LMFDB - Embedded newform 1205.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.38569.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} + 4x - 1 $ x^5 - 5x^3 + 4x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.95408$ of defining polynomial
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.442330 q^{2} -2.59927 q^{3} -1.80434 q^{4} +1.00000 q^{5} -1.14974 q^{6} +1.77251 q^{7} -1.68277 q^{8} +3.75621 q^{9} +O(q^{10})$	\(q+0.442330 q^{2} -2.59927 q^{3} -1.80434 q^{4} +1.00000 q^{5} -1.14974 q^{6} +1.77251 q^{7} -1.68277 q^{8} +3.75621 q^{9} +0.442330 q^{10} -5.16671 q^{11} +4.68998 q^{12} +3.86003 q^{13} +0.784032 q^{14} -2.59927 q^{15} +2.86435 q^{16} +5.69975 q^{17} +1.66149 q^{18} -1.54614 q^{19} -1.80434 q^{20} -4.60723 q^{21} -2.28539 q^{22} -6.38586 q^{23} +4.37399 q^{24} +1.00000 q^{25} +1.70741 q^{26} -1.96561 q^{27} -3.19821 q^{28} +3.55114 q^{29} -1.14974 q^{30} -0.248783 q^{31} +4.63254 q^{32} +13.4297 q^{33} +2.52117 q^{34} +1.77251 q^{35} -6.77750 q^{36} -5.20429 q^{37} -0.683906 q^{38} -10.0333 q^{39} -1.68277 q^{40} +2.30668 q^{41} -2.03791 q^{42} -12.0473 q^{43} +9.32252 q^{44} +3.75621 q^{45} -2.82466 q^{46} +1.78659 q^{47} -7.44522 q^{48} -3.85822 q^{49} +0.442330 q^{50} -14.8152 q^{51} -6.96482 q^{52} -8.80434 q^{53} -0.869446 q^{54} -5.16671 q^{55} -2.98273 q^{56} +4.01885 q^{57} +1.57078 q^{58} -3.45862 q^{59} +4.68998 q^{60} -10.7632 q^{61} -0.110044 q^{62} +6.65791 q^{63} -3.67959 q^{64} +3.86003 q^{65} +5.94034 q^{66} -11.3756 q^{67} -10.2843 q^{68} +16.5986 q^{69} +0.784032 q^{70} +1.11137 q^{71} -6.32086 q^{72} -1.42536 q^{73} -2.30201 q^{74} -2.59927 q^{75} +2.78978 q^{76} -9.15802 q^{77} -4.43801 q^{78} +5.35702 q^{79} +2.86435 q^{80} -6.15950 q^{81} +1.02031 q^{82} +4.69440 q^{83} +8.31302 q^{84} +5.69975 q^{85} -5.32890 q^{86} -9.23038 q^{87} +8.69440 q^{88} +13.0243 q^{89} +1.66149 q^{90} +6.84193 q^{91} +11.5223 q^{92} +0.646654 q^{93} +0.790262 q^{94} -1.54614 q^{95} -12.0412 q^{96} -18.0427 q^{97} -1.70661 q^{98} -19.4073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 5 q^{5} - 8 q^{6} - 10 q^{7} + 6 q^{9}+O(q^{10}) $ 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 5 * q^5 - 8 * q^6 - 10 * q^7 + 6 * q^9	\( 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 5 q^{5} - 8 q^{6} - 10 q^{7} + 6 q^{9} - q^{10} - 3 q^{11} + 8 q^{12} - q^{13} - q^{14} - 5 q^{15} + 15 q^{16} - 5 q^{17} + 4 q^{18} + 3 q^{19} + 3 q^{20} + 11 q^{21} - 13 q^{22} - 8 q^{23} - 14 q^{24} + 5 q^{25} + 14 q^{26} - 14 q^{27} - 17 q^{28} + 9 q^{29} - 8 q^{30} - 16 q^{31} - 16 q^{32} + 23 q^{33} - 10 q^{34} - 10 q^{35} - 17 q^{36} + 7 q^{37} - 22 q^{38} - 19 q^{39} + 9 q^{41} + 17 q^{42} - 32 q^{43} - 8 q^{44} + 6 q^{45} + 5 q^{46} - 7 q^{47} - 6 q^{48} + 9 q^{49} - q^{50} - 8 q^{51} - 10 q^{52} - 32 q^{53} + 32 q^{54} - 3 q^{55} - 18 q^{56} + 3 q^{57} + 11 q^{58} - 8 q^{59} + 8 q^{60} - 12 q^{61} + 17 q^{62} - 11 q^{63} - 16 q^{64} - q^{65} + 15 q^{66} - 5 q^{67} - 2 q^{68} + 7 q^{69} - q^{70} - 11 q^{71} + 7 q^{72} - 29 q^{73} + 10 q^{74} - 5 q^{75} - 8 q^{76} - 5 q^{77} + 2 q^{78} + 16 q^{79} + 15 q^{80} - 15 q^{81} - 2 q^{82} - 10 q^{83} + 5 q^{84} - 5 q^{85} + 14 q^{86} - 37 q^{87} + 10 q^{88} + 9 q^{89} + 4 q^{90} + 12 q^{91} - 25 q^{92} + 15 q^{93} - 11 q^{94} + 3 q^{95} - 3 q^{96} - 43 q^{97} + 30 q^{98} - 30 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 5 * q^5 - 8 * q^6 - 10 * q^7 + 6 * q^9 - q^10 - 3 * q^11 + 8 * q^12 - q^13 - q^14 - 5 * q^15 + 15 * q^16 - 5 * q^17 + 4 * q^18 + 3 * q^19 + 3 * q^20 + 11 * q^21 - 13 * q^22 - 8 * q^23 - 14 * q^24 + 5 * q^25 + 14 * q^26 - 14 * q^27 - 17 * q^28 + 9 * q^29 - 8 * q^30 - 16 * q^31 - 16 * q^32 + 23 * q^33 - 10 * q^34 - 10 * q^35 - 17 * q^36 + 7 * q^37 - 22 * q^38 - 19 * q^39 + 9 * q^41 + 17 * q^42 - 32 * q^43 - 8 * q^44 + 6 * q^45 + 5 * q^46 - 7 * q^47 - 6 * q^48 + 9 * q^49 - q^50 - 8 * q^51 - 10 * q^52 - 32 * q^53 + 32 * q^54 - 3 * q^55 - 18 * q^56 + 3 * q^57 + 11 * q^58 - 8 * q^59 + 8 * q^60 - 12 * q^61 + 17 * q^62 - 11 * q^63 - 16 * q^64 - q^65 + 15 * q^66 - 5 * q^67 - 2 * q^68 + 7 * q^69 - q^70 - 11 * q^71 + 7 * q^72 - 29 * q^73 + 10 * q^74 - 5 * q^75 - 8 * q^76 - 5 * q^77 + 2 * q^78 + 16 * q^79 + 15 * q^80 - 15 * q^81 - 2 * q^82 - 10 * q^83 + 5 * q^84 - 5 * q^85 + 14 * q^86 - 37 * q^87 + 10 * q^88 + 9 * q^89 + 4 * q^90 + 12 * q^91 - 25 * q^92 + 15 * q^93 - 11 * q^94 + 3 * q^95 - 3 * q^96 - 43 * q^97 + 30 * q^98 - 30 * 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 $

$2$	0.442330	0.312774	0.156387	−	0.987696i	$-0.450015\pi$
$2$	0.442330	0.312774	0.156387	+	0.987696i	$0.450015\pi$
$3$	−2.59927	−1.50069	−0.750345	−	0.661046i	$-0.770113\pi$
$3$	−2.59927	−1.50069	−0.750345	+	0.661046i	$0.770113\pi$
$4$	−1.80434	−0.902172
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.14974	−0.469377
$7$	1.77251	0.669945	0.334972	−	0.942228i	$-0.391273\pi$
$7$	1.77251	0.669945	0.334972	+	0.942228i	$0.391273\pi$
$8$	−1.68277	−0.594951
$9$	3.75621	1.25207
$10$	0.442330	0.139877
$11$	−5.16671	−1.55782	−0.778910	−	0.627135i	$-0.784227\pi$
$11$	−5.16671	−1.55782	−0.778910	+	0.627135i	$0.784227\pi$
$12$	4.68998	1.35388
$13$	3.86003	1.07058	0.535290	−	0.844669i	$-0.320202\pi$
$13$	3.86003	1.07058	0.535290	+	0.844669i	$0.320202\pi$
$14$	0.784032	0.209541
$15$	−2.59927	−0.671129
$16$	2.86435	0.716087
$17$	5.69975	1.38239	0.691196	−	0.722668i	$-0.257084\pi$
$17$	5.69975	1.38239	0.691196	+	0.722668i	$0.257084\pi$
$18$	1.66149	0.391616
$19$	−1.54614	−0.354710	−0.177355	−	0.984147i	$-0.556754\pi$
$19$	−1.54614	−0.354710	−0.177355	+	0.984147i	$0.556754\pi$
$20$	−1.80434	−0.403464
$21$	−4.60723	−1.00538
$22$	−2.28539	−0.487246
$23$	−6.38586	−1.33154	−0.665772	−	0.746155i	$-0.731898\pi$
$23$	−6.38586	−1.33154	−0.665772	+	0.746155i	$0.731898\pi$
$24$	4.37399	0.892837
$25$	1.00000	0.200000
$26$	1.70741	0.334850
$27$	−1.96561	−0.378281
$28$	−3.19821	−0.604405
$29$	3.55114	0.659430	0.329715	−	0.944080i	$-0.393047\pi$
$29$	3.55114	0.659430	0.329715	+	0.944080i	$0.393047\pi$
$30$	−1.14974	−0.209912
$31$	−0.248783	−0.0446827	−0.0223414	−	0.999750i	$-0.507112\pi$
$31$	−0.248783	−0.0446827	−0.0223414	+	0.999750i	$0.507112\pi$
$32$	4.63254	0.818924
$33$	13.4297	2.33781
$34$	2.52117	0.432377
$35$	1.77251	0.299608
$36$	−6.77750	−1.12958
$37$	−5.20429	−0.855580	−0.427790	−	0.903878i	$-0.640708\pi$
$37$	−5.20429	−0.855580	−0.427790	+	0.903878i	$0.640708\pi$
$38$	−0.683906	−0.110944
$39$	−10.0333	−1.60661
$40$	−1.68277	−0.266070
$41$	2.30668	0.360242	0.180121	−	0.983644i	$-0.442351\pi$
$41$	2.30668	0.360242	0.180121	+	0.983644i	$0.442351\pi$
$42$	−2.03791	−0.314457
$43$	−12.0473	−1.83720	−0.918602	−	0.395185i	$-0.870680\pi$
$43$	−12.0473	−1.83720	−0.918602	+	0.395185i	$0.870680\pi$
$44$	9.32252	1.40542
$45$	3.75621	0.559943
$46$	−2.82466	−0.416473
$47$	1.78659	0.260601	0.130300	−	0.991475i	$-0.458406\pi$
$47$	1.78659	0.260601	0.130300	+	0.991475i	$0.458406\pi$
$48$	−7.44522	−1.07462
$49$	−3.85822	−0.551174
$50$	0.442330	0.0625549
$51$	−14.8152	−2.07454
$52$	−6.96482	−0.965847
$53$	−8.80434	−1.20937	−0.604685	−	0.796465i	$-0.706701\pi$
$53$	−8.80434	−1.20937	−0.604685	+	0.796465i	$0.706701\pi$
$54$	−0.869446	−0.118317
$55$	−5.16671	−0.696678
$56$	−2.98273	−0.398584
$57$	4.01885	0.532310
$58$	1.57078	0.206253
$59$	−3.45862	−0.450274	−0.225137	−	0.974327i	$-0.572283\pi$
$59$	−3.45862	−0.450274	−0.225137	+	0.974327i	$0.572283\pi$
$60$	4.68998	0.605474
$61$	−10.7632	−1.37809	−0.689043	−	0.724721i	$-0.741969\pi$
$61$	−10.7632	−1.37809	−0.689043	+	0.724721i	$0.741969\pi$
$62$	−0.110044	−0.0139756
$63$	6.65791	0.838818
$64$	−3.67959	−0.459948
$65$	3.86003	0.478778
$66$	5.94034	0.731206
$67$	−11.3756	−1.38976	−0.694878	−	0.719128i	$-0.744542\pi$
$67$	−11.3756	−1.38976	−0.694878	+	0.719128i	$0.744542\pi$
$68$	−10.2843	−1.24716
$69$	16.5986	1.99824
$70$	0.784032	0.0937098
$71$	1.11137	0.131895	0.0659476	−	0.997823i	$-0.478993\pi$
$71$	1.11137	0.131895	0.0659476	+	0.997823i	$0.478993\pi$
$72$	−6.32086	−0.744921
$73$	−1.42536	−0.166826	−0.0834128	−	0.996515i	$-0.526582\pi$
$73$	−1.42536	−0.166826	−0.0834128	+	0.996515i	$0.526582\pi$
$74$	−2.30201	−0.267603
$75$	−2.59927	−0.300138
$76$	2.78978	0.320009
$77$	−9.15802	−1.04365
$78$	−4.43801	−0.502506
$79$	5.35702	0.602712	0.301356	−	0.953512i	$-0.402561\pi$
$79$	5.35702	0.602712	0.301356	+	0.953512i	$0.402561\pi$
$80$	2.86435	0.320244
$81$	−6.15950	−0.684389
$82$	1.02031	0.112675
$83$	4.69440	0.515278	0.257639	−	0.966241i	$-0.417056\pi$
$83$	4.69440	0.515278	0.257639	+	0.966241i	$0.417056\pi$
$84$	8.31302	0.907025
$85$	5.69975	0.618224
$86$	−5.32890	−0.574630
$87$	−9.23038	−0.989601
$88$	8.69440	0.926826
$89$	13.0243	1.38057	0.690286	−	0.723536i	$-0.257485\pi$
$89$	13.0243	1.38057	0.690286	+	0.723536i	$0.257485\pi$
$90$	1.66149	0.175136
$91$	6.84193	0.717229
$92$	11.5223	1.20128
$93$	0.646654	0.0670549
$94$	0.790262	0.0815093
$95$	−1.54614	−0.158631
$96$	−12.0412	−1.22895
$97$	−18.0427	−1.83196	−0.915978	−	0.401228i	$-0.868584\pi$
$97$	−18.0427	−1.83196	−0.915978	+	0.401228i	$0.868584\pi$
$98$	−1.70661	−0.172393
$99$	−19.4073	−1.95050
$100$	−1.80434	−0.180434
$101$	−0.767440	−0.0763631	−0.0381816	−	0.999271i	$-0.512157\pi$
$101$	−0.767440	−0.0763631	−0.0381816	+	0.999271i	$0.512157\pi$
$102$	−6.55320	−0.648863
$103$	4.73756	0.466805	0.233403	−	0.972380i	$-0.425014\pi$
$103$	4.73756	0.466805	0.233403	+	0.972380i	$0.425014\pi$
$104$	−6.49556	−0.636942
$105$	−4.60723	−0.449619
$106$	−3.89442	−0.378260
$107$	−17.6773	−1.70893	−0.854466	−	0.519508i	$-0.826115\pi$
$107$	−17.6773	−1.70893	−0.854466	+	0.519508i	$0.826115\pi$
$108$	3.54663	0.341275
$109$	−8.69294	−0.832633	−0.416316	−	0.909220i	$-0.636679\pi$
$109$	−8.69294	−0.832633	−0.416316	+	0.909220i	$0.636679\pi$
$110$	−2.28539	−0.217903
$111$	13.5274	1.28396
$112$	5.07708	0.479739
$113$	−3.02317	−0.284396	−0.142198	−	0.989838i	$-0.545417\pi$
$113$	−3.02317	−0.284396	−0.142198	+	0.989838i	$0.545417\pi$
$114$	1.77766	0.166493
$115$	−6.38586	−0.595485
$116$	−6.40748	−0.594920
$117$	14.4991	1.34044
$118$	−1.52985	−0.140834
$119$	10.1028	0.926126
$120$	4.37399	0.399289
$121$	15.6949	1.42680
$122$	−4.76088	−0.431030
$123$	−5.99568	−0.540612
$124$	0.448890	0.0403115
$125$	1.00000	0.0894427
$126$	2.94499	0.262361
$127$	−7.12578	−0.632311	−0.316155	−	0.948707i	$-0.602392\pi$
$127$	−7.12578	−0.632311	−0.316155	+	0.948707i	$0.602392\pi$
$128$	−10.8927	−0.962784
$129$	31.3143	2.75707
$130$	1.70741	0.149749
$131$	8.93756	0.780878	0.390439	−	0.920629i	$-0.372323\pi$
$131$	8.93756	0.780878	0.390439	+	0.920629i	$0.372323\pi$
$132$	−24.2318	−2.10910
$133$	−2.74055	−0.237636
$134$	−5.03179	−0.434680
$135$	−1.96561	−0.169172
$136$	−9.59139	−0.822455
$137$	−19.4835	−1.66459	−0.832296	−	0.554332i	$-0.812974\pi$
$137$	−19.4835	−1.66459	−0.832296	+	0.554332i	$0.812974\pi$
$138$	7.34205	0.624997
$139$	14.3856	1.22017	0.610084	−	0.792337i	$-0.291136\pi$
$139$	14.3856	1.22017	0.610084	+	0.792337i	$0.291136\pi$
$140$	−3.19821	−0.270298
$141$	−4.64383	−0.391081
$142$	0.491591	0.0412534
$143$	−19.9436	−1.66777
$144$	10.7591	0.896592
$145$	3.55114	0.294906
$146$	−0.630479	−0.0521788
$147$	10.0286	0.827142
$148$	9.39033	0.771880
$149$	16.1171	1.32036	0.660182	−	0.751106i	$-0.270479\pi$
$149$	16.1171	1.32036	0.660182	+	0.751106i	$0.270479\pi$
$150$	−1.14974	−0.0938755
$151$	5.26264	0.428267	0.214134	−	0.976804i	$-0.431307\pi$
$151$	5.26264	0.428267	0.214134	+	0.976804i	$0.431307\pi$
$152$	2.60181	0.211035
$153$	21.4095	1.73085
$154$	−4.05087	−0.326428
$155$	−0.248783	−0.0199827
$156$	18.1035	1.44944
$157$	−0.335280	−0.0267583	−0.0133791	−	0.999910i	$-0.504259\pi$
$157$	−0.335280	−0.0267583	−0.0133791	+	0.999910i	$0.504259\pi$
$158$	2.36957	0.188513
$159$	22.8849	1.81489
$160$	4.63254	0.366234
$161$	−11.3190	−0.892061
$162$	−2.72453	−0.214059
$163$	23.5461	1.84428	0.922138	−	0.386861i	$-0.126441\pi$
$163$	23.5461	1.84428	0.922138	+	0.386861i	$0.126441\pi$
$164$	−4.16204	−0.325001
$165$	13.4297	1.04550
$166$	2.07647	0.161166
$167$	16.7746	1.29805	0.649027	−	0.760765i	$-0.275176\pi$
$167$	16.7746	1.29805	0.649027	+	0.760765i	$0.275176\pi$
$168$	7.75292	0.598151
$169$	1.89982	0.146140
$170$	2.52117	0.193365
$171$	−5.80765	−0.444122
$172$	21.7376	1.65747
$173$	11.9428	0.907998	0.453999	−	0.891002i	$-0.349997\pi$
$173$	11.9428	0.907998	0.453999	+	0.891002i	$0.349997\pi$
$174$	−4.08287	−0.309522
$175$	1.77251	0.133989
$176$	−14.7992	−1.11553
$177$	8.98990	0.675722
$178$	5.76103	0.431808
$179$	−13.5102	−1.00980	−0.504899	−	0.863178i	$-0.668470\pi$
$179$	−13.5102	−1.00980	−0.504899	+	0.863178i	$0.668470\pi$
$180$	−6.77750	−0.505165
$181$	−20.2476	−1.50500	−0.752498	−	0.658595i	$-0.771151\pi$
$181$	−20.2476	−1.50500	−0.752498	+	0.658595i	$0.771151\pi$
$182$	3.02639	0.224331
$183$	27.9765	2.06808
$184$	10.7460	0.792203
$185$	−5.20429	−0.382627
$186$	0.286034	0.0209731
$187$	−29.4489	−2.15352
$188$	−3.22362	−0.235107
$189$	−3.48405	−0.253427
$190$	−0.683906	−0.0496157
$191$	−3.31200	−0.239648	−0.119824	−	0.992795i	$-0.538233\pi$
$191$	−3.31200	−0.239648	−0.119824	+	0.992795i	$0.538233\pi$
$192$	9.56425	0.690240
$193$	−21.5544	−1.55152	−0.775761	−	0.631026i	$-0.782634\pi$
$193$	−21.5544	−1.55152	−0.775761	+	0.631026i	$0.782634\pi$
$194$	−7.98081	−0.572989
$195$	−10.0333	−0.718497
$196$	6.96156	0.497254
$197$	−2.47264	−0.176168	−0.0880840	−	0.996113i	$-0.528074\pi$
$197$	−2.47264	−0.176168	−0.0880840	+	0.996113i	$0.528074\pi$
$198$	−8.58440	−0.610067
$199$	4.28612	0.303835	0.151917	−	0.988393i	$-0.451455\pi$
$199$	4.28612	0.303835	0.151917	+	0.988393i	$0.451455\pi$
$200$	−1.68277	−0.118990
$201$	29.5684	2.08559
$202$	−0.339461	−0.0238844
$203$	6.29442	0.441782
$204$	26.7317	1.87159
$205$	2.30668	0.161105
$206$	2.09556	0.146005
$207$	−23.9867	−1.66719
$208$	11.0565	0.766628
$209$	7.98847	0.552574
$210$	−2.03791	−0.140629
$211$	−15.5232	−1.06866	−0.534330	−	0.845276i	$-0.679436\pi$
$211$	−15.5232	−1.06866	−0.534330	+	0.845276i	$0.679436\pi$
$212$	15.8861	1.09106
$213$	−2.88875	−0.197934
$214$	−7.81921	−0.534510
$215$	−12.0473	−0.821622
$216$	3.30767	0.225058
$217$	−0.440969	−0.0299349
$218$	−3.84515	−0.260426
$219$	3.70490	0.250354
$220$	9.32252	0.628524
$221$	22.0012	1.47996
$222$	5.98355	0.401590
$223$	−11.7155	−0.784529	−0.392264	−	0.919853i	$-0.628308\pi$
$223$	−11.7155	−0.784529	−0.392264	+	0.919853i	$0.628308\pi$
$224$	8.21120	0.548634
$225$	3.75621	0.250414
$226$	−1.33724	−0.0889517
$227$	20.1580	1.33793	0.668966	−	0.743293i	$-0.266737\pi$
$227$	20.1580	1.33793	0.668966	+	0.743293i	$0.266737\pi$
$228$	−7.25139	−0.480235
$229$	4.98705	0.329553	0.164777	−	0.986331i	$-0.447310\pi$
$229$	4.98705	0.329553	0.164777	+	0.986331i	$0.447310\pi$
$230$	−2.82466	−0.186252
$231$	23.8042	1.56620
$232$	−5.97577	−0.392329
$233$	−5.88574	−0.385588	−0.192794	−	0.981239i	$-0.561755\pi$
$233$	−5.88574	−0.385588	−0.192794	+	0.981239i	$0.561755\pi$
$234$	6.41338	0.419256
$235$	1.78659	0.116544
$236$	6.24055	0.406225
$237$	−13.9243	−0.904483
$238$	4.46879	0.289668
$239$	−21.1934	−1.37089	−0.685443	−	0.728126i	$-0.740392\pi$
$239$	−21.1934	−1.37089	−0.685443	+	0.728126i	$0.740392\pi$
$240$	−7.44522	−0.480587
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	6.94230	0.446268
$243$	21.9070	1.40534
$244$	19.4205	1.24327
$245$	−3.85822	−0.246493
$246$	−2.65207	−0.169090
$247$	−5.96816	−0.379745
$248$	0.418645	0.0265840
$249$	−12.2020	−0.773272
$250$	0.442330	0.0279754
$251$	−9.14871	−0.577461	−0.288731	−	0.957410i	$-0.593233\pi$
$251$	−9.14871	−0.577461	−0.288731	+	0.957410i	$0.593233\pi$
$252$	−12.0132	−0.756759
$253$	32.9939	2.07431
$254$	−3.15195	−0.197771
$255$	−14.8152	−0.927763
$256$	2.54103	0.158814
$257$	24.4085	1.52256	0.761280	−	0.648423i	$-0.224571\pi$
$257$	24.4085	1.52256	0.761280	+	0.648423i	$0.224571\pi$
$258$	13.8513	0.862342
$259$	−9.22464	−0.573191
$260$	−6.96482	−0.431940
$261$	13.3388	0.825654
$262$	3.95335	0.244239
$263$	8.05368	0.496611	0.248306	−	0.968682i	$-0.420126\pi$
$263$	8.05368	0.496611	0.248306	+	0.968682i	$0.420126\pi$
$264$	−22.5991	−1.39088
$265$	−8.80434	−0.540847
$266$	−1.21223	−0.0743264
$267$	−33.8537	−2.07181
$268$	20.5256	1.25380
$269$	8.12648	0.495480	0.247740	−	0.968826i	$-0.420312\pi$
$269$	8.12648	0.495480	0.247740	+	0.968826i	$0.420312\pi$
$270$	−0.869446	−0.0529128
$271$	7.21696	0.438399	0.219199	−	0.975680i	$-0.429655\pi$
$271$	7.21696	0.438399	0.219199	+	0.975680i	$0.429655\pi$
$272$	16.3261	0.989912
$273$	−17.7840	−1.07634
$274$	−8.61815	−0.520642
$275$	−5.16671	−0.311564
$276$	−29.9496	−1.80275
$277$	4.39874	0.264295	0.132147	−	0.991230i	$-0.457813\pi$
$277$	4.39874	0.264295	0.132147	+	0.991230i	$0.457813\pi$
$278$	6.36316	0.381637
$279$	−0.934481	−0.0559459
$280$	−2.98273	−0.178252
$281$	−13.7294	−0.819025	−0.409513	−	0.912304i	$-0.634301\pi$
$281$	−13.7294	−0.819025	−0.409513	+	0.912304i	$0.634301\pi$
$282$	−2.05410	−0.122320
$283$	−15.6129	−0.928088	−0.464044	−	0.885812i	$-0.653602\pi$
$283$	−15.6129	−0.928088	−0.464044	+	0.885812i	$0.653602\pi$
$284$	−2.00529	−0.118992
$285$	4.01885	0.238056
$286$	−8.82166	−0.521636
$287$	4.08860	0.241342
$288$	17.4008	1.02535
$289$	15.4871	0.911006
$290$	1.57078	0.0922391
$291$	46.8978	2.74920
$292$	2.57184	0.150505
$293$	−27.4784	−1.60530	−0.802652	−	0.596447i	$-0.796579\pi$
$293$	−27.4784	−1.60530	−0.802652	+	0.596447i	$0.796579\pi$
$294$	4.43593	0.258709
$295$	−3.45862	−0.201369
$296$	8.75764	0.509028
$297$	10.1557	0.589294
$298$	7.12907	0.412976
$299$	−24.6496	−1.42552
$300$	4.68998	0.270776
$301$	−21.3540	−1.23082
$302$	2.32782	0.133951
$303$	1.99478	0.114597
$304$	−4.42870	−0.254003
$305$	−10.7632	−0.616299
$306$	9.47004	0.541366
$307$	−10.1259	−0.577917	−0.288958	−	0.957342i	$-0.593309\pi$
$307$	−10.1259	−0.577917	−0.288958	+	0.957342i	$0.593309\pi$
$308$	16.5242	0.941555
$309$	−12.3142	−0.700530
$310$	−0.110044	−0.00625008
$311$	6.89127	0.390768	0.195384	−	0.980727i	$-0.437405\pi$
$311$	6.89127	0.390768	0.195384	+	0.980727i	$0.437405\pi$
$312$	16.8837	0.955853
$313$	−22.2496	−1.25762	−0.628811	−	0.777558i	$-0.716458\pi$
$313$	−22.2496	−1.25762	−0.628811	+	0.777558i	$0.716458\pi$
$314$	−0.148304	−0.00836930
$315$	6.65791	0.375131
$316$	−9.66591	−0.543750
$317$	−10.7659	−0.604675	−0.302337	−	0.953201i	$-0.597767\pi$
$317$	−10.7659	−0.604675	−0.302337	+	0.953201i	$0.597767\pi$
$318$	10.1227	0.567651
$319$	−18.3477	−1.02727
$320$	−3.67959	−0.205695
$321$	45.9482	2.56458
$322$	−5.00672	−0.279014
$323$	−8.81263	−0.490348
$324$	11.1139	0.617437
$325$	3.86003	0.214116
$326$	10.4152	0.576842
$327$	22.5953	1.24952
$328$	−3.88162	−0.214327
$329$	3.16674	0.174588
$330$	5.94034	0.327005
$331$	26.5505	1.45935	0.729674	−	0.683795i	$-0.239672\pi$
$331$	26.5505	1.45935	0.729674	+	0.683795i	$0.239672\pi$
$332$	−8.47032	−0.464869
$333$	−19.5484	−1.07125
$334$	7.41989	0.405998
$335$	−11.3756	−0.621518
$336$	−13.1967	−0.719939
$337$	35.7507	1.94746	0.973731	−	0.227701i	$-0.0731209\pi$
$337$	35.7507	1.94746	0.973731	+	0.227701i	$0.0731209\pi$
$338$	0.840347	0.0457089
$339$	7.85804	0.426790
$340$	−10.2843	−0.557745
$341$	1.28539	0.0696076
$342$	−2.56890	−0.138910
$343$	−19.2463	−1.03920
$344$	20.2730	1.09305
$345$	16.5986	0.893638
$346$	5.28268	0.283998
$347$	2.22117	0.119239	0.0596194	−	0.998221i	$-0.481011\pi$
$347$	2.22117	0.119239	0.0596194	+	0.998221i	$0.481011\pi$
$348$	16.6548	0.892790
$349$	−31.8328	−1.70397	−0.851985	−	0.523566i	$-0.824601\pi$
$349$	−31.8328	−1.70397	−0.851985	+	0.523566i	$0.824601\pi$
$350$	0.784032	0.0419083
$351$	−7.58729	−0.404980
$352$	−23.9349	−1.27574
$353$	−26.1958	−1.39426	−0.697131	−	0.716944i	$-0.745540\pi$
$353$	−26.1958	−1.39426	−0.697131	+	0.716944i	$0.745540\pi$
$354$	3.97650	0.211349
$355$	1.11137	0.0589853
$356$	−23.5003	−1.24551
$357$	−26.2600	−1.38983
$358$	−5.97596	−0.315839
$359$	5.74429	0.303172	0.151586	−	0.988444i	$-0.451562\pi$
$359$	5.74429	0.303172	0.151586	+	0.988444i	$0.451562\pi$
$360$	−6.32086	−0.333139
$361$	−16.6094	−0.874181
$362$	−8.95614	−0.470724
$363$	−40.7952	−2.14119
$364$	−12.3452	−0.647064
$365$	−1.42536	−0.0746067
$366$	12.3748	0.646842
$367$	29.6113	1.54570	0.772849	−	0.634590i	$-0.218831\pi$
$367$	29.6113	1.54570	0.772849	+	0.634590i	$0.218831\pi$
$368$	−18.2913	−0.953501
$369$	8.66437	0.451049
$370$	−2.30201	−0.119676
$371$	−15.6058	−0.810211
$372$	−1.16679	−0.0604951
$373$	−37.2280	−1.92759	−0.963797	−	0.266639i	$-0.914087\pi$
$373$	−37.2280	−1.92759	−0.963797	+	0.266639i	$0.914087\pi$
$374$	−13.0261	−0.673565
$375$	−2.59927	−0.134226
$376$	−3.00643	−0.155045
$377$	13.7075	0.705973
$378$	−1.54110	−0.0792655
$379$	9.39554	0.482617	0.241308	−	0.970449i	$-0.422424\pi$
$379$	9.39554	0.482617	0.241308	+	0.970449i	$0.422424\pi$
$380$	2.78978	0.143113
$381$	18.5218	0.948903
$382$	−1.46500	−0.0749557
$383$	−29.8566	−1.52560	−0.762799	−	0.646635i	$-0.776176\pi$
$383$	−29.8566	−1.52560	−0.762799	+	0.646635i	$0.776176\pi$
$384$	28.3130	1.44484
$385$	−9.15802	−0.466736
$386$	−9.53417	−0.485277
$387$	−45.2524	−2.30031
$388$	32.5552	1.65274
$389$	24.7658	1.25567	0.627837	−	0.778345i	$-0.283941\pi$
$389$	24.7658	1.25567	0.627837	+	0.778345i	$0.283941\pi$
$390$	−4.43801	−0.224727
$391$	−36.3978	−1.84072
$392$	6.49251	0.327922
$393$	−23.2311	−1.17186
$394$	−1.09372	−0.0551008
$395$	5.35702	0.269541
$396$	35.0174	1.75969
$397$	−29.2032	−1.46567	−0.732833	−	0.680409i	$-0.761802\pi$
$397$	−29.2032	−1.46567	−0.732833	+	0.680409i	$0.761802\pi$
$398$	1.89588	0.0950318
$399$	7.12344	0.356618
$400$	2.86435	0.143217
$401$	−11.4460	−0.571584	−0.285792	−	0.958292i	$-0.592257\pi$
$401$	−11.4460	−0.571584	−0.285792	+	0.958292i	$0.592257\pi$
$402$	13.0790	0.652320
$403$	−0.960309	−0.0478364
$404$	1.38473	0.0688927
$405$	−6.15950	−0.306068
$406$	2.78421	0.138178
$407$	26.8890	1.33284
$408$	24.9306	1.23425
$409$	9.24486	0.457129	0.228564	−	0.973529i	$-0.426597\pi$
$409$	9.24486	0.457129	0.228564	+	0.973529i	$0.426597\pi$
$410$	1.02031	0.0503896
$411$	50.6430	2.49804
$412$	−8.54819	−0.421139
$413$	−6.13043	−0.301659
$414$	−10.6100	−0.521454
$415$	4.69440	0.230439
$416$	17.8817	0.876723
$417$	−37.3920	−1.83109
$418$	3.53354	0.172831
$419$	−19.5257	−0.953895	−0.476947	−	0.878932i	$-0.658257\pi$
$419$	−19.5257	−0.953895	−0.476947	+	0.878932i	$0.658257\pi$
$420$	8.31302	0.405634
$421$	−9.70110	−0.472802	−0.236401	−	0.971656i	$-0.575968\pi$
$421$	−9.70110	−0.472802	−0.236401	+	0.971656i	$0.575968\pi$
$422$	−6.86636	−0.334249
$423$	6.71081	0.326291
$424$	14.8157	0.719515
$425$	5.69975	0.276478
$426$	−1.27778	−0.0619086
$427$	−19.0778	−0.923241
$428$	31.8960	1.54175
$429$	51.8389	2.50281
$430$	−5.32890	−0.256982
$431$	14.0276	0.675684	0.337842	−	0.941203i	$-0.390303\pi$
$431$	14.0276	0.675684	0.337842	+	0.941203i	$0.390303\pi$
$432$	−5.63018	−0.270882
$433$	18.9459	0.910483	0.455241	−	0.890368i	$-0.349553\pi$
$433$	18.9459	0.910483	0.455241	+	0.890368i	$0.349553\pi$
$434$	−0.195054	−0.00936288
$435$	−9.23038	−0.442563
$436$	15.6851	0.751178
$437$	9.87346	0.472312
$438$	1.63879	0.0783042
$439$	−20.6108	−0.983699	−0.491850	−	0.870680i	$-0.663679\pi$
$439$	−20.6108	−0.983699	−0.491850	+	0.870680i	$0.663679\pi$
$440$	8.69440	0.414489
$441$	−14.4923	−0.690109
$442$	9.73178	0.462893
$443$	4.57030	0.217142	0.108571	−	0.994089i	$-0.465373\pi$
$443$	4.57030	0.217142	0.108571	+	0.994089i	$0.465373\pi$
$444$	−24.4080	−1.15835
$445$	13.0243	0.617411
$446$	−5.18212	−0.245381
$447$	−41.8927	−1.98146
$448$	−6.52209	−0.308140
$449$	8.08757	0.381676	0.190838	−	0.981622i	$-0.438879\pi$
$449$	8.08757	0.381676	0.190838	+	0.981622i	$0.438879\pi$
$450$	1.66149	0.0783232
$451$	−11.9179	−0.561193
$452$	5.45484	0.256574
$453$	−13.6790	−0.642696
$454$	8.91648	0.418471
$455$	6.84193	0.320754
$456$	−6.76282	−0.316698
$457$	9.14520	0.427795	0.213897	−	0.976856i	$-0.431384\pi$
$457$	9.14520	0.427795	0.213897	+	0.976856i	$0.431384\pi$
$458$	2.20592	0.103076
$459$	−11.2034	−0.522932
$460$	11.5223	0.537230
$461$	29.8876	1.39200	0.696001	−	0.718040i	$-0.254961\pi$
$461$	29.8876	1.39200	0.696001	+	0.718040i	$0.254961\pi$
$462$	10.5293	0.489867
$463$	−24.8607	−1.15538	−0.577688	−	0.816258i	$-0.696045\pi$
$463$	−24.8607	−1.15538	−0.577688	+	0.816258i	$0.696045\pi$
$464$	10.1717	0.472209
$465$	0.646654	0.0299879
$466$	−2.60344	−0.120602
$467$	3.70086	0.171255	0.0856277	−	0.996327i	$-0.472710\pi$
$467$	3.70086	0.171255	0.0856277	+	0.996327i	$0.472710\pi$
$468$	−26.1614	−1.20931
$469$	−20.1634	−0.931060
$470$	0.790262	0.0364521
$471$	0.871484	0.0401559
$472$	5.82008	0.267891
$473$	62.2451	2.86203
$474$	−6.15915	−0.282899
$475$	−1.54614	−0.0709420
$476$	−18.2290	−0.835525
$477$	−33.0710	−1.51422
$478$	−9.37447	−0.428778
$479$	−20.3801	−0.931191	−0.465596	−	0.884998i	$-0.654160\pi$
$479$	−20.3801	−0.931191	−0.465596	+	0.884998i	$0.654160\pi$
$480$	−12.0412	−0.549604
$481$	−20.0887	−0.915966
$482$	0.442330	0.0201476
$483$	29.4211	1.33871
$484$	−28.3189	−1.28722
$485$	−18.0427	−0.819276
$486$	9.69013	0.439553
$487$	−10.0732	−0.456460	−0.228230	−	0.973607i	$-0.573294\pi$
$487$	−10.0732	−0.456460	−0.228230	+	0.973607i	$0.573294\pi$
$488$	18.1120	0.819893
$489$	−61.2028	−2.76769
$490$	−1.70661	−0.0770966
$491$	5.76779	0.260297	0.130148	−	0.991495i	$-0.458455\pi$
$491$	5.76779	0.260297	0.130148	+	0.991495i	$0.458455\pi$
$492$	10.8183	0.487725
$493$	20.2406	0.911591
$494$	−2.63990	−0.118775
$495$	−19.4073	−0.872291
$496$	−0.712600	−0.0319967
$497$	1.96991	0.0883625
$498$	−5.39732	−0.241860
$499$	43.3172	1.93914	0.969571	−	0.244810i	$-0.0787256\pi$
$499$	43.3172	1.93914	0.969571	+	0.244810i	$0.0787256\pi$
$500$	−1.80434	−0.0806927
$501$	−43.6016	−1.94798
$502$	−4.04674	−0.180615
$503$	−6.28795	−0.280366	−0.140183	−	0.990126i	$-0.544769\pi$
$503$	−6.28795	−0.280366	−0.140183	+	0.990126i	$0.544769\pi$
$504$	−11.2038	−0.499056
$505$	−0.767440	−0.0341506
$506$	14.5942	0.648790
$507$	−4.93815	−0.219311
$508$	12.8574	0.570453
$509$	1.70229	0.0754525	0.0377263	−	0.999288i	$-0.487989\pi$
$509$	1.70229	0.0754525	0.0377263	+	0.999288i	$0.487989\pi$
$510$	−6.55320	−0.290180
$511$	−2.52646	−0.111764
$512$	22.9093	1.01246
$513$	3.03911	0.134180
$514$	10.7966	0.476218
$515$	4.73756	0.208762
$516$	−56.5018	−2.48735
$517$	−9.23078	−0.405969
$518$	−4.08033	−0.179279
$519$	−31.0427	−1.36262
$520$	−6.49556	−0.284849
$521$	37.0593	1.62360	0.811799	−	0.583937i	$-0.198489\pi$
$521$	37.0593	1.62360	0.811799	+	0.583937i	$0.198489\pi$
$522$	5.90017	0.258243
$523$	−12.2682	−0.536452	−0.268226	−	0.963356i	$-0.586437\pi$
$523$	−12.2682	−0.536452	−0.268226	+	0.963356i	$0.586437\pi$
$524$	−16.1264	−0.704486
$525$	−4.60723	−0.201076
$526$	3.56238	0.155327
$527$	−1.41800	−0.0617690
$528$	38.4673	1.67407
$529$	17.7792	0.773010
$530$	−3.89442	−0.169163
$531$	−12.9913	−0.563776
$532$	4.94490	0.214389
$533$	8.90384	0.385668
$534$	−14.9745	−0.648010
$535$	−17.6773	−0.764257
$536$	19.1426	0.826836
$537$	35.1166	1.51539
$538$	3.59459	0.154974
$539$	19.9343	0.858631
$540$	3.54663	0.152623
$541$	16.5803	0.712842	0.356421	−	0.934325i	$-0.383997\pi$
$541$	16.5803	0.712842	0.356421	+	0.934325i	$0.383997\pi$
$542$	3.19227	0.137120
$543$	52.6291	2.25853
$544$	26.4043	1.13207
$545$	−8.69294	−0.372365
$546$	−7.86640	−0.336651
$547$	12.8563	0.549696	0.274848	−	0.961488i	$-0.411372\pi$
$547$	12.8563	0.549696	0.274848	+	0.961488i	$0.411372\pi$
$548$	35.1550	1.50175
$549$	−40.4288	−1.72546
$550$	−2.28539	−0.0974493
$551$	−5.49058	−0.233906
$552$	−27.9317	−1.18885
$553$	9.49535	0.403783
$554$	1.94569	0.0826646
$555$	13.5274	0.574204
$556$	−25.9565	−1.10080
$557$	−5.75933	−0.244030	−0.122015	−	0.992528i	$-0.538936\pi$
$557$	−5.75933	−0.244030	−0.122015	+	0.992528i	$0.538936\pi$
$558$	−0.413349	−0.0174985
$559$	−46.5031	−1.96687
$560$	5.07708	0.214546
$561$	76.5457	3.23176
$562$	−6.07291	−0.256170
$563$	−0.737140	−0.0310668	−0.0155334	−	0.999879i	$-0.504945\pi$
$563$	−0.737140	−0.0310668	−0.0155334	+	0.999879i	$0.504945\pi$
$564$	8.37907	0.352823
$565$	−3.02317	−0.127186
$566$	−6.90603	−0.290282
$567$	−10.9178	−0.458503
$568$	−1.87018	−0.0784711
$569$	7.28108	0.305239	0.152619	−	0.988285i	$-0.451229\pi$
$569$	7.28108	0.305239	0.152619	+	0.988285i	$0.451229\pi$
$570$	1.77766	0.0744579
$571$	−8.06762	−0.337619	−0.168810	−	0.985649i	$-0.553992\pi$
$571$	−8.06762	−0.337619	−0.168810	+	0.985649i	$0.553992\pi$
$572$	35.9852	1.50462
$573$	8.60879	0.359637
$574$	1.80851	0.0754857
$575$	−6.38586	−0.266309
$576$	−13.8213	−0.575888
$577$	−11.6830	−0.486371	−0.243185	−	0.969980i	$-0.578192\pi$
$577$	−11.6830	−0.486371	−0.243185	+	0.969980i	$0.578192\pi$
$578$	6.85040	0.284939
$579$	56.0259	2.32835
$580$	−6.40748	−0.266056
$581$	8.32086	0.345207
$582$	20.7443	0.859879
$583$	45.4895	1.88398
$584$	2.39856	0.0992530
$585$	14.4991	0.599464
$586$	−12.1545	−0.502098
$587$	15.8053	0.652353	0.326177	−	0.945309i	$-0.394240\pi$
$587$	15.8053	0.652353	0.326177	+	0.945309i	$0.394240\pi$
$588$	−18.0950	−0.746224
$589$	0.384654	0.0158494
$590$	−1.52985	−0.0629830
$591$	6.42705	0.264374
$592$	−14.9069	−0.612669
$593$	47.7031	1.95893	0.979466	−	0.201607i	$-0.0646165\pi$
$593$	47.7031	1.95893	0.979466	+	0.201607i	$0.0646165\pi$
$594$	4.49217	0.184316
$595$	10.1028	0.414176
$596$	−29.0808	−1.19120
$597$	−11.1408	−0.455962
$598$	−10.9033	−0.445867
$599$	32.4012	1.32388	0.661939	−	0.749558i	$-0.269734\pi$
$599$	32.4012	1.32388	0.661939	+	0.749558i	$0.269734\pi$
$600$	4.37399	0.178567
$601$	3.86772	0.157767	0.0788837	−	0.996884i	$-0.474864\pi$
$601$	3.86772	0.157767	0.0788837	+	0.996884i	$0.474864\pi$
$602$	−9.44551	−0.384970
$603$	−42.7294	−1.74007
$604$	−9.49561	−0.386371
$605$	15.6949	0.638086
$606$	0.882352	0.0358431
$607$	30.1532	1.22388	0.611940	−	0.790904i	$-0.290389\pi$
$607$	30.1532	1.22388	0.611940	+	0.790904i	$0.290389\pi$
$608$	−7.16257	−0.290481
$609$	−16.3609	−0.662978
$610$	−4.76088	−0.192762
$611$	6.89629	0.278994
$612$	−38.6300	−1.56153
$613$	−46.4510	−1.87614	−0.938069	−	0.346448i	$-0.887388\pi$
$613$	−46.4510	−1.87614	−0.938069	+	0.346448i	$0.887388\pi$
$614$	−4.47900	−0.180758
$615$	−5.99568	−0.241769
$616$	15.4109	0.620922
$617$	38.9082	1.56639	0.783193	−	0.621779i	$-0.213590\pi$
$617$	38.9082	1.56639	0.783193	+	0.621779i	$0.213590\pi$
$618$	−5.44694	−0.219108
$619$	3.21067	0.129048	0.0645239	−	0.997916i	$-0.479447\pi$
$619$	3.21067	0.129048	0.0645239	+	0.997916i	$0.479447\pi$
$620$	0.448890	0.0180279
$621$	12.5521	0.503698
$622$	3.04822	0.122222
$623$	23.0857	0.924907
$624$	−28.7388	−1.15047
$625$	1.00000	0.0400000
$626$	−9.84166	−0.393352
$627$	−20.7642	−0.829243
$628$	0.604961	0.0241406
$629$	−29.6631	−1.18275
$630$	2.94499	0.117331
$631$	26.4210	1.05180	0.525902	−	0.850545i	$-0.323728\pi$
$631$	26.4210	1.05180	0.525902	+	0.850545i	$0.323728\pi$
$632$	−9.01465	−0.358584
$633$	40.3489	1.60373
$634$	−4.76209	−0.189127
$635$	−7.12578	−0.282778
$636$	−41.2922	−1.63734
$637$	−14.8928	−0.590076
$638$	−8.11573	−0.321305
$639$	4.17454	0.165142
$640$	−10.8927	−0.430570
$641$	26.9059	1.06272	0.531361	−	0.847146i	$-0.321681\pi$
$641$	26.9059	1.06272	0.531361	+	0.847146i	$0.321681\pi$
$642$	20.3242	0.802134
$643$	−1.55606	−0.0613651	−0.0306825	−	0.999529i	$-0.509768\pi$
$643$	−1.55606	−0.0613651	−0.0306825	+	0.999529i	$0.509768\pi$
$644$	20.4233	0.804792
$645$	31.3143	1.23300
$646$	−3.89809	−0.153368
$647$	−47.2518	−1.85766	−0.928829	−	0.370508i	$-0.879184\pi$
$647$	−47.2518	−1.85766	−0.928829	+	0.370508i	$0.879184\pi$
$648$	10.3650	0.407178
$649$	17.8697	0.701447
$650$	1.70741	0.0669700
$651$	1.14620	0.0449231
$652$	−42.4853	−1.66385
$653$	44.0581	1.72412	0.862062	−	0.506802i	$-0.169172\pi$
$653$	44.0581	1.72412	0.862062	+	0.506802i	$0.169172\pi$
$654$	9.99458	0.390819
$655$	8.93756	0.349219
$656$	6.60713	0.257965
$657$	−5.35395	−0.208878
$658$	1.40074	0.0546067
$659$	−31.5091	−1.22742	−0.613711	−	0.789531i	$-0.710324\pi$
$659$	−31.5091	−1.22742	−0.613711	+	0.789531i	$0.710324\pi$
$660$	−24.2318	−0.943220
$661$	−40.7409	−1.58464	−0.792318	−	0.610108i	$-0.791126\pi$
$661$	−40.7409	−1.58464	−0.792318	+	0.610108i	$0.791126\pi$
$662$	11.7441	0.456447
$663$	−57.1870	−2.22096
$664$	−7.89962	−0.306565
$665$	−2.74055	−0.106274
$666$	−8.64685	−0.335059
$667$	−22.6771	−0.878061
$668$	−30.2671	−1.17107
$669$	30.4518	1.17733
$670$	−5.03179	−0.194395
$671$	55.6102	2.14681
$672$	−21.3431	−0.823330
$673$	2.29868	0.0886077	0.0443038	−	0.999018i	$-0.485893\pi$
$673$	2.29868	0.0886077	0.0443038	+	0.999018i	$0.485893\pi$
$674$	15.8136	0.609116
$675$	−1.96561	−0.0756562
$676$	−3.42793	−0.131844
$677$	−5.32208	−0.204544	−0.102272	−	0.994756i	$-0.532611\pi$
$677$	−5.32208	−0.204544	−0.102272	+	0.994756i	$0.532611\pi$
$678$	3.47584	0.133489
$679$	−31.9808	−1.22731
$680$	−9.59139	−0.367813
$681$	−52.3961	−2.00782
$682$	0.568565	0.0217715
$683$	−48.1340	−1.84180	−0.920898	−	0.389803i	$-0.872543\pi$
$683$	−48.1340	−1.84180	−0.920898	+	0.389803i	$0.872543\pi$
$684$	10.4790	0.400675
$685$	−19.4835	−0.744428
$686$	−8.51320	−0.325035
$687$	−12.9627	−0.494558
$688$	−34.5078	−1.31560
$689$	−33.9850	−1.29473
$690$	7.34205	0.279507
$691$	−20.1105	−0.765041	−0.382520	−	0.923947i	$-0.624944\pi$
$691$	−20.1105	−0.765041	−0.382520	+	0.923947i	$0.624944\pi$
$692$	−21.5490	−0.819171
$693$	−34.3995	−1.30673
$694$	0.982490	0.0372948
$695$	14.3856	0.545675
$696$	15.5327	0.588764
$697$	13.1475	0.497996
$698$	−14.0806	−0.532958
$699$	15.2986	0.578647
$700$	−3.19821	−0.120881
$701$	−16.4629	−0.621794	−0.310897	−	0.950444i	$-0.600630\pi$
$701$	−16.4629	−0.621794	−0.310897	+	0.950444i	$0.600630\pi$
$702$	−3.35609	−0.126667
$703$	8.04658	0.303483
$704$	19.0113	0.716517
$705$	−4.64383	−0.174897
$706$	−11.5872	−0.436089
$707$	−1.36029	−0.0511590
$708$	−16.2209	−0.609618
$709$	6.76802	0.254178	0.127089	−	0.991891i	$-0.459437\pi$
$709$	6.76802	0.254178	0.127089	+	0.991891i	$0.459437\pi$
$710$	0.491591	0.0184491
$711$	20.1221	0.754638
$712$	−21.9170	−0.821373
$713$	1.58869	0.0594970
$714$	−11.6156	−0.434702
$715$	−19.9436	−0.745850
$716$	24.3770	0.911012
$717$	55.0874	2.05728
$718$	2.54087	0.0948244
$719$	15.5424	0.579634	0.289817	−	0.957082i	$-0.406406\pi$
$719$	15.5424	0.579634	0.289817	+	0.957082i	$0.406406\pi$
$720$	10.7591	0.400968
$721$	8.39735	0.312734
$722$	−7.34685	−0.273421
$723$	−2.59927	−0.0966680
$724$	36.5337	1.35777
$725$	3.55114	0.131886
$726$	−18.0449	−0.669710
$727$	1.90244	0.0705574	0.0352787	−	0.999378i	$-0.488768\pi$
$727$	1.90244	0.0705574	0.0352787	+	0.999378i	$0.488768\pi$
$728$	−11.5134	−0.426716
$729$	−38.4638	−1.42459
$730$	−0.630479	−0.0233351
$731$	−68.6668	−2.53973
$732$	−50.4792	−1.86576
$733$	18.8761	0.697205	0.348603	−	0.937271i	$-0.386656\pi$
$733$	18.8761	0.697205	0.348603	+	0.937271i	$0.386656\pi$
$734$	13.0980	0.483455
$735$	10.0286	0.369909
$736$	−29.5827	−1.09043
$737$	58.7746	2.16499
$738$	3.83251	0.141077
$739$	−17.2930	−0.636135	−0.318067	−	0.948068i	$-0.603034\pi$
$739$	−17.2930	−0.636135	−0.318067	+	0.948068i	$0.603034\pi$
$740$	9.39033	0.345195
$741$	15.5129	0.569880
$742$	−6.90289	−0.253413
$743$	8.25307	0.302776	0.151388	−	0.988474i	$-0.451626\pi$
$743$	8.25307	0.302776	0.151388	+	0.988474i	$0.451626\pi$
$744$	−1.08817	−0.0398944
$745$	16.1171	0.590485
$746$	−16.4671	−0.602902
$747$	17.6332	0.645164
$748$	53.1360	1.94284
$749$	−31.3332	−1.14489
$750$	−1.14974	−0.0419824
$751$	11.5224	0.420458	0.210229	−	0.977652i	$-0.432579\pi$
$751$	11.5224	0.420458	0.210229	+	0.977652i	$0.432579\pi$
$752$	5.11741	0.186613
$753$	23.7800	0.866590
$754$	6.06324	0.220810
$755$	5.26264	0.191527
$756$	6.28642	0.228635
$757$	−14.1686	−0.514967	−0.257483	−	0.966283i	$-0.582893\pi$
$757$	−14.1686	−0.514967	−0.257483	+	0.966283i	$0.582893\pi$
$758$	4.15593	0.150950
$759$	−85.7600	−3.11289
$760$	2.60181	0.0943777
$761$	35.8383	1.29914	0.649568	−	0.760303i	$-0.274950\pi$
$761$	35.8383	1.29914	0.649568	+	0.760303i	$0.274950\pi$
$762$	8.19276	0.296792
$763$	−15.4083	−0.557818
$764$	5.97599	0.216204
$765$	21.4095	0.774061
$766$	−13.2064	−0.477168
$767$	−13.3504	−0.482054
$768$	−6.60482	−0.238331
$769$	20.1473	0.726531	0.363265	−	0.931686i	$-0.381662\pi$
$769$	20.1473	0.726531	0.363265	+	0.931686i	$0.381662\pi$
$770$	−4.05087	−0.145983
$771$	−63.4443	−2.28489
$772$	38.8916	1.39974
$773$	18.7392	0.674003	0.337001	−	0.941504i	$-0.390587\pi$
$773$	18.7392	0.674003	0.337001	+	0.941504i	$0.390587\pi$
$774$	−20.0165	−0.719478
$775$	−0.248783	−0.00893654
$776$	30.3618	1.08992
$777$	23.9773	0.860182
$778$	10.9546	0.392742
$779$	−3.56646	−0.127782
$780$	18.1035	0.648208
$781$	−5.74211	−0.205469
$782$	−16.0998	−0.575728
$783$	−6.98014	−0.249450
$784$	−11.0513	−0.394689
$785$	−0.335280	−0.0119667
$786$	−10.2758	−0.366527
$787$	3.23213	0.115213	0.0576064	−	0.998339i	$-0.481653\pi$
$787$	3.23213	0.115213	0.0576064	+	0.998339i	$0.481653\pi$
$788$	4.46149	0.158934
$789$	−20.9337	−0.745259
$790$	2.36957	0.0843055
$791$	−5.35859	−0.190529
$792$	32.6580	1.16045
$793$	−41.5462	−1.47535
$794$	−12.9174	−0.458423
$795$	22.8849	0.811643
$796$	−7.73364	−0.274111
$797$	−2.41638	−0.0855926	−0.0427963	−	0.999084i	$-0.513627\pi$
$797$	−2.41638	−0.0855926	−0.0427963	+	0.999084i	$0.513627\pi$
$798$	3.15091	0.111541
$799$	10.1831	0.360252
$800$	4.63254	0.163785
$801$	48.9220	1.72858
$802$	−5.06289	−0.178777
$803$	7.36441	0.259884
$804$	−53.3516	−1.88156
$805$	−11.3190	−0.398942
$806$	−0.424773	−0.0149620
$807$	−21.1229	−0.743563
$808$	1.29143	0.0454323
$809$	−19.5685	−0.687993	−0.343996	−	0.938971i	$-0.611781\pi$
$809$	−19.5685	−0.687993	−0.343996	+	0.938971i	$0.611781\pi$
$810$	−2.72453	−0.0957302
$811$	46.8556	1.64532	0.822661	−	0.568532i	$-0.192489\pi$
$811$	46.8556	1.64532	0.822661	+	0.568532i	$0.192489\pi$
$812$	−11.3573	−0.398563
$813$	−18.7588	−0.657901
$814$	11.8938	0.416878
$815$	23.5461	0.824785
$816$	−42.4358	−1.48555
$817$	18.6269	0.651674
$818$	4.08928	0.142978
$819$	25.6997	0.898022
$820$	−4.16204	−0.145345
$821$	44.6175	1.55716	0.778581	−	0.627545i	$-0.215940\pi$
$821$	44.6175	1.55716	0.778581	+	0.627545i	$0.215940\pi$
$822$	22.4009	0.781322
$823$	−41.3480	−1.44130	−0.720651	−	0.693298i	$-0.756157\pi$
$823$	−41.3480	−1.44130	−0.720651	+	0.693298i	$0.756157\pi$
$824$	−7.97224	−0.277726
$825$	13.4297	0.467561
$826$	−2.71167	−0.0943511
$827$	−38.3649	−1.33408	−0.667040	−	0.745022i	$-0.732439\pi$
$827$	−38.3649	−1.33408	−0.667040	+	0.745022i	$0.732439\pi$
$828$	43.2802	1.50409
$829$	−15.9073	−0.552482	−0.276241	−	0.961088i	$-0.589089\pi$
$829$	−15.9073	−0.552482	−0.276241	+	0.961088i	$0.589089\pi$
$830$	2.07647	0.0720754
$831$	−11.4335	−0.396625
$832$	−14.2033	−0.492411
$833$	−21.9909	−0.761939
$834$	−16.5396	−0.572719
$835$	16.7746	0.580508
$836$	−14.4140	−0.498517
$837$	0.489009	0.0169026
$838$	−8.63682	−0.298354
$839$	18.2936	0.631566	0.315783	−	0.948831i	$-0.397733\pi$
$839$	18.2936	0.631566	0.315783	+	0.948831i	$0.397733\pi$
$840$	7.75292	0.267501
$841$	−16.3894	−0.565152
$842$	−4.29108	−0.147880
$843$	35.6864	1.22910
$844$	28.0091	0.964114
$845$	1.89982	0.0653558
$846$	2.96839	0.102055
$847$	27.8192	0.955880
$848$	−25.2187	−0.866014
$849$	40.5821	1.39277
$850$	2.52117	0.0864753
$851$	33.2339	1.13924
$852$	5.21230	0.178570
$853$	40.3984	1.38322	0.691608	−	0.722273i	$-0.256903\pi$
$853$	40.3984	1.38322	0.691608	+	0.722273i	$0.256903\pi$
$854$	−8.43869	−0.288766
$855$	−5.80765	−0.198617
$856$	29.7470	1.01673
$857$	−6.64571	−0.227013	−0.113507	−	0.993537i	$-0.536208\pi$
$857$	−6.64571	−0.227013	−0.113507	+	0.993537i	$0.536208\pi$
$858$	22.9299	0.782814
$859$	−1.57335	−0.0536820	−0.0268410	−	0.999640i	$-0.508545\pi$
$859$	−1.57335	−0.0536820	−0.0268410	+	0.999640i	$0.508545\pi$
$860$	21.7376	0.741245
$861$	−10.6274	−0.362180
$862$	6.20481	0.211337
$863$	−21.4402	−0.729832	−0.364916	−	0.931040i	$-0.618902\pi$
$863$	−21.4402	−0.729832	−0.364916	+	0.931040i	$0.618902\pi$
$864$	−9.10574	−0.309783
$865$	11.9428	0.406069
$866$	8.38034	0.284776
$867$	−40.2552	−1.36714
$868$	0.795660	0.0270065
$869$	−27.6781	−0.938916
$870$	−4.08287	−0.138422
$871$	−43.9103	−1.48784
$872$	14.6283	0.495375
$873$	−67.7722	−2.29374
$874$	4.36733	0.147727
$875$	1.77251	0.0599217
$876$	−6.68491	−0.225862
$877$	28.3613	0.957693	0.478847	−	0.877899i	$-0.341055\pi$
$877$	28.3613	0.957693	0.478847	+	0.877899i	$0.341055\pi$
$878$	−9.11677	−0.307676
$879$	71.4238	2.40907
$880$	−14.7992	−0.498882
$881$	8.16682	0.275147	0.137574	−	0.990492i	$-0.456070\pi$
$881$	8.16682	0.275147	0.137574	+	0.990492i	$0.456070\pi$
$882$	−6.41037	−0.215849
$883$	3.66300	0.123270	0.0616348	−	0.998099i	$-0.480369\pi$
$883$	3.66300	0.123270	0.0616348	+	0.998099i	$0.480369\pi$
$884$	−39.6977	−1.33518
$885$	8.98990	0.302192
$886$	2.02158	0.0679163
$887$	−20.4754	−0.687496	−0.343748	−	0.939062i	$-0.611697\pi$
$887$	−20.4754	−0.687496	−0.343748	+	0.939062i	$0.611697\pi$
$888$	−22.7635	−0.763893
$889$	−12.6305	−0.423613
$890$	5.76103	0.193110
$891$	31.8243	1.06615
$892$	21.1388	0.707780
$893$	−2.76233	−0.0924377
$894$	−18.5304	−0.619749
$895$	−13.5102	−0.451596
$896$	−19.3073	−0.645012
$897$	64.0710	2.13927
$898$	3.57737	0.119378
$899$	−0.883463	−0.0294651
$900$	−6.77750	−0.225917
$901$	−50.1825	−1.67182
$902$	−5.27165	−0.175527
$903$	55.5049	1.84709
$904$	5.08731	0.169201
$905$	−20.2476	−0.673055
$906$	−6.05064	−0.201019
$907$	10.8243	0.359416	0.179708	−	0.983720i	$-0.442485\pi$
$907$	10.8243	0.359416	0.179708	+	0.983720i	$0.442485\pi$
$908$	−36.3719	−1.20705
$909$	−2.88267	−0.0956121
$910$	3.02639	0.100324
$911$	6.62769	0.219585	0.109793	−	0.993955i	$-0.464981\pi$
$911$	6.62769	0.219585	0.109793	+	0.993955i	$0.464981\pi$
$912$	11.5114	0.381180
$913$	−24.2546	−0.802710
$914$	4.04520	0.133803
$915$	27.9765	0.924873
$916$	−8.99835	−0.297314
$917$	15.8419	0.523145
$918$	−4.95562	−0.163560
$919$	−22.4004	−0.738920	−0.369460	−	0.929247i	$-0.620457\pi$
$919$	−22.4004	−0.738920	−0.369460	+	0.929247i	$0.620457\pi$
$920$	10.7460	0.354284
$921$	26.3200	0.867274
$922$	13.2202	0.435383
$923$	4.28991	0.141204
$924$	−42.9509	−1.41298
$925$	−5.20429	−0.171116
$926$	−10.9966	−0.361372
$927$	17.7953	0.584474
$928$	16.4508	0.540024
$929$	51.0273	1.67415	0.837076	−	0.547087i	$-0.184263\pi$
$929$	51.0273	1.67415	0.837076	+	0.547087i	$0.184263\pi$
$930$	0.286034	0.00937944
$931$	5.96537	0.195507
$932$	10.6199	0.347866
$933$	−17.9123	−0.586422
$934$	1.63700	0.0535643
$935$	−29.4489	−0.963082
$936$	−24.3987	−0.797497
$937$	46.0017	1.50281	0.751405	−	0.659841i	$-0.229376\pi$
$937$	46.0017	1.50281	0.751405	+	0.659841i	$0.229376\pi$
$938$	−8.91887	−0.291212
$939$	57.8328	1.88730
$940$	−3.22362	−0.105143
$941$	−32.8925	−1.07227	−0.536133	−	0.844134i	$-0.680115\pi$
$941$	−32.8925	−1.07227	−0.536133	+	0.844134i	$0.680115\pi$
$942$	0.385483	0.0125597
$943$	−14.7301	−0.479679
$944$	−9.90670	−0.322436
$945$	−3.48405	−0.113336
$946$	27.5329	0.895170
$947$	2.49152	0.0809635	0.0404817	−	0.999180i	$-0.487111\pi$
$947$	2.49152	0.0809635	0.0404817	+	0.999180i	$0.487111\pi$
$948$	25.1243	0.816000
$949$	−5.50193	−0.178600
$950$	−0.683906	−0.0221888
$951$	27.9836	0.907429
$952$	−17.0008	−0.550999
$953$	−8.51021	−0.275673	−0.137836	−	0.990455i	$-0.544015\pi$
$953$	−8.51021	−0.275673	−0.137836	+	0.990455i	$0.544015\pi$
$954$	−14.6283	−0.473608
$955$	−3.31200	−0.107174
$956$	38.2402	1.23678
$957$	47.6907	1.54162
$958$	−9.01473	−0.291253
$959$	−34.5347	−1.11518
$960$	9.56425	0.308685
$961$	−30.9381	−0.998003
$962$	−8.88583	−0.286491
$963$	−66.3998	−2.13970
$964$	−1.80434	−0.0581140
$965$	−21.5544	−0.693862
$966$	13.0138	0.418713
$967$	−25.6155	−0.823740	−0.411870	−	0.911243i	$-0.635124\pi$
$967$	−25.6155	−0.823740	−0.411870	+	0.911243i	$0.635124\pi$
$968$	−26.4109	−0.848878
$969$	22.9064	0.735860
$970$	−7.98081	−0.256249
$971$	−19.1176	−0.613512	−0.306756	−	0.951788i	$-0.599244\pi$
$971$	−19.1176	−0.613512	−0.306756	+	0.951788i	$0.599244\pi$
$972$	−39.5278	−1.26786
$973$	25.4985	0.817445
$974$	−4.45568	−0.142769
$975$	−10.0333	−0.321322
$976$	−30.8295	−0.986829
$977$	31.6150	1.01145	0.505726	−	0.862694i	$-0.331225\pi$
$977$	31.6150	1.01145	0.505726	+	0.862694i	$0.331225\pi$
$978$	−27.0718	−0.865662
$979$	−67.2927	−2.15068
$980$	6.96156	0.222379
$981$	−32.6525	−1.04252
$982$	2.55126	0.0814141
$983$	−26.7309	−0.852585	−0.426292	−	0.904585i	$-0.640181\pi$
$983$	−26.7309	−0.852585	−0.426292	+	0.904585i	$0.640181\pi$
$984$	10.0894	0.321638
$985$	−2.47264	−0.0787847
$986$	8.95302	0.285122
$987$	−8.23122	−0.262003
$988$	10.7686	0.342595
$989$	76.9327	2.44632
$990$	−8.58440	−0.272830
$991$	38.9880	1.23849	0.619247	−	0.785197i	$-0.287438\pi$
$991$	38.9880	1.23849	0.619247	+	0.785197i	$0.287438\pi$
$992$	−1.15250	−0.0365918
$993$	−69.0120	−2.19003
$994$	0.871349	0.0276375
$995$	4.28612	0.135879
$996$	22.0167	0.697625
$997$	−35.3978	−1.12106	−0.560530	−	0.828134i	$-0.689402\pi$
$997$	−35.3978	−1.12106	−0.560530	+	0.828134i	$0.689402\pi$
$998$	19.1605	0.606514
$999$	10.2296	0.323649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.a.1.4	✓	5
5.4	even	2		6025.2.a.e.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.a.1.4	✓	5	1.1	even	1	trivial
6025.2.a.e.1.2		5	5.4	even	2

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q+0.442330 q^{2} -2.59927 q^{3} -1.80434 q^{4} +1.00000 q^{5} -1.14974 q^{6} +1.77251 q^{7} -1.68277 q^{8} +3.75621 q^{9} +O(q^{10})\)	\(q+0.442330 q^{2} -2.59927 q^{3} -1.80434 q^{4} +1.00000 q^{5} -1.14974 q^{6} +1.77251 q^{7} -1.68277 q^{8} +3.75621 q^{9} +0.442330 q^{10} -5.16671 q^{11} +4.68998 q^{12} +3.86003 q^{13} +0.784032 q^{14} -2.59927 q^{15} +2.86435 q^{16} +5.69975 q^{17} +1.66149 q^{18} -1.54614 q^{19} -1.80434 q^{20} -4.60723 q^{21} -2.28539 q^{22} -6.38586 q^{23} +4.37399 q^{24} +1.00000 q^{25} +1.70741 q^{26} -1.96561 q^{27} -3.19821 q^{28} +3.55114 q^{29} -1.14974 q^{30} -0.248783 q^{31} +4.63254 q^{32} +13.4297 q^{33} +2.52117 q^{34} +1.77251 q^{35} -6.77750 q^{36} -5.20429 q^{37} -0.683906 q^{38} -10.0333 q^{39} -1.68277 q^{40} +2.30668 q^{41} -2.03791 q^{42} -12.0473 q^{43} +9.32252 q^{44} +3.75621 q^{45} -2.82466 q^{46} +1.78659 q^{47} -7.44522 q^{48} -3.85822 q^{49} +0.442330 q^{50} -14.8152 q^{51} -6.96482 q^{52} -8.80434 q^{53} -0.869446 q^{54} -5.16671 q^{55} -2.98273 q^{56} +4.01885 q^{57} +1.57078 q^{58} -3.45862 q^{59} +4.68998 q^{60} -10.7632 q^{61} -0.110044 q^{62} +6.65791 q^{63} -3.67959 q^{64} +3.86003 q^{65} +5.94034 q^{66} -11.3756 q^{67} -10.2843 q^{68} +16.5986 q^{69} +0.784032 q^{70} +1.11137 q^{71} -6.32086 q^{72} -1.42536 q^{73} -2.30201 q^{74} -2.59927 q^{75} +2.78978 q^{76} -9.15802 q^{77} -4.43801 q^{78} +5.35702 q^{79} +2.86435 q^{80} -6.15950 q^{81} +1.02031 q^{82} +4.69440 q^{83} +8.31302 q^{84} +5.69975 q^{85} -5.32890 q^{86} -9.23038 q^{87} +8.69440 q^{88} +13.0243 q^{89} +1.66149 q^{90} +6.84193 q^{91} +11.5223 q^{92} +0.646654 q^{93} +0.790262 q^{94} -1.54614 q^{95} -12.0412 q^{96} -18.0427 q^{97} -1.70661 q^{98} -19.4073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 5 q^{5} - 8 q^{6} - 10 q^{7} + 6 q^{9}+O(q^{10}) \) 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 5 * q^5 - 8 * q^6 - 10 * q^7 + 6 * q^9	\( 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 5 q^{5} - 8 q^{6} - 10 q^{7} + 6 q^{9} - q^{10} - 3 q^{11} + 8 q^{12} - q^{13} - q^{14} - 5 q^{15} + 15 q^{16} - 5 q^{17} + 4 q^{18} + 3 q^{19} + 3 q^{20} + 11 q^{21} - 13 q^{22} - 8 q^{23} - 14 q^{24} + 5 q^{25} + 14 q^{26} - 14 q^{27} - 17 q^{28} + 9 q^{29} - 8 q^{30} - 16 q^{31} - 16 q^{32} + 23 q^{33} - 10 q^{34} - 10 q^{35} - 17 q^{36} + 7 q^{37} - 22 q^{38} - 19 q^{39} + 9 q^{41} + 17 q^{42} - 32 q^{43} - 8 q^{44} + 6 q^{45} + 5 q^{46} - 7 q^{47} - 6 q^{48} + 9 q^{49} - q^{50} - 8 q^{51} - 10 q^{52} - 32 q^{53} + 32 q^{54} - 3 q^{55} - 18 q^{56} + 3 q^{57} + 11 q^{58} - 8 q^{59} + 8 q^{60} - 12 q^{61} + 17 q^{62} - 11 q^{63} - 16 q^{64} - q^{65} + 15 q^{66} - 5 q^{67} - 2 q^{68} + 7 q^{69} - q^{70} - 11 q^{71} + 7 q^{72} - 29 q^{73} + 10 q^{74} - 5 q^{75} - 8 q^{76} - 5 q^{77} + 2 q^{78} + 16 q^{79} + 15 q^{80} - 15 q^{81} - 2 q^{82} - 10 q^{83} + 5 q^{84} - 5 q^{85} + 14 q^{86} - 37 q^{87} + 10 q^{88} + 9 q^{89} + 4 q^{90} + 12 q^{91} - 25 q^{92} + 15 q^{93} - 11 q^{94} + 3 q^{95} - 3 q^{96} - 43 q^{97} + 30 q^{98} - 30 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 5 * q^5 - 8 * q^6 - 10 * q^7 + 6 * q^9 - q^10 - 3 * q^11 + 8 * q^12 - q^13 - q^14 - 5 * q^15 + 15 * q^16 - 5 * q^17 + 4 * q^18 + 3 * q^19 + 3 * q^20 + 11 * q^21 - 13 * q^22 - 8 * q^23 - 14 * q^24 + 5 * q^25 + 14 * q^26 - 14 * q^27 - 17 * q^28 + 9 * q^29 - 8 * q^30 - 16 * q^31 - 16 * q^32 + 23 * q^33 - 10 * q^34 - 10 * q^35 - 17 * q^36 + 7 * q^37 - 22 * q^38 - 19 * q^39 + 9 * q^41 + 17 * q^42 - 32 * q^43 - 8 * q^44 + 6 * q^45 + 5 * q^46 - 7 * q^47 - 6 * q^48 + 9 * q^49 - q^50 - 8 * q^51 - 10 * q^52 - 32 * q^53 + 32 * q^54 - 3 * q^55 - 18 * q^56 + 3 * q^57 + 11 * q^58 - 8 * q^59 + 8 * q^60 - 12 * q^61 + 17 * q^62 - 11 * q^63 - 16 * q^64 - q^65 + 15 * q^66 - 5 * q^67 - 2 * q^68 + 7 * q^69 - q^70 - 11 * q^71 + 7 * q^72 - 29 * q^73 + 10 * q^74 - 5 * q^75 - 8 * q^76 - 5 * q^77 + 2 * q^78 + 16 * q^79 + 15 * q^80 - 15 * q^81 - 2 * q^82 - 10 * q^83 + 5 * q^84 - 5 * q^85 + 14 * q^86 - 37 * q^87 + 10 * q^88 + 9 * q^89 + 4 * q^90 + 12 * q^91 - 25 * q^92 + 15 * q^93 - 11 * q^94 + 3 * q^95 - 3 * q^96 - 43 * q^97 + 30 * q^98 - 30 * q^99

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