LMFDB - Embedded newform 231.4.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,4,Mod(1,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("231.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.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:	$13.6294412113$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 28x^{3} - 11x^{2} + 108x - 64 $ x^5 - 28x^3 - 11x^2 + 108*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-4.36278$ of defining polynomial
Character	$\chi$	$=$	231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.36278 q^{2} +3.00000 q^{3} +20.7594 q^{4} -1.66863 q^{5} +16.0883 q^{6} -7.00000 q^{7} +68.4261 q^{8} +9.00000 q^{9} -8.94849 q^{10} +11.0000 q^{11} +62.2783 q^{12} +0.996604 q^{13} -37.5395 q^{14} -5.00588 q^{15} +200.879 q^{16} -99.5115 q^{17} +48.2650 q^{18} +32.8695 q^{19} -34.6398 q^{20} -21.0000 q^{21} +58.9906 q^{22} +72.6019 q^{23} +205.278 q^{24} -122.216 q^{25} +5.34457 q^{26} +27.0000 q^{27} -145.316 q^{28} +45.0027 q^{29} -26.8455 q^{30} -62.8102 q^{31} +529.860 q^{32} +33.0000 q^{33} -533.659 q^{34} +11.6804 q^{35} +186.835 q^{36} -301.317 q^{37} +176.272 q^{38} +2.98981 q^{39} -114.178 q^{40} -307.353 q^{41} -112.618 q^{42} +214.347 q^{43} +228.354 q^{44} -15.0176 q^{45} +389.348 q^{46} -602.899 q^{47} +602.636 q^{48} +49.0000 q^{49} -655.416 q^{50} -298.535 q^{51} +20.6889 q^{52} +592.072 q^{53} +144.795 q^{54} -18.3549 q^{55} -478.983 q^{56} +98.6084 q^{57} +241.339 q^{58} +695.030 q^{59} -103.919 q^{60} +442.815 q^{61} -336.837 q^{62} -63.0000 q^{63} +1234.49 q^{64} -1.66296 q^{65} +176.972 q^{66} -555.143 q^{67} -2065.80 q^{68} +217.806 q^{69} +62.6394 q^{70} -153.352 q^{71} +615.835 q^{72} -147.489 q^{73} -1615.90 q^{74} -366.647 q^{75} +682.352 q^{76} -77.0000 q^{77} +16.0337 q^{78} +676.959 q^{79} -335.192 q^{80} +81.0000 q^{81} -1648.27 q^{82} -222.412 q^{83} -435.948 q^{84} +166.048 q^{85} +1149.50 q^{86} +135.008 q^{87} +752.687 q^{88} -1136.35 q^{89} -80.5364 q^{90} -6.97623 q^{91} +1507.18 q^{92} -188.430 q^{93} -3233.22 q^{94} -54.8469 q^{95} +1589.58 q^{96} +1010.60 q^{97} +262.776 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 15 q^{3} + 21 q^{4} + 7 q^{5} + 15 q^{6} - 35 q^{7} + 60 q^{8} + 45 q^{9} + 55 q^{10} + 55 q^{11} + 63 q^{12} + 111 q^{13} - 35 q^{14} + 21 q^{15} + 201 q^{16} + 136 q^{17} + 45 q^{18} + 111 q^{19}+ \cdots + 495 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 15 * q^3 + 21 * q^4 + 7 * q^5 + 15 * q^6 - 35 * q^7 + 60 * q^8 + 45 * q^9 + 55 * q^10 + 55 * q^11 + 63 * q^12 + 111 * q^13 - 35 * q^14 + 21 * q^15 + 201 * q^16 + 136 * q^17 + 45 * q^18 + 111 * q^19 + 219 * q^20 - 105 * q^21 + 55 * q^22 - 28 * q^23 + 180 * q^24 + 190 * q^25 - q^26 + 135 * q^27 - 147 * q^28 + 61 * q^29 + 165 * q^30 - 280 * q^31 + 535 * q^32 + 165 * q^33 - 572 * q^34 - 49 * q^35 + 189 * q^36 - 41 * q^37 + 267 * q^38 + 333 * q^39 - 336 * q^40 + 426 * q^41 - 105 * q^42 + 424 * q^43 + 231 * q^44 + 63 * q^45 + 140 * q^46 + 75 * q^47 + 603 * q^48 + 245 * q^49 + 490 * q^50 + 408 * q^51 - 269 * q^52 + 1500 * q^53 + 135 * q^54 + 77 * q^55 - 420 * q^56 + 333 * q^57 - 1767 * q^58 + 757 * q^59 + 657 * q^60 + 658 * q^61 - 568 * q^62 - 315 * q^63 - 748 * q^64 + 537 * q^65 + 165 * q^66 - 583 * q^67 - 1650 * q^68 - 84 * q^69 - 385 * q^70 - 764 * q^71 + 540 * q^72 + 875 * q^73 - 825 * q^74 + 570 * q^75 + 213 * q^76 - 385 * q^77 - 3 * q^78 - 244 * q^79 - 2577 * q^80 + 405 * q^81 - 2006 * q^82 + 924 * q^83 - 441 * q^84 - 1402 * q^85 + 1272 * q^86 + 183 * q^87 + 660 * q^88 - 1110 * q^89 + 495 * q^90 - 777 * q^91 - 2046 * q^92 - 840 * q^93 - 3349 * q^94 + 1923 * q^95 + 1605 * q^96 - 852 * q^97 + 245 * q^98 + 495 * 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 $

$2$	5.36278	1.89603	0.948015	−	0.318226i	$-0.103087\pi$
$2$	5.36278	1.89603	0.948015	+	0.318226i	$0.103087\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	20.7594	2.59493
$5$	−1.66863	−0.149247	−0.0746233	−	0.997212i	$-0.523775\pi$
$5$	−1.66863	−0.149247	−0.0746233	+	0.997212i	$0.523775\pi$
$6$	16.0883	1.09467
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	68.4261	3.02403
$9$	9.00000	0.333333
$10$	−8.94849	−0.282976
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	62.2783	1.49818
$13$	0.996604	0.0212622	0.0106311	−	0.999943i	$-0.496616\pi$
$13$	0.996604	0.0212622	0.0106311	+	0.999943i	$0.496616\pi$
$14$	−37.5395	−0.716632
$15$	−5.00588	−0.0861675
$16$	200.879	3.13873
$17$	−99.5115	−1.41971	−0.709856	−	0.704347i	$-0.751240\pi$
$17$	−99.5115	−1.41971	−0.709856	+	0.704347i	$0.751240\pi$
$18$	48.2650	0.632010
$19$	32.8695	0.396883	0.198441	−	0.980113i	$-0.436412\pi$
$19$	32.8695	0.396883	0.198441	+	0.980113i	$0.436412\pi$
$20$	−34.6398	−0.387284
$21$	−21.0000	−0.218218
$22$	58.9906	0.571675
$23$	72.6019	0.658198	0.329099	−	0.944295i	$-0.393255\pi$
$23$	72.6019	0.658198	0.329099	+	0.944295i	$0.393255\pi$
$24$	205.278	1.74593
$25$	−122.216	−0.977725
$26$	5.34457	0.0403137
$27$	27.0000	0.192450
$28$	−145.316	−0.980791
$29$	45.0027	0.288165	0.144082	−	0.989566i	$-0.453977\pi$
$29$	45.0027	0.288165	0.144082	+	0.989566i	$0.453977\pi$
$30$	−26.8455	−0.163376
$31$	−62.8102	−0.363904	−0.181952	−	0.983307i	$-0.558242\pi$
$31$	−62.8102	−0.363904	−0.181952	+	0.983307i	$0.558242\pi$
$32$	529.860	2.92709
$33$	33.0000	0.174078
$34$	−533.659	−2.69182
$35$	11.6804	0.0564099
$36$	186.835	0.864976
$37$	−301.317	−1.33882	−0.669408	−	0.742895i	$-0.733452\pi$
$37$	−301.317	−1.33882	−0.669408	+	0.742895i	$0.733452\pi$
$38$	176.272	0.752502
$39$	2.98981	0.0122757
$40$	−114.178	−0.451327
$41$	−307.353	−1.17074	−0.585371	−	0.810765i	$-0.699051\pi$
$41$	−307.353	−1.17074	−0.585371	+	0.810765i	$0.699051\pi$
$42$	−112.618	−0.413748
$43$	214.347	0.760178	0.380089	−	0.924950i	$-0.375893\pi$
$43$	214.347	0.760178	0.380089	+	0.924950i	$0.375893\pi$
$44$	228.354	0.782401
$45$	−15.0176	−0.0497489
$46$	389.348	1.24796
$47$	−602.899	−1.87110	−0.935552	−	0.353188i	$-0.885098\pi$
$47$	−602.899	−1.87110	−0.935552	+	0.353188i	$0.885098\pi$
$48$	602.636	1.81215
$49$	49.0000	0.142857
$50$	−655.416	−1.85380
$51$	−298.535	−0.819671
$52$	20.6889	0.0551738
$53$	592.072	1.53448	0.767239	−	0.641362i	$-0.221630\pi$
$53$	592.072	1.53448	0.767239	+	0.641362i	$0.221630\pi$
$54$	144.795	0.364891
$55$	−18.3549	−0.0449995
$56$	−478.983	−1.14298
$57$	98.6084	0.229140
$58$	241.339	0.546369
$59$	695.030	1.53365	0.766824	−	0.641857i	$-0.221836\pi$
$59$	695.030	1.53365	0.766824	+	0.641857i	$0.221836\pi$
$60$	−103.919	−0.223599
$61$	442.815	0.929453	0.464726	−	0.885454i	$-0.346153\pi$
$61$	442.815	0.929453	0.464726	+	0.885454i	$0.346153\pi$
$62$	−336.837	−0.689974
$63$	−63.0000	−0.125988
$64$	1234.49	2.41112
$65$	−1.66296	−0.00317331
$66$	176.972	0.330056
$67$	−555.143	−1.01226	−0.506131	−	0.862457i	$-0.668925\pi$
$67$	−555.143	−1.01226	−0.506131	+	0.862457i	$0.668925\pi$
$68$	−2065.80	−3.68405
$69$	217.806	0.380011
$70$	62.6394	0.106955
$71$	−153.352	−0.256331	−0.128166	−	0.991753i	$-0.540909\pi$
$71$	−153.352	−0.256331	−0.128166	+	0.991753i	$0.540909\pi$
$72$	615.835	1.00801
$73$	−147.489	−0.236470	−0.118235	−	0.992986i	$-0.537724\pi$
$73$	−147.489	−0.236470	−0.118235	+	0.992986i	$0.537724\pi$
$74$	−1615.90	−2.53843
$75$	−366.647	−0.564490
$76$	682.352	1.02988
$77$	−77.0000	−0.113961
$78$	16.0337	0.0232751
$79$	676.959	0.964099	0.482050	−	0.876144i	$-0.339893\pi$
$79$	676.959	0.964099	0.482050	+	0.876144i	$0.339893\pi$
$80$	−335.192	−0.468445
$81$	81.0000	0.111111
$82$	−1648.27	−2.21976
$83$	−222.412	−0.294131	−0.147065	−	0.989127i	$-0.546983\pi$
$83$	−222.412	−0.294131	−0.147065	+	0.989127i	$0.546983\pi$
$84$	−435.948	−0.566260
$85$	166.048	0.211887
$86$	1149.50	1.44132
$87$	135.008	0.166372
$88$	752.687	0.911781
$89$	−1136.35	−1.35340	−0.676699	−	0.736260i	$-0.736590\pi$
$89$	−1136.35	−1.35340	−0.676699	+	0.736260i	$0.736590\pi$
$90$	−80.5364	−0.0943253
$91$	−6.97623	−0.00803634
$92$	1507.18	1.70798
$93$	−188.430	−0.210100
$94$	−3233.22	−3.54767
$95$	−54.8469	−0.0592334
$96$	1589.58	1.68996
$97$	1010.60	1.05785	0.528923	−	0.848670i	$-0.322596\pi$
$97$	1010.60	1.05785	0.528923	+	0.848670i	$0.322596\pi$
$98$	262.776	0.270861
$99$	99.0000	0.100504
$100$	−2537.13	−2.53713
$101$	−400.418	−0.394486	−0.197243	−	0.980355i	$-0.563199\pi$
$101$	−400.418	−0.394486	−0.197243	+	0.980355i	$0.563199\pi$
$102$	−1600.98	−1.55412
$103$	−419.845	−0.401636	−0.200818	−	0.979629i	$-0.564360\pi$
$103$	−419.845	−0.401636	−0.200818	+	0.979629i	$0.564360\pi$
$104$	68.1937	0.0642975
$105$	35.0412	0.0325683
$106$	3175.15	2.90941
$107$	2131.99	1.92623	0.963116	−	0.269085i	$-0.0867214\pi$
$107$	2131.99	1.92623	0.963116	+	0.269085i	$0.0867214\pi$
$108$	560.505	0.499394
$109$	−14.0057	−0.0123074	−0.00615369	−	0.999981i	$-0.501959\pi$
$109$	−14.0057	−0.0123074	−0.00615369	+	0.999981i	$0.501959\pi$
$110$	−98.4333	−0.0853205
$111$	−903.950	−0.772965
$112$	−1406.15	−1.18633
$113$	1322.98	1.10137	0.550686	−	0.834712i	$-0.314366\pi$
$113$	1322.98	1.10137	0.550686	+	0.834712i	$0.314366\pi$
$114$	528.816	0.434457
$115$	−121.146	−0.0982338
$116$	934.230	0.747768
$117$	8.96944	0.00708739
$118$	3727.30	2.90784
$119$	696.581	0.536601
$120$	−342.533	−0.260574
$121$	121.000	0.0909091
$122$	2374.72	1.76227
$123$	−922.059	−0.675929
$124$	−1303.90	−0.944306
$125$	412.511	0.295169
$126$	−337.855	−0.238877
$127$	−2199.01	−1.53646	−0.768232	−	0.640172i	$-0.778863\pi$
$127$	−2199.01	−1.53646	−0.768232	+	0.640172i	$0.778863\pi$
$128$	2381.45	1.64447
$129$	643.042	0.438889
$130$	−8.91810	−0.00601668
$131$	1450.27	0.967259	0.483629	−	0.875273i	$-0.339318\pi$
$131$	1450.27	0.967259	0.483629	+	0.875273i	$0.339318\pi$
$132$	685.061	0.451719
$133$	−230.086	−0.150008
$134$	−2977.11	−1.91928
$135$	−45.0529	−0.0287225
$136$	−6809.19	−4.29326
$137$	−893.027	−0.556909	−0.278454	−	0.960449i	$-0.589822\pi$
$137$	−893.027	−0.556909	−0.278454	+	0.960449i	$0.589822\pi$
$138$	1168.05	0.720512
$139$	−530.606	−0.323780	−0.161890	−	0.986809i	$-0.551759\pi$
$139$	−530.606	−0.323780	−0.161890	+	0.986809i	$0.551759\pi$
$140$	242.478	0.146380
$141$	−1808.70	−1.08028
$142$	−822.392	−0.486011
$143$	10.9626	0.00641079
$144$	1807.91	1.04624
$145$	−75.0927	−0.0430076
$146$	−790.954	−0.448355
$147$	147.000	0.0824786
$148$	−6255.17	−3.47413
$149$	2958.97	1.62690	0.813451	−	0.581633i	$-0.197586\pi$
$149$	2958.97	1.62690	0.813451	+	0.581633i	$0.197586\pi$
$150$	−1966.25	−1.07029
$151$	1668.28	0.899092	0.449546	−	0.893257i	$-0.351586\pi$
$151$	1668.28	0.899092	0.449546	+	0.893257i	$0.351586\pi$
$152$	2249.13	1.20019
$153$	−895.604	−0.473237
$154$	−412.934	−0.216073
$155$	104.807	0.0543115
$156$	62.0668	0.0318546
$157$	−1202.63	−0.611342	−0.305671	−	0.952137i	$-0.598881\pi$
$157$	−1202.63	−0.611342	−0.305671	+	0.952137i	$0.598881\pi$
$158$	3630.38	1.82796
$159$	1776.21	0.885931
$160$	−884.139	−0.436858
$161$	−508.214	−0.248775
$162$	434.385	0.210670
$163$	−2534.83	−1.21806	−0.609029	−	0.793148i	$-0.708441\pi$
$163$	−2534.83	−1.21806	−0.609029	+	0.793148i	$0.708441\pi$
$164$	−6380.47	−3.03799
$165$	−55.0647	−0.0259805
$166$	−1192.75	−0.557681
$167$	2424.43	1.12340	0.561700	−	0.827341i	$-0.310147\pi$
$167$	2424.43	1.12340	0.561700	+	0.827341i	$0.310147\pi$
$168$	−1436.95	−0.659898
$169$	−2196.01	−0.999548
$170$	890.478	0.401744
$171$	295.825	0.132294
$172$	4449.73	1.97261
$173$	1977.78	0.869180	0.434590	−	0.900628i	$-0.356893\pi$
$173$	1977.78	0.869180	0.434590	+	0.900628i	$0.356893\pi$
$174$	724.018	0.315447
$175$	855.510	0.369545
$176$	2209.67	0.946363
$177$	2085.09	0.885452
$178$	−6093.97	−2.56608
$179$	1314.89	0.549049	0.274525	−	0.961580i	$-0.411480\pi$
$179$	1314.89	0.549049	0.274525	+	0.961580i	$0.411480\pi$
$180$	−311.758	−0.129095
$181$	2118.94	0.870163	0.435081	−	0.900391i	$-0.356720\pi$
$181$	2118.94	0.870163	0.435081	+	0.900391i	$0.356720\pi$
$182$	−37.4120	−0.0152372
$183$	1328.44	0.536620
$184$	4967.87	1.99041
$185$	502.785	0.199814
$186$	−1010.51	−0.398357
$187$	−1094.63	−0.428059
$188$	−12515.9	−4.85538
$189$	−189.000	−0.0727393
$190$	−294.132	−0.112308
$191$	2136.61	0.809421	0.404711	−	0.914445i	$-0.367372\pi$
$191$	2136.61	0.809421	0.404711	+	0.914445i	$0.367372\pi$
$192$	3703.48	1.39206
$193$	−910.852	−0.339713	−0.169856	−	0.985469i	$-0.554330\pi$
$193$	−910.852	−0.339713	−0.169856	+	0.985469i	$0.554330\pi$
$194$	5419.64	2.00571
$195$	−4.98888	−0.00183211
$196$	1017.21	0.370704
$197$	−2485.86	−0.899038	−0.449519	−	0.893271i	$-0.648405\pi$
$197$	−2485.86	−0.899038	−0.449519	+	0.893271i	$0.648405\pi$
$198$	530.915	0.190558
$199$	−384.145	−0.136841	−0.0684204	−	0.997657i	$-0.521796\pi$
$199$	−384.145	−0.136841	−0.0684204	+	0.997657i	$0.521796\pi$
$200$	−8362.74	−2.95668
$201$	−1665.43	−0.584429
$202$	−2147.36	−0.747958
$203$	−315.019	−0.108916
$204$	−6197.41	−2.12699
$205$	512.857	0.174729
$206$	−2251.54	−0.761515
$207$	653.417	0.219399
$208$	200.196	0.0667362
$209$	361.564	0.119665
$210$	187.918	0.0617504
$211$	3875.31	1.26440	0.632198	−	0.774807i	$-0.282153\pi$
$211$	3875.31	1.26440	0.632198	+	0.774807i	$0.282153\pi$
$212$	12291.1	3.98186
$213$	−460.055	−0.147993
$214$	11433.4	3.65219
$215$	−357.666	−0.113454
$216$	1847.50	0.581976
$217$	439.671	0.137543
$218$	−75.1096	−0.0233352
$219$	−442.468	−0.136526
$220$	−381.037	−0.116771
$221$	−99.1736	−0.0301861
$222$	−4847.69	−1.46557
$223$	449.799	0.135071	0.0675354	−	0.997717i	$-0.478486\pi$
$223$	449.799	0.135071	0.0675354	+	0.997717i	$0.478486\pi$
$224$	−3709.02	−1.10634
$225$	−1099.94	−0.325908
$226$	7094.83	2.08823
$227$	5873.32	1.71729	0.858647	−	0.512567i	$-0.171305\pi$
$227$	5873.32	1.71729	0.858647	+	0.512567i	$0.171305\pi$
$228$	2047.06	0.594603
$229$	4207.68	1.21420	0.607099	−	0.794626i	$-0.292333\pi$
$229$	4207.68	1.21420	0.607099	+	0.794626i	$0.292333\pi$
$230$	−649.677	−0.186254
$231$	−231.000	−0.0657952
$232$	3079.36	0.871421
$233$	5405.81	1.51994	0.759970	−	0.649958i	$-0.225213\pi$
$233$	5405.81	1.51994	0.759970	+	0.649958i	$0.225213\pi$
$234$	48.1011	0.0134379
$235$	1006.01	0.279256
$236$	14428.4	3.97971
$237$	2030.88	0.556623
$238$	3735.61	1.01741
$239$	−5105.16	−1.38170	−0.690848	−	0.723000i	$-0.742763\pi$
$239$	−5105.16	−1.38170	−0.690848	+	0.723000i	$0.742763\pi$
$240$	−1005.58	−0.270457
$241$	254.138	0.0679273	0.0339637	−	0.999423i	$-0.489187\pi$
$241$	254.138	0.0679273	0.0339637	+	0.999423i	$0.489187\pi$
$242$	648.897	0.172366
$243$	243.000	0.0641500
$244$	9192.58	2.41186
$245$	−81.7627	−0.0213209
$246$	−4944.80	−1.28158
$247$	32.7579	0.00843859
$248$	−4297.85	−1.10046
$249$	−667.235	−0.169816
$250$	2212.21	0.559649
$251$	7030.70	1.76802	0.884012	−	0.467464i	$-0.154832\pi$
$251$	7030.70	1.76802	0.884012	+	0.467464i	$0.154832\pi$
$252$	−1307.84	−0.326930
$253$	798.621	0.198454
$254$	−11792.8	−2.91318
$255$	498.143	0.122333
$256$	2895.22	0.706841
$257$	6053.67	1.46933	0.734664	−	0.678431i	$-0.237340\pi$
$257$	6053.67	1.46933	0.734664	+	0.678431i	$0.237340\pi$
$258$	3448.49	0.832146
$259$	2109.22	0.506025
$260$	−34.5221	−0.00823451
$261$	405.024	0.0960550
$262$	7777.50	1.83395
$263$	−6106.79	−1.43179	−0.715895	−	0.698208i	$-0.753981\pi$
$263$	−6106.79	−1.43179	−0.715895	+	0.698208i	$0.753981\pi$
$264$	2258.06	0.526417
$265$	−987.947	−0.229015
$266$	−1233.90	−0.284419
$267$	−3409.04	−0.781384
$268$	−11524.5	−2.62675
$269$	4855.91	1.10063	0.550316	−	0.834956i	$-0.314507\pi$
$269$	4855.91	1.10063	0.550316	+	0.834956i	$0.314507\pi$
$270$	−241.609	−0.0544588
$271$	−8501.09	−1.90555	−0.952775	−	0.303676i	$-0.901786\pi$
$271$	−8501.09	−1.90555	−0.952775	+	0.303676i	$0.901786\pi$
$272$	−19989.7	−4.45609
$273$	−20.9287	−0.00463979
$274$	−4789.11	−1.05592
$275$	−1344.37	−0.294795
$276$	4521.53	0.986101
$277$	−6830.18	−1.48154	−0.740768	−	0.671761i	$-0.765538\pi$
$277$	−6830.18	−1.48154	−0.740768	+	0.671761i	$0.765538\pi$
$278$	−2845.52	−0.613896
$279$	−565.291	−0.121301
$280$	799.243	0.170585
$281$	4987.88	1.05890	0.529452	−	0.848340i	$-0.322397\pi$
$281$	4987.88	1.05890	0.529452	+	0.848340i	$0.322397\pi$
$282$	−9699.66	−2.04825
$283$	−1952.88	−0.410200	−0.205100	−	0.978741i	$-0.565752\pi$
$283$	−1952.88	−0.410200	−0.205100	+	0.978741i	$0.565752\pi$
$284$	−3183.50	−0.665161
$285$	−164.541	−0.0341984
$286$	58.7903	0.0121550
$287$	2151.47	0.442499
$288$	4768.74	0.975697
$289$	4989.55	1.01558
$290$	−402.706	−0.0815438
$291$	3031.81	0.610748
$292$	−3061.80	−0.613624
$293$	−3220.72	−0.642172	−0.321086	−	0.947050i	$-0.604048\pi$
$293$	−3220.72	−0.642172	−0.321086	+	0.947050i	$0.604048\pi$
$294$	788.329	0.156382
$295$	−1159.75	−0.228892
$296$	−20617.9	−4.04862
$297$	297.000	0.0580259
$298$	15868.3	3.08466
$299$	72.3554	0.0139947
$300$	−7611.39	−1.46481
$301$	−1500.43	−0.287320
$302$	8946.64	1.70471
$303$	−1201.25	−0.227757
$304$	6602.78	1.24571
$305$	−738.893	−0.138718
$306$	−4802.93	−0.897272
$307$	−5325.08	−0.989963	−0.494981	−	0.868904i	$-0.664825\pi$
$307$	−5325.08	−0.989963	−0.494981	+	0.868904i	$0.664825\pi$
$308$	−1598.48	−0.295720
$309$	−1259.53	−0.231885
$310$	562.056	0.102976
$311$	−9625.36	−1.75500	−0.877498	−	0.479580i	$-0.840789\pi$
$311$	−9625.36	−1.75500	−0.877498	+	0.479580i	$0.840789\pi$
$312$	204.581	0.0371222
$313$	−4315.55	−0.779327	−0.389664	−	0.920957i	$-0.627409\pi$
$313$	−4315.55	−0.779327	−0.389664	+	0.920957i	$0.627409\pi$
$314$	−6449.46	−1.15912
$315$	105.124	0.0188033
$316$	14053.3	2.50177
$317$	−7399.84	−1.31109	−0.655546	−	0.755155i	$-0.727562\pi$
$317$	−7399.84	−1.31109	−0.655546	+	0.755155i	$0.727562\pi$
$318$	9525.45	1.67975
$319$	495.029	0.0868850
$320$	−2059.91	−0.359852
$321$	6395.96	1.11211
$322$	−2725.44	−0.471686
$323$	−3270.89	−0.563459
$324$	1681.51	0.288325
$325$	−121.801	−0.0207886
$326$	−13593.8	−2.30947
$327$	−42.0171	−0.00710567
$328$	−21031.0	−3.54037
$329$	4220.30	0.707211
$330$	−295.300	−0.0492598
$331$	−4899.29	−0.813562	−0.406781	−	0.913526i	$-0.633349\pi$
$331$	−4899.29	−0.813562	−0.406781	+	0.913526i	$0.633349\pi$
$332$	−4617.14	−0.763248
$333$	−2711.85	−0.446272
$334$	13001.7	2.13000
$335$	926.327	0.151077
$336$	−4218.45	−0.684927
$337$	−1445.02	−0.233577	−0.116788	−	0.993157i	$-0.537260\pi$
$337$	−1445.02	−0.233577	−0.116788	+	0.993157i	$0.537260\pi$
$338$	−11776.7	−1.89517
$339$	3968.93	0.635878
$340$	3447.06	0.549832
$341$	−690.912	−0.109721
$342$	1586.45	0.250834
$343$	−343.000	−0.0539949
$344$	14666.9	2.29880
$345$	−363.437	−0.0567153
$346$	10606.4	1.64799
$347$	4351.93	0.673268	0.336634	−	0.941636i	$-0.390711\pi$
$347$	4351.93	0.673268	0.336634	+	0.941636i	$0.390711\pi$
$348$	2802.69	0.431724
$349$	7971.30	1.22262	0.611309	−	0.791392i	$-0.290643\pi$
$349$	7971.30	1.22262	0.611309	+	0.791392i	$0.290643\pi$
$350$	4587.91	0.700669
$351$	26.9083	0.00409191
$352$	5828.46	0.882551
$353$	−1169.88	−0.176393	−0.0881963	−	0.996103i	$-0.528110\pi$
$353$	−1169.88	−0.176393	−0.0881963	+	0.996103i	$0.528110\pi$
$354$	11181.9	1.67884
$355$	255.887	0.0382565
$356$	−23589.9	−3.51197
$357$	2089.74	0.309806
$358$	7051.49	1.04101
$359$	11998.8	1.76400	0.881998	−	0.471253i	$-0.156198\pi$
$359$	11998.8	1.76400	0.881998	+	0.471253i	$0.156198\pi$
$360$	−1027.60	−0.150442
$361$	−5778.60	−0.842484
$362$	11363.4	1.64985
$363$	363.000	0.0524864
$364$	−144.823	−0.0208537
$365$	246.105	0.0352924
$366$	7124.16	1.01745
$367$	−8489.94	−1.20755	−0.603776	−	0.797154i	$-0.706338\pi$
$367$	−8489.94	−1.20755	−0.603776	+	0.797154i	$0.706338\pi$
$368$	14584.2	2.06590
$369$	−2766.18	−0.390248
$370$	2696.33	0.378853
$371$	−4144.50	−0.579978
$372$	−3911.71	−0.545196
$373$	−13306.1	−1.84708	−0.923542	−	0.383498i	$-0.874719\pi$
$373$	−13306.1	−1.84708	−0.923542	+	0.383498i	$0.874719\pi$
$374$	−5870.25	−0.811613
$375$	1237.53	0.170416
$376$	−41254.0	−5.65828
$377$	44.8498	0.00612701
$378$	−1013.57	−0.137916
$379$	−10645.0	−1.44274	−0.721368	−	0.692552i	$-0.756486\pi$
$379$	−10645.0	−1.44274	−0.721368	+	0.692552i	$0.756486\pi$
$380$	−1138.59	−0.153707
$381$	−6597.04	−0.887078
$382$	11458.2	1.53469
$383$	2299.39	0.306771	0.153385	−	0.988166i	$-0.450982\pi$
$383$	2299.39	0.306771	0.153385	+	0.988166i	$0.450982\pi$
$384$	7144.34	0.949435
$385$	128.484	0.0170082
$386$	−4884.70	−0.644105
$387$	1929.12	0.253393
$388$	20979.5	2.74504
$389$	−3243.77	−0.422791	−0.211395	−	0.977401i	$-0.567801\pi$
$389$	−3243.77	−0.422791	−0.211395	+	0.977401i	$0.567801\pi$
$390$	−26.7543	−0.00347373
$391$	−7224.73	−0.934451
$392$	3352.88	0.432005
$393$	4350.82	0.558447
$394$	−13331.1	−1.70460
$395$	−1129.59	−0.143888
$396$	2055.18	0.260800
$397$	13850.8	1.75102	0.875508	−	0.483203i	$-0.160527\pi$
$397$	13850.8	1.75102	0.875508	+	0.483203i	$0.160527\pi$
$398$	−2060.09	−0.259454
$399$	−690.259	−0.0866070
$400$	−24550.5	−3.06882
$401$	1238.44	0.154227	0.0771133	−	0.997022i	$-0.475430\pi$
$401$	1238.44	0.154227	0.0771133	+	0.997022i	$0.475430\pi$
$402$	−8931.33	−1.10810
$403$	−62.5969	−0.00773740
$404$	−8312.46	−1.02366
$405$	−135.159	−0.0165830
$406$	−1689.38	−0.206508
$407$	−3314.48	−0.403668
$408$	−20427.6	−2.47871
$409$	−3951.51	−0.477726	−0.238863	−	0.971053i	$-0.576775\pi$
$409$	−3951.51	−0.477726	−0.238863	+	0.971053i	$0.576775\pi$
$410$	2750.34	0.331292
$411$	−2679.08	−0.321531
$412$	−8715.74	−1.04222
$413$	−4865.21	−0.579665
$414$	3504.14	0.415988
$415$	371.122	0.0438980
$416$	528.061	0.0622363
$417$	−1591.82	−0.186934
$418$	1938.99	0.226888
$419$	−11603.6	−1.35292	−0.676462	−	0.736477i	$-0.736488\pi$
$419$	−11603.6	−1.35292	−0.676462	+	0.736477i	$0.736488\pi$
$420$	727.435	0.0845124
$421$	−10498.9	−1.21541	−0.607703	−	0.794165i	$-0.707909\pi$
$421$	−10498.9	−1.21541	−0.607703	+	0.794165i	$0.707909\pi$
$422$	20782.5	2.39733
$423$	−5426.09	−0.623702
$424$	40513.1	4.64031
$425$	12161.9	1.38809
$426$	−2467.18	−0.280599
$427$	−3099.70	−0.351300
$428$	44258.8	4.99844
$429$	32.8879	0.00370127
$430$	−1918.08	−0.215112
$431$	−11109.2	−1.24156	−0.620778	−	0.783986i	$-0.713183\pi$
$431$	−11109.2	−1.24156	−0.620778	+	0.783986i	$0.713183\pi$
$432$	5423.72	0.604049
$433$	12535.7	1.39129	0.695644	−	0.718387i	$-0.255119\pi$
$433$	12535.7	1.39129	0.695644	+	0.718387i	$0.255119\pi$
$434$	2357.86	0.260786
$435$	−225.278	−0.0248305
$436$	−290.751	−0.0319368
$437$	2386.39	0.261227
$438$	−2372.86	−0.258858
$439$	2227.80	0.242203	0.121102	−	0.992640i	$-0.461357\pi$
$439$	2227.80	0.242203	0.121102	+	0.992640i	$0.461357\pi$
$440$	−1255.95	−0.136080
$441$	441.000	0.0476190
$442$	−531.846	−0.0572338
$443$	−833.252	−0.0893657	−0.0446828	−	0.999001i	$-0.514228\pi$
$443$	−833.252	−0.0893657	−0.0446828	+	0.999001i	$0.514228\pi$
$444$	−18765.5	−2.00579
$445$	1896.14	0.201990
$446$	2412.17	0.256098
$447$	8876.92	0.939293
$448$	−8641.46	−0.911319
$449$	−4903.89	−0.515432	−0.257716	−	0.966221i	$-0.582970\pi$
$449$	−4903.89	−0.515432	−0.257716	+	0.966221i	$0.582970\pi$
$450$	−5898.75	−0.617932
$451$	−3380.88	−0.352992
$452$	27464.2	2.85798
$453$	5004.85	0.519091
$454$	31497.3	3.25604
$455$	11.6407	0.00119940
$456$	6747.39	0.692929
$457$	12100.7	1.23861	0.619307	−	0.785149i	$-0.287414\pi$
$457$	12100.7	1.23861	0.619307	+	0.785149i	$0.287414\pi$
$458$	22564.9	2.30216
$459$	−2686.81	−0.273224
$460$	−2514.91	−0.254910
$461$	−1271.16	−0.128425	−0.0642125	−	0.997936i	$-0.520454\pi$
$461$	−1271.16	−0.128425	−0.0642125	+	0.997936i	$0.520454\pi$
$462$	−1238.80	−0.124750
$463$	−16020.3	−1.60805	−0.804024	−	0.594596i	$-0.797312\pi$
$463$	−16020.3	−1.60805	−0.804024	+	0.594596i	$0.797312\pi$
$464$	9040.08	0.904472
$465$	314.420	0.0313568
$466$	28990.2	2.88185
$467$	−10696.1	−1.05986	−0.529930	−	0.848042i	$-0.677782\pi$
$467$	−10696.1	−1.05986	−0.529930	+	0.848042i	$0.677782\pi$
$468$	186.200	0.0183913
$469$	3886.00	0.382599
$470$	5395.04	0.529478
$471$	−3607.90	−0.352958
$472$	47558.2	4.63780
$473$	2357.82	0.229202
$474$	10891.2	1.05537
$475$	−4017.17	−0.388043
$476$	14460.6	1.39244
$477$	5328.64	0.511492
$478$	−27377.9	−2.61974
$479$	−12055.2	−1.14993	−0.574963	−	0.818179i	$-0.694984\pi$
$479$	−12055.2	−1.14993	−0.574963	+	0.818179i	$0.694984\pi$
$480$	−2652.42	−0.252220
$481$	−300.293	−0.0284661
$482$	1362.89	0.128792
$483$	−1524.64	−0.143631
$484$	2511.89	0.235903
$485$	−1686.32	−0.157880
$486$	1303.16	0.121630
$487$	−14273.2	−1.32809	−0.664045	−	0.747693i	$-0.731162\pi$
$487$	−14273.2	−1.32809	−0.664045	+	0.747693i	$0.731162\pi$
$488$	30300.1	2.81070
$489$	−7604.50	−0.703246
$490$	−438.476	−0.0404251
$491$	−15616.7	−1.43538	−0.717691	−	0.696362i	$-0.754801\pi$
$491$	−15616.7	−1.43538	−0.717691	+	0.696362i	$0.754801\pi$
$492$	−19141.4	−1.75399
$493$	−4478.28	−0.409111
$494$	175.673	0.0159998
$495$	−165.194	−0.0149998
$496$	−12617.2	−1.14220
$497$	1073.46	0.0968841
$498$	−3578.24	−0.321977
$499$	5820.03	0.522125	0.261062	−	0.965322i	$-0.415927\pi$
$499$	5820.03	0.522125	0.261062	+	0.965322i	$0.415927\pi$
$500$	8563.49	0.765942
$501$	7273.28	0.648596
$502$	37704.1	3.35223
$503$	−1744.38	−0.154629	−0.0773143	−	0.997007i	$-0.524634\pi$
$503$	−1744.38	−0.154629	−0.0773143	+	0.997007i	$0.524634\pi$
$504$	−4310.84	−0.380992
$505$	668.149	0.0588757
$506$	4282.83	0.376275
$507$	−6588.02	−0.577089
$508$	−45650.3	−3.98701
$509$	−4561.13	−0.397187	−0.198594	−	0.980082i	$-0.563637\pi$
$509$	−4561.13	−0.397187	−0.198594	+	0.980082i	$0.563637\pi$
$510$	2671.43	0.231947
$511$	1032.43	0.0893774
$512$	−3525.13	−0.304278
$513$	887.476	0.0763802
$514$	32464.5	2.78589
$515$	700.565	0.0599429
$516$	13349.2	1.13889
$517$	−6631.89	−0.564159
$518$	11311.3	0.959438
$519$	5933.35	0.501822
$520$	−113.790	−0.00959619
$521$	−311.151	−0.0261646	−0.0130823	−	0.999914i	$-0.504164\pi$
$521$	−311.151	−0.0261646	−0.0130823	+	0.999914i	$0.504164\pi$
$522$	2172.06	0.182123
$523$	18159.9	1.51831	0.759154	−	0.650911i	$-0.225613\pi$
$523$	18159.9	1.51831	0.759154	+	0.650911i	$0.225613\pi$
$524$	30106.8	2.50997
$525$	2566.53	0.213357
$526$	−32749.4	−2.71472
$527$	6250.34	0.516639
$528$	6629.00	0.546383
$529$	−6895.96	−0.566776
$530$	−5298.14	−0.434220
$531$	6255.27	0.511216
$532$	−4776.46	−0.389259
$533$	−306.309	−0.0248925
$534$	−18281.9	−1.48153
$535$	−3557.49	−0.287484
$536$	−37986.3	−3.06111
$537$	3944.68	0.316994
$538$	26041.2	2.08683
$539$	539.000	0.0430730
$540$	−935.274	−0.0745329
$541$	10858.8	0.862951	0.431476	−	0.902125i	$-0.357993\pi$
$541$	10858.8	0.862951	0.431476	+	0.902125i	$0.357993\pi$
$542$	−45589.5	−3.61298
$543$	6356.81	0.502389
$544$	−52727.2	−4.15562
$545$	23.3703	0.00183683
$546$	−112.236	−0.00879717
$547$	9560.10	0.747277	0.373638	−	0.927574i	$-0.378110\pi$
$547$	9560.10	0.747277	0.373638	+	0.927574i	$0.378110\pi$
$548$	−18538.7	−1.44514
$549$	3985.33	0.309818
$550$	−7209.58	−0.558941
$551$	1479.21	0.114368
$552$	14903.6	1.14917
$553$	−4738.71	−0.364395
$554$	−36628.8	−2.80904
$555$	1508.36	0.115362
$556$	−11015.1	−0.840186
$557$	−961.471	−0.0731397	−0.0365699	−	0.999331i	$-0.511643\pi$
$557$	−961.471	−0.0731397	−0.0365699	+	0.999331i	$0.511643\pi$
$558$	−3031.53	−0.229991
$559$	213.619	0.0161630
$560$	2346.34	0.177055
$561$	−3283.88	−0.247140
$562$	26748.9	2.00772
$563$	26376.5	1.97449	0.987245	−	0.159206i	$-0.0508935\pi$
$563$	26376.5	1.97449	0.987245	+	0.159206i	$0.0508935\pi$
$564$	−37547.6	−2.80326
$565$	−2207.55	−0.164376
$566$	−10472.9	−0.777751
$567$	−567.000	−0.0419961
$568$	−10493.3	−0.775154
$569$	8256.23	0.608294	0.304147	−	0.952625i	$-0.401629\pi$
$569$	8256.23	0.608294	0.304147	+	0.952625i	$0.401629\pi$
$570$	−882.396	−0.0648412
$571$	−25003.0	−1.83248	−0.916239	−	0.400632i	$-0.868791\pi$
$571$	−25003.0	−1.83248	−0.916239	+	0.400632i	$0.868791\pi$
$572$	227.578	0.0166355
$573$	6409.82	0.467320
$574$	11537.9	0.838992
$575$	−8873.09	−0.643537
$576$	11110.5	0.803708
$577$	−5560.17	−0.401166	−0.200583	−	0.979677i	$-0.564284\pi$
$577$	−5560.17	−0.401166	−0.200583	+	0.979677i	$0.564284\pi$
$578$	26757.9	1.92557
$579$	−2732.56	−0.196133
$580$	−1558.88	−0.111602
$581$	1556.88	0.111171
$582$	16258.9	1.15800
$583$	6512.79	0.462662
$584$	−10092.1	−0.715094
$585$	−14.9666	−0.00105777
$586$	−17272.0	−1.21758
$587$	3926.82	0.276111	0.138055	−	0.990425i	$-0.455915\pi$
$587$	3926.82	0.276111	0.138055	+	0.990425i	$0.455915\pi$
$588$	3051.64	0.214026
$589$	−2064.54	−0.144427
$590$	−6219.47	−0.433986
$591$	−7457.59	−0.519060
$592$	−60528.1	−4.20218
$593$	−14397.6	−0.997027	−0.498514	−	0.866882i	$-0.666121\pi$
$593$	−14397.6	−0.997027	−0.498514	+	0.866882i	$0.666121\pi$
$594$	1592.75	0.110019
$595$	−1162.33	−0.0800858
$596$	61426.6	4.22170
$597$	−1152.44	−0.0790051
$598$	388.026	0.0265344
$599$	−14711.0	−1.00347	−0.501734	−	0.865022i	$-0.667304\pi$
$599$	−14711.0	−1.00347	−0.501734	+	0.865022i	$0.667304\pi$
$600$	−25088.2	−1.70704
$601$	27436.8	1.86218	0.931090	−	0.364790i	$-0.118859\pi$
$601$	27436.8	1.86218	0.931090	+	0.364790i	$0.118859\pi$
$602$	−8046.48	−0.544768
$603$	−4996.29	−0.337420
$604$	34632.6	2.33308
$605$	−201.904	−0.0135679
$606$	−6442.07	−0.431834
$607$	6090.69	0.407271	0.203636	−	0.979047i	$-0.434724\pi$
$607$	6090.69	0.407271	0.203636	+	0.979047i	$0.434724\pi$
$608$	17416.2	1.16171
$609$	−945.056	−0.0628828
$610$	−3962.52	−0.263013
$611$	−600.852	−0.0397837
$612$	−18592.2	−1.22802
$613$	5175.61	0.341013	0.170506	−	0.985357i	$-0.445460\pi$
$613$	5175.61	0.341013	0.170506	+	0.985357i	$0.445460\pi$
$614$	−28557.3	−1.87700
$615$	1538.57	0.100880
$616$	−5268.81	−0.344621
$617$	−10544.9	−0.688044	−0.344022	−	0.938962i	$-0.611789\pi$
$617$	−10544.9	−0.688044	−0.344022	+	0.938962i	$0.611789\pi$
$618$	−6754.61	−0.439661
$619$	−8378.59	−0.544045	−0.272023	−	0.962291i	$-0.587693\pi$
$619$	−8378.59	−0.544045	−0.272023	+	0.962291i	$0.587693\pi$
$620$	2175.73	0.140934
$621$	1960.25	0.126670
$622$	−51618.7	−3.32753
$623$	7954.42	0.511536
$624$	600.589	0.0385302
$625$	14588.6	0.933673
$626$	−23143.4	−1.47763
$627$	1084.69	0.0690885
$628$	−24966.0	−1.58639
$629$	29984.5	1.90073
$630$	563.755	0.0356516
$631$	−2651.03	−0.167251	−0.0836257	−	0.996497i	$-0.526650\pi$
$631$	−2651.03	−0.167251	−0.0836257	+	0.996497i	$0.526650\pi$
$632$	46321.6	2.91547
$633$	11625.9	0.730000
$634$	−39683.7	−2.48587
$635$	3669.33	0.229312
$636$	36873.2	2.29893
$637$	48.8336	0.00303745
$638$	2654.73	0.164737
$639$	−1380.17	−0.0854437
$640$	−3973.75	−0.245431
$641$	−6716.00	−0.413831	−0.206916	−	0.978359i	$-0.566343\pi$
$641$	−6716.00	−0.413831	−0.206916	+	0.978359i	$0.566343\pi$
$642$	34300.1	2.10860
$643$	752.048	0.0461242	0.0230621	−	0.999734i	$-0.492658\pi$
$643$	752.048	0.0461242	0.0230621	+	0.999734i	$0.492658\pi$
$644$	−10550.2	−0.645555
$645$	−1073.00	−0.0655026
$646$	−17541.1	−1.06834
$647$	−10412.8	−0.632717	−0.316358	−	0.948640i	$-0.602460\pi$
$647$	−10412.8	−0.632717	−0.316358	+	0.948640i	$0.602460\pi$
$648$	5542.51	0.336004
$649$	7645.33	0.462412
$650$	−653.190	−0.0394157
$651$	1319.01	0.0794105
$652$	−52621.7	−3.16077
$653$	15442.9	0.925462	0.462731	−	0.886499i	$-0.346870\pi$
$653$	15442.9	0.925462	0.462731	+	0.886499i	$0.346870\pi$
$654$	−225.329	−0.0134726
$655$	−2419.96	−0.144360
$656$	−61740.6	−3.67464
$657$	−1327.40	−0.0788234
$658$	22632.5	1.34089
$659$	−5333.13	−0.315249	−0.157625	−	0.987499i	$-0.550384\pi$
$659$	−5333.13	−0.315249	−0.157625	+	0.987499i	$0.550384\pi$
$660$	−1143.11	−0.0674175
$661$	15118.3	0.889614	0.444807	−	0.895626i	$-0.353272\pi$
$661$	15118.3	0.889614	0.444807	+	0.895626i	$0.353272\pi$
$662$	−26273.8	−1.54254
$663$	−297.521	−0.0174280
$664$	−15218.8	−0.889461
$665$	383.928	0.0223881
$666$	−14543.1	−0.846145
$667$	3267.28	0.189670
$668$	50329.8	2.91514
$669$	1349.40	0.0779831
$670$	4967.69	0.286446
$671$	4870.96	0.280241
$672$	−11127.1	−0.638744
$673$	−813.476	−0.0465931	−0.0232966	−	0.999729i	$-0.507416\pi$
$673$	−813.476	−0.0465931	−0.0232966	+	0.999729i	$0.507416\pi$
$674$	−7749.33	−0.442868
$675$	−3299.82	−0.188163
$676$	−45587.9	−2.59376
$677$	10390.3	0.589854	0.294927	−	0.955520i	$-0.404705\pi$
$677$	10390.3	0.589854	0.294927	+	0.955520i	$0.404705\pi$
$678$	21284.5	1.20564
$679$	−7074.22	−0.399828
$680$	11362.0	0.640754
$681$	17620.0	0.991480
$682$	−3705.21	−0.208035
$683$	24315.7	1.36225	0.681124	−	0.732168i	$-0.261491\pi$
$683$	24315.7	1.36225	0.681124	+	0.732168i	$0.261491\pi$
$684$	6141.17	0.343294
$685$	1490.13	0.0831167
$686$	−1839.43	−0.102376
$687$	12623.0	0.701018
$688$	43057.8	2.38599
$689$	590.061	0.0326263
$690$	−1949.03	−0.107534
$691$	−15379.7	−0.846701	−0.423351	−	0.905966i	$-0.639146\pi$
$691$	−15379.7	−0.846701	−0.423351	+	0.905966i	$0.639146\pi$
$692$	41057.7	2.25546
$693$	−693.000	−0.0379869
$694$	23338.5	1.27654
$695$	885.384	0.0483230
$696$	9238.07	0.503115
$697$	30585.2	1.66212
$698$	42748.3	2.31812
$699$	16217.4	0.877538
$700$	17759.9	0.958944
$701$	−2397.08	−0.129153	−0.0645766	−	0.997913i	$-0.520570\pi$
$701$	−2397.08	−0.129153	−0.0645766	+	0.997913i	$0.520570\pi$
$702$	144.303	0.00775838
$703$	−9904.13	−0.531353
$704$	13579.4	0.726981
$705$	3018.04	0.161228
$706$	−6273.83	−0.334446
$707$	2802.93	0.149102
$708$	43285.3	2.29769
$709$	17121.2	0.906912	0.453456	−	0.891279i	$-0.350191\pi$
$709$	17121.2	0.906912	0.453456	+	0.891279i	$0.350191\pi$
$710$	1372.27	0.0725355
$711$	6092.63	0.321366
$712$	−77755.6	−4.09272
$713$	−4560.14	−0.239521
$714$	11206.8	0.587402
$715$	−18.2926	−0.000956788 0
$716$	27296.5	1.42474
$717$	−15315.5	−0.797723
$718$	64347.2	3.34459
$719$	34131.4	1.77036	0.885179	−	0.465251i	$-0.154036\pi$
$719$	34131.4	1.77036	0.885179	+	0.465251i	$0.154036\pi$
$720$	−3016.73	−0.156148
$721$	2938.91	0.151804
$722$	−30989.4	−1.59737
$723$	762.415	0.0392179
$724$	43988.0	2.25801
$725$	−5500.03	−0.281746
$726$	1946.69	0.0995158
$727$	−1143.65	−0.0583434	−0.0291717	−	0.999574i	$-0.509287\pi$
$727$	−1143.65	−0.0583434	−0.0291717	+	0.999574i	$0.509287\pi$
$728$	−477.356	−0.0243022
$729$	729.000	0.0370370
$730$	1319.81	0.0669154
$731$	−21330.0	−1.07923
$732$	27577.7	1.39249
$733$	24224.7	1.22068	0.610342	−	0.792138i	$-0.291032\pi$
$733$	24224.7	1.22068	0.610342	+	0.792138i	$0.291032\pi$
$734$	−45529.7	−2.28955
$735$	−245.288	−0.0123096
$736$	38468.9	1.92660
$737$	−6106.57	−0.305208
$738$	−14834.4	−0.739921
$739$	25815.9	1.28505	0.642525	−	0.766265i	$-0.277887\pi$
$739$	25815.9	1.28505	0.642525	+	0.766265i	$0.277887\pi$
$740$	10437.5	0.518502
$741$	98.2736	0.00487202
$742$	−22226.1	−1.09966
$743$	−17221.1	−0.850312	−0.425156	−	0.905120i	$-0.639781\pi$
$743$	−17221.1	−0.850312	−0.425156	+	0.905120i	$0.639781\pi$
$744$	−12893.6	−0.635351
$745$	−4937.42	−0.242810
$746$	−71357.5	−3.50212
$747$	−2001.70	−0.0980436
$748$	−22723.8	−1.11078
$749$	−14923.9	−0.728048
$750$	6636.62	0.323113
$751$	−15631.7	−0.759531	−0.379766	−	0.925083i	$-0.623995\pi$
$751$	−15631.7	−0.759531	−0.379766	+	0.925083i	$0.623995\pi$
$752$	−121110.	−5.87289
$753$	21092.1	1.02077
$754$	240.520	0.0116170
$755$	−2783.74	−0.134186
$756$	−3923.53	−0.188753
$757$	24756.7	1.18864	0.594319	−	0.804230i	$-0.297422\pi$
$757$	24756.7	1.18864	0.594319	+	0.804230i	$0.297422\pi$
$758$	−57086.8	−2.73547
$759$	2395.86	0.114578
$760$	−3752.96	−0.179124
$761$	−9087.20	−0.432866	−0.216433	−	0.976297i	$-0.569442\pi$
$761$	−9087.20	−0.432866	−0.216433	+	0.976297i	$0.569442\pi$
$762$	−35378.5	−1.68193
$763$	98.0400	0.00465175
$764$	44354.8	2.10039
$765$	1494.43	0.0706290
$766$	12331.1	0.581647
$767$	692.670	0.0326087
$768$	8685.66	0.408095
$769$	10699.9	0.501753	0.250876	−	0.968019i	$-0.419281\pi$
$769$	10699.9	0.501753	0.250876	+	0.968019i	$0.419281\pi$
$770$	689.033	0.0322481
$771$	18161.0	0.848317
$772$	−18908.8	−0.881531
$773$	−6586.45	−0.306466	−0.153233	−	0.988190i	$-0.548968\pi$
$773$	−6586.45	−0.306466	−0.153233	+	0.988190i	$0.548968\pi$
$774$	10345.5	0.480440
$775$	7676.39	0.355799
$776$	69151.5	3.19896
$777$	6327.65	0.292153
$778$	−17395.6	−0.801623
$779$	−10102.5	−0.464648
$780$	−103.566	−0.00475419
$781$	−1686.87	−0.0772867
$782$	−38744.7	−1.77175
$783$	1215.07	0.0554574
$784$	9843.06	0.448390
$785$	2006.75	0.0912406
$786$	23332.5	1.05883
$787$	−5581.26	−0.252796	−0.126398	−	0.991980i	$-0.540342\pi$
$787$	−5581.26	−0.252796	−0.126398	+	0.991980i	$0.540342\pi$
$788$	−51605.1	−2.33294
$789$	−18320.4	−0.826644
$790$	−6057.76	−0.272817
$791$	−9260.83	−0.416280
$792$	6774.18	0.303927
$793$	441.311	0.0197622
$794$	74279.0	3.31998
$795$	−2963.84	−0.132222
$796$	−7974.64	−0.355092
$797$	−20336.2	−0.903821	−0.451911	−	0.892063i	$-0.649257\pi$
$797$	−20336.2	−0.903821	−0.451911	+	0.892063i	$0.649257\pi$
$798$	−3701.71	−0.164209
$799$	59995.5	2.65643
$800$	−64757.2	−2.86189
$801$	−10227.1	−0.451132
$802$	6641.49	0.292418
$803$	−1622.38	−0.0712985
$804$	−34573.4	−1.51655
$805$	848.019	0.0371289
$806$	−335.693	−0.0146703
$807$	14567.7	0.635450
$808$	−27399.1	−1.19294
$809$	5494.43	0.238781	0.119391	−	0.992847i	$-0.461906\pi$
$809$	5494.43	0.238781	0.119391	+	0.992847i	$0.461906\pi$
$810$	−724.827	−0.0314418
$811$	33839.3	1.46518	0.732590	−	0.680671i	$-0.238312\pi$
$811$	33839.3	1.46518	0.732590	+	0.680671i	$0.238312\pi$
$812$	−6539.61	−0.282630
$813$	−25503.3	−1.10017
$814$	−17774.9	−0.765367
$815$	4229.69	0.181791
$816$	−59969.2	−2.57272
$817$	7045.48	0.301702
$818$	−21191.1	−0.905782
$819$	−62.7860	−0.00267878
$820$	10646.6	0.453410
$821$	35849.2	1.52393	0.761965	−	0.647618i	$-0.224235\pi$
$821$	35849.2	1.52393	0.761965	+	0.647618i	$0.224235\pi$
$822$	−14367.3	−0.609633
$823$	−14873.5	−0.629961	−0.314981	−	0.949098i	$-0.601998\pi$
$823$	−14873.5	−0.629961	−0.314981	+	0.949098i	$0.601998\pi$
$824$	−28728.3	−1.21456
$825$	−4033.12	−0.170200
$826$	−26091.1	−1.09906
$827$	5757.86	0.242104	0.121052	−	0.992646i	$-0.461373\pi$
$827$	5757.86	0.242104	0.121052	+	0.992646i	$0.461373\pi$
$828$	13564.6	0.569326
$829$	−38718.4	−1.62213	−0.811064	−	0.584957i	$-0.801111\pi$
$829$	−38718.4	−1.62213	−0.811064	+	0.584957i	$0.801111\pi$
$830$	1990.25	0.0832319
$831$	−20490.5	−0.855366
$832$	1230.30	0.0512657
$833$	−4876.07	−0.202816
$834$	−8536.57	−0.354433
$835$	−4045.47	−0.167664
$836$	7505.87	0.310521
$837$	−1695.87	−0.0700334
$838$	−62227.8	−2.56518
$839$	−36011.2	−1.48182	−0.740908	−	0.671606i	$-0.765605\pi$
$839$	−36011.2	−1.48182	−0.740908	+	0.671606i	$0.765605\pi$
$840$	2397.73	0.0984876
$841$	−22363.8	−0.916961
$842$	−56303.4	−2.30445
$843$	14963.7	0.611359
$844$	80449.3	3.28102
$845$	3664.32	0.149179
$846$	−29099.0	−1.18256
$847$	−847.000	−0.0343604
$848$	118935.	4.81631
$849$	−5858.63	−0.236829
$850$	65221.5	2.63186
$851$	−21876.2	−0.881205
$852$	−9550.49	−0.384031
$853$	−12086.6	−0.485157	−0.242578	−	0.970132i	$-0.577993\pi$
$853$	−12086.6	−0.485157	−0.242578	+	0.970132i	$0.577993\pi$
$854$	−16623.0	−0.666075
$855$	−493.622	−0.0197445
$856$	145883.	5.82499
$857$	−8653.97	−0.344941	−0.172470	−	0.985015i	$-0.555175\pi$
$857$	−8653.97	−0.344941	−0.172470	+	0.985015i	$0.555175\pi$
$858$	176.371	0.00701772
$859$	−46141.6	−1.83275	−0.916374	−	0.400324i	$-0.868898\pi$
$859$	−46141.6	−1.83275	−0.916374	+	0.400324i	$0.868898\pi$
$860$	−7424.94	−0.294405
$861$	6454.41	0.255477
$862$	−59576.1	−2.35403
$863$	16324.1	0.643893	0.321946	−	0.946758i	$-0.395663\pi$
$863$	16324.1	0.643893	0.321946	+	0.946758i	$0.395663\pi$
$864$	14306.2	0.563319
$865$	−3300.19	−0.129722
$866$	67226.2	2.63792
$867$	14968.6	0.586346
$868$	9127.32	0.356914
$869$	7446.55	0.290687
$870$	−1208.12	−0.0470793
$871$	−553.258	−0.0215229
$872$	−958.356	−0.0372179
$873$	9095.42	0.352615
$874$	12797.7	0.495295
$875$	−2887.58	−0.111563
$876$	−9185.39	−0.354276
$877$	17297.6	0.666017	0.333008	−	0.942924i	$-0.391936\pi$
$877$	17297.6	0.666017	0.333008	+	0.942924i	$0.391936\pi$
$878$	11947.2	0.459225
$879$	−9662.15	−0.370758
$880$	−3687.11	−0.141241
$881$	45762.2	1.75002	0.875009	−	0.484106i	$-0.160855\pi$
$881$	45762.2	1.75002	0.875009	+	0.484106i	$0.160855\pi$
$882$	2364.99	0.0902871
$883$	−1535.96	−0.0585380	−0.0292690	−	0.999572i	$-0.509318\pi$
$883$	−1535.96	−0.0585380	−0.0292690	+	0.999572i	$0.509318\pi$
$884$	−2058.79	−0.0783309
$885$	−3479.24	−0.132151
$886$	−4468.55	−0.169440
$887$	−47975.2	−1.81607	−0.908033	−	0.418899i	$-0.862416\pi$
$887$	−47975.2	−1.81607	−0.908033	+	0.418899i	$0.862416\pi$
$888$	−61853.8	−2.33747
$889$	15393.1	0.580729
$890$	10168.6	0.382979
$891$	891.000	0.0335013
$892$	9337.57	0.350499
$893$	−19817.0	−0.742610
$894$	47605.0	1.78093
$895$	−2194.07	−0.0819437
$896$	−16670.1	−0.621551
$897$	217.066	0.00807985
$898$	−26298.5	−0.977274
$899$	−2826.62	−0.104865
$900$	−22834.2	−0.845710
$901$	−58918.0	−2.17851
$902$	−18130.9	−0.669284
$903$	−4501.29	−0.165884
$904$	90526.0	3.33059
$905$	−3535.72	−0.129869
$906$	26839.9	0.984212
$907$	16461.0	0.602622	0.301311	−	0.953526i	$-0.402576\pi$
$907$	16461.0	0.602622	0.301311	+	0.953526i	$0.402576\pi$
$908$	121927.	4.45626
$909$	−3603.76	−0.131495
$910$	62.4267	0.00227409
$911$	−4712.18	−0.171374	−0.0856869	−	0.996322i	$-0.527308\pi$
$911$	−4712.18	−0.171374	−0.0856869	+	0.996322i	$0.527308\pi$
$912$	19808.3	0.719210
$913$	−2446.53	−0.0886837
$914$	64893.4	2.34845
$915$	−2216.68	−0.0800887
$916$	87349.1	3.15076
$917$	−10151.9	−0.365589
$918$	−14408.8	−0.518040
$919$	16055.3	0.576294	0.288147	−	0.957586i	$-0.406961\pi$
$919$	16055.3	0.576294	0.288147	+	0.957586i	$0.406961\pi$
$920$	−8289.52	−0.297062
$921$	−15975.2	−0.571555
$922$	−6816.97	−0.243498
$923$	−152.831	−0.00545016
$924$	−4795.43	−0.170734
$925$	36825.6	1.30899
$926$	−85913.4	−3.04891
$927$	−3778.60	−0.133879
$928$	23845.1	0.843485
$929$	9378.49	0.331215	0.165607	−	0.986192i	$-0.447042\pi$
$929$	9378.49	0.331215	0.165607	+	0.986192i	$0.447042\pi$
$930$	1686.17	0.0594533
$931$	1610.60	0.0566976
$932$	112222.	3.94414
$933$	−28876.1	−1.01325
$934$	−57360.6	−2.00953
$935$	1826.52	0.0638864
$936$	613.743	0.0214325
$937$	9100.65	0.317295	0.158647	−	0.987335i	$-0.449287\pi$
$937$	9100.65	0.317295	0.158647	+	0.987335i	$0.449287\pi$
$938$	20839.8	0.725419
$939$	−12946.7	−0.449945
$940$	20884.3	0.724650
$941$	9738.84	0.337383	0.168691	−	0.985669i	$-0.446046\pi$
$941$	9738.84	0.337383	0.168691	+	0.985669i	$0.446046\pi$
$942$	−19348.4	−0.669219
$943$	−22314.4	−0.770580
$944$	139617.	4.81371
$945$	315.371	0.0108561
$946$	12644.5	0.434574
$947$	47225.8	1.62052	0.810260	−	0.586071i	$-0.199326\pi$
$947$	47225.8	1.62052	0.810260	+	0.586071i	$0.199326\pi$
$948$	42159.9	1.44440
$949$	−146.989	−0.00502787
$950$	−21543.2	−0.735740
$951$	−22199.5	−0.756960
$952$	47664.3	1.62270
$953$	972.630	0.0330604	0.0165302	−	0.999863i	$-0.494738\pi$
$953$	972.630	0.0330604	0.0165302	+	0.999863i	$0.494738\pi$
$954$	28576.4	0.969805
$955$	−3565.20	−0.120803
$956$	−105980.	−3.58541
$957$	1485.09	0.0501631
$958$	−64649.3	−2.18030
$959$	6251.19	0.210492
$960$	−6179.74	−0.207761
$961$	−25845.9	−0.867574
$962$	−1610.41	−0.0539726
$963$	19187.9	0.642078
$964$	5275.77	0.176267
$965$	1519.87	0.0507010
$966$	−8176.32	−0.272328
$967$	−21987.5	−0.731199	−0.365599	−	0.930772i	$-0.619136\pi$
$967$	−21987.5	−0.731199	−0.365599	+	0.930772i	$0.619136\pi$
$968$	8279.56	0.274912
$969$	−9812.68	−0.325313
$970$	−9043.36	−0.299345
$971$	−18194.5	−0.601326	−0.300663	−	0.953730i	$-0.597208\pi$
$971$	−18194.5	−0.601326	−0.300663	+	0.953730i	$0.597208\pi$
$972$	5044.54	0.166465
$973$	3714.24	0.122377
$974$	−76544.0	−2.51810
$975$	−365.402	−0.0120023
$976$	88952.0	2.91730
$977$	−14356.0	−0.470103	−0.235051	−	0.971983i	$-0.575526\pi$
$977$	−14356.0	−0.470103	−0.235051	+	0.971983i	$0.575526\pi$
$978$	−40781.3	−1.33338
$979$	−12499.8	−0.408065
$980$	−1697.35	−0.0553263
$981$	−126.051	−0.00410246
$982$	−83749.1	−2.72153
$983$	25765.5	0.836005	0.418002	−	0.908446i	$-0.362730\pi$
$983$	25765.5	0.836005	0.418002	+	0.908446i	$0.362730\pi$
$984$	−63092.9	−2.04403
$985$	4147.98	0.134178
$986$	−24016.1	−0.775687
$987$	12660.9	0.408309
$988$	680.035	0.0218976
$989$	15562.0	0.500347
$990$	−885.900	−0.0284402
$991$	7750.45	0.248437	0.124219	−	0.992255i	$-0.460358\pi$
$991$	7750.45	0.248437	0.124219	+	0.992255i	$0.460358\pi$
$992$	−33280.6	−1.06518
$993$	−14697.9	−0.469711
$994$	5756.75	0.183695
$995$	640.995	0.0204230
$996$	−13851.4	−0.440662
$997$	12105.1	0.384528	0.192264	−	0.981343i	$-0.438417\pi$
$997$	12105.1	0.384528	0.192264	+	0.981343i	$0.438417\pi$
$998$	31211.5	0.989964
$999$	−8135.55	−0.257655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.a.l.1.5	✓	5
3.2	odd	2		693.4.a.n.1.1		5
7.6	odd	2		1617.4.a.p.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.l.1.5	✓	5	1.1	even	1	trivial
693.4.a.n.1.1		5	3.2	odd	2
1617.4.a.p.1.5		5	7.6	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.a (trivial)

\(f(q)\)	\(=\)	\(q+5.36278 q^{2} +3.00000 q^{3} +20.7594 q^{4} -1.66863 q^{5} +16.0883 q^{6} -7.00000 q^{7} +68.4261 q^{8} +9.00000 q^{9} -8.94849 q^{10} +11.0000 q^{11} +62.2783 q^{12} +0.996604 q^{13} -37.5395 q^{14} -5.00588 q^{15} +200.879 q^{16} -99.5115 q^{17} +48.2650 q^{18} +32.8695 q^{19} -34.6398 q^{20} -21.0000 q^{21} +58.9906 q^{22} +72.6019 q^{23} +205.278 q^{24} -122.216 q^{25} +5.34457 q^{26} +27.0000 q^{27} -145.316 q^{28} +45.0027 q^{29} -26.8455 q^{30} -62.8102 q^{31} +529.860 q^{32} +33.0000 q^{33} -533.659 q^{34} +11.6804 q^{35} +186.835 q^{36} -301.317 q^{37} +176.272 q^{38} +2.98981 q^{39} -114.178 q^{40} -307.353 q^{41} -112.618 q^{42} +214.347 q^{43} +228.354 q^{44} -15.0176 q^{45} +389.348 q^{46} -602.899 q^{47} +602.636 q^{48} +49.0000 q^{49} -655.416 q^{50} -298.535 q^{51} +20.6889 q^{52} +592.072 q^{53} +144.795 q^{54} -18.3549 q^{55} -478.983 q^{56} +98.6084 q^{57} +241.339 q^{58} +695.030 q^{59} -103.919 q^{60} +442.815 q^{61} -336.837 q^{62} -63.0000 q^{63} +1234.49 q^{64} -1.66296 q^{65} +176.972 q^{66} -555.143 q^{67} -2065.80 q^{68} +217.806 q^{69} +62.6394 q^{70} -153.352 q^{71} +615.835 q^{72} -147.489 q^{73} -1615.90 q^{74} -366.647 q^{75} +682.352 q^{76} -77.0000 q^{77} +16.0337 q^{78} +676.959 q^{79} -335.192 q^{80} +81.0000 q^{81} -1648.27 q^{82} -222.412 q^{83} -435.948 q^{84} +166.048 q^{85} +1149.50 q^{86} +135.008 q^{87} +752.687 q^{88} -1136.35 q^{89} -80.5364 q^{90} -6.97623 q^{91} +1507.18 q^{92} -188.430 q^{93} -3233.22 q^{94} -54.8469 q^{95} +1589.58 q^{96} +1010.60 q^{97} +262.776 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 15 q^{3} + 21 q^{4} + 7 q^{5} + 15 q^{6} - 35 q^{7} + 60 q^{8} + 45 q^{9} + 55 q^{10} + 55 q^{11} + 63 q^{12} + 111 q^{13} - 35 q^{14} + 21 q^{15} + 201 q^{16} + 136 q^{17} + 45 q^{18} + 111 q^{19}+ \cdots + 495 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 15 * q^3 + 21 * q^4 + 7 * q^5 + 15 * q^6 - 35 * q^7 + 60 * q^8 + 45 * q^9 + 55 * q^10 + 55 * q^11 + 63 * q^12 + 111 * q^13 - 35 * q^14 + 21 * q^15 + 201 * q^16 + 136 * q^17 + 45 * q^18 + 111 * q^19 + 219 * q^20 - 105 * q^21 + 55 * q^22 - 28 * q^23 + 180 * q^24 + 190 * q^25 - q^26 + 135 * q^27 - 147 * q^28 + 61 * q^29 + 165 * q^30 - 280 * q^31 + 535 * q^32 + 165 * q^33 - 572 * q^34 - 49 * q^35 + 189 * q^36 - 41 * q^37 + 267 * q^38 + 333 * q^39 - 336 * q^40 + 426 * q^41 - 105 * q^42 + 424 * q^43 + 231 * q^44 + 63 * q^45 + 140 * q^46 + 75 * q^47 + 603 * q^48 + 245 * q^49 + 490 * q^50 + 408 * q^51 - 269 * q^52 + 1500 * q^53 + 135 * q^54 + 77 * q^55 - 420 * q^56 + 333 * q^57 - 1767 * q^58 + 757 * q^59 + 657 * q^60 + 658 * q^61 - 568 * q^62 - 315 * q^63 - 748 * q^64 + 537 * q^65 + 165 * q^66 - 583 * q^67 - 1650 * q^68 - 84 * q^69 - 385 * q^70 - 764 * q^71 + 540 * q^72 + 875 * q^73 - 825 * q^74 + 570 * q^75 + 213 * q^76 - 385 * q^77 - 3 * q^78 - 244 * q^79 - 2577 * q^80 + 405 * q^81 - 2006 * q^82 + 924 * q^83 - 441 * q^84 - 1402 * q^85 + 1272 * q^86 + 183 * q^87 + 660 * q^88 - 1110 * q^89 + 495 * q^90 - 777 * q^91 - 2046 * q^92 - 840 * q^93 - 3349 * q^94 + 1923 * q^95 + 1605 * q^96 - 852 * q^97 + 245 * q^98 + 495 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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