LMFDB - Embedded newform 6026.2.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.11947 q^{3} +1.00000 q^{4} +1.71773 q^{5} -1.11947 q^{6} +3.78646 q^{7} -1.00000 q^{8} -1.74680 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.11947 q^{3} +1.00000 q^{4} +1.71773 q^{5} -1.11947 q^{6} +3.78646 q^{7} -1.00000 q^{8} -1.74680 q^{9} -1.71773 q^{10} -5.02853 q^{11} +1.11947 q^{12} -1.13725 q^{13} -3.78646 q^{14} +1.92293 q^{15} +1.00000 q^{16} -2.02110 q^{17} +1.74680 q^{18} -3.45188 q^{19} +1.71773 q^{20} +4.23882 q^{21} +5.02853 q^{22} -1.00000 q^{23} -1.11947 q^{24} -2.04942 q^{25} +1.13725 q^{26} -5.31387 q^{27} +3.78646 q^{28} +3.63249 q^{29} -1.92293 q^{30} -2.60130 q^{31} -1.00000 q^{32} -5.62926 q^{33} +2.02110 q^{34} +6.50411 q^{35} -1.74680 q^{36} +6.85095 q^{37} +3.45188 q^{38} -1.27311 q^{39} -1.71773 q^{40} +0.0708493 q^{41} -4.23882 q^{42} -10.0539 q^{43} -5.02853 q^{44} -3.00052 q^{45} +1.00000 q^{46} +9.72463 q^{47} +1.11947 q^{48} +7.33731 q^{49} +2.04942 q^{50} -2.26255 q^{51} -1.13725 q^{52} +4.37827 q^{53} +5.31387 q^{54} -8.63764 q^{55} -3.78646 q^{56} -3.86426 q^{57} -3.63249 q^{58} -4.09523 q^{59} +1.92293 q^{60} -7.58965 q^{61} +2.60130 q^{62} -6.61419 q^{63} +1.00000 q^{64} -1.95348 q^{65} +5.62926 q^{66} +6.77221 q^{67} -2.02110 q^{68} -1.11947 q^{69} -6.50411 q^{70} +7.67491 q^{71} +1.74680 q^{72} +0.694157 q^{73} -6.85095 q^{74} -2.29425 q^{75} -3.45188 q^{76} -19.0403 q^{77} +1.27311 q^{78} -6.56104 q^{79} +1.71773 q^{80} -0.708306 q^{81} -0.0708493 q^{82} -6.10921 q^{83} +4.23882 q^{84} -3.47170 q^{85} +10.0539 q^{86} +4.06644 q^{87} +5.02853 q^{88} +0.281878 q^{89} +3.00052 q^{90} -4.30614 q^{91} -1.00000 q^{92} -2.91207 q^{93} -9.72463 q^{94} -5.92938 q^{95} -1.11947 q^{96} -5.35678 q^{97} -7.33731 q^{98} +8.78382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	1.11947	0.646324	0.323162	−	0.946344i	$-0.395254\pi$
$3$	1.11947	0.646324	0.323162	+	0.946344i	$0.395254\pi$
$4$	1.00000	0.500000
$5$	1.71773	0.768190	0.384095	−	0.923294i	$-0.374513\pi$
$5$	1.71773	0.768190	0.384095	+	0.923294i	$0.374513\pi$
$6$	−1.11947	−0.457020
$7$	3.78646	1.43115	0.715574	−	0.698536i	$-0.246165\pi$
$7$	3.78646	1.43115	0.715574	+	0.698536i	$0.246165\pi$
$8$	−1.00000	−0.353553
$9$	−1.74680	−0.582266
$10$	−1.71773	−0.543193
$11$	−5.02853	−1.51616	−0.758079	−	0.652162i	$-0.773862\pi$
$11$	−5.02853	−1.51616	−0.758079	+	0.652162i	$0.773862\pi$
$12$	1.11947	0.323162
$13$	−1.13725	−0.315415	−0.157708	−	0.987486i	$-0.550410\pi$
$13$	−1.13725	−0.315415	−0.157708	+	0.987486i	$0.550410\pi$
$14$	−3.78646	−1.01198
$15$	1.92293	0.496500
$16$	1.00000	0.250000
$17$	−2.02110	−0.490189	−0.245095	−	0.969499i	$-0.578819\pi$
$17$	−2.02110	−0.490189	−0.245095	+	0.969499i	$0.578819\pi$
$18$	1.74680	0.411724
$19$	−3.45188	−0.791915	−0.395958	−	0.918269i	$-0.629587\pi$
$19$	−3.45188	−0.791915	−0.395958	+	0.918269i	$0.629587\pi$
$20$	1.71773	0.384095
$21$	4.23882	0.924985
$22$	5.02853	1.07209
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.11947	−0.228510
$25$	−2.04942	−0.409884
$26$	1.13725	0.223032
$27$	−5.31387	−1.02266
$28$	3.78646	0.715574
$29$	3.63249	0.674536	0.337268	−	0.941409i	$-0.390497\pi$
$29$	3.63249	0.674536	0.337268	+	0.941409i	$0.390497\pi$
$30$	−1.92293	−0.351078
$31$	−2.60130	−0.467208	−0.233604	−	0.972332i	$-0.575052\pi$
$31$	−2.60130	−0.467208	−0.233604	+	0.972332i	$0.575052\pi$
$32$	−1.00000	−0.176777
$33$	−5.62926	−0.979929
$34$	2.02110	0.346616
$35$	6.50411	1.09939
$36$	−1.74680	−0.291133
$37$	6.85095	1.12629	0.563145	−	0.826358i	$-0.309591\pi$
$37$	6.85095	1.12629	0.563145	+	0.826358i	$0.309591\pi$
$38$	3.45188	0.559969
$39$	−1.27311	−0.203860
$40$	−1.71773	−0.271596
$41$	0.0708493	0.0110648	0.00553240	−	0.999985i	$-0.498239\pi$
$41$	0.0708493	0.0110648	0.00553240	+	0.999985i	$0.498239\pi$
$42$	−4.23882	−0.654063
$43$	−10.0539	−1.53321	−0.766604	−	0.642120i	$-0.778055\pi$
$43$	−10.0539	−1.53321	−0.766604	+	0.642120i	$0.778055\pi$
$44$	−5.02853	−0.758079
$45$	−3.00052	−0.447291
$46$	1.00000	0.147442
$47$	9.72463	1.41848	0.709241	−	0.704966i	$-0.249038\pi$
$47$	9.72463	1.41848	0.709241	+	0.704966i	$0.249038\pi$
$48$	1.11947	0.161581
$49$	7.33731	1.04819
$50$	2.04942	0.289831
$51$	−2.26255	−0.316821
$52$	−1.13725	−0.157708
$53$	4.37827	0.601402	0.300701	−	0.953718i	$-0.402779\pi$
$53$	4.37827	0.601402	0.300701	+	0.953718i	$0.402779\pi$
$54$	5.31387	0.723127
$55$	−8.63764	−1.16470
$56$	−3.78646	−0.505988
$57$	−3.86426	−0.511834
$58$	−3.63249	−0.476969
$59$	−4.09523	−0.533153	−0.266577	−	0.963814i	$-0.585893\pi$
$59$	−4.09523	−0.533153	−0.266577	+	0.963814i	$0.585893\pi$
$60$	1.92293	0.248250
$61$	−7.58965	−0.971755	−0.485877	−	0.874027i	$-0.661500\pi$
$61$	−7.58965	−0.971755	−0.485877	+	0.874027i	$0.661500\pi$
$62$	2.60130	0.330366
$63$	−6.61419	−0.833309
$64$	1.00000	0.125000
$65$	−1.95348	−0.242299
$66$	5.62926	0.692915
$67$	6.77221	0.827357	0.413678	−	0.910423i	$-0.364244\pi$
$67$	6.77221	0.827357	0.413678	+	0.910423i	$0.364244\pi$
$68$	−2.02110	−0.245095
$69$	−1.11947	−0.134768
$70$	−6.50411	−0.777389
$71$	7.67491	0.910844	0.455422	−	0.890276i	$-0.349488\pi$
$71$	7.67491	0.910844	0.455422	+	0.890276i	$0.349488\pi$
$72$	1.74680	0.205862
$73$	0.694157	0.0812449	0.0406224	−	0.999175i	$-0.487066\pi$
$73$	0.694157	0.0812449	0.0406224	+	0.999175i	$0.487066\pi$
$74$	−6.85095	−0.796407
$75$	−2.29425	−0.264917
$76$	−3.45188	−0.395958
$77$	−19.0403	−2.16985
$78$	1.27311	0.144151
$79$	−6.56104	−0.738175	−0.369087	−	0.929395i	$-0.620330\pi$
$79$	−6.56104	−0.738175	−0.369087	+	0.929395i	$0.620330\pi$
$80$	1.71773	0.192048
$81$	−0.708306	−0.0787007
$82$	−0.0708493	−0.00782400
$83$	−6.10921	−0.670572	−0.335286	−	0.942116i	$-0.608833\pi$
$83$	−6.10921	−0.670572	−0.335286	+	0.942116i	$0.608833\pi$
$84$	4.23882	0.462493
$85$	−3.47170	−0.376558
$86$	10.0539	1.08414
$87$	4.06644	0.435968
$88$	5.02853	0.536043
$89$	0.281878	0.0298790	0.0149395	−	0.999888i	$-0.495244\pi$
$89$	0.281878	0.0298790	0.0149395	+	0.999888i	$0.495244\pi$
$90$	3.00052	0.316282
$91$	−4.30614	−0.451406
$92$	−1.00000	−0.104257
$93$	−2.91207	−0.301967
$94$	−9.72463	−1.00302
$95$	−5.92938	−0.608342
$96$	−1.11947	−0.114255
$97$	−5.35678	−0.543899	−0.271949	−	0.962312i	$-0.587668\pi$
$97$	−5.35678	−0.543899	−0.271949	+	0.962312i	$0.587668\pi$
$98$	−7.33731	−0.741180
$99$	8.78382	0.882807
$100$	−2.04942	−0.204942
$101$	−0.757584	−0.0753825	−0.0376912	−	0.999289i	$-0.512000\pi$
$101$	−0.757584	−0.0753825	−0.0376912	+	0.999289i	$0.512000\pi$
$102$	2.26255	0.224026
$103$	−4.62928	−0.456137	−0.228068	−	0.973645i	$-0.573241\pi$
$103$	−4.62928	−0.456137	−0.228068	+	0.973645i	$0.573241\pi$
$104$	1.13725	0.111516
$105$	7.28112	0.710565
$106$	−4.37827	−0.425256
$107$	−20.5580	−1.98741	−0.993707	−	0.112009i	$-0.964271\pi$
$107$	−20.5580	−1.98741	−0.993707	+	0.112009i	$0.964271\pi$
$108$	−5.31387	−0.511328
$109$	−20.6989	−1.98260	−0.991299	−	0.131630i	$-0.957979\pi$
$109$	−20.6989	−1.98260	−0.991299	+	0.131630i	$0.957979\pi$
$110$	8.63764	0.823566
$111$	7.66940	0.727947
$112$	3.78646	0.357787
$113$	4.74818	0.446671	0.223336	−	0.974742i	$-0.428305\pi$
$113$	4.74818	0.446671	0.223336	+	0.974742i	$0.428305\pi$
$114$	3.86426	0.361921
$115$	−1.71773	−0.160179
$116$	3.63249	0.337268
$117$	1.98654	0.183656
$118$	4.09523	0.376996
$119$	−7.65283	−0.701534
$120$	−1.92293	−0.175539
$121$	14.2861	1.29874
$122$	7.58965	0.687134
$123$	0.0793133	0.00715144
$124$	−2.60130	−0.233604
$125$	−12.1090	−1.08306
$126$	6.61419	0.589239
$127$	−13.2591	−1.17655	−0.588276	−	0.808660i	$-0.700193\pi$
$127$	−13.2591	−1.17655	−0.588276	+	0.808660i	$0.700193\pi$
$128$	−1.00000	−0.0883883
$129$	−11.2550	−0.990949
$130$	1.95348	0.171331
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−5.62926	−0.489965
$133$	−13.0704	−1.13335
$134$	−6.77221	−0.585030
$135$	−9.12778	−0.785594
$136$	2.02110	0.173308
$137$	2.57060	0.219621	0.109810	−	0.993953i	$-0.464976\pi$
$137$	2.57060	0.219621	0.109810	+	0.993953i	$0.464976\pi$
$138$	1.11947	0.0952952
$139$	−22.8730	−1.94006	−0.970031	−	0.242980i	$-0.921875\pi$
$139$	−22.8730	−1.94006	−0.970031	+	0.242980i	$0.921875\pi$
$140$	6.50411	0.549697
$141$	10.8864	0.916799
$142$	−7.67491	−0.644064
$143$	5.71868	0.478220
$144$	−1.74680	−0.145566
$145$	6.23962	0.518172
$146$	−0.694157	−0.0574488
$147$	8.21386	0.677468
$148$	6.85095	0.563145
$149$	17.0135	1.39380	0.696899	−	0.717170i	$-0.254563\pi$
$149$	17.0135	1.39380	0.696899	+	0.717170i	$0.254563\pi$
$150$	2.29425	0.187325
$151$	−17.0823	−1.39013	−0.695067	−	0.718945i	$-0.744626\pi$
$151$	−17.0823	−1.39013	−0.695067	+	0.718945i	$0.744626\pi$
$152$	3.45188	0.279984
$153$	3.53045	0.285420
$154$	19.0403	1.53432
$155$	−4.46832	−0.358904
$156$	−1.27311	−0.101930
$157$	−9.07778	−0.724486	−0.362243	−	0.932084i	$-0.617989\pi$
$157$	−9.07778	−0.724486	−0.362243	+	0.932084i	$0.617989\pi$
$158$	6.56104	0.521968
$159$	4.90133	0.388700
$160$	−1.71773	−0.135798
$161$	−3.78646	−0.298415
$162$	0.708306	0.0556498
$163$	−9.73473	−0.762483	−0.381242	−	0.924475i	$-0.624503\pi$
$163$	−9.73473	−0.762483	−0.381242	+	0.924475i	$0.624503\pi$
$164$	0.0708493	0.00553240
$165$	−9.66953	−0.752772
$166$	6.10921	0.474166
$167$	8.15347	0.630934	0.315467	−	0.948936i	$-0.397839\pi$
$167$	8.15347	0.630934	0.315467	+	0.948936i	$0.397839\pi$
$168$	−4.23882	−0.327032
$169$	−11.7067	−0.900513
$170$	3.47170	0.266267
$171$	6.02973	0.461105
$172$	−10.0539	−0.766604
$173$	−10.9776	−0.834609	−0.417305	−	0.908767i	$-0.637025\pi$
$173$	−10.9776	−0.834609	−0.417305	+	0.908767i	$0.637025\pi$
$174$	−4.06644	−0.308276
$175$	−7.76005	−0.586605
$176$	−5.02853	−0.379040
$177$	−4.58446	−0.344589
$178$	−0.281878	−0.0211276
$179$	10.2656	0.767287	0.383644	−	0.923481i	$-0.374669\pi$
$179$	10.2656	0.767287	0.383644	+	0.923481i	$0.374669\pi$
$180$	−3.00052	−0.223645
$181$	−17.1571	−1.27528	−0.637639	−	0.770335i	$-0.720089\pi$
$181$	−17.1571	−1.27528	−0.637639	+	0.770335i	$0.720089\pi$
$182$	4.30614	0.319193
$183$	−8.49634	−0.628068
$184$	1.00000	0.0737210
$185$	11.7681	0.865204
$186$	2.91207	0.213523
$187$	10.1632	0.743204
$188$	9.72463	0.709241
$189$	−20.1208	−1.46357
$190$	5.92938	0.430163
$191$	−9.30577	−0.673342	−0.336671	−	0.941622i	$-0.609301\pi$
$191$	−9.30577	−0.673342	−0.336671	+	0.941622i	$0.609301\pi$
$192$	1.11947	0.0807904
$193$	10.0038	0.720092	0.360046	−	0.932935i	$-0.382761\pi$
$193$	10.0038	0.720092	0.360046	+	0.932935i	$0.382761\pi$
$194$	5.35678	0.384594
$195$	−2.18685	−0.156604
$196$	7.33731	0.524094
$197$	6.72942	0.479451	0.239726	−	0.970841i	$-0.422943\pi$
$197$	6.72942	0.479451	0.239726	+	0.970841i	$0.422943\pi$
$198$	−8.78382	−0.624239
$199$	8.96908	0.635801	0.317901	−	0.948124i	$-0.397022\pi$
$199$	8.96908	0.635801	0.317901	+	0.948124i	$0.397022\pi$
$200$	2.04942	0.144916
$201$	7.58125	0.534740
$202$	0.757584	0.0533034
$203$	13.7543	0.965361
$204$	−2.26255	−0.158410
$205$	0.121700	0.00849987
$206$	4.62928	0.322537
$207$	1.74680	0.121411
$208$	−1.13725	−0.0788538
$209$	17.3579	1.20067
$210$	−7.28112	−0.502445
$211$	9.91161	0.682344	0.341172	−	0.940001i	$-0.389176\pi$
$211$	9.91161	0.682344	0.341172	+	0.940001i	$0.389176\pi$
$212$	4.37827	0.300701
$213$	8.59180	0.588700
$214$	20.5580	1.40531
$215$	−17.2699	−1.17780
$216$	5.31387	0.361563
$217$	−9.84974	−0.668644
$218$	20.6989	1.40191
$219$	0.777084	0.0525105
$220$	−8.63764	−0.582349
$221$	2.29849	0.154613
$222$	−7.66940	−0.514736
$223$	−6.93130	−0.464154	−0.232077	−	0.972697i	$-0.574552\pi$
$223$	−6.93130	−0.464154	−0.232077	+	0.972697i	$0.574552\pi$
$224$	−3.78646	−0.252994
$225$	3.57992	0.238661
$226$	−4.74818	−0.315844
$227$	−22.3660	−1.48448	−0.742241	−	0.670133i	$-0.766237\pi$
$227$	−22.3660	−1.48448	−0.742241	+	0.670133i	$0.766237\pi$
$228$	−3.86426	−0.255917
$229$	−6.96193	−0.460057	−0.230029	−	0.973184i	$-0.573882\pi$
$229$	−6.96193	−0.460057	−0.230029	+	0.973184i	$0.573882\pi$
$230$	1.71773	0.113263
$231$	−21.3150	−1.40242
$232$	−3.63249	−0.238484
$233$	−14.4881	−0.949146	−0.474573	−	0.880216i	$-0.657398\pi$
$233$	−14.4881	−0.949146	−0.474573	+	0.880216i	$0.657398\pi$
$234$	−1.98654	−0.129864
$235$	16.7042	1.08966
$236$	−4.09523	−0.266577
$237$	−7.34486	−0.477100
$238$	7.65283	0.496059
$239$	−0.437654	−0.0283095	−0.0141547	−	0.999900i	$-0.504506\pi$
$239$	−0.437654	−0.0283095	−0.0141547	+	0.999900i	$0.504506\pi$
$240$	1.92293	0.124125
$241$	14.7766	0.951842	0.475921	−	0.879488i	$-0.342115\pi$
$241$	14.7766	0.951842	0.475921	+	0.879488i	$0.342115\pi$
$242$	−14.2861	−0.918346
$243$	15.1487	0.971790
$244$	−7.58965	−0.485877
$245$	12.6035	0.805207
$246$	−0.0793133	−0.00505683
$247$	3.92564	0.249782
$248$	2.60130	0.165183
$249$	−6.83904	−0.433407
$250$	12.1090	0.765838
$251$	26.6680	1.68327	0.841634	−	0.540049i	$-0.181594\pi$
$251$	26.6680	1.68327	0.841634	+	0.540049i	$0.181594\pi$
$252$	−6.61419	−0.416655
$253$	5.02853	0.316141
$254$	13.2591	0.831947
$255$	−3.88644	−0.243379
$256$	1.00000	0.0625000
$257$	−1.63010	−0.101683	−0.0508415	−	0.998707i	$-0.516190\pi$
$257$	−1.63010	−0.101683	−0.0508415	+	0.998707i	$0.516190\pi$
$258$	11.2550	0.700707
$259$	25.9409	1.61189
$260$	−1.95348	−0.121150
$261$	−6.34522	−0.392759
$262$	1.00000	0.0617802
$263$	−10.6468	−0.656512	−0.328256	−	0.944589i	$-0.606461\pi$
$263$	−10.6468	−0.656512	−0.328256	+	0.944589i	$0.606461\pi$
$264$	5.62926	0.346457
$265$	7.52067	0.461991
$266$	13.0704	0.801399
$267$	0.315553	0.0193115
$268$	6.77221	0.413678
$269$	−3.27243	−0.199523	−0.0997617	−	0.995011i	$-0.531808\pi$
$269$	−3.27243	−0.199523	−0.0997617	+	0.995011i	$0.531808\pi$
$270$	9.12778	0.555499
$271$	30.6593	1.86242	0.931211	−	0.364482i	$-0.118754\pi$
$271$	30.6593	1.86242	0.931211	+	0.364482i	$0.118754\pi$
$272$	−2.02110	−0.122547
$273$	−4.82058	−0.291755
$274$	−2.57060	−0.155295
$275$	10.3056	0.621449
$276$	−1.11947	−0.0673839
$277$	2.46610	0.148174	0.0740869	−	0.997252i	$-0.476396\pi$
$277$	2.46610	0.148174	0.0740869	+	0.997252i	$0.476396\pi$
$278$	22.8730	1.37183
$279$	4.54395	0.272039
$280$	−6.50411	−0.388695
$281$	22.4296	1.33804	0.669020	−	0.743245i	$-0.266714\pi$
$281$	22.4296	1.33804	0.669020	+	0.743245i	$0.266714\pi$
$282$	−10.8864	−0.648275
$283$	1.27092	0.0755486	0.0377743	−	0.999286i	$-0.487973\pi$
$283$	1.27092	0.0755486	0.0377743	+	0.999286i	$0.487973\pi$
$284$	7.67491	0.455422
$285$	−6.63774	−0.393186
$286$	−5.71868	−0.338152
$287$	0.268268	0.0158354
$288$	1.74680	0.102931
$289$	−12.9152	−0.759715
$290$	−6.23962	−0.366403
$291$	−5.99673	−0.351535
$292$	0.694157	0.0406224
$293$	8.38624	0.489929	0.244965	−	0.969532i	$-0.421224\pi$
$293$	8.38624	0.489929	0.244965	+	0.969532i	$0.421224\pi$
$294$	−8.21386	−0.479042
$295$	−7.03448	−0.409563
$296$	−6.85095	−0.398203
$297$	26.7210	1.55051
$298$	−17.0135	−0.985564
$299$	1.13725	0.0657687
$300$	−2.29425	−0.132459
$301$	−38.0688	−2.19425
$302$	17.0823	0.982974
$303$	−0.848089	−0.0487215
$304$	−3.45188	−0.197979
$305$	−13.0369	−0.746492
$306$	−3.53045	−0.201823
$307$	−0.219042	−0.0125014	−0.00625069	−	0.999980i	$-0.501990\pi$
$307$	−0.219042	−0.0125014	−0.00625069	+	0.999980i	$0.501990\pi$
$308$	−19.0403	−1.08492
$309$	−5.18232	−0.294812
$310$	4.46832	0.253784
$311$	19.9608	1.13188	0.565938	−	0.824448i	$-0.308514\pi$
$311$	19.9608	1.13188	0.565938	+	0.824448i	$0.308514\pi$
$312$	1.27311	0.0720755
$313$	−8.10032	−0.457857	−0.228928	−	0.973443i	$-0.573522\pi$
$313$	−8.10032	−0.457857	−0.228928	+	0.973443i	$0.573522\pi$
$314$	9.07778	0.512289
$315$	−11.3614	−0.640140
$316$	−6.56104	−0.369087
$317$	26.9094	1.51138	0.755690	−	0.654929i	$-0.227302\pi$
$317$	26.9094	1.51138	0.755690	+	0.654929i	$0.227302\pi$
$318$	−4.90133	−0.274853
$319$	−18.2661	−1.02270
$320$	1.71773	0.0960238
$321$	−23.0139	−1.28451
$322$	3.78646	0.211011
$323$	6.97660	0.388188
$324$	−0.708306	−0.0393503
$325$	2.33069	0.129284
$326$	9.73473	0.539157
$327$	−23.1717	−1.28140
$328$	−0.0708493	−0.00391200
$329$	36.8220	2.03006
$330$	9.66953	0.532290
$331$	5.70687	0.313678	0.156839	−	0.987624i	$-0.449870\pi$
$331$	5.70687	0.313678	0.156839	+	0.987624i	$0.449870\pi$
$332$	−6.10921	−0.335286
$333$	−11.9672	−0.655800
$334$	−8.15347	−0.446138
$335$	11.6328	0.635568
$336$	4.23882	0.231246
$337$	−31.2307	−1.70125	−0.850623	−	0.525775i	$-0.823775\pi$
$337$	−31.2307	−1.70125	−0.850623	+	0.525775i	$0.823775\pi$
$338$	11.7067	0.636759
$339$	5.31542	0.288694
$340$	−3.47170	−0.188279
$341$	13.0807	0.708361
$342$	−6.02973	−0.326051
$343$	1.27722	0.0689632
$344$	10.0539	0.542071
$345$	−1.92293	−0.103527
$346$	10.9776	0.590158
$347$	12.5198	0.672098	0.336049	−	0.941845i	$-0.390909\pi$
$347$	12.5198	0.672098	0.336049	+	0.941845i	$0.390909\pi$
$348$	4.06644	0.217984
$349$	2.28939	0.122548	0.0612740	−	0.998121i	$-0.480484\pi$
$349$	2.28939	0.122548	0.0612740	+	0.998121i	$0.480484\pi$
$350$	7.76005	0.414792
$351$	6.04319	0.322561
$352$	5.02853	0.268022
$353$	22.7168	1.20909	0.604546	−	0.796570i	$-0.293355\pi$
$353$	22.7168	1.20909	0.604546	+	0.796570i	$0.293355\pi$
$354$	4.58446	0.243662
$355$	13.1834	0.699702
$356$	0.281878	0.0149395
$357$	−8.56707	−0.453418
$358$	−10.2656	−0.542554
$359$	5.00987	0.264411	0.132206	−	0.991222i	$-0.457794\pi$
$359$	5.00987	0.264411	0.132206	+	0.991222i	$0.457794\pi$
$360$	3.00052	0.158141
$361$	−7.08453	−0.372870
$362$	17.1571	0.901758
$363$	15.9928	0.839405
$364$	−4.30614	−0.225703
$365$	1.19237	0.0624115
$366$	8.49634	0.444111
$367$	12.1325	0.633310	0.316655	−	0.948541i	$-0.397440\pi$
$367$	12.1325	0.633310	0.316655	+	0.948541i	$0.397440\pi$
$368$	−1.00000	−0.0521286
$369$	−0.123759	−0.00644266
$370$	−11.7681	−0.611792
$371$	16.5782	0.860696
$372$	−2.91207	−0.150984
$373$	−30.6721	−1.58814	−0.794071	−	0.607825i	$-0.792042\pi$
$373$	−30.6721	−1.58814	−0.794071	+	0.607825i	$0.792042\pi$
$374$	−10.1632	−0.525525
$375$	−13.5556	−0.700007
$376$	−9.72463	−0.501509
$377$	−4.13103	−0.212759
$378$	20.1208	1.03490
$379$	3.25289	0.167089	0.0835447	−	0.996504i	$-0.473376\pi$
$379$	3.25289	0.167089	0.0835447	+	0.996504i	$0.473376\pi$
$380$	−5.92938	−0.304171
$381$	−14.8431	−0.760433
$382$	9.30577	0.476125
$383$	−25.1366	−1.28442	−0.642209	−	0.766529i	$-0.721982\pi$
$383$	−25.1366	−1.28442	−0.642209	+	0.766529i	$0.721982\pi$
$384$	−1.11947	−0.0571275
$385$	−32.7061	−1.66686
$386$	−10.0038	−0.509182
$387$	17.5622	0.892735
$388$	−5.35678	−0.271949
$389$	−2.28504	−0.115856	−0.0579282	−	0.998321i	$-0.518449\pi$
$389$	−2.28504	−0.115856	−0.0579282	+	0.998321i	$0.518449\pi$
$390$	2.18685	0.110735
$391$	2.02110	0.102211
$392$	−7.33731	−0.370590
$393$	−1.11947	−0.0564696
$394$	−6.72942	−0.339023
$395$	−11.2701	−0.567059
$396$	8.78382	0.441404
$397$	−6.23194	−0.312772	−0.156386	−	0.987696i	$-0.549984\pi$
$397$	−6.23194	−0.312772	−0.156386	+	0.987696i	$0.549984\pi$
$398$	−8.96908	−0.449579
$399$	−14.6319	−0.732510
$400$	−2.04942	−0.102471
$401$	3.09289	0.154452	0.0772258	−	0.997014i	$-0.475394\pi$
$401$	3.09289	0.154452	0.0772258	+	0.997014i	$0.475394\pi$
$402$	−7.58125	−0.378118
$403$	2.95832	0.147364
$404$	−0.757584	−0.0376912
$405$	−1.21668	−0.0604571
$406$	−13.7543	−0.682614
$407$	−34.4502	−1.70763
$408$	2.26255	0.112013
$409$	35.2669	1.74384	0.871918	−	0.489652i	$-0.162876\pi$
$409$	35.2669	1.74384	0.871918	+	0.489652i	$0.162876\pi$
$410$	−0.121700	−0.00601032
$411$	2.87769	0.141946
$412$	−4.62928	−0.228068
$413$	−15.5064	−0.763022
$414$	−1.74680	−0.0858504
$415$	−10.4939	−0.515127
$416$	1.13725	0.0557581
$417$	−25.6055	−1.25391
$418$	−17.3579	−0.849002
$419$	−5.18691	−0.253397	−0.126698	−	0.991941i	$-0.540438\pi$
$419$	−5.18691	−0.253397	−0.126698	+	0.991941i	$0.540438\pi$
$420$	7.28112	0.355282
$421$	22.7698	1.10973	0.554867	−	0.831939i	$-0.312769\pi$
$421$	22.7698	1.10973	0.554867	+	0.831939i	$0.312769\pi$
$422$	−9.91161	−0.482490
$423$	−16.9870	−0.825934
$424$	−4.37827	−0.212628
$425$	4.14208	0.200920
$426$	−8.59180	−0.416274
$427$	−28.7379	−1.39073
$428$	−20.5580	−0.993707
$429$	6.40186	0.309085
$430$	17.2699	0.832827
$431$	27.2797	1.31402	0.657009	−	0.753882i	$-0.271821\pi$
$431$	27.2797	1.31402	0.657009	+	0.753882i	$0.271821\pi$
$432$	−5.31387	−0.255664
$433$	0.185277	0.00890385	0.00445193	−	0.999990i	$-0.498583\pi$
$433$	0.185277	0.00890385	0.00445193	+	0.999990i	$0.498583\pi$
$434$	9.84974	0.472802
$435$	6.98503	0.334907
$436$	−20.6989	−0.991299
$437$	3.45188	0.165126
$438$	−0.777084	−0.0371305
$439$	8.48840	0.405129	0.202565	−	0.979269i	$-0.435072\pi$
$439$	8.48840	0.405129	0.202565	+	0.979269i	$0.435072\pi$
$440$	8.63764	0.411783
$441$	−12.8168	−0.610324
$442$	−2.29849	−0.109328
$443$	−8.73848	−0.415178	−0.207589	−	0.978216i	$-0.566562\pi$
$443$	−8.73848	−0.415178	−0.207589	+	0.978216i	$0.566562\pi$
$444$	7.66940	0.363974
$445$	0.484189	0.0229528
$446$	6.93130	0.328206
$447$	19.0460	0.900844
$448$	3.78646	0.178894
$449$	−34.5338	−1.62975	−0.814875	−	0.579636i	$-0.803195\pi$
$449$	−34.5338	−1.62975	−0.814875	+	0.579636i	$0.803195\pi$
$450$	−3.57992	−0.168759
$451$	−0.356268	−0.0167760
$452$	4.74818	0.223336
$453$	−19.1230	−0.898477
$454$	22.3660	1.04969
$455$	−7.39677	−0.346766
$456$	3.86426	0.180960
$457$	5.56670	0.260399	0.130200	−	0.991488i	$-0.458438\pi$
$457$	5.56670	0.260399	0.130200	+	0.991488i	$0.458438\pi$
$458$	6.96193	0.325310
$459$	10.7399	0.501295
$460$	−1.71773	−0.0800894
$461$	−21.3007	−0.992072	−0.496036	−	0.868302i	$-0.665212\pi$
$461$	−21.3007	−0.992072	−0.496036	+	0.868302i	$0.665212\pi$
$462$	21.3150	0.991664
$463$	8.04899	0.374068	0.187034	−	0.982353i	$-0.440113\pi$
$463$	8.04899	0.374068	0.187034	+	0.982353i	$0.440113\pi$
$464$	3.63249	0.168634
$465$	−5.00213	−0.231968
$466$	14.4881	0.671148
$467$	22.2400	1.02914	0.514572	−	0.857447i	$-0.327951\pi$
$467$	22.2400	1.02914	0.514572	+	0.857447i	$0.327951\pi$
$468$	1.98654	0.0918278
$469$	25.6427	1.18407
$470$	−16.7042	−0.770509
$471$	−10.1623	−0.468252
$472$	4.09523	0.188498
$473$	50.5564	2.32459
$474$	7.34486	0.337360
$475$	7.07434	0.324593
$476$	−7.65283	−0.350767
$477$	−7.64796	−0.350176
$478$	0.437654	0.0200178
$479$	−40.1900	−1.83633	−0.918165	−	0.396199i	$-0.870329\pi$
$479$	−40.1900	−1.83633	−0.918165	+	0.396199i	$0.870329\pi$
$480$	−1.92293	−0.0877695
$481$	−7.79122	−0.355249
$482$	−14.7766	−0.673054
$483$	−4.23882	−0.192873
$484$	14.2861	0.649369
$485$	−9.20148	−0.417818
$486$	−15.1487	−0.687159
$487$	−17.3281	−0.785212	−0.392606	−	0.919707i	$-0.628426\pi$
$487$	−17.3281	−0.785212	−0.392606	+	0.919707i	$0.628426\pi$
$488$	7.58965	0.343567
$489$	−10.8977	−0.492811
$490$	−12.6035	−0.569368
$491$	−22.9947	−1.03774	−0.518868	−	0.854854i	$-0.673646\pi$
$491$	−22.9947	−1.03774	−0.518868	+	0.854854i	$0.673646\pi$
$492$	0.0793133	0.00357572
$493$	−7.34162	−0.330650
$494$	−3.92564	−0.176623
$495$	15.0882	0.678164
$496$	−2.60130	−0.116802
$497$	29.0608	1.30355
$498$	6.83904	0.306465
$499$	4.50534	0.201687	0.100843	−	0.994902i	$-0.467846\pi$
$499$	4.50534	0.201687	0.100843	+	0.994902i	$0.467846\pi$
$500$	−12.1090	−0.541529
$501$	9.12753	0.407788
$502$	−26.6680	−1.19025
$503$	8.98902	0.400801	0.200400	−	0.979714i	$-0.435776\pi$
$503$	8.98902	0.400801	0.200400	+	0.979714i	$0.435776\pi$
$504$	6.61419	0.294619
$505$	−1.30132	−0.0579081
$506$	−5.02853	−0.223545
$507$	−13.1052	−0.582023
$508$	−13.2591	−0.588276
$509$	−8.99235	−0.398579	−0.199290	−	0.979941i	$-0.563863\pi$
$509$	−8.99235	−0.398579	−0.199290	+	0.979941i	$0.563863\pi$
$510$	3.88644	0.172095
$511$	2.62840	0.116274
$512$	−1.00000	−0.0441942
$513$	18.3429	0.809857
$514$	1.63010	0.0719008
$515$	−7.95184	−0.350400
$516$	−11.2550	−0.495474
$517$	−48.9006	−2.15065
$518$	−25.9409	−1.13978
$519$	−12.2890	−0.539428
$520$	1.95348	0.0856657
$521$	−9.42103	−0.412743	−0.206371	−	0.978474i	$-0.566166\pi$
$521$	−9.42103	−0.412743	−0.206371	+	0.978474i	$0.566166\pi$
$522$	6.34522	0.277723
$523$	1.08623	0.0474973	0.0237487	−	0.999718i	$-0.492440\pi$
$523$	1.08623	0.0474973	0.0237487	+	0.999718i	$0.492440\pi$
$524$	−1.00000	−0.0436852
$525$	−8.68710	−0.379136
$526$	10.6468	0.464224
$527$	5.25749	0.229020
$528$	−5.62926	−0.244982
$529$	1.00000	0.0434783
$530$	−7.52067	−0.326677
$531$	7.15353	0.310437
$532$	−13.0704	−0.566674
$533$	−0.0805731	−0.00349001
$534$	−0.315553	−0.0136553
$535$	−35.3130	−1.52671
$536$	−6.77221	−0.292515
$537$	11.4920	0.495916
$538$	3.27243	0.141084
$539$	−36.8959	−1.58922
$540$	−9.12778	−0.392797
$541$	43.9183	1.88819	0.944097	−	0.329669i	$-0.106937\pi$
$541$	43.9183	1.88819	0.944097	+	0.329669i	$0.106937\pi$
$542$	−30.6593	−1.31693
$543$	−19.2068	−0.824242
$544$	2.02110	0.0866540
$545$	−35.5551	−1.52301
$546$	4.82058	0.206302
$547$	−9.03578	−0.386342	−0.193171	−	0.981165i	$-0.561877\pi$
$547$	−9.03578	−0.386342	−0.193171	+	0.981165i	$0.561877\pi$
$548$	2.57060	0.109810
$549$	13.2576	0.565819
$550$	−10.3056	−0.439431
$551$	−12.5389	−0.534175
$552$	1.11947	0.0476476
$553$	−24.8431	−1.05644
$554$	−2.46610	−0.104775
$555$	13.1739	0.559202
$556$	−22.8730	−0.970031
$557$	8.51279	0.360698	0.180349	−	0.983603i	$-0.442277\pi$
$557$	8.51279	0.360698	0.180349	+	0.983603i	$0.442277\pi$
$558$	−4.54395	−0.192361
$559$	11.4338	0.483597
$560$	6.50411	0.274849
$561$	11.3773	0.480351
$562$	−22.4296	−0.946137
$563$	9.95255	0.419450	0.209725	−	0.977760i	$-0.432743\pi$
$563$	9.95255	0.419450	0.209725	+	0.977760i	$0.432743\pi$
$564$	10.8864	0.458399
$565$	8.15607	0.343128
$566$	−1.27092	−0.0534209
$567$	−2.68198	−0.112632
$568$	−7.67491	−0.322032
$569$	−22.5982	−0.947365	−0.473682	−	0.880696i	$-0.657076\pi$
$569$	−22.5982	−0.947365	−0.473682	+	0.880696i	$0.657076\pi$
$570$	6.63774	0.278024
$571$	25.0524	1.04841	0.524205	−	0.851592i	$-0.324362\pi$
$571$	25.0524	1.04841	0.524205	+	0.851592i	$0.324362\pi$
$572$	5.71868	0.239110
$573$	−10.4175	−0.435197
$574$	−0.268268	−0.0111973
$575$	2.04942	0.0854666
$576$	−1.74680	−0.0727832
$577$	31.6088	1.31589	0.657946	−	0.753065i	$-0.271425\pi$
$577$	31.6088	1.31589	0.657946	+	0.753065i	$0.271425\pi$
$578$	12.9152	0.537199
$579$	11.1990	0.465413
$580$	6.23962	0.259086
$581$	−23.1323	−0.959689
$582$	5.99673	0.248572
$583$	−22.0163	−0.911821
$584$	−0.694157	−0.0287244
$585$	3.41233	0.141082
$586$	−8.38624	−0.346432
$587$	−5.66913	−0.233990	−0.116995	−	0.993133i	$-0.537326\pi$
$587$	−5.66913	−0.233990	−0.116995	+	0.993133i	$0.537326\pi$
$588$	8.21386	0.338734
$589$	8.97938	0.369989
$590$	7.03448	0.289605
$591$	7.53335	0.309881
$592$	6.85095	0.281572
$593$	−38.3571	−1.57514	−0.787569	−	0.616226i	$-0.788661\pi$
$593$	−38.3571	−1.57514	−0.787569	+	0.616226i	$0.788661\pi$
$594$	−26.7210	−1.09638
$595$	−13.1455	−0.538911
$596$	17.0135	0.696899
$597$	10.0406	0.410933
$598$	−1.13725	−0.0465055
$599$	−31.7389	−1.29682	−0.648409	−	0.761292i	$-0.724565\pi$
$599$	−31.7389	−1.29682	−0.648409	+	0.761292i	$0.724565\pi$
$600$	2.29425	0.0936625
$601$	33.7116	1.37513	0.687563	−	0.726125i	$-0.258680\pi$
$601$	33.7116	1.37513	0.687563	+	0.726125i	$0.258680\pi$
$602$	38.0688	1.55157
$603$	−11.8297	−0.481742
$604$	−17.0823	−0.695067
$605$	24.5396	0.997678
$606$	0.848089	0.0344513
$607$	7.21595	0.292886	0.146443	−	0.989219i	$-0.453217\pi$
$607$	7.21595	0.292886	0.146443	+	0.989219i	$0.453217\pi$
$608$	3.45188	0.139992
$609$	15.3974	0.623936
$610$	13.0369	0.527850
$611$	−11.0593	−0.447411
$612$	3.53045	0.142710
$613$	9.24872	0.373552	0.186776	−	0.982402i	$-0.440196\pi$
$613$	9.24872	0.373552	0.186776	+	0.982402i	$0.440196\pi$
$614$	0.219042	0.00883981
$615$	0.136239	0.00549367
$616$	19.0403	0.767158
$617$	30.4274	1.22496	0.612480	−	0.790486i	$-0.290172\pi$
$617$	30.4274	1.22496	0.612480	+	0.790486i	$0.290172\pi$
$618$	5.18232	0.208464
$619$	23.3222	0.937398	0.468699	−	0.883358i	$-0.344723\pi$
$619$	23.3222	0.937398	0.468699	+	0.883358i	$0.344723\pi$
$620$	−4.46832	−0.179452
$621$	5.31387	0.213238
$622$	−19.9608	−0.800357
$623$	1.06732	0.0427613
$624$	−1.27311	−0.0509651
$625$	−10.5528	−0.422112
$626$	8.10032	0.323754
$627$	19.4315	0.776021
$628$	−9.07778	−0.362243
$629$	−13.8465	−0.552095
$630$	11.3614	0.452647
$631$	−5.85913	−0.233248	−0.116624	−	0.993176i	$-0.537207\pi$
$631$	−5.85913	−0.233248	−0.116624	+	0.993176i	$0.537207\pi$
$632$	6.56104	0.260984
$633$	11.0957	0.441015
$634$	−26.9094	−1.06871
$635$	−22.7754	−0.903815
$636$	4.90133	0.194350
$637$	−8.34433	−0.330614
$638$	18.2661	0.723161
$639$	−13.4065	−0.530353
$640$	−1.71773	−0.0678991
$641$	36.3729	1.43664	0.718321	−	0.695712i	$-0.244911\pi$
$641$	36.3729	1.43664	0.718321	+	0.695712i	$0.244911\pi$
$642$	23.0139	0.908288
$643$	−39.3201	−1.55063	−0.775317	−	0.631573i	$-0.782410\pi$
$643$	−39.3201	−1.55063	−0.775317	+	0.631573i	$0.782410\pi$
$644$	−3.78646	−0.149208
$645$	−19.3330	−0.761237
$646$	−6.97660	−0.274491
$647$	42.1255	1.65612	0.828062	−	0.560637i	$-0.189444\pi$
$647$	42.1255	1.65612	0.828062	+	0.560637i	$0.189444\pi$
$648$	0.708306	0.0278249
$649$	20.5930	0.808345
$650$	−2.33069	−0.0914173
$651$	−11.0264	−0.432160
$652$	−9.73473	−0.381242
$653$	−28.4950	−1.11510	−0.557548	−	0.830145i	$-0.688258\pi$
$653$	−28.4950	−1.11510	−0.557548	+	0.830145i	$0.688258\pi$
$654$	23.1717	0.906086
$655$	−1.71773	−0.0671171
$656$	0.0708493	0.00276620
$657$	−1.21255	−0.0473061
$658$	−36.8220	−1.43547
$659$	9.45400	0.368275	0.184138	−	0.982900i	$-0.441051\pi$
$659$	9.45400	0.368275	0.184138	+	0.982900i	$0.441051\pi$
$660$	−9.66953	−0.376386
$661$	−28.1789	−1.09603	−0.548016	−	0.836468i	$-0.684617\pi$
$661$	−28.1789	−1.09603	−0.548016	+	0.836468i	$0.684617\pi$
$662$	−5.70687	−0.221804
$663$	2.57308	0.0999301
$664$	6.10921	0.237083
$665$	−22.4514	−0.870628
$666$	11.9672	0.463720
$667$	−3.63249	−0.140650
$668$	8.15347	0.315467
$669$	−7.75934	−0.299994
$670$	−11.6328	−0.449414
$671$	38.1648	1.47333
$672$	−4.23882	−0.163516
$673$	26.0996	1.00607	0.503033	−	0.864267i	$-0.332217\pi$
$673$	26.0996	1.00607	0.503033	+	0.864267i	$0.332217\pi$
$674$	31.2307	1.20296
$675$	10.8904	0.419170
$676$	−11.7067	−0.450257
$677$	4.70817	0.180950	0.0904749	−	0.995899i	$-0.471162\pi$
$677$	4.70817	0.180950	0.0904749	+	0.995899i	$0.471162\pi$
$678$	−5.31542	−0.204137
$679$	−20.2833	−0.778400
$680$	3.47170	0.133134
$681$	−25.0379	−0.959456
$682$	−13.0807	−0.500887
$683$	−14.0487	−0.537560	−0.268780	−	0.963202i	$-0.586620\pi$
$683$	−14.0487	−0.537560	−0.268780	+	0.963202i	$0.586620\pi$
$684$	6.02973	0.230553
$685$	4.41558	0.168711
$686$	−1.27722	−0.0487643
$687$	−7.79364	−0.297346
$688$	−10.0539	−0.383302
$689$	−4.97918	−0.189692
$690$	1.92293	0.0732049
$691$	28.7587	1.09403	0.547017	−	0.837122i	$-0.315763\pi$
$691$	28.7587	1.09403	0.547017	+	0.837122i	$0.315763\pi$
$692$	−10.9776	−0.417305
$693$	33.2596	1.26343
$694$	−12.5198	−0.475245
$695$	−39.2895	−1.49034
$696$	−4.06644	−0.154138
$697$	−0.143194	−0.00542385
$698$	−2.28939	−0.0866545
$699$	−16.2189	−0.613456
$700$	−7.76005	−0.293302
$701$	18.8449	0.711763	0.355881	−	0.934531i	$-0.384181\pi$
$701$	18.8449	0.711763	0.355881	+	0.934531i	$0.384181\pi$
$702$	−6.04319	−0.228085
$703$	−23.6487	−0.891926
$704$	−5.02853	−0.189520
$705$	18.6998	0.704276
$706$	−22.7168	−0.854957
$707$	−2.86857	−0.107884
$708$	−4.58446	−0.172295
$709$	14.0089	0.526115	0.263057	−	0.964780i	$-0.415269\pi$
$709$	14.0089	0.526115	0.263057	+	0.964780i	$0.415269\pi$
$710$	−13.1834	−0.494764
$711$	11.4608	0.429814
$712$	−0.281878	−0.0105638
$713$	2.60130	0.0974195
$714$	8.56707	0.320615
$715$	9.82312	0.367364
$716$	10.2656	0.383644
$717$	−0.489938	−0.0182971
$718$	−5.00987	−0.186967
$719$	28.1173	1.04860	0.524299	−	0.851534i	$-0.324328\pi$
$719$	28.1173	1.04860	0.524299	+	0.851534i	$0.324328\pi$
$720$	−3.00052	−0.111823
$721$	−17.5286	−0.652800
$722$	7.08453	0.263659
$723$	16.5419	0.615198
$724$	−17.1571	−0.637639
$725$	−7.44449	−0.276481
$726$	−15.9928	−0.593549
$727$	−7.63420	−0.283137	−0.141568	−	0.989928i	$-0.545215\pi$
$727$	−7.63420	−0.283137	−0.141568	+	0.989928i	$0.545215\pi$
$728$	4.30614	0.159596
$729$	19.0834	0.706791
$730$	−1.19237	−0.0441316
$731$	20.3200	0.751562
$732$	−8.49634	−0.314034
$733$	16.7518	0.618741	0.309371	−	0.950942i	$-0.399882\pi$
$733$	16.7518	0.618741	0.309371	+	0.950942i	$0.399882\pi$
$734$	−12.1325	−0.447818
$735$	14.1092	0.520424
$736$	1.00000	0.0368605
$737$	−34.0542	−1.25440
$738$	0.123759	0.00455565
$739$	34.9818	1.28683	0.643414	−	0.765519i	$-0.277518\pi$
$739$	34.9818	1.28683	0.643414	+	0.765519i	$0.277518\pi$
$740$	11.7681	0.432602
$741$	4.39461	0.161440
$742$	−16.5782	−0.608604
$743$	11.4003	0.418238	0.209119	−	0.977890i	$-0.432940\pi$
$743$	11.4003	0.418238	0.209119	+	0.977890i	$0.432940\pi$
$744$	2.91207	0.106762
$745$	29.2245	1.07070
$746$	30.6721	1.12299
$747$	10.6715	0.390451
$748$	10.1632	0.371602
$749$	−77.8420	−2.84429
$750$	13.5556	0.494979
$751$	−2.70192	−0.0985946	−0.0492973	−	0.998784i	$-0.515698\pi$
$751$	−2.70192	−0.0985946	−0.0492973	+	0.998784i	$0.515698\pi$
$752$	9.72463	0.354621
$753$	29.8539	1.08794
$754$	4.13103	0.150443
$755$	−29.3426	−1.06789
$756$	−20.1208	−0.731786
$757$	−25.9273	−0.942344	−0.471172	−	0.882041i	$-0.656169\pi$
$757$	−25.9273	−0.942344	−0.471172	+	0.882041i	$0.656169\pi$
$758$	−3.25289	−0.118150
$759$	5.62926	0.204329
$760$	5.92938	0.215081
$761$	−1.33762	−0.0484887	−0.0242444	−	0.999706i	$-0.507718\pi$
$761$	−1.33762	−0.0484887	−0.0242444	+	0.999706i	$0.507718\pi$
$762$	14.8431	0.537707
$763$	−78.3758	−2.83739
$764$	−9.30577	−0.336671
$765$	6.06435	0.219257
$766$	25.1366	0.908221
$767$	4.65728	0.168165
$768$	1.11947	0.0403952
$769$	40.5063	1.46069	0.730347	−	0.683076i	$-0.239358\pi$
$769$	40.5063	1.46069	0.730347	+	0.683076i	$0.239358\pi$
$770$	32.7061	1.17865
$771$	−1.82484	−0.0657202
$772$	10.0038	0.360046
$773$	6.14112	0.220881	0.110440	−	0.993883i	$-0.464774\pi$
$773$	6.14112	0.220881	0.110440	+	0.993883i	$0.464774\pi$
$774$	−17.5622	−0.631259
$775$	5.33115	0.191501
$776$	5.35678	0.192297
$777$	29.0399	1.04180
$778$	2.28504	0.0819228
$779$	−0.244563	−0.00876239
$780$	−2.18685	−0.0783018
$781$	−38.5935	−1.38098
$782$	−2.02110	−0.0722744
$783$	−19.3026	−0.689818
$784$	7.33731	0.262047
$785$	−15.5931	−0.556543
$786$	1.11947	0.0399300
$787$	55.5918	1.98163	0.990817	−	0.135212i	$-0.0431716\pi$
$787$	55.5918	1.98163	0.990817	+	0.135212i	$0.0431716\pi$
$788$	6.72942	0.239726
$789$	−11.9188	−0.424319
$790$	11.2701	0.400971
$791$	17.9788	0.639253
$792$	−8.78382	−0.312120
$793$	8.63130	0.306506
$794$	6.23194	0.221163
$795$	8.41913	0.298596
$796$	8.96908	0.317901
$797$	20.2170	0.716121	0.358061	−	0.933698i	$-0.383438\pi$
$797$	20.2170	0.716121	0.358061	+	0.933698i	$0.383438\pi$
$798$	14.6319	0.517963
$799$	−19.6545	−0.695325
$800$	2.04942	0.0724579
$801$	−0.492384	−0.0173975
$802$	−3.09289	−0.109214
$803$	−3.49059	−0.123180
$804$	7.58125	0.267370
$805$	−6.50411	−0.229240
$806$	−2.95832	−0.104202
$807$	−3.66337	−0.128957
$808$	0.757584	0.0266517
$809$	−23.0017	−0.808698	−0.404349	−	0.914605i	$-0.632502\pi$
$809$	−23.0017	−0.808698	−0.404349	+	0.914605i	$0.632502\pi$
$810$	1.21668	0.0427496
$811$	12.4913	0.438630	0.219315	−	0.975654i	$-0.429618\pi$
$811$	12.4913	0.438630	0.219315	+	0.975654i	$0.429618\pi$
$812$	13.7543	0.482681
$813$	34.3220	1.20373
$814$	34.4502	1.20748
$815$	−16.7216	−0.585732
$816$	−2.26255	−0.0792052
$817$	34.7049	1.21417
$818$	−35.2669	−1.23308
$819$	7.52196	0.262839
$820$	0.121700	0.00424994
$821$	−19.6664	−0.686362	−0.343181	−	0.939269i	$-0.611504\pi$
$821$	−19.6664	−0.686362	−0.343181	+	0.939269i	$0.611504\pi$
$822$	−2.87769	−0.100371
$823$	−30.0960	−1.04908	−0.524541	−	0.851385i	$-0.675763\pi$
$823$	−30.0960	−1.04908	−0.524541	+	0.851385i	$0.675763\pi$
$824$	4.62928	0.161269
$825$	11.5367	0.401657
$826$	15.5064	0.539538
$827$	−15.6806	−0.545269	−0.272634	−	0.962118i	$-0.587895\pi$
$827$	−15.6806	−0.545269	−0.272634	+	0.962118i	$0.587895\pi$
$828$	1.74680	0.0607054
$829$	−5.86794	−0.203802	−0.101901	−	0.994795i	$-0.532492\pi$
$829$	−5.86794	−0.203802	−0.101901	+	0.994795i	$0.532492\pi$
$830$	10.4939	0.364250
$831$	2.76072	0.0957683
$832$	−1.13725	−0.0394269
$833$	−14.8294	−0.513810
$834$	25.6055	0.886647
$835$	14.0054	0.484678
$836$	17.3579	0.600335
$837$	13.8230	0.477792
$838$	5.18691	0.179179
$839$	7.68218	0.265218	0.132609	−	0.991168i	$-0.457665\pi$
$839$	7.68218	0.265218	0.132609	+	0.991168i	$0.457665\pi$
$840$	−7.28112	−0.251223
$841$	−15.8050	−0.545001
$842$	−22.7698	−0.784700
$843$	25.1092	0.864806
$844$	9.91161	0.341172
$845$	−20.1088	−0.691765
$846$	16.9870	0.584024
$847$	54.0939	1.85869
$848$	4.37827	0.150351
$849$	1.42276	0.0488288
$850$	−4.14208	−0.142072
$851$	−6.85095	−0.234848
$852$	8.59180	0.294350
$853$	−50.4283	−1.72663	−0.863315	−	0.504665i	$-0.831616\pi$
$853$	−50.4283	−1.72663	−0.863315	+	0.504665i	$0.831616\pi$
$854$	28.7379	0.983391
$855$	10.3574	0.354217
$856$	20.5580	0.702657
$857$	−40.5583	−1.38544	−0.692722	−	0.721205i	$-0.743589\pi$
$857$	−40.5583	−1.38544	−0.692722	+	0.721205i	$0.743589\pi$
$858$	−6.40186	−0.218556
$859$	−24.8151	−0.846679	−0.423339	−	0.905971i	$-0.639142\pi$
$859$	−24.8151	−0.846679	−0.423339	+	0.905971i	$0.639142\pi$
$860$	−17.2699	−0.588898
$861$	0.300317	0.0102348
$862$	−27.2797	−0.929152
$863$	21.8192	0.742733	0.371366	−	0.928486i	$-0.378889\pi$
$863$	21.8192	0.742733	0.371366	+	0.928486i	$0.378889\pi$
$864$	5.31387	0.180782
$865$	−18.8565	−0.641139
$866$	−0.185277	−0.00629598
$867$	−14.4581	−0.491022
$868$	−9.84974	−0.334322
$869$	32.9924	1.11919
$870$	−6.98503	−0.236815
$871$	−7.70167	−0.260961
$872$	20.6989	0.700954
$873$	9.35721	0.316694
$874$	−3.45188	−0.116762
$875$	−45.8502	−1.55002
$876$	0.777084	0.0262552
$877$	22.5581	0.761733	0.380866	−	0.924630i	$-0.375626\pi$
$877$	22.5581	0.761733	0.380866	+	0.924630i	$0.375626\pi$
$878$	−8.48840	−0.286470
$879$	9.38810	0.316653
$880$	−8.63764	−0.291175
$881$	−12.3252	−0.415248	−0.207624	−	0.978209i	$-0.566573\pi$
$881$	−12.3252	−0.415248	−0.207624	+	0.978209i	$0.566573\pi$
$882$	12.8168	0.431564
$883$	−43.4179	−1.46113	−0.730564	−	0.682844i	$-0.760743\pi$
$883$	−43.4179	−1.46113	−0.730564	+	0.682844i	$0.760743\pi$
$884$	2.29849	0.0773066
$885$	−7.87485	−0.264710
$886$	8.73848	0.293575
$887$	−13.9255	−0.467572	−0.233786	−	0.972288i	$-0.575112\pi$
$887$	−13.9255	−0.467572	−0.233786	+	0.972288i	$0.575112\pi$
$888$	−7.66940	−0.257368
$889$	−50.2050	−1.68382
$890$	−0.484189	−0.0162300
$891$	3.56174	0.119323
$892$	−6.93130	−0.232077
$893$	−33.5682	−1.12332
$894$	−19.0460	−0.636993
$895$	17.6335	0.589423
$896$	−3.78646	−0.126497
$897$	1.27311	0.0425078
$898$	34.5338	1.15241
$899$	−9.44919	−0.315148
$900$	3.57992	0.119331
$901$	−8.84894	−0.294801
$902$	0.356268	0.0118624
$903$	−42.6167	−1.41820
$904$	−4.74818	−0.157922
$905$	−29.4712	−0.979656
$906$	19.1230	0.635319
$907$	1.73046	0.0574590	0.0287295	−	0.999587i	$-0.490854\pi$
$907$	1.73046	0.0574590	0.0287295	+	0.999587i	$0.490854\pi$
$908$	−22.3660	−0.742241
$909$	1.32335	0.0438926
$910$	7.39677	0.245201
$911$	1.21394	0.0402195	0.0201097	−	0.999798i	$-0.493598\pi$
$911$	1.21394	0.0402195	0.0201097	+	0.999798i	$0.493598\pi$
$912$	−3.86426	−0.127958
$913$	30.7203	1.01669
$914$	−5.56670	−0.184130
$915$	−14.5944	−0.482476
$916$	−6.96193	−0.230029
$917$	−3.78646	−0.125040
$918$	−10.7399	−0.354469
$919$	0.857023	0.0282706	0.0141353	−	0.999900i	$-0.495500\pi$
$919$	0.857023	0.0282706	0.0141353	+	0.999900i	$0.495500\pi$
$920$	1.71773	0.0566317
$921$	−0.245210	−0.00807993
$922$	21.3007	0.701501
$923$	−8.72826	−0.287294
$924$	−21.3150	−0.701212
$925$	−14.0405	−0.461648
$926$	−8.04899	−0.264506
$927$	8.08642	0.265593
$928$	−3.63249	−0.119242
$929$	34.7011	1.13851	0.569253	−	0.822162i	$-0.307232\pi$
$929$	34.7011	1.13851	0.569253	+	0.822162i	$0.307232\pi$
$930$	5.00213	0.164026
$931$	−25.3275	−0.830076
$932$	−14.4881	−0.474573
$933$	22.3455	0.731558
$934$	−22.2400	−0.727715
$935$	17.4575	0.570922
$936$	−1.98654	−0.0649321
$937$	−7.49494	−0.244849	−0.122425	−	0.992478i	$-0.539067\pi$
$937$	−7.49494	−0.244849	−0.122425	+	0.992478i	$0.539067\pi$
$938$	−25.6427	−0.837265
$939$	−9.06802	−0.295924
$940$	16.7042	0.544832
$941$	−13.0958	−0.426910	−0.213455	−	0.976953i	$-0.568472\pi$
$941$	−13.0958	−0.426910	−0.213455	+	0.976953i	$0.568472\pi$
$942$	10.1623	0.331104
$943$	−0.0708493	−0.00230717
$944$	−4.09523	−0.133288
$945$	−34.5620	−1.12430
$946$	−50.5564	−1.64373
$947$	−4.96406	−0.161310	−0.0806551	−	0.996742i	$-0.525701\pi$
$947$	−4.96406	−0.161310	−0.0806551	+	0.996742i	$0.525701\pi$
$948$	−7.34486	−0.238550
$949$	−0.789427	−0.0256259
$950$	−7.07434	−0.229522
$951$	30.1241	0.976841
$952$	7.65283	0.248030
$953$	57.0896	1.84931	0.924656	−	0.380803i	$-0.124352\pi$
$953$	57.0896	1.84931	0.924656	+	0.380803i	$0.124352\pi$
$954$	7.64796	0.247612
$955$	−15.9848	−0.517255
$956$	−0.437654	−0.0141547
$957$	−20.4482	−0.660997
$958$	40.1900	1.29848
$959$	9.73347	0.314310
$960$	1.92293	0.0620624
$961$	−24.2332	−0.781717
$962$	7.79122	0.251199
$963$	35.9106	1.15720
$964$	14.7766	0.475921
$965$	17.1839	0.553168
$966$	4.23882	0.136382
$967$	−29.6492	−0.953455	−0.476728	−	0.879051i	$-0.658177\pi$
$967$	−29.6492	−0.953455	−0.476728	+	0.879051i	$0.658177\pi$
$968$	−14.2861	−0.459173
$969$	7.81006	0.250895
$970$	9.20148	0.295442
$971$	−7.32991	−0.235228	−0.117614	−	0.993059i	$-0.537525\pi$
$971$	−7.32991	−0.235228	−0.117614	+	0.993059i	$0.537525\pi$
$972$	15.1487	0.485895
$973$	−86.6078	−2.77652
$974$	17.3281	0.555229
$975$	2.60913	0.0835590
$976$	−7.58965	−0.242939
$977$	19.5965	0.626946	0.313473	−	0.949597i	$-0.398507\pi$
$977$	19.5965	0.626946	0.313473	+	0.949597i	$0.398507\pi$
$978$	10.8977	0.348470
$979$	−1.41743	−0.0453013
$980$	12.6035	0.402604
$981$	36.1568	1.15440
$982$	22.9947	0.733790
$983$	36.0795	1.15076	0.575379	−	0.817887i	$-0.304854\pi$
$983$	36.0795	1.15076	0.575379	+	0.817887i	$0.304854\pi$
$984$	−0.0793133	−0.00252842
$985$	11.5593	0.368310
$986$	7.34162	0.233805
$987$	41.2209	1.31208
$988$	3.92564	0.124891
$989$	10.0539	0.319696
$990$	−15.0882	−0.479534
$991$	−22.5818	−0.717334	−0.358667	−	0.933466i	$-0.616769\pi$
$991$	−22.5818	−0.717334	−0.358667	+	0.933466i	$0.616769\pi$
$992$	2.60130	0.0825914
$993$	6.38864	0.202737
$994$	−29.0608	−0.921752
$995$	15.4064	0.488416
$996$	−6.83904	−0.216703
$997$	8.62626	0.273196	0.136598	−	0.990627i	$-0.456383\pi$
$997$	8.62626	0.273196	0.136598	+	0.990627i	$0.456383\pi$
$998$	−4.50534	−0.142614
$999$	−36.4051	−1.15181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.16	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.16	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.11947 q^{3} +1.00000 q^{4} +1.71773 q^{5} -1.11947 q^{6} +3.78646 q^{7} -1.00000 q^{8} -1.74680 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.11947 q^{3} +1.00000 q^{4} +1.71773 q^{5} -1.11947 q^{6} +3.78646 q^{7} -1.00000 q^{8} -1.74680 q^{9} -1.71773 q^{10} -5.02853 q^{11} +1.11947 q^{12} -1.13725 q^{13} -3.78646 q^{14} +1.92293 q^{15} +1.00000 q^{16} -2.02110 q^{17} +1.74680 q^{18} -3.45188 q^{19} +1.71773 q^{20} +4.23882 q^{21} +5.02853 q^{22} -1.00000 q^{23} -1.11947 q^{24} -2.04942 q^{25} +1.13725 q^{26} -5.31387 q^{27} +3.78646 q^{28} +3.63249 q^{29} -1.92293 q^{30} -2.60130 q^{31} -1.00000 q^{32} -5.62926 q^{33} +2.02110 q^{34} +6.50411 q^{35} -1.74680 q^{36} +6.85095 q^{37} +3.45188 q^{38} -1.27311 q^{39} -1.71773 q^{40} +0.0708493 q^{41} -4.23882 q^{42} -10.0539 q^{43} -5.02853 q^{44} -3.00052 q^{45} +1.00000 q^{46} +9.72463 q^{47} +1.11947 q^{48} +7.33731 q^{49} +2.04942 q^{50} -2.26255 q^{51} -1.13725 q^{52} +4.37827 q^{53} +5.31387 q^{54} -8.63764 q^{55} -3.78646 q^{56} -3.86426 q^{57} -3.63249 q^{58} -4.09523 q^{59} +1.92293 q^{60} -7.58965 q^{61} +2.60130 q^{62} -6.61419 q^{63} +1.00000 q^{64} -1.95348 q^{65} +5.62926 q^{66} +6.77221 q^{67} -2.02110 q^{68} -1.11947 q^{69} -6.50411 q^{70} +7.67491 q^{71} +1.74680 q^{72} +0.694157 q^{73} -6.85095 q^{74} -2.29425 q^{75} -3.45188 q^{76} -19.0403 q^{77} +1.27311 q^{78} -6.56104 q^{79} +1.71773 q^{80} -0.708306 q^{81} -0.0708493 q^{82} -6.10921 q^{83} +4.23882 q^{84} -3.47170 q^{85} +10.0539 q^{86} +4.06644 q^{87} +5.02853 q^{88} +0.281878 q^{89} +3.00052 q^{90} -4.30614 q^{91} -1.00000 q^{92} -2.91207 q^{93} -9.72463 q^{94} -5.92938 q^{95} -1.11947 q^{96} -5.35678 q^{97} -7.33731 q^{98} +8.78382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more