LMFDB - Embedded newform 6010.2.a.h.1.15

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			1.15
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.321033 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.321033 q^{6} -2.34471 q^{7} +1.00000 q^{8} -2.89694 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.321033 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.321033 q^{6} -2.34471 q^{7} +1.00000 q^{8} -2.89694 q^{9} -1.00000 q^{10} +4.30702 q^{11} +0.321033 q^{12} -0.151560 q^{13} -2.34471 q^{14} -0.321033 q^{15} +1.00000 q^{16} -2.90146 q^{17} -2.89694 q^{18} +0.850025 q^{19} -1.00000 q^{20} -0.752730 q^{21} +4.30702 q^{22} +1.17772 q^{23} +0.321033 q^{24} +1.00000 q^{25} -0.151560 q^{26} -1.89311 q^{27} -2.34471 q^{28} -6.06456 q^{29} -0.321033 q^{30} +3.37842 q^{31} +1.00000 q^{32} +1.38269 q^{33} -2.90146 q^{34} +2.34471 q^{35} -2.89694 q^{36} +3.84651 q^{37} +0.850025 q^{38} -0.0486558 q^{39} -1.00000 q^{40} +4.36256 q^{41} -0.752730 q^{42} +2.16365 q^{43} +4.30702 q^{44} +2.89694 q^{45} +1.17772 q^{46} -3.12847 q^{47} +0.321033 q^{48} -1.50232 q^{49} +1.00000 q^{50} -0.931464 q^{51} -0.151560 q^{52} +12.8478 q^{53} -1.89311 q^{54} -4.30702 q^{55} -2.34471 q^{56} +0.272886 q^{57} -6.06456 q^{58} +8.77318 q^{59} -0.321033 q^{60} +4.12343 q^{61} +3.37842 q^{62} +6.79249 q^{63} +1.00000 q^{64} +0.151560 q^{65} +1.38269 q^{66} +11.2919 q^{67} -2.90146 q^{68} +0.378086 q^{69} +2.34471 q^{70} +5.48369 q^{71} -2.89694 q^{72} -1.89647 q^{73} +3.84651 q^{74} +0.321033 q^{75} +0.850025 q^{76} -10.0987 q^{77} -0.0486558 q^{78} -7.14621 q^{79} -1.00000 q^{80} +8.08306 q^{81} +4.36256 q^{82} +12.8931 q^{83} -0.752730 q^{84} +2.90146 q^{85} +2.16365 q^{86} -1.94692 q^{87} +4.30702 q^{88} -3.45632 q^{89} +2.89694 q^{90} +0.355366 q^{91} +1.17772 q^{92} +1.08458 q^{93} -3.12847 q^{94} -0.850025 q^{95} +0.321033 q^{96} -6.67442 q^{97} -1.50232 q^{98} -12.4772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.321033	0.185348	0.0926741	−	0.995696i	$-0.470459\pi$
$3$	0.321033	0.185348	0.0926741	+	0.995696i	$0.470459\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.321033	0.131061
$7$	−2.34471	−0.886219	−0.443109	−	0.896468i	$-0.646125\pi$
$7$	−2.34471	−0.886219	−0.443109	+	0.896468i	$0.646125\pi$
$8$	1.00000	0.353553
$9$	−2.89694	−0.965646
$10$	−1.00000	−0.316228
$11$	4.30702	1.29862	0.649308	−	0.760525i	$-0.275059\pi$
$11$	4.30702	1.29862	0.649308	+	0.760525i	$0.275059\pi$
$12$	0.321033	0.0926741
$13$	−0.151560	−0.0420353	−0.0210176	−	0.999779i	$-0.506691\pi$
$13$	−0.151560	−0.0420353	−0.0210176	+	0.999779i	$0.506691\pi$
$14$	−2.34471	−0.626651
$15$	−0.321033	−0.0828903
$16$	1.00000	0.250000
$17$	−2.90146	−0.703708	−0.351854	−	0.936055i	$-0.614449\pi$
$17$	−2.90146	−0.703708	−0.351854	+	0.936055i	$0.614449\pi$
$18$	−2.89694	−0.682815
$19$	0.850025	0.195009	0.0975046	−	0.995235i	$-0.468914\pi$
$19$	0.850025	0.195009	0.0975046	+	0.995235i	$0.468914\pi$
$20$	−1.00000	−0.223607
$21$	−0.752730	−0.164259
$22$	4.30702	0.918260
$23$	1.17772	0.245571	0.122786	−	0.992433i	$-0.460817\pi$
$23$	1.17772	0.245571	0.122786	+	0.992433i	$0.460817\pi$
$24$	0.321033	0.0655305
$25$	1.00000	0.200000
$26$	−0.151560	−0.0297234
$27$	−1.89311	−0.364329
$28$	−2.34471	−0.443109
$29$	−6.06456	−1.12616	−0.563081	−	0.826402i	$-0.690384\pi$
$29$	−6.06456	−1.12616	−0.563081	+	0.826402i	$0.690384\pi$
$30$	−0.321033	−0.0586123
$31$	3.37842	0.606783	0.303391	−	0.952866i	$-0.401881\pi$
$31$	3.37842	0.606783	0.303391	+	0.952866i	$0.401881\pi$
$32$	1.00000	0.176777
$33$	1.38269	0.240696
$34$	−2.90146	−0.497597
$35$	2.34471	0.396329
$36$	−2.89694	−0.482823
$37$	3.84651	0.632363	0.316181	−	0.948699i	$-0.397599\pi$
$37$	3.84651	0.632363	0.316181	+	0.948699i	$0.397599\pi$
$38$	0.850025	0.137892
$39$	−0.0486558	−0.00779117
$40$	−1.00000	−0.158114
$41$	4.36256	0.681318	0.340659	−	0.940187i	$-0.389350\pi$
$41$	4.36256	0.681318	0.340659	+	0.940187i	$0.389350\pi$
$42$	−0.752730	−0.116149
$43$	2.16365	0.329953	0.164976	−	0.986298i	$-0.447245\pi$
$43$	2.16365	0.329953	0.164976	+	0.986298i	$0.447245\pi$
$44$	4.30702	0.649308
$45$	2.89694	0.431850
$46$	1.17772	0.173645
$47$	−3.12847	−0.456335	−0.228167	−	0.973622i	$-0.573273\pi$
$47$	−3.12847	−0.456335	−0.228167	+	0.973622i	$0.573273\pi$
$48$	0.321033	0.0463371
$49$	−1.50232	−0.214617
$50$	1.00000	0.141421
$51$	−0.931464	−0.130431
$52$	−0.151560	−0.0210176
$53$	12.8478	1.76478	0.882390	−	0.470520i	$-0.155933\pi$
$53$	12.8478	1.76478	0.882390	+	0.470520i	$0.155933\pi$
$54$	−1.89311	−0.257620
$55$	−4.30702	−0.580759
$56$	−2.34471	−0.313326
$57$	0.272886	0.0361446
$58$	−6.06456	−0.796316
$59$	8.77318	1.14217	0.571086	−	0.820891i	$-0.306522\pi$
$59$	8.77318	1.14217	0.571086	+	0.820891i	$0.306522\pi$
$60$	−0.321033	−0.0414451
$61$	4.12343	0.527951	0.263976	−	0.964529i	$-0.414966\pi$
$61$	4.12343	0.527951	0.263976	+	0.964529i	$0.414966\pi$
$62$	3.37842	0.429060
$63$	6.79249	0.855773
$64$	1.00000	0.125000
$65$	0.151560	0.0187988
$66$	1.38269	0.170198
$67$	11.2919	1.37953	0.689763	−	0.724035i	$-0.257715\pi$
$67$	11.2919	1.37953	0.689763	+	0.724035i	$0.257715\pi$
$68$	−2.90146	−0.351854
$69$	0.378086	0.0455162
$70$	2.34471	0.280247
$71$	5.48369	0.650794	0.325397	−	0.945578i	$-0.394502\pi$
$71$	5.48369	0.650794	0.325397	+	0.945578i	$0.394502\pi$
$72$	−2.89694	−0.341407
$73$	−1.89647	−0.221965	−0.110982	−	0.993822i	$-0.535400\pi$
$73$	−1.89647	−0.221965	−0.110982	+	0.993822i	$0.535400\pi$
$74$	3.84651	0.447148
$75$	0.321033	0.0370697
$76$	0.850025	0.0975046
$77$	−10.0987	−1.15086
$78$	−0.0486558	−0.00550919
$79$	−7.14621	−0.804012	−0.402006	−	0.915637i	$-0.631687\pi$
$79$	−7.14621	−0.804012	−0.402006	+	0.915637i	$0.631687\pi$
$80$	−1.00000	−0.111803
$81$	8.08306	0.898118
$82$	4.36256	0.481765
$83$	12.8931	1.41520	0.707602	−	0.706611i	$-0.249777\pi$
$83$	12.8931	1.41520	0.707602	+	0.706611i	$0.249777\pi$
$84$	−0.752730	−0.0821295
$85$	2.90146	0.314708
$86$	2.16365	0.233312
$87$	−1.94692	−0.208732
$88$	4.30702	0.459130
$89$	−3.45632	−0.366369	−0.183184	−	0.983079i	$-0.558641\pi$
$89$	−3.45632	−0.366369	−0.183184	+	0.983079i	$0.558641\pi$
$90$	2.89694	0.305364
$91$	0.355366	0.0372525
$92$	1.17772	0.122786
$93$	1.08458	0.112466
$94$	−3.12847	−0.322678
$95$	−0.850025	−0.0872108
$96$	0.321033	0.0327653
$97$	−6.67442	−0.677684	−0.338842	−	0.940843i	$-0.610035\pi$
$97$	−6.67442	−0.677684	−0.338842	+	0.940843i	$0.610035\pi$
$98$	−1.50232	−0.151757
$99$	−12.4772	−1.25400
$100$	1.00000	0.100000
$101$	−10.9350	−1.08807	−0.544035	−	0.839063i	$-0.683104\pi$
$101$	−10.9350	−1.08807	−0.544035	+	0.839063i	$0.683104\pi$
$102$	−0.931464	−0.0922287
$103$	5.20948	0.513305	0.256652	−	0.966504i	$-0.417380\pi$
$103$	5.20948	0.513305	0.256652	+	0.966504i	$0.417380\pi$
$104$	−0.151560	−0.0148617
$105$	0.752730	0.0734589
$106$	12.8478	1.24789
$107$	−7.53359	−0.728300	−0.364150	−	0.931340i	$-0.618640\pi$
$107$	−7.53359	−0.728300	−0.364150	+	0.931340i	$0.618640\pi$
$108$	−1.89311	−0.182165
$109$	5.91804	0.566845	0.283423	−	0.958995i	$-0.408530\pi$
$109$	5.91804	0.566845	0.283423	+	0.958995i	$0.408530\pi$
$110$	−4.30702	−0.410659
$111$	1.23486	0.117207
$112$	−2.34471	−0.221555
$113$	6.64989	0.625569	0.312784	−	0.949824i	$-0.398738\pi$
$113$	6.64989	0.625569	0.312784	+	0.949824i	$0.398738\pi$
$114$	0.272886	0.0255581
$115$	−1.17772	−0.109823
$116$	−6.06456	−0.563081
$117$	0.439061	0.0405912
$118$	8.77318	0.807637
$119$	6.80310	0.623639
$120$	−0.321033	−0.0293061
$121$	7.55045	0.686404
$122$	4.12343	0.373318
$123$	1.40053	0.126281
$124$	3.37842	0.303391
$125$	−1.00000	−0.0894427
$126$	6.79249	0.605123
$127$	15.9042	1.41127	0.705633	−	0.708578i	$-0.250663\pi$
$127$	15.9042	1.41127	0.705633	+	0.708578i	$0.250663\pi$
$128$	1.00000	0.0883883
$129$	0.694601	0.0611562
$130$	0.151560	0.0132927
$131$	13.9823	1.22164	0.610818	−	0.791771i	$-0.290841\pi$
$131$	13.9823	1.22164	0.610818	+	0.791771i	$0.290841\pi$
$132$	1.38269	0.120348
$133$	−1.99307	−0.172821
$134$	11.2919	0.975472
$135$	1.89311	0.162933
$136$	−2.90146	−0.248798
$137$	−9.68718	−0.827632	−0.413816	−	0.910361i	$-0.635804\pi$
$137$	−9.68718	−0.827632	−0.413816	+	0.910361i	$0.635804\pi$
$138$	0.378086	0.0321848
$139$	10.2590	0.870156	0.435078	−	0.900393i	$-0.356721\pi$
$139$	10.2590	0.870156	0.435078	+	0.900393i	$0.356721\pi$
$140$	2.34471	0.198165
$141$	−1.00434	−0.0845809
$142$	5.48369	0.460181
$143$	−0.652774	−0.0545877
$144$	−2.89694	−0.241412
$145$	6.06456	0.503635
$146$	−1.89647	−0.156953
$147$	−0.482293	−0.0397788
$148$	3.84651	0.316181
$149$	−22.7688	−1.86529	−0.932645	−	0.360794i	$-0.882506\pi$
$149$	−22.7688	−1.86529	−0.932645	+	0.360794i	$0.882506\pi$
$150$	0.321033	0.0262122
$151$	−3.64951	−0.296993	−0.148496	−	0.988913i	$-0.547443\pi$
$151$	−3.64951	−0.296993	−0.148496	+	0.988913i	$0.547443\pi$
$152$	0.850025	0.0689462
$153$	8.40536	0.679533
$154$	−10.0987	−0.813779
$155$	−3.37842	−0.271361
$156$	−0.0486558	−0.00389558
$157$	23.1613	1.84847	0.924236	−	0.381821i	$-0.124703\pi$
$157$	23.1613	1.84847	0.924236	+	0.381821i	$0.124703\pi$
$158$	−7.14621	−0.568522
$159$	4.12456	0.327099
$160$	−1.00000	−0.0790569
$161$	−2.76141	−0.217630
$162$	8.08306	0.635066
$163$	−14.6133	−1.14460	−0.572302	−	0.820043i	$-0.693949\pi$
$163$	−14.6133	−1.14460	−0.572302	+	0.820043i	$0.693949\pi$
$164$	4.36256	0.340659
$165$	−1.38269	−0.107643
$166$	12.8931	1.00070
$167$	18.8141	1.45588	0.727941	−	0.685640i	$-0.240477\pi$
$167$	18.8141	1.45588	0.727941	+	0.685640i	$0.240477\pi$
$168$	−0.752730	−0.0580744
$169$	−12.9770	−0.998233
$170$	2.90146	0.222532
$171$	−2.46247	−0.188310
$172$	2.16365	0.164976
$173$	21.5517	1.63854	0.819271	−	0.573406i	$-0.194378\pi$
$173$	21.5517	1.63854	0.819271	+	0.573406i	$0.194378\pi$
$174$	−1.94692	−0.147596
$175$	−2.34471	−0.177244
$176$	4.30702	0.324654
$177$	2.81648	0.211699
$178$	−3.45632	−0.259062
$179$	−12.3686	−0.924470	−0.462235	−	0.886758i	$-0.652952\pi$
$179$	−12.3686	−0.924470	−0.462235	+	0.886758i	$0.652952\pi$
$180$	2.89694	0.215925
$181$	−4.07510	−0.302900	−0.151450	−	0.988465i	$-0.548394\pi$
$181$	−4.07510	−0.302900	−0.151450	+	0.988465i	$0.548394\pi$
$182$	0.355366	0.0263415
$183$	1.32376	0.0978549
$184$	1.17772	0.0868226
$185$	−3.84651	−0.282801
$186$	1.08458	0.0795255
$187$	−12.4967	−0.913847
$188$	−3.12847	−0.228167
$189$	4.43880	0.322875
$190$	−0.850025	−0.0616673
$191$	21.3120	1.54208	0.771042	−	0.636785i	$-0.219736\pi$
$191$	21.3120	1.54208	0.771042	+	0.636785i	$0.219736\pi$
$192$	0.321033	0.0231685
$193$	3.22833	0.232380	0.116190	−	0.993227i	$-0.462932\pi$
$193$	3.22833	0.232380	0.116190	+	0.993227i	$0.462932\pi$
$194$	−6.67442	−0.479195
$195$	0.0486558	0.00348432
$196$	−1.50232	−0.107308
$197$	17.7112	1.26187	0.630936	−	0.775835i	$-0.282671\pi$
$197$	17.7112	1.26187	0.630936	+	0.775835i	$0.282671\pi$
$198$	−12.4772	−0.886714
$199$	0.0733493	0.00519959	0.00259980	−	0.999997i	$-0.499172\pi$
$199$	0.0733493	0.00519959	0.00259980	+	0.999997i	$0.499172\pi$
$200$	1.00000	0.0707107
$201$	3.62507	0.255693
$202$	−10.9350	−0.769381
$203$	14.2197	0.998025
$204$	−0.931464	−0.0652156
$205$	−4.36256	−0.304695
$206$	5.20948	0.362961
$207$	−3.41178	−0.237135
$208$	−0.151560	−0.0105088
$209$	3.66108	0.253242
$210$	0.752730	0.0519433
$211$	−6.33949	−0.436428	−0.218214	−	0.975901i	$-0.570023\pi$
$211$	−6.33949	−0.436428	−0.218214	+	0.975901i	$0.570023\pi$
$212$	12.8478	0.882390
$213$	1.76044	0.120623
$214$	−7.53359	−0.514986
$215$	−2.16365	−0.147559
$216$	−1.89311	−0.128810
$217$	−7.92143	−0.537742
$218$	5.91804	0.400820
$219$	−0.608829	−0.0411408
$220$	−4.30702	−0.290379
$221$	0.439747	0.0295806
$222$	1.23486	0.0828781
$223$	10.1762	0.681447	0.340723	−	0.940164i	$-0.389328\pi$
$223$	10.1762	0.681447	0.340723	+	0.940164i	$0.389328\pi$
$224$	−2.34471	−0.156663
$225$	−2.89694	−0.193129
$226$	6.64989	0.442344
$227$	17.1555	1.13865	0.569326	−	0.822112i	$-0.307204\pi$
$227$	17.1555	1.13865	0.569326	+	0.822112i	$0.307204\pi$
$228$	0.272886	0.0180723
$229$	25.4373	1.68094	0.840471	−	0.541856i	$-0.182278\pi$
$229$	25.4373	1.68094	0.840471	+	0.541856i	$0.182278\pi$
$230$	−1.17772	−0.0776565
$231$	−3.24202	−0.213310
$232$	−6.06456	−0.398158
$233$	−19.7605	−1.29456	−0.647278	−	0.762254i	$-0.724093\pi$
$233$	−19.7605	−1.29456	−0.647278	+	0.762254i	$0.724093\pi$
$234$	0.439061	0.0287023
$235$	3.12847	0.204079
$236$	8.77318	0.571086
$237$	−2.29417	−0.149022
$238$	6.80310	0.440980
$239$	23.0312	1.48976	0.744882	−	0.667197i	$-0.232506\pi$
$239$	23.0312	1.48976	0.744882	+	0.667197i	$0.232506\pi$
$240$	−0.321033	−0.0207226
$241$	−21.9418	−1.41340	−0.706699	−	0.707515i	$-0.749816\pi$
$241$	−21.9418	−1.41340	−0.706699	+	0.707515i	$0.749816\pi$
$242$	7.55045	0.485361
$243$	8.27426	0.530794
$244$	4.12343	0.263976
$245$	1.50232	0.0959795
$246$	1.40053	0.0892942
$247$	−0.128830	−0.00819727
$248$	3.37842	0.214530
$249$	4.13912	0.262306
$250$	−1.00000	−0.0632456
$251$	21.4800	1.35581	0.677904	−	0.735151i	$-0.262889\pi$
$251$	21.4800	1.35581	0.677904	+	0.735151i	$0.262889\pi$
$252$	6.79249	0.427887
$253$	5.07246	0.318903
$254$	15.9042	0.997916
$255$	0.931464	0.0583306
$256$	1.00000	0.0625000
$257$	−21.8081	−1.36035	−0.680177	−	0.733048i	$-0.738097\pi$
$257$	−21.8081	−1.36035	−0.680177	+	0.733048i	$0.738097\pi$
$258$	0.694601	0.0432440
$259$	−9.01897	−0.560412
$260$	0.151560	0.00939938
$261$	17.5687	1.08747
$262$	13.9823	0.863827
$263$	8.82818	0.544369	0.272185	−	0.962245i	$-0.412254\pi$
$263$	8.82818	0.544369	0.272185	+	0.962245i	$0.412254\pi$
$264$	1.38269	0.0850990
$265$	−12.8478	−0.789233
$266$	−1.99307	−0.122203
$267$	−1.10959	−0.0679058
$268$	11.2919	0.689763
$269$	−16.1412	−0.984145	−0.492072	−	0.870554i	$-0.663761\pi$
$269$	−16.1412	−0.984145	−0.492072	+	0.870554i	$0.663761\pi$
$270$	1.89311	0.115211
$271$	11.6232	0.706060	0.353030	−	0.935612i	$-0.385151\pi$
$271$	11.6232	0.706060	0.353030	+	0.935612i	$0.385151\pi$
$272$	−2.90146	−0.175927
$273$	0.114084	0.00690468
$274$	−9.68718	−0.585224
$275$	4.30702	0.259723
$276$	0.378086	0.0227581
$277$	−2.00332	−0.120368	−0.0601839	−	0.998187i	$-0.519169\pi$
$277$	−2.00332	−0.120368	−0.0601839	+	0.998187i	$0.519169\pi$
$278$	10.2590	0.615293
$279$	−9.78708	−0.585937
$280$	2.34471	0.140123
$281$	−29.1666	−1.73994	−0.869968	−	0.493108i	$-0.835861\pi$
$281$	−29.1666	−1.73994	−0.869968	+	0.493108i	$0.835861\pi$
$282$	−1.00434	−0.0598077
$283$	−26.2792	−1.56214	−0.781068	−	0.624445i	$-0.785325\pi$
$283$	−26.2792	−1.56214	−0.781068	+	0.624445i	$0.785325\pi$
$284$	5.48369	0.325397
$285$	−0.272886	−0.0161644
$286$	−0.652774	−0.0385993
$287$	−10.2290	−0.603797
$288$	−2.89694	−0.170704
$289$	−8.58151	−0.504795
$290$	6.06456	0.356123
$291$	−2.14271	−0.125608
$292$	−1.89647	−0.110982
$293$	33.7640	1.97252	0.986258	−	0.165212i	$-0.0528307\pi$
$293$	33.7640	1.97252	0.986258	+	0.165212i	$0.0528307\pi$
$294$	−0.482293	−0.0281279
$295$	−8.77318	−0.510794
$296$	3.84651	0.223574
$297$	−8.15367	−0.473124
$298$	−22.7688	−1.31896
$299$	−0.178496	−0.0103227
$300$	0.321033	0.0185348
$301$	−5.07313	−0.292410
$302$	−3.64951	−0.210006
$303$	−3.51048	−0.201672
$304$	0.850025	0.0487523
$305$	−4.12343	−0.236107
$306$	8.40536	0.480502
$307$	33.2915	1.90005	0.950023	−	0.312179i	$-0.101059\pi$
$307$	33.2915	1.90005	0.950023	+	0.312179i	$0.101059\pi$
$308$	−10.0987	−0.575429
$309$	1.67241	0.0951402
$310$	−3.37842	−0.191881
$311$	−19.7768	−1.12144	−0.560720	−	0.828006i	$-0.689475\pi$
$311$	−19.7768	−1.12144	−0.560720	+	0.828006i	$0.689475\pi$
$312$	−0.0486558	−0.00275459
$313$	7.51930	0.425016	0.212508	−	0.977159i	$-0.431837\pi$
$313$	7.51930	0.425016	0.212508	+	0.977159i	$0.431837\pi$
$314$	23.1613	1.30707
$315$	−6.79249	−0.382714
$316$	−7.14621	−0.402006
$317$	−26.3118	−1.47782	−0.738910	−	0.673805i	$-0.764659\pi$
$317$	−26.3118	−1.47782	−0.738910	+	0.673805i	$0.764659\pi$
$318$	4.12456	0.231294
$319$	−26.1202	−1.46245
$320$	−1.00000	−0.0559017
$321$	−2.41853	−0.134989
$322$	−2.76141	−0.153888
$323$	−2.46632	−0.137230
$324$	8.08306	0.449059
$325$	−0.151560	−0.00840706
$326$	−14.6133	−0.809357
$327$	1.89988	0.105064
$328$	4.36256	0.240882
$329$	7.33538	0.404412
$330$	−1.38269	−0.0761148
$331$	34.7556	1.91034	0.955170	−	0.296057i	$-0.0956720\pi$
$331$	34.7556	1.91034	0.955170	+	0.296057i	$0.0956720\pi$
$332$	12.8931	0.707602
$333$	−11.1431	−0.610639
$334$	18.8141	1.02946
$335$	−11.2919	−0.616943
$336$	−0.752730	−0.0410648
$337$	36.0840	1.96562	0.982810	−	0.184618i	$-0.0591049\pi$
$337$	36.0840	1.96562	0.982810	+	0.184618i	$0.0591049\pi$
$338$	−12.9770	−0.705857
$339$	2.13483	0.115948
$340$	2.90146	0.157354
$341$	14.5509	0.787978
$342$	−2.46247	−0.133155
$343$	19.9355	1.07642
$344$	2.16365	0.116656
$345$	−0.378086	−0.0203555
$346$	21.5517	1.15862
$347$	−10.1447	−0.544598	−0.272299	−	0.962213i	$-0.587784\pi$
$347$	−10.1447	−0.544598	−0.272299	+	0.962213i	$0.587784\pi$
$348$	−1.94692	−0.104366
$349$	22.0956	1.18275	0.591374	−	0.806397i	$-0.298586\pi$
$349$	22.0956	1.18275	0.591374	+	0.806397i	$0.298586\pi$
$350$	−2.34471	−0.125330
$351$	0.286920	0.0153147
$352$	4.30702	0.229565
$353$	8.98398	0.478169	0.239084	−	0.970999i	$-0.423153\pi$
$353$	8.98398	0.478169	0.239084	+	0.970999i	$0.423153\pi$
$354$	2.81648	0.149694
$355$	−5.48369	−0.291044
$356$	−3.45632	−0.183184
$357$	2.18402	0.115590
$358$	−12.3686	−0.653699
$359$	−23.4608	−1.23821	−0.619107	−	0.785306i	$-0.712505\pi$
$359$	−23.4608	−1.23821	−0.619107	+	0.785306i	$0.712505\pi$
$360$	2.89694	0.152682
$361$	−18.2775	−0.961971
$362$	−4.07510	−0.214183
$363$	2.42394	0.127224
$364$	0.355366	0.0186262
$365$	1.89647	0.0992658
$366$	1.32376	0.0691938
$367$	−21.0118	−1.09681	−0.548405	−	0.836213i	$-0.684765\pi$
$367$	−21.0118	−1.09681	−0.548405	+	0.836213i	$0.684765\pi$
$368$	1.17772	0.0613929
$369$	−12.6381	−0.657912
$370$	−3.84651	−0.199971
$371$	−30.1244	−1.56398
$372$	1.08458	0.0562330
$373$	−22.8935	−1.18538	−0.592689	−	0.805431i	$-0.701934\pi$
$373$	−22.8935	−1.18538	−0.592689	+	0.805431i	$0.701934\pi$
$374$	−12.4967	−0.646187
$375$	−0.321033	−0.0165781
$376$	−3.12847	−0.161339
$377$	0.919148	0.0473385
$378$	4.43880	0.228307
$379$	37.1256	1.90701	0.953507	−	0.301372i	$-0.0974447\pi$
$379$	37.1256	1.90701	0.953507	+	0.301372i	$0.0974447\pi$
$380$	−0.850025	−0.0436054
$381$	5.10575	0.261576
$382$	21.3120	1.09042
$383$	18.3424	0.937253	0.468626	−	0.883396i	$-0.344749\pi$
$383$	18.3424	0.937253	0.468626	+	0.883396i	$0.344749\pi$
$384$	0.321033	0.0163826
$385$	10.0987	0.514679
$386$	3.22833	0.164317
$387$	−6.26795	−0.318618
$388$	−6.67442	−0.338842
$389$	8.01259	0.406254	0.203127	−	0.979152i	$-0.434890\pi$
$389$	8.01259	0.406254	0.203127	+	0.979152i	$0.434890\pi$
$390$	0.0486558	0.00246378
$391$	−3.41711	−0.172811
$392$	−1.50232	−0.0758784
$393$	4.48876	0.226428
$394$	17.7112	0.892279
$395$	7.14621	0.359565
$396$	−12.4772	−0.627002
$397$	20.2147	1.01455	0.507275	−	0.861785i	$-0.330653\pi$
$397$	20.2147	1.01455	0.507275	+	0.861785i	$0.330653\pi$
$398$	0.0733493	0.00367667
$399$	−0.639839	−0.0320320
$400$	1.00000	0.0500000
$401$	−3.11232	−0.155422	−0.0777108	−	0.996976i	$-0.524761\pi$
$401$	−3.11232	−0.155422	−0.0777108	+	0.996976i	$0.524761\pi$
$402$	3.62507	0.180802
$403$	−0.512035	−0.0255063
$404$	−10.9350	−0.544035
$405$	−8.08306	−0.401651
$406$	14.2197	0.705710
$407$	16.5670	0.821197
$408$	−0.931464	−0.0461144
$409$	−27.3963	−1.35466	−0.677329	−	0.735680i	$-0.736863\pi$
$409$	−27.3963	−1.35466	−0.677329	+	0.735680i	$0.736863\pi$
$410$	−4.36256	−0.215452
$411$	−3.10990	−0.153400
$412$	5.20948	0.256652
$413$	−20.5706	−1.01221
$414$	−3.41178	−0.167680
$415$	−12.8931	−0.632899
$416$	−0.151560	−0.00743086
$417$	3.29347	0.161282
$418$	3.66108	0.179069
$419$	−3.33288	−0.162822	−0.0814110	−	0.996681i	$-0.525943\pi$
$419$	−3.33288	−0.162822	−0.0814110	+	0.996681i	$0.525943\pi$
$420$	0.752730	0.0367294
$421$	2.01962	0.0984300	0.0492150	−	0.998788i	$-0.484328\pi$
$421$	2.01962	0.0984300	0.0492150	+	0.998788i	$0.484328\pi$
$422$	−6.33949	−0.308601
$423$	9.06300	0.440658
$424$	12.8478	0.623944
$425$	−2.90146	−0.140742
$426$	1.76044	0.0852937
$427$	−9.66827	−0.467880
$428$	−7.53359	−0.364150
$429$	−0.209562	−0.0101177
$430$	−2.16365	−0.104340
$431$	−38.1102	−1.83570	−0.917851	−	0.396925i	$-0.870077\pi$
$431$	−38.1102	−1.83570	−0.917851	+	0.396925i	$0.870077\pi$
$432$	−1.89311	−0.0910823
$433$	7.36690	0.354030	0.177015	−	0.984208i	$-0.443356\pi$
$433$	7.36690	0.354030	0.177015	+	0.984208i	$0.443356\pi$
$434$	−7.92143	−0.380241
$435$	1.94692	0.0933478
$436$	5.91804	0.283423
$437$	1.00109	0.0478887
$438$	−0.608829	−0.0290910
$439$	−36.3794	−1.73630	−0.868148	−	0.496306i	$-0.834690\pi$
$439$	−36.3794	−1.73630	−0.868148	+	0.496306i	$0.834690\pi$
$440$	−4.30702	−0.205329
$441$	4.35212	0.207244
$442$	0.439747	0.0209166
$443$	−25.2432	−1.19934	−0.599670	−	0.800247i	$-0.704702\pi$
$443$	−25.2432	−1.19934	−0.599670	+	0.800247i	$0.704702\pi$
$444$	1.23486	0.0586037
$445$	3.45632	0.163845
$446$	10.1762	0.481856
$447$	−7.30952	−0.345728
$448$	−2.34471	−0.110777
$449$	12.1827	0.574938	0.287469	−	0.957790i	$-0.407186\pi$
$449$	12.1827	0.574938	0.287469	+	0.957790i	$0.407186\pi$
$450$	−2.89694	−0.136563
$451$	18.7897	0.884771
$452$	6.64989	0.312784
$453$	−1.17161	−0.0550471
$454$	17.1555	0.805149
$455$	−0.355366	−0.0166598
$456$	0.272886	0.0127791
$457$	33.4459	1.56453	0.782266	−	0.622944i	$-0.214064\pi$
$457$	33.4459	1.56453	0.782266	+	0.622944i	$0.214064\pi$
$458$	25.4373	1.18861
$459$	5.49279	0.256381
$460$	−1.17772	−0.0549114
$461$	11.8769	0.553162	0.276581	−	0.960991i	$-0.410799\pi$
$461$	11.8769	0.553162	0.276581	+	0.960991i	$0.410799\pi$
$462$	−3.24202	−0.150833
$463$	−25.8702	−1.20229	−0.601145	−	0.799140i	$-0.705288\pi$
$463$	−25.8702	−1.20229	−0.601145	+	0.799140i	$0.705288\pi$
$464$	−6.06456	−0.281540
$465$	−1.08458	−0.0502964
$466$	−19.7605	−0.915390
$467$	−29.7130	−1.37495	−0.687476	−	0.726207i	$-0.741281\pi$
$467$	−29.7130	−1.37495	−0.687476	+	0.726207i	$0.741281\pi$
$468$	0.439061	0.0202956
$469$	−26.4763	−1.22256
$470$	3.12847	0.144306
$471$	7.43553	0.342611
$472$	8.77318	0.403818
$473$	9.31887	0.428482
$474$	−2.29417	−0.105375
$475$	0.850025	0.0390018
$476$	6.80310	0.311820
$477$	−37.2192	−1.70415
$478$	23.0312	1.05342
$479$	−1.19710	−0.0546969	−0.0273485	−	0.999626i	$-0.508706\pi$
$479$	−1.19710	−0.0546969	−0.0273485	+	0.999626i	$0.508706\pi$
$480$	−0.321033	−0.0146531
$481$	−0.582979	−0.0265816
$482$	−21.9418	−0.999423
$483$	−0.886504	−0.0403373
$484$	7.55045	0.343202
$485$	6.67442	0.303070
$486$	8.27426	0.375328
$487$	−31.3802	−1.42197	−0.710987	−	0.703205i	$-0.751752\pi$
$487$	−31.3802	−1.42197	−0.710987	+	0.703205i	$0.751752\pi$
$488$	4.12343	0.186659
$489$	−4.69135	−0.212150
$490$	1.50232	0.0678677
$491$	20.8352	0.940278	0.470139	−	0.882592i	$-0.344204\pi$
$491$	20.8352	0.940278	0.470139	+	0.882592i	$0.344204\pi$
$492$	1.40053	0.0631406
$493$	17.5961	0.792489
$494$	−0.128830	−0.00579635
$495$	12.4772	0.560807
$496$	3.37842	0.151696
$497$	−12.8577	−0.576745
$498$	4.13912	0.185478
$499$	11.1576	0.499483	0.249741	−	0.968313i	$-0.419654\pi$
$499$	11.1576	0.499483	0.249741	+	0.968313i	$0.419654\pi$
$500$	−1.00000	−0.0447214
$501$	6.03996	0.269845
$502$	21.4800	0.958701
$503$	−30.2780	−1.35003	−0.675015	−	0.737804i	$-0.735863\pi$
$503$	−30.2780	−1.35003	−0.675015	+	0.737804i	$0.735863\pi$
$504$	6.79249	0.302562
$505$	10.9350	0.486600
$506$	5.07246	0.225498
$507$	−4.16605	−0.185021
$508$	15.9042	0.705633
$509$	17.5268	0.776863	0.388431	−	0.921478i	$-0.373017\pi$
$509$	17.5268	0.776863	0.388431	+	0.921478i	$0.373017\pi$
$510$	0.931464	0.0412459
$511$	4.44668	0.196710
$512$	1.00000	0.0441942
$513$	−1.60919	−0.0710475
$514$	−21.8081	−0.961915
$515$	−5.20948	−0.229557
$516$	0.694601	0.0305781
$517$	−13.4744	−0.592604
$518$	−9.01897	−0.396271
$519$	6.91879	0.303701
$520$	0.151560	0.00664636
$521$	13.6637	0.598617	0.299308	−	0.954156i	$-0.403244\pi$
$521$	13.6637	0.598617	0.299308	+	0.954156i	$0.403244\pi$
$522$	17.5687	0.768960
$523$	−9.09377	−0.397643	−0.198821	−	0.980036i	$-0.563711\pi$
$523$	−9.09377	−0.397643	−0.198821	+	0.980036i	$0.563711\pi$
$524$	13.9823	0.610818
$525$	−0.752730	−0.0328518
$526$	8.82818	0.384927
$527$	−9.80237	−0.426998
$528$	1.38269	0.0601741
$529$	−21.6130	−0.939695
$530$	−12.8478	−0.558072
$531$	−25.4154	−1.10293
$532$	−1.99307	−0.0864104
$533$	−0.661192	−0.0286394
$534$	−1.10959	−0.0480167
$535$	7.53359	0.325706
$536$	11.2919	0.487736
$537$	−3.97071	−0.171349
$538$	−16.1412	−0.695896
$539$	−6.47051	−0.278705
$540$	1.89311	0.0814665
$541$	−36.4917	−1.56890	−0.784451	−	0.620191i	$-0.787055\pi$
$541$	−36.4917	−1.56890	−0.784451	+	0.620191i	$0.787055\pi$
$542$	11.6232	0.499260
$543$	−1.30824	−0.0561420
$544$	−2.90146	−0.124399
$545$	−5.91804	−0.253501
$546$	0.114084	0.00488235
$547$	−21.6270	−0.924702	−0.462351	−	0.886697i	$-0.652994\pi$
$547$	−21.6270	−0.924702	−0.462351	+	0.886697i	$0.652994\pi$
$548$	−9.68718	−0.413816
$549$	−11.9453	−0.509814
$550$	4.30702	0.183652
$551$	−5.15503	−0.219612
$552$	0.378086	0.0160924
$553$	16.7558	0.712530
$554$	−2.00332	−0.0851128
$555$	−1.23486	−0.0524167
$556$	10.2590	0.435078
$557$	−6.32452	−0.267978	−0.133989	−	0.990983i	$-0.542779\pi$
$557$	−6.32452	−0.267978	−0.133989	+	0.990983i	$0.542779\pi$
$558$	−9.78708	−0.414320
$559$	−0.327923	−0.0138697
$560$	2.34471	0.0990823
$561$	−4.01184	−0.169380
$562$	−29.1666	−1.23032
$563$	−7.82093	−0.329613	−0.164807	−	0.986326i	$-0.552700\pi$
$563$	−7.82093	−0.329613	−0.164807	+	0.986326i	$0.552700\pi$
$564$	−1.00434	−0.0422904
$565$	−6.64989	−0.279763
$566$	−26.2792	−1.10460
$567$	−18.9525	−0.795929
$568$	5.48369	0.230090
$569$	7.53621	0.315935	0.157967	−	0.987444i	$-0.449506\pi$
$569$	7.53621	0.315935	0.157967	+	0.987444i	$0.449506\pi$
$570$	−0.272886	−0.0114299
$571$	14.5664	0.609586	0.304793	−	0.952419i	$-0.401413\pi$
$571$	14.5664	0.609586	0.304793	+	0.952419i	$0.401413\pi$
$572$	−0.652774	−0.0272939
$573$	6.84185	0.285822
$574$	−10.2290	−0.426949
$575$	1.17772	0.0491143
$576$	−2.89694	−0.120706
$577$	−33.3390	−1.38792	−0.693960	−	0.720013i	$-0.744136\pi$
$577$	−33.3390	−1.38792	−0.693960	+	0.720013i	$0.744136\pi$
$578$	−8.58151	−0.356944
$579$	1.03640	0.0430712
$580$	6.06456	0.251817
$581$	−30.2307	−1.25418
$582$	−2.14271	−0.0888180
$583$	55.3357	2.29177
$584$	−1.89647	−0.0784765
$585$	−0.439061	−0.0181529
$586$	33.7640	1.39478
$587$	−43.9050	−1.81215	−0.906077	−	0.423114i	$-0.860937\pi$
$587$	−43.9050	−1.81215	−0.906077	+	0.423114i	$0.860937\pi$
$588$	−0.482293	−0.0198894
$589$	2.87174	0.118328
$590$	−8.77318	−0.361186
$591$	5.68588	0.233886
$592$	3.84651	0.158091
$593$	−16.2032	−0.665386	−0.332693	−	0.943035i	$-0.607957\pi$
$593$	−16.2032	−0.665386	−0.332693	+	0.943035i	$0.607957\pi$
$594$	−8.15367	−0.334549
$595$	−6.80310	−0.278900
$596$	−22.7688	−0.932645
$597$	0.0235475	0.000963736 0
$598$	−0.178496	−0.00729923
$599$	17.8205	0.728126	0.364063	−	0.931374i	$-0.381389\pi$
$599$	17.8205	0.728126	0.364063	+	0.931374i	$0.381389\pi$
$600$	0.321033	0.0131061
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−5.07313	−0.206765
$603$	−32.7119	−1.33213
$604$	−3.64951	−0.148496
$605$	−7.55045	−0.306969
$606$	−3.51048	−0.142604
$607$	5.62662	0.228378	0.114189	−	0.993459i	$-0.463573\pi$
$607$	5.62662	0.228378	0.114189	+	0.993459i	$0.463573\pi$
$608$	0.850025	0.0344731
$609$	4.56498	0.184982
$610$	−4.12343	−0.166953
$611$	0.474153	0.0191822
$612$	8.40536	0.339767
$613$	17.9431	0.724713	0.362357	−	0.932040i	$-0.381972\pi$
$613$	17.9431	0.724713	0.362357	+	0.932040i	$0.381972\pi$
$614$	33.2915	1.34354
$615$	−1.40053	−0.0564746
$616$	−10.0987	−0.406890
$617$	33.4323	1.34593	0.672967	−	0.739672i	$-0.265019\pi$
$617$	33.4323	1.34593	0.672967	+	0.739672i	$0.265019\pi$
$618$	1.67241	0.0672743
$619$	−2.89611	−0.116404	−0.0582022	−	0.998305i	$-0.518537\pi$
$619$	−2.89611	−0.116404	−0.0582022	+	0.998305i	$0.518537\pi$
$620$	−3.37842	−0.135681
$621$	−2.22955	−0.0894688
$622$	−19.7768	−0.792977
$623$	8.10408	0.324683
$624$	−0.0486558	−0.00194779
$625$	1.00000	0.0400000
$626$	7.51930	0.300532
$627$	1.17533	0.0469380
$628$	23.1613	0.924236
$629$	−11.1605	−0.444999
$630$	−6.79249	−0.270619
$631$	−41.2078	−1.64046	−0.820229	−	0.572035i	$-0.806154\pi$
$631$	−41.2078	−1.64046	−0.820229	+	0.572035i	$0.806154\pi$
$632$	−7.14621	−0.284261
$633$	−2.03518	−0.0808912
$634$	−26.3118	−1.04498
$635$	−15.9042	−0.631137
$636$	4.12456	0.163549
$637$	0.227692	0.00902147
$638$	−26.1202	−1.03411
$639$	−15.8859	−0.628436
$640$	−1.00000	−0.0395285
$641$	−30.7811	−1.21578	−0.607890	−	0.794022i	$-0.707984\pi$
$641$	−30.7811	−1.21578	−0.607890	+	0.794022i	$0.707984\pi$
$642$	−2.41853	−0.0954517
$643$	5.46225	0.215410	0.107705	−	0.994183i	$-0.465650\pi$
$643$	5.46225	0.215410	0.107705	+	0.994183i	$0.465650\pi$
$644$	−2.76141	−0.108815
$645$	−0.694601	−0.0273499
$646$	−2.46632	−0.0970360
$647$	14.4120	0.566596	0.283298	−	0.959032i	$-0.408571\pi$
$647$	14.4120	0.566596	0.283298	+	0.959032i	$0.408571\pi$
$648$	8.08306	0.317533
$649$	37.7863	1.48324
$650$	−0.151560	−0.00594469
$651$	−2.54304	−0.0996695
$652$	−14.6133	−0.572302
$653$	8.47619	0.331699	0.165849	−	0.986151i	$-0.446963\pi$
$653$	8.47619	0.331699	0.165849	+	0.986151i	$0.446963\pi$
$654$	1.89988	0.0742913
$655$	−13.9823	−0.546332
$656$	4.36256	0.170329
$657$	5.49396	0.214340
$658$	7.33538	0.285963
$659$	14.3998	0.560938	0.280469	−	0.959863i	$-0.409510\pi$
$659$	14.3998	0.560938	0.280469	+	0.959863i	$0.409510\pi$
$660$	−1.38269	−0.0538213
$661$	−25.5124	−0.992316	−0.496158	−	0.868232i	$-0.665256\pi$
$661$	−25.5124	−0.992316	−0.496158	+	0.868232i	$0.665256\pi$
$662$	34.7556	1.35081
$663$	0.141173	0.00548271
$664$	12.8931	0.500350
$665$	1.99307	0.0772878
$666$	−11.1431	−0.431787
$667$	−7.14235	−0.276553
$668$	18.8141	0.727941
$669$	3.26688	0.126305
$670$	−11.2919	−0.436244
$671$	17.7597	0.685606
$672$	−0.752730	−0.0290372
$673$	33.5502	1.29326	0.646632	−	0.762802i	$-0.276177\pi$
$673$	33.5502	1.29326	0.646632	+	0.762802i	$0.276177\pi$
$674$	36.0840	1.38990
$675$	−1.89311	−0.0728658
$676$	−12.9770	−0.499117
$677$	14.1461	0.543678	0.271839	−	0.962343i	$-0.412368\pi$
$677$	14.1461	0.543678	0.271839	+	0.962343i	$0.412368\pi$
$678$	2.13483	0.0819877
$679$	15.6496	0.600576
$680$	2.90146	0.111266
$681$	5.50749	0.211047
$682$	14.5509	0.557184
$683$	−5.35864	−0.205043	−0.102521	−	0.994731i	$-0.532691\pi$
$683$	−5.35864	−0.205043	−0.102521	+	0.994731i	$0.532691\pi$
$684$	−2.46247	−0.0941549
$685$	9.68718	0.370128
$686$	19.9355	0.761141
$687$	8.16620	0.311560
$688$	2.16365	0.0824882
$689$	−1.94722	−0.0741830
$690$	−0.378086	−0.0143935
$691$	−24.1494	−0.918688	−0.459344	−	0.888258i	$-0.651915\pi$
$691$	−24.1494	−0.918688	−0.459344	+	0.888258i	$0.651915\pi$
$692$	21.5517	0.819271
$693$	29.2554	1.11132
$694$	−10.1447	−0.385089
$695$	−10.2590	−0.389146
$696$	−1.94692	−0.0737979
$697$	−12.6578	−0.479449
$698$	22.0956	0.836329
$699$	−6.34378	−0.239944
$700$	−2.34471	−0.0886219
$701$	10.3783	0.391982	0.195991	−	0.980606i	$-0.437208\pi$
$701$	10.3783	0.391982	0.195991	+	0.980606i	$0.437208\pi$
$702$	0.286920	0.0108291
$703$	3.26963	0.123317
$704$	4.30702	0.162327
$705$	1.00434	0.0378257
$706$	8.98398	0.338116
$707$	25.6394	0.964268
$708$	2.81648	0.105850
$709$	16.2357	0.609744	0.304872	−	0.952393i	$-0.401386\pi$
$709$	16.2357	0.609744	0.304872	+	0.952393i	$0.401386\pi$
$710$	−5.48369	−0.205799
$711$	20.7021	0.776391
$712$	−3.45632	−0.129531
$713$	3.97883	0.149008
$714$	2.18402	0.0817348
$715$	0.652774	0.0244124
$716$	−12.3686	−0.462235
$717$	7.39376	0.276125
$718$	−23.4608	−0.875550
$719$	−11.9936	−0.447284	−0.223642	−	0.974671i	$-0.571795\pi$
$719$	−11.9936	−0.447284	−0.223642	+	0.974671i	$0.571795\pi$
$720$	2.89694	0.107963
$721$	−12.2147	−0.454900
$722$	−18.2775	−0.680217
$723$	−7.04404	−0.261971
$724$	−4.07510	−0.151450
$725$	−6.06456	−0.225232
$726$	2.42394	0.0899608
$727$	−14.5660	−0.540221	−0.270111	−	0.962829i	$-0.587060\pi$
$727$	−14.5660	−0.540221	−0.270111	+	0.962829i	$0.587060\pi$
$728$	0.355366	0.0131707
$729$	−21.5929	−0.799737
$730$	1.89647	0.0701915
$731$	−6.27774	−0.232191
$732$	1.32376	0.0489274
$733$	41.1765	1.52089	0.760444	−	0.649403i	$-0.224981\pi$
$733$	41.1765	1.52089	0.760444	+	0.649403i	$0.224981\pi$
$734$	−21.0118	−0.775561
$735$	0.482293	0.0177896
$736$	1.17772	0.0434113
$737$	48.6345	1.79147
$738$	−12.6381	−0.465214
$739$	5.78885	0.212946	0.106473	−	0.994316i	$-0.466044\pi$
$739$	5.78885	0.212946	0.106473	+	0.994316i	$0.466044\pi$
$740$	−3.84651	−0.141401
$741$	−0.0413587	−0.00151935
$742$	−30.1244	−1.10590
$743$	−18.0317	−0.661519	−0.330759	−	0.943715i	$-0.607305\pi$
$743$	−18.0317	−0.661519	−0.330759	+	0.943715i	$0.607305\pi$
$744$	1.08458	0.0397628
$745$	22.7688	0.834183
$746$	−22.8935	−0.838189
$747$	−37.3506	−1.36659
$748$	−12.4967	−0.456923
$749$	17.6641	0.645433
$750$	−0.321033	−0.0117225
$751$	−13.4161	−0.489560	−0.244780	−	0.969579i	$-0.578716\pi$
$751$	−13.4161	−0.489560	−0.244780	+	0.969579i	$0.578716\pi$
$752$	−3.12847	−0.114084
$753$	6.89579	0.251297
$754$	0.919148	0.0334734
$755$	3.64951	0.132819
$756$	4.43880	0.161438
$757$	24.8404	0.902841	0.451421	−	0.892311i	$-0.350917\pi$
$757$	24.8404	0.902841	0.451421	+	0.892311i	$0.350917\pi$
$758$	37.1256	1.34846
$759$	1.62843	0.0591081
$760$	−0.850025	−0.0308337
$761$	−8.78430	−0.318431	−0.159215	−	0.987244i	$-0.550896\pi$
$761$	−8.78430	−0.318431	−0.159215	+	0.987244i	$0.550896\pi$
$762$	5.10575	0.184962
$763$	−13.8761	−0.502349
$764$	21.3120	0.771042
$765$	−8.40536	−0.303896
$766$	18.3424	0.662738
$767$	−1.32967	−0.0480115
$768$	0.321033	0.0115843
$769$	37.7680	1.36195	0.680975	−	0.732306i	$-0.261556\pi$
$769$	37.7680	1.36195	0.680975	+	0.732306i	$0.261556\pi$
$770$	10.0987	0.363933
$771$	−7.00112	−0.252139
$772$	3.22833	0.116190
$773$	−2.07521	−0.0746401	−0.0373201	−	0.999303i	$-0.511882\pi$
$773$	−2.07521	−0.0746401	−0.0373201	+	0.999303i	$0.511882\pi$
$774$	−6.26795	−0.225297
$775$	3.37842	0.121357
$776$	−6.67442	−0.239598
$777$	−2.89538	−0.103871
$778$	8.01259	0.287265
$779$	3.70829	0.132863
$780$	0.0486558	0.00174216
$781$	23.6184	0.845131
$782$	−3.41711	−0.122196
$783$	11.4809	0.410293
$784$	−1.50232	−0.0536541
$785$	−23.1613	−0.826662
$786$	4.48876	0.160109
$787$	−15.1359	−0.539535	−0.269768	−	0.962925i	$-0.586947\pi$
$787$	−15.1359	−0.539535	−0.269768	+	0.962925i	$0.586947\pi$
$788$	17.7112	0.630936
$789$	2.83414	0.100898
$790$	7.14621	0.254251
$791$	−15.5921	−0.554391
$792$	−12.4772	−0.443357
$793$	−0.624949	−0.0221926
$794$	20.2147	0.717395
$795$	−4.12456	−0.146283
$796$	0.0733493	0.00259980
$797$	33.3137	1.18003	0.590015	−	0.807392i	$-0.299122\pi$
$797$	33.3137	1.18003	0.590015	+	0.807392i	$0.299122\pi$
$798$	−0.639839	−0.0226501
$799$	9.07715	0.321127
$800$	1.00000	0.0353553
$801$	10.0127	0.353783
$802$	−3.11232	−0.109900
$803$	−8.16814	−0.288247
$804$	3.62507	0.127846
$805$	2.76141	0.0973271
$806$	−0.512035	−0.0180357
$807$	−5.18184	−0.182410
$808$	−10.9350	−0.384691
$809$	1.31239	0.0461412	0.0230706	−	0.999734i	$-0.492656\pi$
$809$	1.31239	0.0461412	0.0230706	+	0.999734i	$0.492656\pi$
$810$	−8.08306	−0.284010
$811$	46.2504	1.62407	0.812035	−	0.583609i	$-0.198360\pi$
$811$	46.2504	1.62407	0.812035	+	0.583609i	$0.198360\pi$
$812$	14.2197	0.499013
$813$	3.73143	0.130867
$814$	16.5670	0.580674
$815$	14.6133	0.511882
$816$	−0.931464	−0.0326078
$817$	1.83915	0.0643439
$818$	−27.3963	−0.957888
$819$	−1.02947	−0.0359727
$820$	−4.36256	−0.152347
$821$	2.52277	0.0880451	0.0440226	−	0.999031i	$-0.485983\pi$
$821$	2.52277	0.0880451	0.0440226	+	0.999031i	$0.485983\pi$
$822$	−3.10990	−0.108470
$823$	27.0537	0.943031	0.471516	−	0.881858i	$-0.343707\pi$
$823$	27.0537	0.943031	0.471516	+	0.881858i	$0.343707\pi$
$824$	5.20948	0.181481
$825$	1.38269	0.0481393
$826$	−20.5706	−0.715743
$827$	15.0034	0.521720	0.260860	−	0.965377i	$-0.415994\pi$
$827$	15.0034	0.521720	0.260860	+	0.965377i	$0.415994\pi$
$828$	−3.41178	−0.118568
$829$	−33.8495	−1.17564	−0.587821	−	0.808991i	$-0.700014\pi$
$829$	−33.8495	−1.17564	−0.587821	+	0.808991i	$0.700014\pi$
$830$	−12.8931	−0.447527
$831$	−0.643131	−0.0223100
$832$	−0.151560	−0.00525441
$833$	4.35892	0.151027
$834$	3.29347	0.114044
$835$	−18.8141	−0.651090
$836$	3.66108	0.126621
$837$	−6.39572	−0.221069
$838$	−3.33288	−0.115132
$839$	−1.95845	−0.0676133	−0.0338066	−	0.999428i	$-0.510763\pi$
$839$	−1.95845	−0.0676133	−0.0338066	+	0.999428i	$0.510763\pi$
$840$	0.752730	0.0259716
$841$	7.77893	0.268239
$842$	2.01962	0.0696005
$843$	−9.36345	−0.322494
$844$	−6.33949	−0.218214
$845$	12.9770	0.446423
$846$	9.06300	0.311592
$847$	−17.7036	−0.608304
$848$	12.8478	0.441195
$849$	−8.43648	−0.289539
$850$	−2.90146	−0.0995194
$851$	4.53011	0.155290
$852$	1.76044	0.0603117
$853$	17.1518	0.587268	0.293634	−	0.955918i	$-0.405135\pi$
$853$	17.1518	0.587268	0.293634	+	0.955918i	$0.405135\pi$
$854$	−9.66827	−0.330841
$855$	2.46247	0.0842147
$856$	−7.53359	−0.257493
$857$	−39.9535	−1.36478	−0.682392	−	0.730986i	$-0.739060\pi$
$857$	−39.9535	−1.36478	−0.682392	+	0.730986i	$0.739060\pi$
$858$	−0.209562	−0.00715432
$859$	−46.4688	−1.58549	−0.792747	−	0.609551i	$-0.791350\pi$
$859$	−46.4688	−1.58549	−0.792747	+	0.609551i	$0.791350\pi$
$860$	−2.16365	−0.0737797
$861$	−3.28383	−0.111913
$862$	−38.1102	−1.29804
$863$	−13.5713	−0.461974	−0.230987	−	0.972957i	$-0.574195\pi$
$863$	−13.5713	−0.461974	−0.230987	+	0.972957i	$0.574195\pi$
$864$	−1.89311	−0.0644049
$865$	−21.5517	−0.732779
$866$	7.36690	0.250337
$867$	−2.75494	−0.0935628
$868$	−7.92143	−0.268871
$869$	−30.7789	−1.04410
$870$	1.94692	0.0660069
$871$	−1.71141	−0.0579888
$872$	5.91804	0.200410
$873$	19.3354	0.654403
$874$	1.00109	0.0338624
$875$	2.34471	0.0792658
$876$	−0.608829	−0.0205704
$877$	52.8279	1.78387	0.891936	−	0.452161i	$-0.149347\pi$
$877$	52.8279	1.78387	0.891936	+	0.452161i	$0.149347\pi$
$878$	−36.3794	−1.22775
$879$	10.8394	0.365602
$880$	−4.30702	−0.145190
$881$	−49.5291	−1.66868	−0.834339	−	0.551251i	$-0.814151\pi$
$881$	−49.5291	−1.66868	−0.834339	+	0.551251i	$0.814151\pi$
$882$	4.35212	0.146543
$883$	−27.1728	−0.914436	−0.457218	−	0.889355i	$-0.651154\pi$
$883$	−27.1728	−0.914436	−0.457218	+	0.889355i	$0.651154\pi$
$884$	0.439747	0.0147903
$885$	−2.81648	−0.0946749
$886$	−25.2432	−0.848062
$887$	51.6010	1.73259	0.866296	−	0.499530i	$-0.166494\pi$
$887$	51.6010	1.73259	0.866296	+	0.499530i	$0.166494\pi$
$888$	1.23486	0.0414391
$889$	−37.2907	−1.25069
$890$	3.45632	0.115856
$891$	34.8139	1.16631
$892$	10.1762	0.340723
$893$	−2.65928	−0.0889895
$894$	−7.30952	−0.244467
$895$	12.3686	0.413435
$896$	−2.34471	−0.0783314
$897$	−0.0573029	−0.00191329
$898$	12.1827	0.406543
$899$	−20.4887	−0.683335
$900$	−2.89694	−0.0965646
$901$	−37.2774	−1.24189
$902$	18.7897	0.625627
$903$	−1.62864	−0.0541978
$904$	6.64989	0.221172
$905$	4.07510	0.135461
$906$	−1.17161	−0.0389242
$907$	15.8778	0.527212	0.263606	−	0.964630i	$-0.415088\pi$
$907$	15.8778	0.527212	0.263606	+	0.964630i	$0.415088\pi$
$908$	17.1555	0.569326
$909$	31.6779	1.05069
$910$	−0.355366	−0.0117803
$911$	25.4708	0.843884	0.421942	−	0.906623i	$-0.361349\pi$
$911$	25.4708	0.843884	0.421942	+	0.906623i	$0.361349\pi$
$912$	0.272886	0.00903616
$913$	55.5310	1.83781
$914$	33.4459	1.10629
$915$	−1.32376	−0.0437620
$916$	25.4373	0.840471
$917$	−32.7844	−1.08264
$918$	5.49279	0.181289
$919$	32.6551	1.07719	0.538596	−	0.842564i	$-0.318955\pi$
$919$	32.6551	1.07719	0.538596	+	0.842564i	$0.318955\pi$
$920$	−1.17772	−0.0388282
$921$	10.6877	0.352170
$922$	11.8769	0.391145
$923$	−0.831110	−0.0273563
$924$	−3.24202	−0.106655
$925$	3.84651	0.126473
$926$	−25.8702	−0.850147
$927$	−15.0915	−0.495671
$928$	−6.06456	−0.199079
$929$	55.1004	1.80779	0.903893	−	0.427759i	$-0.140697\pi$
$929$	55.1004	1.80779	0.903893	+	0.427759i	$0.140697\pi$
$930$	−1.08458	−0.0355649
$931$	−1.27701	−0.0418522
$932$	−19.7605	−0.647278
$933$	−6.34900	−0.207857
$934$	−29.7130	−0.972238
$935$	12.4967	0.408685
$936$	0.439061	0.0143512
$937$	−42.2839	−1.38136	−0.690678	−	0.723163i	$-0.742688\pi$
$937$	−42.2839	−1.38136	−0.690678	+	0.723163i	$0.742688\pi$
$938$	−26.4763	−0.864481
$939$	2.41394	0.0787760
$940$	3.12847	0.102040
$941$	25.6397	0.835829	0.417915	−	0.908486i	$-0.362761\pi$
$941$	25.6397	0.835829	0.417915	+	0.908486i	$0.362761\pi$
$942$	7.43553	0.242263
$943$	5.13787	0.167312
$944$	8.77318	0.285543
$945$	−4.43880	−0.144394
$946$	9.31887	0.302983
$947$	−24.5699	−0.798414	−0.399207	−	0.916861i	$-0.630715\pi$
$947$	−24.5699	−0.798414	−0.399207	+	0.916861i	$0.630715\pi$
$948$	−2.29417	−0.0745111
$949$	0.287430	0.00933036
$950$	0.850025	0.0275785
$951$	−8.44695	−0.273911
$952$	6.80310	0.220490
$953$	−34.2866	−1.11065	−0.555326	−	0.831632i	$-0.687407\pi$
$953$	−34.2866	−1.11065	−0.555326	+	0.831632i	$0.687407\pi$
$954$	−37.2192	−1.20502
$955$	−21.3120	−0.689640
$956$	23.0312	0.744882
$957$	−8.38544	−0.271063
$958$	−1.19710	−0.0386766
$959$	22.7137	0.733463
$960$	−0.321033	−0.0103613
$961$	−19.5863	−0.631815
$962$	−0.582979	−0.0187960
$963$	21.8244	0.703280
$964$	−21.9418	−0.706699
$965$	−3.22833	−0.103924
$966$	−0.886504	−0.0285228
$967$	−52.5731	−1.69064	−0.845319	−	0.534262i	$-0.820590\pi$
$967$	−52.5731	−1.69064	−0.845319	+	0.534262i	$0.820590\pi$
$968$	7.55045	0.242681
$969$	−0.791768	−0.0254353
$970$	6.67442	0.214303
$971$	14.3289	0.459838	0.229919	−	0.973210i	$-0.426154\pi$
$971$	14.3289	0.459838	0.229919	+	0.973210i	$0.426154\pi$
$972$	8.27426	0.265397
$973$	−24.0544	−0.771148
$974$	−31.3802	−1.00549
$975$	−0.0486558	−0.00155823
$976$	4.12343	0.131988
$977$	−44.4430	−1.42186	−0.710929	−	0.703263i	$-0.751725\pi$
$977$	−44.4430	−1.42186	−0.710929	+	0.703263i	$0.751725\pi$
$978$	−4.69135	−0.150013
$979$	−14.8864	−0.475773
$980$	1.50232	0.0479897
$981$	−17.1442	−0.547372
$982$	20.8352	0.664877
$983$	46.3054	1.47691	0.738456	−	0.674301i	$-0.235555\pi$
$983$	46.3054	1.47691	0.738456	+	0.674301i	$0.235555\pi$
$984$	1.40053	0.0446471
$985$	−17.7112	−0.564327
$986$	17.5961	0.560374
$987$	2.35490	0.0749572
$988$	−0.128830	−0.00409864
$989$	2.54817	0.0810270
$990$	12.4772	0.396551
$991$	23.2970	0.740053	0.370027	−	0.929021i	$-0.379349\pi$
$991$	23.2970	0.740053	0.370027	+	0.929021i	$0.379349\pi$
$992$	3.37842	0.107265
$993$	11.1577	0.354078
$994$	−12.8577	−0.407821
$995$	−0.0733493	−0.00232533
$996$	4.13912	0.131153
$997$	12.9217	0.409235	0.204617	−	0.978842i	$-0.434405\pi$
$997$	12.9217	0.409235	0.204617	+	0.978842i	$0.434405\pi$
$998$	11.1576	0.353188
$999$	−7.28187	−0.230388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.15	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.321033 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.321033 q^{6} -2.34471 q^{7} +1.00000 q^{8} -2.89694 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.321033 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.321033 q^{6} -2.34471 q^{7} +1.00000 q^{8} -2.89694 q^{9} -1.00000 q^{10} +4.30702 q^{11} +0.321033 q^{12} -0.151560 q^{13} -2.34471 q^{14} -0.321033 q^{15} +1.00000 q^{16} -2.90146 q^{17} -2.89694 q^{18} +0.850025 q^{19} -1.00000 q^{20} -0.752730 q^{21} +4.30702 q^{22} +1.17772 q^{23} +0.321033 q^{24} +1.00000 q^{25} -0.151560 q^{26} -1.89311 q^{27} -2.34471 q^{28} -6.06456 q^{29} -0.321033 q^{30} +3.37842 q^{31} +1.00000 q^{32} +1.38269 q^{33} -2.90146 q^{34} +2.34471 q^{35} -2.89694 q^{36} +3.84651 q^{37} +0.850025 q^{38} -0.0486558 q^{39} -1.00000 q^{40} +4.36256 q^{41} -0.752730 q^{42} +2.16365 q^{43} +4.30702 q^{44} +2.89694 q^{45} +1.17772 q^{46} -3.12847 q^{47} +0.321033 q^{48} -1.50232 q^{49} +1.00000 q^{50} -0.931464 q^{51} -0.151560 q^{52} +12.8478 q^{53} -1.89311 q^{54} -4.30702 q^{55} -2.34471 q^{56} +0.272886 q^{57} -6.06456 q^{58} +8.77318 q^{59} -0.321033 q^{60} +4.12343 q^{61} +3.37842 q^{62} +6.79249 q^{63} +1.00000 q^{64} +0.151560 q^{65} +1.38269 q^{66} +11.2919 q^{67} -2.90146 q^{68} +0.378086 q^{69} +2.34471 q^{70} +5.48369 q^{71} -2.89694 q^{72} -1.89647 q^{73} +3.84651 q^{74} +0.321033 q^{75} +0.850025 q^{76} -10.0987 q^{77} -0.0486558 q^{78} -7.14621 q^{79} -1.00000 q^{80} +8.08306 q^{81} +4.36256 q^{82} +12.8931 q^{83} -0.752730 q^{84} +2.90146 q^{85} +2.16365 q^{86} -1.94692 q^{87} +4.30702 q^{88} -3.45632 q^{89} +2.89694 q^{90} +0.355366 q^{91} +1.17772 q^{92} +1.08458 q^{93} -3.12847 q^{94} -0.850025 q^{95} +0.321033 q^{96} -6.67442 q^{97} -1.50232 q^{98} -12.4772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 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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