LMFDB - Embedded newform 6014.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.07052 q^{3} +1.00000 q^{4} -1.71120 q^{5} -1.07052 q^{6} -0.903944 q^{7} +1.00000 q^{8} -1.85399 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.07052 q^{3} +1.00000 q^{4} -1.71120 q^{5} -1.07052 q^{6} -0.903944 q^{7} +1.00000 q^{8} -1.85399 q^{9} -1.71120 q^{10} -2.68865 q^{11} -1.07052 q^{12} +3.48897 q^{13} -0.903944 q^{14} +1.83188 q^{15} +1.00000 q^{16} +2.69204 q^{17} -1.85399 q^{18} +2.74341 q^{19} -1.71120 q^{20} +0.967689 q^{21} -2.68865 q^{22} +4.94518 q^{23} -1.07052 q^{24} -2.07178 q^{25} +3.48897 q^{26} +5.19629 q^{27} -0.903944 q^{28} -4.18989 q^{29} +1.83188 q^{30} +1.00000 q^{31} +1.00000 q^{32} +2.87825 q^{33} +2.69204 q^{34} +1.54683 q^{35} -1.85399 q^{36} +1.62440 q^{37} +2.74341 q^{38} -3.73501 q^{39} -1.71120 q^{40} -7.16833 q^{41} +0.967689 q^{42} -6.31452 q^{43} -2.68865 q^{44} +3.17255 q^{45} +4.94518 q^{46} +11.0283 q^{47} -1.07052 q^{48} -6.18288 q^{49} -2.07178 q^{50} -2.88188 q^{51} +3.48897 q^{52} -9.17879 q^{53} +5.19629 q^{54} +4.60083 q^{55} -0.903944 q^{56} -2.93687 q^{57} -4.18989 q^{58} +8.14046 q^{59} +1.83188 q^{60} +6.57676 q^{61} +1.00000 q^{62} +1.67590 q^{63} +1.00000 q^{64} -5.97034 q^{65} +2.87825 q^{66} -1.00348 q^{67} +2.69204 q^{68} -5.29391 q^{69} +1.54683 q^{70} +8.81363 q^{71} -1.85399 q^{72} -7.50514 q^{73} +1.62440 q^{74} +2.21788 q^{75} +2.74341 q^{76} +2.43039 q^{77} -3.73501 q^{78} +8.06001 q^{79} -1.71120 q^{80} -0.000754845 q^{81} -7.16833 q^{82} -12.6677 q^{83} +0.967689 q^{84} -4.60662 q^{85} -6.31452 q^{86} +4.48536 q^{87} -2.68865 q^{88} +2.11333 q^{89} +3.17255 q^{90} -3.15383 q^{91} +4.94518 q^{92} -1.07052 q^{93} +11.0283 q^{94} -4.69453 q^{95} -1.07052 q^{96} -1.00000 q^{97} -6.18288 q^{98} +4.98473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * 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
$3$	−1.07052	−0.618064	−0.309032	−	0.951052i	$-0.600005\pi$
$3$	−1.07052	−0.618064	−0.309032	+	0.951052i	$0.600005\pi$
$4$	1.00000	0.500000
$5$	−1.71120	−0.765274	−0.382637	−	0.923899i	$-0.624984\pi$
$5$	−1.71120	−0.765274	−0.382637	+	0.923899i	$0.624984\pi$
$6$	−1.07052	−0.437037
$7$	−0.903944	−0.341659	−0.170829	−	0.985301i	$-0.554645\pi$
$7$	−0.903944	−0.341659	−0.170829	+	0.985301i	$0.554645\pi$
$8$	1.00000	0.353553
$9$	−1.85399	−0.617996
$10$	−1.71120	−0.541130
$11$	−2.68865	−0.810659	−0.405329	−	0.914171i	$-0.632843\pi$
$11$	−2.68865	−0.810659	−0.405329	+	0.914171i	$0.632843\pi$
$12$	−1.07052	−0.309032
$13$	3.48897	0.967666	0.483833	−	0.875160i	$-0.339244\pi$
$13$	3.48897	0.967666	0.483833	+	0.875160i	$0.339244\pi$
$14$	−0.903944	−0.241589
$15$	1.83188	0.472988
$16$	1.00000	0.250000
$17$	2.69204	0.652915	0.326457	−	0.945212i	$-0.394145\pi$
$17$	2.69204	0.652915	0.326457	+	0.945212i	$0.394145\pi$
$18$	−1.85399	−0.436990
$19$	2.74341	0.629381	0.314690	−	0.949194i	$-0.398099\pi$
$19$	2.74341	0.629381	0.314690	+	0.949194i	$0.398099\pi$
$20$	−1.71120	−0.382637
$21$	0.967689	0.211167
$22$	−2.68865	−0.573222
$23$	4.94518	1.03114	0.515570	−	0.856847i	$-0.327580\pi$
$23$	4.94518	1.03114	0.515570	+	0.856847i	$0.327580\pi$
$24$	−1.07052	−0.218519
$25$	−2.07178	−0.414356
$26$	3.48897	0.684243
$27$	5.19629	1.00003
$28$	−0.903944	−0.170829
$29$	−4.18989	−0.778044	−0.389022	−	0.921229i	$-0.627187\pi$
$29$	−4.18989	−0.778044	−0.389022	+	0.921229i	$0.627187\pi$
$30$	1.83188	0.334453
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	2.87825	0.501039
$34$	2.69204	0.461681
$35$	1.54683	0.261462
$36$	−1.85399	−0.308998
$37$	1.62440	0.267049	0.133525	−	0.991045i	$-0.457370\pi$
$37$	1.62440	0.267049	0.133525	+	0.991045i	$0.457370\pi$
$38$	2.74341	0.445039
$39$	−3.73501	−0.598080
$40$	−1.71120	−0.270565
$41$	−7.16833	−1.11950	−0.559752	−	0.828660i	$-0.689104\pi$
$41$	−7.16833	−1.11950	−0.559752	+	0.828660i	$0.689104\pi$
$42$	0.967689	0.149318
$43$	−6.31452	−0.962956	−0.481478	−	0.876458i	$-0.659900\pi$
$43$	−6.31452	−0.962956	−0.481478	+	0.876458i	$0.659900\pi$
$44$	−2.68865	−0.405329
$45$	3.17255	0.472936
$46$	4.94518	0.729127
$47$	11.0283	1.60865	0.804323	−	0.594193i	$-0.202528\pi$
$47$	11.0283	1.60865	0.804323	+	0.594193i	$0.202528\pi$
$48$	−1.07052	−0.154516
$49$	−6.18288	−0.883269
$50$	−2.07178	−0.292994
$51$	−2.88188	−0.403543
$52$	3.48897	0.483833
$53$	−9.17879	−1.26080	−0.630402	−	0.776269i	$-0.717110\pi$
$53$	−9.17879	−1.26080	−0.630402	+	0.776269i	$0.717110\pi$
$54$	5.19629	0.707125
$55$	4.60083	0.620376
$56$	−0.903944	−0.120795
$57$	−2.93687	−0.388998
$58$	−4.18989	−0.550160
$59$	8.14046	1.05980	0.529899	−	0.848061i	$-0.322230\pi$
$59$	8.14046	1.05980	0.529899	+	0.848061i	$0.322230\pi$
$60$	1.83188	0.236494
$61$	6.57676	0.842068	0.421034	−	0.907045i	$-0.361667\pi$
$61$	6.57676	0.842068	0.421034	+	0.907045i	$0.361667\pi$
$62$	1.00000	0.127000
$63$	1.67590	0.211144
$64$	1.00000	0.125000
$65$	−5.97034	−0.740529
$66$	2.87825	0.354288
$67$	−1.00348	−0.122595	−0.0612974	−	0.998120i	$-0.519524\pi$
$67$	−1.00348	−0.122595	−0.0612974	+	0.998120i	$0.519524\pi$
$68$	2.69204	0.326457
$69$	−5.29391	−0.637311
$70$	1.54683	0.184882
$71$	8.81363	1.04598	0.522992	−	0.852337i	$-0.324816\pi$
$71$	8.81363	1.04598	0.522992	+	0.852337i	$0.324816\pi$
$72$	−1.85399	−0.218495
$73$	−7.50514	−0.878411	−0.439205	−	0.898387i	$-0.644740\pi$
$73$	−7.50514	−0.878411	−0.439205	+	0.898387i	$0.644740\pi$
$74$	1.62440	0.188832
$75$	2.21788	0.256099
$76$	2.74341	0.314690
$77$	2.43039	0.276969
$78$	−3.73501	−0.422906
$79$	8.06001	0.906822	0.453411	−	0.891302i	$-0.350207\pi$
$79$	8.06001	0.906822	0.453411	+	0.891302i	$0.350207\pi$
$80$	−1.71120	−0.191318
$81$	−0.000754845 0	−8.38717e−5 0
$82$	−7.16833	−0.791609
$83$	−12.6677	−1.39046	−0.695231	−	0.718786i	$-0.744698\pi$
$83$	−12.6677	−1.39046	−0.695231	+	0.718786i	$0.744698\pi$
$84$	0.967689	0.105584
$85$	−4.60662	−0.499659
$86$	−6.31452	−0.680912
$87$	4.48536	0.480881
$88$	−2.68865	−0.286611
$89$	2.11333	0.224013	0.112006	−	0.993708i	$-0.464272\pi$
$89$	2.11333	0.224013	0.112006	+	0.993708i	$0.464272\pi$
$90$	3.17255	0.334417
$91$	−3.15383	−0.330612
$92$	4.94518	0.515570
$93$	−1.07052	−0.111008
$94$	11.0283	1.13748
$95$	−4.69453	−0.481648
$96$	−1.07052	−0.109259
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−6.18288	−0.624566
$99$	4.98473	0.500984
$100$	−2.07178	−0.207178
$101$	9.56562	0.951815	0.475907	−	0.879495i	$-0.342120\pi$
$101$	9.56562	0.951815	0.475907	+	0.879495i	$0.342120\pi$
$102$	−2.88188	−0.285348
$103$	−3.93360	−0.387589	−0.193795	−	0.981042i	$-0.562080\pi$
$103$	−3.93360	−0.387589	−0.193795	+	0.981042i	$0.562080\pi$
$104$	3.48897	0.342122
$105$	−1.65591	−0.161601
$106$	−9.17879	−0.891523
$107$	−19.1497	−1.85128	−0.925638	−	0.378411i	$-0.876471\pi$
$107$	−19.1497	−1.85128	−0.925638	+	0.378411i	$0.876471\pi$
$108$	5.19629	0.500013
$109$	−14.0800	−1.34862	−0.674309	−	0.738449i	$-0.735558\pi$
$109$	−14.0800	−1.34862	−0.674309	+	0.738449i	$0.735558\pi$
$110$	4.60083	0.438672
$111$	−1.73895	−0.165054
$112$	−0.903944	−0.0854147
$113$	−1.03738	−0.0975889	−0.0487945	−	0.998809i	$-0.515538\pi$
$113$	−1.03738	−0.0975889	−0.0487945	+	0.998809i	$0.515538\pi$
$114$	−2.93687	−0.275063
$115$	−8.46221	−0.789105
$116$	−4.18989	−0.389022
$117$	−6.46851	−0.598014
$118$	8.14046	0.749390
$119$	−2.43345	−0.223074
$120$	1.83188	0.167227
$121$	−3.77115	−0.342832
$122$	6.57676	0.595432
$123$	7.67383	0.691926
$124$	1.00000	0.0898027
$125$	12.1013	1.08237
$126$	1.67590	0.149301
$127$	−18.7163	−1.66080	−0.830400	−	0.557167i	$-0.811888\pi$
$127$	−18.7163	−1.66080	−0.830400	+	0.557167i	$0.811888\pi$
$128$	1.00000	0.0883883
$129$	6.75982	0.595169
$130$	−5.97034	−0.523633
$131$	−22.3876	−1.95602	−0.978008	−	0.208567i	$-0.933120\pi$
$131$	−22.3876	−1.95602	−0.978008	+	0.208567i	$0.933120\pi$
$132$	2.87825	0.250520
$133$	−2.47989	−0.215033
$134$	−1.00348	−0.0866876
$135$	−8.89191	−0.765293
$136$	2.69204	0.230840
$137$	−5.62065	−0.480204	−0.240102	−	0.970748i	$-0.577181\pi$
$137$	−5.62065	−0.480204	−0.240102	+	0.970748i	$0.577181\pi$
$138$	−5.29391	−0.450647
$139$	−14.6994	−1.24679	−0.623395	−	0.781907i	$-0.714247\pi$
$139$	−14.6994	−1.24679	−0.623395	+	0.781907i	$0.714247\pi$
$140$	1.54683	0.130731
$141$	−11.8060	−0.994247
$142$	8.81363	0.739623
$143$	−9.38062	−0.784447
$144$	−1.85399	−0.154499
$145$	7.16976	0.595416
$146$	−7.50514	−0.621130
$147$	6.61889	0.545917
$148$	1.62440	0.133525
$149$	4.10265	0.336103	0.168051	−	0.985778i	$-0.446253\pi$
$149$	4.10265	0.336103	0.168051	+	0.985778i	$0.446253\pi$
$150$	2.21788	0.181089
$151$	−17.1149	−1.39279	−0.696396	−	0.717658i	$-0.745214\pi$
$151$	−17.1149	−1.39279	−0.696396	+	0.717658i	$0.745214\pi$
$152$	2.74341	0.222520
$153$	−4.99101	−0.403499
$154$	2.43039	0.195846
$155$	−1.71120	−0.137447
$156$	−3.73501	−0.299040
$157$	−3.71980	−0.296872	−0.148436	−	0.988922i	$-0.547424\pi$
$157$	−3.71980	−0.296872	−0.148436	+	0.988922i	$0.547424\pi$
$158$	8.06001	0.641220
$159$	9.82607	0.779258
$160$	−1.71120	−0.135283
$161$	−4.47017	−0.352298
$162$	−0.000754845 0	−5.93062e−5 0
$163$	1.43124	0.112104	0.0560519	−	0.998428i	$-0.482149\pi$
$163$	1.43124	0.112104	0.0560519	+	0.998428i	$0.482149\pi$
$164$	−7.16833	−0.559752
$165$	−4.92528	−0.383432
$166$	−12.6677	−0.983205
$167$	−3.93387	−0.304412	−0.152206	−	0.988349i	$-0.548638\pi$
$167$	−3.93387	−0.304412	−0.152206	+	0.988349i	$0.548638\pi$
$168$	0.967689	0.0746588
$169$	−0.827092	−0.0636224
$170$	−4.60662	−0.353312
$171$	−5.08625	−0.388955
$172$	−6.31452	−0.481478
$173$	4.56557	0.347114	0.173557	−	0.984824i	$-0.444474\pi$
$173$	4.56557	0.347114	0.173557	+	0.984824i	$0.444474\pi$
$174$	4.48536	0.340034
$175$	1.87277	0.141568
$176$	−2.68865	−0.202665
$177$	−8.71452	−0.655023
$178$	2.11333	0.158401
$179$	−8.44096	−0.630907	−0.315454	−	0.948941i	$-0.602157\pi$
$179$	−8.44096	−0.630907	−0.315454	+	0.948941i	$0.602157\pi$
$180$	3.17255	0.236468
$181$	11.6479	0.865780	0.432890	−	0.901447i	$-0.357494\pi$
$181$	11.6479	0.865780	0.432890	+	0.901447i	$0.357494\pi$
$182$	−3.15383	−0.233778
$183$	−7.04055	−0.520452
$184$	4.94518	0.364563
$185$	−2.77968	−0.204366
$186$	−1.07052	−0.0784942
$187$	−7.23795	−0.529291
$188$	11.0283	0.804323
$189$	−4.69715	−0.341668
$190$	−4.69453	−0.340577
$191$	−11.0444	−0.799142	−0.399571	−	0.916702i	$-0.630841\pi$
$191$	−11.0444	−0.799142	−0.399571	+	0.916702i	$0.630841\pi$
$192$	−1.07052	−0.0772580
$193$	−7.55806	−0.544041	−0.272021	−	0.962291i	$-0.587692\pi$
$193$	−7.55806	−0.544041	−0.272021	+	0.962291i	$0.587692\pi$
$194$	−1.00000	−0.0717958
$195$	6.39136	0.457695
$196$	−6.18288	−0.441635
$197$	15.1594	1.08007	0.540033	−	0.841644i	$-0.318412\pi$
$197$	15.1594	1.08007	0.540033	+	0.841644i	$0.318412\pi$
$198$	4.98473	0.354249
$199$	10.6586	0.755570	0.377785	−	0.925893i	$-0.376686\pi$
$199$	10.6586	0.755570	0.377785	+	0.925893i	$0.376686\pi$
$200$	−2.07178	−0.146497
$201$	1.07425	0.0757714
$202$	9.56562	0.673035
$203$	3.78743	0.265825
$204$	−2.88188	−0.201772
$205$	12.2665	0.856727
$206$	−3.93360	−0.274067
$207$	−9.16831	−0.637241
$208$	3.48897	0.241917
$209$	−7.37606	−0.510213
$210$	−1.65591	−0.114269
$211$	−13.1433	−0.904824	−0.452412	−	0.891809i	$-0.649436\pi$
$211$	−13.1433	−0.904824	−0.452412	+	0.891809i	$0.649436\pi$
$212$	−9.17879	−0.630402
$213$	−9.43515	−0.646486
$214$	−19.1497	−1.30905
$215$	10.8054	0.736925
$216$	5.19629	0.353563
$217$	−0.903944	−0.0613637
$218$	−14.0800	−0.953617
$219$	8.03440	0.542914
$220$	4.60083	0.310188
$221$	9.39244	0.631804
$222$	−1.73895	−0.116711
$223$	8.55826	0.573103	0.286552	−	0.958065i	$-0.407491\pi$
$223$	8.55826	0.573103	0.286552	+	0.958065i	$0.407491\pi$
$224$	−0.903944	−0.0603973
$225$	3.84106	0.256071
$226$	−1.03738	−0.0690058
$227$	−11.7534	−0.780098	−0.390049	−	0.920794i	$-0.627542\pi$
$227$	−11.7534	−0.780098	−0.390049	+	0.920794i	$0.627542\pi$
$228$	−2.93687	−0.194499
$229$	−0.639521	−0.0422607	−0.0211304	−	0.999777i	$-0.506727\pi$
$229$	−0.639521	−0.0422607	−0.0211304	+	0.999777i	$0.506727\pi$
$230$	−8.46221	−0.557981
$231$	−2.60178	−0.171185
$232$	−4.18989	−0.275080
$233$	28.4875	1.86628	0.933140	−	0.359513i	$-0.117057\pi$
$233$	28.4875	1.86628	0.933140	+	0.359513i	$0.117057\pi$
$234$	−6.46851	−0.422860
$235$	−18.8717	−1.23105
$236$	8.14046	0.529899
$237$	−8.62839	−0.560474
$238$	−2.43345	−0.157737
$239$	3.59221	0.232361	0.116180	−	0.993228i	$-0.462935\pi$
$239$	3.59221	0.232361	0.116180	+	0.993228i	$0.462935\pi$
$240$	1.83188	0.118247
$241$	−4.65261	−0.299701	−0.149851	−	0.988709i	$-0.547879\pi$
$241$	−4.65261	−0.299701	−0.149851	+	0.988709i	$0.547879\pi$
$242$	−3.77115	−0.242419
$243$	−15.5881	−0.999974
$244$	6.57676	0.421034
$245$	10.5802	0.675943
$246$	7.67383	0.489265
$247$	9.57166	0.609030
$248$	1.00000	0.0635001
$249$	13.5610	0.859395
$250$	12.1013	0.765351
$251$	−6.92543	−0.437129	−0.218565	−	0.975822i	$-0.570137\pi$
$251$	−6.92543	−0.437129	−0.218565	+	0.975822i	$0.570137\pi$
$252$	1.67590	0.105572
$253$	−13.2959	−0.835904
$254$	−18.7163	−1.17436
$255$	4.93148	0.308821
$256$	1.00000	0.0625000
$257$	−6.95060	−0.433567	−0.216783	−	0.976220i	$-0.569557\pi$
$257$	−6.95060	−0.433567	−0.216783	+	0.976220i	$0.569557\pi$
$258$	6.75982	0.420848
$259$	−1.46837	−0.0912398
$260$	−5.97034	−0.370265
$261$	7.76802	0.480828
$262$	−22.3876	−1.38311
$263$	−16.5689	−1.02168	−0.510840	−	0.859676i	$-0.670666\pi$
$263$	−16.5689	−1.02168	−0.510840	+	0.859676i	$0.670666\pi$
$264$	2.87825	0.177144
$265$	15.7068	0.964860
$266$	−2.47989	−0.152052
$267$	−2.26236	−0.138454
$268$	−1.00348	−0.0612974
$269$	3.61232	0.220247	0.110124	−	0.993918i	$-0.464875\pi$
$269$	3.61232	0.220247	0.110124	+	0.993918i	$0.464875\pi$
$270$	−8.89191	−0.541144
$271$	−16.8962	−1.02637	−0.513186	−	0.858277i	$-0.671535\pi$
$271$	−16.8962	−1.02637	−0.513186	+	0.858277i	$0.671535\pi$
$272$	2.69204	0.163229
$273$	3.37624	0.204339
$274$	−5.62065	−0.339556
$275$	5.57030	0.335902
$276$	−5.29391	−0.318656
$277$	7.90907	0.475210	0.237605	−	0.971362i	$-0.423638\pi$
$277$	7.90907	0.475210	0.237605	+	0.971362i	$0.423638\pi$
$278$	−14.6994	−0.881613
$279$	−1.85399	−0.110995
$280$	1.54683	0.0924409
$281$	21.5003	1.28260	0.641299	−	0.767291i	$-0.278396\pi$
$281$	21.5003	1.28260	0.641299	+	0.767291i	$0.278396\pi$
$282$	−11.8060	−0.703038
$283$	−10.0700	−0.598602	−0.299301	−	0.954159i	$-0.596753\pi$
$283$	−10.0700	−0.598602	−0.299301	+	0.954159i	$0.596753\pi$
$284$	8.81363	0.522992
$285$	5.02558	0.297690
$286$	−9.38062	−0.554688
$287$	6.47977	0.382489
$288$	−1.85399	−0.109247
$289$	−9.75294	−0.573702
$290$	7.16976	0.421023
$291$	1.07052	0.0627549
$292$	−7.50514	−0.439205
$293$	−7.30360	−0.426681	−0.213341	−	0.976978i	$-0.568434\pi$
$293$	−7.30360	−0.426681	−0.213341	+	0.976978i	$0.568434\pi$
$294$	6.61889	0.386022
$295$	−13.9300	−0.811035
$296$	1.62440	0.0944162
$297$	−13.9710	−0.810680
$298$	4.10265	0.237660
$299$	17.2536	0.997800
$300$	2.21788	0.128049
$301$	5.70798	0.329002
$302$	−17.1149	−0.984853
$303$	−10.2402	−0.588283
$304$	2.74341	0.157345
$305$	−11.2542	−0.644412
$306$	−4.99101	−0.285317
$307$	34.3882	1.96264	0.981320	−	0.192384i	$-0.0616220\pi$
$307$	34.3882	1.96264	0.981320	+	0.192384i	$0.0616220\pi$
$308$	2.43039	0.138484
$309$	4.21100	0.239555
$310$	−1.71120	−0.0971898
$311$	−8.98536	−0.509513	−0.254756	−	0.967005i	$-0.581995\pi$
$311$	−8.98536	−0.509513	−0.254756	+	0.967005i	$0.581995\pi$
$312$	−3.73501	−0.211453
$313$	−6.32808	−0.357684	−0.178842	−	0.983878i	$-0.557235\pi$
$313$	−6.32808	−0.357684	−0.178842	+	0.983878i	$0.557235\pi$
$314$	−3.71980	−0.209920
$315$	−2.86781	−0.161583
$316$	8.06001	0.453411
$317$	−5.75026	−0.322967	−0.161484	−	0.986875i	$-0.551628\pi$
$317$	−5.75026	−0.322967	−0.161484	+	0.986875i	$0.551628\pi$
$318$	9.82607	0.551019
$319$	11.2652	0.630728
$320$	−1.71120	−0.0956592
$321$	20.5002	1.14421
$322$	−4.47017	−0.249113
$323$	7.38535	0.410932
$324$	−0.000754845 0	−4.19358e−5 0
$325$	−7.22838	−0.400958
$326$	1.43124	0.0792693
$327$	15.0729	0.833533
$328$	−7.16833	−0.395805
$329$	−9.96899	−0.549608
$330$	−4.92528	−0.271128
$331$	−19.6523	−1.08019	−0.540093	−	0.841605i	$-0.681611\pi$
$331$	−19.6523	−1.08019	−0.540093	+	0.841605i	$0.681611\pi$
$332$	−12.6677	−0.695231
$333$	−3.01162	−0.165036
$334$	−3.93387	−0.215252
$335$	1.71716	0.0938185
$336$	0.967689	0.0527918
$337$	−4.40985	−0.240220	−0.120110	−	0.992761i	$-0.538325\pi$
$337$	−4.40985	−0.240220	−0.120110	+	0.992761i	$0.538325\pi$
$338$	−0.827092	−0.0449878
$339$	1.11054	0.0603162
$340$	−4.60662	−0.249829
$341$	−2.68865	−0.145599
$342$	−5.08625	−0.275033
$343$	11.9166	0.643435
$344$	−6.31452	−0.340456
$345$	9.05895	0.487718
$346$	4.56557	0.245446
$347$	−8.01936	−0.430502	−0.215251	−	0.976559i	$-0.569057\pi$
$347$	−8.01936	−0.430502	−0.215251	+	0.976559i	$0.569057\pi$
$348$	4.48536	0.240441
$349$	−2.17779	−0.116575	−0.0582873	−	0.998300i	$-0.518564\pi$
$349$	−2.17779	−0.116575	−0.0582873	+	0.998300i	$0.518564\pi$
$350$	1.87277	0.100104
$351$	18.1297	0.967691
$352$	−2.68865	−0.143306
$353$	7.25687	0.386244	0.193122	−	0.981175i	$-0.438139\pi$
$353$	7.25687	0.386244	0.193122	+	0.981175i	$0.438139\pi$
$354$	−8.71452	−0.463171
$355$	−15.0819	−0.800465
$356$	2.11333	0.112006
$357$	2.60506	0.137874
$358$	−8.44096	−0.446119
$359$	24.9508	1.31685	0.658426	−	0.752645i	$-0.271222\pi$
$359$	24.9508	1.31685	0.658426	+	0.752645i	$0.271222\pi$
$360$	3.17255	0.167208
$361$	−11.4737	−0.603880
$362$	11.6479	0.612199
$363$	4.03709	0.211892
$364$	−3.15383	−0.165306
$365$	12.8428	0.672225
$366$	−7.04055	−0.368015
$367$	1.89102	0.0987106	0.0493553	−	0.998781i	$-0.484283\pi$
$367$	1.89102	0.0987106	0.0493553	+	0.998781i	$0.484283\pi$
$368$	4.94518	0.257785
$369$	13.2900	0.691850
$370$	−2.77968	−0.144508
$371$	8.29712	0.430765
$372$	−1.07052	−0.0555038
$373$	5.90316	0.305654	0.152827	−	0.988253i	$-0.451162\pi$
$373$	5.90316	0.305654	0.152827	+	0.988253i	$0.451162\pi$
$374$	−7.23795	−0.374265
$375$	−12.9546	−0.668974
$376$	11.0283	0.568742
$377$	−14.6184	−0.752887
$378$	−4.69715	−0.241596
$379$	17.3857	0.893041	0.446521	−	0.894773i	$-0.352663\pi$
$379$	17.3857	0.893041	0.446521	+	0.894773i	$0.352663\pi$
$380$	−4.69453	−0.240824
$381$	20.0361	1.02648
$382$	−11.0444	−0.565079
$383$	−0.440804	−0.0225240	−0.0112620	−	0.999937i	$-0.503585\pi$
$383$	−0.440804	−0.0225240	−0.0112620	+	0.999937i	$0.503585\pi$
$384$	−1.07052	−0.0546297
$385$	−4.15889	−0.211957
$386$	−7.55806	−0.384695
$387$	11.7071	0.595103
$388$	−1.00000	−0.0507673
$389$	−14.9920	−0.760123	−0.380062	−	0.924961i	$-0.624097\pi$
$389$	−14.9920	−0.760123	−0.380062	+	0.924961i	$0.624097\pi$
$390$	6.39136	0.323639
$391$	13.3126	0.673247
$392$	−6.18288	−0.312283
$393$	23.9664	1.20894
$394$	15.1594	0.763721
$395$	−13.7923	−0.693967
$396$	4.98473	0.250492
$397$	−20.1226	−1.00993	−0.504963	−	0.863141i	$-0.668494\pi$
$397$	−20.1226	−1.00993	−0.504963	+	0.863141i	$0.668494\pi$
$398$	10.6586	0.534269
$399$	2.65476	0.132904
$400$	−2.07178	−0.103589
$401$	14.3726	0.717735	0.358868	−	0.933388i	$-0.383163\pi$
$401$	14.3726	0.717735	0.358868	+	0.933388i	$0.383163\pi$
$402$	1.07425	0.0535785
$403$	3.48897	0.173798
$404$	9.56562	0.475907
$405$	0.00129169	6.41848e−5 0
$406$	3.78743	0.187967
$407$	−4.36744	−0.216486
$408$	−2.88188	−0.142674
$409$	−9.00634	−0.445335	−0.222667	−	0.974894i	$-0.571476\pi$
$409$	−9.00634	−0.445335	−0.222667	+	0.974894i	$0.571476\pi$
$410$	12.2665	0.605798
$411$	6.01701	0.296797
$412$	−3.93360	−0.193795
$413$	−7.35852	−0.362089
$414$	−9.16831	−0.450598
$415$	21.6770	1.06408
$416$	3.48897	0.171061
$417$	15.7360	0.770596
$418$	−7.37606	−0.360775
$419$	27.2401	1.33076	0.665382	−	0.746503i	$-0.268269\pi$
$419$	27.2401	1.33076	0.665382	+	0.746503i	$0.268269\pi$
$420$	−1.65591	−0.0808003
$421$	−8.62350	−0.420284	−0.210142	−	0.977671i	$-0.567393\pi$
$421$	−8.62350	−0.420284	−0.210142	+	0.977671i	$0.567393\pi$
$422$	−13.1433	−0.639807
$423$	−20.4464	−0.994137
$424$	−9.17879	−0.445762
$425$	−5.57731	−0.270539
$426$	−9.43515	−0.457135
$427$	−5.94502	−0.287700
$428$	−19.1497	−0.925638
$429$	10.0421	0.484839
$430$	10.8054	0.521084
$431$	35.8547	1.72706	0.863529	−	0.504299i	$-0.168249\pi$
$431$	35.8547	1.72706	0.863529	+	0.504299i	$0.168249\pi$
$432$	5.19629	0.250006
$433$	−34.3294	−1.64977	−0.824883	−	0.565303i	$-0.808759\pi$
$433$	−34.3294	−1.64977	−0.824883	+	0.565303i	$0.808759\pi$
$434$	−0.903944	−0.0433907
$435$	−7.67537	−0.368006
$436$	−14.0800	−0.674309
$437$	13.5666	0.648980
$438$	8.03440	0.383898
$439$	−16.2797	−0.776990	−0.388495	−	0.921451i	$-0.627005\pi$
$439$	−16.2797	−0.776990	−0.388495	+	0.921451i	$0.627005\pi$
$440$	4.60083	0.219336
$441$	11.4630	0.545857
$442$	9.39244	0.446753
$443$	−20.3505	−0.966881	−0.483441	−	0.875377i	$-0.660613\pi$
$443$	−20.3505	−0.966881	−0.483441	+	0.875377i	$0.660613\pi$
$444$	−1.73895	−0.0825269
$445$	−3.61634	−0.171431
$446$	8.55826	0.405245
$447$	−4.39197	−0.207733
$448$	−0.903944	−0.0427073
$449$	−12.0062	−0.566606	−0.283303	−	0.959030i	$-0.591430\pi$
$449$	−12.0062	−0.566606	−0.283303	+	0.959030i	$0.591430\pi$
$450$	3.84106	0.181069
$451$	19.2731	0.907536
$452$	−1.03738	−0.0487945
$453$	18.3218	0.860835
$454$	−11.7534	−0.551613
$455$	5.39685	0.253008
$456$	−2.93687	−0.137531
$457$	−21.3699	−0.999640	−0.499820	−	0.866129i	$-0.666600\pi$
$457$	−21.3699	−0.999640	−0.499820	+	0.866129i	$0.666600\pi$
$458$	−0.639521	−0.0298829
$459$	13.9886	0.652932
$460$	−8.46221	−0.394552
$461$	14.1417	0.658645	0.329323	−	0.944217i	$-0.393180\pi$
$461$	14.1417	0.658645	0.329323	+	0.944217i	$0.393180\pi$
$462$	−2.60178	−0.121046
$463$	4.05660	0.188526	0.0942632	−	0.995547i	$-0.469950\pi$
$463$	4.05660	0.188526	0.0942632	+	0.995547i	$0.469950\pi$
$464$	−4.18989	−0.194511
$465$	1.83188	0.0849512
$466$	28.4875	1.31966
$467$	−24.6387	−1.14014	−0.570072	−	0.821595i	$-0.693085\pi$
$467$	−24.6387	−1.14014	−0.570072	+	0.821595i	$0.693085\pi$
$468$	−6.46851	−0.299007
$469$	0.907091	0.0418856
$470$	−18.8717	−0.870487
$471$	3.98211	0.183486
$472$	8.14046	0.374695
$473$	16.9776	0.780629
$474$	−8.62839	−0.396315
$475$	−5.68374	−0.260788
$476$	−2.43345	−0.111537
$477$	17.0174	0.779173
$478$	3.59221	0.164304
$479$	6.90370	0.315438	0.157719	−	0.987484i	$-0.449586\pi$
$479$	6.90370	0.315438	0.157719	+	0.987484i	$0.449586\pi$
$480$	1.83188	0.0836133
$481$	5.66748	0.258415
$482$	−4.65261	−0.211921
$483$	4.78540	0.217743
$484$	−3.77115	−0.171416
$485$	1.71120	0.0777018
$486$	−15.5881	−0.707088
$487$	−33.1771	−1.50340	−0.751699	−	0.659506i	$-0.770766\pi$
$487$	−33.1771	−1.50340	−0.751699	+	0.659506i	$0.770766\pi$
$488$	6.57676	0.297716
$489$	−1.53217	−0.0692873
$490$	10.5802	0.477964
$491$	41.0338	1.85183	0.925915	−	0.377732i	$-0.123296\pi$
$491$	41.0338	1.85183	0.925915	+	0.377732i	$0.123296\pi$
$492$	7.67383	0.345963
$493$	−11.2794	−0.507996
$494$	9.57166	0.430649
$495$	−8.52989	−0.383390
$496$	1.00000	0.0449013
$497$	−7.96703	−0.357370
$498$	13.5610	0.607684
$499$	−26.2154	−1.17356	−0.586781	−	0.809746i	$-0.699605\pi$
$499$	−26.2154	−1.17356	−0.586781	+	0.809746i	$0.699605\pi$
$500$	12.1013	0.541185
$501$	4.21129	0.188146
$502$	−6.92543	−0.309097
$503$	−40.9232	−1.82468	−0.912339	−	0.409437i	$-0.865725\pi$
$503$	−40.9232	−1.82468	−0.912339	+	0.409437i	$0.865725\pi$
$504$	1.67590	0.0746507
$505$	−16.3687	−0.728399
$506$	−13.2959	−0.591073
$507$	0.885417	0.0393228
$508$	−18.7163	−0.830400
$509$	9.01169	0.399436	0.199718	−	0.979853i	$-0.435997\pi$
$509$	9.01169	0.399436	0.199718	+	0.979853i	$0.435997\pi$
$510$	4.93148	0.218370
$511$	6.78423	0.300117
$512$	1.00000	0.0441942
$513$	14.2555	0.629397
$514$	−6.95060	−0.306578
$515$	6.73120	0.296612
$516$	6.75982	0.297584
$517$	−29.6513	−1.30406
$518$	−1.46837	−0.0645163
$519$	−4.88753	−0.214539
$520$	−5.97034	−0.261817
$521$	22.9087	1.00365	0.501824	−	0.864970i	$-0.332662\pi$
$521$	22.9087	1.00365	0.501824	+	0.864970i	$0.332662\pi$
$522$	7.76802	0.339997
$523$	4.78051	0.209037	0.104519	−	0.994523i	$-0.466670\pi$
$523$	4.78051	0.209037	0.104519	+	0.994523i	$0.466670\pi$
$524$	−22.3876	−0.978008
$525$	−2.00484	−0.0874984
$526$	−16.5689	−0.722437
$527$	2.69204	0.117267
$528$	2.87825	0.125260
$529$	1.45479	0.0632516
$530$	15.7068	0.682259
$531$	−15.0923	−0.654951
$532$	−2.47989	−0.107517
$533$	−25.0101	−1.08331
$534$	−2.26236	−0.0979019
$535$	32.7691	1.41673
$536$	−1.00348	−0.0433438
$537$	9.03621	0.389941
$538$	3.61232	0.155738
$539$	16.6236	0.716030
$540$	−8.89191	−0.382647
$541$	0.537865	0.0231246	0.0115623	−	0.999933i	$-0.496320\pi$
$541$	0.537865	0.0231246	0.0115623	+	0.999933i	$0.496320\pi$
$542$	−16.8962	−0.725754
$543$	−12.4693	−0.535107
$544$	2.69204	0.115420
$545$	24.0937	1.03206
$546$	3.37624	0.144490
$547$	4.10892	0.175685	0.0878425	−	0.996134i	$-0.472003\pi$
$547$	4.10892	0.175685	0.0878425	+	0.996134i	$0.472003\pi$
$548$	−5.62065	−0.240102
$549$	−12.1932	−0.520395
$550$	5.57030	0.237518
$551$	−11.4946	−0.489686
$552$	−5.29391	−0.225324
$553$	−7.28580	−0.309824
$554$	7.90907	0.336024
$555$	2.97570	0.126311
$556$	−14.6994	−0.623395
$557$	9.50903	0.402910	0.201455	−	0.979498i	$-0.435433\pi$
$557$	9.50903	0.402910	0.201455	+	0.979498i	$0.435433\pi$
$558$	−1.85399	−0.0784856
$559$	−22.0312	−0.931820
$560$	1.54683	0.0653656
$561$	7.74836	0.327136
$562$	21.5003	0.906934
$563$	−44.5506	−1.87758	−0.938791	−	0.344487i	$-0.888053\pi$
$563$	−44.5506	−1.87758	−0.938791	+	0.344487i	$0.888053\pi$
$564$	−11.8060	−0.497123
$565$	1.77518	0.0746822
$566$	−10.0700	−0.423275
$567$	0.000682338 0	2.86555e−5 0
$568$	8.81363	0.369812
$569$	21.9314	0.919410	0.459705	−	0.888072i	$-0.347955\pi$
$569$	21.9314	0.919410	0.459705	+	0.888072i	$0.347955\pi$
$570$	5.02558	0.210498
$571$	−11.0285	−0.461529	−0.230765	−	0.973010i	$-0.574123\pi$
$571$	−11.0285	−0.461529	−0.230765	+	0.973010i	$0.574123\pi$
$572$	−9.38062	−0.392224
$573$	11.8232	0.493921
$574$	6.47977	0.270460
$575$	−10.2453	−0.427260
$576$	−1.85399	−0.0772496
$577$	40.4784	1.68514	0.842569	−	0.538588i	$-0.181042\pi$
$577$	40.4784	1.68514	0.842569	+	0.538588i	$0.181042\pi$
$578$	−9.75294	−0.405669
$579$	8.09105	0.336253
$580$	7.16976	0.297708
$581$	11.4509	0.475064
$582$	1.07052	0.0443744
$583$	24.6786	1.02208
$584$	−7.50514	−0.310565
$585$	11.0689	0.457645
$586$	−7.30360	−0.301709
$587$	−19.5390	−0.806459	−0.403230	−	0.915099i	$-0.632112\pi$
$587$	−19.5390	−0.806459	−0.403230	+	0.915099i	$0.632112\pi$
$588$	6.61889	0.272959
$589$	2.74341	0.113040
$590$	−13.9300	−0.573489
$591$	−16.2285	−0.667550
$592$	1.62440	0.0667623
$593$	−9.05410	−0.371807	−0.185904	−	0.982568i	$-0.559521\pi$
$593$	−9.05410	−0.371807	−0.185904	+	0.982568i	$0.559521\pi$
$594$	−13.9710	−0.573237
$595$	4.16413	0.170713
$596$	4.10265	0.168051
$597$	−11.4103	−0.466991
$598$	17.2536	0.705551
$599$	−32.7527	−1.33824	−0.669120	−	0.743154i	$-0.733329\pi$
$599$	−32.7527	−1.33824	−0.669120	+	0.743154i	$0.733329\pi$
$600$	2.21788	0.0905446
$601$	3.33441	0.136014	0.0680068	−	0.997685i	$-0.478336\pi$
$601$	3.33441	0.136014	0.0680068	+	0.997685i	$0.478336\pi$
$602$	5.70798	0.232640
$603$	1.86044	0.0757631
$604$	−17.1149	−0.696396
$605$	6.45321	0.262360
$606$	−10.2402	−0.415979
$607$	38.5294	1.56386	0.781930	−	0.623366i	$-0.214235\pi$
$607$	38.5294	1.56386	0.781930	+	0.623366i	$0.214235\pi$
$608$	2.74341	0.111260
$609$	−4.05452	−0.164297
$610$	−11.2542	−0.455668
$611$	38.4775	1.55663
$612$	−4.99101	−0.201750
$613$	42.2323	1.70575	0.852873	−	0.522119i	$-0.174858\pi$
$613$	42.2323	1.70575	0.852873	+	0.522119i	$0.174858\pi$
$614$	34.3882	1.38780
$615$	−13.1315	−0.529513
$616$	2.43039	0.0979232
$617$	−24.2462	−0.976114	−0.488057	−	0.872812i	$-0.662294\pi$
$617$	−24.2462	−0.976114	−0.488057	+	0.872812i	$0.662294\pi$
$618$	4.21100	0.169391
$619$	16.1057	0.647342	0.323671	−	0.946170i	$-0.395083\pi$
$619$	16.1057	0.647342	0.323671	+	0.946170i	$0.395083\pi$
$620$	−1.71120	−0.0687236
$621$	25.6966	1.03117
$622$	−8.98536	−0.360280
$623$	−1.91033	−0.0765359
$624$	−3.73501	−0.149520
$625$	−10.3488	−0.413953
$626$	−6.32808	−0.252921
$627$	7.89621	0.315344
$628$	−3.71980	−0.148436
$629$	4.37294	0.174361
$630$	−2.86781	−0.114256
$631$	−42.0429	−1.67370	−0.836852	−	0.547430i	$-0.815606\pi$
$631$	−42.0429	−1.67370	−0.836852	+	0.547430i	$0.815606\pi$
$632$	8.06001	0.320610
$633$	14.0702	0.559239
$634$	−5.75026	−0.228372
$635$	32.0274	1.27097
$636$	9.82607	0.389629
$637$	−21.5719	−0.854710
$638$	11.2652	0.445992
$639$	−16.3404	−0.646415
$640$	−1.71120	−0.0676413
$641$	21.5838	0.852508	0.426254	−	0.904604i	$-0.359833\pi$
$641$	21.5838	0.852508	0.426254	+	0.904604i	$0.359833\pi$
$642$	20.5002	0.809077
$643$	−34.6674	−1.36715	−0.683575	−	0.729880i	$-0.739576\pi$
$643$	−34.6674	−1.36715	−0.683575	+	0.729880i	$0.739576\pi$
$644$	−4.47017	−0.176149
$645$	−11.5674	−0.455467
$646$	7.38535	0.290573
$647$	−30.4626	−1.19761	−0.598804	−	0.800895i	$-0.704357\pi$
$647$	−30.4626	−1.19761	−0.598804	+	0.800895i	$0.704357\pi$
$648$	−0.000754845 0	−2.96531e−5 0
$649$	−21.8869	−0.859134
$650$	−7.22838	−0.283520
$651$	0.967689	0.0379267
$652$	1.43124	0.0560519
$653$	−2.74723	−0.107507	−0.0537537	−	0.998554i	$-0.517119\pi$
$653$	−2.74723	−0.107507	−0.0537537	+	0.998554i	$0.517119\pi$
$654$	15.0729	0.589397
$655$	38.3098	1.49689
$656$	−7.16833	−0.279876
$657$	13.9145	0.542855
$658$	−9.96899	−0.388632
$659$	−10.9539	−0.426701	−0.213351	−	0.976976i	$-0.568438\pi$
$659$	−10.9539	−0.426701	−0.213351	+	0.976976i	$0.568438\pi$
$660$	−4.92528	−0.191716
$661$	−13.7322	−0.534119	−0.267060	−	0.963680i	$-0.586052\pi$
$661$	−13.7322	−0.534119	−0.267060	+	0.963680i	$0.586052\pi$
$662$	−19.6523	−0.763807
$663$	−10.0548	−0.390495
$664$	−12.6677	−0.491603
$665$	4.24359	0.164559
$666$	−3.01162	−0.116698
$667$	−20.7198	−0.802273
$668$	−3.93387	−0.152206
$669$	−9.16178	−0.354215
$670$	1.71716	0.0663397
$671$	−17.6826	−0.682630
$672$	0.967689	0.0373294
$673$	−15.1801	−0.585151	−0.292576	−	0.956242i	$-0.594512\pi$
$673$	−15.1801	−0.585151	−0.292576	+	0.956242i	$0.594512\pi$
$674$	−4.40985	−0.169861
$675$	−10.7656	−0.414367
$676$	−0.827092	−0.0318112
$677$	13.5138	0.519378	0.259689	−	0.965692i	$-0.416380\pi$
$677$	13.5138	0.519378	0.259689	+	0.965692i	$0.416380\pi$
$678$	1.11054	0.0426500
$679$	0.903944	0.0346902
$680$	−4.60662	−0.176656
$681$	12.5822	0.482151
$682$	−2.68865	−0.102954
$683$	17.6049	0.673634	0.336817	−	0.941570i	$-0.390650\pi$
$683$	17.6049	0.673634	0.336817	+	0.941570i	$0.390650\pi$
$684$	−5.08625	−0.194477
$685$	9.61807	0.367488
$686$	11.9166	0.454978
$687$	0.684619	0.0261199
$688$	−6.31452	−0.240739
$689$	−32.0245	−1.22004
$690$	9.05895	0.344868
$691$	42.6409	1.62213	0.811067	−	0.584953i	$-0.198887\pi$
$691$	42.6409	1.62213	0.811067	+	0.584953i	$0.198887\pi$
$692$	4.56557	0.173557
$693$	−4.50592	−0.171166
$694$	−8.01936	−0.304411
$695$	25.1537	0.954135
$696$	4.48536	0.170017
$697$	−19.2974	−0.730941
$698$	−2.17779	−0.0824306
$699$	−30.4964	−1.15348
$700$	1.87277	0.0707842
$701$	24.8545	0.938743	0.469372	−	0.883001i	$-0.344481\pi$
$701$	24.8545	0.938743	0.469372	+	0.883001i	$0.344481\pi$
$702$	18.1297	0.684261
$703$	4.45638	0.168076
$704$	−2.68865	−0.101332
$705$	20.2025	0.760871
$706$	7.25687	0.273116
$707$	−8.64678	−0.325196
$708$	−8.71452	−0.327512
$709$	2.57456	0.0966894	0.0483447	−	0.998831i	$-0.484605\pi$
$709$	2.57456	0.0966894	0.0483447	+	0.998831i	$0.484605\pi$
$710$	−15.0819	−0.566014
$711$	−14.9432	−0.560413
$712$	2.11333	0.0792004
$713$	4.94518	0.185198
$714$	2.60506	0.0974918
$715$	16.0522	0.600317
$716$	−8.44096	−0.315454
$717$	−3.84553	−0.143614
$718$	24.9508	0.931155
$719$	36.2611	1.35231	0.676155	−	0.736760i	$-0.263645\pi$
$719$	36.2611	1.35231	0.676155	+	0.736760i	$0.263645\pi$
$720$	3.17255	0.118234
$721$	3.55576	0.132423
$722$	−11.4737	−0.427008
$723$	4.98071	0.185235
$724$	11.6479	0.432890
$725$	8.68054	0.322387
$726$	4.03709	0.149830
$727$	−0.373687	−0.0138593	−0.00692965	−	0.999976i	$-0.502206\pi$
$727$	−0.373687	−0.0138593	−0.00692965	+	0.999976i	$0.502206\pi$
$728$	−3.15383	−0.116889
$729$	16.6896	0.618132
$730$	12.8428	0.475335
$731$	−16.9989	−0.628728
$732$	−7.04055	−0.260226
$733$	−25.1577	−0.929222	−0.464611	−	0.885515i	$-0.653806\pi$
$733$	−25.1577	−0.929222	−0.464611	+	0.885515i	$0.653806\pi$
$734$	1.89102	0.0697989
$735$	−11.3263	−0.417776
$736$	4.94518	0.182282
$737$	2.69801	0.0993825
$738$	13.2900	0.489212
$739$	−44.8820	−1.65101	−0.825506	−	0.564393i	$-0.809110\pi$
$739$	−44.8820	−1.65101	−0.825506	+	0.564393i	$0.809110\pi$
$740$	−2.77968	−0.102183
$741$	−10.2466	−0.376420
$742$	8.29712	0.304597
$743$	12.6065	0.462488	0.231244	−	0.972896i	$-0.425720\pi$
$743$	12.6065	0.462488	0.231244	+	0.972896i	$0.425720\pi$
$744$	−1.07052	−0.0392471
$745$	−7.02048	−0.257210
$746$	5.90316	0.216130
$747$	23.4858	0.859301
$748$	−7.23795	−0.264646
$749$	17.3103	0.632505
$750$	−12.9546	−0.473036
$751$	51.2931	1.87171	0.935856	−	0.352382i	$-0.114628\pi$
$751$	51.2931	1.87171	0.935856	+	0.352382i	$0.114628\pi$
$752$	11.0283	0.402161
$753$	7.41380	0.270174
$754$	−14.6184	−0.532371
$755$	29.2871	1.06587
$756$	−4.69715	−0.170834
$757$	40.1908	1.46076	0.730379	−	0.683042i	$-0.239344\pi$
$757$	40.1908	1.46076	0.730379	+	0.683042i	$0.239344\pi$
$758$	17.3857	0.631476
$759$	14.2335	0.516642
$760$	−4.69453	−0.170288
$761$	27.8221	1.00855	0.504275	−	0.863543i	$-0.331760\pi$
$761$	27.8221	1.00855	0.504275	+	0.863543i	$0.331760\pi$
$762$	20.0361	0.725832
$763$	12.7275	0.460767
$764$	−11.0444	−0.399571
$765$	8.54063	0.308787
$766$	−0.440804	−0.0159269
$767$	28.4018	1.02553
$768$	−1.07052	−0.0386290
$769$	9.82074	0.354145	0.177073	−	0.984198i	$-0.443337\pi$
$769$	9.82074	0.354145	0.177073	+	0.984198i	$0.443337\pi$
$770$	−4.15889	−0.149876
$771$	7.44075	0.267972
$772$	−7.55806	−0.272021
$773$	−25.7205	−0.925104	−0.462552	−	0.886592i	$-0.653066\pi$
$773$	−25.7205	−0.925104	−0.462552	+	0.886592i	$0.653066\pi$
$774$	11.7071	0.420802
$775$	−2.07178	−0.0744206
$776$	−1.00000	−0.0358979
$777$	1.57191	0.0563920
$778$	−14.9920	−0.537488
$779$	−19.6656	−0.704594
$780$	6.39136	0.228847
$781$	−23.6968	−0.847937
$782$	13.3126	0.476058
$783$	−21.7719	−0.778064
$784$	−6.18288	−0.220817
$785$	6.36533	0.227188
$786$	23.9664	0.854852
$787$	29.7814	1.06159	0.530797	−	0.847499i	$-0.321893\pi$
$787$	29.7814	1.06159	0.530797	+	0.847499i	$0.321893\pi$
$788$	15.1594	0.540033
$789$	17.7373	0.631464
$790$	−13.7923	−0.490709
$791$	0.937738	0.0333421
$792$	4.98473	0.177125
$793$	22.9461	0.814841
$794$	−20.1226	−0.714126
$795$	−16.8144	−0.596346
$796$	10.6586	0.377785
$797$	−11.8350	−0.419216	−0.209608	−	0.977786i	$-0.567219\pi$
$797$	−11.8350	−0.419216	−0.209608	+	0.977786i	$0.567219\pi$
$798$	2.65476	0.0939777
$799$	29.6886	1.05031
$800$	−2.07178	−0.0732485
$801$	−3.91809	−0.138439
$802$	14.3726	0.507515
$803$	20.1787	0.712091
$804$	1.07425	0.0378857
$805$	7.64936	0.269605
$806$	3.48897	0.122894
$807$	−3.86706	−0.136127
$808$	9.56562	0.336517
$809$	28.9888	1.01919	0.509596	−	0.860414i	$-0.329795\pi$
$809$	28.9888	1.01919	0.509596	+	0.860414i	$0.329795\pi$
$810$	0.00129169	4.53855e−5 0
$811$	3.94448	0.138510	0.0692548	−	0.997599i	$-0.477938\pi$
$811$	3.94448	0.138510	0.0692548	+	0.997599i	$0.477938\pi$
$812$	3.78743	0.132913
$813$	18.0877	0.634364
$814$	−4.36744	−0.153079
$815$	−2.44915	−0.0857900
$816$	−2.88188	−0.100886
$817$	−17.3233	−0.606066
$818$	−9.00634	−0.314899
$819$	5.84717	0.204317
$820$	12.2665	0.428364
$821$	−29.7325	−1.03767	−0.518836	−	0.854874i	$-0.673635\pi$
$821$	−29.7325	−1.03767	−0.518836	+	0.854874i	$0.673635\pi$
$822$	6.01701	0.209867
$823$	17.1032	0.596179	0.298090	−	0.954538i	$-0.403651\pi$
$823$	17.1032	0.596179	0.298090	+	0.954538i	$0.403651\pi$
$824$	−3.93360	−0.137034
$825$	−5.96311	−0.207609
$826$	−7.35852	−0.256036
$827$	−1.77326	−0.0616625	−0.0308312	−	0.999525i	$-0.509815\pi$
$827$	−1.77326	−0.0616625	−0.0308312	+	0.999525i	$0.509815\pi$
$828$	−9.16831	−0.318621
$829$	49.0350	1.70306	0.851529	−	0.524308i	$-0.175676\pi$
$829$	49.0350	1.70306	0.851529	+	0.524308i	$0.175676\pi$
$830$	21.6770	0.752421
$831$	−8.46680	−0.293710
$832$	3.48897	0.120958
$833$	−16.6446	−0.576700
$834$	15.7360	0.544894
$835$	6.73166	0.232959
$836$	−7.37606	−0.255106
$837$	5.19629	0.179610
$838$	27.2401	0.940993
$839$	−34.0506	−1.17556	−0.587779	−	0.809021i	$-0.699998\pi$
$839$	−34.0506	−1.17556	−0.587779	+	0.809021i	$0.699998\pi$
$840$	−1.65591	−0.0571344
$841$	−11.4448	−0.394648
$842$	−8.62350	−0.297185
$843$	−23.0164	−0.792728
$844$	−13.1433	−0.452412
$845$	1.41532	0.0486886
$846$	−20.4464	−0.702961
$847$	3.40891	0.117132
$848$	−9.17879	−0.315201
$849$	10.7802	0.369974
$850$	−5.57731	−0.191300
$851$	8.03294	0.275366
$852$	−9.43515	−0.323243
$853$	−55.7495	−1.90883	−0.954413	−	0.298490i	$-0.903517\pi$
$853$	−55.7495	−1.90883	−0.954413	+	0.298490i	$0.903517\pi$
$854$	−5.94502	−0.203435
$855$	8.70360	0.297657
$856$	−19.1497	−0.654525
$857$	19.3477	0.660905	0.330453	−	0.943823i	$-0.392799\pi$
$857$	19.3477	0.660905	0.330453	+	0.943823i	$0.392799\pi$
$858$	10.0421	0.342833
$859$	−41.3917	−1.41227	−0.706133	−	0.708079i	$-0.749562\pi$
$859$	−41.3917	−1.41227	−0.706133	+	0.708079i	$0.749562\pi$
$860$	10.8054	0.368462
$861$	−6.93671	−0.236403
$862$	35.8547	1.22121
$863$	33.2709	1.13255	0.566277	−	0.824215i	$-0.308383\pi$
$863$	33.2709	1.13255	0.566277	+	0.824215i	$0.308383\pi$
$864$	5.19629	0.176781
$865$	−7.81262	−0.265637
$866$	−34.3294	−1.16656
$867$	10.4407	0.354585
$868$	−0.903944	−0.0306819
$869$	−21.6706	−0.735123
$870$	−7.67537	−0.260219
$871$	−3.50111	−0.118631
$872$	−14.0800	−0.476808
$873$	1.85399	0.0627480
$874$	13.5666	0.458898
$875$	−10.9389	−0.369801
$876$	8.03440	0.271457
$877$	−8.38450	−0.283124	−0.141562	−	0.989929i	$-0.545213\pi$
$877$	−8.38450	−0.283124	−0.141562	+	0.989929i	$0.545213\pi$
$878$	−16.2797	−0.549415
$879$	7.81864	0.263716
$880$	4.60083	0.155094
$881$	5.16055	0.173863	0.0869317	−	0.996214i	$-0.472294\pi$
$881$	5.16055	0.173863	0.0869317	+	0.996214i	$0.472294\pi$
$882$	11.4630	0.385979
$883$	37.3245	1.25607	0.628034	−	0.778186i	$-0.283860\pi$
$883$	37.3245	1.25607	0.628034	+	0.778186i	$0.283860\pi$
$884$	9.39244	0.315902
$885$	14.9123	0.501272
$886$	−20.3505	−0.683688
$887$	−20.2116	−0.678640	−0.339320	−	0.940671i	$-0.610197\pi$
$887$	−20.2116	−0.678640	−0.339320	+	0.940671i	$0.610197\pi$
$888$	−1.73895	−0.0583553
$889$	16.9185	0.567427
$890$	−3.61634	−0.121220
$891$	0.00202951	6.79913e−5 0
$892$	8.55826	0.286552
$893$	30.2552	1.01245
$894$	−4.39197	−0.146889
$895$	14.4442	0.482817
$896$	−0.903944	−0.0301987
$897$	−18.4703	−0.616705
$898$	−12.0062	−0.400651
$899$	−4.18989	−0.139741
$900$	3.84106	0.128035
$901$	−24.7097	−0.823198
$902$	19.2731	0.641725
$903$	−6.11050	−0.203345
$904$	−1.03738	−0.0345029
$905$	−19.9319	−0.662558
$906$	18.3218	0.608702
$907$	−26.6722	−0.885637	−0.442819	−	0.896611i	$-0.646021\pi$
$907$	−26.6722	−0.885637	−0.442819	+	0.896611i	$0.646021\pi$
$908$	−11.7534	−0.390049
$909$	−17.7346	−0.588218
$910$	5.39685	0.178904
$911$	−18.7269	−0.620451	−0.310225	−	0.950663i	$-0.600404\pi$
$911$	−18.7269	−0.620451	−0.310225	+	0.950663i	$0.600404\pi$
$912$	−2.93687	−0.0972494
$913$	34.0591	1.12719
$914$	−21.3699	−0.706852
$915$	12.0478	0.398288
$916$	−0.639521	−0.0211304
$917$	20.2372	0.668290
$918$	13.9886	0.461693
$919$	−22.4067	−0.739128	−0.369564	−	0.929205i	$-0.620493\pi$
$919$	−22.4067	−0.739128	−0.369564	+	0.929205i	$0.620493\pi$
$920$	−8.46221	−0.278991
$921$	−36.8132	−1.21304
$922$	14.1417	0.465733
$923$	30.7505	1.01216
$924$	−2.60178	−0.0855923
$925$	−3.36540	−0.110654
$926$	4.05660	0.133308
$927$	7.29286	0.239529
$928$	−4.18989	−0.137540
$929$	57.6447	1.89126	0.945631	−	0.325241i	$-0.105445\pi$
$929$	57.6447	1.89126	0.945631	+	0.325241i	$0.105445\pi$
$930$	1.83188	0.0600696
$931$	−16.9622	−0.555913
$932$	28.4875	0.933140
$933$	9.61899	0.314912
$934$	−24.6387	−0.806203
$935$	12.3856	0.405053
$936$	−6.46851	−0.211430
$937$	1.25202	0.0409016	0.0204508	−	0.999791i	$-0.493490\pi$
$937$	1.25202	0.0409016	0.0204508	+	0.999791i	$0.493490\pi$
$938$	0.907091	0.0296176
$939$	6.77433	0.221072
$940$	−18.8717	−0.615527
$941$	23.5259	0.766922	0.383461	−	0.923557i	$-0.374732\pi$
$941$	23.5259	0.766922	0.383461	+	0.923557i	$0.374732\pi$
$942$	3.98211	0.129744
$943$	−35.4486	−1.15437
$944$	8.14046	0.264949
$945$	8.03779	0.261469
$946$	16.9776	0.551988
$947$	23.7161	0.770668	0.385334	−	0.922777i	$-0.374086\pi$
$947$	23.7161	0.770668	0.385334	+	0.922777i	$0.374086\pi$
$948$	−8.62839	−0.280237
$949$	−26.1852	−0.850008
$950$	−5.68374	−0.184405
$951$	6.15577	0.199614
$952$	−2.43345	−0.0788686
$953$	60.9906	1.97568	0.987840	−	0.155474i	$-0.0496905\pi$
$953$	60.9906	1.97568	0.987840	+	0.155474i	$0.0496905\pi$
$954$	17.0174	0.550958
$955$	18.8992	0.611562
$956$	3.59221	0.116180
$957$	−12.0596	−0.389831
$958$	6.90370	0.223048
$959$	5.08075	0.164066
$960$	1.83188	0.0591235
$961$	1.00000	0.0322581
$962$	5.66748	0.182727
$963$	35.5034	1.14408
$964$	−4.65261	−0.149851
$965$	12.9334	0.416341
$966$	4.78540	0.153968
$967$	10.3968	0.334337	0.167169	−	0.985928i	$-0.446538\pi$
$967$	10.3968	0.334337	0.167169	+	0.985928i	$0.446538\pi$
$968$	−3.77115	−0.121209
$969$	−7.90616	−0.253982
$970$	1.71120	0.0549434
$971$	−35.8704	−1.15113	−0.575567	−	0.817754i	$-0.695219\pi$
$971$	−35.8704	−1.15113	−0.575567	+	0.817754i	$0.695219\pi$
$972$	−15.5881	−0.499987
$973$	13.2875	0.425977
$974$	−33.1771	−1.06306
$975$	7.73812	0.247818
$976$	6.57676	0.210517
$977$	8.07625	0.258382	0.129191	−	0.991620i	$-0.458762\pi$
$977$	8.07625	0.258382	0.129191	+	0.991620i	$0.458762\pi$
$978$	−1.53217	−0.0489935
$979$	−5.68201	−0.181598
$980$	10.5802	0.337971
$981$	26.1041	0.833441
$982$	41.0338	1.30944
$983$	9.91867	0.316356	0.158178	−	0.987411i	$-0.449438\pi$
$983$	9.91867	0.316356	0.158178	+	0.987411i	$0.449438\pi$
$984$	7.67383	0.244633
$985$	−25.9409	−0.826545
$986$	−11.2794	−0.359208
$987$	10.6720	0.339693
$988$	9.57166	0.304515
$989$	−31.2264	−0.992943
$990$	−8.52989	−0.271098
$991$	10.4790	0.332877	0.166438	−	0.986052i	$-0.446773\pi$
$991$	10.4790	0.332877	0.166438	+	0.986052i	$0.446773\pi$
$992$	1.00000	0.0317500
$993$	21.0381	0.667625
$994$	−7.96703	−0.252699
$995$	−18.2391	−0.578218
$996$	13.5610	0.429697
$997$	0.494612	0.0156645	0.00783227	−	0.999969i	$-0.497507\pi$
$997$	0.494612	0.0156645	0.00783227	+	0.999969i	$0.497507\pi$
$998$	−26.2154	−0.829833
$999$	8.44084	0.267056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.11	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.11	✓	21	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.07052 q^{3} +1.00000 q^{4} -1.71120 q^{5} -1.07052 q^{6} -0.903944 q^{7} +1.00000 q^{8} -1.85399 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.07052 q^{3} +1.00000 q^{4} -1.71120 q^{5} -1.07052 q^{6} -0.903944 q^{7} +1.00000 q^{8} -1.85399 q^{9} -1.71120 q^{10} -2.68865 q^{11} -1.07052 q^{12} +3.48897 q^{13} -0.903944 q^{14} +1.83188 q^{15} +1.00000 q^{16} +2.69204 q^{17} -1.85399 q^{18} +2.74341 q^{19} -1.71120 q^{20} +0.967689 q^{21} -2.68865 q^{22} +4.94518 q^{23} -1.07052 q^{24} -2.07178 q^{25} +3.48897 q^{26} +5.19629 q^{27} -0.903944 q^{28} -4.18989 q^{29} +1.83188 q^{30} +1.00000 q^{31} +1.00000 q^{32} +2.87825 q^{33} +2.69204 q^{34} +1.54683 q^{35} -1.85399 q^{36} +1.62440 q^{37} +2.74341 q^{38} -3.73501 q^{39} -1.71120 q^{40} -7.16833 q^{41} +0.967689 q^{42} -6.31452 q^{43} -2.68865 q^{44} +3.17255 q^{45} +4.94518 q^{46} +11.0283 q^{47} -1.07052 q^{48} -6.18288 q^{49} -2.07178 q^{50} -2.88188 q^{51} +3.48897 q^{52} -9.17879 q^{53} +5.19629 q^{54} +4.60083 q^{55} -0.903944 q^{56} -2.93687 q^{57} -4.18989 q^{58} +8.14046 q^{59} +1.83188 q^{60} +6.57676 q^{61} +1.00000 q^{62} +1.67590 q^{63} +1.00000 q^{64} -5.97034 q^{65} +2.87825 q^{66} -1.00348 q^{67} +2.69204 q^{68} -5.29391 q^{69} +1.54683 q^{70} +8.81363 q^{71} -1.85399 q^{72} -7.50514 q^{73} +1.62440 q^{74} +2.21788 q^{75} +2.74341 q^{76} +2.43039 q^{77} -3.73501 q^{78} +8.06001 q^{79} -1.71120 q^{80} -0.000754845 q^{81} -7.16833 q^{82} -12.6677 q^{83} +0.967689 q^{84} -4.60662 q^{85} -6.31452 q^{86} +4.48536 q^{87} -2.68865 q^{88} +2.11333 q^{89} +3.17255 q^{90} -3.15383 q^{91} +4.94518 q^{92} -1.07052 q^{93} +11.0283 q^{94} -4.69453 q^{95} -1.07052 q^{96} -1.00000 q^{97} -6.18288 q^{98} +4.98473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more