LMFDB - Embedded newform 6015.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40618 q^{2} +1.00000 q^{3} +3.78972 q^{4} -1.00000 q^{5} -2.40618 q^{6} -5.00600 q^{7} -4.30638 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.40618 q^{2} +1.00000 q^{3} +3.78972 q^{4} -1.00000 q^{5} -2.40618 q^{6} -5.00600 q^{7} -4.30638 q^{8} +1.00000 q^{9} +2.40618 q^{10} -3.29153 q^{11} +3.78972 q^{12} -0.878616 q^{13} +12.0454 q^{14} -1.00000 q^{15} +2.78251 q^{16} +4.11498 q^{17} -2.40618 q^{18} -5.70864 q^{19} -3.78972 q^{20} -5.00600 q^{21} +7.92003 q^{22} -6.33673 q^{23} -4.30638 q^{24} +1.00000 q^{25} +2.11411 q^{26} +1.00000 q^{27} -18.9713 q^{28} -6.66565 q^{29} +2.40618 q^{30} -7.43343 q^{31} +1.91753 q^{32} -3.29153 q^{33} -9.90140 q^{34} +5.00600 q^{35} +3.78972 q^{36} -7.47586 q^{37} +13.7360 q^{38} -0.878616 q^{39} +4.30638 q^{40} -4.44549 q^{41} +12.0454 q^{42} +10.2434 q^{43} -12.4740 q^{44} -1.00000 q^{45} +15.2473 q^{46} -1.14869 q^{47} +2.78251 q^{48} +18.0601 q^{49} -2.40618 q^{50} +4.11498 q^{51} -3.32971 q^{52} -7.78186 q^{53} -2.40618 q^{54} +3.29153 q^{55} +21.5578 q^{56} -5.70864 q^{57} +16.0388 q^{58} -13.7047 q^{59} -3.78972 q^{60} +6.51077 q^{61} +17.8862 q^{62} -5.00600 q^{63} -10.1790 q^{64} +0.878616 q^{65} +7.92003 q^{66} +10.2307 q^{67} +15.5946 q^{68} -6.33673 q^{69} -12.0454 q^{70} -2.94662 q^{71} -4.30638 q^{72} -9.03752 q^{73} +17.9883 q^{74} +1.00000 q^{75} -21.6341 q^{76} +16.4774 q^{77} +2.11411 q^{78} -2.87478 q^{79} -2.78251 q^{80} +1.00000 q^{81} +10.6967 q^{82} -10.4097 q^{83} -18.9713 q^{84} -4.11498 q^{85} -24.6475 q^{86} -6.66565 q^{87} +14.1746 q^{88} -12.5790 q^{89} +2.40618 q^{90} +4.39836 q^{91} -24.0144 q^{92} -7.43343 q^{93} +2.76397 q^{94} +5.70864 q^{95} +1.91753 q^{96} +17.2423 q^{97} -43.4559 q^{98} -3.29153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.40618	−1.70143	−0.850714	−	0.525629i	$-0.823830\pi$
$2$	−2.40618	−1.70143	−0.850714	+	0.525629i	$0.823830\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.78972	1.89486
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.40618	−0.982320
$7$	−5.00600	−1.89209	−0.946046	−	0.324033i	$-0.894961\pi$
$7$	−5.00600	−1.89209	−0.946046	+	0.324033i	$0.894961\pi$
$8$	−4.30638	−1.52254
$9$	1.00000	0.333333
$10$	2.40618	0.760902
$11$	−3.29153	−0.992435	−0.496217	−	0.868198i	$-0.665278\pi$
$11$	−3.29153	−0.992435	−0.496217	+	0.868198i	$0.665278\pi$
$12$	3.78972	1.09400
$13$	−0.878616	−0.243684	−0.121842	−	0.992549i	$-0.538880\pi$
$13$	−0.878616	−0.243684	−0.121842	+	0.992549i	$0.538880\pi$
$14$	12.0454	3.21926
$15$	−1.00000	−0.258199
$16$	2.78251	0.695628
$17$	4.11498	0.998030	0.499015	−	0.866593i	$-0.333695\pi$
$17$	4.11498	0.998030	0.499015	+	0.866593i	$0.333695\pi$
$18$	−2.40618	−0.567143
$19$	−5.70864	−1.30965	−0.654826	−	0.755780i	$-0.727258\pi$
$19$	−5.70864	−1.30965	−0.654826	+	0.755780i	$0.727258\pi$
$20$	−3.78972	−0.847406
$21$	−5.00600	−1.09240
$22$	7.92003	1.68856
$23$	−6.33673	−1.32130	−0.660650	−	0.750694i	$-0.729719\pi$
$23$	−6.33673	−1.32130	−0.660650	+	0.750694i	$0.729719\pi$
$24$	−4.30638	−0.879037
$25$	1.00000	0.200000
$26$	2.11411	0.414611
$27$	1.00000	0.192450
$28$	−18.9713	−3.58524
$29$	−6.66565	−1.23778	−0.618890	−	0.785478i	$-0.712417\pi$
$29$	−6.66565	−1.23778	−0.618890	+	0.785478i	$0.712417\pi$
$30$	2.40618	0.439307
$31$	−7.43343	−1.33508	−0.667542	−	0.744572i	$-0.732653\pi$
$31$	−7.43343	−1.33508	−0.667542	+	0.744572i	$0.732653\pi$
$32$	1.91753	0.338975
$33$	−3.29153	−0.572982
$34$	−9.90140	−1.69808
$35$	5.00600	0.846169
$36$	3.78972	0.631619
$37$	−7.47586	−1.22902	−0.614512	−	0.788907i	$-0.710647\pi$
$37$	−7.47586	−1.22902	−0.614512	+	0.788907i	$0.710647\pi$
$38$	13.7360	2.22828
$39$	−0.878616	−0.140691
$40$	4.30638	0.680899
$41$	−4.44549	−0.694270	−0.347135	−	0.937815i	$-0.612845\pi$
$41$	−4.44549	−0.694270	−0.347135	+	0.937815i	$0.612845\pi$
$42$	12.0454	1.85864
$43$	10.2434	1.56210	0.781052	−	0.624466i	$-0.214683\pi$
$43$	10.2434	1.56210	0.781052	+	0.624466i	$0.214683\pi$
$44$	−12.4740	−1.88052
$45$	−1.00000	−0.149071
$46$	15.2473	2.24810
$47$	−1.14869	−0.167554	−0.0837772	−	0.996485i	$-0.526698\pi$
$47$	−1.14869	−0.167554	−0.0837772	+	0.996485i	$0.526698\pi$
$48$	2.78251	0.401621
$49$	18.0601	2.58001
$50$	−2.40618	−0.340286
$51$	4.11498	0.576213
$52$	−3.32971	−0.461747
$53$	−7.78186	−1.06892	−0.534460	−	0.845194i	$-0.679485\pi$
$53$	−7.78186	−1.06892	−0.534460	+	0.845194i	$0.679485\pi$
$54$	−2.40618	−0.327440
$55$	3.29153	0.443830
$56$	21.5578	2.88078
$57$	−5.70864	−0.756128
$58$	16.0388	2.10599
$59$	−13.7047	−1.78420	−0.892099	−	0.451839i	$-0.850768\pi$
$59$	−13.7047	−1.78420	−0.892099	+	0.451839i	$0.850768\pi$
$60$	−3.78972	−0.489250
$61$	6.51077	0.833619	0.416810	−	0.908994i	$-0.363148\pi$
$61$	6.51077	0.833619	0.416810	+	0.908994i	$0.363148\pi$
$62$	17.8862	2.27155
$63$	−5.00600	−0.630697
$64$	−10.1790	−1.27237
$65$	0.878616	0.108979
$66$	7.92003	0.974889
$67$	10.2307	1.24988	0.624942	−	0.780671i	$-0.285122\pi$
$67$	10.2307	1.24988	0.624942	+	0.780671i	$0.285122\pi$
$68$	15.5946	1.89112
$69$	−6.33673	−0.762853
$70$	−12.0454	−1.43970
$71$	−2.94662	−0.349699	−0.174850	−	0.984595i	$-0.555944\pi$
$71$	−2.94662	−0.349699	−0.174850	+	0.984595i	$0.555944\pi$
$72$	−4.30638	−0.507512
$73$	−9.03752	−1.05776	−0.528881	−	0.848696i	$-0.677388\pi$
$73$	−9.03752	−1.05776	−0.528881	+	0.848696i	$0.677388\pi$
$74$	17.9883	2.09110
$75$	1.00000	0.115470
$76$	−21.6341	−2.48160
$77$	16.4774	1.87778
$78$	2.11411	0.239376
$79$	−2.87478	−0.323438	−0.161719	−	0.986837i	$-0.551704\pi$
$79$	−2.87478	−0.323438	−0.161719	+	0.986837i	$0.551704\pi$
$80$	−2.78251	−0.311094
$81$	1.00000	0.111111
$82$	10.6967	1.18125
$83$	−10.4097	−1.14261	−0.571307	−	0.820737i	$-0.693563\pi$
$83$	−10.4097	−1.14261	−0.571307	+	0.820737i	$0.693563\pi$
$84$	−18.9713	−2.06994
$85$	−4.11498	−0.446333
$86$	−24.6475	−2.65781
$87$	−6.66565	−0.714632
$88$	14.1746	1.51102
$89$	−12.5790	−1.33337	−0.666683	−	0.745341i	$-0.732287\pi$
$89$	−12.5790	−1.33337	−0.666683	+	0.745341i	$0.732287\pi$
$90$	2.40618	0.253634
$91$	4.39836	0.461073
$92$	−24.0144	−2.50368
$93$	−7.43343	−0.770811
$94$	2.76397	0.285082
$95$	5.70864	0.585694
$96$	1.91753	0.195707
$97$	17.2423	1.75069	0.875343	−	0.483502i	$-0.160635\pi$
$97$	17.2423	1.75069	0.875343	+	0.483502i	$0.160635\pi$
$98$	−43.4559	−4.38970
$99$	−3.29153	−0.330812
$100$	3.78972	0.378972
$101$	0.0779968	0.00776097	0.00388049	−	0.999992i	$-0.498765\pi$
$101$	0.0779968	0.00776097	0.00388049	+	0.999992i	$0.498765\pi$
$102$	−9.90140	−0.980385
$103$	0.242681	0.0239121	0.0119560	−	0.999929i	$-0.496194\pi$
$103$	0.242681	0.0239121	0.0119560	+	0.999929i	$0.496194\pi$
$104$	3.78366	0.371018
$105$	5.00600	0.488536
$106$	18.7246	1.81869
$107$	−12.7988	−1.23731	−0.618653	−	0.785664i	$-0.712321\pi$
$107$	−12.7988	−1.23731	−0.618653	+	0.785664i	$0.712321\pi$
$108$	3.78972	0.364666
$109$	−15.6345	−1.49752	−0.748759	−	0.662843i	$-0.769350\pi$
$109$	−15.6345	−1.49752	−0.748759	+	0.662843i	$0.769350\pi$
$110$	−7.92003	−0.755145
$111$	−7.47586	−0.709578
$112$	−13.9293	−1.31619
$113$	7.89350	0.742558	0.371279	−	0.928521i	$-0.378919\pi$
$113$	7.89350	0.742558	0.371279	+	0.928521i	$0.378919\pi$
$114$	13.7360	1.28650
$115$	6.33673	0.590903
$116$	−25.2609	−2.34542
$117$	−0.878616	−0.0812281
$118$	32.9760	3.03569
$119$	−20.5996	−1.88836
$120$	4.30638	0.393117
$121$	−0.165806	−0.0150732
$122$	−15.6661	−1.41834
$123$	−4.44549	−0.400837
$124$	−28.1706	−2.52979
$125$	−1.00000	−0.0894427
$126$	12.0454	1.07309
$127$	−5.20848	−0.462178	−0.231089	−	0.972933i	$-0.574229\pi$
$127$	−5.20848	−0.462178	−0.231089	+	0.972933i	$0.574229\pi$
$128$	20.6574	1.82587
$129$	10.2434	0.901882
$130$	−2.11411	−0.185420
$131$	4.02993	0.352097	0.176049	−	0.984381i	$-0.443668\pi$
$131$	4.02993	0.352097	0.176049	+	0.984381i	$0.443668\pi$
$132$	−12.4740	−1.08572
$133$	28.5775	2.47798
$134$	−24.6170	−2.12659
$135$	−1.00000	−0.0860663
$136$	−17.7207	−1.51954
$137$	−15.4985	−1.32413	−0.662063	−	0.749448i	$-0.730319\pi$
$137$	−15.4985	−1.32413	−0.662063	+	0.749448i	$0.730319\pi$
$138$	15.2473	1.29794
$139$	21.6153	1.83338	0.916692	−	0.399595i	$-0.130849\pi$
$139$	21.6153	1.83338	0.916692	+	0.399595i	$0.130849\pi$
$140$	18.9713	1.60337
$141$	−1.14869	−0.0967375
$142$	7.09011	0.594988
$143$	2.89199	0.241841
$144$	2.78251	0.231876
$145$	6.66565	0.553552
$146$	21.7459	1.79971
$147$	18.0601	1.48957
$148$	−28.3314	−2.32883
$149$	−8.79448	−0.720472	−0.360236	−	0.932861i	$-0.617304\pi$
$149$	−8.79448	−0.720472	−0.360236	+	0.932861i	$0.617304\pi$
$150$	−2.40618	−0.196464
$151$	−1.55731	−0.126732	−0.0633661	−	0.997990i	$-0.520184\pi$
$151$	−1.55731	−0.126732	−0.0633661	+	0.997990i	$0.520184\pi$
$152$	24.5836	1.99399
$153$	4.11498	0.332677
$154$	−39.6477	−3.19490
$155$	7.43343	0.597067
$156$	−3.32971	−0.266590
$157$	−4.00590	−0.319705	−0.159853	−	0.987141i	$-0.551102\pi$
$157$	−4.00590	−0.319705	−0.159853	+	0.987141i	$0.551102\pi$
$158$	6.91724	0.550306
$159$	−7.78186	−0.617141
$160$	−1.91753	−0.151594
$161$	31.7217	2.50002
$162$	−2.40618	−0.189048
$163$	23.3821	1.83143	0.915715	−	0.401828i	$-0.131625\pi$
$163$	23.3821	1.83143	0.915715	+	0.401828i	$0.131625\pi$
$164$	−16.8472	−1.31554
$165$	3.29153	0.256246
$166$	25.0477	1.94408
$167$	14.0428	1.08666	0.543332	−	0.839518i	$-0.317163\pi$
$167$	14.0428	1.08666	0.543332	+	0.839518i	$0.317163\pi$
$168$	21.5578	1.66322
$169$	−12.2280	−0.940618
$170$	9.90140	0.759403
$171$	−5.70864	−0.436550
$172$	38.8196	2.95997
$173$	−18.0817	−1.37473	−0.687364	−	0.726313i	$-0.741232\pi$
$173$	−18.0817	−1.37473	−0.687364	+	0.726313i	$0.741232\pi$
$174$	16.0388	1.21590
$175$	−5.00600	−0.378418
$176$	−9.15873	−0.690365
$177$	−13.7047	−1.03011
$178$	30.2673	2.26863
$179$	−3.85860	−0.288406	−0.144203	−	0.989548i	$-0.546062\pi$
$179$	−3.85860	−0.288406	−0.144203	+	0.989548i	$0.546062\pi$
$180$	−3.78972	−0.282469
$181$	−11.4124	−0.848274	−0.424137	−	0.905598i	$-0.639422\pi$
$181$	−11.4124	−0.848274	−0.424137	+	0.905598i	$0.639422\pi$
$182$	−10.5832	−0.784483
$183$	6.51077	0.481290
$184$	27.2884	2.01173
$185$	7.47586	0.549636
$186$	17.8862	1.31148
$187$	−13.5446	−0.990480
$188$	−4.35323	−0.317492
$189$	−5.00600	−0.364133
$190$	−13.7360	−0.996516
$191$	11.6210	0.840866	0.420433	−	0.907324i	$-0.361878\pi$
$191$	11.6210	0.840866	0.420433	+	0.907324i	$0.361878\pi$
$192$	−10.1790	−0.734603
$193$	20.6941	1.48960	0.744798	−	0.667290i	$-0.232546\pi$
$193$	20.6941	1.48960	0.744798	+	0.667290i	$0.232546\pi$
$194$	−41.4880	−2.97867
$195$	0.878616	0.0629190
$196$	68.4426	4.88875
$197$	23.3529	1.66383	0.831914	−	0.554905i	$-0.187245\pi$
$197$	23.3529	1.66383	0.831914	+	0.554905i	$0.187245\pi$
$198$	7.92003	0.562852
$199$	−19.8825	−1.40943	−0.704717	−	0.709488i	$-0.748926\pi$
$199$	−19.8825	−1.40943	−0.704717	+	0.709488i	$0.748926\pi$
$200$	−4.30638	−0.304507
$201$	10.2307	0.721621
$202$	−0.187675	−0.0132047
$203$	33.3683	2.34199
$204$	15.5946	1.09184
$205$	4.44549	0.310487
$206$	−0.583935	−0.0406847
$207$	−6.33673	−0.440433
$208$	−2.44476	−0.169514
$209$	18.7902	1.29974
$210$	−12.0454	−0.831209
$211$	−23.1977	−1.59700	−0.798498	−	0.601997i	$-0.794372\pi$
$211$	−23.1977	−1.59700	−0.798498	+	0.601997i	$0.794372\pi$
$212$	−29.4910	−2.02545
$213$	−2.94662	−0.201899
$214$	30.7962	2.10519
$215$	−10.2434	−0.698594
$216$	−4.30638	−0.293012
$217$	37.2118	2.52610
$218$	37.6196	2.54792
$219$	−9.03752	−0.610699
$220$	12.4740	0.840995
$221$	−3.61549	−0.243204
$222$	17.9883	1.20730
$223$	3.42862	0.229598	0.114799	−	0.993389i	$-0.463378\pi$
$223$	3.42862	0.229598	0.114799	+	0.993389i	$0.463378\pi$
$224$	−9.59918	−0.641372
$225$	1.00000	0.0666667
$226$	−18.9932	−1.26341
$227$	−6.11540	−0.405894	−0.202947	−	0.979190i	$-0.565052\pi$
$227$	−6.11540	−0.405894	−0.202947	+	0.979190i	$0.565052\pi$
$228$	−21.6341	−1.43275
$229$	−9.19193	−0.607420	−0.303710	−	0.952765i	$-0.598225\pi$
$229$	−9.19193	−0.607420	−0.303710	+	0.952765i	$0.598225\pi$
$230$	−15.2473	−1.00538
$231$	16.4774	1.08414
$232$	28.7048	1.88456
$233$	−6.44487	−0.422217	−0.211109	−	0.977463i	$-0.567707\pi$
$233$	−6.44487	−0.422217	−0.211109	+	0.977463i	$0.567707\pi$
$234$	2.11411	0.138204
$235$	1.14869	0.0749326
$236$	−51.9369	−3.38080
$237$	−2.87478	−0.186737
$238$	49.5665	3.21292
$239$	13.3763	0.865239	0.432620	−	0.901577i	$-0.357589\pi$
$239$	13.3763	0.865239	0.432620	+	0.901577i	$0.357589\pi$
$240$	−2.78251	−0.179610
$241$	24.8373	1.59991	0.799956	−	0.600058i	$-0.204856\pi$
$241$	24.8373	1.59991	0.799956	+	0.600058i	$0.204856\pi$
$242$	0.398958	0.0256460
$243$	1.00000	0.0641500
$244$	24.6740	1.57959
$245$	−18.0601	−1.15382
$246$	10.6967	0.681995
$247$	5.01570	0.319141
$248$	32.0112	2.03271
$249$	−10.4097	−0.659688
$250$	2.40618	0.152180
$251$	22.2109	1.40194	0.700968	−	0.713192i	$-0.252751\pi$
$251$	22.2109	1.40194	0.700968	+	0.713192i	$0.252751\pi$
$252$	−18.9713	−1.19508
$253$	20.8576	1.31130
$254$	12.5326	0.786362
$255$	−4.11498	−0.257690
$256$	−29.3475	−1.83422
$257$	−20.8017	−1.29757	−0.648786	−	0.760971i	$-0.724723\pi$
$257$	−20.8017	−1.29757	−0.648786	+	0.760971i	$0.724723\pi$
$258$	−24.6475	−1.53449
$259$	37.4242	2.32543
$260$	3.32971	0.206500
$261$	−6.66565	−0.412593
$262$	−9.69676	−0.599068
$263$	−27.0865	−1.67023	−0.835114	−	0.550077i	$-0.814598\pi$
$263$	−27.0865	−1.67023	−0.835114	+	0.550077i	$0.814598\pi$
$264$	14.1746	0.872386
$265$	7.78186	0.478036
$266$	−68.7626	−4.21611
$267$	−12.5790	−0.769820
$268$	38.7716	2.36835
$269$	6.58075	0.401236	0.200618	−	0.979670i	$-0.435705\pi$
$269$	6.58075	0.401236	0.200618	+	0.979670i	$0.435705\pi$
$270$	2.40618	0.146436
$271$	−2.97893	−0.180957	−0.0904787	−	0.995898i	$-0.528840\pi$
$271$	−2.97893	−0.180957	−0.0904787	+	0.995898i	$0.528840\pi$
$272$	11.4500	0.694257
$273$	4.39836	0.266201
$274$	37.2922	2.25291
$275$	−3.29153	−0.198487
$276$	−24.0144	−1.44550
$277$	29.0253	1.74396	0.871982	−	0.489539i	$-0.162835\pi$
$277$	29.0253	1.74396	0.871982	+	0.489539i	$0.162835\pi$
$278$	−52.0103	−3.11937
$279$	−7.43343	−0.445028
$280$	−21.5578	−1.28832
$281$	16.9046	1.00844	0.504222	−	0.863574i	$-0.331779\pi$
$281$	16.9046	1.00844	0.504222	+	0.863574i	$0.331779\pi$
$282$	2.76397	0.164592
$283$	4.40079	0.261600	0.130800	−	0.991409i	$-0.458245\pi$
$283$	4.40079	0.261600	0.130800	+	0.991409i	$0.458245\pi$
$284$	−11.1669	−0.662631
$285$	5.70864	0.338151
$286$	−6.95867	−0.411475
$287$	22.2542	1.31362
$288$	1.91753	0.112992
$289$	−0.0669196	−0.00393645
$290$	−16.0388	−0.941829
$291$	17.2423	1.01076
$292$	−34.2496	−2.00431
$293$	20.0948	1.17395	0.586976	−	0.809605i	$-0.300318\pi$
$293$	20.0948	1.17395	0.586976	+	0.809605i	$0.300318\pi$
$294$	−43.4559	−2.53440
$295$	13.7047	0.797918
$296$	32.1939	1.87123
$297$	−3.29153	−0.190994
$298$	21.1611	1.22583
$299$	5.56756	0.321980
$300$	3.78972	0.218799
$301$	−51.2785	−2.95565
$302$	3.74717	0.215626
$303$	0.0779968	0.00448080
$304$	−15.8844	−0.911030
$305$	−6.51077	−0.372806
$306$	−9.90140	−0.566025
$307$	−16.9599	−0.967950	−0.483975	−	0.875082i	$-0.660807\pi$
$307$	−16.9599	−0.967950	−0.483975	+	0.875082i	$0.660807\pi$
$308$	62.4448	3.55812
$309$	0.242681	0.0138056
$310$	−17.8862	−1.01587
$311$	−11.3571	−0.644003	−0.322001	−	0.946739i	$-0.604356\pi$
$311$	−11.3571	−0.644003	−0.322001	+	0.946739i	$0.604356\pi$
$312$	3.78366	0.214207
$313$	−4.58030	−0.258894	−0.129447	−	0.991586i	$-0.541320\pi$
$313$	−4.58030	−0.258894	−0.129447	+	0.991586i	$0.541320\pi$
$314$	9.63892	0.543956
$315$	5.00600	0.282056
$316$	−10.8946	−0.612869
$317$	22.3064	1.25285	0.626426	−	0.779481i	$-0.284517\pi$
$317$	22.3064	1.25285	0.626426	+	0.779481i	$0.284517\pi$
$318$	18.7246	1.05002
$319$	21.9402	1.22842
$320$	10.1790	0.569021
$321$	−12.7988	−0.714359
$322$	−76.3282	−4.25361
$323$	−23.4909	−1.30707
$324$	3.78972	0.210540
$325$	−0.878616	−0.0487369
$326$	−56.2617	−3.11605
$327$	−15.6345	−0.864592
$328$	19.1440	1.05705
$329$	5.75037	0.317028
$330$	−7.92003	−0.435983
$331$	−15.7674	−0.866652	−0.433326	−	0.901237i	$-0.642660\pi$
$331$	−15.7674	−0.866652	−0.433326	+	0.901237i	$0.642660\pi$
$332$	−39.4498	−2.16509
$333$	−7.47586	−0.409675
$334$	−33.7895	−1.84888
$335$	−10.2307	−0.558965
$336$	−13.9293	−0.759904
$337$	9.46488	0.515585	0.257792	−	0.966200i	$-0.417005\pi$
$337$	9.46488	0.515585	0.257792	+	0.966200i	$0.417005\pi$
$338$	29.4229	1.60039
$339$	7.89350	0.428716
$340$	−15.5946	−0.845737
$341$	24.4674	1.32498
$342$	13.7360	0.742759
$343$	−55.3668	−2.98953
$344$	−44.1120	−2.37836
$345$	6.33673	0.341158
$346$	43.5079	2.33900
$347$	−27.7079	−1.48744	−0.743720	−	0.668492i	$-0.766940\pi$
$347$	−27.7079	−1.48744	−0.743720	+	0.668492i	$0.766940\pi$
$348$	−25.2609	−1.35413
$349$	11.0871	0.593479	0.296739	−	0.954958i	$-0.404101\pi$
$349$	11.0871	0.593479	0.296739	+	0.954958i	$0.404101\pi$
$350$	12.0454	0.643852
$351$	−0.878616	−0.0468971
$352$	−6.31162	−0.336411
$353$	4.14461	0.220596	0.110298	−	0.993899i	$-0.464820\pi$
$353$	4.14461	0.220596	0.110298	+	0.993899i	$0.464820\pi$
$354$	32.9760	1.75265
$355$	2.94662	0.156390
$356$	−47.6707	−2.52654
$357$	−20.5996	−1.09025
$358$	9.28451	0.490701
$359$	−5.64759	−0.298068	−0.149034	−	0.988832i	$-0.547616\pi$
$359$	−5.64759	−0.298068	−0.149034	+	0.988832i	$0.547616\pi$
$360$	4.30638	0.226966
$361$	13.5886	0.715187
$362$	27.4602	1.44328
$363$	−0.165806	−0.00870254
$364$	16.6685	0.873668
$365$	9.03752	0.473046
$366$	−15.6661	−0.818881
$367$	−29.2875	−1.52880	−0.764398	−	0.644744i	$-0.776964\pi$
$367$	−29.2875	−1.52880	−0.764398	+	0.644744i	$0.776964\pi$
$368$	−17.6320	−0.919133
$369$	−4.44549	−0.231423
$370$	−17.9883	−0.935167
$371$	38.9560	2.02249
$372$	−28.1706	−1.46058
$373$	37.0766	1.91975	0.959876	−	0.280423i	$-0.0904749\pi$
$373$	37.0766	1.91975	0.959876	+	0.280423i	$0.0904749\pi$
$374$	32.5908	1.68523
$375$	−1.00000	−0.0516398
$376$	4.94672	0.255108
$377$	5.85655	0.301627
$378$	12.0454	0.619547
$379$	−16.8058	−0.863257	−0.431629	−	0.902051i	$-0.642061\pi$
$379$	−16.8058	−0.863257	−0.431629	+	0.902051i	$0.642061\pi$
$380$	21.6341	1.10981
$381$	−5.20848	−0.266839
$382$	−27.9623	−1.43067
$383$	9.58040	0.489535	0.244768	−	0.969582i	$-0.421288\pi$
$383$	9.58040	0.489535	0.244768	+	0.969582i	$0.421288\pi$
$384$	20.6574	1.05417
$385$	−16.4774	−0.839768
$386$	−49.7939	−2.53444
$387$	10.2434	0.520702
$388$	65.3433	3.31730
$389$	−27.1425	−1.37618	−0.688090	−	0.725626i	$-0.741550\pi$
$389$	−27.1425	−1.37618	−0.688090	+	0.725626i	$0.741550\pi$
$390$	−2.11411	−0.107052
$391$	−26.0755	−1.31870
$392$	−77.7736	−3.92816
$393$	4.02993	0.203283
$394$	−56.1914	−2.83088
$395$	2.87478	0.144646
$396$	−12.4740	−0.626841
$397$	−32.7343	−1.64289	−0.821444	−	0.570289i	$-0.806831\pi$
$397$	−32.7343	−1.64289	−0.821444	+	0.570289i	$0.806831\pi$
$398$	47.8410	2.39805
$399$	28.5775	1.43066
$400$	2.78251	0.139126
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−24.6170	−1.22779
$403$	6.53113	0.325339
$404$	0.295586	0.0147059
$405$	−1.00000	−0.0496904
$406$	−80.2901	−3.98473
$407$	24.6071	1.21973
$408$	−17.7207	−0.877305
$409$	−31.1840	−1.54195	−0.770974	−	0.636867i	$-0.780230\pi$
$409$	−31.1840	−1.54195	−0.770974	+	0.636867i	$0.780230\pi$
$410$	−10.6967	−0.528271
$411$	−15.4985	−0.764485
$412$	0.919692	0.0453100
$413$	68.6058	3.37587
$414$	15.2473	0.749366
$415$	10.4097	0.510992
$416$	−1.68477	−0.0826029
$417$	21.6153	1.05850
$418$	−45.2126	−2.21142
$419$	28.6564	1.39996	0.699978	−	0.714164i	$-0.253193\pi$
$419$	28.6564	1.39996	0.699978	+	0.714164i	$0.253193\pi$
$420$	18.9713	0.925706
$421$	10.9578	0.534050	0.267025	−	0.963690i	$-0.413959\pi$
$421$	10.9578	0.534050	0.267025	+	0.963690i	$0.413959\pi$
$422$	55.8180	2.71718
$423$	−1.14869	−0.0558514
$424$	33.5116	1.62747
$425$	4.11498	0.199606
$426$	7.09011	0.343517
$427$	−32.5930	−1.57728
$428$	−48.5038	−2.34452
$429$	2.89199	0.139627
$430$	24.6475	1.18861
$431$	−17.7418	−0.854594	−0.427297	−	0.904111i	$-0.640534\pi$
$431$	−17.7418	−0.854594	−0.427297	+	0.904111i	$0.640534\pi$
$432$	2.78251	0.133874
$433$	19.8807	0.955408	0.477704	−	0.878521i	$-0.341469\pi$
$433$	19.8807	0.955408	0.477704	+	0.878521i	$0.341469\pi$
$434$	−89.5384	−4.29798
$435$	6.66565	0.319593
$436$	−59.2505	−2.83758
$437$	36.1741	1.73044
$438$	21.7459	1.03906
$439$	32.7196	1.56162	0.780812	−	0.624767i	$-0.214806\pi$
$439$	32.7196	1.56162	0.780812	+	0.624767i	$0.214806\pi$
$440$	−14.1746	−0.675748
$441$	18.0601	0.860004
$442$	8.69953	0.413794
$443$	−28.5818	−1.35796	−0.678980	−	0.734157i	$-0.737578\pi$
$443$	−28.5818	−1.35796	−0.678980	+	0.734157i	$0.737578\pi$
$444$	−28.3314	−1.34455
$445$	12.5790	0.596300
$446$	−8.24989	−0.390644
$447$	−8.79448	−0.415964
$448$	50.9559	2.40744
$449$	25.0504	1.18220	0.591100	−	0.806598i	$-0.298694\pi$
$449$	25.0504	1.18220	0.591100	+	0.806598i	$0.298694\pi$
$450$	−2.40618	−0.113429
$451$	14.6325	0.689017
$452$	29.9141	1.40704
$453$	−1.55731	−0.0731688
$454$	14.7148	0.690599
$455$	−4.39836	−0.206198
$456$	24.5836	1.15123
$457$	38.2380	1.78870	0.894350	−	0.447368i	$-0.147639\pi$
$457$	38.2380	1.78870	0.894350	+	0.447368i	$0.147639\pi$
$458$	22.1175	1.03348
$459$	4.11498	0.192071
$460$	24.0144	1.11968
$461$	2.70633	0.126047	0.0630233	−	0.998012i	$-0.479926\pi$
$461$	2.70633	0.126047	0.0630233	+	0.998012i	$0.479926\pi$
$462$	−39.6477	−1.84458
$463$	3.80730	0.176940	0.0884700	−	0.996079i	$-0.471802\pi$
$463$	3.80730	0.176940	0.0884700	+	0.996079i	$0.471802\pi$
$464$	−18.5472	−0.861034
$465$	7.43343	0.344717
$466$	15.5075	0.718373
$467$	12.5762	0.581955	0.290978	−	0.956730i	$-0.406020\pi$
$467$	12.5762	0.581955	0.290978	+	0.956730i	$0.406020\pi$
$468$	−3.32971	−0.153916
$469$	−51.2152	−2.36490
$470$	−2.76397	−0.127492
$471$	−4.00590	−0.184582
$472$	59.0176	2.71651
$473$	−33.7165	−1.55029
$474$	6.91724	0.317720
$475$	−5.70864	−0.261930
$476$	−78.0667	−3.57818
$477$	−7.78186	−0.356307
$478$	−32.1858	−1.47214
$479$	3.92411	0.179297	0.0896487	−	0.995973i	$-0.471426\pi$
$479$	3.92411	0.179297	0.0896487	+	0.995973i	$0.471426\pi$
$480$	−1.91753	−0.0875230
$481$	6.56842	0.299494
$482$	−59.7631	−2.72214
$483$	31.7217	1.44339
$484$	−0.628356	−0.0285616
$485$	−17.2423	−0.782931
$486$	−2.40618	−0.109147
$487$	−23.1942	−1.05103	−0.525514	−	0.850785i	$-0.676127\pi$
$487$	−23.1942	−1.05103	−0.525514	+	0.850785i	$0.676127\pi$
$488$	−28.0379	−1.26922
$489$	23.3821	1.05738
$490$	43.4559	1.96314
$491$	−32.6393	−1.47299	−0.736496	−	0.676441i	$-0.763521\pi$
$491$	−32.6393	−1.47299	−0.736496	+	0.676441i	$0.763521\pi$
$492$	−16.8472	−0.759529
$493$	−27.4290	−1.23534
$494$	−12.0687	−0.542996
$495$	3.29153	0.147943
$496$	−20.6836	−0.928721
$497$	14.7508	0.661663
$498$	25.0477	1.12241
$499$	8.79746	0.393828	0.196914	−	0.980421i	$-0.436908\pi$
$499$	8.79746	0.393828	0.196914	+	0.980421i	$0.436908\pi$
$500$	−3.78972	−0.169481
$501$	14.0428	0.627385
$502$	−53.4434	−2.38529
$503$	−24.8524	−1.10811	−0.554056	−	0.832479i	$-0.686921\pi$
$503$	−24.8524	−1.10811	−0.554056	+	0.832479i	$0.686921\pi$
$504$	21.5578	0.960259
$505$	−0.0779968	−0.00347081
$506$	−50.1871	−2.23109
$507$	−12.2280	−0.543066
$508$	−19.7387	−0.875761
$509$	−6.15374	−0.272760	−0.136380	−	0.990657i	$-0.543547\pi$
$509$	−6.15374	−0.272760	−0.136380	+	0.990657i	$0.543547\pi$
$510$	9.90140	0.438441
$511$	45.2419	2.00138
$512$	29.3007	1.29492
$513$	−5.70864	−0.252043
$514$	50.0526	2.20773
$515$	−0.242681	−0.0106938
$516$	38.8196	1.70894
$517$	3.78097	0.166287
$518$	−90.0495	−3.95655
$519$	−18.0817	−0.793700
$520$	−3.78366	−0.165924
$521$	41.4925	1.81782	0.908909	−	0.416995i	$-0.136917\pi$
$521$	41.4925	1.81782	0.908909	+	0.416995i	$0.136917\pi$
$522$	16.0388	0.701998
$523$	19.5469	0.854727	0.427363	−	0.904080i	$-0.359443\pi$
$523$	19.5469	0.854727	0.427363	+	0.904080i	$0.359443\pi$
$524$	15.2723	0.667174
$525$	−5.00600	−0.218480
$526$	65.1752	2.84177
$527$	−30.5884	−1.33245
$528$	−9.15873	−0.398583
$529$	17.1542	0.745834
$530$	−18.7246	−0.813343
$531$	−13.7047	−0.594733
$532$	108.300	4.69542
$533$	3.90588	0.169183
$534$	30.2673	1.30979
$535$	12.7988	0.553340
$536$	−44.0575	−1.90299
$537$	−3.85860	−0.166511
$538$	−15.8345	−0.682674
$539$	−59.4454	−2.56049
$540$	−3.78972	−0.163083
$541$	15.0202	0.645767	0.322883	−	0.946439i	$-0.395348\pi$
$541$	15.0202	0.645767	0.322883	+	0.946439i	$0.395348\pi$
$542$	7.16786	0.307886
$543$	−11.4124	−0.489751
$544$	7.89061	0.338307
$545$	15.6345	0.669710
$546$	−10.5832	−0.452921
$547$	9.05936	0.387350	0.193675	−	0.981066i	$-0.437959\pi$
$547$	9.05936	0.387350	0.193675	+	0.981066i	$0.437959\pi$
$548$	−58.7349	−2.50903
$549$	6.51077	0.277873
$550$	7.92003	0.337711
$551$	38.0518	1.62106
$552$	27.2884	1.16147
$553$	14.3912	0.611974
$554$	−69.8403	−2.96723
$555$	7.47586	0.317333
$556$	81.9157	3.47400
$557$	0.868648	0.0368058	0.0184029	−	0.999831i	$-0.494142\pi$
$557$	0.868648	0.0368058	0.0184029	+	0.999831i	$0.494142\pi$
$558$	17.8862	0.757183
$559$	−9.00002	−0.380660
$560$	13.9293	0.588619
$561$	−13.5446	−0.571854
$562$	−40.6755	−1.71579
$563$	−31.7299	−1.33726	−0.668628	−	0.743597i	$-0.733118\pi$
$563$	−31.7299	−1.33726	−0.668628	+	0.743597i	$0.733118\pi$
$564$	−4.35323	−0.183304
$565$	−7.89350	−0.332082
$566$	−10.5891	−0.445094
$567$	−5.00600	−0.210232
$568$	12.6893	0.532430
$569$	−8.69123	−0.364355	−0.182178	−	0.983266i	$-0.558315\pi$
$569$	−8.69123	−0.364355	−0.182178	+	0.983266i	$0.558315\pi$
$570$	−13.7360	−0.575339
$571$	−28.9001	−1.20943	−0.604716	−	0.796441i	$-0.706714\pi$
$571$	−28.9001	−1.20943	−0.604716	+	0.796441i	$0.706714\pi$
$572$	10.9598	0.458254
$573$	11.6210	0.485474
$574$	−53.5476	−2.23503
$575$	−6.33673	−0.264260
$576$	−10.1790	−0.424123
$577$	−19.6093	−0.816345	−0.408172	−	0.912905i	$-0.633834\pi$
$577$	−19.6093	−0.816345	−0.408172	+	0.912905i	$0.633834\pi$
$578$	0.161021	0.00669759
$579$	20.6941	0.860019
$580$	25.2609	1.04890
$581$	52.1110	2.16193
$582$	−41.4880	−1.71973
$583$	25.6142	1.06083
$584$	38.9190	1.61048
$585$	0.878616	0.0363263
$586$	−48.3518	−1.99739
$587$	−22.1249	−0.913193	−0.456597	−	0.889674i	$-0.650932\pi$
$587$	−22.1249	−0.913193	−0.456597	+	0.889674i	$0.650932\pi$
$588$	68.4426	2.82252
$589$	42.4348	1.74849
$590$	−32.9760	−1.35760
$591$	23.3529	0.960611
$592$	−20.8017	−0.854944
$593$	6.29251	0.258403	0.129201	−	0.991618i	$-0.458759\pi$
$593$	6.29251	0.258403	0.129201	+	0.991618i	$0.458759\pi$
$594$	7.92003	0.324963
$595$	20.5996	0.844502
$596$	−33.3286	−1.36519
$597$	−19.8825	−0.813738
$598$	−13.3966	−0.547826
$599$	−22.6649	−0.926062	−0.463031	−	0.886342i	$-0.653238\pi$
$599$	−22.6649	−0.926062	−0.463031	+	0.886342i	$0.653238\pi$
$600$	−4.30638	−0.175807
$601$	43.4827	1.77369	0.886847	−	0.462063i	$-0.152890\pi$
$601$	43.4827	1.77369	0.886847	+	0.462063i	$0.152890\pi$
$602$	123.386	5.02882
$603$	10.2307	0.416628
$604$	−5.90176	−0.240139
$605$	0.165806	0.00674095
$606$	−0.187675	−0.00762376
$607$	24.5943	0.998250	0.499125	−	0.866530i	$-0.333655\pi$
$607$	24.5943	0.998250	0.499125	+	0.866530i	$0.333655\pi$
$608$	−10.9465	−0.443939
$609$	33.3683	1.35215
$610$	15.6661	0.634302
$611$	1.00926	0.0408304
$612$	15.5946	0.630375
$613$	−34.7196	−1.40231	−0.701156	−	0.713008i	$-0.747332\pi$
$613$	−34.7196	−1.40231	−0.701156	+	0.713008i	$0.747332\pi$
$614$	40.8085	1.64690
$615$	4.44549	0.179260
$616$	−70.9581	−2.85898
$617$	−2.60643	−0.104931	−0.0524655	−	0.998623i	$-0.516708\pi$
$617$	−2.60643	−0.104931	−0.0524655	+	0.998623i	$0.516708\pi$
$618$	−0.583935	−0.0234893
$619$	−8.82980	−0.354899	−0.177450	−	0.984130i	$-0.556785\pi$
$619$	−8.82980	−0.354899	−0.177450	+	0.984130i	$0.556785\pi$
$620$	28.1706	1.13136
$621$	−6.33673	−0.254284
$622$	27.3273	1.09572
$623$	62.9703	2.52285
$624$	−2.44476	−0.0978687
$625$	1.00000	0.0400000
$626$	11.0210	0.440489
$627$	18.7902	0.750407
$628$	−15.1812	−0.605796
$629$	−30.7630	−1.22660
$630$	−12.0454	−0.479899
$631$	5.90883	0.235227	0.117613	−	0.993059i	$-0.462476\pi$
$631$	5.90883	0.235227	0.117613	+	0.993059i	$0.462476\pi$
$632$	12.3799	0.492446
$633$	−23.1977	−0.922027
$634$	−53.6733	−2.13164
$635$	5.20848	0.206692
$636$	−29.4910	−1.16939
$637$	−15.8679	−0.628708
$638$	−52.7921	−2.09006
$639$	−2.94662	−0.116566
$640$	−20.6574	−0.816554
$641$	29.7336	1.17441	0.587203	−	0.809440i	$-0.300229\pi$
$641$	29.7336	1.17441	0.587203	+	0.809440i	$0.300229\pi$
$642$	30.7962	1.21543
$643$	−25.7689	−1.01622	−0.508112	−	0.861291i	$-0.669657\pi$
$643$	−25.7689	−1.01622	−0.508112	+	0.861291i	$0.669657\pi$
$644$	120.216	4.73718
$645$	−10.2434	−0.403334
$646$	56.5235	2.22389
$647$	−29.2720	−1.15080	−0.575400	−	0.817872i	$-0.695153\pi$
$647$	−29.2720	−1.15080	−0.575400	+	0.817872i	$0.695153\pi$
$648$	−4.30638	−0.169171
$649$	45.1095	1.77070
$650$	2.11411	0.0829223
$651$	37.2118	1.45844
$652$	88.6117	3.47030
$653$	33.2261	1.30024	0.650118	−	0.759833i	$-0.274719\pi$
$653$	33.2261	1.30024	0.650118	+	0.759833i	$0.274719\pi$
$654$	37.6196	1.47104
$655$	−4.02993	−0.157463
$656$	−12.3696	−0.482953
$657$	−9.03752	−0.352587
$658$	−13.8364	−0.539401
$659$	−11.5587	−0.450261	−0.225131	−	0.974329i	$-0.572281\pi$
$659$	−11.5587	−0.450261	−0.225131	+	0.974329i	$0.572281\pi$
$660$	12.4740	0.485549
$661$	21.9663	0.854390	0.427195	−	0.904159i	$-0.359502\pi$
$661$	21.9663	0.854390	0.427195	+	0.904159i	$0.359502\pi$
$662$	37.9391	1.47455
$663$	−3.61549	−0.140414
$664$	44.8282	1.73967
$665$	−28.5775	−1.10819
$666$	17.9883	0.697032
$667$	42.2384	1.63548
$668$	53.2182	2.05907
$669$	3.42862	0.132558
$670$	24.6170	0.951040
$671$	−21.4304	−0.827313
$672$	−9.59918	−0.370296
$673$	−2.91044	−0.112189	−0.0560946	−	0.998425i	$-0.517865\pi$
$673$	−2.91044	−0.112189	−0.0560946	+	0.998425i	$0.517865\pi$
$674$	−22.7742	−0.877230
$675$	1.00000	0.0384900
$676$	−46.3408	−1.78234
$677$	28.6175	1.09986	0.549930	−	0.835211i	$-0.314654\pi$
$677$	28.6175	1.09986	0.549930	+	0.835211i	$0.314654\pi$
$678$	−18.9932	−0.729429
$679$	−86.3149	−3.31246
$680$	17.7207	0.679557
$681$	−6.11540	−0.234343
$682$	−58.8730	−2.25436
$683$	8.58691	0.328569	0.164285	−	0.986413i	$-0.447468\pi$
$683$	8.58691	0.328569	0.164285	+	0.986413i	$0.447468\pi$
$684$	−21.6341	−0.827201
$685$	15.4985	0.592167
$686$	133.223	5.08647
$687$	−9.19193	−0.350694
$688$	28.5024	1.08664
$689$	6.83726	0.260479
$690$	−15.2473	−0.580456
$691$	−9.81846	−0.373512	−0.186756	−	0.982406i	$-0.559797\pi$
$691$	−9.81846	−0.373512	−0.186756	+	0.982406i	$0.559797\pi$
$692$	−68.5246	−2.60491
$693$	16.4774	0.625926
$694$	66.6703	2.53077
$695$	−21.6153	−0.819914
$696$	28.7048	1.08805
$697$	−18.2931	−0.692902
$698$	−26.6776	−1.00976
$699$	−6.44487	−0.243767
$700$	−18.9713	−0.717049
$701$	−19.9385	−0.753067	−0.376534	−	0.926403i	$-0.622884\pi$
$701$	−19.9385	−0.753067	−0.376534	+	0.926403i	$0.622884\pi$
$702$	2.11411	0.0797920
$703$	42.6770	1.60959
$704$	33.5044	1.26274
$705$	1.14869	0.0432623
$706$	−9.97270	−0.375328
$707$	−0.390452	−0.0146845
$708$	−51.9369	−1.95191
$709$	35.4498	1.33134	0.665672	−	0.746244i	$-0.268145\pi$
$709$	35.4498	1.33134	0.665672	+	0.746244i	$0.268145\pi$
$710$	−7.09011	−0.266087
$711$	−2.87478	−0.107813
$712$	54.1698	2.03010
$713$	47.1037	1.76405
$714$	49.5665	1.85498
$715$	−2.89199	−0.108154
$716$	−14.6230	−0.546488
$717$	13.3763	0.499546
$718$	13.5891	0.507142
$719$	−12.6259	−0.470868	−0.235434	−	0.971890i	$-0.575651\pi$
$719$	−12.6259	−0.470868	−0.235434	+	0.971890i	$0.575651\pi$
$720$	−2.78251	−0.103698
$721$	−1.21486	−0.0452439
$722$	−32.6965	−1.21684
$723$	24.8373	0.923710
$724$	−43.2496	−1.60736
$725$	−6.66565	−0.247556
$726$	0.398958	0.0148067
$727$	5.07657	0.188279	0.0941397	−	0.995559i	$-0.469990\pi$
$727$	5.07657	0.188279	0.0941397	+	0.995559i	$0.469990\pi$
$728$	−18.9410	−0.702000
$729$	1.00000	0.0370370
$730$	−21.7459	−0.804853
$731$	42.1514	1.55903
$732$	24.6740	0.911977
$733$	−18.9195	−0.698809	−0.349405	−	0.936972i	$-0.613616\pi$
$733$	−18.9195	−0.698809	−0.349405	+	0.936972i	$0.613616\pi$
$734$	70.4711	2.60114
$735$	−18.0601	−0.666156
$736$	−12.1509	−0.447888
$737$	−33.6749	−1.24043
$738$	10.6967	0.393750
$739$	22.2632	0.818964	0.409482	−	0.912318i	$-0.365709\pi$
$739$	22.2632	0.818964	0.409482	+	0.912318i	$0.365709\pi$
$740$	28.3314	1.04148
$741$	5.01570	0.184256
$742$	−93.7353	−3.44113
$743$	32.2303	1.18241	0.591207	−	0.806520i	$-0.298652\pi$
$743$	32.2303	1.18241	0.591207	+	0.806520i	$0.298652\pi$
$744$	32.0112	1.17359
$745$	8.79448	0.322205
$746$	−89.2130	−3.26632
$747$	−10.4097	−0.380871
$748$	−51.3302	−1.87682
$749$	64.0708	2.34110
$750$	2.40618	0.0878614
$751$	25.6680	0.936637	0.468319	−	0.883560i	$-0.344860\pi$
$751$	25.6680	0.936637	0.468319	+	0.883560i	$0.344860\pi$
$752$	−3.19626	−0.116555
$753$	22.2109	0.809408
$754$	−14.0919	−0.513197
$755$	1.55731	0.0566763
$756$	−18.9713	−0.689981
$757$	23.1008	0.839613	0.419807	−	0.907614i	$-0.362098\pi$
$757$	23.1008	0.839613	0.419807	+	0.907614i	$0.362098\pi$
$758$	40.4379	1.46877
$759$	20.8576	0.757082
$760$	−24.5836	−0.891740
$761$	34.7204	1.25861	0.629306	−	0.777157i	$-0.283339\pi$
$761$	34.7204	1.25861	0.629306	+	0.777157i	$0.283339\pi$
$762$	12.5326	0.454007
$763$	78.2666	2.83344
$764$	44.0403	1.59332
$765$	−4.11498	−0.148778
$766$	−23.0522	−0.832909
$767$	12.0412	0.434781
$768$	−29.3475	−1.05899
$769$	−6.59325	−0.237759	−0.118879	−	0.992909i	$-0.537930\pi$
$769$	−6.59325	−0.237759	−0.118879	+	0.992909i	$0.537930\pi$
$770$	39.6477	1.42880
$771$	−20.8017	−0.749154
$772$	78.4249	2.82257
$773$	−2.96849	−0.106769	−0.0533845	−	0.998574i	$-0.517001\pi$
$773$	−2.96849	−0.106769	−0.0533845	+	0.998574i	$0.517001\pi$
$774$	−24.6475	−0.885936
$775$	−7.43343	−0.267017
$776$	−74.2518	−2.66548
$777$	37.4242	1.34259
$778$	65.3098	2.34147
$779$	25.3777	0.909251
$780$	3.32971	0.119223
$781$	9.69890	0.347054
$782$	62.7425	2.24367
$783$	−6.66565	−0.238211
$784$	50.2524	1.79473
$785$	4.00590	0.142977
$786$	−9.69676	−0.345872
$787$	35.6905	1.27223	0.636115	−	0.771594i	$-0.280540\pi$
$787$	35.6905	1.27223	0.636115	+	0.771594i	$0.280540\pi$
$788$	88.5010	3.15272
$789$	−27.0865	−0.964306
$790$	−6.91724	−0.246105
$791$	−39.5149	−1.40499
$792$	14.1746	0.503673
$793$	−5.72047	−0.203140
$794$	78.7647	2.79526
$795$	7.78186	0.275994
$796$	−75.3491	−2.67068
$797$	8.53642	0.302375	0.151188	−	0.988505i	$-0.451690\pi$
$797$	8.53642	0.302375	0.151188	+	0.988505i	$0.451690\pi$
$798$	−68.7626	−2.43417
$799$	−4.72686	−0.167224
$800$	1.91753	0.0677950
$801$	−12.5790	−0.444456
$802$	2.40618	0.0849653
$803$	29.7473	1.04976
$804$	38.7716	1.36737
$805$	−31.7217	−1.11804
$806$	−15.7151	−0.553541
$807$	6.58075	0.231654
$808$	−0.335884	−0.0118164
$809$	15.2968	0.537805	0.268903	−	0.963167i	$-0.413339\pi$
$809$	15.2968	0.537805	0.268903	+	0.963167i	$0.413339\pi$
$810$	2.40618	0.0845446
$811$	49.4592	1.73675	0.868374	−	0.495910i	$-0.165165\pi$
$811$	49.4592	1.73675	0.868374	+	0.495910i	$0.165165\pi$
$812$	126.456	4.43774
$813$	−2.97893	−0.104476
$814$	−59.2091	−2.07528
$815$	−23.3821	−0.819041
$816$	11.4500	0.400830
$817$	−58.4759	−2.04581
$818$	75.0343	2.62351
$819$	4.39836	0.153691
$820$	16.8472	0.588328
$821$	32.3283	1.12826	0.564132	−	0.825685i	$-0.309211\pi$
$821$	32.3283	1.12826	0.564132	+	0.825685i	$0.309211\pi$
$822$	37.2922	1.30072
$823$	−20.6513	−0.719859	−0.359930	−	0.932979i	$-0.617199\pi$
$823$	−20.6513	−0.719859	−0.359930	+	0.932979i	$0.617199\pi$
$824$	−1.04508	−0.0364070
$825$	−3.29153	−0.114596
$826$	−165.078	−5.74380
$827$	−15.3088	−0.532339	−0.266169	−	0.963926i	$-0.585758\pi$
$827$	−15.3088	−0.532339	−0.266169	+	0.963926i	$0.585758\pi$
$828$	−24.0144	−0.834558
$829$	−51.7855	−1.79858	−0.899292	−	0.437348i	$-0.855918\pi$
$829$	−51.7855	−1.79858	−0.899292	+	0.437348i	$0.855918\pi$
$830$	−25.0477	−0.869417
$831$	29.0253	1.00688
$832$	8.94340	0.310056
$833$	74.3169	2.57493
$834$	−52.0103	−1.80097
$835$	−14.0428	−0.485971
$836$	71.2094	2.46283
$837$	−7.43343	−0.256937
$838$	−68.9525	−2.38193
$839$	15.8032	0.545587	0.272794	−	0.962073i	$-0.412052\pi$
$839$	15.8032	0.545587	0.272794	+	0.962073i	$0.412052\pi$
$840$	−21.5578	−0.743814
$841$	15.4308	0.532098
$842$	−26.3664	−0.908648
$843$	16.9046	0.582225
$844$	−87.9128	−3.02608
$845$	12.2280	0.420657
$846$	2.76397	0.0950272
$847$	0.830023	0.0285199
$848$	−21.6531	−0.743571
$849$	4.40079	0.151035
$850$	−9.90140	−0.339615
$851$	47.3725	1.62391
$852$	−11.1669	−0.382570
$853$	23.9271	0.819249	0.409625	−	0.912254i	$-0.365660\pi$
$853$	23.9271	0.819249	0.409625	+	0.912254i	$0.365660\pi$
$854$	78.4246	2.68364
$855$	5.70864	0.195231
$856$	55.1165	1.88384
$857$	−6.10573	−0.208568	−0.104284	−	0.994548i	$-0.533255\pi$
$857$	−6.10573	−0.208568	−0.104284	+	0.994548i	$0.533255\pi$
$858$	−6.95867	−0.237565
$859$	−40.2307	−1.37265	−0.686326	−	0.727294i	$-0.740778\pi$
$859$	−40.2307	−1.37265	−0.686326	+	0.727294i	$0.740778\pi$
$860$	−38.8196	−1.32374
$861$	22.2542	0.758420
$862$	42.6901	1.45403
$863$	−43.1157	−1.46768	−0.733838	−	0.679324i	$-0.762273\pi$
$863$	−43.1157	−1.46768	−0.733838	+	0.679324i	$0.762273\pi$
$864$	1.91753	0.0652358
$865$	18.0817	0.614797
$866$	−47.8367	−1.62556
$867$	−0.0669196	−0.00227271
$868$	141.022	4.78660
$869$	9.46243	0.320991
$870$	−16.0388	−0.543765
$871$	−8.98890	−0.304577
$872$	67.3283	2.28002
$873$	17.2423	0.583562
$874$	−87.0415	−2.94422
$875$	5.00600	0.169234
$876$	−34.2496	−1.15719
$877$	18.5693	0.627041	0.313520	−	0.949581i	$-0.398492\pi$
$877$	18.5693	0.627041	0.313520	+	0.949581i	$0.398492\pi$
$878$	−78.7294	−2.65699
$879$	20.0948	0.677781
$880$	9.15873	0.308741
$881$	4.01512	0.135273	0.0676365	−	0.997710i	$-0.478454\pi$
$881$	4.01512	0.135273	0.0676365	+	0.997710i	$0.478454\pi$
$882$	−43.4559	−1.46323
$883$	9.03801	0.304153	0.152077	−	0.988369i	$-0.451404\pi$
$883$	9.03801	0.304153	0.152077	+	0.988369i	$0.451404\pi$
$884$	−13.7017	−0.460837
$885$	13.7047	0.460678
$886$	68.7729	2.31047
$887$	−27.2903	−0.916319	−0.458160	−	0.888870i	$-0.651491\pi$
$887$	−27.2903	−0.916319	−0.458160	+	0.888870i	$0.651491\pi$
$888$	32.1939	1.08036
$889$	26.0737	0.874483
$890$	−30.2673	−1.01456
$891$	−3.29153	−0.110271
$892$	12.9935	0.435055
$893$	6.55748	0.219438
$894$	21.1611	0.707734
$895$	3.85860	0.128979
$896$	−103.411	−3.45471
$897$	5.56756	0.185895
$898$	−60.2757	−2.01143
$899$	49.5486	1.65254
$900$	3.78972	0.126324
$901$	−32.0222	−1.06681
$902$	−35.2085	−1.17231
$903$	−51.2785	−1.70644
$904$	−33.9924	−1.13057
$905$	11.4124	0.379360
$906$	3.74717	0.124491
$907$	43.6662	1.44991	0.724956	−	0.688795i	$-0.241860\pi$
$907$	43.6662	1.44991	0.724956	+	0.688795i	$0.241860\pi$
$908$	−23.1756	−0.769111
$909$	0.0779968	0.00258699
$910$	10.5832	0.350831
$911$	−11.0350	−0.365605	−0.182802	−	0.983150i	$-0.558517\pi$
$911$	−11.0350	−0.365605	−0.182802	+	0.983150i	$0.558517\pi$
$912$	−15.8844	−0.525984
$913$	34.2639	1.13397
$914$	−92.0077	−3.04334
$915$	−6.51077	−0.215240
$916$	−34.8348	−1.15097
$917$	−20.1739	−0.666200
$918$	−9.90140	−0.326795
$919$	−19.0354	−0.627919	−0.313960	−	0.949436i	$-0.601656\pi$
$919$	−19.0354	−0.627919	−0.313960	+	0.949436i	$0.601656\pi$
$920$	−27.2884	−0.899672
$921$	−16.9599	−0.558846
$922$	−6.51193	−0.214459
$923$	2.58895	0.0852163
$924$	62.4448	2.05428
$925$	−7.47586	−0.245805
$926$	−9.16105	−0.301051
$927$	0.242681	0.00797069
$928$	−12.7816	−0.419576
$929$	−47.3700	−1.55416	−0.777079	−	0.629403i	$-0.783300\pi$
$929$	−47.3700	−1.55416	−0.777079	+	0.629403i	$0.783300\pi$
$930$	−17.8862	−0.586511
$931$	−103.098	−3.37892
$932$	−24.4242	−0.800042
$933$	−11.3571	−0.371815
$934$	−30.2605	−0.990155
$935$	13.5446	0.442956
$936$	3.78366	0.123673
$937$	22.0873	0.721560	0.360780	−	0.932651i	$-0.382511\pi$
$937$	22.0873	0.721560	0.360780	+	0.932651i	$0.382511\pi$
$938$	123.233	4.02370
$939$	−4.58030	−0.149472
$940$	4.35323	0.141987
$941$	−33.4595	−1.09075	−0.545374	−	0.838193i	$-0.683613\pi$
$941$	−33.4595	−1.09075	−0.545374	+	0.838193i	$0.683613\pi$
$942$	9.63892	0.314053
$943$	28.1699	0.917338
$944$	−38.1335	−1.24114
$945$	5.00600	0.162845
$946$	81.1281	2.63770
$947$	−41.9172	−1.36213	−0.681063	−	0.732224i	$-0.738482\pi$
$947$	−41.9172	−1.36213	−0.681063	+	0.732224i	$0.738482\pi$
$948$	−10.8946	−0.353840
$949$	7.94051	0.257760
$950$	13.7360	0.445656
$951$	22.3064	0.723334
$952$	88.7098	2.87510
$953$	−10.6842	−0.346095	−0.173047	−	0.984913i	$-0.555361\pi$
$953$	−10.6842	−0.346095	−0.173047	+	0.984913i	$0.555361\pi$
$954$	18.7246	0.606230
$955$	−11.6210	−0.376047
$956$	50.6923	1.63951
$957$	21.9402	0.709226
$958$	−9.44214	−0.305062
$959$	77.5856	2.50537
$960$	10.1790	0.328524
$961$	24.2559	0.782448
$962$	−15.8048	−0.509567
$963$	−12.7988	−0.412435
$964$	94.1264	3.03161
$965$	−20.6941	−0.666168
$966$	−76.3282	−2.45582
$967$	41.8419	1.34554	0.672772	−	0.739850i	$-0.265104\pi$
$967$	41.8419	1.34554	0.672772	+	0.739850i	$0.265104\pi$
$968$	0.714022	0.0229495
$969$	−23.4909	−0.754638
$970$	41.4880	1.33210
$971$	−51.1562	−1.64168	−0.820840	−	0.571158i	$-0.806494\pi$
$971$	−51.1562	−1.64168	−0.820840	+	0.571158i	$0.806494\pi$
$972$	3.78972	0.121555
$973$	−108.206	−3.46893
$974$	55.8095	1.78825
$975$	−0.878616	−0.0281382
$976$	18.1163	0.579889
$977$	−37.6496	−1.20452	−0.602259	−	0.798301i	$-0.705733\pi$
$977$	−37.6496	−1.20452	−0.602259	+	0.798301i	$0.705733\pi$
$978$	−56.2617	−1.79905
$979$	41.4041	1.32328
$980$	−68.4426	−2.18632
$981$	−15.6345	−0.499173
$982$	78.5362	2.50619
$983$	43.3299	1.38201	0.691005	−	0.722850i	$-0.257168\pi$
$983$	43.3299	1.38201	0.691005	+	0.722850i	$0.257168\pi$
$984$	19.1440	0.610288
$985$	−23.3529	−0.744086
$986$	65.9992	2.10184
$987$	5.75037	0.183036
$988$	19.0081	0.604728
$989$	−64.9097	−2.06401
$990$	−7.92003	−0.251715
$991$	8.31859	0.264249	0.132124	−	0.991233i	$-0.457820\pi$
$991$	8.31859	0.264249	0.132124	+	0.991233i	$0.457820\pi$
$992$	−14.2538	−0.452560
$993$	−15.7674	−0.500362
$994$	−35.4931	−1.12577
$995$	19.8825	0.630318
$996$	−39.4498	−1.25002
$997$	−36.3433	−1.15100	−0.575502	−	0.817800i	$-0.695193\pi$
$997$	−36.3433	−1.15100	−0.575502	+	0.817800i	$0.695193\pi$
$998$	−21.1683	−0.670071
$999$	−7.47586	−0.236526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.4	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.4	✓	39	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40618 q^{2} +1.00000 q^{3} +3.78972 q^{4} -1.00000 q^{5} -2.40618 q^{6} -5.00600 q^{7} -4.30638 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.40618 q^{2} +1.00000 q^{3} +3.78972 q^{4} -1.00000 q^{5} -2.40618 q^{6} -5.00600 q^{7} -4.30638 q^{8} +1.00000 q^{9} +2.40618 q^{10} -3.29153 q^{11} +3.78972 q^{12} -0.878616 q^{13} +12.0454 q^{14} -1.00000 q^{15} +2.78251 q^{16} +4.11498 q^{17} -2.40618 q^{18} -5.70864 q^{19} -3.78972 q^{20} -5.00600 q^{21} +7.92003 q^{22} -6.33673 q^{23} -4.30638 q^{24} +1.00000 q^{25} +2.11411 q^{26} +1.00000 q^{27} -18.9713 q^{28} -6.66565 q^{29} +2.40618 q^{30} -7.43343 q^{31} +1.91753 q^{32} -3.29153 q^{33} -9.90140 q^{34} +5.00600 q^{35} +3.78972 q^{36} -7.47586 q^{37} +13.7360 q^{38} -0.878616 q^{39} +4.30638 q^{40} -4.44549 q^{41} +12.0454 q^{42} +10.2434 q^{43} -12.4740 q^{44} -1.00000 q^{45} +15.2473 q^{46} -1.14869 q^{47} +2.78251 q^{48} +18.0601 q^{49} -2.40618 q^{50} +4.11498 q^{51} -3.32971 q^{52} -7.78186 q^{53} -2.40618 q^{54} +3.29153 q^{55} +21.5578 q^{56} -5.70864 q^{57} +16.0388 q^{58} -13.7047 q^{59} -3.78972 q^{60} +6.51077 q^{61} +17.8862 q^{62} -5.00600 q^{63} -10.1790 q^{64} +0.878616 q^{65} +7.92003 q^{66} +10.2307 q^{67} +15.5946 q^{68} -6.33673 q^{69} -12.0454 q^{70} -2.94662 q^{71} -4.30638 q^{72} -9.03752 q^{73} +17.9883 q^{74} +1.00000 q^{75} -21.6341 q^{76} +16.4774 q^{77} +2.11411 q^{78} -2.87478 q^{79} -2.78251 q^{80} +1.00000 q^{81} +10.6967 q^{82} -10.4097 q^{83} -18.9713 q^{84} -4.11498 q^{85} -24.6475 q^{86} -6.66565 q^{87} +14.1746 q^{88} -12.5790 q^{89} +2.40618 q^{90} +4.39836 q^{91} -24.0144 q^{92} -7.43343 q^{93} +2.76397 q^{94} +5.70864 q^{95} +1.91753 q^{96} +17.2423 q^{97} -43.4559 q^{98} -3.29153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more