LMFDB - Embedded newform 6037.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47379 q^{2} -1.46896 q^{3} +4.11964 q^{4} +2.18568 q^{5} +3.63389 q^{6} -2.37075 q^{7} -5.24354 q^{8} -0.842162 q^{9} +O(q^{10})$	\(q-2.47379 q^{2} -1.46896 q^{3} +4.11964 q^{4} +2.18568 q^{5} +3.63389 q^{6} -2.37075 q^{7} -5.24354 q^{8} -0.842162 q^{9} -5.40693 q^{10} -3.86510 q^{11} -6.05158 q^{12} -4.98021 q^{13} +5.86475 q^{14} -3.21068 q^{15} +4.73215 q^{16} -1.28037 q^{17} +2.08333 q^{18} +0.772103 q^{19} +9.00423 q^{20} +3.48254 q^{21} +9.56146 q^{22} +0.220061 q^{23} +7.70254 q^{24} -0.222783 q^{25} +12.3200 q^{26} +5.64398 q^{27} -9.76665 q^{28} -5.30558 q^{29} +7.94255 q^{30} -1.21044 q^{31} -1.21926 q^{32} +5.67768 q^{33} +3.16737 q^{34} -5.18172 q^{35} -3.46940 q^{36} +0.986815 q^{37} -1.91002 q^{38} +7.31572 q^{39} -11.4607 q^{40} -10.3919 q^{41} -8.61507 q^{42} -1.66810 q^{43} -15.9228 q^{44} -1.84070 q^{45} -0.544384 q^{46} -6.63286 q^{47} -6.95133 q^{48} -1.37952 q^{49} +0.551119 q^{50} +1.88081 q^{51} -20.5167 q^{52} +8.34931 q^{53} -13.9620 q^{54} -8.44790 q^{55} +12.4312 q^{56} -1.13419 q^{57} +13.1249 q^{58} -12.2752 q^{59} -13.2268 q^{60} +2.57632 q^{61} +2.99437 q^{62} +1.99656 q^{63} -6.44811 q^{64} -10.8852 q^{65} -14.0454 q^{66} -9.98001 q^{67} -5.27466 q^{68} -0.323260 q^{69} +12.8185 q^{70} -2.33144 q^{71} +4.41591 q^{72} -6.44092 q^{73} -2.44117 q^{74} +0.327259 q^{75} +3.18078 q^{76} +9.16321 q^{77} -18.0976 q^{78} -7.52346 q^{79} +10.3430 q^{80} -5.76428 q^{81} +25.7074 q^{82} +5.52765 q^{83} +14.3468 q^{84} -2.79848 q^{85} +4.12652 q^{86} +7.79367 q^{87} +20.2668 q^{88} -7.07792 q^{89} +4.55351 q^{90} +11.8069 q^{91} +0.906571 q^{92} +1.77808 q^{93} +16.4083 q^{94} +1.68757 q^{95} +1.79104 q^{96} -4.61343 q^{97} +3.41265 q^{98} +3.25504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.47379	−1.74923	−0.874617	−	0.484815i	$-0.838887\pi$
$2$	−2.47379	−1.74923	−0.874617	+	0.484815i	$0.838887\pi$
$3$	−1.46896	−0.848103	−0.424052	−	0.905638i	$-0.639393\pi$
$3$	−1.46896	−0.848103	−0.424052	+	0.905638i	$0.639393\pi$
$4$	4.11964	2.05982
$5$	2.18568	0.977468	0.488734	−	0.872433i	$-0.337459\pi$
$5$	2.18568	0.977468	0.488734	+	0.872433i	$0.337459\pi$
$6$	3.63389	1.48353
$7$	−2.37075	−0.896061	−0.448030	−	0.894018i	$-0.647874\pi$
$7$	−2.37075	−0.896061	−0.448030	+	0.894018i	$0.647874\pi$
$8$	−5.24354	−1.85387
$9$	−0.842162	−0.280721
$10$	−5.40693	−1.70982
$11$	−3.86510	−1.16537	−0.582686	−	0.812697i	$-0.697998\pi$
$11$	−3.86510	−1.16537	−0.582686	+	0.812697i	$0.697998\pi$
$12$	−6.05158	−1.74694
$13$	−4.98021	−1.38126	−0.690631	−	0.723207i	$-0.742667\pi$
$13$	−4.98021	−1.38126	−0.690631	+	0.723207i	$0.742667\pi$
$14$	5.86475	1.56742
$15$	−3.21068	−0.828994
$16$	4.73215	1.18304
$17$	−1.28037	−0.310535	−0.155268	−	0.987872i	$-0.549624\pi$
$17$	−1.28037	−0.310535	−0.155268	+	0.987872i	$0.549624\pi$
$18$	2.08333	0.491046
$19$	0.772103	0.177133	0.0885663	−	0.996070i	$-0.471771\pi$
$19$	0.772103	0.177133	0.0885663	+	0.996070i	$0.471771\pi$
$20$	9.00423	2.01341
$21$	3.48254	0.759952
$22$	9.56146	2.03851
$23$	0.220061	0.0458858	0.0229429	−	0.999737i	$-0.492696\pi$
$23$	0.220061	0.0458858	0.0229429	+	0.999737i	$0.492696\pi$
$24$	7.70254	1.57228
$25$	−0.222783	−0.0445566
$26$	12.3200	2.41615
$27$	5.64398	1.08618
$28$	−9.76665	−1.84572
$29$	−5.30558	−0.985221	−0.492610	−	0.870250i	$-0.663957\pi$
$29$	−5.30558	−0.985221	−0.492610	+	0.870250i	$0.663957\pi$
$30$	7.94255	1.45010
$31$	−1.21044	−0.217401	−0.108700	−	0.994075i	$-0.534669\pi$
$31$	−1.21044	−0.217401	−0.108700	+	0.994075i	$0.534669\pi$
$32$	−1.21926	−0.215536
$33$	5.67768	0.988356
$34$	3.16737	0.543199
$35$	−5.18172	−0.875871
$36$	−3.46940	−0.578234
$37$	0.986815	0.162231	0.0811157	−	0.996705i	$-0.474152\pi$
$37$	0.986815	0.162231	0.0811157	+	0.996705i	$0.474152\pi$
$38$	−1.91002	−0.309846
$39$	7.31572	1.17145
$40$	−11.4607	−1.81210
$41$	−10.3919	−1.62294	−0.811472	−	0.584392i	$-0.801333\pi$
$41$	−10.3919	−1.62294	−0.811472	+	0.584392i	$0.801333\pi$
$42$	−8.61507	−1.32933
$43$	−1.66810	−0.254382	−0.127191	−	0.991878i	$-0.540596\pi$
$43$	−1.66810	−0.254382	−0.127191	+	0.991878i	$0.540596\pi$
$44$	−15.9228	−2.40046
$45$	−1.84070	−0.274395
$46$	−0.544384	−0.0802650
$47$	−6.63286	−0.967502	−0.483751	−	0.875206i	$-0.660726\pi$
$47$	−6.63286	−0.967502	−0.483751	+	0.875206i	$0.660726\pi$
$48$	−6.95133	−1.00334
$49$	−1.37952	−0.197075
$50$	0.551119	0.0779399
$51$	1.88081	0.263366
$52$	−20.5167	−2.84515
$53$	8.34931	1.14687	0.573433	−	0.819252i	$-0.305611\pi$
$53$	8.34931	1.14687	0.573433	+	0.819252i	$0.305611\pi$
$54$	−13.9620	−1.89999
$55$	−8.44790	−1.13911
$56$	12.4312	1.66118
$57$	−1.13419	−0.150227
$58$	13.1249	1.72338
$59$	−12.2752	−1.59809	−0.799046	−	0.601270i	$-0.794662\pi$
$59$	−12.2752	−1.59809	−0.799046	+	0.601270i	$0.794662\pi$
$60$	−13.2268	−1.70758
$61$	2.57632	0.329864	0.164932	−	0.986305i	$-0.447259\pi$
$61$	2.57632	0.329864	0.164932	+	0.986305i	$0.447259\pi$
$62$	2.99437	0.380285
$63$	1.99656	0.251543
$64$	−6.44811	−0.806014
$65$	−10.8852	−1.35014
$66$	−14.0454	−1.72887
$67$	−9.98001	−1.21925	−0.609626	−	0.792689i	$-0.708680\pi$
$67$	−9.98001	−1.21925	−0.609626	+	0.792689i	$0.708680\pi$
$68$	−5.27466	−0.639647
$69$	−0.323260	−0.0389159
$70$	12.8185	1.53210
$71$	−2.33144	−0.276692	−0.138346	−	0.990384i	$-0.544179\pi$
$71$	−2.33144	−0.276692	−0.138346	+	0.990384i	$0.544179\pi$
$72$	4.41591	0.520420
$73$	−6.44092	−0.753852	−0.376926	−	0.926243i	$-0.623019\pi$
$73$	−6.44092	−0.753852	−0.376926	+	0.926243i	$0.623019\pi$
$74$	−2.44117	−0.283781
$75$	0.327259	0.0377886
$76$	3.18078	0.364861
$77$	9.16321	1.04424
$78$	−18.0976	−2.04915
$79$	−7.52346	−0.846456	−0.423228	−	0.906023i	$-0.639103\pi$
$79$	−7.52346	−0.846456	−0.423228	+	0.906023i	$0.639103\pi$
$80$	10.3430	1.15638
$81$	−5.76428	−0.640475
$82$	25.7074	2.83891
$83$	5.52765	0.606738	0.303369	−	0.952873i	$-0.401889\pi$
$83$	5.52765	0.606738	0.303369	+	0.952873i	$0.401889\pi$
$84$	14.3468	1.56536
$85$	−2.79848	−0.303538
$86$	4.12652	0.444974
$87$	7.79367	0.835569
$88$	20.2668	2.16045
$89$	−7.07792	−0.750258	−0.375129	−	0.926973i	$-0.622402\pi$
$89$	−7.07792	−0.750258	−0.375129	+	0.926973i	$0.622402\pi$
$90$	4.55351	0.479982
$91$	11.8069	1.23770
$92$	0.906571	0.0945165
$93$	1.77808	0.184378
$94$	16.4083	1.69239
$95$	1.68757	0.173141
$96$	1.79104	0.182797
$97$	−4.61343	−0.468423	−0.234211	−	0.972186i	$-0.575251\pi$
$97$	−4.61343	−0.468423	−0.234211	+	0.972186i	$0.575251\pi$
$98$	3.41265	0.344730
$99$	3.25504	0.327144
$100$	−0.917786	−0.0917786
$101$	−6.11949	−0.608912	−0.304456	−	0.952526i	$-0.598475\pi$
$101$	−6.11949	−0.608912	−0.304456	+	0.952526i	$0.598475\pi$
$102$	−4.65273	−0.460689
$103$	−7.91151	−0.779544	−0.389772	−	0.920911i	$-0.627446\pi$
$103$	−7.91151	−0.779544	−0.389772	+	0.920911i	$0.627446\pi$
$104$	26.1140	2.56068
$105$	7.61173	0.742829
$106$	−20.6544	−2.00614
$107$	4.73276	0.457533	0.228767	−	0.973481i	$-0.426531\pi$
$107$	4.73276	0.457533	0.228767	+	0.973481i	$0.426531\pi$
$108$	23.2511	2.23734
$109$	9.14850	0.876267	0.438134	−	0.898910i	$-0.355640\pi$
$109$	9.14850	0.876267	0.438134	+	0.898910i	$0.355640\pi$
$110$	20.8983	1.99258
$111$	−1.44959	−0.137589
$112$	−11.2188	−1.06007
$113$	−11.8129	−1.11127	−0.555634	−	0.831427i	$-0.687524\pi$
$113$	−11.8129	−1.11127	−0.555634	+	0.831427i	$0.687524\pi$
$114$	2.80574	0.262782
$115$	0.480983	0.0448519
$116$	−21.8571	−2.02938
$117$	4.19414	0.387749
$118$	30.3662	2.79544
$119$	3.03544	0.278259
$120$	16.8353	1.53685
$121$	3.93903	0.358093
$122$	−6.37328	−0.577010
$123$	15.2653	1.37642
$124$	−4.98656	−0.447806
$125$	−11.4154	−1.02102
$126$	−4.93907	−0.440007
$127$	16.9039	1.49998	0.749988	−	0.661452i	$-0.230059\pi$
$127$	16.9039	1.49998	0.749988	+	0.661452i	$0.230059\pi$
$128$	18.3898	1.62544
$129$	2.45036	0.215742
$130$	26.9276	2.36171
$131$	10.2085	0.891920	0.445960	−	0.895053i	$-0.352862\pi$
$131$	10.2085	0.891920	0.445960	+	0.895053i	$0.352862\pi$
$132$	23.3900	2.03584
$133$	−1.83047	−0.158722
$134$	24.6885	2.13276
$135$	12.3359	1.06171
$136$	6.71367	0.575693
$137$	10.7157	0.915507	0.457754	−	0.889079i	$-0.348654\pi$
$137$	10.7157	0.915507	0.457754	+	0.889079i	$0.348654\pi$
$138$	0.799677	0.0680731
$139$	−13.5037	−1.14537	−0.572684	−	0.819776i	$-0.694098\pi$
$139$	−13.5037	−1.14537	−0.572684	+	0.819776i	$0.694098\pi$
$140$	−21.3468	−1.80414
$141$	9.74339	0.820542
$142$	5.76750	0.483998
$143$	19.2490	1.60968
$144$	−3.98524	−0.332103
$145$	−11.5963	−0.963021
$146$	15.9335	1.31866
$147$	2.02646	0.167140
$148$	4.06532	0.334167
$149$	−23.1488	−1.89642	−0.948211	−	0.317640i	$-0.897110\pi$
$149$	−23.1488	−1.89642	−0.948211	+	0.317640i	$0.897110\pi$
$150$	−0.809570	−0.0661011
$151$	14.3587	1.16849	0.584247	−	0.811576i	$-0.301390\pi$
$151$	14.3587	1.16849	0.584247	+	0.811576i	$0.301390\pi$
$152$	−4.04855	−0.328381
$153$	1.07828	0.0871737
$154$	−22.6679	−1.82663
$155$	−2.64563	−0.212502
$156$	30.1381	2.41298
$157$	−1.71103	−0.136555	−0.0682776	−	0.997666i	$-0.521750\pi$
$157$	−1.71103	−0.136555	−0.0682776	+	0.997666i	$0.521750\pi$
$158$	18.6115	1.48065
$159$	−12.2648	−0.972661
$160$	−2.66491	−0.210680
$161$	−0.521710	−0.0411165
$162$	14.2596	1.12034
$163$	−14.7782	−1.15752	−0.578760	−	0.815498i	$-0.696463\pi$
$163$	−14.7782	−1.15752	−0.578760	+	0.815498i	$0.696463\pi$
$164$	−42.8109	−3.34297
$165$	12.4096	0.966087
$166$	−13.6742	−1.06133
$167$	11.8405	0.916248	0.458124	−	0.888888i	$-0.348522\pi$
$167$	11.8405	0.916248	0.458124	+	0.888888i	$0.348522\pi$
$168$	−18.2608	−1.40885
$169$	11.8025	0.907885
$170$	6.92286	0.530959
$171$	−0.650236	−0.0497248
$172$	−6.87195	−0.523982
$173$	0.211551	0.0160839	0.00804197	−	0.999968i	$-0.497440\pi$
$173$	0.211551	0.0160839	0.00804197	+	0.999968i	$0.497440\pi$
$174$	−19.2799	−1.46161
$175$	0.528164	0.0399254
$176$	−18.2902	−1.37868
$177$	18.0317	1.35535
$178$	17.5093	1.31238
$179$	−0.884123	−0.0660825	−0.0330412	−	0.999454i	$-0.510519\pi$
$179$	−0.884123	−0.0660825	−0.0330412	+	0.999454i	$0.510519\pi$
$180$	−7.58302	−0.565205
$181$	−23.9100	−1.77722	−0.888608	−	0.458668i	$-0.848327\pi$
$181$	−23.9100	−1.77722	−0.888608	+	0.458668i	$0.848327\pi$
$182$	−29.2077	−2.16502
$183$	−3.78451	−0.279759
$184$	−1.15390	−0.0850665
$185$	2.15687	0.158576
$186$	−4.39860	−0.322521
$187$	4.94876	0.361889
$188$	−27.3250	−1.99288
$189$	−13.3805	−0.973287
$190$	−4.17470	−0.302865
$191$	12.2674	0.887638	0.443819	−	0.896116i	$-0.353623\pi$
$191$	12.2674	0.887638	0.443819	+	0.896116i	$0.353623\pi$
$192$	9.47200	0.683583
$193$	7.62392	0.548782	0.274391	−	0.961618i	$-0.411524\pi$
$193$	7.62392	0.548782	0.274391	+	0.961618i	$0.411524\pi$
$194$	11.4127	0.819381
$195$	15.9899	1.14506
$196$	−5.68314	−0.405938
$197$	−5.52933	−0.393949	−0.196974	−	0.980409i	$-0.563112\pi$
$197$	−5.52933	−0.393949	−0.196974	+	0.980409i	$0.563112\pi$
$198$	−8.05230	−0.572252
$199$	−0.226779	−0.0160759	−0.00803796	−	0.999968i	$-0.502559\pi$
$199$	−0.226779	−0.0160759	−0.00803796	+	0.999968i	$0.502559\pi$
$200$	1.16817	0.0826023
$201$	14.6602	1.03405
$202$	15.1383	1.06513
$203$	12.5782	0.882818
$204$	7.74826	0.542486
$205$	−22.7134	−1.58638
$206$	19.5714	1.36361
$207$	−0.185327	−0.0128811
$208$	−23.5671	−1.63408
$209$	−2.98426	−0.206425
$210$	−18.8298	−1.29938
$211$	−19.3072	−1.32916	−0.664582	−	0.747215i	$-0.731391\pi$
$211$	−19.3072	−1.32916	−0.664582	+	0.747215i	$0.731391\pi$
$212$	34.3961	2.36234
$213$	3.42479	0.234663
$214$	−11.7079	−0.800333
$215$	−3.64593	−0.248651
$216$	−29.5944	−2.01365
$217$	2.86965	0.194804
$218$	−22.6315	−1.53280
$219$	9.46144	0.639345
$220$	−34.8023	−2.34637
$221$	6.37651	0.428931
$222$	3.58598	0.240675
$223$	−6.68365	−0.447570	−0.223785	−	0.974639i	$-0.571841\pi$
$223$	−6.68365	−0.447570	−0.223785	+	0.974639i	$0.571841\pi$
$224$	2.89056	0.193134
$225$	0.187619	0.0125080
$226$	29.2227	1.94387
$227$	−3.12580	−0.207467	−0.103733	−	0.994605i	$-0.533079\pi$
$227$	−3.12580	−0.207467	−0.103733	+	0.994605i	$0.533079\pi$
$228$	−4.67244	−0.309440
$229$	−3.89333	−0.257279	−0.128639	−	0.991691i	$-0.541061\pi$
$229$	−3.89333	−0.257279	−0.128639	+	0.991691i	$0.541061\pi$
$230$	−1.18985	−0.0784565
$231$	−13.4604	−0.885628
$232$	27.8200	1.82647
$233$	−2.28751	−0.149860	−0.0749298	−	0.997189i	$-0.523873\pi$
$233$	−2.28751	−0.149860	−0.0749298	+	0.997189i	$0.523873\pi$
$234$	−10.3754	−0.678263
$235$	−14.4973	−0.945702
$236$	−50.5693	−3.29178
$237$	11.0517	0.717882
$238$	−7.50905	−0.486739
$239$	23.0717	1.49239	0.746193	−	0.665729i	$-0.231879\pi$
$239$	23.0717	1.49239	0.746193	+	0.665729i	$0.231879\pi$
$240$	−15.1934	−0.980730
$241$	8.31031	0.535314	0.267657	−	0.963514i	$-0.413751\pi$
$241$	8.31031	0.535314	0.267657	+	0.963514i	$0.413751\pi$
$242$	−9.74433	−0.626389
$243$	−8.46444	−0.542994
$244$	10.6135	0.679461
$245$	−3.01520	−0.192634
$246$	−37.7631	−2.40769
$247$	−3.84523	−0.244666
$248$	6.34697	0.403033
$249$	−8.11988	−0.514577
$250$	28.2392	1.78600
$251$	−8.28701	−0.523071	−0.261536	−	0.965194i	$-0.584229\pi$
$251$	−8.28701	−0.523071	−0.261536	+	0.965194i	$0.584229\pi$
$252$	8.22510	0.518133
$253$	−0.850557	−0.0534741
$254$	−41.8166	−2.62381
$255$	4.11086	0.257432
$256$	−32.5963	−2.03727
$257$	−26.7133	−1.66633	−0.833164	−	0.553025i	$-0.813473\pi$
$257$	−26.7133	−1.66633	−0.833164	+	0.553025i	$0.813473\pi$
$258$	−6.06169	−0.377384
$259$	−2.33950	−0.145369
$260$	−44.8430	−2.78104
$261$	4.46815	0.276572
$262$	−25.2537	−1.56018
$263$	26.4639	1.63184	0.815918	−	0.578168i	$-0.196232\pi$
$263$	26.4639	1.63184	0.815918	+	0.578168i	$0.196232\pi$
$264$	−29.7711	−1.83229
$265$	18.2490	1.12102
$266$	4.52819	0.277641
$267$	10.3972	0.636297
$268$	−41.1140	−2.51144
$269$	1.35131	0.0823911	0.0411955	−	0.999151i	$-0.486883\pi$
$269$	1.35131	0.0823911	0.0411955	+	0.999151i	$0.486883\pi$
$270$	−30.5166	−1.85718
$271$	−8.02043	−0.487207	−0.243603	−	0.969875i	$-0.578329\pi$
$271$	−8.02043	−0.487207	−0.243603	+	0.969875i	$0.578329\pi$
$272$	−6.05890	−0.367375
$273$	−17.3438	−1.04969
$274$	−26.5085	−1.60144
$275$	0.861080	0.0519250
$276$	−1.33171	−0.0801598
$277$	3.48765	0.209552	0.104776	−	0.994496i	$-0.466587\pi$
$277$	3.48765	0.209552	0.104776	+	0.994496i	$0.466587\pi$
$278$	33.4053	2.00352
$279$	1.01938	0.0610289
$280$	27.1706	1.62375
$281$	6.44566	0.384516	0.192258	−	0.981344i	$-0.438419\pi$
$281$	6.44566	0.384516	0.192258	+	0.981344i	$0.438419\pi$
$282$	−24.1031	−1.43532
$283$	−15.6708	−0.931530	−0.465765	−	0.884908i	$-0.654221\pi$
$283$	−15.6708	−0.931530	−0.465765	+	0.884908i	$0.654221\pi$
$284$	−9.60471	−0.569935
$285$	−2.47897	−0.146842
$286$	−47.6181	−2.81572
$287$	24.6367	1.45426
$288$	1.02681	0.0605054
$289$	−15.3607	−0.903568
$290$	28.6869	1.68455
$291$	6.77693	0.397271
$292$	−26.5343	−1.55280
$293$	−15.3790	−0.898448	−0.449224	−	0.893419i	$-0.648300\pi$
$293$	−15.3790	−0.898448	−0.449224	+	0.893419i	$0.648300\pi$
$294$	−5.01304	−0.292366
$295$	−26.8297	−1.56208
$296$	−5.17441	−0.300756
$297$	−21.8145	−1.26581
$298$	57.2653	3.31729
$299$	−1.09595	−0.0633803
$300$	1.34819	0.0778377
$301$	3.95465	0.227942
$302$	−35.5204	−2.04397
$303$	8.98928	0.516421
$304$	3.65370	0.209554
$305$	5.63103	0.322432
$306$	−2.66744	−0.152487
$307$	26.7178	1.52487	0.762434	−	0.647066i	$-0.224004\pi$
$307$	26.7178	1.52487	0.762434	+	0.647066i	$0.224004\pi$
$308$	37.7491	2.15096
$309$	11.6217	0.661134
$310$	6.54474	0.371716
$311$	−13.3488	−0.756941	−0.378470	−	0.925613i	$-0.623550\pi$
$311$	−13.3488	−0.756941	−0.378470	+	0.925613i	$0.623550\pi$
$312$	−38.3603	−2.17172
$313$	−11.1270	−0.628934	−0.314467	−	0.949268i	$-0.601826\pi$
$313$	−11.1270	−0.628934	−0.314467	+	0.949268i	$0.601826\pi$
$314$	4.23274	0.238867
$315$	4.36385	0.245875
$316$	−30.9939	−1.74355
$317$	21.3453	1.19887	0.599436	−	0.800423i	$-0.295392\pi$
$317$	21.3453	1.19887	0.599436	+	0.800423i	$0.295392\pi$
$318$	30.3405	1.70141
$319$	20.5066	1.14815
$320$	−14.0935	−0.787853
$321$	−6.95223	−0.388036
$322$	1.29060	0.0719224
$323$	−0.988577	−0.0550059
$324$	−23.7467	−1.31926
$325$	1.10951	0.0615444
$326$	36.5582	2.02477
$327$	−13.4388	−0.743165
$328$	54.4904	3.00873
$329$	15.7249	0.866941
$330$	−30.6988	−1.68991
$331$	−14.9182	−0.819976	−0.409988	−	0.912091i	$-0.634467\pi$
$331$	−14.9182	−0.819976	−0.409988	+	0.912091i	$0.634467\pi$
$332$	22.7719	1.24977
$333$	−0.831058	−0.0455417
$334$	−29.2910	−1.60273
$335$	−21.8132	−1.19178
$336$	16.4799	0.899052
$337$	−5.66222	−0.308441	−0.154220	−	0.988036i	$-0.549287\pi$
$337$	−5.66222	−0.308441	−0.154220	+	0.988036i	$0.549287\pi$
$338$	−29.1969	−1.58810
$339$	17.3527	0.942470
$340$	−11.5287	−0.625234
$341$	4.67846	0.253353
$342$	1.60855	0.0869802
$343$	19.8658	1.07265
$344$	8.74673	0.471592
$345$	−0.706544	−0.0380391
$346$	−0.523334	−0.0281346
$347$	12.2096	0.655447	0.327723	−	0.944774i	$-0.393719\pi$
$347$	12.2096	0.655447	0.327723	+	0.944774i	$0.393719\pi$
$348$	32.1071	1.72112
$349$	26.9079	1.44035	0.720173	−	0.693795i	$-0.244063\pi$
$349$	26.9079	1.44035	0.720173	+	0.693795i	$0.244063\pi$
$350$	−1.30657	−0.0698389
$351$	−28.1082	−1.50030
$352$	4.71255	0.251180
$353$	25.7060	1.36819	0.684097	−	0.729391i	$-0.260196\pi$
$353$	25.7060	1.36819	0.684097	+	0.729391i	$0.260196\pi$
$354$	−44.6067	−2.37082
$355$	−5.09580	−0.270457
$356$	−29.1585	−1.54540
$357$	−4.45894	−0.235992
$358$	2.18714	0.115594
$359$	25.9311	1.36859	0.684296	−	0.729205i	$-0.260110\pi$
$359$	25.9311	1.36859	0.684296	+	0.729205i	$0.260110\pi$
$360$	9.65179	0.508694
$361$	−18.4039	−0.968624
$362$	59.1483	3.10877
$363$	−5.78626	−0.303700
$364$	48.6400	2.54943
$365$	−14.0778	−0.736866
$366$	9.36209	0.489364
$367$	−26.0945	−1.36212	−0.681060	−	0.732227i	$-0.738481\pi$
$367$	−26.0945	−1.36212	−0.681060	+	0.732227i	$0.738481\pi$
$368$	1.04136	0.0542846
$369$	8.75167	0.455594
$370$	−5.33564	−0.277387
$371$	−19.7942	−1.02766
$372$	7.32505	0.379786
$373$	14.6171	0.756845	0.378422	−	0.925633i	$-0.376467\pi$
$373$	14.6171	0.756845	0.378422	+	0.925633i	$0.376467\pi$
$374$	−12.2422	−0.633029
$375$	16.7687	0.865931
$376$	34.7797	1.79363
$377$	26.4229	1.36085
$378$	33.1005	1.70251
$379$	−10.7053	−0.549892	−0.274946	−	0.961460i	$-0.588660\pi$
$379$	−10.7053	−0.549892	−0.274946	+	0.961460i	$0.588660\pi$
$380$	6.95219	0.356640
$381$	−24.8311	−1.27213
$382$	−30.3470	−1.55269
$383$	36.2449	1.85203	0.926013	−	0.377492i	$-0.123214\pi$
$383$	36.2449	1.85203	0.926013	+	0.377492i	$0.123214\pi$
$384$	−27.0138	−1.37854
$385$	20.0279	1.02072
$386$	−18.8600	−0.959948
$387$	1.40481	0.0714104
$388$	−19.0057	−0.964866
$389$	−0.668258	−0.0338820	−0.0169410	−	0.999856i	$-0.505393\pi$
$389$	−0.668258	−0.0338820	−0.0169410	+	0.999856i	$0.505393\pi$
$390$	−39.5556	−2.00297
$391$	−0.281759	−0.0142492
$392$	7.23359	0.365351
$393$	−14.9959	−0.756441
$394$	13.6784	0.689108
$395$	−16.4439	−0.827383
$396$	13.4096	0.673858
$397$	4.70934	0.236355	0.118178	−	0.992992i	$-0.462295\pi$
$397$	4.70934	0.236355	0.118178	+	0.992992i	$0.462295\pi$
$398$	0.561003	0.0281205
$399$	2.68888	0.134612
$400$	−1.05424	−0.0527121
$401$	−13.0622	−0.652296	−0.326148	−	0.945319i	$-0.605751\pi$
$401$	−13.0622	−0.652296	−0.326148	+	0.945319i	$0.605751\pi$
$402$	−36.2663	−1.80880
$403$	6.02823	0.300287
$404$	−25.2101	−1.25425
$405$	−12.5989	−0.626044
$406$	−31.1159	−1.54425
$407$	−3.81414	−0.189060
$408$	−9.86211	−0.488247
$409$	−10.4640	−0.517412	−0.258706	−	0.965956i	$-0.583296\pi$
$409$	−10.4640	−0.517412	−0.258706	+	0.965956i	$0.583296\pi$
$410$	56.1883	2.77494
$411$	−15.7410	−0.776445
$412$	−32.5926	−1.60572
$413$	29.1014	1.43199
$414$	0.458460	0.0225321
$415$	12.0817	0.593067
$416$	6.07215	0.297712
$417$	19.8364	0.971391
$418$	7.38243	0.361086
$419$	−11.3593	−0.554938	−0.277469	−	0.960735i	$-0.589496\pi$
$419$	−11.3593	−0.554938	−0.277469	+	0.960735i	$0.589496\pi$
$420$	31.3576	1.53009
$421$	−20.0360	−0.976493	−0.488246	−	0.872706i	$-0.662363\pi$
$421$	−20.0360	−0.976493	−0.488246	+	0.872706i	$0.662363\pi$
$422$	47.7620	2.32502
$423$	5.58594	0.271598
$424$	−43.7800	−2.12614
$425$	0.285245	0.0138364
$426$	−8.47222	−0.410481
$427$	−6.10783	−0.295579
$428$	19.4973	0.942436
$429$	−28.2760	−1.36518
$430$	9.01927	0.434948
$431$	−19.3623	−0.932650	−0.466325	−	0.884613i	$-0.654422\pi$
$431$	−19.3623	−0.932650	−0.466325	+	0.884613i	$0.654422\pi$
$432$	26.7081	1.28500
$433$	−16.3994	−0.788107	−0.394053	−	0.919088i	$-0.628927\pi$
$433$	−16.3994	−0.788107	−0.394053	+	0.919088i	$0.628927\pi$
$434$	−7.09891	−0.340758
$435$	17.0345	0.816742
$436$	37.6885	1.80495
$437$	0.169909	0.00812787
$438$	−23.4056	−1.11836
$439$	9.56807	0.456659	0.228329	−	0.973584i	$-0.426674\pi$
$439$	9.56807	0.456659	0.228329	+	0.973584i	$0.426674\pi$
$440$	44.2969	2.11177
$441$	1.16178	0.0553229
$442$	−15.7742	−0.750300
$443$	10.7900	0.512647	0.256323	−	0.966591i	$-0.417489\pi$
$443$	10.7900	0.512647	0.256323	+	0.966591i	$0.417489\pi$
$444$	−5.97179	−0.283409
$445$	−15.4701	−0.733354
$446$	16.5339	0.782905
$447$	34.0046	1.60836
$448$	15.2869	0.722238
$449$	21.8937	1.03323	0.516615	−	0.856218i	$-0.327192\pi$
$449$	21.8937	1.03323	0.516615	+	0.856218i	$0.327192\pi$
$450$	−0.464131	−0.0218794
$451$	40.1658	1.89133
$452$	−48.6650	−2.28901
$453$	−21.0923	−0.991003
$454$	7.73258	0.362908
$455$	25.8061	1.20981
$456$	5.94716	0.278501
$457$	7.13656	0.333834	0.166917	−	0.985971i	$-0.446619\pi$
$457$	7.13656	0.333834	0.166917	+	0.985971i	$0.446619\pi$
$458$	9.63129	0.450041
$459$	−7.22638	−0.337298
$460$	1.98148	0.0923869
$461$	22.6296	1.05396	0.526982	−	0.849877i	$-0.323324\pi$
$461$	22.6296	1.05396	0.526982	+	0.849877i	$0.323324\pi$
$462$	33.2981	1.54917
$463$	29.6123	1.37620	0.688100	−	0.725616i	$-0.258445\pi$
$463$	29.6123	1.37620	0.688100	+	0.725616i	$0.258445\pi$
$464$	−25.1068	−1.16555
$465$	3.88632	0.180224
$466$	5.65881	0.262139
$467$	−32.3594	−1.49741	−0.748706	−	0.662902i	$-0.769325\pi$
$467$	−32.3594	−1.49741	−0.748706	+	0.662902i	$0.769325\pi$
$468$	17.2784	0.798693
$469$	23.6602	1.09252
$470$	35.8634	1.65425
$471$	2.51344	0.115813
$472$	64.3654	2.96266
$473$	6.44736	0.296450
$474$	−27.3395	−1.25574
$475$	−0.172011	−0.00789242
$476$	12.5049	0.573162
$477$	−7.03147	−0.321949
$478$	−57.0746	−2.61053
$479$	−25.8113	−1.17935	−0.589674	−	0.807641i	$-0.700744\pi$
$479$	−25.8113	−1.17935	−0.589674	+	0.807641i	$0.700744\pi$
$480$	3.91464	0.178678
$481$	−4.91455	−0.224084
$482$	−20.5580	−0.936390
$483$	0.766370	0.0348710
$484$	16.2274	0.737608
$485$	−10.0835	−0.457868
$486$	20.9393	0.949824
$487$	−10.9901	−0.498008	−0.249004	−	0.968502i	$-0.580103\pi$
$487$	−10.9901	−0.498008	−0.249004	+	0.968502i	$0.580103\pi$
$488$	−13.5091	−0.611526
$489$	21.7086	0.981696
$490$	7.45898	0.336962
$491$	36.6058	1.65200	0.825999	−	0.563672i	$-0.190612\pi$
$491$	36.6058	1.65200	0.825999	+	0.563672i	$0.190612\pi$
$492$	62.8874	2.83518
$493$	6.79310	0.305946
$494$	9.51231	0.427979
$495$	7.11450	0.319773
$496$	−5.72796	−0.257193
$497$	5.52728	0.247932
$498$	20.0869	0.900115
$499$	−32.4769	−1.45386	−0.726932	−	0.686710i	$-0.759054\pi$
$499$	−32.4769	−1.45386	−0.726932	+	0.686710i	$0.759054\pi$
$500$	−47.0271	−2.10312
$501$	−17.3932	−0.777073
$502$	20.5003	0.914974
$503$	18.4884	0.824359	0.412179	−	0.911103i	$-0.364768\pi$
$503$	18.4884	0.824359	0.412179	+	0.911103i	$0.364768\pi$
$504$	−10.4690	−0.466328
$505$	−13.3753	−0.595192
$506$	2.10410	0.0935387
$507$	−17.3374	−0.769980
$508$	69.6378	3.08968
$509$	15.2758	0.677090	0.338545	−	0.940950i	$-0.390065\pi$
$509$	15.2758	0.677090	0.338545	+	0.940950i	$0.390065\pi$
$510$	−10.1694	−0.450308
$511$	15.2698	0.675498
$512$	43.8567	1.93821
$513$	4.35773	0.192398
$514$	66.0831	2.91480
$515$	−17.2921	−0.761979
$516$	10.0946	0.444391
$517$	25.6367	1.12750
$518$	5.78742	0.254285
$519$	−0.310760	−0.0136408
$520$	57.0769	2.50299
$521$	0.986700	0.0432281	0.0216141	−	0.999766i	$-0.493119\pi$
$521$	0.986700	0.0432281	0.0216141	+	0.999766i	$0.493119\pi$
$522$	−11.0533	−0.483789
$523$	7.40817	0.323937	0.161968	−	0.986796i	$-0.448216\pi$
$523$	7.40817	0.323937	0.161968	+	0.986796i	$0.448216\pi$
$524$	42.0553	1.83719
$525$	−0.775851	−0.0338609
$526$	−65.4662	−2.85446
$527$	1.54981	0.0675106
$528$	26.8676	1.16926
$529$	−22.9516	−0.997894
$530$	−45.1441	−1.96093
$531$	10.3377	0.448617
$532$	−7.54086	−0.326938
$533$	51.7539	2.24171
$534$	−25.7204	−1.11303
$535$	10.3443	0.447224
$536$	52.3306	2.26034
$537$	1.29874	0.0560448
$538$	−3.34287	−0.144121
$539$	5.33200	0.229665
$540$	50.8197	2.18693
$541$	34.0028	1.46190	0.730948	−	0.682433i	$-0.239078\pi$
$541$	34.0028	1.46190	0.730948	+	0.682433i	$0.239078\pi$
$542$	19.8409	0.852238
$543$	35.1228	1.50726
$544$	1.56110	0.0669316
$545$	19.9957	0.856523
$546$	42.9049	1.83616
$547$	−35.4902	−1.51745	−0.758726	−	0.651410i	$-0.774178\pi$
$547$	−35.4902	−1.51745	−0.758726	+	0.651410i	$0.774178\pi$
$548$	44.1450	1.88578
$549$	−2.16968	−0.0925998
$550$	−2.13013	−0.0908291
$551$	−4.09645	−0.174515
$552$	1.69503	0.0721452
$553$	17.8363	0.758476
$554$	−8.62771	−0.366556
$555$	−3.16835	−0.134489
$556$	−55.6303	−2.35925
$557$	−24.7396	−1.04825	−0.524126	−	0.851641i	$-0.675608\pi$
$557$	−24.7396	−1.04825	−0.524126	+	0.851641i	$0.675608\pi$
$558$	−2.52174	−0.106754
$559$	8.30747	0.351369
$560$	−24.5207	−1.03619
$561$	−7.26952	−0.306920
$562$	−15.9452	−0.672608
$563$	27.5941	1.16295	0.581477	−	0.813563i	$-0.302475\pi$
$563$	27.5941	1.16295	0.581477	+	0.813563i	$0.302475\pi$
$564$	40.1393	1.69017
$565$	−25.8194	−1.08623
$566$	38.7662	1.62946
$567$	13.6657	0.573905
$568$	12.2250	0.512951
$569$	−26.5388	−1.11256	−0.556282	−	0.830993i	$-0.687773\pi$
$569$	−26.5388	−1.11256	−0.556282	+	0.830993i	$0.687773\pi$
$570$	6.13246	0.256861
$571$	−19.5032	−0.816184	−0.408092	−	0.912941i	$-0.633806\pi$
$571$	−19.5032	−0.816184	−0.408092	+	0.912941i	$0.633806\pi$
$572$	79.2991	3.31566
$573$	−18.0203	−0.752809
$574$	−60.9459	−2.54383
$575$	−0.0490258	−0.00204452
$576$	5.43035	0.226265
$577$	−5.90538	−0.245844	−0.122922	−	0.992416i	$-0.539227\pi$
$577$	−5.90538	−0.245844	−0.122922	+	0.992416i	$0.539227\pi$
$578$	37.9990	1.58055
$579$	−11.1992	−0.465424
$580$	−47.7726	−1.98365
$581$	−13.1047	−0.543674
$582$	−16.7647	−0.694920
$583$	−32.2710	−1.33653
$584$	33.7732	1.39755
$585$	9.16708	0.379012
$586$	38.0443	1.57160
$587$	23.1024	0.953540	0.476770	−	0.879028i	$-0.341808\pi$
$587$	23.1024	0.953540	0.476770	+	0.879028i	$0.341808\pi$
$588$	8.34829	0.344278
$589$	−0.934581	−0.0385087
$590$	66.3710	2.73245
$591$	8.12236	0.334109
$592$	4.66976	0.191926
$593$	−11.5850	−0.475737	−0.237869	−	0.971297i	$-0.576449\pi$
$593$	−11.5850	−0.475737	−0.237869	+	0.971297i	$0.576449\pi$
$594$	53.9646	2.21420
$595$	6.63452	0.271989
$596$	−95.3647	−3.90629
$597$	0.333128	0.0136340
$598$	2.71115	0.110867
$599$	30.9145	1.26313	0.631566	−	0.775322i	$-0.282412\pi$
$599$	30.9145	1.26313	0.631566	+	0.775322i	$0.282412\pi$
$600$	−1.71600	−0.0700553
$601$	−39.7960	−1.62331	−0.811657	−	0.584135i	$-0.801434\pi$
$601$	−39.7960	−1.62331	−0.811657	+	0.584135i	$0.801434\pi$
$602$	−9.78297	−0.398724
$603$	8.40479	0.342269
$604$	59.1526	2.40689
$605$	8.60947	0.350025
$606$	−22.2376	−0.903340
$607$	−10.3545	−0.420276	−0.210138	−	0.977672i	$-0.567391\pi$
$607$	−10.3545	−0.420276	−0.210138	+	0.977672i	$0.567391\pi$
$608$	−0.941391	−0.0381785
$609$	−18.4769	−0.748721
$610$	−13.9300	−0.564009
$611$	33.0330	1.33637
$612$	4.44212	0.179562
$613$	17.7475	0.716813	0.358407	−	0.933566i	$-0.383320\pi$
$613$	17.7475	0.716813	0.358407	+	0.933566i	$0.383320\pi$
$614$	−66.0943	−2.66735
$615$	33.3651	1.34541
$616$	−48.0477	−1.93590
$617$	−21.3758	−0.860556	−0.430278	−	0.902696i	$-0.641585\pi$
$617$	−21.3758	−0.860556	−0.430278	+	0.902696i	$0.641585\pi$
$618$	−28.7496	−1.15648
$619$	25.2532	1.01501	0.507506	−	0.861648i	$-0.330568\pi$
$619$	25.2532	1.01501	0.507506	+	0.861648i	$0.330568\pi$
$620$	−10.8990	−0.437716
$621$	1.24202	0.0498404
$622$	33.0221	1.32407
$623$	16.7800	0.672277
$624$	34.6191	1.38587
$625$	−23.8365	−0.953458
$626$	27.5258	1.10015
$627$	4.38375	0.175070
$628$	−7.04884	−0.281279
$629$	−1.26349	−0.0503786
$630$	−10.7952	−0.430093
$631$	5.99689	0.238732	0.119366	−	0.992850i	$-0.461914\pi$
$631$	5.99689	0.238732	0.119366	+	0.992850i	$0.461914\pi$
$632$	39.4496	1.56922
$633$	28.3615	1.12727
$634$	−52.8038	−2.09711
$635$	36.9465	1.46618
$636$	−50.5265	−2.00351
$637$	6.87032	0.272212
$638$	−50.7290	−2.00838
$639$	1.96345	0.0776730
$640$	40.1943	1.58882
$641$	14.2203	0.561667	0.280833	−	0.959757i	$-0.409389\pi$
$641$	14.2203	0.561667	0.280833	+	0.959757i	$0.409389\pi$
$642$	17.1984	0.678765
$643$	−8.46018	−0.333637	−0.166819	−	0.985988i	$-0.553349\pi$
$643$	−8.46018	−0.333637	−0.166819	+	0.985988i	$0.553349\pi$
$644$	−2.14926	−0.0846926
$645$	5.35572	0.210881
$646$	2.44553	0.0962182
$647$	−23.3606	−0.918399	−0.459199	−	0.888333i	$-0.651864\pi$
$647$	−23.3606	−0.918399	−0.459199	+	0.888333i	$0.651864\pi$
$648$	30.2252	1.18736
$649$	47.4448	1.86237
$650$	−2.74469	−0.107655
$651$	−4.21539	−0.165214
$652$	−60.8809	−2.38428
$653$	−40.3587	−1.57936	−0.789680	−	0.613519i	$-0.789753\pi$
$653$	−40.3587	−1.57936	−0.789680	+	0.613519i	$0.789753\pi$
$654$	33.2447	1.29997
$655$	22.3125	0.871823
$656$	−49.1760	−1.92000
$657$	5.42430	0.211622
$658$	−38.9001	−1.51648
$659$	30.7878	1.19932	0.599661	−	0.800254i	$-0.295302\pi$
$659$	30.7878	1.19932	0.599661	+	0.800254i	$0.295302\pi$
$660$	51.1231	1.98996
$661$	−10.9732	−0.426809	−0.213405	−	0.976964i	$-0.568455\pi$
$661$	−10.9732	−0.426809	−0.213405	+	0.976964i	$0.568455\pi$
$662$	36.9044	1.43433
$663$	−9.36683	−0.363778
$664$	−28.9845	−1.12481
$665$	−4.00082	−0.155145
$666$	2.05586	0.0796631
$667$	−1.16755	−0.0452077
$668$	48.7787	1.88730
$669$	9.81800	0.379586
$670$	53.9612	2.08470
$671$	−9.95776	−0.384415
$672$	−4.24611	−0.163797
$673$	5.06520	0.195249	0.0976246	−	0.995223i	$-0.468876\pi$
$673$	5.06520	0.195249	0.0976246	+	0.995223i	$0.468876\pi$
$674$	14.0072	0.539535
$675$	−1.25738	−0.0483967
$676$	48.6221	1.87008
$677$	−3.06697	−0.117873	−0.0589365	−	0.998262i	$-0.518771\pi$
$677$	−3.06697	−0.117873	−0.0589365	+	0.998262i	$0.518771\pi$
$678$	−42.9270	−1.64860
$679$	10.9373	0.419735
$680$	14.6740	0.562721
$681$	4.59167	0.175953
$682$	−11.5735	−0.443173
$683$	−1.58966	−0.0608267	−0.0304133	−	0.999537i	$-0.509682\pi$
$683$	−1.58966	−0.0608267	−0.0304133	+	0.999537i	$0.509682\pi$
$684$	−2.67874	−0.102424
$685$	23.4212	0.894879
$686$	−49.1438	−1.87632
$687$	5.71914	0.218199
$688$	−7.89368	−0.300944
$689$	−41.5813	−1.58412
$690$	1.74784	0.0665392
$691$	24.3903	0.927851	0.463925	−	0.885874i	$-0.346441\pi$
$691$	24.3903	0.927851	0.463925	+	0.885874i	$0.346441\pi$
$692$	0.871515	0.0331300
$693$	−7.71691	−0.293141
$694$	−30.2040	−1.14653
$695$	−29.5148	−1.11956
$696$	−40.8664	−1.54904
$697$	13.3055	0.503981
$698$	−66.5644	−2.51950
$699$	3.36025	0.127096
$700$	2.17584	0.0822392
$701$	28.0625	1.05991	0.529953	−	0.848027i	$-0.322210\pi$
$701$	28.0625	1.05991	0.529953	+	0.848027i	$0.322210\pi$
$702$	69.5338	2.62438
$703$	0.761923	0.0287365
$704$	24.9226	0.939306
$705$	21.2960	0.802053
$706$	−63.5914	−2.39329
$707$	14.5078	0.545623
$708$	74.2842	2.79177
$709$	11.8122	0.443617	0.221808	−	0.975090i	$-0.428804\pi$
$709$	11.8122	0.443617	0.221808	+	0.975090i	$0.428804\pi$
$710$	12.6059	0.473093
$711$	6.33597	0.237618
$712$	37.1134	1.39088
$713$	−0.266369	−0.00997561
$714$	11.0305	0.412805
$715$	42.0723	1.57342
$716$	−3.64227	−0.136118
$717$	−33.8914	−1.26570
$718$	−64.1481	−2.39399
$719$	31.8279	1.18698	0.593490	−	0.804842i	$-0.297750\pi$
$719$	31.8279	1.18698	0.593490	+	0.804842i	$0.297750\pi$
$720$	−8.71047	−0.324620
$721$	18.7562	0.698519
$722$	45.5273	1.69435
$723$	−12.2075	−0.454002
$724$	−98.5005	−3.66074
$725$	1.18199	0.0438981
$726$	14.3140	0.531243
$727$	40.9919	1.52030	0.760152	−	0.649745i	$-0.225124\pi$
$727$	40.9919	1.52030	0.760152	+	0.649745i	$0.225124\pi$
$728$	−61.9098	−2.29453
$729$	29.7267	1.10099
$730$	34.8256	1.28895
$731$	2.13578	0.0789947
$732$	−15.5908	−0.576253
$733$	−41.8046	−1.54409	−0.772045	−	0.635568i	$-0.780766\pi$
$733$	−41.8046	−1.54409	−0.772045	+	0.635568i	$0.780766\pi$
$734$	64.5523	2.38267
$735$	4.42921	0.163374
$736$	−0.268310	−0.00989005
$737$	38.5738	1.42088
$738$	−21.6498	−0.796940
$739$	25.3594	0.932859	0.466430	−	0.884558i	$-0.345540\pi$
$739$	25.3594	0.932859	0.466430	+	0.884558i	$0.345540\pi$
$740$	8.88551	0.326638
$741$	5.64849	0.207502
$742$	48.9666	1.79762
$743$	1.09886	0.0403134	0.0201567	−	0.999797i	$-0.493583\pi$
$743$	1.09886	0.0403134	0.0201567	+	0.999797i	$0.493583\pi$
$744$	−9.32344	−0.341814
$745$	−50.5960	−1.85369
$746$	−36.1597	−1.32390
$747$	−4.65517	−0.170324
$748$	20.3871	0.745427
$749$	−11.2202	−0.409978
$750$	−41.4822	−1.51472
$751$	−33.7558	−1.23177	−0.615884	−	0.787837i	$-0.711201\pi$
$751$	−33.7558	−1.23177	−0.615884	+	0.787837i	$0.711201\pi$
$752$	−31.3877	−1.14459
$753$	12.1733	0.443618
$754$	−65.3647	−2.38044
$755$	31.3836	1.14216
$756$	−55.1227	−2.00479
$757$	20.6483	0.750475	0.375237	−	0.926929i	$-0.377561\pi$
$757$	20.6483	0.750475	0.375237	+	0.926929i	$0.377561\pi$
$758$	26.4826	0.961890
$759$	1.24943	0.0453515
$760$	−8.84886	−0.320982
$761$	8.45805	0.306604	0.153302	−	0.988179i	$-0.451009\pi$
$761$	8.45805	0.306604	0.153302	+	0.988179i	$0.451009\pi$
$762$	61.4269	2.22526
$763$	−21.6888	−0.785189
$764$	50.5373	1.82837
$765$	2.35678	0.0852095
$766$	−89.6622	−3.23963
$767$	61.1330	2.20738
$768$	47.8825	1.72781
$769$	−43.3691	−1.56393	−0.781966	−	0.623321i	$-0.785783\pi$
$769$	−43.3691	−1.56393	−0.781966	+	0.623321i	$0.785783\pi$
$770$	−49.5448	−1.78547
$771$	39.2407	1.41322
$772$	31.4078	1.13039
$773$	−31.1542	−1.12054	−0.560269	−	0.828310i	$-0.689302\pi$
$773$	−31.1542	−1.12054	−0.560269	+	0.828310i	$0.689302\pi$
$774$	−3.47520	−0.124913
$775$	0.269665	0.00968664
$776$	24.1907	0.868396
$777$	3.43662	0.123288
$778$	1.65313	0.0592676
$779$	−8.02362	−0.287476
$780$	65.8725	2.35861
$781$	9.01127	0.322449
$782$	0.697013	0.0249251
$783$	−29.9445	−1.07013
$784$	−6.52811	−0.233147
$785$	−3.73978	−0.133478
$786$	37.0966	1.32319
$787$	22.2358	0.792621	0.396311	−	0.918116i	$-0.370290\pi$
$787$	22.2358	0.792621	0.396311	+	0.918116i	$0.370290\pi$
$788$	−22.7789	−0.811463
$789$	−38.8744	−1.38397
$790$	40.6788	1.44729
$791$	28.0056	0.995764
$792$	−17.0680	−0.606484
$793$	−12.8306	−0.455629
$794$	−11.6499	−0.413440
$795$	−26.8070	−0.950745
$796$	−0.934246	−0.0331135
$797$	−10.9863	−0.389153	−0.194577	−	0.980887i	$-0.562333\pi$
$797$	−10.9863	−0.389153	−0.194577	+	0.980887i	$0.562333\pi$
$798$	−6.65172	−0.235468
$799$	8.49251	0.300444
$800$	0.271630	0.00960356
$801$	5.96076	0.210613
$802$	32.3132	1.14102
$803$	24.8948	0.878519
$804$	60.3948	2.12996
$805$	−1.14029	−0.0401901
$806$	−14.9126	−0.525273
$807$	−1.98502	−0.0698762
$808$	32.0878	1.12885
$809$	26.9226	0.946548	0.473274	−	0.880915i	$-0.343072\pi$
$809$	26.9226	0.946548	0.473274	+	0.880915i	$0.343072\pi$
$810$	31.1670	1.09510
$811$	−6.56174	−0.230414	−0.115207	−	0.993342i	$-0.536753\pi$
$811$	−6.56174	−0.230414	−0.115207	+	0.993342i	$0.536753\pi$
$812$	51.8177	1.81845
$813$	11.7817	0.413202
$814$	9.43539	0.330710
$815$	−32.3005	−1.13144
$816$	8.90027	0.311572
$817$	−1.28794	−0.0450594
$818$	25.8858	0.905074
$819$	−9.94329	−0.347447
$820$	−93.5711	−3.26765
$821$	−18.6500	−0.650891	−0.325445	−	0.945561i	$-0.605514\pi$
$821$	−18.6500	−0.650891	−0.325445	+	0.945561i	$0.605514\pi$
$822$	38.9399	1.35818
$823$	44.5775	1.55387	0.776936	−	0.629579i	$-0.216773\pi$
$823$	44.5775	1.55387	0.776936	+	0.629579i	$0.216773\pi$
$824$	41.4843	1.44518
$825$	−1.26489	−0.0440378
$826$	−71.9908	−2.50488
$827$	18.6174	0.647390	0.323695	−	0.946161i	$-0.395075\pi$
$827$	18.6174	0.647390	0.323695	+	0.946161i	$0.395075\pi$
$828$	−0.763479	−0.0265327
$829$	−15.8680	−0.551117	−0.275558	−	0.961284i	$-0.588863\pi$
$829$	−15.8680	−0.551117	−0.275558	+	0.961284i	$0.588863\pi$
$830$	−29.8876	−1.03741
$831$	−5.12321	−0.177722
$832$	32.1130	1.11332
$833$	1.76630	0.0611986
$834$	−49.0710	−1.69919
$835$	25.8797	0.895603
$836$	−12.2941	−0.425199
$837$	−6.83167	−0.236137
$838$	28.1005	0.970717
$839$	−9.41901	−0.325180	−0.162590	−	0.986694i	$-0.551985\pi$
$839$	−9.41901	−0.325180	−0.162590	+	0.986694i	$0.551985\pi$
$840$	−39.9124	−1.37711
$841$	−0.850872	−0.0293404
$842$	49.5647	1.70811
$843$	−9.46840	−0.326109
$844$	−79.5388	−2.73784
$845$	25.7966	0.887428
$846$	−13.8185	−0.475088
$847$	−9.33846	−0.320873
$848$	39.5102	1.35679
$849$	23.0197	0.790034
$850$	−0.705636	−0.0242031
$851$	0.217159	0.00744412
$852$	14.1089	0.483363
$853$	−54.3194	−1.85986	−0.929931	−	0.367734i	$-0.880134\pi$
$853$	−54.3194	−1.85986	−0.929931	+	0.367734i	$0.880134\pi$
$854$	15.1095	0.517036
$855$	−1.42121	−0.0486044
$856$	−24.8164	−0.848209
$857$	31.2793	1.06848	0.534240	−	0.845333i	$-0.320598\pi$
$857$	31.2793	1.06848	0.534240	+	0.845333i	$0.320598\pi$
$858$	69.9490	2.38802
$859$	3.11068	0.106135	0.0530674	−	0.998591i	$-0.483100\pi$
$859$	3.11068	0.106135	0.0530674	+	0.998591i	$0.483100\pi$
$860$	−15.0199	−0.512175
$861$	−36.1902	−1.23336
$862$	47.8983	1.63142
$863$	26.2309	0.892911	0.446456	−	0.894806i	$-0.352686\pi$
$863$	26.2309	0.892911	0.446456	+	0.894806i	$0.352686\pi$
$864$	−6.88145	−0.234112
$865$	0.462384	0.0157215
$866$	40.5688	1.37858
$867$	22.5642	0.766319
$868$	11.8219	0.401262
$869$	29.0790	0.986436
$870$	−42.1398	−1.42867
$871$	49.7026	1.68411
$872$	−47.9706	−1.62449
$873$	3.88525	0.131496
$874$	−0.420320	−0.0142175
$875$	27.0630	0.914897
$876$	38.9777	1.31693
$877$	−35.0992	−1.18522	−0.592608	−	0.805491i	$-0.701901\pi$
$877$	−35.0992	−1.18522	−0.592608	+	0.805491i	$0.701901\pi$
$878$	−23.6694	−0.798803
$879$	22.5910	0.761977
$880$	−39.9767	−1.34761
$881$	−20.8340	−0.701914	−0.350957	−	0.936392i	$-0.614144\pi$
$881$	−20.8340	−0.701914	−0.350957	+	0.936392i	$0.614144\pi$
$882$	−2.87400	−0.0967728
$883$	2.16972	0.0730168	0.0365084	−	0.999333i	$-0.488376\pi$
$883$	2.16972	0.0730168	0.0365084	+	0.999333i	$0.488376\pi$
$884$	26.2689	0.883520
$885$	39.4116	1.32481
$886$	−26.6921	−0.896740
$887$	−15.2215	−0.511090	−0.255545	−	0.966797i	$-0.582255\pi$
$887$	−15.2215	−0.511090	−0.255545	+	0.966797i	$0.582255\pi$
$888$	7.60099	0.255072
$889$	−40.0749	−1.34407
$890$	38.2698	1.28281
$891$	22.2795	0.746392
$892$	−27.5342	−0.921914
$893$	−5.12125	−0.171376
$894$	−84.1203	−2.81340
$895$	−1.93241	−0.0645935
$896$	−43.5977	−1.45650
$897$	1.60990	0.0537531
$898$	−54.1605	−1.80736
$899$	6.42206	0.214188
$900$	0.772924	0.0257641
$901$	−10.6902	−0.356142
$902$	−99.3618	−3.30839
$903$	−5.80921	−0.193318
$904$	61.9417	2.06015
$905$	−52.2597	−1.73717
$906$	52.1780	1.73350
$907$	16.7529	0.556271	0.278136	−	0.960542i	$-0.410284\pi$
$907$	16.7529	0.556271	0.278136	+	0.960542i	$0.410284\pi$
$908$	−12.8772	−0.427344
$909$	5.15360	0.170934
$910$	−63.8388	−2.11624
$911$	−23.1253	−0.766175	−0.383088	−	0.923712i	$-0.625139\pi$
$911$	−23.1253	−0.766175	−0.383088	+	0.923712i	$0.625139\pi$
$912$	−5.36714	−0.177724
$913$	−21.3649	−0.707076
$914$	−17.6543	−0.583954
$915$	−8.27175	−0.273456
$916$	−16.0391	−0.529948
$917$	−24.2018	−0.799215
$918$	17.8765	0.590014
$919$	−44.7453	−1.47601	−0.738006	−	0.674794i	$-0.764232\pi$
$919$	−44.7453	−1.47601	−0.738006	+	0.674794i	$0.764232\pi$
$920$	−2.52206	−0.0831497
$921$	−39.2474	−1.29325
$922$	−55.9808	−1.84363
$923$	11.6111	0.382184
$924$	−55.4519	−1.82423
$925$	−0.219846	−0.00722848
$926$	−73.2546	−2.40730
$927$	6.66277	0.218834
$928$	6.46886	0.212351
$929$	44.8013	1.46988	0.734941	−	0.678131i	$-0.237210\pi$
$929$	44.8013	1.46988	0.734941	+	0.678131i	$0.237210\pi$
$930$	−9.61395	−0.315254
$931$	−1.06513	−0.0349083
$932$	−9.42370	−0.308684
$933$	19.6088	0.641964
$934$	80.0503	2.61932
$935$	10.8164	0.353735
$936$	−21.9922	−0.718837
$937$	8.42958	0.275382	0.137691	−	0.990475i	$-0.456032\pi$
$937$	8.42958	0.275382	0.137691	+	0.990475i	$0.456032\pi$
$938$	−58.5303	−1.91108
$939$	16.3451	0.533401
$940$	−59.7238	−1.94798
$941$	19.8390	0.646734	0.323367	−	0.946274i	$-0.395185\pi$
$941$	19.8390	0.646734	0.323367	+	0.946274i	$0.395185\pi$
$942$	−6.21771	−0.202584
$943$	−2.28685	−0.0744701
$944$	−58.0879	−1.89060
$945$	−29.2455	−0.951356
$946$	−15.9494	−0.518561
$947$	8.11400	0.263669	0.131835	−	0.991272i	$-0.457913\pi$
$947$	8.11400	0.263669	0.131835	+	0.991272i	$0.457913\pi$
$948$	45.5288	1.47871
$949$	32.0771	1.04127
$950$	0.425520	0.0138057
$951$	−31.3553	−1.01677
$952$	−15.9165	−0.515856
$953$	34.9071	1.13075	0.565376	−	0.824833i	$-0.308731\pi$
$953$	34.9071	1.13075	0.565376	+	0.824833i	$0.308731\pi$
$954$	17.3944	0.563164
$955$	26.8127	0.867638
$956$	95.0472	3.07405
$957$	−30.1233	−0.973749
$958$	63.8517	2.06296
$959$	−25.4044	−0.820350
$960$	20.7028	0.668180
$961$	−29.5348	−0.952737
$962$	12.1576	0.391976
$963$	−3.98575	−0.128439
$964$	34.2355	1.10265
$965$	16.6635	0.536416
$966$	−1.89584	−0.0609976
$967$	−21.3418	−0.686305	−0.343152	−	0.939280i	$-0.611495\pi$
$967$	−21.3418	−0.686305	−0.343152	+	0.939280i	$0.611495\pi$
$968$	−20.6545	−0.663859
$969$	1.45218	0.0466507
$970$	24.9445	0.800919
$971$	−5.56708	−0.178656	−0.0893281	−	0.996002i	$-0.528472\pi$
$971$	−5.56708	−0.178656	−0.0893281	+	0.996002i	$0.528472\pi$
$972$	−34.8705	−1.11847
$973$	32.0139	1.02632
$974$	27.1871	0.871132
$975$	−1.62982	−0.0521960
$976$	12.1915	0.390242
$977$	22.9010	0.732668	0.366334	−	0.930483i	$-0.380613\pi$
$977$	22.9010	0.732668	0.366334	+	0.930483i	$0.380613\pi$
$978$	−53.7025	−1.71722
$979$	27.3569	0.874331
$980$	−12.4215	−0.396792
$981$	−7.70452	−0.245986
$982$	−90.5552	−2.88973
$983$	−14.2190	−0.453517	−0.226759	−	0.973951i	$-0.572813\pi$
$983$	−14.2190	−0.453517	−0.226759	+	0.973951i	$0.572813\pi$
$984$	−80.0441	−2.55171
$985$	−12.0854	−0.385072
$986$	−16.8047	−0.535171
$987$	−23.0992	−0.735255
$988$	−15.8410	−0.503969
$989$	−0.367082	−0.0116725
$990$	−17.5998	−0.559358
$991$	12.0979	0.384301	0.192150	−	0.981365i	$-0.438454\pi$
$991$	12.0979	0.384301	0.192150	+	0.981365i	$0.438454\pi$
$992$	1.47583	0.0468577
$993$	21.9141	0.695424
$994$	−13.6733	−0.433692
$995$	−0.495667	−0.0157137
$996$	−33.4510	−1.05993
$997$	−33.2831	−1.05409	−0.527043	−	0.849839i	$-0.676699\pi$
$997$	−33.2831	−1.05409	−0.527043	+	0.849839i	$0.676699\pi$
$998$	80.3409	2.54315
$999$	5.56956	0.176213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.13	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.13	✓	259	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47379 q^{2} -1.46896 q^{3} +4.11964 q^{4} +2.18568 q^{5} +3.63389 q^{6} -2.37075 q^{7} -5.24354 q^{8} -0.842162 q^{9} +O(q^{10})\)	\(q-2.47379 q^{2} -1.46896 q^{3} +4.11964 q^{4} +2.18568 q^{5} +3.63389 q^{6} -2.37075 q^{7} -5.24354 q^{8} -0.842162 q^{9} -5.40693 q^{10} -3.86510 q^{11} -6.05158 q^{12} -4.98021 q^{13} +5.86475 q^{14} -3.21068 q^{15} +4.73215 q^{16} -1.28037 q^{17} +2.08333 q^{18} +0.772103 q^{19} +9.00423 q^{20} +3.48254 q^{21} +9.56146 q^{22} +0.220061 q^{23} +7.70254 q^{24} -0.222783 q^{25} +12.3200 q^{26} +5.64398 q^{27} -9.76665 q^{28} -5.30558 q^{29} +7.94255 q^{30} -1.21044 q^{31} -1.21926 q^{32} +5.67768 q^{33} +3.16737 q^{34} -5.18172 q^{35} -3.46940 q^{36} +0.986815 q^{37} -1.91002 q^{38} +7.31572 q^{39} -11.4607 q^{40} -10.3919 q^{41} -8.61507 q^{42} -1.66810 q^{43} -15.9228 q^{44} -1.84070 q^{45} -0.544384 q^{46} -6.63286 q^{47} -6.95133 q^{48} -1.37952 q^{49} +0.551119 q^{50} +1.88081 q^{51} -20.5167 q^{52} +8.34931 q^{53} -13.9620 q^{54} -8.44790 q^{55} +12.4312 q^{56} -1.13419 q^{57} +13.1249 q^{58} -12.2752 q^{59} -13.2268 q^{60} +2.57632 q^{61} +2.99437 q^{62} +1.99656 q^{63} -6.44811 q^{64} -10.8852 q^{65} -14.0454 q^{66} -9.98001 q^{67} -5.27466 q^{68} -0.323260 q^{69} +12.8185 q^{70} -2.33144 q^{71} +4.41591 q^{72} -6.44092 q^{73} -2.44117 q^{74} +0.327259 q^{75} +3.18078 q^{76} +9.16321 q^{77} -18.0976 q^{78} -7.52346 q^{79} +10.3430 q^{80} -5.76428 q^{81} +25.7074 q^{82} +5.52765 q^{83} +14.3468 q^{84} -2.79848 q^{85} +4.12652 q^{86} +7.79367 q^{87} +20.2668 q^{88} -7.07792 q^{89} +4.55351 q^{90} +11.8069 q^{91} +0.906571 q^{92} +1.77808 q^{93} +16.4083 q^{94} +1.68757 q^{95} +1.79104 q^{96} -4.61343 q^{97} +3.41265 q^{98} +3.25504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more