LMFDB - Embedded newform 825.4.c.m.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.245110336.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 19x^{4} + 101x^{2} + 100 $ x^6 + 19x^4 + 101x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$1.12946i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.m.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.59486i q^{2} -3.00000i q^{3} -13.1127 q^{4} -13.7846 q^{6} -20.6383i q^{7} +23.4921i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-4.59486i q^{2} -3.00000i q^{3} -13.1127 q^{4} -13.7846 q^{6} -20.6383i q^{7} +23.4921i q^{8} -9.00000 q^{9} +11.0000 q^{11} +39.3381i q^{12} -15.6584i q^{13} -94.8302 q^{14} +3.04132 q^{16} -72.9507i q^{17} +41.3537i q^{18} -61.0513 q^{19} -61.9150 q^{21} -50.5434i q^{22} -13.6605i q^{23} +70.4764 q^{24} -71.9483 q^{26} +27.0000i q^{27} +270.624i q^{28} +31.4663 q^{29} -243.008 q^{31} +173.963i q^{32} -33.0000i q^{33} -335.198 q^{34} +118.014 q^{36} +65.4018i q^{37} +280.522i q^{38} -46.9753 q^{39} -109.087 q^{41} +284.491i q^{42} -121.750i q^{43} -144.240 q^{44} -62.7678 q^{46} +519.530i q^{47} -9.12396i q^{48} -82.9413 q^{49} -218.852 q^{51} +205.324i q^{52} -542.673i q^{53} +124.061 q^{54} +484.839 q^{56} +183.154i q^{57} -144.583i q^{58} -109.478 q^{59} -89.6156 q^{61} +1116.59i q^{62} +185.745i q^{63} +823.664 q^{64} -151.630 q^{66} -488.446i q^{67} +956.581i q^{68} -40.9814 q^{69} +837.423 q^{71} -211.429i q^{72} +351.216i q^{73} +300.512 q^{74} +800.547 q^{76} -227.022i q^{77} +215.845i q^{78} +831.205 q^{79} +81.0000 q^{81} +501.238i q^{82} +1389.13i q^{83} +811.873 q^{84} -559.423 q^{86} -94.3988i q^{87} +258.413i q^{88} -1523.70 q^{89} -323.164 q^{91} +179.125i q^{92} +729.025i q^{93} +2387.17 q^{94} +521.888 q^{96} +426.612i q^{97} +381.103i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9	$ 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9} + 66 q^{11} - 288 q^{14} + 50 q^{16} - 232 q^{19} - 36 q^{21} - 18 q^{24} + 604 q^{26} - 476 q^{29} + 184 q^{31} - 708 q^{34} + 306 q^{36} - 120 q^{39} - 92 q^{41} - 374 q^{44} - 480 q^{46} + 914 q^{49} - 192 q^{51} + 54 q^{54} + 1376 q^{56} - 2472 q^{59} + 684 q^{61} + 3838 q^{64} - 66 q^{66} + 1440 q^{69} + 3632 q^{71} + 3748 q^{74} + 792 q^{76} + 192 q^{79} + 486 q^{81} + 960 q^{84} + 376 q^{86} - 1676 q^{89} + 664 q^{91} + 6224 q^{94} - 1182 q^{96} - 594 q^{99}+O(q^{100}) $ 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9 + 66 * q^11 - 288 * q^14 + 50 * q^16 - 232 * q^19 - 36 * q^21 - 18 * q^24 + 604 * q^26 - 476 * q^29 + 184 * q^31 - 708 * q^34 + 306 * q^36 - 120 * q^39 - 92 * q^41 - 374 * q^44 - 480 * q^46 + 914 * q^49 - 192 * q^51 + 54 * q^54 + 1376 * q^56 - 2472 * q^59 + 684 * q^61 + 3838 * q^64 - 66 * q^66 + 1440 * q^69 + 3632 * q^71 + 3748 * q^74 + 792 * q^76 + 192 * q^79 + 486 * q^81 + 960 * q^84 + 376 * q^86 - 1676 * q^89 + 664 * q^91 + 6224 * q^94 - 1182 * q^96 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	− 4.59486i	− 1.62453i	−0.583291	−	0.812263i	$-0.698235\pi$
$2$	− 4.59486i	− 1.62453i	0.583291	−	0.812263i	$-0.301765\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−13.1127	−1.63909
$5$	0	0
$5$	0	0
$6$	−13.7846	−0.937921
$7$	− 20.6383i	− 1.11437i	−0.830390	−	0.557183i	$-0.811882\pi$
$7$	− 20.6383i	− 1.11437i	0.830390	−	0.557183i	$-0.188118\pi$
$8$	23.4921i	1.03822i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	39.3381i	0.946328i
$13$	− 15.6584i	− 0.334067i	−0.985951	−	0.167033i	$-0.946581\pi$
$13$	− 15.6584i	− 0.334067i	0.985951	−	0.167033i	$-0.0534188\pi$
$14$	−94.8302	−1.81032
$15$	0	0
$16$	3.04132	0.0475206
$17$	− 72.9507i	− 1.04077i	−0.853931	−	0.520387i	$-0.825788\pi$
$17$	− 72.9507i	− 1.04077i	0.853931	−	0.520387i	$-0.174212\pi$
$18$	41.3537i	0.541509i
$19$	−61.0513	−0.737165	−0.368582	−	0.929595i	$-0.620157\pi$
$19$	−61.0513	−0.737165	−0.368582	+	0.929595i	$0.620157\pi$
$20$	0	0
$21$	−61.9150	−0.643379
$22$	− 50.5434i	− 0.489813i
$23$	− 13.6605i	− 0.123844i	−0.998081	−	0.0619218i	$-0.980277\pi$
$23$	− 13.6605i	− 0.123844i	0.998081	−	0.0619218i	$-0.0197229\pi$
$24$	70.4764	0.599414
$25$	0	0
$26$	−71.9483	−0.542701
$27$	27.0000i	0.192450i
$28$	270.624i	1.82654i
$29$	31.4663	0.201487	0.100744	−	0.994912i	$-0.467878\pi$
$29$	31.4663	0.201487	0.100744	+	0.994912i	$0.467878\pi$
$30$	0	0
$31$	−243.008	−1.40792	−0.703961	−	0.710239i	$-0.748587\pi$
$31$	−243.008	−1.40792	−0.703961	+	0.710239i	$0.748587\pi$
$32$	173.963i	0.961016i
$33$	− 33.0000i	− 0.174078i
$34$	−335.198	−1.69076
$35$	0	0
$36$	118.014	0.546363
$37$	65.4018i	0.290594i	0.989388	+	0.145297i	$0.0464138\pi$
$37$	65.4018i	0.290594i	−0.989388	+	0.145297i	$0.953586\pi$
$38$	280.522i	1.19754i
$39$	−46.9753	−0.192874
$40$	0	0
$41$	−109.087	−0.415524	−0.207762	−	0.978179i	$-0.566618\pi$
$41$	−109.087	−0.415524	−0.207762	+	0.978179i	$0.566618\pi$
$42$	284.491i	1.04519i
$43$	− 121.750i	− 0.431783i	−0.976417	−	0.215891i	$-0.930734\pi$
$43$	− 121.750i	− 0.431783i	0.976417	−	0.215891i	$-0.0692657\pi$
$44$	−144.240	−0.494204
$45$	0	0
$46$	−62.7678	−0.201187
$47$	519.530i	1.61237i	0.591665	+	0.806184i	$0.298471\pi$
$47$	519.530i	1.61237i	−0.591665	+	0.806184i	$0.701529\pi$
$48$	− 9.12396i	− 0.0274361i
$49$	−82.9413	−0.241811
$50$	0	0
$51$	−218.852	−0.600891
$52$	205.324i	0.547565i
$53$	− 542.673i	− 1.40645i	−0.710967	−	0.703226i	$-0.751742\pi$
$53$	− 542.673i	− 1.40645i	0.710967	−	0.703226i	$-0.248258\pi$
$54$	124.061	0.312640
$55$	0	0
$56$	484.839	1.15695
$57$	183.154i	0.425602i
$58$	− 144.583i	− 0.327322i
$59$	−109.478	−0.241574	−0.120787	−	0.992678i	$-0.538542\pi$
$59$	−109.478	−0.241574	−0.120787	+	0.992678i	$0.538542\pi$
$60$	0	0
$61$	−89.6156	−0.188100	−0.0940501	−	0.995567i	$-0.529981\pi$
$61$	−89.6156	−0.188100	−0.0940501	+	0.995567i	$0.529981\pi$
$62$	1116.59i	2.28721i
$63$	185.745i	0.371455i
$64$	823.664	1.60872
$65$	0	0
$66$	−151.630	−0.282794
$67$	− 488.446i	− 0.890644i	−0.895371	−	0.445322i	$-0.853089\pi$
$67$	− 488.446i	− 0.890644i	0.895371	−	0.445322i	$-0.146911\pi$
$68$	956.581i	1.70592i
$69$	−40.9814	−0.0715011
$70$	0	0
$71$	837.423	1.39977	0.699887	−	0.714254i	$-0.253234\pi$
$71$	837.423	1.39977	0.699887	+	0.714254i	$0.253234\pi$
$72$	− 211.429i	− 0.346072i
$73$	351.216i	0.563105i	0.959546	+	0.281553i	$0.0908494\pi$
$73$	351.216i	0.563105i	−0.959546	+	0.281553i	$0.909151\pi$
$74$	300.512	0.472078
$75$	0	0
$76$	800.547	1.20828
$77$	− 227.022i	− 0.335994i
$78$	215.845i	0.313328i
$79$	831.205	1.18377	0.591885	−	0.806022i	$-0.298384\pi$
$79$	831.205	1.18377	0.591885	+	0.806022i	$0.298384\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	501.238i	0.675031i
$83$	1389.13i	1.83707i	0.395335	+	0.918537i	$0.370629\pi$
$83$	1389.13i	1.83707i	−0.395335	+	0.918537i	$0.629371\pi$
$84$	811.873	1.05456
$85$	0	0
$86$	−559.423	−0.701443
$87$	− 94.3988i	− 0.116329i
$88$	258.413i	0.313034i
$89$	−1523.70	−1.81474	−0.907369	−	0.420335i	$-0.861912\pi$
$89$	−1523.70	−1.81474	−0.907369	+	0.420335i	$0.861912\pi$
$90$	0	0
$91$	−323.164	−0.372273
$92$	179.125i	0.202990i
$93$	729.025i	0.812864i
$94$	2387.17	2.61933
$95$	0	0
$96$	521.888	0.554843
$97$	426.612i	0.446555i	0.974755	+	0.223278i	$0.0716757\pi$
$97$	426.612i	0.446555i	−0.974755	+	0.223278i	$0.928324\pi$
$98$	381.103i	0.392829i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	74.1387	0.0730403	0.0365202	−	0.999333i	$-0.488373\pi$
$101$	74.1387	0.0730403	0.0365202	+	0.999333i	$0.488373\pi$
$102$	1005.59i	0.976163i
$103$	− 69.3916i	− 0.0663821i	−0.999449	−	0.0331911i	$-0.989433\pi$
$103$	− 69.3916i	− 0.0663821i	0.999449	−	0.0331911i	$-0.0105670\pi$
$104$	367.850	0.346833
$105$	0	0
$106$	−2493.51	−2.28482
$107$	− 1141.71i	− 1.03152i	−0.856733	−	0.515761i	$-0.827509\pi$
$107$	− 1141.71i	− 1.03152i	0.856733	−	0.515761i	$-0.172491\pi$
$108$	− 354.043i	− 0.315443i
$109$	2226.85	1.95682	0.978409	−	0.206680i	$-0.0662659\pi$
$109$	2226.85	1.95682	0.978409	+	0.206680i	$0.0662659\pi$
$110$	0	0
$111$	196.205	0.167775
$112$	− 62.7678i	− 0.0529554i
$113$	− 1719.76i	− 1.43169i	−0.698257	−	0.715847i	$-0.746041\pi$
$113$	− 1719.76i	− 1.43169i	0.698257	−	0.715847i	$-0.253959\pi$
$114$	841.566	0.691402
$115$	0	0
$116$	−412.608	−0.330256
$117$	140.926i	0.111356i
$118$	503.038i	0.392444i
$119$	−1505.58	−1.15980
$120$	0	0
$121$	121.000	0.0909091
$122$	411.771i	0.305574i
$123$	327.260i	0.239903i
$124$	3186.49	2.30771
$125$	0	0
$126$	853.472	0.603439
$127$	1601.63i	1.11907i	0.828807	+	0.559534i	$0.189020\pi$
$127$	1601.63i	1.11907i	−0.828807	+	0.559534i	$0.810980\pi$
$128$	− 2392.91i	− 1.65239i
$129$	−365.249	−0.249290
$130$	0	0
$131$	2004.13	1.33665	0.668327	−	0.743868i	$-0.267011\pi$
$131$	2004.13	1.33665	0.668327	+	0.743868i	$0.267011\pi$
$132$	432.719i	0.285329i
$133$	1260.00i	0.821471i
$134$	−2244.34	−1.44687
$135$	0	0
$136$	1713.77	1.08055
$137$	1672.85i	1.04322i	0.853184	+	0.521610i	$0.174669\pi$
$137$	1672.85i	1.04322i	−0.853184	+	0.521610i	$0.825331\pi$
$138$	188.303i	0.116155i
$139$	−2540.38	−1.55016	−0.775080	−	0.631863i	$-0.782291\pi$
$139$	−2540.38	−1.55016	−0.775080	+	0.631863i	$0.782291\pi$
$140$	0	0
$141$	1558.59	0.930901
$142$	− 3847.84i	− 2.27397i
$143$	− 172.243i	− 0.100725i
$144$	−27.3719	−0.0158402
$145$	0	0
$146$	1613.79	0.914780
$147$	248.824i	0.139610i
$148$	− 857.594i	− 0.476310i
$149$	−3090.68	−1.69932	−0.849658	−	0.527334i	$-0.823192\pi$
$149$	−3090.68	−1.69932	−0.849658	+	0.527334i	$0.823192\pi$
$150$	0	0
$151$	1358.74	0.732267	0.366134	−	0.930562i	$-0.380681\pi$
$151$	1358.74	0.732267	0.366134	+	0.930562i	$0.380681\pi$
$152$	− 1434.22i	− 0.765335i
$153$	656.557i	0.346925i
$154$	−1043.13	−0.545831
$155$	0	0
$156$	615.973	0.316137
$157$	1011.95i	0.514411i	0.966357	+	0.257205i	$0.0828017\pi$
$157$	1011.95i	0.514411i	−0.966357	+	0.257205i	$0.917198\pi$
$158$	− 3819.27i	− 1.92307i
$159$	−1628.02	−0.812015
$160$	0	0
$161$	−281.929	−0.138007
$162$	− 372.183i	− 0.180503i
$163$	− 2816.37i	− 1.35334i	−0.736285	−	0.676672i	$-0.763422\pi$
$163$	− 2816.37i	− 1.35334i	0.736285	−	0.676672i	$-0.236578\pi$
$164$	1430.42	0.681081
$165$	0	0
$166$	6382.87	2.98438
$167$	− 3448.89i	− 1.59810i	−0.601262	−	0.799052i	$-0.705335\pi$
$167$	− 3448.89i	− 1.59810i	0.601262	−	0.799052i	$-0.294665\pi$
$168$	− 1454.52i	− 0.667966i
$169$	1951.81	0.888399
$170$	0	0
$171$	549.462	0.245722
$172$	1596.47i	0.707730i
$173$	− 2287.85i	− 1.00545i	−0.864448	−	0.502723i	$-0.832332\pi$
$173$	− 2287.85i	− 1.00545i	0.864448	−	0.502723i	$-0.167668\pi$
$174$	−433.749	−0.188979
$175$	0	0
$176$	33.4545	0.0143280
$177$	328.435i	0.139473i
$178$	7001.17i	2.94809i
$179$	−3249.06	−1.35668	−0.678340	−	0.734748i	$-0.737300\pi$
$179$	−3249.06	−1.35668	−0.678340	+	0.734748i	$0.737300\pi$
$180$	0	0
$181$	1170.45	0.480655	0.240328	−	0.970692i	$-0.422745\pi$
$181$	1170.45	0.480655	0.240328	+	0.970692i	$0.422745\pi$
$182$	1484.89i	0.604767i
$183$	268.847i	0.108600i
$184$	320.913	0.128576
$185$	0	0
$186$	3349.76	1.32052
$187$	− 802.458i	− 0.313805i
$188$	− 6812.44i	− 2.64281i
$189$	557.235	0.214460
$190$	0	0
$191$	−2760.35	−1.04572	−0.522859	−	0.852419i	$-0.675134\pi$
$191$	−2760.35	−1.04572	−0.522859	+	0.852419i	$0.675134\pi$
$192$	− 2470.99i	− 0.928794i
$193$	− 1250.61i	− 0.466430i	−0.972425	−	0.233215i	$-0.925075\pi$
$193$	− 1250.61i	− 0.466430i	0.972425	−	0.233215i	$-0.0749245\pi$
$194$	1960.22	0.725441
$195$	0	0
$196$	1087.58	0.396350
$197$	143.991i	0.0520756i	0.999661	+	0.0260378i	$0.00828903\pi$
$197$	143.991i	0.0520756i	−0.999661	+	0.0260378i	$0.991711\pi$
$198$	454.891i	0.163271i
$199$	−761.249	−0.271174	−0.135587	−	0.990765i	$-0.543292\pi$
$199$	−761.249	−0.271174	−0.135587	+	0.990765i	$0.543292\pi$
$200$	0	0
$201$	−1465.34	−0.514213
$202$	− 340.657i	− 0.118656i
$203$	− 649.411i	− 0.224531i
$204$	2869.74	0.984913
$205$	0	0
$206$	−318.844	−0.107840
$207$	122.944i	0.0412812i
$208$	− 47.6223i	− 0.0158751i
$209$	−671.564	−0.222263
$210$	0	0
$211$	3976.58	1.29743	0.648717	−	0.761029i	$-0.275306\pi$
$211$	3976.58	1.29743	0.648717	+	0.761029i	$0.275306\pi$
$212$	7115.91i	2.30530i
$213$	− 2512.27i	− 0.808159i
$214$	−5245.97	−1.67573
$215$	0	0
$216$	−634.287	−0.199805
$217$	5015.29i	1.56894i
$218$	− 10232.0i	− 3.17890i
$219$	1053.65	0.325109
$220$	0	0
$221$	−1142.29	−0.347688
$222$	− 901.535i	− 0.272555i
$223$	908.084i	0.272690i	0.990661	+	0.136345i	$0.0435355\pi$
$223$	908.084i	0.272690i	−0.990661	+	0.136345i	$0.956464\pi$
$224$	3590.30	1.07092
$225$	0	0
$226$	−7902.05	−2.32583
$227$	2062.15i	0.602951i	0.953474	+	0.301475i	$0.0974791\pi$
$227$	2062.15i	0.602951i	−0.953474	+	0.301475i	$0.902521\pi$
$228$	− 2401.64i	− 0.697599i
$229$	−4077.47	−1.17662	−0.588312	−	0.808634i	$-0.700207\pi$
$229$	−4077.47	−1.17662	−0.588312	+	0.808634i	$0.700207\pi$
$230$	0	0
$231$	−681.065	−0.193986
$232$	739.209i	0.209187i
$233$	1682.76i	0.473138i	0.971615	+	0.236569i	$0.0760229\pi$
$233$	1682.76i	0.473138i	−0.971615	+	0.236569i	$0.923977\pi$
$234$	647.534	0.180900
$235$	0	0
$236$	1435.56	0.395961
$237$	− 2493.62i	− 0.683450i
$238$	6917.93i	1.88413i
$239$	−4024.96	−1.08934	−0.544672	−	0.838649i	$-0.683346\pi$
$239$	−4024.96	−1.08934	−0.544672	+	0.838649i	$0.683346\pi$
$240$	0	0
$241$	−2784.27	−0.744194	−0.372097	−	0.928194i	$-0.621361\pi$
$241$	−2784.27	−0.744194	−0.372097	+	0.928194i	$0.621361\pi$
$242$	− 555.978i	− 0.147684i
$243$	− 243.000i	− 0.0641500i
$244$	1175.10	0.308313
$245$	0	0
$246$	1503.71	0.389729
$247$	955.968i	0.246262i
$248$	− 5708.78i	− 1.46173i
$249$	4167.40	1.06064
$250$	0	0
$251$	−1827.60	−0.459591	−0.229796	−	0.973239i	$-0.573806\pi$
$251$	−1827.60	−0.459591	−0.229796	+	0.973239i	$0.573806\pi$
$252$	− 2435.62i	− 0.608848i
$253$	− 150.265i	− 0.0373402i
$254$	7359.26	1.81796
$255$	0	0
$256$	−4405.79	−1.07563
$257$	− 585.171i	− 0.142031i	−0.997475	−	0.0710155i	$-0.977376\pi$
$257$	− 585.171i	− 0.142031i	0.997475	−	0.0710155i	$-0.0226240\pi$
$258$	1678.27i	0.404978i
$259$	1349.78	0.323828
$260$	0	0
$261$	−283.196	−0.0671625
$262$	− 9208.69i	− 2.17143i
$263$	− 238.098i	− 0.0558241i	−0.999610	−	0.0279120i	$-0.991114\pi$
$263$	− 238.098i	− 0.0558241i	0.999610	−	0.0279120i	$-0.00888583\pi$
$264$	775.240	0.180730
$265$	0	0
$266$	5789.51	1.33450
$267$	4571.09i	1.04774i
$268$	6404.84i	1.45984i
$269$	−4618.46	−1.04681	−0.523406	−	0.852083i	$-0.675339\pi$
$269$	−4618.46	−1.04681	−0.523406	+	0.852083i	$0.675339\pi$
$270$	0	0
$271$	−143.439	−0.0321525	−0.0160762	−	0.999871i	$-0.505117\pi$
$271$	−143.439	−0.0321525	−0.0160762	+	0.999871i	$0.505117\pi$
$272$	− 221.867i	− 0.0494582i
$273$	969.493i	0.214932i
$274$	7686.51	1.69474
$275$	0	0
$276$	537.376	0.117197
$277$	8602.51i	1.86597i	0.359911	+	0.932987i	$0.382807\pi$
$277$	8602.51i	1.86597i	−0.359911	+	0.932987i	$0.617193\pi$
$278$	11672.7i	2.51828i
$279$	2187.07	0.469307
$280$	0	0
$281$	−2992.81	−0.635360	−0.317680	−	0.948198i	$-0.602904\pi$
$281$	−2992.81	−0.635360	−0.317680	+	0.948198i	$0.602904\pi$
$282$	− 7161.50i	− 1.51227i
$283$	− 6858.89i	− 1.44070i	−0.693610	−	0.720351i	$-0.743981\pi$
$283$	− 6858.89i	− 1.44070i	0.693610	−	0.720351i	$-0.256019\pi$
$284$	−10980.9	−2.29435
$285$	0	0
$286$	−791.431	−0.163630
$287$	2251.37i	0.463046i
$288$	− 1565.66i	− 0.320339i
$289$	−408.809	−0.0832096
$290$	0	0
$291$	1279.84	0.257819
$292$	− 4605.39i	− 0.922979i
$293$	4049.70i	0.807461i	0.914878	+	0.403731i	$0.132287\pi$
$293$	4049.70i	0.807461i	−0.914878	+	0.403731i	$0.867713\pi$
$294$	1143.31	0.226800
$295$	0	0
$296$	−1536.43	−0.301699
$297$	297.000i	0.0580259i
$298$	14201.2i	2.76059i
$299$	−213.901	−0.0413720
$300$	0	0
$301$	−2512.71	−0.481164
$302$	− 6243.20i	− 1.18959i
$303$	− 222.416i	− 0.0421699i
$304$	−185.677	−0.0350305
$305$	0	0
$306$	3016.78	0.563588
$307$	9572.69i	1.77962i	0.456335	+	0.889808i	$0.349162\pi$
$307$	9572.69i	1.77962i	−0.456335	+	0.889808i	$0.650838\pi$
$308$	2976.87i	0.550724i
$309$	−208.175	−0.0383257
$310$	0	0
$311$	5396.42	0.983932	0.491966	−	0.870614i	$-0.336278\pi$
$311$	5396.42	0.983932	0.491966	+	0.870614i	$0.336278\pi$
$312$	− 1103.55i	− 0.200244i
$313$	9755.04i	1.76162i	0.473469	+	0.880811i	$0.343002\pi$
$313$	9755.04i	1.76162i	−0.473469	+	0.880811i	$0.656998\pi$
$314$	4649.77	0.835674
$315$	0	0
$316$	−10899.3	−1.94030
$317$	4353.75i	0.771391i	0.922626	+	0.385695i	$0.126038\pi$
$317$	4353.75i	0.771391i	−0.922626	+	0.385695i	$0.873962\pi$
$318$	7480.52i	1.31914i
$319$	346.129	0.0607508
$320$	0	0
$321$	−3425.12	−0.595549
$322$	1295.42i	0.224196i
$323$	4453.74i	0.767221i
$324$	−1062.13	−0.182121
$325$	0	0
$326$	−12940.8	−2.19854
$327$	− 6680.54i	− 1.12977i
$328$	− 2562.68i	− 0.431404i
$329$	10722.2	1.79677
$330$	0	0
$331$	5387.64	0.894656	0.447328	−	0.894370i	$-0.352376\pi$
$331$	5387.64	0.894656	0.447328	+	0.894370i	$0.352376\pi$
$332$	− 18215.3i	− 3.01113i
$333$	− 588.616i	− 0.0968648i
$334$	−15847.2	−2.59616
$335$	0	0
$336$	−188.303	−0.0305738
$337$	4500.27i	0.727434i	0.931509	+	0.363717i	$0.118492\pi$
$337$	4500.27i	0.727434i	−0.931509	+	0.363717i	$0.881508\pi$
$338$	− 8968.30i	− 1.44323i
$339$	−5159.28	−0.826589
$340$	0	0
$341$	−2673.09	−0.424504
$342$	− 2524.70i	− 0.399181i
$343$	− 5367.18i	− 0.844899i
$344$	2860.16	0.448283
$345$	0	0
$346$	−10512.4	−1.63337
$347$	− 5906.32i	− 0.913740i	−0.889533	−	0.456870i	$-0.848970\pi$
$347$	− 5906.32i	− 0.913740i	0.889533	−	0.456870i	$-0.151030\pi$
$348$	1237.82i	0.190673i
$349$	−3636.26	−0.557721	−0.278860	−	0.960332i	$-0.589957\pi$
$349$	−3636.26	−0.557721	−0.278860	+	0.960332i	$0.589957\pi$
$350$	0	0
$351$	422.778	0.0642912
$352$	1913.59i	0.289757i
$353$	210.408i	0.0317248i	0.999874	+	0.0158624i	$0.00504938\pi$
$353$	210.408i	0.0317248i	−0.999874	+	0.0158624i	$0.994951\pi$
$354$	1509.11	0.226577
$355$	0	0
$356$	19979.8	2.97451
$357$	4516.75i	0.669612i
$358$	14928.9i	2.20396i
$359$	−2499.68	−0.367488	−0.183744	−	0.982974i	$-0.558822\pi$
$359$	−2499.68	−0.367488	−0.183744	+	0.982974i	$0.558822\pi$
$360$	0	0
$361$	−3131.74	−0.456588
$362$	− 5378.03i	− 0.780837i
$363$	− 363.000i	− 0.0524864i
$364$	4237.56	0.610188
$365$	0	0
$366$	1235.31	0.176423
$367$	− 5748.70i	− 0.817656i	−0.912612	−	0.408828i	$-0.865938\pi$
$367$	− 5748.70i	− 0.817656i	0.912612	−	0.408828i	$-0.134062\pi$
$368$	− 41.5458i	− 0.00588512i
$369$	981.781	0.138508
$370$	0	0
$371$	−11199.9	−1.56730
$372$	− 9559.48i	− 1.33236i
$373$	4467.78i	0.620196i	0.950705	+	0.310098i	$0.100362\pi$
$373$	4467.78i	0.620196i	−0.950705	+	0.310098i	$0.899638\pi$
$374$	−3687.18	−0.509785
$375$	0	0
$376$	−12204.9	−1.67398
$377$	− 492.712i	− 0.0673103i
$378$	− 2560.42i	− 0.348396i
$379$	−7804.08	−1.05770	−0.528851	−	0.848715i	$-0.677377\pi$
$379$	−7804.08	−1.05770	−0.528851	+	0.848715i	$0.677377\pi$
$380$	0	0
$381$	4804.89	0.646094
$382$	12683.4i	1.69880i
$383$	− 11161.1i	− 1.48904i	−0.667597	−	0.744522i	$-0.732677\pi$
$383$	− 11161.1i	− 1.48904i	0.667597	−	0.744522i	$-0.267323\pi$
$384$	−7178.74	−0.954007
$385$	0	0
$386$	−5746.38	−0.757728
$387$	1095.75i	0.143928i
$388$	− 5594.04i	− 0.731944i
$389$	−8490.24	−1.10661	−0.553306	−	0.832978i	$-0.686634\pi$
$389$	−8490.24	−1.10661	−0.553306	+	0.832978i	$0.686634\pi$
$390$	0	0
$391$	−996.540	−0.128893
$392$	− 1948.47i	− 0.251052i
$393$	− 6012.39i	− 0.771717i
$394$	661.616	0.0845983
$395$	0	0
$396$	1298.16	0.164735
$397$	− 6019.74i	− 0.761013i	−0.924778	−	0.380507i	$-0.875750\pi$
$397$	− 6019.74i	− 0.761013i	0.924778	−	0.380507i	$-0.124250\pi$
$398$	3497.83i	0.440529i
$399$	3779.99	0.474277
$400$	0	0
$401$	−10398.8	−1.29499	−0.647495	−	0.762069i	$-0.724184\pi$
$401$	−10398.8	−1.29499	−0.647495	+	0.762069i	$0.724184\pi$
$402$	6733.01i	0.835354i
$403$	3805.13i	0.470340i
$404$	−972.158	−0.119720
$405$	0	0
$406$	−2983.95	−0.364756
$407$	719.420i	0.0876175i
$408$	− 5141.30i	− 0.623854i
$409$	4733.68	0.572287	0.286144	−	0.958187i	$-0.407627\pi$
$409$	4733.68	0.572287	0.286144	+	0.958187i	$0.407627\pi$
$410$	0	0
$411$	5018.55	0.602304
$412$	909.911i	0.108806i
$413$	2259.45i	0.269202i
$414$	564.910	0.0670624
$415$	0	0
$416$	2723.98	0.321044
$417$	7621.14i	0.894985i
$418$	3085.74i	0.361073i
$419$	8117.57	0.946466	0.473233	−	0.880937i	$-0.343087\pi$
$419$	8117.57	0.946466	0.473233	+	0.880937i	$0.343087\pi$
$420$	0	0
$421$	−9484.27	−1.09795	−0.548973	−	0.835840i	$-0.684981\pi$
$421$	−9484.27	−1.09795	−0.548973	+	0.835840i	$0.684981\pi$
$422$	− 18271.8i	− 2.10772i
$423$	− 4675.77i	− 0.537456i
$424$	12748.5	1.46020
$425$	0	0
$426$	−11543.5	−1.31288
$427$	1849.52i	0.209612i
$428$	14970.8i	1.69075i
$429$	−516.728	−0.0581536
$430$	0	0
$431$	9335.16	1.04329	0.521646	−	0.853162i	$-0.325318\pi$
$431$	9335.16	1.04329	0.521646	+	0.853162i	$0.325318\pi$
$432$	82.1157i	0.00914535i
$433$	− 2983.02i	− 0.331074i	−0.986204	−	0.165537i	$-0.947064\pi$
$433$	− 2983.02i	− 0.331074i	0.986204	−	0.165537i	$-0.0529357\pi$
$434$	23044.5	2.54878
$435$	0	0
$436$	−29200.0	−3.20739
$437$	833.988i	0.0912931i
$438$	− 4841.36i	− 0.528148i
$439$	5232.32	0.568850	0.284425	−	0.958698i	$-0.408197\pi$
$439$	5232.32	0.568850	0.284425	+	0.958698i	$0.408197\pi$
$440$	0	0
$441$	746.472	0.0806038
$442$	5248.68i	0.564828i
$443$	7517.71i	0.806269i	0.915141	+	0.403135i	$0.132079\pi$
$443$	7517.71i	0.806269i	−0.915141	+	0.403135i	$0.867921\pi$
$444$	−2572.78	−0.274997
$445$	0	0
$446$	4172.52	0.442992
$447$	9272.03i	0.981101i
$448$	− 16999.1i	− 1.79270i
$449$	−16070.9	−1.68916	−0.844581	−	0.535428i	$-0.820150\pi$
$449$	−16070.9	−1.68916	−0.844581	+	0.535428i	$0.820150\pi$
$450$	0	0
$451$	−1199.96	−0.125285
$452$	22550.7i	2.34667i
$453$	− 4076.21i	− 0.422775i
$454$	9475.29	0.979510
$455$	0	0
$456$	−4302.67	−0.441867
$457$	− 9718.51i	− 0.994776i	−0.867528	−	0.497388i	$-0.834293\pi$
$457$	− 9718.51i	− 0.994776i	0.867528	−	0.497388i	$-0.165707\pi$
$458$	18735.4i	1.91146i
$459$	1969.67	0.200297
$460$	0	0
$461$	−14538.0	−1.46877	−0.734385	−	0.678733i	$-0.762529\pi$
$461$	−14538.0	−1.46877	−0.734385	+	0.678733i	$0.762529\pi$
$462$	3129.40i	0.315136i
$463$	− 9978.17i	− 1.00157i	−0.865573	−	0.500783i	$-0.833045\pi$
$463$	− 9978.17i	− 1.00157i	0.865573	−	0.500783i	$-0.166955\pi$
$464$	95.6990	0.00957481
$465$	0	0
$466$	7732.03	0.768625
$467$	− 15188.2i	− 1.50498i	−0.658605	−	0.752489i	$-0.728853\pi$
$467$	− 15188.2i	− 1.50498i	0.658605	−	0.752489i	$-0.271147\pi$
$468$	− 1847.92i	− 0.182522i
$469$	−10080.7	−0.992503
$470$	0	0
$471$	3035.85	0.296995
$472$	− 2571.88i	− 0.250806i
$473$	− 1339.25i	− 0.130187i
$474$	−11457.8	−1.11028
$475$	0	0
$476$	19742.3	1.90102
$477$	4884.06i	0.468817i
$478$	18494.1i	1.76967i
$479$	−11330.8	−1.08083	−0.540415	−	0.841399i	$-0.681733\pi$
$479$	−11330.8	−1.08083	−0.540415	+	0.841399i	$0.681733\pi$
$480$	0	0
$481$	1024.09	0.0970779
$482$	12793.3i	1.20896i
$483$	845.788i	0.0796784i
$484$	−1586.64	−0.149008
$485$	0	0
$486$	−1116.55	−0.104213
$487$	− 19086.9i	− 1.77599i	−0.459850	−	0.887997i	$-0.652097\pi$
$487$	− 19086.9i	− 1.77599i	0.459850	−	0.887997i	$-0.347903\pi$
$488$	− 2105.26i	− 0.195288i
$489$	−8449.11	−0.781353
$490$	0	0
$491$	−8112.85	−0.745677	−0.372839	−	0.927896i	$-0.621616\pi$
$491$	−8112.85	−0.745677	−0.372839	+	0.927896i	$0.621616\pi$
$492$	− 4291.27i	− 0.393222i
$493$	− 2295.49i	− 0.209703i
$494$	4392.53	0.400060
$495$	0	0
$496$	−739.066	−0.0669053
$497$	− 17283.0i	− 1.55986i
$498$	− 19148.6i	− 1.72303i
$499$	−18329.1	−1.64433	−0.822167	−	0.569246i	$-0.807235\pi$
$499$	−18329.1	−1.64433	−0.822167	+	0.569246i	$0.807235\pi$
$500$	0	0
$501$	−10346.7	−0.922666
$502$	8397.58i	0.746618i
$503$	7739.57i	0.686064i	0.939324	+	0.343032i	$0.111454\pi$
$503$	7739.57i	0.686064i	−0.939324	+	0.343032i	$0.888546\pi$
$504$	−4363.55	−0.385651
$505$	0	0
$506$	−690.446	−0.0606602
$507$	− 5855.44i	− 0.512918i
$508$	− 21001.7i	− 1.83425i
$509$	−15914.9	−1.38589	−0.692943	−	0.720993i	$-0.743686\pi$
$509$	−15914.9	−1.38589	−0.692943	+	0.720993i	$0.743686\pi$
$510$	0	0
$511$	7248.51	0.627505
$512$	1100.65i	0.0950048i
$513$	− 1648.38i	− 0.141867i
$514$	−2688.78	−0.230733
$515$	0	0
$516$	4789.40	0.408608
$517$	5714.83i	0.486147i
$518$	− 6202.07i	− 0.526068i
$519$	−6863.56	−0.580495
$520$	0	0
$521$	2274.50	0.191262	0.0956312	−	0.995417i	$-0.469513\pi$
$521$	2274.50	0.191262	0.0956312	+	0.995417i	$0.469513\pi$
$522$	1301.25i	0.109107i
$523$	10971.1i	0.917274i	0.888624	+	0.458637i	$0.151662\pi$
$523$	10971.1i	0.917274i	−0.888624	+	0.458637i	$0.848338\pi$
$524$	−26279.6	−2.19089
$525$	0	0
$526$	−1094.02	−0.0906877
$527$	17727.6i	1.46533i
$528$	− 100.364i	− 0.00827228i
$529$	11980.4	0.984663
$530$	0	0
$531$	985.306	0.0805247
$532$	− 16522.0i	− 1.34646i
$533$	1708.13i	0.138813i
$534$	21003.5	1.70208
$535$	0	0
$536$	11474.6	0.924680
$537$	9747.17i	0.783280i
$538$	21221.2i	1.70058i
$539$	−912.355	−0.0729089
$540$	0	0
$541$	5313.05	0.422229	0.211115	−	0.977461i	$-0.432291\pi$
$541$	5313.05	0.422229	0.211115	+	0.977461i	$0.432291\pi$
$542$	659.084i	0.0522326i
$543$	− 3511.34i	− 0.277506i
$544$	12690.7	1.00020
$545$	0	0
$546$	4454.68	0.349162
$547$	− 20685.1i	− 1.61688i	−0.588581	−	0.808439i	$-0.700313\pi$
$547$	− 20685.1i	− 1.61688i	0.588581	−	0.808439i	$-0.299687\pi$
$548$	− 21935.6i	− 1.70993i
$549$	806.541	0.0627000
$550$	0	0
$551$	−1921.06	−0.148529
$552$	− 962.739i	− 0.0742335i
$553$	− 17154.7i	− 1.31915i
$554$	39527.3	3.03132
$555$	0	0
$556$	33311.2	2.54085
$557$	10853.8i	0.825659i	0.910808	+	0.412830i	$0.135460\pi$
$557$	10853.8i	0.825659i	−0.910808	+	0.412830i	$0.864540\pi$
$558$	− 10049.3i	− 0.762402i
$559$	−1906.41	−0.144244
$560$	0	0
$561$	−2407.37	−0.181175
$562$	13751.5i	1.03216i
$563$	− 15381.2i	− 1.15141i	−0.817658	−	0.575704i	$-0.804728\pi$
$563$	− 15381.2i	− 1.15141i	0.817658	−	0.575704i	$-0.195272\pi$
$564$	−20437.3	−1.52583
$565$	0	0
$566$	−31515.6	−2.34046
$567$	− 1671.71i	− 0.123818i
$568$	19672.9i	1.45327i
$569$	1348.88	0.0993814	0.0496907	−	0.998765i	$-0.484176\pi$
$569$	1348.88	0.0993814	0.0496907	+	0.998765i	$0.484176\pi$
$570$	0	0
$571$	3463.51	0.253841	0.126920	−	0.991913i	$-0.459491\pi$
$571$	3463.51	0.253841	0.126920	+	0.991913i	$0.459491\pi$
$572$	2258.57i	0.165097i
$573$	8281.05i	0.603745i
$574$	10344.7	0.752231
$575$	0	0
$576$	−7412.97	−0.536239
$577$	− 12052.6i	− 0.869598i	−0.900528	−	0.434799i	$-0.856819\pi$
$577$	− 12052.6i	− 0.869598i	0.900528	−	0.434799i	$-0.143181\pi$
$578$	1878.42i	0.135176i
$579$	−3751.83	−0.269293
$580$	0	0
$581$	28669.4	2.04717
$582$	− 5880.66i	− 0.418834i
$583$	− 5969.41i	− 0.424061i
$584$	−8250.80	−0.584624
$585$	0	0
$586$	18607.8	1.31174
$587$	11133.1i	0.782813i	0.920218	+	0.391407i	$0.128011\pi$
$587$	11133.1i	0.782813i	−0.920218	+	0.391407i	$0.871989\pi$
$588$	− 3262.75i	− 0.228833i
$589$	14836.0	1.03787
$590$	0	0
$591$	431.972	0.0300659
$592$	198.908i	0.0138092i
$593$	− 7939.69i	− 0.549821i	−0.961470	−	0.274911i	$-0.911352\pi$
$593$	− 7939.69i	− 0.549821i	0.961470	−	0.274911i	$-0.0886482\pi$
$594$	1364.67	0.0942646
$595$	0	0
$596$	40527.1	2.78533
$597$	2283.75i	0.156562i
$598$	982.846i	0.0672100i
$599$	19474.7	1.32840	0.664202	−	0.747553i	$-0.268771\pi$
$599$	19474.7	1.32840	0.664202	+	0.747553i	$0.268771\pi$
$600$	0	0
$601$	−19946.1	−1.35377	−0.676887	−	0.736087i	$-0.736671\pi$
$601$	−19946.1	−1.35377	−0.676887	+	0.736087i	$0.736671\pi$
$602$	11545.6i	0.781664i
$603$	4396.01i	0.296881i
$604$	−17816.7	−1.20025
$605$	0	0
$606$	−1021.97	−0.0685061
$607$	− 1427.44i	− 0.0954496i	−0.998861	−	0.0477248i	$-0.984803\pi$
$607$	− 1427.44i	− 0.0954496i	0.998861	−	0.0477248i	$-0.0151970\pi$
$608$	− 10620.6i	− 0.708427i
$609$	−1948.23	−0.129633
$610$	0	0
$611$	8135.03	0.538638
$612$	− 8609.23i	− 0.568640i
$613$	− 8029.40i	− 0.529045i	−0.964380	−	0.264522i	$-0.914786\pi$
$613$	− 8029.40i	− 0.529045i	0.964380	−	0.264522i	$-0.0852143\pi$
$614$	43985.1	2.89103
$615$	0	0
$616$	5333.22	0.348834
$617$	− 20795.5i	− 1.35688i	−0.734655	−	0.678440i	$-0.762656\pi$
$617$	− 20795.5i	− 1.35688i	0.734655	−	0.678440i	$-0.237344\pi$
$618$	956.533i	0.0622612i
$619$	−1677.43	−0.108920	−0.0544602	−	0.998516i	$-0.517344\pi$
$619$	−1677.43	−0.108920	−0.0544602	+	0.998516i	$0.517344\pi$
$620$	0	0
$621$	368.832	0.0238337
$622$	− 24795.8i	− 1.59842i
$623$	31446.6i	2.02228i
$624$	−142.867	−0.00916547
$625$	0	0
$626$	44823.0	2.86180
$627$	2014.69i	0.128324i
$628$	− 13269.4i	− 0.843165i
$629$	4771.11	0.302443
$630$	0	0
$631$	−25225.2	−1.59144	−0.795719	−	0.605666i	$-0.792907\pi$
$631$	−25225.2	−1.59144	−0.795719	+	0.605666i	$0.792907\pi$
$632$	19526.8i	1.22901i
$633$	− 11929.7i	− 0.749074i
$634$	20004.8	1.25315
$635$	0	0
$636$	21347.7	1.33096
$637$	1298.73i	0.0807812i
$638$	− 1590.41i	− 0.0986912i
$639$	−7536.81	−0.466591
$640$	0	0
$641$	15165.3	0.934468	0.467234	−	0.884134i	$-0.345251\pi$
$641$	15165.3	0.934468	0.467234	+	0.884134i	$0.345251\pi$
$642$	15737.9i	0.967486i
$643$	27156.1i	1.66553i	0.553630	+	0.832763i	$0.313242\pi$
$643$	27156.1i	1.66553i	−0.553630	+	0.832763i	$0.686758\pi$
$644$	3696.85	0.226206
$645$	0	0
$646$	20464.3	1.24637
$647$	− 29154.9i	− 1.77156i	−0.464110	−	0.885778i	$-0.653626\pi$
$647$	− 29154.9i	− 1.77156i	0.464110	−	0.885778i	$-0.346374\pi$
$648$	1902.86i	0.115357i
$649$	−1204.26	−0.0728374
$650$	0	0
$651$	15045.9	0.905828
$652$	36930.2i	2.21825i
$653$	− 19141.7i	− 1.14713i	−0.819161	−	0.573564i	$-0.805560\pi$
$653$	− 19141.7i	− 1.14713i	0.819161	−	0.573564i	$-0.194440\pi$
$654$	−30696.1	−1.83534
$655$	0	0
$656$	−331.768	−0.0197460
$657$	− 3160.94i	− 0.187702i
$658$	− 49267.2i	− 2.91890i
$659$	24939.6	1.47422	0.737110	−	0.675773i	$-0.236190\pi$
$659$	24939.6	1.47422	0.737110	+	0.675773i	$0.236190\pi$
$660$	0	0
$661$	22617.7	1.33090	0.665452	−	0.746440i	$-0.268239\pi$
$661$	22617.7	1.33090	0.665452	+	0.746440i	$0.268239\pi$
$662$	− 24755.4i	− 1.45339i
$663$	3426.88i	0.200738i
$664$	−32633.7	−1.90728
$665$	0	0
$666$	−2704.61	−0.157359
$667$	− 429.843i	− 0.0249529i
$668$	45224.3i	2.61943i
$669$	2724.25	0.157438
$670$	0	0
$671$	−985.772	−0.0567143
$672$	− 10770.9i	− 0.618298i
$673$	− 13855.8i	− 0.793615i	−0.917902	−	0.396807i	$-0.870118\pi$
$673$	− 13855.8i	− 0.793615i	0.917902	−	0.396807i	$-0.129882\pi$
$674$	20678.1	1.18174
$675$	0	0
$676$	−25593.5	−1.45616
$677$	24992.8i	1.41884i	0.704787	+	0.709419i	$0.251043\pi$
$677$	24992.8i	1.41884i	−0.704787	+	0.709419i	$0.748957\pi$
$678$	23706.1i	1.34282i
$679$	8804.57	0.497626
$680$	0	0
$681$	6186.46	0.348114
$682$	12282.5i	0.689619i
$683$	− 14420.5i	− 0.807887i	−0.914784	−	0.403943i	$-0.867639\pi$
$683$	− 14420.5i	− 0.807887i	0.914784	−	0.403943i	$-0.132361\pi$
$684$	−7204.93	−0.402759
$685$	0	0
$686$	−24661.4	−1.37256
$687$	12232.4i	0.679324i
$688$	− 370.280i	− 0.0205186i
$689$	−8497.42	−0.469849
$690$	0	0
$691$	30552.4	1.68201	0.841005	−	0.541027i	$-0.181964\pi$
$691$	30552.4	1.68201	0.841005	+	0.541027i	$0.181964\pi$
$692$	29999.9i	1.64801i
$693$	2043.20i	0.111998i
$694$	−27138.7	−1.48440
$695$	0	0
$696$	2217.63	0.120774
$697$	7957.96i	0.432467i
$698$	16708.1i	0.906032i
$699$	5048.27	0.273166
$700$	0	0
$701$	−9151.47	−0.493076	−0.246538	−	0.969133i	$-0.579293\pi$
$701$	−9151.47	−0.493076	−0.246538	+	0.969133i	$0.579293\pi$
$702$	− 1942.60i	− 0.104443i
$703$	− 3992.86i	− 0.214216i
$704$	9060.30	0.485047
$705$	0	0
$706$	966.793	0.0515378
$707$	− 1530.10i	− 0.0813937i
$708$	− 4306.67i	− 0.228608i
$709$	6261.96	0.331697	0.165848	−	0.986151i	$-0.446964\pi$
$709$	6261.96	0.331697	0.165848	+	0.986151i	$0.446964\pi$
$710$	0	0
$711$	−7480.85	−0.394590
$712$	− 35794.9i	− 1.88409i
$713$	3319.60i	0.174362i
$714$	20753.8	1.08780
$715$	0	0
$716$	42603.9	2.22372
$717$	12074.9i	0.628933i
$718$	11485.7i	0.596995i
$719$	18228.7	0.945500	0.472750	−	0.881197i	$-0.343261\pi$
$719$	18228.7	0.945500	0.472750	+	0.881197i	$0.343261\pi$
$720$	0	0
$721$	−1432.13	−0.0739740
$722$	14389.9i	0.741740i
$723$	8352.81i	0.429660i
$724$	−15347.7	−0.787836
$725$	0	0
$726$	−1667.93	−0.0852655
$727$	7233.66i	0.369026i	0.982830	+	0.184513i	$0.0590707\pi$
$727$	7233.66i	0.369026i	−0.982830	+	0.184513i	$0.940929\pi$
$728$	− 7591.81i	− 0.386499i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−8881.73	−0.449388
$732$	− 3525.31i	− 0.178004i
$733$	− 13444.8i	− 0.677485i	−0.940879	−	0.338743i	$-0.889998\pi$
$733$	− 13444.8i	− 0.677485i	0.940879	−	0.338743i	$-0.110002\pi$
$734$	−26414.4	−1.32830
$735$	0	0
$736$	2376.41	0.119016
$737$	− 5372.90i	− 0.268539i
$738$	− 4511.14i	− 0.225010i
$739$	−18490.9	−0.920432	−0.460216	−	0.887807i	$-0.652228\pi$
$739$	−18490.9	−0.920432	−0.460216	+	0.887807i	$0.652228\pi$
$740$	0	0
$741$	2867.90	0.142180
$742$	51461.8i	2.54612i
$743$	− 25160.9i	− 1.24235i	−0.783674	−	0.621173i	$-0.786657\pi$
$743$	− 25160.9i	− 1.24235i	0.783674	−	0.621173i	$-0.213343\pi$
$744$	−17126.3	−0.843927
$745$	0	0
$746$	20528.8	1.00752
$747$	− 12502.2i	− 0.612358i
$748$	10522.4i	0.514354i
$749$	−23562.9	−1.14949
$750$	0	0
$751$	−13419.5	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$751$	−13419.5	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$752$	1580.06i	0.0766207i
$753$	5482.81i	0.265345i
$754$	−2263.94	−0.109347
$755$	0	0
$756$	−7306.86	−0.351518
$757$	7014.90i	0.336804i	0.985718	+	0.168402i	$0.0538607\pi$
$757$	7014.90i	0.336804i	−0.985718	+	0.168402i	$0.946139\pi$
$758$	35858.6i	1.71826i
$759$	−450.795	−0.0215584
$760$	0	0
$761$	−30156.9	−1.43651	−0.718256	−	0.695779i	$-0.755059\pi$
$761$	−30156.9	−1.43651	−0.718256	+	0.695779i	$0.755059\pi$
$762$	− 22077.8i	− 1.04960i
$763$	− 45958.4i	− 2.18061i
$764$	36195.7	1.71402
$765$	0	0
$766$	−51283.5	−2.41899
$767$	1714.26i	0.0807019i
$768$	13217.4i	0.621017i
$769$	−11292.2	−0.529530	−0.264765	−	0.964313i	$-0.585294\pi$
$769$	−11292.2	−0.529530	−0.264765	+	0.964313i	$0.585294\pi$
$770$	0	0
$771$	−1755.51	−0.0820016
$772$	16398.9i	0.764519i
$773$	8524.10i	0.396624i	0.980139	+	0.198312i	$0.0635460\pi$
$773$	8524.10i	0.396624i	−0.980139	+	0.198312i	$0.936454\pi$
$774$	5034.80	0.233814
$775$	0	0
$776$	−10022.0	−0.463621
$777$	− 4049.35i	− 0.186962i
$778$	39011.4i	1.79772i
$779$	6659.89	0.306310
$780$	0	0
$781$	9211.66	0.422047
$782$	4578.96i	0.209390i
$783$	849.589i	0.0387763i
$784$	−252.251	−0.0114910
$785$	0	0
$786$	−27626.1	−1.25368
$787$	14983.9i	0.678676i	0.940665	+	0.339338i	$0.110203\pi$
$787$	14983.9i	0.678676i	−0.940665	+	0.339338i	$0.889797\pi$
$788$	− 1888.10i	− 0.0853565i
$789$	−714.293	−0.0322300
$790$	0	0
$791$	−35493.0	−1.59543
$792$	− 2325.72i	− 0.104345i
$793$	1403.24i	0.0628380i
$794$	−27659.9	−1.23629
$795$	0	0
$796$	9982.04	0.444477
$797$	− 37172.3i	− 1.65208i	−0.563610	−	0.826041i	$-0.690588\pi$
$797$	− 37172.3i	− 1.65208i	0.563610	−	0.826041i	$-0.309412\pi$
$798$	− 17368.5i	− 0.770475i
$799$	37900.1	1.67811
$800$	0	0
$801$	13713.3	0.604913
$802$	47781.0i	2.10375i
$803$	3863.37i	0.169783i
$804$	19214.5	0.842841
$805$	0	0
$806$	17484.0	0.764080
$807$	13855.4i	0.604378i
$808$	1741.68i	0.0758316i
$809$	−23797.1	−1.03419	−0.517096	−	0.855928i	$-0.672987\pi$
$809$	−23797.1	−1.03419	−0.517096	+	0.855928i	$0.672987\pi$
$810$	0	0
$811$	8988.35	0.389178	0.194589	−	0.980885i	$-0.437663\pi$
$811$	8988.35	0.389178	0.194589	+	0.980885i	$0.437663\pi$
$812$	8515.54i	0.368026i
$813$	430.318i	0.0185633i
$814$	3305.63	0.142337
$815$	0	0
$816$	−665.600	−0.0285547
$817$	7432.98i	0.318295i
$818$	− 21750.6i	− 0.929696i
$819$	2908.48	0.124091
$820$	0	0
$821$	−25156.8	−1.06940	−0.534702	−	0.845041i	$-0.679576\pi$
$821$	−25156.8	−1.06940	−0.534702	+	0.845041i	$0.679576\pi$
$822$	− 23059.5i	− 0.978459i
$823$	1318.51i	0.0558447i	0.999610	+	0.0279224i	$0.00888912\pi$
$823$	1318.51i	0.0558447i	−0.999610	+	0.0279224i	$0.991111\pi$
$824$	1630.16	0.0689189
$825$	0	0
$826$	10381.9	0.437326
$827$	− 124.982i	− 0.00525519i	−0.999997	−	0.00262760i	$-0.999164\pi$
$827$	− 124.982i	− 0.00525519i	0.999997	−	0.00262760i	$-0.000836391\pi$
$828$	− 1612.13i	− 0.0676635i
$829$	8886.80	0.372318	0.186159	−	0.982520i	$-0.440396\pi$
$829$	8886.80	0.372318	0.186159	+	0.982520i	$0.440396\pi$
$830$	0	0
$831$	25807.5	1.07732
$832$	− 12897.3i	− 0.537419i
$833$	6050.63i	0.251671i
$834$	35018.0	1.45393
$835$	0	0
$836$	8806.02	0.364309
$837$	− 6561.22i	− 0.270955i
$838$	− 37299.1i	− 1.53756i
$839$	−2995.21	−0.123249	−0.0616247	−	0.998099i	$-0.519628\pi$
$839$	−2995.21	−0.123249	−0.0616247	+	0.998099i	$0.519628\pi$
$840$	0	0
$841$	−23398.9	−0.959403
$842$	43578.8i	1.78364i
$843$	8978.43i	0.366825i
$844$	−52143.6	−2.12661
$845$	0	0
$846$	−21484.5	−0.873111
$847$	− 2497.24i	− 0.101306i
$848$	− 1650.44i	− 0.0668355i
$849$	−20576.7	−0.831789
$850$	0	0
$851$	893.418	0.0359882
$852$	32942.7i	1.32464i
$853$	18130.5i	0.727757i	0.931446	+	0.363878i	$0.118548\pi$
$853$	18130.5i	0.727757i	−0.931446	+	0.363878i	$0.881452\pi$
$854$	8498.27	0.340521
$855$	0	0
$856$	26821.1	1.07094
$857$	− 26394.1i	− 1.05205i	−0.850470	−	0.526024i	$-0.823682\pi$
$857$	− 26394.1i	− 1.05205i	0.850470	−	0.526024i	$-0.176318\pi$
$858$	2374.29i	0.0944720i
$859$	29456.2	1.17000	0.585002	−	0.811032i	$-0.301094\pi$
$859$	29456.2	1.17000	0.585002	+	0.811032i	$0.301094\pi$
$860$	0	0
$861$	6754.12	0.267340
$862$	− 42893.7i	− 1.69486i
$863$	− 762.616i	− 0.0300808i	−0.999887	−	0.0150404i	$-0.995212\pi$
$863$	− 762.616i	− 0.0300808i	0.999887	−	0.0150404i	$-0.00478769\pi$
$864$	−4696.99	−0.184948
$865$	0	0
$866$	−13706.6	−0.537838
$867$	1226.43i	0.0480411i
$868$	− 65764.0i	− 2.57163i
$869$	9143.26	0.356920
$870$	0	0
$871$	−7648.29	−0.297535
$872$	52313.3i	2.03160i
$873$	− 3839.51i	− 0.148852i
$874$	3832.06	0.148308
$875$	0	0
$876$	−13816.2	−0.532882
$877$	− 44767.2i	− 1.72369i	−0.507168	−	0.861847i	$-0.669308\pi$
$877$	− 44767.2i	− 1.72369i	0.507168	−	0.861847i	$-0.330692\pi$
$878$	− 24041.8i	− 0.924112i
$879$	12149.1	0.466188
$880$	0	0
$881$	−32057.9	−1.22595	−0.612973	−	0.790104i	$-0.710027\pi$
$881$	−32057.9	−1.22595	−0.612973	+	0.790104i	$0.710027\pi$
$882$	− 3429.93i	− 0.130943i
$883$	7078.95i	0.269791i	0.990860	+	0.134896i	$0.0430699\pi$
$883$	7078.95i	0.269791i	−0.990860	+	0.134896i	$0.956930\pi$
$884$	14978.6	0.569891
$885$	0	0
$886$	34542.8	1.30981
$887$	25148.1i	0.951964i	0.879455	+	0.475982i	$0.157907\pi$
$887$	25148.1i	0.951964i	−0.879455	+	0.475982i	$0.842093\pi$
$888$	4609.28i	0.174186i
$889$	33055.0	1.24705
$890$	0	0
$891$	891.000	0.0335013
$892$	− 11907.4i	− 0.446963i
$893$	− 31718.0i	− 1.18858i
$894$	42603.6	1.59382
$895$	0	0
$896$	−49385.8	−1.84137
$897$	641.704i	0.0238862i
$898$	73843.6i	2.74409i
$899$	−7646.56	−0.283679
$900$	0	0
$901$	−39588.4	−1.46380
$902$	5513.62i	0.203529i
$903$	7538.14i	0.277800i
$904$	40400.8	1.48641
$905$	0	0
$906$	−18729.6	−0.686809
$907$	− 1269.76i	− 0.0464848i	−0.999730	−	0.0232424i	$-0.992601\pi$
$907$	− 1269.76i	− 0.0464848i	0.999730	−	0.0232424i	$-0.00739895\pi$
$908$	− 27040.4i	− 0.988289i
$909$	−667.248	−0.0243468
$910$	0	0
$911$	−33783.1	−1.22863	−0.614316	−	0.789060i	$-0.710568\pi$
$911$	−33783.1	−1.22863	−0.614316	+	0.789060i	$0.710568\pi$
$912$	557.030i	0.0202249i
$913$	15280.5i	0.553899i
$914$	−44655.1	−1.61604
$915$	0	0
$916$	53466.6	1.92859
$917$	− 41361.9i	− 1.48952i
$918$	− 9050.35i	− 0.325388i
$919$	−39262.5	−1.40930	−0.704652	−	0.709553i	$-0.748897\pi$
$919$	−39262.5	−1.40930	−0.704652	+	0.709553i	$0.748897\pi$
$920$	0	0
$921$	28718.1	1.02746
$922$	66800.1i	2.38606i
$923$	− 13112.7i	− 0.467618i
$924$	8930.61	0.317960
$925$	0	0
$926$	−45848.3	−1.62707
$927$	624.525i	0.0221274i
$928$	5473.95i	0.193633i
$929$	21175.0	0.747825	0.373913	−	0.927464i	$-0.378016\pi$
$929$	21175.0	0.747825	0.373913	+	0.927464i	$0.378016\pi$
$930$	0	0
$931$	5063.68	0.178255
$932$	− 22065.5i	− 0.775515i
$933$	− 16189.3i	− 0.568073i
$934$	−69787.5	−2.44488
$935$	0	0
$936$	−3310.65	−0.115611
$937$	5135.11i	0.179036i	0.995985	+	0.0895180i	$0.0285327\pi$
$937$	5135.11i	0.179036i	−0.995985	+	0.0895180i	$0.971467\pi$
$938$	46319.4i	1.61235i
$939$	29265.1	1.01707
$940$	0	0
$941$	−9702.77	−0.336133	−0.168067	−	0.985776i	$-0.553752\pi$
$941$	−9702.77	−0.336133	−0.168067	+	0.985776i	$0.553752\pi$
$942$	− 13949.3i	− 0.482477i
$943$	1490.18i	0.0514600i
$944$	−332.959	−0.0114798
$945$	0	0
$946$	−6153.65	−0.211493
$947$	699.579i	0.0240055i	0.999928	+	0.0120028i	$0.00382069\pi$
$947$	699.579i	0.0240055i	−0.999928	+	0.0120028i	$0.996179\pi$
$948$	32698.0i	1.12024i
$949$	5499.49	0.188115
$950$	0	0
$951$	13061.2	0.445363
$952$	− 35369.3i	− 1.20412i
$953$	42039.3i	1.42895i	0.699663	+	0.714473i	$0.253333\pi$
$953$	42039.3i	1.42895i	−0.699663	+	0.714473i	$0.746667\pi$
$954$	22441.6	0.761606
$955$	0	0
$956$	52778.1	1.78553
$957$	− 1038.39i	− 0.0350745i
$958$	52063.4i	1.75584i
$959$	34524.9	1.16253
$960$	0	0
$961$	29262.0	0.982243
$962$	− 4705.55i	− 0.157706i
$963$	10275.3i	0.343841i
$964$	36509.3	1.21980
$965$	0	0
$966$	3886.27	0.129440
$967$	32794.8i	1.09060i	0.838242	+	0.545299i	$0.183584\pi$
$967$	32794.8i	1.09060i	−0.838242	+	0.545299i	$0.816416\pi$
$968$	2842.55i	0.0943832i
$969$	13361.2	0.442955
$970$	0	0
$971$	−3322.53	−0.109810	−0.0549048	−	0.998492i	$-0.517486\pi$
$971$	−3322.53	−0.109810	−0.0549048	+	0.998492i	$0.517486\pi$
$972$	3186.39i	0.105148i
$973$	52429.3i	1.72745i
$974$	−87701.4	−2.88515
$975$	0	0
$976$	−272.550	−0.00893864
$977$	− 22192.5i	− 0.726716i	−0.931650	−	0.363358i	$-0.881630\pi$
$977$	− 22192.5i	− 0.726716i	0.931650	−	0.363358i	$-0.118370\pi$
$978$	38822.4i	1.26933i
$979$	−16760.7	−0.547164
$980$	0	0
$981$	−20041.6	−0.652272
$982$	37277.4i	1.21137i
$983$	7383.09i	0.239556i	0.992801	+	0.119778i	$0.0382183\pi$
$983$	7383.09i	0.239556i	−0.992801	+	0.119778i	$0.961782\pi$
$984$	−7688.04	−0.249071
$985$	0	0
$986$	−10547.4	−0.340668
$987$	− 32166.7i	− 1.03736i
$988$	− 12535.3i	− 0.403645i
$989$	−1663.16	−0.0534735
$990$	0	0
$991$	46260.8	1.48287	0.741434	−	0.671026i	$-0.234146\pi$
$991$	46260.8	1.48287	0.741434	+	0.671026i	$0.234146\pi$
$992$	− 42274.3i	− 1.35304i
$993$	− 16162.9i	− 0.516530i
$994$	−79413.1	−2.53403
$995$	0	0
$996$	−54645.9	−1.73847
$997$	− 41196.8i	− 1.30864i	−0.756217	−	0.654320i	$-0.772955\pi$
$997$	− 41196.8i	− 1.30864i	0.756217	−	0.654320i	$-0.227045\pi$
$998$	84219.5i	2.67127i
$999$	−1765.85	−0.0559249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.m.199.1		6
5.2	odd	4		165.4.a.g.1.3	✓	3
5.3	odd	4		825.4.a.p.1.1		3
5.4	even	2	inner	825.4.c.m.199.6		6
15.2	even	4		495.4.a.i.1.1		3
15.8	even	4		2475.4.a.z.1.3		3
55.32	even	4		1815.4.a.q.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.g.1.3	✓	3	5.2	odd	4
495.4.a.i.1.1		3	15.2	even	4
825.4.a.p.1.1		3	5.3	odd	4
825.4.c.m.199.1		6	1.1	even	1	trivial
825.4.c.m.199.6		6	5.4	even	2	inner
1815.4.a.q.1.1		3	55.32	even	4
2475.4.a.z.1.3		3	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.59486i q^{2} -3.00000i q^{3} -13.1127 q^{4} -13.7846 q^{6} -20.6383i q^{7} +23.4921i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-4.59486i q^{2} -3.00000i q^{3} -13.1127 q^{4} -13.7846 q^{6} -20.6383i q^{7} +23.4921i q^{8} -9.00000 q^{9} +11.0000 q^{11} +39.3381i q^{12} -15.6584i q^{13} -94.8302 q^{14} +3.04132 q^{16} -72.9507i q^{17} +41.3537i q^{18} -61.0513 q^{19} -61.9150 q^{21} -50.5434i q^{22} -13.6605i q^{23} +70.4764 q^{24} -71.9483 q^{26} +27.0000i q^{27} +270.624i q^{28} +31.4663 q^{29} -243.008 q^{31} +173.963i q^{32} -33.0000i q^{33} -335.198 q^{34} +118.014 q^{36} +65.4018i q^{37} +280.522i q^{38} -46.9753 q^{39} -109.087 q^{41} +284.491i q^{42} -121.750i q^{43} -144.240 q^{44} -62.7678 q^{46} +519.530i q^{47} -9.12396i q^{48} -82.9413 q^{49} -218.852 q^{51} +205.324i q^{52} -542.673i q^{53} +124.061 q^{54} +484.839 q^{56} +183.154i q^{57} -144.583i q^{58} -109.478 q^{59} -89.6156 q^{61} +1116.59i q^{62} +185.745i q^{63} +823.664 q^{64} -151.630 q^{66} -488.446i q^{67} +956.581i q^{68} -40.9814 q^{69} +837.423 q^{71} -211.429i q^{72} +351.216i q^{73} +300.512 q^{74} +800.547 q^{76} -227.022i q^{77} +215.845i q^{78} +831.205 q^{79} +81.0000 q^{81} +501.238i q^{82} +1389.13i q^{83} +811.873 q^{84} -559.423 q^{86} -94.3988i q^{87} +258.413i q^{88} -1523.70 q^{89} -323.164 q^{91} +179.125i q^{92} +729.025i q^{93} +2387.17 q^{94} +521.888 q^{96} +426.612i q^{97} +381.103i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9	\( 6 q - 34 q^{4} - 6 q^{6} - 54 q^{9} + 66 q^{11} - 288 q^{14} + 50 q^{16} - 232 q^{19} - 36 q^{21} - 18 q^{24} + 604 q^{26} - 476 q^{29} + 184 q^{31} - 708 q^{34} + 306 q^{36} - 120 q^{39} - 92 q^{41} - 374 q^{44} - 480 q^{46} + 914 q^{49} - 192 q^{51} + 54 q^{54} + 1376 q^{56} - 2472 q^{59} + 684 q^{61} + 3838 q^{64} - 66 q^{66} + 1440 q^{69} + 3632 q^{71} + 3748 q^{74} + 792 q^{76} + 192 q^{79} + 486 q^{81} + 960 q^{84} + 376 q^{86} - 1676 q^{89} + 664 q^{91} + 6224 q^{94} - 1182 q^{96} - 594 q^{99}+O(q^{100}) \) 6 * q - 34 * q^4 - 6 * q^6 - 54 * q^9 + 66 * q^11 - 288 * q^14 + 50 * q^16 - 232 * q^19 - 36 * q^21 - 18 * q^24 + 604 * q^26 - 476 * q^29 + 184 * q^31 - 708 * q^34 + 306 * q^36 - 120 * q^39 - 92 * q^41 - 374 * q^44 - 480 * q^46 + 914 * q^49 - 192 * q^51 + 54 * q^54 + 1376 * q^56 - 2472 * q^59 + 684 * q^61 + 3838 * q^64 - 66 * q^66 + 1440 * q^69 + 3632 * q^71 + 3748 * q^74 + 792 * q^76 + 192 * q^79 + 486 * q^81 + 960 * q^84 + 376 * q^86 - 1676 * q^89 + 664 * q^91 + 6224 * q^94 - 1182 * q^96 - 594 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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