LMFDB - Embedded newform 1150.4.b.n.599.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(599,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.599");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 136x^{6} + 5308x^{4} + 58833x^{2} + 116964 $ x^8 + 136x^6 + 5308x^4 + 58833*x^2 + 116964
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.2
Root			$-1.58997i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.4.b.n.599.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -0.589969i q^{3} -4.00000 q^{4} -1.17994 q^{6} -18.5077i q^{7} +8.00000i q^{8} +26.6519 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -0.589969i q^{3} -4.00000 q^{4} -1.17994 q^{6} -18.5077i q^{7} +8.00000i q^{8} +26.6519 q^{9} +47.9296 q^{11} +2.35988i q^{12} -42.3717i q^{13} -37.0155 q^{14} +16.0000 q^{16} +1.70534i q^{17} -53.3039i q^{18} -21.4208 q^{19} -10.9190 q^{21} -95.8592i q^{22} +23.0000i q^{23} +4.71976 q^{24} -84.7434 q^{26} -31.6530i q^{27} +74.0310i q^{28} -57.6332 q^{29} +295.699 q^{31} -32.0000i q^{32} -28.2770i q^{33} +3.41069 q^{34} -106.608 q^{36} -7.85184i q^{37} +42.8416i q^{38} -24.9980 q^{39} +465.929 q^{41} +21.8380i q^{42} -182.374i q^{43} -191.718 q^{44} +46.0000 q^{46} +449.193i q^{47} -9.43951i q^{48} +0.463605 q^{49} +1.00610 q^{51} +169.487i q^{52} +368.316i q^{53} -63.3060 q^{54} +148.062 q^{56} +12.6376i q^{57} +115.266i q^{58} +377.032 q^{59} +849.042 q^{61} -591.398i q^{62} -493.267i q^{63} -64.0000 q^{64} -56.5540 q^{66} +92.3424i q^{67} -6.82138i q^{68} +13.5693 q^{69} -626.854 q^{71} +213.215i q^{72} -439.227i q^{73} -15.7037 q^{74} +85.6831 q^{76} -887.068i q^{77} +49.9960i q^{78} -641.707 q^{79} +700.928 q^{81} -931.859i q^{82} +609.932i q^{83} +43.6760 q^{84} -364.747 q^{86} +34.0018i q^{87} +383.437i q^{88} -1122.87 q^{89} -784.204 q^{91} -92.0000i q^{92} -174.453i q^{93} +898.386 q^{94} -18.8790 q^{96} -1428.80i q^{97} -0.927209i q^{98} +1277.42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 16 q^{6} - 64 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 + 16 * q^6 - 64 * q^9	$ 8 q - 32 q^{4} + 16 q^{6} - 64 q^{9} - 78 q^{11} - 4 q^{14} + 128 q^{16} - 106 q^{19} + 600 q^{21} - 64 q^{24} + 80 q^{26} - 322 q^{29} + 776 q^{31} - 92 q^{34} + 256 q^{36} - 2094 q^{39} + 968 q^{41} + 312 q^{44} + 368 q^{46} - 3286 q^{49} + 3650 q^{51} + 548 q^{54} + 16 q^{56} + 188 q^{59} + 2306 q^{61} - 512 q^{64} - 348 q^{66} - 184 q^{69} + 400 q^{71} + 1864 q^{74} + 424 q^{76} + 1816 q^{79} - 2112 q^{81} - 2400 q^{84} - 3576 q^{86} + 3568 q^{89} + 4658 q^{91} - 1060 q^{94} + 256 q^{96} + 5330 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 16 * q^6 - 64 * q^9 - 78 * q^11 - 4 * q^14 + 128 * q^16 - 106 * q^19 + 600 * q^21 - 64 * q^24 + 80 * q^26 - 322 * q^29 + 776 * q^31 - 92 * q^34 + 256 * q^36 - 2094 * q^39 + 968 * q^41 + 312 * q^44 + 368 * q^46 - 3286 * q^49 + 3650 * q^51 + 548 * q^54 + 16 * q^56 + 188 * q^59 + 2306 * q^61 - 512 * q^64 - 348 * q^66 - 184 * q^69 + 400 * q^71 + 1864 * q^74 + 424 * q^76 + 1816 * q^79 - 2112 * q^81 - 2400 * q^84 - 3576 * q^86 + 3568 * q^89 + 4658 * q^91 - 1060 * q^94 + 256 * q^96 + 5330 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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
$3$	− 0.589969i	− 0.113540i	−0.998387	−	0.0567698i	$-0.981920\pi$
$3$	− 0.589969i	− 0.113540i	0.998387	−	0.0567698i	$-0.0180801\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.17994	−0.0802847
$7$	− 18.5077i	− 0.999324i	−0.866220	−	0.499662i	$-0.833458\pi$
$7$	− 18.5077i	− 0.999324i	0.866220	−	0.499662i	$-0.166542\pi$
$8$	8.00000i	0.353553i
$9$	26.6519	0.987109
$10$	0	0
$11$	47.9296	1.31376	0.656878	−	0.753997i	$-0.271877\pi$
$11$	47.9296	1.31376	0.656878	+	0.753997i	$0.271877\pi$
$12$	2.35988i	0.0567698i
$13$	− 42.3717i	− 0.903984i	−0.892022	−	0.451992i	$-0.850714\pi$
$13$	− 42.3717i	− 0.903984i	0.892022	−	0.451992i	$-0.149286\pi$
$14$	−37.0155	−0.706629
$15$	0	0
$16$	16.0000	0.250000
$17$	1.70534i	0.0243298i	0.999926	+	0.0121649i	$0.00387230\pi$
$17$	1.70534i	0.0243298i	−0.999926	+	0.0121649i	$0.996128\pi$
$18$	− 53.3039i	− 0.697991i
$19$	−21.4208	−0.258645	−0.129323	−	0.991603i	$-0.541280\pi$
$19$	−21.4208	−0.258645	−0.129323	+	0.991603i	$0.541280\pi$
$20$	0	0
$21$	−10.9190	−0.113463
$22$	− 95.8592i	− 0.928966i
$23$	23.0000i	0.208514i
$23$	23.0000i	0.208514i
$24$	4.71976	0.0401423
$25$	0	0
$26$	−84.7434	−0.639213
$27$	− 31.6530i	− 0.225616i
$28$	74.0310i	0.499662i
$29$	−57.6332	−0.369042	−0.184521	−	0.982829i	$-0.559073\pi$
$29$	−57.6332	−0.369042	−0.184521	+	0.982829i	$0.559073\pi$
$30$	0	0
$31$	295.699	1.71320	0.856599	−	0.515983i	$-0.172573\pi$
$31$	295.699	1.71320	0.856599	+	0.515983i	$0.172573\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 28.2770i	− 0.149163i
$34$	3.41069	0.0172038
$35$	0	0
$36$	−106.608	−0.493554
$37$	− 7.85184i	− 0.0348874i	−0.999848	−	0.0174437i	$-0.994447\pi$
$37$	− 7.85184i	− 0.0348874i	0.999848	−	0.0174437i	$-0.00555279\pi$
$38$	42.8416i	0.182890i
$39$	−24.9980	−0.102638
$40$	0	0
$41$	465.929	1.77478	0.887390	−	0.461020i	$-0.152516\pi$
$41$	465.929	1.77478	0.887390	+	0.461020i	$0.152516\pi$
$42$	21.8380i	0.0802304i
$43$	− 182.374i	− 0.646784i	−0.946265	−	0.323392i	$-0.895177\pi$
$43$	− 182.374i	− 0.646784i	0.946265	−	0.323392i	$-0.104823\pi$
$44$	−191.718	−0.656878
$45$	0	0
$46$	46.0000	0.147442
$47$	449.193i	1.39408i	0.717035	+	0.697038i	$0.245499\pi$
$47$	449.193i	1.39408i	−0.717035	+	0.697038i	$0.754501\pi$
$48$	− 9.43951i	− 0.0283849i
$49$	0.463605	0.00135162
$50$	0	0
$51$	1.00610	0.00276240
$52$	169.487i	0.451992i
$53$	368.316i	0.954567i	0.878749	+	0.477283i	$0.158379\pi$
$53$	368.316i	0.954567i	−0.878749	+	0.477283i	$0.841621\pi$
$54$	−63.3060	−0.159534
$55$	0	0
$56$	148.062	0.353314
$57$	12.6376i	0.0293665i
$58$	115.266i	0.260952i
$59$	377.032	0.831955	0.415977	−	0.909375i	$-0.363440\pi$
$59$	377.032	0.831955	0.415977	+	0.909375i	$0.363440\pi$
$60$	0	0
$61$	849.042	1.78211	0.891055	−	0.453896i	$-0.149966\pi$
$61$	849.042	1.78211	0.891055	+	0.453896i	$0.149966\pi$
$62$	− 591.398i	− 1.21141i
$63$	− 493.267i	− 0.986441i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−56.5540	−0.105474
$67$	92.3424i	0.168379i	0.996450	+	0.0841897i	$0.0268302\pi$
$67$	92.3424i	0.168379i	−0.996450	+	0.0841897i	$0.973170\pi$
$68$	− 6.82138i	− 0.0121649i
$69$	13.5693	0.0236747
$70$	0	0
$71$	−626.854	−1.04780	−0.523901	−	0.851779i	$-0.675524\pi$
$71$	−626.854	−1.04780	−0.523901	+	0.851779i	$0.675524\pi$
$72$	213.215i	0.348996i
$73$	− 439.227i	− 0.704214i	−0.935960	−	0.352107i	$-0.885465\pi$
$73$	− 439.227i	− 0.704214i	0.935960	−	0.352107i	$-0.114535\pi$
$74$	−15.7037	−0.0246691
$75$	0	0
$76$	85.6831	0.129323
$77$	− 887.068i	− 1.31287i
$78$	49.9960i	0.0725761i
$79$	−641.707	−0.913894	−0.456947	−	0.889494i	$-0.651057\pi$
$79$	−641.707	−0.913894	−0.456947	+	0.889494i	$0.651057\pi$
$80$	0	0
$81$	700.928	0.961492
$82$	− 931.859i	− 1.25496i
$83$	609.932i	0.806611i	0.915065	+	0.403306i	$0.132139\pi$
$83$	609.932i	0.806611i	−0.915065	+	0.403306i	$0.867861\pi$
$84$	43.6760	0.0567315
$85$	0	0
$86$	−364.747	−0.457346
$87$	34.0018i	0.0419009i
$88$	383.437i	0.464483i
$89$	−1122.87	−1.33735	−0.668673	−	0.743557i	$-0.733137\pi$
$89$	−1122.87	−1.33735	−0.668673	+	0.743557i	$0.733137\pi$
$90$	0	0
$91$	−784.204	−0.903373
$92$	− 92.0000i	− 0.104257i
$93$	− 174.453i	− 0.194516i
$94$	898.386	0.985760
$95$	0	0
$96$	−18.8790	−0.0200712
$97$	− 1428.80i	− 1.49559i	−0.663930	−	0.747795i	$-0.731113\pi$
$97$	− 1428.80i	− 1.49559i	0.663930	−	0.747795i	$-0.268887\pi$
$98$	− 0.927209i	0 0.000955737i
$99$	1277.42	1.29682
$100$	0	0
$101$	−1512.15	−1.48975	−0.744875	−	0.667204i	$-0.767491\pi$
$101$	−1512.15	−1.48975	−0.744875	+	0.667204i	$0.767491\pi$
$102$	− 2.01220i	− 0.00195331i
$103$	− 957.279i	− 0.915762i	−0.889013	−	0.457881i	$-0.848609\pi$
$103$	− 957.279i	− 0.915762i	0.889013	−	0.457881i	$-0.151391\pi$
$104$	338.974	0.319607
$105$	0	0
$106$	736.631	0.674981
$107$	− 1742.16i	− 1.57403i	−0.616936	−	0.787013i	$-0.711626\pi$
$107$	− 1742.16i	− 1.57403i	0.616936	−	0.787013i	$-0.288374\pi$
$108$	126.612i	0.112808i
$109$	−1166.77	−1.02529	−0.512644	−	0.858601i	$-0.671334\pi$
$109$	−1166.77	−1.02529	−0.512644	+	0.858601i	$0.671334\pi$
$110$	0	0
$111$	−4.63234	−0.00396111
$112$	− 296.124i	− 0.249831i
$113$	393.287i	0.327410i	0.986509	+	0.163705i	$0.0523445\pi$
$113$	393.287i	0.327410i	−0.986509	+	0.163705i	$0.947655\pi$
$114$	25.2752	0.0207653
$115$	0	0
$116$	230.533	0.184521
$117$	− 1129.29i	− 0.892331i
$118$	− 754.063i	− 0.588281i
$119$	31.5621	0.0243134
$120$	0	0
$121$	966.245	0.725954
$122$	− 1698.08i	− 1.26014i
$123$	− 274.884i	− 0.201508i
$124$	−1182.80	−0.856599
$125$	0	0
$126$	−986.534	−0.697519
$127$	− 1067.87i	− 0.746127i	−0.927806	−	0.373063i	$-0.878307\pi$
$127$	− 1067.87i	− 0.746127i	0.927806	−	0.373063i	$-0.121693\pi$
$128$	128.000i	0.0883883i
$129$	−107.595	−0.0734357
$130$	0	0
$131$	−175.497	−0.117047	−0.0585237	−	0.998286i	$-0.518639\pi$
$131$	−175.497	−0.117047	−0.0585237	+	0.998286i	$0.518639\pi$
$132$	113.108i	0.0745817i
$133$	396.450i	0.258471i
$134$	184.685	0.119062
$135$	0	0
$136$	−13.6428	−0.00860189
$137$	475.898i	0.296779i	0.988929	+	0.148389i	$0.0474089\pi$
$137$	475.898i	0.296779i	−0.988929	+	0.148389i	$0.952591\pi$
$138$	− 27.1386i	− 0.0167405i
$139$	−153.167	−0.0934638	−0.0467319	−	0.998907i	$-0.514881\pi$
$139$	−153.167	−0.0934638	−0.0467319	+	0.998907i	$0.514881\pi$
$140$	0	0
$141$	265.010	0.158283
$142$	1253.71i	0.740907i
$143$	− 2030.86i	− 1.18761i
$144$	426.431	0.246777
$145$	0	0
$146$	−878.454	−0.497954
$147$	− 0.273513i	0 0.000153462i
$148$	31.4074i	0.0174437i
$149$	−506.906	−0.278707	−0.139353	−	0.990243i	$-0.544502\pi$
$149$	−506.906	−0.278707	−0.139353	+	0.990243i	$0.544502\pi$
$150$	0	0
$151$	2437.84	1.31383	0.656916	−	0.753964i	$-0.271861\pi$
$151$	2437.84	1.31383	0.656916	+	0.753964i	$0.271861\pi$
$152$	− 171.366i	− 0.0914450i
$153$	45.4507i	0.0240162i
$154$	−1774.14	−0.928338
$155$	0	0
$156$	99.9920	0.0513190
$157$	255.966i	0.130117i	0.997881	+	0.0650584i	$0.0207234\pi$
$157$	255.966i	0.130117i	−0.997881	+	0.0650584i	$0.979277\pi$
$158$	1283.41i	0.646221i
$159$	217.295	0.108381
$160$	0	0
$161$	425.678	0.208373
$162$	− 1401.86i	− 0.679878i
$163$	− 321.632i	− 0.154553i	−0.997010	−	0.0772767i	$-0.975378\pi$
$163$	− 321.632i	− 0.154553i	0.997010	−	0.0772767i	$-0.0246225\pi$
$164$	−1863.72	−0.887390
$165$	0	0
$166$	1219.86	0.570360
$167$	− 2926.22i	− 1.35591i	−0.735102	−	0.677957i	$-0.762866\pi$
$167$	− 2926.22i	− 1.35591i	0.735102	−	0.677957i	$-0.237134\pi$
$168$	− 87.3520i	− 0.0401152i
$169$	401.640	0.182813
$170$	0	0
$171$	−570.905	−0.255311
$172$	729.495i	0.323392i
$173$	− 1811.84i	− 0.796254i	−0.917330	−	0.398127i	$-0.869660\pi$
$173$	− 1811.84i	− 0.796254i	0.917330	−	0.398127i	$-0.130340\pi$
$174$	68.0037	0.0296284
$175$	0	0
$176$	766.873	0.328439
$177$	− 222.437i	− 0.0944599i
$178$	2245.74i	0.945646i
$179$	−912.664	−0.381093	−0.190547	−	0.981678i	$-0.561026\pi$
$179$	−912.664	−0.381093	−0.190547	+	0.981678i	$0.561026\pi$
$180$	0	0
$181$	3670.55	1.50735	0.753673	−	0.657249i	$-0.228280\pi$
$181$	3670.55	1.50735	0.753673	+	0.657249i	$0.228280\pi$
$182$	1568.41i	0.638781i
$183$	− 500.909i	− 0.202340i
$184$	−184.000	−0.0737210
$185$	0	0
$186$	−348.907	−0.137544
$187$	81.7364i	0.0319634i
$188$	− 1796.77i	− 0.697038i
$189$	−585.826	−0.225463
$190$	0	0
$191$	−1840.96	−0.697419	−0.348710	−	0.937231i	$-0.613380\pi$
$191$	−1840.96	−0.697419	−0.348710	+	0.937231i	$0.613380\pi$
$192$	37.7580i	0.0141925i
$193$	611.817i	0.228184i	0.993470	+	0.114092i	$0.0363959\pi$
$193$	611.817i	0.228184i	−0.993470	+	0.114092i	$0.963604\pi$
$194$	−2857.59	−1.05754
$195$	0	0
$196$	−1.85442	−0.000675808 0
$197$	2830.26i	1.02359i	0.859107	+	0.511796i	$0.171020\pi$
$197$	2830.26i	1.02359i	−0.859107	+	0.511796i	$0.828980\pi$
$198$	− 2554.83i	− 0.916990i
$199$	1162.74	0.414195	0.207097	−	0.978320i	$-0.433598\pi$
$199$	1162.74	0.414195	0.207097	+	0.978320i	$0.433598\pi$
$200$	0	0
$201$	54.4792	0.0191177
$202$	3024.31i	1.05341i
$203$	1066.66i	0.368792i
$204$	−4.02440	−0.00138120
$205$	0	0
$206$	−1914.56	−0.647542
$207$	612.995i	0.205826i
$208$	− 677.947i	− 0.225996i
$209$	−1026.69	−0.339797
$210$	0	0
$211$	1399.58	0.456641	0.228320	−	0.973586i	$-0.426677\pi$
$211$	1399.58	0.456641	0.228320	+	0.973586i	$0.426677\pi$
$212$	− 1473.26i	− 0.477283i
$213$	369.825i	0.118967i
$214$	−3484.32	−1.11300
$215$	0	0
$216$	253.224	0.0797672
$217$	− 5472.72i	− 1.71204i
$218$	2333.54i	0.724988i
$219$	−259.130	−0.0799562
$220$	0	0
$221$	72.2583	0.0219938
$222$	9.26469i	0.00280092i
$223$	− 4257.98i	− 1.27863i	−0.768943	−	0.639317i	$-0.779217\pi$
$223$	− 4257.98i	− 1.27863i	0.768943	−	0.639317i	$-0.220783\pi$
$224$	−592.248	−0.176657
$225$	0	0
$226$	786.574	0.231514
$227$	− 4025.03i	− 1.17688i	−0.808542	−	0.588438i	$-0.799743\pi$
$227$	− 4025.03i	− 1.17688i	0.808542	−	0.588438i	$-0.200257\pi$
$228$	− 50.5504i	− 0.0146833i
$229$	−3623.04	−1.04549	−0.522745	−	0.852489i	$-0.675092\pi$
$229$	−3623.04	−1.04549	−0.522745	+	0.852489i	$0.675092\pi$
$230$	0	0
$231$	−523.343	−0.149063
$232$	− 461.066i	− 0.130476i
$233$	− 6502.81i	− 1.82838i	−0.405282	−	0.914192i	$-0.632827\pi$
$233$	− 6502.81i	− 1.82838i	0.405282	−	0.914192i	$-0.367173\pi$
$234$	−2258.58	−0.630973
$235$	0	0
$236$	−1508.13	−0.415977
$237$	378.587i	0.103763i
$238$	− 63.1241i	− 0.0171921i
$239$	2690.07	0.728059	0.364030	−	0.931387i	$-0.381401\pi$
$239$	2690.07	0.728059	0.364030	+	0.931387i	$0.381401\pi$
$240$	0	0
$241$	−44.6958	−0.0119465	−0.00597326	−	0.999982i	$-0.501901\pi$
$241$	−44.6958	−0.0119465	−0.00597326	+	0.999982i	$0.501901\pi$
$242$	− 1932.49i	− 0.513327i
$243$	− 1268.16i	− 0.334783i
$244$	−3396.17	−0.891055
$245$	0	0
$246$	−549.768	−0.142488
$247$	907.635i	0.233811i
$248$	2365.59i	0.605707i
$249$	359.841	0.0915824
$250$	0	0
$251$	−6801.41	−1.71036	−0.855181	−	0.518329i	$-0.826554\pi$
$251$	−6801.41	−1.71036	−0.855181	+	0.518329i	$0.826554\pi$
$252$	1973.07i	0.493221i
$253$	1102.38i	0.273937i
$254$	−2135.74	−0.527591
$255$	0	0
$256$	256.000	0.0625000
$257$	5576.00i	1.35339i	0.736263	+	0.676695i	$0.236589\pi$
$257$	5576.00i	1.35339i	−0.736263	+	0.676695i	$0.763411\pi$
$258$	215.190i	0.0519269i
$259$	−145.320	−0.0348638
$260$	0	0
$261$	−1536.04	−0.364285
$262$	350.993i	0.0827651i
$263$	5669.58i	1.32928i	0.747163	+	0.664641i	$0.231415\pi$
$263$	5669.58i	1.32928i	−0.747163	+	0.664641i	$0.768585\pi$
$264$	226.216	0.0527372
$265$	0	0
$266$	792.900	0.182766
$267$	662.458i	0.151842i
$268$	− 369.370i	− 0.0841897i
$269$	−6040.21	−1.36906	−0.684532	−	0.728983i	$-0.739994\pi$
$269$	−6040.21	−1.36906	−0.684532	+	0.728983i	$0.739994\pi$
$270$	0	0
$271$	−6899.26	−1.54650	−0.773248	−	0.634104i	$-0.781369\pi$
$271$	−6899.26	−1.54650	−0.773248	+	0.634104i	$0.781369\pi$
$272$	27.2855i	0.00608245i
$273$	462.657i	0.102569i
$274$	951.795	0.209854
$275$	0	0
$276$	−54.2772	−0.0118373
$277$	5617.68i	1.21853i	0.792965	+	0.609267i	$0.208536\pi$
$277$	5617.68i	1.21853i	−0.792965	+	0.609267i	$0.791464\pi$
$278$	306.334i	0.0660889i
$279$	7880.96	1.69111
$280$	0	0
$281$	3069.89	0.651723	0.325861	−	0.945418i	$-0.394346\pi$
$281$	3069.89	0.651723	0.325861	+	0.945418i	$0.394346\pi$
$282$	− 530.020i	− 0.111923i
$283$	− 1404.86i	− 0.295089i	−0.989055	−	0.147544i	$-0.952863\pi$
$283$	− 1404.86i	− 0.295089i	0.989055	−	0.147544i	$-0.0471369\pi$
$284$	2507.42	0.523901
$285$	0	0
$286$	−4061.72	−0.839770
$287$	− 8623.30i	− 1.77358i
$288$	− 852.862i	− 0.174498i
$289$	4910.09	0.999408
$290$	0	0
$291$	−842.946	−0.169809
$292$	1756.91i	0.352107i
$293$	2407.05i	0.479936i	0.970781	+	0.239968i	$0.0771369\pi$
$293$	2407.05i	0.479936i	−0.970781	+	0.239968i	$0.922863\pi$
$294$	−0.547025	−0.000108514 0
$295$	0	0
$296$	62.8147	0.0123346
$297$	− 1517.12i	− 0.296404i
$298$	1013.81i	0.197076i
$299$	974.549	0.188494
$300$	0	0
$301$	−3375.33	−0.646347
$302$	− 4875.68i	− 0.929020i
$303$	892.124i	0.169146i
$304$	−342.732	−0.0646614
$305$	0	0
$306$	90.9015	0.0169820
$307$	− 459.743i	− 0.0854689i	−0.999086	−	0.0427344i	$-0.986393\pi$
$307$	− 459.743i	− 0.0854689i	0.999086	−	0.0427344i	$-0.0136069\pi$
$308$	3548.27i	0.656434i
$309$	−564.765	−0.103975
$310$	0	0
$311$	4119.48	0.751107	0.375553	−	0.926801i	$-0.377453\pi$
$311$	4119.48	0.751107	0.375553	+	0.926801i	$0.377453\pi$
$312$	− 199.984i	− 0.0362880i
$313$	− 1684.15i	− 0.304133i	−0.988370	−	0.152066i	$-0.951407\pi$
$313$	− 1684.15i	− 0.304133i	0.988370	−	0.152066i	$-0.0485927\pi$
$314$	511.933	0.0920065
$315$	0	0
$316$	2566.83	0.456947
$317$	8686.47i	1.53906i	0.638613	+	0.769528i	$0.279508\pi$
$317$	8686.47i	1.53906i	−0.638613	+	0.769528i	$0.720492\pi$
$318$	− 434.590i	− 0.0766371i
$319$	−2762.34	−0.484831
$320$	0	0
$321$	−1027.82	−0.178714
$322$	− 851.356i	− 0.147342i
$323$	− 36.5298i	− 0.00629279i
$324$	−2803.71	−0.480746
$325$	0	0
$326$	−643.265	−0.109286
$327$	688.360i	0.116411i
$328$	3727.44i	0.627479i
$329$	8313.55	1.39313
$330$	0	0
$331$	4307.91	0.715359	0.357680	−	0.933844i	$-0.383568\pi$
$331$	4307.91	0.715359	0.357680	+	0.933844i	$0.383568\pi$
$332$	− 2439.73i	− 0.403306i
$333$	− 209.267i	− 0.0344377i
$334$	−5852.44	−0.958776
$335$	0	0
$336$	−174.704	−0.0283657
$337$	− 290.156i	− 0.0469015i	−0.999725	−	0.0234507i	$-0.992535\pi$
$337$	− 290.156i	− 0.0469015i	0.999725	−	0.0234507i	$-0.00746529\pi$
$338$	− 803.280i	− 0.129268i
$339$	232.027	0.0371740
$340$	0	0
$341$	14172.7	2.25072
$342$	1141.81i	0.180532i
$343$	− 6356.73i	− 1.00067i
$344$	1458.99	0.228673
$345$	0	0
$346$	−3623.69	−0.563037
$347$	1042.94i	0.161349i	0.996741	+	0.0806743i	$0.0257074\pi$
$347$	1042.94i	0.161349i	−0.996741	+	0.0806743i	$0.974293\pi$
$348$	− 136.007i	− 0.0209505i
$349$	1819.56	0.279080	0.139540	−	0.990216i	$-0.455438\pi$
$349$	1819.56	0.279080	0.139540	+	0.990216i	$0.455438\pi$
$350$	0	0
$351$	−1341.19	−0.203953
$352$	− 1533.75i	− 0.232241i
$353$	4514.29i	0.680656i	0.940307	+	0.340328i	$0.110538\pi$
$353$	4514.29i	0.680656i	−0.940307	+	0.340328i	$0.889462\pi$
$354$	−444.874	−0.0667932
$355$	0	0
$356$	4491.47	0.668673
$357$	− 18.6207i	− 0.00276053i
$358$	1825.33i	0.269474i
$359$	−11527.9	−1.69476	−0.847379	−	0.530988i	$-0.821821\pi$
$359$	−11527.9	−1.69476	−0.847379	+	0.530988i	$0.821821\pi$
$360$	0	0
$361$	−6400.15	−0.933103
$362$	− 7341.10i	− 1.06585i
$363$	− 570.055i	− 0.0824246i
$364$	3136.82	0.451686
$365$	0	0
$366$	−1001.82	−0.143076
$367$	6894.09i	0.980568i	0.871563	+	0.490284i	$0.163107\pi$
$367$	6894.09i	0.980568i	−0.871563	+	0.490284i	$0.836893\pi$
$368$	368.000i	0.0521286i
$369$	12417.9	1.75190
$370$	0	0
$371$	6816.69	0.953922
$372$	697.814i	0.0972580i
$373$	− 7733.25i	− 1.07349i	−0.843744	−	0.536746i	$-0.819653\pi$
$373$	− 7733.25i	− 1.07349i	0.843744	−	0.536746i	$-0.180347\pi$
$374$	163.473	0.0226016
$375$	0	0
$376$	−3593.54	−0.492880
$377$	2442.02i	0.333608i
$378$	1171.65i	0.159427i
$379$	9495.72	1.28697	0.643486	−	0.765458i	$-0.277488\pi$
$379$	9495.72	1.28697	0.643486	+	0.765458i	$0.277488\pi$
$380$	0	0
$381$	−630.011	−0.0847150
$382$	3681.92i	0.493150i
$383$	12877.0i	1.71797i	0.511998	+	0.858987i	$0.328906\pi$
$383$	12877.0i	1.71797i	−0.511998	+	0.858987i	$0.671094\pi$
$384$	75.5161	0.0100356
$385$	0	0
$386$	1223.63	0.161351
$387$	− 4860.61i	− 0.638447i
$388$	5715.18i	0.747795i
$389$	8200.40	1.06884	0.534418	−	0.845221i	$-0.320531\pi$
$389$	8200.40	1.06884	0.534418	+	0.845221i	$0.320531\pi$
$390$	0	0
$391$	−39.2229	−0.00507312
$392$	3.70884i	0 0.000477869i
$393$	103.538i	0.0132895i
$394$	5660.52	0.723789
$395$	0	0
$396$	−5109.66	−0.648410
$397$	7842.68i	0.991468i	0.868475	+	0.495734i	$0.165101\pi$
$397$	7842.68i	0.991468i	−0.868475	+	0.495734i	$0.834899\pi$
$398$	− 2325.49i	− 0.292880i
$399$	233.893	0.0293467
$400$	0	0
$401$	−14534.2	−1.80999	−0.904993	−	0.425427i	$-0.860124\pi$
$401$	−14534.2	−1.80999	−0.904993	+	0.425427i	$0.860124\pi$
$402$	− 108.958i	− 0.0135183i
$403$	− 12529.3i	− 1.54870i
$404$	6048.61	0.744875
$405$	0	0
$406$	2133.32	0.260776
$407$	− 376.335i	− 0.0458335i
$408$	8.04881i	0 0.000976655i
$409$	−13388.0	−1.61857	−0.809283	−	0.587419i	$-0.800144\pi$
$409$	−13388.0	−1.61857	−0.809283	+	0.587419i	$0.800144\pi$
$410$	0	0
$411$	280.765	0.0336962
$412$	3829.12i	0.457881i
$413$	− 6978.00i	− 0.831393i
$414$	1225.99	0.145541
$415$	0	0
$416$	−1355.89	−0.159803
$417$	90.3640i	0.0106119i
$418$	2053.38i	0.240273i
$419$	3103.10	0.361805	0.180903	−	0.983501i	$-0.442098\pi$
$419$	3103.10	0.361805	0.180903	+	0.983501i	$0.442098\pi$
$420$	0	0
$421$	−6075.82	−0.703367	−0.351684	−	0.936119i	$-0.614391\pi$
$421$	−6075.82	−0.703367	−0.351684	+	0.936119i	$0.614391\pi$
$422$	− 2799.16i	− 0.322894i
$423$	11971.9i	1.37610i
$424$	−2946.53	−0.337490
$425$	0	0
$426$	739.649	0.0841224
$427$	− 15713.8i	− 1.78090i
$428$	6968.63i	0.787013i
$429$	−1198.14	−0.134841
$430$	0	0
$431$	14120.3	1.57808	0.789040	−	0.614341i	$-0.210578\pi$
$431$	14120.3	1.57808	0.789040	+	0.614341i	$0.210578\pi$
$432$	− 506.448i	− 0.0564039i
$433$	− 8555.96i	− 0.949592i	−0.880096	−	0.474796i	$-0.842522\pi$
$433$	− 8555.96i	− 0.949592i	0.880096	−	0.474796i	$-0.157478\pi$
$434$	−10945.4	−1.21060
$435$	0	0
$436$	4667.09	0.512644
$437$	− 492.678i	− 0.0539313i
$438$	518.261i	0.0565376i
$439$	10894.1	1.18439	0.592194	−	0.805796i	$-0.298262\pi$
$439$	10894.1	1.18439	0.592194	+	0.805796i	$0.298262\pi$
$440$	0	0
$441$	12.3560	0.00133419
$442$	− 144.517i	− 0.0155519i
$443$	− 16120.5i	− 1.72891i	−0.502708	−	0.864456i	$-0.667663\pi$
$443$	− 16120.5i	− 1.72891i	0.502708	−	0.864456i	$-0.332337\pi$
$444$	18.5294	0.00198055
$445$	0	0
$446$	−8515.96	−0.904130
$447$	299.059i	0.0316443i
$448$	1184.50i	0.124915i
$449$	−4811.29	−0.505699	−0.252849	−	0.967506i	$-0.581368\pi$
$449$	−4811.29	−0.505699	−0.252849	+	0.967506i	$0.581368\pi$
$450$	0	0
$451$	22331.8	2.33163
$452$	− 1573.15i	− 0.163705i
$453$	− 1438.25i	− 0.149172i
$454$	−8050.06	−0.832177
$455$	0	0
$456$	−101.101	−0.0103826
$457$	− 226.329i	− 0.0231667i	−0.999933	−	0.0115834i	$-0.996313\pi$
$457$	− 226.329i	− 0.0231667i	0.999933	−	0.0115834i	$-0.00368718\pi$
$458$	7246.08i	0.739273i
$459$	53.9793	0.00548919
$460$	0	0
$461$	−4349.17	−0.439395	−0.219697	−	0.975568i	$-0.570507\pi$
$461$	−4349.17	−0.439395	−0.219697	+	0.975568i	$0.570507\pi$
$462$	1046.69i	0.105403i
$463$	989.313i	0.0993030i	0.998767	+	0.0496515i	$0.0158111\pi$
$463$	989.313i	0.0993030i	−0.998767	+	0.0496515i	$0.984189\pi$
$464$	−922.131	−0.0922605
$465$	0	0
$466$	−13005.6	−1.29286
$467$	8512.91i	0.843535i	0.906704	+	0.421767i	$0.138590\pi$
$467$	8512.91i	0.843535i	−0.906704	+	0.421767i	$0.861410\pi$
$468$	4517.15i	0.446165i
$469$	1709.05	0.168266
$470$	0	0
$471$	151.012	0.0147734
$472$	3016.25i	0.294140i
$473$	− 8741.10i	− 0.849717i
$474$	757.175	0.0733717
$475$	0	0
$476$	−126.248	−0.0121567
$477$	9816.33i	0.942261i
$478$	− 5380.14i	− 0.514816i
$479$	12058.6	1.15025	0.575125	−	0.818065i	$-0.304953\pi$
$479$	12058.6	1.15025	0.575125	+	0.818065i	$0.304953\pi$
$480$	0	0
$481$	−332.696	−0.0315377
$482$	89.3916i	0.00844746i
$483$	− 251.137i	− 0.0236587i
$484$	−3864.98	−0.362977
$485$	0	0
$486$	−2536.31	−0.236727
$487$	11605.3i	1.07985i	0.841714	+	0.539924i	$0.181547\pi$
$487$	11605.3i	1.07985i	−0.841714	+	0.539924i	$0.818453\pi$
$488$	6792.34i	0.630071i
$489$	−189.753	−0.0175479
$490$	0	0
$491$	−4651.88	−0.427569	−0.213785	−	0.976881i	$-0.568579\pi$
$491$	−4651.88	−0.427569	−0.213785	+	0.976881i	$0.568579\pi$
$492$	1099.54i	0.100754i
$493$	− 98.2845i	− 0.00897872i
$494$	1815.27	0.165330
$495$	0	0
$496$	4731.19	0.428300
$497$	11601.6i	1.04709i
$498$	− 719.682i	− 0.0647585i
$499$	7953.03	0.713480	0.356740	−	0.934204i	$-0.383888\pi$
$499$	7953.03	0.713480	0.356740	+	0.934204i	$0.383888\pi$
$500$	0	0
$501$	−1726.38	−0.153950
$502$	13602.8i	1.20941i
$503$	11805.6i	1.04649i	0.852182	+	0.523245i	$0.175279\pi$
$503$	11805.6i	1.04649i	−0.852182	+	0.523245i	$0.824721\pi$
$504$	3946.14	0.348760
$505$	0	0
$506$	2204.76	0.193703
$507$	− 236.955i	− 0.0207565i
$508$	4271.48i	0.373063i
$509$	2732.89	0.237983	0.118991	−	0.992895i	$-0.462034\pi$
$509$	2732.89	0.237983	0.118991	+	0.992895i	$0.462034\pi$
$510$	0	0
$511$	−8129.09	−0.703738
$512$	− 512.000i	− 0.0441942i
$513$	678.032i	0.0583545i
$514$	11152.0	0.956992
$515$	0	0
$516$	430.380	0.0367178
$517$	21529.6i	1.83147i
$518$	290.640i	0.0246525i
$519$	−1068.93	−0.0904065
$520$	0	0
$521$	14710.9	1.23704	0.618518	−	0.785771i	$-0.287733\pi$
$521$	14710.9	1.23704	0.618518	+	0.785771i	$0.287733\pi$
$522$	3072.07i	0.257588i
$523$	7034.35i	0.588127i	0.955786	+	0.294064i	$0.0950078\pi$
$523$	7034.35i	0.588127i	−0.955786	+	0.294064i	$0.904992\pi$
$524$	701.987	0.0585237
$525$	0	0
$526$	11339.2	0.939944
$527$	504.269i	0.0416818i
$528$	− 452.432i	− 0.0372908i
$529$	−529.000	−0.0434783
$530$	0	0
$531$	10048.6	0.821230
$532$	− 1585.80i	− 0.129235i
$533$	− 19742.2i	− 1.60437i
$534$	1324.92	0.107368
$535$	0	0
$536$	−738.739	−0.0595311
$537$	538.444i	0.0432692i
$538$	12080.4i	0.968075i
$539$	22.2204	0.00177569
$540$	0	0
$541$	1552.90	0.123409	0.0617045	−	0.998094i	$-0.480346\pi$
$541$	1552.90	0.123409	0.0617045	+	0.998094i	$0.480346\pi$
$542$	13798.5i	1.09354i
$543$	− 2165.51i	− 0.171144i
$544$	54.5710	0.00430094
$545$	0	0
$546$	925.313	0.0725270
$547$	174.657i	0.0136523i	0.999977	+	0.00682614i	$0.00217284\pi$
$547$	174.657i	0.0136523i	−0.999977	+	0.00682614i	$0.997827\pi$
$548$	− 1903.59i	− 0.148389i
$549$	22628.6	1.75914
$550$	0	0
$551$	1234.55	0.0954510
$552$	108.554i	0.00837026i
$553$	11876.5i	0.913276i
$554$	11235.4	0.861633
$555$	0	0
$556$	612.669	0.0467319
$557$	− 1990.63i	− 0.151429i	−0.997130	−	0.0757143i	$-0.975876\pi$
$557$	− 1990.63i	− 0.151429i	0.997130	−	0.0757143i	$-0.0241237\pi$
$558$	− 15761.9i	− 1.19580i
$559$	−7727.48	−0.584683
$560$	0	0
$561$	48.2220	0.00362912
$562$	− 6139.78i	− 0.460838i
$563$	− 208.006i	− 0.0155709i	−0.999970	−	0.00778543i	$-0.997522\pi$
$563$	− 208.006i	− 0.0155709i	0.999970	−	0.00778543i	$-0.00247820\pi$
$564$	−1060.04	−0.0791414
$565$	0	0
$566$	−2809.71	−0.208659
$567$	− 12972.6i	− 0.960842i
$568$	− 5014.83i	− 0.370454i
$569$	3003.05	0.221256	0.110628	−	0.993862i	$-0.464714\pi$
$569$	3003.05	0.221256	0.110628	+	0.993862i	$0.464714\pi$
$570$	0	0
$571$	−10796.1	−0.791249	−0.395624	−	0.918412i	$-0.629472\pi$
$571$	−10796.1	−0.791249	−0.395624	+	0.918412i	$0.629472\pi$
$572$	8123.43i	0.593807i
$573$	1086.11i	0.0791847i
$574$	−17246.6	−1.25411
$575$	0	0
$576$	−1705.72	−0.123389
$577$	− 26011.3i	− 1.87671i	−0.345667	−	0.938357i	$-0.612347\pi$
$577$	− 26011.3i	− 1.87671i	0.345667	−	0.938357i	$-0.387653\pi$
$578$	− 9820.18i	− 0.706688i
$579$	360.953	0.0259079
$580$	0	0
$581$	11288.5	0.806066
$582$	1685.89i	0.120073i
$583$	17653.2i	1.25407i
$584$	3513.81	0.248977
$585$	0	0
$586$	4814.09	0.339366
$587$	− 2774.97i	− 0.195120i	−0.995230	−	0.0975598i	$-0.968896\pi$
$587$	− 2774.97i	− 0.195120i	0.995230	−	0.0975598i	$-0.0311037\pi$
$588$	1.09405i	0 7.67311e-5i
$589$	−6334.11	−0.443111
$590$	0	0
$591$	1669.77	0.116218
$592$	− 125.629i	− 0.00872185i
$593$	2384.07i	0.165096i	0.996587	+	0.0825481i	$0.0263058\pi$
$593$	2384.07i	0.165096i	−0.996587	+	0.0825481i	$0.973694\pi$
$594$	−3034.23	−0.209589
$595$	0	0
$596$	2027.62	0.139353
$597$	− 685.984i	− 0.0470276i
$598$	− 1949.10i	− 0.133285i
$599$	1090.87	0.0744102	0.0372051	−	0.999308i	$-0.488155\pi$
$599$	1090.87	0.0744102	0.0372051	+	0.999308i	$0.488155\pi$
$600$	0	0
$601$	−5192.37	−0.352414	−0.176207	−	0.984353i	$-0.556383\pi$
$601$	−5192.37	−0.352414	−0.176207	+	0.984353i	$0.556383\pi$
$602$	6750.65i	0.457036i
$603$	2461.10i	0.166209i
$604$	−9751.36	−0.656916
$605$	0	0
$606$	1784.25	0.119604
$607$	1205.44i	0.0806054i	0.999188	+	0.0403027i	$0.0128322\pi$
$607$	1205.44i	0.0806054i	−0.999188	+	0.0403027i	$0.987168\pi$
$608$	685.465i	0.0457225i
$609$	629.297	0.0418726
$610$	0	0
$611$	19033.1	1.26022
$612$	− 181.803i	− 0.0120081i
$613$	14243.2i	0.938466i	0.883075	+	0.469233i	$0.155469\pi$
$613$	14243.2i	0.938466i	−0.883075	+	0.469233i	$0.844531\pi$
$614$	−919.487	−0.0604356
$615$	0	0
$616$	7096.55	0.464169
$617$	− 422.492i	− 0.0275671i	−0.999905	−	0.0137835i	$-0.995612\pi$
$617$	− 422.492i	− 0.0275671i	0.999905	−	0.0137835i	$-0.00438757\pi$
$618$	1129.53i	0.0735217i
$619$	8826.35	0.573119	0.286560	−	0.958062i	$-0.407488\pi$
$619$	8826.35	0.573119	0.286560	+	0.958062i	$0.407488\pi$
$620$	0	0
$621$	728.019	0.0470441
$622$	− 8238.96i	− 0.531113i
$623$	20781.7i	1.33644i
$624$	−399.968	−0.0256595
$625$	0	0
$626$	−3368.29	−0.215054
$627$	605.715i	0.0385804i
$628$	− 1023.87i	− 0.0650584i
$629$	13.3901	0.000848804 0
$630$	0	0
$631$	−19684.1	−1.24186	−0.620929	−	0.783867i	$-0.713244\pi$
$631$	−19684.1	−1.24186	−0.620929	+	0.783867i	$0.713244\pi$
$632$	− 5133.65i	− 0.323110i
$633$	− 825.710i	− 0.0518468i
$634$	17372.9	1.08828
$635$	0	0
$636$	−869.180	−0.0541906
$637$	− 19.6437i	− 0.00122184i
$638$	5524.67i	0.342827i
$639$	−16706.9	−1.03429
$640$	0	0
$641$	15113.1	0.931253	0.465626	−	0.884981i	$-0.345829\pi$
$641$	15113.1	0.931253	0.465626	+	0.884981i	$0.345829\pi$
$642$	2055.64i	0.126370i
$643$	16917.8i	1.03760i	0.854897	+	0.518798i	$0.173620\pi$
$643$	16917.8i	1.03760i	−0.854897	+	0.518798i	$0.826380\pi$
$644$	−1702.71	−0.104187
$645$	0	0
$646$	−73.0596	−0.00444968
$647$	19564.5i	1.18881i	0.804166	+	0.594405i	$0.202612\pi$
$647$	19564.5i	1.18881i	−0.804166	+	0.594405i	$0.797388\pi$
$648$	5607.42i	0.339939i
$649$	18071.0	1.09299
$650$	0	0
$651$	−3228.74	−0.194384
$652$	1286.53i	0.0772767i
$653$	22735.0i	1.36247i	0.732067	+	0.681233i	$0.238556\pi$
$653$	22735.0i	1.36247i	−0.732067	+	0.681233i	$0.761444\pi$
$654$	1376.72	0.0823149
$655$	0	0
$656$	7454.87	0.443695
$657$	− 11706.2i	− 0.695136i
$658$	− 16627.1i	− 0.985094i
$659$	30730.7	1.81654	0.908269	−	0.418388i	$-0.137405\pi$
$659$	30730.7	1.81654	0.908269	+	0.418388i	$0.137405\pi$
$660$	0	0
$661$	−29204.3	−1.71848	−0.859240	−	0.511573i	$-0.829063\pi$
$661$	−29204.3	−1.71848	−0.859240	+	0.511573i	$0.829063\pi$
$662$	− 8615.81i	− 0.505835i
$663$	− 42.6302i	− 0.00249716i
$664$	−4879.45	−0.285180
$665$	0	0
$666$	−418.533	−0.0243511
$667$	− 1325.56i	− 0.0769506i
$668$	11704.9i	0.677957i
$669$	−2512.08	−0.145176
$670$	0	0
$671$	40694.2	2.34126
$672$	349.408i	0.0200576i
$673$	17530.1i	1.00406i	0.864849	+	0.502032i	$0.167414\pi$
$673$	17530.1i	1.00406i	−0.864849	+	0.502032i	$0.832586\pi$
$674$	−580.312	−0.0331644
$675$	0	0
$676$	−1606.56	−0.0914064
$677$	− 20553.4i	− 1.16681i	−0.812180	−	0.583407i	$-0.801719\pi$
$677$	− 20553.4i	− 1.16681i	0.812180	−	0.583407i	$-0.198281\pi$
$678$	− 464.055i	− 0.0262860i
$679$	−26443.8	−1.49458
$680$	0	0
$681$	−2374.65	−0.133622
$682$	− 28345.5i	− 1.59150i
$683$	− 13174.8i	− 0.738098i	−0.929410	−	0.369049i	$-0.879684\pi$
$683$	− 13174.8i	− 0.738098i	0.929410	−	0.369049i	$-0.120316\pi$
$684$	2283.62	0.127656
$685$	0	0
$686$	−12713.5	−0.707584
$687$	2137.48i	0.118705i
$688$	− 2917.98i	− 0.161696i
$689$	15606.2	0.862913
$690$	0	0
$691$	−14800.8	−0.814831	−0.407415	−	0.913243i	$-0.633570\pi$
$691$	−14800.8	−0.814831	−0.407415	+	0.913243i	$0.633570\pi$
$692$	7247.38i	0.398127i
$693$	− 23642.1i	− 1.29594i
$694$	2085.88	0.114091
$695$	0	0
$696$	−272.015	−0.0148142
$697$	794.570i	0.0431800i
$698$	− 3639.13i	− 0.197339i
$699$	−3836.46	−0.207594
$700$	0	0
$701$	−12311.5	−0.663336	−0.331668	−	0.943396i	$-0.607611\pi$
$701$	−12311.5	−0.663336	−0.331668	+	0.943396i	$0.607611\pi$
$702$	2682.38i	0.144217i
$703$	168.192i	0.00902347i
$704$	−3067.49	−0.164219
$705$	0	0
$706$	9028.59	0.481297
$707$	27986.5i	1.48874i
$708$	889.749i	0.0472299i
$709$	−3893.89	−0.206260	−0.103130	−	0.994668i	$-0.532886\pi$
$709$	−3893.89	−0.206260	−0.103130	+	0.994668i	$0.532886\pi$
$710$	0	0
$711$	−17102.7	−0.902113
$712$	− 8982.94i	− 0.472823i
$713$	6801.08i	0.357227i
$714$	−37.2413	−0.00195199
$715$	0	0
$716$	3650.65	0.190547
$717$	− 1587.06i	− 0.0826636i
$718$	23055.8i	1.19838i
$719$	19942.5	1.03440	0.517198	−	0.855866i	$-0.326975\pi$
$719$	19942.5	1.03440	0.517198	+	0.855866i	$0.326975\pi$
$720$	0	0
$721$	−17717.1	−0.915143
$722$	12800.3i	0.659803i
$723$	26.3692i	0.00135640i
$724$	−14682.2	−0.753673
$725$	0	0
$726$	−1140.11	−0.0582830
$727$	36167.0i	1.84506i	0.385926	+	0.922530i	$0.373882\pi$
$727$	36167.0i	1.84506i	−0.385926	+	0.922530i	$0.626118\pi$
$728$	− 6273.63i	− 0.319391i
$729$	18176.9	0.923481
$730$	0	0
$731$	311.010	0.0157361
$732$	2003.64i	0.101170i
$733$	11669.5i	0.588025i	0.955802	+	0.294013i	$0.0949908\pi$
$733$	11669.5i	0.588025i	−0.955802	+	0.294013i	$0.905009\pi$
$734$	13788.2	0.693366
$735$	0	0
$736$	736.000	0.0368605
$737$	4425.93i	0.221209i
$738$	− 24835.8i	− 1.23878i
$739$	−75.0536	−0.00373598	−0.00186799	−	0.999998i	$-0.500595\pi$
$739$	−75.0536	−0.00373598	−0.00186799	+	0.999998i	$0.500595\pi$
$740$	0	0
$741$	535.477	0.0265469
$742$	− 13633.4i	− 0.674524i
$743$	− 28279.8i	− 1.39635i	−0.715929	−	0.698173i	$-0.753997\pi$
$743$	− 28279.8i	− 1.39635i	0.715929	−	0.698173i	$-0.246003\pi$
$744$	1395.63	0.0687718
$745$	0	0
$746$	−15466.5	−0.759074
$747$	16255.9i	0.796213i
$748$	− 326.946i	− 0.0159817i
$749$	−32243.4	−1.57296
$750$	0	0
$751$	−17268.1	−0.839044	−0.419522	−	0.907745i	$-0.637802\pi$
$751$	−17268.1	−0.839044	−0.419522	+	0.907745i	$0.637802\pi$
$752$	7187.09i	0.348519i
$753$	4012.62i	0.194194i
$754$	4884.03	0.235897
$755$	0	0
$756$	2343.30	0.112732
$757$	− 12525.8i	− 0.601400i	−0.953719	−	0.300700i	$-0.902780\pi$
$757$	− 12525.8i	− 0.601400i	0.953719	−	0.300700i	$-0.0972202\pi$
$758$	− 18991.4i	− 0.910026i
$759$	650.371	0.0311027
$760$	0	0
$761$	−18670.1	−0.889343	−0.444672	−	0.895694i	$-0.646680\pi$
$761$	−18670.1	−0.889343	−0.444672	+	0.895694i	$0.646680\pi$
$762$	1260.02i	0.0599026i
$763$	21594.3i	1.02460i
$764$	7363.83	0.348710
$765$	0	0
$766$	25754.0	1.21479
$767$	− 15975.5i	− 0.752074i
$768$	− 151.032i	− 0.00709623i
$769$	32969.6	1.54605	0.773027	−	0.634373i	$-0.218742\pi$
$769$	32969.6	1.54605	0.773027	+	0.634373i	$0.218742\pi$
$770$	0	0
$771$	3289.67	0.153664
$772$	− 2447.27i	− 0.114092i
$773$	23251.3i	1.08188i	0.841062	+	0.540938i	$0.181931\pi$
$773$	23251.3i	1.08188i	−0.841062	+	0.540938i	$0.818069\pi$
$774$	−9721.23	−0.451450
$775$	0	0
$776$	11430.4	0.528771
$777$	85.7342i	0.00395843i
$778$	− 16400.8i	− 0.755781i
$779$	−9980.57	−0.459039
$780$	0	0
$781$	−30044.8	−1.37655
$782$	78.4458i	0.00358723i
$783$	1824.26i	0.0832617i
$784$	7.41767	0.000337904 0
$785$	0	0
$786$	207.075	0.00939712
$787$	− 29782.8i	− 1.34897i	−0.738288	−	0.674486i	$-0.764365\pi$
$787$	− 29782.8i	− 1.34897i	0.738288	−	0.674486i	$-0.235635\pi$
$788$	− 11321.0i	− 0.511796i
$789$	3344.88	0.150926
$790$	0	0
$791$	7278.86	0.327189
$792$	10219.3i	0.458495i
$793$	− 35975.3i	− 1.61100i
$794$	15685.4	0.701073
$795$	0	0
$796$	−4650.98	−0.207097
$797$	35307.2i	1.56919i	0.620008	+	0.784596i	$0.287129\pi$
$797$	35307.2i	1.56919i	−0.620008	+	0.784596i	$0.712871\pi$
$798$	− 467.787i	− 0.0207512i
$799$	−766.029	−0.0339176
$800$	0	0
$801$	−29926.6	−1.32011
$802$	29068.4i	1.27985i
$803$	− 21052.0i	− 0.925165i
$804$	−217.917	−0.00955887
$805$	0	0
$806$	−25058.5	−1.09510
$807$	3563.54i	0.155443i
$808$	− 12097.2i	− 0.526706i
$809$	−7752.46	−0.336912	−0.168456	−	0.985709i	$-0.553878\pi$
$809$	−7752.46	−0.336912	−0.168456	+	0.985709i	$0.553878\pi$
$810$	0	0
$811$	23471.6	1.01627	0.508137	−	0.861276i	$-0.330334\pi$
$811$	23471.6	1.01627	0.508137	+	0.861276i	$0.330334\pi$
$812$	− 4266.64i	− 0.184396i
$813$	4070.35i	0.175589i
$814$	−752.671	−0.0324092
$815$	0	0
$816$	16.0976	0.000690600 0
$817$	3906.59i	0.167288i
$818$	26776.0i	1.14450i
$819$	−20900.6	−0.891727
$820$	0	0
$821$	2467.55	0.104894	0.0524470	−	0.998624i	$-0.483298\pi$
$821$	2467.55	0.104894	0.0524470	+	0.998624i	$0.483298\pi$
$822$	− 561.530i	− 0.0238268i
$823$	− 21984.5i	− 0.931144i	−0.885010	−	0.465572i	$-0.845849\pi$
$823$	− 21984.5i	− 0.931144i	0.885010	−	0.465572i	$-0.154151\pi$
$824$	7658.23	0.323771
$825$	0	0
$826$	−13956.0	−0.587883
$827$	− 587.293i	− 0.0246943i	−0.999924	−	0.0123472i	$-0.996070\pi$
$827$	− 587.293i	− 0.0246943i	0.999924	−	0.0123472i	$-0.00393032\pi$
$828$	− 2451.98i	− 0.102913i
$829$	−41822.8	−1.75219	−0.876096	−	0.482137i	$-0.839861\pi$
$829$	−41822.8	−1.75219	−0.876096	+	0.482137i	$0.839861\pi$
$830$	0	0
$831$	3314.26	0.138352
$832$	2711.79i	0.112998i
$833$	0.790605i	0 3.28846e-5i
$834$	180.728	0.00750371
$835$	0	0
$836$	4106.76	0.169898
$837$	− 9359.77i	− 0.386524i
$838$	− 6206.20i	− 0.255835i
$839$	10126.5	0.416693	0.208346	−	0.978055i	$-0.433192\pi$
$839$	10126.5	0.416693	0.208346	+	0.978055i	$0.433192\pi$
$840$	0	0
$841$	−21067.4	−0.863808
$842$	12151.6i	0.497356i
$843$	− 1811.14i	− 0.0739964i
$844$	−5598.33	−0.228320
$845$	0	0
$846$	23943.7	0.973052
$847$	− 17883.0i	− 0.725463i
$848$	5893.05i	0.238642i
$849$	−828.822	−0.0335043
$850$	0	0
$851$	180.592	0.00727453
$852$	− 1479.30i	− 0.0594835i
$853$	− 11584.4i	− 0.464995i	−0.972597	−	0.232498i	$-0.925310\pi$
$853$	− 11584.4i	− 0.464995i	0.972597	−	0.232498i	$-0.0746898\pi$
$854$	−31427.7	−1.25929
$855$	0	0
$856$	13937.3	0.556502
$857$	− 9221.47i	− 0.367561i	−0.982967	−	0.183780i	$-0.941166\pi$
$857$	− 9221.47i	− 0.367561i	0.982967	−	0.183780i	$-0.0588335\pi$
$858$	2396.29i	0.0953472i
$859$	−34654.2	−1.37647	−0.688235	−	0.725488i	$-0.741614\pi$
$859$	−34654.2	−1.37647	−0.688235	+	0.725488i	$0.741614\pi$
$860$	0	0
$861$	−5087.48	−0.201372
$862$	− 28240.7i	− 1.11587i
$863$	− 42887.7i	− 1.69167i	−0.533441	−	0.845837i	$-0.679101\pi$
$863$	− 42887.7i	− 1.69167i	0.533441	−	0.845837i	$-0.320899\pi$
$864$	−1012.90	−0.0398836
$865$	0	0
$866$	−17111.9	−0.671463
$867$	− 2896.80i	− 0.113472i
$868$	21890.9i	0.856020i
$869$	−30756.7	−1.20063
$870$	0	0
$871$	3912.70	0.152212
$872$	− 9334.17i	− 0.362494i
$873$	− 38080.2i	− 1.47631i
$874$	−985.356	−0.0381352
$875$	0	0
$876$	1036.52	0.0399781
$877$	45935.5i	1.76868i	0.466846	+	0.884339i	$0.345390\pi$
$877$	45935.5i	1.76868i	−0.466846	+	0.884339i	$0.654610\pi$
$878$	− 21788.2i	− 0.837488i
$879$	1420.08	0.0544917
$880$	0	0
$881$	−71.9309	−0.00275075	−0.00137538	−	0.999999i	$-0.500438\pi$
$881$	−71.9309	−0.00275075	−0.00137538	+	0.999999i	$0.500438\pi$
$882$	− 24.7119i	0 0.000943417i
$883$	− 20003.8i	− 0.762379i	−0.924497	−	0.381189i	$-0.875515\pi$
$883$	− 20003.8i	− 0.762379i	0.924497	−	0.381189i	$-0.124485\pi$
$884$	−289.033	−0.0109969
$885$	0	0
$886$	−32241.0	−1.22253
$887$	26357.3i	0.997737i	0.866678	+	0.498869i	$0.166251\pi$
$887$	26357.3i	0.997737i	−0.866678	+	0.498869i	$0.833749\pi$
$888$	− 37.0588i	− 0.00140046i
$889$	−19763.9	−0.745623
$890$	0	0
$891$	33595.2	1.26317
$892$	17031.9i	0.639317i
$893$	− 9622.06i	− 0.360571i
$894$	598.118	0.0223759
$895$	0	0
$896$	2368.99	0.0883286
$897$	− 574.954i	− 0.0214015i
$898$	9622.57i	0.357583i
$899$	−17042.1	−0.632242
$900$	0	0
$901$	−628.105	−0.0232244
$902$	− 44663.6i	− 1.64871i
$903$	1991.34i	0.0733860i
$904$	−3146.30	−0.115757
$905$	0	0
$906$	−2876.50	−0.105481
$907$	− 39300.4i	− 1.43875i	−0.694620	−	0.719377i	$-0.744428\pi$
$907$	− 39300.4i	− 1.43875i	0.694620	−	0.719377i	$-0.255572\pi$
$908$	16100.1i	0.588438i
$909$	−40301.8	−1.47055
$910$	0	0
$911$	31099.2	1.13103	0.565513	−	0.824740i	$-0.308678\pi$
$911$	31099.2	1.13103	0.565513	+	0.824740i	$0.308678\pi$
$912$	202.202i	0.00734163i
$913$	29233.8i	1.05969i
$914$	−452.657	−0.0163814
$915$	0	0
$916$	14492.2	0.522745
$917$	3248.05i	0.116968i
$918$	− 107.959i	− 0.00388144i
$919$	−18935.8	−0.679690	−0.339845	−	0.940481i	$-0.610375\pi$
$919$	−18935.8	−0.679690	−0.339845	+	0.940481i	$0.610375\pi$
$920$	0	0
$921$	−271.235	−0.00970411
$922$	8698.33i	0.310699i
$923$	26560.9i	0.947195i
$924$	2093.37	0.0745313
$925$	0	0
$926$	1978.63	0.0702178
$927$	− 25513.3i	− 0.903957i
$928$	1844.26i	0.0652380i
$929$	−40156.1	−1.41817	−0.709085	−	0.705123i	$-0.750892\pi$
$929$	−40156.1	−1.41817	−0.709085	+	0.705123i	$0.750892\pi$
$930$	0	0
$931$	−9.93077	−0.000349590 0
$932$	26011.2i	0.914192i
$933$	− 2430.37i	− 0.0852804i
$934$	17025.8	0.596469
$935$	0	0
$936$	9034.30	0.315486
$937$	126.898i	0.00442432i	0.999998	+	0.00221216i	$0.000704153\pi$
$937$	126.898i	0.00442432i	−0.999998	+	0.00221216i	$0.999296\pi$
$938$	− 3418.10i	− 0.118982i
$939$	−993.594	−0.0345311
$940$	0	0
$941$	−19266.6	−0.667452	−0.333726	−	0.942670i	$-0.608306\pi$
$941$	−19266.6	−0.667452	−0.333726	+	0.942670i	$0.608306\pi$
$942$	− 302.025i	− 0.0104464i
$943$	10716.4i	0.370067i
$944$	6032.51	0.207989
$945$	0	0
$946$	−17482.2	−0.600840
$947$	− 54560.4i	− 1.87220i	−0.351732	−	0.936101i	$-0.614407\pi$
$947$	− 54560.4i	− 1.87220i	0.351732	−	0.936101i	$-0.385593\pi$
$948$	− 1514.35i	− 0.0518816i
$949$	−18610.8	−0.636598
$950$	0	0
$951$	5124.75	0.174744
$952$	252.497i	0.00859607i
$953$	44976.2i	1.52877i	0.644758	+	0.764387i	$0.276958\pi$
$953$	44976.2i	1.52877i	−0.644758	+	0.764387i	$0.723042\pi$
$954$	19632.7	0.666279
$955$	0	0
$956$	−10760.3	−0.364030
$957$	1629.69i	0.0550476i
$958$	− 24117.1i	− 0.813350i
$959$	8807.79	0.296578
$960$	0	0
$961$	57647.0	1.93505
$962$	665.391i	0.0223005i
$963$	− 46431.9i	− 1.55374i
$964$	178.783	0.00597326
$965$	0	0
$966$	−502.274	−0.0167292
$967$	− 39431.7i	− 1.31131i	−0.755059	−	0.655656i	$-0.772392\pi$
$967$	− 39431.7i	− 1.31131i	0.755059	−	0.655656i	$-0.227608\pi$
$968$	7729.96i	0.256664i
$969$	−21.5515	−0.000714482 0
$970$	0	0
$971$	20249.9	0.669258	0.334629	−	0.942350i	$-0.391389\pi$
$971$	20249.9	0.669258	0.334629	+	0.942350i	$0.391389\pi$
$972$	5072.63i	0.167392i
$973$	2834.78i	0.0934006i
$974$	23210.6	0.763567
$975$	0	0
$976$	13584.7	0.445527
$977$	− 9673.55i	− 0.316770i	−0.987377	−	0.158385i	$-0.949371\pi$
$977$	− 9673.55i	− 0.316770i	0.987377	−	0.158385i	$-0.0506287\pi$
$978$	379.507i	0.0124083i
$979$	−53818.6	−1.75695
$980$	0	0
$981$	−31096.7	−1.01207
$982$	9303.77i	0.302337i
$983$	17264.3i	0.560168i	0.959975	+	0.280084i	$0.0903623\pi$
$983$	17264.3i	0.560168i	−0.959975	+	0.280084i	$0.909638\pi$
$984$	2199.07	0.0712438
$985$	0	0
$986$	−196.569	−0.00634891
$987$	− 4904.74i	− 0.158176i
$988$	− 3630.54i	− 0.116906i
$989$	4194.60	0.134864
$990$	0	0
$991$	23892.9	0.765876	0.382938	−	0.923774i	$-0.374912\pi$
$991$	23892.9	0.765876	0.382938	+	0.923774i	$0.374912\pi$
$992$	− 9462.37i	− 0.302854i
$993$	− 2541.53i	− 0.0812217i
$994$	23203.3	0.740406
$995$	0	0
$996$	−1439.36	−0.0457912
$997$	− 35830.2i	− 1.13817i	−0.822280	−	0.569083i	$-0.807298\pi$
$997$	− 35830.2i	− 1.13817i	0.822280	−	0.569083i	$-0.192702\pi$
$998$	− 15906.1i	− 0.504507i
$999$	−248.534	−0.00787115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.b.n.599.2		8
5.2	odd	4		1150.4.a.p.1.2		4
5.3	odd	4		230.4.a.h.1.3	✓	4
5.4	even	2	inner	1150.4.b.n.599.7		8
15.8	even	4		2070.4.a.bj.1.2		4
20.3	even	4		1840.4.a.m.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.3	✓	4	5.3	odd	4
1150.4.a.p.1.2		4	5.2	odd	4
1150.4.b.n.599.2		8	1.1	even	1	trivial
1150.4.b.n.599.7		8	5.4	even	2	inner
1840.4.a.m.1.2		4	20.3	even	4
2070.4.a.bj.1.2		4	15.8	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -0.589969i q^{3} -4.00000 q^{4} -1.17994 q^{6} -18.5077i q^{7} +8.00000i q^{8} +26.6519 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -0.589969i q^{3} -4.00000 q^{4} -1.17994 q^{6} -18.5077i q^{7} +8.00000i q^{8} +26.6519 q^{9} +47.9296 q^{11} +2.35988i q^{12} -42.3717i q^{13} -37.0155 q^{14} +16.0000 q^{16} +1.70534i q^{17} -53.3039i q^{18} -21.4208 q^{19} -10.9190 q^{21} -95.8592i q^{22} +23.0000i q^{23} +4.71976 q^{24} -84.7434 q^{26} -31.6530i q^{27} +74.0310i q^{28} -57.6332 q^{29} +295.699 q^{31} -32.0000i q^{32} -28.2770i q^{33} +3.41069 q^{34} -106.608 q^{36} -7.85184i q^{37} +42.8416i q^{38} -24.9980 q^{39} +465.929 q^{41} +21.8380i q^{42} -182.374i q^{43} -191.718 q^{44} +46.0000 q^{46} +449.193i q^{47} -9.43951i q^{48} +0.463605 q^{49} +1.00610 q^{51} +169.487i q^{52} +368.316i q^{53} -63.3060 q^{54} +148.062 q^{56} +12.6376i q^{57} +115.266i q^{58} +377.032 q^{59} +849.042 q^{61} -591.398i q^{62} -493.267i q^{63} -64.0000 q^{64} -56.5540 q^{66} +92.3424i q^{67} -6.82138i q^{68} +13.5693 q^{69} -626.854 q^{71} +213.215i q^{72} -439.227i q^{73} -15.7037 q^{74} +85.6831 q^{76} -887.068i q^{77} +49.9960i q^{78} -641.707 q^{79} +700.928 q^{81} -931.859i q^{82} +609.932i q^{83} +43.6760 q^{84} -364.747 q^{86} +34.0018i q^{87} +383.437i q^{88} -1122.87 q^{89} -784.204 q^{91} -92.0000i q^{92} -174.453i q^{93} +898.386 q^{94} -18.8790 q^{96} -1428.80i q^{97} -0.927209i q^{98} +1277.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 16 q^{6} - 64 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 + 16 * q^6 - 64 * q^9	\( 8 q - 32 q^{4} + 16 q^{6} - 64 q^{9} - 78 q^{11} - 4 q^{14} + 128 q^{16} - 106 q^{19} + 600 q^{21} - 64 q^{24} + 80 q^{26} - 322 q^{29} + 776 q^{31} - 92 q^{34} + 256 q^{36} - 2094 q^{39} + 968 q^{41} + 312 q^{44} + 368 q^{46} - 3286 q^{49} + 3650 q^{51} + 548 q^{54} + 16 q^{56} + 188 q^{59} + 2306 q^{61} - 512 q^{64} - 348 q^{66} - 184 q^{69} + 400 q^{71} + 1864 q^{74} + 424 q^{76} + 1816 q^{79} - 2112 q^{81} - 2400 q^{84} - 3576 q^{86} + 3568 q^{89} + 4658 q^{91} - 1060 q^{94} + 256 q^{96} + 5330 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 16 * q^6 - 64 * q^9 - 78 * q^11 - 4 * q^14 + 128 * q^16 - 106 * q^19 + 600 * q^21 - 64 * q^24 + 80 * q^26 - 322 * q^29 + 776 * q^31 - 92 * q^34 + 256 * q^36 - 2094 * q^39 + 968 * q^41 + 312 * q^44 + 368 * q^46 - 3286 * q^49 + 3650 * q^51 + 548 * q^54 + 16 * q^56 + 188 * q^59 + 2306 * q^61 - 512 * q^64 - 348 * q^66 - 184 * q^69 + 400 * q^71 + 1864 * q^74 + 424 * q^76 + 1816 * q^79 - 2112 * q^81 - 2400 * q^84 - 3576 * q^86 + 3568 * q^89 + 4658 * q^91 - 1060 * q^94 + 256 * q^96 + 5330 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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