LMFDB - Embedded newform 529.4.a.m.1.12

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			1.12
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)

$f(q)$	$=$	\(q-0.525953 q^{2} +5.51332 q^{3} -7.72337 q^{4} +13.2745 q^{5} -2.89975 q^{6} -8.04220 q^{7} +8.26975 q^{8} +3.39674 q^{9} -6.98174 q^{10} +13.2705 q^{11} -42.5815 q^{12} -71.9274 q^{13} +4.22982 q^{14} +73.1864 q^{15} +57.4375 q^{16} -113.151 q^{17} -1.78653 q^{18} -19.3870 q^{19} -102.524 q^{20} -44.3393 q^{21} -6.97966 q^{22} +45.5938 q^{24} +51.2112 q^{25} +37.8304 q^{26} -130.132 q^{27} +62.1129 q^{28} -77.0710 q^{29} -38.4926 q^{30} +240.220 q^{31} -96.3674 q^{32} +73.1646 q^{33} +59.5121 q^{34} -106.756 q^{35} -26.2343 q^{36} -261.861 q^{37} +10.1966 q^{38} -396.559 q^{39} +109.776 q^{40} +115.325 q^{41} +23.3204 q^{42} -352.920 q^{43} -102.493 q^{44} +45.0899 q^{45} +385.301 q^{47} +316.671 q^{48} -278.323 q^{49} -26.9347 q^{50} -623.838 q^{51} +555.522 q^{52} +279.112 q^{53} +68.4435 q^{54} +176.159 q^{55} -66.5070 q^{56} -106.887 q^{57} +40.5357 q^{58} +503.910 q^{59} -565.246 q^{60} -643.723 q^{61} -126.344 q^{62} -27.3173 q^{63} -408.815 q^{64} -954.797 q^{65} -38.4811 q^{66} -472.252 q^{67} +873.908 q^{68} +56.1486 q^{70} +168.643 q^{71} +28.0902 q^{72} -667.140 q^{73} +137.727 q^{74} +282.344 q^{75} +149.733 q^{76} -106.724 q^{77} +208.571 q^{78} -826.993 q^{79} +762.451 q^{80} -809.174 q^{81} -60.6553 q^{82} +822.468 q^{83} +342.449 q^{84} -1502.02 q^{85} +185.619 q^{86} -424.917 q^{87} +109.744 q^{88} -562.870 q^{89} -23.7152 q^{90} +578.454 q^{91} +1324.41 q^{93} -202.650 q^{94} -257.351 q^{95} -531.305 q^{96} -21.3397 q^{97} +146.385 q^{98} +45.0765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.525953	−0.185952	−0.0929762	−	0.995668i	$-0.529638\pi$
$2$	−0.525953	−0.185952	−0.0929762	+	0.995668i	$0.529638\pi$
$3$	5.51332	1.06104	0.530520	−	0.847673i	$-0.321997\pi$
$3$	5.51332	1.06104	0.530520	+	0.847673i	$0.321997\pi$
$4$	−7.72337	−0.965422
$5$	13.2745	1.18730	0.593652	−	0.804722i	$-0.297686\pi$
$5$	13.2745	1.18730	0.593652	+	0.804722i	$0.297686\pi$
$6$	−2.89975	−0.197303
$7$	−8.04220	−0.434238	−0.217119	−	0.976145i	$-0.569666\pi$
$7$	−8.04220	−0.434238	−0.217119	+	0.976145i	$0.569666\pi$
$8$	8.26975	0.365475
$9$	3.39674	0.125805
$10$	−6.98174	−0.220782
$11$	13.2705	0.363746	0.181873	−	0.983322i	$-0.441784\pi$
$11$	13.2705	0.363746	0.181873	+	0.983322i	$0.441784\pi$
$12$	−42.5815	−1.02435
$13$	−71.9274	−1.53454	−0.767272	−	0.641322i	$-0.778386\pi$
$13$	−71.9274	−1.53454	−0.767272	+	0.641322i	$0.778386\pi$
$14$	4.22982	0.0807476
$15$	73.1864	1.25978
$16$	57.4375	0.897461
$17$	−113.151	−1.61430	−0.807152	−	0.590344i	$-0.798992\pi$
$17$	−113.151	−1.61430	−0.807152	+	0.590344i	$0.798992\pi$
$18$	−1.78653	−0.0233938
$19$	−19.3870	−0.234088	−0.117044	−	0.993127i	$-0.537342\pi$
$19$	−19.3870	−0.234088	−0.117044	+	0.993127i	$0.537342\pi$
$20$	−102.524	−1.14625
$21$	−44.3393	−0.460744
$22$	−6.97966	−0.0676395
$23$	0	0
$23$	0	0
$24$	45.5938	0.387783
$25$	51.2112	0.409689
$26$	37.8304	0.285352
$27$	−130.132	−0.927555
$28$	62.1129	0.419223
$29$	−77.0710	−0.493508	−0.246754	−	0.969078i	$-0.579364\pi$
$29$	−77.0710	−0.493508	−0.246754	+	0.969078i	$0.579364\pi$
$30$	−38.4926	−0.234258
$31$	240.220	1.39177	0.695884	−	0.718154i	$-0.255013\pi$
$31$	240.220	1.39177	0.695884	+	0.718154i	$0.255013\pi$
$32$	−96.3674	−0.532360
$33$	73.1646	0.385949
$34$	59.5121	0.300184
$35$	−106.756	−0.515572
$36$	−26.2343	−0.121455
$37$	−261.861	−1.16351	−0.581753	−	0.813366i	$-0.697633\pi$
$37$	−261.861	−1.16351	−0.581753	+	0.813366i	$0.697633\pi$
$38$	10.1966	0.0435293
$39$	−396.559	−1.62821
$40$	109.776	0.433930
$41$	115.325	0.439285	0.219642	−	0.975580i	$-0.429511\pi$
$41$	115.325	0.439285	0.219642	+	0.975580i	$0.429511\pi$
$42$	23.3204	0.0856764
$43$	−352.920	−1.25162	−0.625812	−	0.779974i	$-0.715232\pi$
$43$	−352.920	−1.25162	−0.625812	+	0.779974i	$0.715232\pi$
$44$	−102.493	−0.351168
$45$	45.0899	0.149369
$46$	0	0
$47$	385.301	1.19579	0.597893	−	0.801576i	$-0.296005\pi$
$47$	385.301	1.19579	0.597893	+	0.801576i	$0.296005\pi$
$48$	316.671	0.952241
$49$	−278.323	−0.811437
$50$	−26.9347	−0.0761827
$51$	−623.838	−1.71284
$52$	555.522	1.48148
$53$	279.112	0.723377	0.361688	−	0.932299i	$-0.382200\pi$
$53$	279.112	0.723377	0.361688	+	0.932299i	$0.382200\pi$
$54$	68.4435	0.172481
$55$	176.159	0.431877
$56$	−66.5070	−0.158703
$57$	−106.887	−0.248377
$58$	40.5357	0.0917689
$59$	503.910	1.11192	0.555962	−	0.831208i	$-0.312350\pi$
$59$	503.910	1.11192	0.555962	+	0.831208i	$0.312350\pi$
$60$	−565.246	−1.21622
$61$	−643.723	−1.35115	−0.675576	−	0.737290i	$-0.736105\pi$
$61$	−643.723	−1.35115	−0.675576	+	0.737290i	$0.736105\pi$
$62$	−126.344	−0.258803
$63$	−27.3173	−0.0546294
$64$	−408.815	−0.798467
$65$	−954.797	−1.82197
$66$	−38.4811	−0.0717681
$67$	−472.252	−0.861116	−0.430558	−	0.902563i	$-0.641683\pi$
$67$	−472.252	−0.861116	−0.430558	+	0.902563i	$0.641683\pi$
$68$	873.908	1.55848
$69$	0	0
$70$	56.1486	0.0958719
$71$	168.643	0.281890	0.140945	−	0.990017i	$-0.454986\pi$
$71$	168.643	0.281890	0.140945	+	0.990017i	$0.454986\pi$
$72$	28.0902	0.0459787
$73$	−667.140	−1.06963	−0.534814	−	0.844970i	$-0.679618\pi$
$73$	−667.140	−1.06963	−0.534814	+	0.844970i	$0.679618\pi$
$74$	137.727	0.216357
$75$	282.344	0.434697
$76$	149.733	0.225994
$77$	−106.724	−0.157952
$78$	208.571	0.302770
$79$	−826.993	−1.17777	−0.588886	−	0.808216i	$-0.700433\pi$
$79$	−826.993	−1.17777	−0.588886	+	0.808216i	$0.700433\pi$
$80$	762.451	1.06556
$81$	−809.174	−1.10998
$82$	−60.6553	−0.0816860
$83$	822.468	1.08768	0.543841	−	0.839188i	$-0.316969\pi$
$83$	822.468	1.08768	0.543841	+	0.839188i	$0.316969\pi$
$84$	342.449	0.444812
$85$	−1502.02	−1.91667
$86$	185.619	0.232743
$87$	−424.917	−0.523631
$88$	109.744	0.132940
$89$	−562.870	−0.670383	−0.335191	−	0.942150i	$-0.608801\pi$
$89$	−562.870	−0.670383	−0.335191	+	0.942150i	$0.608801\pi$
$90$	−23.7152	−0.0277755
$91$	578.454	0.666357
$92$	0	0
$93$	1324.41	1.47672
$94$	−202.650	−0.222359
$95$	−257.351	−0.277934
$96$	−531.305	−0.564855
$97$	−21.3397	−0.0223374	−0.0111687	−	0.999938i	$-0.503555\pi$
$97$	−21.3397	−0.0223374	−0.0111687	+	0.999938i	$0.503555\pi$
$98$	146.385	0.150889
$99$	45.0765	0.0457612
$100$	−395.523	−0.395523
$101$	1528.03	1.50539	0.752696	−	0.658368i	$-0.228753\pi$
$101$	1528.03	1.50539	0.752696	+	0.658368i	$0.228753\pi$
$102$	328.110	0.318507
$103$	1063.46	1.01734	0.508668	−	0.860963i	$-0.330138\pi$
$103$	1063.46	1.01734	0.508668	+	0.860963i	$0.330138\pi$
$104$	−594.822	−0.560837
$105$	−588.580	−0.547043
$106$	−146.800	−0.134514
$107$	214.676	0.193958	0.0969789	−	0.995286i	$-0.469082\pi$
$107$	214.676	0.193958	0.0969789	+	0.995286i	$0.469082\pi$
$108$	1005.06	0.895482
$109$	−1445.44	−1.27016	−0.635081	−	0.772446i	$-0.719033\pi$
$109$	−1445.44	−1.27016	−0.635081	+	0.772446i	$0.719033\pi$
$110$	−92.6512	−0.0803086
$111$	−1443.73	−1.23453
$112$	−461.924	−0.389712
$113$	−541.575	−0.450860	−0.225430	−	0.974259i	$-0.572379\pi$
$113$	−541.575	−0.450860	−0.225430	+	0.974259i	$0.572379\pi$
$114$	56.2173	0.0461863
$115$	0	0
$116$	595.248	0.476443
$117$	−244.319	−0.193054
$118$	−265.033	−0.206765
$119$	909.984	0.700992
$120$	605.233	0.460417
$121$	−1154.89	−0.867689
$122$	338.568	0.251250
$123$	635.821	0.466098
$124$	−1855.31	−1.34364
$125$	−979.506	−0.700878
$126$	14.3676	0.0101585
$127$	518.539	0.362306	0.181153	−	0.983455i	$-0.442017\pi$
$127$	518.539	0.362306	0.181153	+	0.983455i	$0.442017\pi$
$128$	985.957	0.680837
$129$	−1945.76	−1.32802
$130$	502.178	0.338799
$131$	−854.590	−0.569969	−0.284984	−	0.958532i	$-0.591988\pi$
$131$	−854.590	−0.569969	−0.284984	+	0.958532i	$0.591988\pi$
$132$	−565.077	−0.372603
$133$	155.914	0.101650
$134$	248.382	0.160127
$135$	−1727.44	−1.10129
$136$	−935.731	−0.589988
$137$	−77.0997	−0.0480808	−0.0240404	−	0.999711i	$-0.507653\pi$
$137$	−77.0997	−0.0480808	−0.0240404	+	0.999711i	$0.507653\pi$
$138$	0	0
$139$	−396.171	−0.241747	−0.120873	−	0.992668i	$-0.538570\pi$
$139$	−396.171	−0.241747	−0.120873	+	0.992668i	$0.538570\pi$
$140$	824.515	0.497745
$141$	2124.29	1.26878
$142$	−88.6981	−0.0524181
$143$	−954.512	−0.558184
$144$	195.100	0.112905
$145$	−1023.08	−0.585943
$146$	350.884	0.198900
$147$	−1534.48	−0.860967
$148$	2022.45	1.12327
$149$	−2573.73	−1.41509	−0.707544	−	0.706669i	$-0.750197\pi$
$149$	−2573.73	−1.41509	−0.707544	+	0.706669i	$0.750197\pi$
$150$	−148.500	−0.0808329
$151$	−2431.61	−1.31048	−0.655238	−	0.755422i	$-0.727432\pi$
$151$	−2431.61	−1.31048	−0.655238	+	0.755422i	$0.727432\pi$
$152$	−160.325	−0.0855534
$153$	−384.345	−0.203088
$154$	56.1318	0.0293716
$155$	3188.79	1.65245
$156$	3062.77	1.57191
$157$	3218.49	1.63607	0.818037	−	0.575166i	$-0.195063\pi$
$157$	3218.49	1.63607	0.818037	+	0.575166i	$0.195063\pi$
$158$	434.960	0.219010
$159$	1538.83	0.767531
$160$	−1279.23	−0.632073
$161$	0	0
$162$	425.587	0.206403
$163$	563.274	0.270669	0.135334	−	0.990800i	$-0.456789\pi$
$163$	563.274	0.270669	0.135334	+	0.990800i	$0.456789\pi$
$164$	−890.694	−0.424095
$165$	971.220	0.458239
$166$	−432.580	−0.202257
$167$	234.737	0.108770	0.0543848	−	0.998520i	$-0.482680\pi$
$167$	234.737	0.108770	0.0543848	+	0.998520i	$0.482680\pi$
$168$	−366.675	−0.168390
$169$	2976.55	1.35482
$170$	789.991	0.356409
$171$	−65.8525	−0.0294495
$172$	2725.74	1.20835
$173$	2291.27	1.00695	0.503475	−	0.864010i	$-0.332055\pi$
$173$	2291.27	1.00695	0.503475	+	0.864010i	$0.332055\pi$
$174$	223.486	0.0973705
$175$	−411.851	−0.177903
$176$	762.224	0.326448
$177$	2778.22	1.17980
$178$	296.043	0.124659
$179$	−2111.14	−0.881531	−0.440766	−	0.897622i	$-0.645293\pi$
$179$	−2111.14	−0.881531	−0.440766	+	0.897622i	$0.645293\pi$
$180$	−348.246	−0.144204
$181$	809.218	0.332313	0.166157	−	0.986099i	$-0.446864\pi$
$181$	809.218	0.332313	0.166157	+	0.986099i	$0.446864\pi$
$182$	−304.240	−0.123911
$183$	−3549.06	−1.43363
$184$	0	0
$185$	−3476.06	−1.38143
$186$	−696.578	−0.274600
$187$	−1501.57	−0.587197
$188$	−2975.83	−1.15444
$189$	1046.55	0.402780
$190$	135.355	0.0516824
$191$	49.6795	0.0188203	0.00941017	−	0.999956i	$-0.497005\pi$
$191$	49.6795	0.0188203	0.00941017	+	0.999956i	$0.497005\pi$
$192$	−2253.93	−0.847205
$193$	171.160	0.0638360	0.0319180	−	0.999490i	$-0.489838\pi$
$193$	171.160	0.0638360	0.0319180	+	0.999490i	$0.489838\pi$
$194$	11.2237	0.00415368
$195$	−5264.10	−1.93318
$196$	2149.59	0.783379
$197$	2835.30	1.02541	0.512707	−	0.858564i	$-0.328643\pi$
$197$	2835.30	1.02541	0.512707	+	0.858564i	$0.328643\pi$
$198$	−23.7081	−0.00850940
$199$	−958.983	−0.341611	−0.170805	−	0.985305i	$-0.554637\pi$
$199$	−958.983	−0.341611	−0.170805	+	0.985305i	$0.554637\pi$
$200$	423.504	0.149731
$201$	−2603.68	−0.913678
$202$	−803.671	−0.279931
$203$	619.820	0.214300
$204$	4818.14	1.65361
$205$	1530.87	0.521564
$206$	−559.328	−0.189176
$207$	0	0
$208$	−4131.33	−1.37719
$209$	−257.275	−0.0851486
$210$	309.565	0.101724
$211$	1906.86	0.622149	0.311074	−	0.950386i	$-0.399311\pi$
$211$	1906.86	0.622149	0.311074	+	0.950386i	$0.399311\pi$
$212$	−2155.69	−0.698364
$213$	929.781	0.299097
$214$	−112.909	−0.0360669
$215$	−4684.83	−1.48606
$216$	−1076.16	−0.338998
$217$	−1931.90	−0.604359
$218$	760.231	0.236190
$219$	−3678.16	−1.13492
$220$	−1360.54	−0.416943
$221$	8138.66	2.47722
$222$	759.332	0.229563
$223$	2767.85	0.831160	0.415580	−	0.909557i	$-0.363579\pi$
$223$	2767.85	0.831160	0.415580	+	0.909557i	$0.363579\pi$
$224$	775.006	0.231171
$225$	173.951	0.0515411
$226$	284.843	0.0838384
$227$	4644.75	1.35808	0.679038	−	0.734103i	$-0.262397\pi$
$227$	4644.75	1.35808	0.679038	+	0.734103i	$0.262397\pi$
$228$	825.525	0.239788
$229$	1988.68	0.573868	0.286934	−	0.957950i	$-0.407364\pi$
$229$	1988.68	0.573868	0.286934	+	0.957950i	$0.407364\pi$
$230$	0	0
$231$	−588.404	−0.167594
$232$	−637.358	−0.180365
$233$	−406.618	−0.114328	−0.0571640	−	0.998365i	$-0.518206\pi$
$233$	−406.618	−0.114328	−0.0571640	+	0.998365i	$0.518206\pi$
$234$	128.500	0.0358988
$235$	5114.67	1.41976
$236$	−3891.88	−1.07348
$237$	−4559.48	−1.24966
$238$	−478.609	−0.130351
$239$	3556.38	0.962523	0.481262	−	0.876577i	$-0.340179\pi$
$239$	3556.38	0.962523	0.481262	+	0.876577i	$0.340179\pi$
$240$	4203.64	1.13060
$241$	5.01372	0.00134009	0.000670046	−	1.00000i	$-0.499787\pi$
$241$	5.01372	0.00134009	0.000670046		1.00000i	$0.499787\pi$
$242$	607.420	0.161349
$243$	−947.664	−0.250176
$244$	4971.72	1.30443
$245$	−3694.59	−0.963422
$246$	−334.412	−0.0866721
$247$	1394.45	0.359218
$248$	1986.56	0.508656
$249$	4534.53	1.15407
$250$	515.174	0.130330
$251$	6847.71	1.72201	0.861003	−	0.508599i	$-0.169836\pi$
$251$	6847.71	1.72201	0.861003	+	0.508599i	$0.169836\pi$
$252$	210.982	0.0527404
$253$	0	0
$254$	−272.727	−0.0673717
$255$	−8281.12	−2.03366
$256$	2751.95	0.671864
$257$	7842.78	1.90358	0.951789	−	0.306755i	$-0.0992432\pi$
$257$	7842.78	1.90358	0.951789	+	0.306755i	$0.0992432\pi$
$258$	1023.38	0.246949
$259$	2105.94	0.505239
$260$	7374.25	1.75897
$261$	−261.790	−0.0620858
$262$	449.474	0.105987
$263$	−1276.75	−0.299344	−0.149672	−	0.988736i	$-0.547822\pi$
$263$	−1276.75	−0.299344	−0.149672	+	0.988736i	$0.547822\pi$
$264$	605.053	0.141055
$265$	3705.06	0.858868
$266$	−82.0034	−0.0189021
$267$	−3103.28	−0.711303
$268$	3647.38	0.831340
$269$	−207.570	−0.0470475	−0.0235237	−	0.999723i	$-0.507489\pi$
$269$	−207.570	−0.0470475	−0.0235237	+	0.999723i	$0.507489\pi$
$270$	908.550	0.204787
$271$	−2881.93	−0.645996	−0.322998	−	0.946400i	$-0.604691\pi$
$271$	−2881.93	−0.645996	−0.322998	+	0.946400i	$0.604691\pi$
$272$	−6499.11	−1.44877
$273$	3189.21	0.707031
$274$	40.5508	0.00894075
$275$	679.598	0.149023
$276$	0	0
$277$	722.581	0.156735	0.0783676	−	0.996925i	$-0.475029\pi$
$277$	722.581	0.156735	0.0783676	+	0.996925i	$0.475029\pi$
$278$	208.367	0.0449534
$279$	815.965	0.175092
$280$	−882.845	−0.188429
$281$	4966.45	1.05435	0.527177	−	0.849756i	$-0.323251\pi$
$281$	4966.45	1.05435	0.527177	+	0.849756i	$0.323251\pi$
$282$	−1117.28	−0.235932
$283$	1267.55	0.266248	0.133124	−	0.991099i	$-0.457499\pi$
$283$	1267.55	0.266248	0.133124	+	0.991099i	$0.457499\pi$
$284$	−1302.49	−0.272143
$285$	−1418.86	−0.294899
$286$	502.028	0.103796
$287$	−927.463	−0.190754
$288$	−327.335	−0.0669737
$289$	7890.16	1.60598
$290$	538.089	0.108958
$291$	−117.653	−0.0237008
$292$	5152.57	1.03264
$293$	−2043.84	−0.407517	−0.203758	−	0.979021i	$-0.565316\pi$
$293$	−2043.84	−0.407517	−0.203758	+	0.979021i	$0.565316\pi$
$294$	807.067	0.160099
$295$	6689.13	1.32019
$296$	−2165.53	−0.425232
$297$	−1726.92	−0.337395
$298$	1353.66	0.263139
$299$	0	0
$300$	−2180.65	−0.419666
$301$	2838.26	0.543503
$302$	1278.91	0.243686
$303$	8424.52	1.59728
$304$	−1113.54	−0.210085
$305$	−8545.08	−1.60423
$306$	202.147	0.0377647
$307$	−3436.97	−0.638951	−0.319476	−	0.947594i	$-0.603507\pi$
$307$	−3436.97	−0.638951	−0.319476	+	0.947594i	$0.603507\pi$
$308$	824.270	0.152491
$309$	5863.18	1.07943
$310$	−1677.15	−0.307277
$311$	884.496	0.161271	0.0806353	−	0.996744i	$-0.474305\pi$
$311$	884.496	0.161271	0.0806353	+	0.996744i	$0.474305\pi$
$312$	−3279.44	−0.595070
$313$	−2367.43	−0.427524	−0.213762	−	0.976886i	$-0.568572\pi$
$313$	−2367.43	−0.427524	−0.213762	+	0.976886i	$0.568572\pi$
$314$	−1692.77	−0.304232
$315$	−362.622	−0.0648617
$316$	6387.18	1.13705
$317$	−208.007	−0.0368544	−0.0184272	−	0.999830i	$-0.505866\pi$
$317$	−208.007	−0.0368544	−0.0184272	+	0.999830i	$0.505866\pi$
$318$	−809.354	−0.142724
$319$	−1022.77	−0.179511
$320$	−5426.80	−0.948023
$321$	1183.58	0.205797
$322$	0	0
$323$	2193.66	0.377889
$324$	6249.55	1.07160
$325$	−3683.48	−0.628686
$326$	−296.256	−0.0503315
$327$	−7969.15	−1.34769
$328$	953.705	0.160547
$329$	−3098.67	−0.519256
$330$	−510.816	−0.0852106
$331$	−8595.84	−1.42740	−0.713701	−	0.700451i	$-0.752982\pi$
$331$	−8595.84	−1.42740	−0.713701	+	0.700451i	$0.752982\pi$
$332$	−6352.23	−1.05007
$333$	−889.475	−0.146375
$334$	−123.461	−0.0202260
$335$	−6268.89	−1.02241
$336$	−2546.74	−0.413500
$337$	1404.45	0.227018	0.113509	−	0.993537i	$-0.463791\pi$
$337$	1404.45	0.227018	0.113509	+	0.993537i	$0.463791\pi$
$338$	−1565.52	−0.251933
$339$	−2985.88	−0.478380
$340$	11600.7	1.85039
$341$	3187.84	0.506250
$342$	34.6353	0.00547621
$343$	4996.81	0.786595
$344$	−2918.56	−0.457437
$345$	0	0
$346$	−1205.10	−0.187245
$347$	−2840.44	−0.439431	−0.219716	−	0.975564i	$-0.570513\pi$
$347$	−2840.44	−0.439431	−0.219716	+	0.975564i	$0.570513\pi$
$348$	3281.79	0.505525
$349$	−7353.34	−1.12784	−0.563919	−	0.825830i	$-0.690707\pi$
$349$	−7353.34	−1.12784	−0.563919	+	0.825830i	$0.690707\pi$
$350$	216.614	0.0330814
$351$	9360.08	1.42337
$352$	−1278.84	−0.193644
$353$	12156.5	1.83293	0.916466	−	0.400112i	$-0.131029\pi$
$353$	12156.5	1.83293	0.916466	+	0.400112i	$0.131029\pi$
$354$	−1461.21	−0.219386
$355$	2238.64	0.334689
$356$	4347.25	0.647202
$357$	5017.04	0.743781
$358$	1110.36	0.163923
$359$	−852.313	−0.125302	−0.0626509	−	0.998035i	$-0.519955\pi$
$359$	−852.313	−0.125302	−0.0626509	+	0.998035i	$0.519955\pi$
$360$	372.882	0.0545906
$361$	−6483.15	−0.945203
$362$	−425.611	−0.0617945
$363$	−6367.30	−0.920652
$364$	−4467.62	−0.643316
$365$	−8855.92	−1.26997
$366$	1866.64	0.266586
$367$	−13521.3	−1.92318	−0.961591	−	0.274485i	$-0.911493\pi$
$367$	−13521.3	−1.92318	−0.961591	+	0.274485i	$0.911493\pi$
$368$	0	0
$369$	391.728	0.0552643
$370$	1828.25	0.256881
$371$	−2244.67	−0.314118
$372$	−10228.9	−1.42566
$373$	2211.99	0.307058	0.153529	−	0.988144i	$-0.450936\pi$
$373$	2211.99	0.307058	0.153529	+	0.988144i	$0.450936\pi$
$374$	789.756	0.109191
$375$	−5400.34	−0.743659
$376$	3186.35	0.437030
$377$	5543.51	0.757309
$378$	−550.437	−0.0748979
$379$	−952.236	−0.129058	−0.0645291	−	0.997916i	$-0.520555\pi$
$379$	−952.236	−0.129058	−0.0645291	+	0.997916i	$0.520555\pi$
$380$	1987.62	0.268323
$381$	2858.87	0.384421
$382$	−26.1291	−0.00349969
$383$	3882.00	0.517913	0.258957	−	0.965889i	$-0.416621\pi$
$383$	3882.00	0.517913	0.258957	+	0.965889i	$0.416621\pi$
$384$	5435.90	0.722395
$385$	−1416.70	−0.187537
$386$	−90.0220	−0.0118705
$387$	−1198.78	−0.157461
$388$	164.815	0.0215650
$389$	−8820.82	−1.14970	−0.574850	−	0.818259i	$-0.694940\pi$
$389$	−8820.82	−1.14970	−0.574850	+	0.818259i	$0.694940\pi$
$390$	2768.67	0.359480
$391$	0	0
$392$	−2301.66	−0.296560
$393$	−4711.63	−0.604759
$394$	−1491.23	−0.190678
$395$	−10977.9	−1.39837
$396$	−348.142	−0.0441788
$397$	−2109.41	−0.266671	−0.133336	−	0.991071i	$-0.542569\pi$
$397$	−2109.41	−0.266671	−0.133336	+	0.991071i	$0.542569\pi$
$398$	504.380	0.0635233
$399$	859.604	0.107855
$400$	2941.44	0.367680
$401$	−5935.80	−0.739202	−0.369601	−	0.929191i	$-0.620506\pi$
$401$	−5935.80	−0.739202	−0.369601	+	0.929191i	$0.620506\pi$
$402$	1369.41	0.169901
$403$	−17278.4	−2.13573
$404$	−11801.5	−1.45334
$405$	−10741.3	−1.31788
$406$	−325.996	−0.0398496
$407$	−3475.03	−0.423221
$408$	−5158.99	−0.626000
$409$	−7541.71	−0.911769	−0.455884	−	0.890039i	$-0.650677\pi$
$409$	−7541.71	−0.911769	−0.455884	+	0.890039i	$0.650677\pi$
$410$	−805.166	−0.0969861
$411$	−425.076	−0.0510157
$412$	−8213.48	−0.982158
$413$	−4052.55	−0.482840
$414$	0	0
$415$	10917.8	1.29141
$416$	6931.46	0.816929
$417$	−2184.22	−0.256503
$418$	135.314	0.0158336
$419$	−13311.0	−1.55200	−0.775998	−	0.630736i	$-0.782753\pi$
$419$	−13311.0	−1.55200	−0.775998	+	0.630736i	$0.782753\pi$
$420$	4545.82	0.528127
$421$	−12336.5	−1.42813	−0.714065	−	0.700080i	$-0.753148\pi$
$421$	−12336.5	−1.42813	−0.714065	+	0.700080i	$0.753148\pi$
$422$	−1002.92	−0.115690
$423$	1308.77	0.150436
$424$	2308.19	0.264376
$425$	−5794.60	−0.661363
$426$	−489.021	−0.0556177
$427$	5176.95	0.586722
$428$	−1658.02	−0.187251
$429$	−5262.53	−0.592255
$430$	2464.00	0.276336
$431$	−2767.60	−0.309306	−0.154653	−	0.987969i	$-0.549426\pi$
$431$	−2767.60	−0.309306	−0.154653	+	0.987969i	$0.549426\pi$
$432$	−7474.48	−0.832445
$433$	−3315.68	−0.367994	−0.183997	−	0.982927i	$-0.558904\pi$
$433$	−3315.68	−0.367994	−0.183997	+	0.982927i	$0.558904\pi$
$434$	1016.09	0.112382
$435$	−5640.55	−0.621709
$436$	11163.6	1.22624
$437$	0	0
$438$	1934.54	0.211041
$439$	7003.61	0.761421	0.380711	−	0.924694i	$-0.375679\pi$
$439$	7003.61	0.761421	0.380711	+	0.924694i	$0.375679\pi$
$440$	1456.79	0.157840
$441$	−945.391	−0.102083
$442$	−4280.55	−0.460645
$443$	4437.22	0.475888	0.237944	−	0.971279i	$-0.423526\pi$
$443$	4437.22	0.475888	0.237944	+	0.971279i	$0.423526\pi$
$444$	11150.4	1.19184
$445$	−7471.79	−0.795948
$446$	−1455.76	−0.154556
$447$	−14189.8	−1.50147
$448$	3287.77	0.346725
$449$	−3830.58	−0.402620	−0.201310	−	0.979528i	$-0.564520\pi$
$449$	−3830.58	−0.402620	−0.201310	+	0.979528i	$0.564520\pi$
$450$	−91.4901	−0.00958419
$451$	1530.41	0.159788
$452$	4182.79	0.435270
$453$	−13406.3	−1.39047
$454$	−2442.92	−0.252537
$455$	7678.67	0.791168
$456$	−883.926	−0.0907755
$457$	−15001.0	−1.53549	−0.767745	−	0.640755i	$-0.778621\pi$
$457$	−15001.0	−1.53549	−0.767745	+	0.640755i	$0.778621\pi$
$458$	−1045.95	−0.106712
$459$	14724.6	1.49736
$460$	0	0
$461$	2747.37	0.277566	0.138783	−	0.990323i	$-0.455681\pi$
$461$	2747.37	0.277566	0.138783	+	0.990323i	$0.455681\pi$
$462$	309.473	0.0311645
$463$	−4823.85	−0.484198	−0.242099	−	0.970252i	$-0.577836\pi$
$463$	−4823.85	−0.484198	−0.242099	+	0.970252i	$0.577836\pi$
$464$	−4426.76	−0.442904
$465$	17580.8	1.75332
$466$	213.862	0.0212596
$467$	13563.8	1.34403	0.672013	−	0.740539i	$-0.265430\pi$
$467$	13563.8	1.34403	0.672013	+	0.740539i	$0.265430\pi$
$468$	1886.96	0.186378
$469$	3797.94	0.373929
$470$	−2690.07	−0.264008
$471$	17744.6	1.73594
$472$	4167.21	0.406380
$473$	−4683.43	−0.455273
$474$	2398.07	0.232378
$475$	−992.829	−0.0959034
$476$	−7028.14	−0.676753
$477$	948.071	0.0910046
$478$	−1870.49	−0.178984
$479$	−16542.5	−1.57797	−0.788983	−	0.614415i	$-0.789392\pi$
$479$	−16542.5	−1.57797	−0.788983	+	0.614415i	$0.789392\pi$
$480$	−7052.78	−0.670654
$481$	18835.0	1.78545
$482$	−2.63698	−0.000249193 0
$483$	0	0
$484$	8919.68	0.837686
$485$	−283.274	−0.0265212
$486$	498.427	0.0465208
$487$	19230.5	1.78936	0.894681	−	0.446705i	$-0.147403\pi$
$487$	19230.5	1.78936	0.894681	+	0.446705i	$0.147403\pi$
$488$	−5323.43	−0.493812
$489$	3105.51	0.287190
$490$	1943.18	0.179151
$491$	15572.7	1.43134	0.715670	−	0.698439i	$-0.246122\pi$
$491$	15572.7	1.43134	0.715670	+	0.698439i	$0.246122\pi$
$492$	−4910.69	−0.449981
$493$	8720.66	0.796671
$494$	−733.417	−0.0667975
$495$	598.365	0.0543324
$496$	13797.6	1.24906
$497$	−1356.26	−0.122407
$498$	−2384.95	−0.214603
$499$	−4494.97	−0.403251	−0.201626	−	0.979463i	$-0.564622\pi$
$499$	−4494.97	−0.403251	−0.201626	+	0.979463i	$0.564622\pi$
$500$	7565.09	0.676643
$501$	1294.18	0.115409
$502$	−3601.57	−0.320211
$503$	−3972.18	−0.352109	−0.176055	−	0.984380i	$-0.556334\pi$
$503$	−3972.18	−0.352109	−0.176055	+	0.984380i	$0.556334\pi$
$504$	−225.907	−0.0199657
$505$	20283.8	1.78736
$506$	0	0
$507$	16410.7	1.43752
$508$	−4004.87	−0.349778
$509$	12507.6	1.08917	0.544586	−	0.838705i	$-0.316687\pi$
$509$	12507.6	1.08917	0.544586	+	0.838705i	$0.316687\pi$
$510$	4355.48	0.378164
$511$	5365.28	0.464473
$512$	−9335.05	−0.805772
$513$	2522.87	0.217130
$514$	−4124.93	−0.353975
$515$	14116.8	1.20789
$516$	15027.9	1.28210
$517$	5113.14	0.434963
$518$	−1107.63	−0.0939503
$519$	12632.5	1.06841
$520$	−7895.93	−0.665884
$521$	−15846.0	−1.33249	−0.666245	−	0.745733i	$-0.732099\pi$
$521$	−15846.0	−1.33249	−0.666245	+	0.745733i	$0.732099\pi$
$522$	137.689	0.0115450
$523$	6140.30	0.513377	0.256689	−	0.966494i	$-0.417368\pi$
$523$	6140.30	0.513377	0.256689	+	0.966494i	$0.417368\pi$
$524$	6600.32	0.550260
$525$	−2270.67	−0.188762
$526$	671.508	0.0556638
$527$	−27181.2	−2.24674
$528$	4202.39	0.346374
$529$	0	0
$530$	−1948.69	−0.159709
$531$	1711.65	0.139886
$532$	−1204.18	−0.0981351
$533$	−8294.99	−0.674101
$534$	1632.18	0.132268
$535$	2849.70	0.230287
$536$	−3905.41	−0.314716
$537$	−11639.4	−0.935340
$538$	109.172	0.00874859
$539$	−3693.48	−0.295157
$540$	13341.6	1.06321
$541$	−8637.61	−0.686432	−0.343216	−	0.939257i	$-0.611516\pi$
$541$	−8637.61	−0.686432	−0.343216	+	0.939257i	$0.611516\pi$
$542$	1515.76	0.120125
$543$	4461.48	0.352598
$544$	10904.1	0.859391
$545$	−19187.4	−1.50807
$546$	−1677.37	−0.131474
$547$	−11081.5	−0.866197	−0.433098	−	0.901347i	$-0.642580\pi$
$547$	−11081.5	−0.866197	−0.433098	+	0.901347i	$0.642580\pi$
$548$	595.470	0.0464183
$549$	−2186.56	−0.169982
$550$	−357.436	−0.0277112
$551$	1494.17	0.115524
$552$	0	0
$553$	6650.85	0.511434
$554$	−380.043	−0.0291453
$555$	−19164.7	−1.46576
$556$	3059.78	0.233388
$557$	−20212.8	−1.53760	−0.768800	−	0.639490i	$-0.779146\pi$
$557$	−20212.8	−1.53760	−0.768800	+	0.639490i	$0.779146\pi$
$558$	−429.159	−0.0325587
$559$	25384.6	1.92067
$560$	−6131.79	−0.462706
$561$	−8278.65	−0.623039
$562$	−2612.12	−0.196060
$563$	−23081.6	−1.72784	−0.863921	−	0.503628i	$-0.831998\pi$
$563$	−23081.6	−1.72784	−0.863921	+	0.503628i	$0.831998\pi$
$564$	−16406.7	−1.22491
$565$	−7189.12	−0.535307
$566$	−666.673	−0.0495095
$567$	6507.54	0.481995
$568$	1394.63	0.103024
$569$	−7342.08	−0.540942	−0.270471	−	0.962728i	$-0.587179\pi$
$569$	−7342.08	−0.540942	−0.270471	+	0.962728i	$0.587179\pi$
$570$	746.254	0.0548371
$571$	8612.40	0.631204	0.315602	−	0.948892i	$-0.397794\pi$
$571$	8612.40	0.631204	0.315602	+	0.948892i	$0.397794\pi$
$572$	7372.05	0.538883
$573$	273.899	0.0199691
$574$	487.802	0.0354712
$575$	0	0
$576$	−1388.64	−0.100451
$577$	−2681.66	−0.193482	−0.0967409	−	0.995310i	$-0.530842\pi$
$577$	−2681.66	−0.193482	−0.0967409	+	0.995310i	$0.530842\pi$
$578$	−4149.85	−0.298635
$579$	943.660	0.0677326
$580$	7901.59	0.565682
$581$	−6614.46	−0.472313
$582$	61.8799	0.00440722
$583$	3703.95	0.263125
$584$	−5517.08	−0.390922
$585$	−3243.20	−0.229213
$586$	1074.96	0.0757787
$587$	11195.6	0.787212	0.393606	−	0.919279i	$-0.371227\pi$
$587$	11195.6	0.787212	0.393606	+	0.919279i	$0.371227\pi$
$588$	11851.4	0.831196
$589$	−4657.14	−0.325796
$590$	−3518.17	−0.245493
$591$	15631.9	1.08800
$592$	−15040.6	−1.04420
$593$	1586.06	0.109835	0.0549173	−	0.998491i	$-0.482510\pi$
$593$	1586.06	0.109835	0.0549173	+	0.998491i	$0.482510\pi$
$594$	908.280	0.0627393
$595$	12079.5	0.832290
$596$	19877.9	1.36616
$597$	−5287.19	−0.362463
$598$	0	0
$599$	−15953.8	−1.08824	−0.544118	−	0.839009i	$-0.683136\pi$
$599$	−15953.8	−1.08824	−0.544118	+	0.839009i	$0.683136\pi$
$600$	2334.91	0.158871
$601$	26086.6	1.77054	0.885271	−	0.465076i	$-0.153973\pi$
$601$	26086.6	1.77054	0.885271	+	0.465076i	$0.153973\pi$
$602$	−1492.79	−0.101066
$603$	−1604.12	−0.108333
$604$	18780.3	1.26516
$605$	−15330.6	−1.03021
$606$	−4430.90	−0.297018
$607$	6777.03	0.453165	0.226583	−	0.973992i	$-0.427245\pi$
$607$	6777.03	0.453165	0.226583	+	0.973992i	$0.427245\pi$
$608$	1868.27	0.124619
$609$	3417.27	0.227381
$610$	4494.31	0.298310
$611$	−27713.7	−1.83499
$612$	2968.44	0.196065
$613$	−4054.63	−0.267154	−0.133577	−	0.991038i	$-0.542646\pi$
$613$	−4054.63	−0.267154	−0.133577	+	0.991038i	$0.542646\pi$
$614$	1807.68	0.118815
$615$	8440.18	0.553400
$616$	−882.582	−0.0577276
$617$	−24978.8	−1.62984	−0.814919	−	0.579575i	$-0.803218\pi$
$617$	−24978.8	−1.62984	−0.814919	+	0.579575i	$0.803218\pi$
$618$	−3083.76	−0.200723
$619$	9933.57	0.645014	0.322507	−	0.946567i	$-0.395474\pi$
$619$	9933.57	0.645014	0.322507	+	0.946567i	$0.395474\pi$
$620$	−24628.2	−1.59531
$621$	0	0
$622$	−465.203	−0.0299886
$623$	4526.71	0.291106
$624$	−22777.3	−1.46126
$625$	−19403.8	−1.24184
$626$	1245.16	0.0794992
$627$	−1418.44	−0.0903461
$628$	−24857.6	−1.57950
$629$	29629.9	1.87825
$630$	190.722	0.0120612
$631$	−7605.27	−0.479811	−0.239906	−	0.970796i	$-0.577117\pi$
$631$	−7605.27	−0.479811	−0.239906	+	0.970796i	$0.577117\pi$
$632$	−6839.03	−0.430446
$633$	10513.1	0.660124
$634$	109.402	0.00685316
$635$	6883.32	0.430167
$636$	−11885.0	−0.740991
$637$	20019.0	1.24519
$638$	537.929	0.0333806
$639$	572.835	0.0354632
$640$	13088.0	0.808360
$641$	−3860.63	−0.237887	−0.118944	−	0.992901i	$-0.537951\pi$
$641$	−3860.63	−0.237887	−0.118944	+	0.992901i	$0.537951\pi$
$642$	−622.506	−0.0382684
$643$	−10167.9	−0.623612	−0.311806	−	0.950146i	$-0.600934\pi$
$643$	−10167.9	−0.623612	−0.311806	+	0.950146i	$0.600934\pi$
$644$	0	0
$645$	−25829.0	−1.57677
$646$	−1153.76	−0.0702694
$647$	9334.86	0.567220	0.283610	−	0.958940i	$-0.408468\pi$
$647$	9334.86	0.567220	0.283610	+	0.958940i	$0.408468\pi$
$648$	−6691.67	−0.405669
$649$	6687.14	0.404458
$650$	1937.34	0.116906
$651$	−10651.2	−0.641248
$652$	−4350.38	−0.261310
$653$	14456.3	0.866337	0.433169	−	0.901313i	$-0.357395\pi$
$653$	14456.3	0.866337	0.433169	+	0.901313i	$0.357395\pi$
$654$	4191.40	0.250607
$655$	−11344.2	−0.676726
$656$	6623.95	0.394241
$657$	−2266.10	−0.134565
$658$	1629.76	0.0965570
$659$	16757.3	0.990548	0.495274	−	0.868737i	$-0.335068\pi$
$659$	16757.3	0.990548	0.495274	+	0.868737i	$0.335068\pi$
$660$	−7501.09	−0.442393
$661$	8857.65	0.521214	0.260607	−	0.965445i	$-0.416077\pi$
$661$	8857.65	0.521214	0.260607	+	0.965445i	$0.416077\pi$
$662$	4521.00	0.265429
$663$	44871.1	2.62843
$664$	6801.61	0.397521
$665$	2069.67	0.120689
$666$	467.822	0.0272188
$667$	0	0
$668$	−1812.96	−0.105009
$669$	15260.0	0.881894
$670$	3297.14	0.190119
$671$	−8542.53	−0.491476
$672$	4272.86	0.245282
$673$	4643.19	0.265946	0.132973	−	0.991120i	$-0.457548\pi$
$673$	4643.19	0.265946	0.132973	+	0.991120i	$0.457548\pi$
$674$	−738.673	−0.0422145
$675$	−6664.23	−0.380010
$676$	−22989.0	−1.30798
$677$	−5056.01	−0.287028	−0.143514	−	0.989648i	$-0.545840\pi$
$677$	−5056.01	−0.287028	−0.143514	+	0.989648i	$0.545840\pi$
$678$	1570.43	0.0889559
$679$	171.619	0.00969973
$680$	−12421.3	−0.700494
$681$	25608.0	1.44097
$682$	−1676.65	−0.0941384
$683$	20822.5	1.16655	0.583274	−	0.812276i	$-0.301771\pi$
$683$	20822.5	1.16655	0.583274	+	0.812276i	$0.301771\pi$
$684$	508.604	0.0284312
$685$	−1023.46	−0.0570865
$686$	−2628.08	−0.146269
$687$	10964.2	0.608897
$688$	−20270.9	−1.12328
$689$	−20075.8	−1.11005
$690$	0	0
$691$	−14920.6	−0.821429	−0.410715	−	0.911764i	$-0.634721\pi$
$691$	−14920.6	−0.821429	−0.410715	+	0.911764i	$0.634721\pi$
$692$	−17696.4	−0.972132
$693$	−362.514	−0.0198712
$694$	1493.94	0.0817133
$695$	−5258.96	−0.287027
$696$	−3513.96	−0.191374
$697$	−13049.1	−0.709139
$698$	3867.51	0.209724
$699$	−2241.82	−0.121307
$700$	3180.88	0.171751
$701$	−20379.9	−1.09806	−0.549030	−	0.835803i	$-0.685003\pi$
$701$	−20379.9	−1.09806	−0.549030	+	0.835803i	$0.685003\pi$
$702$	−4922.96	−0.264680
$703$	5076.69	0.272363
$704$	−5425.18	−0.290439
$705$	28198.8	1.50642
$706$	−6393.75	−0.340838
$707$	−12288.7	−0.653698
$708$	−21457.2	−1.13900
$709$	6321.71	0.334861	0.167431	−	0.985884i	$-0.446453\pi$
$709$	6321.71	0.334861	0.167431	+	0.985884i	$0.446453\pi$
$710$	−1177.42	−0.0622362
$711$	−2809.08	−0.148170
$712$	−4654.79	−0.245008
$713$	0	0
$714$	−2638.72	−0.138308
$715$	−12670.6	−0.662734
$716$	16305.1	0.851049
$717$	19607.5	1.02128
$718$	448.277	0.0233002
$719$	−30340.8	−1.57374	−0.786872	−	0.617117i	$-0.788301\pi$
$719$	−30340.8	−1.57374	−0.786872	+	0.617117i	$0.788301\pi$
$720$	2589.85	0.134053
$721$	−8552.54	−0.441766
$722$	3409.83	0.175763
$723$	27.6423	0.00142189
$724$	−6249.89	−0.320822
$725$	−3946.90	−0.202185
$726$	3348.90	0.171198
$727$	−36267.5	−1.85019	−0.925093	−	0.379740i	$-0.876013\pi$
$727$	−36267.5	−1.85019	−0.925093	+	0.379740i	$0.876013\pi$
$728$	4783.68	0.243537
$729$	16622.9	0.844532
$730$	4657.80	0.236155
$731$	39933.3	2.02050
$732$	27410.7	1.38405
$733$	29209.9	1.47189	0.735943	−	0.677044i	$-0.236739\pi$
$733$	29209.9	1.47189	0.735943	+	0.677044i	$0.236739\pi$
$734$	7111.59	0.357620
$735$	−20369.5	−1.02223
$736$	0	0
$737$	−6267.02	−0.313227
$738$	−206.030	−0.0102765
$739$	−31867.0	−1.58626	−0.793130	−	0.609053i	$-0.791550\pi$
$739$	−31867.0	−1.58626	−0.793130	+	0.609053i	$0.791550\pi$
$740$	26846.9	1.33367
$741$	7688.07	0.381145
$742$	1180.59	0.0584110
$743$	32890.4	1.62400	0.812000	−	0.583658i	$-0.198379\pi$
$743$	32890.4	1.62400	0.812000	+	0.583658i	$0.198379\pi$
$744$	10952.6	0.539704
$745$	−34164.9	−1.68014
$746$	−1163.40	−0.0570982
$747$	2793.71	0.136836
$748$	11597.2	0.566892
$749$	−1726.47	−0.0842239
$750$	2840.32	0.138285
$751$	−24756.8	−1.20292	−0.601458	−	0.798904i	$-0.705413\pi$
$751$	−24756.8	−1.20292	−0.601458	+	0.798904i	$0.705413\pi$
$752$	22130.7	1.07317
$753$	37753.7	1.82712
$754$	−2915.63	−0.140823
$755$	−32278.4	−1.55593
$756$	−8082.91	−0.388852
$757$	14933.4	0.716992	0.358496	−	0.933531i	$-0.383290\pi$
$757$	14933.4	0.716992	0.358496	+	0.933531i	$0.383290\pi$
$758$	500.831	0.0239987
$759$	0	0
$760$	−2128.23	−0.101578
$761$	1953.15	0.0930375	0.0465187	−	0.998917i	$-0.485187\pi$
$761$	1953.15	0.0930375	0.0465187	+	0.998917i	$0.485187\pi$
$762$	−1503.63	−0.0714840
$763$	11624.5	0.551552
$764$	−383.693	−0.0181696
$765$	−5101.97	−0.241127
$766$	−2041.75	−0.0963072
$767$	−36244.9	−1.70629
$768$	15172.4	0.712874
$769$	35847.6	1.68101	0.840505	−	0.541803i	$-0.182258\pi$
$769$	35847.6	1.68101	0.840505	+	0.541803i	$0.182258\pi$
$770$	745.119	0.0348730
$771$	43239.8	2.01977
$772$	−1321.93	−0.0616287
$773$	31989.4	1.48846	0.744231	−	0.667923i	$-0.232816\pi$
$773$	31989.4	1.48846	0.744231	+	0.667923i	$0.232816\pi$
$774$	630.501	0.0292802
$775$	12302.0	0.570192
$776$	−176.474	−0.00816374
$777$	11610.7	0.536078
$778$	4639.34	0.213790
$779$	−2235.79	−0.102831
$780$	40656.6	1.86633
$781$	2237.97	0.102536
$782$	0	0
$783$	10029.4	0.457756
$784$	−15986.2	−0.728233
$785$	42723.7	1.94252
$786$	2478.10	0.112456
$787$	−147.774	−0.00669322	−0.00334661	−	0.999994i	$-0.501065\pi$
$787$	−147.774	−0.00669322	−0.00334661	+	0.999994i	$0.501065\pi$
$788$	−21898.0	−0.989956
$789$	−7039.11	−0.317616
$790$	5773.85	0.260031
$791$	4355.46	0.195780
$792$	372.771	0.0167246
$793$	46301.3	2.07340
$794$	1109.45	0.0495881
$795$	20427.2	0.911293
$796$	7406.59	0.329798
$797$	−9020.44	−0.400904	−0.200452	−	0.979704i	$-0.564241\pi$
$797$	−9020.44	−0.400904	−0.200452	+	0.979704i	$0.564241\pi$
$798$	−452.111	−0.0200558
$799$	−43597.3	−1.93036
$800$	−4935.09	−0.218102
$801$	−1911.92	−0.0843376
$802$	3121.95	0.137456
$803$	−8853.28	−0.389073
$804$	20109.2	0.882084
$805$	0	0
$806$	9087.62	0.397144
$807$	−1144.40	−0.0499192
$808$	12636.4	0.550183
$809$	27220.0	1.18295	0.591473	−	0.806325i	$-0.298547\pi$
$809$	27220.0	1.18295	0.591473	+	0.806325i	$0.298547\pi$
$810$	5649.44	0.245063
$811$	−5041.04	−0.218267	−0.109134	−	0.994027i	$-0.534808\pi$
$811$	−5041.04	−0.218267	−0.109134	+	0.994027i	$0.534808\pi$
$812$	−4787.10	−0.206890
$813$	−15889.0	−0.685428
$814$	1827.70	0.0786989
$815$	7477.16	0.321366
$816$	−35831.7	−1.53721
$817$	6842.05	0.292990
$818$	3966.58	0.169546
$819$	1964.86	0.0838312
$820$	−11823.5	−0.503529
$821$	−46345.6	−1.97013	−0.985063	−	0.172196i	$-0.944914\pi$
$821$	−46345.6	−1.97013	−0.985063	+	0.172196i	$0.944914\pi$
$822$	223.570	0.00948649
$823$	18019.6	0.763213	0.381606	−	0.924325i	$-0.375371\pi$
$823$	18019.6	0.763213	0.381606	+	0.924325i	$0.375371\pi$
$824$	8794.53	0.371811
$825$	3746.84	0.158119
$826$	2131.45	0.0897852
$827$	20971.1	0.881783	0.440892	−	0.897560i	$-0.354662\pi$
$827$	20971.1	0.881783	0.440892	+	0.897560i	$0.354662\pi$
$828$	0	0
$829$	−21672.6	−0.907987	−0.453993	−	0.891005i	$-0.650001\pi$
$829$	−21672.6	−0.907987	−0.453993	+	0.891005i	$0.650001\pi$
$830$	−5742.26	−0.240141
$831$	3983.82	0.166302
$832$	29405.0	1.22528
$833$	31492.5	1.30991
$834$	1148.80	0.0476973
$835$	3116.01	0.129142
$836$	1987.03	0.0822043
$837$	−31260.4	−1.29094
$838$	7000.97	0.288597
$839$	−10256.1	−0.422028	−0.211014	−	0.977483i	$-0.567677\pi$
$839$	−10256.1	−0.422028	−0.211014	+	0.977483i	$0.567677\pi$
$840$	−4867.41	−0.199930
$841$	−18449.1	−0.756450
$842$	6488.40	0.265564
$843$	27381.6	1.11871
$844$	−14727.4	−0.600636
$845$	39512.0	1.60859
$846$	−688.351	−0.0279740
$847$	9287.89	0.376784
$848$	16031.5	0.649202
$849$	6988.43	0.282500
$850$	3047.69	0.122982
$851$	0	0
$852$	−7181.05	−0.288754
$853$	−31765.3	−1.27506	−0.637528	−	0.770427i	$-0.720043\pi$
$853$	−31765.3	−1.27506	−0.637528	+	0.770427i	$0.720043\pi$
$854$	−2722.83	−0.109102
$855$	−874.156	−0.0349655
$856$	1775.32	0.0708867
$857$	−8899.70	−0.354735	−0.177368	−	0.984145i	$-0.556758\pi$
$857$	−8899.70	−0.354735	−0.177368	+	0.984145i	$0.556758\pi$
$858$	2767.84	0.110131
$859$	−32318.1	−1.28368	−0.641839	−	0.766839i	$-0.721828\pi$
$859$	−32318.1	−1.28368	−0.641839	+	0.766839i	$0.721828\pi$
$860$	36182.7	1.43467
$861$	−5113.41	−0.202398
$862$	1455.63	0.0575162
$863$	−36462.4	−1.43823	−0.719116	−	0.694890i	$-0.755453\pi$
$863$	−36462.4	−1.43823	−0.719116	+	0.694890i	$0.755453\pi$
$864$	12540.5	0.493793
$865$	30415.4	1.19556
$866$	1743.89	0.0684294
$867$	43501.0	1.70400
$868$	14920.8	0.583461
$869$	−10974.6	−0.428410
$870$	2966.66	0.115608
$871$	33967.8	1.32142
$872$	−11953.4	−0.464212
$873$	−72.4856	−0.00281016
$874$	0	0
$875$	7877.39	0.304348
$876$	28407.8	1.09567
$877$	−34016.2	−1.30975	−0.654873	−	0.755739i	$-0.727278\pi$
$877$	−34016.2	−1.30975	−0.654873	+	0.755739i	$0.727278\pi$
$878$	−3683.57	−0.141588
$879$	−11268.4	−0.432392
$880$	10118.1	0.387593
$881$	15355.4	0.587215	0.293607	−	0.955926i	$-0.405144\pi$
$881$	15355.4	0.587215	0.293607	+	0.955926i	$0.405144\pi$
$882$	497.231	0.0189826
$883$	9153.83	0.348868	0.174434	−	0.984669i	$-0.444190\pi$
$883$	9153.83	0.348868	0.174434	+	0.984669i	$0.444190\pi$
$884$	−62857.9	−2.39156
$885$	36879.3	1.40077
$886$	−2333.77	−0.0884926
$887$	23619.1	0.894083	0.447042	−	0.894513i	$-0.352478\pi$
$887$	23619.1	0.894083	0.447042	+	0.894513i	$0.352478\pi$
$888$	−11939.3	−0.451188
$889$	−4170.19	−0.157327
$890$	3929.81	0.148008
$891$	−10738.1	−0.403750
$892$	−21377.1	−0.802420
$893$	−7469.82	−0.279920
$894$	7463.17	0.279201
$895$	−28024.3	−1.04665
$896$	−7929.27	−0.295645
$897$	0	0
$898$	2014.70	0.0748681
$899$	−18514.0	−0.686848
$900$	−1343.49	−0.0497589
$901$	−31581.8	−1.16775
$902$	−804.926	−0.0297130
$903$	15648.2	0.576678
$904$	−4478.70	−0.164778
$905$	10741.9	0.394557
$906$	7051.07	0.258561
$907$	19901.5	0.728575	0.364287	−	0.931287i	$-0.381313\pi$
$907$	19901.5	0.728575	0.364287	+	0.931287i	$0.381313\pi$
$908$	−35873.2	−1.31112
$909$	5190.32	0.189386
$910$	−4038.62	−0.147120
$911$	15534.2	0.564951	0.282475	−	0.959275i	$-0.408844\pi$
$911$	15534.2	0.564951	0.282475	+	0.959275i	$0.408844\pi$
$912$	−6139.30	−0.222908
$913$	10914.6	0.395640
$914$	7889.84	0.285528
$915$	−47111.8	−1.70215
$916$	−15359.3	−0.554025
$917$	6872.79	0.247502
$918$	−7744.46	−0.278437
$919$	5021.93	0.180259	0.0901296	−	0.995930i	$-0.471272\pi$
$919$	5021.93	0.180259	0.0901296	+	0.995930i	$0.471272\pi$
$920$	0	0
$921$	−18949.1	−0.677953
$922$	−1444.99	−0.0516140
$923$	−12130.0	−0.432572
$924$	4544.47	0.161799
$925$	−13410.2	−0.476676
$926$	2537.12	0.0900377
$927$	3612.29	0.127986
$928$	7427.13	0.262724
$929$	33025.9	1.16635	0.583177	−	0.812345i	$-0.301809\pi$
$929$	33025.9	1.16635	0.583177	+	0.812345i	$0.301809\pi$
$930$	−9246.69	−0.326033
$931$	5395.84	0.189948
$932$	3140.46	0.110375
$933$	4876.51	0.171114
$934$	−7133.94	−0.249925
$935$	−19932.5	−0.697180
$936$	−2020.46	−0.0705562
$937$	−19265.7	−0.671700	−0.335850	−	0.941916i	$-0.609023\pi$
$937$	−19265.7	−0.671700	−0.335850	+	0.941916i	$0.609023\pi$
$938$	−1997.54	−0.0695330
$939$	−13052.4	−0.453620
$940$	−39502.5	−1.37067
$941$	51333.4	1.77834	0.889172	−	0.457573i	$-0.151281\pi$
$941$	51333.4	1.77834	0.889172	+	0.457573i	$0.151281\pi$
$942$	−9332.82	−0.322802
$943$	0	0
$944$	28943.3	0.997908
$945$	13892.4	0.478222
$946$	2463.26	0.0846592
$947$	−39799.6	−1.36570	−0.682848	−	0.730560i	$-0.739259\pi$
$947$	−39799.6	−1.36570	−0.682848	+	0.730560i	$0.739259\pi$
$948$	35214.6	1.20645
$949$	47985.6	1.64139
$950$	522.181	0.0178335
$951$	−1146.81	−0.0391040
$952$	7525.34	0.256195
$953$	15167.6	0.515559	0.257779	−	0.966204i	$-0.417009\pi$
$953$	15167.6	0.515559	0.257779	+	0.966204i	$0.417009\pi$
$954$	−498.641	−0.0169225
$955$	659.469	0.0223454
$956$	−27467.2	−0.929241
$957$	−5638.86	−0.190469
$958$	8700.57	0.293427
$959$	620.051	0.0208785
$960$	−29919.7	−1.00589
$961$	27914.7	0.937017
$962$	−9906.31	−0.332009
$963$	729.198	0.0244009
$964$	−38.7229	−0.00129375
$965$	2272.05	0.0757928
$966$	0	0
$967$	−14243.5	−0.473673	−0.236836	−	0.971550i	$-0.576110\pi$
$967$	−14243.5	−0.473673	−0.236836	+	0.971550i	$0.576110\pi$
$968$	−9550.69	−0.317119
$969$	12094.3	0.400956
$970$	148.989	0.00493168
$971$	−53306.9	−1.76179	−0.880896	−	0.473309i	$-0.843059\pi$
$971$	−53306.9	−1.76179	−0.880896	+	0.473309i	$0.843059\pi$
$972$	7319.16	0.241525
$973$	3186.09	0.104976
$974$	−10114.4	−0.332736
$975$	−20308.2	−0.667061
$976$	−36973.8	−1.21261
$977$	2388.35	0.0782090	0.0391045	−	0.999235i	$-0.487549\pi$
$977$	2388.35	0.0782090	0.0391045	+	0.999235i	$0.487549\pi$
$978$	−1633.35	−0.0534037
$979$	−7469.56	−0.243849
$980$	28534.7	0.930109
$981$	−4909.77	−0.159793
$982$	−8190.53	−0.266161
$983$	−10132.0	−0.328749	−0.164375	−	0.986398i	$-0.552561\pi$
$983$	−10132.0	−0.328749	−0.164375	+	0.986398i	$0.552561\pi$
$984$	5258.09	0.170347
$985$	37637.0	1.21748
$986$	−4586.66	−0.148143
$987$	−17084.0	−0.550951
$988$	−10769.9	−0.346797
$989$	0	0
$990$	−314.712	−0.0101032
$991$	55273.5	1.77177	0.885883	−	0.463908i	$-0.153553\pi$
$991$	55273.5	1.77177	0.885883	+	0.463908i	$0.153553\pi$
$992$	−23149.4	−0.740921
$993$	−47391.6	−1.51453
$994$	713.328	0.0227620
$995$	−12730.0	−0.405596
$996$	−35021.9	−1.11417
$997$	11176.8	0.355037	0.177519	−	0.984117i	$-0.443193\pi$
$997$	11176.8	0.355037	0.177519	+	0.984117i	$0.443193\pi$
$998$	2364.14	0.0749856
$999$	34076.6	1.07922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.12		25
23.5	odd	22		23.4.c.a.2.3	✓	50
23.14	odd	22		23.4.c.a.12.3	yes	50
23.22	odd	2		529.4.a.n.1.12		25
69.5	even	22		207.4.i.a.163.3		50
69.14	even	22		207.4.i.a.127.3		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.2.3	✓	50	23.5	odd	22
23.4.c.a.12.3	yes	50	23.14	odd	22
207.4.i.a.127.3		50	69.14	even	22
207.4.i.a.163.3		50	69.5	even	22
529.4.a.m.1.12		25	1.1	even	1	trivial
529.4.a.n.1.12		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)

\(f(q)\)	\(=\)	\(q-0.525953 q^{2} +5.51332 q^{3} -7.72337 q^{4} +13.2745 q^{5} -2.89975 q^{6} -8.04220 q^{7} +8.26975 q^{8} +3.39674 q^{9} -6.98174 q^{10} +13.2705 q^{11} -42.5815 q^{12} -71.9274 q^{13} +4.22982 q^{14} +73.1864 q^{15} +57.4375 q^{16} -113.151 q^{17} -1.78653 q^{18} -19.3870 q^{19} -102.524 q^{20} -44.3393 q^{21} -6.97966 q^{22} +45.5938 q^{24} +51.2112 q^{25} +37.8304 q^{26} -130.132 q^{27} +62.1129 q^{28} -77.0710 q^{29} -38.4926 q^{30} +240.220 q^{31} -96.3674 q^{32} +73.1646 q^{33} +59.5121 q^{34} -106.756 q^{35} -26.2343 q^{36} -261.861 q^{37} +10.1966 q^{38} -396.559 q^{39} +109.776 q^{40} +115.325 q^{41} +23.3204 q^{42} -352.920 q^{43} -102.493 q^{44} +45.0899 q^{45} +385.301 q^{47} +316.671 q^{48} -278.323 q^{49} -26.9347 q^{50} -623.838 q^{51} +555.522 q^{52} +279.112 q^{53} +68.4435 q^{54} +176.159 q^{55} -66.5070 q^{56} -106.887 q^{57} +40.5357 q^{58} +503.910 q^{59} -565.246 q^{60} -643.723 q^{61} -126.344 q^{62} -27.3173 q^{63} -408.815 q^{64} -954.797 q^{65} -38.4811 q^{66} -472.252 q^{67} +873.908 q^{68} +56.1486 q^{70} +168.643 q^{71} +28.0902 q^{72} -667.140 q^{73} +137.727 q^{74} +282.344 q^{75} +149.733 q^{76} -106.724 q^{77} +208.571 q^{78} -826.993 q^{79} +762.451 q^{80} -809.174 q^{81} -60.6553 q^{82} +822.468 q^{83} +342.449 q^{84} -1502.02 q^{85} +185.619 q^{86} -424.917 q^{87} +109.744 q^{88} -562.870 q^{89} -23.7152 q^{90} +578.454 q^{91} +1324.41 q^{93} -202.650 q^{94} -257.351 q^{95} -531.305 q^{96} -21.3397 q^{97} +146.385 q^{98} +45.0765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 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

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Database

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