LMFDB - Embedded newform 1573.4.a.h.1.14

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			1.14
Root			$-3.84909$ 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)

$f(q)$	$=$	$q+3.84909 q^{2} -0.121722 q^{3} +6.81551 q^{4} +8.75953 q^{5} -0.468519 q^{6} -0.407809 q^{7} -4.55922 q^{8} -26.9852 q^{9} +O(q^{10})$	\(q+3.84909 q^{2} -0.121722 q^{3} +6.81551 q^{4} +8.75953 q^{5} -0.468519 q^{6} -0.407809 q^{7} -4.55922 q^{8} -26.9852 q^{9} +33.7162 q^{10} -0.829597 q^{12} -13.0000 q^{13} -1.56969 q^{14} -1.06623 q^{15} -72.0729 q^{16} +32.1743 q^{17} -103.868 q^{18} +114.541 q^{19} +59.7007 q^{20} +0.0496393 q^{21} -119.286 q^{23} +0.554957 q^{24} -48.2706 q^{25} -50.0382 q^{26} +6.57118 q^{27} -2.77942 q^{28} -31.5471 q^{29} -4.10401 q^{30} +85.1733 q^{31} -240.942 q^{32} +123.842 q^{34} -3.57222 q^{35} -183.918 q^{36} -60.5880 q^{37} +440.880 q^{38} +1.58239 q^{39} -39.9366 q^{40} +108.934 q^{41} +0.191066 q^{42} -409.923 q^{43} -236.378 q^{45} -459.141 q^{46} -507.006 q^{47} +8.77286 q^{48} -342.834 q^{49} -185.798 q^{50} -3.91632 q^{51} -88.6016 q^{52} +64.2070 q^{53} +25.2931 q^{54} +1.85929 q^{56} -13.9422 q^{57} -121.428 q^{58} +652.386 q^{59} -7.26688 q^{60} -724.537 q^{61} +327.840 q^{62} +11.0048 q^{63} -350.823 q^{64} -113.874 q^{65} -396.525 q^{67} +219.284 q^{68} +14.5197 q^{69} -13.7498 q^{70} -51.0899 q^{71} +123.031 q^{72} -372.151 q^{73} -233.209 q^{74} +5.87559 q^{75} +780.658 q^{76} +6.09075 q^{78} -736.822 q^{79} -631.325 q^{80} +727.800 q^{81} +419.297 q^{82} -836.545 q^{83} +0.338317 q^{84} +281.832 q^{85} -1577.83 q^{86} +3.83998 q^{87} -1156.63 q^{89} -909.839 q^{90} +5.30152 q^{91} -812.991 q^{92} -10.3675 q^{93} -1951.51 q^{94} +1003.33 q^{95} +29.3279 q^{96} +1595.13 q^{97} -1319.60 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.84909	1.36086	0.680430	−	0.732813i	$-0.261793\pi$
$2$	3.84909	1.36086	0.680430	+	0.732813i	$0.261793\pi$
$3$	−0.121722	−0.0234254	−0.0117127	−	0.999931i	$-0.503728\pi$
$3$	−0.121722	−0.0234254	−0.0117127	+	0.999931i	$0.503728\pi$
$4$	6.81551	0.851938
$5$	8.75953	0.783476	0.391738	−	0.920077i	$-0.371874\pi$
$5$	8.75953	0.783476	0.391738	+	0.920077i	$0.371874\pi$
$6$	−0.468519	−0.0318787
$7$	−0.407809	−0.0220196	−0.0110098	−	0.999939i	$-0.503505\pi$
$7$	−0.407809	−0.0220196	−0.0110098	+	0.999939i	$0.503505\pi$
$8$	−4.55922	−0.201491
$9$	−26.9852	−0.999451
$10$	33.7162	1.06620
$11$	0	0
$11$	0	0
$12$	−0.829597	−0.0199570
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−1.56969	−0.0299656
$15$	−1.06623	−0.0183533
$16$	−72.0729	−1.12614
$17$	32.1743	0.459025	0.229512	−	0.973306i	$-0.426287\pi$
$17$	32.1743	0.459025	0.229512	+	0.973306i	$0.426287\pi$
$18$	−103.868	−1.36011
$19$	114.541	1.38303	0.691516	−	0.722361i	$-0.256943\pi$
$19$	114.541	1.38303	0.691516	+	0.722361i	$0.256943\pi$
$20$	59.7007	0.667474
$21$	0.0496393	0.000515818 0
$22$	0	0
$23$	−119.286	−1.08142	−0.540712	−	0.841208i	$-0.681845\pi$
$23$	−119.286	−1.08142	−0.540712	+	0.841208i	$0.681845\pi$
$24$	0.554957	0.00472001
$25$	−48.2706	−0.386165
$26$	−50.0382	−0.377434
$27$	6.57118	0.0468380
$28$	−2.77942	−0.0187594
$29$	−31.5471	−0.202005	−0.101003	−	0.994886i	$-0.532205\pi$
$29$	−31.5471	−0.202005	−0.101003	+	0.994886i	$0.532205\pi$
$30$	−4.10401	−0.0249762
$31$	85.1733	0.493470	0.246735	−	0.969083i	$-0.420642\pi$
$31$	85.1733	0.493470	0.246735	+	0.969083i	$0.420642\pi$
$32$	−240.942	−1.33103
$33$	0	0
$34$	123.842	0.624668
$35$	−3.57222	−0.0172518
$36$	−183.918	−0.851471
$37$	−60.5880	−0.269206	−0.134603	−	0.990900i	$-0.542976\pi$
$37$	−60.5880	−0.269206	−0.134603	+	0.990900i	$0.542976\pi$
$38$	440.880	1.88211
$39$	1.58239	0.00649704
$40$	−39.9366	−0.157863
$41$	108.934	0.414942	0.207471	−	0.978241i	$-0.433477\pi$
$41$	108.934	0.414942	0.207471	+	0.978241i	$0.433477\pi$
$42$	0.191066	0.000701956 0
$43$	−409.923	−1.45378	−0.726892	−	0.686752i	$-0.759036\pi$
$43$	−409.923	−1.45378	−0.726892	+	0.686752i	$0.759036\pi$
$44$	0	0
$45$	−236.378	−0.783046
$46$	−459.141	−1.47167
$47$	−507.006	−1.57350	−0.786750	−	0.617272i	$-0.788238\pi$
$47$	−507.006	−1.57350	−0.786750	+	0.617272i	$0.788238\pi$
$48$	8.77286	0.0263803
$49$	−342.834	−0.999515
$50$	−185.798	−0.525516
$51$	−3.91632	−0.0107528
$52$	−88.6016	−0.236285
$53$	64.2070	0.166406	0.0832029	−	0.996533i	$-0.473485\pi$
$53$	64.2070	0.166406	0.0832029	+	0.996533i	$0.473485\pi$
$54$	25.2931	0.0637399
$55$	0	0
$56$	1.85929	0.00443675
$57$	−13.9422	−0.0323981
$58$	−121.428	−0.274901
$59$	652.386	1.43955	0.719775	−	0.694208i	$-0.244245\pi$
$59$	652.386	1.43955	0.719775	+	0.694208i	$0.244245\pi$
$60$	−7.26688	−0.0156358
$61$	−724.537	−1.52078	−0.760389	−	0.649467i	$-0.774992\pi$
$61$	−724.537	−1.52078	−0.760389	+	0.649467i	$0.774992\pi$
$62$	327.840	0.671543
$63$	11.0048	0.0220075
$64$	−350.823	−0.685200
$65$	−113.874	−0.217297
$66$	0	0
$67$	−396.525	−0.723034	−0.361517	−	0.932366i	$-0.617741\pi$
$67$	−396.525	−0.723034	−0.361517	+	0.932366i	$0.617741\pi$
$68$	219.284	0.391061
$69$	14.5197	0.0253328
$70$	−13.7498	−0.0234773
$71$	−51.0899	−0.0853980	−0.0426990	−	0.999088i	$-0.513596\pi$
$71$	−51.0899	−0.0853980	−0.0426990	+	0.999088i	$0.513596\pi$
$72$	123.031	0.201380
$73$	−372.151	−0.596671	−0.298335	−	0.954461i	$-0.596431\pi$
$73$	−372.151	−0.596671	−0.298335	+	0.954461i	$0.596431\pi$
$74$	−233.209	−0.366351
$75$	5.87559	0.00904607
$76$	780.658	1.17826
$77$	0	0
$78$	6.09075	0.00884156
$79$	−736.822	−1.04935	−0.524677	−	0.851301i	$-0.675814\pi$
$79$	−736.822	−1.04935	−0.524677	+	0.851301i	$0.675814\pi$
$80$	−631.325	−0.882304
$81$	727.800	0.998354
$82$	419.297	0.564678
$83$	−836.545	−1.10630	−0.553149	−	0.833082i	$-0.686574\pi$
$83$	−836.545	−1.10630	−0.553149	+	0.833082i	$0.686574\pi$
$84$	0.338317	0.000439445 0
$85$	281.832	0.359635
$86$	−1577.83	−1.97840
$87$	3.83998	0.00473205
$88$	0	0
$89$	−1156.63	−1.37756	−0.688780	−	0.724971i	$-0.741853\pi$
$89$	−1156.63	−1.37756	−0.688780	+	0.724971i	$0.741853\pi$
$90$	−909.839	−1.06562
$91$	5.30152	0.00610714
$92$	−812.991	−0.921307
$93$	−10.3675	−0.0115597
$94$	−1951.51	−2.14131
$95$	1003.33	1.08357
$96$	29.3279	0.0311798
$97$	1595.13	1.66970	0.834851	−	0.550476i	$-0.185554\pi$
$97$	1595.13	1.66970	0.834851	+	0.550476i	$0.185554\pi$
$98$	−1319.60	−1.36020
$99$	0	0
$100$	−328.989	−0.328989
$101$	−869.163	−0.856287	−0.428143	−	0.903711i	$-0.640832\pi$
$101$	−869.163	−0.856287	−0.428143	+	0.903711i	$0.640832\pi$
$102$	−15.0743	−0.0146331
$103$	−78.0844	−0.0746979	−0.0373489	−	0.999302i	$-0.511891\pi$
$103$	−78.0844	−0.0746979	−0.0373489	+	0.999302i	$0.511891\pi$
$104$	59.2699	0.0558836
$105$	0.434817	0.000404131 0
$106$	247.139	0.226455
$107$	702.839	0.635009	0.317505	−	0.948257i	$-0.397155\pi$
$107$	702.839	0.635009	0.317505	+	0.948257i	$0.397155\pi$
$108$	44.7859	0.0399031
$109$	340.307	0.299042	0.149521	−	0.988759i	$-0.452227\pi$
$109$	340.307	0.299042	0.149521	+	0.988759i	$0.452227\pi$
$110$	0	0
$111$	7.37489	0.00630625
$112$	29.3920	0.0247972
$113$	202.163	0.168300	0.0841501	−	0.996453i	$-0.473182\pi$
$113$	202.163	0.168300	0.0841501	+	0.996453i	$0.473182\pi$
$114$	−53.6648	−0.0440892
$115$	−1044.89	−0.847270
$116$	−215.010	−0.172096
$117$	350.807	0.277198
$118$	2511.09	1.95902
$119$	−13.1210	−0.0101075
$120$	4.86117	0.00369802
$121$	0	0
$122$	−2788.81	−2.06957
$123$	−13.2597	−0.00972019
$124$	580.499	0.420406
$125$	−1517.77	−1.08603
$126$	42.3585	0.0299492
$127$	495.587	0.346269	0.173135	−	0.984898i	$-0.444610\pi$
$127$	495.587	0.346269	0.173135	+	0.984898i	$0.444610\pi$
$128$	577.184	0.398565
$129$	49.8967	0.0340555
$130$	−438.311	−0.295711
$131$	−428.883	−0.286043	−0.143022	−	0.989720i	$-0.545682\pi$
$131$	−428.883	−0.286043	−0.143022	+	0.989720i	$0.545682\pi$
$132$	0	0
$133$	−46.7110	−0.0304538
$134$	−1526.26	−0.983947
$135$	57.5605	0.0366964
$136$	−146.690	−0.0924893
$137$	−148.921	−0.0928701	−0.0464350	−	0.998921i	$-0.514786\pi$
$137$	−148.921	−0.0928701	−0.0464350	+	0.998921i	$0.514786\pi$
$138$	55.8875	0.0344744
$139$	1389.37	0.847806	0.423903	−	0.905708i	$-0.360660\pi$
$139$	1389.37	0.847806	0.423903	+	0.905708i	$0.360660\pi$
$140$	−24.3465	−0.0146975
$141$	61.7138	0.0368599
$142$	−196.650	−0.116215
$143$	0	0
$144$	1944.90	1.12552
$145$	−276.338	−0.158266
$146$	−1432.44	−0.811985
$147$	41.7304	0.0234140
$148$	−412.938	−0.229347
$149$	257.396	0.141521	0.0707607	−	0.997493i	$-0.477457\pi$
$149$	257.396	0.141521	0.0707607	+	0.997493i	$0.477457\pi$
$150$	22.6157	0.0123104
$151$	2641.69	1.42369	0.711846	−	0.702336i	$-0.247859\pi$
$151$	2641.69	1.42369	0.711846	+	0.702336i	$0.247859\pi$
$152$	−522.219	−0.278668
$153$	−868.230	−0.458773
$154$	0	0
$155$	746.078	0.386622
$156$	10.7848	0.00553508
$157$	−2348.68	−1.19392	−0.596959	−	0.802271i	$-0.703625\pi$
$157$	−2348.68	−1.19392	−0.596959	+	0.802271i	$0.703625\pi$
$158$	−2836.10	−1.42802
$159$	−7.81540	−0.00389812
$160$	−2110.53	−1.04283
$161$	48.6457	0.0238125
$162$	2801.37	1.35862
$163$	−2063.15	−0.991401	−0.495700	−	0.868494i	$-0.665089\pi$
$163$	−2063.15	−0.991401	−0.495700	+	0.868494i	$0.665089\pi$
$164$	742.441	0.353505
$165$	0	0
$166$	−3219.94	−1.50552
$167$	−1584.35	−0.734135	−0.367067	−	0.930194i	$-0.619638\pi$
$167$	−1584.35	−0.734135	−0.367067	+	0.930194i	$0.619638\pi$
$168$	−0.226317	−0.000103933 0
$169$	169.000	0.0769231
$170$	1084.80	0.489413
$171$	−3090.92	−1.38227
$172$	−2793.84	−1.23853
$173$	−443.898	−0.195081	−0.0975403	−	0.995232i	$-0.531097\pi$
$173$	−443.898	−0.195081	−0.0975403	+	0.995232i	$0.531097\pi$
$174$	14.7804	0.00643966
$175$	19.6852	0.00850320
$176$	0	0
$177$	−79.4097	−0.0337220
$178$	−4451.98	−1.87466
$179$	4163.54	1.73853	0.869266	−	0.494345i	$-0.164592\pi$
$179$	4163.54	1.73853	0.869266	+	0.494345i	$0.164592\pi$
$180$	−1611.03	−0.667107
$181$	2047.58	0.840861	0.420430	−	0.907325i	$-0.361879\pi$
$181$	2047.58	0.840861	0.420430	+	0.907325i	$0.361879\pi$
$182$	20.4060	0.00831096
$183$	88.1921	0.0356249
$184$	543.849	0.217897
$185$	−530.722	−0.210916
$186$	−39.9053	−0.0157312
$187$	0	0
$188$	−3455.50	−1.34052
$189$	−2.67979	−0.00103135
$190$	3861.90	1.47459
$191$	1735.93	0.657631	0.328816	−	0.944394i	$-0.393351\pi$
$191$	1735.93	0.657631	0.328816	+	0.944394i	$0.393351\pi$
$192$	42.7028	0.0160511
$193$	−2621.44	−0.977696	−0.488848	−	0.872369i	$-0.662583\pi$
$193$	−2621.44	−0.977696	−0.488848	+	0.872369i	$0.662583\pi$
$194$	6139.81	2.27223
$195$	13.8610	0.00509028
$196$	−2336.59	−0.851525
$197$	4571.10	1.65319	0.826593	−	0.562800i	$-0.190276\pi$
$197$	4571.10	1.65319	0.826593	+	0.562800i	$0.190276\pi$
$198$	0	0
$199$	2942.54	1.04820	0.524099	−	0.851658i	$-0.324402\pi$
$199$	2942.54	1.04820	0.524099	+	0.851658i	$0.324402\pi$
$200$	220.076	0.0778087
$201$	48.2658	0.0169374
$202$	−3345.49	−1.16529
$203$	12.8652	0.00444808
$204$	−26.6917	−0.00916076
$205$	954.211	0.325098
$206$	−300.554	−0.101653
$207$	3218.94	1.08083
$208$	936.948	0.312335
$209$	0	0
$210$	1.67365	0.000549966 0
$211$	−74.2760	−0.0242340	−0.0121170	−	0.999927i	$-0.503857\pi$
$211$	−74.2760	−0.0242340	−0.0121170	+	0.999927i	$0.503857\pi$
$212$	437.603	0.141767
$213$	6.21877	0.00200048
$214$	2705.29	0.864159
$215$	−3590.74	−1.13901
$216$	−29.9595	−0.00943743
$217$	−34.7344	−0.0108660
$218$	1309.87	0.406953
$219$	45.2990	0.0139773
$220$	0	0
$221$	−418.266	−0.127311
$222$	28.3866	0.00858192
$223$	1164.43	0.349667	0.174833	−	0.984598i	$-0.444061\pi$
$223$	1164.43	0.349667	0.174833	+	0.984598i	$0.444061\pi$
$224$	98.2581	0.0293087
$225$	1302.59	0.385953
$226$	778.145	0.229033
$227$	−3614.45	−1.05683	−0.528413	−	0.848987i	$-0.677213\pi$
$227$	−3614.45	−1.05683	−0.528413	+	0.848987i	$0.677213\pi$
$228$	−95.0232	−0.0276012
$229$	1029.98	0.297218	0.148609	−	0.988896i	$-0.452520\pi$
$229$	1029.98	0.297218	0.148609	+	0.988896i	$0.452520\pi$
$230$	−4021.86	−1.15302
$231$	0	0
$232$	143.830	0.0407022
$233$	2111.70	0.593742	0.296871	−	0.954918i	$-0.404057\pi$
$233$	2111.70	0.593742	0.296871	+	0.954918i	$0.404057\pi$
$234$	1350.29	0.377227
$235$	−4441.14	−1.23280
$236$	4446.34	1.22641
$237$	89.6875	0.0245815
$238$	−50.5038	−0.0137549
$239$	14.1121	0.00381941	0.00190970	−	0.999998i	$-0.499392\pi$
$239$	14.1121	0.00381941	0.00190970	+	0.999998i	$0.499392\pi$
$240$	76.8461	0.0206683
$241$	−7098.82	−1.89741	−0.948703	−	0.316168i	$-0.897604\pi$
$241$	−7098.82	−1.89741	−0.948703	+	0.316168i	$0.897604\pi$
$242$	0	0
$243$	−266.011	−0.0702248
$244$	−4938.09	−1.29561
$245$	−3003.06	−0.783096
$246$	−51.0377	−0.0132278
$247$	−1489.04	−0.383584
$248$	−388.324	−0.0994298
$249$	101.826	0.0259155
$250$	−5842.03	−1.47793
$251$	−4101.64	−1.03145	−0.515723	−	0.856755i	$-0.672477\pi$
$251$	−4101.64	−1.03145	−0.515723	+	0.856755i	$0.672477\pi$
$252$	75.0033	0.0187491
$253$	0	0
$254$	1907.56	0.471224
$255$	−34.3051	−0.00842459
$256$	5028.21	1.22759
$257$	1002.92	0.243426	0.121713	−	0.992565i	$-0.461161\pi$
$257$	1002.92	0.243426	0.121713	+	0.992565i	$0.461161\pi$
$258$	192.057	0.0463447
$259$	24.7083	0.00592780
$260$	−776.108	−0.185124
$261$	851.305	0.201894
$262$	−1650.81	−0.389265
$263$	−5585.19	−1.30950	−0.654748	−	0.755847i	$-0.727225\pi$
$263$	−5585.19	−1.30950	−0.654748	+	0.755847i	$0.727225\pi$
$264$	0	0
$265$	562.423	0.130375
$266$	−179.795	−0.0414434
$267$	140.788	0.0322699
$268$	−2702.52	−0.615980
$269$	3049.66	0.691230	0.345615	−	0.938376i	$-0.387670\pi$
$269$	3049.66	0.691230	0.345615	+	0.938376i	$0.387670\pi$
$270$	221.556	0.0499387
$271$	−2079.37	−0.466098	−0.233049	−	0.972465i	$-0.574870\pi$
$271$	−2079.37	−0.466098	−0.233049	+	0.972465i	$0.574870\pi$
$272$	−2318.90	−0.516926
$273$	−0.645311	−0.000143062 0
$274$	−573.211	−0.126383
$275$	0	0
$276$	98.9589	0.0215820
$277$	467.707	0.101450	0.0507252	−	0.998713i	$-0.483847\pi$
$277$	467.707	0.101450	0.0507252	+	0.998713i	$0.483847\pi$
$278$	5347.82	1.15374
$279$	−2298.42	−0.493199
$280$	16.2865	0.00347609
$281$	−666.062	−0.141402	−0.0707010	−	0.997498i	$-0.522524\pi$
$281$	−666.062	−0.141402	−0.0707010	+	0.997498i	$0.522524\pi$
$282$	237.542	0.0501611
$283$	1863.64	0.391456	0.195728	−	0.980658i	$-0.437293\pi$
$283$	1863.64	0.391456	0.195728	+	0.980658i	$0.437293\pi$
$284$	−348.204	−0.0727539
$285$	−122.127	−0.0253831
$286$	0	0
$287$	−44.4243	−0.00913687
$288$	6501.85	1.33030
$289$	−3877.81	−0.789296
$290$	−1063.65	−0.215378
$291$	−194.163	−0.0391135
$292$	−2536.40	−0.508327
$293$	−6579.27	−1.31183	−0.655913	−	0.754836i	$-0.727716\pi$
$293$	−6579.27	−1.31183	−0.655913	+	0.754836i	$0.727716\pi$
$294$	160.624	0.0318632
$295$	5714.60	1.12785
$296$	276.234	0.0542425
$297$	0	0
$298$	990.741	0.192591
$299$	1550.71	0.299933
$300$	40.0452	0.00770669
$301$	167.170	0.0320118
$302$	10168.1	1.93744
$303$	105.796	0.0200589
$304$	−8255.33	−1.55749
$305$	−6346.61	−1.19149
$306$	−3341.90	−0.624325
$307$	−775.289	−0.144131	−0.0720653	−	0.997400i	$-0.522959\pi$
$307$	−775.289	−0.144131	−0.0720653	+	0.997400i	$0.522959\pi$
$308$	0	0
$309$	9.50458	0.00174983
$310$	2871.72	0.526138
$311$	9865.33	1.79875	0.899375	−	0.437178i	$-0.144022\pi$
$311$	9865.33	1.79875	0.899375	+	0.437178i	$0.144022\pi$
$312$	−7.21445	−0.00130909
$313$	−4849.80	−0.875804	−0.437902	−	0.899023i	$-0.644278\pi$
$313$	−4849.80	−0.875804	−0.437902	+	0.899023i	$0.644278\pi$
$314$	−9040.29	−1.62476
$315$	96.3969	0.0172424
$316$	−5021.82	−0.893985
$317$	−728.252	−0.129031	−0.0645153	−	0.997917i	$-0.520550\pi$
$317$	−728.252	−0.129031	−0.0645153	+	0.997917i	$0.520550\pi$
$318$	−30.0822	−0.00530480
$319$	0	0
$320$	−3073.04	−0.536838
$321$	−85.5510	−0.0148754
$322$	187.242	0.0324055
$323$	3685.29	0.634845
$324$	4960.33	0.850536
$325$	627.518	0.107103
$326$	−7941.25	−1.34916
$327$	−41.4229	−0.00700517
$328$	−496.654	−0.0836072
$329$	206.762	0.0346478
$330$	0	0
$331$	8561.62	1.42172	0.710859	−	0.703334i	$-0.248306\pi$
$331$	8561.62	1.42172	0.710859	+	0.703334i	$0.248306\pi$
$332$	−5701.48	−0.942498
$333$	1634.98	0.269058
$334$	−6098.30	−0.999054
$335$	−3473.37	−0.566480
$336$	−3.57765	−0.000580883 0
$337$	−8960.93	−1.44847	−0.724233	−	0.689556i	$-0.757806\pi$
$337$	−8960.93	−1.44847	−0.724233	+	0.689556i	$0.757806\pi$
$338$	650.497	0.104681
$339$	−24.6077	−0.00394250
$340$	1920.83	0.306387
$341$	0	0
$342$	−11897.2	−1.88108
$343$	279.689	0.0440286
$344$	1868.93	0.292924
$345$	127.186	0.0198476
$346$	−1708.60	−0.265477
$347$	−2934.02	−0.453909	−0.226954	−	0.973905i	$-0.572877\pi$
$347$	−2934.02	−0.453909	−0.226954	+	0.973905i	$0.572877\pi$
$348$	26.1714	0.00403142
$349$	9028.51	1.38477	0.692385	−	0.721528i	$-0.256560\pi$
$349$	9028.51	1.38477	0.692385	+	0.721528i	$0.256560\pi$
$350$	75.7701	0.0115717
$351$	−85.4254	−0.0129905
$352$	0	0
$353$	3682.13	0.555184	0.277592	−	0.960699i	$-0.410464\pi$
$353$	3682.13	0.555184	0.277592	+	0.960699i	$0.410464\pi$
$354$	−305.655	−0.0458910
$355$	−447.524	−0.0669073
$356$	−7883.04	−1.17360
$357$	1.59711	0.000236773 0
$358$	16025.8	2.36590
$359$	−5237.52	−0.769988	−0.384994	−	0.922919i	$-0.625796\pi$
$359$	−5237.52	−0.769988	−0.384994	+	0.922919i	$0.625796\pi$
$360$	1077.70	0.157777
$361$	6260.73	0.912776
$362$	7881.34	1.14429
$363$	0	0
$364$	36.1325	0.00520291
$365$	−3259.87	−0.467478
$366$	339.460	0.0484804
$367$	−3567.20	−0.507373	−0.253687	−	0.967286i	$-0.581643\pi$
$367$	−3567.20	−0.507373	−0.253687	+	0.967286i	$0.581643\pi$
$368$	8597.26	1.21783
$369$	−2939.61	−0.414715
$370$	−2042.80	−0.287027
$371$	−26.1842	−0.00366419
$372$	−70.6595	−0.00984818
$373$	−2334.33	−0.324040	−0.162020	−	0.986787i	$-0.551801\pi$
$373$	−2334.33	−0.324040	−0.162020	+	0.986787i	$0.551801\pi$
$374$	0	0
$375$	184.746	0.0254406
$376$	2311.55	0.317046
$377$	410.112	0.0560262
$378$	−10.3147	−0.00140353
$379$	2659.08	0.360390	0.180195	−	0.983631i	$-0.442327\pi$
$379$	2659.08	0.360390	0.180195	+	0.983631i	$0.442327\pi$
$380$	6838.19	0.923137
$381$	−60.3238	−0.00811150
$382$	6681.76	0.894944
$383$	−3127.66	−0.417273	−0.208637	−	0.977993i	$-0.566903\pi$
$383$	−3127.66	−0.417273	−0.208637	+	0.977993i	$0.566903\pi$
$384$	−70.2559	−0.00933654
$385$	0	0
$386$	−10090.2	−1.33051
$387$	11061.9	1.45299
$388$	10871.6	1.42248
$389$	792.648	0.103313	0.0516566	−	0.998665i	$-0.483550\pi$
$389$	792.648	0.103313	0.0516566	+	0.998665i	$0.483550\pi$
$390$	53.3521	0.00692715
$391$	−3837.93	−0.496400
$392$	1563.05	0.201393
$393$	52.2045	0.00670068
$394$	17594.6	2.24975
$395$	−6454.22	−0.822144
$396$	0	0
$397$	−1499.00	−0.189503	−0.0947514	−	0.995501i	$-0.530206\pi$
$397$	−1499.00	−0.189503	−0.0947514	+	0.995501i	$0.530206\pi$
$398$	11326.1	1.42645
$399$	5.68576	0.000713393 0
$400$	3479.00	0.434875
$401$	−9262.17	−1.15344	−0.576721	−	0.816941i	$-0.695668\pi$
$401$	−9262.17	−1.15344	−0.576721	+	0.816941i	$0.695668\pi$
$402$	185.780	0.0230494
$403$	−1107.25	−0.136864
$404$	−5923.79	−0.729504
$405$	6375.19	0.782187
$406$	49.5193	0.00605321
$407$	0	0
$408$	17.8554	0.00216660
$409$	12143.6	1.46813	0.734064	−	0.679080i	$-0.237621\pi$
$409$	12143.6	1.46813	0.734064	+	0.679080i	$0.237621\pi$
$410$	3672.85	0.442412
$411$	18.1270	0.00217552
$412$	−532.185	−0.0636380
$413$	−266.049	−0.0316983
$414$	12390.0	1.47086
$415$	−7327.74	−0.866758
$416$	3132.24	0.369160
$417$	−169.117	−0.0198602
$418$	0	0
$419$	11269.1	1.31391	0.656957	−	0.753928i	$-0.271843\pi$
$419$	11269.1	1.31391	0.656957	+	0.753928i	$0.271843\pi$
$420$	2.96350	0.000344295 0
$421$	13674.7	1.58305	0.791526	−	0.611135i	$-0.209287\pi$
$421$	13674.7	1.58305	0.791526	+	0.611135i	$0.209287\pi$
$422$	−285.895	−0.0329791
$423$	13681.7	1.57264
$424$	−292.734	−0.0335293
$425$	−1553.07	−0.177259
$426$	23.9366	0.00272238
$427$	295.473	0.0334870
$428$	4790.20	0.540989
$429$	0	0
$430$	−13821.1	−1.55003
$431$	−8117.08	−0.907160	−0.453580	−	0.891216i	$-0.649853\pi$
$431$	−8117.08	−0.907160	−0.453580	+	0.891216i	$0.649853\pi$
$432$	−473.604	−0.0527461
$433$	1001.71	0.111175	0.0555877	−	0.998454i	$-0.482297\pi$
$433$	1001.71	0.111175	0.0555877	+	0.998454i	$0.482297\pi$
$434$	−133.696	−0.0147871
$435$	33.6364	0.00370745
$436$	2319.37	0.254765
$437$	−13663.1	−1.49564
$438$	174.360	0.0190211
$439$	8656.97	0.941173	0.470586	−	0.882354i	$-0.344042\pi$
$439$	8656.97	0.941173	0.470586	+	0.882354i	$0.344042\pi$
$440$	0	0
$441$	9251.43	0.998967
$442$	−1609.94	−0.173252
$443$	−4013.69	−0.430466	−0.215233	−	0.976563i	$-0.569051\pi$
$443$	−4013.69	−0.430466	−0.215233	+	0.976563i	$0.569051\pi$
$444$	50.2636	0.00537254
$445$	−10131.6	−1.07928
$446$	4481.98	0.475847
$447$	−31.3307	−0.00331520
$448$	143.069	0.0150878
$449$	13668.0	1.43660	0.718298	−	0.695736i	$-0.244922\pi$
$449$	13668.0	1.43660	0.718298	+	0.695736i	$0.244922\pi$
$450$	5013.79	0.525228
$451$	0	0
$452$	1377.84	0.143381
$453$	−321.551	−0.0333506
$454$	−13912.4	−1.43819
$455$	46.4388	0.00478480
$456$	63.5656	0.00652792
$457$	−7754.10	−0.793701	−0.396851	−	0.917883i	$-0.629897\pi$
$457$	−7754.10	−0.793701	−0.396851	+	0.917883i	$0.629897\pi$
$458$	3964.48	0.404471
$459$	211.423	0.0214998
$460$	−7121.42	−0.721822
$461$	−1130.14	−0.114178	−0.0570889	−	0.998369i	$-0.518182\pi$
$461$	−1130.14	−0.114178	−0.0570889	+	0.998369i	$0.518182\pi$
$462$	0	0
$463$	9312.20	0.934718	0.467359	−	0.884068i	$-0.345206\pi$
$463$	9312.20	0.934718	0.467359	+	0.884068i	$0.345206\pi$
$464$	2273.69	0.227486
$465$	−90.8141	−0.00905678
$466$	8128.12	0.808000
$467$	2923.78	0.289714	0.144857	−	0.989453i	$-0.453728\pi$
$467$	2923.78	0.289714	0.144857	+	0.989453i	$0.453728\pi$
$468$	2390.93	0.236156
$469$	161.707	0.0159209
$470$	−17094.3	−1.67767
$471$	285.886	0.0279680
$472$	−2974.37	−0.290056
$473$	0	0
$474$	345.215	0.0334520
$475$	−5528.98	−0.534078
$476$	−89.4261	−0.00861100
$477$	−1732.64	−0.166314
$478$	54.3189	0.00519768
$479$	−6069.62	−0.578973	−0.289487	−	0.957182i	$-0.593485\pi$
$479$	−6069.62	−0.578973	−0.289487	+	0.957182i	$0.593485\pi$
$480$	256.898	0.0244287
$481$	787.644	0.0746642
$482$	−27324.0	−2.58210
$483$	−5.92125	−0.000557818 0
$484$	0	0
$485$	13972.6	1.30817
$486$	−1023.90	−0.0955661
$487$	8265.98	0.769132	0.384566	−	0.923097i	$-0.374351\pi$
$487$	8265.98	0.769132	0.384566	+	0.923097i	$0.374351\pi$
$488$	3303.33	0.306423
$489$	251.131	0.0232240
$490$	−11559.1	−1.06568
$491$	12158.3	1.11751	0.558754	−	0.829333i	$-0.311280\pi$
$491$	12158.3	1.11751	0.558754	+	0.829333i	$0.311280\pi$
$492$	−90.3714	−0.00828101
$493$	−1015.01	−0.0927254
$494$	−5731.44	−0.522004
$495$	0	0
$496$	−6138.68	−0.555716
$497$	20.8349	0.00188043
$498$	391.937	0.0352673
$499$	−8490.56	−0.761703	−0.380852	−	0.924636i	$-0.624369\pi$
$499$	−8490.56	−0.761703	−0.380852	+	0.924636i	$0.624369\pi$
$500$	−10344.4	−0.925228
$501$	192.850	0.0171974
$502$	−15787.6	−1.40365
$503$	18493.9	1.63937	0.819686	−	0.572813i	$-0.194148\pi$
$503$	18493.9	1.63937	0.819686	+	0.572813i	$0.194148\pi$
$504$	−50.1733	−0.00443432
$505$	−7613.46	−0.670880
$506$	0	0
$507$	−20.5710	−0.00180195
$508$	3377.67	0.295000
$509$	16681.2	1.45261	0.726306	−	0.687371i	$-0.241235\pi$
$509$	16681.2	1.45261	0.726306	+	0.687371i	$0.241235\pi$
$510$	−132.044	−0.0114647
$511$	151.767	0.0131385
$512$	14736.6	1.27201
$513$	752.672	0.0647784
$514$	3860.33	0.331269
$515$	−683.982	−0.0585240
$516$	340.071	0.0290132
$517$	0	0
$518$	95.1046	0.00806690
$519$	54.0321	0.00456984
$520$	519.176	0.0437834
$521$	15605.0	1.31222	0.656110	−	0.754665i	$-0.272201\pi$
$521$	15605.0	1.31222	0.656110	+	0.754665i	$0.272201\pi$
$522$	3276.75	0.274750
$523$	14039.8	1.17383	0.586917	−	0.809647i	$-0.300341\pi$
$523$	14039.8	1.17383	0.586917	+	0.809647i	$0.300341\pi$
$524$	−2923.06	−0.243691
$525$	−2.39612	−0.000199191 0
$526$	−21497.9	−1.78204
$527$	2740.39	0.226515
$528$	0	0
$529$	2062.03	0.169478
$530$	2164.82	0.177422
$531$	−17604.8	−1.43876
$532$	−318.359	−0.0259448
$533$	−1416.14	−0.115084
$534$	541.904	0.0439148
$535$	6156.54	0.497515
$536$	1807.85	0.145685
$537$	−506.794	−0.0407258
$538$	11738.4	0.940667
$539$	0	0
$540$	392.304	0.0312631
$541$	3771.26	0.299703	0.149852	−	0.988709i	$-0.452120\pi$
$541$	3771.26	0.299703	0.149852	+	0.988709i	$0.452120\pi$
$542$	−8003.68	−0.634294
$543$	−249.236	−0.0196975
$544$	−7752.13	−0.610974
$545$	2980.93	0.234292
$546$	−2.48386	−0.000194688 0
$547$	7376.99	0.576631	0.288316	−	0.957535i	$-0.406905\pi$
$547$	7376.99	0.576631	0.288316	+	0.957535i	$0.406905\pi$
$548$	−1014.97	−0.0791196
$549$	19551.8	1.51994
$550$	0	0
$551$	−3613.45	−0.279380
$552$	−66.1984	−0.00510433
$553$	300.483	0.0231064
$554$	1800.25	0.138060
$555$	64.6006	0.00494080
$556$	9469.27	0.722278
$557$	19281.0	1.46672	0.733361	−	0.679840i	$-0.237951\pi$
$557$	19281.0	1.46672	0.733361	+	0.679840i	$0.237951\pi$
$558$	−8846.81	−0.671175
$559$	5329.00	0.403207
$560$	257.460	0.0194280
$561$	0	0
$562$	−2563.73	−0.192428
$563$	−15156.5	−1.13458	−0.567291	−	0.823517i	$-0.692009\pi$
$563$	−15156.5	−1.13458	−0.567291	+	0.823517i	$0.692009\pi$
$564$	420.611	0.0314023
$565$	1770.85	0.131859
$566$	7173.32	0.532716
$567$	−296.803	−0.0219834
$568$	232.930	0.0172069
$569$	1086.47	0.0800478	0.0400239	−	0.999199i	$-0.487257\pi$
$569$	1086.47	0.0800478	0.0400239	+	0.999199i	$0.487257\pi$
$570$	−470.079	−0.0345429
$571$	6714.60	0.492115	0.246057	−	0.969255i	$-0.420865\pi$
$571$	6714.60	0.492115	0.246057	+	0.969255i	$0.420865\pi$
$572$	0	0
$573$	−211.301	−0.0154053
$574$	−170.993	−0.0124340
$575$	5757.98	0.417608
$576$	9467.01	0.684824
$577$	−7797.71	−0.562605	−0.281302	−	0.959619i	$-0.590766\pi$
$577$	−7797.71	−0.562605	−0.281302	+	0.959619i	$0.590766\pi$
$578$	−14926.1	−1.07412
$579$	319.087	0.0229029
$580$	−1883.38	−0.134833
$581$	341.151	0.0243603
$582$	−747.350	−0.0532279
$583$	0	0
$584$	1696.72	0.120224
$585$	3072.91	0.217178
$586$	−25324.2	−1.78521
$587$	238.651	0.0167806	0.00839028	−	0.999965i	$-0.497329\pi$
$587$	238.651	0.0167806	0.00839028	+	0.999965i	$0.497329\pi$
$588$	284.414	0.0199473
$589$	9755.86	0.682484
$590$	21996.0	1.53485
$591$	−556.404	−0.0387266
$592$	4366.75	0.303163
$593$	−20491.3	−1.41902	−0.709509	−	0.704697i	$-0.751083\pi$
$593$	−20491.3	−1.41902	−0.709509	+	0.704697i	$0.751083\pi$
$594$	0	0
$595$	−114.934	−0.00791902
$596$	1754.28	0.120568
$597$	−358.172	−0.0245545
$598$	5968.83	0.408167
$599$	−24400.5	−1.66440	−0.832200	−	0.554476i	$-0.812919\pi$
$599$	−24400.5	−1.66440	−0.832200	+	0.554476i	$0.812919\pi$
$600$	−26.7881	−0.00182270
$601$	21807.0	1.48007	0.740037	−	0.672566i	$-0.234808\pi$
$601$	21807.0	1.48007	0.740037	+	0.672566i	$0.234808\pi$
$602$	643.454	0.0435635
$603$	10700.3	0.722637
$604$	18004.4	1.21290
$605$	0	0
$606$	407.219	0.0272973
$607$	−26069.1	−1.74318	−0.871591	−	0.490233i	$-0.836912\pi$
$607$	−26069.1	−1.74318	−0.871591	+	0.490233i	$0.836912\pi$
$608$	−27597.8	−1.84085
$609$	−1.56598	−0.000104198 0
$610$	−24428.7	−1.62146
$611$	6591.08	0.436410
$612$	−5917.43	−0.390846
$613$	22395.2	1.47559	0.737793	−	0.675027i	$-0.235868\pi$
$613$	22395.2	1.47559	0.737793	+	0.675027i	$0.235868\pi$
$614$	−2984.16	−0.196141
$615$	−116.148	−0.00761554
$616$	0	0
$617$	23250.4	1.51706	0.758531	−	0.651637i	$-0.225917\pi$
$617$	23250.4	1.51706	0.758531	+	0.651637i	$0.225917\pi$
$618$	36.5840	0.00238127
$619$	8266.53	0.536769	0.268384	−	0.963312i	$-0.413510\pi$
$619$	8266.53	0.536769	0.268384	+	0.963312i	$0.413510\pi$
$620$	5084.90	0.329378
$621$	−783.847	−0.0506517
$622$	37972.5	2.44785
$623$	471.685	0.0303333
$624$	−114.047	−0.00731657
$625$	−7261.12	−0.464712
$626$	−18667.3	−1.19185
$627$	0	0
$628$	−16007.5	−1.01715
$629$	−1949.38	−0.123572
$630$	371.040	0.0234645
$631$	−25952.6	−1.63734	−0.818668	−	0.574268i	$-0.805287\pi$
$631$	−25952.6	−1.63734	−0.818668	+	0.574268i	$0.805287\pi$
$632$	3359.34	0.211435
$633$	9.04103	0.000567691 0
$634$	−2803.11	−0.175593
$635$	4341.11	0.271294
$636$	−53.2659	−0.00332096
$637$	4456.84	0.277216
$638$	0	0
$639$	1378.67	0.0853512
$640$	5055.86	0.312266
$641$	−28725.1	−1.77000	−0.885002	−	0.465587i	$-0.845843\pi$
$641$	−28725.1	−1.77000	−0.885002	+	0.465587i	$0.845843\pi$
$642$	−329.293	−0.0202433
$643$	−12743.6	−0.781583	−0.390792	−	0.920479i	$-0.627799\pi$
$643$	−12743.6	−0.781583	−0.390792	+	0.920479i	$0.627799\pi$
$644$	331.545	0.0202868
$645$	437.072	0.0266817
$646$	14185.0	0.863935
$647$	2810.68	0.170787	0.0853934	−	0.996347i	$-0.472785\pi$
$647$	2810.68	0.170787	0.0853934	+	0.996347i	$0.472785\pi$
$648$	−3318.20	−0.201159
$649$	0	0
$650$	2415.37	0.145752
$651$	4.22794	0.000254541 0
$652$	−14061.4	−0.844612
$653$	33285.6	1.99474	0.997369	−	0.0724880i	$-0.0230939\pi$
$653$	33285.6	1.99474	0.997369	+	0.0724880i	$0.0230939\pi$
$654$	−159.440	−0.00953305
$655$	−3756.82	−0.224108
$656$	−7851.19	−0.467283
$657$	10042.6	0.596344
$658$	795.845	0.0471508
$659$	−10002.1	−0.591240	−0.295620	−	0.955306i	$-0.595526\pi$
$659$	−10002.1	−0.591240	−0.295620	+	0.955306i	$0.595526\pi$
$660$	0	0
$661$	−1409.40	−0.0829338	−0.0414669	−	0.999140i	$-0.513203\pi$
$661$	−1409.40	−0.0829338	−0.0414669	+	0.999140i	$0.513203\pi$
$662$	32954.4	1.93476
$663$	50.9122	0.00298230
$664$	3813.99	0.222909
$665$	−409.166	−0.0238598
$666$	6293.18	0.366150
$667$	3763.11	0.218453
$668$	−10798.1	−0.625438
$669$	−141.736	−0.00819109
$670$	−13369.3	−0.770899
$671$	0	0
$672$	−11.9602	−0.000686568 0
$673$	−23293.6	−1.33418	−0.667090	−	0.744977i	$-0.732460\pi$
$673$	−23293.6	−1.33418	−0.667090	+	0.744977i	$0.732460\pi$
$674$	−34491.4	−1.97116
$675$	−317.195	−0.0180872
$676$	1151.82	0.0655337
$677$	−21956.9	−1.24649	−0.623243	−	0.782028i	$-0.714185\pi$
$677$	−21956.9	−1.24649	−0.623243	+	0.782028i	$0.714185\pi$
$678$	−94.7173	−0.00536519
$679$	−650.509	−0.0367662
$680$	−1284.93	−0.0724632
$681$	439.958	0.0247566
$682$	0	0
$683$	653.143	0.0365913	0.0182956	−	0.999833i	$-0.494176\pi$
$683$	653.143	0.0365913	0.0182956	+	0.999833i	$0.494176\pi$
$684$	−21066.2	−1.17761
$685$	−1304.48	−0.0727615
$686$	1076.55	0.0599167
$687$	−125.371	−0.00696244
$688$	29544.4	1.63716
$689$	−834.691	−0.0461527
$690$	489.549	0.0270099
$691$	−26352.4	−1.45078	−0.725392	−	0.688336i	$-0.758342\pi$
$691$	−26352.4	−1.45078	−0.725392	+	0.688336i	$0.758342\pi$
$692$	−3025.39	−0.166197
$693$	0	0
$694$	−11293.3	−0.617706
$695$	12170.2	0.664236
$696$	−17.5073	−0.000953466 0
$697$	3504.88	0.190469
$698$	34751.5	1.88448
$699$	−257.040	−0.0139087
$700$	134.165	0.00724420
$701$	−434.358	−0.0234029	−0.0117015	−	0.999932i	$-0.503725\pi$
$701$	−434.358	−0.0234029	−0.0117015	+	0.999932i	$0.503725\pi$
$702$	−328.810	−0.0176783
$703$	−6939.83	−0.372320
$704$	0	0
$705$	540.584	0.0288788
$706$	14172.9	0.755527
$707$	354.452	0.0188551
$708$	−541.218	−0.0287291
$709$	−34325.5	−1.81823	−0.909113	−	0.416549i	$-0.863240\pi$
$709$	−34325.5	−1.81823	−0.909113	+	0.416549i	$0.863240\pi$
$710$	−1722.56	−0.0910515
$711$	19883.3	1.04878
$712$	5273.34	0.277566
$713$	−10159.9	−0.533650
$714$	6.14743	0.000322215 0
$715$	0	0
$716$	28376.6	1.48112
$717$	−1.71776	−8.94712e−5 0
$718$	−20159.7	−1.04785
$719$	8201.41	0.425398	0.212699	−	0.977118i	$-0.431775\pi$
$719$	8201.41	0.425398	0.212699	+	0.977118i	$0.431775\pi$
$720$	17036.4	0.881819
$721$	31.8435	0.00164482
$722$	24098.1	1.24216
$723$	864.082	0.0444475
$724$	13955.3	0.716361
$725$	1522.80	0.0780073
$726$	0	0
$727$	14515.1	0.740489	0.370244	−	0.928934i	$-0.379274\pi$
$727$	14515.1	0.740489	0.370244	+	0.928934i	$0.379274\pi$
$728$	−24.1708	−0.00123053
$729$	−19618.2	−0.996709
$730$	−12547.5	−0.636171
$731$	−13189.0	−0.667323
$732$	601.074	0.0303502
$733$	−36317.6	−1.83004	−0.915020	−	0.403408i	$-0.867826\pi$
$733$	−36317.6	−1.83004	−0.915020	+	0.403408i	$0.867826\pi$
$734$	−13730.5	−0.690464
$735$	365.539	0.0183444
$736$	28740.8	1.43940
$737$	0	0
$738$	−11314.8	−0.564368
$739$	−32609.8	−1.62324	−0.811618	−	0.584189i	$-0.801413\pi$
$739$	−32609.8	−1.62324	−0.811618	+	0.584189i	$0.801413\pi$
$740$	−3617.14	−0.179688
$741$	181.249	0.00898561
$742$	−100.785	−0.00498645
$743$	−15261.1	−0.753532	−0.376766	−	0.926308i	$-0.622964\pi$
$743$	−15261.1	−0.753532	−0.376766	+	0.926308i	$0.622964\pi$
$744$	47.2675	0.00232918
$745$	2254.67	0.110879
$746$	−8985.05	−0.440973
$747$	22574.3	1.10569
$748$	0	0
$749$	−286.624	−0.0139827
$750$	711.104	0.0346211
$751$	−20205.3	−0.981761	−0.490880	−	0.871227i	$-0.663325\pi$
$751$	−20205.3	−0.981761	−0.490880	+	0.871227i	$0.663325\pi$
$752$	36541.4	1.77198
$753$	499.260	0.0241621
$754$	1578.56	0.0762437
$755$	23139.9	1.11543
$756$	−18.2641	−0.000878650 0
$757$	31358.6	1.50561	0.752804	−	0.658244i	$-0.228701\pi$
$757$	31358.6	1.50561	0.752804	+	0.658244i	$0.228701\pi$
$758$	10235.1	0.490440
$759$	0	0
$760$	−4574.40	−0.218330
$761$	15060.4	0.717397	0.358699	−	0.933453i	$-0.383221\pi$
$761$	15060.4	0.717397	0.358699	+	0.933453i	$0.383221\pi$
$762$	−232.192	−0.0110386
$763$	−138.780	−0.00658478
$764$	11831.2	0.560261
$765$	−7605.29	−0.359438
$766$	−12038.6	−0.567850
$767$	−8481.02	−0.399259
$768$	−612.044	−0.0287568
$769$	6749.67	0.316514	0.158257	−	0.987398i	$-0.449413\pi$
$769$	6749.67	0.316514	0.158257	+	0.987398i	$0.449413\pi$
$770$	0	0
$771$	−122.077	−0.00570235
$772$	−17866.4	−0.832937
$773$	−31990.6	−1.48851	−0.744257	−	0.667893i	$-0.767196\pi$
$773$	−31990.6	−1.48851	−0.744257	+	0.667893i	$0.767196\pi$
$774$	42578.1	1.97731
$775$	−4111.36	−0.190561
$776$	−7272.56	−0.336430
$777$	−3.00755	−0.000138861 0
$778$	3050.98	0.140595
$779$	12477.5	0.573878
$780$	94.4695	0.00433660
$781$	0	0
$782$	−14772.5	−0.675531
$783$	−207.302	−0.00946151
$784$	24709.0	1.12559
$785$	−20573.4	−0.935407
$786$	200.940	0.00911869
$787$	−35406.7	−1.60370	−0.801851	−	0.597525i	$-0.796151\pi$
$787$	−35406.7	−1.60370	−0.801851	+	0.597525i	$0.796151\pi$
$788$	31154.4	1.40841
$789$	679.840	0.0306755
$790$	−24842.9	−1.11882
$791$	−82.4440	−0.00370590
$792$	0	0
$793$	9418.99	0.421788
$794$	−5769.79	−0.257887
$795$	−68.4592	−0.00305409
$796$	20054.9	0.893000
$797$	−18386.9	−0.817187	−0.408594	−	0.912716i	$-0.633981\pi$
$797$	−18386.9	−0.817187	−0.408594	+	0.912716i	$0.633981\pi$
$798$	21.8850	0.000970828 0
$799$	−16312.6	−0.722275
$800$	11630.4	0.513996
$801$	31211.9	1.37680
$802$	−35650.9	−1.56967
$803$	0	0
$804$	328.956	0.0144296
$805$	426.114	0.0186566
$806$	−4261.92	−0.186253
$807$	−371.210	−0.0161923
$808$	3962.71	0.172534
$809$	33502.4	1.45597	0.727987	−	0.685591i	$-0.240456\pi$
$809$	33502.4	1.45597	0.727987	+	0.685591i	$0.240456\pi$
$810$	24538.7	1.06445
$811$	−30012.7	−1.29949	−0.649745	−	0.760152i	$-0.725124\pi$
$811$	−30012.7	−1.29949	−0.649745	+	0.760152i	$0.725124\pi$
$812$	87.6828	0.00378949
$813$	253.105	0.0109185
$814$	0	0
$815$	−18072.2	−0.776739
$816$	282.261	0.0121092
$817$	−46953.2	−2.01063
$818$	46742.0	1.99792
$819$	−143.062	−0.00610379
$820$	6503.43	0.276963
$821$	−30554.0	−1.29883	−0.649417	−	0.760433i	$-0.724987\pi$
$821$	−30554.0	−1.29883	−0.649417	+	0.760433i	$0.724987\pi$
$822$	69.7724	0.00296058
$823$	−14528.0	−0.615326	−0.307663	−	0.951495i	$-0.599547\pi$
$823$	−14528.0	−0.615326	−0.307663	+	0.951495i	$0.599547\pi$
$824$	356.004	0.0150510
$825$	0	0
$826$	−1024.05	−0.0431370
$827$	15277.8	0.642395	0.321198	−	0.947012i	$-0.395915\pi$
$827$	15277.8	0.642395	0.321198	+	0.947012i	$0.395915\pi$
$828$	21938.7	0.920801
$829$	36367.8	1.52365	0.761826	−	0.647782i	$-0.224303\pi$
$829$	36367.8	1.52365	0.761826	+	0.647782i	$0.224303\pi$
$830$	−28205.2	−1.17954
$831$	−56.9302	−0.00237652
$832$	4560.69	0.190040
$833$	−11030.4	−0.458802
$834$	−650.947	−0.0270269
$835$	−13878.1	−0.575177
$836$	0	0
$837$	559.689	0.0231131
$838$	43375.7	1.78805
$839$	19342.0	0.795901	0.397950	−	0.917407i	$-0.369722\pi$
$839$	19342.0	0.795901	0.397950	+	0.917407i	$0.369722\pi$
$840$	−1.98243	−8.14289e−5 0
$841$	−23393.8	−0.959194
$842$	52635.3	2.15431
$843$	81.0744	0.00331240
$844$	−506.229	−0.0206459
$845$	1480.36	0.0602674
$846$	52662.0	2.14014
$847$	0	0
$848$	−4627.58	−0.187396
$849$	−226.846	−0.00917000
$850$	−5977.92	−0.241225
$851$	7227.27	0.291125
$852$	42.3841	0.00170429
$853$	33629.9	1.34990	0.674950	−	0.737863i	$-0.264165\pi$
$853$	33629.9	1.34990	0.674950	+	0.737863i	$0.264165\pi$
$854$	1137.30	0.0455710
$855$	−27075.0	−1.08298
$856$	−3204.40	−0.127949
$857$	7790.66	0.310530	0.155265	−	0.987873i	$-0.450377\pi$
$857$	7790.66	0.310530	0.155265	+	0.987873i	$0.450377\pi$
$858$	0	0
$859$	−35052.5	−1.39229	−0.696145	−	0.717901i	$-0.745103\pi$
$859$	−35052.5	−1.39229	−0.696145	+	0.717901i	$0.745103\pi$
$860$	−24472.7	−0.970363
$861$	5.40741	0.000214035 0
$862$	−31243.4	−1.23452
$863$	42114.2	1.66116	0.830581	−	0.556898i	$-0.188008\pi$
$863$	42114.2	1.66116	0.830581	+	0.556898i	$0.188008\pi$
$864$	−1583.27	−0.0623426
$865$	−3888.34	−0.152841
$866$	3855.66	0.151294
$867$	472.015	0.0184896
$868$	−236.733	−0.00925718
$869$	0	0
$870$	129.470	0.00504532
$871$	5154.83	0.200533
$872$	−1551.54	−0.0602542
$873$	−43044.9	−1.66879
$874$	−52590.6	−2.03536
$875$	618.960	0.0239139
$876$	308.735	0.0119078
$877$	24510.4	0.943738	0.471869	−	0.881669i	$-0.343579\pi$
$877$	24510.4	0.943738	0.471869	+	0.881669i	$0.343579\pi$
$878$	33321.5	1.28080
$879$	800.842	0.0307301
$880$	0	0
$881$	723.525	0.0276687	0.0138344	−	0.999904i	$-0.495596\pi$
$881$	723.525	0.0276687	0.0138344	+	0.999904i	$0.495596\pi$
$882$	35609.6	1.35945
$883$	26035.6	0.992262	0.496131	−	0.868248i	$-0.334754\pi$
$883$	26035.6	0.992262	0.496131	+	0.868248i	$0.334754\pi$
$884$	−2850.70	−0.108461
$885$	−695.592	−0.0264204
$886$	−15449.1	−0.585803
$887$	−17142.3	−0.648910	−0.324455	−	0.945901i	$-0.605181\pi$
$887$	−17142.3	−0.648910	−0.324455	+	0.945901i	$0.605181\pi$
$888$	−33.6238	−0.00127065
$889$	−202.105	−0.00762472
$890$	−38997.3	−1.46876
$891$	0	0
$892$	7936.15	0.297895
$893$	−58073.2	−2.17620
$894$	−120.595	−0.00451152
$895$	36470.6	1.36210
$896$	−235.381	−0.00877624
$897$	−188.756	−0.00702605
$898$	52609.3	1.95500
$899$	−2686.97	−0.0996835
$900$	8877.82	0.328808
$901$	2065.82	0.0763843
$902$	0	0
$903$	−20.3483	−0.000749889 0
$904$	−921.707	−0.0339110
$905$	17935.9	0.658794
$906$	−1237.68	−0.0453854
$907$	−54015.7	−1.97747	−0.988733	−	0.149687i	$-0.952173\pi$
$907$	−54015.7	−1.97747	−0.988733	+	0.149687i	$0.952173\pi$
$908$	−24634.3	−0.900351
$909$	23454.5	0.855817
$910$	178.747	0.00651144
$911$	27595.2	1.00359	0.501795	−	0.864987i	$-0.332673\pi$
$911$	27595.2	1.00359	0.501795	+	0.864987i	$0.332673\pi$
$912$	1004.86	0.0364847
$913$	0	0
$914$	−29846.2	−1.08012
$915$	772.522	0.0279112
$916$	7019.82	0.253211
$917$	174.902	0.00629857
$918$	813.788	0.0292582
$919$	−39835.7	−1.42988	−0.714940	−	0.699186i	$-0.753546\pi$
$919$	−39835.7	−1.42988	−0.714940	+	0.699186i	$0.753546\pi$
$920$	4763.86	0.170717
$921$	94.3697	0.00337632
$922$	−4350.02	−0.155380
$923$	664.169	0.0236852
$924$	0	0
$925$	2924.62	0.103958
$926$	35843.5	1.27202
$927$	2107.12	0.0746569
$928$	7601.01	0.268874
$929$	17741.7	0.626573	0.313286	−	0.949659i	$-0.398570\pi$
$929$	17741.7	0.626573	0.313286	+	0.949659i	$0.398570\pi$
$930$	−349.552	−0.0123250
$931$	−39268.6	−1.38236
$932$	14392.3	0.505832
$933$	−1200.83	−0.0421365
$934$	11253.9	0.394260
$935$	0	0
$936$	−1599.41	−0.0558529
$937$	20545.5	0.716321	0.358160	−	0.933660i	$-0.383404\pi$
$937$	20545.5	0.716321	0.358160	+	0.933660i	$0.383404\pi$
$938$	622.423	0.0216661
$939$	590.327	0.0205161
$940$	−30268.6	−1.05027
$941$	−40544.7	−1.40459	−0.702296	−	0.711885i	$-0.747841\pi$
$941$	−40544.7	−1.40459	−0.702296	+	0.711885i	$0.747841\pi$
$942$	1100.40	0.0380606
$943$	−12994.3	−0.448729
$944$	−47019.4	−1.62113
$945$	−23.4737	−0.000808041 0
$946$	0	0
$947$	45060.9	1.54623	0.773117	−	0.634264i	$-0.218697\pi$
$947$	45060.9	1.54623	0.773117	+	0.634264i	$0.218697\pi$
$948$	611.266	0.0209420
$949$	4837.96	0.165487
$950$	−21281.6	−0.726805
$951$	88.6443	0.00302260
$952$	59.8214	0.00203658
$953$	−9709.99	−0.330050	−0.165025	−	0.986289i	$-0.552770\pi$
$953$	−9709.99	−0.330050	−0.165025	+	0.986289i	$0.552770\pi$
$954$	−6669.08	−0.226331
$955$	15205.9	0.515238
$956$	96.1814	0.00325390
$957$	0	0
$958$	−23362.5	−0.787901
$959$	60.7314	0.00204496
$960$	374.057	0.0125757
$961$	−22536.5	−0.756487
$962$	3031.71	0.101607
$963$	−18966.2	−0.634661
$964$	−48382.0	−1.61647
$965$	−22962.6	−0.766001
$966$	−22.7914	−0.000759112 0
$967$	−21031.5	−0.699409	−0.349705	−	0.936860i	$-0.613718\pi$
$967$	−21031.5	−0.699409	−0.349705	+	0.936860i	$0.613718\pi$
$968$	0	0
$969$	−448.581	−0.0148715
$970$	53781.9	1.78024
$971$	24480.2	0.809070	0.404535	−	0.914523i	$-0.367433\pi$
$971$	24480.2	0.809070	0.404535	+	0.914523i	$0.367433\pi$
$972$	−1813.00	−0.0598272
$973$	−566.598	−0.0186684
$974$	31816.5	1.04668
$975$	−76.3827	−0.00250893
$976$	52219.5	1.71261
$977$	−11726.8	−0.384004	−0.192002	−	0.981394i	$-0.561498\pi$
$977$	−11726.8	−0.384004	−0.192002	+	0.981394i	$0.561498\pi$
$978$	966.625	0.0316045
$979$	0	0
$980$	−20467.4	−0.667150
$981$	−9183.25	−0.298877
$982$	46798.4	1.52077
$983$	−13935.7	−0.452168	−0.226084	−	0.974108i	$-0.572592\pi$
$983$	−13935.7	−0.452168	−0.226084	+	0.974108i	$0.572592\pi$
$984$	60.4538	0.00195853
$985$	40040.7	1.29523
$986$	−3906.85	−0.126186
$987$	−25.1674	−0.000811640 0
$988$	−10148.5	−0.326790
$989$	48897.9	1.57216
$990$	0	0
$991$	13493.3	0.432523	0.216262	−	0.976335i	$-0.430614\pi$
$991$	13493.3	0.432523	0.216262	+	0.976335i	$0.430614\pi$
$992$	−20521.8	−0.656821
$993$	−1042.14	−0.0333043
$994$	80.1956	0.00255900
$995$	25775.3	0.821238
$996$	693.995	0.0220784
$997$	−4779.22	−0.151815	−0.0759075	−	0.997115i	$-0.524185\pi$
$997$	−4779.22	−0.151815	−0.0759075	+	0.997115i	$0.524185\pi$
$998$	−32681.0	−1.03657
$999$	−398.135	−0.0126090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.h.1.14	✓	15
11.10	odd	2		1573.4.a.k.1.2	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1573.4.a.h.1.14	✓	15	1.1	even	1	trivial
1573.4.a.k.1.2	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)

\(f(q)\)	\(=\)	\(q+3.84909 q^{2} -0.121722 q^{3} +6.81551 q^{4} +8.75953 q^{5} -0.468519 q^{6} -0.407809 q^{7} -4.55922 q^{8} -26.9852 q^{9} +O(q^{10})\)	\(q+3.84909 q^{2} -0.121722 q^{3} +6.81551 q^{4} +8.75953 q^{5} -0.468519 q^{6} -0.407809 q^{7} -4.55922 q^{8} -26.9852 q^{9} +33.7162 q^{10} -0.829597 q^{12} -13.0000 q^{13} -1.56969 q^{14} -1.06623 q^{15} -72.0729 q^{16} +32.1743 q^{17} -103.868 q^{18} +114.541 q^{19} +59.7007 q^{20} +0.0496393 q^{21} -119.286 q^{23} +0.554957 q^{24} -48.2706 q^{25} -50.0382 q^{26} +6.57118 q^{27} -2.77942 q^{28} -31.5471 q^{29} -4.10401 q^{30} +85.1733 q^{31} -240.942 q^{32} +123.842 q^{34} -3.57222 q^{35} -183.918 q^{36} -60.5880 q^{37} +440.880 q^{38} +1.58239 q^{39} -39.9366 q^{40} +108.934 q^{41} +0.191066 q^{42} -409.923 q^{43} -236.378 q^{45} -459.141 q^{46} -507.006 q^{47} +8.77286 q^{48} -342.834 q^{49} -185.798 q^{50} -3.91632 q^{51} -88.6016 q^{52} +64.2070 q^{53} +25.2931 q^{54} +1.85929 q^{56} -13.9422 q^{57} -121.428 q^{58} +652.386 q^{59} -7.26688 q^{60} -724.537 q^{61} +327.840 q^{62} +11.0048 q^{63} -350.823 q^{64} -113.874 q^{65} -396.525 q^{67} +219.284 q^{68} +14.5197 q^{69} -13.7498 q^{70} -51.0899 q^{71} +123.031 q^{72} -372.151 q^{73} -233.209 q^{74} +5.87559 q^{75} +780.658 q^{76} +6.09075 q^{78} -736.822 q^{79} -631.325 q^{80} +727.800 q^{81} +419.297 q^{82} -836.545 q^{83} +0.338317 q^{84} +281.832 q^{85} -1577.83 q^{86} +3.83998 q^{87} -1156.63 q^{89} -909.839 q^{90} +5.30152 q^{91} -812.991 q^{92} -10.3675 q^{93} -1951.51 q^{94} +1003.33 q^{95} +29.3279 q^{96} +1595.13 q^{97} -1319.60 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) \) 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

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Database

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