LMFDB - Embedded newform 529.4.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, 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("529.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.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:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.34818 q^{2} -4.97765 q^{3} +20.6030 q^{4} -16.6747 q^{5} +26.6214 q^{6} +7.69394 q^{7} -67.4034 q^{8} -2.22303 q^{9} +89.1791 q^{10} -18.6441 q^{11} -102.555 q^{12} +29.5700 q^{13} -41.1486 q^{14} +83.0005 q^{15} +195.661 q^{16} -44.2479 q^{17} +11.8892 q^{18} -57.7509 q^{19} -343.549 q^{20} -38.2977 q^{21} +99.7120 q^{22} +335.510 q^{24} +153.044 q^{25} -158.146 q^{26} +145.462 q^{27} +158.519 q^{28} -130.893 q^{29} -443.902 q^{30} +152.368 q^{31} -507.204 q^{32} +92.8038 q^{33} +236.646 q^{34} -128.294 q^{35} -45.8012 q^{36} +85.8578 q^{37} +308.862 q^{38} -147.189 q^{39} +1123.93 q^{40} +334.244 q^{41} +204.823 q^{42} +199.918 q^{43} -384.125 q^{44} +37.0683 q^{45} +126.827 q^{47} -973.932 q^{48} -283.803 q^{49} -818.507 q^{50} +220.250 q^{51} +609.233 q^{52} +759.122 q^{53} -777.957 q^{54} +310.884 q^{55} -518.598 q^{56} +287.464 q^{57} +700.040 q^{58} +741.673 q^{59} +1710.06 q^{60} +262.966 q^{61} -814.890 q^{62} -17.1039 q^{63} +1147.33 q^{64} -493.070 q^{65} -496.331 q^{66} +102.208 q^{67} -911.641 q^{68} +686.139 q^{70} +275.514 q^{71} +149.840 q^{72} -610.501 q^{73} -459.183 q^{74} -761.799 q^{75} -1189.84 q^{76} -143.447 q^{77} +787.194 q^{78} -994.915 q^{79} -3262.58 q^{80} -664.036 q^{81} -1787.60 q^{82} -370.778 q^{83} -789.050 q^{84} +737.818 q^{85} -1069.20 q^{86} +651.540 q^{87} +1256.68 q^{88} -748.991 q^{89} -198.248 q^{90} +227.510 q^{91} -758.432 q^{93} -678.295 q^{94} +962.976 q^{95} +2524.68 q^{96} +370.644 q^{97} +1517.83 q^{98} +41.4464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Coefficient data

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

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

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

$2$	−5.34818	−1.89087	−0.945434	−	0.325814i	$-0.894362\pi$
$2$	−5.34818	−1.89087	−0.945434	+	0.325814i	$0.894362\pi$
$3$	−4.97765	−0.957949	−0.478974	−	0.877829i	$-0.658991\pi$
$3$	−4.97765	−0.957949	−0.478974	+	0.877829i	$0.658991\pi$
$4$	20.6030	2.57538
$5$	−16.6747	−1.49143	−0.745713	−	0.666267i	$-0.767891\pi$
$5$	−16.6747	−1.49143	−0.745713	+	0.666267i	$0.767891\pi$
$6$	26.6214	1.81135
$7$	7.69394	0.415434	0.207717	−	0.978189i	$-0.433397\pi$
$7$	7.69394	0.415434	0.207717	+	0.978189i	$0.433397\pi$
$8$	−67.4034	−2.97884
$9$	−2.22303	−0.0823345
$10$	89.1791	2.82009
$11$	−18.6441	−0.511037	−0.255519	−	0.966804i	$-0.582246\pi$
$11$	−18.6441	−0.511037	−0.255519	+	0.966804i	$0.582246\pi$
$12$	−102.555	−2.46708
$13$	29.5700	0.630865	0.315433	−	0.948948i	$-0.397850\pi$
$13$	29.5700	0.630865	0.315433	+	0.948948i	$0.397850\pi$
$14$	−41.1486	−0.785531
$15$	83.0005	1.42871
$16$	195.661	3.05721
$17$	−44.2479	−0.631276	−0.315638	−	0.948880i	$-0.602218\pi$
$17$	−44.2479	−0.631276	−0.315638	+	0.948880i	$0.602218\pi$
$18$	11.8892	0.155684
$19$	−57.7509	−0.697314	−0.348657	−	0.937250i	$-0.613362\pi$
$19$	−57.7509	−0.697314	−0.348657	+	0.937250i	$0.613362\pi$
$20$	−343.549	−3.84099
$21$	−38.2977	−0.397964
$22$	99.7120	0.966304
$23$	0	0
$23$	0	0
$24$	335.510	2.85357
$25$	153.044	1.22435
$26$	−158.146	−1.19288
$27$	145.462	1.03682
$28$	158.519	1.06990
$29$	−130.893	−0.838146	−0.419073	−	0.907952i	$-0.637645\pi$
$29$	−130.893	−0.838146	−0.419073	+	0.907952i	$0.637645\pi$
$30$	−443.902	−2.70150
$31$	152.368	0.882775	0.441388	−	0.897316i	$-0.354486\pi$
$31$	152.368	0.882775	0.441388	+	0.897316i	$0.354486\pi$
$32$	−507.204	−2.80193
$33$	92.8038	0.489547
$34$	236.646	1.19366
$35$	−128.294	−0.619589
$36$	−45.8012	−0.212043
$37$	85.8578	0.381485	0.190742	−	0.981640i	$-0.438910\pi$
$37$	85.8578	0.381485	0.190742	+	0.981640i	$0.438910\pi$
$38$	308.862	1.31853
$39$	−147.189	−0.604337
$40$	1123.93	4.44271
$41$	334.244	1.27317	0.636587	−	0.771205i	$-0.280345\pi$
$41$	334.244	1.27317	0.636587	+	0.771205i	$0.280345\pi$
$42$	204.823	0.752498
$43$	199.918	0.709003	0.354502	−	0.935055i	$-0.384651\pi$
$43$	199.918	0.709003	0.354502	+	0.935055i	$0.384651\pi$
$44$	−384.125	−1.31612
$45$	37.0683	0.122796
$46$	0	0
$47$	126.827	0.393610	0.196805	−	0.980443i	$-0.436943\pi$
$47$	126.827	0.393610	0.196805	+	0.980443i	$0.436943\pi$
$48$	−973.932	−2.92865
$49$	−283.803	−0.827415
$50$	−818.507	−2.31509
$51$	220.250	0.604730
$52$	609.233	1.62472
$53$	759.122	1.96742	0.983711	−	0.179755i	$-0.0575306\pi$
$53$	759.122	1.96742	0.983711	+	0.179755i	$0.0575306\pi$
$54$	−777.957	−1.96049
$55$	310.884	0.762174
$56$	−518.598	−1.23751
$57$	287.464	0.667991
$58$	700.040	1.58482
$59$	741.673	1.63657	0.818284	−	0.574814i	$-0.194926\pi$
$59$	741.673	1.63657	0.818284	+	0.574814i	$0.194926\pi$
$60$	1710.06	3.67947
$61$	262.966	0.551956	0.275978	−	0.961164i	$-0.410998\pi$
$61$	262.966	0.551956	0.275978	+	0.961164i	$0.410998\pi$
$62$	−814.890	−1.66921
$63$	−17.1039	−0.0342045
$64$	1147.33	2.24088
$65$	−493.070	−0.940889
$66$	−496.331	−0.925669
$67$	102.208	0.186369	0.0931847	−	0.995649i	$-0.470295\pi$
$67$	102.208	0.186369	0.0931847	+	0.995649i	$0.470295\pi$
$68$	−911.641	−1.62578
$69$	0	0
$70$	686.139	1.17156
$71$	275.514	0.460528	0.230264	−	0.973128i	$-0.426041\pi$
$71$	275.514	0.460528	0.230264	+	0.973128i	$0.426041\pi$
$72$	149.840	0.245261
$73$	−610.501	−0.978819	−0.489410	−	0.872054i	$-0.662788\pi$
$73$	−610.501	−0.978819	−0.489410	+	0.872054i	$0.662788\pi$
$74$	−459.183	−0.721338
$75$	−761.799	−1.17287
$76$	−1189.84	−1.79585
$77$	−143.447	−0.212302
$78$	787.194	1.14272
$79$	−994.915	−1.41692	−0.708460	−	0.705751i	$-0.750610\pi$
$79$	−994.915	−1.41692	−0.708460	+	0.705751i	$0.750610\pi$
$80$	−3262.58	−4.55960
$81$	−664.036	−0.910887
$82$	−1787.60	−2.40741
$83$	−370.778	−0.490340	−0.245170	−	0.969480i	$-0.578844\pi$
$83$	−370.778	−0.490340	−0.245170	+	0.969480i	$0.578844\pi$
$84$	−789.050	−1.02491
$85$	737.818	0.941501
$86$	−1069.20	−1.34063
$87$	651.540	0.802901
$88$	1256.68	1.52230
$89$	−748.991	−0.892055	−0.446028	−	0.895019i	$-0.647162\pi$
$89$	−748.991	−0.892055	−0.446028	+	0.895019i	$0.647162\pi$
$90$	−198.248	−0.232191
$91$	227.510	0.262083
$92$	0	0
$93$	−758.432	−0.845653
$94$	−678.295	−0.744264
$95$	962.976	1.03999
$96$	2524.68	2.68411
$97$	370.644	0.387971	0.193985	−	0.981004i	$-0.437859\pi$
$97$	370.644	0.387971	0.193985	+	0.981004i	$0.437859\pi$
$98$	1517.83	1.56453
$99$	41.4464	0.0420760
$100$	3153.17	3.15317
$101$	−593.204	−0.584416	−0.292208	−	0.956355i	$-0.594390\pi$
$101$	−593.204	−0.584416	−0.292208	+	0.956355i	$0.594390\pi$
$102$	−1177.94	−1.14346
$103$	1122.77	1.07408	0.537038	−	0.843558i	$-0.319543\pi$
$103$	1122.77	1.07408	0.537038	+	0.843558i	$0.319543\pi$
$104$	−1993.12	−1.87925
$105$	638.601	0.593534
$106$	−4059.92	−3.72014
$107$	−1063.85	−0.961177	−0.480588	−	0.876946i	$-0.659577\pi$
$107$	−1063.85	−0.961177	−0.480588	+	0.876946i	$0.659577\pi$
$108$	2996.96	2.67021
$109$	−1264.21	−1.11092	−0.555458	−	0.831545i	$-0.687457\pi$
$109$	−1264.21	−1.11092	−0.555458	+	0.831545i	$0.687457\pi$
$110$	−1662.66	−1.44117
$111$	−427.370	−0.365443
$112$	1505.41	1.27007
$113$	750.868	0.625095	0.312547	−	0.949902i	$-0.398818\pi$
$113$	750.868	0.625095	0.312547	+	0.949902i	$0.398818\pi$
$114$	−1537.41	−1.26308
$115$	0	0
$116$	−2696.80	−2.15855
$117$	−65.7351	−0.0519420
$118$	−3966.60	−3.09453
$119$	−340.441	−0.262253
$120$	−5594.52	−4.25589
$121$	−983.397	−0.738841
$122$	−1406.39	−1.04368
$123$	−1663.75	−1.21964
$124$	3139.24	2.27348
$125$	−467.623	−0.334604
$126$	91.4746	0.0646763
$127$	353.105	0.246716	0.123358	−	0.992362i	$-0.460634\pi$
$127$	353.105	0.246716	0.123358	+	0.992362i	$0.460634\pi$
$128$	−2078.50	−1.43528
$129$	−995.119	−0.679189
$130$	2637.03	1.77910
$131$	838.237	0.559062	0.279531	−	0.960137i	$-0.409821\pi$
$131$	838.237	0.559062	0.279531	+	0.960137i	$0.409821\pi$
$132$	1912.04	1.26077
$133$	−444.332	−0.289688
$134$	−546.629	−0.352400
$135$	−2425.53	−1.54634
$136$	2982.46	1.88047
$137$	−1875.91	−1.16985	−0.584926	−	0.811087i	$-0.698876\pi$
$137$	−1875.91	−1.16985	−0.584926	+	0.811087i	$0.698876\pi$
$138$	0	0
$139$	−1414.19	−0.862950	−0.431475	−	0.902125i	$-0.642007\pi$
$139$	−1414.19	−0.862950	−0.431475	+	0.902125i	$0.642007\pi$
$140$	−2643.24	−1.59568
$141$	−631.301	−0.377058
$142$	−1473.50	−0.870797
$143$	−551.307	−0.322396
$144$	−434.961	−0.251714
$145$	2182.60	1.25003
$146$	3265.07	1.85082
$147$	1412.67	0.792621
$148$	1768.93	0.982469
$149$	−2605.92	−1.43279	−0.716395	−	0.697695i	$-0.754209\pi$
$149$	−2605.92	−1.43279	−0.716395	+	0.697695i	$0.754209\pi$
$150$	4074.24	2.21773
$151$	948.694	0.511282	0.255641	−	0.966772i	$-0.417713\pi$
$151$	948.694	0.511282	0.255641	+	0.966772i	$0.417713\pi$
$152$	3892.61	2.07718
$153$	98.3644	0.0519758
$154$	767.179	0.401435
$155$	−2540.68	−1.31659
$156$	−3032.55	−1.55640
$157$	2023.07	1.02840	0.514199	−	0.857671i	$-0.328089\pi$
$157$	2023.07	1.02840	0.514199	+	0.857671i	$0.328089\pi$
$158$	5320.99	2.67921
$159$	−3778.64	−1.88469
$160$	8457.46	4.17888
$161$	0	0
$162$	3551.39	1.72237
$163$	278.635	0.133892	0.0669460	−	0.997757i	$-0.478674\pi$
$163$	278.635	0.133892	0.0669460	+	0.997757i	$0.478674\pi$
$164$	6886.45	3.27891
$165$	−1547.47	−0.730124
$166$	1982.99	0.927168
$167$	−643.623	−0.298234	−0.149117	−	0.988820i	$-0.547643\pi$
$167$	−643.623	−0.298234	−0.149117	+	0.988820i	$0.547643\pi$
$168$	2581.40	1.18547
$169$	−1322.61	−0.602009
$170$	−3945.98	−1.78025
$171$	128.382	0.0574130
$172$	4118.91	1.82595
$173$	2041.44	0.897155	0.448577	−	0.893744i	$-0.351931\pi$
$173$	2041.44	0.897155	0.448577	+	0.893744i	$0.351931\pi$
$174$	−3484.55	−1.51818
$175$	1177.51	0.508637
$176$	−3647.93	−1.56235
$177$	−3691.78	−1.56775
$178$	4005.74	1.68676
$179$	4024.47	1.68046	0.840231	−	0.542228i	$-0.182419\pi$
$179$	4024.47	1.68046	0.840231	+	0.542228i	$0.182419\pi$
$180$	763.719	0.316246
$181$	−3924.12	−1.61148	−0.805738	−	0.592272i	$-0.798231\pi$
$181$	−3924.12	−1.61148	−0.805738	+	0.592272i	$0.798231\pi$
$182$	−1216.77	−0.495564
$183$	−1308.95	−0.528745
$184$	0	0
$185$	−1431.65	−0.568957
$186$	4056.23	1.59902
$187$	824.962	0.322605
$188$	2613.03	1.01370
$189$	1119.18	0.430730
$190$	−5150.17	−1.96649
$191$	−4468.66	−1.69288	−0.846442	−	0.532481i	$-0.821260\pi$
$191$	−4468.66	−1.69288	−0.846442	+	0.532481i	$0.821260\pi$
$192$	−5711.01	−2.14665
$193$	3009.79	1.12254	0.561268	−	0.827634i	$-0.310314\pi$
$193$	3009.79	1.12254	0.561268	+	0.827634i	$0.310314\pi$
$194$	−1982.27	−0.733602
$195$	2454.33	0.901323
$196$	−5847.21	−2.13091
$197$	4993.28	1.80587	0.902935	−	0.429776i	$-0.141408\pi$
$197$	4993.28	1.80587	0.902935	+	0.429776i	$0.141408\pi$
$198$	−221.663	−0.0795601
$199$	−1501.04	−0.534702	−0.267351	−	0.963599i	$-0.586148\pi$
$199$	−1501.04	−0.534702	−0.267351	+	0.963599i	$0.586148\pi$
$200$	−10315.7	−3.64714
$201$	−508.758	−0.178532
$202$	3172.56	1.10505
$203$	−1007.08	−0.348194
$204$	4537.83	1.55741
$205$	−5573.40	−1.89885
$206$	−6004.78	−2.03094
$207$	0	0
$208$	5785.71	1.92869
$209$	1076.71	0.356353
$210$	−3415.36	−1.12229
$211$	456.647	0.148990	0.0744950	−	0.997221i	$-0.476266\pi$
$211$	456.647	0.148990	0.0744950	+	0.997221i	$0.476266\pi$
$212$	15640.2	5.06686
$213$	−1371.41	−0.441162
$214$	5689.64	1.81746
$215$	−3333.56	−1.05743
$216$	−9804.63	−3.08852
$217$	1172.31	0.366735
$218$	6761.25	2.10060
$219$	3038.86	0.937658
$220$	6405.16	1.96289
$221$	−1308.41	−0.398250
$222$	2285.65	0.691004
$223$	497.395	0.149363	0.0746817	−	0.997207i	$-0.476206\pi$
$223$	497.395	0.149363	0.0746817	+	0.997207i	$0.476206\pi$
$224$	−3902.40	−1.16402
$225$	−340.222	−0.100806
$226$	−4015.78	−1.18197
$227$	−3287.13	−0.961122	−0.480561	−	0.876961i	$-0.659567\pi$
$227$	−3287.13	−0.961122	−0.480561	+	0.876961i	$0.659567\pi$
$228$	5922.62	1.72033
$229$	3859.28	1.11366	0.556830	−	0.830626i	$-0.312017\pi$
$229$	3859.28	1.11366	0.556830	+	0.830626i	$0.312017\pi$
$230$	0	0
$231$	714.027	0.203375
$232$	8822.64	2.49670
$233$	738.467	0.207633	0.103817	−	0.994596i	$-0.466894\pi$
$233$	738.467	0.207633	0.103817	+	0.994596i	$0.466894\pi$
$234$	351.563	0.0982154
$235$	−2114.80	−0.587040
$236$	15280.7	4.21479
$237$	4952.34	1.35734
$238$	1820.74	0.495886
$239$	1851.62	0.501136	0.250568	−	0.968099i	$-0.419383\pi$
$239$	1851.62	0.501136	0.250568	+	0.968099i	$0.419383\pi$
$240$	16240.0	4.36786
$241$	−3417.63	−0.913482	−0.456741	−	0.889600i	$-0.650983\pi$
$241$	−3417.63	−0.913482	−0.456741	+	0.889600i	$0.650983\pi$
$242$	5259.39	1.39705
$243$	−622.134	−0.164238
$244$	5417.89	1.42150
$245$	4732.32	1.23403
$246$	8898.03	2.30617
$247$	−1707.70	−0.439911
$248$	−10270.1	−2.62964
$249$	1845.60	0.469720
$250$	2500.93	0.632692
$251$	5508.42	1.38521	0.692607	−	0.721315i	$-0.256462\pi$
$251$	5508.42	1.38521	0.692607	+	0.721315i	$0.256462\pi$
$252$	−352.392	−0.0880897
$253$	0	0
$254$	−1888.47	−0.466508
$255$	−3672.60	−0.901910
$256$	1937.56	0.473038
$257$	−6346.62	−1.54043	−0.770217	−	0.637782i	$-0.779852\pi$
$257$	−6346.62	−1.54043	−0.770217	+	0.637782i	$0.779852\pi$
$258$	5322.08	1.28426
$259$	660.585	0.158482
$260$	−10158.7	−2.42315
$261$	290.980	0.0690084
$262$	−4483.04	−1.05711
$263$	789.729	0.185159	0.0925794	−	0.995705i	$-0.470489\pi$
$263$	789.729	0.185159	0.0925794	+	0.995705i	$0.470489\pi$
$264$	−6255.29	−1.45828
$265$	−12658.1	−2.93427
$266$	2376.37	0.547761
$267$	3728.22	0.854543
$268$	2105.81	0.479972
$269$	2117.33	0.479909	0.239955	−	0.970784i	$-0.422867\pi$
$269$	2117.33	0.479909	0.239955	+	0.970784i	$0.422867\pi$
$270$	12972.2	2.92393
$271$	−2544.85	−0.570438	−0.285219	−	0.958462i	$-0.592066\pi$
$271$	−2544.85	−0.570438	−0.285219	+	0.958462i	$0.592066\pi$
$272$	−8657.59	−1.92994
$273$	−1132.47	−0.251062
$274$	10032.7	2.21203
$275$	−2853.37	−0.625689
$276$	0	0
$277$	6965.82	1.51096	0.755479	−	0.655172i	$-0.227404\pi$
$277$	6965.82	1.51096	0.755479	+	0.655172i	$0.227404\pi$
$278$	7563.35	1.63172
$279$	−338.718	−0.0726829
$280$	8647.44	1.84565
$281$	−6549.77	−1.39049	−0.695243	−	0.718775i	$-0.744703\pi$
$281$	−6549.77	−1.39049	−0.695243	+	0.718775i	$0.744703\pi$
$282$	3376.32	0.712967
$283$	−2573.93	−0.540651	−0.270325	−	0.962769i	$-0.587131\pi$
$283$	−2573.93	−0.540651	−0.270325	+	0.962769i	$0.587131\pi$
$284$	5676.42	1.18603
$285$	−4793.35	−0.996259
$286$	2948.49	0.609608
$287$	2571.66	0.528920
$288$	1127.53	0.230696
$289$	−2955.12	−0.601491
$290$	−11672.9	−2.36365
$291$	−1844.93	−0.371656
$292$	−12578.2	−2.52083
$293$	−4751.08	−0.947308	−0.473654	−	0.880711i	$-0.657065\pi$
$293$	−4751.08	−0.947308	−0.473654	+	0.880711i	$0.657065\pi$
$294$	−7555.23	−1.49874
$295$	−12367.1	−2.44082
$296$	−5787.11	−1.13638
$297$	−2712.01	−0.529854
$298$	13937.0	2.70922
$299$	0	0
$300$	−15695.4	−3.02058
$301$	1538.15	0.294544
$302$	−5073.79	−0.966768
$303$	2952.76	0.559841
$304$	−11299.6	−2.13183
$305$	−4384.86	−0.823201
$306$	−526.071	−0.0982793
$307$	−5666.81	−1.05349	−0.526745	−	0.850023i	$-0.676588\pi$
$307$	−5666.81	−1.05349	−0.526745	+	0.850023i	$0.676588\pi$
$308$	−2955.44	−0.546759
$309$	−5588.76	−1.02891
$310$	13588.0	2.48951
$311$	−3426.13	−0.624689	−0.312344	−	0.949969i	$-0.601114\pi$
$311$	−3426.13	−0.624689	−0.312344	+	0.949969i	$0.601114\pi$
$312$	9921.05	1.80022
$313$	−6836.57	−1.23459	−0.617294	−	0.786733i	$-0.711771\pi$
$313$	−6836.57	−1.23459	−0.617294	+	0.786733i	$0.711771\pi$
$314$	−10819.7	−1.94456
$315$	285.201	0.0510135
$316$	−20498.3	−3.64911
$317$	1273.47	0.225631	0.112815	−	0.993616i	$-0.464013\pi$
$317$	1273.47	0.225631	0.112815	+	0.993616i	$0.464013\pi$
$318$	20208.9	3.56370
$319$	2440.38	0.428324
$320$	−19131.4	−3.34211
$321$	5295.45	0.920758
$322$	0	0
$323$	2555.35	0.440197
$324$	−13681.2	−2.34588
$325$	4525.51	0.772401
$326$	−1490.19	−0.253172
$327$	6292.82	1.06420
$328$	−22529.2	−3.79258
$329$	975.802	0.163519
$330$	8276.15	1.38057
$331$	4370.21	0.725706	0.362853	−	0.931846i	$-0.381803\pi$
$331$	4370.21	0.725706	0.362853	+	0.931846i	$0.381803\pi$
$332$	−7639.17	−1.26281
$333$	−190.865	−0.0314094
$334$	3442.21	0.563921
$335$	−1704.29	−0.277956
$336$	−7493.38	−1.21666
$337$	5637.57	0.911269	0.455635	−	0.890167i	$-0.349412\pi$
$337$	5637.57	0.911269	0.455635	+	0.890167i	$0.349412\pi$
$338$	7073.58	1.13832
$339$	−3737.56	−0.598809
$340$	15201.3	2.42472
$341$	−2840.76	−0.451131
$342$	−686.611	−0.108560
$343$	−4822.59	−0.759170
$344$	−13475.1	−2.11201
$345$	0	0
$346$	−10918.0	−1.69640
$347$	−3968.72	−0.613982	−0.306991	−	0.951712i	$-0.599322\pi$
$347$	−3968.72	−0.613982	−0.306991	+	0.951712i	$0.599322\pi$
$348$	13423.7	2.06778
$349$	222.016	0.0340523	0.0170262	−	0.999855i	$-0.494580\pi$
$349$	222.016	0.0340523	0.0170262	+	0.999855i	$0.494580\pi$
$350$	−6297.55	−0.961766
$351$	4301.31	0.654094
$352$	9456.37	1.43189
$353$	2223.61	0.335272	0.167636	−	0.985849i	$-0.446387\pi$
$353$	2223.61	0.335272	0.167636	+	0.985849i	$0.446387\pi$
$354$	19744.3	2.96440
$355$	−4594.10	−0.686843
$356$	−15431.5	−2.29738
$357$	1694.59	0.251225
$358$	−21523.6	−3.17753
$359$	4487.81	0.659770	0.329885	−	0.944021i	$-0.392990\pi$
$359$	4487.81	0.659770	0.329885	+	0.944021i	$0.392990\pi$
$360$	−2498.53	−0.365789
$361$	−3523.83	−0.513753
$362$	20986.9	3.04709
$363$	4895.01	0.707772
$364$	4687.40	0.674963
$365$	10179.9	1.45984
$366$	7000.50	0.999787
$367$	3655.81	0.519978	0.259989	−	0.965612i	$-0.416281\pi$
$367$	3655.81	0.519978	0.259989	+	0.965612i	$0.416281\pi$
$368$	0	0
$369$	−743.035	−0.104826
$370$	7656.72	1.07582
$371$	5840.64	0.817334
$372$	−15626.0	−2.17788
$373$	−4245.19	−0.589297	−0.294649	−	0.955606i	$-0.595203\pi$
$373$	−4245.19	−0.589297	−0.294649	+	0.955606i	$0.595203\pi$
$374$	−4412.05	−0.610004
$375$	2327.66	0.320533
$376$	−8548.59	−1.17250
$377$	−3870.51	−0.528757
$378$	−5985.56	−0.814454
$379$	−7047.58	−0.955171	−0.477586	−	0.878585i	$-0.658488\pi$
$379$	−7047.58	−0.955171	−0.477586	+	0.878585i	$0.658488\pi$
$380$	19840.2	2.67838
$381$	−1757.63	−0.236342
$382$	23899.2	3.20102
$383$	−9245.97	−1.23354	−0.616771	−	0.787142i	$-0.711560\pi$
$383$	−9245.97	−1.23354	−0.616771	+	0.787142i	$0.711560\pi$
$384$	10346.1	1.37492
$385$	2391.92	0.316633
$386$	−16096.9	−2.12257
$387$	−444.423	−0.0583754
$388$	7636.39	0.999173
$389$	4195.74	0.546870	0.273435	−	0.961891i	$-0.411840\pi$
$389$	4195.74	0.546870	0.273435	+	0.961891i	$0.411840\pi$
$390$	−13126.2	−1.70428
$391$	0	0
$392$	19129.3	2.46473
$393$	−4172.45	−0.535552
$394$	−26705.0	−3.41466
$395$	16589.9	2.11323
$396$	853.923	0.108362
$397$	7766.52	0.981840	0.490920	−	0.871205i	$-0.336661\pi$
$397$	7766.52	0.981840	0.490920	+	0.871205i	$0.336661\pi$
$398$	8027.82	1.01105
$399$	2211.73	0.277506
$400$	29944.8	3.74309
$401$	15563.0	1.93811	0.969054	−	0.246849i	$-0.0793953\pi$
$401$	15563.0	1.93811	0.969054	+	0.246849i	$0.0793953\pi$
$402$	2720.93	0.337581
$403$	4505.52	0.556912
$404$	−12221.8	−1.50509
$405$	11072.6	1.35852
$406$	5386.07	0.658389
$407$	−1600.74	−0.194953
$408$	−14845.6	−1.80139
$409$	568.129	0.0686851	0.0343425	−	0.999410i	$-0.489066\pi$
$409$	568.129	0.0686851	0.0343425	+	0.999410i	$0.489066\pi$
$410$	29807.6	3.59047
$411$	9337.61	1.12066
$412$	23132.5	2.76616
$413$	5706.39	0.679886
$414$	0	0
$415$	6182.60	0.731306
$416$	−14998.0	−1.76764
$417$	7039.34	0.826662
$418$	−5758.46	−0.673817
$419$	−13017.7	−1.51779	−0.758896	−	0.651212i	$-0.774261\pi$
$419$	−13017.7	−1.51779	−0.758896	+	0.651212i	$0.774261\pi$
$420$	13157.1	1.52858
$421$	8342.69	0.965791	0.482895	−	0.875678i	$-0.339585\pi$
$421$	8342.69	0.965791	0.482895	+	0.875678i	$0.339585\pi$
$422$	−2442.23	−0.281720
$423$	−281.941	−0.0324077
$424$	−51167.4	−5.86063
$425$	−6771.87	−0.772904
$426$	7334.55	0.834179
$427$	2023.24	0.229301
$428$	−21918.5	−2.47540
$429$	2744.21	0.308838
$430$	17828.5	1.99945
$431$	4666.29	0.521502	0.260751	−	0.965406i	$-0.416030\pi$
$431$	4666.29	0.521502	0.260751	+	0.965406i	$0.416030\pi$
$432$	28461.3	3.16977
$433$	735.157	0.0815922	0.0407961	−	0.999167i	$-0.487011\pi$
$433$	735.157	0.0815922	0.0407961	+	0.999167i	$0.487011\pi$
$434$	−6269.72	−0.693447
$435$	−10864.2	−1.19747
$436$	−26046.7	−2.86103
$437$	0	0
$438$	−16252.4	−1.77299
$439$	4550.38	0.494710	0.247355	−	0.968925i	$-0.420439\pi$
$439$	4550.38	0.494710	0.247355	+	0.968925i	$0.420439\pi$
$440$	−20954.6	−2.27039
$441$	630.904	0.0681248
$442$	6997.62	0.753038
$443$	−6681.96	−0.716635	−0.358318	−	0.933600i	$-0.616649\pi$
$443$	−6681.96	−0.716635	−0.358318	+	0.933600i	$0.616649\pi$
$444$	−8805.13	−0.941155
$445$	12489.2	1.33043
$446$	−2660.16	−0.282427
$447$	12971.4	1.37254
$448$	8827.51	0.930938
$449$	13.1976	0.00138715	0.000693576	−	1.00000i	$-0.499779\pi$
$449$	13.1976	0.00138715	0.000693576		1.00000i	$0.499779\pi$
$450$	1819.57	0.190612
$451$	−6231.68	−0.650640
$452$	15470.2	1.60986
$453$	−4722.27	−0.489782
$454$	17580.2	1.81735
$455$	−3793.65	−0.390877
$456$	−19376.0	−1.98984
$457$	4649.93	0.475962	0.237981	−	0.971270i	$-0.423514\pi$
$457$	4649.93	0.475962	0.237981	+	0.971270i	$0.423514\pi$
$458$	−20640.1	−2.10578
$459$	−6436.38	−0.654520
$460$	0	0
$461$	−7703.46	−0.778277	−0.389139	−	0.921179i	$-0.627227\pi$
$461$	−7703.46	−0.778277	−0.389139	+	0.921179i	$0.627227\pi$
$462$	−3818.75	−0.384554
$463$	3025.26	0.303662	0.151831	−	0.988406i	$-0.451483\pi$
$463$	3025.26	0.303662	0.151831	+	0.988406i	$0.451483\pi$
$464$	−25610.7	−2.56239
$465$	12646.6	1.26123
$466$	−3949.46	−0.392607
$467$	−18570.7	−1.84015	−0.920075	−	0.391743i	$-0.871872\pi$
$467$	−18570.7	−1.84015	−0.920075	+	0.391743i	$0.871872\pi$
$468$	−1354.34	−0.133770
$469$	786.386	0.0774242
$470$	11310.3	1.11001
$471$	−10070.1	−0.985152
$472$	−49991.2	−4.87507
$473$	−3727.28	−0.362327
$474$	−26486.0	−2.56654
$475$	−8838.42	−0.853757
$476$	−7014.12	−0.675402
$477$	−1687.55	−0.161987
$478$	−9902.80	−0.947581
$479$	12817.1	1.22261	0.611304	−	0.791396i	$-0.290645\pi$
$479$	12817.1	1.22261	0.611304	+	0.791396i	$0.290645\pi$
$480$	−42098.2	−4.00315
$481$	2538.82	0.240666
$482$	18278.1	1.72727
$483$	0	0
$484$	−20261.0	−1.90280
$485$	−6180.36	−0.578630
$486$	3327.29	0.310553
$487$	19367.1	1.80206	0.901032	−	0.433753i	$-0.142811\pi$
$487$	19367.1	1.80206	0.901032	+	0.433753i	$0.142811\pi$
$488$	−17724.8	−1.64419
$489$	−1386.95	−0.128262
$490$	−25309.3	−2.33338
$491$	−4004.55	−0.368071	−0.184036	−	0.982920i	$-0.558916\pi$
$491$	−4004.55	−0.368071	−0.184036	+	0.982920i	$0.558916\pi$
$492$	−34278.3	−3.14103
$493$	5791.74	0.529101
$494$	9133.07	0.831814
$495$	−691.105	−0.0627532
$496$	29812.4	2.69883
$497$	2119.79	0.191319
$498$	−9870.63	−0.888179
$499$	1554.44	0.139452	0.0697258	−	0.997566i	$-0.477788\pi$
$499$	1554.44	0.139452	0.0697258	+	0.997566i	$0.477788\pi$
$500$	−9634.46	−0.861733
$501$	3203.73	0.285693
$502$	−29460.1	−2.61926
$503$	−15826.7	−1.40294	−0.701468	−	0.712701i	$-0.747472\pi$
$503$	−15826.7	−1.40294	−0.701468	+	0.712701i	$0.747472\pi$
$504$	1152.86	0.101890
$505$	9891.47	0.871613
$506$	0	0
$507$	6583.50	0.576694
$508$	7275.03	0.635388
$509$	5819.10	0.506733	0.253366	−	0.967370i	$-0.418462\pi$
$509$	5819.10	0.506733	0.253366	+	0.967370i	$0.418462\pi$
$510$	19641.7	1.70539
$511$	−4697.16	−0.406635
$512$	6265.60	0.540826
$513$	−8400.56	−0.722989
$514$	33942.9	2.91276
$515$	−18721.8	−1.60191
$516$	−20502.5	−1.74917
$517$	−2364.58	−0.201149
$518$	−3532.93	−0.299668
$519$	−10161.6	−0.859428
$520$	33234.6	2.80276
$521$	−597.668	−0.0502578	−0.0251289	−	0.999684i	$-0.508000\pi$
$521$	−597.668	−0.0502578	−0.0251289	+	0.999684i	$0.508000\pi$
$522$	−1556.21	−0.130486
$523$	4621.46	0.386391	0.193195	−	0.981160i	$-0.438115\pi$
$523$	4621.46	0.386391	0.193195	+	0.981160i	$0.438115\pi$
$524$	17270.2	1.43980
$525$	−5861.24	−0.487248
$526$	−4223.61	−0.350111
$527$	−6741.95	−0.557275
$528$	18158.1	1.49665
$529$	0	0
$530$	67697.8	5.54831
$531$	−1648.76	−0.134746
$532$	−9154.59	−0.746056
$533$	9883.61	0.803202
$534$	−19939.2	−1.61583
$535$	17739.3	1.43352
$536$	−6889.20	−0.555164
$537$	−20032.4	−1.60980
$538$	−11323.8	−0.907445
$539$	5291.26	0.422840
$540$	−49973.2	−3.98242
$541$	−2051.95	−0.163068	−0.0815342	−	0.996671i	$-0.525982\pi$
$541$	−2051.95	−0.163068	−0.0815342	+	0.996671i	$0.525982\pi$
$542$	13610.3	1.07862
$543$	19532.9	1.54371
$544$	22442.7	1.76879
$545$	21080.3	1.65685
$546$	6056.63	0.474725
$547$	−14848.8	−1.16067	−0.580336	−	0.814377i	$-0.697079\pi$
$547$	−14848.8	−1.16067	−0.580336	+	0.814377i	$0.697079\pi$
$548$	−38649.4	−3.01281
$549$	−584.581	−0.0454450
$550$	15260.3	1.18310
$551$	7559.19	0.584451
$552$	0	0
$553$	−7654.82	−0.588637
$554$	−37254.5	−2.85702
$555$	7126.25	0.545031
$556$	−29136.6	−2.22243
$557$	3987.17	0.303307	0.151653	−	0.988434i	$-0.451540\pi$
$557$	3987.17	0.303307	0.151653	+	0.988434i	$0.451540\pi$
$558$	1811.53	0.137434
$559$	5911.57	0.447286
$560$	−25102.1	−1.89421
$561$	−4106.37	−0.309039
$562$	35029.3	2.62922
$563$	1529.20	0.114473	0.0572365	−	0.998361i	$-0.481771\pi$
$563$	1529.20	0.114473	0.0572365	+	0.998361i	$0.481771\pi$
$564$	−13006.7	−0.971068
$565$	−12520.5	−0.932283
$566$	13765.8	1.02230
$567$	−5109.06	−0.378413
$568$	−18570.6	−1.37184
$569$	−1502.71	−0.110715	−0.0553575	−	0.998467i	$-0.517630\pi$
$569$	−1502.71	−0.110715	−0.0553575	+	0.998467i	$0.517630\pi$
$570$	25635.7	1.88379
$571$	18439.0	1.35140	0.675698	−	0.737179i	$-0.263842\pi$
$571$	18439.0	1.35140	0.675698	+	0.737179i	$0.263842\pi$
$572$	−11358.6	−0.830292
$573$	22243.4	1.62170
$574$	−13753.7	−1.00012
$575$	0	0
$576$	−2550.55	−0.184502
$577$	7047.28	0.508462	0.254231	−	0.967144i	$-0.418178\pi$
$577$	7047.28	0.508462	0.254231	+	0.967144i	$0.418178\pi$
$578$	15804.5	1.13734
$579$	−14981.7	−1.07533
$580$	44968.1	3.21931
$581$	−2852.75	−0.203704
$582$	9867.04	0.702753
$583$	−14153.1	−1.00543
$584$	41149.9	2.91574
$585$	1096.11	0.0774676
$586$	25409.7	1.79123
$587$	443.692	0.0311978	0.0155989	−	0.999878i	$-0.495035\pi$
$587$	443.692	0.0311978	0.0155989	+	0.999878i	$0.495035\pi$
$588$	29105.4	2.04130
$589$	−8799.37	−0.615571
$590$	66141.7	4.61527
$591$	−24854.8	−1.72993
$592$	16799.0	1.16628
$593$	−3597.92	−0.249155	−0.124577	−	0.992210i	$-0.539757\pi$
$593$	−3597.92	−0.249155	−0.124577	+	0.992210i	$0.539757\pi$
$594$	14504.3	1.00188
$595$	5676.73	0.391131
$596$	−53690.0	−3.68998
$597$	7471.63	0.512217
$598$	0	0
$599$	−18693.3	−1.27510	−0.637552	−	0.770407i	$-0.720053\pi$
$599$	−18693.3	−1.27510	−0.637552	+	0.770407i	$0.720053\pi$
$600$	51347.8	3.49378
$601$	−1362.47	−0.0924732	−0.0462366	−	0.998931i	$-0.514723\pi$
$601$	−1362.47	−0.0924732	−0.0462366	+	0.998931i	$0.514723\pi$
$602$	−8226.33	−0.556944
$603$	−227.213	−0.0153446
$604$	19546.0	1.31675
$605$	16397.8	1.10193
$606$	−15791.9	−1.05858
$607$	−24186.6	−1.61730	−0.808652	−	0.588288i	$-0.799802\pi$
$607$	−24186.6	−1.61730	−0.808652	+	0.588288i	$0.799802\pi$
$608$	29291.5	1.95383
$609$	5012.91	0.333552
$610$	23451.0	1.55656
$611$	3750.29	0.248315
$612$	2026.61	0.133857
$613$	−4575.06	−0.301444	−0.150722	−	0.988576i	$-0.548160\pi$
$613$	−4575.06	−0.301444	−0.150722	+	0.988576i	$0.548160\pi$
$614$	30307.1	1.99201
$615$	27742.4	1.81900
$616$	9668.79	0.632413
$617$	513.945	0.0335343	0.0167671	−	0.999859i	$-0.494663\pi$
$617$	513.945	0.0335343	0.0167671	+	0.999859i	$0.494663\pi$
$618$	29889.7	1.94553
$619$	21594.8	1.40221	0.701105	−	0.713058i	$-0.252690\pi$
$619$	21594.8	1.40221	0.701105	+	0.713058i	$0.252690\pi$
$620$	−52345.7	−3.39073
$621$	0	0
$622$	18323.6	1.18120
$623$	−5762.70	−0.370590
$624$	−28799.2	−1.84758
$625$	−11333.0	−0.725315
$626$	36563.2	2.33444
$627$	−5359.50	−0.341368
$628$	41681.4	2.64852
$629$	−3799.03	−0.240822
$630$	−1525.31	−0.0964599
$631$	−28382.2	−1.79062	−0.895309	−	0.445446i	$-0.853045\pi$
$631$	−28382.2	−1.79062	−0.895309	+	0.445446i	$0.853045\pi$
$632$	67060.7	4.22077
$633$	−2273.03	−0.142725
$634$	−6810.73	−0.426638
$635$	−5887.90	−0.367959
$636$	−77851.5	−4.85379
$637$	−8392.07	−0.521987
$638$	−13051.6	−0.809904
$639$	−612.476	−0.0379173
$640$	34658.3	2.14061
$641$	4764.70	0.293595	0.146798	−	0.989167i	$-0.453103\pi$
$641$	4764.70	0.293595	0.146798	+	0.989167i	$0.453103\pi$
$642$	−28321.0	−1.74103
$643$	19.9338	0.00122257	0.000611284	−	1.00000i	$-0.499805\pi$
$643$	19.9338	0.00122257	0.000611284		1.00000i	$0.499805\pi$
$644$	0	0
$645$	16593.3	1.01296
$646$	−13666.5	−0.832355
$647$	−25204.3	−1.53151	−0.765753	−	0.643134i	$-0.777634\pi$
$647$	−25204.3	−1.53151	−0.765753	+	0.643134i	$0.777634\pi$
$648$	44758.3	2.71338
$649$	−13827.8	−0.836347
$650$	−24203.3	−1.46051
$651$	−5835.34	−0.351313
$652$	5740.73	0.344823
$653$	27495.2	1.64773	0.823866	−	0.566785i	$-0.191813\pi$
$653$	27495.2	1.64773	0.823866	+	0.566785i	$0.191813\pi$
$654$	−33655.1	−2.01226
$655$	−13977.3	−0.833799
$656$	65398.6	3.89236
$657$	1357.16	0.0805906
$658$	−5218.77	−0.309193
$659$	−18633.5	−1.10146	−0.550728	−	0.834685i	$-0.685650\pi$
$659$	−18633.5	−1.10146	−0.550728	+	0.834685i	$0.685650\pi$
$660$	−31882.6	−1.88035
$661$	3032.20	0.178425	0.0892123	−	0.996013i	$-0.471565\pi$
$661$	3032.20	0.178425	0.0892123	+	0.996013i	$0.471565\pi$
$662$	−23372.7	−1.37221
$663$	6512.81	0.381503
$664$	24991.7	1.46064
$665$	7409.08	0.432048
$666$	1020.78	0.0593910
$667$	0	0
$668$	−13260.6	−0.768066
$669$	−2475.86	−0.143083
$670$	9114.85	0.525578
$671$	−4902.76	−0.282070
$672$	19424.8	1.11507
$673$	6139.01	0.351622	0.175811	−	0.984424i	$-0.443745\pi$
$673$	6139.01	0.351622	0.175811	+	0.984424i	$0.443745\pi$
$674$	−30150.7	−1.72309
$675$	22262.1	1.26943
$676$	−27249.9	−1.55040
$677$	−7923.34	−0.449806	−0.224903	−	0.974381i	$-0.572206\pi$
$677$	−7923.34	−0.449806	−0.224903	+	0.974381i	$0.572206\pi$
$678$	19989.1	1.13227
$679$	2851.71	0.161176
$680$	−49731.4	−2.80458
$681$	16362.2	0.920705
$682$	15192.9	0.853029
$683$	−2879.93	−0.161343	−0.0806716	−	0.996741i	$-0.525706\pi$
$683$	−2879.93	−0.161343	−0.0806716	+	0.996741i	$0.525706\pi$
$684$	2645.06	0.147860
$685$	31280.1	1.74475
$686$	25792.1	1.43549
$687$	−19210.1	−1.06683
$688$	39116.1	2.16757
$689$	22447.3	1.24118
$690$	0	0
$691$	3629.33	0.199807	0.0999033	−	0.994997i	$-0.468147\pi$
$691$	3629.33	0.199807	0.0999033	+	0.994997i	$0.468147\pi$
$692$	42059.9	2.31051
$693$	318.886	0.0174798
$694$	21225.4	1.16096
$695$	23581.1	1.28703
$696$	−43916.0	−2.39171
$697$	−14789.6	−0.803724
$698$	−1187.38	−0.0643885
$699$	−3675.83	−0.198902
$700$	24260.3	1.30993
$701$	29193.0	1.57290	0.786452	−	0.617651i	$-0.211916\pi$
$701$	29193.0	1.57290	0.786452	+	0.617651i	$0.211916\pi$
$702$	−23004.2	−1.23681
$703$	−4958.37	−0.266015
$704$	−21391.0	−1.14517
$705$	10526.7	0.562354
$706$	−11892.3	−0.633954
$707$	−4564.08	−0.242786
$708$	−76062.0	−4.03755
$709$	2328.75	0.123354	0.0616771	−	0.998096i	$-0.480355\pi$
$709$	2328.75	0.123354	0.0616771	+	0.998096i	$0.480355\pi$
$710$	24570.1	1.29873
$711$	2211.73	0.116661
$712$	50484.6	2.65729
$713$	0	0
$714$	−9062.99	−0.475034
$715$	9192.85	0.480829
$716$	82916.3	4.32783
$717$	−9216.71	−0.480062
$718$	−24001.6	−1.24754
$719$	−6248.25	−0.324089	−0.162045	−	0.986783i	$-0.551809\pi$
$719$	−6248.25	−0.324089	−0.162045	+	0.986783i	$0.551809\pi$
$720$	7252.82	0.375412
$721$	8638.53	0.446208
$722$	18846.1	0.971440
$723$	17011.8	0.875068
$724$	−80848.8	−4.15017
$725$	−20032.4	−1.02619
$726$	−26179.4	−1.33830
$727$	−25579.0	−1.30491	−0.652457	−	0.757826i	$-0.726262\pi$
$727$	−25579.0	−1.30491	−0.652457	+	0.757826i	$0.726262\pi$
$728$	−15335.0	−0.780702
$729$	21025.7	1.06822
$730$	−54443.9	−2.76036
$731$	−8845.93	−0.447577
$732$	−26968.4	−1.36172
$733$	19555.6	0.985407	0.492704	−	0.870197i	$-0.336009\pi$
$733$	19555.6	0.985407	0.492704	+	0.870197i	$0.336009\pi$
$734$	−19552.0	−0.983210
$735$	−23555.8	−1.18214
$736$	0	0
$737$	−1905.58	−0.0952417
$738$	3973.89	0.198213
$739$	1767.88	0.0880005	0.0440002	−	0.999032i	$-0.485990\pi$
$739$	1767.88	0.0880005	0.0440002	+	0.999032i	$0.485990\pi$
$740$	−29496.3	−1.46528
$741$	8500.30	0.421412
$742$	−31236.8	−1.54547
$743$	24114.0	1.19065	0.595327	−	0.803483i	$-0.297022\pi$
$743$	24114.0	1.19065	0.595327	+	0.803483i	$0.297022\pi$
$744$	51120.9	2.51906
$745$	43452.9	2.13690
$746$	22704.1	1.11428
$747$	824.252	0.0403719
$748$	16996.7	0.830832
$749$	−8185.17	−0.399305
$750$	−12448.8	−0.606086
$751$	8161.37	0.396555	0.198277	−	0.980146i	$-0.436465\pi$
$751$	8161.37	0.396555	0.198277	+	0.980146i	$0.436465\pi$
$752$	24815.2	1.20335
$753$	−27419.0	−1.32696
$754$	20700.2	0.999811
$755$	−15819.1	−0.762540
$756$	23058.4	1.10930
$757$	−22301.0	−1.07073	−0.535365	−	0.844621i	$-0.679826\pi$
$757$	−22301.0	−1.07073	−0.535365	+	0.844621i	$0.679826\pi$
$758$	37691.7	1.80610
$759$	0	0
$760$	−64907.8	−3.09797
$761$	15601.5	0.743174	0.371587	−	0.928398i	$-0.378814\pi$
$761$	15601.5	0.743174	0.371587	+	0.928398i	$0.378814\pi$
$762$	9400.13	0.446891
$763$	−9726.80	−0.461512
$764$	−92068.0	−4.35982
$765$	−1640.19	−0.0775180
$766$	49449.1	2.33247
$767$	21931.3	1.03245
$768$	−9644.50	−0.453146
$769$	−18247.5	−0.855686	−0.427843	−	0.903853i	$-0.640726\pi$
$769$	−18247.5	−0.855686	−0.427843	+	0.903853i	$0.640726\pi$
$770$	−12792.4	−0.598711
$771$	31591.2	1.47566
$772$	62010.9	2.89096
$773$	15455.8	0.719154	0.359577	−	0.933115i	$-0.382921\pi$
$773$	15455.8	0.719154	0.359577	+	0.933115i	$0.382921\pi$
$774$	2376.86	0.110380
$775$	23318.9	1.08083
$776$	−24982.7	−1.15570
$777$	−3288.16	−0.151817
$778$	−22439.6	−1.03406
$779$	−19302.9	−0.887802
$780$	50566.6	2.32125
$781$	−5136.71	−0.235347
$782$	0	0
$783$	−19040.0	−0.869007
$784$	−55529.3	−2.52958
$785$	−33734.0	−1.53378
$786$	22315.0	1.01266
$787$	−41756.5	−1.89131	−0.945653	−	0.325178i	$-0.894576\pi$
$787$	−41756.5	−1.89131	−0.945653	+	0.325178i	$0.894576\pi$
$788$	102877.	4.65081
$789$	−3930.99	−0.177373
$790$	−88725.6	−3.99584
$791$	5777.14	0.259686
$792$	−2793.63	−0.125338
$793$	7775.90	0.348210
$794$	−41536.7	−1.85653
$795$	63007.5	2.81088
$796$	−30925.9	−1.37706
$797$	35471.1	1.57647	0.788237	−	0.615372i	$-0.210994\pi$
$797$	35471.1	1.57647	0.788237	+	0.615372i	$0.210994\pi$
$798$	−11828.7	−0.524727
$799$	−5611.84	−0.248476
$800$	−77624.6	−3.43055
$801$	1665.03	0.0734469
$802$	−83234.0	−3.66471
$803$	11382.3	0.500213
$804$	−10482.0	−0.459789
$805$	0	0
$806$	−24096.3	−1.05305
$807$	−10539.3	−0.459728
$808$	39984.0	1.74088
$809$	38812.7	1.68675	0.843375	−	0.537325i	$-0.180565\pi$
$809$	38812.7	1.68675	0.843375	+	0.537325i	$0.180565\pi$
$810$	−59218.1	−2.56878
$811$	−22669.5	−0.981546	−0.490773	−	0.871287i	$-0.663286\pi$
$811$	−22669.5	−0.981546	−0.490773	+	0.871287i	$0.663286\pi$
$812$	−20749.0	−0.896733
$813$	12667.4	0.546450
$814$	8561.06	0.368630
$815$	−4646.14	−0.199690
$816$	43094.4	1.84878
$817$	−11545.4	−0.494398
$818$	−3038.46	−0.129874
$819$	−505.762	−0.0215785
$820$	−114829.	−4.89025
$821$	−20935.8	−0.889967	−0.444984	−	0.895539i	$-0.646791\pi$
$821$	−20935.8	−0.889967	−0.444984	+	0.895539i	$0.646791\pi$
$822$	−49939.2	−2.11902
$823$	−14199.6	−0.601417	−0.300708	−	0.953716i	$-0.597223\pi$
$823$	−14199.6	−0.601417	−0.300708	+	0.953716i	$0.597223\pi$
$824$	−75678.6	−3.19950
$825$	14203.1	0.599378
$826$	−30518.8	−1.28557
$827$	−44936.9	−1.88949	−0.944746	−	0.327803i	$-0.893692\pi$
$827$	−44936.9	−1.88949	−0.944746	+	0.327803i	$0.893692\pi$
$828$	0	0
$829$	−9240.93	−0.387154	−0.193577	−	0.981085i	$-0.562009\pi$
$829$	−9240.93	−0.387154	−0.193577	+	0.981085i	$0.562009\pi$
$830$	−33065.7	−1.38280
$831$	−34673.4	−1.44742
$832$	33926.6	1.41370
$833$	12557.7	0.522327
$834$	−37647.7	−1.56311
$835$	10732.2	0.444794
$836$	22183.6	0.917745
$837$	22163.7	0.915280
$838$	69620.9	2.86994
$839$	−32694.8	−1.34535	−0.672675	−	0.739938i	$-0.734855\pi$
$839$	−32694.8	−1.34535	−0.672675	+	0.739938i	$0.734855\pi$
$840$	−43043.9	−1.76804
$841$	−7255.99	−0.297511
$842$	−44618.2	−1.82618
$843$	32602.4	1.33201
$844$	9408.32	0.383706
$845$	22054.1	0.897852
$846$	1507.87	0.0612786
$847$	−7566.20	−0.306940
$848$	148531.	6.01482
$849$	12812.1	0.517915
$850$	36217.2	1.46146
$851$	0	0
$852$	−28255.2	−1.13616
$853$	43809.9	1.75853	0.879263	−	0.476337i	$-0.158036\pi$
$853$	43809.9	1.75853	0.879263	+	0.476337i	$0.158036\pi$
$854$	−10820.7	−0.433578
$855$	−2140.73	−0.0856272
$856$	71706.8	2.86319
$857$	4605.22	0.183561	0.0917803	−	0.995779i	$-0.470744\pi$
$857$	4605.22	0.183561	0.0917803	+	0.995779i	$0.470744\pi$
$858$	−14676.5	−0.583973
$859$	−16963.5	−0.673792	−0.336896	−	0.941542i	$-0.609377\pi$
$859$	−16963.5	−0.673792	−0.336896	+	0.941542i	$0.609377\pi$
$860$	−68681.4	−2.72327
$861$	−12800.8	−0.506678
$862$	−24956.2	−0.986091
$863$	−9074.76	−0.357947	−0.178974	−	0.983854i	$-0.557278\pi$
$863$	−9074.76	−0.357947	−0.178974	+	0.983854i	$0.557278\pi$
$864$	−73778.9	−2.90510
$865$	−34040.3	−1.33804
$866$	−3931.76	−0.154280
$867$	14709.6	0.576197
$868$	24153.1	0.944482
$869$	18549.3	0.724099
$870$	58103.7	2.26425
$871$	3022.31	0.117574
$872$	85212.4	3.30924
$873$	−823.953	−0.0319434
$874$	0	0
$875$	−3597.87	−0.139006
$876$	62609.8	2.41483
$877$	16087.6	0.619429	0.309715	−	0.950830i	$-0.399766\pi$
$877$	16087.6	0.619429	0.309715	+	0.950830i	$0.399766\pi$
$878$	−24336.3	−0.935432
$879$	23649.2	0.907472
$880$	60827.9	2.33012
$881$	−11415.0	−0.436528	−0.218264	−	0.975890i	$-0.570039\pi$
$881$	−11415.0	−0.436528	−0.218264	+	0.975890i	$0.570039\pi$
$882$	−3374.19	−0.128815
$883$	−37562.2	−1.43156	−0.715781	−	0.698324i	$-0.753929\pi$
$883$	−37562.2	−1.43156	−0.715781	+	0.698324i	$0.753929\pi$
$884$	−26957.3	−1.02565
$885$	61559.2	2.33818
$886$	35736.3	1.35506
$887$	−30871.9	−1.16863	−0.584316	−	0.811526i	$-0.698637\pi$
$887$	−30871.9	−1.16863	−0.584316	+	0.811526i	$0.698637\pi$
$888$	28806.2	1.08859
$889$	2716.77	0.102494
$890$	−66794.4	−2.51568
$891$	12380.4	0.465497
$892$	10247.9	0.384668
$893$	−7324.39	−0.274470
$894$	−69373.2	−2.59529
$895$	−67106.6	−2.50629
$896$	−15991.9	−0.596263
$897$	0	0
$898$	−70.5829	−0.00262292
$899$	−19943.9	−0.739895
$900$	−7009.60	−0.259615
$901$	−33589.5	−1.24199
$902$	33328.2	1.23027
$903$	−7656.39	−0.282158
$904$	−50611.0	−1.86206
$905$	65433.3	2.40340
$906$	25255.5	0.926114
$907$	15486.0	0.566928	0.283464	−	0.958983i	$-0.408516\pi$
$907$	15486.0	0.566928	0.283464	+	0.958983i	$0.408516\pi$
$908$	−67724.9	−2.47525
$909$	1318.71	0.0481176
$910$	20289.1	0.739097
$911$	−7113.72	−0.258713	−0.129357	−	0.991598i	$-0.541291\pi$
$911$	−7113.72	−0.258713	−0.129357	+	0.991598i	$0.541291\pi$
$912$	56245.4	2.04219
$913$	6912.83	0.250582
$914$	−24868.7	−0.899981
$915$	21826.3	0.788584
$916$	79512.8	2.86810
$917$	6449.35	0.232253
$918$	34422.9	1.23761
$919$	−28732.6	−1.03134	−0.515669	−	0.856788i	$-0.672457\pi$
$919$	−28732.6	−1.03134	−0.515669	+	0.856788i	$0.672457\pi$
$920$	0	0
$921$	28207.4	1.00919
$922$	41199.5	1.47162
$923$	8146.95	0.290531
$924$	14711.1	0.523767
$925$	13140.0	0.467072
$926$	−16179.6	−0.574185
$927$	−2495.96	−0.0884336
$928$	66389.6	2.34843
$929$	11558.1	0.408192	0.204096	−	0.978951i	$-0.434575\pi$
$929$	11558.1	0.408192	0.204096	+	0.978951i	$0.434575\pi$
$930$	−67636.3	−2.38482
$931$	16389.9	0.576968
$932$	15214.7	0.534735
$933$	17054.1	0.598420
$934$	99319.5	3.47948
$935$	−13756.0	−0.481142
$936$	4430.77	0.154727
$937$	−9644.45	−0.336255	−0.168127	−	0.985765i	$-0.553772\pi$
$937$	−9644.45	−0.336255	−0.168127	+	0.985765i	$0.553772\pi$
$938$	−4205.74	−0.146399
$939$	34030.0	1.18267
$940$	−43571.3	−1.51185
$941$	14437.1	0.500143	0.250072	−	0.968227i	$-0.419546\pi$
$941$	14437.1	0.500143	0.250072	+	0.968227i	$0.419546\pi$
$942$	53856.8	1.86279
$943$	0	0
$944$	145117.	5.00333
$945$	−18661.9	−0.642403
$946$	19934.2	0.685113
$947$	−44849.3	−1.53897	−0.769486	−	0.638664i	$-0.779487\pi$
$947$	−44849.3	−1.53897	−0.769486	+	0.638664i	$0.779487\pi$
$948$	102033.	3.49566
$949$	−18052.5	−0.617503
$950$	47269.5	1.61434
$951$	−6338.86	−0.216143
$952$	22946.9	0.781210
$953$	−56306.6	−1.91390	−0.956952	−	0.290247i	$-0.906263\pi$
$953$	−56306.6	−1.91390	−0.956952	+	0.290247i	$0.906263\pi$
$954$	9025.33	0.306296
$955$	74513.3	2.52481
$956$	38149.0	1.29061
$957$	−12147.4	−0.410312
$958$	−68548.3	−2.31179
$959$	−14433.1	−0.485996
$960$	95229.1	3.20157
$961$	−6575.10	−0.220708
$962$	−13578.1	−0.455067
$963$	2364.96	0.0791380
$964$	−70413.6	−2.35256
$965$	−50187.2	−1.67418
$966$	0	0
$967$	30681.6	1.02033	0.510163	−	0.860078i	$-0.329585\pi$
$967$	30681.6	1.02033	0.510163	+	0.860078i	$0.329585\pi$
$968$	66284.3	2.20089
$969$	−12719.7	−0.421686
$970$	33053.7	1.09411
$971$	32313.5	1.06796	0.533980	−	0.845497i	$-0.320696\pi$
$971$	32313.5	1.06796	0.533980	+	0.845497i	$0.320696\pi$
$972$	−12817.9	−0.422976
$973$	−10880.7	−0.358499
$974$	−103579.	−3.40746
$975$	−22526.4	−0.739921
$976$	51452.2	1.68744
$977$	34011.4	1.11374	0.556868	−	0.830601i	$-0.312003\pi$
$977$	34011.4	1.11374	0.556868	+	0.830601i	$0.312003\pi$
$978$	7417.65	0.242526
$979$	13964.3	0.455873
$980$	97500.2	3.17809
$981$	2810.39	0.0914667
$982$	21417.1	0.695974
$983$	−19406.4	−0.629673	−0.314836	−	0.949146i	$-0.601950\pi$
$983$	−19406.4	−0.629673	−0.314836	+	0.949146i	$0.601950\pi$
$984$	112142.	3.63310
$985$	−83261.2	−2.69332
$986$	−30975.3	−1.00046
$987$	−4857.20	−0.156643
$988$	−35183.7	−1.13294
$989$	0	0
$990$	3696.15	0.118658
$991$	−15089.6	−0.483689	−0.241844	−	0.970315i	$-0.577752\pi$
$991$	−15089.6	−0.483689	−0.241844	+	0.970315i	$0.577752\pi$
$992$	−77281.5	−2.47348
$993$	−21753.4	−0.695189
$994$	−11337.0	−0.361759
$995$	25029.3	0.797469
$996$	38025.1	1.20971
$997$	−53588.1	−1.70226	−0.851130	−	0.524955i	$-0.824082\pi$
$997$	−53588.1	−1.70226	−0.851130	+	0.524955i	$0.824082\pi$
$998$	−8313.44	−0.263685
$999$	12489.0	0.395532

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.1		25
23.17	odd	22		23.4.c.a.13.5	✓	50
23.19	odd	22		23.4.c.a.16.5	yes	50
23.22	odd	2		529.4.a.n.1.1		25
69.17	even	22		207.4.i.a.82.1		50
69.65	even	22		207.4.i.a.154.1		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.13.5	✓	50	23.17	odd	22
23.4.c.a.16.5	yes	50	23.19	odd	22
207.4.i.a.82.1		50	69.17	even	22
207.4.i.a.154.1		50	69.65	even	22
529.4.a.m.1.1		25	1.1	even	1	trivial
529.4.a.n.1.1		25	23.22	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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-5.34818 q^{2} -4.97765 q^{3} +20.6030 q^{4} -16.6747 q^{5} +26.6214 q^{6} +7.69394 q^{7} -67.4034 q^{8} -2.22303 q^{9} +89.1791 q^{10} -18.6441 q^{11} -102.555 q^{12} +29.5700 q^{13} -41.1486 q^{14} +83.0005 q^{15} +195.661 q^{16} -44.2479 q^{17} +11.8892 q^{18} -57.7509 q^{19} -343.549 q^{20} -38.2977 q^{21} +99.7120 q^{22} +335.510 q^{24} +153.044 q^{25} -158.146 q^{26} +145.462 q^{27} +158.519 q^{28} -130.893 q^{29} -443.902 q^{30} +152.368 q^{31} -507.204 q^{32} +92.8038 q^{33} +236.646 q^{34} -128.294 q^{35} -45.8012 q^{36} +85.8578 q^{37} +308.862 q^{38} -147.189 q^{39} +1123.93 q^{40} +334.244 q^{41} +204.823 q^{42} +199.918 q^{43} -384.125 q^{44} +37.0683 q^{45} +126.827 q^{47} -973.932 q^{48} -283.803 q^{49} -818.507 q^{50} +220.250 q^{51} +609.233 q^{52} +759.122 q^{53} -777.957 q^{54} +310.884 q^{55} -518.598 q^{56} +287.464 q^{57} +700.040 q^{58} +741.673 q^{59} +1710.06 q^{60} +262.966 q^{61} -814.890 q^{62} -17.1039 q^{63} +1147.33 q^{64} -493.070 q^{65} -496.331 q^{66} +102.208 q^{67} -911.641 q^{68} +686.139 q^{70} +275.514 q^{71} +149.840 q^{72} -610.501 q^{73} -459.183 q^{74} -761.799 q^{75} -1189.84 q^{76} -143.447 q^{77} +787.194 q^{78} -994.915 q^{79} -3262.58 q^{80} -664.036 q^{81} -1787.60 q^{82} -370.778 q^{83} -789.050 q^{84} +737.818 q^{85} -1069.20 q^{86} +651.540 q^{87} +1256.68 q^{88} -748.991 q^{89} -198.248 q^{90} +227.510 q^{91} -758.432 q^{93} -678.295 q^{94} +962.976 q^{95} +2524.68 q^{96} +370.644 q^{97} +1517.83 q^{98} +41.4464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

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Database

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