LMFDB - Embedded newform 1573.4.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 69 x^{13} + 418 x^{12} + 1806 x^{11} - 10742 x^{10} - 24098 x^{9} + 129758 x^{8} + \cdots + 47232 $ x^15 - 6x^14 - 69x^13 + 418x^12 + 1806x^11 - 10742x^10 - 24098x^9 + 129758x^8 + 183825x^7 - 750764x^6 - 813769x^5 + 1744424x^4 + 1731312x^3 - 516000x^2 - 352704x + 47232
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.65412$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65412 q^{2} +7.25625 q^{3} -0.955648 q^{4} +11.9209 q^{5} -19.2590 q^{6} +3.65834 q^{7} +23.7694 q^{8} +25.6532 q^{9} +O(q^{10})$	\(q-2.65412 q^{2} +7.25625 q^{3} -0.955648 q^{4} +11.9209 q^{5} -19.2590 q^{6} +3.65834 q^{7} +23.7694 q^{8} +25.6532 q^{9} -31.6396 q^{10} -6.93442 q^{12} -13.0000 q^{13} -9.70966 q^{14} +86.5014 q^{15} -55.4416 q^{16} -118.137 q^{17} -68.0866 q^{18} -69.1714 q^{19} -11.3922 q^{20} +26.5458 q^{21} +208.988 q^{23} +172.476 q^{24} +17.1090 q^{25} +34.5036 q^{26} -9.77282 q^{27} -3.49608 q^{28} -39.8398 q^{29} -229.585 q^{30} -104.663 q^{31} -43.0064 q^{32} +313.550 q^{34} +43.6108 q^{35} -24.5154 q^{36} -337.188 q^{37} +183.589 q^{38} -94.3313 q^{39} +283.353 q^{40} -25.9773 q^{41} -70.4558 q^{42} -366.694 q^{43} +305.810 q^{45} -554.678 q^{46} -274.572 q^{47} -402.298 q^{48} -329.617 q^{49} -45.4095 q^{50} -857.231 q^{51} +12.4234 q^{52} +84.7894 q^{53} +25.9382 q^{54} +86.9563 q^{56} -501.925 q^{57} +105.740 q^{58} +50.5991 q^{59} -82.6649 q^{60} -213.089 q^{61} +277.788 q^{62} +93.8480 q^{63} +557.677 q^{64} -154.972 q^{65} +420.089 q^{67} +112.897 q^{68} +1516.47 q^{69} -115.748 q^{70} +276.541 q^{71} +609.760 q^{72} -1167.74 q^{73} +894.938 q^{74} +124.148 q^{75} +66.1036 q^{76} +250.366 q^{78} +23.3747 q^{79} -660.916 q^{80} -763.550 q^{81} +68.9468 q^{82} -731.478 q^{83} -25.3685 q^{84} -1408.30 q^{85} +973.251 q^{86} -289.088 q^{87} +494.579 q^{89} -811.657 q^{90} -47.5584 q^{91} -199.719 q^{92} -759.459 q^{93} +728.748 q^{94} -824.589 q^{95} -312.065 q^{96} +1554.47 q^{97} +874.842 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) $ 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9} + 16 q^{10} - 3 q^{12} - 195 q^{13} + 60 q^{14} + 202 q^{15} + 282 q^{16} - 136 q^{17} - 351 q^{18} - 136 q^{19} - 62 q^{20} - 625 q^{21} - 176 q^{23} + 227 q^{24} + 479 q^{25} + 78 q^{26} - 13 q^{27} + 86 q^{28} - 344 q^{29} - 542 q^{30} + 275 q^{31} + 170 q^{32} - 1505 q^{34} - 655 q^{35} + 623 q^{36} + 346 q^{37} - 848 q^{38} - 26 q^{39} - 256 q^{40} - 38 q^{41} + 575 q^{42} - 534 q^{43} - 633 q^{45} + 375 q^{46} + 276 q^{47} - 723 q^{48} + 773 q^{49} - 1684 q^{50} - 1111 q^{51} - 702 q^{52} + 706 q^{53} + 178 q^{54} - 2056 q^{56} - 1320 q^{57} - 983 q^{58} - 174 q^{59} + 2004 q^{60} - 1078 q^{61} - 1365 q^{62} + 2055 q^{63} + 1338 q^{64} + 26 q^{65} - 260 q^{67} - 559 q^{68} + 154 q^{69} - 1161 q^{70} + 2910 q^{71} - 6171 q^{72} - 1000 q^{73} - 688 q^{74} - 553 q^{75} - 178 q^{76} - 325 q^{78} + 386 q^{79} + 1702 q^{80} - 2805 q^{81} + 3380 q^{82} - 4318 q^{83} - 6681 q^{84} + 1391 q^{85} + 4139 q^{86} - 3144 q^{87} - 810 q^{89} + 3789 q^{90} + 364 q^{91} - 4857 q^{92} + 394 q^{93} + 116 q^{94} - 5204 q^{95} + 893 q^{96} - 1860 q^{97} - 8 q^{98}+O(q^{100}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9 + 16 * q^10 - 3 * q^12 - 195 * q^13 + 60 * q^14 + 202 * q^15 + 282 * q^16 - 136 * q^17 - 351 * q^18 - 136 * q^19 - 62 * q^20 - 625 * q^21 - 176 * q^23 + 227 * q^24 + 479 * q^25 + 78 * q^26 - 13 * q^27 + 86 * q^28 - 344 * q^29 - 542 * q^30 + 275 * q^31 + 170 * q^32 - 1505 * q^34 - 655 * q^35 + 623 * q^36 + 346 * q^37 - 848 * q^38 - 26 * q^39 - 256 * q^40 - 38 * q^41 + 575 * q^42 - 534 * q^43 - 633 * q^45 + 375 * q^46 + 276 * q^47 - 723 * q^48 + 773 * q^49 - 1684 * q^50 - 1111 * q^51 - 702 * q^52 + 706 * q^53 + 178 * q^54 - 2056 * q^56 - 1320 * q^57 - 983 * q^58 - 174 * q^59 + 2004 * q^60 - 1078 * q^61 - 1365 * q^62 + 2055 * q^63 + 1338 * q^64 + 26 * q^65 - 260 * q^67 - 559 * q^68 + 154 * q^69 - 1161 * q^70 + 2910 * q^71 - 6171 * q^72 - 1000 * q^73 - 688 * q^74 - 553 * q^75 - 178 * q^76 - 325 * q^78 + 386 * q^79 + 1702 * q^80 - 2805 * q^81 + 3380 * q^82 - 4318 * q^83 - 6681 * q^84 + 1391 * q^85 + 4139 * q^86 - 3144 * q^87 - 810 * q^89 + 3789 * q^90 + 364 * q^91 - 4857 * q^92 + 394 * q^93 + 116 * q^94 - 5204 * q^95 + 893 * q^96 - 1860 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−2.65412	−0.938373	−0.469187	−	0.883099i	$-0.655453\pi$
$2$	−2.65412	−0.938373	−0.469187	+	0.883099i	$0.655453\pi$
$3$	7.25625	1.39647	0.698233	−	0.715870i	$-0.253970\pi$
$3$	7.25625	1.39647	0.698233	+	0.715870i	$0.253970\pi$
$4$	−0.955648	−0.119456
$5$	11.9209	1.06624	0.533121	−	0.846039i	$-0.321019\pi$
$5$	11.9209	1.06624	0.533121	+	0.846039i	$0.321019\pi$
$6$	−19.2590	−1.31041
$7$	3.65834	0.197532	0.0987658	−	0.995111i	$-0.468511\pi$
$7$	3.65834	0.197532	0.0987658	+	0.995111i	$0.468511\pi$
$8$	23.7694	1.05047
$9$	25.6532	0.950118
$10$	−31.6396	−1.00053
$11$	0	0
$11$	0	0
$12$	−6.93442	−0.166816
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−9.70966	−0.185358
$15$	86.5014	1.48897
$16$	−55.4416	−0.866274
$17$	−118.137	−1.68544	−0.842718	−	0.538355i	$-0.819046\pi$
$17$	−118.137	−1.68544	−0.842718	+	0.538355i	$0.819046\pi$
$18$	−68.0866	−0.891565
$19$	−69.1714	−0.835211	−0.417606	−	0.908628i	$-0.637131\pi$
$19$	−69.1714	−0.835211	−0.417606	+	0.908628i	$0.637131\pi$
$20$	−11.3922	−0.127369
$21$	26.5458	0.275846
$22$	0	0
$23$	208.988	1.89465	0.947325	−	0.320275i	$-0.103775\pi$
$23$	208.988	1.89465	0.947325	+	0.320275i	$0.103775\pi$
$24$	172.476	1.46694
$25$	17.1090	0.136872
$26$	34.5036	0.260258
$27$	−9.77282	−0.0696585
$28$	−3.49608	−0.0235963
$29$	−39.8398	−0.255106	−0.127553	−	0.991832i	$-0.540712\pi$
$29$	−39.8398	−0.255106	−0.127553	+	0.991832i	$0.540712\pi$
$30$	−229.585	−1.39721
$31$	−104.663	−0.606387	−0.303193	−	0.952929i	$-0.598053\pi$
$31$	−104.663	−0.606387	−0.303193	+	0.952929i	$0.598053\pi$
$32$	−43.0064	−0.237579
$33$	0	0
$34$	313.550	1.58157
$35$	43.6108	0.210617
$36$	−24.5154	−0.113497
$37$	−337.188	−1.49820	−0.749100	−	0.662457i	$-0.769514\pi$
$37$	−337.188	−1.49820	−0.749100	+	0.662457i	$0.769514\pi$
$38$	183.589	0.783740
$39$	−94.3313	−0.387310
$40$	283.353	1.12005
$41$	−25.9773	−0.0989505	−0.0494753	−	0.998775i	$-0.515755\pi$
$41$	−25.9773	−0.0989505	−0.0494753	+	0.998775i	$0.515755\pi$
$42$	−70.4558	−0.258847
$43$	−366.694	−1.30047	−0.650237	−	0.759732i	$-0.725330\pi$
$43$	−366.694	−1.30047	−0.650237	+	0.759732i	$0.725330\pi$
$44$	0	0
$45$	305.810	1.01306
$46$	−554.678	−1.77789
$47$	−274.572	−0.852138	−0.426069	−	0.904691i	$-0.640102\pi$
$47$	−274.572	−0.852138	−0.426069	+	0.904691i	$0.640102\pi$
$48$	−402.298	−1.20972
$49$	−329.617	−0.960981
$50$	−45.4095	−0.128437
$51$	−857.231	−2.35365
$52$	12.4234	0.0331311
$53$	84.7894	0.219749	0.109875	−	0.993945i	$-0.464955\pi$
$53$	84.7894	0.219749	0.109875	+	0.993945i	$0.464955\pi$
$54$	25.9382	0.0653657
$55$	0	0
$56$	86.9563	0.207500
$57$	−501.925	−1.16634
$58$	105.740	0.239385
$59$	50.5991	0.111651	0.0558257	−	0.998441i	$-0.482221\pi$
$59$	50.5991	0.111651	0.0558257	+	0.998441i	$0.482221\pi$
$60$	−82.6649	−0.177867
$61$	−213.089	−0.447266	−0.223633	−	0.974673i	$-0.571792\pi$
$61$	−213.089	−0.447266	−0.223633	+	0.974673i	$0.571792\pi$
$62$	277.788	0.569017
$63$	93.8480	0.187678
$64$	557.677	1.08921
$65$	−154.972	−0.295722
$66$	0	0
$67$	420.089	0.766000	0.383000	−	0.923748i	$-0.374891\pi$
$67$	420.089	0.766000	0.383000	+	0.923748i	$0.374891\pi$
$68$	112.897	0.201336
$69$	1516.47	2.64581
$70$	−115.748	−0.197637
$71$	276.541	0.462245	0.231122	−	0.972925i	$-0.425760\pi$
$71$	276.541	0.462245	0.231122	+	0.972925i	$0.425760\pi$
$72$	609.760	0.998068
$73$	−1167.74	−1.87224	−0.936120	−	0.351680i	$-0.885610\pi$
$73$	−1167.74	−1.87224	−0.936120	+	0.351680i	$0.885610\pi$
$74$	894.938	1.40587
$75$	124.148	0.191138
$76$	66.1036	0.0997710
$77$	0	0
$78$	250.366	0.363441
$79$	23.3747	0.0332893	0.0166446	−	0.999861i	$-0.494702\pi$
$79$	23.3747	0.0332893	0.0166446	+	0.999861i	$0.494702\pi$
$80$	−660.916	−0.923658
$81$	−763.550	−1.04739
$82$	68.9468	0.0928525
$83$	−731.478	−0.967351	−0.483676	−	0.875247i	$-0.660699\pi$
$83$	−731.478	−0.967351	−0.483676	+	0.875247i	$0.660699\pi$
$84$	−25.3685	−0.0329515
$85$	−1408.30	−1.79708
$86$	973.251	1.22033
$87$	−289.088	−0.356247
$88$	0	0
$89$	494.579	0.589048	0.294524	−	0.955644i	$-0.404839\pi$
$89$	494.579	0.589048	0.294524	+	0.955644i	$0.404839\pi$
$90$	−811.657	−0.950624
$91$	−47.5584	−0.0547854
$92$	−199.719	−0.226327
$93$	−759.459	−0.846799
$94$	728.748	0.799623
$95$	−824.589	−0.890537
$96$	−312.065	−0.331771
$97$	1554.47	1.62714	0.813568	−	0.581469i	$-0.197522\pi$
$97$	1554.47	1.62714	0.813568	+	0.581469i	$0.197522\pi$
$98$	874.842	0.901759
$99$	0	0
$100$	−16.3502	−0.0163502
$101$	509.777	0.502225	0.251113	−	0.967958i	$-0.419204\pi$
$101$	509.777	0.502225	0.251113	+	0.967958i	$0.419204\pi$
$102$	2275.19	2.20861
$103$	−1021.84	−0.977521	−0.488761	−	0.872418i	$-0.662551\pi$
$103$	−1021.84	−0.977521	−0.488761	+	0.872418i	$0.662551\pi$
$104$	−309.002	−0.291347
$105$	316.451	0.294119
$106$	−225.041	−0.206207
$107$	−689.844	−0.623269	−0.311634	−	0.950202i	$-0.600876\pi$
$107$	−689.844	−0.623269	−0.311634	+	0.950202i	$0.600876\pi$
$108$	9.33938	0.00832113
$109$	−525.557	−0.461828	−0.230914	−	0.972974i	$-0.574172\pi$
$109$	−525.557	−0.461828	−0.230914	+	0.972974i	$0.574172\pi$
$110$	0	0
$111$	−2446.72	−2.09219
$112$	−202.824	−0.171117
$113$	479.225	0.398953	0.199477	−	0.979903i	$-0.436076\pi$
$113$	479.225	0.398953	0.199477	+	0.979903i	$0.436076\pi$
$114$	1332.17	1.09447
$115$	2491.33	2.02015
$116$	38.0729	0.0304739
$117$	−333.491	−0.263515
$118$	−134.296	−0.104771
$119$	−432.185	−0.332927
$120$	2056.08	1.56412
$121$	0	0
$122$	565.563	0.419702
$123$	−188.498	−0.138181
$124$	100.021	0.0724366
$125$	−1286.16	−0.920303
$126$	−249.084	−0.176112
$127$	850.217	0.594052	0.297026	−	0.954869i	$-0.404005\pi$
$127$	850.217	0.594052	0.297026	+	0.954869i	$0.404005\pi$
$128$	−1136.09	−0.784508
$129$	−2660.83	−1.81607
$130$	411.315	0.277498
$131$	2570.68	1.71451	0.857256	−	0.514891i	$-0.172168\pi$
$131$	2570.68	1.71451	0.857256	+	0.514891i	$0.172168\pi$
$132$	0	0
$133$	−253.052	−0.164981
$134$	−1114.97	−0.718794
$135$	−116.501	−0.0742728
$136$	−2808.04	−1.77050
$137$	90.5655	0.0564784	0.0282392	−	0.999601i	$-0.491010\pi$
$137$	90.5655	0.0564784	0.0282392	+	0.999601i	$0.491010\pi$
$138$	−4024.88	−2.48276
$139$	2339.29	1.42745	0.713727	−	0.700424i	$-0.247006\pi$
$139$	2339.29	1.42745	0.713727	+	0.700424i	$0.247006\pi$
$140$	−41.6766	−0.0251594
$141$	−1992.37	−1.18998
$142$	−733.973	−0.433758
$143$	0	0
$144$	−1422.25	−0.823063
$145$	−474.929	−0.272005
$146$	3099.32	1.75686
$147$	−2391.78	−1.34198
$148$	322.233	0.178969
$149$	−426.255	−0.234364	−0.117182	−	0.993110i	$-0.537386\pi$
$149$	−426.255	−0.234364	−0.117182	+	0.993110i	$0.537386\pi$
$150$	−329.502	−0.179358
$151$	−2609.19	−1.40618	−0.703088	−	0.711103i	$-0.748196\pi$
$151$	−2609.19	−1.40618	−0.703088	+	0.711103i	$0.748196\pi$
$152$	−1644.16	−0.877362
$153$	−3030.59	−1.60136
$154$	0	0
$155$	−1247.68	−0.646555
$156$	90.1475	0.0462665
$157$	−350.937	−0.178394	−0.0891969	−	0.996014i	$-0.528430\pi$
$157$	−350.937	−0.178394	−0.0891969	+	0.996014i	$0.528430\pi$
$158$	−62.0391	−0.0312378
$159$	615.253	0.306873
$160$	−512.677	−0.253317
$161$	764.547	0.374253
$162$	2026.55	0.982846
$163$	266.357	0.127992	0.0639959	−	0.997950i	$-0.479616\pi$
$163$	266.357	0.127992	0.0639959	+	0.997950i	$0.479616\pi$
$164$	24.8251	0.0118202
$165$	0	0
$166$	1941.43	0.907736
$167$	3635.80	1.68471	0.842356	−	0.538922i	$-0.181168\pi$
$167$	3635.80	1.68471	0.842356	+	0.538922i	$0.181168\pi$
$168$	630.977	0.289767
$169$	169.000	0.0769231
$170$	3737.81	1.68633
$171$	−1774.47	−0.793549
$172$	350.431	0.155349
$173$	1534.28	0.674274	0.337137	−	0.941456i	$-0.390541\pi$
$173$	1534.28	0.674274	0.337137	+	0.941456i	$0.390541\pi$
$174$	767.274	0.334292
$175$	62.5906	0.0270366
$176$	0	0
$177$	367.160	0.155918
$178$	−1312.67	−0.552747
$179$	3820.80	1.59542	0.797709	−	0.603042i	$-0.206045\pi$
$179$	3820.80	1.59542	0.797709	+	0.603042i	$0.206045\pi$
$180$	−292.247	−0.121016
$181$	−4155.41	−1.70646	−0.853229	−	0.521536i	$-0.825359\pi$
$181$	−4155.41	−1.70646	−0.853229	+	0.521536i	$0.825359\pi$
$182$	126.226	0.0514091
$183$	−1546.23	−0.624592
$184$	4967.50	1.99027
$185$	−4019.61	−1.59744
$186$	2015.70	0.794613
$187$	0	0
$188$	262.394	0.101793
$189$	−35.7523	−0.0137598
$190$	2188.56	0.835656
$191$	4287.34	1.62419	0.812096	−	0.583524i	$-0.198327\pi$
$191$	4287.34	1.62419	0.812096	+	0.583524i	$0.198327\pi$
$192$	4046.64	1.52105
$193$	−1907.21	−0.711314	−0.355657	−	0.934617i	$-0.615743\pi$
$193$	−1907.21	−0.711314	−0.355657	+	0.934617i	$0.615743\pi$
$194$	−4125.74	−1.52686
$195$	−1124.52	−0.412966
$196$	314.998	0.114795
$197$	−131.036	−0.0473904	−0.0236952	−	0.999719i	$-0.507543\pi$
$197$	−131.036	−0.0473904	−0.0236952	+	0.999719i	$0.507543\pi$
$198$	0	0
$199$	−3451.55	−1.22952	−0.614759	−	0.788715i	$-0.710747\pi$
$199$	−3451.55	−1.22952	−0.614759	+	0.788715i	$0.710747\pi$
$200$	406.671	0.143780
$201$	3048.27	1.06969
$202$	−1353.01	−0.471274
$203$	−145.748	−0.0503915
$204$	819.212	0.281158
$205$	−309.674	−0.105505
$206$	2712.08	0.917280
$207$	5361.20	1.80014
$208$	720.740	0.240261
$209$	0	0
$210$	−839.900	−0.275993
$211$	4232.37	1.38089	0.690447	−	0.723383i	$-0.257414\pi$
$211$	4232.37	1.38089	0.690447	+	0.723383i	$0.257414\pi$
$212$	−81.0288	−0.0262504
$213$	2006.65	0.645509
$214$	1830.93	0.584859
$215$	−4371.35	−1.38662
$216$	−232.294	−0.0731740
$217$	−382.892	−0.119781
$218$	1394.89	0.433367
$219$	−8473.41	−2.61452
$220$	0	0
$221$	1535.78	0.467456
$222$	6493.90	1.96325
$223$	−4194.21	−1.25948	−0.629742	−	0.776804i	$-0.716840\pi$
$223$	−4194.21	−1.25948	−0.629742	+	0.776804i	$0.716840\pi$
$224$	−157.332	−0.0469294
$225$	438.901	0.130045
$226$	−1271.92	−0.374367
$227$	3450.40	1.00886	0.504430	−	0.863452i	$-0.331703\pi$
$227$	3450.40	1.00886	0.504430	+	0.863452i	$0.331703\pi$
$228$	479.664	0.139327
$229$	21.9236	0.00632643	0.00316321	−	0.999995i	$-0.498993\pi$
$229$	21.9236	0.00632643	0.00316321	+	0.999995i	$0.498993\pi$
$230$	−6612.29	−1.89566
$231$	0	0
$232$	−946.968	−0.267981
$233$	915.102	0.257298	0.128649	−	0.991690i	$-0.458936\pi$
$233$	915.102	0.257298	0.128649	+	0.991690i	$0.458936\pi$
$234$	885.126	0.247276
$235$	−3273.16	−0.908585
$236$	−48.3549	−0.0133374
$237$	169.612	0.0464874
$238$	1147.07	0.312410
$239$	5797.13	1.56898	0.784488	−	0.620143i	$-0.212926\pi$
$239$	5797.13	1.56898	0.784488	+	0.620143i	$0.212926\pi$
$240$	−4795.77	−1.28986
$241$	64.3466	0.0171989	0.00859944	−	0.999963i	$-0.497263\pi$
$241$	64.3466	0.0171989	0.00859944	+	0.999963i	$0.497263\pi$
$242$	0	0
$243$	−5276.65	−1.39299
$244$	203.638	0.0534286
$245$	−3929.34	−1.02464
$246$	500.296	0.129665
$247$	899.229	0.231646
$248$	−2487.77	−0.636989
$249$	−5307.79	−1.35087
$250$	3413.63	0.863588
$251$	−2028.54	−0.510122	−0.255061	−	0.966925i	$-0.582096\pi$
$251$	−2028.54	−0.510122	−0.255061	+	0.966925i	$0.582096\pi$
$252$	−89.6857	−0.0224193
$253$	0	0
$254$	−2256.58	−0.557442
$255$	−10219.0	−2.50957
$256$	−1446.10	−0.353051
$257$	−5817.42	−1.41199	−0.705994	−	0.708218i	$-0.749499\pi$
$257$	−5817.42	−1.41199	−0.705994	+	0.708218i	$0.749499\pi$
$258$	7062.15	1.70415
$259$	−1233.55	−0.295942
$260$	148.099	0.0353258
$261$	−1022.02	−0.242381
$262$	−6822.88	−1.60885
$263$	70.7961	0.0165988	0.00829938	−	0.999966i	$-0.497358\pi$
$263$	70.7961	0.0165988	0.00829938	+	0.999966i	$0.497358\pi$
$264$	0	0
$265$	1010.77	0.234306
$266$	671.631	0.154813
$267$	3588.79	0.822586
$268$	−401.457	−0.0915034
$269$	1248.77	0.283043	0.141521	−	0.989935i	$-0.454801\pi$
$269$	1248.77	0.283043	0.141521	+	0.989935i	$0.454801\pi$
$270$	309.208	0.0696956
$271$	−3911.83	−0.876852	−0.438426	−	0.898767i	$-0.644464\pi$
$271$	−3911.83	−0.876852	−0.438426	+	0.898767i	$0.644464\pi$
$272$	6549.69	1.46005
$273$	−345.096	−0.0765060
$274$	−240.372	−0.0529978
$275$	0	0
$276$	−1449.21	−0.316058
$277$	−6314.04	−1.36958	−0.684790	−	0.728740i	$-0.740106\pi$
$277$	−6314.04	−1.36958	−0.684790	+	0.728740i	$0.740106\pi$
$278$	−6208.76	−1.33948
$279$	−2684.93	−0.576139
$280$	1036.60	0.221246
$281$	−919.436	−0.195192	−0.0975960	−	0.995226i	$-0.531115\pi$
$281$	−919.436	−0.195192	−0.0975960	+	0.995226i	$0.531115\pi$
$282$	5287.98	1.11665
$283$	−4031.48	−0.846807	−0.423403	−	0.905941i	$-0.639165\pi$
$283$	−4031.48	−0.846807	−0.423403	+	0.905941i	$0.639165\pi$
$284$	−264.276	−0.0552179
$285$	−5983.43	−1.24361
$286$	0	0
$287$	−95.0337	−0.0195459
$288$	−1103.25	−0.225728
$289$	9043.33	1.84070
$290$	1260.52	0.255242
$291$	11279.6	2.27224
$292$	1115.95	0.223650
$293$	6110.44	1.21835	0.609173	−	0.793037i	$-0.291501\pi$
$293$	6110.44	1.21835	0.609173	+	0.793037i	$0.291501\pi$
$294$	6348.07	1.25928
$295$	603.189	0.119048
$296$	−8014.75	−1.57381
$297$	0	0
$298$	1131.33	0.219921
$299$	−2716.84	−0.525481
$300$	−118.641	−0.0228325
$301$	−1341.49	−0.256885
$302$	6925.09	1.31952
$303$	3699.07	0.701340
$304$	3834.97	0.723522
$305$	−2540.22	−0.476894
$306$	8043.55	1.50268
$307$	7585.80	1.41024	0.705122	−	0.709086i	$-0.250892\pi$
$307$	7585.80	1.41024	0.705122	+	0.709086i	$0.250892\pi$
$308$	0	0
$309$	−7414.71	−1.36508
$310$	3311.49	0.606710
$311$	4317.06	0.787132	0.393566	−	0.919296i	$-0.371241\pi$
$311$	4317.06	0.787132	0.393566	+	0.919296i	$0.371241\pi$
$312$	−2242.19	−0.406857
$313$	−5998.86	−1.08331	−0.541654	−	0.840601i	$-0.682202\pi$
$313$	−5998.86	−1.08331	−0.541654	+	0.840601i	$0.682202\pi$
$314$	931.429	0.167400
$315$	1118.76	0.200111
$316$	−22.3380	−0.00397661
$317$	−5519.25	−0.977892	−0.488946	−	0.872314i	$-0.662618\pi$
$317$	−5519.25	−0.977892	−0.488946	+	0.872314i	$0.662618\pi$
$318$	−1632.95	−0.287961
$319$	0	0
$320$	6648.03	1.16136
$321$	−5005.68	−0.870374
$322$	−2029.20	−0.351189
$323$	8171.70	1.40770
$324$	729.685	0.125118
$325$	−222.418	−0.0379616
$326$	−706.942	−0.120104
$327$	−3813.57	−0.644927
$328$	−617.464	−0.103944
$329$	−1004.48	−0.168324
$330$	0	0
$331$	−1738.83	−0.288746	−0.144373	−	0.989523i	$-0.546116\pi$
$331$	−1738.83	−0.288746	−0.144373	+	0.989523i	$0.546116\pi$
$332$	699.036	0.115556
$333$	−8649.95	−1.42347
$334$	−9649.86	−1.58089
$335$	5007.86	0.816742
$336$	−1471.74	−0.238958
$337$	−2884.79	−0.466304	−0.233152	−	0.972440i	$-0.574904\pi$
$337$	−2884.79	−0.466304	−0.233152	+	0.972440i	$0.574904\pi$
$338$	−448.546	−0.0721825
$339$	3477.38	0.557125
$340$	1345.84	0.214672
$341$	0	0
$342$	4709.65	0.744645
$343$	−2460.66	−0.387356
$344$	−8716.09	−1.36611
$345$	18077.7	2.82108
$346$	−4072.17	−0.632720
$347$	1392.68	0.215455	0.107728	−	0.994180i	$-0.465643\pi$
$347$	1392.68	0.215455	0.107728	+	0.994180i	$0.465643\pi$
$348$	276.266	0.0425558
$349$	−7018.70	−1.07651	−0.538256	−	0.842782i	$-0.680916\pi$
$349$	−7018.70	−1.07651	−0.538256	+	0.842782i	$0.680916\pi$
$350$	−166.123	−0.0253704
$351$	127.047	0.0193198
$352$	0	0
$353$	−1312.46	−0.197891	−0.0989453	−	0.995093i	$-0.531547\pi$
$353$	−1312.46	−0.197891	−0.0989453	+	0.995093i	$0.531547\pi$
$354$	−974.486	−0.146309
$355$	3296.63	0.492865
$356$	−472.644	−0.0703654
$357$	−3136.04	−0.464921
$358$	−10140.9	−1.49710
$359$	−195.398	−0.0287262	−0.0143631	−	0.999897i	$-0.504572\pi$
$359$	−195.398	−0.0287262	−0.0143631	+	0.999897i	$0.504572\pi$
$360$	7268.92	1.06418
$361$	−2074.31	−0.302422
$362$	11029.0	1.60129
$363$	0	0
$364$	45.4491	0.00654445
$365$	−13920.6	−1.99626
$366$	4103.87	0.586100
$367$	−1608.80	−0.228825	−0.114412	−	0.993433i	$-0.536499\pi$
$367$	−1608.80	−0.228825	−0.114412	+	0.993433i	$0.536499\pi$
$368$	−11586.6	−1.64129
$369$	−666.400	−0.0940147
$370$	10668.5	1.49900
$371$	310.188	0.0434074
$372$	725.776	0.101155
$373$	5197.94	0.721552	0.360776	−	0.932652i	$-0.382512\pi$
$373$	5197.94	0.721552	0.360776	+	0.932652i	$0.382512\pi$
$374$	0	0
$375$	−9332.72	−1.28517
$376$	−6526.41	−0.895143
$377$	517.918	0.0707537
$378$	94.8908	0.0129118
$379$	−6330.50	−0.857984	−0.428992	−	0.903308i	$-0.641131\pi$
$379$	−6330.50	−0.857984	−0.428992	+	0.903308i	$0.641131\pi$
$380$	788.017	0.106380
$381$	6169.39	0.829573
$382$	−11379.1	−1.52410
$383$	−13372.4	−1.78406	−0.892031	−	0.451974i	$-0.850720\pi$
$383$	−13372.4	−1.78406	−0.892031	+	0.451974i	$0.850720\pi$
$384$	−8243.75	−1.09554
$385$	0	0
$386$	5061.95	0.667478
$387$	−9406.88	−1.23560
$388$	−1485.52	−0.194371
$389$	−11984.5	−1.56205	−0.781025	−	0.624500i	$-0.785303\pi$
$389$	−11984.5	−1.56205	−0.781025	+	0.624500i	$0.785303\pi$
$390$	2984.61	0.387516
$391$	−24689.2	−3.19331
$392$	−7834.78	−1.00948
$393$	18653.5	2.39426
$394$	347.784	0.0444699
$395$	278.648	0.0354945
$396$	0	0
$397$	−3857.35	−0.487645	−0.243822	−	0.969820i	$-0.578401\pi$
$397$	−3857.35	−0.487645	−0.243822	+	0.969820i	$0.578401\pi$
$398$	9160.84	1.15375
$399$	−1836.21	−0.230390
$400$	−948.552	−0.118569
$401$	−5026.35	−0.625945	−0.312973	−	0.949762i	$-0.601325\pi$
$401$	−5026.35	−0.625945	−0.312973	+	0.949762i	$0.601325\pi$
$402$	−8090.48	−1.00377
$403$	1360.62	0.168181
$404$	−487.168	−0.0599938
$405$	−9102.24	−1.11678
$406$	386.831	0.0472860
$407$	0	0
$408$	−20375.8	−2.47244
$409$	13907.1	1.68132	0.840662	−	0.541560i	$-0.182166\pi$
$409$	13907.1	1.68132	0.840662	+	0.541560i	$0.182166\pi$
$410$	821.912	0.0990032
$411$	657.166	0.0788701
$412$	976.518	0.116771
$413$	185.108	0.0220547
$414$	−14229.3	−1.68920
$415$	−8719.91	−1.03143
$416$	559.083	0.0658926
$417$	16974.5	1.99339
$418$	0	0
$419$	−10562.2	−1.23150	−0.615751	−	0.787941i	$-0.711147\pi$
$419$	−10562.2	−1.23150	−0.615751	+	0.787941i	$0.711147\pi$
$420$	−302.416	−0.0351343
$421$	−3567.35	−0.412974	−0.206487	−	0.978449i	$-0.566203\pi$
$421$	−3567.35	−0.412974	−0.206487	+	0.978449i	$0.566203\pi$
$422$	−11233.2	−1.29579
$423$	−7043.65	−0.809631
$424$	2015.39	0.230839
$425$	−2021.21	−0.230690
$426$	−5325.89	−0.605728
$427$	−779.550	−0.0883491
$428$	659.249	0.0744532
$429$	0	0
$430$	11602.1	1.30117
$431$	−9345.52	−1.04445	−0.522225	−	0.852808i	$-0.674898\pi$
$431$	−9345.52	−1.04445	−0.522225	+	0.852808i	$0.674898\pi$
$432$	541.820	0.0603434
$433$	−11741.5	−1.30314	−0.651572	−	0.758587i	$-0.725890\pi$
$433$	−11741.5	−1.30314	−0.651572	+	0.758587i	$0.725890\pi$
$434$	1016.24	0.112399
$435$	−3446.20	−0.379845
$436$	502.248	0.0551681
$437$	−14456.0	−1.58243
$438$	22489.4	2.45340
$439$	7285.94	0.792116	0.396058	−	0.918225i	$-0.370378\pi$
$439$	7285.94	0.792116	0.396058	+	0.918225i	$0.370378\pi$
$440$	0	0
$441$	−8455.72	−0.913046
$442$	−4076.14	−0.438648
$443$	5133.90	0.550607	0.275303	−	0.961357i	$-0.411222\pi$
$443$	5133.90	0.550607	0.275303	+	0.961357i	$0.411222\pi$
$444$	2338.21	0.249924
$445$	5895.85	0.628068
$446$	11131.9	1.18187
$447$	−3093.02	−0.327281
$448$	2040.17	0.215154
$449$	14201.9	1.49272	0.746358	−	0.665545i	$-0.231801\pi$
$449$	14201.9	1.49272	0.746358	+	0.665545i	$0.231801\pi$
$450$	−1164.90	−0.122031
$451$	0	0
$452$	−457.971	−0.0476574
$453$	−18932.9	−1.96368
$454$	−9157.78	−0.946687
$455$	−566.941	−0.0584145
$456$	−11930.4	−1.22521
$457$	3389.75	0.346971	0.173485	−	0.984836i	$-0.444497\pi$
$457$	3389.75	0.346971	0.173485	+	0.984836i	$0.444497\pi$
$458$	−58.1879	−0.00593655
$459$	1154.53	0.117405
$460$	−2380.84	−0.241320
$461$	−9476.05	−0.957361	−0.478681	−	0.877989i	$-0.658885\pi$
$461$	−9476.05	−0.957361	−0.478681	+	0.877989i	$0.658885\pi$
$462$	0	0
$463$	13680.5	1.37319	0.686593	−	0.727042i	$-0.259106\pi$
$463$	13680.5	1.37319	0.686593	+	0.727042i	$0.259106\pi$
$464$	2208.78	0.220992
$465$	−9053.48	−0.902892
$466$	−2428.79	−0.241441
$467$	−15708.2	−1.55651	−0.778255	−	0.627948i	$-0.783895\pi$
$467$	−15708.2	−1.55651	−0.778255	+	0.627948i	$0.783895\pi$
$468$	318.701	0.0314785
$469$	1536.83	0.151309
$470$	8687.36	0.852592
$471$	−2546.49	−0.249121
$472$	1202.71	0.117286
$473$	0	0
$474$	−450.172	−0.0436225
$475$	−1183.46	−0.114317
$476$	413.016	0.0397701
$477$	2175.12	0.208788
$478$	−15386.3	−1.47229
$479$	6522.42	0.622165	0.311083	−	0.950383i	$-0.399308\pi$
$479$	6522.42	0.622165	0.311083	+	0.950383i	$0.399308\pi$
$480$	−3720.11	−0.353748
$481$	4383.45	0.415526
$482$	−170.784	−0.0161390
$483$	5547.75	0.522632
$484$	0	0
$485$	18530.7	1.73492
$486$	14004.8	1.30715
$487$	−2305.77	−0.214547	−0.107274	−	0.994230i	$-0.534212\pi$
$487$	−2305.77	−0.214547	−0.107274	+	0.994230i	$0.534212\pi$
$488$	−5064.98	−0.469838
$489$	1932.75	0.178736
$490$	10428.9	0.961493
$491$	11832.4	1.08756	0.543779	−	0.839229i	$-0.316993\pi$
$491$	11832.4	1.08756	0.543779	+	0.839229i	$0.316993\pi$
$492$	180.138	0.0165066
$493$	4706.56	0.429965
$494$	−2386.66	−0.217370
$495$	0	0
$496$	5802.67	0.525297
$497$	1011.68	0.0913079
$498$	14087.5	1.26762
$499$	18835.6	1.68977	0.844886	−	0.534947i	$-0.179668\pi$
$499$	18835.6	1.68977	0.844886	+	0.534947i	$0.179668\pi$
$500$	1229.12	0.109936
$501$	26382.3	2.35264
$502$	5384.00	0.478684
$503$	−7262.23	−0.643752	−0.321876	−	0.946782i	$-0.604313\pi$
$503$	−7262.23	−0.643752	−0.321876	+	0.946782i	$0.604313\pi$
$504$	2230.71	0.197150
$505$	6077.03	0.535494
$506$	0	0
$507$	1226.31	0.107420
$508$	−812.508	−0.0709630
$509$	1174.43	0.102271	0.0511355	−	0.998692i	$-0.483716\pi$
$509$	1174.43	0.102271	0.0511355	+	0.998692i	$0.483716\pi$
$510$	27122.5	2.35491
$511$	−4271.98	−0.369827
$512$	12926.8	1.11580
$513$	676.000	0.0581796
$514$	15440.1	1.32497
$515$	−12181.3	−1.04227
$516$	2542.81	0.216940
$517$	0	0
$518$	3273.98	0.277704
$519$	11133.1	0.941601
$520$	−3683.59	−0.310647
$521$	−16777.8	−1.41084	−0.705422	−	0.708787i	$-0.749243\pi$
$521$	−16777.8	−1.41084	−0.705422	+	0.708787i	$0.749243\pi$
$522$	2712.56	0.227444
$523$	−15496.2	−1.29560	−0.647802	−	0.761809i	$-0.724312\pi$
$523$	−15496.2	−1.29560	−0.647802	+	0.761809i	$0.724312\pi$
$524$	−2456.66	−0.204809
$525$	454.173	0.0377557
$526$	−187.901	−0.0155758
$527$	12364.5	1.02203
$528$	0	0
$529$	31508.8	2.58970
$530$	−2682.70	−0.219866
$531$	1298.03	0.106082
$532$	241.829	0.0197079
$533$	337.705	0.0274439
$534$	−9525.08	−0.771892
$535$	−8223.60	−0.664556
$536$	9985.25	0.804658
$537$	27724.7	2.22795
$538$	−3314.37	−0.265600
$539$	0	0
$540$	111.334	0.00887234
$541$	−21385.1	−1.69948	−0.849740	−	0.527203i	$-0.823241\pi$
$541$	−21385.1	−1.69948	−0.849740	+	0.527203i	$0.823241\pi$
$542$	10382.5	0.822814
$543$	−30152.7	−2.38301
$544$	5080.64	0.400424
$545$	−6265.14	−0.492420
$546$	915.925	0.0717911
$547$	−13035.2	−1.01891	−0.509457	−	0.860496i	$-0.670154\pi$
$547$	−13035.2	−1.01891	−0.509457	+	0.860496i	$0.670154\pi$
$548$	−86.5488	−0.00674668
$549$	−5466.40	−0.424955
$550$	0	0
$551$	2755.78	0.213067
$552$	36045.4	2.77934
$553$	85.5124	0.00657569
$554$	16758.2	1.28518
$555$	−29167.3	−2.23078
$556$	−2235.54	−0.170518
$557$	8408.36	0.639630	0.319815	−	0.947480i	$-0.396379\pi$
$557$	8408.36	0.639630	0.319815	+	0.947480i	$0.396379\pi$
$558$	7126.14	0.540633
$559$	4767.03	0.360686
$560$	−2417.85	−0.182452
$561$	0	0
$562$	2440.29	0.183163
$563$	−20172.3	−1.51005	−0.755026	−	0.655695i	$-0.772376\pi$
$563$	−20172.3	−1.51005	−0.755026	+	0.655695i	$0.772376\pi$
$564$	1904.00	0.142150
$565$	5712.82	0.425381
$566$	10700.0	0.794621
$567$	−2793.32	−0.206893
$568$	6573.20	0.485573
$569$	−5311.64	−0.391345	−0.195673	−	0.980669i	$-0.562689\pi$
$569$	−5311.64	−0.391345	−0.195673	+	0.980669i	$0.562689\pi$
$570$	15880.7	1.16697
$571$	−11829.7	−0.867003	−0.433502	−	0.901153i	$-0.642722\pi$
$571$	−11829.7	−0.867003	−0.433502	+	0.901153i	$0.642722\pi$
$572$	0	0
$573$	31110.0	2.26813
$574$	252.231	0.0183413
$575$	3575.58	0.259325
$576$	14306.2	1.03488
$577$	25425.2	1.83442	0.917212	−	0.398398i	$-0.130434\pi$
$577$	25425.2	1.83442	0.917212	+	0.398398i	$0.130434\pi$
$578$	−24002.1	−1.72726
$579$	−13839.2	−0.993326
$580$	453.865	0.0324926
$581$	−2675.99	−0.191082
$582$	−29937.4	−2.13221
$583$	0	0
$584$	−27756.4	−1.96673
$585$	−3975.53	−0.280971
$586$	−16217.8	−1.14326
$587$	21455.2	1.50860	0.754302	−	0.656527i	$-0.227975\pi$
$587$	21455.2	1.50860	0.754302	+	0.656527i	$0.227975\pi$
$588$	2285.70	0.160307
$589$	7239.67	0.506461
$590$	−1600.94	−0.111711
$591$	−950.828	−0.0661791
$592$	18694.2	1.29785
$593$	17282.1	1.19678	0.598389	−	0.801206i	$-0.295808\pi$
$593$	17282.1	1.19678	0.598389	+	0.801206i	$0.295808\pi$
$594$	0	0
$595$	−5152.05	−0.354981
$596$	407.350	0.0279962
$597$	−25045.3	−1.71698
$598$	7210.82	0.493097
$599$	−15202.5	−1.03699	−0.518494	−	0.855081i	$-0.673507\pi$
$599$	−15202.5	−1.03699	−0.518494	+	0.855081i	$0.673507\pi$
$600$	2950.91	0.200784
$601$	10441.4	0.708674	0.354337	−	0.935118i	$-0.384707\pi$
$601$	10441.4	0.708674	0.354337	+	0.935118i	$0.384707\pi$
$602$	3560.48	0.241054
$603$	10776.6	0.727791
$604$	2493.46	0.167976
$605$	0	0
$606$	−9817.78	−0.658119
$607$	6894.27	0.461005	0.230502	−	0.973072i	$-0.425963\pi$
$607$	6894.27	0.461005	0.230502	+	0.973072i	$0.425963\pi$
$608$	2974.81	0.198429
$609$	−1057.58	−0.0703700
$610$	6742.05	0.447504
$611$	3569.44	0.236340
$612$	2896.18	0.191293
$613$	−17081.9	−1.12550	−0.562749	−	0.826628i	$-0.690256\pi$
$613$	−17081.9	−1.12550	−0.562749	+	0.826628i	$0.690256\pi$
$614$	−20133.6	−1.32333
$615$	−2247.07	−0.147334
$616$	0	0
$617$	6937.92	0.452691	0.226345	−	0.974047i	$-0.427322\pi$
$617$	6937.92	0.452691	0.226345	+	0.974047i	$0.427322\pi$
$618$	19679.5	1.28095
$619$	29140.4	1.89217	0.946083	−	0.323924i	$-0.105002\pi$
$619$	29140.4	1.89217	0.946083	+	0.323924i	$0.105002\pi$
$620$	1192.34	0.0772349
$621$	−2042.40	−0.131978
$622$	−11458.0	−0.738623
$623$	1809.34	0.116356
$624$	5229.87	0.335517
$625$	−17470.9	−1.11814
$626$	15921.7	1.01655
$627$	0	0
$628$	335.372	0.0213102
$629$	39834.4	2.52512
$630$	−2969.32	−0.187778
$631$	2040.36	0.128725	0.0643624	−	0.997927i	$-0.479499\pi$
$631$	2040.36	0.128725	0.0643624	+	0.997927i	$0.479499\pi$
$632$	555.601	0.0349693
$633$	30711.2	1.92837
$634$	14648.7	0.917627
$635$	10135.4	0.633403
$636$	−587.965	−0.0366578
$637$	4285.02	0.266528
$638$	0	0
$639$	7094.16	0.439187
$640$	−13543.3	−0.836476
$641$	−24930.0	−1.53615	−0.768077	−	0.640357i	$-0.778786\pi$
$641$	−24930.0	−1.53615	−0.768077	+	0.640357i	$0.778786\pi$
$642$	13285.7	0.816736
$643$	4466.15	0.273916	0.136958	−	0.990577i	$-0.456267\pi$
$643$	4466.15	0.273916	0.136958	+	0.990577i	$0.456267\pi$
$644$	−730.638	−0.0447068
$645$	−31719.6	−1.93637
$646$	−21688.7	−1.32094
$647$	19433.7	1.18086	0.590432	−	0.807087i	$-0.298957\pi$
$647$	19433.7	1.18086	0.590432	+	0.807087i	$0.298957\pi$
$648$	−18149.1	−1.10025
$649$	0	0
$650$	590.323	0.0356221
$651$	−2778.36	−0.167269
$652$	−254.543	−0.0152894
$653$	17998.5	1.07862	0.539308	−	0.842109i	$-0.318686\pi$
$653$	17998.5	1.07862	0.539308	+	0.842109i	$0.318686\pi$
$654$	10121.7	0.605182
$655$	30644.9	1.82808
$656$	1440.22	0.0857183
$657$	−29956.2	−1.77885
$658$	2666.00	0.157951
$659$	−26500.3	−1.56647	−0.783236	−	0.621725i	$-0.786432\pi$
$659$	−26500.3	−1.56647	−0.783236	+	0.621725i	$0.786432\pi$
$660$	0	0
$661$	18345.2	1.07950	0.539748	−	0.841827i	$-0.318520\pi$
$661$	18345.2	1.07950	0.539748	+	0.841827i	$0.318520\pi$
$662$	4615.06	0.270951
$663$	11144.0	0.652786
$664$	−17386.8	−1.01617
$665$	−3016.62	−0.175909
$666$	22958.0	1.33574
$667$	−8326.03	−0.483336
$668$	−3474.55	−0.201249
$669$	−30434.2	−1.75883
$670$	−13291.5	−0.766409
$671$	0	0
$672$	−1141.64	−0.0655353
$673$	9762.57	0.559167	0.279583	−	0.960121i	$-0.409804\pi$
$673$	9762.57	0.559167	0.279583	+	0.960121i	$0.409804\pi$
$674$	7656.58	0.437567
$675$	−167.204	−0.00953432
$676$	−161.505	−0.00918893
$677$	33675.6	1.91175	0.955876	−	0.293769i	$-0.0949097\pi$
$677$	33675.6	1.91175	0.955876	+	0.293769i	$0.0949097\pi$
$678$	−9229.38	−0.522791
$679$	5686.77	0.321411
$680$	−33474.5	−1.88778
$681$	25037.0	1.40884
$682$	0	0
$683$	−377.701	−0.0211601	−0.0105800	−	0.999944i	$-0.503368\pi$
$683$	−377.701	−0.0211601	−0.0105800	+	0.999944i	$0.503368\pi$
$684$	1695.77	0.0947942
$685$	1079.63	0.0602196
$686$	6530.88	0.363484
$687$	159.083	0.00883464
$688$	20330.1	1.12657
$689$	−1102.26	−0.0609475
$690$	−47980.4	−2.64722
$691$	11848.0	0.652269	0.326135	−	0.945323i	$-0.394254\pi$
$691$	11848.0	0.652269	0.326135	+	0.945323i	$0.394254\pi$
$692$	−1466.24	−0.0805461
$693$	0	0
$694$	−3696.34	−0.202177
$695$	27886.6	1.52201
$696$	−6871.44	−0.374226
$697$	3068.88	0.166775
$698$	18628.5	1.01017
$699$	6640.21	0.359307
$700$	−59.8146	−0.00322969
$701$	−15697.1	−0.845753	−0.422876	−	0.906187i	$-0.638980\pi$
$701$	−15697.1	−0.845753	−0.422876	+	0.906187i	$0.638980\pi$
$702$	−337.197	−0.0181292
$703$	23323.8	1.25131
$704$	0	0
$705$	−23750.9	−1.26881
$706$	3483.44	0.185695
$707$	1864.94	0.0992053
$708$	−350.875	−0.0186253
$709$	9213.20	0.488024	0.244012	−	0.969772i	$-0.421536\pi$
$709$	9213.20	0.488024	0.244012	+	0.969772i	$0.421536\pi$
$710$	−8749.65	−0.462491
$711$	599.634	0.0316288
$712$	11755.8	0.618776
$713$	−21873.2	−1.14889
$714$	8323.43	0.436269
$715$	0	0
$716$	−3651.34	−0.190582
$717$	42065.5	2.19102
$718$	518.610	0.0269559
$719$	−36648.2	−1.90090	−0.950451	−	0.310875i	$-0.899378\pi$
$719$	−36648.2	−1.90090	−0.950451	+	0.310875i	$0.899378\pi$
$720$	−16954.6	−0.877584
$721$	−3738.23	−0.193091
$722$	5505.48	0.283785
$723$	466.915	0.0240177
$724$	3971.11	0.203847
$725$	−681.622	−0.0349170
$726$	0	0
$727$	22446.3	1.14510	0.572551	−	0.819869i	$-0.305954\pi$
$727$	22446.3	1.14510	0.572551	+	0.819869i	$0.305954\pi$
$728$	−1130.43	−0.0575503
$729$	−17672.8	−0.897872
$730$	36946.8	1.87324
$731$	43320.1	2.19187
$732$	1477.65	0.0746112
$733$	3022.40	0.152299	0.0761493	−	0.997096i	$-0.475737\pi$
$733$	3022.40	0.152299	0.0761493	+	0.997096i	$0.475737\pi$
$734$	4269.95	0.214723
$735$	−28512.3	−1.43087
$736$	−8987.80	−0.450129
$737$	0	0
$738$	1768.71	0.0882208
$739$	−19115.4	−0.951519	−0.475759	−	0.879576i	$-0.657827\pi$
$739$	−19115.4	−0.951519	−0.475759	+	0.879576i	$0.657827\pi$
$740$	3841.33	0.190824
$741$	6525.03	0.323486
$742$	−823.276	−0.0407324
$743$	33948.7	1.67625	0.838127	−	0.545475i	$-0.183651\pi$
$743$	33948.7	1.67625	0.838127	+	0.545475i	$0.183651\pi$
$744$	−18051.9	−0.889534
$745$	−5081.37	−0.249889
$746$	−13795.9	−0.677085
$747$	−18764.7	−0.919098
$748$	0	0
$749$	−2523.68	−0.123115
$750$	24770.2	1.20597
$751$	−6253.37	−0.303847	−0.151923	−	0.988392i	$-0.548547\pi$
$751$	−6253.37	−0.303847	−0.151923	+	0.988392i	$0.548547\pi$
$752$	15222.7	0.738185
$753$	−14719.6	−0.712368
$754$	−1374.62	−0.0663933
$755$	−31104.0	−1.49932
$756$	34.1666	0.00164369
$757$	−8127.80	−0.390237	−0.195119	−	0.980780i	$-0.562509\pi$
$757$	−8127.80	−0.390237	−0.195119	+	0.980780i	$0.562509\pi$
$758$	16801.9	0.805109
$759$	0	0
$760$	−19600.0	−0.935480
$761$	−28337.6	−1.34985	−0.674925	−	0.737886i	$-0.735824\pi$
$761$	−28337.6	−1.34985	−0.674925	+	0.737886i	$0.735824\pi$
$762$	−16374.3	−0.778449
$763$	−1922.66	−0.0912256
$764$	−4097.18	−0.194020
$765$	−36127.5	−1.70744
$766$	35491.9	1.67412
$767$	−657.788	−0.0309666
$768$	−10493.2	−0.493023
$769$	39008.9	1.82925	0.914627	−	0.404298i	$-0.132484\pi$
$769$	39008.9	1.82925	0.914627	+	0.404298i	$0.132484\pi$
$770$	0	0
$771$	−42212.7	−1.97179
$772$	1822.62	0.0849708
$773$	−28664.4	−1.33375	−0.666875	−	0.745170i	$-0.732368\pi$
$773$	−28664.4	−1.33375	−0.666875	+	0.745170i	$0.732368\pi$
$774$	24967.0	1.15946
$775$	−1790.68	−0.0829976
$776$	36948.7	1.70925
$777$	−8950.94	−0.413273
$778$	31808.3	1.46579
$779$	1796.89	0.0826446
$780$	1074.64	0.0493313
$781$	0	0
$782$	65528.0	2.99652
$783$	389.348	0.0177703
$784$	18274.5	0.832473
$785$	−4183.50	−0.190211
$786$	−49508.5	−2.24671
$787$	30674.2	1.38935	0.694674	−	0.719324i	$-0.255549\pi$
$787$	30674.2	1.38935	0.694674	+	0.719324i	$0.255549\pi$
$788$	125.224	0.00566107
$789$	513.714	0.0231796
$790$	−739.566	−0.0333070
$791$	1753.17	0.0788059
$792$	0	0
$793$	2770.15	0.124049
$794$	10237.9	0.457592
$795$	7334.40	0.327200
$796$	3298.47	0.146873
$797$	19464.2	0.865067	0.432533	−	0.901618i	$-0.357620\pi$
$797$	19464.2	0.865067	0.432533	+	0.901618i	$0.357620\pi$
$798$	4873.52	0.216192
$799$	32437.1	1.43622
$800$	−735.798	−0.0325180
$801$	12687.5	0.559665
$802$	13340.5	0.587370
$803$	0	0
$804$	−2913.07	−0.127781
$805$	9114.13	0.399044
$806$	−3611.24	−0.157817
$807$	9061.35	0.395260
$808$	12117.1	0.527571
$809$	36315.3	1.57822	0.789108	−	0.614254i	$-0.210543\pi$
$809$	36315.3	1.57822	0.789108	+	0.614254i	$0.210543\pi$
$810$	24158.4	1.04795
$811$	26546.5	1.14941	0.574706	−	0.818360i	$-0.305116\pi$
$811$	26546.5	1.14941	0.574706	+	0.818360i	$0.305116\pi$
$812$	139.283	0.00601957
$813$	−28385.2	−1.22449
$814$	0	0
$815$	3175.22	0.136470
$816$	47526.2	2.03891
$817$	25364.8	1.08617
$818$	−36911.1	−1.57771
$819$	−1220.02	−0.0520526
$820$	295.939	0.0126032
$821$	−1315.87	−0.0559369	−0.0279684	−	0.999609i	$-0.508904\pi$
$821$	−1315.87	−0.0559369	−0.0279684	+	0.999609i	$0.508904\pi$
$822$	−1744.20	−0.0740096
$823$	37438.8	1.58570	0.792852	−	0.609414i	$-0.208595\pi$
$823$	37438.8	1.58570	0.792852	+	0.609414i	$0.208595\pi$
$824$	−24288.4	−1.02685
$825$	0	0
$826$	−491.300	−0.0206955
$827$	6124.33	0.257514	0.128757	−	0.991676i	$-0.458901\pi$
$827$	6124.33	0.257514	0.128757	+	0.991676i	$0.458901\pi$
$828$	−5123.42	−0.215038
$829$	−24945.5	−1.04511	−0.522553	−	0.852607i	$-0.675020\pi$
$829$	−24945.5	−1.04511	−0.522553	+	0.852607i	$0.675020\pi$
$830$	23143.7	0.967867
$831$	−45816.2	−1.91257
$832$	−7249.79	−0.302093
$833$	38939.9	1.61967
$834$	−45052.3	−1.87054
$835$	43342.2	1.79631
$836$	0	0
$837$	1022.85	0.0422400
$838$	28033.5	1.15561
$839$	22137.1	0.910913	0.455456	−	0.890258i	$-0.349476\pi$
$839$	22137.1	0.910913	0.455456	+	0.890258i	$0.349476\pi$
$840$	7521.84	0.308962
$841$	−22801.8	−0.934921
$842$	9468.17	0.387523
$843$	−6671.66	−0.272579
$844$	−4044.66	−0.164956
$845$	2014.64	0.0820186
$846$	18694.7	0.759736
$847$	0	0
$848$	−4700.85	−0.190363
$849$	−29253.4	−1.18254
$850$	5364.53	0.216473
$851$	−70468.2	−2.83856
$852$	−1917.65	−0.0771100
$853$	19392.0	0.778391	0.389196	−	0.921155i	$-0.372753\pi$
$853$	19392.0	0.778391	0.389196	+	0.921155i	$0.372753\pi$
$854$	2069.02	0.0829044
$855$	−21153.3	−0.846116
$856$	−16397.2	−0.654724
$857$	−34648.6	−1.38107	−0.690534	−	0.723300i	$-0.742624\pi$
$857$	−34648.6	−1.38107	−0.690534	+	0.723300i	$0.742624\pi$
$858$	0	0
$859$	−14702.9	−0.584001	−0.292000	−	0.956418i	$-0.594321\pi$
$859$	−14702.9	−0.584001	−0.292000	+	0.956418i	$0.594321\pi$
$860$	4177.47	0.165640
$861$	−689.588	−0.0272951
$862$	24804.1	0.980084
$863$	−36311.0	−1.43226	−0.716130	−	0.697967i	$-0.754088\pi$
$863$	−36311.0	−1.43226	−0.716130	+	0.697967i	$0.754088\pi$
$864$	420.294	0.0165494
$865$	18290.1	0.718939
$866$	31163.4	1.22284
$867$	65620.7	2.57047
$868$	365.910	0.0143085
$869$	0	0
$870$	9146.63	0.356437
$871$	−5461.16	−0.212450
$872$	−12492.2	−0.485135
$873$	39877.0	1.54597
$874$	38367.9	1.48491
$875$	−4705.22	−0.181789
$876$	8097.60	0.312320
$877$	−29264.2	−1.12678	−0.563388	−	0.826192i	$-0.690502\pi$
$877$	−29264.2	−1.12678	−0.563388	+	0.826192i	$0.690502\pi$
$878$	−19337.8	−0.743301
$879$	44338.9	1.70138
$880$	0	0
$881$	−28265.2	−1.08091	−0.540453	−	0.841375i	$-0.681747\pi$
$881$	−28265.2	−1.08091	−0.540453	+	0.841375i	$0.681747\pi$
$882$	22442.5	0.856777
$883$	20701.2	0.788958	0.394479	−	0.918905i	$-0.370925\pi$
$883$	20701.2	0.788958	0.394479	+	0.918905i	$0.370925\pi$
$884$	−1467.67	−0.0558404
$885$	4376.89	0.166246
$886$	−13626.0	−0.516675
$887$	−26638.8	−1.00839	−0.504195	−	0.863590i	$-0.668211\pi$
$887$	−26638.8	−1.00839	−0.504195	+	0.863590i	$0.668211\pi$
$888$	−58157.1	−2.19777
$889$	3110.38	0.117344
$890$	−15648.3	−0.589362
$891$	0	0
$892$	4008.19	0.150453
$893$	18992.6	0.711715
$894$	8209.24	0.307112
$895$	45547.5	1.70110
$896$	−4156.20	−0.154965
$897$	−19714.1	−0.733817
$898$	−37693.5	−1.40072
$899$	4169.75	0.154693
$900$	−419.435	−0.0155346
$901$	−10016.8	−0.370373
$902$	0	0
$903$	−9734.20	−0.358731
$904$	11390.9	0.419087
$905$	−49536.4	−1.81950
$906$	50250.2	1.84266
$907$	−29219.3	−1.06969	−0.534845	−	0.844950i	$-0.679630\pi$
$907$	−29219.3	−1.06969	−0.534845	+	0.844950i	$0.679630\pi$
$908$	−3297.37	−0.120514
$909$	13077.4	0.477173
$910$	1504.73	0.0548146
$911$	10621.1	0.386269	0.193135	−	0.981172i	$-0.438135\pi$
$911$	10621.1	0.386269	0.193135	+	0.981172i	$0.438135\pi$
$912$	27827.5	1.01037
$913$	0	0
$914$	−8996.79	−0.325588
$915$	−18432.5	−0.665966
$916$	−20.9512	−0.000755730 0
$917$	9404.40	0.338670
$918$	−3064.26	−0.110170
$919$	−30526.1	−1.09571	−0.547857	−	0.836572i	$-0.684556\pi$
$919$	−30526.1	−1.09571	−0.547857	+	0.836572i	$0.684556\pi$
$920$	59217.3	2.12211
$921$	55044.5	1.96936
$922$	25150.6	0.898362
$923$	−3595.03	−0.128204
$924$	0	0
$925$	−5768.97	−0.205062
$926$	−36309.6	−1.28856
$927$	−26213.4	−0.928761
$928$	1713.37	0.0606078
$929$	3377.13	0.119268	0.0596340	−	0.998220i	$-0.481007\pi$
$929$	3377.13	0.119268	0.0596340	+	0.998220i	$0.481007\pi$
$930$	24029.0	0.847250
$931$	22800.0	0.802622
$932$	−874.516	−0.0307358
$933$	31325.7	1.09920
$934$	41691.5	1.46059
$935$	0	0
$936$	−7926.88	−0.276814
$937$	29378.2	1.02427	0.512137	−	0.858904i	$-0.328854\pi$
$937$	29378.2	1.02427	0.512137	+	0.858904i	$0.328854\pi$
$938$	−4078.92	−0.141985
$939$	−43529.2	−1.51280
$940$	3127.99	0.108536
$941$	20768.4	0.719481	0.359741	−	0.933052i	$-0.382865\pi$
$941$	20768.4	0.719481	0.359741	+	0.933052i	$0.382865\pi$
$942$	6758.68	0.233768
$943$	−5428.93	−0.187476
$944$	−2805.29	−0.0967208
$945$	−426.201	−0.0146712
$946$	0	0
$947$	−18055.0	−0.619544	−0.309772	−	0.950811i	$-0.600253\pi$
$947$	−18055.0	−0.619544	−0.309772	+	0.950811i	$0.600253\pi$
$948$	−162.090	−0.00555320
$949$	15180.6	0.519266
$950$	3141.04	0.107272
$951$	−40049.0	−1.36559
$952$	−10272.8	−0.349729
$953$	−36155.2	−1.22894	−0.614471	−	0.788940i	$-0.710630\pi$
$953$	−36155.2	−1.22894	−0.614471	+	0.788940i	$0.710630\pi$
$954$	−5773.02	−0.195921
$955$	51109.1	1.73178
$956$	−5540.02	−0.187424
$957$	0	0
$958$	−17311.3	−0.583823
$959$	331.319	0.0111563
$960$	48239.8	1.62181
$961$	−18836.7	−0.632295
$962$	−11634.2	−0.389918
$963$	−17696.7	−0.592179
$964$	−61.4927	−0.00205451
$965$	−22735.7	−0.758433
$966$	−14724.4	−0.490424
$967$	30043.5	0.999104	0.499552	−	0.866284i	$-0.333498\pi$
$967$	30043.5	0.999104	0.499552	+	0.866284i	$0.333498\pi$
$968$	0	0
$969$	59295.9	1.96580
$970$	−49182.8	−1.62800
$971$	−30546.5	−1.00956	−0.504781	−	0.863247i	$-0.668427\pi$
$971$	−30546.5	−1.00956	−0.504781	+	0.863247i	$0.668427\pi$
$972$	5042.62	0.166401
$973$	8557.91	0.281967
$974$	6119.79	0.201325
$975$	−1613.92	−0.0530120
$976$	11814.0	0.387455
$977$	47290.9	1.54859	0.774293	−	0.632827i	$-0.218105\pi$
$977$	47290.9	1.54859	0.774293	+	0.632827i	$0.218105\pi$
$978$	−5129.75	−0.167721
$979$	0	0
$980$	3755.07	0.122399
$981$	−13482.2	−0.438791
$982$	−31404.7	−1.02053
$983$	−8300.42	−0.269321	−0.134660	−	0.990892i	$-0.542994\pi$
$983$	−8300.42	−0.269321	−0.134660	+	0.990892i	$0.542994\pi$
$984$	−4480.47	−0.145155
$985$	−1562.07	−0.0505296
$986$	−12491.8	−0.403467
$987$	−7288.74	−0.235059
$988$	−859.346	−0.0276715
$989$	−76634.6	−2.46394
$990$	0	0
$991$	26782.9	0.858514	0.429257	−	0.903182i	$-0.358775\pi$
$991$	26782.9	0.858514	0.429257	+	0.903182i	$0.358775\pi$
$992$	4501.17	0.144065
$993$	−12617.4	−0.403223
$994$	−2685.12	−0.0856809
$995$	−41145.8	−1.31096
$996$	5072.38	0.161370
$997$	56493.9	1.79456	0.897281	−	0.441459i	$-0.145539\pi$
$997$	56493.9	1.79456	0.897281	+	0.441459i	$0.145539\pi$
$998$	−49991.9	−1.58564
$999$	3295.28	0.104362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.h.1.6	✓	15
11.10	odd	2		1573.4.a.k.1.10	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1573.4.a.h.1.6	✓	15	1.1	even	1	trivial
1573.4.a.k.1.10	yes	15	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65412 q^{2} +7.25625 q^{3} -0.955648 q^{4} +11.9209 q^{5} -19.2590 q^{6} +3.65834 q^{7} +23.7694 q^{8} +25.6532 q^{9} +O(q^{10})\)	\(q-2.65412 q^{2} +7.25625 q^{3} -0.955648 q^{4} +11.9209 q^{5} -19.2590 q^{6} +3.65834 q^{7} +23.7694 q^{8} +25.6532 q^{9} -31.6396 q^{10} -6.93442 q^{12} -13.0000 q^{13} -9.70966 q^{14} +86.5014 q^{15} -55.4416 q^{16} -118.137 q^{17} -68.0866 q^{18} -69.1714 q^{19} -11.3922 q^{20} +26.5458 q^{21} +208.988 q^{23} +172.476 q^{24} +17.1090 q^{25} +34.5036 q^{26} -9.77282 q^{27} -3.49608 q^{28} -39.8398 q^{29} -229.585 q^{30} -104.663 q^{31} -43.0064 q^{32} +313.550 q^{34} +43.6108 q^{35} -24.5154 q^{36} -337.188 q^{37} +183.589 q^{38} -94.3313 q^{39} +283.353 q^{40} -25.9773 q^{41} -70.4558 q^{42} -366.694 q^{43} +305.810 q^{45} -554.678 q^{46} -274.572 q^{47} -402.298 q^{48} -329.617 q^{49} -45.4095 q^{50} -857.231 q^{51} +12.4234 q^{52} +84.7894 q^{53} +25.9382 q^{54} +86.9563 q^{56} -501.925 q^{57} +105.740 q^{58} +50.5991 q^{59} -82.6649 q^{60} -213.089 q^{61} +277.788 q^{62} +93.8480 q^{63} +557.677 q^{64} -154.972 q^{65} +420.089 q^{67} +112.897 q^{68} +1516.47 q^{69} -115.748 q^{70} +276.541 q^{71} +609.760 q^{72} -1167.74 q^{73} +894.938 q^{74} +124.148 q^{75} +66.1036 q^{76} +250.366 q^{78} +23.3747 q^{79} -660.916 q^{80} -763.550 q^{81} +68.9468 q^{82} -731.478 q^{83} -25.3685 q^{84} -1408.30 q^{85} +973.251 q^{86} -289.088 q^{87} +494.579 q^{89} -811.657 q^{90} -47.5584 q^{91} -199.719 q^{92} -759.459 q^{93} +728.748 q^{94} -824.589 q^{95} -312.065 q^{96} +1554.47 q^{97} +874.842 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9} + 16 q^{10} - 3 q^{12} - 195 q^{13} + 60 q^{14} + 202 q^{15} + 282 q^{16} - 136 q^{17} - 351 q^{18} - 136 q^{19} - 62 q^{20} - 625 q^{21} - 176 q^{23} + 227 q^{24} + 479 q^{25} + 78 q^{26} - 13 q^{27} + 86 q^{28} - 344 q^{29} - 542 q^{30} + 275 q^{31} + 170 q^{32} - 1505 q^{34} - 655 q^{35} + 623 q^{36} + 346 q^{37} - 848 q^{38} - 26 q^{39} - 256 q^{40} - 38 q^{41} + 575 q^{42} - 534 q^{43} - 633 q^{45} + 375 q^{46} + 276 q^{47} - 723 q^{48} + 773 q^{49} - 1684 q^{50} - 1111 q^{51} - 702 q^{52} + 706 q^{53} + 178 q^{54} - 2056 q^{56} - 1320 q^{57} - 983 q^{58} - 174 q^{59} + 2004 q^{60} - 1078 q^{61} - 1365 q^{62} + 2055 q^{63} + 1338 q^{64} + 26 q^{65} - 260 q^{67} - 559 q^{68} + 154 q^{69} - 1161 q^{70} + 2910 q^{71} - 6171 q^{72} - 1000 q^{73} - 688 q^{74} - 553 q^{75} - 178 q^{76} - 325 q^{78} + 386 q^{79} + 1702 q^{80} - 2805 q^{81} + 3380 q^{82} - 4318 q^{83} - 6681 q^{84} + 1391 q^{85} + 4139 q^{86} - 3144 q^{87} - 810 q^{89} + 3789 q^{90} + 364 q^{91} - 4857 q^{92} + 394 q^{93} + 116 q^{94} - 5204 q^{95} + 893 q^{96} - 1860 q^{97} - 8 q^{98}+O(q^{100}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9 + 16 * q^10 - 3 * q^12 - 195 * q^13 + 60 * q^14 + 202 * q^15 + 282 * q^16 - 136 * q^17 - 351 * q^18 - 136 * q^19 - 62 * q^20 - 625 * q^21 - 176 * q^23 + 227 * q^24 + 479 * q^25 + 78 * q^26 - 13 * q^27 + 86 * q^28 - 344 * q^29 - 542 * q^30 + 275 * q^31 + 170 * q^32 - 1505 * q^34 - 655 * q^35 + 623 * q^36 + 346 * q^37 - 848 * q^38 - 26 * q^39 - 256 * q^40 - 38 * q^41 + 575 * q^42 - 534 * q^43 - 633 * q^45 + 375 * q^46 + 276 * q^47 - 723 * q^48 + 773 * q^49 - 1684 * q^50 - 1111 * q^51 - 702 * q^52 + 706 * q^53 + 178 * q^54 - 2056 * q^56 - 1320 * q^57 - 983 * q^58 - 174 * q^59 + 2004 * q^60 - 1078 * q^61 - 1365 * q^62 + 2055 * q^63 + 1338 * q^64 + 26 * q^65 - 260 * q^67 - 559 * q^68 + 154 * q^69 - 1161 * q^70 + 2910 * q^71 - 6171 * q^72 - 1000 * q^73 - 688 * q^74 - 553 * q^75 - 178 * q^76 - 325 * q^78 + 386 * q^79 + 1702 * q^80 - 2805 * q^81 + 3380 * q^82 - 4318 * q^83 - 6681 * q^84 + 1391 * q^85 + 4139 * q^86 - 3144 * q^87 - 810 * q^89 + 3789 * q^90 + 364 * q^91 - 4857 * q^92 + 394 * q^93 + 116 * q^94 - 5204 * q^95 + 893 * q^96 - 1860 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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