LMFDB - Embedded newform 529.4.a.m.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,4,Mod(1,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [25,0,-1,80,-51] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			1.14
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)

$f(q)$	$=$	\(q+0.929572 q^{2} +0.505183 q^{3} -7.13590 q^{4} +10.4946 q^{5} +0.469604 q^{6} +30.2596 q^{7} -14.0699 q^{8} -26.7448 q^{9} +9.75547 q^{10} -36.7763 q^{11} -3.60494 q^{12} -65.2752 q^{13} +28.1284 q^{14} +5.30169 q^{15} +44.0082 q^{16} +36.6778 q^{17} -24.8612 q^{18} -42.1700 q^{19} -74.8883 q^{20} +15.2866 q^{21} -34.1862 q^{22} -7.10788 q^{24} -14.8637 q^{25} -60.6779 q^{26} -27.1510 q^{27} -215.929 q^{28} +57.5815 q^{29} +4.92830 q^{30} -58.5416 q^{31} +153.468 q^{32} -18.5788 q^{33} +34.0947 q^{34} +317.562 q^{35} +190.848 q^{36} -288.712 q^{37} -39.2000 q^{38} -32.9759 q^{39} -147.658 q^{40} -350.300 q^{41} +14.2100 q^{42} +186.494 q^{43} +262.432 q^{44} -280.675 q^{45} +217.230 q^{47} +22.2322 q^{48} +572.642 q^{49} -13.8169 q^{50} +18.5290 q^{51} +465.797 q^{52} -145.484 q^{53} -25.2388 q^{54} -385.952 q^{55} -425.749 q^{56} -21.3036 q^{57} +53.5262 q^{58} -800.665 q^{59} -37.8323 q^{60} -598.596 q^{61} -54.4186 q^{62} -809.286 q^{63} -209.406 q^{64} -685.036 q^{65} -17.2703 q^{66} +415.191 q^{67} -261.729 q^{68} +295.196 q^{70} -949.038 q^{71} +376.297 q^{72} -417.817 q^{73} -268.379 q^{74} -7.50889 q^{75} +300.921 q^{76} -1112.83 q^{77} -30.6535 q^{78} +82.7395 q^{79} +461.848 q^{80} +708.393 q^{81} -325.629 q^{82} -71.0365 q^{83} -109.084 q^{84} +384.919 q^{85} +173.359 q^{86} +29.0892 q^{87} +517.438 q^{88} -737.250 q^{89} -260.908 q^{90} -1975.20 q^{91} -29.5742 q^{93} +201.931 q^{94} -442.557 q^{95} +77.5295 q^{96} -1473.90 q^{97} +532.311 q^{98} +983.573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.929572	0.328653	0.164327	−	0.986406i	$-0.447455\pi$
$2$	0.929572	0.328653	0.164327	+	0.986406i	$0.447455\pi$
$3$	0.505183	0.0972226	0.0486113	−	0.998818i	$-0.484520\pi$
$3$	0.505183	0.0972226	0.0486113	+	0.998818i	$0.484520\pi$
$4$	−7.13590	−0.891987
$5$	10.4946	0.938664	0.469332	−	0.883022i	$-0.344495\pi$
$5$	10.4946	0.938664	0.469332	+	0.883022i	$0.344495\pi$
$6$	0.469604	0.0319525
$7$	30.2596	1.63386	0.816932	−	0.576735i	$-0.195673\pi$
$7$	30.2596	1.63386	0.816932	+	0.576735i	$0.195673\pi$
$8$	−14.0699	−0.621808
$9$	−26.7448	−0.990548
$10$	9.75547	0.308495
$11$	−36.7763	−1.00804	−0.504021	−	0.863691i	$-0.668147\pi$
$11$	−36.7763	−1.00804	−0.504021	+	0.863691i	$0.668147\pi$
$12$	−3.60494	−0.0867213
$13$	−65.2752	−1.39262	−0.696310	−	0.717741i	$-0.745176\pi$
$13$	−65.2752	−1.39262	−0.696310	+	0.717741i	$0.745176\pi$
$14$	28.1284	0.536974
$15$	5.30169	0.0912593
$16$	44.0082	0.687628
$17$	36.6778	0.523275	0.261638	−	0.965166i	$-0.415737\pi$
$17$	36.6778	0.523275	0.261638	+	0.965166i	$0.415737\pi$
$18$	−24.8612	−0.325547
$19$	−42.1700	−0.509182	−0.254591	−	0.967049i	$-0.581941\pi$
$19$	−42.1700	−0.509182	−0.254591	+	0.967049i	$0.581941\pi$
$20$	−74.8883	−0.837276
$21$	15.2866	0.158848
$22$	−34.1862	−0.331296
$23$	0	0
$23$	0	0
$24$	−7.10788	−0.0604537
$25$	−14.8637	−0.118909
$26$	−60.6779	−0.457689
$27$	−27.1510	−0.193526
$28$	−215.929	−1.45738
$29$	57.5815	0.368711	0.184356	−	0.982860i	$-0.440980\pi$
$29$	57.5815	0.368711	0.184356	+	0.982860i	$0.440980\pi$
$30$	4.92830	0.0299927
$31$	−58.5416	−0.339173	−0.169587	−	0.985515i	$-0.554243\pi$
$31$	−58.5416	−0.339173	−0.169587	+	0.985515i	$0.554243\pi$
$32$	153.468	0.847799
$33$	−18.5788	−0.0980044
$34$	34.0947	0.171976
$35$	317.562	1.53365
$36$	190.848	0.883556
$37$	−288.712	−1.28281	−0.641405	−	0.767203i	$-0.721648\pi$
$37$	−288.712	−1.28281	−0.641405	+	0.767203i	$0.721648\pi$
$38$	−39.2000	−0.167344
$39$	−32.9759	−0.135394
$40$	−147.658	−0.583669
$41$	−350.300	−1.33433	−0.667166	−	0.744909i	$-0.732493\pi$
$41$	−350.300	−1.33433	−0.667166	+	0.744909i	$0.732493\pi$
$42$	14.2100	0.0522060
$43$	186.494	0.661396	0.330698	−	0.943737i	$-0.392716\pi$
$43$	186.494	0.661396	0.330698	+	0.943737i	$0.392716\pi$
$44$	262.432	0.899160
$45$	−280.675	−0.929792
$46$	0	0
$47$	217.230	0.674176	0.337088	−	0.941473i	$-0.390558\pi$
$47$	217.230	0.674176	0.337088	+	0.941473i	$0.390558\pi$
$48$	22.2322	0.0668529
$49$	572.642	1.66951
$50$	−13.8169	−0.0390800
$51$	18.5290	0.0508742
$52$	465.797	1.24220
$53$	−145.484	−0.377052	−0.188526	−	0.982068i	$-0.560371\pi$
$53$	−145.484	−0.377052	−0.188526	+	0.982068i	$0.560371\pi$
$54$	−25.2388	−0.0636030
$55$	−385.952	−0.946213
$56$	−425.749	−1.01595
$57$	−21.3036	−0.0495040
$58$	53.5262	0.121178
$59$	−800.665	−1.76674	−0.883370	−	0.468676i	$-0.844731\pi$
$59$	−800.665	−1.76674	−0.883370	+	0.468676i	$0.844731\pi$
$60$	−37.8323	−0.0814021
$61$	−598.596	−1.25643	−0.628216	−	0.778039i	$-0.716215\pi$
$61$	−598.596	−1.25643	−0.628216	+	0.778039i	$0.716215\pi$
$62$	−54.4186	−0.111470
$63$	−809.286	−1.61842
$64$	−209.406	−0.408996
$65$	−685.036	−1.30720
$66$	−17.2703	−0.0322095
$67$	415.191	0.757069	0.378535	−	0.925587i	$-0.376428\pi$
$67$	415.191	0.757069	0.378535	+	0.925587i	$0.376428\pi$
$68$	−261.729	−0.466755
$69$	0	0
$70$	295.196	0.504039
$71$	−949.038	−1.58634	−0.793170	−	0.609001i	$-0.791571\pi$
$71$	−949.038	−1.58634	−0.793170	+	0.609001i	$0.791571\pi$
$72$	376.297	0.615930
$73$	−417.817	−0.669887	−0.334943	−	0.942238i	$-0.608717\pi$
$73$	−417.817	−0.669887	−0.334943	+	0.942238i	$0.608717\pi$
$74$	−268.379	−0.421600
$75$	−7.50889	−0.0115607
$76$	300.921	0.454184
$77$	−1112.83	−1.64700
$78$	−30.6535	−0.0444977
$79$	82.7395	0.117834	0.0589172	−	0.998263i	$-0.481235\pi$
$79$	82.7395	0.117834	0.0589172	+	0.998263i	$0.481235\pi$
$80$	461.848	0.645452
$81$	708.393	0.971733
$82$	−325.629	−0.438532
$83$	−71.0365	−0.0939430	−0.0469715	−	0.998896i	$-0.514957\pi$
$83$	−71.0365	−0.0939430	−0.0469715	+	0.998896i	$0.514957\pi$
$84$	−109.084	−0.141691
$85$	384.919	0.491180
$86$	173.359	0.217370
$87$	29.0892	0.0358470
$88$	517.438	0.626808
$89$	−737.250	−0.878071	−0.439036	−	0.898470i	$-0.644680\pi$
$89$	−737.250	−0.878071	−0.439036	+	0.898470i	$0.644680\pi$
$90$	−260.908	−0.305579
$91$	−1975.20	−2.27535
$92$	0	0
$93$	−29.5742	−0.0329753
$94$	201.931	0.221570
$95$	−442.557	−0.477951
$96$	77.5295	0.0824252
$97$	−1473.90	−1.54280	−0.771401	−	0.636350i	$-0.780444\pi$
$97$	−1473.90	−1.54280	−0.771401	+	0.636350i	$0.780444\pi$
$98$	532.311	0.548690
$99$	983.573	0.998514
$100$	106.066	0.106066
$101$	571.898	0.563425	0.281713	−	0.959499i	$-0.409098\pi$
$101$	571.898	0.563425	0.281713	+	0.959499i	$0.409098\pi$
$102$	17.2241	0.0167200
$103$	255.521	0.244439	0.122220	−	0.992503i	$-0.460999\pi$
$103$	255.521	0.244439	0.122220	+	0.992503i	$0.460999\pi$
$104$	918.415	0.865942
$105$	160.427	0.149105
$106$	−135.238	−0.123919
$107$	694.013	0.627035	0.313518	−	0.949582i	$-0.398492\pi$
$107$	694.013	0.627035	0.313518	+	0.949582i	$0.398492\pi$
$108$	193.746	0.172623
$109$	162.205	0.142536	0.0712679	−	0.997457i	$-0.477295\pi$
$109$	162.205	0.142536	0.0712679	+	0.997457i	$0.477295\pi$
$110$	−358.770	−0.310976
$111$	−145.852	−0.124718
$112$	1331.67	1.12349
$113$	2011.80	1.67482	0.837409	−	0.546577i	$-0.184069\pi$
$113$	2011.80	1.67482	0.837409	+	0.546577i	$0.184069\pi$
$114$	−19.8032	−0.0162696
$115$	0	0
$116$	−410.896	−0.328885
$117$	1745.77	1.37946
$118$	−744.275	−0.580645
$119$	1109.86	0.854961
$120$	−74.5942	−0.0567458
$121$	21.4936	0.0161485
$122$	−556.438	−0.412930
$123$	−176.965	−0.129727
$124$	417.746	0.302538
$125$	−1467.81	−1.05028
$126$	−752.289	−0.531899
$127$	−536.927	−0.375154	−0.187577	−	0.982250i	$-0.560063\pi$
$127$	−536.927	−0.375154	−0.187577	+	0.982250i	$0.560063\pi$
$128$	−1422.40	−0.982217
$129$	94.2134	0.0643026
$130$	−636.790	−0.429617
$131$	545.888	0.364080	0.182040	−	0.983291i	$-0.441730\pi$
$131$	545.888	0.364080	0.182040	+	0.983291i	$0.441730\pi$
$132$	132.576	0.0874187
$133$	−1276.05	−0.831934
$134$	385.950	0.248813
$135$	−284.938	−0.181656
$136$	−516.054	−0.325377
$137$	728.474	0.454290	0.227145	−	0.973861i	$-0.427061\pi$
$137$	728.474	0.454290	0.227145	+	0.973861i	$0.427061\pi$
$138$	0	0
$139$	1952.77	1.19159	0.595796	−	0.803135i	$-0.296837\pi$
$139$	1952.77	1.19159	0.595796	+	0.803135i	$0.296837\pi$
$140$	−2266.09	−1.36799
$141$	109.741	0.0655451
$142$	−882.199	−0.521356
$143$	2400.58	1.40382
$144$	−1176.99	−0.681128
$145$	604.294	0.346096
$146$	−388.391	−0.220161
$147$	289.289	0.162314
$148$	2060.22	1.14425
$149$	1446.99	0.795585	0.397793	−	0.917475i	$-0.369776\pi$
$149$	1446.99	0.795585	0.397793	+	0.917475i	$0.369776\pi$
$150$	−6.98005	−0.00379946
$151$	356.783	0.192282	0.0961410	−	0.995368i	$-0.469350\pi$
$151$	356.783	0.192282	0.0961410	+	0.995368i	$0.469350\pi$
$152$	593.328	0.316613
$153$	−980.941	−0.518329
$154$	−1034.46	−0.541293
$155$	−614.369	−0.318370
$156$	235.313	0.120770
$157$	−2361.17	−1.20027	−0.600134	−	0.799899i	$-0.704886\pi$
$157$	−2361.17	−1.20027	−0.600134	+	0.799899i	$0.704886\pi$
$158$	76.9123	0.0387267
$159$	−73.4961	−0.0366580
$160$	1610.58	0.795798
$161$	0	0
$162$	658.502	0.319363
$163$	904.786	0.434775	0.217387	−	0.976085i	$-0.430246\pi$
$163$	904.786	0.434775	0.217387	+	0.976085i	$0.430246\pi$
$164$	2499.70	1.19021
$165$	−194.976	−0.0919932
$166$	−66.0335	−0.0308747
$167$	−363.482	−0.168426	−0.0842129	−	0.996448i	$-0.526838\pi$
$167$	−363.482	−0.168426	−0.0842129	+	0.996448i	$0.526838\pi$
$168$	−215.081	−0.0987731
$169$	2063.85	0.939393
$170$	357.810	0.161428
$171$	1127.83	0.504369
$172$	−1330.80	−0.589956
$173$	−403.664	−0.177399	−0.0886993	−	0.996058i	$-0.528271\pi$
$173$	−403.664	−0.177399	−0.0886993	+	0.996058i	$0.528271\pi$
$174$	27.0405	0.0117812
$175$	−449.769	−0.194282
$176$	−1618.46	−0.693158
$177$	−404.482	−0.171767
$178$	−685.327	−0.288581
$179$	3531.72	1.47471	0.737354	−	0.675506i	$-0.236075\pi$
$179$	3531.72	1.47471	0.737354	+	0.675506i	$0.236075\pi$
$180$	2002.87	0.829362
$181$	−374.126	−0.153638	−0.0768191	−	0.997045i	$-0.524476\pi$
$181$	−374.126	−0.153638	−0.0768191	+	0.997045i	$0.524476\pi$
$182$	−1836.09	−0.747802
$183$	−302.401	−0.122154
$184$	0	0
$185$	−3029.91	−1.20413
$186$	−27.4914	−0.0108374
$187$	−1348.87	−0.527484
$188$	−1550.13	−0.601356
$189$	−821.577	−0.316195
$190$	−411.388	−0.157080
$191$	−3712.31	−1.40635	−0.703177	−	0.711015i	$-0.748236\pi$
$191$	−3712.31	−1.40635	−0.703177	+	0.711015i	$0.748236\pi$
$192$	−105.788	−0.0397637
$193$	−3046.61	−1.13627	−0.568135	−	0.822935i	$-0.692335\pi$
$193$	−3046.61	−1.13627	−0.568135	+	0.822935i	$0.692335\pi$
$194$	−1370.09	−0.507047
$195$	−346.069	−0.127090
$196$	−4086.31	−1.48918
$197$	4466.37	1.61531	0.807654	−	0.589657i	$-0.200737\pi$
$197$	4466.37	1.61531	0.807654	+	0.589657i	$0.200737\pi$
$198$	914.302	0.328165
$199$	5180.23	1.84531	0.922655	−	0.385626i	$-0.126015\pi$
$199$	5180.23	1.84531	0.922655	+	0.385626i	$0.126015\pi$
$200$	209.131	0.0739388
$201$	209.747	0.0736042
$202$	531.620	0.185172
$203$	1742.39	0.602423
$204$	−132.221	−0.0453791
$205$	−3676.25	−1.25249
$206$	237.525	0.0803357
$207$	0	0
$208$	−2872.64	−0.957605
$209$	1550.86	0.513277
$210$	149.128	0.0490039
$211$	4171.06	1.36089	0.680445	−	0.732799i	$-0.261786\pi$
$211$	4171.06	1.36089	0.680445	+	0.732799i	$0.261786\pi$
$212$	1038.16	0.336326
$213$	−479.438	−0.154228
$214$	645.135	0.206077
$215$	1957.17	0.620828
$216$	382.011	0.120336
$217$	−1771.44	−0.554163
$218$	150.781	0.0468449
$219$	−211.074	−0.0651281
$220$	2754.11	0.844010
$221$	−2394.15	−0.728724
$222$	−135.580	−0.0409890
$223$	−3011.36	−0.904285	−0.452143	−	0.891946i	$-0.649340\pi$
$223$	−3011.36	−0.904285	−0.452143	+	0.891946i	$0.649340\pi$
$224$	4643.88	1.38519
$225$	397.526	0.117786
$226$	1870.11	0.550434
$227$	−363.862	−0.106389	−0.0531946	−	0.998584i	$-0.516940\pi$
$227$	−363.862	−0.106389	−0.0531946	+	0.998584i	$0.516940\pi$
$228$	152.020	0.0441569
$229$	4638.08	1.33840	0.669198	−	0.743084i	$-0.266638\pi$
$229$	4638.08	1.33840	0.669198	+	0.743084i	$0.266638\pi$
$230$	0	0
$231$	−562.185	−0.160126
$232$	−810.166	−0.229267
$233$	−6420.52	−1.80525	−0.902623	−	0.430433i	$-0.858361\pi$
$233$	−6420.52	−1.80525	−0.902623	+	0.430433i	$0.858361\pi$
$234$	1622.82	0.453363
$235$	2279.74	0.632825
$236$	5713.46	1.57591
$237$	41.7986	0.0114562
$238$	1031.69	0.280986
$239$	−1241.97	−0.336135	−0.168067	−	0.985776i	$-0.553753\pi$
$239$	−1241.97	−0.336135	−0.168067	+	0.985776i	$0.553753\pi$
$240$	233.318	0.0627525
$241$	299.554	0.0800663	0.0400332	−	0.999198i	$-0.487254\pi$
$241$	299.554	0.0800663	0.0400332	+	0.999198i	$0.487254\pi$
$242$	19.9799	0.00530725
$243$	1090.94	0.288000
$244$	4271.52	1.12072
$245$	6009.64	1.56711
$246$	−164.502	−0.0426352
$247$	2752.65	0.709098
$248$	823.674	0.210901
$249$	−35.8864	−0.00913338
$250$	−1364.44	−0.345178
$251$	−3478.23	−0.874678	−0.437339	−	0.899297i	$-0.644079\pi$
$251$	−3478.23	−0.874678	−0.437339	+	0.899297i	$0.644079\pi$
$252$	5774.98	1.44361
$253$	0	0
$254$	−499.112	−0.123296
$255$	194.454	0.0477538
$256$	353.024	0.0861874
$257$	−3168.54	−0.769058	−0.384529	−	0.923113i	$-0.625636\pi$
$257$	−3168.54	−0.769058	−0.384529	+	0.923113i	$0.625636\pi$
$258$	87.5782	0.0211332
$259$	−8736.30	−2.09594
$260$	4888.34	1.16601
$261$	−1540.01	−0.365226
$262$	507.442	0.119656
$263$	6391.26	1.49849	0.749243	−	0.662295i	$-0.230417\pi$
$263$	6391.26	1.49849	0.749243	+	0.662295i	$0.230417\pi$
$264$	261.401	0.0609399
$265$	−1526.79	−0.353925
$266$	−1186.18	−0.273418
$267$	−372.446	−0.0853683
$268$	−2962.76	−0.675296
$269$	5422.53	1.22906	0.614531	−	0.788893i	$-0.289345\pi$
$269$	5422.53	1.22906	0.614531	+	0.788893i	$0.289345\pi$
$270$	−264.870	−0.0597019
$271$	1728.18	0.387379	0.193689	−	0.981063i	$-0.437955\pi$
$271$	1728.18	0.387379	0.193689	+	0.981063i	$0.437955\pi$
$272$	1614.13	0.359819
$273$	−997.837	−0.221216
$274$	677.168	0.149304
$275$	546.631	0.119866
$276$	0	0
$277$	1790.89	0.388463	0.194232	−	0.980956i	$-0.437779\pi$
$277$	1790.89	0.388463	0.194232	+	0.980956i	$0.437779\pi$
$278$	1815.24	0.391621
$279$	1565.68	0.335967
$280$	−4468.06	−0.953635
$281$	5903.46	1.25328	0.626639	−	0.779310i	$-0.284430\pi$
$281$	5903.46	1.25328	0.626639	+	0.779310i	$0.284430\pi$
$282$	102.012	0.0215416
$283$	−7327.59	−1.53915	−0.769576	−	0.638555i	$-0.779532\pi$
$283$	−7327.59	−1.53915	−0.769576	+	0.638555i	$0.779532\pi$
$284$	6772.24	1.41499
$285$	−223.572	−0.0464676
$286$	2231.51	0.461370
$287$	−10599.9	−2.18012
$288$	−4104.47	−0.839785
$289$	−3567.74	−0.726183
$290$	561.735	0.113746
$291$	−744.589	−0.149995
$292$	2981.50	0.597530
$293$	1562.43	0.311530	0.155765	−	0.987794i	$-0.450216\pi$
$293$	1562.43	0.311530	0.155765	+	0.987794i	$0.450216\pi$
$294$	268.915	0.0533450
$295$	−8402.65	−1.65838
$296$	4062.15	0.797661
$297$	998.511	0.195082
$298$	1345.08	0.261472
$299$	0	0
$300$	53.5826	0.0103120
$301$	5643.22	1.08063
$302$	331.655	0.0631941
$303$	288.913	0.0547776
$304$	−1855.83	−0.350128
$305$	−6282.02	−1.17937
$306$	−911.855	−0.170351
$307$	−584.640	−0.108688	−0.0543439	−	0.998522i	$-0.517307\pi$
$307$	−584.640	−0.108688	−0.0543439	+	0.998522i	$0.517307\pi$
$308$	7941.07	1.46910
$309$	129.085	0.0237650
$310$	−571.100	−0.104633
$311$	2343.59	0.427309	0.213654	−	0.976909i	$-0.431463\pi$
$311$	2343.59	0.427309	0.213654	+	0.976909i	$0.431463\pi$
$312$	463.968	0.0841891
$313$	3503.27	0.632641	0.316320	−	0.948652i	$-0.397553\pi$
$313$	3503.27	0.632641	0.316320	+	0.948652i	$0.397553\pi$
$314$	−2194.88	−0.394472
$315$	−8493.12	−1.51915
$316$	−590.420	−0.105107
$317$	−291.844	−0.0517084	−0.0258542	−	0.999666i	$-0.508231\pi$
$317$	−291.844	−0.0517084	−0.0258542	+	0.999666i	$0.508231\pi$
$318$	−68.3199	−0.0120478
$319$	−2117.63	−0.371676
$320$	−2197.63	−0.383910
$321$	350.604	0.0609620
$322$	0	0
$323$	−1546.70	−0.266443
$324$	−5055.02	−0.866773
$325$	970.230	0.165596
$326$	841.063	0.142890
$327$	81.9432	0.0138577
$328$	4928.68	0.829698
$329$	6573.29	1.10151
$330$	−181.244	−0.0302339
$331$	−2124.61	−0.352807	−0.176404	−	0.984318i	$-0.556446\pi$
$331$	−2124.61	−0.352807	−0.176404	+	0.984318i	$0.556446\pi$
$332$	506.909	0.0837959
$333$	7721.54	1.27068
$334$	−337.883	−0.0553537
$335$	4357.26	0.710634
$336$	672.737	0.109229
$337$	−264.713	−0.0427889	−0.0213944	−	0.999771i	$-0.506811\pi$
$337$	−264.713	−0.0427889	−0.0213944	+	0.999771i	$0.506811\pi$
$338$	1918.49	0.308735
$339$	1016.33	0.162830
$340$	−2746.74	−0.438126
$341$	2152.94	0.341901
$342$	1048.40	0.165763
$343$	6948.86	1.09389
$344$	−2623.95	−0.411261
$345$	0	0
$346$	−375.234	−0.0583027
$347$	1281.55	0.198263	0.0991317	−	0.995074i	$-0.468393\pi$
$347$	1281.55	0.198263	0.0991317	+	0.995074i	$0.468393\pi$
$348$	−207.578	−0.0319751
$349$	8705.35	1.33521	0.667603	−	0.744517i	$-0.267320\pi$
$349$	8705.35	1.33521	0.667603	+	0.744517i	$0.267320\pi$
$350$	−418.092	−0.0638514
$351$	1772.28	0.269509
$352$	−5643.98	−0.854617
$353$	−4960.03	−0.747863	−0.373931	−	0.927456i	$-0.621990\pi$
$353$	−4960.03	−0.747863	−0.373931	+	0.927456i	$0.621990\pi$
$354$	−375.995	−0.0564518
$355$	−9959.76	−1.48904
$356$	5260.94	0.783228
$357$	560.680	0.0831215
$358$	3282.98	0.484668
$359$	−9394.15	−1.38107	−0.690535	−	0.723299i	$-0.742625\pi$
$359$	−9394.15	−1.38107	−0.690535	+	0.723299i	$0.742625\pi$
$360$	3949.08	0.578152
$361$	−5080.69	−0.740734
$362$	−347.777	−0.0504937
$363$	10.8582	0.00157000
$364$	14094.8	2.02958
$365$	−4384.81	−0.628799
$366$	−281.103	−0.0401462
$367$	−3557.98	−0.506063	−0.253032	−	0.967458i	$-0.581428\pi$
$367$	−3557.98	−0.506063	−0.253032	+	0.967458i	$0.581428\pi$
$368$	0	0
$369$	9368.69	1.32172
$370$	−2816.52	−0.395740
$371$	−4402.28	−0.616052
$372$	211.039	0.0294135
$373$	−2036.18	−0.282653	−0.141326	−	0.989963i	$-0.545137\pi$
$373$	−2036.18	−0.282653	−0.141326	+	0.989963i	$0.545137\pi$
$374$	−1253.88	−0.173359
$375$	−741.514	−0.102111
$376$	−3056.41	−0.419208
$377$	−3758.64	−0.513475
$378$	−763.714	−0.103919
$379$	6940.66	0.940680	0.470340	−	0.882485i	$-0.344131\pi$
$379$	6940.66	0.940680	0.470340	+	0.882485i	$0.344131\pi$
$380$	3158.04	0.426326
$381$	−271.246	−0.0364734
$382$	−3450.86	−0.462203
$383$	−6218.78	−0.829673	−0.414837	−	0.909896i	$-0.636161\pi$
$383$	−6218.78	−0.829673	−0.414837	+	0.909896i	$0.636161\pi$
$384$	−718.574	−0.0954936
$385$	−11678.7	−1.54598
$386$	−2832.05	−0.373439
$387$	−4987.73	−0.655144
$388$	10517.6	1.37616
$389$	−1498.75	−0.195346	−0.0976728	−	0.995219i	$-0.531140\pi$
$389$	−1498.75	−0.195346	−0.0976728	+	0.995219i	$0.531140\pi$
$390$	−321.696	−0.0417684
$391$	0	0
$392$	−8057.01	−1.03811
$393$	275.773	0.0353968
$394$	4151.81	0.530876
$395$	868.316	0.110607
$396$	−7018.68	−0.890661
$397$	10983.0	1.38847	0.694233	−	0.719750i	$-0.255744\pi$
$397$	10983.0	1.38847	0.694233	+	0.719750i	$0.255744\pi$
$398$	4815.39	0.606467
$399$	−644.637	−0.0808828
$400$	−654.124	−0.0817655
$401$	−3456.81	−0.430486	−0.215243	−	0.976561i	$-0.569054\pi$
$401$	−3456.81	−0.430486	−0.215243	+	0.976561i	$0.569054\pi$
$402$	194.975	0.0241903
$403$	3821.31	0.472340
$404$	−4081.00	−0.502568
$405$	7434.29	0.912131
$406$	1619.68	0.197988
$407$	10617.7	1.29313
$408$	−260.702	−0.0316340
$409$	11470.8	1.38678	0.693389	−	0.720563i	$-0.256117\pi$
$409$	11470.8	1.38678	0.693389	+	0.720563i	$0.256117\pi$
$410$	−3417.34	−0.411635
$411$	368.013	0.0441672
$412$	−1823.37	−0.218037
$413$	−24227.8	−2.88661
$414$	0	0
$415$	−745.499	−0.0881809
$416$	−10017.6	−1.18066
$417$	986.504	0.115850
$418$	1441.63	0.168690
$419$	−4497.28	−0.524359	−0.262179	−	0.965019i	$-0.584441\pi$
$419$	−4497.28	−0.524359	−0.262179	+	0.965019i	$0.584441\pi$
$420$	−1144.79	−0.133000
$421$	3908.00	0.452409	0.226205	−	0.974080i	$-0.427368\pi$
$421$	3908.00	0.452409	0.226205	+	0.974080i	$0.427368\pi$
$422$	3877.30	0.447261
$423$	−5809.77	−0.667803
$424$	2046.95	0.234454
$425$	−545.168	−0.0622224
$426$	−445.672	−0.0506875
$427$	−18113.3	−2.05284
$428$	−4952.41	−0.559308
$429$	1212.73	0.136483
$430$	1819.33	0.204037
$431$	−10563.4	−1.18056	−0.590281	−	0.807198i	$-0.700983\pi$
$431$	−10563.4	−1.18056	−0.590281	+	0.807198i	$0.700983\pi$
$432$	−1194.86	−0.133074
$433$	−5752.34	−0.638430	−0.319215	−	0.947682i	$-0.603419\pi$
$433$	−5752.34	−0.638430	−0.319215	+	0.947682i	$0.603419\pi$
$434$	−1646.68	−0.182127
$435$	305.279	0.0336483
$436$	−1157.48	−0.127140
$437$	0	0
$438$	−196.208	−0.0214046
$439$	6120.04	0.665361	0.332681	−	0.943040i	$-0.392047\pi$
$439$	6120.04	0.665361	0.332681	+	0.943040i	$0.392047\pi$
$440$	5430.30	0.588362
$441$	−15315.2	−1.65373
$442$	−2225.54	−0.239498
$443$	421.355	0.0451900	0.0225950	−	0.999745i	$-0.492807\pi$
$443$	421.355	0.0451900	0.0225950	+	0.999745i	$0.492807\pi$
$444$	1040.79	0.111247
$445$	−7737.13	−0.824214
$446$	−2799.28	−0.297196
$447$	730.996	0.0773488
$448$	−6336.54	−0.668244
$449$	87.6960	0.00921744	0.00460872	−	0.999989i	$-0.498533\pi$
$449$	87.6960	0.00921744	0.00460872	+	0.999989i	$0.498533\pi$
$450$	369.529	0.0387106
$451$	12882.7	1.34506
$452$	−14356.0	−1.49392
$453$	180.241	0.0186941
$454$	−338.235	−0.0349651
$455$	−20728.9	−2.13579
$456$	299.739	0.0307820
$457$	−10926.7	−1.11845	−0.559223	−	0.829017i	$-0.688900\pi$
$457$	−10926.7	−1.11845	−0.559223	+	0.829017i	$0.688900\pi$
$458$	4311.43	0.439868
$459$	−995.839	−0.101267
$460$	0	0
$461$	16330.7	1.64988	0.824940	−	0.565221i	$-0.191209\pi$
$461$	16330.7	1.64988	0.824940	+	0.565221i	$0.191209\pi$
$462$	−522.591	−0.0526259
$463$	10924.1	1.09651	0.548256	−	0.836311i	$-0.315292\pi$
$463$	10924.1	1.09651	0.548256	+	0.836311i	$0.315292\pi$
$464$	2534.06	0.253536
$465$	−310.369	−0.0309527
$466$	−5968.33	−0.593300
$467$	2389.48	0.236771	0.118386	−	0.992968i	$-0.462228\pi$
$467$	2389.48	0.236771	0.118386	+	0.992968i	$0.462228\pi$
$468$	−12457.6	−1.23046
$469$	12563.5	1.23695
$470$	2119.18	0.207980
$471$	−1192.83	−0.116693
$472$	11265.3	1.09857
$473$	−6858.54	−0.666714
$474$	38.8548	0.00376510
$475$	626.802	0.0605466
$476$	−7919.82	−0.762614
$477$	3890.94	0.373488
$478$	−1154.50	−0.110472
$479$	−8981.11	−0.856696	−0.428348	−	0.903614i	$-0.640904\pi$
$479$	−8981.11	−0.856696	−0.428348	+	0.903614i	$0.640904\pi$
$480$	813.639	0.0773696
$481$	18845.7	1.78647
$482$	278.457	0.0263141
$483$	0	0
$484$	−153.376	−0.0144042
$485$	−15468.0	−1.44817
$486$	1014.11	0.0946523
$487$	−8484.20	−0.789437	−0.394719	−	0.918802i	$-0.629158\pi$
$487$	−8484.20	−0.789437	−0.394719	+	0.918802i	$0.629158\pi$
$488$	8422.19	0.781259
$489$	457.083	0.0422699
$490$	5586.39	0.515035
$491$	−1421.07	−0.130615	−0.0653074	−	0.997865i	$-0.520803\pi$
$491$	−1421.07	−0.130615	−0.0653074	+	0.997865i	$0.520803\pi$
$492$	1262.81	0.115715
$493$	2111.97	0.192937
$494$	2558.79	0.233047
$495$	10322.2	0.937269
$496$	−2576.31	−0.233225
$497$	−28717.5	−2.59186
$498$	−33.3590	−0.00300171
$499$	6053.06	0.543030	0.271515	−	0.962434i	$-0.412475\pi$
$499$	6053.06	0.543030	0.271515	+	0.962434i	$0.412475\pi$
$500$	10474.1	0.936836
$501$	−183.625	−0.0163748
$502$	−3233.27	−0.287466
$503$	−1616.88	−0.143327	−0.0716634	−	0.997429i	$-0.522831\pi$
$503$	−1616.88	−0.143327	−0.0716634	+	0.997429i	$0.522831\pi$
$504$	11386.6	1.00635
$505$	6001.83	0.528867
$506$	0	0
$507$	1042.62	0.0913302
$508$	3831.45	0.334632
$509$	−14178.3	−1.23466	−0.617330	−	0.786704i	$-0.711786\pi$
$509$	−14178.3	−1.23466	−0.617330	+	0.786704i	$0.711786\pi$
$510$	180.759	0.0156944
$511$	−12643.0	−1.09450
$512$	11707.4	1.01054
$513$	1144.96	0.0985401
$514$	−2945.38	−0.252753
$515$	2681.59	0.229446
$516$	−672.297	−0.0573571
$517$	−7988.91	−0.679598
$518$	−8121.02	−0.688836
$519$	−203.924	−0.0172472
$520$	9638.38	0.812829
$521$	−10315.7	−0.867449	−0.433725	−	0.901045i	$-0.642801\pi$
$521$	−10315.7	−0.867449	−0.433725	+	0.901045i	$0.642801\pi$
$522$	−1431.55	−0.120033
$523$	−79.7623	−0.00666876	−0.00333438	−	0.999994i	$-0.501061\pi$
$523$	−79.7623	−0.00666876	−0.00333438	+	0.999994i	$0.501061\pi$
$524$	−3895.40	−0.324754
$525$	−227.216	−0.0188886
$526$	5941.14	0.492483
$527$	−2147.18	−0.177481
$528$	−817.617	−0.0673906
$529$	0	0
$530$	−1419.26	−0.116319
$531$	21413.6	1.75004
$532$	9105.73	0.742074
$533$	22865.9	1.85822
$534$	−346.216	−0.0280566
$535$	7283.38	0.588576
$536$	−5841.69	−0.470751
$537$	1784.16	0.143375
$538$	5040.63	0.403935
$539$	−21059.6	−1.68294
$540$	2033.29	0.162035
$541$	21296.9	1.69247	0.846234	−	0.532812i	$-0.178865\pi$
$541$	21296.9	1.69247	0.846234	+	0.532812i	$0.178865\pi$
$542$	1606.47	0.127313
$543$	−189.002	−0.0149371
$544$	5628.87	0.443632
$545$	1702.27	0.133793
$546$	−927.561	−0.0727032
$547$	−18547.5	−1.44979	−0.724894	−	0.688861i	$-0.758111\pi$
$547$	−18547.5	−1.44979	−0.724894	+	0.688861i	$0.758111\pi$
$548$	−5198.31	−0.405221
$549$	16009.3	1.24456
$550$	508.133	0.0393943
$551$	−2428.21	−0.187741
$552$	0	0
$553$	2503.66	0.192525
$554$	1664.76	0.127670
$555$	−1530.66	−0.117068
$556$	−13934.7	−1.06289
$557$	−4307.03	−0.327639	−0.163819	−	0.986490i	$-0.552381\pi$
$557$	−4307.03	−0.327639	−0.163819	+	0.986490i	$0.552381\pi$
$558$	1455.41	0.110417
$559$	−12173.4	−0.921073
$560$	13975.3	1.05458
$561$	−681.429	−0.0512833
$562$	5487.69	0.411894
$563$	1775.12	0.132882	0.0664408	−	0.997790i	$-0.478836\pi$
$563$	1775.12	0.132882	0.0664408	+	0.997790i	$0.478836\pi$
$564$	−783.100	−0.0584654
$565$	21113.0	1.57209
$566$	−6811.52	−0.505847
$567$	21435.7	1.58768
$568$	13352.9	0.986398
$569$	−3766.88	−0.277532	−0.138766	−	0.990325i	$-0.544314\pi$
$569$	−3766.88	−0.277532	−0.138766	+	0.990325i	$0.544314\pi$
$570$	−207.826	−0.0152717
$571$	9128.39	0.669022	0.334511	−	0.942392i	$-0.391429\pi$
$571$	9128.39	0.669022	0.334511	+	0.942392i	$0.391429\pi$
$572$	−17130.3	−1.25219
$573$	−1875.40	−0.136729
$574$	−9853.38	−0.716502
$575$	0	0
$576$	5600.52	0.405130
$577$	−6763.76	−0.488005	−0.244003	−	0.969775i	$-0.578461\pi$
$577$	−6763.76	−0.488005	−0.244003	+	0.969775i	$0.578461\pi$
$578$	−3316.47	−0.238662
$579$	−1539.10	−0.110471
$580$	−4312.18	−0.308713
$581$	−2149.53	−0.153490
$582$	−692.149	−0.0492964
$583$	5350.36	0.380084
$584$	5878.64	0.416541
$585$	18321.1	1.29485
$586$	1452.39	0.102385
$587$	−3956.59	−0.278204	−0.139102	−	0.990278i	$-0.544422\pi$
$587$	−3956.59	−0.278204	−0.139102	+	0.990278i	$0.544422\pi$
$588$	−2064.34	−0.144782
$589$	2468.70	0.172701
$590$	−7810.86	−0.545031
$591$	2256.33	0.157044
$592$	−12705.7	−0.882096
$593$	1784.21	0.123556	0.0617779	−	0.998090i	$-0.480323\pi$
$593$	1784.21	0.123556	0.0617779	+	0.998090i	$0.480323\pi$
$594$	928.188	0.0641145
$595$	11647.5	0.802521
$596$	−10325.6	−0.709652
$597$	2616.96	0.179406
$598$	0	0
$599$	−21692.8	−1.47970	−0.739851	−	0.672771i	$-0.765104\pi$
$599$	−21692.8	−1.47970	−0.739851	+	0.672771i	$0.765104\pi$
$600$	105.649	0.00718852
$601$	2781.39	0.188777	0.0943886	−	0.995535i	$-0.469910\pi$
$601$	2781.39	0.188777	0.0943886	+	0.995535i	$0.469910\pi$
$602$	5245.77	0.355153
$603$	−11104.2	−0.749913
$604$	−2545.96	−0.171513
$605$	225.567	0.0151580
$606$	268.565	0.0180029
$607$	−24744.7	−1.65462	−0.827312	−	0.561743i	$-0.810131\pi$
$607$	−24744.7	−1.65462	−0.827312	+	0.561743i	$0.810131\pi$
$608$	−6471.74	−0.431684
$609$	880.227	0.0585691
$610$	−5839.58	−0.387603
$611$	−14179.7	−0.938871
$612$	6999.89	0.462343
$613$	8345.37	0.549863	0.274932	−	0.961464i	$-0.411345\pi$
$613$	8345.37	0.549863	0.274932	+	0.961464i	$0.411345\pi$
$614$	−543.465	−0.0357206
$615$	−1857.18	−0.121770
$616$	15657.5	1.02412
$617$	15792.2	1.03042	0.515211	−	0.857064i	$-0.327714\pi$
$617$	15792.2	1.03042	0.515211	+	0.857064i	$0.327714\pi$
$618$	119.994	0.00781044
$619$	−19030.0	−1.23567	−0.617835	−	0.786308i	$-0.711990\pi$
$619$	−19030.0	−1.23567	−0.617835	+	0.786308i	$0.711990\pi$
$620$	4384.08	0.283982
$621$	0	0
$622$	2178.54	0.140436
$623$	−22308.9	−1.43465
$624$	−1451.21	−0.0931008
$625$	−13546.1	−0.866951
$626$	3256.54	0.207919
$627$	783.466	0.0499021
$628$	16849.1	1.07062
$629$	−10589.3	−0.671263
$630$	−7894.96	−0.499274
$631$	−4214.18	−0.265870	−0.132935	−	0.991125i	$-0.542440\pi$
$631$	−4214.18	−0.265870	−0.132935	+	0.991125i	$0.542440\pi$
$632$	−1164.14	−0.0732703
$633$	2107.15	0.132309
$634$	−271.290	−0.0169941
$635$	−5634.82	−0.352144
$636$	524.460	0.0326984
$637$	−37379.3	−2.32499
$638$	−1968.49	−0.122153
$639$	25381.8	1.57135
$640$	−14927.5	−0.921972
$641$	−26926.4	−1.65917	−0.829587	−	0.558378i	$-0.811424\pi$
$641$	−26926.4	−1.65917	−0.829587	+	0.558378i	$0.811424\pi$
$642$	325.911	0.0200354
$643$	4923.29	0.301953	0.150976	−	0.988537i	$-0.451758\pi$
$643$	4923.29	0.301953	0.150976	+	0.988537i	$0.451758\pi$
$644$	0	0
$645$	988.731	0.0603585
$646$	−1437.77	−0.0875672
$647$	−2007.97	−0.122011	−0.0610057	−	0.998137i	$-0.519431\pi$
$647$	−2007.97	−0.122011	−0.0610057	+	0.998137i	$0.519431\pi$
$648$	−9967.02	−0.604231
$649$	29445.5	1.78095
$650$	901.898	0.0544236
$651$	−894.903	−0.0538771
$652$	−6456.46	−0.387814
$653$	9349.83	0.560317	0.280158	−	0.959954i	$-0.409613\pi$
$653$	9349.83	0.560317	0.280158	+	0.959954i	$0.409613\pi$
$654$	76.1721	0.00455438
$655$	5728.87	0.341749
$656$	−15416.0	−0.917524
$657$	11174.4	0.663555
$658$	6110.34	0.362015
$659$	−26550.3	−1.56943	−0.784715	−	0.619857i	$-0.787191\pi$
$659$	−26550.3	−1.56943	−0.784715	+	0.619857i	$0.787191\pi$
$660$	1391.33	0.0820568
$661$	21621.2	1.27226	0.636132	−	0.771580i	$-0.280533\pi$
$661$	21621.2	1.27226	0.636132	+	0.771580i	$0.280533\pi$
$662$	−1974.98	−0.115951
$663$	−1209.49	−0.0708484
$664$	999.477	0.0584145
$665$	−13391.6	−0.780907
$666$	7177.73	0.417615
$667$	0	0
$668$	2593.77	0.150234
$669$	−1521.29	−0.0879169
$670$	4050.38	0.233552
$671$	22014.1	1.26654
$672$	2346.01	0.134671
$673$	−15816.8	−0.905931	−0.452966	−	0.891528i	$-0.649634\pi$
$673$	−15816.8	−0.905931	−0.452966	+	0.891528i	$0.649634\pi$
$674$	−246.070	−0.0140627
$675$	403.563	0.0230121
$676$	−14727.4	−0.837926
$677$	2288.74	0.129931	0.0649656	−	0.997888i	$-0.479306\pi$
$677$	2288.74	0.129931	0.0649656	+	0.997888i	$0.479306\pi$
$678$	944.750	0.0535146
$679$	−44599.5	−2.52073
$680$	−5415.77	−0.305419
$681$	−183.817	−0.0103434
$682$	2001.31	0.112367
$683$	19860.7	1.11266	0.556330	−	0.830961i	$-0.312209\pi$
$683$	19860.7	1.11266	0.556330	+	0.830961i	$0.312209\pi$
$684$	−8048.06	−0.449891
$685$	7645.03	0.426426
$686$	6459.46	0.359509
$687$	2343.08	0.130122
$688$	8207.25	0.454794
$689$	9496.49	0.525091
$690$	0	0
$691$	−11436.4	−0.629609	−0.314804	−	0.949157i	$-0.601939\pi$
$691$	−11436.4	−0.629609	−0.314804	+	0.949157i	$0.601939\pi$
$692$	2880.50	0.158237
$693$	29762.5	1.63143
$694$	1191.30	0.0651599
$695$	20493.5	1.11851
$696$	−409.282	−0.0222900
$697$	−12848.2	−0.698223
$698$	8092.25	0.438820
$699$	−3243.54	−0.175511
$700$	3209.50	0.173297
$701$	−19366.2	−1.04344	−0.521721	−	0.853116i	$-0.674710\pi$
$701$	−19366.2	−1.04344	−0.521721	+	0.853116i	$0.674710\pi$
$702$	1647.46	0.0885749
$703$	12175.0	0.653184
$704$	7701.17	0.412285
$705$	1151.69	0.0615248
$706$	−4610.70	−0.245788
$707$	17305.4	0.920560
$708$	2886.35	0.153214
$709$	9108.02	0.482453	0.241226	−	0.970469i	$-0.422450\pi$
$709$	9108.02	0.482453	0.241226	+	0.970469i	$0.422450\pi$
$710$	−9258.31	−0.489378
$711$	−2212.85	−0.116721
$712$	10373.0	0.545991
$713$	0	0
$714$	521.193	0.0273181
$715$	25193.1	1.31772
$716$	−25202.0	−1.31542
$717$	−627.421	−0.0326799
$718$	−8732.54	−0.453893
$719$	−3320.22	−0.172216	−0.0861079	−	0.996286i	$-0.527443\pi$
$719$	−3320.22	−0.172216	−0.0861079	+	0.996286i	$0.527443\pi$
$720$	−12352.0	−0.639351
$721$	7731.96	0.399380
$722$	−4722.87	−0.243444
$723$	151.330	0.00778425
$724$	2669.72	0.137043
$725$	−855.874	−0.0438432
$726$	10.0935	0.000515984 0
$727$	31049.1	1.58397	0.791986	−	0.610539i	$-0.209047\pi$
$727$	31049.1	1.58397	0.791986	+	0.610539i	$0.209047\pi$
$728$	27790.8	1.41483
$729$	−18575.5	−0.943733
$730$	−4076.00	−0.206657
$731$	6840.18	0.346092
$732$	2157.90	0.108959
$733$	26190.8	1.31975	0.659876	−	0.751374i	$-0.270609\pi$
$733$	26190.8	1.31975	0.659876	+	0.751374i	$0.270609\pi$
$734$	−3307.40	−0.166319
$735$	3035.97	0.152358
$736$	0	0
$737$	−15269.2	−0.763157
$738$	8708.87	0.434387
$739$	−29002.9	−1.44369	−0.721847	−	0.692053i	$-0.756707\pi$
$739$	−29002.9	−1.44369	−0.721847	+	0.692053i	$0.756707\pi$
$740$	21621.1	1.07407
$741$	1390.59	0.0689403
$742$	−4092.24	−0.202467
$743$	8442.89	0.416877	0.208439	−	0.978035i	$-0.433162\pi$
$743$	8442.89	0.416877	0.208439	+	0.978035i	$0.433162\pi$
$744$	416.106	0.0205043
$745$	15185.6	0.746787
$746$	−1892.78	−0.0928947
$747$	1899.86	0.0930550
$748$	9625.42	0.470509
$749$	21000.5	1.02449
$750$	−689.290	−0.0335591
$751$	10264.8	0.498758	0.249379	−	0.968406i	$-0.419774\pi$
$751$	10264.8	0.498758	0.249379	+	0.968406i	$0.419774\pi$
$752$	9559.90	0.463582
$753$	−1757.15	−0.0850385
$754$	−3493.93	−0.168755
$755$	3744.29	0.180488
$756$	5862.69	0.282042
$757$	−16443.5	−0.789499	−0.394749	−	0.918789i	$-0.629169\pi$
$757$	−16443.5	−0.789499	−0.394749	+	0.918789i	$0.629169\pi$
$758$	6451.84	0.309158
$759$	0	0
$760$	6226.73	0.297194
$761$	768.989	0.0366305	0.0183153	−	0.999832i	$-0.494170\pi$
$761$	768.989	0.0366305	0.0183153	+	0.999832i	$0.494170\pi$
$762$	−252.143	−0.0119871
$763$	4908.25	0.232884
$764$	26490.7	1.25445
$765$	−10294.6	−0.486537
$766$	−5780.80	−0.272675
$767$	52263.5	2.46040
$768$	178.342	0.00837936
$769$	36463.7	1.70990	0.854951	−	0.518709i	$-0.173587\pi$
$769$	36463.7	1.70990	0.854951	+	0.518709i	$0.173587\pi$
$770$	−10856.2	−0.508092
$771$	−1600.69	−0.0747698
$772$	21740.3	1.01354
$773$	−23350.4	−1.08649	−0.543244	−	0.839575i	$-0.682804\pi$
$773$	−23350.4	−1.08649	−0.543244	+	0.839575i	$0.682804\pi$
$774$	−4636.46	−0.215315
$775$	870.143	0.0403309
$776$	20737.6	0.959326
$777$	−4413.43	−0.203772
$778$	−1393.19	−0.0642010
$779$	14772.1	0.679418
$780$	2469.51	0.113362
$781$	34902.1	1.59910
$782$	0	0
$783$	−1563.39	−0.0713552
$784$	25200.9	1.14800
$785$	−24779.5	−1.12665
$786$	256.351	0.0116333
$787$	−26050.4	−1.17992	−0.589959	−	0.807433i	$-0.700856\pi$
$787$	−26050.4	−1.17992	−0.589959	+	0.807433i	$0.700856\pi$
$788$	−31871.5	−1.44083
$789$	3228.76	0.145687
$790$	807.162	0.0363513
$791$	60876.3	2.73642
$792$	−13838.8	−0.620883
$793$	39073.4	1.74973
$794$	10209.5	0.456324
$795$	−771.311	−0.0344095
$796$	−36965.6	−1.64599
$797$	−1255.25	−0.0557880	−0.0278940	−	0.999611i	$-0.508880\pi$
$797$	−1255.25	−0.0557880	−0.0278940	+	0.999611i	$0.508880\pi$
$798$	−599.236	−0.0265824
$799$	7967.53	0.352780
$800$	−2281.10	−0.100811
$801$	19717.6	0.869771
$802$	−3213.35	−0.141481
$803$	15365.7	0.675274
$804$	−1496.74	−0.0656540
$805$	0	0
$806$	3552.18	0.155236
$807$	2739.37	0.119493
$808$	−8046.54	−0.350342
$809$	−36116.2	−1.56956	−0.784782	−	0.619772i	$-0.787225\pi$
$809$	−36116.2	−1.56956	−0.784782	+	0.619772i	$0.787225\pi$
$810$	6910.71	0.299775
$811$	2736.30	0.118476	0.0592382	−	0.998244i	$-0.481133\pi$
$811$	2736.30	0.118476	0.0592382	+	0.998244i	$0.481133\pi$
$812$	−12433.5	−0.537354
$813$	873.049	0.0376620
$814$	9869.96	0.424990
$815$	9495.35	0.408108
$816$	815.429	0.0349825
$817$	−7864.44	−0.336771
$818$	10662.9	0.455769
$819$	52826.3	2.25384
$820$	26233.3	1.11720
$821$	39943.7	1.69798	0.848991	−	0.528407i	$-0.177211\pi$
$821$	39943.7	1.69798	0.848991	+	0.528407i	$0.177211\pi$
$822$	342.094	0.0145157
$823$	22498.7	0.952925	0.476462	−	0.879195i	$-0.341919\pi$
$823$	22498.7	0.952925	0.476462	+	0.879195i	$0.341919\pi$
$824$	−3595.16	−0.151994
$825$	276.149	0.0116537
$826$	−22521.5	−0.948694
$827$	1455.02	0.0611802	0.0305901	−	0.999532i	$-0.490261\pi$
$827$	1455.02	0.0611802	0.0305901	+	0.999532i	$0.490261\pi$
$828$	0	0
$829$	26124.8	1.09451	0.547257	−	0.836964i	$-0.315672\pi$
$829$	26124.8	1.09451	0.547257	+	0.836964i	$0.315672\pi$
$830$	−692.994	−0.0289809
$831$	904.729	0.0377674
$832$	13669.0	0.569577
$833$	21003.3	0.873613
$834$	917.027	0.0380744
$835$	−3814.59	−0.158095
$836$	−11066.7	−0.457836
$837$	1589.46	0.0656389
$838$	−4180.54	−0.172332
$839$	−22967.6	−0.945090	−0.472545	−	0.881307i	$-0.656665\pi$
$839$	−22967.6	−0.945090	−0.472545	+	0.881307i	$0.656665\pi$
$840$	−2257.19	−0.0927148
$841$	−21073.4	−0.864052
$842$	3632.77	0.148686
$843$	2982.33	0.121847
$844$	−29764.3	−1.21390
$845$	21659.2	0.881775
$846$	−5400.60	−0.219476
$847$	650.388	0.0263844
$848$	−6402.49	−0.259272
$849$	−3701.78	−0.149640
$850$	−506.773	−0.0204496
$851$	0	0
$852$	3421.22	0.137569
$853$	−30675.1	−1.23130	−0.615648	−	0.788021i	$-0.711106\pi$
$853$	−30675.1	−1.23130	−0.615648	+	0.788021i	$0.711106\pi$
$854$	−16837.6	−0.674672
$855$	11836.1	0.473433
$856$	−9764.70	−0.389895
$857$	10501.3	0.418573	0.209287	−	0.977854i	$-0.432886\pi$
$857$	10501.3	0.418573	0.209287	+	0.977854i	$0.432886\pi$
$858$	1127.32	0.0448556
$859$	−6550.81	−0.260199	−0.130099	−	0.991501i	$-0.541530\pi$
$859$	−6550.81	−0.260199	−0.130099	+	0.991501i	$0.541530\pi$
$860$	−13966.2	−0.553771
$861$	−5354.90	−0.211956
$862$	−9819.47	−0.387996
$863$	−35060.1	−1.38292	−0.691461	−	0.722414i	$-0.743032\pi$
$863$	−35060.1	−1.38292	−0.691461	+	0.722414i	$0.743032\pi$
$864$	−4166.80	−0.164071
$865$	−4236.28	−0.166518
$866$	−5347.22	−0.209822
$867$	−1802.36	−0.0706013
$868$	12640.8	0.494306
$869$	−3042.85	−0.118782
$870$	283.779	0.0110586
$871$	−27101.6	−1.05431
$872$	−2282.21	−0.0886299
$873$	39419.1	1.52822
$874$	0	0
$875$	−44415.3	−1.71601
$876$	1506.20	0.0580934
$877$	18548.2	0.714172	0.357086	−	0.934071i	$-0.383770\pi$
$877$	18548.2	0.714172	0.357086	+	0.934071i	$0.383770\pi$
$878$	5689.01	0.218673
$879$	789.314	0.0302877
$880$	−16985.0	−0.650642
$881$	38133.3	1.45828	0.729140	−	0.684365i	$-0.239920\pi$
$881$	38133.3	1.45828	0.729140	+	0.684365i	$0.239920\pi$
$882$	−14236.6	−0.543503
$883$	−41211.3	−1.57064	−0.785318	−	0.619092i	$-0.787501\pi$
$883$	−41211.3	−1.57064	−0.785318	+	0.619092i	$0.787501\pi$
$884$	17084.4	0.650013
$885$	−4244.88	−0.161232
$886$	391.680	0.0148518
$887$	−11653.4	−0.441130	−0.220565	−	0.975372i	$-0.570790\pi$
$887$	−11653.4	−0.441130	−0.220565	+	0.975372i	$0.570790\pi$
$888$	2052.13	0.0775506
$889$	−16247.2	−0.612950
$890$	−7192.22	−0.270881
$891$	−26052.1	−0.979547
$892$	21488.8	0.806611
$893$	−9160.59	−0.343278
$894$	679.513	0.0254209
$895$	37063.9	1.38426
$896$	−43041.3	−1.60481
$897$	0	0
$898$	81.5197	0.00302934
$899$	−3370.91	−0.125057
$900$	−2836.71	−0.105063
$901$	−5336.04	−0.197302
$902$	11975.4	0.442059
$903$	2850.86	0.105062
$904$	−28305.9	−1.04141
$905$	−3926.29	−0.144215
$906$	167.547	0.00614389
$907$	−5172.81	−0.189372	−0.0946860	−	0.995507i	$-0.530185\pi$
$907$	−5172.81	−0.189372	−0.0946860	+	0.995507i	$0.530185\pi$
$908$	2596.48	0.0948978
$909$	−15295.3	−0.558100
$910$	−19269.0	−0.701935
$911$	24937.2	0.906922	0.453461	−	0.891276i	$-0.350189\pi$
$911$	24937.2	0.906922	0.453461	+	0.891276i	$0.350189\pi$
$912$	−937.532	−0.0340403
$913$	2612.46	0.0946985
$914$	−10157.2	−0.367581
$915$	−3173.57	−0.114661
$916$	−33096.8	−1.19383
$917$	16518.3	0.594856
$918$	−925.704	−0.0332819
$919$	−3145.70	−0.112913	−0.0564564	−	0.998405i	$-0.517980\pi$
$919$	−3145.70	−0.112913	−0.0564564	+	0.998405i	$0.517980\pi$
$920$	0	0
$921$	−295.350	−0.0105669
$922$	15180.5	0.542238
$923$	61948.6	2.20917
$924$	4011.69	0.142830
$925$	4291.32	0.152538
$926$	10154.7	0.360372
$927$	−6833.86	−0.242129
$928$	8836.92	0.312593
$929$	−43571.3	−1.53878	−0.769391	−	0.638778i	$-0.779440\pi$
$929$	−43571.3	−1.53878	−0.769391	+	0.638778i	$0.779440\pi$
$930$	−288.510	−0.0101727
$931$	−24148.3	−0.850084
$932$	45816.2	1.61026
$933$	1183.94	0.0415441
$934$	2221.20	0.0778156
$935$	−14155.9	−0.495130
$936$	−24562.8	−0.857757
$937$	5850.96	0.203994	0.101997	−	0.994785i	$-0.467477\pi$
$937$	5850.96	0.203994	0.101997	+	0.994785i	$0.467477\pi$
$938$	11678.7	0.406527
$939$	1769.79	0.0615069
$940$	−16268.0	−0.564471
$941$	−52094.7	−1.80472	−0.902358	−	0.430986i	$-0.858166\pi$
$941$	−52094.7	−1.80472	−0.902358	+	0.430986i	$0.858166\pi$
$942$	−1108.82	−0.0383516
$943$	0	0
$944$	−35235.8	−1.21486
$945$	−8622.11	−0.296801
$946$	−6375.50	−0.219118
$947$	−25167.2	−0.863596	−0.431798	−	0.901970i	$-0.642121\pi$
$947$	−25167.2	−0.863596	−0.431798	+	0.901970i	$0.642121\pi$
$948$	−298.270	−0.0102187
$949$	27273.1	0.932899
$950$	582.657	0.0198988
$951$	−147.435	−0.00502723
$952$	−15615.6	−0.531621
$953$	−18123.4	−0.616028	−0.308014	−	0.951382i	$-0.599664\pi$
$953$	−18123.4	−0.616028	−0.308014	+	0.951382i	$0.599664\pi$
$954$	3616.91	0.122748
$955$	−38959.2	−1.32009
$956$	8862.55	0.299828
$957$	−1069.79	−0.0361353
$958$	−8348.58	−0.281556
$959$	22043.3	0.742247
$960$	−1110.21	−0.0373247
$961$	−26363.9	−0.884961
$962$	17518.5	0.587128
$963$	−18561.2	−0.621109
$964$	−2137.59	−0.0714181
$965$	−31972.9	−1.06658
$966$	0	0
$967$	45040.1	1.49782	0.748910	−	0.662671i	$-0.230577\pi$
$967$	45040.1	1.49782	0.748910	+	0.662671i	$0.230577\pi$
$968$	−302.413	−0.0100412
$969$	−781.369	−0.0259042
$970$	−14378.6	−0.475947
$971$	16722.5	0.552678	0.276339	−	0.961060i	$-0.410879\pi$
$971$	16722.5	0.552678	0.276339	+	0.961060i	$0.410879\pi$
$972$	−7784.87	−0.256893
$973$	59089.8	1.94690
$974$	−7886.67	−0.259451
$975$	490.144	0.0160997
$976$	−26343.1	−0.863958
$977$	24491.0	0.801983	0.400992	−	0.916082i	$-0.368666\pi$
$977$	24491.0	0.801983	0.400992	+	0.916082i	$0.368666\pi$
$978$	424.891	0.0138921
$979$	27113.3	0.885132
$980$	−42884.1	−1.39784
$981$	−4338.13	−0.141189
$982$	−1320.98	−0.0429270
$983$	−43577.9	−1.41396	−0.706979	−	0.707235i	$-0.749942\pi$
$983$	−43577.9	−1.41396	−0.706979	+	0.707235i	$0.749942\pi$
$984$	2489.89	0.0806653
$985$	46872.7	1.51623
$986$	1963.22	0.0634095
$987$	3320.72	0.107092
$988$	−19642.6	−0.632506
$989$	0	0
$990$	9595.22	0.308037
$991$	−29438.9	−0.943651	−0.471825	−	0.881692i	$-0.656405\pi$
$991$	−29438.9	−0.943651	−0.471825	+	0.881692i	$0.656405\pi$
$992$	−8984.25	−0.287551
$993$	−1073.32	−0.0343008
$994$	−26695.0	−0.851824
$995$	54364.4	1.73213
$996$	256.082	0.00814686
$997$	−55586.4	−1.76574	−0.882868	−	0.469621i	$-0.844390\pi$
$997$	−55586.4	−1.76574	−0.882868	+	0.469621i	$0.844390\pi$
$998$	5626.75	0.178469
$999$	7838.81	0.248257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.14		25
23.7	odd	22		23.4.c.a.3.2	✓	50
23.10	odd	22		23.4.c.a.8.2	yes	50
23.22	odd	2		529.4.a.n.1.14		25
69.53	even	22		207.4.i.a.118.4		50
69.56	even	22		207.4.i.a.100.4		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.3.2	✓	50	23.7	odd	22
23.4.c.a.8.2	yes	50	23.10	odd	22
207.4.i.a.100.4		50	69.56	even	22
207.4.i.a.118.4		50	69.53	even	22
529.4.a.m.1.14		25	1.1	even	1	trivial
529.4.a.n.1.14		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)

\(f(q)\)	\(=\)	\(q+0.929572 q^{2} +0.505183 q^{3} -7.13590 q^{4} +10.4946 q^{5} +0.469604 q^{6} +30.2596 q^{7} -14.0699 q^{8} -26.7448 q^{9} +9.75547 q^{10} -36.7763 q^{11} -3.60494 q^{12} -65.2752 q^{13} +28.1284 q^{14} +5.30169 q^{15} +44.0082 q^{16} +36.6778 q^{17} -24.8612 q^{18} -42.1700 q^{19} -74.8883 q^{20} +15.2866 q^{21} -34.1862 q^{22} -7.10788 q^{24} -14.8637 q^{25} -60.6779 q^{26} -27.1510 q^{27} -215.929 q^{28} +57.5815 q^{29} +4.92830 q^{30} -58.5416 q^{31} +153.468 q^{32} -18.5788 q^{33} +34.0947 q^{34} +317.562 q^{35} +190.848 q^{36} -288.712 q^{37} -39.2000 q^{38} -32.9759 q^{39} -147.658 q^{40} -350.300 q^{41} +14.2100 q^{42} +186.494 q^{43} +262.432 q^{44} -280.675 q^{45} +217.230 q^{47} +22.2322 q^{48} +572.642 q^{49} -13.8169 q^{50} +18.5290 q^{51} +465.797 q^{52} -145.484 q^{53} -25.2388 q^{54} -385.952 q^{55} -425.749 q^{56} -21.3036 q^{57} +53.5262 q^{58} -800.665 q^{59} -37.8323 q^{60} -598.596 q^{61} -54.4186 q^{62} -809.286 q^{63} -209.406 q^{64} -685.036 q^{65} -17.2703 q^{66} +415.191 q^{67} -261.729 q^{68} +295.196 q^{70} -949.038 q^{71} +376.297 q^{72} -417.817 q^{73} -268.379 q^{74} -7.50889 q^{75} +300.921 q^{76} -1112.83 q^{77} -30.6535 q^{78} +82.7395 q^{79} +461.848 q^{80} +708.393 q^{81} -325.629 q^{82} -71.0365 q^{83} -109.084 q^{84} +384.919 q^{85} +173.359 q^{86} +29.0892 q^{87} +517.438 q^{88} -737.250 q^{89} -260.908 q^{90} -1975.20 q^{91} -29.5742 q^{93} +201.931 q^{94} -442.557 q^{95} +77.5295 q^{96} -1473.90 q^{97} +532.311 q^{98} +983.573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 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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