LMFDB - Embedded newform 6034.2.a.l.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-1.35221$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.35221 q^{3} +1.00000 q^{4} +2.46727 q^{5} +1.35221 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.17152 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.35221 q^{3} +1.00000 q^{4} +2.46727 q^{5} +1.35221 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.17152 q^{9} +2.46727 q^{10} -3.61409 q^{11} +1.35221 q^{12} -4.55617 q^{13} -1.00000 q^{14} +3.33628 q^{15} +1.00000 q^{16} -6.23091 q^{17} -1.17152 q^{18} -0.0439905 q^{19} +2.46727 q^{20} -1.35221 q^{21} -3.61409 q^{22} -0.857918 q^{23} +1.35221 q^{24} +1.08743 q^{25} -4.55617 q^{26} -5.64078 q^{27} -1.00000 q^{28} -6.72083 q^{29} +3.33628 q^{30} -0.329418 q^{31} +1.00000 q^{32} -4.88702 q^{33} -6.23091 q^{34} -2.46727 q^{35} -1.17152 q^{36} +7.43728 q^{37} -0.0439905 q^{38} -6.16091 q^{39} +2.46727 q^{40} +8.00012 q^{41} -1.35221 q^{42} +4.47562 q^{43} -3.61409 q^{44} -2.89045 q^{45} -0.857918 q^{46} -10.1996 q^{47} +1.35221 q^{48} +1.00000 q^{49} +1.08743 q^{50} -8.42552 q^{51} -4.55617 q^{52} -4.27740 q^{53} -5.64078 q^{54} -8.91693 q^{55} -1.00000 q^{56} -0.0594846 q^{57} -6.72083 q^{58} +6.40429 q^{59} +3.33628 q^{60} +5.51992 q^{61} -0.329418 q^{62} +1.17152 q^{63} +1.00000 q^{64} -11.2413 q^{65} -4.88702 q^{66} -2.91057 q^{67} -6.23091 q^{68} -1.16009 q^{69} -2.46727 q^{70} -5.91123 q^{71} -1.17152 q^{72} -6.88924 q^{73} +7.43728 q^{74} +1.47043 q^{75} -0.0439905 q^{76} +3.61409 q^{77} -6.16091 q^{78} +12.1235 q^{79} +2.46727 q^{80} -4.11299 q^{81} +8.00012 q^{82} -16.5831 q^{83} -1.35221 q^{84} -15.3733 q^{85} +4.47562 q^{86} -9.08799 q^{87} -3.61409 q^{88} -17.4985 q^{89} -2.89045 q^{90} +4.55617 q^{91} -0.857918 q^{92} -0.445443 q^{93} -10.1996 q^{94} -0.108537 q^{95} +1.35221 q^{96} +8.60922 q^{97} +1.00000 q^{98} +4.23397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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
$3$	1.35221	0.780701	0.390350	−	0.920666i	$-0.372354\pi$
$3$	1.35221	0.780701	0.390350	+	0.920666i	$0.372354\pi$
$4$	1.00000	0.500000
$5$	2.46727	1.10340	0.551699	−	0.834044i	$-0.313980\pi$
$5$	2.46727	1.10340	0.551699	+	0.834044i	$0.313980\pi$
$6$	1.35221	0.552039
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.17152	−0.390506
$10$	2.46727	0.780220
$11$	−3.61409	−1.08969	−0.544844	−	0.838537i	$-0.683411\pi$
$11$	−3.61409	−1.08969	−0.544844	+	0.838537i	$0.683411\pi$
$12$	1.35221	0.390350
$13$	−4.55617	−1.26365	−0.631827	−	0.775110i	$-0.717695\pi$
$13$	−4.55617	−1.26365	−0.631827	+	0.775110i	$0.717695\pi$
$14$	−1.00000	−0.267261
$15$	3.33628	0.861423
$16$	1.00000	0.250000
$17$	−6.23091	−1.51122	−0.755609	−	0.655023i	$-0.772659\pi$
$17$	−6.23091	−1.51122	−0.755609	+	0.655023i	$0.772659\pi$
$18$	−1.17152	−0.276130
$19$	−0.0439905	−0.0100921	−0.00504606	−	0.999987i	$-0.501606\pi$
$19$	−0.0439905	−0.0100921	−0.00504606	+	0.999987i	$0.501606\pi$
$20$	2.46727	0.551699
$21$	−1.35221	−0.295077
$22$	−3.61409	−0.770526
$23$	−0.857918	−0.178888	−0.0894442	−	0.995992i	$-0.528509\pi$
$23$	−0.857918	−0.178888	−0.0894442	+	0.995992i	$0.528509\pi$
$24$	1.35221	0.276019
$25$	1.08743	0.217485
$26$	−4.55617	−0.893538
$27$	−5.64078	−1.08557
$28$	−1.00000	−0.188982
$29$	−6.72083	−1.24803	−0.624013	−	0.781414i	$-0.714499\pi$
$29$	−6.72083	−1.24803	−0.624013	+	0.781414i	$0.714499\pi$
$30$	3.33628	0.609118
$31$	−0.329418	−0.0591651	−0.0295826	−	0.999562i	$-0.509418\pi$
$31$	−0.329418	−0.0591651	−0.0295826	+	0.999562i	$0.509418\pi$
$32$	1.00000	0.176777
$33$	−4.88702	−0.850721
$34$	−6.23091	−1.06859
$35$	−2.46727	−0.417045
$36$	−1.17152	−0.195253
$37$	7.43728	1.22268	0.611341	−	0.791367i	$-0.290630\pi$
$37$	7.43728	1.22268	0.611341	+	0.791367i	$0.290630\pi$
$38$	−0.0439905	−0.00713621
$39$	−6.16091	−0.986536
$40$	2.46727	0.390110
$41$	8.00012	1.24941	0.624705	−	0.780861i	$-0.285219\pi$
$41$	8.00012	1.24941	0.624705	+	0.780861i	$0.285219\pi$
$42$	−1.35221	−0.208651
$43$	4.47562	0.682525	0.341263	−	0.939968i	$-0.389145\pi$
$43$	4.47562	0.682525	0.341263	+	0.939968i	$0.389145\pi$
$44$	−3.61409	−0.544844
$45$	−2.89045	−0.430883
$46$	−0.857918	−0.126493
$47$	−10.1996	−1.48776	−0.743882	−	0.668311i	$-0.767018\pi$
$47$	−10.1996	−1.48776	−0.743882	+	0.668311i	$0.767018\pi$
$48$	1.35221	0.195175
$49$	1.00000	0.142857
$50$	1.08743	0.153785
$51$	−8.42552	−1.17981
$52$	−4.55617	−0.631827
$53$	−4.27740	−0.587547	−0.293773	−	0.955875i	$-0.594911\pi$
$53$	−4.27740	−0.587547	−0.293773	+	0.955875i	$0.594911\pi$
$54$	−5.64078	−0.767613
$55$	−8.91693	−1.20236
$56$	−1.00000	−0.133631
$57$	−0.0594846	−0.00787893
$58$	−6.72083	−0.882488
$59$	6.40429	0.833767	0.416884	−	0.908960i	$-0.363122\pi$
$59$	6.40429	0.833767	0.416884	+	0.908960i	$0.363122\pi$
$60$	3.33628	0.430712
$61$	5.51992	0.706754	0.353377	−	0.935481i	$-0.385033\pi$
$61$	5.51992	0.706754	0.353377	+	0.935481i	$0.385033\pi$
$62$	−0.329418	−0.0418361
$63$	1.17152	0.147597
$64$	1.00000	0.125000
$65$	−11.2413	−1.39431
$66$	−4.88702	−0.601550
$67$	−2.91057	−0.355583	−0.177791	−	0.984068i	$-0.556895\pi$
$67$	−2.91057	−0.355583	−0.177791	+	0.984068i	$0.556895\pi$
$68$	−6.23091	−0.755609
$69$	−1.16009	−0.139658
$70$	−2.46727	−0.294895
$71$	−5.91123	−0.701534	−0.350767	−	0.936463i	$-0.614079\pi$
$71$	−5.91123	−0.701534	−0.350767	+	0.936463i	$0.614079\pi$
$72$	−1.17152	−0.138065
$73$	−6.88924	−0.806325	−0.403162	−	0.915128i	$-0.632089\pi$
$73$	−6.88924	−0.806325	−0.403162	+	0.915128i	$0.632089\pi$
$74$	7.43728	0.864566
$75$	1.47043	0.169791
$76$	−0.0439905	−0.00504606
$77$	3.61409	0.411864
$78$	−6.16091	−0.697586
$79$	12.1235	1.36400	0.681998	−	0.731354i	$-0.261111\pi$
$79$	12.1235	1.36400	0.681998	+	0.731354i	$0.261111\pi$
$80$	2.46727	0.275849
$81$	−4.11299	−0.456999
$82$	8.00012	0.883466
$83$	−16.5831	−1.82023	−0.910114	−	0.414358i	$-0.864006\pi$
$83$	−16.5831	−1.82023	−0.910114	+	0.414358i	$0.864006\pi$
$84$	−1.35221	−0.147539
$85$	−15.3733	−1.66747
$86$	4.47562	0.482618
$87$	−9.08799	−0.974335
$88$	−3.61409	−0.385263
$89$	−17.4985	−1.85483	−0.927416	−	0.374031i	$-0.877976\pi$
$89$	−17.4985	−1.85483	−0.927416	+	0.374031i	$0.877976\pi$
$90$	−2.89045	−0.304681
$91$	4.55617	0.477616
$92$	−0.857918	−0.0894442
$93$	−0.445443	−0.0461903
$94$	−10.1996	−1.05201
$95$	−0.108537	−0.0111356
$96$	1.35221	0.138010
$97$	8.60922	0.874133	0.437067	−	0.899429i	$-0.356017\pi$
$97$	8.60922	0.874133	0.437067	+	0.899429i	$0.356017\pi$
$98$	1.00000	0.101015
$99$	4.23397	0.425530
$100$	1.08743	0.108743
$101$	−0.210773	−0.0209727	−0.0104863	−	0.999945i	$-0.503338\pi$
$101$	−0.210773	−0.0209727	−0.0104863	+	0.999945i	$0.503338\pi$
$102$	−8.42552	−0.834251
$103$	4.15357	0.409263	0.204632	−	0.978839i	$-0.434400\pi$
$103$	4.15357	0.409263	0.204632	+	0.978839i	$0.434400\pi$
$104$	−4.55617	−0.446769
$105$	−3.33628	−0.325587
$106$	−4.27740	−0.415458
$107$	8.41635	0.813639	0.406820	−	0.913508i	$-0.366638\pi$
$107$	8.41635	0.813639	0.406820	+	0.913508i	$0.366638\pi$
$108$	−5.64078	−0.542785
$109$	−3.07137	−0.294184	−0.147092	−	0.989123i	$-0.546991\pi$
$109$	−3.07137	−0.294184	−0.147092	+	0.989123i	$0.546991\pi$
$110$	−8.91693	−0.850196
$111$	10.0568	0.954549
$112$	−1.00000	−0.0944911
$113$	2.13157	0.200521	0.100260	−	0.994961i	$-0.468032\pi$
$113$	2.13157	0.200521	0.100260	+	0.994961i	$0.468032\pi$
$114$	−0.0594846	−0.00557125
$115$	−2.11672	−0.197385
$116$	−6.72083	−0.624013
$117$	5.33764	0.493465
$118$	6.40429	0.589563
$119$	6.23091	0.571186
$120$	3.33628	0.304559
$121$	2.06163	0.187421
$122$	5.51992	0.499750
$123$	10.8179	0.975415
$124$	−0.329418	−0.0295826
$125$	−9.65338	−0.863425
$126$	1.17152	0.104367
$127$	−8.58936	−0.762182	−0.381091	−	0.924538i	$-0.624452\pi$
$127$	−8.58936	−0.762182	−0.381091	+	0.924538i	$0.624452\pi$
$128$	1.00000	0.0883883
$129$	6.05199	0.532848
$130$	−11.2413	−0.985927
$131$	4.86423	0.424990	0.212495	−	0.977162i	$-0.431841\pi$
$131$	4.86423	0.424990	0.212495	+	0.977162i	$0.431841\pi$
$132$	−4.88702	−0.425360
$133$	0.0439905	0.00381446
$134$	−2.91057	−0.251435
$135$	−13.9173	−1.19781
$136$	−6.23091	−0.534296
$137$	−14.6037	−1.24768	−0.623839	−	0.781553i	$-0.714428\pi$
$137$	−14.6037	−1.24768	−0.623839	+	0.781553i	$0.714428\pi$
$138$	−1.16009	−0.0987533
$139$	10.5497	0.894815	0.447407	−	0.894330i	$-0.352347\pi$
$139$	10.5497	0.894815	0.447407	+	0.894330i	$0.352347\pi$
$140$	−2.46727	−0.208522
$141$	−13.7920	−1.16150
$142$	−5.91123	−0.496060
$143$	16.4664	1.37699
$144$	−1.17152	−0.0976265
$145$	−16.5821	−1.37707
$146$	−6.88924	−0.570158
$147$	1.35221	0.111529
$148$	7.43728	0.611341
$149$	21.7848	1.78468	0.892340	−	0.451363i	$-0.149062\pi$
$149$	21.7848	1.78468	0.892340	+	0.451363i	$0.149062\pi$
$150$	1.47043	0.120060
$151$	−18.2824	−1.48780	−0.743901	−	0.668290i	$-0.767027\pi$
$151$	−18.2824	−1.48780	−0.743901	+	0.668290i	$0.767027\pi$
$152$	−0.0439905	−0.00356810
$153$	7.29962	0.590140
$154$	3.61409	0.291231
$155$	−0.812762	−0.0652826
$156$	−6.16091	−0.493268
$157$	24.5315	1.95782	0.978912	−	0.204283i	$-0.0654863\pi$
$157$	24.5315	1.95782	0.978912	+	0.204283i	$0.0654863\pi$
$158$	12.1235	0.964491
$159$	−5.78396	−0.458698
$160$	2.46727	0.195055
$161$	0.857918	0.0676134
$162$	−4.11299	−0.323147
$163$	16.7494	1.31192	0.655958	−	0.754797i	$-0.272265\pi$
$163$	16.7494	1.31192	0.655958	+	0.754797i	$0.272265\pi$
$164$	8.00012	0.624705
$165$	−12.0576	−0.938683
$166$	−16.5831	−1.28710
$167$	1.41790	0.109720	0.0548602	−	0.998494i	$-0.482529\pi$
$167$	1.41790	0.109720	0.0548602	+	0.998494i	$0.482529\pi$
$168$	−1.35221	−0.104326
$169$	7.75867	0.596821
$170$	−15.3733	−1.17908
$171$	0.0515357	0.00394104
$172$	4.47562	0.341263
$173$	−2.38807	−0.181561	−0.0907807	−	0.995871i	$-0.528936\pi$
$173$	−2.38807	−0.181561	−0.0907807	+	0.995871i	$0.528936\pi$
$174$	−9.08799	−0.688959
$175$	−1.08743	−0.0822017
$176$	−3.61409	−0.272422
$177$	8.65997	0.650923
$178$	−17.4985	−1.31156
$179$	−14.4821	−1.08244	−0.541222	−	0.840880i	$-0.682038\pi$
$179$	−14.4821	−1.08244	−0.541222	+	0.840880i	$0.682038\pi$
$180$	−2.89045	−0.215442
$181$	0.726434	0.0539954	0.0269977	−	0.999635i	$-0.491405\pi$
$181$	0.726434	0.0539954	0.0269977	+	0.999635i	$0.491405\pi$
$182$	4.55617	0.337726
$183$	7.46412	0.551763
$184$	−0.857918	−0.0632466
$185$	18.3498	1.34910
$186$	−0.445443	−0.0326615
$187$	22.5190	1.64676
$188$	−10.1996	−0.743882
$189$	5.64078	0.410307
$190$	−0.108537	−0.00787407
$191$	−22.2354	−1.60890	−0.804448	−	0.594024i	$-0.797539\pi$
$191$	−22.2354	−1.60890	−0.804448	+	0.594024i	$0.797539\pi$
$192$	1.35221	0.0975876
$193$	6.43981	0.463547	0.231774	−	0.972770i	$-0.425547\pi$
$193$	6.43981	0.463547	0.231774	+	0.972770i	$0.425547\pi$
$194$	8.60922	0.618106
$195$	−15.2006	−1.08854
$196$	1.00000	0.0714286
$197$	1.59642	0.113740	0.0568701	−	0.998382i	$-0.481888\pi$
$197$	1.59642	0.113740	0.0568701	+	0.998382i	$0.481888\pi$
$198$	4.23397	0.300895
$199$	−14.5094	−1.02855	−0.514273	−	0.857627i	$-0.671938\pi$
$199$	−14.5094	−1.02855	−0.514273	+	0.857627i	$0.671938\pi$
$200$	1.08743	0.0768927
$201$	−3.93571	−0.277604
$202$	−0.210773	−0.0148299
$203$	6.72083	0.471710
$204$	−8.42552	−0.589904
$205$	19.7385	1.37859
$206$	4.15357	0.289393
$207$	1.00507	0.0698570
$208$	−4.55617	−0.315913
$209$	0.158986	0.0109973
$210$	−3.33628	−0.230225
$211$	−23.2915	−1.60345	−0.801727	−	0.597691i	$-0.796085\pi$
$211$	−23.2915	−1.60345	−0.801727	+	0.597691i	$0.796085\pi$
$212$	−4.27740	−0.293773
$213$	−7.99325	−0.547688
$214$	8.41635	0.575330
$215$	11.0426	0.753096
$216$	−5.64078	−0.383807
$217$	0.329418	0.0223623
$218$	−3.07137	−0.208019
$219$	−9.31573	−0.629499
$220$	−8.91693	−0.601180
$221$	28.3891	1.90966
$222$	10.0568	0.674968
$223$	11.6516	0.780251	0.390126	−	0.920762i	$-0.372432\pi$
$223$	11.6516	0.780251	0.390126	+	0.920762i	$0.372432\pi$
$224$	−1.00000	−0.0668153
$225$	−1.27394	−0.0849293
$226$	2.13157	0.141790
$227$	−28.5583	−1.89548	−0.947740	−	0.319043i	$-0.896639\pi$
$227$	−28.5583	−1.89548	−0.947740	+	0.319043i	$0.896639\pi$
$228$	−0.0594846	−0.00393947
$229$	1.27546	0.0842845	0.0421423	−	0.999112i	$-0.486582\pi$
$229$	1.27546	0.0842845	0.0421423	+	0.999112i	$0.486582\pi$
$230$	−2.11672	−0.139572
$231$	4.88702	0.321542
$232$	−6.72083	−0.441244
$233$	25.4829	1.66944	0.834720	−	0.550675i	$-0.185630\pi$
$233$	25.4829	1.66944	0.834720	+	0.550675i	$0.185630\pi$
$234$	5.33764	0.348932
$235$	−25.1652	−1.64160
$236$	6.40429	0.416884
$237$	16.3935	1.06487
$238$	6.23091	0.403890
$239$	−3.28337	−0.212384	−0.106192	−	0.994346i	$-0.533866\pi$
$239$	−3.28337	−0.212384	−0.106192	+	0.994346i	$0.533866\pi$
$240$	3.33628	0.215356
$241$	2.12768	0.137056	0.0685280	−	0.997649i	$-0.478170\pi$
$241$	2.12768	0.137056	0.0685280	+	0.997649i	$0.478170\pi$
$242$	2.06163	0.132527
$243$	11.3607	0.728790
$244$	5.51992	0.353377
$245$	2.46727	0.157628
$246$	10.8179	0.689722
$247$	0.200428	0.0127530
$248$	−0.329418	−0.0209180
$249$	−22.4239	−1.42105
$250$	−9.65338	−0.610533
$251$	−2.35540	−0.148672	−0.0743358	−	0.997233i	$-0.523684\pi$
$251$	−2.35540	−0.148672	−0.0743358	+	0.997233i	$0.523684\pi$
$252$	1.17152	0.0737987
$253$	3.10059	0.194933
$254$	−8.58936	−0.538944
$255$	−20.7880	−1.30180
$256$	1.00000	0.0625000
$257$	2.97291	0.185445	0.0927226	−	0.995692i	$-0.470443\pi$
$257$	2.97291	0.185445	0.0927226	+	0.995692i	$0.470443\pi$
$258$	6.05199	0.376780
$259$	−7.43728	−0.462130
$260$	−11.2413	−0.697156
$261$	7.87357	0.487362
$262$	4.86423	0.300513
$263$	30.2951	1.86808	0.934038	−	0.357173i	$-0.116259\pi$
$263$	30.2951	1.86808	0.934038	+	0.357173i	$0.116259\pi$
$264$	−4.88702	−0.300775
$265$	−10.5535	−0.648297
$266$	0.0439905	0.00269723
$267$	−23.6617	−1.44807
$268$	−2.91057	−0.177791
$269$	−13.3075	−0.811372	−0.405686	−	0.914013i	$-0.632967\pi$
$269$	−13.3075	−0.811372	−0.405686	+	0.914013i	$0.632967\pi$
$270$	−13.9173	−0.846983
$271$	−2.83784	−0.172386	−0.0861932	−	0.996278i	$-0.527470\pi$
$271$	−2.83784	−0.172386	−0.0861932	+	0.996278i	$0.527470\pi$
$272$	−6.23091	−0.377804
$273$	6.16091	0.372875
$274$	−14.6037	−0.882242
$275$	−3.93005	−0.236991
$276$	−1.16009	−0.0698291
$277$	−9.90856	−0.595348	−0.297674	−	0.954668i	$-0.596211\pi$
$277$	−9.90856	−0.595348	−0.297674	+	0.954668i	$0.596211\pi$
$278$	10.5497	0.632730
$279$	0.385919	0.0231043
$280$	−2.46727	−0.147448
$281$	1.68871	0.100740	0.0503701	−	0.998731i	$-0.483960\pi$
$281$	1.68871	0.100740	0.0503701	+	0.998731i	$0.483960\pi$
$282$	−13.7920	−0.821304
$283$	12.0077	0.713783	0.356891	−	0.934146i	$-0.383837\pi$
$283$	12.0077	0.713783	0.356891	+	0.934146i	$0.383837\pi$
$284$	−5.91123	−0.350767
$285$	−0.146765	−0.00869359
$286$	16.4664	0.973678
$287$	−8.00012	−0.472232
$288$	−1.17152	−0.0690324
$289$	21.8242	1.28378
$290$	−16.5821	−0.973735
$291$	11.6415	0.682437
$292$	−6.88924	−0.403162
$293$	−13.0320	−0.761340	−0.380670	−	0.924711i	$-0.624307\pi$
$293$	−13.0320	−0.761340	−0.380670	+	0.924711i	$0.624307\pi$
$294$	1.35221	0.0788627
$295$	15.8011	0.919977
$296$	7.43728	0.432283
$297$	20.3863	1.18293
$298$	21.7848	1.26196
$299$	3.90882	0.226053
$300$	1.47043	0.0848955
$301$	−4.47562	−0.257970
$302$	−18.2824	−1.05204
$303$	−0.285010	−0.0163734
$304$	−0.0439905	−0.00252303
$305$	13.6191	0.779830
$306$	7.29962	0.417292
$307$	32.0555	1.82950	0.914751	−	0.404019i	$-0.132387\pi$
$307$	32.0555	1.82950	0.914751	+	0.404019i	$0.132387\pi$
$308$	3.61409	0.205932
$309$	5.61651	0.319512
$310$	−0.812762	−0.0461618
$311$	26.6948	1.51372	0.756862	−	0.653575i	$-0.226731\pi$
$311$	26.6948	1.51372	0.756862	+	0.653575i	$0.226731\pi$
$312$	−6.16091	−0.348793
$313$	−16.6593	−0.941637	−0.470818	−	0.882230i	$-0.656041\pi$
$313$	−16.6593	−0.941637	−0.470818	+	0.882230i	$0.656041\pi$
$314$	24.5315	1.38439
$315$	2.89045	0.162859
$316$	12.1235	0.681998
$317$	−11.3687	−0.638528	−0.319264	−	0.947666i	$-0.603436\pi$
$317$	−11.3687	−0.638528	−0.319264	+	0.947666i	$0.603436\pi$
$318$	−5.78396	−0.324349
$319$	24.2897	1.35996
$320$	2.46727	0.137925
$321$	11.3807	0.635209
$322$	0.857918	0.0478099
$323$	0.274101	0.0152514
$324$	−4.11299	−0.228499
$325$	−4.95450	−0.274826
$326$	16.7494	0.927665
$327$	−4.15315	−0.229670
$328$	8.00012	0.441733
$329$	10.1996	0.562322
$330$	−12.0576	−0.663749
$331$	27.6932	1.52216	0.761079	−	0.648659i	$-0.224670\pi$
$331$	27.6932	1.52216	0.761079	+	0.648659i	$0.224670\pi$
$332$	−16.5831	−0.910114
$333$	−8.71291	−0.477465
$334$	1.41790	0.0775841
$335$	−7.18116	−0.392349
$336$	−1.35221	−0.0737693
$337$	3.69179	0.201105	0.100552	−	0.994932i	$-0.467939\pi$
$337$	3.69179	0.201105	0.100552	+	0.994932i	$0.467939\pi$
$338$	7.75867	0.422016
$339$	2.88233	0.156547
$340$	−15.3733	−0.833736
$341$	1.19054	0.0644716
$342$	0.0515357	0.00278673
$343$	−1.00000	−0.0539949
$344$	4.47562	0.241309
$345$	−2.86225	−0.154099
$346$	−2.38807	−0.128383
$347$	14.4936	0.778059	0.389030	−	0.921225i	$-0.372810\pi$
$347$	14.4936	0.778059	0.389030	+	0.921225i	$0.372810\pi$
$348$	−9.08799	−0.487168
$349$	−0.449641	−0.0240687	−0.0120344	−	0.999928i	$-0.503831\pi$
$349$	−0.449641	−0.0240687	−0.0120344	+	0.999928i	$0.503831\pi$
$350$	−1.08743	−0.0581254
$351$	25.7004	1.37178
$352$	−3.61409	−0.192632
$353$	5.83050	0.310326	0.155163	−	0.987889i	$-0.450410\pi$
$353$	5.83050	0.310326	0.155163	+	0.987889i	$0.450410\pi$
$354$	8.65997	0.460272
$355$	−14.5846	−0.774071
$356$	−17.4985	−0.927416
$357$	8.42552	0.445926
$358$	−14.4821	−0.765404
$359$	11.1179	0.586780	0.293390	−	0.955993i	$-0.405217\pi$
$359$	11.1179	0.586780	0.293390	+	0.955993i	$0.405217\pi$
$360$	−2.89045	−0.152340
$361$	−18.9981	−0.999898
$362$	0.726434	0.0381805
$363$	2.78776	0.146320
$364$	4.55617	0.238808
$365$	−16.9976	−0.889697
$366$	7.46412	0.390156
$367$	10.9654	0.572389	0.286194	−	0.958172i	$-0.407610\pi$
$367$	10.9654	0.572389	0.286194	+	0.958172i	$0.407610\pi$
$368$	−0.857918	−0.0447221
$369$	−9.37229	−0.487902
$370$	18.3498	0.953960
$371$	4.27740	0.222072
$372$	−0.445443	−0.0230951
$373$	−0.642662	−0.0332758	−0.0166379	−	0.999862i	$-0.505296\pi$
$373$	−0.642662	−0.0332758	−0.0166379	+	0.999862i	$0.505296\pi$
$374$	22.5190	1.16443
$375$	−13.0534	−0.674076
$376$	−10.1996	−0.526004
$377$	30.6212	1.57707
$378$	5.64078	0.290131
$379$	−15.8865	−0.816034	−0.408017	−	0.912974i	$-0.633780\pi$
$379$	−15.8865	−0.816034	−0.408017	+	0.912974i	$0.633780\pi$
$380$	−0.108537	−0.00556781
$381$	−11.6146	−0.595036
$382$	−22.2354	−1.13766
$383$	12.0002	0.613183	0.306592	−	0.951841i	$-0.400811\pi$
$383$	12.0002	0.613183	0.306592	+	0.951841i	$0.400811\pi$
$384$	1.35221	0.0690049
$385$	8.91693	0.454449
$386$	6.43981	0.327777
$387$	−5.24327	−0.266530
$388$	8.60922	0.437067
$389$	−29.4418	−1.49276	−0.746380	−	0.665521i	$-0.768210\pi$
$389$	−29.4418	−1.49276	−0.746380	+	0.665521i	$0.768210\pi$
$390$	−15.2006	−0.769714
$391$	5.34561	0.270339
$392$	1.00000	0.0505076
$393$	6.57748	0.331790
$394$	1.59642	0.0804264
$395$	29.9119	1.50503
$396$	4.23397	0.212765
$397$	−38.3265	−1.92355	−0.961775	−	0.273841i	$-0.911706\pi$
$397$	−38.3265	−1.92355	−0.961775	+	0.273841i	$0.911706\pi$
$398$	−14.5094	−0.727292
$399$	0.0594846	0.00297796
$400$	1.08743	0.0543713
$401$	−20.6821	−1.03282	−0.516408	−	0.856342i	$-0.672731\pi$
$401$	−20.6821	−1.03282	−0.516408	+	0.856342i	$0.672731\pi$
$402$	−3.93571	−0.196295
$403$	1.50088	0.0747643
$404$	−0.210773	−0.0104863
$405$	−10.1479	−0.504251
$406$	6.72083	0.333549
$407$	−26.8790	−1.33234
$408$	−8.42552	−0.417125
$409$	22.0533	1.09046	0.545232	−	0.838285i	$-0.316441\pi$
$409$	22.0533	1.09046	0.545232	+	0.838285i	$0.316441\pi$
$410$	19.7385	0.974813
$411$	−19.7473	−0.974064
$412$	4.15357	0.204632
$413$	−6.40429	−0.315134
$414$	1.00507	0.0493964
$415$	−40.9149	−2.00843
$416$	−4.55617	−0.223385
$417$	14.2655	0.698583
$418$	0.158986	0.00777624
$419$	14.1427	0.690915	0.345457	−	0.938434i	$-0.387724\pi$
$419$	14.1427	0.690915	0.345457	+	0.938434i	$0.387724\pi$
$420$	−3.33628	−0.162794
$421$	20.0792	0.978601	0.489301	−	0.872115i	$-0.337252\pi$
$421$	20.0792	0.978601	0.489301	+	0.872115i	$0.337252\pi$
$422$	−23.2915	−1.13381
$423$	11.9490	0.580981
$424$	−4.27740	−0.207729
$425$	−6.77565	−0.328668
$426$	−7.99325	−0.387274
$427$	−5.51992	−0.267128
$428$	8.41635	0.406820
$429$	22.2661	1.07502
$430$	11.0426	0.532519
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.64078	−0.271392
$433$	−5.12584	−0.246332	−0.123166	−	0.992386i	$-0.539305\pi$
$433$	−5.12584	−0.246332	−0.123166	+	0.992386i	$0.539305\pi$
$434$	0.329418	0.0158125
$435$	−22.4225	−1.07508
$436$	−3.07137	−0.147092
$437$	0.0377403	0.00180536
$438$	−9.31573	−0.445123
$439$	5.46458	0.260810	0.130405	−	0.991461i	$-0.458372\pi$
$439$	5.46458	0.260810	0.130405	+	0.991461i	$0.458372\pi$
$440$	−8.91693	−0.425098
$441$	−1.17152	−0.0557866
$442$	28.3891	1.35033
$443$	−10.3639	−0.492404	−0.246202	−	0.969218i	$-0.579183\pi$
$443$	−10.3639	−0.492404	−0.246202	+	0.969218i	$0.579183\pi$
$444$	10.0568	0.477274
$445$	−43.1734	−2.04662
$446$	11.6516	0.551721
$447$	29.4577	1.39330
$448$	−1.00000	−0.0472456
$449$	−13.0593	−0.616306	−0.308153	−	0.951337i	$-0.599711\pi$
$449$	−13.0593	−0.616306	−0.308153	+	0.951337i	$0.599711\pi$
$450$	−1.27394	−0.0600541
$451$	−28.9131	−1.36147
$452$	2.13157	0.100260
$453$	−24.7217	−1.16153
$454$	−28.5583	−1.34031
$455$	11.2413	0.527000
$456$	−0.0594846	−0.00278562
$457$	−34.3068	−1.60480	−0.802402	−	0.596784i	$-0.796445\pi$
$457$	−34.3068	−1.60480	−0.802402	+	0.596784i	$0.796445\pi$
$458$	1.27546	0.0595981
$459$	35.1472	1.64053
$460$	−2.11672	−0.0986924
$461$	−13.2879	−0.618879	−0.309440	−	0.950919i	$-0.600141\pi$
$461$	−13.2879	−0.618879	−0.309440	+	0.950919i	$0.600141\pi$
$462$	4.88702	0.227365
$463$	−16.0159	−0.744320	−0.372160	−	0.928169i	$-0.621383\pi$
$463$	−16.0159	−0.744320	−0.372160	+	0.928169i	$0.621383\pi$
$464$	−6.72083	−0.312007
$465$	−1.09903	−0.0509662
$466$	25.4829	1.18047
$467$	9.61836	0.445084	0.222542	−	0.974923i	$-0.428564\pi$
$467$	9.61836	0.445084	0.222542	+	0.974923i	$0.428564\pi$
$468$	5.33764	0.246732
$469$	2.91057	0.134398
$470$	−25.1652	−1.16078
$471$	33.1718	1.52847
$472$	6.40429	0.294781
$473$	−16.1753	−0.743740
$474$	16.3935	0.752979
$475$	−0.0478365	−0.00219489
$476$	6.23091	0.285593
$477$	5.01106	0.229441
$478$	−3.28337	−0.150178
$479$	−15.2691	−0.697663	−0.348832	−	0.937185i	$-0.613421\pi$
$479$	−15.2691	−0.697663	−0.348832	+	0.937185i	$0.613421\pi$
$480$	3.33628	0.152280
$481$	−33.8855	−1.54505
$482$	2.12768	0.0969133
$483$	1.16009	0.0527859
$484$	2.06163	0.0937104
$485$	21.2413	0.964516
$486$	11.3607	0.515332
$487$	−31.9172	−1.44630	−0.723152	−	0.690689i	$-0.757307\pi$
$487$	−31.9172	−1.44630	−0.723152	+	0.690689i	$0.757307\pi$
$488$	5.51992	0.249875
$489$	22.6488	1.02421
$490$	2.46727	0.111460
$491$	36.7161	1.65697	0.828487	−	0.560008i	$-0.189202\pi$
$491$	36.7161	1.65697	0.828487	+	0.560008i	$0.189202\pi$
$492$	10.8179	0.487707
$493$	41.8769	1.88604
$494$	0.200428	0.00901770
$495$	10.4464	0.469529
$496$	−0.329418	−0.0147913
$497$	5.91123	0.265155
$498$	−22.4239	−1.00484
$499$	−1.32810	−0.0594539	−0.0297269	−	0.999558i	$-0.509464\pi$
$499$	−1.32810	−0.0594539	−0.0297269	+	0.999558i	$0.509464\pi$
$500$	−9.65338	−0.431712
$501$	1.91731	0.0856589
$502$	−2.35540	−0.105127
$503$	−31.5474	−1.40663	−0.703315	−	0.710878i	$-0.748298\pi$
$503$	−31.5474	−1.40663	−0.703315	+	0.710878i	$0.748298\pi$
$504$	1.17152	0.0521836
$505$	−0.520034	−0.0231412
$506$	3.10059	0.137838
$507$	10.4914	0.465939
$508$	−8.58936	−0.381091
$509$	−18.9968	−0.842018	−0.421009	−	0.907056i	$-0.638324\pi$
$509$	−18.9968	−0.842018	−0.421009	+	0.907056i	$0.638324\pi$
$510$	−20.7880	−0.920510
$511$	6.88924	0.304762
$512$	1.00000	0.0441942
$513$	0.248141	0.0109557
$514$	2.97291	0.131130
$515$	10.2480	0.451580
$516$	6.05199	0.266424
$517$	36.8623	1.62120
$518$	−7.43728	−0.326775
$519$	−3.22918	−0.141745
$520$	−11.2413	−0.492964
$521$	−10.4693	−0.458669	−0.229334	−	0.973348i	$-0.573655\pi$
$521$	−10.4693	−0.458669	−0.229334	+	0.973348i	$0.573655\pi$
$522$	7.87357	0.344617
$523$	44.6251	1.95132	0.975660	−	0.219288i	$-0.0703733\pi$
$523$	44.6251	1.95132	0.975660	+	0.219288i	$0.0703733\pi$
$524$	4.86423	0.212495
$525$	−1.47043	−0.0641749
$526$	30.2951	1.32093
$527$	2.05257	0.0894114
$528$	−4.88702	−0.212680
$529$	−22.2640	−0.967999
$530$	−10.5535	−0.458415
$531$	−7.50274	−0.325591
$532$	0.0439905	0.00190723
$533$	−36.4499	−1.57882
$534$	−23.6617	−1.02394
$535$	20.7654	0.897767
$536$	−2.91057	−0.125717
$537$	−19.5829	−0.845065
$538$	−13.3075	−0.573727
$539$	−3.61409	−0.155670
$540$	−13.9173	−0.598907
$541$	−8.40932	−0.361545	−0.180772	−	0.983525i	$-0.557860\pi$
$541$	−8.40932	−0.361545	−0.180772	+	0.983525i	$0.557860\pi$
$542$	−2.83784	−0.121896
$543$	0.982294	0.0421543
$544$	−6.23091	−0.267148
$545$	−7.57790	−0.324602
$546$	6.16091	0.263663
$547$	−26.7573	−1.14406	−0.572030	−	0.820233i	$-0.693844\pi$
$547$	−26.7573	−1.14406	−0.572030	+	0.820233i	$0.693844\pi$
$548$	−14.6037	−0.623839
$549$	−6.46669	−0.275992
$550$	−3.93005	−0.167578
$551$	0.295653	0.0125952
$552$	−1.16009	−0.0493767
$553$	−12.1235	−0.515542
$554$	−9.90856	−0.420974
$555$	24.8128	1.05325
$556$	10.5497	0.447407
$557$	16.4315	0.696227	0.348113	−	0.937452i	$-0.386822\pi$
$557$	16.4315	0.696227	0.348113	+	0.937452i	$0.386822\pi$
$558$	0.385919	0.0163372
$559$	−20.3917	−0.862475
$560$	−2.46727	−0.104261
$561$	30.4506	1.28562
$562$	1.68871	0.0712341
$563$	−19.2764	−0.812402	−0.406201	−	0.913784i	$-0.633147\pi$
$563$	−19.2764	−0.812402	−0.406201	+	0.913784i	$0.633147\pi$
$564$	−13.7920	−0.580750
$565$	5.25915	0.221254
$566$	12.0077	0.504721
$567$	4.11299	0.172729
$568$	−5.91123	−0.248030
$569$	2.60969	0.109404	0.0547020	−	0.998503i	$-0.482579\pi$
$569$	2.60969	0.109404	0.0547020	+	0.998503i	$0.482579\pi$
$570$	−0.146765	−0.00614730
$571$	21.8914	0.916125	0.458063	−	0.888920i	$-0.348544\pi$
$571$	21.8914	0.916125	0.458063	+	0.888920i	$0.348544\pi$
$572$	16.4664	0.688494
$573$	−30.0670	−1.25607
$574$	−8.00012	−0.333919
$575$	−0.932923	−0.0389056
$576$	−1.17152	−0.0488133
$577$	32.6596	1.35964	0.679819	−	0.733380i	$-0.262058\pi$
$577$	32.6596	1.35964	0.679819	+	0.733380i	$0.262058\pi$
$578$	21.8242	0.907768
$579$	8.70799	0.361892
$580$	−16.5821	−0.688534
$581$	16.5831	0.687982
$582$	11.6415	0.482556
$583$	15.4589	0.640243
$584$	−6.88924	−0.285079
$585$	13.1694	0.544487
$586$	−13.0320	−0.538349
$587$	4.31527	0.178110	0.0890552	−	0.996027i	$-0.471615\pi$
$587$	4.31527	0.178110	0.0890552	+	0.996027i	$0.471615\pi$
$588$	1.35221	0.0557643
$589$	0.0144913	0.000597102 0
$590$	15.8011	0.650522
$591$	2.15870	0.0887970
$592$	7.43728	0.305670
$593$	10.0326	0.411991	0.205996	−	0.978553i	$-0.433957\pi$
$593$	10.0326	0.411991	0.205996	+	0.978553i	$0.433957\pi$
$594$	20.3863	0.836460
$595$	15.3733	0.630245
$596$	21.7848	0.892340
$597$	−19.6198	−0.802987
$598$	3.90882	0.159844
$599$	−12.7059	−0.519150	−0.259575	−	0.965723i	$-0.583583\pi$
$599$	−12.7059	−0.519150	−0.259575	+	0.965723i	$0.583583\pi$
$600$	1.47043	0.0600302
$601$	−25.3883	−1.03561	−0.517805	−	0.855499i	$-0.673251\pi$
$601$	−25.3883	−1.03561	−0.517805	+	0.855499i	$0.673251\pi$
$602$	−4.47562	−0.182413
$603$	3.40979	0.138857
$604$	−18.2824	−0.743901
$605$	5.08660	0.206800
$606$	−0.285010	−0.0115777
$607$	12.9737	0.526586	0.263293	−	0.964716i	$-0.415191\pi$
$607$	12.9737	0.526586	0.263293	+	0.964716i	$0.415191\pi$
$608$	−0.0439905	−0.00178405
$609$	9.08799	0.368264
$610$	13.6191	0.551423
$611$	46.4711	1.88002
$612$	7.29962	0.295070
$613$	−43.3705	−1.75172	−0.875859	−	0.482568i	$-0.839704\pi$
$613$	−43.3705	−1.75172	−0.875859	+	0.482568i	$0.839704\pi$
$614$	32.0555	1.29365
$615$	26.6906	1.07627
$616$	3.61409	0.145616
$617$	19.6821	0.792370	0.396185	−	0.918171i	$-0.370334\pi$
$617$	19.6821	0.792370	0.396185	+	0.918171i	$0.370334\pi$
$618$	5.61651	0.225929
$619$	−29.8253	−1.19878	−0.599391	−	0.800457i	$-0.704590\pi$
$619$	−29.8253	−1.19878	−0.599391	+	0.800457i	$0.704590\pi$
$620$	−0.812762	−0.0326413
$621$	4.83933	0.194196
$622$	26.6948	1.07036
$623$	17.4985	0.701061
$624$	−6.16091	−0.246634
$625$	−29.2546	−1.17019
$626$	−16.6593	−0.665838
$627$	0.214983	0.00858558
$628$	24.5315	0.978912
$629$	−46.3410	−1.84774
$630$	2.89045	0.115158
$631$	39.1087	1.55689	0.778446	−	0.627711i	$-0.216008\pi$
$631$	39.1087	1.55689	0.778446	+	0.627711i	$0.216008\pi$
$632$	12.1235	0.482246
$633$	−31.4951	−1.25182
$634$	−11.3687	−0.451508
$635$	−21.1923	−0.840990
$636$	−5.78396	−0.229349
$637$	−4.55617	−0.180522
$638$	24.2897	0.961637
$639$	6.92512	0.273953
$640$	2.46727	0.0975275
$641$	5.29763	0.209244	0.104622	−	0.994512i	$-0.466637\pi$
$641$	5.29763	0.209244	0.104622	+	0.994512i	$0.466637\pi$
$642$	11.3807	0.449161
$643$	−21.4537	−0.846053	−0.423026	−	0.906117i	$-0.639032\pi$
$643$	−21.4537	−0.846053	−0.423026	+	0.906117i	$0.639032\pi$
$644$	0.857918	0.0338067
$645$	14.9319	0.587943
$646$	0.274101	0.0107844
$647$	−43.3354	−1.70369	−0.851845	−	0.523793i	$-0.824516\pi$
$647$	−43.3354	−1.70369	−0.851845	+	0.523793i	$0.824516\pi$
$648$	−4.11299	−0.161573
$649$	−23.1457	−0.908547
$650$	−4.95450	−0.194331
$651$	0.445443	0.0174583
$652$	16.7494	0.655958
$653$	35.4657	1.38788	0.693940	−	0.720033i	$-0.255873\pi$
$653$	35.4657	1.38788	0.693940	+	0.720033i	$0.255873\pi$
$654$	−4.15315	−0.162401
$655$	12.0014	0.468932
$656$	8.00012	0.312352
$657$	8.07087	0.314875
$658$	10.1996	0.397622
$659$	17.8435	0.695084	0.347542	−	0.937664i	$-0.387016\pi$
$659$	17.8435	0.695084	0.347542	+	0.937664i	$0.387016\pi$
$660$	−12.0576	−0.469341
$661$	−24.1492	−0.939296	−0.469648	−	0.882854i	$-0.655619\pi$
$661$	−24.1492	−0.939296	−0.469648	+	0.882854i	$0.655619\pi$
$662$	27.6932	1.07633
$663$	38.3881	1.49087
$664$	−16.5831	−0.643548
$665$	0.108537	0.00420887
$666$	−8.71291	−0.337618
$667$	5.76592	0.223257
$668$	1.41790	0.0548602
$669$	15.7555	0.609143
$670$	−7.18116	−0.277433
$671$	−19.9495	−0.770141
$672$	−1.35221	−0.0521628
$673$	−49.7872	−1.91915	−0.959577	−	0.281445i	$-0.909186\pi$
$673$	−49.7872	−1.91915	−0.959577	+	0.281445i	$0.909186\pi$
$674$	3.69179	0.142203
$675$	−6.13394	−0.236095
$676$	7.75867	0.298410
$677$	11.6725	0.448611	0.224306	−	0.974519i	$-0.427989\pi$
$677$	11.6725	0.448611	0.224306	+	0.974519i	$0.427989\pi$
$678$	2.88233	0.110695
$679$	−8.60922	−0.330391
$680$	−15.3733	−0.589541
$681$	−38.6169	−1.47980
$682$	1.19054	0.0455883
$683$	20.5026	0.784512	0.392256	−	0.919856i	$-0.371695\pi$
$683$	20.5026	0.784512	0.392256	+	0.919856i	$0.371695\pi$
$684$	0.0515357	0.00197052
$685$	−36.0313	−1.37668
$686$	−1.00000	−0.0381802
$687$	1.72469	0.0658010
$688$	4.47562	0.170631
$689$	19.4886	0.742456
$690$	−2.86225	−0.108964
$691$	−25.5432	−0.971710	−0.485855	−	0.874039i	$-0.661492\pi$
$691$	−25.5432	−0.971710	−0.485855	+	0.874039i	$0.661492\pi$
$692$	−2.38807	−0.0907807
$693$	−4.23397	−0.160835
$694$	14.4936	0.550171
$695$	26.0290	0.987336
$696$	−9.08799	−0.344480
$697$	−49.8480	−1.88813
$698$	−0.449641	−0.0170192
$699$	34.4583	1.30333
$700$	−1.08743	−0.0411009
$701$	−16.1035	−0.608221	−0.304111	−	0.952637i	$-0.598359\pi$
$701$	−16.1035	−0.608221	−0.304111	+	0.952637i	$0.598359\pi$
$702$	25.7004	0.969998
$703$	−0.327170	−0.0123395
$704$	−3.61409	−0.136211
$705$	−34.0287	−1.28159
$706$	5.83050	0.219434
$707$	0.210773	0.00792693
$708$	8.65997	0.325461
$709$	15.9071	0.597404	0.298702	−	0.954346i	$-0.403446\pi$
$709$	15.9071	0.597404	0.298702	+	0.954346i	$0.403446\pi$
$710$	−14.5846	−0.547351
$711$	−14.2029	−0.532649
$712$	−17.4985	−0.655782
$713$	0.282613	0.0105840
$714$	8.42552	0.315317
$715$	40.6271	1.51937
$716$	−14.4821	−0.541222
$717$	−4.43982	−0.165808
$718$	11.1179	0.414916
$719$	−50.8393	−1.89599	−0.947993	−	0.318291i	$-0.896891\pi$
$719$	−50.8393	−1.89599	−0.947993	+	0.318291i	$0.896891\pi$
$720$	−2.89045	−0.107721
$721$	−4.15357	−0.154687
$722$	−18.9981	−0.707035
$723$	2.87708	0.107000
$724$	0.726434	0.0269977
$725$	−7.30841	−0.271427
$726$	2.78776	0.103464
$727$	−26.1972	−0.971601	−0.485801	−	0.874070i	$-0.661472\pi$
$727$	−26.1972	−0.971601	−0.485801	+	0.874070i	$0.661472\pi$
$728$	4.55617	0.168863
$729$	27.7011	1.02597
$730$	−16.9976	−0.629110
$731$	−27.8872	−1.03144
$732$	7.46412	0.275882
$733$	1.64887	0.0609024	0.0304512	−	0.999536i	$-0.490306\pi$
$733$	1.64887	0.0609024	0.0304512	+	0.999536i	$0.490306\pi$
$734$	10.9654	0.404740
$735$	3.33628	0.123060
$736$	−0.857918	−0.0316233
$737$	10.5191	0.387474
$738$	−9.37229	−0.344999
$739$	−34.3068	−1.26200	−0.630999	−	0.775784i	$-0.717355\pi$
$739$	−34.3068	−1.26200	−0.630999	+	0.775784i	$0.717355\pi$
$740$	18.3498	0.674552
$741$	0.271022	0.00995624
$742$	4.27740	0.157028
$743$	30.9174	1.13425	0.567125	−	0.823632i	$-0.308056\pi$
$743$	30.9174	1.13425	0.567125	+	0.823632i	$0.308056\pi$
$744$	−0.445443	−0.0163307
$745$	53.7490	1.96921
$746$	−0.642662	−0.0235295
$747$	19.4274	0.710810
$748$	22.5190	0.823378
$749$	−8.41635	−0.307527
$750$	−13.0534	−0.476644
$751$	−23.5847	−0.860617	−0.430308	−	0.902682i	$-0.641595\pi$
$751$	−23.5847	−0.860617	−0.430308	+	0.902682i	$0.641595\pi$
$752$	−10.1996	−0.371941
$753$	−3.18500	−0.116068
$754$	30.6212	1.11516
$755$	−45.1077	−1.64164
$756$	5.64078	0.205153
$757$	12.9700	0.471403	0.235701	−	0.971826i	$-0.424261\pi$
$757$	12.9700	0.471403	0.235701	+	0.971826i	$0.424261\pi$
$758$	−15.8865	−0.577023
$759$	4.19266	0.152184
$760$	−0.108537	−0.00393704
$761$	−46.6100	−1.68961	−0.844806	−	0.535073i	$-0.820284\pi$
$761$	−46.6100	−1.68961	−0.844806	+	0.535073i	$0.820284\pi$
$762$	−11.6146	−0.420754
$763$	3.07137	0.111191
$764$	−22.2354	−0.804448
$765$	18.0101	0.651158
$766$	12.0002	0.433586
$767$	−29.1790	−1.05359
$768$	1.35221	0.0487938
$769$	32.8471	1.18450	0.592248	−	0.805756i	$-0.298241\pi$
$769$	32.8471	1.18450	0.592248	+	0.805756i	$0.298241\pi$
$770$	8.91693	0.321344
$771$	4.02001	0.144777
$772$	6.43981	0.231774
$773$	21.5533	0.775220	0.387610	−	0.921823i	$-0.373301\pi$
$773$	21.5533	0.775220	0.387610	+	0.921823i	$0.373301\pi$
$774$	−5.24327	−0.188465
$775$	−0.358217	−0.0128675
$776$	8.60922	0.309053
$777$	−10.0568	−0.360785
$778$	−29.4418	−1.05554
$779$	−0.351930	−0.0126092
$780$	−15.2006	−0.544270
$781$	21.3637	0.764454
$782$	5.34561	0.191159
$783$	37.9107	1.35482
$784$	1.00000	0.0357143
$785$	60.5258	2.16026
$786$	6.57748	0.234611
$787$	−19.6699	−0.701155	−0.350577	−	0.936534i	$-0.614015\pi$
$787$	−19.6699	−0.701155	−0.350577	+	0.936534i	$0.614015\pi$
$788$	1.59642	0.0568701
$789$	40.9655	1.45841
$790$	29.9119	1.06422
$791$	−2.13157	−0.0757897
$792$	4.23397	0.150448
$793$	−25.1497	−0.893092
$794$	−38.3265	−1.36016
$795$	−14.2706	−0.506126
$796$	−14.5094	−0.514273
$797$	−42.5143	−1.50593	−0.752966	−	0.658059i	$-0.771378\pi$
$797$	−42.5143	−1.50593	−0.752966	+	0.658059i	$0.771378\pi$
$798$	0.0594846	0.00210573
$799$	63.5528	2.24834
$800$	1.08743	0.0384463
$801$	20.4998	0.724324
$802$	−20.6821	−0.730312
$803$	24.8983	0.878643
$804$	−3.93571	−0.138802
$805$	2.11672	0.0746045
$806$	1.50088	0.0528663
$807$	−17.9946	−0.633439
$808$	−0.210773	−0.00741497
$809$	−12.3300	−0.433501	−0.216750	−	0.976227i	$-0.569546\pi$
$809$	−12.3300	−0.433501	−0.216750	+	0.976227i	$0.569546\pi$
$810$	−10.1479	−0.356559
$811$	−48.5626	−1.70526	−0.852632	−	0.522511i	$-0.824995\pi$
$811$	−48.5626	−1.70526	−0.852632	+	0.522511i	$0.824995\pi$
$812$	6.72083	0.235855
$813$	−3.83736	−0.134582
$814$	−26.8790	−0.942108
$815$	41.3254	1.44756
$816$	−8.42552	−0.294952
$817$	−0.196885	−0.00688813
$818$	22.0533	0.771075
$819$	−5.33764	−0.186512
$820$	19.7385	0.689297
$821$	−3.65654	−0.127614	−0.0638071	−	0.997962i	$-0.520324\pi$
$821$	−3.65654	−0.127614	−0.0638071	+	0.997962i	$0.520324\pi$
$822$	−19.7473	−0.688767
$823$	22.4454	0.782398	0.391199	−	0.920306i	$-0.372060\pi$
$823$	22.4454	0.782398	0.391199	+	0.920306i	$0.372060\pi$
$824$	4.15357	0.144696
$825$	−5.31427	−0.185019
$826$	−6.40429	−0.222834
$827$	19.2366	0.668922	0.334461	−	0.942410i	$-0.391446\pi$
$827$	19.2366	0.668922	0.334461	+	0.942410i	$0.391446\pi$
$828$	1.00507	0.0349285
$829$	−5.70353	−0.198092	−0.0990459	−	0.995083i	$-0.531579\pi$
$829$	−5.70353	−0.198092	−0.0990459	+	0.995083i	$0.531579\pi$
$830$	−40.9149	−1.42018
$831$	−13.3985	−0.464789
$832$	−4.55617	−0.157957
$833$	−6.23091	−0.215888
$834$	14.2655	0.493973
$835$	3.49835	0.121065
$836$	0.158986	0.00549864
$837$	1.85817	0.0642279
$838$	14.1427	0.488550
$839$	−17.7968	−0.614415	−0.307208	−	0.951642i	$-0.599395\pi$
$839$	−17.7968	−0.614415	−0.307208	+	0.951642i	$0.599395\pi$
$840$	−3.33628	−0.115113
$841$	16.1695	0.557570
$842$	20.0792	0.691976
$843$	2.28350	0.0786480
$844$	−23.2915	−0.801727
$845$	19.1427	0.658530
$846$	11.9490	0.410816
$847$	−2.06163	−0.0708384
$848$	−4.27740	−0.146887
$849$	16.2370	0.557251
$850$	−6.77565	−0.232403
$851$	−6.38058	−0.218723
$852$	−7.99325	−0.273844
$853$	−18.7651	−0.642505	−0.321252	−	0.946994i	$-0.604104\pi$
$853$	−18.7651	−0.642505	−0.321252	+	0.946994i	$0.604104\pi$
$854$	−5.51992	−0.188888
$855$	0.127153	0.00434853
$856$	8.41635	0.287665
$857$	−48.6512	−1.66189	−0.830946	−	0.556353i	$-0.812200\pi$
$857$	−48.6512	−1.66189	−0.830946	+	0.556353i	$0.812200\pi$
$858$	22.2661	0.760151
$859$	−24.4775	−0.835162	−0.417581	−	0.908640i	$-0.637122\pi$
$859$	−24.4775	−0.835162	−0.417581	+	0.908640i	$0.637122\pi$
$860$	11.0426	0.376548
$861$	−10.8179	−0.368672
$862$	1.00000	0.0340601
$863$	15.7936	0.537621	0.268811	−	0.963193i	$-0.413369\pi$
$863$	15.7936	0.537621	0.268811	+	0.963193i	$0.413369\pi$
$864$	−5.64078	−0.191903
$865$	−5.89201	−0.200334
$866$	−5.12584	−0.174183
$867$	29.5110	1.00225
$868$	0.329418	0.0111812
$869$	−43.8153	−1.48633
$870$	−22.4225	−0.760195
$871$	13.2610	0.449333
$872$	−3.07137	−0.104010
$873$	−10.0859	−0.341354
$874$	0.0377403	0.00127658
$875$	9.65338	0.326344
$876$	−9.31573	−0.314749
$877$	6.13888	0.207295	0.103648	−	0.994614i	$-0.466949\pi$
$877$	6.13888	0.207295	0.103648	+	0.994614i	$0.466949\pi$
$878$	5.46458	0.184421
$879$	−17.6221	−0.594379
$880$	−8.91693	−0.300590
$881$	−19.6015	−0.660392	−0.330196	−	0.943912i	$-0.607115\pi$
$881$	−19.6015	−0.660392	−0.330196	+	0.943912i	$0.607115\pi$
$882$	−1.17152	−0.0394471
$883$	53.5845	1.80326	0.901631	−	0.432506i	$-0.142371\pi$
$883$	53.5845	1.80326	0.901631	+	0.432506i	$0.142371\pi$
$884$	28.3891	0.954828
$885$	21.3665	0.718227
$886$	−10.3639	−0.348182
$887$	28.3618	0.952297	0.476149	−	0.879365i	$-0.342032\pi$
$887$	28.3618	0.952297	0.476149	+	0.879365i	$0.342032\pi$
$888$	10.0568	0.337484
$889$	8.58936	0.288078
$890$	−43.1734	−1.44718
$891$	14.8647	0.497986
$892$	11.6516	0.390126
$893$	0.448686	0.0150147
$894$	29.4577	0.985213
$895$	−35.7313	−1.19437
$896$	−1.00000	−0.0334077
$897$	5.28556	0.176480
$898$	−13.0593	−0.435794
$899$	2.21396	0.0738397
$900$	−1.27394	−0.0424647
$901$	26.6521	0.887911
$902$	−28.9131	−0.962702
$903$	−6.05199	−0.201398
$904$	2.13157	0.0708948
$905$	1.79231	0.0595784
$906$	−24.7217	−0.821325
$907$	17.2018	0.571178	0.285589	−	0.958352i	$-0.407811\pi$
$907$	17.2018	0.571178	0.285589	+	0.958352i	$0.407811\pi$
$908$	−28.5583	−0.947740
$909$	0.246924	0.00818997
$910$	11.2413	0.372646
$911$	5.18677	0.171845	0.0859227	−	0.996302i	$-0.472616\pi$
$911$	5.18677	0.171845	0.0859227	+	0.996302i	$0.472616\pi$
$912$	−0.0594846	−0.00196973
$913$	59.9327	1.98348
$914$	−34.3068	−1.13477
$915$	18.4160	0.608814
$916$	1.27546	0.0421423
$917$	−4.86423	−0.160631
$918$	35.1472	1.16003
$919$	39.9905	1.31917	0.659583	−	0.751632i	$-0.270733\pi$
$919$	39.9905	1.31917	0.659583	+	0.751632i	$0.270733\pi$
$920$	−2.11672	−0.0697861
$921$	43.3458	1.42829
$922$	−13.2879	−0.437614
$923$	26.9326	0.886496
$924$	4.88702	0.160771
$925$	8.08750	0.265915
$926$	−16.0159	−0.526314
$927$	−4.86598	−0.159820
$928$	−6.72083	−0.220622
$929$	17.6071	0.577669	0.288835	−	0.957379i	$-0.406732\pi$
$929$	17.6071	0.577669	0.288835	+	0.957379i	$0.406732\pi$
$930$	−1.09903	−0.0360386
$931$	−0.0439905	−0.00144173
$932$	25.4829	0.834720
$933$	36.0971	1.18177
$934$	9.61836	0.314722
$935$	55.5606	1.81703
$936$	5.33764	0.174466
$937$	6.91886	0.226029	0.113015	−	0.993593i	$-0.463949\pi$
$937$	6.91886	0.226029	0.113015	+	0.993593i	$0.463949\pi$
$938$	2.91057	0.0950335
$939$	−22.5269	−0.735136
$940$	−25.1652	−0.820798
$941$	−52.2686	−1.70391	−0.851954	−	0.523617i	$-0.824582\pi$
$941$	−52.2686	−1.70391	−0.851954	+	0.523617i	$0.824582\pi$
$942$	33.1718	1.08079
$943$	−6.86345	−0.223505
$944$	6.40429	0.208442
$945$	13.9173	0.452731
$946$	−16.1753	−0.525903
$947$	−2.36249	−0.0767708	−0.0383854	−	0.999263i	$-0.512221\pi$
$947$	−2.36249	−0.0767708	−0.0383854	+	0.999263i	$0.512221\pi$
$948$	16.3935	0.532437
$949$	31.3886	1.01892
$950$	−0.0478365	−0.00155202
$951$	−15.3729	−0.498500
$952$	6.23091	0.201945
$953$	0.795488	0.0257684	0.0128842	−	0.999917i	$-0.495899\pi$
$953$	0.795488	0.0257684	0.0128842	+	0.999917i	$0.495899\pi$
$954$	5.01106	0.162239
$955$	−54.8607	−1.77525
$956$	−3.28337	−0.106192
$957$	32.8448	1.06172
$958$	−15.2691	−0.493322
$959$	14.6037	0.471578
$960$	3.33628	0.107678
$961$	−30.8915	−0.996499
$962$	−33.8855	−1.09251
$963$	−9.85991	−0.317731
$964$	2.12768	0.0685280
$965$	15.8887	0.511477
$966$	1.16009	0.0373252
$967$	28.0545	0.902172	0.451086	−	0.892480i	$-0.351037\pi$
$967$	28.0545	0.902172	0.451086	+	0.892480i	$0.351037\pi$
$968$	2.06163	0.0662633
$969$	0.370643	0.0119068
$970$	21.2413	0.682016
$971$	36.9820	1.18681	0.593404	−	0.804905i	$-0.297784\pi$
$971$	36.9820	1.18681	0.593404	+	0.804905i	$0.297784\pi$
$972$	11.3607	0.364395
$973$	−10.5497	−0.338208
$974$	−31.9172	−1.02269
$975$	−6.69954	−0.214557
$976$	5.51992	0.176688
$977$	45.4777	1.45496	0.727480	−	0.686129i	$-0.240691\pi$
$977$	45.4777	1.45496	0.727480	+	0.686129i	$0.240691\pi$
$978$	22.6488	0.724229
$979$	63.2410	2.02119
$980$	2.46727	0.0788141
$981$	3.59817	0.114881
$982$	36.7161	1.17166
$983$	−30.9793	−0.988085	−0.494043	−	0.869438i	$-0.664481\pi$
$983$	−30.9793	−0.988085	−0.494043	+	0.869438i	$0.664481\pi$
$984$	10.8179	0.344861
$985$	3.93880	0.125501
$986$	41.8769	1.33363
$987$	13.7920	0.439005
$988$	0.200428	0.00637648
$989$	−3.83971	−0.122096
$990$	10.4464	0.332007
$991$	9.05110	0.287518	0.143759	−	0.989613i	$-0.454081\pi$
$991$	9.05110	0.287518	0.143759	+	0.989613i	$0.454081\pi$
$992$	−0.329418	−0.0104590
$993$	37.4472	1.18835
$994$	5.91123	0.187493
$995$	−35.7987	−1.13489
$996$	−22.4239	−0.710527
$997$	−6.57533	−0.208243	−0.104121	−	0.994565i	$-0.533203\pi$
$997$	−6.57533	−0.208243	−0.104121	+	0.994565i	$0.533203\pi$
$998$	−1.32810	−0.0420402
$999$	−41.9521	−1.32731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.14	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.14	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.35221 q^{3} +1.00000 q^{4} +2.46727 q^{5} +1.35221 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.17152 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.35221 q^{3} +1.00000 q^{4} +2.46727 q^{5} +1.35221 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.17152 q^{9} +2.46727 q^{10} -3.61409 q^{11} +1.35221 q^{12} -4.55617 q^{13} -1.00000 q^{14} +3.33628 q^{15} +1.00000 q^{16} -6.23091 q^{17} -1.17152 q^{18} -0.0439905 q^{19} +2.46727 q^{20} -1.35221 q^{21} -3.61409 q^{22} -0.857918 q^{23} +1.35221 q^{24} +1.08743 q^{25} -4.55617 q^{26} -5.64078 q^{27} -1.00000 q^{28} -6.72083 q^{29} +3.33628 q^{30} -0.329418 q^{31} +1.00000 q^{32} -4.88702 q^{33} -6.23091 q^{34} -2.46727 q^{35} -1.17152 q^{36} +7.43728 q^{37} -0.0439905 q^{38} -6.16091 q^{39} +2.46727 q^{40} +8.00012 q^{41} -1.35221 q^{42} +4.47562 q^{43} -3.61409 q^{44} -2.89045 q^{45} -0.857918 q^{46} -10.1996 q^{47} +1.35221 q^{48} +1.00000 q^{49} +1.08743 q^{50} -8.42552 q^{51} -4.55617 q^{52} -4.27740 q^{53} -5.64078 q^{54} -8.91693 q^{55} -1.00000 q^{56} -0.0594846 q^{57} -6.72083 q^{58} +6.40429 q^{59} +3.33628 q^{60} +5.51992 q^{61} -0.329418 q^{62} +1.17152 q^{63} +1.00000 q^{64} -11.2413 q^{65} -4.88702 q^{66} -2.91057 q^{67} -6.23091 q^{68} -1.16009 q^{69} -2.46727 q^{70} -5.91123 q^{71} -1.17152 q^{72} -6.88924 q^{73} +7.43728 q^{74} +1.47043 q^{75} -0.0439905 q^{76} +3.61409 q^{77} -6.16091 q^{78} +12.1235 q^{79} +2.46727 q^{80} -4.11299 q^{81} +8.00012 q^{82} -16.5831 q^{83} -1.35221 q^{84} -15.3733 q^{85} +4.47562 q^{86} -9.08799 q^{87} -3.61409 q^{88} -17.4985 q^{89} -2.89045 q^{90} +4.55617 q^{91} -0.857918 q^{92} -0.445443 q^{93} -10.1996 q^{94} -0.108537 q^{95} +1.35221 q^{96} +8.60922 q^{97} +1.00000 q^{98} +4.23397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more