LMFDB - Embedded newform 1849.4.a.m.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.06596 q^{2} +8.82751 q^{3} +17.6640 q^{4} -4.85016 q^{5} -44.7198 q^{6} +30.6269 q^{7} -48.9575 q^{8} +50.9249 q^{9} +O(q^{10})$	\(q-5.06596 q^{2} +8.82751 q^{3} +17.6640 q^{4} -4.85016 q^{5} -44.7198 q^{6} +30.6269 q^{7} -48.9575 q^{8} +50.9249 q^{9} +24.5707 q^{10} +43.3053 q^{11} +155.929 q^{12} -7.16422 q^{13} -155.155 q^{14} -42.8148 q^{15} +106.705 q^{16} +28.9099 q^{17} -257.984 q^{18} -109.979 q^{19} -85.6731 q^{20} +270.359 q^{21} -219.383 q^{22} -61.7030 q^{23} -432.172 q^{24} -101.476 q^{25} +36.2937 q^{26} +211.197 q^{27} +540.993 q^{28} +12.3736 q^{29} +216.898 q^{30} -190.094 q^{31} -148.903 q^{32} +382.278 q^{33} -146.456 q^{34} -148.545 q^{35} +899.537 q^{36} +315.869 q^{37} +557.151 q^{38} -63.2422 q^{39} +237.451 q^{40} +15.9534 q^{41} -1369.63 q^{42} +764.945 q^{44} -246.993 q^{45} +312.585 q^{46} +351.451 q^{47} +941.938 q^{48} +595.007 q^{49} +514.074 q^{50} +255.202 q^{51} -126.549 q^{52} +515.962 q^{53} -1069.92 q^{54} -210.038 q^{55} -1499.42 q^{56} -970.842 q^{57} -62.6840 q^{58} +392.768 q^{59} -756.280 q^{60} -78.1107 q^{61} +963.011 q^{62} +1559.67 q^{63} -99.3004 q^{64} +34.7476 q^{65} -1936.61 q^{66} +277.176 q^{67} +510.664 q^{68} -544.683 q^{69} +752.525 q^{70} -812.995 q^{71} -2493.15 q^{72} -352.767 q^{73} -1600.18 q^{74} -895.780 q^{75} -1942.67 q^{76} +1326.31 q^{77} +320.383 q^{78} +827.162 q^{79} -517.535 q^{80} +489.370 q^{81} -80.8196 q^{82} +878.314 q^{83} +4775.62 q^{84} -140.217 q^{85} +109.228 q^{87} -2120.12 q^{88} +370.282 q^{89} +1251.26 q^{90} -219.418 q^{91} -1089.92 q^{92} -1678.06 q^{93} -1780.44 q^{94} +533.416 q^{95} -1314.44 q^{96} +1105.48 q^{97} -3014.28 q^{98} +2205.32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.06596	−1.79109	−0.895544	−	0.444972i	$-0.853214\pi$
$2$	−5.06596	−1.79109	−0.895544	+	0.444972i	$0.853214\pi$
$3$	8.82751	1.69885	0.849427	−	0.527706i	$-0.176948\pi$
$3$	8.82751	1.69885	0.849427	+	0.527706i	$0.176948\pi$
$4$	17.6640	2.20800
$5$	−4.85016	−0.433811	−0.216906	−	0.976193i	$-0.569596\pi$
$5$	−4.85016	−0.433811	−0.216906	+	0.976193i	$0.569596\pi$
$6$	−44.7198	−3.04280
$7$	30.6269	1.65370	0.826848	−	0.562425i	$-0.190131\pi$
$7$	30.6269	1.65370	0.826848	+	0.562425i	$0.190131\pi$
$8$	−48.9575	−2.16364
$9$	50.9249	1.88611
$10$	24.5707	0.776994
$11$	43.3053	1.18700	0.593502	−	0.804833i	$-0.297745\pi$
$11$	43.3053	1.18700	0.593502	+	0.804833i	$0.297745\pi$
$12$	155.929	3.75107
$13$	−7.16422	−0.152846	−0.0764229	−	0.997075i	$-0.524350\pi$
$13$	−7.16422	−0.152846	−0.0764229	+	0.997075i	$0.524350\pi$
$14$	−155.155	−2.96192
$15$	−42.8148	−0.736982
$16$	106.705	1.66726
$17$	28.9099	0.412451	0.206226	−	0.978504i	$-0.433882\pi$
$17$	28.9099	0.412451	0.206226	+	0.978504i	$0.433882\pi$
$18$	−257.984	−3.37818
$19$	−109.979	−1.32795	−0.663973	−	0.747757i	$-0.731131\pi$
$19$	−109.979	−1.32795	−0.663973	+	0.747757i	$0.731131\pi$
$20$	−85.6731	−0.957855
$21$	270.359	2.80939
$22$	−219.383	−2.12603
$23$	−61.7030	−0.559390	−0.279695	−	0.960089i	$-0.590233\pi$
$23$	−61.7030	−0.559390	−0.279695	+	0.960089i	$0.590233\pi$
$24$	−432.172	−3.67570
$25$	−101.476	−0.811808
$26$	36.2937	0.273761
$27$	211.197	1.50536
$28$	540.993	3.65136
$29$	12.3736	0.0792314	0.0396157	−	0.999215i	$-0.487387\pi$
$29$	12.3736	0.0792314	0.0396157	+	0.999215i	$0.487387\pi$
$30$	216.898	1.32000
$31$	−190.094	−1.10135	−0.550677	−	0.834719i	$-0.685630\pi$
$31$	−190.094	−1.10135	−0.550677	+	0.834719i	$0.685630\pi$
$32$	−148.903	−0.822582
$33$	382.278	2.01655
$34$	−146.456	−0.738737
$35$	−148.545	−0.717392
$36$	899.537	4.16452
$37$	315.869	1.40348	0.701738	−	0.712435i	$-0.252408\pi$
$37$	315.869	1.40348	0.701738	+	0.712435i	$0.252408\pi$
$38$	557.151	2.37847
$39$	−63.2422	−0.259663
$40$	237.451	0.938609
$41$	15.9534	0.0607685	0.0303843	−	0.999538i	$-0.490327\pi$
$41$	15.9534	0.0607685	0.0303843	+	0.999538i	$0.490327\pi$
$42$	−1369.63	−5.03187
$43$	0	0
$43$	0	0
$44$	764.945	2.62090
$45$	−246.993	−0.818214
$46$	312.585	1.00192
$47$	351.451	1.09073	0.545365	−	0.838198i	$-0.316391\pi$
$47$	351.451	1.09073	0.545365	+	0.838198i	$0.316391\pi$
$48$	941.938	2.83244
$49$	595.007	1.73471
$50$	514.074	1.45402
$51$	255.202	0.700695
$52$	−126.549	−0.337484
$53$	515.962	1.33722	0.668611	−	0.743612i	$-0.266889\pi$
$53$	515.962	1.33722	0.668611	+	0.743612i	$0.266889\pi$
$54$	−1069.92	−2.69624
$55$	−210.038	−0.514935
$56$	−1499.42	−3.57800
$57$	−970.842	−2.25599
$58$	−62.6840	−0.141911
$59$	392.768	0.866679	0.433339	−	0.901231i	$-0.357335\pi$
$59$	392.768	0.866679	0.433339	+	0.901231i	$0.357335\pi$
$60$	−756.280	−1.62726
$61$	−78.1107	−0.163952	−0.0819759	−	0.996634i	$-0.526123\pi$
$61$	−78.1107	−0.163952	−0.0819759	+	0.996634i	$0.526123\pi$
$62$	963.011	1.97262
$63$	1559.67	3.11905
$64$	−99.3004	−0.193946
$65$	34.7476	0.0663062
$66$	−1936.61	−3.61181
$67$	277.176	0.505409	0.252704	−	0.967544i	$-0.418680\pi$
$67$	277.176	0.505409	0.252704	+	0.967544i	$0.418680\pi$
$68$	510.664	0.910692
$69$	−544.683	−0.950321
$70$	752.525	1.28491
$71$	−812.995	−1.35894	−0.679470	−	0.733703i	$-0.737790\pi$
$71$	−812.995	−1.35894	−0.679470	+	0.733703i	$0.737790\pi$
$72$	−2493.15	−4.08084
$73$	−352.767	−0.565592	−0.282796	−	0.959180i	$-0.591262\pi$
$73$	−352.767	−0.565592	−0.282796	+	0.959180i	$0.591262\pi$
$74$	−1600.18	−2.51375
$75$	−895.780	−1.37914
$76$	−1942.67	−2.93210
$77$	1326.31	1.96294
$78$	320.383	0.465079
$79$	827.162	1.17801	0.589006	−	0.808128i	$-0.299519\pi$
$79$	827.162	1.17801	0.589006	+	0.808128i	$0.299519\pi$
$80$	−517.535	−0.723277
$81$	489.370	0.671289
$82$	−80.8196	−0.108842
$83$	878.314	1.16154	0.580768	−	0.814069i	$-0.302752\pi$
$83$	878.314	1.16154	0.580768	+	0.814069i	$0.302752\pi$
$84$	4775.62	6.20313
$85$	−140.217	−0.178926
$86$	0	0
$87$	109.228	0.134603
$88$	−2120.12	−2.56824
$89$	370.282	0.441009	0.220504	−	0.975386i	$-0.429230\pi$
$89$	370.282	0.441009	0.220504	+	0.975386i	$0.429230\pi$
$90$	1251.26	1.46549
$91$	−219.418	−0.252761
$92$	−1089.92	−1.23513
$93$	−1678.06	−1.87104
$94$	−1780.44	−1.95360
$95$	533.416	0.576077
$96$	−1314.44	−1.39745
$97$	1105.48	1.15716	0.578580	−	0.815625i	$-0.303607\pi$
$97$	1105.48	1.15716	0.578580	+	0.815625i	$0.303607\pi$
$98$	−3014.28	−3.10703
$99$	2205.32	2.23881
$100$	−1792.47	−1.79247
$101$	1299.31	1.28006	0.640030	−	0.768350i	$-0.278922\pi$
$101$	1299.31	1.28006	0.640030	+	0.768350i	$0.278922\pi$
$102$	−1292.84	−1.25501
$103$	−110.713	−0.105911	−0.0529556	−	0.998597i	$-0.516864\pi$
$103$	−110.713	−0.105911	−0.0529556	+	0.998597i	$0.516864\pi$
$104$	350.742	0.330703
$105$	−1311.28	−1.21874
$106$	−2613.84	−2.39509
$107$	386.179	0.348910	0.174455	−	0.984665i	$-0.444184\pi$
$107$	386.179	0.348910	0.174455	+	0.984665i	$0.444184\pi$
$108$	3730.58	3.32384
$109$	822.569	0.722824	0.361412	−	0.932406i	$-0.382295\pi$
$109$	822.569	0.722824	0.361412	+	0.932406i	$0.382295\pi$
$110$	1064.04	0.922295
$111$	2788.34	2.38430
$112$	3268.04	2.75715
$113$	511.636	0.425935	0.212967	−	0.977059i	$-0.431687\pi$
$113$	511.636	0.425935	0.212967	+	0.977059i	$0.431687\pi$
$114$	4918.25	4.04067
$115$	299.269	0.242669
$116$	218.566	0.174943
$117$	−364.837	−0.288283
$118$	−1989.75	−1.55230
$119$	885.419	0.682069
$120$	2096.10	1.59456
$121$	544.350	0.408978
$122$	395.706	0.293652
$123$	140.829	0.103237
$124$	−3357.83	−2.43179
$125$	1098.44	0.785982
$126$	−7901.23	−5.58649
$127$	2062.93	1.44138	0.720689	−	0.693258i	$-0.243825\pi$
$127$	2062.93	1.44138	0.720689	+	0.693258i	$0.243825\pi$
$128$	1694.28	1.16996
$129$	0	0
$130$	−176.030	−0.118760
$131$	−729.542	−0.486568	−0.243284	−	0.969955i	$-0.578225\pi$
$131$	−729.542	−0.486568	−0.243284	+	0.969955i	$0.578225\pi$
$132$	6752.56	4.45253
$133$	−3368.32	−2.19602
$134$	−1404.16	−0.905232
$135$	−1024.34	−0.653044
$136$	−1415.35	−0.892394
$137$	2915.57	1.81821	0.909103	−	0.416571i	$-0.136768\pi$
$137$	2915.57	1.81821	0.909103	+	0.416571i	$0.136768\pi$
$138$	2759.35	1.70211
$139$	1774.39	1.08275	0.541374	−	0.840782i	$-0.317904\pi$
$139$	1774.39	1.08275	0.541374	+	0.840782i	$0.317904\pi$
$140$	−2623.90	−1.58400
$141$	3102.43	1.85299
$142$	4118.60	2.43398
$143$	−310.249	−0.181429
$144$	5433.93	3.14463
$145$	−60.0137	−0.0343715
$146$	1787.10	1.01303
$147$	5252.42	2.94702
$148$	5579.52	3.09887
$149$	−2231.35	−1.22684	−0.613421	−	0.789756i	$-0.710207\pi$
$149$	−2231.35	−1.22684	−0.613421	+	0.789756i	$0.710207\pi$
$150$	4537.99	2.47017
$151$	−556.506	−0.299919	−0.149960	−	0.988692i	$-0.547914\pi$
$151$	−556.506	−0.299919	−0.149960	+	0.988692i	$0.547914\pi$
$152$	5384.30	2.87319
$153$	1472.23	0.777927
$154$	−6719.03	−3.51581
$155$	921.987	0.477779
$156$	−1117.11	−0.573336
$157$	−2701.43	−1.37323	−0.686616	−	0.727020i	$-0.740905\pi$
$157$	−2701.43	−1.37323	−0.686616	+	0.727020i	$0.740905\pi$
$158$	−4190.37	−2.10993
$159$	4554.66	2.27175
$160$	722.204	0.356845
$161$	−1889.77	−0.925061
$162$	−2479.13	−1.20234
$163$	187.621	0.0901572	0.0450786	−	0.998983i	$-0.485646\pi$
$163$	187.621	0.0901572	0.0450786	+	0.998983i	$0.485646\pi$
$164$	281.802	0.134177
$165$	−1854.11	−0.874800
$166$	−4449.51	−2.08041
$167$	1855.32	0.859696	0.429848	−	0.902901i	$-0.358567\pi$
$167$	1855.32	0.859696	0.429848	+	0.902901i	$0.358567\pi$
$168$	−13236.1	−6.07849
$169$	−2145.67	−0.976638
$170$	710.336	0.320472
$171$	−5600.68	−2.50465
$172$	0	0
$173$	−2134.76	−0.938166	−0.469083	−	0.883154i	$-0.655416\pi$
$173$	−2134.76	−0.938166	−0.469083	+	0.883154i	$0.655416\pi$
$174$	−553.343	−0.241085
$175$	−3107.89	−1.34248
$176$	4620.89	1.97905
$177$	3467.16	1.47236
$178$	−1875.83	−0.789886
$179$	51.6348	0.0215607	0.0107803	−	0.999942i	$-0.496568\pi$
$179$	51.6348	0.0215607	0.0107803	+	0.999942i	$0.496568\pi$
$180$	−4362.89	−1.80662
$181$	−3723.19	−1.52897	−0.764483	−	0.644644i	$-0.777006\pi$
$181$	−3723.19	−1.52897	−0.764483	+	0.644644i	$0.777006\pi$
$182$	1111.56	0.452717
$183$	−689.523	−0.278530
$184$	3020.82	1.21031
$185$	−1532.02	−0.608843
$186$	8500.99	3.35120
$187$	1251.95	0.489581
$188$	6208.02	2.40833
$189$	6468.30	2.48942
$190$	−2702.27	−1.03181
$191$	−2771.97	−1.05012	−0.525059	−	0.851066i	$-0.675957\pi$
$191$	−2771.97	−1.05012	−0.525059	+	0.851066i	$0.675957\pi$
$192$	−876.575	−0.329486
$193$	−4314.92	−1.60930	−0.804650	−	0.593749i	$-0.797647\pi$
$193$	−4314.92	−1.60930	−0.804650	+	0.593749i	$0.797647\pi$
$194$	−5600.33	−2.07258
$195$	306.734	0.112645
$196$	10510.2	3.83025
$197$	3482.35	1.25943	0.629714	−	0.776827i	$-0.283172\pi$
$197$	3482.35	1.25943	0.629714	+	0.776827i	$0.283172\pi$
$198$	−11172.1	−4.00992
$199$	3321.96	1.18335	0.591677	−	0.806175i	$-0.298466\pi$
$199$	3321.96	1.18335	0.591677	+	0.806175i	$0.298466\pi$
$200$	4968.01	1.75646
$201$	2446.77	0.858616
$202$	−6582.25	−2.29270
$203$	378.964	0.131025
$204$	4507.89	1.54713
$205$	−77.3767	−0.0263621
$206$	560.868	0.189697
$207$	−3142.21	−1.05507
$208$	−764.457	−0.254834
$209$	−4762.68	−1.57628
$210$	6642.92	2.18288
$211$	2954.93	0.964103	0.482051	−	0.876143i	$-0.339892\pi$
$211$	2954.93	0.964103	0.482051	+	0.876143i	$0.339892\pi$
$212$	9113.95	2.95259
$213$	−7176.72	−2.30864
$214$	−1956.37	−0.624929
$215$	0	0
$216$	−10339.7	−3.25706
$217$	−5822.00	−1.82130
$218$	−4167.11	−1.29464
$219$	−3114.05	−0.960859
$220$	−3710.10	−1.13698
$221$	−207.117	−0.0630415
$222$	−14125.6	−4.27050
$223$	−2029.04	−0.609302	−0.304651	−	0.952464i	$-0.598540\pi$
$223$	−2029.04	−0.609302	−0.304651	+	0.952464i	$0.598540\pi$
$224$	−4560.44	−1.36030
$225$	−5167.65	−1.53116
$226$	−2591.93	−0.762887
$227$	−959.022	−0.280408	−0.140204	−	0.990123i	$-0.544776\pi$
$227$	−959.022	−0.280408	−0.140204	+	0.990123i	$0.544776\pi$
$228$	−17149.0	−4.98122
$229$	1848.66	0.533462	0.266731	−	0.963771i	$-0.414056\pi$
$229$	1848.66	0.533462	0.266731	+	0.963771i	$0.414056\pi$
$230$	−1516.09	−0.434642
$231$	11708.0	3.33476
$232$	−605.778	−0.171428
$233$	3792.22	1.06625	0.533126	−	0.846036i	$-0.321017\pi$
$233$	3792.22	1.06625	0.533126	+	0.846036i	$0.321017\pi$
$234$	1848.25	0.516341
$235$	−1704.59	−0.473171
$236$	6937.85	1.91363
$237$	7301.78	2.00127
$238$	−4485.50	−1.22165
$239$	−3009.11	−0.814407	−0.407204	−	0.913337i	$-0.633496\pi$
$239$	−3009.11	−0.814407	−0.407204	+	0.913337i	$0.633496\pi$
$240$	−4568.54	−1.22874
$241$	−4896.13	−1.30866	−0.654330	−	0.756209i	$-0.727049\pi$
$241$	−4896.13	−1.30866	−0.654330	+	0.756209i	$0.727049\pi$
$242$	−2757.66	−0.732516
$243$	−1382.40	−0.364942
$244$	−1379.75	−0.362005
$245$	−2885.87	−0.752538
$246$	−713.435	−0.184906
$247$	787.915	0.202971
$248$	9306.54	2.38293
$249$	7753.32	1.97328
$250$	−5564.68	−1.40776
$251$	5960.08	1.49879	0.749396	−	0.662122i	$-0.230344\pi$
$251$	5960.08	1.49879	0.749396	+	0.662122i	$0.230344\pi$
$252$	27550.0	6.88685
$253$	−2672.07	−0.663998
$254$	−10450.7	−2.58164
$255$	−1237.77	−0.303969
$256$	−7788.75	−1.90155
$257$	1196.29	0.290359	0.145180	−	0.989405i	$-0.453624\pi$
$257$	1196.29	0.290359	0.145180	+	0.989405i	$0.453624\pi$
$258$	0	0
$259$	9674.10	2.32092
$260$	613.781	0.146404
$261$	630.122	0.149439
$262$	3695.84	0.871486
$263$	3362.66	0.788406	0.394203	−	0.919023i	$-0.371021\pi$
$263$	3362.66	0.788406	0.394203	+	0.919023i	$0.371021\pi$
$264$	−18715.4	−4.36307
$265$	−2502.50	−0.580102
$266$	17063.8	3.93327
$267$	3268.66	0.749210
$268$	4896.03	1.11594
$269$	6643.64	1.50584	0.752918	−	0.658114i	$-0.228646\pi$
$269$	6643.64	1.50584	0.752918	+	0.658114i	$0.228646\pi$
$270$	5189.26	1.16966
$271$	166.303	0.0372776	0.0186388	−	0.999826i	$-0.494067\pi$
$271$	166.303	0.0372776	0.0186388	+	0.999826i	$0.494067\pi$
$272$	3084.82	0.687665
$273$	−1936.91	−0.429404
$274$	−14770.2	−3.25657
$275$	−4394.45	−0.963619
$276$	−9621.29	−2.09831
$277$	−3864.62	−0.838276	−0.419138	−	0.907923i	$-0.637668\pi$
$277$	−3864.62	−0.838276	−0.419138	+	0.907923i	$0.637668\pi$
$278$	−8989.00	−1.93930
$279$	−9680.53	−2.07727
$280$	7272.40	1.55217
$281$	−1246.51	−0.264629	−0.132314	−	0.991208i	$-0.542241\pi$
$281$	−1246.51	−0.264629	−0.132314	+	0.991208i	$0.542241\pi$
$282$	−15716.8	−3.31887
$283$	−6319.00	−1.32730	−0.663650	−	0.748043i	$-0.730993\pi$
$283$	−6319.00	−1.32730	−0.663650	+	0.748043i	$0.730993\pi$
$284$	−14360.7	−3.00054
$285$	4708.74	0.978672
$286$	1571.71	0.324955
$287$	488.604	0.100493
$288$	−7582.87	−1.55148
$289$	−4077.22	−0.829884
$290$	304.027	0.0615624
$291$	9758.64	1.96585
$292$	−6231.27	−1.24883
$293$	2834.42	0.565148	0.282574	−	0.959245i	$-0.408812\pi$
$293$	2834.42	0.565148	0.282574	+	0.959245i	$0.408812\pi$
$294$	−26608.6	−5.27838
$295$	−1904.99	−0.375975
$296$	−15464.2	−3.03661
$297$	9145.94	1.78687
$298$	11303.9	2.19738
$299$	442.054	0.0855004
$300$	−15823.1	−3.04515
$301$	0	0
$302$	2819.24	0.537182
$303$	11469.7	2.17463
$304$	−11735.3	−2.21403
$305$	378.849	0.0711241
$306$	−7458.27	−1.39334
$307$	1401.16	0.260484	0.130242	−	0.991482i	$-0.458425\pi$
$307$	1401.16	0.260484	0.130242	+	0.991482i	$0.458425\pi$
$308$	23427.9	4.33418
$309$	−977.319	−0.179928
$310$	−4670.75	−0.855745
$311$	5013.93	0.914193	0.457096	−	0.889417i	$-0.348889\pi$
$311$	5013.93	0.914193	0.457096	+	0.889417i	$0.348889\pi$
$312$	3096.18	0.561816
$313$	4379.26	0.790832	0.395416	−	0.918502i	$-0.370600\pi$
$313$	4379.26	0.790832	0.395416	+	0.918502i	$0.370600\pi$
$314$	13685.3	2.45958
$315$	−7564.64	−1.35308
$316$	14611.0	2.60105
$317$	−4850.35	−0.859377	−0.429689	−	0.902977i	$-0.641377\pi$
$317$	−4850.35	−0.859377	−0.429689	+	0.902977i	$0.641377\pi$
$318$	−23073.7	−4.06890
$319$	535.841	0.0940480
$320$	481.622	0.0841360
$321$	3409.00	0.592747
$322$	9573.51	1.65687
$323$	−3179.48	−0.547713
$324$	8644.22	1.48221
$325$	726.996	0.124081
$326$	−950.483	−0.161480
$327$	7261.23	1.22797
$328$	−781.040	−0.131481
$329$	10763.8	1.80374
$330$	9392.84	1.56685
$331$	−9025.47	−1.49875	−0.749373	−	0.662148i	$-0.769645\pi$
$331$	−9025.47	−1.49875	−0.749373	+	0.662148i	$0.769645\pi$
$332$	15514.5	2.56467
$333$	16085.6	2.64710
$334$	−9399.01	−1.53979
$335$	−1344.34	−0.219252
$336$	28848.6	4.68399
$337$	9048.02	1.46254	0.731272	−	0.682086i	$-0.238927\pi$
$337$	9048.02	1.46254	0.731272	+	0.682086i	$0.238927\pi$
$338$	10869.9	1.74925
$339$	4516.47	0.723601
$340$	−2476.80	−0.395068
$341$	−8232.09	−1.30731
$342$	28372.8	4.48604
$343$	7718.18	1.21499
$344$	0	0
$345$	2641.80	0.412260
$346$	10814.6	1.68034
$347$	−6296.43	−0.974093	−0.487047	−	0.873376i	$-0.661926\pi$
$347$	−6296.43	−0.974093	−0.487047	+	0.873376i	$0.661926\pi$
$348$	1929.40	0.297203
$349$	−7027.07	−1.07780	−0.538898	−	0.842371i	$-0.681159\pi$
$349$	−7027.07	−1.07780	−0.538898	+	0.842371i	$0.681159\pi$
$350$	15744.5	2.40451
$351$	−1513.06	−0.230089
$352$	−6448.30	−0.976408
$353$	−2172.15	−0.327513	−0.163757	−	0.986501i	$-0.552361\pi$
$353$	−2172.15	−0.327513	−0.163757	+	0.986501i	$0.552361\pi$
$354$	−17564.5	−2.63713
$355$	3943.15	0.589523
$356$	6540.66	0.973748
$357$	7816.04	1.15874
$358$	−261.580	−0.0386171
$359$	−2727.76	−0.401018	−0.200509	−	0.979692i	$-0.564260\pi$
$359$	−2727.76	−0.401018	−0.200509	+	0.979692i	$0.564260\pi$
$360$	12092.2	1.77032
$361$	5236.43	0.763439
$362$	18861.6	2.73851
$363$	4805.25	0.694794
$364$	−3875.79	−0.558096
$365$	1710.97	0.245360
$366$	3493.10	0.498872
$367$	−2687.77	−0.382290	−0.191145	−	0.981562i	$-0.561220\pi$
$367$	−2687.77	−0.382290	−0.191145	+	0.981562i	$0.561220\pi$
$368$	−6584.01	−0.932650
$369$	812.427	0.114616
$370$	7761.14	1.09049
$371$	15802.3	2.21136
$372$	−29641.2	−4.13125
$373$	345.178	0.0479159	0.0239580	−	0.999713i	$-0.492373\pi$
$373$	345.178	0.0479159	0.0239580	+	0.999713i	$0.492373\pi$
$374$	−6342.34	−0.876884
$375$	9696.52	1.33527
$376$	−17206.1	−2.35994
$377$	−88.6469	−0.0121102
$378$	−32768.2	−4.45877
$379$	11658.8	1.58014	0.790069	−	0.613018i	$-0.210045\pi$
$379$	11658.8	1.58014	0.790069	+	0.613018i	$0.210045\pi$
$380$	9422.26	1.27198
$381$	18210.5	2.44869
$382$	14042.7	1.88086
$383$	−4928.81	−0.657573	−0.328786	−	0.944404i	$-0.606640\pi$
$383$	−4928.81	−0.657573	−0.328786	+	0.944404i	$0.606640\pi$
$384$	14956.2	1.98759
$385$	−6432.80	−0.851547
$386$	21859.3	2.88240
$387$	0	0
$388$	19527.2	2.55501
$389$	−2861.06	−0.372909	−0.186455	−	0.982464i	$-0.559700\pi$
$389$	−2861.06	−0.372909	−0.186455	+	0.982464i	$0.559700\pi$
$390$	−1553.91	−0.201757
$391$	−1783.82	−0.230721
$392$	−29130.0	−3.75329
$393$	−6440.04	−0.826608
$394$	−17641.5	−2.25575
$395$	−4011.86	−0.511035
$396$	38954.7	4.94330
$397$	−3321.07	−0.419848	−0.209924	−	0.977718i	$-0.567322\pi$
$397$	−3321.07	−0.419848	−0.209924	+	0.977718i	$0.567322\pi$
$398$	−16828.9	−2.11949
$399$	−29733.9	−3.73072
$400$	−10828.0	−1.35350
$401$	−6827.29	−0.850221	−0.425111	−	0.905141i	$-0.639765\pi$
$401$	−6827.29	−0.850221	−0.425111	+	0.905141i	$0.639765\pi$
$402$	−12395.2	−1.53786
$403$	1361.88	0.168337
$404$	22951.0	2.82637
$405$	−2373.52	−0.291213
$406$	−1919.82	−0.234677
$407$	13678.8	1.66593
$408$	−12494.0	−1.51605
$409$	−393.294	−0.0475480	−0.0237740	−	0.999717i	$-0.507568\pi$
$409$	−393.294	−0.0475480	−0.0237740	+	0.999717i	$0.507568\pi$
$410$	391.988	0.0472168
$411$	25737.2	3.08887
$412$	−1955.63	−0.233852
$413$	12029.3	1.43322
$414$	15918.3	1.88972
$415$	−4259.96	−0.503887
$416$	1066.78	0.125728
$417$	15663.4	1.83943
$418$	24127.6	2.82325
$419$	2349.47	0.273936	0.136968	−	0.990576i	$-0.456264\pi$
$419$	2349.47	0.273936	0.136968	+	0.990576i	$0.456264\pi$
$420$	−23162.5	−2.69099
$421$	−7675.61	−0.888567	−0.444283	−	0.895886i	$-0.646542\pi$
$421$	−7675.61	−0.888567	−0.444283	+	0.895886i	$0.646542\pi$
$422$	−14969.6	−1.72679
$423$	17897.6	2.05723
$424$	−25260.2	−2.89326
$425$	−2933.66	−0.334831
$426$	36357.0	4.13498
$427$	−2392.29	−0.271126
$428$	6821.47	0.770393
$429$	−2738.72	−0.308221
$430$	0	0
$431$	−9866.87	−1.10272	−0.551358	−	0.834269i	$-0.685890\pi$
$431$	−9866.87	−1.10272	−0.551358	+	0.834269i	$0.685890\pi$
$432$	22535.7	2.50984
$433$	16541.1	1.83583	0.917917	−	0.396772i	$-0.129870\pi$
$433$	16541.1	1.83583	0.917917	+	0.396772i	$0.129870\pi$
$434$	29494.0	3.26212
$435$	−529.771	−0.0583921
$436$	14529.9	1.59600
$437$	6786.04	0.742839
$438$	15775.7	1.72098
$439$	−17269.4	−1.87750	−0.938750	−	0.344598i	$-0.888015\pi$
$439$	−17269.4	−1.87750	−0.938750	+	0.344598i	$0.888015\pi$
$440$	10282.9	1.11413
$441$	30300.6	3.27185
$442$	1049.25	0.112913
$443$	−9711.01	−1.04150	−0.520749	−	0.853710i	$-0.674347\pi$
$443$	−9711.01	−1.04150	−0.520749	+	0.853710i	$0.674347\pi$
$444$	49253.2	5.26454
$445$	−1795.92	−0.191315
$446$	10279.0	1.09131
$447$	−19697.3	−2.08422
$448$	−3041.26	−0.320728
$449$	16237.2	1.70664	0.853319	−	0.521389i	$-0.174586\pi$
$449$	16237.2	1.70664	0.853319	+	0.521389i	$0.174586\pi$
$450$	26179.1	2.74244
$451$	690.869	0.0721325
$452$	9037.53	0.940464
$453$	−4912.56	−0.509519
$454$	4858.37	0.502235
$455$	1064.21	0.109650
$456$	47530.0	4.88113
$457$	−8381.58	−0.857930	−0.428965	−	0.903321i	$-0.641122\pi$
$457$	−8381.58	−0.857930	−0.428965	+	0.903321i	$0.641122\pi$
$458$	−9365.24	−0.955478
$459$	6105.67	0.620889
$460$	5286.29	0.535814
$461$	8799.93	0.889053	0.444527	−	0.895766i	$-0.353372\pi$
$461$	8799.93	0.889053	0.444527	+	0.895766i	$0.353372\pi$
$462$	−59312.2	−5.97285
$463$	310.339	0.0311505	0.0155752	−	0.999879i	$-0.495042\pi$
$463$	310.339	0.0311505	0.0155752	+	0.999879i	$0.495042\pi$
$464$	1320.32	0.132100
$465$	8138.85	0.811677
$466$	−19211.3	−1.90975
$467$	−18227.0	−1.80609	−0.903046	−	0.429544i	$-0.858674\pi$
$467$	−18227.0	−1.80609	−0.903046	+	0.429544i	$0.858674\pi$
$468$	−6444.48	−0.636530
$469$	8489.03	0.835793
$470$	8635.39	0.847492
$471$	−23846.9	−2.33292
$472$	−19228.9	−1.87518
$473$	0	0
$474$	−36990.5	−3.58446
$475$	11160.2	1.07804
$476$	15640.0	1.50601
$477$	26275.3	2.52214
$478$	15244.1	1.45868
$479$	8438.76	0.804962	0.402481	−	0.915428i	$-0.368148\pi$
$479$	8438.76	0.804962	0.402481	+	0.915428i	$0.368148\pi$
$480$	6375.26	0.606228
$481$	−2262.96	−0.214516
$482$	24803.6	2.34393
$483$	−16682.0	−1.57154
$484$	9615.40	0.903024
$485$	−5361.76	−0.501989
$486$	7003.19	0.653644
$487$	−11705.3	−1.08916	−0.544579	−	0.838710i	$-0.683310\pi$
$487$	−11705.3	−1.08916	−0.544579	+	0.838710i	$0.683310\pi$
$488$	3824.11	0.354732
$489$	1656.23	0.153164
$490$	14619.7	1.34786
$491$	7645.39	0.702712	0.351356	−	0.936242i	$-0.385721\pi$
$491$	7645.39	0.702712	0.351356	+	0.936242i	$0.385721\pi$
$492$	2487.61	0.227947
$493$	357.718	0.0326791
$494$	−3991.55	−0.363539
$495$	−10696.1	−0.971223
$496$	−20284.0	−1.83625
$497$	−24899.5	−2.24728
$498$	−39278.1	−3.53432
$499$	−14595.7	−1.30940	−0.654701	−	0.755888i	$-0.727205\pi$
$499$	−14595.7	−1.30940	−0.654701	+	0.755888i	$0.727205\pi$
$500$	19402.9	1.73545
$501$	16377.9	1.46050
$502$	−30193.5	−2.68447
$503$	21378.2	1.89504	0.947521	−	0.319695i	$-0.103580\pi$
$503$	21378.2	1.89504	0.947521	+	0.319695i	$0.103580\pi$
$504$	−76357.5	−6.74848
$505$	−6301.85	−0.555304
$506$	13536.6	1.18928
$507$	−18940.9	−1.65917
$508$	36439.5	3.18256
$509$	5614.26	0.488895	0.244448	−	0.969663i	$-0.421393\pi$
$509$	5614.26	0.488895	0.244448	+	0.969663i	$0.421393\pi$
$510$	6270.50	0.544436
$511$	−10804.2	−0.935318
$512$	25903.3	2.23589
$513$	−23227.3	−1.99904
$514$	−6060.35	−0.520059
$515$	536.975	0.0459455
$516$	0	0
$517$	15219.7	1.29470
$518$	−49008.6	−4.15698
$519$	−18844.6	−1.59381
$520$	−1701.15	−0.143463
$521$	−20123.3	−1.69217	−0.846083	−	0.533051i	$-0.821045\pi$
$521$	−20123.3	−1.69217	−0.846083	+	0.533051i	$0.821045\pi$
$522$	−3192.17	−0.267658
$523$	−10084.7	−0.843161	−0.421580	−	0.906791i	$-0.638525\pi$
$523$	−10084.7	−0.843161	−0.421580	+	0.906791i	$0.638525\pi$
$524$	−12886.6	−1.07434
$525$	−27435.0	−2.28068
$526$	−17035.1	−1.41211
$527$	−5495.60	−0.454255
$528$	40790.9	3.36211
$529$	−8359.74	−0.687083
$530$	12677.6	1.03901
$531$	20001.7	1.63465
$532$	−59498.0	−4.84881
$533$	−114.294	−0.00928822
$534$	−16558.9	−1.34190
$535$	−1873.03	−0.151361
$536$	−13569.8	−1.09352
$537$	455.806	0.0366285
$538$	−33656.4	−2.69709
$539$	25766.9	2.05911
$540$	−18093.9	−1.44192
$541$	15986.6	1.27046	0.635228	−	0.772325i	$-0.280906\pi$
$541$	15986.6	1.27046	0.635228	+	0.772325i	$0.280906\pi$
$542$	−842.488	−0.0667674
$543$	−32866.5	−2.59749
$544$	−4304.77	−0.339275
$545$	−3989.59	−0.313569
$546$	9812.32	0.769100
$547$	17522.6	1.36968	0.684839	−	0.728694i	$-0.259873\pi$
$547$	17522.6	1.36968	0.684839	+	0.728694i	$0.259873\pi$
$548$	51500.7	4.01460
$549$	−3977.78	−0.309230
$550$	22262.1	1.72593
$551$	−1360.83	−0.105215
$552$	26666.3	2.05615
$553$	25333.4	1.94808
$554$	19578.0	1.50143
$555$	−13523.9	−1.03434
$556$	31342.8	2.39071
$557$	−8382.77	−0.637683	−0.318842	−	0.947808i	$-0.603294\pi$
$557$	−8382.77	−0.637683	−0.318842	+	0.947808i	$0.603294\pi$
$558$	49041.2	3.72057
$559$	0	0
$560$	−15850.5	−1.19608
$561$	11051.6	0.831727
$562$	6314.78	0.473973
$563$	−12120.0	−0.907274	−0.453637	−	0.891187i	$-0.649874\pi$
$563$	−12120.0	−0.907274	−0.453637	+	0.891187i	$0.649874\pi$
$564$	54801.4	4.09141
$565$	−2481.51	−0.184775
$566$	32011.9	2.37731
$567$	14987.9	1.11011
$568$	39802.2	2.94025
$569$	−17232.2	−1.26962	−0.634809	−	0.772669i	$-0.718921\pi$
$569$	−17232.2	−1.26962	−0.634809	+	0.772669i	$0.718921\pi$
$570$	−23854.3	−1.75289
$571$	22460.6	1.64614	0.823070	−	0.567940i	$-0.192259\pi$
$571$	22460.6	1.64614	0.823070	+	0.567940i	$0.192259\pi$
$572$	−5480.23	−0.400594
$573$	−24469.6	−1.78400
$574$	−2475.25	−0.179991
$575$	6261.37	0.454117
$576$	−5056.86	−0.365803
$577$	−8020.32	−0.578666	−0.289333	−	0.957229i	$-0.593433\pi$
$577$	−8020.32	−0.578666	−0.289333	+	0.957229i	$0.593433\pi$
$578$	20655.1	1.48640
$579$	−38090.0	−2.73397
$580$	−1060.08	−0.0758922
$581$	26900.0	1.92083
$582$	−49436.9	−3.52101
$583$	22343.9	1.58729
$584$	17270.6	1.22374
$585$	1769.52	0.125061
$586$	−14359.1	−1.01223
$587$	24191.0	1.70097	0.850485	−	0.525999i	$-0.176308\pi$
$587$	24191.0	1.70097	0.850485	+	0.525999i	$0.176308\pi$
$588$	92778.8	6.50703
$589$	20906.4	1.46254
$590$	9650.59	0.673404
$591$	30740.5	2.13958
$592$	33704.8	2.33996
$593$	5438.90	0.376642	0.188321	−	0.982108i	$-0.439695\pi$
$593$	5438.90	0.376642	0.188321	+	0.982108i	$0.439695\pi$
$594$	−46333.0	−3.20045
$595$	−4294.42	−0.295889
$596$	−39414.6	−2.70887
$597$	29324.6	2.01035
$598$	−2239.43	−0.153139
$599$	2473.44	0.168718	0.0843589	−	0.996435i	$-0.473116\pi$
$599$	2473.44	0.168718	0.0843589	+	0.996435i	$0.473116\pi$
$600$	43855.1	2.98396
$601$	−848.130	−0.0575639	−0.0287820	−	0.999586i	$-0.509163\pi$
$601$	−848.130	−0.0575639	−0.0287820	+	0.999586i	$0.509163\pi$
$602$	0	0
$603$	14115.1	0.953254
$604$	−9830.11	−0.662221
$605$	−2640.18	−0.177419
$606$	−58104.8	−3.89496
$607$	18623.2	1.24529	0.622647	−	0.782503i	$-0.286057\pi$
$607$	18623.2	1.24529	0.622647	+	0.782503i	$0.286057\pi$
$608$	16376.3	1.09234
$609$	3345.30	0.222592
$610$	−1919.24	−0.127390
$611$	−2517.87	−0.166714
$612$	26005.5	1.71766
$613$	11171.9	0.736101	0.368050	−	0.929806i	$-0.380025\pi$
$613$	11171.9	0.736101	0.368050	+	0.929806i	$0.380025\pi$
$614$	−7098.23	−0.466549
$615$	−683.043	−0.0447853
$616$	−64932.6	−4.24710
$617$	−14502.5	−0.946271	−0.473136	−	0.880990i	$-0.656878\pi$
$617$	−14502.5	−0.946271	−0.473136	+	0.880990i	$0.656878\pi$
$618$	4951.06	0.322267
$619$	−12437.5	−0.807604	−0.403802	−	0.914846i	$-0.632312\pi$
$619$	−12437.5	−0.807604	−0.403802	+	0.914846i	$0.632312\pi$
$620$	16286.0	1.05494
$621$	−13031.5	−0.842085
$622$	−25400.4	−1.63740
$623$	11340.6	0.729295
$624$	−6748.25	−0.432926
$625$	7356.87	0.470840
$626$	−22185.2	−1.41645
$627$	−42042.6	−2.67786
$628$	−47718.1	−3.03210
$629$	9131.74	0.578865
$630$	38322.2	2.42348
$631$	4221.19	0.266312	0.133156	−	0.991095i	$-0.457489\pi$
$631$	4221.19	0.266312	0.133156	+	0.991095i	$0.457489\pi$
$632$	−40495.8	−2.54879
$633$	26084.6	1.63787
$634$	24571.7	1.53922
$635$	−10005.5	−0.625286
$636$	80453.4	5.01602
$637$	−4262.76	−0.265144
$638$	−2714.55	−0.168448
$639$	−41401.7	−2.56311
$640$	−8217.51	−0.507540
$641$	−4237.88	−0.261133	−0.130566	−	0.991440i	$-0.541680\pi$
$641$	−4237.88	−0.261133	−0.130566	+	0.991440i	$0.541680\pi$
$642$	−17269.9	−1.06166
$643$	28189.2	1.72888	0.864442	−	0.502733i	$-0.167672\pi$
$643$	28189.2	1.72888	0.864442	+	0.502733i	$0.167672\pi$
$644$	−33380.9	−2.04253
$645$	0	0
$646$	16107.2	0.981002
$647$	1645.74	0.100001	0.0500006	−	0.998749i	$-0.484078\pi$
$647$	1645.74	0.100001	0.0500006	+	0.998749i	$0.484078\pi$
$648$	−23958.3	−1.45242
$649$	17008.9	1.02875
$650$	−3682.94	−0.222241
$651$	−51393.7	−3.09413
$652$	3314.14	0.199067
$653$	10616.3	0.636215	0.318107	−	0.948055i	$-0.396953\pi$
$653$	10616.3	0.636215	0.318107	+	0.948055i	$0.396953\pi$
$654$	−36785.2	−2.19941
$655$	3538.39	0.211079
$656$	1702.31	0.101317
$657$	−17964.6	−1.06677
$658$	−54529.2	−3.23066
$659$	−6339.95	−0.374764	−0.187382	−	0.982287i	$-0.560000\pi$
$659$	−6339.95	−0.374764	−0.187382	+	0.982287i	$0.560000\pi$
$660$	−32750.9	−1.93156
$661$	−4182.89	−0.246136	−0.123068	−	0.992398i	$-0.539273\pi$
$661$	−4182.89	−0.246136	−0.123068	+	0.992398i	$0.539273\pi$
$662$	45722.7	2.68439
$663$	−1828.32	−0.107098
$664$	−43000.0	−2.51314
$665$	16336.9	0.952657
$666$	−81489.1	−4.74120
$667$	−763.485	−0.0443212
$668$	32772.4	1.89821
$669$	−17911.3	−1.03511
$670$	6810.40	0.392700
$671$	−3382.61	−0.194611
$672$	−40257.3	−2.31095
$673$	−12968.1	−0.742769	−0.371385	−	0.928479i	$-0.621117\pi$
$673$	−12968.1	−0.742769	−0.371385	+	0.928479i	$0.621117\pi$
$674$	−45837.0	−2.61955
$675$	−21431.4	−1.22207
$676$	−37901.2	−2.15642
$677$	9410.58	0.534236	0.267118	−	0.963664i	$-0.413929\pi$
$677$	9410.58	0.534236	0.267118	+	0.963664i	$0.413929\pi$
$678$	−22880.3	−1.29603
$679$	33857.5	1.91359
$680$	6864.69	0.387130
$681$	−8465.77	−0.476372
$682$	41703.5	2.34151
$683$	−1974.70	−0.110629	−0.0553146	−	0.998469i	$-0.517616\pi$
$683$	−1974.70	−0.110629	−0.0553146	+	0.998469i	$0.517616\pi$
$684$	−98930.3	−5.53026
$685$	−14141.0	−0.788758
$686$	−39100.0	−2.17616
$687$	16319.0	0.906274
$688$	0	0
$689$	−3696.46	−0.204389
$690$	−13383.3	−0.738394
$691$	−27230.2	−1.49911	−0.749555	−	0.661942i	$-0.769732\pi$
$691$	−27230.2	−1.49911	−0.749555	+	0.661942i	$0.769732\pi$
$692$	−37708.4	−2.07147
$693$	67542.0	3.70232
$694$	31897.5	1.74469
$695$	−8606.07	−0.469708
$696$	−5347.51	−0.291231
$697$	461.212	0.0250641
$698$	35598.9	1.93043
$699$	33475.9	1.81141
$700$	−54897.8	−2.96420
$701$	−8960.38	−0.482780	−0.241390	−	0.970428i	$-0.577603\pi$
$701$	−8960.38	−0.482780	−0.241390	+	0.970428i	$0.577603\pi$
$702$	7665.11	0.412109
$703$	−34739.1	−1.86374
$704$	−4300.23	−0.230215
$705$	−15047.3	−0.803849
$706$	11004.1	0.586605
$707$	39793.8	2.11683
$708$	61243.9	3.25097
$709$	21760.4	1.15265	0.576324	−	0.817221i	$-0.304487\pi$
$709$	21760.4	1.15265	0.576324	+	0.817221i	$0.304487\pi$
$710$	−19975.9	−1.05589
$711$	42123.1	2.22186
$712$	−18128.1	−0.954182
$713$	11729.4	0.616085
$714$	−39595.8	−2.07540
$715$	1504.75	0.0787058
$716$	912.077	0.0476060
$717$	−26563.0	−1.38356
$718$	13818.7	0.718259
$719$	−4608.63	−0.239044	−0.119522	−	0.992832i	$-0.538136\pi$
$719$	−4608.63	−0.239044	−0.119522	+	0.992832i	$0.538136\pi$
$720$	−26355.4	−1.36418
$721$	−3390.79	−0.175145
$722$	−26527.6	−1.36739
$723$	−43220.6	−2.22322
$724$	−65766.5	−3.37596
$725$	−1255.62	−0.0643207
$726$	−24343.2	−1.24444
$727$	−10414.3	−0.531288	−0.265644	−	0.964071i	$-0.585585\pi$
$727$	−10414.3	−0.531288	−0.265644	+	0.964071i	$0.585585\pi$
$728$	10742.1	0.546882
$729$	−25416.1	−1.29127
$730$	−8667.74	−0.439462
$731$	0	0
$732$	−12179.7	−0.614994
$733$	−11963.2	−0.602823	−0.301411	−	0.953494i	$-0.597458\pi$
$733$	−11963.2	−0.602823	−0.301411	+	0.953494i	$0.597458\pi$
$734$	13616.1	0.684715
$735$	−25475.1	−1.27845
$736$	9187.77	0.460144
$737$	12003.2	0.599922
$738$	−4115.73	−0.205287
$739$	16512.6	0.821954	0.410977	−	0.911646i	$-0.365188\pi$
$739$	16512.6	0.821954	0.410977	+	0.911646i	$0.365188\pi$
$740$	−27061.5	−1.34433
$741$	6955.32	0.344818
$742$	−80053.9	−3.96074
$743$	−899.266	−0.0444022	−0.0222011	−	0.999754i	$-0.507067\pi$
$743$	−899.266	−0.0444022	−0.0222011	+	0.999754i	$0.507067\pi$
$744$	82153.5	4.04824
$745$	10822.4	0.532218
$746$	−1748.66	−0.0858216
$747$	44728.0	2.19078
$748$	22114.5	1.08100
$749$	11827.5	0.576991
$750$	−49122.2	−2.39159
$751$	−7351.82	−0.357219	−0.178610	−	0.983920i	$-0.557160\pi$
$751$	−7351.82	−0.357219	−0.178610	+	0.983920i	$0.557160\pi$
$752$	37501.5	1.81854
$753$	52612.6	2.54623
$754$	449.082	0.0216904
$755$	2699.14	0.130108
$756$	114256.	5.49663
$757$	38577.9	1.85223	0.926116	−	0.377239i	$-0.123127\pi$
$757$	38577.9	1.85223	0.926116	+	0.377239i	$0.123127\pi$
$758$	−59063.0	−2.83017
$759$	−23587.7	−1.12803
$760$	−26114.7	−1.24642
$761$	−33258.2	−1.58424	−0.792121	−	0.610364i	$-0.791023\pi$
$761$	−33258.2	−1.58424	−0.792121	+	0.610364i	$0.791023\pi$
$762$	−92253.7	−4.38583
$763$	25192.7	1.19533
$764$	−48964.0	−2.31866
$765$	−7140.55	−0.337473
$766$	24969.2	1.17777
$767$	−2813.88	−0.132468
$768$	−68755.2	−3.23046
$769$	−11273.5	−0.528653	−0.264326	−	0.964433i	$-0.585150\pi$
$769$	−11273.5	−0.528653	−0.264326	+	0.964433i	$0.585150\pi$
$770$	32588.3	1.52520
$771$	10560.2	0.493278
$772$	−76218.8	−3.55334
$773$	−7430.64	−0.345746	−0.172873	−	0.984944i	$-0.555305\pi$
$773$	−7430.64	−0.345746	−0.172873	+	0.984944i	$0.555305\pi$
$774$	0	0
$775$	19290.0	0.894087
$776$	−54121.6	−2.50367
$777$	85398.2	3.94291
$778$	14494.1	0.667914
$779$	−1754.55	−0.0806973
$780$	5418.16	0.248719
$781$	−35207.0	−1.61307
$782$	9036.79	0.413242
$783$	2613.26	0.119272
$784$	63490.1	2.89222
$785$	13102.4	0.595724
$786$	32625.0	1.48053
$787$	17586.2	0.796542	0.398271	−	0.917268i	$-0.369610\pi$
$787$	17586.2	0.796542	0.398271	+	0.917268i	$0.369610\pi$
$788$	61512.2	2.78082
$789$	29683.9	1.33939
$790$	20324.0	0.915309
$791$	15669.8	0.704367
$792$	−107967.	−4.84398
$793$	559.602	0.0250594
$794$	16824.4	0.751985
$795$	−22090.8	−0.985509
$796$	58679.1	2.61285
$797$	−43685.1	−1.94154	−0.970769	−	0.240017i	$-0.922847\pi$
$797$	−43685.1	−1.94154	−0.970769	+	0.240017i	$0.922847\pi$
$798$	150631.	6.68204
$799$	10160.4	0.449873
$800$	15110.1	0.667778
$801$	18856.5	0.831789
$802$	34586.8	1.52282
$803$	−15276.7	−0.671360
$804$	43219.7	1.89582
$805$	9165.68	0.401302
$806$	−6899.22	−0.301507
$807$	58646.8	2.55820
$808$	−63610.9	−2.76958
$809$	−32083.2	−1.39430	−0.697149	−	0.716926i	$-0.745548\pi$
$809$	−32083.2	−1.39430	−0.697149	+	0.716926i	$0.745548\pi$
$810$	12024.2	0.521588
$811$	14345.1	0.621114	0.310557	−	0.950555i	$-0.399485\pi$
$811$	14345.1	0.621114	0.310557	+	0.950555i	$0.399485\pi$
$812$	6694.01	0.289303
$813$	1468.05	0.0633291
$814$	−69296.4	−2.98383
$815$	−909.992	−0.0391112
$816$	27231.3	1.16824
$817$	0	0
$818$	1992.41	0.0851628
$819$	−11173.8	−0.476733
$820$	−1366.78	−0.0582074
$821$	−3389.64	−0.144092	−0.0720458	−	0.997401i	$-0.522953\pi$
$821$	−3389.64	−0.144092	−0.0720458	+	0.997401i	$0.522953\pi$
$822$	−130384.	−5.53244
$823$	30885.8	1.30815	0.654077	−	0.756428i	$-0.273057\pi$
$823$	30885.8	1.30815	0.654077	+	0.756428i	$0.273057\pi$
$824$	5420.22	0.229153
$825$	−38792.0	−1.63705
$826$	−60939.8	−2.56703
$827$	−47108.5	−1.98080	−0.990400	−	0.138230i	$-0.955859\pi$
$827$	−47108.5	−1.98080	−0.990400	+	0.138230i	$0.955859\pi$
$828$	−55504.1	−2.32959
$829$	4723.48	0.197893	0.0989465	−	0.995093i	$-0.468453\pi$
$829$	4723.48	0.197893	0.0989465	+	0.995093i	$0.468453\pi$
$830$	21580.8	0.902507
$831$	−34114.9	−1.42411
$832$	711.410	0.0296439
$833$	17201.6	0.715485
$834$	−79350.5	−3.29458
$835$	−8998.61	−0.372946
$836$	−84128.0	−3.48042
$837$	−40147.3	−1.65794
$838$	−11902.3	−0.490643
$839$	−40785.4	−1.67827	−0.839135	−	0.543923i	$-0.816938\pi$
$839$	−40785.4	−1.67827	−0.839135	+	0.543923i	$0.816938\pi$
$840$	64197.1	2.63692
$841$	−24235.9	−0.993722
$842$	38884.4	1.59150
$843$	−11003.6	−0.449565
$844$	52195.8	2.12874
$845$	10406.9	0.423676
$846$	−90668.5	−3.68469
$847$	16671.7	0.676326
$848$	55055.6	2.22950
$849$	−55781.0	−2.25489
$850$	14861.8	0.599712
$851$	−19490.1	−0.785090
$852$	−126770.	−5.09748
$853$	1082.07	0.0434344	0.0217172	−	0.999764i	$-0.493087\pi$
$853$	1082.07	0.0434344	0.0217172	+	0.999764i	$0.493087\pi$
$854$	12119.3	0.485612
$855$	27164.1	1.08654
$856$	−18906.4	−0.754914
$857$	−21093.7	−0.840780	−0.420390	−	0.907343i	$-0.638107\pi$
$857$	−21093.7	−0.840780	−0.420390	+	0.907343i	$0.638107\pi$
$858$	13874.3	0.552051
$859$	−29598.4	−1.17565	−0.587826	−	0.808987i	$-0.700016\pi$
$859$	−29598.4	−1.17565	−0.587826	+	0.808987i	$0.700016\pi$
$860$	0	0
$861$	4313.16	0.170722
$862$	49985.2	1.97506
$863$	−8596.06	−0.339065	−0.169533	−	0.985525i	$-0.554226\pi$
$863$	−8596.06	−0.339065	−0.169533	+	0.985525i	$0.554226\pi$
$864$	−31447.9	−1.23829
$865$	10353.9	0.406987
$866$	−83796.8	−3.28814
$867$	−35991.7	−1.40985
$868$	−102840.	−4.02144
$869$	35820.5	1.39831
$870$	2683.80	0.104586
$871$	−1985.75	−0.0772497
$872$	−40270.9	−1.56393
$873$	56296.5	2.18253
$874$	−34377.9	−1.33049
$875$	33641.9	1.29978
$876$	−55006.6	−2.12158
$877$	50561.5	1.94680	0.973399	−	0.229118i	$-0.0735841\pi$
$877$	50561.5	1.94680	0.973399	+	0.229118i	$0.0735841\pi$
$878$	87486.1	3.36277
$879$	25020.8	0.960104
$880$	−22412.0	−0.858533
$881$	27431.1	1.04901	0.524504	−	0.851408i	$-0.324251\pi$
$881$	27431.1	1.04901	0.524504	+	0.851408i	$0.324251\pi$
$882$	−153502.	−5.86018
$883$	−23591.8	−0.899124	−0.449562	−	0.893249i	$-0.648420\pi$
$883$	−23591.8	−0.899124	−0.449562	+	0.893249i	$0.648420\pi$
$884$	−3658.51	−0.139196
$885$	−16816.3	−0.638726
$886$	49195.6	1.86542
$887$	4274.07	0.161792	0.0808959	−	0.996723i	$-0.474222\pi$
$887$	4274.07	0.161792	0.0808959	+	0.996723i	$0.474222\pi$
$888$	−136510.	−5.15876
$889$	63181.0	2.38360
$890$	9098.09	0.342661
$891$	21192.3	0.796823
$892$	−35840.9	−1.34534
$893$	−38652.3	−1.44843
$894$	99785.6	3.73303
$895$	−250.437	−0.00935327
$896$	51890.5	1.93475
$897$	3902.23	0.145253
$898$	−82257.1	−3.05674
$899$	−2352.14	−0.0872618
$900$	−91281.4	−3.38079
$901$	14916.4	0.551539
$902$	−3499.92	−0.129196
$903$	0	0
$904$	−25048.4	−0.921568
$905$	18058.1	0.663282
$906$	24886.8	0.912593
$907$	24783.6	0.907306	0.453653	−	0.891178i	$-0.350120\pi$
$907$	24783.6	0.907306	0.453653	+	0.891178i	$0.350120\pi$
$908$	−16940.2	−0.619140
$909$	66167.1	2.41433
$910$	−5391.25	−0.196394
$911$	20642.1	0.750717	0.375359	−	0.926880i	$-0.377520\pi$
$911$	20642.1	0.750717	0.375359	+	0.926880i	$0.377520\pi$
$912$	−103594.	−3.76132
$913$	38035.7	1.37875
$914$	42460.8	1.53663
$915$	3344.29	0.120829
$916$	32654.7	1.17788
$917$	−22343.6	−0.804636
$918$	−30931.1	−1.11207
$919$	−8222.09	−0.295127	−0.147563	−	0.989053i	$-0.547143\pi$
$919$	−8222.09	−0.295127	−0.147563	+	0.989053i	$0.547143\pi$
$920$	−14651.5	−0.525048
$921$	12368.8	0.442524
$922$	−44580.1	−1.59237
$923$	5824.47	0.207708
$924$	206810.	7.36314
$925$	−32053.2	−1.13935
$926$	−1572.17	−0.0557933
$927$	−5638.04	−0.199760
$928$	−1842.46	−0.0651743
$929$	−29894.5	−1.05577	−0.527883	−	0.849317i	$-0.677014\pi$
$929$	−29894.5	−1.05577	−0.527883	+	0.849317i	$0.677014\pi$
$930$	−41231.1	−1.45379
$931$	−65438.4	−2.30360
$932$	66985.8	2.35429
$933$	44260.5	1.55308
$934$	92337.3	3.23487
$935$	−6072.16	−0.212386
$936$	17861.5	0.623740
$937$	9082.43	0.316660	0.158330	−	0.987386i	$-0.449389\pi$
$937$	9082.43	0.316660	0.158330	+	0.987386i	$0.449389\pi$
$938$	−43005.1	−1.49698
$939$	38658.0	1.34351
$940$	−30109.9	−1.04476
$941$	−12593.5	−0.436275	−0.218138	−	0.975918i	$-0.569998\pi$
$941$	−12593.5	−0.436275	−0.218138	+	0.975918i	$0.569998\pi$
$942$	120807.	4.17847
$943$	−984.375	−0.0339933
$944$	41910.2	1.44498
$945$	−31372.3	−1.07994
$946$	0	0
$947$	−23530.7	−0.807438	−0.403719	−	0.914883i	$-0.632283\pi$
$947$	−23530.7	−0.807438	−0.403719	+	0.914883i	$0.632283\pi$
$948$	128979.	4.41881
$949$	2527.30	0.0864485
$950$	−56537.4	−1.93086
$951$	−42816.5	−1.45996
$952$	−43347.9	−1.47575
$953$	46996.0	1.59743	0.798715	−	0.601709i	$-0.205513\pi$
$953$	46996.0	1.59743	0.798715	+	0.601709i	$0.205513\pi$
$954$	−133110.	−4.51738
$955$	13444.5	0.455553
$956$	−53153.0	−1.79821
$957$	4730.14	0.159774
$958$	−42750.5	−1.44176
$959$	89295.0	3.00676
$960$	4251.52	0.142935
$961$	6344.86	0.212979
$962$	11464.1	0.384216
$963$	19666.1	0.658081
$964$	−86485.2	−2.88952
$965$	20928.1	0.698133
$966$	84510.2	2.81477
$967$	−6956.63	−0.231345	−0.115672	−	0.993287i	$-0.536902\pi$
$967$	−6956.63	−0.231345	−0.115672	+	0.993287i	$0.536902\pi$
$968$	−26650.0	−0.884880
$969$	−28066.9	−0.930484
$970$	27162.5	0.899107
$971$	−443.315	−0.0146516	−0.00732578	−	0.999973i	$-0.502332\pi$
$971$	−443.315	−0.0146516	−0.00732578	+	0.999973i	$0.502332\pi$
$972$	−24418.7	−0.805793
$973$	54344.1	1.79054
$974$	59298.8	1.95078
$975$	6417.56	0.210796
$976$	−8334.80	−0.273351
$977$	−6508.62	−0.213131	−0.106566	−	0.994306i	$-0.533985\pi$
$977$	−6508.62	−0.213131	−0.106566	+	0.994306i	$0.533985\pi$
$978$	−8390.39	−0.274330
$979$	16035.2	0.523479
$980$	−50976.1	−1.66160
$981$	41889.2	1.36332
$982$	−38731.3	−1.25862
$983$	−13296.1	−0.431413	−0.215707	−	0.976458i	$-0.569205\pi$
$983$	−13296.1	−0.431413	−0.215707	+	0.976458i	$0.569205\pi$
$984$	−6894.64	−0.223367
$985$	−16889.9	−0.546354
$986$	−1812.19	−0.0585312
$987$	95017.9	3.06429
$988$	13917.7	0.448160
$989$	0	0
$990$	54186.2	1.73955
$991$	−26922.0	−0.862973	−0.431486	−	0.902119i	$-0.642011\pi$
$991$	−26922.0	−0.862973	−0.431486	+	0.902119i	$0.642011\pi$
$992$	28305.7	0.905953
$993$	−79672.4	−2.54615
$994$	126140.	4.02507
$995$	−16112.0	−0.513352
$996$	136955.	4.35700
$997$	28805.6	0.915026	0.457513	−	0.889203i	$-0.348740\pi$
$997$	28805.6	0.915026	0.457513	+	0.889203i	$0.348740\pi$
$998$	73941.1	2.34525
$999$	66710.6	2.11274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.9	✓	110
43.42	odd	2	inner	1849.4.a.m.1.102	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.9	✓	110	1.1	even	1	trivial
1849.4.a.m.1.102	yes	110	43.42	odd	2	inner

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-5.06596 q^{2} +8.82751 q^{3} +17.6640 q^{4} -4.85016 q^{5} -44.7198 q^{6} +30.6269 q^{7} -48.9575 q^{8} +50.9249 q^{9} +O(q^{10})\)	\(q-5.06596 q^{2} +8.82751 q^{3} +17.6640 q^{4} -4.85016 q^{5} -44.7198 q^{6} +30.6269 q^{7} -48.9575 q^{8} +50.9249 q^{9} +24.5707 q^{10} +43.3053 q^{11} +155.929 q^{12} -7.16422 q^{13} -155.155 q^{14} -42.8148 q^{15} +106.705 q^{16} +28.9099 q^{17} -257.984 q^{18} -109.979 q^{19} -85.6731 q^{20} +270.359 q^{21} -219.383 q^{22} -61.7030 q^{23} -432.172 q^{24} -101.476 q^{25} +36.2937 q^{26} +211.197 q^{27} +540.993 q^{28} +12.3736 q^{29} +216.898 q^{30} -190.094 q^{31} -148.903 q^{32} +382.278 q^{33} -146.456 q^{34} -148.545 q^{35} +899.537 q^{36} +315.869 q^{37} +557.151 q^{38} -63.2422 q^{39} +237.451 q^{40} +15.9534 q^{41} -1369.63 q^{42} +764.945 q^{44} -246.993 q^{45} +312.585 q^{46} +351.451 q^{47} +941.938 q^{48} +595.007 q^{49} +514.074 q^{50} +255.202 q^{51} -126.549 q^{52} +515.962 q^{53} -1069.92 q^{54} -210.038 q^{55} -1499.42 q^{56} -970.842 q^{57} -62.6840 q^{58} +392.768 q^{59} -756.280 q^{60} -78.1107 q^{61} +963.011 q^{62} +1559.67 q^{63} -99.3004 q^{64} +34.7476 q^{65} -1936.61 q^{66} +277.176 q^{67} +510.664 q^{68} -544.683 q^{69} +752.525 q^{70} -812.995 q^{71} -2493.15 q^{72} -352.767 q^{73} -1600.18 q^{74} -895.780 q^{75} -1942.67 q^{76} +1326.31 q^{77} +320.383 q^{78} +827.162 q^{79} -517.535 q^{80} +489.370 q^{81} -80.8196 q^{82} +878.314 q^{83} +4775.62 q^{84} -140.217 q^{85} +109.228 q^{87} -2120.12 q^{88} +370.282 q^{89} +1251.26 q^{90} -219.418 q^{91} -1089.92 q^{92} -1678.06 q^{93} -1780.44 q^{94} +533.416 q^{95} -1314.44 q^{96} +1105.48 q^{97} -3014.28 q^{98} +2205.32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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