LMFDB - Embedded newform 6010.2.a.f.1.8

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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.51693 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51693 q^{6} -1.44279 q^{7} +1.00000 q^{8} -0.698933 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.51693 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51693 q^{6} -1.44279 q^{7} +1.00000 q^{8} -0.698933 q^{9} -1.00000 q^{10} +3.70234 q^{11} -1.51693 q^{12} -2.24813 q^{13} -1.44279 q^{14} +1.51693 q^{15} +1.00000 q^{16} +1.48782 q^{17} -0.698933 q^{18} -6.06979 q^{19} -1.00000 q^{20} +2.18861 q^{21} +3.70234 q^{22} +2.81079 q^{23} -1.51693 q^{24} +1.00000 q^{25} -2.24813 q^{26} +5.61101 q^{27} -1.44279 q^{28} +0.753284 q^{29} +1.51693 q^{30} +6.62522 q^{31} +1.00000 q^{32} -5.61618 q^{33} +1.48782 q^{34} +1.44279 q^{35} -0.698933 q^{36} +6.78867 q^{37} -6.06979 q^{38} +3.41025 q^{39} -1.00000 q^{40} -1.29325 q^{41} +2.18861 q^{42} -11.8236 q^{43} +3.70234 q^{44} +0.698933 q^{45} +2.81079 q^{46} +5.22916 q^{47} -1.51693 q^{48} -4.91834 q^{49} +1.00000 q^{50} -2.25692 q^{51} -2.24813 q^{52} +10.6019 q^{53} +5.61101 q^{54} -3.70234 q^{55} -1.44279 q^{56} +9.20743 q^{57} +0.753284 q^{58} -1.75309 q^{59} +1.51693 q^{60} -7.55068 q^{61} +6.62522 q^{62} +1.00842 q^{63} +1.00000 q^{64} +2.24813 q^{65} -5.61618 q^{66} -4.43992 q^{67} +1.48782 q^{68} -4.26376 q^{69} +1.44279 q^{70} -4.51814 q^{71} -0.698933 q^{72} -13.0540 q^{73} +6.78867 q^{74} -1.51693 q^{75} -6.06979 q^{76} -5.34172 q^{77} +3.41025 q^{78} -4.39884 q^{79} -1.00000 q^{80} -6.41470 q^{81} -1.29325 q^{82} -5.76469 q^{83} +2.18861 q^{84} -1.48782 q^{85} -11.8236 q^{86} -1.14268 q^{87} +3.70234 q^{88} +7.81189 q^{89} +0.698933 q^{90} +3.24359 q^{91} +2.81079 q^{92} -10.0500 q^{93} +5.22916 q^{94} +6.06979 q^{95} -1.51693 q^{96} -14.6497 q^{97} -4.91834 q^{98} -2.58769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.51693	−0.875798	−0.437899	−	0.899024i	$-0.644277\pi$
$3$	−1.51693	−0.875798	−0.437899	+	0.899024i	$0.644277\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.51693	−0.619283
$7$	−1.44279	−0.545325	−0.272663	−	0.962110i	$-0.587904\pi$
$7$	−1.44279	−0.545325	−0.272663	+	0.962110i	$0.587904\pi$
$8$	1.00000	0.353553
$9$	−0.698933	−0.232978
$10$	−1.00000	−0.316228
$11$	3.70234	1.11630	0.558149	−	0.829741i	$-0.311512\pi$
$11$	3.70234	1.11630	0.558149	+	0.829741i	$0.311512\pi$
$12$	−1.51693	−0.437899
$13$	−2.24813	−0.623520	−0.311760	−	0.950161i	$-0.600918\pi$
$13$	−2.24813	−0.623520	−0.311760	+	0.950161i	$0.600918\pi$
$14$	−1.44279	−0.385603
$15$	1.51693	0.391669
$16$	1.00000	0.250000
$17$	1.48782	0.360850	0.180425	−	0.983589i	$-0.442253\pi$
$17$	1.48782	0.360850	0.180425	+	0.983589i	$0.442253\pi$
$18$	−0.698933	−0.164740
$19$	−6.06979	−1.39251	−0.696253	−	0.717797i	$-0.745151\pi$
$19$	−6.06979	−1.39251	−0.696253	+	0.717797i	$0.745151\pi$
$20$	−1.00000	−0.223607
$21$	2.18861	0.477595
$22$	3.70234	0.789342
$23$	2.81079	0.586090	0.293045	−	0.956099i	$-0.405331\pi$
$23$	2.81079	0.586090	0.293045	+	0.956099i	$0.405331\pi$
$24$	−1.51693	−0.309641
$25$	1.00000	0.200000
$26$	−2.24813	−0.440895
$27$	5.61101	1.07984
$28$	−1.44279	−0.272663
$29$	0.753284	0.139881	0.0699407	−	0.997551i	$-0.477719\pi$
$29$	0.753284	0.139881	0.0699407	+	0.997551i	$0.477719\pi$
$30$	1.51693	0.276952
$31$	6.62522	1.18993	0.594963	−	0.803753i	$-0.297167\pi$
$31$	6.62522	1.18993	0.594963	+	0.803753i	$0.297167\pi$
$32$	1.00000	0.176777
$33$	−5.61618	−0.977651
$34$	1.48782	0.255160
$35$	1.44279	0.243877
$36$	−0.698933	−0.116489
$37$	6.78867	1.11605	0.558025	−	0.829824i	$-0.311559\pi$
$37$	6.78867	1.11605	0.558025	+	0.829824i	$0.311559\pi$
$38$	−6.06979	−0.984650
$39$	3.41025	0.546077
$40$	−1.00000	−0.158114
$41$	−1.29325	−0.201972	−0.100986	−	0.994888i	$-0.532200\pi$
$41$	−1.29325	−0.201972	−0.100986	+	0.994888i	$0.532200\pi$
$42$	2.18861	0.337711
$43$	−11.8236	−1.80308	−0.901542	−	0.432692i	$-0.857564\pi$
$43$	−11.8236	−1.80308	−0.901542	+	0.432692i	$0.857564\pi$
$44$	3.70234	0.558149
$45$	0.698933	0.104191
$46$	2.81079	0.414428
$47$	5.22916	0.762751	0.381376	−	0.924420i	$-0.375450\pi$
$47$	5.22916	0.762751	0.381376	+	0.924420i	$0.375450\pi$
$48$	−1.51693	−0.218950
$49$	−4.91834	−0.702620
$50$	1.00000	0.141421
$51$	−2.25692	−0.316032
$52$	−2.24813	−0.311760
$53$	10.6019	1.45629	0.728144	−	0.685425i	$-0.240383\pi$
$53$	10.6019	1.45629	0.728144	+	0.685425i	$0.240383\pi$
$54$	5.61101	0.763562
$55$	−3.70234	−0.499223
$56$	−1.44279	−0.192802
$57$	9.20743	1.21955
$58$	0.753284	0.0989110
$59$	−1.75309	−0.228233	−0.114116	−	0.993467i	$-0.536404\pi$
$59$	−1.75309	−0.228233	−0.114116	+	0.993467i	$0.536404\pi$
$60$	1.51693	0.195834
$61$	−7.55068	−0.966765	−0.483382	−	0.875409i	$-0.660592\pi$
$61$	−7.55068	−0.966765	−0.483382	+	0.875409i	$0.660592\pi$
$62$	6.62522	0.841404
$63$	1.00842	0.127049
$64$	1.00000	0.125000
$65$	2.24813	0.278846
$66$	−5.61618	−0.691304
$67$	−4.43992	−0.542423	−0.271211	−	0.962520i	$-0.587424\pi$
$67$	−4.43992	−0.542423	−0.271211	+	0.962520i	$0.587424\pi$
$68$	1.48782	0.180425
$69$	−4.26376	−0.513297
$70$	1.44279	0.172447
$71$	−4.51814	−0.536205	−0.268102	−	0.963390i	$-0.586397\pi$
$71$	−4.51814	−0.536205	−0.268102	+	0.963390i	$0.586397\pi$
$72$	−0.698933	−0.0823700
$73$	−13.0540	−1.52786	−0.763929	−	0.645300i	$-0.776732\pi$
$73$	−13.0540	−1.52786	−0.763929	+	0.645300i	$0.776732\pi$
$74$	6.78867	0.789167
$75$	−1.51693	−0.175160
$76$	−6.06979	−0.696253
$77$	−5.34172	−0.608745
$78$	3.41025	0.386135
$79$	−4.39884	−0.494908	−0.247454	−	0.968900i	$-0.579594\pi$
$79$	−4.39884	−0.494908	−0.247454	+	0.968900i	$0.579594\pi$
$80$	−1.00000	−0.111803
$81$	−6.41470	−0.712744
$82$	−1.29325	−0.142816
$83$	−5.76469	−0.632757	−0.316379	−	0.948633i	$-0.602467\pi$
$83$	−5.76469	−0.632757	−0.316379	+	0.948633i	$0.602467\pi$
$84$	2.18861	0.238797
$85$	−1.48782	−0.161377
$86$	−11.8236	−1.27497
$87$	−1.14268	−0.122508
$88$	3.70234	0.394671
$89$	7.81189	0.828058	0.414029	−	0.910264i	$-0.364121\pi$
$89$	7.81189	0.828058	0.414029	+	0.910264i	$0.364121\pi$
$90$	0.698933	0.0736740
$91$	3.24359	0.340021
$92$	2.81079	0.293045
$93$	−10.0500	−1.04213
$94$	5.22916	0.539347
$95$	6.06979	0.622747
$96$	−1.51693	−0.154821
$97$	−14.6497	−1.48745	−0.743727	−	0.668483i	$-0.766944\pi$
$97$	−14.6497	−1.48745	−0.743727	+	0.668483i	$0.766944\pi$
$98$	−4.91834	−0.496828
$99$	−2.58769	−0.260072
$100$	1.00000	0.100000
$101$	12.0406	1.19809	0.599043	−	0.800717i	$-0.295548\pi$
$101$	12.0406	1.19809	0.599043	+	0.800717i	$0.295548\pi$
$102$	−2.25692	−0.223468
$103$	−10.1669	−1.00177	−0.500887	−	0.865513i	$-0.666993\pi$
$103$	−10.1669	−1.00177	−0.500887	+	0.865513i	$0.666993\pi$
$104$	−2.24813	−0.220447
$105$	−2.18861	−0.213587
$106$	10.6019	1.02975
$107$	12.5378	1.21208	0.606039	−	0.795435i	$-0.292758\pi$
$107$	12.5378	1.21208	0.606039	+	0.795435i	$0.292758\pi$
$108$	5.61101	0.539920
$109$	5.17606	0.495777	0.247889	−	0.968789i	$-0.420263\pi$
$109$	5.17606	0.495777	0.247889	+	0.968789i	$0.420263\pi$
$110$	−3.70234	−0.353004
$111$	−10.2979	−0.977435
$112$	−1.44279	−0.136331
$113$	−1.34296	−0.126335	−0.0631674	−	0.998003i	$-0.520120\pi$
$113$	−1.34296	−0.126335	−0.0631674	+	0.998003i	$0.520120\pi$
$114$	9.20743	0.862355
$115$	−2.81079	−0.262107
$116$	0.753284	0.0699407
$117$	1.57129	0.145266
$118$	−1.75309	−0.161385
$119$	−2.14663	−0.196781
$120$	1.51693	0.138476
$121$	2.70732	0.246120
$122$	−7.55068	−0.683606
$123$	1.96177	0.176887
$124$	6.62522	0.594963
$125$	−1.00000	−0.0894427
$126$	1.00842	0.0898369
$127$	−11.6113	−1.03034	−0.515168	−	0.857089i	$-0.672271\pi$
$127$	−11.6113	−1.03034	−0.515168	+	0.857089i	$0.672271\pi$
$128$	1.00000	0.0883883
$129$	17.9355	1.57914
$130$	2.24813	0.197174
$131$	−18.4830	−1.61486	−0.807432	−	0.589961i	$-0.799143\pi$
$131$	−18.4830	−1.61486	−0.807432	+	0.589961i	$0.799143\pi$
$132$	−5.61618	−0.488826
$133$	8.75746	0.759368
$134$	−4.43992	−0.383551
$135$	−5.61101	−0.482919
$136$	1.48782	0.127580
$137$	−4.33213	−0.370119	−0.185059	−	0.982727i	$-0.559248\pi$
$137$	−4.33213	−0.370119	−0.185059	+	0.982727i	$0.559248\pi$
$138$	−4.26376	−0.362956
$139$	0.901260	0.0764439	0.0382219	−	0.999269i	$-0.487831\pi$
$139$	0.901260	0.0764439	0.0382219	+	0.999269i	$0.487831\pi$
$140$	1.44279	0.121938
$141$	−7.93225	−0.668016
$142$	−4.51814	−0.379154
$143$	−8.32335	−0.696033
$144$	−0.698933	−0.0582444
$145$	−0.753284	−0.0625568
$146$	−13.0540	−1.08036
$147$	7.46077	0.615354
$148$	6.78867	0.558025
$149$	−3.88375	−0.318169	−0.159085	−	0.987265i	$-0.550854\pi$
$149$	−3.88375	−0.318169	−0.159085	+	0.987265i	$0.550854\pi$
$150$	−1.51693	−0.123857
$151$	19.6323	1.59766	0.798829	−	0.601558i	$-0.205453\pi$
$151$	19.6323	1.59766	0.798829	+	0.601558i	$0.205453\pi$
$152$	−6.06979	−0.492325
$153$	−1.03989	−0.0840700
$154$	−5.34172	−0.430448
$155$	−6.62522	−0.532151
$156$	3.41025	0.273039
$157$	−11.9869	−0.956655	−0.478328	−	0.878182i	$-0.658757\pi$
$157$	−11.9869	−0.956655	−0.478328	+	0.878182i	$0.658757\pi$
$158$	−4.39884	−0.349953
$159$	−16.0824	−1.27541
$160$	−1.00000	−0.0790569
$161$	−4.05539	−0.319610
$162$	−6.41470	−0.503986
$163$	−13.5214	−1.05908	−0.529539	−	0.848286i	$-0.677635\pi$
$163$	−13.5214	−1.05908	−0.529539	+	0.848286i	$0.677635\pi$
$164$	−1.29325	−0.100986
$165$	5.61618	0.437219
$166$	−5.76469	−0.447427
$167$	−9.36271	−0.724508	−0.362254	−	0.932079i	$-0.617993\pi$
$167$	−9.36271	−0.724508	−0.362254	+	0.932079i	$0.617993\pi$
$168$	2.18861	0.168855
$169$	−7.94590	−0.611223
$170$	−1.48782	−0.114111
$171$	4.24238	0.324423
$172$	−11.8236	−0.901542
$173$	−12.2556	−0.931779	−0.465890	−	0.884843i	$-0.654266\pi$
$173$	−12.2556	−0.931779	−0.465890	+	0.884843i	$0.654266\pi$
$174$	−1.14268	−0.0866261
$175$	−1.44279	−0.109065
$176$	3.70234	0.279074
$177$	2.65931	0.199886
$178$	7.81189	0.585526
$179$	17.1199	1.27960	0.639799	−	0.768542i	$-0.279018\pi$
$179$	17.1199	1.27960	0.639799	+	0.768542i	$0.279018\pi$
$180$	0.698933	0.0520954
$181$	12.2866	0.913256	0.456628	−	0.889658i	$-0.349057\pi$
$181$	12.2866	0.913256	0.456628	+	0.889658i	$0.349057\pi$
$182$	3.24359	0.240431
$183$	11.4538	0.846691
$184$	2.81079	0.207214
$185$	−6.78867	−0.499113
$186$	−10.0500	−0.736900
$187$	5.50843	0.402816
$188$	5.22916	0.381376
$189$	−8.09554	−0.588864
$190$	6.06979	0.440349
$191$	14.9736	1.08345	0.541725	−	0.840556i	$-0.317771\pi$
$191$	14.9736	1.08345	0.541725	+	0.840556i	$0.317771\pi$
$192$	−1.51693	−0.109475
$193$	−2.28076	−0.164173	−0.0820864	−	0.996625i	$-0.526158\pi$
$193$	−2.28076	−0.164173	−0.0820864	+	0.996625i	$0.526158\pi$
$194$	−14.6497	−1.05179
$195$	−3.41025	−0.244213
$196$	−4.91834	−0.351310
$197$	−3.53756	−0.252041	−0.126020	−	0.992028i	$-0.540220\pi$
$197$	−3.53756	−0.252041	−0.126020	+	0.992028i	$0.540220\pi$
$198$	−2.58769	−0.183899
$199$	−0.474746	−0.0336538	−0.0168269	−	0.999858i	$-0.505356\pi$
$199$	−0.474746	−0.0336538	−0.0168269	+	0.999858i	$0.505356\pi$
$200$	1.00000	0.0707107
$201$	6.73504	0.475053
$202$	12.0406	0.847175
$203$	−1.08683	−0.0762808
$204$	−2.25692	−0.158016
$205$	1.29325	0.0903247
$206$	−10.1669	−0.708361
$207$	−1.96455	−0.136546
$208$	−2.24813	−0.155880
$209$	−22.4724	−1.55445
$210$	−2.18861	−0.151029
$211$	−6.28010	−0.432340	−0.216170	−	0.976356i	$-0.569356\pi$
$211$	−6.28010	−0.432340	−0.216170	+	0.976356i	$0.569356\pi$
$212$	10.6019	0.728144
$213$	6.85369	0.469607
$214$	12.5378	0.857069
$215$	11.8236	0.806363
$216$	5.61101	0.381781
$217$	−9.55884	−0.648896
$218$	5.17606	0.350567
$219$	19.8020	1.33810
$220$	−3.70234	−0.249612
$221$	−3.34483	−0.224997
$222$	−10.2979	−0.691151
$223$	10.8613	0.727330	0.363665	−	0.931530i	$-0.381525\pi$
$223$	10.8613	0.727330	0.363665	+	0.931530i	$0.381525\pi$
$224$	−1.44279	−0.0964008
$225$	−0.698933	−0.0465955
$226$	−1.34296	−0.0893321
$227$	−22.8338	−1.51553	−0.757765	−	0.652527i	$-0.773709\pi$
$227$	−22.8338	−1.51553	−0.757765	+	0.652527i	$0.773709\pi$
$228$	9.20743	0.609777
$229$	2.26452	0.149644	0.0748220	−	0.997197i	$-0.476161\pi$
$229$	2.26452	0.149644	0.0748220	+	0.997197i	$0.476161\pi$
$230$	−2.81079	−0.185338
$231$	8.10299	0.533138
$232$	0.753284	0.0494555
$233$	−14.3422	−0.939588	−0.469794	−	0.882776i	$-0.655672\pi$
$233$	−14.3422	−0.939588	−0.469794	+	0.882776i	$0.655672\pi$
$234$	1.57129	0.102719
$235$	−5.22916	−0.341113
$236$	−1.75309	−0.114116
$237$	6.67272	0.433440
$238$	−2.14663	−0.139145
$239$	−7.24899	−0.468898	−0.234449	−	0.972128i	$-0.575329\pi$
$239$	−7.24899	−0.468898	−0.234449	+	0.972128i	$0.575329\pi$
$240$	1.51693	0.0979172
$241$	−16.1862	−1.04264	−0.521322	−	0.853360i	$-0.674561\pi$
$241$	−16.1862	−1.04264	−0.521322	+	0.853360i	$0.674561\pi$
$242$	2.70732	0.174033
$243$	−7.10241	−0.455620
$244$	−7.55068	−0.483382
$245$	4.91834	0.314221
$246$	1.96177	0.125078
$247$	13.6457	0.868255
$248$	6.62522	0.420702
$249$	8.74462	0.554167
$250$	−1.00000	−0.0632456
$251$	−9.35987	−0.590789	−0.295395	−	0.955375i	$-0.595451\pi$
$251$	−9.35987	−0.590789	−0.295395	+	0.955375i	$0.595451\pi$
$252$	1.00842	0.0635243
$253$	10.4065	0.654251
$254$	−11.6113	−0.728558
$255$	2.25692	0.141334
$256$	1.00000	0.0625000
$257$	18.3587	1.14518	0.572592	−	0.819841i	$-0.305938\pi$
$257$	18.3587	1.14518	0.572592	+	0.819841i	$0.305938\pi$
$258$	17.9355	1.11662
$259$	−9.79466	−0.608610
$260$	2.24813	0.139423
$261$	−0.526495	−0.0325892
$262$	−18.4830	−1.14188
$263$	−19.6261	−1.21020	−0.605099	−	0.796150i	$-0.706867\pi$
$263$	−19.6261	−1.21020	−0.605099	+	0.796150i	$0.706867\pi$
$264$	−5.61618	−0.345652
$265$	−10.6019	−0.651271
$266$	8.75746	0.536955
$267$	−11.8501	−0.725212
$268$	−4.43992	−0.271211
$269$	16.3925	0.999469	0.499735	−	0.866179i	$-0.333431\pi$
$269$	16.3925	0.999469	0.499735	+	0.866179i	$0.333431\pi$
$270$	−5.61101	−0.341475
$271$	−5.95875	−0.361968	−0.180984	−	0.983486i	$-0.557928\pi$
$271$	−5.95875	−0.361968	−0.180984	+	0.983486i	$0.557928\pi$
$272$	1.48782	0.0902126
$273$	−4.92029	−0.297790
$274$	−4.33213	−0.261714
$275$	3.70234	0.223260
$276$	−4.26376	−0.256648
$277$	−23.2890	−1.39930	−0.699650	−	0.714486i	$-0.746661\pi$
$277$	−23.2890	−1.39930	−0.699650	+	0.714486i	$0.746661\pi$
$278$	0.901260	0.0540540
$279$	−4.63058	−0.277226
$280$	1.44279	0.0862235
$281$	−9.23470	−0.550896	−0.275448	−	0.961316i	$-0.588826\pi$
$281$	−9.23470	−0.550896	−0.275448	+	0.961316i	$0.588826\pi$
$282$	−7.93225	−0.472359
$283$	−12.1457	−0.721989	−0.360994	−	0.932568i	$-0.617563\pi$
$283$	−12.1457	−0.721989	−0.360994	+	0.932568i	$0.617563\pi$
$284$	−4.51814	−0.268102
$285$	−9.20743	−0.545401
$286$	−8.32335	−0.492170
$287$	1.86590	0.110141
$288$	−0.698933	−0.0411850
$289$	−14.7864	−0.869787
$290$	−0.753284	−0.0442344
$291$	22.2226	1.30271
$292$	−13.0540	−0.763929
$293$	0.713364	0.0416751	0.0208376	−	0.999783i	$-0.493367\pi$
$293$	0.713364	0.0416751	0.0208376	+	0.999783i	$0.493367\pi$
$294$	7.46077	0.435121
$295$	1.75309	0.102069
$296$	6.78867	0.394583
$297$	20.7739	1.20542
$298$	−3.88375	−0.224980
$299$	−6.31903	−0.365439
$300$	−1.51693	−0.0875798
$301$	17.0590	0.983267
$302$	19.6323	1.12971
$303$	−18.2647	−1.04928
$304$	−6.06979	−0.348126
$305$	7.55068	0.432350
$306$	−1.03989	−0.0594465
$307$	4.34550	0.248011	0.124005	−	0.992282i	$-0.460426\pi$
$307$	4.34550	0.248011	0.124005	+	0.992282i	$0.460426\pi$
$308$	−5.34172	−0.304373
$309$	15.4224	0.877352
$310$	−6.62522	−0.376287
$311$	9.01185	0.511015	0.255508	−	0.966807i	$-0.417757\pi$
$311$	9.01185	0.511015	0.255508	+	0.966807i	$0.417757\pi$
$312$	3.41025	0.193068
$313$	−12.2902	−0.694682	−0.347341	−	0.937739i	$-0.612915\pi$
$313$	−12.2902	−0.694682	−0.347341	+	0.937739i	$0.612915\pi$
$314$	−11.9869	−0.676457
$315$	−1.00842	−0.0568178
$316$	−4.39884	−0.247454
$317$	−23.4866	−1.31914	−0.659569	−	0.751644i	$-0.729261\pi$
$317$	−23.4866	−1.31914	−0.659569	+	0.751644i	$0.729261\pi$
$318$	−16.0824	−0.901854
$319$	2.78891	0.156149
$320$	−1.00000	−0.0559017
$321$	−19.0190	−1.06154
$322$	−4.05539	−0.225998
$323$	−9.03078	−0.502486
$324$	−6.41470	−0.356372
$325$	−2.24813	−0.124704
$326$	−13.5214	−0.748881
$327$	−7.85171	−0.434201
$328$	−1.29325	−0.0714080
$329$	−7.54460	−0.415947
$330$	5.61618	0.309161
$331$	17.5531	0.964804	0.482402	−	0.875950i	$-0.339764\pi$
$331$	17.5531	0.964804	0.482402	+	0.875950i	$0.339764\pi$
$332$	−5.76469	−0.316379
$333$	−4.74482	−0.260015
$334$	−9.36271	−0.512305
$335$	4.43992	0.242579
$336$	2.18861	0.119399
$337$	−35.8513	−1.95294	−0.976472	−	0.215642i	$-0.930816\pi$
$337$	−35.8513	−1.95294	−0.976472	+	0.215642i	$0.930816\pi$
$338$	−7.94590	−0.432200
$339$	2.03717	0.110644
$340$	−1.48782	−0.0806886
$341$	24.5288	1.32831
$342$	4.24238	0.229401
$343$	17.1957	0.928482
$344$	−11.8236	−0.637486
$345$	4.26376	0.229553
$346$	−12.2556	−0.658868
$347$	16.9464	0.909731	0.454865	−	0.890560i	$-0.349687\pi$
$347$	16.9464	0.909731	0.454865	+	0.890560i	$0.349687\pi$
$348$	−1.14268	−0.0612539
$349$	−26.0755	−1.39579	−0.697896	−	0.716200i	$-0.745880\pi$
$349$	−26.0755	−1.39579	−0.697896	+	0.716200i	$0.745880\pi$
$350$	−1.44279	−0.0771206
$351$	−12.6143	−0.673301
$352$	3.70234	0.197335
$353$	−27.9624	−1.48829	−0.744145	−	0.668018i	$-0.767143\pi$
$353$	−27.9624	−1.48829	−0.744145	+	0.668018i	$0.767143\pi$
$354$	2.65931	0.141341
$355$	4.51814	0.239798
$356$	7.81189	0.414029
$357$	3.25627	0.172340
$358$	17.1199	0.904812
$359$	4.94512	0.260994	0.130497	−	0.991449i	$-0.458343\pi$
$359$	4.94512	0.260994	0.130497	+	0.991449i	$0.458343\pi$
$360$	0.698933	0.0368370
$361$	17.8424	0.939072
$362$	12.2866	0.645770
$363$	−4.10681	−0.215552
$364$	3.24359	0.170010
$365$	13.0540	0.683279
$366$	11.4538	0.598701
$367$	−26.7591	−1.39681	−0.698406	−	0.715702i	$-0.746107\pi$
$367$	−26.7591	−1.39681	−0.698406	+	0.715702i	$0.746107\pi$
$368$	2.81079	0.146523
$369$	0.903897	0.0470550
$370$	−6.78867	−0.352926
$371$	−15.2964	−0.794150
$372$	−10.0500	−0.521067
$373$	5.84571	0.302679	0.151340	−	0.988482i	$-0.451641\pi$
$373$	5.84571	0.302679	0.151340	+	0.988482i	$0.451641\pi$
$374$	5.50843	0.284834
$375$	1.51693	0.0783338
$376$	5.22916	0.269673
$377$	−1.69348	−0.0872188
$378$	−8.09554	−0.416389
$379$	−14.1478	−0.726724	−0.363362	−	0.931648i	$-0.618371\pi$
$379$	−14.1478	−0.726724	−0.363362	+	0.931648i	$0.618371\pi$
$380$	6.06979	0.311374
$381$	17.6135	0.902367
$382$	14.9736	0.766115
$383$	−4.37680	−0.223644	−0.111822	−	0.993728i	$-0.535669\pi$
$383$	−4.37680	−0.223644	−0.111822	+	0.993728i	$0.535669\pi$
$384$	−1.51693	−0.0774104
$385$	5.34172	0.272239
$386$	−2.28076	−0.116088
$387$	8.26391	0.420078
$388$	−14.6497	−0.743727
$389$	−4.37190	−0.221664	−0.110832	−	0.993839i	$-0.535352\pi$
$389$	−4.37190	−0.221664	−0.110832	+	0.993839i	$0.535352\pi$
$390$	−3.41025	−0.172685
$391$	4.18196	0.211491
$392$	−4.91834	−0.248414
$393$	28.0373	1.41429
$394$	−3.53756	−0.178220
$395$	4.39884	0.221330
$396$	−2.58769	−0.130036
$397$	−5.29107	−0.265551	−0.132776	−	0.991146i	$-0.542389\pi$
$397$	−5.29107	−0.265551	−0.132776	+	0.991146i	$0.542389\pi$
$398$	−0.474746	−0.0237969
$399$	−13.2844	−0.665054
$400$	1.00000	0.0500000
$401$	18.9343	0.945532	0.472766	−	0.881188i	$-0.343256\pi$
$401$	18.9343	0.945532	0.472766	+	0.881188i	$0.343256\pi$
$402$	6.73504	0.335913
$403$	−14.8944	−0.741942
$404$	12.0406	0.599043
$405$	6.41470	0.318749
$406$	−1.08683	−0.0539387
$407$	25.1340	1.24584
$408$	−2.25692	−0.111734
$409$	14.7708	0.730367	0.365184	−	0.930936i	$-0.381006\pi$
$409$	14.7708	0.730367	0.365184	+	0.930936i	$0.381006\pi$
$410$	1.29325	0.0638692
$411$	6.57153	0.324149
$412$	−10.1669	−0.500887
$413$	2.52935	0.124461
$414$	−1.96455	−0.0965525
$415$	5.76469	0.282978
$416$	−2.24813	−0.110224
$417$	−1.36715	−0.0669494
$418$	−22.4724	−1.09916
$419$	17.4520	0.852585	0.426293	−	0.904585i	$-0.359819\pi$
$419$	17.4520	0.852585	0.426293	+	0.904585i	$0.359819\pi$
$420$	−2.18861	−0.106793
$421$	5.78247	0.281820	0.140910	−	0.990022i	$-0.454997\pi$
$421$	5.78247	0.281820	0.140910	+	0.990022i	$0.454997\pi$
$422$	−6.28010	−0.305710
$423$	−3.65483	−0.177704
$424$	10.6019	0.514875
$425$	1.48782	0.0721701
$426$	6.85369	0.332062
$427$	10.8941	0.527201
$428$	12.5378	0.606039
$429$	12.6259	0.609585
$430$	11.8236	0.570185
$431$	5.56901	0.268250	0.134125	−	0.990964i	$-0.457178\pi$
$431$	5.56901	0.268250	0.134125	+	0.990964i	$0.457178\pi$
$432$	5.61101	0.269960
$433$	−32.4534	−1.55961	−0.779805	−	0.626023i	$-0.784682\pi$
$433$	−32.4534	−1.55961	−0.779805	+	0.626023i	$0.784682\pi$
$434$	−9.55884	−0.458839
$435$	1.14268	0.0547872
$436$	5.17606	0.247889
$437$	−17.0609	−0.816134
$438$	19.8020	0.946177
$439$	2.42418	0.115700	0.0578499	−	0.998325i	$-0.481576\pi$
$439$	2.42418	0.115700	0.0578499	+	0.998325i	$0.481576\pi$
$440$	−3.70234	−0.176502
$441$	3.43759	0.163695
$442$	−3.34483	−0.159097
$443$	−15.6505	−0.743579	−0.371790	−	0.928317i	$-0.621256\pi$
$443$	−15.6505	−0.743579	−0.371790	+	0.928317i	$0.621256\pi$
$444$	−10.2979	−0.488717
$445$	−7.81189	−0.370319
$446$	10.8613	0.514300
$447$	5.89136	0.278652
$448$	−1.44279	−0.0681656
$449$	−0.127414	−0.00601306	−0.00300653	−	0.999995i	$-0.500957\pi$
$449$	−0.127414	−0.00601306	−0.00300653	+	0.999995i	$0.500957\pi$
$450$	−0.698933	−0.0329480
$451$	−4.78806	−0.225461
$452$	−1.34296	−0.0631674
$453$	−29.7808	−1.39923
$454$	−22.8338	−1.07164
$455$	−3.24359	−0.152062
$456$	9.20743	0.431177
$457$	21.9431	1.02645	0.513227	−	0.858253i	$-0.328450\pi$
$457$	21.9431	1.02645	0.513227	+	0.858253i	$0.328450\pi$
$458$	2.26452	0.105814
$459$	8.34820	0.389660
$460$	−2.81079	−0.131054
$461$	1.98645	0.0925181	0.0462591	−	0.998929i	$-0.485270\pi$
$461$	1.98645	0.0925181	0.0462591	+	0.998929i	$0.485270\pi$
$462$	8.10299	0.376985
$463$	−22.8078	−1.05997	−0.529985	−	0.848007i	$-0.677802\pi$
$463$	−22.8078	−1.05997	−0.529985	+	0.848007i	$0.677802\pi$
$464$	0.753284	0.0349703
$465$	10.0500	0.466057
$466$	−14.3422	−0.664389
$467$	13.5961	0.629151	0.314575	−	0.949232i	$-0.398138\pi$
$467$	13.5961	0.629151	0.314575	+	0.949232i	$0.398138\pi$
$468$	1.57129	0.0726330
$469$	6.40590	0.295797
$470$	−5.22916	−0.241203
$471$	18.1832	0.837837
$472$	−1.75309	−0.0806925
$473$	−43.7750	−2.01278
$474$	6.67272	0.306488
$475$	−6.06979	−0.278501
$476$	−2.14663	−0.0983904
$477$	−7.41004	−0.339282
$478$	−7.24899	−0.331561
$479$	5.41038	0.247207	0.123603	−	0.992332i	$-0.460555\pi$
$479$	5.41038	0.247207	0.123603	+	0.992332i	$0.460555\pi$
$480$	1.51693	0.0692379
$481$	−15.2618	−0.695879
$482$	−16.1862	−0.737260
$483$	6.15173	0.279914
$484$	2.70732	0.123060
$485$	14.6497	0.665210
$486$	−7.10241	−0.322172
$487$	38.3374	1.73723	0.868617	−	0.495483i	$-0.165009\pi$
$487$	38.3374	1.73723	0.868617	+	0.495483i	$0.165009\pi$
$488$	−7.55068	−0.341803
$489$	20.5110	0.927538
$490$	4.91834	0.222188
$491$	15.8272	0.714270	0.357135	−	0.934053i	$-0.383754\pi$
$491$	15.8272	0.714270	0.357135	+	0.934053i	$0.383754\pi$
$492$	1.96177	0.0884435
$493$	1.12075	0.0504762
$494$	13.6457	0.613949
$495$	2.58769	0.116308
$496$	6.62522	0.297481
$497$	6.51875	0.292406
$498$	8.74462	0.391856
$499$	−2.98013	−0.133409	−0.0667045	−	0.997773i	$-0.521248\pi$
$499$	−2.98013	−0.133409	−0.0667045	+	0.997773i	$0.521248\pi$
$500$	−1.00000	−0.0447214
$501$	14.2025	0.634523
$502$	−9.35987	−0.417751
$503$	10.0533	0.448256	0.224128	−	0.974560i	$-0.428047\pi$
$503$	10.0533	0.448256	0.224128	+	0.974560i	$0.428047\pi$
$504$	1.00842	0.0449184
$505$	−12.0406	−0.535801
$506$	10.4065	0.462625
$507$	12.0534	0.535308
$508$	−11.6113	−0.515168
$509$	−14.1456	−0.626993	−0.313496	−	0.949589i	$-0.601500\pi$
$509$	−14.1456	−0.626993	−0.313496	+	0.949589i	$0.601500\pi$
$510$	2.25692	0.0999381
$511$	18.8343	0.833180
$512$	1.00000	0.0441942
$513$	−34.0577	−1.50368
$514$	18.3587	0.809767
$515$	10.1669	0.448007
$516$	17.9355	0.789569
$517$	19.3601	0.851457
$518$	−9.79466	−0.430352
$519$	18.5909	0.816051
$520$	2.24813	0.0985871
$521$	−3.14996	−0.138002	−0.0690011	−	0.997617i	$-0.521981\pi$
$521$	−3.14996	−0.138002	−0.0690011	+	0.997617i	$0.521981\pi$
$522$	−0.526495	−0.0230441
$523$	8.56097	0.374345	0.187172	−	0.982327i	$-0.440068\pi$
$523$	8.56097	0.374345	0.187172	+	0.982327i	$0.440068\pi$
$524$	−18.4830	−0.807432
$525$	2.18861	0.0955190
$526$	−19.6261	−0.855739
$527$	9.85717	0.429385
$528$	−5.61618	−0.244413
$529$	−15.0995	−0.656498
$530$	−10.6019	−0.460518
$531$	1.22529	0.0531732
$532$	8.75746	0.379684
$533$	2.90740	0.125934
$534$	−11.8501	−0.512802
$535$	−12.5378	−0.542058
$536$	−4.43992	−0.191775
$537$	−25.9696	−1.12067
$538$	16.3925	0.706732
$539$	−18.2094	−0.784333
$540$	−5.61101	−0.241459
$541$	8.05710	0.346402	0.173201	−	0.984887i	$-0.444589\pi$
$541$	8.05710	0.346402	0.173201	+	0.984887i	$0.444589\pi$
$542$	−5.95875	−0.255950
$543$	−18.6379	−0.799828
$544$	1.48782	0.0637899
$545$	−5.17606	−0.221718
$546$	−4.92029	−0.210569
$547$	16.6397	0.711460	0.355730	−	0.934589i	$-0.384232\pi$
$547$	16.6397	0.711460	0.355730	+	0.934589i	$0.384232\pi$
$548$	−4.33213	−0.185059
$549$	5.27741	0.225235
$550$	3.70234	0.157868
$551$	−4.57228	−0.194786
$552$	−4.26376	−0.181478
$553$	6.34662	0.269886
$554$	−23.2890	−0.989454
$555$	10.2979	0.437122
$556$	0.901260	0.0382219
$557$	0.613566	0.0259976	0.0129988	−	0.999916i	$-0.495862\pi$
$557$	0.613566	0.0259976	0.0129988	+	0.999916i	$0.495862\pi$
$558$	−4.63058	−0.196028
$559$	26.5810	1.12426
$560$	1.44279	0.0609692
$561$	−8.35589	−0.352786
$562$	−9.23470	−0.389542
$563$	35.9434	1.51484	0.757418	−	0.652931i	$-0.226461\pi$
$563$	35.9434	1.51484	0.757418	+	0.652931i	$0.226461\pi$
$564$	−7.93225	−0.334008
$565$	1.34296	0.0564986
$566$	−12.1457	−0.510523
$567$	9.25509	0.388677
$568$	−4.51814	−0.189577
$569$	21.7297	0.910955	0.455478	−	0.890247i	$-0.349469\pi$
$569$	21.7297	0.910955	0.455478	+	0.890247i	$0.349469\pi$
$570$	−9.20743	−0.385657
$571$	2.69182	0.112649	0.0563246	−	0.998413i	$-0.482062\pi$
$571$	2.69182	0.112649	0.0563246	+	0.998413i	$0.482062\pi$
$572$	−8.32335	−0.348017
$573$	−22.7138	−0.948884
$574$	1.86590	0.0778811
$575$	2.81079	0.117218
$576$	−0.698933	−0.0291222
$577$	−40.0102	−1.66565	−0.832824	−	0.553538i	$-0.813277\pi$
$577$	−40.0102	−1.66565	−0.832824	+	0.553538i	$0.813277\pi$
$578$	−14.7864	−0.615032
$579$	3.45975	0.143782
$580$	−0.753284	−0.0312784
$581$	8.31727	0.345058
$582$	22.2226	0.921155
$583$	39.2520	1.62565
$584$	−13.0540	−0.540180
$585$	−1.57129	−0.0649650
$586$	0.713364	0.0294688
$587$	18.4962	0.763421	0.381710	−	0.924282i	$-0.375335\pi$
$587$	18.4962	0.763421	0.381710	+	0.924282i	$0.375335\pi$
$588$	7.46077	0.307677
$589$	−40.2137	−1.65698
$590$	1.75309	0.0721736
$591$	5.36622	0.220737
$592$	6.78867	0.279013
$593$	26.1260	1.07287	0.536433	−	0.843943i	$-0.319771\pi$
$593$	26.1260	1.07287	0.536433	+	0.843943i	$0.319771\pi$
$594$	20.7739	0.852362
$595$	2.14663	0.0880030
$596$	−3.88375	−0.159085
$597$	0.720154	0.0294740
$598$	−6.31903	−0.258404
$599$	18.0516	0.737568	0.368784	−	0.929515i	$-0.379774\pi$
$599$	18.0516	0.737568	0.368784	+	0.929515i	$0.379774\pi$
$600$	−1.51693	−0.0619283
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	17.0590	0.695275
$603$	3.10321	0.126372
$604$	19.6323	0.798829
$605$	−2.70732	−0.110068
$606$	−18.2647	−0.741955
$607$	16.5481	0.671666	0.335833	−	0.941922i	$-0.390982\pi$
$607$	16.5481	0.671666	0.335833	+	0.941922i	$0.390982\pi$
$608$	−6.06979	−0.246163
$609$	1.64865	0.0668066
$610$	7.55068	0.305718
$611$	−11.7558	−0.475590
$612$	−1.03989	−0.0420350
$613$	−3.65477	−0.147615	−0.0738073	−	0.997273i	$-0.523515\pi$
$613$	−3.65477	−0.147615	−0.0738073	+	0.997273i	$0.523515\pi$
$614$	4.34550	0.175370
$615$	−1.96177	−0.0791062
$616$	−5.34172	−0.215224
$617$	−0.426034	−0.0171515	−0.00857573	−	0.999963i	$-0.502730\pi$
$617$	−0.426034	−0.0171515	−0.00857573	+	0.999963i	$0.502730\pi$
$618$	15.4224	0.620381
$619$	−17.2743	−0.694312	−0.347156	−	0.937807i	$-0.612852\pi$
$619$	−17.2743	−0.694312	−0.347156	+	0.937807i	$0.612852\pi$
$620$	−6.62522	−0.266075
$621$	15.7714	0.632883
$622$	9.01185	0.361342
$623$	−11.2710	−0.451561
$624$	3.41025	0.136519
$625$	1.00000	0.0400000
$626$	−12.2902	−0.491214
$627$	34.0890	1.36139
$628$	−11.9869	−0.478328
$629$	10.1003	0.402727
$630$	−1.00842	−0.0401763
$631$	−4.06934	−0.161998	−0.0809988	−	0.996714i	$-0.525811\pi$
$631$	−4.06934	−0.161998	−0.0809988	+	0.996714i	$0.525811\pi$
$632$	−4.39884	−0.174976
$633$	9.52645	0.378642
$634$	−23.4866	−0.932771
$635$	11.6113	0.460780
$636$	−16.0824	−0.637707
$637$	11.0571	0.438098
$638$	2.78891	0.110414
$639$	3.15788	0.124924
$640$	−1.00000	−0.0395285
$641$	24.9367	0.984940	0.492470	−	0.870329i	$-0.336094\pi$
$641$	24.9367	0.984940	0.492470	+	0.870329i	$0.336094\pi$
$642$	−19.0190	−0.750619
$643$	37.3568	1.47321	0.736605	−	0.676324i	$-0.236428\pi$
$643$	37.3568	1.47321	0.736605	+	0.676324i	$0.236428\pi$
$644$	−4.05539	−0.159805
$645$	−17.9355	−0.706212
$646$	−9.03078	−0.355311
$647$	−32.3686	−1.27254	−0.636270	−	0.771466i	$-0.719524\pi$
$647$	−32.3686	−1.27254	−0.636270	+	0.771466i	$0.719524\pi$
$648$	−6.41470	−0.251993
$649$	−6.49054	−0.254776
$650$	−2.24813	−0.0881790
$651$	14.5001	0.568302
$652$	−13.5214	−0.529539
$653$	23.2079	0.908195	0.454097	−	0.890952i	$-0.349962\pi$
$653$	23.2079	0.908195	0.454097	+	0.890952i	$0.349962\pi$
$654$	−7.85171	−0.307026
$655$	18.4830	0.722189
$656$	−1.29325	−0.0504931
$657$	9.12389	0.355957
$658$	−7.54460	−0.294119
$659$	4.47924	0.174486	0.0872432	−	0.996187i	$-0.472194\pi$
$659$	4.47924	0.174486	0.0872432	+	0.996187i	$0.472194\pi$
$660$	5.61618	0.218609
$661$	−14.6997	−0.571754	−0.285877	−	0.958266i	$-0.592285\pi$
$661$	−14.6997	−0.571754	−0.285877	+	0.958266i	$0.592285\pi$
$662$	17.5531	0.682219
$663$	5.07386	0.197052
$664$	−5.76469	−0.223713
$665$	−8.75746	−0.339600
$666$	−4.74482	−0.183858
$667$	2.11732	0.0819831
$668$	−9.36271	−0.362254
$669$	−16.4759	−0.636994
$670$	4.43992	0.171529
$671$	−27.9552	−1.07920
$672$	2.18861	0.0844276
$673$	38.2145	1.47306	0.736529	−	0.676406i	$-0.236463\pi$
$673$	38.2145	1.47306	0.736529	+	0.676406i	$0.236463\pi$
$674$	−35.8513	−1.38094
$675$	5.61101	0.215968
$676$	−7.94590	−0.305612
$677$	47.2850	1.81731	0.908655	−	0.417547i	$-0.137110\pi$
$677$	47.2850	1.81731	0.908655	+	0.417547i	$0.137110\pi$
$678$	2.03717	0.0782369
$679$	21.1366	0.811147
$680$	−1.48782	−0.0570555
$681$	34.6372	1.32730
$682$	24.5288	0.939257
$683$	19.9612	0.763793	0.381896	−	0.924205i	$-0.375271\pi$
$683$	19.9612	0.763793	0.381896	+	0.924205i	$0.375271\pi$
$684$	4.24238	0.162211
$685$	4.33213	0.165522
$686$	17.1957	0.656536
$687$	−3.43512	−0.131058
$688$	−11.8236	−0.450771
$689$	−23.8345	−0.908024
$690$	4.26376	0.162319
$691$	26.2966	1.00037	0.500186	−	0.865918i	$-0.333265\pi$
$691$	26.2966	1.00037	0.500186	+	0.865918i	$0.333265\pi$
$692$	−12.2556	−0.465890
$693$	3.73350	0.141824
$694$	16.9464	0.643277
$695$	−0.901260	−0.0341867
$696$	−1.14268	−0.0433130
$697$	−1.92413	−0.0728818
$698$	−26.0755	−0.986973
$699$	21.7561	0.822890
$700$	−1.44279	−0.0545325
$701$	−18.9599	−0.716106	−0.358053	−	0.933701i	$-0.616559\pi$
$701$	−18.9599	−0.716106	−0.358053	+	0.933701i	$0.616559\pi$
$702$	−12.6143	−0.476096
$703$	−41.2058	−1.55411
$704$	3.70234	0.139537
$705$	7.93225	0.298746
$706$	−27.9624	−1.05238
$707$	−17.3721	−0.653347
$708$	2.65931	0.0999430
$709$	−15.3777	−0.577522	−0.288761	−	0.957401i	$-0.593243\pi$
$709$	−15.3777	−0.577522	−0.288761	+	0.957401i	$0.593243\pi$
$710$	4.51814	0.169563
$711$	3.07449	0.115303
$712$	7.81189	0.292763
$713$	18.6221	0.697403
$714$	3.25627	0.121863
$715$	8.32335	0.311276
$716$	17.1199	0.639799
$717$	10.9962	0.410660
$718$	4.94512	0.184550
$719$	−45.8528	−1.71002	−0.855011	−	0.518610i	$-0.826450\pi$
$719$	−45.8528	−1.71002	−0.855011	+	0.518610i	$0.826450\pi$
$720$	0.698933	0.0260477
$721$	14.6687	0.546292
$722$	17.8424	0.664024
$723$	24.5532	0.913145
$724$	12.2866	0.456628
$725$	0.753284	0.0279763
$726$	−4.10681	−0.152418
$727$	−4.86045	−0.180264	−0.0901320	−	0.995930i	$-0.528729\pi$
$727$	−4.86045	−0.180264	−0.0901320	+	0.995930i	$0.528729\pi$
$728$	3.24359	0.120216
$729$	30.0179	1.11177
$730$	13.0540	0.483151
$731$	−17.5915	−0.650643
$732$	11.4538	0.423345
$733$	34.5612	1.27655	0.638273	−	0.769810i	$-0.279649\pi$
$733$	34.5612	1.27655	0.638273	+	0.769810i	$0.279649\pi$
$734$	−26.7591	−0.987695
$735$	−7.46077	−0.275195
$736$	2.81079	0.103607
$737$	−16.4381	−0.605505
$738$	0.903897	0.0332729
$739$	9.17058	0.337345	0.168673	−	0.985672i	$-0.446052\pi$
$739$	9.17058	0.337345	0.168673	+	0.985672i	$0.446052\pi$
$740$	−6.78867	−0.249556
$741$	−20.6995	−0.760416
$742$	−15.2964	−0.561549
$743$	−52.1851	−1.91449	−0.957243	−	0.289286i	$-0.906582\pi$
$743$	−52.1851	−1.91449	−0.957243	+	0.289286i	$0.906582\pi$
$744$	−10.0500	−0.368450
$745$	3.88375	0.142290
$746$	5.84571	0.214026
$747$	4.02913	0.147418
$748$	5.50843	0.201408
$749$	−18.0895	−0.660977
$750$	1.51693	0.0553903
$751$	−21.7836	−0.794895	−0.397448	−	0.917625i	$-0.630104\pi$
$751$	−21.7836	−0.794895	−0.397448	+	0.917625i	$0.630104\pi$
$752$	5.22916	0.190688
$753$	14.1982	0.517412
$754$	−1.69348	−0.0616730
$755$	−19.6323	−0.714494
$756$	−8.09554	−0.294432
$757$	−10.9739	−0.398853	−0.199427	−	0.979913i	$-0.563908\pi$
$757$	−10.9739	−0.398853	−0.199427	+	0.979913i	$0.563908\pi$
$758$	−14.1478	−0.513871
$759$	−15.7859	−0.572992
$760$	6.06979	0.220174
$761$	−34.6463	−1.25593	−0.627963	−	0.778243i	$-0.716111\pi$
$761$	−34.6463	−1.25593	−0.627963	+	0.778243i	$0.716111\pi$
$762$	17.6135	0.638070
$763$	−7.46800	−0.270360
$764$	14.9736	0.541725
$765$	1.03989	0.0375973
$766$	−4.37680	−0.158140
$767$	3.94118	0.142308
$768$	−1.51693	−0.0547374
$769$	35.7596	1.28952	0.644762	−	0.764383i	$-0.276956\pi$
$769$	35.7596	1.28952	0.644762	+	0.764383i	$0.276956\pi$
$770$	5.34172	0.192502
$771$	−27.8488	−1.00295
$772$	−2.28076	−0.0820864
$773$	−32.3920	−1.16506	−0.582529	−	0.812810i	$-0.697937\pi$
$773$	−32.3920	−1.16506	−0.582529	+	0.812810i	$0.697937\pi$
$774$	8.26391	0.297040
$775$	6.62522	0.237985
$776$	−14.6497	−0.525895
$777$	14.8578	0.533020
$778$	−4.37190	−0.156740
$779$	7.84978	0.281248
$780$	−3.41025	−0.122107
$781$	−16.7277	−0.598564
$782$	4.18196	0.149547
$783$	4.22668	0.151049
$784$	−4.91834	−0.175655
$785$	11.9869	0.427829
$786$	28.0373	1.00006
$787$	16.5964	0.591596	0.295798	−	0.955250i	$-0.404414\pi$
$787$	16.5964	0.591596	0.295798	+	0.955250i	$0.404414\pi$
$788$	−3.53756	−0.126020
$789$	29.7714	1.05989
$790$	4.39884	0.156504
$791$	1.93761	0.0688935
$792$	−2.58769	−0.0919494
$793$	16.9749	0.602797
$794$	−5.29107	−0.187773
$795$	16.0824	0.570382
$796$	−0.474746	−0.0168269
$797$	−34.9257	−1.23713	−0.618566	−	0.785733i	$-0.712286\pi$
$797$	−34.9257	−1.23713	−0.618566	+	0.785733i	$0.712286\pi$
$798$	−13.2844	−0.470264
$799$	7.78007	0.275239
$800$	1.00000	0.0353553
$801$	−5.45998	−0.192919
$802$	18.9343	0.668592
$803$	−48.3305	−1.70554
$804$	6.73504	0.237526
$805$	4.05539	0.142934
$806$	−14.8944	−0.524632
$807$	−24.8663	−0.875333
$808$	12.0406	0.423588
$809$	23.8821	0.839651	0.419826	−	0.907605i	$-0.362091\pi$
$809$	23.8821	0.839651	0.419826	+	0.907605i	$0.362091\pi$
$810$	6.41470	0.225389
$811$	−20.1084	−0.706100	−0.353050	−	0.935604i	$-0.614855\pi$
$811$	−20.1084	−0.706100	−0.353050	+	0.935604i	$0.614855\pi$
$812$	−1.08683	−0.0381404
$813$	9.03898	0.317011
$814$	25.1340	0.880945
$815$	13.5214	0.473634
$816$	−2.25692	−0.0790080
$817$	71.7668	2.51080
$818$	14.7708	0.516448
$819$	−2.26705	−0.0792173
$820$	1.29325	0.0451624
$821$	−0.0839354	−0.00292937	−0.00146468	−	0.999999i	$-0.500466\pi$
$821$	−0.0839354	−0.00292937	−0.00146468	+	0.999999i	$0.500466\pi$
$822$	6.57153	0.229208
$823$	5.05120	0.176074	0.0880369	−	0.996117i	$-0.471941\pi$
$823$	5.05120	0.176074	0.0880369	+	0.996117i	$0.471941\pi$
$824$	−10.1669	−0.354180
$825$	−5.61618	−0.195530
$826$	2.52935	0.0880073
$827$	30.3291	1.05465	0.527323	−	0.849665i	$-0.323196\pi$
$827$	30.3291	1.05465	0.527323	+	0.849665i	$0.323196\pi$
$828$	−1.96455	−0.0682729
$829$	−39.7639	−1.38106	−0.690528	−	0.723306i	$-0.742622\pi$
$829$	−39.7639	−1.38106	−0.690528	+	0.723306i	$0.742622\pi$
$830$	5.76469	0.200095
$831$	35.3277	1.22550
$832$	−2.24813	−0.0779400
$833$	−7.31763	−0.253541
$834$	−1.36715	−0.0473404
$835$	9.36271	0.324010
$836$	−22.4724	−0.777225
$837$	37.1742	1.28493
$838$	17.4520	0.602869
$839$	23.2841	0.803855	0.401927	−	0.915672i	$-0.368340\pi$
$839$	23.2841	0.803855	0.401927	+	0.915672i	$0.368340\pi$
$840$	−2.18861	−0.0755144
$841$	−28.4326	−0.980433
$842$	5.78247	0.199277
$843$	14.0084	0.482474
$844$	−6.28010	−0.216170
$845$	7.94590	0.273347
$846$	−3.65483	−0.125656
$847$	−3.90611	−0.134216
$848$	10.6019	0.364072
$849$	18.4242	0.632317
$850$	1.48782	0.0510319
$851$	19.0815	0.654106
$852$	6.85369	0.234804
$853$	−40.4949	−1.38652	−0.693259	−	0.720688i	$-0.743826\pi$
$853$	−40.4949	−1.38652	−0.693259	+	0.720688i	$0.743826\pi$
$854$	10.8941	0.372788
$855$	−4.24238	−0.145086
$856$	12.5378	0.428534
$857$	−4.81200	−0.164375	−0.0821873	−	0.996617i	$-0.526191\pi$
$857$	−4.81200	−0.164375	−0.0821873	+	0.996617i	$0.526191\pi$
$858$	12.6259	0.431042
$859$	21.6160	0.737529	0.368765	−	0.929523i	$-0.379781\pi$
$859$	21.6160	0.737529	0.368765	+	0.929523i	$0.379781\pi$
$860$	11.8236	0.403182
$861$	−2.83043	−0.0964609
$862$	5.56901	0.189681
$863$	−2.20575	−0.0750845	−0.0375422	−	0.999295i	$-0.511953\pi$
$863$	−2.20575	−0.0750845	−0.0375422	+	0.999295i	$0.511953\pi$
$864$	5.61101	0.190890
$865$	12.2556	0.416704
$866$	−32.4534	−1.10281
$867$	22.4299	0.761758
$868$	−9.55884	−0.324448
$869$	−16.2860	−0.552465
$870$	1.14268	0.0387404
$871$	9.98153	0.338211
$872$	5.17606	0.175284
$873$	10.2392	0.346544
$874$	−17.0609	−0.577094
$875$	1.44279	0.0487754
$876$	19.8020	0.669048
$877$	−39.6013	−1.33724	−0.668620	−	0.743605i	$-0.733115\pi$
$877$	−39.6013	−1.33724	−0.668620	+	0.743605i	$0.733115\pi$
$878$	2.42418	0.0818122
$879$	−1.08212	−0.0364990
$880$	−3.70234	−0.124806
$881$	12.0985	0.407610	0.203805	−	0.979012i	$-0.434669\pi$
$881$	12.0985	0.407610	0.203805	+	0.979012i	$0.434669\pi$
$882$	3.43759	0.115750
$883$	−31.2565	−1.05186	−0.525932	−	0.850527i	$-0.676283\pi$
$883$	−31.2565	−1.05186	−0.525932	+	0.850527i	$0.676283\pi$
$884$	−3.34483	−0.112499
$885$	−2.65931	−0.0893917
$886$	−15.6505	−0.525790
$887$	−26.3958	−0.886285	−0.443142	−	0.896451i	$-0.646136\pi$
$887$	−26.3958	−0.886285	−0.443142	+	0.896451i	$0.646136\pi$
$888$	−10.2979	−0.345575
$889$	16.7527	0.561868
$890$	−7.81189	−0.261855
$891$	−23.7494	−0.795634
$892$	10.8613	0.363665
$893$	−31.7399	−1.06214
$894$	5.89136	0.197037
$895$	−17.1199	−0.572254
$896$	−1.44279	−0.0482004
$897$	9.58550	0.320051
$898$	−0.127414	−0.00425187
$899$	4.99067	0.166448
$900$	−0.698933	−0.0232978
$901$	15.7738	0.525502
$902$	−4.78806	−0.159425
$903$	−25.8773	−0.861143
$904$	−1.34296	−0.0446661
$905$	−12.2866	−0.408421
$906$	−29.7808	−0.989402
$907$	−25.0968	−0.833325	−0.416662	−	0.909061i	$-0.636800\pi$
$907$	−25.0968	−0.833325	−0.416662	+	0.909061i	$0.636800\pi$
$908$	−22.8338	−0.757765
$909$	−8.41558	−0.279127
$910$	−3.24359	−0.107524
$911$	1.39455	0.0462034	0.0231017	−	0.999733i	$-0.492646\pi$
$911$	1.39455	0.0462034	0.0231017	+	0.999733i	$0.492646\pi$
$912$	9.20743	0.304888
$913$	−21.3428	−0.706345
$914$	21.9431	0.725812
$915$	−11.4538	−0.378652
$916$	2.26452	0.0748220
$917$	26.6671	0.880626
$918$	8.34820	0.275532
$919$	27.9190	0.920963	0.460482	−	0.887669i	$-0.347677\pi$
$919$	27.9190	0.920963	0.460482	+	0.887669i	$0.347677\pi$
$920$	−2.81079	−0.0926690
$921$	−6.59181	−0.217208
$922$	1.98645	0.0654202
$923$	10.1574	0.334334
$924$	8.10299	0.266569
$925$	6.78867	0.223210
$926$	−22.8078	−0.749511
$927$	7.10597	0.233391
$928$	0.753284	0.0247278
$929$	1.76298	0.0578415	0.0289208	−	0.999582i	$-0.490793\pi$
$929$	1.76298	0.0578415	0.0289208	+	0.999582i	$0.490793\pi$
$930$	10.0500	0.329552
$931$	29.8533	0.978403
$932$	−14.3422	−0.469794
$933$	−13.6703	−0.447546
$934$	13.5961	0.444877
$935$	−5.50843	−0.180145
$936$	1.57129	0.0513593
$937$	−55.0086	−1.79705	−0.898526	−	0.438920i	$-0.855361\pi$
$937$	−55.0086	−1.79705	−0.898526	+	0.438920i	$0.855361\pi$
$938$	6.40590	0.209160
$939$	18.6433	0.608401
$940$	−5.22916	−0.170556
$941$	−29.9149	−0.975196	−0.487598	−	0.873068i	$-0.662127\pi$
$941$	−29.9149	−0.975196	−0.487598	+	0.873068i	$0.662127\pi$
$942$	18.1832	0.592440
$943$	−3.63506	−0.118374
$944$	−1.75309	−0.0570582
$945$	8.09554	0.263348
$946$	−43.7750	−1.42325
$947$	24.0877	0.782745	0.391373	−	0.920232i	$-0.372000\pi$
$947$	24.0877	0.782745	0.391373	+	0.920232i	$0.372000\pi$
$948$	6.67272	0.216720
$949$	29.3472	0.952650
$950$	−6.06979	−0.196930
$951$	35.6274	1.15530
$952$	−2.14663	−0.0695725
$953$	−23.5579	−0.763114	−0.381557	−	0.924345i	$-0.624612\pi$
$953$	−23.5579	−0.763114	−0.381557	+	0.924345i	$0.624612\pi$
$954$	−7.41004	−0.239909
$955$	−14.9736	−0.484534
$956$	−7.24899	−0.234449
$957$	−4.23058	−0.136755
$958$	5.41038	0.174801
$959$	6.25038	0.201835
$960$	1.51693	0.0489586
$961$	12.8936	0.415922
$962$	−15.2618	−0.492061
$963$	−8.76310	−0.282387
$964$	−16.1862	−0.521322
$965$	2.28076	0.0734203
$966$	6.15173	0.197929
$967$	35.5537	1.14333	0.571665	−	0.820487i	$-0.306298\pi$
$967$	35.5537	1.14333	0.571665	+	0.820487i	$0.306298\pi$
$968$	2.70732	0.0870167
$969$	13.6990	0.440077
$970$	14.6497	0.470375
$971$	40.1283	1.28778	0.643890	−	0.765118i	$-0.277319\pi$
$971$	40.1283	1.28778	0.643890	+	0.765118i	$0.277319\pi$
$972$	−7.10241	−0.227810
$973$	−1.30033	−0.0416868
$974$	38.3374	1.22841
$975$	3.41025	0.109215
$976$	−7.55068	−0.241691
$977$	56.1091	1.79509	0.897545	−	0.440922i	$-0.145349\pi$
$977$	56.1091	1.79509	0.897545	+	0.440922i	$0.145349\pi$
$978$	20.5110	0.655868
$979$	28.9223	0.924360
$980$	4.91834	0.157111
$981$	−3.61772	−0.115505
$982$	15.8272	0.505065
$983$	21.5162	0.686261	0.343130	−	0.939288i	$-0.388513\pi$
$983$	21.5162	0.686261	0.343130	+	0.939288i	$0.388513\pi$
$984$	1.96177	0.0625390
$985$	3.53756	0.112716
$986$	1.12075	0.0356921
$987$	11.4446	0.364286
$988$	13.6457	0.434127
$989$	−33.2337	−1.05677
$990$	2.58769	0.0822421
$991$	29.5773	0.939554	0.469777	−	0.882785i	$-0.344334\pi$
$991$	29.5773	0.939554	0.469777	+	0.882785i	$0.344334\pi$
$992$	6.62522	0.210351
$993$	−26.6267	−0.844974
$994$	6.51875	0.206762
$995$	0.474746	0.0150504
$996$	8.74462	0.277084
$997$	14.1643	0.448587	0.224294	−	0.974522i	$-0.427993\pi$
$997$	14.1643	0.448587	0.224294	+	0.974522i	$0.427993\pi$
$998$	−2.98013	−0.0943345
$999$	38.0913	1.20516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.8	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.51693 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51693 q^{6} -1.44279 q^{7} +1.00000 q^{8} -0.698933 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.51693 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51693 q^{6} -1.44279 q^{7} +1.00000 q^{8} -0.698933 q^{9} -1.00000 q^{10} +3.70234 q^{11} -1.51693 q^{12} -2.24813 q^{13} -1.44279 q^{14} +1.51693 q^{15} +1.00000 q^{16} +1.48782 q^{17} -0.698933 q^{18} -6.06979 q^{19} -1.00000 q^{20} +2.18861 q^{21} +3.70234 q^{22} +2.81079 q^{23} -1.51693 q^{24} +1.00000 q^{25} -2.24813 q^{26} +5.61101 q^{27} -1.44279 q^{28} +0.753284 q^{29} +1.51693 q^{30} +6.62522 q^{31} +1.00000 q^{32} -5.61618 q^{33} +1.48782 q^{34} +1.44279 q^{35} -0.698933 q^{36} +6.78867 q^{37} -6.06979 q^{38} +3.41025 q^{39} -1.00000 q^{40} -1.29325 q^{41} +2.18861 q^{42} -11.8236 q^{43} +3.70234 q^{44} +0.698933 q^{45} +2.81079 q^{46} +5.22916 q^{47} -1.51693 q^{48} -4.91834 q^{49} +1.00000 q^{50} -2.25692 q^{51} -2.24813 q^{52} +10.6019 q^{53} +5.61101 q^{54} -3.70234 q^{55} -1.44279 q^{56} +9.20743 q^{57} +0.753284 q^{58} -1.75309 q^{59} +1.51693 q^{60} -7.55068 q^{61} +6.62522 q^{62} +1.00842 q^{63} +1.00000 q^{64} +2.24813 q^{65} -5.61618 q^{66} -4.43992 q^{67} +1.48782 q^{68} -4.26376 q^{69} +1.44279 q^{70} -4.51814 q^{71} -0.698933 q^{72} -13.0540 q^{73} +6.78867 q^{74} -1.51693 q^{75} -6.06979 q^{76} -5.34172 q^{77} +3.41025 q^{78} -4.39884 q^{79} -1.00000 q^{80} -6.41470 q^{81} -1.29325 q^{82} -5.76469 q^{83} +2.18861 q^{84} -1.48782 q^{85} -11.8236 q^{86} -1.14268 q^{87} +3.70234 q^{88} +7.81189 q^{89} +0.698933 q^{90} +3.24359 q^{91} +2.81079 q^{92} -10.0500 q^{93} +5.22916 q^{94} +6.06979 q^{95} -1.51693 q^{96} -14.6497 q^{97} -4.91834 q^{98} -2.58769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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