LMFDB - Embedded newform 1617.4.a.bd.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.a (trivial)

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:	yes
Analytic conductor:	$95.4060884793$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 92 x^{14} + 346 x^{13} + 3385 x^{12} - 11756 x^{11} - 63875 x^{10} + 199466 x^{9} + \cdots - 738304 $ x^16 - 4x^15 - 92x^14 + 346x^13 + 3385x^12 - 11756x^11 - 63875x^10 + 199466x^9 + 657606x^8 - 1772388x^7 - 3590705x^6 + 7831536x^5 + 8898560x^4 - 14389664x^3 - 4854640x^2 + 6896896*x - 738304
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-5.13282$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.13282 q^{2} +3.00000 q^{3} +18.3458 q^{4} -11.5297 q^{5} +15.3984 q^{6} +53.1030 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.13282 q^{2} +3.00000 q^{3} +18.3458 q^{4} -11.5297 q^{5} +15.3984 q^{6} +53.1030 q^{8} +9.00000 q^{9} -59.1800 q^{10} -11.0000 q^{11} +55.0374 q^{12} -63.3138 q^{13} -34.5892 q^{15} +125.802 q^{16} -76.6459 q^{17} +46.1953 q^{18} -125.580 q^{19} -211.522 q^{20} -56.4610 q^{22} -59.1091 q^{23} +159.309 q^{24} +7.93498 q^{25} -324.978 q^{26} +27.0000 q^{27} -93.6214 q^{29} -177.540 q^{30} +317.611 q^{31} +220.893 q^{32} -33.0000 q^{33} -393.409 q^{34} +165.112 q^{36} +5.39627 q^{37} -644.578 q^{38} -189.941 q^{39} -612.264 q^{40} +131.138 q^{41} +247.074 q^{43} -201.804 q^{44} -103.768 q^{45} -303.396 q^{46} -509.625 q^{47} +377.405 q^{48} +40.7288 q^{50} -229.938 q^{51} -1161.54 q^{52} -417.681 q^{53} +138.586 q^{54} +126.827 q^{55} -376.739 q^{57} -480.541 q^{58} -353.552 q^{59} -634.567 q^{60} +98.3192 q^{61} +1630.24 q^{62} +127.388 q^{64} +729.992 q^{65} -169.383 q^{66} +933.448 q^{67} -1406.13 q^{68} -177.327 q^{69} +16.4318 q^{71} +477.927 q^{72} -722.452 q^{73} +27.6980 q^{74} +23.8049 q^{75} -2303.86 q^{76} -974.934 q^{78} +541.853 q^{79} -1450.46 q^{80} +81.0000 q^{81} +673.108 q^{82} +1353.74 q^{83} +883.708 q^{85} +1268.18 q^{86} -280.864 q^{87} -584.133 q^{88} +140.357 q^{89} -532.620 q^{90} -1084.40 q^{92} +952.834 q^{93} -2615.81 q^{94} +1447.90 q^{95} +662.678 q^{96} -342.747 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9} - 178 q^{10} - 176 q^{11} + 216 q^{12} - 104 q^{13} + 220 q^{16} - 220 q^{17} - 36 q^{18} - 152 q^{19} - 182 q^{20} + 44 q^{22} - 180 q^{23} - 198 q^{24} + 284 q^{25} - 10 q^{26} + 432 q^{27} - 604 q^{29} - 534 q^{30} - 380 q^{31} - 592 q^{32} - 528 q^{33} - 632 q^{34} + 648 q^{36} + 148 q^{37} - 266 q^{38} - 312 q^{39} - 1792 q^{40} - 60 q^{41} + 252 q^{43} - 792 q^{44} - 116 q^{46} - 1468 q^{47} + 660 q^{48} - 850 q^{50} - 660 q^{51} - 310 q^{52} - 1456 q^{53} - 108 q^{54} - 456 q^{57} - 1350 q^{58} - 1312 q^{59} - 546 q^{60} - 2880 q^{61} - 708 q^{62} + 630 q^{64} - 4064 q^{65} + 132 q^{66} + 1220 q^{67} - 4956 q^{68} - 540 q^{69} - 2040 q^{71} - 594 q^{72} - 1628 q^{73} - 3126 q^{74} + 852 q^{75} - 6286 q^{76} - 30 q^{78} - 416 q^{79} + 874 q^{80} + 1296 q^{81} - 3040 q^{82} - 3724 q^{83} + 628 q^{85} - 1608 q^{86} - 1812 q^{87} + 726 q^{88} - 752 q^{89} - 1602 q^{90} - 32 q^{92} - 1140 q^{93} - 610 q^{94} - 912 q^{95} - 1776 q^{96} - 1088 q^{97} - 1584 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9 - 178 * q^10 - 176 * q^11 + 216 * q^12 - 104 * q^13 + 220 * q^16 - 220 * q^17 - 36 * q^18 - 152 * q^19 - 182 * q^20 + 44 * q^22 - 180 * q^23 - 198 * q^24 + 284 * q^25 - 10 * q^26 + 432 * q^27 - 604 * q^29 - 534 * q^30 - 380 * q^31 - 592 * q^32 - 528 * q^33 - 632 * q^34 + 648 * q^36 + 148 * q^37 - 266 * q^38 - 312 * q^39 - 1792 * q^40 - 60 * q^41 + 252 * q^43 - 792 * q^44 - 116 * q^46 - 1468 * q^47 + 660 * q^48 - 850 * q^50 - 660 * q^51 - 310 * q^52 - 1456 * q^53 - 108 * q^54 - 456 * q^57 - 1350 * q^58 - 1312 * q^59 - 546 * q^60 - 2880 * q^61 - 708 * q^62 + 630 * q^64 - 4064 * q^65 + 132 * q^66 + 1220 * q^67 - 4956 * q^68 - 540 * q^69 - 2040 * q^71 - 594 * q^72 - 1628 * q^73 - 3126 * q^74 + 852 * q^75 - 6286 * q^76 - 30 * q^78 - 416 * q^79 + 874 * q^80 + 1296 * q^81 - 3040 * q^82 - 3724 * q^83 + 628 * q^85 - 1608 * q^86 - 1812 * q^87 + 726 * q^88 - 752 * q^89 - 1602 * q^90 - 32 * q^92 - 1140 * q^93 - 610 * q^94 - 912 * q^95 - 1776 * q^96 - 1088 * q^97 - 1584 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	5.13282	1.81472	0.907362	−	0.420350i	$-0.138093\pi$
$2$	5.13282	1.81472	0.907362	+	0.420350i	$0.138093\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	18.3458	2.29322
$5$	−11.5297	−1.03125	−0.515626	−	0.856814i	$-0.672441\pi$
$5$	−11.5297	−1.03125	−0.515626	+	0.856814i	$0.672441\pi$
$6$	15.3984	1.04773
$7$	0	0
$7$	0	0
$8$	53.1030	2.34684
$9$	9.00000	0.333333
$10$	−59.1800	−1.87144
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	55.0374	1.32399
$13$	−63.3138	−1.35078	−0.675388	−	0.737462i	$-0.736024\pi$
$13$	−63.3138	−1.35078	−0.675388	+	0.737462i	$0.736024\pi$
$14$	0	0
$15$	−34.5892	−0.595393
$16$	125.802	1.96565
$17$	−76.6459	−1.09349	−0.546746	−	0.837298i	$-0.684134\pi$
$17$	−76.6459	−1.09349	−0.546746	+	0.837298i	$0.684134\pi$
$18$	46.1953	0.604908
$19$	−125.580	−1.51632	−0.758158	−	0.652071i	$-0.773900\pi$
$19$	−125.580	−1.51632	−0.758158	+	0.652071i	$0.773900\pi$
$20$	−211.522	−2.36489
$21$	0	0
$22$	−56.4610	−0.547160
$23$	−59.1091	−0.535874	−0.267937	−	0.963436i	$-0.586342\pi$
$23$	−59.1091	−0.535874	−0.267937	+	0.963436i	$0.586342\pi$
$24$	159.309	1.35495
$25$	7.93498	0.0634799
$26$	−324.978	−2.45129
$27$	27.0000	0.192450
$28$	0	0
$29$	−93.6214	−0.599485	−0.299742	−	0.954020i	$-0.596901\pi$
$29$	−93.6214	−0.599485	−0.299742	+	0.954020i	$0.596901\pi$
$30$	−177.540	−1.08047
$31$	317.611	1.84015	0.920076	−	0.391740i	$-0.128127\pi$
$31$	317.611	1.84015	0.920076	+	0.391740i	$0.128127\pi$
$32$	220.893	1.22027
$33$	−33.0000	−0.174078
$34$	−393.409	−1.98439
$35$	0	0
$36$	165.112	0.764408
$37$	5.39627	0.0239768	0.0119884	−	0.999928i	$-0.496184\pi$
$37$	5.39627	0.0239768	0.0119884	+	0.999928i	$0.496184\pi$
$38$	−644.578	−2.75169
$39$	−189.941	−0.779871
$40$	−612.264	−2.42019
$41$	131.138	0.499520	0.249760	−	0.968308i	$-0.419648\pi$
$41$	131.138	0.499520	0.249760	+	0.968308i	$0.419648\pi$
$42$	0	0
$43$	247.074	0.876242	0.438121	−	0.898916i	$-0.355644\pi$
$43$	247.074	0.876242	0.438121	+	0.898916i	$0.355644\pi$
$44$	−201.804	−0.691433
$45$	−103.768	−0.343751
$46$	−303.396	−0.972463
$47$	−509.625	−1.58163	−0.790813	−	0.612058i	$-0.790342\pi$
$47$	−509.625	−1.58163	−0.790813	+	0.612058i	$0.790342\pi$
$48$	377.405	1.13487
$49$	0	0
$50$	40.7288	0.115198
$51$	−229.938	−0.631328
$52$	−1161.54	−3.09763
$53$	−417.681	−1.08251	−0.541253	−	0.840860i	$-0.682050\pi$
$53$	−417.681	−1.08251	−0.541253	+	0.840860i	$0.682050\pi$
$54$	138.586	0.349244
$55$	126.827	0.310934
$56$	0	0
$57$	−376.739	−0.875445
$58$	−480.541	−1.08790
$59$	−353.552	−0.780144	−0.390072	−	0.920784i	$-0.627550\pi$
$59$	−353.552	−0.780144	−0.390072	+	0.920784i	$0.627550\pi$
$60$	−634.567	−1.36537
$61$	98.3192	0.206369	0.103184	−	0.994662i	$-0.467097\pi$
$61$	98.3192	0.206369	0.103184	+	0.994662i	$0.467097\pi$
$62$	1630.24	3.33937
$63$	0	0
$64$	127.388	0.248805
$65$	729.992	1.39299
$66$	−169.383	−0.315903
$67$	933.448	1.70207	0.851036	−	0.525107i	$-0.175975\pi$
$67$	933.448	1.70207	0.851036	+	0.525107i	$0.175975\pi$
$68$	−1406.13	−2.50762
$69$	−177.327	−0.309387
$70$	0	0
$71$	16.4318	0.0274661	0.0137330	−	0.999906i	$-0.495629\pi$
$71$	16.4318	0.0274661	0.0137330	+	0.999906i	$0.495629\pi$
$72$	477.927	0.782282
$73$	−722.452	−1.15831	−0.579155	−	0.815217i	$-0.696617\pi$
$73$	−722.452	−1.15831	−0.579155	+	0.815217i	$0.696617\pi$
$74$	27.6980	0.0435112
$75$	23.8049	0.0366501
$76$	−2303.86	−3.47725
$77$	0	0
$78$	−974.934	−1.41525
$79$	541.853	0.771686	0.385843	−	0.922564i	$-0.373911\pi$
$79$	541.853	0.771686	0.385843	+	0.922564i	$0.373911\pi$
$80$	−1450.46	−2.02708
$81$	81.0000	0.111111
$82$	673.108	0.906492
$83$	1353.74	1.79027	0.895134	−	0.445798i	$-0.147080\pi$
$83$	1353.74	1.79027	0.895134	+	0.445798i	$0.147080\pi$
$84$	0	0
$85$	883.708	1.12767
$86$	1268.18	1.59014
$87$	−280.864	−0.346113
$88$	−584.133	−0.707600
$89$	140.357	0.167166	0.0835831	−	0.996501i	$-0.473364\pi$
$89$	140.357	0.167166	0.0835831	+	0.996501i	$0.473364\pi$
$90$	−532.620	−0.623812
$91$	0	0
$92$	−1084.40	−1.22888
$93$	952.834	1.06241
$94$	−2615.81	−2.87022
$95$	1447.90	1.56370
$96$	662.678	0.704524
$97$	−342.747	−0.358770	−0.179385	−	0.983779i	$-0.557411\pi$
$97$	−342.747	−0.358770	−0.179385	+	0.983779i	$0.557411\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	145.574	0.145574
$101$	617.643	0.608493	0.304246	−	0.952593i	$-0.401595\pi$
$101$	617.643	0.608493	0.304246	+	0.952593i	$0.401595\pi$
$102$	−1180.23	−1.14569
$103$	−971.198	−0.929077	−0.464539	−	0.885553i	$-0.653780\pi$
$103$	−971.198	−0.929077	−0.464539	+	0.885553i	$0.653780\pi$
$104$	−3362.16	−3.17006
$105$	0	0
$106$	−2143.88	−1.96445
$107$	893.927	0.807656	0.403828	−	0.914835i	$-0.367679\pi$
$107$	893.927	0.807656	0.403828	+	0.914835i	$0.367679\pi$
$108$	495.336	0.441331
$109$	−1180.97	−1.03776	−0.518882	−	0.854846i	$-0.673651\pi$
$109$	−1180.97	−1.03776	−0.518882	+	0.854846i	$0.673651\pi$
$110$	650.980	0.564260
$111$	16.1888	0.0138430
$112$	0	0
$113$	−761.508	−0.633953	−0.316976	−	0.948433i	$-0.602668\pi$
$113$	−761.508	−0.633953	−0.316976	+	0.948433i	$0.602668\pi$
$114$	−1933.73	−1.58869
$115$	681.513	0.552621
$116$	−1717.56	−1.37475
$117$	−569.824	−0.450259
$118$	−1814.72	−1.41575
$119$	0	0
$120$	−1836.79	−1.39730
$121$	121.000	0.0909091
$122$	504.654	0.374502
$123$	393.414	0.288398
$124$	5826.83	4.21988
$125$	1349.73	0.965788
$126$	0	0
$127$	−952.564	−0.665562	−0.332781	−	0.943004i	$-0.607987\pi$
$127$	−952.564	−0.665562	−0.332781	+	0.943004i	$0.607987\pi$
$128$	−1113.28	−0.768760
$129$	741.221	0.505899
$130$	3746.91	2.52789
$131$	−1431.36	−0.954647	−0.477324	−	0.878728i	$-0.658393\pi$
$131$	−1431.36	−0.954647	−0.477324	+	0.878728i	$0.658393\pi$
$132$	−605.411	−0.399199
$133$	0	0
$134$	4791.22	3.08879
$135$	−311.303	−0.198464
$136$	−4070.13	−2.56626
$137$	1668.78	1.04068	0.520342	−	0.853958i	$-0.325805\pi$
$137$	1668.78	1.04068	0.520342	+	0.853958i	$0.325805\pi$
$138$	−910.188	−0.561452
$139$	−37.4592	−0.0228579	−0.0114289	−	0.999935i	$-0.503638\pi$
$139$	−37.4592	−0.0228579	−0.0114289	+	0.999935i	$0.503638\pi$
$140$	0	0
$141$	−1528.88	−0.913152
$142$	84.3412	0.0498434
$143$	696.452	0.407274
$144$	1132.22	0.655217
$145$	1079.43	0.618220
$146$	−3708.21	−2.10201
$147$	0	0
$148$	98.9988	0.0549841
$149$	−1698.36	−0.933792	−0.466896	−	0.884312i	$-0.654628\pi$
$149$	−1698.36	−0.933792	−0.466896	+	0.884312i	$0.654628\pi$
$150$	122.186	0.0665099
$151$	1760.09	0.948570	0.474285	−	0.880371i	$-0.342707\pi$
$151$	1760.09	0.948570	0.474285	+	0.880371i	$0.342707\pi$
$152$	−6668.67	−3.55856
$153$	−689.813	−0.364497
$154$	0	0
$155$	−3661.98	−1.89766
$156$	−3484.63	−1.78842
$157$	2513.62	1.27776	0.638881	−	0.769306i	$-0.279398\pi$
$157$	2513.62	1.27776	0.638881	+	0.769306i	$0.279398\pi$
$158$	2781.23	1.40040
$159$	−1253.04	−0.624985
$160$	−2546.84	−1.25841
$161$	0	0
$162$	415.758	0.201636
$163$	−3641.75	−1.74996	−0.874981	−	0.484158i	$-0.839126\pi$
$163$	−3641.75	−1.74996	−0.874981	+	0.484158i	$0.839126\pi$
$164$	2405.83	1.14551
$165$	380.482	0.179518
$166$	6948.49	3.24884
$167$	−661.218	−0.306387	−0.153193	−	0.988196i	$-0.548956\pi$
$167$	−661.218	−0.306387	−0.153193	+	0.988196i	$0.548956\pi$
$168$	0	0
$169$	1811.64	0.824597
$170$	4535.91	2.04640
$171$	−1130.22	−0.505438
$172$	4532.76	2.00942
$173$	67.1784	0.0295230	0.0147615	−	0.999891i	$-0.495301\pi$
$173$	67.1784	0.0295230	0.0147615	+	0.999891i	$0.495301\pi$
$174$	−1441.62	−0.628099
$175$	0	0
$176$	−1383.82	−0.592666
$177$	−1060.66	−0.450417
$178$	720.425	0.303360
$179$	2125.50	0.887528	0.443764	−	0.896144i	$-0.353643\pi$
$179$	2125.50	0.887528	0.443764	+	0.896144i	$0.353643\pi$
$180$	−1903.70	−0.788297
$181$	−3512.97	−1.44263	−0.721317	−	0.692605i	$-0.756463\pi$
$181$	−3512.97	−1.44263	−0.721317	+	0.692605i	$0.756463\pi$
$182$	0	0
$183$	294.958	0.119147
$184$	−3138.87	−1.25761
$185$	−62.2176	−0.0247261
$186$	4890.72	1.92798
$187$	843.105	0.329700
$188$	−9349.47	−3.62702
$189$	0	0
$190$	7431.82	2.83769
$191$	2938.27	1.11312	0.556559	−	0.830808i	$-0.312121\pi$
$191$	2938.27	1.11312	0.556559	+	0.830808i	$0.312121\pi$
$192$	382.164	0.143647
$193$	−3856.91	−1.43848	−0.719239	−	0.694762i	$-0.755510\pi$
$193$	−3856.91	−1.43848	−0.719239	+	0.694762i	$0.755510\pi$
$194$	−1759.26	−0.651069
$195$	2189.98	0.804243
$196$	0	0
$197$	−4322.67	−1.56334	−0.781668	−	0.623695i	$-0.785631\pi$
$197$	−4322.67	−1.56334	−0.781668	+	0.623695i	$0.785631\pi$
$198$	−508.149	−0.182387
$199$	−3382.38	−1.20488	−0.602438	−	0.798165i	$-0.705804\pi$
$199$	−3382.38	−1.20488	−0.602438	+	0.798165i	$0.705804\pi$
$200$	421.372	0.148977
$201$	2800.35	0.982692
$202$	3170.25	1.10425
$203$	0	0
$204$	−4218.39	−1.44778
$205$	−1511.99	−0.515131
$206$	−4984.98	−1.68602
$207$	−531.982	−0.178625
$208$	−7964.99	−2.65516
$209$	1381.38	0.457186
$210$	0	0
$211$	3843.23	1.25393	0.626963	−	0.779049i	$-0.284298\pi$
$211$	3843.23	1.25393	0.626963	+	0.779049i	$0.284298\pi$
$212$	−7662.68	−2.48243
$213$	49.2953	0.0158575
$214$	4588.36	1.46567
$215$	−2848.70	−0.903626
$216$	1433.78	0.451651
$217$	0	0
$218$	−6061.69	−1.88325
$219$	−2167.36	−0.668751
$220$	2326.74	0.713041
$221$	4852.75	1.47706
$222$	83.0941	0.0251212
$223$	3919.57	1.17701	0.588507	−	0.808492i	$-0.299716\pi$
$223$	3919.57	1.17701	0.588507	+	0.808492i	$0.299716\pi$
$224$	0	0
$225$	71.4148	0.0211600
$226$	−3908.68	−1.15045
$227$	341.454	0.0998374	0.0499187	−	0.998753i	$-0.484104\pi$
$227$	341.454	0.0998374	0.0499187	+	0.998753i	$0.484104\pi$
$228$	−6911.58	−2.00759
$229$	−250.650	−0.0723294	−0.0361647	−	0.999346i	$-0.511514\pi$
$229$	−250.650	−0.0723294	−0.0361647	+	0.999346i	$0.511514\pi$
$230$	3498.08	1.00285
$231$	0	0
$232$	−4971.58	−1.40690
$233$	−4769.89	−1.34114	−0.670571	−	0.741845i	$-0.733951\pi$
$233$	−4769.89	−1.34114	−0.670571	+	0.741845i	$0.733951\pi$
$234$	−2924.80	−0.817096
$235$	5875.85	1.63105
$236$	−6486.19	−1.78905
$237$	1625.56	0.445533
$238$	0	0
$239$	−3797.01	−1.02765	−0.513825	−	0.857895i	$-0.671772\pi$
$239$	−3797.01	−1.02765	−0.513825	+	0.857895i	$0.671772\pi$
$240$	−4351.39	−1.17034
$241$	−2382.59	−0.636831	−0.318415	−	0.947951i	$-0.603151\pi$
$241$	−2382.59	−0.636831	−0.318415	+	0.947951i	$0.603151\pi$
$242$	621.071	0.164975
$243$	243.000	0.0641500
$244$	1803.74	0.473249
$245$	0	0
$246$	2019.32	0.523363
$247$	7950.94	2.04820
$248$	16866.1	4.31855
$249$	4061.22	1.03361
$250$	6927.91	1.75264
$251$	−7297.08	−1.83501	−0.917506	−	0.397723i	$-0.869801\pi$
$251$	−7297.08	−1.83501	−0.917506	+	0.397723i	$0.869801\pi$
$252$	0	0
$253$	650.200	0.161572
$254$	−4889.34	−1.20781
$255$	2651.12	0.651058
$256$	−6733.38	−1.64389
$257$	5744.14	1.39420	0.697101	−	0.716973i	$-0.254473\pi$
$257$	5744.14	1.39420	0.697101	+	0.716973i	$0.254473\pi$
$258$	3804.55	0.918066
$259$	0	0
$260$	13392.3	3.19444
$261$	−842.593	−0.199828
$262$	−7346.92	−1.73242
$263$	−1824.20	−0.427699	−0.213850	−	0.976867i	$-0.568600\pi$
$263$	−1824.20	−0.427699	−0.213850	+	0.976867i	$0.568600\pi$
$264$	−1752.40	−0.408533
$265$	4815.75	1.11634
$266$	0	0
$267$	421.070	0.0965134
$268$	17124.9	3.90323
$269$	1645.21	0.372900	0.186450	−	0.982464i	$-0.440302\pi$
$269$	1645.21	0.372900	0.186450	+	0.982464i	$0.440302\pi$
$270$	−1597.86	−0.360158
$271$	3574.07	0.801142	0.400571	−	0.916266i	$-0.368812\pi$
$271$	3574.07	0.801142	0.400571	+	0.916266i	$0.368812\pi$
$272$	−9642.19	−2.14943
$273$	0	0
$274$	8565.55	1.88855
$275$	−87.2848	−0.0191399
$276$	−3253.21	−0.709493
$277$	−2014.96	−0.437067	−0.218533	−	0.975829i	$-0.570127\pi$
$277$	−2014.96	−0.437067	−0.218533	+	0.975829i	$0.570127\pi$
$278$	−192.271	−0.0414808
$279$	2858.50	0.613384
$280$	0	0
$281$	−3975.15	−0.843905	−0.421953	−	0.906618i	$-0.638655\pi$
$281$	−3975.15	−0.843905	−0.421953	+	0.906618i	$0.638655\pi$
$282$	−7847.43	−1.65712
$283$	8014.56	1.68345	0.841724	−	0.539908i	$-0.181541\pi$
$283$	8014.56	1.68345	0.841724	+	0.539908i	$0.181541\pi$
$284$	301.454	0.0629859
$285$	4343.71	0.902804
$286$	3574.76	0.739091
$287$	0	0
$288$	1988.04	0.406757
$289$	961.599	0.195725
$290$	5540.52	1.12190
$291$	−1028.24	−0.207136
$292$	−13254.0	−2.65626
$293$	−6400.81	−1.27624	−0.638122	−	0.769936i	$-0.720288\pi$
$293$	−6400.81	−1.27624	−0.638122	+	0.769936i	$0.720288\pi$
$294$	0	0
$295$	4076.36	0.804525
$296$	286.558	0.0562698
$297$	−297.000	−0.0580259
$298$	−8717.37	−1.69458
$299$	3742.42	0.723846
$300$	436.721	0.0840469
$301$	0	0
$302$	9034.21	1.72139
$303$	1852.93	0.351314
$304$	−15798.2	−2.98055
$305$	−1133.60	−0.212818
$306$	−3540.68	−0.661462
$307$	−2915.78	−0.542060	−0.271030	−	0.962571i	$-0.587364\pi$
$307$	−2915.78	−0.542060	−0.271030	+	0.962571i	$0.587364\pi$
$308$	0	0
$309$	−2913.59	−0.536403
$310$	−18796.3	−3.44373
$311$	8268.72	1.50764	0.753820	−	0.657081i	$-0.228209\pi$
$311$	8268.72	1.50764	0.753820	+	0.657081i	$0.228209\pi$
$312$	−10086.5	−1.83024
$313$	8675.89	1.56674	0.783371	−	0.621554i	$-0.213498\pi$
$313$	8675.89	1.56674	0.783371	+	0.621554i	$0.213498\pi$
$314$	12901.9	2.31878
$315$	0	0
$316$	9940.72	1.76965
$317$	7010.56	1.24212	0.621060	−	0.783763i	$-0.286702\pi$
$317$	7010.56	1.24212	0.621060	+	0.783763i	$0.286702\pi$
$318$	−6431.63	−1.13418
$319$	1029.84	0.180752
$320$	−1468.75	−0.256580
$321$	2681.78	0.466300
$322$	0	0
$323$	9625.18	1.65808
$324$	1486.01	0.254803
$325$	−502.394	−0.0857471
$326$	−18692.4	−3.17570
$327$	−3542.90	−0.599153
$328$	6963.83	1.17230
$329$	0	0
$330$	1952.94	0.325775
$331$	11213.0	1.86200	0.930998	−	0.365024i	$-0.118939\pi$
$331$	11213.0	1.86200	0.930998	+	0.365024i	$0.118939\pi$
$332$	24835.4	4.10548
$333$	48.5664	0.00799226
$334$	−3393.91	−0.556008
$335$	−10762.4	−1.75527
$336$	0	0
$337$	−8703.83	−1.40691	−0.703454	−	0.710741i	$-0.748360\pi$
$337$	−8703.83	−1.40691	−0.703454	+	0.710741i	$0.748360\pi$
$338$	9298.81	1.49642
$339$	−2284.52	−0.366013
$340$	16212.3	2.58599
$341$	−3493.73	−0.554827
$342$	−5801.20	−0.917231
$343$	0	0
$344$	13120.4	2.05640
$345$	2044.54	0.319056
$346$	344.814	0.0535761
$347$	7707.75	1.19243	0.596216	−	0.802824i	$-0.296670\pi$
$347$	7707.75	1.19243	0.596216	+	0.802824i	$0.296670\pi$
$348$	−5152.68	−0.793714
$349$	2452.90	0.376220	0.188110	−	0.982148i	$-0.439764\pi$
$349$	2452.90	0.376220	0.188110	+	0.982148i	$0.439764\pi$
$350$	0	0
$351$	−1709.47	−0.259957
$352$	−2429.82	−0.367926
$353$	3252.77	0.490446	0.245223	−	0.969467i	$-0.421139\pi$
$353$	3252.77	0.490446	0.245223	+	0.969467i	$0.421139\pi$
$354$	−5444.15	−0.817382
$355$	−189.454	−0.0283244
$356$	2574.96	0.383349
$357$	0	0
$358$	10909.8	1.61062
$359$	−5224.30	−0.768044	−0.384022	−	0.923324i	$-0.625461\pi$
$359$	−5224.30	−0.768044	−0.384022	+	0.923324i	$0.625461\pi$
$360$	−5510.38	−0.806729
$361$	8911.29	1.29921
$362$	−18031.4	−2.61798
$363$	363.000	0.0524864
$364$	0	0
$365$	8329.69	1.19451
$366$	1513.96	0.216219
$367$	−1492.03	−0.212217	−0.106108	−	0.994355i	$-0.533839\pi$
$367$	−1492.03	−0.212217	−0.106108	+	0.994355i	$0.533839\pi$
$368$	−7436.03	−1.05334
$369$	1180.24	0.166507
$370$	−319.351	−0.0448710
$371$	0	0
$372$	17480.5	2.43635
$373$	−6747.40	−0.936641	−0.468320	−	0.883559i	$-0.655141\pi$
$373$	−6747.40	−0.936641	−0.468320	+	0.883559i	$0.655141\pi$
$374$	4327.50	0.598315
$375$	4049.19	0.557598
$376$	−27062.6	−3.71183
$377$	5927.53	0.809770
$378$	0	0
$379$	−5626.78	−0.762608	−0.381304	−	0.924450i	$-0.624525\pi$
$379$	−5626.78	−0.762608	−0.381304	+	0.924450i	$0.624525\pi$
$380$	26562.9	3.58592
$381$	−2857.69	−0.384262
$382$	15081.6	2.02000
$383$	−13533.7	−1.80558	−0.902792	−	0.430077i	$-0.858486\pi$
$383$	−13533.7	−1.80558	−0.902792	+	0.430077i	$0.858486\pi$
$384$	−3339.85	−0.443844
$385$	0	0
$386$	−19796.8	−2.61044
$387$	2223.66	0.292081
$388$	−6287.97	−0.822740
$389$	1020.34	0.132991	0.0664953	−	0.997787i	$-0.478818\pi$
$389$	1020.34	0.132991	0.0664953	+	0.997787i	$0.478818\pi$
$390$	11240.7	1.45948
$391$	4530.47	0.585974
$392$	0	0
$393$	−4294.09	−0.551166
$394$	−22187.4	−2.83702
$395$	−6247.42	−0.795802
$396$	−1816.23	−0.230478
$397$	−9905.14	−1.25220	−0.626102	−	0.779741i	$-0.715351\pi$
$397$	−9905.14	−1.25220	−0.626102	+	0.779741i	$0.715351\pi$
$398$	−17361.1	−2.18652
$399$	0	0
$400$	998.235	0.124779
$401$	−8359.90	−1.04108	−0.520541	−	0.853837i	$-0.674270\pi$
$401$	−8359.90	−1.04108	−0.520541	+	0.853837i	$0.674270\pi$
$402$	14373.7	1.78332
$403$	−20109.2	−2.48563
$404$	11331.2	1.39541
$405$	−933.909	−0.114584
$406$	0	0
$407$	−59.3589	−0.00722927
$408$	−12210.4	−1.48163
$409$	6259.46	0.756749	0.378375	−	0.925653i	$-0.376483\pi$
$409$	6259.46	0.756749	0.378375	+	0.925653i	$0.376483\pi$
$410$	−7760.76	−0.934821
$411$	5006.35	0.600839
$412$	−17817.4	−2.13058
$413$	0	0
$414$	−2730.56	−0.324154
$415$	−15608.3	−1.84622
$416$	−13985.6	−1.64831
$417$	−112.378	−0.0131970
$418$	7090.36	0.829667
$419$	5166.29	0.602362	0.301181	−	0.953567i	$-0.402619\pi$
$419$	5166.29	0.602362	0.301181	+	0.953567i	$0.402619\pi$
$420$	0	0
$421$	13553.1	1.56898	0.784488	−	0.620144i	$-0.212926\pi$
$421$	13553.1	1.56898	0.784488	+	0.620144i	$0.212926\pi$
$422$	19726.6	2.27553
$423$	−4586.63	−0.527209
$424$	−22180.1	−2.54047
$425$	−608.184	−0.0694147
$426$	253.024	0.0287771
$427$	0	0
$428$	16399.8	1.85214
$429$	2089.36	0.235140
$430$	−14621.8	−1.63983
$431$	8658.56	0.967676	0.483838	−	0.875158i	$-0.339242\pi$
$431$	8658.56	0.967676	0.483838	+	0.875158i	$0.339242\pi$
$432$	3396.65	0.378290
$433$	6704.16	0.744068	0.372034	−	0.928219i	$-0.378660\pi$
$433$	6704.16	0.744068	0.372034	+	0.928219i	$0.378660\pi$
$434$	0	0
$435$	3238.29	0.356929
$436$	−21665.8	−2.37982
$437$	7422.91	0.812553
$438$	−11124.6	−1.21360
$439$	11735.0	1.27581	0.637905	−	0.770115i	$-0.279801\pi$
$439$	11735.0	1.27581	0.637905	+	0.770115i	$0.279801\pi$
$440$	6734.91	0.729714
$441$	0	0
$442$	24908.3	2.68046
$443$	−13176.2	−1.41314	−0.706571	−	0.707642i	$-0.749759\pi$
$443$	−13176.2	−1.41314	−0.706571	+	0.707642i	$0.749759\pi$
$444$	296.996	0.0317451
$445$	−1618.28	−0.172390
$446$	20118.4	2.13596
$447$	−5095.08	−0.539125
$448$	0	0
$449$	−12641.7	−1.32873	−0.664364	−	0.747410i	$-0.731297\pi$
$449$	−12641.7	−1.32873	−0.664364	+	0.747410i	$0.731297\pi$
$450$	366.559	0.0383995
$451$	−1442.52	−0.150611
$452$	−13970.5	−1.45380
$453$	5280.27	0.547657
$454$	1752.62	0.181177
$455$	0	0
$456$	−20006.0	−2.05453
$457$	−7953.85	−0.814147	−0.407074	−	0.913395i	$-0.633451\pi$
$457$	−7953.85	−0.814147	−0.407074	+	0.913395i	$0.633451\pi$
$458$	−1286.54	−0.131258
$459$	−2069.44	−0.210443
$460$	12502.9	1.26728
$461$	−935.141	−0.0944769	−0.0472385	−	0.998884i	$-0.515042\pi$
$461$	−935.141	−0.0944769	−0.0472385	+	0.998884i	$0.515042\pi$
$462$	0	0
$463$	−13447.2	−1.34978	−0.674888	−	0.737920i	$-0.735808\pi$
$463$	−13447.2	−1.34978	−0.674888	+	0.737920i	$0.735808\pi$
$464$	−11777.7	−1.17838
$465$	−10985.9	−1.09561
$466$	−24483.0	−2.43380
$467$	12565.6	1.24511	0.622556	−	0.782575i	$-0.286094\pi$
$467$	12565.6	1.24511	0.622556	+	0.782575i	$0.286094\pi$
$468$	−10453.9	−1.03254
$469$	0	0
$470$	30159.6	2.95991
$471$	7540.85	0.737716
$472$	−18774.7	−1.83088
$473$	−2717.81	−0.264197
$474$	8343.69	0.808520
$475$	−996.474	−0.0962555
$476$	0	0
$477$	−3759.13	−0.360835
$478$	−19489.4	−1.86490
$479$	19388.5	1.84944	0.924721	−	0.380647i	$-0.124299\pi$
$479$	19388.5	1.84944	0.924721	+	0.380647i	$0.124299\pi$
$480$	−7640.51	−0.726542
$481$	−341.658	−0.0323873
$482$	−12229.4	−1.15567
$483$	0	0
$484$	2219.84	0.208475
$485$	3951.79	0.369982
$486$	1247.27	0.116415
$487$	13720.5	1.27667	0.638333	−	0.769760i	$-0.279624\pi$
$487$	13720.5	1.27667	0.638333	+	0.769760i	$0.279624\pi$
$488$	5221.05	0.484315
$489$	−10925.2	−1.01034
$490$	0	0
$491$	3428.83	0.315154	0.157577	−	0.987507i	$-0.449632\pi$
$491$	3428.83	0.315154	0.157577	+	0.987507i	$0.449632\pi$
$492$	7217.50	0.661362
$493$	7175.70	0.655532
$494$	40810.7	3.71692
$495$	1141.44	0.103645
$496$	39956.1	3.61710
$497$	0	0
$498$	20845.5	1.87572
$499$	2916.86	0.261676	0.130838	−	0.991404i	$-0.458233\pi$
$499$	2916.86	0.261676	0.130838	+	0.991404i	$0.458233\pi$
$500$	24761.9	2.21477
$501$	−1983.66	−0.176893
$502$	−37454.6	−3.33004
$503$	7277.00	0.645060	0.322530	−	0.946559i	$-0.395467\pi$
$503$	7277.00	0.645060	0.322530	+	0.946559i	$0.395467\pi$
$504$	0	0
$505$	−7121.27	−0.627509
$506$	3337.36	0.293209
$507$	5434.92	0.476081
$508$	−17475.5	−1.52628
$509$	−11383.3	−0.991272	−0.495636	−	0.868530i	$-0.665065\pi$
$509$	−11383.3	−0.991272	−0.495636	+	0.868530i	$0.665065\pi$
$510$	13607.7	1.18149
$511$	0	0
$512$	−25654.9	−2.21445
$513$	−3390.66	−0.291815
$514$	29483.6	2.53009
$515$	11197.7	0.958113
$516$	13598.3	1.16014
$517$	5605.88	0.476878
$518$	0	0
$519$	201.535	0.0170451
$520$	38764.8	3.26913
$521$	−17015.1	−1.43080	−0.715400	−	0.698716i	$-0.753755\pi$
$521$	−17015.1	−1.43080	−0.715400	+	0.698716i	$0.753755\pi$
$522$	−4324.87	−0.362633
$523$	19038.3	1.59175	0.795875	−	0.605461i	$-0.207011\pi$
$523$	19038.3	1.59175	0.795875	+	0.605461i	$0.207011\pi$
$524$	−26259.5	−2.18922
$525$	0	0
$526$	−9363.27	−0.776156
$527$	−24343.6	−2.01219
$528$	−4151.46	−0.342176
$529$	−8673.12	−0.712839
$530$	24718.4	2.02584
$531$	−3181.97	−0.260048
$532$	0	0
$533$	−8302.86	−0.674740
$534$	2161.28	0.175145
$535$	−10306.7	−0.832896
$536$	49568.9	3.99450
$537$	6376.51	0.512415
$538$	8444.55	0.676711
$539$	0	0
$540$	−5711.10	−0.455123
$541$	−14785.7	−1.17502	−0.587512	−	0.809216i	$-0.699892\pi$
$541$	−14785.7	−1.17502	−0.587512	+	0.809216i	$0.699892\pi$
$542$	18345.1	1.45385
$543$	−10538.9	−0.832905
$544$	−16930.5	−1.33436
$545$	13616.3	1.07019
$546$	0	0
$547$	−23452.8	−1.83322	−0.916608	−	0.399786i	$-0.869084\pi$
$547$	−23452.8	−1.83322	−0.916608	+	0.399786i	$0.869084\pi$
$548$	30615.1	2.38652
$549$	884.873	0.0687895
$550$	−448.017	−0.0347336
$551$	11757.0	0.909008
$552$	−9416.62	−0.726083
$553$	0	0
$554$	−10342.4	−0.793155
$555$	−186.653	−0.0142756
$556$	−687.218	−0.0524183
$557$	23429.6	1.78230	0.891151	−	0.453706i	$-0.149898\pi$
$557$	23429.6	1.78230	0.891151	+	0.453706i	$0.149898\pi$
$558$	14672.2	1.11312
$559$	−15643.2	−1.18361
$560$	0	0
$561$	2529.32	0.190353
$562$	−20403.7	−1.53145
$563$	−15441.6	−1.15593	−0.577964	−	0.816062i	$-0.696152\pi$
$563$	−15441.6	−1.15593	−0.577964	+	0.816062i	$0.696152\pi$
$564$	−28048.4	−2.09406
$565$	8779.99	0.653765
$566$	41137.2	3.05499
$567$	0	0
$568$	872.576	0.0644586
$569$	−7917.89	−0.583366	−0.291683	−	0.956515i	$-0.594215\pi$
$569$	−7917.89	−0.583366	−0.291683	+	0.956515i	$0.594215\pi$
$570$	22295.5	1.63834
$571$	14744.0	1.08059	0.540294	−	0.841476i	$-0.318313\pi$
$571$	14744.0	1.08059	0.540294	+	0.841476i	$0.318313\pi$
$572$	12777.0	0.933971
$573$	8814.80	0.642659
$574$	0	0
$575$	−469.030	−0.0340172
$576$	1146.49	0.0829349
$577$	12982.9	0.936714	0.468357	−	0.883539i	$-0.344846\pi$
$577$	12982.9	0.936714	0.468357	+	0.883539i	$0.344846\pi$
$578$	4935.71	0.355188
$579$	−11570.7	−0.830506
$580$	19803.0	1.41772
$581$	0	0
$582$	−5277.77	−0.375895
$583$	4594.49	0.326388
$584$	−38364.4	−2.71837
$585$	6569.93	0.464330
$586$	−32854.2	−2.31603
$587$	4553.10	0.320148	0.160074	−	0.987105i	$-0.448827\pi$
$587$	4553.10	0.320148	0.160074	+	0.987105i	$0.448827\pi$
$588$	0	0
$589$	−39885.6	−2.79025
$590$	20923.2	1.45999
$591$	−12968.0	−0.902593
$592$	678.860	0.0471300
$593$	−7841.38	−0.543013	−0.271507	−	0.962437i	$-0.587522\pi$
$593$	−7841.38	−0.543013	−0.271507	+	0.962437i	$0.587522\pi$
$594$	−1524.45	−0.105301
$595$	0	0
$596$	−31157.8	−2.14140
$597$	−10147.1	−0.695636
$598$	19209.2	1.31358
$599$	−57.6863	−0.00393489	−0.00196744	−	0.999998i	$-0.500626\pi$
$599$	−57.6863	−0.00393489	−0.00196744	+	0.999998i	$0.500626\pi$
$600$	1264.12	0.0860121
$601$	2853.32	0.193659	0.0968297	−	0.995301i	$-0.469130\pi$
$601$	2853.32	0.193659	0.0968297	+	0.995301i	$0.469130\pi$
$602$	0	0
$603$	8401.04	0.567358
$604$	32290.2	2.17528
$605$	−1395.10	−0.0937501
$606$	9510.74	0.637537
$607$	−17920.7	−1.19832	−0.599159	−	0.800630i	$-0.704498\pi$
$607$	−17920.7	−1.19832	−0.599159	+	0.800630i	$0.704498\pi$
$608$	−27739.7	−1.85032
$609$	0	0
$610$	−5818.53	−0.386206
$611$	32266.3	2.13642
$612$	−12655.2	−0.835874
$613$	25237.4	1.66285	0.831427	−	0.555634i	$-0.187524\pi$
$613$	25237.4	1.66285	0.831427	+	0.555634i	$0.187524\pi$
$614$	−14966.2	−0.983690
$615$	−4535.97	−0.297411
$616$	0	0
$617$	−23363.5	−1.52444	−0.762221	−	0.647317i	$-0.775891\pi$
$617$	−23363.5	−1.52444	−0.762221	+	0.647317i	$0.775891\pi$
$618$	−14954.9	−0.973424
$619$	1294.69	0.0840675	0.0420338	−	0.999116i	$-0.486616\pi$
$619$	1294.69	0.0840675	0.0420338	+	0.999116i	$0.486616\pi$
$620$	−67181.9	−4.35176
$621$	−1595.95	−0.103129
$622$	42441.8	2.73595
$623$	0	0
$624$	−23895.0	−1.53296
$625$	−16553.9	−1.05945
$626$	44531.7	2.84320
$627$	4144.13	0.263957
$628$	46114.3	2.93019
$629$	−413.602	−0.0262184
$630$	0	0
$631$	−22757.6	−1.43576	−0.717880	−	0.696167i	$-0.754887\pi$
$631$	−22757.6	−1.43576	−0.717880	+	0.696167i	$0.754887\pi$
$632$	28774.0	1.81103
$633$	11529.7	0.723955
$634$	35983.9	2.25411
$635$	10982.8	0.686362
$636$	−22988.0	−1.43323
$637$	0	0
$638$	5285.96	0.328014
$639$	147.886	0.00915536
$640$	12835.9	0.792785
$641$	−17410.7	−1.07282	−0.536412	−	0.843956i	$-0.680221\pi$
$641$	−17410.7	−1.07282	−0.536412	+	0.843956i	$0.680221\pi$
$642$	13765.1	0.846206
$643$	17445.4	1.06995	0.534976	−	0.844867i	$-0.320321\pi$
$643$	17445.4	1.06995	0.534976	+	0.844867i	$0.320321\pi$
$644$	0	0
$645$	−8546.09	−0.521709
$646$	49404.3	3.00896
$647$	−19957.1	−1.21267	−0.606334	−	0.795210i	$-0.707360\pi$
$647$	−19957.1	−1.21267	−0.606334	+	0.795210i	$0.707360\pi$
$648$	4301.35	0.260761
$649$	3889.07	0.235222
$650$	−2578.70	−0.155607
$651$	0	0
$652$	−66810.8	−4.01305
$653$	4722.22	0.282993	0.141497	−	0.989939i	$-0.454809\pi$
$653$	4722.22	0.282993	0.141497	+	0.989939i	$0.454809\pi$
$654$	−18185.1	−1.08730
$655$	16503.3	0.984482
$656$	16497.4	0.981883
$657$	−6502.07	−0.386103
$658$	0	0
$659$	−3272.39	−0.193436	−0.0967178	−	0.995312i	$-0.530834\pi$
$659$	−3272.39	−0.193436	−0.0967178	+	0.995312i	$0.530834\pi$
$660$	6980.23	0.411675
$661$	11324.5	0.666374	0.333187	−	0.942861i	$-0.391876\pi$
$661$	11324.5	0.666374	0.333187	+	0.942861i	$0.391876\pi$
$662$	57554.1	3.37901
$663$	14558.2	0.852783
$664$	71887.7	4.20148
$665$	0	0
$666$	249.282	0.0145037
$667$	5533.88	0.321248
$668$	−12130.6	−0.702614
$669$	11758.7	0.679549
$670$	−55241.5	−3.18532
$671$	−1081.51	−0.0622225
$672$	0	0
$673$	13490.0	0.772664	0.386332	−	0.922360i	$-0.373742\pi$
$673$	13490.0	0.772664	0.386332	+	0.922360i	$0.373742\pi$
$674$	−44675.2	−2.55315
$675$	214.245	0.0122167
$676$	33236.0	1.89099
$677$	−18900.9	−1.07300	−0.536500	−	0.843900i	$-0.680254\pi$
$677$	−18900.9	−1.07300	−0.536500	+	0.843900i	$0.680254\pi$
$678$	−11726.0	−0.664212
$679$	0	0
$680$	46927.6	2.64646
$681$	1024.36	0.0576411
$682$	−17932.7	−1.00686
$683$	−13268.5	−0.743347	−0.371673	−	0.928364i	$-0.621216\pi$
$683$	−13268.5	−0.743347	−0.371673	+	0.928364i	$0.621216\pi$
$684$	−20734.8	−1.15908
$685$	−19240.6	−1.07321
$686$	0	0
$687$	−751.951	−0.0417594
$688$	31082.3	1.72239
$689$	26445.0	1.46222
$690$	10494.2	0.578998
$691$	24465.7	1.34692	0.673458	−	0.739225i	$-0.264808\pi$
$691$	24465.7	1.34692	0.673458	+	0.739225i	$0.264808\pi$
$692$	1232.44	0.0677028
$693$	0	0
$694$	39562.5	2.16393
$695$	431.895	0.0235722
$696$	−14914.7	−0.812273
$697$	−10051.2	−0.546222
$698$	12590.3	0.682735
$699$	−14309.7	−0.774309
$700$	0	0
$701$	−25741.3	−1.38693	−0.693464	−	0.720492i	$-0.743916\pi$
$701$	−25741.3	−1.38693	−0.693464	+	0.720492i	$0.743916\pi$
$702$	−8774.41	−0.471750
$703$	−677.662	−0.0363564
$704$	−1401.27	−0.0750174
$705$	17627.5	0.941690
$706$	16695.9	0.890025
$707$	0	0
$708$	−19458.6	−1.03291
$709$	18210.7	0.964623	0.482311	−	0.876000i	$-0.339797\pi$
$709$	18210.7	0.964623	0.482311	+	0.876000i	$0.339797\pi$
$710$	−972.432	−0.0514010
$711$	4876.67	0.257229
$712$	7453.37	0.392313
$713$	−18773.7	−0.986089
$714$	0	0
$715$	−8029.91	−0.420002
$716$	38994.0	2.03530
$717$	−11391.0	−0.593314
$718$	−26815.4	−1.39379
$719$	−5676.21	−0.294419	−0.147209	−	0.989105i	$-0.547029\pi$
$719$	−5676.21	−0.294419	−0.147209	+	0.989105i	$0.547029\pi$
$720$	−13054.2	−0.675694
$721$	0	0
$722$	45740.0	2.35771
$723$	−7147.77	−0.367674
$724$	−64448.2	−3.30828
$725$	−742.884	−0.0380552
$726$	1863.21	0.0952483
$727$	−28482.7	−1.45305	−0.726523	−	0.687142i	$-0.758865\pi$
$727$	−28482.7	−1.45305	−0.726523	+	0.687142i	$0.758865\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	42754.8	2.16770
$731$	−18937.2	−0.958164
$732$	5411.23	0.273231
$733$	−2599.36	−0.130981	−0.0654907	−	0.997853i	$-0.520861\pi$
$733$	−2599.36	−0.130981	−0.0654907	+	0.997853i	$0.520861\pi$
$734$	−7658.34	−0.385115
$735$	0	0
$736$	−13056.8	−0.653912
$737$	−10267.9	−0.513194
$738$	6057.97	0.302164
$739$	26783.3	1.33320	0.666602	−	0.745414i	$-0.267748\pi$
$739$	26783.3	1.33320	0.666602	+	0.745414i	$0.267748\pi$
$740$	−1141.43	−0.0567025
$741$	23852.8	1.18253
$742$	0	0
$743$	10596.8	0.523229	0.261614	−	0.965172i	$-0.415745\pi$
$743$	10596.8	0.523229	0.261614	+	0.965172i	$0.415745\pi$
$744$	50598.4	2.49332
$745$	19581.7	0.962975
$746$	−34633.1	−1.69974
$747$	12183.7	0.596756
$748$	15467.4	0.756077
$749$	0	0
$750$	20783.7	1.01189
$751$	36992.3	1.79743	0.898713	−	0.438537i	$-0.144503\pi$
$751$	36992.3	1.79743	0.898713	+	0.438537i	$0.144503\pi$
$752$	−64111.7	−3.10893
$753$	−21891.2	−1.05944
$754$	30424.9	1.46951
$755$	−20293.4	−0.978214
$756$	0	0
$757$	22057.3	1.05903	0.529515	−	0.848300i	$-0.322374\pi$
$757$	22057.3	1.05903	0.529515	+	0.848300i	$0.322374\pi$
$758$	−28881.2	−1.38392
$759$	1950.60	0.0932836
$760$	76888.1	3.66977
$761$	−16948.7	−0.807347	−0.403674	−	0.914903i	$-0.632267\pi$
$761$	−16948.7	−0.807347	−0.403674	+	0.914903i	$0.632267\pi$
$762$	−14668.0	−0.697330
$763$	0	0
$764$	53904.8	2.55263
$765$	7953.37	0.375889
$766$	−69465.9	−3.27664
$767$	22384.7	1.05380
$768$	−20200.1	−0.949102
$769$	−24621.4	−1.15458	−0.577288	−	0.816540i	$-0.695889\pi$
$769$	−24621.4	−1.15458	−0.577288	+	0.816540i	$0.695889\pi$
$770$	0	0
$771$	17232.4	0.804942
$772$	−70758.1	−3.29875
$773$	−10553.6	−0.491057	−0.245529	−	0.969389i	$-0.578962\pi$
$773$	−10553.6	−0.491057	−0.245529	+	0.969389i	$0.578962\pi$
$774$	11413.7	0.530046
$775$	2520.24	0.116813
$776$	−18200.9	−0.841978
$777$	0	0
$778$	5237.22	0.241341
$779$	−16468.3	−0.757430
$780$	40176.8	1.84431
$781$	−180.749	−0.00828133
$782$	23254.1	1.06338
$783$	−2527.78	−0.115371
$784$	0	0
$785$	−28981.4	−1.31769
$786$	−22040.8	−1.00021
$787$	−33839.2	−1.53270	−0.766352	−	0.642421i	$-0.777930\pi$
$787$	−33839.2	−1.53270	−0.766352	+	0.642421i	$0.777930\pi$
$788$	−79302.7	−3.58508
$789$	−5472.59	−0.246932
$790$	−32066.9	−1.44416
$791$	0	0
$792$	−5257.20	−0.235867
$793$	−6224.96	−0.278758
$794$	−50841.3	−2.27240
$795$	14447.2	0.644517
$796$	−62052.4	−2.76305
$797$	−11136.3	−0.494941	−0.247471	−	0.968895i	$-0.579599\pi$
$797$	−11136.3	−0.494941	−0.247471	+	0.968895i	$0.579599\pi$
$798$	0	0
$799$	39060.7	1.72950
$800$	1752.78	0.0774627
$801$	1263.21	0.0557220
$802$	−42909.8	−1.88928
$803$	7946.98	0.349244
$804$	51374.6	2.25353
$805$	0	0
$806$	−103217.	−4.51074
$807$	4935.63	0.215294
$808$	32798.7	1.42804
$809$	−27719.1	−1.20464	−0.602318	−	0.798256i	$-0.705756\pi$
$809$	−27719.1	−1.20464	−0.602318	+	0.798256i	$0.705756\pi$
$810$	−4793.58	−0.207937
$811$	10035.8	0.434531	0.217266	−	0.976113i	$-0.430286\pi$
$811$	10035.8	0.434531	0.217266	+	0.976113i	$0.430286\pi$
$812$	0	0
$813$	10722.2	0.462540
$814$	−304.678	−0.0131191
$815$	41988.4	1.80465
$816$	−28926.6	−1.24097
$817$	−31027.5	−1.32866
$818$	32128.7	1.37329
$819$	0	0
$820$	−27738.6	−1.18131
$821$	−15926.4	−0.677023	−0.338512	−	0.940962i	$-0.609923\pi$
$821$	−15926.4	−0.677023	−0.338512	+	0.940962i	$0.609923\pi$
$822$	25696.7	1.09036
$823$	−22827.4	−0.966843	−0.483422	−	0.875388i	$-0.660606\pi$
$823$	−22827.4	−0.966843	−0.483422	+	0.875388i	$0.660606\pi$
$824$	−51573.6	−2.18040
$825$	−261.854	−0.0110504
$826$	0	0
$827$	4962.86	0.208677	0.104338	−	0.994542i	$-0.466728\pi$
$827$	4962.86	0.208677	0.104338	+	0.994542i	$0.466728\pi$
$828$	−9759.63	−0.409626
$829$	−19638.7	−0.822775	−0.411388	−	0.911460i	$-0.634956\pi$
$829$	−19638.7	−0.822775	−0.411388	+	0.911460i	$0.634956\pi$
$830$	−80114.3	−3.35037
$831$	−6044.89	−0.252341
$832$	−8065.42	−0.336079
$833$	0	0
$834$	−576.813	−0.0239489
$835$	7623.68	0.315962
$836$	25342.5	1.04843
$837$	8575.51	0.354137
$838$	26517.6	1.09312
$839$	15068.6	0.620055	0.310027	−	0.950728i	$-0.399662\pi$
$839$	15068.6	0.620055	0.310027	+	0.950728i	$0.399662\pi$
$840$	0	0
$841$	−15624.0	−0.640618
$842$	69565.7	2.84726
$843$	−11925.4	−0.487229
$844$	70507.0	2.87553
$845$	−20887.7	−0.850367
$846$	−23542.3	−0.956739
$847$	0	0
$848$	−52544.9	−2.12783
$849$	24043.7	0.971939
$850$	−3121.70	−0.125969
$851$	−318.968	−0.0128485
$852$	904.361	0.0363649
$853$	−27659.6	−1.11025	−0.555127	−	0.831765i	$-0.687330\pi$
$853$	−27659.6	−1.11025	−0.555127	+	0.831765i	$0.687330\pi$
$854$	0	0
$855$	13031.1	0.521234
$856$	47470.2	1.89544
$857$	−32225.5	−1.28448	−0.642241	−	0.766502i	$-0.721995\pi$
$857$	−32225.5	−1.28448	−0.642241	+	0.766502i	$0.721995\pi$
$858$	10724.3	0.426714
$859$	2202.26	0.0874740	0.0437370	−	0.999043i	$-0.486074\pi$
$859$	2202.26	0.0874740	0.0437370	+	0.999043i	$0.486074\pi$
$860$	−52261.6	−2.07222
$861$	0	0
$862$	44442.8	1.75607
$863$	−35825.3	−1.41310	−0.706551	−	0.707662i	$-0.749750\pi$
$863$	−35825.3	−1.41310	−0.706551	+	0.707662i	$0.749750\pi$
$864$	5964.11	0.234841
$865$	−774.550	−0.0304456
$866$	34411.2	1.35028
$867$	2884.80	0.113002
$868$	0	0
$869$	−5960.38	−0.232672
$870$	16621.6	0.647728
$871$	−59100.2	−2.29912
$872$	−62713.0	−2.43547
$873$	−3084.72	−0.119590
$874$	38100.4	1.47456
$875$	0	0
$876$	−39761.9	−1.53360
$877$	−12497.0	−0.481178	−0.240589	−	0.970627i	$-0.577341\pi$
$877$	−12497.0	−0.481178	−0.240589	+	0.970627i	$0.577341\pi$
$878$	60233.6	2.31524
$879$	−19202.4	−0.736839
$880$	15955.1	0.611188
$881$	−17244.8	−0.659469	−0.329735	−	0.944074i	$-0.606959\pi$
$881$	−17244.8	−0.659469	−0.329735	+	0.944074i	$0.606959\pi$
$882$	0	0
$883$	8348.44	0.318174	0.159087	−	0.987265i	$-0.449145\pi$
$883$	8348.44	0.318174	0.159087	+	0.987265i	$0.449145\pi$
$884$	89027.5	3.38724
$885$	12229.1	0.464493
$886$	−67631.2	−2.56446
$887$	37814.8	1.43145	0.715725	−	0.698383i	$-0.246097\pi$
$887$	37814.8	1.43145	0.715725	+	0.698383i	$0.246097\pi$
$888$	859.675	0.0324874
$889$	0	0
$890$	−8306.32	−0.312841
$891$	−891.000	−0.0335013
$892$	71907.7	2.69916
$893$	63998.6	2.39824
$894$	−26152.1	−0.978364
$895$	−24506.5	−0.915265
$896$	0	0
$897$	11227.3	0.417912
$898$	−64887.5	−2.41127
$899$	−29735.2	−1.10314
$900$	1310.16	0.0485245
$901$	32013.5	1.18371
$902$	−7404.19	−0.273318
$903$	0	0
$904$	−40438.4	−1.48779
$905$	40503.6	1.48772
$906$	27102.6	0.993847
$907$	5967.62	0.218469	0.109235	−	0.994016i	$-0.465160\pi$
$907$	5967.62	0.218469	0.109235	+	0.994016i	$0.465160\pi$
$908$	6264.24	0.228949
$909$	5558.79	0.202831
$910$	0	0
$911$	7038.10	0.255964	0.127982	−	0.991777i	$-0.459150\pi$
$911$	7038.10	0.255964	0.127982	+	0.991777i	$0.459150\pi$
$912$	−47394.5	−1.72082
$913$	−14891.1	−0.539786
$914$	−40825.6	−1.47745
$915$	−3400.79	−0.122870
$916$	−4598.38	−0.165868
$917$	0	0
$918$	−10622.1	−0.381895
$919$	34623.3	1.24278	0.621392	−	0.783500i	$-0.286567\pi$
$919$	34623.3	1.24278	0.621392	+	0.783500i	$0.286567\pi$
$920$	36190.4	1.29691
$921$	−8747.35	−0.312959
$922$	−4799.91	−0.171450
$923$	−1040.36	−0.0371005
$924$	0	0
$925$	42.8193	0.00152204
$926$	−69022.2	−2.44947
$927$	−8740.78	−0.309692
$928$	−20680.3	−0.731535
$929$	−37754.6	−1.33336	−0.666678	−	0.745346i	$-0.732284\pi$
$929$	−37754.6	−1.33336	−0.666678	+	0.745346i	$0.732284\pi$
$930$	−56388.8	−1.98824
$931$	0	0
$932$	−87507.5	−3.07554
$933$	24806.2	0.870436
$934$	64497.0	2.25953
$935$	−9720.79	−0.340004
$936$	−30259.4	−1.05669
$937$	−2820.23	−0.0983275	−0.0491637	−	0.998791i	$-0.515656\pi$
$937$	−2820.23	−0.0983275	−0.0491637	+	0.998791i	$0.515656\pi$
$938$	0	0
$939$	26027.7	0.904559
$940$	107797.	3.74037
$941$	−27271.0	−0.944750	−0.472375	−	0.881398i	$-0.656603\pi$
$941$	−27271.0	−0.944750	−0.472375	+	0.881398i	$0.656603\pi$
$942$	38705.8	1.33875
$943$	−7751.45	−0.267680
$944$	−44477.4	−1.53349
$945$	0	0
$946$	−13950.0	−0.479445
$947$	−16823.3	−0.577280	−0.288640	−	0.957438i	$-0.593203\pi$
$947$	−16823.3	−0.577280	−0.288640	+	0.957438i	$0.593203\pi$
$948$	29822.2	1.02171
$949$	45741.2	1.56462
$950$	−5114.72	−0.174677
$951$	21031.7	0.717138
$952$	0	0
$953$	−27233.5	−0.925685	−0.462843	−	0.886440i	$-0.653171\pi$
$953$	−27233.5	−0.925685	−0.462843	+	0.886440i	$0.653171\pi$
$954$	−19294.9	−0.654817
$955$	−33877.5	−1.14790
$956$	−69659.2	−2.35663
$957$	3089.51	0.104357
$958$	99517.5	3.35623
$959$	0	0
$960$	−4406.25	−0.148137
$961$	71086.0	2.38616
$962$	−1753.67	−0.0587740
$963$	8045.34	0.269219
$964$	−43710.5	−1.46040
$965$	44469.2	1.48343
$966$	0	0
$967$	13998.5	0.465524	0.232762	−	0.972534i	$-0.425224\pi$
$967$	13998.5	0.465524	0.232762	+	0.972534i	$0.425224\pi$
$968$	6425.47	0.213350
$969$	28875.5	0.957292
$970$	20283.8	0.671416
$971$	18955.5	0.626478	0.313239	−	0.949674i	$-0.398586\pi$
$971$	18955.5	0.626478	0.313239	+	0.949674i	$0.398586\pi$
$972$	4458.03	0.147110
$973$	0	0
$974$	70425.0	2.31680
$975$	−1507.18	−0.0495061
$976$	12368.7	0.405649
$977$	8054.22	0.263743	0.131872	−	0.991267i	$-0.457901\pi$
$977$	8054.22	0.263743	0.131872	+	0.991267i	$0.457901\pi$
$978$	−56077.3	−1.83349
$979$	−1543.92	−0.0504025
$980$	0	0
$981$	−10628.7	−0.345921
$982$	17599.5	0.571918
$983$	49882.2	1.61851	0.809255	−	0.587457i	$-0.199871\pi$
$983$	49882.2	1.61851	0.809255	+	0.587457i	$0.199871\pi$
$984$	20891.5	0.676826
$985$	49839.2	1.61219
$986$	36831.5	1.18961
$987$	0	0
$988$	145866.	4.69699
$989$	−14604.3	−0.469555
$990$	5858.82	0.188087
$991$	21603.0	0.692473	0.346237	−	0.938147i	$-0.387459\pi$
$991$	21603.0	0.692473	0.346237	+	0.938147i	$0.387459\pi$
$992$	70158.1	2.24549
$993$	33638.9	1.07502
$994$	0	0
$995$	38998.0	1.24253
$996$	74506.3	2.37030
$997$	−52100.9	−1.65502	−0.827509	−	0.561452i	$-0.810243\pi$
$997$	−52100.9	−1.65502	−0.827509	+	0.561452i	$0.810243\pi$
$998$	14971.7	0.474870
$999$	145.699	0.00461433

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.bd.1.16	yes	16
7.6	odd	2		1617.4.a.bc.1.16	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.bc.1.16	✓	16	7.6	odd	2
1617.4.a.bd.1.16	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+5.13282 q^{2} +3.00000 q^{3} +18.3458 q^{4} -11.5297 q^{5} +15.3984 q^{6} +53.1030 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.13282 q^{2} +3.00000 q^{3} +18.3458 q^{4} -11.5297 q^{5} +15.3984 q^{6} +53.1030 q^{8} +9.00000 q^{9} -59.1800 q^{10} -11.0000 q^{11} +55.0374 q^{12} -63.3138 q^{13} -34.5892 q^{15} +125.802 q^{16} -76.6459 q^{17} +46.1953 q^{18} -125.580 q^{19} -211.522 q^{20} -56.4610 q^{22} -59.1091 q^{23} +159.309 q^{24} +7.93498 q^{25} -324.978 q^{26} +27.0000 q^{27} -93.6214 q^{29} -177.540 q^{30} +317.611 q^{31} +220.893 q^{32} -33.0000 q^{33} -393.409 q^{34} +165.112 q^{36} +5.39627 q^{37} -644.578 q^{38} -189.941 q^{39} -612.264 q^{40} +131.138 q^{41} +247.074 q^{43} -201.804 q^{44} -103.768 q^{45} -303.396 q^{46} -509.625 q^{47} +377.405 q^{48} +40.7288 q^{50} -229.938 q^{51} -1161.54 q^{52} -417.681 q^{53} +138.586 q^{54} +126.827 q^{55} -376.739 q^{57} -480.541 q^{58} -353.552 q^{59} -634.567 q^{60} +98.3192 q^{61} +1630.24 q^{62} +127.388 q^{64} +729.992 q^{65} -169.383 q^{66} +933.448 q^{67} -1406.13 q^{68} -177.327 q^{69} +16.4318 q^{71} +477.927 q^{72} -722.452 q^{73} +27.6980 q^{74} +23.8049 q^{75} -2303.86 q^{76} -974.934 q^{78} +541.853 q^{79} -1450.46 q^{80} +81.0000 q^{81} +673.108 q^{82} +1353.74 q^{83} +883.708 q^{85} +1268.18 q^{86} -280.864 q^{87} -584.133 q^{88} +140.357 q^{89} -532.620 q^{90} -1084.40 q^{92} +952.834 q^{93} -2615.81 q^{94} +1447.90 q^{95} +662.678 q^{96} -342.747 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9} - 178 q^{10} - 176 q^{11} + 216 q^{12} - 104 q^{13} + 220 q^{16} - 220 q^{17} - 36 q^{18} - 152 q^{19} - 182 q^{20} + 44 q^{22} - 180 q^{23} - 198 q^{24} + 284 q^{25} - 10 q^{26} + 432 q^{27} - 604 q^{29} - 534 q^{30} - 380 q^{31} - 592 q^{32} - 528 q^{33} - 632 q^{34} + 648 q^{36} + 148 q^{37} - 266 q^{38} - 312 q^{39} - 1792 q^{40} - 60 q^{41} + 252 q^{43} - 792 q^{44} - 116 q^{46} - 1468 q^{47} + 660 q^{48} - 850 q^{50} - 660 q^{51} - 310 q^{52} - 1456 q^{53} - 108 q^{54} - 456 q^{57} - 1350 q^{58} - 1312 q^{59} - 546 q^{60} - 2880 q^{61} - 708 q^{62} + 630 q^{64} - 4064 q^{65} + 132 q^{66} + 1220 q^{67} - 4956 q^{68} - 540 q^{69} - 2040 q^{71} - 594 q^{72} - 1628 q^{73} - 3126 q^{74} + 852 q^{75} - 6286 q^{76} - 30 q^{78} - 416 q^{79} + 874 q^{80} + 1296 q^{81} - 3040 q^{82} - 3724 q^{83} + 628 q^{85} - 1608 q^{86} - 1812 q^{87} + 726 q^{88} - 752 q^{89} - 1602 q^{90} - 32 q^{92} - 1140 q^{93} - 610 q^{94} - 912 q^{95} - 1776 q^{96} - 1088 q^{97} - 1584 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9 - 178 * q^10 - 176 * q^11 + 216 * q^12 - 104 * q^13 + 220 * q^16 - 220 * q^17 - 36 * q^18 - 152 * q^19 - 182 * q^20 + 44 * q^22 - 180 * q^23 - 198 * q^24 + 284 * q^25 - 10 * q^26 + 432 * q^27 - 604 * q^29 - 534 * q^30 - 380 * q^31 - 592 * q^32 - 528 * q^33 - 632 * q^34 + 648 * q^36 + 148 * q^37 - 266 * q^38 - 312 * q^39 - 1792 * q^40 - 60 * q^41 + 252 * q^43 - 792 * q^44 - 116 * q^46 - 1468 * q^47 + 660 * q^48 - 850 * q^50 - 660 * q^51 - 310 * q^52 - 1456 * q^53 - 108 * q^54 - 456 * q^57 - 1350 * q^58 - 1312 * q^59 - 546 * q^60 - 2880 * q^61 - 708 * q^62 + 630 * q^64 - 4064 * q^65 + 132 * q^66 + 1220 * q^67 - 4956 * q^68 - 540 * q^69 - 2040 * q^71 - 594 * q^72 - 1628 * q^73 - 3126 * q^74 + 852 * q^75 - 6286 * q^76 - 30 * q^78 - 416 * q^79 + 874 * q^80 + 1296 * q^81 - 3040 * q^82 - 3724 * q^83 + 628 * q^85 - 1608 * q^86 - 1812 * q^87 + 726 * q^88 - 752 * q^89 - 1602 * q^90 - 32 * q^92 - 1140 * q^93 - 610 * q^94 - 912 * q^95 - 1776 * q^96 - 1088 * q^97 - 1584 * q^99

Introduction

L-functions

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Varieties

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Database

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