LMFDB - Embedded newform 950.2.b.f.799.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.b (of order $2$, degree $1$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.4
Root			$1.56155i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.f.799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.56155i q^{3} -1.00000 q^{4} -1.56155 q^{6} -1.56155i q^{7} -1.00000i q^{8} +0.561553 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.56155i q^{3} -1.00000 q^{4} -1.56155 q^{6} -1.56155i q^{7} -1.00000i q^{8} +0.561553 q^{9} +4.00000 q^{11} -1.56155i q^{12} -6.68466i q^{13} +1.56155 q^{14} +1.00000 q^{16} -7.56155i q^{17} +0.561553i q^{18} +1.00000 q^{19} +2.43845 q^{21} +4.00000i q^{22} -4.68466i q^{23} +1.56155 q^{24} +6.68466 q^{26} +5.56155i q^{27} +1.56155i q^{28} -6.68466 q^{29} +3.12311 q^{31} +1.00000i q^{32} +6.24621i q^{33} +7.56155 q^{34} -0.561553 q^{36} +6.00000i q^{37} +1.00000i q^{38} +10.4384 q^{39} -4.24621 q^{41} +2.43845i q^{42} -11.1231i q^{43} -4.00000 q^{44} +4.68466 q^{46} +10.2462i q^{47} +1.56155i q^{48} +4.56155 q^{49} +11.8078 q^{51} +6.68466i q^{52} -0.438447i q^{53} -5.56155 q^{54} -1.56155 q^{56} +1.56155i q^{57} -6.68466i q^{58} +1.56155 q^{59} +2.87689 q^{61} +3.12311i q^{62} -0.876894i q^{63} -1.00000 q^{64} -6.24621 q^{66} -1.56155i q^{67} +7.56155i q^{68} +7.31534 q^{69} -6.24621 q^{71} -0.561553i q^{72} +10.6847i q^{73} -6.00000 q^{74} -1.00000 q^{76} -6.24621i q^{77} +10.4384i q^{78} -3.12311 q^{79} -7.00000 q^{81} -4.24621i q^{82} +11.1231i q^{83} -2.43845 q^{84} +11.1231 q^{86} -10.4384i q^{87} -4.00000i q^{88} -2.00000 q^{89} -10.4384 q^{91} +4.68466i q^{92} +4.87689i q^{93} -10.2462 q^{94} -1.56155 q^{96} -6.00000i q^{97} +4.56155i q^{98} +2.24621 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{6} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^6 - 6 * q^9	$ 4 q - 4 q^{4} + 2 q^{6} - 6 q^{9} + 16 q^{11} - 2 q^{14} + 4 q^{16} + 4 q^{19} + 18 q^{21} - 2 q^{24} + 2 q^{26} - 2 q^{29} - 4 q^{31} + 22 q^{34} + 6 q^{36} + 50 q^{39} + 16 q^{41} - 16 q^{44} - 6 q^{46} + 10 q^{49} + 6 q^{51} - 14 q^{54} + 2 q^{56} - 2 q^{59} + 28 q^{61} - 4 q^{64} + 8 q^{66} + 54 q^{69} + 8 q^{71} - 24 q^{74} - 4 q^{76} + 4 q^{79} - 28 q^{81} - 18 q^{84} + 28 q^{86} - 8 q^{89} - 50 q^{91} - 8 q^{94} + 2 q^{96} - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^6 - 6 * q^9 + 16 * q^11 - 2 * q^14 + 4 * q^16 + 4 * q^19 + 18 * q^21 - 2 * q^24 + 2 * q^26 - 2 * q^29 - 4 * q^31 + 22 * q^34 + 6 * q^36 + 50 * q^39 + 16 * q^41 - 16 * q^44 - 6 * q^46 + 10 * q^49 + 6 * q^51 - 14 * q^54 + 2 * q^56 - 2 * q^59 + 28 * q^61 - 4 * q^64 + 8 * q^66 + 54 * q^69 + 8 * q^71 - 24 * q^74 - 4 * q^76 + 4 * q^79 - 28 * q^81 - 18 * q^84 + 28 * q^86 - 8 * q^89 - 50 * q^91 - 8 * q^94 + 2 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.56155i	0.901563i	0.892634	+	0.450781i	$0.148855\pi$
$3$	1.56155i	0.901563i	−0.892634	+	0.450781i	$0.851145\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.56155	−0.637501
$7$	− 1.56155i	− 0.590211i	−0.955465	−	0.295106i	$-0.904645\pi$
$7$	− 1.56155i	− 0.590211i	0.955465	−	0.295106i	$-0.0953549\pi$
$8$	− 1.00000i	− 0.353553i
$9$	0.561553	0.187184
$10$	0	0
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	− 1.56155i	− 0.450781i
$13$	− 6.68466i	− 1.85399i	−0.375073	−	0.926995i	$-0.622382\pi$
$13$	− 6.68466i	− 1.85399i	0.375073	−	0.926995i	$-0.377618\pi$
$14$	1.56155	0.417343
$15$	0	0
$16$	1.00000	0.250000
$17$	− 7.56155i	− 1.83395i	−0.398949	−	0.916973i	$-0.630625\pi$
$17$	− 7.56155i	− 1.83395i	0.398949	−	0.916973i	$-0.369375\pi$
$18$	0.561553i	0.132359i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	2.43845	0.532113
$22$	4.00000i	0.852803i
$23$	− 4.68466i	− 0.976819i	−0.872615	−	0.488409i	$-0.837577\pi$
$23$	− 4.68466i	− 0.976819i	0.872615	−	0.488409i	$-0.162423\pi$
$24$	1.56155	0.318751
$25$	0	0
$26$	6.68466	1.31097
$27$	5.56155i	1.07032i
$28$	1.56155i	0.295106i
$29$	−6.68466	−1.24131	−0.620655	−	0.784084i	$-0.713133\pi$
$29$	−6.68466	−1.24131	−0.620655	+	0.784084i	$0.713133\pi$
$30$	0	0
$31$	3.12311	0.560926	0.280463	−	0.959865i	$-0.409512\pi$
$31$	3.12311	0.560926	0.280463	+	0.959865i	$0.409512\pi$
$32$	1.00000i	0.176777i
$33$	6.24621i	1.08733i
$34$	7.56155	1.29680
$35$	0	0
$36$	−0.561553	−0.0935921
$37$	6.00000i	0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$37$	6.00000i	0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$38$	1.00000i	0.162221i
$39$	10.4384	1.67149
$40$	0	0
$41$	−4.24621	−0.663147	−0.331573	−	0.943429i	$-0.607579\pi$
$41$	−4.24621	−0.663147	−0.331573	+	0.943429i	$0.607579\pi$
$42$	2.43845i	0.376261i
$43$	− 11.1231i	− 1.69626i	−0.529790	−	0.848129i	$-0.677729\pi$
$43$	− 11.1231i	− 1.69626i	0.529790	−	0.848129i	$-0.322271\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	4.68466	0.690715
$47$	10.2462i	1.49456i	0.664507	+	0.747282i	$0.268641\pi$
$47$	10.2462i	1.49456i	−0.664507	+	0.747282i	$0.731359\pi$
$48$	1.56155i	0.225391i
$49$	4.56155	0.651650
$50$	0	0
$51$	11.8078	1.65342
$52$	6.68466i	0.926995i
$53$	− 0.438447i	− 0.0602254i	−0.999547	−	0.0301127i	$-0.990413\pi$
$53$	− 0.438447i	− 0.0602254i	0.999547	−	0.0301127i	$-0.00958661\pi$
$54$	−5.56155	−0.756831
$55$	0	0
$56$	−1.56155	−0.208671
$57$	1.56155i	0.206833i
$58$	− 6.68466i	− 0.877739i
$59$	1.56155	0.203297	0.101648	−	0.994820i	$-0.467588\pi$
$59$	1.56155	0.203297	0.101648	+	0.994820i	$0.467588\pi$
$60$	0	0
$61$	2.87689	0.368349	0.184174	−	0.982894i	$-0.441039\pi$
$61$	2.87689	0.368349	0.184174	+	0.982894i	$0.441039\pi$
$62$	3.12311i	0.396635i
$63$	− 0.876894i	− 0.110478i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−6.24621	−0.768855
$67$	− 1.56155i	− 0.190774i	−0.995440	−	0.0953870i	$-0.969591\pi$
$67$	− 1.56155i	− 0.190774i	0.995440	−	0.0953870i	$-0.0304089\pi$
$68$	7.56155i	0.916973i
$69$	7.31534	0.880664
$70$	0	0
$71$	−6.24621	−0.741289	−0.370644	−	0.928775i	$-0.620863\pi$
$71$	−6.24621	−0.741289	−0.370644	+	0.928775i	$0.620863\pi$
$72$	− 0.561553i	− 0.0661796i
$73$	10.6847i	1.25054i	0.780407	+	0.625272i	$0.215012\pi$
$73$	10.6847i	1.25054i	−0.780407	+	0.625272i	$0.784988\pi$
$74$	−6.00000	−0.697486
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 6.24621i	− 0.711822i
$78$	10.4384i	1.18192i
$79$	−3.12311	−0.351377	−0.175688	−	0.984446i	$-0.556215\pi$
$79$	−3.12311	−0.351377	−0.175688	+	0.984446i	$0.556215\pi$
$80$	0	0
$81$	−7.00000	−0.777778
$82$	− 4.24621i	− 0.468916i
$83$	11.1231i	1.22092i	0.792047	+	0.610460i	$0.209015\pi$
$83$	11.1231i	1.22092i	−0.792047	+	0.610460i	$0.790985\pi$
$84$	−2.43845	−0.266056
$85$	0	0
$86$	11.1231	1.19944
$87$	− 10.4384i	− 1.11912i
$88$	− 4.00000i	− 0.426401i
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	−10.4384	−1.09425
$92$	4.68466i	0.488409i
$93$	4.87689i	0.505710i
$94$	−10.2462	−1.05682
$95$	0	0
$96$	−1.56155	−0.159375
$97$	− 6.00000i	− 0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$97$	− 6.00000i	− 0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$98$	4.56155i	0.460786i
$99$	2.24621	0.225753
$100$	0	0
$101$	7.36932	0.733274	0.366637	−	0.930364i	$-0.380509\pi$
$101$	7.36932	0.733274	0.366637	+	0.930364i	$0.380509\pi$
$102$	11.8078i	1.16914i
$103$	− 14.2462i	− 1.40372i	−0.712314	−	0.701860i	$-0.752353\pi$
$103$	− 14.2462i	− 1.40372i	0.712314	−	0.701860i	$-0.247647\pi$
$104$	−6.68466	−0.655485
$105$	0	0
$106$	0.438447	0.0425858
$107$	9.56155i	0.924350i	0.886789	+	0.462175i	$0.152931\pi$
$107$	9.56155i	0.924350i	−0.886789	+	0.462175i	$0.847069\pi$
$108$	− 5.56155i	− 0.535161i
$109$	−3.56155	−0.341135	−0.170567	−	0.985346i	$-0.554560\pi$
$109$	−3.56155	−0.341135	−0.170567	+	0.985346i	$0.554560\pi$
$110$	0	0
$111$	−9.36932	−0.889296
$112$	− 1.56155i	− 0.147553i
$113$	17.1231i	1.61081i	0.592727	+	0.805403i	$0.298051\pi$
$113$	17.1231i	1.61081i	−0.592727	+	0.805403i	$0.701949\pi$
$114$	−1.56155	−0.146253
$115$	0	0
$116$	6.68466	0.620655
$117$	− 3.75379i	− 0.347038i
$118$	1.56155i	0.143753i
$119$	−11.8078	−1.08242
$120$	0	0
$121$	5.00000	0.454545
$122$	2.87689i	0.260462i
$123$	− 6.63068i	− 0.597869i
$124$	−3.12311	−0.280463
$125$	0	0
$126$	0.876894	0.0781200
$127$	− 4.87689i	− 0.432754i	−0.976310	−	0.216377i	$-0.930576\pi$
$127$	− 4.87689i	− 0.432754i	0.976310	−	0.216377i	$-0.0694241\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	17.3693	1.52928
$130$	0	0
$131$	16.4924	1.44095	0.720475	−	0.693481i	$-0.243924\pi$
$131$	16.4924	1.44095	0.720475	+	0.693481i	$0.243924\pi$
$132$	− 6.24621i	− 0.543663i
$133$	− 1.56155i	− 0.135404i
$134$	1.56155	0.134898
$135$	0	0
$136$	−7.56155	−0.648398
$137$	− 5.80776i	− 0.496191i	−0.968736	−	0.248095i	$-0.920195\pi$
$137$	− 5.80776i	− 0.496191i	0.968736	−	0.248095i	$-0.0798046\pi$
$138$	7.31534i	0.622723i
$139$	16.4924	1.39887	0.699435	−	0.714697i	$-0.253435\pi$
$139$	16.4924	1.39887	0.699435	+	0.714697i	$0.253435\pi$
$140$	0	0
$141$	−16.0000	−1.34744
$142$	− 6.24621i	− 0.524170i
$143$	− 26.7386i	− 2.23600i
$144$	0.561553	0.0467961
$145$	0	0
$146$	−10.6847	−0.884269
$147$	7.12311i	0.587504i
$148$	− 6.00000i	− 0.493197i
$149$	11.3693	0.931411	0.465705	−	0.884940i	$-0.345801\pi$
$149$	11.3693	0.931411	0.465705	+	0.884940i	$0.345801\pi$
$150$	0	0
$151$	−3.12311	−0.254155	−0.127077	−	0.991893i	$-0.540560\pi$
$151$	−3.12311	−0.254155	−0.127077	+	0.991893i	$0.540560\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	− 4.24621i	− 0.343286i
$154$	6.24621	0.503334
$155$	0	0
$156$	−10.4384	−0.835745
$157$	3.75379i	0.299585i	0.988717	+	0.149792i	$0.0478606\pi$
$157$	3.75379i	0.299585i	−0.988717	+	0.149792i	$0.952139\pi$
$158$	− 3.12311i	− 0.248461i
$159$	0.684658	0.0542969
$160$	0	0
$161$	−7.31534	−0.576530
$162$	− 7.00000i	− 0.549972i
$163$	9.36932i	0.733862i	0.930248	+	0.366931i	$0.119591\pi$
$163$	9.36932i	0.733862i	−0.930248	+	0.366931i	$0.880409\pi$
$164$	4.24621	0.331573
$165$	0	0
$166$	−11.1231	−0.863320
$167$	− 17.3693i	− 1.34408i	−0.740516	−	0.672039i	$-0.765419\pi$
$167$	− 17.3693i	− 1.34408i	0.740516	−	0.672039i	$-0.234581\pi$
$168$	− 2.43845i	− 0.188130i
$169$	−31.6847	−2.43728
$170$	0	0
$171$	0.561553	0.0429430
$172$	11.1231i	0.848129i
$173$	3.75379i	0.285395i	0.989766	+	0.142698i	$0.0455777\pi$
$173$	3.75379i	0.285395i	−0.989766	+	0.142698i	$0.954422\pi$
$174$	10.4384	0.791337
$175$	0	0
$176$	4.00000	0.301511
$177$	2.43845i	0.183285i
$178$	− 2.00000i	− 0.149906i
$179$	5.75379	0.430058	0.215029	−	0.976608i	$-0.431015\pi$
$179$	5.75379	0.430058	0.215029	+	0.976608i	$0.431015\pi$
$180$	0	0
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	− 10.4384i	− 0.773749i
$183$	4.49242i	0.332089i
$184$	−4.68466	−0.345358
$185$	0	0
$186$	−4.87689	−0.357591
$187$	− 30.2462i	− 2.21182i
$188$	− 10.2462i	− 0.747282i
$189$	8.68466	0.631716
$190$	0	0
$191$	8.68466	0.628400	0.314200	−	0.949357i	$-0.398264\pi$
$191$	8.68466	0.628400	0.314200	+	0.949357i	$0.398264\pi$
$192$	− 1.56155i	− 0.112695i
$193$	18.4924i	1.33111i	0.746347	+	0.665557i	$0.231806\pi$
$193$	18.4924i	1.33111i	−0.746347	+	0.665557i	$0.768194\pi$
$194$	6.00000	0.430775
$195$	0	0
$196$	−4.56155	−0.325825
$197$	3.75379i	0.267446i	0.991019	+	0.133723i	$0.0426933\pi$
$197$	3.75379i	0.267446i	−0.991019	+	0.133723i	$0.957307\pi$
$198$	2.24621i	0.159631i
$199$	3.80776	0.269925	0.134963	−	0.990851i	$-0.456909\pi$
$199$	3.80776	0.269925	0.134963	+	0.990851i	$0.456909\pi$
$200$	0	0
$201$	2.43845	0.171995
$202$	7.36932i	0.518503i
$203$	10.4384i	0.732635i
$204$	−11.8078	−0.826709
$205$	0	0
$206$	14.2462	0.992581
$207$	− 2.63068i	− 0.182845i
$208$	− 6.68466i	− 0.463498i
$209$	4.00000	0.276686
$210$	0	0
$211$	20.6847	1.42399	0.711995	−	0.702184i	$-0.247792\pi$
$211$	20.6847	1.42399	0.711995	+	0.702184i	$0.247792\pi$
$212$	0.438447i	0.0301127i
$213$	− 9.75379i	− 0.668319i
$214$	−9.56155	−0.653614
$215$	0	0
$216$	5.56155	0.378416
$217$	− 4.87689i	− 0.331065i
$218$	− 3.56155i	− 0.241219i
$219$	−16.6847	−1.12744
$220$	0	0
$221$	−50.5464	−3.40012
$222$	− 9.36932i	− 0.628827i
$223$	1.36932i	0.0916962i	0.998948	+	0.0458481i	$0.0145990\pi$
$223$	1.36932i	0.0916962i	−0.998948	+	0.0458481i	$0.985401\pi$
$224$	1.56155	0.104336
$225$	0	0
$226$	−17.1231	−1.13901
$227$	2.93087i	0.194529i	0.995259	+	0.0972643i	$0.0310092\pi$
$227$	2.93087i	0.194529i	−0.995259	+	0.0972643i	$0.968991\pi$
$228$	− 1.56155i	− 0.103416i
$229$	−18.4924	−1.22201	−0.611007	−	0.791625i	$-0.709235\pi$
$229$	−18.4924	−1.22201	−0.611007	+	0.791625i	$0.709235\pi$
$230$	0	0
$231$	9.75379	0.641752
$232$	6.68466i	0.438869i
$233$	10.0000i	0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$	10.0000i	0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	3.75379	0.245393
$235$	0	0
$236$	−1.56155	−0.101648
$237$	− 4.87689i	− 0.316788i
$238$	− 11.8078i	− 0.765384i
$239$	5.56155	0.359747	0.179873	−	0.983690i	$-0.442431\pi$
$239$	5.56155	0.359747	0.179873	+	0.983690i	$0.442431\pi$
$240$	0	0
$241$	14.8769	0.958305	0.479153	−	0.877732i	$-0.340944\pi$
$241$	14.8769	0.958305	0.479153	+	0.877732i	$0.340944\pi$
$242$	5.00000i	0.321412i
$243$	5.75379i	0.369106i
$244$	−2.87689	−0.184174
$245$	0	0
$246$	6.63068	0.422757
$247$	− 6.68466i	− 0.425335i
$248$	− 3.12311i	− 0.198317i
$249$	−17.3693	−1.10074
$250$	0	0
$251$	−10.2462	−0.646735	−0.323368	−	0.946273i	$-0.604815\pi$
$251$	−10.2462	−0.646735	−0.323368	+	0.946273i	$0.604815\pi$
$252$	0.876894i	0.0552392i
$253$	− 18.7386i	− 1.17809i
$254$	4.87689	0.306004
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 14.0000i	− 0.873296i	−0.899632	−	0.436648i	$-0.856166\pi$
$257$	− 14.0000i	− 0.873296i	0.899632	−	0.436648i	$-0.143834\pi$
$258$	17.3693i	1.08137i
$259$	9.36932	0.582181
$260$	0	0
$261$	−3.75379	−0.232354
$262$	16.4924i	1.01891i
$263$	− 5.75379i	− 0.354794i	−0.984139	−	0.177397i	$-0.943232\pi$
$263$	− 5.75379i	− 0.354794i	0.984139	−	0.177397i	$-0.0567676\pi$
$264$	6.24621	0.384428
$265$	0	0
$266$	1.56155	0.0957449
$267$	− 3.12311i	− 0.191131i
$268$	1.56155i	0.0953870i
$269$	26.0000	1.58525	0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000	1.58525	0.792624	+	0.609711i	$0.208714\pi$
$270$	0	0
$271$	6.93087	0.421020	0.210510	−	0.977592i	$-0.432487\pi$
$271$	6.93087	0.421020	0.210510	+	0.977592i	$0.432487\pi$
$272$	− 7.56155i	− 0.458486i
$273$	− 16.3002i	− 0.986532i
$274$	5.80776	0.350860
$275$	0	0
$276$	−7.31534	−0.440332
$277$	− 9.12311i	− 0.548154i	−0.961708	−	0.274077i	$-0.911628\pi$
$277$	− 9.12311i	− 0.548154i	0.961708	−	0.274077i	$-0.0883724\pi$
$278$	16.4924i	0.989150i
$279$	1.75379	0.104997
$280$	0	0
$281$	2.00000	0.119310	0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000	0.119310	0.0596550	+	0.998219i	$0.481000\pi$
$282$	− 16.0000i	− 0.952786i
$283$	− 12.8769i	− 0.765452i	−0.923862	−	0.382726i	$-0.874985\pi$
$283$	− 12.8769i	− 0.765452i	0.923862	−	0.382726i	$-0.125015\pi$
$284$	6.24621	0.370644
$285$	0	0
$286$	26.7386	1.58109
$287$	6.63068i	0.391397i
$288$	0.561553i	0.0330898i
$289$	−40.1771	−2.36336
$290$	0	0
$291$	9.36932	0.549239
$292$	− 10.6847i	− 0.625272i
$293$	23.1771i	1.35402i	0.735974	+	0.677010i	$0.236725\pi$
$293$	23.1771i	1.35402i	−0.735974	+	0.677010i	$0.763275\pi$
$294$	−7.12311	−0.415428
$295$	0	0
$296$	6.00000	0.348743
$297$	22.2462i	1.29086i
$298$	11.3693i	0.658607i
$299$	−31.3153	−1.81101
$300$	0	0
$301$	−17.3693	−1.00115
$302$	− 3.12311i	− 0.179715i
$303$	11.5076i	0.661093i
$304$	1.00000	0.0573539
$305$	0	0
$306$	4.24621	0.242740
$307$	0.492423i	0.0281040i	0.999901	+	0.0140520i	$0.00447304\pi$
$307$	0.492423i	0.0281040i	−0.999901	+	0.0140520i	$0.995527\pi$
$308$	6.24621i	0.355911i
$309$	22.2462	1.26554
$310$	0	0
$311$	8.68466	0.492462	0.246231	−	0.969211i	$-0.420808\pi$
$311$	8.68466	0.492462	0.246231	+	0.969211i	$0.420808\pi$
$312$	− 10.4384i	− 0.590961i
$313$	− 32.0540i	− 1.81180i	−0.423494	−	0.905899i	$-0.639197\pi$
$313$	− 32.0540i	− 1.81180i	0.423494	−	0.905899i	$-0.360803\pi$
$314$	−3.75379	−0.211839
$315$	0	0
$316$	3.12311	0.175688
$317$	24.0540i	1.35101i	0.737357	+	0.675503i	$0.236073\pi$
$317$	24.0540i	1.35101i	−0.737357	+	0.675503i	$0.763927\pi$
$318$	0.684658i	0.0383937i
$319$	−26.7386	−1.49708
$320$	0	0
$321$	−14.9309	−0.833360
$322$	− 7.31534i	− 0.407668i
$323$	− 7.56155i	− 0.420736i
$324$	7.00000	0.388889
$325$	0	0
$326$	−9.36932	−0.518918
$327$	− 5.56155i	− 0.307555i
$328$	4.24621i	0.234458i
$329$	16.0000	0.882109
$330$	0	0
$331$	1.56155	0.0858307	0.0429154	−	0.999079i	$-0.486335\pi$
$331$	1.56155	0.0858307	0.0429154	+	0.999079i	$0.486335\pi$
$332$	− 11.1231i	− 0.610460i
$333$	3.36932i	0.184637i
$334$	17.3693	0.950407
$335$	0	0
$336$	2.43845	0.133028
$337$	26.0000i	1.41631i	0.706057	+	0.708155i	$0.250472\pi$
$337$	26.0000i	1.41631i	−0.706057	+	0.708155i	$0.749528\pi$
$338$	− 31.6847i	− 1.72342i
$339$	−26.7386	−1.45224
$340$	0	0
$341$	12.4924	0.676503
$342$	0.561553i	0.0303653i
$343$	− 18.0540i	− 0.974823i
$344$	−11.1231	−0.599718
$345$	0	0
$346$	−3.75379	−0.201805
$347$	33.3693i	1.79136i	0.444700	+	0.895679i	$0.353310\pi$
$347$	33.3693i	1.79136i	−0.444700	+	0.895679i	$0.646690\pi$
$348$	10.4384i	0.559560i
$349$	−20.2462	−1.08375	−0.541877	−	0.840458i	$-0.682286\pi$
$349$	−20.2462	−1.08375	−0.541877	+	0.840458i	$0.682286\pi$
$350$	0	0
$351$	37.1771	1.98437
$352$	4.00000i	0.213201i
$353$	24.9309i	1.32694i	0.748205	+	0.663468i	$0.230916\pi$
$353$	24.9309i	1.32694i	−0.748205	+	0.663468i	$0.769084\pi$
$354$	−2.43845	−0.129602
$355$	0	0
$356$	2.00000	0.106000
$357$	− 18.4384i	− 0.975866i
$358$	5.75379i	0.304097i
$359$	−5.56155	−0.293528	−0.146764	−	0.989172i	$-0.546886\pi$
$359$	−5.56155	−0.293528	−0.146764	+	0.989172i	$0.546886\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 18.0000i	− 0.946059i
$363$	7.80776i	0.409801i
$364$	10.4384	0.547123
$365$	0	0
$366$	−4.49242	−0.234823
$367$	10.2462i	0.534848i	0.963579	+	0.267424i	$0.0861724\pi$
$367$	10.2462i	0.534848i	−0.963579	+	0.267424i	$0.913828\pi$
$368$	− 4.68466i	− 0.244205i
$369$	−2.38447	−0.124131
$370$	0	0
$371$	−0.684658	−0.0355457
$372$	− 4.87689i	− 0.252855i
$373$	− 27.5616i	− 1.42708i	−0.700613	−	0.713542i	$-0.747090\pi$
$373$	− 27.5616i	− 1.42708i	0.700613	−	0.713542i	$-0.252910\pi$
$374$	30.2462	1.56399
$375$	0	0
$376$	10.2462	0.528408
$377$	44.6847i	2.30138i
$378$	8.68466i	0.446691i
$379$	−6.43845	−0.330721	−0.165360	−	0.986233i	$-0.552879\pi$
$379$	−6.43845	−0.330721	−0.165360	+	0.986233i	$0.552879\pi$
$380$	0	0
$381$	7.61553	0.390155
$382$	8.68466i	0.444346i
$383$	30.2462i	1.54551i	0.634705	+	0.772755i	$0.281122\pi$
$383$	30.2462i	1.54551i	−0.634705	+	0.772755i	$0.718878\pi$
$384$	1.56155	0.0796877
$385$	0	0
$386$	−18.4924	−0.941240
$387$	− 6.24621i	− 0.317513i
$388$	6.00000i	0.304604i
$389$	−1.12311	−0.0569437	−0.0284719	−	0.999595i	$-0.509064\pi$
$389$	−1.12311	−0.0569437	−0.0284719	+	0.999595i	$0.509064\pi$
$390$	0	0
$391$	−35.4233	−1.79143
$392$	− 4.56155i	− 0.230393i
$393$	25.7538i	1.29911i
$394$	−3.75379	−0.189113
$395$	0	0
$396$	−2.24621	−0.112876
$397$	− 1.12311i	− 0.0563671i	−0.999603	−	0.0281835i	$-0.991028\pi$
$397$	− 1.12311i	− 0.0563671i	0.999603	−	0.0281835i	$-0.00897228\pi$
$398$	3.80776i	0.190866i
$399$	2.43845	0.122075
$400$	0	0
$401$	−20.2462	−1.01105	−0.505524	−	0.862813i	$-0.668701\pi$
$401$	−20.2462	−1.01105	−0.505524	+	0.862813i	$0.668701\pi$
$402$	2.43845i	0.121619i
$403$	− 20.8769i	− 1.03995i
$404$	−7.36932	−0.366637
$405$	0	0
$406$	−10.4384	−0.518051
$407$	24.0000i	1.18964i
$408$	− 11.8078i	− 0.584571i
$409$	24.7386	1.22325	0.611623	−	0.791149i	$-0.290517\pi$
$409$	24.7386	1.22325	0.611623	+	0.791149i	$0.290517\pi$
$410$	0	0
$411$	9.06913	0.447347
$412$	14.2462i	0.701860i
$413$	− 2.43845i	− 0.119988i
$414$	2.63068	0.129291
$415$	0	0
$416$	6.68466	0.327742
$417$	25.7538i	1.26117i
$418$	4.00000i	0.195646i
$419$	33.8617	1.65425	0.827127	−	0.562015i	$-0.189974\pi$
$419$	33.8617	1.65425	0.827127	+	0.562015i	$0.189974\pi$
$420$	0	0
$421$	4.93087	0.240316	0.120158	−	0.992755i	$-0.461660\pi$
$421$	4.93087	0.240316	0.120158	+	0.992755i	$0.461660\pi$
$422$	20.6847i	1.00691i
$423$	5.75379i	0.279759i
$424$	−0.438447	−0.0212929
$425$	0	0
$426$	9.75379	0.472573
$427$	− 4.49242i	− 0.217404i
$428$	− 9.56155i	− 0.462175i
$429$	41.7538	2.01589
$430$	0	0
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	5.56155i	0.267580i
$433$	39.3693i	1.89197i	0.324212	+	0.945984i	$0.394901\pi$
$433$	39.3693i	1.89197i	−0.324212	+	0.945984i	$0.605099\pi$
$434$	4.87689	0.234098
$435$	0	0
$436$	3.56155	0.170567
$437$	− 4.68466i	− 0.224098i
$438$	− 16.6847i	− 0.797224i
$439$	4.87689	0.232761	0.116381	−	0.993205i	$-0.462871\pi$
$439$	4.87689	0.232761	0.116381	+	0.993205i	$0.462871\pi$
$440$	0	0
$441$	2.56155	0.121979
$442$	− 50.5464i	− 2.40425i
$443$	− 14.2462i	− 0.676858i	−0.940992	−	0.338429i	$-0.890105\pi$
$443$	− 14.2462i	− 0.676858i	0.940992	−	0.338429i	$-0.109895\pi$
$444$	9.36932	0.444648
$445$	0	0
$446$	−1.36932	−0.0648390
$447$	17.7538i	0.839725i
$448$	1.56155i	0.0737764i
$449$	−20.7386	−0.978717	−0.489358	−	0.872083i	$-0.662769\pi$
$449$	−20.7386	−0.978717	−0.489358	+	0.872083i	$0.662769\pi$
$450$	0	0
$451$	−16.9848	−0.799785
$452$	− 17.1231i	− 0.805403i
$453$	− 4.87689i	− 0.229136i
$454$	−2.93087	−0.137553
$455$	0	0
$456$	1.56155	0.0731264
$457$	− 18.6847i	− 0.874031i	−0.899454	−	0.437016i	$-0.856035\pi$
$457$	− 18.6847i	− 0.874031i	0.899454	−	0.437016i	$-0.143965\pi$
$458$	− 18.4924i	− 0.864094i
$459$	42.0540	1.96291
$460$	0	0
$461$	20.2462	0.942960	0.471480	−	0.881877i	$-0.343720\pi$
$461$	20.2462	0.942960	0.471480	+	0.881877i	$0.343720\pi$
$462$	9.75379i	0.453787i
$463$	− 13.7538i	− 0.639193i	−0.947554	−	0.319596i	$-0.896453\pi$
$463$	− 13.7538i	− 0.639193i	0.947554	−	0.319596i	$-0.103547\pi$
$464$	−6.68466	−0.310327
$465$	0	0
$466$	−10.0000	−0.463241
$467$	− 1.75379i	− 0.0811557i	−0.999176	−	0.0405778i	$-0.987080\pi$
$467$	− 1.75379i	− 0.0811557i	0.999176	−	0.0405778i	$-0.0129199\pi$
$468$	3.75379i	0.173519i
$469$	−2.43845	−0.112597
$470$	0	0
$471$	−5.86174	−0.270095
$472$	− 1.56155i	− 0.0718763i
$473$	− 44.4924i	− 2.04576i
$474$	4.87689	0.224003
$475$	0	0
$476$	11.8078	0.541208
$477$	− 0.246211i	− 0.0112732i
$478$	5.56155i	0.254380i
$479$	−32.0000	−1.46212	−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000	−1.46212	−0.731059	+	0.682315i	$0.760973\pi$
$480$	0	0
$481$	40.1080	1.82877
$482$	14.8769i	0.677624i
$483$	− 11.4233i	− 0.519778i
$484$	−5.00000	−0.227273
$485$	0	0
$486$	−5.75379	−0.260997
$487$	− 23.6155i	− 1.07012i	−0.844814	−	0.535061i	$-0.820289\pi$
$487$	− 23.6155i	− 1.07012i	0.844814	−	0.535061i	$-0.179711\pi$
$488$	− 2.87689i	− 0.130231i
$489$	−14.6307	−0.661622
$490$	0	0
$491$	7.12311	0.321461	0.160731	−	0.986998i	$-0.448615\pi$
$491$	7.12311	0.321461	0.160731	+	0.986998i	$0.448615\pi$
$492$	6.63068i	0.298934i
$493$	50.5464i	2.27650i
$494$	6.68466	0.300757
$495$	0	0
$496$	3.12311	0.140232
$497$	9.75379i	0.437517i
$498$	− 17.3693i	− 0.778338i
$499$	32.1080	1.43735	0.718675	−	0.695347i	$-0.244749\pi$
$499$	32.1080	1.43735	0.718675	+	0.695347i	$0.244749\pi$
$500$	0	0
$501$	27.1231	1.21177
$502$	− 10.2462i	− 0.457311i
$503$	30.0540i	1.34004i	0.742343	+	0.670020i	$0.233715\pi$
$503$	30.0540i	1.34004i	−0.742343	+	0.670020i	$0.766285\pi$
$504$	−0.876894	−0.0390600
$505$	0	0
$506$	18.7386	0.833034
$507$	− 49.4773i	− 2.19736i
$508$	4.87689i	0.216377i
$509$	30.4924	1.35155	0.675776	−	0.737107i	$-0.263808\pi$
$509$	30.4924	1.35155	0.675776	+	0.737107i	$0.263808\pi$
$510$	0	0
$511$	16.6847	0.738086
$512$	1.00000i	0.0441942i
$513$	5.56155i	0.245549i
$514$	14.0000	0.617514
$515$	0	0
$516$	−17.3693	−0.764642
$517$	40.9848i	1.80251i
$518$	9.36932i	0.411664i
$519$	−5.86174	−0.257302
$520$	0	0
$521$	5.12311	0.224447	0.112224	−	0.993683i	$-0.464203\pi$
$521$	5.12311	0.224447	0.112224	+	0.993683i	$0.464203\pi$
$522$	− 3.75379i	− 0.164299i
$523$	− 19.3153i	− 0.844601i	−0.906456	−	0.422300i	$-0.861223\pi$
$523$	− 19.3153i	− 0.844601i	0.906456	−	0.422300i	$-0.138777\pi$
$524$	−16.4924	−0.720475
$525$	0	0
$526$	5.75379	0.250877
$527$	− 23.6155i	− 1.02871i
$528$	6.24621i	0.271831i
$529$	1.05398	0.0458250
$530$	0	0
$531$	0.876894	0.0380540
$532$	1.56155i	0.0677019i
$533$	28.3845i	1.22947i
$534$	3.12311	0.135150
$535$	0	0
$536$	−1.56155	−0.0674488
$537$	8.98485i	0.387725i
$538$	26.0000i	1.12094i
$539$	18.2462	0.785920
$540$	0	0
$541$	−41.6155	−1.78919	−0.894596	−	0.446877i	$-0.852536\pi$
$541$	−41.6155	−1.78919	−0.894596	+	0.446877i	$0.852536\pi$
$542$	6.93087i	0.297706i
$543$	− 28.1080i	− 1.20623i
$544$	7.56155	0.324199
$545$	0	0
$546$	16.3002	0.697584
$547$	16.4924i	0.705165i	0.935781	+	0.352583i	$0.114696\pi$
$547$	16.4924i	0.705165i	−0.935781	+	0.352583i	$0.885304\pi$
$548$	5.80776i	0.248095i
$549$	1.61553	0.0689491
$550$	0	0
$551$	−6.68466	−0.284776
$552$	− 7.31534i	− 0.311362i
$553$	4.87689i	0.207387i
$554$	9.12311	0.387604
$555$	0	0
$556$	−16.4924	−0.699435
$557$	1.61553i	0.0684521i	0.999414	+	0.0342261i	$0.0108966\pi$
$557$	1.61553i	0.0684521i	−0.999414	+	0.0342261i	$0.989103\pi$
$558$	1.75379i	0.0742438i
$559$	−74.3542	−3.14485
$560$	0	0
$561$	47.2311	1.99410
$562$	2.00000i	0.0843649i
$563$	24.4924i	1.03223i	0.856519	+	0.516116i	$0.172623\pi$
$563$	24.4924i	1.03223i	−0.856519	+	0.516116i	$0.827377\pi$
$564$	16.0000	0.673722
$565$	0	0
$566$	12.8769	0.541256
$567$	10.9309i	0.459053i
$568$	6.24621i	0.262085i
$569$	−5.12311	−0.214772	−0.107386	−	0.994217i	$-0.534248\pi$
$569$	−5.12311	−0.214772	−0.107386	+	0.994217i	$0.534248\pi$
$570$	0	0
$571$	−19.6155	−0.820884	−0.410442	−	0.911887i	$-0.634626\pi$
$571$	−19.6155	−0.820884	−0.410442	+	0.911887i	$0.634626\pi$
$572$	26.7386i	1.11800i
$573$	13.5616i	0.566542i
$574$	−6.63068	−0.276759
$575$	0	0
$576$	−0.561553	−0.0233980
$577$	22.6847i	0.944375i	0.881498	+	0.472187i	$0.156535\pi$
$577$	22.6847i	0.944375i	−0.881498	+	0.472187i	$0.843465\pi$
$578$	− 40.1771i	− 1.67115i
$579$	−28.8769	−1.20008
$580$	0	0
$581$	17.3693	0.720601
$582$	9.36932i	0.388371i
$583$	− 1.75379i	− 0.0726345i
$584$	10.6847	0.442134
$585$	0	0
$586$	−23.1771	−0.957436
$587$	− 17.3693i	− 0.716908i	−0.933547	−	0.358454i	$-0.883304\pi$
$587$	− 17.3693i	− 0.716908i	0.933547	−	0.358454i	$-0.116696\pi$
$588$	− 7.12311i	− 0.293752i
$589$	3.12311	0.128685
$590$	0	0
$591$	−5.86174	−0.241120
$592$	6.00000i	0.246598i
$593$	24.2462i	0.995673i	0.867271	+	0.497836i	$0.165872\pi$
$593$	24.2462i	0.995673i	−0.867271	+	0.497836i	$0.834128\pi$
$594$	−22.2462	−0.912773
$595$	0	0
$596$	−11.3693	−0.465705
$597$	5.94602i	0.243355i
$598$	− 31.3153i	− 1.28058i
$599$	−45.8617	−1.87386	−0.936930	−	0.349517i	$-0.886346\pi$
$599$	−45.8617	−1.87386	−0.936930	+	0.349517i	$0.886346\pi$
$600$	0	0
$601$	18.0000	0.734235	0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000	0.734235	0.367118	+	0.930175i	$0.380345\pi$
$602$	− 17.3693i	− 0.707921i
$603$	− 0.876894i	− 0.0357099i
$604$	3.12311	0.127077
$605$	0	0
$606$	−11.5076	−0.467463
$607$	12.8769i	0.522657i	0.965250	+	0.261329i	$0.0841606\pi$
$607$	12.8769i	0.522657i	−0.965250	+	0.261329i	$0.915839\pi$
$608$	1.00000i	0.0405554i
$609$	−16.3002	−0.660517
$610$	0	0
$611$	68.4924	2.77091
$612$	4.24621i	0.171643i
$613$	− 19.3693i	− 0.782319i	−0.920323	−	0.391160i	$-0.872074\pi$
$613$	− 19.3693i	− 0.782319i	0.920323	−	0.391160i	$-0.127926\pi$
$614$	−0.492423	−0.0198726
$615$	0	0
$616$	−6.24621	−0.251667
$617$	4.24621i	0.170946i	0.996340	+	0.0854730i	$0.0272401\pi$
$617$	4.24621i	0.170946i	−0.996340	+	0.0854730i	$0.972760\pi$
$618$	22.2462i	0.894874i
$619$	36.0000	1.44696	0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000	1.44696	0.723481	+	0.690344i	$0.242541\pi$
$620$	0	0
$621$	26.0540	1.04551
$622$	8.68466i	0.348223i
$623$	3.12311i	0.125125i
$624$	10.4384	0.417872
$625$	0	0
$626$	32.0540	1.28113
$627$	6.24621i	0.249450i
$628$	− 3.75379i	− 0.149792i
$629$	45.3693	1.80899
$630$	0	0
$631$	12.4924	0.497315	0.248658	−	0.968591i	$-0.420011\pi$
$631$	12.4924	0.497315	0.248658	+	0.968591i	$0.420011\pi$
$632$	3.12311i	0.124230i
$633$	32.3002i	1.28382i
$634$	−24.0540	−0.955305
$635$	0	0
$636$	−0.684658	−0.0271485
$637$	− 30.4924i	− 1.20815i
$638$	− 26.7386i	− 1.05859i
$639$	−3.50758	−0.138758
$640$	0	0
$641$	−35.8617	−1.41645	−0.708227	−	0.705985i	$-0.750505\pi$
$641$	−35.8617	−1.41645	−0.708227	+	0.705985i	$0.750505\pi$
$642$	− 14.9309i	− 0.589274i
$643$	7.61553i	0.300327i	0.988661	+	0.150164i	$0.0479800\pi$
$643$	7.61553i	0.300327i	−0.988661	+	0.150164i	$0.952020\pi$
$644$	7.31534	0.288265
$645$	0	0
$646$	7.56155	0.297505
$647$	− 9.56155i	− 0.375903i	−0.982178	−	0.187952i	$-0.939815\pi$
$647$	− 9.56155i	− 0.375903i	0.982178	−	0.187952i	$-0.0601848\pi$
$648$	7.00000i	0.274986i
$649$	6.24621	0.245185
$650$	0	0
$651$	7.61553	0.298476
$652$	− 9.36932i	− 0.366931i
$653$	1.12311i	0.0439505i	0.999759	+	0.0219753i	$0.00699551\pi$
$653$	1.12311i	0.0439505i	−0.999759	+	0.0219753i	$0.993004\pi$
$654$	5.56155	0.217474
$655$	0	0
$656$	−4.24621	−0.165787
$657$	6.00000i	0.234082i
$658$	16.0000i	0.623745i
$659$	42.9309	1.67235	0.836175	−	0.548463i	$-0.184787\pi$
$659$	42.9309	1.67235	0.836175	+	0.548463i	$0.184787\pi$
$660$	0	0
$661$	9.80776	0.381478	0.190739	−	0.981641i	$-0.438912\pi$
$661$	9.80776	0.381478	0.190739	+	0.981641i	$0.438912\pi$
$662$	1.56155i	0.0606915i
$663$	− 78.9309i	− 3.06542i
$664$	11.1231	0.431660
$665$	0	0
$666$	−3.36932	−0.130558
$667$	31.3153i	1.21253i
$668$	17.3693i	0.672039i
$669$	−2.13826	−0.0826699
$670$	0	0
$671$	11.5076	0.444245
$672$	2.43845i	0.0940651i
$673$	− 3.36932i	− 0.129878i	−0.997889	−	0.0649388i	$-0.979315\pi$
$673$	− 3.36932i	− 0.129878i	0.997889	−	0.0649388i	$-0.0206852\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	31.6847	1.21864
$677$	− 36.4384i	− 1.40044i	−0.713926	−	0.700222i	$-0.753085\pi$
$677$	− 36.4384i	− 1.40044i	0.713926	−	0.700222i	$-0.246915\pi$
$678$	− 26.7386i	− 1.02689i
$679$	−9.36932	−0.359561
$680$	0	0
$681$	−4.57671	−0.175380
$682$	12.4924i	0.478360i
$683$	4.00000i	0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$	4.00000i	0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$	−0.561553	−0.0214715
$685$	0	0
$686$	18.0540	0.689304
$687$	− 28.8769i	− 1.10172i
$688$	− 11.1231i	− 0.424064i
$689$	−2.93087	−0.111657
$690$	0	0
$691$	−8.87689	−0.337693	−0.168846	−	0.985642i	$-0.554004\pi$
$691$	−8.87689	−0.337693	−0.168846	+	0.985642i	$0.554004\pi$
$692$	− 3.75379i	− 0.142698i
$693$	− 3.50758i	− 0.133242i
$694$	−33.3693	−1.26668
$695$	0	0
$696$	−10.4384	−0.395668
$697$	32.1080i	1.21618i
$698$	− 20.2462i	− 0.766330i
$699$	−15.6155	−0.590634
$700$	0	0
$701$	−29.1231	−1.09996	−0.549982	−	0.835176i	$-0.685366\pi$
$701$	−29.1231	−1.09996	−0.549982	+	0.835176i	$0.685366\pi$
$702$	37.1771i	1.40316i
$703$	6.00000i	0.226294i
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−24.9309	−0.938286
$707$	− 11.5076i	− 0.432787i
$708$	− 2.43845i	− 0.0916425i
$709$	−38.0000	−1.42712	−0.713560	−	0.700594i	$-0.752918\pi$
$709$	−38.0000	−1.42712	−0.713560	+	0.700594i	$0.752918\pi$
$710$	0	0
$711$	−1.75379	−0.0657722
$712$	2.00000i	0.0749532i
$713$	− 14.6307i	− 0.547923i
$714$	18.4384	0.690042
$715$	0	0
$716$	−5.75379	−0.215029
$717$	8.68466i	0.324335i
$718$	− 5.56155i	− 0.207555i
$719$	29.5616	1.10246	0.551230	−	0.834353i	$-0.314159\pi$
$719$	29.5616	1.10246	0.551230	+	0.834353i	$0.314159\pi$
$720$	0	0
$721$	−22.2462	−0.828492
$722$	1.00000i	0.0372161i
$723$	23.2311i	0.863972i
$724$	18.0000	0.668965
$725$	0	0
$726$	−7.80776	−0.289773
$727$	36.6847i	1.36056i	0.732953	+	0.680279i	$0.238142\pi$
$727$	36.6847i	1.36056i	−0.732953	+	0.680279i	$0.761858\pi$
$728$	10.4384i	0.386875i
$729$	−29.9848	−1.11055
$730$	0	0
$731$	−84.1080	−3.11084
$732$	− 4.49242i	− 0.166045i
$733$	− 45.1231i	− 1.66666i	−0.552776	−	0.833330i	$-0.686431\pi$
$733$	− 45.1231i	− 1.66666i	0.552776	−	0.833330i	$-0.313569\pi$
$734$	−10.2462	−0.378195
$735$	0	0
$736$	4.68466	0.172679
$737$	− 6.24621i	− 0.230082i
$738$	− 2.38447i	− 0.0877736i
$739$	−16.8769	−0.620827	−0.310413	−	0.950602i	$-0.600467\pi$
$739$	−16.8769	−0.620827	−0.310413	+	0.950602i	$0.600467\pi$
$740$	0	0
$741$	10.4384	0.383466
$742$	− 0.684658i	− 0.0251346i
$743$	27.1231i	0.995050i	0.867450	+	0.497525i	$0.165758\pi$
$743$	27.1231i	0.995050i	−0.867450	+	0.497525i	$0.834242\pi$
$744$	4.87689	0.178796
$745$	0	0
$746$	27.5616	1.00910
$747$	6.24621i	0.228537i
$748$	30.2462i	1.10591i
$749$	14.9309	0.545562
$750$	0	0
$751$	−43.1231	−1.57358	−0.786792	−	0.617218i	$-0.788260\pi$
$751$	−43.1231	−1.57358	−0.786792	+	0.617218i	$0.788260\pi$
$752$	10.2462i	0.373641i
$753$	− 16.0000i	− 0.583072i
$754$	−44.6847	−1.62732
$755$	0	0
$756$	−8.68466	−0.315858
$757$	− 9.50758i	− 0.345559i	−0.984961	−	0.172779i	$-0.944725\pi$
$757$	− 9.50758i	− 0.345559i	0.984961	−	0.172779i	$-0.0552748\pi$
$758$	− 6.43845i	− 0.233855i
$759$	29.2614	1.06212
$760$	0	0
$761$	−28.5464	−1.03481	−0.517403	−	0.855742i	$-0.673101\pi$
$761$	−28.5464	−1.03481	−0.517403	+	0.855742i	$0.673101\pi$
$762$	7.61553i	0.275881i
$763$	5.56155i	0.201342i
$764$	−8.68466	−0.314200
$765$	0	0
$766$	−30.2462	−1.09284
$767$	− 10.4384i	− 0.376910i
$768$	1.56155i	0.0563477i
$769$	−31.5616	−1.13814	−0.569069	−	0.822290i	$-0.692696\pi$
$769$	−31.5616	−1.13814	−0.569069	+	0.822290i	$0.692696\pi$
$770$	0	0
$771$	21.8617	0.787331
$772$	− 18.4924i	− 0.665557i
$773$	− 9.80776i	− 0.352761i	−0.984322	−	0.176380i	$-0.943561\pi$
$773$	− 9.80776i	− 0.352761i	0.984322	−	0.176380i	$-0.0564389\pi$
$774$	6.24621	0.224515
$775$	0	0
$776$	−6.00000	−0.215387
$777$	14.6307i	0.524873i
$778$	− 1.12311i	− 0.0402653i
$779$	−4.24621	−0.152136
$780$	0	0
$781$	−24.9848	−0.894028
$782$	− 35.4233i	− 1.26673i
$783$	− 37.1771i	− 1.32860i
$784$	4.56155	0.162913
$785$	0	0
$786$	−25.7538	−0.918607
$787$	− 31.8078i	− 1.13382i	−0.823778	−	0.566912i	$-0.808138\pi$
$787$	− 31.8078i	− 1.13382i	0.823778	−	0.566912i	$-0.191862\pi$
$788$	− 3.75379i	− 0.133723i
$789$	8.98485	0.319869
$790$	0	0
$791$	26.7386	0.950716
$792$	− 2.24621i	− 0.0798156i
$793$	− 19.2311i	− 0.682915i
$794$	1.12311	0.0398575
$795$	0	0
$796$	−3.80776	−0.134963
$797$	− 42.3002i	− 1.49835i	−0.662372	−	0.749175i	$-0.730450\pi$
$797$	− 42.3002i	− 1.49835i	0.662372	−	0.749175i	$-0.269550\pi$
$798$	2.43845i	0.0863201i
$799$	77.4773	2.74095
$800$	0	0
$801$	−1.12311	−0.0396830
$802$	− 20.2462i	− 0.714919i
$803$	42.7386i	1.50821i
$804$	−2.43845	−0.0859974
$805$	0	0
$806$	20.8769	0.735357
$807$	40.6004i	1.42920i
$808$	− 7.36932i	− 0.259252i
$809$	8.43845	0.296680	0.148340	−	0.988936i	$-0.452607\pi$
$809$	8.43845	0.296680	0.148340	+	0.988936i	$0.452607\pi$
$810$	0	0
$811$	−0.192236	−0.00675032	−0.00337516	−	0.999994i	$-0.501074\pi$
$811$	−0.192236	−0.00675032	−0.00337516	+	0.999994i	$0.501074\pi$
$812$	− 10.4384i	− 0.366318i
$813$	10.8229i	0.379576i
$814$	−24.0000	−0.841200
$815$	0	0
$816$	11.8078	0.413354
$817$	− 11.1231i	− 0.389148i
$818$	24.7386i	0.864966i
$819$	−5.86174	−0.204826
$820$	0	0
$821$	7.36932	0.257191	0.128595	−	0.991697i	$-0.458953\pi$
$821$	7.36932	0.257191	0.128595	+	0.991697i	$0.458953\pi$
$822$	9.06913i	0.316322i
$823$	− 33.5616i	− 1.16988i	−0.811076	−	0.584941i	$-0.801118\pi$
$823$	− 33.5616i	− 1.16988i	0.811076	−	0.584941i	$-0.198882\pi$
$824$	−14.2462	−0.496290
$825$	0	0
$826$	2.43845	0.0848444
$827$	6.43845i	0.223887i	0.993715	+	0.111943i	$0.0357075\pi$
$827$	6.43845i	0.223887i	−0.993715	+	0.111943i	$0.964292\pi$
$828$	2.63068i	0.0914226i
$829$	−16.0540	−0.557578	−0.278789	−	0.960352i	$-0.589933\pi$
$829$	−16.0540	−0.557578	−0.278789	+	0.960352i	$0.589933\pi$
$830$	0	0
$831$	14.2462	0.494196
$832$	6.68466i	0.231749i
$833$	− 34.4924i	− 1.19509i
$834$	−25.7538	−0.891781
$835$	0	0
$836$	−4.00000	−0.138343
$837$	17.3693i	0.600371i
$838$	33.8617i	1.16973i
$839$	12.4924	0.431286	0.215643	−	0.976472i	$-0.430815\pi$
$839$	12.4924	0.431286	0.215643	+	0.976472i	$0.430815\pi$
$840$	0	0
$841$	15.6847	0.540850
$842$	4.93087i	0.169929i
$843$	3.12311i	0.107565i
$844$	−20.6847	−0.711995
$845$	0	0
$846$	−5.75379	−0.197819
$847$	− 7.80776i	− 0.268278i
$848$	− 0.438447i	− 0.0150563i
$849$	20.1080	0.690103
$850$	0	0
$851$	28.1080	0.963528
$852$	9.75379i	0.334159i
$853$	24.7386i	0.847035i	0.905888	+	0.423517i	$0.139205\pi$
$853$	24.7386i	0.847035i	−0.905888	+	0.423517i	$0.860795\pi$
$854$	4.49242	0.153728
$855$	0	0
$856$	9.56155	0.326807
$857$	− 39.3693i	− 1.34483i	−0.740174	−	0.672415i	$-0.765257\pi$
$857$	− 39.3693i	− 1.34483i	0.740174	−	0.672415i	$-0.234743\pi$
$858$	41.7538i	1.42545i
$859$	−12.9848	−0.443037	−0.221519	−	0.975156i	$-0.571101\pi$
$859$	−12.9848	−0.443037	−0.221519	+	0.975156i	$0.571101\pi$
$860$	0	0
$861$	−10.3542	−0.352869
$862$	− 16.0000i	− 0.544962i
$863$	− 14.2462i	− 0.484947i	−0.970158	−	0.242473i	$-0.922041\pi$
$863$	− 14.2462i	− 0.484947i	0.970158	−	0.242473i	$-0.0779587\pi$
$864$	−5.56155	−0.189208
$865$	0	0
$866$	−39.3693	−1.33782
$867$	− 62.7386i	− 2.13072i
$868$	4.87689i	0.165533i
$869$	−12.4924	−0.423776
$870$	0	0
$871$	−10.4384	−0.353693
$872$	3.56155i	0.120609i
$873$	− 3.36932i	− 0.114034i
$874$	4.68466	0.158461
$875$	0	0
$876$	16.6847	0.563722
$877$	− 24.9309i	− 0.841856i	−0.907094	−	0.420928i	$-0.861705\pi$
$877$	− 24.9309i	− 0.841856i	0.907094	−	0.420928i	$-0.138295\pi$
$878$	4.87689i	0.164587i
$879$	−36.1922	−1.22073
$880$	0	0
$881$	−22.9848	−0.774379	−0.387190	−	0.922000i	$-0.626554\pi$
$881$	−22.9848	−0.774379	−0.387190	+	0.922000i	$0.626554\pi$
$882$	2.56155i	0.0862520i
$883$	− 47.6155i	− 1.60239i	−0.598403	−	0.801195i	$-0.704198\pi$
$883$	− 47.6155i	− 1.60239i	0.598403	−	0.801195i	$-0.295802\pi$
$884$	50.5464	1.70006
$885$	0	0
$886$	14.2462	0.478611
$887$	4.49242i	0.150841i	0.997152	+	0.0754204i	$0.0240299\pi$
$887$	4.49242i	0.150841i	−0.997152	+	0.0754204i	$0.975970\pi$
$888$	9.36932i	0.314414i
$889$	−7.61553	−0.255417
$890$	0	0
$891$	−28.0000	−0.938035
$892$	− 1.36932i	− 0.0458481i
$893$	10.2462i	0.342876i
$894$	−17.7538	−0.593776
$895$	0	0
$896$	−1.56155	−0.0521678
$897$	− 48.9006i	− 1.63274i
$898$	− 20.7386i	− 0.692057i
$899$	−20.8769	−0.696283
$900$	0	0
$901$	−3.31534	−0.110450
$902$	− 16.9848i	− 0.565533i
$903$	− 27.1231i	− 0.902600i
$904$	17.1231	0.569506
$905$	0	0
$906$	4.87689	0.162024
$907$	− 25.1771i	− 0.835991i	−0.908449	−	0.417996i	$-0.862733\pi$
$907$	− 25.1771i	− 0.835991i	0.908449	−	0.417996i	$-0.137267\pi$
$908$	− 2.93087i	− 0.0972643i
$909$	4.13826	0.137257
$910$	0	0
$911$	−28.4924	−0.943996	−0.471998	−	0.881600i	$-0.656467\pi$
$911$	−28.4924	−0.943996	−0.471998	+	0.881600i	$0.656467\pi$
$912$	1.56155i	0.0517082i
$913$	44.4924i	1.47248i
$914$	18.6847	0.618034
$915$	0	0
$916$	18.4924	0.611007
$917$	− 25.7538i	− 0.850465i
$918$	42.0540i	1.38799i
$919$	30.9309	1.02032	0.510158	−	0.860081i	$-0.329587\pi$
$919$	30.9309	1.02032	0.510158	+	0.860081i	$0.329587\pi$
$920$	0	0
$921$	−0.768944	−0.0253376
$922$	20.2462i	0.666773i
$923$	41.7538i	1.37434i
$924$	−9.75379	−0.320876
$925$	0	0
$926$	13.7538	0.451978
$927$	− 8.00000i	− 0.262754i
$928$	− 6.68466i	− 0.219435i
$929$	−34.3002	−1.12535	−0.562676	−	0.826677i	$-0.690228\pi$
$929$	−34.3002	−1.12535	−0.562676	+	0.826677i	$0.690228\pi$
$930$	0	0
$931$	4.56155	0.149499
$932$	− 10.0000i	− 0.327561i
$933$	13.5616i	0.443985i
$934$	1.75379	0.0573857
$935$	0	0
$936$	−3.75379	−0.122696
$937$	− 36.4384i	− 1.19039i	−0.803580	−	0.595196i	$-0.797074\pi$
$937$	− 36.4384i	− 1.19039i	0.803580	−	0.595196i	$-0.202926\pi$
$938$	− 2.43845i	− 0.0796181i
$939$	50.0540	1.63345
$940$	0	0
$941$	34.1922	1.11464	0.557318	−	0.830299i	$-0.311831\pi$
$941$	34.1922	1.11464	0.557318	+	0.830299i	$0.311831\pi$
$942$	− 5.86174i	− 0.190986i
$943$	19.8920i	0.647774i
$944$	1.56155	0.0508242
$945$	0	0
$946$	44.4924	1.44657
$947$	17.7538i	0.576921i	0.957492	+	0.288460i	$0.0931433\pi$
$947$	17.7538i	0.576921i	−0.957492	+	0.288460i	$0.906857\pi$
$948$	4.87689i	0.158394i
$949$	71.4233	2.31850
$950$	0	0
$951$	−37.5616	−1.21802
$952$	11.8078i	0.382692i
$953$	− 30.1080i	− 0.975292i	−0.873041	−	0.487646i	$-0.837856\pi$
$953$	− 30.1080i	− 0.975292i	0.873041	−	0.487646i	$-0.162144\pi$
$954$	0.246211	0.00797138
$955$	0	0
$956$	−5.56155	−0.179873
$957$	− 41.7538i	− 1.34971i
$958$	− 32.0000i	− 1.03387i
$959$	−9.06913	−0.292857
$960$	0	0
$961$	−21.2462	−0.685362
$962$	40.1080i	1.29313i
$963$	5.36932i	0.173024i
$964$	−14.8769	−0.479153
$965$	0	0
$966$	11.4233	0.367538
$967$	48.4924i	1.55941i	0.626146	+	0.779706i	$0.284631\pi$
$967$	48.4924i	1.55941i	−0.626146	+	0.779706i	$0.715369\pi$
$968$	− 5.00000i	− 0.160706i
$969$	11.8078	0.379320
$970$	0	0
$971$	−23.5076	−0.754394	−0.377197	−	0.926133i	$-0.623112\pi$
$971$	−23.5076	−0.754394	−0.377197	+	0.926133i	$0.623112\pi$
$972$	− 5.75379i	− 0.184553i
$973$	− 25.7538i	− 0.825629i
$974$	23.6155	0.756690
$975$	0	0
$976$	2.87689	0.0920871
$977$	20.7386i	0.663488i	0.943370	+	0.331744i	$0.107637\pi$
$977$	20.7386i	0.663488i	−0.943370	+	0.331744i	$0.892363\pi$
$978$	− 14.6307i	− 0.467838i
$979$	−8.00000	−0.255681
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	7.12311i	0.227307i
$983$	27.1231i	0.865093i	0.901612	+	0.432546i	$0.142385\pi$
$983$	27.1231i	0.865093i	−0.901612	+	0.432546i	$0.857615\pi$
$984$	−6.63068	−0.211378
$985$	0	0
$986$	−50.5464	−1.60973
$987$	24.9848i	0.795276i
$988$	6.68466i	0.212667i
$989$	−52.1080	−1.65694
$990$	0	0
$991$	11.1231	0.353337	0.176669	−	0.984270i	$-0.443468\pi$
$991$	11.1231	0.353337	0.176669	+	0.984270i	$0.443468\pi$
$992$	3.12311i	0.0991587i
$993$	2.43845i	0.0773818i
$994$	−9.75379	−0.309371
$995$	0	0
$996$	17.3693	0.550368
$997$	− 32.7386i	− 1.03684i	−0.855125	−	0.518421i	$-0.826520\pi$
$997$	− 32.7386i	− 1.03684i	0.855125	−	0.518421i	$-0.173480\pi$
$998$	32.1080i	1.01636i
$999$	−33.3693	−1.05576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.b.f.799.4		4
5.2	odd	4		190.2.a.d.1.2	✓	2
5.3	odd	4		950.2.a.h.1.1		2
5.4	even	2	inner	950.2.b.f.799.1		4
15.2	even	4		1710.2.a.w.1.2		2
15.8	even	4		8550.2.a.br.1.1		2
20.3	even	4		7600.2.a.y.1.2		2
20.7	even	4		1520.2.a.n.1.1		2
35.27	even	4		9310.2.a.bc.1.1		2
40.27	even	4		6080.2.a.bb.1.2		2
40.37	odd	4		6080.2.a.bh.1.1		2
95.37	even	4		3610.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.d.1.2	✓	2	5.2	odd	4
950.2.a.h.1.1		2	5.3	odd	4
950.2.b.f.799.1		4	5.4	even	2	inner
950.2.b.f.799.4		4	1.1	even	1	trivial
1520.2.a.n.1.1		2	20.7	even	4
1710.2.a.w.1.2		2	15.2	even	4
3610.2.a.t.1.1		2	95.37	even	4
6080.2.a.bb.1.2		2	40.27	even	4
6080.2.a.bh.1.1		2	40.37	odd	4
7600.2.a.y.1.2		2	20.3	even	4
8550.2.a.br.1.1		2	15.8	even	4
9310.2.a.bc.1.1		2	35.27	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.56155i q^{3} -1.00000 q^{4} -1.56155 q^{6} -1.56155i q^{7} -1.00000i q^{8} +0.561553 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.56155i q^{3} -1.00000 q^{4} -1.56155 q^{6} -1.56155i q^{7} -1.00000i q^{8} +0.561553 q^{9} +4.00000 q^{11} -1.56155i q^{12} -6.68466i q^{13} +1.56155 q^{14} +1.00000 q^{16} -7.56155i q^{17} +0.561553i q^{18} +1.00000 q^{19} +2.43845 q^{21} +4.00000i q^{22} -4.68466i q^{23} +1.56155 q^{24} +6.68466 q^{26} +5.56155i q^{27} +1.56155i q^{28} -6.68466 q^{29} +3.12311 q^{31} +1.00000i q^{32} +6.24621i q^{33} +7.56155 q^{34} -0.561553 q^{36} +6.00000i q^{37} +1.00000i q^{38} +10.4384 q^{39} -4.24621 q^{41} +2.43845i q^{42} -11.1231i q^{43} -4.00000 q^{44} +4.68466 q^{46} +10.2462i q^{47} +1.56155i q^{48} +4.56155 q^{49} +11.8078 q^{51} +6.68466i q^{52} -0.438447i q^{53} -5.56155 q^{54} -1.56155 q^{56} +1.56155i q^{57} -6.68466i q^{58} +1.56155 q^{59} +2.87689 q^{61} +3.12311i q^{62} -0.876894i q^{63} -1.00000 q^{64} -6.24621 q^{66} -1.56155i q^{67} +7.56155i q^{68} +7.31534 q^{69} -6.24621 q^{71} -0.561553i q^{72} +10.6847i q^{73} -6.00000 q^{74} -1.00000 q^{76} -6.24621i q^{77} +10.4384i q^{78} -3.12311 q^{79} -7.00000 q^{81} -4.24621i q^{82} +11.1231i q^{83} -2.43845 q^{84} +11.1231 q^{86} -10.4384i q^{87} -4.00000i q^{88} -2.00000 q^{89} -10.4384 q^{91} +4.68466i q^{92} +4.87689i q^{93} -10.2462 q^{94} -1.56155 q^{96} -6.00000i q^{97} +4.56155i q^{98} +2.24621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^6 - 6 * q^9	\( 4 q - 4 q^{4} + 2 q^{6} - 6 q^{9} + 16 q^{11} - 2 q^{14} + 4 q^{16} + 4 q^{19} + 18 q^{21} - 2 q^{24} + 2 q^{26} - 2 q^{29} - 4 q^{31} + 22 q^{34} + 6 q^{36} + 50 q^{39} + 16 q^{41} - 16 q^{44} - 6 q^{46} + 10 q^{49} + 6 q^{51} - 14 q^{54} + 2 q^{56} - 2 q^{59} + 28 q^{61} - 4 q^{64} + 8 q^{66} + 54 q^{69} + 8 q^{71} - 24 q^{74} - 4 q^{76} + 4 q^{79} - 28 q^{81} - 18 q^{84} + 28 q^{86} - 8 q^{89} - 50 q^{91} - 8 q^{94} + 2 q^{96} - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^6 - 6 * q^9 + 16 * q^11 - 2 * q^14 + 4 * q^16 + 4 * q^19 + 18 * q^21 - 2 * q^24 + 2 * q^26 - 2 * q^29 - 4 * q^31 + 22 * q^34 + 6 * q^36 + 50 * q^39 + 16 * q^41 - 16 * q^44 - 6 * q^46 + 10 * q^49 + 6 * q^51 - 14 * q^54 + 2 * q^56 - 2 * q^59 + 28 * q^61 - 4 * q^64 + 8 * q^66 + 54 * q^69 + 8 * q^71 - 24 * q^74 - 4 * q^76 + 4 * q^79 - 28 * q^81 - 18 * q^84 + 28 * q^86 - 8 * q^89 - 50 * q^91 - 8 * q^94 + 2 * q^96 - 24 * q^99

Introduction

L-functions

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