LMFDB - Embedded newform 1150.4.b.n.599.8

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			599.8
Root			$8.73081i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.4.b.n.599.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +7.73081i q^{3} -4.00000 q^{4} -15.4616 q^{6} -23.5622i q^{7} -8.00000i q^{8} -32.7654 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +7.73081i q^{3} -4.00000 q^{4} -15.4616 q^{6} -23.5622i q^{7} -8.00000i q^{8} -32.7654 q^{9} -32.1352 q^{11} -30.9232i q^{12} +40.0811i q^{13} +47.1245 q^{14} +16.0000 q^{16} -126.165i q^{17} -65.5308i q^{18} -0.232742 q^{19} +182.155 q^{21} -64.2704i q^{22} -23.0000i q^{23} +61.8465 q^{24} -80.1621 q^{26} -44.5711i q^{27} +94.2490i q^{28} +137.226 q^{29} +112.866 q^{31} +32.0000i q^{32} -248.431i q^{33} +252.331 q^{34} +131.062 q^{36} -45.7057i q^{37} -0.465483i q^{38} -309.859 q^{39} -135.385 q^{41} +364.310i q^{42} +543.528i q^{43} +128.541 q^{44} +46.0000 q^{46} -26.4344i q^{47} +123.693i q^{48} -212.180 q^{49} +975.359 q^{51} -160.324i q^{52} +43.6958i q^{53} +89.1422 q^{54} -188.498 q^{56} -1.79928i q^{57} +274.451i q^{58} -202.248 q^{59} +150.279 q^{61} +225.732i q^{62} +772.026i q^{63} -64.0000 q^{64} +496.862 q^{66} +420.722i q^{67} +504.661i q^{68} +177.809 q^{69} +667.381 q^{71} +262.123i q^{72} +602.960i q^{73} +91.4115 q^{74} +0.930966 q^{76} +757.178i q^{77} -619.718i q^{78} +1378.88 q^{79} -540.095 q^{81} -270.769i q^{82} -485.178i q^{83} -728.621 q^{84} -1087.06 q^{86} +1060.86i q^{87} +257.082i q^{88} +1127.71 q^{89} +944.400 q^{91} +92.0000i q^{92} +872.545i q^{93} +52.8688 q^{94} -247.386 q^{96} +1486.24i q^{97} -424.359i q^{98} +1052.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	7.73081i	1.48779i	0.668294	+	0.743897i	$0.267025\pi$
$3$	7.73081i	1.48779i	−0.668294	+	0.743897i	$0.732975\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−15.4616	−1.05203
$7$	− 23.5622i	− 1.27224i	−0.771589	−	0.636121i	$-0.780538\pi$
$7$	− 23.5622i	− 1.27224i	0.771589	−	0.636121i	$-0.219462\pi$
$8$	− 8.00000i	− 0.353553i
$9$	−32.7654	−1.21353
$10$	0	0
$11$	−32.1352	−0.880830	−0.440415	−	0.897794i	$-0.645169\pi$
$11$	−32.1352	−0.880830	−0.440415	+	0.897794i	$0.645169\pi$
$12$	− 30.9232i	− 0.743897i
$13$	40.0811i	0.855115i	0.903988	+	0.427557i	$0.140626\pi$
$13$	40.0811i	0.855115i	−0.903988	+	0.427557i	$0.859374\pi$
$14$	47.1245	0.899611
$15$	0	0
$16$	16.0000	0.250000
$17$	− 126.165i	− 1.79997i	−0.435916	−	0.899987i	$-0.643576\pi$
$17$	− 126.165i	− 1.79997i	0.435916	−	0.899987i	$-0.356424\pi$
$18$	− 65.5308i	− 0.858097i
$19$	−0.232742	−0.00281024	−0.00140512	−	0.999999i	$-0.500447\pi$
$19$	−0.232742	−0.00281024	−0.00140512	+	0.999999i	$0.500447\pi$
$20$	0	0
$21$	182.155	1.89283
$22$	− 64.2704i	− 0.622841i
$23$	− 23.0000i	− 0.208514i
$23$	− 23.0000i	− 0.208514i
$24$	61.8465	0.526015
$25$	0	0
$26$	−80.1621	−0.604657
$27$	− 44.5711i	− 0.317693i
$28$	94.2490i	0.636121i
$29$	137.226	0.878695	0.439347	−	0.898317i	$-0.355210\pi$
$29$	137.226	0.878695	0.439347	+	0.898317i	$0.355210\pi$
$30$	0	0
$31$	112.866	0.653914	0.326957	−	0.945039i	$-0.393977\pi$
$31$	112.866	0.653914	0.326957	+	0.945039i	$0.393977\pi$
$32$	32.0000i	0.176777i
$33$	− 248.431i	− 1.31049i
$34$	252.331	1.27277
$35$	0	0
$36$	131.062	0.606766
$37$	− 45.7057i	− 0.203080i	−0.994831	−	0.101540i	$-0.967623\pi$
$37$	− 45.7057i	− 0.203080i	0.994831	−	0.101540i	$-0.0323771\pi$
$38$	− 0.465483i	− 0.00198714i
$39$	−309.859	−1.27223
$40$	0	0
$41$	−135.385	−0.515696	−0.257848	−	0.966186i	$-0.583013\pi$
$41$	−135.385	−0.515696	−0.257848	+	0.966186i	$0.583013\pi$
$42$	364.310i	1.33844i
$43$	543.528i	1.92761i	0.266608	+	0.963805i	$0.414097\pi$
$43$	543.528i	1.92761i	−0.266608	+	0.963805i	$0.585903\pi$
$44$	128.541	0.440415
$45$	0	0
$46$	46.0000	0.147442
$47$	− 26.4344i	− 0.0820394i	−0.999158	−	0.0410197i	$-0.986939\pi$
$47$	− 26.4344i	− 0.0820394i	0.999158	−	0.0410197i	$-0.0130606\pi$
$48$	123.693i	0.371949i
$49$	−212.180	−0.618599
$50$	0	0
$51$	975.359	2.67799
$52$	− 160.324i	− 0.427557i
$53$	43.6958i	0.113247i	0.998396	+	0.0566235i	$0.0180335\pi$
$53$	43.6958i	0.113247i	−0.998396	+	0.0566235i	$0.981967\pi$
$54$	89.1422	0.224643
$55$	0	0
$56$	−188.498	−0.449805
$57$	− 1.79928i	− 0.00418106i
$58$	274.451i	0.621331i
$59$	−202.248	−0.446278	−0.223139	−	0.974787i	$-0.571630\pi$
$59$	−202.248	−0.446278	−0.223139	+	0.974787i	$0.571630\pi$
$60$	0	0
$61$	150.279	0.315430	0.157715	−	0.987485i	$-0.449587\pi$
$61$	150.279	0.315430	0.157715	+	0.987485i	$0.449587\pi$
$62$	225.732i	0.462387i
$63$	772.026i	1.54391i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	496.862	0.926659
$67$	420.722i	0.767155i	0.923509	+	0.383577i	$0.125308\pi$
$67$	420.722i	0.767155i	−0.923509	+	0.383577i	$0.874692\pi$
$68$	504.661i	0.899987i
$69$	177.809	0.310227
$70$	0	0
$71$	667.381	1.11554	0.557771	−	0.829995i	$-0.311657\pi$
$71$	667.381	1.11554	0.557771	+	0.829995i	$0.311657\pi$
$72$	262.123i	0.429049i
$73$	602.960i	0.966728i	0.875420	+	0.483364i	$0.160585\pi$
$73$	602.960i	0.966728i	−0.875420	+	0.483364i	$0.839415\pi$
$74$	91.4115	0.143600
$75$	0	0
$76$	0.930966	0.00140512
$77$	757.178i	1.12063i
$78$	− 619.718i	− 0.899606i
$79$	1378.88	1.96374	0.981872	−	0.189545i	$-0.0607013\pi$
$79$	1378.88	1.96374	0.981872	+	0.189545i	$0.0607013\pi$
$80$	0	0
$81$	−540.095	−0.740871
$82$	− 270.769i	− 0.364652i
$83$	− 485.178i	− 0.641629i	−0.947142	−	0.320815i	$-0.896043\pi$
$83$	− 485.178i	− 0.641629i	0.947142	−	0.320815i	$-0.103957\pi$
$84$	−728.621	−0.946417
$85$	0	0
$86$	−1087.06	−1.36303
$87$	1060.86i	1.30732i
$88$	257.082i	0.311420i
$89$	1127.71	1.34311	0.671556	−	0.740954i	$-0.265626\pi$
$89$	1127.71	1.34311	0.671556	+	0.740954i	$0.265626\pi$
$90$	0	0
$91$	944.400	1.08791
$92$	92.0000i	0.104257i
$93$	872.545i	0.972890i
$94$	52.8688	0.0580106
$95$	0	0
$96$	−247.386	−0.263007
$97$	1486.24i	1.55572i	0.628441	+	0.777858i	$0.283694\pi$
$97$	1486.24i	1.55572i	−0.628441	+	0.777858i	$0.716306\pi$
$98$	− 424.359i	− 0.437416i
$99$	1052.92	1.06892
$100$	0	0
$101$	1888.86	1.86087	0.930437	−	0.366451i	$-0.119427\pi$
$101$	1888.86	1.86087	0.930437	+	0.366451i	$0.119427\pi$
$102$	1950.72i	1.89363i
$103$	− 1497.17i	− 1.43224i	−0.697979	−	0.716118i	$-0.745917\pi$
$103$	− 1497.17i	− 1.43224i	0.697979	−	0.716118i	$-0.254083\pi$
$104$	320.649	0.302329
$105$	0	0
$106$	−87.3917	−0.0800777
$107$	585.150i	0.528678i	0.964430	+	0.264339i	$0.0851538\pi$
$107$	585.150i	0.528678i	−0.964430	+	0.264339i	$0.914846\pi$
$108$	178.284i	0.158846i
$109$	139.166	0.122290	0.0611452	−	0.998129i	$-0.480525\pi$
$109$	139.166	0.122290	0.0611452	+	0.998129i	$0.480525\pi$
$110$	0	0
$111$	353.342	0.302142
$112$	− 376.996i	− 0.318060i
$113$	− 1293.18i	− 1.07656i	−0.842765	−	0.538282i	$-0.819073\pi$
$113$	− 1293.18i	− 1.07656i	0.842765	−	0.538282i	$-0.180927\pi$
$114$	3.59856	0.00295646
$115$	0	0
$116$	−548.902	−0.439347
$117$	− 1313.27i	− 1.03771i
$118$	− 404.495i	− 0.315566i
$119$	−2972.74	−2.29000
$120$	0	0
$121$	−298.328	−0.224138
$122$	300.557i	0.223043i
$123$	− 1046.63i	− 0.767250i
$124$	−451.464	−0.326957
$125$	0	0
$126$	−1544.05	−1.09171
$127$	1298.43i	0.907221i	0.891200	+	0.453610i	$0.149864\pi$
$127$	1298.43i	0.907221i	−0.891200	+	0.453610i	$0.850136\pi$
$128$	− 128.000i	− 0.0883883i
$129$	−4201.91	−2.86789
$130$	0	0
$131$	−525.247	−0.350313	−0.175157	−	0.984541i	$-0.556043\pi$
$131$	−525.247	−0.350313	−0.175157	+	0.984541i	$0.556043\pi$
$132$	993.725i	0.655247i
$133$	5.48392i	0.00357531i
$134$	−841.444	−0.542460
$135$	0	0
$136$	−1009.32	−0.636387
$137$	2428.12i	1.51422i	0.653288	+	0.757109i	$0.273389\pi$
$137$	2428.12i	1.51422i	−0.653288	+	0.757109i	$0.726611\pi$
$138$	355.617i	0.219363i
$139$	−2456.46	−1.49895	−0.749476	−	0.662031i	$-0.769695\pi$
$139$	−2456.46	−1.49895	−0.749476	+	0.662031i	$0.769695\pi$
$140$	0	0
$141$	204.359	0.122058
$142$	1334.76i	0.788808i
$143$	− 1288.01i	− 0.753211i
$144$	−524.246	−0.303383
$145$	0	0
$146$	−1205.92	−0.683580
$147$	− 1640.32i	− 0.920349i
$148$	182.823i	0.101540i
$149$	2405.39	1.32253	0.661266	−	0.750151i	$-0.270019\pi$
$149$	2405.39	1.32253	0.661266	+	0.750151i	$0.270019\pi$
$150$	0	0
$151$	−649.276	−0.349916	−0.174958	−	0.984576i	$-0.555979\pi$
$151$	−649.276	−0.349916	−0.174958	+	0.984576i	$0.555979\pi$
$152$	1.86193i	0 0.000993570i
$153$	4133.85i	2.18433i
$154$	−1514.36	−0.792404
$155$	0	0
$156$	1239.44	0.636117
$157$	− 3665.04i	− 1.86307i	−0.363650	−	0.931536i	$-0.618470\pi$
$157$	− 3665.04i	− 1.86307i	0.363650	−	0.931536i	$-0.381530\pi$
$158$	2757.75i	1.38858i
$159$	−337.804	−0.168488
$160$	0	0
$161$	−541.932	−0.265281
$162$	− 1080.19i	− 0.523875i
$163$	− 1055.27i	− 0.507088i	−0.967324	−	0.253544i	$-0.918404\pi$
$163$	− 1055.27i	− 0.507088i	0.967324	−	0.253544i	$-0.0815963\pi$
$164$	541.539	0.257848
$165$	0	0
$166$	970.356	0.453700
$167$	731.805i	0.339095i	0.985522	+	0.169547i	$0.0542306\pi$
$167$	731.805i	0.339095i	−0.985522	+	0.169547i	$0.945769\pi$
$168$	− 1457.24i	− 0.669218i
$169$	590.507	0.268779
$170$	0	0
$171$	7.62587	0.00341032
$172$	− 2174.11i	− 0.963805i
$173$	− 521.773i	− 0.229304i	−0.993406	−	0.114652i	$-0.963425\pi$
$173$	− 521.773i	− 0.229304i	0.993406	−	0.114652i	$-0.0365754\pi$
$174$	−2121.73	−0.924413
$175$	0	0
$176$	−514.163	−0.220208
$177$	− 1563.54i	− 0.663970i
$178$	2255.42i	0.949723i
$179$	1183.07	0.494005	0.247002	−	0.969015i	$-0.420554\pi$
$179$	1183.07	0.494005	0.247002	+	0.969015i	$0.420554\pi$
$180$	0	0
$181$	1723.92	0.707946	0.353973	−	0.935256i	$-0.384830\pi$
$181$	1723.92	0.707946	0.353973	+	0.935256i	$0.384830\pi$
$182$	1888.80i	0.769270i
$183$	1161.78i	0.469295i
$184$	−184.000	−0.0737210
$185$	0	0
$186$	−1745.09	−0.687937
$187$	4054.35i	1.58547i
$188$	105.738i	0.0410197i
$189$	−1050.20	−0.404182
$190$	0	0
$191$	−2798.12	−1.06002	−0.530012	−	0.847990i	$-0.677813\pi$
$191$	−2798.12	−1.06002	−0.530012	+	0.847990i	$0.677813\pi$
$192$	− 494.772i	− 0.185974i
$193$	− 497.686i	− 0.185618i	−0.995684	−	0.0928089i	$-0.970415\pi$
$193$	− 497.686i	− 0.185618i	0.995684	−	0.0928089i	$-0.0295846\pi$
$194$	−2972.47	−1.10006
$195$	0	0
$196$	848.718	0.309300
$197$	− 296.489i	− 0.107228i	−0.998562	−	0.0536141i	$-0.982926\pi$
$197$	− 296.489i	− 0.107228i	0.998562	−	0.0536141i	$-0.0170741\pi$
$198$	2105.85i	0.755838i
$199$	−2347.43	−0.836207	−0.418103	−	0.908399i	$-0.637305\pi$
$199$	−2347.43	−0.836207	−0.418103	+	0.908399i	$0.637305\pi$
$200$	0	0
$201$	−3252.52	−1.14137
$202$	3777.71i	1.31584i
$203$	− 3233.34i	− 1.11791i
$204$	−3901.44	−1.33900
$205$	0	0
$206$	2994.34	1.01274
$207$	753.604i	0.253039i
$208$	641.297i	0.213779i
$209$	7.47920	0.00247535
$210$	0	0
$211$	2838.61	0.926153	0.463076	−	0.886318i	$-0.346746\pi$
$211$	2838.61	0.926153	0.463076	+	0.886318i	$0.346746\pi$
$212$	− 174.783i	− 0.0566235i
$213$	5159.39i	1.65970i
$214$	−1170.30	−0.373832
$215$	0	0
$216$	−356.569	−0.112321
$217$	− 2659.38i	− 0.831937i
$218$	278.331i	0.0864723i
$219$	−4661.37	−1.43829
$220$	0	0
$221$	5056.84	1.53918
$222$	706.685i	0.213647i
$223$	− 2124.68i	− 0.638024i	−0.947751	−	0.319012i	$-0.896649\pi$
$223$	− 2124.68i	− 0.638024i	0.947751	−	0.319012i	$-0.103351\pi$
$224$	753.992	0.224903
$225$	0	0
$226$	2586.35	0.761246
$227$	− 1551.97i	− 0.453780i	−0.973920	−	0.226890i	$-0.927144\pi$
$227$	− 1551.97i	− 0.453780i	0.973920	−	0.226890i	$-0.0728557\pi$
$228$	7.19712i	0.00209053i
$229$	158.531	0.0457469	0.0228735	−	0.999738i	$-0.492719\pi$
$229$	158.531	0.0457469	0.0228735	+	0.999738i	$0.492719\pi$
$230$	0	0
$231$	−5853.60	−1.66727
$232$	− 1097.80i	− 0.310666i
$233$	− 728.999i	− 0.204971i	−0.994734	−	0.102486i	$-0.967320\pi$
$233$	− 728.999i	− 0.204971i	0.994734	−	0.102486i	$-0.0326796\pi$
$234$	2626.54	0.733772
$235$	0	0
$236$	808.991	0.223139
$237$	10659.8i	2.92165i
$238$	− 5945.47i	− 1.61928i
$239$	6201.60	1.67844	0.839222	−	0.543789i	$-0.183011\pi$
$239$	6201.60	1.67844	0.839222	+	0.543789i	$0.183011\pi$
$240$	0	0
$241$	−7223.04	−1.93061	−0.965305	−	0.261126i	$-0.915906\pi$
$241$	−7223.04	−1.93061	−0.965305	+	0.261126i	$0.915906\pi$
$242$	− 596.656i	− 0.158490i
$243$	− 5378.79i	− 1.41996i
$244$	−601.115	−0.157715
$245$	0	0
$246$	2093.27	0.542527
$247$	− 9.32853i	− 0.00240308i
$248$	− 902.928i	− 0.231193i
$249$	3750.82	0.954612
$250$	0	0
$251$	5042.78	1.26812	0.634059	−	0.773285i	$-0.281388\pi$
$251$	5042.78	1.26812	0.634059	+	0.773285i	$0.281388\pi$
$252$	− 3088.10i	− 0.771954i
$253$	739.110i	0.183666i
$254$	−2596.86	−0.641502
$255$	0	0
$256$	256.000	0.0625000
$257$	− 2981.15i	− 0.723577i	−0.932260	−	0.361788i	$-0.882166\pi$
$257$	− 2981.15i	− 0.723577i	0.932260	−	0.361788i	$-0.117834\pi$
$258$	− 8403.82i	− 2.02790i
$259$	−1076.93	−0.258367
$260$	0	0
$261$	−4496.25	−1.06632
$262$	− 1050.49i	− 0.247709i
$263$	7242.86i	1.69815i	0.528271	+	0.849076i	$0.322841\pi$
$263$	7242.86i	1.69815i	−0.528271	+	0.849076i	$0.677159\pi$
$264$	−1987.45	−0.463330
$265$	0	0
$266$	−10.9678	−0.00252812
$267$	8718.10i	1.99827i
$268$	− 1682.89i	− 0.383577i
$269$	2567.58	0.581962	0.290981	−	0.956729i	$-0.406018\pi$
$269$	2567.58	0.581962	0.290981	+	0.956729i	$0.406018\pi$
$270$	0	0
$271$	8066.27	1.80808	0.904042	−	0.427443i	$-0.140586\pi$
$271$	8066.27	1.80808	0.904042	+	0.427443i	$0.140586\pi$
$272$	− 2018.64i	− 0.449994i
$273$	7300.98i	1.61859i
$274$	−4856.23	−1.07071
$275$	0	0
$276$	−711.234	−0.155113
$277$	− 8991.54i	− 1.95036i	−0.221418	−	0.975179i	$-0.571068\pi$
$277$	− 8991.54i	− 1.95036i	0.221418	−	0.975179i	$-0.428932\pi$
$278$	− 4912.92i	− 1.05992i
$279$	−3698.10	−0.793546
$280$	0	0
$281$	968.130	0.205529	0.102765	−	0.994706i	$-0.467231\pi$
$281$	968.130	0.205529	0.102765	+	0.994706i	$0.467231\pi$
$282$	408.718i	0.0863079i
$283$	− 2252.65i	− 0.473167i	−0.971611	−	0.236583i	$-0.923972\pi$
$283$	− 2252.65i	− 0.473167i	0.971611	−	0.236583i	$-0.0760277\pi$
$284$	−2669.52	−0.557771
$285$	0	0
$286$	2576.03	0.532600
$287$	3189.97i	0.656090i
$288$	− 1048.49i	− 0.214524i
$289$	−11004.7	−2.23991
$290$	0	0
$291$	−11489.8	−2.31458
$292$	− 2411.84i	− 0.483364i
$293$	2734.35i	0.545196i	0.962128	+	0.272598i	$0.0878829\pi$
$293$	2734.35i	0.545196i	−0.962128	+	0.272598i	$0.912117\pi$
$294$	3280.64	0.650785
$295$	0	0
$296$	−365.646	−0.0717998
$297$	1432.30i	0.279834i
$298$	4810.78i	0.935172i
$299$	921.865	0.178304
$300$	0	0
$301$	12806.7	2.45239
$302$	− 1298.55i	− 0.247428i
$303$	14602.4i	2.76860i
$304$	−3.72387	−0.000702560 0
$305$	0	0
$306$	−8267.71	−1.54455
$307$	7977.09i	1.48299i	0.670961	+	0.741493i	$0.265882\pi$
$307$	7977.09i	1.48299i	−0.670961	+	0.741493i	$0.734118\pi$
$308$	− 3028.71i	− 0.560314i
$309$	11574.3	2.13087
$310$	0	0
$311$	7729.43	1.40931	0.704655	−	0.709550i	$-0.251102\pi$
$311$	7729.43	1.40931	0.704655	+	0.709550i	$0.251102\pi$
$312$	2478.87i	0.449803i
$313$	5506.25i	0.994350i	0.867650	+	0.497175i	$0.165629\pi$
$313$	5506.25i	0.994350i	−0.867650	+	0.497175i	$0.834371\pi$
$314$	7330.08	1.31739
$315$	0	0
$316$	−5515.51	−0.981872
$317$	− 5231.37i	− 0.926887i	−0.886126	−	0.463443i	$-0.846614\pi$
$317$	− 5231.37i	− 0.926887i	0.886126	−	0.463443i	$-0.153386\pi$
$318$	− 675.608i	− 0.119139i
$319$	−4409.77	−0.773981
$320$	0	0
$321$	−4523.68	−0.786565
$322$	− 1083.86i	− 0.187582i
$323$	29.3639i	0.00505836i
$324$	2160.38	0.370435
$325$	0	0
$326$	2110.55	0.358566
$327$	1075.86i	0.181943i
$328$	1083.08i	0.182326i
$329$	−622.854	−0.104374
$330$	0	0
$331$	−3551.61	−0.589771	−0.294885	−	0.955533i	$-0.595281\pi$
$331$	−3551.61	−0.589771	−0.294885	+	0.955533i	$0.595281\pi$
$332$	1940.71i	0.320815i
$333$	1497.57i	0.246445i
$334$	−1463.61	−0.239776
$335$	0	0
$336$	2914.48	0.473209
$337$	7002.99i	1.13198i	0.824412	+	0.565990i	$0.191506\pi$
$337$	7002.99i	1.13198i	−0.824412	+	0.565990i	$0.808494\pi$
$338$	1181.01i	0.190055i
$339$	9997.29	1.60171
$340$	0	0
$341$	−3626.97	−0.575987
$342$	15.2517i	0.00241146i
$343$	− 3082.42i	− 0.485234i
$344$	4348.22	0.681513
$345$	0	0
$346$	1043.55	0.162143
$347$	10268.2i	1.58854i	0.607562	+	0.794272i	$0.292148\pi$
$347$	10268.2i	1.58854i	−0.607562	+	0.794272i	$0.707852\pi$
$348$	− 4243.46i	− 0.653659i
$349$	−4515.58	−0.692588	−0.346294	−	0.938126i	$-0.612560\pi$
$349$	−4515.58	−0.692588	−0.346294	+	0.938126i	$0.612560\pi$
$350$	0	0
$351$	1786.46	0.271664
$352$	− 1028.33i	− 0.155710i
$353$	7838.63i	1.18189i	0.806711	+	0.590947i	$0.201246\pi$
$353$	7838.63i	1.18189i	−0.806711	+	0.590947i	$0.798754\pi$
$354$	3127.08	0.469498
$355$	0	0
$356$	−4510.84	−0.671556
$357$	− 22981.7i	− 3.40705i
$358$	2366.14i	0.349314i
$359$	12464.8	1.83250	0.916250	−	0.400606i	$-0.131201\pi$
$359$	12464.8	1.83250	0.916250	+	0.400606i	$0.131201\pi$
$360$	0	0
$361$	−6858.95	−0.999992
$362$	3447.85i	0.500594i
$363$	− 2306.32i	− 0.333472i
$364$	−3777.60	−0.543956
$365$	0	0
$366$	−2323.55	−0.331842
$367$	− 3936.14i	− 0.559850i	−0.960022	−	0.279925i	$-0.909690\pi$
$367$	− 3936.14i	− 0.559850i	0.960022	−	0.279925i	$-0.0903096\pi$
$368$	− 368.000i	− 0.0521286i
$369$	4435.93	0.625814
$370$	0	0
$371$	1029.57	0.144077
$372$	− 3490.18i	− 0.486445i
$373$	1920.72i	0.266625i	0.991074	+	0.133313i	$0.0425614\pi$
$373$	1920.72i	0.266625i	−0.991074	+	0.133313i	$0.957439\pi$
$374$	−8108.69	−1.12110
$375$	0	0
$376$	−211.475	−0.0290053
$377$	5500.15i	0.751385i
$378$	− 2100.39i	− 0.285800i
$379$	13074.5	1.77201	0.886004	−	0.463678i	$-0.153470\pi$
$379$	13074.5	1.77201	0.886004	+	0.463678i	$0.153470\pi$
$380$	0	0
$381$	−10037.9	−1.34976
$382$	− 5596.23i	− 0.749550i
$383$	8838.22i	1.17914i	0.807716	+	0.589571i	$0.200703\pi$
$383$	8838.22i	1.17914i	−0.807716	+	0.589571i	$0.799297\pi$
$384$	989.543	0.131504
$385$	0	0
$386$	995.372	0.131252
$387$	− 17808.9i	− 2.33922i
$388$	− 5944.94i	− 0.777858i
$389$	12687.3	1.65365	0.826827	−	0.562456i	$-0.190144\pi$
$389$	12687.3	1.65365	0.826827	+	0.562456i	$0.190144\pi$
$390$	0	0
$391$	−2901.80	−0.375321
$392$	1697.44i	0.218708i
$393$	− 4060.58i	− 0.521194i
$394$	592.977	0.0758218
$395$	0	0
$396$	−4211.69	−0.534458
$397$	− 8060.49i	− 1.01900i	−0.860470	−	0.509501i	$-0.829830\pi$
$397$	− 8060.49i	− 1.01900i	0.860470	−	0.509501i	$-0.170170\pi$
$398$	− 4694.87i	− 0.591287i
$399$	−42.3951	−0.00531932
$400$	0	0
$401$	12325.1	1.53488	0.767440	−	0.641121i	$-0.221530\pi$
$401$	12325.1	1.53488	0.767440	+	0.641121i	$0.221530\pi$
$402$	− 6505.04i	− 0.807070i
$403$	4523.79i	0.559171i
$404$	−7555.43	−0.930437
$405$	0	0
$406$	6466.69	0.790483
$407$	1468.76i	0.178879i
$408$	− 7802.87i	− 0.946813i
$409$	10806.7	1.30650	0.653250	−	0.757143i	$-0.273405\pi$
$409$	10806.7	1.30650	0.653250	+	0.757143i	$0.273405\pi$
$410$	0	0
$411$	−18771.3	−2.25285
$412$	5988.67i	0.716118i
$413$	4765.41i	0.567774i
$414$	−1507.21	−0.178926
$415$	0	0
$416$	−1282.59	−0.151164
$417$	− 18990.4i	− 2.23013i
$418$	14.9584i	0.00175033i
$419$	1823.74	0.212639	0.106319	−	0.994332i	$-0.466093\pi$
$419$	1823.74	0.212639	0.106319	+	0.994332i	$0.466093\pi$
$420$	0	0
$421$	5995.43	0.694060	0.347030	−	0.937854i	$-0.387190\pi$
$421$	5995.43	0.694060	0.347030	+	0.937854i	$0.387190\pi$
$422$	5677.23i	0.654889i
$423$	866.133i	0.0995575i
$424$	349.567	0.0400388
$425$	0	0
$426$	−10318.8	−1.17358
$427$	− 3540.91i	− 0.401303i
$428$	− 2340.60i	− 0.264339i
$429$	9957.39	1.12062
$430$	0	0
$431$	3887.80	0.434499	0.217249	−	0.976116i	$-0.430292\pi$
$431$	3887.80	0.434499	0.217249	+	0.976116i	$0.430292\pi$
$432$	− 713.137i	− 0.0794232i
$433$	− 4422.93i	− 0.490884i	−0.969411	−	0.245442i	$-0.921067\pi$
$433$	− 4422.93i	− 0.490884i	0.969411	−	0.245442i	$-0.0789330\pi$
$434$	5318.75	0.588268
$435$	0	0
$436$	−556.662	−0.0611452
$437$	5.35306i	0 0.000585976i
$438$	− 9322.74i	− 1.01703i
$439$	1748.08	0.190048	0.0950242	−	0.995475i	$-0.469707\pi$
$439$	1748.08	0.190048	0.0950242	+	0.995475i	$0.469707\pi$
$440$	0	0
$441$	6952.14	0.750690
$442$	10113.7i	1.08837i
$443$	3371.31i	0.361571i	0.983523	+	0.180785i	$0.0578639\pi$
$443$	3371.31i	0.361571i	−0.983523	+	0.180785i	$0.942136\pi$
$444$	−1413.37	−0.151071
$445$	0	0
$446$	4249.37	0.451151
$447$	18595.6i	1.96766i
$448$	1507.98i	0.159030i
$449$	−13314.7	−1.39947	−0.699734	−	0.714404i	$-0.746698\pi$
$449$	−13314.7	−1.39947	−0.699734	+	0.714404i	$0.746698\pi$
$450$	0	0
$451$	4350.61	0.454240
$452$	5172.70i	0.538282i
$453$	− 5019.43i	− 0.520603i
$454$	3103.94	0.320871
$455$	0	0
$456$	−14.3942	−0.00147823
$457$	− 3767.20i	− 0.385607i	−0.981237	−	0.192803i	$-0.938242\pi$
$457$	− 3767.20i	− 0.385607i	0.981237	−	0.192803i	$-0.0617579\pi$
$458$	317.063i	0.0323480i
$459$	−5623.32	−0.571839
$460$	0	0
$461$	9674.06	0.977366	0.488683	−	0.872461i	$-0.337477\pi$
$461$	9674.06	0.977366	0.488683	+	0.872461i	$0.337477\pi$
$462$	− 11707.2i	− 1.17893i
$463$	2977.73i	0.298892i	0.988770	+	0.149446i	$0.0477490\pi$
$463$	2977.73i	0.298892i	−0.988770	+	0.149446i	$0.952251\pi$
$464$	2195.61	0.219674
$465$	0	0
$466$	1458.00	0.144937
$467$	10701.0i	1.06035i	0.847888	+	0.530176i	$0.177874\pi$
$467$	10701.0i	1.06035i	−0.847888	+	0.530176i	$0.822126\pi$
$468$	5253.09i	0.518855i
$469$	9913.16	0.976006
$470$	0	0
$471$	28333.7	2.77187
$472$	1617.98i	0.157783i
$473$	− 17466.4i	− 1.69790i
$474$	−21319.7	−2.06592
$475$	0	0
$476$	11890.9	1.14500
$477$	− 1431.71i	− 0.137429i
$478$	12403.2i	1.18684i
$479$	−2337.15	−0.222937	−0.111469	−	0.993768i	$-0.535555\pi$
$479$	−2337.15	−0.222937	−0.111469	+	0.993768i	$0.535555\pi$
$480$	0	0
$481$	1831.94	0.173657
$482$	− 14446.1i	− 1.36515i
$483$	− 4189.57i	− 0.394683i
$484$	1193.31	0.112069
$485$	0	0
$486$	10757.6	1.00406
$487$	7183.85i	0.668442i	0.942495	+	0.334221i	$0.108473\pi$
$487$	7183.85i	0.668442i	−0.942495	+	0.334221i	$0.891527\pi$
$488$	− 1202.23i	− 0.111521i
$489$	8158.12	0.754443
$490$	0	0
$491$	−12084.2	−1.11070	−0.555350	−	0.831617i	$-0.687416\pi$
$491$	−12084.2	−1.11070	−0.555350	+	0.831617i	$0.687416\pi$
$492$	4186.53i	0.383625i
$493$	− 17313.1i	− 1.58163i
$494$	18.6571	0.00169923
$495$	0	0
$496$	1805.86	0.163478
$497$	− 15725.0i	− 1.41924i
$498$	7501.64i	0.675013i
$499$	−7145.78	−0.641060	−0.320530	−	0.947238i	$-0.603861\pi$
$499$	−7145.78	−0.641060	−0.320530	+	0.947238i	$0.603861\pi$
$500$	0	0
$501$	−5657.45	−0.504503
$502$	10085.6i	0.896695i
$503$	20436.2i	1.81154i	0.423771	+	0.905770i	$0.360706\pi$
$503$	20436.2i	1.81154i	−0.423771	+	0.905770i	$0.639294\pi$
$504$	6176.21	0.545854
$505$	0	0
$506$	−1478.22	−0.129871
$507$	4565.10i	0.399888i
$508$	− 5193.72i	− 0.453610i
$509$	−19721.7	−1.71738	−0.858690	−	0.512495i	$-0.828721\pi$
$509$	−19721.7	−1.71738	−0.858690	+	0.512495i	$0.828721\pi$
$510$	0	0
$511$	14207.1	1.22991
$512$	512.000i	0.0441942i
$513$	10.3735i	0 0.000892794i
$514$	5962.30	0.511646
$515$	0	0
$516$	16807.6	1.43394
$517$	849.475i	0.0722628i
$518$	− 2153.86i	− 0.182693i
$519$	4033.73	0.341158
$520$	0	0
$521$	3483.23	0.292904	0.146452	−	0.989218i	$-0.453215\pi$
$521$	3483.23	0.292904	0.146452	+	0.989218i	$0.453215\pi$
$522$	− 8992.50i	− 0.754006i
$523$	15689.0i	1.31172i	0.754881	+	0.655862i	$0.227695\pi$
$523$	15689.0i	1.31172i	−0.754881	+	0.655862i	$0.772305\pi$
$524$	2100.99	0.175157
$525$	0	0
$526$	−14485.7	−1.20077
$527$	− 14239.8i	− 1.17703i
$528$	− 3974.90i	− 0.327624i
$529$	−529.000	−0.0434783
$530$	0	0
$531$	6626.72	0.541573
$532$	− 21.9357i	− 0.00178765i
$533$	− 5426.36i	− 0.440979i
$534$	−17436.2	−1.41299
$535$	0	0
$536$	3365.78	0.271230
$537$	9146.09i	0.734977i
$538$	5135.15i	0.411510i
$539$	6818.43	0.544881
$540$	0	0
$541$	7620.73	0.605621	0.302810	−	0.953051i	$-0.402075\pi$
$541$	7620.73	0.605621	0.302810	+	0.953051i	$0.402075\pi$
$542$	16132.5i	1.27851i
$543$	13327.3i	1.05328i
$544$	4037.29	0.318194
$545$	0	0
$546$	−14602.0	−1.14452
$547$	− 5925.62i	− 0.463183i	−0.972813	−	0.231592i	$-0.925607\pi$
$547$	− 5925.62i	− 0.463183i	0.972813	−	0.231592i	$-0.0743933\pi$
$548$	− 9712.47i	− 0.757109i
$549$	−4923.94	−0.382784
$550$	0	0
$551$	−31.9381	−0.00246934
$552$	− 1422.47i	− 0.109682i
$553$	− 32489.4i	− 2.49836i
$554$	17983.1	1.37911
$555$	0	0
$556$	9825.85	0.749476
$557$	5456.16i	0.415054i	0.978229	+	0.207527i	$0.0665414\pi$
$557$	5456.16i	0.415054i	−0.978229	+	0.207527i	$0.933459\pi$
$558$	− 7396.20i	− 0.561122i
$559$	−21785.2	−1.64833
$560$	0	0
$561$	−31343.4	−2.35886
$562$	1936.26i	0.145331i
$563$	− 9194.29i	− 0.688265i	−0.938921	−	0.344132i	$-0.888173\pi$
$563$	− 9194.29i	− 0.688265i	0.938921	−	0.344132i	$-0.111827\pi$
$564$	−817.437	−0.0610289
$565$	0	0
$566$	4505.30	0.334580
$567$	12725.8i	0.942567i
$568$	− 5339.05i	− 0.394404i
$569$	−338.831	−0.0249640	−0.0124820	−	0.999922i	$-0.503973\pi$
$569$	−338.831	−0.0249640	−0.0124820	+	0.999922i	$0.503973\pi$
$570$	0	0
$571$	−1725.34	−0.126451	−0.0632254	−	0.997999i	$-0.520139\pi$
$571$	−1725.34	−0.126451	−0.0632254	+	0.997999i	$0.520139\pi$
$572$	5152.06i	0.376605i
$573$	− 21631.7i	− 1.57710i
$574$	−6379.93	−0.463926
$575$	0	0
$576$	2096.98	0.151692
$577$	− 23300.0i	− 1.68109i	−0.541738	−	0.840547i	$-0.682234\pi$
$577$	− 23300.0i	− 1.68109i	0.541738	−	0.840547i	$-0.317766\pi$
$578$	− 22009.3i	− 1.58385i
$579$	3847.52	0.276161
$580$	0	0
$581$	−11431.9	−0.816307
$582$	− 22979.6i	− 1.63666i
$583$	− 1404.18i	− 0.0997513i
$584$	4823.68	0.341790
$585$	0	0
$586$	−5468.70	−0.385512
$587$	− 15653.3i	− 1.10065i	−0.834950	−	0.550325i	$-0.814504\pi$
$587$	− 15653.3i	− 1.10065i	0.834950	−	0.550325i	$-0.185496\pi$
$588$	6561.28i	0.460174i
$589$	−26.2686	−0.00183766
$590$	0	0
$591$	2292.10	0.159533
$592$	− 731.292i	− 0.0507701i
$593$	− 2658.08i	− 0.184072i	−0.995756	−	0.0920358i	$-0.970663\pi$
$593$	− 2658.08i	− 0.184072i	0.995756	−	0.0920358i	$-0.0293374\pi$
$594$	−2864.60	−0.197872
$595$	0	0
$596$	−9621.57	−0.661266
$597$	− 18147.6i	− 1.24410i
$598$	1843.73i	0.126080i
$599$	−19417.6	−1.32451	−0.662256	−	0.749278i	$-0.730401\pi$
$599$	−19417.6	−1.32451	−0.662256	+	0.749278i	$0.730401\pi$
$600$	0	0
$601$	−18469.0	−1.25352	−0.626760	−	0.779213i	$-0.715619\pi$
$601$	−18469.0	−1.25352	−0.626760	+	0.779213i	$0.715619\pi$
$602$	25613.5i	1.73410i
$603$	− 13785.1i	− 0.930968i
$604$	2597.10	0.174958
$605$	0	0
$606$	−29204.8	−1.95770
$607$	− 3968.56i	− 0.265369i	−0.991158	−	0.132684i	$-0.957640\pi$
$607$	− 3968.56i	− 0.265369i	0.991158	−	0.132684i	$-0.0423596\pi$
$608$	− 7.44773i	0 0.000496785i
$609$	24996.4	1.66322
$610$	0	0
$611$	1059.52	0.0701531
$612$	− 16535.4i	− 1.09216i
$613$	− 11478.7i	− 0.756311i	−0.925742	−	0.378156i	$-0.876558\pi$
$613$	− 11478.7i	− 0.756311i	0.925742	−	0.378156i	$-0.123442\pi$
$614$	−15954.2	−1.04863
$615$	0	0
$616$	6057.42	0.396202
$617$	15691.1i	1.02382i	0.859039	+	0.511911i	$0.171062\pi$
$617$	15691.1i	1.02382i	−0.859039	+	0.511911i	$0.828938\pi$
$618$	23148.6i	1.50676i
$619$	18249.4	1.18499	0.592494	−	0.805575i	$-0.298144\pi$
$619$	18249.4	1.18499	0.592494	+	0.805575i	$0.298144\pi$
$620$	0	0
$621$	−1025.14	−0.0662436
$622$	15458.9i	0.996533i
$623$	− 26571.4i	− 1.70876i
$624$	−4957.75	−0.318059
$625$	0	0
$626$	−11012.5	−0.703111
$627$	57.8203i	0.00368281i
$628$	14660.2i	0.931536i
$629$	−5766.48	−0.365540
$630$	0	0
$631$	−23528.8	−1.48442	−0.742208	−	0.670169i	$-0.766222\pi$
$631$	−23528.8	−1.48442	−0.742208	+	0.670169i	$0.766222\pi$
$632$	− 11031.0i	− 0.694288i
$633$	21944.8i	1.37793i
$634$	10462.7	0.655408
$635$	0	0
$636$	1351.22	0.0842441
$637$	− 8504.38i	− 0.528973i
$638$	− 8819.55i	− 0.547287i
$639$	−21867.0	−1.35375
$640$	0	0
$641$	3748.79	0.230996	0.115498	−	0.993308i	$-0.463154\pi$
$641$	3748.79	0.230996	0.115498	+	0.993308i	$0.463154\pi$
$642$	− 9047.36i	− 0.556185i
$643$	15924.3i	0.976660i	0.872659	+	0.488330i	$0.162394\pi$
$643$	15924.3i	0.976660i	−0.872659	+	0.488330i	$0.837606\pi$
$644$	2167.73	0.132640
$645$	0	0
$646$	−58.7278	−0.00357680
$647$	2854.11i	0.173426i	0.996233	+	0.0867129i	$0.0276363\pi$
$647$	2854.11i	0.173426i	−0.996233	+	0.0867129i	$0.972364\pi$
$648$	4320.76i	0.261937i
$649$	6499.27	0.393095
$650$	0	0
$651$	20559.1	1.23775
$652$	4221.09i	0.253544i
$653$	7925.97i	0.474988i	0.971389	+	0.237494i	$0.0763260\pi$
$653$	7925.97i	0.474988i	−0.971389	+	0.237494i	$0.923674\pi$
$654$	−2151.72	−0.128653
$655$	0	0
$656$	−2166.15	−0.128924
$657$	− 19756.2i	− 1.17316i
$658$	− 1245.71i	− 0.0738035i
$659$	5799.43	0.342813	0.171406	−	0.985200i	$-0.445169\pi$
$659$	5799.43	0.342813	0.171406	+	0.985200i	$0.445169\pi$
$660$	0	0
$661$	22324.8	1.31367	0.656833	−	0.754036i	$-0.271896\pi$
$661$	22324.8	1.31367	0.656833	+	0.754036i	$0.271896\pi$
$662$	− 7103.22i	− 0.417031i
$663$	39093.4i	2.28999i
$664$	−3881.42	−0.226850
$665$	0	0
$666$	−2995.13	−0.174263
$667$	− 3156.19i	− 0.183221i
$668$	− 2927.22i	− 0.169547i
$669$	16425.5	0.949249
$670$	0	0
$671$	−4829.24	−0.277840
$672$	5828.97i	0.334609i
$673$	− 23253.5i	− 1.33188i	−0.746005	−	0.665940i	$-0.768031\pi$
$673$	− 23253.5i	− 1.33188i	0.746005	−	0.665940i	$-0.231969\pi$
$674$	−14006.0	−0.800430
$675$	0	0
$676$	−2362.03	−0.134389
$677$	19003.7i	1.07884i	0.842038	+	0.539419i	$0.181356\pi$
$677$	19003.7i	1.07884i	−0.842038	+	0.539419i	$0.818644\pi$
$678$	19994.6i	1.13258i
$679$	35019.1	1.97925
$680$	0	0
$681$	11998.0	0.675131
$682$	− 7253.94i	− 0.407284i
$683$	− 11222.5i	− 0.628722i	−0.949304	−	0.314361i	$-0.898210\pi$
$683$	− 11222.5i	− 0.628722i	0.949304	−	0.314361i	$-0.101790\pi$
$684$	−30.5035	−0.00170516
$685$	0	0
$686$	6164.85	0.343112
$687$	1225.58i	0.0680620i
$688$	8696.45i	0.481902i
$689$	−1751.38	−0.0968391
$690$	0	0
$691$	4297.68	0.236601	0.118301	−	0.992978i	$-0.462255\pi$
$691$	4297.68	0.236601	0.118301	+	0.992978i	$0.462255\pi$
$692$	2087.09i	0.114652i
$693$	− 24809.2i	− 1.35992i
$694$	−20536.4	−1.12327
$695$	0	0
$696$	8486.92	0.462206
$697$	17080.8i	0.928240i
$698$	− 9031.15i	− 0.489734i
$699$	5635.75	0.304955
$700$	0	0
$701$	25769.6	1.38845	0.694225	−	0.719758i	$-0.255747\pi$
$701$	25769.6	1.38845	0.694225	+	0.719758i	$0.255747\pi$
$702$	3572.91i	0.192095i
$703$	10.6376i	0 0.000570705i
$704$	2056.65	0.110104
$705$	0	0
$706$	−15677.3	−0.835725
$707$	− 44505.7i	− 2.36748i
$708$	6254.15i	0.331985i
$709$	4900.01	0.259554	0.129777	−	0.991543i	$-0.458574\pi$
$709$	4900.01	0.259554	0.129777	+	0.991543i	$0.458574\pi$
$710$	0	0
$711$	−45179.4	−2.38307
$712$	− 9021.67i	− 0.474862i
$713$	− 2595.92i	− 0.136350i
$714$	45963.3	2.40915
$715$	0	0
$716$	−4732.28	−0.247002
$717$	47943.4i	2.49718i
$718$	24929.6i	1.29577i
$719$	−7631.85	−0.395855	−0.197928	−	0.980217i	$-0.563421\pi$
$719$	−7631.85	−0.395855	−0.197928	+	0.980217i	$0.563421\pi$
$720$	0	0
$721$	−35276.6	−1.82215
$722$	− 13717.9i	− 0.707101i
$723$	− 55839.9i	− 2.87235i
$724$	−6895.70	−0.353973
$725$	0	0
$726$	4612.64	0.235800
$727$	36985.6i	1.88682i	0.331628	+	0.943410i	$0.392402\pi$
$727$	36985.6i	1.88682i	−0.331628	+	0.943410i	$0.607598\pi$
$728$	− 7555.20i	− 0.384635i
$729$	26999.8	1.37173
$730$	0	0
$731$	68574.3	3.46965
$732$	− 4647.10i	− 0.234647i
$733$	− 22227.3i	− 1.12003i	−0.828482	−	0.560015i	$-0.810795\pi$
$733$	− 22227.3i	− 1.12003i	0.828482	−	0.560015i	$-0.189205\pi$
$734$	7872.29	0.395874
$735$	0	0
$736$	736.000	0.0368605
$737$	− 13520.0i	− 0.675733i
$738$	8871.86i	0.442517i
$739$	17899.1	0.890974	0.445487	−	0.895288i	$-0.353030\pi$
$739$	17899.1	0.890974	0.445487	+	0.895288i	$0.353030\pi$
$740$	0	0
$741$	72.1171	0.00357529
$742$	2059.14i	0.101878i
$743$	− 29843.4i	− 1.47355i	−0.676137	−	0.736776i	$-0.736347\pi$
$743$	− 29843.4i	− 1.47355i	0.676137	−	0.736776i	$-0.263653\pi$
$744$	6980.36	0.343968
$745$	0	0
$746$	−3841.44	−0.188532
$747$	15897.0i	0.778638i
$748$	− 16217.4i	− 0.792736i
$749$	13787.4	0.672606
$750$	0	0
$751$	−9399.65	−0.456722	−0.228361	−	0.973577i	$-0.573337\pi$
$751$	−9399.65	−0.456722	−0.228361	+	0.973577i	$0.573337\pi$
$752$	− 422.950i	− 0.0205098i
$753$	38984.8i	1.88670i
$754$	−11000.3	−0.531309
$755$	0	0
$756$	4200.78	0.202091
$757$	− 29871.6i	− 1.43422i	−0.696961	−	0.717109i	$-0.745465\pi$
$757$	− 29871.6i	− 1.43422i	0.696961	−	0.717109i	$-0.254535\pi$
$758$	26149.0i	1.25300i
$759$	−5713.92	−0.273257
$760$	0	0
$761$	−273.955	−0.0130497	−0.00652487	−	0.999979i	$-0.502077\pi$
$761$	−273.955	−0.0130497	−0.00652487	+	0.999979i	$0.502077\pi$
$762$	− 20075.8i	− 0.954423i
$763$	− 3279.05i	− 0.155583i
$764$	11192.5	0.530012
$765$	0	0
$766$	−17676.4	−0.833780
$767$	− 8106.31i	− 0.381619i
$768$	1979.09i	0.0929872i
$769$	13273.8	0.622450	0.311225	−	0.950336i	$-0.399261\pi$
$769$	13273.8	0.622450	0.311225	+	0.950336i	$0.399261\pi$
$770$	0	0
$771$	23046.7	1.07653
$772$	1990.74i	0.0928089i
$773$	34161.1i	1.58951i	0.606933	+	0.794753i	$0.292400\pi$
$773$	34161.1i	1.58951i	−0.606933	+	0.794753i	$0.707600\pi$
$774$	35617.8	1.65408
$775$	0	0
$776$	11889.9	0.550028
$777$	− 8325.54i	− 0.384398i
$778$	25374.6i	1.16931i
$779$	31.5096	0.00144923
$780$	0	0
$781$	−21446.4	−0.982603
$782$	− 5803.60i	− 0.265392i
$783$	− 6116.29i	− 0.279155i
$784$	−3394.87	−0.154650
$785$	0	0
$786$	8121.17	0.368540
$787$	38489.6i	1.74334i	0.490095	+	0.871669i	$0.336962\pi$
$787$	38489.6i	1.74334i	−0.490095	+	0.871669i	$0.663038\pi$
$788$	1185.95i	0.0536141i
$789$	−55993.2	−2.52650
$790$	0	0
$791$	−30470.1	−1.36965
$792$	− 8423.38i	− 0.377919i
$793$	6023.33i	0.269729i
$794$	16121.0	0.720544
$795$	0	0
$796$	9389.73	0.418103
$797$	− 17176.8i	− 0.763405i	−0.924285	−	0.381702i	$-0.875338\pi$
$797$	− 17176.8i	− 0.763405i	0.924285	−	0.381702i	$-0.124662\pi$
$798$	− 84.7902i	− 0.00376133i
$799$	−3335.10	−0.147669
$800$	0	0
$801$	−36949.8	−1.62991
$802$	24650.2i	1.08532i
$803$	− 19376.2i	− 0.851523i
$804$	13010.1	0.570684
$805$	0	0
$806$	−9047.58	−0.395394
$807$	19849.4i	0.865841i
$808$	− 15110.9i	− 0.657918i
$809$	−8226.61	−0.357518	−0.178759	−	0.983893i	$-0.557208\pi$
$809$	−8226.61	−0.357518	−0.178759	+	0.983893i	$0.557208\pi$
$810$	0	0
$811$	27867.9	1.20662	0.603312	−	0.797505i	$-0.293847\pi$
$811$	27867.9	1.20662	0.603312	+	0.797505i	$0.293847\pi$
$812$	12933.4i	0.558956i
$813$	62358.8i	2.69006i
$814$	−2937.53	−0.126487
$815$	0	0
$816$	15605.7	0.669498
$817$	− 126.502i	− 0.00541705i
$818$	21613.5i	0.923835i
$819$	−30943.6	−1.32022
$820$	0	0
$821$	−17637.5	−0.749761	−0.374880	−	0.927073i	$-0.622316\pi$
$821$	−17637.5	−0.749761	−0.374880	+	0.927073i	$0.622316\pi$
$822$	− 37542.6i	− 1.59300i
$823$	28048.6i	1.18799i	0.804470	+	0.593993i	$0.202449\pi$
$823$	28048.6i	1.18799i	−0.804470	+	0.593993i	$0.797551\pi$
$824$	−11977.3	−0.506372
$825$	0	0
$826$	−9530.82	−0.401477
$827$	32592.9i	1.37046i	0.728329	+	0.685228i	$0.240297\pi$
$827$	32592.9i	1.37046i	−0.728329	+	0.685228i	$0.759703\pi$
$828$	− 3014.42i	− 0.126520i
$829$	−18815.9	−0.788303	−0.394152	−	0.919045i	$-0.628962\pi$
$829$	−18815.9	−0.788303	−0.394152	+	0.919045i	$0.628962\pi$
$830$	0	0
$831$	69511.9	2.90173
$832$	− 2565.19i	− 0.106889i
$833$	26769.7i	1.11346i
$834$	37980.9	1.57694
$835$	0	0
$836$	−29.9168	−0.00123767
$837$	− 5030.56i	− 0.207744i
$838$	3647.48i	0.150358i
$839$	−7612.72	−0.313254	−0.156627	−	0.987658i	$-0.550062\pi$
$839$	−7612.72	−0.313254	−0.156627	+	0.987658i	$0.550062\pi$
$840$	0	0
$841$	−5558.14	−0.227896
$842$	11990.9i	0.490775i
$843$	7484.43i	0.305786i
$844$	−11354.5	−0.463076
$845$	0	0
$846$	−1732.27	−0.0703978
$847$	7029.28i	0.285158i
$848$	699.134i	0.0283117i
$849$	17414.8	0.703975
$850$	0	0
$851$	−1051.23	−0.0423452
$852$	− 20637.6i	− 0.829849i
$853$	− 31421.4i	− 1.26125i	−0.776086	−	0.630627i	$-0.782798\pi$
$853$	− 31421.4i	− 1.26125i	0.776086	−	0.630627i	$-0.217202\pi$
$854$	7081.81	0.283764
$855$	0	0
$856$	4681.20	0.186916
$857$	− 20909.5i	− 0.833435i	−0.909036	−	0.416718i	$-0.863180\pi$
$857$	− 20909.5i	− 0.833435i	0.909036	−	0.416718i	$-0.136820\pi$
$858$	19914.8i	0.792400i
$859$	−23304.5	−0.925655	−0.462828	−	0.886448i	$-0.653165\pi$
$859$	−23304.5	−0.925655	−0.462828	+	0.886448i	$0.653165\pi$
$860$	0	0
$861$	−24661.0	−0.976127
$862$	7775.61i	0.307237i
$863$	− 19146.3i	− 0.755211i	−0.925966	−	0.377606i	$-0.876747\pi$
$863$	− 19146.3i	− 0.755211i	0.925966	−	0.377606i	$-0.123253\pi$
$864$	1426.27	0.0561607
$865$	0	0
$866$	8845.87	0.347107
$867$	− 85075.0i	− 3.33252i
$868$	10637.5i	0.415968i
$869$	−44310.5	−1.72972
$870$	0	0
$871$	−16863.0	−0.656005
$872$	− 1113.32i	− 0.0432362i
$873$	− 48697.1i	− 1.88791i
$874$	−10.7061	−0.000414347 0
$875$	0	0
$876$	18645.5	0.719146
$877$	− 31389.0i	− 1.20859i	−0.796762	−	0.604293i	$-0.793456\pi$
$877$	− 31389.0i	− 1.20859i	0.796762	−	0.604293i	$-0.206544\pi$
$878$	3496.16i	0.134384i
$879$	−21138.7	−0.811139
$880$	0	0
$881$	44496.3	1.70161	0.850806	−	0.525480i	$-0.176114\pi$
$881$	44496.3	1.70161	0.850806	+	0.525480i	$0.176114\pi$
$882$	13904.3i	0.530818i
$883$	8906.65i	0.339448i	0.985492	+	0.169724i	$0.0542876\pi$
$883$	8906.65i	0.339448i	−0.985492	+	0.169724i	$0.945712\pi$
$884$	−20227.4	−0.769592
$885$	0	0
$886$	−6742.62	−0.255669
$887$	36584.7i	1.38489i	0.721472	+	0.692444i	$0.243466\pi$
$887$	36584.7i	1.38489i	−0.721472	+	0.692444i	$0.756534\pi$
$888$	− 2826.74i	− 0.106823i
$889$	30593.9	1.15420
$890$	0	0
$891$	17356.1	0.652581
$892$	8498.74i	0.319012i
$893$	6.15238i	0 0.000230551i
$894$	−37191.2	−1.39134
$895$	0	0
$896$	−3015.97	−0.112451
$897$	7126.76i	0.265279i
$898$	− 26629.5i	− 0.989573i
$899$	15488.1	0.574591
$900$	0	0
$901$	5512.90	0.203842
$902$	8701.23i	0.321197i
$903$	99006.4i	3.64865i
$904$	−10345.4	−0.380623
$905$	0	0
$906$	10038.9	0.368122
$907$	21346.1i	0.781463i	0.920505	+	0.390731i	$0.127778\pi$
$907$	21346.1i	0.781463i	−0.920505	+	0.390731i	$0.872222\pi$
$908$	6207.89i	0.226890i
$909$	−61889.1	−2.25823
$910$	0	0
$911$	−10208.0	−0.371246	−0.185623	−	0.982621i	$-0.559430\pi$
$911$	−10208.0	−0.371246	−0.185623	+	0.982621i	$0.559430\pi$
$912$	− 28.7885i	− 0.00104527i
$913$	15591.3i	0.565166i
$914$	7534.40	0.272665
$915$	0	0
$916$	−634.125	−0.0228735
$917$	12376.0i	0.445683i
$918$	− 11246.6i	− 0.404351i
$919$	−1758.00	−0.0631025	−0.0315513	−	0.999502i	$-0.510045\pi$
$919$	−1758.00	−0.0631025	−0.0315513	+	0.999502i	$0.510045\pi$
$920$	0	0
$921$	−61669.3	−2.20638
$922$	19348.1i	0.691102i
$923$	26749.3i	0.953917i
$924$	23414.4	0.833633
$925$	0	0
$926$	−5955.46	−0.211348
$927$	49055.3i	1.73807i
$928$	4391.22i	0.155333i
$929$	845.008	0.0298426	0.0149213	−	0.999889i	$-0.495250\pi$
$929$	845.008	0.0298426	0.0149213	+	0.999889i	$0.495250\pi$
$930$	0	0
$931$	49.3830	0.00173841
$932$	2915.99i	0.102486i
$933$	59754.7i	2.09676i
$934$	−21402.0	−0.749782
$935$	0	0
$936$	−10506.2	−0.366886
$937$	− 3851.61i	− 0.134287i	−0.997743	−	0.0671433i	$-0.978612\pi$
$937$	− 3851.61i	− 0.134287i	0.997743	−	0.0671433i	$-0.0213885\pi$
$938$	19826.3i	0.690141i
$939$	−42567.7	−1.47939
$940$	0	0
$941$	−4379.36	−0.151714	−0.0758571	−	0.997119i	$-0.524169\pi$
$941$	−4379.36	−0.151714	−0.0758571	+	0.997119i	$0.524169\pi$
$942$	56667.5i	1.96001i
$943$	3113.85i	0.107530i
$944$	−3235.96	−0.111570
$945$	0	0
$946$	34932.8	1.20059
$947$	− 29746.9i	− 1.02074i	−0.859954	−	0.510371i	$-0.829508\pi$
$947$	− 29746.9i	− 1.02074i	0.859954	−	0.510371i	$-0.170492\pi$
$948$	− 42639.3i	− 1.46082i
$949$	−24167.3	−0.826663
$950$	0	0
$951$	40442.7	1.37902
$952$	23781.9i	0.809638i
$953$	4306.61i	0.146385i	0.997318	+	0.0731924i	$0.0233187\pi$
$953$	4306.61i	0.146385i	−0.997318	+	0.0731924i	$0.976681\pi$
$954$	2863.42	0.0971769
$955$	0	0
$956$	−24806.4	−0.839222
$957$	− 34091.1i	− 1.15152i
$958$	− 4674.29i	− 0.157640i
$959$	57211.9	1.92645
$960$	0	0
$961$	−17052.3	−0.572397
$962$	3663.87i	0.122794i
$963$	− 19172.7i	− 0.641568i
$964$	28892.2	0.965305
$965$	0	0
$966$	8379.14	0.279083
$967$	12233.4i	0.406824i	0.979093	+	0.203412i	$0.0652031\pi$
$967$	12233.4i	0.406824i	−0.979093	+	0.203412i	$0.934797\pi$
$968$	2386.63i	0.0792449i
$969$	−227.007	−0.00752581
$970$	0	0
$971$	48207.7	1.59326	0.796631	−	0.604465i	$-0.206613\pi$
$971$	48207.7	1.59326	0.796631	+	0.604465i	$0.206613\pi$
$972$	21515.2i	0.709978i
$973$	57879.8i	1.90703i
$974$	−14367.7	−0.472660
$975$	0	0
$976$	2404.46	0.0788575
$977$	− 28662.9i	− 0.938595i	−0.883040	−	0.469298i	$-0.844507\pi$
$977$	− 28662.9i	− 0.938595i	0.883040	−	0.469298i	$-0.155493\pi$
$978$	16316.2i	0.533472i
$979$	−36239.2	−1.18305
$980$	0	0
$981$	−4559.81	−0.148403
$982$	− 24168.4i	− 0.785383i
$983$	− 20944.1i	− 0.679567i	−0.940504	−	0.339783i	$-0.889646\pi$
$983$	− 20944.1i	− 0.679567i	0.940504	−	0.339783i	$-0.110354\pi$
$984$	−8373.06	−0.271264
$985$	0	0
$986$	34626.2	1.11838
$987$	− 4815.16i	− 0.155287i
$988$	37.3141i	0.00120154i
$989$	12501.1	0.401934
$990$	0	0
$991$	−36440.2	−1.16808	−0.584038	−	0.811727i	$-0.698528\pi$
$991$	−36440.2	−1.16808	−0.584038	+	0.811727i	$0.698528\pi$
$992$	3611.71i	0.115597i
$993$	− 27456.8i	− 0.877458i
$994$	31450.0	1.00355
$995$	0	0
$996$	−15003.3	−0.477306
$997$	11945.0i	0.379439i	0.981838	+	0.189720i	$0.0607579\pi$
$997$	11945.0i	0.379439i	−0.981838	+	0.189720i	$0.939242\pi$
$998$	− 14291.6i	− 0.453298i
$999$	−2037.15	−0.0645172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.b.n.599.8		8
5.2	odd	4		230.4.a.h.1.4	✓	4
5.3	odd	4		1150.4.a.p.1.1		4
5.4	even	2	inner	1150.4.b.n.599.1		8
15.2	even	4		2070.4.a.bj.1.3		4
20.7	even	4		1840.4.a.m.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.4	✓	4	5.2	odd	4
1150.4.a.p.1.1		4	5.3	odd	4
1150.4.b.n.599.1		8	5.4	even	2	inner
1150.4.b.n.599.8		8	1.1	even	1	trivial
1840.4.a.m.1.1		4	20.7	even	4
2070.4.a.bj.1.3		4	15.2	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)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +7.73081i q^{3} -4.00000 q^{4} -15.4616 q^{6} -23.5622i q^{7} -8.00000i q^{8} -32.7654 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +7.73081i q^{3} -4.00000 q^{4} -15.4616 q^{6} -23.5622i q^{7} -8.00000i q^{8} -32.7654 q^{9} -32.1352 q^{11} -30.9232i q^{12} +40.0811i q^{13} +47.1245 q^{14} +16.0000 q^{16} -126.165i q^{17} -65.5308i q^{18} -0.232742 q^{19} +182.155 q^{21} -64.2704i q^{22} -23.0000i q^{23} +61.8465 q^{24} -80.1621 q^{26} -44.5711i q^{27} +94.2490i q^{28} +137.226 q^{29} +112.866 q^{31} +32.0000i q^{32} -248.431i q^{33} +252.331 q^{34} +131.062 q^{36} -45.7057i q^{37} -0.465483i q^{38} -309.859 q^{39} -135.385 q^{41} +364.310i q^{42} +543.528i q^{43} +128.541 q^{44} +46.0000 q^{46} -26.4344i q^{47} +123.693i q^{48} -212.180 q^{49} +975.359 q^{51} -160.324i q^{52} +43.6958i q^{53} +89.1422 q^{54} -188.498 q^{56} -1.79928i q^{57} +274.451i q^{58} -202.248 q^{59} +150.279 q^{61} +225.732i q^{62} +772.026i q^{63} -64.0000 q^{64} +496.862 q^{66} +420.722i q^{67} +504.661i q^{68} +177.809 q^{69} +667.381 q^{71} +262.123i q^{72} +602.960i q^{73} +91.4115 q^{74} +0.930966 q^{76} +757.178i q^{77} -619.718i q^{78} +1378.88 q^{79} -540.095 q^{81} -270.769i q^{82} -485.178i q^{83} -728.621 q^{84} -1087.06 q^{86} +1060.86i q^{87} +257.082i q^{88} +1127.71 q^{89} +944.400 q^{91} +92.0000i q^{92} +872.545i q^{93} +52.8688 q^{94} -247.386 q^{96} +1486.24i q^{97} -424.359i q^{98} +1052.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 16 q^{6} - 64 q^{9}+O(q^{10}) \) 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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