LMFDB - Embedded newform 529.4.a.m.1.7

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			1.7
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)

$f(q)$	$=$	\(q-3.19041 q^{2} +1.55052 q^{3} +2.17871 q^{4} -19.2991 q^{5} -4.94680 q^{6} +19.8587 q^{7} +18.5723 q^{8} -24.5959 q^{9} +61.5722 q^{10} -17.2315 q^{11} +3.37814 q^{12} +37.7704 q^{13} -63.3574 q^{14} -29.9238 q^{15} -76.6829 q^{16} +22.1500 q^{17} +78.4709 q^{18} -6.74712 q^{19} -42.0473 q^{20} +30.7914 q^{21} +54.9754 q^{22} +28.7968 q^{24} +247.457 q^{25} -120.503 q^{26} -80.0006 q^{27} +43.2664 q^{28} +226.669 q^{29} +95.4691 q^{30} +292.339 q^{31} +96.0716 q^{32} -26.7178 q^{33} -70.6675 q^{34} -383.256 q^{35} -53.5873 q^{36} +113.785 q^{37} +21.5261 q^{38} +58.5639 q^{39} -358.429 q^{40} -443.225 q^{41} -98.2371 q^{42} -277.826 q^{43} -37.5424 q^{44} +474.679 q^{45} -75.1817 q^{47} -118.899 q^{48} +51.3683 q^{49} -789.489 q^{50} +34.3441 q^{51} +82.2909 q^{52} +195.931 q^{53} +255.235 q^{54} +332.553 q^{55} +368.822 q^{56} -10.4616 q^{57} -723.168 q^{58} -354.359 q^{59} -65.1953 q^{60} -36.1334 q^{61} -932.682 q^{62} -488.442 q^{63} +306.956 q^{64} -728.937 q^{65} +85.2407 q^{66} +40.3882 q^{67} +48.2585 q^{68} +1222.74 q^{70} +635.069 q^{71} -456.802 q^{72} +354.930 q^{73} -363.022 q^{74} +383.688 q^{75} -14.7000 q^{76} -342.195 q^{77} -186.843 q^{78} -726.065 q^{79} +1479.91 q^{80} +540.046 q^{81} +1414.07 q^{82} -1190.42 q^{83} +67.0856 q^{84} -427.476 q^{85} +886.379 q^{86} +351.456 q^{87} -320.028 q^{88} -1622.29 q^{89} -1514.42 q^{90} +750.072 q^{91} +453.279 q^{93} +239.860 q^{94} +130.214 q^{95} +148.961 q^{96} -621.081 q^{97} -163.886 q^{98} +423.823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.19041	−1.12798	−0.563990	−	0.825782i	$-0.690734\pi$
$2$	−3.19041	−1.12798	−0.563990	+	0.825782i	$0.690734\pi$
$3$	1.55052	0.298398	0.149199	−	0.988807i	$-0.452330\pi$
$3$	1.55052	0.298398	0.149199	+	0.988807i	$0.452330\pi$
$4$	2.17871	0.272339
$5$	−19.2991	−1.72617	−0.863084	−	0.505060i	$-0.831470\pi$
$5$	−19.2991	−1.72617	−0.863084	+	0.505060i	$0.831470\pi$
$6$	−4.94680	−0.336587
$7$	19.8587	1.07227	0.536135	−	0.844132i	$-0.319884\pi$
$7$	19.8587	1.07227	0.536135	+	0.844132i	$0.319884\pi$
$8$	18.5723	0.820787
$9$	−24.5959	−0.910958
$10$	61.5722	1.94708
$11$	−17.2315	−0.472317	−0.236158	−	0.971715i	$-0.575888\pi$
$11$	−17.2315	−0.472317	−0.236158	+	0.971715i	$0.575888\pi$
$12$	3.37814	0.0812655
$13$	37.7704	0.805817	0.402909	−	0.915240i	$-0.367999\pi$
$13$	37.7704	0.805817	0.402909	+	0.915240i	$0.367999\pi$
$14$	−63.3574	−1.20950
$15$	−29.9238	−0.515086
$16$	−76.6829	−1.19817
$17$	22.1500	0.316010	0.158005	−	0.987438i	$-0.449494\pi$
$17$	22.1500	0.316010	0.158005	+	0.987438i	$0.449494\pi$
$18$	78.4709	1.02754
$19$	−6.74712	−0.0814681	−0.0407341	−	0.999170i	$-0.512970\pi$
$19$	−6.74712	−0.0814681	−0.0407341	+	0.999170i	$0.512970\pi$
$20$	−42.0473	−0.470103
$21$	30.7914	0.319963
$22$	54.9754	0.532764
$23$	0	0
$23$	0	0
$24$	28.7968	0.244921
$25$	247.457	1.97966
$26$	−120.503	−0.908946
$27$	−80.0006	−0.570227
$28$	43.2664	0.292021
$29$	226.669	1.45143	0.725715	−	0.687996i	$-0.241509\pi$
$29$	226.669	1.45143	0.725715	+	0.687996i	$0.241509\pi$
$30$	95.4691	0.581006
$31$	292.339	1.69373	0.846866	−	0.531806i	$-0.178487\pi$
$31$	292.339	1.69373	0.846866	+	0.531806i	$0.178487\pi$
$32$	96.0716	0.530725
$33$	−26.7178	−0.140938
$34$	−70.6675	−0.356452
$35$	−383.256	−1.85092
$36$	−53.5873	−0.248090
$37$	113.785	0.505573	0.252786	−	0.967522i	$-0.418653\pi$
$37$	113.785	0.505573	0.252786	+	0.967522i	$0.418653\pi$
$38$	21.5261	0.0918944
$39$	58.5639	0.240455
$40$	−358.429	−1.41682
$41$	−443.225	−1.68830	−0.844148	−	0.536110i	$-0.819893\pi$
$41$	−443.225	−1.68830	−0.844148	+	0.536110i	$0.819893\pi$
$42$	−98.2371	−0.360912
$43$	−277.826	−0.985304	−0.492652	−	0.870226i	$-0.663972\pi$
$43$	−277.826	−0.985304	−0.492652	+	0.870226i	$0.663972\pi$
$44$	−37.5424	−0.128630
$45$	474.679	1.57247
$46$	0	0
$47$	−75.1817	−0.233327	−0.116664	−	0.993171i	$-0.537220\pi$
$47$	−75.1817	−0.233327	−0.116664	+	0.993171i	$0.537220\pi$
$48$	−118.899	−0.357532
$49$	51.3683	0.149762
$50$	−789.489	−2.23301
$51$	34.3441	0.0942967
$52$	82.2909	0.219456
$53$	195.931	0.507796	0.253898	−	0.967231i	$-0.418287\pi$
$53$	195.931	0.507796	0.253898	+	0.967231i	$0.418287\pi$
$54$	255.235	0.643204
$55$	332.553	0.815298
$56$	368.822	0.880105
$57$	−10.4616	−0.0243100
$58$	−723.168	−1.63718
$59$	−354.359	−0.781926	−0.390963	−	0.920406i	$-0.627858\pi$
$59$	−354.359	−0.781926	−0.390963	+	0.920406i	$0.627858\pi$
$60$	−65.1953	−0.140278
$61$	−36.1334	−0.0758427	−0.0379214	−	0.999281i	$-0.512074\pi$
$61$	−36.1334	−0.0758427	−0.0379214	+	0.999281i	$0.512074\pi$
$62$	−932.682	−1.91050
$63$	−488.442	−0.976793
$64$	306.956	0.599523
$65$	−728.937	−1.39098
$66$	85.2407	0.158976
$67$	40.3882	0.0736449	0.0368224	−	0.999322i	$-0.488276\pi$
$67$	40.3882	0.0736449	0.0368224	+	0.999322i	$0.488276\pi$
$68$	48.2585	0.0860617
$69$	0	0
$70$	1222.74	2.08780
$71$	635.069	1.06153	0.530766	−	0.847518i	$-0.321904\pi$
$71$	635.069	1.06153	0.530766	+	0.847518i	$0.321904\pi$
$72$	−456.802	−0.747703
$73$	354.930	0.569060	0.284530	−	0.958667i	$-0.408162\pi$
$73$	354.930	0.569060	0.284530	+	0.958667i	$0.408162\pi$
$74$	−363.022	−0.570276
$75$	383.688	0.590726
$76$	−14.7000	−0.0221870
$77$	−342.195	−0.506451
$78$	−186.843	−0.271228
$79$	−726.065	−1.03403	−0.517017	−	0.855975i	$-0.672958\pi$
$79$	−726.065	−1.03403	−0.517017	+	0.855975i	$0.672958\pi$
$80$	1479.91	2.06824
$81$	540.046	0.740804
$82$	1414.07	1.90436
$83$	−1190.42	−1.57428	−0.787141	−	0.616774i	$-0.788439\pi$
$83$	−1190.42	−1.57428	−0.787141	+	0.616774i	$0.788439\pi$
$84$	67.0856	0.0871385
$85$	−427.476	−0.545486
$86$	886.379	1.11140
$87$	351.456	0.433104
$88$	−320.028	−0.387671
$89$	−1622.29	−1.93216	−0.966079	−	0.258246i	$-0.916856\pi$
$89$	−1622.29	−1.93216	−0.966079	+	0.258246i	$0.916856\pi$
$90$	−1514.42	−1.77371
$91$	750.072	0.864053
$92$	0	0
$93$	453.279	0.505407
$94$	239.860	0.263188
$95$	130.214	0.140628
$96$	148.961	0.158368
$97$	−621.081	−0.650116	−0.325058	−	0.945694i	$-0.605384\pi$
$97$	−621.081	−0.650116	−0.325058	+	0.945694i	$0.605384\pi$
$98$	−163.886	−0.168928
$99$	423.823	0.430261
$100$	539.138	0.539138
$101$	−608.309	−0.599297	−0.299649	−	0.954050i	$-0.596869\pi$
$101$	−608.309	−0.599297	−0.299649	+	0.954050i	$0.596869\pi$
$102$	−109.572	−0.106365
$103$	−1037.77	−0.992762	−0.496381	−	0.868105i	$-0.665338\pi$
$103$	−1037.77	−0.992762	−0.496381	+	0.868105i	$0.665338\pi$
$104$	701.483	0.661405
$105$	−594.248	−0.552311
$106$	−625.100	−0.572784
$107$	−1329.55	−1.20124	−0.600619	−	0.799535i	$-0.705079\pi$
$107$	−1329.55	−1.20124	−0.600619	+	0.799535i	$0.705079\pi$
$108$	−174.298	−0.155295
$109$	1222.75	1.07448	0.537242	−	0.843428i	$-0.319466\pi$
$109$	1222.75	1.07448	0.537242	+	0.843428i	$0.319466\pi$
$110$	−1060.98	−0.919640
$111$	176.427	0.150862
$112$	−1522.82	−1.28476
$113$	−727.319	−0.605490	−0.302745	−	0.953072i	$-0.597903\pi$
$113$	−727.319	−0.605490	−0.302745	+	0.953072i	$0.597903\pi$
$114$	33.3767	0.0274211
$115$	0	0
$116$	493.848	0.395281
$117$	−928.996	−0.734066
$118$	1130.55	0.881997
$119$	439.870	0.338847
$120$	−555.753	−0.422776
$121$	−1034.08	−0.776917
$122$	115.280	0.0855491
$123$	−687.231	−0.503785
$124$	636.923	0.461269
$125$	−2363.32	−1.69105
$126$	1558.33	1.10180
$127$	540.736	0.377815	0.188908	−	0.981995i	$-0.439505\pi$
$127$	540.736	0.377815	0.188908	+	0.981995i	$0.439505\pi$
$128$	−1747.89	−1.20698
$129$	−430.776	−0.294013
$130$	2325.61	1.56899
$131$	48.5943	0.0324100	0.0162050	−	0.999869i	$-0.494842\pi$
$131$	48.5943	0.0324100	0.0162050	+	0.999869i	$0.494842\pi$
$132$	−58.2104	−0.0383830
$133$	−133.989	−0.0873558
$134$	−128.855	−0.0830700
$135$	1543.94	0.984307
$136$	411.376	0.259377
$137$	−1628.45	−1.01553	−0.507766	−	0.861495i	$-0.669529\pi$
$137$	−1628.45	−1.01553	−0.507766	+	0.861495i	$0.669529\pi$
$138$	0	0
$139$	1143.09	0.697524	0.348762	−	0.937211i	$-0.386602\pi$
$139$	1143.09	0.697524	0.348762	+	0.937211i	$0.386602\pi$
$140$	−835.005	−0.504077
$141$	−116.571	−0.0696245
$142$	−2026.13	−1.19739
$143$	−650.839	−0.380601
$144$	1886.08	1.09148
$145$	−4374.53	−2.50541
$146$	−1132.37	−0.641889
$147$	79.6478	0.0446887
$148$	247.906	0.137687
$149$	352.672	0.193906	0.0969530	−	0.995289i	$-0.469090\pi$
$149$	352.672	0.193906	0.0969530	+	0.995289i	$0.469090\pi$
$150$	−1224.12	−0.666327
$151$	966.880	0.521083	0.260542	−	0.965463i	$-0.416099\pi$
$151$	966.880	0.521083	0.260542	+	0.965463i	$0.416099\pi$
$152$	−125.309	−0.0668680
$153$	−544.799	−0.287872
$154$	1091.74	0.571266
$155$	−5641.90	−2.92367
$156$	127.594	0.0654852
$157$	−1212.39	−0.616303	−0.308152	−	0.951337i	$-0.599710\pi$
$157$	−1212.39	−0.616303	−0.308152	+	0.951337i	$0.599710\pi$
$158$	2316.45	1.16637
$159$	303.796	0.151526
$160$	−1854.10	−0.916121
$161$	0	0
$162$	−1722.97	−0.835612
$163$	772.621	0.371266	0.185633	−	0.982619i	$-0.440566\pi$
$163$	772.621	0.371266	0.185633	+	0.982619i	$0.440566\pi$
$164$	−965.660	−0.459789
$165$	515.630	0.243283
$166$	3797.92	1.77576
$167$	−2462.48	−1.14103	−0.570517	−	0.821286i	$-0.693257\pi$
$167$	−2462.48	−1.14103	−0.570517	+	0.821286i	$0.693257\pi$
$168$	571.867	0.262622
$169$	−770.396	−0.350658
$170$	1363.82	0.615297
$171$	165.951	0.0742141
$172$	−605.303	−0.268337
$173$	540.078	0.237349	0.118675	−	0.992933i	$-0.462135\pi$
$173$	540.078	0.237349	0.118675	+	0.992933i	$0.462135\pi$
$174$	−1121.29	−0.488533
$175$	4914.18	2.12273
$176$	1321.36	0.565916
$177$	−549.442	−0.233325
$178$	5175.76	2.17944
$179$	1547.02	0.645978	0.322989	−	0.946403i	$-0.395312\pi$
$179$	1547.02	0.645978	0.322989	+	0.946403i	$0.395312\pi$
$180$	1034.19	0.428244
$181$	−1404.76	−0.576877	−0.288438	−	0.957498i	$-0.593136\pi$
$181$	−1404.76	−0.576877	−0.288438	+	0.957498i	$0.593136\pi$
$182$	−2393.04	−0.974635
$183$	−56.0256	−0.0226313
$184$	0	0
$185$	−2195.96	−0.872704
$186$	−1446.15	−0.570089
$187$	−381.677	−0.149257
$188$	−163.799	−0.0635441
$189$	−1588.71	−0.611437
$190$	−415.435	−0.158625
$191$	3186.91	1.20731	0.603656	−	0.797245i	$-0.293710\pi$
$191$	3186.91	1.20731	0.603656	+	0.797245i	$0.293710\pi$
$192$	475.942	0.178897
$193$	−3363.83	−1.25458	−0.627289	−	0.778786i	$-0.715836\pi$
$193$	−3363.83	−1.25458	−0.627289	+	0.778786i	$0.715836\pi$
$194$	1981.50	0.733318
$195$	−1130.23	−0.415065
$196$	111.917	0.0407860
$197$	1025.25	0.370794	0.185397	−	0.982664i	$-0.440643\pi$
$197$	1025.25	0.370794	0.185397	+	0.982664i	$0.440643\pi$
$198$	−1352.17	−0.485326
$199$	−1924.81	−0.685658	−0.342829	−	0.939398i	$-0.611385\pi$
$199$	−1924.81	−0.685658	−0.342829	+	0.939398i	$0.611385\pi$
$200$	4595.84	1.62488
$201$	62.6229	0.0219755
$202$	1940.75	0.675995
$203$	4501.36	1.55632
$204$	74.8259	0.0256807
$205$	8553.87	2.91428
$206$	3310.91	1.11982
$207$	0	0
$208$	−2896.34	−0.965507
$209$	116.263	0.0384788
$210$	1895.89	0.622995
$211$	4157.97	1.35662	0.678309	−	0.734777i	$-0.262713\pi$
$211$	4157.97	1.35662	0.678309	+	0.734777i	$0.262713\pi$
$212$	426.877	0.138293
$213$	984.689	0.316759
$214$	4241.81	1.35497
$215$	5361.81	1.70080
$216$	−1485.79	−0.468035
$217$	5805.48	1.81614
$218$	−3901.09	−1.21200
$219$	550.327	0.169807
$220$	724.536	0.222037
$221$	836.614	0.254646
$222$	−562.874	−0.170169
$223$	−1252.06	−0.375983	−0.187991	−	0.982171i	$-0.560198\pi$
$223$	−1252.06	−0.375983	−0.187991	+	0.982171i	$0.560198\pi$
$224$	1907.86	0.569081
$225$	−6086.42	−1.80338
$226$	2320.44	0.682981
$227$	3523.38	1.03020	0.515099	−	0.857131i	$-0.327755\pi$
$227$	3523.38	1.03020	0.515099	+	0.857131i	$0.327755\pi$
$228$	−22.7927	−0.00662055
$229$	686.340	0.198055	0.0990275	−	0.995085i	$-0.468427\pi$
$229$	686.340	0.198055	0.0990275	+	0.995085i	$0.468427\pi$
$230$	0	0
$231$	−530.581	−0.151124
$232$	4209.77	1.19131
$233$	−949.949	−0.267095	−0.133548	−	0.991042i	$-0.542637\pi$
$233$	−949.949	−0.267095	−0.133548	+	0.991042i	$0.542637\pi$
$234$	2963.88	0.828012
$235$	1450.94	0.402762
$236$	−772.047	−0.212949
$237$	−1125.78	−0.308554
$238$	−1403.37	−0.382213
$239$	3808.49	1.03076	0.515378	−	0.856963i	$-0.327651\pi$
$239$	3808.49	1.03076	0.515378	+	0.856963i	$0.327651\pi$
$240$	2294.64	0.617160
$241$	−3055.59	−0.816713	−0.408357	−	0.912822i	$-0.633898\pi$
$241$	−3055.59	−0.816713	−0.408357	+	0.912822i	$0.633898\pi$
$242$	3299.13	0.876347
$243$	2997.37	0.791281
$244$	−78.7242	−0.0206549
$245$	−991.365	−0.258514
$246$	2192.55	0.568259
$247$	−254.841	−0.0656485
$248$	5429.41	1.39019
$249$	−1845.77	−0.469763
$250$	7539.95	1.90747
$251$	958.620	0.241066	0.120533	−	0.992709i	$-0.461540\pi$
$251$	958.620	0.241066	0.120533	+	0.992709i	$0.461540\pi$
$252$	−1064.18	−0.266019
$253$	0	0
$254$	−1725.17	−0.426168
$255$	−662.811	−0.162772
$256$	3120.83	0.761921
$257$	3288.89	0.798271	0.399135	−	0.916892i	$-0.369310\pi$
$257$	3288.89	0.798271	0.399135	+	0.916892i	$0.369310\pi$
$258$	1374.35	0.331641
$259$	2259.63	0.542110
$260$	−1588.14	−0.378817
$261$	−5575.13	−1.32219
$262$	−155.036	−0.0365578
$263$	−2275.07	−0.533410	−0.266705	−	0.963778i	$-0.585935\pi$
$263$	−2275.07	−0.533410	−0.266705	+	0.963778i	$0.585935\pi$
$264$	−496.210	−0.115680
$265$	−3781.30	−0.876542
$266$	427.480	0.0985356
$267$	−2515.39	−0.576553
$268$	87.9943	0.0200564
$269$	−2902.01	−0.657764	−0.328882	−	0.944371i	$-0.606672\pi$
$269$	−2902.01	−0.657764	−0.328882	+	0.944371i	$0.606672\pi$
$270$	−4925.81	−1.11028
$271$	3352.53	0.751483	0.375741	−	0.926725i	$-0.377388\pi$
$271$	3352.53	0.751483	0.375741	+	0.926725i	$0.377388\pi$
$272$	−1698.53	−0.378633
$273$	1163.00	0.257832
$274$	5195.43	1.14550
$275$	−4264.05	−0.935025
$276$	0	0
$277$	−6066.83	−1.31596	−0.657979	−	0.753036i	$-0.728588\pi$
$277$	−6066.83	−1.31596	−0.657979	+	0.753036i	$0.728588\pi$
$278$	−3646.93	−0.786793
$279$	−7190.34	−1.54292
$280$	−7117.94	−1.51921
$281$	1946.68	0.413271	0.206635	−	0.978418i	$-0.433749\pi$
$281$	1946.68	0.413271	0.206635	+	0.978418i	$0.433749\pi$
$282$	371.909	0.0785350
$283$	−3619.04	−0.760175	−0.380088	−	0.924951i	$-0.624106\pi$
$283$	−3619.04	−0.760175	−0.380088	+	0.924951i	$0.624106\pi$
$284$	1383.63	0.289097
$285$	201.899	0.0419631
$286$	2076.44	0.429310
$287$	−8801.88	−1.81031
$288$	−2362.96	−0.483469
$289$	−4422.38	−0.900138
$290$	13956.5	2.82605
$291$	−963.001	−0.193994
$292$	773.290	0.154977
$293$	2366.36	0.471823	0.235912	−	0.971775i	$-0.424192\pi$
$293$	2366.36	0.471823	0.235912	+	0.971775i	$0.424192\pi$
$294$	−254.109	−0.0504080
$295$	6838.83	1.34974
$296$	2113.25	0.414968
$297$	1378.53	0.269328
$298$	−1125.17	−0.218722
$299$	0	0
$300$	835.946	0.160878
$301$	−5517.27	−1.05651
$302$	−3084.74	−0.587771
$303$	−943.197	−0.178829
$304$	517.389	0.0976127
$305$	697.343	0.130917
$306$	1738.13	0.324713
$307$	326.171	0.0606370	0.0303185	−	0.999540i	$-0.490348\pi$
$307$	326.171	0.0606370	0.0303185	+	0.999540i	$0.490348\pi$
$308$	−745.544	−0.137926
$309$	−1609.09	−0.296239
$310$	18000.0	3.29784
$311$	−306.470	−0.0558789	−0.0279395	−	0.999610i	$-0.508895\pi$
$311$	−306.470	−0.0558789	−0.0279395	+	0.999610i	$0.508895\pi$
$312$	1087.67	0.197362
$313$	4458.02	0.805055	0.402527	−	0.915408i	$-0.368132\pi$
$313$	4458.02	0.805055	0.402527	+	0.915408i	$0.368132\pi$
$314$	3868.03	0.695178
$315$	9426.52	1.68611
$316$	−1581.89	−0.281608
$317$	−8877.46	−1.57290	−0.786448	−	0.617657i	$-0.788082\pi$
$317$	−8877.46	−1.57290	−0.786448	+	0.617657i	$0.788082\pi$
$318$	−969.232	−0.170918
$319$	−3905.85	−0.685534
$320$	−5923.98	−1.03488
$321$	−2061.50	−0.358447
$322$	0	0
$323$	−149.449	−0.0257447
$324$	1176.60	0.201750
$325$	9346.55	1.59524
$326$	−2464.98	−0.418781
$327$	1895.91	0.320624
$328$	−8231.71	−1.38573
$329$	−1493.01	−0.250190
$330$	−1645.07	−0.274419
$331$	−2163.47	−0.359259	−0.179630	−	0.983734i	$-0.557490\pi$
$331$	−2163.47	−0.359259	−0.179630	+	0.983734i	$0.557490\pi$
$332$	−2593.58	−0.428738
$333$	−2798.65	−0.460556
$334$	7856.33	1.28706
$335$	−779.458	−0.127123
$336$	−2361.17	−0.383371
$337$	−3371.87	−0.545038	−0.272519	−	0.962150i	$-0.587857\pi$
$337$	−3371.87	−0.545038	−0.272519	+	0.962150i	$0.587857\pi$
$338$	2457.88	0.395536
$339$	−1127.72	−0.180677
$340$	−931.347	−0.148557
$341$	−5037.44	−0.799978
$342$	−529.452	−0.0837120
$343$	−5791.43	−0.911684
$344$	−5159.87	−0.808725
$345$	0	0
$346$	−1723.07	−0.267725
$347$	−1676.46	−0.259358	−0.129679	−	0.991556i	$-0.541395\pi$
$347$	−1676.46	−0.259358	−0.129679	+	0.991556i	$0.541395\pi$
$348$	765.722	0.117951
$349$	1161.04	0.178077	0.0890385	−	0.996028i	$-0.471621\pi$
$349$	1161.04	0.178077	0.0890385	+	0.996028i	$0.471621\pi$
$350$	−15678.2	−2.39439
$351$	−3021.66	−0.459499
$352$	−1655.45	−0.250670
$353$	−1837.85	−0.277107	−0.138554	−	0.990355i	$-0.544245\pi$
$353$	−1837.85	−0.277107	−0.138554	+	0.990355i	$0.544245\pi$
$354$	1752.95	0.263186
$355$	−12256.3	−1.83238
$356$	−3534.50	−0.526202
$357$	682.029	0.101112
$358$	−4935.64	−0.728650
$359$	−13137.1	−1.93133	−0.965666	−	0.259787i	$-0.916348\pi$
$359$	−13137.1	−1.93133	−0.965666	+	0.259787i	$0.916348\pi$
$360$	8815.89	1.29066
$361$	−6813.48	−0.993363
$362$	4481.75	0.650705
$363$	−1603.36	−0.231831
$364$	1634.19	0.235315
$365$	−6849.84	−0.982294
$366$	178.745	0.0255277
$367$	9390.56	1.33565	0.667825	−	0.744319i	$-0.267226\pi$
$367$	9390.56	1.33565	0.667825	+	0.744319i	$0.267226\pi$
$368$	0	0
$369$	10901.5	1.53797
$370$	7006.01	0.984392
$371$	3890.94	0.544494
$372$	987.564	0.137642
$373$	12801.7	1.77707	0.888534	−	0.458811i	$-0.151724\pi$
$373$	12801.7	1.77707	0.888534	+	0.458811i	$0.151724\pi$
$374$	1217.71	0.168358
$375$	−3664.38	−0.504607
$376$	−1396.30	−0.191512
$377$	8561.40	1.16959
$378$	5068.63	0.689689
$379$	6576.73	0.891356	0.445678	−	0.895193i	$-0.352963\pi$
$379$	6576.73	0.891356	0.445678	+	0.895193i	$0.352963\pi$
$380$	283.698	0.0382984
$381$	838.424	0.112739
$382$	−10167.5	−1.36182
$383$	5752.89	0.767517	0.383759	−	0.923433i	$-0.374629\pi$
$383$	5752.89	0.767517	0.383759	+	0.923433i	$0.374629\pi$
$384$	−2710.14	−0.360159
$385$	6604.06	0.874219
$386$	10732.0	1.41514
$387$	6833.38	0.897571
$388$	−1353.16	−0.177052
$389$	−5859.60	−0.763736	−0.381868	−	0.924217i	$-0.624719\pi$
$389$	−5859.60	−0.763736	−0.381868	+	0.924217i	$0.624719\pi$
$390$	3605.91	0.468185
$391$	0	0
$392$	954.028	0.122923
$393$	75.3466	0.00967108
$394$	−3270.98	−0.418248
$395$	14012.4	1.78492
$396$	923.388	0.117177
$397$	10657.5	1.34732	0.673661	−	0.739041i	$-0.264721\pi$
$397$	10657.5	1.34732	0.673661	+	0.739041i	$0.264721\pi$
$398$	6140.93	0.773409
$399$	−207.753	−0.0260668
$400$	−18975.7	−2.37197
$401$	−6687.73	−0.832841	−0.416420	−	0.909172i	$-0.636716\pi$
$401$	−6687.73	−0.832841	−0.416420	+	0.909172i	$0.636716\pi$
$402$	−199.793	−0.0247879
$403$	11041.8	1.36484
$404$	−1325.33	−0.163212
$405$	−10422.4	−1.27875
$406$	−14361.2	−1.75550
$407$	−1960.69	−0.238790
$408$	637.848	0.0773975
$409$	5118.39	0.618797	0.309399	−	0.950932i	$-0.399872\pi$
$409$	5118.39	0.618797	0.309399	+	0.950932i	$0.399872\pi$
$410$	−27290.3	−3.28725
$411$	−2524.95	−0.303033
$412$	−2261.00	−0.270368
$413$	−7037.12	−0.838436
$414$	0	0
$415$	22974.0	2.71747
$416$	3628.66	0.427668
$417$	1772.39	0.208140
$418$	−370.926	−0.0434033
$419$	−11267.7	−1.31375	−0.656877	−	0.753998i	$-0.728123\pi$
$419$	−11267.7	−1.31375	−0.656877	+	0.753998i	$0.728123\pi$
$420$	−1294.69	−0.150416
$421$	−9880.23	−1.14378	−0.571892	−	0.820329i	$-0.693790\pi$
$421$	−9880.23	−1.14378	−0.571892	+	0.820329i	$0.693790\pi$
$422$	−13265.6	−1.53024
$423$	1849.16	0.212551
$424$	3638.89	0.416793
$425$	5481.17	0.625590
$426$	−3141.56	−0.357298
$427$	−717.562	−0.0813238
$428$	−2896.71	−0.327144
$429$	−1009.14	−0.113571
$430$	−17106.4	−1.91847
$431$	3597.69	0.402075	0.201038	−	0.979583i	$-0.435569\pi$
$431$	3597.69	0.402075	0.201038	+	0.979583i	$0.435569\pi$
$432$	6134.68	0.683229
$433$	14357.9	1.59352	0.796761	−	0.604294i	$-0.206545\pi$
$433$	14357.9	1.59352	0.796761	+	0.604294i	$0.206545\pi$
$434$	−18521.9	−2.04857
$435$	−6782.81	−0.747611
$436$	2664.03	0.292624
$437$	0	0
$438$	−1755.77	−0.191539
$439$	−13097.5	−1.42394	−0.711971	−	0.702209i	$-0.752197\pi$
$439$	−13097.5	−1.42394	−0.711971	+	0.702209i	$0.752197\pi$
$440$	6176.26	0.669186
$441$	−1263.45	−0.136427
$442$	−2669.14	−0.287236
$443$	−9920.87	−1.06401	−0.532003	−	0.846743i	$-0.678560\pi$
$443$	−9920.87	−1.06401	−0.532003	+	0.846743i	$0.678560\pi$
$444$	384.383	0.0410856
$445$	31308.8	3.33523
$446$	3994.59	0.424101
$447$	546.826	0.0578612
$448$	6095.74	0.642850
$449$	−11647.7	−1.22425	−0.612127	−	0.790759i	$-0.709686\pi$
$449$	−11647.7	−1.22425	−0.612127	+	0.790759i	$0.709686\pi$
$450$	19418.2	2.03418
$451$	7637.42	0.797410
$452$	−1584.62	−0.164899
$453$	1499.17	0.155490
$454$	−11241.0	−1.16204
$455$	−14475.7	−1.49150
$456$	−194.295	−0.0199533
$457$	−4382.80	−0.448619	−0.224309	−	0.974518i	$-0.572013\pi$
$457$	−4382.80	−0.448619	−0.224309	+	0.974518i	$0.572013\pi$
$458$	−2189.70	−0.223402
$459$	−1772.01	−0.180197
$460$	0	0
$461$	−2500.17	−0.252591	−0.126296	−	0.991993i	$-0.540309\pi$
$461$	−2500.17	−0.252591	−0.126296	+	0.991993i	$0.540309\pi$
$462$	1692.77	0.170465
$463$	−11935.3	−1.19801	−0.599005	−	0.800745i	$-0.704437\pi$
$463$	−11935.3	−1.19801	−0.599005	+	0.800745i	$0.704437\pi$
$464$	−17381.7	−1.73906
$465$	−8747.90	−0.872417
$466$	3030.73	0.301278
$467$	14879.3	1.47437	0.737184	−	0.675692i	$-0.236155\pi$
$467$	14879.3	1.47437	0.737184	+	0.675692i	$0.236155\pi$
$468$	−2024.02	−0.199915
$469$	802.058	0.0789672
$470$	−4629.10	−0.454308
$471$	−1879.85	−0.183904
$472$	−6581.26	−0.641795
$473$	4787.35	0.465375
$474$	3591.70	0.348043
$475$	−1669.62	−0.161279
$476$	958.351	0.0922814
$477$	−4819.10	−0.462581
$478$	−12150.6	−1.16267
$479$	−13932.8	−1.32903	−0.664513	−	0.747276i	$-0.731361\pi$
$479$	−13932.8	−1.32903	−0.664513	+	0.747276i	$0.731361\pi$
$480$	−2874.82	−0.273369
$481$	4297.72	0.407399
$482$	9748.58	0.921236
$483$	0	0
$484$	−2252.96	−0.211585
$485$	11986.3	1.12221
$486$	−9562.84	−0.892550
$487$	−15845.1	−1.47435	−0.737175	−	0.675702i	$-0.763841\pi$
$487$	−15845.1	−1.47435	−0.737175	+	0.675702i	$0.763841\pi$
$488$	−671.080	−0.0622507
$489$	1197.97	0.110785
$490$	3162.86	0.291599
$491$	−3273.12	−0.300843	−0.150421	−	0.988622i	$-0.548063\pi$
$491$	−3273.12	−0.300843	−0.150421	+	0.988622i	$0.548063\pi$
$492$	−1497.28	−0.137200
$493$	5020.73	0.458666
$494$	813.048	0.0740501
$495$	−8179.42	−0.742702
$496$	−22417.4	−2.02938
$497$	12611.6	1.13825
$498$	5888.76	0.529883
$499$	−13135.4	−1.17840	−0.589202	−	0.807986i	$-0.700558\pi$
$499$	−13135.4	−1.17840	−0.589202	+	0.807986i	$0.700558\pi$
$500$	−5148.99	−0.460540
$501$	−3818.14	−0.340483
$502$	−3058.39	−0.271918
$503$	10138.3	0.898698	0.449349	−	0.893356i	$-0.351656\pi$
$503$	10138.3	0.898698	0.449349	+	0.893356i	$0.351656\pi$
$504$	−9071.49	−0.801739
$505$	11739.8	1.03449
$506$	0	0
$507$	−1194.52	−0.104636
$508$	1178.11	0.102894
$509$	−1804.96	−0.157178	−0.0785888	−	0.996907i	$-0.525041\pi$
$509$	−1804.96	−0.157178	−0.0785888	+	0.996907i	$0.525041\pi$
$510$	2114.64	0.183604
$511$	7048.45	0.610186
$512$	4026.37	0.347543
$513$	539.773	0.0464553
$514$	−10492.9	−0.900433
$515$	20028.1	1.71367
$516$	−938.537	−0.0800713
$517$	1295.49	0.110204
$518$	−7209.14	−0.611490
$519$	837.404	0.0708246
$520$	−13538.0	−1.14170
$521$	1473.76	0.123928	0.0619641	−	0.998078i	$-0.480264\pi$
$521$	1473.76	0.123928	0.0619641	+	0.998078i	$0.480264\pi$
$522$	17787.0	1.49141
$523$	−54.1107	−0.00452408	−0.00226204	−	0.999997i	$-0.500720\pi$
$523$	−54.1107	−0.00452408	−0.00226204	+	0.999997i	$0.500720\pi$
$524$	105.873	0.00882650
$525$	7619.55	0.633418
$526$	7258.41	0.601676
$527$	6475.31	0.535236
$528$	2048.80	0.168868
$529$	0	0
$530$	12063.9	0.988721
$531$	8715.78	0.712302
$532$	−291.924	−0.0237904
$533$	−16740.8	−1.36046
$534$	8025.14	0.650340
$535$	25659.2	2.07354
$536$	750.102	0.0604468
$537$	2398.70	0.192759
$538$	9258.59	0.741945
$539$	−885.152	−0.0707350
$540$	3363.81	0.268065
$541$	−3147.39	−0.250123	−0.125062	−	0.992149i	$-0.539913\pi$
$541$	−3147.39	−0.250123	−0.125062	+	0.992149i	$0.539913\pi$
$542$	−10696.0	−0.847658
$543$	−2178.11	−0.172139
$544$	2127.98	0.167714
$545$	−23598.1	−1.85474
$546$	−3710.46	−0.290829
$547$	1092.23	0.0853752	0.0426876	−	0.999088i	$-0.486408\pi$
$547$	1092.23	0.0853752	0.0426876	+	0.999088i	$0.486408\pi$
$548$	−3547.93	−0.276569
$549$	888.732	0.0690895
$550$	13604.1	1.05469
$551$	−1529.37	−0.118245
$552$	0	0
$553$	−14418.7	−1.10876
$554$	19355.7	1.48437
$555$	−3404.89	−0.260413
$556$	2490.47	0.189963
$557$	15256.2	1.16055	0.580274	−	0.814421i	$-0.302945\pi$
$557$	15256.2	1.16055	0.580274	+	0.814421i	$0.302945\pi$
$558$	22940.1	1.74038
$559$	−10493.6	−0.793975
$560$	29389.2	2.21771
$561$	−591.799	−0.0445379
$562$	−6210.70	−0.466161
$563$	−14937.8	−1.11821	−0.559107	−	0.829096i	$-0.688856\pi$
$563$	−14937.8	−1.11821	−0.559107	+	0.829096i	$0.688856\pi$
$564$	−253.975	−0.0189615
$565$	14036.6	1.04518
$566$	11546.2	0.857462
$567$	10724.6	0.794341
$568$	11794.7	0.871292
$569$	−6987.69	−0.514831	−0.257416	−	0.966301i	$-0.582871\pi$
$569$	−6987.69	−0.514831	−0.257416	+	0.966301i	$0.582871\pi$
$570$	−644.141	−0.0473335
$571$	−13846.6	−1.01482	−0.507411	−	0.861704i	$-0.669397\pi$
$571$	−13846.6	−1.01482	−0.507411	+	0.861704i	$0.669397\pi$
$572$	−1417.99	−0.103652
$573$	4941.38	0.360260
$574$	28081.6	2.04199
$575$	0	0
$576$	−7549.84	−0.546140
$577$	−4051.08	−0.292286	−0.146143	−	0.989264i	$-0.546686\pi$
$577$	−4051.08	−0.292286	−0.146143	+	0.989264i	$0.546686\pi$
$578$	14109.2	1.01534
$579$	−5215.70	−0.374364
$580$	−9530.84	−0.682322
$581$	−23640.2	−1.68805
$582$	3072.37	0.218821
$583$	−3376.18	−0.239841
$584$	6591.86	0.467077
$585$	17928.8	1.26712
$586$	−7549.66	−0.532207
$587$	−17976.8	−1.26402	−0.632012	−	0.774959i	$-0.717771\pi$
$587$	−17976.8	−1.26402	−0.632012	+	0.774959i	$0.717771\pi$
$588$	173.530	0.0121705
$589$	−1972.45	−0.137985
$590$	−21818.7	−1.52248
$591$	1589.68	0.110644
$592$	−8725.39	−0.605762
$593$	22373.5	1.54936	0.774680	−	0.632354i	$-0.217911\pi$
$593$	22373.5	1.54936	0.774680	+	0.632354i	$0.217911\pi$
$594$	−4398.07	−0.303796
$595$	−8489.12	−0.584908
$596$	768.370	0.0528082
$597$	−2984.46	−0.204599
$598$	0	0
$599$	6088.93	0.415337	0.207669	−	0.978199i	$-0.433412\pi$
$599$	6088.93	0.415337	0.207669	+	0.978199i	$0.433412\pi$
$600$	7125.96	0.484860
$601$	4618.28	0.313450	0.156725	−	0.987642i	$-0.449906\pi$
$601$	4618.28	0.313450	0.156725	+	0.987642i	$0.449906\pi$
$602$	17602.3	1.19172
$603$	−993.384	−0.0670874
$604$	2106.55	0.141911
$605$	19956.8	1.34109
$606$	3009.19	0.201716
$607$	−21555.2	−1.44135	−0.720673	−	0.693275i	$-0.756167\pi$
$607$	−21555.2	−1.44135	−0.720673	+	0.693275i	$0.756167\pi$
$608$	−648.206	−0.0432372
$609$	6979.47	0.464404
$610$	−2224.81	−0.147672
$611$	−2839.64	−0.188019
$612$	−1186.96	−0.0783987
$613$	−11049.5	−0.728034	−0.364017	−	0.931392i	$-0.618595\pi$
$613$	−11049.5	−0.728034	−0.364017	+	0.931392i	$0.618595\pi$
$614$	−1040.62	−0.0683973
$615$	13263.0	0.869617
$616$	−6355.34	−0.415688
$617$	6319.90	0.412366	0.206183	−	0.978513i	$-0.433896\pi$
$617$	6319.90	0.412366	0.206183	+	0.978513i	$0.433896\pi$
$618$	5133.64	0.334151
$619$	−15420.9	−1.00132	−0.500662	−	0.865643i	$-0.666910\pi$
$619$	−15420.9	−1.00132	−0.500662	+	0.865643i	$0.666910\pi$
$620$	−12292.1	−0.796229
$621$	0	0
$622$	977.766	0.0630303
$623$	−32216.5	−2.07179
$624$	−4490.85	−0.288106
$625$	14677.9	0.939384
$626$	−14222.9	−0.908086
$627$	180.268	0.0114820
$628$	−2641.46	−0.167843
$629$	2520.34	0.159766
$630$	−30074.5	−1.90190
$631$	30890.3	1.94885	0.974424	−	0.224718i	$-0.0721462\pi$
$631$	30890.3	1.94885	0.974424	+	0.224718i	$0.0721462\pi$
$632$	−13484.7	−0.848722
$633$	6447.03	0.404813
$634$	28322.7	1.77420
$635$	−10435.7	−0.652173
$636$	661.883	0.0412663
$637$	1940.20	0.120681
$638$	12461.3	0.773269
$639$	−15620.1	−0.967012
$640$	33732.7	2.08344
$641$	4693.19	0.289189	0.144594	−	0.989491i	$-0.453812\pi$
$641$	4693.19	0.289189	0.144594	+	0.989491i	$0.453812\pi$
$642$	6577.02	0.404322
$643$	−31374.5	−1.92425	−0.962123	−	0.272615i	$-0.912112\pi$
$643$	−31374.5	−1.92425	−0.962123	+	0.272615i	$0.912112\pi$
$644$	0	0
$645$	8313.61	0.507516
$646$	476.802	0.0290395
$647$	−20657.7	−1.25524	−0.627620	−	0.778520i	$-0.715971\pi$
$647$	−20657.7	−1.25524	−0.627620	+	0.778520i	$0.715971\pi$
$648$	10029.9	0.608042
$649$	6106.13	0.369317
$650$	−29819.3	−1.79940
$651$	9001.53	0.541932
$652$	1683.32	0.101110
$653$	10213.7	0.612088	0.306044	−	0.952017i	$-0.400995\pi$
$653$	10213.7	0.612088	0.306044	+	0.952017i	$0.400995\pi$
$654$	−6048.73	−0.361657
$655$	−937.829	−0.0559451
$656$	33987.8	2.02287
$657$	−8729.81	−0.518390
$658$	4763.32	0.282209
$659$	−1863.82	−0.110173	−0.0550867	−	0.998482i	$-0.517544\pi$
$659$	−1863.82	−0.110173	−0.0550867	+	0.998482i	$0.517544\pi$
$660$	1123.41	0.0662556
$661$	7888.30	0.464174	0.232087	−	0.972695i	$-0.425445\pi$
$661$	7888.30	0.464174	0.232087	+	0.972695i	$0.425445\pi$
$662$	6902.34	0.405237
$663$	1297.19	0.0759859
$664$	−22108.8	−1.29215
$665$	2585.87	0.150791
$666$	8928.84	0.519498
$667$	0	0
$668$	−5365.04	−0.310748
$669$	−1941.35	−0.112193
$670$	2486.79	0.143393
$671$	622.631	0.0358218
$672$	2958.18	0.169813
$673$	−13840.8	−0.792754	−0.396377	−	0.918088i	$-0.629733\pi$
$673$	−13840.8	−0.792754	−0.396377	+	0.918088i	$0.629733\pi$
$674$	10757.7	0.614792
$675$	−19796.7	−1.12885
$676$	−1678.47	−0.0954979
$677$	−4298.48	−0.244024	−0.122012	−	0.992529i	$-0.538935\pi$
$677$	−4298.48	−0.244024	−0.122012	+	0.992529i	$0.538935\pi$
$678$	3597.90	0.203800
$679$	−12333.9	−0.697100
$680$	−7939.21	−0.447728
$681$	5463.08	0.307409
$682$	16071.5	0.902359
$683$	8793.73	0.492654	0.246327	−	0.969187i	$-0.420776\pi$
$683$	8793.73	0.492654	0.246327	+	0.969187i	$0.420776\pi$
$684$	361.560	0.0202114
$685$	31427.7	1.75298
$686$	18477.0	1.02836
$687$	1064.19	0.0590993
$688$	21304.5	1.18056
$689$	7400.40	0.409191
$690$	0	0
$691$	−27329.1	−1.50456	−0.752279	−	0.658845i	$-0.771045\pi$
$691$	−27329.1	−1.50456	−0.752279	+	0.658845i	$0.771045\pi$
$692$	1176.68	0.0646394
$693$	8416.58	0.461355
$694$	5348.60	0.292551
$695$	−22060.7	−1.20404
$696$	6527.35	0.355486
$697$	−9817.43	−0.533518
$698$	−3704.18	−0.200867
$699$	−1472.92	−0.0797008
$700$	10706.6	0.578101
$701$	103.178	0.00555917	0.00277959	−	0.999996i	$-0.499115\pi$
$701$	103.178	0.00555917	0.00277959	+	0.999996i	$0.499115\pi$
$702$	9640.32	0.518305
$703$	−767.723	−0.0411881
$704$	−5289.30	−0.283165
$705$	2249.72	0.120184
$706$	5863.49	0.312571
$707$	−12080.2	−0.642608
$708$	−1197.08	−0.0635436
$709$	−12420.3	−0.657906	−0.328953	−	0.944346i	$-0.606696\pi$
$709$	−12420.3	−0.657906	−0.328953	+	0.944346i	$0.606696\pi$
$710$	39102.6	2.06689
$711$	17858.2	0.941963
$712$	−30129.6	−1.58589
$713$	0	0
$714$	−2175.95	−0.114052
$715$	12560.6	0.656981
$716$	3370.52	0.175925
$717$	5905.15	0.307576
$718$	41912.6	2.17850
$719$	−6934.64	−0.359692	−0.179846	−	0.983695i	$-0.557560\pi$
$719$	−6934.64	−0.359692	−0.179846	+	0.983695i	$0.557560\pi$
$720$	−36399.8	−1.88408
$721$	−20608.8	−1.06451
$722$	21737.8	1.12049
$723$	−4737.76	−0.243706
$724$	−3060.56	−0.157106
$725$	56091.0	2.87333
$726$	5115.37	0.261500
$727$	10473.0	0.534283	0.267142	−	0.963657i	$-0.413921\pi$
$727$	10473.0	0.534283	0.267142	+	0.963657i	$0.413921\pi$
$728$	13930.5	0.709204
$729$	−9933.75	−0.504687
$730$	21853.8	1.10801
$731$	−6153.85	−0.311366
$732$	−122.064	−0.00616340
$733$	31375.5	1.58101	0.790504	−	0.612457i	$-0.209819\pi$
$733$	31375.5	1.58101	0.790504	+	0.612457i	$0.209819\pi$
$734$	−29959.7	−1.50659
$735$	−1537.13	−0.0771402
$736$	0	0
$737$	−695.948	−0.0347837
$738$	−34780.3	−1.73480
$739$	27631.1	1.37541	0.687705	−	0.725991i	$-0.258618\pi$
$739$	27631.1	1.37541	0.687705	+	0.725991i	$0.258618\pi$
$740$	−4784.36	−0.237671
$741$	−395.137	−0.0195894
$742$	−12413.7	−0.614179
$743$	−30157.8	−1.48908	−0.744538	−	0.667580i	$-0.767330\pi$
$743$	−30157.8	−1.48908	−0.744538	+	0.667580i	$0.767330\pi$
$744$	8418.43	0.414831
$745$	−6806.26	−0.334714
$746$	−40842.6	−2.00450
$747$	29279.4	1.43410
$748$	−831.564	−0.0406484
$749$	−26403.2	−1.28805
$750$	11690.9	0.569187
$751$	30644.0	1.48897	0.744483	−	0.667641i	$-0.232696\pi$
$751$	30644.0	1.48897	0.744483	+	0.667641i	$0.232696\pi$
$752$	5765.15	0.279566
$753$	1486.36	0.0719337
$754$	−27314.4	−1.31927
$755$	−18660.0	−0.899477
$756$	−3461.34	−0.166518
$757$	−8621.61	−0.413947	−0.206973	−	0.978347i	$-0.566361\pi$
$757$	−8621.61	−0.413947	−0.206973	+	0.978347i	$0.566361\pi$
$758$	−20982.5	−1.00543
$759$	0	0
$760$	2418.36	0.115425
$761$	7583.96	0.361259	0.180630	−	0.983551i	$-0.442186\pi$
$761$	7583.96	0.361259	0.180630	+	0.983551i	$0.442186\pi$
$762$	−2674.91	−0.127168
$763$	24282.3	1.15214
$764$	6943.36	0.328798
$765$	10514.1	0.496915
$766$	−18354.1	−0.865744
$767$	−13384.3	−0.630090
$768$	4838.92	0.227356
$769$	−33771.6	−1.58366	−0.791830	−	0.610742i	$-0.790871\pi$
$769$	−33771.6	−1.58366	−0.791830	+	0.610742i	$0.790871\pi$
$770$	−21069.7	−0.986102
$771$	5099.51	0.238203
$772$	−7328.82	−0.341671
$773$	26394.7	1.22814	0.614069	−	0.789252i	$-0.289532\pi$
$773$	26394.7	1.22814	0.614069	+	0.789252i	$0.289532\pi$
$774$	−21801.3	−1.01244
$775$	72341.4	3.35301
$776$	−11534.9	−0.533607
$777$	3503.61	0.161765
$778$	18694.5	0.861479
$779$	2990.49	0.137542
$780$	−2462.45	−0.113038
$781$	−10943.2	−0.501379
$782$	0	0
$783$	−18133.7	−0.827644
$784$	−3939.07	−0.179440
$785$	23398.2	1.06384
$786$	−240.387	−0.0109088
$787$	−27561.5	−1.24836	−0.624181	−	0.781280i	$-0.714567\pi$
$787$	−27561.5	−1.24836	−0.624181	+	0.781280i	$0.714567\pi$
$788$	2233.73	0.100982
$789$	−3527.55	−0.159169
$790$	−44705.4	−2.01335
$791$	−14443.6	−0.649249
$792$	7871.36	0.353152
$793$	−1364.77	−0.0611154
$794$	−34001.9	−1.51975
$795$	−5863.00	−0.261559
$796$	−4193.60	−0.186732
$797$	−21730.1	−0.965772	−0.482886	−	0.875683i	$-0.660411\pi$
$797$	−21730.1	−0.965772	−0.482886	+	0.875683i	$0.660411\pi$
$798$	662.817	0.0294029
$799$	−1665.27	−0.0737336
$800$	23773.6	1.05065
$801$	39901.6	1.76012
$802$	21336.6	0.939428
$803$	−6115.96	−0.268777
$804$	136.437	0.00598479
$805$	0	0
$806$	−35227.8	−1.53951
$807$	−4499.63	−0.196276
$808$	−11297.7	−0.491895
$809$	−32140.5	−1.39679	−0.698393	−	0.715714i	$-0.746101\pi$
$809$	−32140.5	−1.39679	−0.698393	+	0.715714i	$0.746101\pi$
$810$	33251.8	1.44241
$811$	18711.8	0.810185	0.405093	−	0.914276i	$-0.367239\pi$
$811$	18711.8	0.810185	0.405093	+	0.914276i	$0.367239\pi$
$812$	9807.18	0.423848
$813$	5198.18	0.224241
$814$	6255.40	0.269351
$815$	−14910.9	−0.640868
$816$	−2633.60	−0.112984
$817$	1874.53	0.0802709
$818$	−16329.8	−0.697991
$819$	−18448.7	−0.787117
$820$	18636.4	0.793673
$821$	28478.0	1.21058	0.605292	−	0.796003i	$-0.293056\pi$
$821$	28478.0	1.21058	0.605292	+	0.796003i	$0.293056\pi$
$822$	8055.63	0.341816
$823$	−19614.8	−0.830775	−0.415388	−	0.909645i	$-0.636354\pi$
$823$	−19614.8	−0.830775	−0.415388	+	0.909645i	$0.636354\pi$
$824$	−19273.8	−0.814846
$825$	−6611.50	−0.279010
$826$	22451.3	0.945739
$827$	1466.89	0.0616793	0.0308396	−	0.999524i	$-0.490182\pi$
$827$	1466.89	0.0616793	0.0308396	+	0.999524i	$0.490182\pi$
$828$	0	0
$829$	35248.9	1.47677	0.738387	−	0.674378i	$-0.235588\pi$
$829$	35248.9	1.47677	0.738387	+	0.674378i	$0.235588\pi$
$830$	−73296.6	−3.06526
$831$	−9406.76	−0.392680
$832$	11593.8	0.483106
$833$	1137.81	0.0473262
$834$	−5654.65	−0.234778
$835$	47523.8	1.96962
$836$	253.303	0.0104793
$837$	−23387.3	−0.965812
$838$	35948.6	1.48189
$839$	−5241.54	−0.215683	−0.107842	−	0.994168i	$-0.534394\pi$
$839$	−5241.54	−0.215683	−0.107842	+	0.994168i	$0.534394\pi$
$840$	−11036.5	−0.453329
$841$	26990.1	1.10665
$842$	31522.0	1.29017
$843$	3018.37	0.123319
$844$	9059.02	0.369460
$845$	14868.0	0.605295
$846$	−5899.58	−0.239754
$847$	−20535.4	−0.833065
$848$	−15024.6	−0.608426
$849$	−5611.40	−0.226835
$850$	−17487.2	−0.705654
$851$	0	0
$852$	2145.35	0.0862660
$853$	1078.39	0.0432866	0.0216433	−	0.999766i	$-0.493110\pi$
$853$	1078.39	0.0432866	0.0216433	+	0.999766i	$0.493110\pi$
$854$	2289.32	0.0917316
$855$	−3202.72	−0.128106
$856$	−24692.8	−0.985961
$857$	−37733.4	−1.50402	−0.752012	−	0.659149i	$-0.770917\pi$
$857$	−37733.4	−1.50402	−0.752012	+	0.659149i	$0.770917\pi$
$858$	3219.57	0.128105
$859$	−14792.4	−0.587555	−0.293778	−	0.955874i	$-0.594913\pi$
$859$	−14792.4	−0.587555	−0.293778	+	0.955874i	$0.594913\pi$
$860$	11681.8	0.463194
$861$	−13647.5	−0.540193
$862$	−11478.1	−0.453533
$863$	32572.4	1.28479	0.642396	−	0.766373i	$-0.277940\pi$
$863$	32572.4	1.28479	0.642396	+	0.766373i	$0.277940\pi$
$864$	−7685.78	−0.302634
$865$	−10423.0	−0.409704
$866$	−45807.5	−1.79746
$867$	−6857.00	−0.268600
$868$	12648.5	0.494605
$869$	12511.2	0.488392
$870$	21639.9	0.843290
$871$	1525.48	0.0593443
$872$	22709.4	0.881922
$873$	15276.0	0.592229
$874$	0	0
$875$	−46932.4	−1.81326
$876$	1199.00	0.0462450
$877$	−12833.0	−0.494115	−0.247058	−	0.969001i	$-0.579464\pi$
$877$	−12833.0	−0.494115	−0.247058	+	0.969001i	$0.579464\pi$
$878$	41786.5	1.60618
$879$	3669.10	0.140791
$880$	−25501.1	−0.976866
$881$	−32284.2	−1.23460	−0.617299	−	0.786729i	$-0.711773\pi$
$881$	−32284.2	−1.23460	−0.617299	+	0.786729i	$0.711773\pi$
$882$	4030.92	0.153887
$883$	19698.0	0.750724	0.375362	−	0.926878i	$-0.377518\pi$
$883$	19698.0	0.750724	0.375362	+	0.926878i	$0.377518\pi$
$884$	1822.74	0.0693500
$885$	10603.8	0.402759
$886$	31651.6	1.20018
$887$	7425.12	0.281072	0.140536	−	0.990076i	$-0.455117\pi$
$887$	7425.12	0.281072	0.140536	+	0.990076i	$0.455117\pi$
$888$	3276.65	0.123826
$889$	10738.3	0.405120
$890$	−99887.8	−3.76207
$891$	−9305.78	−0.349894
$892$	−2727.88	−0.102395
$893$	507.260	0.0190087
$894$	−1744.60	−0.0652663
$895$	−29856.3	−1.11507
$896$	−34710.8	−1.29420
$897$	0	0
$898$	37161.0	1.38093
$899$	66264.4	2.45833
$900$	−13260.6	−0.491132
$901$	4339.87	0.160468
$902$	−24366.5	−0.899463
$903$	−8554.65	−0.315261
$904$	−13508.0	−0.496978
$905$	27110.6	0.995786
$906$	−4782.96	−0.175390
$907$	20674.0	0.756857	0.378428	−	0.925631i	$-0.376465\pi$
$907$	20674.0	0.756857	0.378428	+	0.925631i	$0.376465\pi$
$908$	7676.43	0.280563
$909$	14961.9	0.545935
$910$	46183.5	1.68238
$911$	15326.3	0.557389	0.278695	−	0.960380i	$-0.410098\pi$
$911$	15326.3	0.557389	0.278695	+	0.960380i	$0.410098\pi$
$912$	802.223	0.0291275
$913$	20512.6	0.743559
$914$	13982.9	0.506033
$915$	1081.25	0.0390655
$916$	1495.34	0.0539381
$917$	965.021	0.0347522
$918$	5653.45	0.203259
$919$	40794.3	1.46429	0.732143	−	0.681151i	$-0.238520\pi$
$919$	40794.3	1.46429	0.732143	+	0.681151i	$0.238520\pi$
$920$	0	0
$921$	505.736	0.0180940
$922$	7976.57	0.284918
$923$	23986.8	0.855401
$924$	−1155.98	−0.0411570
$925$	28157.0	1.00086
$926$	38078.4	1.35133
$927$	25524.9	0.904365
$928$	21776.5	0.770311
$929$	−33287.1	−1.17558	−0.587791	−	0.809013i	$-0.700002\pi$
$929$	−33287.1	−1.17558	−0.587791	+	0.809013i	$0.700002\pi$
$930$	27909.4	0.984069
$931$	−346.588	−0.0122008
$932$	−2069.67	−0.0727405
$933$	−475.189	−0.0166742
$934$	−47470.9	−1.66306
$935$	7366.04	0.257642
$936$	−17253.6	−0.602512
$937$	−23880.2	−0.832586	−0.416293	−	0.909231i	$-0.636671\pi$
$937$	−23880.2	−0.832586	−0.416293	+	0.909231i	$0.636671\pi$
$938$	−2558.89	−0.0890734
$939$	6912.26	0.240227
$940$	3161.19	0.109688
$941$	49973.0	1.73121	0.865607	−	0.500723i	$-0.166933\pi$
$941$	49973.0	1.73121	0.865607	+	0.500723i	$0.166933\pi$
$942$	5997.48	0.207440
$943$	0	0
$944$	27173.3	0.936881
$945$	30660.7	1.05544
$946$	−15273.6	−0.524934
$947$	24406.2	0.837482	0.418741	−	0.908106i	$-0.362472\pi$
$947$	24406.2	0.837482	0.418741	+	0.908106i	$0.362472\pi$
$948$	−2452.75	−0.0840314
$949$	13405.8	0.458559
$950$	5326.78	0.181919
$951$	−13764.7	−0.469349
$952$	8169.40	0.278122
$953$	34507.8	1.17295	0.586473	−	0.809969i	$-0.300516\pi$
$953$	34507.8	1.17295	0.586473	+	0.809969i	$0.300516\pi$
$954$	15374.9	0.521782
$955$	−61504.7	−2.08402
$956$	8297.60	0.280715
$957$	−6056.11	−0.204562
$958$	44451.2	1.49912
$959$	−32338.9	−1.08893
$960$	−9185.27	−0.308806
$961$	55671.3	1.86873
$962$	−13711.5	−0.459538
$963$	32701.5	1.09428
$964$	−6657.25	−0.222423
$965$	64919.0	2.16561
$966$	0	0
$967$	−5389.43	−0.179227	−0.0896134	−	0.995977i	$-0.528563\pi$
$967$	−5389.43	−0.179227	−0.0896134	+	0.995977i	$0.528563\pi$
$968$	−19205.2	−0.637684
$969$	−231.724	−0.00768218
$970$	−38241.3	−1.26583
$971$	3602.54	0.119064	0.0595319	−	0.998226i	$-0.481039\pi$
$971$	3602.54	0.119064	0.0595319	+	0.998226i	$0.481039\pi$
$972$	6530.41	0.215497
$973$	22700.3	0.747934
$974$	50552.2	1.66304
$975$	14492.0	0.476017
$976$	2770.81	0.0908725
$977$	−6831.70	−0.223711	−0.111855	−	0.993724i	$-0.535679\pi$
$977$	−6831.70	−0.223711	−0.111855	+	0.993724i	$0.535679\pi$
$978$	−3822.01	−0.124963
$979$	27954.4	0.912590
$980$	−2159.90	−0.0704035
$981$	−30074.7	−0.978810
$982$	10442.6	0.339345
$983$	29777.6	0.966182	0.483091	−	0.875570i	$-0.339514\pi$
$983$	29777.6	0.966182	0.483091	+	0.875570i	$0.339514\pi$
$984$	−12763.5	−0.413500
$985$	−19786.5	−0.640052
$986$	−16018.2	−0.517366
$987$	−2314.95	−0.0746562
$988$	−555.226	−0.0178786
$989$	0	0
$990$	26095.7	0.837753
$991$	26349.2	0.844612	0.422306	−	0.906453i	$-0.361221\pi$
$991$	26349.2	0.844612	0.422306	+	0.906453i	$0.361221\pi$
$992$	28085.5	0.898907
$993$	−3354.50	−0.107202
$994$	−40236.3	−1.28392
$995$	37147.2	1.18356
$996$	−4021.40	−0.127935
$997$	−5799.36	−0.184220	−0.0921101	−	0.995749i	$-0.529361\pi$
$997$	−5799.36	−0.184220	−0.0921101	+	0.995749i	$0.529361\pi$
$998$	41907.4	1.32922
$999$	−9102.90	−0.288291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.7		25
23.5	odd	22		23.4.c.a.2.2	✓	50
23.14	odd	22		23.4.c.a.12.2	yes	50
23.22	odd	2		529.4.a.n.1.7		25
69.5	even	22		207.4.i.a.163.4		50
69.14	even	22		207.4.i.a.127.4		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.2.2	✓	50	23.5	odd	22
23.4.c.a.12.2	yes	50	23.14	odd	22
207.4.i.a.127.4		50	69.14	even	22
207.4.i.a.163.4		50	69.5	even	22
529.4.a.m.1.7		25	1.1	even	1	trivial
529.4.a.n.1.7		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-3.19041 q^{2} +1.55052 q^{3} +2.17871 q^{4} -19.2991 q^{5} -4.94680 q^{6} +19.8587 q^{7} +18.5723 q^{8} -24.5959 q^{9} +61.5722 q^{10} -17.2315 q^{11} +3.37814 q^{12} +37.7704 q^{13} -63.3574 q^{14} -29.9238 q^{15} -76.6829 q^{16} +22.1500 q^{17} +78.4709 q^{18} -6.74712 q^{19} -42.0473 q^{20} +30.7914 q^{21} +54.9754 q^{22} +28.7968 q^{24} +247.457 q^{25} -120.503 q^{26} -80.0006 q^{27} +43.2664 q^{28} +226.669 q^{29} +95.4691 q^{30} +292.339 q^{31} +96.0716 q^{32} -26.7178 q^{33} -70.6675 q^{34} -383.256 q^{35} -53.5873 q^{36} +113.785 q^{37} +21.5261 q^{38} +58.5639 q^{39} -358.429 q^{40} -443.225 q^{41} -98.2371 q^{42} -277.826 q^{43} -37.5424 q^{44} +474.679 q^{45} -75.1817 q^{47} -118.899 q^{48} +51.3683 q^{49} -789.489 q^{50} +34.3441 q^{51} +82.2909 q^{52} +195.931 q^{53} +255.235 q^{54} +332.553 q^{55} +368.822 q^{56} -10.4616 q^{57} -723.168 q^{58} -354.359 q^{59} -65.1953 q^{60} -36.1334 q^{61} -932.682 q^{62} -488.442 q^{63} +306.956 q^{64} -728.937 q^{65} +85.2407 q^{66} +40.3882 q^{67} +48.2585 q^{68} +1222.74 q^{70} +635.069 q^{71} -456.802 q^{72} +354.930 q^{73} -363.022 q^{74} +383.688 q^{75} -14.7000 q^{76} -342.195 q^{77} -186.843 q^{78} -726.065 q^{79} +1479.91 q^{80} +540.046 q^{81} +1414.07 q^{82} -1190.42 q^{83} +67.0856 q^{84} -427.476 q^{85} +886.379 q^{86} +351.456 q^{87} -320.028 q^{88} -1622.29 q^{89} -1514.42 q^{90} +750.072 q^{91} +453.279 q^{93} +239.860 q^{94} +130.214 q^{95} +148.961 q^{96} -621.081 q^{97} -163.886 q^{98} +423.823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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