LMFDB - Embedded newform 1050.3.q.c.199.5

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			199.5
Root			$1.56290 + 0.418778i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.c.649.5

$q$-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	$-0.590080\pi$
$13$	−7.26007			−0.558467			−0.279233	+	0.960223i	$0.590080\pi$
$14$	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	−0.696426	−	0.717628i	$-0.745228\pi$
$17$	4.64561	−	8.04643i	0.273271	−	0.473319i	0.969697	+	0.244309i	$0.0785611\pi$
$18$	−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	−0.541767	−	0.840529i	$-0.682244\pi$
$23$	−1.94880	+	1.12514i	−0.0847306	+	0.0489192i	0.457036	+	0.889448i	$0.348911\pi$
$24$	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	−0.850623	−	0.525775i	$-0.823775\pi$
$37$	−30.3622	+	17.5296i	−0.820600	+	0.473774i	0.0300231	+	0.999549i	$0.490442\pi$
$38$	−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	$-0.870547\pi$
$43$		−	34.0190i		−	0.791140i	0.918436	−	0.395570i	$-0.129453\pi$
$44$	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	$-0.958904\pi$
$47$	−28.5448	−	49.4411i	−0.607337	−	1.05194i	0.384340	−	0.923191i	$-0.374429\pi$
$48$	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	0.376480	−	0.926425i	$-0.377134\pi$
$53$	−12.5922	−	7.27009i	−0.237588	−	0.137172i	−0.614068	+	0.789253i	$0.710468\pi$
$54$	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	0.784402	−	0.620252i	$-0.212970\pi$
$67$	42.8431	+	24.7355i	0.639449	+	0.369186i	−0.144953	+	0.989439i	$0.546303\pi$
$68$	−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	$0.357302\pi$
$73$	−41.1525	+	71.2783i	−0.563733	+	0.976415i	−0.997166	+	0.0752290i	$0.976031\pi$
$74$	−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	$-0.686116\pi$
$83$	−91.6237			−1.10390			−0.551950	+	0.833877i	$0.686116\pi$
$84$	−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	$-0.397415\pi$
$97$	61.4455			0.633459			0.316729	+	0.948516i	$0.397415\pi$
$98$	−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	$-0.834748\pi$
$103$	−88.9709	−	154.102i	−0.863795	−	1.49614i	0.00444312	−	0.999990i	$-0.498586\pi$
$104$			20.5346i			0.197448i
$105$		0			0
$106$	−20.5629			−0.193990
$107$	−73.5871	+	42.4855i	−0.687730	+	0.397061i	−0.802761	−	0.596301i	$-0.796637\pi$
$107$	−73.5871	+	42.4855i	−0.687730	+	0.397061i	0.115031	+	0.993362i	$0.463303\pi$
$108$	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	$-0.881717\pi$
$113$		−	82.0616i		−	0.726209i	0.931748	−	0.363105i	$-0.118283\pi$
$114$	−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	$0.275651\pi$
$127$			193.480i			1.52346i	−0.647892	+	0.761732i	$0.724349\pi$
$128$	−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	0.503988	−	0.863711i	$-0.331866\pi$
$137$	1.09408	+	0.631666i	0.00798597	+	0.00461070i	−0.496002	+	0.868322i	$0.665199\pi$
$138$	−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	$-0.634368\pi$
$157$	91.8687	−	159.121i	0.585151	−	1.01351i	0.994857	−	0.101294i	$-0.0322982\pi$
$158$	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	−0.140977	−	0.990013i	$-0.545024\pi$
$163$	105.283	−	60.7854i	0.645911	−	0.372917i	0.786888	+	0.617096i	$0.211691\pi$
$164$	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	$-0.408539\pi$
$167$	94.6539			0.566790			0.283395	+	0.959003i	$0.408539\pi$
$168$	−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	$-0.895057\pi$
$173$	−130.346	−	225.766i	−0.753445	−	1.30501i	0.192699	−	0.981258i	$-0.438276\pi$
$174$		−	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	0.917129	−	0.398591i	$-0.130501\pi$
$193$	198.887	+	114.828i	1.03050	+	0.594961i	0.113374	+	0.993552i	$0.463834\pi$
$194$	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	$-0.803579\pi$
$197$		−	227.989i		−	1.15730i	0.815574	−	0.578652i	$-0.196421\pi$
$198$	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	$-0.256776\pi$
$223$	308.586			1.38379			0.691896	+	0.721997i	$0.256776\pi$
$224$	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	−0.733976	−	0.679175i	$-0.762338\pi$
$227$	50.2112	−	86.9683i	0.221195	−	0.383120i	0.955171	+	0.296055i	$0.0956711\pi$
$228$	−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	0.205017	−	0.978758i	$-0.434275\pi$
$233$	269.151	−	155.395i	1.15516	−	0.666929i	0.950138	+	0.311829i	$0.100942\pi$
$234$	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	0.844752	−	0.535159i	$-0.179748\pi$
$257$	−10.5589	−	18.2886i	−0.0410852	−	0.0711617i	−0.885837	+	0.463997i	$0.846415\pi$
$258$	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	0.971703	−	0.236205i	$-0.0759038\pi$
$263$	329.538	+	190.259i	1.25299	+	0.723417i	0.281292	+	0.959622i	$0.409237\pi$
$264$	−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	$0.00708542\pi$
$277$	420.736	+	242.912i	1.51890	+	0.876940i	0.519152	+	0.854682i	$0.326248\pi$
$278$	−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	−0.999680	−	0.0253131i	$-0.991942\pi$
$283$	−135.251	+	234.261i	−0.477918	+	0.827778i	0.521762	+	0.853091i	$0.325275\pi$
$284$	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	$-0.494768\pi$
$293$	9.63230			0.0328747			0.0164374	+	0.999865i	$0.494768\pi$
$294$	−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	$-0.523891\pi$
$307$	−46.0412			−0.149971			−0.0749857	+	0.997185i	$0.523891\pi$
$308$	−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	0.998839	−	0.0481706i	$-0.0153391\pi$
$313$	143.261	+	248.135i	0.457703	+	0.792764i	−0.541137	+	0.840935i	$0.682006\pi$
$314$		−	259.844i		−	0.827529i
$315$		0			0
$316$	223.412			0.707001
$317$	1.18545	−	0.684418i	0.00373958	−	0.00215905i	−0.498129	−	0.867103i	$-0.665979\pi$
$317$	1.18545	−	0.684418i	0.00373958	−	0.00215905i	0.501869	+	0.864944i	$0.332646\pi$
$318$	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	$0.0675436\pi$
$337$			141.948i			0.421211i	−0.977571	+	0.210606i	$0.932456\pi$
$338$	−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	0.153926	−	0.988082i	$-0.450808\pi$
$347$	−216.811	−	125.176i	−0.624815	−	0.360737i	−0.778741	+	0.627345i	$0.784142\pi$
$348$	−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	−0.948985	−	0.315322i	$-0.897887\pi$
$353$	−71.0997	+	123.148i	−0.201416	+	0.348862i	0.747569	+	0.664184i	$0.231221\pi$
$354$	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	$0.413090\pi$
$367$	−256.576	+	444.403i	−0.699117	+	1.21091i	−0.968773	+	0.247950i	$0.920243\pi$
$368$	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	−0.999380	−	0.0352027i	$-0.988792\pi$
$373$	−547.782	+	316.262i	−1.46858	+	0.847887i	−0.469204	+	0.883090i	$0.655459\pi$
$374$	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	0.956943	−	0.290276i	$-0.0937472\pi$
$383$	86.9735	+	150.642i	0.227085	+	0.393322i	−0.729858	+	0.683599i	$0.760414\pi$
$384$		−	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	$0.000787951\pi$
$397$	199.350	+	345.285i	0.502142	+	0.869736i	−0.497855	+	0.867260i	$0.665879\pi$
$398$	−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	$-0.233374\pi$
$433$	643.490			1.48612			0.743060	+	0.669224i	$0.233374\pi$
$434$	−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	−0.563137	−	0.826364i	$-0.690406\pi$
$443$	−57.1705	+	33.0074i	−0.129053	+	0.0745089i	0.434084	+	0.900873i	$0.357072\pi$
$444$	−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	−0.573007	−	0.819551i	$-0.694223\pi$
$457$	−68.4395	+	39.5136i	−0.149758	+	0.0864629i	0.423248	+	0.906014i	$0.360890\pi$
$458$	−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	$-0.919355\pi$
$463$		−	232.103i		−	0.501303i	0.968077	−	0.250652i	$-0.0806449\pi$
$464$	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	$-0.904328\pi$
$467$	−342.768	−	593.692i	−0.733979	−	1.27129i	0.221191	−	0.975230i	$-0.429006\pi$
$468$	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	−0.0140085	−	0.999902i	$-0.504459\pi$
$487$	−431.946	−	249.384i	−0.886953	−	0.512083i	−0.872945	+	0.487819i	$0.837793\pi$
$488$	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	$-0.282582\pi$
$503$	634.940			1.26231			0.631153	+	0.775658i	$0.282582\pi$
$504$	−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	0.997188	−	0.0749389i	$-0.0238762\pi$
$523$	226.823	+	392.868i	0.433695	+	0.751182i	−0.563493	+	0.826121i	$0.690543\pi$
$524$			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	$-0.854996\pi$
$547$		−	481.306i		−	0.879901i	0.898022	−	0.439950i	$-0.145004\pi$
$548$	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	0.582199	−	0.813046i	$-0.302192\pi$
$557$	94.2333	+	54.4056i	0.169180	+	0.0976762i	−0.413019	+	0.910722i	$0.635526\pi$
$558$	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	$0.346283\pi$
$563$	−301.097	+	521.516i	−0.534809	+	0.926316i	−0.999173	+	0.0406717i	$0.987050\pi$
$564$	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	−0.998646	−	0.0520155i	$-0.983435\pi$
$577$	−262.117	+	454.001i	−0.454276	+	0.786830i	0.544370	+	0.838845i	$0.316769\pi$
$578$	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	$-0.312799\pi$
$587$	651.322			1.10958			0.554789	+	0.831991i	$0.312799\pi$
$588$	−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	$-0.963905\pi$
$593$	−352.706	−	610.904i	−0.594782	−	1.03019i	0.398796	−	0.917040i	$-0.369428\pi$
$594$			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	$-0.935353\pi$
$607$	−403.291	−	698.521i	−0.664401	−	1.15078i	0.315047	−	0.949076i	$-0.397980\pi$
$608$	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	0.942014	−	0.335574i	$-0.108930\pi$
$613$	688.035	+	397.237i	1.12241	+	0.648021i	0.180392	+	0.983595i	$0.442263\pi$
$614$	−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	$-0.971851\pi$
$617$		−	108.982i		−	0.176633i	0.996092	−	0.0883164i	$-0.0281487\pi$
$618$	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	$-0.725224\pi$
$643$	−835.879			−1.29997			−0.649984	+	0.759948i	$0.725224\pi$
$644$	−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	−0.997679	−	0.0680932i	$-0.978308\pi$
$647$	−284.595	+	492.933i	−0.439869	+	0.761876i	0.557810	+	0.829969i	$0.311642\pi$
$648$	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	−0.216751	−	0.976227i	$-0.569546\pi$
$653$	339.763	−	196.162i	0.520311	−	0.300402i	0.737062	+	0.675825i	$0.236213\pi$
$654$	−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	$-0.846407\pi$
$673$		−	624.569i		−	0.928038i	0.885825	−	0.464019i	$-0.153593\pi$
$674$	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	$0.0291957\pi$
$677$	390.778	+	676.847i	0.577220	+	0.999774i	−0.418577	+	0.908181i	$0.637471\pi$
$678$	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	0.434133	−	0.900849i	$-0.357055\pi$
$683$	−88.0791	−	50.8525i	−0.128959	−	0.0744546i	−0.563092	+	0.826394i	$0.690388\pi$
$684$	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	$-0.502960\pi$
$727$	−13.5224			−0.0186003			−0.00930013	+	0.999957i	$0.502960\pi$
$728$	−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	0.968624	−	0.248529i	$-0.0799472\pi$
$733$	197.235	+	341.622i	0.269080	+	0.466060i	−0.699545	+	0.714589i	$0.746614\pi$
$734$			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	$0.0925241\pi$
$743$			425.883i			0.573194i	−0.958051	+	0.286597i	$0.907476\pi$
$744$	−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	$-0.801816\pi$
$757$		−	882.903i		−	1.16632i	0.812358	−	0.583159i	$-0.198184\pi$
$758$	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	$0.479494\pi$
$773$	−643.167	+	1114.00i	−0.832041	+	1.44114i	−0.896417	+	0.443211i	$0.853839\pi$
$774$	−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	$0.385139\pi$
$787$	−498.736	+	863.836i	−0.633718	+	1.09763i	−0.986785	+	0.162034i	$0.948195\pi$
$788$	−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	$-0.291369\pi$
$797$	971.547			1.21901			0.609503	+	0.792784i	$0.291369\pi$
$798$	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	0.715970	−	0.698131i	$-0.245985\pi$
$823$	386.279	+	223.018i	0.469355	+	0.270982i	−0.246615	+	0.969114i	$0.579318\pi$
$824$	−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	$0.139681\pi$
$827$			702.737i			0.849743i	−0.905254	+	0.424871i	$0.860319\pi$
$828$	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	$-0.696826\pi$
$853$	−988.948			−1.15938			−0.579688	+	0.814838i	$0.696826\pi$
$854$	−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	−0.741170	−	0.671317i	$-0.765729\pi$
$857$	180.649	−	312.893i	0.210792	−	0.365103i	0.951963	+	0.306214i	$0.0990623\pi$
$858$	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	0.168417	−	0.985716i	$-0.446135\pi$
$863$	954.720	−	551.208i	1.10628	−	0.638711i	0.937863	+	0.347005i	$0.112801\pi$
$864$	−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	−0.792186	−	0.610280i	$-0.791057\pi$
$877$	−578.610	+	334.061i	−0.659761	+	0.380913i	0.132425	+	0.991193i	$0.457724\pi$
$878$	−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	$0.00920962\pi$
$883$			51.0884i			0.0578577i	−0.999581	+	0.0289289i	$0.990790\pi$
$884$	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	0.857317	−	0.514788i	$-0.172130\pi$
$887$	−15.2220	−	26.3653i	−0.0171612	−	0.0297241i	−0.874478	+	0.485064i	$0.838796\pi$
$888$	−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	0.132993	−	0.991117i	$-0.457541\pi$
$907$	−597.571	−	345.008i	−0.658844	−	0.380384i	−0.791836	+	0.610733i	$0.790875\pi$
$908$	−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	$-0.678637\pi$
$937$	−997.355			−1.06441			−0.532206	+	0.846615i	$0.678637\pi$
$938$	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	−0.744008	−	0.668171i	$-0.767077\pi$
$947$	−508.878	+	293.801i	−0.537358	+	0.310244i	0.206650	+	0.978415i	$0.433744\pi$
$948$	−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	$0.0744547\pi$
$953$			441.771i			0.463558i	−0.972768	+	0.231779i	$0.925545\pi$
$954$	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	$-0.695191\pi$
$967$		−	1581.63i		−	1.63561i	0.575497	−	0.817804i	$-0.304809\pi$
$968$	−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	0.403351	−	0.915045i	$-0.367845\pi$
$977$	−183.114	−	105.721i	−0.187425	−	0.108210i	−0.590777	+	0.806835i	$0.701179\pi$
$978$	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	−0.674939	−	0.737874i	$-0.735830\pi$
$983$	296.422	−	513.418i	0.301548	−	0.522297i	0.976487	+	0.215577i	$0.0691633\pi$
$984$	−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	−0.809549	−	0.587052i	$-0.800288\pi$
$997$	103.317	−	178.950i	0.103628	−	0.179489i	0.913177	+	0.407564i	$0.133622\pi$
$998$	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.199.5		16
5.2	odd	4		210.3.o.a.31.3	✓	8
5.3	odd	4		1050.3.p.b.451.2		8
5.4	even	2	inner	1050.3.q.c.199.4		16
7.5	odd	6	inner	1050.3.q.c.649.4		16
15.2	even	4		630.3.v.b.451.2		8
35.12	even	12		210.3.o.a.61.3	yes	8
35.17	even	12		1470.3.f.a.391.4		8
35.19	odd	6	inner	1050.3.q.c.649.5		16
35.32	odd	12		1470.3.f.a.391.1		8
35.33	even	12		1050.3.p.b.901.2		8
105.47	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	5.2	odd	4
210.3.o.a.61.3	yes	8	35.12	even	12
630.3.v.b.271.2		8	105.47	odd	12
630.3.v.b.451.2		8	15.2	even	4
1050.3.p.b.451.2		8	5.3	odd	4
1050.3.p.b.901.2		8	35.33	even	12
1050.3.q.c.199.4		16	5.4	even	2	inner
1050.3.q.c.199.5		16	1.1	even	1	trivial
1050.3.q.c.649.4		16	7.5	odd	6	inner
1050.3.q.c.649.5		16	35.19	odd	6	inner
1470.3.f.a.391.1		8	35.32	odd	12
1470.3.f.a.391.4		8	35.17	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

Modular forms

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