LMFDB - Embedded newform 1369.4.a.j.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1369,4,Mod(1,1369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1369, 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("1369.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1369 = 37^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1369.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:	$80.7736147979$
Analytic rank:	$1$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 37)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1369.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.11167 q^{2} -3.42317 q^{3} -6.76419 q^{4} -19.9955 q^{5} +3.80543 q^{6} -25.5427 q^{7} +16.4129 q^{8} -15.2819 q^{9} +O(q^{10})$	\(q-1.11167 q^{2} -3.42317 q^{3} -6.76419 q^{4} -19.9955 q^{5} +3.80543 q^{6} -25.5427 q^{7} +16.4129 q^{8} -15.2819 q^{9} +22.2284 q^{10} -23.3078 q^{11} +23.1550 q^{12} -42.1767 q^{13} +28.3950 q^{14} +68.4482 q^{15} +35.8679 q^{16} -100.134 q^{17} +16.9884 q^{18} +44.7534 q^{19} +135.254 q^{20} +87.4370 q^{21} +25.9105 q^{22} -59.4052 q^{23} -56.1841 q^{24} +274.822 q^{25} +46.8865 q^{26} +144.738 q^{27} +172.776 q^{28} -190.025 q^{29} -76.0916 q^{30} +126.310 q^{31} -171.176 q^{32} +79.7865 q^{33} +111.316 q^{34} +510.740 q^{35} +103.370 q^{36} -49.7509 q^{38} +144.378 q^{39} -328.185 q^{40} -87.5963 q^{41} -97.2009 q^{42} +376.859 q^{43} +157.658 q^{44} +305.570 q^{45} +66.0389 q^{46} -172.215 q^{47} -122.782 q^{48} +309.429 q^{49} -305.511 q^{50} +342.775 q^{51} +285.291 q^{52} -469.103 q^{53} -160.901 q^{54} +466.052 q^{55} -419.229 q^{56} -153.199 q^{57} +211.245 q^{58} +505.457 q^{59} -462.997 q^{60} -192.714 q^{61} -140.415 q^{62} +390.341 q^{63} -96.6518 q^{64} +843.346 q^{65} -88.6961 q^{66} +629.122 q^{67} +677.325 q^{68} +203.354 q^{69} -567.774 q^{70} -91.4841 q^{71} -250.820 q^{72} -44.1056 q^{73} -940.762 q^{75} -302.721 q^{76} +595.344 q^{77} -160.500 q^{78} -496.507 q^{79} -717.198 q^{80} -82.8518 q^{81} +97.3781 q^{82} -512.325 q^{83} -591.441 q^{84} +2002.23 q^{85} -418.942 q^{86} +650.489 q^{87} -382.548 q^{88} +433.085 q^{89} -339.693 q^{90} +1077.31 q^{91} +401.829 q^{92} -432.382 q^{93} +191.446 q^{94} -894.869 q^{95} +585.965 q^{96} +738.356 q^{97} -343.983 q^{98} +356.188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 36 q^{3} + 144 q^{4} - 84 q^{7} + 216 q^{9}+O(q^{10}) $ 48 * q - 36 * q^3 + 144 * q^4 - 84 * q^7 + 216 * q^9	$ 48 q - 36 q^{3} + 144 q^{4} - 84 q^{7} + 216 q^{9} - 114 q^{10} - 270 q^{11} - 270 q^{12} + 192 q^{16} - 666 q^{21} + 732 q^{25} - 378 q^{26} - 414 q^{27} + 240 q^{28} + 840 q^{30} - 648 q^{33} - 432 q^{34} - 852 q^{36} - 2526 q^{38} - 522 q^{40} - 3096 q^{41} - 1662 q^{44} - 2970 q^{46} - 2370 q^{47} - 4326 q^{48} - 120 q^{49} - 4326 q^{53} - 1398 q^{58} - 2790 q^{62} + 390 q^{63} - 3024 q^{64} - 1842 q^{65} + 2844 q^{67} - 1320 q^{70} - 2640 q^{71} - 7002 q^{73} - 5604 q^{75} + 2904 q^{77} + 462 q^{78} - 6000 q^{81} - 4476 q^{83} - 17148 q^{84} + 1452 q^{85} - 5856 q^{86} - 13956 q^{90} - 7782 q^{95} - 6198 q^{99}+O(q^{100}) $ 48 * q - 36 * q^3 + 144 * q^4 - 84 * q^7 + 216 * q^9 - 114 * q^10 - 270 * q^11 - 270 * q^12 + 192 * q^16 - 666 * q^21 + 732 * q^25 - 378 * q^26 - 414 * q^27 + 240 * q^28 + 840 * q^30 - 648 * q^33 - 432 * q^34 - 852 * q^36 - 2526 * q^38 - 522 * q^40 - 3096 * q^41 - 1662 * q^44 - 2970 * q^46 - 2370 * q^47 - 4326 * q^48 - 120 * q^49 - 4326 * q^53 - 1398 * q^58 - 2790 * q^62 + 390 * q^63 - 3024 * q^64 - 1842 * q^65 + 2844 * q^67 - 1320 * q^70 - 2640 * q^71 - 7002 * q^73 - 5604 * q^75 + 2904 * q^77 + 462 * q^78 - 6000 * q^81 - 4476 * q^83 - 17148 * q^84 + 1452 * q^85 - 5856 * q^86 - 13956 * q^90 - 7782 * q^95 - 6198 * 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 $

$2$	−1.11167	−0.393034	−0.196517	−	0.980500i	$-0.562963\pi$
$2$	−1.11167	−0.393034	−0.196517	+	0.980500i	$0.562963\pi$
$3$	−3.42317	−0.658789	−0.329395	−	0.944192i	$-0.606845\pi$
$3$	−3.42317	−0.658789	−0.329395	+	0.944192i	$0.606845\pi$
$4$	−6.76419	−0.845524
$5$	−19.9955	−1.78846	−0.894228	−	0.447612i	$-0.852275\pi$
$5$	−19.9955	−1.78846	−0.894228	+	0.447612i	$0.852275\pi$
$6$	3.80543	0.258927
$7$	−25.5427	−1.37918	−0.689588	−	0.724202i	$-0.742208\pi$
$7$	−25.5427	−1.37918	−0.689588	+	0.724202i	$0.742208\pi$
$8$	16.4129	0.725354
$9$	−15.2819	−0.565997
$10$	22.2284	0.702924
$11$	−23.3078	−0.638869	−0.319435	−	0.947608i	$-0.603493\pi$
$11$	−23.3078	−0.638869	−0.319435	+	0.947608i	$0.603493\pi$
$12$	23.1550	0.557022
$13$	−42.1767	−0.899824	−0.449912	−	0.893073i	$-0.648545\pi$
$13$	−42.1767	−0.899824	−0.449912	+	0.893073i	$0.648545\pi$
$14$	28.3950	0.542063
$15$	68.4482	1.17822
$16$	35.8679	0.560436
$17$	−100.134	−1.42859	−0.714295	−	0.699845i	$-0.753252\pi$
$17$	−100.134	−1.42859	−0.714295	+	0.699845i	$0.753252\pi$
$18$	16.9884	0.222456
$19$	44.7534	0.540376	0.270188	−	0.962808i	$-0.412914\pi$
$19$	44.7534	0.540376	0.270188	+	0.962808i	$0.412914\pi$
$20$	135.254	1.51218
$21$	87.4370	0.908586
$22$	25.9105	0.251097
$23$	−59.4052	−0.538559	−0.269279	−	0.963062i	$-0.586785\pi$
$23$	−59.4052	−0.538559	−0.269279	+	0.963062i	$0.586785\pi$
$24$	−56.1841	−0.477855
$25$	274.822	2.19858
$26$	46.8865	0.353661
$27$	144.738	1.03166
$28$	172.776	1.16613
$29$	−190.025	−1.21679	−0.608394	−	0.793635i	$-0.708186\pi$
$29$	−190.025	−1.21679	−0.608394	+	0.793635i	$0.708186\pi$
$30$	−76.0916	−0.463079
$31$	126.310	0.731807	0.365903	−	0.930653i	$-0.380760\pi$
$31$	126.310	0.731807	0.365903	+	0.930653i	$0.380760\pi$
$32$	−171.176	−0.945624
$33$	79.7865	0.420880
$34$	111.316	0.561484
$35$	510.740	2.46660
$36$	103.370	0.478564
$37$	0	0
$37$	0	0
$38$	−49.7509	−0.212386
$39$	144.378	0.592794
$40$	−328.185	−1.29726
$41$	−87.5963	−0.333665	−0.166832	−	0.985985i	$-0.553354\pi$
$41$	−87.5963	−0.333665	−0.166832	+	0.985985i	$0.553354\pi$
$42$	−97.2009	−0.357105
$43$	376.859	1.33652	0.668261	−	0.743927i	$-0.267039\pi$
$43$	376.859	1.33652	0.668261	+	0.743927i	$0.267039\pi$
$44$	157.658	0.540180
$45$	305.570	1.01226
$46$	66.0389	0.211672
$47$	−172.215	−0.534471	−0.267236	−	0.963631i	$-0.586110\pi$
$47$	−172.215	−0.534471	−0.267236	+	0.963631i	$0.586110\pi$
$48$	−122.782	−0.369209
$49$	309.429	0.902126
$50$	−305.511	−0.864115
$51$	342.775	0.941139
$52$	285.291	0.760823
$53$	−469.103	−1.21578	−0.607889	−	0.794022i	$-0.707984\pi$
$53$	−469.103	−1.21578	−0.607889	+	0.794022i	$0.707984\pi$
$54$	−160.901	−0.405478
$55$	466.052	1.14259
$56$	−419.229	−1.00039
$57$	−153.199	−0.355994
$58$	211.245	0.478239
$59$	505.457	1.11534	0.557668	−	0.830064i	$-0.311696\pi$
$59$	505.457	1.11534	0.557668	+	0.830064i	$0.311696\pi$
$60$	−462.997	−0.996210
$61$	−192.714	−0.404499	−0.202250	−	0.979334i	$-0.564825\pi$
$61$	−192.714	−0.404499	−0.202250	+	0.979334i	$0.564825\pi$
$62$	−140.415	−0.287625
$63$	390.341	0.780609
$64$	−96.6518	−0.188773
$65$	843.346	1.60929
$66$	−88.6961	−0.165420
$67$	629.122	1.14716	0.573578	−	0.819151i	$-0.305555\pi$
$67$	629.122	1.14716	0.573578	+	0.819151i	$0.305555\pi$
$68$	677.325	1.20791
$69$	203.354	0.354797
$70$	−567.774	−0.969456
$71$	−91.4841	−0.152918	−0.0764589	−	0.997073i	$-0.524361\pi$
$71$	−91.4841	−0.152918	−0.0764589	+	0.997073i	$0.524361\pi$
$72$	−250.820	−0.410548
$73$	−44.1056	−0.0707146	−0.0353573	−	0.999375i	$-0.511257\pi$
$73$	−44.1056	−0.0707146	−0.0353573	+	0.999375i	$0.511257\pi$
$74$	0	0
$75$	−940.762	−1.44840
$76$	−302.721	−0.456901
$77$	595.344	0.881113
$78$	−160.500	−0.232988
$79$	−496.507	−0.707106	−0.353553	−	0.935414i	$-0.615027\pi$
$79$	−496.507	−0.707106	−0.353553	+	0.935414i	$0.615027\pi$
$80$	−717.198	−1.00231
$81$	−82.8518	−0.113651
$82$	97.3781	0.131142
$83$	−512.325	−0.677530	−0.338765	−	0.940871i	$-0.610009\pi$
$83$	−512.325	−0.677530	−0.338765	+	0.940871i	$0.610009\pi$
$84$	−591.441	−0.768232
$85$	2002.23	2.55497
$86$	−418.942	−0.525299
$87$	650.489	0.801607
$88$	−382.548	−0.463406
$89$	433.085	0.515808	0.257904	−	0.966171i	$-0.416968\pi$
$89$	433.085	0.515808	0.257904	+	0.966171i	$0.416968\pi$
$90$	−339.693	−0.397853
$91$	1077.31	1.24101
$92$	401.829	0.455364
$93$	−432.382	−0.482106
$94$	191.446	0.210065
$95$	−894.869	−0.966438
$96$	585.965	0.622967
$97$	738.356	0.772874	0.386437	−	0.922316i	$-0.373706\pi$
$97$	738.356	0.772874	0.386437	+	0.922316i	$0.373706\pi$
$98$	−343.983	−0.354566
$99$	356.188	0.361598
$100$	−1858.95	−1.85895
$101$	−1303.39	−1.28408	−0.642040	−	0.766671i	$-0.721912\pi$
$101$	−1303.39	−1.28408	−0.642040	+	0.766671i	$0.721912\pi$
$102$	−381.052	−0.369900
$103$	1087.53	1.04036	0.520181	−	0.854056i	$-0.325864\pi$
$103$	1087.53	1.04036	0.520181	+	0.854056i	$0.325864\pi$
$104$	−692.241	−0.652690
$105$	−1748.35	−1.62497
$106$	521.487	0.477842
$107$	1183.74	1.06950	0.534748	−	0.845012i	$-0.320407\pi$
$107$	1183.74	1.06950	0.534748	+	0.845012i	$0.320407\pi$
$108$	−979.037	−0.872295
$109$	−1598.64	−1.40479	−0.702393	−	0.711789i	$-0.747885\pi$
$109$	−1598.64	−1.40479	−0.702393	+	0.711789i	$0.747885\pi$
$110$	−518.095	−0.449077
$111$	0	0
$112$	−916.162	−0.772939
$113$	−332.356	−0.276685	−0.138342	−	0.990384i	$-0.544177\pi$
$113$	−332.356	−0.276685	−0.138342	+	0.990384i	$0.544177\pi$
$114$	170.306	0.139918
$115$	1187.84	0.963188
$116$	1285.37	1.02882
$117$	644.540	0.509297
$118$	−561.900	−0.438365
$119$	2557.69	1.97028
$120$	1123.43	0.854623
$121$	−787.747	−0.591846
$122$	214.234	0.158982
$123$	299.857	0.219815
$124$	−854.387	−0.618760
$125$	−2995.77	−2.14360
$126$	−433.930	−0.306806
$127$	−1442.17	−1.00766	−0.503828	−	0.863804i	$-0.668075\pi$
$127$	−1442.17	−1.00766	−0.503828	+	0.863804i	$0.668075\pi$
$128$	1476.85	1.01982
$129$	−1290.05	−0.880486
$130$	−937.521	−0.632508
$131$	833.202	0.555704	0.277852	−	0.960624i	$-0.410378\pi$
$131$	833.202	0.555704	0.277852	+	0.960624i	$0.410378\pi$
$132$	−539.692	−0.355865
$133$	−1143.12	−0.745273
$134$	−699.374	−0.450871
$135$	−2894.12	−1.84508
$136$	−1643.48	−1.03623
$137$	−1960.61	−1.22268	−0.611338	−	0.791370i	$-0.709368\pi$
$137$	−1960.61	−1.22268	−0.611338	+	0.791370i	$0.709368\pi$
$138$	−226.062	−0.139447
$139$	−2067.01	−1.26131	−0.630654	−	0.776064i	$-0.717213\pi$
$139$	−2067.01	−1.26131	−0.630654	+	0.776064i	$0.717213\pi$
$140$	−3454.75	−2.08557
$141$	589.522	0.352104
$142$	101.700	0.0601019
$143$	983.045	0.574870
$144$	−548.130	−0.317205
$145$	3799.66	2.17617
$146$	49.0307	0.0277932
$147$	−1059.23	−0.594311
$148$	0	0
$149$	541.015	0.297461	0.148730	−	0.988878i	$-0.452481\pi$
$149$	541.015	0.297461	0.148730	+	0.988878i	$0.452481\pi$
$150$	1045.82	0.569270
$151$	2551.82	1.37526	0.687629	−	0.726063i	$-0.258652\pi$
$151$	2551.82	1.37526	0.687629	+	0.726063i	$0.258652\pi$
$152$	734.532	0.391963
$153$	1530.24	0.808577
$154$	−661.825	−0.346308
$155$	−2525.64	−1.30880
$156$	−976.600	−0.501222
$157$	−2046.16	−1.04014	−0.520068	−	0.854125i	$-0.674093\pi$
$157$	−2046.16	−1.04014	−0.520068	+	0.854125i	$0.674093\pi$
$158$	551.951	0.277917
$159$	1605.82	0.800942
$160$	3422.76	1.69121
$161$	1517.37	0.742767
$162$	92.1037	0.0446688
$163$	1479.80	0.711087	0.355544	−	0.934660i	$-0.384296\pi$
$163$	1479.80	0.711087	0.355544	+	0.934660i	$0.384296\pi$
$164$	592.519	0.282122
$165$	−1595.38	−0.752726
$166$	569.536	0.266292
$167$	531.569	0.246312	0.123156	−	0.992387i	$-0.460698\pi$
$167$	531.569	0.246312	0.123156	+	0.992387i	$0.460698\pi$
$168$	1435.09	0.659047
$169$	−418.128	−0.190318
$170$	−2225.82	−1.00419
$171$	−683.917	−0.305851
$172$	−2549.15	−1.13006
$173$	1760.32	0.773609	0.386804	−	0.922162i	$-0.373579\pi$
$173$	1760.32	0.773609	0.386804	+	0.922162i	$0.373579\pi$
$174$	−723.128	−0.315059
$175$	−7019.69	−3.03222
$176$	−836.001	−0.358045
$177$	−1730.26	−0.734772
$178$	−481.447	−0.202730
$179$	−1662.63	−0.694250	−0.347125	−	0.937819i	$-0.612842\pi$
$179$	−1662.63	−0.694250	−0.347125	+	0.937819i	$0.612842\pi$
$180$	−2066.94	−0.855890
$181$	−2335.79	−0.959216	−0.479608	−	0.877483i	$-0.659221\pi$
$181$	−2335.79	−0.959216	−0.479608	+	0.877483i	$0.659221\pi$
$182$	−1197.61	−0.487761
$183$	659.692	0.266480
$184$	−975.011	−0.390646
$185$	0	0
$186$	480.665	0.189484
$187$	2333.90	0.912682
$188$	1164.90	0.451909
$189$	−3697.00	−1.42284
$190$	994.797	0.379843
$191$	2130.20	0.806992	0.403496	−	0.914981i	$-0.367795\pi$
$191$	2130.20	0.806992	0.403496	+	0.914981i	$0.367795\pi$
$192$	330.856	0.124362
$193$	1610.96	0.600825	0.300412	−	0.953809i	$-0.402876\pi$
$193$	1610.96	0.600825	0.300412	+	0.953809i	$0.402876\pi$
$194$	−820.807	−0.303766
$195$	−2886.92	−1.06019
$196$	−2093.04	−0.762769
$197$	537.802	0.194502	0.0972509	−	0.995260i	$-0.468995\pi$
$197$	537.802	0.194502	0.0972509	+	0.995260i	$0.468995\pi$
$198$	−395.962	−0.142120
$199$	4117.85	1.46687	0.733433	−	0.679761i	$-0.237917\pi$
$199$	4117.85	1.46687	0.733433	+	0.679761i	$0.237917\pi$
$200$	4510.62	1.59474
$201$	−2153.59	−0.755734
$202$	1448.94	0.504687
$203$	4853.76	1.67816
$204$	−2318.60	−0.795756
$205$	1751.54	0.596745
$206$	−1208.97	−0.408898
$207$	907.825	0.304822
$208$	−1512.79	−0.504293
$209$	−1043.10	−0.345229
$210$	1943.59	0.638667
$211$	3378.65	1.10235	0.551175	−	0.834389i	$-0.314180\pi$
$211$	3378.65	1.10235	0.551175	+	0.834389i	$0.314180\pi$
$212$	3173.10	1.02797
$213$	313.166	0.100741
$214$	−1315.92	−0.420348
$215$	−7535.50	−2.39031
$216$	2375.57	0.748320
$217$	−3226.31	−1.00929
$218$	1777.15	0.552129
$219$	150.981	0.0465860
$220$	−3152.47	−0.966087
$221$	4223.31	1.28548
$222$	0	0
$223$	−1495.97	−0.449226	−0.224613	−	0.974448i	$-0.572112\pi$
$223$	−1495.97	−0.449226	−0.224613	+	0.974448i	$0.572112\pi$
$224$	4372.30	1.30418
$225$	−4199.80	−1.24439
$226$	369.469	0.108747
$227$	−747.510	−0.218564	−0.109282	−	0.994011i	$-0.534855\pi$
$227$	−747.510	−0.218564	−0.109282	+	0.994011i	$0.534855\pi$
$228$	1036.26	0.301001
$229$	−4044.86	−1.16721	−0.583607	−	0.812036i	$-0.698359\pi$
$229$	−4044.86	−1.16721	−0.583607	+	0.812036i	$0.698359\pi$
$230$	−1320.48	−0.378566
$231$	−2037.96	−0.580468
$232$	−3118.87	−0.882602
$233$	4563.67	1.28316	0.641580	−	0.767056i	$-0.278279\pi$
$233$	4563.67	1.28316	0.641580	+	0.767056i	$0.278279\pi$
$234$	−716.515	−0.200171
$235$	3443.54	0.955879
$236$	−3419.01	−0.943044
$237$	1699.63	0.465834
$238$	−2843.30	−0.774385
$239$	−5479.35	−1.48297	−0.741484	−	0.670970i	$-0.765878\pi$
$239$	−5479.35	−1.48297	−0.741484	+	0.670970i	$0.765878\pi$
$240$	2455.09	0.660314
$241$	−2920.97	−0.780731	−0.390365	−	0.920660i	$-0.627651\pi$
$241$	−2920.97	−0.780731	−0.390365	+	0.920660i	$0.627651\pi$
$242$	875.713	0.232616
$243$	−3624.31	−0.956790
$244$	1303.55	0.342014
$245$	−6187.21	−1.61341
$246$	−333.342	−0.0863947
$247$	−1887.55	−0.486243
$248$	2073.12	0.530819
$249$	1753.78	0.446350
$250$	3330.30	0.842507
$251$	−799.293	−0.201000	−0.100500	−	0.994937i	$-0.532044\pi$
$251$	−799.293	−0.201000	−0.100500	+	0.994937i	$0.532044\pi$
$252$	−2640.34	−0.660024
$253$	1384.60	0.344069
$254$	1603.22	0.396043
$255$	−6853.97	−1.68319
$256$	−868.558	−0.212050
$257$	6975.17	1.69299	0.846496	−	0.532395i	$-0.178708\pi$
$257$	6975.17	1.69299	0.846496	+	0.532395i	$0.178708\pi$
$258$	1434.11	0.346061
$259$	0	0
$260$	−5704.55	−1.36070
$261$	2903.95	0.688698
$262$	−926.244	−0.218410
$263$	5691.13	1.33434	0.667168	−	0.744908i	$-0.267506\pi$
$263$	5691.13	1.33434	0.667168	+	0.744908i	$0.267506\pi$
$264$	1309.53	0.305287
$265$	9379.97	2.17437
$266$	1270.77	0.292918
$267$	−1482.52	−0.339809
$268$	−4255.50	−0.969948
$269$	−652.759	−0.147953	−0.0739766	−	0.997260i	$-0.523569\pi$
$269$	−652.759	−0.147953	−0.0739766	+	0.997260i	$0.523569\pi$
$270$	3217.30	0.725180
$271$	−69.6551	−0.0156134	−0.00780672	−	0.999970i	$-0.502485\pi$
$271$	−69.6551	−0.0156134	−0.00780672	+	0.999970i	$0.502485\pi$
$272$	−3591.59	−0.800632
$273$	−3687.80	−0.817567
$274$	2179.55	0.480553
$275$	−6405.49	−1.40460
$276$	−1375.53	−0.299989
$277$	4846.96	1.05136	0.525678	−	0.850684i	$-0.323812\pi$
$277$	4846.96	1.05136	0.525678	+	0.850684i	$0.323812\pi$
$278$	2297.83	0.495737
$279$	−1930.26	−0.414200
$280$	8382.72	1.78915
$281$	−615.814	−0.130734	−0.0653672	−	0.997861i	$-0.520822\pi$
$281$	−615.814	−0.130734	−0.0653672	+	0.997861i	$0.520822\pi$
$282$	−655.352	−0.138389
$283$	3631.25	0.762740	0.381370	−	0.924422i	$-0.375452\pi$
$283$	3631.25	0.762740	0.381370	+	0.924422i	$0.375452\pi$
$284$	618.816	0.129296
$285$	3063.29	0.636679
$286$	−1092.82	−0.225943
$287$	2237.45	0.460182
$288$	2615.90	0.535220
$289$	5113.78	1.04087
$290$	−4223.96	−0.855309
$291$	−2527.52	−0.509161
$292$	298.339	0.0597909
$293$	−1810.47	−0.360986	−0.180493	−	0.983576i	$-0.557769\pi$
$293$	−1810.47	−0.360986	−0.180493	+	0.983576i	$0.557769\pi$
$294$	1177.51	0.233584
$295$	−10106.9	−1.99473
$296$	0	0
$297$	−3373.53	−0.659097
$298$	−601.429	−0.116912
$299$	2505.52	0.484608
$300$	6363.50	1.22466
$301$	−9625.99	−1.84330
$302$	−2836.77	−0.540523
$303$	4461.72	0.845938
$304$	1605.21	0.302846
$305$	3853.41	0.723429
$306$	−1701.11	−0.317798
$307$	−1547.66	−0.287719	−0.143860	−	0.989598i	$-0.545951\pi$
$307$	−1547.66	−0.287719	−0.143860	+	0.989598i	$0.545951\pi$
$308$	−4027.02	−0.745003
$309$	−3722.79	−0.685379
$310$	2807.68	0.514404
$311$	7065.39	1.28824	0.644118	−	0.764926i	$-0.277224\pi$
$311$	7065.39	1.28824	0.644118	+	0.764926i	$0.277224\pi$
$312$	2369.66	0.429986
$313$	10488.4	1.89405	0.947027	−	0.321155i	$-0.104071\pi$
$313$	10488.4	1.89405	0.947027	+	0.321155i	$0.104071\pi$
$314$	2274.65	0.408809
$315$	−7805.08	−1.39608
$316$	3358.47	0.597875
$317$	−6641.12	−1.17666	−0.588332	−	0.808619i	$-0.700215\pi$
$317$	−6641.12	−1.17666	−0.588332	+	0.808619i	$0.700215\pi$
$318$	−1785.14	−0.314797
$319$	4429.07	0.777368
$320$	1932.61	0.337612
$321$	−4052.13	−0.704572
$322$	−1686.81	−0.291933
$323$	−4481.33	−0.771975
$324$	560.426	0.0960949
$325$	−11591.1	−1.97833
$326$	−1645.05	−0.279481
$327$	5472.41	0.925458
$328$	−1437.71	−0.242025
$329$	4398.84	0.737130
$330$	1773.53	0.295847
$331$	−6935.24	−1.15165	−0.575824	−	0.817574i	$-0.695319\pi$
$331$	−6935.24	−1.15165	−0.575824	+	0.817574i	$0.695319\pi$
$332$	3465.47	0.572868
$333$	0	0
$334$	−590.929	−0.0968089
$335$	−12579.6	−2.05164
$336$	3136.18	0.509204
$337$	−5095.44	−0.823639	−0.411819	−	0.911265i	$-0.635107\pi$
$337$	−5095.44	−0.823639	−0.411819	+	0.911265i	$0.635107\pi$
$338$	464.819	0.0748013
$339$	1137.71	0.182277
$340$	−13543.5	−2.16029
$341$	−2944.01	−0.467529
$342$	760.289	0.120210
$343$	857.488	0.134985
$344$	6185.34	0.969451
$345$	−4066.18	−0.634538
$346$	−1956.89	−0.304054
$347$	1620.40	0.250685	0.125342	−	0.992114i	$-0.459997\pi$
$347$	1620.40	0.250685	0.125342	+	0.992114i	$0.459997\pi$
$348$	−4400.04	−0.677778
$349$	7536.90	1.15599	0.577996	−	0.816040i	$-0.303835\pi$
$349$	7536.90	1.15599	0.577996	+	0.816040i	$0.303835\pi$
$350$	7803.57	1.19177
$351$	−6104.57	−0.928314
$352$	3989.74	0.604130
$353$	−2379.20	−0.358730	−0.179365	−	0.983783i	$-0.557404\pi$
$353$	−2379.20	−0.358730	−0.179365	+	0.983783i	$0.557404\pi$
$354$	1923.48	0.288790
$355$	1829.27	0.273487
$356$	−2929.47	−0.436128
$357$	−8755.40	−1.29800
$358$	1848.29	0.272864
$359$	−8706.93	−1.28004	−0.640019	−	0.768359i	$-0.721074\pi$
$359$	−8706.93	−1.28004	−0.640019	+	0.768359i	$0.721074\pi$
$360$	5015.29	0.734247
$361$	−4856.13	−0.707994
$362$	2596.63	0.377004
$363$	2696.59	0.389902
$364$	−7287.11	−1.04931
$365$	881.915	0.126470
$366$	−733.358	−0.104736
$367$	−911.766	−0.129683	−0.0648417	−	0.997896i	$-0.520654\pi$
$367$	−911.766	−0.129683	−0.0648417	+	0.997896i	$0.520654\pi$
$368$	−2130.74	−0.301827
$369$	1338.64	0.188853
$370$	0	0
$371$	11982.2	1.67677
$372$	2924.71	0.407633
$373$	7071.17	0.981585	0.490792	−	0.871277i	$-0.336707\pi$
$373$	7071.17	0.981585	0.490792	+	0.871277i	$0.336707\pi$
$374$	−2594.52	−0.358715
$375$	10255.0	1.41218
$376$	−2826.55	−0.387681
$377$	8014.64	1.09489
$378$	4109.84	0.559226
$379$	12264.9	1.66228	0.831140	−	0.556063i	$-0.187688\pi$
$379$	12264.9	1.66228	0.831140	+	0.556063i	$0.187688\pi$
$380$	6053.07	0.817147
$381$	4936.80	0.663832
$382$	−2368.07	−0.317175
$383$	−9089.33	−1.21265	−0.606323	−	0.795219i	$-0.707356\pi$
$383$	−9089.33	−1.21265	−0.606323	+	0.795219i	$0.707356\pi$
$384$	−5055.52	−0.671845
$385$	−11904.2	−1.57583
$386$	−1790.85	−0.236145
$387$	−5759.12	−0.756467
$388$	−4994.39	−0.653483
$389$	−14771.6	−1.92532	−0.962662	−	0.270706i	$-0.912743\pi$
$389$	−14771.6	−1.92532	−0.962662	+	0.270706i	$0.912743\pi$
$390$	3209.29	0.416689
$391$	5948.47	0.769379
$392$	5078.63	0.654361
$393$	−2852.19	−0.366092
$394$	−597.858	−0.0764458
$395$	9927.93	1.26463
$396$	−2409.32	−0.305740
$397$	−14138.2	−1.78735	−0.893673	−	0.448718i	$-0.851881\pi$
$397$	−14138.2	−1.78735	−0.893673	+	0.448718i	$0.851881\pi$
$398$	−4577.68	−0.576529
$399$	3913.10	0.490978
$400$	9857.28	1.23216
$401$	3651.51	0.454732	0.227366	−	0.973809i	$-0.426989\pi$
$401$	3651.51	0.454732	0.227366	+	0.973809i	$0.426989\pi$
$402$	2394.08	0.297029
$403$	−5327.35	−0.658497
$404$	8816.38	1.08572
$405$	1656.67	0.203260
$406$	−5395.77	−0.659576
$407$	0	0
$408$	5625.93	0.682659
$409$	−2681.26	−0.324156	−0.162078	−	0.986778i	$-0.551820\pi$
$409$	−2681.26	−0.324156	−0.162078	+	0.986778i	$0.551820\pi$
$410$	−1947.13	−0.234541
$411$	6711.51	0.805485
$412$	−7356.25	−0.879651
$413$	−12910.7	−1.53824
$414$	−1009.20	−0.119806
$415$	10244.2	1.21173
$416$	7219.65	0.850895
$417$	7075.74	0.830936
$418$	1159.58	0.135687
$419$	5987.71	0.698136	0.349068	−	0.937097i	$-0.386498\pi$
$419$	5987.71	0.698136	0.349068	+	0.937097i	$0.386498\pi$
$420$	11826.2	1.37395
$421$	4083.70	0.472749	0.236375	−	0.971662i	$-0.424041\pi$
$421$	4083.70	0.472749	0.236375	+	0.971662i	$0.424041\pi$
$422$	−3755.94	−0.433261
$423$	2631.78	0.302509
$424$	−7699.33	−0.881870
$425$	−27519.0	−3.14086
$426$	−348.136	−0.0395945
$427$	4922.43	0.557876
$428$	−8007.02	−0.904284
$429$	−3365.13	−0.378718
$430$	8376.97	0.939473
$431$	4819.55	0.538631	0.269315	−	0.963052i	$-0.413203\pi$
$431$	4819.55	0.538631	0.269315	+	0.963052i	$0.413203\pi$
$432$	5191.45	0.578180
$433$	2047.99	0.227298	0.113649	−	0.993521i	$-0.463746\pi$
$433$	2047.99	0.227298	0.113649	+	0.993521i	$0.463746\pi$
$434$	3586.58	0.396685
$435$	−13006.9	−1.43364
$436$	10813.5	1.18778
$437$	−2658.59	−0.291024
$438$	−167.841	−0.0183099
$439$	10003.1	1.08753	0.543763	−	0.839239i	$-0.316999\pi$
$439$	10003.1	1.08753	0.543763	+	0.839239i	$0.316999\pi$
$440$	7649.26	0.828782
$441$	−4728.67	−0.510600
$442$	−4694.92	−0.505237
$443$	14926.1	1.60081	0.800405	−	0.599459i	$-0.204618\pi$
$443$	14926.1	1.60081	0.800405	+	0.599459i	$0.204618\pi$
$444$	0	0
$445$	−8659.77	−0.922500
$446$	1663.02	0.176561
$447$	−1851.99	−0.195964
$448$	2468.75	0.260351
$449$	−2968.11	−0.311968	−0.155984	−	0.987760i	$-0.549855\pi$
$449$	−2968.11	−0.311968	−0.155984	+	0.987760i	$0.549855\pi$
$450$	4668.79	0.489086
$451$	2041.68	0.213168
$452$	2248.12	0.233944
$453$	−8735.30	−0.906005
$454$	830.983	0.0859030
$455$	−21541.3	−2.21950
$456$	−2514.43	−0.258221
$457$	7673.51	0.785452	0.392726	−	0.919656i	$-0.371532\pi$
$457$	7673.51	0.785452	0.392726	+	0.919656i	$0.371532\pi$
$458$	4496.54	0.458755
$459$	−14493.2	−1.47382
$460$	−8034.78	−0.814399
$461$	15850.2	1.60134	0.800669	−	0.599107i	$-0.204478\pi$
$461$	15850.2	1.60134	0.800669	+	0.599107i	$0.204478\pi$
$462$	2265.54	0.228144
$463$	16842.7	1.69059	0.845297	−	0.534296i	$-0.179423\pi$
$463$	16842.7	1.69059	0.845297	+	0.534296i	$0.179423\pi$
$464$	−6815.81	−0.681931
$465$	8645.71	0.862226
$466$	−5073.29	−0.504326
$467$	5171.45	0.512433	0.256217	−	0.966619i	$-0.417524\pi$
$467$	5171.45	0.512433	0.256217	+	0.966619i	$0.417524\pi$
$468$	−4359.79	−0.430623
$469$	−16069.5	−1.58213
$470$	−3828.07	−0.375693
$471$	7004.35	0.685231
$472$	8296.00	0.809013
$473$	−8783.75	−0.853863
$474$	−1889.42	−0.183089
$475$	12299.2	1.18806
$476$	−17300.7	−1.66592
$477$	7168.79	0.688127
$478$	6091.21	0.582857
$479$	−7321.72	−0.698409	−0.349205	−	0.937046i	$-0.613548\pi$
$479$	−7321.72	−0.698409	−0.349205	+	0.937046i	$0.613548\pi$
$480$	−11716.7	−1.11415
$481$	0	0
$482$	3247.15	0.306854
$483$	−5194.21	−0.489327
$484$	5328.47	0.500420
$485$	−14763.8	−1.38225
$486$	4029.03	0.376051
$487$	−8135.40	−0.756982	−0.378491	−	0.925605i	$-0.623557\pi$
$487$	−8135.40	−0.756982	−0.378491	+	0.925605i	$0.623557\pi$
$488$	−3162.99	−0.293405
$489$	−5065.62	−0.468457
$490$	6878.12	0.634126
$491$	−6570.04	−0.603874	−0.301937	−	0.953328i	$-0.597633\pi$
$491$	−6570.04	−0.603874	−0.301937	+	0.953328i	$0.597633\pi$
$492$	−2028.29	−0.185859
$493$	19028.0	1.73829
$494$	2098.33	0.191110
$495$	−7122.16	−0.646702
$496$	4530.48	0.410130
$497$	2336.75	0.210901
$498$	−1949.62	−0.175431
$499$	21994.3	1.97314	0.986571	−	0.163330i	$-0.0522237\pi$
$499$	21994.3	1.97314	0.986571	+	0.163330i	$0.0522237\pi$
$500$	20264.0	1.81246
$501$	−1819.65	−0.162268
$502$	888.548	0.0789997
$503$	−9258.86	−0.820740	−0.410370	−	0.911919i	$-0.634600\pi$
$503$	−9258.86	−0.820740	−0.410370	+	0.911919i	$0.634600\pi$
$504$	6406.62	0.566218
$505$	26062.0	2.29652
$506$	−1539.22	−0.135231
$507$	1431.32	0.125379
$508$	9755.14	0.851997
$509$	7999.47	0.696602	0.348301	−	0.937383i	$-0.386759\pi$
$509$	7999.47	0.696602	0.348301	+	0.937383i	$0.386759\pi$
$510$	7619.34	0.661550
$511$	1126.57	0.0975278
$512$	−10849.3	−0.936475
$513$	6477.53	0.557485
$514$	−7754.07	−0.665404
$515$	−21745.7	−1.86064
$516$	8726.16	0.744473
$517$	4013.95	0.341457
$518$	0	0
$519$	−6025.86	−0.509645
$520$	13841.7	1.16731
$521$	−4955.58	−0.416714	−0.208357	−	0.978053i	$-0.566812\pi$
$521$	−4955.58	−0.416714	−0.208357	+	0.978053i	$0.566812\pi$
$522$	−3228.23	−0.270682
$523$	−7891.55	−0.659796	−0.329898	−	0.944017i	$-0.607014\pi$
$523$	−7891.55	−0.659796	−0.329898	+	0.944017i	$0.607014\pi$
$524$	−5635.94	−0.469861
$525$	24029.6	1.99760
$526$	−6326.65	−0.524439
$527$	−12647.9	−1.04545
$528$	2861.77	0.235876
$529$	−8638.02	−0.709955
$530$	−10427.4	−0.854600
$531$	−7724.34	−0.631276
$532$	7732.30	0.630146
$533$	3694.52	0.300239
$534$	1648.07	0.133556
$535$	−23669.4	−1.91275
$536$	10325.7	0.832094
$537$	5691.46	0.457364
$538$	725.651	0.0581507
$539$	−7212.11	−0.576341
$540$	19576.4	1.56006
$541$	12398.5	0.985308	0.492654	−	0.870225i	$-0.336027\pi$
$541$	12398.5	0.985308	0.492654	+	0.870225i	$0.336027\pi$
$542$	77.4333	0.00613662
$543$	7995.81	0.631921
$544$	17140.5	1.35091
$545$	31965.6	2.51240
$546$	4099.61	0.321332
$547$	23971.4	1.87375	0.936875	−	0.349665i	$-0.113705\pi$
$547$	23971.4	1.87375	0.936875	+	0.349665i	$0.113705\pi$
$548$	13262.0	1.03380
$549$	2945.03	0.228945
$550$	7120.78	0.552057
$551$	−8504.29	−0.657522
$552$	3337.63	0.257353
$553$	12682.1	0.975224
$554$	−5388.21	−0.413219
$555$	0	0
$556$	13981.7	1.06647
$557$	−6264.14	−0.476518	−0.238259	−	0.971202i	$-0.576577\pi$
$557$	−6264.14	−0.476518	−0.238259	+	0.971202i	$0.576577\pi$
$558$	2145.81	0.162795
$559$	−15894.7	−1.20263
$560$	18319.2	1.38237
$561$	−7989.33	−0.601265
$562$	684.580	0.0513831
$563$	−17210.2	−1.28832	−0.644159	−	0.764891i	$-0.722793\pi$
$563$	−17210.2	−1.28832	−0.644159	+	0.764891i	$0.722793\pi$
$564$	−3987.64	−0.297713
$565$	6645.64	0.494839
$566$	−4036.75	−0.299783
$567$	2116.26	0.156745
$568$	−1501.52	−0.110920
$569$	−6594.00	−0.485826	−0.242913	−	0.970048i	$-0.578103\pi$
$569$	−6594.00	−0.485826	−0.242913	+	0.970048i	$0.578103\pi$
$570$	−3405.36	−0.250237
$571$	16743.2	1.22711	0.613556	−	0.789651i	$-0.289738\pi$
$571$	16743.2	1.22711	0.613556	+	0.789651i	$0.289738\pi$
$572$	−6649.51	−0.486066
$573$	−7292.02	−0.531638
$574$	−2487.30	−0.180867
$575$	−16325.9	−1.18406
$576$	1477.02	0.106845
$577$	−1090.81	−0.0787022	−0.0393511	−	0.999225i	$-0.512529\pi$
$577$	−1090.81	−0.0787022	−0.0393511	+	0.999225i	$0.512529\pi$
$578$	−5684.83	−0.409096
$579$	−5514.58	−0.395817
$580$	−25701.7	−1.84001
$581$	13086.2	0.934433
$582$	2809.76	0.200118
$583$	10933.8	0.776724
$584$	−723.899	−0.0512931
$585$	−12887.9	−0.910855
$586$	2012.65	0.141880
$587$	12521.8	0.880461	0.440231	−	0.897885i	$-0.354897\pi$
$587$	12521.8	0.880461	0.440231	+	0.897885i	$0.354897\pi$
$588$	7164.83	0.502504
$589$	5652.82	0.395450
$590$	11235.5	0.783997
$591$	−1840.99	−0.128136
$592$	0	0
$593$	−2022.44	−0.140053	−0.0700265	−	0.997545i	$-0.522308\pi$
$593$	−2022.44	−0.140053	−0.0700265	+	0.997545i	$0.522308\pi$
$594$	3750.24	0.259048
$595$	−51142.4	−3.52375
$596$	−3659.53	−0.251510
$597$	−14096.1	−0.966356
$598$	−2785.30	−0.190467
$599$	16912.1	1.15361	0.576804	−	0.816882i	$-0.304300\pi$
$599$	16912.1	1.15361	0.576804	+	0.816882i	$0.304300\pi$
$600$	−15440.6	−1.05060
$601$	−20980.2	−1.42396	−0.711981	−	0.702198i	$-0.752202\pi$
$601$	−20980.2	−1.42396	−0.711981	+	0.702198i	$0.752202\pi$
$602$	10700.9	0.724479
$603$	−9614.18	−0.649286
$604$	−17261.0	−1.16281
$605$	15751.4	1.05849
$606$	−4959.96	−0.332483
$607$	10586.6	0.707903	0.353952	−	0.935264i	$-0.384838\pi$
$607$	10586.6	0.707903	0.353952	+	0.935264i	$0.384838\pi$
$608$	−7660.72	−0.510992
$609$	−16615.3	−1.10556
$610$	−4283.72	−0.284332
$611$	7263.46	0.480930
$612$	−10350.8	−0.683671
$613$	−8535.63	−0.562400	−0.281200	−	0.959649i	$-0.590732\pi$
$613$	−8535.63	−0.562400	−0.281200	+	0.959649i	$0.590732\pi$
$614$	1720.49	0.113084
$615$	−5995.81	−0.393129
$616$	9771.31	0.639119
$617$	12282.6	0.801427	0.400714	−	0.916203i	$-0.368762\pi$
$617$	12282.6	0.801427	0.400714	+	0.916203i	$0.368762\pi$
$618$	4138.51	0.269377
$619$	644.810	0.0418693	0.0209347	−	0.999781i	$-0.493336\pi$
$619$	644.810	0.0418693	0.0209347	+	0.999781i	$0.493336\pi$
$620$	17083.9	1.10663
$621$	−8598.20	−0.555610
$622$	−7854.37	−0.506321
$623$	−11062.2	−0.711390
$624$	5178.53	0.332223
$625$	25549.3	1.63516
$626$	−11659.6	−0.744428
$627$	3570.72	0.227433
$628$	13840.6	0.879460
$629$	0	0
$630$	8676.66	0.548709
$631$	−14261.8	−0.899764	−0.449882	−	0.893088i	$-0.648534\pi$
$631$	−14261.8	−0.899764	−0.449882	+	0.893088i	$0.648534\pi$
$632$	−8149.11	−0.512902
$633$	−11565.7	−0.726217
$634$	7382.72	0.462469
$635$	28837.0	1.80215
$636$	−10862.1	−0.677216
$637$	−13050.7	−0.811754
$638$	−4923.66	−0.305532
$639$	1398.05	0.0865510
$640$	−29530.5	−1.82390
$641$	17844.8	1.09957	0.549786	−	0.835305i	$-0.314709\pi$
$641$	17844.8	1.09957	0.549786	+	0.835305i	$0.314709\pi$
$642$	4504.62	0.276921
$643$	8374.09	0.513596	0.256798	−	0.966465i	$-0.417333\pi$
$643$	8374.09	0.513596	0.256798	+	0.966465i	$0.417333\pi$
$644$	−10263.8	−0.628028
$645$	25795.3	1.57471
$646$	4981.75	0.303412
$647$	−509.698	−0.0309711	−0.0154855	−	0.999880i	$-0.504929\pi$
$647$	−509.698	−0.0309711	−0.0154855	+	0.999880i	$0.504929\pi$
$648$	−1359.84	−0.0824374
$649$	−11781.1	−0.712554
$650$	12885.4	0.777551
$651$	11044.2	0.664909
$652$	−10009.7	−0.601241
$653$	23855.1	1.42959	0.714796	−	0.699333i	$-0.246519\pi$
$653$	23855.1	1.42959	0.714796	+	0.699333i	$0.246519\pi$
$654$	−6083.50	−0.363737
$655$	−16660.3	−0.993851
$656$	−3141.89	−0.186998
$657$	674.017	0.0400242
$658$	−4890.05	−0.289717
$659$	3774.69	0.223127	0.111564	−	0.993757i	$-0.464414\pi$
$659$	3774.69	0.223127	0.111564	+	0.993757i	$0.464414\pi$
$660$	10791.4	0.636448
$661$	−8978.60	−0.528331	−0.264166	−	0.964477i	$-0.585097\pi$
$661$	−8978.60	−0.528331	−0.264166	+	0.964477i	$0.585097\pi$
$662$	7709.69	0.452637
$663$	−14457.1	−0.846859
$664$	−8408.74	−0.491449
$665$	22857.4	1.33289
$666$	0	0
$667$	11288.5	0.655312
$668$	−3595.64	−0.208263
$669$	5120.95	0.295945
$670$	13984.4	0.806363
$671$	4491.73	0.258422
$672$	−14967.1	−0.859181
$673$	−1138.53	−0.0652113	−0.0326057	−	0.999468i	$-0.510381\pi$
$673$	−1138.53	−0.0652113	−0.0326057	+	0.999468i	$0.510381\pi$
$674$	5664.44	0.323718
$675$	39777.2	2.26819
$676$	2828.30	0.160918
$677$	−3755.81	−0.213216	−0.106608	−	0.994301i	$-0.533999\pi$
$677$	−3755.81	−0.213216	−0.106608	+	0.994301i	$0.533999\pi$
$678$	−1264.76	−0.0716411
$679$	−18859.6	−1.06593
$680$	32862.4	1.85326
$681$	2558.85	0.143988
$682$	3272.77	0.183755
$683$	6229.76	0.349012	0.174506	−	0.984656i	$-0.444167\pi$
$683$	6229.76	0.349012	0.174506	+	0.984656i	$0.444167\pi$
$684$	4626.15	0.258604
$685$	39203.5	2.18670
$686$	−953.242	−0.0530538
$687$	13846.2	0.768948
$688$	13517.1	0.749034
$689$	19785.2	1.09399
$690$	4520.24	0.249395
$691$	15328.9	0.843907	0.421954	−	0.906617i	$-0.361344\pi$
$691$	15328.9	0.843907	0.421954	+	0.906617i	$0.361344\pi$
$692$	−11907.1	−0.654105
$693$	−9097.99	−0.498707
$694$	−1801.35	−0.0985277
$695$	41331.1	2.25579
$696$	10676.4	0.581449
$697$	8771.36	0.476670
$698$	−8378.53	−0.454344
$699$	−15622.2	−0.845332
$700$	47482.6	2.56382
$701$	−3059.61	−0.164850	−0.0824250	−	0.996597i	$-0.526266\pi$
$701$	−3059.61	−0.164850	−0.0824250	+	0.996597i	$0.526266\pi$
$702$	6786.26	0.364859
$703$	0	0
$704$	2252.74	0.120601
$705$	−11787.8	−0.629723
$706$	2644.88	0.140993
$707$	33292.1	1.77097
$708$	11703.8	0.621267
$709$	29519.7	1.56366	0.781830	−	0.623491i	$-0.214286\pi$
$709$	29519.7	1.56366	0.781830	+	0.623491i	$0.214286\pi$
$710$	−2033.55	−0.107490
$711$	7587.57	0.400220
$712$	7108.17	0.374143
$713$	−7503.49	−0.394121
$714$	9733.10	0.510157
$715$	−19656.5	−1.02813
$716$	11246.3	0.587005
$717$	18756.7	0.976964
$718$	9679.21	0.503099
$719$	30325.1	1.57293	0.786463	−	0.617637i	$-0.211910\pi$
$719$	30325.1	1.57293	0.786463	+	0.617637i	$0.211910\pi$
$720$	10960.1	0.567306
$721$	−27778.4	−1.43484
$722$	5398.41	0.278266
$723$	9998.97	0.514337
$724$	15799.7	0.811040
$725$	−52223.2	−2.67520
$726$	−2997.71	−0.153245
$727$	−24006.6	−1.22470	−0.612350	−	0.790587i	$-0.709776\pi$
$727$	−24006.6	−1.22470	−0.612350	+	0.790587i	$0.709776\pi$
$728$	17681.7	0.900175
$729$	14643.6	0.743974
$730$	−980.396	−0.0497070
$731$	−37736.3	−1.90934
$732$	−4462.28	−0.225315
$733$	15097.2	0.760746	0.380373	−	0.924833i	$-0.375796\pi$
$733$	15097.2	0.760746	0.380373	+	0.924833i	$0.375796\pi$
$734$	1013.58	0.0509700
$735$	21179.9	1.06290
$736$	10168.8	0.509274
$737$	−14663.4	−0.732883
$738$	−1488.12	−0.0742257
$739$	−36358.0	−1.80981	−0.904905	−	0.425614i	$-0.860058\pi$
$739$	−36358.0	−1.80981	−0.904905	+	0.425614i	$0.860058\pi$
$740$	0	0
$741$	6461.40	0.320331
$742$	−13320.2	−0.659029
$743$	8085.01	0.399206	0.199603	−	0.979877i	$-0.436035\pi$
$743$	8085.01	0.399206	0.199603	+	0.979877i	$0.436035\pi$
$744$	−7096.63	−0.349698
$745$	−10817.9	−0.531996
$746$	−7860.79	−0.385796
$747$	7829.31	0.383480
$748$	−15786.9	−0.771695
$749$	−30235.8	−1.47502
$750$	−11400.2	−0.555035
$751$	14523.8	0.705701	0.352851	−	0.935680i	$-0.385212\pi$
$751$	14523.8	0.705701	0.352851	+	0.935680i	$0.385212\pi$
$752$	−6176.99	−0.299537
$753$	2736.12	0.132416
$754$	−8909.62	−0.430331
$755$	−51025.0	−2.45959
$756$	25007.2	1.20305
$757$	−14760.3	−0.708682	−0.354341	−	0.935116i	$-0.615295\pi$
$757$	−14760.3	−0.708682	−0.354341	+	0.935116i	$0.615295\pi$
$758$	−13634.5	−0.653333
$759$	−4739.74	−0.226669
$760$	−14687.4	−0.701009
$761$	−3700.20	−0.176258	−0.0881288	−	0.996109i	$-0.528089\pi$
$761$	−3700.20	−0.176258	−0.0881288	+	0.996109i	$0.528089\pi$
$762$	−5488.09	−0.260909
$763$	40833.5	1.93745
$764$	−14409.1	−0.682332
$765$	−30597.9	−1.44610
$766$	10104.3	0.476611
$767$	−21318.5	−1.00361
$768$	2973.22	0.139696
$769$	−18470.1	−0.866123	−0.433062	−	0.901364i	$-0.642567\pi$
$769$	−18470.1	−0.866123	−0.433062	+	0.901364i	$0.642567\pi$
$770$	13233.5	0.619356
$771$	−23877.2	−1.11533
$772$	−10896.8	−0.508012
$773$	9271.86	0.431417	0.215709	−	0.976458i	$-0.430794\pi$
$773$	9271.86	0.431417	0.215709	+	0.976458i	$0.430794\pi$
$774$	6402.23	0.297317
$775$	34712.8	1.60893
$776$	12118.6	0.560607
$777$	0	0
$778$	16421.1	0.756718
$779$	−3920.23	−0.180304
$780$	19527.7	0.896413
$781$	2132.29	0.0976945
$782$	−6612.73	−0.302392
$783$	−27503.9	−1.25531
$784$	11098.6	0.505583
$785$	40914.1	1.86024
$786$	3170.69	0.143886
$787$	15810.0	0.716096	0.358048	−	0.933703i	$-0.383442\pi$
$787$	15810.0	0.716096	0.358048	+	0.933703i	$0.383442\pi$
$788$	−3637.80	−0.164456
$789$	−19481.7	−0.879046
$790$	−11036.6	−0.497042
$791$	8489.26	0.381597
$792$	5846.06	0.262286
$793$	8128.02	0.363978
$794$	15717.0	0.702488
$795$	−32109.2	−1.43245
$796$	−27853.9	−1.24027
$797$	4937.77	0.219454	0.109727	−	0.993962i	$-0.465002\pi$
$797$	4937.77	0.219454	0.109727	+	0.993962i	$0.465002\pi$
$798$	−4350.07	−0.192971
$799$	17244.6	0.763540
$800$	−47043.0	−2.07903
$801$	−6618.37	−0.291946
$802$	−4059.27	−0.178725
$803$	1028.00	0.0451774
$804$	14567.3	0.638991
$805$	−30340.6	−1.32841
$806$	5922.24	0.258812
$807$	2234.51	0.0974700
$808$	−21392.4	−0.931413
$809$	−2304.82	−0.100164	−0.0500822	−	0.998745i	$-0.515948\pi$
$809$	−2304.82	−0.100164	−0.0500822	+	0.998745i	$0.515948\pi$
$810$	−1841.66	−0.0798882
$811$	−36004.0	−1.55891	−0.779453	−	0.626461i	$-0.784503\pi$
$811$	−36004.0	−1.55891	−0.779453	+	0.626461i	$0.784503\pi$
$812$	−32831.8	−1.41893
$813$	238.441	0.0102860
$814$	0	0
$815$	−29589.5	−1.27175
$816$	12294.6	0.527448
$817$	16865.7	0.722224
$818$	2980.67	0.127404
$819$	−16463.3	−0.702410
$820$	−11847.7	−0.504562
$821$	−27100.7	−1.15203	−0.576017	−	0.817438i	$-0.695394\pi$
$821$	−27100.7	−1.15203	−0.576017	+	0.817438i	$0.695394\pi$
$822$	−7460.98	−0.316583
$823$	15685.5	0.664353	0.332177	−	0.943217i	$-0.392217\pi$
$823$	15685.5	0.664353	0.332177	+	0.943217i	$0.392217\pi$
$824$	17849.5	0.754630
$825$	21927.1	0.925337
$826$	14352.4	0.604583
$827$	−30698.2	−1.29079	−0.645393	−	0.763851i	$-0.723306\pi$
$827$	−30698.2	−1.29079	−0.645393	+	0.763851i	$0.723306\pi$
$828$	−6140.71	−0.257735
$829$	−8598.09	−0.360222	−0.180111	−	0.983646i	$-0.557646\pi$
$829$	−8598.09	−0.360222	−0.180111	+	0.983646i	$0.557646\pi$
$830$	−11388.2	−0.476252
$831$	−16592.0	−0.692622
$832$	4076.45	0.169862
$833$	−30984.3	−1.28877
$834$	−7865.87	−0.326586
$835$	−10629.0	−0.440518
$836$	7055.75	0.291900
$837$	18281.9	0.754977
$838$	−6656.35	−0.274391
$839$	509.803	0.0209778	0.0104889	−	0.999945i	$-0.496661\pi$
$839$	509.803	0.0209778	0.0104889	+	0.999945i	$0.496661\pi$
$840$	−28695.5	−1.17868
$841$	11720.7	0.480572
$842$	−4539.72	−0.185807
$843$	2108.03	0.0861264
$844$	−22853.9	−0.932064
$845$	8360.69	0.340375
$846$	−2925.66	−0.118896
$847$	20121.2	0.816260
$848$	−16825.7	−0.681366
$849$	−12430.4	−0.502485
$850$	30592.0	1.23447
$851$	0	0
$852$	−2118.31	−0.0851787
$853$	572.535	0.0229815	0.0114908	−	0.999934i	$-0.496342\pi$
$853$	572.535	0.0229815	0.0114908	+	0.999934i	$0.496342\pi$
$854$	−5472.10	−0.219264
$855$	13675.3	0.547001
$856$	19428.5	0.775763
$857$	−22531.6	−0.898092	−0.449046	−	0.893509i	$-0.648236\pi$
$857$	−22531.6	−0.898092	−0.449046	+	0.893509i	$0.648236\pi$
$858$	3740.91	0.148849
$859$	45265.2	1.79794	0.898969	−	0.438012i	$-0.144317\pi$
$859$	45265.2	1.79794	0.898969	+	0.438012i	$0.144317\pi$
$860$	50971.6	2.02107
$861$	−7659.16	−0.303163
$862$	−5357.74	−0.211700
$863$	−20447.2	−0.806527	−0.403263	−	0.915084i	$-0.632124\pi$
$863$	−20447.2	−0.806527	−0.403263	+	0.915084i	$0.632124\pi$
$864$	−24775.7	−0.975564
$865$	−35198.5	−1.38356
$866$	−2276.69	−0.0893360
$867$	−17505.3	−0.685712
$868$	21823.4	0.853379
$869$	11572.5	0.451749
$870$	14459.3	0.563469
$871$	−26534.3	−1.03224
$872$	−26238.3	−1.01897
$873$	−11283.5	−0.437444
$874$	2955.47	0.114382
$875$	76520.0	2.95640
$876$	−1021.26	−0.0393896
$877$	−273.973	−0.0105489	−0.00527447	−	0.999986i	$-0.501679\pi$
$877$	−273.973	−0.0105489	−0.00527447	+	0.999986i	$0.501679\pi$
$878$	−11120.2	−0.427435
$879$	6197.56	0.237814
$880$	16716.3	0.640348
$881$	18867.8	0.721537	0.360768	−	0.932655i	$-0.382514\pi$
$881$	18867.8	0.721537	0.360768	+	0.932655i	$0.382514\pi$
$882$	5256.71	0.200683
$883$	−13253.7	−0.505121	−0.252561	−	0.967581i	$-0.581273\pi$
$883$	−13253.7	−0.505121	−0.252561	+	0.967581i	$0.581273\pi$
$884$	−28567.3	−1.08690
$885$	34597.6	1.31411
$886$	−16592.8	−0.629173
$887$	−44618.2	−1.68899	−0.844494	−	0.535565i	$-0.820099\pi$
$887$	−44618.2	−1.68899	−0.844494	+	0.535565i	$0.820099\pi$
$888$	0	0
$889$	36837.0	1.38973
$890$	9626.79	0.362574
$891$	1931.09	0.0726083
$892$	10119.0	0.379831
$893$	−7707.21	−0.288815
$894$	2058.79	0.0770205
$895$	33245.2	1.24163
$896$	−37722.8	−1.40651
$897$	−8576.81	−0.319254
$898$	3299.55	0.122614
$899$	−24002.2	−0.890453
$900$	28408.3	1.05216
$901$	46973.1	1.73685
$902$	−2269.67	−0.0837823
$903$	32951.4	1.21435
$904$	−5454.92	−0.200695
$905$	46705.4	1.71552
$906$	9710.75	0.356091
$907$	−19222.8	−0.703730	−0.351865	−	0.936051i	$-0.614452\pi$
$907$	−19222.8	−0.703730	−0.351865	+	0.936051i	$0.614452\pi$
$908$	5056.30	0.184801
$909$	19918.3	0.726785
$910$	23946.8	0.872339
$911$	465.333	0.0169233	0.00846167	−	0.999964i	$-0.497307\pi$
$911$	465.333	0.0169233	0.00846167	+	0.999964i	$0.497307\pi$
$912$	−5494.90	−0.199511
$913$	11941.2	0.432853
$914$	−8530.39	−0.308709
$915$	−13190.9	−0.476587
$916$	27360.2	0.986907
$917$	−21282.2	−0.766413
$918$	16111.6	0.579262
$919$	−9871.63	−0.354336	−0.177168	−	0.984181i	$-0.556694\pi$
$919$	−9871.63	−0.354336	−0.177168	+	0.984181i	$0.556694\pi$
$920$	19495.9	0.698652
$921$	5297.92	0.189546
$922$	−17620.1	−0.629380
$923$	3858.50	0.137599
$924$	13785.2	0.490800
$925$	0	0
$926$	−18723.5	−0.664461
$927$	−16619.5	−0.588841
$928$	32527.8	1.15062
$929$	−52109.0	−1.84030	−0.920150	−	0.391565i	$-0.871934\pi$
$929$	−52109.0	−1.84030	−0.920150	+	0.391565i	$0.871934\pi$
$930$	−9611.16	−0.338884
$931$	13848.0	0.487487
$932$	−30869.6	−1.08494
$933$	−24186.0	−0.848677
$934$	−5748.94	−0.201404
$935$	−46667.6	−1.63229
$936$	10578.8	0.369421
$937$	−26347.2	−0.918598	−0.459299	−	0.888282i	$-0.651899\pi$
$937$	−26347.2	−0.918598	−0.459299	+	0.888282i	$0.651899\pi$
$938$	17863.9	0.621831
$939$	−35903.5	−1.24778
$940$	−23292.7	−0.808219
$941$	−48923.6	−1.69486	−0.847430	−	0.530907i	$-0.821851\pi$
$941$	−48923.6	−1.69486	−0.847430	+	0.530907i	$0.821851\pi$
$942$	−7786.52	−0.269319
$943$	5203.68	0.179698
$944$	18129.7	0.625074
$945$	73923.6	2.54469
$946$	9764.61	0.335597
$947$	7583.78	0.260232	0.130116	−	0.991499i	$-0.458465\pi$
$947$	7583.78	0.260232	0.130116	+	0.991499i	$0.458465\pi$
$948$	−11496.6	−0.393874
$949$	1860.23	0.0636307
$950$	−13672.6	−0.466947
$951$	22733.7	0.775174
$952$	41979.0	1.42915
$953$	24502.0	0.832842	0.416421	−	0.909172i	$-0.363284\pi$
$953$	24502.0	0.832842	0.416421	+	0.909172i	$0.363284\pi$
$954$	−7969.32	−0.270457
$955$	−42594.4	−1.44327
$956$	37063.4	1.25389
$957$	−15161.5	−0.512122
$958$	8139.33	0.274499
$959$	50079.4	1.68628
$960$	−6615.64	−0.222415
$961$	−13836.7	−0.464459
$962$	0	0
$963$	−18089.7	−0.605331
$964$	19758.0	0.660127
$965$	−32212.0	−1.07455
$966$	5774.24	0.192322
$967$	−20531.1	−0.682767	−0.341384	−	0.939924i	$-0.610896\pi$
$967$	−20531.1	−0.682767	−0.341384	+	0.939924i	$0.610896\pi$
$968$	−12929.2	−0.429298
$969$	15340.4	0.508569
$970$	16412.5	0.543271
$971$	−46996.9	−1.55325	−0.776623	−	0.629965i	$-0.783069\pi$
$971$	−46996.9	−1.55325	−0.776623	+	0.629965i	$0.783069\pi$
$972$	24515.6	0.808989
$973$	52797.1	1.73956
$974$	9043.87	0.297520
$975$	39678.2	1.30330
$976$	−6912.23	−0.226696
$977$	−3008.67	−0.0985218	−0.0492609	−	0.998786i	$-0.515687\pi$
$977$	−3008.67	−0.0985218	−0.0492609	+	0.998786i	$0.515687\pi$
$978$	5631.29	0.184119
$979$	−10094.3	−0.329534
$980$	41851.5	1.36418
$981$	24430.2	0.795104
$982$	7303.71	0.237343
$983$	−4739.23	−0.153772	−0.0768861	−	0.997040i	$-0.524498\pi$
$983$	−4739.23	−0.153772	−0.0768861	+	0.997040i	$0.524498\pi$
$984$	4921.52	0.159443
$985$	−10753.7	−0.347858
$986$	−21152.8	−0.683207
$987$	−15058.0	−0.485613
$988$	12767.8	0.411130
$989$	−22387.4	−0.719795
$990$	7917.48	0.254176
$991$	18821.8	0.603323	0.301662	−	0.953415i	$-0.402459\pi$
$991$	18821.8	0.603323	0.301662	+	0.953415i	$0.402459\pi$
$992$	−21621.3	−0.692014
$993$	23740.5	0.758693
$994$	−2597.69	−0.0828911
$995$	−82338.6	−2.62343
$996$	−11862.9	−0.377399
$997$	35682.9	1.13349	0.566744	−	0.823894i	$-0.308203\pi$
$997$	35682.9	1.13349	0.566744	+	0.823894i	$0.308203\pi$
$998$	−24450.3	−0.775512
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1369.4.a.j.1.20		48
37.2	odd	36		37.4.h.a.4.4	✓	48
37.19	odd	36		37.4.h.a.28.4	yes	48
37.36	even	2	inner	1369.4.a.j.1.29		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.4.h.a.4.4	✓	48	37.2	odd	36
37.4.h.a.28.4	yes	48	37.19	odd	36
1369.4.a.j.1.20		48	1.1	even	1	trivial
1369.4.a.j.1.29		48	37.36	even	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:	\( N \)	\(=\)	\( 1369 = 37^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1369.a (trivial)

\(f(q)\)	\(=\)	\(q-1.11167 q^{2} -3.42317 q^{3} -6.76419 q^{4} -19.9955 q^{5} +3.80543 q^{6} -25.5427 q^{7} +16.4129 q^{8} -15.2819 q^{9} +O(q^{10})\)	\(q-1.11167 q^{2} -3.42317 q^{3} -6.76419 q^{4} -19.9955 q^{5} +3.80543 q^{6} -25.5427 q^{7} +16.4129 q^{8} -15.2819 q^{9} +22.2284 q^{10} -23.3078 q^{11} +23.1550 q^{12} -42.1767 q^{13} +28.3950 q^{14} +68.4482 q^{15} +35.8679 q^{16} -100.134 q^{17} +16.9884 q^{18} +44.7534 q^{19} +135.254 q^{20} +87.4370 q^{21} +25.9105 q^{22} -59.4052 q^{23} -56.1841 q^{24} +274.822 q^{25} +46.8865 q^{26} +144.738 q^{27} +172.776 q^{28} -190.025 q^{29} -76.0916 q^{30} +126.310 q^{31} -171.176 q^{32} +79.7865 q^{33} +111.316 q^{34} +510.740 q^{35} +103.370 q^{36} -49.7509 q^{38} +144.378 q^{39} -328.185 q^{40} -87.5963 q^{41} -97.2009 q^{42} +376.859 q^{43} +157.658 q^{44} +305.570 q^{45} +66.0389 q^{46} -172.215 q^{47} -122.782 q^{48} +309.429 q^{49} -305.511 q^{50} +342.775 q^{51} +285.291 q^{52} -469.103 q^{53} -160.901 q^{54} +466.052 q^{55} -419.229 q^{56} -153.199 q^{57} +211.245 q^{58} +505.457 q^{59} -462.997 q^{60} -192.714 q^{61} -140.415 q^{62} +390.341 q^{63} -96.6518 q^{64} +843.346 q^{65} -88.6961 q^{66} +629.122 q^{67} +677.325 q^{68} +203.354 q^{69} -567.774 q^{70} -91.4841 q^{71} -250.820 q^{72} -44.1056 q^{73} -940.762 q^{75} -302.721 q^{76} +595.344 q^{77} -160.500 q^{78} -496.507 q^{79} -717.198 q^{80} -82.8518 q^{81} +97.3781 q^{82} -512.325 q^{83} -591.441 q^{84} +2002.23 q^{85} -418.942 q^{86} +650.489 q^{87} -382.548 q^{88} +433.085 q^{89} -339.693 q^{90} +1077.31 q^{91} +401.829 q^{92} -432.382 q^{93} +191.446 q^{94} -894.869 q^{95} +585.965 q^{96} +738.356 q^{97} -343.983 q^{98} +356.188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 36 q^{3} + 144 q^{4} - 84 q^{7} + 216 q^{9}+O(q^{10}) \) 48 * q - 36 * q^3 + 144 * q^4 - 84 * q^7 + 216 * q^9	\( 48 q - 36 q^{3} + 144 q^{4} - 84 q^{7} + 216 q^{9} - 114 q^{10} - 270 q^{11} - 270 q^{12} + 192 q^{16} - 666 q^{21} + 732 q^{25} - 378 q^{26} - 414 q^{27} + 240 q^{28} + 840 q^{30} - 648 q^{33} - 432 q^{34} - 852 q^{36} - 2526 q^{38} - 522 q^{40} - 3096 q^{41} - 1662 q^{44} - 2970 q^{46} - 2370 q^{47} - 4326 q^{48} - 120 q^{49} - 4326 q^{53} - 1398 q^{58} - 2790 q^{62} + 390 q^{63} - 3024 q^{64} - 1842 q^{65} + 2844 q^{67} - 1320 q^{70} - 2640 q^{71} - 7002 q^{73} - 5604 q^{75} + 2904 q^{77} + 462 q^{78} - 6000 q^{81} - 4476 q^{83} - 17148 q^{84} + 1452 q^{85} - 5856 q^{86} - 13956 q^{90} - 7782 q^{95} - 6198 q^{99}+O(q^{100}) \) 48 * q - 36 * q^3 + 144 * q^4 - 84 * q^7 + 216 * q^9 - 114 * q^10 - 270 * q^11 - 270 * q^12 + 192 * q^16 - 666 * q^21 + 732 * q^25 - 378 * q^26 - 414 * q^27 + 240 * q^28 + 840 * q^30 - 648 * q^33 - 432 * q^34 - 852 * q^36 - 2526 * q^38 - 522 * q^40 - 3096 * q^41 - 1662 * q^44 - 2970 * q^46 - 2370 * q^47 - 4326 * q^48 - 120 * q^49 - 4326 * q^53 - 1398 * q^58 - 2790 * q^62 + 390 * q^63 - 3024 * q^64 - 1842 * q^65 + 2844 * q^67 - 1320 * q^70 - 2640 * q^71 - 7002 * q^73 - 5604 * q^75 + 2904 * q^77 + 462 * q^78 - 6000 * q^81 - 4476 * q^83 - 17148 * q^84 + 1452 * q^85 - 5856 * q^86 - 13956 * q^90 - 7782 * q^95 - 6198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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