LMFDB - Embedded newform 2401.4.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,4,Mod(1,2401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2401.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2401.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:	$141.663585924$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.93571 q^{2} +3.09696 q^{3} +7.48982 q^{4} +18.2977 q^{5} -12.1887 q^{6} +2.00794 q^{8} -17.4089 q^{9} +O(q^{10})$	\(q-3.93571 q^{2} +3.09696 q^{3} +7.48982 q^{4} +18.2977 q^{5} -12.1887 q^{6} +2.00794 q^{8} -17.4089 q^{9} -72.0144 q^{10} +11.1264 q^{11} +23.1956 q^{12} +32.1274 q^{13} +56.6671 q^{15} -67.8212 q^{16} -68.2593 q^{17} +68.5163 q^{18} -113.492 q^{19} +137.046 q^{20} -43.7905 q^{22} +151.295 q^{23} +6.21849 q^{24} +209.805 q^{25} -126.444 q^{26} -137.532 q^{27} -183.747 q^{29} -223.025 q^{30} -167.796 q^{31} +250.861 q^{32} +34.4581 q^{33} +268.649 q^{34} -130.389 q^{36} +255.519 q^{37} +446.673 q^{38} +99.4970 q^{39} +36.7406 q^{40} +238.493 q^{41} -90.2895 q^{43} +83.3350 q^{44} -318.542 q^{45} -595.452 q^{46} -353.761 q^{47} -210.039 q^{48} -825.732 q^{50} -211.396 q^{51} +240.628 q^{52} +231.242 q^{53} +541.287 q^{54} +203.588 q^{55} -351.481 q^{57} +723.174 q^{58} -238.752 q^{59} +424.426 q^{60} -33.1087 q^{61} +660.396 q^{62} -444.747 q^{64} +587.856 q^{65} -135.617 q^{66} -505.936 q^{67} -511.249 q^{68} +468.553 q^{69} +683.159 q^{71} -34.9559 q^{72} -587.218 q^{73} -1005.65 q^{74} +649.757 q^{75} -850.037 q^{76} -391.592 q^{78} -50.1378 q^{79} -1240.97 q^{80} +44.1082 q^{81} -938.639 q^{82} -559.144 q^{83} -1248.99 q^{85} +355.353 q^{86} -569.055 q^{87} +22.3412 q^{88} +1171.00 q^{89} +1253.69 q^{90} +1133.17 q^{92} -519.656 q^{93} +1392.30 q^{94} -2076.65 q^{95} +776.905 q^{96} -5.56045 q^{97} -193.699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) $ 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.93571	−1.39148	−0.695742	−	0.718292i	$-0.744924\pi$
$2$	−3.93571	−1.39148	−0.695742	+	0.718292i	$0.744924\pi$
$3$	3.09696	0.596009	0.298005	−	0.954564i	$-0.403679\pi$
$3$	3.09696	0.596009	0.298005	+	0.954564i	$0.403679\pi$
$4$	7.48982	0.936227
$5$	18.2977	1.63659	0.818297	−	0.574795i	$-0.194918\pi$
$5$	18.2977	1.63659	0.818297	+	0.574795i	$0.194918\pi$
$6$	−12.1887	−0.829337
$7$	0	0
$7$	0	0
$8$	2.00794	0.0887390
$9$	−17.4089	−0.644773
$10$	−72.0144	−2.27729
$11$	11.1264	0.304977	0.152489	−	0.988305i	$-0.451271\pi$
$11$	11.1264	0.304977	0.152489	+	0.988305i	$0.451271\pi$
$12$	23.1956	0.558000
$13$	32.1274	0.685425	0.342713	−	0.939440i	$-0.388654\pi$
$13$	32.1274	0.685425	0.342713	+	0.939440i	$0.388654\pi$
$14$	0	0
$15$	56.6671	0.975425
$16$	−67.8212	−1.05971
$17$	−68.2593	−0.973842	−0.486921	−	0.873446i	$-0.661880\pi$
$17$	−68.2593	−0.973842	−0.486921	+	0.873446i	$0.661880\pi$
$18$	68.5163	0.897191
$19$	−113.492	−1.37036	−0.685182	−	0.728372i	$-0.740278\pi$
$19$	−113.492	−1.37036	−0.685182	+	0.728372i	$0.740278\pi$
$20$	137.046	1.53222
$21$	0	0
$22$	−43.7905	−0.424371
$23$	151.295	1.37161	0.685807	−	0.727784i	$-0.259449\pi$
$23$	151.295	1.37161	0.685807	+	0.727784i	$0.259449\pi$
$24$	6.21849	0.0528893
$25$	209.805	1.67844
$26$	−126.444	−0.953758
$27$	−137.532	−0.980300
$28$	0	0
$29$	−183.747	−1.17658	−0.588291	−	0.808649i	$-0.700199\pi$
$29$	−183.747	−1.17658	−0.588291	+	0.808649i	$0.700199\pi$
$30$	−223.025	−1.35729
$31$	−167.796	−0.972162	−0.486081	−	0.873914i	$-0.661574\pi$
$31$	−167.796	−0.972162	−0.486081	+	0.873914i	$0.661574\pi$
$32$	250.861	1.38582
$33$	34.4581	0.181769
$34$	268.649	1.35508
$35$	0	0
$36$	−130.389	−0.603654
$37$	255.519	1.13533	0.567663	−	0.823261i	$-0.307848\pi$
$37$	255.519	1.13533	0.567663	+	0.823261i	$0.307848\pi$
$38$	446.673	1.90684
$39$	99.4970	0.408520
$40$	36.7406	0.145230
$41$	238.493	0.908447	0.454223	−	0.890888i	$-0.349917\pi$
$41$	238.493	0.908447	0.454223	+	0.890888i	$0.349917\pi$
$42$	0	0
$43$	−90.2895	−0.320210	−0.160105	−	0.987100i	$-0.551183\pi$
$43$	−90.2895	−0.320210	−0.160105	+	0.987100i	$0.551183\pi$
$44$	83.3350	0.285528
$45$	−318.542	−1.05523
$46$	−595.452	−1.90858
$47$	−353.761	−1.09790	−0.548950	−	0.835855i	$-0.684972\pi$
$47$	−353.761	−1.09790	−0.548950	+	0.835855i	$0.684972\pi$
$48$	−210.039	−0.631595
$49$	0	0
$50$	−825.732	−2.33552
$51$	−211.396	−0.580419
$52$	240.628	0.641714
$53$	231.242	0.599311	0.299656	−	0.954047i	$-0.403128\pi$
$53$	231.242	0.599311	0.299656	+	0.954047i	$0.403128\pi$
$54$	541.287	1.36407
$55$	203.588	0.499124
$56$	0	0
$57$	−351.481	−0.816750
$58$	723.174	1.63720
$59$	−238.752	−0.526827	−0.263414	−	0.964683i	$-0.584848\pi$
$59$	−238.752	−0.526827	−0.263414	+	0.964683i	$0.584848\pi$
$60$	424.426	0.913220
$61$	−33.1087	−0.0694940	−0.0347470	−	0.999396i	$-0.511063\pi$
$61$	−33.1087	−0.0694940	−0.0347470	+	0.999396i	$0.511063\pi$
$62$	660.396	1.35275
$63$	0	0
$64$	−444.747	−0.868646
$65$	587.856	1.12176
$66$	−135.617	−0.252929
$67$	−505.936	−0.922537	−0.461268	−	0.887261i	$-0.652605\pi$
$67$	−505.936	−0.922537	−0.461268	+	0.887261i	$0.652605\pi$
$68$	−511.249	−0.911737
$69$	468.553	0.817494
$70$	0	0
$71$	683.159	1.14192	0.570958	−	0.820979i	$-0.306572\pi$
$71$	683.159	1.14192	0.570958	+	0.820979i	$0.306572\pi$
$72$	−34.9559	−0.0572165
$73$	−587.218	−0.941489	−0.470745	−	0.882269i	$-0.656015\pi$
$73$	−587.218	−0.941489	−0.470745	+	0.882269i	$0.656015\pi$
$74$	−1005.65	−1.57979
$75$	649.757	1.00037
$76$	−850.037	−1.28297
$77$	0	0
$78$	−391.592	−0.568449
$79$	−50.1378	−0.0714043	−0.0357022	−	0.999362i	$-0.511367\pi$
$79$	−50.1378	−0.0714043	−0.0357022	+	0.999362i	$0.511367\pi$
$80$	−1240.97	−1.73431
$81$	44.1082	0.0605050
$82$	−938.639	−1.26409
$83$	−559.144	−0.739446	−0.369723	−	0.929142i	$-0.620547\pi$
$83$	−559.144	−0.739446	−0.369723	+	0.929142i	$0.620547\pi$
$84$	0	0
$85$	−1248.99	−1.59378
$86$	355.353	0.445566
$87$	−569.055	−0.701254
$88$	22.3412	0.0270634
$89$	1171.00	1.39468	0.697338	−	0.716743i	$-0.254368\pi$
$89$	1171.00	1.39468	0.697338	+	0.716743i	$0.254368\pi$
$90$	1253.69	1.46834
$91$	0	0
$92$	1133.17	1.28414
$93$	−519.656	−0.579418
$94$	1392.30	1.52771
$95$	−2076.65	−2.24273
$96$	776.905	0.825964
$97$	−5.56045	−0.00582039	−0.00291019	−	0.999996i	$-0.500926\pi$
$97$	−5.56045	−0.00582039	−0.00291019	+	0.999996i	$0.500926\pi$
$98$	0	0
$99$	−193.699	−0.196641
$100$	1571.40	1.57140
$101$	−1560.22	−1.53710	−0.768552	−	0.639787i	$-0.779023\pi$
$101$	−1560.22	−1.53710	−0.768552	+	0.639787i	$0.779023\pi$
$102$	831.993	0.807643
$103$	−958.221	−0.916663	−0.458332	−	0.888781i	$-0.651553\pi$
$103$	−958.221	−0.916663	−0.458332	+	0.888781i	$0.651553\pi$
$104$	64.5097	0.0608240
$105$	0	0
$106$	−910.100	−0.833932
$107$	−1596.71	−1.44262	−0.721308	−	0.692614i	$-0.756459\pi$
$107$	−1596.71	−1.44262	−0.721308	+	0.692614i	$0.756459\pi$
$108$	−1030.09	−0.917783
$109$	−1383.90	−1.21609	−0.608044	−	0.793904i	$-0.708045\pi$
$109$	−1383.90	−1.21609	−0.608044	+	0.793904i	$0.708045\pi$
$110$	−801.264	−0.694523
$111$	791.330	0.676664
$112$	0	0
$113$	2107.11	1.75416	0.877080	−	0.480345i	$-0.159489\pi$
$113$	2107.11	1.75416	0.877080	+	0.480345i	$0.159489\pi$
$114$	1383.33	1.13649
$115$	2768.34	2.24477
$116$	−1376.23	−1.10155
$117$	−559.301	−0.441944
$118$	939.657	0.733071
$119$	0	0
$120$	113.784	0.0865583
$121$	−1207.20	−0.906989
$122$	130.306	0.0966998
$123$	738.602	0.541443
$124$	−1256.76	−0.910165
$125$	1551.74	1.11033
$126$	0	0
$127$	−2051.74	−1.43356	−0.716781	−	0.697299i	$-0.754385\pi$
$127$	−2051.74	−1.43356	−0.716781	+	0.697299i	$0.754385\pi$
$128$	−256.493	−0.177117
$129$	−279.622	−0.190848
$130$	−2313.63	−1.56092
$131$	−158.468	−0.105691	−0.0528453	−	0.998603i	$-0.516829\pi$
$131$	−158.468	−0.105691	−0.0528453	+	0.998603i	$0.516829\pi$
$132$	258.085	0.170177
$133$	0	0
$134$	1991.22	1.28369
$135$	−2516.52	−1.60435
$136$	−137.060	−0.0864178
$137$	−70.9378	−0.0442381	−0.0221191	−	0.999755i	$-0.507041\pi$
$137$	−70.9378	−0.0442381	−0.0221191	+	0.999755i	$0.507041\pi$
$138$	−1844.09	−1.13753
$139$	−1374.54	−0.838753	−0.419377	−	0.907812i	$-0.637751\pi$
$139$	−1374.54	−0.838753	−0.419377	+	0.907812i	$0.637751\pi$
$140$	0	0
$141$	−1095.58	−0.654358
$142$	−2688.72	−1.58896
$143$	357.464	0.209039
$144$	1180.69	0.683270
$145$	−3362.14	−1.92559
$146$	2311.12	1.31007
$147$	0	0
$148$	1913.79	1.06292
$149$	349.364	0.192087	0.0960436	−	0.995377i	$-0.469381\pi$
$149$	349.364	0.192087	0.0960436	+	0.995377i	$0.469381\pi$
$150$	−2557.26	−1.39199
$151$	−1660.64	−0.894975	−0.447488	−	0.894290i	$-0.647681\pi$
$151$	−1660.64	−0.894975	−0.447488	+	0.894290i	$0.647681\pi$
$152$	−227.885	−0.121605
$153$	1188.32	0.627907
$154$	0	0
$155$	−3070.28	−1.59104
$156$	745.215	0.382467
$157$	−3076.18	−1.56373	−0.781867	−	0.623446i	$-0.785732\pi$
$157$	−3076.18	−1.56373	−0.781867	+	0.623446i	$0.785732\pi$
$158$	197.328	0.0993580
$159$	716.145	0.357195
$160$	4590.18	2.26803
$161$	0	0
$162$	−173.597	−0.0841918
$163$	−2772.40	−1.33222	−0.666108	−	0.745855i	$-0.732041\pi$
$163$	−2772.40	−1.33222	−0.666108	+	0.745855i	$0.732041\pi$
$164$	1786.27	0.850513
$165$	630.503	0.297483
$166$	2200.63	1.02893
$167$	593.286	0.274909	0.137455	−	0.990508i	$-0.456108\pi$
$167$	593.286	0.274909	0.137455	+	0.990508i	$0.456108\pi$
$168$	0	0
$169$	−1164.83	−0.530192
$170$	4915.65	2.21772
$171$	1975.77	0.883574
$172$	−676.251	−0.299789
$173$	1622.53	0.713058	0.356529	−	0.934284i	$-0.383960\pi$
$173$	1622.53	0.713058	0.356529	+	0.934284i	$0.383960\pi$
$174$	2239.64	0.975784
$175$	0	0
$176$	−754.609	−0.323186
$177$	−739.403	−0.313994
$178$	−4608.73	−1.94067
$179$	2025.46	0.845756	0.422878	−	0.906187i	$-0.361020\pi$
$179$	2025.46	0.845756	0.422878	+	0.906187i	$0.361020\pi$
$180$	−2385.82	−0.987936
$181$	2765.94	1.13586	0.567930	−	0.823077i	$-0.307745\pi$
$181$	2765.94	1.13586	0.567930	+	0.823077i	$0.307745\pi$
$182$	0	0
$183$	−102.536	−0.0414191
$184$	303.790	0.121716
$185$	4675.40	1.85807
$186$	2045.22	0.806250
$187$	−759.483	−0.297000
$188$	−2649.60	−1.02788
$189$	0	0
$190$	8173.08	3.12072
$191$	976.430	0.369906	0.184953	−	0.982747i	$-0.440787\pi$
$191$	976.430	0.369906	0.184953	+	0.982747i	$0.440787\pi$
$192$	−1377.36	−0.517721
$193$	4578.51	1.70761	0.853805	−	0.520593i	$-0.174289\pi$
$193$	4578.51	1.70761	0.853805	+	0.520593i	$0.174289\pi$
$194$	21.8843	0.00809898
$195$	1820.57	0.668581
$196$	0	0
$197$	1085.93	0.392737	0.196369	−	0.980530i	$-0.437085\pi$
$197$	1085.93	0.392737	0.196369	+	0.980530i	$0.437085\pi$
$198$	762.343	0.273623
$199$	2662.01	0.948267	0.474133	−	0.880453i	$-0.342761\pi$
$199$	2662.01	0.948267	0.474133	+	0.880453i	$0.342761\pi$
$200$	421.275	0.148943
$201$	−1566.86	−0.549840
$202$	6140.57	2.13886
$203$	0	0
$204$	−1583.32	−0.543404
$205$	4363.87	1.48676
$206$	3771.28	1.27552
$207$	−2633.87	−0.884379
$208$	−2178.92	−0.726349
$209$	−1262.77	−0.417930
$210$	0	0
$211$	3338.26	1.08917	0.544586	−	0.838705i	$-0.316687\pi$
$211$	3338.26	1.08917	0.544586	+	0.838705i	$0.316687\pi$
$212$	1731.96	0.561091
$213$	2115.71	0.680593
$214$	6284.19	2.00738
$215$	−1652.09	−0.524053
$216$	−276.156	−0.0869909
$217$	0	0
$218$	5446.63	1.69217
$219$	−1818.59	−0.561136
$220$	1524.84	0.467293
$221$	−2192.99	−0.667496
$222$	−3114.45	−0.941568
$223$	272.956	0.0819663	0.0409832	−	0.999160i	$-0.486951\pi$
$223$	272.956	0.0819663	0.0409832	+	0.999160i	$0.486951\pi$
$224$	0	0
$225$	−3652.47	−1.08221
$226$	−8292.96	−2.44088
$227$	−3637.99	−1.06371	−0.531855	−	0.846836i	$-0.678505\pi$
$227$	−3637.99	−1.06371	−0.531855	+	0.846836i	$0.678505\pi$
$228$	−2632.53	−0.764664
$229$	853.825	0.246386	0.123193	−	0.992383i	$-0.460687\pi$
$229$	853.825	0.246386	0.123193	+	0.992383i	$0.460687\pi$
$230$	−10895.4	−3.12357
$231$	0	0
$232$	−368.951	−0.104409
$233$	−6233.09	−1.75255	−0.876273	−	0.481816i	$-0.839977\pi$
$233$	−6233.09	−1.75255	−0.876273	+	0.481816i	$0.839977\pi$
$234$	2201.25	0.614958
$235$	−6473.00	−1.79682
$236$	−1788.21	−0.493230
$237$	−155.275	−0.0425577
$238$	0	0
$239$	4372.77	1.18348	0.591739	−	0.806130i	$-0.298442\pi$
$239$	4372.77	1.18348	0.591739	+	0.806130i	$0.298442\pi$
$240$	−3843.23	−1.03366
$241$	−374.956	−0.100220	−0.0501101	−	0.998744i	$-0.515957\pi$
$241$	−374.956	−0.100220	−0.0501101	+	0.998744i	$0.515957\pi$
$242$	4751.20	1.26206
$243$	3849.97	1.01636
$244$	−247.978	−0.0650621
$245$	0	0
$246$	−2906.92	−0.753409
$247$	−3646.21	−0.939283
$248$	−336.923	−0.0862687
$249$	−1731.64	−0.440717
$250$	−6107.18	−1.54501
$251$	5177.11	1.30190	0.650949	−	0.759122i	$-0.274371\pi$
$251$	5177.11	1.30190	0.650949	+	0.759122i	$0.274371\pi$
$252$	0	0
$253$	1683.37	0.418311
$254$	8075.04	1.99478
$255$	−3868.05	−0.949910
$256$	4567.46	1.11510
$257$	−2579.54	−0.626099	−0.313049	−	0.949737i	$-0.601351\pi$
$257$	−2579.54	−0.626099	−0.313049	+	0.949737i	$0.601351\pi$
$258$	1100.51	0.265562
$259$	0	0
$260$	4402.94	1.05023
$261$	3198.82	0.758629
$262$	623.686	0.147067
$263$	−3988.24	−0.935078	−0.467539	−	0.883973i	$-0.654859\pi$
$263$	−3988.24	−0.935078	−0.467539	+	0.883973i	$0.654859\pi$
$264$	69.1897	0.0161300
$265$	4231.19	0.980829
$266$	0	0
$267$	3626.54	0.831239
$268$	−3789.37	−0.863704
$269$	−3146.82	−0.713252	−0.356626	−	0.934247i	$-0.616073\pi$
$269$	−3146.82	−0.713252	−0.356626	+	0.934247i	$0.616073\pi$
$270$	9904.30	2.23243
$271$	−2115.95	−0.474298	−0.237149	−	0.971473i	$-0.576213\pi$
$271$	−2115.95	−0.474298	−0.237149	+	0.971473i	$0.576213\pi$
$272$	4629.42	1.03199
$273$	0	0
$274$	279.190	0.0615566
$275$	2334.39	0.511886
$276$	3509.37	0.765360
$277$	−3176.01	−0.688910	−0.344455	−	0.938803i	$-0.611936\pi$
$277$	−3176.01	−0.688910	−0.344455	+	0.938803i	$0.611936\pi$
$278$	5409.78	1.16711
$279$	2921.14	0.626824
$280$	0	0
$281$	1518.75	0.322424	0.161212	−	0.986920i	$-0.448460\pi$
$281$	1518.75	0.322424	0.161212	+	0.986920i	$0.448460\pi$
$282$	4311.89	0.910529
$283$	−1518.90	−0.319044	−0.159522	−	0.987194i	$-0.550995\pi$
$283$	−1518.90	−0.319044	−0.159522	+	0.987194i	$0.550995\pi$
$284$	5116.74	1.06909
$285$	−6431.28	−1.33669
$286$	−1406.87	−0.290875
$287$	0	0
$288$	−4367.21	−0.893542
$289$	−253.671	−0.0516326
$290$	13232.4	2.67942
$291$	−17.2205	−0.00346901
$292$	−4398.16	−0.881448
$293$	6408.29	1.27774	0.638868	−	0.769317i	$-0.279403\pi$
$293$	6408.29	1.27774	0.638868	+	0.769317i	$0.279403\pi$
$294$	0	0
$295$	−4368.60	−0.862202
$296$	513.065	0.100748
$297$	−1530.25	−0.298969
$298$	−1374.99	−0.267286
$299$	4860.70	0.940139
$300$	4866.56	0.936570
$301$	0	0
$302$	6535.81	1.24534
$303$	−4831.93	−0.916129
$304$	7697.19	1.45218
$305$	−605.812	−0.113733
$306$	−4676.87	−0.873722
$307$	4645.18	0.863565	0.431783	−	0.901978i	$-0.357885\pi$
$307$	4645.18	0.863565	0.431783	+	0.901978i	$0.357885\pi$
$308$	0	0
$309$	−2967.57	−0.546340
$310$	12083.7	2.21390
$311$	829.604	0.151262	0.0756311	−	0.997136i	$-0.475903\pi$
$311$	829.604	0.151262	0.0756311	+	0.997136i	$0.475903\pi$
$312$	199.784	0.0362517
$313$	−7156.11	−1.29229	−0.646146	−	0.763214i	$-0.723620\pi$
$313$	−7156.11	−1.29229	−0.646146	+	0.763214i	$0.723620\pi$
$314$	12107.0	2.17591
$315$	0	0
$316$	−375.523	−0.0668507
$317$	3114.62	0.551844	0.275922	−	0.961180i	$-0.411017\pi$
$317$	3114.62	0.551844	0.275922	+	0.961180i	$0.411017\pi$
$318$	−2818.54	−0.497031
$319$	−2044.45	−0.358831
$320$	−8137.84	−1.42162
$321$	−4944.94	−0.859813
$322$	0	0
$323$	7746.91	1.33452
$324$	330.362	0.0566465
$325$	6740.49	1.15045
$326$	10911.4	1.85376
$327$	−4285.87	−0.724799
$328$	478.878	0.0806147
$329$	0	0
$330$	−2481.48	−0.413942
$331$	−8372.51	−1.39032	−0.695158	−	0.718857i	$-0.744666\pi$
$331$	−8372.51	−1.39032	−0.695158	+	0.718857i	$0.744666\pi$
$332$	−4187.88	−0.692289
$333$	−4448.29	−0.732027
$334$	−2335.00	−0.382532
$335$	−9257.46	−1.50982
$336$	0	0
$337$	4752.53	0.768210	0.384105	−	0.923290i	$-0.374510\pi$
$337$	4752.53	0.768210	0.384105	+	0.923290i	$0.374510\pi$
$338$	4584.44	0.737753
$339$	6525.62	1.04550
$340$	−9354.68	−1.49214
$341$	−1866.97	−0.296487
$342$	−7776.07	−1.22948
$343$	0	0
$344$	−181.295	−0.0284151
$345$	8573.43	1.33791
$346$	−6385.82	−0.992208
$347$	−5903.14	−0.913248	−0.456624	−	0.889660i	$-0.650941\pi$
$347$	−5903.14	−0.913248	−0.456624	+	0.889660i	$0.650941\pi$
$348$	−4262.12	−0.656533
$349$	−446.879	−0.0685412	−0.0342706	−	0.999413i	$-0.510911\pi$
$349$	−446.879	−0.0685412	−0.0342706	+	0.999413i	$0.510911\pi$
$350$	0	0
$351$	−4418.55	−0.671923
$352$	2791.19	0.422645
$353$	−7681.47	−1.15820	−0.579098	−	0.815258i	$-0.696595\pi$
$353$	−7681.47	−1.15820	−0.579098	+	0.815258i	$0.696595\pi$
$354$	2910.08	0.436917
$355$	12500.2	1.86885
$356$	8770.60	1.30573
$357$	0	0
$358$	−7971.64	−1.17686
$359$	9406.07	1.38282	0.691411	−	0.722461i	$-0.256989\pi$
$359$	9406.07	1.38282	0.691411	+	0.722461i	$0.256989\pi$
$360$	−639.612	−0.0936402
$361$	6021.51	0.877900
$362$	−10885.9	−1.58053
$363$	−3738.65	−0.540574
$364$	0	0
$365$	−10744.7	−1.54084
$366$	403.552	0.0576340
$367$	445.233	0.0633268	0.0316634	−	0.999499i	$-0.489920\pi$
$367$	445.233	0.0633268	0.0316634	+	0.999499i	$0.489920\pi$
$368$	−10261.0	−1.45351
$369$	−4151.89	−0.585742
$370$	−18401.0	−2.58547
$371$	0	0
$372$	−3892.13	−0.542467
$373$	9545.30	1.32503	0.662516	−	0.749048i	$-0.269489\pi$
$373$	9545.30	1.32503	0.662516	+	0.749048i	$0.269489\pi$
$374$	2989.11	0.413270
$375$	4805.66	0.661768
$376$	−710.328	−0.0974266
$377$	−5903.30	−0.806460
$378$	0	0
$379$	321.340	0.0435518	0.0217759	−	0.999763i	$-0.493068\pi$
$379$	321.340	0.0435518	0.0217759	+	0.999763i	$0.493068\pi$
$380$	−15553.7	−2.09971
$381$	−6354.14	−0.854416
$382$	−3842.95	−0.514718
$383$	−4423.96	−0.590219	−0.295110	−	0.955463i	$-0.595356\pi$
$383$	−4423.96	−0.590219	−0.295110	+	0.955463i	$0.595356\pi$
$384$	−794.348	−0.105563
$385$	0	0
$386$	−18019.7	−2.37611
$387$	1571.84	0.206462
$388$	−41.6467	−0.00544921
$389$	−9517.64	−1.24052	−0.620262	−	0.784395i	$-0.712974\pi$
$389$	−9517.64	−1.24052	−0.620262	+	0.784395i	$0.712974\pi$
$390$	−7165.22	−0.930320
$391$	−10327.3	−1.33573
$392$	0	0
$393$	−490.770	−0.0629925
$394$	−4273.90	−0.546488
$395$	−917.405	−0.116860
$396$	−1450.77	−0.184101
$397$	1484.81	0.187710	0.0938548	−	0.995586i	$-0.470081\pi$
$397$	1484.81	0.187710	0.0938548	+	0.995586i	$0.470081\pi$
$398$	−10476.9	−1.31950
$399$	0	0
$400$	−14229.2	−1.77865
$401$	6186.84	0.770464	0.385232	−	0.922820i	$-0.374121\pi$
$401$	6186.84	0.770464	0.385232	+	0.922820i	$0.374121\pi$
$402$	6166.72	0.765094
$403$	−5390.84	−0.666345
$404$	−11685.8	−1.43908
$405$	807.077	0.0990222
$406$	0	0
$407$	2843.02	0.346248
$408$	−424.469	−0.0515058
$409$	−10738.0	−1.29819	−0.649093	−	0.760709i	$-0.724851\pi$
$409$	−10738.0	−1.29819	−0.649093	+	0.760709i	$0.724851\pi$
$410$	−17174.9	−2.06880
$411$	−219.691	−0.0263663
$412$	−7176.90	−0.858205
$413$	0	0
$414$	10366.1	1.23060
$415$	−10231.0	−1.21017
$416$	8059.51	0.949879
$417$	−4256.88	−0.499905
$418$	4969.88	0.581543
$419$	−4920.15	−0.573663	−0.286832	−	0.957981i	$-0.592602\pi$
$419$	−4920.15	−0.573663	−0.286832	+	0.957981i	$0.592602\pi$
$420$	0	0
$421$	−11804.0	−1.36648	−0.683242	−	0.730192i	$-0.739431\pi$
$421$	−11804.0	−1.36648	−0.683242	+	0.730192i	$0.739431\pi$
$422$	−13138.4	−1.51557
$423$	6158.57	0.707896
$424$	464.318	0.0531823
$425$	−14321.1	−1.63454
$426$	−8326.83	−0.947034
$427$	0	0
$428$	−11959.1	−1.35062
$429$	1107.05	0.124589
$430$	6502.14	0.729212
$431$	2901.97	0.324323	0.162161	−	0.986764i	$-0.448153\pi$
$431$	2901.97	0.324323	0.162161	+	0.986764i	$0.448153\pi$
$432$	9327.60	1.03883
$433$	−398.338	−0.0442099	−0.0221049	−	0.999756i	$-0.507037\pi$
$433$	−398.338	−0.0442099	−0.0221049	+	0.999756i	$0.507037\pi$
$434$	0	0
$435$	−10412.4	−1.14767
$436$	−10365.2	−1.13853
$437$	−17170.8	−1.87961
$438$	7157.44	0.780812
$439$	4977.64	0.541161	0.270580	−	0.962697i	$-0.412784\pi$
$439$	4977.64	0.541161	0.270580	+	0.962697i	$0.412784\pi$
$440$	408.792	0.0442918
$441$	0	0
$442$	8630.98	0.928810
$443$	−2201.59	−0.236119	−0.118059	−	0.993007i	$-0.537667\pi$
$443$	−2201.59	−0.236119	−0.118059	+	0.993007i	$0.537667\pi$
$444$	5926.92	0.633512
$445$	21426.6	2.28252
$446$	−1074.28	−0.114055
$447$	1081.96	0.114486
$448$	0	0
$449$	18314.1	1.92494	0.962468	−	0.271395i	$-0.0874851\pi$
$449$	18314.1	1.92494	0.962468	+	0.271395i	$0.0874851\pi$
$450$	14375.1	1.50588
$451$	2653.58	0.277056
$452$	15781.8	1.64229
$453$	−5142.94	−0.533414
$454$	14318.1	1.48013
$455$	0	0
$456$	−705.750	−0.0724776
$457$	−8747.89	−0.895425	−0.447712	−	0.894178i	$-0.647761\pi$
$457$	−8747.89	−0.895425	−0.447712	+	0.894178i	$0.647761\pi$
$458$	−3360.41	−0.342842
$459$	9387.85	0.954657
$460$	20734.4	2.10162
$461$	−9307.86	−0.940370	−0.470185	−	0.882568i	$-0.655813\pi$
$461$	−9307.86	−0.940370	−0.470185	+	0.882568i	$0.655813\pi$
$462$	0	0
$463$	−14225.1	−1.42785	−0.713927	−	0.700220i	$-0.753085\pi$
$463$	−14225.1	−1.42785	−0.713927	+	0.700220i	$0.753085\pi$
$464$	12461.9	1.24683
$465$	−9508.50	−0.948272
$466$	24531.6	2.43864
$467$	−5884.52	−0.583090	−0.291545	−	0.956557i	$-0.594169\pi$
$467$	−5884.52	−0.583090	−0.291545	+	0.956557i	$0.594169\pi$
$468$	−4189.06	−0.413760
$469$	0	0
$470$	25475.8	2.50024
$471$	−9526.80	−0.931999
$472$	−479.398	−0.0467501
$473$	−1004.60	−0.0976567
$474$	611.115	0.0592183
$475$	−23811.3	−2.30008
$476$	0	0
$477$	−4025.66	−0.386420
$478$	−17210.0	−1.64679
$479$	−12489.8	−1.19138	−0.595692	−	0.803213i	$-0.703122\pi$
$479$	−12489.8	−1.19138	−0.595692	+	0.803213i	$0.703122\pi$
$480$	14215.6	1.35177
$481$	8209.15	0.778181
$482$	1475.72	0.139455
$483$	0	0
$484$	−9041.72	−0.849147
$485$	−101.743	−0.00952562
$486$	−15152.4	−1.41425
$487$	8170.07	0.760208	0.380104	−	0.924944i	$-0.375888\pi$
$487$	8170.07	0.760208	0.380104	+	0.924944i	$0.375888\pi$
$488$	−66.4801	−0.00616683
$489$	−8586.00	−0.794013
$490$	0	0
$491$	5894.06	0.541741	0.270871	−	0.962616i	$-0.412688\pi$
$491$	5894.06	0.541741	0.270871	+	0.962616i	$0.412688\pi$
$492$	5531.99	0.506913
$493$	12542.4	1.14581
$494$	14350.4	1.30700
$495$	−3544.24	−0.321822
$496$	11380.1	1.03021
$497$	0	0
$498$	6815.25	0.613250
$499$	7089.14	0.635979	0.317989	−	0.948094i	$-0.396992\pi$
$499$	7089.14	0.635979	0.317989	+	0.948094i	$0.396992\pi$
$500$	11622.2	1.03952
$501$	1837.38	0.163849
$502$	−20375.6	−1.81157
$503$	2916.01	0.258486	0.129243	−	0.991613i	$-0.458745\pi$
$503$	2916.01	0.258486	0.129243	+	0.991613i	$0.458745\pi$
$504$	0	0
$505$	−28548.4	−2.51562
$506$	−6625.26	−0.582073
$507$	−3607.43	−0.315999
$508$	−15367.1	−1.34214
$509$	−11495.4	−1.00104	−0.500518	−	0.865726i	$-0.666857\pi$
$509$	−11495.4	−1.00104	−0.500518	+	0.865726i	$0.666857\pi$
$510$	15223.5	1.32178
$511$	0	0
$512$	−15924.2	−1.37453
$513$	15608.9	1.34337
$514$	10152.3	0.871206
$515$	−17533.2	−1.50021
$516$	−2094.32	−0.178677
$517$	−3936.10	−0.334834
$518$	0	0
$519$	5024.92	0.424989
$520$	1180.38	0.0995442
$521$	−16479.2	−1.38574	−0.692868	−	0.721064i	$-0.743653\pi$
$521$	−16479.2	−1.38574	−0.692868	+	0.721064i	$0.743653\pi$
$522$	−12589.6	−1.05562
$523$	−12363.5	−1.03369	−0.516844	−	0.856080i	$-0.672893\pi$
$523$	−12363.5	−1.03369	−0.516844	+	0.856080i	$0.672893\pi$
$524$	−1186.90	−0.0989503
$525$	0	0
$526$	15696.6	1.30115
$527$	11453.6	0.946732
$528$	−2336.99	−0.192622
$529$	10723.1	0.881324
$530$	−16652.7	−1.36481
$531$	4156.39	0.339684
$532$	0	0
$533$	7662.15	0.622673
$534$	−14273.0	−1.15666
$535$	−29216.1	−2.36098
$536$	−1015.89	−0.0818650
$537$	6272.77	0.504078
$538$	12385.0	0.992479
$539$	0	0
$540$	−18848.3	−1.50204
$541$	−5706.02	−0.453458	−0.226729	−	0.973958i	$-0.572803\pi$
$541$	−5706.02	−0.453458	−0.226729	+	0.973958i	$0.572803\pi$
$542$	8327.76	0.659978
$543$	8565.98	0.676983
$544$	−17123.6	−1.34957
$545$	−25322.1	−1.99024
$546$	0	0
$547$	6452.32	0.504354	0.252177	−	0.967681i	$-0.418854\pi$
$547$	6452.32	0.504354	0.252177	+	0.967681i	$0.418854\pi$
$548$	−531.311	−0.0414169
$549$	576.385	0.0448078
$550$	−9187.46	−0.712281
$551$	20853.8	1.61235
$552$	940.823	0.0725437
$553$	0	0
$554$	12499.9	0.958607
$555$	14479.5	1.10743
$556$	−10295.0	−0.785263
$557$	8462.90	0.643778	0.321889	−	0.946777i	$-0.395682\pi$
$557$	8462.90	0.643778	0.321889	+	0.946777i	$0.395682\pi$
$558$	−11496.7	−0.872215
$559$	−2900.76	−0.219480
$560$	0	0
$561$	−2352.09	−0.177014
$562$	−5977.36	−0.448647
$563$	−16622.0	−1.24429	−0.622145	−	0.782902i	$-0.713738\pi$
$563$	−16622.0	−1.24429	−0.622145	+	0.782902i	$0.713738\pi$
$564$	−8205.70	−0.612628
$565$	38555.2	2.87085
$566$	5977.96	0.443944
$567$	0	0
$568$	1371.74	0.101333
$569$	−5553.95	−0.409198	−0.204599	−	0.978846i	$-0.565589\pi$
$569$	−5553.95	−0.409198	−0.204599	+	0.978846i	$0.565589\pi$
$570$	25311.7	1.85998
$571$	17365.2	1.27270	0.636351	−	0.771399i	$-0.280443\pi$
$571$	17365.2	1.27270	0.636351	+	0.771399i	$0.280443\pi$
$572$	2677.34	0.195708
$573$	3023.96	0.220467
$574$	0	0
$575$	31742.4	2.30217
$576$	7742.54	0.560080
$577$	−14165.9	−1.02207	−0.511035	−	0.859560i	$-0.670738\pi$
$577$	−14165.9	−1.02207	−0.511035	+	0.859560i	$0.670738\pi$
$578$	998.376	0.0718460
$579$	14179.5	1.01775
$580$	−25181.8	−1.80279
$581$	0	0
$582$	67.7747	0.00482707
$583$	2572.90	0.182776
$584$	−1179.10	−0.0835469
$585$	−10233.9	−0.723283
$586$	−25221.2	−1.77795
$587$	−13013.6	−0.915043	−0.457521	−	0.889199i	$-0.651263\pi$
$587$	−13013.6	−0.915043	−0.457521	+	0.889199i	$0.651263\pi$
$588$	0	0
$589$	19043.5	1.33222
$590$	17193.5	1.19974
$591$	3363.07	0.234075
$592$	−17329.6	−1.20311
$593$	−1489.95	−0.103179	−0.0515894	−	0.998668i	$-0.516429\pi$
$593$	−1489.95	−0.103179	−0.0515894	+	0.998668i	$0.516429\pi$
$594$	6022.60	0.416011
$595$	0	0
$596$	2616.67	0.179837
$597$	8244.13	0.565176
$598$	−19130.3	−1.30819
$599$	−11764.0	−0.802446	−0.401223	−	0.915980i	$-0.631415\pi$
$599$	−11764.0	−0.802446	−0.401223	+	0.915980i	$0.631415\pi$
$600$	1304.67	0.0887715
$601$	−11373.3	−0.771925	−0.385962	−	0.922515i	$-0.626131\pi$
$601$	−11373.3	−0.771925	−0.385962	+	0.922515i	$0.626131\pi$
$602$	0	0
$603$	8807.78	0.594827
$604$	−12437.9	−0.837900
$605$	−22089.0	−1.48437
$606$	19017.1	1.27478
$607$	20896.4	1.39730	0.698648	−	0.715465i	$-0.253785\pi$
$607$	20896.4	1.39730	0.698648	+	0.715465i	$0.253785\pi$
$608$	−28470.8	−1.89909
$609$	0	0
$610$	2384.30	0.158258
$611$	−11365.4	−0.752528
$612$	8900.27	0.587863
$613$	−4220.00	−0.278049	−0.139024	−	0.990289i	$-0.544397\pi$
$613$	−4220.00	−0.278049	−0.139024	+	0.990289i	$0.544397\pi$
$614$	−18282.1	−1.20164
$615$	13514.7	0.886122
$616$	0	0
$617$	−250.008	−0.0163127	−0.00815634	−	0.999967i	$-0.502596\pi$
$617$	−250.008	−0.0163127	−0.00815634	+	0.999967i	$0.502596\pi$
$618$	11679.5	0.760223
$619$	10844.4	0.704158	0.352079	−	0.935970i	$-0.385475\pi$
$619$	10844.4	0.704158	0.352079	+	0.935970i	$0.385475\pi$
$620$	−22995.8	−1.48957
$621$	−20807.9	−1.34459
$622$	−3265.08	−0.210479
$623$	0	0
$624$	−6748.01	−0.432911
$625$	2167.54	0.138722
$626$	28164.4	1.79820
$627$	−3910.73	−0.249090
$628$	−23040.0	−1.46401
$629$	−17441.5	−1.10563
$630$	0	0
$631$	−12729.0	−0.803061	−0.401531	−	0.915846i	$-0.631522\pi$
$631$	−12729.0	−0.803061	−0.401531	+	0.915846i	$0.631522\pi$
$632$	−100.673	−0.00633635
$633$	10338.4	0.649157
$634$	−12258.2	−0.767882
$635$	−37542.0	−2.34616
$636$	5363.80	0.334416
$637$	0	0
$638$	8046.35	0.499307
$639$	−11893.0	−0.736277
$640$	−4693.23	−0.289869
$641$	−9838.08	−0.606210	−0.303105	−	0.952957i	$-0.598023\pi$
$641$	−9838.08	−0.606210	−0.303105	+	0.952957i	$0.598023\pi$
$642$	19461.9	1.19642
$643$	16456.6	1.00931	0.504655	−	0.863321i	$-0.331620\pi$
$643$	16456.6	1.00931	0.504655	+	0.863321i	$0.331620\pi$
$644$	0	0
$645$	−5116.44	−0.312341
$646$	−30489.6	−1.85696
$647$	8370.82	0.508641	0.254321	−	0.967120i	$-0.418148\pi$
$647$	8370.82	0.508641	0.254321	+	0.967120i	$0.418148\pi$
$648$	88.5664	0.00536916
$649$	−2656.46	−0.160670
$650$	−26528.6	−1.60083
$651$	0	0
$652$	−20764.8	−1.24726
$653$	9681.16	0.580173	0.290087	−	0.957000i	$-0.406316\pi$
$653$	9681.16	0.580173	0.290087	+	0.957000i	$0.406316\pi$
$654$	16868.0	1.00855
$655$	−2899.61	−0.172972
$656$	−16174.9	−0.962687
$657$	10222.8	0.607047
$658$	0	0
$659$	3978.93	0.235200	0.117600	−	0.993061i	$-0.462480\pi$
$659$	3978.93	0.235200	0.117600	+	0.993061i	$0.462480\pi$
$660$	4722.35	0.278511
$661$	23777.7	1.39916	0.699581	−	0.714554i	$-0.253370\pi$
$661$	23777.7	1.39916	0.699581	+	0.714554i	$0.253370\pi$
$662$	32951.8	1.93460
$663$	−6791.60	−0.397834
$664$	−1122.72	−0.0656177
$665$	0	0
$666$	17507.2	1.01860
$667$	−27799.9	−1.61382
$668$	4443.61	0.257378
$669$	845.333	0.0488527
$670$	36434.7	2.10089
$671$	−368.382	−0.0211941
$672$	0	0
$673$	−6783.00	−0.388507	−0.194254	−	0.980951i	$-0.562228\pi$
$673$	−6783.00	−0.388507	−0.194254	+	0.980951i	$0.562228\pi$
$674$	−18704.6	−1.06895
$675$	−28855.0	−1.64538
$676$	−8724.38	−0.496380
$677$	19979.7	1.13424	0.567121	−	0.823635i	$-0.308057\pi$
$677$	19979.7	1.13424	0.567121	+	0.823635i	$0.308057\pi$
$678$	−25682.9	−1.45479
$679$	0	0
$680$	−2507.88	−0.141431
$681$	−11266.7	−0.633981
$682$	7347.86	0.412557
$683$	7057.33	0.395375	0.197688	−	0.980265i	$-0.436657\pi$
$683$	7057.33	0.395375	0.197688	+	0.980265i	$0.436657\pi$
$684$	14798.2	0.827226
$685$	−1298.00	−0.0723998
$686$	0	0
$687$	2644.26	0.146848
$688$	6123.54	0.339328
$689$	7429.19	0.410783
$690$	−33742.5	−1.86168
$691$	−9084.49	−0.500131	−0.250065	−	0.968229i	$-0.580452\pi$
$691$	−9084.49	−0.500131	−0.250065	+	0.968229i	$0.580452\pi$
$692$	12152.5	0.667584
$693$	0	0
$694$	23233.0	1.27077
$695$	−25150.8	−1.37270
$696$	−1142.63	−0.0622286
$697$	−16279.3	−0.884683
$698$	1758.79	0.0953740
$699$	−19303.6	−1.04453
$700$	0	0
$701$	15607.4	0.840920	0.420460	−	0.907311i	$-0.361869\pi$
$701$	15607.4	0.840920	0.420460	+	0.907311i	$0.361869\pi$
$702$	17390.1	0.934969
$703$	−28999.4	−1.55581
$704$	−4948.45	−0.264917
$705$	−20046.6	−1.07092
$706$	30232.0	1.61161
$707$	0	0
$708$	−5537.99	−0.293970
$709$	−14222.5	−0.753367	−0.376684	−	0.926342i	$-0.622936\pi$
$709$	−14222.5	−0.753367	−0.376684	+	0.926342i	$0.622936\pi$
$710$	−49197.3	−2.60048
$711$	872.842	0.0460396
$712$	2351.30	0.123762
$713$	−25386.6	−1.33343
$714$	0	0
$715$	6540.75	0.342112
$716$	15170.3	0.791819
$717$	13542.3	0.705363
$718$	−37019.6	−1.92418
$719$	2333.58	0.121040	0.0605200	−	0.998167i	$-0.480724\pi$
$719$	2333.58	0.121040	0.0605200	+	0.998167i	$0.480724\pi$
$720$	21603.9	1.11824
$721$	0	0
$722$	−23698.9	−1.22158
$723$	−1161.22	−0.0597321
$724$	20716.4	1.06342
$725$	−38551.0	−1.97482
$726$	14714.2	0.752200
$727$	21602.3	1.10204	0.551020	−	0.834492i	$-0.314239\pi$
$727$	21602.3	1.10204	0.551020	+	0.834492i	$0.314239\pi$
$728$	0	0
$729$	10732.3	0.545256
$730$	42288.2	2.14405
$731$	6163.09	0.311833
$732$	−767.977	−0.0387776
$733$	33179.7	1.67192	0.835961	−	0.548789i	$-0.184911\pi$
$733$	33179.7	1.67192	0.835961	+	0.548789i	$0.184911\pi$
$734$	−1752.31	−0.0881183
$735$	0	0
$736$	37953.9	1.90082
$737$	−5629.27	−0.281353
$738$	16340.6	0.815050
$739$	−19573.5	−0.974322	−0.487161	−	0.873312i	$-0.661968\pi$
$739$	−19573.5	−0.974322	−0.487161	+	0.873312i	$0.661968\pi$
$740$	35017.9	1.73957
$741$	−11292.2	−0.559821
$742$	0	0
$743$	27842.0	1.37473	0.687365	−	0.726312i	$-0.258767\pi$
$743$	27842.0	1.37473	0.687365	+	0.726312i	$0.258767\pi$
$744$	−1043.44	−0.0514170
$745$	6392.55	0.314369
$746$	−37567.6	−1.84376
$747$	9734.06	0.476775
$748$	−5688.39	−0.278059
$749$	0	0
$750$	−18913.7	−0.920840
$751$	−29613.8	−1.43891	−0.719455	−	0.694539i	$-0.755608\pi$
$751$	−29613.8	−1.43891	−0.719455	+	0.694539i	$0.755608\pi$
$752$	23992.5	1.16345
$753$	16033.3	0.775943
$754$	23233.7	1.12218
$755$	−30385.9	−1.46471
$756$	0	0
$757$	7371.98	0.353949	0.176974	−	0.984215i	$-0.443369\pi$
$757$	7371.98	0.353949	0.176974	+	0.984215i	$0.443369\pi$
$758$	−1264.70	−0.0606016
$759$	5213.33	0.249317
$760$	−4169.77	−0.199018
$761$	−24101.3	−1.14806	−0.574029	−	0.818835i	$-0.694620\pi$
$761$	−24101.3	−1.14806	−0.574029	+	0.818835i	$0.694620\pi$
$762$	25008.1	1.18891
$763$	0	0
$764$	7313.28	0.346316
$765$	21743.4	1.02763
$766$	17411.4	0.821281
$767$	−7670.46	−0.361101
$768$	14145.2	0.664611
$769$	−34245.7	−1.60589	−0.802947	−	0.596051i	$-0.796736\pi$
$769$	−34245.7	−1.60589	−0.802947	+	0.596051i	$0.796736\pi$
$770$	0	0
$771$	−7988.73	−0.373161
$772$	34292.2	1.59871
$773$	21268.3	0.989609	0.494804	−	0.869004i	$-0.335240\pi$
$773$	21268.3	0.989609	0.494804	+	0.869004i	$0.335240\pi$
$774$	−6186.30	−0.287289
$775$	−35204.4	−1.63172
$776$	−11.1650	−0.000516496 0
$777$	0	0
$778$	37458.7	1.72617
$779$	−27067.1	−1.24490
$780$	13635.7	0.625944
$781$	7601.13	0.348259
$782$	40645.1	1.85865
$783$	25271.1	1.15340
$784$	0	0
$785$	−56287.0	−2.55920
$786$	1931.53	0.0876531
$787$	−1773.26	−0.0803173	−0.0401587	−	0.999193i	$-0.512786\pi$
$787$	−1773.26	−0.0803173	−0.0401587	+	0.999193i	$0.512786\pi$
$788$	8133.41	0.367691
$789$	−12351.4	−0.557315
$790$	3610.64	0.162609
$791$	0	0
$792$	−388.935	−0.0174497
$793$	−1063.70	−0.0476329
$794$	−5843.80	−0.261195
$795$	13103.8	0.584583
$796$	19938.0	0.887793
$797$	−4473.60	−0.198825	−0.0994123	−	0.995046i	$-0.531696\pi$
$797$	−4473.60	−0.198825	−0.0994123	+	0.995046i	$0.531696\pi$
$798$	0	0
$799$	24147.4	1.06918
$800$	52631.9	2.32602
$801$	−20385.8	−0.899249
$802$	−24349.6	−1.07209
$803$	−6533.66	−0.287133
$804$	−11735.5	−0.514776
$805$	0	0
$806$	21216.8	0.927208
$807$	−9745.56	−0.425105
$808$	−3132.82	−0.136401
$809$	−15255.6	−0.662989	−0.331494	−	0.943457i	$-0.607553\pi$
$809$	−15255.6	−0.662989	−0.331494	+	0.943457i	$0.607553\pi$
$810$	−3176.42	−0.137788
$811$	4911.79	0.212671	0.106336	−	0.994330i	$-0.466088\pi$
$811$	4911.79	0.212671	0.106336	+	0.994330i	$0.466088\pi$
$812$	0	0
$813$	−6553.00	−0.282686
$814$	−11189.3	−0.481799
$815$	−50728.5	−2.18030
$816$	14337.1	0.615073
$817$	10247.2	0.438804
$818$	42261.5	1.80640
$819$	0	0
$820$	32684.5	1.39194
$821$	22792.2	0.968884	0.484442	−	0.874823i	$-0.339023\pi$
$821$	22792.2	0.968884	0.484442	+	0.874823i	$0.339023\pi$
$822$	864.640	0.0366883
$823$	17358.6	0.735216	0.367608	−	0.929981i	$-0.380177\pi$
$823$	17358.6	0.735216	0.367608	+	0.929981i	$0.380177\pi$
$824$	−1924.05	−0.0813438
$825$	7229.49	0.305089
$826$	0	0
$827$	−34567.7	−1.45349	−0.726745	−	0.686907i	$-0.758968\pi$
$827$	−34567.7	−1.45349	−0.726745	+	0.686907i	$0.758968\pi$
$828$	−19727.2	−0.827980
$829$	568.054	0.0237990	0.0118995	−	0.999929i	$-0.496212\pi$
$829$	568.054	0.0237990	0.0118995	+	0.999929i	$0.496212\pi$
$830$	40266.4	1.68394
$831$	−9835.96	−0.410597
$832$	−14288.6	−0.595392
$833$	0	0
$834$	16753.8	0.695609
$835$	10855.8	0.449915
$836$	−9457.89	−0.391277
$837$	23077.3	0.953011
$838$	19364.3	0.798243
$839$	−28050.8	−1.15426	−0.577129	−	0.816653i	$-0.695827\pi$
$839$	−28050.8	−1.15426	−0.577129	+	0.816653i	$0.695827\pi$
$840$	0	0
$841$	9373.83	0.384347
$842$	46457.0	1.90144
$843$	4703.50	0.192167
$844$	25003.0	1.01971
$845$	−21313.7	−0.867709
$846$	−24238.4	−0.985026
$847$	0	0
$848$	−15683.1	−0.635094
$849$	−4703.98	−0.190153
$850$	56363.9	2.27443
$851$	38658.6	1.55723
$852$	15846.3	0.637189
$853$	8242.71	0.330862	0.165431	−	0.986221i	$-0.447099\pi$
$853$	8242.71	0.330862	0.165431	+	0.986221i	$0.447099\pi$
$854$	0	0
$855$	36152.1	1.44605
$856$	−3206.09	−0.128016
$857$	21781.0	0.868175	0.434087	−	0.900871i	$-0.357071\pi$
$857$	21781.0	0.868175	0.434087	+	0.900871i	$0.357071\pi$
$858$	−4357.02	−0.173364
$859$	46751.1	1.85696	0.928480	−	0.371383i	$-0.121116\pi$
$859$	46751.1	1.85696	0.928480	+	0.371383i	$0.121116\pi$
$860$	−12373.8	−0.490633
$861$	0	0
$862$	−11421.3	−0.451290
$863$	−20805.6	−0.820663	−0.410331	−	0.911936i	$-0.634587\pi$
$863$	−20805.6	−0.820663	−0.410331	+	0.911936i	$0.634587\pi$
$864$	−34501.5	−1.35852
$865$	29688.6	1.16699
$866$	1567.74	0.0615173
$867$	−785.608	−0.0307735
$868$	0	0
$869$	−557.856	−0.0217767
$870$	40980.1	1.59696
$871$	−16254.4	−0.632330
$872$	−2778.78	−0.107914
$873$	96.8011	0.00375283
$874$	67579.2	2.61545
$875$	0	0
$876$	−13620.9	−0.525351
$877$	3507.96	0.135069	0.0675345	−	0.997717i	$-0.478487\pi$
$877$	3507.96	0.135069	0.0675345	+	0.997717i	$0.478487\pi$
$878$	−19590.5	−0.753017
$879$	19846.2	0.761542
$880$	−13807.6	−0.528925
$881$	−29531.8	−1.12934	−0.564671	−	0.825316i	$-0.690997\pi$
$881$	−29531.8	−1.12934	−0.564671	+	0.825316i	$0.690997\pi$
$882$	0	0
$883$	−41514.5	−1.58219	−0.791096	−	0.611692i	$-0.790489\pi$
$883$	−41514.5	−1.58219	−0.791096	+	0.611692i	$0.790489\pi$
$884$	−16425.1	−0.624928
$885$	−13529.4	−0.513881
$886$	8664.81	0.328555
$887$	−36859.9	−1.39530	−0.697652	−	0.716437i	$-0.745772\pi$
$887$	−36859.9	−1.39530	−0.697652	+	0.716437i	$0.745772\pi$
$888$	1588.94	0.0600466
$889$	0	0
$890$	−84329.1	−3.17609
$891$	490.767	0.0184527
$892$	2044.39	0.0767391
$893$	40149.1	1.50452
$894$	−4258.30	−0.159305
$895$	37061.3	1.38416
$896$	0	0
$897$	15053.4	0.560332
$898$	−72079.0	−2.67852
$899$	30831.9	1.14383
$900$	−27356.3	−1.01320
$901$	−15784.4	−0.583634
$902$	−10443.7	−0.385518
$903$	0	0
$904$	4230.94	0.155662
$905$	50610.2	1.85894
$906$	20241.1	0.742236
$907$	−17428.2	−0.638031	−0.319016	−	0.947749i	$-0.603352\pi$
$907$	−17428.2	−0.638031	−0.319016	+	0.947749i	$0.603352\pi$
$908$	−27247.9	−0.995874
$909$	27161.6	0.991083
$910$	0	0
$911$	−14994.7	−0.545333	−0.272666	−	0.962109i	$-0.587906\pi$
$911$	−14994.7	−0.545333	−0.272666	+	0.962109i	$0.587906\pi$
$912$	23837.8	0.865515
$913$	−6221.28	−0.225514
$914$	34429.2	1.24597
$915$	−1876.17	−0.0677862
$916$	6394.99	0.230673
$917$	0	0
$918$	−36947.9	−1.32839
$919$	24719.2	0.887280	0.443640	−	0.896205i	$-0.353687\pi$
$919$	24719.2	0.887280	0.443640	+	0.896205i	$0.353687\pi$
$920$	5558.65	0.199199
$921$	14385.9	0.514693
$922$	36633.1	1.30851
$923$	21948.1	0.782698
$924$	0	0
$925$	53609.2	1.90558
$926$	55985.9	1.98684
$927$	16681.5	0.591040
$928$	−46094.9	−1.63054
$929$	41255.1	1.45698	0.728490	−	0.685056i	$-0.240222\pi$
$929$	41255.1	1.45698	0.728490	+	0.685056i	$0.240222\pi$
$930$	37422.7	1.31950
$931$	0	0
$932$	−46684.7	−1.64078
$933$	2569.25	0.0901536
$934$	23159.8	0.811361
$935$	−13896.8	−0.486068
$936$	−1123.04	−0.0392177
$937$	30271.6	1.05542	0.527711	−	0.849424i	$-0.323050\pi$
$937$	30271.6	1.05542	0.527711	+	0.849424i	$0.323050\pi$
$938$	0	0
$939$	−22162.1	−0.770218
$940$	−48481.6	−1.68223
$941$	−49515.6	−1.71537	−0.857685	−	0.514175i	$-0.828098\pi$
$941$	−49515.6	−1.71537	−0.857685	+	0.514175i	$0.828098\pi$
$942$	37494.7	1.29686
$943$	36082.7	1.24604
$944$	16192.4	0.558282
$945$	0	0
$946$	3953.82	0.135888
$947$	−48772.3	−1.67359	−0.836794	−	0.547518i	$-0.815573\pi$
$947$	−48772.3	−1.67359	−0.836794	+	0.547518i	$0.815573\pi$
$948$	−1162.98	−0.0398436
$949$	−18865.8	−0.645321
$950$	93714.3	3.20052
$951$	9645.84	0.328904
$952$	0	0
$953$	−43341.2	−1.47320	−0.736599	−	0.676329i	$-0.763570\pi$
$953$	−43341.2	−1.47320	−0.736599	+	0.676329i	$0.763570\pi$
$954$	15843.8	0.537697
$955$	17866.4	0.605386
$956$	32751.3	1.10800
$957$	−6331.56	−0.213867
$958$	49156.2	1.65779
$959$	0	0
$960$	−25202.5	−0.847300
$961$	−1635.54	−0.0549006
$962$	−32308.8	−1.08283
$963$	27796.9	0.930160
$964$	−2808.35	−0.0938288
$965$	83776.2	2.79466
$966$	0	0
$967$	−636.799	−0.0211769	−0.0105885	−	0.999944i	$-0.503370\pi$
$967$	−636.799	−0.0211769	−0.0105885	+	0.999944i	$0.503370\pi$
$968$	−2423.98	−0.0804853
$969$	23991.8	0.795385
$970$	400.432	0.0132547
$971$	19763.9	0.653195	0.326598	−	0.945163i	$-0.394098\pi$
$971$	19763.9	0.653195	0.326598	+	0.945163i	$0.394098\pi$
$972$	28835.6	0.951545
$973$	0	0
$974$	−32155.0	−1.05782
$975$	20875.0	0.685676
$976$	2245.47	0.0736432
$977$	40980.6	1.34195	0.670975	−	0.741480i	$-0.265876\pi$
$977$	40980.6	1.34195	0.670975	+	0.741480i	$0.265876\pi$
$978$	33792.0	1.10486
$979$	13029.1	0.425344
$980$	0	0
$981$	24092.1	0.784100
$982$	−23197.3	−0.753824
$983$	−9296.84	−0.301651	−0.150826	−	0.988560i	$-0.548193\pi$
$983$	−9296.84	−0.301651	−0.150826	+	0.988560i	$0.548193\pi$
$984$	1483.06	0.0480471
$985$	19870.0	0.642752
$986$	−49363.3	−1.59437
$987$	0	0
$988$	−27309.5	−0.879382
$989$	−13660.3	−0.439204
$990$	13949.1	0.447810
$991$	6575.47	0.210774	0.105387	−	0.994431i	$-0.466392\pi$
$991$	6575.47	0.210774	0.105387	+	0.994431i	$0.466392\pi$
$992$	−42093.4	−1.34725
$993$	−25929.3	−0.828641
$994$	0	0
$995$	48708.6	1.55193
$996$	−12969.7	−0.412611
$997$	5380.51	0.170915	0.0854576	−	0.996342i	$-0.472765\pi$
$997$	5380.51	0.170915	0.0854576	+	0.996342i	$0.472765\pi$
$998$	−27900.8	−0.884954
$999$	−35142.1	−1.11296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.7		39
7.6	odd	2		2401.4.a.d.1.7		39
49.20	odd	14		49.4.e.a.8.3	✓	78
49.27	odd	14		49.4.e.a.43.3	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.3	✓	78	49.20	odd	14
49.4.e.a.43.3	yes	78	49.27	odd	14
2401.4.a.c.1.7		39	1.1	even	1	trivial
2401.4.a.d.1.7		39	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-3.93571 q^{2} +3.09696 q^{3} +7.48982 q^{4} +18.2977 q^{5} -12.1887 q^{6} +2.00794 q^{8} -17.4089 q^{9} +O(q^{10})\)	\(q-3.93571 q^{2} +3.09696 q^{3} +7.48982 q^{4} +18.2977 q^{5} -12.1887 q^{6} +2.00794 q^{8} -17.4089 q^{9} -72.0144 q^{10} +11.1264 q^{11} +23.1956 q^{12} +32.1274 q^{13} +56.6671 q^{15} -67.8212 q^{16} -68.2593 q^{17} +68.5163 q^{18} -113.492 q^{19} +137.046 q^{20} -43.7905 q^{22} +151.295 q^{23} +6.21849 q^{24} +209.805 q^{25} -126.444 q^{26} -137.532 q^{27} -183.747 q^{29} -223.025 q^{30} -167.796 q^{31} +250.861 q^{32} +34.4581 q^{33} +268.649 q^{34} -130.389 q^{36} +255.519 q^{37} +446.673 q^{38} +99.4970 q^{39} +36.7406 q^{40} +238.493 q^{41} -90.2895 q^{43} +83.3350 q^{44} -318.542 q^{45} -595.452 q^{46} -353.761 q^{47} -210.039 q^{48} -825.732 q^{50} -211.396 q^{51} +240.628 q^{52} +231.242 q^{53} +541.287 q^{54} +203.588 q^{55} -351.481 q^{57} +723.174 q^{58} -238.752 q^{59} +424.426 q^{60} -33.1087 q^{61} +660.396 q^{62} -444.747 q^{64} +587.856 q^{65} -135.617 q^{66} -505.936 q^{67} -511.249 q^{68} +468.553 q^{69} +683.159 q^{71} -34.9559 q^{72} -587.218 q^{73} -1005.65 q^{74} +649.757 q^{75} -850.037 q^{76} -391.592 q^{78} -50.1378 q^{79} -1240.97 q^{80} +44.1082 q^{81} -938.639 q^{82} -559.144 q^{83} -1248.99 q^{85} +355.353 q^{86} -569.055 q^{87} +22.3412 q^{88} +1171.00 q^{89} +1253.69 q^{90} +1133.17 q^{92} -519.656 q^{93} +1392.30 q^{94} -2076.65 q^{95} +776.905 q^{96} -5.56045 q^{97} -193.699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Introduction

L-functions

Modular forms

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Database

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