LMFDB - Embedded newform 1150.4.b.n.599.3

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			599.3
Root			$3.74869i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.4.b.n.599.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +4.74869i q^{3} -4.00000 q^{4} +9.49738 q^{6} +29.3684i q^{7} +8.00000i q^{8} +4.44993 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +4.74869i q^{3} -4.00000 q^{4} +9.49738 q^{6} +29.3684i q^{7} +8.00000i q^{8} +4.44993 q^{9} -38.1645 q^{11} -18.9948i q^{12} +22.5396i q^{13} +58.7368 q^{14} +16.0000 q^{16} -104.049i q^{17} -8.89986i q^{18} -142.000 q^{19} -139.461 q^{21} +76.3291i q^{22} +23.0000i q^{23} -37.9895 q^{24} +45.0792 q^{26} +149.346i q^{27} -117.474i q^{28} -241.429 q^{29} +99.2706 q^{31} -32.0000i q^{32} -181.232i q^{33} -208.097 q^{34} -17.7997 q^{36} +59.9452i q^{37} +284.000i q^{38} -107.034 q^{39} +249.248 q^{41} +278.923i q^{42} +163.863i q^{43} +152.658 q^{44} +46.0000 q^{46} -205.591i q^{47} +75.9791i q^{48} -519.502 q^{49} +494.095 q^{51} -90.1584i q^{52} -491.274i q^{53} +298.692 q^{54} -234.947 q^{56} -674.313i q^{57} +482.858i q^{58} -433.734 q^{59} +660.902 q^{61} -198.541i q^{62} +130.687i q^{63} -64.0000 q^{64} -362.463 q^{66} -323.564i q^{67} +416.195i q^{68} -109.220 q^{69} +893.243 q^{71} +35.5994i q^{72} -196.273i q^{73} +119.890 q^{74} +567.999 q^{76} -1120.83i q^{77} +214.067i q^{78} +500.211 q^{79} -589.050 q^{81} -498.496i q^{82} -800.944i q^{83} +557.846 q^{84} +327.726 q^{86} -1146.47i q^{87} -305.316i q^{88} +729.016 q^{89} -661.952 q^{91} -92.0000i q^{92} +471.405i q^{93} -411.181 q^{94} +151.958 q^{96} +1139.96i q^{97} +1039.00i q^{98} -169.829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	4.74869i	0.913886i	0.889496	+	0.456943i	$0.151056\pi$
$3$	4.74869i	0.913886i	−0.889496	+	0.456943i	$0.848944\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	9.49738	0.646215
$7$	29.3684i	1.58574i	0.609388	+	0.792872i	$0.291415\pi$
$7$	29.3684i	1.58574i	−0.609388	+	0.792872i	$0.708585\pi$
$8$	8.00000i	0.353553i
$9$	4.44993	0.164812
$10$	0	0
$11$	−38.1645	−1.04609	−0.523047	−	0.852304i	$-0.675205\pi$
$11$	−38.1645	−1.04609	−0.523047	+	0.852304i	$0.675205\pi$
$12$	− 18.9948i	− 0.456943i
$13$	22.5396i	0.480874i	0.970665	+	0.240437i	$0.0772907\pi$
$13$	22.5396i	0.480874i	−0.970665	+	0.240437i	$0.922709\pi$
$14$	58.7368	1.12129
$15$	0	0
$16$	16.0000	0.250000
$17$	− 104.049i	− 1.48444i	−0.670155	−	0.742221i	$-0.733772\pi$
$17$	− 104.049i	− 1.48444i	0.670155	−	0.742221i	$-0.266228\pi$
$18$	− 8.89986i	− 0.116540i
$19$	−142.000	−1.71458	−0.857289	−	0.514835i	$-0.827853\pi$
$19$	−142.000	−1.71458	−0.857289	+	0.514835i	$0.827853\pi$
$20$	0	0
$21$	−139.461	−1.44919
$22$	76.3291i	0.739701i
$23$	23.0000i	0.208514i
$23$	23.0000i	0.208514i
$24$	−37.9895	−0.323108
$25$	0	0
$26$	45.0792	0.340029
$27$	149.346i	1.06451i
$28$	− 117.474i	− 0.792872i
$29$	−241.429	−1.54594	−0.772969	−	0.634444i	$-0.781229\pi$
$29$	−241.429	−1.54594	−0.772969	+	0.634444i	$0.781229\pi$
$30$	0	0
$31$	99.2706	0.575146	0.287573	−	0.957759i	$-0.407152\pi$
$31$	99.2706	0.575146	0.287573	+	0.957759i	$0.407152\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 181.232i	− 0.956011i
$34$	−208.097	−1.04966
$35$	0	0
$36$	−17.7997	−0.0824061
$37$	59.9452i	0.266349i	0.991093	+	0.133175i	$0.0425171\pi$
$37$	59.9452i	0.266349i	−0.991093	+	0.133175i	$0.957483\pi$
$38$	284.000i	1.21239i
$39$	−107.034	−0.439464
$40$	0	0
$41$	249.248	0.949414	0.474707	−	0.880144i	$-0.342554\pi$
$41$	249.248	0.949414	0.474707	+	0.880144i	$0.342554\pi$
$42$	278.923i	1.02473i
$43$	163.863i	0.581136i	0.956854	+	0.290568i	$0.0938442\pi$
$43$	163.863i	0.581136i	−0.956854	+	0.290568i	$0.906156\pi$
$44$	152.658	0.523047
$45$	0	0
$46$	46.0000	0.147442
$47$	− 205.591i	− 0.638052i	−0.947746	−	0.319026i	$-0.896644\pi$
$47$	− 205.591i	− 0.638052i	0.947746	−	0.319026i	$-0.103356\pi$
$48$	75.9791i	0.228472i
$49$	−519.502	−1.51458
$50$	0	0
$51$	494.095	1.35661
$52$	− 90.1584i	− 0.240437i
$53$	− 491.274i	− 1.27324i	−0.771178	−	0.636620i	$-0.780332\pi$
$53$	− 491.274i	− 1.27324i	0.771178	−	0.636620i	$-0.219668\pi$
$54$	298.692	0.752719
$55$	0	0
$56$	−234.947	−0.560645
$57$	− 674.313i	− 1.56693i
$58$	482.858i	1.09314i
$59$	−433.734	−0.957074	−0.478537	−	0.878067i	$-0.658833\pi$
$59$	−433.734	−0.957074	−0.478537	+	0.878067i	$0.658833\pi$
$60$	0	0
$61$	660.902	1.38721	0.693605	−	0.720355i	$-0.256021\pi$
$61$	660.902	1.38721	0.693605	+	0.720355i	$0.256021\pi$
$62$	− 198.541i	− 0.406690i
$63$	130.687i	0.261350i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−362.463	−0.676002
$67$	− 323.564i	− 0.589995i	−0.955498	−	0.294997i	$-0.904681\pi$
$67$	− 323.564i	− 0.589995i	0.955498	−	0.294997i	$-0.0953188\pi$
$68$	416.195i	0.742221i
$69$	−109.220	−0.190558
$70$	0	0
$71$	893.243	1.49308	0.746538	−	0.665342i	$-0.231714\pi$
$71$	893.243	1.49308	0.746538	+	0.665342i	$0.231714\pi$
$72$	35.5994i	0.0582699i
$73$	− 196.273i	− 0.314685i	−0.987544	−	0.157343i	$-0.949707\pi$
$73$	− 196.273i	− 0.314685i	0.987544	−	0.157343i	$-0.0502927\pi$
$74$	119.890	0.188337
$75$	0	0
$76$	567.999	0.857289
$77$	− 1120.83i	− 1.65884i
$78$	214.067i	0.310748i
$79$	500.211	0.712381	0.356191	−	0.934413i	$-0.384075\pi$
$79$	500.211	0.712381	0.356191	+	0.934413i	$0.384075\pi$
$80$	0	0
$81$	−589.050	−0.808025
$82$	− 498.496i	− 0.671337i
$83$	− 800.944i	− 1.05922i	−0.848242	−	0.529609i	$-0.822339\pi$
$83$	− 800.944i	− 1.05922i	0.848242	−	0.529609i	$-0.177661\pi$
$84$	557.846	0.724595
$85$	0	0
$86$	327.726	0.410925
$87$	− 1146.47i	− 1.41281i
$88$	− 305.316i	− 0.369850i
$89$	729.016	0.868264	0.434132	−	0.900849i	$-0.357055\pi$
$89$	729.016	0.868264	0.434132	+	0.900849i	$0.357055\pi$
$90$	0	0
$91$	−661.952	−0.762543
$92$	− 92.0000i	− 0.104257i
$93$	471.405i	0.525618i
$94$	−411.181	−0.451171
$95$	0	0
$96$	151.958	0.161554
$97$	1139.96i	1.19325i	0.802520	+	0.596626i	$0.203492\pi$
$97$	1139.96i	1.19325i	−0.802520	+	0.596626i	$0.796508\pi$
$98$	1039.00i	1.07097i
$99$	−169.829	−0.172409
$100$	0	0
$101$	−1669.38	−1.64465	−0.822326	−	0.569017i	$-0.807324\pi$
$101$	−1669.38	−1.64465	−0.822326	+	0.569017i	$0.807324\pi$
$102$	− 988.190i	− 0.959269i
$103$	1110.63i	1.06246i	0.847228	+	0.531229i	$0.178270\pi$
$103$	1110.63i	1.06246i	−0.847228	+	0.531229i	$0.821730\pi$
$104$	−180.317	−0.170015
$105$	0	0
$106$	−982.549	−0.900317
$107$	39.1892i	0.0354071i	0.999843	+	0.0177036i	$0.00563551\pi$
$107$	39.1892i	0.0354071i	−0.999843	+	0.0177036i	$0.994364\pi$
$108$	− 597.384i	− 0.532253i
$109$	−807.545	−0.709622	−0.354811	−	0.934938i	$-0.615455\pi$
$109$	−807.545	−0.709622	−0.354811	+	0.934938i	$0.615455\pi$
$110$	0	0
$111$	−284.661	−0.243413
$112$	469.894i	0.396436i
$113$	− 1066.58i	− 0.887923i	−0.896046	−	0.443961i	$-0.853573\pi$
$113$	− 1066.58i	− 0.887923i	0.896046	−	0.443961i	$-0.146427\pi$
$114$	−1348.63	−1.10799
$115$	0	0
$116$	965.715	0.772969
$117$	100.300i	0.0792539i
$118$	867.468i	0.676753i
$119$	3055.74	2.35395
$120$	0	0
$121$	125.532	0.0943139
$122$	− 1321.80i	− 0.980906i
$123$	1183.60i	0.867657i
$124$	−397.082	−0.287573
$125$	0	0
$126$	261.374	0.184802
$127$	− 641.707i	− 0.448364i	−0.974547	−	0.224182i	$-0.928029\pi$
$127$	− 641.707i	− 0.448364i	0.974547	−	0.224182i	$-0.0719711\pi$
$128$	128.000i	0.0883883i
$129$	−778.134	−0.531092
$130$	0	0
$131$	2389.92	1.59396	0.796979	−	0.604007i	$-0.206430\pi$
$131$	2389.92	1.59396	0.796979	+	0.604007i	$0.206430\pi$
$132$	724.926i	0.478006i
$133$	− 4170.31i	− 2.71888i
$134$	−647.128	−0.417189
$135$	0	0
$136$	832.390	0.524830
$137$	899.291i	0.560814i	0.959881	+	0.280407i	$0.0904695\pi$
$137$	899.291i	0.560814i	−0.959881	+	0.280407i	$0.909530\pi$
$138$	218.440i	0.134745i
$139$	−309.341	−0.188762	−0.0943811	−	0.995536i	$-0.530087\pi$
$139$	−309.341	−0.188762	−0.0943811	+	0.995536i	$0.530087\pi$
$140$	0	0
$141$	976.286	0.583107
$142$	− 1786.49i	− 1.05576i
$143$	− 860.214i	− 0.503040i
$144$	71.1989	0.0412030
$145$	0	0
$146$	−392.546	−0.222516
$147$	− 2466.96i	− 1.38416i
$148$	− 239.781i	− 0.133175i
$149$	−2560.87	−1.40802	−0.704010	−	0.710190i	$-0.748609\pi$
$149$	−2560.87	−1.40802	−0.704010	+	0.710190i	$0.748609\pi$
$150$	0	0
$151$	−2463.15	−1.32747	−0.663737	−	0.747966i	$-0.731031\pi$
$151$	−2463.15	−1.32747	−0.663737	+	0.747966i	$0.731031\pi$
$152$	− 1136.00i	− 0.606195i
$153$	− 463.009i	− 0.244654i
$154$	−2241.66	−1.17298
$155$	0	0
$156$	428.135	0.219732
$157$	− 566.720i	− 0.288084i	−0.989572	−	0.144042i	$-0.953990\pi$
$157$	− 566.720i	− 0.288084i	0.989572	−	0.144042i	$-0.0460100\pi$
$158$	− 1000.42i	− 0.503730i
$159$	2332.91	1.16360
$160$	0	0
$161$	−675.473	−0.330650
$162$	1178.10i	0.571360i
$163$	− 960.902i	− 0.461740i	−0.972985	−	0.230870i	$-0.925843\pi$
$163$	− 960.902i	− 0.461740i	0.972985	−	0.230870i	$-0.0741573\pi$
$164$	−996.992	−0.474707
$165$	0	0
$166$	−1601.89	−0.748980
$167$	− 4224.70i	− 1.95759i	−0.204847	−	0.978794i	$-0.565670\pi$
$167$	− 4224.70i	− 1.95759i	0.204847	−	0.978794i	$-0.434330\pi$
$168$	− 1115.69i	− 0.512366i
$169$	1688.97	0.768760
$170$	0	0
$171$	−631.889	−0.282583
$172$	− 655.451i	− 0.290568i
$173$	− 3448.98i	− 1.51573i	−0.652412	−	0.757865i	$-0.726243\pi$
$173$	− 3448.98i	− 1.51573i	0.652412	−	0.757865i	$-0.273757\pi$
$174$	−2292.94	−0.999008
$175$	0	0
$176$	−610.633	−0.261524
$177$	− 2059.67i	− 0.874657i
$178$	− 1458.03i	− 0.613955i
$179$	−1457.82	−0.608728	−0.304364	−	0.952556i	$-0.598444\pi$
$179$	−1457.82	−0.608728	−0.304364	+	0.952556i	$0.598444\pi$
$180$	0	0
$181$	−3634.97	−1.49274	−0.746368	−	0.665534i	$-0.768204\pi$
$181$	−3634.97	−1.49274	−0.746368	+	0.665534i	$0.768204\pi$
$182$	1323.90i	0.539199i
$183$	3138.42i	1.26775i
$184$	−184.000	−0.0737210
$185$	0	0
$186$	942.811	0.371668
$187$	3970.97i	1.55287i
$188$	822.362i	0.319026i
$189$	−4386.05	−1.68803
$190$	0	0
$191$	448.811	0.170025	0.0850127	−	0.996380i	$-0.472907\pi$
$191$	448.811	0.170025	0.0850127	+	0.996380i	$0.472907\pi$
$192$	− 303.916i	− 0.114236i
$193$	− 4259.35i	− 1.58857i	−0.607544	−	0.794286i	$-0.707845\pi$
$193$	− 4259.35i	− 1.58857i	0.607544	−	0.794286i	$-0.292155\pi$
$194$	2279.92	0.843756
$195$	0	0
$196$	2078.01	0.757292
$197$	− 1767.37i	− 0.639189i	−0.947554	−	0.319594i	$-0.896453\pi$
$197$	− 1767.37i	− 0.639189i	0.947554	−	0.319594i	$-0.103547\pi$
$198$	339.659i	0.121912i
$199$	−1004.29	−0.357750	−0.178875	−	0.983872i	$-0.557246\pi$
$199$	−1004.29	−0.357750	−0.178875	+	0.983872i	$0.557246\pi$
$200$	0	0
$201$	1536.51	0.539188
$202$	3338.76i	1.16294i
$203$	− 7090.37i	− 2.45146i
$204$	−1976.38	−0.678305
$205$	0	0
$206$	2221.25	0.751272
$207$	102.348i	0.0343657i
$208$	360.634i	0.120218i
$209$	5419.36	1.79361
$210$	0	0
$211$	5395.17	1.76028	0.880140	−	0.474714i	$-0.157449\pi$
$211$	5395.17	1.76028	0.880140	+	0.474714i	$0.157449\pi$
$212$	1965.10i	0.636620i
$213$	4241.74i	1.36450i
$214$	78.3783	0.0250366
$215$	0	0
$216$	−1194.77	−0.376360
$217$	2915.42i	0.912034i
$218$	1615.09i	0.501779i
$219$	932.041	0.287587
$220$	0	0
$221$	2345.22	0.713830
$222$	569.322i	0.172119i
$223$	1504.79i	0.451876i	0.974142	+	0.225938i	$0.0725447\pi$
$223$	1504.79i	0.451876i	−0.974142	+	0.225938i	$0.927455\pi$
$224$	939.788	0.280323
$225$	0	0
$226$	−2133.16	−0.627856
$227$	− 1779.44i	− 0.520288i	−0.965570	−	0.260144i	$-0.916230\pi$
$227$	− 1779.44i	− 0.520288i	0.965570	−	0.260144i	$-0.0837700\pi$
$228$	2697.25i	0.783465i
$229$	−3976.16	−1.14739	−0.573694	−	0.819070i	$-0.694490\pi$
$229$	−3976.16	−1.14739	−0.573694	+	0.819070i	$0.694490\pi$
$230$	0	0
$231$	5322.48	1.51599
$232$	− 1931.43i	− 0.546572i
$233$	2311.12i	0.649815i	0.945746	+	0.324907i	$0.105333\pi$
$233$	2311.12i	0.649815i	−0.945746	+	0.324907i	$0.894667\pi$
$234$	200.599	0.0560410
$235$	0	0
$236$	1734.94	0.478537
$237$	2375.35i	0.651035i
$238$	− 6111.49i	− 1.66449i
$239$	−824.267	−0.223085	−0.111543	−	0.993760i	$-0.535579\pi$
$239$	−824.267	−0.223085	−0.111543	+	0.993760i	$0.535579\pi$
$240$	0	0
$241$	3641.83	0.973406	0.486703	−	0.873567i	$-0.338199\pi$
$241$	3641.83	0.973406	0.486703	+	0.873567i	$0.338199\pi$
$242$	− 251.064i	− 0.0666900i
$243$	1235.13i	0.326063i
$244$	−2643.61	−0.693605
$245$	0	0
$246$	2367.20	0.613526
$247$	− 3200.62i	− 0.824496i
$248$	794.165i	0.203345i
$249$	3803.44	0.968004
$250$	0	0
$251$	−7767.51	−1.95331	−0.976655	−	0.214813i	$-0.931086\pi$
$251$	−7767.51	−1.95331	−0.976655	+	0.214813i	$0.931086\pi$
$252$	− 522.749i	− 0.130675i
$253$	− 877.784i	− 0.218126i
$254$	−1283.41	−0.317042
$255$	0	0
$256$	256.000	0.0625000
$257$	− 1501.17i	− 0.364359i	−0.983265	−	0.182179i	$-0.941685\pi$
$257$	− 1501.17i	− 0.364359i	0.983265	−	0.182179i	$-0.0583151\pi$
$258$	1556.27i	0.375539i
$259$	−1760.49	−0.422362
$260$	0	0
$261$	−1074.34	−0.254789
$262$	− 4779.84i	− 1.12710i
$263$	5430.98i	1.27334i	0.771136	+	0.636671i	$0.219689\pi$
$263$	5430.98i	1.27334i	−0.771136	+	0.636671i	$0.780311\pi$
$264$	1449.85	0.338001
$265$	0	0
$266$	−8340.61	−1.92254
$267$	3461.87i	0.793494i
$268$	1294.26i	0.294997i
$269$	5014.20	1.13651	0.568255	−	0.822852i	$-0.307619\pi$
$269$	5014.20	1.13651	0.568255	+	0.822852i	$0.307619\pi$
$270$	0	0
$271$	7215.54	1.61739	0.808695	−	0.588228i	$-0.200174\pi$
$271$	7215.54	1.61739	0.808695	+	0.588228i	$0.200174\pi$
$272$	− 1664.78i	− 0.371111i
$273$	− 3143.41i	− 0.696877i
$274$	1798.58	0.396556
$275$	0	0
$276$	436.880	0.0952792
$277$	− 7439.60i	− 1.61373i	−0.590738	−	0.806863i	$-0.701163\pi$
$277$	− 7439.60i	− 1.61373i	0.590738	−	0.806863i	$-0.298837\pi$
$278$	618.681i	0.133475i
$279$	441.747	0.0947910
$280$	0	0
$281$	−2605.59	−0.553155	−0.276578	−	0.960992i	$-0.589200\pi$
$281$	−2605.59	−0.553155	−0.276578	+	0.960992i	$0.589200\pi$
$282$	− 1952.57i	− 0.412319i
$283$	7162.57i	1.50449i	0.658884	+	0.752245i	$0.271029\pi$
$283$	7162.57i	1.50449i	−0.658884	+	0.752245i	$0.728971\pi$
$284$	−3572.97	−0.746538
$285$	0	0
$286$	−1720.43	−0.355703
$287$	7320.01i	1.50553i
$288$	− 142.398i	− 0.0291349i
$289$	−5913.13	−1.20357
$290$	0	0
$291$	−5413.32	−1.09050
$292$	785.093i	0.157343i
$293$	− 9310.55i	− 1.85641i	−0.372069	−	0.928205i	$-0.621351\pi$
$293$	− 9310.55i	− 1.85641i	0.372069	−	0.928205i	$-0.378649\pi$
$294$	−4933.91	−0.978747
$295$	0	0
$296$	−479.562	−0.0941687
$297$	− 5699.72i	− 1.11357i
$298$	5121.74i	0.995620i
$299$	−518.411	−0.100269
$300$	0	0
$301$	−4812.39	−0.921533
$302$	4926.31i	0.938666i
$303$	− 7927.38i	− 1.50302i
$304$	−2272.00	−0.428645
$305$	0	0
$306$	−926.018	−0.172997
$307$	3359.07i	0.624470i	0.950005	+	0.312235i	$0.101078\pi$
$307$	3359.07i	0.624470i	−0.950005	+	0.312235i	$0.898922\pi$
$308$	4483.32i	0.829419i
$309$	−5274.02	−0.970966
$310$	0	0
$311$	−5509.20	−1.00450	−0.502248	−	0.864724i	$-0.667493\pi$
$311$	−5509.20	−1.00450	−0.502248	+	0.864724i	$0.667493\pi$
$312$	− 856.269i	− 0.155374i
$313$	− 2401.42i	− 0.433661i	−0.976209	−	0.216831i	$-0.930428\pi$
$313$	− 2401.42i	− 0.433661i	0.976209	−	0.216831i	$-0.0695720\pi$
$314$	−1133.44	−0.203706
$315$	0	0
$316$	−2000.84	−0.356191
$317$	− 1057.36i	− 0.187341i	−0.995603	−	0.0936704i	$-0.970140\pi$
$317$	− 1057.36i	− 0.187341i	0.995603	−	0.0936704i	$-0.0298600\pi$
$318$	− 4665.82i	− 0.822787i
$319$	9214.02	1.61720
$320$	0	0
$321$	−186.097	−0.0323581
$322$	1350.95i	0.233805i
$323$	14774.9i	2.54519i
$324$	2356.20	0.404012
$325$	0	0
$326$	−1921.80	−0.326500
$327$	− 3834.78i	− 0.648514i
$328$	1993.98i	0.335669i
$329$	6037.86	1.01179
$330$	0	0
$331$	−9680.21	−1.60747	−0.803735	−	0.594987i	$-0.797157\pi$
$331$	−9680.21	−1.60747	−0.803735	+	0.594987i	$0.797157\pi$
$332$	3203.78i	0.529609i
$333$	266.752i	0.0438976i
$334$	−8449.40	−1.38422
$335$	0	0
$336$	−2231.38	−0.362297
$337$	467.694i	0.0755991i	0.999285	+	0.0377996i	$0.0120348\pi$
$337$	467.694i	0.0755991i	−0.999285	+	0.0377996i	$0.987965\pi$
$338$	− 3377.93i	− 0.543596i
$339$	5064.85	0.811460
$340$	0	0
$341$	−3788.62	−0.601657
$342$	1263.78i	0.199817i
$343$	− 5183.59i	− 0.815998i
$344$	−1310.90	−0.205463
$345$	0	0
$346$	−6897.96	−1.07178
$347$	3371.55i	0.521597i	0.965393	+	0.260798i	$0.0839858\pi$
$347$	3371.55i	0.521597i	−0.965393	+	0.260798i	$0.916014\pi$
$348$	4585.88i	0.706406i
$349$	−10958.7	−1.68082	−0.840412	−	0.541947i	$-0.817687\pi$
$349$	−10958.7	−1.68082	−0.840412	+	0.541947i	$0.817687\pi$
$350$	0	0
$351$	−3366.20	−0.511893
$352$	1221.27i	0.184925i
$353$	1584.76i	0.238947i	0.992837	+	0.119474i	$0.0381207\pi$
$353$	1584.76i	0.238947i	−0.992837	+	0.119474i	$0.961879\pi$
$354$	−4119.34	−0.618476
$355$	0	0
$356$	−2916.06	−0.434132
$357$	14510.8i	2.15124i
$358$	2915.63i	0.430436i
$359$	−5130.67	−0.754280	−0.377140	−	0.926156i	$-0.623092\pi$
$359$	−5130.67	−0.754280	−0.377140	+	0.926156i	$0.623092\pi$
$360$	0	0
$361$	13304.9	1.93978
$362$	7269.94i	1.05552i
$363$	596.112i	0.0861922i
$364$	2647.81	0.381271
$365$	0	0
$366$	6276.84	0.896437
$367$	2811.27i	0.399856i	0.979811	+	0.199928i	$0.0640708\pi$
$367$	2811.27i	0.399856i	−0.979811	+	0.199928i	$0.935929\pi$
$368$	368.000i	0.0521286i
$369$	1109.14	0.156475
$370$	0	0
$371$	14427.9	2.01903
$372$	− 1885.62i	− 0.262809i
$373$	1952.42i	0.271026i	0.990776	+	0.135513i	$0.0432682\pi$
$373$	1952.42i	0.271026i	−0.990776	+	0.135513i	$0.956732\pi$
$374$	7941.94	1.09804
$375$	0	0
$376$	1644.72	0.225586
$377$	− 5441.71i	− 0.743401i
$378$	8772.10i	1.19362i
$379$	−9609.27	−1.30236	−0.651181	−	0.758923i	$-0.725726\pi$
$379$	−9609.27	−1.30236	−0.651181	+	0.758923i	$0.725726\pi$
$380$	0	0
$381$	3047.27	0.409754
$382$	− 897.623i	− 0.120226i
$383$	− 5027.44i	− 0.670732i	−0.942088	−	0.335366i	$-0.891140\pi$
$383$	− 5027.44i	− 0.670732i	0.942088	−	0.335366i	$-0.108860\pi$
$384$	−607.833	−0.0807769
$385$	0	0
$386$	−8518.70	−1.12329
$387$	729.178i	0.0957783i
$388$	− 4559.84i	− 0.596626i
$389$	−5892.29	−0.767997	−0.383999	−	0.923334i	$-0.625453\pi$
$389$	−5892.29	−0.767997	−0.383999	+	0.923334i	$0.625453\pi$
$390$	0	0
$391$	2393.12	0.309528
$392$	− 4156.02i	− 0.535486i
$393$	11349.0i	1.45670i
$394$	−3534.75	−0.451975
$395$	0	0
$396$	679.318	0.0862046
$397$	− 2454.41i	− 0.310285i	−0.987892	−	0.155143i	$-0.950416\pi$
$397$	− 2454.41i	− 0.310285i	0.987892	−	0.155143i	$-0.0495837\pi$
$398$	2008.58i	0.252967i
$399$	19803.5	2.48475
$400$	0	0
$401$	9458.39	1.17788	0.588939	−	0.808177i	$-0.299546\pi$
$401$	9458.39	1.17788	0.588939	+	0.808177i	$0.299546\pi$
$402$	− 3073.01i	− 0.381264i
$403$	2237.52i	0.276573i
$404$	6677.53	0.822326
$405$	0	0
$406$	−14180.7	−1.73345
$407$	− 2287.78i	− 0.278627i
$408$	3952.76i	0.479634i
$409$	5857.25	0.708123	0.354062	−	0.935222i	$-0.384800\pi$
$409$	5857.25	0.708123	0.354062	+	0.935222i	$0.384800\pi$
$410$	0	0
$411$	−4270.45	−0.512521
$412$	− 4442.51i	− 0.531229i
$413$	− 12738.1i	− 1.51767i
$414$	204.697	0.0243002
$415$	0	0
$416$	721.267	0.0850073
$417$	− 1468.96i	− 0.172507i
$418$	− 10838.7i	− 1.26827i
$419$	5252.61	0.612426	0.306213	−	0.951963i	$-0.400938\pi$
$419$	5252.61	0.612426	0.306213	+	0.951963i	$0.400938\pi$
$420$	0	0
$421$	−203.517	−0.0235602	−0.0117801	−	0.999931i	$-0.503750\pi$
$421$	−203.517	−0.0235602	−0.0117801	+	0.999931i	$0.503750\pi$
$422$	− 10790.3i	− 1.24471i
$423$	− 914.863i	− 0.105159i
$424$	3930.20	0.450158
$425$	0	0
$426$	8483.47	0.964849
$427$	19409.6i	2.19976i
$428$	− 156.757i	− 0.0177036i
$429$	4084.89	0.459721
$430$	0	0
$431$	3107.72	0.347317	0.173659	−	0.984806i	$-0.444441\pi$
$431$	3107.72	0.347317	0.173659	+	0.984806i	$0.444441\pi$
$432$	2389.54i	0.266126i
$433$	5713.46i	0.634114i	0.948406	+	0.317057i	$0.102695\pi$
$433$	5713.46i	0.634114i	−0.948406	+	0.317057i	$0.897305\pi$
$434$	5830.83	0.644905
$435$	0	0
$436$	3230.18	0.354811
$437$	− 3266.00i	− 0.357514i
$438$	− 1864.08i	− 0.203354i
$439$	4587.14	0.498706	0.249353	−	0.968413i	$-0.419782\pi$
$439$	4587.14	0.498706	0.249353	+	0.968413i	$0.419782\pi$
$440$	0	0
$441$	−2311.75	−0.249622
$442$	− 4690.43i	− 0.504754i
$443$	− 5268.01i	− 0.564990i	−0.959269	−	0.282495i	$-0.908838\pi$
$443$	− 5268.01i	− 0.564990i	0.959269	−	0.282495i	$-0.0911621\pi$
$444$	1138.64	0.121707
$445$	0	0
$446$	3009.58	0.319525
$447$	− 12160.8i	− 1.28677i
$448$	− 1879.58i	− 0.198218i
$449$	−16866.8	−1.77282	−0.886409	−	0.462902i	$-0.846808\pi$
$449$	−16866.8	−1.77282	−0.886409	+	0.462902i	$0.846808\pi$
$450$	0	0
$451$	−9512.43	−0.993177
$452$	4266.31i	0.443961i
$453$	− 11696.8i	− 1.21316i
$454$	−3558.87	−0.367899
$455$	0	0
$456$	5394.51	0.553993
$457$	9124.25i	0.933948i	0.884271	+	0.466974i	$0.154656\pi$
$457$	9124.25i	0.933948i	−0.884271	+	0.466974i	$0.845344\pi$
$458$	7952.31i	0.811326i
$459$	15539.3	1.58020
$460$	0	0
$461$	6011.92	0.607382	0.303691	−	0.952771i	$-0.401781\pi$
$461$	6011.92	0.607382	0.303691	+	0.952771i	$0.401781\pi$
$462$	− 10645.0i	− 1.07197i
$463$	8584.09i	0.861634i	0.902439	+	0.430817i	$0.141775\pi$
$463$	8584.09i	0.861634i	−0.902439	+	0.430817i	$0.858225\pi$
$464$	−3862.86	−0.386484
$465$	0	0
$466$	4622.25	0.459488
$467$	3954.09i	0.391806i	0.980623	+	0.195903i	$0.0627639\pi$
$467$	3954.09i	0.391806i	−0.980623	+	0.195903i	$0.937236\pi$
$468$	− 401.198i	− 0.0396269i
$469$	9502.56	0.935581
$470$	0	0
$471$	2691.18	0.263276
$472$	− 3469.87i	− 0.338377i
$473$	− 6253.75i	− 0.607923i
$474$	4750.69	0.460351
$475$	0	0
$476$	−12223.0	−1.17697
$477$	− 2186.14i	− 0.209845i
$478$	1648.53i	0.157745i
$479$	95.3377	0.00909413	0.00454707	−	0.999990i	$-0.498553\pi$
$479$	95.3377	0.00909413	0.00454707	+	0.999990i	$0.498553\pi$
$480$	0	0
$481$	−1351.14	−0.128080
$482$	− 7283.66i	− 0.688302i
$483$	− 3207.61i	− 0.302177i
$484$	−502.127	−0.0471570
$485$	0	0
$486$	2470.25	0.230561
$487$	13915.2i	1.29478i	0.762158	+	0.647391i	$0.224140\pi$
$487$	13915.2i	1.29478i	−0.762158	+	0.647391i	$0.775860\pi$
$488$	5287.22i	0.490453i
$489$	4563.03	0.421978
$490$	0	0
$491$	6291.33	0.578256	0.289128	−	0.957290i	$-0.406635\pi$
$491$	6291.33	0.578256	0.289128	+	0.957290i	$0.406635\pi$
$492$	− 4734.41i	− 0.433828i
$493$	25120.3i	2.29486i
$494$	−6401.24	−0.583007
$495$	0	0
$496$	1588.33	0.143786
$497$	26233.1i	2.36764i
$498$	− 7606.87i	− 0.684482i
$499$	638.332	0.0572658	0.0286329	−	0.999590i	$-0.490885\pi$
$499$	638.332	0.0572658	0.0286329	+	0.999590i	$0.490885\pi$
$500$	0	0
$501$	20061.8	1.78901
$502$	15535.0i	1.38120i
$503$	− 15063.4i	− 1.33527i	−0.744487	−	0.667637i	$-0.767306\pi$
$503$	− 15063.4i	− 1.33527i	0.744487	−	0.667637i	$-0.232694\pi$
$504$	−1045.50	−0.0924011
$505$	0	0
$506$	−1755.57	−0.154238
$507$	8020.38i	0.702559i
$508$	2566.83i	0.224182i
$509$	13623.1	1.18631	0.593157	−	0.805087i	$-0.297881\pi$
$509$	13623.1	1.18631	0.593157	+	0.805087i	$0.297881\pi$
$510$	0	0
$511$	5764.23	0.499010
$512$	− 512.000i	− 0.0441942i
$513$	− 21207.1i	− 1.82518i
$514$	−3002.33	−0.257640
$515$	0	0
$516$	3112.54	0.265546
$517$	7846.27i	0.667463i
$518$	3520.99i	0.298655i
$519$	16378.2	1.38520
$520$	0	0
$521$	−21659.4	−1.82133	−0.910666	−	0.413143i	$-0.864431\pi$
$521$	−21659.4	−1.82133	−0.910666	+	0.413143i	$0.864431\pi$
$522$	2148.68i	0.180163i
$523$	3813.85i	0.318868i	0.987209	+	0.159434i	$0.0509669\pi$
$523$	3813.85i	0.318868i	−0.987209	+	0.159434i	$0.949033\pi$
$524$	−9559.69	−0.796979
$525$	0	0
$526$	10862.0	0.900388
$527$	− 10329.0i	− 0.853771i
$528$	− 2899.71i	− 0.239003i
$529$	−529.000	−0.0434783
$530$	0	0
$531$	−1930.09	−0.157737
$532$	16681.2i	1.35944i
$533$	5617.95i	0.456549i
$534$	6923.74	0.561085
$535$	0	0
$536$	2588.51	0.208595
$537$	− 6922.72i	− 0.556308i
$538$	− 10028.4i	− 0.803634i
$539$	19826.6	1.58440
$540$	0	0
$541$	9727.32	0.773031	0.386516	−	0.922283i	$-0.373679\pi$
$541$	9727.32	0.773031	0.386516	+	0.922283i	$0.373679\pi$
$542$	− 14431.1i	− 1.14367i
$543$	− 17261.3i	− 1.36419i
$544$	−3329.56	−0.262415
$545$	0	0
$546$	−6286.81	−0.492767
$547$	782.647i	0.0611766i	0.999532	+	0.0305883i	$0.00973807\pi$
$547$	782.647i	0.0611766i	−0.999532	+	0.0305883i	$0.990262\pi$
$548$	− 3597.16i	− 0.280407i
$549$	2940.97	0.228629
$550$	0	0
$551$	34282.8	2.65063
$552$	− 873.759i	− 0.0673726i
$553$	14690.4i	1.12965i
$554$	−14879.2	−1.14108
$555$	0	0
$556$	1237.36	0.0943811
$557$	3472.87i	0.264184i	0.991237	+	0.132092i	$0.0421694\pi$
$557$	3472.87i	0.264184i	−0.991237	+	0.132092i	$0.957831\pi$
$558$	− 883.494i	− 0.0670274i
$559$	−3693.40	−0.279453
$560$	0	0
$561$	−18856.9	−1.41914
$562$	5211.18i	0.391140i
$563$	− 7544.75i	− 0.564784i	−0.959299	−	0.282392i	$-0.908872\pi$
$563$	− 7544.75i	− 0.564784i	0.959299	−	0.282392i	$-0.0911279\pi$
$564$	−3905.14	−0.291554
$565$	0	0
$566$	14325.1	1.06383
$567$	− 17299.5i	− 1.28132i
$568$	7145.94i	0.527882i
$569$	−13222.5	−0.974193	−0.487096	−	0.873348i	$-0.661944\pi$
$569$	−13222.5	−0.974193	−0.487096	+	0.873348i	$0.661944\pi$
$570$	0	0
$571$	4069.49	0.298254	0.149127	−	0.988818i	$-0.452354\pi$
$571$	4069.49	0.298254	0.149127	+	0.988818i	$0.452354\pi$
$572$	3440.85i	0.251520i
$573$	2131.27i	0.155384i
$574$	14640.0	1.06457
$575$	0	0
$576$	−284.795	−0.0206015
$577$	846.627i	0.0610841i	0.999533	+	0.0305421i	$0.00972336\pi$
$577$	846.627i	0.0610841i	−0.999533	+	0.0305421i	$0.990277\pi$
$578$	11826.3i	0.851051i
$579$	20226.3	1.45177
$580$	0	0
$581$	23522.4	1.67965
$582$	10826.6i	0.771097i
$583$	18749.3i	1.33193i
$584$	1570.19	0.111258
$585$	0	0
$586$	−18621.1	−1.31268
$587$	4702.77i	0.330672i	0.986237	+	0.165336i	$0.0528708\pi$
$587$	4702.77i	0.330672i	−0.986237	+	0.165336i	$0.947129\pi$
$588$	9867.82i	0.692079i
$589$	−14096.4	−0.986133
$590$	0	0
$591$	8392.71	0.584146
$592$	959.123i	0.0665874i
$593$	14016.5i	0.970640i	0.874337	+	0.485320i	$0.161297\pi$
$593$	14016.5i	0.970640i	−0.874337	+	0.485320i	$0.838703\pi$
$594$	−11399.4	−0.787415
$595$	0	0
$596$	10243.5	0.704010
$597$	− 4769.07i	− 0.326943i
$598$	1036.82i	0.0709010i
$599$	−12885.0	−0.878910	−0.439455	−	0.898265i	$-0.644828\pi$
$599$	−12885.0	−0.878910	−0.439455	+	0.898265i	$0.644828\pi$
$600$	0	0
$601$	−4753.41	−0.322622	−0.161311	−	0.986904i	$-0.551572\pi$
$601$	−4753.41	−0.322622	−0.161311	+	0.986904i	$0.551572\pi$
$602$	9624.77i	0.651622i
$603$	− 1439.84i	− 0.0972383i
$604$	9852.61	0.663737
$605$	0	0
$606$	−15854.8	−1.06280
$607$	− 6800.06i	− 0.454705i	−0.973813	−	0.227352i	$-0.926993\pi$
$607$	− 6800.06i	− 0.454705i	0.973813	−	0.227352i	$-0.0730070\pi$
$608$	4543.99i	0.303097i
$609$	33670.0	2.24036
$610$	0	0
$611$	4633.93	0.306823
$612$	1852.04i	0.122327i
$613$	− 20842.3i	− 1.37327i	−0.727003	−	0.686634i	$-0.759087\pi$
$613$	− 20842.3i	− 1.37327i	0.727003	−	0.686634i	$-0.240913\pi$
$614$	6718.14	0.441567
$615$	0	0
$616$	8966.65	0.586488
$617$	18917.7i	1.23436i	0.786823	+	0.617179i	$0.211724\pi$
$617$	18917.7i	1.23436i	−0.786823	+	0.617179i	$0.788276\pi$
$618$	10548.0i	0.686577i
$619$	28044.8	1.82103	0.910513	−	0.413480i	$-0.135687\pi$
$619$	28044.8	1.82103	0.910513	+	0.413480i	$0.135687\pi$
$620$	0	0
$621$	−3434.96	−0.221965
$622$	11018.4i	0.710285i
$623$	21410.0i	1.37684i
$624$	−1712.54	−0.109866
$625$	0	0
$626$	−4802.83	−0.306645
$627$	25734.9i	1.63916i
$628$	2266.88i	0.144042i
$629$	6237.22	0.395380
$630$	0	0
$631$	−25796.2	−1.62746	−0.813732	−	0.581241i	$-0.802567\pi$
$631$	−25796.2	−1.62746	−0.813732	+	0.581241i	$0.802567\pi$
$632$	4001.69i	0.251865i
$633$	25620.0i	1.60870i
$634$	−2114.71	−0.132470
$635$	0	0
$636$	−9331.64	−0.581798
$637$	− 11709.4i	− 0.728324i
$638$	− 18428.0i	− 1.14353i
$639$	3974.87	0.246077
$640$	0	0
$641$	−26482.3	−1.63181	−0.815903	−	0.578188i	$-0.803760\pi$
$641$	−26482.3	−1.63181	−0.815903	+	0.578188i	$0.803760\pi$
$642$	372.195i	0.0228806i
$643$	− 30458.1i	− 1.86804i	−0.357219	−	0.934020i	$-0.616275\pi$
$643$	− 30458.1i	− 1.86804i	0.357219	−	0.934020i	$-0.383725\pi$
$644$	2701.89	0.165325
$645$	0	0
$646$	29549.8	1.79972
$647$	− 6746.24i	− 0.409926i	−0.978770	−	0.204963i	$-0.934293\pi$
$647$	− 6746.24i	− 0.409926i	0.978770	−	0.204963i	$-0.0657074\pi$
$648$	− 4712.40i	− 0.285680i
$649$	16553.3	1.00119
$650$	0	0
$651$	−13844.4	−0.833495
$652$	3843.61i	0.230870i
$653$	− 12976.2i	− 0.777640i	−0.921314	−	0.388820i	$-0.872883\pi$
$653$	− 12976.2i	− 0.777640i	0.921314	−	0.388820i	$-0.127117\pi$
$654$	−7669.57	−0.458569
$655$	0	0
$656$	3987.97	0.237354
$657$	− 873.401i	− 0.0518640i
$658$	− 12075.7i	− 0.715442i
$659$	6538.56	0.386504	0.193252	−	0.981149i	$-0.438097\pi$
$659$	6538.56	0.386504	0.193252	+	0.981149i	$0.438097\pi$
$660$	0	0
$661$	−25177.1	−1.48151	−0.740753	−	0.671777i	$-0.765531\pi$
$661$	−25177.1	−1.48151	−0.740753	+	0.671777i	$0.765531\pi$
$662$	19360.4i	1.13665i
$663$	11136.7i	0.652359i
$664$	6407.55	0.374490
$665$	0	0
$666$	533.504	0.0310403
$667$	− 5552.86i	− 0.322350i
$668$	16898.8i	0.978794i
$669$	−7145.79	−0.412963
$670$	0	0
$671$	−25223.0	−1.45115
$672$	4462.77i	0.256183i
$673$	− 18339.3i	− 1.05041i	−0.850975	−	0.525207i	$-0.823988\pi$
$673$	− 18339.3i	− 1.05041i	0.850975	−	0.525207i	$-0.176012\pi$
$674$	935.388	0.0534567
$675$	0	0
$676$	−6755.86	−0.384380
$677$	31876.9i	1.80965i	0.425789	+	0.904823i	$0.359997\pi$
$677$	31876.9i	1.80965i	−0.425789	+	0.904823i	$0.640003\pi$
$678$	− 10129.7i	− 0.573789i
$679$	−33478.8	−1.89219
$680$	0	0
$681$	8450.00	0.475484
$682$	7577.23i	0.425436i
$683$	28843.7i	1.61592i	0.589239	+	0.807959i	$0.299428\pi$
$683$	28843.7i	1.61592i	−0.589239	+	0.807959i	$0.700572\pi$
$684$	2527.56	0.141292
$685$	0	0
$686$	−10367.2	−0.576998
$687$	− 18881.5i	− 1.04858i
$688$	2621.80i	0.145284i
$689$	11073.1	0.612268
$690$	0	0
$691$	−18327.7	−1.00900	−0.504499	−	0.863413i	$-0.668323\pi$
$691$	−18327.7	−1.00900	−0.504499	+	0.863413i	$0.668323\pi$
$692$	13795.9i	0.757865i
$693$	− 4987.62i	− 0.273397i
$694$	6743.09	0.368825
$695$	0	0
$696$	9171.77	0.499504
$697$	− 25933.9i	− 1.40935i
$698$	21917.5i	1.18852i
$699$	−10974.8	−0.593857
$700$	0	0
$701$	−8329.48	−0.448788	−0.224394	−	0.974499i	$-0.572040\pi$
$701$	−8329.48	−0.448788	−0.224394	+	0.974499i	$0.572040\pi$
$702$	6732.40i	0.361963i
$703$	− 8512.20i	− 0.456677i
$704$	2442.53	0.130762
$705$	0	0
$706$	3169.52	0.168961
$707$	− 49027.1i	− 2.60800i
$708$	8238.68i	0.437328i
$709$	6169.85	0.326818	0.163409	−	0.986558i	$-0.447751\pi$
$709$	6169.85	0.326818	0.163409	+	0.986558i	$0.447751\pi$
$710$	0	0
$711$	2225.90	0.117409
$712$	5832.12i	0.306978i
$713$	2283.22i	0.119926i
$714$	29021.6	1.52115
$715$	0	0
$716$	5831.27	0.304364
$717$	− 3914.19i	− 0.203875i
$718$	10261.3i	0.533356i
$719$	−28740.8	−1.49075	−0.745377	−	0.666644i	$-0.767730\pi$
$719$	−28740.8	−1.49075	−0.745377	+	0.666644i	$0.767730\pi$
$720$	0	0
$721$	−32617.3	−1.68479
$722$	− 26609.9i	− 1.37163i
$723$	17293.9i	0.889583i
$724$	14539.9	0.746368
$725$	0	0
$726$	1192.22	0.0609471
$727$	11174.0i	0.570041i	0.958521	+	0.285021i	$0.0920004\pi$
$727$	11174.0i	0.570041i	−0.958521	+	0.285021i	$0.908000\pi$
$728$	− 5295.62i	− 0.269600i
$729$	−21769.6	−1.10601
$730$	0	0
$731$	17049.7	0.862663
$732$	− 12553.7i	− 0.633876i
$733$	23560.7i	1.18722i	0.804751	+	0.593612i	$0.202299\pi$
$733$	23560.7i	1.18722i	−0.804751	+	0.593612i	$0.797701\pi$
$734$	5622.54	0.282741
$735$	0	0
$736$	736.000	0.0368605
$737$	12348.7i	0.617191i
$738$	− 2218.27i	− 0.110645i
$739$	−22713.6	−1.13063	−0.565313	−	0.824877i	$-0.691245\pi$
$739$	−22713.6	−1.13063	−0.565313	+	0.824877i	$0.691245\pi$
$740$	0	0
$741$	15198.8	0.753495
$742$	− 28855.9i	− 1.42767i
$743$	15882.7i	0.784224i	0.919917	+	0.392112i	$0.128255\pi$
$743$	15882.7i	0.784224i	−0.919917	+	0.392112i	$0.871745\pi$
$744$	−3771.24	−0.185834
$745$	0	0
$746$	3904.84	0.191644
$747$	− 3564.14i	− 0.174572i
$748$	− 15883.9i	− 0.776433i
$749$	−1150.92	−0.0561466
$750$	0	0
$751$	−30250.6	−1.46985	−0.734927	−	0.678146i	$-0.762784\pi$
$751$	−30250.6	−1.46985	−0.734927	+	0.678146i	$0.762784\pi$
$752$	− 3289.45i	− 0.159513i
$753$	− 36885.5i	− 1.78510i
$754$	−10883.4	−0.525664
$755$	0	0
$756$	17544.2	0.844017
$757$	− 9611.05i	− 0.461453i	−0.973019	−	0.230726i	$-0.925890\pi$
$757$	− 9611.05i	− 0.461453i	0.973019	−	0.230726i	$-0.0741102\pi$
$758$	19218.5i	0.920908i
$759$	4168.33	0.199342
$760$	0	0
$761$	5892.64	0.280694	0.140347	−	0.990102i	$-0.455178\pi$
$761$	5892.64	0.280694	0.140347	+	0.990102i	$0.455178\pi$
$762$	− 6094.54i	− 0.289740i
$763$	− 23716.3i	− 1.12528i
$764$	−1795.25	−0.0850127
$765$	0	0
$766$	−10054.9	−0.474279
$767$	− 9776.19i	− 0.460232i
$768$	1215.67i	0.0571179i
$769$	−1683.72	−0.0789553	−0.0394777	−	0.999220i	$-0.512569\pi$
$769$	−1683.72	−0.0789553	−0.0394777	+	0.999220i	$0.512569\pi$
$770$	0	0
$771$	7128.57	0.332982
$772$	17037.4i	0.794286i
$773$	− 19880.8i	− 0.925048i	−0.886607	−	0.462524i	$-0.846944\pi$
$773$	− 19880.8i	− 0.925048i	0.886607	−	0.462524i	$-0.153056\pi$
$774$	1458.36	0.0677255
$775$	0	0
$776$	−9119.68	−0.421878
$777$	− 8360.04i	− 0.385991i
$778$	11784.6i	0.543056i
$779$	−35393.2	−1.62785
$780$	0	0
$781$	−34090.2	−1.56190
$782$	− 4786.24i	− 0.218869i
$783$	− 36056.4i	− 1.64566i
$784$	−8312.04	−0.378646
$785$	0	0
$786$	22698.0	1.03004
$787$	− 7622.64i	− 0.345258i	−0.984987	−	0.172629i	$-0.944774\pi$
$787$	− 7622.64i	− 0.345258i	0.984987	−	0.172629i	$-0.0552261\pi$
$788$	7069.50i	0.319594i
$789$	−25790.1	−1.16369
$790$	0	0
$791$	31323.7	1.40802
$792$	− 1358.64i	− 0.0609558i
$793$	14896.5i	0.667074i
$794$	−4908.82	−0.219405
$795$	0	0
$796$	4017.16	0.178875
$797$	− 22380.9i	− 0.994693i	−0.867552	−	0.497347i	$-0.834308\pi$
$797$	− 22380.9i	− 0.994693i	0.867552	−	0.497347i	$-0.165692\pi$
$798$	− 39607.0i	− 1.75698i
$799$	−21391.4	−0.947152
$800$	0	0
$801$	3244.07	0.143100
$802$	− 18916.8i	− 0.832886i
$803$	7490.67i	0.329191i
$804$	−6146.03	−0.269594
$805$	0	0
$806$	4475.04	0.195566
$807$	23810.9i	1.03864i
$808$	− 13355.1i	− 0.581472i
$809$	−8117.18	−0.352762	−0.176381	−	0.984322i	$-0.556439\pi$
$809$	−8117.18	−0.352762	−0.176381	+	0.984322i	$0.556439\pi$
$810$	0	0
$811$	7221.05	0.312658	0.156329	−	0.987705i	$-0.450034\pi$
$811$	7221.05	0.312658	0.156329	+	0.987705i	$0.450034\pi$
$812$	28361.5i	1.22573i
$813$	34264.4i	1.47811i
$814$	−4575.56	−0.197019
$815$	0	0
$816$	7905.52	0.339153
$817$	− 23268.5i	− 0.996403i
$818$	− 11714.5i	− 0.500719i
$819$	−2945.64	−0.125676
$820$	0	0
$821$	34803.3	1.47947	0.739735	−	0.672899i	$-0.234951\pi$
$821$	34803.3	1.47947	0.739735	+	0.672899i	$0.234951\pi$
$822$	8540.91i	0.362407i
$823$	− 490.883i	− 0.0207911i	−0.999946	−	0.0103956i	$-0.996691\pi$
$823$	− 490.883i	− 0.0207911i	0.999946	−	0.0103956i	$-0.00330907\pi$
$824$	−8885.01	−0.375636
$825$	0	0
$826$	−25476.1	−1.07316
$827$	30952.0i	1.30146i	0.759310	+	0.650729i	$0.225537\pi$
$827$	30952.0i	1.30146i	−0.759310	+	0.650729i	$0.774463\pi$
$828$	− 409.393i	− 0.0171829i
$829$	−8587.63	−0.359784	−0.179892	−	0.983686i	$-0.557575\pi$
$829$	−8587.63	−0.359784	−0.179892	+	0.983686i	$0.557575\pi$
$830$	0	0
$831$	35328.4	1.47476
$832$	− 1442.53i	− 0.0601092i
$833$	54053.5i	2.24831i
$834$	−2937.93	−0.121981
$835$	0	0
$836$	−21677.4	−0.896806
$837$	14825.7i	0.612246i
$838$	− 10505.2i	− 0.433051i
$839$	−3077.94	−0.126653	−0.0633267	−	0.997993i	$-0.520171\pi$
$839$	−3077.94	−0.126653	−0.0633267	+	0.997993i	$0.520171\pi$
$840$	0	0
$841$	33898.9	1.38992
$842$	407.035i	0.0166596i
$843$	− 12373.2i	− 0.505521i
$844$	−21580.7	−0.880140
$845$	0	0
$846$	−1829.73	−0.0743585
$847$	3686.67i	0.149558i
$848$	− 7860.39i	− 0.318310i
$849$	−34012.8	−1.37493
$850$	0	0
$851$	−1378.74	−0.0555377
$852$	− 16966.9i	− 0.682251i
$853$	9193.14i	0.369012i	0.982831	+	0.184506i	$0.0590685\pi$
$853$	9193.14i	0.369012i	−0.982831	+	0.184506i	$0.940932\pi$
$854$	38819.3	1.55547
$855$	0	0
$856$	−313.513	−0.0125183
$857$	21445.8i	0.854813i	0.904059	+	0.427407i	$0.140573\pi$
$857$	21445.8i	0.854813i	−0.904059	+	0.427407i	$0.859427\pi$
$858$	− 8169.78i	− 0.325072i
$859$	40276.7	1.59979	0.799897	−	0.600137i	$-0.204887\pi$
$859$	40276.7	1.59979	0.799897	+	0.600137i	$0.204887\pi$
$860$	0	0
$861$	−34760.5	−1.37588
$862$	− 6215.44i	− 0.245590i
$863$	− 43713.4i	− 1.72424i	−0.506703	−	0.862120i	$-0.669136\pi$
$863$	− 43713.4i	− 1.72424i	0.506703	−	0.862120i	$-0.330864\pi$
$864$	4779.07	0.188180
$865$	0	0
$866$	11426.9	0.448386
$867$	− 28079.6i	− 1.09992i
$868$	− 11661.7i	− 0.456017i
$869$	−19090.3	−0.745218
$870$	0	0
$871$	7293.01	0.283713
$872$	− 6460.36i	− 0.250889i
$873$	5072.74i	0.196662i
$874$	−6531.99	−0.252801
$875$	0	0
$876$	−3728.16	−0.143793
$877$	24740.5i	0.952596i	0.879284	+	0.476298i	$0.158022\pi$
$877$	24740.5i	0.952596i	−0.879284	+	0.476298i	$0.841978\pi$
$878$	− 9174.27i	− 0.352639i
$879$	44212.9	1.69655
$880$	0	0
$881$	−44027.2	−1.68367	−0.841835	−	0.539735i	$-0.818524\pi$
$881$	−44027.2	−1.68367	−0.841835	+	0.539735i	$0.818524\pi$
$882$	4623.50i	0.176509i
$883$	− 30245.0i	− 1.15269i	−0.817207	−	0.576344i	$-0.804479\pi$
$883$	− 30245.0i	− 1.15269i	0.817207	−	0.576344i	$-0.195521\pi$
$884$	−9380.87	−0.356915
$885$	0	0
$886$	−10536.0	−0.399509
$887$	− 7317.82i	− 0.277010i	−0.990362	−	0.138505i	$-0.955770\pi$
$887$	− 7317.82i	− 0.277010i	0.990362	−	0.138505i	$-0.0442298\pi$
$888$	− 2277.29i	− 0.0860595i
$889$	18845.9	0.710991
$890$	0	0
$891$	22480.8	0.845270
$892$	− 6019.17i	− 0.225938i
$893$	29193.8i	1.09399i
$894$	−24321.6	−0.909883
$895$	0	0
$896$	−3759.15	−0.140161
$897$	− 2461.77i	− 0.0916346i
$898$	33733.7i	1.25357i
$899$	−23966.8	−0.889140
$900$	0	0
$901$	−51116.5	−1.89005
$902$	19024.9i	0.702282i
$903$	− 22852.5i	− 0.842176i
$904$	8532.63	0.313928
$905$	0	0
$906$	−23393.5	−0.857834
$907$	− 35436.0i	− 1.29728i	−0.761096	−	0.648640i	$-0.775338\pi$
$907$	− 35436.0i	− 1.29728i	0.761096	−	0.648640i	$-0.224662\pi$
$908$	7117.75i	0.260144i
$909$	−7428.63	−0.271058
$910$	0	0
$911$	−11359.1	−0.413112	−0.206556	−	0.978435i	$-0.566225\pi$
$911$	−11359.1	−0.413112	−0.206556	+	0.978435i	$0.566225\pi$
$912$	− 10789.0i	− 0.391732i
$913$	30567.7i	1.10804i
$914$	18248.5	0.660401
$915$	0	0
$916$	15904.6	0.573694
$917$	70188.2i	2.52761i
$918$	− 31078.5i	− 1.11737i
$919$	−40517.5	−1.45435	−0.727175	−	0.686452i	$-0.759167\pi$
$919$	−40517.5	−1.45435	−0.727175	+	0.686452i	$0.759167\pi$
$920$	0	0
$921$	−15951.2	−0.570695
$922$	− 12023.8i	− 0.429484i
$923$	20133.3i	0.717982i
$924$	−21289.9	−0.757995
$925$	0	0
$926$	17168.2	0.609267
$927$	4942.21i	0.175106i
$928$	7725.72i	0.273286i
$929$	−16242.2	−0.573614	−0.286807	−	0.957988i	$-0.592594\pi$
$929$	−16242.2	−0.573614	−0.286807	+	0.957988i	$0.592594\pi$
$930$	0	0
$931$	73769.2	2.59687
$932$	− 9244.50i	− 0.324907i
$933$	− 26161.5i	− 0.917994i
$934$	7908.19	0.277049
$935$	0	0
$936$	−802.397	−0.0280205
$937$	− 47445.0i	− 1.65417i	−0.562074	−	0.827087i	$-0.689996\pi$
$937$	− 47445.0i	− 1.65417i	0.562074	−	0.827087i	$-0.310004\pi$
$938$	− 19005.1i	− 0.661556i
$939$	11403.6	0.396317
$940$	0	0
$941$	−48063.5	−1.66506	−0.832532	−	0.553976i	$-0.813110\pi$
$941$	−48063.5	−1.66506	−0.832532	+	0.553976i	$0.813110\pi$
$942$	− 5382.36i	− 0.186164i
$943$	5732.70i	0.197967i
$944$	−6939.74	−0.239268
$945$	0	0
$946$	−12507.5	−0.429867
$947$	13745.4i	0.471663i	0.971794	+	0.235831i	$0.0757813\pi$
$947$	13745.4i	0.471663i	−0.971794	+	0.235831i	$0.924219\pi$
$948$	− 9501.39i	− 0.325518i
$949$	4423.92	0.151324
$950$	0	0
$951$	5021.06	0.171208
$952$	24445.9i	0.832245i
$953$	13999.1i	0.475839i	0.971285	+	0.237920i	$0.0764655\pi$
$953$	13999.1i	0.475839i	−0.971285	+	0.237920i	$0.923535\pi$
$954$	−4372.27	−0.148383
$955$	0	0
$956$	3297.07	0.111543
$957$	43754.5i	1.47793i
$958$	− 190.675i	− 0.00643052i
$959$	−26410.7	−0.889308
$960$	0	0
$961$	−19936.4	−0.669207
$962$	2702.28i	0.0905666i
$963$	174.389i	0.00583552i
$964$	−14567.3	−0.486703
$965$	0	0
$966$	−6415.23	−0.213671
$967$	− 800.187i	− 0.0266104i	−0.999911	−	0.0133052i	$-0.995765\pi$
$967$	− 800.187i	− 0.0266104i	0.999911	−	0.0133052i	$-0.00423530\pi$
$968$	1004.25i	0.0333450i
$969$	−70161.4	−2.32602
$970$	0	0
$971$	−11363.5	−0.375563	−0.187782	−	0.982211i	$-0.560130\pi$
$971$	−11363.5	−0.375563	−0.187782	+	0.982211i	$0.560130\pi$
$972$	− 4940.50i	− 0.163032i
$973$	− 9084.84i	− 0.299328i
$974$	27830.4	0.915549
$975$	0	0
$976$	10574.4	0.346803
$977$	− 17444.0i	− 0.571220i	−0.958346	−	0.285610i	$-0.907804\pi$
$977$	− 17444.0i	− 0.571220i	0.958346	−	0.285610i	$-0.0921962\pi$
$978$	− 9126.06i	− 0.298384i
$979$	−27822.5	−0.908286
$980$	0	0
$981$	−3593.52	−0.116954
$982$	− 12582.7i	− 0.408889i
$983$	54032.7i	1.75318i	0.481237	+	0.876590i	$0.340188\pi$
$983$	54032.7i	1.75318i	−0.481237	+	0.876590i	$0.659812\pi$
$984$	−9468.81	−0.306763
$985$	0	0
$986$	50240.7	1.62271
$987$	28671.9i	0.924659i
$988$	12802.5i	0.412248i
$989$	−3768.84	−0.121175
$990$	0	0
$991$	28869.3	0.925392	0.462696	−	0.886517i	$-0.346882\pi$
$991$	28869.3	0.925392	0.462696	+	0.886517i	$0.346882\pi$
$992$	− 3176.66i	− 0.101672i
$993$	− 45968.3i	− 1.46904i
$994$	52466.2	1.67417
$995$	0	0
$996$	−15213.7	−0.484002
$997$	3358.78i	0.106694i	0.998576	+	0.0533469i	$0.0169889\pi$
$997$	3358.78i	0.106694i	−0.998576	+	0.0533469i	$0.983011\pi$
$998$	− 1276.66i	− 0.0404931i
$999$	−8952.57	−0.283530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.b.n.599.3		8
5.2	odd	4		1150.4.a.p.1.3		4
5.3	odd	4		230.4.a.h.1.2	✓	4
5.4	even	2	inner	1150.4.b.n.599.6		8
15.8	even	4		2070.4.a.bj.1.4		4
20.3	even	4		1840.4.a.m.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.2	✓	4	5.3	odd	4
1150.4.a.p.1.3		4	5.2	odd	4
1150.4.b.n.599.3		8	1.1	even	1	trivial
1150.4.b.n.599.6		8	5.4	even	2	inner
1840.4.a.m.1.3		4	20.3	even	4
2070.4.a.bj.1.4		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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +4.74869i q^{3} -4.00000 q^{4} +9.49738 q^{6} +29.3684i q^{7} +8.00000i q^{8} +4.44993 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +4.74869i q^{3} -4.00000 q^{4} +9.49738 q^{6} +29.3684i q^{7} +8.00000i q^{8} +4.44993 q^{9} -38.1645 q^{11} -18.9948i q^{12} +22.5396i q^{13} +58.7368 q^{14} +16.0000 q^{16} -104.049i q^{17} -8.89986i q^{18} -142.000 q^{19} -139.461 q^{21} +76.3291i q^{22} +23.0000i q^{23} -37.9895 q^{24} +45.0792 q^{26} +149.346i q^{27} -117.474i q^{28} -241.429 q^{29} +99.2706 q^{31} -32.0000i q^{32} -181.232i q^{33} -208.097 q^{34} -17.7997 q^{36} +59.9452i q^{37} +284.000i q^{38} -107.034 q^{39} +249.248 q^{41} +278.923i q^{42} +163.863i q^{43} +152.658 q^{44} +46.0000 q^{46} -205.591i q^{47} +75.9791i q^{48} -519.502 q^{49} +494.095 q^{51} -90.1584i q^{52} -491.274i q^{53} +298.692 q^{54} -234.947 q^{56} -674.313i q^{57} +482.858i q^{58} -433.734 q^{59} +660.902 q^{61} -198.541i q^{62} +130.687i q^{63} -64.0000 q^{64} -362.463 q^{66} -323.564i q^{67} +416.195i q^{68} -109.220 q^{69} +893.243 q^{71} +35.5994i q^{72} -196.273i q^{73} +119.890 q^{74} +567.999 q^{76} -1120.83i q^{77} +214.067i q^{78} +500.211 q^{79} -589.050 q^{81} -498.496i q^{82} -800.944i q^{83} +557.846 q^{84} +327.726 q^{86} -1146.47i q^{87} -305.316i q^{88} +729.016 q^{89} -661.952 q^{91} -92.0000i q^{92} +471.405i q^{93} -411.181 q^{94} +151.958 q^{96} +1139.96i q^{97} +1039.00i q^{98} -169.829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 16 q^{6} - 64 q^{9}+O(q^{10}) \) 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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