LMFDB - Embedded newform 1573.4.a.h.1.7

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			1.7
Root			$0.460593$ 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)

$f(q)$	$=$	$q-0.460593 q^{2} -6.09765 q^{3} -7.78785 q^{4} +15.2965 q^{5} +2.80854 q^{6} +15.1681 q^{7} +7.27177 q^{8} +10.1814 q^{9} +O(q^{10})$	\(q-0.460593 q^{2} -6.09765 q^{3} -7.78785 q^{4} +15.2965 q^{5} +2.80854 q^{6} +15.1681 q^{7} +7.27177 q^{8} +10.1814 q^{9} -7.04544 q^{10} +47.4876 q^{12} -13.0000 q^{13} -6.98630 q^{14} -93.2725 q^{15} +58.9535 q^{16} +53.9478 q^{17} -4.68947 q^{18} -66.3695 q^{19} -119.127 q^{20} -92.4895 q^{21} -50.1184 q^{23} -44.3408 q^{24} +108.982 q^{25} +5.98771 q^{26} +102.554 q^{27} -118.127 q^{28} +118.110 q^{29} +42.9607 q^{30} -322.580 q^{31} -85.3278 q^{32} -24.8480 q^{34} +232.018 q^{35} -79.2910 q^{36} -32.1765 q^{37} +30.5693 q^{38} +79.2695 q^{39} +111.232 q^{40} -27.4066 q^{41} +42.6000 q^{42} -333.814 q^{43} +155.739 q^{45} +23.0842 q^{46} -408.579 q^{47} -359.478 q^{48} -112.930 q^{49} -50.1962 q^{50} -328.955 q^{51} +101.242 q^{52} +91.6536 q^{53} -47.2357 q^{54} +110.299 q^{56} +404.698 q^{57} -54.4006 q^{58} +606.073 q^{59} +726.393 q^{60} +673.975 q^{61} +148.578 q^{62} +154.432 q^{63} -432.327 q^{64} -198.854 q^{65} +61.5821 q^{67} -420.137 q^{68} +305.604 q^{69} -106.866 q^{70} +721.468 q^{71} +74.0366 q^{72} +637.757 q^{73} +14.8202 q^{74} -664.532 q^{75} +516.876 q^{76} -36.5110 q^{78} +185.484 q^{79} +901.780 q^{80} -900.237 q^{81} +12.6233 q^{82} +665.368 q^{83} +720.295 q^{84} +825.210 q^{85} +153.752 q^{86} -720.193 q^{87} -407.360 q^{89} -71.7322 q^{90} -197.185 q^{91} +390.314 q^{92} +1966.98 q^{93} +188.189 q^{94} -1015.22 q^{95} +520.299 q^{96} -942.625 q^{97} +52.0148 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.460593	−0.162844	−0.0814221	−	0.996680i	$-0.525946\pi$
$2$	−0.460593	−0.162844	−0.0814221	+	0.996680i	$0.525946\pi$
$3$	−6.09765	−1.17349	−0.586747	−	0.809770i	$-0.699592\pi$
$3$	−6.09765	−1.17349	−0.586747	+	0.809770i	$0.699592\pi$
$4$	−7.78785	−0.973482
$5$	15.2965	1.36816	0.684078	−	0.729408i	$-0.260205\pi$
$5$	15.2965	1.36816	0.684078	+	0.729408i	$0.260205\pi$
$6$	2.80854	0.191097
$7$	15.1681	0.818998	0.409499	−	0.912311i	$-0.365704\pi$
$7$	15.1681	0.818998	0.409499	+	0.912311i	$0.365704\pi$
$8$	7.27177	0.321370
$9$	10.1814	0.377088
$10$	−7.04544	−0.222796
$11$	0	0
$11$	0	0
$12$	47.4876	1.14237
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−6.98630	−0.133369
$15$	−93.2725	−1.60552
$16$	58.9535	0.921149
$17$	53.9478	0.769662	0.384831	−	0.922987i	$-0.374260\pi$
$17$	53.9478	0.769662	0.384831	+	0.922987i	$0.374260\pi$
$18$	−4.68947	−0.0614066
$19$	−66.3695	−0.801380	−0.400690	−	0.916214i	$-0.631230\pi$
$19$	−66.3695	−0.801380	−0.400690	+	0.916214i	$0.631230\pi$
$20$	−119.127	−1.33188
$21$	−92.4895	−0.961089
$22$	0	0
$23$	−50.1184	−0.454365	−0.227183	−	0.973852i	$-0.572951\pi$
$23$	−50.1184	−0.454365	−0.227183	+	0.973852i	$0.572951\pi$
$24$	−44.3408	−0.377126
$25$	108.982	0.871853
$26$	5.98771	0.0451649
$27$	102.554	0.730984
$28$	−118.127	−0.797280
$29$	118.110	0.756291	0.378146	−	0.925746i	$-0.376562\pi$
$29$	118.110	0.756291	0.378146	+	0.925746i	$0.376562\pi$
$30$	42.9607	0.261450
$31$	−322.580	−1.86894	−0.934470	−	0.356043i	$-0.884126\pi$
$31$	−322.580	−1.86894	−0.934470	+	0.356043i	$0.884126\pi$
$32$	−85.3278	−0.471374
$33$	0	0
$34$	−24.8480	−0.125335
$35$	232.018	1.12052
$36$	−79.2910	−0.367088
$37$	−32.1765	−0.142967	−0.0714835	−	0.997442i	$-0.522773\pi$
$37$	−32.1765	−0.142967	−0.0714835	+	0.997442i	$0.522773\pi$
$38$	30.5693	0.130500
$39$	79.2695	0.325469
$40$	111.232	0.439685
$41$	−27.4066	−0.104395	−0.0521975	−	0.998637i	$-0.516623\pi$
$41$	−27.4066	−0.104395	−0.0521975	+	0.998637i	$0.516623\pi$
$42$	42.6000	0.156508
$43$	−333.814	−1.18386	−0.591932	−	0.805988i	$-0.701635\pi$
$43$	−333.814	−1.18386	−0.591932	+	0.805988i	$0.701635\pi$
$44$	0	0
$45$	155.739	0.515915
$46$	23.0842	0.0739907
$47$	−408.579	−1.26803	−0.634015	−	0.773321i	$-0.718594\pi$
$47$	−408.579	−1.26803	−0.634015	+	0.773321i	$0.718594\pi$
$48$	−359.478	−1.08096
$49$	−112.930	−0.329242
$50$	−50.1962	−0.141976
$51$	−328.955	−0.903194
$52$	101.242	0.269995
$53$	91.6536	0.237540	0.118770	−	0.992922i	$-0.462105\pi$
$53$	91.6536	0.237540	0.118770	+	0.992922i	$0.462105\pi$
$54$	−47.2357	−0.119036
$55$	0	0
$56$	110.299	0.263201
$57$	404.698	0.940414
$58$	−54.4006	−0.123158
$59$	606.073	1.33736	0.668678	−	0.743552i	$-0.266861\pi$
$59$	606.073	1.33736	0.668678	+	0.743552i	$0.266861\pi$
$60$	726.393	1.56295
$61$	673.975	1.41465	0.707325	−	0.706888i	$-0.249902\pi$
$61$	673.975	1.41465	0.707325	+	0.706888i	$0.249902\pi$
$62$	148.578	0.304346
$63$	154.432	0.308834
$64$	−432.327	−0.844388
$65$	−198.854	−0.379458
$66$	0	0
$67$	61.5821	0.112290	0.0561451	−	0.998423i	$-0.482119\pi$
$67$	61.5821	0.112290	0.0561451	+	0.998423i	$0.482119\pi$
$68$	−420.137	−0.749252
$69$	305.604	0.533195
$70$	−106.866	−0.182470
$71$	721.468	1.20595	0.602976	−	0.797760i	$-0.293982\pi$
$71$	721.468	1.20595	0.602976	+	0.797760i	$0.293982\pi$
$72$	74.0366	0.121185
$73$	637.757	1.02252	0.511259	−	0.859427i	$-0.329179\pi$
$73$	637.757	1.02252	0.511259	+	0.859427i	$0.329179\pi$
$74$	14.8202	0.0232813
$75$	−664.532	−1.02311
$76$	516.876	0.780129
$77$	0	0
$78$	−36.5110	−0.0530007
$79$	185.484	0.264159	0.132080	−	0.991239i	$-0.457835\pi$
$79$	185.484	0.264159	0.132080	+	0.991239i	$0.457835\pi$
$80$	901.780	1.26028
$81$	−900.237	−1.23489
$82$	12.6233	0.0170001
$83$	665.368	0.879923	0.439962	−	0.898017i	$-0.354992\pi$
$83$	665.368	0.879923	0.439962	+	0.898017i	$0.354992\pi$
$84$	720.295	0.935603
$85$	825.210	1.05302
$86$	153.752	0.192785
$87$	−720.193	−0.887503
$88$	0	0
$89$	−407.360	−0.485169	−0.242585	−	0.970130i	$-0.577995\pi$
$89$	−407.360	−0.485169	−0.242585	+	0.970130i	$0.577995\pi$
$90$	−71.7322	−0.0840138
$91$	−197.185	−0.227149
$92$	390.314	0.442316
$93$	1966.98	2.19319
$94$	188.189	0.206491
$95$	−1015.22	−1.09641
$96$	520.299	0.553154
$97$	−942.625	−0.986691	−0.493346	−	0.869833i	$-0.664226\pi$
$97$	−942.625	−0.986691	−0.493346	+	0.869833i	$0.664226\pi$
$98$	52.0148	0.0536152
$99$	0	0
$100$	−848.733	−0.848733
$101$	−550.030	−0.541881	−0.270941	−	0.962596i	$-0.587335\pi$
$101$	−550.030	−0.541881	−0.270941	+	0.962596i	$0.587335\pi$
$102$	151.514	0.147080
$103$	−401.751	−0.384328	−0.192164	−	0.981363i	$-0.561550\pi$
$103$	−401.751	−0.384328	−0.192164	+	0.981363i	$0.561550\pi$
$104$	−94.5331	−0.0891320
$105$	−1414.76	−1.31492
$106$	−42.2150	−0.0386819
$107$	848.429	0.766549	0.383275	−	0.923634i	$-0.374796\pi$
$107$	848.429	0.766549	0.383275	+	0.923634i	$0.374796\pi$
$108$	−798.677	−0.711599
$109$	494.730	0.434739	0.217369	−	0.976089i	$-0.430252\pi$
$109$	494.730	0.434739	0.217369	+	0.976089i	$0.430252\pi$
$110$	0	0
$111$	196.201	0.167771
$112$	894.210	0.754419
$113$	1571.50	1.30826	0.654132	−	0.756380i	$-0.273034\pi$
$113$	1571.50	1.30826	0.654132	+	0.756380i	$0.273034\pi$
$114$	−186.401	−0.153141
$115$	−766.633	−0.621643
$116$	−919.822	−0.736236
$117$	−132.358	−0.104585
$118$	−279.153	−0.217781
$119$	818.283	0.630352
$120$	−678.256	−0.515967
$121$	0	0
$122$	−310.428	−0.230368
$123$	167.116	0.122507
$124$	2512.21	1.81938
$125$	−245.024	−0.175325
$126$	−71.1301	−0.0502919
$127$	−2314.26	−1.61699	−0.808495	−	0.588503i	$-0.799718\pi$
$127$	−2314.26	−1.61699	−0.808495	+	0.588503i	$0.799718\pi$
$128$	881.749	0.608877
$129$	2035.48	1.38926
$130$	91.5907	0.0617926
$131$	961.977	0.641590	0.320795	−	0.947149i	$-0.396050\pi$
$131$	961.977	0.641590	0.320795	+	0.947149i	$0.396050\pi$
$132$	0	0
$133$	−1006.70	−0.656328
$134$	−28.3643	−0.0182858
$135$	1568.72	1.00010
$136$	392.296	0.247346
$137$	418.692	0.261104	0.130552	−	0.991441i	$-0.458325\pi$
$137$	418.692	0.261104	0.130552	+	0.991441i	$0.458325\pi$
$138$	−140.759	−0.0868277
$139$	−2841.86	−1.73412	−0.867062	−	0.498201i	$-0.833994\pi$
$139$	−2841.86	−1.73412	−0.867062	+	0.498201i	$0.833994\pi$
$140$	−1806.92	−1.09080
$141$	2491.37	1.48802
$142$	−332.303	−0.196382
$143$	0	0
$144$	600.227	0.347354
$145$	1806.66	1.03473
$146$	−293.746	−0.166511
$147$	688.608	0.386364
$148$	250.586	0.139176
$149$	−2523.79	−1.38763	−0.693815	−	0.720153i	$-0.744072\pi$
$149$	−2523.79	−1.38763	−0.693815	+	0.720153i	$0.744072\pi$
$150$	306.079	0.166608
$151$	−3421.46	−1.84394	−0.921968	−	0.387266i	$-0.873419\pi$
$151$	−3421.46	−1.84394	−0.921968	+	0.387266i	$0.873419\pi$
$152$	−482.624	−0.257539
$153$	549.262	0.290230
$154$	0	0
$155$	−4934.34	−2.55700
$156$	−617.339	−0.316838
$157$	−1093.76	−0.555998	−0.277999	−	0.960581i	$-0.589671\pi$
$157$	−1093.76	−0.555998	−0.277999	+	0.960581i	$0.589671\pi$
$158$	−85.4327	−0.0430168
$159$	−558.872	−0.278751
$160$	−1305.21	−0.644913
$161$	−760.198	−0.372124
$162$	414.643	0.201095
$163$	3459.01	1.66215	0.831075	−	0.556160i	$-0.187726\pi$
$163$	3459.01	1.66215	0.831075	+	0.556160i	$0.187726\pi$
$164$	213.439	0.101627
$165$	0	0
$166$	−306.464	−0.143290
$167$	−3189.17	−1.47776	−0.738878	−	0.673840i	$-0.764644\pi$
$167$	−3189.17	−1.47776	−0.738878	+	0.673840i	$0.764644\pi$
$168$	−672.563	−0.308865
$169$	169.000	0.0769231
$170$	−380.086	−0.171478
$171$	−675.733	−0.302191
$172$	2599.70	1.15247
$173$	2867.43	1.26016	0.630078	−	0.776532i	$-0.283023\pi$
$173$	2867.43	1.26016	0.630078	+	0.776532i	$0.283023\pi$
$174$	331.716	0.144525
$175$	1653.04	0.714046
$176$	0	0
$177$	−3695.62	−1.56938
$178$	187.627	0.0790070
$179$	330.834	0.138143	0.0690717	−	0.997612i	$-0.477996\pi$
$179$	330.834	0.138143	0.0690717	+	0.997612i	$0.477996\pi$
$180$	−1212.87	−0.502234
$181$	−2983.98	−1.22540	−0.612701	−	0.790315i	$-0.709917\pi$
$181$	−2983.98	−1.22540	−0.612701	+	0.790315i	$0.709917\pi$
$182$	90.8219	0.0369899
$183$	−4109.67	−1.66008
$184$	−364.449	−0.146019
$185$	−492.186	−0.195601
$186$	−905.978	−0.357148
$187$	0	0
$188$	3181.95	1.23440
$189$	1555.55	0.598674
$190$	467.603	0.178545
$191$	−3935.96	−1.49108	−0.745539	−	0.666462i	$-0.767808\pi$
$191$	−3935.96	−1.49108	−0.745539	+	0.666462i	$0.767808\pi$
$192$	2636.18	0.990884
$193$	−1040.51	−0.388072	−0.194036	−	0.980994i	$-0.562158\pi$
$193$	−1040.51	−0.388072	−0.194036	+	0.980994i	$0.562158\pi$
$194$	434.166	0.160677
$195$	1212.54	0.445292
$196$	879.483	0.320511
$197$	−1480.11	−0.535298	−0.267649	−	0.963517i	$-0.586247\pi$
$197$	−1480.11	−0.535298	−0.267649	+	0.963517i	$0.586247\pi$
$198$	0	0
$199$	1286.73	0.458361	0.229181	−	0.973384i	$-0.426395\pi$
$199$	1286.73	0.458361	0.229181	+	0.973384i	$0.426395\pi$
$200$	792.490	0.280187
$201$	−375.506	−0.131772
$202$	253.340	0.0882422
$203$	1791.50	0.619401
$204$	2561.85	0.879243
$205$	−419.224	−0.142829
$206$	185.044	0.0625855
$207$	−510.274	−0.171336
$208$	−766.396	−0.255481
$209$	0	0
$210$	651.630	0.214127
$211$	−5575.45	−1.81910	−0.909550	−	0.415595i	$-0.863573\pi$
$211$	−5575.45	−1.81910	−0.909550	+	0.415595i	$0.863573\pi$
$212$	−713.785	−0.231240
$213$	−4399.26	−1.41518
$214$	−390.781	−0.124828
$215$	−5106.17	−1.61971
$216$	745.751	0.234916
$217$	−4892.92	−1.53066
$218$	−227.869	−0.0707947
$219$	−3888.82	−1.19992
$220$	0	0
$221$	−701.321	−0.213466
$222$	−90.3687	−0.0273205
$223$	2396.54	0.719660	0.359830	−	0.933018i	$-0.382835\pi$
$223$	2396.54	0.719660	0.359830	+	0.933018i	$0.382835\pi$
$224$	−1294.26	−0.386054
$225$	1109.58	0.328765
$226$	−723.819	−0.213043
$227$	−3968.95	−1.16048	−0.580239	−	0.814446i	$-0.697041\pi$
$227$	−3968.95	−1.16048	−0.580239	+	0.814446i	$0.697041\pi$
$228$	−3151.73	−0.915476
$229$	−635.796	−0.183470	−0.0917349	−	0.995783i	$-0.529241\pi$
$229$	−635.796	−0.183470	−0.0917349	+	0.995783i	$0.529241\pi$
$230$	353.106	0.101231
$231$	0	0
$232$	858.868	0.243049
$233$	−1333.88	−0.375043	−0.187522	−	0.982260i	$-0.560045\pi$
$233$	−1333.88	−0.375043	−0.187522	+	0.982260i	$0.560045\pi$
$234$	60.9631	0.0170311
$235$	−6249.81	−1.73486
$236$	−4720.01	−1.30189
$237$	−1131.02	−0.309989
$238$	−376.895	−0.102649
$239$	502.325	0.135953	0.0679764	−	0.997687i	$-0.478346\pi$
$239$	502.325	0.135953	0.0679764	+	0.997687i	$0.478346\pi$
$240$	−5498.74	−1.47893
$241$	−3710.42	−0.991740	−0.495870	−	0.868397i	$-0.665151\pi$
$241$	−3710.42	−0.991740	−0.495870	+	0.868397i	$0.665151\pi$
$242$	0	0
$243$	2720.37	0.718155
$244$	−5248.82	−1.37714
$245$	−1727.43	−0.450455
$246$	−76.9725	−0.0199495
$247$	862.804	0.222263
$248$	−2345.73	−0.600621
$249$	−4057.18	−1.03258
$250$	112.856	0.0285507
$251$	5287.21	1.32958	0.664792	−	0.747029i	$-0.268520\pi$
$251$	5287.21	1.32958	0.664792	+	0.747029i	$0.268520\pi$
$252$	−1202.69	−0.300644
$253$	0	0
$254$	1065.93	0.263317
$255$	−5031.84	−1.23571
$256$	3052.49	0.745236
$257$	2746.82	0.666700	0.333350	−	0.942803i	$-0.391821\pi$
$257$	2746.82	0.666700	0.333350	+	0.942803i	$0.391821\pi$
$258$	−937.529	−0.226233
$259$	−488.054	−0.117090
$260$	1548.65	0.369396
$261$	1202.52	0.285188
$262$	−443.080	−0.104479
$263$	−915.340	−0.214610	−0.107305	−	0.994226i	$-0.534222\pi$
$263$	−915.340	−0.214610	−0.107305	+	0.994226i	$0.534222\pi$
$264$	0	0
$265$	1401.98	0.324991
$266$	463.677	0.106879
$267$	2483.94	0.569343
$268$	−479.592	−0.109313
$269$	7033.92	1.59430	0.797148	−	0.603784i	$-0.206341\pi$
$269$	7033.92	1.59430	0.797148	+	0.603784i	$0.206341\pi$
$270$	−722.539	−0.162861
$271$	−3005.16	−0.673619	−0.336809	−	0.941573i	$-0.609348\pi$
$271$	−3005.16	−0.673619	−0.336809	+	0.941573i	$0.609348\pi$
$272$	3180.41	0.708973
$273$	1202.36	0.266558
$274$	−192.847	−0.0425193
$275$	0	0
$276$	−2380.00	−0.519055
$277$	−4329.80	−0.939180	−0.469590	−	0.882885i	$-0.655598\pi$
$277$	−4329.80	−0.939180	−0.469590	+	0.882885i	$0.655598\pi$
$278$	1308.94	0.282392
$279$	−3284.31	−0.704754
$280$	1687.18	0.360101
$281$	−3998.95	−0.848959	−0.424479	−	0.905438i	$-0.639543\pi$
$281$	−3998.95	−0.848959	−0.424479	+	0.905438i	$0.639543\pi$
$282$	−1147.51	−0.242316
$283$	256.940	0.0539699	0.0269850	−	0.999636i	$-0.491409\pi$
$283$	256.940	0.0539699	0.0269850	+	0.999636i	$0.491409\pi$
$284$	−5618.69	−1.17397
$285$	6190.45	1.28663
$286$	0	0
$287$	−415.705	−0.0854993
$288$	−868.754	−0.177749
$289$	−2002.64	−0.407620
$290$	−832.136	−0.168499
$291$	5747.80	1.15788
$292$	−4966.76	−0.995402
$293$	5282.27	1.05322	0.526610	−	0.850107i	$-0.323463\pi$
$293$	5282.27	1.05322	0.526610	+	0.850107i	$0.323463\pi$
$294$	−317.168	−0.0629171
$295$	9270.77	1.82971
$296$	−233.980	−0.0459453
$297$	0	0
$298$	1162.44	0.225968
$299$	651.539	0.126018
$300$	5175.28	0.995983
$301$	−5063.31	−0.969583
$302$	1575.90	0.300274
$303$	3353.89	0.635894
$304$	−3912.72	−0.738190
$305$	10309.4	1.93546
$306$	−252.986	−0.0472623
$307$	−586.545	−0.109042	−0.0545210	−	0.998513i	$-0.517363\pi$
$307$	−586.545	−0.109042	−0.0545210	+	0.998513i	$0.517363\pi$
$308$	0	0
$309$	2449.74	0.451006
$310$	2272.72	0.416393
$311$	−8175.90	−1.49072	−0.745358	−	0.666664i	$-0.767722\pi$
$311$	−8175.90	−1.49072	−0.745358	+	0.666664i	$0.767722\pi$
$312$	576.430	0.104596
$313$	1194.49	0.215708	0.107854	−	0.994167i	$-0.465602\pi$
$313$	1194.49	0.215708	0.107854	+	0.994167i	$0.465602\pi$
$314$	503.779	0.0905411
$315$	2362.26	0.422534
$316$	−1444.52	−0.257154
$317$	5687.61	1.00772	0.503861	−	0.863785i	$-0.331912\pi$
$317$	5687.61	1.00772	0.503861	+	0.863785i	$0.331912\pi$
$318$	257.413	0.0453930
$319$	0	0
$320$	−6613.07	−1.15526
$321$	−5173.43	−0.899541
$322$	350.142	0.0605983
$323$	−3580.49	−0.616792
$324$	7010.91	1.20215
$325$	−1416.76	−0.241809
$326$	−1593.20	−0.270672
$327$	−3016.69	−0.510163
$328$	−199.295	−0.0335494
$329$	−6197.35	−1.03851
$330$	0	0
$331$	−127.649	−0.0211971	−0.0105986	−	0.999944i	$-0.503374\pi$
$331$	−127.649	−0.0211971	−0.0105986	+	0.999944i	$0.503374\pi$
$332$	−5181.79	−0.856589
$333$	−327.600	−0.0539111
$334$	1468.91	0.240644
$335$	941.988	0.153631
$336$	−5452.58	−0.885306
$337$	−8115.26	−1.31177	−0.655884	−	0.754861i	$-0.727704\pi$
$337$	−8115.26	−1.31177	−0.655884	+	0.754861i	$0.727704\pi$
$338$	−77.8402	−0.0125265
$339$	−9582.43	−1.53524
$340$	−6426.62	−1.02509
$341$	0	0
$342$	311.238	0.0492100
$343$	−6915.57	−1.08865
$344$	−2427.42	−0.380459
$345$	4674.66	0.729494
$346$	−1320.72	−0.205209
$347$	5610.36	0.867954	0.433977	−	0.900924i	$-0.357110\pi$
$347$	5610.36	0.867954	0.433977	+	0.900924i	$0.357110\pi$
$348$	5608.76	0.863968
$349$	−2440.19	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$349$	−2440.19	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$350$	−761.378	−0.116278
$351$	−1333.20	−0.202738
$352$	0	0
$353$	8473.65	1.27764	0.638820	−	0.769356i	$-0.279423\pi$
$353$	8473.65	1.27764	0.638820	+	0.769356i	$0.279423\pi$
$354$	1702.18	0.255564
$355$	11035.9	1.64993
$356$	3172.46	0.472303
$357$	−4989.61	−0.739714
$358$	−152.380	−0.0224958
$359$	3351.74	0.492753	0.246376	−	0.969174i	$-0.420760\pi$
$359$	3351.74	0.492753	0.246376	+	0.969174i	$0.420760\pi$
$360$	1132.50	0.165800
$361$	−2454.09	−0.357791
$362$	1374.40	0.199550
$363$	0	0
$364$	1535.65	0.221126
$365$	9755.42	1.39896
$366$	1892.88	0.270335
$367$	−5340.29	−0.759567	−0.379783	−	0.925075i	$-0.624001\pi$
$367$	−5340.29	−0.759567	−0.379783	+	0.925075i	$0.624001\pi$
$368$	−2954.65	−0.418538
$369$	−279.037	−0.0393661
$370$	226.697	0.0318525
$371$	1390.21	0.194544
$372$	−15318.6	−2.13503
$373$	11825.2	1.64152	0.820760	−	0.571274i	$-0.193550\pi$
$373$	11825.2	1.64152	0.820760	+	0.571274i	$0.193550\pi$
$374$	0	0
$375$	1494.07	0.205743
$376$	−2971.09	−0.407507
$377$	−1535.43	−0.209757
$378$	−716.474	−0.0974906
$379$	−9087.61	−1.23166	−0.615830	−	0.787879i	$-0.711179\pi$
$379$	−9087.61	−1.23166	−0.615830	+	0.787879i	$0.711179\pi$
$380$	7906.38	1.06734
$381$	14111.6	1.89753
$382$	1812.87	0.242813
$383$	−6021.23	−0.803318	−0.401659	−	0.915789i	$-0.631566\pi$
$383$	−6021.23	−0.803318	−0.401659	+	0.915789i	$0.631566\pi$
$384$	−5376.60	−0.714514
$385$	0	0
$386$	479.254	0.0631953
$387$	−3398.68	−0.446421
$388$	7341.02	0.960526
$389$	2234.89	0.291295	0.145647	−	0.989337i	$-0.453474\pi$
$389$	2234.89	0.291295	0.145647	+	0.989337i	$0.453474\pi$
$390$	−558.488	−0.0725132
$391$	−2703.77	−0.349708
$392$	−821.202	−0.105809
$393$	−5865.80	−0.752902
$394$	681.729	0.0871701
$395$	2837.25	0.361411
$396$	0	0
$397$	−2136.22	−0.270060	−0.135030	−	0.990841i	$-0.543113\pi$
$397$	−2136.22	−0.270060	−0.135030	+	0.990841i	$0.543113\pi$
$398$	−592.659	−0.0746415
$399$	6138.49	0.770197
$400$	6424.85	0.803106
$401$	9584.99	1.19364	0.596822	−	0.802373i	$-0.296430\pi$
$401$	9584.99	1.19364	0.596822	+	0.802373i	$0.296430\pi$
$402$	172.955	0.0214583
$403$	4193.54	0.518351
$404$	4283.55	0.527512
$405$	−13770.4	−1.68953
$406$	−825.151	−0.100866
$407$	0	0
$408$	−2392.09	−0.290260
$409$	−2244.00	−0.271293	−0.135646	−	0.990757i	$-0.543311\pi$
$409$	−2244.00	−0.271293	−0.135646	+	0.990757i	$0.543311\pi$
$410$	193.092	0.0232588
$411$	−2553.04	−0.306404
$412$	3128.78	0.374136
$413$	9192.95	1.09529
$414$	235.028	0.0279010
$415$	10177.8	1.20387
$416$	1109.26	0.130736
$417$	17328.7	2.03498
$418$	0	0
$419$	−9472.49	−1.10444	−0.552221	−	0.833698i	$-0.686220\pi$
$419$	−9472.49	−1.10444	−0.552221	+	0.833698i	$0.686220\pi$
$420$	11018.0	1.28005
$421$	−16811.4	−1.94617	−0.973083	−	0.230453i	$-0.925979\pi$
$421$	−16811.4	−1.94617	−0.973083	+	0.230453i	$0.925979\pi$
$422$	2568.01	0.296230
$423$	−4159.90	−0.478158
$424$	666.485	0.0763381
$425$	5879.32	0.671032
$426$	2026.27	0.230453
$427$	10222.9	1.15860
$428$	−6607.44	−0.746222
$429$	0	0
$430$	2351.87	0.263761
$431$	16856.8	1.88391	0.941955	−	0.335739i	$-0.108986\pi$
$431$	16856.8	1.88391	0.941955	+	0.335739i	$0.108986\pi$
$432$	6045.93	0.673344
$433$	−4199.40	−0.466074	−0.233037	−	0.972468i	$-0.574866\pi$
$433$	−4199.40	−0.466074	−0.233037	+	0.972468i	$0.574866\pi$
$434$	2253.64	0.249259
$435$	−11016.4	−1.21424
$436$	−3852.88	−0.423210
$437$	3326.33	0.364119
$438$	1791.16	0.195400
$439$	−8470.73	−0.920925	−0.460462	−	0.887679i	$-0.652316\pi$
$439$	−8470.73	−0.920925	−0.460462	+	0.887679i	$0.652316\pi$
$440$	0	0
$441$	−1149.78	−0.124153
$442$	323.024	0.0347617
$443$	−8141.88	−0.873211	−0.436605	−	0.899653i	$-0.643819\pi$
$443$	−8141.88	−0.873211	−0.436605	+	0.899653i	$0.643819\pi$
$444$	−1527.98	−0.163322
$445$	−6231.16	−0.663787
$446$	−1103.83	−0.117192
$447$	15389.2	1.62838
$448$	−6557.56	−0.691552
$449$	8418.84	0.884876	0.442438	−	0.896799i	$-0.354114\pi$
$449$	8418.84	0.884876	0.442438	+	0.896799i	$0.354114\pi$
$450$	−511.066	−0.0535375
$451$	0	0
$452$	−12238.6	−1.27357
$453$	20862.9	2.16385
$454$	1828.07	0.188977
$455$	−3016.23	−0.310776
$456$	2942.87	0.302221
$457$	−15206.3	−1.55650	−0.778252	−	0.627953i	$-0.783893\pi$
$457$	−15206.3	−1.55650	−0.778252	+	0.627953i	$0.783893\pi$
$458$	292.843	0.0298770
$459$	5532.57	0.562611
$460$	5970.43	0.605158
$461$	13607.8	1.37479	0.687393	−	0.726285i	$-0.258755\pi$
$461$	13607.8	1.37479	0.687393	+	0.726285i	$0.258755\pi$
$462$	0	0
$463$	8150.46	0.818108	0.409054	−	0.912510i	$-0.365859\pi$
$463$	8150.46	0.818108	0.409054	+	0.912510i	$0.365859\pi$
$464$	6962.99	0.696657
$465$	30087.9	3.00063
$466$	614.374	0.0610736
$467$	12503.4	1.23895	0.619476	−	0.785016i	$-0.287345\pi$
$467$	12503.4	1.23895	0.619476	+	0.785016i	$0.287345\pi$
$468$	1030.78	0.101812
$469$	934.080	0.0919655
$470$	2878.62	0.282512
$471$	6669.38	0.652461
$472$	4407.22	0.429786
$473$	0	0
$474$	520.939	0.0504800
$475$	−7233.06	−0.698685
$476$	−6372.67	−0.613636
$477$	933.160	0.0895733
$478$	−231.367	−0.0221391
$479$	8789.34	0.838403	0.419202	−	0.907893i	$-0.362310\pi$
$479$	8789.34	0.838403	0.419202	+	0.907893i	$0.362310\pi$
$480$	7958.73	0.756802
$481$	418.294	0.0396519
$482$	1708.99	0.161499
$483$	4635.42	0.436686
$484$	0	0
$485$	−14418.8	−1.34995
$486$	−1252.98	−0.116947
$487$	−2735.77	−0.254558	−0.127279	−	0.991867i	$-0.540624\pi$
$487$	−2735.77	−0.254558	−0.127279	+	0.991867i	$0.540624\pi$
$488$	4900.99	0.454626
$489$	−21091.8	−1.95052
$490$	795.642	0.0733540
$491$	−18713.6	−1.72002	−0.860012	−	0.510273i	$-0.829544\pi$
$491$	−18713.6	−1.72002	−0.860012	+	0.510273i	$0.829544\pi$
$492$	−1301.48	−0.119258
$493$	6371.76	0.582089
$494$	−397.401	−0.0361942
$495$	0	0
$496$	−19017.2	−1.72157
$497$	10943.3	0.987672
$498$	1868.71	0.168150
$499$	32.7265	0.00293595	0.00146797	−	0.999999i	$-0.499533\pi$
$499$	32.7265	0.00293595	0.00146797	+	0.999999i	$0.499533\pi$
$500$	1908.21	0.170676
$501$	19446.4	1.73414
$502$	−2435.25	−0.216515
$503$	20953.7	1.85741	0.928707	−	0.370813i	$-0.120921\pi$
$503$	20953.7	1.85741	0.928707	+	0.370813i	$0.120921\pi$
$504$	1122.99	0.0992500
$505$	−8413.51	−0.741379
$506$	0	0
$507$	−1030.50	−0.0902688
$508$	18023.2	1.57411
$509$	−21626.7	−1.88327	−0.941636	−	0.336632i	$-0.890712\pi$
$509$	−21626.7	−1.88327	−0.941636	+	0.336632i	$0.890712\pi$
$510$	2317.63	0.201228
$511$	9673.53	0.837440
$512$	−8459.94	−0.730235
$513$	−6806.47	−0.585795
$514$	−1265.17	−0.108568
$515$	−6145.37	−0.525820
$516$	−15852.0	−1.35242
$517$	0	0
$518$	224.794	0.0190674
$519$	−17484.6	−1.47878
$520$	−1446.02	−0.121947
$521$	−2525.15	−0.212339	−0.106170	−	0.994348i	$-0.533859\pi$
$521$	−2525.15	−0.212339	−0.106170	+	0.994348i	$0.533859\pi$
$522$	−553.872	−0.0464412
$523$	−14741.4	−1.23250	−0.616249	−	0.787552i	$-0.711348\pi$
$523$	−14741.4	−1.23250	−0.616249	+	0.787552i	$0.711348\pi$
$524$	−7491.74	−0.624577
$525$	−10079.7	−0.837929
$526$	421.599	0.0349479
$527$	−17402.5	−1.43845
$528$	0	0
$529$	−9655.15	−0.793552
$530$	−645.740	−0.0529230
$531$	6170.65	0.504300
$532$	7840.01	0.638924
$533$	356.286	0.0289540
$534$	−1144.08	−0.0927142
$535$	12978.0	1.04876
$536$	447.811	0.0360867
$537$	−2017.31	−0.162110
$538$	−3239.77	−0.259622
$539$	0	0
$540$	−12216.9	−0.973579
$541$	4883.90	0.388124	0.194062	−	0.980989i	$-0.437834\pi$
$541$	4883.90	0.388124	0.194062	+	0.980989i	$0.437834\pi$
$542$	1384.16	0.109695
$543$	18195.3	1.43800
$544$	−4603.24	−0.362799
$545$	7567.62	0.594791
$546$	−553.800	−0.0434074
$547$	−25011.3	−1.95504	−0.977519	−	0.210849i	$-0.932377\pi$
$547$	−25011.3	−1.95504	−0.977519	+	0.210849i	$0.932377\pi$
$548$	−3260.72	−0.254180
$549$	6861.99	0.533447
$550$	0	0
$551$	−7838.90	−0.606077
$552$	2222.29	0.171353
$553$	2813.43	0.216346
$554$	1994.28	0.152940
$555$	3001.18	0.229537
$556$	22132.0	1.68814
$557$	−18354.2	−1.39622	−0.698110	−	0.715991i	$-0.745975\pi$
$557$	−18354.2	−1.39622	−0.698110	+	0.715991i	$0.745975\pi$
$558$	1512.73	0.114765
$559$	4339.58	0.328345
$560$	13678.2	1.03216
$561$	0	0
$562$	1841.89	0.138248
$563$	−18508.0	−1.38547	−0.692733	−	0.721194i	$-0.743594\pi$
$563$	−18508.0	−1.38547	−0.692733	+	0.721194i	$0.743594\pi$
$564$	−19402.5	−1.44857
$565$	24038.3	1.78991
$566$	−118.345	−0.00878869
$567$	−13654.8	−1.01137
$568$	5246.35	0.387557
$569$	−11981.7	−0.882778	−0.441389	−	0.897316i	$-0.645514\pi$
$569$	−11981.7	−0.882778	−0.441389	+	0.897316i	$0.645514\pi$
$570$	−2851.28	−0.209521
$571$	7951.96	0.582801	0.291400	−	0.956601i	$-0.405879\pi$
$571$	7951.96	0.582801	0.291400	+	0.956601i	$0.405879\pi$
$572$	0	0
$573$	24000.1	1.74977
$574$	191.471	0.0139231
$575$	−5461.98	−0.396140
$576$	−4401.68	−0.318408
$577$	−18170.7	−1.31101	−0.655506	−	0.755190i	$-0.727545\pi$
$577$	−18170.7	−1.31101	−0.655506	+	0.755190i	$0.727545\pi$
$578$	922.400	0.0663785
$579$	6344.70	0.455400
$580$	−14070.0	−1.00729
$581$	10092.3	0.720656
$582$	−2647.40	−0.188553
$583$	0	0
$584$	4637.62	0.328607
$585$	−2024.61	−0.143089
$586$	−2432.98	−0.171511
$587$	−12648.4	−0.889365	−0.444682	−	0.895688i	$-0.646683\pi$
$587$	−12648.4	−0.889365	−0.444682	+	0.895688i	$0.646683\pi$
$588$	−5362.78	−0.376118
$589$	21409.5	1.49773
$590$	−4270.05	−0.297958
$591$	9025.21	0.628169
$592$	−1896.91	−0.131694
$593$	−10554.1	−0.730866	−0.365433	−	0.930838i	$-0.619079\pi$
$593$	−10554.1	−0.730866	−0.365433	+	0.930838i	$0.619079\pi$
$594$	0	0
$595$	12516.8	0.862420
$596$	19654.9	1.35083
$597$	−7846.03	−0.537884
$598$	−300.094	−0.0205213
$599$	23100.4	1.57572	0.787861	−	0.615853i	$-0.211189\pi$
$599$	23100.4	1.57572	0.787861	+	0.615853i	$0.211189\pi$
$600$	−4832.33	−0.328798
$601$	−12866.2	−0.873252	−0.436626	−	0.899643i	$-0.643827\pi$
$601$	−12866.2	−0.873252	−0.436626	+	0.899643i	$0.643827\pi$
$602$	2332.13	0.157891
$603$	626.990	0.0423433
$604$	26645.8	1.79504
$605$	0	0
$606$	−1544.78	−0.103552
$607$	−15851.3	−1.05994	−0.529971	−	0.848016i	$-0.677797\pi$
$607$	−15851.3	−1.05994	−0.529971	+	0.848016i	$0.677797\pi$
$608$	5663.16	0.377749
$609$	−10923.9	−0.726863
$610$	−4748.45	−0.315179
$611$	5311.53	0.351688
$612$	−4277.58	−0.282534
$613$	−1838.69	−0.121149	−0.0605743	−	0.998164i	$-0.519293\pi$
$613$	−1838.69	−0.121149	−0.0605743	+	0.998164i	$0.519293\pi$
$614$	270.158	0.0177569
$615$	2556.29	0.167609
$616$	0	0
$617$	20653.2	1.34759	0.673796	−	0.738917i	$-0.264662\pi$
$617$	20653.2	1.34759	0.673796	+	0.738917i	$0.264662\pi$
$618$	−1128.33	−0.0734437
$619$	−20029.3	−1.30056	−0.650278	−	0.759697i	$-0.725347\pi$
$619$	−20029.3	−1.30056	−0.650278	+	0.759697i	$0.725347\pi$
$620$	38427.9	2.48920
$621$	−5139.85	−0.332134
$622$	3765.76	0.242755
$623$	−6178.85	−0.397352
$624$	4673.21	0.299805
$625$	−17370.7	−1.11173
$626$	−550.174	−0.0351268
$627$	0	0
$628$	8518.06	0.541254
$629$	−1735.85	−0.110036
$630$	−1088.04	−0.0688071
$631$	14099.0	0.889499	0.444750	−	0.895655i	$-0.353293\pi$
$631$	14099.0	0.889499	0.444750	+	0.895655i	$0.353293\pi$
$632$	1348.80	0.0848929
$633$	33997.2	2.13470
$634$	−2619.67	−0.164102
$635$	−35400.0	−2.21230
$636$	4352.41	0.271359
$637$	1468.09	0.0913154
$638$	0	0
$639$	7345.54	0.454749
$640$	13487.6	0.833040
$641$	−12016.0	−0.740409	−0.370204	−	0.928950i	$-0.620712\pi$
$641$	−12016.0	−0.740409	−0.370204	+	0.928950i	$0.620712\pi$
$642$	2382.84	0.146485
$643$	1550.60	0.0951008	0.0475504	−	0.998869i	$-0.484859\pi$
$643$	1550.60	0.0951008	0.0475504	+	0.998869i	$0.484859\pi$
$644$	5920.31	0.362256
$645$	31135.7	1.90072
$646$	1649.15	0.100441
$647$	2798.03	0.170018	0.0850091	−	0.996380i	$-0.472908\pi$
$647$	2798.03	0.170018	0.0850091	+	0.996380i	$0.472908\pi$
$648$	−6546.32	−0.396857
$649$	0	0
$650$	652.550	0.0393771
$651$	29835.3	1.79622
$652$	−26938.3	−1.61807
$653$	−26132.2	−1.56605	−0.783027	−	0.621988i	$-0.786325\pi$
$653$	−26132.2	−1.56605	−0.783027	+	0.621988i	$0.786325\pi$
$654$	1389.47	0.0830771
$655$	14714.8	0.877796
$656$	−1615.72	−0.0961634
$657$	6493.24	0.385579
$658$	2854.46	0.169116
$659$	−25067.0	−1.48175	−0.740874	−	0.671644i	$-0.765588\pi$
$659$	−25067.0	−1.48175	−0.740874	+	0.671644i	$0.765588\pi$
$660$	0	0
$661$	25175.2	1.48139	0.740696	−	0.671840i	$-0.234496\pi$
$661$	25175.2	1.48139	0.740696	+	0.671840i	$0.234496\pi$
$662$	58.7944	0.00345183
$663$	4276.41	0.250501
$664$	4838.41	0.282781
$665$	−15398.9	−0.897960
$666$	150.890	0.00877911
$667$	−5919.47	−0.343633
$668$	24836.8	1.43857
$669$	−14613.3	−0.844516
$670$	−433.873	−0.0250179
$671$	0	0
$672$	7891.93	0.453032
$673$	−19571.8	−1.12101	−0.560504	−	0.828152i	$-0.689392\pi$
$673$	−19571.8	−1.12101	−0.560504	+	0.828152i	$0.689392\pi$
$674$	3737.83	0.213614
$675$	11176.5	0.637310
$676$	−1316.15	−0.0748832
$677$	−3451.02	−0.195914	−0.0979569	−	0.995191i	$-0.531231\pi$
$677$	−3451.02	−0.195914	−0.0979569	+	0.995191i	$0.531231\pi$
$678$	4413.60	0.250005
$679$	−14297.8	−0.808098
$680$	6000.74	0.338409
$681$	24201.3	1.36181
$682$	0	0
$683$	1697.19	0.0950824	0.0475412	−	0.998869i	$-0.484861\pi$
$683$	1697.19	0.0950824	0.0475412	+	0.998869i	$0.484861\pi$
$684$	5262.51	0.294177
$685$	6404.51	0.357232
$686$	3185.26	0.177280
$687$	3876.87	0.215301
$688$	−19679.5	−1.09051
$689$	−1191.50	−0.0658816
$690$	−2153.12	−0.118794
$691$	−15604.9	−0.859101	−0.429551	−	0.903043i	$-0.641328\pi$
$691$	−15604.9	−0.859101	−0.429551	+	0.903043i	$0.641328\pi$
$692$	−22331.2	−1.22674
$693$	0	0
$694$	−2584.09	−0.141341
$695$	−43470.3	−2.37255
$696$	−5237.08	−0.285217
$697$	−1478.53	−0.0803489
$698$	1123.93	0.0609478
$699$	8133.51	0.440111
$700$	−12873.6	−0.695111
$701$	−6578.36	−0.354438	−0.177219	−	0.984171i	$-0.556710\pi$
$701$	−6578.36	−0.354438	−0.177219	+	0.984171i	$0.556710\pi$
$702$	614.064	0.0330148
$703$	2135.54	0.114571
$704$	0	0
$705$	38109.2	2.03585
$706$	−3902.90	−0.208056
$707$	−8342.88	−0.443800
$708$	28781.0	1.52776
$709$	−23783.1	−1.25979	−0.629896	−	0.776679i	$-0.716903\pi$
$709$	−23783.1	−1.25979	−0.629896	+	0.776679i	$0.716903\pi$
$710$	−5083.06	−0.268682
$711$	1888.48	0.0996113
$712$	−2962.23	−0.155919
$713$	16167.2	0.849181
$714$	2298.18	0.120458
$715$	0	0
$716$	−2576.48	−0.134480
$717$	−3063.00	−0.159540
$718$	−1543.79	−0.0802419
$719$	15412.9	0.799450	0.399725	−	0.916635i	$-0.369106\pi$
$719$	15412.9	0.799450	0.399725	+	0.916635i	$0.369106\pi$
$720$	9181.35	0.475235
$721$	−6093.79	−0.314763
$722$	1130.33	0.0582641
$723$	22624.9	1.16380
$724$	23238.8	1.19291
$725$	12871.8	0.659375
$726$	0	0
$727$	10692.5	0.545477	0.272739	−	0.962088i	$-0.412071\pi$
$727$	10692.5	0.545477	0.272739	+	0.962088i	$0.412071\pi$
$728$	−1433.88	−0.0729989
$729$	7718.53	0.392142
$730$	−4493.28	−0.227813
$731$	−18008.5	−0.911176
$732$	32005.5	1.61606
$733$	1843.31	0.0928844	0.0464422	−	0.998921i	$-0.485212\pi$
$733$	1843.31	0.0928844	0.0464422	+	0.998921i	$0.485212\pi$
$734$	2459.70	0.123691
$735$	10533.3	0.528606
$736$	4276.49	0.214176
$737$	0	0
$738$	128.523	0.00641054
$739$	24309.8	1.21008	0.605041	−	0.796194i	$-0.293157\pi$
$739$	24309.8	1.21008	0.605041	+	0.796194i	$0.293157\pi$
$740$	3833.07	0.190414
$741$	−5261.08	−0.260824
$742$	−640.320	−0.0316804
$743$	−7007.90	−0.346023	−0.173011	−	0.984920i	$-0.555350\pi$
$743$	−7007.90	−0.346023	−0.173011	+	0.984920i	$0.555350\pi$
$744$	14303.5	0.704825
$745$	−38605.0	−1.89850
$746$	−5446.61	−0.267312
$747$	6774.36	0.331808
$748$	0	0
$749$	12869.0	0.627802
$750$	−688.159	−0.0335040
$751$	9977.32	0.484790	0.242395	−	0.970178i	$-0.422067\pi$
$751$	9977.32	0.484790	0.242395	+	0.970178i	$0.422067\pi$
$752$	−24087.2	−1.16804
$753$	−32239.5	−1.56026
$754$	707.207	0.0341578
$755$	−52336.2	−2.52279
$756$	−12114.4	−0.582798
$757$	33732.2	1.61958	0.809788	−	0.586723i	$-0.199582\pi$
$757$	33732.2	1.61958	0.809788	+	0.586723i	$0.199582\pi$
$758$	4185.69	0.200569
$759$	0	0
$760$	−7382.44	−0.352354
$761$	−30690.6	−1.46193	−0.730967	−	0.682413i	$-0.760931\pi$
$761$	−30690.6	−1.46193	−0.730967	+	0.682413i	$0.760931\pi$
$762$	−6499.69	−0.309001
$763$	7504.09	0.356050
$764$	30652.7	1.45154
$765$	8401.77	0.397081
$766$	2773.34	0.130816
$767$	−7878.95	−0.370916
$768$	−18613.0	−0.874530
$769$	12985.5	0.608933	0.304467	−	0.952523i	$-0.401522\pi$
$769$	12985.5	0.608933	0.304467	+	0.952523i	$0.401522\pi$
$770$	0	0
$771$	−16749.1	−0.782368
$772$	8103.38	0.377781
$773$	−10488.7	−0.488035	−0.244018	−	0.969771i	$-0.578466\pi$
$773$	−10488.7	−0.488035	−0.244018	+	0.969771i	$0.578466\pi$
$774$	1565.41	0.0726970
$775$	−35155.3	−1.62944
$776$	−6854.55	−0.317093
$777$	2975.99	0.137404
$778$	−1029.38	−0.0474357
$779$	1818.97	0.0836601
$780$	−9443.10	−0.433484
$781$	0	0
$782$	1245.34	0.0569479
$783$	12112.7	0.552837
$784$	−6657.62	−0.303281
$785$	−16730.7	−0.760693
$786$	2701.75	0.122606
$787$	11131.4	0.504180	0.252090	−	0.967704i	$-0.418882\pi$
$787$	11131.4	0.504180	0.252090	+	0.967704i	$0.418882\pi$
$788$	11526.9	0.521103
$789$	5581.43	0.251843
$790$	−1306.82	−0.0588538
$791$	23836.5	1.07147
$792$	0	0
$793$	−8761.68	−0.392353
$794$	983.930	0.0439778
$795$	−8548.76	−0.381375
$796$	−10020.9	−0.446206
$797$	−23227.3	−1.03231	−0.516156	−	0.856494i	$-0.672638\pi$
$797$	−23227.3	−1.03231	−0.516156	+	0.856494i	$0.672638\pi$
$798$	−2827.34	−0.125422
$799$	−22041.9	−0.975955
$800$	−9299.16	−0.410969
$801$	−4147.48	−0.182951
$802$	−4414.78	−0.194378
$803$	0	0
$804$	2924.39	0.128278
$805$	−11628.3	−0.509124
$806$	−1931.52	−0.0844104
$807$	−42890.4	−1.87090
$808$	−3999.69	−0.174144
$809$	19819.7	0.861341	0.430670	−	0.902509i	$-0.358277\pi$
$809$	19819.7	0.861341	0.430670	+	0.902509i	$0.358277\pi$
$810$	6342.56	0.275130
$811$	−12691.4	−0.549512	−0.274756	−	0.961514i	$-0.588597\pi$
$811$	−12691.4	−0.549512	−0.274756	+	0.961514i	$0.588597\pi$
$812$	−13951.9	−0.602976
$813$	18324.4	0.790488
$814$	0	0
$815$	52910.6	2.27408
$816$	−19393.0	−0.831976
$817$	22155.1	0.948725
$818$	1033.57	0.0441784
$819$	−2007.61	−0.0856552
$820$	3264.86	0.139041
$821$	5011.90	0.213053	0.106527	−	0.994310i	$-0.466027\pi$
$821$	5011.90	0.213053	0.106527	+	0.994310i	$0.466027\pi$
$822$	1175.91	0.0498962
$823$	2964.04	0.125541	0.0627703	−	0.998028i	$-0.480006\pi$
$823$	2964.04	0.125541	0.0627703	+	0.998028i	$0.480006\pi$
$824$	−2921.44	−0.123511
$825$	0	0
$826$	−4234.21	−0.178362
$827$	21651.8	0.910408	0.455204	−	0.890387i	$-0.349566\pi$
$827$	21651.8	0.910408	0.455204	+	0.890387i	$0.349566\pi$
$828$	3973.94	0.166792
$829$	31704.6	1.32828	0.664141	−	0.747607i	$-0.268797\pi$
$829$	31704.6	1.32828	0.664141	+	0.747607i	$0.268797\pi$
$830$	−4687.81	−0.196044
$831$	26401.6	1.10212
$832$	5620.25	0.234191
$833$	−6092.33	−0.253405
$834$	−7981.46	−0.331385
$835$	−48783.0	−2.02180
$836$	0	0
$837$	−33081.9	−1.36616
$838$	4362.96	0.179852
$839$	4433.44	0.182431	0.0912154	−	0.995831i	$-0.470925\pi$
$839$	4433.44	0.182431	0.0912154	+	0.995831i	$0.470925\pi$
$840$	−10287.8	−0.422576
$841$	−10439.1	−0.428023
$842$	7743.20	0.316922
$843$	24384.2	0.996248
$844$	43420.8	1.77086
$845$	2585.10	0.105243
$846$	1916.02	0.0778653
$847$	0	0
$848$	5403.30	0.218809
$849$	−1566.73	−0.0633334
$850$	−2707.97	−0.109274
$851$	1612.63	0.0649592
$852$	34260.8	1.37765
$853$	−48187.1	−1.93423	−0.967114	−	0.254345i	$-0.918140\pi$
$853$	−48187.1	−1.93423	−0.967114	+	0.254345i	$0.918140\pi$
$854$	−4708.59	−0.188671
$855$	−10336.3	−0.413444
$856$	6169.59	0.246346
$857$	39097.9	1.55841	0.779206	−	0.626768i	$-0.215623\pi$
$857$	39097.9	1.55841	0.779206	+	0.626768i	$0.215623\pi$
$858$	0	0
$859$	1584.32	0.0629293	0.0314647	−	0.999505i	$-0.489983\pi$
$859$	1584.32	0.0629293	0.0314647	+	0.999505i	$0.489983\pi$
$860$	39766.1	1.57676
$861$	2534.83	0.100333
$862$	−7764.14	−0.306784
$863$	−36411.8	−1.43624	−0.718118	−	0.695921i	$-0.754996\pi$
$863$	−36411.8	−1.43624	−0.718118	+	0.695921i	$0.754996\pi$
$864$	−8750.72	−0.344566
$865$	43861.6	1.72409
$866$	1934.21	0.0758975
$867$	12211.4	0.478339
$868$	38105.3	1.49007
$869$	0	0
$870$	5074.08	0.197733
$871$	−800.567	−0.0311437
$872$	3597.56	0.139712
$873$	−9597.21	−0.372069
$874$	−1532.09	−0.0592947
$875$	−3716.54	−0.143591
$876$	30285.6	1.16810
$877$	23475.7	0.903899	0.451949	−	0.892044i	$-0.350729\pi$
$877$	23475.7	0.903899	0.451949	+	0.892044i	$0.350729\pi$
$878$	3901.56	0.149967
$879$	−32209.4	−1.23595
$880$	0	0
$881$	14503.6	0.554639	0.277320	−	0.960778i	$-0.410554\pi$
$881$	14503.6	0.554639	0.277320	+	0.960778i	$0.410554\pi$
$882$	529.582	0.0202176
$883$	8195.21	0.312334	0.156167	−	0.987731i	$-0.450086\pi$
$883$	8195.21	0.312334	0.156167	+	0.987731i	$0.450086\pi$
$884$	5461.79	0.207805
$885$	−56529.9	−2.14716
$886$	3750.09	0.142197
$887$	45753.7	1.73197	0.865985	−	0.500069i	$-0.166692\pi$
$887$	45753.7	1.73197	0.865985	+	0.500069i	$0.166692\pi$
$888$	1426.73	0.0539165
$889$	−35102.9	−1.32431
$890$	2870.03	0.108094
$891$	0	0
$892$	−18663.9	−0.700576
$893$	27117.2	1.01617
$894$	−7088.15	−0.265172
$895$	5060.58	0.189002
$896$	13374.4	0.498669
$897$	−3972.86	−0.147882
$898$	−3877.66	−0.144097
$899$	−38099.9	−1.41346
$900$	−8641.27	−0.320047
$901$	4944.51	0.182825
$902$	0	0
$903$	30874.3	1.13780
$904$	11427.6	0.420437
$905$	−45644.4	−1.67654
$906$	−9609.29	−0.352370
$907$	40948.6	1.49909	0.749546	−	0.661952i	$-0.230272\pi$
$907$	40948.6	1.49909	0.749546	+	0.661952i	$0.230272\pi$
$908$	30909.6	1.12970
$909$	−5600.06	−0.204337
$910$	1389.25	0.0506080
$911$	−3615.42	−0.131487	−0.0657433	−	0.997837i	$-0.520942\pi$
$911$	−3615.42	−0.131487	−0.0657433	+	0.997837i	$0.520942\pi$
$912$	23858.4	0.866261
$913$	0	0
$914$	7003.93	0.253467
$915$	−62863.3	−2.27125
$916$	4951.49	0.178605
$917$	14591.3	0.525461
$918$	−2548.26	−0.0916179
$919$	332.592	0.0119382	0.00596910	−	0.999982i	$-0.498100\pi$
$919$	332.592	0.0119382	0.00596910	+	0.999982i	$0.498100\pi$
$920$	−5574.79	−0.199777
$921$	3576.55	0.127960
$922$	−6267.64	−0.223876
$923$	−9379.09	−0.334471
$924$	0	0
$925$	−3506.64	−0.124646
$926$	−3754.05	−0.133224
$927$	−4090.38	−0.144925
$928$	−10078.0	−0.356496
$929$	−2723.57	−0.0961868	−0.0480934	−	0.998843i	$-0.515315\pi$
$929$	−2723.57	−0.0961868	−0.0480934	+	0.998843i	$0.515315\pi$
$930$	−13858.3	−0.488635
$931$	7495.12	0.263848
$932$	10388.0	0.365098
$933$	49853.8	1.74935
$934$	−5759.00	−0.201756
$935$	0	0
$936$	−962.476	−0.0336106
$937$	−7194.98	−0.250853	−0.125427	−	0.992103i	$-0.540030\pi$
$937$	−7194.98	−0.250853	−0.125427	+	0.992103i	$0.540030\pi$
$938$	−430.231	−0.0149760
$939$	−7283.59	−0.253132
$940$	48672.6	1.68886
$941$	37735.9	1.30729	0.653643	−	0.756803i	$-0.273240\pi$
$941$	37735.9	1.30729	0.653643	+	0.756803i	$0.273240\pi$
$942$	−3071.87	−0.106249
$943$	1373.58	0.0474335
$944$	35730.1	1.23190
$945$	23794.4	0.819080
$946$	0	0
$947$	−161.336	−0.00553612	−0.00276806	−	0.999996i	$-0.500881\pi$
$947$	−161.336	−0.00553612	−0.00276806	+	0.999996i	$0.500881\pi$
$948$	8808.20	0.301769
$949$	−8290.84	−0.283595
$950$	3331.50	0.113777
$951$	−34681.1	−1.18256
$952$	5950.37	0.202576
$953$	14926.5	0.507363	0.253682	−	0.967288i	$-0.418358\pi$
$953$	14926.5	0.507363	0.253682	+	0.967288i	$0.418358\pi$
$954$	−429.807	−0.0145865
$955$	−60206.2	−2.04003
$956$	−3912.03	−0.132348
$957$	0	0
$958$	−4048.31	−0.136529
$959$	6350.75	0.213844
$960$	40324.2	1.35568
$961$	74267.0	2.49293
$962$	−192.663	−0.00645708
$963$	8638.17	0.289056
$964$	28896.2	0.965441
$965$	−15916.2	−0.530943
$966$	−2135.04	−0.0711117
$967$	−16090.2	−0.535084	−0.267542	−	0.963546i	$-0.586211\pi$
$967$	−16090.2	−0.535084	−0.267542	+	0.963546i	$0.586211\pi$
$968$	0	0
$969$	21832.6	0.723801
$970$	6641.21	0.219831
$971$	41457.3	1.37016	0.685082	−	0.728466i	$-0.259767\pi$
$971$	41457.3	1.37016	0.685082	+	0.728466i	$0.259767\pi$
$972$	−21185.8	−0.699111
$973$	−43105.4	−1.42024
$974$	1260.08	0.0414532
$975$	8638.92	0.283761
$976$	39733.2	1.30310
$977$	47867.4	1.56747	0.783733	−	0.621098i	$-0.213313\pi$
$977$	47867.4	1.56747	0.783733	+	0.621098i	$0.213313\pi$
$978$	9714.75	0.317631
$979$	0	0
$980$	13453.0	0.438510
$981$	5037.03	0.163935
$982$	8619.34	0.280096
$983$	9453.88	0.306747	0.153373	−	0.988168i	$-0.450986\pi$
$983$	9453.88	0.306747	0.153373	+	0.988168i	$0.450986\pi$
$984$	1215.23	0.0393701
$985$	−22640.5	−0.732371
$986$	−2934.79	−0.0947898
$987$	37789.3	1.21869
$988$	−6719.39	−0.216369
$989$	16730.2	0.537907
$990$	0	0
$991$	−51881.9	−1.66305	−0.831525	−	0.555487i	$-0.812532\pi$
$991$	−51881.9	−1.66305	−0.831525	+	0.555487i	$0.812532\pi$
$992$	27525.1	0.880969
$993$	778.361	0.0248747
$994$	−5040.39	−0.160837
$995$	19682.4	0.627110
$996$	31596.8	1.00520
$997$	−17248.2	−0.547900	−0.273950	−	0.961744i	$-0.588330\pi$
$997$	−17248.2	−0.547900	−0.273950	+	0.961744i	$0.588330\pi$
$998$	−15.0736	−0.000478102 0
$999$	−3299.83	−0.104506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.h.1.7	✓	15
11.10	odd	2		1573.4.a.k.1.9	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1573.4.a.h.1.7	✓	15	1.1	even	1	trivial
1573.4.a.k.1.9	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)

\(f(q)\)	\(=\)	\(q-0.460593 q^{2} -6.09765 q^{3} -7.78785 q^{4} +15.2965 q^{5} +2.80854 q^{6} +15.1681 q^{7} +7.27177 q^{8} +10.1814 q^{9} +O(q^{10})\)	\(q-0.460593 q^{2} -6.09765 q^{3} -7.78785 q^{4} +15.2965 q^{5} +2.80854 q^{6} +15.1681 q^{7} +7.27177 q^{8} +10.1814 q^{9} -7.04544 q^{10} +47.4876 q^{12} -13.0000 q^{13} -6.98630 q^{14} -93.2725 q^{15} +58.9535 q^{16} +53.9478 q^{17} -4.68947 q^{18} -66.3695 q^{19} -119.127 q^{20} -92.4895 q^{21} -50.1184 q^{23} -44.3408 q^{24} +108.982 q^{25} +5.98771 q^{26} +102.554 q^{27} -118.127 q^{28} +118.110 q^{29} +42.9607 q^{30} -322.580 q^{31} -85.3278 q^{32} -24.8480 q^{34} +232.018 q^{35} -79.2910 q^{36} -32.1765 q^{37} +30.5693 q^{38} +79.2695 q^{39} +111.232 q^{40} -27.4066 q^{41} +42.6000 q^{42} -333.814 q^{43} +155.739 q^{45} +23.0842 q^{46} -408.579 q^{47} -359.478 q^{48} -112.930 q^{49} -50.1962 q^{50} -328.955 q^{51} +101.242 q^{52} +91.6536 q^{53} -47.2357 q^{54} +110.299 q^{56} +404.698 q^{57} -54.4006 q^{58} +606.073 q^{59} +726.393 q^{60} +673.975 q^{61} +148.578 q^{62} +154.432 q^{63} -432.327 q^{64} -198.854 q^{65} +61.5821 q^{67} -420.137 q^{68} +305.604 q^{69} -106.866 q^{70} +721.468 q^{71} +74.0366 q^{72} +637.757 q^{73} +14.8202 q^{74} -664.532 q^{75} +516.876 q^{76} -36.5110 q^{78} +185.484 q^{79} +901.780 q^{80} -900.237 q^{81} +12.6233 q^{82} +665.368 q^{83} +720.295 q^{84} +825.210 q^{85} +153.752 q^{86} -720.193 q^{87} -407.360 q^{89} -71.7322 q^{90} -197.185 q^{91} +390.314 q^{92} +1966.98 q^{93} +188.189 q^{94} -1015.22 q^{95} +520.299 q^{96} -942.625 q^{97} +52.0148 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) \) 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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