LMFDB - Embedded newform 1150.4.b.n.599.4

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			599.4
Root			$6.57209i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.4.b.n.599.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +7.57209i q^{3} -4.00000 q^{4} +15.1442 q^{6} -35.4229i q^{7} +8.00000i q^{8} -30.3365 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +7.57209i q^{3} -4.00000 q^{4} +15.1442 q^{6} -35.4229i q^{7} +8.00000i q^{8} -30.3365 q^{9} -16.6298 q^{11} -30.2883i q^{12} +79.9132i q^{13} -70.8458 q^{14} +16.0000 q^{16} -46.8219i q^{17} +60.6730i q^{18} +110.653 q^{19} +268.225 q^{21} +33.2597i q^{22} +23.0000i q^{23} -60.5767 q^{24} +159.826 q^{26} -25.2641i q^{27} +141.692i q^{28} +0.836422 q^{29} -119.836 q^{31} -32.0000i q^{32} -125.923i q^{33} -93.6438 q^{34} +121.346 q^{36} +368.201i q^{37} -221.307i q^{38} -605.109 q^{39} -95.7927 q^{41} -536.450i q^{42} -331.961i q^{43} +66.5193 q^{44} +46.0000 q^{46} -535.037i q^{47} +121.153i q^{48} -911.782 q^{49} +354.539 q^{51} -319.653i q^{52} -409.345i q^{53} -50.5282 q^{54} +283.383 q^{56} +837.876i q^{57} -1.67284i q^{58} +352.950 q^{59} -507.223 q^{61} +239.672i q^{62} +1074.61i q^{63} -64.0000 q^{64} -251.845 q^{66} -820.056i q^{67} +187.288i q^{68} -174.158 q^{69} -733.770 q^{71} -242.692i q^{72} +91.4599i q^{73} +736.402 q^{74} -442.613 q^{76} +589.077i q^{77} +1210.22i q^{78} -329.381 q^{79} -627.783 q^{81} +191.585i q^{82} +753.834i q^{83} -1072.90 q^{84} -663.922 q^{86} +6.33346i q^{87} -133.039i q^{88} +1050.14 q^{89} +2830.76 q^{91} -92.0000i q^{92} -907.407i q^{93} -1070.07 q^{94} +242.307 q^{96} -271.928i q^{97} +1823.56i q^{98} +504.491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	7.57209i	1.45725i	0.684914	+	0.728624i	$0.259840\pi$
$3$	7.57209i	1.45725i	−0.684914	+	0.728624i	$0.740160\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	15.1442	1.03043
$7$	− 35.4229i	− 1.91266i	−0.292294	−	0.956328i	$-0.594419\pi$
$7$	− 35.4229i	− 1.91266i	0.292294	−	0.956328i	$-0.405581\pi$
$8$	8.00000i	0.353553i
$9$	−30.3365	−1.12357
$10$	0	0
$11$	−16.6298	−0.455826	−0.227913	−	0.973682i	$-0.573190\pi$
$11$	−16.6298	−0.455826	−0.227913	+	0.973682i	$0.573190\pi$
$12$	− 30.2883i	− 0.728624i
$13$	79.9132i	1.70492i	0.522795	+	0.852459i	$0.324889\pi$
$13$	79.9132i	1.70492i	−0.522795	+	0.852459i	$0.675111\pi$
$14$	−70.8458	−1.35245
$15$	0	0
$16$	16.0000	0.250000
$17$	− 46.8219i	− 0.667999i	−0.942573	−	0.333999i	$-0.891602\pi$
$17$	− 46.8219i	− 0.667999i	0.942573	−	0.333999i	$-0.108398\pi$
$18$	60.6730i	0.794486i
$19$	110.653	1.33608	0.668042	−	0.744123i	$-0.267132\pi$
$19$	110.653	1.33608	0.668042	+	0.744123i	$0.267132\pi$
$20$	0	0
$21$	268.225	2.78722
$22$	33.2597i	0.322318i
$23$	23.0000i	0.208514i
$23$	23.0000i	0.208514i
$24$	−60.5767	−0.515215
$25$	0	0
$26$	159.826	1.20556
$27$	− 25.2641i	− 0.180077i
$28$	141.692i	0.956328i
$29$	0.836422	0.00535585	0.00267793	−	0.999996i	$-0.499148\pi$
$29$	0.836422	0.00535585	0.00267793	+	0.999996i	$0.499148\pi$
$30$	0	0
$31$	−119.836	−0.694295	−0.347147	−	0.937811i	$-0.612850\pi$
$31$	−119.836	−0.694295	−0.347147	+	0.937811i	$0.612850\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 125.923i	− 0.664252i
$34$	−93.6438	−0.472346
$35$	0	0
$36$	121.346	0.561787
$37$	368.201i	1.63600i	0.575221	+	0.817998i	$0.304916\pi$
$37$	368.201i	1.63600i	−0.575221	+	0.817998i	$0.695084\pi$
$38$	− 221.307i	− 0.944755i
$39$	−605.109	−2.48449
$40$	0	0
$41$	−95.7927	−0.364886	−0.182443	−	0.983216i	$-0.558400\pi$
$41$	−95.7927	−0.364886	−0.182443	+	0.983216i	$0.558400\pi$
$42$	− 536.450i	− 1.97086i
$43$	− 331.961i	− 1.17729i	−0.808390	−	0.588647i	$-0.799661\pi$
$43$	− 331.961i	− 1.17729i	0.808390	−	0.588647i	$-0.200339\pi$
$44$	66.5193	0.227913
$45$	0	0
$46$	46.0000	0.147442
$47$	− 535.037i	− 1.66049i	−0.557397	−	0.830246i	$-0.688200\pi$
$47$	− 535.037i	− 1.66049i	0.557397	−	0.830246i	$-0.311800\pi$
$48$	121.153i	0.364312i
$49$	−911.782	−2.65826
$50$	0	0
$51$	354.539	0.973440
$52$	− 319.653i	− 0.852459i
$53$	− 409.345i	− 1.06090i	−0.847715	−	0.530452i	$-0.822022\pi$
$53$	− 409.345i	− 1.06090i	0.847715	−	0.530452i	$-0.177978\pi$
$54$	−50.5282	−0.127334
$55$	0	0
$56$	283.383	0.676226
$57$	837.876i	1.94701i
$58$	− 1.67284i	− 0.00378716i
$59$	352.950	0.778817	0.389408	−	0.921065i	$-0.372679\pi$
$59$	352.950	0.778817	0.389408	+	0.921065i	$0.372679\pi$
$60$	0	0
$61$	−507.223	−1.06464	−0.532322	−	0.846542i	$-0.678680\pi$
$61$	−507.223	−1.06464	−0.532322	+	0.846542i	$0.678680\pi$
$62$	239.672i	0.490941i
$63$	1074.61i	2.14901i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−251.845	−0.469697
$67$	− 820.056i	− 1.49531i	−0.664087	−	0.747655i	$-0.731180\pi$
$67$	− 820.056i	− 1.49531i	0.664087	−	0.747655i	$-0.268820\pi$
$68$	187.288i	0.333999i
$69$	−174.158	−0.303857
$70$	0	0
$71$	−733.770	−1.22651	−0.613257	−	0.789884i	$-0.710141\pi$
$71$	−733.770	−1.22651	−0.613257	+	0.789884i	$0.710141\pi$
$72$	− 242.692i	− 0.397243i
$73$	91.4599i	0.146638i	0.997309	+	0.0733190i	$0.0233591\pi$
$73$	91.4599i	0.146638i	−0.997309	+	0.0733190i	$0.976641\pi$
$74$	736.402	1.15682
$75$	0	0
$76$	−442.613	−0.668042
$77$	589.077i	0.871838i
$78$	1210.22i	1.75680i
$79$	−329.381	−0.469092	−0.234546	−	0.972105i	$-0.575360\pi$
$79$	−329.381	−0.469092	−0.234546	+	0.972105i	$0.575360\pi$
$80$	0	0
$81$	−627.783	−0.861156
$82$	191.585i	0.258013i
$83$	753.834i	0.996916i	0.866914	+	0.498458i	$0.166100\pi$
$83$	753.834i	0.996916i	−0.866914	+	0.498458i	$0.833900\pi$
$84$	−1072.90	−1.39361
$85$	0	0
$86$	−663.922	−0.832472
$87$	6.33346i	0.00780481i
$88$	− 133.039i	− 0.161159i
$89$	1050.14	1.25073	0.625365	−	0.780332i	$-0.284950\pi$
$89$	1050.14	1.25073	0.625365	+	0.780332i	$0.284950\pi$
$90$	0	0
$91$	2830.76	3.26092
$92$	− 92.0000i	− 0.104257i
$93$	− 907.407i	− 1.01176i
$94$	−1070.07	−1.17415
$95$	0	0
$96$	242.307	0.257608
$97$	− 271.928i	− 0.284641i	−0.989821	−	0.142320i	$-0.954544\pi$
$97$	− 271.928i	− 0.284641i	0.989821	−	0.142320i	$-0.0454563\pi$
$98$	1823.56i	1.87967i
$99$	504.491	0.512154
$100$	0	0
$101$	1658.68	1.63410	0.817052	−	0.576563i	$-0.195607\pi$
$101$	1658.68	1.63410	0.817052	+	0.576563i	$0.195607\pi$
$102$	− 709.079i	− 0.688326i
$103$	− 1735.52i	− 1.66025i	−0.557580	−	0.830123i	$-0.688270\pi$
$103$	− 1735.52i	− 1.66025i	0.557580	−	0.830123i	$-0.311730\pi$
$104$	−639.305	−0.602779
$105$	0	0
$106$	−818.691	−0.750172
$107$	− 1629.88i	− 1.47258i	−0.676664	−	0.736292i	$-0.736575\pi$
$107$	− 1629.88i	− 1.47258i	0.676664	−	0.736292i	$-0.263425\pi$
$108$	101.056i	0.0900385i
$109$	432.151	0.379748	0.189874	−	0.981808i	$-0.439192\pi$
$109$	432.151	0.379748	0.189874	+	0.981808i	$0.439192\pi$
$110$	0	0
$111$	−2788.05	−2.38405
$112$	− 566.766i	− 0.478164i
$113$	240.115i	0.199895i	0.994993	+	0.0999476i	$0.0318675\pi$
$113$	240.115i	0.199895i	−0.994993	+	0.0999476i	$0.968132\pi$
$114$	1675.75	1.37674
$115$	0	0
$116$	−3.34569	−0.00267793
$117$	− 2424.28i	− 1.91560i
$118$	− 705.900i	− 0.550707i
$119$	−1658.57	−1.27765
$120$	0	0
$121$	−1054.45	−0.792223
$122$	1014.45i	0.752817i
$123$	− 725.350i	− 0.531729i
$124$	479.343	0.347147
$125$	0	0
$126$	2149.21	1.51958
$127$	− 210.993i	− 0.147422i	−0.997280	−	0.0737110i	$-0.976516\pi$
$127$	− 210.993i	− 0.147422i	0.997280	−	0.0737110i	$-0.0234842\pi$
$128$	128.000i	0.0883883i
$129$	2513.64	1.71561
$130$	0	0
$131$	−746.178	−0.497663	−0.248832	−	0.968547i	$-0.580047\pi$
$131$	−746.178	−0.497663	−0.248832	+	0.968547i	$0.580047\pi$
$132$	503.690i	0.332126i
$133$	− 3919.66i	− 2.55547i
$134$	−1640.11	−1.05734
$135$	0	0
$136$	374.575	0.236173
$137$	− 2420.07i	− 1.50920i	−0.656184	−	0.754601i	$-0.727830\pi$
$137$	− 2420.07i	− 1.50920i	0.656184	−	0.754601i	$-0.272170\pi$
$138$	348.316i	0.214860i
$139$	−924.030	−0.563850	−0.281925	−	0.959436i	$-0.590973\pi$
$139$	−924.030	−0.563850	−0.281925	+	0.959436i	$0.590973\pi$
$140$	0	0
$141$	4051.34	2.41975
$142$	1467.54i	0.867276i
$143$	− 1328.94i	− 0.777145i
$144$	−485.384	−0.280893
$145$	0	0
$146$	182.920	0.103689
$147$	− 6904.09i	− 3.87374i
$148$	− 1472.80i	− 0.817998i
$149$	−430.614	−0.236760	−0.118380	−	0.992968i	$-0.537770\pi$
$149$	−430.614	−0.236760	−0.118380	+	0.992968i	$0.537770\pi$
$150$	0	0
$151$	−25.4118	−0.0136953	−0.00684763	−	0.999977i	$-0.502180\pi$
$151$	−25.4118	−0.0136953	−0.00684763	+	0.999977i	$0.502180\pi$
$152$	885.226i	0.472377i
$153$	1420.41i	0.750546i
$154$	1178.15	0.616483
$155$	0	0
$156$	2420.44	1.24224
$157$	− 1580.29i	− 0.803317i	−0.915790	−	0.401658i	$-0.868434\pi$
$157$	− 1580.29i	− 0.803317i	0.915790	−	0.401658i	$-0.131566\pi$
$158$	658.762i	0.331698i
$159$	3099.60	1.54600
$160$	0	0
$161$	814.727	0.398817
$162$	1255.57i	0.608930i
$163$	− 458.739i	− 0.220437i	−0.993907	−	0.110218i	$-0.964845\pi$
$163$	− 458.739i	− 0.220437i	0.993907	−	0.110218i	$-0.0351550\pi$
$164$	383.171	0.182443
$165$	0	0
$166$	1507.67	0.704926
$167$	− 561.275i	− 0.260076i	−0.991509	−	0.130038i	$-0.958490\pi$
$167$	− 561.275i	− 0.260076i	0.991509	−	0.130038i	$-0.0415100\pi$
$168$	2145.80i	0.985430i
$169$	−4189.11	−1.90674
$170$	0	0
$171$	−3356.83	−1.50119
$172$	1327.84i	0.588647i
$173$	− 1573.95i	− 0.691705i	−0.938289	−	0.345852i	$-0.887590\pi$
$173$	− 1573.95i	− 0.691705i	0.938289	−	0.345852i	$-0.112410\pi$
$174$	12.6669	0.00551883
$175$	0	0
$176$	−266.077	−0.113956
$177$	2672.57i	1.13493i
$178$	− 2100.29i	− 0.884400i
$179$	−2215.59	−0.925145	−0.462572	−	0.886581i	$-0.653073\pi$
$179$	−2215.59	−0.925145	−0.462572	+	0.886581i	$0.653073\pi$
$180$	0	0
$181$	873.497	0.358710	0.179355	−	0.983784i	$-0.442599\pi$
$181$	873.497	0.358710	0.179355	+	0.983784i	$0.442599\pi$
$182$	− 5661.51i	− 2.30582i
$183$	− 3840.74i	− 1.55145i
$184$	−184.000	−0.0737210
$185$	0	0
$186$	−1814.81	−0.715422
$187$	778.641i	0.304491i
$188$	2140.15i	0.830246i
$189$	−894.928	−0.344425
$190$	0	0
$191$	−2497.74	−0.946230	−0.473115	−	0.881001i	$-0.656870\pi$
$191$	−2497.74	−0.946230	−0.473115	+	0.881001i	$0.656870\pi$
$192$	− 484.613i	− 0.182156i
$193$	− 909.155i	− 0.339080i	−0.985523	−	0.169540i	$-0.945772\pi$
$193$	− 909.155i	− 0.339080i	0.985523	−	0.169540i	$-0.0542282\pi$
$194$	−543.857	−0.201271
$195$	0	0
$196$	3647.13	1.32913
$197$	608.627i	0.220116i	0.993925	+	0.110058i	$0.0351037\pi$
$197$	608.627i	0.220116i	−0.993925	+	0.110058i	$0.964896\pi$
$198$	− 1008.98i	− 0.362147i
$199$	2304.98	0.821083	0.410542	−	0.911842i	$-0.365340\pi$
$199$	2304.98	0.821083	0.410542	+	0.911842i	$0.365340\pi$
$200$	0	0
$201$	6209.54	2.17904
$202$	− 3317.36i	− 1.15549i
$203$	− 29.6285i	− 0.0102439i
$204$	−1418.16	−0.486720
$205$	0	0
$206$	−3471.03	−1.17397
$207$	− 697.739i	− 0.234281i
$208$	1278.61i	0.426229i
$209$	−1840.15	−0.609022
$210$	0	0
$211$	−4373.37	−1.42690	−0.713448	−	0.700708i	$-0.752868\pi$
$211$	−4373.37	−1.42690	−0.713448	+	0.700708i	$0.752868\pi$
$212$	1637.38i	0.530452i
$213$	− 5556.17i	− 1.78733i
$214$	−3259.76	−1.04127
$215$	0	0
$216$	202.113	0.0636668
$217$	4244.93i	1.32795i
$218$	− 864.303i	− 0.268523i
$219$	−692.542	−0.213688
$220$	0	0
$221$	3741.69	1.13888
$222$	5576.10i	1.68578i
$223$	− 5439.50i	− 1.63343i	−0.577038	−	0.816717i	$-0.695792\pi$
$223$	− 5439.50i	− 1.63343i	0.577038	−	0.816717i	$-0.304208\pi$
$224$	−1133.53	−0.338113
$225$	0	0
$226$	480.231	0.141347
$227$	216.498i	0.0633017i	0.999499	+	0.0316508i	$0.0100765\pi$
$227$	216.498i	0.0633017i	−0.999499	+	0.0316508i	$0.989924\pi$
$228$	− 3351.51i	− 0.973504i
$229$	924.664	0.266828	0.133414	−	0.991060i	$-0.457406\pi$
$229$	924.664	0.266828	0.133414	+	0.991060i	$0.457406\pi$
$230$	0	0
$231$	−4460.54	−1.27049
$232$	6.69138i	0.00189358i
$233$	2369.69i	0.666280i	0.942877	+	0.333140i	$0.108108\pi$
$233$	2369.69i	0.666280i	−0.942877	+	0.333140i	$0.891892\pi$
$234$	−4848.57	−1.35453
$235$	0	0
$236$	−1411.80	−0.389408
$237$	− 2494.10i	− 0.683584i
$238$	3317.14i	0.903437i
$239$	2769.60	0.749583	0.374791	−	0.927109i	$-0.377714\pi$
$239$	2769.60	0.749583	0.374791	+	0.927109i	$0.377714\pi$
$240$	0	0
$241$	−5334.10	−1.42572	−0.712862	−	0.701305i	$-0.752601\pi$
$241$	−5334.10	−1.42572	−0.712862	+	0.701305i	$0.752601\pi$
$242$	2108.90i	0.560186i
$243$	− 5435.76i	− 1.43500i
$244$	2028.89	0.532322
$245$	0	0
$246$	−1450.70	−0.375989
$247$	8842.66i	2.27791i
$248$	− 958.686i	− 0.245470i
$249$	−5708.10	−1.45275
$250$	0	0
$251$	4677.13	1.17617	0.588084	−	0.808800i	$-0.299882\pi$
$251$	4677.13	1.17617	0.588084	+	0.808800i	$0.299882\pi$
$252$	− 4298.42i	− 1.07451i
$253$	− 382.486i	− 0.0950463i
$254$	−421.986	−0.104243
$255$	0	0
$256$	256.000	0.0625000
$257$	− 2602.99i	− 0.631789i	−0.948794	−	0.315895i	$-0.897695\pi$
$257$	− 2602.99i	− 0.631789i	0.948794	−	0.315895i	$-0.102305\pi$
$258$	− 5027.28i	− 1.21312i
$259$	13042.7	3.12910
$260$	0	0
$261$	−25.3741	−0.00601769
$262$	1492.36i	0.351901i
$263$	3411.30i	0.799809i	0.916557	+	0.399904i	$0.130957\pi$
$263$	3411.30i	0.799809i	−0.916557	+	0.399904i	$0.869043\pi$
$264$	1007.38	0.234848
$265$	0	0
$266$	−7839.32	−1.80699
$267$	7951.77i	1.82262i
$268$	3280.22i	0.747655i
$269$	−4366.56	−0.989718	−0.494859	−	0.868973i	$-0.664780\pi$
$269$	−4366.56	−0.989718	−0.494859	+	0.868973i	$0.664780\pi$
$270$	0	0
$271$	5682.45	1.27374	0.636872	−	0.770970i	$-0.280228\pi$
$271$	5682.45	1.27374	0.636872	+	0.770970i	$0.280228\pi$
$272$	− 749.150i	− 0.167000i
$273$	21434.7i	4.75197i
$274$	−4840.14	−1.06717
$275$	0	0
$276$	696.632	0.151929
$277$	− 1884.62i	− 0.408794i	−0.978888	−	0.204397i	$-0.934477\pi$
$277$	− 1884.62i	− 0.408794i	0.978888	−	0.204397i	$-0.0655234\pi$
$278$	1848.06i	0.398702i
$279$	3635.39	0.780091
$280$	0	0
$281$	−2706.42	−0.574561	−0.287281	−	0.957846i	$-0.592751\pi$
$281$	−2706.42	−0.574561	−0.287281	+	0.957846i	$0.592751\pi$
$282$	− 8102.69i	− 1.71102i
$283$	5963.64i	1.25266i	0.779560	+	0.626328i	$0.215443\pi$
$283$	5963.64i	1.25266i	−0.779560	+	0.626328i	$0.784557\pi$
$284$	2935.08	0.613257
$285$	0	0
$286$	−2657.89	−0.549525
$287$	3393.26i	0.697901i
$288$	970.767i	0.198622i
$289$	2720.71	0.553778
$290$	0	0
$291$	2059.06	0.414792
$292$	− 365.840i	− 0.0733190i
$293$	4735.85i	0.944272i	0.881526	+	0.472136i	$0.156517\pi$
$293$	4735.85i	0.944272i	−0.881526	+	0.472136i	$0.843483\pi$
$294$	−13808.2	−2.73915
$295$	0	0
$296$	−2945.61	−0.578412
$297$	420.138i	0.0820837i
$298$	861.227i	0.167415i
$299$	−1838.00	−0.355500
$300$	0	0
$301$	−11759.0	−2.25176
$302$	50.8236i	0.00968401i
$303$	12559.6i	2.38130i
$304$	1770.45	0.334021
$305$	0	0
$306$	2840.82	0.530716
$307$	− 769.241i	− 0.143006i	−0.997440	−	0.0715031i	$-0.977220\pi$
$307$	− 769.241i	− 0.143006i	0.997440	−	0.0715031i	$-0.0227796\pi$
$308$	− 2356.31i	− 0.435919i
$309$	13141.5	2.41939
$310$	0	0
$311$	−5592.71	−1.01972	−0.509861	−	0.860257i	$-0.670303\pi$
$311$	−5592.71	−1.01972	−0.509861	+	0.860257i	$0.670303\pi$
$312$	− 4840.87i	− 0.878399i
$313$	− 9777.19i	− 1.76562i	−0.469729	−	0.882811i	$-0.655648\pi$
$313$	− 9777.19i	− 1.76562i	0.469729	−	0.882811i	$-0.344352\pi$
$314$	−3160.58	−0.568031
$315$	0	0
$316$	1317.52	0.234546
$317$	1868.51i	0.331060i	0.986205	+	0.165530i	$0.0529335\pi$
$317$	1868.51i	0.331060i	−0.986205	+	0.165530i	$0.947066\pi$
$318$	− 6199.20i	− 1.09319i
$319$	−13.9096	−0.00244134
$320$	0	0
$321$	12341.6	2.14592
$322$	− 1629.45i	− 0.282006i
$323$	− 5181.00i	− 0.892503i
$324$	2511.13	0.430578
$325$	0	0
$326$	−917.477	−0.155872
$327$	3272.29i	0.553388i
$328$	− 766.342i	− 0.129007i
$329$	−18952.6	−3.17595
$330$	0	0
$331$	6966.91	1.15691	0.578454	−	0.815715i	$-0.303656\pi$
$331$	6966.91	1.15691	0.578454	+	0.815715i	$0.303656\pi$
$332$	− 3015.34i	− 0.498458i
$333$	− 11169.9i	− 1.83816i
$334$	−1122.55	−0.183902
$335$	0	0
$336$	4291.60	0.696804
$337$	− 17.5487i	− 0.00283661i	−0.999999	−	0.00141830i	$-0.999549\pi$
$337$	− 17.5487i	− 0.00283661i	0.999999	−	0.00141830i	$-0.000451460\pi$
$338$	8378.23i	1.34827i
$339$	−1818.17	−0.291297
$340$	0	0
$341$	1992.85	0.316477
$342$	6713.66i	1.06150i
$343$	20147.9i	3.17167i
$344$	2655.69	0.416236
$345$	0	0
$346$	−3147.89	−0.489109
$347$	− 9859.30i	− 1.52529i	−0.646818	−	0.762644i	$-0.723901\pi$
$347$	− 9859.30i	− 1.52529i	0.646818	−	0.762644i	$-0.276099\pi$
$348$	− 25.3338i	− 0.00390240i
$349$	−7200.25	−1.10436	−0.552178	−	0.833726i	$-0.686203\pi$
$349$	−7200.25	−1.10436	−0.552178	+	0.833726i	$0.686203\pi$
$350$	0	0
$351$	2018.93	0.307016
$352$	532.155i	0.0805794i
$353$	6054.58i	0.912897i	0.889750	+	0.456449i	$0.150879\pi$
$353$	6054.58i	0.912897i	−0.889750	+	0.456449i	$0.849121\pi$
$354$	5345.14	0.802516
$355$	0	0
$356$	−4200.57	−0.625365
$357$	− 12558.8i	− 1.86186i
$358$	4431.18i	0.654176i
$359$	−2734.26	−0.401974	−0.200987	−	0.979594i	$-0.564415\pi$
$359$	−2734.26	−0.401974	−0.200987	+	0.979594i	$0.564415\pi$
$360$	0	0
$361$	5385.16	0.785123
$362$	− 1746.99i	− 0.253646i
$363$	− 7984.37i	− 1.15447i
$364$	−11323.0	−1.63046
$365$	0	0
$366$	−7681.47	−1.09704
$367$	− 2465.50i	− 0.350676i	−0.984508	−	0.175338i	$-0.943898\pi$
$367$	− 2465.50i	− 0.350676i	0.984508	−	0.175338i	$-0.0561018\pi$
$368$	368.000i	0.0521286i
$369$	2906.01	0.409976
$370$	0	0
$371$	−14500.2	−2.02915
$372$	3629.63i	0.505880i
$373$	− 5704.45i	− 0.791863i	−0.918280	−	0.395932i	$-0.870422\pi$
$373$	− 5704.45i	− 0.791863i	0.918280	−	0.395932i	$-0.129578\pi$
$374$	1557.28	0.215308
$375$	0	0
$376$	4280.29	0.587073
$377$	66.8411i	0.00913128i
$378$	1789.86i	0.243546i
$379$	−10231.9	−1.38675	−0.693376	−	0.720576i	$-0.743878\pi$
$379$	−10231.9	−1.38675	−0.693376	+	0.720576i	$0.743878\pi$
$380$	0	0
$381$	1597.66	0.214830
$382$	4995.47i	0.669086i
$383$	− 6321.34i	− 0.843356i	−0.906746	−	0.421678i	$-0.861441\pi$
$383$	− 6321.34i	− 0.843356i	0.906746	−	0.421678i	$-0.138559\pi$
$384$	−969.227	−0.128804
$385$	0	0
$386$	−1818.31	−0.239766
$387$	10070.5i	1.32278i
$388$	1087.71i	0.142320i
$389$	925.594	0.120641	0.0603207	−	0.998179i	$-0.480788\pi$
$389$	925.594	0.120641	0.0603207	+	0.998179i	$0.480788\pi$
$390$	0	0
$391$	1076.90	0.139287
$392$	− 7294.25i	− 0.939835i
$393$	− 5650.13i	− 0.725219i
$394$	1217.25	0.155646
$395$	0	0
$396$	−2017.96	−0.256077
$397$	− 2706.75i	− 0.342187i	−0.985255	−	0.171093i	$-0.945270\pi$
$397$	− 2706.75i	− 0.342187i	0.985255	−	0.171093i	$-0.0547299\pi$
$398$	− 4609.96i	− 0.580594i
$399$	29680.0	3.72396
$400$	0	0
$401$	−14095.3	−1.75532	−0.877661	−	0.479281i	$-0.840897\pi$
$401$	−14095.3	−1.75532	−0.877661	+	0.479281i	$0.840897\pi$
$402$	− 12419.1i	− 1.54081i
$403$	− 9576.45i	− 1.18372i
$404$	−6634.71	−0.817052
$405$	0	0
$406$	−59.2570	−0.00724353
$407$	− 6123.12i	− 0.745729i
$408$	2836.32i	0.344163i
$409$	10846.0	1.31125	0.655625	−	0.755087i	$-0.272405\pi$
$409$	10846.0	1.31125	0.655625	+	0.755087i	$0.272405\pi$
$410$	0	0
$411$	18325.0	2.19928
$412$	6942.06i	0.830123i
$413$	− 12502.5i	− 1.48961i
$414$	−1395.48	−0.165662
$415$	0	0
$416$	2557.22	0.301390
$417$	− 6996.84i	− 0.821670i
$418$	3680.29i	0.430644i
$419$	5626.55	0.656026	0.328013	−	0.944673i	$-0.393621\pi$
$419$	5626.55	0.656026	0.328013	+	0.944673i	$0.393621\pi$
$420$	0	0
$421$	−7109.09	−0.822983	−0.411491	−	0.911414i	$-0.634992\pi$
$421$	−7109.09	−0.822983	−0.411491	+	0.911414i	$0.634992\pi$
$422$	8746.74i	1.00897i
$423$	16231.1i	1.86568i
$424$	3274.76	0.375086
$425$	0	0
$426$	−11112.3	−1.26384
$427$	17967.3i	2.03630i
$428$	6519.52i	0.736292i
$429$	10062.9	1.13249
$430$	0	0
$431$	4464.14	0.498909	0.249455	−	0.968387i	$-0.419749\pi$
$431$	4464.14	0.498909	0.249455	+	0.968387i	$0.419749\pi$
$432$	− 404.226i	− 0.0450192i
$433$	− 11009.4i	− 1.22189i	−0.791672	−	0.610947i	$-0.790789\pi$
$433$	− 11009.4i	− 1.22189i	0.791672	−	0.610947i	$-0.209211\pi$
$434$	8489.86	0.939001
$435$	0	0
$436$	−1728.61	−0.189874
$437$	2545.03i	0.278593i
$438$	1385.08i	0.151100i
$439$	3052.70	0.331885	0.165943	−	0.986135i	$-0.446933\pi$
$439$	3052.70	0.331885	0.165943	+	0.986135i	$0.446933\pi$
$440$	0	0
$441$	27660.2	2.98675
$442$	− 7483.37i	− 0.805312i
$443$	4465.82i	0.478956i	0.970902	+	0.239478i	$0.0769764\pi$
$443$	4465.82i	0.478956i	−0.970902	+	0.239478i	$0.923024\pi$
$444$	11152.2	1.19203
$445$	0	0
$446$	−10879.0	−1.15501
$447$	− 3260.64i	− 0.345018i
$448$	2267.07i	0.239082i
$449$	−9040.14	−0.950179	−0.475090	−	0.879937i	$-0.657584\pi$
$449$	−9040.14	−0.950179	−0.475090	+	0.879937i	$0.657584\pi$
$450$	0	0
$451$	1593.02	0.166324
$452$	− 960.462i	− 0.0999476i
$453$	− 192.420i	− 0.0199574i
$454$	432.996	0.0447610
$455$	0	0
$456$	−6703.01	−0.688371
$457$	7756.88i	0.793986i	0.917822	+	0.396993i	$0.129946\pi$
$457$	7756.88i	0.793986i	−0.917822	+	0.396993i	$0.870054\pi$
$458$	− 1849.33i	− 0.188676i
$459$	−1182.91	−0.120291
$460$	0	0
$461$	7064.19	0.713692	0.356846	−	0.934163i	$-0.383852\pi$
$461$	7064.19	0.713692	0.356846	+	0.934163i	$0.383852\pi$
$462$	8921.08i	0.898369i
$463$	− 12599.7i	− 1.26470i	−0.774682	−	0.632350i	$-0.782090\pi$
$463$	− 12599.7i	− 1.26470i	0.774682	−	0.632350i	$-0.217910\pi$
$464$	13.3828	0.00133896
$465$	0	0
$466$	4739.37	0.471131
$467$	14746.0i	1.46117i	0.682824	+	0.730583i	$0.260751\pi$
$467$	14746.0i	1.46117i	−0.682824	+	0.730583i	$0.739249\pi$
$468$	9697.14i	0.957800i
$469$	−29048.8	−2.86002
$470$	0	0
$471$	11966.1	1.17063
$472$	2823.60i	0.275353i
$473$	5520.46i	0.536641i
$474$	−4988.20	−0.483367
$475$	0	0
$476$	6634.27	0.638826
$477$	12418.1i	1.19200i
$478$	− 5539.19i	− 0.530035i
$479$	17411.2	1.66084	0.830418	−	0.557141i	$-0.188102\pi$
$479$	17411.2	1.66084	0.830418	+	0.557141i	$0.188102\pi$
$480$	0	0
$481$	−29424.1	−2.78924
$482$	10668.2i	1.00814i
$483$	6169.18i	0.581175i
$484$	4217.79	0.396111
$485$	0	0
$486$	−10871.5	−1.01470
$487$	1320.34i	0.122855i	0.998112	+	0.0614276i	$0.0195653\pi$
$487$	1320.34i	0.122855i	−0.998112	+	0.0614276i	$0.980435\pi$
$488$	− 4057.78i	− 0.376408i
$489$	3473.61	0.321231
$490$	0	0
$491$	17115.8	1.57317	0.786583	−	0.617485i	$-0.211848\pi$
$491$	17115.8	1.57317	0.786583	+	0.617485i	$0.211848\pi$
$492$	2901.40i	0.265864i
$493$	− 39.1629i	− 0.00357770i
$494$	17685.3	1.61073
$495$	0	0
$496$	−1917.37	−0.173574
$497$	25992.3i	2.34590i
$498$	11416.2i	1.02725i
$499$	−17540.6	−1.57360	−0.786798	−	0.617210i	$-0.788263\pi$
$499$	−17540.6	−1.57360	−0.786798	+	0.617210i	$0.788263\pi$
$500$	0	0
$501$	4250.02	0.378996
$502$	− 9354.27i	− 0.831676i
$503$	4934.98i	0.437455i	0.975786	+	0.218727i	$0.0701905\pi$
$503$	4934.98i	0.437455i	−0.975786	+	0.218727i	$0.929809\pi$
$504$	−8596.85	−0.759790
$505$	0	0
$506$	−764.972	−0.0672079
$507$	− 31720.3i	− 2.77860i
$508$	843.972i	0.0737110i
$509$	−11927.3	−1.03865	−0.519323	−	0.854578i	$-0.673816\pi$
$509$	−11927.3	−1.03865	−0.519323	+	0.854578i	$0.673816\pi$
$510$	0	0
$511$	3239.78	0.280468
$512$	− 512.000i	− 0.0441942i
$513$	− 2795.56i	− 0.240598i
$514$	−5205.97	−0.446743
$515$	0	0
$516$	−10054.6	−0.857804
$517$	8897.57i	0.756895i
$518$	− 26085.5i	− 2.21261i
$519$	11918.1	1.00799
$520$	0	0
$521$	−9592.76	−0.806653	−0.403327	−	0.915056i	$-0.632146\pi$
$521$	−9592.76	−0.806653	−0.403327	+	0.915056i	$0.632146\pi$
$522$	50.7482i	0.00425515i
$523$	− 6525.20i	− 0.545558i	−0.962077	−	0.272779i	$-0.912057\pi$
$523$	− 6525.20i	− 0.545558i	0.962077	−	0.272779i	$-0.0879428\pi$
$524$	2984.71	0.248832
$525$	0	0
$526$	6822.60	0.565550
$527$	5610.94i	0.463788i
$528$	− 2014.76i	− 0.166063i
$529$	−529.000	−0.0434783
$530$	0	0
$531$	−10707.3	−0.875058
$532$	15678.6i	1.27774i
$533$	− 7655.10i	− 0.622100i
$534$	15903.5	1.28879
$535$	0	0
$536$	6560.45	0.528672
$537$	− 16776.6i	− 1.34817i
$538$	8733.13i	0.699836i
$539$	15162.8	1.21170
$540$	0	0
$541$	5634.05	0.447739	0.223870	−	0.974619i	$-0.428131\pi$
$541$	5634.05	0.447739	0.223870	+	0.974619i	$0.428131\pi$
$542$	− 11364.9i	− 0.900673i
$543$	6614.19i	0.522729i
$544$	−1498.30	−0.118087
$545$	0	0
$546$	42869.5	3.36015
$547$	6093.08i	0.476273i	0.971232	+	0.238136i	$0.0765365\pi$
$547$	6093.08i	0.476273i	−0.971232	+	0.238136i	$0.923463\pi$
$548$	9680.29i	0.754601i
$549$	15387.4	1.19620
$550$	0	0
$551$	92.5529	0.00715587
$552$	− 1393.26i	− 0.107430i
$553$	11667.6i	0.897212i
$554$	−3769.24	−0.289061
$555$	0	0
$556$	3696.12	0.281925
$557$	21461.9i	1.63262i	0.577612	+	0.816311i	$0.303985\pi$
$557$	21461.9i	1.63262i	−0.577612	+	0.816311i	$0.696015\pi$
$558$	− 7270.79i	− 0.551608i
$559$	26528.1	2.00719
$560$	0	0
$561$	−5895.93	−0.443719
$562$	5412.85i	0.406276i
$563$	11038.5i	0.826316i	0.910659	+	0.413158i	$0.135574\pi$
$563$	11038.5i	0.826316i	−0.910659	+	0.413158i	$0.864426\pi$
$564$	−16205.4	−1.20988
$565$	0	0
$566$	11927.3	0.885761
$567$	22237.9i	1.64710i
$568$	− 5870.16i	− 0.433638i
$569$	19210.3	1.41535	0.707677	−	0.706536i	$-0.249743\pi$
$569$	19210.3	1.41535	0.707677	+	0.706536i	$0.249743\pi$
$570$	0	0
$571$	−11967.0	−0.877066	−0.438533	−	0.898715i	$-0.644502\pi$
$571$	−11967.0	−0.877066	−0.438533	+	0.898715i	$0.644502\pi$
$572$	5315.77i	0.388573i
$573$	− 18913.1i	− 1.37889i
$574$	6786.51	0.493490
$575$	0	0
$576$	1941.53	0.140447
$577$	− 14982.3i	− 1.08097i	−0.841352	−	0.540487i	$-0.818240\pi$
$577$	− 14982.3i	− 1.08097i	0.841352	−	0.540487i	$-0.181760\pi$
$578$	− 5441.42i	− 0.391580i
$579$	6884.20	0.494124
$580$	0	0
$581$	26703.0	1.90676
$582$	− 4118.13i	− 0.293302i
$583$	6807.35i	0.483587i
$584$	−731.679	−0.0518444
$585$	0	0
$586$	9471.71	0.667701
$587$	24002.9i	1.68774i	0.536547	+	0.843871i	$0.319729\pi$
$587$	24002.9i	1.68774i	−0.536547	+	0.843871i	$0.680271\pi$
$588$	27616.4i	1.93687i
$589$	−13260.2	−0.927637
$590$	0	0
$591$	−4608.58	−0.320764
$592$	5891.21i	0.408999i
$593$	− 5124.67i	− 0.354882i	−0.984131	−	0.177441i	$-0.943218\pi$
$593$	− 5124.67i	− 0.354882i	0.984131	−	0.177441i	$-0.0567819\pi$
$594$	840.276	0.0580420
$595$	0	0
$596$	1722.45	0.118380
$597$	17453.5i	1.19652i
$598$	3676.01i	0.251376i
$599$	23776.8	1.62186	0.810928	−	0.585146i	$-0.198963\pi$
$599$	23776.8	1.62186	0.810928	+	0.585146i	$0.198963\pi$
$600$	0	0
$601$	−25435.3	−1.72633	−0.863166	−	0.504920i	$-0.831522\pi$
$601$	−25435.3	−1.72633	−0.863166	+	0.504920i	$0.831522\pi$
$602$	23518.1i	1.59223i
$603$	24877.6i	1.68009i
$604$	101.647	0.00684763
$605$	0	0
$606$	25119.3	1.68383
$607$	− 7445.94i	− 0.497894i	−0.968517	−	0.248947i	$-0.919916\pi$
$607$	− 7445.94i	− 0.497894i	0.968517	−	0.248947i	$-0.0800844\pi$
$608$	− 3540.91i	− 0.236189i
$609$	224.349	0.0149279
$610$	0	0
$611$	42756.5	2.83100
$612$	− 5681.65i	− 0.375273i
$613$	12874.4i	0.848275i	0.905598	+	0.424138i	$0.139423\pi$
$613$	12874.4i	0.848275i	−0.905598	+	0.424138i	$0.860577\pi$
$614$	−1538.48	−0.101121
$615$	0	0
$616$	−4712.62	−0.308241
$617$	− 19247.2i	− 1.25585i	−0.778272	−	0.627927i	$-0.783904\pi$
$617$	− 19247.2i	− 1.25585i	0.778272	−	0.627927i	$-0.216096\pi$
$618$	− 26282.9i	− 1.71077i
$619$	14496.4	0.941293	0.470647	−	0.882322i	$-0.344021\pi$
$619$	14496.4	0.941293	0.470647	+	0.882322i	$0.344021\pi$
$620$	0	0
$621$	581.074	0.0375486
$622$	11185.4i	0.721052i
$623$	− 37199.1i	− 2.39222i
$624$	−9681.75	−0.621122
$625$	0	0
$626$	−19554.4	−1.24848
$627$	− 13933.7i	− 0.887496i
$628$	6321.15i	0.401658i
$629$	17239.9	1.09284
$630$	0	0
$631$	−18030.9	−1.13756	−0.568779	−	0.822490i	$-0.692584\pi$
$631$	−18030.9	−1.13756	−0.568779	+	0.822490i	$0.692584\pi$
$632$	− 2635.05i	− 0.165849i
$633$	− 33115.5i	− 2.07934i
$634$	3737.03	0.234095
$635$	0	0
$636$	−12398.4	−0.773000
$637$	− 72863.4i	− 4.53211i
$638$	27.8191i	0.00172628i
$639$	22260.0	1.37808
$640$	0	0
$641$	11776.4	0.725646	0.362823	−	0.931858i	$-0.381813\pi$
$641$	11776.4	0.725646	0.362823	+	0.931858i	$0.381813\pi$
$642$	− 24683.2i	− 1.51740i
$643$	− 20207.4i	− 1.23935i	−0.784858	−	0.619676i	$-0.787264\pi$
$643$	− 20207.4i	− 1.23935i	0.784858	−	0.619676i	$-0.212736\pi$
$644$	−3258.91	−0.199408
$645$	0	0
$646$	−10362.0	−0.631095
$647$	21452.8i	1.30355i	0.758412	+	0.651776i	$0.225976\pi$
$647$	21452.8i	1.30355i	−0.758412	+	0.651776i	$0.774024\pi$
$648$	− 5022.26i	− 0.304465i
$649$	−5869.50	−0.355005
$650$	0	0
$651$	−32143.0	−1.93515
$652$	1834.95i	0.110218i
$653$	15095.2i	0.904624i	0.891860	+	0.452312i	$0.149401\pi$
$653$	15095.2i	0.904624i	−0.891860	+	0.452312i	$0.850599\pi$
$654$	6544.57	0.391304
$655$	0	0
$656$	−1532.68	−0.0912214
$657$	− 2774.57i	− 0.164759i
$658$	37905.1i	2.24574i
$659$	−6964.68	−0.411693	−0.205846	−	0.978584i	$-0.565995\pi$
$659$	−6964.68	−0.411693	−0.205846	+	0.978584i	$0.565995\pi$
$660$	0	0
$661$	−17380.4	−1.02272	−0.511361	−	0.859366i	$-0.670858\pi$
$661$	−17380.4	−1.02272	−0.511361	+	0.859366i	$0.670858\pi$
$662$	− 13933.8i	− 0.818057i
$663$	28332.4i	1.65964i
$664$	−6030.67	−0.352463
$665$	0	0
$666$	−22339.8	−1.29978
$667$	19.2377i	0.00111677i
$668$	2245.10i	0.130038i
$669$	41188.3	2.38032
$670$	0	0
$671$	8435.04	0.485292
$672$	− 8583.21i	− 0.492715i
$673$	− 12383.2i	− 0.709271i	−0.935005	−	0.354635i	$-0.884605\pi$
$673$	− 12383.2i	− 0.709271i	0.935005	−	0.354635i	$-0.115395\pi$
$674$	−35.0973	−0.00200578
$675$	0	0
$676$	16756.5	0.953371
$677$	− 8375.74i	− 0.475489i	−0.971328	−	0.237744i	$-0.923592\pi$
$677$	− 8375.74i	− 0.475489i	0.971328	−	0.237744i	$-0.0764080\pi$
$678$	3636.35i	0.205978i
$679$	−9632.49	−0.544420
$680$	0	0
$681$	−1639.34	−0.0922463
$682$	− 3985.70i	− 0.223783i
$683$	4434.66i	0.248444i	0.992254	+	0.124222i	$0.0396436\pi$
$683$	4434.66i	0.248444i	−0.992254	+	0.124222i	$0.960356\pi$
$684$	13427.3	0.750595
$685$	0	0
$686$	40295.8	2.24271
$687$	7001.64i	0.388834i
$688$	− 5311.38i	− 0.294323i
$689$	32712.1	1.80875
$690$	0	0
$691$	11032.8	0.607389	0.303694	−	0.952770i	$-0.401780\pi$
$691$	11032.8	0.607389	0.303694	+	0.952770i	$0.401780\pi$
$692$	6295.79i	0.345852i
$693$	− 17870.5i	− 0.979574i
$694$	−19718.6	−1.07854
$695$	0	0
$696$	−50.6677	−0.00275942
$697$	4485.20i	0.243743i
$698$	14400.5i	0.780898i
$699$	−17943.5	−0.970936
$700$	0	0
$701$	3708.40	0.199806	0.0999032	−	0.994997i	$-0.468147\pi$
$701$	3708.40	0.199806	0.0999032	+	0.994997i	$0.468147\pi$
$702$	− 4037.87i	− 0.217093i
$703$	40742.6i	2.18583i
$704$	1064.31	0.0569782
$705$	0	0
$706$	12109.2	0.645516
$707$	− 58755.2i	− 3.12548i
$708$	− 10690.3i	− 0.567465i
$709$	6315.04	0.334508	0.167254	−	0.985914i	$-0.446510\pi$
$709$	6315.04	0.334508	0.167254	+	0.985914i	$0.446510\pi$
$710$	0	0
$711$	9992.26	0.527059
$712$	8401.15i	0.442200i
$713$	− 2756.22i	− 0.144770i
$714$	−25117.6	−1.31653
$715$	0	0
$716$	8862.36	0.462572
$717$	20971.6i	1.09233i
$718$	5468.52i	0.284239i
$719$	−24736.9	−1.28307	−0.641536	−	0.767093i	$-0.721703\pi$
$719$	−24736.9	−1.28307	−0.641536	+	0.767093i	$0.721703\pi$
$720$	0	0
$721$	−61477.0	−3.17548
$722$	− 10770.3i	− 0.555165i
$723$	− 40390.2i	− 2.07763i
$724$	−3493.99	−0.179355
$725$	0	0
$726$	−15968.7	−0.816330
$727$	33283.6i	1.69797i	0.528420	+	0.848983i	$0.322785\pi$
$727$	33283.6i	1.69797i	−0.528420	+	0.848983i	$0.677215\pi$
$728$	22646.0i	1.15291i
$729$	24209.9	1.22999
$730$	0	0
$731$	−15543.1	−0.786430
$732$	15362.9i	0.775725i
$733$	33636.5i	1.69494i	0.530841	+	0.847471i	$0.321876\pi$
$733$	33636.5i	1.69494i	−0.530841	+	0.847471i	$0.678124\pi$
$734$	−4931.00	−0.247965
$735$	0	0
$736$	736.000	0.0368605
$737$	13637.4i	0.681601i
$738$	− 5812.03i	− 0.289897i
$739$	−36575.5	−1.82064	−0.910319	−	0.413907i	$-0.864164\pi$
$739$	−36575.5	−1.82064	−0.910319	+	0.413907i	$0.864164\pi$
$740$	0	0
$741$	−66957.3	−3.31949
$742$	29000.4i	1.43482i
$743$	17704.7i	0.874190i	0.899415	+	0.437095i	$0.143993\pi$
$743$	17704.7i	0.874190i	−0.899415	+	0.437095i	$0.856007\pi$
$744$	7259.25	0.357711
$745$	0	0
$746$	−11408.9	−0.559932
$747$	− 22868.7i	− 1.12011i
$748$	− 3114.56i	− 0.152246i
$749$	−57735.1	−2.81655
$750$	0	0
$751$	8858.37	0.430421	0.215211	−	0.976568i	$-0.430956\pi$
$751$	8858.37	0.430421	0.215211	+	0.976568i	$0.430956\pi$
$752$	− 8560.59i	− 0.415123i
$753$	35415.7i	1.71397i
$754$	133.682	0.00645679
$755$	0	0
$756$	3579.71	0.172213
$757$	7899.26i	0.379265i	0.981855	+	0.189633i	$0.0607297\pi$
$757$	7899.26i	0.379265i	−0.981855	+	0.189633i	$0.939270\pi$
$758$	20463.9i	0.980582i
$759$	2896.22	0.138506
$760$	0	0
$761$	23437.4	1.11643	0.558216	−	0.829696i	$-0.311486\pi$
$761$	23437.4	1.11643	0.558216	+	0.829696i	$0.311486\pi$
$762$	− 3195.31i	− 0.151908i
$763$	− 15308.1i	− 0.726329i
$764$	9990.95	0.473115
$765$	0	0
$766$	−12642.7	−0.596343
$767$	28205.4i	1.32782i
$768$	1938.45i	0.0910780i
$769$	−31447.7	−1.47468	−0.737342	−	0.675519i	$-0.763919\pi$
$769$	−31447.7	−1.47468	−0.737342	+	0.675519i	$0.763919\pi$
$770$	0	0
$771$	19710.0	0.920674
$772$	3636.62i	0.169540i
$773$	− 2397.42i	− 0.111551i	−0.998443	−	0.0557756i	$-0.982237\pi$
$773$	− 2397.42i	− 0.111551i	0.998443	−	0.0557756i	$-0.0177632\pi$
$774$	20141.1	0.935343
$775$	0	0
$776$	2175.43	0.100636
$777$	98760.8i	4.55987i
$778$	− 1851.19i	− 0.0853063i
$779$	−10599.8	−0.487518
$780$	0	0
$781$	12202.5	0.559077
$782$	− 2153.81i	− 0.0984911i
$783$	− 21.1314i	0 0.000964465i
$784$	−14588.5	−0.664564
$785$	0	0
$786$	−11300.3	−0.512807
$787$	− 19407.0i	− 0.879014i	−0.898239	−	0.439507i	$-0.855153\pi$
$787$	− 19407.0i	− 0.879014i	0.898239	−	0.439507i	$-0.144847\pi$
$788$	− 2434.51i	− 0.110058i
$789$	−25830.7	−1.16552
$790$	0	0
$791$	8505.58	0.382331
$792$	4035.93i	0.181074i
$793$	− 40533.8i	− 1.81513i
$794$	−5413.51	−0.241962
$795$	0	0
$796$	−9219.91	−0.410542
$797$	− 28631.1i	− 1.27248i	−0.771491	−	0.636240i	$-0.780489\pi$
$797$	− 28631.1i	− 1.27248i	0.771491	−	0.636240i	$-0.219511\pi$
$798$	− 59360.0i	− 2.63324i
$799$	−25051.4	−1.10921
$800$	0	0
$801$	−31857.6	−1.40529
$802$	28190.6i	1.24120i
$803$	− 1520.96i	− 0.0668414i
$804$	−24838.1	−1.08952
$805$	0	0
$806$	−19152.9	−0.837013
$807$	− 33064.0i	− 1.44227i
$808$	13269.4i	0.577743i
$809$	9191.25	0.399440	0.199720	−	0.979853i	$-0.435997\pi$
$809$	9191.25	0.399440	0.199720	+	0.979853i	$0.435997\pi$
$810$	0	0
$811$	−567.477	−0.0245706	−0.0122853	−	0.999925i	$-0.503911\pi$
$811$	−567.477	−0.0245706	−0.0122853	+	0.999925i	$0.503911\pi$
$812$	118.514i	0.00512195i
$813$	43028.0i	1.85616i
$814$	−12246.2	−0.527310
$815$	0	0
$816$	5672.63	0.243360
$817$	− 36732.6i	− 1.57296i
$818$	− 21692.0i	− 0.927193i
$819$	−85875.2	−3.66388
$820$	0	0
$821$	−6057.35	−0.257494	−0.128747	−	0.991677i	$-0.541096\pi$
$821$	−6057.35	−0.257494	−0.128747	+	0.991677i	$0.541096\pi$
$822$	− 36650.0i	− 1.55513i
$823$	21327.0i	0.903294i	0.892197	+	0.451647i	$0.149163\pi$
$823$	21327.0i	0.903294i	−0.892197	+	0.451647i	$0.850837\pi$
$824$	13884.1	0.586986
$825$	0	0
$826$	−25005.0	−1.05331
$827$	− 27553.8i	− 1.15857i	−0.815124	−	0.579286i	$-0.803332\pi$
$827$	− 27553.8i	− 1.15857i	0.815124	−	0.579286i	$-0.196668\pi$
$828$	2790.96i	0.117141i
$829$	−11181.6	−0.468461	−0.234231	−	0.972181i	$-0.575257\pi$
$829$	−11181.6	−0.468461	−0.234231	+	0.972181i	$0.575257\pi$
$830$	0	0
$831$	14270.5	0.595715
$832$	− 5114.44i	− 0.213115i
$833$	42691.4i	1.77571i
$834$	−13993.7	−0.581009
$835$	0	0
$836$	7360.59	0.304511
$837$	3027.54i	0.125026i
$838$	− 11253.1i	− 0.463881i
$839$	−9811.83	−0.403745	−0.201872	−	0.979412i	$-0.564703\pi$
$839$	−9811.83	−0.403745	−0.201872	+	0.979412i	$0.564703\pi$
$840$	0	0
$841$	−24388.3	−0.999971
$842$	14218.2i	0.581937i
$843$	− 20493.3i	− 0.837279i
$844$	17493.5	0.713448
$845$	0	0
$846$	32462.3	1.31924
$847$	37351.6i	1.51525i
$848$	− 6549.53i	− 0.265226i
$849$	−45157.2	−1.82543
$850$	0	0
$851$	−8468.62	−0.341129
$852$	22224.7i	0.893667i
$853$	24030.8i	0.964594i	0.876008	+	0.482297i	$0.160197\pi$
$853$	24030.8i	0.964594i	−0.876008	+	0.482297i	$0.839803\pi$
$854$	35934.6	1.43988
$855$	0	0
$856$	13039.0	0.520637
$857$	− 16934.8i	− 0.675008i	−0.941324	−	0.337504i	$-0.890417\pi$
$857$	− 16934.8i	− 0.675008i	0.941324	−	0.337504i	$-0.109583\pi$
$858$	− 20125.7i	− 0.800794i
$859$	31057.0	1.23359	0.616793	−	0.787125i	$-0.288432\pi$
$859$	31057.0	1.23359	0.616793	+	0.787125i	$0.288432\pi$
$860$	0	0
$861$	−25694.0	−1.01701
$862$	− 8928.27i	− 0.352782i
$863$	16157.8i	0.637332i	0.947867	+	0.318666i	$0.103235\pi$
$863$	16157.8i	0.637332i	−0.947867	+	0.318666i	$0.896765\pi$
$864$	−808.451	−0.0318334
$865$	0	0
$866$	−22018.9	−0.864009
$867$	20601.4i	0.806992i
$868$	− 16979.7i	− 0.663974i
$869$	5477.55	0.213824
$870$	0	0
$871$	65533.3	2.54938
$872$	3457.21i	0.134261i
$873$	8249.35i	0.319815i
$874$	5090.05	0.196995
$875$	0	0
$876$	2770.17	0.106844
$877$	− 32473.9i	− 1.25036i	−0.780480	−	0.625180i	$-0.785025\pi$
$877$	− 32473.9i	− 1.25036i	0.780480	−	0.625180i	$-0.214975\pi$
$878$	− 6105.41i	− 0.234678i
$879$	−35860.3	−1.37604
$880$	0	0
$881$	−15703.2	−0.600517	−0.300258	−	0.953858i	$-0.597073\pi$
$881$	−15703.2	−0.600517	−0.300258	+	0.953858i	$0.597073\pi$
$882$	− 55320.5i	− 2.11195i
$883$	14330.4i	0.546155i	0.961992	+	0.273078i	$0.0880416\pi$
$883$	14330.4i	0.546155i	−0.961992	+	0.273078i	$0.911958\pi$
$884$	−14966.7	−0.569441
$885$	0	0
$886$	8931.65	0.338673
$887$	23238.2i	0.879664i	0.898080	+	0.439832i	$0.144962\pi$
$887$	23238.2i	0.879664i	−0.898080	+	0.439832i	$0.855038\pi$
$888$	− 22304.4i	− 0.842890i
$889$	−7473.98	−0.281968
$890$	0	0
$891$	10439.9	0.392537
$892$	21758.0i	0.816717i
$893$	− 59203.6i	− 2.21856i
$894$	−6521.29	−0.243965
$895$	0	0
$896$	4534.13	0.169057
$897$	− 13917.5i	− 0.518052i
$898$	18080.3i	0.671878i
$899$	−100.233	−0.00371854
$900$	0	0
$901$	−19166.3	−0.708683
$902$	− 3186.03i	− 0.117609i
$903$	− 89040.4i	− 3.28137i
$904$	−1920.92	−0.0706736
$905$	0	0
$906$	−384.841	−0.0141120
$907$	− 3667.46i	− 0.134263i	−0.997744	−	0.0671313i	$-0.978615\pi$
$907$	− 3667.46i	− 0.134263i	0.997744	−	0.0671313i	$-0.0213846\pi$
$908$	− 865.992i	− 0.0316508i
$909$	−50318.4	−1.83604
$910$	0	0
$911$	21457.9	0.780385	0.390192	−	0.920733i	$-0.372409\pi$
$911$	21457.9	0.780385	0.390192	+	0.920733i	$0.372409\pi$
$912$	13406.0i	0.486752i
$913$	− 12536.1i	− 0.454420i
$914$	15513.8	0.561433
$915$	0	0
$916$	−3698.66	−0.133414
$917$	26431.8i	0.951859i
$918$	2365.83i	0.0850587i
$919$	11109.3	0.398762	0.199381	−	0.979922i	$-0.436107\pi$
$919$	11109.3	0.398762	0.199381	+	0.979922i	$0.436107\pi$
$920$	0	0
$921$	5824.76	0.208396
$922$	− 14128.4i	− 0.504657i
$923$	− 58637.9i	− 2.09110i
$924$	17842.2	0.635243
$925$	0	0
$926$	−25199.3	−0.894279
$927$	52649.4i	1.86541i
$928$	− 26.7655i	0 0.000946790i
$929$	20804.3	0.734732	0.367366	−	0.930076i	$-0.380260\pi$
$929$	20804.3	0.734732	0.367366	+	0.930076i	$0.380260\pi$
$930$	0	0
$931$	−100892.	−3.55166
$932$	− 9478.75i	− 0.333140i
$933$	− 42348.5i	− 1.48599i
$934$	29492.0	1.03320
$935$	0	0
$936$	19394.3	0.677267
$937$	− 35550.5i	− 1.23947i	−0.784811	−	0.619735i	$-0.787240\pi$
$937$	− 35550.5i	− 1.23947i	0.784811	−	0.619735i	$-0.212760\pi$
$938$	58097.5i	2.02234i
$939$	74033.7	2.57295
$940$	0	0
$941$	49674.4	1.72087	0.860436	−	0.509558i	$-0.170191\pi$
$941$	49674.4	1.72087	0.860436	+	0.509558i	$0.170191\pi$
$942$	− 23932.2i	− 0.827762i
$943$	− 2203.23i	− 0.0760839i
$944$	5647.20	0.194704
$945$	0	0
$946$	11040.9	0.379462
$947$	33466.2i	1.14837i	0.818726	+	0.574184i	$0.194681\pi$
$947$	33466.2i	1.14837i	−0.818726	+	0.574184i	$0.805319\pi$
$948$	9976.41i	0.341792i
$949$	−7308.85	−0.250006
$950$	0	0
$951$	−14148.5	−0.482437
$952$	− 13268.5i	− 0.451718i
$953$	17298.4i	0.587984i	0.955808	+	0.293992i	$0.0949839\pi$
$953$	17298.4i	0.587984i	−0.955808	+	0.293992i	$0.905016\pi$
$954$	24836.2	0.842874
$955$	0	0
$956$	−11078.4	−0.374791
$957$	− 105.324i	− 0.00355763i
$958$	− 34822.5i	− 1.17439i
$959$	−85726.0	−2.88659
$960$	0	0
$961$	−15430.4	−0.517955
$962$	58848.2i	1.97229i
$963$	49444.8i	1.65456i
$964$	21336.4	0.712862
$965$	0	0
$966$	12338.4	0.410953
$967$	− 14869.7i	− 0.494495i	−0.968952	−	0.247248i	$-0.920474\pi$
$967$	− 14869.7i	− 0.494495i	0.968952	−	0.247248i	$-0.0795261\pi$
$968$	− 8435.59i	− 0.280093i
$969$	39231.0	1.30060
$970$	0	0
$971$	26634.9	0.880283	0.440142	−	0.897928i	$-0.354928\pi$
$971$	26634.9	0.880283	0.440142	+	0.897928i	$0.354928\pi$
$972$	21743.0i	0.717498i
$973$	32731.8i	1.07845i
$974$	2640.69	0.0868717
$975$	0	0
$976$	−8115.57	−0.266161
$977$	40803.6i	1.33615i	0.744092	+	0.668077i	$0.232882\pi$
$977$	40803.6i	1.33615i	−0.744092	+	0.668077i	$0.767118\pi$
$978$	− 6947.22i	− 0.227145i
$979$	−17463.7	−0.570115
$980$	0	0
$981$	−13109.9	−0.426675
$982$	− 34231.6i	− 1.11240i
$983$	18615.8i	0.604021i	0.953305	+	0.302011i	$0.0976578\pi$
$983$	18615.8i	0.604021i	−0.953305	+	0.302011i	$0.902342\pi$
$984$	5802.80	0.187995
$985$	0	0
$986$	−78.3257	−0.00252982
$987$	− 143510.i	− 4.62815i
$988$	− 35370.6i	− 1.13896i
$989$	7635.11	0.245483
$990$	0	0
$991$	46185.1	1.48044	0.740220	−	0.672364i	$-0.234721\pi$
$991$	46185.1	1.48044	0.740220	+	0.672364i	$0.234721\pi$
$992$	3834.74i	0.122735i
$993$	52754.1i	1.68590i
$994$	51984.5	1.65880
$995$	0	0
$996$	22832.4	0.726377
$997$	16544.3i	0.525541i	0.964858	+	0.262771i	$0.0846363\pi$
$997$	16544.3i	0.525541i	−0.964858	+	0.262771i	$0.915364\pi$
$998$	35081.2i	1.11270i
$999$	9302.26	0.294605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.b.n.599.4		8
5.2	odd	4		1150.4.a.p.1.4		4
5.3	odd	4		230.4.a.h.1.1	✓	4
5.4	even	2	inner	1150.4.b.n.599.5		8
15.8	even	4		2070.4.a.bj.1.1		4
20.3	even	4		1840.4.a.m.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.1	✓	4	5.3	odd	4
1150.4.a.p.1.4		4	5.2	odd	4
1150.4.b.n.599.4		8	1.1	even	1	trivial
1150.4.b.n.599.5		8	5.4	even	2	inner
1840.4.a.m.1.4		4	20.3	even	4
2070.4.a.bj.1.1		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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +7.57209i q^{3} -4.00000 q^{4} +15.1442 q^{6} -35.4229i q^{7} +8.00000i q^{8} -30.3365 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +7.57209i q^{3} -4.00000 q^{4} +15.1442 q^{6} -35.4229i q^{7} +8.00000i q^{8} -30.3365 q^{9} -16.6298 q^{11} -30.2883i q^{12} +79.9132i q^{13} -70.8458 q^{14} +16.0000 q^{16} -46.8219i q^{17} +60.6730i q^{18} +110.653 q^{19} +268.225 q^{21} +33.2597i q^{22} +23.0000i q^{23} -60.5767 q^{24} +159.826 q^{26} -25.2641i q^{27} +141.692i q^{28} +0.836422 q^{29} -119.836 q^{31} -32.0000i q^{32} -125.923i q^{33} -93.6438 q^{34} +121.346 q^{36} +368.201i q^{37} -221.307i q^{38} -605.109 q^{39} -95.7927 q^{41} -536.450i q^{42} -331.961i q^{43} +66.5193 q^{44} +46.0000 q^{46} -535.037i q^{47} +121.153i q^{48} -911.782 q^{49} +354.539 q^{51} -319.653i q^{52} -409.345i q^{53} -50.5282 q^{54} +283.383 q^{56} +837.876i q^{57} -1.67284i q^{58} +352.950 q^{59} -507.223 q^{61} +239.672i q^{62} +1074.61i q^{63} -64.0000 q^{64} -251.845 q^{66} -820.056i q^{67} +187.288i q^{68} -174.158 q^{69} -733.770 q^{71} -242.692i q^{72} +91.4599i q^{73} +736.402 q^{74} -442.613 q^{76} +589.077i q^{77} +1210.22i q^{78} -329.381 q^{79} -627.783 q^{81} +191.585i q^{82} +753.834i q^{83} -1072.90 q^{84} -663.922 q^{86} +6.33346i q^{87} -133.039i q^{88} +1050.14 q^{89} +2830.76 q^{91} -92.0000i q^{92} -907.407i q^{93} -1070.07 q^{94} +242.307 q^{96} -271.928i q^{97} +1823.56i q^{98} +504.491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 16 q^{6} - 64 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more