LMFDB - Embedded newform 209.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,4,Mod(1,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, 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("209.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	209.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:	$12.3313991912$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 91 x^{11} + 176 x^{10} + 3117 x^{9} - 5786 x^{8} - 49725 x^{7} + 87196 x^{6} + \cdots - 86016 $ x^13 - 2x^12 - 91x^11 + 176x^10 + 3117x^9 - 5786x^8 - 49725x^7 + 87196x^6 + 366602x^5 - 590896x^4 - 1017888x^3 + 1444096x^2 + 115200x - 86016
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.62918$ of defining polynomial
Character	$\chi$	$=$	209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.62918 q^{2} +10.0382 q^{3} +23.6877 q^{4} -2.17343 q^{5} -56.5070 q^{6} +1.58350 q^{7} -88.3091 q^{8} +73.7660 q^{9} +12.2346 q^{10} -11.0000 q^{11} +237.783 q^{12} +48.8093 q^{13} -8.91380 q^{14} -21.8174 q^{15} +307.606 q^{16} +50.8475 q^{17} -415.242 q^{18} -19.0000 q^{19} -51.4836 q^{20} +15.8955 q^{21} +61.9210 q^{22} -29.9557 q^{23} -886.467 q^{24} -120.276 q^{25} -274.757 q^{26} +469.447 q^{27} +37.5094 q^{28} +59.8413 q^{29} +122.814 q^{30} +229.019 q^{31} -1025.10 q^{32} -110.420 q^{33} -286.230 q^{34} -3.44162 q^{35} +1747.35 q^{36} +30.5522 q^{37} +106.955 q^{38} +489.959 q^{39} +191.934 q^{40} -44.1228 q^{41} -89.4787 q^{42} +279.983 q^{43} -260.565 q^{44} -160.325 q^{45} +168.626 q^{46} -337.116 q^{47} +3087.82 q^{48} -340.493 q^{49} +677.057 q^{50} +510.419 q^{51} +1156.18 q^{52} +108.326 q^{53} -2642.61 q^{54} +23.9077 q^{55} -139.837 q^{56} -190.726 q^{57} -336.857 q^{58} +147.196 q^{59} -516.804 q^{60} +457.035 q^{61} -1289.19 q^{62} +116.808 q^{63} +3309.63 q^{64} -106.084 q^{65} +621.577 q^{66} -265.095 q^{67} +1204.46 q^{68} -300.702 q^{69} +19.3735 q^{70} +746.973 q^{71} -6514.20 q^{72} -643.087 q^{73} -171.984 q^{74} -1207.36 q^{75} -450.067 q^{76} -17.4185 q^{77} -2758.07 q^{78} -543.570 q^{79} -668.561 q^{80} +2720.74 q^{81} +248.375 q^{82} +766.485 q^{83} +376.528 q^{84} -110.514 q^{85} -1576.07 q^{86} +600.700 q^{87} +971.400 q^{88} -377.916 q^{89} +902.500 q^{90} +77.2894 q^{91} -709.581 q^{92} +2298.94 q^{93} +1897.69 q^{94} +41.2952 q^{95} -10290.2 q^{96} +661.607 q^{97} +1916.70 q^{98} -811.426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 2 q^{2} + 11 q^{3} + 82 q^{4} + 8 q^{5} + 13 q^{6} + 39 q^{7} + 6 q^{8} + 156 q^{9} + 124 q^{10} - 143 q^{11} + 247 q^{12} - 23 q^{13} + 47 q^{14} + 278 q^{15} + 526 q^{16} + 73 q^{17} - 165 q^{18}+ \cdots - 1716 q^{99}+O(q^{100}) $ 13 * q - 2 * q^2 + 11 * q^3 + 82 * q^4 + 8 * q^5 + 13 * q^6 + 39 * q^7 + 6 * q^8 + 156 * q^9 + 124 * q^10 - 143 * q^11 + 247 * q^12 - 23 * q^13 + 47 * q^14 + 278 * q^15 + 526 * q^16 + 73 * q^17 - 165 * q^18 - 247 * q^19 + 142 * q^20 + 77 * q^21 + 22 * q^22 + 185 * q^23 - 251 * q^24 + 641 * q^25 - 47 * q^26 + 1109 * q^27 + 289 * q^28 - 41 * q^29 + 520 * q^30 + 930 * q^31 - 194 * q^32 - 121 * q^33 - 333 * q^34 + 122 * q^35 + 1469 * q^36 + 1094 * q^37 + 38 * q^38 + 543 * q^39 + 2084 * q^40 - 766 * q^41 - 1277 * q^42 + 1024 * q^43 - 902 * q^44 - 348 * q^45 + 1927 * q^46 + 516 * q^47 + 3067 * q^48 + 1966 * q^49 + 3066 * q^50 + 1975 * q^51 - 553 * q^52 + 1017 * q^53 - 2231 * q^54 - 88 * q^55 - 1793 * q^56 - 209 * q^57 - 159 * q^58 + 15 * q^59 - 3158 * q^60 - 862 * q^61 - 3298 * q^62 + 552 * q^63 + 3694 * q^64 - 1640 * q^65 - 143 * q^66 + 621 * q^67 - 1533 * q^68 + 335 * q^69 - 3250 * q^70 + 632 * q^71 - 8349 * q^72 - 629 * q^73 - 4086 * q^74 - 2759 * q^75 - 1558 * q^76 - 429 * q^77 - 5813 * q^78 + 2444 * q^79 + 2810 * q^80 + 2265 * q^81 - 846 * q^82 + 732 * q^83 - 761 * q^84 - 3786 * q^85 - 4664 * q^86 - 1185 * q^87 - 66 * q^88 + 3178 * q^89 - 6174 * q^90 + 1349 * q^91 - 1677 * q^92 + 1328 * q^93 + 3156 * q^94 - 152 * q^95 - 13811 * q^96 + 1410 * q^97 - 6273 * q^98 - 1716 * q^99

Coefficient data

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

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

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

$2$	−5.62918	−1.99022	−0.995109	−	0.0987859i	$-0.968504\pi$
$2$	−5.62918	−1.99022	−0.995109	+	0.0987859i	$0.968504\pi$
$3$	10.0382	1.93186	0.965929	−	0.258809i	$-0.0833299\pi$
$3$	10.0382	1.93186	0.965929	+	0.258809i	$0.0833299\pi$
$4$	23.6877	2.96097
$5$	−2.17343	−0.194398	−0.0971988	−	0.995265i	$-0.530988\pi$
$5$	−2.17343	−0.194398	−0.0971988	+	0.995265i	$0.530988\pi$
$6$	−56.5070	−3.84482
$7$	1.58350	0.0855008	0.0427504	−	0.999086i	$-0.486388\pi$
$7$	1.58350	0.0855008	0.0427504	+	0.999086i	$0.486388\pi$
$8$	−88.3091	−3.90275
$9$	73.7660	2.73207
$10$	12.2346	0.386893
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	237.783	5.72016
$13$	48.8093	1.04133	0.520664	−	0.853762i	$-0.325684\pi$
$13$	48.8093	1.04133	0.520664	+	0.853762i	$0.325684\pi$
$14$	−8.91380	−0.170165
$15$	−21.8174	−0.375548
$16$	307.606	4.80635
$17$	50.8475	0.725431	0.362716	−	0.931900i	$-0.381850\pi$
$17$	50.8475	0.725431	0.362716	+	0.931900i	$0.381850\pi$
$18$	−415.242	−5.43742
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−51.4836	−0.575604
$21$	15.8955	0.165175
$22$	61.9210	0.600073
$23$	−29.9557	−0.271573	−0.135787	−	0.990738i	$-0.543356\pi$
$23$	−29.9557	−0.271573	−0.135787	+	0.990738i	$0.543356\pi$
$24$	−886.467	−7.53955
$25$	−120.276	−0.962210
$26$	−274.757	−2.07247
$27$	469.447	3.34612
$28$	37.5094	0.253165
$29$	59.8413	0.383181	0.191590	−	0.981475i	$-0.438635\pi$
$29$	59.8413	0.383181	0.191590	+	0.981475i	$0.438635\pi$
$30$	122.814	0.747423
$31$	229.019	1.32687	0.663436	−	0.748233i	$-0.269098\pi$
$31$	229.019	1.32687	0.663436	+	0.748233i	$0.269098\pi$
$32$	−1025.10	−5.66294
$33$	−110.420	−0.582477
$34$	−286.230	−1.44377
$35$	−3.44162	−0.0166212
$36$	1747.35	8.08957
$37$	30.5522	0.135750	0.0678750	−	0.997694i	$-0.478378\pi$
$37$	30.5522	0.135750	0.0678750	+	0.997694i	$0.478378\pi$
$38$	106.955	0.456587
$39$	489.959	2.01170
$40$	191.934	0.758685
$41$	−44.1228	−0.168069	−0.0840345	−	0.996463i	$-0.526781\pi$
$41$	−44.1228	−0.168069	−0.0840345	+	0.996463i	$0.526781\pi$
$42$	−89.4787	−0.328735
$43$	279.983	0.992953	0.496476	−	0.868050i	$-0.334627\pi$
$43$	279.983	0.992953	0.496476	+	0.868050i	$0.334627\pi$
$44$	−260.565	−0.892765
$45$	−160.325	−0.531108
$46$	168.626	0.540490
$47$	−337.116	−1.04624	−0.523121	−	0.852258i	$-0.675232\pi$
$47$	−337.116	−1.04624	−0.523121	+	0.852258i	$0.675232\pi$
$48$	3087.82	9.28518
$49$	−340.493	−0.992690
$50$	677.057	1.91501
$51$	510.419	1.40143
$52$	1156.18	3.08334
$53$	108.326	0.280749	0.140374	−	0.990099i	$-0.455169\pi$
$53$	108.326	0.280749	0.140374	+	0.990099i	$0.455169\pi$
$54$	−2642.61	−6.65950
$55$	23.9077	0.0586131
$56$	−139.837	−0.333688
$57$	−190.726	−0.443198
$58$	−336.857	−0.762613
$59$	147.196	0.324801	0.162401	−	0.986725i	$-0.448076\pi$
$59$	147.196	0.324801	0.162401	+	0.986725i	$0.448076\pi$
$60$	−516.804	−1.11199
$61$	457.035	0.959300	0.479650	−	0.877460i	$-0.340764\pi$
$61$	457.035	0.959300	0.479650	+	0.877460i	$0.340764\pi$
$62$	−1289.19	−2.64076
$63$	116.808	0.233594
$64$	3309.63	6.46412
$65$	−106.084	−0.202432
$66$	621.577	1.15926
$67$	−265.095	−0.483381	−0.241690	−	0.970353i	$-0.577702\pi$
$67$	−265.095	−0.483381	−0.241690	+	0.970353i	$0.577702\pi$
$68$	1204.46	2.14798
$69$	−300.702	−0.524641
$70$	19.3735	0.0330797
$71$	746.973	1.24858	0.624292	−	0.781191i	$-0.285388\pi$
$71$	746.973	1.24858	0.624292	+	0.781191i	$0.285388\pi$
$72$	−6514.20	−10.6626
$73$	−643.087	−1.03106	−0.515532	−	0.856870i	$-0.672406\pi$
$73$	−643.087	−1.03106	−0.515532	+	0.856870i	$0.672406\pi$
$74$	−171.984	−0.270172
$75$	−1207.36	−1.85885
$76$	−450.067	−0.679292
$77$	−17.4185	−0.0257795
$78$	−2758.07	−4.00372
$79$	−543.570	−0.774132	−0.387066	−	0.922052i	$-0.626511\pi$
$79$	−543.570	−0.774132	−0.387066	+	0.922052i	$0.626511\pi$
$80$	−668.561	−0.934343
$81$	2720.74	3.73215
$82$	248.375	0.334494
$83$	766.485	1.01365	0.506823	−	0.862050i	$-0.330820\pi$
$83$	766.485	1.01365	0.506823	+	0.862050i	$0.330820\pi$
$84$	376.528	0.489079
$85$	−110.514	−0.141022
$86$	−1576.07	−1.97619
$87$	600.700	0.740250
$88$	971.400	1.17672
$89$	−377.916	−0.450101	−0.225051	−	0.974347i	$-0.572255\pi$
$89$	−377.916	−0.450101	−0.225051	+	0.974347i	$0.572255\pi$
$90$	902.500	1.05702
$91$	77.2894	0.0890344
$92$	−709.581	−0.804119
$93$	2298.94	2.56333
$94$	1897.69	2.08225
$95$	41.2952	0.0445979
$96$	−10290.2	−10.9400
$97$	661.607	0.692536	0.346268	−	0.938136i	$-0.387449\pi$
$97$	661.607	0.692536	0.346268	+	0.938136i	$0.387449\pi$
$98$	1916.70	1.97567
$99$	−811.426	−0.823751
$100$	−2849.07	−2.84907
$101$	258.982	0.255145	0.127573	−	0.991829i	$-0.459281\pi$
$101$	258.982	0.255145	0.127573	+	0.991829i	$0.459281\pi$
$102$	−2873.24	−2.78915
$103$	−888.492	−0.849958	−0.424979	−	0.905203i	$-0.639719\pi$
$103$	−888.492	−0.849958	−0.424979	+	0.905203i	$0.639719\pi$
$104$	−4310.31	−4.06404
$105$	−34.5478	−0.0321097
$106$	−609.785	−0.558751
$107$	704.131	0.636176	0.318088	−	0.948061i	$-0.396959\pi$
$107$	704.131	0.636176	0.318088	+	0.948061i	$0.396959\pi$
$108$	11120.1	9.90774
$109$	1846.39	1.62249	0.811247	−	0.584704i	$-0.198789\pi$
$109$	1846.39	1.62249	0.811247	+	0.584704i	$0.198789\pi$
$110$	−134.581	−0.116653
$111$	306.690	0.262249
$112$	487.094	0.410947
$113$	−1239.58	−1.03195	−0.515974	−	0.856604i	$-0.672570\pi$
$113$	−1239.58	−1.03195	−0.515974	+	0.856604i	$0.672570\pi$
$114$	1073.63	0.882061
$115$	65.1066	0.0527932
$116$	1417.50	1.13458
$117$	3600.47	2.84498
$118$	−828.593	−0.646425
$119$	80.5169	0.0620250
$120$	1926.67	1.46567
$121$	121.000	0.0909091
$122$	−2572.73	−1.90922
$123$	−442.915	−0.324685
$124$	5424.94	3.92882
$125$	533.091	0.381449
$126$	−657.535	−0.464904
$127$	−1524.76	−1.06536	−0.532678	−	0.846318i	$-0.678814\pi$
$127$	−1524.76	−1.06536	−0.532678	+	0.846318i	$0.678814\pi$
$128$	−10429.7	−7.20207
$129$	2810.53	1.91824
$130$	597.165	0.402883
$131$	−1354.99	−0.903712	−0.451856	−	0.892091i	$-0.649238\pi$
$131$	−1354.99	−0.903712	−0.451856	+	0.892091i	$0.649238\pi$
$132$	−2615.61	−1.72469
$133$	−30.0865	−0.0196152
$134$	1492.27	0.962032
$135$	−1020.31	−0.650477
$136$	−4490.30	−2.83118
$137$	−2504.42	−1.56181	−0.780903	−	0.624652i	$-0.785241\pi$
$137$	−2504.42	−1.56181	−0.780903	+	0.624652i	$0.785241\pi$
$138$	1692.71	1.04415
$139$	−1374.36	−0.838643	−0.419322	−	0.907838i	$-0.637732\pi$
$139$	−1374.36	−0.838643	−0.419322	+	0.907838i	$0.637732\pi$
$140$	−81.5242	−0.0492147
$141$	−3384.04	−2.02119
$142$	−4204.85	−2.48495
$143$	−536.903	−0.313972
$144$	22690.9	13.1313
$145$	−130.061	−0.0744894
$146$	3620.06	2.05204
$147$	−3417.94	−1.91773
$148$	723.712	0.401951
$149$	−3053.35	−1.67879	−0.839396	−	0.543520i	$-0.817091\pi$
$149$	−3053.35	−1.67879	−0.839396	+	0.543520i	$0.817091\pi$
$150$	6796.45	3.69952
$151$	−42.8789	−0.0231088	−0.0115544	−	0.999933i	$-0.503678\pi$
$151$	−42.8789	−0.0231088	−0.0115544	+	0.999933i	$0.503678\pi$
$152$	1677.87	0.895352
$153$	3750.82	1.98193
$154$	98.0518	0.0513067
$155$	−497.757	−0.257941
$156$	11606.0	5.95657
$157$	−2412.15	−1.22618	−0.613090	−	0.790013i	$-0.710074\pi$
$157$	−2412.15	−1.22618	−0.613090	+	0.790013i	$0.710074\pi$
$158$	3059.86	1.54069
$159$	1087.40	0.542366
$160$	2227.99	1.10086
$161$	−47.4347	−0.0232197
$162$	−15315.5	−7.42779
$163$	−1927.73	−0.926328	−0.463164	−	0.886273i	$-0.653286\pi$
$163$	−1927.73	−0.926328	−0.463164	+	0.886273i	$0.653286\pi$
$164$	−1045.17	−0.497646
$165$	239.991	0.113232
$166$	−4314.69	−2.01738
$167$	2083.92	0.965622	0.482811	−	0.875725i	$-0.339616\pi$
$167$	2083.92	0.965622	0.482811	+	0.875725i	$0.339616\pi$
$168$	−1403.72	−0.644638
$169$	185.350	0.0843650
$170$	622.101	0.280665
$171$	−1401.55	−0.626780
$172$	6632.15	2.94010
$173$	889.638	0.390971	0.195485	−	0.980707i	$-0.437372\pi$
$173$	889.638	0.390971	0.195485	+	0.980707i	$0.437372\pi$
$174$	−3381.45	−1.47326
$175$	−190.457	−0.0822697
$176$	−3383.67	−1.44917
$177$	1477.59	0.627470
$178$	2127.36	0.895800
$179$	−2660.34	−1.11086	−0.555428	−	0.831564i	$-0.687446\pi$
$179$	−2660.34	−1.11086	−0.555428	+	0.831564i	$0.687446\pi$
$180$	−3797.74	−1.57259
$181$	2582.66	1.06060	0.530298	−	0.847811i	$-0.322080\pi$
$181$	2582.66	1.06060	0.530298	+	0.847811i	$0.322080\pi$
$182$	−435.077	−0.177198
$183$	4587.82	1.85323
$184$	2645.36	1.05988
$185$	−66.4030	−0.0263895
$186$	−12941.2	−5.10158
$187$	−559.323	−0.218726
$188$	−7985.50	−3.09789
$189$	743.368	0.286096
$190$	−232.458	−0.0887594
$191$	1848.27	0.700190	0.350095	−	0.936714i	$-0.386149\pi$
$191$	1848.27	0.700190	0.350095	+	0.936714i	$0.386149\pi$
$192$	33222.8	12.4878
$193$	−1588.06	−0.592285	−0.296142	−	0.955144i	$-0.595700\pi$
$193$	−1588.06	−0.592285	−0.296142	+	0.955144i	$0.595700\pi$
$194$	−3724.31	−1.37830
$195$	−1064.89	−0.391069
$196$	−8065.49	−2.93932
$197$	−1885.40	−0.681875	−0.340938	−	0.940086i	$-0.610744\pi$
$197$	−1885.40	−0.681875	−0.340938	+	0.940086i	$0.610744\pi$
$198$	4567.66	1.63944
$199$	1372.30	0.488842	0.244421	−	0.969669i	$-0.421402\pi$
$199$	1372.30	0.488842	0.244421	+	0.969669i	$0.421402\pi$
$200$	10621.5	3.75526
$201$	−2661.08	−0.933822
$202$	−1457.86	−0.507794
$203$	94.7585	0.0327623
$204$	12090.7	4.14958
$205$	95.8979	0.0326722
$206$	5001.48	1.69160
$207$	−2209.71	−0.741958
$208$	15014.1	5.00499
$209$	209.000	0.0691714
$210$	194.476	0.0639053
$211$	−2677.68	−0.873645	−0.436822	−	0.899548i	$-0.643896\pi$
$211$	−2677.68	−0.873645	−0.436822	+	0.899548i	$0.643896\pi$
$212$	2565.99	0.831287
$213$	7498.28	2.41208
$214$	−3963.68	−1.26613
$215$	−608.523	−0.193028
$216$	−41456.5	−13.0590
$217$	362.651	0.113449
$218$	−10393.7	−3.22911
$219$	−6455.45	−1.99187
$220$	566.320	0.173551
$221$	2481.83	0.755412
$222$	−1726.41	−0.521933
$223$	−1230.38	−0.369473	−0.184737	−	0.982788i	$-0.559143\pi$
$223$	−1230.38	−0.369473	−0.184737	+	0.982788i	$0.559143\pi$
$224$	−1623.24	−0.484186
$225$	−8872.29	−2.62883
$226$	6977.84	2.05380
$227$	−2478.72	−0.724752	−0.362376	−	0.932032i	$-0.618034\pi$
$227$	−2478.72	−0.724752	−0.362376	+	0.932032i	$0.618034\pi$
$228$	−4517.87	−1.31230
$229$	−5486.63	−1.58326	−0.791630	−	0.611001i	$-0.790767\pi$
$229$	−5486.63	−1.58326	−0.791630	+	0.611001i	$0.790767\pi$
$230$	−366.497	−0.105070
$231$	−174.851	−0.0498023
$232$	−5284.53	−1.49546
$233$	1054.22	0.296412	0.148206	−	0.988957i	$-0.452650\pi$
$233$	1054.22	0.296412	0.148206	+	0.988957i	$0.452650\pi$
$234$	−20267.7	−5.66214
$235$	732.698	0.203387
$236$	3486.74	0.961725
$237$	−5456.48	−1.49551
$238$	−453.245	−0.123443
$239$	157.540	0.0426377	0.0213188	−	0.999773i	$-0.493213\pi$
$239$	157.540	0.0426377	0.0213188	+	0.999773i	$0.493213\pi$
$240$	−6711.17	−1.80502
$241$	−1989.66	−0.531805	−0.265903	−	0.964000i	$-0.585670\pi$
$241$	−1989.66	−0.531805	−0.265903	+	0.964000i	$0.585670\pi$
$242$	−681.131	−0.180929
$243$	14636.3	3.86386
$244$	10826.1	2.84045
$245$	740.037	0.192976
$246$	2493.25	0.646194
$247$	−927.377	−0.238897
$248$	−20224.4	−5.17844
$249$	7694.15	1.95822
$250$	−3000.87	−0.759166
$251$	3911.56	0.983648	0.491824	−	0.870695i	$-0.336330\pi$
$251$	3911.56	0.983648	0.491824	+	0.870695i	$0.336330\pi$
$252$	2766.92	0.691665
$253$	329.512	0.0818824
$254$	8583.13	2.12029
$255$	−1109.36	−0.272435
$256$	32233.7	7.86957
$257$	117.568	0.0285358	0.0142679	−	0.999898i	$-0.495458\pi$
$257$	117.568	0.0285358	0.0142679	+	0.999898i	$0.495458\pi$
$258$	−15821.0	−3.81772
$259$	48.3793	0.0116067
$260$	−2512.88	−0.599393
$261$	4414.25	1.04688
$262$	7627.51	1.79858
$263$	−6832.09	−1.60184	−0.800922	−	0.598769i	$-0.795657\pi$
$263$	−6832.09	−1.60184	−0.800922	+	0.598769i	$0.795657\pi$
$264$	9751.13	2.27326
$265$	−235.438	−0.0545769
$266$	169.362	0.0390386
$267$	−3793.61	−0.869532
$268$	−6279.49	−1.43127
$269$	760.862	0.172456	0.0862278	−	0.996275i	$-0.472519\pi$
$269$	760.862	0.172456	0.0862278	+	0.996275i	$0.472519\pi$
$270$	5743.52	1.29459
$271$	−2203.58	−0.493941	−0.246970	−	0.969023i	$-0.579435\pi$
$271$	−2203.58	−0.493941	−0.246970	+	0.969023i	$0.579435\pi$
$272$	15641.0	3.48668
$273$	775.849	0.172002
$274$	14097.9	3.10833
$275$	1323.04	0.290117
$276$	−7122.94	−1.55344
$277$	3847.52	0.834567	0.417284	−	0.908776i	$-0.362982\pi$
$277$	3847.52	0.834567	0.417284	+	0.908776i	$0.362982\pi$
$278$	7736.51	1.66908
$279$	16893.8	3.62511
$280$	303.927	0.0648682
$281$	5965.21	1.26639	0.633194	−	0.773994i	$-0.281744\pi$
$281$	5965.21	1.26639	0.633194	+	0.773994i	$0.281744\pi$
$282$	19049.4	4.02261
$283$	−6968.74	−1.46378	−0.731888	−	0.681425i	$-0.761360\pi$
$283$	−6968.74	−1.46378	−0.731888	+	0.681425i	$0.761360\pi$
$284$	17694.1	3.69701
$285$	414.530	0.0861567
$286$	3022.32	0.624873
$287$	−69.8684	−0.0143700
$288$	−75617.5	−15.4715
$289$	−2327.53	−0.473749
$290$	732.136	0.148250
$291$	6641.36	1.33788
$292$	−15233.3	−3.05294
$293$	4916.72	0.980334	0.490167	−	0.871629i	$-0.336936\pi$
$293$	4916.72	0.980334	0.490167	+	0.871629i	$0.336936\pi$
$294$	19240.2	3.81671
$295$	−319.920	−0.0631406
$296$	−2698.04	−0.529798
$297$	−5163.92	−1.00889
$298$	17187.9	3.34116
$299$	−1462.12	−0.282797
$300$	−28599.6	−5.50400
$301$	443.352	0.0848983
$302$	241.373	0.0459916
$303$	2599.72	0.492904
$304$	−5844.52	−1.10265
$305$	−993.334	−0.186486
$306$	−21114.0	−3.94447
$307$	5505.90	1.02358	0.511788	−	0.859112i	$-0.328983\pi$
$307$	5505.90	1.02358	0.511788	+	0.859112i	$0.328983\pi$
$308$	−412.604	−0.0763321
$309$	−8918.88	−1.64200
$310$	2801.96	0.513358
$311$	9389.51	1.71199	0.855997	−	0.516980i	$-0.172944\pi$
$311$	9389.51	1.71199	0.855997	+	0.516980i	$0.172944\pi$
$312$	−43267.8	−7.85115
$313$	−6970.63	−1.25880	−0.629398	−	0.777083i	$-0.716699\pi$
$313$	−6970.63	−1.25880	−0.629398	+	0.777083i	$0.716699\pi$
$314$	13578.4	2.44036
$315$	−253.875	−0.0454102
$316$	−12875.9	−2.29218
$317$	−326.797	−0.0579014	−0.0289507	−	0.999581i	$-0.509217\pi$
$317$	−326.797	−0.0579014	−0.0289507	+	0.999581i	$0.509217\pi$
$318$	−6121.16	−1.07943
$319$	−658.254	−0.115533
$320$	−7193.25	−1.25661
$321$	7068.22	1.22900
$322$	267.019	0.0462123
$323$	−966.103	−0.166425
$324$	64448.0	11.0508
$325$	−5870.60	−1.00198
$326$	10851.5	1.84359
$327$	18534.4	3.13443
$328$	3896.45	0.655931
$329$	−533.822	−0.0894546
$330$	−1350.96	−0.225356
$331$	−1572.30	−0.261092	−0.130546	−	0.991442i	$-0.541673\pi$
$331$	−1572.30	−0.261092	−0.130546	+	0.991442i	$0.541673\pi$
$332$	18156.3	3.00137
$333$	2253.71	0.370879
$334$	−11730.8	−1.92180
$335$	576.165	0.0939680
$336$	4889.56	0.793891
$337$	−7617.59	−1.23133	−0.615663	−	0.788010i	$-0.711112\pi$
$337$	−7617.59	−1.23133	−0.615663	+	0.788010i	$0.711112\pi$
$338$	−1043.37	−0.167905
$339$	−12443.2	−1.99358
$340$	−2617.81	−0.417561
$341$	−2519.21	−0.400067
$342$	7889.60	1.24743
$343$	−1082.31	−0.170377
$344$	−24725.0	−3.87524
$345$	653.554	0.101989
$346$	−5007.94	−0.778117
$347$	−9768.47	−1.51124	−0.755618	−	0.655013i	$-0.772663\pi$
$347$	−9768.47	−1.51124	−0.755618	+	0.655013i	$0.772663\pi$
$348$	14229.2	2.19186
$349$	−2950.04	−0.452470	−0.226235	−	0.974073i	$-0.572642\pi$
$349$	−2950.04	−0.452470	−0.226235	+	0.974073i	$0.572642\pi$
$350$	1072.12	0.163735
$351$	22913.4	3.48441
$352$	11276.1	1.70744
$353$	−10041.1	−1.51398	−0.756991	−	0.653425i	$-0.773331\pi$
$353$	−10041.1	−1.51398	−0.756991	+	0.653425i	$0.773331\pi$
$354$	−8317.60	−1.24880
$355$	−1623.49	−0.242722
$356$	−8951.97	−1.33273
$357$	808.247	0.119823
$358$	14975.6	2.21085
$359$	982.859	0.144494	0.0722470	−	0.997387i	$-0.476983\pi$
$359$	982.859	0.144494	0.0722470	+	0.997387i	$0.476983\pi$
$360$	14158.2	2.07278
$361$	361.000	0.0526316
$362$	−14538.3	−2.11082
$363$	1214.63	0.175623
$364$	1830.81	0.263628
$365$	1397.71	0.200436
$366$	−25825.7	−3.68833
$367$	−9105.92	−1.29516	−0.647582	−	0.761996i	$-0.724220\pi$
$367$	−9105.92	−1.29516	−0.647582	+	0.761996i	$0.724220\pi$
$368$	−9214.55	−1.30528
$369$	−3254.76	−0.459176
$370$	373.795	0.0525208
$371$	171.533	0.0240042
$372$	54456.7	7.58992
$373$	−10470.1	−1.45340	−0.726702	−	0.686953i	$-0.758948\pi$
$373$	−10470.1	−1.45340	−0.726702	+	0.686953i	$0.758948\pi$
$374$	3148.53	0.435312
$375$	5351.29	0.736905
$376$	29770.4	4.08322
$377$	2920.81	0.399017
$378$	−4184.56	−0.569393
$379$	12680.1	1.71855	0.859277	−	0.511510i	$-0.170914\pi$
$379$	12680.1	1.71855	0.859277	+	0.511510i	$0.170914\pi$
$380$	978.189	0.132053
$381$	−15305.8	−2.05811
$382$	−10404.3	−1.39353
$383$	3880.72	0.517742	0.258871	−	0.965912i	$-0.416649\pi$
$383$	3880.72	0.517742	0.258871	+	0.965912i	$0.416649\pi$
$384$	−104696.	−13.9134
$385$	37.8578	0.00501147
$386$	8939.48	1.17878
$387$	20653.2	2.71282
$388$	15672.0	2.05058
$389$	12623.5	1.64534	0.822671	−	0.568518i	$-0.192483\pi$
$389$	12623.5	1.64534	0.822671	+	0.568518i	$0.192483\pi$
$390$	5994.47	0.778313
$391$	−1523.17	−0.197008
$392$	30068.6	3.87422
$393$	−13601.7	−1.74584
$394$	10613.3	1.35708
$395$	1181.41	0.150489
$396$	−19220.8	−2.43910
$397$	−8104.35	−1.02455	−0.512274	−	0.858822i	$-0.671197\pi$
$397$	−8104.35	−1.02455	−0.512274	+	0.858822i	$0.671197\pi$
$398$	−7724.92	−0.972902
$399$	−302.015	−0.0378938
$400$	−36997.7	−4.62472
$401$	3453.29	0.430047	0.215024	−	0.976609i	$-0.431017\pi$
$401$	3453.29	0.430047	0.215024	+	0.976609i	$0.431017\pi$
$402$	14979.7	1.85851
$403$	11178.3	1.38171
$404$	6134.69	0.755476
$405$	−5913.33	−0.725520
$406$	−533.413	−0.0652040
$407$	−336.074	−0.0409301
$408$	−45074.6	−5.46943
$409$	−307.510	−0.0371770	−0.0185885	−	0.999827i	$-0.505917\pi$
$409$	−307.510	−0.0371770	−0.0185885	+	0.999827i	$0.505917\pi$
$410$	−539.827	−0.0650248
$411$	−25140.0	−3.01719
$412$	−21046.3	−2.51670
$413$	233.084	0.0277708
$414$	12438.9	1.47666
$415$	−1665.90	−0.197051
$416$	−50034.5	−5.89698
$417$	−13796.1	−1.62014
$418$	−1176.50	−0.137666
$419$	−1856.97	−0.216513	−0.108257	−	0.994123i	$-0.534527\pi$
$419$	−1856.97	−0.216513	−0.108257	+	0.994123i	$0.534527\pi$
$420$	−818.358	−0.0950757
$421$	10492.3	1.21464	0.607321	−	0.794457i	$-0.292244\pi$
$421$	10492.3	1.21464	0.607321	+	0.794457i	$0.292244\pi$
$422$	15073.2	1.73874
$423$	−24867.7	−2.85841
$424$	−9566.14	−1.09569
$425$	−6115.74	−0.698017
$426$	−42209.2	−4.80057
$427$	723.713	0.0820210
$428$	16679.3	1.88370
$429$	−5389.55	−0.606550
$430$	3425.49	0.384167
$431$	4910.65	0.548811	0.274405	−	0.961614i	$-0.411519\pi$
$431$	4910.65	0.548811	0.274405	+	0.961614i	$0.411519\pi$
$432$	144405.	16.0826
$433$	5459.77	0.605958	0.302979	−	0.952997i	$-0.402019\pi$
$433$	5459.77	0.605958	0.302979	+	0.952997i	$0.402019\pi$
$434$	−2041.43	−0.225787
$435$	−1305.58	−0.143903
$436$	43736.7	4.80415
$437$	569.158	0.0623032
$438$	36338.9	3.96425
$439$	9674.02	1.05174	0.525872	−	0.850564i	$-0.323739\pi$
$439$	9674.02	1.05174	0.525872	+	0.850564i	$0.323739\pi$
$440$	−2111.27	−0.228752
$441$	−25116.8	−2.71210
$442$	−13970.7	−1.50343
$443$	−3314.76	−0.355505	−0.177753	−	0.984075i	$-0.556883\pi$
$443$	−3314.76	−0.355505	−0.177753	+	0.984075i	$0.556883\pi$
$444$	7264.78	0.776512
$445$	821.375	0.0874986
$446$	6926.06	0.735332
$447$	−30650.2	−3.24319
$448$	5240.79	0.552688
$449$	−14828.8	−1.55861	−0.779305	−	0.626644i	$-0.784428\pi$
$449$	−14828.8	−1.55861	−0.779305	+	0.626644i	$0.784428\pi$
$450$	49943.8	5.23194
$451$	485.351	0.0506747
$452$	−29362.9	−3.05556
$453$	−430.428	−0.0446430
$454$	13953.2	1.44241
$455$	−167.983	−0.0173081
$456$	16842.9	1.72969
$457$	8906.30	0.911639	0.455820	−	0.890072i	$-0.349346\pi$
$457$	8906.30	0.911639	0.455820	+	0.890072i	$0.349346\pi$
$458$	30885.2	3.15103
$459$	23870.2	2.42738
$460$	1542.23	0.156319
$461$	5846.42	0.590661	0.295331	−	0.955395i	$-0.404570\pi$
$461$	5846.42	0.590661	0.295331	+	0.955395i	$0.404570\pi$
$462$	984.266	0.0991173
$463$	18029.8	1.80976	0.904879	−	0.425669i	$-0.139961\pi$
$463$	18029.8	1.80976	0.904879	+	0.425669i	$0.139961\pi$
$464$	18407.6	1.84170
$465$	−4996.59	−0.498304
$466$	−5934.38	−0.589924
$467$	−5105.03	−0.505851	−0.252926	−	0.967486i	$-0.581393\pi$
$467$	−5105.03	−0.505851	−0.252926	+	0.967486i	$0.581393\pi$
$468$	85286.9	8.42390
$469$	−419.777	−0.0413294
$470$	−4124.49	−0.404784
$471$	−24213.7	−2.36880
$472$	−12998.7	−1.26762
$473$	−3079.81	−0.299387
$474$	30715.5	2.97639
$475$	2285.25	0.220746
$476$	1907.26	0.183654
$477$	7990.75	0.767026
$478$	−886.821	−0.0848582
$479$	−1008.00	−0.0961516	−0.0480758	−	0.998844i	$-0.515309\pi$
$479$	−1008.00	−0.0961516	−0.0480758	+	0.998844i	$0.515309\pi$
$480$	22365.0	2.12671
$481$	1491.23	0.141360
$482$	11200.1	1.05841
$483$	−476.160	−0.0448572
$484$	2866.21	0.269179
$485$	−1437.96	−0.134627
$486$	−82390.3	−7.68992
$487$	−8551.87	−0.795733	−0.397867	−	0.917443i	$-0.630249\pi$
$487$	−8551.87	−0.795733	−0.397867	+	0.917443i	$0.630249\pi$
$488$	−40360.3	−3.74391
$489$	−19351.0	−1.78953
$490$	−4165.81	−0.384065
$491$	4870.52	0.447665	0.223832	−	0.974628i	$-0.428143\pi$
$491$	4870.52	0.447665	0.223832	+	0.974628i	$0.428143\pi$
$492$	−10491.6	−0.961382
$493$	3042.78	0.277971
$494$	5220.38	0.475457
$495$	1763.58	0.160135
$496$	70447.7	6.37741
$497$	1182.83	0.106755
$498$	−43311.8	−3.89729
$499$	1737.82	0.155903	0.0779514	−	0.996957i	$-0.475162\pi$
$499$	1737.82	0.155903	0.0779514	+	0.996957i	$0.475162\pi$
$500$	12627.7	1.12946
$501$	20918.9	1.86544
$502$	−22018.9	−1.95767
$503$	8680.66	0.769486	0.384743	−	0.923024i	$-0.374290\pi$
$503$	8680.66	0.769486	0.384743	+	0.923024i	$0.374290\pi$
$504$	−10315.2	−0.911660
$505$	−562.879	−0.0495996
$506$	−1854.89	−0.162964
$507$	1860.58	0.162981
$508$	−36118.0	−3.15448
$509$	11094.7	0.966141	0.483071	−	0.875581i	$-0.339521\pi$
$509$	11094.7	0.966141	0.483071	+	0.875581i	$0.339521\pi$
$510$	6244.79	0.542204
$511$	−1018.33	−0.0881568
$512$	−98012.0	−8.46008
$513$	−8919.50	−0.767652
$514$	−661.812	−0.0567924
$515$	1931.07	0.165230
$516$	66575.0	5.67985
$517$	3708.27	0.315454
$518$	−272.336	−0.0230999
$519$	8930.39	0.755300
$520$	9368.15	0.790040
$521$	17892.1	1.50455	0.752273	−	0.658852i	$-0.228958\pi$
$521$	17892.1	1.50455	0.752273	+	0.658852i	$0.228958\pi$
$522$	−24848.6	−2.08351
$523$	−660.395	−0.0552143	−0.0276071	−	0.999619i	$-0.508789\pi$
$523$	−660.395	−0.0552143	−0.0276071	+	0.999619i	$0.508789\pi$
$524$	−32096.7	−2.67586
$525$	−1911.85	−0.158933
$526$	38459.1	3.18802
$527$	11645.0	0.962554
$528$	−33966.0	−2.79959
$529$	−11269.7	−0.926248
$530$	1325.33	0.108620
$531$	10858.0	0.887381
$532$	−712.680	−0.0580800
$533$	−2153.60	−0.175015
$534$	21354.9	1.73056
$535$	−1530.38	−0.123671
$536$	23410.3	1.88651
$537$	−26705.1	−2.14602
$538$	−4283.03	−0.343224
$539$	3745.42	0.299307
$540$	−24168.8	−1.92604
$541$	−4518.62	−0.359095	−0.179548	−	0.983749i	$-0.557463\pi$
$541$	−4518.62	−0.359095	−0.179548	+	0.983749i	$0.557463\pi$
$542$	12404.4	0.983049
$543$	25925.4	2.04892
$544$	−52123.8	−4.10807
$545$	−4012.99	−0.315409
$546$	−4367.40	−0.342321
$547$	1450.22	0.113358	0.0566790	−	0.998392i	$-0.481949\pi$
$547$	1450.22	0.113358	0.0566790	+	0.998392i	$0.481949\pi$
$548$	−59324.1	−4.62445
$549$	33713.6	2.62088
$550$	−7447.63	−0.577396
$551$	−1136.98	−0.0879077
$552$	26554.7	2.04754
$553$	−860.742	−0.0661889
$554$	−21658.4	−1.66097
$555$	−666.569	−0.0509807
$556$	−32555.4	−2.48319
$557$	9000.42	0.684668	0.342334	−	0.939578i	$-0.388783\pi$
$557$	9000.42	0.684668	0.342334	+	0.939578i	$0.388783\pi$
$558$	−95098.3	−7.21475
$559$	13665.8	1.03399
$560$	−1058.67	−0.0798871
$561$	−5614.61	−0.422547
$562$	−33579.3	−2.52039
$563$	15050.8	1.12667	0.563335	−	0.826228i	$-0.309518\pi$
$563$	15050.8	1.12667	0.563335	+	0.826228i	$0.309518\pi$
$564$	−80160.3	−5.98467
$565$	2694.15	0.200608
$566$	39228.3	2.91323
$567$	4308.28	0.319102
$568$	−65964.5	−4.87290
$569$	−15142.9	−1.11568	−0.557840	−	0.829948i	$-0.688370\pi$
$569$	−15142.9	−1.11568	−0.557840	+	0.829948i	$0.688370\pi$
$570$	−2333.47	−0.171471
$571$	19227.6	1.40919	0.704596	−	0.709608i	$-0.251128\pi$
$571$	19227.6	1.40919	0.704596	+	0.709608i	$0.251128\pi$
$572$	−12718.0	−0.929661
$573$	18553.4	1.35267
$574$	393.302	0.0285995
$575$	3602.95	0.261310
$576$	244138.	17.6604
$577$	13397.4	0.966625	0.483313	−	0.875448i	$-0.339433\pi$
$577$	13397.4	0.966625	0.483313	+	0.875448i	$0.339433\pi$
$578$	13102.1	0.942864
$579$	−15941.3	−1.14421
$580$	−3080.84	−0.220561
$581$	1213.73	0.0866676
$582$	−37385.4	−2.66267
$583$	−1191.58	−0.0846489
$584$	56790.4	4.02398
$585$	−7825.37	−0.553058
$586$	−27677.1	−1.95108
$587$	9119.43	0.641225	0.320613	−	0.947210i	$-0.396111\pi$
$587$	9119.43	0.641225	0.320613	+	0.947210i	$0.396111\pi$
$588$	−80963.2	−5.67835
$589$	−4351.36	−0.304405
$590$	1800.89	0.125663
$591$	−18926.1	−1.31729
$592$	9398.05	0.652462
$593$	21237.3	1.47068	0.735340	−	0.677698i	$-0.237022\pi$
$593$	21237.3	1.47068	0.735340	+	0.677698i	$0.237022\pi$
$594$	29068.7	2.00791
$595$	−174.998	−0.0120575
$596$	−72326.9	−4.97085
$597$	13775.4	0.944373
$598$	8230.52	0.562828
$599$	18566.7	1.26647	0.633235	−	0.773960i	$-0.281727\pi$
$599$	18566.7	1.26647	0.633235	+	0.773960i	$0.281727\pi$
$600$	106621.	7.25463
$601$	−14151.5	−0.960485	−0.480242	−	0.877136i	$-0.659451\pi$
$601$	−14151.5	−0.960485	−0.480242	+	0.877136i	$0.659451\pi$
$602$	−2495.71	−0.168966
$603$	−19555.0	−1.32063
$604$	−1015.70	−0.0684245
$605$	−262.985	−0.0176725
$606$	−14634.3	−0.980986
$607$	−16435.0	−1.09897	−0.549486	−	0.835503i	$-0.685176\pi$
$607$	−16435.0	−1.09897	−0.549486	+	0.835503i	$0.685176\pi$
$608$	19476.9	1.29917
$609$	951.207	0.0632920
$610$	5591.66	0.371147
$611$	−16454.4	−1.08948
$612$	88848.3	5.86843
$613$	−11170.1	−0.735983	−0.367992	−	0.929829i	$-0.619954\pi$
$613$	−11170.1	−0.735983	−0.367992	+	0.929829i	$0.619954\pi$
$614$	−30993.7	−2.03714
$615$	962.645	0.0631180
$616$	1538.21	0.100611
$617$	−12177.1	−0.794541	−0.397271	−	0.917701i	$-0.630043\pi$
$617$	−12177.1	−0.794541	−0.397271	+	0.917701i	$0.630043\pi$
$618$	50206.0	3.26793
$619$	14948.4	0.970642	0.485321	−	0.874336i	$-0.338703\pi$
$619$	14948.4	0.970642	0.485321	+	0.874336i	$0.338703\pi$
$620$	−11790.7	−0.763753
$621$	−14062.6	−0.908716
$622$	−52855.3	−3.40724
$623$	−598.429	−0.0384840
$624$	150715.	9.66893
$625$	13875.9	0.888057
$626$	39239.0	2.50528
$627$	2097.99	0.133629
$628$	−57138.2	−3.63067
$629$	1553.50	0.0984772
$630$	1429.11	0.0903762
$631$	−2802.70	−0.176820	−0.0884102	−	0.996084i	$-0.528179\pi$
$631$	−2802.70	−0.176820	−0.0884102	+	0.996084i	$0.528179\pi$
$632$	48002.2	3.02124
$633$	−26879.1	−1.68776
$634$	1839.60	0.115236
$635$	3313.95	0.207102
$636$	25758.0	1.60593
$637$	−16619.2	−1.03372
$638$	3705.43	0.229936
$639$	55101.2	3.41122
$640$	22668.3	1.40007
$641$	793.890	0.0489185	0.0244593	−	0.999701i	$-0.492214\pi$
$641$	793.890	0.0489185	0.0244593	+	0.999701i	$0.492214\pi$
$642$	−39788.3	−2.44598
$643$	4344.62	0.266462	0.133231	−	0.991085i	$-0.457465\pi$
$643$	4344.62	0.266462	0.133231	+	0.991085i	$0.457465\pi$
$644$	−1123.62	−0.0687529
$645$	−6108.49	−0.372902
$646$	5438.37	0.331223
$647$	−4860.64	−0.295350	−0.147675	−	0.989036i	$-0.547179\pi$
$647$	−4860.64	−0.295350	−0.147675	+	0.989036i	$0.547179\pi$
$648$	−240266.	−14.5656
$649$	−1619.16	−0.0979313
$650$	33046.7	1.99415
$651$	3640.37	0.219166
$652$	−45663.5	−2.74283
$653$	−20401.8	−1.22264	−0.611321	−	0.791382i	$-0.709362\pi$
$653$	−20401.8	−1.22264	−0.611321	+	0.791382i	$0.709362\pi$
$654$	−104334.	−6.23819
$655$	2944.98	0.175680
$656$	−13572.5	−0.807798
$657$	−47437.9	−2.81694
$658$	3004.98	0.178034
$659$	22495.6	1.32975	0.664875	−	0.746955i	$-0.268485\pi$
$659$	22495.6	1.32975	0.664875	+	0.746955i	$0.268485\pi$
$660$	5684.85	0.335276
$661$	−3331.21	−0.196020	−0.0980098	−	0.995185i	$-0.531248\pi$
$661$	−3331.21	−0.196020	−0.0980098	+	0.995185i	$0.531248\pi$
$662$	8850.75	0.519629
$663$	24913.2	1.45935
$664$	−67687.6	−3.95601
$665$	65.3908	0.00381315
$666$	−12686.6	−0.738129
$667$	−1792.58	−0.104062
$668$	49363.4	2.85917
$669$	−12350.9	−0.713770
$670$	−3243.34	−0.187017
$671$	−5027.38	−0.289240
$672$	−16294.5	−0.935378
$673$	−24944.3	−1.42872	−0.714361	−	0.699777i	$-0.753283\pi$
$673$	−24944.3	−1.42872	−0.714361	+	0.699777i	$0.753283\pi$
$674$	42880.9	2.45061
$675$	−56463.3	−3.21967
$676$	4390.52	0.249802
$677$	23004.0	1.30593	0.652964	−	0.757389i	$-0.273525\pi$
$677$	23004.0	1.30593	0.652964	+	0.757389i	$0.273525\pi$
$678$	70045.2	3.96765
$679$	1047.65	0.0592124
$680$	9759.35	0.550374
$681$	−24882.0	−1.40012
$682$	14181.1	0.796220
$683$	9990.42	0.559697	0.279848	−	0.960044i	$-0.409716\pi$
$683$	9990.42	0.559697	0.279848	+	0.960044i	$0.409716\pi$
$684$	−33199.6	−1.85588
$685$	5443.19	0.303611
$686$	6092.52	0.339086
$687$	−55076.0	−3.05863
$688$	86124.5	4.77248
$689$	5287.30	0.292352
$690$	−3678.98	−0.202980
$691$	−4683.53	−0.257844	−0.128922	−	0.991655i	$-0.541152\pi$
$691$	−4683.53	−0.257844	−0.128922	+	0.991655i	$0.541152\pi$
$692$	21073.5	1.15765
$693$	−1284.89	−0.0704314
$694$	54988.5	3.00769
$695$	2987.07	0.163030
$696$	−53047.3	−2.88901
$697$	−2243.54	−0.121922
$698$	16606.3	0.900514
$699$	10582.5	0.572626
$700$	−4511.49	−0.243598
$701$	−30340.8	−1.63474	−0.817372	−	0.576110i	$-0.804570\pi$
$701$	−30340.8	−1.63474	−0.817372	+	0.576110i	$0.804570\pi$
$702$	−128984.	−6.93473
$703$	−580.491	−0.0311432
$704$	−36405.9	−1.94901
$705$	7354.98	0.392914
$706$	56523.4	3.01315
$707$	410.097	0.0218151
$708$	35000.6	1.85792
$709$	−14079.4	−0.745785	−0.372893	−	0.927874i	$-0.621634\pi$
$709$	−14079.4	−0.745785	−0.372893	+	0.927874i	$0.621634\pi$
$710$	9138.95	0.483069
$711$	−40097.0	−2.11498
$712$	33373.4	1.75663
$713$	−6860.41	−0.360343
$714$	−4549.77	−0.238475
$715$	1166.92	0.0610355
$716$	−63017.5	−3.28921
$717$	1581.42	0.0823699
$718$	−5532.70	−0.287574
$719$	21941.5	1.13808	0.569041	−	0.822309i	$-0.307315\pi$
$719$	21941.5	1.13808	0.569041	+	0.822309i	$0.307315\pi$
$720$	−49317.1	−2.55269
$721$	−1406.92	−0.0726721
$722$	−2032.14	−0.104748
$723$	−19972.6	−1.02737
$724$	61177.4	3.14039
$725$	−7197.48	−0.368700
$726$	−6837.35	−0.349529
$727$	10903.1	0.556224	0.278112	−	0.960549i	$-0.410291\pi$
$727$	10903.1	0.556224	0.278112	+	0.960549i	$0.410291\pi$
$728$	−6825.36	−0.347479
$729$	73462.4	3.73228
$730$	−7867.94	−0.398912
$731$	14236.4	0.720319
$732$	108675.	5.48735
$733$	33298.0	1.67788	0.838942	−	0.544220i	$-0.183174\pi$
$733$	33298.0	1.67788	0.838942	+	0.544220i	$0.183174\pi$
$734$	51258.9	2.57766
$735$	7428.66	0.372803
$736$	30707.6	1.53790
$737$	2916.04	0.145745
$738$	18321.7	0.913861
$739$	−797.502	−0.0396977	−0.0198489	−	0.999803i	$-0.506319\pi$
$739$	−797.502	−0.0396977	−0.0198489	+	0.999803i	$0.506319\pi$
$740$	−1572.94	−0.0781383
$741$	−9309.22	−0.461515
$742$	−965.594	−0.0477737
$743$	−30701.6	−1.51593	−0.757963	−	0.652298i	$-0.773805\pi$
$743$	−30701.6	−1.51593	−0.757963	+	0.652298i	$0.773805\pi$
$744$	−203018.	−10.0040
$745$	6636.24	0.326353
$746$	58937.9	2.89259
$747$	56540.5	2.76936
$748$	−13249.1	−0.647639
$749$	1114.99	0.0543936
$750$	−30123.4	−1.46660
$751$	4727.79	0.229719	0.114860	−	0.993382i	$-0.463358\pi$
$751$	4727.79	0.229719	0.114860	+	0.993382i	$0.463358\pi$
$752$	−103699.	−5.02861
$753$	39265.1	1.90027
$754$	−16441.8	−0.794131
$755$	93.1943	0.00449230
$756$	17608.7	0.847120
$757$	18149.4	0.871402	0.435701	−	0.900092i	$-0.356501\pi$
$757$	18149.4	0.871402	0.435701	+	0.900092i	$0.356501\pi$
$758$	−71378.5	−3.42030
$759$	3307.72	0.158185
$760$	−3646.74	−0.174054
$761$	32588.1	1.55232	0.776162	−	0.630533i	$-0.217164\pi$
$761$	32588.1	1.55232	0.776162	+	0.630533i	$0.217164\pi$
$762$	86159.4	4.09610
$763$	2923.75	0.138725
$764$	43781.3	2.07324
$765$	−8152.14	−0.385283
$766$	−21845.3	−1.03042
$767$	7184.53	0.338225
$768$	323570.	15.2029
$769$	8274.90	0.388037	0.194019	−	0.980998i	$-0.437848\pi$
$769$	8274.90	0.388037	0.194019	+	0.980998i	$0.437848\pi$
$770$	−213.109	−0.00997391
$771$	1180.17	0.0551270
$772$	−37617.5	−1.75373
$773$	26523.6	1.23414	0.617069	−	0.786909i	$-0.288320\pi$
$773$	26523.6	1.23414	0.617069	+	0.786909i	$0.288320\pi$
$774$	−116261.	−5.39910
$775$	−27545.5	−1.27673
$776$	−58425.9	−2.70279
$777$	485.642	0.0224225
$778$	−71060.1	−3.27459
$779$	838.333	0.0385577
$780$	−25224.9	−1.15794
$781$	−8216.70	−0.376462
$782$	8574.21	0.392088
$783$	28092.3	1.28217
$784$	−104738.	−4.77121
$785$	5242.63	0.238366
$786$	76566.7	3.47461
$787$	−8455.16	−0.382965	−0.191483	−	0.981496i	$-0.561330\pi$
$787$	−8455.16	−0.382965	−0.191483	+	0.981496i	$0.561330\pi$
$788$	−44660.9	−2.01901
$789$	−68582.1	−3.09453
$790$	−6650.38	−0.299506
$791$	−1962.88	−0.0882324
$792$	71656.3	3.21489
$793$	22307.6	0.998947
$794$	45620.9	2.03907
$795$	−2363.38	−0.105435
$796$	32506.6	1.44744
$797$	15760.8	0.700473	0.350236	−	0.936661i	$-0.386101\pi$
$797$	15760.8	0.700473	0.350236	+	0.936661i	$0.386101\pi$
$798$	1700.10	0.0754170
$799$	−17141.5	−0.758977
$800$	123295.	5.44893
$801$	−27877.3	−1.22971
$802$	−19439.2	−0.855887
$803$	7073.96	0.310877
$804$	−63035.0	−2.76502
$805$	103.096	0.00451386
$806$	−62924.5	−2.74990
$807$	7637.70	0.333160
$808$	−22870.5	−0.995767
$809$	−2909.63	−0.126449	−0.0632244	−	0.997999i	$-0.520138\pi$
$809$	−2909.63	−0.126449	−0.0632244	+	0.997999i	$0.520138\pi$
$810$	33287.2	1.44394
$811$	22893.2	0.991233	0.495616	−	0.868542i	$-0.334942\pi$
$811$	22893.2	0.991233	0.495616	+	0.868542i	$0.334942\pi$
$812$	2244.61	0.0970079
$813$	−22120.0	−0.954223
$814$	1891.82	0.0814599
$815$	4189.79	0.180076
$816$	157008.	6.73576
$817$	−5319.67	−0.227799
$818$	1731.03	0.0739902
$819$	5701.33	0.243249
$820$	2271.60	0.0967412
$821$	−27306.7	−1.16079	−0.580397	−	0.814334i	$-0.697103\pi$
$821$	−27306.7	−1.16079	−0.580397	+	0.814334i	$0.697103\pi$
$822$	141518.	6.00486
$823$	11324.7	0.479653	0.239827	−	0.970816i	$-0.422909\pi$
$823$	11324.7	0.479653	0.239827	+	0.970816i	$0.422909\pi$
$824$	78461.9	3.31717
$825$	13281.0	0.560465
$826$	−1312.07	−0.0552699
$827$	−44894.9	−1.88772	−0.943862	−	0.330340i	$-0.892837\pi$
$827$	−44894.9	−1.88772	−0.943862	+	0.330340i	$0.892837\pi$
$828$	−52342.9	−2.19691
$829$	−13391.2	−0.561034	−0.280517	−	0.959849i	$-0.590506\pi$
$829$	−13391.2	−0.561034	−0.280517	+	0.959849i	$0.590506\pi$
$830$	9377.68	0.392173
$831$	38622.3	1.61226
$832$	161541.	6.73127
$833$	−17313.2	−0.720128
$834$	77660.8	3.22443
$835$	−4529.26	−0.187715
$836$	4950.73	0.204814
$837$	107512.	4.43987
$838$	10453.3	0.430909
$839$	−21482.9	−0.883994	−0.441997	−	0.897016i	$-0.645730\pi$
$839$	−21482.9	−0.883994	−0.441997	+	0.897016i	$0.645730\pi$
$840$	3050.88	0.125316
$841$	−20808.0	−0.853173
$842$	−59063.2	−2.41740
$843$	59880.1	2.44648
$844$	−63428.1	−2.58683
$845$	−402.845	−0.0164004
$846$	139985.	5.68886
$847$	191.603	0.00777280
$848$	33321.7	1.34938
$849$	−69953.8	−2.82781
$850$	34426.7	1.38921
$851$	−915.211	−0.0368661
$852$	177617.	7.14210
$853$	34746.6	1.39473	0.697363	−	0.716718i	$-0.254357\pi$
$853$	34746.6	1.39473	0.697363	+	0.716718i	$0.254357\pi$
$854$	−4073.92	−0.163240
$855$	3046.18	0.121845
$856$	−62181.1	−2.48284
$857$	−4839.63	−0.192904	−0.0964520	−	0.995338i	$-0.530749\pi$
$857$	−4839.63	−0.192904	−0.0964520	+	0.995338i	$0.530749\pi$
$858$	30338.8	1.20717
$859$	33496.2	1.33047	0.665235	−	0.746634i	$-0.268331\pi$
$859$	33496.2	1.33047	0.665235	+	0.746634i	$0.268331\pi$
$860$	−14414.5	−0.571548
$861$	−701.354	−0.0277608
$862$	−27642.9	−1.09225
$863$	19334.5	0.762636	0.381318	−	0.924444i	$-0.375470\pi$
$863$	19334.5	0.762636	0.381318	+	0.924444i	$0.375470\pi$
$864$	−481231.	−18.9488
$865$	−1933.57	−0.0760038
$866$	−30734.0	−1.20599
$867$	−23364.3	−0.915216
$868$	8590.37	0.335917
$869$	5979.27	0.233409
$870$	7349.35	0.286398
$871$	−12939.1	−0.503358
$872$	−163053.	−6.33218
$873$	48804.1	1.89206
$874$	−3203.89	−0.123997
$875$	844.148	0.0326142
$876$	−152915.	−5.89785
$877$	−7181.41	−0.276510	−0.138255	−	0.990397i	$-0.544149\pi$
$877$	−7181.41	−0.276510	−0.138255	+	0.990397i	$0.544149\pi$
$878$	−54456.8	−2.09320
$879$	49355.1	1.89387
$880$	7354.17	0.281715
$881$	−39644.4	−1.51607	−0.758033	−	0.652216i	$-0.773839\pi$
$881$	−39644.4	−1.51607	−0.758033	+	0.652216i	$0.773839\pi$
$882$	141387.	5.39767
$883$	−7245.50	−0.276139	−0.138069	−	0.990423i	$-0.544090\pi$
$883$	−7245.50	−0.276139	−0.138069	+	0.990423i	$0.544090\pi$
$884$	58789.0	2.23675
$885$	−3211.43	−0.121979
$886$	18659.4	0.707532
$887$	−32690.9	−1.23749	−0.618746	−	0.785591i	$-0.712359\pi$
$887$	−32690.9	−1.23749	−0.618746	+	0.785591i	$0.712359\pi$
$888$	−27083.5	−1.02349
$889$	−2414.45	−0.0910888
$890$	−4623.67	−0.174141
$891$	−29928.1	−1.12528
$892$	−29145.0	−1.09400
$893$	6405.20	0.240024
$894$	172536.	6.45465
$895$	5782.07	0.215948
$896$	−16515.4	−0.615783
$897$	−14677.0	−0.546324
$898$	83474.3	3.10197
$899$	13704.8	0.508431
$900$	−210164.	−7.78386
$901$	5508.09	0.203664
$902$	−2732.13	−0.100854
$903$	4450.47	0.164011
$904$	109466.	4.02743
$905$	−5613.24	−0.206177
$906$	2422.96	0.0888492
$907$	50455.7	1.84714	0.923568	−	0.383434i	$-0.125259\pi$
$907$	50455.7	1.84714	0.923568	+	0.383434i	$0.125259\pi$
$908$	−58715.3	−2.14597
$909$	19104.0	0.697075
$910$	945.609	0.0344468
$911$	13736.4	0.499569	0.249785	−	0.968301i	$-0.419640\pi$
$911$	13736.4	0.499569	0.249785	+	0.968301i	$0.419640\pi$
$912$	−58668.6	−2.13017
$913$	−8431.34	−0.305626
$914$	−50135.2	−1.81436
$915$	−9971.31	−0.360264
$916$	−129966.	−4.68798
$917$	−2145.63	−0.0772682
$918$	−134370.	−4.83101
$919$	2873.98	0.103160	0.0515800	−	0.998669i	$-0.483574\pi$
$919$	2873.98	0.103160	0.0515800	+	0.998669i	$0.483574\pi$
$920$	−5749.50	−0.206039
$921$	55269.4	1.97740
$922$	−32910.6	−1.17554
$923$	36459.3	1.30019
$924$	−4141.81	−0.147463
$925$	−3674.70	−0.130620
$926$	−101493.	−3.60181
$927$	−65540.4	−2.32215
$928$	−61343.3	−2.16993
$929$	−37090.3	−1.30990	−0.654948	−	0.755674i	$-0.727310\pi$
$929$	−37090.3	−1.30990	−0.654948	+	0.755674i	$0.727310\pi$
$930$	28126.7	0.991734
$931$	6469.36	0.227739
$932$	24972.0	0.877666
$933$	94254.0	3.30733
$934$	28737.1	1.00675
$935$	1215.65	0.0425198
$936$	−317954.	−11.1033
$937$	33019.5	1.15123	0.575614	−	0.817721i	$-0.304763\pi$
$937$	33019.5	1.15123	0.575614	+	0.817721i	$0.304763\pi$
$938$	2363.00	0.0822546
$939$	−69972.8	−2.43182
$940$	17355.9	0.602222
$941$	−17507.5	−0.606513	−0.303257	−	0.952909i	$-0.598074\pi$
$941$	−17507.5	−0.606513	−0.303257	+	0.952909i	$0.598074\pi$
$942$	136303.	4.71443
$943$	1321.73	0.0456430
$944$	45278.4	1.56111
$945$	−1615.66	−0.0556163
$946$	17336.8	0.595844
$947$	−15368.9	−0.527373	−0.263687	−	0.964608i	$-0.584938\pi$
$947$	−15368.9	−0.527373	−0.263687	+	0.964608i	$0.584938\pi$
$948$	−129252.	−4.42816
$949$	−31388.6	−1.07368
$950$	−12864.1	−0.439333
$951$	−3280.46	−0.111857
$952$	−7110.37	−0.242068
$953$	19354.5	0.657875	0.328938	−	0.944352i	$-0.393309\pi$
$953$	19354.5	0.657875	0.328938	+	0.944352i	$0.393309\pi$
$954$	−44981.4	−1.52655
$955$	−4017.09	−0.136115
$956$	3731.76	0.126249
$957$	−6607.70	−0.223194
$958$	5674.21	0.191363
$959$	−3965.75	−0.133536
$960$	−72207.5	−2.42759
$961$	22658.6	0.760587
$962$	−8394.42	−0.281338
$963$	51940.9	1.73808
$964$	−47130.4	−1.57466
$965$	3451.54	0.115139
$966$	2680.39	0.0892756
$967$	−8986.83	−0.298859	−0.149430	−	0.988772i	$-0.547744\pi$
$967$	−8986.83	−0.298859	−0.149430	+	0.988772i	$0.547744\pi$
$968$	−10685.4	−0.354795
$969$	−9697.96	−0.321510
$970$	8094.53	0.267938
$971$	−16014.7	−0.529284	−0.264642	−	0.964347i	$-0.585254\pi$
$971$	−16014.7	−0.529284	−0.264642	+	0.964347i	$0.585254\pi$
$972$	346700.	11.4408
$973$	−2176.29	−0.0717047
$974$	48140.1	1.58368
$975$	−58930.4	−1.93568
$976$	140587.	4.61073
$977$	42465.7	1.39058	0.695291	−	0.718728i	$-0.255276\pi$
$977$	42465.7	1.39058	0.695291	+	0.718728i	$0.255276\pi$
$978$	108930.	3.56156
$979$	4157.08	0.135711
$980$	17529.8	0.571397
$981$	136200.	4.43277
$982$	−27417.0	−0.890950
$983$	−9815.35	−0.318475	−0.159238	−	0.987240i	$-0.550904\pi$
$983$	−9815.35	−0.318475	−0.159238	+	0.987240i	$0.550904\pi$
$984$	39113.4	1.26716
$985$	4097.79	0.132555
$986$	−17128.4	−0.553223
$987$	−5358.62	−0.172813
$988$	−21967.5	−0.707366
$989$	−8387.07	−0.269659
$990$	−9927.50	−0.318704
$991$	−1750.83	−0.0561220	−0.0280610	−	0.999606i	$-0.508933\pi$
$991$	−1750.83	−0.0561220	−0.0280610	+	0.999606i	$0.508933\pi$
$992$	−234767.	−7.51398
$993$	−15783.1	−0.504392
$994$	−6658.37	−0.212465
$995$	−2982.59	−0.0950297
$996$	182257.	5.79823
$997$	−4947.66	−0.157166	−0.0785828	−	0.996908i	$-0.525039\pi$
$997$	−4947.66	−0.157166	−0.0785828	+	0.996908i	$0.525039\pi$
$998$	−9782.51	−0.310280
$999$	14342.6	0.454235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.4.a.c.1.1	✓	13
3.2	odd	2		1881.4.a.k.1.13		13
11.10	odd	2		2299.4.a.k.1.13		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.4.a.c.1.1	✓	13	1.1	even	1	trivial
1881.4.a.k.1.13		13	3.2	odd	2
2299.4.a.k.1.13		13	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	209.a (trivial)

\(f(q)\)	\(=\)	\(q-5.62918 q^{2} +10.0382 q^{3} +23.6877 q^{4} -2.17343 q^{5} -56.5070 q^{6} +1.58350 q^{7} -88.3091 q^{8} +73.7660 q^{9} +12.2346 q^{10} -11.0000 q^{11} +237.783 q^{12} +48.8093 q^{13} -8.91380 q^{14} -21.8174 q^{15} +307.606 q^{16} +50.8475 q^{17} -415.242 q^{18} -19.0000 q^{19} -51.4836 q^{20} +15.8955 q^{21} +61.9210 q^{22} -29.9557 q^{23} -886.467 q^{24} -120.276 q^{25} -274.757 q^{26} +469.447 q^{27} +37.5094 q^{28} +59.8413 q^{29} +122.814 q^{30} +229.019 q^{31} -1025.10 q^{32} -110.420 q^{33} -286.230 q^{34} -3.44162 q^{35} +1747.35 q^{36} +30.5522 q^{37} +106.955 q^{38} +489.959 q^{39} +191.934 q^{40} -44.1228 q^{41} -89.4787 q^{42} +279.983 q^{43} -260.565 q^{44} -160.325 q^{45} +168.626 q^{46} -337.116 q^{47} +3087.82 q^{48} -340.493 q^{49} +677.057 q^{50} +510.419 q^{51} +1156.18 q^{52} +108.326 q^{53} -2642.61 q^{54} +23.9077 q^{55} -139.837 q^{56} -190.726 q^{57} -336.857 q^{58} +147.196 q^{59} -516.804 q^{60} +457.035 q^{61} -1289.19 q^{62} +116.808 q^{63} +3309.63 q^{64} -106.084 q^{65} +621.577 q^{66} -265.095 q^{67} +1204.46 q^{68} -300.702 q^{69} +19.3735 q^{70} +746.973 q^{71} -6514.20 q^{72} -643.087 q^{73} -171.984 q^{74} -1207.36 q^{75} -450.067 q^{76} -17.4185 q^{77} -2758.07 q^{78} -543.570 q^{79} -668.561 q^{80} +2720.74 q^{81} +248.375 q^{82} +766.485 q^{83} +376.528 q^{84} -110.514 q^{85} -1576.07 q^{86} +600.700 q^{87} +971.400 q^{88} -377.916 q^{89} +902.500 q^{90} +77.2894 q^{91} -709.581 q^{92} +2298.94 q^{93} +1897.69 q^{94} +41.2952 q^{95} -10290.2 q^{96} +661.607 q^{97} +1916.70 q^{98} -811.426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 2 q^{2} + 11 q^{3} + 82 q^{4} + 8 q^{5} + 13 q^{6} + 39 q^{7} + 6 q^{8} + 156 q^{9} + 124 q^{10} - 143 q^{11} + 247 q^{12} - 23 q^{13} + 47 q^{14} + 278 q^{15} + 526 q^{16} + 73 q^{17} - 165 q^{18}+ \cdots - 1716 q^{99}+O(q^{100}) \) 13 * q - 2 * q^2 + 11 * q^3 + 82 * q^4 + 8 * q^5 + 13 * q^6 + 39 * q^7 + 6 * q^8 + 156 * q^9 + 124 * q^10 - 143 * q^11 + 247 * q^12 - 23 * q^13 + 47 * q^14 + 278 * q^15 + 526 * q^16 + 73 * q^17 - 165 * q^18 - 247 * q^19 + 142 * q^20 + 77 * q^21 + 22 * q^22 + 185 * q^23 - 251 * q^24 + 641 * q^25 - 47 * q^26 + 1109 * q^27 + 289 * q^28 - 41 * q^29 + 520 * q^30 + 930 * q^31 - 194 * q^32 - 121 * q^33 - 333 * q^34 + 122 * q^35 + 1469 * q^36 + 1094 * q^37 + 38 * q^38 + 543 * q^39 + 2084 * q^40 - 766 * q^41 - 1277 * q^42 + 1024 * q^43 - 902 * q^44 - 348 * q^45 + 1927 * q^46 + 516 * q^47 + 3067 * q^48 + 1966 * q^49 + 3066 * q^50 + 1975 * q^51 - 553 * q^52 + 1017 * q^53 - 2231 * q^54 - 88 * q^55 - 1793 * q^56 - 209 * q^57 - 159 * q^58 + 15 * q^59 - 3158 * q^60 - 862 * q^61 - 3298 * q^62 + 552 * q^63 + 3694 * q^64 - 1640 * q^65 - 143 * q^66 + 621 * q^67 - 1533 * q^68 + 335 * q^69 - 3250 * q^70 + 632 * q^71 - 8349 * q^72 - 629 * q^73 - 4086 * q^74 - 2759 * q^75 - 1558 * q^76 - 429 * q^77 - 5813 * q^78 + 2444 * q^79 + 2810 * q^80 + 2265 * q^81 - 846 * q^82 + 732 * q^83 - 761 * q^84 - 3786 * q^85 - 4664 * q^86 - 1185 * q^87 - 66 * q^88 + 3178 * q^89 - 6174 * q^90 + 1349 * q^91 - 1677 * q^92 + 1328 * q^93 + 3156 * q^94 - 152 * q^95 - 13811 * q^96 + 1410 * q^97 - 6273 * q^98 - 1716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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