LMFDB - Embedded newform 6026.2.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.05724 q^{3} +1.00000 q^{4} -2.13811 q^{5} +1.05724 q^{6} +3.42578 q^{7} -1.00000 q^{8} -1.88224 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.05724 q^{3} +1.00000 q^{4} -2.13811 q^{5} +1.05724 q^{6} +3.42578 q^{7} -1.00000 q^{8} -1.88224 q^{9} +2.13811 q^{10} -2.88880 q^{11} -1.05724 q^{12} +1.88300 q^{13} -3.42578 q^{14} +2.26050 q^{15} +1.00000 q^{16} +4.09799 q^{17} +1.88224 q^{18} -3.98884 q^{19} -2.13811 q^{20} -3.62188 q^{21} +2.88880 q^{22} +1.00000 q^{23} +1.05724 q^{24} -0.428488 q^{25} -1.88300 q^{26} +5.16171 q^{27} +3.42578 q^{28} +7.47426 q^{29} -2.26050 q^{30} -8.99847 q^{31} -1.00000 q^{32} +3.05415 q^{33} -4.09799 q^{34} -7.32470 q^{35} -1.88224 q^{36} -5.04641 q^{37} +3.98884 q^{38} -1.99079 q^{39} +2.13811 q^{40} +8.18175 q^{41} +3.62188 q^{42} +0.248678 q^{43} -2.88880 q^{44} +4.02444 q^{45} -1.00000 q^{46} -6.96367 q^{47} -1.05724 q^{48} +4.73599 q^{49} +0.428488 q^{50} -4.33257 q^{51} +1.88300 q^{52} +6.38409 q^{53} -5.16171 q^{54} +6.17656 q^{55} -3.42578 q^{56} +4.21717 q^{57} -7.47426 q^{58} +11.2269 q^{59} +2.26050 q^{60} -1.76733 q^{61} +8.99847 q^{62} -6.44815 q^{63} +1.00000 q^{64} -4.02606 q^{65} -3.05415 q^{66} -15.5338 q^{67} +4.09799 q^{68} -1.05724 q^{69} +7.32470 q^{70} +9.84931 q^{71} +1.88224 q^{72} +2.29095 q^{73} +5.04641 q^{74} +0.453015 q^{75} -3.98884 q^{76} -9.89639 q^{77} +1.99079 q^{78} +0.874389 q^{79} -2.13811 q^{80} +0.189559 q^{81} -8.18175 q^{82} -9.68880 q^{83} -3.62188 q^{84} -8.76196 q^{85} -0.248678 q^{86} -7.90209 q^{87} +2.88880 q^{88} -0.610099 q^{89} -4.02444 q^{90} +6.45075 q^{91} +1.00000 q^{92} +9.51355 q^{93} +6.96367 q^{94} +8.52858 q^{95} +1.05724 q^{96} +5.60934 q^{97} -4.73599 q^{98} +5.43741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	−1.05724	−0.610398	−0.305199	−	0.952289i	$-0.598723\pi$
$3$	−1.05724	−0.610398	−0.305199	+	0.952289i	$0.598723\pi$
$4$	1.00000	0.500000
$5$	−2.13811	−0.956192	−0.478096	−	0.878308i	$-0.658673\pi$
$5$	−2.13811	−0.956192	−0.478096	+	0.878308i	$0.658673\pi$
$6$	1.05724	0.431617
$7$	3.42578	1.29482	0.647412	−	0.762140i	$-0.275851\pi$
$7$	3.42578	1.29482	0.647412	+	0.762140i	$0.275851\pi$
$8$	−1.00000	−0.353553
$9$	−1.88224	−0.627414
$10$	2.13811	0.676130
$11$	−2.88880	−0.871005	−0.435503	−	0.900188i	$-0.643429\pi$
$11$	−2.88880	−0.871005	−0.435503	+	0.900188i	$0.643429\pi$
$12$	−1.05724	−0.305199
$13$	1.88300	0.522251	0.261125	−	0.965305i	$-0.415906\pi$
$13$	1.88300	0.522251	0.261125	+	0.965305i	$0.415906\pi$
$14$	−3.42578	−0.915579
$15$	2.26050	0.583658
$16$	1.00000	0.250000
$17$	4.09799	0.993909	0.496955	−	0.867777i	$-0.334452\pi$
$17$	4.09799	0.993909	0.496955	+	0.867777i	$0.334452\pi$
$18$	1.88224	0.443649
$19$	−3.98884	−0.915103	−0.457552	−	0.889183i	$-0.651273\pi$
$19$	−3.98884	−0.915103	−0.457552	+	0.889183i	$0.651273\pi$
$20$	−2.13811	−0.478096
$21$	−3.62188	−0.790359
$22$	2.88880	0.615894
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.05724	0.215808
$25$	−0.428488	−0.0856975
$26$	−1.88300	−0.369287
$27$	5.16171	0.993371
$28$	3.42578	0.647412
$29$	7.47426	1.38794	0.693968	−	0.720006i	$-0.255861\pi$
$29$	7.47426	1.38794	0.693968	+	0.720006i	$0.255861\pi$
$30$	−2.26050	−0.412708
$31$	−8.99847	−1.61617	−0.808087	−	0.589064i	$-0.799497\pi$
$31$	−8.99847	−1.61617	−0.808087	+	0.589064i	$0.799497\pi$
$32$	−1.00000	−0.176777
$33$	3.05415	0.531660
$34$	−4.09799	−0.702800
$35$	−7.32470	−1.23810
$36$	−1.88224	−0.313707
$37$	−5.04641	−0.829625	−0.414813	−	0.909907i	$-0.636153\pi$
$37$	−5.04641	−0.829625	−0.414813	+	0.909907i	$0.636153\pi$
$38$	3.98884	0.647076
$39$	−1.99079	−0.318781
$40$	2.13811	0.338065
$41$	8.18175	1.27777	0.638887	−	0.769301i	$-0.279395\pi$
$41$	8.18175	1.27777	0.638887	+	0.769301i	$0.279395\pi$
$42$	3.62188	0.558868
$43$	0.248678	0.0379230	0.0189615	−	0.999820i	$-0.493964\pi$
$43$	0.248678	0.0379230	0.0189615	+	0.999820i	$0.493964\pi$
$44$	−2.88880	−0.435503
$45$	4.02444	0.599928
$46$	−1.00000	−0.147442
$47$	−6.96367	−1.01576	−0.507878	−	0.861429i	$-0.669570\pi$
$47$	−6.96367	−1.01576	−0.507878	+	0.861429i	$0.669570\pi$
$48$	−1.05724	−0.152600
$49$	4.73599	0.676570
$50$	0.428488	0.0605973
$51$	−4.33257	−0.606681
$52$	1.88300	0.261125
$53$	6.38409	0.876922	0.438461	−	0.898750i	$-0.355524\pi$
$53$	6.38409	0.876922	0.438461	+	0.898750i	$0.355524\pi$
$54$	−5.16171	−0.702419
$55$	6.17656	0.832848
$56$	−3.42578	−0.457789
$57$	4.21717	0.558577
$58$	−7.47426	−0.981418
$59$	11.2269	1.46161	0.730806	−	0.682585i	$-0.239144\pi$
$59$	11.2269	1.46161	0.730806	+	0.682585i	$0.239144\pi$
$60$	2.26050	0.291829
$61$	−1.76733	−0.226283	−0.113141	−	0.993579i	$-0.536091\pi$
$61$	−1.76733	−0.226283	−0.113141	+	0.993579i	$0.536091\pi$
$62$	8.99847	1.14281
$63$	−6.44815	−0.812391
$64$	1.00000	0.125000
$65$	−4.02606	−0.499372
$66$	−3.05415	−0.375940
$67$	−15.5338	−1.89776	−0.948880	−	0.315638i	$-0.897782\pi$
$67$	−15.5338	−1.89776	−0.948880	+	0.315638i	$0.897782\pi$
$68$	4.09799	0.496955
$69$	−1.05724	−0.127277
$70$	7.32470	0.875469
$71$	9.84931	1.16890	0.584449	−	0.811430i	$-0.301311\pi$
$71$	9.84931	1.16890	0.584449	+	0.811430i	$0.301311\pi$
$72$	1.88224	0.221824
$73$	2.29095	0.268135	0.134068	−	0.990972i	$-0.457196\pi$
$73$	2.29095	0.268135	0.134068	+	0.990972i	$0.457196\pi$
$74$	5.04641	0.586634
$75$	0.453015	0.0523096
$76$	−3.98884	−0.457552
$77$	−9.89639	−1.12780
$78$	1.99079	0.225412
$79$	0.874389	0.0983765	0.0491883	−	0.998790i	$-0.484337\pi$
$79$	0.874389	0.0983765	0.0491883	+	0.998790i	$0.484337\pi$
$80$	−2.13811	−0.239048
$81$	0.189559	0.0210621
$82$	−8.18175	−0.903523
$83$	−9.68880	−1.06348	−0.531742	−	0.846906i	$-0.678462\pi$
$83$	−9.68880	−1.06348	−0.531742	+	0.846906i	$0.678462\pi$
$84$	−3.62188	−0.395179
$85$	−8.76196	−0.950368
$86$	−0.248678	−0.0268156
$87$	−7.90209	−0.847193
$88$	2.88880	0.307947
$89$	−0.610099	−0.0646704	−0.0323352	−	0.999477i	$-0.510294\pi$
$89$	−0.610099	−0.0646704	−0.0323352	+	0.999477i	$0.510294\pi$
$90$	−4.02444	−0.424213
$91$	6.45075	0.676223
$92$	1.00000	0.104257
$93$	9.51355	0.986510
$94$	6.96367	0.718248
$95$	8.52858	0.875014
$96$	1.05724	0.107904
$97$	5.60934	0.569542	0.284771	−	0.958596i	$-0.408082\pi$
$97$	5.60934	0.569542	0.284771	+	0.958596i	$0.408082\pi$
$98$	−4.73599	−0.478407
$99$	5.43741	0.546481
$100$	−0.428488	−0.0428488
$101$	−1.95082	−0.194113	−0.0970567	−	0.995279i	$-0.530943\pi$
$101$	−1.95082	−0.194113	−0.0970567	+	0.995279i	$0.530943\pi$
$102$	4.33257	0.428988
$103$	13.6416	1.34414	0.672072	−	0.740485i	$-0.265404\pi$
$103$	13.6416	1.34414	0.672072	+	0.740485i	$0.265404\pi$
$104$	−1.88300	−0.184643
$105$	7.74397	0.755734
$106$	−6.38409	−0.620077
$107$	−9.13236	−0.882859	−0.441430	−	0.897296i	$-0.645528\pi$
$107$	−9.13236	−0.882859	−0.441430	+	0.897296i	$0.645528\pi$
$108$	5.16171	0.496685
$109$	−0.273264	−0.0261739	−0.0130870	−	0.999914i	$-0.504166\pi$
$109$	−0.273264	−0.0261739	−0.0130870	+	0.999914i	$0.504166\pi$
$110$	−6.17656	−0.588912
$111$	5.33527	0.506402
$112$	3.42578	0.323706
$113$	−2.15872	−0.203075	−0.101538	−	0.994832i	$-0.532376\pi$
$113$	−2.15872	−0.203075	−0.101538	+	0.994832i	$0.532376\pi$
$114$	−4.21717	−0.394974
$115$	−2.13811	−0.199380
$116$	7.47426	0.693968
$117$	−3.54426	−0.327667
$118$	−11.2269	−1.03352
$119$	14.0388	1.28694
$120$	−2.26050	−0.206354
$121$	−2.65485	−0.241350
$122$	1.76733	0.160006
$123$	−8.65008	−0.779951
$124$	−8.99847	−0.808087
$125$	11.6067	1.03813
$126$	6.44815	0.574447
$127$	9.72670	0.863105	0.431552	−	0.902088i	$-0.357966\pi$
$127$	9.72670	0.863105	0.431552	+	0.902088i	$0.357966\pi$
$128$	−1.00000	−0.0883883
$129$	−0.262912	−0.0231481
$130$	4.02606	0.353109
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	3.05415	0.265830
$133$	−13.6649	−1.18490
$134$	15.5338	1.34192
$135$	−11.0363	−0.949853
$136$	−4.09799	−0.351400
$137$	16.4538	1.40574	0.702871	−	0.711318i	$-0.251901\pi$
$137$	16.4538	1.40574	0.702871	+	0.711318i	$0.251901\pi$
$138$	1.05724	0.0899983
$139$	−15.7089	−1.33241	−0.666206	−	0.745768i	$-0.732083\pi$
$139$	−15.7089	−1.33241	−0.666206	+	0.745768i	$0.732083\pi$
$140$	−7.32470	−0.619050
$141$	7.36228	0.620015
$142$	−9.84931	−0.826536
$143$	−5.43961	−0.454883
$144$	−1.88224	−0.156853
$145$	−15.9808	−1.32713
$146$	−2.29095	−0.189600
$147$	−5.00708	−0.412977
$148$	−5.04641	−0.414813
$149$	10.0073	0.819827	0.409914	−	0.912124i	$-0.365559\pi$
$149$	10.0073	0.819827	0.409914	+	0.912124i	$0.365559\pi$
$150$	−0.453015	−0.0369885
$151$	−3.07867	−0.250539	−0.125269	−	0.992123i	$-0.539980\pi$
$151$	−3.07867	−0.250539	−0.125269	+	0.992123i	$0.539980\pi$
$152$	3.98884	0.323538
$153$	−7.71341	−0.623592
$154$	9.89639	0.797474
$155$	19.2397	1.54537
$156$	−1.99079	−0.159390
$157$	−11.6045	−0.926143	−0.463072	−	0.886321i	$-0.653253\pi$
$157$	−11.6045	−0.926143	−0.463072	+	0.886321i	$0.653253\pi$
$158$	−0.874389	−0.0695627
$159$	−6.74952	−0.535272
$160$	2.13811	0.169032
$161$	3.42578	0.269990
$162$	−0.189559	−0.0148931
$163$	−12.1993	−0.955520	−0.477760	−	0.878491i	$-0.658551\pi$
$163$	−12.1993	−0.955520	−0.477760	+	0.878491i	$0.658551\pi$
$164$	8.18175	0.638887
$165$	−6.53012	−0.508369
$166$	9.68880	0.751997
$167$	−19.8800	−1.53836	−0.769180	−	0.639032i	$-0.779335\pi$
$167$	−19.8800	−1.53836	−0.769180	+	0.639032i	$0.779335\pi$
$168$	3.62188	0.279434
$169$	−9.45431	−0.727254
$170$	8.76196	0.672011
$171$	7.50796	0.574148
$172$	0.248678	0.0189615
$173$	−13.0623	−0.993106	−0.496553	−	0.868006i	$-0.665401\pi$
$173$	−13.0623	−0.993106	−0.496553	+	0.868006i	$0.665401\pi$
$174$	7.90209	0.599056
$175$	−1.46791	−0.110963
$176$	−2.88880	−0.217751
$177$	−11.8695	−0.892166
$178$	0.610099	0.0457289
$179$	−4.59658	−0.343565	−0.171782	−	0.985135i	$-0.554953\pi$
$179$	−4.59658	−0.343565	−0.171782	+	0.985135i	$0.554953\pi$
$180$	4.02444	0.299964
$181$	−6.40419	−0.476020	−0.238010	−	0.971263i	$-0.576495\pi$
$181$	−6.40419	−0.476020	−0.238010	+	0.971263i	$0.576495\pi$
$182$	−6.45075	−0.478162
$183$	1.86849	0.138123
$184$	−1.00000	−0.0737210
$185$	10.7898	0.793281
$186$	−9.51355	−0.697568
$187$	−11.8383	−0.865700
$188$	−6.96367	−0.507878
$189$	17.6829	1.28624
$190$	−8.52858	−0.618728
$191$	8.96653	0.648795	0.324398	−	0.945921i	$-0.394838\pi$
$191$	8.96653	0.648795	0.324398	+	0.945921i	$0.394838\pi$
$192$	−1.05724	−0.0762998
$193$	19.7194	1.41944	0.709718	−	0.704486i	$-0.248822\pi$
$193$	19.7194	1.41944	0.709718	+	0.704486i	$0.248822\pi$
$194$	−5.60934	−0.402727
$195$	4.25652	0.304816
$196$	4.73599	0.338285
$197$	−21.0521	−1.49990	−0.749950	−	0.661495i	$-0.769922\pi$
$197$	−21.0521	−1.49990	−0.749950	+	0.661495i	$0.769922\pi$
$198$	−5.43741	−0.386420
$199$	10.0749	0.714188	0.357094	−	0.934068i	$-0.383768\pi$
$199$	10.0749	0.714188	0.357094	+	0.934068i	$0.383768\pi$
$200$	0.428488	0.0302986
$201$	16.4230	1.15839
$202$	1.95082	0.137259
$203$	25.6052	1.79713
$204$	−4.33257	−0.303340
$205$	−17.4935	−1.22180
$206$	−13.6416	−0.950454
$207$	−1.88224	−0.130825
$208$	1.88300	0.130563
$209$	11.5230	0.797059
$210$	−7.74397	−0.534385
$211$	9.93841	0.684188	0.342094	−	0.939666i	$-0.388864\pi$
$211$	9.93841	0.684188	0.342094	+	0.939666i	$0.388864\pi$
$212$	6.38409	0.438461
$213$	−10.4131	−0.713494
$214$	9.13236	0.624276
$215$	−0.531700	−0.0362616
$216$	−5.16171	−0.351210
$217$	−30.8268	−2.09266
$218$	0.273264	0.0185078
$219$	−2.42208	−0.163669
$220$	6.17656	0.416424
$221$	7.71653	0.519070
$222$	−5.33527	−0.358080
$223$	−1.24087	−0.0830947	−0.0415474	−	0.999137i	$-0.513229\pi$
$223$	−1.24087	−0.0830947	−0.0415474	+	0.999137i	$0.513229\pi$
$224$	−3.42578	−0.228895
$225$	0.806517	0.0537678
$226$	2.15872	0.143596
$227$	27.6748	1.83684	0.918419	−	0.395609i	$-0.129467\pi$
$227$	27.6748	1.83684	0.918419	+	0.395609i	$0.129467\pi$
$228$	4.21717	0.279289
$229$	27.1412	1.79354	0.896772	−	0.442494i	$-0.145906\pi$
$229$	27.1412	1.79354	0.896772	+	0.442494i	$0.145906\pi$
$230$	2.13811	0.140983
$231$	10.4629	0.688406
$232$	−7.47426	−0.490709
$233$	−10.2090	−0.668812	−0.334406	−	0.942429i	$-0.608536\pi$
$233$	−10.2090	−0.668812	−0.334406	+	0.942429i	$0.608536\pi$
$234$	3.54426	0.231696
$235$	14.8891	0.971257
$236$	11.2269	0.730806
$237$	−0.924440	−0.0600489
$238$	−14.0388	−0.910002
$239$	−0.963565	−0.0623278	−0.0311639	−	0.999514i	$-0.509921\pi$
$239$	−0.963565	−0.0623278	−0.0311639	+	0.999514i	$0.509921\pi$
$240$	2.26050	0.145914
$241$	8.62238	0.555417	0.277708	−	0.960665i	$-0.410425\pi$
$241$	8.62238	0.555417	0.277708	+	0.960665i	$0.410425\pi$
$242$	2.65485	0.170660
$243$	−15.6855	−1.00623
$244$	−1.76733	−0.113141
$245$	−10.1261	−0.646930
$246$	8.65008	0.551509
$247$	−7.51099	−0.477913
$248$	8.99847	0.571404
$249$	10.2434	0.649149
$250$	−11.6067	−0.734072
$251$	4.66001	0.294137	0.147069	−	0.989126i	$-0.453016\pi$
$251$	4.66001	0.294137	0.147069	+	0.989126i	$0.453016\pi$
$252$	−6.44815	−0.406195
$253$	−2.88880	−0.181617
$254$	−9.72670	−0.610307
$255$	9.26350	0.580103
$256$	1.00000	0.0625000
$257$	9.82881	0.613104	0.306552	−	0.951854i	$-0.400825\pi$
$257$	9.82881	0.613104	0.306552	+	0.951854i	$0.400825\pi$
$258$	0.262912	0.0163682
$259$	−17.2879	−1.07422
$260$	−4.02606	−0.249686
$261$	−14.0684	−0.870810
$262$	−1.00000	−0.0617802
$263$	17.8668	1.10171	0.550857	−	0.834599i	$-0.314301\pi$
$263$	17.8668	1.10171	0.550857	+	0.834599i	$0.314301\pi$
$264$	−3.05415	−0.187970
$265$	−13.6499	−0.838505
$266$	13.6649	0.837849
$267$	0.645022	0.0394747
$268$	−15.5338	−0.948880
$269$	−12.9576	−0.790040	−0.395020	−	0.918672i	$-0.629262\pi$
$269$	−12.9576	−0.790040	−0.395020	+	0.918672i	$0.629262\pi$
$270$	11.0363	0.671647
$271$	−14.2166	−0.863595	−0.431797	−	0.901971i	$-0.642120\pi$
$271$	−14.2166	−0.863595	−0.431797	+	0.901971i	$0.642120\pi$
$272$	4.09799	0.248477
$273$	−6.82000	−0.412765
$274$	−16.4538	−0.994009
$275$	1.23781	0.0746430
$276$	−1.05724	−0.0636384
$277$	20.6973	1.24358	0.621790	−	0.783184i	$-0.286406\pi$
$277$	20.6973	1.24358	0.621790	+	0.783184i	$0.286406\pi$
$278$	15.7089	0.942157
$279$	16.9373	1.01401
$280$	7.32470	0.437734
$281$	−31.3920	−1.87269	−0.936344	−	0.351084i	$-0.885813\pi$
$281$	−31.3920	−1.87269	−0.936344	+	0.351084i	$0.885813\pi$
$282$	−7.36228	−0.438417
$283$	6.28213	0.373434	0.186717	−	0.982414i	$-0.440215\pi$
$283$	6.28213	0.373434	0.186717	+	0.982414i	$0.440215\pi$
$284$	9.84931	0.584449
$285$	−9.01676	−0.534107
$286$	5.43961	0.321651
$287$	28.0289	1.65449
$288$	1.88224	0.110912
$289$	−0.206455	−0.0121444
$290$	15.9808	0.938424
$291$	−5.93042	−0.347647
$292$	2.29095	0.134068
$293$	−22.8404	−1.33435	−0.667175	−	0.744901i	$-0.732497\pi$
$293$	−22.8404	−1.33435	−0.667175	+	0.744901i	$0.732497\pi$
$294$	5.00708	0.292019
$295$	−24.0043	−1.39758
$296$	5.04641	0.293317
$297$	−14.9111	−0.865231
$298$	−10.0073	−0.579705
$299$	1.88300	0.108897
$300$	0.453015	0.0261548
$301$	0.851915	0.0491036
$302$	3.07867	0.177158
$303$	2.06248	0.118486
$304$	−3.98884	−0.228776
$305$	3.77873	0.216370
$306$	7.71341	0.440946
$307$	−21.2908	−1.21513	−0.607564	−	0.794271i	$-0.707853\pi$
$307$	−21.2908	−1.21513	−0.607564	+	0.794271i	$0.707853\pi$
$308$	−9.89639	−0.563899
$309$	−14.4224	−0.820464
$310$	−19.2397	−1.09274
$311$	1.17285	0.0665065	0.0332532	−	0.999447i	$-0.489413\pi$
$311$	1.17285	0.0665065	0.0332532	+	0.999447i	$0.489413\pi$
$312$	1.99079	0.112706
$313$	−7.39068	−0.417746	−0.208873	−	0.977943i	$-0.566980\pi$
$313$	−7.39068	−0.417746	−0.208873	+	0.977943i	$0.566980\pi$
$314$	11.6045	0.654882
$315$	13.7869	0.776801
$316$	0.874389	0.0491883
$317$	−17.9224	−1.00662	−0.503311	−	0.864105i	$-0.667885\pi$
$317$	−17.9224	−1.00662	−0.503311	+	0.864105i	$0.667885\pi$
$318$	6.74952	0.378494
$319$	−21.5916	−1.20890
$320$	−2.13811	−0.119524
$321$	9.65511	0.538896
$322$	−3.42578	−0.190911
$323$	−16.3462	−0.909529
$324$	0.189559	0.0105310
$325$	−0.806843	−0.0447556
$326$	12.1993	0.675654
$327$	0.288906	0.0159765
$328$	−8.18175	−0.451761
$329$	−23.8560	−1.31522
$330$	6.53012	0.359471
$331$	−26.2243	−1.44142	−0.720708	−	0.693238i	$-0.756183\pi$
$331$	−26.2243	−1.44142	−0.720708	+	0.693238i	$0.756183\pi$
$332$	−9.68880	−0.531742
$333$	9.49857	0.520518
$334$	19.8800	1.08779
$335$	33.2130	1.81462
$336$	−3.62188	−0.197590
$337$	−20.9240	−1.13980	−0.569901	−	0.821713i	$-0.693019\pi$
$337$	−20.9240	−1.13980	−0.569901	+	0.821713i	$0.693019\pi$
$338$	9.45431	0.514246
$339$	2.28228	0.123957
$340$	−8.76196	−0.475184
$341$	25.9948	1.40770
$342$	−7.50796	−0.405984
$343$	−7.75601	−0.418785
$344$	−0.248678	−0.0134078
$345$	2.26050	0.121701
$346$	13.0623	0.702232
$347$	20.5743	1.10449	0.552243	−	0.833683i	$-0.313772\pi$
$347$	20.5743	1.10449	0.552243	+	0.833683i	$0.313772\pi$
$348$	−7.90209	−0.423597
$349$	−12.3675	−0.662015	−0.331008	−	0.943628i	$-0.607389\pi$
$349$	−12.3675	−0.662015	−0.331008	+	0.943628i	$0.607389\pi$
$350$	1.46791	0.0784628
$351$	9.71950	0.518788
$352$	2.88880	0.153973
$353$	12.8737	0.685198	0.342599	−	0.939482i	$-0.388693\pi$
$353$	12.8737	0.685198	0.342599	+	0.939482i	$0.388693\pi$
$354$	11.8695	0.630857
$355$	−21.0589	−1.11769
$356$	−0.610099	−0.0323352
$357$	−14.8424	−0.785545
$358$	4.59658	0.242937
$359$	20.2210	1.06722	0.533612	−	0.845730i	$-0.320834\pi$
$359$	20.2210	1.06722	0.533612	+	0.845730i	$0.320834\pi$
$360$	−4.02444	−0.212107
$361$	−3.08914	−0.162586
$362$	6.40419	0.336597
$363$	2.80682	0.147320
$364$	6.45075	0.338111
$365$	−4.89830	−0.256389
$366$	−1.86849	−0.0976675
$367$	−17.6959	−0.923720	−0.461860	−	0.886953i	$-0.652818\pi$
$367$	−17.6959	−0.923720	−0.461860	+	0.886953i	$0.652818\pi$
$368$	1.00000	0.0521286
$369$	−15.4000	−0.801693
$370$	−10.7898	−0.560934
$371$	21.8705	1.13546
$372$	9.51355	0.493255
$373$	−18.3029	−0.947688	−0.473844	−	0.880609i	$-0.657134\pi$
$373$	−18.3029	−0.947688	−0.473844	+	0.880609i	$0.657134\pi$
$374$	11.8383	0.612142
$375$	−12.2711	−0.633676
$376$	6.96367	0.359124
$377$	14.0740	0.724850
$378$	−17.6829	−0.909509
$379$	−30.3097	−1.55690	−0.778451	−	0.627705i	$-0.783994\pi$
$379$	−30.3097	−1.55690	−0.778451	+	0.627705i	$0.783994\pi$
$380$	8.52858	0.437507
$381$	−10.2835	−0.526838
$382$	−8.96653	−0.458768
$383$	−33.3270	−1.70293	−0.851464	−	0.524413i	$-0.824285\pi$
$383$	−33.3270	−1.70293	−0.851464	+	0.524413i	$0.824285\pi$
$384$	1.05724	0.0539521
$385$	21.1596	1.07839
$386$	−19.7194	−1.00369
$387$	−0.468071	−0.0237934
$388$	5.60934	0.284771
$389$	−31.9039	−1.61759	−0.808795	−	0.588090i	$-0.799880\pi$
$389$	−31.9039	−1.61759	−0.808795	+	0.588090i	$0.799880\pi$
$390$	−4.25652	−0.215537
$391$	4.09799	0.207244
$392$	−4.73599	−0.239204
$393$	−1.05724	−0.0533307
$394$	21.0521	1.06059
$395$	−1.86954	−0.0940668
$396$	5.43741	0.273240
$397$	−26.3120	−1.32056	−0.660280	−	0.751020i	$-0.729562\pi$
$397$	−26.3120	−1.32056	−0.660280	+	0.751020i	$0.729562\pi$
$398$	−10.0749	−0.505007
$399$	14.4471	0.723259
$400$	−0.428488	−0.0214244
$401$	−11.2889	−0.563740	−0.281870	−	0.959453i	$-0.590955\pi$
$401$	−11.2889	−0.563740	−0.281870	+	0.959453i	$0.590955\pi$
$402$	−16.4230	−0.819105
$403$	−16.9441	−0.844048
$404$	−1.95082	−0.0970567
$405$	−0.405297	−0.0201394
$406$	−25.6052	−1.27076
$407$	14.5781	0.722608
$408$	4.33257	0.214494
$409$	−17.6148	−0.870995	−0.435498	−	0.900190i	$-0.643428\pi$
$409$	−17.6148	−0.870995	−0.435498	+	0.900190i	$0.643428\pi$
$410$	17.4935	0.863941
$411$	−17.3956	−0.858062
$412$	13.6416	0.672072
$413$	38.4608	1.89253
$414$	1.88224	0.0925071
$415$	20.7157	1.01689
$416$	−1.88300	−0.0923217
$417$	16.6081	0.813302
$418$	−11.5230	−0.563606
$419$	−9.48791	−0.463515	−0.231757	−	0.972774i	$-0.574448\pi$
$419$	−9.48791	−0.463515	−0.231757	+	0.972774i	$0.574448\pi$
$420$	7.74397	0.377867
$421$	37.8882	1.84656	0.923279	−	0.384131i	$-0.125499\pi$
$421$	37.8882	1.84656	0.923279	+	0.384131i	$0.125499\pi$
$422$	−9.93841	−0.483794
$423$	13.1073	0.637299
$424$	−6.38409	−0.310039
$425$	−1.75594	−0.0851755
$426$	10.4131	0.504516
$427$	−6.05447	−0.292996
$428$	−9.13236	−0.441430
$429$	5.75098	0.277660
$430$	0.531700	0.0256408
$431$	−30.4416	−1.46632	−0.733159	−	0.680057i	$-0.761955\pi$
$431$	−30.4416	−1.46632	−0.733159	+	0.680057i	$0.761955\pi$
$432$	5.16171	0.248343
$433$	−23.7947	−1.14350	−0.571751	−	0.820427i	$-0.693736\pi$
$433$	−23.7947	−1.14350	−0.571751	+	0.820427i	$0.693736\pi$
$434$	30.8268	1.47973
$435$	16.8955	0.810079
$436$	−0.273264	−0.0130870
$437$	−3.98884	−0.190812
$438$	2.42208	0.115732
$439$	−24.4063	−1.16485	−0.582424	−	0.812885i	$-0.697896\pi$
$439$	−24.4063	−1.16485	−0.582424	+	0.812885i	$0.697896\pi$
$440$	−6.17656	−0.294456
$441$	−8.91427	−0.424489
$442$	−7.71653	−0.367038
$443$	−8.82371	−0.419227	−0.209614	−	0.977784i	$-0.567221\pi$
$443$	−8.82371	−0.419227	−0.209614	+	0.977784i	$0.567221\pi$
$444$	5.33527	0.253201
$445$	1.30446	0.0618373
$446$	1.24087	0.0587569
$447$	−10.5801	−0.500421
$448$	3.42578	0.161853
$449$	32.3312	1.52580	0.762902	−	0.646515i	$-0.223774\pi$
$449$	32.3312	1.52580	0.762902	+	0.646515i	$0.223774\pi$
$450$	−0.806517	−0.0380196
$451$	−23.6354	−1.11295
$452$	−2.15872	−0.101538
$453$	3.25490	0.152929
$454$	−27.6748	−1.29884
$455$	−13.7924	−0.646599
$456$	−4.21717	−0.197487
$457$	0.481915	0.0225430	0.0112715	−	0.999936i	$-0.496412\pi$
$457$	0.481915	0.0225430	0.0112715	+	0.999936i	$0.496412\pi$
$458$	−27.1412	−1.26823
$459$	21.1526	0.987320
$460$	−2.13811	−0.0996899
$461$	−11.0216	−0.513329	−0.256664	−	0.966501i	$-0.582623\pi$
$461$	−11.0216	−0.513329	−0.256664	+	0.966501i	$0.582623\pi$
$462$	−10.4629	−0.486777
$463$	−16.3035	−0.757690	−0.378845	−	0.925460i	$-0.623679\pi$
$463$	−16.3035	−0.757690	−0.378845	+	0.925460i	$0.623679\pi$
$464$	7.47426	0.346984
$465$	−20.3410	−0.943292
$466$	10.2090	0.472921
$467$	−5.72416	−0.264883	−0.132441	−	0.991191i	$-0.542282\pi$
$467$	−5.72416	−0.264883	−0.132441	+	0.991191i	$0.542282\pi$
$468$	−3.54426	−0.163834
$469$	−53.2155	−2.45727
$470$	−14.8891	−0.686782
$471$	12.2688	0.565316
$472$	−11.2269	−0.516758
$473$	−0.718379	−0.0330311
$474$	0.924440	0.0424610
$475$	1.70917	0.0784220
$476$	14.0388	0.643469
$477$	−12.0164	−0.550193
$478$	0.963565	0.0440724
$479$	−19.4595	−0.889129	−0.444564	−	0.895747i	$-0.646641\pi$
$479$	−19.4595	−0.889129	−0.444564	+	0.895747i	$0.646641\pi$
$480$	−2.26050	−0.103177
$481$	−9.50240	−0.433272
$482$	−8.62238	−0.392739
$483$	−3.62188	−0.164801
$484$	−2.65485	−0.120675
$485$	−11.9934	−0.544591
$486$	15.6855	0.711510
$487$	−25.7071	−1.16490	−0.582449	−	0.812867i	$-0.697905\pi$
$487$	−25.7071	−1.16490	−0.582449	+	0.812867i	$0.697905\pi$
$488$	1.76733	0.0800031
$489$	12.8976	0.583248
$490$	10.1261	0.457449
$491$	31.0924	1.40318	0.701590	−	0.712580i	$-0.252474\pi$
$491$	31.0924	1.40318	0.701590	+	0.712580i	$0.252474\pi$
$492$	−8.65008	−0.389976
$493$	30.6295	1.37948
$494$	7.51099	0.337936
$495$	−11.6258	−0.522540
$496$	−8.99847	−0.404043
$497$	33.7416	1.51352
$498$	−10.2434	−0.459017
$499$	41.1280	1.84114	0.920572	−	0.390573i	$-0.127723\pi$
$499$	41.1280	1.84114	0.920572	+	0.390573i	$0.127723\pi$
$500$	11.6067	0.519067
$501$	21.0180	0.939013
$502$	−4.66001	−0.207987
$503$	19.8371	0.884491	0.442245	−	0.896894i	$-0.354182\pi$
$503$	19.8371	0.884491	0.442245	+	0.896894i	$0.354182\pi$
$504$	6.44815	0.287223
$505$	4.17106	0.185610
$506$	2.88880	0.128423
$507$	9.99548	0.443915
$508$	9.72670	0.431552
$509$	−38.2365	−1.69480	−0.847401	−	0.530954i	$-0.821834\pi$
$509$	−38.2365	−1.69480	−0.847401	+	0.530954i	$0.821834\pi$
$510$	−9.26350	−0.410195
$511$	7.84829	0.347188
$512$	−1.00000	−0.0441942
$513$	−20.5892	−0.909037
$514$	−9.82881	−0.433530
$515$	−29.1672	−1.28526
$516$	−0.262912	−0.0115741
$517$	20.1166	0.884728
$518$	17.2879	0.759587
$519$	13.8100	0.606191
$520$	4.02606	0.176555
$521$	0.456619	0.0200048	0.0100024	−	0.999950i	$-0.496816\pi$
$521$	0.456619	0.0200048	0.0100024	+	0.999950i	$0.496816\pi$
$522$	14.0684	0.615756
$523$	6.95728	0.304221	0.152110	−	0.988364i	$-0.451393\pi$
$523$	6.95728	0.304221	0.152110	+	0.988364i	$0.451393\pi$
$524$	1.00000	0.0436852
$525$	1.55193	0.0677318
$526$	−17.8668	−0.779030
$527$	−36.8757	−1.60633
$528$	3.05415	0.132915
$529$	1.00000	0.0434783
$530$	13.6499	0.592913
$531$	−21.1317	−0.917036
$532$	−13.6649	−0.592449
$533$	15.4062	0.667318
$534$	−0.645022	−0.0279128
$535$	19.5260	0.844182
$536$	15.5338	0.670959
$537$	4.85970	0.209711
$538$	12.9576	0.558643
$539$	−13.6813	−0.589296
$540$	−11.0363	−0.474926
$541$	11.4234	0.491128	0.245564	−	0.969380i	$-0.421027\pi$
$541$	11.4234	0.491128	0.245564	+	0.969380i	$0.421027\pi$
$542$	14.2166	0.610654
$543$	6.77078	0.290562
$544$	−4.09799	−0.175700
$545$	0.584268	0.0250273
$546$	6.82000	0.291869
$547$	20.4916	0.876156	0.438078	−	0.898937i	$-0.355659\pi$
$547$	20.4916	0.876156	0.438078	+	0.898937i	$0.355659\pi$
$548$	16.4538	0.702871
$549$	3.32653	0.141973
$550$	−1.23781	−0.0527805
$551$	−29.8136	−1.27010
$552$	1.05724	0.0449992
$553$	2.99547	0.127380
$554$	−20.6973	−0.879343
$555$	−11.4074	−0.484217
$556$	−15.7089	−0.666206
$557$	34.4423	1.45937	0.729684	−	0.683784i	$-0.239667\pi$
$557$	34.4423	1.45937	0.729684	+	0.683784i	$0.239667\pi$
$558$	−16.9373	−0.717013
$559$	0.468260	0.0198053
$560$	−7.32470	−0.309525
$561$	12.5159	0.528422
$562$	31.3920	1.32419
$563$	−38.3357	−1.61566	−0.807829	−	0.589416i	$-0.799358\pi$
$563$	−38.3357	−1.61566	−0.807829	+	0.589416i	$0.799358\pi$
$564$	7.36228	0.310008
$565$	4.61558	0.194179
$566$	−6.28213	−0.264058
$567$	0.649387	0.0272717
$568$	−9.84931	−0.413268
$569$	−43.3728	−1.81828	−0.909141	−	0.416488i	$-0.863261\pi$
$569$	−43.3728	−1.81828	−0.909141	+	0.416488i	$0.863261\pi$
$570$	9.01676	0.377671
$571$	10.9007	0.456182	0.228091	−	0.973640i	$-0.426752\pi$
$571$	10.9007	0.456182	0.228091	+	0.973640i	$0.426752\pi$
$572$	−5.43961	−0.227441
$573$	−9.47978	−0.396024
$574$	−28.0289	−1.16990
$575$	−0.428488	−0.0178692
$576$	−1.88224	−0.0784267
$577$	−2.45423	−0.102171	−0.0510855	−	0.998694i	$-0.516268\pi$
$577$	−2.45423	−0.102171	−0.0510855	+	0.998694i	$0.516268\pi$
$578$	0.206455	0.00858740
$579$	−20.8482	−0.866421
$580$	−15.9808	−0.663566
$581$	−33.1917	−1.37702
$582$	5.93042	0.245824
$583$	−18.4423	−0.763803
$584$	−2.29095	−0.0948001
$585$	7.57802	0.313313
$586$	22.8404	0.943528
$587$	10.3726	0.428125	0.214062	−	0.976820i	$-0.431330\pi$
$587$	10.3726	0.428125	0.214062	+	0.976820i	$0.431330\pi$
$588$	−5.00708	−0.206489
$589$	35.8935	1.47897
$590$	24.0043	0.988240
$591$	22.2571	0.915536
$592$	−5.04641	−0.207406
$593$	31.5489	1.29556	0.647779	−	0.761828i	$-0.275698\pi$
$593$	31.5489	1.29556	0.647779	+	0.761828i	$0.275698\pi$
$594$	14.9111	0.611811
$595$	−30.0166	−1.23056
$596$	10.0073	0.409914
$597$	−10.6516	−0.435939
$598$	−1.88300	−0.0770017
$599$	−41.5870	−1.69920	−0.849599	−	0.527429i	$-0.823156\pi$
$599$	−41.5870	−1.69920	−0.849599	+	0.527429i	$0.823156\pi$
$600$	−0.453015	−0.0184942
$601$	11.8948	0.485199	0.242599	−	0.970127i	$-0.422000\pi$
$601$	11.8948	0.485199	0.242599	+	0.970127i	$0.422000\pi$
$602$	−0.851915	−0.0347215
$603$	29.2384	1.19068
$604$	−3.07867	−0.125269
$605$	5.67637	0.230777
$606$	−2.06248	−0.0837826
$607$	−4.77299	−0.193730	−0.0968648	−	0.995298i	$-0.530881\pi$
$607$	−4.77299	−0.193730	−0.0968648	+	0.995298i	$0.530881\pi$
$608$	3.98884	0.161769
$609$	−27.0709	−1.09697
$610$	−3.77873	−0.152997
$611$	−13.1126	−0.530479
$612$	−7.71341	−0.311796
$613$	12.8111	0.517434	0.258717	−	0.965953i	$-0.416700\pi$
$613$	12.8111	0.517434	0.258717	+	0.965953i	$0.416700\pi$
$614$	21.2908	0.859225
$615$	18.4948	0.745783
$616$	9.89639	0.398737
$617$	−34.1863	−1.37629	−0.688144	−	0.725574i	$-0.741574\pi$
$617$	−34.1863	−1.37629	−0.688144	+	0.725574i	$0.741574\pi$
$618$	14.4224	0.580155
$619$	−17.0595	−0.685678	−0.342839	−	0.939394i	$-0.611389\pi$
$619$	−17.0595	−0.685678	−0.342839	+	0.939394i	$0.611389\pi$
$620$	19.2397	0.772686
$621$	5.16171	0.207132
$622$	−1.17285	−0.0470272
$623$	−2.09007	−0.0837368
$624$	−1.99079	−0.0796952
$625$	−22.6740	−0.906958
$626$	7.39068	0.295391
$627$	−12.1825	−0.486524
$628$	−11.6045	−0.463072
$629$	−20.6802	−0.824572
$630$	−13.7869	−0.549281
$631$	7.17481	0.285625	0.142812	−	0.989750i	$-0.454385\pi$
$631$	7.17481	0.285625	0.142812	+	0.989750i	$0.454385\pi$
$632$	−0.874389	−0.0347813
$633$	−10.5073	−0.417627
$634$	17.9224	0.711790
$635$	−20.7967	−0.825294
$636$	−6.74952	−0.267636
$637$	8.91787	0.353339
$638$	21.5916	0.854820
$639$	−18.5388	−0.733383
$640$	2.13811	0.0845162
$641$	2.70971	0.107027	0.0535135	−	0.998567i	$-0.482958\pi$
$641$	2.70971	0.107027	0.0535135	+	0.998567i	$0.482958\pi$
$642$	−9.65511	−0.381057
$643$	−49.2001	−1.94026	−0.970132	−	0.242577i	$-0.922007\pi$
$643$	−49.2001	−1.94026	−0.970132	+	0.242577i	$0.922007\pi$
$644$	3.42578	0.134995
$645$	0.562135	0.0221340
$646$	16.3462	0.643134
$647$	−36.8361	−1.44818	−0.724089	−	0.689707i	$-0.757739\pi$
$647$	−36.8361	−1.44818	−0.724089	+	0.689707i	$0.757739\pi$
$648$	−0.189559	−0.00744657
$649$	−32.4321	−1.27307
$650$	0.806843	0.0316470
$651$	32.5914	1.27736
$652$	−12.1993	−0.477760
$653$	−28.7965	−1.12689	−0.563447	−	0.826152i	$-0.690525\pi$
$653$	−28.7965	−1.12689	−0.563447	+	0.826152i	$0.690525\pi$
$654$	−0.288906	−0.0112971
$655$	−2.13811	−0.0835429
$656$	8.18175	0.319443
$657$	−4.31212	−0.168232
$658$	23.8560	0.930004
$659$	−36.0407	−1.40395	−0.701973	−	0.712203i	$-0.747697\pi$
$659$	−36.0407	−1.40395	−0.701973	+	0.712203i	$0.747697\pi$
$660$	−6.53012	−0.254184
$661$	−13.7737	−0.535736	−0.267868	−	0.963456i	$-0.586319\pi$
$661$	−13.7737	−0.535736	−0.267868	+	0.963456i	$0.586319\pi$
$662$	26.2243	1.01924
$663$	−8.15823	−0.316839
$664$	9.68880	0.375998
$665$	29.2171	1.13299
$666$	−9.49857	−0.368062
$667$	7.47426	0.289404
$668$	−19.8800	−0.769180
$669$	1.31190	0.0507209
$670$	−33.2130	−1.28313
$671$	5.10544	0.197093
$672$	3.62188	0.139717
$673$	−6.37154	−0.245605	−0.122802	−	0.992431i	$-0.539188\pi$
$673$	−6.37154	−0.245605	−0.122802	+	0.992431i	$0.539188\pi$
$674$	20.9240	0.805962
$675$	−2.21173	−0.0851294
$676$	−9.45431	−0.363627
$677$	−12.2470	−0.470689	−0.235345	−	0.971912i	$-0.575622\pi$
$677$	−12.2470	−0.470689	−0.235345	+	0.971912i	$0.575622\pi$
$678$	−2.28228	−0.0876506
$679$	19.2164	0.737457
$680$	8.76196	0.336006
$681$	−29.2589	−1.12120
$682$	−25.9948	−0.995391
$683$	−35.7312	−1.36722	−0.683608	−	0.729849i	$-0.739590\pi$
$683$	−35.7312	−1.36722	−0.683608	+	0.729849i	$0.739590\pi$
$684$	7.50796	0.287074
$685$	−35.1800	−1.34416
$686$	7.75601	0.296126
$687$	−28.6948	−1.09478
$688$	0.248678	0.00948074
$689$	12.0212	0.457973
$690$	−2.26050	−0.0860556
$691$	−15.4716	−0.588568	−0.294284	−	0.955718i	$-0.595081\pi$
$691$	−15.4716	−0.588568	−0.294284	+	0.955718i	$0.595081\pi$
$692$	−13.0623	−0.496553
$693$	18.6274	0.707596
$694$	−20.5743	−0.780990
$695$	33.5874	1.27404
$696$	7.90209	0.299528
$697$	33.5287	1.26999
$698$	12.3675	0.468116
$699$	10.7933	0.408242
$700$	−1.46791	−0.0554816
$701$	28.4299	1.07378	0.536892	−	0.843651i	$-0.319598\pi$
$701$	28.4299	1.07378	0.536892	+	0.843651i	$0.319598\pi$
$702$	−9.71950	−0.366839
$703$	20.1293	0.759193
$704$	−2.88880	−0.108876
$705$	−15.7414	−0.592854
$706$	−12.8737	−0.484508
$707$	−6.68307	−0.251343
$708$	−11.8695	−0.446083
$709$	−24.8867	−0.934641	−0.467321	−	0.884088i	$-0.654781\pi$
$709$	−24.8867	−0.934641	−0.467321	+	0.884088i	$0.654781\pi$
$710$	21.0589	0.790327
$711$	−1.64581	−0.0617228
$712$	0.610099	0.0228644
$713$	−8.99847	−0.336995
$714$	14.8424	0.555464
$715$	11.6305	0.434955
$716$	−4.59658	−0.171782
$717$	1.01872	0.0380448
$718$	−20.2210	−0.754641
$719$	5.40032	0.201398	0.100699	−	0.994917i	$-0.467892\pi$
$719$	5.40032	0.201398	0.100699	+	0.994917i	$0.467892\pi$
$720$	4.02444	0.149982
$721$	46.7331	1.74043
$722$	3.08914	0.114966
$723$	−9.11594	−0.339025
$724$	−6.40419	−0.238010
$725$	−3.20263	−0.118943
$726$	−2.80682	−0.104171
$727$	19.7868	0.733850	0.366925	−	0.930250i	$-0.380410\pi$
$727$	19.7868	0.733850	0.366925	+	0.930250i	$0.380410\pi$
$728$	−6.45075	−0.239081
$729$	16.0147	0.593137
$730$	4.89830	0.181294
$731$	1.01908	0.0376920
$732$	1.86849	0.0690613
$733$	−27.2188	−1.00535	−0.502675	−	0.864475i	$-0.667651\pi$
$733$	−27.2188	−1.00535	−0.502675	+	0.864475i	$0.667651\pi$
$734$	17.6959	0.653169
$735$	10.7057	0.394885
$736$	−1.00000	−0.0368605
$737$	44.8741	1.65296
$738$	15.4000	0.566883
$739$	13.4289	0.493991	0.246995	−	0.969017i	$-0.420557\pi$
$739$	13.4289	0.493991	0.246995	+	0.969017i	$0.420557\pi$
$740$	10.7898	0.396640
$741$	7.94093	0.291717
$742$	−21.8705	−0.802891
$743$	18.8940	0.693153	0.346576	−	0.938022i	$-0.387344\pi$
$743$	18.8940	0.693153	0.346576	+	0.938022i	$0.387344\pi$
$744$	−9.51355	−0.348784
$745$	−21.3966	−0.783912
$746$	18.3029	0.670117
$747$	18.2367	0.667244
$748$	−11.8383	−0.432850
$749$	−31.2855	−1.14315
$750$	12.2711	0.448076
$751$	−0.708626	−0.0258581	−0.0129291	−	0.999916i	$-0.504116\pi$
$751$	−0.708626	−0.0258581	−0.0129291	+	0.999916i	$0.504116\pi$
$752$	−6.96367	−0.253939
$753$	−4.92676	−0.179541
$754$	−14.0740	−0.512546
$755$	6.58254	0.239563
$756$	17.6829	0.643120
$757$	−13.2334	−0.480976	−0.240488	−	0.970652i	$-0.577307\pi$
$757$	−13.2334	−0.480976	−0.240488	+	0.970652i	$0.577307\pi$
$758$	30.3097	1.10090
$759$	3.05415	0.110859
$760$	−8.52858	−0.309364
$761$	49.8216	1.80603	0.903016	−	0.429606i	$-0.141348\pi$
$761$	49.8216	1.80603	0.903016	+	0.429606i	$0.141348\pi$
$762$	10.2835	0.372531
$763$	−0.936142	−0.0338906
$764$	8.96653	0.324398
$765$	16.4921	0.596274
$766$	33.3270	1.20415
$767$	21.1402	0.763328
$768$	−1.05724	−0.0381499
$769$	51.8616	1.87018	0.935089	−	0.354413i	$-0.115319\pi$
$769$	51.8616	1.87018	0.935089	+	0.354413i	$0.115319\pi$
$770$	−21.1596	−0.762538
$771$	−10.3914	−0.374238
$772$	19.7194	0.709718
$773$	−6.66148	−0.239597	−0.119798	−	0.992798i	$-0.538225\pi$
$773$	−6.66148	−0.239597	−0.119798	+	0.992798i	$0.538225\pi$
$774$	0.468071	0.0168245
$775$	3.85573	0.138502
$776$	−5.60934	−0.201363
$777$	18.2775	0.655701
$778$	31.9039	1.14381
$779$	−32.6357	−1.16929
$780$	4.25652	0.152408
$781$	−28.4527	−1.01812
$782$	−4.09799	−0.146544
$783$	38.5799	1.37873
$784$	4.73599	0.169142
$785$	24.8118	0.885570
$786$	1.05724	0.0377105
$787$	14.4552	0.515270	0.257635	−	0.966242i	$-0.417057\pi$
$787$	14.4552	0.515270	0.257635	+	0.966242i	$0.417057\pi$
$788$	−21.0521	−0.749950
$789$	−18.8895	−0.672485
$790$	1.86954	0.0665153
$791$	−7.39530	−0.262947
$792$	−5.43741	−0.193210
$793$	−3.32788	−0.118176
$794$	26.3120	0.933776
$795$	14.4312	0.511822
$796$	10.0749	0.357094
$797$	24.4618	0.866482	0.433241	−	0.901278i	$-0.357370\pi$
$797$	24.4618	0.866482	0.433241	+	0.901278i	$0.357370\pi$
$798$	−14.4471	−0.511422
$799$	−28.5371	−1.00957
$800$	0.428488	0.0151493
$801$	1.14835	0.0405751
$802$	11.2889	0.398624
$803$	−6.61809	−0.233547
$804$	16.4230	0.579195
$805$	−7.32470	−0.258162
$806$	16.9441	0.596832
$807$	13.6993	0.482239
$808$	1.95082	0.0686295
$809$	−10.3920	−0.365363	−0.182682	−	0.983172i	$-0.558478\pi$
$809$	−10.3920	−0.365363	−0.182682	+	0.983172i	$0.558478\pi$
$810$	0.405297	0.0142407
$811$	4.30770	0.151264	0.0756319	−	0.997136i	$-0.475903\pi$
$811$	4.30770	0.151264	0.0756319	+	0.997136i	$0.475903\pi$
$812$	25.6052	0.898566
$813$	15.0303	0.527137
$814$	−14.5781	−0.510961
$815$	26.0833	0.913660
$816$	−4.33257	−0.151670
$817$	−0.991935	−0.0347034
$818$	17.6148	0.615887
$819$	−12.1419	−0.424272
$820$	−17.4935	−0.610898
$821$	1.10610	0.0386031	0.0193016	−	0.999814i	$-0.493856\pi$
$821$	1.10610	0.0386031	0.0193016	+	0.999814i	$0.493856\pi$
$822$	17.3956	0.606741
$823$	−44.3392	−1.54557	−0.772783	−	0.634670i	$-0.781136\pi$
$823$	−44.3392	−1.54557	−0.772783	+	0.634670i	$0.781136\pi$
$824$	−13.6416	−0.475227
$825$	−1.30867	−0.0455619
$826$	−38.4608	−1.33822
$827$	1.51438	0.0526600	0.0263300	−	0.999653i	$-0.491618\pi$
$827$	1.51438	0.0526600	0.0263300	+	0.999653i	$0.491618\pi$
$828$	−1.88224	−0.0654124
$829$	11.9940	0.416567	0.208284	−	0.978068i	$-0.433212\pi$
$829$	11.9940	0.416567	0.208284	+	0.978068i	$0.433212\pi$
$830$	−20.7157	−0.719053
$831$	−21.8820	−0.759079
$832$	1.88300	0.0652813
$833$	19.4080	0.672449
$834$	−16.6081	−0.575091
$835$	42.5056	1.47097
$836$	11.5230	0.398530
$837$	−46.4475	−1.60546
$838$	9.48791	0.327754
$839$	−29.6034	−1.02202	−0.511012	−	0.859574i	$-0.670729\pi$
$839$	−29.6034	−1.02202	−0.511012	+	0.859574i	$0.670729\pi$
$840$	−7.74397	−0.267192
$841$	26.8646	0.926364
$842$	−37.8882	−1.30571
$843$	33.1889	1.14309
$844$	9.93841	0.342094
$845$	20.2143	0.695394
$846$	−13.1073	−0.450639
$847$	−9.09495	−0.312506
$848$	6.38409	0.219230
$849$	−6.64173	−0.227944
$850$	1.75594	0.0602282
$851$	−5.04641	−0.172989
$852$	−10.4131	−0.356747
$853$	−20.4826	−0.701311	−0.350656	−	0.936505i	$-0.614041\pi$
$853$	−20.4826	−0.701311	−0.350656	+	0.936505i	$0.614041\pi$
$854$	6.05447	0.207180
$855$	−16.0528	−0.548996
$856$	9.13236	0.312138
$857$	45.7255	1.56195	0.780976	−	0.624561i	$-0.214722\pi$
$857$	45.7255	1.56195	0.780976	+	0.624561i	$0.214722\pi$
$858$	−5.75098	−0.196335
$859$	9.25702	0.315845	0.157923	−	0.987451i	$-0.449520\pi$
$859$	9.25702	0.315845	0.157923	+	0.987451i	$0.449520\pi$
$860$	−0.531700	−0.0181308
$861$	−29.6333	−1.00990
$862$	30.4416	1.03684
$863$	−49.0948	−1.67121	−0.835603	−	0.549334i	$-0.814881\pi$
$863$	−49.0948	−1.67121	−0.835603	+	0.549334i	$0.814881\pi$
$864$	−5.16171	−0.175605
$865$	27.9286	0.949600
$866$	23.7947	0.808578
$867$	0.218273	0.00741294
$868$	−30.8268	−1.04633
$869$	−2.52593	−0.0856864
$870$	−16.8955	−0.572812
$871$	−29.2502	−0.991106
$872$	0.273264	0.00925388
$873$	−10.5581	−0.357339
$874$	3.98884	0.134925
$875$	39.7620	1.34420
$876$	−2.42208	−0.0818347
$877$	−50.5971	−1.70854	−0.854272	−	0.519827i	$-0.825996\pi$
$877$	−50.5971	−1.70854	−0.854272	+	0.519827i	$0.825996\pi$
$878$	24.4063	0.823672
$879$	24.1478	0.814485
$880$	6.17656	0.208212
$881$	27.7363	0.934459	0.467229	−	0.884136i	$-0.345252\pi$
$881$	27.7363	0.934459	0.467229	+	0.884136i	$0.345252\pi$
$882$	8.91427	0.300159
$883$	27.8821	0.938306	0.469153	−	0.883117i	$-0.344559\pi$
$883$	27.8821	0.938306	0.469153	+	0.883117i	$0.344559\pi$
$884$	7.71653	0.259535
$885$	25.3783	0.853082
$886$	8.82371	0.296438
$887$	47.1150	1.58197	0.790984	−	0.611837i	$-0.209569\pi$
$887$	47.1150	1.58197	0.790984	+	0.611837i	$0.209569\pi$
$888$	−5.33527	−0.179040
$889$	33.3216	1.11757
$890$	−1.30446	−0.0437255
$891$	−0.547597	−0.0183452
$892$	−1.24087	−0.0415474
$893$	27.7770	0.929521
$894$	10.5801	0.353851
$895$	9.82800	0.328514
$896$	−3.42578	−0.114447
$897$	−1.99079	−0.0664704
$898$	−32.3312	−1.07891
$899$	−67.2569	−2.24314
$900$	0.806517	0.0268839
$901$	26.1619	0.871581
$902$	23.6354	0.786973
$903$	−0.900680	−0.0299727
$904$	2.15872	0.0717979
$905$	13.6929	0.455166
$906$	−3.25490	−0.108137
$907$	44.1631	1.46641	0.733207	−	0.680006i	$-0.238023\pi$
$907$	44.1631	1.46641	0.733207	+	0.680006i	$0.238023\pi$
$908$	27.6748	0.918419
$909$	3.67191	0.121789
$910$	13.7924	0.457214
$911$	17.0393	0.564538	0.282269	−	0.959335i	$-0.408913\pi$
$911$	17.0393	0.564538	0.282269	+	0.959335i	$0.408913\pi$
$912$	4.21717	0.139644
$913$	27.9890	0.926300
$914$	−0.481915	−0.0159403
$915$	−3.99503	−0.132072
$916$	27.1412	0.896772
$917$	3.42578	0.113129
$918$	−21.1526	−0.698141
$919$	−44.1611	−1.45674	−0.728371	−	0.685183i	$-0.759722\pi$
$919$	−44.1611	−1.45674	−0.728371	+	0.685183i	$0.759722\pi$
$920$	2.13811	0.0704914
$921$	22.5095	0.741712
$922$	11.0216	0.362978
$923$	18.5463	0.610458
$924$	10.4629	0.344203
$925$	2.16233	0.0710968
$926$	16.3035	0.535768
$927$	−25.6768	−0.843335
$928$	−7.47426	−0.245355
$929$	47.3416	1.55323	0.776613	−	0.629978i	$-0.216936\pi$
$929$	47.3416	1.55323	0.776613	+	0.629978i	$0.216936\pi$
$930$	20.3410	0.667008
$931$	−18.8911	−0.619131
$932$	−10.2090	−0.334406
$933$	−1.23999	−0.0405954
$934$	5.72416	0.187300
$935$	25.3115	0.827775
$936$	3.54426	0.115848
$937$	3.19381	0.104337	0.0521686	−	0.998638i	$-0.483387\pi$
$937$	3.19381	0.104337	0.0521686	+	0.998638i	$0.483387\pi$
$938$	53.2155	1.73755
$939$	7.81373	0.254991
$940$	14.8891	0.485629
$941$	−42.9033	−1.39861	−0.699304	−	0.714825i	$-0.746506\pi$
$941$	−42.9033	−1.39861	−0.699304	+	0.714825i	$0.746506\pi$
$942$	−12.2688	−0.399739
$943$	8.18175	0.266434
$944$	11.2269	0.365403
$945$	−37.8079	−1.22989
$946$	0.718379	0.0233565
$947$	−28.5902	−0.929057	−0.464528	−	0.885558i	$-0.653776\pi$
$947$	−28.5902	−0.929057	−0.464528	+	0.885558i	$0.653776\pi$
$948$	−0.924440	−0.0300244
$949$	4.31386	0.140034
$950$	−1.70917	−0.0554528
$951$	18.9483	0.614441
$952$	−14.0388	−0.455001
$953$	−45.5680	−1.47609	−0.738047	−	0.674749i	$-0.764252\pi$
$953$	−45.5680	−1.47609	−0.738047	+	0.674749i	$0.764252\pi$
$954$	12.0164	0.389045
$955$	−19.1714	−0.620373
$956$	−0.963565	−0.0311639
$957$	22.8275	0.737910
$958$	19.4595	0.628709
$959$	56.3671	1.82019
$960$	2.26050	0.0729572
$961$	49.9725	1.61202
$962$	9.50240	0.306370
$963$	17.1893	0.553918
$964$	8.62238	0.277708
$965$	−42.1623	−1.35725
$966$	3.62188	0.116532
$967$	8.85805	0.284856	0.142428	−	0.989805i	$-0.454509\pi$
$967$	8.85805	0.284856	0.142428	+	0.989805i	$0.454509\pi$
$968$	2.65485	0.0853302
$969$	17.2819	0.555175
$970$	11.9934	0.385084
$971$	27.7455	0.890394	0.445197	−	0.895433i	$-0.353134\pi$
$971$	27.7455	0.890394	0.445197	+	0.895433i	$0.353134\pi$
$972$	−15.6855	−0.503113
$973$	−53.8153	−1.72524
$974$	25.7071	0.823707
$975$	0.853027	0.0273187
$976$	−1.76733	−0.0565707
$977$	48.7651	1.56013	0.780067	−	0.625696i	$-0.215185\pi$
$977$	48.7651	1.56013	0.780067	+	0.625696i	$0.215185\pi$
$978$	−12.8976	−0.412418
$979$	1.76245	0.0563282
$980$	−10.1261	−0.323465
$981$	0.514348	0.0164219
$982$	−31.0924	−0.992199
$983$	32.6228	1.04051	0.520253	−	0.854012i	$-0.325837\pi$
$983$	32.6228	1.04051	0.520253	+	0.854012i	$0.325837\pi$
$984$	8.65008	0.275754
$985$	45.0117	1.43419
$986$	−30.6295	−0.975441
$987$	25.2216	0.802811
$988$	−7.51099	−0.238957
$989$	0.248678	0.00790749
$990$	11.6258	0.369492
$991$	48.1910	1.53084	0.765419	−	0.643532i	$-0.222532\pi$
$991$	48.1910	1.53084	0.765419	+	0.643532i	$0.222532\pi$
$992$	8.99847	0.285702
$993$	27.7254	0.879838
$994$	−33.7416	−1.07022
$995$	−21.5412	−0.682900
$996$	10.2434	0.324574
$997$	19.8878	0.629853	0.314927	−	0.949116i	$-0.398020\pi$
$997$	19.8878	0.629853	0.314927	+	0.949116i	$0.398020\pi$
$998$	−41.1280	−1.30189
$999$	−26.0481	−0.824125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.9	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.9	✓	25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.05724 q^{3} +1.00000 q^{4} -2.13811 q^{5} +1.05724 q^{6} +3.42578 q^{7} -1.00000 q^{8} -1.88224 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.05724 q^{3} +1.00000 q^{4} -2.13811 q^{5} +1.05724 q^{6} +3.42578 q^{7} -1.00000 q^{8} -1.88224 q^{9} +2.13811 q^{10} -2.88880 q^{11} -1.05724 q^{12} +1.88300 q^{13} -3.42578 q^{14} +2.26050 q^{15} +1.00000 q^{16} +4.09799 q^{17} +1.88224 q^{18} -3.98884 q^{19} -2.13811 q^{20} -3.62188 q^{21} +2.88880 q^{22} +1.00000 q^{23} +1.05724 q^{24} -0.428488 q^{25} -1.88300 q^{26} +5.16171 q^{27} +3.42578 q^{28} +7.47426 q^{29} -2.26050 q^{30} -8.99847 q^{31} -1.00000 q^{32} +3.05415 q^{33} -4.09799 q^{34} -7.32470 q^{35} -1.88224 q^{36} -5.04641 q^{37} +3.98884 q^{38} -1.99079 q^{39} +2.13811 q^{40} +8.18175 q^{41} +3.62188 q^{42} +0.248678 q^{43} -2.88880 q^{44} +4.02444 q^{45} -1.00000 q^{46} -6.96367 q^{47} -1.05724 q^{48} +4.73599 q^{49} +0.428488 q^{50} -4.33257 q^{51} +1.88300 q^{52} +6.38409 q^{53} -5.16171 q^{54} +6.17656 q^{55} -3.42578 q^{56} +4.21717 q^{57} -7.47426 q^{58} +11.2269 q^{59} +2.26050 q^{60} -1.76733 q^{61} +8.99847 q^{62} -6.44815 q^{63} +1.00000 q^{64} -4.02606 q^{65} -3.05415 q^{66} -15.5338 q^{67} +4.09799 q^{68} -1.05724 q^{69} +7.32470 q^{70} +9.84931 q^{71} +1.88224 q^{72} +2.29095 q^{73} +5.04641 q^{74} +0.453015 q^{75} -3.98884 q^{76} -9.89639 q^{77} +1.99079 q^{78} +0.874389 q^{79} -2.13811 q^{80} +0.189559 q^{81} -8.18175 q^{82} -9.68880 q^{83} -3.62188 q^{84} -8.76196 q^{85} -0.248678 q^{86} -7.90209 q^{87} +2.88880 q^{88} -0.610099 q^{89} -4.02444 q^{90} +6.45075 q^{91} +1.00000 q^{92} +9.51355 q^{93} +6.96367 q^{94} +8.52858 q^{95} +1.05724 q^{96} +5.60934 q^{97} -4.73599 q^{98} +5.43741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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