LMFDB - Embedded newform 950.4.b.i.799.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,4,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, 4, names="a")

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
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:	$56.0518145055$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 37x^{2} + 324 $ x^4 + 37*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$-4.77200i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.4.b.i.799.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +0.227998i q^{3} -4.00000 q^{4} +0.455996 q^{6} -8.08801i q^{7} +8.00000i q^{8} +26.9480 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +0.227998i q^{3} -4.00000 q^{4} +0.455996 q^{6} -8.08801i q^{7} +8.00000i q^{8} +26.9480 q^{9} -12.7720 q^{11} -0.911993i q^{12} -47.0360i q^{13} -16.1760 q^{14} +16.0000 q^{16} +31.4560i q^{17} -53.8960i q^{18} -19.0000 q^{19} +1.84405 q^{21} +25.5440i q^{22} -19.0360i q^{23} -1.82399 q^{24} -94.0720 q^{26} +12.3000i q^{27} +32.3520i q^{28} -91.2120 q^{29} +293.968 q^{31} -32.0000i q^{32} -2.91199i q^{33} +62.9120 q^{34} -107.792 q^{36} -215.616i q^{37} +38.0000i q^{38} +10.7241 q^{39} -67.7200 q^{41} -3.68810i q^{42} +308.596i q^{43} +51.0880 q^{44} -38.0720 q^{46} -108.812i q^{47} +3.64797i q^{48} +277.584 q^{49} -7.17191 q^{51} +188.144i q^{52} -682.124i q^{53} +24.6001 q^{54} +64.7041 q^{56} -4.33196i q^{57} +182.424i q^{58} +250.300 q^{59} -317.692 q^{61} -587.936i q^{62} -217.956i q^{63} -64.0000 q^{64} -5.82399 q^{66} -940.444i q^{67} -125.824i q^{68} +4.34018 q^{69} -395.552 q^{71} +215.584i q^{72} +975.048i q^{73} -431.232 q^{74} +76.0000 q^{76} +103.300i q^{77} -21.4483i q^{78} -922.776 q^{79} +724.792 q^{81} +135.440i q^{82} -1163.77i q^{83} -7.37620 q^{84} +617.192 q^{86} -20.7962i q^{87} -102.176i q^{88} -685.136 q^{89} -380.428 q^{91} +76.1441i q^{92} +67.0242i q^{93} -217.624 q^{94} +7.29594 q^{96} -211.256i q^{97} -555.168i q^{98} -344.180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9}+O(q^{10}) $ 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9	$ 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9} - 34 q^{11} + 72 q^{14} + 64 q^{16} - 76 q^{19} - 454 q^{21} - 144 q^{24} + 68 q^{26} - 6 q^{29} + 424 q^{31} + 320 q^{34} + 184 q^{36} - 1102 q^{39} - 100 q^{41} + 136 q^{44} + 292 q^{46} - 120 q^{49} - 866 q^{51} - 756 q^{54} - 288 q^{56} + 574 q^{59} + 626 q^{61} - 256 q^{64} - 160 q^{66} - 1606 q^{69} + 400 q^{71} - 768 q^{74} + 304 q^{76} - 2700 q^{79} + 2284 q^{81} + 1816 q^{84} + 2708 q^{86} + 472 q^{89} - 4102 q^{91} + 1556 q^{94} + 576 q^{96} - 266 q^{99}+O(q^{100}) $ 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9 - 34 * q^11 + 72 * q^14 + 64 * q^16 - 76 * q^19 - 454 * q^21 - 144 * q^24 + 68 * q^26 - 6 * q^29 + 424 * q^31 + 320 * q^34 + 184 * q^36 - 1102 * q^39 - 100 * q^41 + 136 * q^44 + 292 * q^46 - 120 * q^49 - 866 * q^51 - 756 * q^54 - 288 * q^56 + 574 * q^59 + 626 * q^61 - 256 * q^64 - 160 * q^66 - 1606 * q^69 + 400 * q^71 - 768 * q^74 + 304 * q^76 - 2700 * q^79 + 2284 * q^81 + 1816 * q^84 + 2708 * q^86 + 472 * q^89 - 4102 * q^91 + 1556 * q^94 + 576 * q^96 - 266 * 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 $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	0.227998i	0.0438783i	0.999759	+	0.0219391i	$0.00698400\pi$
$3$	0.227998i	0.0438783i	−0.999759	+	0.0219391i	$0.993016\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.455996	0.0310266
$7$	− 8.08801i	− 0.436711i	−0.975869	−	0.218356i	$-0.929931\pi$
$7$	− 8.08801i	− 0.436711i	0.975869	−	0.218356i	$-0.0700693\pi$
$8$	8.00000i	0.353553i
$9$	26.9480	0.998075
$10$	0	0
$11$	−12.7720	−0.350082	−0.175041	−	0.984561i	$-0.556006\pi$
$11$	−12.7720	−0.350082	−0.175041	+	0.984561i	$0.556006\pi$
$12$	− 0.911993i	− 0.0219391i
$13$	− 47.0360i	− 1.00350i	−0.865014	−	0.501748i	$-0.832691\pi$
$13$	− 47.0360i	− 1.00350i	0.865014	−	0.501748i	$-0.167309\pi$
$14$	−16.1760	−0.308802
$15$	0	0
$16$	16.0000	0.250000
$17$	31.4560i	0.448776i	0.974500	+	0.224388i	$0.0720384\pi$
$17$	31.4560i	0.448776i	−0.974500	+	0.224388i	$0.927962\pi$
$18$	− 53.8960i	− 0.705745i
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	1.84405	0.0191621
$22$	25.5440i	0.247545i
$23$	− 19.0360i	− 0.172578i	−0.996270	−	0.0862888i	$-0.972499\pi$
$23$	− 19.0360i	− 0.172578i	0.996270	−	0.0862888i	$-0.0275008\pi$
$24$	−1.82399	−0.0155133
$25$	0	0
$26$	−94.0720	−0.709579
$27$	12.3000i	0.0876720i
$28$	32.3520i	0.218356i
$29$	−91.2120	−0.584057	−0.292028	−	0.956410i	$-0.594330\pi$
$29$	−91.2120	−0.584057	−0.292028	+	0.956410i	$0.594330\pi$
$30$	0	0
$31$	293.968	1.70317	0.851584	−	0.524218i	$-0.175642\pi$
$31$	293.968	1.70317	0.851584	+	0.524218i	$0.175642\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 2.91199i	− 0.0153610i
$34$	62.9120	0.317333
$35$	0	0
$36$	−107.792	−0.499037
$37$	− 215.616i	− 0.958029i	−0.877807	−	0.479014i	$-0.840994\pi$
$37$	− 215.616i	− 0.958029i	0.877807	−	0.479014i	$-0.159006\pi$
$38$	38.0000i	0.162221i
$39$	10.7241	0.0440317
$40$	0	0
$41$	−67.7200	−0.257953	−0.128977	−	0.991648i	$-0.541169\pi$
$41$	−67.7200	−0.257953	−0.128977	+	0.991648i	$0.541169\pi$
$42$	− 3.68810i	− 0.0135497i
$43$	308.596i	1.09443i	0.836992	+	0.547214i	$0.184312\pi$
$43$	308.596i	1.09443i	−0.836992	+	0.547214i	$0.815688\pi$
$44$	51.0880	0.175041
$45$	0	0
$46$	−38.0720	−0.122031
$47$	− 108.812i	− 0.337700i	−0.985642	−	0.168850i	$-0.945995\pi$
$47$	− 108.812i	− 0.337700i	0.985642	−	0.168850i	$-0.0540053\pi$
$48$	3.64797i	0.0109696i
$49$	277.584	0.809283
$50$	0	0
$51$	−7.17191	−0.0196915
$52$	188.144i	0.501748i
$53$	− 682.124i	− 1.76787i	−0.467613	−	0.883933i	$-0.654886\pi$
$53$	− 682.124i	− 1.76787i	0.467613	−	0.883933i	$-0.345114\pi$
$54$	24.6001	0.0619935
$55$	0	0
$56$	64.7041	0.154401
$57$	− 4.33196i	− 0.0100664i
$58$	182.424i	0.412991i
$59$	250.300	0.552310	0.276155	−	0.961113i	$-0.410940\pi$
$59$	250.300	0.552310	0.276155	+	0.961113i	$0.410940\pi$
$60$	0	0
$61$	−317.692	−0.666825	−0.333412	−	0.942781i	$-0.608200\pi$
$61$	−317.692	−0.666825	−0.333412	+	0.942781i	$0.608200\pi$
$62$	− 587.936i	− 1.20432i
$63$	− 217.956i	− 0.435871i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−5.82399	−0.0108619
$67$	− 940.444i	− 1.71483i	−0.514626	−	0.857414i	$-0.672069\pi$
$67$	− 940.444i	− 1.71483i	0.514626	−	0.857414i	$-0.327931\pi$
$68$	− 125.824i	− 0.224388i
$69$	4.34018	0.00757241
$70$	0	0
$71$	−395.552	−0.661175	−0.330587	−	0.943775i	$-0.607247\pi$
$71$	−395.552	−0.661175	−0.330587	+	0.943775i	$0.607247\pi$
$72$	215.584i	0.352873i
$73$	975.048i	1.56330i	0.623718	+	0.781649i	$0.285621\pi$
$73$	975.048i	1.56330i	−0.623718	+	0.781649i	$0.714379\pi$
$74$	−431.232	−0.677429
$75$	0	0
$76$	76.0000	0.114708
$77$	103.300i	0.152885i
$78$	− 21.4483i	− 0.0311351i
$79$	−922.776	−1.31418	−0.657091	−	0.753811i	$-0.728213\pi$
$79$	−922.776	−1.31418	−0.657091	+	0.753811i	$0.728213\pi$
$80$	0	0
$81$	724.792	0.994228
$82$	135.440i	0.182401i
$83$	− 1163.77i	− 1.53904i	−0.638624	−	0.769519i	$-0.720496\pi$
$83$	− 1163.77i	− 1.53904i	0.638624	−	0.769519i	$-0.279504\pi$
$84$	−7.37620	−0.00958107
$85$	0	0
$86$	617.192	0.773878
$87$	− 20.7962i	− 0.0256274i
$88$	− 102.176i	− 0.123773i
$89$	−685.136	−0.816003	−0.408002	−	0.912981i	$-0.633774\pi$
$89$	−685.136	−0.816003	−0.408002	+	0.912981i	$0.633774\pi$
$90$	0	0
$91$	−380.428	−0.438238
$92$	76.1441i	0.0862888i
$93$	67.0242i	0.0747321i
$94$	−217.624	−0.238790
$95$	0	0
$96$	7.29594	0.00775665
$97$	− 211.256i	− 0.221132i	−0.993869	−	0.110566i	$-0.964734\pi$
$97$	− 211.256i	− 0.221132i	0.993869	−	0.110566i	$-0.0352663\pi$
$98$	− 555.168i	− 0.572250i
$99$	−344.180	−0.349408
$100$	0	0
$101$	−1703.55	−1.67831	−0.839157	−	0.543889i	$-0.816951\pi$
$101$	−1703.55	−1.67831	−0.839157	+	0.543889i	$0.816951\pi$
$102$	14.3438i	0.0139240i
$103$	− 1393.52i	− 1.33308i	−0.745468	−	0.666542i	$-0.767774\pi$
$103$	− 1393.52i	− 1.33308i	0.745468	−	0.666542i	$-0.232226\pi$
$104$	376.288	0.354789
$105$	0	0
$106$	−1364.25	−1.25007
$107$	− 907.996i	− 0.820367i	−0.912003	−	0.410184i	$-0.865465\pi$
$107$	− 907.996i	− 0.820367i	0.912003	−	0.410184i	$-0.134535\pi$
$108$	− 49.2002i	− 0.0438360i
$109$	−862.077	−0.757541	−0.378770	−	0.925491i	$-0.623653\pi$
$109$	−862.077	−0.757541	−0.378770	+	0.925491i	$0.623653\pi$
$110$	0	0
$111$	49.1601	0.0420366
$112$	− 129.408i	− 0.109178i
$113$	1502.72i	1.25101i	0.780220	+	0.625505i	$0.215107\pi$
$113$	1502.72i	1.25101i	−0.780220	+	0.625505i	$0.784893\pi$
$114$	−8.66393	−0.00711799
$115$	0	0
$116$	364.848	0.292028
$117$	− 1267.53i	− 1.00156i
$118$	− 500.600i	− 0.390542i
$119$	254.416	0.195986
$120$	0	0
$121$	−1167.88	−0.877443
$122$	635.384i	0.471516i
$123$	− 15.4400i	− 0.0113185i
$124$	−1175.87	−0.851584
$125$	0	0
$126$	−435.912	−0.308207
$127$	− 389.280i	− 0.271992i	−0.990709	−	0.135996i	$-0.956577\pi$
$127$	− 389.280i	− 0.271992i	0.990709	−	0.135996i	$-0.0434234\pi$
$128$	128.000i	0.0883883i
$129$	−70.3593	−0.0480216
$130$	0	0
$131$	−268.308	−0.178948	−0.0894739	−	0.995989i	$-0.528519\pi$
$131$	−268.308	−0.178948	−0.0894739	+	0.995989i	$0.528519\pi$
$132$	11.6480i	0.00768050i
$133$	153.672i	0.100188i
$134$	−1880.89	−1.21257
$135$	0	0
$136$	−251.648	−0.158666
$137$	− 2657.33i	− 1.65716i	−0.559871	−	0.828580i	$-0.689149\pi$
$137$	− 2657.33i	− 1.65716i	0.559871	−	0.828580i	$-0.310851\pi$
$138$	− 8.68036i	− 0.00535450i
$139$	2859.92	1.74514	0.872572	−	0.488486i	$-0.162451\pi$
$139$	2859.92	1.74514	0.872572	+	0.488486i	$0.162451\pi$
$140$	0	0
$141$	24.8090	0.0148177
$142$	791.104i	0.467521i
$143$	600.744i	0.351306i
$144$	431.168	0.249519
$145$	0	0
$146$	1950.10	1.10542
$147$	63.2887i	0.0355099i
$148$	862.464i	0.479014i
$149$	−311.812	−0.171440	−0.0857202	−	0.996319i	$-0.527319\pi$
$149$	−311.812	−0.171440	−0.0857202	+	0.996319i	$0.527319\pi$
$150$	0	0
$151$	−1462.32	−0.788093	−0.394046	−	0.919091i	$-0.628925\pi$
$151$	−1462.32	−0.788093	−0.394046	+	0.919091i	$0.628925\pi$
$152$	− 152.000i	− 0.0811107i
$153$	847.677i	0.447912i
$154$	206.600	0.108106
$155$	0	0
$156$	−42.8965	−0.0220158
$157$	− 4.38395i	− 0.00222852i	−0.999999	−	0.00111426i	$-0.999645\pi$
$157$	− 4.38395i	− 0.00222852i	0.999999	−	0.00111426i	$-0.000354680\pi$
$158$	1845.55i	0.929267i
$159$	155.523	0.0775709
$160$	0	0
$161$	−153.964	−0.0753666
$162$	− 1449.58i	− 0.703025i
$163$	− 1777.89i	− 0.854325i	−0.904175	−	0.427162i	$-0.859513\pi$
$163$	− 1777.89i	− 0.854325i	0.904175	−	0.427162i	$-0.140487\pi$
$164$	270.880	0.128977
$165$	0	0
$166$	−2327.54	−1.08826
$167$	− 893.064i	− 0.413817i	−0.978360	−	0.206908i	$-0.933660\pi$
$167$	− 893.064i	− 0.413817i	0.978360	−	0.206908i	$-0.0663402\pi$
$168$	14.7524i	0.00677484i
$169$	−15.3876	−0.00700391
$170$	0	0
$171$	−512.012	−0.228974
$172$	− 1234.38i	− 0.547214i
$173$	− 2452.56i	− 1.07783i	−0.842360	−	0.538915i	$-0.818834\pi$
$173$	− 2452.56i	− 1.07783i	0.842360	−	0.538915i	$-0.181166\pi$
$174$	−41.5923	−0.0181213
$175$	0	0
$176$	−204.352	−0.0875205
$177$	57.0679i	0.0242344i
$178$	1370.27i	0.577002i
$179$	2064.81	0.862185	0.431092	−	0.902308i	$-0.358128\pi$
$179$	2064.81	0.862185	0.431092	+	0.902308i	$0.358128\pi$
$180$	0	0
$181$	−2518.54	−1.03426	−0.517132	−	0.855906i	$-0.673000\pi$
$181$	−2518.54	−1.03426	−0.517132	+	0.855906i	$0.673000\pi$
$182$	760.855i	0.309881i
$183$	− 72.4332i	− 0.0292591i
$184$	152.288	0.0610154
$185$	0	0
$186$	134.048	0.0528436
$187$	− 401.756i	− 0.157109i
$188$	435.249i	0.168850i
$189$	99.4829	0.0382874
$190$	0	0
$191$	−4206.38	−1.59352	−0.796761	−	0.604294i	$-0.793455\pi$
$191$	−4206.38	−1.59352	−0.796761	+	0.604294i	$0.793455\pi$
$192$	− 14.5919i	− 0.00548478i
$193$	3245.82i	1.21056i	0.796011	+	0.605282i	$0.206940\pi$
$193$	3245.82i	1.21056i	−0.796011	+	0.605282i	$0.793060\pi$
$194$	−422.512	−0.156364
$195$	0	0
$196$	−1110.34	−0.404642
$197$	1734.71i	0.627377i	0.949526	+	0.313688i	$0.101565\pi$
$197$	1734.71i	0.627377i	−0.949526	+	0.313688i	$0.898435\pi$
$198$	688.360i	0.247069i
$199$	−380.792	−0.135646	−0.0678232	−	0.997697i	$-0.521605\pi$
$199$	−380.792	−0.135646	−0.0678232	+	0.997697i	$0.521605\pi$
$200$	0	0
$201$	214.420	0.0752437
$202$	3407.10i	1.18675i
$203$	737.724i	0.255064i
$204$	28.6876	0.00984576
$205$	0	0
$206$	−2787.04	−0.942633
$207$	− 512.983i	− 0.172245i
$208$	− 752.576i	− 0.250874i
$209$	242.668	0.0803143
$210$	0	0
$211$	1010.44	0.329675	0.164837	−	0.986321i	$-0.447290\pi$
$211$	1010.44	0.329675	0.164837	+	0.986321i	$0.447290\pi$
$212$	2728.50i	0.883933i
$213$	− 90.1852i	− 0.0290112i
$214$	−1815.99	−0.580087
$215$	0	0
$216$	−98.4004	−0.0309967
$217$	− 2377.62i	− 0.743793i
$218$	1724.15i	0.535662i
$219$	−222.309	−0.0685948
$220$	0	0
$221$	1479.57	0.450345
$222$	− 98.3201i	− 0.0297244i
$223$	3398.70i	1.02060i	0.859996	+	0.510301i	$0.170466\pi$
$223$	3398.70i	1.02060i	−0.859996	+	0.510301i	$0.829534\pi$
$224$	−258.816	−0.0772004
$225$	0	0
$226$	3005.44	0.884597
$227$	− 5760.80i	− 1.68439i	−0.539169	−	0.842197i	$-0.681262\pi$
$227$	− 5760.80i	− 1.68439i	0.539169	−	0.842197i	$-0.318738\pi$
$228$	17.3279i	0.00503318i
$229$	2179.00	0.628786	0.314393	−	0.949293i	$-0.398199\pi$
$229$	2179.00	0.628786	0.314393	+	0.949293i	$0.398199\pi$
$230$	0	0
$231$	−23.5522	−0.00670832
$232$	− 729.696i	− 0.206495i
$233$	− 2808.49i	− 0.789659i	−0.918754	−	0.394830i	$-0.870804\pi$
$233$	− 2808.49i	− 0.789659i	0.918754	−	0.394830i	$-0.129196\pi$
$234$	−2535.06	−0.708213
$235$	0	0
$236$	−1001.20	−0.276155
$237$	− 210.391i	− 0.0576640i
$238$	− 508.833i	− 0.138583i
$239$	−6285.67	−1.70120	−0.850599	−	0.525815i	$-0.823761\pi$
$239$	−6285.67	−1.70120	−0.850599	+	0.525815i	$0.823761\pi$
$240$	0	0
$241$	1129.22	0.301825	0.150912	−	0.988547i	$-0.451779\pi$
$241$	1129.22	0.301825	0.150912	+	0.988547i	$0.451779\pi$
$242$	2335.75i	0.620446i
$243$	497.352i	0.131297i
$244$	1270.77	0.333412
$245$	0	0
$246$	−30.8801	−0.00800342
$247$	893.684i	0.230218i
$248$	2351.74i	0.602161i
$249$	265.337	0.0675303
$250$	0	0
$251$	−2873.73	−0.722661	−0.361331	−	0.932438i	$-0.617677\pi$
$251$	−2873.73	−0.722661	−0.361331	+	0.932438i	$0.617677\pi$
$252$	871.823i	0.217935i
$253$	243.128i	0.0604163i
$254$	−778.559	−0.192327
$255$	0	0
$256$	256.000	0.0625000
$257$	3712.18i	0.901008i	0.892774	+	0.450504i	$0.148756\pi$
$257$	3712.18i	0.901008i	−0.892774	+	0.450504i	$0.851244\pi$
$258$	140.719i	0.0339564i
$259$	−1743.90	−0.418382
$260$	0	0
$261$	−2457.98	−0.582932
$262$	536.616i	0.126535i
$263$	1263.04i	0.296130i	0.988978	+	0.148065i	$0.0473044\pi$
$263$	1263.04i	0.296130i	−0.988978	+	0.148065i	$0.952696\pi$
$264$	23.2959	0.00543093
$265$	0	0
$266$	307.344	0.0708439
$267$	− 156.210i	− 0.0358048i
$268$	3761.78i	0.857414i
$269$	5484.39	1.24308	0.621541	−	0.783381i	$-0.286507\pi$
$269$	5484.39	1.24308	0.621541	+	0.783381i	$0.286507\pi$
$270$	0	0
$271$	−3217.66	−0.721251	−0.360625	−	0.932711i	$-0.617437\pi$
$271$	−3217.66	−0.721251	−0.360625	+	0.932711i	$0.617437\pi$
$272$	503.296i	0.112194i
$273$	− 86.7368i	− 0.0192291i
$274$	−5314.66	−1.17179
$275$	0	0
$276$	−17.3607	−0.00378620
$277$	− 7668.13i	− 1.66330i	−0.555302	−	0.831649i	$-0.687397\pi$
$277$	− 7668.13i	− 1.66330i	0.555302	−	0.831649i	$-0.312603\pi$
$278$	− 5719.83i	− 1.23400i
$279$	7921.86	1.69989
$280$	0	0
$281$	1126.81	0.239216	0.119608	−	0.992821i	$-0.461836\pi$
$281$	1126.81	0.239216	0.119608	+	0.992821i	$0.461836\pi$
$282$	− 49.6179i	− 0.0104777i
$283$	− 1502.63i	− 0.315625i	−0.987469	−	0.157813i	$-0.949556\pi$
$283$	− 1502.63i	− 0.315625i	0.987469	−	0.157813i	$-0.0504442\pi$
$284$	1582.21	0.330587
$285$	0	0
$286$	1201.49	0.248411
$287$	547.720i	0.112651i
$288$	− 862.337i	− 0.176436i
$289$	3923.52	0.798600
$290$	0	0
$291$	48.1659	0.00970288
$292$	− 3900.19i	− 0.781649i
$293$	− 452.324i	− 0.0901878i	−0.998983	−	0.0450939i	$-0.985641\pi$
$293$	− 452.324i	− 0.0901878i	0.998983	−	0.0450939i	$-0.0143587\pi$
$294$	126.577	0.0251093
$295$	0	0
$296$	1724.93	0.338714
$297$	− 157.096i	− 0.0306924i
$298$	623.623i	0.121227i
$299$	−895.379	−0.173181
$300$	0	0
$301$	2495.93	0.477950
$302$	2924.64i	0.557266i
$303$	− 388.407i	− 0.0736415i
$304$	−304.000	−0.0573539
$305$	0	0
$306$	1695.35	0.316722
$307$	2333.46i	0.433803i	0.976194	+	0.216901i	$0.0695950\pi$
$307$	2333.46i	0.433803i	−0.976194	+	0.216901i	$0.930405\pi$
$308$	− 413.200i	− 0.0764424i
$309$	317.720	0.0584934
$310$	0	0
$311$	10476.1	1.91011	0.955055	−	0.296429i	$-0.0957959\pi$
$311$	10476.1	1.91011	0.955055	+	0.296429i	$0.0957959\pi$
$312$	85.7930i	0.0155675i
$313$	4160.33i	0.751297i	0.926762	+	0.375648i	$0.122580\pi$
$313$	4160.33i	0.751297i	−0.926762	+	0.375648i	$0.877420\pi$
$314$	−8.76790	−0.00157580
$315$	0	0
$316$	3691.10	0.657091
$317$	7508.56i	1.33036i	0.746685	+	0.665178i	$0.231644\pi$
$317$	7508.56i	1.33036i	−0.746685	+	0.665178i	$0.768356\pi$
$318$	− 311.046i	− 0.0548509i
$319$	1164.96	0.204468
$320$	0	0
$321$	207.021	0.0359963
$322$	307.927i	0.0532922i
$323$	− 597.664i	− 0.102956i
$324$	−2899.17	−0.497114
$325$	0	0
$326$	−3555.78	−0.604099
$327$	− 196.552i	− 0.0332396i
$328$	− 541.760i	− 0.0912003i
$329$	−880.073	−0.147477
$330$	0	0
$331$	10386.8	1.72480	0.862400	−	0.506227i	$-0.168960\pi$
$331$	10386.8	1.72480	0.862400	+	0.506227i	$0.168960\pi$
$332$	4655.07i	0.769519i
$333$	− 5810.43i	− 0.956184i
$334$	−1786.13	−0.292613
$335$	0	0
$336$	29.5048	0.00479053
$337$	− 5618.29i	− 0.908153i	−0.890963	−	0.454077i	$-0.849969\pi$
$337$	− 5618.29i	− 0.908153i	0.890963	−	0.454077i	$-0.150031\pi$
$338$	30.7752i	0.00495251i
$339$	−342.617	−0.0548921
$340$	0	0
$341$	−3754.56	−0.596249
$342$	1024.02i	0.161909i
$343$	− 5019.29i	− 0.790135i
$344$	−2468.77	−0.386939
$345$	0	0
$346$	−4905.12	−0.762142
$347$	− 1814.32i	− 0.280686i	−0.990103	−	0.140343i	$-0.955180\pi$
$347$	− 1814.32i	− 0.280686i	0.990103	−	0.140343i	$-0.0448205\pi$
$348$	83.1847i	0.0128137i
$349$	816.757	0.125272	0.0626361	−	0.998036i	$-0.480049\pi$
$349$	816.757	0.125272	0.0626361	+	0.998036i	$0.480049\pi$
$350$	0	0
$351$	578.545	0.0879785
$352$	408.704i	0.0618864i
$353$	11090.4i	1.67219i	0.548585	+	0.836095i	$0.315167\pi$
$353$	11090.4i	1.67219i	−0.548585	+	0.836095i	$0.684833\pi$
$354$	114.136	0.0171363
$355$	0	0
$356$	2740.55	0.408002
$357$	58.0064i	0.00859951i
$358$	− 4129.62i	− 0.609657i
$359$	3211.68	0.472161	0.236081	−	0.971733i	$-0.424137\pi$
$359$	3211.68	0.472161	0.236081	+	0.971733i	$0.424137\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	5037.09i	0.731335i
$363$	− 266.274i	− 0.0385007i
$364$	1521.71	0.219119
$365$	0	0
$366$	−144.866	−0.0206893
$367$	− 8077.81i	− 1.14893i	−0.818528	−	0.574466i	$-0.805210\pi$
$367$	− 8077.81i	− 1.14893i	0.818528	−	0.574466i	$-0.194790\pi$
$368$	− 304.576i	− 0.0431444i
$369$	−1824.92	−0.257457
$370$	0	0
$371$	−5517.02	−0.772048
$372$	− 268.097i	− 0.0373660i
$373$	− 5088.15i	− 0.706312i	−0.935564	−	0.353156i	$-0.885108\pi$
$373$	− 5088.15i	− 0.706312i	0.935564	−	0.353156i	$-0.114892\pi$
$374$	−803.512	−0.111093
$375$	0	0
$376$	870.497	0.119395
$377$	4290.25i	0.586099i
$378$	− 198.966i	− 0.0270733i
$379$	−2547.00	−0.345199	−0.172600	−	0.984992i	$-0.555217\pi$
$379$	−2547.00	−0.345199	−0.172600	+	0.984992i	$0.555217\pi$
$380$	0	0
$381$	88.7550	0.0119345
$382$	8412.76i	1.12679i
$383$	− 7056.11i	− 0.941384i	−0.882297	−	0.470692i	$-0.844004\pi$
$383$	− 7056.11i	− 0.941384i	0.882297	−	0.470692i	$-0.155996\pi$
$384$	−29.1838	−0.00387833
$385$	0	0
$386$	6491.63	0.855999
$387$	8316.05i	1.09232i
$388$	845.023i	0.110566i
$389$	−4728.25	−0.616277	−0.308138	−	0.951342i	$-0.599706\pi$
$389$	−4728.25	−0.616277	−0.308138	+	0.951342i	$0.599706\pi$
$390$	0	0
$391$	598.797	0.0774488
$392$	2220.67i	0.286125i
$393$	− 61.1737i	− 0.00785192i
$394$	3469.43	0.443622
$395$	0	0
$396$	1376.72	0.174704
$397$	− 740.837i	− 0.0936563i	−0.998903	−	0.0468281i	$-0.985089\pi$
$397$	− 740.837i	− 0.0936563i	0.998903	−	0.0468281i	$-0.0149113\pi$
$398$	761.584i	0.0959165i
$399$	−35.0370	−0.00439610
$400$	0	0
$401$	1879.58	0.234070	0.117035	−	0.993128i	$-0.462661\pi$
$401$	1879.58	0.234070	0.117035	+	0.993128i	$0.462661\pi$
$402$	− 428.839i	− 0.0532053i
$403$	− 13827.1i	− 1.70912i
$404$	6814.21	0.839157
$405$	0	0
$406$	1475.45	0.180358
$407$	2753.85i	0.335389i
$408$	− 57.3753i	− 0.00696201i
$409$	1715.45	0.207393	0.103697	−	0.994609i	$-0.466933\pi$
$409$	1715.45	0.207393	0.103697	+	0.994609i	$0.466933\pi$
$410$	0	0
$411$	605.866	0.0727133
$412$	5574.08i	0.666542i
$413$	− 2024.43i	− 0.241200i
$414$	−1025.97	−0.121796
$415$	0	0
$416$	−1505.15	−0.177395
$417$	652.056i	0.0765739i
$418$	− 485.336i	− 0.0567908i
$419$	−2497.15	−0.291155	−0.145578	−	0.989347i	$-0.546504\pi$
$419$	−2497.15	−0.291155	−0.145578	+	0.989347i	$0.546504\pi$
$420$	0	0
$421$	6582.52	0.762024	0.381012	−	0.924570i	$-0.375576\pi$
$421$	6582.52	0.762024	0.381012	+	0.924570i	$0.375576\pi$
$422$	− 2020.87i	− 0.233115i
$423$	− 2932.27i	− 0.337049i
$424$	5456.99	0.625035
$425$	0	0
$426$	−180.370	−0.0205140
$427$	2569.50i	0.291210i
$428$	3631.99i	0.410184i
$429$	−136.969	−0.0154147
$430$	0	0
$431$	8875.72	0.991946	0.495973	−	0.868338i	$-0.334812\pi$
$431$	8875.72	0.991946	0.495973	+	0.868338i	$0.334812\pi$
$432$	196.801i	0.0219180i
$433$	− 3636.90i	− 0.403645i	−0.979422	−	0.201822i	$-0.935314\pi$
$433$	− 3636.90i	− 0.403645i	0.979422	−	0.201822i	$-0.0646863\pi$
$434$	−4755.23	−0.525941
$435$	0	0
$436$	3448.31	0.378770
$437$	361.684i	0.0395920i
$438$	444.618i	0.0485039i
$439$	10979.4	1.19366	0.596829	−	0.802368i	$-0.296427\pi$
$439$	10979.4	1.19366	0.596829	+	0.802368i	$0.296427\pi$
$440$	0	0
$441$	7480.34	0.807725
$442$	− 2959.13i	− 0.318442i
$443$	1300.16i	0.139442i	0.997567	+	0.0697208i	$0.0222108\pi$
$443$	1300.16i	0.139442i	−0.997567	+	0.0697208i	$0.977789\pi$
$444$	−196.640	−0.0210183
$445$	0	0
$446$	6797.41	0.721674
$447$	− 71.0925i	− 0.00752250i
$448$	517.632i	0.0545889i
$449$	15875.2	1.66859	0.834296	−	0.551317i	$-0.185875\pi$
$449$	15875.2	1.66859	0.834296	+	0.551317i	$0.185875\pi$
$450$	0	0
$451$	864.920	0.0903049
$452$	− 6010.88i	− 0.625505i
$453$	− 333.406i	− 0.0345801i
$454$	−11521.6	−1.19105
$455$	0	0
$456$	34.6557	0.00355900
$457$	− 3115.66i	− 0.318916i	−0.987205	−	0.159458i	$-0.949025\pi$
$457$	− 3115.66i	− 0.318916i	0.987205	−	0.159458i	$-0.0509746\pi$
$458$	− 4357.99i	− 0.444619i
$459$	−386.910	−0.0393451
$460$	0	0
$461$	13479.7	1.36185	0.680924	−	0.732354i	$-0.261578\pi$
$461$	13479.7	1.36185	0.680924	+	0.732354i	$0.261578\pi$
$462$	47.1044i	0.00474350i
$463$	7946.19i	0.797604i	0.917037	+	0.398802i	$0.130574\pi$
$463$	7946.19i	0.797604i	−0.917037	+	0.398802i	$0.869426\pi$
$464$	−1459.39	−0.146014
$465$	0	0
$466$	−5616.99	−0.558373
$467$	9148.37i	0.906501i	0.891383	+	0.453250i	$0.149736\pi$
$467$	9148.37i	0.906501i	−0.891383	+	0.453250i	$0.850264\pi$
$468$	5070.11i	0.500782i
$469$	−7606.32	−0.748885
$470$	0	0
$471$	0.999532	9.77834e−5 0
$472$	2002.40i	0.195271i
$473$	− 3941.39i	− 0.383140i
$474$	−420.782	−0.0407746
$475$	0	0
$476$	−1017.67	−0.0979929
$477$	− 18381.9i	− 1.76446i
$478$	12571.3i	1.20293i
$479$	−7664.64	−0.731120	−0.365560	−	0.930788i	$-0.619122\pi$
$479$	−7664.64	−0.731120	−0.365560	+	0.930788i	$0.619122\pi$
$480$	0	0
$481$	−10141.7	−0.961378
$482$	− 2258.45i	− 0.213422i
$483$	− 35.1034i	− 0.00330696i
$484$	4671.50	0.438721
$485$	0	0
$486$	994.705	0.0928410
$487$	5347.21i	0.497547i	0.968562	+	0.248774i	$0.0800275\pi$
$487$	5347.21i	0.497547i	−0.968562	+	0.248774i	$0.919973\pi$
$488$	− 2541.54i	− 0.235758i
$489$	405.355	0.0374863
$490$	0	0
$491$	13647.2	1.25436	0.627178	−	0.778876i	$-0.284210\pi$
$491$	13647.2	1.25436	0.627178	+	0.778876i	$0.284210\pi$
$492$	61.7601i	0.00565927i
$493$	− 2869.17i	− 0.262111i
$494$	1787.37	0.162789
$495$	0	0
$496$	4703.49	0.425792
$497$	3199.23i	0.288743i
$498$	− 530.674i	− 0.0477511i
$499$	19351.6	1.73607	0.868034	−	0.496504i	$-0.165383\pi$
$499$	19351.6	1.73607	0.868034	+	0.496504i	$0.165383\pi$
$500$	0	0
$501$	203.617	0.0181576
$502$	5747.45i	0.510999i
$503$	− 19259.1i	− 1.70720i	−0.520929	−	0.853600i	$-0.674414\pi$
$503$	− 19259.1i	− 1.70720i	0.520929	−	0.853600i	$-0.325586\pi$
$504$	1743.65	0.154104
$505$	0	0
$506$	486.256	0.0427208
$507$	− 3.50834i	0 0.000307319i
$508$	1557.12i	0.135996i
$509$	−3595.77	−0.313123	−0.156561	−	0.987668i	$-0.550041\pi$
$509$	−3595.77	−0.313123	−0.156561	+	0.987668i	$0.550041\pi$
$510$	0	0
$511$	7886.20	0.682710
$512$	− 512.000i	− 0.0441942i
$513$	− 233.701i	− 0.0201133i
$514$	7424.35	0.637109
$515$	0	0
$516$	281.437	0.0240108
$517$	1389.75i	0.118223i
$518$	3487.81i	0.295841i
$519$	559.179	0.0472933
$520$	0	0
$521$	−15211.0	−1.27909	−0.639544	−	0.768754i	$-0.720877\pi$
$521$	−15211.0	−1.27909	−0.639544	+	0.768754i	$0.720877\pi$
$522$	4915.97i	0.412195i
$523$	18307.1i	1.53062i	0.643662	+	0.765310i	$0.277414\pi$
$523$	18307.1i	1.53062i	−0.643662	+	0.765310i	$0.722586\pi$
$524$	1073.23	0.0894739
$525$	0	0
$526$	2526.07	0.209395
$527$	9247.06i	0.764342i
$528$	− 46.5919i	− 0.00384025i
$529$	11804.6	0.970217
$530$	0	0
$531$	6745.09	0.551247
$532$	− 614.689i	− 0.0500942i
$533$	3185.28i	0.258855i
$534$	−312.420	−0.0253178
$535$	0	0
$536$	7523.55	0.606284
$537$	470.773i	0.0378312i
$538$	− 10968.8i	− 0.878992i
$539$	−3545.31	−0.283316
$540$	0	0
$541$	9102.17	0.723351	0.361676	−	0.932304i	$-0.382205\pi$
$541$	9102.17	0.723351	0.361676	+	0.932304i	$0.382205\pi$
$542$	6435.32i	0.510001i
$543$	− 574.223i	− 0.0453817i
$544$	1006.59	0.0793332
$545$	0	0
$546$	−173.474	−0.0135970
$547$	9218.75i	0.720595i	0.932837	+	0.360297i	$0.117325\pi$
$547$	9218.75i	0.720595i	−0.932837	+	0.360297i	$0.882675\pi$
$548$	10629.3i	0.828580i
$549$	−8561.17	−0.665541
$550$	0	0
$551$	1733.03	0.133992
$552$	34.7214i	0.00267725i
$553$	7463.42i	0.573918i
$554$	−15336.3	−1.17613
$555$	0	0
$556$	−11439.7	−0.872572
$557$	13435.1i	1.02202i	0.859575	+	0.511010i	$0.170728\pi$
$557$	13435.1i	1.02202i	−0.859575	+	0.511010i	$0.829272\pi$
$558$	− 15843.7i	− 1.20200i
$559$	14515.1	1.09825
$560$	0	0
$561$	91.5996	0.00689365
$562$	− 2253.62i	− 0.169151i
$563$	11941.5i	0.893916i	0.894555	+	0.446958i	$0.147493\pi$
$563$	11941.5i	0.893916i	−0.894555	+	0.446958i	$0.852507\pi$
$564$	−99.2359	−0.00740884
$565$	0	0
$566$	−3005.26	−0.223181
$567$	− 5862.12i	− 0.434191i
$568$	− 3164.42i	− 0.233761i
$569$	6378.91	0.469979	0.234989	−	0.971998i	$-0.424494\pi$
$569$	6378.91	0.469979	0.234989	+	0.971998i	$0.424494\pi$
$570$	0	0
$571$	24903.9	1.82521	0.912605	−	0.408843i	$-0.134068\pi$
$571$	24903.9	1.82521	0.912605	+	0.408843i	$0.134068\pi$
$572$	− 2402.98i	− 0.175653i
$573$	− 959.046i	− 0.0699210i
$574$	1095.44	0.0796564
$575$	0	0
$576$	−1724.67	−0.124759
$577$	11414.7i	0.823568i	0.911281	+	0.411784i	$0.135094\pi$
$577$	11414.7i	0.823568i	−0.911281	+	0.411784i	$0.864906\pi$
$578$	− 7847.04i	− 0.564695i
$579$	−740.040	−0.0531175
$580$	0	0
$581$	−9412.57	−0.672115
$582$	− 96.3319i	− 0.00686097i
$583$	8712.09i	0.618899i
$584$	−7800.39	−0.552709
$585$	0	0
$586$	−904.648	−0.0637724
$587$	− 20732.1i	− 1.45776i	−0.684641	−	0.728881i	$-0.740041\pi$
$587$	− 20732.1i	− 1.45776i	0.684641	−	0.728881i	$-0.259959\pi$
$588$	− 253.155i	− 0.0177550i
$589$	−5585.39	−0.390734
$590$	0	0
$591$	−395.511	−0.0275282
$592$	− 3449.86i	− 0.239507i
$593$	18010.5i	1.24722i	0.781735	+	0.623611i	$0.214335\pi$
$593$	18010.5i	1.24722i	−0.781735	+	0.623611i	$0.785665\pi$
$594$	−314.192	−0.0217028
$595$	0	0
$596$	1247.25	0.0857202
$597$	− 86.8199i	− 0.00595193i
$598$	1790.76i	0.122457i
$599$	−27944.7	−1.90616	−0.953080	−	0.302719i	$-0.902106\pi$
$599$	−27944.7	−1.90616	−0.953080	+	0.302719i	$0.902106\pi$
$600$	0	0
$601$	−11598.1	−0.787179	−0.393590	−	0.919286i	$-0.628767\pi$
$601$	−11598.1	−0.787179	−0.393590	+	0.919286i	$0.628767\pi$
$602$	− 4991.85i	− 0.337961i
$603$	− 25343.1i	− 1.71153i
$604$	5849.28	0.394046
$605$	0	0
$606$	−776.813	−0.0520724
$607$	− 20170.5i	− 1.34876i	−0.738385	−	0.674379i	$-0.764411\pi$
$607$	− 20170.5i	− 1.34876i	0.738385	−	0.674379i	$-0.235589\pi$
$608$	608.000i	0.0405554i
$609$	−168.200	−0.0111918
$610$	0	0
$611$	−5118.09	−0.338880
$612$	− 3390.71i	− 0.223956i
$613$	14618.3i	0.963174i	0.876398	+	0.481587i	$0.159939\pi$
$613$	14618.3i	0.963174i	−0.876398	+	0.481587i	$0.840061\pi$
$614$	4666.91	0.306745
$615$	0	0
$616$	−826.400	−0.0540530
$617$	17538.1i	1.14434i	0.820134	+	0.572171i	$0.193899\pi$
$617$	17538.1i	1.14434i	−0.820134	+	0.572171i	$0.806101\pi$
$618$	− 635.440i	− 0.0413611i
$619$	8815.75	0.572431	0.286216	−	0.958165i	$-0.407603\pi$
$619$	8815.75	0.572431	0.286216	+	0.958165i	$0.407603\pi$
$620$	0	0
$621$	234.144	0.0151302
$622$	− 20952.2i	− 1.35065i
$623$	5541.39i	0.356358i
$624$	171.586	0.0110079
$625$	0	0
$626$	8320.66	0.531247
$627$	55.3279i	0.00352405i
$628$	17.5358i	0.00111426i
$629$	6782.42	0.429941
$630$	0	0
$631$	−22170.8	−1.39874	−0.699370	−	0.714759i	$-0.746536\pi$
$631$	−22170.8	−1.39874	−0.699370	+	0.714759i	$0.746536\pi$
$632$	− 7382.21i	− 0.464634i
$633$	230.378i	0.0144655i
$634$	15017.1	0.940703
$635$	0	0
$636$	−622.092	−0.0387855
$637$	− 13056.5i	− 0.812112i
$638$	− 2329.92i	− 0.144581i
$639$	−10659.3	−0.659902
$640$	0	0
$641$	−22067.7	−1.35978	−0.679891	−	0.733313i	$-0.737973\pi$
$641$	−22067.7	−1.35978	−0.679891	+	0.733313i	$0.737973\pi$
$642$	− 414.043i	− 0.0254532i
$643$	− 11795.4i	− 0.723428i	−0.932289	−	0.361714i	$-0.882192\pi$
$643$	− 11795.4i	− 0.723428i	0.932289	−	0.361714i	$-0.117808\pi$
$644$	615.854	0.0376833
$645$	0	0
$646$	−1195.33	−0.0728012
$647$	9716.04i	0.590382i	0.955438	+	0.295191i	$0.0953832\pi$
$647$	9716.04i	0.590382i	−0.955438	+	0.295191i	$0.904617\pi$
$648$	5798.34i	0.351513i
$649$	−3196.83	−0.193354
$650$	0	0
$651$	542.092	0.0326363
$652$	7111.55i	0.427162i
$653$	− 10311.9i	− 0.617969i	−0.951067	−	0.308985i	$-0.900011\pi$
$653$	− 10311.9i	− 0.617969i	0.951067	−	0.308985i	$-0.0999892\pi$
$654$	−393.104	−0.0235039
$655$	0	0
$656$	−1083.52	−0.0644884
$657$	26275.6i	1.56029i
$658$	1760.15i	0.104282i
$659$	−4019.80	−0.237616	−0.118808	−	0.992917i	$-0.537907\pi$
$659$	−4019.80	−0.237616	−0.118808	+	0.992917i	$0.537907\pi$
$660$	0	0
$661$	−22702.6	−1.33590	−0.667951	−	0.744206i	$-0.732828\pi$
$661$	−22702.6	−1.33590	−0.667951	+	0.744206i	$0.732828\pi$
$662$	− 20773.6i	− 1.21962i
$663$	337.338i	0.0197604i
$664$	9310.15	0.544132
$665$	0	0
$666$	−11620.9	−0.676124
$667$	1736.31i	0.100795i
$668$	3572.26i	0.206908i
$669$	−774.898	−0.0447822
$670$	0	0
$671$	4057.57	0.233443
$672$	− 59.0096i	− 0.00338742i
$673$	11132.8i	0.637652i	0.947813	+	0.318826i	$0.103289\pi$
$673$	11132.8i	0.637652i	−0.947813	+	0.318826i	$0.896711\pi$
$674$	−11236.6	−0.642161
$675$	0	0
$676$	61.5503	0.00350195
$677$	13967.0i	0.792903i	0.918056	+	0.396452i	$0.129759\pi$
$677$	13967.0i	0.792903i	−0.918056	+	0.396452i	$0.870241\pi$
$678$	685.235i	0.0388146i
$679$	−1708.64	−0.0965707
$680$	0	0
$681$	1313.45	0.0739083
$682$	7509.12i	0.421612i
$683$	1173.88i	0.0657648i	0.999459	+	0.0328824i	$0.0104687\pi$
$683$	1173.88i	0.0657648i	−0.999459	+	0.0328824i	$0.989531\pi$
$684$	2048.05	0.114487
$685$	0	0
$686$	−10038.6	−0.558709
$687$	496.807i	0.0275901i
$688$	4937.54i	0.273607i
$689$	−32084.4	−1.77405
$690$	0	0
$691$	8713.33	0.479697	0.239849	−	0.970810i	$-0.422902\pi$
$691$	8713.33	0.479697	0.239849	+	0.970810i	$0.422902\pi$
$692$	9810.24i	0.538915i
$693$	2783.73i	0.152590i
$694$	−3628.64	−0.198475
$695$	0	0
$696$	166.369	0.00906065
$697$	− 2130.20i	− 0.115763i
$698$	− 1633.51i	− 0.0885809i
$699$	640.331	0.0346489
$700$	0	0
$701$	−31003.4	−1.67045	−0.835223	−	0.549912i	$-0.814661\pi$
$701$	−31003.4	−1.67045	−0.835223	+	0.549912i	$0.814661\pi$
$702$	− 1157.09i	− 0.0622102i
$703$	4096.70i	0.219787i
$704$	817.408	0.0437603
$705$	0	0
$706$	22180.8	1.18242
$707$	13778.3i	0.732939i
$708$	− 228.272i	− 0.0121172i
$709$	12145.1	0.643328	0.321664	−	0.946854i	$-0.395758\pi$
$709$	12145.1	0.643328	0.321664	+	0.946854i	$0.395758\pi$
$710$	0	0
$711$	−24867.0	−1.31165
$712$	− 5481.09i	− 0.288501i
$713$	− 5595.98i	− 0.293929i
$714$	116.013	0.00608078
$715$	0	0
$716$	−8259.24	−0.431092
$717$	− 1433.12i	− 0.0746456i
$718$	− 6423.36i	− 0.333868i
$719$	−24787.8	−1.28572	−0.642858	−	0.765985i	$-0.722252\pi$
$719$	−24787.8	−1.28572	−0.642858	+	0.765985i	$0.722252\pi$
$720$	0	0
$721$	−11270.8	−0.582173
$722$	− 722.000i	− 0.0372161i
$723$	257.461i	0.0132435i
$724$	10074.2	0.517132
$725$	0	0
$726$	−532.547	−0.0272241
$727$	− 19335.6i	− 0.986409i	−0.869914	−	0.493204i	$-0.835826\pi$
$727$	− 19335.6i	− 0.986409i	0.869914	−	0.493204i	$-0.164174\pi$
$728$	− 3043.42i	− 0.154941i
$729$	19456.0	0.988467
$730$	0	0
$731$	−9707.19	−0.491154
$732$	289.733i	0.0146296i
$733$	20204.5i	1.01810i	0.860735	+	0.509052i	$0.170004\pi$
$733$	20204.5i	1.01810i	−0.860735	+	0.509052i	$0.829996\pi$
$734$	−16155.6	−0.812418
$735$	0	0
$736$	−609.153	−0.0305077
$737$	12011.4i	0.600331i
$738$	3649.84i	0.182049i
$739$	−15643.7	−0.778706	−0.389353	−	0.921089i	$-0.627301\pi$
$739$	−15643.7	−0.778706	−0.389353	+	0.921089i	$0.627301\pi$
$740$	0	0
$741$	−203.758	−0.0101016
$742$	11034.0i	0.545920i
$743$	− 4500.20i	− 0.222202i	−0.993809	−	0.111101i	$-0.964562\pi$
$743$	− 4500.20i	− 0.222202i	0.993809	−	0.111101i	$-0.0354377\pi$
$744$	−536.193	−0.0264218
$745$	0	0
$746$	−10176.3	−0.499438
$747$	− 31361.2i	− 1.53608i
$748$	1607.02i	0.0785543i
$749$	−7343.88	−0.358264
$750$	0	0
$751$	35080.2	1.70452	0.852261	−	0.523117i	$-0.175231\pi$
$751$	35080.2	1.70452	0.852261	+	0.523117i	$0.175231\pi$
$752$	− 1740.99i	− 0.0844249i
$753$	− 655.204i	− 0.0317091i
$754$	8580.50	0.414434
$755$	0	0
$756$	−397.931	−0.0191437
$757$	10391.8i	0.498938i	0.968383	+	0.249469i	$0.0802560\pi$
$757$	10391.8i	0.498938i	−0.968383	+	0.249469i	$0.919744\pi$
$758$	5094.00i	0.244093i
$759$	−55.4328	−0.00265096
$760$	0	0
$761$	11810.5	0.562590	0.281295	−	0.959621i	$-0.409236\pi$
$761$	11810.5	0.562590	0.281295	+	0.959621i	$0.409236\pi$
$762$	− 177.510i	− 0.00843899i
$763$	6972.48i	0.330827i
$764$	16825.5	0.796761
$765$	0	0
$766$	−14112.2	−0.665659
$767$	− 11773.1i	− 0.554241i
$768$	58.3675i	0.00274239i
$769$	−35125.5	−1.64715	−0.823574	−	0.567209i	$-0.808023\pi$
$769$	−35125.5	−1.64715	−0.823574	+	0.567209i	$0.808023\pi$
$770$	0	0
$771$	−846.369	−0.0395347
$772$	− 12983.3i	− 0.605282i
$773$	20001.5i	0.930665i	0.885136	+	0.465332i	$0.154065\pi$
$773$	20001.5i	0.930665i	−0.885136	+	0.465332i	$0.845935\pi$
$774$	16632.1	0.772388
$775$	0	0
$776$	1690.05	0.0781819
$777$	− 397.607i	− 0.0183579i
$778$	9456.49i	0.435773i
$779$	1286.68	0.0591786
$780$	0	0
$781$	5051.99	0.231465
$782$	− 1197.59i	− 0.0547646i
$783$	− 1121.91i	− 0.0512055i
$784$	4441.35	0.202321
$785$	0	0
$786$	−122.347	−0.00555214
$787$	− 13593.3i	− 0.615690i	−0.951437	−	0.307845i	$-0.900392\pi$
$787$	− 13593.3i	− 0.615690i	0.951437	−	0.307845i	$-0.0996078\pi$
$788$	− 6938.85i	− 0.313688i
$789$	−287.970	−0.0129937
$790$	0	0
$791$	12154.0	0.546330
$792$	− 2753.44i	− 0.123534i
$793$	14943.0i	0.669156i
$794$	−1481.67	−0.0662250
$795$	0	0
$796$	1523.17	0.0678232
$797$	6946.75i	0.308741i	0.988013	+	0.154370i	$0.0493349\pi$
$797$	6946.75i	0.308741i	−0.988013	+	0.154370i	$0.950665\pi$
$798$	70.0739i	0.00310851i
$799$	3422.79	0.151552
$800$	0	0
$801$	−18463.1	−0.814432
$802$	− 3759.17i	− 0.165512i
$803$	− 12453.3i	− 0.547283i
$804$	−857.678	−0.0376219
$805$	0	0
$806$	−27654.2	−1.20853
$807$	1250.43i	0.0545443i
$808$	− 13628.4i	− 0.593374i
$809$	−24987.2	−1.08591	−0.542955	−	0.839762i	$-0.682695\pi$
$809$	−24987.2	−1.08591	−0.542955	+	0.839762i	$0.682695\pi$
$810$	0	0
$811$	−23172.5	−1.00332	−0.501662	−	0.865064i	$-0.667278\pi$
$811$	−23172.5	−1.00332	−0.501662	+	0.865064i	$0.667278\pi$
$812$	− 2950.89i	− 0.127532i
$813$	− 733.621i	− 0.0316472i
$814$	5507.70	0.237156
$815$	0	0
$816$	−114.751	−0.00492288
$817$	− 5863.32i	− 0.251079i
$818$	− 3430.91i	− 0.146649i
$819$	−10251.8	−0.437394
$820$	0	0
$821$	30703.8	1.30520	0.652600	−	0.757703i	$-0.273678\pi$
$821$	30703.8	1.30520	0.652600	+	0.757703i	$0.273678\pi$
$822$	− 1211.73i	− 0.0514161i
$823$	− 15940.1i	− 0.675135i	−0.941301	−	0.337568i	$-0.890396\pi$
$823$	− 15940.1i	− 0.675135i	0.941301	−	0.337568i	$-0.109604\pi$
$824$	11148.2	0.471316
$825$	0	0
$826$	−4048.86	−0.170554
$827$	6662.20i	0.280130i	0.990142	+	0.140065i	$0.0447311\pi$
$827$	6662.20i	0.280130i	−0.990142	+	0.140065i	$0.955269\pi$
$828$	2051.93i	0.0861227i
$829$	20606.0	0.863299	0.431649	−	0.902041i	$-0.357932\pi$
$829$	20606.0	0.863299	0.431649	+	0.902041i	$0.357932\pi$
$830$	0	0
$831$	1748.32	0.0729826
$832$	3010.31i	0.125437i
$833$	8731.69i	0.363187i
$834$	1304.11	0.0541459
$835$	0	0
$836$	−970.672	−0.0401572
$837$	3615.82i	0.149320i
$838$	4994.31i	0.205878i
$839$	45717.9	1.88124	0.940618	−	0.339468i	$-0.110247\pi$
$839$	45717.9	1.88124	0.940618	+	0.339468i	$0.110247\pi$
$840$	0	0
$841$	−16069.4	−0.658878
$842$	− 13165.0i	− 0.538833i
$843$	256.910i	0.0104964i
$844$	−4041.75	−0.164837
$845$	0	0
$846$	−5864.54	−0.238330
$847$	9445.79i	0.383189i
$848$	− 10914.0i	− 0.441967i
$849$	342.597	0.0138491
$850$	0	0
$851$	−4104.47	−0.165334
$852$	360.741i	0.0145056i
$853$	17230.4i	0.691626i	0.938303	+	0.345813i	$0.112397\pi$
$853$	17230.4i	0.691626i	−0.938303	+	0.345813i	$0.887603\pi$
$854$	5138.99	0.205917
$855$	0	0
$856$	7263.97	0.290044
$857$	− 44484.4i	− 1.77311i	−0.462619	−	0.886557i	$-0.653090\pi$
$857$	− 44484.4i	− 1.77311i	0.462619	−	0.886557i	$-0.346910\pi$
$858$	273.937i	0.0108998i
$859$	23213.4	0.922039	0.461019	−	0.887390i	$-0.347484\pi$
$859$	23213.4	0.922039	0.461019	+	0.887390i	$0.347484\pi$
$860$	0	0
$861$	−124.879	−0.00494294
$862$	− 17751.4i	− 0.701411i
$863$	− 9640.68i	− 0.380270i	−0.981758	−	0.190135i	$-0.939107\pi$
$863$	− 9640.68i	− 0.380270i	0.981758	−	0.190135i	$-0.0608925\pi$
$864$	393.601	0.0154984
$865$	0	0
$866$	−7273.79	−0.285420
$867$	894.555i	0.0350412i
$868$	9510.46i	0.371897i
$869$	11785.7	0.460072
$870$	0	0
$871$	−44234.8	−1.72082
$872$	− 6896.61i	− 0.267831i
$873$	− 5692.93i	− 0.220706i
$874$	723.369	0.0279958
$875$	0	0
$876$	889.237	0.0342974
$877$	9499.62i	0.365769i	0.983134	+	0.182885i	$0.0585434\pi$
$877$	9499.62i	0.365769i	−0.983134	+	0.182885i	$0.941457\pi$
$878$	− 21958.7i	− 0.844044i
$879$	103.129	0.00395729
$880$	0	0
$881$	−8252.54	−0.315590	−0.157795	−	0.987472i	$-0.550439\pi$
$881$	−8252.54	−0.315590	−0.157795	+	0.987472i	$0.550439\pi$
$882$	− 14960.7i	− 0.571148i
$883$	− 34768.9i	− 1.32510i	−0.749016	−	0.662552i	$-0.769474\pi$
$883$	− 34768.9i	− 1.32510i	0.749016	−	0.662552i	$-0.230526\pi$
$884$	−5918.26	−0.225173
$885$	0	0
$886$	2600.33	0.0986000
$887$	3288.58i	0.124487i	0.998061	+	0.0622433i	$0.0198255\pi$
$887$	3288.58i	0.124487i	−0.998061	+	0.0622433i	$0.980175\pi$
$888$	393.280i	0.0148622i
$889$	−3148.50	−0.118782
$890$	0	0
$891$	−9257.05	−0.348061
$892$	− 13594.8i	− 0.510301i
$893$	2067.43i	0.0774736i
$894$	−142.185	−0.00531921
$895$	0	0
$896$	1035.26	0.0386002
$897$	− 204.145i	− 0.00759888i
$898$	− 31750.4i	− 1.17987i
$899$	−26813.4	−0.994747
$900$	0	0
$901$	21456.9	0.793377
$902$	− 1729.84i	− 0.0638552i
$903$	569.067i	0.0209716i
$904$	−12021.8	−0.442299
$905$	0	0
$906$	−666.813	−0.0244518
$907$	− 37686.1i	− 1.37966i	−0.723973	−	0.689828i	$-0.757686\pi$
$907$	− 37686.1i	− 1.37966i	0.723973	−	0.689828i	$-0.242314\pi$
$908$	23043.2i	0.842197i
$909$	−45907.4	−1.67508
$910$	0	0
$911$	15090.9	0.548828	0.274414	−	0.961612i	$-0.411516\pi$
$911$	15090.9	0.548828	0.274414	+	0.961612i	$0.411516\pi$
$912$	− 69.3114i	− 0.00251659i
$913$	14863.7i	0.538790i
$914$	−6231.32	−0.225508
$915$	0	0
$916$	−8715.98	−0.314393
$917$	2170.08i	0.0781485i
$918$	773.820i	0.0278212i
$919$	−43617.4	−1.56562	−0.782810	−	0.622261i	$-0.786214\pi$
$919$	−43617.4	−1.56562	−0.782810	+	0.622261i	$0.786214\pi$
$920$	0	0
$921$	−532.024	−0.0190345
$922$	− 26959.4i	− 0.962972i
$923$	18605.2i	0.663486i
$924$	94.2089	0.00335416
$925$	0	0
$926$	15892.4	0.563991
$927$	− 37552.6i	− 1.33052i
$928$	2918.79i	0.103248i
$929$	−32446.2	−1.14588	−0.572942	−	0.819596i	$-0.694198\pi$
$929$	−32446.2	−1.14588	−0.572942	+	0.819596i	$0.694198\pi$
$930$	0	0
$931$	−5274.10	−0.185662
$932$	11234.0i	0.394830i
$933$	2388.53i	0.0838123i
$934$	18296.7	0.640993
$935$	0	0
$936$	10140.2	0.354106
$937$	28355.4i	0.988614i	0.869287	+	0.494307i	$0.164578\pi$
$937$	28355.4i	0.988614i	−0.869287	+	0.494307i	$0.835422\pi$
$938$	15212.6i	0.529542i
$939$	−948.548	−0.0329656
$940$	0	0
$941$	−48970.8	−1.69650	−0.848248	−	0.529599i	$-0.822342\pi$
$941$	−48970.8	−1.69650	−0.848248	+	0.529599i	$0.822342\pi$
$942$	− 1.99906i	0 6.91433e-5i
$943$	1289.12i	0.0445170i
$944$	4004.80	0.138078
$945$	0	0
$946$	−7882.78	−0.270921
$947$	9198.84i	0.315652i	0.987467	+	0.157826i	$0.0504485\pi$
$947$	9198.84i	0.315652i	−0.987467	+	0.157826i	$0.949552\pi$
$948$	841.565i	0.0288320i
$949$	45862.4	1.56876
$950$	0	0
$951$	−1711.94	−0.0583737
$952$	2035.33i	0.0692914i
$953$	28428.9i	0.966321i	0.875532	+	0.483160i	$0.160511\pi$
$953$	28428.9i	0.966321i	−0.875532	+	0.483160i	$0.839489\pi$
$954$	−36763.8	−1.24766
$955$	0	0
$956$	25142.7	0.850599
$957$	265.609i	0.00897170i
$958$	15329.3i	0.516980i
$959$	−21492.5	−0.723700
$960$	0	0
$961$	56626.2	1.90078
$962$	20283.4i	0.679797i
$963$	− 24468.7i	− 0.818788i
$964$	−4516.90	−0.150912
$965$	0	0
$966$	−70.2068	−0.00233837
$967$	22315.5i	0.742109i	0.928611	+	0.371054i	$0.121004\pi$
$967$	22315.5i	0.742109i	−0.928611	+	0.371054i	$0.878996\pi$
$968$	− 9343.01i	− 0.310223i
$969$	136.266	0.00451755
$970$	0	0
$971$	208.410	0.00688795	0.00344398	−	0.999994i	$-0.498904\pi$
$971$	208.410	0.00688795	0.00344398	+	0.999994i	$0.498904\pi$
$972$	− 1989.41i	− 0.0656485i
$973$	− 23131.0i	− 0.762124i
$974$	10694.4	0.351819
$975$	0	0
$976$	−5083.08	−0.166706
$977$	− 35744.3i	− 1.17048i	−0.810860	−	0.585241i	$-0.801000\pi$
$977$	− 35744.3i	− 1.17048i	0.810860	−	0.585241i	$-0.199000\pi$
$978$	− 810.710i	− 0.0265068i
$979$	8750.56	0.285668
$980$	0	0
$981$	−23231.3	−0.756082
$982$	− 27294.3i	− 0.886963i
$983$	− 36175.5i	− 1.17377i	−0.809669	−	0.586887i	$-0.800353\pi$
$983$	− 36175.5i	− 1.17377i	0.809669	−	0.586887i	$-0.199647\pi$
$984$	123.520	0.00400171
$985$	0	0
$986$	−5738.33	−0.185340
$987$	− 200.655i	− 0.00647104i
$988$	− 3574.74i	− 0.115109i
$989$	5874.44	0.188874
$990$	0	0
$991$	34654.3	1.11083	0.555413	−	0.831575i	$-0.312560\pi$
$991$	34654.3	1.11083	0.555413	+	0.831575i	$0.312560\pi$
$992$	− 9406.98i	− 0.301081i
$993$	2368.17i	0.0756812i
$994$	6398.46	0.204172
$995$	0	0
$996$	−1061.35	−0.0337652
$997$	− 4756.72i	− 0.151100i	−0.997142	−	0.0755501i	$-0.975929\pi$
$997$	− 4756.72i	− 0.151100i	0.997142	−	0.0755501i	$-0.0240713\pi$
$998$	− 38703.3i	− 1.22759i
$999$	2652.09	0.0839923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.4.b.i.799.1		4
5.2	odd	4		38.4.a.c.1.1	✓	2
5.3	odd	4		950.4.a.e.1.2		2
5.4	even	2	inner	950.4.b.i.799.4		4
15.2	even	4		342.4.a.h.1.1		2
20.7	even	4		304.4.a.c.1.2		2
35.27	even	4		1862.4.a.e.1.2		2
40.27	even	4		1216.4.a.p.1.1		2
40.37	odd	4		1216.4.a.g.1.2		2
95.37	even	4		722.4.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.a.c.1.1	✓	2	5.2	odd	4
304.4.a.c.1.2		2	20.7	even	4
342.4.a.h.1.1		2	15.2	even	4
722.4.a.f.1.2		2	95.37	even	4
950.4.a.e.1.2		2	5.3	odd	4
950.4.b.i.799.1		4	1.1	even	1	trivial
950.4.b.i.799.4		4	5.4	even	2	inner
1216.4.a.g.1.2		2	40.37	odd	4
1216.4.a.p.1.1		2	40.27	even	4
1862.4.a.e.1.2		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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +0.227998i q^{3} -4.00000 q^{4} +0.455996 q^{6} -8.08801i q^{7} +8.00000i q^{8} +26.9480 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +0.227998i q^{3} -4.00000 q^{4} +0.455996 q^{6} -8.08801i q^{7} +8.00000i q^{8} +26.9480 q^{9} -12.7720 q^{11} -0.911993i q^{12} -47.0360i q^{13} -16.1760 q^{14} +16.0000 q^{16} +31.4560i q^{17} -53.8960i q^{18} -19.0000 q^{19} +1.84405 q^{21} +25.5440i q^{22} -19.0360i q^{23} -1.82399 q^{24} -94.0720 q^{26} +12.3000i q^{27} +32.3520i q^{28} -91.2120 q^{29} +293.968 q^{31} -32.0000i q^{32} -2.91199i q^{33} +62.9120 q^{34} -107.792 q^{36} -215.616i q^{37} +38.0000i q^{38} +10.7241 q^{39} -67.7200 q^{41} -3.68810i q^{42} +308.596i q^{43} +51.0880 q^{44} -38.0720 q^{46} -108.812i q^{47} +3.64797i q^{48} +277.584 q^{49} -7.17191 q^{51} +188.144i q^{52} -682.124i q^{53} +24.6001 q^{54} +64.7041 q^{56} -4.33196i q^{57} +182.424i q^{58} +250.300 q^{59} -317.692 q^{61} -587.936i q^{62} -217.956i q^{63} -64.0000 q^{64} -5.82399 q^{66} -940.444i q^{67} -125.824i q^{68} +4.34018 q^{69} -395.552 q^{71} +215.584i q^{72} +975.048i q^{73} -431.232 q^{74} +76.0000 q^{76} +103.300i q^{77} -21.4483i q^{78} -922.776 q^{79} +724.792 q^{81} +135.440i q^{82} -1163.77i q^{83} -7.37620 q^{84} +617.192 q^{86} -20.7962i q^{87} -102.176i q^{88} -685.136 q^{89} -380.428 q^{91} +76.1441i q^{92} +67.0242i q^{93} -217.624 q^{94} +7.29594 q^{96} -211.256i q^{97} -555.168i q^{98} -344.180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9}+O(q^{10}) \) 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9	\( 4 q - 16 q^{4} + 36 q^{6} - 46 q^{9} - 34 q^{11} + 72 q^{14} + 64 q^{16} - 76 q^{19} - 454 q^{21} - 144 q^{24} + 68 q^{26} - 6 q^{29} + 424 q^{31} + 320 q^{34} + 184 q^{36} - 1102 q^{39} - 100 q^{41} + 136 q^{44} + 292 q^{46} - 120 q^{49} - 866 q^{51} - 756 q^{54} - 288 q^{56} + 574 q^{59} + 626 q^{61} - 256 q^{64} - 160 q^{66} - 1606 q^{69} + 400 q^{71} - 768 q^{74} + 304 q^{76} - 2700 q^{79} + 2284 q^{81} + 1816 q^{84} + 2708 q^{86} + 472 q^{89} - 4102 q^{91} + 1556 q^{94} + 576 q^{96} - 266 q^{99}+O(q^{100}) \) 4 * q - 16 * q^4 + 36 * q^6 - 46 * q^9 - 34 * q^11 + 72 * q^14 + 64 * q^16 - 76 * q^19 - 454 * q^21 - 144 * q^24 + 68 * q^26 - 6 * q^29 + 424 * q^31 + 320 * q^34 + 184 * q^36 - 1102 * q^39 - 100 * q^41 + 136 * q^44 + 292 * q^46 - 120 * q^49 - 866 * q^51 - 756 * q^54 - 288 * q^56 + 574 * q^59 + 626 * q^61 - 256 * q^64 - 160 * q^66 - 1606 * q^69 + 400 * q^71 - 768 * q^74 + 304 * q^76 - 2700 * q^79 + 2284 * q^81 + 1816 * q^84 + 2708 * q^86 + 472 * q^89 - 4102 * q^91 + 1556 * q^94 + 576 * q^96 - 266 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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