LMFDB - Embedded newform 2401.4.a.c.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.07454 q^{2} -7.56379 q^{3} -3.69627 q^{4} +6.53935 q^{5} +15.6914 q^{6} +24.2644 q^{8} +30.2110 q^{9} +O(q^{10})$	\(q-2.07454 q^{2} -7.56379 q^{3} -3.69627 q^{4} +6.53935 q^{5} +15.6914 q^{6} +24.2644 q^{8} +30.2110 q^{9} -13.5662 q^{10} -8.40368 q^{11} +27.9578 q^{12} +91.4293 q^{13} -49.4623 q^{15} -20.7674 q^{16} +114.282 q^{17} -62.6739 q^{18} -46.8704 q^{19} -24.1712 q^{20} +17.4338 q^{22} -82.8941 q^{23} -183.531 q^{24} -82.2369 q^{25} -189.674 q^{26} -24.2870 q^{27} +146.963 q^{29} +102.612 q^{30} -148.432 q^{31} -151.032 q^{32} +63.5637 q^{33} -237.082 q^{34} -111.668 q^{36} -216.068 q^{37} +97.2347 q^{38} -691.552 q^{39} +158.674 q^{40} +210.053 q^{41} +5.30278 q^{43} +31.0623 q^{44} +197.560 q^{45} +171.967 q^{46} -183.454 q^{47} +157.080 q^{48} +170.604 q^{50} -864.403 q^{51} -337.948 q^{52} -83.9016 q^{53} +50.3845 q^{54} -54.9546 q^{55} +354.518 q^{57} -304.880 q^{58} -554.273 q^{59} +182.826 q^{60} -328.452 q^{61} +307.928 q^{62} +479.463 q^{64} +597.888 q^{65} -131.866 q^{66} +362.660 q^{67} -422.416 q^{68} +626.994 q^{69} +586.467 q^{71} +733.051 q^{72} -369.093 q^{73} +448.242 q^{74} +622.023 q^{75} +173.246 q^{76} +1434.65 q^{78} -714.661 q^{79} -135.805 q^{80} -631.994 q^{81} -435.763 q^{82} -1250.48 q^{83} +747.328 q^{85} -11.0008 q^{86} -1111.59 q^{87} -203.910 q^{88} +1167.95 q^{89} -409.847 q^{90} +306.399 q^{92} +1122.71 q^{93} +380.583 q^{94} -306.502 q^{95} +1142.38 q^{96} -1210.74 q^{97} -253.883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.07454	−0.733462	−0.366731	−	0.930327i	$-0.619523\pi$
$2$	−2.07454	−0.733462	−0.366731	+	0.930327i	$0.619523\pi$
$3$	−7.56379	−1.45565	−0.727826	−	0.685762i	$-0.759469\pi$
$3$	−7.56379	−1.45565	−0.727826	+	0.685762i	$0.759469\pi$
$4$	−3.69627	−0.462034
$5$	6.53935	0.584897	0.292449	−	0.956281i	$-0.405530\pi$
$5$	6.53935	0.584897	0.292449	+	0.956281i	$0.405530\pi$
$6$	15.6914	1.06767
$7$	0	0
$7$	0	0
$8$	24.2644	1.07235
$9$	30.2110	1.11892
$10$	−13.5662	−0.429000
$11$	−8.40368	−0.230346	−0.115173	−	0.993345i	$-0.536742\pi$
$11$	−8.40368	−0.230346	−0.115173	+	0.993345i	$0.536742\pi$
$12$	27.9578	0.672561
$13$	91.4293	1.95061	0.975305	−	0.220864i	$-0.0708876\pi$
$13$	91.4293	1.95061	0.975305	+	0.220864i	$0.0708876\pi$
$14$	0	0
$15$	−49.4623	−0.851407
$16$	−20.7674	−0.324491
$17$	114.282	1.63043	0.815217	−	0.579155i	$-0.196618\pi$
$17$	114.282	1.63043	0.815217	+	0.579155i	$0.196618\pi$
$18$	−62.6739	−0.820688
$19$	−46.8704	−0.565937	−0.282969	−	0.959129i	$-0.591319\pi$
$19$	−46.8704	−0.565937	−0.282969	+	0.959129i	$0.591319\pi$
$20$	−24.1712	−0.270242
$21$	0	0
$22$	17.4338	0.168950
$23$	−82.8941	−0.751505	−0.375752	−	0.926720i	$-0.622616\pi$
$23$	−82.8941	−0.751505	−0.375752	+	0.926720i	$0.622616\pi$
$24$	−183.531	−1.56096
$25$	−82.2369	−0.657895
$26$	−189.674	−1.43070
$27$	−24.2870	−0.173113
$28$	0	0
$29$	146.963	0.941044	0.470522	−	0.882388i	$-0.344066\pi$
$29$	146.963	0.941044	0.470522	+	0.882388i	$0.344066\pi$
$30$	102.612	0.624475
$31$	−148.432	−0.859972	−0.429986	−	0.902836i	$-0.641481\pi$
$31$	−148.432	−0.859972	−0.429986	+	0.902836i	$0.641481\pi$
$32$	−151.032	−0.834345
$33$	63.5637	0.335304
$34$	−237.082	−1.19586
$35$	0	0
$36$	−111.668	−0.516981
$37$	−216.068	−0.960035	−0.480018	−	0.877259i	$-0.659370\pi$
$37$	−216.068	−0.960035	−0.480018	+	0.877259i	$0.659370\pi$
$38$	97.2347	0.415093
$39$	−691.552	−2.83941
$40$	158.674	0.627212
$41$	210.053	0.800115	0.400058	−	0.916490i	$-0.368990\pi$
$41$	210.053	0.800115	0.400058	+	0.916490i	$0.368990\pi$
$42$	0	0
$43$	5.30278	0.0188062	0.00940310	−	0.999956i	$-0.497007\pi$
$43$	5.30278	0.0188062	0.00940310	+	0.999956i	$0.497007\pi$
$44$	31.0623	0.106428
$45$	197.560	0.654456
$46$	171.967	0.551200
$47$	−183.454	−0.569351	−0.284676	−	0.958624i	$-0.591886\pi$
$47$	−183.454	−0.569351	−0.284676	+	0.958624i	$0.591886\pi$
$48$	157.080	0.472345
$49$	0	0
$50$	170.604	0.482541
$51$	−864.403	−2.37335
$52$	−337.948	−0.901248
$53$	−83.9016	−0.217449	−0.108724	−	0.994072i	$-0.534677\pi$
$53$	−83.9016	−0.217449	−0.108724	+	0.994072i	$0.534677\pi$
$54$	50.3845	0.126972
$55$	−54.9546	−0.134729
$56$	0	0
$57$	354.518	0.823808
$58$	−304.880	−0.690220
$59$	−554.273	−1.22305	−0.611527	−	0.791223i	$-0.709445\pi$
$59$	−554.273	−1.22305	−0.611527	+	0.791223i	$0.709445\pi$
$60$	182.826	0.393379
$61$	−328.452	−0.689410	−0.344705	−	0.938711i	$-0.612021\pi$
$61$	−328.452	−0.689410	−0.344705	+	0.938711i	$0.612021\pi$
$62$	307.928	0.630756
$63$	0	0
$64$	479.463	0.936450
$65$	597.888	1.14091
$66$	−131.866	−0.245932
$67$	362.660	0.661282	0.330641	−	0.943757i	$-0.392735\pi$
$67$	362.660	0.661282	0.330641	+	0.943757i	$0.392735\pi$
$68$	−422.416	−0.753316
$69$	626.994	1.09393
$70$	0	0
$71$	586.467	0.980294	0.490147	−	0.871640i	$-0.336943\pi$
$71$	586.467	0.980294	0.490147	+	0.871640i	$0.336943\pi$
$72$	733.051	1.19987
$73$	−369.093	−0.591767	−0.295884	−	0.955224i	$-0.595614\pi$
$73$	−369.093	−0.591767	−0.295884	+	0.955224i	$0.595614\pi$
$74$	448.242	0.704149
$75$	622.023	0.957667
$76$	173.246	0.261482
$77$	0	0
$78$	1434.65	2.08260
$79$	−714.661	−1.01779	−0.508897	−	0.860828i	$-0.669946\pi$
$79$	−714.661	−1.01779	−0.508897	+	0.860828i	$0.669946\pi$
$80$	−135.805	−0.189794
$81$	−631.994	−0.866933
$82$	−435.763	−0.586854
$83$	−1250.48	−1.65371	−0.826855	−	0.562415i	$-0.809872\pi$
$83$	−1250.48	−1.65371	−0.826855	+	0.562415i	$0.809872\pi$
$84$	0	0
$85$	747.328	0.953637
$86$	−11.0008	−0.0137936
$87$	−1111.59	−1.36983
$88$	−203.910	−0.247010
$89$	1167.95	1.39104	0.695519	−	0.718508i	$-0.255175\pi$
$89$	1167.95	1.39104	0.695519	+	0.718508i	$0.255175\pi$
$90$	−409.847	−0.480018
$91$	0	0
$92$	306.399	0.347221
$93$	1122.71	1.25182
$94$	380.583	0.417597
$95$	−306.502	−0.331015
$96$	1142.38	1.21452
$97$	−1210.74	−1.26735	−0.633673	−	0.773601i	$-0.718453\pi$
$97$	−1210.74	−1.26735	−0.633673	+	0.773601i	$0.718453\pi$
$98$	0	0
$99$	−253.883	−0.257740
$100$	303.970	0.303970
$101$	900.857	0.887511	0.443756	−	0.896148i	$-0.353646\pi$
$101$	900.857	0.887511	0.443756	+	0.896148i	$0.353646\pi$
$102$	1793.24	1.74076
$103$	867.306	0.829692	0.414846	−	0.909892i	$-0.363836\pi$
$103$	867.306	0.829692	0.414846	+	0.909892i	$0.363836\pi$
$104$	2218.48	2.09173
$105$	0	0
$106$	174.058	0.159490
$107$	241.830	0.218492	0.109246	−	0.994015i	$-0.465156\pi$
$107$	241.830	0.218492	0.109246	+	0.994015i	$0.465156\pi$
$108$	89.7715	0.0799840
$109$	1366.64	1.20093	0.600463	−	0.799653i	$-0.294983\pi$
$109$	1366.64	1.20093	0.600463	+	0.799653i	$0.294983\pi$
$110$	114.006	0.0988183
$111$	1634.29	1.39748
$112$	0	0
$113$	551.415	0.459051	0.229526	−	0.973303i	$-0.426283\pi$
$113$	551.415	0.459051	0.229526	+	0.973303i	$0.426283\pi$
$114$	−735.463	−0.604232
$115$	−542.073	−0.439553
$116$	−543.214	−0.434794
$117$	2762.17	2.18258
$118$	1149.86	0.897064
$119$	0	0
$120$	−1200.17	−0.913003
$121$	−1260.38	−0.946941
$122$	681.388	0.505655
$123$	−1588.80	−1.16469
$124$	548.644	0.397336
$125$	−1355.19	−0.969698
$126$	0	0
$127$	−1046.07	−0.730895	−0.365447	−	0.930832i	$-0.619084\pi$
$127$	−1046.07	−0.730895	−0.365447	+	0.930832i	$0.619084\pi$
$128$	213.594	0.147494
$129$	−40.1091	−0.0273753
$130$	−1240.34	−0.836811
$131$	−402.233	−0.268269	−0.134134	−	0.990963i	$-0.542825\pi$
$131$	−402.233	−0.268269	−0.134134	+	0.990963i	$0.542825\pi$
$132$	−234.949	−0.154922
$133$	0	0
$134$	−752.353	−0.485025
$135$	−158.821	−0.101253
$136$	2772.98	1.74839
$137$	−1545.80	−0.963992	−0.481996	−	0.876173i	$-0.660088\pi$
$137$	−1545.80	−0.963992	−0.481996	+	0.876173i	$0.660088\pi$
$138$	−1300.73	−0.802356
$139$	−1426.24	−0.870301	−0.435150	−	0.900358i	$-0.643305\pi$
$139$	−1426.24	−0.870301	−0.435150	+	0.900358i	$0.643305\pi$
$140$	0	0
$141$	1387.61	0.828777
$142$	−1216.65	−0.719008
$143$	−768.342	−0.449315
$144$	−627.403	−0.363080
$145$	961.040	0.550414
$146$	765.698	0.434039
$147$	0	0
$148$	798.645	0.443569
$149$	337.916	0.185793	0.0928965	−	0.995676i	$-0.470387\pi$
$149$	337.916	0.185793	0.0928965	+	0.995676i	$0.470387\pi$
$150$	−1290.41	−0.702412
$151$	3312.97	1.78547	0.892735	−	0.450581i	$-0.148783\pi$
$151$	3312.97	1.78547	0.892735	+	0.450581i	$0.148783\pi$
$152$	−1137.28	−0.606881
$153$	3452.56	1.82433
$154$	0	0
$155$	−970.647	−0.502995
$156$	2556.17	1.31190
$157$	1781.50	0.905599	0.452799	−	0.891612i	$-0.350425\pi$
$157$	1781.50	0.905599	0.452799	+	0.891612i	$0.350425\pi$
$158$	1482.60	0.746512
$159$	634.615	0.316530
$160$	−987.654	−0.488006
$161$	0	0
$162$	1311.10	0.635862
$163$	−3670.72	−1.76388	−0.881941	−	0.471359i	$-0.843764\pi$
$163$	−3670.72	−1.76388	−0.881941	+	0.471359i	$0.843764\pi$
$164$	−776.412	−0.369681
$165$	415.665	0.196118
$166$	2594.17	1.21293
$167$	−1800.21	−0.834160	−0.417080	−	0.908870i	$-0.636946\pi$
$167$	−1800.21	−0.834160	−0.417080	+	0.908870i	$0.636946\pi$
$168$	0	0
$169$	6162.31	2.80488
$170$	−1550.36	−0.699456
$171$	−1416.00	−0.633241
$172$	−19.6005	−0.00868910
$173$	3771.86	1.65762	0.828812	−	0.559527i	$-0.189017\pi$
$173$	3771.86	1.65762	0.828812	+	0.559527i	$0.189017\pi$
$174$	2306.05	1.00472
$175$	0	0
$176$	174.523	0.0747451
$177$	4192.41	1.78034
$178$	−2422.96	−1.02027
$179$	1704.39	0.711688	0.355844	−	0.934545i	$-0.384193\pi$
$179$	1704.39	0.711688	0.355844	+	0.934545i	$0.384193\pi$
$180$	−730.236	−0.302381
$181$	−3314.29	−1.36105	−0.680523	−	0.732727i	$-0.738247\pi$
$181$	−3314.29	−1.36105	−0.680523	+	0.732727i	$0.738247\pi$
$182$	0	0
$183$	2484.34	1.00354
$184$	−2011.38	−0.805873
$185$	−1412.94	−0.561522
$186$	−2329.10	−0.918162
$187$	−960.387	−0.375564
$188$	678.096	0.263060
$189$	0	0
$190$	635.852	0.242787
$191$	2602.75	0.986014	0.493007	−	0.870025i	$-0.335898\pi$
$191$	2602.75	0.986014	0.493007	+	0.870025i	$0.335898\pi$
$192$	−3626.56	−1.36315
$193$	−1809.02	−0.674694	−0.337347	−	0.941380i	$-0.609530\pi$
$193$	−1809.02	−0.674694	−0.337347	+	0.941380i	$0.609530\pi$
$194$	2511.74	0.929549
$195$	−4522.30	−1.66076
$196$	0	0
$197$	−11.0014	−0.00397876	−0.00198938	−	0.999998i	$-0.500633\pi$
$197$	−11.0014	−0.00397876	−0.00198938	+	0.999998i	$0.500633\pi$
$198$	526.692	0.189042
$199$	166.785	0.0594124	0.0297062	−	0.999559i	$-0.490543\pi$
$199$	166.785	0.0594124	0.0297062	+	0.999559i	$0.490543\pi$
$200$	−1995.43	−0.705491
$201$	−2743.08	−0.962597
$202$	−1868.87	−0.650955
$203$	0	0
$204$	3195.07	1.09657
$205$	1373.61	0.467985
$206$	−1799.26	−0.608547
$207$	−2504.31	−0.840877
$208$	−1898.75	−0.632954
$209$	393.884	0.130361
$210$	0	0
$211$	−17.8394	−0.00582046	−0.00291023	−	0.999996i	$-0.500926\pi$
$211$	−17.8394	−0.00582046	−0.00291023	+	0.999996i	$0.500926\pi$
$212$	310.123	0.100469
$213$	−4435.92	−1.42697
$214$	−501.688	−0.160255
$215$	34.6767	0.0109997
$216$	−589.311	−0.185637
$217$	0	0
$218$	−2835.16	−0.880832
$219$	2791.74	0.861408
$220$	203.127	0.0622492
$221$	10448.7	3.18034
$222$	−3390.41	−1.02500
$223$	2185.49	0.656284	0.328142	−	0.944628i	$-0.393578\pi$
$223$	2185.49	0.656284	0.328142	+	0.944628i	$0.393578\pi$
$224$	0	0
$225$	−2484.46	−0.736135
$226$	−1143.93	−0.336697
$227$	3227.55	0.943700	0.471850	−	0.881679i	$-0.343586\pi$
$227$	3227.55	0.943700	0.471850	+	0.881679i	$0.343586\pi$
$228$	−1310.40	−0.380627
$229$	−2694.41	−0.777517	−0.388758	−	0.921340i	$-0.627096\pi$
$229$	−2694.41	−0.777517	−0.388758	+	0.921340i	$0.627096\pi$
$230$	1124.55	0.322395
$231$	0	0
$232$	3565.96	1.00912
$233$	−1080.66	−0.303848	−0.151924	−	0.988392i	$-0.548547\pi$
$233$	−1080.66	−0.303848	−0.151924	+	0.988392i	$0.548547\pi$
$234$	−5730.23	−1.60084
$235$	−1199.67	−0.333012
$236$	2048.74	0.565093
$237$	5405.55	1.48155
$238$	0	0
$239$	−1489.11	−0.403022	−0.201511	−	0.979486i	$-0.564585\pi$
$239$	−1489.11	−0.403022	−0.201511	+	0.979486i	$0.564585\pi$
$240$	1027.20	0.276274
$241$	−633.713	−0.169382	−0.0846910	−	0.996407i	$-0.526990\pi$
$241$	−633.713	−0.169382	−0.0846910	+	0.996407i	$0.526990\pi$
$242$	2614.71	0.694545
$243$	5436.02	1.43507
$244$	1214.05	0.318531
$245$	0	0
$246$	3296.02	0.854255
$247$	−4285.33	−1.10392
$248$	−3601.61	−0.922187
$249$	9458.37	2.40723
$250$	2811.41	0.711237
$251$	−1725.00	−0.433789	−0.216895	−	0.976195i	$-0.569593\pi$
$251$	−1725.00	−0.433789	−0.216895	+	0.976195i	$0.569593\pi$
$252$	0	0
$253$	696.615	0.173106
$254$	2170.12	0.536083
$255$	−5652.63	−1.38816
$256$	−4278.81	−1.04463
$257$	−631.459	−0.153266	−0.0766330	−	0.997059i	$-0.524417\pi$
$257$	−631.459	−0.153266	−0.0766330	+	0.997059i	$0.524417\pi$
$258$	83.2081	0.0200787
$259$	0	0
$260$	−2209.96	−0.527137
$261$	4439.88	1.05296
$262$	834.449	0.196765
$263$	−318.169	−0.0745976	−0.0372988	−	0.999304i	$-0.511875\pi$
$263$	−318.169	−0.0745976	−0.0372988	+	0.999304i	$0.511875\pi$
$264$	1542.34	0.359561
$265$	−548.662	−0.127185
$266$	0	0
$267$	−8834.12	−2.02487
$268$	−1340.49	−0.305535
$269$	−3670.08	−0.831854	−0.415927	−	0.909398i	$-0.636543\pi$
$269$	−3670.08	−0.831854	−0.415927	+	0.909398i	$0.636543\pi$
$270$	329.482	0.0742653
$271$	−791.880	−0.177503	−0.0887515	−	0.996054i	$-0.528288\pi$
$271$	−791.880	−0.177503	−0.0887515	+	0.996054i	$0.528288\pi$
$272$	−2373.33	−0.529060
$273$	0	0
$274$	3206.83	0.707051
$275$	691.093	0.151543
$276$	−2317.54	−0.505433
$277$	5264.93	1.14202	0.571009	−	0.820944i	$-0.306552\pi$
$277$	5264.93	1.14202	0.571009	+	0.820944i	$0.306552\pi$
$278$	2958.79	0.638332
$279$	−4484.27	−0.962244
$280$	0	0
$281$	−8453.37	−1.79461	−0.897306	−	0.441409i	$-0.854479\pi$
$281$	−8453.37	−1.79461	−0.897306	+	0.441409i	$0.854479\pi$
$282$	−2878.65	−0.607877
$283$	−8151.83	−1.71228	−0.856141	−	0.516742i	$-0.827145\pi$
$283$	−8151.83	−1.71228	−0.856141	+	0.516742i	$0.827145\pi$
$284$	−2167.74	−0.452929
$285$	2318.32	0.481843
$286$	1593.96	0.329555
$287$	0	0
$288$	−4562.84	−0.933568
$289$	8147.31	1.65832
$290$	−1993.72	−0.403708
$291$	9157.82	1.84481
$292$	1364.27	0.273417
$293$	1115.42	0.222401	0.111201	−	0.993798i	$-0.464530\pi$
$293$	1115.42	0.222401	0.111201	+	0.993798i	$0.464530\pi$
$294$	0	0
$295$	−3624.59	−0.715361
$296$	−5242.76	−1.02949
$297$	204.101	0.0398758
$298$	−701.021	−0.136272
$299$	−7578.95	−1.46589
$300$	−2299.17	−0.442475
$301$	0	0
$302$	−6872.91	−1.30957
$303$	−6813.90	−1.29191
$304$	973.376	0.183641
$305$	−2147.86	−0.403234
$306$	−7162.48	−1.33808
$307$	−6836.09	−1.27087	−0.635433	−	0.772156i	$-0.719178\pi$
$307$	−6836.09	−1.27087	−0.635433	+	0.772156i	$0.719178\pi$
$308$	0	0
$309$	−6560.13	−1.20774
$310$	2013.65	0.368928
$311$	1361.00	0.248152	0.124076	−	0.992273i	$-0.460403\pi$
$311$	1361.00	0.248152	0.124076	+	0.992273i	$0.460403\pi$
$312$	−16780.1	−3.04483
$313$	−260.048	−0.0469610	−0.0234805	−	0.999724i	$-0.507475\pi$
$313$	−260.048	−0.0469610	−0.0234805	+	0.999724i	$0.507475\pi$
$314$	−3695.79	−0.664222
$315$	0	0
$316$	2641.58	0.470255
$317$	8847.24	1.56754	0.783771	−	0.621050i	$-0.213294\pi$
$317$	8847.24	1.56754	0.783771	+	0.621050i	$0.213294\pi$
$318$	−1316.53	−0.232162
$319$	−1235.03	−0.216766
$320$	3135.37	0.547727
$321$	−1829.16	−0.318048
$322$	0	0
$323$	−5356.43	−0.922724
$324$	2336.02	0.400552
$325$	−7518.86	−1.28330
$326$	7615.06	1.29374
$327$	−10337.0	−1.74813
$328$	5096.81	0.858000
$329$	0	0
$330$	−862.315	−0.143845
$331$	5714.03	0.948857	0.474428	−	0.880294i	$-0.342655\pi$
$331$	5714.03	0.948857	0.474428	+	0.880294i	$0.342655\pi$
$332$	4622.11	0.764070
$333$	−6527.61	−1.07421
$334$	3734.62	0.611824
$335$	2371.56	0.386782
$336$	0	0
$337$	−1132.57	−0.183071	−0.0915357	−	0.995802i	$-0.529178\pi$
$337$	−1132.57	−0.183071	−0.0915357	+	0.995802i	$0.529178\pi$
$338$	−12784.0	−2.05727
$339$	−4170.79	−0.668219
$340$	−2762.33	−0.440613
$341$	1247.37	0.198091
$342$	2937.55	0.464458
$343$	0	0
$344$	128.669	0.0201667
$345$	4100.13	0.639837
$346$	−7824.88	−1.21580
$347$	−10513.8	−1.62654	−0.813270	−	0.581887i	$-0.802315\pi$
$347$	−10513.8	−1.62654	−0.813270	+	0.581887i	$0.802315\pi$
$348$	4108.76	0.632909
$349$	−8551.16	−1.31156	−0.655778	−	0.754954i	$-0.727659\pi$
$349$	−8551.16	−1.31156	−0.655778	+	0.754954i	$0.727659\pi$
$350$	0	0
$351$	−2220.55	−0.337675
$352$	1269.23	0.192188
$353$	−10386.6	−1.56607	−0.783034	−	0.621978i	$-0.786329\pi$
$353$	−10386.6	−1.56607	−0.783034	+	0.621978i	$0.786329\pi$
$354$	−8697.33	−1.30581
$355$	3835.11	0.573371
$356$	−4317.06	−0.642707
$357$	0	0
$358$	−3535.83	−0.521996
$359$	6645.98	0.977051	0.488526	−	0.872550i	$-0.337535\pi$
$359$	6645.98	0.977051	0.488526	+	0.872550i	$0.337535\pi$
$360$	4793.68	0.701803
$361$	−4662.16	−0.679715
$362$	6875.64	0.998275
$363$	9533.24	1.37842
$364$	0	0
$365$	−2413.63	−0.346123
$366$	−5153.88	−0.736059
$367$	524.741	0.0746355	0.0373178	−	0.999303i	$-0.488119\pi$
$367$	524.741	0.0746355	0.0373178	+	0.999303i	$0.488119\pi$
$368$	1721.49	0.243856
$369$	6345.90	0.895269
$370$	2931.21	0.411855
$371$	0	0
$372$	−4149.83	−0.578384
$373$	−10708.2	−1.48646	−0.743228	−	0.669038i	$-0.766706\pi$
$373$	−10708.2	−1.48646	−0.743228	+	0.669038i	$0.766706\pi$
$374$	1992.36	0.275462
$375$	10250.4	1.41154
$376$	−4451.40	−0.610541
$377$	13436.7	1.83561
$378$	0	0
$379$	−3522.69	−0.477437	−0.238719	−	0.971089i	$-0.576727\pi$
$379$	−3522.69	−0.477437	−0.238719	+	0.971089i	$0.576727\pi$
$380$	1132.92	0.152940
$381$	7912.25	1.06393
$382$	−5399.52	−0.723203
$383$	393.288	0.0524702	0.0262351	−	0.999656i	$-0.491648\pi$
$383$	393.288	0.0524702	0.0262351	+	0.999656i	$0.491648\pi$
$384$	−1615.58	−0.214700
$385$	0	0
$386$	3752.88	0.494862
$387$	160.202	0.0210427
$388$	4475.24	0.585557
$389$	−10262.2	−1.33757	−0.668784	−	0.743457i	$-0.733185\pi$
$389$	−10262.2	−1.33757	−0.668784	+	0.743457i	$0.733185\pi$
$390$	9381.71	1.21811
$391$	−9473.28	−1.22528
$392$	0	0
$393$	3042.40	0.390506
$394$	22.8228	0.00291827
$395$	−4673.42	−0.595305
$396$	938.422	0.119084
$397$	−2302.60	−0.291094	−0.145547	−	0.989351i	$-0.546494\pi$
$397$	−2302.60	−0.291094	−0.145547	+	0.989351i	$0.546494\pi$
$398$	−346.002	−0.0435767
$399$	0	0
$400$	1707.85	0.213481
$401$	−3181.74	−0.396230	−0.198115	−	0.980179i	$-0.563482\pi$
$401$	−3181.74	−0.396230	−0.198115	+	0.980179i	$0.563482\pi$
$402$	5690.64	0.706028
$403$	−13571.0	−1.67747
$404$	−3329.81	−0.410060
$405$	−4132.83	−0.507067
$406$	0	0
$407$	1815.76	0.221140
$408$	−20974.2	−2.54505
$409$	−1418.50	−0.171492	−0.0857459	−	0.996317i	$-0.527327\pi$
$409$	−1418.50	−0.171492	−0.0857459	+	0.996317i	$0.527327\pi$
$410$	−2849.61	−0.343249
$411$	11692.1	1.40324
$412$	−3205.80	−0.383346
$413$	0	0
$414$	5195.30	0.616751
$415$	−8177.32	−0.967251
$416$	−13808.8	−1.62748
$417$	10787.8	1.26686
$418$	−817.129	−0.0956151
$419$	5887.58	0.686461	0.343231	−	0.939251i	$-0.388479\pi$
$419$	5887.58	0.686461	0.343231	+	0.939251i	$0.388479\pi$
$420$	0	0
$421$	10540.7	1.22024	0.610121	−	0.792308i	$-0.291121\pi$
$421$	10540.7	1.22024	0.610121	+	0.792308i	$0.291121\pi$
$422$	37.0087	0.00426909
$423$	−5542.32	−0.637061
$424$	−2035.82	−0.233180
$425$	−9398.17	−1.07265
$426$	9202.50	1.04663
$427$	0	0
$428$	−893.871	−0.100951
$429$	5811.58	0.654046
$430$	−71.9384	−0.00806785
$431$	9150.95	1.02270	0.511352	−	0.859371i	$-0.329145\pi$
$431$	9150.95	1.02270	0.511352	+	0.859371i	$0.329145\pi$
$432$	504.379	0.0561734
$433$	2197.22	0.243861	0.121930	−	0.992539i	$-0.461092\pi$
$433$	2197.22	0.243861	0.121930	+	0.992539i	$0.461092\pi$
$434$	0	0
$435$	−7269.11	−0.801212
$436$	−5051.49	−0.554868
$437$	3885.28	0.425305
$438$	−5791.58	−0.631810
$439$	10774.2	1.17135	0.585675	−	0.810546i	$-0.300830\pi$
$439$	10774.2	1.17135	0.585675	+	0.810546i	$0.300830\pi$
$440$	−1333.44	−0.144476
$441$	0	0
$442$	−21676.3	−2.33266
$443$	10195.0	1.09340	0.546702	−	0.837327i	$-0.315883\pi$
$443$	10195.0	1.09340	0.546702	+	0.837327i	$0.315883\pi$
$444$	−6040.78	−0.645682
$445$	7637.63	0.813614
$446$	−4533.89	−0.481359
$447$	−2555.93	−0.270450
$448$	0	0
$449$	9496.70	0.998167	0.499084	−	0.866554i	$-0.333670\pi$
$449$	9496.70	0.998167	0.499084	+	0.866554i	$0.333670\pi$
$450$	5154.11	0.539927
$451$	−1765.22	−0.184303
$452$	−2038.18	−0.212097
$453$	−25058.7	−2.59902
$454$	−6695.69	−0.692168
$455$	0	0
$456$	8602.17	0.883407
$457$	11967.2	1.22495	0.612477	−	0.790488i	$-0.290173\pi$
$457$	11967.2	1.22495	0.612477	+	0.790488i	$0.290173\pi$
$458$	5589.66	0.570279
$459$	−2775.56	−0.282249
$460$	2003.65	0.203088
$461$	−18749.3	−1.89423	−0.947116	−	0.320893i	$-0.896017\pi$
$461$	−18749.3	−1.89423	−0.947116	+	0.320893i	$0.896017\pi$
$462$	0	0
$463$	−14442.8	−1.44971	−0.724853	−	0.688903i	$-0.758092\pi$
$463$	−14442.8	−1.44971	−0.724853	+	0.688903i	$0.758092\pi$
$464$	−3052.03	−0.305360
$465$	7341.78	0.732186
$466$	2241.88	0.222861
$467$	1948.19	0.193044	0.0965218	−	0.995331i	$-0.469228\pi$
$467$	1948.19	0.193044	0.0965218	+	0.995331i	$0.469228\pi$
$468$	−10209.7	−1.00843
$469$	0	0
$470$	2488.77	0.244252
$471$	−13474.9	−1.31824
$472$	−13449.1	−1.31154
$473$	−44.5629	−0.00433193
$474$	−11214.0	−1.08666
$475$	3854.48	0.372327
$476$	0	0
$477$	−2534.75	−0.243309
$478$	3089.21	0.295601
$479$	−14900.9	−1.42137	−0.710686	−	0.703509i	$-0.751615\pi$
$479$	−14900.9	−1.42137	−0.710686	+	0.703509i	$0.751615\pi$
$480$	7470.41	0.710367
$481$	−19754.9	−1.87265
$482$	1314.66	0.124235
$483$	0	0
$484$	4658.70	0.437519
$485$	−7917.49	−0.741267
$486$	−11277.3	−1.05257
$487$	284.500	0.0264721	0.0132361	−	0.999912i	$-0.495787\pi$
$487$	284.500	0.0264721	0.0132361	+	0.999912i	$0.495787\pi$
$488$	−7969.70	−0.739285
$489$	27764.6	2.56760
$490$	0	0
$491$	3697.12	0.339814	0.169907	−	0.985460i	$-0.445653\pi$
$491$	3697.12	0.339814	0.169907	+	0.985460i	$0.445653\pi$
$492$	5872.62	0.538126
$493$	16795.1	1.53431
$494$	8890.10	0.809685
$495$	−1660.23	−0.150751
$496$	3082.54	0.279053
$497$	0	0
$498$	−19621.8	−1.76561
$499$	−17743.1	−1.59176	−0.795882	−	0.605451i	$-0.792993\pi$
$499$	−17743.1	−1.59176	−0.795882	+	0.605451i	$0.792993\pi$
$500$	5009.17	0.448034
$501$	13616.4	1.21425
$502$	3578.59	0.318168
$503$	10055.9	0.891395	0.445698	−	0.895184i	$-0.352956\pi$
$503$	10055.9	0.891395	0.445698	+	0.895184i	$0.352956\pi$
$504$	0	0
$505$	5891.02	0.519103
$506$	−1445.16	−0.126967
$507$	−46610.5	−4.08293
$508$	3866.56	0.337698
$509$	−3080.10	−0.268218	−0.134109	−	0.990967i	$-0.542817\pi$
$509$	−3080.10	−0.268218	−0.134109	+	0.990967i	$0.542817\pi$
$510$	11726.6	1.01816
$511$	0	0
$512$	7167.82	0.618703
$513$	1138.34	0.0979710
$514$	1309.99	0.112415
$515$	5671.62	0.485284
$516$	148.254	0.0126483
$517$	1541.69	0.131148
$518$	0	0
$519$	−28529.6	−2.41293
$520$	14507.4	1.22345
$521$	14546.6	1.22322	0.611612	−	0.791158i	$-0.290522\pi$
$521$	14546.6	1.22322	0.611612	+	0.791158i	$0.290522\pi$
$522$	−9210.72	−0.772304
$523$	−6580.46	−0.550179	−0.275089	−	0.961419i	$-0.588707\pi$
$523$	−6580.46	−0.550179	−0.275089	+	0.961419i	$0.588707\pi$
$524$	1486.76	0.123949
$525$	0	0
$526$	660.056	0.0547145
$527$	−16963.0	−1.40213
$528$	−1320.05	−0.108803
$529$	−5295.57	−0.435241
$530$	1138.22	0.0932854
$531$	−16745.1	−1.36851
$532$	0	0
$533$	19205.0	1.56071
$534$	18326.8	1.48516
$535$	1581.41	0.127795
$536$	8799.72	0.709123
$537$	−12891.7	−1.03597
$538$	7613.73	0.610133
$539$	0	0
$540$	587.047	0.0467824
$541$	−6460.51	−0.513418	−0.256709	−	0.966489i	$-0.582638\pi$
$541$	−6460.51	−0.513418	−0.256709	+	0.966489i	$0.582638\pi$
$542$	1642.79	0.130192
$543$	25068.6	1.98121
$544$	−17260.2	−1.36034
$545$	8936.97	0.702418
$546$	0	0
$547$	4861.18	0.379980	0.189990	−	0.981786i	$-0.439154\pi$
$547$	4861.18	0.379980	0.189990	+	0.981786i	$0.439154\pi$
$548$	5713.71	0.445397
$549$	−9922.85	−0.771397
$550$	−1433.70	−0.111151
$551$	−6888.20	−0.532572
$552$	15213.6	1.17307
$553$	0	0
$554$	−10922.3	−0.837627
$555$	10687.2	0.817381
$556$	5271.76	0.402109
$557$	−914.583	−0.0695730	−0.0347865	−	0.999395i	$-0.511075\pi$
$557$	−914.583	−0.0695730	−0.0347865	+	0.999395i	$0.511075\pi$
$558$	9302.80	0.705769
$559$	484.829	0.0366835
$560$	0	0
$561$	7264.17	0.546690
$562$	17536.9	1.31628
$563$	11944.8	0.894159	0.447080	−	0.894494i	$-0.352464\pi$
$563$	11944.8	0.894159	0.447080	+	0.894494i	$0.352464\pi$
$564$	−5128.97	−0.382923
$565$	3605.90	0.268498
$566$	16911.3	1.25589
$567$	0	0
$568$	14230.3	1.05121
$569$	2883.12	0.212420	0.106210	−	0.994344i	$-0.466128\pi$
$569$	2883.12	0.212420	0.106210	+	0.994344i	$0.466128\pi$
$570$	−4809.45	−0.353414
$571$	10891.5	0.798241	0.399120	−	0.916899i	$-0.369316\pi$
$571$	10891.5	0.798241	0.399120	+	0.916899i	$0.369316\pi$
$572$	2840.00	0.207599
$573$	−19686.7	−1.43529
$574$	0	0
$575$	6816.95	0.494411
$576$	14485.0	1.04782
$577$	−1506.90	−0.108723	−0.0543614	−	0.998521i	$-0.517312\pi$
$577$	−1506.90	−0.108723	−0.0543614	+	0.998521i	$0.517312\pi$
$578$	−16901.9	−1.21631
$579$	13683.0	0.982120
$580$	−3552.27	−0.254310
$581$	0	0
$582$	−18998.3	−1.35310
$583$	705.082	0.0500884
$584$	−8955.82	−0.634579
$585$	18062.8	1.27659
$586$	−2313.99	−0.163123
$587$	−6284.62	−0.441898	−0.220949	−	0.975285i	$-0.570915\pi$
$587$	−6284.62	−0.441898	−0.220949	+	0.975285i	$0.570915\pi$
$588$	0	0
$589$	6957.06	0.486690
$590$	7519.36	0.524690
$591$	83.2122	0.00579170
$592$	4487.16	0.311522
$593$	−3538.29	−0.245026	−0.122513	−	0.992467i	$-0.539095\pi$
$593$	−3538.29	−0.245026	−0.122513	+	0.992467i	$0.539095\pi$
$594$	−423.415	−0.0292474
$595$	0	0
$596$	−1249.03	−0.0858427
$597$	−1261.53	−0.0864838
$598$	15722.8	1.07518
$599$	12860.6	0.877243	0.438622	−	0.898672i	$-0.355467\pi$
$599$	12860.6	0.877243	0.438622	+	0.898672i	$0.355467\pi$
$600$	15093.0	1.02695
$601$	7937.34	0.538721	0.269360	−	0.963039i	$-0.413188\pi$
$601$	7937.34	0.538721	0.269360	+	0.963039i	$0.413188\pi$
$602$	0	0
$603$	10956.3	0.739925
$604$	−12245.7	−0.824948
$605$	−8242.06	−0.553863
$606$	14135.7	0.947565
$607$	−22918.5	−1.53251	−0.766255	−	0.642537i	$-0.777882\pi$
$607$	−22918.5	−1.53251	−0.766255	+	0.642537i	$0.777882\pi$
$608$	7078.96	0.472187
$609$	0	0
$610$	4455.83	0.295757
$611$	−16773.1	−1.11058
$612$	−12761.6	−0.842904
$613$	23252.8	1.53209	0.766046	−	0.642786i	$-0.222221\pi$
$613$	23252.8	1.53209	0.766046	+	0.642786i	$0.222221\pi$
$614$	14181.8	0.932132
$615$	−10389.7	−0.681224
$616$	0	0
$617$	20195.3	1.31772	0.658861	−	0.752265i	$-0.271039\pi$
$617$	20195.3	1.31772	0.658861	+	0.752265i	$0.271039\pi$
$618$	13609.3	0.885833
$619$	2442.15	0.158576	0.0792878	−	0.996852i	$-0.474735\pi$
$619$	2442.15	0.158576	0.0792878	+	0.996852i	$0.474735\pi$
$620$	3587.78	0.232401
$621$	2013.25	0.130095
$622$	−2823.45	−0.182010
$623$	0	0
$624$	14361.7	0.921362
$625$	1417.52	0.0907211
$626$	539.481	0.0344441
$627$	−2979.26	−0.189761
$628$	−6584.90	−0.418418
$629$	−24692.6	−1.56527
$630$	0	0
$631$	−8011.55	−0.505443	−0.252722	−	0.967539i	$-0.581326\pi$
$631$	−8011.55	−0.505443	−0.252722	+	0.967539i	$0.581326\pi$
$632$	−17340.8	−1.09143
$633$	134.934	0.00847257
$634$	−18354.0	−1.14973
$635$	−6840.62	−0.427498
$636$	−2345.71	−0.146247
$637$	0	0
$638$	2562.12	0.158989
$639$	17717.7	1.09687
$640$	1396.77	0.0862690
$641$	−2508.93	−0.154597	−0.0772986	−	0.997008i	$-0.524629\pi$
$641$	−2508.93	−0.154597	−0.0772986	+	0.997008i	$0.524629\pi$
$642$	3794.66	0.233276
$643$	−8970.56	−0.550178	−0.275089	−	0.961419i	$-0.588707\pi$
$643$	−8970.56	−0.550178	−0.275089	+	0.961419i	$0.588707\pi$
$644$	0	0
$645$	−262.288	−0.0160117
$646$	11112.1	0.676782
$647$	−7418.05	−0.450747	−0.225374	−	0.974272i	$-0.572360\pi$
$647$	−7418.05	−0.450747	−0.225374	+	0.974272i	$0.572360\pi$
$648$	−15335.0	−0.929651
$649$	4657.93	0.281726
$650$	15598.2	0.941249
$651$	0	0
$652$	13568.0	0.814974
$653$	−403.130	−0.0241588	−0.0120794	−	0.999927i	$-0.503845\pi$
$653$	−403.130	−0.0241588	−0.0120794	+	0.999927i	$0.503845\pi$
$654$	21444.6	1.28219
$655$	−2630.34	−0.156910
$656$	−4362.25	−0.259630
$657$	−11150.6	−0.662143
$658$	0	0
$659$	30749.9	1.81767	0.908835	−	0.417156i	$-0.136973\pi$
$659$	30749.9	1.81767	0.908835	+	0.417156i	$0.136973\pi$
$660$	−1536.41	−0.0906133
$661$	−19037.3	−1.12022	−0.560111	−	0.828418i	$-0.689241\pi$
$661$	−19037.3	−1.12022	−0.560111	+	0.828418i	$0.689241\pi$
$662$	−11854.0	−0.695950
$663$	−79031.8	−4.62947
$664$	−30342.2	−1.77335
$665$	0	0
$666$	13541.8	0.787890
$667$	−12182.3	−0.707199
$668$	6654.08	0.385410
$669$	−16530.6	−0.955321
$670$	−4919.90	−0.283690
$671$	2760.21	0.158803
$672$	0	0
$673$	−3237.24	−0.185418	−0.0927090	−	0.995693i	$-0.529553\pi$
$673$	−3237.24	−0.185418	−0.0927090	+	0.995693i	$0.529553\pi$
$674$	2349.57	0.134276
$675$	1997.29	0.113890
$676$	−22777.6	−1.29595
$677$	1857.69	0.105461	0.0527304	−	0.998609i	$-0.483208\pi$
$677$	1857.69	0.105461	0.0527304	+	0.998609i	$0.483208\pi$
$678$	8652.49	0.490113
$679$	0	0
$680$	18133.5	1.02263
$681$	−24412.5	−1.37370
$682$	−2587.73	−0.145292
$683$	14382.7	0.805766	0.402883	−	0.915251i	$-0.368008\pi$
$683$	14382.7	0.805766	0.402883	+	0.915251i	$0.368008\pi$
$684$	5233.92	0.292579
$685$	−10108.5	−0.563836
$686$	0	0
$687$	20379.9	1.13179
$688$	−110.125	−0.00610243
$689$	−7671.07	−0.424157
$690$	−8505.90	−0.469296
$691$	9836.11	0.541510	0.270755	−	0.962648i	$-0.412727\pi$
$691$	9836.11	0.541510	0.270755	+	0.962648i	$0.412727\pi$
$692$	−13941.8	−0.765879
$693$	0	0
$694$	21811.3	1.19300
$695$	−9326.66	−0.509037
$696$	−26972.2	−1.46893
$697$	24005.2	1.30454
$698$	17739.7	0.961976
$699$	8173.92	0.442297
$700$	0	0
$701$	−2247.39	−0.121088	−0.0605440	−	0.998166i	$-0.519284\pi$
$701$	−2247.39	−0.121088	−0.0605440	+	0.998166i	$0.519284\pi$
$702$	4606.62	0.247672
$703$	10127.2	0.543320
$704$	−4029.25	−0.215707
$705$	9074.05	0.484750
$706$	21547.4	1.14865
$707$	0	0
$708$	−15496.3	−0.822579
$709$	3934.15	0.208392	0.104196	−	0.994557i	$-0.466773\pi$
$709$	3934.15	0.208392	0.104196	+	0.994557i	$0.466773\pi$
$710$	−7956.11	−0.420546
$711$	−21590.6	−1.13883
$712$	28339.6	1.49167
$713$	12304.1	0.646273
$714$	0	0
$715$	−5024.46	−0.262803
$716$	−6299.89	−0.328824
$717$	11263.3	0.586660
$718$	−13787.4	−0.716630
$719$	17106.3	0.887283	0.443641	−	0.896204i	$-0.353686\pi$
$719$	17106.3	0.887283	0.443641	+	0.896204i	$0.353686\pi$
$720$	−4102.81	−0.212365
$721$	0	0
$722$	9671.86	0.498545
$723$	4793.27	0.246561
$724$	12250.5	0.628849
$725$	−12085.7	−0.619108
$726$	−19777.1	−1.01102
$727$	13467.7	0.687053	0.343527	−	0.939143i	$-0.388378\pi$
$727$	13467.7	0.687053	0.343527	+	0.939143i	$0.388378\pi$
$728$	0	0
$729$	−24053.1	−1.22202
$730$	5007.17	0.253868
$731$	606.011	0.0306623
$732$	−9182.81	−0.463670
$733$	25838.5	1.30200	0.650999	−	0.759078i	$-0.274350\pi$
$733$	25838.5	1.30200	0.650999	+	0.759078i	$0.274350\pi$
$734$	−1088.60	−0.0547423
$735$	0	0
$736$	12519.7	0.627014
$737$	−3047.67	−0.152324
$738$	−13164.8	−0.656645
$739$	−15022.9	−0.747801	−0.373900	−	0.927469i	$-0.621980\pi$
$739$	−15022.9	−0.747801	−0.373900	+	0.927469i	$0.621980\pi$
$740$	5222.62	0.259442
$741$	32413.3	1.60693
$742$	0	0
$743$	25755.6	1.27171	0.635855	−	0.771808i	$-0.280647\pi$
$743$	25755.6	1.27171	0.635855	+	0.771808i	$0.280647\pi$
$744$	27241.8	1.34238
$745$	2209.75	0.108670
$746$	22214.6	1.09026
$747$	−37778.2	−1.85038
$748$	3549.85	0.173523
$749$	0	0
$750$	−21264.9	−1.03531
$751$	−10026.7	−0.487191	−0.243596	−	0.969877i	$-0.578327\pi$
$751$	−10026.7	−0.487191	−0.243596	+	0.969877i	$0.578327\pi$
$752$	3809.86	0.184749
$753$	13047.5	0.631446
$754$	−27875.0	−1.34635
$755$	21664.7	1.04432
$756$	0	0
$757$	−20442.9	−0.981520	−0.490760	−	0.871295i	$-0.663281\pi$
$757$	−20442.9	−0.981520	−0.490760	+	0.871295i	$0.663281\pi$
$758$	7307.98	0.350182
$759$	−5269.05	−0.251982
$760$	−7437.09	−0.354963
$761$	9533.05	0.454104	0.227052	−	0.973883i	$-0.427091\pi$
$761$	9533.05	0.454104	0.227052	+	0.973883i	$0.427091\pi$
$762$	−16414.3	−0.780351
$763$	0	0
$764$	−9620.49	−0.455572
$765$	22577.5	1.06705
$766$	−815.893	−0.0384849
$767$	−50676.8	−2.38570
$768$	32364.0	1.52062
$769$	−11738.9	−0.550478	−0.275239	−	0.961376i	$-0.588757\pi$
$769$	−11738.9	−0.550478	−0.275239	+	0.961376i	$0.588757\pi$
$770$	0	0
$771$	4776.23	0.223102
$772$	6686.62	0.311732
$773$	−596.028	−0.0277331	−0.0138665	−	0.999904i	$-0.504414\pi$
$773$	−596.028	−0.0277331	−0.0138665	+	0.999904i	$0.504414\pi$
$774$	−332.346	−0.0154340
$775$	12206.6	0.565771
$776$	−29378.0	−1.35903
$777$	0	0
$778$	21289.4	0.981055
$779$	−9845.26	−0.452815
$780$	16715.7	0.767329
$781$	−4928.48	−0.225807
$782$	19652.7	0.898695
$783$	−3569.29	−0.162907
$784$	0	0
$785$	11649.8	0.529682
$786$	−6311.60	−0.286421
$787$	3812.88	0.172700	0.0863498	−	0.996265i	$-0.472480\pi$
$787$	3812.88	0.172700	0.0863498	+	0.996265i	$0.472480\pi$
$788$	40.6641	0.00183832
$789$	2406.57	0.108588
$790$	9695.21	0.436633
$791$	0	0
$792$	−6160.33	−0.276386
$793$	−30030.1	−1.34477
$794$	4776.84	0.213506
$795$	4149.97	0.185137
$796$	−616.482	−0.0274505
$797$	−28185.0	−1.25265	−0.626327	−	0.779561i	$-0.715442\pi$
$797$	−28185.0	−1.25265	−0.626327	+	0.779561i	$0.715442\pi$
$798$	0	0
$799$	−20965.4	−0.928290
$800$	12420.4	0.548911
$801$	35284.9	1.55647
$802$	6600.65	0.290620
$803$	3101.74	0.136311
$804$	10139.2	0.444753
$805$	0	0
$806$	28153.6	1.23036
$807$	27759.7	1.21089
$808$	21858.8	0.951719
$809$	−24087.3	−1.04680	−0.523402	−	0.852086i	$-0.675337\pi$
$809$	−24087.3	−1.04680	−0.523402	+	0.852086i	$0.675337\pi$
$810$	8573.73	0.371914
$811$	−19749.8	−0.855127	−0.427564	−	0.903985i	$-0.640628\pi$
$811$	−19749.8	−0.855127	−0.427564	+	0.903985i	$0.640628\pi$
$812$	0	0
$813$	5989.62	0.258383
$814$	−3766.88	−0.162198
$815$	−24004.1	−1.03169
$816$	17951.4	0.770128
$817$	−248.543	−0.0106431
$818$	2942.73	0.125783
$819$	0	0
$820$	−5077.23	−0.216225
$821$	2330.66	0.0990750	0.0495375	−	0.998772i	$-0.484225\pi$
$821$	2330.66	0.0990750	0.0495375	+	0.998772i	$0.484225\pi$
$822$	−24255.8	−1.02922
$823$	1891.75	0.0801243	0.0400621	−	0.999197i	$-0.487244\pi$
$823$	1891.75	0.0801243	0.0400621	+	0.999197i	$0.487244\pi$
$824$	21044.7	0.889716
$825$	−5227.28	−0.220595
$826$	0	0
$827$	18190.5	0.764869	0.382434	−	0.923983i	$-0.375086\pi$
$827$	18190.5	0.764869	0.382434	+	0.923983i	$0.375086\pi$
$828$	9256.61	0.388514
$829$	28991.4	1.21461	0.607305	−	0.794469i	$-0.292251\pi$
$829$	28991.4	1.21461	0.607305	+	0.794469i	$0.292251\pi$
$830$	16964.2	0.709441
$831$	−39822.9	−1.66238
$832$	43836.9	1.82665
$833$	0	0
$834$	−22379.7	−0.929190
$835$	−11772.2	−0.487898
$836$	−1455.90	−0.0602314
$837$	3604.97	0.148872
$838$	−12214.0	−0.503493
$839$	−25059.2	−1.03115	−0.515577	−	0.856843i	$-0.672422\pi$
$839$	−25059.2	−1.03115	−0.515577	+	0.856843i	$0.672422\pi$
$840$	0	0
$841$	−2790.99	−0.114437
$842$	−21867.1	−0.895000
$843$	63939.6	2.61233
$844$	65.9394	0.00268925
$845$	40297.5	1.64056
$846$	11497.8	0.467260
$847$	0	0
$848$	1742.42	0.0705600
$849$	61658.8	2.49249
$850$	19496.9	0.786751
$851$	17910.7	0.721471
$852$	16396.4	0.659307
$853$	6918.03	0.277689	0.138845	−	0.990314i	$-0.455661\pi$
$853$	6918.03	0.277689	0.138845	+	0.990314i	$0.455661\pi$
$854$	0	0
$855$	−9259.72	−0.370381
$856$	5867.87	0.234299
$857$	24255.8	0.966818	0.483409	−	0.875395i	$-0.339398\pi$
$857$	24255.8	0.966818	0.483409	+	0.875395i	$0.339398\pi$
$858$	−12056.4	−0.479718
$859$	22220.3	0.882592	0.441296	−	0.897361i	$-0.354519\pi$
$859$	22220.3	0.882592	0.441296	+	0.897361i	$0.354519\pi$
$860$	−128.175	−0.00508223
$861$	0	0
$862$	−18984.0	−0.750115
$863$	−39489.0	−1.55761	−0.778807	−	0.627264i	$-0.784175\pi$
$863$	−39489.0	−1.55761	−0.778807	+	0.627264i	$0.784175\pi$
$864$	3668.13	0.144436
$865$	24665.5	0.969540
$866$	−4558.23	−0.178863
$867$	−61624.5	−2.41393
$868$	0	0
$869$	6005.78	0.234445
$870$	15080.1	0.587658
$871$	33157.7	1.28990
$872$	33160.8	1.28781
$873$	−36577.8	−1.41806
$874$	−8060.18	−0.311945
$875$	0	0
$876$	−10319.0	−0.398000
$877$	21117.1	0.813082	0.406541	−	0.913633i	$-0.366735\pi$
$877$	21117.1	0.813082	0.406541	+	0.913633i	$0.366735\pi$
$878$	−22351.5	−0.859140
$879$	−8436.82	−0.323739
$880$	1141.26	0.0437182
$881$	−38687.6	−1.47948	−0.739738	−	0.672895i	$-0.765051\pi$
$881$	−38687.6	−1.47948	−0.739738	+	0.672895i	$0.765051\pi$
$882$	0	0
$883$	−9650.36	−0.367792	−0.183896	−	0.982946i	$-0.558871\pi$
$883$	−9650.36	−0.367792	−0.183896	+	0.982946i	$0.558871\pi$
$884$	−38621.2	−1.46943
$885$	27415.6	1.04132
$886$	−21149.9	−0.801969
$887$	−1995.40	−0.0755342	−0.0377671	−	0.999287i	$-0.512025\pi$
$887$	−1995.40	−0.0755342	−0.0377671	+	0.999287i	$0.512025\pi$
$888$	39655.1	1.49858
$889$	0	0
$890$	−15844.6	−0.596755
$891$	5311.07	0.199694
$892$	−8078.17	−0.303225
$893$	8598.56	0.322217
$894$	5302.38	0.198365
$895$	11145.6	0.416265
$896$	0	0
$897$	57325.6	2.13383
$898$	−19701.3	−0.732117
$899$	−21813.9	−0.809271
$900$	9183.22	0.340119
$901$	−9588.42	−0.354536
$902$	3662.02	0.135179
$903$	0	0
$904$	13379.8	0.492262
$905$	−21673.3	−0.796072
$906$	51985.3	1.90629
$907$	−20056.3	−0.734244	−0.367122	−	0.930173i	$-0.619657\pi$
$907$	−20056.3	−0.734244	−0.367122	+	0.930173i	$0.619657\pi$
$908$	−11929.9	−0.436022
$909$	27215.8	0.993058
$910$	0	0
$911$	17721.8	0.644513	0.322256	−	0.946652i	$-0.395559\pi$
$911$	17721.8	0.644513	0.322256	+	0.946652i	$0.395559\pi$
$912$	−7362.42	−0.267318
$913$	10508.6	0.380925
$914$	−24826.6	−0.898457
$915$	16246.0	0.586968
$916$	9959.26	0.359239
$917$	0	0
$918$	5758.03	0.207019
$919$	−38297.6	−1.37467	−0.687335	−	0.726340i	$-0.741220\pi$
$919$	−38297.6	−1.37467	−0.687335	+	0.726340i	$0.741220\pi$
$920$	−13153.1	−0.471353
$921$	51706.7	1.84994
$922$	38896.2	1.38935
$923$	53620.3	1.91217
$924$	0	0
$925$	17768.7	0.631602
$926$	29962.2	1.06330
$927$	26202.2	0.928362
$928$	−22196.1	−0.785155
$929$	3816.73	0.134793	0.0673965	−	0.997726i	$-0.478531\pi$
$929$	3816.73	0.134793	0.0673965	+	0.997726i	$0.478531\pi$
$930$	−15230.8	−0.537031
$931$	0	0
$932$	3994.43	0.140388
$933$	−10294.3	−0.361223
$934$	−4041.60	−0.141590
$935$	−6280.31	−0.219666
$936$	67022.4	2.34049
$937$	17295.4	0.603007	0.301503	−	0.953465i	$-0.402512\pi$
$937$	17295.4	0.603007	0.301503	+	0.953465i	$0.402512\pi$
$938$	0	0
$939$	1966.95	0.0683589
$940$	4434.31	0.153863
$941$	−29474.0	−1.02107	−0.510534	−	0.859858i	$-0.670552\pi$
$941$	−29474.0	−1.02107	−0.510534	+	0.859858i	$0.670552\pi$
$942$	27954.2	0.966877
$943$	−17412.1	−0.601291
$944$	11510.8	0.396870
$945$	0	0
$946$	92.4476	0.00317730
$947$	−34834.6	−1.19532	−0.597662	−	0.801748i	$-0.703904\pi$
$947$	−34834.6	−1.19532	−0.597662	+	0.801748i	$0.703904\pi$
$948$	−19980.4	−0.684528
$949$	−33745.9	−1.15431
$950$	−7996.28	−0.273088
$951$	−66918.7	−2.28180
$952$	0	0
$953$	−52629.5	−1.78892	−0.894458	−	0.447151i	$-0.852439\pi$
$953$	−52629.5	−1.78892	−0.894458	+	0.447151i	$0.852439\pi$
$954$	5258.44	0.178457
$955$	17020.3	0.576717
$956$	5504.14	0.186210
$957$	9341.49	0.315535
$958$	30912.5	1.04252
$959$	0	0
$960$	−23715.3	−0.797301
$961$	−7759.02	−0.260448
$962$	40982.4	1.37352
$963$	7305.93	0.244476
$964$	2342.38	0.0782602
$965$	−11829.8	−0.394627
$966$	0	0
$967$	−14976.1	−0.498033	−0.249017	−	0.968499i	$-0.580107\pi$
$967$	−14976.1	−0.498033	−0.249017	+	0.968499i	$0.580107\pi$
$968$	−30582.3	−1.01545
$969$	40514.9	1.34317
$970$	16425.2	0.543691
$971$	−2836.59	−0.0937493	−0.0468746	−	0.998901i	$-0.514926\pi$
$971$	−2836.59	−0.0937493	−0.0468746	+	0.998901i	$0.514926\pi$
$972$	−20093.0	−0.663049
$973$	0	0
$974$	−590.207	−0.0194163
$975$	56871.1	1.86803
$976$	6821.09	0.223707
$977$	−37168.3	−1.21711	−0.608556	−	0.793511i	$-0.708251\pi$
$977$	−37168.3	−1.21711	−0.608556	+	0.793511i	$0.708251\pi$
$978$	−57598.8	−1.88324
$979$	−9815.07	−0.320420
$980$	0	0
$981$	41287.7	1.34374
$982$	−7669.83	−0.249240
$983$	23250.8	0.754412	0.377206	−	0.926129i	$-0.376885\pi$
$983$	23250.8	0.754412	0.377206	+	0.926129i	$0.376885\pi$
$984$	−38551.2	−1.24895
$985$	−71.9419	−0.00232717
$986$	−34842.2	−1.12536
$987$	0	0
$988$	15839.7	0.510050
$989$	−439.569	−0.0141329
$990$	3444.22	0.110570
$991$	−21786.8	−0.698366	−0.349183	−	0.937054i	$-0.613541\pi$
$991$	−21786.8	−0.698366	−0.349183	+	0.937054i	$0.613541\pi$
$992$	22418.0	0.717513
$993$	−43219.8	−1.38121
$994$	0	0
$995$	1090.66	0.0347501
$996$	−34960.7	−1.11222
$997$	24932.9	0.792008	0.396004	−	0.918249i	$-0.370397\pi$
$997$	24932.9	0.792008	0.396004	+	0.918249i	$0.370397\pi$
$998$	36808.8	1.16750
$999$	5247.64	0.166194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.15		39
7.6	odd	2		2401.4.a.d.1.15		39
49.13	odd	14		49.4.e.a.22.9	✓	78
49.34	odd	14		49.4.e.a.29.9	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.22.9	✓	78	49.13	odd	14
49.4.e.a.29.9	yes	78	49.34	odd	14
2401.4.a.c.1.15		39	1.1	even	1	trivial
2401.4.a.d.1.15		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)

\(f(q)\)	\(=\)	\(q-2.07454 q^{2} -7.56379 q^{3} -3.69627 q^{4} +6.53935 q^{5} +15.6914 q^{6} +24.2644 q^{8} +30.2110 q^{9} +O(q^{10})\)	\(q-2.07454 q^{2} -7.56379 q^{3} -3.69627 q^{4} +6.53935 q^{5} +15.6914 q^{6} +24.2644 q^{8} +30.2110 q^{9} -13.5662 q^{10} -8.40368 q^{11} +27.9578 q^{12} +91.4293 q^{13} -49.4623 q^{15} -20.7674 q^{16} +114.282 q^{17} -62.6739 q^{18} -46.8704 q^{19} -24.1712 q^{20} +17.4338 q^{22} -82.8941 q^{23} -183.531 q^{24} -82.2369 q^{25} -189.674 q^{26} -24.2870 q^{27} +146.963 q^{29} +102.612 q^{30} -148.432 q^{31} -151.032 q^{32} +63.5637 q^{33} -237.082 q^{34} -111.668 q^{36} -216.068 q^{37} +97.2347 q^{38} -691.552 q^{39} +158.674 q^{40} +210.053 q^{41} +5.30278 q^{43} +31.0623 q^{44} +197.560 q^{45} +171.967 q^{46} -183.454 q^{47} +157.080 q^{48} +170.604 q^{50} -864.403 q^{51} -337.948 q^{52} -83.9016 q^{53} +50.3845 q^{54} -54.9546 q^{55} +354.518 q^{57} -304.880 q^{58} -554.273 q^{59} +182.826 q^{60} -328.452 q^{61} +307.928 q^{62} +479.463 q^{64} +597.888 q^{65} -131.866 q^{66} +362.660 q^{67} -422.416 q^{68} +626.994 q^{69} +586.467 q^{71} +733.051 q^{72} -369.093 q^{73} +448.242 q^{74} +622.023 q^{75} +173.246 q^{76} +1434.65 q^{78} -714.661 q^{79} -135.805 q^{80} -631.994 q^{81} -435.763 q^{82} -1250.48 q^{83} +747.328 q^{85} -11.0008 q^{86} -1111.59 q^{87} -203.910 q^{88} +1167.95 q^{89} -409.847 q^{90} +306.399 q^{92} +1122.71 q^{93} +380.583 q^{94} -306.502 q^{95} +1142.38 q^{96} -1210.74 q^{97} -253.883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 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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