LMFDB - Embedded newform 1859.4.a.q.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.24016 q^{2} -4.67403 q^{3} +9.97893 q^{4} -7.09125 q^{5} +19.8186 q^{6} -21.9298 q^{7} -8.39097 q^{8} -5.15349 q^{9} +O(q^{10})$	\(q-4.24016 q^{2} -4.67403 q^{3} +9.97893 q^{4} -7.09125 q^{5} +19.8186 q^{6} -21.9298 q^{7} -8.39097 q^{8} -5.15349 q^{9} +30.0680 q^{10} +11.0000 q^{11} -46.6418 q^{12} +92.9860 q^{14} +33.1447 q^{15} -44.2524 q^{16} +66.7503 q^{17} +21.8516 q^{18} +59.2420 q^{19} -70.7631 q^{20} +102.501 q^{21} -46.6417 q^{22} +51.3838 q^{23} +39.2196 q^{24} -74.7142 q^{25} +150.286 q^{27} -218.836 q^{28} +235.050 q^{29} -140.539 q^{30} -269.681 q^{31} +254.765 q^{32} -51.4143 q^{33} -283.032 q^{34} +155.510 q^{35} -51.4263 q^{36} -51.2079 q^{37} -251.195 q^{38} +59.5024 q^{40} +430.757 q^{41} -434.619 q^{42} +93.5129 q^{43} +109.768 q^{44} +36.5447 q^{45} -217.875 q^{46} -608.482 q^{47} +206.837 q^{48} +137.918 q^{49} +316.800 q^{50} -311.993 q^{51} +13.2710 q^{53} -637.237 q^{54} -78.0037 q^{55} +184.013 q^{56} -276.899 q^{57} -996.651 q^{58} +49.3230 q^{59} +330.748 q^{60} +309.887 q^{61} +1143.49 q^{62} +113.015 q^{63} -726.224 q^{64} +218.005 q^{66} -236.624 q^{67} +666.097 q^{68} -240.169 q^{69} -659.387 q^{70} -481.950 q^{71} +43.2428 q^{72} +205.221 q^{73} +217.130 q^{74} +349.216 q^{75} +591.172 q^{76} -241.228 q^{77} +613.679 q^{79} +313.805 q^{80} -563.297 q^{81} -1826.48 q^{82} -277.796 q^{83} +1022.85 q^{84} -473.343 q^{85} -396.509 q^{86} -1098.63 q^{87} -92.3007 q^{88} +752.231 q^{89} -154.955 q^{90} +512.756 q^{92} +1260.49 q^{93} +2580.06 q^{94} -420.100 q^{95} -1190.78 q^{96} -133.966 q^{97} -584.794 q^{98} -56.6884 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * 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 $

$2$	−4.24016	−1.49912	−0.749561	−	0.661935i	$-0.769735\pi$
$2$	−4.24016	−1.49912	−0.749561	+	0.661935i	$0.769735\pi$
$3$	−4.67403	−0.899517	−0.449758	−	0.893150i	$-0.648490\pi$
$3$	−4.67403	−0.899517	−0.449758	+	0.893150i	$0.648490\pi$
$4$	9.97893	1.24737
$5$	−7.09125	−0.634261	−0.317130	−	0.948382i	$-0.602719\pi$
$5$	−7.09125	−0.634261	−0.317130	+	0.948382i	$0.602719\pi$
$6$	19.8186	1.34848
$7$	−21.9298	−1.18410	−0.592050	−	0.805901i	$-0.701681\pi$
$7$	−21.9298	−1.18410	−0.592050	+	0.805901i	$0.701681\pi$
$8$	−8.39097	−0.370832
$9$	−5.15349	−0.190870
$10$	30.0680	0.950834
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−46.6418	−1.12203
$13$	0	0
$13$	0	0
$14$	92.9860	1.77511
$15$	33.1447	0.570528
$16$	−44.2524	−0.691444
$17$	66.7503	0.952313	0.476157	−	0.879360i	$-0.342030\pi$
$17$	66.7503	0.952313	0.476157	+	0.879360i	$0.342030\pi$
$18$	21.8516	0.286137
$19$	59.2420	0.715318	0.357659	−	0.933852i	$-0.383575\pi$
$19$	59.2420	0.715318	0.357659	+	0.933852i	$0.383575\pi$
$20$	−70.7631	−0.791155
$21$	102.501	1.06512
$22$	−46.6417	−0.452002
$23$	51.3838	0.465838	0.232919	−	0.972496i	$-0.425172\pi$
$23$	51.3838	0.465838	0.232919	+	0.972496i	$0.425172\pi$
$24$	39.2196	0.333569
$25$	−74.7142	−0.597714
$26$	0	0
$27$	150.286	1.07121
$28$	−218.836	−1.47701
$29$	235.050	1.50510	0.752548	−	0.658538i	$-0.228825\pi$
$29$	235.050	1.50510	0.752548	+	0.658538i	$0.228825\pi$
$30$	−140.539	−0.855291
$31$	−269.681	−1.56245	−0.781227	−	0.624246i	$-0.785406\pi$
$31$	−269.681	−1.56245	−0.781227	+	0.624246i	$0.785406\pi$
$32$	254.765	1.40739
$33$	−51.4143	−0.271214
$34$	−283.032	−1.42763
$35$	155.510	0.751028
$36$	−51.4263	−0.238085
$37$	−51.2079	−0.227528	−0.113764	−	0.993508i	$-0.536291\pi$
$37$	−51.2079	−0.227528	−0.113764	+	0.993508i	$0.536291\pi$
$38$	−251.195	−1.07235
$39$	0	0
$40$	59.5024	0.235204
$41$	430.757	1.64080	0.820402	−	0.571787i	$-0.193750\pi$
$41$	430.757	1.64080	0.820402	+	0.571787i	$0.193750\pi$
$42$	−434.619	−1.59674
$43$	93.5129	0.331642	0.165821	−	0.986156i	$-0.446973\pi$
$43$	93.5129	0.331642	0.165821	+	0.986156i	$0.446973\pi$
$44$	109.768	0.376095
$45$	36.5447	0.121061
$46$	−217.875	−0.698348
$47$	−608.482	−1.88843	−0.944215	−	0.329331i	$-0.893177\pi$
$47$	−608.482	−1.88843	−0.944215	+	0.329331i	$0.893177\pi$
$48$	206.837	0.621965
$49$	137.918	0.402093
$50$	316.800	0.896045
$51$	−311.993	−0.856622
$52$	0	0
$53$	13.2710	0.0343946	0.0171973	−	0.999852i	$-0.494526\pi$
$53$	13.2710	0.0343946	0.0171973	+	0.999852i	$0.494526\pi$
$54$	−637.237	−1.60587
$55$	−78.0037	−0.191237
$56$	184.013	0.439102
$57$	−276.899	−0.643441
$58$	−996.651	−2.25632
$59$	49.3230	0.108836	0.0544179	−	0.998518i	$-0.482670\pi$
$59$	49.3230	0.108836	0.0544179	+	0.998518i	$0.482670\pi$
$60$	330.748	0.711657
$61$	309.887	0.650443	0.325221	−	0.945638i	$-0.394561\pi$
$61$	309.887	0.650443	0.325221	+	0.945638i	$0.394561\pi$
$62$	1143.49	2.34231
$63$	113.015	0.226009
$64$	−726.224	−1.41841
$65$	0	0
$66$	218.005	0.406583
$67$	−236.624	−0.431465	−0.215733	−	0.976452i	$-0.569214\pi$
$67$	−236.624	−0.431465	−0.215733	+	0.976452i	$0.569214\pi$
$68$	666.097	1.18788
$69$	−240.169	−0.419029
$70$	−659.387	−1.12588
$71$	−481.950	−0.805590	−0.402795	−	0.915290i	$-0.631961\pi$
$71$	−481.950	−0.805590	−0.402795	+	0.915290i	$0.631961\pi$
$72$	43.2428	0.0707807
$73$	205.221	0.329031	0.164515	−	0.986375i	$-0.447394\pi$
$73$	205.221	0.329031	0.164515	+	0.986375i	$0.447394\pi$
$74$	217.130	0.341092
$75$	349.216	0.537653
$76$	591.172	0.892264
$77$	−241.228	−0.357020
$78$	0	0
$79$	613.679	0.873978	0.436989	−	0.899467i	$-0.356045\pi$
$79$	613.679	0.873978	0.436989	+	0.899467i	$0.356045\pi$
$80$	313.805	0.438556
$81$	−563.297	−0.772699
$82$	−1826.48	−2.45977
$83$	−277.796	−0.367375	−0.183687	−	0.982985i	$-0.558803\pi$
$83$	−277.796	−0.367375	−0.183687	+	0.982985i	$0.558803\pi$
$84$	1022.85	1.32859
$85$	−473.343	−0.604015
$86$	−396.509	−0.497171
$87$	−1098.63	−1.35386
$88$	−92.3007	−0.111810
$89$	752.231	0.895914	0.447957	−	0.894055i	$-0.352152\pi$
$89$	752.231	0.895914	0.447957	+	0.894055i	$0.352152\pi$
$90$	−154.955	−0.181486
$91$	0	0
$92$	512.756	0.581070
$93$	1260.49	1.40545
$94$	2580.06	2.83099
$95$	−420.100	−0.453698
$96$	−1190.78	−1.26597
$97$	−133.966	−0.140229	−0.0701146	−	0.997539i	$-0.522336\pi$
$97$	−133.966	−0.140229	−0.0701146	+	0.997539i	$0.522336\pi$
$98$	−584.794	−0.602787
$99$	−56.6884	−0.0575495
$100$	−745.568	−0.745568
$101$	265.568	0.261633	0.130817	−	0.991407i	$-0.458240\pi$
$101$	265.568	0.261633	0.130817	+	0.991407i	$0.458240\pi$
$102$	1322.90	1.28418
$103$	−518.171	−0.495698	−0.247849	−	0.968799i	$-0.579724\pi$
$103$	−518.171	−0.495698	−0.247849	+	0.968799i	$0.579724\pi$
$104$	0	0
$105$	−726.858	−0.675562
$106$	−56.2712	−0.0515617
$107$	−220.264	−0.199007	−0.0995035	−	0.995037i	$-0.531725\pi$
$107$	−220.264	−0.199007	−0.0995035	+	0.995037i	$0.531725\pi$
$108$	1499.70	1.33619
$109$	−2042.49	−1.79481	−0.897407	−	0.441203i	$-0.854552\pi$
$109$	−2042.49	−1.79481	−0.897407	+	0.441203i	$0.854552\pi$
$110$	330.748	0.286687
$111$	239.347	0.204665
$112$	970.448	0.818739
$113$	305.200	0.254078	0.127039	−	0.991898i	$-0.459453\pi$
$113$	305.200	0.254078	0.127039	+	0.991898i	$0.459453\pi$
$114$	1174.09	0.964596
$115$	−364.376	−0.295463
$116$	2345.55	1.87741
$117$	0	0
$118$	−209.137	−0.163158
$119$	−1463.82	−1.12763
$120$	−278.116	−0.211570
$121$	121.000	0.0909091
$122$	−1313.97	−0.975093
$123$	−2013.37	−1.47593
$124$	−2691.13	−1.94895
$125$	1416.22	1.01337
$126$	−479.202	−0.338815
$127$	969.403	0.677328	0.338664	−	0.940907i	$-0.390025\pi$
$127$	969.403	0.677328	0.338664	+	0.940907i	$0.390025\pi$
$128$	1041.18	0.718973
$129$	−437.082	−0.298317
$130$	0	0
$131$	−2614.84	−1.74396	−0.871982	−	0.489538i	$-0.837165\pi$
$131$	−2614.84	−1.74396	−0.871982	+	0.489538i	$0.837165\pi$
$132$	−513.059	−0.338304
$133$	−1299.17	−0.847008
$134$	1003.32	0.646819
$135$	−1065.72	−0.679425
$136$	−560.100	−0.353148
$137$	−2843.30	−1.77314	−0.886568	−	0.462599i	$-0.846917\pi$
$137$	−2843.30	−1.77314	−0.886568	+	0.462599i	$0.846917\pi$
$138$	1018.36	0.628175
$139$	1067.01	0.651097	0.325548	−	0.945525i	$-0.394451\pi$
$139$	1067.01	0.651097	0.325548	+	0.945525i	$0.394451\pi$
$140$	1551.82	0.936807
$141$	2844.06	1.69867
$142$	2043.54	1.20768
$143$	0	0
$144$	228.054	0.131976
$145$	−1666.80	−0.954623
$146$	−870.167	−0.493257
$147$	−644.632	−0.361690
$148$	−511.000	−0.283810
$149$	−2262.74	−1.24410	−0.622050	−	0.782977i	$-0.713700\pi$
$149$	−2262.74	−1.24410	−0.622050	+	0.782977i	$0.713700\pi$
$150$	−1480.73	−0.806008
$151$	910.311	0.490597	0.245298	−	0.969448i	$-0.421114\pi$
$151$	910.311	0.490597	0.245298	+	0.969448i	$0.421114\pi$
$152$	−497.098	−0.265263
$153$	−343.997	−0.181768
$154$	1022.85	0.535216
$155$	1912.37	0.991004
$156$	0	0
$157$	−2143.13	−1.08943	−0.544715	−	0.838621i	$-0.683362\pi$
$157$	−2143.13	−1.08943	−0.544715	+	0.838621i	$0.683362\pi$
$158$	−2602.09	−1.31020
$159$	−62.0291	−0.0309385
$160$	−1806.60	−0.892652
$161$	−1126.84	−0.551599
$162$	2388.47	1.15837
$163$	−795.705	−0.382358	−0.191179	−	0.981555i	$-0.561231\pi$
$163$	−795.705	−0.382358	−0.191179	+	0.981555i	$0.561231\pi$
$164$	4298.50	2.04668
$165$	364.591	0.172021
$166$	1177.90	0.550739
$167$	−3614.99	−1.67507	−0.837534	−	0.546385i	$-0.816004\pi$
$167$	−3614.99	−1.67507	−0.837534	+	0.546385i	$0.816004\pi$
$168$	−860.080	−0.394980
$169$	0	0
$170$	2007.05	0.905492
$171$	−305.303	−0.136533
$172$	933.159	0.413678
$173$	3401.12	1.49469	0.747347	−	0.664433i	$-0.231327\pi$
$173$	3401.12	1.49469	0.747347	+	0.664433i	$0.231327\pi$
$174$	4658.37	2.02960
$175$	1638.47	0.707753
$176$	−486.776	−0.208478
$177$	−230.537	−0.0978996
$178$	−3189.58	−1.34308
$179$	−2814.02	−1.17503	−0.587513	−	0.809214i	$-0.699893\pi$
$179$	−2814.02	−1.17503	−0.587513	+	0.809214i	$0.699893\pi$
$180$	364.677	0.151008
$181$	83.4174	0.0342562	0.0171281	−	0.999853i	$-0.494548\pi$
$181$	83.4174	0.0342562	0.0171281	+	0.999853i	$0.494548\pi$
$182$	0	0
$183$	−1448.42	−0.585084
$184$	−431.160	−0.172748
$185$	363.128	0.144312
$186$	−5344.70	−2.10695
$187$	734.253	0.287133
$188$	−6071.99	−2.35556
$189$	−3295.75	−1.26842
$190$	1781.29	0.680149
$191$	2642.78	1.00118	0.500588	−	0.865686i	$-0.333117\pi$
$191$	2642.78	1.00118	0.500588	+	0.865686i	$0.333117\pi$
$192$	3394.39	1.27588
$193$	2249.08	0.838821	0.419411	−	0.907797i	$-0.362237\pi$
$193$	2249.08	0.838821	0.419411	+	0.907797i	$0.362237\pi$
$194$	568.039	0.210221
$195$	0	0
$196$	1376.27	0.501558
$197$	−3387.41	−1.22509	−0.612545	−	0.790435i	$-0.709854\pi$
$197$	−3387.41	−1.22509	−0.612545	+	0.790435i	$0.709854\pi$
$198$	240.368	0.0862736
$199$	580.047	0.206625	0.103313	−	0.994649i	$-0.467056\pi$
$199$	580.047	0.206625	0.103313	+	0.994649i	$0.467056\pi$
$200$	626.924	0.221651
$201$	1105.99	0.388110
$202$	−1126.05	−0.392220
$203$	−5154.62	−1.78218
$204$	−3113.35	−1.06852
$205$	−3054.61	−1.04070
$206$	2197.12	0.743111
$207$	−264.806	−0.0889144
$208$	0	0
$209$	651.662	0.215677
$210$	3081.99	1.01275
$211$	−2628.70	−0.857665	−0.428833	−	0.903384i	$-0.641075\pi$
$211$	−2628.70	−0.857665	−0.428833	+	0.903384i	$0.641075\pi$
$212$	132.431	0.0429027
$213$	2252.64	0.724642
$214$	933.955	0.298336
$215$	−663.123	−0.210347
$216$	−1261.05	−0.397238
$217$	5914.06	1.85010
$218$	8660.46	2.69065
$219$	−959.206	−0.295969
$220$	−778.394	−0.238542
$221$	0	0
$222$	−1014.87	−0.306818
$223$	2393.89	0.718865	0.359432	−	0.933171i	$-0.382970\pi$
$223$	2393.89	0.718865	0.359432	+	0.933171i	$0.382970\pi$
$224$	−5586.95	−1.66649
$225$	385.039	0.114086
$226$	−1294.10	−0.380894
$227$	−4902.25	−1.43336	−0.716682	−	0.697400i	$-0.754340\pi$
$227$	−4902.25	−1.43336	−0.716682	+	0.697400i	$0.754340\pi$
$228$	−2763.15	−0.802606
$229$	−4644.63	−1.34029	−0.670143	−	0.742232i	$-0.733767\pi$
$229$	−4644.63	−1.34029	−0.670143	+	0.742232i	$0.733767\pi$
$230$	1545.01	0.442934
$231$	1127.51	0.321145
$232$	−1972.30	−0.558138
$233$	1240.22	0.348711	0.174355	−	0.984683i	$-0.444216\pi$
$233$	1240.22	0.348711	0.174355	+	0.984683i	$0.444216\pi$
$234$	0	0
$235$	4314.89	1.19776
$236$	492.191	0.135758
$237$	−2868.35	−0.786157
$238$	6206.84	1.69046
$239$	3091.87	0.836805	0.418402	−	0.908262i	$-0.362590\pi$
$239$	3091.87	0.836805	0.418402	+	0.908262i	$0.362590\pi$
$240$	−1466.73	−0.394488
$241$	−3964.99	−1.05978	−0.529891	−	0.848065i	$-0.677767\pi$
$241$	−3964.99	−1.05978	−0.529891	+	0.848065i	$0.677767\pi$
$242$	−513.059	−0.136284
$243$	−1424.86	−0.376152
$244$	3092.34	0.811340
$245$	−978.011	−0.255032
$246$	8537.00	2.21260
$247$	0	0
$248$	2262.88	0.579408
$249$	1298.43	0.330460
$250$	−6005.01	−1.51916
$251$	3703.27	0.931269	0.465635	−	0.884977i	$-0.345826\pi$
$251$	3703.27	0.931269	0.465635	+	0.884977i	$0.345826\pi$
$252$	1127.77	0.281916
$253$	565.222	0.140455
$254$	−4110.42	−1.01540
$255$	2212.42	0.543321
$256$	1395.01	0.340578
$257$	−3635.60	−0.882422	−0.441211	−	0.897403i	$-0.645451\pi$
$257$	−3635.60	−0.882422	−0.441211	+	0.897403i	$0.645451\pi$
$258$	1853.30	0.447214
$259$	1122.98	0.269416
$260$	0	0
$261$	−1211.33	−0.287278
$262$	11087.3	2.61441
$263$	7580.91	1.77741	0.888705	−	0.458480i	$-0.151606\pi$
$263$	7580.91	1.77741	0.888705	+	0.458480i	$0.151606\pi$
$264$	431.416	0.100575
$265$	−94.1081	−0.0218151
$266$	5508.67	1.26977
$267$	−3515.95	−0.805889
$268$	−2361.25	−0.538195
$269$	−5590.70	−1.26718	−0.633590	−	0.773669i	$-0.718419\pi$
$269$	−5590.70	−1.26718	−0.633590	+	0.773669i	$0.718419\pi$
$270$	4518.81	1.01854
$271$	7315.01	1.63969	0.819844	−	0.572587i	$-0.194060\pi$
$271$	7315.01	1.63969	0.819844	+	0.572587i	$0.194060\pi$
$272$	−2953.86	−0.658471
$273$	0	0
$274$	12056.0	2.65815
$275$	−821.856	−0.180217
$276$	−2396.63	−0.522682
$277$	3382.47	0.733693	0.366846	−	0.930282i	$-0.380437\pi$
$277$	3382.47	0.733693	0.366846	+	0.930282i	$0.380437\pi$
$278$	−4524.28	−0.976073
$279$	1389.80	0.298226
$280$	−1304.88	−0.278505
$281$	8791.63	1.86642	0.933211	−	0.359330i	$-0.116995\pi$
$281$	8791.63	1.86642	0.933211	+	0.359330i	$0.116995\pi$
$282$	−12059.3	−2.54652
$283$	−3057.43	−0.642210	−0.321105	−	0.947044i	$-0.604054\pi$
$283$	−3057.43	−0.642210	−0.321105	+	0.947044i	$0.604054\pi$
$284$	−4809.34	−1.00487
$285$	1963.56	0.408109
$286$	0	0
$287$	−9446.44	−1.94288
$288$	−1312.93	−0.268629
$289$	−457.397	−0.0930992
$290$	7067.50	1.43110
$291$	626.162	0.126138
$292$	2047.88	0.410422
$293$	3514.95	0.700838	0.350419	−	0.936593i	$-0.386039\pi$
$293$	3514.95	0.700838	0.350419	+	0.936593i	$0.386039\pi$
$294$	2733.34	0.542217
$295$	−349.762	−0.0690303
$296$	429.684	0.0843746
$297$	1653.15	0.322981
$298$	9594.38	1.86506
$299$	0	0
$300$	3484.80	0.670650
$301$	−2050.72	−0.392697
$302$	−3859.86	−0.735464
$303$	−1241.27	−0.235344
$304$	−2621.60	−0.494602
$305$	−2197.49	−0.412550
$306$	1458.60	0.272492
$307$	−2625.58	−0.488110	−0.244055	−	0.969761i	$-0.578478\pi$
$307$	−2625.58	−0.488110	−0.244055	+	0.969761i	$0.578478\pi$
$308$	−2407.20	−0.445334
$309$	2421.94	0.445888
$310$	−8108.76	−1.48564
$311$	1733.33	0.316040	0.158020	−	0.987436i	$-0.449489\pi$
$311$	1733.33	0.316040	0.158020	+	0.987436i	$0.449489\pi$
$312$	0	0
$313$	1841.16	0.332487	0.166243	−	0.986085i	$-0.446836\pi$
$313$	1841.16	0.332487	0.166243	+	0.986085i	$0.446836\pi$
$314$	9087.21	1.63319
$315$	−801.419	−0.143349
$316$	6123.86	1.09017
$317$	833.013	0.147592	0.0737960	−	0.997273i	$-0.476489\pi$
$317$	833.013	0.147592	0.0737960	+	0.997273i	$0.476489\pi$
$318$	263.013	0.0463806
$319$	2585.55	0.453803
$320$	5149.83	0.899639
$321$	1029.52	0.179010
$322$	4777.98	0.826914
$323$	3954.42	0.681207
$324$	−5621.10	−0.963838
$325$	0	0
$326$	3373.91	0.573202
$327$	9546.64	1.61447
$328$	−3614.47	−0.608463
$329$	13343.9	2.23609
$330$	−1545.92	−0.257880
$331$	9652.61	1.60289	0.801444	−	0.598070i	$-0.204066\pi$
$331$	9652.61	1.60289	0.801444	+	0.598070i	$0.204066\pi$
$332$	−2772.11	−0.458251
$333$	263.899	0.0434282
$334$	15328.1	2.51113
$335$	1677.96	0.273662
$336$	−4535.90	−0.736469
$337$	−763.625	−0.123434	−0.0617171	−	0.998094i	$-0.519658\pi$
$337$	−763.625	−0.123434	−0.0617171	+	0.998094i	$0.519658\pi$
$338$	0	0
$339$	−1426.51	−0.228547
$340$	−4723.46	−0.753428
$341$	−2966.49	−0.471098
$342$	1294.53	0.204679
$343$	4497.42	0.707981
$344$	−784.664	−0.122983
$345$	1703.10	0.265773
$346$	−14421.3	−2.24073
$347$	−8173.00	−1.26441	−0.632204	−	0.774802i	$-0.717850\pi$
$347$	−8173.00	−1.26441	−0.632204	+	0.774802i	$0.717850\pi$
$348$	−10963.2	−1.68876
$349$	5361.96	0.822404	0.411202	−	0.911544i	$-0.365109\pi$
$349$	5361.96	0.822404	0.411202	+	0.911544i	$0.365109\pi$
$350$	−6947.37	−1.06101
$351$	0	0
$352$	2802.41	0.424344
$353$	−8837.64	−1.33252	−0.666261	−	0.745719i	$-0.732106\pi$
$353$	−8837.64	−1.33252	−0.666261	+	0.745719i	$0.732106\pi$
$354$	977.514	0.146763
$355$	3417.62	0.510954
$356$	7506.46	1.11753
$357$	6841.95	1.01433
$358$	11931.9	1.76151
$359$	3018.10	0.443702	0.221851	−	0.975081i	$-0.428790\pi$
$359$	3018.10	0.443702	0.221851	+	0.975081i	$0.428790\pi$
$360$	−306.645	−0.0448934
$361$	−3349.39	−0.488320
$362$	−353.703	−0.0513542
$363$	−565.557	−0.0817742
$364$	0	0
$365$	−1455.27	−0.208691
$366$	6141.53	0.877112
$367$	10177.0	1.44751	0.723754	−	0.690058i	$-0.242415\pi$
$367$	10177.0	1.44751	0.723754	+	0.690058i	$0.242415\pi$
$368$	−2273.86	−0.322101
$369$	−2219.90	−0.313180
$370$	−1539.72	−0.216341
$371$	−291.031	−0.0407267
$372$	12578.4	1.75312
$373$	7046.39	0.978145	0.489073	−	0.872243i	$-0.337335\pi$
$373$	7046.39	0.978145	0.489073	+	0.872243i	$0.337335\pi$
$374$	−3113.35	−0.430448
$375$	−6619.46	−0.911540
$376$	5105.75	0.700290
$377$	0	0
$378$	13974.5	1.90151
$379$	7985.27	1.08226	0.541129	−	0.840939i	$-0.317997\pi$
$379$	7985.27	1.08226	0.541129	+	0.840939i	$0.317997\pi$
$380$	−4192.14	−0.565928
$381$	−4531.01	−0.609267
$382$	−11205.8	−1.50088
$383$	−3978.90	−0.530841	−0.265421	−	0.964133i	$-0.585511\pi$
$383$	−3978.90	−0.530841	−0.265421	+	0.964133i	$0.585511\pi$
$384$	−4866.52	−0.646728
$385$	1710.61	0.226443
$386$	−9536.46	−1.25750
$387$	−481.918	−0.0633004
$388$	−1336.84	−0.174917
$389$	15195.4	1.98056	0.990281	−	0.139080i	$-0.0444145\pi$
$389$	15195.4	1.98056	0.990281	+	0.139080i	$0.0444145\pi$
$390$	0	0
$391$	3429.89	0.443624
$392$	−1157.27	−0.149109
$393$	12221.8	1.56872
$394$	14363.1	1.83656
$395$	−4351.75	−0.554330
$396$	−565.689	−0.0717852
$397$	14186.5	1.79346	0.896728	−	0.442582i	$-0.145938\pi$
$397$	14186.5	1.79346	0.896728	+	0.442582i	$0.145938\pi$
$398$	−2459.49	−0.309756
$399$	6072.34	0.761898
$400$	3306.28	0.413285
$401$	−951.991	−0.118554	−0.0592770	−	0.998242i	$-0.518880\pi$
$401$	−951.991	−0.118554	−0.0592770	+	0.998242i	$0.518880\pi$
$402$	−4689.55	−0.581825
$403$	0	0
$404$	2650.08	0.326353
$405$	3994.48	0.490092
$406$	21856.4	2.67171
$407$	−563.287	−0.0686022
$408$	2617.92	0.317663
$409$	−8933.82	−1.08007	−0.540035	−	0.841642i	$-0.681589\pi$
$409$	−8933.82	−1.08007	−0.540035	+	0.841642i	$0.681589\pi$
$410$	12952.0	1.56013
$411$	13289.7	1.59496
$412$	−5170.79	−0.618317
$413$	−1081.65	−0.128873
$414$	1122.82	0.133294
$415$	1969.92	0.233011
$416$	0	0
$417$	−4987.22	−0.585672
$418$	−2763.15	−0.323325
$419$	−2318.98	−0.270381	−0.135190	−	0.990820i	$-0.543165\pi$
$419$	−2318.98	−0.270381	−0.135190	+	0.990820i	$0.543165\pi$
$420$	−7253.26	−0.842673
$421$	−8670.81	−1.00378	−0.501888	−	0.864933i	$-0.667361\pi$
$421$	−8670.81	−1.00378	−0.501888	+	0.864933i	$0.667361\pi$
$422$	11146.1	1.28574
$423$	3135.80	0.360444
$424$	−111.357	−0.0127546
$425$	−4987.20	−0.569211
$426$	−9551.57	−1.08633
$427$	−6795.78	−0.770189
$428$	−2198.00	−0.248235
$429$	0	0
$430$	2811.75	0.315336
$431$	14566.2	1.62790	0.813952	−	0.580932i	$-0.197312\pi$
$431$	14566.2	1.62790	0.813952	+	0.580932i	$0.197312\pi$
$432$	−6650.53	−0.740680
$433$	−7554.66	−0.838462	−0.419231	−	0.907880i	$-0.637700\pi$
$433$	−7554.66	−0.838462	−0.419231	+	0.907880i	$0.637700\pi$
$434$	−25076.5	−2.77353
$435$	7790.67	0.858699
$436$	−20381.8	−2.23879
$437$	3044.08	0.333222
$438$	4067.18	0.443693
$439$	−5581.68	−0.606832	−0.303416	−	0.952858i	$-0.598127\pi$
$439$	−5581.68	−0.606832	−0.303416	+	0.952858i	$0.598127\pi$
$440$	654.527	0.0709167
$441$	−710.759	−0.0767475
$442$	0	0
$443$	−2734.15	−0.293236	−0.146618	−	0.989193i	$-0.546839\pi$
$443$	−2734.15	−0.293236	−0.146618	+	0.989193i	$0.546839\pi$
$444$	2388.43	0.255292
$445$	−5334.26	−0.568243
$446$	−10150.5	−1.07767
$447$	10576.1	1.11909
$448$	15926.0	1.67953
$449$	3874.13	0.407197	0.203599	−	0.979054i	$-0.434736\pi$
$449$	3874.13	0.407197	0.203599	+	0.979054i	$0.434736\pi$
$450$	−1632.62	−0.171028
$451$	4738.33	0.494721
$452$	3045.57	0.316928
$453$	−4254.82	−0.441300
$454$	20786.3	2.14879
$455$	0	0
$456$	2323.45	0.238608
$457$	4639.46	0.474890	0.237445	−	0.971401i	$-0.423690\pi$
$457$	4639.46	0.474890	0.237445	+	0.971401i	$0.423690\pi$
$458$	19693.9	2.00925
$459$	10031.7	1.02012
$460$	−3636.08	−0.368550
$461$	11086.5	1.12007	0.560033	−	0.828471i	$-0.310789\pi$
$461$	11086.5	1.12007	0.560033	+	0.828471i	$0.310789\pi$
$462$	−4780.81	−0.481436
$463$	404.461	0.0405981	0.0202990	−	0.999794i	$-0.493538\pi$
$463$	404.461	0.0405981	0.0202990	+	0.999794i	$0.493538\pi$
$464$	−10401.5	−1.04069
$465$	−8938.48	−0.891424
$466$	−5258.73	−0.522760
$467$	3379.87	0.334908	0.167454	−	0.985880i	$-0.446446\pi$
$467$	3379.87	0.334908	0.167454	+	0.985880i	$0.446446\pi$
$468$	0	0
$469$	5189.12	0.510898
$470$	−18295.8	−1.79558
$471$	10017.1	0.979960
$472$	−413.868	−0.0403598
$473$	1028.64	0.0999937
$474$	12162.3	1.17855
$475$	−4426.22	−0.427555
$476$	−14607.4	−1.40657
$477$	−68.3920	−0.00656490
$478$	−13110.0	−1.25447
$479$	20773.9	1.98159	0.990796	−	0.135362i	$-0.0432196\pi$
$479$	20773.9	1.98159	0.990796	+	0.135362i	$0.0432196\pi$
$480$	8444.10	0.802956
$481$	0	0
$482$	16812.2	1.58874
$483$	5266.88	0.496172
$484$	1207.45	0.113397
$485$	949.989	0.0889418
$486$	6041.64	0.563898
$487$	−19174.2	−1.78412	−0.892062	−	0.451914i	$-0.850742\pi$
$487$	−19174.2	−1.78412	−0.892062	+	0.451914i	$0.850742\pi$
$488$	−2600.25	−0.241205
$489$	3719.14	0.343938
$490$	4146.92	0.382324
$491$	−10932.0	−1.00480	−0.502399	−	0.864636i	$-0.667549\pi$
$491$	−10932.0	−1.00480	−0.502399	+	0.864636i	$0.667549\pi$
$492$	−20091.3	−1.84103
$493$	15689.7	1.43332
$494$	0	0
$495$	401.991	0.0365014
$496$	11934.0	1.08035
$497$	10569.1	0.953899
$498$	−5505.53	−0.495399
$499$	1703.59	0.152832	0.0764162	−	0.997076i	$-0.475652\pi$
$499$	1703.59	0.152832	0.0764162	+	0.997076i	$0.475652\pi$
$500$	14132.4	1.26404
$501$	16896.6	1.50675
$502$	−15702.5	−1.39609
$503$	−11735.8	−1.04030	−0.520151	−	0.854074i	$-0.674124\pi$
$503$	−11735.8	−1.04030	−0.520151	+	0.854074i	$0.674124\pi$
$504$	−948.307	−0.0838114
$505$	−1883.21	−0.165944
$506$	−2396.63	−0.210560
$507$	0	0
$508$	9673.60	0.844875
$509$	10412.6	0.906736	0.453368	−	0.891323i	$-0.350222\pi$
$509$	10412.6	0.906736	0.453368	+	0.891323i	$0.350222\pi$
$510$	−9381.00	−0.814505
$511$	−4500.45	−0.389605
$512$	−14244.5	−1.22954
$513$	8903.25	0.766254
$514$	15415.5	1.32286
$515$	3674.48	0.314401
$516$	−4361.61	−0.372111
$517$	−6693.30	−0.569383
$518$	−4761.62	−0.403887
$519$	−15896.9	−1.34450
$520$	0	0
$521$	−1352.97	−0.113771	−0.0568854	−	0.998381i	$-0.518117\pi$
$521$	−1352.97	−0.113771	−0.0568854	+	0.998381i	$0.518117\pi$
$522$	5136.23	0.430664
$523$	−11349.5	−0.948912	−0.474456	−	0.880279i	$-0.657355\pi$
$523$	−11349.5	−0.948912	−0.474456	+	0.880279i	$0.657355\pi$
$524$	−26093.3	−2.17536
$525$	−7658.25	−0.636635
$526$	−32144.2	−2.66455
$527$	−18001.3	−1.48795
$528$	2275.21	0.187530
$529$	−9526.70	−0.782995
$530$	399.033	0.0327036
$531$	−254.186	−0.0207735
$532$	−12964.3	−1.05653
$533$	0	0
$534$	14908.2	1.20813
$535$	1561.95	0.126222
$536$	1985.50	0.160001
$537$	13152.8	1.05696
$538$	23705.5	1.89966
$539$	1517.10	0.121236
$540$	−10634.7	−0.847491
$541$	2095.88	0.166560	0.0832800	−	0.996526i	$-0.473460\pi$
$541$	2095.88	0.166560	0.0832800	+	0.996526i	$0.473460\pi$
$542$	−31016.8	−2.45809
$543$	−389.895	−0.0308140
$544$	17005.6	1.34028
$545$	14483.8	1.13838
$546$	0	0
$547$	−5559.49	−0.434564	−0.217282	−	0.976109i	$-0.569719\pi$
$547$	−5559.49	−0.434564	−0.217282	+	0.976109i	$0.569719\pi$
$548$	−28373.1	−2.21175
$549$	−1597.00	−0.124150
$550$	3484.80	0.270168
$551$	13924.9	1.07662
$552$	2015.25	0.155389
$553$	−13457.9	−1.03488
$554$	−14342.2	−1.09989
$555$	−1697.27	−0.129811
$556$	10647.6	0.812156
$557$	9561.11	0.727320	0.363660	−	0.931532i	$-0.381527\pi$
$557$	9561.11	0.727320	0.363660	+	0.931532i	$0.381527\pi$
$558$	−5892.96	−0.447077
$559$	0	0
$560$	−6881.69	−0.519294
$561$	−3431.92	−0.258281
$562$	−37277.9	−2.79799
$563$	1311.44	0.0981714	0.0490857	−	0.998795i	$-0.484369\pi$
$563$	1311.44	0.0981714	0.0490857	+	0.998795i	$0.484369\pi$
$564$	28380.7	2.11887
$565$	−2164.25	−0.161152
$566$	12964.0	0.962751
$567$	12353.0	0.914953
$568$	4044.02	0.298739
$569$	10477.5	0.771949	0.385975	−	0.922509i	$-0.373865\pi$
$569$	10477.5	0.771949	0.385975	+	0.922509i	$0.373865\pi$
$570$	−8325.79	−0.611805
$571$	−21757.4	−1.59460	−0.797302	−	0.603581i	$-0.793740\pi$
$571$	−21757.4	−1.59460	−0.797302	+	0.603581i	$0.793740\pi$
$572$	0	0
$573$	−12352.4	−0.900574
$574$	40054.4	2.91261
$575$	−3839.10	−0.278438
$576$	3742.59	0.270731
$577$	929.841	0.0670880	0.0335440	−	0.999437i	$-0.489321\pi$
$577$	929.841	0.0670880	0.0335440	+	0.999437i	$0.489321\pi$
$578$	1939.43	0.139567
$579$	−10512.3	−0.754534
$580$	−16632.9	−1.19076
$581$	6092.03	0.435008
$582$	−2655.03	−0.189097
$583$	145.981	0.0103704
$584$	−1722.00	−0.122015
$585$	0	0
$586$	−14903.9	−1.05064
$587$	−26386.5	−1.85534	−0.927671	−	0.373398i	$-0.878192\pi$
$587$	−26386.5	−1.85534	−0.927671	+	0.373398i	$0.878192\pi$
$588$	−6432.74	−0.451159
$589$	−15976.4	−1.11765
$590$	1483.05	0.103485
$591$	15832.8	1.10199
$592$	2266.07	0.157323
$593$	13062.4	0.904568	0.452284	−	0.891874i	$-0.350609\pi$
$593$	13062.4	0.904568	0.452284	+	0.891874i	$0.350609\pi$
$594$	−7009.61	−0.484188
$595$	10380.3	0.715214
$596$	−22579.7	−1.55185
$597$	−2711.15	−0.185863
$598$	0	0
$599$	−8132.90	−0.554760	−0.277380	−	0.960760i	$-0.589466\pi$
$599$	−8132.90	−0.554760	−0.277380	+	0.960760i	$0.589466\pi$
$600$	−2930.26	−0.199379
$601$	22217.0	1.50790	0.753951	−	0.656930i	$-0.228145\pi$
$601$	22217.0	1.50790	0.753951	+	0.656930i	$0.228145\pi$
$602$	8695.39	0.588700
$603$	1219.44	0.0823538
$604$	9083.93	0.611954
$605$	−858.041	−0.0576601
$606$	5263.18	0.352809
$607$	4888.27	0.326868	0.163434	−	0.986554i	$-0.447743\pi$
$607$	4888.27	0.326868	0.163434	+	0.986554i	$0.447743\pi$
$608$	15092.8	1.00673
$609$	24092.8	1.60310
$610$	9317.69	0.618463
$611$	0	0
$612$	−3432.72	−0.226731
$613$	−28779.2	−1.89621	−0.948107	−	0.317952i	$-0.897005\pi$
$613$	−28779.2	−1.89621	−0.948107	+	0.317952i	$0.897005\pi$
$614$	11132.9	0.731736
$615$	14277.3	0.936125
$616$	2024.14	0.132394
$617$	20851.5	1.36053	0.680267	−	0.732965i	$-0.261864\pi$
$617$	20851.5	1.36053	0.680267	+	0.732965i	$0.261864\pi$
$618$	−10269.4	−0.668441
$619$	−14647.2	−0.951086	−0.475543	−	0.879692i	$-0.657748\pi$
$619$	−14647.2	−0.951086	−0.475543	+	0.879692i	$0.657748\pi$
$620$	19083.4	1.23614
$621$	7722.28	0.499009
$622$	−7349.61	−0.473782
$623$	−16496.3	−1.06085
$624$	0	0
$625$	−703.515	−0.0450250
$626$	−7806.79	−0.498438
$627$	−3045.88	−0.194005
$628$	−21386.2	−1.35892
$629$	−3418.14	−0.216678
$630$	3398.14	0.214897
$631$	27274.6	1.72074	0.860369	−	0.509672i	$-0.170233\pi$
$631$	27274.6	1.72074	0.860369	+	0.509672i	$0.170233\pi$
$632$	−5149.36	−0.324099
$633$	12286.6	0.771484
$634$	−3532.11	−0.221258
$635$	−6874.28	−0.429602
$636$	−618.984	−0.0385917
$637$	0	0
$638$	−10963.2	−0.680307
$639$	2483.72	0.153763
$640$	−7383.29	−0.456016
$641$	−31976.9	−1.97038	−0.985188	−	0.171475i	$-0.945147\pi$
$641$	−31976.9	−1.97038	−0.985188	+	0.171475i	$0.945147\pi$
$642$	−4365.33	−0.268358
$643$	−20735.0	−1.27171	−0.635854	−	0.771809i	$-0.719352\pi$
$643$	−20735.0	−1.27171	−0.635854	+	0.771809i	$0.719352\pi$
$644$	−11244.7	−0.688045
$645$	3099.46	0.189211
$646$	−16767.4	−1.02121
$647$	−28082.8	−1.70641	−0.853207	−	0.521572i	$-0.825346\pi$
$647$	−28082.8	−1.70641	−0.853207	+	0.521572i	$0.825346\pi$
$648$	4726.61	0.286541
$649$	542.554	0.0328152
$650$	0	0
$651$	−27642.5	−1.66420
$652$	−7940.28	−0.476941
$653$	−16318.0	−0.977907	−0.488954	−	0.872310i	$-0.662621\pi$
$653$	−16318.0	−0.977907	−0.488954	+	0.872310i	$0.662621\pi$
$654$	−40479.2	−2.42028
$655$	18542.4	1.10613
$656$	−19062.0	−1.13452
$657$	−1057.60	−0.0628021
$658$	−56580.3	−3.35217
$659$	19663.7	1.16235	0.581176	−	0.813778i	$-0.302593\pi$
$659$	19663.7	1.16235	0.581176	+	0.813778i	$0.302593\pi$
$660$	3638.23	0.214573
$661$	29680.0	1.74648	0.873238	−	0.487295i	$-0.162016\pi$
$661$	29680.0	1.74648	0.873238	+	0.487295i	$0.162016\pi$
$662$	−40928.6	−2.40292
$663$	0	0
$664$	2330.98	0.136234
$665$	9212.72	0.537224
$666$	−1118.97	−0.0651042
$667$	12077.8	0.701130
$668$	−36073.7	−2.08942
$669$	−11189.1	−0.646631
$670$	−7114.80	−0.410252
$671$	3408.76	0.196116
$672$	26113.6	1.49904
$673$	−3409.13	−0.195264	−0.0976318	−	0.995223i	$-0.531127\pi$
$673$	−3409.13	−0.195264	−0.0976318	+	0.995223i	$0.531127\pi$
$674$	3237.89	0.185043
$675$	−11228.5	−0.640275
$676$	0	0
$677$	3762.66	0.213605	0.106803	−	0.994280i	$-0.465939\pi$
$677$	3762.66	0.213605	0.106803	+	0.994280i	$0.465939\pi$
$678$	6048.64	0.342620
$679$	2937.86	0.166045
$680$	3971.81	0.223988
$681$	22913.2	1.28934
$682$	12578.4	0.706233
$683$	4032.46	0.225912	0.112956	−	0.993600i	$-0.463968\pi$
$683$	4032.46	0.225912	0.112956	+	0.993600i	$0.463968\pi$
$684$	−3046.60	−0.170306
$685$	20162.5	1.12463
$686$	−19069.7	−1.06135
$687$	21709.1	1.20561
$688$	−4138.17	−0.229312
$689$	0	0
$690$	−7221.41	−0.398427
$691$	−4066.80	−0.223891	−0.111945	−	0.993714i	$-0.535708\pi$
$691$	−4066.80	−0.223891	−0.111945	+	0.993714i	$0.535708\pi$
$692$	33939.5	1.86443
$693$	1243.17	0.0681443
$694$	34654.8	1.89550
$695$	−7566.42	−0.412965
$696$	9218.59	0.502054
$697$	28753.2	1.56256
$698$	−22735.5	−1.23288
$699$	−5796.83	−0.313671
$700$	16350.2	0.882827
$701$	−4431.35	−0.238759	−0.119379	−	0.992849i	$-0.538090\pi$
$701$	−4431.35	−0.238759	−0.119379	+	0.992849i	$0.538090\pi$
$702$	0	0
$703$	−3033.66	−0.162755
$704$	−7988.46	−0.427665
$705$	−20167.9	−1.07740
$706$	37473.0	1.99761
$707$	−5823.86	−0.309800
$708$	−2300.51	−0.122117
$709$	23644.0	1.25243	0.626213	−	0.779652i	$-0.284604\pi$
$709$	23644.0	1.25243	0.626213	+	0.779652i	$0.284604\pi$
$710$	−14491.3	−0.765982
$711$	−3162.59	−0.166816
$712$	−6311.95	−0.332234
$713$	−13857.2	−0.727851
$714$	−29010.9	−1.52060
$715$	0	0
$716$	−28080.9	−1.46569
$717$	−14451.5	−0.752720
$718$	−12797.2	−0.665164
$719$	19407.6	1.00665	0.503325	−	0.864097i	$-0.332110\pi$
$719$	19407.6	1.00665	0.503325	+	0.864097i	$0.332110\pi$
$720$	−1617.19	−0.0837071
$721$	11363.4	0.586956
$722$	14201.9	0.732051
$723$	18532.5	0.953292
$724$	832.416	0.0427300
$725$	−17561.6	−0.899616
$726$	2398.05	0.122590
$727$	1282.55	0.0654293	0.0327147	−	0.999465i	$-0.489585\pi$
$727$	1282.55	0.0654293	0.0327147	+	0.999465i	$0.489585\pi$
$728$	0	0
$729$	21868.9	1.11105
$730$	6170.57	0.312854
$731$	6242.02	0.315827
$732$	−14453.7	−0.729814
$733$	26511.4	1.33591	0.667953	−	0.744203i	$-0.267171\pi$
$733$	26511.4	1.33591	0.667953	+	0.744203i	$0.267171\pi$
$734$	−43152.1	−2.16999
$735$	4571.25	0.229405
$736$	13090.8	0.655616
$737$	−2602.86	−0.130092
$738$	9412.74	0.469495
$739$	26682.3	1.32818	0.664090	−	0.747653i	$-0.268819\pi$
$739$	26682.3	1.32818	0.664090	+	0.747653i	$0.268819\pi$
$740$	3623.63	0.180010
$741$	0	0
$742$	1234.02	0.0610542
$743$	−23434.9	−1.15712	−0.578562	−	0.815639i	$-0.696386\pi$
$743$	−23434.9	−1.15712	−0.578562	+	0.815639i	$0.696386\pi$
$744$	−10576.8	−0.521187
$745$	16045.7	0.789084
$746$	−29877.8	−1.46636
$747$	1431.62	0.0701208
$748$	7327.06	0.358160
$749$	4830.36	0.235644
$750$	28067.6	1.36651
$751$	−7130.60	−0.346470	−0.173235	−	0.984881i	$-0.555422\pi$
$751$	−7130.60	−0.346470	−0.173235	+	0.984881i	$0.555422\pi$
$752$	26926.8	1.30574
$753$	−17309.2	−0.837692
$754$	0	0
$755$	−6455.24	−0.311166
$756$	−32888.1	−1.58218
$757$	−3099.17	−0.148799	−0.0743997	−	0.997228i	$-0.523704\pi$
$757$	−3099.17	−0.148799	−0.0743997	+	0.997228i	$0.523704\pi$
$758$	−33858.8	−1.62244
$759$	−2641.86	−0.126342
$760$	3525.04	0.168246
$761$	−13473.1	−0.641789	−0.320894	−	0.947115i	$-0.603983\pi$
$761$	−13473.1	−0.641789	−0.320894	+	0.947115i	$0.603983\pi$
$762$	19212.2	0.913366
$763$	44791.4	2.12524
$764$	26372.1	1.24883
$765$	2439.37	0.115288
$766$	16871.2	0.795796
$767$	0	0
$768$	−6520.31	−0.306356
$769$	6731.80	0.315676	0.157838	−	0.987465i	$-0.449548\pi$
$769$	6731.80	0.315676	0.157838	+	0.987465i	$0.449548\pi$
$770$	−7253.25	−0.339466
$771$	16992.9	0.793753
$772$	22443.4	1.04632
$773$	−37119.1	−1.72714	−0.863571	−	0.504227i	$-0.831778\pi$
$773$	−37119.1	−1.72714	−0.863571	+	0.504227i	$0.831778\pi$
$774$	2043.41	0.0948950
$775$	20149.0	0.933901
$776$	1124.11	0.0520014
$777$	−5248.84	−0.242344
$778$	−64431.0	−2.96910
$779$	25518.9	1.17370
$780$	0	0
$781$	−5301.45	−0.242895
$782$	−14543.3	−0.665046
$783$	35324.8	1.61227
$784$	−6103.20	−0.278025
$785$	15197.5	0.690983
$786$	−51822.4	−2.35171
$787$	9400.60	0.425788	0.212894	−	0.977075i	$-0.431711\pi$
$787$	9400.60	0.425788	0.212894	+	0.977075i	$0.431711\pi$
$788$	−33802.7	−1.52814
$789$	−35433.4	−1.59881
$790$	18452.1	0.831008
$791$	−6692.99	−0.300854
$792$	475.670	0.0213412
$793$	0	0
$794$	−60153.1	−2.68861
$795$	439.863	0.0196231
$796$	5788.25	0.257737
$797$	31897.0	1.41763	0.708815	−	0.705395i	$-0.249230\pi$
$797$	31897.0	1.41763	0.708815	+	0.705395i	$0.249230\pi$
$798$	−25747.7	−1.14218
$799$	−40616.3	−1.79838
$800$	−19034.6	−0.841216
$801$	−3876.62	−0.171003
$802$	4036.59	0.177727
$803$	2257.43	0.0992065
$804$	11036.5	0.484116
$805$	7990.70	0.349857
$806$	0	0
$807$	26131.1	1.13985
$808$	−2228.37	−0.0970220
$809$	−31105.0	−1.35179	−0.675893	−	0.737000i	$-0.736242\pi$
$809$	−31105.0	−1.35179	−0.675893	+	0.737000i	$0.736242\pi$
$810$	−16937.2	−0.734708
$811$	−16013.6	−0.693359	−0.346679	−	0.937984i	$-0.612691\pi$
$811$	−16013.6	−0.693359	−0.346679	+	0.937984i	$0.612691\pi$
$812$	−51437.6	−2.22304
$813$	−34190.6	−1.47493
$814$	2388.42	0.102843
$815$	5642.54	0.242515
$816$	13806.4	0.592306
$817$	5539.89	0.237229
$818$	37880.8	1.61916
$819$	0	0
$820$	−30481.7	−1.29813
$821$	−8078.04	−0.343393	−0.171696	−	0.985150i	$-0.554925\pi$
$821$	−8078.04	−0.343393	−0.171696	+	0.985150i	$0.554925\pi$
$822$	−56350.2	−2.39105
$823$	−9380.35	−0.397301	−0.198650	−	0.980070i	$-0.563656\pi$
$823$	−9380.35	−0.397301	−0.198650	+	0.980070i	$0.563656\pi$
$824$	4347.95	0.183821
$825$	3841.38	0.162109
$826$	4586.35	0.193196
$827$	228.009	0.00958723	0.00479361	−	0.999989i	$-0.498474\pi$
$827$	228.009	0.00958723	0.00479361	+	0.999989i	$0.498474\pi$
$828$	−2642.48	−0.110909
$829$	37075.9	1.55331	0.776657	−	0.629923i	$-0.216914\pi$
$829$	37075.9	1.55331	0.776657	+	0.629923i	$0.216914\pi$
$830$	−8352.78	−0.349312
$831$	−15809.7	−0.659969
$832$	0	0
$833$	9206.07	0.382919
$834$	21146.6	0.877994
$835$	25634.8	1.06243
$836$	6502.89	0.269028
$837$	−40529.3	−1.67371
$838$	9832.83	0.405333
$839$	−3197.98	−0.131593	−0.0657964	−	0.997833i	$-0.520959\pi$
$839$	−3197.98	−0.131593	−0.0657964	+	0.997833i	$0.520959\pi$
$840$	6099.04	0.250520
$841$	30859.7	1.26531
$842$	36765.6	1.50478
$843$	−41092.3	−1.67888
$844$	−26231.6	−1.06982
$845$	0	0
$846$	−13296.3	−0.540350
$847$	−2653.51	−0.107645
$848$	−587.274	−0.0237819
$849$	14290.5	0.577679
$850$	21146.5	0.853316
$851$	−2631.26	−0.105991
$852$	22479.0	0.903893
$853$	−21166.3	−0.849615	−0.424808	−	0.905284i	$-0.639658\pi$
$853$	−21166.3	−0.849615	−0.424808	+	0.905284i	$0.639658\pi$
$854$	28815.2	1.15461
$855$	2164.98	0.0865973
$856$	1848.23	0.0737981
$857$	16653.9	0.663813	0.331906	−	0.943312i	$-0.392308\pi$
$857$	16653.9	0.663813	0.331906	+	0.943312i	$0.392308\pi$
$858$	0	0
$859$	−21558.3	−0.856296	−0.428148	−	0.903709i	$-0.640834\pi$
$859$	−21558.3	−0.856296	−0.428148	+	0.903709i	$0.640834\pi$
$860$	−6617.26	−0.262380
$861$	44152.9	1.74765
$862$	−61762.8	−2.44043
$863$	−34009.4	−1.34148	−0.670738	−	0.741694i	$-0.734022\pi$
$863$	−34009.4	−1.34148	−0.670738	+	0.741694i	$0.734022\pi$
$864$	38287.7	1.50761
$865$	−24118.2	−0.948026
$866$	32033.0	1.25696
$867$	2137.88	0.0837443
$868$	59016.0	2.30776
$869$	6750.46	0.263514
$870$	−33033.7	−1.28729
$871$	0	0
$872$	17138.4	0.665575
$873$	690.394	0.0267655
$874$	−12907.4	−0.499541
$875$	−31057.5	−1.19993
$876$	−9571.85	−0.369181
$877$	26342.8	1.01429	0.507145	−	0.861861i	$-0.330701\pi$
$877$	26342.8	1.01429	0.507145	+	0.861861i	$0.330701\pi$
$878$	23667.2	0.909715
$879$	−16429.0	−0.630415
$880$	3451.85	0.132229
$881$	−11157.3	−0.426672	−0.213336	−	0.976979i	$-0.568433\pi$
$881$	−11157.3	−0.426672	−0.213336	+	0.976979i	$0.568433\pi$
$882$	3013.73	0.115054
$883$	−8074.37	−0.307728	−0.153864	−	0.988092i	$-0.549172\pi$
$883$	−8074.37	−0.307728	−0.153864	+	0.988092i	$0.549172\pi$
$884$	0	0
$885$	1634.80	0.0620939
$886$	11593.2	0.439597
$887$	5859.32	0.221800	0.110900	−	0.993832i	$-0.464627\pi$
$887$	5859.32	0.221800	0.110900	+	0.993832i	$0.464627\pi$
$888$	−2008.35	−0.0758963
$889$	−21258.9	−0.802024
$890$	22618.1	0.851865
$891$	−6196.27	−0.232977
$892$	23888.5	0.896687
$893$	−36047.7	−1.35083
$894$	−44844.4	−1.67765
$895$	19954.9	0.745273
$896$	−22833.0	−0.851336
$897$	0	0
$898$	−16426.9	−0.610438
$899$	−63388.6	−2.35164
$900$	3842.27	0.142306
$901$	885.844	0.0327544
$902$	−20091.3	−0.741647
$903$	9585.13	0.353237
$904$	−2560.92	−0.0942202
$905$	−591.534	−0.0217273
$906$	18041.1	0.661562
$907$	−25392.2	−0.929584	−0.464792	−	0.885420i	$-0.653871\pi$
$907$	−25392.2	−0.929584	−0.464792	+	0.885420i	$0.653871\pi$
$908$	−48919.2	−1.78793
$909$	−1368.60	−0.0499379
$910$	0	0
$911$	−29302.8	−1.06569	−0.532845	−	0.846213i	$-0.678877\pi$
$911$	−29302.8	−1.06569	−0.532845	+	0.846213i	$0.678877\pi$
$912$	12253.4	0.444903
$913$	−3055.76	−0.110768
$914$	−19672.0	−0.711918
$915$	10271.1	0.371096
$916$	−46348.4	−1.67183
$917$	57342.9	2.06503
$918$	−42535.8	−1.52929
$919$	48756.0	1.75007	0.875033	−	0.484062i	$-0.160839\pi$
$919$	48756.0	1.75007	0.875033	+	0.484062i	$0.160839\pi$
$920$	3057.46	0.109567
$921$	12272.0	0.439063
$922$	−47008.5	−1.67911
$923$	0	0
$924$	11251.3	0.400586
$925$	3825.96	0.135996
$926$	−1714.98	−0.0608615
$927$	2670.39	0.0946138
$928$	59882.6	2.11826
$929$	44326.0	1.56544	0.782718	−	0.622377i	$-0.213833\pi$
$929$	44326.0	1.56544	0.782718	+	0.622377i	$0.213833\pi$
$930$	37900.6	1.33635
$931$	8170.54	0.287625
$932$	12376.1	0.434970
$933$	−8101.65	−0.284283
$934$	−14331.2	−0.502067
$935$	−5206.77	−0.182117
$936$	0	0
$937$	−24188.6	−0.843338	−0.421669	−	0.906750i	$-0.638556\pi$
$937$	−24188.6	−0.843338	−0.421669	+	0.906750i	$0.638556\pi$
$938$	−22002.7	−0.765899
$939$	−8605.61	−0.299077
$940$	43058.0	1.49404
$941$	−41690.4	−1.44428	−0.722141	−	0.691746i	$-0.756842\pi$
$941$	−41690.4	−1.44428	−0.722141	+	0.691746i	$0.756842\pi$
$942$	−42473.9	−1.46908
$943$	22134.0	0.764349
$944$	−2182.66	−0.0752539
$945$	23371.0	0.804507
$946$	−4361.60	−0.149903
$947$	−58047.8	−1.99187	−0.995935	−	0.0900730i	$-0.971290\pi$
$947$	−58047.8	−1.99187	−0.995935	+	0.0900730i	$0.971290\pi$
$948$	−28623.1	−0.980626
$949$	0	0
$950$	18767.9	0.640958
$951$	−3893.53	−0.132762
$952$	12282.9	0.418163
$953$	3231.23	0.109832	0.0549160	−	0.998491i	$-0.482511\pi$
$953$	3231.23	0.109832	0.0549160	+	0.998491i	$0.482511\pi$
$954$	289.993	0.00984158
$955$	−18740.6	−0.635006
$956$	30853.5	1.04380
$957$	−12084.9	−0.408204
$958$	−88084.5	−2.97065
$959$	62353.1	2.09957
$960$	−24070.5	−0.809240
$961$	42936.7	1.44127
$962$	0	0
$963$	1135.13	0.0379845
$964$	−39566.4	−1.32194
$965$	−15948.8	−0.532031
$966$	−22332.4	−0.743822
$967$	−41056.2	−1.36533	−0.682667	−	0.730729i	$-0.739180\pi$
$967$	−41056.2	−1.36533	−0.682667	+	0.730729i	$0.739180\pi$
$968$	−1015.31	−0.0337120
$969$	−18483.1	−0.612757
$970$	−4028.10	−0.133335
$971$	33340.7	1.10191	0.550955	−	0.834535i	$-0.314264\pi$
$971$	33340.7	1.10191	0.550955	+	0.834535i	$0.314264\pi$
$972$	−14218.6	−0.469199
$973$	−23399.3	−0.770964
$974$	81301.8	2.67462
$975$	0	0
$976$	−13713.3	−0.449745
$977$	−4013.69	−0.131432	−0.0657161	−	0.997838i	$-0.520933\pi$
$977$	−4013.69	−0.131432	−0.0657161	+	0.997838i	$0.520933\pi$
$978$	−15769.8	−0.515604
$979$	8274.54	0.270128
$980$	−9759.50	−0.318118
$981$	10525.9	0.342576
$982$	46353.5	1.50631
$983$	868.813	0.0281901	0.0140950	−	0.999901i	$-0.495513\pi$
$983$	868.813	0.0281901	0.0140950	+	0.999901i	$0.495513\pi$
$984$	16894.1	0.547322
$985$	24021.0	0.777027
$986$	−66526.7	−2.14873
$987$	−62369.8	−2.01140
$988$	0	0
$989$	4805.05	0.154491
$990$	−1704.51	−0.0547200
$991$	14068.4	0.450958	0.225479	−	0.974248i	$-0.427605\pi$
$991$	14068.4	0.450958	0.225479	+	0.974248i	$0.427605\pi$
$992$	−68705.2	−2.19898
$993$	−45116.6	−1.44182
$994$	−44814.6	−1.43001
$995$	−4113.26	−0.131054
$996$	12956.9	0.412204
$997$	23082.2	0.733220	0.366610	−	0.930375i	$-0.380518\pi$
$997$	23082.2	0.733220	0.366610	+	0.930375i	$0.380518\pi$
$998$	−7223.51	−0.229114
$999$	−7695.84	−0.243729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.9	yes	51
13.12	even	2		1859.4.a.p.1.43	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.43	✓	51	13.12	even	2
1859.4.a.q.1.9	yes	51	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-4.24016 q^{2} -4.67403 q^{3} +9.97893 q^{4} -7.09125 q^{5} +19.8186 q^{6} -21.9298 q^{7} -8.39097 q^{8} -5.15349 q^{9} +O(q^{10})\)	\(q-4.24016 q^{2} -4.67403 q^{3} +9.97893 q^{4} -7.09125 q^{5} +19.8186 q^{6} -21.9298 q^{7} -8.39097 q^{8} -5.15349 q^{9} +30.0680 q^{10} +11.0000 q^{11} -46.6418 q^{12} +92.9860 q^{14} +33.1447 q^{15} -44.2524 q^{16} +66.7503 q^{17} +21.8516 q^{18} +59.2420 q^{19} -70.7631 q^{20} +102.501 q^{21} -46.6417 q^{22} +51.3838 q^{23} +39.2196 q^{24} -74.7142 q^{25} +150.286 q^{27} -218.836 q^{28} +235.050 q^{29} -140.539 q^{30} -269.681 q^{31} +254.765 q^{32} -51.4143 q^{33} -283.032 q^{34} +155.510 q^{35} -51.4263 q^{36} -51.2079 q^{37} -251.195 q^{38} +59.5024 q^{40} +430.757 q^{41} -434.619 q^{42} +93.5129 q^{43} +109.768 q^{44} +36.5447 q^{45} -217.875 q^{46} -608.482 q^{47} +206.837 q^{48} +137.918 q^{49} +316.800 q^{50} -311.993 q^{51} +13.2710 q^{53} -637.237 q^{54} -78.0037 q^{55} +184.013 q^{56} -276.899 q^{57} -996.651 q^{58} +49.3230 q^{59} +330.748 q^{60} +309.887 q^{61} +1143.49 q^{62} +113.015 q^{63} -726.224 q^{64} +218.005 q^{66} -236.624 q^{67} +666.097 q^{68} -240.169 q^{69} -659.387 q^{70} -481.950 q^{71} +43.2428 q^{72} +205.221 q^{73} +217.130 q^{74} +349.216 q^{75} +591.172 q^{76} -241.228 q^{77} +613.679 q^{79} +313.805 q^{80} -563.297 q^{81} -1826.48 q^{82} -277.796 q^{83} +1022.85 q^{84} -473.343 q^{85} -396.509 q^{86} -1098.63 q^{87} -92.3007 q^{88} +752.231 q^{89} -154.955 q^{90} +512.756 q^{92} +1260.49 q^{93} +2580.06 q^{94} -420.100 q^{95} -1190.78 q^{96} -133.966 q^{97} -584.794 q^{98} -56.6884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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