LMFDB - Embedded newform 1573.4.a.k.1.4

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:	$0$
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			1.4
Root			$-3.04830$ 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)

$f(q)$	$=$	$q-3.04830 q^{2} +7.84090 q^{3} +1.29211 q^{4} -10.4483 q^{5} -23.9014 q^{6} -17.4647 q^{7} +20.4476 q^{8} +34.4796 q^{9} +O(q^{10})$	\(q-3.04830 q^{2} +7.84090 q^{3} +1.29211 q^{4} -10.4483 q^{5} -23.9014 q^{6} -17.4647 q^{7} +20.4476 q^{8} +34.4796 q^{9} +31.8495 q^{10} +10.1313 q^{12} +13.0000 q^{13} +53.2377 q^{14} -81.9239 q^{15} -72.6673 q^{16} +80.1657 q^{17} -105.104 q^{18} +53.2690 q^{19} -13.5003 q^{20} -136.939 q^{21} -77.5267 q^{23} +160.328 q^{24} -15.8334 q^{25} -39.6278 q^{26} +58.6470 q^{27} -22.5663 q^{28} -67.3407 q^{29} +249.728 q^{30} +15.3347 q^{31} +57.9303 q^{32} -244.369 q^{34} +182.476 q^{35} +44.5513 q^{36} +251.763 q^{37} -162.380 q^{38} +101.932 q^{39} -213.643 q^{40} +376.773 q^{41} +417.431 q^{42} -186.795 q^{43} -360.253 q^{45} +236.324 q^{46} -488.422 q^{47} -569.777 q^{48} -37.9833 q^{49} +48.2649 q^{50} +628.571 q^{51} +16.7974 q^{52} -366.416 q^{53} -178.773 q^{54} -357.113 q^{56} +417.677 q^{57} +205.274 q^{58} +27.8944 q^{59} -105.854 q^{60} -540.280 q^{61} -46.7447 q^{62} -602.177 q^{63} +404.750 q^{64} -135.828 q^{65} +608.159 q^{67} +103.583 q^{68} -607.879 q^{69} -556.242 q^{70} -1180.76 q^{71} +705.027 q^{72} +82.2687 q^{73} -767.447 q^{74} -124.148 q^{75} +68.8292 q^{76} -310.718 q^{78} +416.410 q^{79} +759.249 q^{80} -471.105 q^{81} -1148.52 q^{82} +1036.97 q^{83} -176.940 q^{84} -837.594 q^{85} +569.405 q^{86} -528.011 q^{87} +830.391 q^{89} +1098.16 q^{90} -227.041 q^{91} -100.173 q^{92} +120.238 q^{93} +1488.85 q^{94} -556.570 q^{95} +454.225 q^{96} +823.686 q^{97} +115.784 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.04830	−1.07774	−0.538868	−	0.842390i	$-0.681148\pi$
$2$	−3.04830	−1.07774	−0.538868	+	0.842390i	$0.681148\pi$
$3$	7.84090	1.50898	0.754490	−	0.656311i	$-0.227884\pi$
$3$	7.84090	1.50898	0.754490	+	0.656311i	$0.227884\pi$
$4$	1.29211	0.161513
$5$	−10.4483	−0.934523	−0.467261	−	0.884119i	$-0.654759\pi$
$5$	−10.4483	−0.934523	−0.467261	+	0.884119i	$0.654759\pi$
$6$	−23.9014	−1.62628
$7$	−17.4647	−0.943007	−0.471503	−	0.881864i	$-0.656288\pi$
$7$	−17.4647	−0.943007	−0.471503	+	0.881864i	$0.656288\pi$
$8$	20.4476	0.903667
$9$	34.4796	1.27702
$10$	31.8495	1.00717
$11$	0	0
$11$	0	0
$12$	10.1313	0.243720
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	53.2377	1.01631
$15$	−81.9239	−1.41018
$16$	−72.6673	−1.13543
$17$	80.1657	1.14371	0.571854	−	0.820355i	$-0.306224\pi$
$17$	80.1657	1.14371	0.571854	+	0.820355i	$0.306224\pi$
$18$	−105.104	−1.37629
$19$	53.2690	0.643197	0.321599	−	0.946876i	$-0.395780\pi$
$19$	53.2690	0.643197	0.321599	+	0.946876i	$0.395780\pi$
$20$	−13.5003	−0.150938
$21$	−136.939	−1.42298
$22$	0	0
$23$	−77.5267	−0.702845	−0.351422	−	0.936217i	$-0.614302\pi$
$23$	−77.5267	−0.702845	−0.351422	+	0.936217i	$0.614302\pi$
$24$	160.328	1.36362
$25$	−15.8334	−0.126667
$26$	−39.6278	−0.298910
$27$	58.6470	0.418023
$28$	−22.5663	−0.152308
$29$	−67.3407	−0.431202	−0.215601	−	0.976482i	$-0.569171\pi$
$29$	−67.3407	−0.431202	−0.215601	+	0.976482i	$0.569171\pi$
$30$	249.728	1.51980
$31$	15.3347	0.0888449	0.0444225	−	0.999013i	$-0.485855\pi$
$31$	15.3347	0.0888449	0.0444225	+	0.999013i	$0.485855\pi$
$32$	57.9303	0.320023
$33$	0	0
$34$	−244.369	−1.23262
$35$	182.476	0.881261
$36$	44.5513	0.206256
$37$	251.763	1.11864	0.559318	−	0.828953i	$-0.311063\pi$
$37$	251.763	1.11864	0.559318	+	0.828953i	$0.311063\pi$
$38$	−162.380	−0.693197
$39$	101.932	0.418516
$40$	−213.643	−0.844497
$41$	376.773	1.43517	0.717586	−	0.696470i	$-0.245247\pi$
$41$	376.773	1.43517	0.717586	+	0.696470i	$0.245247\pi$
$42$	417.431	1.53359
$43$	−186.795	−0.662463	−0.331232	−	0.943549i	$-0.607464\pi$
$43$	−186.795	−0.662463	−0.331232	+	0.943549i	$0.607464\pi$
$44$	0	0
$45$	−360.253	−1.19341
$46$	236.324	0.757481
$47$	−488.422	−1.51582	−0.757911	−	0.652358i	$-0.773780\pi$
$47$	−488.422	−1.51582	−0.757911	+	0.652358i	$0.773780\pi$
$48$	−569.777	−1.71334
$49$	−37.9833	−0.110739
$50$	48.2649	0.136514
$51$	628.571	1.72583
$52$	16.7974	0.0447957
$53$	−366.416	−0.949643	−0.474822	−	0.880082i	$-0.657487\pi$
$53$	−366.416	−0.949643	−0.474822	+	0.880082i	$0.657487\pi$
$54$	−178.773	−0.450518
$55$	0	0
$56$	−357.113	−0.852164
$57$	417.677	0.970573
$58$	205.274	0.464721
$59$	27.8944	0.0615515	0.0307757	−	0.999526i	$-0.490202\pi$
$59$	27.8944	0.0615515	0.0307757	+	0.999526i	$0.490202\pi$
$60$	−105.854	−0.227762
$61$	−540.280	−1.13403	−0.567015	−	0.823708i	$-0.691902\pi$
$61$	−540.280	−1.13403	−0.567015	+	0.823708i	$0.691902\pi$
$62$	−46.7447	−0.0957513
$63$	−602.177	−1.20424
$64$	404.750	0.790527
$65$	−135.828	−0.259190
$66$	0	0
$67$	608.159	1.10893	0.554466	−	0.832206i	$-0.312923\pi$
$67$	608.159	1.10893	0.554466	+	0.832206i	$0.312923\pi$
$68$	103.583	0.184724
$69$	−607.879	−1.06058
$70$	−556.242	−0.949766
$71$	−1180.76	−1.97368	−0.986838	−	0.161711i	$-0.948299\pi$
$71$	−1180.76	−1.97368	−0.986838	+	0.161711i	$0.948299\pi$
$72$	705.027	1.15400
$73$	82.2687	0.131902	0.0659508	−	0.997823i	$-0.478992\pi$
$73$	82.2687	0.131902	0.0659508	+	0.997823i	$0.478992\pi$
$74$	−767.447	−1.20559
$75$	−124.148	−0.191138
$76$	68.8292	0.103885
$77$	0	0
$78$	−310.718	−0.451049
$79$	416.410	0.593035	0.296518	−	0.955027i	$-0.404175\pi$
$79$	416.410	0.593035	0.296518	+	0.955027i	$0.404175\pi$
$80$	759.249	1.06108
$81$	−471.105	−0.646234
$82$	−1148.52	−1.54674
$83$	1036.97	1.37135	0.685675	−	0.727908i	$-0.259507\pi$
$83$	1036.97	1.37135	0.685675	+	0.727908i	$0.259507\pi$
$84$	−176.940	−0.229830
$85$	−837.594	−1.06882
$86$	569.405	0.713960
$87$	−528.011	−0.650675
$88$	0	0
$89$	830.391	0.989003	0.494502	−	0.869177i	$-0.335351\pi$
$89$	830.391	0.989003	0.494502	+	0.869177i	$0.335351\pi$
$90$	1098.16	1.28618
$91$	−227.041	−0.261543
$92$	−100.173	−0.113519
$93$	120.238	0.134065
$94$	1488.85	1.63365
$95$	−556.570	−0.601083
$96$	454.225	0.482908
$97$	823.686	0.862192	0.431096	−	0.902306i	$-0.358127\pi$
$97$	823.686	0.862192	0.431096	+	0.902306i	$0.358127\pi$
$98$	115.784	0.119347
$99$	0	0
$100$	−20.4584	−0.0204584
$101$	991.921	0.977226	0.488613	−	0.872501i	$-0.337503\pi$
$101$	991.921	0.977226	0.488613	+	0.872501i	$0.337503\pi$
$102$	−1916.07	−1.85999
$103$	408.601	0.390880	0.195440	−	0.980716i	$-0.437387\pi$
$103$	408.601	0.390880	0.195440	+	0.980716i	$0.437387\pi$
$104$	265.819	0.250632
$105$	1430.78	1.32981
$106$	1116.94	1.02346
$107$	−929.987	−0.840236	−0.420118	−	0.907470i	$-0.638011\pi$
$107$	−929.987	−0.840236	−0.420118	+	0.907470i	$0.638011\pi$
$108$	75.7782	0.0675163
$109$	160.203	0.140776	0.0703882	−	0.997520i	$-0.477576\pi$
$109$	160.203	0.140776	0.0703882	+	0.997520i	$0.477576\pi$
$110$	0	0
$111$	1974.04	1.68800
$112$	1269.11	1.07071
$113$	1096.27	0.912639	0.456319	−	0.889816i	$-0.349167\pi$
$113$	1096.27	0.912639	0.456319	+	0.889816i	$0.349167\pi$
$114$	−1273.20	−1.04602
$115$	810.021	0.656825
$116$	−87.0113	−0.0696448
$117$	448.235	0.354183
$118$	−85.0302	−0.0663362
$119$	−1400.07	−1.07852
$120$	−1675.15	−1.27433
$121$	0	0
$122$	1646.93	1.22218
$123$	2954.24	2.16565
$124$	19.8141	0.0143496
$125$	1471.47	1.05290
$126$	1835.61	1.29785
$127$	755.663	0.527986	0.263993	−	0.964525i	$-0.414960\pi$
$127$	755.663	0.527986	0.263993	+	0.964525i	$0.414960\pi$
$128$	−1697.24	−1.17200
$129$	−1464.64	−0.999645
$130$	414.043	0.279338
$131$	2049.77	1.36709	0.683547	−	0.729906i	$-0.260436\pi$
$131$	2049.77	1.36709	0.683547	+	0.729906i	$0.260436\pi$
$132$	0	0
$133$	−930.329	−0.606539
$134$	−1853.85	−1.19513
$135$	−612.761	−0.390652
$136$	1639.20	1.03353
$137$	1021.82	0.637226	0.318613	−	0.947885i	$-0.396783\pi$
$137$	1021.82	0.637226	0.318613	+	0.947885i	$0.396783\pi$
$138$	1852.99	1.14302
$139$	602.831	0.367852	0.183926	−	0.982940i	$-0.441119\pi$
$139$	602.831	0.367852	0.183926	+	0.982940i	$0.441119\pi$
$140$	235.779	0.142335
$141$	−3829.66	−2.28735
$142$	3599.32	2.12710
$143$	0	0
$144$	−2505.54	−1.44997
$145$	703.594	0.402968
$146$	−250.779	−0.142155
$147$	−297.823	−0.167102
$148$	325.304	0.180674
$149$	976.886	0.537111	0.268556	−	0.963264i	$-0.413454\pi$
$149$	976.886	0.537111	0.268556	+	0.963264i	$0.413454\pi$
$150$	378.440	0.205997
$151$	2480.46	1.33680	0.668400	−	0.743802i	$-0.266979\pi$
$151$	2480.46	1.33680	0.668400	+	0.743802i	$0.266979\pi$
$152$	1089.23	0.581236
$153$	2764.09	1.46054
$154$	0	0
$155$	−160.221	−0.0830276
$156$	131.706	0.0675959
$157$	2261.20	1.14945	0.574725	−	0.818347i	$-0.305109\pi$
$157$	2261.20	1.14945	0.574725	+	0.818347i	$0.305109\pi$
$158$	−1269.34	−0.639135
$159$	−2873.03	−1.43299
$160$	−605.272	−0.299068
$161$	1353.98	0.662787
$162$	1436.07	0.696470
$163$	1482.92	0.712584	0.356292	−	0.934375i	$-0.384041\pi$
$163$	1482.92	0.712584	0.356292	+	0.934375i	$0.384041\pi$
$164$	486.831	0.231799
$165$	0	0
$166$	−3160.99	−1.47795
$167$	2460.07	1.13991	0.569957	−	0.821674i	$-0.306960\pi$
$167$	2460.07	1.13991	0.569957	+	0.821674i	$0.306960\pi$
$168$	−2800.08	−1.28590
$169$	169.000	0.0769231
$170$	2553.23	1.15191
$171$	1836.70	0.821378
$172$	−241.359	−0.106997
$173$	−4497.61	−1.97657	−0.988287	−	0.152608i	$-0.951233\pi$
$173$	−4497.61	−1.97657	−0.988287	+	0.152608i	$0.951233\pi$
$174$	1609.53	0.701255
$175$	276.526	0.119448
$176$	0	0
$177$	218.717	0.0928800
$178$	−2531.28	−1.06588
$179$	−1474.63	−0.615750	−0.307875	−	0.951427i	$-0.599618\pi$
$179$	−1474.63	−0.615750	−0.307875	+	0.951427i	$0.599618\pi$
$180$	−465.485	−0.192751
$181$	152.510	0.0626295	0.0313148	−	0.999510i	$-0.490031\pi$
$181$	152.510	0.0626295	0.0313148	+	0.999510i	$0.490031\pi$
$182$	692.089	0.281874
$183$	−4236.28	−1.71123
$184$	−1585.24	−0.635138
$185$	−2630.49	−1.04539
$186$	−366.520	−0.144487
$187$	0	0
$188$	−631.092	−0.244825
$189$	−1024.25	−0.394199
$190$	1696.59	0.647808
$191$	1281.24	0.485379	0.242690	−	0.970104i	$-0.421970\pi$
$191$	1281.24	0.485379	0.242690	+	0.970104i	$0.421970\pi$
$192$	3173.60	1.19289
$193$	−2558.69	−0.954292	−0.477146	−	0.878824i	$-0.658329\pi$
$193$	−2558.69	−0.954292	−0.477146	+	0.878824i	$0.658329\pi$
$194$	−2510.84	−0.929215
$195$	−1065.01	−0.391113
$196$	−49.0785	−0.0178857
$197$	4552.85	1.64659	0.823293	−	0.567617i	$-0.192134\pi$
$197$	4552.85	1.64659	0.823293	+	0.567617i	$0.192134\pi$
$198$	0	0
$199$	−4197.88	−1.49538	−0.747688	−	0.664050i	$-0.768836\pi$
$199$	−4197.88	−1.49538	−0.747688	+	0.664050i	$0.768836\pi$
$200$	−323.756	−0.114465
$201$	4768.51	1.67336
$202$	−3023.67	−1.05319
$203$	1176.09	0.406626
$204$	812.181	0.278745
$205$	−3936.63	−1.34120
$206$	−1245.54	−0.421265
$207$	−2673.09	−0.897549
$208$	−944.675	−0.314911
$209$	0	0
$210$	−4361.43	−1.43318
$211$	5890.12	1.92176	0.960882	−	0.276957i	$-0.0893260\pi$
$211$	5890.12	1.92176	0.960882	+	0.276957i	$0.0893260\pi$
$212$	−473.448	−0.153380
$213$	−9258.25	−2.97824
$214$	2834.87	0.905552
$215$	1951.68	0.619087
$216$	1199.19	0.377754
$217$	−267.816	−0.0837814
$218$	−488.345	−0.151720
$219$	645.060	0.199037
$220$	0	0
$221$	1042.15	0.317208
$222$	−6017.47	−1.81922
$223$	3816.32	1.14601	0.573004	−	0.819553i	$-0.305778\pi$
$223$	3816.32	1.14601	0.573004	+	0.819553i	$0.305778\pi$
$224$	−1011.74	−0.301784
$225$	−545.930	−0.161757
$226$	−3341.75	−0.983583
$227$	−2512.37	−0.734589	−0.367295	−	0.930105i	$-0.619716\pi$
$227$	−2512.37	−0.734589	−0.367295	+	0.930105i	$0.619716\pi$
$228$	539.683	0.156760
$229$	−6568.50	−1.89545	−0.947726	−	0.319086i	$-0.896624\pi$
$229$	−6568.50	−1.89545	−0.947726	+	0.319086i	$0.896624\pi$
$230$	−2469.18	−0.707883
$231$	0	0
$232$	−1376.96	−0.389663
$233$	2278.71	0.640701	0.320351	−	0.947299i	$-0.396199\pi$
$233$	2278.71	0.640701	0.320351	+	0.947299i	$0.396199\pi$
$234$	−1366.35	−0.381715
$235$	5103.17	1.41657
$236$	36.0425	0.00994138
$237$	3265.03	0.894879
$238$	4267.84	1.16236
$239$	6162.16	1.66777	0.833885	−	0.551938i	$-0.186111\pi$
$239$	6162.16	1.66777	0.833885	+	0.551938i	$0.186111\pi$
$240$	5953.19	1.60115
$241$	−4554.46	−1.21734	−0.608670	−	0.793424i	$-0.708297\pi$
$241$	−4554.46	−1.21734	−0.608670	+	0.793424i	$0.708297\pi$
$242$	0	0
$243$	−5277.35	−1.39318
$244$	−698.099	−0.183161
$245$	396.860	0.103488
$246$	−9005.39	−2.33399
$247$	692.497	0.178391
$248$	313.558	0.0802862
$249$	8130.76	2.06934
$250$	−4485.47	−1.13474
$251$	3136.97	0.788861	0.394430	−	0.918926i	$-0.370942\pi$
$251$	3136.97	0.788861	0.394430	+	0.918926i	$0.370942\pi$
$252$	−778.077	−0.194501
$253$	0	0
$254$	−2303.49	−0.569030
$255$	−6567.49	−1.61283
$256$	1935.69	0.472580
$257$	−587.868	−0.142686	−0.0713428	−	0.997452i	$-0.522728\pi$
$257$	−587.868	−0.142686	−0.0713428	+	0.997452i	$0.522728\pi$
$258$	4464.65	1.07735
$259$	−4396.97	−1.05488
$260$	−175.504	−0.0418626
$261$	−2321.88	−0.550655
$262$	−6248.31	−1.47337
$263$	−4976.91	−1.16688	−0.583440	−	0.812156i	$-0.698294\pi$
$263$	−4976.91	−1.16688	−0.583440	+	0.812156i	$0.698294\pi$
$264$	0	0
$265$	3828.42	0.887463
$266$	2835.92	0.653689
$267$	6511.01	1.49239
$268$	785.806	0.179107
$269$	4620.43	1.04726	0.523629	−	0.851946i	$-0.324578\pi$
$269$	4620.43	1.04726	0.523629	+	0.851946i	$0.324578\pi$
$270$	1867.88	0.421020
$271$	3469.18	0.777629	0.388815	−	0.921316i	$-0.372885\pi$
$271$	3469.18	0.777629	0.388815	+	0.921316i	$0.372885\pi$
$272$	−5825.43	−1.29860
$273$	−1780.21	−0.394663
$274$	−3114.81	−0.686761
$275$	0	0
$276$	−785.444	−0.171298
$277$	−7292.73	−1.58187	−0.790935	−	0.611900i	$-0.790405\pi$
$277$	−7292.73	−1.58187	−0.790935	+	0.611900i	$0.790405\pi$
$278$	−1837.61	−0.396447
$279$	528.735	0.113457
$280$	3731.21	0.796366
$281$	1457.78	0.309479	0.154740	−	0.987955i	$-0.450546\pi$
$281$	1457.78	0.309479	0.154740	+	0.987955i	$0.450546\pi$
$282$	11673.9	2.46515
$283$	150.436	0.0315988	0.0157994	−	0.999875i	$-0.494971\pi$
$283$	150.436	0.0315988	0.0157994	+	0.999875i	$0.494971\pi$
$284$	−1525.67	−0.318775
$285$	−4364.01	−0.907022
$286$	0	0
$287$	−6580.24	−1.35338
$288$	1997.42	0.408677
$289$	1513.54	0.308069
$290$	−2144.76	−0.434293
$291$	6458.44	1.30103
$292$	106.300	0.0213039
$293$	−6900.87	−1.37595	−0.687975	−	0.725734i	$-0.741500\pi$
$293$	−6900.87	−1.37595	−0.687975	+	0.725734i	$0.741500\pi$
$294$	907.853	0.180092
$295$	−291.448	−0.0575212
$296$	5147.95	1.01087
$297$	0	0
$298$	−2977.84	−0.578864
$299$	−1007.85	−0.194934
$300$	−160.413	−0.0308714
$301$	3262.32	0.624707
$302$	−7561.17	−1.44072
$303$	7777.55	1.47462
$304$	−3870.92	−0.730304
$305$	5645.00	1.05978
$306$	−8425.75	−1.57408
$307$	50.8375	0.00945098	0.00472549	−	0.999989i	$-0.498496\pi$
$307$	50.8375	0.00945098	0.00472549	+	0.999989i	$0.498496\pi$
$308$	0	0
$309$	3203.80	0.589830
$310$	488.402	0.0894818
$311$	7624.75	1.39023	0.695113	−	0.718901i	$-0.255354\pi$
$311$	7624.75	1.39023	0.695113	+	0.718901i	$0.255354\pi$
$312$	2084.26	0.378199
$313$	7560.97	1.36540	0.682702	−	0.730697i	$-0.260805\pi$
$313$	7560.97	1.36540	0.682702	+	0.730697i	$0.260805\pi$
$314$	−6892.82	−1.23880
$315$	6291.72	1.12539
$316$	538.046	0.0957831
$317$	8710.54	1.54332	0.771661	−	0.636035i	$-0.219426\pi$
$317$	8710.54	1.54332	0.771661	+	0.636035i	$0.219426\pi$
$318$	8757.84	1.54439
$319$	0	0
$320$	−4228.94	−0.738765
$321$	−7291.93	−1.26790
$322$	−4127.34	−0.714309
$323$	4270.35	0.735630
$324$	−608.718	−0.104375
$325$	−205.834	−0.0351312
$326$	−4520.38	−0.767977
$327$	1256.13	0.212429
$328$	7704.12	1.29692
$329$	8530.15	1.42943
$330$	0	0
$331$	6645.66	1.10356	0.551780	−	0.833990i	$-0.313949\pi$
$331$	6645.66	1.10356	0.551780	+	0.833990i	$0.313949\pi$
$332$	1339.87	0.221491
$333$	8680.68	1.42852
$334$	−7499.01	−1.22853
$335$	−6354.22	−1.03632
$336$	9951.00	1.61569
$337$	−1308.28	−0.211473	−0.105737	−	0.994394i	$-0.533720\pi$
$337$	−1308.28	−0.211473	−0.105737	+	0.994394i	$0.533720\pi$
$338$	−515.162	−0.0829027
$339$	8595.72	1.37715
$340$	−1082.26	−0.172629
$341$	0	0
$342$	−5598.79	−0.885228
$343$	6653.77	1.04743
$344$	−3819.51	−0.598646
$345$	6351.29	0.991136
$346$	13710.1	2.13022
$347$	8499.42	1.31491	0.657453	−	0.753495i	$-0.271634\pi$
$347$	8499.42	1.31491	0.657453	+	0.753495i	$0.271634\pi$
$348$	−682.246	−0.105093
$349$	−1493.51	−0.229071	−0.114535	−	0.993419i	$-0.536538\pi$
$349$	−1493.51	−0.229071	−0.114535	+	0.993419i	$0.536538\pi$
$350$	−842.933	−0.128733
$351$	762.411	0.115939
$352$	0	0
$353$	10082.4	1.52020	0.760100	−	0.649806i	$-0.225150\pi$
$353$	10082.4	1.52020	0.760100	+	0.649806i	$0.225150\pi$
$354$	−666.713	−0.100100
$355$	12337.0	1.84445
$356$	1072.95	0.159737
$357$	−10977.8	−1.62747
$358$	4495.12	0.663615
$359$	−7181.99	−1.05585	−0.527926	−	0.849290i	$-0.677030\pi$
$359$	−7181.99	−1.05585	−0.527926	+	0.849290i	$0.677030\pi$
$360$	−7366.32	−1.07844
$361$	−4021.41	−0.586297
$362$	−464.894	−0.0674980
$363$	0	0
$364$	−293.362	−0.0422427
$365$	−859.566	−0.123265
$366$	12913.4	1.84425
$367$	−455.980	−0.0648554	−0.0324277	−	0.999474i	$-0.510324\pi$
$367$	−455.980	−0.0648554	−0.0324277	+	0.999474i	$0.510324\pi$
$368$	5633.66	0.798029
$369$	12991.0	1.83275
$370$	8018.50	1.12665
$371$	6399.35	0.895520
$372$	155.360	0.0216533
$373$	8380.87	1.16339	0.581696	−	0.813407i	$-0.302389\pi$
$373$	8380.87	1.16339	0.581696	+	0.813407i	$0.302389\pi$
$374$	0	0
$375$	11537.6	1.58880
$376$	−9987.07	−1.36980
$377$	−875.429	−0.119594
$378$	3122.23	0.424842
$379$	−782.703	−0.106081	−0.0530405	−	0.998592i	$-0.516891\pi$
$379$	−782.703	−0.106081	−0.0530405	+	0.998592i	$0.516891\pi$
$380$	−719.147	−0.0970828
$381$	5925.08	0.796721
$382$	−3905.61	−0.523111
$383$	9755.24	1.30149	0.650743	−	0.759298i	$-0.274457\pi$
$383$	9755.24	1.30149	0.650743	+	0.759298i	$0.274457\pi$
$384$	−13307.9	−1.76853
$385$	0	0
$386$	7799.64	1.02847
$387$	−6440.61	−0.845981
$388$	1064.29	0.139256
$389$	−5193.48	−0.676914	−0.338457	−	0.940982i	$-0.609905\pi$
$389$	−5193.48	−0.676914	−0.338457	+	0.940982i	$0.609905\pi$
$390$	3246.47	0.421516
$391$	−6214.98	−0.803850
$392$	−776.669	−0.100071
$393$	16072.0	2.06292
$394$	−13878.4	−1.77458
$395$	−4350.77	−0.554205
$396$	0	0
$397$	6592.31	0.833396	0.416698	−	0.909045i	$-0.363187\pi$
$397$	6592.31	0.833396	0.416698	+	0.909045i	$0.363187\pi$
$398$	12796.4	1.61162
$399$	−7294.61	−0.915257
$400$	1150.57	0.143821
$401$	−8166.00	−1.01693	−0.508467	−	0.861081i	$-0.669788\pi$
$401$	−8166.00	−1.01693	−0.508467	+	0.861081i	$0.669788\pi$
$402$	−14535.8	−1.80344
$403$	199.351	0.0246412
$404$	1281.67	0.157835
$405$	4922.24	0.603921
$406$	−3585.06	−0.438235
$407$	0	0
$408$	12852.8	1.55958
$409$	410.335	0.0496082	0.0248041	−	0.999692i	$-0.492104\pi$
$409$	410.335	0.0496082	0.0248041	+	0.999692i	$0.492104\pi$
$410$	12000.0	1.44546
$411$	8011.98	0.961561
$412$	527.956	0.0631323
$413$	−487.167	−0.0580434
$414$	8148.37	0.967321
$415$	−10834.5	−1.28156
$416$	753.094	0.0887583
$417$	4726.73	0.555082
$418$	0	0
$419$	13457.4	1.56906	0.784532	−	0.620088i	$-0.212903\pi$
$419$	13457.4	1.56906	0.784532	+	0.620088i	$0.212903\pi$
$420$	1848.72	0.214781
$421$	3027.78	0.350511	0.175255	−	0.984523i	$-0.443925\pi$
$421$	3027.78	0.350511	0.175255	+	0.984523i	$0.443925\pi$
$422$	−17954.8	−2.07115
$423$	−16840.6	−1.93574
$424$	−7492.34	−0.858161
$425$	−1269.30	−0.144870
$426$	28221.9	3.20975
$427$	9435.84	1.06940
$428$	−1201.64	−0.135709
$429$	0	0
$430$	−5949.31	−0.667212
$431$	6192.47	0.692067	0.346033	−	0.938222i	$-0.387528\pi$
$431$	6192.47	0.692067	0.346033	+	0.938222i	$0.387528\pi$
$432$	−4261.72	−0.474635
$433$	−2121.11	−0.235413	−0.117707	−	0.993048i	$-0.537554\pi$
$433$	−2121.11	−0.235413	−0.117707	+	0.993048i	$0.537554\pi$
$434$	816.383	0.0902941
$435$	5516.81	0.608071
$436$	206.999	0.0227373
$437$	−4129.77	−0.452068
$438$	−1966.33	−0.214509
$439$	13914.2	1.51273	0.756367	−	0.654148i	$-0.226973\pi$
$439$	13914.2	1.51273	0.756367	+	0.654148i	$0.226973\pi$
$440$	0	0
$441$	−1309.65	−0.141416
$442$	−3176.79	−0.341866
$443$	−9407.56	−1.00895	−0.504477	−	0.863425i	$-0.668315\pi$
$443$	−9407.56	−1.00895	−0.504477	+	0.863425i	$0.668315\pi$
$444$	2550.67	0.272634
$445$	−8676.16	−0.924246
$446$	−11633.3	−1.23509
$447$	7659.66	0.810491
$448$	−7068.85	−0.745472
$449$	−682.686	−0.0717549	−0.0358775	−	0.999356i	$-0.511423\pi$
$449$	−682.686	−0.0717549	−0.0358775	+	0.999356i	$0.511423\pi$
$450$	1664.16	0.174331
$451$	0	0
$452$	1416.49	0.147403
$453$	19449.0	2.01721
$454$	7658.44	0.791692
$455$	2372.19	0.244418
$456$	8540.51	0.877074
$457$	−8126.75	−0.831846	−0.415923	−	0.909400i	$-0.636541\pi$
$457$	−8126.75	−0.831846	−0.415923	+	0.909400i	$0.636541\pi$
$458$	20022.7	2.04280
$459$	4701.48	0.478097
$460$	1046.63	0.106086
$461$	10093.9	1.01979	0.509894	−	0.860237i	$-0.329685\pi$
$461$	10093.9	1.01979	0.509894	+	0.860237i	$0.329685\pi$
$462$	0	0
$463$	−161.556	−0.0162163	−0.00810817	−	0.999967i	$-0.502581\pi$
$463$	−161.556	−0.0162163	−0.00810817	+	0.999967i	$0.502581\pi$
$464$	4893.47	0.489598
$465$	−1256.28	−0.125287
$466$	−6946.19	−0.690507
$467$	−3326.27	−0.329596	−0.164798	−	0.986327i	$-0.552697\pi$
$467$	−3326.27	−0.329596	−0.164798	+	0.986327i	$0.552697\pi$
$468$	579.168	0.0572052
$469$	−10621.3	−1.04573
$470$	−15556.0	−1.52669
$471$	17729.9	1.73450
$472$	570.374	0.0556220
$473$	0	0
$474$	−9952.77	−0.964443
$475$	−843.430	−0.0814721
$476$	−1809.04	−0.174196
$477$	−12633.9	−1.21272
$478$	−18784.1	−1.79741
$479$	−7542.27	−0.719447	−0.359723	−	0.933059i	$-0.617129\pi$
$479$	−7542.27	−0.719447	−0.359723	+	0.933059i	$0.617129\pi$
$480$	−4745.87	−0.451289
$481$	3272.91	0.310254
$482$	13883.4	1.31197
$483$	10616.4	1.00013
$484$	0	0
$485$	−8606.11	−0.805738
$486$	16086.9	1.50148
$487$	−12686.1	−1.18041	−0.590206	−	0.807252i	$-0.700954\pi$
$487$	−12686.1	−1.18041	−0.590206	+	0.807252i	$0.700954\pi$
$488$	−11047.5	−1.02478
$489$	11627.4	1.07528
$490$	−1209.75	−0.111532
$491$	13549.8	1.24541	0.622703	−	0.782458i	$-0.286034\pi$
$491$	13549.8	1.24541	0.622703	+	0.782458i	$0.286034\pi$
$492$	3817.19	0.349781
$493$	−5398.41	−0.493169
$494$	−2110.94	−0.192258
$495$	0	0
$496$	−1114.33	−0.100877
$497$	20621.7	1.86119
$498$	−24785.0	−2.23020
$499$	−14538.2	−1.30425	−0.652123	−	0.758113i	$-0.726121\pi$
$499$	−14538.2	−1.30425	−0.652123	+	0.758113i	$0.726121\pi$
$500$	1901.29	0.170057
$501$	19289.1	1.72011
$502$	−9562.42	−0.850183
$503$	16031.1	1.42105	0.710526	−	0.703671i	$-0.248457\pi$
$503$	16031.1	1.42105	0.710526	+	0.703671i	$0.248457\pi$
$504$	−12313.1	−1.08823
$505$	−10363.9	−0.913240
$506$	0	0
$507$	1325.11	0.116075
$508$	976.397	0.0852768
$509$	−8274.70	−0.720569	−0.360284	−	0.932843i	$-0.617320\pi$
$509$	−8274.70	−0.720569	−0.360284	+	0.932843i	$0.617320\pi$
$510$	20019.6	1.73821
$511$	−1436.80	−0.124384
$512$	7677.36	0.662685
$513$	3124.07	0.268871
$514$	1791.99	0.153777
$515$	−4269.18	−0.365286
$516$	−1892.47	−0.161456
$517$	0	0
$518$	13403.2	1.13688
$519$	−35265.3	−2.98261
$520$	−2777.36	−0.234221
$521$	−19947.8	−1.67741	−0.838703	−	0.544589i	$-0.816686\pi$
$521$	−19947.8	−1.67741	−0.838703	+	0.544589i	$0.816686\pi$
$522$	7077.78	0.593460
$523$	−9418.37	−0.787450	−0.393725	−	0.919228i	$-0.628814\pi$
$523$	−9418.37	−0.787450	−0.393725	+	0.919228i	$0.628814\pi$
$524$	2648.52	0.220804
$525$	2168.21	0.180245
$526$	15171.1	1.25759
$527$	1229.32	0.101613
$528$	0	0
$529$	−6156.61	−0.506009
$530$	−11670.1	−0.956450
$531$	961.787	0.0786027
$532$	−1202.08	−0.0979642
$533$	4898.05	0.398045
$534$	−19847.5	−1.60840
$535$	9716.76	0.785219
$536$	12435.4	1.00210
$537$	−11562.4	−0.929155
$538$	−14084.4	−1.12867
$539$	0	0
$540$	−791.752	−0.0630955
$541$	−20665.4	−1.64228	−0.821140	−	0.570728i	$-0.806661\pi$
$541$	−20665.4	−1.64228	−0.821140	+	0.570728i	$0.806661\pi$
$542$	−10575.1	−0.838079
$543$	1195.81	0.0945068
$544$	4644.02	0.366013
$545$	−1673.84	−0.131559
$546$	5426.60	0.425343
$547$	−13691.2	−1.07019	−0.535093	−	0.844793i	$-0.679723\pi$
$547$	−13691.2	−1.07019	−0.535093	+	0.844793i	$0.679723\pi$
$548$	1320.30	0.102920
$549$	−18628.7	−1.44818
$550$	0	0
$551$	−3587.17	−0.277348
$552$	−12429.7	−0.958410
$553$	−7272.49	−0.559236
$554$	22230.4	1.70484
$555$	−20625.4	−1.57747
$556$	778.922	0.0594130
$557$	−18001.2	−1.36936	−0.684682	−	0.728842i	$-0.740059\pi$
$557$	−18001.2	−1.36936	−0.684682	+	0.728842i	$0.740059\pi$
$558$	−1611.74	−0.122277
$559$	−2428.33	−0.183734
$560$	−13260.1	−1.00061
$561$	0	0
$562$	−4443.73	−0.333537
$563$	6078.61	0.455032	0.227516	−	0.973774i	$-0.426940\pi$
$563$	6078.61	0.455032	0.227516	+	0.973774i	$0.426940\pi$
$564$	−4948.33	−0.369437
$565$	−11454.1	−0.852882
$566$	−458.572	−0.0340552
$567$	8227.72	0.609403
$568$	−24143.9	−1.78355
$569$	5443.40	0.401053	0.200527	−	0.979688i	$-0.435735\pi$
$569$	5443.40	0.401053	0.200527	+	0.979688i	$0.435735\pi$
$570$	13302.8	0.977530
$571$	4537.77	0.332574	0.166287	−	0.986077i	$-0.446822\pi$
$571$	4537.77	0.332574	0.166287	+	0.986077i	$0.446822\pi$
$572$	0	0
$573$	10046.1	0.732428
$574$	20058.5	1.45858
$575$	1227.51	0.0890274
$576$	13955.6	1.00952
$577$	−16056.4	−1.15847	−0.579235	−	0.815161i	$-0.696649\pi$
$577$	−16056.4	−1.15847	−0.579235	+	0.815161i	$0.696649\pi$
$578$	−4613.73	−0.332017
$579$	−20062.4	−1.44001
$580$	909.118	0.0650846
$581$	−18110.4	−1.29319
$582$	−19687.2	−1.40217
$583$	0	0
$584$	1682.20	0.119195
$585$	−4683.29	−0.330992
$586$	21035.9	1.48291
$587$	18480.8	1.29946	0.649731	−	0.760165i	$-0.274882\pi$
$587$	18480.8	1.29946	0.649731	+	0.760165i	$0.274882\pi$
$588$	−384.819	−0.0269892
$589$	816.864	0.0571448
$590$	888.420	0.0619927
$591$	35698.5	2.48467
$592$	−18294.9	−1.27013
$593$	16507.6	1.14315	0.571573	−	0.820551i	$-0.306333\pi$
$593$	16507.6	1.14315	0.571573	+	0.820551i	$0.306333\pi$
$594$	0	0
$595$	14628.4	1.00791
$596$	1262.24	0.0867506
$597$	−32915.1	−2.25649
$598$	3072.22	0.210087
$599$	20635.1	1.40756	0.703781	−	0.710417i	$-0.251494\pi$
$599$	20635.1	1.40756	0.703781	+	0.710417i	$0.251494\pi$
$600$	−2538.54	−0.172725
$601$	10193.7	0.691865	0.345932	−	0.938259i	$-0.387563\pi$
$601$	10193.7	0.691865	0.345932	+	0.938259i	$0.387563\pi$
$602$	−9944.51	−0.673269
$603$	20969.1	1.41613
$604$	3205.01	0.215911
$605$	0	0
$606$	−23708.3	−1.58925
$607$	14643.2	0.979158	0.489579	−	0.871959i	$-0.337150\pi$
$607$	14643.2	0.979158	0.489579	+	0.871959i	$0.337150\pi$
$608$	3085.89	0.205838
$609$	9221.57	0.613591
$610$	−17207.6	−1.14216
$611$	−6349.48	−0.420413
$612$	3571.49	0.235897
$613$	−24115.6	−1.58894	−0.794470	−	0.607304i	$-0.792251\pi$
$613$	−24115.6	−1.58894	−0.794470	+	0.607304i	$0.792251\pi$
$614$	−154.968	−0.0101857
$615$	−30866.7	−2.02385
$616$	0	0
$617$	5353.36	0.349300	0.174650	−	0.984631i	$-0.444121\pi$
$617$	5353.36	0.349300	0.174650	+	0.984631i	$0.444121\pi$
$618$	−9766.12	−0.635681
$619$	22942.2	1.48970	0.744852	−	0.667230i	$-0.232520\pi$
$619$	22942.2	1.48970	0.744852	+	0.667230i	$0.232520\pi$
$620$	−207.023	−0.0134101
$621$	−4546.71	−0.293805
$622$	−23242.5	−1.49830
$623$	−14502.6	−0.932637
$624$	−7407.10	−0.475194
$625$	−13395.1	−0.857288
$626$	−23048.1	−1.47154
$627$	0	0
$628$	2921.71	0.185651
$629$	20182.7	1.27939
$630$	−19179.0	−1.21287
$631$	2562.47	0.161664	0.0808321	−	0.996728i	$-0.474242\pi$
$631$	2562.47	0.161664	0.0808321	+	0.996728i	$0.474242\pi$
$632$	8514.60	0.535906
$633$	46183.8	2.89991
$634$	−26552.3	−1.66329
$635$	−7895.38	−0.493415
$636$	−3712.26	−0.231447
$637$	−493.783	−0.0307133
$638$	0	0
$639$	−40712.3	−2.52043
$640$	17733.2	1.09526
$641$	−3746.10	−0.230830	−0.115415	−	0.993317i	$-0.536820\pi$
$641$	−3746.10	−0.230830	−0.115415	+	0.993317i	$0.536820\pi$
$642$	22228.0	1.36646
$643$	−17190.8	−1.05434	−0.527168	−	0.849761i	$-0.676746\pi$
$643$	−17190.8	−1.05434	−0.527168	+	0.849761i	$0.676746\pi$
$644$	1749.49	0.107049
$645$	15302.9	0.934191
$646$	−13017.3	−0.792815
$647$	−26594.3	−1.61597	−0.807984	−	0.589205i	$-0.799441\pi$
$647$	−26594.3	−1.61597	−0.807984	+	0.589205i	$0.799441\pi$
$648$	−9632.99	−0.583981
$649$	0	0
$650$	627.444	0.0378621
$651$	−2099.92	−0.126424
$652$	1916.09	0.115092
$653$	16019.5	0.960018	0.480009	−	0.877264i	$-0.340633\pi$
$653$	16019.5	0.960018	0.480009	+	0.877264i	$0.340633\pi$
$654$	−3829.06	−0.228942
$655$	−21416.6	−1.27758
$656$	−27379.1	−1.62953
$657$	2836.59	0.168442
$658$	−26002.4	−1.54055
$659$	2693.80	0.159234	0.0796172	−	0.996826i	$-0.474630\pi$
$659$	2693.80	0.159234	0.0796172	+	0.996826i	$0.474630\pi$
$660$	0	0
$661$	19207.5	1.13023	0.565117	−	0.825010i	$-0.308831\pi$
$661$	19207.5	1.13023	0.565117	+	0.825010i	$0.308831\pi$
$662$	−20257.9	−1.18935
$663$	8171.42	0.478660
$664$	21203.6	1.23924
$665$	9720.34	0.566825
$666$	−26461.3	−1.53957
$667$	5220.70	0.303068
$668$	3178.67	0.184111
$669$	29923.4	1.72930
$670$	19369.5	1.11688
$671$	0	0
$672$	−7932.92	−0.455386
$673$	−1909.68	−0.109380	−0.0546899	−	0.998503i	$-0.517417\pi$
$673$	−1909.68	−0.109380	−0.0546899	+	0.998503i	$0.517417\pi$
$674$	3988.02	0.227912
$675$	−928.582	−0.0529499
$676$	218.366	0.0124241
$677$	−11495.3	−0.652583	−0.326291	−	0.945269i	$-0.605799\pi$
$677$	−11495.3	−0.652583	−0.326291	+	0.945269i	$0.605799\pi$
$678$	−26202.3	−1.48421
$679$	−14385.5	−0.813053
$680$	−17126.8	−0.965859
$681$	−19699.2	−1.10848
$682$	0	0
$683$	3936.68	0.220546	0.110273	−	0.993901i	$-0.464828\pi$
$683$	3936.68	0.220546	0.110273	+	0.993901i	$0.464828\pi$
$684$	2373.21	0.132663
$685$	−10676.3	−0.595502
$686$	−20282.7	−1.12886
$687$	−51502.9	−2.86020
$688$	13573.9	0.752179
$689$	−4763.41	−0.263384
$690$	−19360.6	−1.06818
$691$	13955.6	0.768299	0.384150	−	0.923271i	$-0.374495\pi$
$691$	13955.6	0.768299	0.384150	+	0.923271i	$0.374495\pi$
$692$	−5811.39	−0.319243
$693$	0	0
$694$	−25908.7	−1.41712
$695$	−6298.55	−0.343766
$696$	−10796.6	−0.587993
$697$	30204.3	1.64142
$698$	4552.66	0.246878
$699$	17867.1	0.966806
$700$	357.301	0.0192924
$701$	21944.3	1.18235	0.591173	−	0.806544i	$-0.298665\pi$
$701$	21944.3	1.18235	0.591173	+	0.806544i	$0.298665\pi$
$702$	−2324.06	−0.124951
$703$	13411.1	0.719504
$704$	0	0
$705$	40013.4	2.13758
$706$	−30734.1	−1.63837
$707$	−17323.6	−0.921531
$708$	282.605	0.0150013
$709$	7288.13	0.386053	0.193026	−	0.981194i	$-0.438170\pi$
$709$	7288.13	0.386053	0.193026	+	0.981194i	$0.438170\pi$
$710$	−37606.7	−1.98782
$711$	14357.7	0.757320
$712$	16979.5	0.893729
$713$	−1188.85	−0.0624442
$714$	33463.6	1.75399
$715$	0	0
$716$	−1905.38	−0.0994518
$717$	48316.9	2.51663
$718$	21892.8	1.13793
$719$	36744.7	1.90591	0.952954	−	0.303115i	$-0.0980266\pi$
$719$	36744.7	1.90591	0.952954	+	0.303115i	$0.0980266\pi$
$720$	26178.6	1.35503
$721$	−7136.10	−0.368602
$722$	12258.4	0.631873
$723$	−35711.1	−1.83694
$724$	197.058	0.0101155
$725$	1066.23	0.0546191
$726$	0	0
$727$	8229.31	0.419819	0.209909	−	0.977721i	$-0.432683\pi$
$727$	8229.31	0.419819	0.209909	+	0.977721i	$0.432683\pi$
$728$	−4642.46	−0.236348
$729$	−28659.3	−1.45605
$730$	2620.21	0.132847
$731$	−14974.5	−0.757665
$732$	−5473.72	−0.276386
$733$	30208.8	1.52222	0.761110	−	0.648623i	$-0.224655\pi$
$733$	30208.8	1.52222	0.761110	+	0.648623i	$0.224655\pi$
$734$	1389.96	0.0698970
$735$	3111.74	0.156161
$736$	−4491.14	−0.224926
$737$	0	0
$738$	−39600.4	−1.97522
$739$	−21305.3	−1.06053	−0.530263	−	0.847833i	$-0.677907\pi$
$739$	−21305.3	−1.06053	−0.530263	+	0.847833i	$0.677907\pi$
$740$	−3398.87	−0.168844
$741$	5429.80	0.269188
$742$	−19507.1	−0.965133
$743$	19246.6	0.950324	0.475162	−	0.879898i	$-0.342389\pi$
$743$	19246.6	0.950324	0.475162	+	0.879898i	$0.342389\pi$
$744$	2458.58	0.121150
$745$	−10206.8	−0.501943
$746$	−25547.4	−1.25383
$747$	35754.3	1.75125
$748$	0	0
$749$	16242.0	0.792348
$750$	−35170.1	−1.71231
$751$	−20791.4	−1.01024	−0.505120	−	0.863049i	$-0.668552\pi$
$751$	−20791.4	−1.01024	−0.505120	+	0.863049i	$0.668552\pi$
$752$	35492.3	1.72110
$753$	24596.7	1.19038
$754$	2668.57	0.128890
$755$	−25916.5	−1.24927
$756$	−1323.45	−0.0636683
$757$	−12952.7	−0.621896	−0.310948	−	0.950427i	$-0.600647\pi$
$757$	−12952.7	−0.621896	−0.310948	+	0.950427i	$0.600647\pi$
$758$	2385.91	0.114327
$759$	0	0
$760$	−11380.5	−0.543178
$761$	4482.10	0.213504	0.106752	−	0.994286i	$-0.465955\pi$
$761$	4482.10	0.213504	0.106752	+	0.994286i	$0.465955\pi$
$762$	−18061.4	−0.858655
$763$	−2797.90	−0.132753
$764$	1655.50	0.0783952
$765$	−28879.9	−1.36491
$766$	−29736.8	−1.40266
$767$	362.627	0.0170713
$768$	15177.5	0.713115
$769$	24493.9	1.14860	0.574300	−	0.818645i	$-0.305274\pi$
$769$	24493.9	1.14860	0.574300	+	0.818645i	$0.305274\pi$
$770$	0	0
$771$	−4609.41	−0.215310
$772$	−3306.10	−0.154131
$773$	17199.8	0.800301	0.400150	−	0.916449i	$-0.368958\pi$
$773$	17199.8	0.800301	0.400150	+	0.916449i	$0.368958\pi$
$774$	19632.9	0.911744
$775$	−242.801	−0.0112537
$776$	16842.4	0.779135
$777$	−34476.1	−1.59179
$778$	15831.3	0.729535
$779$	20070.3	0.923099
$780$	−1376.11	−0.0631699
$781$	0	0
$782$	18945.1	0.866337
$783$	−3949.33	−0.180252
$784$	2760.15	0.125735
$785$	−23625.7	−1.07419
$786$	−48992.3	−2.22328
$787$	−4203.43	−0.190389	−0.0951945	−	0.995459i	$-0.530347\pi$
$787$	−4203.43	−0.190389	−0.0951945	+	0.995459i	$0.530347\pi$
$788$	5882.77	0.265945
$789$	−39023.4	−1.76080
$790$	13262.4	0.597286
$791$	−19146.0	−0.860624
$792$	0	0
$793$	−7023.64	−0.314523
$794$	−20095.3	−0.898181
$795$	30018.2	1.33917
$796$	−5424.11	−0.241523
$797$	29590.4	1.31512	0.657558	−	0.753404i	$-0.271590\pi$
$797$	29590.4	1.31512	0.657558	+	0.753404i	$0.271590\pi$
$798$	22236.1	0.986404
$799$	−39154.7	−1.73366
$800$	−917.234	−0.0405364
$801$	28631.6	1.26298
$802$	24892.4	1.09599
$803$	0	0
$804$	6161.42	0.270269
$805$	−14146.8	−0.619390
$806$	−607.681	−0.0265566
$807$	36228.3	1.58029
$808$	20282.5	0.883087
$809$	22306.7	0.969423	0.484712	−	0.874674i	$-0.338925\pi$
$809$	22306.7	0.969423	0.484712	+	0.874674i	$0.338925\pi$
$810$	−15004.4	−0.650867
$811$	−29725.4	−1.28705	−0.643527	−	0.765424i	$-0.722530\pi$
$811$	−29725.4	−1.28705	−0.643527	+	0.765424i	$0.722530\pi$
$812$	1519.63	0.0656755
$813$	27201.5	1.17343
$814$	0	0
$815$	−15494.0	−0.665926
$816$	−45676.6	−1.95956
$817$	−9950.37	−0.426095
$818$	−1250.82	−0.0534645
$819$	−7828.31	−0.333997
$820$	−5086.54	−0.216622
$821$	30623.9	1.30180	0.650902	−	0.759162i	$-0.274391\pi$
$821$	30623.9	1.30180	0.650902	+	0.759162i	$0.274391\pi$
$822$	−24422.9	−1.03631
$823$	31687.7	1.34212	0.671058	−	0.741405i	$-0.265840\pi$
$823$	31687.7	1.34212	0.671058	+	0.741405i	$0.265840\pi$
$824$	8354.92	0.353225
$825$	0	0
$826$	1485.03	0.0625555
$827$	−4744.08	−0.199477	−0.0997387	−	0.995014i	$-0.531801\pi$
$827$	−4744.08	−0.199477	−0.0997387	+	0.995014i	$0.531801\pi$
$828$	−3453.92	−0.144966
$829$	−23419.2	−0.981159	−0.490580	−	0.871396i	$-0.663215\pi$
$829$	−23419.2	−0.981159	−0.490580	+	0.871396i	$0.663215\pi$
$830$	33026.9	1.38118
$831$	−57181.6	−2.38701
$832$	5261.75	0.219253
$833$	−3044.96	−0.126653
$834$	−14408.5	−0.598231
$835$	−25703.5	−1.06528
$836$	0	0
$837$	899.335	0.0371393
$838$	−41022.2	−1.69104
$839$	−22363.7	−0.920239	−0.460120	−	0.887857i	$-0.652193\pi$
$839$	−22363.7	−0.920239	−0.460120	+	0.887857i	$0.652193\pi$
$840$	29256.0	1.20170
$841$	−19854.2	−0.814065
$842$	−9229.57	−0.377758
$843$	11430.3	0.466998
$844$	7610.65	0.310390
$845$	−1765.76	−0.0718864
$846$	51335.1	2.08621
$847$	0	0
$848$	26626.5	1.07825
$849$	1179.55	0.0476820
$850$	3869.19	0.156132
$851$	−19518.3	−0.786227
$852$	−11962.6	−0.481025
$853$	−8888.09	−0.356767	−0.178384	−	0.983961i	$-0.557087\pi$
$853$	−8888.09	−0.356767	−0.178384	+	0.983961i	$0.557087\pi$
$854$	−28763.2	−1.15253
$855$	−19190.3	−0.767597
$856$	−19016.0	−0.759293
$857$	−24013.3	−0.957152	−0.478576	−	0.878046i	$-0.658847\pi$
$857$	−24013.3	−0.957152	−0.478576	+	0.878046i	$0.658847\pi$
$858$	0	0
$859$	−34041.5	−1.35213	−0.676067	−	0.736841i	$-0.736317\pi$
$859$	−34041.5	−1.35213	−0.676067	+	0.736841i	$0.736317\pi$
$860$	2521.78	0.0999908
$861$	−51594.9	−2.04222
$862$	−18876.5	−0.745865
$863$	−13583.4	−0.535789	−0.267894	−	0.963448i	$-0.586328\pi$
$863$	−13583.4	−0.535789	−0.267894	+	0.963448i	$0.586328\pi$
$864$	3397.44	0.133777
$865$	46992.3	1.84715
$866$	6465.76	0.253713
$867$	11867.5	0.464871
$868$	−346.047	−0.0135318
$869$	0	0
$870$	−16816.9	−0.655339
$871$	7906.07	0.307562
$872$	3275.77	0.127215
$873$	28400.4	1.10104
$874$	12588.8	0.487210
$875$	−25698.8	−0.992888
$876$	833.486	0.0321471
$877$	4982.94	0.191861	0.0959304	−	0.995388i	$-0.469417\pi$
$877$	4982.94	0.191861	0.0959304	+	0.995388i	$0.469417\pi$
$878$	−42414.7	−1.63033
$879$	−54109.0	−2.07628
$880$	0	0
$881$	6944.27	0.265560	0.132780	−	0.991146i	$-0.457610\pi$
$881$	6944.27	0.265560	0.132780	+	0.991146i	$0.457610\pi$
$882$	3992.20	0.152409
$883$	−26384.2	−1.00555	−0.502774	−	0.864418i	$-0.667687\pi$
$883$	−26384.2	−1.00555	−0.502774	+	0.864418i	$0.667687\pi$
$884$	1346.57	0.0512332
$885$	−2285.21	−0.0867984
$886$	28677.0	1.08739
$887$	−1306.21	−0.0494454	−0.0247227	−	0.999694i	$-0.507870\pi$
$887$	−1306.21	−0.0494454	−0.0247227	+	0.999694i	$0.507870\pi$
$888$	40364.6	1.52539
$889$	−13197.5	−0.497895
$890$	26447.5	0.996092
$891$	0	0
$892$	4931.09	0.185095
$893$	−26017.7	−0.974973
$894$	−23348.9	−0.873494
$895$	15407.4	0.575432
$896$	29641.8	1.10521
$897$	−7902.42	−0.294152
$898$	2081.03	0.0773328
$899$	−1032.65	−0.0383101
$900$	−705.400	−0.0261259
$901$	−29374.0	−1.08612
$902$	0	0
$903$	25579.5	0.942671
$904$	22416.1	0.824721
$905$	−1593.46	−0.0585287
$906$	−59286.3	−2.17401
$907$	−48885.7	−1.78966	−0.894831	−	0.446404i	$-0.852704\pi$
$907$	−48885.7	−1.78966	−0.894831	+	0.446404i	$0.852704\pi$
$908$	−3246.25	−0.118646
$909$	34201.1	1.24794
$910$	−7231.15	−0.263418
$911$	−29503.0	−1.07297	−0.536486	−	0.843909i	$-0.680249\pi$
$911$	−29503.0	−1.07297	−0.536486	+	0.843909i	$0.680249\pi$
$912$	−30351.5	−1.10201
$913$	0	0
$914$	24772.7	0.896509
$915$	44261.8	1.59918
$916$	−8487.19	−0.306141
$917$	−35798.7	−1.28918
$918$	−14331.5	−0.515262
$919$	25816.9	0.926684	0.463342	−	0.886180i	$-0.346650\pi$
$919$	25816.9	0.926684	0.463342	+	0.886180i	$0.346650\pi$
$920$	16563.0	0.593550
$921$	398.612	0.0142613
$922$	−30769.3	−1.09906
$923$	−15349.9	−0.547399
$924$	0	0
$925$	−3986.26	−0.141695
$926$	492.472	0.0174769
$927$	14088.4	0.499163
$928$	−3901.06	−0.137994
$929$	−14202.9	−0.501596	−0.250798	−	0.968039i	$-0.580693\pi$
$929$	−14202.9	−0.501596	−0.250798	+	0.968039i	$0.580693\pi$
$930$	3829.51	0.135026
$931$	−2023.33	−0.0712267
$932$	2944.34	0.103482
$933$	59784.9	2.09782
$934$	10139.5	0.355218
$935$	0	0
$936$	9165.35	0.320063
$937$	55535.3	1.93624	0.968122	−	0.250480i	$-0.0805884\pi$
$937$	55535.3	1.93624	0.968122	+	0.250480i	$0.0805884\pi$
$938$	32377.0	1.12702
$939$	59284.8	2.06037
$940$	6593.83	0.228795
$941$	−27893.4	−0.966311	−0.483156	−	0.875535i	$-0.660509\pi$
$941$	−27893.4	−0.966311	−0.483156	+	0.875535i	$0.660509\pi$
$942$	−54045.8	−1.86933
$943$	−29210.0	−1.00870
$944$	−2027.01	−0.0698872
$945$	10701.7	0.368388
$946$	0	0
$947$	−33283.9	−1.14211	−0.571057	−	0.820910i	$-0.693466\pi$
$947$	−33283.9	−1.14211	−0.571057	+	0.820910i	$0.693466\pi$
$948$	4218.76	0.144535
$949$	1069.49	0.0365829
$950$	2571.02	0.0878053
$951$	68298.4	2.32884
$952$	−28628.2	−0.974627
$953$	−26366.7	−0.896224	−0.448112	−	0.893977i	$-0.647903\pi$
$953$	−26366.7	−0.896224	−0.448112	+	0.893977i	$0.647903\pi$
$954$	38511.8	1.30699
$955$	−13386.8	−0.453598
$956$	7962.17	0.269367
$957$	0	0
$958$	22991.1	0.775373
$959$	−17845.8	−0.600908
$960$	−33158.7	−1.11478
$961$	−29555.8	−0.992107
$962$	−9976.81	−0.334371
$963$	−32065.6	−1.07300
$964$	−5884.85	−0.196616
$965$	26733.9	0.891808
$966$	−32362.0	−1.07788
$967$	−40336.7	−1.34141	−0.670703	−	0.741726i	$-0.734008\pi$
$967$	−40336.7	−1.34141	−0.670703	+	0.741726i	$0.734008\pi$
$968$	0	0
$969$	33483.4	1.11005
$970$	26234.0	0.868373
$971$	33695.9	1.11365	0.556824	−	0.830631i	$-0.312020\pi$
$971$	33695.9	1.11365	0.556824	+	0.830631i	$0.312020\pi$
$972$	−6818.90	−0.225017
$973$	−10528.3	−0.346887
$974$	38670.9	1.27217
$975$	−1613.93	−0.0530123
$976$	39260.7	1.28761
$977$	−9413.52	−0.308255	−0.154127	−	0.988051i	$-0.549257\pi$
$977$	−9413.52	−0.308255	−0.154127	+	0.988051i	$0.549257\pi$
$978$	−35443.8	−1.15886
$979$	0	0
$980$	512.786	0.0167146
$981$	5523.73	0.179775
$982$	−41303.9	−1.34222
$983$	−37657.2	−1.22185	−0.610925	−	0.791689i	$-0.709202\pi$
$983$	−37657.2	−1.22185	−0.610925	+	0.791689i	$0.709202\pi$
$984$	60407.2	1.95702
$985$	−47569.5	−1.53877
$986$	16456.0	0.531506
$987$	66884.0	2.15698
$988$	894.780	0.0288125
$989$	14481.6	0.465609
$990$	0	0
$991$	55077.2	1.76547	0.882737	−	0.469868i	$-0.155698\pi$
$991$	55077.2	1.76547	0.882737	+	0.469868i	$0.155698\pi$
$992$	888.344	0.0284324
$993$	52107.9	1.66525
$994$	−62861.1	−2.00587
$995$	43860.6	1.39746
$996$	10505.8	0.334226
$997$	27419.6	0.870999	0.435500	−	0.900189i	$-0.356572\pi$
$997$	27419.6	0.870999	0.435500	+	0.900189i	$0.356572\pi$
$998$	44316.7	1.40563
$999$	14765.1	0.467616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.k.1.4	yes	15
11.10	odd	2		1573.4.a.h.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1573.4.a.h.1.12	✓	15	11.10	odd	2
1573.4.a.k.1.4	yes	15	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-3.04830 q^{2} +7.84090 q^{3} +1.29211 q^{4} -10.4483 q^{5} -23.9014 q^{6} -17.4647 q^{7} +20.4476 q^{8} +34.4796 q^{9} +O(q^{10})\)	\(q-3.04830 q^{2} +7.84090 q^{3} +1.29211 q^{4} -10.4483 q^{5} -23.9014 q^{6} -17.4647 q^{7} +20.4476 q^{8} +34.4796 q^{9} +31.8495 q^{10} +10.1313 q^{12} +13.0000 q^{13} +53.2377 q^{14} -81.9239 q^{15} -72.6673 q^{16} +80.1657 q^{17} -105.104 q^{18} +53.2690 q^{19} -13.5003 q^{20} -136.939 q^{21} -77.5267 q^{23} +160.328 q^{24} -15.8334 q^{25} -39.6278 q^{26} +58.6470 q^{27} -22.5663 q^{28} -67.3407 q^{29} +249.728 q^{30} +15.3347 q^{31} +57.9303 q^{32} -244.369 q^{34} +182.476 q^{35} +44.5513 q^{36} +251.763 q^{37} -162.380 q^{38} +101.932 q^{39} -213.643 q^{40} +376.773 q^{41} +417.431 q^{42} -186.795 q^{43} -360.253 q^{45} +236.324 q^{46} -488.422 q^{47} -569.777 q^{48} -37.9833 q^{49} +48.2649 q^{50} +628.571 q^{51} +16.7974 q^{52} -366.416 q^{53} -178.773 q^{54} -357.113 q^{56} +417.677 q^{57} +205.274 q^{58} +27.8944 q^{59} -105.854 q^{60} -540.280 q^{61} -46.7447 q^{62} -602.177 q^{63} +404.750 q^{64} -135.828 q^{65} +608.159 q^{67} +103.583 q^{68} -607.879 q^{69} -556.242 q^{70} -1180.76 q^{71} +705.027 q^{72} +82.2687 q^{73} -767.447 q^{74} -124.148 q^{75} +68.8292 q^{76} -310.718 q^{78} +416.410 q^{79} +759.249 q^{80} -471.105 q^{81} -1148.52 q^{82} +1036.97 q^{83} -176.940 q^{84} -837.594 q^{85} +569.405 q^{86} -528.011 q^{87} +830.391 q^{89} +1098.16 q^{90} -227.041 q^{91} -100.173 q^{92} +120.238 q^{93} +1488.85 q^{94} -556.570 q^{95} +454.225 q^{96} +823.686 q^{97} +115.784 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} - 25 q^{6} + 28 q^{7} + 108 q^{8} + 133 q^{9}+O(q^{10}) \) 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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