LMFDB - Embedded newform 798.4.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,4,Mod(1,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, 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("798.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	798.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:	$47.0835241846$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.3221.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 2 $ x^3 - x^2 - 9*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.66246$ of defining polynomial
Character	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.50237 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.50237 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +15.0047 q^{10} -24.9448 q^{11} -12.0000 q^{12} -48.9543 q^{13} -14.0000 q^{14} -22.5071 q^{15} +16.0000 q^{16} +118.406 q^{17} +18.0000 q^{18} +19.0000 q^{19} +30.0095 q^{20} +21.0000 q^{21} -49.8897 q^{22} +123.563 q^{23} -24.0000 q^{24} -68.7145 q^{25} -97.9086 q^{26} -27.0000 q^{27} -28.0000 q^{28} +234.799 q^{29} -45.0142 q^{30} +46.8201 q^{31} +32.0000 q^{32} +74.8345 q^{33} +236.813 q^{34} -52.5166 q^{35} +36.0000 q^{36} -196.536 q^{37} +38.0000 q^{38} +146.863 q^{39} +60.0189 q^{40} -60.9418 q^{41} +42.0000 q^{42} +560.657 q^{43} -99.7794 q^{44} +67.5213 q^{45} +247.126 q^{46} +247.524 q^{47} -48.0000 q^{48} +49.0000 q^{49} -137.429 q^{50} -355.219 q^{51} -195.817 q^{52} -436.128 q^{53} -54.0000 q^{54} -187.145 q^{55} -56.0000 q^{56} -57.0000 q^{57} +469.598 q^{58} +283.152 q^{59} -90.0284 q^{60} -4.73816 q^{61} +93.6401 q^{62} -63.0000 q^{63} +64.0000 q^{64} -367.273 q^{65} +149.669 q^{66} -392.460 q^{67} +473.625 q^{68} -370.690 q^{69} -105.033 q^{70} +1013.20 q^{71} +72.0000 q^{72} -55.8537 q^{73} -393.073 q^{74} +206.143 q^{75} +76.0000 q^{76} +174.614 q^{77} +293.726 q^{78} +58.2148 q^{79} +120.038 q^{80} +81.0000 q^{81} -121.884 q^{82} +1358.66 q^{83} +84.0000 q^{84} +888.327 q^{85} +1121.31 q^{86} -704.397 q^{87} -199.559 q^{88} -1005.23 q^{89} +135.043 q^{90} +342.680 q^{91} +494.253 q^{92} -140.460 q^{93} +495.049 q^{94} +142.545 q^{95} -96.0000 q^{96} +1450.61 q^{97} +98.0000 q^{98} -224.504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} - 12 q^{11} - 36 q^{12} + 6 q^{13} - 42 q^{14} + 48 q^{16} + 72 q^{17} + 54 q^{18} + 57 q^{19} + 63 q^{21} - 24 q^{22} - 16 q^{23} - 72 q^{24} - 143 q^{25} + 12 q^{26} - 81 q^{27} - 84 q^{28} + 52 q^{29} + 248 q^{31} + 96 q^{32} + 36 q^{33} + 144 q^{34} + 108 q^{36} + 130 q^{37} + 114 q^{38} - 18 q^{39} + 438 q^{41} + 126 q^{42} + 676 q^{43} - 48 q^{44} - 32 q^{46} + 1098 q^{47} - 144 q^{48} + 147 q^{49} - 286 q^{50} - 216 q^{51} + 24 q^{52} + 8 q^{53} - 162 q^{54} + 392 q^{55} - 168 q^{56} - 171 q^{57} + 104 q^{58} + 1012 q^{59} + 274 q^{61} + 496 q^{62} - 189 q^{63} + 192 q^{64} - 536 q^{65} + 72 q^{66} + 144 q^{67} + 288 q^{68} + 48 q^{69} + 606 q^{71} + 216 q^{72} + 362 q^{73} + 260 q^{74} + 429 q^{75} + 228 q^{76} + 84 q^{77} - 36 q^{78} + 752 q^{79} + 243 q^{81} + 876 q^{82} + 2010 q^{83} + 252 q^{84} + 840 q^{85} + 1352 q^{86} - 156 q^{87} - 96 q^{88} + 950 q^{89} - 42 q^{91} - 64 q^{92} - 744 q^{93} + 2196 q^{94} - 288 q^{96} + 1470 q^{97} + 294 q^{98} - 108 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 - 12 * q^11 - 36 * q^12 + 6 * q^13 - 42 * q^14 + 48 * q^16 + 72 * q^17 + 54 * q^18 + 57 * q^19 + 63 * q^21 - 24 * q^22 - 16 * q^23 - 72 * q^24 - 143 * q^25 + 12 * q^26 - 81 * q^27 - 84 * q^28 + 52 * q^29 + 248 * q^31 + 96 * q^32 + 36 * q^33 + 144 * q^34 + 108 * q^36 + 130 * q^37 + 114 * q^38 - 18 * q^39 + 438 * q^41 + 126 * q^42 + 676 * q^43 - 48 * q^44 - 32 * q^46 + 1098 * q^47 - 144 * q^48 + 147 * q^49 - 286 * q^50 - 216 * q^51 + 24 * q^52 + 8 * q^53 - 162 * q^54 + 392 * q^55 - 168 * q^56 - 171 * q^57 + 104 * q^58 + 1012 * q^59 + 274 * q^61 + 496 * q^62 - 189 * q^63 + 192 * q^64 - 536 * q^65 + 72 * q^66 + 144 * q^67 + 288 * q^68 + 48 * q^69 + 606 * q^71 + 216 * q^72 + 362 * q^73 + 260 * q^74 + 429 * q^75 + 228 * q^76 + 84 * q^77 - 36 * q^78 + 752 * q^79 + 243 * q^81 + 876 * q^82 + 2010 * q^83 + 252 * q^84 + 840 * q^85 + 1352 * q^86 - 156 * q^87 - 96 * q^88 + 950 * q^89 - 42 * q^91 - 64 * q^92 - 744 * q^93 + 2196 * q^94 - 288 * q^96 + 1470 * q^97 + 294 * q^98 - 108 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	7.50237	0.671032	0.335516	−	0.942034i	$-0.391089\pi$
$5$	7.50237	0.671032	0.335516	+	0.942034i	$0.391089\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	15.0047	0.474491
$11$	−24.9448	−0.683741	−0.341871	−	0.939747i	$-0.611060\pi$
$11$	−24.9448	−0.683741	−0.341871	+	0.939747i	$0.611060\pi$
$12$	−12.0000	−0.288675
$13$	−48.9543	−1.04442	−0.522211	−	0.852816i	$-0.674893\pi$
$13$	−48.9543	−1.04442	−0.522211	+	0.852816i	$0.674893\pi$
$14$	−14.0000	−0.267261
$15$	−22.5071	−0.387421
$16$	16.0000	0.250000
$17$	118.406	1.68928	0.844639	−	0.535336i	$-0.179815\pi$
$17$	118.406	1.68928	0.844639	+	0.535336i	$0.179815\pi$
$18$	18.0000	0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	30.0095	0.335516
$21$	21.0000	0.218218
$22$	−49.8897	−0.483478
$23$	123.563	1.12020	0.560102	−	0.828423i	$-0.310762\pi$
$23$	123.563	1.12020	0.560102	+	0.828423i	$0.310762\pi$
$24$	−24.0000	−0.204124
$25$	−68.7145	−0.549716
$26$	−97.9086	−0.738518
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	234.799	1.50349	0.751743	−	0.659456i	$-0.229214\pi$
$29$	234.799	1.50349	0.751743	+	0.659456i	$0.229214\pi$
$30$	−45.0142	−0.273948
$31$	46.8201	0.271262	0.135631	−	0.990759i	$-0.456694\pi$
$31$	46.8201	0.271262	0.135631	+	0.990759i	$0.456694\pi$
$32$	32.0000	0.176777
$33$	74.8345	0.394758
$34$	236.813	1.19450
$35$	−52.5166	−0.253626
$36$	36.0000	0.166667
$37$	−196.536	−0.873254	−0.436627	−	0.899643i	$-0.643827\pi$
$37$	−196.536	−0.873254	−0.436627	+	0.899643i	$0.643827\pi$
$38$	38.0000	0.162221
$39$	146.863	0.602997
$40$	60.0189	0.237246
$41$	−60.9418	−0.232134	−0.116067	−	0.993241i	$-0.537029\pi$
$41$	−60.9418	−0.232134	−0.116067	+	0.993241i	$0.537029\pi$
$42$	42.0000	0.154303
$43$	560.657	1.98836	0.994179	−	0.107745i	$-0.0343630\pi$
$43$	560.657	1.98836	0.994179	+	0.107745i	$0.0343630\pi$
$44$	−99.7794	−0.341871
$45$	67.5213	0.223677
$46$	247.126	0.792104
$47$	247.524	0.768195	0.384097	−	0.923293i	$-0.374513\pi$
$47$	247.524	0.768195	0.384097	+	0.923293i	$0.374513\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−137.429	−0.388708
$51$	−355.219	−0.975305
$52$	−195.817	−0.522211
$53$	−436.128	−1.13032	−0.565158	−	0.824983i	$-0.691185\pi$
$53$	−436.128	−1.13032	−0.565158	+	0.824983i	$0.691185\pi$
$54$	−54.0000	−0.136083
$55$	−187.145	−0.458812
$56$	−56.0000	−0.133631
$57$	−57.0000	−0.132453
$58$	469.598	1.06312
$59$	283.152	0.624800	0.312400	−	0.949951i	$-0.398867\pi$
$59$	283.152	0.624800	0.312400	+	0.949951i	$0.398867\pi$
$60$	−90.0284	−0.193710
$61$	−4.73816	−0.00994523	−0.00497261	−	0.999988i	$-0.501583\pi$
$61$	−4.73816	−0.00994523	−0.00497261	+	0.999988i	$0.501583\pi$
$62$	93.6401	0.191811
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−367.273	−0.700841
$66$	149.669	0.279136
$67$	−392.460	−0.715620	−0.357810	−	0.933794i	$-0.616477\pi$
$67$	−392.460	−0.715620	−0.357810	+	0.933794i	$0.616477\pi$
$68$	473.625	0.844639
$69$	−370.690	−0.646751
$70$	−105.033	−0.179341
$71$	1013.20	1.69359	0.846794	−	0.531921i	$-0.178530\pi$
$71$	1013.20	1.69359	0.846794	+	0.531921i	$0.178530\pi$
$72$	72.0000	0.117851
$73$	−55.8537	−0.0895505	−0.0447752	−	0.998997i	$-0.514257\pi$
$73$	−55.8537	−0.0895505	−0.0447752	+	0.998997i	$0.514257\pi$
$74$	−393.073	−0.617484
$75$	206.143	0.317379
$76$	76.0000	0.114708
$77$	174.614	0.258430
$78$	293.726	0.426383
$79$	58.2148	0.0829072	0.0414536	−	0.999140i	$-0.486801\pi$
$79$	58.2148	0.0829072	0.0414536	+	0.999140i	$0.486801\pi$
$80$	120.038	0.167758
$81$	81.0000	0.111111
$82$	−121.884	−0.164144
$83$	1358.66	1.79677	0.898384	−	0.439210i	$-0.144742\pi$
$83$	1358.66	1.79677	0.898384	+	0.439210i	$0.144742\pi$
$84$	84.0000	0.109109
$85$	888.327	1.13356
$86$	1121.31	1.40598
$87$	−704.397	−0.868038
$88$	−199.559	−0.241739
$89$	−1005.23	−1.19723	−0.598617	−	0.801035i	$-0.704283\pi$
$89$	−1005.23	−1.19723	−0.598617	+	0.801035i	$0.704283\pi$
$90$	135.043	0.158164
$91$	342.680	0.394754
$92$	494.253	0.560102
$93$	−140.460	−0.156613
$94$	495.049	0.543196
$95$	142.545	0.153945
$96$	−96.0000	−0.102062
$97$	1450.61	1.51843	0.759213	−	0.650842i	$-0.225584\pi$
$97$	1450.61	1.51843	0.759213	+	0.650842i	$0.225584\pi$
$98$	98.0000	0.101015
$99$	−224.504	−0.227914
$100$	−274.858	−0.274858
$101$	1204.15	1.18631	0.593157	−	0.805086i	$-0.297881\pi$
$101$	1204.15	1.18631	0.593157	+	0.805086i	$0.297881\pi$
$102$	−710.438	−0.689645
$103$	293.215	0.280498	0.140249	−	0.990116i	$-0.455210\pi$
$103$	293.215	0.280498	0.140249	+	0.990116i	$0.455210\pi$
$104$	−391.634	−0.369259
$105$	157.550	0.146431
$106$	−872.255	−0.799254
$107$	1375.55	1.24280	0.621399	−	0.783494i	$-0.286565\pi$
$107$	1375.55	1.24280	0.621399	+	0.783494i	$0.286565\pi$
$108$	−108.000	−0.0962250
$109$	1008.27	0.886009	0.443004	−	0.896519i	$-0.353913\pi$
$109$	1008.27	0.886009	0.443004	+	0.896519i	$0.353913\pi$
$110$	−374.291	−0.324429
$111$	589.609	0.504173
$112$	−112.000	−0.0944911
$113$	2.90985	0.00242244	0.00121122	−	0.999999i	$-0.499614\pi$
$113$	2.90985	0.00242244	0.00121122	+	0.999999i	$0.499614\pi$
$114$	−114.000	−0.0936586
$115$	927.017	0.751693
$116$	939.196	0.751743
$117$	−440.589	−0.348141
$118$	566.303	0.441800
$119$	−828.844	−0.638487
$120$	−180.057	−0.136974
$121$	−708.755	−0.532498
$122$	−9.47632	−0.00703234
$123$	182.825	0.134023
$124$	187.280	0.135631
$125$	−1453.32	−1.03991
$126$	−126.000	−0.0890871
$127$	−2710.94	−1.89415	−0.947077	−	0.321008i	$-0.895978\pi$
$127$	−2710.94	−1.89415	−0.947077	+	0.321008i	$0.895978\pi$
$128$	128.000	0.0883883
$129$	−1681.97	−1.14798
$130$	−734.546	−0.495569
$131$	1617.00	1.07846	0.539230	−	0.842159i	$-0.318715\pi$
$131$	1617.00	1.07846	0.539230	+	0.842159i	$0.318715\pi$
$132$	299.338	0.197379
$133$	−133.000	−0.0867110
$134$	−784.919	−0.506020
$135$	−202.564	−0.129140
$136$	947.250	0.597250
$137$	−1677.17	−1.04591	−0.522956	−	0.852360i	$-0.675171\pi$
$137$	−1677.17	−1.04591	−0.522956	+	0.852360i	$0.675171\pi$
$138$	−741.379	−0.457322
$139$	438.603	0.267639	0.133819	−	0.991006i	$-0.457276\pi$
$139$	438.603	0.267639	0.133819	+	0.991006i	$0.457276\pi$
$140$	−210.066	−0.126813
$141$	−742.573	−0.443517
$142$	2026.40	1.19755
$143$	1221.16	0.714114
$144$	144.000	0.0833333
$145$	1761.55	1.00889
$146$	−111.707	−0.0633217
$147$	−147.000	−0.0824786
$148$	−786.146	−0.436627
$149$	1875.61	1.03125	0.515625	−	0.856815i	$-0.327560\pi$
$149$	1875.61	1.03125	0.515625	+	0.856815i	$0.327560\pi$
$150$	412.287	0.224421
$151$	−118.513	−0.0638706	−0.0319353	−	0.999490i	$-0.510167\pi$
$151$	−118.513	−0.0638706	−0.0319353	+	0.999490i	$0.510167\pi$
$152$	152.000	0.0811107
$153$	1065.66	0.563093
$154$	349.228	0.182738
$155$	351.261	0.182026
$156$	587.452	0.301499
$157$	1402.23	0.712801	0.356401	−	0.934333i	$-0.384004\pi$
$157$	1402.23	0.712801	0.356401	+	0.934333i	$0.384004\pi$
$158$	116.430	0.0586243
$159$	1308.38	0.652588
$160$	240.076	0.118623
$161$	−864.943	−0.423398
$162$	162.000	0.0785674
$163$	1188.77	0.571238	0.285619	−	0.958343i	$-0.407801\pi$
$163$	1188.77	0.571238	0.285619	+	0.958343i	$0.407801\pi$
$164$	−243.767	−0.116067
$165$	561.436	0.264895
$166$	2717.31	1.27051
$167$	3337.16	1.54633	0.773166	−	0.634204i	$-0.218672\pi$
$167$	3337.16	1.54633	0.773166	+	0.634204i	$0.218672\pi$
$168$	168.000	0.0771517
$169$	199.525	0.0908169
$170$	1776.65	0.801548
$171$	171.000	0.0764719
$172$	2242.63	0.994179
$173$	−942.581	−0.414237	−0.207119	−	0.978316i	$-0.566409\pi$
$173$	−942.581	−0.414237	−0.207119	+	0.978316i	$0.566409\pi$
$174$	−1408.79	−0.613795
$175$	481.001	0.207773
$176$	−399.117	−0.170935
$177$	−849.455	−0.360728
$178$	−2010.45	−0.846572
$179$	−2995.02	−1.25061	−0.625303	−	0.780382i	$-0.715025\pi$
$179$	−2995.02	−1.25061	−0.625303	+	0.780382i	$0.715025\pi$
$180$	270.085	0.111839
$181$	−381.091	−0.156499	−0.0782493	−	0.996934i	$-0.524933\pi$
$181$	−381.091	−0.156499	−0.0782493	+	0.996934i	$0.524933\pi$
$182$	685.360	0.279133
$183$	14.2145	0.00574188
$184$	988.506	0.396052
$185$	−1474.49	−0.585981
$186$	−280.920	−0.110742
$187$	−2953.63	−1.15503
$188$	990.098	0.384097
$189$	189.000	0.0727393
$190$	285.090	0.108856
$191$	−2956.94	−1.12019	−0.560097	−	0.828427i	$-0.689236\pi$
$191$	−2956.94	−1.12019	−0.560097	+	0.828427i	$0.689236\pi$
$192$	−192.000	−0.0721688
$193$	−1186.06	−0.442356	−0.221178	−	0.975233i	$-0.570990\pi$
$193$	−1186.06	−0.442356	−0.221178	+	0.975233i	$0.570990\pi$
$194$	2901.22	1.07369
$195$	1101.82	0.404630
$196$	196.000	0.0714286
$197$	−725.731	−0.262468	−0.131234	−	0.991351i	$-0.541894\pi$
$197$	−725.731	−0.262468	−0.131234	+	0.991351i	$0.541894\pi$
$198$	−449.007	−0.161159
$199$	2239.04	0.797594	0.398797	−	0.917039i	$-0.369428\pi$
$199$	2239.04	0.797594	0.398797	+	0.917039i	$0.369428\pi$
$200$	−549.716	−0.194354
$201$	1177.38	0.413164
$202$	2408.31	0.838851
$203$	−1643.59	−0.568264
$204$	−1420.88	−0.487653
$205$	−457.208	−0.155770
$206$	586.430	0.198342
$207$	1112.07	0.373402
$208$	−783.269	−0.261105
$209$	−473.952	−0.156861
$210$	315.099	0.103543
$211$	605.109	0.197429	0.0987143	−	0.995116i	$-0.468527\pi$
$211$	605.109	0.197429	0.0987143	+	0.995116i	$0.468527\pi$
$212$	−1744.51	−0.565158
$213$	−3039.60	−0.977793
$214$	2751.10	0.878791
$215$	4206.25	1.33425
$216$	−216.000	−0.0680414
$217$	−327.740	−0.102528
$218$	2016.54	0.626503
$219$	167.561	0.0517020
$220$	−748.581	−0.229406
$221$	−5796.50	−1.76432
$222$	1179.22	0.356504
$223$	−3078.18	−0.924349	−0.462175	−	0.886789i	$-0.652931\pi$
$223$	−3078.18	−0.924349	−0.462175	+	0.886789i	$0.652931\pi$
$224$	−224.000	−0.0668153
$225$	−618.430	−0.183239
$226$	5.81969	0.00171292
$227$	−5083.30	−1.48630	−0.743151	−	0.669124i	$-0.766669\pi$
$227$	−5083.30	−1.48630	−0.743151	+	0.669124i	$0.766669\pi$
$228$	−228.000	−0.0662266
$229$	−1933.70	−0.558001	−0.279000	−	0.960291i	$-0.590003\pi$
$229$	−1933.70	−0.558001	−0.279000	+	0.960291i	$0.590003\pi$
$230$	1854.03	0.531528
$231$	−523.842	−0.149205
$232$	1878.39	0.531562
$233$	−1383.70	−0.389053	−0.194526	−	0.980897i	$-0.562317\pi$
$233$	−1383.70	−0.389053	−0.194526	+	0.980897i	$0.562317\pi$
$234$	−881.178	−0.246173
$235$	1857.02	0.515483
$236$	1132.61	0.312400
$237$	−174.644	−0.0478665
$238$	−1657.69	−0.451479
$239$	−7015.77	−1.89880	−0.949398	−	0.314075i	$-0.898306\pi$
$239$	−7015.77	−1.89880	−0.949398	+	0.314075i	$0.898306\pi$
$240$	−360.114	−0.0968551
$241$	−3436.82	−0.918611	−0.459305	−	0.888278i	$-0.651902\pi$
$241$	−3436.82	−0.918611	−0.459305	+	0.888278i	$0.651902\pi$
$242$	−1417.51	−0.376533
$243$	−243.000	−0.0641500
$244$	−18.9526	−0.00497261
$245$	367.616	0.0958617
$246$	365.651	0.0947684
$247$	−930.132	−0.239607
$248$	374.561	0.0959057
$249$	−4075.97	−1.03737
$250$	−2906.63	−0.735327
$251$	4866.74	1.22385	0.611924	−	0.790916i	$-0.290396\pi$
$251$	4866.74	1.22385	0.611924	+	0.790916i	$0.290396\pi$
$252$	−252.000	−0.0629941
$253$	−3082.27	−0.765930
$254$	−5421.89	−1.33937
$255$	−2664.98	−0.654461
$256$	256.000	0.0625000
$257$	−5496.38	−1.33407	−0.667033	−	0.745028i	$-0.732436\pi$
$257$	−5496.38	−1.33407	−0.667033	+	0.745028i	$0.732436\pi$
$258$	−3363.94	−0.811743
$259$	1375.76	0.330059
$260$	−1469.09	−0.350420
$261$	2113.19	0.501162
$262$	3234.01	0.762586
$263$	−101.702	−0.0238449	−0.0119224	−	0.999929i	$-0.503795\pi$
$263$	−101.702	−0.0238449	−0.0119224	+	0.999929i	$0.503795\pi$
$264$	598.676	0.139568
$265$	−3271.99	−0.758478
$266$	−266.000	−0.0613139
$267$	3015.68	0.691223
$268$	−1569.84	−0.357810
$269$	4714.72	1.06863	0.534316	−	0.845285i	$-0.320569\pi$
$269$	4714.72	1.06863	0.534316	+	0.845285i	$0.320569\pi$
$270$	−405.128	−0.0913159
$271$	4539.90	1.01764	0.508818	−	0.860874i	$-0.330083\pi$
$271$	4539.90	1.01764	0.508818	+	0.860874i	$0.330083\pi$
$272$	1894.50	0.422320
$273$	−1028.04	−0.227912
$274$	−3354.33	−0.739572
$275$	1714.07	0.375863
$276$	−1482.76	−0.323375
$277$	−738.963	−0.160289	−0.0801444	−	0.996783i	$-0.525538\pi$
$277$	−738.963	−0.160289	−0.0801444	+	0.996783i	$0.525538\pi$
$278$	877.205	0.189249
$279$	421.381	0.0904208
$280$	−420.133	−0.0896704
$281$	−6160.82	−1.30791	−0.653957	−	0.756532i	$-0.726892\pi$
$281$	−6160.82	−1.30791	−0.653957	+	0.756532i	$0.726892\pi$
$282$	−1485.15	−0.313614
$283$	−4667.01	−0.980301	−0.490150	−	0.871638i	$-0.663058\pi$
$283$	−4667.01	−0.980301	−0.490150	+	0.871638i	$0.663058\pi$
$284$	4052.80	0.846794
$285$	−427.635	−0.0888804
$286$	2442.32	0.504955
$287$	426.592	0.0877385
$288$	288.000	0.0589256
$289$	9107.04	1.85366
$290$	3523.10	0.713391
$291$	−4351.84	−0.876664
$292$	−223.415	−0.0447752
$293$	8928.57	1.78025	0.890124	−	0.455718i	$-0.150618\pi$
$293$	8928.57	1.78025	0.890124	+	0.455718i	$0.150618\pi$
$294$	−294.000	−0.0583212
$295$	2124.31	0.419261
$296$	−1572.29	−0.308742
$297$	673.511	0.131586
$298$	3751.22	0.729203
$299$	−6048.95	−1.16997
$300$	824.574	0.158689
$301$	−3924.60	−0.751528
$302$	−237.026	−0.0451633
$303$	−3612.46	−0.684919
$304$	304.000	0.0573539
$305$	−35.5474	−0.00667357
$306$	2131.31	0.398167
$307$	284.685	0.0529246	0.0264623	−	0.999650i	$-0.491576\pi$
$307$	284.685	0.0529246	0.0264623	+	0.999650i	$0.491576\pi$
$308$	698.456	0.129215
$309$	−879.645	−0.161946
$310$	702.523	0.128712
$311$	−1113.22	−0.202974	−0.101487	−	0.994837i	$-0.532360\pi$
$311$	−1113.22	−0.202974	−0.101487	+	0.994837i	$0.532360\pi$
$312$	1174.90	0.213192
$313$	−5122.62	−0.925073	−0.462536	−	0.886600i	$-0.653061\pi$
$313$	−5122.62	−0.925073	−0.462536	+	0.886600i	$0.653061\pi$
$314$	2804.45	0.504027
$315$	−472.649	−0.0845421
$316$	232.859	0.0414536
$317$	−3860.02	−0.683912	−0.341956	−	0.939716i	$-0.611089\pi$
$317$	−3860.02	−0.683912	−0.341956	+	0.939716i	$0.611089\pi$
$318$	2616.77	0.461450
$319$	−5857.02	−1.02800
$320$	480.152	0.0838790
$321$	−4126.65	−0.717530
$322$	−1729.89	−0.299387
$323$	2249.72	0.387547
$324$	324.000	0.0555556
$325$	3363.87	0.574135
$326$	2377.54	0.403926
$327$	−3024.82	−0.511537
$328$	−487.534	−0.0820719
$329$	−1732.67	−0.290350
$330$	1122.87	0.187309
$331$	7957.46	1.32139	0.660697	−	0.750653i	$-0.270261\pi$
$331$	7957.46	1.32139	0.660697	+	0.750653i	$0.270261\pi$
$332$	5434.62	0.898384
$333$	−1768.83	−0.291085
$334$	6674.32	1.09342
$335$	−2944.38	−0.480204
$336$	336.000	0.0545545
$337$	9552.05	1.54402	0.772008	−	0.635613i	$-0.219253\pi$
$337$	9552.05	1.54402	0.772008	+	0.635613i	$0.219253\pi$
$338$	399.049	0.0642172
$339$	−8.72954	−0.00139859
$340$	3553.31	0.566780
$341$	−1167.92	−0.185473
$342$	342.000	0.0540738
$343$	−343.000	−0.0539949
$344$	4485.25	0.702990
$345$	−2781.05	−0.433990
$346$	−1885.16	−0.292910
$347$	1169.20	0.180881	0.0904406	−	0.995902i	$-0.471172\pi$
$347$	1169.20	0.180881	0.0904406	+	0.995902i	$0.471172\pi$
$348$	−2817.59	−0.434019
$349$	−4490.36	−0.688721	−0.344361	−	0.938837i	$-0.611904\pi$
$349$	−4490.36	−0.688721	−0.344361	+	0.938837i	$0.611904\pi$
$350$	962.003	0.146918
$351$	1321.77	0.200999
$352$	−798.235	−0.120870
$353$	1818.89	0.274248	0.137124	−	0.990554i	$-0.456214\pi$
$353$	1818.89	0.274248	0.137124	+	0.990554i	$0.456214\pi$
$354$	−1698.91	−0.255073
$355$	7601.40	1.13645
$356$	−4020.91	−0.598617
$357$	2486.53	0.368631
$358$	−5990.05	−0.884312
$359$	−6254.14	−0.919446	−0.459723	−	0.888062i	$-0.652051\pi$
$359$	−6254.14	−0.919446	−0.459723	+	0.888062i	$0.652051\pi$
$360$	540.170	0.0790819
$361$	361.000	0.0526316
$362$	−762.181	−0.110661
$363$	2126.26	0.307438
$364$	1370.72	0.197377
$365$	−419.035	−0.0600912
$366$	28.4289	0.00406012
$367$	−11279.9	−1.60438	−0.802190	−	0.597069i	$-0.796332\pi$
$367$	−11279.9	−1.60438	−0.802190	+	0.597069i	$0.796332\pi$
$368$	1977.01	0.280051
$369$	−548.476	−0.0773781
$370$	−2948.98	−0.414351
$371$	3052.89	0.427219
$372$	−561.841	−0.0783067
$373$	−1648.80	−0.228878	−0.114439	−	0.993430i	$-0.536507\pi$
$373$	−1648.80	−0.228878	−0.114439	+	0.993430i	$0.536507\pi$
$374$	−5907.25	−0.816729
$375$	4359.95	0.600392
$376$	1980.20	0.271598
$377$	−11494.4	−1.57027
$378$	378.000	0.0514344
$379$	−10749.8	−1.45694	−0.728469	−	0.685079i	$-0.759768\pi$
$379$	−10749.8	−1.45694	−0.728469	+	0.685079i	$0.759768\pi$
$380$	570.180	0.0769727
$381$	8132.83	1.09359
$382$	−5913.89	−0.792097
$383$	10114.2	1.34938	0.674688	−	0.738103i	$-0.264278\pi$
$383$	10114.2	1.34938	0.674688	+	0.738103i	$0.264278\pi$
$384$	−384.000	−0.0510310
$385$	1310.02	0.173415
$386$	−2372.13	−0.312793
$387$	5045.91	0.662786
$388$	5802.45	0.759213
$389$	−9406.46	−1.22603	−0.613016	−	0.790071i	$-0.710044\pi$
$389$	−9406.46	−1.22603	−0.613016	+	0.790071i	$0.710044\pi$
$390$	2203.64	0.286117
$391$	14630.7	1.89234
$392$	392.000	0.0505076
$393$	−4851.01	−0.622649
$394$	−1451.46	−0.185593
$395$	436.748	0.0556334
$396$	−898.014	−0.113957
$397$	10856.4	1.37247	0.686233	−	0.727382i	$-0.259263\pi$
$397$	10856.4	1.37247	0.686233	+	0.727382i	$0.259263\pi$
$398$	4478.08	0.563984
$399$	399.000	0.0500626
$400$	−1099.43	−0.137429
$401$	−4145.71	−0.516277	−0.258138	−	0.966108i	$-0.583109\pi$
$401$	−4145.71	−0.516277	−0.258138	+	0.966108i	$0.583109\pi$
$402$	2354.76	0.292151
$403$	−2292.04	−0.283312
$404$	4816.62	0.593157
$405$	607.692	0.0745591
$406$	−3287.19	−0.401823
$407$	4902.57	0.597080
$408$	−2841.75	−0.344823
$409$	2751.21	0.332613	0.166306	−	0.986074i	$-0.446816\pi$
$409$	2751.21	0.332613	0.166306	+	0.986074i	$0.446816\pi$
$410$	−914.415	−0.110146
$411$	5031.50	0.603858
$412$	1172.86	0.140249
$413$	−1982.06	−0.236152
$414$	2224.14	0.264035
$415$	10193.1	1.20569
$416$	−1566.54	−0.184629
$417$	−1315.81	−0.154521
$418$	−947.904	−0.110917
$419$	−4697.24	−0.547673	−0.273837	−	0.961776i	$-0.588293\pi$
$419$	−4697.24	−0.547673	−0.273837	+	0.961776i	$0.588293\pi$
$420$	630.199	0.0732156
$421$	−274.561	−0.0317845	−0.0158922	−	0.999874i	$-0.505059\pi$
$421$	−274.561	−0.0317845	−0.0158922	+	0.999874i	$0.505059\pi$
$422$	1210.22	0.139603
$423$	2227.72	0.256065
$424$	−3489.02	−0.399627
$425$	−8136.23	−0.928623
$426$	−6079.20	−0.691404
$427$	33.1671	0.00375894
$428$	5502.20	0.621399
$429$	−3663.47	−0.412294
$430$	8412.51	0.943458
$431$	−1218.84	−0.136216	−0.0681082	−	0.997678i	$-0.521696\pi$
$431$	−1218.84	−0.136216	−0.0681082	+	0.997678i	$0.521696\pi$
$432$	−432.000	−0.0481125
$433$	−2166.59	−0.240462	−0.120231	−	0.992746i	$-0.538363\pi$
$433$	−2166.59	−0.240462	−0.120231	+	0.992746i	$0.538363\pi$
$434$	−655.481	−0.0724979
$435$	−5284.65	−0.582481
$436$	4033.09	0.443004
$437$	2347.70	0.256993
$438$	335.122	0.0365588
$439$	16365.3	1.77921	0.889607	−	0.456727i	$-0.150979\pi$
$439$	16365.3	1.77921	0.889607	+	0.456727i	$0.150979\pi$
$440$	−1497.16	−0.162215
$441$	441.000	0.0476190
$442$	−11593.0	−1.24756
$443$	−11343.2	−1.21655	−0.608277	−	0.793724i	$-0.708139\pi$
$443$	−11343.2	−1.21655	−0.608277	+	0.793724i	$0.708139\pi$
$444$	2358.44	0.252087
$445$	−7541.58	−0.803383
$446$	−6156.35	−0.653614
$447$	−5626.84	−0.595392
$448$	−448.000	−0.0472456
$449$	−10979.8	−1.15405	−0.577025	−	0.816726i	$-0.695787\pi$
$449$	−10979.8	−1.15405	−0.577025	+	0.816726i	$0.695787\pi$
$450$	−1236.86	−0.129569
$451$	1520.18	0.158720
$452$	11.6394	0.00121122
$453$	355.539	0.0368757
$454$	−10166.6	−1.05097
$455$	2570.91	0.264893
$456$	−456.000	−0.0468293
$457$	1690.86	0.173075	0.0865375	−	0.996249i	$-0.472420\pi$
$457$	1690.86	0.173075	0.0865375	+	0.996249i	$0.472420\pi$
$458$	−3867.39	−0.394566
$459$	−3196.97	−0.325102
$460$	3708.07	0.375847
$461$	10023.1	1.01263	0.506313	−	0.862350i	$-0.331008\pi$
$461$	10023.1	1.01263	0.506313	+	0.862350i	$0.331008\pi$
$462$	−1047.68	−0.105504
$463$	14429.4	1.44836	0.724181	−	0.689609i	$-0.242218\pi$
$463$	14429.4	1.44836	0.724181	+	0.689609i	$0.242218\pi$
$464$	3756.78	0.375871
$465$	−1053.78	−0.105093
$466$	−2767.40	−0.275102
$467$	5390.79	0.534167	0.267084	−	0.963673i	$-0.413940\pi$
$467$	5390.79	0.534167	0.267084	+	0.963673i	$0.413940\pi$
$468$	−1762.36	−0.174070
$469$	2747.22	0.270479
$470$	3714.04	0.364502
$471$	−4206.68	−0.411536
$472$	2265.21	0.220900
$473$	−13985.5	−1.35952
$474$	−349.289	−0.0338467
$475$	−1305.58	−0.126113
$476$	−3315.38	−0.319244
$477$	−3925.15	−0.376772
$478$	−14031.5	−1.34265
$479$	−9074.96	−0.865648	−0.432824	−	0.901478i	$-0.642483\pi$
$479$	−9074.96	−0.865648	−0.432824	+	0.901478i	$0.642483\pi$
$480$	−720.227	−0.0684869
$481$	9621.31	0.912045
$482$	−6873.64	−0.649556
$483$	2594.83	0.244449
$484$	−2835.02	−0.266249
$485$	10883.0	1.01891
$486$	−486.000	−0.0453609
$487$	−14265.8	−1.32741	−0.663704	−	0.747996i	$-0.731016\pi$
$487$	−14265.8	−1.32741	−0.663704	+	0.747996i	$0.731016\pi$
$488$	−37.9053	−0.00351617
$489$	−3566.31	−0.329804
$490$	735.232	0.0677845
$491$	−15562.0	−1.43035	−0.715175	−	0.698945i	$-0.753653\pi$
$491$	−15562.0	−1.43035	−0.715175	+	0.698945i	$0.753653\pi$
$492$	731.301	0.0670114
$493$	27801.7	2.53981
$494$	−1860.26	−0.169428
$495$	−1684.31	−0.152937
$496$	749.121	0.0678156
$497$	−7092.40	−0.640116
$498$	−8151.93	−0.733528
$499$	16557.5	1.48540	0.742701	−	0.669623i	$-0.233544\pi$
$499$	16557.5	1.48540	0.742701	+	0.669623i	$0.233544\pi$
$500$	−5813.27	−0.519955
$501$	−10011.5	−0.892775
$502$	9733.48	0.865392
$503$	−9599.06	−0.850896	−0.425448	−	0.904983i	$-0.639884\pi$
$503$	−9599.06	−0.850896	−0.425448	+	0.904983i	$0.639884\pi$
$504$	−504.000	−0.0445435
$505$	9034.01	0.796055
$506$	−6164.53	−0.541594
$507$	−598.574	−0.0524331
$508$	−10843.8	−0.947077
$509$	−15584.0	−1.35707	−0.678535	−	0.734568i	$-0.737385\pi$
$509$	−15584.0	−1.35707	−0.678535	+	0.734568i	$0.737385\pi$
$510$	−5329.96	−0.462774
$511$	390.976	0.0338469
$512$	512.000	0.0441942
$513$	−513.000	−0.0441511
$514$	−10992.8	−0.943327
$515$	2199.81	0.188223
$516$	−6727.88	−0.573989
$517$	−6174.46	−0.525246
$518$	2751.51	0.233387
$519$	2827.74	0.239160
$520$	−2938.19	−0.247785
$521$	−7270.38	−0.611365	−0.305682	−	0.952134i	$-0.598885\pi$
$521$	−7270.38	−0.611365	−0.305682	+	0.952134i	$0.598885\pi$
$522$	4226.38	0.354375
$523$	19238.3	1.60847	0.804235	−	0.594311i	$-0.202575\pi$
$523$	19238.3	1.60847	0.804235	+	0.594311i	$0.202575\pi$
$524$	6468.01	0.539230
$525$	−1443.00	−0.119958
$526$	−203.404	−0.0168609
$527$	5543.79	0.458238
$528$	1197.35	0.0986895
$529$	3100.87	0.254859
$530$	−6543.98	−0.536325
$531$	2548.36	0.208267
$532$	−532.000	−0.0433555
$533$	2983.36	0.242446
$534$	6031.36	0.488769
$535$	10319.9	0.833958
$536$	−3139.68	−0.253010
$537$	8985.07	0.722038
$538$	9429.45	0.755636
$539$	−1222.30	−0.0976773
$540$	−810.256	−0.0645701
$541$	−20566.7	−1.63444	−0.817219	−	0.576328i	$-0.804485\pi$
$541$	−20566.7	−1.63444	−0.817219	+	0.576328i	$0.804485\pi$
$542$	9079.80	0.719577
$543$	1143.27	0.0903545
$544$	3789.00	0.298625
$545$	7564.43	0.594540
$546$	−2056.08	−0.161158
$547$	−15609.6	−1.22014	−0.610070	−	0.792348i	$-0.708859\pi$
$547$	−15609.6	−1.22014	−0.610070	+	0.792348i	$0.708859\pi$
$548$	−6708.67	−0.522956
$549$	−42.6434	−0.00331508
$550$	3428.14	0.265776
$551$	4461.18	0.344923
$552$	−2965.52	−0.228661
$553$	−407.503	−0.0313360
$554$	−1477.93	−0.113341
$555$	4423.47	0.338317
$556$	1754.41	0.133819
$557$	14517.8	1.10438	0.552190	−	0.833719i	$-0.313792\pi$
$557$	14517.8	1.10438	0.552190	+	0.833719i	$0.313792\pi$
$558$	842.761	0.0639371
$559$	−27446.6	−2.07668
$560$	−840.265	−0.0634066
$561$	8860.88	0.666857
$562$	−12321.6	−0.924835
$563$	4522.48	0.338543	0.169272	−	0.985569i	$-0.445858\pi$
$563$	4522.48	0.338543	0.169272	+	0.985569i	$0.445858\pi$
$564$	−2970.29	−0.221759
$565$	21.8307	0.00162553
$566$	−9334.03	−0.693177
$567$	−567.000	−0.0419961
$568$	8105.60	0.598774
$569$	7222.80	0.532154	0.266077	−	0.963952i	$-0.414272\pi$
$569$	7222.80	0.532154	0.266077	+	0.963952i	$0.414272\pi$
$570$	−855.270	−0.0628479
$571$	17601.1	1.28999	0.644995	−	0.764187i	$-0.276859\pi$
$571$	17601.1	1.28999	0.644995	+	0.764187i	$0.276859\pi$
$572$	4884.63	0.357057
$573$	8870.83	0.646744
$574$	853.185	0.0620405
$575$	−8490.58	−0.615794
$576$	576.000	0.0416667
$577$	−3836.50	−0.276803	−0.138402	−	0.990376i	$-0.544196\pi$
$577$	−3836.50	−0.276803	−0.138402	+	0.990376i	$0.544196\pi$
$578$	18214.1	1.31074
$579$	3558.19	0.255395
$580$	7046.19	0.504444
$581$	−9510.59	−0.679115
$582$	−8703.67	−0.619895
$583$	10879.1	0.772844
$584$	−446.830	−0.0316609
$585$	−3305.46	−0.233614
$586$	17857.1	1.25883
$587$	−22655.3	−1.59299	−0.796493	−	0.604647i	$-0.793314\pi$
$587$	−22655.3	−1.59299	−0.796493	+	0.604647i	$0.793314\pi$
$588$	−588.000	−0.0412393
$589$	889.581	0.0622318
$590$	4248.61	0.296462
$591$	2177.19	0.151536
$592$	−3144.58	−0.218313
$593$	24398.4	1.68958	0.844792	−	0.535094i	$-0.179724\pi$
$593$	24398.4	1.68958	0.844792	+	0.535094i	$0.179724\pi$
$594$	1347.02	0.0930454
$595$	−6218.29	−0.428445
$596$	7502.45	0.515625
$597$	−6717.12	−0.460491
$598$	−12097.9	−0.827291
$599$	−21559.7	−1.47063	−0.735313	−	0.677728i	$-0.762965\pi$
$599$	−21559.7	−1.47063	−0.735313	+	0.677728i	$0.762965\pi$
$600$	1649.15	0.112210
$601$	14996.6	1.01785	0.508923	−	0.860812i	$-0.330044\pi$
$601$	14996.6	1.01785	0.508923	+	0.860812i	$0.330044\pi$
$602$	−7849.19	−0.531411
$603$	−3532.14	−0.238540
$604$	−474.052	−0.0319353
$605$	−5317.34	−0.357323
$606$	−7224.92	−0.484311
$607$	−9498.91	−0.635171	−0.317585	−	0.948230i	$-0.602872\pi$
$607$	−9498.91	−0.635171	−0.317585	+	0.948230i	$0.602872\pi$
$608$	608.000	0.0405554
$609$	4930.78	0.328087
$610$	−71.0948	−0.00471893
$611$	−12117.4	−0.802319
$612$	4262.63	0.281546
$613$	16464.6	1.08483	0.542413	−	0.840112i	$-0.317511\pi$
$613$	16464.6	1.08483	0.542413	+	0.840112i	$0.317511\pi$
$614$	569.370	0.0374233
$615$	1371.62	0.0899336
$616$	1396.91	0.0913688
$617$	28452.3	1.85648	0.928240	−	0.371982i	$-0.121322\pi$
$617$	28452.3	1.85648	0.928240	+	0.371982i	$0.121322\pi$
$618$	−1759.29	−0.114513
$619$	11718.1	0.760888	0.380444	−	0.924804i	$-0.375771\pi$
$619$	11718.1	0.760888	0.380444	+	0.924804i	$0.375771\pi$
$620$	1405.05	0.0910129
$621$	−3336.21	−0.215584
$622$	−2226.44	−0.143524
$623$	7036.59	0.452512
$624$	2349.81	0.150749
$625$	−2314.01	−0.148097
$626$	−10245.2	−0.654125
$627$	1421.86	0.0905637
$628$	5608.90	0.356401
$629$	−23271.1	−1.47517
$630$	−945.298	−0.0597803
$631$	8917.95	0.562628	0.281314	−	0.959616i	$-0.409230\pi$
$631$	8917.95	0.562628	0.281314	+	0.959616i	$0.409230\pi$
$632$	465.718	0.0293121
$633$	−1815.33	−0.113985
$634$	−7720.03	−0.483599
$635$	−20338.5	−1.27104
$636$	5233.53	0.326294
$637$	−2398.76	−0.149203
$638$	−11714.0	−0.726902
$639$	9118.80	0.564529
$640$	960.303	0.0593114
$641$	−27736.7	−1.70910	−0.854551	−	0.519367i	$-0.826168\pi$
$641$	−27736.7	−1.70910	−0.854551	+	0.519367i	$0.826168\pi$
$642$	−8253.30	−0.507370
$643$	−19356.4	−1.18716	−0.593578	−	0.804776i	$-0.702285\pi$
$643$	−19356.4	−1.18716	−0.593578	+	0.804776i	$0.702285\pi$
$644$	−3459.77	−0.211699
$645$	−12618.8	−0.770330
$646$	4499.44	0.274037
$647$	24062.2	1.46211	0.731054	−	0.682320i	$-0.239029\pi$
$647$	24062.2	1.46211	0.731054	+	0.682320i	$0.239029\pi$
$648$	648.000	0.0392837
$649$	−7063.17	−0.427201
$650$	6727.74	0.405975
$651$	983.221	0.0591943
$652$	4755.08	0.285619
$653$	−6599.94	−0.395522	−0.197761	−	0.980250i	$-0.563367\pi$
$653$	−6599.94	−0.395522	−0.197761	+	0.980250i	$0.563367\pi$
$654$	−6049.63	−0.361712
$655$	12131.4	0.723681
$656$	−975.068	−0.0580336
$657$	−502.684	−0.0298502
$658$	−3465.34	−0.205309
$659$	744.463	0.0440063	0.0220031	−	0.999758i	$-0.492996\pi$
$659$	744.463	0.0440063	0.0220031	+	0.999758i	$0.492996\pi$
$660$	2245.74	0.132448
$661$	−3629.01	−0.213544	−0.106772	−	0.994284i	$-0.534051\pi$
$661$	−3629.01	−0.213544	−0.106772	+	0.994284i	$0.534051\pi$
$662$	15914.9	0.934367
$663$	17389.5	1.01863
$664$	10869.2	0.635254
$665$	−997.815	−0.0581859
$666$	−3537.66	−0.205828
$667$	29012.5	1.68421
$668$	13348.6	0.773166
$669$	9234.53	0.533673
$670$	−5888.75	−0.339556
$671$	118.193	0.00679996
$672$	672.000	0.0385758
$673$	−3205.20	−0.183583	−0.0917916	−	0.995778i	$-0.529259\pi$
$673$	−3205.20	−0.183583	−0.0917916	+	0.995778i	$0.529259\pi$
$674$	19104.1	1.09178
$675$	1855.29	0.105793
$676$	798.099	0.0454084
$677$	−5732.42	−0.325428	−0.162714	−	0.986673i	$-0.552025\pi$
$677$	−5732.42	−0.325428	−0.162714	+	0.986673i	$0.552025\pi$
$678$	−17.4591	−0.000988955 0
$679$	−10154.3	−0.573911
$680$	7106.62	0.400774
$681$	15249.9	0.858117
$682$	−2335.84	−0.131149
$683$	29489.8	1.65212	0.826058	−	0.563585i	$-0.190578\pi$
$683$	29489.8	1.65212	0.826058	+	0.563585i	$0.190578\pi$
$684$	684.000	0.0382360
$685$	−12582.7	−0.701841
$686$	−686.000	−0.0381802
$687$	5801.09	0.322162
$688$	8970.51	0.497089
$689$	21350.3	1.18053
$690$	−5562.10	−0.306878
$691$	−8654.43	−0.476455	−0.238227	−	0.971209i	$-0.576566\pi$
$691$	−8654.43	−0.476455	−0.238227	+	0.971209i	$0.576566\pi$
$692$	−3770.32	−0.207119
$693$	1571.53	0.0861433
$694$	2338.39	0.127902
$695$	3290.56	0.179594
$696$	−5635.18	−0.306898
$697$	−7215.89	−0.392139
$698$	−8980.73	−0.486999
$699$	4151.11	0.224620
$700$	1924.01	0.103887
$701$	16379.1	0.882494	0.441247	−	0.897386i	$-0.354536\pi$
$701$	16379.1	0.882494	0.441247	+	0.897386i	$0.354536\pi$
$702$	2643.53	0.142128
$703$	−3734.19	−0.200338
$704$	−1596.47	−0.0854676
$705$	−5571.06	−0.297614
$706$	3637.77	0.193923
$707$	−8429.08	−0.448385
$708$	−3397.82	−0.180364
$709$	7840.50	0.415312	0.207656	−	0.978202i	$-0.433417\pi$
$709$	7840.50	0.415312	0.207656	+	0.978202i	$0.433417\pi$
$710$	15202.8	0.803593
$711$	523.933	0.0276357
$712$	−8041.82	−0.423286
$713$	5785.24	0.303869
$714$	4973.06	0.260661
$715$	9161.57	0.479194
$716$	−11980.1	−0.625303
$717$	21047.3	1.09627
$718$	−12508.3	−0.650146
$719$	5719.40	0.296659	0.148329	−	0.988938i	$-0.452610\pi$
$719$	5719.40	0.296659	0.148329	+	0.988938i	$0.452610\pi$
$720$	1080.34	0.0559193
$721$	−2052.51	−0.106018
$722$	722.000	0.0372161
$723$	10310.5	0.530360
$724$	−1524.36	−0.0782493
$725$	−16134.1	−0.826490
$726$	4252.53	0.217391
$727$	29571.7	1.50860	0.754301	−	0.656529i	$-0.227976\pi$
$727$	29571.7	1.50860	0.754301	+	0.656529i	$0.227976\pi$
$728$	2741.44	0.139567
$729$	729.000	0.0370370
$730$	−838.070	−0.0424909
$731$	66385.3	3.35889
$732$	56.8579	0.00287094
$733$	−5307.52	−0.267446	−0.133723	−	0.991019i	$-0.542693\pi$
$733$	−5307.52	−0.267446	−0.133723	+	0.991019i	$0.542693\pi$
$734$	−22559.8	−1.13447
$735$	−1102.85	−0.0553458
$736$	3954.02	0.198026
$737$	9789.84	0.489299
$738$	−1096.95	−0.0547146
$739$	6507.76	0.323940	0.161970	−	0.986796i	$-0.448215\pi$
$739$	6507.76	0.323940	0.161970	+	0.986796i	$0.448215\pi$
$740$	−5897.96	−0.292991
$741$	2790.40	0.138337
$742$	6105.79	0.302090
$743$	−28299.7	−1.39733	−0.698664	−	0.715450i	$-0.746222\pi$
$743$	−28299.7	−1.39733	−0.698664	+	0.715450i	$0.746222\pi$
$744$	−1123.68	−0.0553712
$745$	14071.5	0.692001
$746$	−3297.60	−0.161841
$747$	12227.9	0.598923
$748$	−11814.5	−0.577515
$749$	−9628.85	−0.469734
$750$	8719.90	0.424541
$751$	19539.3	0.949402	0.474701	−	0.880147i	$-0.342556\pi$
$751$	19539.3	0.949402	0.474701	+	0.880147i	$0.342556\pi$
$752$	3960.39	0.192049
$753$	−14600.2	−0.706589
$754$	−22988.8	−1.11035
$755$	−889.128	−0.0428592
$756$	756.000	0.0363696
$757$	−33939.1	−1.62951	−0.814754	−	0.579807i	$-0.803128\pi$
$757$	−33939.1	−1.62951	−0.814754	+	0.579807i	$0.803128\pi$
$758$	−21499.6	−1.03021
$759$	9246.80	0.442210
$760$	1140.36	0.0544279
$761$	22124.4	1.05389	0.526944	−	0.849900i	$-0.323338\pi$
$761$	22124.4	1.05389	0.526944	+	0.849900i	$0.323338\pi$
$762$	16265.7	0.773285
$763$	−7057.90	−0.334880
$764$	−11827.8	−0.560097
$765$	7994.95	0.377853
$766$	20228.4	0.954153
$767$	−13861.5	−0.652555
$768$	−768.000	−0.0360844
$769$	−17253.5	−0.809074	−0.404537	−	0.914522i	$-0.632567\pi$
$769$	−17253.5	−0.809074	−0.404537	+	0.914522i	$0.632567\pi$
$770$	2620.04	0.122623
$771$	16489.1	0.770223
$772$	−4744.26	−0.221178
$773$	26514.6	1.23372	0.616859	−	0.787074i	$-0.288405\pi$
$773$	26514.6	1.23372	0.616859	+	0.787074i	$0.288405\pi$
$774$	10091.8	0.468660
$775$	−3217.22	−0.149117
$776$	11604.9	0.536845
$777$	−4127.27	−0.190560
$778$	−18812.9	−0.866935
$779$	−1157.89	−0.0532553
$780$	4407.28	0.202315
$781$	−25274.1	−1.15798
$782$	29261.3	1.33809
$783$	−6339.57	−0.289346
$784$	784.000	0.0357143
$785$	10520.0	0.478313
$786$	−9702.02	−0.440279
$787$	5212.77	0.236106	0.118053	−	0.993007i	$-0.462335\pi$
$787$	5212.77	0.236106	0.118053	+	0.993007i	$0.462335\pi$
$788$	−2902.92	−0.131234
$789$	305.106	0.0137669
$790$	873.497	0.0393388
$791$	−20.3689	−0.000915594 0
$792$	−1796.03	−0.0805797
$793$	231.953	0.0103870
$794$	21712.9	0.970480
$795$	9815.97	0.437908
$796$	8956.16	0.398797
$797$	−10848.4	−0.482146	−0.241073	−	0.970507i	$-0.577499\pi$
$797$	−10848.4	−0.482146	−0.241073	+	0.970507i	$0.577499\pi$
$798$	798.000	0.0353996
$799$	29308.4	1.29769
$800$	−2198.86	−0.0971770
$801$	−9047.04	−0.399078
$802$	−8291.42	−0.365063
$803$	1393.26	0.0612293
$804$	4709.51	0.206582
$805$	−6489.12	−0.284113
$806$	−4584.09	−0.200332
$807$	−14144.2	−0.616974
$808$	9633.23	0.419426
$809$	−869.934	−0.0378062	−0.0189031	−	0.999821i	$-0.506017\pi$
$809$	−869.934	−0.0378062	−0.0189031	+	0.999821i	$0.506017\pi$
$810$	1215.38	0.0527213
$811$	26441.7	1.14487	0.572437	−	0.819949i	$-0.305998\pi$
$811$	26441.7	1.14487	0.572437	+	0.819949i	$0.305998\pi$
$812$	−6574.37	−0.284132
$813$	−13619.7	−0.587532
$814$	9805.14	0.422199
$815$	8918.60	0.383319
$816$	−5683.50	−0.243826
$817$	10652.5	0.456160
$818$	5502.42	0.235193
$819$	3084.12	0.131585
$820$	−1828.83	−0.0778848
$821$	−34499.3	−1.46654	−0.733272	−	0.679935i	$-0.762008\pi$
$821$	−34499.3	−1.46654	−0.733272	+	0.679935i	$0.762008\pi$
$822$	10063.0	0.426992
$823$	2238.24	0.0947995	0.0473997	−	0.998876i	$-0.484907\pi$
$823$	2238.24	0.0947995	0.0473997	+	0.998876i	$0.484907\pi$
$824$	2345.72	0.0991712
$825$	−5142.22	−0.217005
$826$	−3964.12	−0.166985
$827$	37009.4	1.55616	0.778080	−	0.628165i	$-0.216194\pi$
$827$	37009.4	1.55616	0.778080	+	0.628165i	$0.216194\pi$
$828$	4448.28	0.186701
$829$	−46472.3	−1.94698	−0.973492	−	0.228722i	$-0.926545\pi$
$829$	−46472.3	−1.94698	−0.973492	+	0.228722i	$0.926545\pi$
$830$	20386.3	0.852551
$831$	2216.89	0.0925428
$832$	−3133.08	−0.130553
$833$	5801.91	0.241326
$834$	−2631.62	−0.109263
$835$	25036.6	1.03764
$836$	−1895.81	−0.0784305
$837$	−1264.14	−0.0522045
$838$	−9394.47	−0.387263
$839$	8318.33	0.342289	0.171145	−	0.985246i	$-0.445253\pi$
$839$	8318.33	0.342289	0.171145	+	0.985246i	$0.445253\pi$
$840$	1260.40	0.0517713
$841$	30741.6	1.26047
$842$	−549.121	−0.0224750
$843$	18482.5	0.755124
$844$	2420.44	0.0987143
$845$	1496.91	0.0609410
$846$	4455.44	0.181065
$847$	4961.28	0.201265
$848$	−6978.04	−0.282579
$849$	14001.0	0.565977
$850$	−16272.5	−0.656636
$851$	−24284.7	−0.978223
$852$	−12158.4	−0.488897
$853$	10045.6	0.403230	0.201615	−	0.979465i	$-0.435381\pi$
$853$	10045.6	0.403230	0.201615	+	0.979465i	$0.435381\pi$
$854$	66.3342	0.00265797
$855$	1282.90	0.0513151
$856$	11004.4	0.439396
$857$	−5533.17	−0.220548	−0.110274	−	0.993901i	$-0.535173\pi$
$857$	−5533.17	−0.220548	−0.110274	+	0.993901i	$0.535173\pi$
$858$	−7326.95	−0.291536
$859$	21840.8	0.867520	0.433760	−	0.901029i	$-0.357187\pi$
$859$	21840.8	0.867520	0.433760	+	0.901029i	$0.357187\pi$
$860$	16825.0	0.667126
$861$	−1279.78	−0.0506558
$862$	−2437.67	−0.0963196
$863$	17369.2	0.685116	0.342558	−	0.939497i	$-0.388707\pi$
$863$	17369.2	0.685116	0.342558	+	0.939497i	$0.388707\pi$
$864$	−864.000	−0.0340207
$865$	−7071.59	−0.277967
$866$	−4333.19	−0.170032
$867$	−27321.1	−1.07021
$868$	−1310.96	−0.0512638
$869$	−1452.16	−0.0566871
$870$	−10569.3	−0.411876
$871$	19212.6	0.747410
$872$	8066.18	0.313251
$873$	13055.5	0.506142
$874$	4695.40	0.181721
$875$	10173.2	0.393049
$876$	670.245	0.0258510
$877$	46675.8	1.79718	0.898592	−	0.438784i	$-0.144591\pi$
$877$	46675.8	1.79718	0.898592	+	0.438784i	$0.144591\pi$
$878$	32730.7	1.25809
$879$	−26785.7	−1.02783
$880$	−2994.33	−0.114703
$881$	3245.03	0.124095	0.0620476	−	0.998073i	$-0.480237\pi$
$881$	3245.03	0.124095	0.0620476	+	0.998073i	$0.480237\pi$
$882$	882.000	0.0336718
$883$	−40654.8	−1.54943	−0.774713	−	0.632312i	$-0.782106\pi$
$883$	−40654.8	−1.54943	−0.774713	+	0.632312i	$0.782106\pi$
$884$	−23186.0	−0.882160
$885$	−6372.92	−0.242060
$886$	−22686.5	−0.860234
$887$	−5034.69	−0.190585	−0.0952923	−	0.995449i	$-0.530379\pi$
$887$	−5034.69	−0.190585	−0.0952923	+	0.995449i	$0.530379\pi$
$888$	4716.88	0.178252
$889$	18976.6	0.715923
$890$	−15083.2	−0.568077
$891$	−2020.53	−0.0759712
$892$	−12312.7	−0.462175
$893$	4702.96	0.176236
$894$	−11253.7	−0.421006
$895$	−22469.8	−0.839197
$896$	−896.000	−0.0334077
$897$	18146.9	0.675480
$898$	−21959.6	−0.816037
$899$	10993.3	0.407839
$900$	−2473.72	−0.0916193
$901$	−51640.2	−1.90942
$902$	3040.37	0.112232
$903$	11773.8	0.433895
$904$	23.2788	0.000856460 0
$905$	−2859.08	−0.105016
$906$	711.078	0.0260751
$907$	4939.49	0.180830	0.0904152	−	0.995904i	$-0.471181\pi$
$907$	4939.49	0.180830	0.0904152	+	0.995904i	$0.471181\pi$
$908$	−20333.2	−0.743151
$909$	10837.4	0.395438
$910$	5141.83	0.187308
$911$	30257.4	1.10041	0.550205	−	0.835030i	$-0.314550\pi$
$911$	30257.4	1.10041	0.550205	+	0.835030i	$0.314550\pi$
$912$	−912.000	−0.0331133
$913$	−33891.4	−1.22852
$914$	3381.73	0.122382
$915$	106.642	0.00385299
$916$	−7734.78	−0.279000
$917$	−11319.0	−0.407619
$918$	−6393.94	−0.229882
$919$	2470.91	0.0886917	0.0443459	−	0.999016i	$-0.485880\pi$
$919$	2470.91	0.0886917	0.0443459	+	0.999016i	$0.485880\pi$
$920$	7416.13	0.265764
$921$	−854.055	−0.0305560
$922$	20046.1	0.716035
$923$	−49600.5	−1.76882
$924$	−2095.37	−0.0746023
$925$	13504.9	0.480042
$926$	28858.8	1.02415
$927$	2638.94	0.0934995
$928$	7513.57	0.265781
$929$	33803.3	1.19381	0.596905	−	0.802312i	$-0.296397\pi$
$929$	33803.3	1.19381	0.596905	+	0.802312i	$0.296397\pi$
$930$	−2107.57	−0.0743117
$931$	931.000	0.0327737
$932$	−5534.81	−0.194526
$933$	3339.66	0.117187
$934$	10781.6	0.377713
$935$	−22159.2	−0.775062
$936$	−3524.71	−0.123086
$937$	41209.8	1.43678	0.718392	−	0.695639i	$-0.244879\pi$
$937$	41209.8	1.43678	0.718392	+	0.695639i	$0.244879\pi$
$938$	5494.43	0.191258
$939$	15367.9	0.534091
$940$	7428.08	0.257742
$941$	−2743.53	−0.0950441	−0.0475221	−	0.998870i	$-0.515132\pi$
$941$	−2743.53	−0.0950441	−0.0475221	+	0.998870i	$0.515132\pi$
$942$	−8413.36	−0.291000
$943$	−7530.16	−0.260038
$944$	4530.42	0.156200
$945$	1417.95	0.0488104
$946$	−27971.0	−0.961327
$947$	29793.3	1.02234	0.511168	−	0.859481i	$-0.329213\pi$
$947$	29793.3	1.02234	0.511168	+	0.859481i	$0.329213\pi$
$948$	−698.577	−0.0239333
$949$	2734.28	0.0935285
$950$	−2611.15	−0.0891757
$951$	11580.1	0.394857
$952$	−6630.75	−0.225739
$953$	−23878.0	−0.811633	−0.405816	−	0.913955i	$-0.633013\pi$
$953$	−23878.0	−0.811633	−0.405816	+	0.913955i	$0.633013\pi$
$954$	−7850.30	−0.266418
$955$	−22184.1	−0.751686
$956$	−28063.1	−0.949398
$957$	17571.1	0.593513
$958$	−18149.9	−0.612106
$959$	11740.2	0.395318
$960$	−1440.45	−0.0484276
$961$	−27598.9	−0.926417
$962$	19242.6	0.644914
$963$	12379.9	0.414266
$964$	−13747.3	−0.459305
$965$	−8898.29	−0.296835
$966$	5189.66	0.172851
$967$	−32332.2	−1.07521	−0.537607	−	0.843196i	$-0.680672\pi$
$967$	−32332.2	−1.07521	−0.537607	+	0.843196i	$0.680672\pi$
$968$	−5670.04	−0.188266
$969$	−6749.16	−0.223750
$970$	21766.0	0.720480
$971$	−4053.08	−0.133954	−0.0669771	−	0.997755i	$-0.521335\pi$
$971$	−4053.08	−0.133954	−0.0669771	+	0.997755i	$0.521335\pi$
$972$	−972.000	−0.0320750
$973$	−3070.22	−0.101158
$974$	−28531.7	−0.938619
$975$	−10091.6	−0.331477
$976$	−75.8105	−0.00248631
$977$	34508.2	1.13000	0.565002	−	0.825089i	$-0.308875\pi$
$977$	34508.2	1.13000	0.565002	+	0.825089i	$0.308875\pi$
$978$	−7132.63	−0.233207
$979$	25075.2	0.818598
$980$	1470.46	0.0479309
$981$	9074.45	0.295336
$982$	−31124.0	−1.01141
$983$	−14410.2	−0.467561	−0.233780	−	0.972289i	$-0.575110\pi$
$983$	−14410.2	−0.467561	−0.233780	+	0.972289i	$0.575110\pi$
$984$	1462.60	0.0473842
$985$	−5444.70	−0.176124
$986$	55603.3	1.79591
$987$	5198.01	0.167634
$988$	−3720.53	−0.119803
$989$	69276.6	2.22737
$990$	−3368.62	−0.108143
$991$	−58507.4	−1.87543	−0.937713	−	0.347410i	$-0.887061\pi$
$991$	−58507.4	−1.87543	−0.937713	+	0.347410i	$0.887061\pi$
$992$	1498.24	0.0479529
$993$	−23872.4	−0.762907
$994$	−14184.8	−0.452630
$995$	16798.1	0.535211
$996$	−16303.9	−0.518683
$997$	10024.4	0.318431	0.159216	−	0.987244i	$-0.449104\pi$
$997$	10024.4	0.318431	0.159216	+	0.987244i	$0.449104\pi$
$998$	33115.0	1.05034
$999$	5306.48	0.168058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.h.1.3	✓	3
3.2	odd	2		2394.4.a.l.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.h.1.3	✓	3	1.1	even	1	trivial
2394.4.a.l.1.1		3	3.2	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.50237 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.50237 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +15.0047 q^{10} -24.9448 q^{11} -12.0000 q^{12} -48.9543 q^{13} -14.0000 q^{14} -22.5071 q^{15} +16.0000 q^{16} +118.406 q^{17} +18.0000 q^{18} +19.0000 q^{19} +30.0095 q^{20} +21.0000 q^{21} -49.8897 q^{22} +123.563 q^{23} -24.0000 q^{24} -68.7145 q^{25} -97.9086 q^{26} -27.0000 q^{27} -28.0000 q^{28} +234.799 q^{29} -45.0142 q^{30} +46.8201 q^{31} +32.0000 q^{32} +74.8345 q^{33} +236.813 q^{34} -52.5166 q^{35} +36.0000 q^{36} -196.536 q^{37} +38.0000 q^{38} +146.863 q^{39} +60.0189 q^{40} -60.9418 q^{41} +42.0000 q^{42} +560.657 q^{43} -99.7794 q^{44} +67.5213 q^{45} +247.126 q^{46} +247.524 q^{47} -48.0000 q^{48} +49.0000 q^{49} -137.429 q^{50} -355.219 q^{51} -195.817 q^{52} -436.128 q^{53} -54.0000 q^{54} -187.145 q^{55} -56.0000 q^{56} -57.0000 q^{57} +469.598 q^{58} +283.152 q^{59} -90.0284 q^{60} -4.73816 q^{61} +93.6401 q^{62} -63.0000 q^{63} +64.0000 q^{64} -367.273 q^{65} +149.669 q^{66} -392.460 q^{67} +473.625 q^{68} -370.690 q^{69} -105.033 q^{70} +1013.20 q^{71} +72.0000 q^{72} -55.8537 q^{73} -393.073 q^{74} +206.143 q^{75} +76.0000 q^{76} +174.614 q^{77} +293.726 q^{78} +58.2148 q^{79} +120.038 q^{80} +81.0000 q^{81} -121.884 q^{82} +1358.66 q^{83} +84.0000 q^{84} +888.327 q^{85} +1121.31 q^{86} -704.397 q^{87} -199.559 q^{88} -1005.23 q^{89} +135.043 q^{90} +342.680 q^{91} +494.253 q^{92} -140.460 q^{93} +495.049 q^{94} +142.545 q^{95} -96.0000 q^{96} +1450.61 q^{97} +98.0000 q^{98} -224.504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} - 12 q^{11} - 36 q^{12} + 6 q^{13} - 42 q^{14} + 48 q^{16} + 72 q^{17} + 54 q^{18} + 57 q^{19} + 63 q^{21} - 24 q^{22} - 16 q^{23} - 72 q^{24} - 143 q^{25} + 12 q^{26} - 81 q^{27} - 84 q^{28} + 52 q^{29} + 248 q^{31} + 96 q^{32} + 36 q^{33} + 144 q^{34} + 108 q^{36} + 130 q^{37} + 114 q^{38} - 18 q^{39} + 438 q^{41} + 126 q^{42} + 676 q^{43} - 48 q^{44} - 32 q^{46} + 1098 q^{47} - 144 q^{48} + 147 q^{49} - 286 q^{50} - 216 q^{51} + 24 q^{52} + 8 q^{53} - 162 q^{54} + 392 q^{55} - 168 q^{56} - 171 q^{57} + 104 q^{58} + 1012 q^{59} + 274 q^{61} + 496 q^{62} - 189 q^{63} + 192 q^{64} - 536 q^{65} + 72 q^{66} + 144 q^{67} + 288 q^{68} + 48 q^{69} + 606 q^{71} + 216 q^{72} + 362 q^{73} + 260 q^{74} + 429 q^{75} + 228 q^{76} + 84 q^{77} - 36 q^{78} + 752 q^{79} + 243 q^{81} + 876 q^{82} + 2010 q^{83} + 252 q^{84} + 840 q^{85} + 1352 q^{86} - 156 q^{87} - 96 q^{88} + 950 q^{89} - 42 q^{91} - 64 q^{92} - 744 q^{93} + 2196 q^{94} - 288 q^{96} + 1470 q^{97} + 294 q^{98} - 108 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 - 12 * q^11 - 36 * q^12 + 6 * q^13 - 42 * q^14 + 48 * q^16 + 72 * q^17 + 54 * q^18 + 57 * q^19 + 63 * q^21 - 24 * q^22 - 16 * q^23 - 72 * q^24 - 143 * q^25 + 12 * q^26 - 81 * q^27 - 84 * q^28 + 52 * q^29 + 248 * q^31 + 96 * q^32 + 36 * q^33 + 144 * q^34 + 108 * q^36 + 130 * q^37 + 114 * q^38 - 18 * q^39 + 438 * q^41 + 126 * q^42 + 676 * q^43 - 48 * q^44 - 32 * q^46 + 1098 * q^47 - 144 * q^48 + 147 * q^49 - 286 * q^50 - 216 * q^51 + 24 * q^52 + 8 * q^53 - 162 * q^54 + 392 * q^55 - 168 * q^56 - 171 * q^57 + 104 * q^58 + 1012 * q^59 + 274 * q^61 + 496 * q^62 - 189 * q^63 + 192 * q^64 - 536 * q^65 + 72 * q^66 + 144 * q^67 + 288 * q^68 + 48 * q^69 + 606 * q^71 + 216 * q^72 + 362 * q^73 + 260 * q^74 + 429 * q^75 + 228 * q^76 + 84 * q^77 - 36 * q^78 + 752 * q^79 + 243 * q^81 + 876 * q^82 + 2010 * q^83 + 252 * q^84 + 840 * q^85 + 1352 * q^86 - 156 * q^87 - 96 * q^88 + 950 * q^89 - 42 * q^91 - 64 * q^92 - 744 * q^93 + 2196 * q^94 - 288 * q^96 + 1470 * q^97 + 294 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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