LMFDB - Embedded newform 77.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,4,Mod(1,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	77.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:	$4.54314707044$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.509800.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} + 5x + 15 $ x^4 - x^3 - 10x^2 + 5x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.59222$ of defining polynomial
Character	$\chi$	$=$	77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.05706 q^{2} -9.64416 q^{3} +17.5738 q^{4} +12.9427 q^{5} +48.7711 q^{6} -7.00000 q^{7} -48.4155 q^{8} +66.0098 q^{9} -65.4521 q^{10} +11.0000 q^{11} -169.485 q^{12} -55.5473 q^{13} +35.3994 q^{14} -124.822 q^{15} +104.249 q^{16} +59.2511 q^{17} -333.816 q^{18} -33.1777 q^{19} +227.453 q^{20} +67.5091 q^{21} -55.6276 q^{22} +26.0532 q^{23} +466.927 q^{24} +42.5139 q^{25} +280.906 q^{26} -376.217 q^{27} -123.017 q^{28} -188.479 q^{29} +631.230 q^{30} -278.333 q^{31} -139.870 q^{32} -106.086 q^{33} -299.636 q^{34} -90.5990 q^{35} +1160.05 q^{36} +201.567 q^{37} +167.781 q^{38} +535.707 q^{39} -626.628 q^{40} -126.784 q^{41} -341.398 q^{42} -454.826 q^{43} +193.312 q^{44} +854.347 q^{45} -131.753 q^{46} -129.710 q^{47} -1005.40 q^{48} +49.0000 q^{49} -214.995 q^{50} -571.427 q^{51} -976.179 q^{52} +79.8855 q^{53} +1902.55 q^{54} +142.370 q^{55} +338.908 q^{56} +319.971 q^{57} +953.150 q^{58} -593.670 q^{59} -2193.60 q^{60} -49.8622 q^{61} +1407.55 q^{62} -462.069 q^{63} -126.661 q^{64} -718.932 q^{65} +536.482 q^{66} +295.997 q^{67} +1041.27 q^{68} -251.262 q^{69} +458.164 q^{70} +546.422 q^{71} -3195.90 q^{72} -809.232 q^{73} -1019.34 q^{74} -410.011 q^{75} -583.059 q^{76} -77.0000 q^{77} -2709.10 q^{78} -375.244 q^{79} +1349.27 q^{80} +1846.03 q^{81} +641.154 q^{82} +85.9037 q^{83} +1186.39 q^{84} +766.870 q^{85} +2300.08 q^{86} +1817.72 q^{87} -532.570 q^{88} +750.306 q^{89} -4320.48 q^{90} +388.831 q^{91} +457.856 q^{92} +2684.29 q^{93} +655.953 q^{94} -429.409 q^{95} +1348.93 q^{96} -451.876 q^{97} -247.796 q^{98} +726.108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{3} + 22 q^{4} - 18 q^{5} + 2 q^{6} - 28 q^{7} - 60 q^{8} + 66 q^{9} - 92 q^{10} + 44 q^{11} - 186 q^{12} - 134 q^{13} + 28 q^{14} - 62 q^{15} - 6 q^{16} - 74 q^{17} - 256 q^{18} - 164 q^{19}+ \cdots + 726 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 12 * q^3 + 22 * q^4 - 18 * q^5 + 2 * q^6 - 28 * q^7 - 60 * q^8 + 66 * q^9 - 92 * q^10 + 44 * q^11 - 186 * q^12 - 134 * q^13 + 28 * q^14 - 62 * q^15 - 6 * q^16 - 74 * q^17 - 256 * q^18 - 164 * q^19 + 116 * q^20 + 84 * q^21 - 44 * q^22 + 194 * q^23 + 570 * q^24 + 38 * q^25 + 734 * q^26 - 510 * q^27 - 154 * q^28 - 108 * q^29 + 1252 * q^30 - 412 * q^31 - 4 * q^32 - 132 * q^33 - 346 * q^34 + 126 * q^35 + 1518 * q^36 + 286 * q^37 + 224 * q^38 - 256 * q^39 - 540 * q^40 - 18 * q^41 - 14 * q^42 - 496 * q^43 + 242 * q^44 + 580 * q^45 - 284 * q^46 + 62 * q^47 - 862 * q^48 + 196 * q^49 + 212 * q^50 - 508 * q^51 - 822 * q^52 - 828 * q^53 + 2420 * q^54 - 198 * q^55 + 420 * q^56 + 700 * q^57 + 1388 * q^58 - 1224 * q^59 - 1776 * q^60 - 350 * q^61 - 878 * q^62 - 462 * q^63 - 718 * q^64 - 396 * q^65 + 22 * q^66 - 1498 * q^67 + 1058 * q^68 - 386 * q^69 + 644 * q^70 + 2326 * q^71 - 3000 * q^72 - 1630 * q^73 - 1156 * q^74 - 1362 * q^75 - 3152 * q^76 - 308 * q^77 - 2464 * q^78 - 1020 * q^79 + 3072 * q^80 + 1128 * q^81 + 2118 * q^82 - 1920 * q^83 + 1302 * q^84 + 2008 * q^85 + 1056 * q^86 + 1640 * q^87 - 660 * q^88 + 1550 * q^89 - 5780 * q^90 + 938 * q^91 + 2592 * q^92 + 6046 * q^93 - 1042 * q^94 + 2332 * q^95 + 4082 * q^96 - 2202 * q^97 - 196 * q^98 + 726 * 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 $

$2$	−5.05706	−1.78794	−0.893970	−	0.448127i	$-0.852091\pi$
$2$	−5.05706	−1.78794	−0.893970	+	0.448127i	$0.852091\pi$
$3$	−9.64416	−1.85602	−0.928010	−	0.372556i	$-0.878482\pi$
$3$	−9.64416	−1.85602	−0.928010	+	0.372556i	$0.878482\pi$
$4$	17.5738	2.19673
$5$	12.9427	1.15763	0.578816	−	0.815458i	$-0.303515\pi$
$5$	12.9427	1.15763	0.578816	+	0.815458i	$0.303515\pi$
$6$	48.7711	3.31845
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−48.4155	−2.13968
$9$	66.0098	2.44481
$10$	−65.4521	−2.06978
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−169.485	−4.07717
$13$	−55.5473	−1.18508	−0.592540	−	0.805541i	$-0.701875\pi$
$13$	−55.5473	−1.18508	−0.592540	+	0.805541i	$0.701875\pi$
$14$	35.3994	0.675778
$15$	−124.822	−2.14859
$16$	104.249	1.62889
$17$	59.2511	0.845324	0.422662	−	0.906287i	$-0.361096\pi$
$17$	59.2511	0.845324	0.422662	+	0.906287i	$0.361096\pi$
$18$	−333.816	−4.37117
$19$	−33.1777	−0.400604	−0.200302	−	0.979734i	$-0.564192\pi$
$19$	−33.1777	−0.400604	−0.200302	+	0.979734i	$0.564192\pi$
$20$	227.453	2.54300
$21$	67.5091	0.701510
$22$	−55.6276	−0.539084
$23$	26.0532	0.236195	0.118097	−	0.993002i	$-0.462321\pi$
$23$	26.0532	0.236195	0.118097	+	0.993002i	$0.462321\pi$
$24$	466.927	3.97129
$25$	42.5139	0.340111
$26$	280.906	2.11885
$27$	−376.217	−2.68159
$28$	−123.017	−0.830286
$29$	−188.479	−1.20689	−0.603443	−	0.797406i	$-0.706205\pi$
$29$	−188.479	−1.20689	−0.603443	+	0.797406i	$0.706205\pi$
$30$	631.230	3.84155
$31$	−278.333	−1.61259	−0.806293	−	0.591516i	$-0.798529\pi$
$31$	−278.333	−1.61259	−0.806293	+	0.591516i	$0.798529\pi$
$32$	−139.870	−0.772682
$33$	−106.086	−0.559611
$34$	−299.636	−1.51139
$35$	−90.5990	−0.437544
$36$	1160.05	5.37059
$37$	201.567	0.895608	0.447804	−	0.894132i	$-0.352206\pi$
$37$	201.567	0.895608	0.447804	+	0.894132i	$0.352206\pi$
$38$	167.781	0.716256
$39$	535.707	2.19953
$40$	−626.628	−2.47696
$41$	−126.784	−0.482935	−0.241467	−	0.970409i	$-0.577629\pi$
$41$	−126.784	−0.482935	−0.241467	+	0.970409i	$0.577629\pi$
$42$	−341.398	−1.25426
$43$	−454.826	−1.61303	−0.806514	−	0.591214i	$-0.798649\pi$
$43$	−454.826	−1.61303	−0.806514	+	0.591214i	$0.798649\pi$
$44$	193.312	0.662339
$45$	854.347	2.83019
$46$	−131.753	−0.422302
$47$	−129.710	−0.402558	−0.201279	−	0.979534i	$-0.564510\pi$
$47$	−129.710	−0.402558	−0.201279	+	0.979534i	$0.564510\pi$
$48$	−1005.40	−3.02326
$49$	49.0000	0.142857
$50$	−214.995	−0.608098
$51$	−571.427	−1.56894
$52$	−976.179	−2.60330
$53$	79.8855	0.207040	0.103520	−	0.994627i	$-0.466989\pi$
$53$	79.8855	0.207040	0.103520	+	0.994627i	$0.466989\pi$
$54$	1902.55	4.79453
$55$	142.370	0.349039
$56$	338.908	0.808724
$57$	319.971	0.743529
$58$	953.150	2.15784
$59$	−593.670	−1.30999	−0.654994	−	0.755634i	$-0.727329\pi$
$59$	−593.670	−1.30999	−0.654994	+	0.755634i	$0.727329\pi$
$60$	−2193.60	−4.71987
$61$	−49.8622	−0.104659	−0.0523295	−	0.998630i	$-0.516665\pi$
$61$	−49.8622	−0.104659	−0.0523295	+	0.998630i	$0.516665\pi$
$62$	1407.55	2.88321
$63$	−462.069	−0.924051
$64$	−126.661	−0.247385
$65$	−718.932	−1.37189
$66$	536.482	1.00055
$67$	295.997	0.539728	0.269864	−	0.962898i	$-0.413021\pi$
$67$	295.997	0.539728	0.269864	+	0.962898i	$0.413021\pi$
$68$	1041.27	1.85695
$69$	−251.262	−0.438382
$70$	458.164	0.782302
$71$	546.422	0.913357	0.456679	−	0.889632i	$-0.349039\pi$
$71$	546.422	0.913357	0.456679	+	0.889632i	$0.349039\pi$
$72$	−3195.90	−5.23111
$73$	−809.232	−1.29744	−0.648722	−	0.761025i	$-0.724696\pi$
$73$	−809.232	−1.29744	−0.648722	+	0.761025i	$0.724696\pi$
$74$	−1019.34	−1.60129
$75$	−410.011	−0.631253
$76$	−583.059	−0.880019
$77$	−77.0000	−0.113961
$78$	−2709.10	−3.93263
$79$	−375.244	−0.534408	−0.267204	−	0.963640i	$-0.586100\pi$
$79$	−375.244	−0.534408	−0.267204	+	0.963640i	$0.586100\pi$
$80$	1349.27	1.88566
$81$	1846.03	2.53228
$82$	641.154	0.863459
$83$	85.9037	0.113604	0.0568022	−	0.998385i	$-0.481910\pi$
$83$	85.9037	0.113604	0.0568022	+	0.998385i	$0.481910\pi$
$84$	1186.39	1.54103
$85$	766.870	0.978574
$86$	2300.08	2.88400
$87$	1817.72	2.24000
$88$	−532.570	−0.645138
$89$	750.306	0.893621	0.446810	−	0.894629i	$-0.352560\pi$
$89$	750.306	0.893621	0.446810	+	0.894629i	$0.352560\pi$
$90$	−4320.48	−5.06021
$91$	388.831	0.447918
$92$	457.856	0.518856
$93$	2684.29	2.99299
$94$	655.953	0.719749
$95$	−429.409	−0.463752
$96$	1348.93	1.43411
$97$	−451.876	−0.473001	−0.236500	−	0.971631i	$-0.576000\pi$
$97$	−451.876	−0.473001	−0.236500	+	0.971631i	$0.576000\pi$
$98$	−247.796	−0.255420
$99$	726.108	0.737138
$100$	747.132	0.747132
$101$	−1414.20	−1.39325	−0.696626	−	0.717434i	$-0.745316\pi$
$101$	−1414.20	−1.39325	−0.696626	+	0.717434i	$0.745316\pi$
$102$	2889.74	2.80517
$103$	−27.8798	−0.0266707	−0.0133354	−	0.999911i	$-0.504245\pi$
$103$	−27.8798	−0.0266707	−0.0133354	+	0.999911i	$0.504245\pi$
$104$	2689.35	2.53569
$105$	873.751	0.812090
$106$	−403.985	−0.370175
$107$	−778.142	−0.703045	−0.351523	−	0.936179i	$-0.614336\pi$
$107$	−778.142	−0.703045	−0.351523	+	0.936179i	$0.614336\pi$
$108$	−6611.58	−5.89074
$109$	−219.545	−0.192923	−0.0964615	−	0.995337i	$-0.530752\pi$
$109$	−219.545	−0.192923	−0.0964615	+	0.995337i	$0.530752\pi$
$110$	−719.973	−0.624061
$111$	−1943.95	−1.66227
$112$	−729.744	−0.615664
$113$	607.402	0.505660	0.252830	−	0.967511i	$-0.418639\pi$
$113$	607.402	0.505660	0.252830	+	0.967511i	$0.418639\pi$
$114$	−1618.11	−1.32939
$115$	337.200	0.273426
$116$	−3312.30	−2.65120
$117$	−3666.67	−2.89729
$118$	3002.22	2.34218
$119$	−414.758	−0.319502
$120$	6043.30	4.59729
$121$	121.000	0.0909091
$122$	252.156	0.187124
$123$	1222.73	0.896337
$124$	−4891.39	−3.54242
$125$	−1067.59	−0.763908
$126$	2336.71	1.65215
$127$	1949.05	1.36181	0.680905	−	0.732372i	$-0.261587\pi$
$127$	1949.05	1.36181	0.680905	+	0.732372i	$0.261587\pi$
$128$	1759.49	1.21499
$129$	4386.41	2.99381
$130$	3635.68	2.45285
$131$	−1782.57	−1.18888	−0.594442	−	0.804138i	$-0.702627\pi$
$131$	−1782.57	−1.18888	−0.594442	+	0.804138i	$0.702627\pi$
$132$	−1864.33	−1.22931
$133$	232.244	0.151414
$134$	−1496.87	−0.965001
$135$	−4869.27	−3.10430
$136$	−2868.67	−1.80872
$137$	−3080.56	−1.92109	−0.960546	−	0.278120i	$-0.910289\pi$
$137$	−3080.56	−1.92109	−0.960546	+	0.278120i	$0.910289\pi$
$138$	1270.65	0.783801
$139$	1171.35	0.714769	0.357384	−	0.933957i	$-0.383669\pi$
$139$	1171.35	0.714769	0.357384	+	0.933957i	$0.383669\pi$
$140$	−1592.17	−0.961165
$141$	1250.95	0.747155
$142$	−2763.29	−1.63303
$143$	−611.020	−0.357315
$144$	6881.47	3.98233
$145$	−2439.43	−1.39713
$146$	4092.33	2.31975
$147$	−472.564	−0.265146
$148$	3542.31	1.96741
$149$	1237.66	0.680492	0.340246	−	0.940337i	$-0.389490\pi$
$149$	1237.66	0.680492	0.340246	+	0.940337i	$0.389490\pi$
$150$	2073.45	1.12864
$151$	1581.62	0.852388	0.426194	−	0.904632i	$-0.359854\pi$
$151$	1581.62	0.852388	0.426194	+	0.904632i	$0.359854\pi$
$152$	1606.31	0.857165
$153$	3911.16	2.06666
$154$	389.394	0.203755
$155$	−3602.39	−1.86678
$156$	9414.42	4.83178
$157$	−3209.77	−1.63164	−0.815821	−	0.578304i	$-0.803715\pi$
$157$	−3209.77	−1.63164	−0.815821	+	0.578304i	$0.803715\pi$
$158$	1897.63	0.955489
$159$	−770.428	−0.384270
$160$	−1810.30	−0.894481
$161$	−182.373	−0.0892732
$162$	−9335.50	−4.52757
$163$	−139.967	−0.0672579	−0.0336290	−	0.999434i	$-0.510706\pi$
$163$	−139.967	−0.0672579	−0.0336290	+	0.999434i	$0.510706\pi$
$164$	−2228.08	−1.06088
$165$	−1373.04	−0.647823
$166$	−434.420	−0.203118
$167$	1425.74	0.660641	0.330320	−	0.943869i	$-0.392843\pi$
$167$	1425.74	0.660641	0.330320	+	0.943869i	$0.392843\pi$
$168$	−3268.49	−1.50101
$169$	888.497	0.404414
$170$	−3878.11	−1.74963
$171$	−2190.05	−0.979400
$172$	−7993.03	−3.54339
$173$	1527.01	0.671077	0.335538	−	0.942027i	$-0.391082\pi$
$173$	1527.01	0.671077	0.335538	+	0.942027i	$0.391082\pi$
$174$	−9192.33	−4.00499
$175$	−297.597	−0.128550
$176$	1146.74	0.491130
$177$	5725.45	2.43136
$178$	−3794.34	−1.59774
$179$	4512.37	1.88419	0.942095	−	0.335346i	$-0.108853\pi$
$179$	4512.37	1.88419	0.942095	+	0.335346i	$0.108853\pi$
$180$	15014.2	6.21716
$181$	−2973.55	−1.22112	−0.610559	−	0.791970i	$-0.709055\pi$
$181$	−2973.55	−1.22112	−0.610559	+	0.791970i	$0.709055\pi$
$182$	−1966.34	−0.800851
$183$	480.879	0.194249
$184$	−1261.38	−0.505381
$185$	2608.83	1.03678
$186$	−13574.6	−5.35129
$187$	651.762	0.254875
$188$	−2279.51	−0.884311
$189$	2633.52	1.01355
$190$	2171.55	0.829161
$191$	−1275.56	−0.483225	−0.241613	−	0.970373i	$-0.577676\pi$
$191$	−1275.56	−0.483225	−0.241613	+	0.970373i	$0.577676\pi$
$192$	1221.54	0.459151
$193$	−121.983	−0.0454950	−0.0227475	−	0.999741i	$-0.507241\pi$
$193$	−121.983	−0.0454950	−0.0227475	+	0.999741i	$0.507241\pi$
$194$	2285.17	0.845697
$195$	6933.50	2.54625
$196$	861.118	0.313819
$197$	−3483.97	−1.26001	−0.630007	−	0.776589i	$-0.716948\pi$
$197$	−3483.97	−1.26001	−0.630007	+	0.776589i	$0.716948\pi$
$198$	−3671.97	−1.31796
$199$	2655.65	0.946002	0.473001	−	0.881062i	$-0.343171\pi$
$199$	2655.65	0.946002	0.473001	+	0.881062i	$0.343171\pi$
$200$	−2058.33	−0.727730
$201$	−2854.64	−1.00175
$202$	7151.71	2.49105
$203$	1319.35	0.456160
$204$	−10042.2	−3.44653
$205$	−1640.93	−0.559061
$206$	140.990	0.0476856
$207$	1719.77	0.577451
$208$	−5790.75	−1.93037
$209$	−364.954	−0.120787
$210$	−4418.61	−1.45197
$211$	1909.91	0.623147	0.311573	−	0.950222i	$-0.399144\pi$
$211$	1909.91	0.623147	0.311573	+	0.950222i	$0.399144\pi$
$212$	1403.89	0.454811
$213$	−5269.78	−1.69521
$214$	3935.11	1.25700
$215$	−5886.68	−1.86729
$216$	18214.7	5.73776
$217$	1948.33	0.609500
$218$	1110.25	0.344935
$219$	7804.37	2.40808
$220$	2501.99	0.766745
$221$	−3291.24	−1.00178
$222$	9830.66	2.97203
$223$	−4381.22	−1.31564	−0.657821	−	0.753174i	$-0.728522\pi$
$223$	−4381.22	−1.31564	−0.657821	+	0.753174i	$0.728522\pi$
$224$	979.092	0.292046
$225$	2806.33	0.831507
$226$	−3071.67	−0.904090
$227$	1711.28	0.500359	0.250180	−	0.968199i	$-0.419510\pi$
$227$	1711.28	0.500359	0.250180	+	0.968199i	$0.419510\pi$
$228$	5623.11	1.63333
$229$	2617.84	0.755423	0.377712	−	0.925923i	$-0.376711\pi$
$229$	2617.84	0.755423	0.377712	+	0.925923i	$0.376711\pi$
$230$	−1705.24	−0.488870
$231$	742.600	0.211513
$232$	9125.31	2.58235
$233$	3593.09	1.01026	0.505131	−	0.863043i	$-0.331444\pi$
$233$	3593.09	1.01026	0.505131	+	0.863043i	$0.331444\pi$
$234$	18542.5	5.18019
$235$	−1678.81	−0.466014
$236$	−10433.1	−2.87769
$237$	3618.91	0.991871
$238$	2097.45	0.571251
$239$	1841.19	0.498312	0.249156	−	0.968463i	$-0.419847\pi$
$239$	1841.19	0.498312	0.249156	+	0.968463i	$0.419847\pi$
$240$	−13012.6	−3.49982
$241$	2209.45	0.590552	0.295276	−	0.955412i	$-0.404588\pi$
$241$	2209.45	0.590552	0.295276	+	0.955412i	$0.404588\pi$
$242$	−611.904	−0.162540
$243$	−7645.58	−2.01837
$244$	−876.270	−0.229907
$245$	634.193	0.165376
$246$	−6183.39	−1.60260
$247$	1842.93	0.474748
$248$	13475.6	3.45042
$249$	−828.469	−0.210852
$250$	5398.89	1.36582
$251$	1066.68	0.268240	0.134120	−	0.990965i	$-0.457179\pi$
$251$	1066.68	0.268240	0.134120	+	0.990965i	$0.457179\pi$
$252$	−8120.33	−2.02989
$253$	286.586	0.0712154
$254$	−9856.44	−2.43483
$255$	−7395.82	−1.81625
$256$	−7884.58	−1.92495
$257$	2990.18	0.725769	0.362884	−	0.931834i	$-0.381792\pi$
$257$	2990.18	0.725769	0.362884	+	0.931834i	$0.381792\pi$
$258$	−22182.3	−5.35276
$259$	−1410.97	−0.338508
$260$	−12634.4	−3.01366
$261$	−12441.5	−2.95061
$262$	9014.56	2.12565
$263$	4240.32	0.994181	0.497090	−	0.867699i	$-0.334402\pi$
$263$	4240.32	0.994181	0.497090	+	0.867699i	$0.334402\pi$
$264$	5136.19	1.19739
$265$	1033.93	0.239676
$266$	−1174.47	−0.270719
$267$	−7236.07	−1.65858
$268$	5201.80	1.18564
$269$	5364.21	1.21584	0.607922	−	0.793997i	$-0.292003\pi$
$269$	5364.21	1.21584	0.607922	+	0.793997i	$0.292003\pi$
$270$	24624.2	5.55030
$271$	1476.11	0.330876	0.165438	−	0.986220i	$-0.447096\pi$
$271$	1476.11	0.330876	0.165438	+	0.986220i	$0.447096\pi$
$272$	6176.88	1.37694
$273$	−3749.95	−0.831345
$274$	15578.6	3.43480
$275$	467.653	0.102547
$276$	−4415.63	−0.963007
$277$	2371.67	0.514439	0.257219	−	0.966353i	$-0.417194\pi$
$277$	2371.67	0.514439	0.257219	+	0.966353i	$0.417194\pi$
$278$	−5923.60	−1.27796
$279$	−18372.7	−3.94246
$280$	4386.39	0.936204
$281$	−1619.54	−0.343821	−0.171911	−	0.985113i	$-0.554994\pi$
$281$	−1619.54	−0.343821	−0.171911	+	0.985113i	$0.554994\pi$
$282$	−6326.12	−1.33587
$283$	−3779.82	−0.793947	−0.396973	−	0.917830i	$-0.629939\pi$
$283$	−3779.82	−0.793947	−0.396973	+	0.917830i	$0.629939\pi$
$284$	9602.73	2.00640
$285$	4141.29	0.860733
$286$	3089.96	0.638858
$287$	887.488	0.182532
$288$	−9232.82	−1.88906
$289$	−1402.31	−0.285427
$290$	12336.4	2.49798
$291$	4357.97	0.877899
$292$	−14221.3	−2.85014
$293$	2884.18	0.575070	0.287535	−	0.957770i	$-0.407164\pi$
$293$	2884.18	0.575070	0.287535	+	0.957770i	$0.407164\pi$
$294$	2389.78	0.474065
$295$	−7683.70	−1.51648
$296$	−9758.98	−1.91632
$297$	−4138.39	−0.808531
$298$	−6258.93	−1.21668
$299$	−1447.19	−0.279909
$300$	−7205.46	−1.38669
$301$	3183.78	0.609668
$302$	−7998.35	−1.52402
$303$	13638.8	2.58590
$304$	−3458.74	−0.652541
$305$	−645.352	−0.121156
$306$	−19779.0	−3.69506
$307$	−4242.88	−0.788774	−0.394387	−	0.918944i	$-0.629043\pi$
$307$	−4242.88	−0.788774	−0.394387	+	0.918944i	$0.629043\pi$
$308$	−1353.19	−0.250341
$309$	268.878	0.0495013
$310$	18217.5	3.33769
$311$	−9658.23	−1.76099	−0.880495	−	0.474055i	$-0.842790\pi$
$311$	−9658.23	−1.76099	−0.880495	+	0.474055i	$0.842790\pi$
$312$	−25936.5	−4.70630
$313$	10683.6	1.92930	0.964651	−	0.263529i	$-0.0848866\pi$
$313$	10683.6	1.92930	0.964651	+	0.263529i	$0.0848866\pi$
$314$	16232.0	2.91728
$315$	−5980.43	−1.06971
$316$	−6594.47	−1.17395
$317$	−2077.90	−0.368160	−0.184080	−	0.982911i	$-0.558931\pi$
$317$	−2077.90	−0.368160	−0.184080	+	0.982911i	$0.558931\pi$
$318$	3896.10	0.687052
$319$	−2073.27	−0.363890
$320$	−1639.34	−0.286380
$321$	7504.53	1.30487
$322$	922.269	0.159615
$323$	−1965.81	−0.338640
$324$	32441.9	5.56274
$325$	−2361.53	−0.403059
$326$	707.820	0.120253
$327$	2117.33	0.358069
$328$	6138.31	1.03333
$329$	907.973	0.152153
$330$	6943.53	1.15827
$331$	−11020.5	−1.83004	−0.915019	−	0.403410i	$-0.867825\pi$
$331$	−11020.5	−1.83004	−0.915019	+	0.403410i	$0.867825\pi$
$332$	1509.66	0.249558
$333$	13305.4	2.18959
$334$	−7210.05	−1.18119
$335$	3831.00	0.624806
$336$	7037.77	1.14268
$337$	−5932.54	−0.958950	−0.479475	−	0.877556i	$-0.659173\pi$
$337$	−5932.54	−0.958950	−0.479475	+	0.877556i	$0.659173\pi$
$338$	−4493.18	−0.723068
$339$	−5857.88	−0.938515
$340$	13476.9	2.14966
$341$	−3061.67	−0.486213
$342$	11075.2	1.75111
$343$	−343.000	−0.0539949
$344$	22020.6	3.45137
$345$	−3252.01	−0.507485
$346$	−7722.17	−1.19985
$347$	−4115.57	−0.636701	−0.318351	−	0.947973i	$-0.603129\pi$
$347$	−4115.57	−0.636701	−0.318351	+	0.947973i	$0.603129\pi$
$348$	31944.4	4.92069
$349$	−3760.31	−0.576746	−0.288373	−	0.957518i	$-0.593114\pi$
$349$	−3760.31	−0.576746	−0.288373	+	0.957518i	$0.593114\pi$
$350$	1504.97	0.229840
$351$	20897.8	3.17790
$352$	−1538.57	−0.232972
$353$	−888.701	−0.133997	−0.0669983	−	0.997753i	$-0.521342\pi$
$353$	−888.701	−0.133997	−0.0669983	+	0.997753i	$0.521342\pi$
$354$	−28953.9	−4.34713
$355$	7072.18	1.05733
$356$	13185.8	1.96304
$357$	3999.99	0.593003
$358$	−22819.3	−3.36882
$359$	10561.1	1.55263	0.776314	−	0.630347i	$-0.217087\pi$
$359$	10561.1	1.55263	0.776314	+	0.630347i	$0.217087\pi$
$360$	−41363.6	−6.05570
$361$	−5758.24	−0.839516
$362$	15037.4	2.18329
$363$	−1166.94	−0.168729
$364$	6833.25	0.983955
$365$	−10473.7	−1.50196
$366$	−2431.83	−0.347306
$367$	2773.62	0.394500	0.197250	−	0.980353i	$-0.436799\pi$
$367$	2773.62	0.394500	0.197250	+	0.980353i	$0.436799\pi$
$368$	2716.03	0.384736
$369$	−8368.99	−1.18068
$370$	−13193.0	−1.85371
$371$	−559.198	−0.0782537
$372$	47173.3	6.57479
$373$	−11360.2	−1.57697	−0.788484	−	0.615056i	$-0.789134\pi$
$373$	−11360.2	−1.57697	−0.788484	+	0.615056i	$0.789134\pi$
$374$	−3296.00	−0.455701
$375$	10296.1	1.41783
$376$	6279.99	0.861346
$377$	10469.5	1.43026
$378$	−13317.9	−1.81216
$379$	−10948.5	−1.48387	−0.741936	−	0.670470i	$-0.766092\pi$
$379$	−10948.5	−1.48387	−0.741936	+	0.670470i	$0.766092\pi$
$380$	−7546.37	−1.01874
$381$	−18796.9	−2.52755
$382$	6450.56	0.863978
$383$	11122.1	1.48385	0.741923	−	0.670485i	$-0.233914\pi$
$383$	11122.1	1.48385	0.741923	+	0.670485i	$0.233914\pi$
$384$	−16968.8	−2.25505
$385$	−996.589	−0.131924
$386$	616.875	0.0813423
$387$	−30023.0	−3.94355
$388$	−7941.20	−1.03906
$389$	−7938.70	−1.03473	−0.517363	−	0.855766i	$-0.673086\pi$
$389$	−7938.70	−1.03473	−0.517363	+	0.855766i	$0.673086\pi$
$390$	−35063.1	−4.55254
$391$	1543.68	0.199661
$392$	−2372.36	−0.305669
$393$	17191.4	2.20659
$394$	17618.7	2.25283
$395$	−4856.67	−0.618647
$396$	12760.5	1.61929
$397$	1060.60	0.134080	0.0670402	−	0.997750i	$-0.478644\pi$
$397$	1060.60	0.134080	0.0670402	+	0.997750i	$0.478644\pi$
$398$	−13429.8	−1.69139
$399$	−2239.79	−0.281028
$400$	4432.04	0.554005
$401$	−2776.24	−0.345733	−0.172866	−	0.984945i	$-0.555303\pi$
$401$	−2776.24	−0.345733	−0.172866	+	0.984945i	$0.555303\pi$
$402$	14436.1	1.79106
$403$	15460.7	1.91104
$404$	−24853.0	−3.06060
$405$	23892.7	2.93145
$406$	−6672.05	−0.815587
$407$	2217.24	0.270036
$408$	27665.9	3.35703
$409$	8725.98	1.05494	0.527472	−	0.849573i	$-0.323140\pi$
$409$	8725.98	1.05494	0.527472	+	0.849573i	$0.323140\pi$
$410$	8298.27	0.999567
$411$	29709.4	3.56559
$412$	−489.956	−0.0585883
$413$	4155.69	0.495129
$414$	−8696.98	−1.03245
$415$	1111.83	0.131512
$416$	7769.41	0.915689
$417$	−11296.7	−1.32662
$418$	1845.59	0.215959
$419$	−2390.49	−0.278719	−0.139359	−	0.990242i	$-0.544504\pi$
$419$	−2390.49	−0.278719	−0.139359	+	0.990242i	$0.544504\pi$
$420$	15355.2	1.78394
$421$	−8626.42	−0.998636	−0.499318	−	0.866419i	$-0.666416\pi$
$421$	−8626.42	−0.998636	−0.499318	+	0.866419i	$0.666416\pi$
$422$	−9658.55	−1.11415
$423$	−8562.17	−0.984177
$424$	−3867.69	−0.442999
$425$	2519.00	0.287504
$426$	26649.6	3.03093
$427$	349.035	0.0395574
$428$	−13674.9	−1.54440
$429$	5892.77	0.663184
$430$	29769.3	3.33861
$431$	4143.05	0.463025	0.231512	−	0.972832i	$-0.425633\pi$
$431$	4143.05	0.463025	0.231512	+	0.972832i	$0.425633\pi$
$432$	−39220.3	−4.36803
$433$	161.696	0.0179460	0.00897302	−	0.999960i	$-0.497144\pi$
$433$	161.696	0.0179460	0.00897302	+	0.999960i	$0.497144\pi$
$434$	−9852.84	−1.08975
$435$	23526.3	2.59310
$436$	−3858.25	−0.423800
$437$	−864.386	−0.0946205
$438$	−39467.1	−4.30551
$439$	12921.0	1.40475	0.702376	−	0.711806i	$-0.252123\pi$
$439$	12921.0	1.40475	0.702376	+	0.711806i	$0.252123\pi$
$440$	−6892.90	−0.746833
$441$	3234.48	0.349258
$442$	16644.0	1.79112
$443$	−10175.2	−1.09128	−0.545640	−	0.838020i	$-0.683713\pi$
$443$	−10175.2	−1.09128	−0.545640	+	0.838020i	$0.683713\pi$
$444$	−34162.7	−3.65155
$445$	9711.00	1.03448
$446$	22156.1	2.35229
$447$	−11936.2	−1.26301
$448$	886.626	0.0935026
$449$	3995.27	0.419930	0.209965	−	0.977709i	$-0.432665\pi$
$449$	3995.27	0.419930	0.209965	+	0.977709i	$0.432665\pi$
$450$	−14191.8	−1.48668
$451$	−1394.62	−0.145610
$452$	10674.4	1.11080
$453$	−15253.4	−1.58205
$454$	−8654.04	−0.894613
$455$	5032.53	0.518524
$456$	−15491.5	−1.59092
$457$	12445.5	1.27391	0.636956	−	0.770900i	$-0.280193\pi$
$457$	12445.5	1.27391	0.636956	+	0.770900i	$0.280193\pi$
$458$	−13238.6	−1.35065
$459$	−22291.3	−2.26682
$460$	5925.89	0.600644
$461$	11977.5	1.21009	0.605043	−	0.796193i	$-0.293156\pi$
$461$	11977.5	1.21009	0.605043	+	0.796193i	$0.293156\pi$
$462$	−3755.37	−0.378173
$463$	17335.0	1.74002	0.870009	−	0.493037i	$-0.164113\pi$
$463$	17335.0	1.74002	0.870009	+	0.493037i	$0.164113\pi$
$464$	−19648.8	−1.96589
$465$	34742.0	3.46478
$466$	−18170.4	−1.80629
$467$	4014.05	0.397747	0.198874	−	0.980025i	$-0.436272\pi$
$467$	4014.05	0.397747	0.198874	+	0.980025i	$0.436272\pi$
$468$	−64437.4	−6.36457
$469$	−2071.98	−0.203998
$470$	8489.82	0.833204
$471$	30955.6	3.02836
$472$	28742.8	2.80296
$473$	−5003.08	−0.486346
$474$	−18301.0	−1.77341
$475$	−1410.51	−0.136250
$476$	−7288.89	−0.701861
$477$	5273.23	0.506173
$478$	−9310.99	−0.890952
$479$	−6809.91	−0.649588	−0.324794	−	0.945785i	$-0.605295\pi$
$479$	−6809.91	−0.649588	−0.324794	+	0.945785i	$0.605295\pi$
$480$	17458.8	1.66017
$481$	−11196.5	−1.06137
$482$	−11173.3	−1.05587
$483$	1758.83	0.165693
$484$	2126.43	0.199703
$485$	−5848.51	−0.547561
$486$	38664.2	3.60873
$487$	−16342.2	−1.52060	−0.760302	−	0.649570i	$-0.774949\pi$
$487$	−16342.2	−1.52060	−0.760302	+	0.649570i	$0.774949\pi$
$488$	2414.10	0.223937
$489$	1349.86	0.124832
$490$	−3207.15	−0.295682
$491$	1686.53	0.155014	0.0775070	−	0.996992i	$-0.475304\pi$
$491$	1686.53	0.155014	0.0775070	+	0.996992i	$0.475304\pi$
$492$	21488.0	1.96901
$493$	−11167.6	−1.02021
$494$	−9319.79	−0.848821
$495$	9397.81	0.853334
$496$	−29016.0	−2.62673
$497$	−3824.95	−0.345217
$498$	4189.62	0.376991
$499$	1992.19	0.178723	0.0893616	−	0.995999i	$-0.471517\pi$
$499$	1992.19	0.178723	0.0893616	+	0.995999i	$0.471517\pi$
$500$	−18761.7	−1.67810
$501$	−13750.1	−1.22616
$502$	−5394.27	−0.479597
$503$	11525.3	1.02165	0.510824	−	0.859685i	$-0.329340\pi$
$503$	11525.3	1.02165	0.510824	+	0.859685i	$0.329340\pi$
$504$	22371.3	1.97718
$505$	−18303.6	−1.61287
$506$	−1449.28	−0.127329
$507$	−8568.81	−0.750600
$508$	34252.2	2.99153
$509$	−12191.9	−1.06168	−0.530842	−	0.847471i	$-0.678124\pi$
$509$	−12191.9	−1.06168	−0.530842	+	0.847471i	$0.678124\pi$
$510$	37401.1	3.24735
$511$	5664.63	0.490388
$512$	25796.8	2.22670
$513$	12482.0	1.07426
$514$	−15121.5	−1.29763
$515$	−360.841	−0.0308748
$516$	77086.1	6.57660
$517$	−1426.81	−0.121376
$518$	7135.37	0.605232
$519$	−14726.7	−1.24553
$520$	34807.4	2.93540
$521$	11196.1	0.941482	0.470741	−	0.882271i	$-0.343987\pi$
$521$	11196.1	0.941482	0.470741	+	0.882271i	$0.343987\pi$
$522$	62917.3	5.27551
$523$	−11969.2	−1.00072	−0.500361	−	0.865817i	$-0.666799\pi$
$523$	−11969.2	−1.00072	−0.500361	+	0.865817i	$0.666799\pi$
$524$	−31326.6	−2.61166
$525$	2870.08	0.238591
$526$	−21443.6	−1.77754
$527$	−16491.6	−1.36316
$528$	−11059.4	−0.911547
$529$	−11488.2	−0.944212
$530$	−5228.67	−0.428526
$531$	−39188.1	−3.20267
$532$	4081.41	0.332616
$533$	7042.50	0.572316
$534$	36593.2	2.96544
$535$	−10071.3	−0.813867
$536$	−14330.8	−1.15485
$537$	−43518.0	−3.49709
$538$	−27127.1	−2.17385
$539$	539.000	0.0430730
$540$	−85571.8	−6.81931
$541$	10468.1	0.831905	0.415953	−	0.909386i	$-0.363448\pi$
$541$	10468.1	0.831905	0.415953	+	0.909386i	$0.363448\pi$
$542$	−7464.78	−0.591587
$543$	28677.4	2.26642
$544$	−8287.47	−0.653166
$545$	−2841.51	−0.223334
$546$	18963.7	1.48639
$547$	−18969.5	−1.48277	−0.741386	−	0.671078i	$-0.765831\pi$
$547$	−18969.5	−1.48277	−0.741386	+	0.671078i	$0.765831\pi$
$548$	−54137.2	−4.22012
$549$	−3291.39	−0.255871
$550$	−2364.95	−0.183349
$551$	6253.30	0.483484
$552$	12165.0	0.937998
$553$	2626.71	0.201987
$554$	−11993.6	−0.919786
$555$	−25160.0	−1.92429
$556$	20585.2	1.57015
$557$	11524.3	0.876658	0.438329	−	0.898815i	$-0.355570\pi$
$557$	11524.3	0.876658	0.438329	+	0.898815i	$0.355570\pi$
$558$	92912.1	7.04889
$559$	25264.3	1.91157
$560$	−9444.87	−0.712712
$561$	−6285.70	−0.473053
$562$	8190.12	0.614732
$563$	14117.8	1.05683	0.528415	−	0.848986i	$-0.322787\pi$
$563$	14117.8	1.05683	0.528415	+	0.848986i	$0.322787\pi$
$564$	21984.0	1.64130
$565$	7861.43	0.585368
$566$	19114.8	1.41953
$567$	−12922.2	−0.957113
$568$	−26455.3	−1.95429
$569$	−16291.9	−1.20034	−0.600168	−	0.799874i	$-0.704899\pi$
$569$	−16291.9	−1.20034	−0.600168	+	0.799874i	$0.704899\pi$
$570$	−20942.7	−1.53894
$571$	4581.10	0.335750	0.167875	−	0.985808i	$-0.446310\pi$
$571$	4581.10	0.335750	0.167875	+	0.985808i	$0.446310\pi$
$572$	−10738.0	−0.784925
$573$	12301.7	0.896876
$574$	−4488.08	−0.326357
$575$	1107.62	0.0803324
$576$	−8360.87	−0.604808
$577$	20971.6	1.51310	0.756550	−	0.653935i	$-0.226883\pi$
$577$	20971.6	1.51310	0.756550	+	0.653935i	$0.226883\pi$
$578$	7091.54	0.510327
$579$	1176.42	0.0844396
$580$	−42870.2	−3.06912
$581$	−601.326	−0.0429384
$582$	−22038.5	−1.56963
$583$	878.740	0.0624249
$584$	39179.4	2.77612
$585$	−47456.6	−3.35400
$586$	−14585.5	−1.02819
$587$	26603.0	1.87057	0.935283	−	0.353900i	$-0.115145\pi$
$587$	26603.0	1.87057	0.935283	+	0.353900i	$0.115145\pi$
$588$	−8304.76	−0.582453
$589$	9234.45	0.646008
$590$	38856.9	2.71138
$591$	33600.0	2.33861
$592$	21013.2	1.45885
$593$	−13431.6	−0.930135	−0.465068	−	0.885275i	$-0.653970\pi$
$593$	−13431.6	−0.930135	−0.465068	+	0.885275i	$0.653970\pi$
$594$	20928.1	1.44561
$595$	−5368.09	−0.369866
$596$	21750.5	1.49486
$597$	−25611.6	−1.75580
$598$	7318.50	0.500461
$599$	−7329.80	−0.499979	−0.249990	−	0.968249i	$-0.580427\pi$
$599$	−7329.80	−0.499979	−0.249990	+	0.968249i	$0.580427\pi$
$600$	19850.9	1.35068
$601$	−9241.26	−0.627219	−0.313610	−	0.949552i	$-0.601538\pi$
$601$	−9241.26	−0.627219	−0.313610	+	0.949552i	$0.601538\pi$
$602$	−16100.6	−1.09005
$603$	19538.7	1.31953
$604$	27795.2	1.87247
$605$	1566.07	0.105239
$606$	−68972.3	−4.62344
$607$	11068.2	0.740109	0.370054	−	0.929010i	$-0.379339\pi$
$607$	11068.2	0.740109	0.370054	+	0.929010i	$0.379339\pi$
$608$	4640.57	0.309539
$609$	−12724.1	−0.846642
$610$	3263.58	0.216621
$611$	7205.06	0.477063
$612$	68734.1	4.53988
$613$	−22528.7	−1.48438	−0.742191	−	0.670189i	$-0.766213\pi$
$613$	−22528.7	−1.48438	−0.742191	+	0.670189i	$0.766213\pi$
$614$	21456.5	1.41028
$615$	15825.4	1.03763
$616$	3727.99	0.243839
$617$	6859.59	0.447579	0.223790	−	0.974637i	$-0.428157\pi$
$617$	6859.59	0.447579	0.223790	+	0.974637i	$0.428157\pi$
$618$	−1359.73	−0.0885055
$619$	14905.2	0.967833	0.483917	−	0.875114i	$-0.339214\pi$
$619$	14905.2	0.967833	0.483917	+	0.875114i	$0.339214\pi$
$620$	−63307.8	−4.10081
$621$	−9801.68	−0.633378
$622$	48842.2	3.14854
$623$	−5252.14	−0.337757
$624$	55847.0	3.58280
$625$	−19131.8	−1.22444
$626$	−54027.5	−3.44948
$627$	3519.68	0.224182
$628$	−56408.1	−3.58428
$629$	11943.1	0.757079
$630$	30243.4	1.91258
$631$	20709.3	1.30653	0.653267	−	0.757128i	$-0.273398\pi$
$631$	20709.3	1.30653	0.653267	+	0.757128i	$0.273398\pi$
$632$	18167.6	1.14346
$633$	−18419.5	−1.15657
$634$	10508.1	0.658248
$635$	25225.9	1.57647
$636$	−13539.4	−0.844138
$637$	−2721.82	−0.169297
$638$	10484.7	0.650613
$639$	36069.2	2.23298
$640$	22772.6	1.40651
$641$	30663.6	1.88945	0.944727	−	0.327859i	$-0.106327\pi$
$641$	30663.6	1.88945	0.944727	+	0.327859i	$0.106327\pi$
$642$	−37950.8	−2.33302
$643$	−12820.9	−0.786326	−0.393163	−	0.919469i	$-0.628619\pi$
$643$	−12820.9	−0.786326	−0.393163	+	0.919469i	$0.628619\pi$
$644$	−3204.99	−0.196109
$645$	56772.1	3.46573
$646$	9941.23	0.605468
$647$	−21345.2	−1.29701	−0.648506	−	0.761209i	$-0.724606\pi$
$647$	−21345.2	−1.29701	−0.648506	+	0.761209i	$0.724606\pi$
$648$	−89376.6	−5.41828
$649$	−6530.37	−0.394976
$650$	11942.4	0.720645
$651$	−18790.0	−1.13124
$652$	−2459.75	−0.147748
$653$	−17194.7	−1.03044	−0.515222	−	0.857057i	$-0.672291\pi$
$653$	−17194.7	−1.03044	−0.515222	+	0.857057i	$0.672291\pi$
$654$	−10707.5	−0.640206
$655$	−23071.3	−1.37629
$656$	−13217.1	−0.786649
$657$	−53417.3	−3.17200
$658$	−4591.67	−0.272040
$659$	27892.6	1.64877	0.824386	−	0.566027i	$-0.191520\pi$
$659$	27892.6	1.64877	0.824386	+	0.566027i	$0.191520\pi$
$660$	−24129.6	−1.42309
$661$	−17082.0	−1.00516	−0.502582	−	0.864529i	$-0.667617\pi$
$661$	−17082.0	−1.00516	−0.502582	+	0.864529i	$0.667617\pi$
$662$	55731.4	3.27200
$663$	31741.2	1.85932
$664$	−4159.07	−0.243077
$665$	3005.86	0.175282
$666$	−67286.4	−3.91486
$667$	−4910.49	−0.285060
$668$	25055.7	1.45125
$669$	42253.2	2.44186
$670$	−19373.6	−1.11712
$671$	−548.484	−0.0315559
$672$	−9442.52	−0.542044
$673$	−27727.6	−1.58814	−0.794071	−	0.607825i	$-0.792042\pi$
$673$	−27727.6	−1.58814	−0.794071	+	0.607825i	$0.792042\pi$
$674$	30001.2	1.71454
$675$	−15994.5	−0.912040
$676$	15614.3	0.888388
$677$	−3018.10	−0.171337	−0.0856685	−	0.996324i	$-0.527303\pi$
$677$	−3018.10	−0.171337	−0.0856685	+	0.996324i	$0.527303\pi$
$678$	29623.7	1.67801
$679$	3163.13	0.178778
$680$	−37128.4	−2.09384
$681$	−16503.9	−0.928677
$682$	15483.0	0.869320
$683$	33614.8	1.88321	0.941607	−	0.336714i	$-0.109316\pi$
$683$	33614.8	1.88321	0.941607	+	0.336714i	$0.109316\pi$
$684$	−38487.6	−2.15148
$685$	−39870.8	−2.22392
$686$	1734.57	0.0965397
$687$	−25246.9	−1.40208
$688$	−47415.2	−2.62745
$689$	−4437.42	−0.245359
$690$	16445.6	0.907352
$691$	−14923.1	−0.821565	−0.410783	−	0.911733i	$-0.634744\pi$
$691$	−14923.1	−0.821565	−0.410783	+	0.911733i	$0.634744\pi$
$692$	26835.4	1.47417
$693$	−5082.76	−0.278612
$694$	20812.7	1.13838
$695$	15160.5	0.827439
$696$	−88005.9	−4.79290
$697$	−7512.09	−0.408236
$698$	19016.1	1.03119
$699$	−34652.3	−1.87507
$700$	−5229.93	−0.282389
$701$	15440.5	0.831928	0.415964	−	0.909381i	$-0.363444\pi$
$701$	15440.5	0.831928	0.415964	+	0.909381i	$0.363444\pi$
$702$	−105682.	−5.68190
$703$	−6687.54	−0.358784
$704$	−1393.27	−0.0745893
$705$	16190.7	0.864930
$706$	4494.21	0.239578
$707$	9899.43	0.526600
$708$	100618.	5.34105
$709$	25441.7	1.34765	0.673825	−	0.738891i	$-0.264650\pi$
$709$	25441.7	1.34765	0.673825	+	0.738891i	$0.264650\pi$
$710$	−35764.5	−1.89044
$711$	−24769.8	−1.30652
$712$	−36326.4	−1.91206
$713$	−7251.49	−0.380884
$714$	−20228.2	−1.06025
$715$	−7908.26	−0.413639
$716$	79299.6	4.13906
$717$	−17756.7	−0.924876
$718$	−53408.1	−2.77601
$719$	−11335.3	−0.587951	−0.293976	−	0.955813i	$-0.594978\pi$
$719$	−11335.3	−0.587951	−0.293976	+	0.955813i	$0.594978\pi$
$720$	89064.9	4.61007
$721$	195.159	0.0100806
$722$	29119.8	1.50101
$723$	−21308.3	−1.09608
$724$	−52256.8	−2.68247
$725$	−8012.98	−0.410475
$726$	5901.30	0.301677
$727$	−11169.8	−0.569830	−0.284915	−	0.958553i	$-0.591965\pi$
$727$	−11169.8	−0.569830	−0.284915	+	0.958553i	$0.591965\pi$
$728$	−18825.4	−0.958402
$729$	23892.3	1.21386
$730$	52965.9	2.68542
$731$	−26948.9	−1.36353
$732$	8450.89	0.426713
$733$	25635.5	1.29177	0.645885	−	0.763435i	$-0.276488\pi$
$733$	25635.5	1.29177	0.645885	+	0.763435i	$0.276488\pi$
$734$	−14026.3	−0.705343
$735$	−6116.26	−0.306941
$736$	−3644.08	−0.182503
$737$	3255.97	0.162734
$738$	42322.5	2.11099
$739$	20947.2	1.04270	0.521350	−	0.853343i	$-0.325429\pi$
$739$	20947.2	1.04270	0.521350	+	0.853343i	$0.325429\pi$
$740$	45847.2	2.27753
$741$	−17773.5	−0.881141
$742$	2827.90	0.139913
$743$	−4063.24	−0.200627	−0.100314	−	0.994956i	$-0.531985\pi$
$743$	−4063.24	−0.200627	−0.100314	+	0.994956i	$0.531985\pi$
$744$	−129961.	−6.40405
$745$	16018.7	0.787759
$746$	57449.2	2.81952
$747$	5670.49	0.277741
$748$	11454.0	0.559891
$749$	5446.99	0.265726
$750$	−52067.7	−2.53499
$751$	24644.9	1.19747	0.598737	−	0.800945i	$-0.295669\pi$
$751$	24644.9	1.19747	0.598737	+	0.800945i	$0.295669\pi$
$752$	−13522.2	−0.655724
$753$	−10287.2	−0.497859
$754$	−52944.9	−2.55721
$755$	20470.5	0.986751
$756$	46281.1	2.22649
$757$	−17258.3	−0.828618	−0.414309	−	0.910136i	$-0.635977\pi$
$757$	−17258.3	−0.828618	−0.414309	+	0.910136i	$0.635977\pi$
$758$	55367.3	2.65308
$759$	−2763.88	−0.132177
$760$	20790.0	0.992282
$761$	12931.6	0.615990	0.307995	−	0.951388i	$-0.400342\pi$
$761$	12931.6	0.615990	0.307995	+	0.951388i	$0.400342\pi$
$762$	95057.1	4.51910
$763$	1536.82	0.0729180
$764$	−22416.4	−1.06152
$765$	50621.0	2.39243
$766$	−56245.1	−2.65303
$767$	32976.7	1.55244
$768$	76040.1	3.57274
$769$	13584.8	0.637034	0.318517	−	0.947917i	$-0.396815\pi$
$769$	13584.8	0.637034	0.318517	+	0.947917i	$0.396815\pi$
$770$	5039.81	0.235873
$771$	−28837.8	−1.34704
$772$	−2143.71	−0.0999402
$773$	2239.95	0.104224	0.0521121	−	0.998641i	$-0.483405\pi$
$773$	2239.95	0.104224	0.0521121	+	0.998641i	$0.483405\pi$
$774$	151828.	7.05083
$775$	−11833.0	−0.548458
$776$	21877.8	1.01207
$777$	13607.6	0.628277
$778$	40146.5	1.85003
$779$	4206.40	0.193466
$780$	121848.	5.59342
$781$	6010.64	0.275388
$782$	−7806.50	−0.356982
$783$	70909.1	3.23638
$784$	5108.21	0.232699
$785$	−41543.2	−1.88884
$786$	−86937.9	−3.94526
$787$	10614.2	0.480758	0.240379	−	0.970679i	$-0.422728\pi$
$787$	10614.2	0.480758	0.240379	+	0.970679i	$0.422728\pi$
$788$	−61226.8	−2.76791
$789$	−40894.4	−1.84522
$790$	24560.5	1.10610
$791$	−4251.82	−0.191122
$792$	−35154.9	−1.57724
$793$	2769.71	0.124029
$794$	−5363.51	−0.239728
$795$	−9971.43	−0.444843
$796$	46670.1	2.07811
$797$	1020.65	0.0453616	0.0226808	−	0.999743i	$-0.492780\pi$
$797$	1020.65	0.0453616	0.0226808	+	0.999743i	$0.492780\pi$
$798$	11326.8	0.502460
$799$	−7685.49	−0.340292
$800$	−5946.43	−0.262798
$801$	49527.6	2.18473
$802$	14039.6	0.618150
$803$	−8901.55	−0.391194
$804$	−50167.0	−2.20057
$805$	−2360.40	−0.103345
$806$	−78185.5	−3.41683
$807$	−51733.3	−2.25663
$808$	68469.4	2.98112
$809$	−44041.1	−1.91397	−0.956985	−	0.290139i	$-0.906298\pi$
$809$	−44041.1	−1.91397	−0.956985	+	0.290139i	$0.906298\pi$
$810$	−120827.	−5.24126
$811$	−16722.4	−0.724048	−0.362024	−	0.932169i	$-0.617914\pi$
$811$	−16722.4	−0.724048	−0.362024	+	0.932169i	$0.617914\pi$
$812$	23186.1	1.00206
$813$	−14235.9	−0.614113
$814$	−11212.7	−0.482808
$815$	−1811.55	−0.0778599
$816$	−59570.8	−2.55563
$817$	15090.0	0.646186
$818$	−44127.8	−1.88618
$819$	25666.7	1.09507
$820$	−28837.4	−1.22811
$821$	30420.1	1.29314	0.646570	−	0.762855i	$-0.276203\pi$
$821$	30420.1	1.29314	0.646570	+	0.762855i	$0.276203\pi$
$822$	−150242.	−6.37506
$823$	−330.412	−0.0139945	−0.00699724	−	0.999976i	$-0.502227\pi$
$823$	−330.412	−0.0139945	−0.00699724	+	0.999976i	$0.502227\pi$
$824$	1349.82	0.0570668
$825$	−4510.12	−0.190330
$826$	−21015.6	−0.885261
$827$	4475.72	0.188194	0.0940968	−	0.995563i	$-0.470004\pi$
$827$	4475.72	0.188194	0.0940968	+	0.995563i	$0.470004\pi$
$828$	30223.0	1.26850
$829$	−10923.6	−0.457651	−0.228825	−	0.973467i	$-0.573489\pi$
$829$	−10923.6	−0.457651	−0.228825	+	0.973467i	$0.573489\pi$
$830$	−5622.58	−0.235136
$831$	−22872.7	−0.954809
$832$	7035.67	0.293170
$833$	2903.30	0.120761
$834$	57128.1	2.37193
$835$	18452.9	0.764779
$836$	−6413.65	−0.265336
$837$	104714.	4.32430
$838$	12088.8	0.498332
$839$	−28354.8	−1.16677	−0.583383	−	0.812197i	$-0.698271\pi$
$839$	−28354.8	−1.16677	−0.583383	+	0.812197i	$0.698271\pi$
$840$	−42303.1	−1.73761
$841$	11135.4	0.456574
$842$	43624.3	1.78550
$843$	15619.1	0.638139
$844$	33564.5	1.36888
$845$	11499.6	0.468162
$846$	43299.4	1.75965
$847$	−847.000	−0.0343604
$848$	8327.99	0.337246
$849$	36453.2	1.47358
$850$	−12738.7	−0.514040
$851$	5251.49	0.211538
$852$	−92610.3	−3.72392
$853$	39699.8	1.59355	0.796774	−	0.604278i	$-0.206538\pi$
$853$	39699.8	1.59355	0.796774	+	0.604278i	$0.206538\pi$
$854$	−1765.09	−0.0707262
$855$	−28345.2	−1.13378
$856$	37674.1	1.50429
$857$	6093.09	0.242866	0.121433	−	0.992600i	$-0.461251\pi$
$857$	6093.09	0.242866	0.121433	+	0.992600i	$0.461251\pi$
$858$	−29800.1	−1.18573
$859$	20688.1	0.821733	0.410867	−	0.911695i	$-0.365226\pi$
$859$	20688.1	0.821733	0.410867	+	0.911695i	$0.365226\pi$
$860$	−103452.	−4.10194
$861$	−8559.08	−0.338783
$862$	−20951.6	−0.827860
$863$	−38835.1	−1.53182	−0.765910	−	0.642948i	$-0.777711\pi$
$863$	−38835.1	−1.53182	−0.765910	+	0.642948i	$0.777711\pi$
$864$	52621.6	2.07202
$865$	19763.6	0.776860
$866$	−817.708	−0.0320864
$867$	13524.1	0.529759
$868$	34239.7	1.33891
$869$	−4127.68	−0.161130
$870$	−118974.	−4.63631
$871$	−16441.8	−0.639621
$872$	10629.4	0.412794
$873$	−29828.3	−1.15640
$874$	4371.25	0.169176
$875$	7473.16	0.288730
$876$	137153.	5.28991
$877$	−14454.3	−0.556543	−0.278272	−	0.960502i	$-0.589762\pi$
$877$	−14454.3	−0.556543	−0.278272	+	0.960502i	$0.589762\pi$
$878$	−65342.3	−2.51161
$879$	−27815.5	−1.06734
$880$	14841.9	0.568547
$881$	−21890.5	−0.837130	−0.418565	−	0.908187i	$-0.637467\pi$
$881$	−21890.5	−0.837130	−0.418565	+	0.908187i	$0.637467\pi$
$882$	−16357.0	−0.624453
$883$	−34415.2	−1.31162	−0.655812	−	0.754924i	$-0.727674\pi$
$883$	−34415.2	−1.31162	−0.655812	+	0.754924i	$0.727674\pi$
$884$	−57839.7	−2.20063
$885$	74102.9	2.81462
$886$	51456.4	1.95114
$887$	−288.789	−0.0109319	−0.00546594	−	0.999985i	$-0.501740\pi$
$887$	−288.789	−0.0109319	−0.00546594	+	0.999985i	$0.501740\pi$
$888$	94117.2	3.55672
$889$	−13643.3	−0.514716
$890$	−49109.1	−1.84960
$891$	20306.4	0.763512
$892$	−76994.9	−2.89011
$893$	4303.49	0.161266
$894$	60362.1	2.25818
$895$	58402.3	2.18120
$896$	−12316.5	−0.459223
$897$	13956.9	0.519517
$898$	−20204.3	−0.750809
$899$	52460.1	1.94621
$900$	49318.1	1.82660
$901$	4733.30	0.175016
$902$	7052.69	0.260343
$903$	−30704.9	−1.13156
$904$	−29407.7	−1.08195
$905$	−38485.9	−1.41361
$906$	77137.4	2.82861
$907$	−36248.0	−1.32701	−0.663503	−	0.748174i	$-0.730931\pi$
$907$	−36248.0	−1.32701	−0.663503	+	0.748174i	$0.730931\pi$
$908$	30073.7	1.09915
$909$	−93351.4	−3.40624
$910$	−25449.8	−0.927090
$911$	−4600.52	−0.167313	−0.0836564	−	0.996495i	$-0.526660\pi$
$911$	−4600.52	−0.167313	−0.0836564	+	0.996495i	$0.526660\pi$
$912$	33356.7	1.21113
$913$	944.941	0.0342530
$914$	−62937.8	−2.27768
$915$	6223.88	0.224869
$916$	46005.6	1.65946
$917$	12478.0	0.449356
$918$	112728.	4.05293
$919$	−46257.9	−1.66040	−0.830200	−	0.557466i	$-0.811774\pi$
$919$	−46257.9	−1.66040	−0.830200	+	0.557466i	$0.811774\pi$
$920$	−16325.7	−0.585046
$921$	40919.0	1.46398
$922$	−60571.1	−2.16356
$923$	−30352.2	−1.08240
$924$	13050.3	0.464637
$925$	8569.42	0.304606
$926$	−87664.3	−3.11105
$927$	−1840.34	−0.0652048
$928$	26362.6	0.932539
$929$	−3303.31	−0.116661	−0.0583305	−	0.998297i	$-0.518578\pi$
$929$	−3303.31	−0.116661	−0.0583305	+	0.998297i	$0.518578\pi$
$930$	−175693.	−6.19482
$931$	−1625.71	−0.0572291
$932$	63144.3	2.21927
$933$	93145.5	3.26843
$934$	−20299.3	−0.711148
$935$	8435.57	0.295051
$936$	177523.	6.19929
$937$	−44736.9	−1.55975	−0.779877	−	0.625932i	$-0.784719\pi$
$937$	−44736.9	−1.55975	−0.779877	+	0.625932i	$0.784719\pi$
$938$	10478.1	0.364736
$939$	−103034.	−3.58082
$940$	−29503.1	−1.02371
$941$	−21009.4	−0.727829	−0.363914	−	0.931432i	$-0.618560\pi$
$941$	−21009.4	−0.727829	−0.363914	+	0.931432i	$0.618560\pi$
$942$	−156544.	−5.41453
$943$	−3303.13	−0.114067
$944$	−61889.6	−2.13383
$945$	34084.9	1.17331
$946$	25300.9	0.869558
$947$	11343.0	0.389227	0.194613	−	0.980880i	$-0.437655\pi$
$947$	11343.0	0.389227	0.194613	+	0.980880i	$0.437655\pi$
$948$	63598.1	2.17887
$949$	44950.6	1.53758
$950$	7133.04	0.243607
$951$	20039.6	0.683312
$952$	20080.7	0.683634
$953$	−45452.4	−1.54496	−0.772481	−	0.635038i	$-0.780985\pi$
$953$	−45452.4	−1.54496	−0.772481	+	0.635038i	$0.780985\pi$
$954$	−26667.0	−0.905007
$955$	−16509.2	−0.559397
$956$	32356.7	1.09466
$957$	19995.0	0.675387
$958$	34438.1	1.16142
$959$	21563.9	0.726105
$960$	15810.0	0.531527
$961$	47678.5	1.60043
$962$	56621.5	1.89766
$963$	−51365.0	−1.71881
$964$	38828.5	1.29728
$965$	−1578.79	−0.0526664
$966$	−8894.52	−0.296249
$967$	4435.17	0.147493	0.0737464	−	0.997277i	$-0.476504\pi$
$967$	4435.17	0.147493	0.0737464	+	0.997277i	$0.476504\pi$
$968$	−5858.27	−0.194517
$969$	18958.6	0.628523
$970$	29576.2	0.979006
$971$	−33349.3	−1.10219	−0.551097	−	0.834441i	$-0.685791\pi$
$971$	−33349.3	−1.10219	−0.551097	+	0.834441i	$0.685791\pi$
$972$	−134362.	−4.43382
$973$	−8199.47	−0.270157
$974$	82643.3	2.71875
$975$	22775.0	0.748085
$976$	−5198.09	−0.170478
$977$	−39719.6	−1.30066	−0.650328	−	0.759653i	$-0.725369\pi$
$977$	−39719.6	−1.30066	−0.650328	+	0.759653i	$0.725369\pi$
$978$	−6826.33	−0.223192
$979$	8253.36	0.269437
$980$	11145.2	0.363286
$981$	−14492.1	−0.471660
$982$	−8528.86	−0.277156
$983$	16117.6	0.522963	0.261482	−	0.965208i	$-0.415789\pi$
$983$	16117.6	0.522963	0.261482	+	0.965208i	$0.415789\pi$
$984$	−59198.8	−1.91788
$985$	−45092.1	−1.45863
$986$	56475.2	1.82407
$987$	−8756.64	−0.282398
$988$	32387.3	1.04289
$989$	−11849.7	−0.380989
$990$	−47525.3	−1.52571
$991$	−14926.8	−0.478471	−0.239236	−	0.970962i	$-0.576897\pi$
$991$	−14926.8	−0.478471	−0.239236	+	0.970962i	$0.576897\pi$
$992$	38930.6	1.24602
$993$	106284.	3.39659
$994$	19343.0	0.617227
$995$	34371.4	1.09512
$996$	−14559.4	−0.463185
$997$	51206.2	1.62660	0.813298	−	0.581847i	$-0.197670\pi$
$997$	51206.2	1.62660	0.813298	+	0.581847i	$0.197670\pi$
$998$	−10074.6	−0.319546
$999$	−75833.2	−2.40166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.4.a.c.1.1	✓	4
3.2	odd	2		693.4.a.m.1.4		4
4.3	odd	2		1232.4.a.w.1.4		4
5.4	even	2		1925.4.a.q.1.4		4
7.6	odd	2		539.4.a.f.1.1		4
11.10	odd	2		847.4.a.e.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.a.c.1.1	✓	4	1.1	even	1	trivial
539.4.a.f.1.1		4	7.6	odd	2
693.4.a.m.1.4		4	3.2	odd	2
847.4.a.e.1.4		4	11.10	odd	2
1232.4.a.w.1.4		4	4.3	odd	2
1925.4.a.q.1.4		4	5.4	even	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.a (trivial)

\(f(q)\)	\(=\)	\(q-5.05706 q^{2} -9.64416 q^{3} +17.5738 q^{4} +12.9427 q^{5} +48.7711 q^{6} -7.00000 q^{7} -48.4155 q^{8} +66.0098 q^{9} -65.4521 q^{10} +11.0000 q^{11} -169.485 q^{12} -55.5473 q^{13} +35.3994 q^{14} -124.822 q^{15} +104.249 q^{16} +59.2511 q^{17} -333.816 q^{18} -33.1777 q^{19} +227.453 q^{20} +67.5091 q^{21} -55.6276 q^{22} +26.0532 q^{23} +466.927 q^{24} +42.5139 q^{25} +280.906 q^{26} -376.217 q^{27} -123.017 q^{28} -188.479 q^{29} +631.230 q^{30} -278.333 q^{31} -139.870 q^{32} -106.086 q^{33} -299.636 q^{34} -90.5990 q^{35} +1160.05 q^{36} +201.567 q^{37} +167.781 q^{38} +535.707 q^{39} -626.628 q^{40} -126.784 q^{41} -341.398 q^{42} -454.826 q^{43} +193.312 q^{44} +854.347 q^{45} -131.753 q^{46} -129.710 q^{47} -1005.40 q^{48} +49.0000 q^{49} -214.995 q^{50} -571.427 q^{51} -976.179 q^{52} +79.8855 q^{53} +1902.55 q^{54} +142.370 q^{55} +338.908 q^{56} +319.971 q^{57} +953.150 q^{58} -593.670 q^{59} -2193.60 q^{60} -49.8622 q^{61} +1407.55 q^{62} -462.069 q^{63} -126.661 q^{64} -718.932 q^{65} +536.482 q^{66} +295.997 q^{67} +1041.27 q^{68} -251.262 q^{69} +458.164 q^{70} +546.422 q^{71} -3195.90 q^{72} -809.232 q^{73} -1019.34 q^{74} -410.011 q^{75} -583.059 q^{76} -77.0000 q^{77} -2709.10 q^{78} -375.244 q^{79} +1349.27 q^{80} +1846.03 q^{81} +641.154 q^{82} +85.9037 q^{83} +1186.39 q^{84} +766.870 q^{85} +2300.08 q^{86} +1817.72 q^{87} -532.570 q^{88} +750.306 q^{89} -4320.48 q^{90} +388.831 q^{91} +457.856 q^{92} +2684.29 q^{93} +655.953 q^{94} -429.409 q^{95} +1348.93 q^{96} -451.876 q^{97} -247.796 q^{98} +726.108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{3} + 22 q^{4} - 18 q^{5} + 2 q^{6} - 28 q^{7} - 60 q^{8} + 66 q^{9} - 92 q^{10} + 44 q^{11} - 186 q^{12} - 134 q^{13} + 28 q^{14} - 62 q^{15} - 6 q^{16} - 74 q^{17} - 256 q^{18} - 164 q^{19}+ \cdots + 726 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^3 + 22 * q^4 - 18 * q^5 + 2 * q^6 - 28 * q^7 - 60 * q^8 + 66 * q^9 - 92 * q^10 + 44 * q^11 - 186 * q^12 - 134 * q^13 + 28 * q^14 - 62 * q^15 - 6 * q^16 - 74 * q^17 - 256 * q^18 - 164 * q^19 + 116 * q^20 + 84 * q^21 - 44 * q^22 + 194 * q^23 + 570 * q^24 + 38 * q^25 + 734 * q^26 - 510 * q^27 - 154 * q^28 - 108 * q^29 + 1252 * q^30 - 412 * q^31 - 4 * q^32 - 132 * q^33 - 346 * q^34 + 126 * q^35 + 1518 * q^36 + 286 * q^37 + 224 * q^38 - 256 * q^39 - 540 * q^40 - 18 * q^41 - 14 * q^42 - 496 * q^43 + 242 * q^44 + 580 * q^45 - 284 * q^46 + 62 * q^47 - 862 * q^48 + 196 * q^49 + 212 * q^50 - 508 * q^51 - 822 * q^52 - 828 * q^53 + 2420 * q^54 - 198 * q^55 + 420 * q^56 + 700 * q^57 + 1388 * q^58 - 1224 * q^59 - 1776 * q^60 - 350 * q^61 - 878 * q^62 - 462 * q^63 - 718 * q^64 - 396 * q^65 + 22 * q^66 - 1498 * q^67 + 1058 * q^68 - 386 * q^69 + 644 * q^70 + 2326 * q^71 - 3000 * q^72 - 1630 * q^73 - 1156 * q^74 - 1362 * q^75 - 3152 * q^76 - 308 * q^77 - 2464 * q^78 - 1020 * q^79 + 3072 * q^80 + 1128 * q^81 + 2118 * q^82 - 1920 * q^83 + 1302 * q^84 + 2008 * q^85 + 1056 * q^86 + 1640 * q^87 - 660 * q^88 + 1550 * q^89 - 5780 * q^90 + 938 * q^91 + 2592 * q^92 + 6046 * q^93 - 1042 * q^94 + 2332 * q^95 + 4082 * q^96 - 2202 * q^97 - 196 * q^98 + 726 * q^99

Introduction

L-functions

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Database

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