LMFDB - Embedded newform 6010.2.a.h.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.41587 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.41587 q^{6} +2.06613 q^{7} +1.00000 q^{8} -0.995326 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.41587 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.41587 q^{6} +2.06613 q^{7} +1.00000 q^{8} -0.995326 q^{9} -1.00000 q^{10} +0.693026 q^{11} +1.41587 q^{12} -2.14922 q^{13} +2.06613 q^{14} -1.41587 q^{15} +1.00000 q^{16} +2.17699 q^{17} -0.995326 q^{18} +0.722882 q^{19} -1.00000 q^{20} +2.92536 q^{21} +0.693026 q^{22} +7.23604 q^{23} +1.41587 q^{24} +1.00000 q^{25} -2.14922 q^{26} -5.65684 q^{27} +2.06613 q^{28} +1.93721 q^{29} -1.41587 q^{30} +6.20494 q^{31} +1.00000 q^{32} +0.981231 q^{33} +2.17699 q^{34} -2.06613 q^{35} -0.995326 q^{36} -0.815624 q^{37} +0.722882 q^{38} -3.04301 q^{39} -1.00000 q^{40} +2.04076 q^{41} +2.92536 q^{42} +5.06569 q^{43} +0.693026 q^{44} +0.995326 q^{45} +7.23604 q^{46} -2.87389 q^{47} +1.41587 q^{48} -2.73112 q^{49} +1.00000 q^{50} +3.08232 q^{51} -2.14922 q^{52} -2.22421 q^{53} -5.65684 q^{54} -0.693026 q^{55} +2.06613 q^{56} +1.02350 q^{57} +1.93721 q^{58} -3.31115 q^{59} -1.41587 q^{60} +8.53996 q^{61} +6.20494 q^{62} -2.05647 q^{63} +1.00000 q^{64} +2.14922 q^{65} +0.981231 q^{66} +11.0905 q^{67} +2.17699 q^{68} +10.2453 q^{69} -2.06613 q^{70} -2.45407 q^{71} -0.995326 q^{72} -1.59861 q^{73} -0.815624 q^{74} +1.41587 q^{75} +0.722882 q^{76} +1.43188 q^{77} -3.04301 q^{78} -5.78572 q^{79} -1.00000 q^{80} -5.02335 q^{81} +2.04076 q^{82} +6.17404 q^{83} +2.92536 q^{84} -2.17699 q^{85} +5.06569 q^{86} +2.74283 q^{87} +0.693026 q^{88} +5.59992 q^{89} +0.995326 q^{90} -4.44057 q^{91} +7.23604 q^{92} +8.78536 q^{93} -2.87389 q^{94} -0.722882 q^{95} +1.41587 q^{96} -10.8879 q^{97} -2.73112 q^{98} -0.689786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * 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
$3$	1.41587	0.817450	0.408725	−	0.912658i	$-0.365973\pi$
$3$	1.41587	0.817450	0.408725	+	0.912658i	$0.365973\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.41587	0.578025
$7$	2.06613	0.780923	0.390461	−	0.920619i	$-0.372315\pi$
$7$	2.06613	0.780923	0.390461	+	0.920619i	$0.372315\pi$
$8$	1.00000	0.353553
$9$	−0.995326	−0.331775
$10$	−1.00000	−0.316228
$11$	0.693026	0.208955	0.104478	−	0.994527i	$-0.466683\pi$
$11$	0.693026	0.208955	0.104478	+	0.994527i	$0.466683\pi$
$12$	1.41587	0.408725
$13$	−2.14922	−0.596088	−0.298044	−	0.954552i	$-0.596334\pi$
$13$	−2.14922	−0.596088	−0.298044	+	0.954552i	$0.596334\pi$
$14$	2.06613	0.552196
$15$	−1.41587	−0.365575
$16$	1.00000	0.250000
$17$	2.17699	0.527998	0.263999	−	0.964523i	$-0.414958\pi$
$17$	2.17699	0.527998	0.263999	+	0.964523i	$0.414958\pi$
$18$	−0.995326	−0.234600
$19$	0.722882	0.165841	0.0829203	−	0.996556i	$-0.473575\pi$
$19$	0.722882	0.165841	0.0829203	+	0.996556i	$0.473575\pi$
$20$	−1.00000	−0.223607
$21$	2.92536	0.638366
$22$	0.693026	0.147754
$23$	7.23604	1.50882	0.754409	−	0.656405i	$-0.227924\pi$
$23$	7.23604	1.50882	0.754409	+	0.656405i	$0.227924\pi$
$24$	1.41587	0.289012
$25$	1.00000	0.200000
$26$	−2.14922	−0.421498
$27$	−5.65684	−1.08866
$28$	2.06613	0.390461
$29$	1.93721	0.359732	0.179866	−	0.983691i	$-0.442434\pi$
$29$	1.93721	0.359732	0.179866	+	0.983691i	$0.442434\pi$
$30$	−1.41587	−0.258500
$31$	6.20494	1.11444	0.557220	−	0.830365i	$-0.311868\pi$
$31$	6.20494	1.11444	0.557220	+	0.830365i	$0.311868\pi$
$32$	1.00000	0.176777
$33$	0.981231	0.170810
$34$	2.17699	0.373351
$35$	−2.06613	−0.349239
$36$	−0.995326	−0.165888
$37$	−0.815624	−0.134088	−0.0670439	−	0.997750i	$-0.521357\pi$
$37$	−0.815624	−0.134088	−0.0670439	+	0.997750i	$0.521357\pi$
$38$	0.722882	0.117267
$39$	−3.04301	−0.487272
$40$	−1.00000	−0.158114
$41$	2.04076	0.318713	0.159356	−	0.987221i	$-0.449058\pi$
$41$	2.04076	0.318713	0.159356	+	0.987221i	$0.449058\pi$
$42$	2.92536	0.451393
$43$	5.06569	0.772511	0.386256	−	0.922392i	$-0.373768\pi$
$43$	5.06569	0.772511	0.386256	+	0.922392i	$0.373768\pi$
$44$	0.693026	0.104478
$45$	0.995326	0.148374
$46$	7.23604	1.06690
$47$	−2.87389	−0.419199	−0.209600	−	0.977787i	$-0.567216\pi$
$47$	−2.87389	−0.419199	−0.209600	+	0.977787i	$0.567216\pi$
$48$	1.41587	0.204363
$49$	−2.73112	−0.390159
$50$	1.00000	0.141421
$51$	3.08232	0.431612
$52$	−2.14922	−0.298044
$53$	−2.22421	−0.305518	−0.152759	−	0.988263i	$-0.548816\pi$
$53$	−2.22421	−0.305518	−0.152759	+	0.988263i	$0.548816\pi$
$54$	−5.65684	−0.769799
$55$	−0.693026	−0.0934476
$56$	2.06613	0.276098
$57$	1.02350	0.135566
$58$	1.93721	0.254369
$59$	−3.31115	−0.431075	−0.215538	−	0.976496i	$-0.569150\pi$
$59$	−3.31115	−0.431075	−0.215538	+	0.976496i	$0.569150\pi$
$60$	−1.41587	−0.182787
$61$	8.53996	1.09343	0.546715	−	0.837319i	$-0.315878\pi$
$61$	8.53996	1.09343	0.546715	+	0.837319i	$0.315878\pi$
$62$	6.20494	0.788029
$63$	−2.05647	−0.259091
$64$	1.00000	0.125000
$65$	2.14922	0.266579
$66$	0.981231	0.120781
$67$	11.0905	1.35492	0.677461	−	0.735559i	$-0.263080\pi$
$67$	11.0905	1.35492	0.677461	+	0.735559i	$0.263080\pi$
$68$	2.17699	0.263999
$69$	10.2453	1.23338
$70$	−2.06613	−0.246950
$71$	−2.45407	−0.291245	−0.145622	−	0.989340i	$-0.546518\pi$
$71$	−2.45407	−0.291245	−0.145622	+	0.989340i	$0.546518\pi$
$72$	−0.995326	−0.117300
$73$	−1.59861	−0.187103	−0.0935514	−	0.995614i	$-0.529822\pi$
$73$	−1.59861	−0.187103	−0.0935514	+	0.995614i	$0.529822\pi$
$74$	−0.815624	−0.0948144
$75$	1.41587	0.163490
$76$	0.722882	0.0829203
$77$	1.43188	0.163178
$78$	−3.04301	−0.344553
$79$	−5.78572	−0.650944	−0.325472	−	0.945552i	$-0.605523\pi$
$79$	−5.78572	−0.650944	−0.325472	+	0.945552i	$0.605523\pi$
$80$	−1.00000	−0.111803
$81$	−5.02335	−0.558150
$82$	2.04076	0.225364
$83$	6.17404	0.677689	0.338844	−	0.940842i	$-0.389964\pi$
$83$	6.17404	0.677689	0.338844	+	0.940842i	$0.389964\pi$
$84$	2.92536	0.319183
$85$	−2.17699	−0.236128
$86$	5.06569	0.546248
$87$	2.74283	0.294063
$88$	0.693026	0.0738768
$89$	5.59992	0.593590	0.296795	−	0.954941i	$-0.404082\pi$
$89$	5.59992	0.593590	0.296795	+	0.954941i	$0.404082\pi$
$90$	0.995326	0.104917
$91$	−4.44057	−0.465499
$92$	7.23604	0.754409
$93$	8.78536	0.911000
$94$	−2.87389	−0.296419
$95$	−0.722882	−0.0741662
$96$	1.41587	0.144506
$97$	−10.8879	−1.10550	−0.552751	−	0.833346i	$-0.686422\pi$
$97$	−10.8879	−1.10550	−0.552751	+	0.833346i	$0.686422\pi$
$98$	−2.73112	−0.275884
$99$	−0.689786	−0.0693261
$100$	1.00000	0.100000
$101$	−1.75104	−0.174235	−0.0871173	−	0.996198i	$-0.527766\pi$
$101$	−1.75104	−0.174235	−0.0871173	+	0.996198i	$0.527766\pi$
$102$	3.08232	0.305196
$103$	17.7226	1.74626	0.873132	−	0.487485i	$-0.162085\pi$
$103$	17.7226	1.74626	0.873132	+	0.487485i	$0.162085\pi$
$104$	−2.14922	−0.210749
$105$	−2.92536	−0.285486
$106$	−2.22421	−0.216034
$107$	17.2133	1.66408	0.832038	−	0.554718i	$-0.187174\pi$
$107$	17.2133	1.66408	0.832038	+	0.554718i	$0.187174\pi$
$108$	−5.65684	−0.544330
$109$	6.77532	0.648958	0.324479	−	0.945893i	$-0.394811\pi$
$109$	6.77532	0.648958	0.324479	+	0.945893i	$0.394811\pi$
$110$	−0.693026	−0.0660774
$111$	−1.15481	−0.109610
$112$	2.06613	0.195231
$113$	1.35435	0.127406	0.0637032	−	0.997969i	$-0.479709\pi$
$113$	1.35435	0.127406	0.0637032	+	0.997969i	$0.479709\pi$
$114$	1.02350	0.0958599
$115$	−7.23604	−0.674764
$116$	1.93721	0.179866
$117$	2.13918	0.197767
$118$	−3.31115	−0.304816
$119$	4.49794	0.412325
$120$	−1.41587	−0.129250
$121$	−10.5197	−0.956338
$122$	8.53996	0.773172
$123$	2.88944	0.260532
$124$	6.20494	0.557220
$125$	−1.00000	−0.0894427
$126$	−2.05647	−0.183205
$127$	−14.6933	−1.30382	−0.651909	−	0.758297i	$-0.726032\pi$
$127$	−14.6933	−1.30382	−0.651909	+	0.758297i	$0.726032\pi$
$128$	1.00000	0.0883883
$129$	7.17234	0.631489
$130$	2.14922	0.188499
$131$	20.1536	1.76083	0.880413	−	0.474207i	$-0.157265\pi$
$131$	20.1536	1.76083	0.880413	+	0.474207i	$0.157265\pi$
$132$	0.981231	0.0854052
$133$	1.49357	0.129509
$134$	11.0905	0.958075
$135$	5.65684	0.486863
$136$	2.17699	0.186675
$137$	−2.87670	−0.245773	−0.122886	−	0.992421i	$-0.539215\pi$
$137$	−2.87670	−0.245773	−0.122886	+	0.992421i	$0.539215\pi$
$138$	10.2453	0.872134
$139$	13.7622	1.16730	0.583648	−	0.812007i	$-0.301625\pi$
$139$	13.7622	1.16730	0.583648	+	0.812007i	$0.301625\pi$
$140$	−2.06613	−0.174620
$141$	−4.06904	−0.342675
$142$	−2.45407	−0.205941
$143$	−1.48947	−0.124556
$144$	−0.995326	−0.0829438
$145$	−1.93721	−0.160877
$146$	−1.59861	−0.132302
$147$	−3.86689	−0.318936
$148$	−0.815624	−0.0670439
$149$	20.5309	1.68195	0.840977	−	0.541071i	$-0.181981\pi$
$149$	20.5309	1.68195	0.840977	+	0.541071i	$0.181981\pi$
$150$	1.41587	0.115605
$151$	−6.98229	−0.568210	−0.284105	−	0.958793i	$-0.591696\pi$
$151$	−6.98229	−0.568210	−0.284105	+	0.958793i	$0.591696\pi$
$152$	0.722882	0.0586335
$153$	−2.16681	−0.175177
$154$	1.43188	0.115384
$155$	−6.20494	−0.498393
$156$	−3.04301	−0.243636
$157$	9.08588	0.725132	0.362566	−	0.931958i	$-0.381901\pi$
$157$	9.08588	0.725132	0.362566	+	0.931958i	$0.381901\pi$
$158$	−5.78572	−0.460287
$159$	−3.14918	−0.249746
$160$	−1.00000	−0.0790569
$161$	14.9506	1.17827
$162$	−5.02335	−0.394672
$163$	14.5723	1.14139	0.570697	−	0.821161i	$-0.306673\pi$
$163$	14.5723	1.14139	0.570697	+	0.821161i	$0.306673\pi$
$164$	2.04076	0.159356
$165$	−0.981231	−0.0763887
$166$	6.17404	0.479198
$167$	−11.2047	−0.867043	−0.433522	−	0.901143i	$-0.642729\pi$
$167$	−11.2047	−0.867043	−0.433522	+	0.901143i	$0.642729\pi$
$168$	2.92536	0.225696
$169$	−8.38083	−0.644679
$170$	−2.17699	−0.166968
$171$	−0.719503	−0.0550218
$172$	5.06569	0.386256
$173$	−14.7791	−1.12364	−0.561818	−	0.827261i	$-0.689898\pi$
$173$	−14.7791	−1.12364	−0.561818	+	0.827261i	$0.689898\pi$
$174$	2.74283	0.207934
$175$	2.06613	0.156185
$176$	0.693026	0.0522388
$177$	−4.68814	−0.352382
$178$	5.59992	0.419732
$179$	−4.77643	−0.357007	−0.178504	−	0.983939i	$-0.557126\pi$
$179$	−4.77643	−0.357007	−0.178504	+	0.983939i	$0.557126\pi$
$180$	0.995326	0.0741872
$181$	−9.05373	−0.672959	−0.336479	−	0.941691i	$-0.609236\pi$
$181$	−9.05373	−0.672959	−0.336479	+	0.941691i	$0.609236\pi$
$182$	−4.44057	−0.329157
$183$	12.0914	0.893824
$184$	7.23604	0.533448
$185$	0.815624	0.0599659
$186$	8.78536	0.644174
$187$	1.50871	0.110328
$188$	−2.87389	−0.209600
$189$	−11.6878	−0.850159
$190$	−0.722882	−0.0524434
$191$	3.66734	0.265359	0.132680	−	0.991159i	$-0.457642\pi$
$191$	3.66734	0.265359	0.132680	+	0.991159i	$0.457642\pi$
$192$	1.41587	0.102181
$193$	−8.25428	−0.594156	−0.297078	−	0.954853i	$-0.596012\pi$
$193$	−8.25428	−0.594156	−0.297078	+	0.954853i	$0.596012\pi$
$194$	−10.8879	−0.781708
$195$	3.04301	0.217915
$196$	−2.73112	−0.195080
$197$	−22.0096	−1.56812	−0.784060	−	0.620685i	$-0.786855\pi$
$197$	−22.0096	−1.56812	−0.784060	+	0.620685i	$0.786855\pi$
$198$	−0.689786	−0.0490210
$199$	24.0436	1.70441	0.852203	−	0.523212i	$-0.175266\pi$
$199$	24.0436	1.70441	0.852203	+	0.523212i	$0.175266\pi$
$200$	1.00000	0.0707107
$201$	15.7027	1.10758
$202$	−1.75104	−0.123203
$203$	4.00253	0.280923
$204$	3.08232	0.215806
$205$	−2.04076	−0.142533
$206$	17.7226	1.23479
$207$	−7.20221	−0.500588
$208$	−2.14922	−0.149022
$209$	0.500976	0.0346532
$210$	−2.92536	−0.201869
$211$	10.9323	0.752609	0.376305	−	0.926496i	$-0.377195\pi$
$211$	10.9323	0.752609	0.376305	+	0.926496i	$0.377195\pi$
$212$	−2.22421	−0.152759
$213$	−3.47464	−0.238078
$214$	17.2133	1.17668
$215$	−5.06569	−0.345478
$216$	−5.65684	−0.384899
$217$	12.8202	0.870292
$218$	6.77532	0.458883
$219$	−2.26341	−0.152947
$220$	−0.693026	−0.0467238
$221$	−4.67884	−0.314733
$222$	−1.15481	−0.0775061
$223$	2.47659	0.165845	0.0829225	−	0.996556i	$-0.473575\pi$
$223$	2.47659	0.165845	0.0829225	+	0.996556i	$0.473575\pi$
$224$	2.06613	0.138049
$225$	−0.995326	−0.0663550
$226$	1.35435	0.0900900
$227$	−18.3683	−1.21915	−0.609575	−	0.792729i	$-0.708660\pi$
$227$	−18.3683	−1.21915	−0.609575	+	0.792729i	$0.708660\pi$
$228$	1.02350	0.0677832
$229$	−16.8398	−1.11281	−0.556404	−	0.830912i	$-0.687819\pi$
$229$	−16.8398	−1.11281	−0.556404	+	0.830912i	$0.687819\pi$
$230$	−7.23604	−0.477130
$231$	2.02735	0.133390
$232$	1.93721	0.127184
$233$	7.03142	0.460644	0.230322	−	0.973115i	$-0.426022\pi$
$233$	7.03142	0.460644	0.230322	+	0.973115i	$0.426022\pi$
$234$	2.13918	0.139842
$235$	2.87389	0.187472
$236$	−3.31115	−0.215538
$237$	−8.19180	−0.532115
$238$	4.49794	0.291558
$239$	−13.0641	−0.845044	−0.422522	−	0.906353i	$-0.638855\pi$
$239$	−13.0641	−0.845044	−0.422522	+	0.906353i	$0.638855\pi$
$240$	−1.41587	−0.0913937
$241$	−9.38159	−0.604321	−0.302161	−	0.953257i	$-0.597708\pi$
$241$	−9.38159	−0.604321	−0.302161	+	0.953257i	$0.597708\pi$
$242$	−10.5197	−0.676233
$243$	9.85814	0.632400
$244$	8.53996	0.546715
$245$	2.73112	0.174485
$246$	2.88944	0.184224
$247$	−1.55364	−0.0988555
$248$	6.20494	0.394014
$249$	8.74161	0.553977
$250$	−1.00000	−0.0632456
$251$	−14.8197	−0.935408	−0.467704	−	0.883885i	$-0.654919\pi$
$251$	−14.8197	−0.935408	−0.467704	+	0.883885i	$0.654919\pi$
$252$	−2.05647	−0.129545
$253$	5.01476	0.315275
$254$	−14.6933	−0.921939
$255$	−3.08232	−0.193023
$256$	1.00000	0.0625000
$257$	17.0719	1.06491	0.532457	−	0.846457i	$-0.321269\pi$
$257$	17.0719	1.06491	0.532457	+	0.846457i	$0.321269\pi$
$258$	7.17234	0.446530
$259$	−1.68518	−0.104712
$260$	2.14922	0.133289
$261$	−1.92816	−0.119350
$262$	20.1536	1.24509
$263$	8.40937	0.518544	0.259272	−	0.965804i	$-0.416517\pi$
$263$	8.40937	0.518544	0.259272	+	0.965804i	$0.416517\pi$
$264$	0.981231	0.0603906
$265$	2.22421	0.136632
$266$	1.49357	0.0915765
$267$	7.92873	0.485230
$268$	11.0905	0.677461
$269$	−26.1346	−1.59346	−0.796728	−	0.604338i	$-0.793438\pi$
$269$	−26.1346	−1.59346	−0.796728	+	0.604338i	$0.793438\pi$
$270$	5.65684	0.344264
$271$	−17.0311	−1.03457	−0.517284	−	0.855814i	$-0.673057\pi$
$271$	−17.0311	−1.03457	−0.517284	+	0.855814i	$0.673057\pi$
$272$	2.17699	0.131999
$273$	−6.28725	−0.380522
$274$	−2.87670	−0.173788
$275$	0.693026	0.0417910
$276$	10.2453	0.616692
$277$	−22.3005	−1.33991	−0.669954	−	0.742403i	$-0.733686\pi$
$277$	−22.3005	−1.33991	−0.669954	+	0.742403i	$0.733686\pi$
$278$	13.7622	0.825403
$279$	−6.17594	−0.369744
$280$	−2.06613	−0.123475
$281$	11.5379	0.688292	0.344146	−	0.938916i	$-0.388168\pi$
$281$	11.5379	0.688292	0.344146	+	0.938916i	$0.388168\pi$
$282$	−4.06904	−0.242308
$283$	1.04795	0.0622944	0.0311472	−	0.999515i	$-0.490084\pi$
$283$	1.04795	0.0622944	0.0311472	+	0.999515i	$0.490084\pi$
$284$	−2.45407	−0.145622
$285$	−1.02350	−0.0606271
$286$	−1.48947	−0.0880741
$287$	4.21646	0.248890
$288$	−0.995326	−0.0586501
$289$	−12.2607	−0.721218
$290$	−1.93721	−0.113757
$291$	−15.4159	−0.903693
$292$	−1.59861	−0.0935514
$293$	−16.6303	−0.971555	−0.485777	−	0.874083i	$-0.661463\pi$
$293$	−16.6303	−0.971555	−0.485777	+	0.874083i	$0.661463\pi$
$294$	−3.86689	−0.225522
$295$	3.31115	0.192783
$296$	−0.815624	−0.0474072
$297$	−3.92034	−0.227481
$298$	20.5309	1.18932
$299$	−15.5519	−0.899388
$300$	1.41587	0.0817450
$301$	10.4664	0.603272
$302$	−6.98229	−0.401785
$303$	−2.47923	−0.142428
$304$	0.722882	0.0414601
$305$	−8.53996	−0.488997
$306$	−2.16681	−0.123869
$307$	20.3313	1.16037	0.580186	−	0.814484i	$-0.302980\pi$
$307$	20.3313	1.16037	0.580186	+	0.814484i	$0.302980\pi$
$308$	1.43188	0.0815889
$309$	25.0929	1.42748
$310$	−6.20494	−0.352417
$311$	26.5179	1.50369	0.751846	−	0.659339i	$-0.229164\pi$
$311$	26.5179	1.50369	0.751846	+	0.659339i	$0.229164\pi$
$312$	−3.04301	−0.172277
$313$	−3.17313	−0.179356	−0.0896779	−	0.995971i	$-0.528584\pi$
$313$	−3.17313	−0.179356	−0.0896779	+	0.995971i	$0.528584\pi$
$314$	9.08588	0.512746
$315$	2.05647	0.115869
$316$	−5.78572	−0.325472
$317$	−18.5584	−1.04234	−0.521172	−	0.853451i	$-0.674505\pi$
$317$	−18.5584	−1.04234	−0.521172	+	0.853451i	$0.674505\pi$
$318$	−3.14918	−0.176597
$319$	1.34254	0.0751677
$320$	−1.00000	−0.0559017
$321$	24.3718	1.36030
$322$	14.9506	0.833163
$323$	1.57371	0.0875634
$324$	−5.02335	−0.279075
$325$	−2.14922	−0.119218
$326$	14.5723	0.807088
$327$	9.59294	0.530491
$328$	2.04076	0.112682
$329$	−5.93782	−0.327362
$330$	−0.981231	−0.0540150
$331$	11.2400	0.617804	0.308902	−	0.951094i	$-0.400039\pi$
$331$	11.2400	0.617804	0.308902	+	0.951094i	$0.400039\pi$
$332$	6.17404	0.338844
$333$	0.811812	0.0444870
$334$	−11.2047	−0.613092
$335$	−11.0905	−0.605940
$336$	2.92536	0.159591
$337$	−12.1914	−0.664107	−0.332054	−	0.943261i	$-0.607741\pi$
$337$	−12.1914	−0.664107	−0.332054	+	0.943261i	$0.607741\pi$
$338$	−8.38083	−0.455857
$339$	1.91758	0.104148
$340$	−2.17699	−0.118064
$341$	4.30019	0.232868
$342$	−0.719503	−0.0389063
$343$	−20.1057	−1.08561
$344$	5.06569	0.273124
$345$	−10.2453	−0.551586
$346$	−14.7791	−0.794531
$347$	−32.0304	−1.71948	−0.859740	−	0.510732i	$-0.829375\pi$
$347$	−32.0304	−1.71948	−0.859740	+	0.510732i	$0.829375\pi$
$348$	2.74283	0.147031
$349$	13.4376	0.719300	0.359650	−	0.933087i	$-0.382896\pi$
$349$	13.4376	0.719300	0.359650	+	0.933087i	$0.382896\pi$
$350$	2.06613	0.110439
$351$	12.1578	0.648937
$352$	0.693026	0.0369384
$353$	−2.11720	−0.112687	−0.0563437	−	0.998411i	$-0.517944\pi$
$353$	−2.11720	−0.112687	−0.0563437	+	0.998411i	$0.517944\pi$
$354$	−4.68814	−0.249172
$355$	2.45407	0.130249
$356$	5.59992	0.296795
$357$	6.36848	0.337056
$358$	−4.77643	−0.252442
$359$	33.8442	1.78623	0.893113	−	0.449832i	$-0.148516\pi$
$359$	33.8442	1.78623	0.893113	+	0.449832i	$0.148516\pi$
$360$	0.995326	0.0524583
$361$	−18.4774	−0.972497
$362$	−9.05373	−0.475854
$363$	−14.8945	−0.781758
$364$	−4.44057	−0.232749
$365$	1.59861	0.0836749
$366$	12.0914	0.632029
$367$	0.437345	0.0228292	0.0114146	−	0.999935i	$-0.496367\pi$
$367$	0.437345	0.0228292	0.0114146	+	0.999935i	$0.496367\pi$
$368$	7.23604	0.377204
$369$	−2.03122	−0.105741
$370$	0.815624	0.0424023
$371$	−4.59550	−0.238586
$372$	8.78536	0.455500
$373$	−24.7553	−1.28178	−0.640890	−	0.767633i	$-0.721434\pi$
$373$	−24.7553	−1.28178	−0.640890	+	0.767633i	$0.721434\pi$
$374$	1.50871	0.0780135
$375$	−1.41587	−0.0731150
$376$	−2.87389	−0.148209
$377$	−4.16351	−0.214432
$378$	−11.6878	−0.601154
$379$	−13.5596	−0.696511	−0.348256	−	0.937400i	$-0.613226\pi$
$379$	−13.5596	−0.696511	−0.348256	+	0.937400i	$0.613226\pi$
$380$	−0.722882	−0.0370831
$381$	−20.8037	−1.06581
$382$	3.66734	0.187637
$383$	12.4858	0.637995	0.318998	−	0.947756i	$-0.396654\pi$
$383$	12.4858	0.637995	0.318998	+	0.947756i	$0.396654\pi$
$384$	1.41587	0.0722531
$385$	−1.43188	−0.0729754
$386$	−8.25428	−0.420132
$387$	−5.04202	−0.256300
$388$	−10.8879	−0.552751
$389$	13.1633	0.667404	0.333702	−	0.942679i	$-0.391702\pi$
$389$	13.1633	0.667404	0.333702	+	0.942679i	$0.391702\pi$
$390$	3.04301	0.154089
$391$	15.7528	0.796652
$392$	−2.73112	−0.137942
$393$	28.5348	1.43939
$394$	−22.0096	−1.10883
$395$	5.78572	0.291111
$396$	−0.689786	−0.0346631
$397$	13.2207	0.663529	0.331764	−	0.943362i	$-0.392356\pi$
$397$	13.2207	0.663529	0.331764	+	0.943362i	$0.392356\pi$
$398$	24.0436	1.20520
$399$	2.11469	0.105867
$400$	1.00000	0.0500000
$401$	−4.13155	−0.206320	−0.103160	−	0.994665i	$-0.532895\pi$
$401$	−4.13155	−0.206320	−0.103160	+	0.994665i	$0.532895\pi$
$402$	15.7027	0.783178
$403$	−13.3358	−0.664304
$404$	−1.75104	−0.0871173
$405$	5.02335	0.249612
$406$	4.00253	0.198642
$407$	−0.565249	−0.0280183
$408$	3.08232	0.152598
$409$	5.43209	0.268600	0.134300	−	0.990941i	$-0.457121\pi$
$409$	5.43209	0.268600	0.134300	+	0.990941i	$0.457121\pi$
$410$	−2.04076	−0.100786
$411$	−4.07301	−0.200907
$412$	17.7226	0.873132
$413$	−6.84126	−0.336636
$414$	−7.20221	−0.353969
$415$	−6.17404	−0.303072
$416$	−2.14922	−0.105374
$417$	19.4854	0.954206
$418$	0.500976	0.0245035
$419$	−10.5230	−0.514080	−0.257040	−	0.966401i	$-0.582747\pi$
$419$	−10.5230	−0.514080	−0.257040	+	0.966401i	$0.582747\pi$
$420$	−2.92536	−0.142743
$421$	2.63413	0.128380	0.0641899	−	0.997938i	$-0.479554\pi$
$421$	2.63413	0.128380	0.0641899	+	0.997938i	$0.479554\pi$
$422$	10.9323	0.532175
$423$	2.86045	0.139080
$424$	−2.22421	−0.108017
$425$	2.17699	0.105600
$426$	−3.47464	−0.168347
$427$	17.6447	0.853885
$428$	17.2133	0.832038
$429$	−2.10889	−0.101818
$430$	−5.06569	−0.244289
$431$	38.3675	1.84810	0.924049	−	0.382273i	$-0.124859\pi$
$431$	38.3675	1.84810	0.924049	+	0.382273i	$0.124859\pi$
$432$	−5.65684	−0.272165
$433$	21.9841	1.05649	0.528244	−	0.849093i	$-0.322851\pi$
$433$	21.9841	1.05649	0.528244	+	0.849093i	$0.322851\pi$
$434$	12.8202	0.615390
$435$	−2.74283	−0.131509
$436$	6.77532	0.324479
$437$	5.23080	0.250223
$438$	−2.26341	−0.108150
$439$	−17.4418	−0.832450	−0.416225	−	0.909262i	$-0.636647\pi$
$439$	−17.4418	−0.832450	−0.416225	+	0.909262i	$0.636647\pi$
$440$	−0.693026	−0.0330387
$441$	2.71835	0.129445
$442$	−4.67884	−0.222550
$443$	−26.1819	−1.24394	−0.621970	−	0.783041i	$-0.713668\pi$
$443$	−26.1819	−1.24394	−0.621970	+	0.783041i	$0.713668\pi$
$444$	−1.15481	−0.0548051
$445$	−5.59992	−0.265462
$446$	2.47659	0.117270
$447$	29.0689	1.37491
$448$	2.06613	0.0976154
$449$	−3.73111	−0.176082	−0.0880411	−	0.996117i	$-0.528061\pi$
$449$	−3.73111	−0.176082	−0.0880411	+	0.996117i	$0.528061\pi$
$450$	−0.995326	−0.0469201
$451$	1.41430	0.0665966
$452$	1.35435	0.0637032
$453$	−9.88598	−0.464484
$454$	−18.3683	−0.862069
$455$	4.44057	0.208177
$456$	1.02350	0.0479300
$457$	−16.9678	−0.793720	−0.396860	−	0.917879i	$-0.629900\pi$
$457$	−16.9678	−0.793720	−0.396860	+	0.917879i	$0.629900\pi$
$458$	−16.8398	−0.786874
$459$	−12.3149	−0.574810
$460$	−7.23604	−0.337382
$461$	−9.68521	−0.451085	−0.225543	−	0.974233i	$-0.572416\pi$
$461$	−9.68521	−0.451085	−0.225543	+	0.974233i	$0.572416\pi$
$462$	2.02735	0.0943208
$463$	−16.2512	−0.755256	−0.377628	−	0.925957i	$-0.623260\pi$
$463$	−16.2512	−0.755256	−0.377628	+	0.925957i	$0.623260\pi$
$464$	1.93721	0.0899329
$465$	−8.78536	−0.407411
$466$	7.03142	0.325724
$467$	6.91105	0.319805	0.159903	−	0.987133i	$-0.448882\pi$
$467$	6.91105	0.319805	0.159903	+	0.987133i	$0.448882\pi$
$468$	2.13918	0.0988836
$469$	22.9144	1.05809
$470$	2.87389	0.132562
$471$	12.8644	0.592759
$472$	−3.31115	−0.152408
$473$	3.51066	0.161420
$474$	−8.19180	−0.376262
$475$	0.722882	0.0331681
$476$	4.49794	0.206163
$477$	2.21381	0.101363
$478$	−13.0641	−0.597536
$479$	28.7121	1.31189	0.655944	−	0.754810i	$-0.272271\pi$
$479$	28.7121	1.31189	0.655944	+	0.754810i	$0.272271\pi$
$480$	−1.41587	−0.0646251
$481$	1.75296	0.0799281
$482$	−9.38159	−0.427320
$483$	21.1680	0.963177
$484$	−10.5197	−0.478169
$485$	10.8879	0.494396
$486$	9.85814	0.447174
$487$	1.48753	0.0674066	0.0337033	−	0.999432i	$-0.489270\pi$
$487$	1.48753	0.0674066	0.0337033	+	0.999432i	$0.489270\pi$
$488$	8.53996	0.386586
$489$	20.6325	0.933033
$490$	2.73112	0.123379
$491$	5.09667	0.230010	0.115005	−	0.993365i	$-0.463312\pi$
$491$	5.09667	0.230010	0.115005	+	0.993365i	$0.463312\pi$
$492$	2.88944	0.130266
$493$	4.21729	0.189937
$494$	−1.55364	−0.0699014
$495$	0.689786	0.0310036
$496$	6.20494	0.278610
$497$	−5.07043	−0.227440
$498$	8.74161	0.391721
$499$	−28.6710	−1.28349	−0.641745	−	0.766918i	$-0.721789\pi$
$499$	−28.6710	−1.28349	−0.641745	+	0.766918i	$0.721789\pi$
$500$	−1.00000	−0.0447214
$501$	−15.8643	−0.708765
$502$	−14.8197	−0.661433
$503$	24.4158	1.08865	0.544323	−	0.838876i	$-0.316786\pi$
$503$	24.4158	1.08865	0.544323	+	0.838876i	$0.316786\pi$
$504$	−2.05647	−0.0916025
$505$	1.75104	0.0779201
$506$	5.01476	0.222933
$507$	−11.8661	−0.526993
$508$	−14.6933	−0.651909
$509$	−29.0429	−1.28730	−0.643651	−	0.765319i	$-0.722581\pi$
$509$	−29.0429	−1.28730	−0.643651	+	0.765319i	$0.722581\pi$
$510$	−3.08232	−0.136488
$511$	−3.30293	−0.146113
$512$	1.00000	0.0441942
$513$	−4.08923	−0.180544
$514$	17.0719	0.753008
$515$	−17.7226	−0.780953
$516$	7.17234	0.315745
$517$	−1.99168	−0.0875939
$518$	−1.68518	−0.0740427
$519$	−20.9252	−0.918516
$520$	2.14922	0.0942497
$521$	2.73703	0.119912	0.0599558	−	0.998201i	$-0.480904\pi$
$521$	2.73703	0.119912	0.0599558	+	0.998201i	$0.480904\pi$
$522$	−1.92816	−0.0843932
$523$	−12.8267	−0.560873	−0.280437	−	0.959873i	$-0.590479\pi$
$523$	−12.8267	−0.560873	−0.280437	+	0.959873i	$0.590479\pi$
$524$	20.1536	0.880413
$525$	2.92536	0.127673
$526$	8.40937	0.366666
$527$	13.5081	0.588422
$528$	0.981231	0.0427026
$529$	29.3602	1.27653
$530$	2.22421	0.0966134
$531$	3.29567	0.143020
$532$	1.49357	0.0647544
$533$	−4.38604	−0.189981
$534$	7.92873	0.343110
$535$	−17.2133	−0.744197
$536$	11.0905	0.479037
$537$	−6.76278	−0.291836
$538$	−26.1346	−1.12674
$539$	−1.89273	−0.0815258
$540$	5.65684	0.243432
$541$	−21.0373	−0.904464	−0.452232	−	0.891900i	$-0.649372\pi$
$541$	−21.0373	−0.904464	−0.452232	+	0.891900i	$0.649372\pi$
$542$	−17.0311	−0.731550
$543$	−12.8189	−0.550110
$544$	2.17699	0.0933377
$545$	−6.77532	−0.290223
$546$	−6.28725	−0.269070
$547$	0.679703	0.0290620	0.0145310	−	0.999894i	$-0.495374\pi$
$547$	0.679703	0.0290620	0.0145310	+	0.999894i	$0.495374\pi$
$548$	−2.87670	−0.122886
$549$	−8.50004	−0.362773
$550$	0.693026	0.0295507
$551$	1.40038	0.0596581
$552$	10.2453	0.436067
$553$	−11.9540	−0.508337
$554$	−22.3005	−0.947457
$555$	1.15481	0.0490191
$556$	13.7622	0.583648
$557$	−4.30300	−0.182324	−0.0911620	−	0.995836i	$-0.529058\pi$
$557$	−4.30300	−0.182324	−0.0911620	+	0.995836i	$0.529058\pi$
$558$	−6.17594	−0.261448
$559$	−10.8873	−0.460484
$560$	−2.06613	−0.0873098
$561$	2.13613	0.0901875
$562$	11.5379	0.486696
$563$	−10.1342	−0.427105	−0.213552	−	0.976932i	$-0.568503\pi$
$563$	−10.1342	−0.427105	−0.213552	+	0.976932i	$0.568503\pi$
$564$	−4.06904	−0.171337
$565$	−1.35435	−0.0569779
$566$	1.04795	0.0440488
$567$	−10.3789	−0.435872
$568$	−2.45407	−0.102971
$569$	11.4107	0.478362	0.239181	−	0.970975i	$-0.423121\pi$
$569$	11.4107	0.478362	0.239181	+	0.970975i	$0.423121\pi$
$570$	−1.02350	−0.0428699
$571$	−26.6501	−1.11527	−0.557635	−	0.830086i	$-0.688291\pi$
$571$	−26.6501	−1.11527	−0.557635	+	0.830086i	$0.688291\pi$
$572$	−1.48947	−0.0622778
$573$	5.19245	0.216918
$574$	4.21646	0.175992
$575$	7.23604	0.301764
$576$	−0.995326	−0.0414719
$577$	−3.48014	−0.144880	−0.0724400	−	0.997373i	$-0.523079\pi$
$577$	−3.48014	−0.144880	−0.0724400	+	0.997373i	$0.523079\pi$
$578$	−12.2607	−0.509978
$579$	−11.6870	−0.485693
$580$	−1.93721	−0.0804384
$581$	12.7564	0.529223
$582$	−15.4159	−0.639008
$583$	−1.54143	−0.0638396
$584$	−1.59861	−0.0661508
$585$	−2.13918	−0.0884441
$586$	−16.6303	−0.686993
$587$	−17.2767	−0.713087	−0.356543	−	0.934279i	$-0.616045\pi$
$587$	−17.2767	−0.713087	−0.356543	+	0.934279i	$0.616045\pi$
$588$	−3.86689	−0.159468
$589$	4.48544	0.184820
$590$	3.31115	0.136318
$591$	−31.1626	−1.28186
$592$	−0.815624	−0.0335220
$593$	−38.6787	−1.58835	−0.794173	−	0.607692i	$-0.792095\pi$
$593$	−38.6787	−1.58835	−0.794173	+	0.607692i	$0.792095\pi$
$594$	−3.92034	−0.160853
$595$	−4.49794	−0.184398
$596$	20.5309	0.840977
$597$	34.0425	1.39327
$598$	−15.5519	−0.635963
$599$	17.8002	0.727296	0.363648	−	0.931536i	$-0.381531\pi$
$599$	17.8002	0.727296	0.363648	+	0.931536i	$0.381531\pi$
$600$	1.41587	0.0578025
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	10.4664	0.426578
$603$	−11.0387	−0.449530
$604$	−6.98229	−0.284105
$605$	10.5197	0.427687
$606$	−2.47923	−0.100712
$607$	7.38581	0.299781	0.149890	−	0.988703i	$-0.452108\pi$
$607$	7.38581	0.299781	0.149890	+	0.988703i	$0.452108\pi$
$608$	0.722882	0.0293168
$609$	5.66704	0.229640
$610$	−8.53996	−0.345773
$611$	6.17663	0.249880
$612$	−2.16681	−0.0875883
$613$	−25.6651	−1.03660	−0.518302	−	0.855198i	$-0.673436\pi$
$613$	−25.6651	−1.03660	−0.518302	+	0.855198i	$0.673436\pi$
$614$	20.3313	0.820506
$615$	−2.88944	−0.116513
$616$	1.43188	0.0576921
$617$	−24.8641	−1.00099	−0.500496	−	0.865739i	$-0.666849\pi$
$617$	−24.8641	−1.00099	−0.500496	+	0.865739i	$0.666849\pi$
$618$	25.0929	1.00938
$619$	21.6600	0.870591	0.435295	−	0.900288i	$-0.356644\pi$
$619$	21.6600	0.870591	0.435295	+	0.900288i	$0.356644\pi$
$620$	−6.20494	−0.249197
$621$	−40.9331	−1.64259
$622$	26.5179	1.06327
$623$	11.5701	0.463548
$624$	−3.04301	−0.121818
$625$	1.00000	0.0400000
$626$	−3.17313	−0.126824
$627$	0.709315	0.0283273
$628$	9.08588	0.362566
$629$	−1.77561	−0.0707981
$630$	2.05647	0.0819317
$631$	27.6216	1.09960	0.549800	−	0.835296i	$-0.314704\pi$
$631$	27.6216	1.09960	0.549800	+	0.835296i	$0.314704\pi$
$632$	−5.78572	−0.230144
$633$	15.4786	0.615220
$634$	−18.5584	−0.737049
$635$	14.6933	0.583085
$636$	−3.14918	−0.124873
$637$	5.86978	0.232569
$638$	1.34254	0.0531516
$639$	2.44260	0.0966278
$640$	−1.00000	−0.0395285
$641$	−10.0682	−0.397671	−0.198835	−	0.980033i	$-0.563716\pi$
$641$	−10.0682	−0.397671	−0.198835	+	0.980033i	$0.563716\pi$
$642$	24.3718	0.961877
$643$	41.0823	1.62013	0.810063	−	0.586343i	$-0.199433\pi$
$643$	41.0823	1.62013	0.810063	+	0.586343i	$0.199433\pi$
$644$	14.9506	0.589135
$645$	−7.17234	−0.282411
$646$	1.57371	0.0619167
$647$	17.6668	0.694552	0.347276	−	0.937763i	$-0.387107\pi$
$647$	17.6668	0.694552	0.347276	+	0.937763i	$0.387107\pi$
$648$	−5.02335	−0.197336
$649$	−2.29471	−0.0900753
$650$	−2.14922	−0.0842995
$651$	18.1517	0.711421
$652$	14.5723	0.570697
$653$	40.4316	1.58221	0.791106	−	0.611679i	$-0.209506\pi$
$653$	40.4316	1.58221	0.791106	+	0.611679i	$0.209506\pi$
$654$	9.59294	0.375114
$655$	−20.1536	−0.787466
$656$	2.04076	0.0796781
$657$	1.59113	0.0620761
$658$	−5.93782	−0.231480
$659$	−25.6785	−1.00029	−0.500146	−	0.865941i	$-0.666720\pi$
$659$	−25.6785	−1.00029	−0.500146	+	0.865941i	$0.666720\pi$
$660$	−0.981231	−0.0381944
$661$	−35.9623	−1.39877	−0.699386	−	0.714744i	$-0.746543\pi$
$661$	−35.9623	−1.39877	−0.699386	+	0.714744i	$0.746543\pi$
$662$	11.2400	0.436853
$663$	−6.62461	−0.257278
$664$	6.17404	0.239599
$665$	−1.49357	−0.0579181
$666$	0.811812	0.0314571
$667$	14.0177	0.542769
$668$	−11.2047	−0.433522
$669$	3.50652	0.135570
$670$	−11.0905	−0.428464
$671$	5.91841	0.228478
$672$	2.92536	0.112848
$673$	−1.97935	−0.0762984	−0.0381492	−	0.999272i	$-0.512146\pi$
$673$	−1.97935	−0.0762984	−0.0381492	+	0.999272i	$0.512146\pi$
$674$	−12.1914	−0.469595
$675$	−5.65684	−0.217732
$676$	−8.38083	−0.322340
$677$	19.2161	0.738536	0.369268	−	0.929323i	$-0.379608\pi$
$677$	19.2161	0.738536	0.369268	+	0.929323i	$0.379608\pi$
$678$	1.91758	0.0736441
$679$	−22.4959	−0.863312
$680$	−2.17699	−0.0834838
$681$	−26.0071	−0.996594
$682$	4.30019	0.164663
$683$	−6.72223	−0.257219	−0.128609	−	0.991695i	$-0.541051\pi$
$683$	−6.72223	−0.257219	−0.128609	+	0.991695i	$0.541051\pi$
$684$	−0.719503	−0.0275109
$685$	2.87670	0.109913
$686$	−20.1057	−0.767640
$687$	−23.8429	−0.909665
$688$	5.06569	0.193128
$689$	4.78032	0.182116
$690$	−10.2453	−0.390030
$691$	5.83669	0.222038	0.111019	−	0.993818i	$-0.464589\pi$
$691$	5.83669	0.222038	0.111019	+	0.993818i	$0.464589\pi$
$692$	−14.7791	−0.561818
$693$	−1.42519	−0.0541384
$694$	−32.0304	−1.21586
$695$	−13.7622	−0.522030
$696$	2.74283	0.103967
$697$	4.44271	0.168279
$698$	13.4376	0.508622
$699$	9.95554	0.376553
$700$	2.06613	0.0780923
$701$	−30.9321	−1.16829	−0.584146	−	0.811649i	$-0.698570\pi$
$701$	−30.9321	−1.16829	−0.584146	+	0.811649i	$0.698570\pi$
$702$	12.1578	0.458868
$703$	−0.589601	−0.0222372
$704$	0.693026	0.0261194
$705$	4.06904	0.153249
$706$	−2.11720	−0.0796820
$707$	−3.61787	−0.136064
$708$	−4.68814	−0.176191
$709$	−43.9891	−1.65204	−0.826022	−	0.563637i	$-0.809402\pi$
$709$	−43.9891	−1.65204	−0.826022	+	0.563637i	$0.809402\pi$
$710$	2.45407	0.0920997
$711$	5.75868	0.215967
$712$	5.59992	0.209866
$713$	44.8992	1.68149
$714$	6.36848	0.238334
$715$	1.48947	0.0557029
$716$	−4.77643	−0.178504
$717$	−18.4970	−0.690782
$718$	33.8442	1.26305
$719$	−23.5042	−0.876559	−0.438280	−	0.898839i	$-0.644412\pi$
$719$	−23.5042	−0.876559	−0.438280	+	0.898839i	$0.644412\pi$
$720$	0.995326	0.0370936
$721$	36.6172	1.36370
$722$	−18.4774	−0.687659
$723$	−13.2831	−0.494003
$724$	−9.05373	−0.336479
$725$	1.93721	0.0719463
$726$	−14.8945	−0.552787
$727$	26.5100	0.983200	0.491600	−	0.870821i	$-0.336412\pi$
$727$	26.5100	0.983200	0.491600	+	0.870821i	$0.336412\pi$
$728$	−4.44057	−0.164579
$729$	29.0278	1.07511
$730$	1.59861	0.0591671
$731$	11.0280	0.407884
$732$	12.0914	0.446912
$733$	−9.37663	−0.346334	−0.173167	−	0.984892i	$-0.555400\pi$
$733$	−9.37663	−0.346334	−0.173167	+	0.984892i	$0.555400\pi$
$734$	0.437345	0.0161427
$735$	3.86689	0.142632
$736$	7.23604	0.266724
$737$	7.68601	0.283118
$738$	−2.03122	−0.0747701
$739$	−35.5119	−1.30633	−0.653164	−	0.757216i	$-0.726559\pi$
$739$	−35.5119	−1.30633	−0.653164	+	0.757216i	$0.726559\pi$
$740$	0.815624	0.0299829
$741$	−2.19974	−0.0808095
$742$	−4.59550	−0.168706
$743$	38.1387	1.39917	0.699587	−	0.714548i	$-0.253367\pi$
$743$	38.1387	1.39917	0.699587	+	0.714548i	$0.253367\pi$
$744$	8.78536	0.322087
$745$	−20.5309	−0.752193
$746$	−24.7553	−0.906355
$747$	−6.14518	−0.224840
$748$	1.50871	0.0551639
$749$	35.5650	1.29952
$750$	−1.41587	−0.0517001
$751$	48.8588	1.78288	0.891441	−	0.453137i	$-0.149695\pi$
$751$	48.8588	1.78288	0.891441	+	0.453137i	$0.149695\pi$
$752$	−2.87389	−0.104800
$753$	−20.9826	−0.764650
$754$	−4.16351	−0.151626
$755$	6.98229	0.254111
$756$	−11.6878	−0.425080
$757$	−52.1715	−1.89621	−0.948103	−	0.317963i	$-0.897001\pi$
$757$	−52.1715	−1.89621	−0.948103	+	0.317963i	$0.897001\pi$
$758$	−13.5596	−0.492508
$759$	7.10022	0.257722
$760$	−0.722882	−0.0262217
$761$	−25.5439	−0.925967	−0.462983	−	0.886367i	$-0.653221\pi$
$761$	−25.5439	−0.925967	−0.462983	+	0.886367i	$0.653221\pi$
$762$	−20.8037	−0.753639
$763$	13.9987	0.506786
$764$	3.66734	0.132680
$765$	2.16681	0.0783413
$766$	12.4858	0.451131
$767$	7.11641	0.256959
$768$	1.41587	0.0510906
$769$	−28.2660	−1.01930	−0.509648	−	0.860383i	$-0.670224\pi$
$769$	−28.2660	−1.01930	−0.509648	+	0.860383i	$0.670224\pi$
$770$	−1.43188	−0.0516014
$771$	24.1715	0.870514
$772$	−8.25428	−0.297078
$773$	26.5979	0.956661	0.478330	−	0.878180i	$-0.341242\pi$
$773$	26.5979	0.956661	0.478330	+	0.878180i	$0.341242\pi$
$774$	−5.04202	−0.181232
$775$	6.20494	0.222888
$776$	−10.8879	−0.390854
$777$	−2.38599	−0.0855971
$778$	13.1633	0.471926
$779$	1.47523	0.0528555
$780$	3.04301	0.108957
$781$	−1.70074	−0.0608571
$782$	15.7528	0.563318
$783$	−10.9585	−0.391625
$784$	−2.73112	−0.0975398
$785$	−9.08588	−0.324289
$786$	28.5348	1.01780
$787$	−36.8847	−1.31480	−0.657398	−	0.753544i	$-0.728343\pi$
$787$	−36.8847	−1.31480	−0.657398	+	0.753544i	$0.728343\pi$
$788$	−22.0096	−0.784060
$789$	11.9065	0.423884
$790$	5.78572	0.205847
$791$	2.79826	0.0994946
$792$	−0.689786	−0.0245105
$793$	−18.3543	−0.651780
$794$	13.2207	0.469186
$795$	3.14918	0.111690
$796$	24.0436	0.852203
$797$	−5.55923	−0.196918	−0.0984589	−	0.995141i	$-0.531391\pi$
$797$	−5.55923	−0.196918	−0.0984589	+	0.995141i	$0.531391\pi$
$798$	2.11469	0.0748592
$799$	−6.25642	−0.221336
$800$	1.00000	0.0353553
$801$	−5.57374	−0.196939
$802$	−4.13155	−0.145890
$803$	−1.10788	−0.0390961
$804$	15.7027	0.553791
$805$	−14.9506	−0.526939
$806$	−13.3358	−0.469734
$807$	−37.0031	−1.30257
$808$	−1.75104	−0.0616013
$809$	−39.6500	−1.39402	−0.697009	−	0.717062i	$-0.745486\pi$
$809$	−39.6500	−1.39402	−0.697009	+	0.717062i	$0.745486\pi$
$810$	5.02335	0.176503
$811$	0.765038	0.0268641	0.0134321	−	0.999910i	$-0.495724\pi$
$811$	0.765038	0.0268641	0.0134321	+	0.999910i	$0.495724\pi$
$812$	4.00253	0.140461
$813$	−24.1138	−0.845708
$814$	−0.565249	−0.0198120
$815$	−14.5723	−0.510447
$816$	3.08232	0.107903
$817$	3.66190	0.128114
$818$	5.43209	0.189929
$819$	4.41982	0.154441
$820$	−2.04076	−0.0712663
$821$	42.4215	1.48052	0.740261	−	0.672320i	$-0.234702\pi$
$821$	42.4215	1.48052	0.740261	+	0.672320i	$0.234702\pi$
$822$	−4.07301	−0.142063
$823$	−27.5115	−0.958992	−0.479496	−	0.877544i	$-0.659181\pi$
$823$	−27.5115	−0.958992	−0.479496	+	0.877544i	$0.659181\pi$
$824$	17.7226	0.617397
$825$	0.981231	0.0341621
$826$	−6.84126	−0.238038
$827$	−0.281703	−0.00979577	−0.00489789	−	0.999988i	$-0.501559\pi$
$827$	−0.281703	−0.00979577	−0.00489789	+	0.999988i	$0.501559\pi$
$828$	−7.20221	−0.250294
$829$	−36.1179	−1.25443	−0.627213	−	0.778848i	$-0.715804\pi$
$829$	−36.1179	−1.25443	−0.627213	+	0.778848i	$0.715804\pi$
$830$	−6.17404	−0.214304
$831$	−31.5745	−1.09531
$832$	−2.14922	−0.0745110
$833$	−5.94561	−0.206003
$834$	19.4854	0.674725
$835$	11.2047	0.387754
$836$	0.500976	0.0173266
$837$	−35.1004	−1.21325
$838$	−10.5230	−0.363509
$839$	−37.7926	−1.30475	−0.652373	−	0.757898i	$-0.726226\pi$
$839$	−37.7926	−1.30475	−0.652373	+	0.757898i	$0.726226\pi$
$840$	−2.92536	−0.100934
$841$	−25.2472	−0.870593
$842$	2.63413	0.0907782
$843$	16.3361	0.562644
$844$	10.9323	0.376305
$845$	8.38083	0.288309
$846$	2.86045	0.0983444
$847$	−21.7351	−0.746826
$848$	−2.22421	−0.0763796
$849$	1.48376	0.0509226
$850$	2.17699	0.0746701
$851$	−5.90189	−0.202314
$852$	−3.47464	−0.119039
$853$	12.8577	0.440238	0.220119	−	0.975473i	$-0.429355\pi$
$853$	12.8577	0.440238	0.220119	+	0.975473i	$0.429355\pi$
$854$	17.6447	0.603788
$855$	0.719503	0.0246065
$856$	17.2133	0.588340
$857$	35.9043	1.22647	0.613234	−	0.789902i	$-0.289868\pi$
$857$	35.9043	1.22647	0.613234	+	0.789902i	$0.289868\pi$
$858$	−2.10889	−0.0719962
$859$	−20.7291	−0.707267	−0.353633	−	0.935384i	$-0.615054\pi$
$859$	−20.7291	−0.707267	−0.353633	+	0.935384i	$0.615054\pi$
$860$	−5.06569	−0.172739
$861$	5.96994	0.203455
$862$	38.3675	1.30680
$863$	1.27846	0.0435192	0.0217596	−	0.999763i	$-0.493073\pi$
$863$	1.27846	0.0435192	0.0217596	+	0.999763i	$0.493073\pi$
$864$	−5.65684	−0.192450
$865$	14.7791	0.502505
$866$	21.9841	0.747050
$867$	−17.3595	−0.589560
$868$	12.8202	0.435146
$869$	−4.00965	−0.136018
$870$	−2.74283	−0.0929908
$871$	−23.8360	−0.807653
$872$	6.77532	0.229441
$873$	10.8370	0.366778
$874$	5.23080	0.176935
$875$	−2.06613	−0.0698479
$876$	−2.26341	−0.0764736
$877$	−1.76598	−0.0596328	−0.0298164	−	0.999555i	$-0.509492\pi$
$877$	−1.76598	−0.0596328	−0.0298164	+	0.999555i	$0.509492\pi$
$878$	−17.4418	−0.588631
$879$	−23.5463	−0.794198
$880$	−0.693026	−0.0233619
$881$	42.9186	1.44596	0.722982	−	0.690867i	$-0.242771\pi$
$881$	42.9186	1.44596	0.722982	+	0.690867i	$0.242771\pi$
$882$	2.71835	0.0915316
$883$	−21.8477	−0.735235	−0.367617	−	0.929977i	$-0.619826\pi$
$883$	−21.8477	−0.735235	−0.367617	+	0.929977i	$0.619826\pi$
$884$	−4.67884	−0.157366
$885$	4.68814	0.157590
$886$	−26.1819	−0.879599
$887$	−49.0465	−1.64682	−0.823410	−	0.567447i	$-0.807931\pi$
$887$	−49.0465	−1.64682	−0.823410	+	0.567447i	$0.807931\pi$
$888$	−1.15481	−0.0387530
$889$	−30.3582	−1.01818
$890$	−5.59992	−0.187710
$891$	−3.48131	−0.116628
$892$	2.47659	0.0829225
$893$	−2.07748	−0.0695203
$894$	29.0689	0.972211
$895$	4.77643	0.159659
$896$	2.06613	0.0690245
$897$	−22.0193	−0.735205
$898$	−3.73111	−0.124509
$899$	12.0203	0.400899
$900$	−0.995326	−0.0331775
$901$	−4.84208	−0.161313
$902$	1.41430	0.0470909
$903$	14.8190	0.493145
$904$	1.35435	0.0450450
$905$	9.05373	0.300956
$906$	−9.88598	−0.328440
$907$	12.9473	0.429909	0.214955	−	0.976624i	$-0.431040\pi$
$907$	12.9473	0.429909	0.214955	+	0.976624i	$0.431040\pi$
$908$	−18.3683	−0.609575
$909$	1.74285	0.0578067
$910$	4.44057	0.147204
$911$	8.52068	0.282303	0.141151	−	0.989988i	$-0.454920\pi$
$911$	8.52068	0.282303	0.141151	+	0.989988i	$0.454920\pi$
$912$	1.02350	0.0338916
$913$	4.27877	0.141607
$914$	−16.9678	−0.561245
$915$	−12.0914	−0.399730
$916$	−16.8398	−0.556404
$917$	41.6399	1.37507
$918$	−12.3149	−0.406452
$919$	17.4399	0.575288	0.287644	−	0.957737i	$-0.407128\pi$
$919$	17.4399	0.575288	0.287644	+	0.957737i	$0.407128\pi$
$920$	−7.23604	−0.238565
$921$	28.7865	0.948546
$922$	−9.68521	−0.318966
$923$	5.27435	0.173607
$924$	2.02735	0.0666949
$925$	−0.815624	−0.0268176
$926$	−16.2512	−0.534047
$927$	−17.6398	−0.579367
$928$	1.93721	0.0635921
$929$	−27.1204	−0.889790	−0.444895	−	0.895583i	$-0.646759\pi$
$929$	−27.1204	−0.889790	−0.444895	+	0.895583i	$0.646759\pi$
$930$	−8.78536	−0.288083
$931$	−1.97428	−0.0647043
$932$	7.03142	0.230322
$933$	37.5458	1.22919
$934$	6.91105	0.226137
$935$	−1.50871	−0.0493401
$936$	2.13918	0.0699212
$937$	−32.4493	−1.06007	−0.530035	−	0.847975i	$-0.677821\pi$
$937$	−32.4493	−1.06007	−0.530035	+	0.847975i	$0.677821\pi$
$938$	22.9144	0.748183
$939$	−4.49272	−0.146614
$940$	2.87389	0.0937358
$941$	45.6524	1.48822	0.744112	−	0.668055i	$-0.232873\pi$
$941$	45.6524	1.48822	0.744112	+	0.668055i	$0.232873\pi$
$942$	12.8644	0.419144
$943$	14.7670	0.480879
$944$	−3.31115	−0.107769
$945$	11.6878	0.380203
$946$	3.51066	0.114141
$947$	3.21953	0.104621	0.0523103	−	0.998631i	$-0.483342\pi$
$947$	3.21953	0.104621	0.0523103	+	0.998631i	$0.483342\pi$
$948$	−8.19180	−0.266057
$949$	3.43577	0.111530
$950$	0.722882	0.0234534
$951$	−26.2762	−0.852065
$952$	4.49794	0.145779
$953$	26.8935	0.871167	0.435584	−	0.900148i	$-0.356542\pi$
$953$	26.8935	0.871167	0.435584	+	0.900148i	$0.356542\pi$
$954$	2.21381	0.0716747
$955$	−3.66734	−0.118672
$956$	−13.0641	−0.422522
$957$	1.90085	0.0614459
$958$	28.7121	0.927645
$959$	−5.94362	−0.191930
$960$	−1.41587	−0.0456969
$961$	7.50132	0.241978
$962$	1.75296	0.0565177
$963$	−17.1329	−0.552099
$964$	−9.38159	−0.302161
$965$	8.25428	0.265715
$966$	21.1680	0.681069
$967$	−39.9841	−1.28580	−0.642901	−	0.765950i	$-0.722269\pi$
$967$	−39.9841	−1.28580	−0.642901	+	0.765950i	$0.722269\pi$
$968$	−10.5197	−0.338116
$969$	2.22816	0.0715788
$970$	10.8879	0.349591
$971$	41.3880	1.32820	0.664101	−	0.747643i	$-0.268814\pi$
$971$	41.3880	1.32820	0.664101	+	0.747643i	$0.268814\pi$
$972$	9.85814	0.316200
$973$	28.4345	0.911568
$974$	1.48753	0.0476637
$975$	−3.04301	−0.0974544
$976$	8.53996	0.273357
$977$	6.28911	0.201207	0.100603	−	0.994927i	$-0.467923\pi$
$977$	6.28911	0.201207	0.100603	+	0.994927i	$0.467923\pi$
$978$	20.6325	0.659754
$979$	3.88089	0.124034
$980$	2.73112	0.0872423
$981$	−6.74365	−0.215308
$982$	5.09667	0.162641
$983$	14.9253	0.476043	0.238022	−	0.971260i	$-0.423501\pi$
$983$	14.9253	0.476043	0.238022	+	0.971260i	$0.423501\pi$
$984$	2.88944	0.0921119
$985$	22.0096	0.701285
$986$	4.21729	0.134306
$987$	−8.40715	−0.267602
$988$	−1.55364	−0.0494278
$989$	36.6555	1.16558
$990$	0.689786	0.0219228
$991$	−5.99151	−0.190326	−0.0951632	−	0.995462i	$-0.530337\pi$
$991$	−5.99151	−0.190326	−0.0951632	+	0.995462i	$0.530337\pi$
$992$	6.20494	0.197007
$993$	15.9143	0.505024
$994$	−5.07043	−0.160824
$995$	−24.0436	−0.762233
$996$	8.74161	0.276988
$997$	21.3416	0.675896	0.337948	−	0.941165i	$-0.390267\pi$
$997$	21.3416	0.675896	0.337948	+	0.941165i	$0.390267\pi$
$998$	−28.6710	−0.907565
$999$	4.61386	0.145976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.20	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.20	✓	28	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.41587 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.41587 q^{6} +2.06613 q^{7} +1.00000 q^{8} -0.995326 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.41587 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.41587 q^{6} +2.06613 q^{7} +1.00000 q^{8} -0.995326 q^{9} -1.00000 q^{10} +0.693026 q^{11} +1.41587 q^{12} -2.14922 q^{13} +2.06613 q^{14} -1.41587 q^{15} +1.00000 q^{16} +2.17699 q^{17} -0.995326 q^{18} +0.722882 q^{19} -1.00000 q^{20} +2.92536 q^{21} +0.693026 q^{22} +7.23604 q^{23} +1.41587 q^{24} +1.00000 q^{25} -2.14922 q^{26} -5.65684 q^{27} +2.06613 q^{28} +1.93721 q^{29} -1.41587 q^{30} +6.20494 q^{31} +1.00000 q^{32} +0.981231 q^{33} +2.17699 q^{34} -2.06613 q^{35} -0.995326 q^{36} -0.815624 q^{37} +0.722882 q^{38} -3.04301 q^{39} -1.00000 q^{40} +2.04076 q^{41} +2.92536 q^{42} +5.06569 q^{43} +0.693026 q^{44} +0.995326 q^{45} +7.23604 q^{46} -2.87389 q^{47} +1.41587 q^{48} -2.73112 q^{49} +1.00000 q^{50} +3.08232 q^{51} -2.14922 q^{52} -2.22421 q^{53} -5.65684 q^{54} -0.693026 q^{55} +2.06613 q^{56} +1.02350 q^{57} +1.93721 q^{58} -3.31115 q^{59} -1.41587 q^{60} +8.53996 q^{61} +6.20494 q^{62} -2.05647 q^{63} +1.00000 q^{64} +2.14922 q^{65} +0.981231 q^{66} +11.0905 q^{67} +2.17699 q^{68} +10.2453 q^{69} -2.06613 q^{70} -2.45407 q^{71} -0.995326 q^{72} -1.59861 q^{73} -0.815624 q^{74} +1.41587 q^{75} +0.722882 q^{76} +1.43188 q^{77} -3.04301 q^{78} -5.78572 q^{79} -1.00000 q^{80} -5.02335 q^{81} +2.04076 q^{82} +6.17404 q^{83} +2.92536 q^{84} -2.17699 q^{85} +5.06569 q^{86} +2.74283 q^{87} +0.693026 q^{88} +5.59992 q^{89} +0.995326 q^{90} -4.44057 q^{91} +7.23604 q^{92} +8.78536 q^{93} -2.87389 q^{94} -0.722882 q^{95} +1.41587 q^{96} -10.8879 q^{97} -2.73112 q^{98} -0.689786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * q^99

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