LMFDB - Embedded newform 1617.4.a.q.1.6

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:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 38x^{5} + 73x^{4} + 383x^{3} - 256x^{2} - 676x - 224 $ x^7 - 3x^6 - 38x^5 + 73x^4 + 383x^3 - 256x^2 - 676x - 224
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$4.28176$ 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)

$f(q)$	$=$	$q+3.28176 q^{2} -3.00000 q^{3} +2.76992 q^{4} -6.75357 q^{5} -9.84527 q^{6} -17.1638 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.28176 q^{2} -3.00000 q^{3} +2.76992 q^{4} -6.75357 q^{5} -9.84527 q^{6} -17.1638 q^{8} +9.00000 q^{9} -22.1636 q^{10} +11.0000 q^{11} -8.30977 q^{12} +17.8121 q^{13} +20.2607 q^{15} -78.4869 q^{16} +122.219 q^{17} +29.5358 q^{18} -52.2268 q^{19} -18.7069 q^{20} +36.0993 q^{22} -128.320 q^{23} +51.4915 q^{24} -79.3892 q^{25} +58.4548 q^{26} -27.0000 q^{27} -216.778 q^{29} +66.4908 q^{30} -252.292 q^{31} -120.264 q^{32} -33.0000 q^{33} +401.092 q^{34} +24.9293 q^{36} +356.315 q^{37} -171.396 q^{38} -53.4362 q^{39} +115.917 q^{40} +276.938 q^{41} -327.683 q^{43} +30.4692 q^{44} -60.7822 q^{45} -421.116 q^{46} +469.742 q^{47} +235.461 q^{48} -260.536 q^{50} -366.657 q^{51} +49.3380 q^{52} -124.727 q^{53} -88.6074 q^{54} -74.2893 q^{55} +156.681 q^{57} -711.413 q^{58} +449.091 q^{59} +56.1207 q^{60} -356.246 q^{61} -827.962 q^{62} +233.217 q^{64} -120.295 q^{65} -108.298 q^{66} -253.661 q^{67} +338.537 q^{68} +384.961 q^{69} +812.727 q^{71} -154.475 q^{72} -183.554 q^{73} +1169.34 q^{74} +238.168 q^{75} -144.664 q^{76} -175.364 q^{78} +1303.73 q^{79} +530.067 q^{80} +81.0000 q^{81} +908.844 q^{82} +1111.30 q^{83} -825.414 q^{85} -1075.37 q^{86} +650.335 q^{87} -188.802 q^{88} +1015.26 q^{89} -199.472 q^{90} -355.437 q^{92} +756.877 q^{93} +1541.58 q^{94} +352.718 q^{95} +360.793 q^{96} +902.429 q^{97} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9	\( 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9} - 49 q^{10} + 77 q^{11} - 90 q^{12} + 92 q^{13} - 60 q^{15} + 218 q^{16} + 170 q^{17} - 36 q^{18} + 76 q^{19} + 569 q^{20} - 44 q^{22} - 56 q^{23} + 117 q^{24} + 53 q^{25} + 109 q^{26} - 189 q^{27} - 472 q^{29} + 147 q^{30} + 290 q^{31} - 1046 q^{32} - 231 q^{33} + 344 q^{34} + 270 q^{36} - 66 q^{37} + 385 q^{38} - 276 q^{39} - 800 q^{40} - 166 q^{41} - 76 q^{43} + 330 q^{44} + 180 q^{45} - 528 q^{46} + 1082 q^{47} - 654 q^{48} - 569 q^{50} - 510 q^{51} + 1065 q^{52} - 150 q^{53} + 108 q^{54} + 220 q^{55} - 228 q^{57} + 1457 q^{58} + 1284 q^{59} - 1707 q^{60} - 764 q^{61} - 296 q^{62} + 1661 q^{64} + 2722 q^{65} + 132 q^{66} - 658 q^{67} - 360 q^{68} + 168 q^{69} - 272 q^{71} - 351 q^{72} + 1658 q^{73} + 613 q^{74} - 159 q^{75} - 1757 q^{76} - 327 q^{78} + 792 q^{79} + 5079 q^{80} + 567 q^{81} + 3208 q^{82} - 770 q^{83} - 776 q^{85} - 478 q^{86} + 1416 q^{87} - 429 q^{88} + 656 q^{89} - 441 q^{90} - 3916 q^{92} - 870 q^{93} - 849 q^{94} - 1636 q^{95} + 3138 q^{96} + 608 q^{97} + 693 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9 - 49 * q^10 + 77 * q^11 - 90 * q^12 + 92 * q^13 - 60 * q^15 + 218 * q^16 + 170 * q^17 - 36 * q^18 + 76 * q^19 + 569 * q^20 - 44 * q^22 - 56 * q^23 + 117 * q^24 + 53 * q^25 + 109 * q^26 - 189 * q^27 - 472 * q^29 + 147 * q^30 + 290 * q^31 - 1046 * q^32 - 231 * q^33 + 344 * q^34 + 270 * q^36 - 66 * q^37 + 385 * q^38 - 276 * q^39 - 800 * q^40 - 166 * q^41 - 76 * q^43 + 330 * q^44 + 180 * q^45 - 528 * q^46 + 1082 * q^47 - 654 * q^48 - 569 * q^50 - 510 * q^51 + 1065 * q^52 - 150 * q^53 + 108 * q^54 + 220 * q^55 - 228 * q^57 + 1457 * q^58 + 1284 * q^59 - 1707 * q^60 - 764 * q^61 - 296 * q^62 + 1661 * q^64 + 2722 * q^65 + 132 * q^66 - 658 * q^67 - 360 * q^68 + 168 * q^69 - 272 * q^71 - 351 * q^72 + 1658 * q^73 + 613 * q^74 - 159 * q^75 - 1757 * q^76 - 327 * q^78 + 792 * q^79 + 5079 * q^80 + 567 * q^81 + 3208 * q^82 - 770 * q^83 - 776 * q^85 - 478 * q^86 + 1416 * q^87 - 429 * q^88 + 656 * q^89 - 441 * q^90 - 3916 * q^92 - 870 * q^93 - 849 * q^94 - 1636 * q^95 + 3138 * q^96 + 608 * q^97 + 693 * 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 $

$2$	3.28176	1.16028	0.580138	−	0.814518i	$-0.302999\pi$
$2$	3.28176	1.16028	0.580138	+	0.814518i	$0.302999\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	2.76992	0.346240
$5$	−6.75357	−0.604058	−0.302029	−	0.953299i	$-0.597664\pi$
$5$	−6.75357	−0.604058	−0.302029	+	0.953299i	$0.597664\pi$
$6$	−9.84527	−0.669886
$7$	0	0
$7$	0	0
$8$	−17.1638	−0.758542
$9$	9.00000	0.333333
$10$	−22.1636	−0.700874
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−8.30977	−0.199902
$13$	17.8121	0.380014	0.190007	−	0.981783i	$-0.439149\pi$
$13$	17.8121	0.380014	0.190007	+	0.981783i	$0.439149\pi$
$14$	0	0
$15$	20.2607	0.348753
$16$	−78.4869	−1.22636
$17$	122.219	1.74367	0.871836	−	0.489798i	$-0.162929\pi$
$17$	122.219	1.74367	0.871836	+	0.489798i	$0.162929\pi$
$18$	29.5358	0.386759
$19$	−52.2268	−0.630614	−0.315307	−	0.948990i	$-0.602107\pi$
$19$	−52.2268	−0.630614	−0.315307	+	0.948990i	$0.602107\pi$
$20$	−18.7069	−0.209149
$21$	0	0
$22$	36.0993	0.349836
$23$	−128.320	−1.16333	−0.581666	−	0.813428i	$-0.697599\pi$
$23$	−128.320	−1.16333	−0.581666	+	0.813428i	$0.697599\pi$
$24$	51.4915	0.437944
$25$	−79.3892	−0.635114
$26$	58.4548	0.440921
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−216.778	−1.38809	−0.694047	−	0.719930i	$-0.744174\pi$
$29$	−216.778	−1.38809	−0.694047	+	0.719930i	$0.744174\pi$
$30$	66.4908	0.404650
$31$	−252.292	−1.46171	−0.730856	−	0.682532i	$-0.760879\pi$
$31$	−252.292	−1.46171	−0.730856	+	0.682532i	$0.760879\pi$
$32$	−120.264	−0.664372
$33$	−33.0000	−0.174078
$34$	401.092	2.02314
$35$	0	0
$36$	24.9293	0.115413
$37$	356.315	1.58318	0.791591	−	0.611051i	$-0.209253\pi$
$37$	356.315	1.58318	0.791591	+	0.611051i	$0.209253\pi$
$38$	−171.396	−0.731686
$39$	−53.4362	−0.219401
$40$	115.917	0.458203
$41$	276.938	1.05489	0.527445	−	0.849589i	$-0.323150\pi$
$41$	276.938	1.05489	0.527445	+	0.849589i	$0.323150\pi$
$42$	0	0
$43$	−327.683	−1.16212	−0.581060	−	0.813861i	$-0.697362\pi$
$43$	−327.683	−1.16212	−0.581060	+	0.813861i	$0.697362\pi$
$44$	30.4692	0.104395
$45$	−60.7822	−0.201353
$46$	−421.116	−1.34979
$47$	469.742	1.45785	0.728924	−	0.684595i	$-0.240021\pi$
$47$	469.742	1.45785	0.728924	+	0.684595i	$0.240021\pi$
$48$	235.461	0.708038
$49$	0	0
$50$	−260.536	−0.736907
$51$	−366.657	−1.00671
$52$	49.3380	0.131576
$53$	−124.727	−0.323255	−0.161627	−	0.986852i	$-0.551674\pi$
$53$	−124.727	−0.323255	−0.161627	+	0.986852i	$0.551674\pi$
$54$	−88.6074	−0.223295
$55$	−74.2893	−0.182130
$56$	0	0
$57$	156.681	0.364085
$58$	−711.413	−1.61057
$59$	449.091	0.990960	0.495480	−	0.868619i	$-0.334992\pi$
$59$	449.091	0.990960	0.495480	+	0.868619i	$0.334992\pi$
$60$	56.1207	0.120752
$61$	−356.246	−0.747748	−0.373874	−	0.927480i	$-0.621971\pi$
$61$	−356.246	−0.747748	−0.373874	+	0.927480i	$0.621971\pi$
$62$	−827.962	−1.69599
$63$	0	0
$64$	233.217	0.455503
$65$	−120.295	−0.229550
$66$	−108.298	−0.201978
$67$	−253.661	−0.462532	−0.231266	−	0.972891i	$-0.574287\pi$
$67$	−253.661	−0.462532	−0.231266	+	0.972891i	$0.574287\pi$
$68$	338.537	0.603730
$69$	384.961	0.671650
$70$	0	0
$71$	812.727	1.35849	0.679246	−	0.733910i	$-0.262307\pi$
$71$	812.727	1.35849	0.679246	+	0.733910i	$0.262307\pi$
$72$	−154.475	−0.252847
$73$	−183.554	−0.294292	−0.147146	−	0.989115i	$-0.547009\pi$
$73$	−183.554	−0.294292	−0.147146	+	0.989115i	$0.547009\pi$
$74$	1169.34	1.83693
$75$	238.168	0.366683
$76$	−144.664	−0.218344
$77$	0	0
$78$	−175.364	−0.254566
$79$	1303.73	1.85672	0.928360	−	0.371683i	$-0.121219\pi$
$79$	1303.73	1.85672	0.928360	+	0.371683i	$0.121219\pi$
$80$	530.067	0.740791
$81$	81.0000	0.111111
$82$	908.844	1.22396
$83$	1111.30	1.46966	0.734828	−	0.678253i	$-0.237263\pi$
$83$	1111.30	1.46966	0.734828	+	0.678253i	$0.237263\pi$
$84$	0	0
$85$	−825.414	−1.05328
$86$	−1075.37	−1.34838
$87$	650.335	0.801416
$88$	−188.802	−0.228709
$89$	1015.26	1.20919	0.604593	−	0.796535i	$-0.293336\pi$
$89$	1015.26	1.20919	0.604593	+	0.796535i	$0.293336\pi$
$90$	−199.472	−0.233625
$91$	0	0
$92$	−355.437	−0.402792
$93$	756.877	0.843919
$94$	1541.58	1.69151
$95$	352.718	0.380927
$96$	360.793	0.383575
$97$	902.429	0.944616	0.472308	−	0.881434i	$-0.343421\pi$
$97$	902.429	0.944616	0.472308	+	0.881434i	$0.343421\pi$
$98$	0	0
$99$	99.0000	0.100504
$100$	−219.902	−0.219902
$101$	−1631.36	−1.60719	−0.803594	−	0.595177i	$-0.797082\pi$
$101$	−1631.36	−1.60719	−0.803594	+	0.595177i	$0.797082\pi$
$102$	−1203.28	−1.16806
$103$	1769.77	1.69301	0.846506	−	0.532379i	$-0.178702\pi$
$103$	1769.77	1.69301	0.846506	+	0.532379i	$0.178702\pi$
$104$	−305.723	−0.288256
$105$	0	0
$106$	−409.322	−0.375065
$107$	914.631	0.826361	0.413181	−	0.910649i	$-0.364418\pi$
$107$	914.631	0.826361	0.413181	+	0.910649i	$0.364418\pi$
$108$	−74.7879	−0.0666340
$109$	1548.11	1.36039	0.680195	−	0.733031i	$-0.261895\pi$
$109$	1548.11	1.36039	0.680195	+	0.733031i	$0.261895\pi$
$110$	−243.799	−0.211322
$111$	−1068.94	−0.914051
$112$	0	0
$113$	−828.758	−0.689938	−0.344969	−	0.938614i	$-0.612111\pi$
$113$	−828.758	−0.689938	−0.344969	+	0.938614i	$0.612111\pi$
$114$	514.187	0.422439
$115$	866.620	0.702720
$116$	−600.459	−0.480614
$117$	160.309	0.126671
$118$	1473.81	1.14979
$119$	0	0
$120$	−347.752	−0.264544
$121$	121.000	0.0909091
$122$	−1169.11	−0.867594
$123$	−830.815	−0.609041
$124$	−698.831	−0.506103
$125$	1380.36	0.987704
$126$	0	0
$127$	2135.81	1.49231	0.746153	−	0.665775i	$-0.231899\pi$
$127$	2135.81	1.49231	0.746153	+	0.665775i	$0.231899\pi$
$128$	1727.48	1.19288
$129$	983.048	0.670950
$130$	−394.779	−0.266342
$131$	2525.27	1.68422	0.842112	−	0.539302i	$-0.181312\pi$
$131$	2525.27	1.68422	0.842112	+	0.539302i	$0.181312\pi$
$132$	−91.4075	−0.0602727
$133$	0	0
$134$	−832.454	−0.536665
$135$	182.347	0.116251
$136$	−2097.74	−1.32265
$137$	−2651.92	−1.65378	−0.826892	−	0.562360i	$-0.809894\pi$
$137$	−2651.92	−1.65378	−0.826892	+	0.562360i	$0.809894\pi$
$138$	1263.35	0.779299
$139$	110.894	0.0676685	0.0338342	−	0.999427i	$-0.489228\pi$
$139$	110.894	0.0676685	0.0338342	+	0.999427i	$0.489228\pi$
$140$	0	0
$141$	−1409.22	−0.841689
$142$	2667.17	1.57623
$143$	195.933	0.114578
$144$	−706.382	−0.408786
$145$	1464.03	0.838489
$146$	−602.378	−0.341460
$147$	0	0
$148$	986.964	0.548162
$149$	−2458.42	−1.35169	−0.675844	−	0.737045i	$-0.736221\pi$
$149$	−2458.42	−1.35169	−0.675844	+	0.737045i	$0.736221\pi$
$150$	781.608	0.425454
$151$	−809.708	−0.436378	−0.218189	−	0.975906i	$-0.570015\pi$
$151$	−809.708	−0.436378	−0.218189	+	0.975906i	$0.570015\pi$
$152$	896.413	0.478347
$153$	1099.97	0.581224
$154$	0	0
$155$	1703.88	0.882958
$156$	−148.014	−0.0759655
$157$	232.487	0.118182	0.0590908	−	0.998253i	$-0.481180\pi$
$157$	232.487	0.118182	0.0590908	+	0.998253i	$0.481180\pi$
$158$	4278.52	2.15431
$159$	374.180	0.186631
$160$	812.213	0.401319
$161$	0	0
$162$	265.822	0.128920
$163$	758.198	0.364335	0.182168	−	0.983268i	$-0.441689\pi$
$163$	758.198	0.364335	0.182168	+	0.983268i	$0.441689\pi$
$164$	767.098	0.365246
$165$	222.868	0.105153
$166$	3647.03	1.70521
$167$	−1906.88	−0.883585	−0.441793	−	0.897117i	$-0.645657\pi$
$167$	−1906.88	−0.883585	−0.441793	+	0.897117i	$0.645657\pi$
$168$	0	0
$169$	−1879.73	−0.855590
$170$	−2708.81	−1.22209
$171$	−470.042	−0.210205
$172$	−907.656	−0.402373
$173$	−988.890	−0.434589	−0.217295	−	0.976106i	$-0.569723\pi$
$173$	−988.890	−0.434589	−0.217295	+	0.976106i	$0.569723\pi$
$174$	2134.24	0.929864
$175$	0	0
$176$	−863.356	−0.369761
$177$	−1347.27	−0.572131
$178$	3331.84	1.40299
$179$	−136.047	−0.0568081	−0.0284041	−	0.999597i	$-0.509043\pi$
$179$	−136.047	−0.0568081	−0.0284041	+	0.999597i	$0.509043\pi$
$180$	−168.362	−0.0697164
$181$	743.405	0.305286	0.152643	−	0.988281i	$-0.451221\pi$
$181$	743.405	0.305286	0.152643	+	0.988281i	$0.451221\pi$
$182$	0	0
$183$	1068.74	0.431712
$184$	2202.47	0.882435
$185$	−2406.40	−0.956334
$186$	2483.89	0.979179
$187$	1344.41	0.525737
$188$	1301.15	0.504766
$189$	0	0
$190$	1157.53	0.441981
$191$	503.013	0.190559	0.0952795	−	0.995451i	$-0.469626\pi$
$191$	503.013	0.190559	0.0952795	+	0.995451i	$0.469626\pi$
$192$	−699.652	−0.262985
$193$	−1917.95	−0.715320	−0.357660	−	0.933852i	$-0.616425\pi$
$193$	−1917.95	−0.715320	−0.357660	+	0.933852i	$0.616425\pi$
$194$	2961.55	1.09602
$195$	360.885	0.132531
$196$	0	0
$197$	1501.16	0.542911	0.271455	−	0.962451i	$-0.412495\pi$
$197$	1501.16	0.542911	0.271455	+	0.962451i	$0.412495\pi$
$198$	324.894	0.116612
$199$	−553.640	−0.197219	−0.0986094	−	0.995126i	$-0.531439\pi$
$199$	−553.640	−0.197219	−0.0986094	+	0.995126i	$0.531439\pi$
$200$	1362.62	0.481760
$201$	760.984	0.267043
$202$	−5353.72	−1.86478
$203$	0	0
$204$	−1015.61	−0.348564
$205$	−1870.32	−0.637215
$206$	5807.94	1.96436
$207$	−1154.88	−0.387777
$208$	−1398.01	−0.466033
$209$	−574.495	−0.190137
$210$	0	0
$211$	294.245	0.0960033	0.0480016	−	0.998847i	$-0.484715\pi$
$211$	294.245	0.0960033	0.0480016	+	0.998847i	$0.484715\pi$
$212$	−345.483	−0.111924
$213$	−2438.18	−0.784326
$214$	3001.59	0.958807
$215$	2213.03	0.701988
$216$	463.424	0.145981
$217$	0	0
$218$	5080.53	1.57843
$219$	550.661	0.169910
$220$	−205.776	−0.0630609
$221$	2176.97	0.662619
$222$	−3508.01	−1.06055
$223$	−4711.62	−1.41486	−0.707429	−	0.706784i	$-0.750145\pi$
$223$	−4711.62	−1.41486	−0.707429	+	0.706784i	$0.750145\pi$
$224$	0	0
$225$	−714.503	−0.211705
$226$	−2719.78	−0.800519
$227$	−4579.56	−1.33901	−0.669507	−	0.742805i	$-0.733495\pi$
$227$	−4579.56	−1.33901	−0.669507	+	0.742805i	$0.733495\pi$
$228$	433.993	0.126061
$229$	−335.719	−0.0968774	−0.0484387	−	0.998826i	$-0.515425\pi$
$229$	−335.719	−0.0968774	−0.0484387	+	0.998826i	$0.515425\pi$
$230$	2844.04	0.815349
$231$	0	0
$232$	3720.75	1.05293
$233$	−5850.58	−1.64500	−0.822498	−	0.568768i	$-0.807420\pi$
$233$	−5850.58	−1.64500	−0.822498	+	0.568768i	$0.807420\pi$
$234$	526.093	0.146974
$235$	−3172.44	−0.880625
$236$	1243.95	0.343110
$237$	−3911.18	−1.07198
$238$	0	0
$239$	4484.88	1.21382	0.606909	−	0.794771i	$-0.292409\pi$
$239$	4484.88	1.21382	0.606909	+	0.794771i	$0.292409\pi$
$240$	−1590.20	−0.427696
$241$	4127.57	1.10324	0.551618	−	0.834097i	$-0.314011\pi$
$241$	4127.57	1.10324	0.551618	+	0.834097i	$0.314011\pi$
$242$	397.092	0.105480
$243$	−243.000	−0.0641500
$244$	−986.774	−0.258901
$245$	0	0
$246$	−2726.53	−0.706656
$247$	−930.267	−0.239642
$248$	4330.30	1.10877
$249$	−3333.91	−0.848506
$250$	4530.00	1.14601
$251$	−3879.13	−0.975492	−0.487746	−	0.872986i	$-0.662181\pi$
$251$	−3879.13	−0.975492	−0.487746	+	0.872986i	$0.662181\pi$
$252$	0	0
$253$	−1411.52	−0.350758
$254$	7009.22	1.73149
$255$	2476.24	0.608111
$256$	3803.42	0.928569
$257$	5630.47	1.36661	0.683306	−	0.730132i	$-0.260542\pi$
$257$	5630.47	1.36661	0.683306	+	0.730132i	$0.260542\pi$
$258$	3226.12	0.778487
$259$	0	0
$260$	−333.208	−0.0794796
$261$	−1951.00	−0.462698
$262$	8287.30	1.95417
$263$	5344.23	1.25300	0.626501	−	0.779421i	$-0.284486\pi$
$263$	5344.23	1.25300	0.626501	+	0.779421i	$0.284486\pi$
$264$	566.407	0.132045
$265$	842.350	0.195265
$266$	0	0
$267$	−3045.78	−0.698124
$268$	−702.622	−0.160147
$269$	4100.27	0.929360	0.464680	−	0.885479i	$-0.346169\pi$
$269$	4100.27	0.929360	0.464680	+	0.885479i	$0.346169\pi$
$270$	598.417	0.134883
$271$	3691.68	0.827504	0.413752	−	0.910390i	$-0.364218\pi$
$271$	3691.68	0.827504	0.413752	+	0.910390i	$0.364218\pi$
$272$	−9592.58	−2.13837
$273$	0	0
$274$	−8702.94	−1.91885
$275$	−873.281	−0.191494
$276$	1066.31	0.232552
$277$	−471.856	−0.102350	−0.0511752	−	0.998690i	$-0.516297\pi$
$277$	−471.856	−0.102350	−0.0511752	+	0.998690i	$0.516297\pi$
$278$	363.928	0.0785141
$279$	−2270.63	−0.487237
$280$	0	0
$281$	8693.78	1.84565	0.922825	−	0.385220i	$-0.125875\pi$
$281$	8693.78	1.84565	0.922825	+	0.385220i	$0.125875\pi$
$282$	−4624.73	−0.976592
$283$	−6176.66	−1.29740	−0.648700	−	0.761044i	$-0.724687\pi$
$283$	−6176.66	−1.29740	−0.648700	+	0.761044i	$0.724687\pi$
$284$	2251.19	0.470365
$285$	−1058.15	−0.219928
$286$	643.003	0.132943
$287$	0	0
$288$	−1082.38	−0.221457
$289$	10024.4	2.04039
$290$	4804.58	0.972879
$291$	−2707.29	−0.545374
$292$	−508.430	−0.101896
$293$	−5119.89	−1.02084	−0.510422	−	0.859924i	$-0.670511\pi$
$293$	−5119.89	−1.02084	−0.510422	+	0.859924i	$0.670511\pi$
$294$	0	0
$295$	−3032.97	−0.598597
$296$	−6115.73	−1.20091
$297$	−297.000	−0.0580259
$298$	−8067.93	−1.56833
$299$	−2285.65	−0.442082
$300$	659.706	0.126961
$301$	0	0
$302$	−2657.27	−0.506319
$303$	4894.07	0.927911
$304$	4099.12	0.773358
$305$	2405.93	0.451683
$306$	3609.83	0.674380
$307$	3768.12	0.700515	0.350257	−	0.936653i	$-0.386094\pi$
$307$	3768.12	0.700515	0.350257	+	0.936653i	$0.386094\pi$
$308$	0	0
$309$	−5309.30	−0.977461
$310$	5591.70	1.02448
$311$	1648.46	0.300564	0.150282	−	0.988643i	$-0.451982\pi$
$311$	1648.46	0.300564	0.150282	+	0.988643i	$0.451982\pi$
$312$	917.170	0.166425
$313$	6367.07	1.14980	0.574901	−	0.818223i	$-0.305041\pi$
$313$	6367.07	1.14980	0.574901	+	0.818223i	$0.305041\pi$
$314$	762.967	0.137123
$315$	0	0
$316$	3611.23	0.642871
$317$	−9865.83	−1.74801	−0.874006	−	0.485914i	$-0.838487\pi$
$317$	−9865.83	−1.74801	−0.874006	+	0.485914i	$0.838487\pi$
$318$	1227.97	0.216544
$319$	−2384.56	−0.418526
$320$	−1575.05	−0.275150
$321$	−2743.89	−0.477100
$322$	0	0
$323$	−6383.10	−1.09958
$324$	224.364	0.0384712
$325$	−1414.09	−0.241352
$326$	2488.22	0.422729
$327$	−4644.34	−0.785421
$328$	−4753.33	−0.800178
$329$	0	0
$330$	731.398	0.122007
$331$	114.633	0.0190357	0.00951786	−	0.999955i	$-0.496970\pi$
$331$	114.633	0.0190357	0.00951786	+	0.999955i	$0.496970\pi$
$332$	3078.23	0.508854
$333$	3206.83	0.527728
$334$	−6257.91	−1.02520
$335$	1713.12	0.279396
$336$	0	0
$337$	−2135.08	−0.345119	−0.172560	−	0.984999i	$-0.555204\pi$
$337$	−2135.08	−0.345119	−0.172560	+	0.984999i	$0.555204\pi$
$338$	−6168.82	−0.992720
$339$	2486.27	0.398336
$340$	−2286.33	−0.364688
$341$	−2775.22	−0.440722
$342$	−1542.56	−0.243895
$343$	0	0
$344$	5624.29	0.881516
$345$	−2599.86	−0.405715
$346$	−3245.30	−0.504243
$347$	3039.47	0.470223	0.235112	−	0.971968i	$-0.424454\pi$
$347$	3039.47	0.470223	0.235112	+	0.971968i	$0.424454\pi$
$348$	1801.38	0.277483
$349$	7938.30	1.21756	0.608778	−	0.793340i	$-0.291660\pi$
$349$	7938.30	1.21756	0.608778	+	0.793340i	$0.291660\pi$
$350$	0	0
$351$	−480.926	−0.0731336
$352$	−1322.91	−0.200316
$353$	7723.11	1.16447	0.582237	−	0.813019i	$-0.302177\pi$
$353$	7723.11	1.16447	0.582237	+	0.813019i	$0.302177\pi$
$354$	−4421.42	−0.663830
$355$	−5488.81	−0.820608
$356$	2812.20	0.418669
$357$	0	0
$358$	−446.474	−0.0659131
$359$	2452.64	0.360572	0.180286	−	0.983614i	$-0.442298\pi$
$359$	2452.64	0.360572	0.180286	+	0.983614i	$0.442298\pi$
$360$	1043.26	0.152734
$361$	−4131.36	−0.602327
$362$	2439.67	0.354217
$363$	−363.000	−0.0524864
$364$	0	0
$365$	1239.64	0.177770
$366$	3507.34	0.500906
$367$	9657.52	1.37362	0.686810	−	0.726837i	$-0.259010\pi$
$367$	9657.52	1.37362	0.686810	+	0.726837i	$0.259010\pi$
$368$	10071.5	1.42666
$369$	2492.45	0.351630
$370$	−7897.21	−1.10961
$371$	0	0
$372$	2096.49	0.292199
$373$	4354.09	0.604413	0.302207	−	0.953242i	$-0.402277\pi$
$373$	4354.09	0.604413	0.302207	+	0.953242i	$0.402277\pi$
$374$	4412.02	0.610000
$375$	−4141.07	−0.570251
$376$	−8062.57	−1.10584
$377$	−3861.27	−0.527494
$378$	0	0
$379$	13976.7	1.89429	0.947143	−	0.320813i	$-0.103956\pi$
$379$	13976.7	1.89429	0.947143	+	0.320813i	$0.103956\pi$
$380$	977.001	0.131892
$381$	−6407.44	−0.861583
$382$	1650.77	0.221101
$383$	−401.811	−0.0536072	−0.0268036	−	0.999641i	$-0.508533\pi$
$383$	−401.811	−0.0536072	−0.0268036	+	0.999641i	$0.508533\pi$
$384$	−5182.43	−0.688710
$385$	0	0
$386$	−6294.23	−0.829968
$387$	−2949.14	−0.387373
$388$	2499.66	0.327064
$389$	8270.03	1.07791	0.538955	−	0.842334i	$-0.318819\pi$
$389$	8270.03	1.07791	0.538955	+	0.842334i	$0.318819\pi$
$390$	1184.34	0.153772
$391$	−15683.2	−2.02847
$392$	0	0
$393$	−7575.80	−0.972388
$394$	4926.45	0.629926
$395$	−8804.82	−1.12157
$396$	274.222	0.0347985
$397$	2987.83	0.377720	0.188860	−	0.982004i	$-0.439521\pi$
$397$	2987.83	0.377720	0.188860	+	0.982004i	$0.439521\pi$
$398$	−1816.91	−0.228828
$399$	0	0
$400$	6231.02	0.778877
$401$	13101.6	1.63158	0.815790	−	0.578348i	$-0.196303\pi$
$401$	13101.6	1.63158	0.815790	+	0.578348i	$0.196303\pi$
$402$	2497.36	0.309844
$403$	−4493.85	−0.555470
$404$	−4518.73	−0.556474
$405$	−547.040	−0.0671176
$406$	0	0
$407$	3919.46	0.477348
$408$	6293.23	0.763631
$409$	−3200.71	−0.386956	−0.193478	−	0.981105i	$-0.561977\pi$
$409$	−3200.71	−0.386956	−0.193478	+	0.981105i	$0.561977\pi$
$410$	−6137.95	−0.739346
$411$	7955.75	0.954813
$412$	4902.12	0.586189
$413$	0	0
$414$	−3790.04	−0.449928
$415$	−7505.27	−0.887758
$416$	−2142.15	−0.252470
$417$	−332.682	−0.0390684
$418$	−1885.35	−0.220612
$419$	6153.32	0.717444	0.358722	−	0.933444i	$-0.383213\pi$
$419$	6153.32	0.717444	0.358722	+	0.933444i	$0.383213\pi$
$420$	0	0
$421$	1378.63	0.159597	0.0797985	−	0.996811i	$-0.474572\pi$
$421$	1378.63	0.159597	0.0797985	+	0.996811i	$0.474572\pi$
$422$	965.642	0.111390
$423$	4227.67	0.485949
$424$	2140.79	0.245202
$425$	−9702.86	−1.10743
$426$	−8001.52	−0.910035
$427$	0	0
$428$	2533.46	0.286120
$429$	−587.798	−0.0661519
$430$	7262.63	0.814500
$431$	9715.83	1.08584	0.542918	−	0.839786i	$-0.317320\pi$
$431$	9715.83	1.08584	0.542918	+	0.839786i	$0.317320\pi$
$432$	2119.15	0.236013
$433$	−10762.5	−1.19449	−0.597245	−	0.802059i	$-0.703738\pi$
$433$	−10762.5	−1.19449	−0.597245	+	0.802059i	$0.703738\pi$
$434$	0	0
$435$	−4392.08	−0.484102
$436$	4288.16	0.471022
$437$	6701.76	0.733612
$438$	1807.13	0.197142
$439$	−1969.87	−0.214161	−0.107081	−	0.994250i	$-0.534150\pi$
$439$	−1969.87	−0.214161	−0.107081	+	0.994250i	$0.534150\pi$
$440$	1275.09	0.138153
$441$	0	0
$442$	7144.28	0.768821
$443$	−7607.02	−0.815847	−0.407924	−	0.913016i	$-0.633747\pi$
$443$	−7607.02	−0.815847	−0.407924	+	0.913016i	$0.633747\pi$
$444$	−2960.89	−0.316481
$445$	−6856.64	−0.730418
$446$	−15462.4	−1.64163
$447$	7375.26	0.780398
$448$	0	0
$449$	−8031.40	−0.844154	−0.422077	−	0.906560i	$-0.638699\pi$
$449$	−8031.40	−0.844154	−0.422077	+	0.906560i	$0.638699\pi$
$450$	−2344.82	−0.245636
$451$	3046.32	0.318062
$452$	−2295.60	−0.238884
$453$	2429.13	0.251943
$454$	−15029.0	−1.55363
$455$	0	0
$456$	−2689.24	−0.276174
$457$	7534.58	0.771232	0.385616	−	0.922659i	$-0.373989\pi$
$457$	7534.58	0.771232	0.385616	+	0.922659i	$0.373989\pi$
$458$	−1101.75	−0.112405
$459$	−3299.91	−0.335570
$460$	2400.47	0.243310
$461$	−8884.86	−0.897634	−0.448817	−	0.893624i	$-0.648154\pi$
$461$	−8884.86	−0.897634	−0.448817	+	0.893624i	$0.648154\pi$
$462$	0	0
$463$	−5561.05	−0.558194	−0.279097	−	0.960263i	$-0.590035\pi$
$463$	−5561.05	−0.558194	−0.279097	+	0.960263i	$0.590035\pi$
$464$	17014.3	1.70230
$465$	−5111.63	−0.509776
$466$	−19200.2	−1.90865
$467$	−2089.35	−0.207032	−0.103516	−	0.994628i	$-0.533009\pi$
$467$	−2089.35	−0.207032	−0.103516	+	0.994628i	$0.533009\pi$
$468$	444.042	0.0438587
$469$	0	0
$470$	−10411.2	−1.02177
$471$	−697.462	−0.0682322
$472$	−7708.12	−0.751684
$473$	−3604.51	−0.350392
$474$	−12835.5	−1.24379
$475$	4146.25	0.400511
$476$	0	0
$477$	−1122.54	−0.107752
$478$	14718.3	1.40836
$479$	−5442.60	−0.519162	−0.259581	−	0.965721i	$-0.583584\pi$
$479$	−5442.60	−0.519162	−0.259581	+	0.965721i	$0.583584\pi$
$480$	−2436.64	−0.231702
$481$	6346.70	0.601631
$482$	13545.7	1.28006
$483$	0	0
$484$	335.161	0.0314764
$485$	−6094.62	−0.570603
$486$	−797.467	−0.0744317
$487$	−957.632	−0.0891056	−0.0445528	−	0.999007i	$-0.514186\pi$
$487$	−957.632	−0.0891056	−0.0445528	+	0.999007i	$0.514186\pi$
$488$	6114.55	0.567198
$489$	−2274.59	−0.210349
$490$	0	0
$491$	679.047	0.0624134	0.0312067	−	0.999513i	$-0.490065\pi$
$491$	679.047	0.0624134	0.0312067	+	0.999513i	$0.490065\pi$
$492$	−2301.29	−0.210875
$493$	−26494.4	−2.42038
$494$	−3052.91	−0.278051
$495$	−668.604	−0.0607101
$496$	19801.6	1.79258
$497$	0	0
$498$	−10941.1	−0.984502
$499$	−12101.7	−1.08566	−0.542830	−	0.839842i	$-0.682647\pi$
$499$	−12101.7	−1.08566	−0.542830	+	0.839842i	$0.682647\pi$
$500$	3823.49	0.341983
$501$	5720.64	0.510138
$502$	−12730.4	−1.13184
$503$	4866.88	0.431418	0.215709	−	0.976458i	$-0.430794\pi$
$503$	4866.88	0.431418	0.215709	+	0.976458i	$0.430794\pi$
$504$	0	0
$505$	11017.5	0.970835
$506$	−4632.27	−0.406976
$507$	5639.19	0.493975
$508$	5916.04	0.516697
$509$	4331.00	0.377148	0.188574	−	0.982059i	$-0.439613\pi$
$509$	4331.00	0.377148	0.188574	+	0.982059i	$0.439613\pi$
$510$	8126.42	0.705577
$511$	0	0
$512$	−1337.92	−0.115485
$513$	1410.12	0.121362
$514$	18477.8	1.58565
$515$	−11952.2	−1.02268
$516$	2722.97	0.232310
$517$	5167.16	0.439558
$518$	0	0
$519$	2966.67	0.250910
$520$	2064.72	0.174123
$521$	−19981.5	−1.68024	−0.840120	−	0.542400i	$-0.817516\pi$
$521$	−19981.5	−1.68024	−0.840120	+	0.542400i	$0.817516\pi$
$522$	−6402.72	−0.536857
$523$	10712.5	0.895646	0.447823	−	0.894122i	$-0.352199\pi$
$523$	10712.5	0.895646	0.447823	+	0.894122i	$0.352199\pi$
$524$	6994.79	0.583147
$525$	0	0
$526$	17538.5	1.45383
$527$	−30834.9	−2.54874
$528$	2590.07	0.213482
$529$	4299.08	0.353339
$530$	2764.39	0.226561
$531$	4041.82	0.330320
$532$	0	0
$533$	4932.84	0.400873
$534$	−9995.52	−0.810016
$535$	−6177.03	−0.499170
$536$	4353.80	0.350850
$537$	408.142	0.0327982
$538$	13456.1	1.07831
$539$	0	0
$540$	505.086	0.0402508
$541$	9069.69	0.720770	0.360385	−	0.932804i	$-0.382645\pi$
$541$	9069.69	0.720770	0.360385	+	0.932804i	$0.382645\pi$
$542$	12115.2	0.960133
$543$	−2230.21	−0.176257
$544$	−14698.6	−1.15845
$545$	−10455.3	−0.821754
$546$	0	0
$547$	7312.52	0.571592	0.285796	−	0.958291i	$-0.407742\pi$
$547$	7312.52	0.571592	0.285796	+	0.958291i	$0.407742\pi$
$548$	−7345.61	−0.572607
$549$	−3206.21	−0.249249
$550$	−2865.90	−0.222186
$551$	11321.6	0.875350
$552$	−6607.40	−0.509474
$553$	0	0
$554$	−1548.52	−0.118755
$555$	7219.19	0.552140
$556$	307.168	0.0234296
$557$	6814.05	0.518349	0.259175	−	0.965830i	$-0.416549\pi$
$557$	6814.05	0.518349	0.259175	+	0.965830i	$0.416549\pi$
$558$	−7451.66	−0.565329
$559$	−5836.70	−0.441621
$560$	0	0
$561$	−4033.22	−0.303534
$562$	28530.9	2.14146
$563$	5261.17	0.393840	0.196920	−	0.980420i	$-0.436906\pi$
$563$	5261.17	0.393840	0.196920	+	0.980420i	$0.436906\pi$
$564$	−3903.45	−0.291427
$565$	5597.08	0.416763
$566$	−20270.3	−1.50534
$567$	0	0
$568$	−13949.5	−1.03047
$569$	−1406.56	−0.103631	−0.0518157	−	0.998657i	$-0.516501\pi$
$569$	−1406.56	−0.103631	−0.0518157	+	0.998657i	$0.516501\pi$
$570$	−3472.60	−0.255178
$571$	3482.55	0.255237	0.127618	−	0.991823i	$-0.459267\pi$
$571$	3482.55	0.255237	0.127618	+	0.991823i	$0.459267\pi$
$572$	542.718	0.0396717
$573$	−1509.04	−0.110019
$574$	0	0
$575$	10187.2	0.738848
$576$	2098.96	0.151834
$577$	−18790.4	−1.35572	−0.677862	−	0.735189i	$-0.737093\pi$
$577$	−18790.4	−1.35572	−0.677862	+	0.735189i	$0.737093\pi$
$578$	32897.8	2.36742
$579$	5753.84	0.412990
$580$	4055.25	0.290319
$581$	0	0
$582$	−8884.65	−0.632785
$583$	−1371.99	−0.0974650
$584$	3150.48	0.223233
$585$	−1082.66	−0.0765168
$586$	−16802.2	−1.18446
$587$	−6640.97	−0.466954	−0.233477	−	0.972362i	$-0.575010\pi$
$587$	−6640.97	−0.466954	−0.233477	+	0.972362i	$0.575010\pi$
$588$	0	0
$589$	13176.4	0.921775
$590$	−9953.46	−0.694538
$591$	−4503.49	−0.313450
$592$	−27966.0	−1.94155
$593$	−10326.6	−0.715111	−0.357555	−	0.933892i	$-0.616390\pi$
$593$	−10326.6	−0.715111	−0.357555	+	0.933892i	$0.616390\pi$
$594$	−974.682	−0.0673260
$595$	0	0
$596$	−6809.63	−0.468009
$597$	1660.92	0.113864
$598$	−7500.94	−0.512937
$599$	16028.7	1.09335	0.546673	−	0.837346i	$-0.315894\pi$
$599$	16028.7	1.09335	0.546673	+	0.837346i	$0.315894\pi$
$600$	−4087.87	−0.278144
$601$	−15127.4	−1.02672	−0.513359	−	0.858174i	$-0.671599\pi$
$601$	−15127.4	−1.02672	−0.513359	+	0.858174i	$0.671599\pi$
$602$	0	0
$603$	−2282.95	−0.154177
$604$	−2242.83	−0.151092
$605$	−817.183	−0.0549144
$606$	16061.1	1.07663
$607$	10397.7	0.695273	0.347636	−	0.937629i	$-0.386984\pi$
$607$	10397.7	0.695273	0.347636	+	0.937629i	$0.386984\pi$
$608$	6281.02	0.418962
$609$	0	0
$610$	7895.69	0.524077
$611$	8367.07	0.554002
$612$	3046.83	0.201243
$613$	−10563.3	−0.695998	−0.347999	−	0.937495i	$-0.613139\pi$
$613$	−10563.3	−0.695998	−0.347999	+	0.937495i	$0.613139\pi$
$614$	12366.1	0.812791
$615$	5610.97	0.367896
$616$	0	0
$617$	−6430.19	−0.419562	−0.209781	−	0.977748i	$-0.567275\pi$
$617$	−6430.19	−0.419562	−0.209781	+	0.977748i	$0.567275\pi$
$618$	−17423.8	−1.13412
$619$	−10321.3	−0.670192	−0.335096	−	0.942184i	$-0.608769\pi$
$619$	−10321.3	−0.670192	−0.335096	+	0.942184i	$0.608769\pi$
$620$	4719.60	0.305716
$621$	3464.65	0.223883
$622$	5409.83	0.348737
$623$	0	0
$624$	4194.04	0.269064
$625$	601.302	0.0384834
$626$	20895.2	1.33409
$627$	1723.49	0.109776
$628$	643.972	0.0409192
$629$	43548.4	2.76055
$630$	0	0
$631$	611.526	0.0385808	0.0192904	−	0.999814i	$-0.493859\pi$
$631$	611.526	0.0385808	0.0192904	+	0.999814i	$0.493859\pi$
$632$	−22377.0	−1.40840
$633$	−882.736	−0.0554275
$634$	−32377.2	−2.02818
$635$	−14424.4	−0.901439
$636$	1036.45	0.0646193
$637$	0	0
$638$	−7825.55	−0.485606
$639$	7314.55	0.452831
$640$	−11666.6	−0.720570
$641$	−18150.6	−1.11842	−0.559208	−	0.829028i	$-0.688895\pi$
$641$	−18150.6	−1.11842	−0.559208	+	0.829028i	$0.688895\pi$
$642$	−9004.78	−0.553568
$643$	13159.4	0.807087	0.403544	−	0.914960i	$-0.367778\pi$
$643$	13159.4	0.807087	0.403544	+	0.914960i	$0.367778\pi$
$644$	0	0
$645$	−6639.09	−0.405293
$646$	−20947.8	−1.27582
$647$	−24884.3	−1.51206	−0.756029	−	0.654538i	$-0.772863\pi$
$647$	−24884.3	−1.51206	−0.756029	+	0.654538i	$0.772863\pi$
$648$	−1390.27	−0.0842824
$649$	4940.00	0.298786
$650$	−4640.68	−0.280035
$651$	0	0
$652$	2100.15	0.126148
$653$	−4885.33	−0.292768	−0.146384	−	0.989228i	$-0.546764\pi$
$653$	−4885.33	−0.292768	−0.146384	+	0.989228i	$0.546764\pi$
$654$	−15241.6	−0.911306
$655$	−17054.6	−1.01737
$656$	−21736.0	−1.29367
$657$	−1651.98	−0.0980974
$658$	0	0
$659$	−20779.0	−1.22827	−0.614137	−	0.789199i	$-0.710496\pi$
$659$	−20779.0	−1.22827	−0.614137	+	0.789199i	$0.710496\pi$
$660$	617.327	0.0364082
$661$	17316.9	1.01899	0.509494	−	0.860474i	$-0.329833\pi$
$661$	17316.9	1.01899	0.509494	+	0.860474i	$0.329833\pi$
$662$	376.199	0.0220867
$663$	−6530.91	−0.382563
$664$	−19074.2	−1.11480
$665$	0	0
$666$	10524.0	0.612310
$667$	27817.0	1.61481
$668$	−5281.91	−0.305933
$669$	14134.9	0.816869
$670$	5622.04	0.324177
$671$	−3918.71	−0.225454
$672$	0	0
$673$	−17229.3	−0.986837	−0.493419	−	0.869792i	$-0.664253\pi$
$673$	−17229.3	−0.986837	−0.493419	+	0.869792i	$0.664253\pi$
$674$	−7006.81	−0.400434
$675$	2143.51	0.122228
$676$	−5206.71	−0.296240
$677$	21397.7	1.21474	0.607371	−	0.794418i	$-0.292224\pi$
$677$	21397.7	1.21474	0.607371	+	0.794418i	$0.292224\pi$
$678$	8159.35	0.462180
$679$	0	0
$680$	14167.3	0.798956
$681$	13738.7	0.773081
$682$	−9107.58	−0.511360
$683$	−14885.4	−0.833930	−0.416965	−	0.908923i	$-0.636906\pi$
$683$	−14885.4	−0.833930	−0.416965	+	0.908923i	$0.636906\pi$
$684$	−1301.98	−0.0727813
$685$	17909.9	0.998982
$686$	0	0
$687$	1007.16	0.0559322
$688$	25718.8	1.42517
$689$	−2221.64	−0.122841
$690$	−8532.11	−0.470742
$691$	−19287.3	−1.06183	−0.530914	−	0.847426i	$-0.678151\pi$
$691$	−19287.3	−1.06183	−0.530914	+	0.847426i	$0.678151\pi$
$692$	−2739.15	−0.150472
$693$	0	0
$694$	9974.81	0.545589
$695$	−748.932	−0.0408757
$696$	−11162.2	−0.607907
$697$	33847.1	1.83938
$698$	26051.6	1.41270
$699$	17551.7	0.949739
$700$	0	0
$701$	604.072	0.0325471	0.0162735	−	0.999868i	$-0.494820\pi$
$701$	604.072	0.0325471	0.0162735	+	0.999868i	$0.494820\pi$
$702$	−1578.28	−0.0848552
$703$	−18609.2	−0.998376
$704$	2565.39	0.137339
$705$	9517.31	0.508429
$706$	25345.4	1.35111
$707$	0	0
$708$	−3731.84	−0.198095
$709$	−23186.8	−1.22821	−0.614104	−	0.789225i	$-0.710483\pi$
$709$	−23186.8	−1.22821	−0.614104	+	0.789225i	$0.710483\pi$
$710$	−18012.9	−0.952132
$711$	11733.5	0.618906
$712$	−17425.8	−0.917217
$713$	32374.2	1.70045
$714$	0	0
$715$	−1323.25	−0.0692120
$716$	−376.841	−0.0196693
$717$	−13454.6	−0.700798
$718$	8048.96	0.418363
$719$	30988.9	1.60736	0.803680	−	0.595062i	$-0.202873\pi$
$719$	30988.9	1.60736	0.803680	+	0.595062i	$0.202873\pi$
$720$	4770.61	0.246930
$721$	0	0
$722$	−13558.1	−0.698865
$723$	−12382.7	−0.636954
$724$	2059.17	0.105703
$725$	17209.9	0.881597
$726$	−1191.28	−0.0608987
$727$	31303.5	1.59695	0.798476	−	0.602027i	$-0.205640\pi$
$727$	31303.5	1.59695	0.798476	+	0.602027i	$0.205640\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	4068.21	0.206262
$731$	−40049.0	−2.02636
$732$	2960.32	0.149476
$733$	17655.8	0.889674	0.444837	−	0.895611i	$-0.353262\pi$
$733$	17655.8	0.889674	0.444837	+	0.895611i	$0.353262\pi$
$734$	31693.6	1.59378
$735$	0	0
$736$	15432.3	0.772885
$737$	−2790.27	−0.139459
$738$	8179.60	0.407988
$739$	1049.63	0.0522479	0.0261240	−	0.999659i	$-0.491684\pi$
$739$	1049.63	0.0522479	0.0261240	+	0.999659i	$0.491684\pi$
$740$	−6665.54	−0.331122
$741$	2790.80	0.138357
$742$	0	0
$743$	−9514.08	−0.469768	−0.234884	−	0.972023i	$-0.575471\pi$
$743$	−9514.08	−0.469768	−0.234884	+	0.972023i	$0.575471\pi$
$744$	−12990.9	−0.640148
$745$	16603.1	0.816498
$746$	14289.1	0.701286
$747$	10001.7	0.489885
$748$	3723.91	0.182031
$749$	0	0
$750$	−13590.0	−0.661649
$751$	8530.03	0.414468	0.207234	−	0.978291i	$-0.433554\pi$
$751$	8530.03	0.414468	0.207234	+	0.978291i	$0.433554\pi$
$752$	−36868.6	−1.78784
$753$	11637.4	0.563200
$754$	−12671.7	−0.612039
$755$	5468.43	0.263598
$756$	0	0
$757$	−9141.66	−0.438916	−0.219458	−	0.975622i	$-0.570429\pi$
$757$	−9141.66	−0.438916	−0.219458	+	0.975622i	$0.570429\pi$
$758$	45868.1	2.19789
$759$	4234.57	0.202510
$760$	−6053.99	−0.288949
$761$	−38289.7	−1.82391	−0.911957	−	0.410285i	$-0.865429\pi$
$761$	−38289.7	−1.82391	−0.911957	+	0.410285i	$0.865429\pi$
$762$	−21027.7	−0.999674
$763$	0	0
$764$	1393.31	0.0659792
$765$	−7428.73	−0.351093
$766$	−1318.64	−0.0621992
$767$	7999.23	0.376578
$768$	−11410.3	−0.536109
$769$	4475.76	0.209883	0.104941	−	0.994478i	$-0.466534\pi$
$769$	4475.76	0.209883	0.104941	+	0.994478i	$0.466534\pi$
$770$	0	0
$771$	−16891.4	−0.789014
$772$	−5312.56	−0.247673
$773$	−37847.5	−1.76103	−0.880517	−	0.474014i	$-0.842805\pi$
$773$	−37847.5	−1.76103	−0.880517	+	0.474014i	$0.842805\pi$
$774$	−9678.37	−0.449460
$775$	20029.3	0.928353
$776$	−15489.1	−0.716531
$777$	0	0
$778$	27140.2	1.25067
$779$	−14463.6	−0.665228
$780$	999.624	0.0458876
$781$	8940.00	0.409601
$782$	−51468.3	−2.35358
$783$	5853.01	0.267139
$784$	0	0
$785$	−1570.12	−0.0713885
$786$	−24861.9	−1.12824
$787$	8335.43	0.377543	0.188771	−	0.982021i	$-0.439550\pi$
$787$	8335.43	0.377543	0.188771	+	0.982021i	$0.439550\pi$
$788$	4158.10	0.187978
$789$	−16032.7	−0.723421
$790$	−28895.3	−1.30133
$791$	0	0
$792$	−1699.22	−0.0762363
$793$	−6345.47	−0.284154
$794$	9805.33	0.438260
$795$	−2527.05	−0.112736
$796$	−1533.54	−0.0682851
$797$	32982.2	1.46586	0.732930	−	0.680304i	$-0.238152\pi$
$797$	32982.2	1.46586	0.732930	+	0.680304i	$0.238152\pi$
$798$	0	0
$799$	57411.3	2.54201
$800$	9547.68	0.421952
$801$	9137.35	0.403062
$802$	42996.3	1.89308
$803$	−2019.09	−0.0887324
$804$	2107.87	0.0924611
$805$	0	0
$806$	−14747.7	−0.644499
$807$	−12300.8	−0.536566
$808$	28000.3	1.21912
$809$	7819.98	0.339847	0.169923	−	0.985457i	$-0.445648\pi$
$809$	7819.98	0.339847	0.169923	+	0.985457i	$0.445648\pi$
$810$	−1795.25	−0.0778749
$811$	36536.5	1.58196	0.790981	−	0.611841i	$-0.209571\pi$
$811$	36536.5	1.58196	0.790981	+	0.611841i	$0.209571\pi$
$812$	0	0
$813$	−11075.0	−0.477760
$814$	12862.7	0.553855
$815$	−5120.54	−0.220080
$816$	28777.7	1.23459
$817$	17113.8	0.732849
$818$	−10503.9	−0.448975
$819$	0	0
$820$	−5180.66	−0.220630
$821$	23473.7	0.997854	0.498927	−	0.866644i	$-0.333728\pi$
$821$	23473.7	0.997854	0.498927	+	0.866644i	$0.333728\pi$
$822$	26108.8	1.10785
$823$	42257.8	1.78981	0.894905	−	0.446257i	$-0.147243\pi$
$823$	42257.8	1.78981	0.894905	+	0.446257i	$0.147243\pi$
$824$	−30376.0	−1.28422
$825$	2619.84	0.110559
$826$	0	0
$827$	−8822.43	−0.370962	−0.185481	−	0.982648i	$-0.559384\pi$
$827$	−8822.43	−0.370962	−0.185481	+	0.982648i	$0.559384\pi$
$828$	−3198.94	−0.134264
$829$	−17839.9	−0.747414	−0.373707	−	0.927547i	$-0.621913\pi$
$829$	−17839.9	−0.747414	−0.373707	+	0.927547i	$0.621913\pi$
$830$	−24630.5	−1.03004
$831$	1415.57	0.0590921
$832$	4154.08	0.173097
$833$	0	0
$834$	−1091.78	−0.0453301
$835$	12878.3	0.533737
$836$	−1591.31	−0.0658332
$837$	6811.89	0.281306
$838$	20193.7	0.832434
$839$	−25570.4	−1.05219	−0.526096	−	0.850425i	$-0.676345\pi$
$839$	−25570.4	−1.05219	−0.526096	+	0.850425i	$0.676345\pi$
$840$	0	0
$841$	22603.8	0.926803
$842$	4524.33	0.185177
$843$	−26081.3	−1.06559
$844$	815.037	0.0332402
$845$	12694.9	0.516826
$846$	13874.2	0.563835
$847$	0	0
$848$	9789.40	0.396426
$849$	18530.0	0.749054
$850$	−31842.4	−1.28492
$851$	−45722.4	−1.84177
$852$	−6753.58	−0.271565
$853$	4696.01	0.188497	0.0942487	−	0.995549i	$-0.469955\pi$
$853$	4696.01	0.188497	0.0942487	+	0.995549i	$0.469955\pi$
$854$	0	0
$855$	3174.46	0.126976
$856$	−15698.6	−0.626829
$857$	−9754.99	−0.388826	−0.194413	−	0.980920i	$-0.562280\pi$
$857$	−9754.99	−0.388826	−0.194413	+	0.980920i	$0.562280\pi$
$858$	−1929.01	−0.0767544
$859$	−33316.1	−1.32332	−0.661659	−	0.749805i	$-0.730147\pi$
$859$	−33316.1	−1.32332	−0.661659	+	0.749805i	$0.730147\pi$
$860$	6129.92	0.243057
$861$	0	0
$862$	31885.0	1.25987
$863$	−22080.9	−0.870966	−0.435483	−	0.900197i	$-0.643422\pi$
$863$	−22080.9	−0.870966	−0.435483	+	0.900197i	$0.643422\pi$
$864$	3247.13	0.127858
$865$	6678.54	0.262517
$866$	−35320.0	−1.38594
$867$	−30073.3	−1.17802
$868$	0	0
$869$	14341.0	0.559822
$870$	−14413.7	−0.561692
$871$	−4518.23	−0.175768
$872$	−26571.6	−1.03191
$873$	8121.86	0.314872
$874$	21993.5	0.851193
$875$	0	0
$876$	1525.29	0.0588296
$877$	18330.7	0.705797	0.352898	−	0.935662i	$-0.385196\pi$
$877$	18330.7	0.705797	0.352898	+	0.935662i	$0.385196\pi$
$878$	−6464.63	−0.248486
$879$	15359.7	0.589384
$880$	5830.74	0.223357
$881$	−11826.1	−0.452251	−0.226125	−	0.974098i	$-0.572606\pi$
$881$	−11826.1	−0.452251	−0.226125	+	0.974098i	$0.572606\pi$
$882$	0	0
$883$	31967.1	1.21832	0.609161	−	0.793046i	$-0.291506\pi$
$883$	31967.1	1.21832	0.609161	+	0.793046i	$0.291506\pi$
$884$	6030.04	0.229426
$885$	9098.90	0.345600
$886$	−24964.4	−0.946608
$887$	16538.0	0.626035	0.313017	−	0.949747i	$-0.398660\pi$
$887$	16538.0	0.626035	0.313017	+	0.949747i	$0.398660\pi$
$888$	18347.2	0.693346
$889$	0	0
$890$	−22501.8	−0.847487
$891$	891.000	0.0335013
$892$	−13050.8	−0.489881
$893$	−24533.1	−0.919339
$894$	24203.8	0.905477
$895$	918.806	0.0343154
$896$	0	0
$897$	6856.94	0.255236
$898$	−26357.1	−0.979451
$899$	54691.5	2.02899
$900$	−1979.12	−0.0733007
$901$	−15243.9	−0.563650
$902$	9997.29	0.369039
$903$	0	0
$904$	14224.7	0.523347
$905$	−5020.64	−0.184411
$906$	7971.80	0.292324
$907$	−15747.6	−0.576507	−0.288253	−	0.957554i	$-0.593075\pi$
$907$	−15747.6	−0.576507	−0.288253	+	0.957554i	$0.593075\pi$
$908$	−12685.0	−0.463621
$909$	−14682.2	−0.535730
$910$	0	0
$911$	−4092.46	−0.148836	−0.0744179	−	0.997227i	$-0.523710\pi$
$911$	−4092.46	−0.148836	−0.0744179	+	0.997227i	$0.523710\pi$
$912$	−12297.4	−0.446498
$913$	12224.3	0.443118
$914$	24726.7	0.894842
$915$	−7217.80	−0.260779
$916$	−929.916	−0.0335429
$917$	0	0
$918$	−10829.5	−0.389354
$919$	30830.7	1.10665	0.553324	−	0.832966i	$-0.313359\pi$
$919$	30830.7	1.10665	0.553324	+	0.832966i	$0.313359\pi$
$920$	−14874.5	−0.533042
$921$	−11304.4	−0.404443
$922$	−29157.9	−1.04150
$923$	14476.3	0.516246
$924$	0	0
$925$	−28287.5	−1.00550
$926$	−18250.0	−0.647659
$927$	15927.9	0.564337
$928$	26070.7	0.922211
$929$	−28745.2	−1.01518	−0.507589	−	0.861599i	$-0.669463\pi$
$929$	−28745.2	−1.01518	−0.507589	+	0.861599i	$0.669463\pi$
$930$	−16775.1	−0.591481
$931$	0	0
$932$	−16205.6	−0.569564
$933$	−4945.37	−0.173531
$934$	−6856.75	−0.240214
$935$	−9079.56	−0.317576
$936$	−2751.51	−0.0960854
$937$	3547.77	0.123693	0.0618466	−	0.998086i	$-0.480301\pi$
$937$	3547.77	0.123693	0.0618466	+	0.998086i	$0.480301\pi$
$938$	0	0
$939$	−19101.2	−0.663839
$940$	−8787.40	−0.304908
$941$	39138.8	1.35589	0.677943	−	0.735115i	$-0.262872\pi$
$941$	39138.8	1.35589	0.677943	+	0.735115i	$0.262872\pi$
$942$	−2288.90	−0.0791681
$943$	−35536.8	−1.22719
$944$	−35247.7	−1.21527
$945$	0	0
$946$	−11829.1	−0.406552
$947$	14322.1	0.491451	0.245726	−	0.969339i	$-0.420974\pi$
$947$	14322.1	0.491451	0.245726	+	0.969339i	$0.420974\pi$
$948$	−10833.7	−0.371162
$949$	−3269.47	−0.111835
$950$	13607.0	0.464704
$951$	29597.5	1.00922
$952$	0	0
$953$	−2937.41	−0.0998447	−0.0499223	−	0.998753i	$-0.515897\pi$
$953$	−2937.41	−0.0998447	−0.0499223	+	0.998753i	$0.515897\pi$
$954$	−3683.90	−0.125022
$955$	−3397.14	−0.115109
$956$	12422.8	0.420273
$957$	7153.68	0.241636
$958$	−17861.3	−0.602371
$959$	0	0
$960$	4725.15	0.158858
$961$	33860.4	1.13660
$962$	20828.3	0.698058
$963$	8231.68	0.275454
$964$	11433.0	0.381985
$965$	12953.0	0.432095
$966$	0	0
$967$	18616.7	0.619101	0.309551	−	0.950883i	$-0.399821\pi$
$967$	18616.7	0.619101	0.309551	+	0.950883i	$0.399821\pi$
$968$	−2076.82	−0.0689583
$969$	19149.3	0.634845
$970$	−20001.1	−0.662057
$971$	42729.0	1.41219	0.706097	−	0.708115i	$-0.250454\pi$
$971$	42729.0	1.41219	0.706097	+	0.708115i	$0.250454\pi$
$972$	−673.091	−0.0222113
$973$	0	0
$974$	−3142.71	−0.103387
$975$	4242.26	0.139345
$976$	27960.6	0.917007
$977$	−10239.5	−0.335301	−0.167651	−	0.985846i	$-0.553618\pi$
$977$	−10239.5	−0.335301	−0.167651	+	0.985846i	$0.553618\pi$
$978$	−7464.66	−0.244063
$979$	11167.9	0.364583
$980$	0	0
$981$	13933.0	0.453463
$982$	2228.47	0.0724168
$983$	−30603.1	−0.992969	−0.496485	−	0.868046i	$-0.665376\pi$
$983$	−30603.1	−0.992969	−0.496485	+	0.868046i	$0.665376\pi$
$984$	14260.0	0.461983
$985$	−10138.2	−0.327949
$986$	−86948.1	−2.80831
$987$	0	0
$988$	−2576.77	−0.0829736
$989$	42048.3	1.35193
$990$	−2194.20	−0.0704405
$991$	−37134.4	−1.19033	−0.595163	−	0.803605i	$-0.702913\pi$
$991$	−37134.4	−1.19033	−0.595163	+	0.803605i	$0.702913\pi$
$992$	30341.7	0.971120
$993$	−343.900	−0.0109903
$994$	0	0
$995$	3739.05	0.119132
$996$	−9234.68	−0.293787
$997$	−49777.9	−1.58123	−0.790613	−	0.612317i	$-0.790238\pi$
$997$	−49777.9	−1.58123	−0.790613	+	0.612317i	$0.790238\pi$
$998$	−39714.7	−1.25967
$999$	−9620.49	−0.304684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.q.1.6	✓	7
7.6	odd	2		1617.4.a.r.1.6	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.q.1.6	✓	7	1.1	even	1	trivial
1617.4.a.r.1.6	yes	7	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+3.28176 q^{2} -3.00000 q^{3} +2.76992 q^{4} -6.75357 q^{5} -9.84527 q^{6} -17.1638 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.28176 q^{2} -3.00000 q^{3} +2.76992 q^{4} -6.75357 q^{5} -9.84527 q^{6} -17.1638 q^{8} +9.00000 q^{9} -22.1636 q^{10} +11.0000 q^{11} -8.30977 q^{12} +17.8121 q^{13} +20.2607 q^{15} -78.4869 q^{16} +122.219 q^{17} +29.5358 q^{18} -52.2268 q^{19} -18.7069 q^{20} +36.0993 q^{22} -128.320 q^{23} +51.4915 q^{24} -79.3892 q^{25} +58.4548 q^{26} -27.0000 q^{27} -216.778 q^{29} +66.4908 q^{30} -252.292 q^{31} -120.264 q^{32} -33.0000 q^{33} +401.092 q^{34} +24.9293 q^{36} +356.315 q^{37} -171.396 q^{38} -53.4362 q^{39} +115.917 q^{40} +276.938 q^{41} -327.683 q^{43} +30.4692 q^{44} -60.7822 q^{45} -421.116 q^{46} +469.742 q^{47} +235.461 q^{48} -260.536 q^{50} -366.657 q^{51} +49.3380 q^{52} -124.727 q^{53} -88.6074 q^{54} -74.2893 q^{55} +156.681 q^{57} -711.413 q^{58} +449.091 q^{59} +56.1207 q^{60} -356.246 q^{61} -827.962 q^{62} +233.217 q^{64} -120.295 q^{65} -108.298 q^{66} -253.661 q^{67} +338.537 q^{68} +384.961 q^{69} +812.727 q^{71} -154.475 q^{72} -183.554 q^{73} +1169.34 q^{74} +238.168 q^{75} -144.664 q^{76} -175.364 q^{78} +1303.73 q^{79} +530.067 q^{80} +81.0000 q^{81} +908.844 q^{82} +1111.30 q^{83} -825.414 q^{85} -1075.37 q^{86} +650.335 q^{87} -188.802 q^{88} +1015.26 q^{89} -199.472 q^{90} -355.437 q^{92} +756.877 q^{93} +1541.58 q^{94} +352.718 q^{95} +360.793 q^{96} +902.429 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9	\( 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9} - 49 q^{10} + 77 q^{11} - 90 q^{12} + 92 q^{13} - 60 q^{15} + 218 q^{16} + 170 q^{17} - 36 q^{18} + 76 q^{19} + 569 q^{20} - 44 q^{22} - 56 q^{23} + 117 q^{24} + 53 q^{25} + 109 q^{26} - 189 q^{27} - 472 q^{29} + 147 q^{30} + 290 q^{31} - 1046 q^{32} - 231 q^{33} + 344 q^{34} + 270 q^{36} - 66 q^{37} + 385 q^{38} - 276 q^{39} - 800 q^{40} - 166 q^{41} - 76 q^{43} + 330 q^{44} + 180 q^{45} - 528 q^{46} + 1082 q^{47} - 654 q^{48} - 569 q^{50} - 510 q^{51} + 1065 q^{52} - 150 q^{53} + 108 q^{54} + 220 q^{55} - 228 q^{57} + 1457 q^{58} + 1284 q^{59} - 1707 q^{60} - 764 q^{61} - 296 q^{62} + 1661 q^{64} + 2722 q^{65} + 132 q^{66} - 658 q^{67} - 360 q^{68} + 168 q^{69} - 272 q^{71} - 351 q^{72} + 1658 q^{73} + 613 q^{74} - 159 q^{75} - 1757 q^{76} - 327 q^{78} + 792 q^{79} + 5079 q^{80} + 567 q^{81} + 3208 q^{82} - 770 q^{83} - 776 q^{85} - 478 q^{86} + 1416 q^{87} - 429 q^{88} + 656 q^{89} - 441 q^{90} - 3916 q^{92} - 870 q^{93} - 849 q^{94} - 1636 q^{95} + 3138 q^{96} + 608 q^{97} + 693 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9 - 49 * q^10 + 77 * q^11 - 90 * q^12 + 92 * q^13 - 60 * q^15 + 218 * q^16 + 170 * q^17 - 36 * q^18 + 76 * q^19 + 569 * q^20 - 44 * q^22 - 56 * q^23 + 117 * q^24 + 53 * q^25 + 109 * q^26 - 189 * q^27 - 472 * q^29 + 147 * q^30 + 290 * q^31 - 1046 * q^32 - 231 * q^33 + 344 * q^34 + 270 * q^36 - 66 * q^37 + 385 * q^38 - 276 * q^39 - 800 * q^40 - 166 * q^41 - 76 * q^43 + 330 * q^44 + 180 * q^45 - 528 * q^46 + 1082 * q^47 - 654 * q^48 - 569 * q^50 - 510 * q^51 + 1065 * q^52 - 150 * q^53 + 108 * q^54 + 220 * q^55 - 228 * q^57 + 1457 * q^58 + 1284 * q^59 - 1707 * q^60 - 764 * q^61 - 296 * q^62 + 1661 * q^64 + 2722 * q^65 + 132 * q^66 - 658 * q^67 - 360 * q^68 + 168 * q^69 - 272 * q^71 - 351 * q^72 + 1658 * q^73 + 613 * q^74 - 159 * q^75 - 1757 * q^76 - 327 * q^78 + 792 * q^79 + 5079 * q^80 + 567 * q^81 + 3208 * q^82 - 770 * q^83 - 776 * q^85 - 478 * q^86 + 1416 * q^87 - 429 * q^88 + 656 * q^89 - 441 * q^90 - 3916 * q^92 - 870 * q^93 - 849 * q^94 - 1636 * q^95 + 3138 * q^96 + 608 * q^97 + 693 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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