136i
$47$	28.5448	+	49.4411i	0.607337	+	1.05194i	0.991677	+	0.128747i	$0.0410956\pi$
$47$	28.5448	+	49.4411i	0.607337	+	1.05194i	−0.384340	+	0.923191i	$0.625571\pi$
$48$	−6.92820			−0.144338
$49$	−35.9317	+	33.3154i	−0.733300	+	0.679906i
$50$		0			0
$51$	8.04643	+	13.9368i	0.157773	+	0.273271i
$52$	7.26007	−	12.5748i	0.139617	−	0.241823i
$53$	12.5922	+	7.27009i	0.237588	+	0.137172i	0.614068	−	0.789253i	$-0.289532\pi$
$53$	12.5922	+	7.27009i	0.237588	+	0.137172i	−0.376480	+	0.926425i	$0.622866\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	18.4317	−	7.23003i	0.329137	−	0.129108i
$57$			10.5247i			0.184644i
$58$	51.6992	−	29.8485i	0.891365	−	0.514630i
$59$	−50.1067	−	28.9291i	−0.849266	−	0.490324i	0.0111375	−	0.999938i	$-0.496455\pi$
$59$	−50.1067	−	28.9291i	−0.849266	−	0.490324i	−0.860403	+	0.509614i	$0.829788\pi$
$60$		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	$0.348634\pi$
$62$	1.72325			0.0277944
$63$	−13.0963	+	16.4161i	−0.207877	+	0.260573i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−26.1434	−	15.0939i	−0.396112	−	0.228695i
$67$	−42.8431	−	24.7355i	−0.639449	−	0.369186i	0.144953	−	0.989439i	$-0.453697\pi$
$67$	−42.8431	−	24.7355i	−0.639449	−	0.369186i	−0.784402	+	0.620252i	$0.787030\pi$
$68$	9.29122	+	16.0929i	0.136636	+	0.236660i
$69$		−	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	$0.244960\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	41.1525	−	71.2783i	0.563733	−	0.976415i	−0.433433	−	0.901186i	$-0.642698\pi$
$73$	41.1525	−	71.2783i	0.563733	−	0.976415i	0.997166	−	0.0752290i	$-0.0239688\pi$
$74$	−24.7906	+	42.9387i	−0.335009	+	0.580252i
$75$		0			0
$76$			12.1529i			0.159906i
$77$	85.3029	+	12.8732i	1.10783	+	0.167185i
$78$			17.7835i			0.227993i
$79$	55.8530	+	96.7403i	0.707001	+	1.22456i	0.965965	+	0.258674i	$0.0832855\pi$
$79$	55.8530	+	96.7403i	0.707001	+	1.22456i	−0.258964	+	0.965887i	$0.583381\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−40.9281	−	70.8895i	−0.499123	−	0.864507i
$83$	91.6237			1.10390			0.551950	−	0.833877i	$-0.313884\pi$
$83$	91.6237			1.10390			0.551950	+	0.833877i	$0.313884\pi$
$84$	−15.1223	+	18.9557i	−0.180027	+	0.225663i
$85$		0			0
$86$	−24.0551	−	41.6646i	−0.279710	−	0.484472i
$87$	−36.5568	+	63.3183i	−0.420194	+	0.727797i
$88$	−30.1878	−	17.4289i	−0.343043	−	0.198056i
$89$	−110.673	+	63.8973i	−1.24352	+	0.717947i	−0.969809	−	0.243864i	$-0.921585\pi$
$89$	−110.673	+	63.8973i	−1.24352	+	0.717947i	−0.273712	+	0.961812i	$0.588252\pi$
$90$		0			0
$91$	−18.5582	−	47.3108i	−0.203936	−	0.519899i
$92$		−	4.50057i		−	0.0489192i
$93$	−1.82779	+	1.05527i	−0.0196536	+	0.0113470i
$94$	−69.9203	−	40.3685i	−0.743833	−	0.429452i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	−61.4455			−0.633459			−0.316729	−	0.948516i	$-0.602585\pi$
$97$	−61.4455			−0.633459			−0.316729	+	0.948516i	$0.602585\pi$
$98$	20.4496	−	66.2104i	0.208669	−	0.675616i
$99$	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	$0.567134\pi$
$102$	−19.7096	−	11.3794i	−0.193232	−	0.111562i
$103$	88.9709	+	154.102i	0.863795	+	1.49614i	0.868238	+	0.496147i	$0.165252\pi$
$103$	88.9709	+	154.102i	0.863795	+	1.49614i	−0.00444312	+	0.999990i	$0.501414\pi$
$104$			20.5346i			0.197448i
$105$		0			0
$106$	−20.5629			−0.193990
$107$	73.5871	−	42.4855i	0.687730	−	0.397061i	−0.115031	−	0.993362i	$-0.536697\pi$
$107$	73.5871	−	42.4855i	0.687730	−	0.397061i	0.802761	+	0.596301i	$0.203363\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	−86.4291	+	149.700i	−0.792928	+	1.37339i	0.131219	+	0.991353i	$0.458111\pi$
$109$	−86.4291	+	149.700i	−0.792928	+	1.37339i	−0.924147	+	0.382037i	$0.875223\pi$
$110$		0			0
$111$		−	60.7244i		−	0.547067i
$112$	−17.4617	+	21.8881i	−0.155908	+	0.195429i
$113$			82.0616i			0.726209i	0.931748	+	0.363105i	$0.118283\pi$
$113$			82.0616i			0.726209i	−0.931748	+	0.363105i	$0.881717\pi$
$114$	−7.44209	−	12.8901i	−0.0652815	−	0.113071i
$115$		0			0
$116$	−42.2122	+	73.1137i	−0.363898	+	0.630290i
$117$	−10.8901	−	18.8622i	−0.0930778	−	0.161215i
$118$	81.8238			0.693422
$119$	64.3103	+	9.70520i	0.540423	+	0.0815563i
$120$		0			0
$121$	−15.4418	−	26.7460i	−0.127618	−	0.221042i
$122$	4.14501	−	7.17937i	0.0339755	−	0.0588473i
$123$	86.8216	+	50.1265i	0.705867	+	0.407532i
$124$	−2.11055	+	1.21852i	−0.0170205	+	0.00982681i
$125$		0			0
$126$	4.43168	−	29.3660i	0.0351720	−	0.233063i
$127$		−	193.480i		−	1.52346i	−0.647892	−	0.761732i	$-0.724349\pi$
$127$		−	193.480i		−	1.52346i	0.647892	−	0.761732i	$-0.275651\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	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	$0.576285\pi$
$132$	42.6920			0.323424
$133$	33.2504	+	26.5263i	0.250003	+	0.199446i
$134$	69.9625			0.522108
$135$		0			0
$136$	−22.7587	−	13.1398i	−0.167344	−	0.0966159i
$137$	−1.09408	−	0.631666i	−0.00798597	−	0.00461070i	0.496002	−	0.868322i	$-0.334801\pi$
$137$	−1.09408	−	0.631666i	−0.00798597	−	0.00461070i	−0.503988	+	0.863711i	$0.668134\pi$
$138$	2.75603	+	4.77358i	0.0199712	+	0.0345911i
$139$		−	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
$142$	−124.907	+	72.1153i	−0.879629	+	0.507854i
$143$	−44.7369	+	77.4866i	−0.312846	+	0.541865i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			116.397i			0.797239i
$147$	18.8553	+	82.7495i	0.128268	+	0.562922i
$148$		−	70.1185i		−	0.473774i
$149$	144.863	+	250.910i	0.972233	+	1.68396i	0.688780	+	0.724971i	$0.258147\pi$
$149$	144.863	+	250.910i	0.972233	+	1.68396i	0.283453	+	0.958986i	$0.408520\pi$
$150$		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	$0.293646\pi$
$152$	−8.59339	−	14.8842i	−0.0565354	−	0.0979223i
$153$	27.8737			0.182181
$154$	−113.577	+	44.5518i	−0.737513	+	0.289298i
$155$		0			0
$156$	−12.5748	−	21.7802i	−0.0806077	−	0.139617i
$157$	−91.8687	+	159.121i	−0.585151	+	1.01351i	0.409705	+	0.912218i	$0.365632\pi$
$157$	−91.8687	+	159.121i	−0.585151	+	1.01351i	−0.994857	+	0.101294i	$0.967702\pi$
$158$	−136.811	−	78.9881i	−0.865895	−	0.499925i
$159$	21.8103	−	12.5922i	0.137172	−	0.0791960i
$160$		0			0
$161$	−12.3136	−	9.82345i	−0.0764821	−	0.0610152i
$162$		−	12.7279i		−	0.0785674i
$163$	−105.283	+	60.7854i	−0.645911	+	0.372917i	−0.786888	−	0.617096i	$-0.788309\pi$
$163$	−105.283	+	60.7854i	−0.645911	+	0.372917i	0.140977	+	0.990013i	$0.454976\pi$
$164$	100.253	+	57.8811i	0.611298	+	0.352933i
$165$		0			0
$166$	−112.216	+	64.7878i	−0.675998	+	0.390288i
$167$	−94.6539			−0.566790			−0.283395	−	0.959003i	$-0.591461\pi$
$167$	−94.6539			−0.566790			−0.283395	+	0.959003i	$0.591461\pi$
$168$	5.11726	−	33.9089i	0.0304599	−	0.201839i
$169$	−116.291			−0.688115
$170$		0			0
$171$	15.7871	+	9.11466i	0.0923220	+	0.0533021i
$172$	58.9227	+	34.0190i	0.342574	+	0.197785i
$173$	130.346	+	225.766i	0.753445	+	1.30501i	0.946144	+	0.323747i	$0.104943\pi$
$173$	130.346	+	225.766i	0.753445	+	1.30501i	−0.192699	+	0.981258i	$0.561724\pi$
$174$		−	103.398i		−	0.594244i
$175$		0			0
$176$	49.2964			0.280093
$177$	−86.7873	+	50.1067i	−0.490324	+	0.283089i
$178$	90.3645	−	156.516i	0.507666	−	0.879302i
$179$	153.264	−	265.462i	0.856225	−	1.48303i	−0.0192782	−	0.999814i	$-0.506137\pi$
$179$	153.264	−	265.462i	0.856225	−	1.48303i	0.875504	−	0.483212i	$-0.160530\pi$
$180$		0			0
$181$		−	314.885i		−	1.73970i	−0.493318	−	0.869849i	$-0.664216\pi$
$181$		−	314.885i		−	1.73970i	0.493318	−	0.869849i	$-0.335784\pi$
$182$	56.1828	+	44.8211i	0.308697	+	0.246270i
$183$			10.1532i			0.0554817i
$184$	3.18238	+	5.51205i	0.0172956	+	0.0299568i
$185$		0			0
$186$	1.49238	−	2.58488i	0.00802356	−	0.0138972i
$187$	−57.2530	−	99.1651i	−0.306166	−	0.530295i
$188$	114.179			0.607337
$189$	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	$0.756950\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	−198.887	−	114.828i	−1.03050	−	0.594961i	−0.113374	−	0.993552i	$-0.536166\pi$
$193$	−198.887	−	114.828i	−1.03050	−	0.594961i	−0.917129	+	0.398591i	$0.869499\pi$
$194$	75.2551	−	43.4485i	0.387913	−	0.223962i
$195$		0			0
$196$	21.7723	+	95.5509i	0.111083	+	0.487504i
$197$			227.989i			1.15730i	0.815574	+	0.578652i	$0.196421\pi$
$197$			227.989i			1.15730i	−0.815574	+	0.578652i	$0.803579\pi$
$198$	−45.2817	+	26.1434i	−0.228695	+	0.132037i
$199$	−9.56623	−	5.52307i	−0.0480715	−	0.0277541i	0.475772	−	0.879569i	$-0.342169\pi$
$199$	−9.56623	−	5.52307i	−0.0480715	−	0.0277541i	−0.523843	+	0.851815i	$0.675502\pi$
$200$		0			0
$201$	−74.2064	+	42.8431i	−0.369186	+	0.213150i
$202$	−87.8781			−0.435040
$203$	107.903	+	275.079i	0.531541	+	1.35507i
$204$	32.1857			0.157773
$205$		0			0
$206$	−217.933	−	125.824i	−1.05793	−	0.610796i
$207$	−5.84641	−	3.37543i	−0.0282435	−	0.0163064i
$208$	−14.5201	−	25.1496i	−0.0698083	−	0.120912i
$209$		−	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	$0.383369\pi$
$212$	25.1843	−	14.5402i	0.118794	−	0.0685858i
$213$	88.3228	−	152.980i	0.414661	−	0.718214i
$214$	−60.0836	+	104.068i	−0.280765	+	0.486298i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−1.27282	+	8.43417i	−0.00586552	+	0.0388671i
$218$		−	244.458i		−	1.12137i
$219$	−71.2783	−	123.458i	−0.325472	−	0.563733i
$220$		0			0
$221$	−33.7274	+	58.4176i	−0.152613	+	0.264333i
$222$	42.9387	+	74.3719i	0.193417	+	0.335009i
$223$	−308.586			−1.38379			−0.691896	−	0.721997i	$-0.743224\pi$
$223$	−308.586			−1.38379			−0.691896	+	0.721997i	$0.743224\pi$
$224$	5.90890	−	39.1546i	0.0263790	−	0.174797i
$225$		0			0
$226$	−58.0263	−	100.505i	−0.256754	−	0.444710i
$227$	−50.2112	+	86.9683i	−0.221195	+	0.383120i	−0.955171	−	0.296055i	$-0.904329\pi$
$227$	−50.2112	+	86.9683i	−0.221195	+	0.383120i	0.733976	+	0.679175i	$0.237662\pi$
$228$	18.2293	+	10.5247i	0.0799532	+	0.0461610i
$229$	−277.125	+	159.998i	−1.21015	+	0.698682i	−0.962793	−	0.270241i	$-0.912897\pi$
$229$	−277.125	+	159.998i	−1.21015	+	0.698682i	−0.247361	+	0.968923i	$0.579563\pi$
$230$		0			0
$231$	93.1843	−	116.806i	0.403395	−	0.505653i
$232$		−	119.394i		−	0.514630i
$233$	−269.151	+	155.395i	−1.15516	+	0.666929i	−0.950138	−	0.311829i	$-0.899058\pi$
$233$	−269.151	+	155.395i	−1.15516	+	0.666929i	−0.205017	+	0.978758i	$0.565725\pi$
$234$	26.6752	+	15.4009i	0.113997	+	0.0658159i
$235$		0			0
$236$	−100.213	+	57.8582i	−0.424633	+	0.245162i
$237$	193.481			0.816374
$238$	−85.6264	+	33.5879i	−0.359775	+	0.141126i
$239$	−136.263			−0.570139			−0.285069	−	0.958507i	$-0.592017\pi$
$239$	−136.263			−0.570139			−0.285069	+	0.958507i	$0.592017\pi$
$240$		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	$0.370861\pi$
$242$	37.8246	+	21.8380i	0.156300	+	0.0902398i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			11.7239i			0.0480486i
$245$		0			0
$246$	−141.779			−0.576338
$247$	−38.2050	+	22.0577i	−0.154676	+	0.0893024i
$248$	1.72325	−	2.98476i	0.00694860	−	0.0120353i
$249$	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	$-0.0634289\pi$
$252$	15.3372	+	39.0995i	0.0608619	+	0.155157i
$253$			27.7328i			0.109616i
$254$	136.811	+	236.964i	0.538626	+	0.932928i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	10.5589	+	18.2886i	0.0410852	+	0.0711617i	0.885837	−	0.463997i	$-0.153585\pi$
$257$	10.5589	+	18.2886i	0.0410852	+	0.0711617i	−0.844752	+	0.535159i	$0.820252\pi$
$258$	−83.3292			−0.322982
$259$	−191.845	−	153.049i	−0.740715	−	0.590921i
$260$		0			0
$261$	63.3183	+	109.671i	0.242599	+	0.420194i
$262$	128.067	−	221.819i	0.488806	−	0.846637i
$263$	−329.538	−	190.259i	−1.25299	−	0.723417i	−0.281292	−	0.959622i	$-0.590763\pi$
$263$	−329.538	−	190.259i	−1.25299	−	0.723417i	−0.971703	+	0.236205i	$0.924096\pi$
$264$	−52.2868	+	30.1878i	−0.198056	+	0.114348i
$265$		0			0
$266$	−59.4802	−	8.97628i	−0.223610	−	0.0337454i
$267$			221.347i			0.829014i
$268$	−85.6862	+	49.4709i	−0.319725	+	0.184593i
$269$	−14.5415	−	8.39551i	−0.0540574	−	0.0312101i	0.472728	−	0.881209i	$-0.343269\pi$
$269$	−14.5415	−	8.39551i	−0.0540574	−	0.0312101i	−0.526785	+	0.849998i	$0.676603\pi$
$270$		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	$0.0944209\pi$
$272$	37.1649			0.136636
$273$	−87.0381	−	13.1351i	−0.318821	−	0.0481139i
$274$	1.78662			0.00652051
$275$		0			0
$276$	−6.75086	−	3.89761i	−0.0244596	−	0.0141218i
$277$	−420.736	−	242.912i	−1.51890	−	0.876940i	−0.999752	−	0.0222577i	$-0.992915\pi$
$277$	−420.736	−	242.912i	−1.51890	−	0.876940i	−0.519152	−	0.854682i	$-0.673752\pi$
$278$	8.57912	+	14.8595i	0.0308601	+	0.0534513i
$279$			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	$0.278526\pi$
$282$	−121.106	+	69.9203i	−0.429452	+	0.247944i
$283$	135.251	−	234.261i	0.477918	−	0.827778i	−0.521762	−	0.853091i	$-0.674725\pi$
$283$	135.251	−	234.261i	0.477918	−	0.827778i	0.999680	+	0.0253131i	$0.00805826\pi$
$284$	101.986	−	176.646i	0.359107	−	0.621992i
$285$		0			0
$286$		−	126.535i		−	0.442431i
$287$	377.187	−	147.956i	1.31424	−	0.515525i
$288$		−	16.9706i		−	0.0589256i
$289$	101.337	+	175.520i	0.350646	+	0.607336i
$290$		0			0
$291$	−53.2134	+	92.1683i	−0.182864	+	0.316729i
$292$	−82.3051	−	142.557i	−0.281867	−	0.488207i
$293$	−9.63230			−0.0328747			−0.0164374	−	0.999865i	$-0.505232\pi$
$293$	−9.63230			−0.0328747			−0.0164374	+	0.999865i	$0.505232\pi$
$294$	−81.6057	−	88.0143i	−0.277570	−	0.299368i
$295$		0			0
$296$	49.5813	+	85.8773i	0.167504	+	0.290126i
$297$	32.0190	−	55.4585i	0.107808	−	0.186729i
$298$	−354.840	−	204.867i	−1.19074	−	0.687472i
$299$	14.1484	−	8.16861i	0.0473192	−	0.0273198i
$300$		0			0
$301$	221.688	−	86.9594i	0.736504	−	0.288902i
$302$		−	165.892i		−	0.549310i
$303$	93.2088	−	53.8141i	0.307620	−	0.177604i
$304$	21.0494	+	12.1529i	0.0692415	+	0.0399766i
$305$		0			0
$306$	−34.1381	+	19.7096i	−0.111562	+	0.0644106i
$307$	46.0412			0.149971			0.0749857	−	0.997185i	$-0.476109\pi$
$307$	46.0412			0.149971			0.0749857	+	0.997185i	$0.476109\pi$
$308$	107.600	−	134.876i	0.349350	−	0.437908i
$309$	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	$0.914389\pi$
$312$	30.8019	+	17.7835i	0.0987239	+	0.0569983i
$313$	−143.261	−	248.135i	−0.457703	−	0.792764i	0.541137	−	0.840935i	$-0.317994\pi$
$313$	−143.261	−	248.135i	−0.457703	−	0.792764i	−0.998839	+	0.0481706i	$0.984661\pi$
$314$		−	259.844i		−	0.827529i
$315$		0			0
$316$	223.412			0.707001
$317$	−1.18545	+	0.684418i	−0.00373958	+	0.00215905i	−0.501869	−	0.864944i	$-0.667354\pi$
$317$	−1.18545	+	0.684418i	−0.00373958	+	0.00215905i	0.498129	+	0.867103i	$0.334021\pi$
$318$	−17.8080	+	30.8444i	−0.0560001	+	0.0969949i
$319$	260.114	−	450.531i	0.815404	−	1.41232i
$320$		0			0
$321$		−	147.174i		−	0.458487i
$322$	22.0273	+	3.32418i	0.0684077	+	0.0103235i
$323$		−	56.4575i		−	0.174791i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	85.9636	−	148.893i	0.263692	−	0.456728i
$327$	149.700	+	259.287i	0.457797	+	0.792928i
$328$	−163.712			−0.499123
$329$	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	$0.636342\pi$
$332$	91.6237	−	158.697i	0.275975	−	0.478003i
$333$	−91.0866	−	52.5889i	−0.273533	−	0.157925i
$334$	115.927	−	66.9304i	0.347087	−	0.200391i
$335$		0			0
$336$	17.7099	+	45.1482i	0.0527080	+	0.134370i
$337$		−	141.948i		−	0.421211i	−0.977571	−	0.210606i	$-0.932456\pi$
$337$		−	141.948i		−	0.421211i	0.977571	−	0.210606i	$-0.0675436\pi$
$338$	142.427	−	82.2305i	0.421383	−	0.243285i
$339$	123.092	+	71.0675i	0.363105	+	0.209639i
$340$		0			0
$341$	13.0053	−	7.50861i	0.0381387	−	0.0220194i
$342$	−25.7802			−0.0753806
$343$	308.951	+	148.991i	0.900732	+	0.434376i
$344$	−96.2203			−0.279710
$345$		0			0
$346$	−319.281	−	184.337i	−0.922778	−	0.532766i
$347$	216.811	+	125.176i	0.624815	+	0.360737i	0.778741	−	0.627345i	$-0.215858\pi$
$347$	216.811	+	125.176i	0.624815	+	0.360737i	−0.153926	+	0.988082i	$0.549192\pi$
$348$	73.1137	+	126.637i	0.210097	+	0.363898i
$349$		−	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
$352$	−60.3756	+	34.8578i	−0.171521	+	0.0990280i
$353$	71.0997	−	123.148i	0.201416	−	0.348862i	−0.747569	−	0.664184i	$-0.768779\pi$
$353$	71.0997	−	123.148i	0.201416	−	0.348862i	0.948985	+	0.315322i	$0.102113\pi$
$354$	70.8615	−	122.736i	0.200174	−	0.346711i
$355$		0			0
$356$			255.589i			0.717947i
$357$	70.2522	−	88.0605i	0.196785	−	0.246668i
$358$			433.497i			1.21089i
$359$	−328.443	−	568.880i	−0.914884	−	1.58462i	−0.807072	−	0.590453i	$-0.798949\pi$
$359$	−328.443	−	568.880i	−0.914884	−	1.58462i	−0.107812	−	0.994171i	$-0.534384\pi$
$360$		0			0
$361$	−162.038	+	280.659i	−0.448860	+	0.777448i
$362$	222.658	+	385.654i	0.615076	+	1.06534i
$363$	−53.4921			−0.147361
$364$	−100.503	−	15.1671i	−0.276107	−	0.0416678i
$365$		0			0
$366$	−7.17937	−	12.4350i	−0.0196158	−	0.0339755i
$367$	256.576	−	444.403i	0.699117	−	1.21091i	−0.269655	−	0.962957i	$-0.586910\pi$
$367$	256.576	−	444.403i	0.699117	−	1.21091i	0.968773	−	0.247950i	$-0.0797569\pi$
$368$	−7.79522	−	4.50057i	−0.0211827	−	0.0122298i
$369$	150.379	−	86.8216i	0.407532	−	0.235289i
$370$		0			0
$371$	15.1880	−	100.642i	0.0409381	−	0.271271i
$372$			4.22109i			0.0113470i
$373$	547.782	−	316.262i	1.46858	−	0.847887i	0.469204	−	0.883090i	$-0.344541\pi$
$373$	547.782	−	316.262i	1.46858	−	0.847887i	0.999380	+	0.0352027i	$0.0112077\pi$
$374$	140.241	+	80.9679i	0.374975	+	0.216492i
$375$		0			0
$376$	−139.841	+	80.7370i	−0.371916	+	0.214726i
$377$	−306.463			−0.812900
$378$	−40.2110	−	32.0792i	−0.106378	−	0.0848656i
$379$	617.180			1.62844			0.814222	−	0.580553i	$-0.197164\pi$
$379$	617.180			1.62844			0.814222	+	0.580553i	$0.197164\pi$
$380$		0			0
$381$	−290.220	−	167.559i	−0.761732	−	0.439786i
$382$	−111.193	−	64.1976i	−0.291082	−	0.168057i
$383$	−86.9735	−	150.642i	−0.227085	−	0.393322i	0.729858	−	0.683599i	$-0.239586\pi$
$383$	−86.9735	−	150.642i	−0.227085	−	0.393322i	−0.956943	+	0.290276i	$0.906253\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	324.781			0.841402
$387$	88.3840	−	51.0285i	0.228382	−	0.131857i
$388$	−61.4455	+	106.427i	−0.158365	+	0.274296i
$389$	98.0961	−	169.907i	0.252175	−	0.436780i	−0.711949	−	0.702231i	$-0.752187\pi$
$389$	98.0961	−	169.907i	0.252175	−	0.436780i	0.964124	+	0.265451i	$0.0855208\pi$
$390$		0			0
$391$			20.9079i			0.0534729i
$392$	−94.2301	−	101.630i	−0.240383	−	0.259261i
$393$			313.699i			0.798217i
$394$	−161.213	−	279.228i	−0.409169	−	0.708702i
$395$		0			0
$396$	36.9723	−	64.0379i	0.0933645	−	0.161712i
$397$	−199.350	−	345.285i	−0.502142	−	0.869736i	−0.999997	−	0.00247542i	$-0.999212\pi$
$397$	−199.350	−	345.285i	−0.502142	−	0.869736i	0.497855	−	0.867260i	$-0.334121\pi$
$398$	15.6216			0.0392502
$399$	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	$0.975849\pi$
$402$	60.5893	−	104.944i	0.150720	−	0.261054i
$403$	−7.66135	−	4.42328i	−0.0190108	−	0.0109759i
$404$	107.628	−	62.1392i	0.266407	−	0.153810i
$405$		0			0
$406$	−326.664	−	260.603i	−0.804591	−	0.641880i
$407$			432.074i			1.06161i
$408$	−39.4193	+	22.7587i	−0.0966159	+	0.0557812i
$409$	−293.397	−	169.393i	−0.717352	−	0.414163i	0.0964252	−	0.995340i	$-0.469259\pi$
$409$	−293.397	−	169.393i	−0.717352	−	0.414163i	−0.813777	+	0.581177i	$0.802592\pi$
$410$		0			0
$411$	−1.89500	+	1.09408i	−0.00461070	+	0.00266199i
$412$	355.884			0.863795
$413$	−60.4361	+	400.473i	−0.146334	+	0.969668i
$414$	9.54715			0.0230608
$415$		0			0
$416$	35.5669	+	20.5346i	0.0854974	+	0.0493619i
$417$	−18.1991	−	10.5072i	−0.0436428	−	0.0251972i
$418$	52.9529	+	91.7171i	0.126682	+	0.219419i
$419$		−	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	$0.583195\pi$
$422$	−185.166	+	106.905i	−0.438781	+	0.253330i
$423$	85.6345	−	148.323i	0.202446	−	0.350646i
$424$	−20.5629	+	35.6160i	−0.0484975	+	0.0840001i
$425$		0			0
$426$			249.815i			0.586420i
$427$	32.0766	+	25.5898i	0.0751209	+	0.0599293i
$428$		−	169.942i		−	0.397061i
$429$	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	$0.0590814\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	−643.490			−1.48612			−0.743060	−	0.669224i	$-0.766626\pi$
$433$	−643.490			−1.48612			−0.743060	+	0.669224i	$0.766626\pi$
$434$	−4.40498	−	11.2297i	−0.0101497	−	0.0258749i
$435$		0			0
$436$	172.858	+	299.399i	0.396464	+	0.686695i
$437$	−6.83686	+	11.8418i	−0.0156450	+	0.0270979i
$438$	174.595	+	100.803i	0.398620	+	0.230143i
$439$	−494.013	+	285.218i	−1.12531	+	0.649700i	−0.942752	−	0.333494i	$-0.891772\pi$
$439$	−494.013	+	285.218i	−1.12531	+	0.649700i	−0.182562	+	0.983194i	$0.558439\pi$
$440$		0			0
$441$	140.453	+	43.3802i	0.318488	+	0.0983677i
$442$		−	95.3956i		−	0.215827i
$443$	57.1705	−	33.0074i	0.129053	−	0.0745089i	−0.434084	−	0.900873i	$-0.642928\pi$
$443$	57.1705	−	33.0074i	0.129053	−	0.0745089i	0.563137	+	0.826364i	$0.309594\pi$
$444$	−105.178	−	60.7244i	−0.236887	−	0.136767i
$445$		0			0
$446$	377.939	−	218.203i	0.847396	−	0.489244i
$447$	501.819			1.12264
$448$	20.4496	+	52.1327i	0.0456464	+	0.116368i
$449$	−515.072			−1.14715			−0.573577	−	0.819152i	$-0.694445\pi$
$449$	−515.072			−1.14715			−0.573577	+	0.819152i	$0.694445\pi$
$450$		0			0
$451$	−617.764	−	356.666i	−1.36977	−	0.790834i
$452$	142.135	+	82.0616i	0.314458	+	0.181552i
$453$	101.588	+	175.955i	0.224255	+	0.388421i
$454$		−	142.019i		−	0.312816i
$455$		0			0
$456$	−29.7684			−0.0652815
$457$	68.4395	−	39.5136i	0.149758	−	0.0864629i	−0.423248	−	0.906014i	$-0.639110\pi$
$457$	68.4395	−	39.5136i	0.149758	−	0.0864629i	0.573007	+	0.819551i	$0.305777\pi$
$458$	226.272	−	391.914i	0.494043	−	0.855708i
$459$	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	$-0.00330854\pi$
$462$	−31.5328	+	208.948i	−0.0682529	+	0.452269i
$463$			232.103i			0.501303i	0.968077	+	0.250652i	$0.0806449\pi$
$463$			232.103i			0.501303i	−0.968077	+	0.250652i	$0.919355\pi$
$464$	84.4244	+	146.227i	0.181949	+	0.315145i
$465$		0			0
$466$	219.761	−	380.637i	0.471590	−	0.816818i
$467$	342.768	+	593.692i	0.733979	+	1.27129i	0.955170	+	0.296058i	$0.0956722\pi$
$467$	342.768	+	593.692i	0.733979	+	1.27129i	−0.221191	+	0.975230i	$0.570994\pi$
$468$	−43.5604			−0.0930778
$469$	−51.6752	+	342.419i	−0.110182	+	0.730105i
$470$		0			0
$471$	159.121	+	275.606i	0.337837	+	0.585151i
$472$	81.8238	−	141.723i	0.173356	−	0.300261i
$473$	−363.085	−	209.627i	−0.767621	−	0.443186i
$474$	−236.964	+	136.811i	−0.499925	+	0.288632i
$475$		0			0
$476$	81.1202	−	101.684i	0.170421	−	0.213621i
$477$		−	43.6206i		−	0.0914477i
$478$	166.888	−	96.3526i	0.349137	−	0.201575i
$479$	544.818	+	314.551i	1.13741	+	0.656682i	0.945787	−	0.324787i	$-0.105293\pi$
$479$	544.818	+	314.551i	1.13741	+	0.656682i	0.191619	+	0.981469i	$0.438626\pi$
$480$		0			0
$481$	220.432	−	127.266i	0.458278	−	0.264587i
$482$	−546.140			−1.13307
$483$	−25.3991	+	9.96307i	−0.0525861	+	0.0206275i
$484$	−61.7673			−0.127618
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	431.946	+	249.384i	0.886953	+	0.512083i	0.872945	−	0.487819i	$-0.162207\pi$
$487$	431.946	+	249.384i	0.886953	+	0.512083i	0.0140085	+	0.999902i	$0.495541\pi$
$488$	−8.29002	−	14.3587i	−0.0169877	−	0.0294236i
$489$			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	$0.445741\pi$
$492$	173.643	−	100.253i	0.352933	−	0.203766i
$493$	196.101	−	339.658i	0.397772	−	0.688961i
$494$	31.1943	−	54.0301i	0.0631463	−	0.109373i
$495$		0			0
$496$			4.87410i			0.00982681i
$497$	−260.698	−	664.603i	−0.524543	−	1.33723i
$498$			224.431i			0.450665i
$499$	18.1531	+	31.4421i	0.0363790	+	0.0630102i	0.883642	−	0.468164i	$-0.155084\pi$
$499$	18.1531	+	31.4421i	0.0363790	+	0.0630102i	−0.847263	+	0.531174i	$0.821751\pi$
$500$		0			0
$501$	−81.9727	+	141.981i	−0.163618	+	0.283395i
$502$	70.2664	+	121.705i	0.139973	+	0.242440i
$503$	−634.940			−1.26231			−0.631153	−	0.775658i	$-0.717418\pi$
$503$	−634.940			−1.26231			−0.631153	+	0.775658i	$0.717418\pi$
$504$	−46.4317	−	37.0419i	−0.0921263	−	0.0734958i
$505$		0			0
$506$	−19.6100	−	33.9656i	−0.0387550	−	0.0671256i
$507$	−100.711	+	174.437i	−0.198642	+	0.344057i
$508$	−335.117	−	193.480i	−0.659680	−	0.380866i
$509$	−500.864	+	289.174i	−0.984015	+	0.568121i	−0.903480	−	0.428631i	$-0.858996\pi$
$509$	−500.864	+	289.174i	−0.984015	+	0.568121i	−0.0805350	+	0.996752i	$0.525663\pi$
$510$		0			0
$511$	−569.685	−	85.9723i	−1.11484	−	0.168243i
$512$		−	22.6274i		−	0.0441942i
$513$	27.3440	−	15.7871i	0.0533021	−	0.0307740i
$514$	−25.8639	−	14.9325i	−0.0503189	−	0.0290516i
$515$		0			0
$516$	102.057	−	58.9227i	0.197785	−	0.114191i
$517$	−703.579			−1.36089
$518$	343.183	+	51.7904i	0.662516	+	0.0999815i
$519$	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	$0.875725\pi$
$522$	−155.098	−	89.5456i	−0.297122	−	0.171543i
$523$	−226.823	−	392.868i	−0.433695	−	0.751182i	0.563493	−	0.826121i	$-0.309457\pi$
$523$	−226.823	−	392.868i	−0.433695	−	0.751182i	−0.997188	+	0.0749389i	$0.976124\pi$
$524$			362.229i			0.691276i
$525$		0			0
$526$	538.133			1.02307
$527$	9.80477	−	5.66079i	0.0186049	−	0.0107415i
$528$	42.6920	−	73.9447i	0.0808560	−	0.140047i
$529$	−261.968	+	453.742i	−0.495214	+	0.857735i
$530$		0			0
$531$			173.575i			0.326882i
$532$	79.1953	−	31.0652i	0.148863	−	0.0583933i
$533$			420.220i			0.788406i
$534$	−156.516	−	271.093i	−0.293101	−	0.507666i
$535$		0			0
$536$	69.9625	−	121.179i	0.130527	−	0.226079i
$537$	−265.462	−	459.793i	−0.494342	−	0.856225i
$538$	23.7461			0.0441377
$539$	−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	$0.654533\pi$
$542$	−261.398	+	452.754i	−0.482284	+	0.835340i
$543$	−472.328	−	272.699i	−0.869849	−	0.502208i
$544$	−45.5175	+	26.2795i	−0.0836718	+	0.0483080i
$545$		0			0
$546$	115.887	−	45.4581i	0.212248	−	0.0832566i
$547$			481.306i			0.879901i	0.898022	+	0.439950i	$0.145004\pi$
$547$			481.306i			0.879901i	−0.898022	+	0.439950i	$0.854996\pi$
$548$	−2.18815	+	1.26333i	−0.00399298	+	0.00230535i
$549$	15.2297	+	8.79289i	0.0277409	+	0.0160162i
$550$		0			0
$551$	222.136	−	128.250i	0.403150	−	0.232759i
$552$	11.0241			0.0199712
$553$	487.645	−	611.259i	0.881817	−	1.10535i
$554$	687.060			1.24018
$555$		0			0
$556$	−21.0145	−	12.1327i	−0.0377958	−	0.0218214i
$557$	−94.2333	−	54.4056i	−0.169180	−	0.0976762i	0.413019	−	0.910722i	$-0.364474\pi$
$557$	−94.2333	−	54.4056i	−0.169180	−	0.0976762i	−0.582199	+	0.813046i	$0.697808\pi$
$558$	−2.58488	−	4.47714i	−0.00463240	−	0.00802356i
$559$			246.980i			0.441825i
$560$		0			0
$561$	−198.330			−0.353530
$562$	−441.195	+	254.724i	−0.785044	+	0.453245i
$563$	301.097	−	521.516i	0.534809	−	0.926316i	−0.464364	−	0.885645i	$-0.653717\pi$
$563$	301.097	−	521.516i	0.534809	−	0.926316i	0.999173	−	0.0406717i	$-0.0129498\pi$
$564$	98.8822	−	171.269i	0.175323	−	0.303669i
$565$		0			0
$566$			382.547i			0.675878i
$567$	62.2946	+	9.40101i	0.109867	+	0.0165803i
$568$			288.461i			0.507854i
$569$	−4.76685	−	8.25642i	−0.00837759	−	0.0145104i	0.861806	−	0.507238i	$-0.169333\pi$
$569$	−4.76685	−	8.25642i	−0.00837759	−	0.0145104i	−0.870184	+	0.492727i	$0.836000\pi$
$570$		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	$0.837084\pi$
$572$	89.4739	+	154.973i	0.156423	+	0.270932i
$573$	157.251			0.274435
$574$	−357.337	+	447.919i	−0.622538	+	0.780347i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	262.117	−	454.001i	0.454276	−	0.786830i	−0.544370	−	0.838845i	$-0.683231\pi$
$577$	262.117	−	454.001i	0.454276	−	0.786830i	0.998646	+	0.0520155i	$0.0165645\pi$
$578$	−248.223	−	143.312i	−0.429452	−	0.247944i
$579$	−344.483	+	198.887i	−0.594961	+	0.343501i
$580$		0			0
$581$	−234.209	−	597.073i	−0.403113	−	1.02767i
$582$		−	150.510i		−	0.258608i
$583$	−155.187	+	89.5974i	−0.266187	+	0.153683i
$584$	201.605	+	116.397i	0.345215	+	0.199310i
$585$		0			0
$586$	11.7971	−	6.81106i	0.0201316	−	0.0116230i
$587$	−651.322			−1.10958			−0.554789	−	0.831991i	$-0.687201\pi$
$587$	−651.322			−1.10958			−0.554789	+	0.831991i	$0.687201\pi$
$588$	162.182	+	50.0911i	0.275819	+	0.0851889i
$589$	7.40429			0.0125710
$590$		0			0
$591$	341.984	+	197.444i	0.578652	+	0.334085i
$592$	−121.449	−	70.1185i	−0.205150	−	0.118443i
$593$	352.706	+	610.904i	0.594782	+	1.03019i	0.993578	+	0.113152i	$0.0360948\pi$
$593$	352.706	+	610.904i	0.594782	+	1.03019i	−0.398796	+	0.917040i	$0.630572\pi$
$594$			90.5633i			0.152464i
$595$		0			0
$596$	579.451			0.972233
$597$	−16.5692	+	9.56623i	−0.0277541	+	0.0160238i
$598$	−11.5522	+	20.0089i	−0.0193180	+	0.0334597i
$599$	−296.910	+	514.263i	−0.495676	+	0.858535i	−0.999988	−	0.00498610i	$-0.998413\pi$
$599$	−296.910	+	514.263i	−0.495676	+	0.858535i	0.504312	+	0.863522i	$0.331746\pi$
$600$		0			0
$601$			12.1644i			0.0202403i	0.999949	+	0.0101202i	$0.00322140\pi$
$601$			12.1644i			0.0202403i	−0.999949	+	0.0101202i	$0.996779\pi$
$602$	−210.021	+	263.260i	−0.348873	+	0.437309i
$603$			148.413i			0.246124i
$604$	117.303	+	203.175i	0.194211	+	0.336383i
$605$		0			0
$606$	−76.1047	+	131.817i	−0.125585	+	0.217520i
$607$	403.291	+	698.521i	0.664401	+	1.15078i	0.979447	+	0.201700i	$0.0646465\pi$
$607$	403.291	+	698.521i	0.664401	+	1.15078i	−0.315047	+	0.949076i	$0.602020\pi$
$608$	−34.3736			−0.0565354
$609$	506.066	+	76.3714i	0.830978	+	0.125405i
$610$		0			0
$611$	207.237	+	358.946i	0.339178	+	0.587473i
$612$	27.8737	−	48.2786i	0.0455452	−	0.0788866i
$613$	−688.035	−	397.237i	−1.12241	−	0.648021i	−0.180392	−	0.983595i	$-0.557737\pi$
$613$	−688.035	−	397.237i	−1.12241	−	0.648021i	−0.942014	+	0.335574i	$0.891070\pi$
$614$	−56.3887	+	32.5560i	−0.0918383	+	0.0530229i
$615$		0			0
$616$	−36.4110	+	241.273i	−0.0591087	+	0.391677i
$617$			108.982i			0.176633i	0.996092	+	0.0883164i	$0.0281487\pi$
$617$			108.982i			0.176633i	−0.996092	+	0.0883164i	$0.971851\pi$
$618$	−377.472	+	217.933i	−0.610796	+	0.352643i
$619$	310.725	+	179.397i	0.501979	+	0.289818i	0.729531	−	0.683948i	$-0.239739\pi$
$619$	310.725	+	179.397i	0.501979	+	0.289818i	−0.227551	+	0.973766i	$0.573072\pi$
$620$		0			0
$621$	−10.1263	+	5.84641i	−0.0163064	+	0.00941451i
$622$	617.533			0.992819
$623$	699.296	+	557.878i	1.12246	+	0.895470i
$624$	−50.2992			−0.0806077
$625$		0			0
$626$	350.916	+	202.602i	0.560569	+	0.323645i
$627$	−112.330	−	64.8538i	−0.179155	−	0.103435i
$628$	183.737	+	318.243i	0.292576	+	0.506756i
$629$			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	$0.661262\pi$
$632$	−273.623	+	157.976i	−0.432948	+	0.249962i
$633$	130.932	−	226.781i	0.206843	−	0.358263i
$634$	0.967913	−	1.67647i	0.00152668	−	0.00264428i
$635$		0			0
$636$		−	50.3687i		−	0.0791960i
$637$	−260.866	+	241.872i	−0.409523	+	0.379705i
$638$			735.713i			1.15316i
$639$	−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	$0.912104\pi$
$642$	104.068	+	180.251i	0.162099	+	0.280765i
$643$	835.879			1.29997			0.649984	−	0.759948i	$-0.274776\pi$
$643$	835.879			1.29997			0.649984	+	0.759948i	$0.274776\pi$
$644$	−29.3283	+	11.5044i	−0.0455409	+	0.0178639i
$645$		0			0
$646$	39.9215	+	69.1461i	0.0617980	+	0.107037i
$647$	284.595	−	492.933i	0.439869	−	0.761876i	−0.557810	−	0.829969i	$-0.688358\pi$
$647$	284.595	−	492.933i	0.439869	−	0.761876i	0.997679	+	0.0680932i	$0.0216915\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	617.520	−	356.525i	0.951495	−	0.549346i
$650$		0			0
$651$	11.5490	+	9.21343i	0.0177403	+	0.0141527i
$652$			243.142i			0.372917i
$653$	−339.763	+	196.162i	−0.520311	+	0.300402i	−0.737062	−	0.675825i	$-0.763787\pi$
$653$	−339.763	+	196.162i	−0.520311	+	0.300402i	0.216751	+	0.976227i	$0.430454\pi$
$654$	−366.688	−	211.707i	−0.560684	−	0.323711i
$655$		0			0
$656$	200.506	−	115.762i	0.305649	−	0.176467i
$657$	−246.915			−0.375822
$658$	−84.3343	+	558.831i	−0.128168	+	0.849288i
$659$	−505.063			−0.766408			−0.383204	−	0.923664i	$-0.625179\pi$
$659$	−505.063			−0.766408			−0.383204	+	0.923664i	$0.625179\pi$
$660$		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	$0.738396\pi$
$662$	−470.343	−	271.553i	−0.710488	−	0.410201i
$663$	58.4176	+	101.182i	0.0881110	+	0.152613i
$664$			259.151i			0.390288i
$665$		0			0
$666$	148.744			0.223339
$667$	−82.2633	+	47.4948i	−0.123333	+	0.0712065i
$668$	−94.6539	+	163.945i	−0.141698	+	0.245427i
$669$	−267.243	+	462.878i	−0.399466	+	0.691896i
$670$		0			0
$671$		−	72.2430i		−	0.107665i
$672$	−53.6147	−	42.7723i	−0.0797838	−	0.0636492i
$673$			624.569i			0.928038i	0.885825	+	0.464019i	$0.153593\pi$
$673$			624.569i			0.928038i	−0.885825	+	0.464019i	$0.846407\pi$
$674$	100.373	+	173.850i	0.148921	+	0.257938i
$675$		0			0
$676$	−116.291	+	201.423i	−0.172029	+	0.297963i
$677$	−390.778	−	676.847i	−0.577220	−	0.999774i	−0.995797	−	0.0915926i	$-0.970804\pi$
$677$	−390.778	−	676.847i	−0.577220	−	0.999774i	0.418577	−	0.908181i	$-0.362529\pi$
$678$	−201.009			−0.296474
$679$	157.067	+	400.415i	0.231321	+	0.589712i
$680$		0			0
$681$	86.9683	+	150.634i	0.127707	+	0.221195i
$682$	−10.6188	+	18.3923i	−0.0155701	+	0.0269681i
$683$	88.0791	+	50.8525i	0.128959	+	0.0744546i	0.563092	−	0.826394i	$-0.309612\pi$
$683$	88.0791	+	50.8525i	0.128959	+	0.0744546i	−0.434133	+	0.900849i	$0.642945\pi$
$684$	31.5741	−	18.2293i	0.0461610	−	0.0266511i
$685$		0			0
$686$	−483.739	+	35.9855i	−0.705158	+	0.0524570i
$687$			554.250i			0.806769i
$688$	117.845	−	68.0380i	0.171287	−	0.0988925i
$689$	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	$0.155414\pi$
$692$	521.384			0.753445
$693$	−94.5087	−	240.933i	−0.136376	−	0.347667i
$694$	−354.051			−0.510160
$695$		0			0
$696$	−179.091	−	103.398i	−0.257315	−	0.148561i
$697$	−465.736	−	268.893i	−0.668201	−	0.385786i
$698$	138.019	+	239.055i	0.197734	+	0.342486i
$699$			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	$0.692170\pi$
$702$	46.2028	−	26.6752i	0.0658159	−	0.0379988i
$703$	−106.518	+	184.494i	−0.151519	+	0.262438i
$704$	49.2964	−	85.3839i	0.0700233	−	0.121284i
$705$		0			0
$706$			201.100i			0.284845i
$707$	64.9079	−	430.104i	0.0918075	−	0.608351i
$708$			200.427i			0.283089i
$709$	514.532	+	891.196i	0.725715	+	1.25698i	0.958679	+	0.284490i	$0.0918243\pi$
$709$	514.532	+	891.196i	0.725715	+	1.25698i	−0.232964	+	0.972485i	$0.574842\pi$
$710$		0			0
$711$	167.559	−	290.221i	0.235667	−	0.408187i
$712$	−180.729	−	313.032i	−0.253833	−	0.439651i
$713$	−2.74203			−0.00384576
$714$	−23.7728	+	157.527i	−0.0332952	+	0.220627i
$715$		0			0
$716$	−306.529	−	530.923i	−0.428113	−	0.741513i
$717$	−118.007	+	204.395i	−0.164585	+	0.285069i
$718$	804.518	+	464.489i	1.12050	+	0.646920i
$719$	136.549	−	78.8367i	0.189915	−	0.109648i	−0.402028	−	0.915628i	$-0.631694\pi$
$719$	136.549	−	78.8367i	0.189915	−	0.109648i	0.591943	+	0.805980i	$0.298361\pi$
$720$		0			0
$721$	776.792	−	973.702i	1.07738	−	1.35049i
$722$		−	458.314i		−	0.634784i
$723$	579.269	−	334.441i	0.801202	−	0.462574i
$724$	−545.397	−	314.885i	−0.753311	−	0.434925i
$725$		0			0
$726$	65.5141	−	37.8246i	0.0902398	−	0.0521000i
$727$	13.5224			0.0186003			0.00930013	−	0.999957i	$-0.497040\pi$
$727$	13.5224			0.0186003			0.00930013	+	0.999957i	$0.497040\pi$
$728$	133.815	−	52.4905i	0.183812	−	0.0721023i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−273.732	−	158.039i	−0.374462	−	0.216196i
$732$	17.5858	+	10.1532i	0.0240243	+	0.0138704i
$733$	−197.235	−	341.622i	−0.269080	−	0.466060i	0.699545	−	0.714589i	$-0.253386\pi$
$733$	−197.235	−	341.622i	−0.269080	−	0.466060i	−0.968624	+	0.248529i	$0.920053\pi$
$734$			725.707i			0.988701i
$735$		0			0
$736$	12.7295			0.0172956
$737$	528.003	−	304.843i	0.716422	−	0.413626i
$738$	−122.784	+	212.669i	−0.166374	+	0.288169i
$739$	475.080	−	822.863i	0.642869	−	1.11348i	−0.341920	−	0.939729i	$-0.611077\pi$
$739$	475.080	−	822.863i	0.642869	−	1.11348i	0.984789	−	0.173753i	$-0.0555895\pi$
$740$		0			0
$741$			76.4101i			0.103118i
$742$	52.5630	+	134.000i	0.0708396	+	0.180593i
$743$		−	425.883i		−	0.573194i	−0.958051	−	0.286597i	$-0.907476\pi$
$743$		−	425.883i		−	0.573194i	0.958051	−	0.286597i	$-0.0925241\pi$
$744$	−2.98476	−	5.16976i	−0.00401178	−	0.00694860i
$745$		0			0
$746$	−447.262	+	774.680i	−0.599547	+	1.03845i
$747$	−137.436	−	238.045i	−0.183983	−	0.318669i
$748$	−229.012			−0.306166
$749$	−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	$0.695151\pi$
$752$	114.179	−	197.764i	0.151834	−	0.262985i
$753$	−149.058	−	86.0584i	−0.197952	−	0.114287i
$754$	375.340	−	216.702i	0.497798	−	0.287404i
$755$		0			0
$756$	71.9316	+	10.8553i	0.0951477	+	0.0143589i
$757$			882.903i			1.16632i	0.812358	+	0.583159i	$0.198184\pi$
$757$			882.903i			1.16632i	−0.812358	+	0.583159i	$0.801816\pi$
$758$	−755.889	+	436.412i	−0.997214	+	0.575742i
$759$	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	$0.600548\pi$
$762$	473.927			0.621952
$763$	1196.46	+	180.560i	1.56810	+	0.236645i
$764$	181.578			0.237668
$765$		0			0
$766$	213.041	+	122.999i	0.278121	+	0.160573i
$767$	−363.778	−	210.027i	−0.474287	−	0.273829i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$			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
$772$	−397.774	+	229.655i	−0.515252	+	0.297481i
$773$	643.167	−	1114.00i	0.832041	−	1.44114i	−0.0643767	−	0.997926i	$-0.520506\pi$
$773$	643.167	−	1114.00i	0.832041	−	1.44114i	0.896417	−	0.443211i	$-0.146161\pi$
$774$	−72.1652	+	124.994i	−0.0932367	+	0.161491i
$775$		0			0
$776$		−	173.794i		−	0.223962i
$777$	−395.716	+	155.224i	−0.509287	+	0.199773i
$778$			277.458i			0.356629i
$779$	−175.855	−	304.591i	−0.225745	−	0.391002i
$780$		0			0
$781$	−628.446	+	1088.50i	−0.804668	+	1.39373i
$782$	−14.7841	−	25.6068i	−0.0189055	−	0.0327453i
$783$	219.341			0.280129
$784$	187.271	+	57.8402i	0.238866	+	0.0737758i
$785$		0			0
$786$	−221.819	−	384.202i	−0.282212	−	0.488806i
$787$	498.736	−	863.836i	0.633718	−	1.09763i	−0.353067	−	0.935598i	$-0.614861\pi$
$787$	498.736	−	863.836i	0.633718	−	1.09763i	0.986785	−	0.162034i	$-0.0518054\pi$
$788$	394.889	+	227.989i	0.501128	+	0.289326i
$789$	−570.776	+	329.538i	−0.723417	+	0.417665i
$790$		0			0
$791$	534.761	−	209.766i	0.676057	−	0.265191i
$792$			104.574i			0.132037i
$793$	−36.8563	+	21.2790i	−0.0464770	+	0.0268335i
$794$	488.307	+	281.924i	0.614996	+	0.355068i
$795$		0			0
$796$	−19.1325	+	11.0461i	−0.0240358	+	0.0138771i
$797$	−971.547			−1.21901			−0.609503	−	0.792784i	$-0.708631\pi$
$797$	−971.547			−1.21901			−0.609503	+	0.792784i	$0.708631\pi$
$798$	−64.9758	+	81.4466i	−0.0814233	+	0.102063i
$799$	−530.433			−0.663871
$800$		0			0
$801$	332.020	+	191.692i	0.414507	+	0.239316i
$802$	425.230	+	245.507i	0.530212	+	0.306118i
$803$	507.168	+	878.441i	0.631592	+	1.09395i
$804$			171.372i			0.213150i
$805$		0			0
$806$	12.5109			0.0155223
$807$	−25.1865	+	14.5415i	−0.0312101	+	0.0180191i
$808$	−87.8781	+	152.209i	−0.108760	+	0.188378i
$809$	−652.112	+	1129.49i	−0.806072	+	1.39616i	0.109493	+	0.993988i	$0.465077\pi$
$809$	−652.112	+	1129.49i	−0.806072	+	1.39616i	−0.915565	+	0.402170i	$0.868256\pi$
$810$		0			0
$811$		−	210.763i		−	0.259880i	−0.991522	−	0.129940i	$-0.958521\pi$
$811$		−	210.763i		−	0.259880i	0.991522	−	0.129940i	$-0.0414785\pi$
$812$	584.354	+	88.1861i	0.719648	+	0.108604i
$813$		−	640.291i		−	0.787566i
$814$	−305.523	−	529.181i	−0.375335	−	0.650099i
$815$		0			0
$816$	32.1857	−	55.7473i	0.0394433	−	0.0683178i
$817$	−103.357	−	179.020i	−0.126508	−	0.219119i
$818$	479.115			0.585716
$819$	−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	$0.687874\pi$
$822$	1.54726	−	2.67993i	0.00188231	−	0.00326026i
$823$	−386.279	−	223.018i	−0.469355	−	0.270982i	0.246615	−	0.969114i	$-0.420682\pi$
$823$	−386.279	−	223.018i	−0.469355	−	0.270982i	−0.715970	+	0.698131i	$0.754015\pi$
$824$	−435.867	+	251.648i	−0.528964	+	0.305398i
$825$		0			0
$826$	−209.158	−	533.212i	−0.253218	−	0.645535i
$827$		−	702.737i		−	0.849743i	−0.905254	−	0.424871i	$-0.860319\pi$
$827$		−	702.737i		−	0.849743i	0.905254	−	0.424871i	$-0.139681\pi$
$828$	−11.6928	+	6.75086i	−0.0141218	+	0.00815321i
$829$	361.023	+	208.437i	0.435492	+	0.251431i	0.701683	−	0.712489i	$-0.252432\pi$
$829$	361.023	+	208.437i	0.435492	+	0.251431i	−0.266192	+	0.963920i	$0.585765\pi$
$830$		0			0
$831$	−728.737	+	420.736i	−0.876940	+	0.506301i
$832$	−58.0805			−0.0698083
$833$	−101.145	−	443.892i	−0.121423	−	0.532883i
$834$	29.7189			0.0356342
$835$		0			0
$836$	−129.708	−	74.8867i	−0.155153	−	0.0895774i
$837$	5.48336	+	3.16582i	0.00655121	+	0.00378234i
$838$	261.286	+	452.560i	0.311797	+	0.540047i
$839$			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
$842$	266.469	−	153.846i	0.316472	−	0.182715i
$843$	311.972	−	540.351i	0.370073	−	0.640986i
$844$	151.187	−	261.864i	0.179132	−	0.310265i
$845$		0			0
$846$			242.211i			0.286301i
$847$	−134.820	+	168.996i	−0.159174	+	0.199523i
$848$		−	58.1607i		−	0.0685858i
$849$	−234.261	−	405.752i	−0.275926	−	0.477918i
$850$		0			0
$851$	39.4467	−	68.3236i	0.0463533	−	0.0802863i
$852$	−176.646	−	305.959i	−0.207331	−	0.359107i
$853$	988.948			1.15938			0.579688	−	0.814838i	$-0.303174\pi$
$853$	988.948			1.15938			0.579688	+	0.814838i	$0.303174\pi$
$854$	−57.3804	−	8.65939i	−0.0671902	−	0.0101398i
$855$		0			0
$856$	120.167	+	208.136i	0.140382	+	0.243149i
$857$	−180.649	+	312.893i	−0.210792	+	0.365103i	−0.951963	−	0.306214i	$-0.900938\pi$
$857$	−180.649	+	312.893i	−0.210792	+	0.365103i	0.741170	+	0.671317i	$0.234271\pi$
$858$	−189.803	−	109.583i	−0.221215	−	0.127719i
$859$	608.464	−	351.297i	0.708339	−	0.408960i	−0.102106	−	0.994773i	$-0.532558\pi$
$859$	608.464	−	351.297i	0.708339	−	0.408960i	0.810446	+	0.585814i	$0.199225\pi$
$860$		0			0
$861$	104.720	−	693.913i	0.121626	−	0.805939i
$862$			404.226i			0.468940i
$863$	−954.720	+	551.208i	−1.10628	+	0.638711i	−0.937863	−	0.347005i	$-0.887199\pi$
$863$	−954.720	+	551.208i	−1.10628	+	0.638711i	−0.168417	+	0.985716i	$0.553865\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	788.111	−	455.016i	0.910059	−	0.525423i
$867$	351.040			0.404891
$868$	13.3356	+	10.6388i	0.0153636	+	0.0122566i
$869$	−1376.68			−1.58421
$870$		0			0
$871$	−311.044	−	179.581i	−0.357111	−	0.206178i
$872$	−423.414	−	244.458i	−0.485567	−	0.280342i
$873$	92.1683	+	159.640i	0.105576	+	0.182864i
$874$		−	19.3376i		−	0.0221254i
$875$		0			0
$876$	−285.113			−0.325472
$877$	578.610	−	334.061i	0.659761	−	0.380913i	−0.132425	−	0.991193i	$-0.542276\pi$
$877$	578.610	−	334.061i	0.659761	−	0.380913i	0.792186	+	0.610280i	$0.208943\pi$
$878$	403.360	−	698.640i	0.459408	−	0.795717i
$879$	−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	$0.997221\pi$
$882$	−202.694	+	46.1859i	−0.229812	+	0.0523650i
$883$		−	51.0884i		−	0.0578577i	−0.999581	−	0.0289289i	$-0.990790\pi$
$883$		−	51.0884i		−	0.0578577i	0.999581	−	0.0289289i	$-0.00920962\pi$
$884$	67.4549	+	116.835i	0.0763064	+	0.132167i
$885$		0			0
$886$	−46.6796	+	80.8514i	−0.0526857	+	0.0912543i
$887$	15.2220	+	26.3653i	0.0171612	+	0.0297241i	0.874478	−	0.485064i	$-0.161204\pi$
$887$	15.2220	+	26.3653i	0.0171612	+	0.0297241i	−0.857317	+	0.514788i	$0.827870\pi$
$888$	171.755			0.193417
$889$	−1260.83	+	494.574i	−1.41825	+	0.556326i
$890$		0			0
$891$	−55.4585	−	96.0569i	−0.0622430	−	0.107808i
$892$	−308.586	+	534.486i	−0.345948	+	0.599200i
$893$	−300.426	−	173.451i	−0.336423	−	0.194234i
$894$	−614.600	+	354.840i	−0.687472	+	0.396912i
$895$		0			0
$896$	−61.9089	−	49.3891i	−0.0690948	−	0.0551218i
$897$		−	28.2969i		−	0.0315462i
$898$	630.832	−	364.211i	0.702485	−	0.405580i
$899$	44.5454	+	25.7183i	0.0495500	+	0.0286077i
$900$		0			0
$901$	−116.997	+	67.5480i	−0.129852	+	0.0749700i
$902$	1008.80			1.11841
$903$	61.5480	−	407.841i	0.0681595	−	0.451651i
$904$	−232.105			−0.256754
$905$		0			0
$906$	−248.838	−	143.666i	−0.274655	−	0.158572i
$907$	597.571	+	345.008i	0.658844	+	0.380384i	0.791836	−	0.610733i	$-0.209125\pi$
$907$	597.571	+	345.008i	0.658844	+	0.380384i	−0.132993	+	0.991117i	$0.542459\pi$
$908$	100.422	+	173.937i	0.110597	+	0.191560i
$909$		−	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	$0.546380\pi$
$912$	36.4587	−	21.0494i	0.0399766	−	0.0230805i
$913$	−564.590	+	977.899i	−0.618390	+	1.07108i
$914$	−55.8806	+	96.7881i	−0.0611385	+	0.105895i
$915$		0			0
$916$			639.993i			0.698682i
$917$	991.063	+	790.641i	1.08077	+	0.862204i
$918$			68.2762i			0.0743750i
$919$	269.068	+	466.039i	0.292783	+	0.507115i	0.974467	−	0.224532i	$-0.0720853\pi$
$919$	269.068	+	466.039i	0.292783	+	0.507115i	−0.681684	+	0.731647i	$0.738752\pi$
$920$		0			0
$921$	39.8729	−	69.0618i	0.0432930	−	0.0749857i
$922$	6.77632	+	11.7369i	0.00734959	+	0.0127299i
$923$	740.428			0.802198
$924$	−109.129	−	278.206i	−0.118105	−	0.301088i
$925$		0			0
$926$	−164.122	−	284.267i	−0.177237	−	0.306984i
$927$	266.913	−	462.306i	0.287932	−	0.498712i
$928$	−206.797	−	119.394i	−0.222841	−	0.128658i
$929$	770.069	−	444.600i	0.828922	−	0.478579i	−0.0245611	−	0.999698i	$-0.507819\pi$
$929$	770.069	−	444.600i	0.828922	−	0.478579i	0.853484	+	0.521120i	$0.174485\pi$
$930$		0			0
$931$	87.8657	−	284.486i	0.0943778	−	0.305570i
$932$			621.578i			0.666929i
$933$	−654.993	+	378.160i	−0.702029	+	0.405317i
$934$	−839.607	−	484.747i	−0.898937	−	0.519001i
$935$		0			0
$936$	53.3504	−	30.8019i	0.0569983	−	0.0329080i
$937$	997.355			1.06441			0.532206	−	0.846615i	$-0.321363\pi$
$937$	997.355			1.06441			0.532206	+	0.846615i	$0.321363\pi$
$938$	−178.838	−	455.916i	−0.190659	−	0.486051i
$939$	−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	$0.866930\pi$
$942$	−389.766	−	225.032i	−0.413764	−	0.238887i
$943$	65.1245	+	112.799i	0.0690609	+	0.119617i
$944$			231.433i			0.245162i
$945$		0			0
$946$	592.915			0.626760
$947$	508.878	−	293.801i	0.537358	−	0.310244i	−0.206650	−	0.978415i	$-0.566256\pi$
$947$	508.878	−	293.801i	0.537358	−	0.310244i	0.744008	+	0.668171i	$0.232923\pi$
$948$	193.481	−	335.118i	0.204093	−	0.353500i
$949$	298.770	−	517.485i	0.314826	−	0.545295i
$950$		0			0
$951$			2.37089i			0.00249305i
$952$	−27.4504	+	181.897i	−0.0288345	+	0.191068i
$953$		−	441.771i		−	0.463558i	−0.972768	−	0.231779i	$-0.925545\pi$
$953$		−	441.771i		−	0.463558i	0.972768	−	0.231779i	$-0.0744547\pi$
$954$	30.8444	+	53.4241i	0.0323316	+	0.0560001i
$955$		0			0
$956$	−136.263	+	236.015i	−0.142535	+	0.246877i
$957$	−450.531	−	780.342i	−0.470774	−	0.815404i
$958$	−889.684			−0.928688
$959$	−1.31962	+	8.74431i	−0.00137604	+	0.00911815i
$960$		0			0
$961$	−479.758	−	830.965i	−0.499227	−	0.864687i
$962$	−179.982	+	311.738i	−0.187091	+	0.324051i
$963$	−220.761	−	127.457i	−0.229243	−	0.132354i
$964$	668.883	−	386.179i	0.693862	−	0.400601i
$965$		0			0
$966$	24.0624	−	30.1621i	0.0249094	−	0.0312237i
$967$			1581.63i			1.63561i	0.575497	+	0.817804i	$0.304809\pi$
$967$			1581.63i			1.63561i	−0.575497	+	0.817804i	$0.695191\pi$
$968$	75.6492	−	43.6761i	0.0781500	−	0.0451199i
$969$	−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	$0.233866\pi$
$972$	31.1769			0.0320750
$973$	−79.0638	+	31.0136i	−0.0812577	+	0.0318742i
$974$	−705.365			−0.724194
$975$		0			0
$976$	20.3063	+	11.7239i	0.0208056	+	0.0120121i
$977$	183.114	+	105.721i	0.187425	+	0.108210i	0.590777	−	0.806835i	$-0.298821\pi$
$977$	183.114	+	105.721i	0.187425	+	0.108210i	−0.403351	+	0.915045i	$0.632155\pi$
$978$	−148.893	−	257.891i	−0.152243	−	0.263692i
$979$		−	1574.96i		−	1.60874i
$980$		0			0
$981$	518.575			0.528618
$982$	−204.022	+	117.792i	−0.207762	+	0.119951i
$983$	−296.422	+	513.418i	−0.301548	+	0.522297i	−0.976487	−	0.215577i	$-0.930837\pi$
$983$	−296.422	+	513.418i	−0.301548	+	0.522297i	0.674939	+	0.737874i	$0.264170\pi$
$984$	−141.779	+	245.569i	−0.144084	+	0.249562i
$985$		0			0
$986$			554.659i			0.562534i
$987$	−252.763	−	644.374i	−0.256092	−	0.652861i
$988$			88.2308i			0.0893024i
$989$	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	$0.105268\pi$
$992$	−3.44651	−	5.96953i	−0.00347430	−	0.00601767i
$993$	665.166			0.669855
$994$	789.233	+	629.628i	0.793997	+	0.633428i
$995$		0			0
$996$	−158.697	−	274.871i	−0.159334	−	0.275975i
$997$	−103.317	+	178.950i	−0.103628	+	0.179489i	−0.913177	−	0.407564i	$-0.866378\pi$
$997$	−103.317	+	178.950i	−0.103628	+	0.179489i	0.809549	+	0.587052i	$0.199712\pi$
$998$	−44.4658	−	25.6724i	−0.0445550	−	0.0257238i
$999$	−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.q.c.199.4		16
5.2	odd	4		1050.3.p.b.451.2		8
5.3	odd	4		210.3.o.a.31.3	✓	8
5.4	even	2	inner	1050.3.q.c.199.5		16
7.5	odd	6	inner	1050.3.q.c.649.5		16
15.8	even	4		630.3.v.b.451.2		8
35.3	even	12		1470.3.f.a.391.4		8
35.12	even	12		1050.3.p.b.901.2		8
35.18	odd	12		1470.3.f.a.391.1		8
35.19	odd	6	inner	1050.3.q.c.649.4		16
35.33	even	12		210.3.o.a.61.3	yes	8
105.68	odd	12		630.3.v.b.271.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.3	✓	8	5.3	odd	4
210.3.o.a.61.3	yes	8	35.33	even	12
630.3.v.b.271.2		8	105.68	odd	12
630.3.v.b.451.2		8	15.8	even	4
1050.3.p.b.451.2		8	5.2	odd	4
1050.3.p.b.901.2		8	35.12	even	12
1050.3.q.c.199.4		16	1.1	even	1	trivial
1050.3.q.c.199.5		16	5.4	even	2	inner
1050.3.q.c.649.4		16	35.19	odd	6	inner
1050.3.q.c.649.5		16	7.5	odd	6	inner
1470.3.f.a.391.1		8	35.18	odd	12
1470.3.f.a.391.4		8	35.3	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.55620 - 6.51658i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.55620 - 6.51658i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-6.16205 + 10.6730i) q^{11} +(-1.73205 - 3.00000i) q^{12} +7.26007 q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.64561 + 8.04643i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-5.26235 + 3.03822i) q^{19} +(-11.9886 - 1.80922i) q^{21} -17.4289i q^{22} +(1.94880 - 1.12514i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-8.89173 + 5.13364i) q^{26} -5.19615 q^{27} +(-13.8433 - 2.08911i) q^{28} -42.2122 q^{29} +(-1.05527 - 0.609262i) q^{31} +(4.89898 + 2.82843i) q^{32} +(10.6730 + 18.4862i) q^{33} -13.1398i q^{34} -6.00000 q^{36} +(30.3622 - 17.5296i) q^{37} +(4.29669 - 7.44209i) q^{38} +(6.28740 - 10.8901i) q^{39} +57.8811i q^{41} +(15.9623 - 6.26139i) q^{42} +34.0190i q^{43} +(12.3241 + 21.3460i) q^{44} +(-1.59119 + 2.75603i) q^{46} +(28.5448 + 49.4411i) q^{47} -6.92820 q^{48} +(-35.9317 + 33.3154i) q^{49} +(8.04643 + 13.9368i) q^{51} +(7.26007 - 12.5748i) q^{52} +(12.5922 + 7.27009i) q^{53} +(6.36396 - 3.67423i) q^{54} +(18.4317 - 7.23003i) q^{56} +10.5247i q^{57} +(51.6992 - 29.8485i) q^{58} +(-50.1067 - 28.9291i) q^{59} +(-5.07658 + 2.93096i) q^{61} +1.72325 q^{62} +(-13.0963 + 16.4161i) q^{63} -8.00000 q^{64} +(-26.1434 - 15.0939i) q^{66} +(-42.8431 - 24.7355i) q^{67} +(9.29122 + 16.0929i) q^{68} -3.89761i q^{69} +101.986 q^{71} +(7.34847 - 4.24264i) q^{72} +(41.1525 - 71.2783i) q^{73} +(-24.7906 + 42.9387i) q^{74} +12.1529i q^{76} +(85.3029 + 12.8732i) q^{77} +17.7835i q^{78} +(55.8530 + 96.7403i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-40.9281 - 70.8895i) q^{82} +91.6237 q^{83} +(-15.1223 + 18.9557i) q^{84} +(-24.0551 - 41.6646i) q^{86} +(-36.5568 + 63.3183i) q^{87} +(-30.1878 - 17.4289i) q^{88} +(-110.673 + 63.8973i) q^{89} +(-18.5582 - 47.3108i) q^{91} -4.50057i q^{92} +(-1.82779 + 1.05527i) q^{93} +(-69.9203 - 40.3685i) q^{94} +(8.48528 - 4.89898i) q^{96} -61.4455 q^{97} +(20.4496 - 66.2104i) q^{98} +36.9723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^9	\( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 80 q^{14} - 32 q^{16} - 216 q^{19} - 192 q^{26} - 144 q^{29} - 264 q^{31} - 96 q^{36} - 48 q^{39} + 16 q^{44} + 16 q^{46} - 312 q^{49} + 168 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 128 q^{64} - 144 q^{66} + 16 q^{71} + 32 q^{74} - 24 q^{79} - 72 q^{81} - 80 q^{86} - 984 q^{89} - 616 q^{91} - 960 q^{94} + 48 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 80 * q^14 - 32 * q^16 - 216 * q^19 - 192 * q^26 - 144 * q^29 - 264 * q^31 - 96 * q^36 - 48 * q^39 + 16 * q^44 + 16 * q^46 - 312 * q^49 + 168 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 128 * q^64 - 144 * q^66 + 16 * q^71 + 32 * q^74 - 24 * q^79 - 72 * q^81 - 80 * q^86 - 984 * q^89 - 616 * q^91 - 960 * q^94 + 48 * q^99

Introduction

L-functions

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