LMFDB - Embedded newform 6422.2.a.bm.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} + \cdots + 358 $ x^14 - 4x^13 - 22x^12 + 98x^11 + 164x^10 - 912x^9 - 374x^8 + 3996x^7 - 817x^6 - 8194x^5 + 4418x^4 + 6430x^3 - 4327x^2 - 922*x + 358
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.64536$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.64536 q^{3} +1.00000 q^{4} +3.69209 q^{5} +2.64536 q^{6} -4.07315 q^{7} -1.00000 q^{8} +3.99793 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.64536 q^{3} +1.00000 q^{4} +3.69209 q^{5} +2.64536 q^{6} -4.07315 q^{7} -1.00000 q^{8} +3.99793 q^{9} -3.69209 q^{10} -5.71070 q^{11} -2.64536 q^{12} +4.07315 q^{14} -9.76691 q^{15} +1.00000 q^{16} +3.36481 q^{17} -3.99793 q^{18} -1.00000 q^{19} +3.69209 q^{20} +10.7749 q^{21} +5.71070 q^{22} +1.44687 q^{23} +2.64536 q^{24} +8.63155 q^{25} -2.63988 q^{27} -4.07315 q^{28} +3.22743 q^{29} +9.76691 q^{30} -5.87017 q^{31} -1.00000 q^{32} +15.1069 q^{33} -3.36481 q^{34} -15.0384 q^{35} +3.99793 q^{36} -11.7794 q^{37} +1.00000 q^{38} -3.69209 q^{40} -1.52210 q^{41} -10.7749 q^{42} +1.05141 q^{43} -5.71070 q^{44} +14.7607 q^{45} -1.44687 q^{46} +3.95928 q^{47} -2.64536 q^{48} +9.59054 q^{49} -8.63155 q^{50} -8.90113 q^{51} -7.94818 q^{53} +2.63988 q^{54} -21.0844 q^{55} +4.07315 q^{56} +2.64536 q^{57} -3.22743 q^{58} +1.81375 q^{59} -9.76691 q^{60} -13.8390 q^{61} +5.87017 q^{62} -16.2842 q^{63} +1.00000 q^{64} -15.1069 q^{66} +12.3611 q^{67} +3.36481 q^{68} -3.82750 q^{69} +15.0384 q^{70} -7.39827 q^{71} -3.99793 q^{72} -1.81541 q^{73} +11.7794 q^{74} -22.8336 q^{75} -1.00000 q^{76} +23.2605 q^{77} +4.47510 q^{79} +3.69209 q^{80} -5.01035 q^{81} +1.52210 q^{82} +7.57752 q^{83} +10.7749 q^{84} +12.4232 q^{85} -1.05141 q^{86} -8.53771 q^{87} +5.71070 q^{88} +4.91489 q^{89} -14.7607 q^{90} +1.44687 q^{92} +15.5287 q^{93} -3.95928 q^{94} -3.69209 q^{95} +2.64536 q^{96} -12.0199 q^{97} -9.59054 q^{98} -22.8310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.64536	−1.52730	−0.763650	−	0.645631i	$-0.776594\pi$
$3$	−2.64536	−1.52730	−0.763650	+	0.645631i	$0.776594\pi$
$4$	1.00000	0.500000
$5$	3.69209	1.65115	0.825577	−	0.564289i	$-0.190850\pi$
$5$	3.69209	1.65115	0.825577	+	0.564289i	$0.190850\pi$
$6$	2.64536	1.07996
$7$	−4.07315	−1.53951	−0.769753	−	0.638342i	$-0.779621\pi$
$7$	−4.07315	−1.53951	−0.769753	+	0.638342i	$0.779621\pi$
$8$	−1.00000	−0.353553
$9$	3.99793	1.33264
$10$	−3.69209	−1.16754
$11$	−5.71070	−1.72184	−0.860921	−	0.508739i	$-0.830112\pi$
$11$	−5.71070	−1.72184	−0.860921	+	0.508739i	$0.830112\pi$
$12$	−2.64536	−0.763650
$13$	0	0
$13$	0	0
$14$	4.07315	1.08859
$15$	−9.76691	−2.52181
$16$	1.00000	0.250000
$17$	3.36481	0.816086	0.408043	−	0.912963i	$-0.366211\pi$
$17$	3.36481	0.816086	0.408043	+	0.912963i	$0.366211\pi$
$18$	−3.99793	−0.942321
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.69209	0.825577
$21$	10.7749	2.35129
$22$	5.71070	1.21753
$23$	1.44687	0.301694	0.150847	−	0.988557i	$-0.451800\pi$
$23$	1.44687	0.301694	0.150847	+	0.988557i	$0.451800\pi$
$24$	2.64536	0.539982
$25$	8.63155	1.72631
$26$	0	0
$27$	−2.63988	−0.508045
$28$	−4.07315	−0.769753
$29$	3.22743	0.599318	0.299659	−	0.954046i	$-0.403127\pi$
$29$	3.22743	0.599318	0.299659	+	0.954046i	$0.403127\pi$
$30$	9.76691	1.78319
$31$	−5.87017	−1.05431	−0.527157	−	0.849768i	$-0.676742\pi$
$31$	−5.87017	−1.05431	−0.527157	+	0.849768i	$0.676742\pi$
$32$	−1.00000	−0.176777
$33$	15.1069	2.62977
$34$	−3.36481	−0.577060
$35$	−15.0384	−2.54196
$36$	3.99793	0.666321
$37$	−11.7794	−1.93651	−0.968257	−	0.249958i	$-0.919583\pi$
$37$	−11.7794	−1.93651	−0.968257	+	0.249958i	$0.919583\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−3.69209	−0.583771
$41$	−1.52210	−0.237713	−0.118856	−	0.992911i	$-0.537923\pi$
$41$	−1.52210	−0.237713	−0.118856	+	0.992911i	$0.537923\pi$
$42$	−10.7749	−1.66261
$43$	1.05141	0.160338	0.0801689	−	0.996781i	$-0.474454\pi$
$43$	1.05141	0.160338	0.0801689	+	0.996781i	$0.474454\pi$
$44$	−5.71070	−0.860921
$45$	14.7607	2.20040
$46$	−1.44687	−0.213330
$47$	3.95928	0.577521	0.288760	−	0.957401i	$-0.406757\pi$
$47$	3.95928	0.577521	0.288760	+	0.957401i	$0.406757\pi$
$48$	−2.64536	−0.381825
$49$	9.59054	1.37008
$50$	−8.63155	−1.22069
$51$	−8.90113	−1.24641
$52$	0	0
$53$	−7.94818	−1.09177	−0.545883	−	0.837861i	$-0.683806\pi$
$53$	−7.94818	−1.09177	−0.545883	+	0.837861i	$0.683806\pi$
$54$	2.63988	0.359242
$55$	−21.0844	−2.84302
$56$	4.07315	0.544297
$57$	2.64536	0.350386
$58$	−3.22743	−0.423782
$59$	1.81375	0.236130	0.118065	−	0.993006i	$-0.462331\pi$
$59$	1.81375	0.236130	0.118065	+	0.993006i	$0.462331\pi$
$60$	−9.76691	−1.26090
$61$	−13.8390	−1.77190	−0.885950	−	0.463782i	$-0.846492\pi$
$61$	−13.8390	−1.77190	−0.885950	+	0.463782i	$0.846492\pi$
$62$	5.87017	0.745512
$63$	−16.2842	−2.05161
$64$	1.00000	0.125000
$65$	0	0
$66$	−15.1069	−1.85953
$67$	12.3611	1.51015	0.755075	−	0.655638i	$-0.227600\pi$
$67$	12.3611	1.51015	0.755075	+	0.655638i	$0.227600\pi$
$68$	3.36481	0.408043
$69$	−3.82750	−0.460777
$70$	15.0384	1.79744
$71$	−7.39827	−0.878013	−0.439006	−	0.898484i	$-0.644669\pi$
$71$	−7.39827	−0.878013	−0.439006	+	0.898484i	$0.644669\pi$
$72$	−3.99793	−0.471160
$73$	−1.81541	−0.212477	−0.106239	−	0.994341i	$-0.533881\pi$
$73$	−1.81541	−0.212477	−0.106239	+	0.994341i	$0.533881\pi$
$74$	11.7794	1.36932
$75$	−22.8336	−2.63659
$76$	−1.00000	−0.114708
$77$	23.2605	2.65078
$78$	0	0
$79$	4.47510	0.503488	0.251744	−	0.967794i	$-0.418996\pi$
$79$	4.47510	0.503488	0.251744	+	0.967794i	$0.418996\pi$
$80$	3.69209	0.412789
$81$	−5.01035	−0.556706
$82$	1.52210	0.168088
$83$	7.57752	0.831741	0.415870	−	0.909424i	$-0.363477\pi$
$83$	7.57752	0.831741	0.415870	+	0.909424i	$0.363477\pi$
$84$	10.7749	1.17564
$85$	12.4232	1.34748
$86$	−1.05141	−0.113376
$87$	−8.53771	−0.915338
$88$	5.71070	0.608763
$89$	4.91489	0.520977	0.260489	−	0.965477i	$-0.416116\pi$
$89$	4.91489	0.520977	0.260489	+	0.965477i	$0.416116\pi$
$90$	−14.7607	−1.55592
$91$	0	0
$92$	1.44687	0.150847
$93$	15.5287	1.61025
$94$	−3.95928	−0.408369
$95$	−3.69209	−0.378801
$96$	2.64536	0.269991
$97$	−12.0199	−1.22044	−0.610220	−	0.792232i	$-0.708919\pi$
$97$	−12.0199	−1.22044	−0.610220	+	0.792232i	$0.708919\pi$
$98$	−9.59054	−0.968791
$99$	−22.8310	−2.29460
$100$	8.63155	0.863155
$101$	−1.83721	−0.182810	−0.0914048	−	0.995814i	$-0.529136\pi$
$101$	−1.83721	−0.182810	−0.0914048	+	0.995814i	$0.529136\pi$
$102$	8.90113	0.881343
$103$	−6.16843	−0.607794	−0.303897	−	0.952705i	$-0.598288\pi$
$103$	−6.16843	−0.607794	−0.303897	+	0.952705i	$0.598288\pi$
$104$	0	0
$105$	39.7821	3.88233
$106$	7.94818	0.771996
$107$	10.5729	1.02212	0.511059	−	0.859545i	$-0.329253\pi$
$107$	10.5729	1.02212	0.511059	+	0.859545i	$0.329253\pi$
$108$	−2.63988	−0.254023
$109$	−13.2819	−1.27217	−0.636087	−	0.771618i	$-0.719448\pi$
$109$	−13.2819	−1.27217	−0.636087	+	0.771618i	$0.719448\pi$
$110$	21.0844	2.01032
$111$	31.1606	2.95764
$112$	−4.07315	−0.384876
$113$	0.835180	0.0785671	0.0392836	−	0.999228i	$-0.487492\pi$
$113$	0.835180	0.0785671	0.0392836	+	0.999228i	$0.487492\pi$
$114$	−2.64536	−0.247761
$115$	5.34199	0.498143
$116$	3.22743	0.299659
$117$	0	0
$118$	−1.81375	−0.166969
$119$	−13.7054	−1.25637
$120$	9.76691	0.891593
$121$	21.6121	1.96474
$122$	13.8390	1.25292
$123$	4.02651	0.363058
$124$	−5.87017	−0.527157
$125$	13.4080	1.19925
$126$	16.2842	1.45071
$127$	−2.39635	−0.212642	−0.106321	−	0.994332i	$-0.533907\pi$
$127$	−2.39635	−0.212642	−0.106321	+	0.994332i	$0.533907\pi$
$128$	−1.00000	−0.0883883
$129$	−2.78135	−0.244884
$130$	0	0
$131$	−17.2306	−1.50544	−0.752722	−	0.658338i	$-0.771260\pi$
$131$	−17.2306	−1.50544	−0.752722	+	0.658338i	$0.771260\pi$
$132$	15.1069	1.31488
$133$	4.07315	0.353187
$134$	−12.3611	−1.06784
$135$	−9.74668	−0.838861
$136$	−3.36481	−0.288530
$137$	−8.92384	−0.762415	−0.381207	−	0.924490i	$-0.624492\pi$
$137$	−8.92384	−0.762415	−0.381207	+	0.924490i	$0.624492\pi$
$138$	3.82750	0.325819
$139$	6.45019	0.547098	0.273549	−	0.961858i	$-0.411802\pi$
$139$	6.45019	0.547098	0.273549	+	0.961858i	$0.411802\pi$
$140$	−15.0384	−1.27098
$141$	−10.4737	−0.882047
$142$	7.39827	0.620849
$143$	0	0
$144$	3.99793	0.333161
$145$	11.9160	0.989567
$146$	1.81541	0.150244
$147$	−25.3704	−2.09252
$148$	−11.7794	−0.968257
$149$	20.8111	1.70491	0.852456	−	0.522798i	$-0.175112\pi$
$149$	20.8111	1.70491	0.852456	+	0.522798i	$0.175112\pi$
$150$	22.8336	1.86435
$151$	4.58277	0.372941	0.186470	−	0.982461i	$-0.440295\pi$
$151$	4.58277	0.372941	0.186470	+	0.982461i	$0.440295\pi$
$152$	1.00000	0.0811107
$153$	13.4523	1.08755
$154$	−23.2605	−1.87439
$155$	−21.6732	−1.74083
$156$	0	0
$157$	24.2979	1.93918	0.969590	−	0.244735i	$-0.0787009\pi$
$157$	24.2979	1.93918	0.969590	+	0.244735i	$0.0787009\pi$
$158$	−4.47510	−0.356020
$159$	21.0258	1.66745
$160$	−3.69209	−0.291886
$161$	−5.89333	−0.464460
$162$	5.01035	0.393650
$163$	2.85635	0.223727	0.111863	−	0.993724i	$-0.464318\pi$
$163$	2.85635	0.223727	0.111863	+	0.993724i	$0.464318\pi$
$164$	−1.52210	−0.118856
$165$	55.7759	4.34215
$166$	−7.57752	−0.588129
$167$	1.46405	0.113291	0.0566457	−	0.998394i	$-0.481959\pi$
$167$	1.46405	0.113291	0.0566457	+	0.998394i	$0.481959\pi$
$168$	−10.7749	−0.831305
$169$	0	0
$170$	−12.4232	−0.952815
$171$	−3.99793	−0.305729
$172$	1.05141	0.0801689
$173$	13.2182	1.00496	0.502481	−	0.864588i	$-0.332421\pi$
$173$	13.2182	1.00496	0.502481	+	0.864588i	$0.332421\pi$
$174$	8.53771	0.647242
$175$	−35.1576	−2.65766
$176$	−5.71070	−0.430460
$177$	−4.79803	−0.360642
$178$	−4.91489	−0.368387
$179$	6.06621	0.453410	0.226705	−	0.973963i	$-0.427205\pi$
$179$	6.06621	0.453410	0.226705	+	0.973963i	$0.427205\pi$
$180$	14.7607	1.10020
$181$	−1.78374	−0.132584	−0.0662922	−	0.997800i	$-0.521117\pi$
$181$	−1.78374	−0.132584	−0.0662922	+	0.997800i	$0.521117\pi$
$182$	0	0
$183$	36.6091	2.70622
$184$	−1.44687	−0.106665
$185$	−43.4905	−3.19748
$186$	−15.5287	−1.13862
$187$	−19.2154	−1.40517
$188$	3.95928	0.288760
$189$	10.7526	0.782139
$190$	3.69209	0.267853
$191$	−0.968814	−0.0701009	−0.0350505	−	0.999386i	$-0.511159\pi$
$191$	−0.968814	−0.0701009	−0.0350505	+	0.999386i	$0.511159\pi$
$192$	−2.64536	−0.190912
$193$	4.87685	0.351043	0.175522	−	0.984476i	$-0.443839\pi$
$193$	4.87685	0.351043	0.175522	+	0.984476i	$0.443839\pi$
$194$	12.0199	0.862982
$195$	0	0
$196$	9.59054	0.685039
$197$	9.87125	0.703297	0.351649	−	0.936132i	$-0.385621\pi$
$197$	9.87125	0.703297	0.351649	+	0.936132i	$0.385621\pi$
$198$	22.8310	1.62253
$199$	−12.6371	−0.895821	−0.447910	−	0.894078i	$-0.647832\pi$
$199$	−12.6371	−0.895821	−0.447910	+	0.894078i	$0.647832\pi$
$200$	−8.63155	−0.610343
$201$	−32.6996	−2.30645
$202$	1.83721	0.129266
$203$	−13.1458	−0.922654
$204$	−8.90113	−0.623204
$205$	−5.61974	−0.392500
$206$	6.16843	0.429775
$207$	5.78450	0.402050
$208$	0	0
$209$	5.71070	0.395017
$210$	−39.7821	−2.74523
$211$	−24.5263	−1.68846	−0.844232	−	0.535978i	$-0.819943\pi$
$211$	−24.5263	−1.68846	−0.844232	+	0.535978i	$0.819943\pi$
$212$	−7.94818	−0.545883
$213$	19.5711	1.34099
$214$	−10.5729	−0.722747
$215$	3.88189	0.264743
$216$	2.63988	0.179621
$217$	23.9101	1.62312
$218$	13.2819	0.899562
$219$	4.80240	0.324516
$220$	−21.0844	−1.42151
$221$	0	0
$222$	−31.1606	−2.09136
$223$	−18.6888	−1.25149	−0.625746	−	0.780027i	$-0.715205\pi$
$223$	−18.6888	−1.25149	−0.625746	+	0.780027i	$0.715205\pi$
$224$	4.07315	0.272149
$225$	34.5083	2.30055
$226$	−0.835180	−0.0555553
$227$	12.4603	0.827019	0.413510	−	0.910500i	$-0.364303\pi$
$227$	12.4603	0.827019	0.413510	+	0.910500i	$0.364303\pi$
$228$	2.64536	0.175193
$229$	4.67305	0.308804	0.154402	−	0.988008i	$-0.450655\pi$
$229$	4.67305	0.308804	0.154402	+	0.988008i	$0.450655\pi$
$230$	−5.34199	−0.352240
$231$	−61.5325	−4.04854
$232$	−3.22743	−0.211891
$233$	−23.0917	−1.51279	−0.756395	−	0.654115i	$-0.773041\pi$
$233$	−23.0917	−1.51279	−0.756395	+	0.654115i	$0.773041\pi$
$234$	0	0
$235$	14.6180	0.953576
$236$	1.81375	0.118065
$237$	−11.8383	−0.768977
$238$	13.7054	0.888387
$239$	2.59543	0.167884	0.0839421	−	0.996471i	$-0.473249\pi$
$239$	2.59543	0.167884	0.0839421	+	0.996471i	$0.473249\pi$
$240$	−9.76691	−0.630452
$241$	−15.3195	−0.986817	−0.493409	−	0.869798i	$-0.664249\pi$
$241$	−15.3195	−0.986817	−0.493409	+	0.869798i	$0.664249\pi$
$242$	−21.6121	−1.38928
$243$	21.1738	1.35830
$244$	−13.8390	−0.885950
$245$	35.4092	2.26221
$246$	−4.02651	−0.256721
$247$	0	0
$248$	5.87017	0.372756
$249$	−20.0453	−1.27032
$250$	−13.4080	−0.847997
$251$	−1.15980	−0.0732056	−0.0366028	−	0.999330i	$-0.511654\pi$
$251$	−1.15980	−0.0732056	−0.0366028	+	0.999330i	$0.511654\pi$
$252$	−16.2842	−1.02581
$253$	−8.26266	−0.519469
$254$	2.39635	0.150360
$255$	−32.8638	−2.05801
$256$	1.00000	0.0625000
$257$	22.5442	1.40627	0.703134	−	0.711057i	$-0.251783\pi$
$257$	22.5442	1.40627	0.703134	+	0.711057i	$0.251783\pi$
$258$	2.78135	0.173159
$259$	47.9791	2.98127
$260$	0	0
$261$	12.9030	0.798677
$262$	17.2306	1.06451
$263$	9.07631	0.559669	0.279835	−	0.960048i	$-0.409720\pi$
$263$	9.07631	0.559669	0.279835	+	0.960048i	$0.409720\pi$
$264$	−15.1069	−0.929763
$265$	−29.3454	−1.80268
$266$	−4.07315	−0.249741
$267$	−13.0017	−0.795688
$268$	12.3611	0.755075
$269$	−5.25303	−0.320283	−0.160142	−	0.987094i	$-0.551195\pi$
$269$	−5.25303	−0.320283	−0.160142	+	0.987094i	$0.551195\pi$
$270$	9.74668	0.593164
$271$	−8.97271	−0.545053	−0.272527	−	0.962148i	$-0.587859\pi$
$271$	−8.97271	−0.545053	−0.272527	+	0.962148i	$0.587859\pi$
$272$	3.36481	0.204021
$273$	0	0
$274$	8.92384	0.539109
$275$	−49.2922	−2.97243
$276$	−3.82750	−0.230388
$277$	20.1053	1.20801	0.604006	−	0.796979i	$-0.293570\pi$
$277$	20.1053	1.20801	0.604006	+	0.796979i	$0.293570\pi$
$278$	−6.45019	−0.386857
$279$	−23.4685	−1.40502
$280$	15.0384	0.898719
$281$	−24.3409	−1.45206	−0.726029	−	0.687664i	$-0.758636\pi$
$281$	−24.3409	−1.45206	−0.726029	+	0.687664i	$0.758636\pi$
$282$	10.4737	0.623702
$283$	−15.9644	−0.948983	−0.474491	−	0.880260i	$-0.657368\pi$
$283$	−15.9644	−0.948983	−0.474491	+	0.880260i	$0.657368\pi$
$284$	−7.39827	−0.439006
$285$	9.76691	0.578542
$286$	0	0
$287$	6.19975	0.365960
$288$	−3.99793	−0.235580
$289$	−5.67806	−0.334004
$290$	−11.9160	−0.699730
$291$	31.7971	1.86398
$292$	−1.81541	−0.106239
$293$	3.84316	0.224520	0.112260	−	0.993679i	$-0.464191\pi$
$293$	3.84316	0.224520	0.112260	+	0.993679i	$0.464191\pi$
$294$	25.3704	1.47963
$295$	6.69654	0.389888
$296$	11.7794	0.684661
$297$	15.0756	0.874773
$298$	−20.8111	−1.20556
$299$	0	0
$300$	−22.8336	−1.31830
$301$	−4.28253	−0.246841
$302$	−4.58277	−0.263709
$303$	4.86009	0.279205
$304$	−1.00000	−0.0573539
$305$	−51.0948	−2.92568
$306$	−13.4523	−0.769015
$307$	0.652509	0.0372407	0.0186203	−	0.999827i	$-0.494073\pi$
$307$	0.652509	0.0372407	0.0186203	+	0.999827i	$0.494073\pi$
$308$	23.2605	1.32539
$309$	16.3177	0.928283
$310$	21.6732	1.23096
$311$	16.0752	0.911543	0.455772	−	0.890097i	$-0.349363\pi$
$311$	16.0752	0.911543	0.455772	+	0.890097i	$0.349363\pi$
$312$	0	0
$313$	11.4119	0.645041	0.322520	−	0.946563i	$-0.395470\pi$
$313$	11.4119	0.645041	0.322520	+	0.946563i	$0.395470\pi$
$314$	−24.2979	−1.37121
$315$	−60.1226	−3.38753
$316$	4.47510	0.251744
$317$	−10.0084	−0.562127	−0.281064	−	0.959689i	$-0.590687\pi$
$317$	−10.0084	−0.562127	−0.281064	+	0.959689i	$0.590687\pi$
$318$	−21.0258	−1.17907
$319$	−18.4309	−1.03193
$320$	3.69209	0.206394
$321$	−27.9691	−1.56108
$322$	5.89333	0.328422
$323$	−3.36481	−0.187223
$324$	−5.01035	−0.278353
$325$	0	0
$326$	−2.85635	−0.158199
$327$	35.1354	1.94299
$328$	1.52210	0.0840441
$329$	−16.1268	−0.889097
$330$	−55.7759	−3.07036
$331$	−5.08261	−0.279365	−0.139683	−	0.990196i	$-0.544608\pi$
$331$	−5.08261	−0.279365	−0.139683	+	0.990196i	$0.544608\pi$
$332$	7.57752	0.415870
$333$	−47.0930	−2.58068
$334$	−1.46405	−0.0801091
$335$	45.6384	2.49349
$336$	10.7749	0.587821
$337$	25.9786	1.41514	0.707572	−	0.706641i	$-0.249790\pi$
$337$	25.9786	1.41514	0.707572	+	0.706641i	$0.249790\pi$
$338$	0	0
$339$	−2.20935	−0.119995
$340$	12.4232	0.673742
$341$	33.5228	1.81536
$342$	3.99793	0.216183
$343$	−10.5517	−0.569736
$344$	−1.05141	−0.0566880
$345$	−14.1315	−0.760814
$346$	−13.2182	−0.710616
$347$	7.50336	0.402801	0.201401	−	0.979509i	$-0.435451\pi$
$347$	7.50336	0.402801	0.201401	+	0.979509i	$0.435451\pi$
$348$	−8.53771	−0.457669
$349$	15.6461	0.837517	0.418758	−	0.908098i	$-0.362465\pi$
$349$	15.6461	0.837517	0.418758	+	0.908098i	$0.362465\pi$
$350$	35.1576	1.87925
$351$	0	0
$352$	5.71070	0.304381
$353$	25.0341	1.33243	0.666215	−	0.745759i	$-0.267913\pi$
$353$	25.0341	1.33243	0.666215	+	0.745759i	$0.267913\pi$
$354$	4.79803	0.255012
$355$	−27.3151	−1.44973
$356$	4.91489	0.260489
$357$	36.2556	1.91885
$358$	−6.06621	−0.320609
$359$	1.57542	0.0831474	0.0415737	−	0.999135i	$-0.486763\pi$
$359$	1.57542	0.0831474	0.0415737	+	0.999135i	$0.486763\pi$
$360$	−14.7607	−0.777958
$361$	1.00000	0.0526316
$362$	1.78374	0.0937514
$363$	−57.1718	−3.00074
$364$	0	0
$365$	−6.70265	−0.350833
$366$	−36.6091	−1.91359
$367$	6.87895	0.359078	0.179539	−	0.983751i	$-0.442539\pi$
$367$	6.87895	0.359078	0.179539	+	0.983751i	$0.442539\pi$
$368$	1.44687	0.0754235
$369$	−6.08526	−0.316786
$370$	43.4905	2.26096
$371$	32.3741	1.68078
$372$	15.5287	0.805126
$373$	−22.2616	−1.15266	−0.576332	−	0.817216i	$-0.695516\pi$
$373$	−22.2616	−1.15266	−0.576332	+	0.817216i	$0.695516\pi$
$374$	19.2154	0.993605
$375$	−35.4690	−1.83161
$376$	−3.95928	−0.204184
$377$	0	0
$378$	−10.7526	−0.553055
$379$	−16.1270	−0.828388	−0.414194	−	0.910189i	$-0.635936\pi$
$379$	−16.1270	−0.828388	−0.414194	+	0.910189i	$0.635936\pi$
$380$	−3.69209	−0.189400
$381$	6.33921	0.324767
$382$	0.968814	0.0495688
$383$	20.6401	1.05466	0.527330	−	0.849660i	$-0.323193\pi$
$383$	20.6401	1.05466	0.527330	+	0.849660i	$0.323193\pi$
$384$	2.64536	0.134995
$385$	85.8800	4.37685
$386$	−4.87685	−0.248225
$387$	4.20345	0.213673
$388$	−12.0199	−0.610220
$389$	33.3483	1.69082	0.845412	−	0.534115i	$-0.179355\pi$
$389$	33.3483	1.69082	0.845412	+	0.534115i	$0.179355\pi$
$390$	0	0
$391$	4.86845	0.246208
$392$	−9.59054	−0.484395
$393$	45.5811	2.29926
$394$	−9.87125	−0.497306
$395$	16.5225	0.831336
$396$	−22.8310	−1.14730
$397$	15.6201	0.783950	0.391975	−	0.919976i	$-0.371792\pi$
$397$	15.6201	0.783950	0.391975	+	0.919976i	$0.371792\pi$
$398$	12.6371	0.633441
$399$	−10.7749	−0.539422
$400$	8.63155	0.431577
$401$	25.8655	1.29166	0.645831	−	0.763480i	$-0.276511\pi$
$401$	25.8655	1.29166	0.645831	+	0.763480i	$0.276511\pi$
$402$	32.6996	1.63091
$403$	0	0
$404$	−1.83721	−0.0914048
$405$	−18.4987	−0.919207
$406$	13.1458	0.652415
$407$	67.2684	3.33437
$408$	8.90113	0.440672
$409$	25.0621	1.23924	0.619622	−	0.784901i	$-0.287286\pi$
$409$	25.0621	1.23924	0.619622	+	0.784901i	$0.287286\pi$
$410$	5.61974	0.277539
$411$	23.6068	1.16444
$412$	−6.16843	−0.303897
$413$	−7.38768	−0.363524
$414$	−5.78450	−0.284293
$415$	27.9769	1.37333
$416$	0	0
$417$	−17.0631	−0.835582
$418$	−5.71070	−0.279319
$419$	33.4995	1.63656	0.818278	−	0.574823i	$-0.194929\pi$
$419$	33.4995	1.63656	0.818278	+	0.574823i	$0.194929\pi$
$420$	39.7821	1.94117
$421$	−24.5268	−1.19536	−0.597682	−	0.801733i	$-0.703911\pi$
$421$	−24.5268	−1.19536	−0.597682	+	0.801733i	$0.703911\pi$
$422$	24.5263	1.19392
$423$	15.8289	0.769629
$424$	7.94818	0.385998
$425$	29.0435	1.40882
$426$	−19.5711	−0.948222
$427$	56.3682	2.72785
$428$	10.5729	0.511059
$429$	0	0
$430$	−3.88189	−0.187201
$431$	26.6431	1.28335	0.641677	−	0.766975i	$-0.278239\pi$
$431$	26.6431	1.28335	0.641677	+	0.766975i	$0.278239\pi$
$432$	−2.63988	−0.127011
$433$	−6.43476	−0.309235	−0.154617	−	0.987974i	$-0.549414\pi$
$433$	−6.43476	−0.309235	−0.154617	+	0.987974i	$0.549414\pi$
$434$	−23.9101	−1.14772
$435$	−31.5220	−1.51136
$436$	−13.2819	−0.636087
$437$	−1.44687	−0.0692133
$438$	−4.80240	−0.229468
$439$	8.71522	0.415955	0.207977	−	0.978134i	$-0.433312\pi$
$439$	8.71522	0.415955	0.207977	+	0.978134i	$0.433312\pi$
$440$	21.0844	1.00516
$441$	38.3423	1.82582
$442$	0	0
$443$	17.0013	0.807758	0.403879	−	0.914813i	$-0.367662\pi$
$443$	17.0013	0.807758	0.403879	+	0.914813i	$0.367662\pi$
$444$	31.1606	1.47882
$445$	18.1462	0.860214
$446$	18.6888	0.884939
$447$	−55.0529	−2.60391
$448$	−4.07315	−0.192438
$449$	−23.9354	−1.12958	−0.564790	−	0.825235i	$-0.691043\pi$
$449$	−23.9354	−1.12958	−0.564790	+	0.825235i	$0.691043\pi$
$450$	−34.5083	−1.62674
$451$	8.69227	0.409303
$452$	0.835180	0.0392836
$453$	−12.1231	−0.569592
$454$	−12.4603	−0.584791
$455$	0	0
$456$	−2.64536	−0.123880
$457$	15.3842	0.719645	0.359822	−	0.933021i	$-0.382837\pi$
$457$	15.3842	0.719645	0.359822	+	0.933021i	$0.382837\pi$
$458$	−4.67305	−0.218357
$459$	−8.88269	−0.414609
$460$	5.34199	0.249072
$461$	31.8581	1.48378	0.741889	−	0.670522i	$-0.233930\pi$
$461$	31.8581	1.48378	0.741889	+	0.670522i	$0.233930\pi$
$462$	61.5325	2.86275
$463$	13.3282	0.619413	0.309706	−	0.950832i	$-0.399769\pi$
$463$	13.3282	0.619413	0.309706	+	0.950832i	$0.399769\pi$
$464$	3.22743	0.149830
$465$	57.3334	2.65877
$466$	23.0917	1.06970
$467$	−20.7094	−0.958317	−0.479159	−	0.877728i	$-0.659058\pi$
$467$	−20.7094	−0.958317	−0.479159	+	0.877728i	$0.659058\pi$
$468$	0	0
$469$	−50.3487	−2.32488
$470$	−14.6180	−0.674280
$471$	−64.2766	−2.96171
$472$	−1.81375	−0.0834847
$473$	−6.00426	−0.276076
$474$	11.8383	0.543749
$475$	−8.63155	−0.396043
$476$	−13.7054	−0.628184
$477$	−31.7763	−1.45494
$478$	−2.59543	−0.118712
$479$	22.2365	1.01601	0.508006	−	0.861354i	$-0.330383\pi$
$479$	22.2365	1.01601	0.508006	+	0.861354i	$0.330383\pi$
$480$	9.76691	0.445797
$481$	0	0
$482$	15.3195	0.697785
$483$	15.5900	0.709369
$484$	21.6121	0.982368
$485$	−44.3787	−2.01513
$486$	−21.1738	−0.960464
$487$	−29.8911	−1.35450	−0.677248	−	0.735755i	$-0.736828\pi$
$487$	−29.8911	−1.35450	−0.677248	+	0.735755i	$0.736828\pi$
$488$	13.8390	0.626461
$489$	−7.55608	−0.341698
$490$	−35.4092	−1.59962
$491$	4.95716	0.223713	0.111857	−	0.993724i	$-0.464320\pi$
$491$	4.95716	0.223713	0.111857	+	0.993724i	$0.464320\pi$
$492$	4.02651	0.181529
$493$	10.8597	0.489095
$494$	0	0
$495$	−84.2941	−3.78874
$496$	−5.87017	−0.263578
$497$	30.1342	1.35171
$498$	20.0453	0.898250
$499$	34.1608	1.52925	0.764624	−	0.644476i	$-0.222924\pi$
$499$	34.1608	1.52925	0.764624	+	0.644476i	$0.222924\pi$
$500$	13.4080	0.599625
$501$	−3.87293	−0.173030
$502$	1.15980	0.0517642
$503$	17.0392	0.759739	0.379869	−	0.925040i	$-0.375969\pi$
$503$	17.0392	0.759739	0.379869	+	0.925040i	$0.375969\pi$
$504$	16.2842	0.725354
$505$	−6.78316	−0.301847
$506$	8.26266	0.367320
$507$	0	0
$508$	−2.39635	−0.106321
$509$	16.0583	0.711774	0.355887	−	0.934529i	$-0.384179\pi$
$509$	16.0583	0.711774	0.355887	+	0.934529i	$0.384179\pi$
$510$	32.8638	1.45523
$511$	7.39442	0.327110
$512$	−1.00000	−0.0441942
$513$	2.63988	0.116554
$514$	−22.5442	−0.994382
$515$	−22.7744	−1.00356
$516$	−2.78135	−0.122442
$517$	−22.6103	−0.994399
$518$	−47.9791	−2.10808
$519$	−34.9669	−1.53488
$520$	0	0
$521$	0.834968	0.0365806	0.0182903	−	0.999833i	$-0.494178\pi$
$521$	0.834968	0.0365806	0.0182903	+	0.999833i	$0.494178\pi$
$522$	−12.9030	−0.564750
$523$	32.9981	1.44290	0.721452	−	0.692464i	$-0.243475\pi$
$523$	32.9981	1.44290	0.721452	+	0.692464i	$0.243475\pi$
$524$	−17.2306	−0.752722
$525$	93.0045	4.05905
$526$	−9.07631	−0.395746
$527$	−19.7520	−0.860410
$528$	15.1069	0.657442
$529$	−20.9066	−0.908981
$530$	29.3454	1.27468
$531$	7.25125	0.314677
$532$	4.07315	0.176593
$533$	0	0
$534$	13.0017	0.562637
$535$	39.0361	1.68768
$536$	−12.3611	−0.533919
$537$	−16.0473	−0.692493
$538$	5.25303	0.226474
$539$	−54.7687	−2.35906
$540$	−9.74668	−0.419431
$541$	−22.7980	−0.980162	−0.490081	−	0.871677i	$-0.663033\pi$
$541$	−22.7980	−0.980162	−0.490081	+	0.871677i	$0.663033\pi$
$542$	8.97271	0.385411
$543$	4.71864	0.202496
$544$	−3.36481	−0.144265
$545$	−49.0379	−2.10055
$546$	0	0
$547$	20.9305	0.894923	0.447462	−	0.894303i	$-0.352328\pi$
$547$	20.9305	0.894923	0.447462	+	0.894303i	$0.352328\pi$
$548$	−8.92384	−0.381207
$549$	−55.3272	−2.36131
$550$	49.2922	2.10183
$551$	−3.22743	−0.137493
$552$	3.82750	0.162909
$553$	−18.2277	−0.775123
$554$	−20.1053	−0.854194
$555$	115.048	4.88351
$556$	6.45019	0.273549
$557$	18.6052	0.788329	0.394165	−	0.919040i	$-0.371034\pi$
$557$	18.6052	0.788329	0.394165	+	0.919040i	$0.371034\pi$
$558$	23.4685	0.993502
$559$	0	0
$560$	−15.0384	−0.635490
$561$	50.8317	2.14612
$562$	24.3409	1.02676
$563$	−22.4154	−0.944698	−0.472349	−	0.881412i	$-0.656594\pi$
$563$	−22.4154	−0.944698	−0.472349	+	0.881412i	$0.656594\pi$
$564$	−10.4737	−0.441024
$565$	3.08356	0.129726
$566$	15.9644	0.671032
$567$	20.4079	0.857052
$568$	7.39827	0.310424
$569$	−13.2448	−0.555252	−0.277626	−	0.960689i	$-0.589548\pi$
$569$	−13.2448	−0.555252	−0.277626	+	0.960689i	$0.589548\pi$
$570$	−9.76691	−0.409091
$571$	4.19781	0.175673	0.0878364	−	0.996135i	$-0.472005\pi$
$571$	4.19781	0.175673	0.0878364	+	0.996135i	$0.472005\pi$
$572$	0	0
$573$	2.56286	0.107065
$574$	−6.19975	−0.258773
$575$	12.4888	0.520817
$576$	3.99793	0.166580
$577$	37.6214	1.56620	0.783100	−	0.621896i	$-0.213637\pi$
$577$	37.6214	1.56620	0.783100	+	0.621896i	$0.213637\pi$
$578$	5.67806	0.236176
$579$	−12.9010	−0.536148
$580$	11.9160	0.494783
$581$	−30.8644	−1.28047
$582$	−31.7971	−1.31803
$583$	45.3897	1.87985
$584$	1.81541	0.0751220
$585$	0	0
$586$	−3.84316	−0.158760
$587$	−11.4562	−0.472848	−0.236424	−	0.971650i	$-0.575975\pi$
$587$	−11.4562	−0.472848	−0.236424	+	0.971650i	$0.575975\pi$
$588$	−25.3704	−1.04626
$589$	5.87017	0.241876
$590$	−6.69654	−0.275692
$591$	−26.1130	−1.07415
$592$	−11.7794	−0.484128
$593$	−6.46021	−0.265289	−0.132644	−	0.991164i	$-0.542347\pi$
$593$	−6.46021	−0.265289	−0.132644	+	0.991164i	$0.542347\pi$
$594$	−15.0756	−0.618558
$595$	−50.6015	−2.07446
$596$	20.8111	0.852456
$597$	33.4297	1.36819
$598$	0	0
$599$	30.4777	1.24529	0.622643	−	0.782506i	$-0.286059\pi$
$599$	30.4777	1.24529	0.622643	+	0.782506i	$0.286059\pi$
$600$	22.8336	0.932176
$601$	3.37027	0.137476	0.0687380	−	0.997635i	$-0.478103\pi$
$601$	3.37027	0.137476	0.0687380	+	0.997635i	$0.478103\pi$
$602$	4.28253	0.174543
$603$	49.4188	2.01249
$604$	4.58277	0.186470
$605$	79.7939	3.24408
$606$	−4.86009	−0.197428
$607$	27.6119	1.12073	0.560367	−	0.828245i	$-0.310660\pi$
$607$	27.6119	1.12073	0.560367	+	0.828245i	$0.310660\pi$
$608$	1.00000	0.0405554
$609$	34.7754	1.40917
$610$	51.0948	2.06877
$611$	0	0
$612$	13.4523	0.543776
$613$	25.4038	1.02605	0.513025	−	0.858374i	$-0.328525\pi$
$613$	25.4038	1.02605	0.513025	+	0.858374i	$0.328525\pi$
$614$	−0.652509	−0.0263331
$615$	14.8662	0.599465
$616$	−23.2605	−0.937194
$617$	−24.9963	−1.00631	−0.503156	−	0.864195i	$-0.667828\pi$
$617$	−24.9963	−1.00631	−0.503156	+	0.864195i	$0.667828\pi$
$618$	−16.3177	−0.656395
$619$	−23.2145	−0.933071	−0.466536	−	0.884502i	$-0.654498\pi$
$619$	−23.2145	−0.933071	−0.466536	+	0.884502i	$0.654498\pi$
$620$	−21.6732	−0.870417
$621$	−3.81957	−0.153274
$622$	−16.0752	−0.644558
$623$	−20.0191	−0.802048
$624$	0	0
$625$	6.34590	0.253836
$626$	−11.4119	−0.456113
$627$	−15.1069	−0.603310
$628$	24.2979	0.969590
$629$	−39.6353	−1.58036
$630$	60.1226	2.39534
$631$	11.8881	0.473258	0.236629	−	0.971600i	$-0.423957\pi$
$631$	11.8881	0.473258	0.236629	+	0.971600i	$0.423957\pi$
$632$	−4.47510	−0.178010
$633$	64.8810	2.57879
$634$	10.0084	0.397484
$635$	−8.84754	−0.351104
$636$	21.0258	0.833727
$637$	0	0
$638$	18.4309	0.729685
$639$	−29.5777	−1.17008
$640$	−3.69209	−0.145943
$641$	−7.87488	−0.311039	−0.155520	−	0.987833i	$-0.549705\pi$
$641$	−7.87488	−0.311039	−0.155520	+	0.987833i	$0.549705\pi$
$642$	27.9691	1.10385
$643$	−24.4983	−0.966118	−0.483059	−	0.875588i	$-0.660474\pi$
$643$	−24.4983	−0.966118	−0.483059	+	0.875588i	$0.660474\pi$
$644$	−5.89333	−0.232230
$645$	−10.2690	−0.404341
$646$	3.36481	0.132387
$647$	−0.0754726	−0.00296713	−0.00148357	−	0.999999i	$-0.500472\pi$
$647$	−0.0754726	−0.00296713	−0.00148357	+	0.999999i	$0.500472\pi$
$648$	5.01035	0.196825
$649$	−10.3578	−0.406579
$650$	0	0
$651$	−63.2508	−2.47899
$652$	2.85635	0.111863
$653$	−11.4887	−0.449589	−0.224795	−	0.974406i	$-0.572171\pi$
$653$	−11.4887	−0.449589	−0.224795	+	0.974406i	$0.572171\pi$
$654$	−35.1354	−1.37390
$655$	−63.6170	−2.48572
$656$	−1.52210	−0.0594281
$657$	−7.25786	−0.283156
$658$	16.1268	0.628686
$659$	−35.7443	−1.39240	−0.696201	−	0.717847i	$-0.745128\pi$
$659$	−35.7443	−1.39240	−0.696201	+	0.717847i	$0.745128\pi$
$660$	55.7759	2.17107
$661$	−45.0084	−1.75062	−0.875311	−	0.483560i	$-0.839343\pi$
$661$	−45.0084	−1.75062	−0.875311	+	0.483560i	$0.839343\pi$
$662$	5.08261	0.197541
$663$	0	0
$664$	−7.57752	−0.294065
$665$	15.0384	0.583166
$666$	47.0930	1.82482
$667$	4.66968	0.180811
$668$	1.46405	0.0566457
$669$	49.4385	1.91140
$670$	−45.6384	−1.76316
$671$	79.0302	3.05093
$672$	−10.7749	−0.415652
$673$	22.0218	0.848876	0.424438	−	0.905457i	$-0.360472\pi$
$673$	22.0218	0.848876	0.424438	+	0.905457i	$0.360472\pi$
$674$	−25.9786	−1.00066
$675$	−22.7863	−0.877044
$676$	0	0
$677$	−10.7766	−0.414178	−0.207089	−	0.978322i	$-0.566399\pi$
$677$	−10.7766	−0.414178	−0.207089	+	0.978322i	$0.566399\pi$
$678$	2.20935	0.0848496
$679$	48.9590	1.87887
$680$	−12.4232	−0.476407
$681$	−32.9620	−1.26311
$682$	−33.5228	−1.28365
$683$	−8.14237	−0.311559	−0.155780	−	0.987792i	$-0.549789\pi$
$683$	−8.14237	−0.311559	−0.155780	+	0.987792i	$0.549789\pi$
$684$	−3.99793	−0.152865
$685$	−32.9476	−1.25886
$686$	10.5517	0.402864
$687$	−12.3619	−0.471636
$688$	1.05141	0.0400845
$689$	0	0
$690$	14.1315	0.537977
$691$	2.44900	0.0931642	0.0465821	−	0.998914i	$-0.485167\pi$
$691$	2.44900	0.0931642	0.0465821	+	0.998914i	$0.485167\pi$
$692$	13.2182	0.502481
$693$	92.9940	3.53255
$694$	−7.50336	−0.284823
$695$	23.8147	0.903343
$696$	8.53771	0.323621
$697$	−5.12158	−0.193994
$698$	−15.6461	−0.592214
$699$	61.0860	2.31048
$700$	−35.1576	−1.32883
$701$	−15.1790	−0.573303	−0.286651	−	0.958035i	$-0.592542\pi$
$701$	−15.1790	−0.573303	−0.286651	+	0.958035i	$0.592542\pi$
$702$	0	0
$703$	11.7794	0.444267
$704$	−5.71070	−0.215230
$705$	−38.6700	−1.45640
$706$	−25.0341	−0.942171
$707$	7.48325	0.281436
$708$	−4.79803	−0.180321
$709$	41.5587	1.56077	0.780384	−	0.625300i	$-0.215024\pi$
$709$	41.5587	1.56077	0.780384	+	0.625300i	$0.215024\pi$
$710$	27.3151	1.02512
$711$	17.8911	0.670970
$712$	−4.91489	−0.184193
$713$	−8.49339	−0.318080
$714$	−36.2556	−1.35683
$715$	0	0
$716$	6.06621	0.226705
$717$	−6.86583	−0.256409
$718$	−1.57542	−0.0587941
$719$	−35.8196	−1.33585	−0.667923	−	0.744230i	$-0.732817\pi$
$719$	−35.8196	−1.33585	−0.667923	+	0.744230i	$0.732817\pi$
$720$	14.7607	0.550100
$721$	25.1249	0.935702
$722$	−1.00000	−0.0372161
$723$	40.5256	1.50716
$724$	−1.78374	−0.0662922
$725$	27.8577	1.03461
$726$	57.1718	2.12184
$727$	38.2749	1.41954	0.709769	−	0.704434i	$-0.248799\pi$
$727$	38.2749	1.41954	0.709769	+	0.704434i	$0.248799\pi$
$728$	0	0
$729$	−40.9813	−1.51783
$730$	6.70265	0.248076
$731$	3.53778	0.130849
$732$	36.6091	1.35311
$733$	40.4747	1.49497	0.747483	−	0.664281i	$-0.231262\pi$
$733$	40.4747	1.49497	0.747483	+	0.664281i	$0.231262\pi$
$734$	−6.87895	−0.253907
$735$	−93.6700	−3.45507
$736$	−1.44687	−0.0533325
$737$	−70.5906	−2.60024
$738$	6.08526	0.224001
$739$	26.3003	0.967473	0.483736	−	0.875214i	$-0.339279\pi$
$739$	26.3003	0.967473	0.483736	+	0.875214i	$0.339279\pi$
$740$	−43.4905	−1.59874
$741$	0	0
$742$	−32.3741	−1.18849
$743$	10.8639	0.398558	0.199279	−	0.979943i	$-0.436140\pi$
$743$	10.8639	0.398558	0.199279	+	0.979943i	$0.436140\pi$
$744$	−15.5287	−0.569310
$745$	76.8366	2.81507
$746$	22.2616	0.815056
$747$	30.2944	1.10841
$748$	−19.2154	−0.702585
$749$	−43.0649	−1.57356
$750$	35.4690	1.29515
$751$	−4.01104	−0.146365	−0.0731825	−	0.997319i	$-0.523316\pi$
$751$	−4.01104	−0.146365	−0.0731825	+	0.997319i	$0.523316\pi$
$752$	3.95928	0.144380
$753$	3.06808	0.111807
$754$	0	0
$755$	16.9200	0.615783
$756$	10.7526	0.391069
$757$	−16.4737	−0.598747	−0.299374	−	0.954136i	$-0.596778\pi$
$757$	−16.4737	−0.598747	−0.299374	+	0.954136i	$0.596778\pi$
$758$	16.1270	0.585759
$759$	21.8577	0.793385
$760$	3.69209	0.133926
$761$	25.0513	0.908108	0.454054	−	0.890974i	$-0.349977\pi$
$761$	25.0513	0.908108	0.454054	+	0.890974i	$0.349977\pi$
$762$	−6.33921	−0.229645
$763$	54.0991	1.95852
$764$	−0.968814	−0.0350505
$765$	49.6670	1.79571
$766$	−20.6401	−0.745758
$767$	0	0
$768$	−2.64536	−0.0954562
$769$	−43.1208	−1.55498	−0.777488	−	0.628898i	$-0.783506\pi$
$769$	−43.1208	−1.55498	−0.777488	+	0.628898i	$0.783506\pi$
$770$	−85.8800	−3.09490
$771$	−59.6375	−2.14779
$772$	4.87685	0.175522
$773$	31.9839	1.15038	0.575191	−	0.818019i	$-0.304928\pi$
$773$	31.9839	1.15038	0.575191	+	0.818019i	$0.304928\pi$
$774$	−4.20345	−0.151090
$775$	−50.6687	−1.82007
$776$	12.0199	0.431491
$777$	−126.922	−4.55330
$778$	−33.3483	−1.19559
$779$	1.52210	0.0545350
$780$	0	0
$781$	42.2493	1.51180
$782$	−4.86845	−0.174095
$783$	−8.52003	−0.304481
$784$	9.59054	0.342519
$785$	89.7099	3.20189
$786$	−45.5811	−1.62583
$787$	48.3455	1.72333	0.861666	−	0.507476i	$-0.169421\pi$
$787$	48.3455	1.72333	0.861666	+	0.507476i	$0.169421\pi$
$788$	9.87125	0.351649
$789$	−24.0101	−0.854783
$790$	−16.5225	−0.587844
$791$	−3.40181	−0.120954
$792$	22.8310	0.811263
$793$	0	0
$794$	−15.6201	−0.554336
$795$	77.6292	2.75322
$796$	−12.6371	−0.447910
$797$	−34.6328	−1.22676	−0.613378	−	0.789790i	$-0.710190\pi$
$797$	−34.6328	−1.22676	−0.613378	+	0.789790i	$0.710190\pi$
$798$	10.7749	0.381429
$799$	13.3222	0.471307
$800$	−8.63155	−0.305171
$801$	19.6494	0.694277
$802$	−25.8655	−0.913343
$803$	10.3672	0.365852
$804$	−32.6996	−1.15323
$805$	−21.7587	−0.766894
$806$	0	0
$807$	13.8962	0.489168
$808$	1.83721	0.0646330
$809$	9.58073	0.336840	0.168420	−	0.985715i	$-0.446133\pi$
$809$	9.58073	0.336840	0.168420	+	0.985715i	$0.446133\pi$
$810$	18.4987	0.649977
$811$	−25.3774	−0.891120	−0.445560	−	0.895252i	$-0.646995\pi$
$811$	−25.3774	−0.891120	−0.445560	+	0.895252i	$0.646995\pi$
$812$	−13.1458	−0.461327
$813$	23.7361	0.832460
$814$	−67.2684	−2.35775
$815$	10.5459	0.369408
$816$	−8.90113	−0.311602
$817$	−1.05141	−0.0367840
$818$	−25.0621	−0.876277
$819$	0	0
$820$	−5.61974	−0.196250
$821$	22.9906	0.802378	0.401189	−	0.915995i	$-0.368597\pi$
$821$	22.9906	0.802378	0.401189	+	0.915995i	$0.368597\pi$
$822$	−23.6068	−0.823380
$823$	28.1221	0.980274	0.490137	−	0.871645i	$-0.336947\pi$
$823$	28.1221	0.980274	0.490137	+	0.871645i	$0.336947\pi$
$824$	6.16843	0.214887
$825$	130.396	4.53979
$826$	7.38768	0.257050
$827$	5.48117	0.190599	0.0952996	−	0.995449i	$-0.469619\pi$
$827$	5.48117	0.190599	0.0952996	+	0.995449i	$0.469619\pi$
$828$	5.78450	0.201025
$829$	32.8268	1.14012	0.570060	−	0.821603i	$-0.306920\pi$
$829$	32.8268	1.14012	0.570060	+	0.821603i	$0.306920\pi$
$830$	−27.9769	−0.971092
$831$	−53.1859	−1.84500
$832$	0	0
$833$	32.2703	1.11810
$834$	17.0631	0.590846
$835$	5.40540	0.187062
$836$	5.71070	0.197509
$837$	15.4965	0.535639
$838$	−33.4995	−1.15722
$839$	27.9746	0.965792	0.482896	−	0.875678i	$-0.339585\pi$
$839$	27.9746	0.965792	0.482896	+	0.875678i	$0.339585\pi$
$840$	−39.7821	−1.37261
$841$	−18.5837	−0.640818
$842$	24.5268	0.845250
$843$	64.3905	2.21773
$844$	−24.5263	−0.844232
$845$	0	0
$846$	−15.8289	−0.544210
$847$	−88.0293	−3.02472
$848$	−7.94818	−0.272942
$849$	42.2315	1.44938
$850$	−29.0435	−0.996184
$851$	−17.0432	−0.584234
$852$	19.5711	0.670494
$853$	39.8121	1.36314	0.681571	−	0.731752i	$-0.261297\pi$
$853$	39.8121	1.36314	0.681571	+	0.731752i	$0.261297\pi$
$854$	−56.3682	−1.92888
$855$	−14.7607	−0.504806
$856$	−10.5729	−0.361374
$857$	12.1105	0.413688	0.206844	−	0.978374i	$-0.433681\pi$
$857$	12.1105	0.413688	0.206844	+	0.978374i	$0.433681\pi$
$858$	0	0
$859$	40.0749	1.36734	0.683670	−	0.729792i	$-0.260383\pi$
$859$	40.0749	1.36734	0.683670	+	0.729792i	$0.260383\pi$
$860$	3.88189	0.132371
$861$	−16.4006	−0.558930
$862$	−26.6431	−0.907468
$863$	−42.3184	−1.44054	−0.720268	−	0.693696i	$-0.755981\pi$
$863$	−42.3184	−1.44054	−0.720268	+	0.693696i	$0.755981\pi$
$864$	2.63988	0.0898106
$865$	48.8029	1.65935
$866$	6.43476	0.218662
$867$	15.0205	0.510124
$868$	23.9101	0.811561
$869$	−25.5560	−0.866927
$870$	31.5220	1.06870
$871$	0	0
$872$	13.2819	0.449781
$873$	−48.0549	−1.62641
$874$	1.44687	0.0489412
$875$	−54.6129	−1.84625
$876$	4.80240	0.162258
$877$	14.6765	0.495590	0.247795	−	0.968812i	$-0.420294\pi$
$877$	14.6765	0.495590	0.247795	+	0.968812i	$0.420294\pi$
$878$	−8.71522	−0.294124
$879$	−10.1665	−0.342909
$880$	−21.0844	−0.710756
$881$	6.78736	0.228672	0.114336	−	0.993442i	$-0.463526\pi$
$881$	6.78736	0.228672	0.114336	+	0.993442i	$0.463526\pi$
$882$	−38.3423	−1.29105
$883$	9.45762	0.318274	0.159137	−	0.987256i	$-0.449129\pi$
$883$	9.45762	0.318274	0.159137	+	0.987256i	$0.449129\pi$
$884$	0	0
$885$	−17.7148	−0.595475
$886$	−17.0013	−0.571171
$887$	−20.1547	−0.676729	−0.338365	−	0.941015i	$-0.609874\pi$
$887$	−20.1547	−0.676729	−0.338365	+	0.941015i	$0.609874\pi$
$888$	−31.1606	−1.04568
$889$	9.76069	0.327363
$890$	−18.1462	−0.608263
$891$	28.6126	0.958559
$892$	−18.6888	−0.625746
$893$	−3.95928	−0.132492
$894$	55.0529	1.84124
$895$	22.3970	0.748650
$896$	4.07315	0.136074
$897$	0	0
$898$	23.9354	0.798733
$899$	−18.9456	−0.631869
$900$	34.5083	1.15028
$901$	−26.7441	−0.890975
$902$	−8.69227	−0.289421
$903$	11.3288	0.377000
$904$	−0.835180	−0.0277777
$905$	−6.58574	−0.218917
$906$	12.1231	0.402763
$907$	−15.3249	−0.508856	−0.254428	−	0.967092i	$-0.581887\pi$
$907$	−15.3249	−0.508856	−0.254428	+	0.967092i	$0.581887\pi$
$908$	12.4603	0.413510
$909$	−7.34505	−0.243620
$910$	0	0
$911$	−26.3683	−0.873622	−0.436811	−	0.899553i	$-0.643892\pi$
$911$	−26.3683	−0.873622	−0.436811	+	0.899553i	$0.643892\pi$
$912$	2.64536	0.0875966
$913$	−43.2729	−1.43212
$914$	−15.3842	−0.508866
$915$	135.164	4.46839
$916$	4.67305	0.154402
$917$	70.1828	2.31764
$918$	8.88269	0.293173
$919$	−14.6439	−0.483059	−0.241529	−	0.970394i	$-0.577649\pi$
$919$	−14.6439	−0.483059	−0.241529	+	0.970394i	$0.577649\pi$
$920$	−5.34199	−0.176120
$921$	−1.72612	−0.0568776
$922$	−31.8581	−1.04919
$923$	0	0
$924$	−61.5325	−2.02427
$925$	−101.674	−3.34302
$926$	−13.3282	−0.437991
$927$	−24.6609	−0.809972
$928$	−3.22743	−0.105946
$929$	−38.3329	−1.25766	−0.628831	−	0.777542i	$-0.716466\pi$
$929$	−38.3329	−1.25766	−0.628831	+	0.777542i	$0.716466\pi$
$930$	−57.3334	−1.88004
$931$	−9.59054	−0.314317
$932$	−23.0917	−0.756395
$933$	−42.5248	−1.39220
$934$	20.7094	0.677633
$935$	−70.9451	−2.32015
$936$	0	0
$937$	15.1582	0.495197	0.247598	−	0.968863i	$-0.420359\pi$
$937$	15.1582	0.495197	0.247598	+	0.968863i	$0.420359\pi$
$938$	50.3487	1.64394
$939$	−30.1887	−0.985170
$940$	14.6180	0.476788
$941$	9.28052	0.302536	0.151268	−	0.988493i	$-0.451664\pi$
$941$	9.28052	0.302536	0.151268	+	0.988493i	$0.451664\pi$
$942$	64.2766	2.09424
$943$	−2.20229	−0.0717164
$944$	1.81375	0.0590326
$945$	39.6997	1.29143
$946$	6.00426	0.195215
$947$	−12.9919	−0.422180	−0.211090	−	0.977467i	$-0.567701\pi$
$947$	−12.9919	−0.422180	−0.211090	+	0.977467i	$0.567701\pi$
$948$	−11.8383	−0.384489
$949$	0	0
$950$	8.63155	0.280044
$951$	26.4758	0.858537
$952$	13.7054	0.444193
$953$	−48.1633	−1.56016	−0.780082	−	0.625678i	$-0.784822\pi$
$953$	−48.1633	−1.56016	−0.780082	+	0.625678i	$0.784822\pi$
$954$	31.7763	1.02879
$955$	−3.57695	−0.115747
$956$	2.59543	0.0839421
$957$	48.7563	1.57607
$958$	−22.2365	−0.718428
$959$	36.3481	1.17374
$960$	−9.76691	−0.315226
$961$	3.45889	0.111577
$962$	0	0
$963$	42.2696	1.36212
$964$	−15.3195	−0.493409
$965$	18.0058	0.579626
$966$	−15.5900	−0.501599
$967$	23.8315	0.766370	0.383185	−	0.923672i	$-0.374827\pi$
$967$	23.8315	0.766370	0.383185	+	0.923672i	$0.374827\pi$
$968$	−21.6121	−0.694639
$969$	8.90113	0.285945
$970$	44.3787	1.42492
$971$	11.9585	0.383766	0.191883	−	0.981418i	$-0.438541\pi$
$971$	11.9585	0.383766	0.191883	+	0.981418i	$0.438541\pi$
$972$	21.1738	0.679151
$973$	−26.2726	−0.842260
$974$	29.8911	0.957773
$975$	0	0
$976$	−13.8390	−0.442975
$977$	14.2230	0.455034	0.227517	−	0.973774i	$-0.426939\pi$
$977$	14.2230	0.455034	0.227517	+	0.973774i	$0.426939\pi$
$978$	7.55608	0.241617
$979$	−28.0675	−0.897040
$980$	35.4092	1.13110
$981$	−53.1000	−1.69535
$982$	−4.95716	−0.158189
$983$	−39.9576	−1.27445	−0.637224	−	0.770678i	$-0.719918\pi$
$983$	−39.9576	−1.27445	−0.637224	+	0.770678i	$0.719918\pi$
$984$	−4.02651	−0.128360
$985$	36.4456	1.16125
$986$	−10.8597	−0.345843
$987$	42.6611	1.35792
$988$	0	0
$989$	1.52125	0.0483730
$990$	84.2941	2.67904
$991$	47.6597	1.51396	0.756981	−	0.653437i	$-0.226674\pi$
$991$	47.6597	1.51396	0.756981	+	0.653437i	$0.226674\pi$
$992$	5.87017	0.186378
$993$	13.4453	0.426675
$994$	−30.1342	−0.955800
$995$	−46.6574	−1.47914
$996$	−20.0453	−0.635158
$997$	55.1765	1.74746	0.873729	−	0.486414i	$-0.161695\pi$
$997$	55.1765	1.74746	0.873729	+	0.486414i	$0.161695\pi$
$998$	−34.1608	−1.08134
$999$	31.0961	0.983837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bm.1.2		14
13.6	odd	12		494.2.m.b.153.14	✓	28
13.11	odd	12		494.2.m.b.381.14	yes	28
13.12	even	2		6422.2.a.bn.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.14	✓	28	13.6	odd	12
494.2.m.b.381.14	yes	28	13.11	odd	12
6422.2.a.bm.1.2		14	1.1	even	1	trivial
6422.2.a.bn.1.2		14	13.12	even	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:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.64536 q^{3} +1.00000 q^{4} +3.69209 q^{5} +2.64536 q^{6} -4.07315 q^{7} -1.00000 q^{8} +3.99793 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.64536 q^{3} +1.00000 q^{4} +3.69209 q^{5} +2.64536 q^{6} -4.07315 q^{7} -1.00000 q^{8} +3.99793 q^{9} -3.69209 q^{10} -5.71070 q^{11} -2.64536 q^{12} +4.07315 q^{14} -9.76691 q^{15} +1.00000 q^{16} +3.36481 q^{17} -3.99793 q^{18} -1.00000 q^{19} +3.69209 q^{20} +10.7749 q^{21} +5.71070 q^{22} +1.44687 q^{23} +2.64536 q^{24} +8.63155 q^{25} -2.63988 q^{27} -4.07315 q^{28} +3.22743 q^{29} +9.76691 q^{30} -5.87017 q^{31} -1.00000 q^{32} +15.1069 q^{33} -3.36481 q^{34} -15.0384 q^{35} +3.99793 q^{36} -11.7794 q^{37} +1.00000 q^{38} -3.69209 q^{40} -1.52210 q^{41} -10.7749 q^{42} +1.05141 q^{43} -5.71070 q^{44} +14.7607 q^{45} -1.44687 q^{46} +3.95928 q^{47} -2.64536 q^{48} +9.59054 q^{49} -8.63155 q^{50} -8.90113 q^{51} -7.94818 q^{53} +2.63988 q^{54} -21.0844 q^{55} +4.07315 q^{56} +2.64536 q^{57} -3.22743 q^{58} +1.81375 q^{59} -9.76691 q^{60} -13.8390 q^{61} +5.87017 q^{62} -16.2842 q^{63} +1.00000 q^{64} -15.1069 q^{66} +12.3611 q^{67} +3.36481 q^{68} -3.82750 q^{69} +15.0384 q^{70} -7.39827 q^{71} -3.99793 q^{72} -1.81541 q^{73} +11.7794 q^{74} -22.8336 q^{75} -1.00000 q^{76} +23.2605 q^{77} +4.47510 q^{79} +3.69209 q^{80} -5.01035 q^{81} +1.52210 q^{82} +7.57752 q^{83} +10.7749 q^{84} +12.4232 q^{85} -1.05141 q^{86} -8.53771 q^{87} +5.71070 q^{88} +4.91489 q^{89} -14.7607 q^{90} +1.44687 q^{92} +15.5287 q^{93} -3.95928 q^{94} -3.69209 q^{95} +2.64536 q^{96} -12.0199 q^{97} -9.59054 q^{98} -22.8310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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