LMFDB - Embedded newform 161.4.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, 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("161.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 76 x^{10} + 311 x^{9} + 1979 x^{8} - 8466 x^{7} - 19942 x^{6} + 95647 x^{5} + \cdots - 70656 $ x^12 - 4x^11 - 76x^10 + 311x^9 + 1979x^8 - 8466x^7 - 19942x^6 + 95647x^5 + 50294x^4 - 400320x^3 + 178432x^2 + 227072*x - 70656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.89764$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.89764 q^{2} +7.57994 q^{3} +15.9869 q^{4} -14.0191 q^{5} -37.1238 q^{6} +7.00000 q^{7} -39.1171 q^{8} +30.4555 q^{9} +68.6607 q^{10} +35.1776 q^{11} +121.180 q^{12} +16.8491 q^{13} -34.2835 q^{14} -106.264 q^{15} +63.6863 q^{16} -71.4072 q^{17} -149.160 q^{18} +133.530 q^{19} -224.123 q^{20} +53.0596 q^{21} -172.287 q^{22} +23.0000 q^{23} -296.505 q^{24} +71.5361 q^{25} -82.5207 q^{26} +26.1922 q^{27} +111.908 q^{28} +240.517 q^{29} +520.444 q^{30} +105.085 q^{31} +1.02401 q^{32} +266.644 q^{33} +349.727 q^{34} -98.1339 q^{35} +486.889 q^{36} +329.378 q^{37} -653.982 q^{38} +127.715 q^{39} +548.388 q^{40} -304.814 q^{41} -259.867 q^{42} +140.198 q^{43} +562.381 q^{44} -426.959 q^{45} -112.646 q^{46} +298.500 q^{47} +482.738 q^{48} +49.0000 q^{49} -350.358 q^{50} -541.262 q^{51} +269.365 q^{52} +292.191 q^{53} -128.280 q^{54} -493.159 q^{55} -273.820 q^{56} +1012.15 q^{57} -1177.97 q^{58} -62.9889 q^{59} -1698.84 q^{60} +593.679 q^{61} -514.667 q^{62} +213.188 q^{63} -514.506 q^{64} -236.209 q^{65} -1305.93 q^{66} +744.666 q^{67} -1141.58 q^{68} +174.339 q^{69} +480.625 q^{70} -277.419 q^{71} -1191.33 q^{72} -551.265 q^{73} -1613.18 q^{74} +542.239 q^{75} +2134.73 q^{76} +246.243 q^{77} -625.502 q^{78} -929.896 q^{79} -892.827 q^{80} -623.762 q^{81} +1492.87 q^{82} -749.978 q^{83} +848.259 q^{84} +1001.07 q^{85} -686.640 q^{86} +1823.10 q^{87} -1376.05 q^{88} +1124.37 q^{89} +2091.09 q^{90} +117.943 q^{91} +367.699 q^{92} +796.534 q^{93} -1461.95 q^{94} -1871.97 q^{95} +7.76194 q^{96} -1462.41 q^{97} -239.985 q^{98} +1071.35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * 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 $

$2$	−4.89764	−1.73158	−0.865789	−	0.500409i	$-0.833183\pi$
$2$	−4.89764	−1.73158	−0.865789	+	0.500409i	$0.833183\pi$
$3$	7.57994	1.45876	0.729380	−	0.684109i	$-0.239809\pi$
$3$	7.57994	1.45876	0.729380	+	0.684109i	$0.239809\pi$
$4$	15.9869	1.99837
$5$	−14.0191	−1.25391	−0.626955	−	0.779056i	$-0.715699\pi$
$5$	−14.0191	−1.25391	−0.626955	+	0.779056i	$0.715699\pi$
$6$	−37.1238	−2.52596
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−39.1171	−1.72875
$9$	30.4555	1.12798
$10$	68.6607	2.17124
$11$	35.1776	0.964222	0.482111	−	0.876110i	$-0.339870\pi$
$11$	35.1776	0.964222	0.482111	+	0.876110i	$0.339870\pi$
$12$	121.180	2.91513
$13$	16.8491	0.359468	0.179734	−	0.983715i	$-0.442476\pi$
$13$	16.8491	0.359468	0.179734	+	0.983715i	$0.442476\pi$
$14$	−34.2835	−0.654475
$15$	−106.264	−1.82915
$16$	63.6863	0.995098
$17$	−71.4072	−1.01875	−0.509376	−	0.860544i	$-0.670124\pi$
$17$	−71.4072	−1.01875	−0.509376	+	0.860544i	$0.670124\pi$
$18$	−149.160	−1.95319
$19$	133.530	1.61231	0.806154	−	0.591706i	$-0.201545\pi$
$19$	133.530	1.61231	0.806154	+	0.591706i	$0.201545\pi$
$20$	−224.123	−2.50577
$21$	53.0596	0.551359
$22$	−172.287	−1.66963
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−296.505	−2.52183
$25$	71.5361	0.572289
$26$	−82.5207	−0.622448
$27$	26.1922	0.186692
$28$	111.908	0.755311
$29$	240.517	1.54010	0.770049	−	0.637985i	$-0.220232\pi$
$29$	240.517	1.54010	0.770049	+	0.637985i	$0.220232\pi$
$30$	520.444	3.16732
$31$	105.085	0.608830	0.304415	−	0.952539i	$-0.401539\pi$
$31$	105.085	0.608830	0.304415	+	0.952539i	$0.401539\pi$
$32$	1.02401	0.00565692
$33$	266.644	1.40657
$34$	349.727	1.76405
$35$	−98.1339	−0.473933
$36$	486.889	2.25412
$37$	329.378	1.46350	0.731749	−	0.681574i	$-0.238704\pi$
$37$	329.378	1.46350	0.731749	+	0.681574i	$0.238704\pi$
$38$	−653.982	−2.79184
$39$	127.715	0.524378
$40$	548.388	2.16769
$41$	−304.814	−1.16107	−0.580535	−	0.814235i	$-0.697157\pi$
$41$	−304.814	−1.16107	−0.580535	+	0.814235i	$0.697157\pi$
$42$	−259.867	−0.954722
$43$	140.198	0.497209	0.248605	−	0.968605i	$-0.420028\pi$
$43$	140.198	0.497209	0.248605	+	0.968605i	$0.420028\pi$
$44$	562.381	1.92687
$45$	−426.959	−1.41438
$46$	−112.646	−0.361059
$47$	298.500	0.926398	0.463199	−	0.886254i	$-0.346702\pi$
$47$	298.500	0.926398	0.463199	+	0.886254i	$0.346702\pi$
$48$	482.738	1.45161
$49$	49.0000	0.142857
$50$	−350.358	−0.990963
$51$	−541.262	−1.48612
$52$	269.365	0.718349
$53$	292.191	0.757273	0.378636	−	0.925545i	$-0.376393\pi$
$53$	292.191	0.757273	0.378636	+	0.925545i	$0.376393\pi$
$54$	−128.280	−0.323272
$55$	−493.159	−1.20905
$56$	−273.820	−0.653405
$57$	1012.15	2.35197
$58$	−1177.97	−2.66680
$59$	−62.9889	−0.138991	−0.0694954	−	0.997582i	$-0.522139\pi$
$59$	−62.9889	−0.138991	−0.0694954	+	0.997582i	$0.522139\pi$
$60$	−1698.84	−3.65531
$61$	593.679	1.24611	0.623056	−	0.782177i	$-0.285891\pi$
$61$	593.679	1.24611	0.623056	+	0.782177i	$0.285891\pi$
$62$	−514.667	−1.05424
$63$	213.188	0.426336
$64$	−514.506	−1.00489
$65$	−236.209	−0.450741
$66$	−1305.93	−2.43558
$67$	744.666	1.35784	0.678921	−	0.734211i	$-0.262448\pi$
$67$	744.666	1.35784	0.678921	+	0.734211i	$0.262448\pi$
$68$	−1141.58	−2.03584
$69$	174.339	0.304172
$70$	480.625	0.820653
$71$	−277.419	−0.463712	−0.231856	−	0.972750i	$-0.574480\pi$
$71$	−277.419	−0.463712	−0.231856	+	0.972750i	$0.574480\pi$
$72$	−1191.33	−1.94999
$73$	−551.265	−0.883845	−0.441922	−	0.897053i	$-0.645703\pi$
$73$	−551.265	−0.883845	−0.441922	+	0.897053i	$0.645703\pi$
$74$	−1613.18	−2.53416
$75$	542.239	0.834832
$76$	2134.73	3.22198
$77$	246.243	0.364442
$78$	−625.502	−0.908002
$79$	−929.896	−1.32432	−0.662161	−	0.749361i	$-0.730361\pi$
$79$	−929.896	−1.32432	−0.662161	+	0.749361i	$0.730361\pi$
$80$	−892.827	−1.24776
$81$	−623.762	−0.855641
$82$	1492.87	2.01049
$83$	−749.978	−0.991817	−0.495909	−	0.868375i	$-0.665165\pi$
$83$	−749.978	−0.991817	−0.495909	+	0.868375i	$0.665165\pi$
$84$	848.259	1.10182
$85$	1001.07	1.27742
$86$	−686.640	−0.860957
$87$	1823.10	2.24663
$88$	−1376.05	−1.66690
$89$	1124.37	1.33914	0.669568	−	0.742751i	$-0.266479\pi$
$89$	1124.37	1.33914	0.669568	+	0.742751i	$0.266479\pi$
$90$	2091.09	2.44912
$91$	117.943	0.135866
$92$	367.699	0.416688
$93$	796.534	0.888137
$94$	−1461.95	−1.60413
$95$	−1871.97	−2.02169
$96$	7.76194	0.00825208
$97$	−1462.41	−1.53078	−0.765390	−	0.643567i	$-0.777454\pi$
$97$	−1462.41	−1.53078	−0.765390	+	0.643567i	$0.777454\pi$
$98$	−239.985	−0.247368
$99$	1071.35	1.08762
$100$	1143.64	1.14364
$101$	1371.39	1.35107	0.675536	−	0.737327i	$-0.263912\pi$
$101$	1371.39	1.35107	0.675536	+	0.737327i	$0.263912\pi$
$102$	2650.91	2.57333
$103$	−1361.55	−1.30250	−0.651251	−	0.758863i	$-0.725755\pi$
$103$	−1361.55	−1.30250	−0.651251	+	0.758863i	$0.725755\pi$
$104$	−659.086	−0.621430
$105$	−743.849	−0.691355
$106$	−1431.05	−1.31128
$107$	−1384.47	−1.25086	−0.625430	−	0.780280i	$-0.715076\pi$
$107$	−1384.47	−1.25086	−0.625430	+	0.780280i	$0.715076\pi$
$108$	418.732	0.373079
$109$	859.747	0.755494	0.377747	−	0.925909i	$-0.376699\pi$
$109$	859.747	0.755494	0.377747	+	0.925909i	$0.376699\pi$
$110$	2415.32	2.09356
$111$	2496.67	2.13489
$112$	445.804	0.376112
$113$	−746.954	−0.621836	−0.310918	−	0.950437i	$-0.600637\pi$
$113$	−746.954	−0.621836	−0.310918	+	0.950437i	$0.600637\pi$
$114$	−4957.14	−4.07262
$115$	−322.440	−0.261458
$116$	3845.12	3.07768
$117$	513.146	0.405473
$118$	308.497	0.240674
$119$	−499.851	−0.385052
$120$	4156.75	3.16214
$121$	−93.5377	−0.0702762
$122$	−2907.63	−2.15774
$123$	−2310.47	−1.69372
$124$	1679.98	1.21667
$125$	749.518	0.536311
$126$	−1044.12	−0.738235
$127$	−2746.70	−1.91914	−0.959569	−	0.281475i	$-0.909177\pi$
$127$	−2746.70	−1.91914	−0.959569	+	0.281475i	$0.909177\pi$
$128$	2511.67	1.73440
$129$	1062.69	0.725309
$130$	1156.87	0.780493
$131$	−1586.65	−1.05822	−0.529108	−	0.848554i	$-0.677474\pi$
$131$	−1586.65	−1.05822	−0.529108	+	0.848554i	$0.677474\pi$
$132$	4262.82	2.81084
$133$	934.709	0.609395
$134$	−3647.11	−2.35121
$135$	−367.192	−0.234095
$136$	2793.24	1.76117
$137$	1352.96	0.843729	0.421865	−	0.906659i	$-0.361376\pi$
$137$	1352.96	0.843729	0.421865	+	0.906659i	$0.361376\pi$
$138$	−853.848	−0.526699
$139$	−1160.94	−0.708417	−0.354209	−	0.935166i	$-0.615250\pi$
$139$	−1160.94	−0.708417	−0.354209	+	0.935166i	$0.615250\pi$
$140$	−1568.86	−0.947092
$141$	2262.61	1.35139
$142$	1358.70	0.802954
$143$	592.709	0.346607
$144$	1939.60	1.12245
$145$	−3371.84	−1.93114
$146$	2699.90	1.53045
$147$	371.417	0.208394
$148$	5265.74	2.92460
$149$	−547.404	−0.300974	−0.150487	−	0.988612i	$-0.548084\pi$
$149$	−547.404	−0.300974	−0.150487	+	0.988612i	$0.548084\pi$
$150$	−2655.69	−1.44558
$151$	1894.02	1.02075	0.510373	−	0.859953i	$-0.329507\pi$
$151$	1894.02	1.02075	0.510373	+	0.859953i	$0.329507\pi$
$152$	−5223.30	−2.78727
$153$	−2174.74	−1.14913
$154$	−1206.01	−0.631059
$155$	−1473.19	−0.763418
$156$	2041.77	1.04790
$157$	1632.57	0.829891	0.414946	−	0.909846i	$-0.363801\pi$
$157$	1632.57	0.829891	0.414946	+	0.909846i	$0.363801\pi$
$158$	4554.30	2.29317
$159$	2214.79	1.10468
$160$	−14.3557	−0.00709326
$161$	161.000	0.0788110
$162$	3054.97	1.48161
$163$	−1994.34	−0.958338	−0.479169	−	0.877723i	$-0.659062\pi$
$163$	−1994.34	−0.958338	−0.479169	+	0.877723i	$0.659062\pi$
$164$	−4873.03	−2.32024
$165$	−3738.12	−1.76371
$166$	3673.13	1.71741
$167$	37.7222	0.0174792	0.00873962	−	0.999962i	$-0.497218\pi$
$167$	37.7222	0.0174792	0.00873962	+	0.999962i	$0.497218\pi$
$168$	−2075.54	−0.953161
$169$	−1913.11	−0.870782
$170$	−4902.87	−2.21196
$171$	4066.71	1.81865
$172$	2241.33	0.993605
$173$	−3701.46	−1.62669	−0.813344	−	0.581784i	$-0.802355\pi$
$173$	−3701.46	−1.62669	−0.813344	+	0.581784i	$0.802355\pi$
$174$	−8928.91	−3.89022
$175$	500.753	0.216305
$176$	2240.33	0.959496
$177$	−477.452	−0.202754
$178$	−5506.77	−2.31882
$179$	1615.16	0.674430	0.337215	−	0.941428i	$-0.390515\pi$
$179$	1615.16	0.674430	0.337215	+	0.941428i	$0.390515\pi$
$180$	−6825.76	−2.82646
$181$	−2592.58	−1.06467	−0.532333	−	0.846535i	$-0.678685\pi$
$181$	−2592.58	−1.06467	−0.532333	+	0.846535i	$0.678685\pi$
$182$	−577.645	−0.235263
$183$	4500.05	1.81778
$184$	−899.693	−0.360469
$185$	−4617.60	−1.83509
$186$	−3901.14	−1.53788
$187$	−2511.93	−0.982304
$188$	4772.09	1.85128
$189$	183.345	0.0705630
$190$	9168.26	3.50071
$191$	3725.70	1.41142	0.705712	−	0.708499i	$-0.250627\pi$
$191$	3725.70	1.41142	0.705712	+	0.708499i	$0.250627\pi$
$192$	−3899.92	−1.46590
$193$	1936.79	0.722347	0.361173	−	0.932499i	$-0.382376\pi$
$193$	1936.79	0.722347	0.361173	+	0.932499i	$0.382376\pi$
$194$	7162.38	2.65067
$195$	−1790.45	−0.657522
$196$	783.359	0.285481
$197$	151.465	0.0547788	0.0273894	−	0.999625i	$-0.491281\pi$
$197$	151.465	0.0547788	0.0273894	+	0.999625i	$0.491281\pi$
$198$	−5247.09	−1.88330
$199$	3213.25	1.14463	0.572314	−	0.820035i	$-0.306046\pi$
$199$	3213.25	1.14463	0.572314	+	0.820035i	$0.306046\pi$
$200$	−2798.28	−0.989343
$201$	5644.52	1.98077
$202$	−6716.57	−2.33949
$203$	1683.62	0.582102
$204$	−8653.12	−2.96980
$205$	4273.22	1.45588
$206$	6668.39	2.25538
$207$	700.476	0.235200
$208$	1073.05	0.357706
$209$	4697.26	1.55462
$210$	3643.11	1.19714
$211$	3721.23	1.21412	0.607061	−	0.794655i	$-0.292348\pi$
$211$	3721.23	1.21412	0.607061	+	0.794655i	$0.292348\pi$
$212$	4671.23	1.51331
$213$	−2102.82	−0.676445
$214$	6780.66	2.16596
$215$	−1965.45	−0.623455
$216$	−1024.56	−0.322744
$217$	735.592	0.230116
$218$	−4210.73	−1.30820
$219$	−4178.55	−1.28932
$220$	−7884.10	−2.41612
$221$	−1203.15	−0.366209
$222$	−12227.8	−3.69673
$223$	2213.82	0.664791	0.332396	−	0.943140i	$-0.392143\pi$
$223$	2213.82	0.664791	0.332396	+	0.943140i	$0.392143\pi$
$224$	7.16808	0.00213811
$225$	2178.66	0.645530
$226$	3658.32	1.07676
$227$	−924.567	−0.270333	−0.135167	−	0.990823i	$-0.543157\pi$
$227$	−924.567	−0.270333	−0.135167	+	0.990823i	$0.543157\pi$
$228$	16181.1	4.70010
$229$	5561.96	1.60500	0.802500	−	0.596652i	$-0.203503\pi$
$229$	5561.96	1.60500	0.802500	+	0.596652i	$0.203503\pi$
$230$	1579.20	0.452735
$231$	1866.51	0.531633
$232$	−9408.32	−2.66244
$233$	−978.431	−0.275104	−0.137552	−	0.990495i	$-0.543923\pi$
$233$	−978.431	−0.275104	−0.137552	+	0.990495i	$0.543923\pi$
$234$	−2513.21	−0.702109
$235$	−4184.71	−1.16162
$236$	−1007.00	−0.277754
$237$	−7048.56	−1.93187
$238$	2448.09	0.666749
$239$	−3086.70	−0.835407	−0.417703	−	0.908583i	$-0.637165\pi$
$239$	−3086.70	−0.835407	−0.417703	+	0.908583i	$0.637165\pi$
$240$	−6767.57	−1.82019
$241$	−4927.18	−1.31696	−0.658480	−	0.752598i	$-0.728800\pi$
$241$	−4927.18	−1.31696	−0.658480	+	0.752598i	$0.728800\pi$
$242$	458.114	0.121689
$243$	−5435.27	−1.43487
$244$	9491.10	2.49019
$245$	−686.938	−0.179130
$246$	11315.9	2.93281
$247$	2249.85	0.579574
$248$	−4110.60	−1.05251
$249$	−5684.79	−1.44682
$250$	−3670.87	−0.928665
$251$	3873.90	0.974177	0.487089	−	0.873353i	$-0.338059\pi$
$251$	3873.90	0.974177	0.487089	+	0.873353i	$0.338059\pi$
$252$	3408.22	0.851976
$253$	809.084	0.201054
$254$	13452.4	3.32314
$255$	7588.03	1.86345
$256$	−8185.24	−1.99835
$257$	4056.98	0.984697	0.492349	−	0.870398i	$-0.336138\pi$
$257$	4056.98	0.984697	0.492349	+	0.870398i	$0.336138\pi$
$258$	−5204.69	−1.25593
$259$	2305.65	0.553150
$260$	−3776.26	−0.900745
$261$	7325.05	1.73720
$262$	7770.86	1.83239
$263$	−3089.32	−0.724318	−0.362159	−	0.932116i	$-0.617960\pi$
$263$	−3089.32	−0.724318	−0.362159	+	0.932116i	$0.617960\pi$
$264$	−10430.3	−2.43160
$265$	−4096.26	−0.949552
$266$	−4577.87	−1.05522
$267$	8522.66	1.95348
$268$	11904.9	2.71347
$269$	−7152.14	−1.62109	−0.810546	−	0.585675i	$-0.800830\pi$
$269$	−7152.14	−1.62109	−0.810546	+	0.585675i	$0.800830\pi$
$270$	1798.37	0.405354
$271$	−5385.90	−1.20727	−0.603635	−	0.797261i	$-0.706281\pi$
$271$	−5385.90	−1.20727	−0.603635	+	0.797261i	$0.706281\pi$
$272$	−4547.66	−1.01376
$273$	894.004	0.198196
$274$	−6626.30	−1.46098
$275$	2516.47	0.551813
$276$	2787.14	0.607848
$277$	−6955.45	−1.50871	−0.754354	−	0.656467i	$-0.772050\pi$
$277$	−6955.45	−1.50871	−0.754354	+	0.656467i	$0.772050\pi$
$278$	5685.89	1.22668
$279$	3200.40	0.686748
$280$	3838.72	0.819311
$281$	3088.75	0.655728	0.327864	−	0.944725i	$-0.393671\pi$
$281$	3088.75	0.655728	0.327864	+	0.944725i	$0.393671\pi$
$282$	−11081.5	−2.34004
$283$	3113.25	0.653934	0.326967	−	0.945036i	$-0.393973\pi$
$283$	3113.25	0.653934	0.326967	+	0.945036i	$0.393973\pi$
$284$	−4435.08	−0.926667
$285$	−14189.4	−2.94916
$286$	−2902.88	−0.600178
$287$	−2133.70	−0.438843
$288$	31.1867	0.00638089
$289$	185.994	0.0378576
$290$	16514.1	3.34393
$291$	−11085.0	−2.23304
$292$	−8813.03	−1.76624
$293$	2979.02	0.593980	0.296990	−	0.954881i	$-0.404017\pi$
$293$	2979.02	0.593980	0.296990	+	0.954881i	$0.404017\pi$
$294$	−1819.07	−0.360851
$295$	883.050	0.174282
$296$	−12884.3	−2.53002
$297$	921.378	0.180013
$298$	2680.99	0.521160
$299$	387.528	0.0749543
$300$	8668.73	1.66830
$301$	981.386	0.187927
$302$	−9276.21	−1.76750
$303$	10395.0	1.97089
$304$	8504.02	1.60441
$305$	−8322.87	−1.56251
$306$	10651.1	1.98981
$307$	98.3382	0.0182816	0.00914081	−	0.999958i	$-0.497090\pi$
$307$	98.3382	0.0182816	0.00914081	+	0.999958i	$0.497090\pi$
$308$	3936.67	0.728287
$309$	−10320.5	−1.90004
$310$	7215.18	1.32192
$311$	3614.30	0.658997	0.329499	−	0.944156i	$-0.393120\pi$
$311$	3614.30	0.658997	0.329499	+	0.944156i	$0.393120\pi$
$312$	−4995.83	−0.906517
$313$	−3891.47	−0.702744	−0.351372	−	0.936236i	$-0.614285\pi$
$313$	−3891.47	−0.702744	−0.351372	+	0.936236i	$0.614285\pi$
$314$	−7995.73	−1.43702
$315$	−2988.71	−0.534587
$316$	−14866.2	−2.64648
$317$	−551.746	−0.0977576	−0.0488788	−	0.998805i	$-0.515565\pi$
$317$	−551.746	−0.0977576	−0.0488788	+	0.998805i	$0.515565\pi$
$318$	−10847.2	−1.91284
$319$	8460.80	1.48500
$320$	7212.92	1.26005
$321$	−10494.2	−1.82470
$322$	−788.521	−0.136468
$323$	−9535.00	−1.64254
$324$	−9972.04	−1.70988
$325$	1205.32	0.205720
$326$	9767.58	1.65944
$327$	6516.83	1.10208
$328$	11923.4	2.00720
$329$	2089.50	0.350145
$330$	18308.0	3.05400
$331$	2521.09	0.418645	0.209323	−	0.977847i	$-0.432874\pi$
$331$	2521.09	0.418645	0.209323	+	0.977847i	$0.432874\pi$
$332$	−11989.8	−1.98201
$333$	10031.4	1.65080
$334$	−184.750	−0.0302667
$335$	−10439.6	−1.70261
$336$	3379.17	0.548657
$337$	−97.0240	−0.0156832	−0.00784160	−	0.999969i	$-0.502496\pi$
$337$	−97.0240	−0.0156832	−0.00784160	+	0.999969i	$0.502496\pi$
$338$	9369.73	1.50783
$339$	−5661.87	−0.907110
$340$	16004.0	2.55276
$341$	3696.62	0.587047
$342$	−19917.3	−3.14914
$343$	343.000	0.0539949
$344$	−5484.14	−0.859549
$345$	−2444.08	−0.381405
$346$	18128.4	2.81674
$347$	1470.36	0.227473	0.113737	−	0.993511i	$-0.463718\pi$
$347$	1470.36	0.227473	0.113737	+	0.993511i	$0.463718\pi$
$348$	29145.8	4.48959
$349$	6640.36	1.01848	0.509241	−	0.860624i	$-0.329926\pi$
$349$	6640.36	1.01848	0.509241	+	0.860624i	$0.329926\pi$
$350$	−2452.51	−0.374549
$351$	441.314	0.0671099
$352$	36.0222	0.00545452
$353$	846.354	0.127612	0.0638058	−	0.997962i	$-0.479676\pi$
$353$	846.354	0.127612	0.0638058	+	0.997962i	$0.479676\pi$
$354$	2338.39	0.351085
$355$	3889.17	0.581453
$356$	17975.2	2.67608
$357$	−3788.84	−0.561699
$358$	−7910.50	−1.16783
$359$	509.029	0.0748343	0.0374172	−	0.999300i	$-0.488087\pi$
$359$	509.029	0.0748343	0.0374172	+	0.999300i	$0.488087\pi$
$360$	16701.4	2.44511
$361$	10971.2	1.59954
$362$	12697.5	1.84355
$363$	−709.010	−0.102516
$364$	1885.55	0.271510
$365$	7728.25	1.10826
$366$	−22039.6	−3.14763
$367$	−3417.70	−0.486110	−0.243055	−	0.970013i	$-0.578149\pi$
$367$	−3417.70	−0.486110	−0.243055	+	0.970013i	$0.578149\pi$
$368$	1464.78	0.207492
$369$	−9283.24	−1.30966
$370$	22615.3	3.17761
$371$	2045.33	0.286222
$372$	12734.1	1.77482
$373$	−13091.1	−1.81724	−0.908619	−	0.417625i	$-0.862863\pi$
$373$	−13091.1	−1.81724	−0.908619	+	0.417625i	$0.862863\pi$
$374$	12302.6	1.70094
$375$	5681.30	0.782349
$376$	−11676.5	−1.60151
$377$	4052.48	0.553617
$378$	−897.960	−0.122185
$379$	−314.160	−0.0425787	−0.0212893	−	0.999773i	$-0.506777\pi$
$379$	−314.160	−0.0425787	−0.0212893	+	0.999773i	$0.506777\pi$
$380$	−29927.1	−4.04007
$381$	−20819.8	−2.79956
$382$	−18247.1	−2.44399
$383$	4196.06	0.559814	0.279907	−	0.960027i	$-0.409696\pi$
$383$	4196.06	0.559814	0.279907	+	0.960027i	$0.409696\pi$
$384$	19038.3	2.53007
$385$	−3452.11	−0.456977
$386$	−9485.69	−1.25080
$387$	4269.79	0.560842
$388$	−23379.5	−3.05906
$389$	12186.3	1.58836	0.794179	−	0.607684i	$-0.207901\pi$
$389$	12186.3	1.58836	0.794179	+	0.607684i	$0.207901\pi$
$390$	8768.99	1.13855
$391$	−1642.37	−0.212425
$392$	−1916.74	−0.246964
$393$	−12026.7	−1.54368
$394$	−741.821	−0.0948538
$395$	13036.3	1.66058
$396$	17127.6	2.17347
$397$	−14249.9	−1.80146	−0.900731	−	0.434377i	$-0.856969\pi$
$397$	−14249.9	−1.80146	−0.900731	+	0.434377i	$0.856969\pi$
$398$	−15737.3	−1.98201
$399$	7085.04	0.888961
$400$	4555.87	0.569484
$401$	11729.8	1.46074	0.730369	−	0.683053i	$-0.239348\pi$
$401$	11729.8	1.46074	0.730369	+	0.683053i	$0.239348\pi$
$402$	−27644.9	−3.42985
$403$	1770.58	0.218855
$404$	21924.3	2.69993
$405$	8744.61	1.07290
$406$	−8245.76	−1.00796
$407$	11586.7	1.41114
$408$	21172.6	2.56912
$409$	−8062.38	−0.974716	−0.487358	−	0.873202i	$-0.662039\pi$
$409$	−8062.38	−0.974716	−0.487358	+	0.873202i	$0.662039\pi$
$410$	−20928.7	−2.52097
$411$	10255.3	1.23080
$412$	−21767.0	−2.60287
$413$	−440.922	−0.0525336
$414$	−3430.68	−0.407268
$415$	10514.0	1.24365
$416$	17.2536	0.00203348
$417$	−8799.89	−1.03341
$418$	−23005.5	−2.69195
$419$	−7705.35	−0.898404	−0.449202	−	0.893430i	$-0.648292\pi$
$419$	−7705.35	−0.898404	−0.449202	+	0.893430i	$0.648292\pi$
$420$	−11891.9	−1.38158
$421$	7993.86	0.925408	0.462704	−	0.886513i	$-0.346879\pi$
$421$	7993.86	0.925408	0.462704	+	0.886513i	$0.346879\pi$
$422$	−18225.3	−2.10235
$423$	9090.95	1.04496
$424$	−11429.7	−1.30913
$425$	−5108.19	−0.583021
$426$	10298.9	1.17132
$427$	4155.75	0.470986
$428$	−22133.5	−2.49968
$429$	4492.70	0.505617
$430$	9626.10	1.07956
$431$	−7237.36	−0.808843	−0.404422	−	0.914573i	$-0.632527\pi$
$431$	−7237.36	−0.808843	−0.404422	+	0.914573i	$0.632527\pi$
$432$	1668.08	0.185777
$433$	−13092.0	−1.45303	−0.726513	−	0.687153i	$-0.758860\pi$
$433$	−13092.0	−1.45303	−0.726513	+	0.687153i	$0.758860\pi$
$434$	−3602.67	−0.398464
$435$	−25558.3	−2.81707
$436$	13744.7	1.50975
$437$	3071.19	0.336189
$438$	20465.1	2.23255
$439$	−263.091	−0.0286029	−0.0143014	−	0.999898i	$-0.504552\pi$
$439$	−263.091	−0.0286029	−0.0143014	+	0.999898i	$0.504552\pi$
$440$	19291.0	2.09014
$441$	1492.32	0.161140
$442$	5892.58	0.634121
$443$	13153.4	1.41070	0.705349	−	0.708860i	$-0.250790\pi$
$443$	13153.4	1.41070	0.705349	+	0.708860i	$0.250790\pi$
$444$	39914.0	4.26629
$445$	−15762.7	−1.67915
$446$	−10842.5	−1.15114
$447$	−4149.29	−0.439048
$448$	−3601.54	−0.379814
$449$	11598.8	1.21911	0.609555	−	0.792744i	$-0.291348\pi$
$449$	11598.8	1.21911	0.609555	+	0.792744i	$0.291348\pi$
$450$	−10670.3	−1.11779
$451$	−10722.6	−1.11953
$452$	−11941.5	−1.24266
$453$	14356.5	1.48902
$454$	4528.20	0.468103
$455$	−1653.46	−0.170364
$456$	−39592.3	−4.06596
$457$	5365.07	0.549163	0.274582	−	0.961564i	$-0.411461\pi$
$457$	5365.07	0.549163	0.274582	+	0.961564i	$0.411461\pi$
$458$	−27240.5	−2.77918
$459$	−1870.31	−0.190193
$460$	−5154.82	−0.522489
$461$	700.237	0.0707446	0.0353723	−	0.999374i	$-0.488738\pi$
$461$	700.237	0.0707446	0.0353723	+	0.999374i	$0.488738\pi$
$462$	−9141.49	−0.920564
$463$	3526.32	0.353957	0.176979	−	0.984215i	$-0.443368\pi$
$463$	3526.32	0.353957	0.176979	+	0.984215i	$0.443368\pi$
$464$	15317.6	1.53255
$465$	−11166.7	−1.11364
$466$	4792.01	0.476364
$467$	714.018	0.0707512	0.0353756	−	0.999374i	$-0.488737\pi$
$467$	714.018	0.0707512	0.0353756	+	0.999374i	$0.488737\pi$
$468$	8203.62	0.810283
$469$	5212.66	0.513216
$470$	20495.2	2.01143
$471$	12374.8	1.21061
$472$	2463.94	0.240280
$473$	4931.83	0.479420
$474$	34521.3	3.34518
$475$	9552.21	0.922706
$476$	−7991.07	−0.769475
$477$	8898.80	0.854189
$478$	15117.6	1.44657
$479$	−1380.74	−0.131707	−0.0658533	−	0.997829i	$-0.520977\pi$
$479$	−1380.74	−0.131707	−0.0658533	+	0.997829i	$0.520977\pi$
$480$	−108.816	−0.0103474
$481$	5549.71	0.526081
$482$	24131.6	2.28042
$483$	1220.37	0.114966
$484$	−1495.38	−0.140438
$485$	20501.8	1.91946
$486$	26620.0	2.48459
$487$	−1245.71	−0.115910	−0.0579552	−	0.998319i	$-0.518458\pi$
$487$	−1245.71	−0.115910	−0.0579552	+	0.998319i	$0.518458\pi$
$488$	−23223.0	−2.15421
$489$	−15117.0	−1.39798
$490$	3364.38	0.310178
$491$	13384.2	1.23019	0.615094	−	0.788454i	$-0.289118\pi$
$491$	13384.2	1.23019	0.615094	+	0.788454i	$0.289118\pi$
$492$	−36937.3	−3.38468
$493$	−17174.6	−1.56898
$494$	−11019.0	−1.00358
$495$	−15019.4	−1.36378
$496$	6692.44	0.605846
$497$	−1941.93	−0.175267
$498$	27842.1	2.50529
$499$	−17600.2	−1.57894	−0.789471	−	0.613788i	$-0.789645\pi$
$499$	−17600.2	−1.57894	−0.789471	+	0.613788i	$0.789645\pi$
$500$	11982.5	1.07175
$501$	285.932	0.0254980
$502$	−18973.0	−1.68686
$503$	−17189.1	−1.52371	−0.761854	−	0.647749i	$-0.775711\pi$
$503$	−17189.1	−1.52371	−0.761854	+	0.647749i	$0.775711\pi$
$504$	−8339.31	−0.737028
$505$	−19225.7	−1.69412
$506$	−3962.61	−0.348141
$507$	−14501.2	−1.27026
$508$	−43911.3	−3.83514
$509$	−4387.71	−0.382086	−0.191043	−	0.981582i	$-0.561187\pi$
$509$	−4387.71	−0.382086	−0.191043	+	0.981582i	$0.561187\pi$
$510$	−37163.5	−3.22672
$511$	−3858.85	−0.334062
$512$	19995.0	1.72590
$513$	3497.44	0.301005
$514$	−19869.6	−1.70508
$515$	19087.8	1.63322
$516$	16989.2	1.44943
$517$	10500.5	0.893253
$518$	−11292.2	−0.957823
$519$	−28056.8	−2.37295
$520$	9239.82	0.779217
$521$	10646.2	0.895236	0.447618	−	0.894225i	$-0.352273\pi$
$521$	10646.2	0.895236	0.447618	+	0.894225i	$0.352273\pi$
$522$	−35875.5	−3.00810
$523$	−16978.5	−1.41954	−0.709768	−	0.704436i	$-0.751200\pi$
$523$	−16978.5	−1.41954	−0.709768	+	0.704436i	$0.751200\pi$
$524$	−25365.7	−2.11470
$525$	3795.67	0.315537
$526$	15130.4	1.25421
$527$	−7503.80	−0.620248
$528$	16981.6	1.39967
$529$	529.000	0.0434783
$530$	20062.0	1.64422
$531$	−1918.36	−0.156779
$532$	14943.1	1.21779
$533$	−5135.82	−0.417368
$534$	−41741.0	−3.38260
$535$	19409.1	1.56847
$536$	−29129.2	−2.34737
$537$	12242.8	0.983832
$538$	35028.7	2.80705
$539$	1723.70	0.137746
$540$	−5870.26	−0.467807
$541$	−13975.9	−1.11067	−0.555333	−	0.831628i	$-0.687409\pi$
$541$	−13975.9	−1.11067	−0.555333	+	0.831628i	$0.687409\pi$
$542$	26378.2	2.09048
$543$	−19651.6	−1.55309
$544$	−73.1218	−0.00576300
$545$	−12052.9	−0.947320
$546$	−4378.51	−0.343192
$547$	18965.2	1.48243	0.741217	−	0.671265i	$-0.234249\pi$
$547$	18965.2	1.48243	0.741217	+	0.671265i	$0.234249\pi$
$548$	21629.6	1.68608
$549$	18080.8	1.40559
$550$	−12324.8	−0.955508
$551$	32116.2	2.48311
$552$	−6819.62	−0.525838
$553$	−6509.27	−0.500547
$554$	34065.3	2.61245
$555$	−35001.1	−2.67696
$556$	−18559.9	−1.41568
$557$	−7420.49	−0.564482	−0.282241	−	0.959344i	$-0.591078\pi$
$557$	−7420.49	−0.564482	−0.282241	+	0.959344i	$0.591078\pi$
$558$	−15674.4	−1.18916
$559$	2362.20	0.178731
$560$	−6249.79	−0.471610
$561$	−19040.3	−1.43295
$562$	−15127.6	−1.13545
$563$	3213.41	0.240549	0.120275	−	0.992741i	$-0.461623\pi$
$563$	3213.41	0.240549	0.120275	+	0.992741i	$0.461623\pi$
$564$	36172.2	2.70057
$565$	10471.6	0.779727
$566$	−15247.6	−1.13234
$567$	−4366.34	−0.323402
$568$	10851.8	0.801642
$569$	−7889.49	−0.581274	−0.290637	−	0.956833i	$-0.593867\pi$
$569$	−7889.49	−0.581274	−0.290637	+	0.956833i	$0.593867\pi$
$570$	69494.8	5.10670
$571$	18255.0	1.33791	0.668956	−	0.743302i	$-0.266741\pi$
$571$	18255.0	1.33791	0.668956	+	0.743302i	$0.266741\pi$
$572$	9475.60	0.692648
$573$	28240.6	2.05893
$574$	10450.1	0.759892
$575$	1645.33	0.119330
$576$	−15669.5	−1.13350
$577$	4723.25	0.340783	0.170391	−	0.985376i	$-0.445497\pi$
$577$	4723.25	0.340783	0.170391	+	0.985376i	$0.445497\pi$
$578$	−910.933	−0.0655533
$579$	14680.7	1.05373
$580$	−53905.3	−3.85913
$581$	−5249.85	−0.374872
$582$	54290.4	3.86668
$583$	10278.6	0.730179
$584$	21563.9	1.52794
$585$	−7193.86	−0.508427
$586$	−14590.2	−1.02852
$587$	−9362.17	−0.658293	−0.329147	−	0.944279i	$-0.606761\pi$
$587$	−9362.17	−0.658293	−0.329147	+	0.944279i	$0.606761\pi$
$588$	5937.81	0.416448
$589$	14031.9	0.981622
$590$	−4324.86	−0.301783
$591$	1148.09	0.0799091
$592$	20976.9	1.45632
$593$	−25733.2	−1.78202	−0.891008	−	0.453988i	$-0.850001\pi$
$593$	−25733.2	−1.78202	−0.891008	+	0.453988i	$0.850001\pi$
$594$	−4512.58	−0.311706
$595$	7007.47	0.482821
$596$	−8751.30	−0.601455
$597$	24356.2	1.66974
$598$	−1897.98	−0.129789
$599$	−18606.5	−1.26918	−0.634591	−	0.772848i	$-0.718831\pi$
$599$	−18606.5	−1.26918	−0.634591	+	0.772848i	$0.718831\pi$
$600$	−21210.8	−1.44321
$601$	−17493.3	−1.18730	−0.593651	−	0.804723i	$-0.702314\pi$
$601$	−17493.3	−1.18730	−0.593651	+	0.804723i	$0.702314\pi$
$602$	−4806.48	−0.325411
$603$	22679.2	1.53162
$604$	30279.5	2.03982
$605$	1311.32	0.0881200
$606$	−50911.2	−3.41275
$607$	−11212.7	−0.749771	−0.374885	−	0.927071i	$-0.622318\pi$
$607$	−11212.7	−0.749771	−0.374885	+	0.927071i	$0.622318\pi$
$608$	136.736	0.00912069
$609$	12761.7	0.849148
$610$	40762.4	2.70561
$611$	5029.44	0.333011
$612$	−34767.4	−2.29639
$613$	25386.1	1.67265	0.836326	−	0.548232i	$-0.184699\pi$
$613$	25386.1	1.67265	0.836326	+	0.548232i	$0.184699\pi$
$614$	−481.625	−0.0316561
$615$	32390.8	2.12378
$616$	−9632.32	−0.630028
$617$	−202.481	−0.0132116	−0.00660581	−	0.999978i	$-0.502103\pi$
$617$	−202.481	−0.0132116	−0.00660581	+	0.999978i	$0.502103\pi$
$618$	50546.0	3.29006
$619$	15754.9	1.02301	0.511504	−	0.859281i	$-0.329088\pi$
$619$	15754.9	1.02301	0.511504	+	0.859281i	$0.329088\pi$
$620$	−23551.8	−1.52559
$621$	602.420	0.0389280
$622$	−17701.6	−1.14111
$623$	7870.59	0.506146
$624$	8133.68	0.521808
$625$	−19449.6	−1.24477
$626$	19059.0	1.21686
$627$	35604.9	2.26782
$628$	26099.7	1.65843
$629$	−23520.0	−1.49094
$630$	14637.7	0.925680
$631$	−11543.0	−0.728242	−0.364121	−	0.931352i	$-0.618630\pi$
$631$	−11543.0	−0.728242	−0.364121	+	0.931352i	$0.618630\pi$
$632$	36374.8	2.28942
$633$	28206.7	1.77111
$634$	2702.26	0.169275
$635$	38506.4	2.40642
$636$	35407.6	2.20755
$637$	825.604	0.0513526
$638$	−41438.0	−2.57139
$639$	−8448.92	−0.523058
$640$	−35211.5	−2.17478
$641$	−3765.88	−0.232049	−0.116024	−	0.993246i	$-0.537015\pi$
$641$	−3765.88	−0.232049	−0.116024	+	0.993246i	$0.537015\pi$
$642$	51397.0	3.15962
$643$	−18886.8	−1.15835	−0.579176	−	0.815202i	$-0.696626\pi$
$643$	−18886.8	−1.15835	−0.579176	+	0.815202i	$0.696626\pi$
$644$	2573.89	0.157493
$645$	−14898.0	−0.909471
$646$	46699.0	2.84419
$647$	−20512.8	−1.24643	−0.623215	−	0.782051i	$-0.714174\pi$
$647$	−20512.8	−1.24643	−0.623215	+	0.782051i	$0.714174\pi$
$648$	24399.8	1.47919
$649$	−2215.80	−0.134018
$650$	−5903.21	−0.356220
$651$	5575.74	0.335684
$652$	−31883.4	−1.91511
$653$	14632.7	0.876909	0.438455	−	0.898753i	$-0.355526\pi$
$653$	14632.7	0.876909	0.438455	+	0.898753i	$0.355526\pi$
$654$	−31917.1	−1.90834
$655$	22243.5	1.32691
$656$	−19412.5	−1.15538
$657$	−16789.0	−0.996959
$658$	−10233.6	−0.606304
$659$	−13652.1	−0.806994	−0.403497	−	0.914981i	$-0.632205\pi$
$659$	−13652.1	−0.806994	−0.403497	+	0.914981i	$0.632205\pi$
$660$	−59761.0	−3.52453
$661$	−6188.35	−0.364144	−0.182072	−	0.983285i	$-0.558280\pi$
$661$	−6188.35	−0.364144	−0.182072	+	0.983285i	$0.558280\pi$
$662$	−12347.4	−0.724917
$663$	−9119.76	−0.534212
$664$	29337.0	1.71460
$665$	−13103.8	−0.764126
$666$	−49130.0	−2.85848
$667$	5531.89	0.321133
$668$	603.062	0.0349299
$669$	16780.6	0.969771
$670$	51129.3	2.94821
$671$	20884.2	1.20153
$672$	54.3336	0.00311899
$673$	27024.1	1.54785	0.773925	−	0.633277i	$-0.218291\pi$
$673$	27024.1	1.54785	0.773925	+	0.633277i	$0.218291\pi$
$674$	475.189	0.0271567
$675$	1873.69	0.106842
$676$	−30584.7	−1.74014
$677$	18115.8	1.02843	0.514214	−	0.857662i	$-0.328084\pi$
$677$	18115.8	1.02843	0.514214	+	0.857662i	$0.328084\pi$
$678$	27729.8	1.57073
$679$	−10236.9	−0.578580
$680$	−39158.9	−2.20834
$681$	−7008.16	−0.394351
$682$	−18104.7	−1.01652
$683$	−18663.6	−1.04560	−0.522800	−	0.852455i	$-0.675113\pi$
$683$	−18663.6	−1.04560	−0.522800	+	0.852455i	$0.675113\pi$
$684$	65014.2	3.63433
$685$	−18967.3	−1.05796
$686$	−1679.89	−0.0934965
$687$	42159.3	2.34131
$688$	8928.69	0.494772
$689$	4923.14	0.272216
$690$	11970.2	0.660432
$691$	−4808.47	−0.264722	−0.132361	−	0.991202i	$-0.542256\pi$
$691$	−4808.47	−0.264722	−0.132361	+	0.991202i	$0.542256\pi$
$692$	−59175.0	−3.25071
$693$	7499.45	0.411083
$694$	−7201.31	−0.393888
$695$	16275.4	0.888291
$696$	−71314.5	−3.88386
$697$	21765.9	1.18284
$698$	−32522.1	−1.76358
$699$	−7416.45	−0.401310
$700$	8005.49	0.432256
$701$	−13236.7	−0.713188	−0.356594	−	0.934259i	$-0.616062\pi$
$701$	−13236.7	−0.713188	−0.356594	+	0.934259i	$0.616062\pi$
$702$	−2161.40	−0.116206
$703$	43981.8	2.35961
$704$	−18099.1	−0.968940
$705$	−31719.8	−1.69452
$706$	−4145.14	−0.220969
$707$	9599.71	0.510657
$708$	−7632.99	−0.405177
$709$	3430.92	0.181736	0.0908681	−	0.995863i	$-0.471036\pi$
$709$	3430.92	0.181736	0.0908681	+	0.995863i	$0.471036\pi$
$710$	−19047.8	−1.00683
$711$	−28320.4	−1.49381
$712$	−43982.1	−2.31503
$713$	2416.94	0.126950
$714$	18556.4	0.972626
$715$	−8309.27	−0.434614
$716$	25821.5	1.34776
$717$	−23397.0	−1.21866
$718$	−2493.04	−0.129582
$719$	−3473.95	−0.180190	−0.0900950	−	0.995933i	$-0.528717\pi$
$719$	−3473.95	−0.180190	−0.0900950	+	0.995933i	$0.528717\pi$
$720$	−27191.4	−1.40745
$721$	−9530.86	−0.492299
$722$	−53733.2	−2.76972
$723$	−37347.7	−1.92113
$724$	−41447.3	−2.12759
$725$	17205.6	0.881381
$726$	3472.48	0.177515
$727$	30372.8	1.54947	0.774736	−	0.632285i	$-0.217883\pi$
$727$	30372.8	1.54947	0.774736	+	0.632285i	$0.217883\pi$
$728$	−4613.61	−0.234879
$729$	−24357.4	−1.23749
$730$	−37850.2	−1.91904
$731$	−10011.2	−0.506533
$732$	71942.0	3.63258
$733$	1787.59	0.0900765	0.0450383	−	0.998985i	$-0.485659\pi$
$733$	1787.59	0.0900765	0.0450383	+	0.998985i	$0.485659\pi$
$734$	16738.7	0.841737
$735$	−5206.94	−0.261308
$736$	23.5523	0.00117955
$737$	26195.6	1.30926
$738$	45466.0	2.26779
$739$	17095.5	0.850971	0.425485	−	0.904965i	$-0.360103\pi$
$739$	17095.5	0.850971	0.425485	+	0.904965i	$0.360103\pi$
$740$	−73821.1	−3.66719
$741$	17053.7	0.845459
$742$	−10017.3	−0.495616
$743$	−10540.7	−0.520459	−0.260230	−	0.965547i	$-0.583798\pi$
$743$	−10540.7	−0.520459	−0.260230	+	0.965547i	$0.583798\pi$
$744$	−31158.1	−1.53537
$745$	7674.13	0.377394
$746$	64115.4	3.14669
$747$	−22840.9	−1.11875
$748$	−40158.1	−1.96300
$749$	−9691.31	−0.472781
$750$	−27825.0	−1.35470
$751$	−29453.8	−1.43114	−0.715570	−	0.698541i	$-0.753833\pi$
$751$	−29453.8	−1.43114	−0.715570	+	0.698541i	$0.753833\pi$
$752$	19010.4	0.921857
$753$	29363.9	1.42109
$754$	−19847.6	−0.958631
$755$	−26552.4	−1.27992
$756$	2931.13	0.141011
$757$	11615.2	0.557675	0.278838	−	0.960338i	$-0.410051\pi$
$757$	11615.2	0.557675	0.278838	+	0.960338i	$0.410051\pi$
$758$	1538.64	0.0737283
$759$	6132.81	0.293290
$760$	73226.2	3.49499
$761$	−38984.8	−1.85703	−0.928513	−	0.371299i	$-0.878912\pi$
$761$	−38984.8	−1.85703	−0.928513	+	0.371299i	$0.878912\pi$
$762$	101968.	4.84766
$763$	6018.23	0.285550
$764$	59562.4	2.82054
$765$	30488.0	1.44091
$766$	−20550.8	−0.969362
$767$	−1061.30	−0.0499628
$768$	−62043.6	−2.91511
$769$	−23455.3	−1.09990	−0.549948	−	0.835199i	$-0.685352\pi$
$769$	−23455.3	−1.09990	−0.549948	+	0.835199i	$0.685352\pi$
$770$	16907.2	0.791291
$771$	30751.6	1.43644
$772$	30963.3	1.44351
$773$	−30007.9	−1.39626	−0.698131	−	0.715970i	$-0.745985\pi$
$773$	−30007.9	−1.39626	−0.698131	+	0.715970i	$0.745985\pi$
$774$	−20911.9	−0.971142
$775$	7517.34	0.348427
$776$	57205.4	2.64633
$777$	17476.7	0.806913
$778$	−59684.3	−2.75037
$779$	−40701.7	−1.87200
$780$	−28623.8	−1.31397
$781$	−9758.93	−0.447122
$782$	8043.73	0.367830
$783$	6299.66	0.287524
$784$	3120.63	0.142157
$785$	−22887.2	−1.04061
$786$	58902.6	2.67301
$787$	675.486	0.0305953	0.0152976	−	0.999883i	$-0.495130\pi$
$787$	675.486	0.0305953	0.0152976	+	0.999883i	$0.495130\pi$
$788$	2421.46	0.109468
$789$	−23416.9	−1.05661
$790$	−63847.4	−2.87543
$791$	−5228.68	−0.235032
$792$	−41908.1	−1.88023
$793$	10002.9	0.447938
$794$	69790.8	3.11937
$795$	−31049.4	−1.38517
$796$	51369.9	2.28738
$797$	9305.07	0.413554	0.206777	−	0.978388i	$-0.433703\pi$
$797$	9305.07	0.413554	0.206777	+	0.978388i	$0.433703\pi$
$798$	−34700.0	−1.53931
$799$	−21315.1	−0.943770
$800$	73.2538	0.00323739
$801$	34243.2	1.51052
$802$	−57448.2	−2.52938
$803$	−19392.2	−0.852222
$804$	90238.6	3.95829
$805$	−2257.08	−0.0988219
$806$	−8671.65	−0.378965
$807$	−54212.8	−2.36478
$808$	−53644.7	−2.33566
$809$	23243.3	1.01013	0.505063	−	0.863083i	$-0.331469\pi$
$809$	23243.3	1.01013	0.505063	+	0.863083i	$0.331469\pi$
$810$	−42828.0	−1.85780
$811$	−12897.3	−0.558429	−0.279214	−	0.960229i	$-0.590074\pi$
$811$	−12897.3	−0.558429	−0.279214	+	0.960229i	$0.590074\pi$
$812$	26915.9	1.16325
$813$	−40824.8	−1.76112
$814$	−56747.7	−2.44349
$815$	27959.0	1.20167
$816$	−34471.0	−1.47883
$817$	18720.6	0.801654
$818$	39486.7	1.68780
$819$	3592.02	0.153254
$820$	68315.7	2.90937
$821$	21029.3	0.893944	0.446972	−	0.894548i	$-0.352502\pi$
$821$	21029.3	0.893944	0.446972	+	0.894548i	$0.352502\pi$
$822$	−50227.0	−2.13122
$823$	43489.8	1.84199	0.920995	−	0.389575i	$-0.127378\pi$
$823$	43489.8	1.84199	0.920995	+	0.389575i	$0.127378\pi$
$824$	53259.9	2.25170
$825$	19074.7	0.804963
$826$	2159.48	0.0909660
$827$	−22733.5	−0.955892	−0.477946	−	0.878389i	$-0.658618\pi$
$827$	−22733.5	−0.955892	−0.477946	+	0.878389i	$0.658618\pi$
$828$	11198.4	0.470016
$829$	19130.8	0.801496	0.400748	−	0.916188i	$-0.368750\pi$
$829$	19130.8	0.801496	0.400748	+	0.916188i	$0.368750\pi$
$830$	−51494.1	−2.15348
$831$	−52721.9	−2.20084
$832$	−8668.94	−0.361228
$833$	−3498.95	−0.145536
$834$	43098.7	1.78943
$835$	−528.833	−0.0219174
$836$	75094.7	3.10670
$837$	2752.39	0.113664
$838$	37738.1	1.55566
$839$	17347.5	0.713830	0.356915	−	0.934137i	$-0.383829\pi$
$839$	17347.5	0.713830	0.356915	+	0.934137i	$0.383829\pi$
$840$	29097.2	1.19518
$841$	33459.3	1.37190
$842$	−39151.1	−1.60242
$843$	23412.6	0.956550
$844$	59491.0	2.42626
$845$	26820.1	1.09188
$846$	−44524.3	−1.80943
$847$	−654.764	−0.0265619
$848$	18608.5	0.753561
$849$	23598.2	0.953933
$850$	25018.1	1.00955
$851$	7575.70	0.305160
$852$	−33617.6	−1.35178
$853$	26880.8	1.07899	0.539497	−	0.841988i	$-0.318615\pi$
$853$	26880.8	1.07899	0.539497	+	0.841988i	$0.318615\pi$
$854$	−20353.4	−0.815549
$855$	−57011.8	−2.28042
$856$	54156.6	2.16242
$857$	−8911.42	−0.355202	−0.177601	−	0.984103i	$-0.556834\pi$
$857$	−8911.42	−0.355202	−0.177601	+	0.984103i	$0.556834\pi$
$858$	−22003.6	−0.875515
$859$	31980.1	1.27025	0.635126	−	0.772408i	$-0.280948\pi$
$859$	31980.1	1.27025	0.635126	+	0.772408i	$0.280948\pi$
$860$	−31421.6	−1.24589
$861$	−16173.3	−0.640167
$862$	35446.0	1.40058
$863$	−40155.9	−1.58392	−0.791960	−	0.610573i	$-0.790939\pi$
$863$	−40155.9	−1.58392	−0.791960	+	0.610573i	$0.790939\pi$
$864$	26.8211	0.00105610
$865$	51891.3	2.03972
$866$	64119.8	2.51603
$867$	1409.82	0.0552251
$868$	11759.8	0.459856
$869$	−32711.5	−1.27694
$870$	125176.	4.87799
$871$	12546.9	0.488101
$872$	−33630.8	−1.30606
$873$	−44538.5	−1.72669
$874$	−15041.6	−0.582139
$875$	5246.62	0.202707
$876$	−66802.2	−2.57653
$877$	26935.8	1.03712	0.518561	−	0.855041i	$-0.326468\pi$
$877$	26935.8	1.03712	0.518561	+	0.855041i	$0.326468\pi$
$878$	1288.53	0.0495281
$879$	22580.8	0.866475
$880$	−31407.5	−1.20312
$881$	−19935.6	−0.762369	−0.381184	−	0.924499i	$-0.624484\pi$
$881$	−19935.6	−0.762369	−0.381184	+	0.924499i	$0.624484\pi$
$882$	−7308.84	−0.279027
$883$	−33663.8	−1.28299	−0.641494	−	0.767128i	$-0.721685\pi$
$883$	−33663.8	−1.28299	−0.641494	+	0.767128i	$0.721685\pi$
$884$	−19234.6	−0.731820
$885$	6693.46	0.254235
$886$	−64420.9	−2.44273
$887$	−7663.47	−0.290095	−0.145047	−	0.989425i	$-0.546333\pi$
$887$	−7663.47	−0.290095	−0.145047	+	0.989425i	$0.546333\pi$
$888$	−97662.3	−3.69069
$889$	−19226.9	−0.725366
$890$	77200.1	2.90759
$891$	−21942.5	−0.825028
$892$	35392.2	1.32850
$893$	39858.7	1.49364
$894$	20321.7	0.760247
$895$	−22643.2	−0.845675
$896$	17581.7	0.655540
$897$	2937.44	0.109340
$898$	−56806.7	−2.11098
$899$	25274.6	0.937658
$900$	34830.1	1.29001
$901$	−20864.5	−0.771474
$902$	52515.5	1.93855
$903$	7438.84	0.274141
$904$	29218.7	1.07500
$905$	36345.7	1.33500
$906$	−70313.1	−2.57836
$907$	−10916.0	−0.399623	−0.199812	−	0.979834i	$-0.564033\pi$
$907$	−10916.0	−0.399623	−0.199812	+	0.979834i	$0.564033\pi$
$908$	−14781.0	−0.540224
$909$	41766.2	1.52398
$910$	8098.08	0.294999
$911$	20013.4	0.727853	0.363926	−	0.931428i	$-0.381436\pi$
$911$	20013.4	0.727853	0.363926	+	0.931428i	$0.381436\pi$
$912$	64460.0	2.34044
$913$	−26382.4	−0.956332
$914$	−26276.2	−0.950919
$915$	−63086.8	−2.27933
$916$	88918.7	3.20738
$917$	−11106.6	−0.399968
$918$	9160.12	0.329334
$919$	12422.4	0.445894	0.222947	−	0.974831i	$-0.428432\pi$
$919$	12422.4	0.445894	0.222947	+	0.974831i	$0.428432\pi$
$920$	12612.9	0.451995
$921$	745.397	0.0266685
$922$	−3429.51	−0.122500
$923$	−4674.25	−0.166690
$924$	29839.7	1.06240
$925$	23562.4	0.837543
$926$	−17270.7	−0.612904
$927$	−41466.7	−1.46920
$928$	246.292	0.00871221
$929$	−34451.3	−1.21670	−0.608348	−	0.793670i	$-0.708168\pi$
$929$	−34451.3	−1.21670	−0.608348	+	0.793670i	$0.708168\pi$
$930$	54690.6	1.92836
$931$	6542.96	0.230330
$932$	−15642.1	−0.549758
$933$	27396.2	0.961318
$934$	−3497.01	−0.122511
$935$	35215.1	1.23172
$936$	−20072.8	−0.700961
$937$	5456.58	0.190244	0.0951221	−	0.995466i	$-0.469676\pi$
$937$	5456.58	0.190244	0.0951221	+	0.995466i	$0.469676\pi$
$938$	−25529.8	−0.888674
$939$	−29497.1	−1.02513
$940$	−66900.6	−2.32134
$941$	12069.3	0.418115	0.209058	−	0.977903i	$-0.432960\pi$
$941$	12069.3	0.418115	0.209058	+	0.977903i	$0.432960\pi$
$942$	−60607.1	−2.09627
$943$	−7010.71	−0.242100
$944$	−4011.53	−0.138310
$945$	−2570.34	−0.0884796
$946$	−24154.3	−0.830153
$947$	12456.5	0.427436	0.213718	−	0.976895i	$-0.431443\pi$
$947$	12456.5	0.427436	0.213718	+	0.976895i	$0.431443\pi$
$948$	−112685.	−3.86058
$949$	−9288.29	−0.317714
$950$	−46783.3	−1.59774
$951$	−4182.20	−0.142605
$952$	19552.7	0.665659
$953$	−2930.03	−0.0995940	−0.0497970	−	0.998759i	$-0.515857\pi$
$953$	−2930.03	−0.0995940	−0.0497970	+	0.998759i	$0.515857\pi$
$954$	−43583.2	−1.47910
$955$	−52231.1	−1.76980
$956$	−49346.9	−1.66945
$957$	64132.3	2.16625
$958$	6762.35	0.228060
$959$	9470.70	0.318900
$960$	54673.5	1.83810
$961$	−18748.2	−0.629326
$962$	−27180.5	−0.910951
$963$	−42164.8	−1.41095
$964$	−78770.4	−2.63177
$965$	−27152.1	−0.905757
$966$	−5976.94	−0.199073
$967$	20405.2	0.678580	0.339290	−	0.940682i	$-0.389813\pi$
$967$	20405.2	0.678580	0.339290	+	0.940682i	$0.389813\pi$
$968$	3658.92	0.121490
$969$	−72274.7	−2.39608
$970$	−100410.	−3.32369
$971$	−19526.9	−0.645362	−0.322681	−	0.946508i	$-0.604584\pi$
$971$	−19526.9	−0.645362	−0.322681	+	0.946508i	$0.604584\pi$
$972$	−86893.2	−2.86739
$973$	−8126.61	−0.267757
$974$	6101.03	0.200708
$975$	9136.22	0.300096
$976$	37809.2	1.24000
$977$	33801.9	1.10688	0.553438	−	0.832890i	$-0.313315\pi$
$977$	33801.9	1.10688	0.553438	+	0.832890i	$0.313315\pi$
$978$	74037.7	2.42072
$979$	39552.6	1.29122
$980$	−10982.0	−0.357967
$981$	26184.0	0.852182
$982$	−65551.3	−2.13017
$983$	−24200.6	−0.785228	−0.392614	−	0.919703i	$-0.628429\pi$
$983$	−24200.6	−0.785228	−0.392614	+	0.919703i	$0.628429\pi$
$984$	90378.8	2.92802
$985$	−2123.41	−0.0686877
$986$	84115.3	2.71681
$987$	15838.3	0.510778
$988$	35968.2	1.15820
$989$	3224.55	0.103675
$990$	73559.6	2.36149
$991$	−51314.2	−1.64485	−0.822426	−	0.568872i	$-0.807380\pi$
$991$	−51314.2	−1.64485	−0.822426	+	0.568872i	$0.807380\pi$
$992$	107.608	0.00344410
$993$	19109.7	0.610703
$994$	9510.90	0.303488
$995$	−45046.9	−1.43526
$996$	−90882.3	−2.89128
$997$	−20618.9	−0.654970	−0.327485	−	0.944856i	$-0.606201\pi$
$997$	−20618.9	−0.654970	−0.327485	+	0.944856i	$0.606201\pi$
$998$	86199.4	2.73406
$999$	8627.13	0.273224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.2	✓	12
3.2	odd	2		1449.4.a.o.1.11		12
7.6	odd	2		1127.4.a.h.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.2	✓	12	1.1	even	1	trivial
1127.4.a.h.1.2		12	7.6	odd	2
1449.4.a.o.1.11		12	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q-4.89764 q^{2} +7.57994 q^{3} +15.9869 q^{4} -14.0191 q^{5} -37.1238 q^{6} +7.00000 q^{7} -39.1171 q^{8} +30.4555 q^{9} +68.6607 q^{10} +35.1776 q^{11} +121.180 q^{12} +16.8491 q^{13} -34.2835 q^{14} -106.264 q^{15} +63.6863 q^{16} -71.4072 q^{17} -149.160 q^{18} +133.530 q^{19} -224.123 q^{20} +53.0596 q^{21} -172.287 q^{22} +23.0000 q^{23} -296.505 q^{24} +71.5361 q^{25} -82.5207 q^{26} +26.1922 q^{27} +111.908 q^{28} +240.517 q^{29} +520.444 q^{30} +105.085 q^{31} +1.02401 q^{32} +266.644 q^{33} +349.727 q^{34} -98.1339 q^{35} +486.889 q^{36} +329.378 q^{37} -653.982 q^{38} +127.715 q^{39} +548.388 q^{40} -304.814 q^{41} -259.867 q^{42} +140.198 q^{43} +562.381 q^{44} -426.959 q^{45} -112.646 q^{46} +298.500 q^{47} +482.738 q^{48} +49.0000 q^{49} -350.358 q^{50} -541.262 q^{51} +269.365 q^{52} +292.191 q^{53} -128.280 q^{54} -493.159 q^{55} -273.820 q^{56} +1012.15 q^{57} -1177.97 q^{58} -62.9889 q^{59} -1698.84 q^{60} +593.679 q^{61} -514.667 q^{62} +213.188 q^{63} -514.506 q^{64} -236.209 q^{65} -1305.93 q^{66} +744.666 q^{67} -1141.58 q^{68} +174.339 q^{69} +480.625 q^{70} -277.419 q^{71} -1191.33 q^{72} -551.265 q^{73} -1613.18 q^{74} +542.239 q^{75} +2134.73 q^{76} +246.243 q^{77} -625.502 q^{78} -929.896 q^{79} -892.827 q^{80} -623.762 q^{81} +1492.87 q^{82} -749.978 q^{83} +848.259 q^{84} +1001.07 q^{85} -686.640 q^{86} +1823.10 q^{87} -1376.05 q^{88} +1124.37 q^{89} +2091.09 q^{90} +117.943 q^{91} +367.699 q^{92} +796.534 q^{93} -1461.95 q^{94} -1871.97 q^{95} +7.76194 q^{96} -1462.41 q^{97} -239.985 q^{98} +1071.35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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