LMFDB - Embedded newform 363.4.a.i.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,4,Mod(1,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	363.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-1,-6,33,-14,3,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$21.4176933321$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{97}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 24 $ x^2 - x - 24
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.42443$ of defining polynomial
Character	$\chi$	$=$	363.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.42443 q^{2} -3.00000 q^{3} +11.5756 q^{4} +2.84886 q^{5} -13.2733 q^{6} -31.6977 q^{7} +15.8199 q^{8} +9.00000 q^{9} +12.6046 q^{10} -34.7267 q^{12} -5.15114 q^{13} -140.244 q^{14} -8.54657 q^{15} -22.6107 q^{16} -121.942 q^{17} +39.8199 q^{18} -34.8489 q^{19} +32.9772 q^{20} +95.0931 q^{21} +116.244 q^{23} -47.4596 q^{24} -116.884 q^{25} -22.7909 q^{26} -27.0000 q^{27} -366.919 q^{28} +69.4534 q^{29} -37.8137 q^{30} +140.605 q^{31} -226.598 q^{32} -539.524 q^{34} -90.3023 q^{35} +104.180 q^{36} -420.070 q^{37} -154.186 q^{38} +15.4534 q^{39} +45.0685 q^{40} +322.058 q^{41} +420.733 q^{42} -321.035 q^{43} +25.6397 q^{45} +514.315 q^{46} -231.408 q^{47} +67.8322 q^{48} +661.745 q^{49} -517.145 q^{50} +365.826 q^{51} -59.6274 q^{52} +4.91916 q^{53} -119.460 q^{54} -501.453 q^{56} +104.547 q^{57} +307.292 q^{58} +406.443 q^{59} -98.9315 q^{60} +556.431 q^{61} +622.095 q^{62} -285.279 q^{63} -821.683 q^{64} -14.6749 q^{65} +84.7452 q^{67} -1411.55 q^{68} -348.733 q^{69} -399.536 q^{70} +49.0808 q^{71} +142.379 q^{72} -785.884 q^{73} -1858.57 q^{74} +350.652 q^{75} -403.395 q^{76} +68.3726 q^{78} +383.118 q^{79} -64.4147 q^{80} +81.0000 q^{81} +1424.92 q^{82} +930.211 q^{83} +1100.76 q^{84} -347.395 q^{85} -1420.40 q^{86} -208.360 q^{87} -732.559 q^{89} +113.441 q^{90} +163.279 q^{91} +1345.59 q^{92} -421.814 q^{93} -1023.85 q^{94} -99.2794 q^{95} +679.795 q^{96} -1171.49 q^{97} +2927.84 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 6 q^{3} + 33 q^{4} - 14 q^{5} + 3 q^{6} - 24 q^{7} - 57 q^{8} + 18 q^{9} + 104 q^{10} - 99 q^{12} - 30 q^{13} - 182 q^{14} + 42 q^{15} + 201 q^{16} - 106 q^{17} - 9 q^{18} - 50 q^{19} - 328 q^{20}+ \cdots + 4467 q^{98}+O(q^{100}) $ 2 * q - q^2 - 6 * q^3 + 33 * q^4 - 14 * q^5 + 3 * q^6 - 24 * q^7 - 57 * q^8 + 18 * q^9 + 104 * q^10 - 99 * q^12 - 30 * q^13 - 182 * q^14 + 42 * q^15 + 201 * q^16 - 106 * q^17 - 9 * q^18 - 50 * q^19 - 328 * q^20 + 72 * q^21 + 134 * q^23 + 171 * q^24 + 42 * q^25 + 112 * q^26 - 54 * q^27 - 202 * q^28 + 198 * q^29 - 312 * q^30 + 360 * q^31 - 857 * q^32 - 626 * q^34 - 220 * q^35 + 297 * q^36 - 328 * q^37 - 72 * q^38 + 90 * q^39 + 1272 * q^40 + 782 * q^41 + 546 * q^42 - 386 * q^43 - 126 * q^45 + 418 * q^46 + 266 * q^47 - 603 * q^48 + 378 * q^49 - 1379 * q^50 + 318 * q^51 - 592 * q^52 - 522 * q^53 + 27 * q^54 - 1062 * q^56 + 150 * q^57 - 390 * q^58 - 172 * q^59 + 984 * q^60 + 778 * q^61 - 568 * q^62 - 216 * q^63 + 809 * q^64 + 404 * q^65 - 776 * q^67 - 1070 * q^68 - 402 * q^69 + 304 * q^70 + 630 * q^71 - 513 * q^72 - 1296 * q^73 - 2358 * q^74 - 126 * q^75 - 728 * q^76 - 336 * q^78 - 652 * q^79 - 3832 * q^80 + 162 * q^81 - 1070 * q^82 + 324 * q^83 + 606 * q^84 - 616 * q^85 - 1068 * q^86 - 594 * q^87 - 756 * q^89 + 936 * q^90 - 28 * q^91 + 1726 * q^92 - 1080 * q^93 - 3722 * q^94 + 156 * q^95 + 2571 * q^96 - 452 * q^97 + 4467 * q^98

Coefficient data

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

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

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

$2$	4.42443	1.56427	0.782136	−	0.623108i	$-0.214130\pi$
$2$	4.42443	1.56427	0.782136	+	0.623108i	$0.214130\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	11.5756	1.44695
$5$	2.84886	0.254810	0.127405	−	0.991851i	$-0.459335\pi$
$5$	2.84886	0.254810	0.127405	+	0.991851i	$0.459335\pi$
$6$	−13.2733	−0.903133
$7$	−31.6977	−1.71152	−0.855758	−	0.517377i	$-0.826909\pi$
$7$	−31.6977	−1.71152	−0.855758	+	0.517377i	$0.826909\pi$
$8$	15.8199	0.699146
$9$	9.00000	0.333333
$10$	12.6046	0.398591
$11$	0	0
$11$	0	0
$12$	−34.7267	−0.835395
$13$	−5.15114	−0.109898	−0.0549488	−	0.998489i	$-0.517500\pi$
$13$	−5.15114	−0.109898	−0.0549488	+	0.998489i	$0.517500\pi$
$14$	−140.244	−2.67728
$15$	−8.54657	−0.147114
$16$	−22.6107	−0.353293
$17$	−121.942	−1.73972	−0.869861	−	0.493297i	$-0.835792\pi$
$17$	−121.942	−1.73972	−0.869861	+	0.493297i	$0.835792\pi$
$18$	39.8199	0.521424
$19$	−34.8489	−0.420783	−0.210391	−	0.977617i	$-0.567474\pi$
$19$	−34.8489	−0.420783	−0.210391	+	0.977617i	$0.567474\pi$
$20$	32.9772	0.368696
$21$	95.0931	0.988144
$22$	0	0
$23$	116.244	1.05385	0.526926	−	0.849911i	$-0.323344\pi$
$23$	116.244	1.05385	0.526926	+	0.849911i	$0.323344\pi$
$24$	−47.4596	−0.403652
$25$	−116.884	−0.935072
$26$	−22.7909	−0.171910
$27$	−27.0000	−0.192450
$28$	−366.919	−2.47647
$29$	69.4534	0.444730	0.222365	−	0.974963i	$-0.428622\pi$
$29$	69.4534	0.444730	0.222365	+	0.974963i	$0.428622\pi$
$30$	−37.8137	−0.230127
$31$	140.605	0.814623	0.407312	−	0.913289i	$-0.366466\pi$
$31$	140.605	0.814623	0.407312	+	0.913289i	$0.366466\pi$
$32$	−226.598	−1.25179
$33$	0	0
$34$	−539.524	−2.72140
$35$	−90.3023	−0.436111
$36$	104.180	0.482315
$37$	−420.070	−1.86646	−0.933232	−	0.359276i	$-0.883024\pi$
$37$	−420.070	−1.86646	−0.933232	+	0.359276i	$0.883024\pi$
$38$	−154.186	−0.658219
$39$	15.4534	0.0634495
$40$	45.0685	0.178149
$41$	322.058	1.22676	0.613378	−	0.789789i	$-0.289810\pi$
$41$	322.058	1.22676	0.613378	+	0.789789i	$0.289810\pi$
$42$	420.733	1.54573
$43$	−321.035	−1.13854	−0.569272	−	0.822149i	$-0.692775\pi$
$43$	−321.035	−1.13854	−0.569272	+	0.822149i	$0.692775\pi$
$44$	0	0
$45$	25.6397	0.0849365
$46$	514.315	1.64851
$47$	−231.408	−0.718176	−0.359088	−	0.933304i	$-0.616912\pi$
$47$	−231.408	−0.718176	−0.359088	+	0.933304i	$0.616912\pi$
$48$	67.8322	0.203974
$49$	661.745	1.92929
$50$	−517.145	−1.46271
$51$	365.826	1.00443
$52$	−59.6274	−0.159016
$53$	4.91916	0.0127490	0.00637452	−	0.999980i	$-0.497971\pi$
$53$	4.91916	0.0127490	0.00637452	+	0.999980i	$0.497971\pi$
$54$	−119.460	−0.301044
$55$	0	0
$56$	−501.453	−1.19660
$57$	104.547	0.242939
$58$	307.292	0.695679
$59$	406.443	0.896854	0.448427	−	0.893820i	$-0.351984\pi$
$59$	406.443	0.896854	0.448427	+	0.893820i	$0.351984\pi$
$60$	−98.9315	−0.212867
$61$	556.431	1.16793	0.583964	−	0.811779i	$-0.301501\pi$
$61$	556.431	1.16793	0.583964	+	0.811779i	$0.301501\pi$
$62$	622.095	1.27429
$63$	−285.279	−0.570505
$64$	−821.683	−1.60485
$65$	−14.6749	−0.0280030
$66$	0	0
$67$	84.7452	0.154526	0.0772632	−	0.997011i	$-0.475382\pi$
$67$	84.7452	0.154526	0.0772632	+	0.997011i	$0.475382\pi$
$68$	−1411.55	−2.51728
$69$	−348.733	−0.608442
$70$	−399.536	−0.682196
$71$	49.0808	0.0820398	0.0410199	−	0.999158i	$-0.486939\pi$
$71$	49.0808	0.0820398	0.0410199	+	0.999158i	$0.486939\pi$
$72$	142.379	0.233049
$73$	−785.884	−1.26001	−0.630005	−	0.776591i	$-0.716947\pi$
$73$	−785.884	−1.26001	−0.630005	+	0.776591i	$0.716947\pi$
$74$	−1858.57	−2.91966
$75$	350.652	0.539864
$76$	−403.395	−0.608850
$77$	0	0
$78$	68.3726	0.0992522
$79$	383.118	0.545622	0.272811	−	0.962068i	$-0.412047\pi$
$79$	383.118	0.545622	0.272811	+	0.962068i	$0.412047\pi$
$80$	−64.4147	−0.0900223
$81$	81.0000	0.111111
$82$	1424.92	1.91898
$83$	930.211	1.23017	0.615084	−	0.788462i	$-0.289122\pi$
$83$	930.211	1.23017	0.615084	+	0.788462i	$0.289122\pi$
$84$	1100.76	1.42979
$85$	−347.395	−0.443298
$86$	−1420.40	−1.78099
$87$	−208.360	−0.256765
$88$	0	0
$89$	−732.559	−0.872484	−0.436242	−	0.899829i	$-0.643691\pi$
$89$	−732.559	−0.872484	−0.436242	+	0.899829i	$0.643691\pi$
$90$	113.441	0.132864
$91$	163.279	0.188092
$92$	1345.59	1.52487
$93$	−421.814	−0.470323
$94$	−1023.85	−1.12342
$95$	−99.2794	−0.107220
$96$	679.795	0.722722
$97$	−1171.49	−1.22626	−0.613128	−	0.789984i	$-0.710089\pi$
$97$	−1171.49	−1.22626	−0.613128	+	0.789984i	$0.710089\pi$
$98$	2927.84	3.01793
$99$	0	0
$100$	−1353.00	−1.35300
$101$	1221.27	1.20318	0.601589	−	0.798806i	$-0.294535\pi$
$101$	1221.27	1.20318	0.601589	+	0.798806i	$0.294535\pi$
$102$	1618.57	1.57120
$103$	516.745	0.494334	0.247167	−	0.968973i	$-0.420500\pi$
$103$	516.745	0.494334	0.247167	+	0.968973i	$0.420500\pi$
$104$	−81.4903	−0.0768345
$105$	270.907	0.251789
$106$	21.7645	0.0199430
$107$	152.025	0.137353	0.0686765	−	0.997639i	$-0.478122\pi$
$107$	152.025	0.137353	0.0686765	+	0.997639i	$0.478122\pi$
$108$	−312.540	−0.278465
$109$	−2170.32	−1.90714	−0.953572	−	0.301164i	$-0.902625\pi$
$109$	−2170.32	−1.90714	−0.953572	+	0.301164i	$0.902625\pi$
$110$	0	0
$111$	1260.21	1.07760
$112$	716.708	0.604666
$113$	−646.397	−0.538123	−0.269062	−	0.963123i	$-0.586714\pi$
$113$	−646.397	−0.538123	−0.269062	+	0.963123i	$0.586714\pi$
$114$	462.559	0.380023
$115$	331.163	0.268532
$116$	803.963	0.643501
$117$	−46.3603	−0.0366326
$118$	1798.28	1.40292
$119$	3865.28	2.97756
$120$	−135.206	−0.102854
$121$	0	0
$122$	2461.89	1.82696
$123$	−966.174	−0.708268
$124$	1627.58	1.17872
$125$	−689.093	−0.493075
$126$	−1262.20	−0.892425
$127$	993.304	0.694027	0.347014	−	0.937860i	$-0.387196\pi$
$127$	993.304	0.694027	0.347014	+	0.937860i	$0.387196\pi$
$128$	−1822.69	−1.25863
$129$	963.105	0.657339
$130$	−64.9279	−0.0438043
$131$	−385.814	−0.257318	−0.128659	−	0.991689i	$-0.541067\pi$
$131$	−385.814	−0.257318	−0.128659	+	0.991689i	$0.541067\pi$
$132$	0	0
$133$	1104.63	0.720177
$134$	374.949	0.241721
$135$	−76.9192	−0.0490381
$136$	−1929.11	−1.21632
$137$	884.840	0.551803	0.275901	−	0.961186i	$-0.411024\pi$
$137$	884.840	0.551803	0.275901	+	0.961186i	$0.411024\pi$
$138$	−1542.94	−0.951769
$139$	1091.94	0.666312	0.333156	−	0.942872i	$-0.391886\pi$
$139$	1091.94	0.666312	0.333156	+	0.942872i	$0.391886\pi$
$140$	−1045.30	−0.631029
$141$	694.223	0.414639
$142$	217.155	0.128333
$143$	0	0
$144$	−203.497	−0.117764
$145$	197.863	0.113322
$146$	−3477.09	−1.97100
$147$	−1985.24	−1.11387
$148$	−4862.55	−2.70067
$149$	−297.014	−0.163304	−0.0816522	−	0.996661i	$-0.526020\pi$
$149$	−297.014	−0.163304	−0.0816522	+	0.996661i	$0.526020\pi$
$150$	1551.43	0.844494
$151$	1887.86	1.01743	0.508716	−	0.860935i	$-0.330120\pi$
$151$	1887.86	1.01743	0.508716	+	0.860935i	$0.330120\pi$
$152$	−551.304	−0.294189
$153$	−1097.48	−0.579907
$154$	0	0
$155$	400.562	0.207574
$156$	178.882	0.0918080
$157$	−56.5343	−0.0287384	−0.0143692	−	0.999897i	$-0.504574\pi$
$157$	−56.5343	−0.0287384	−0.0143692	+	0.999897i	$0.504574\pi$
$158$	1695.08	0.853501
$159$	−14.7575	−0.00736066
$160$	−645.547	−0.318968
$161$	−3684.68	−1.80369
$162$	358.379	0.173808
$163$	−49.2338	−0.0236582	−0.0118291	−	0.999930i	$-0.503765\pi$
$163$	−49.2338	−0.0236582	−0.0118291	+	0.999930i	$0.503765\pi$
$164$	3728.01	1.77505
$165$	0	0
$166$	4115.65	1.92432
$167$	−2068.75	−0.958589	−0.479294	−	0.877654i	$-0.659107\pi$
$167$	−2068.75	−0.958589	−0.479294	+	0.877654i	$0.659107\pi$
$168$	1504.36	0.690857
$169$	−2170.47	−0.987923
$170$	−1537.03	−0.693438
$171$	−313.640	−0.140261
$172$	−3716.17	−1.64741
$173$	604.012	0.265446	0.132723	−	0.991153i	$-0.457628\pi$
$173$	604.012	0.265446	0.132723	+	0.991153i	$0.457628\pi$
$174$	−921.875	−0.401650
$175$	3704.96	1.60039
$176$	0	0
$177$	−1219.33	−0.517799
$178$	−3241.15	−1.36480
$179$	−2132.02	−0.890251	−0.445126	−	0.895468i	$-0.646841\pi$
$179$	−2132.02	−0.890251	−0.445126	+	0.895468i	$0.646841\pi$
$180$	296.794	0.122899
$181$	−589.371	−0.242031	−0.121015	−	0.992651i	$-0.538615\pi$
$181$	−589.371	−0.242031	−0.121015	+	0.992651i	$0.538615\pi$
$182$	722.418	0.294226
$183$	−1669.29	−0.674304
$184$	1838.97	0.736796
$185$	−1196.72	−0.475593
$186$	−1866.28	−0.735713
$187$	0	0
$188$	−2678.68	−1.03916
$189$	855.838	0.329381
$190$	−439.255	−0.167720
$191$	−2160.90	−0.818624	−0.409312	−	0.912395i	$-0.634231\pi$
$191$	−2160.90	−0.818624	−0.409312	+	0.912395i	$0.634231\pi$
$192$	2465.05	0.926560
$193$	1490.91	0.556052	0.278026	−	0.960574i	$-0.410320\pi$
$193$	1490.91	0.556052	0.278026	+	0.960574i	$0.410320\pi$
$194$	−5183.18	−1.91820
$195$	44.0246	0.0161675
$196$	7660.08	2.79157
$197$	230.529	0.0833732	0.0416866	−	0.999131i	$-0.486727\pi$
$197$	230.529	0.0833732	0.0416866	+	0.999131i	$0.486727\pi$
$198$	0	0
$199$	22.4007	0.00797963	0.00398982	−	0.999992i	$-0.498730\pi$
$199$	22.4007	0.00797963	0.00398982	+	0.999992i	$0.498730\pi$
$200$	−1849.09	−0.653752
$201$	−254.236	−0.0892159
$202$	5403.43	1.88210
$203$	−2201.51	−0.761163
$204$	4234.65	1.45336
$205$	917.497	0.312589
$206$	2286.30	0.773273
$207$	1046.20	0.351284
$208$	116.471	0.0388260
$209$	0	0
$210$	1198.61	0.393866
$211$	1051.64	0.343117	0.171558	−	0.985174i	$-0.445120\pi$
$211$	1051.64	0.343117	0.171558	+	0.985174i	$0.445120\pi$
$212$	56.9421	0.0184472
$213$	−147.243	−0.0473657
$214$	672.622	0.214857
$215$	−914.583	−0.290112
$216$	−427.136	−0.134551
$217$	−4456.84	−1.39424
$218$	−9602.42	−2.98329
$219$	2357.65	0.727467
$220$	0	0
$221$	628.141	0.191191
$222$	5575.71	1.68566
$223$	3861.80	1.15966	0.579832	−	0.814736i	$-0.303118\pi$
$223$	3861.80	1.15966	0.579832	+	0.814736i	$0.303118\pi$
$224$	7182.65	2.14246
$225$	−1051.96	−0.311691
$226$	−2859.94	−0.841771
$227$	872.721	0.255174	0.127587	−	0.991827i	$-0.459277\pi$
$227$	872.721	0.255174	0.127587	+	0.991827i	$0.459277\pi$
$228$	1210.19	0.351520
$229$	1841.72	0.531459	0.265730	−	0.964048i	$-0.414387\pi$
$229$	1841.72	0.531459	0.265730	+	0.964048i	$0.414387\pi$
$230$	1465.21	0.420057
$231$	0	0
$232$	1098.74	0.310931
$233$	−3932.14	−1.10559	−0.552796	−	0.833317i	$-0.686439\pi$
$233$	−3932.14	−1.10559	−0.552796	+	0.833317i	$0.686439\pi$
$234$	−205.118	−0.0573033
$235$	−659.248	−0.182998
$236$	4704.81	1.29770
$237$	−1149.35	−0.315015
$238$	17101.7	4.65772
$239$	−4772.10	−1.29155	−0.645777	−	0.763526i	$-0.723466\pi$
$239$	−4772.10	−1.29155	−0.645777	+	0.763526i	$0.723466\pi$
$240$	193.244	0.0519744
$241$	−3988.84	−1.06616	−0.533078	−	0.846066i	$-0.678965\pi$
$241$	−3988.84	−1.06616	−0.533078	+	0.846066i	$0.678965\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	6441.00	1.68993
$245$	1885.22	0.491601
$246$	−4274.77	−1.10792
$247$	179.511	0.0462431
$248$	2224.34	0.569540
$249$	−2790.63	−0.710238
$250$	−3048.84	−0.771303
$251$	−5474.22	−1.37661	−0.688306	−	0.725421i	$-0.741645\pi$
$251$	−5474.22	−1.37661	−0.688306	+	0.725421i	$0.741645\pi$
$252$	−3302.27	−0.825491
$253$	0	0
$254$	4394.80	1.08565
$255$	1042.19	0.255938
$256$	−1490.90	−0.363989
$257$	−6434.01	−1.56164	−0.780822	−	0.624754i	$-0.785199\pi$
$257$	−6434.01	−1.56164	−0.780822	+	0.624754i	$0.785199\pi$
$258$	4261.19	1.02826
$259$	13315.3	3.19448
$260$	−169.870	−0.0405188
$261$	625.081	0.148243
$262$	−1707.01	−0.402516
$263$	−7589.00	−1.77931	−0.889654	−	0.456636i	$-0.849054\pi$
$263$	−7589.00	−1.77931	−0.889654	+	0.456636i	$0.849054\pi$
$264$	0	0
$265$	14.0140	0.00324858
$266$	4887.35	1.12655
$267$	2197.68	0.503729
$268$	980.974	0.223591
$269$	478.178	0.108383	0.0541914	−	0.998531i	$-0.482742\pi$
$269$	478.178	0.108383	0.0541914	+	0.998531i	$0.482742\pi$
$270$	−340.323	−0.0767090
$271$	122.323	0.0274192	0.0137096	−	0.999906i	$-0.495636\pi$
$271$	122.323	0.0274192	0.0137096	+	0.999906i	$0.495636\pi$
$272$	2757.20	0.614631
$273$	−489.838	−0.108595
$274$	3914.91	0.863170
$275$	0	0
$276$	−4036.78	−0.880383
$277$	−8199.41	−1.77854	−0.889269	−	0.457385i	$-0.848786\pi$
$277$	−8199.41	−1.77854	−0.889269	+	0.457385i	$0.848786\pi$
$278$	4831.22	1.04229
$279$	1265.44	0.271541
$280$	−1428.57	−0.304905
$281$	−6943.79	−1.47413	−0.737067	−	0.675820i	$-0.763790\pi$
$281$	−6943.79	−1.47413	−0.737067	+	0.675820i	$0.763790\pi$
$282$	3071.54	0.648609
$283$	−1035.14	−0.217429	−0.108715	−	0.994073i	$-0.534673\pi$
$283$	−1035.14	−0.217429	−0.108715	+	0.994073i	$0.534673\pi$
$284$	568.139	0.118707
$285$	297.838	0.0619032
$286$	0	0
$287$	−10208.5	−2.09961
$288$	−2039.39	−0.417264
$289$	9956.85	2.02663
$290$	875.430	0.177266
$291$	3514.47	0.707979
$292$	−9097.06	−1.82317
$293$	6144.81	1.22520	0.612600	−	0.790393i	$-0.290124\pi$
$293$	6144.81	1.22520	0.612600	+	0.790393i	$0.290124\pi$
$294$	−8783.53	−1.74240
$295$	1157.90	0.228527
$296$	−6645.45	−1.30493
$297$	0	0
$298$	−1314.12	−0.255452
$299$	−598.791	−0.115816
$300$	4059.00	0.781154
$301$	10176.1	1.94864
$302$	8352.72	1.59154
$303$	−3663.81	−0.694655
$304$	787.958	0.148659
$305$	1585.19	0.297599
$306$	−4855.71	−0.907133
$307$	2186.09	0.406406	0.203203	−	0.979137i	$-0.434865\pi$
$307$	2186.09	0.406406	0.203203	+	0.979137i	$0.434865\pi$
$308$	0	0
$309$	−1550.24	−0.285404
$310$	1772.26	0.324702
$311$	−7484.83	−1.36471	−0.682357	−	0.731019i	$-0.739045\pi$
$311$	−7484.83	−1.36471	−0.682357	+	0.731019i	$0.739045\pi$
$312$	244.471	0.0443604
$313$	−6833.33	−1.23400	−0.617001	−	0.786962i	$-0.711653\pi$
$313$	−6833.33	−1.23400	−0.617001	+	0.786962i	$0.711653\pi$
$314$	−250.132	−0.0449546
$315$	−812.721	−0.145370
$316$	4434.81	0.789485
$317$	924.265	0.163760	0.0818800	−	0.996642i	$-0.473908\pi$
$317$	924.265	0.163760	0.0818800	+	0.996642i	$0.473908\pi$
$318$	−65.2934	−0.0115141
$319$	0	0
$320$	−2340.86	−0.408931
$321$	−456.074	−0.0793008
$322$	−16302.6	−2.82145
$323$	4249.54	0.732046
$324$	937.621	0.160772
$325$	602.086	0.102762
$326$	−217.831	−0.0370078
$327$	6510.95	1.10109
$328$	5094.91	0.857681
$329$	7335.10	1.22917
$330$	0	0
$331$	−9820.46	−1.63076	−0.815380	−	0.578927i	$-0.803472\pi$
$331$	−9820.46	−1.63076	−0.815380	+	0.578927i	$0.803472\pi$
$332$	10767.7	1.77999
$333$	−3780.63	−0.622154
$334$	−9153.02	−1.49949
$335$	241.427	0.0393748
$336$	−2150.12	−0.349104
$337$	−600.808	−0.0971161	−0.0485580	−	0.998820i	$-0.515463\pi$
$337$	−600.808	−0.0971161	−0.0485580	+	0.998820i	$0.515463\pi$
$338$	−9603.07	−1.54538
$339$	1939.19	0.310686
$340$	−4021.30	−0.641428
$341$	0	0
$342$	−1387.68	−0.219406
$343$	−10103.5	−1.59049
$344$	−5078.73	−0.796008
$345$	−993.490	−0.155037
$346$	2672.41	0.415230
$347$	3143.41	0.486303	0.243152	−	0.969988i	$-0.421819\pi$
$347$	3143.41	0.486303	0.243152	+	0.969988i	$0.421819\pi$
$348$	−2411.89	−0.371525
$349$	−720.663	−0.110533	−0.0552667	−	0.998472i	$-0.517601\pi$
$349$	−720.663	−0.110533	−0.0552667	+	0.998472i	$0.517601\pi$
$350$	16392.3	2.50345
$351$	139.081	0.0211498
$352$	0	0
$353$	1207.12	0.182007	0.0910034	−	0.995851i	$-0.470993\pi$
$353$	1207.12	0.182007	0.0910034	+	0.995851i	$0.470993\pi$
$354$	−5394.83	−0.809978
$355$	139.824	0.0209045
$356$	−8479.79	−1.26244
$357$	−11595.8	−1.71910
$358$	−9432.99	−1.39260
$359$	−8748.31	−1.28612	−0.643062	−	0.765814i	$-0.722336\pi$
$359$	−8748.31	−1.28612	−0.643062	+	0.765814i	$0.722336\pi$
$360$	405.617	0.0593830
$361$	−5644.56	−0.822942
$362$	−2607.63	−0.378602
$363$	0	0
$364$	1890.05	0.272158
$365$	−2238.87	−0.321063
$366$	−7385.66	−1.05479
$367$	−6730.45	−0.957293	−0.478647	−	0.878008i	$-0.658872\pi$
$367$	−6730.45	−0.957293	−0.478647	+	0.878008i	$0.658872\pi$
$368$	−2628.37	−0.372318
$369$	2898.52	0.408919
$370$	−5294.81	−0.743956
$371$	−155.926	−0.0218202
$372$	−4882.73	−0.680532
$373$	227.394	0.0315657	0.0157828	−	0.999875i	$-0.494976\pi$
$373$	227.394	0.0315657	0.0157828	+	0.999875i	$0.494976\pi$
$374$	0	0
$375$	2067.28	0.284677
$376$	−3660.84	−0.502110
$377$	−357.764	−0.0488748
$378$	3786.60	0.515242
$379$	11356.2	1.53913	0.769565	−	0.638568i	$-0.220473\pi$
$379$	11356.2	1.53913	0.769565	+	0.638568i	$0.220473\pi$
$380$	−1149.22	−0.155141
$381$	−2979.91	−0.400697
$382$	−9560.74	−1.28055
$383$	10753.6	1.43468	0.717338	−	0.696725i	$-0.245360\pi$
$383$	10753.6	1.43468	0.717338	+	0.696725i	$0.245360\pi$
$384$	5468.07	0.726670
$385$	0	0
$386$	6596.43	0.869817
$387$	−2889.32	−0.379515
$388$	−13560.7	−1.77433
$389$	−11727.1	−1.52850	−0.764252	−	0.644918i	$-0.776891\pi$
$389$	−11727.1	−1.52850	−0.764252	+	0.644918i	$0.776891\pi$
$390$	194.784	0.0252904
$391$	−14175.1	−1.83341
$392$	10468.7	1.34885
$393$	1157.44	0.148563
$394$	1019.96	0.130418
$395$	1091.45	0.139030
$396$	0	0
$397$	−359.905	−0.0454990	−0.0227495	−	0.999741i	$-0.507242\pi$
$397$	−359.905	−0.0454990	−0.0227495	+	0.999741i	$0.507242\pi$
$398$	99.1105	0.0124823
$399$	−3313.89	−0.415794
$400$	2642.83	0.330354
$401$	−4066.71	−0.506438	−0.253219	−	0.967409i	$-0.581489\pi$
$401$	−4066.71	−0.506438	−0.253219	+	0.967409i	$0.581489\pi$
$402$	−1124.85	−0.139558
$403$	−724.274	−0.0895252
$404$	14136.9	1.74093
$405$	230.757	0.0283122
$406$	−9740.45	−1.19067
$407$	0	0
$408$	5787.32	0.702242
$409$	13488.8	1.63076	0.815379	−	0.578927i	$-0.196528\pi$
$409$	13488.8	1.63076	0.815379	+	0.578927i	$0.196528\pi$
$410$	4059.40	0.488975
$411$	−2654.52	−0.318584
$412$	5981.62	0.715275
$413$	−12883.3	−1.53498
$414$	4628.83	0.549504
$415$	2650.04	0.313459
$416$	1167.24	0.137569
$417$	−3275.83	−0.384695
$418$	0	0
$419$	−7040.12	−0.820841	−0.410420	−	0.911896i	$-0.634618\pi$
$419$	−7040.12	−0.820841	−0.410420	+	0.911896i	$0.634618\pi$
$420$	3135.90	0.364325
$421$	9171.74	1.06177	0.530883	−	0.847445i	$-0.321860\pi$
$421$	9171.74	1.06177	0.530883	+	0.847445i	$0.321860\pi$
$422$	4652.89	0.536728
$423$	−2082.67	−0.239392
$424$	77.8204	0.00891343
$425$	14253.1	1.62677
$426$	−651.464	−0.0740928
$427$	−17637.6	−1.99893
$428$	1759.77	0.198742
$429$	0	0
$430$	−4046.51	−0.453814
$431$	−992.995	−0.110976	−0.0554882	−	0.998459i	$-0.517672\pi$
$431$	−992.995	−0.110976	−0.0554882	+	0.998459i	$0.517672\pi$
$432$	610.490	0.0679912
$433$	3790.21	0.420660	0.210330	−	0.977630i	$-0.432546\pi$
$433$	3790.21	0.420660	0.210330	+	0.977630i	$0.432546\pi$
$434$	−19719.0	−2.18097
$435$	−593.589	−0.0654262
$436$	−25122.7	−2.75954
$437$	−4050.98	−0.443443
$438$	10431.3	1.13796
$439$	5136.97	0.558483	0.279242	−	0.960221i	$-0.409917\pi$
$439$	5136.97	0.558483	0.279242	+	0.960221i	$0.409917\pi$
$440$	0	0
$441$	5955.71	0.643095
$442$	2779.16	0.299075
$443$	10676.8	1.14508	0.572541	−	0.819876i	$-0.305958\pi$
$443$	10676.8	1.14508	0.572541	+	0.819876i	$0.305958\pi$
$444$	14587.7	1.55923
$445$	−2086.96	−0.222317
$446$	17086.2	1.81403
$447$	891.042	0.0942838
$448$	26045.5	2.74672
$449$	10529.9	1.10676	0.553379	−	0.832929i	$-0.313338\pi$
$449$	10529.9	1.10676	0.553379	+	0.832929i	$0.313338\pi$
$450$	−4654.30	−0.487569
$451$	0	0
$452$	−7482.42	−0.778636
$453$	−5663.59	−0.587414
$454$	3861.29	0.399162
$455$	465.160	0.0479275
$456$	1653.91	0.169850
$457$	14072.5	1.44045	0.720225	−	0.693741i	$-0.244039\pi$
$457$	14072.5	1.44045	0.720225	+	0.693741i	$0.244039\pi$
$458$	8148.55	0.831347
$459$	3292.43	0.334810
$460$	3833.41	0.388551
$461$	30.8173	0.00311346	0.00155673	−	0.999999i	$-0.499504\pi$
$461$	30.8173	0.00311346	0.00155673	+	0.999999i	$0.499504\pi$
$462$	0	0
$463$	17591.3	1.76573	0.882867	−	0.469622i	$-0.155610\pi$
$463$	17591.3	1.76573	0.882867	+	0.469622i	$0.155610\pi$
$464$	−1570.39	−0.157120
$465$	−1201.69	−0.119843
$466$	−17397.5	−1.72945
$467$	13273.1	1.31522	0.657609	−	0.753360i	$-0.271568\pi$
$467$	13273.1	1.31522	0.657609	+	0.753360i	$0.271568\pi$
$468$	−536.647	−0.0530053
$469$	−2686.23	−0.264474
$470$	−2916.79	−0.286259
$471$	169.603	0.0165921
$472$	6429.87	0.627031
$473$	0	0
$474$	−5085.23	−0.492769
$475$	4073.27	0.393462
$476$	44742.9	4.30837
$477$	44.2724	0.00424968
$478$	−21113.8	−2.02034
$479$	−2496.68	−0.238155	−0.119077	−	0.992885i	$-0.537994\pi$
$479$	−2496.68	−0.238155	−0.119077	+	0.992885i	$0.537994\pi$
$480$	1936.64	0.184156
$481$	2163.84	0.205120
$482$	−17648.3	−1.66776
$483$	11054.0	1.04136
$484$	0	0
$485$	−3337.41	−0.312462
$486$	−1075.14	−0.100348
$487$	−3464.42	−0.322357	−0.161178	−	0.986925i	$-0.551529\pi$
$487$	−3464.42	−0.322357	−0.161178	+	0.986925i	$0.551529\pi$
$488$	8802.65	0.816552
$489$	147.701	0.0136591
$490$	8341.01	0.768997
$491$	16224.6	1.49125	0.745625	−	0.666366i	$-0.232151\pi$
$491$	16224.6	1.49125	0.745625	+	0.666366i	$0.232151\pi$
$492$	−11184.0	−1.02483
$493$	−8469.29	−0.773707
$494$	794.236	0.0723367
$495$	0	0
$496$	−3179.17	−0.287800
$497$	−1555.75	−0.140412
$498$	−12347.0	−1.11100
$499$	9993.81	0.896562	0.448281	−	0.893893i	$-0.352036\pi$
$499$	9993.81	0.896562	0.448281	+	0.893893i	$0.352036\pi$
$500$	−7976.65	−0.713453
$501$	6206.24	0.553441
$502$	−24220.3	−2.15340
$503$	15334.8	1.35933	0.679667	−	0.733520i	$-0.262124\pi$
$503$	15334.8	1.35933	0.679667	+	0.733520i	$0.262124\pi$
$504$	−4513.08	−0.398866
$505$	3479.23	0.306581
$506$	0	0
$507$	6511.40	0.570377
$508$	11498.1	1.00422
$509$	−7291.23	−0.634927	−0.317464	−	0.948270i	$-0.602831\pi$
$509$	−7291.23	−0.634927	−0.317464	+	0.948270i	$0.602831\pi$
$510$	4611.08	0.400357
$511$	24910.7	2.15653
$512$	7985.14	0.689251
$513$	940.919	0.0809797
$514$	−28466.8	−2.44283
$515$	1472.13	0.125961
$516$	11148.5	0.951134
$517$	0	0
$518$	58912.5	4.99704
$519$	−1812.04	−0.153255
$520$	−232.154	−0.0195782
$521$	16794.3	1.41223	0.706114	−	0.708098i	$-0.250447\pi$
$521$	16794.3	1.41223	0.706114	+	0.708098i	$0.250447\pi$
$522$	2765.63	0.231893
$523$	21009.4	1.75655	0.878275	−	0.478157i	$-0.158695\pi$
$523$	21009.4	1.75655	0.878275	+	0.478157i	$0.158695\pi$
$524$	−4466.01	−0.372326
$525$	−11114.9	−0.923986
$526$	−33577.0	−2.78332
$527$	−17145.6	−1.41722
$528$	0	0
$529$	1345.73	0.110605
$530$	62.0039	0.00508166
$531$	3657.99	0.298951
$532$	12786.7	1.04206
$533$	−1658.97	−0.134818
$534$	9723.46	0.787969
$535$	433.097	0.0349989
$536$	1340.66	0.108036
$537$	6396.07	0.513987
$538$	2115.66	0.169540
$539$	0	0
$540$	−890.383	−0.0709555
$541$	16802.8	1.33532	0.667662	−	0.744464i	$-0.267295\pi$
$541$	16802.8	1.33532	0.667662	+	0.744464i	$0.267295\pi$
$542$	541.211	0.0428911
$543$	1768.11	0.139737
$544$	27631.9	2.17777
$545$	−6182.93	−0.485959
$546$	−2167.25	−0.169872
$547$	−16784.5	−1.31198	−0.655990	−	0.754770i	$-0.727749\pi$
$547$	−16784.5	−1.31198	−0.655990	+	0.754770i	$0.727749\pi$
$548$	10242.5	0.798429
$549$	5007.88	0.389309
$550$	0	0
$551$	−2420.37	−0.187135
$552$	−5516.91	−0.425390
$553$	−12144.0	−0.933840
$554$	−36277.7	−2.78212
$555$	3590.16	0.274584
$556$	12639.9	0.964117
$557$	−18127.0	−1.37893	−0.689467	−	0.724317i	$-0.742155\pi$
$557$	−18127.0	−1.37893	−0.689467	+	0.724317i	$0.742155\pi$
$558$	5598.85	0.424764
$559$	1653.70	0.125123
$560$	2041.80	0.154075
$561$	0	0
$562$	−30722.3	−2.30595
$563$	−2090.88	−0.156518	−0.0782592	−	0.996933i	$-0.524936\pi$
$563$	−2090.88	−0.156518	−0.0782592	+	0.996933i	$0.524936\pi$
$564$	8036.03	0.599961
$565$	−1841.49	−0.137119
$566$	−4579.89	−0.340119
$567$	−2567.51	−0.190168
$568$	776.452	0.0573578
$569$	−6249.23	−0.460424	−0.230212	−	0.973140i	$-0.573942\pi$
$569$	−6249.23	−0.460424	−0.230212	+	0.973140i	$0.573942\pi$
$570$	1317.76	0.0968335
$571$	−6048.79	−0.443317	−0.221659	−	0.975124i	$-0.571147\pi$
$571$	−6048.79	−0.443317	−0.221659	+	0.975124i	$0.571147\pi$
$572$	0	0
$573$	6482.69	0.472633
$574$	−45166.8	−3.28437
$575$	−13587.1	−0.985428
$576$	−7395.15	−0.534950
$577$	−15729.1	−1.13486	−0.567429	−	0.823423i	$-0.692062\pi$
$577$	−15729.1	−1.13486	−0.567429	+	0.823423i	$0.692062\pi$
$578$	44053.4	3.17021
$579$	−4472.73	−0.321037
$580$	2290.38	0.163970
$581$	−29485.6	−2.10545
$582$	15549.5	1.10747
$583$	0	0
$584$	−12432.6	−0.880931
$585$	−132.074	−0.00933433
$586$	27187.3	1.91655
$587$	15620.5	1.09835	0.549173	−	0.835709i	$-0.314943\pi$
$587$	15620.5	1.09835	0.549173	+	0.835709i	$0.314943\pi$
$588$	−22980.2	−1.61172
$589$	−4899.91	−0.342780
$590$	5123.04	0.357478
$591$	−691.587	−0.0481355
$592$	9498.09	0.659407
$593$	493.541	0.0341776	0.0170888	−	0.999854i	$-0.494560\pi$
$593$	493.541	0.0341776	0.0170888	+	0.999854i	$0.494560\pi$
$594$	0	0
$595$	11011.6	0.758711
$596$	−3438.11	−0.236293
$597$	−67.2022	−0.00460704
$598$	−2649.31	−0.181168
$599$	−12455.1	−0.849585	−0.424793	−	0.905291i	$-0.639653\pi$
$599$	−12455.1	−0.849585	−0.424793	+	0.905291i	$0.639653\pi$
$600$	5547.27	0.377444
$601$	−12454.8	−0.845329	−0.422664	−	0.906286i	$-0.638905\pi$
$601$	−12454.8	−0.845329	−0.422664	+	0.906286i	$0.638905\pi$
$602$	45023.3	3.04820
$603$	762.707	0.0515088
$604$	21853.1	1.47217
$605$	0	0
$606$	−16210.3	−1.08663
$607$	4243.19	0.283733	0.141867	−	0.989886i	$-0.454690\pi$
$607$	4243.19	0.283733	0.141867	+	0.989886i	$0.454690\pi$
$608$	7896.70	0.526732
$609$	6604.54	0.439458
$610$	7013.57	0.465526
$611$	1192.01	0.0789259
$612$	−12703.9	−0.839095
$613$	−5733.14	−0.377748	−0.188874	−	0.982001i	$-0.560484\pi$
$613$	−5733.14	−0.377748	−0.188874	+	0.982001i	$0.560484\pi$
$614$	9672.18	0.635729
$615$	−2752.49	−0.180473
$616$	0	0
$617$	15642.1	1.02063	0.510314	−	0.859988i	$-0.329529\pi$
$617$	15642.1	1.02063	0.510314	+	0.859988i	$0.329529\pi$
$618$	−6858.91	−0.446449
$619$	−7467.40	−0.484879	−0.242440	−	0.970167i	$-0.577948\pi$
$619$	−7467.40	−0.484879	−0.242440	+	0.970167i	$0.577948\pi$
$620$	4636.74	0.300348
$621$	−3138.60	−0.202814
$622$	−33116.1	−2.13478
$623$	23220.4	1.49327
$624$	−349.413	−0.0224162
$625$	12647.4	0.809432
$626$	−30233.6	−1.93031
$627$	0	0
$628$	−654.416	−0.0415829
$629$	51224.2	3.24713
$630$	−3595.82	−0.227399
$631$	−1486.38	−0.0937745	−0.0468872	−	0.998900i	$-0.514930\pi$
$631$	−1486.38	−0.0937745	−0.0468872	+	0.998900i	$0.514930\pi$
$632$	6060.87	0.381469
$633$	−3154.91	−0.198099
$634$	4089.35	0.256165
$635$	2829.78	0.176845
$636$	−170.826	−0.0106505
$637$	−3408.74	−0.212024
$638$	0	0
$639$	441.728	0.0273466
$640$	−5192.58	−0.320711
$641$	12386.0	0.763211	0.381606	−	0.924325i	$-0.375371\pi$
$641$	12386.0	0.763211	0.381606	+	0.924325i	$0.375371\pi$
$642$	−2017.87	−0.124048
$643$	−14458.1	−0.886737	−0.443369	−	0.896339i	$-0.646217\pi$
$643$	−14458.1	−0.886737	−0.443369	+	0.896339i	$0.646217\pi$
$644$	−42652.3	−2.60984
$645$	2743.75	0.167496
$646$	18801.8	1.14512
$647$	15792.8	0.959625	0.479813	−	0.877371i	$-0.340705\pi$
$647$	15792.8	0.959625	0.479813	+	0.877371i	$0.340705\pi$
$648$	1281.41	0.0776828
$649$	0	0
$650$	2663.89	0.160748
$651$	13370.5	0.804965
$652$	−569.909	−0.0342321
$653$	−3179.93	−0.190567	−0.0952837	−	0.995450i	$-0.530376\pi$
$653$	−3179.93	−0.190567	−0.0952837	+	0.995450i	$0.530376\pi$
$654$	28807.3	1.72240
$655$	−1099.13	−0.0655672
$656$	−7281.96	−0.433404
$657$	−7072.96	−0.420003
$658$	32453.6	1.92276
$659$	−11593.5	−0.685308	−0.342654	−	0.939462i	$-0.611326\pi$
$659$	−11593.5	−0.685308	−0.342654	+	0.939462i	$0.611326\pi$
$660$	0	0
$661$	3233.88	0.190293	0.0951464	−	0.995463i	$-0.469668\pi$
$661$	3233.88	0.190293	0.0951464	+	0.995463i	$0.469668\pi$
$662$	−43449.9	−2.55095
$663$	−1884.42	−0.110384
$664$	14715.8	0.860066
$665$	3146.93	0.183508
$666$	−16727.1	−0.973219
$667$	8073.56	0.468680
$668$	−23946.9	−1.38703
$669$	−11585.4	−0.669532
$670$	1068.18	0.0615929
$671$	0	0
$672$	−21548.0	−1.23695
$673$	5495.72	0.314776	0.157388	−	0.987537i	$-0.449693\pi$
$673$	5495.72	0.314776	0.157388	+	0.987537i	$0.449693\pi$
$674$	−2658.23	−0.151916
$675$	3155.87	0.179955
$676$	−25124.4	−1.42947
$677$	−33836.7	−1.92090	−0.960451	−	0.278448i	$-0.910180\pi$
$677$	−33836.7	−1.92090	−0.960451	+	0.278448i	$0.910180\pi$
$678$	8579.82	0.485997
$679$	37133.6	2.09876
$680$	−5495.75	−0.309930
$681$	−2618.16	−0.147325
$682$	0	0
$683$	−21080.3	−1.18099	−0.590493	−	0.807043i	$-0.701067\pi$
$683$	−21080.3	−1.18099	−0.590493	+	0.807043i	$0.701067\pi$
$684$	−3630.56	−0.202950
$685$	2520.78	0.140605
$686$	−44702.2	−2.48796
$687$	−5525.16	−0.306838
$688$	7258.84	0.402239
$689$	−25.3393	−0.00140109
$690$	−4395.63	−0.242520
$691$	11811.3	0.650253	0.325127	−	0.945671i	$-0.394593\pi$
$691$	11811.3	0.650253	0.325127	+	0.945671i	$0.394593\pi$
$692$	6991.79	0.384087
$693$	0	0
$694$	13907.8	0.760711
$695$	3110.79	0.169783
$696$	−3296.23	−0.179516
$697$	−39272.4	−2.13422
$698$	−3188.52	−0.172904
$699$	11796.4	0.638313
$700$	42887.0	2.31568
$701$	−4244.99	−0.228718	−0.114359	−	0.993440i	$-0.536481\pi$
$701$	−4244.99	−0.228718	−0.114359	+	0.993440i	$0.536481\pi$
$702$	615.353	0.0330841
$703$	14639.0	0.785376
$704$	0	0
$705$	1977.74	0.105654
$706$	5340.81	0.284708
$707$	−38711.5	−2.05926
$708$	−14114.4	−0.749227
$709$	−898.822	−0.0476107	−0.0238053	−	0.999717i	$-0.507578\pi$
$709$	−898.822	−0.0476107	−0.0238053	+	0.999717i	$0.507578\pi$
$710$	618.643	0.0327004
$711$	3448.06	0.181874
$712$	−11589.0	−0.609993
$713$	16344.5	0.858493
$714$	−51305.0	−2.68913
$715$	0	0
$716$	−24679.4	−1.28815
$717$	14316.3	0.745679
$718$	−38706.3	−2.01185
$719$	10741.8	0.557165	0.278582	−	0.960412i	$-0.410135\pi$
$719$	10741.8	0.557165	0.278582	+	0.960412i	$0.410135\pi$
$720$	−579.733	−0.0300074
$721$	−16379.6	−0.846061
$722$	−24973.9	−1.28730
$723$	11966.5	0.615546
$724$	−6822.30	−0.350206
$725$	−8117.99	−0.415855
$726$	0	0
$727$	16794.2	0.856758	0.428379	−	0.903599i	$-0.359085\pi$
$727$	16794.2	0.856758	0.428379	+	0.903599i	$0.359085\pi$
$728$	2583.06	0.131503
$729$	729.000	0.0370370
$730$	−9905.73	−0.502229
$731$	39147.7	1.98075
$732$	−19323.0	−0.975681
$733$	−8659.40	−0.436347	−0.218173	−	0.975910i	$-0.570010\pi$
$733$	−8659.40	−0.436347	−0.218173	+	0.975910i	$0.570010\pi$
$734$	−29778.4	−1.49747
$735$	−5655.65	−0.283826
$736$	−26340.8	−1.31920
$737$	0	0
$738$	12824.3	0.639660
$739$	−16705.7	−0.831567	−0.415783	−	0.909464i	$-0.636493\pi$
$739$	−16705.7	−0.831567	−0.415783	+	0.909464i	$0.636493\pi$
$740$	−13852.7	−0.688157
$741$	−538.534	−0.0266984
$742$	−689.884	−0.0341327
$743$	−1292.12	−0.0637996	−0.0318998	−	0.999491i	$-0.510156\pi$
$743$	−1292.12	−0.0637996	−0.0318998	+	0.999491i	$0.510156\pi$
$744$	−6673.03	−0.328824
$745$	−846.151	−0.0416115
$746$	1006.09	0.0493773
$747$	8371.90	0.410056
$748$	0	0
$749$	−4818.83	−0.235082
$750$	9146.53	0.445312
$751$	−14980.4	−0.727886	−0.363943	−	0.931421i	$-0.618570\pi$
$751$	−14980.4	−0.727886	−0.363943	+	0.931421i	$0.618570\pi$
$752$	5232.30	0.253726
$753$	16422.7	0.794787
$754$	−1582.90	−0.0764535
$755$	5378.25	0.259251
$756$	9906.82	0.476597
$757$	3003.41	0.144202	0.0721010	−	0.997397i	$-0.477030\pi$
$757$	3003.41	0.144202	0.0721010	+	0.997397i	$0.477030\pi$
$758$	50244.8	2.40762
$759$	0	0
$760$	−1570.59	−0.0749621
$761$	20375.0	0.970555	0.485277	−	0.874360i	$-0.338719\pi$
$761$	20375.0	0.970555	0.485277	+	0.874360i	$0.338719\pi$
$762$	−13184.4	−0.626799
$763$	68794.1	3.26411
$764$	−25013.6	−1.18450
$765$	−3126.56	−0.147766
$766$	47578.4	2.24422
$767$	−2093.65	−0.0985621
$768$	4472.70	0.210149
$769$	12372.4	0.580184	0.290092	−	0.956999i	$-0.406314\pi$
$769$	12372.4	0.580184	0.290092	+	0.956999i	$0.406314\pi$
$770$	0	0
$771$	19302.0	0.901615
$772$	17258.1	0.804578
$773$	21023.6	0.978225	0.489113	−	0.872221i	$-0.337321\pi$
$773$	21023.6	0.978225	0.489113	+	0.872221i	$0.337321\pi$
$774$	−12783.6	−0.593664
$775$	−16434.4	−0.761732
$776$	−18532.8	−0.857331
$777$	−39945.8	−1.84433
$778$	−51885.7	−2.39099
$779$	−11223.4	−0.516198
$780$	509.610	0.0233935
$781$	0	0
$782$	−62716.6	−2.86795
$783$	−1875.24	−0.0855884
$784$	−14962.5	−0.681602
$785$	−161.058	−0.00732281
$786$	5121.02	0.232393
$787$	−30286.2	−1.37177	−0.685886	−	0.727709i	$-0.740585\pi$
$787$	−30286.2	−1.37177	−0.685886	+	0.727709i	$0.740585\pi$
$788$	2668.51	0.120637
$789$	22767.0	1.02728
$790$	4829.03	0.217480
$791$	20489.3	0.921007
$792$	0	0
$793$	−2866.25	−0.128353
$794$	−1592.37	−0.0711729
$795$	−42.0420	−0.00187557
$796$	259.301	0.0115461
$797$	32337.8	1.43722	0.718610	−	0.695413i	$-0.244779\pi$
$797$	32337.8	1.43722	0.718610	+	0.695413i	$0.244779\pi$
$798$	−14662.1	−0.650415
$799$	28218.3	1.24943
$800$	26485.7	1.17052
$801$	−6593.03	−0.290828
$802$	−17992.9	−0.792207
$803$	0	0
$804$	−2942.92	−0.129091
$805$	−10497.1	−0.459596
$806$	−3204.50	−0.140042
$807$	−1434.53	−0.0625749
$808$	19320.3	0.841197
$809$	891.707	0.0387525	0.0193762	−	0.999812i	$-0.493832\pi$
$809$	891.707	0.0387525	0.0193762	+	0.999812i	$0.493832\pi$
$810$	1020.97	0.0442879
$811$	10114.9	0.437957	0.218978	−	0.975730i	$-0.429728\pi$
$811$	10114.9	0.437957	0.218978	+	0.975730i	$0.429728\pi$
$812$	−25483.8	−1.10136
$813$	−366.970	−0.0158305
$814$	0	0
$815$	−140.260	−0.00602833
$816$	−8271.59	−0.354857
$817$	11187.7	0.479080
$818$	59680.4	2.55095
$819$	1469.51	0.0626972
$820$	10620.6	0.452300
$821$	−10833.5	−0.460525	−0.230262	−	0.973129i	$-0.573958\pi$
$821$	−10833.5	−0.460525	−0.230262	+	0.973129i	$0.573958\pi$
$822$	−11744.7	−0.498351
$823$	31958.5	1.35359	0.676794	−	0.736173i	$-0.263369\pi$
$823$	31958.5	1.35359	0.676794	+	0.736173i	$0.263369\pi$
$824$	8174.84	0.345612
$825$	0	0
$826$	−57001.3	−2.40112
$827$	−34847.3	−1.46525	−0.732624	−	0.680634i	$-0.761704\pi$
$827$	−34847.3	−1.46525	−0.732624	+	0.680634i	$0.761704\pi$
$828$	12110.3	0.508289
$829$	6537.91	0.273910	0.136955	−	0.990577i	$-0.456268\pi$
$829$	6537.91	0.273910	0.136955	+	0.990577i	$0.456268\pi$
$830$	11724.9	0.490334
$831$	24598.2	1.02684
$832$	4232.60	0.176369
$833$	−80694.5	−3.35642
$834$	−14493.7	−0.601768
$835$	−5893.56	−0.244258
$836$	0	0
$837$	−3796.32	−0.156774
$838$	−31148.5	−1.28402
$839$	2710.34	0.111527	0.0557635	−	0.998444i	$-0.482241\pi$
$839$	2710.34	0.111527	0.0557635	+	0.998444i	$0.482241\pi$
$840$	4285.71	0.176037
$841$	−19565.2	−0.802215
$842$	40579.7	1.66089
$843$	20831.4	0.851092
$844$	12173.3	0.496471
$845$	−6183.35	−0.251732
$846$	−9214.62	−0.374474
$847$	0	0
$848$	−111.226	−0.00450414
$849$	3105.41	0.125533
$850$	63061.7	2.54470
$851$	−48830.8	−1.96698
$852$	−1704.42	−0.0685356
$853$	−9759.32	−0.391738	−0.195869	−	0.980630i	$-0.562753\pi$
$853$	−9759.32	−0.391738	−0.195869	+	0.980630i	$0.562753\pi$
$854$	−78036.2	−3.12687
$855$	−893.515	−0.0357398
$856$	2405.01	0.0960298
$857$	13649.8	0.544072	0.272036	−	0.962287i	$-0.412303\pi$
$857$	13649.8	0.544072	0.272036	+	0.962287i	$0.412303\pi$
$858$	0	0
$859$	7796.42	0.309674	0.154837	−	0.987940i	$-0.450515\pi$
$859$	7796.42	0.309674	0.154837	+	0.987940i	$0.450515\pi$
$860$	−10586.8	−0.419776
$861$	30625.5	1.21221
$862$	−4393.43	−0.173597
$863$	7183.57	0.283350	0.141675	−	0.989913i	$-0.454751\pi$
$863$	7183.57	0.283350	0.141675	+	0.989913i	$0.454751\pi$
$864$	6118.16	0.240907
$865$	1720.75	0.0676383
$866$	16769.5	0.658026
$867$	−29870.6	−1.17008
$868$	−51590.5	−2.01739
$869$	0	0
$870$	−2626.29	−0.102344
$871$	−436.534	−0.0169821
$872$	−34334.1	−1.33337
$873$	−10543.4	−0.408752
$874$	−17923.3	−0.693666
$875$	21842.7	0.843905
$876$	27291.2	1.05261
$877$	−17063.1	−0.656991	−0.328495	−	0.944506i	$-0.606542\pi$
$877$	−17063.1	−0.656991	−0.328495	+	0.944506i	$0.606542\pi$
$878$	22728.2	0.873620
$879$	−18434.4	−0.707369
$880$	0	0
$881$	−32174.9	−1.23042	−0.615210	−	0.788363i	$-0.710929\pi$
$881$	−32174.9	−1.23042	−0.615210	+	0.788363i	$0.710929\pi$
$882$	26350.6	1.00598
$883$	2843.68	0.108378	0.0541889	−	0.998531i	$-0.482743\pi$
$883$	2843.68	0.108378	0.0541889	+	0.998531i	$0.482743\pi$
$884$	7271.09	0.276644
$885$	−3473.69	−0.131940
$886$	47238.9	1.79122
$887$	31417.8	1.18930	0.594649	−	0.803985i	$-0.297291\pi$
$887$	31417.8	1.18930	0.594649	+	0.803985i	$0.297291\pi$
$888$	19936.4	0.753401
$889$	−31485.5	−1.18784
$890$	−9233.59	−0.347765
$891$	0	0
$892$	44702.5	1.67797
$893$	8064.30	0.302196
$894$	3942.35	0.147485
$895$	−6073.83	−0.226845
$896$	57775.1	2.15416
$897$	1796.37	0.0668664
$898$	46588.6	1.73127
$899$	9765.47	0.362288
$900$	−12177.0	−0.451000
$901$	−599.852	−0.0221798
$902$	0	0
$903$	−30528.2	−1.12505
$904$	−10225.9	−0.376227
$905$	−1679.03	−0.0616718
$906$	−25058.1	−0.918875
$907$	12253.1	0.448573	0.224287	−	0.974523i	$-0.427995\pi$
$907$	12253.1	0.448573	0.224287	+	0.974523i	$0.427995\pi$
$908$	10102.2	0.369223
$909$	10991.4	0.401059
$910$	2058.07	0.0749717
$911$	−48422.4	−1.76104	−0.880518	−	0.474012i	$-0.842805\pi$
$911$	−48422.4	−1.76104	−0.880518	+	0.474012i	$0.842805\pi$
$912$	−2363.87	−0.0858286
$913$	0	0
$914$	62262.9	2.25326
$915$	−4755.57	−0.171819
$916$	21318.9	0.768993
$917$	12229.4	0.440404
$918$	14567.1	0.523733
$919$	−5546.18	−0.199077	−0.0995385	−	0.995034i	$-0.531737\pi$
$919$	−5546.18	−0.199077	−0.0995385	+	0.995034i	$0.531737\pi$
$920$	5238.96	0.187743
$921$	−6558.26	−0.234638
$922$	136.349	0.00487030
$923$	−252.822	−0.00901598
$924$	0	0
$925$	49099.5	1.74528
$926$	77831.3	2.76209
$927$	4650.71	0.164778
$928$	−15738.0	−0.556709
$929$	−35684.5	−1.26025	−0.630125	−	0.776494i	$-0.716996\pi$
$929$	−35684.5	−1.26025	−0.630125	+	0.776494i	$0.716996\pi$
$930$	−5316.78	−0.187467
$931$	−23061.1	−0.811811
$932$	−45516.7	−1.59973
$933$	22454.5	0.787918
$934$	58726.0	2.05736
$935$	0	0
$936$	−733.413	−0.0256115
$937$	48903.6	1.70503	0.852514	−	0.522705i	$-0.175077\pi$
$937$	48903.6	1.70503	0.852514	+	0.522705i	$0.175077\pi$
$938$	−11885.0	−0.413710
$939$	20500.0	0.712451
$940$	−7631.17	−0.264789
$941$	23741.9	0.822490	0.411245	−	0.911525i	$-0.365094\pi$
$941$	23741.9	0.822490	0.411245	+	0.911525i	$0.365094\pi$
$942$	750.396	0.0259546
$943$	37437.4	1.29282
$944$	−9189.97	−0.316852
$945$	2438.16	0.0839295
$946$	0	0
$947$	37612.4	1.29064	0.645321	−	0.763911i	$-0.276724\pi$
$947$	37612.4	1.29064	0.645321	+	0.763911i	$0.276724\pi$
$948$	−13304.4	−0.455810
$949$	4048.20	0.138472
$950$	18021.9	0.615482
$951$	−2772.80	−0.0945469
$952$	61148.2	2.08175
$953$	48294.3	1.64156	0.820779	−	0.571246i	$-0.193540\pi$
$953$	48294.3	1.64156	0.820779	+	0.571246i	$0.193540\pi$
$954$	195.880	0.00664765
$955$	−6156.09	−0.208593
$956$	−55239.8	−1.86881
$957$	0	0
$958$	−11046.4	−0.372539
$959$	−28047.4	−0.944419
$960$	7022.57	0.236096
$961$	−10021.4	−0.336389
$962$	9573.76	0.320863
$963$	1368.22	0.0457843
$964$	−46173.1	−1.54267
$965$	4247.39	0.141687
$966$	48907.8	1.62897
$967$	−1840.92	−0.0612204	−0.0306102	−	0.999531i	$-0.509745\pi$
$967$	−1840.92	−0.0612204	−0.0306102	+	0.999531i	$0.509745\pi$
$968$	0	0
$969$	−12748.6	−0.422647
$970$	−14766.1	−0.488775
$971$	31461.8	1.03981	0.519906	−	0.854223i	$-0.325967\pi$
$971$	31461.8	1.03981	0.519906	+	0.854223i	$0.325967\pi$
$972$	−2812.86	−0.0928217
$973$	−34612.1	−1.14040
$974$	−15328.1	−0.504254
$975$	−1806.26	−0.0593298
$976$	−12581.3	−0.412620
$977$	−7040.11	−0.230535	−0.115268	−	0.993334i	$-0.536773\pi$
$977$	−7040.11	−0.230535	−0.115268	+	0.993334i	$0.536773\pi$
$978$	653.494	0.0213665
$979$	0	0
$980$	21822.5	0.711320
$981$	−19532.9	−0.635715
$982$	71784.4	2.33272
$983$	−24610.9	−0.798541	−0.399270	−	0.916833i	$-0.630737\pi$
$983$	−24610.9	−0.798541	−0.399270	+	0.916833i	$0.630737\pi$
$984$	−15284.7	−0.495183
$985$	656.744	0.0212443
$986$	−37471.8	−1.21029
$987$	−22005.3	−0.709662
$988$	2077.95	0.0669112
$989$	−37318.5	−1.19986
$990$	0	0
$991$	−40003.3	−1.28229	−0.641144	−	0.767421i	$-0.721540\pi$
$991$	−40003.3	−1.28229	−0.641144	+	0.767421i	$0.721540\pi$
$992$	−31860.8	−1.01974
$993$	29461.4	0.941519
$994$	−6883.31	−0.219643
$995$	63.8165	0.00203329
$996$	−32303.2	−1.02768
$997$	7342.61	0.233242	0.116621	−	0.993176i	$-0.462794\pi$
$997$	7342.61	0.233242	0.116621	+	0.993176i	$0.462794\pi$
$998$	44216.9	1.40247
$999$	11341.9	0.359201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.4.a.i.1.2		2
3.2	odd	2		1089.4.a.u.1.1		2
11.10	odd	2		33.4.a.c.1.1	✓	2
33.32	even	2		99.4.a.f.1.2		2
44.43	even	2		528.4.a.p.1.2		2
55.32	even	4		825.4.c.h.199.2		4
55.43	even	4		825.4.c.h.199.3		4
55.54	odd	2		825.4.a.l.1.2		2
77.76	even	2		1617.4.a.k.1.1		2
88.21	odd	2		2112.4.a.bn.1.1		2
88.43	even	2		2112.4.a.bg.1.1		2
132.131	odd	2		1584.4.a.bj.1.1		2
165.164	even	2		2475.4.a.p.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.a.c.1.1	✓	2	11.10	odd	2
99.4.a.f.1.2		2	33.32	even	2
363.4.a.i.1.2		2	1.1	even	1	trivial
528.4.a.p.1.2		2	44.43	even	2
825.4.a.l.1.2		2	55.54	odd	2
825.4.c.h.199.2		4	55.32	even	4
825.4.c.h.199.3		4	55.43	even	4
1089.4.a.u.1.1		2	3.2	odd	2
1584.4.a.bj.1.1		2	132.131	odd	2
1617.4.a.k.1.1		2	77.76	even	2
2112.4.a.bg.1.1		2	88.43	even	2
2112.4.a.bn.1.1		2	88.21	odd	2
2475.4.a.p.1.1		2	165.164	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

\(f(q)\)	\(=\)	\(q+4.42443 q^{2} -3.00000 q^{3} +11.5756 q^{4} +2.84886 q^{5} -13.2733 q^{6} -31.6977 q^{7} +15.8199 q^{8} +9.00000 q^{9} +12.6046 q^{10} -34.7267 q^{12} -5.15114 q^{13} -140.244 q^{14} -8.54657 q^{15} -22.6107 q^{16} -121.942 q^{17} +39.8199 q^{18} -34.8489 q^{19} +32.9772 q^{20} +95.0931 q^{21} +116.244 q^{23} -47.4596 q^{24} -116.884 q^{25} -22.7909 q^{26} -27.0000 q^{27} -366.919 q^{28} +69.4534 q^{29} -37.8137 q^{30} +140.605 q^{31} -226.598 q^{32} -539.524 q^{34} -90.3023 q^{35} +104.180 q^{36} -420.070 q^{37} -154.186 q^{38} +15.4534 q^{39} +45.0685 q^{40} +322.058 q^{41} +420.733 q^{42} -321.035 q^{43} +25.6397 q^{45} +514.315 q^{46} -231.408 q^{47} +67.8322 q^{48} +661.745 q^{49} -517.145 q^{50} +365.826 q^{51} -59.6274 q^{52} +4.91916 q^{53} -119.460 q^{54} -501.453 q^{56} +104.547 q^{57} +307.292 q^{58} +406.443 q^{59} -98.9315 q^{60} +556.431 q^{61} +622.095 q^{62} -285.279 q^{63} -821.683 q^{64} -14.6749 q^{65} +84.7452 q^{67} -1411.55 q^{68} -348.733 q^{69} -399.536 q^{70} +49.0808 q^{71} +142.379 q^{72} -785.884 q^{73} -1858.57 q^{74} +350.652 q^{75} -403.395 q^{76} +68.3726 q^{78} +383.118 q^{79} -64.4147 q^{80} +81.0000 q^{81} +1424.92 q^{82} +930.211 q^{83} +1100.76 q^{84} -347.395 q^{85} -1420.40 q^{86} -208.360 q^{87} -732.559 q^{89} +113.441 q^{90} +163.279 q^{91} +1345.59 q^{92} -421.814 q^{93} -1023.85 q^{94} -99.2794 q^{95} +679.795 q^{96} -1171.49 q^{97} +2927.84 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 6 q^{3} + 33 q^{4} - 14 q^{5} + 3 q^{6} - 24 q^{7} - 57 q^{8} + 18 q^{9} + 104 q^{10} - 99 q^{12} - 30 q^{13} - 182 q^{14} + 42 q^{15} + 201 q^{16} - 106 q^{17} - 9 q^{18} - 50 q^{19} - 328 q^{20}+ \cdots + 4467 q^{98}+O(q^{100}) \) 2 * q - q^2 - 6 * q^3 + 33 * q^4 - 14 * q^5 + 3 * q^6 - 24 * q^7 - 57 * q^8 + 18 * q^9 + 104 * q^10 - 99 * q^12 - 30 * q^13 - 182 * q^14 + 42 * q^15 + 201 * q^16 - 106 * q^17 - 9 * q^18 - 50 * q^19 - 328 * q^20 + 72 * q^21 + 134 * q^23 + 171 * q^24 + 42 * q^25 + 112 * q^26 - 54 * q^27 - 202 * q^28 + 198 * q^29 - 312 * q^30 + 360 * q^31 - 857 * q^32 - 626 * q^34 - 220 * q^35 + 297 * q^36 - 328 * q^37 - 72 * q^38 + 90 * q^39 + 1272 * q^40 + 782 * q^41 + 546 * q^42 - 386 * q^43 - 126 * q^45 + 418 * q^46 + 266 * q^47 - 603 * q^48 + 378 * q^49 - 1379 * q^50 + 318 * q^51 - 592 * q^52 - 522 * q^53 + 27 * q^54 - 1062 * q^56 + 150 * q^57 - 390 * q^58 - 172 * q^59 + 984 * q^60 + 778 * q^61 - 568 * q^62 - 216 * q^63 + 809 * q^64 + 404 * q^65 - 776 * q^67 - 1070 * q^68 - 402 * q^69 + 304 * q^70 + 630 * q^71 - 513 * q^72 - 1296 * q^73 - 2358 * q^74 - 126 * q^75 - 728 * q^76 - 336 * q^78 - 652 * q^79 - 3832 * q^80 + 162 * q^81 - 1070 * q^82 + 324 * q^83 + 606 * q^84 - 616 * q^85 - 1068 * q^86 - 594 * q^87 - 756 * q^89 + 936 * q^90 - 28 * q^91 + 1726 * q^92 - 1080 * q^93 - 3722 * q^94 + 156 * q^95 + 2571 * q^96 - 452 * q^97 + 4467 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more