LMFDB - Embedded newform 4017.2.a.i.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.307676 q^{2} -1.00000 q^{3} -1.90534 q^{4} -1.88076 q^{5} +0.307676 q^{6} -3.18485 q^{7} +1.20158 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.307676 q^{2} -1.00000 q^{3} -1.90534 q^{4} -1.88076 q^{5} +0.307676 q^{6} -3.18485 q^{7} +1.20158 q^{8} +1.00000 q^{9} +0.578664 q^{10} -3.08877 q^{11} +1.90534 q^{12} -1.00000 q^{13} +0.979900 q^{14} +1.88076 q^{15} +3.44098 q^{16} -4.84630 q^{17} -0.307676 q^{18} +5.64948 q^{19} +3.58348 q^{20} +3.18485 q^{21} +0.950339 q^{22} +6.40749 q^{23} -1.20158 q^{24} -1.46274 q^{25} +0.307676 q^{26} -1.00000 q^{27} +6.06820 q^{28} +1.13654 q^{29} -0.578664 q^{30} +1.55491 q^{31} -3.46186 q^{32} +3.08877 q^{33} +1.49109 q^{34} +5.98994 q^{35} -1.90534 q^{36} +9.63312 q^{37} -1.73821 q^{38} +1.00000 q^{39} -2.25988 q^{40} -2.54543 q^{41} -0.979900 q^{42} -4.37951 q^{43} +5.88514 q^{44} -1.88076 q^{45} -1.97143 q^{46} +9.16997 q^{47} -3.44098 q^{48} +3.14325 q^{49} +0.450049 q^{50} +4.84630 q^{51} +1.90534 q^{52} +2.80479 q^{53} +0.307676 q^{54} +5.80924 q^{55} -3.82684 q^{56} -5.64948 q^{57} -0.349686 q^{58} -3.55846 q^{59} -3.58348 q^{60} +8.59913 q^{61} -0.478409 q^{62} -3.18485 q^{63} -5.81682 q^{64} +1.88076 q^{65} -0.950339 q^{66} -10.8138 q^{67} +9.23383 q^{68} -6.40749 q^{69} -1.84296 q^{70} +1.88052 q^{71} +1.20158 q^{72} +12.0563 q^{73} -2.96388 q^{74} +1.46274 q^{75} -10.7641 q^{76} +9.83726 q^{77} -0.307676 q^{78} +7.69423 q^{79} -6.47165 q^{80} +1.00000 q^{81} +0.783166 q^{82} +0.322186 q^{83} -6.06820 q^{84} +9.11473 q^{85} +1.34747 q^{86} -1.13654 q^{87} -3.71139 q^{88} -11.6204 q^{89} +0.578664 q^{90} +3.18485 q^{91} -12.2084 q^{92} -1.55491 q^{93} -2.82138 q^{94} -10.6253 q^{95} +3.46186 q^{96} -11.5520 q^{97} -0.967101 q^{98} -3.08877 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	−0.307676	−0.217560	−0.108780	−	0.994066i	$-0.534694\pi$
$2$	−0.307676	−0.217560	−0.108780	+	0.994066i	$0.534694\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.90534	−0.952668
$5$	−1.88076	−0.841102	−0.420551	−	0.907269i	$-0.638163\pi$
$5$	−1.88076	−0.841102	−0.420551	+	0.907269i	$0.638163\pi$
$6$	0.307676	0.125608
$7$	−3.18485	−1.20376	−0.601879	−	0.798587i	$-0.705581\pi$
$7$	−3.18485	−1.20376	−0.601879	+	0.798587i	$0.705581\pi$
$8$	1.20158	0.424822
$9$	1.00000	0.333333
$10$	0.578664	0.182990
$11$	−3.08877	−0.931299	−0.465650	−	0.884969i	$-0.654179\pi$
$11$	−3.08877	−0.931299	−0.465650	+	0.884969i	$0.654179\pi$
$12$	1.90534	0.550023
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.979900	0.261889
$15$	1.88076	0.485610
$16$	3.44098	0.860244
$17$	−4.84630	−1.17540	−0.587700	−	0.809079i	$-0.699967\pi$
$17$	−4.84630	−1.17540	−0.587700	+	0.809079i	$0.699967\pi$
$18$	−0.307676	−0.0725198
$19$	5.64948	1.29608	0.648039	−	0.761607i	$-0.275589\pi$
$19$	5.64948	1.29608	0.648039	+	0.761607i	$0.275589\pi$
$20$	3.58348	0.801291
$21$	3.18485	0.694991
$22$	0.950339	0.202613
$23$	6.40749	1.33605	0.668027	−	0.744137i	$-0.267139\pi$
$23$	6.40749	1.33605	0.668027	+	0.744137i	$0.267139\pi$
$24$	−1.20158	−0.245271
$25$	−1.46274	−0.292547
$26$	0.307676	0.0603402
$27$	−1.00000	−0.192450
$28$	6.06820	1.14678
$29$	1.13654	0.211051	0.105525	−	0.994417i	$-0.466348\pi$
$29$	1.13654	0.211051	0.105525	+	0.994417i	$0.466348\pi$
$30$	−0.578664	−0.105649
$31$	1.55491	0.279271	0.139635	−	0.990203i	$-0.455407\pi$
$31$	1.55491	0.279271	0.139635	+	0.990203i	$0.455407\pi$
$32$	−3.46186	−0.611976
$33$	3.08877	0.537686
$34$	1.49109	0.255720
$35$	5.98994	1.01248
$36$	−1.90534	−0.317556
$37$	9.63312	1.58367	0.791837	−	0.610732i	$-0.209125\pi$
$37$	9.63312	1.58367	0.791837	+	0.610732i	$0.209125\pi$
$38$	−1.73821	−0.281974
$39$	1.00000	0.160128
$40$	−2.25988	−0.357318
$41$	−2.54543	−0.397529	−0.198764	−	0.980047i	$-0.563693\pi$
$41$	−2.54543	−0.397529	−0.198764	+	0.980047i	$0.563693\pi$
$42$	−0.979900	−0.151202
$43$	−4.37951	−0.667868	−0.333934	−	0.942596i	$-0.608376\pi$
$43$	−4.37951	−0.667868	−0.333934	+	0.942596i	$0.608376\pi$
$44$	5.88514	0.887219
$45$	−1.88076	−0.280367
$46$	−1.97143	−0.290671
$47$	9.16997	1.33758	0.668789	−	0.743453i	$-0.266813\pi$
$47$	9.16997	1.33758	0.668789	+	0.743453i	$0.266813\pi$
$48$	−3.44098	−0.496662
$49$	3.14325	0.449035
$50$	0.450049	0.0636465
$51$	4.84630	0.678618
$52$	1.90534	0.264223
$53$	2.80479	0.385267	0.192634	−	0.981271i	$-0.438297\pi$
$53$	2.80479	0.385267	0.192634	+	0.981271i	$0.438297\pi$
$54$	0.307676	0.0418694
$55$	5.80924	0.783318
$56$	−3.82684	−0.511383
$57$	−5.64948	−0.748291
$58$	−0.349686	−0.0459161
$59$	−3.55846	−0.463272	−0.231636	−	0.972803i	$-0.574408\pi$
$59$	−3.55846	−0.463272	−0.231636	+	0.972803i	$0.574408\pi$
$60$	−3.58348	−0.462625
$61$	8.59913	1.10101	0.550503	−	0.834833i	$-0.314436\pi$
$61$	8.59913	1.10101	0.550503	+	0.834833i	$0.314436\pi$
$62$	−0.478409	−0.0607580
$63$	−3.18485	−0.401253
$64$	−5.81682	−0.727103
$65$	1.88076	0.233280
$66$	−0.950339	−0.116979
$67$	−10.8138	−1.32112	−0.660560	−	0.750773i	$-0.729681\pi$
$67$	−10.8138	−1.32112	−0.660560	+	0.750773i	$0.729681\pi$
$68$	9.23383	1.11977
$69$	−6.40749	−0.771371
$70$	−1.84296	−0.220276
$71$	1.88052	0.223176	0.111588	−	0.993755i	$-0.464406\pi$
$71$	1.88052	0.223176	0.111588	+	0.993755i	$0.464406\pi$
$72$	1.20158	0.141607
$73$	12.0563	1.41108	0.705542	−	0.708668i	$-0.250704\pi$
$73$	12.0563	1.41108	0.705542	+	0.708668i	$0.250704\pi$
$74$	−2.96388	−0.344544
$75$	1.46274	0.168902
$76$	−10.7641	−1.23473
$77$	9.83726	1.12106
$78$	−0.307676	−0.0348374
$79$	7.69423	0.865669	0.432834	−	0.901474i	$-0.357514\pi$
$79$	7.69423	0.865669	0.432834	+	0.901474i	$0.357514\pi$
$80$	−6.47165	−0.723553
$81$	1.00000	0.111111
$82$	0.783166	0.0864862
$83$	0.322186	0.0353645	0.0176823	−	0.999844i	$-0.494371\pi$
$83$	0.322186	0.0353645	0.0176823	+	0.999844i	$0.494371\pi$
$84$	−6.06820	−0.662095
$85$	9.11473	0.988631
$86$	1.34747	0.145301
$87$	−1.13654	−0.121850
$88$	−3.71139	−0.395636
$89$	−11.6204	−1.23176	−0.615882	−	0.787839i	$-0.711200\pi$
$89$	−11.6204	−1.23176	−0.615882	+	0.787839i	$0.711200\pi$
$90$	0.578664	0.0609966
$91$	3.18485	0.333863
$92$	−12.2084	−1.27281
$93$	−1.55491	−0.161237
$94$	−2.82138	−0.291003
$95$	−10.6253	−1.09013
$96$	3.46186	0.353324
$97$	−11.5520	−1.17293	−0.586463	−	0.809976i	$-0.699480\pi$
$97$	−11.5520	−1.17293	−0.586463	+	0.809976i	$0.699480\pi$
$98$	−0.967101	−0.0976920
$99$	−3.08877	−0.310433
$100$	2.78701	0.278701
$101$	−3.57364	−0.355590	−0.177795	−	0.984068i	$-0.556896\pi$
$101$	−3.57364	−0.355590	−0.177795	+	0.984068i	$0.556896\pi$
$102$	−1.49109	−0.147640
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.20158	−0.117824
$105$	−5.98994	−0.584558
$106$	−0.862965	−0.0838186
$107$	−5.85682	−0.566200	−0.283100	−	0.959090i	$-0.591363\pi$
$107$	−5.85682	−0.566200	−0.283100	+	0.959090i	$0.591363\pi$
$108$	1.90534	0.183341
$109$	10.8377	1.03806	0.519032	−	0.854755i	$-0.326293\pi$
$109$	10.8377	1.03806	0.519032	+	0.854755i	$0.326293\pi$
$110$	−1.78736	−0.170418
$111$	−9.63312	−0.914335
$112$	−10.9590	−1.03553
$113$	4.69516	0.441684	0.220842	−	0.975310i	$-0.429120\pi$
$113$	4.69516	0.441684	0.220842	+	0.975310i	$0.429120\pi$
$114$	1.73821	0.162798
$115$	−12.0510	−1.12376
$116$	−2.16549	−0.201061
$117$	−1.00000	−0.0924500
$118$	1.09485	0.100789
$119$	15.4347	1.41490
$120$	2.25988	0.206298
$121$	−1.45950	−0.132682
$122$	−2.64574	−0.239534
$123$	2.54543	0.229513
$124$	−2.96263	−0.266052
$125$	12.1549	1.08716
$126$	0.979900	0.0872964
$127$	−2.70854	−0.240344	−0.120172	−	0.992753i	$-0.538345\pi$
$127$	−2.70854	−0.240344	−0.120172	+	0.992753i	$0.538345\pi$
$128$	8.71341	0.770164
$129$	4.37951	0.385594
$130$	−0.578664	−0.0507522
$131$	12.9163	1.12850	0.564250	−	0.825604i	$-0.309165\pi$
$131$	12.9163	1.12850	0.564250	+	0.825604i	$0.309165\pi$
$132$	−5.88514	−0.512236
$133$	−17.9927	−1.56017
$134$	3.32715	0.287422
$135$	1.88076	0.161870
$136$	−5.82320	−0.499335
$137$	8.60965	0.735572	0.367786	−	0.929911i	$-0.380116\pi$
$137$	8.60965	0.735572	0.367786	+	0.929911i	$0.380116\pi$
$138$	1.97143	0.167819
$139$	5.89105	0.499672	0.249836	−	0.968288i	$-0.419623\pi$
$139$	5.89105	0.499672	0.249836	+	0.968288i	$0.419623\pi$
$140$	−11.4128	−0.964561
$141$	−9.16997	−0.772251
$142$	−0.578589	−0.0485541
$143$	3.08877	0.258296
$144$	3.44098	0.286748
$145$	−2.13756	−0.177515
$146$	−3.70943	−0.306995
$147$	−3.14325	−0.259251
$148$	−18.3543	−1.50872
$149$	−17.5425	−1.43714	−0.718570	−	0.695455i	$-0.755203\pi$
$149$	−17.5425	−1.43714	−0.718570	+	0.695455i	$0.755203\pi$
$150$	−0.450049	−0.0367463
$151$	−10.6190	−0.864158	−0.432079	−	0.901836i	$-0.642220\pi$
$151$	−10.6190	−0.864158	−0.432079	+	0.901836i	$0.642220\pi$
$152$	6.78828	0.550602
$153$	−4.84630	−0.391800
$154$	−3.02669	−0.243897
$155$	−2.92442	−0.234895
$156$	−1.90534	−0.152549
$157$	−21.7611	−1.73673	−0.868363	−	0.495929i	$-0.834828\pi$
$157$	−21.7611	−1.73673	−0.868363	+	0.495929i	$0.834828\pi$
$158$	−2.36733	−0.188334
$159$	−2.80479	−0.222434
$160$	6.51093	0.514734
$161$	−20.4069	−1.60829
$162$	−0.307676	−0.0241733
$163$	−3.33751	−0.261414	−0.130707	−	0.991421i	$-0.541725\pi$
$163$	−3.33751	−0.261414	−0.130707	+	0.991421i	$0.541725\pi$
$164$	4.84989	0.378713
$165$	−5.80924	−0.452249
$166$	−0.0991289	−0.00769389
$167$	−0.598074	−0.0462804	−0.0231402	−	0.999732i	$-0.507366\pi$
$167$	−0.598074	−0.0462804	−0.0231402	+	0.999732i	$0.507366\pi$
$168$	3.82684	0.295247
$169$	1.00000	0.0769231
$170$	−2.80438	−0.215086
$171$	5.64948	0.432026
$172$	8.34443	0.636257
$173$	−5.96891	−0.453808	−0.226904	−	0.973917i	$-0.572860\pi$
$173$	−5.96891	−0.453808	−0.226904	+	0.973917i	$0.572860\pi$
$174$	0.349686	0.0265097
$175$	4.65859	0.352157
$176$	−10.6284	−0.801144
$177$	3.55846	0.267470
$178$	3.57532	0.267982
$179$	10.9281	0.816806	0.408403	−	0.912802i	$-0.366086\pi$
$179$	10.9281	0.816806	0.408403	+	0.912802i	$0.366086\pi$
$180$	3.58348	0.267097
$181$	13.9425	1.03634	0.518170	−	0.855277i	$-0.326613\pi$
$181$	13.9425	1.03634	0.518170	+	0.855277i	$0.326613\pi$
$182$	−0.979900	−0.0726350
$183$	−8.59913	−0.635666
$184$	7.69909	0.567584
$185$	−18.1176	−1.33203
$186$	0.478409	0.0350786
$187$	14.9691	1.09465
$188$	−17.4719	−1.27427
$189$	3.18485	0.231664
$190$	3.26915	0.237169
$191$	−1.92904	−0.139580	−0.0697901	−	0.997562i	$-0.522233\pi$
$191$	−1.92904	−0.139580	−0.0697901	+	0.997562i	$0.522233\pi$
$192$	5.81682	0.419793
$193$	14.3650	1.03402	0.517009	−	0.855980i	$-0.327045\pi$
$193$	14.3650	1.03402	0.517009	+	0.855980i	$0.327045\pi$
$194$	3.55427	0.255181
$195$	−1.88076	−0.134684
$196$	−5.98894	−0.427782
$197$	−2.82201	−0.201060	−0.100530	−	0.994934i	$-0.532054\pi$
$197$	−2.82201	−0.201060	−0.100530	+	0.994934i	$0.532054\pi$
$198$	0.950339	0.0675377
$199$	8.66955	0.614568	0.307284	−	0.951618i	$-0.400580\pi$
$199$	8.66955	0.614568	0.307284	+	0.951618i	$0.400580\pi$
$200$	−1.75759	−0.124280
$201$	10.8138	0.762749
$202$	1.09952	0.0773621
$203$	−3.61971	−0.254054
$204$	−9.23383	−0.646497
$205$	4.78734	0.334362
$206$	0.307676	0.0214368
$207$	6.40749	0.445351
$208$	−3.44098	−0.238589
$209$	−17.4499	−1.20704
$210$	1.84296	0.127176
$211$	−16.1177	−1.10959	−0.554793	−	0.831988i	$-0.687203\pi$
$211$	−16.1177	−1.10959	−0.554793	+	0.831988i	$0.687203\pi$
$212$	−5.34406	−0.367032
$213$	−1.88052	−0.128851
$214$	1.80200	0.123182
$215$	8.23680	0.561745
$216$	−1.20158	−0.0817569
$217$	−4.95216	−0.336175
$218$	−3.33450	−0.225841
$219$	−12.0563	−0.814690
$220$	−11.0686	−0.746241
$221$	4.84630	0.325997
$222$	2.96388	0.198922
$223$	7.00485	0.469080	0.234540	−	0.972107i	$-0.424642\pi$
$223$	7.00485	0.469080	0.234540	+	0.972107i	$0.424642\pi$
$224$	11.0255	0.736671
$225$	−1.46274	−0.0975158
$226$	−1.44459	−0.0960925
$227$	−21.0854	−1.39948	−0.699742	−	0.714396i	$-0.746702\pi$
$227$	−21.0854	−1.39948	−0.699742	+	0.714396i	$0.746702\pi$
$228$	10.7641	0.712873
$229$	22.7471	1.50317	0.751584	−	0.659637i	$-0.229290\pi$
$229$	22.7471	1.50317	0.751584	+	0.659637i	$0.229290\pi$
$230$	3.70778	0.244484
$231$	−9.83726	−0.647244
$232$	1.36564	0.0896588
$233$	−10.4279	−0.683157	−0.341578	−	0.939853i	$-0.610961\pi$
$233$	−10.4279	−0.683157	−0.341578	+	0.939853i	$0.610961\pi$
$234$	0.307676	0.0201134
$235$	−17.2465	−1.12504
$236$	6.78006	0.441345
$237$	−7.69423	−0.499794
$238$	−4.74889	−0.307825
$239$	−24.4288	−1.58017	−0.790083	−	0.612999i	$-0.789963\pi$
$239$	−24.4288	−1.58017	−0.790083	+	0.612999i	$0.789963\pi$
$240$	6.47165	0.417743
$241$	−22.1839	−1.42899	−0.714495	−	0.699641i	$-0.753343\pi$
$241$	−22.1839	−1.42899	−0.714495	+	0.699641i	$0.753343\pi$
$242$	0.449053	0.0288662
$243$	−1.00000	−0.0641500
$244$	−16.3842	−1.04889
$245$	−5.91170	−0.377685
$246$	−0.783166	−0.0499328
$247$	−5.64948	−0.359468
$248$	1.86835	0.118640
$249$	−0.322186	−0.0204177
$250$	−3.73976	−0.236523
$251$	−14.8665	−0.938367	−0.469184	−	0.883101i	$-0.655452\pi$
$251$	−14.8665	−0.938367	−0.469184	+	0.883101i	$0.655452\pi$
$252$	6.06820	0.382261
$253$	−19.7913	−1.24427
$254$	0.833353	0.0522892
$255$	−9.11473	−0.570787
$256$	8.95274	0.559546
$257$	14.5541	0.907861	0.453931	−	0.891037i	$-0.350021\pi$
$257$	14.5541	0.907861	0.453931	+	0.891037i	$0.350021\pi$
$258$	−1.34747	−0.0838897
$259$	−30.6800	−1.90636
$260$	−3.58348	−0.222238
$261$	1.13654	0.0703502
$262$	−3.97402	−0.245516
$263$	14.1420	0.872031	0.436016	−	0.899939i	$-0.356389\pi$
$263$	14.1420	0.872031	0.436016	+	0.899939i	$0.356389\pi$
$264$	3.71139	0.228421
$265$	−5.27514	−0.324049
$266$	5.53592	0.339429
$267$	11.6204	0.711159
$268$	20.6040	1.25859
$269$	−11.5513	−0.704298	−0.352149	−	0.935944i	$-0.614549\pi$
$269$	−11.5513	−0.704298	−0.352149	+	0.935944i	$0.614549\pi$
$270$	−0.578664	−0.0352164
$271$	22.1927	1.34811	0.674056	−	0.738680i	$-0.264551\pi$
$271$	22.1927	1.34811	0.674056	+	0.738680i	$0.264551\pi$
$272$	−16.6760	−1.01113
$273$	−3.18485	−0.192756
$274$	−2.64898	−0.160031
$275$	4.51806	0.272449
$276$	12.2084	0.734860
$277$	−12.3917	−0.744545	−0.372273	−	0.928123i	$-0.621421\pi$
$277$	−12.3917	−0.744545	−0.372273	+	0.928123i	$0.621421\pi$
$278$	−1.81253	−0.108708
$279$	1.55491	0.0930902
$280$	7.19737	0.430125
$281$	3.61441	0.215618	0.107809	−	0.994172i	$-0.465617\pi$
$281$	3.61441	0.215618	0.107809	+	0.994172i	$0.465617\pi$
$282$	2.82138	0.168010
$283$	−15.2073	−0.903979	−0.451990	−	0.892023i	$-0.649286\pi$
$283$	−15.2073	−0.903979	−0.451990	+	0.892023i	$0.649286\pi$
$284$	−3.58302	−0.212613
$285$	10.6253	0.629389
$286$	−0.950339	−0.0561947
$287$	8.10680	0.478529
$288$	−3.46186	−0.203992
$289$	6.48662	0.381566
$290$	0.657677	0.0386201
$291$	11.5520	0.677190
$292$	−22.9713	−1.34429
$293$	2.48970	0.145450	0.0727250	−	0.997352i	$-0.476830\pi$
$293$	2.48970	0.145450	0.0727250	+	0.997352i	$0.476830\pi$
$294$	0.967101	0.0564025
$295$	6.69262	0.389659
$296$	11.5749	0.672779
$297$	3.08877	0.179229
$298$	5.39741	0.312663
$299$	−6.40749	−0.370554
$300$	−2.78701	−0.160908
$301$	13.9481	0.803953
$302$	3.26719	0.188006
$303$	3.57364	0.205300
$304$	19.4397	1.11494
$305$	−16.1729	−0.926059
$306$	1.49109	0.0852398
$307$	−6.08504	−0.347292	−0.173646	−	0.984808i	$-0.555555\pi$
$307$	−6.08504	−0.347292	−0.173646	+	0.984808i	$0.555555\pi$
$308$	−18.7433	−1.06800
$309$	1.00000	0.0568880
$310$	0.899773	0.0511037
$311$	−12.0311	−0.682222	−0.341111	−	0.940023i	$-0.610803\pi$
$311$	−12.0311	−0.682222	−0.341111	+	0.940023i	$0.610803\pi$
$312$	1.20158	0.0680259
$313$	−1.97990	−0.111911	−0.0559553	−	0.998433i	$-0.517820\pi$
$313$	−1.97990	−0.111911	−0.0559553	+	0.998433i	$0.517820\pi$
$314$	6.69537	0.377841
$315$	5.98994	0.337495
$316$	−14.6601	−0.824695
$317$	−32.9689	−1.85172	−0.925859	−	0.377868i	$-0.876657\pi$
$317$	−32.9689	−1.85172	−0.925859	+	0.377868i	$0.876657\pi$
$318$	0.862965	0.0483927
$319$	−3.51052	−0.196551
$320$	10.9401	0.611568
$321$	5.85682	0.326896
$322$	6.27869	0.349898
$323$	−27.3791	−1.52341
$324$	−1.90534	−0.105852
$325$	1.46274	0.0811381
$326$	1.02687	0.0568731
$327$	−10.8377	−0.599327
$328$	−3.05853	−0.168879
$329$	−29.2049	−1.61012
$330$	1.78736	0.0983910
$331$	19.4708	1.07021	0.535106	−	0.844785i	$-0.320272\pi$
$331$	19.4708	1.07021	0.535106	+	0.844785i	$0.320272\pi$
$332$	−0.613873	−0.0336907
$333$	9.63312	0.527892
$334$	0.184013	0.0100687
$335$	20.3382	1.11120
$336$	10.9590	0.597861
$337$	2.33313	0.127094	0.0635469	−	0.997979i	$-0.479759\pi$
$337$	2.33313	0.127094	0.0635469	+	0.997979i	$0.479759\pi$
$338$	−0.307676	−0.0167353
$339$	−4.69516	−0.255006
$340$	−17.3666	−0.941837
$341$	−4.80277	−0.260085
$342$	−1.73821	−0.0939914
$343$	12.2832	0.663228
$344$	−5.26231	−0.283725
$345$	12.0510	0.648801
$346$	1.83649	0.0987303
$347$	−15.0170	−0.806154	−0.403077	−	0.915166i	$-0.632059\pi$
$347$	−15.0170	−0.806154	−0.403077	+	0.915166i	$0.632059\pi$
$348$	2.16549	0.116083
$349$	24.2169	1.29630	0.648150	−	0.761513i	$-0.275543\pi$
$349$	24.2169	1.29630	0.648150	+	0.761513i	$0.275543\pi$
$350$	−1.43334	−0.0766150
$351$	1.00000	0.0533761
$352$	10.6929	0.569933
$353$	12.2564	0.652343	0.326172	−	0.945311i	$-0.394241\pi$
$353$	12.2564	0.652343	0.326172	+	0.945311i	$0.394241\pi$
$354$	−1.09485	−0.0581907
$355$	−3.53680	−0.187714
$356$	22.1408	1.17346
$357$	−15.4347	−0.816892
$358$	−3.36232	−0.177704
$359$	−3.43630	−0.181361	−0.0906806	−	0.995880i	$-0.528904\pi$
$359$	−3.43630	−0.181361	−0.0906806	+	0.995880i	$0.528904\pi$
$360$	−2.25988	−0.119106
$361$	12.9166	0.679820
$362$	−4.28978	−0.225466
$363$	1.45950	0.0766039
$364$	−6.06820	−0.318060
$365$	−22.6750	−1.18687
$366$	2.64574	0.138295
$367$	−13.3035	−0.694436	−0.347218	−	0.937784i	$-0.612874\pi$
$367$	−13.3035	−0.694436	−0.347218	+	0.937784i	$0.612874\pi$
$368$	22.0480	1.14933
$369$	−2.54543	−0.132510
$370$	5.57434	0.289796
$371$	−8.93282	−0.463769
$372$	2.96263	0.153605
$373$	16.0952	0.833379	0.416689	−	0.909049i	$-0.363190\pi$
$373$	16.0952	0.833379	0.416689	+	0.909049i	$0.363190\pi$
$374$	−4.60563	−0.238151
$375$	−12.1549	−0.627675
$376$	11.0184	0.568232
$377$	−1.13654	−0.0585349
$378$	−0.979900	−0.0504006
$379$	15.9649	0.820063	0.410032	−	0.912071i	$-0.365518\pi$
$379$	15.9649	0.820063	0.410032	+	0.912071i	$0.365518\pi$
$380$	20.2448	1.03854
$381$	2.70854	0.138763
$382$	0.593517	0.0303670
$383$	−37.7966	−1.93132	−0.965659	−	0.259814i	$-0.916339\pi$
$383$	−37.7966	−1.93132	−0.965659	+	0.259814i	$0.916339\pi$
$384$	−8.71341	−0.444654
$385$	−18.5015	−0.942926
$386$	−4.41977	−0.224960
$387$	−4.37951	−0.222623
$388$	22.0104	1.11741
$389$	−13.6873	−0.693974	−0.346987	−	0.937870i	$-0.612795\pi$
$389$	−13.6873	−0.693974	−0.346987	+	0.937870i	$0.612795\pi$
$390$	0.578664	0.0293018
$391$	−31.0526	−1.57040
$392$	3.77685	0.190760
$393$	−12.9163	−0.651540
$394$	0.868264	0.0437425
$395$	−14.4710	−0.728116
$396$	5.88514	0.295740
$397$	26.1528	1.31257	0.656286	−	0.754512i	$-0.272126\pi$
$397$	26.1528	1.31257	0.656286	+	0.754512i	$0.272126\pi$
$398$	−2.66741	−0.133705
$399$	17.9927	0.900762
$400$	−5.03324	−0.251662
$401$	5.55625	0.277466	0.138733	−	0.990330i	$-0.455697\pi$
$401$	5.55625	0.277466	0.138733	+	0.990330i	$0.455697\pi$
$402$	−3.32715	−0.165943
$403$	−1.55491	−0.0774557
$404$	6.80898	0.338759
$405$	−1.88076	−0.0934558
$406$	1.11370	0.0552719
$407$	−29.7545	−1.47488
$408$	5.82320	0.288291
$409$	39.1900	1.93782	0.968911	−	0.247411i	$-0.0795798\pi$
$409$	39.1900	1.93782	0.968911	+	0.247411i	$0.0795798\pi$
$410$	−1.47295	−0.0727437
$411$	−8.60965	−0.424683
$412$	1.90534	0.0938692
$413$	11.3332	0.557668
$414$	−1.97143	−0.0968904
$415$	−0.605955	−0.0297452
$416$	3.46186	0.169732
$417$	−5.89105	−0.288486
$418$	5.36892	0.262602
$419$	−6.97151	−0.340581	−0.170290	−	0.985394i	$-0.554471\pi$
$419$	−6.97151	−0.340581	−0.170290	+	0.985394i	$0.554471\pi$
$420$	11.4128	0.556890
$421$	36.6348	1.78547	0.892736	−	0.450581i	$-0.148783\pi$
$421$	36.6348	1.78547	0.892736	+	0.450581i	$0.148783\pi$
$422$	4.95901	0.241401
$423$	9.16997	0.445859
$424$	3.37017	0.163670
$425$	7.08886	0.343860
$426$	0.578589	0.0280327
$427$	−27.3869	−1.32535
$428$	11.1592	0.539400
$429$	−3.08877	−0.149127
$430$	−2.53426	−0.122213
$431$	−1.50312	−0.0724026	−0.0362013	−	0.999345i	$-0.511526\pi$
$431$	−1.50312	−0.0724026	−0.0362013	+	0.999345i	$0.511526\pi$
$432$	−3.44098	−0.165554
$433$	−18.3430	−0.881508	−0.440754	−	0.897628i	$-0.645289\pi$
$433$	−18.3430	−0.881508	−0.440754	+	0.897628i	$0.645289\pi$
$434$	1.52366	0.0731380
$435$	2.13756	0.102488
$436$	−20.6495	−0.988930
$437$	36.1989	1.73163
$438$	3.70943	0.177244
$439$	−11.1018	−0.529860	−0.264930	−	0.964268i	$-0.585349\pi$
$439$	−11.1018	−0.529860	−0.264930	+	0.964268i	$0.585349\pi$
$440$	6.98025	0.332770
$441$	3.14325	0.149678
$442$	−1.49109	−0.0709238
$443$	−32.6500	−1.55125	−0.775623	−	0.631196i	$-0.782564\pi$
$443$	−32.6500	−1.55125	−0.775623	+	0.631196i	$0.782564\pi$
$444$	18.3543	0.871058
$445$	21.8553	1.03604
$446$	−2.15522	−0.102053
$447$	17.5425	0.829733
$448$	18.5257	0.875256
$449$	23.1801	1.09394	0.546968	−	0.837153i	$-0.315782\pi$
$449$	23.1801	1.09394	0.546968	+	0.837153i	$0.315782\pi$
$450$	0.450049	0.0212155
$451$	7.86224	0.370218
$452$	−8.94586	−0.420778
$453$	10.6190	0.498922
$454$	6.48745	0.304471
$455$	−5.98994	−0.280813
$456$	−6.78828	−0.317890
$457$	13.6550	0.638756	0.319378	−	0.947627i	$-0.396526\pi$
$457$	13.6550	0.638756	0.319378	+	0.947627i	$0.396526\pi$
$458$	−6.99872	−0.327029
$459$	4.84630	0.226206
$460$	22.9611	1.07057
$461$	−16.8038	−0.782629	−0.391315	−	0.920257i	$-0.627980\pi$
$461$	−16.8038	−0.782629	−0.391315	+	0.920257i	$0.627980\pi$
$462$	3.02669	0.140814
$463$	−11.2077	−0.520868	−0.260434	−	0.965492i	$-0.583866\pi$
$463$	−11.2077	−0.520868	−0.260434	+	0.965492i	$0.583866\pi$
$464$	3.91081	0.181555
$465$	2.92442	0.135617
$466$	3.20842	0.148627
$467$	3.25959	0.150836	0.0754180	−	0.997152i	$-0.475971\pi$
$467$	3.25959	0.150836	0.0754180	+	0.997152i	$0.475971\pi$
$468$	1.90534	0.0880742
$469$	34.4404	1.59031
$470$	5.30633	0.244763
$471$	21.7611	1.00270
$472$	−4.27576	−0.196808
$473$	13.5273	0.621985
$474$	2.36733	0.108735
$475$	−8.26370	−0.379165
$476$	−29.4083	−1.34793
$477$	2.80479	0.128422
$478$	7.51614	0.343780
$479$	36.7358	1.67850	0.839250	−	0.543746i	$-0.182994\pi$
$479$	36.7358	1.67850	0.839250	+	0.543746i	$0.182994\pi$
$480$	−6.51093	−0.297182
$481$	−9.63312	−0.439232
$482$	6.82544	0.310890
$483$	20.4069	0.928544
$484$	2.78084	0.126402
$485$	21.7265	0.986551
$486$	0.307676	0.0139565
$487$	−27.8171	−1.26051	−0.630257	−	0.776386i	$-0.717051\pi$
$487$	−27.8171	−1.26051	−0.630257	+	0.776386i	$0.717051\pi$
$488$	10.3325	0.467731
$489$	3.33751	0.150927
$490$	1.81889	0.0821689
$491$	−8.60689	−0.388424	−0.194212	−	0.980960i	$-0.562215\pi$
$491$	−8.60689	−0.388424	−0.194212	+	0.980960i	$0.562215\pi$
$492$	−4.84989	−0.218650
$493$	−5.50802	−0.248069
$494$	1.73821	0.0782056
$495$	5.80924	0.261106
$496$	5.35042	0.240241
$497$	−5.98916	−0.268650
$498$	0.0991289	0.00444207
$499$	32.0695	1.43563	0.717813	−	0.696236i	$-0.245143\pi$
$499$	32.0695	1.43563	0.717813	+	0.696236i	$0.245143\pi$
$500$	−23.1591	−1.03571
$501$	0.598074	0.0267200
$502$	4.57407	0.204151
$503$	−26.1216	−1.16470	−0.582352	−	0.812937i	$-0.697868\pi$
$503$	−26.1216	−1.16470	−0.582352	+	0.812937i	$0.697868\pi$
$504$	−3.82684	−0.170461
$505$	6.72116	0.299088
$506$	6.08929	0.270702
$507$	−1.00000	−0.0444116
$508$	5.16069	0.228968
$509$	40.6560	1.80205	0.901024	−	0.433770i	$-0.142817\pi$
$509$	40.6560	1.80205	0.901024	+	0.433770i	$0.142817\pi$
$510$	2.80438	0.124180
$511$	−38.3975	−1.69861
$512$	−20.1814	−0.891899
$513$	−5.64948	−0.249430
$514$	−4.47795	−0.197514
$515$	1.88076	0.0828762
$516$	−8.34443	−0.367343
$517$	−28.3239	−1.24568
$518$	9.43949	0.414747
$519$	5.96891	0.262006
$520$	2.25988	0.0991022
$521$	−5.42218	−0.237550	−0.118775	−	0.992921i	$-0.537897\pi$
$521$	−5.42218	−0.237550	−0.118775	+	0.992921i	$0.537897\pi$
$522$	−0.349686	−0.0153054
$523$	13.9749	0.611080	0.305540	−	0.952179i	$-0.401163\pi$
$523$	13.9749	0.611080	0.305540	+	0.952179i	$0.401163\pi$
$524$	−24.6098	−1.07509
$525$	−4.65859	−0.203318
$526$	−4.35114	−0.189719
$527$	−7.53557	−0.328255
$528$	10.6284	0.462541
$529$	18.0559	0.785038
$530$	1.62303	0.0705000
$531$	−3.55846	−0.154424
$532$	34.2822	1.48632
$533$	2.54543	0.110255
$534$	−3.57532	−0.154719
$535$	11.0153	0.476232
$536$	−12.9936	−0.561240
$537$	−10.9281	−0.471583
$538$	3.55407	0.153227
$539$	−9.70877	−0.418186
$540$	−3.58348	−0.154208
$541$	5.62038	0.241639	0.120819	−	0.992674i	$-0.461448\pi$
$541$	5.62038	0.241639	0.120819	+	0.992674i	$0.461448\pi$
$542$	−6.82816	−0.293295
$543$	−13.9425	−0.598331
$544$	16.7772	0.719316
$545$	−20.3831	−0.873118
$546$	0.979900	0.0419358
$547$	28.7866	1.23083	0.615413	−	0.788205i	$-0.288989\pi$
$547$	28.7866	1.23083	0.615413	+	0.788205i	$0.288989\pi$
$548$	−16.4043	−0.700756
$549$	8.59913	0.367002
$550$	−1.39010	−0.0592739
$551$	6.42087	0.273538
$552$	−7.69909	−0.327695
$553$	−24.5049	−1.04206
$554$	3.81263	0.161983
$555$	18.1176	0.769049
$556$	−11.2244	−0.476022
$557$	−17.2323	−0.730157	−0.365079	−	0.930977i	$-0.618958\pi$
$557$	−17.2323	−0.730157	−0.365079	+	0.930977i	$0.618958\pi$
$558$	−0.478409	−0.0202527
$559$	4.37951	0.185233
$560$	20.6112	0.870983
$561$	−14.9691	−0.631996
$562$	−1.11207	−0.0469097
$563$	23.3887	0.985715	0.492857	−	0.870110i	$-0.335952\pi$
$563$	23.3887	0.985715	0.492857	+	0.870110i	$0.335952\pi$
$564$	17.4719	0.735698
$565$	−8.83048	−0.371501
$566$	4.67891	0.196669
$567$	−3.18485	−0.133751
$568$	2.25958	0.0948101
$569$	−23.0674	−0.967034	−0.483517	−	0.875335i	$-0.660641\pi$
$569$	−23.0674	−0.967034	−0.483517	+	0.875335i	$0.660641\pi$
$570$	−3.26915	−0.136930
$571$	−24.9603	−1.04456	−0.522278	−	0.852776i	$-0.674918\pi$
$571$	−24.9603	−1.04456	−0.522278	+	0.852776i	$0.674918\pi$
$572$	−5.88514	−0.246070
$573$	1.92904	0.0805866
$574$	−2.49426	−0.104109
$575$	−9.37247	−0.390859
$576$	−5.81682	−0.242368
$577$	−32.3961	−1.34867	−0.674334	−	0.738426i	$-0.735569\pi$
$577$	−32.3961	−1.34867	−0.674334	+	0.738426i	$0.735569\pi$
$578$	−1.99577	−0.0830133
$579$	−14.3650	−0.596990
$580$	4.07278	0.169113
$581$	−1.02611	−0.0425704
$582$	−3.55427	−0.147329
$583$	−8.66334	−0.358799
$584$	14.4866	0.599459
$585$	1.88076	0.0777599
$586$	−0.766021	−0.0316440
$587$	3.85697	0.159194	0.0795971	−	0.996827i	$-0.474637\pi$
$587$	3.85697	0.159194	0.0795971	+	0.996827i	$0.474637\pi$
$588$	5.98894	0.246980
$589$	8.78445	0.361957
$590$	−2.05916	−0.0847741
$591$	2.82201	0.116082
$592$	33.1473	1.36235
$593$	−27.0531	−1.11094	−0.555469	−	0.831537i	$-0.687461\pi$
$593$	−27.0531	−1.11094	−0.555469	+	0.831537i	$0.687461\pi$
$594$	−0.950339	−0.0389929
$595$	−29.0290	−1.19007
$596$	33.4244	1.36912
$597$	−8.66955	−0.354821
$598$	1.97143	0.0806177
$599$	−15.6622	−0.639939	−0.319970	−	0.947428i	$-0.603673\pi$
$599$	−15.6622	−0.639939	−0.319970	+	0.947428i	$0.603673\pi$
$600$	1.75759	0.0717534
$601$	35.9604	1.46686	0.733428	−	0.679767i	$-0.237919\pi$
$601$	35.9604	1.46686	0.733428	+	0.679767i	$0.237919\pi$
$602$	−4.29148	−0.174908
$603$	−10.8138	−0.440373
$604$	20.2327	0.823256
$605$	2.74497	0.111599
$606$	−1.09952	−0.0446650
$607$	17.3658	0.704855	0.352427	−	0.935839i	$-0.385356\pi$
$607$	17.3658	0.704855	0.352427	+	0.935839i	$0.385356\pi$
$608$	−19.5577	−0.793169
$609$	3.61971	0.146678
$610$	4.97601	0.201473
$611$	−9.16997	−0.370977
$612$	9.23383	0.373255
$613$	14.8285	0.598916	0.299458	−	0.954109i	$-0.403194\pi$
$613$	14.8285	0.598916	0.299458	+	0.954109i	$0.403194\pi$
$614$	1.87222	0.0755566
$615$	−4.78734	−0.193044
$616$	11.8202	0.476250
$617$	−13.3967	−0.539332	−0.269666	−	0.962954i	$-0.586913\pi$
$617$	−13.3967	−0.539332	−0.269666	+	0.962954i	$0.586913\pi$
$618$	−0.307676	−0.0123765
$619$	−37.9635	−1.52588	−0.762941	−	0.646468i	$-0.776245\pi$
$619$	−37.9635	−1.52588	−0.762941	+	0.646468i	$0.776245\pi$
$620$	5.57200	0.223777
$621$	−6.40749	−0.257124
$622$	3.70168	0.148424
$623$	37.0093	1.48275
$624$	3.44098	0.137749
$625$	−15.5467	−0.621869
$626$	0.609167	0.0243472
$627$	17.4499	0.696883
$628$	41.4622	1.65452
$629$	−46.6850	−1.86145
$630$	−1.84296	−0.0734252
$631$	−14.0261	−0.558370	−0.279185	−	0.960237i	$-0.590064\pi$
$631$	−14.0261	−0.558370	−0.279185	+	0.960237i	$0.590064\pi$
$632$	9.24521	0.367755
$633$	16.1177	0.640620
$634$	10.1437	0.402859
$635$	5.09413	0.202154
$636$	5.34406	0.211906
$637$	−3.14325	−0.124540
$638$	1.08010	0.0427616
$639$	1.88052	0.0743921
$640$	−16.3878	−0.647786
$641$	2.49012	0.0983537	0.0491768	−	0.998790i	$-0.484340\pi$
$641$	2.49012	0.0983537	0.0491768	+	0.998790i	$0.484340\pi$
$642$	−1.80200	−0.0711193
$643$	26.3218	1.03803	0.519015	−	0.854765i	$-0.326299\pi$
$643$	26.3218	1.03803	0.519015	+	0.854765i	$0.326299\pi$
$644$	38.8819	1.53216
$645$	−8.23680	−0.324324
$646$	8.42387	0.331433
$647$	−5.50523	−0.216433	−0.108216	−	0.994127i	$-0.534514\pi$
$647$	−5.50523	−0.216433	−0.108216	+	0.994127i	$0.534514\pi$
$648$	1.20158	0.0472024
$649$	10.9913	0.431445
$650$	−0.450049	−0.0176524
$651$	4.95216	0.194090
$652$	6.35908	0.249041
$653$	−37.3824	−1.46289	−0.731443	−	0.681903i	$-0.761153\pi$
$653$	−37.3824	−1.46289	−0.731443	+	0.681903i	$0.761153\pi$
$654$	3.33450	0.130389
$655$	−24.2924	−0.949183
$656$	−8.75875	−0.341972
$657$	12.0563	0.470361
$658$	8.98565	0.350297
$659$	10.5790	0.412100	0.206050	−	0.978541i	$-0.433939\pi$
$659$	10.5790	0.412100	0.206050	+	0.978541i	$0.433939\pi$
$660$	11.0686	0.430843
$661$	20.5956	0.801077	0.400538	−	0.916280i	$-0.368823\pi$
$661$	20.5956	0.801077	0.400538	+	0.916280i	$0.368823\pi$
$662$	−5.99069	−0.232835
$663$	−4.84630	−0.188215
$664$	0.387131	0.0150236
$665$	33.8400	1.31226
$666$	−2.96388	−0.114848
$667$	7.28238	0.281975
$668$	1.13953	0.0440898
$669$	−7.00485	−0.270823
$670$	−6.25758	−0.241751
$671$	−26.5607	−1.02537
$672$	−11.0255	−0.425317
$673$	−3.75259	−0.144652	−0.0723258	−	0.997381i	$-0.523042\pi$
$673$	−3.75259	−0.144652	−0.0723258	+	0.997381i	$0.523042\pi$
$674$	−0.717847	−0.0276504
$675$	1.46274	0.0563008
$676$	−1.90534	−0.0732821
$677$	13.8921	0.533915	0.266958	−	0.963708i	$-0.413982\pi$
$677$	13.8921	0.533915	0.266958	+	0.963708i	$0.413982\pi$
$678$	1.44459	0.0554790
$679$	36.7913	1.41192
$680$	10.9520	0.419992
$681$	21.0854	0.807993
$682$	1.47770	0.0565839
$683$	−8.53370	−0.326533	−0.163266	−	0.986582i	$-0.552203\pi$
$683$	−8.53370	−0.326533	−0.163266	+	0.986582i	$0.552203\pi$
$684$	−10.7641	−0.411578
$685$	−16.1927	−0.618691
$686$	−3.77923	−0.144292
$687$	−22.7471	−0.867855
$688$	−15.0698	−0.574530
$689$	−2.80479	−0.106854
$690$	−3.70778	−0.141153
$691$	−30.4960	−1.16012	−0.580062	−	0.814572i	$-0.696972\pi$
$691$	−30.4960	−1.16012	−0.580062	+	0.814572i	$0.696972\pi$
$692$	11.3728	0.432328
$693$	9.83726	0.373687
$694$	4.62036	0.175387
$695$	−11.0797	−0.420275
$696$	−1.36564	−0.0517646
$697$	12.3359	0.467256
$698$	−7.45094	−0.282022
$699$	10.4279	0.394421
$700$	−8.87619	−0.335488
$701$	27.9782	1.05672	0.528361	−	0.849020i	$-0.322807\pi$
$701$	27.9782	1.05672	0.528361	+	0.849020i	$0.322807\pi$
$702$	−0.307676	−0.0116125
$703$	54.4221	2.05257
$704$	17.9668	0.677150
$705$	17.2465	0.649541
$706$	−3.77100	−0.141923
$707$	11.3815	0.428045
$708$	−6.78006	−0.254810
$709$	−30.6880	−1.15251	−0.576256	−	0.817270i	$-0.695487\pi$
$709$	−30.6880	−1.15251	−0.576256	+	0.817270i	$0.695487\pi$
$710$	1.08819	0.0408390
$711$	7.69423	0.288556
$712$	−13.9628	−0.523280
$713$	9.96308	0.373120
$714$	4.74889	0.177723
$715$	−5.80924	−0.217253
$716$	−20.8217	−0.778145
$717$	24.4288	0.912310
$718$	1.05727	0.0394568
$719$	−44.5388	−1.66102	−0.830509	−	0.557005i	$-0.811951\pi$
$719$	−44.5388	−1.66102	−0.830509	+	0.557005i	$0.811951\pi$
$720$	−6.47165	−0.241184
$721$	3.18485	0.118610
$722$	−3.97412	−0.147901
$723$	22.1839	0.825027
$724$	−26.5652	−0.987288
$725$	−1.66246	−0.0617423
$726$	−0.449053	−0.0166659
$727$	50.9168	1.88840	0.944200	−	0.329373i	$-0.106837\pi$
$727$	50.9168	1.88840	0.944200	+	0.329373i	$0.106837\pi$
$728$	3.82684	0.141832
$729$	1.00000	0.0370370
$730$	6.97656	0.258214
$731$	21.2244	0.785013
$732$	16.3842	0.605579
$733$	−15.9817	−0.590297	−0.295149	−	0.955451i	$-0.595369\pi$
$733$	−15.9817	−0.590297	−0.295149	+	0.955451i	$0.595369\pi$
$734$	4.09316	0.151081
$735$	5.91170	0.218056
$736$	−22.1818	−0.817632
$737$	33.4014	1.23036
$738$	0.783166	0.0288287
$739$	38.9167	1.43157	0.715787	−	0.698319i	$-0.246068\pi$
$739$	38.9167	1.43157	0.715787	+	0.698319i	$0.246068\pi$
$740$	34.5201	1.26898
$741$	5.64948	0.207539
$742$	2.74841	0.100897
$743$	−23.3053	−0.854989	−0.427495	−	0.904018i	$-0.640604\pi$
$743$	−23.3053	−0.854989	−0.427495	+	0.904018i	$0.640604\pi$
$744$	−1.86835	−0.0684969
$745$	32.9933	1.20878
$746$	−4.95211	−0.181310
$747$	0.322186	0.0117882
$748$	−28.5212	−1.04284
$749$	18.6531	0.681568
$750$	3.73976	0.136557
$751$	−36.6145	−1.33608	−0.668042	−	0.744124i	$-0.732867\pi$
$751$	−36.6145	−1.33608	−0.668042	+	0.744124i	$0.732867\pi$
$752$	31.5536	1.15064
$753$	14.8665	0.541767
$754$	0.349686	0.0127348
$755$	19.9717	0.726845
$756$	−6.06820	−0.220698
$757$	−23.5592	−0.856274	−0.428137	−	0.903714i	$-0.640830\pi$
$757$	−23.5592	−0.856274	−0.428137	+	0.903714i	$0.640830\pi$
$758$	−4.91202	−0.178413
$759$	19.7913	0.718377
$760$	−12.7671	−0.463113
$761$	−31.4673	−1.14069	−0.570345	−	0.821405i	$-0.693191\pi$
$761$	−31.4673	−1.14069	−0.570345	+	0.821405i	$0.693191\pi$
$762$	−0.833353	−0.0301892
$763$	−34.5164	−1.24958
$764$	3.67546	0.132974
$765$	9.11473	0.329544
$766$	11.6291	0.420177
$767$	3.55846	0.128489
$768$	−8.95274	−0.323054
$769$	28.0815	1.01264	0.506322	−	0.862344i	$-0.331005\pi$
$769$	28.0815	1.01264	0.506322	+	0.862344i	$0.331005\pi$
$770$	5.69247	0.205142
$771$	−14.5541	−0.524154
$772$	−27.3702	−0.985075
$773$	32.5055	1.16914	0.584571	−	0.811343i	$-0.301263\pi$
$773$	32.5055	1.16914	0.584571	+	0.811343i	$0.301263\pi$
$774$	1.34747	0.0484337
$775$	−2.27443	−0.0816999
$776$	−13.8806	−0.498284
$777$	30.6800	1.10064
$778$	4.21125	0.150981
$779$	−14.3803	−0.515229
$780$	3.58348	0.128309
$781$	−5.80848	−0.207844
$782$	9.55413	0.341655
$783$	−1.13654	−0.0406167
$784$	10.8158	0.386280
$785$	40.9275	1.46076
$786$	3.97402	0.141749
$787$	−51.9820	−1.85296	−0.926479	−	0.376347i	$-0.877180\pi$
$787$	−51.9820	−1.85296	−0.926479	+	0.376347i	$0.877180\pi$
$788$	5.37688	0.191543
$789$	−14.1420	−0.503467
$790$	4.45238	0.158408
$791$	−14.9534	−0.531680
$792$	−3.71139	−0.131879
$793$	−8.59913	−0.305364
$794$	−8.04659	−0.285563
$795$	5.27514	0.187090
$796$	−16.5184	−0.585479
$797$	43.8739	1.55409	0.777046	−	0.629443i	$-0.216717\pi$
$797$	43.8739	1.55409	0.777046	+	0.629443i	$0.216717\pi$
$798$	−5.53592	−0.195969
$799$	−44.4404	−1.57219
$800$	5.06379	0.179032
$801$	−11.6204	−0.410588
$802$	−1.70952	−0.0603653
$803$	−37.2392	−1.31414
$804$	−20.6040	−0.726646
$805$	38.3804	1.35273
$806$	0.478409	0.0168512
$807$	11.5513	0.406627
$808$	−4.29400	−0.151062
$809$	45.2447	1.59072	0.795359	−	0.606138i	$-0.207282\pi$
$809$	45.2447	1.59072	0.795359	+	0.606138i	$0.207282\pi$
$810$	0.578664	0.0203322
$811$	−12.8457	−0.451073	−0.225537	−	0.974235i	$-0.572414\pi$
$811$	−12.8457	−0.451073	−0.225537	+	0.974235i	$0.572414\pi$
$812$	6.89677	0.242029
$813$	−22.1927	−0.778333
$814$	9.15473	0.320873
$815$	6.27706	0.219876
$816$	16.6760	0.583777
$817$	−24.7419	−0.865610
$818$	−12.0578	−0.421591
$819$	3.18485	0.111288
$820$	−9.12149	−0.318536
$821$	−27.8055	−0.970419	−0.485210	−	0.874398i	$-0.661257\pi$
$821$	−27.8055	−0.970419	−0.485210	+	0.874398i	$0.661257\pi$
$822$	2.64898	0.0923937
$823$	7.74762	0.270065	0.135032	−	0.990841i	$-0.456886\pi$
$823$	7.74762	0.270065	0.135032	+	0.990841i	$0.456886\pi$
$824$	−1.20158	−0.0418589
$825$	−4.51806	−0.157299
$826$	−3.48694	−0.121326
$827$	16.9179	0.588292	0.294146	−	0.955761i	$-0.404965\pi$
$827$	16.9179	0.588292	0.294146	+	0.955761i	$0.404965\pi$
$828$	−12.2084	−0.424272
$829$	−6.60452	−0.229384	−0.114692	−	0.993401i	$-0.536588\pi$
$829$	−6.60452	−0.229384	−0.114692	+	0.993401i	$0.536588\pi$
$830$	0.186438	0.00647135
$831$	12.3917	0.429864
$832$	5.81682	0.201662
$833$	−15.2331	−0.527796
$834$	1.81253	0.0627629
$835$	1.12483	0.0389265
$836$	33.2480	1.14991
$837$	−1.55491	−0.0537457
$838$	2.14496	0.0740966
$839$	16.7790	0.579275	0.289637	−	0.957136i	$-0.406465\pi$
$839$	16.7790	0.579275	0.289637	+	0.957136i	$0.406465\pi$
$840$	−7.19737	−0.248333
$841$	−27.7083	−0.955458
$842$	−11.2716	−0.388446
$843$	−3.61441	−0.124487
$844$	30.7096	1.05707
$845$	−1.88076	−0.0647002
$846$	−2.82138	−0.0970009
$847$	4.64828	0.159717
$848$	9.65121	0.331424
$849$	15.2073	0.521913
$850$	−2.18107	−0.0748101
$851$	61.7241	2.11587
$852$	3.58302	0.122752
$853$	13.9971	0.479251	0.239626	−	0.970865i	$-0.422975\pi$
$853$	13.9971	0.479251	0.239626	+	0.970865i	$0.422975\pi$
$854$	8.42629	0.288342
$855$	−10.6253	−0.363378
$856$	−7.03741	−0.240534
$857$	−50.1498	−1.71308	−0.856542	−	0.516078i	$-0.827392\pi$
$857$	−50.1498	−1.71308	−0.856542	+	0.516078i	$0.827392\pi$
$858$	0.950339	0.0324440
$859$	−6.62371	−0.225998	−0.112999	−	0.993595i	$-0.536046\pi$
$859$	−6.62371	−0.225998	−0.112999	+	0.993595i	$0.536046\pi$
$860$	−15.6939	−0.535157
$861$	−8.10680	−0.276279
$862$	0.462473	0.0157519
$863$	−51.4156	−1.75021	−0.875103	−	0.483937i	$-0.839207\pi$
$863$	−51.4156	−1.75021	−0.875103	+	0.483937i	$0.839207\pi$
$864$	3.46186	0.117775
$865$	11.2261	0.381699
$866$	5.64369	0.191780
$867$	−6.48662	−0.220297
$868$	9.43553	0.320263
$869$	−23.7657	−0.806196
$870$	−0.657677	−0.0222973
$871$	10.8138	0.366413
$872$	13.0223	0.440992
$873$	−11.5520	−0.390976
$874$	−11.1375	−0.376733
$875$	−38.7114	−1.30868
$876$	22.9713	0.776129
$877$	52.8446	1.78444	0.892218	−	0.451606i	$-0.149149\pi$
$877$	52.8446	1.78444	0.892218	+	0.451606i	$0.149149\pi$
$878$	3.41575	0.115276
$879$	−2.48970	−0.0839755
$880$	19.9894	0.673844
$881$	53.8292	1.81355	0.906775	−	0.421614i	$-0.138536\pi$
$881$	53.8292	1.81355	0.906775	+	0.421614i	$0.138536\pi$
$882$	−0.967101	−0.0325640
$883$	−22.7835	−0.766726	−0.383363	−	0.923598i	$-0.625234\pi$
$883$	−22.7835	−0.766726	−0.383363	+	0.923598i	$0.625234\pi$
$884$	−9.23383	−0.310567
$885$	−6.69262	−0.224970
$886$	10.0456	0.337489
$887$	18.2571	0.613015	0.306507	−	0.951868i	$-0.400840\pi$
$887$	18.2571	0.613015	0.306507	+	0.951868i	$0.400840\pi$
$888$	−11.5749	−0.388429
$889$	8.62630	0.289317
$890$	−6.72433	−0.225400
$891$	−3.08877	−0.103478
$892$	−13.3466	−0.446877
$893$	51.8055	1.73361
$894$	−5.39741	−0.180516
$895$	−20.5532	−0.687017
$896$	−27.7509	−0.927092
$897$	6.40749	0.213940
$898$	−7.13195	−0.237996
$899$	1.76722	0.0589402
$900$	2.78701	0.0929002
$901$	−13.5928	−0.452843
$902$	−2.41902	−0.0805445
$903$	−13.9481	−0.464162
$904$	5.64160	0.187637
$905$	−26.2226	−0.871668
$906$	−3.26719	−0.108545
$907$	−19.5780	−0.650075	−0.325038	−	0.945701i	$-0.605377\pi$
$907$	−19.5780	−0.650075	−0.325038	+	0.945701i	$0.605377\pi$
$908$	40.1747	1.33324
$909$	−3.57364	−0.118530
$910$	1.84296	0.0610934
$911$	−38.5379	−1.27682	−0.638409	−	0.769698i	$-0.720407\pi$
$911$	−38.5379	−1.27682	−0.638409	+	0.769698i	$0.720407\pi$
$912$	−19.4397	−0.643713
$913$	−0.995159	−0.0329350
$914$	−4.20132	−0.138967
$915$	16.1729	0.534660
$916$	−43.3408	−1.43202
$917$	−41.1363	−1.35844
$918$	−1.49109	−0.0492132
$919$	−12.6247	−0.416452	−0.208226	−	0.978081i	$-0.566769\pi$
$919$	−12.6247	−0.416452	−0.208226	+	0.978081i	$0.566769\pi$
$920$	−14.4801	−0.477396
$921$	6.08504	0.200509
$922$	5.17011	0.170268
$923$	−1.88052	−0.0618980
$924$	18.7433	0.616609
$925$	−14.0907	−0.463300
$926$	3.44835	0.113320
$927$	−1.00000	−0.0328443
$928$	−3.93455	−0.129158
$929$	10.1397	0.332674	0.166337	−	0.986069i	$-0.446806\pi$
$929$	10.1397	0.332674	0.166337	+	0.986069i	$0.446806\pi$
$930$	−0.899773	−0.0295047
$931$	17.7577	0.581985
$932$	19.8687	0.650821
$933$	12.0311	0.393881
$934$	−1.00290	−0.0328158
$935$	−28.1533	−0.920712
$936$	−1.20158	−0.0392748
$937$	45.9657	1.50163	0.750816	−	0.660511i	$-0.229660\pi$
$937$	45.9657	1.50163	0.750816	+	0.660511i	$0.229660\pi$
$938$	−10.5965	−0.345987
$939$	1.97990	0.0646116
$940$	32.8604	1.07179
$941$	12.4186	0.404836	0.202418	−	0.979299i	$-0.435120\pi$
$941$	12.4186	0.404836	0.202418	+	0.979299i	$0.435120\pi$
$942$	−6.69537	−0.218147
$943$	−16.3098	−0.531120
$944$	−12.2446	−0.398527
$945$	−5.98994	−0.194853
$946$	−4.16202	−0.135319
$947$	17.5035	0.568788	0.284394	−	0.958707i	$-0.408208\pi$
$947$	17.5035	0.568788	0.284394	+	0.958707i	$0.408208\pi$
$948$	14.6601	0.476138
$949$	−12.0563	−0.391364
$950$	2.54254	0.0824909
$951$	32.9689	1.06909
$952$	18.5460	0.601079
$953$	16.1961	0.524644	0.262322	−	0.964980i	$-0.415512\pi$
$953$	16.1961	0.524644	0.262322	+	0.964980i	$0.415512\pi$
$954$	−0.862965	−0.0279395
$955$	3.62806	0.117401
$956$	46.5450	1.50537
$957$	3.51052	0.113479
$958$	−11.3027	−0.365174
$959$	−27.4204	−0.885451
$960$	−10.9401	−0.353089
$961$	−28.5822	−0.922008
$962$	2.96388	0.0955592
$963$	−5.85682	−0.188733
$964$	42.2677	1.36135
$965$	−27.0172	−0.869714
$966$	−6.27869	−0.202014
$967$	34.4075	1.10647	0.553235	−	0.833026i	$-0.313393\pi$
$967$	34.4075	1.10647	0.553235	+	0.833026i	$0.313393\pi$
$968$	−1.75370	−0.0563661
$969$	27.3791	0.879542
$970$	−6.68472	−0.214634
$971$	50.2690	1.61321	0.806604	−	0.591092i	$-0.201303\pi$
$971$	50.2690	1.61321	0.806604	+	0.591092i	$0.201303\pi$
$972$	1.90534	0.0611137
$973$	−18.7621	−0.601485
$974$	8.55865	0.274237
$975$	−1.46274	−0.0468451
$976$	29.5894	0.947134
$977$	26.7966	0.857298	0.428649	−	0.903471i	$-0.358990\pi$
$977$	26.7966	0.857298	0.428649	+	0.903471i	$0.358990\pi$
$978$	−1.02687	−0.0328357
$979$	35.8928	1.14714
$980$	11.2638	0.359808
$981$	10.8377	0.346021
$982$	2.64813	0.0845053
$983$	−13.2492	−0.422583	−0.211291	−	0.977423i	$-0.567767\pi$
$983$	−13.2492	−0.422583	−0.211291	+	0.977423i	$0.567767\pi$
$984$	3.05853	0.0975022
$985$	5.30753	0.169112
$986$	1.69468	0.0539698
$987$	29.2049	0.929603
$988$	10.7641	0.342453
$989$	−28.0616	−0.892308
$990$	−1.78736	−0.0568061
$991$	18.5577	0.589505	0.294752	−	0.955574i	$-0.404763\pi$
$991$	18.5577	0.589505	0.294752	+	0.955574i	$0.404763\pi$
$992$	−5.38289	−0.170907
$993$	−19.4708	−0.617887
$994$	1.84272	0.0584475
$995$	−16.3054	−0.516915
$996$	0.613873	0.0194513
$997$	−21.5801	−0.683448	−0.341724	−	0.939800i	$-0.611011\pi$
$997$	−21.5801	−0.683448	−0.341724	+	0.939800i	$0.611011\pi$
$998$	−9.86699	−0.312334
$999$	−9.63312	−0.304778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.12	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.12	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.307676 q^{2} -1.00000 q^{3} -1.90534 q^{4} -1.88076 q^{5} +0.307676 q^{6} -3.18485 q^{7} +1.20158 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.307676 q^{2} -1.00000 q^{3} -1.90534 q^{4} -1.88076 q^{5} +0.307676 q^{6} -3.18485 q^{7} +1.20158 q^{8} +1.00000 q^{9} +0.578664 q^{10} -3.08877 q^{11} +1.90534 q^{12} -1.00000 q^{13} +0.979900 q^{14} +1.88076 q^{15} +3.44098 q^{16} -4.84630 q^{17} -0.307676 q^{18} +5.64948 q^{19} +3.58348 q^{20} +3.18485 q^{21} +0.950339 q^{22} +6.40749 q^{23} -1.20158 q^{24} -1.46274 q^{25} +0.307676 q^{26} -1.00000 q^{27} +6.06820 q^{28} +1.13654 q^{29} -0.578664 q^{30} +1.55491 q^{31} -3.46186 q^{32} +3.08877 q^{33} +1.49109 q^{34} +5.98994 q^{35} -1.90534 q^{36} +9.63312 q^{37} -1.73821 q^{38} +1.00000 q^{39} -2.25988 q^{40} -2.54543 q^{41} -0.979900 q^{42} -4.37951 q^{43} +5.88514 q^{44} -1.88076 q^{45} -1.97143 q^{46} +9.16997 q^{47} -3.44098 q^{48} +3.14325 q^{49} +0.450049 q^{50} +4.84630 q^{51} +1.90534 q^{52} +2.80479 q^{53} +0.307676 q^{54} +5.80924 q^{55} -3.82684 q^{56} -5.64948 q^{57} -0.349686 q^{58} -3.55846 q^{59} -3.58348 q^{60} +8.59913 q^{61} -0.478409 q^{62} -3.18485 q^{63} -5.81682 q^{64} +1.88076 q^{65} -0.950339 q^{66} -10.8138 q^{67} +9.23383 q^{68} -6.40749 q^{69} -1.84296 q^{70} +1.88052 q^{71} +1.20158 q^{72} +12.0563 q^{73} -2.96388 q^{74} +1.46274 q^{75} -10.7641 q^{76} +9.83726 q^{77} -0.307676 q^{78} +7.69423 q^{79} -6.47165 q^{80} +1.00000 q^{81} +0.783166 q^{82} +0.322186 q^{83} -6.06820 q^{84} +9.11473 q^{85} +1.34747 q^{86} -1.13654 q^{87} -3.71139 q^{88} -11.6204 q^{89} +0.578664 q^{90} +3.18485 q^{91} -12.2084 q^{92} -1.55491 q^{93} -2.82138 q^{94} -10.6253 q^{95} +3.46186 q^{96} -11.5520 q^{97} -0.967101 q^{98} -3.08877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more