LMFDB - Embedded newform 2671.2.a.b.1.55

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.55
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.239313 q^{2} +1.33956 q^{3} -1.94273 q^{4} +3.18454 q^{5} -0.320575 q^{6} -0.0212892 q^{7} +0.943545 q^{8} -1.20557 q^{9} +O(q^{10})$	\(q-0.239313 q^{2} +1.33956 q^{3} -1.94273 q^{4} +3.18454 q^{5} -0.320575 q^{6} -0.0212892 q^{7} +0.943545 q^{8} -1.20557 q^{9} -0.762101 q^{10} +4.76179 q^{11} -2.60241 q^{12} +2.84917 q^{13} +0.00509477 q^{14} +4.26590 q^{15} +3.65966 q^{16} +0.435106 q^{17} +0.288508 q^{18} +1.09198 q^{19} -6.18670 q^{20} -0.0285182 q^{21} -1.13956 q^{22} +5.16760 q^{23} +1.26394 q^{24} +5.14130 q^{25} -0.681842 q^{26} -5.63363 q^{27} +0.0413591 q^{28} +0.0588219 q^{29} -1.02088 q^{30} -4.60784 q^{31} -2.76289 q^{32} +6.37872 q^{33} -0.104126 q^{34} -0.0677962 q^{35} +2.34209 q^{36} -2.75049 q^{37} -0.261324 q^{38} +3.81664 q^{39} +3.00476 q^{40} -6.36101 q^{41} +0.00682477 q^{42} +1.13555 q^{43} -9.25087 q^{44} -3.83918 q^{45} -1.23667 q^{46} +9.46509 q^{47} +4.90234 q^{48} -6.99955 q^{49} -1.23038 q^{50} +0.582853 q^{51} -5.53516 q^{52} +6.31080 q^{53} +1.34820 q^{54} +15.1641 q^{55} -0.0200873 q^{56} +1.46278 q^{57} -0.0140768 q^{58} -8.37431 q^{59} -8.28748 q^{60} +5.82832 q^{61} +1.10271 q^{62} +0.0256655 q^{63} -6.65812 q^{64} +9.07329 q^{65} -1.52651 q^{66} +7.76195 q^{67} -0.845294 q^{68} +6.92234 q^{69} +0.0162245 q^{70} +3.25499 q^{71} -1.13751 q^{72} -4.59395 q^{73} +0.658227 q^{74} +6.88710 q^{75} -2.12142 q^{76} -0.101374 q^{77} -0.913371 q^{78} +6.82619 q^{79} +11.6543 q^{80} -3.92990 q^{81} +1.52227 q^{82} +1.79125 q^{83} +0.0554031 q^{84} +1.38561 q^{85} -0.271753 q^{86} +0.0787957 q^{87} +4.49296 q^{88} -13.2202 q^{89} +0.918764 q^{90} -0.0606564 q^{91} -10.0393 q^{92} -6.17250 q^{93} -2.26512 q^{94} +3.47745 q^{95} -3.70107 q^{96} +18.6939 q^{97} +1.67508 q^{98} -5.74066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * 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 $

$2$	−0.239313	−0.169220	−0.0846098	−	0.996414i	$-0.526964\pi$
$2$	−0.239313	−0.169220	−0.0846098	+	0.996414i	$0.526964\pi$
$3$	1.33956	0.773398	0.386699	−	0.922206i	$-0.373615\pi$
$3$	1.33956	0.773398	0.386699	+	0.922206i	$0.373615\pi$
$4$	−1.94273	−0.971365
$5$	3.18454	1.42417	0.712085	−	0.702093i	$-0.247751\pi$
$5$	3.18454	1.42417	0.712085	+	0.702093i	$0.247751\pi$
$6$	−0.320575	−0.130874
$7$	−0.0212892	−0.00804655	−0.00402327	−	0.999992i	$-0.501281\pi$
$7$	−0.0212892	−0.00804655	−0.00402327	+	0.999992i	$0.501281\pi$
$8$	0.943545	0.333594
$9$	−1.20557	−0.401856
$10$	−0.762101	−0.240997
$11$	4.76179	1.43573	0.717867	−	0.696181i	$-0.245119\pi$
$11$	4.76179	1.43573	0.717867	+	0.696181i	$0.245119\pi$
$12$	−2.60241	−0.751251
$13$	2.84917	0.790217	0.395108	−	0.918634i	$-0.370707\pi$
$13$	2.84917	0.790217	0.395108	+	0.918634i	$0.370707\pi$
$14$	0.00509477	0.00136163
$15$	4.26590	1.10145
$16$	3.65966	0.914914
$17$	0.435106	0.105529	0.0527644	−	0.998607i	$-0.483197\pi$
$17$	0.435106	0.105529	0.0527644	+	0.998607i	$0.483197\pi$
$18$	0.288508	0.0680019
$19$	1.09198	0.250517	0.125259	−	0.992124i	$-0.460024\pi$
$19$	1.09198	0.250517	0.125259	+	0.992124i	$0.460024\pi$
$20$	−6.18670	−1.38339
$21$	−0.0285182	−0.00622318
$22$	−1.13956	−0.242954
$23$	5.16760	1.07752	0.538760	−	0.842459i	$-0.318893\pi$
$23$	5.16760	1.07752	0.538760	+	0.842459i	$0.318893\pi$
$24$	1.26394	0.258000
$25$	5.14130	1.02826
$26$	−0.681842	−0.133720
$27$	−5.63363	−1.08419
$28$	0.0413591	0.00781613
$29$	0.0588219	0.0109230	0.00546148	−	0.999985i	$-0.498262\pi$
$29$	0.0588219	0.0109230	0.00546148	+	0.999985i	$0.498262\pi$
$30$	−1.02088	−0.186387
$31$	−4.60784	−0.827592	−0.413796	−	0.910370i	$-0.635797\pi$
$31$	−4.60784	−0.827592	−0.413796	+	0.910370i	$0.635797\pi$
$32$	−2.76289	−0.488415
$33$	6.37872	1.11039
$34$	−0.104126	−0.0178575
$35$	−0.0677962	−0.0114597
$36$	2.34209	0.390349
$37$	−2.75049	−0.452178	−0.226089	−	0.974107i	$-0.572594\pi$
$37$	−2.75049	−0.452178	−0.226089	+	0.974107i	$0.572594\pi$
$38$	−0.261324	−0.0423924
$39$	3.81664	0.611152
$40$	3.00476	0.475094
$41$	−6.36101	−0.993423	−0.496712	−	0.867916i	$-0.665459\pi$
$41$	−6.36101	−0.993423	−0.496712	+	0.867916i	$0.665459\pi$
$42$	0.00682477	0.00105308
$43$	1.13555	0.173170	0.0865852	−	0.996244i	$-0.472405\pi$
$43$	1.13555	0.173170	0.0865852	+	0.996244i	$0.472405\pi$
$44$	−9.25087	−1.39462
$45$	−3.83918	−0.572311
$46$	−1.23667	−0.182337
$47$	9.46509	1.38063	0.690313	−	0.723511i	$-0.257473\pi$
$47$	9.46509	1.38063	0.690313	+	0.723511i	$0.257473\pi$
$48$	4.90234	0.707592
$49$	−6.99955	−0.999935
$50$	−1.23038	−0.174002
$51$	0.582853	0.0816157
$52$	−5.53516	−0.767589
$53$	6.31080	0.866854	0.433427	−	0.901189i	$-0.357304\pi$
$53$	6.31080	0.866854	0.433427	+	0.901189i	$0.357304\pi$
$54$	1.34820	0.183467
$55$	15.1641	2.04473
$56$	−0.0200873	−0.00268428
$57$	1.46278	0.193749
$58$	−0.0140768	−0.00184838
$59$	−8.37431	−1.09024	−0.545121	−	0.838357i	$-0.683516\pi$
$59$	−8.37431	−1.09024	−0.545121	+	0.838357i	$0.683516\pi$
$60$	−8.28748	−1.06991
$61$	5.82832	0.746241	0.373120	−	0.927783i	$-0.378288\pi$
$61$	5.82832	0.746241	0.373120	+	0.927783i	$0.378288\pi$
$62$	1.10271	0.140045
$63$	0.0256655	0.00323355
$64$	−6.65812	−0.832265
$65$	9.07329	1.12540
$66$	−1.52651	−0.187900
$67$	7.76195	0.948273	0.474137	−	0.880451i	$-0.342760\pi$
$67$	7.76195	0.948273	0.474137	+	0.880451i	$0.342760\pi$
$68$	−0.845294	−0.102507
$69$	6.92234	0.833351
$70$	0.0162245	0.00193920
$71$	3.25499	0.386297	0.193148	−	0.981170i	$-0.438130\pi$
$71$	3.25499	0.386297	0.193148	+	0.981170i	$0.438130\pi$
$72$	−1.13751	−0.134057
$73$	−4.59395	−0.537681	−0.268841	−	0.963185i	$-0.586640\pi$
$73$	−4.59395	−0.537681	−0.268841	+	0.963185i	$0.586640\pi$
$74$	0.658227	0.0765174
$75$	6.88710	0.795253
$76$	−2.12142	−0.243343
$77$	−0.101374	−0.0115527
$78$	−0.913371	−0.103419
$79$	6.82619	0.768006	0.384003	−	0.923332i	$-0.374545\pi$
$79$	6.82619	0.768006	0.384003	+	0.923332i	$0.374545\pi$
$80$	11.6543	1.30299
$81$	−3.92990	−0.436656
$82$	1.52227	0.168107
$83$	1.79125	0.196615	0.0983077	−	0.995156i	$-0.468657\pi$
$83$	1.79125	0.196615	0.0983077	+	0.995156i	$0.468657\pi$
$84$	0.0554031	0.00604498
$85$	1.38561	0.150291
$86$	−0.271753	−0.0293038
$87$	0.0787957	0.00844779
$88$	4.49296	0.478951
$89$	−13.2202	−1.40134	−0.700669	−	0.713487i	$-0.747115\pi$
$89$	−13.2202	−1.40134	−0.700669	+	0.713487i	$0.747115\pi$
$90$	0.918764	0.0968463
$91$	−0.0606564	−0.00635852
$92$	−10.0393	−1.04666
$93$	−6.17250	−0.640058
$94$	−2.26512	−0.233629
$95$	3.47745	0.356779
$96$	−3.70107	−0.377739
$97$	18.6939	1.89807	0.949037	−	0.315164i	$-0.102059\pi$
$97$	18.6939	1.89807	0.949037	+	0.315164i	$0.102059\pi$
$98$	1.67508	0.169209
$99$	−5.74066	−0.576958
$100$	−9.98815	−0.998815
$101$	8.69369	0.865054	0.432527	−	0.901621i	$-0.357622\pi$
$101$	8.69369	0.865054	0.432527	+	0.901621i	$0.357622\pi$
$102$	−0.139484	−0.0138110
$103$	1.81807	0.179140	0.0895700	−	0.995981i	$-0.471451\pi$
$103$	1.81807	0.179140	0.0895700	+	0.995981i	$0.471451\pi$
$104$	2.68832	0.263611
$105$	−0.0908174	−0.00886287
$106$	−1.51025	−0.146689
$107$	1.91819	0.185438	0.0927192	−	0.995692i	$-0.470444\pi$
$107$	1.91819	0.185438	0.0927192	+	0.995692i	$0.470444\pi$
$108$	10.9446	1.05315
$109$	6.84586	0.655715	0.327857	−	0.944727i	$-0.393673\pi$
$109$	6.84586	0.655715	0.327857	+	0.944727i	$0.393673\pi$
$110$	−3.62896	−0.346008
$111$	−3.68446	−0.349713
$112$	−0.0779110	−0.00736190
$113$	6.43168	0.605041	0.302521	−	0.953143i	$-0.402172\pi$
$113$	6.43168	0.605041	0.302521	+	0.953143i	$0.402172\pi$
$114$	−0.350061	−0.0327862
$115$	16.4564	1.53457
$116$	−0.114275	−0.0106102
$117$	−3.43487	−0.317553
$118$	2.00408	0.184490
$119$	−0.00926305	−0.000849143 0
$120$	4.02507	0.367436
$121$	11.6746	1.06133
$122$	−1.39479	−0.126279
$123$	−8.52099	−0.768311
$124$	8.95179	0.803894
$125$	0.449966	0.0402462
$126$	−0.00614209	−0.000547181 0
$127$	0.0879967	0.00780845	0.00390422	−	0.999992i	$-0.498757\pi$
$127$	0.0879967	0.00780845	0.00390422	+	0.999992i	$0.498757\pi$
$128$	7.11916	0.629251
$129$	1.52115	0.133930
$130$	−2.17135	−0.190440
$131$	−5.03568	−0.439969	−0.219985	−	0.975503i	$-0.570601\pi$
$131$	−5.03568	−0.439969	−0.219985	+	0.975503i	$0.570601\pi$
$132$	−12.3921	−1.07860
$133$	−0.0232473	−0.00201580
$134$	−1.85753	−0.160466
$135$	−17.9405	−1.54407
$136$	0.410542	0.0352037
$137$	−2.80298	−0.239475	−0.119737	−	0.992806i	$-0.538205\pi$
$137$	−2.80298	−0.239475	−0.119737	+	0.992806i	$0.538205\pi$
$138$	−1.65660	−0.141019
$139$	−18.4566	−1.56547	−0.782734	−	0.622357i	$-0.786175\pi$
$139$	−18.4566	−1.56547	−0.782734	+	0.622357i	$0.786175\pi$
$140$	0.131710	0.0111315
$141$	12.6791	1.06777
$142$	−0.778961	−0.0653690
$143$	13.5671	1.13454
$144$	−4.41197	−0.367664
$145$	0.187321	0.0155561
$146$	1.09939	0.0909862
$147$	−9.37634	−0.773348
$148$	5.34346	0.439230
$149$	−1.43391	−0.117470	−0.0587352	−	0.998274i	$-0.518707\pi$
$149$	−1.43391	−0.117470	−0.0587352	+	0.998274i	$0.518707\pi$
$150$	−1.64817	−0.134572
$151$	22.9337	1.86632	0.933161	−	0.359460i	$-0.117039\pi$
$151$	22.9337	1.86632	0.933161	+	0.359460i	$0.117039\pi$
$152$	1.03033	0.0835709
$153$	−0.524550	−0.0424074
$154$	0.0242602	0.00195494
$155$	−14.6739	−1.17863
$156$	−7.41470	−0.593651
$157$	−9.65252	−0.770355	−0.385177	−	0.922843i	$-0.625860\pi$
$157$	−9.65252	−0.770355	−0.385177	+	0.922843i	$0.625860\pi$
$158$	−1.63359	−0.129962
$159$	8.45372	0.670423
$160$	−8.79854	−0.695586
$161$	−0.110014	−0.00867032
$162$	0.940475	0.0738907
$163$	10.7883	0.845008	0.422504	−	0.906361i	$-0.361151\pi$
$163$	10.7883	0.845008	0.422504	+	0.906361i	$0.361151\pi$
$164$	12.3577	0.964976
$165$	20.3133	1.58139
$166$	−0.428669	−0.0332712
$167$	−16.7884	−1.29913	−0.649565	−	0.760306i	$-0.725049\pi$
$167$	−16.7884	−1.29913	−0.649565	+	0.760306i	$0.725049\pi$
$168$	−0.0269082	−0.00207601
$169$	−4.88224	−0.375557
$170$	−0.331595	−0.0254322
$171$	−1.31645	−0.100672
$172$	−2.20607	−0.168212
$173$	−2.71821	−0.206662	−0.103331	−	0.994647i	$-0.532950\pi$
$173$	−2.71821	−0.206662	−0.103331	+	0.994647i	$0.532950\pi$
$174$	−0.0188568	−0.00142953
$175$	−0.109454	−0.00827394
$176$	17.4265	1.31357
$177$	−11.2179	−0.843191
$178$	3.16376	0.237134
$179$	−15.8899	−1.18767	−0.593835	−	0.804587i	$-0.702387\pi$
$179$	−15.8899	−1.18767	−0.593835	+	0.804587i	$0.702387\pi$
$180$	7.45849	0.555923
$181$	9.54727	0.709643	0.354821	−	0.934934i	$-0.384542\pi$
$181$	9.54727	0.709643	0.354821	+	0.934934i	$0.384542\pi$
$182$	0.0145158	0.00107599
$183$	7.80741	0.577141
$184$	4.87587	0.359454
$185$	−8.75905	−0.643978
$186$	1.47716	0.108310
$187$	2.07188	0.151511
$188$	−18.3881	−1.34109
$189$	0.119935	0.00872400
$190$	−0.832198	−0.0603740
$191$	0.0878846	0.00635911	0.00317955	−	0.999995i	$-0.498988\pi$
$191$	0.0878846	0.00635911	0.00317955	+	0.999995i	$0.498988\pi$
$192$	−8.91898	−0.643672
$193$	3.69895	0.266257	0.133128	−	0.991099i	$-0.457498\pi$
$193$	3.69895	0.266257	0.133128	+	0.991099i	$0.457498\pi$
$194$	−4.47368	−0.321191
$195$	12.1543	0.870384
$196$	13.5982	0.971302
$197$	−4.01600	−0.286128	−0.143064	−	0.989713i	$-0.545695\pi$
$197$	−4.01600	−0.286128	−0.143064	+	0.989713i	$0.545695\pi$
$198$	1.37381	0.0976326
$199$	6.56566	0.465427	0.232713	−	0.972545i	$-0.425240\pi$
$199$	6.56566	0.465427	0.232713	+	0.972545i	$0.425240\pi$
$200$	4.85105	0.343021
$201$	10.3976	0.733392
$202$	−2.08051	−0.146384
$203$	−0.00125227	−8.78921e−5 0
$204$	−1.13233	−0.0792786
$205$	−20.2569	−1.41480
$206$	−0.435088	−0.0303140
$207$	−6.22990	−0.433008
$208$	10.4270	0.722981
$209$	5.19977	0.359676
$210$	0.0217337	0.00149977
$211$	−17.6712	−1.21653	−0.608267	−	0.793733i	$-0.708135\pi$
$211$	−17.6712	−1.21653	−0.608267	+	0.793733i	$0.708135\pi$
$212$	−12.2602	−0.842032
$213$	4.36027	0.298761
$214$	−0.459047	−0.0313798
$215$	3.61622	0.246624
$216$	−5.31558	−0.361680
$217$	0.0980971	0.00665926
$218$	−1.63830	−0.110960
$219$	−6.15389	−0.415841
$220$	−29.4598	−1.98618
$221$	1.23969	0.0833906
$222$	0.881738	0.0591784
$223$	3.79236	0.253955	0.126977	−	0.991906i	$-0.459472\pi$
$223$	3.79236	0.253955	0.126977	+	0.991906i	$0.459472\pi$
$224$	0.0588197	0.00393005
$225$	−6.19818	−0.413212
$226$	−1.53918	−0.102385
$227$	−0.580144	−0.0385055	−0.0192527	−	0.999815i	$-0.506129\pi$
$227$	−0.580144	−0.0385055	−0.0192527	+	0.999815i	$0.506129\pi$
$228$	−2.84178	−0.188201
$229$	16.1248	1.06555	0.532777	−	0.846256i	$-0.321149\pi$
$229$	16.1248	1.06555	0.532777	+	0.846256i	$0.321149\pi$
$230$	−3.93824	−0.259680
$231$	−0.135798	−0.00893483
$232$	0.0555011	0.00364383
$233$	5.01125	0.328298	0.164149	−	0.986436i	$-0.447512\pi$
$233$	5.01125	0.328298	0.164149	+	0.986436i	$0.447512\pi$
$234$	0.822007	0.0537363
$235$	30.1420	1.96624
$236$	16.2690	1.05902
$237$	9.14412	0.593974
$238$	0.00221677	0.000143692 0
$239$	4.16317	0.269293	0.134647	−	0.990894i	$-0.457010\pi$
$239$	4.16317	0.269293	0.134647	+	0.990894i	$0.457010\pi$
$240$	15.6117	1.00773
$241$	20.9865	1.35186	0.675930	−	0.736966i	$-0.263742\pi$
$241$	20.9865	1.35186	0.675930	+	0.736966i	$0.263742\pi$
$242$	−2.79389	−0.179598
$243$	11.6365	0.746484
$244$	−11.3229	−0.724872
$245$	−22.2903	−1.42408
$246$	2.03918	0.130013
$247$	3.11123	0.197963
$248$	−4.34770	−0.276080
$249$	2.39950	0.152062
$250$	−0.107683	−0.00681044
$251$	6.64717	0.419565	0.209783	−	0.977748i	$-0.432724\pi$
$251$	6.64717	0.419565	0.209783	+	0.977748i	$0.432724\pi$
$252$	−0.0498612	−0.00314096
$253$	24.6070	1.54703
$254$	−0.0210587	−0.00132134
$255$	1.85612	0.116235
$256$	11.6125	0.725783
$257$	6.08189	0.379378	0.189689	−	0.981844i	$-0.439252\pi$
$257$	6.08189	0.379378	0.189689	+	0.981844i	$0.439252\pi$
$258$	−0.364030	−0.0226635
$259$	0.0585557	0.00363847
$260$	−17.6269	−1.09318
$261$	−0.0709138	−0.00438946
$262$	1.20510	0.0744514
$263$	−18.5419	−1.14334	−0.571672	−	0.820482i	$-0.693705\pi$
$263$	−18.5419	−1.14334	−0.571672	+	0.820482i	$0.693705\pi$
$264$	6.01861	0.370420
$265$	20.0970	1.23455
$266$	0.00556338	0.000341113 0
$267$	−17.7093	−1.08379
$268$	−15.0794	−0.921119
$269$	−3.95440	−0.241104	−0.120552	−	0.992707i	$-0.538466\pi$
$269$	−3.95440	−0.241104	−0.120552	+	0.992707i	$0.538466\pi$
$270$	4.29339	0.261288
$271$	−8.57994	−0.521194	−0.260597	−	0.965448i	$-0.583919\pi$
$271$	−8.57994	−0.521194	−0.260597	+	0.965448i	$0.583919\pi$
$272$	1.59234	0.0965498
$273$	−0.0812531	−0.00491766
$274$	0.670788	0.0405238
$275$	24.4818	1.47631
$276$	−13.4482	−0.809488
$277$	−4.31950	−0.259534	−0.129767	−	0.991545i	$-0.541423\pi$
$277$	−4.31950	−0.259534	−0.129767	+	0.991545i	$0.541423\pi$
$278$	4.41690	0.264908
$279$	5.55506	0.332573
$280$	−0.0639688	−0.00382287
$281$	−7.15391	−0.426767	−0.213383	−	0.976969i	$-0.568448\pi$
$281$	−7.15391	−0.426767	−0.213383	+	0.976969i	$0.568448\pi$
$282$	−3.03427	−0.180688
$283$	1.95363	0.116131	0.0580655	−	0.998313i	$-0.481507\pi$
$283$	1.95363	0.116131	0.0580655	+	0.998313i	$0.481507\pi$
$284$	−6.32357	−0.375235
$285$	4.65827	0.275932
$286$	−3.24679	−0.191987
$287$	0.135421	0.00799363
$288$	3.33086	0.196273
$289$	−16.8107	−0.988864
$290$	−0.0448282	−0.00263240
$291$	25.0416	1.46797
$292$	8.92480	0.522285
$293$	5.44102	0.317868	0.158934	−	0.987289i	$-0.449194\pi$
$293$	5.44102	0.317868	0.158934	+	0.987289i	$0.449194\pi$
$294$	2.24388	0.130866
$295$	−26.6683	−1.55269
$296$	−2.59521	−0.150844
$297$	−26.8261	−1.55661
$298$	0.343153	0.0198783
$299$	14.7234	0.851475
$300$	−13.3798	−0.772481
$301$	−0.0241750	−0.00139342
$302$	−5.48833	−0.315818
$303$	11.6458	0.669031
$304$	3.99627	0.229202
$305$	18.5605	1.06277
$306$	0.125532	0.00717616
$307$	5.30339	0.302681	0.151340	−	0.988482i	$-0.451641\pi$
$307$	5.30339	0.302681	0.151340	+	0.988482i	$0.451641\pi$
$308$	0.196943	0.0112219
$309$	2.43543	0.138547
$310$	3.51164	0.199448
$311$	0.308317	0.0174831	0.00874154	−	0.999962i	$-0.497217\pi$
$311$	0.308317	0.0174831	0.00874154	+	0.999962i	$0.497217\pi$
$312$	3.60117	0.203876
$313$	16.4371	0.929081	0.464541	−	0.885552i	$-0.346219\pi$
$313$	16.4371	0.929081	0.464541	+	0.885552i	$0.346219\pi$
$314$	2.30997	0.130359
$315$	0.0817329	0.00460513
$316$	−13.2614	−0.746014
$317$	−2.00837	−0.112801	−0.0564007	−	0.998408i	$-0.517962\pi$
$317$	−2.00837	−0.112801	−0.0564007	+	0.998408i	$0.517962\pi$
$318$	−2.02308	−0.113449
$319$	0.280098	0.0156825
$320$	−21.2030	−1.18529
$321$	2.56954	0.143418
$322$	0.0263277	0.00146719
$323$	0.475127	0.0264368
$324$	7.63473	0.424152
$325$	14.6484	0.812548
$326$	−2.58179	−0.142992
$327$	9.17047	0.507128
$328$	−6.00190	−0.331400
$329$	−0.201504	−0.0111093
$330$	−4.86123	−0.267602
$331$	−18.8349	−1.03526	−0.517631	−	0.855604i	$-0.673186\pi$
$331$	−18.8349	−1.03526	−0.517631	+	0.855604i	$0.673186\pi$
$332$	−3.47992	−0.190985
$333$	3.31590	0.181710
$334$	4.01769	0.219838
$335$	24.7182	1.35050
$336$	−0.104367	−0.00569368
$337$	−30.3639	−1.65403	−0.827014	−	0.562182i	$-0.809962\pi$
$337$	−30.3639	−1.65403	−0.827014	+	0.562182i	$0.809962\pi$
$338$	1.16838	0.0635516
$339$	8.61564	0.467938
$340$	−2.69187	−0.145987
$341$	−21.9416	−1.18820
$342$	0.315044	0.0170356
$343$	0.298039	0.0160926
$344$	1.07145	0.0577685
$345$	22.0445	1.18683
$346$	0.650503	0.0349712
$347$	7.93588	0.426020	0.213010	−	0.977050i	$-0.431673\pi$
$347$	7.93588	0.426020	0.213010	+	0.977050i	$0.431673\pi$
$348$	−0.153079	−0.00820589
$349$	−2.55875	−0.136967	−0.0684835	−	0.997652i	$-0.521816\pi$
$349$	−2.55875	−0.136967	−0.0684835	+	0.997652i	$0.521816\pi$
$350$	0.0261937	0.00140011
$351$	−16.0512	−0.856747
$352$	−13.1563	−0.701234
$353$	−13.1595	−0.700412	−0.350206	−	0.936673i	$-0.613888\pi$
$353$	−13.1595	−0.700412	−0.350206	+	0.936673i	$0.613888\pi$
$354$	2.68459	0.142684
$355$	10.3657	0.550152
$356$	25.6832	1.36121
$357$	−0.0124085	−0.000656725 0
$358$	3.80266	0.200977
$359$	−14.5025	−0.765413	−0.382707	−	0.923870i	$-0.625008\pi$
$359$	−14.5025	−0.765413	−0.382707	+	0.923870i	$0.625008\pi$
$360$	−3.62244	−0.190919
$361$	−17.8076	−0.937241
$362$	−2.28478	−0.120085
$363$	15.6389	0.820830
$364$	0.117839	0.00617644
$365$	−14.6296	−0.765749
$366$	−1.86841	−0.0976635
$367$	24.1077	1.25841	0.629205	−	0.777239i	$-0.283380\pi$
$367$	24.1077	1.25841	0.629205	+	0.777239i	$0.283380\pi$
$368$	18.9117	0.985838
$369$	7.66864	0.399213
$370$	2.09615	0.108974
$371$	−0.134352	−0.00697519
$372$	11.9915	0.621730
$373$	12.7807	0.661761	0.330880	−	0.943673i	$-0.392654\pi$
$373$	12.7807	0.661761	0.330880	+	0.943673i	$0.392654\pi$
$374$	−0.495828	−0.0256387
$375$	0.602758	0.0311263
$376$	8.93074	0.460568
$377$	0.167594	0.00863151
$378$	−0.0287020	−0.00147627
$379$	−23.3055	−1.19712	−0.598562	−	0.801077i	$-0.704261\pi$
$379$	−23.3055	−1.19712	−0.598562	+	0.801077i	$0.704261\pi$
$380$	−6.75575	−0.346562
$381$	0.117877	0.00603903
$382$	−0.0210319	−0.00107609
$383$	−16.5095	−0.843598	−0.421799	−	0.906689i	$-0.638601\pi$
$383$	−16.5095	−0.843598	−0.421799	+	0.906689i	$0.638601\pi$
$384$	9.53657	0.486661
$385$	−0.322831	−0.0164530
$386$	−0.885207	−0.0450558
$387$	−1.36899	−0.0695896
$388$	−36.3171	−1.84372
$389$	−22.0102	−1.11596	−0.557981	−	0.829854i	$-0.688424\pi$
$389$	−22.0102	−1.11596	−0.557981	+	0.829854i	$0.688424\pi$
$390$	−2.90867	−0.147286
$391$	2.24846	0.113709
$392$	−6.60439	−0.333572
$393$	−6.74562	−0.340271
$394$	0.961079	0.0484185
$395$	21.7383	1.09377
$396$	11.1525	0.560437
$397$	6.32697	0.317541	0.158771	−	0.987315i	$-0.449247\pi$
$397$	6.32697	0.317541	0.158771	+	0.987315i	$0.449247\pi$
$398$	−1.57124	−0.0787594
$399$	−0.0311413	−0.00155901
$400$	18.8154	0.940769
$401$	−16.8186	−0.839879	−0.419940	−	0.907552i	$-0.637949\pi$
$401$	−16.8186	−0.839879	−0.419940	+	0.907552i	$0.637949\pi$
$402$	−2.48828	−0.124104
$403$	−13.1285	−0.653978
$404$	−16.8895	−0.840283
$405$	−12.5149	−0.621872
$406$	0.000299684 0	1.48731e−5 0
$407$	−13.0973	−0.649207
$408$	0.549948	0.0272265
$409$	−5.79047	−0.286320	−0.143160	−	0.989700i	$-0.545726\pi$
$409$	−5.79047	−0.286320	−0.143160	+	0.989700i	$0.545726\pi$
$410$	4.84773	0.239413
$411$	−3.75477	−0.185209
$412$	−3.53202	−0.174010
$413$	0.178282	0.00877269
$414$	1.49089	0.0732734
$415$	5.70431	0.280014
$416$	−7.87194	−0.385954
$417$	−24.7238	−1.21073
$418$	−1.24437	−0.0608642
$419$	−1.51557	−0.0740405	−0.0370203	−	0.999315i	$-0.511787\pi$
$419$	−1.51557	−0.0740405	−0.0370203	+	0.999315i	$0.511787\pi$
$420$	0.176434	0.00860908
$421$	−24.9274	−1.21489	−0.607443	−	0.794363i	$-0.707805\pi$
$421$	−24.9274	−1.21489	−0.607443	+	0.794363i	$0.707805\pi$
$422$	4.22894	0.205861
$423$	−11.4108	−0.554813
$424$	5.95452	0.289177
$425$	2.23701	0.108511
$426$	−1.04347	−0.0505562
$427$	−0.124080	−0.00600466
$428$	−3.72652	−0.180128
$429$	18.1740	0.877451
$430$	−0.865407	−0.0417336
$431$	−20.4563	−0.985346	−0.492673	−	0.870214i	$-0.663980\pi$
$431$	−20.4563	−0.985346	−0.492673	+	0.870214i	$0.663980\pi$
$432$	−20.6171	−0.991943
$433$	12.1615	0.584446	0.292223	−	0.956350i	$-0.405605\pi$
$433$	12.1615	0.584446	0.292223	+	0.956350i	$0.405605\pi$
$434$	−0.0234759	−0.00112688
$435$	0.250928	0.0120311
$436$	−13.2997	−0.636938
$437$	5.64291	0.269937
$438$	1.47270	0.0703685
$439$	−6.54257	−0.312260	−0.156130	−	0.987737i	$-0.549902\pi$
$439$	−6.54257	−0.312260	−0.156130	+	0.987737i	$0.549902\pi$
$440$	14.3080	0.682108
$441$	8.43843	0.401830
$442$	−0.296674	−0.0141113
$443$	−23.7790	−1.12977	−0.564886	−	0.825169i	$-0.691080\pi$
$443$	−23.7790	−1.12977	−0.564886	+	0.825169i	$0.691080\pi$
$444$	7.15791	0.339699
$445$	−42.1002	−1.99574
$446$	−0.907559	−0.0429742
$447$	−1.92081	−0.0908514
$448$	0.141746	0.00669686
$449$	37.1800	1.75463	0.877315	−	0.479914i	$-0.159332\pi$
$449$	37.1800	1.75463	0.877315	+	0.479914i	$0.159332\pi$
$450$	1.48330	0.0699236
$451$	−30.2898	−1.42629
$452$	−12.4950	−0.587716
$453$	30.7212	1.44341
$454$	0.138836	0.00651588
$455$	−0.193163	−0.00905561
$456$	1.38019	0.0646335
$457$	−11.1527	−0.521703	−0.260851	−	0.965379i	$-0.584003\pi$
$457$	−11.1527	−0.521703	−0.260851	+	0.965379i	$0.584003\pi$
$458$	−3.85886	−0.180313
$459$	−2.45123	−0.114413
$460$	−31.9704	−1.49063
$461$	13.3646	0.622451	0.311226	−	0.950336i	$-0.399261\pi$
$461$	13.3646	0.622451	0.311226	+	0.950336i	$0.399261\pi$
$462$	0.0324981	0.00151195
$463$	−15.9862	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$463$	−15.9862	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$464$	0.215268	0.00999357
$465$	−19.6566	−0.911551
$466$	−1.19926	−0.0555544
$467$	−10.5163	−0.486636	−0.243318	−	0.969947i	$-0.578236\pi$
$467$	−10.5163	−0.486636	−0.243318	+	0.969947i	$0.578236\pi$
$468$	6.67302	0.308460
$469$	−0.165245	−0.00763033
$470$	−7.21335	−0.332727
$471$	−12.9302	−0.595791
$472$	−7.90154	−0.363698
$473$	5.40727	0.248627
$474$	−2.18830	−0.100512
$475$	5.61419	0.257597
$476$	0.0179956	0.000824827 0
$477$	−7.60809	−0.348351
$478$	−0.996300	−0.0455697
$479$	−3.80135	−0.173688	−0.0868439	−	0.996222i	$-0.527678\pi$
$479$	−3.80135	−0.173688	−0.0868439	+	0.996222i	$0.527678\pi$
$480$	−11.7862	−0.537964
$481$	−7.83661	−0.357319
$482$	−5.02234	−0.228761
$483$	−0.147371	−0.00670560
$484$	−22.6806	−1.03094
$485$	59.5314	2.70318
$486$	−2.78477	−0.126320
$487$	24.0516	1.08988	0.544942	−	0.838474i	$-0.316552\pi$
$487$	24.0516	1.08988	0.544942	+	0.838474i	$0.316552\pi$
$488$	5.49929	0.248941
$489$	14.4517	0.653527
$490$	5.33436	0.240982
$491$	−21.7135	−0.979917	−0.489959	−	0.871746i	$-0.662988\pi$
$491$	−21.7135	−0.979917	−0.489959	+	0.871746i	$0.662988\pi$
$492$	16.5540	0.746311
$493$	0.0255938	0.00115269
$494$	−0.744557	−0.0334992
$495$	−18.2814	−0.821686
$496$	−16.8631	−0.757176
$497$	−0.0692961	−0.00310835
$498$	−0.574230	−0.0257318
$499$	39.6080	1.77310	0.886548	−	0.462636i	$-0.153096\pi$
$499$	39.6080	1.77310	0.886548	+	0.462636i	$0.153096\pi$
$500$	−0.874162	−0.0390937
$501$	−22.4892	−1.00474
$502$	−1.59075	−0.0709987
$503$	43.6477	1.94615	0.973076	−	0.230483i	$-0.0740305\pi$
$503$	43.6477	1.94615	0.973076	+	0.230483i	$0.0740305\pi$
$504$	0.0242166	0.00107869
$505$	27.6854	1.23198
$506$	−5.88878	−0.261788
$507$	−6.54008	−0.290455
$508$	−0.170954	−0.00758485
$509$	11.9846	0.531206	0.265603	−	0.964083i	$-0.414429\pi$
$509$	11.9846	0.531206	0.265603	+	0.964083i	$0.414429\pi$
$510$	−0.444193	−0.0196692
$511$	0.0978014	0.00432648
$512$	−17.0173	−0.752067
$513$	−6.15180	−0.271609
$514$	−1.45547	−0.0641982
$515$	5.78973	0.255126
$516$	−2.95518	−0.130094
$517$	45.0708	1.98221
$518$	−0.0140131	−0.000615701 0
$519$	−3.64122	−0.159832
$520$	8.56106	0.375427
$521$	0.691677	0.0303029	0.0151515	−	0.999885i	$-0.495177\pi$
$521$	0.691677	0.0303029	0.0151515	+	0.999885i	$0.495177\pi$
$522$	0.0169706	0.000742782 0
$523$	−25.2683	−1.10491	−0.552453	−	0.833544i	$-0.686308\pi$
$523$	−25.2683	−1.10491	−0.552453	+	0.833544i	$0.686308\pi$
$524$	9.78296	0.427371
$525$	−0.146621	−0.00639904
$526$	4.43732	0.193476
$527$	−2.00490	−0.0873348
$528$	23.3439	1.01591
$529$	3.70413	0.161049
$530$	−4.80946	−0.208910
$531$	10.0958	0.438121
$532$	0.0451632	0.00195808
$533$	−18.1236	−0.785020
$534$	4.23806	0.183399
$535$	6.10855	0.264096
$536$	7.32375	0.316338
$537$	−21.2856	−0.918541
$538$	0.946338	0.0407995
$539$	−33.3304	−1.43564
$540$	34.8536	1.49986
$541$	−32.3769	−1.39199	−0.695996	−	0.718045i	$-0.745037\pi$
$541$	−32.3769	−1.39199	−0.695996	+	0.718045i	$0.745037\pi$
$542$	2.05329	0.0881963
$543$	12.7892	0.548836
$544$	−1.20215	−0.0515418
$545$	21.8009	0.933849
$546$	0.0194449	0.000832165 0
$547$	−15.1797	−0.649038	−0.324519	−	0.945879i	$-0.605202\pi$
$547$	−15.1797	−0.649038	−0.324519	+	0.945879i	$0.605202\pi$
$548$	5.44543	0.232617
$549$	−7.02644	−0.299881
$550$	−5.85880	−0.249820
$551$	0.0642323	0.00273639
$552$	6.53154	0.278001
$553$	−0.145324	−0.00617980
$554$	1.03371	0.0439182
$555$	−11.7333	−0.498051
$556$	35.8562	1.52064
$557$	−33.4104	−1.41564	−0.707822	−	0.706391i	$-0.750322\pi$
$557$	−33.4104	−1.41564	−0.707822	+	0.706391i	$0.750322\pi$
$558$	−1.32940	−0.0562779
$559$	3.23539	0.136842
$560$	−0.248111	−0.0104846
$561$	2.77542	0.117178
$562$	1.71202	0.0722173
$563$	−7.71048	−0.324958	−0.162479	−	0.986712i	$-0.551949\pi$
$563$	−7.71048	−0.324958	−0.162479	+	0.986712i	$0.551949\pi$
$564$	−24.6320	−1.03720
$565$	20.4819	0.861682
$566$	−0.467527	−0.0196516
$567$	0.0836643	0.00351357
$568$	3.07123	0.128866
$569$	28.7361	1.20468	0.602340	−	0.798240i	$-0.294235\pi$
$569$	28.7361	1.20468	0.602340	+	0.798240i	$0.294235\pi$
$570$	−1.11478	−0.0466931
$571$	4.94052	0.206754	0.103377	−	0.994642i	$-0.467035\pi$
$571$	4.94052	0.206754	0.103377	+	0.994642i	$0.467035\pi$
$572$	−26.3573	−1.10205
$573$	0.117727	0.00491812
$574$	−0.0324079	−0.00135268
$575$	26.5682	1.10797
$576$	8.02681	0.334451
$577$	1.90858	0.0794550	0.0397275	−	0.999211i	$-0.487351\pi$
$577$	1.90858	0.0794550	0.0397275	+	0.999211i	$0.487351\pi$
$578$	4.02301	0.167335
$579$	4.95499	0.205922
$580$	−0.363914	−0.0151107
$581$	−0.0381342	−0.00158207
$582$	−5.99278	−0.248409
$583$	30.0507	1.24457
$584$	−4.33460	−0.179367
$585$	−10.9385	−0.452250
$586$	−1.30211	−0.0537895
$587$	−16.7860	−0.692832	−0.346416	−	0.938081i	$-0.612601\pi$
$587$	−16.7860	−0.692832	−0.346416	+	0.938081i	$0.612601\pi$
$588$	18.2157	0.751203
$589$	−5.03166	−0.207326
$590$	6.38207	0.262746
$591$	−5.37969	−0.221291
$592$	−10.0659	−0.413704
$593$	34.7412	1.42665	0.713325	−	0.700833i	$-0.247188\pi$
$593$	34.7412	1.42665	0.713325	+	0.700833i	$0.247188\pi$
$594$	6.41984	0.263409
$595$	−0.0294986	−0.00120932
$596$	2.78570	0.114107
$597$	8.79512	0.359960
$598$	−3.52349	−0.144086
$599$	−12.2079	−0.498799	−0.249400	−	0.968401i	$-0.580233\pi$
$599$	−12.2079	−0.498799	−0.249400	+	0.968401i	$0.580233\pi$
$600$	6.49829	0.265291
$601$	−15.1163	−0.616605	−0.308302	−	0.951288i	$-0.599761\pi$
$601$	−15.1163	−0.616605	−0.308302	+	0.951288i	$0.599761\pi$
$602$	0.00578539	0.000235795 0
$603$	−9.35756	−0.381069
$604$	−44.5541	−1.81288
$605$	37.1783	1.51151
$606$	−2.78698	−0.113213
$607$	−23.5460	−0.955701	−0.477850	−	0.878441i	$-0.658584\pi$
$607$	−23.5460	−0.955701	−0.477850	+	0.878441i	$0.658584\pi$
$608$	−3.01702	−0.122356
$609$	−0.00167750	−6.79755e−5 0
$610$	−4.44177	−0.179842
$611$	26.9676	1.09099
$612$	1.01906	0.0411930
$613$	−5.31358	−0.214614	−0.107307	−	0.994226i	$-0.534223\pi$
$613$	−5.31358	−0.214614	−0.107307	+	0.994226i	$0.534223\pi$
$614$	−1.26917	−0.0512195
$615$	−27.1354	−1.09421
$616$	−0.0956514	−0.00385391
$617$	17.8019	0.716677	0.358339	−	0.933592i	$-0.383343\pi$
$617$	17.8019	0.716677	0.358339	+	0.933592i	$0.383343\pi$
$618$	−0.582828	−0.0234448
$619$	−24.4521	−0.982812	−0.491406	−	0.870931i	$-0.663517\pi$
$619$	−24.4521	−0.982812	−0.491406	+	0.870931i	$0.663517\pi$
$620$	28.5073	1.14488
$621$	−29.1124	−1.16824
$622$	−0.0737843	−0.00295848
$623$	0.281447	0.0112759
$624$	13.9676	0.559152
$625$	−24.2736	−0.970942
$626$	−3.93361	−0.157219
$627$	6.96543	0.278172
$628$	18.7522	0.748296
$629$	−1.19676	−0.0477178
$630$	−0.0195597	−0.000779278 0
$631$	−27.4869	−1.09423	−0.547117	−	0.837056i	$-0.684275\pi$
$631$	−27.4869	−1.09423	−0.547117	+	0.837056i	$0.684275\pi$
$632$	6.44082	0.256202
$633$	−23.6717	−0.940865
$634$	0.480628	0.0190882
$635$	0.280229	0.0111206
$636$	−16.4233	−0.651225
$637$	−19.9429	−0.790166
$638$	−0.0670309	−0.00265378
$639$	−3.92412	−0.155236
$640$	22.6712	0.896160
$641$	−24.5068	−0.967959	−0.483980	−	0.875079i	$-0.660809\pi$
$641$	−24.5068	−0.967959	−0.483980	+	0.875079i	$0.660809\pi$
$642$	−0.614923	−0.0242691
$643$	−13.9690	−0.550883	−0.275441	−	0.961318i	$-0.588824\pi$
$643$	−13.9690	−0.550883	−0.275441	+	0.961318i	$0.588824\pi$
$644$	0.213727	0.00842204
$645$	4.84416	0.190738
$646$	−0.113704	−0.00447362
$647$	−47.4488	−1.86540	−0.932702	−	0.360648i	$-0.882555\pi$
$647$	−47.4488	−1.86540	−0.932702	+	0.360648i	$0.882555\pi$
$648$	−3.70804	−0.145666
$649$	−39.8767	−1.56530
$650$	−3.50555	−0.137499
$651$	0.131407	0.00515026
$652$	−20.9588	−0.820811
$653$	28.0976	1.09954	0.549772	−	0.835315i	$-0.314715\pi$
$653$	28.0976	1.09954	0.549772	+	0.835315i	$0.314715\pi$
$654$	−2.19461	−0.0858160
$655$	−16.0363	−0.626591
$656$	−23.2791	−0.908897
$657$	5.53832	0.216070
$658$	0.0482224	0.00187991
$659$	17.3819	0.677102	0.338551	−	0.940948i	$-0.390063\pi$
$659$	17.3819	0.677102	0.338551	+	0.940948i	$0.390063\pi$
$660$	−39.4632	−1.53610
$661$	−34.2536	−1.33231	−0.666155	−	0.745813i	$-0.732061\pi$
$661$	−34.2536	−1.33231	−0.666155	+	0.745813i	$0.732061\pi$
$662$	4.50744	0.175187
$663$	1.66065	0.0644941
$664$	1.69013	0.0655896
$665$	−0.0740320	−0.00287084
$666$	−0.793538	−0.0307490
$667$	0.303968	0.0117697
$668$	32.6154	1.26193
$669$	5.08010	0.196408
$670$	−5.91539	−0.228531
$671$	27.7532	1.07140
$672$	0.0787927	0.00303950
$673$	−36.0998	−1.39155	−0.695773	−	0.718262i	$-0.744938\pi$
$673$	−36.0998	−1.39155	−0.695773	+	0.718262i	$0.744938\pi$
$674$	7.26647	0.279894
$675$	−28.9642	−1.11483
$676$	9.48488	0.364803
$677$	24.1006	0.926261	0.463131	−	0.886290i	$-0.346726\pi$
$677$	24.1006	0.926261	0.463131	+	0.886290i	$0.346726\pi$
$678$	−2.06183	−0.0791842
$679$	−0.397977	−0.0152729
$680$	1.30739	0.0501361
$681$	−0.777140	−0.0297801
$682$	5.25089	0.201067
$683$	−11.5776	−0.443006	−0.221503	−	0.975160i	$-0.571096\pi$
$683$	−11.5776	−0.443006	−0.221503	+	0.975160i	$0.571096\pi$
$684$	2.55752	0.0977891
$685$	−8.92620	−0.341052
$686$	−0.0713244	−0.00272318
$687$	21.6001	0.824097
$688$	4.15574	0.158436
$689$	17.9805	0.685003
$690$	−5.27552	−0.200836
$691$	−0.866803	−0.0329747	−0.0164874	−	0.999864i	$-0.505248\pi$
$691$	−0.866803	−0.0329747	−0.0164874	+	0.999864i	$0.505248\pi$
$692$	5.28075	0.200744
$693$	0.122214	0.00464252
$694$	−1.89916	−0.0720910
$695$	−58.7758	−2.22949
$696$	0.0743473	0.00281813
$697$	−2.76772	−0.104835
$698$	0.612342	0.0231775
$699$	6.71289	0.253905
$700$	0.212639	0.00803701
$701$	37.7372	1.42531	0.712657	−	0.701512i	$-0.247491\pi$
$701$	37.7372	1.42531	0.712657	+	0.701512i	$0.247491\pi$
$702$	3.84124	0.144978
$703$	−3.00348	−0.113278
$704$	−31.7045	−1.19491
$705$	40.3771	1.52069
$706$	3.14925	0.118523
$707$	−0.185081	−0.00696070
$708$	21.7934	0.819046
$709$	48.7806	1.83199	0.915997	−	0.401185i	$-0.131402\pi$
$709$	48.7806	1.83199	0.915997	+	0.401185i	$0.131402\pi$
$710$	−2.48063	−0.0930965
$711$	−8.22943	−0.308628
$712$	−12.4738	−0.467477
$713$	−23.8115	−0.891747
$714$	0.00296950	0.000111131 0
$715$	43.2051	1.61578
$716$	30.8698	1.15366
$717$	5.57684	0.208271
$718$	3.47064	0.129523
$719$	−40.3846	−1.50609	−0.753045	−	0.657969i	$-0.771416\pi$
$719$	−40.3846	−1.50609	−0.753045	+	0.657969i	$0.771416\pi$
$720$	−14.0501	−0.523616
$721$	−0.0387053	−0.00144146
$722$	4.26158	0.158600
$723$	28.1128	1.04553
$724$	−18.5478	−0.689322
$725$	0.302421	0.0112316
$726$	−3.74259	−0.138901
$727$	−37.1197	−1.37669	−0.688347	−	0.725382i	$-0.741663\pi$
$727$	−37.1197	−1.37669	−0.688347	+	0.725382i	$0.741663\pi$
$728$	−0.0572321	−0.00212116
$729$	27.3776	1.01398
$730$	3.50105	0.129580
$731$	0.494087	0.0182745
$732$	−15.1677	−0.560614
$733$	−14.1028	−0.520900	−0.260450	−	0.965487i	$-0.583871\pi$
$733$	−14.1028	−0.520900	−0.260450	+	0.965487i	$0.583871\pi$
$734$	−5.76927	−0.212948
$735$	−29.8593	−1.10138
$736$	−14.2775	−0.526277
$737$	36.9608	1.36147
$738$	−1.83520	−0.0675547
$739$	−2.12928	−0.0783267	−0.0391633	−	0.999233i	$-0.512469\pi$
$739$	−2.12928	−0.0783267	−0.0391633	+	0.999233i	$0.512469\pi$
$740$	17.0165	0.625538
$741$	4.16769	0.153104
$742$	0.0321520	0.00118034
$743$	17.6849	0.648796	0.324398	−	0.945921i	$-0.394838\pi$
$743$	17.6849	0.648796	0.324398	+	0.945921i	$0.394838\pi$
$744$	−5.82403	−0.213519
$745$	−4.56634	−0.167298
$746$	−3.05859	−0.111983
$747$	−2.15948	−0.0790111
$748$	−4.02511	−0.147173
$749$	−0.0408367	−0.00149214
$750$	−0.144248	−0.00526718
$751$	−37.2172	−1.35808	−0.679038	−	0.734103i	$-0.737603\pi$
$751$	−37.2172	−1.35808	−0.679038	+	0.734103i	$0.737603\pi$
$752$	34.6390	1.26315
$753$	8.90431	0.324491
$754$	−0.0401073	−0.00146062
$755$	73.0334	2.65796
$756$	−0.233002	−0.00847419
$757$	−8.45222	−0.307201	−0.153601	−	0.988133i	$-0.549087\pi$
$757$	−8.45222	−0.307201	−0.153601	+	0.988133i	$0.549087\pi$
$758$	5.57730	0.202577
$759$	32.9627	1.19647
$760$	3.28113	0.119019
$761$	−26.8512	−0.973355	−0.486677	−	0.873582i	$-0.661791\pi$
$761$	−26.8512	−0.973355	−0.486677	+	0.873582i	$0.661791\pi$
$762$	−0.0282095	−0.00102192
$763$	−0.145743	−0.00527624
$764$	−0.170736	−0.00617701
$765$	−1.67045	−0.0603953
$766$	3.95094	0.142753
$767$	−23.8598	−0.861528
$768$	15.5557	0.561319
$769$	−41.6031	−1.50024	−0.750122	−	0.661299i	$-0.770005\pi$
$769$	−41.6031	−1.50024	−0.750122	+	0.661299i	$0.770005\pi$
$770$	0.0772576	0.00278417
$771$	8.14708	0.293410
$772$	−7.18607	−0.258632
$773$	11.4779	0.412833	0.206417	−	0.978464i	$-0.433820\pi$
$773$	11.4779	0.412833	0.206417	+	0.978464i	$0.433820\pi$
$774$	0.327616	0.0117759
$775$	−23.6903	−0.850980
$776$	17.6385	0.633186
$777$	0.0784391	0.00281399
$778$	5.26732	0.188843
$779$	−6.94609	−0.248870
$780$	−23.6124	−0.845460
$781$	15.4996	0.554619
$782$	−0.538084	−0.0192419
$783$	−0.331381	−0.0118426
$784$	−25.6159	−0.914855
$785$	−30.7388	−1.09712
$786$	1.61431	0.0575806
$787$	19.0838	0.680264	0.340132	−	0.940378i	$-0.389528\pi$
$787$	19.0838	0.680264	0.340132	+	0.940378i	$0.389528\pi$
$788$	7.80200	0.277935
$789$	−24.8381	−0.884260
$790$	−5.20224	−0.185088
$791$	−0.136925	−0.00486849
$792$	−5.41657	−0.192470
$793$	16.6059	0.589692
$794$	−1.51412	−0.0537342
$795$	26.9212	0.954796
$796$	−12.7553	−0.452099
$797$	13.6833	0.484686	0.242343	−	0.970191i	$-0.422084\pi$
$797$	13.6833	0.484686	0.242343	+	0.970191i	$0.422084\pi$
$798$	0.00745250	0.000263816 0
$799$	4.11832	0.145696
$800$	−14.2049	−0.502217
$801$	15.9378	0.563136
$802$	4.02490	0.142124
$803$	−21.8754	−0.771967
$804$	−20.1998	−0.712391
$805$	−0.350344	−0.0123480
$806$	3.14182	0.110666
$807$	−5.29717	−0.186469
$808$	8.20289	0.288577
$809$	10.8988	0.383182	0.191591	−	0.981475i	$-0.438635\pi$
$809$	10.8988	0.383182	0.191591	+	0.981475i	$0.438635\pi$
$810$	2.99498	0.105233
$811$	−5.70642	−0.200380	−0.100190	−	0.994968i	$-0.531945\pi$
$811$	−5.70642	−0.200380	−0.100190	+	0.994968i	$0.531945\pi$
$812$	0.00243282	8.53753e−5 0
$813$	−11.4934	−0.403090
$814$	3.13434	0.109859
$815$	34.3559	1.20344
$816$	2.13304	0.0746714
$817$	1.24000	0.0433822
$818$	1.38573	0.0484510
$819$	0.0731254	0.00255521
$820$	39.3537	1.37429
$821$	24.7044	0.862189	0.431095	−	0.902307i	$-0.358128\pi$
$821$	24.7044	0.862189	0.431095	+	0.902307i	$0.358128\pi$
$822$	0.898564	0.0313410
$823$	16.3046	0.568344	0.284172	−	0.958773i	$-0.408281\pi$
$823$	16.3046	0.568344	0.284172	+	0.958773i	$0.408281\pi$
$824$	1.71543	0.0597600
$825$	32.7949	1.14177
$826$	−0.0426652	−0.00148451
$827$	−2.16490	−0.0752808	−0.0376404	−	0.999291i	$-0.511984\pi$
$827$	−2.16490	−0.0752808	−0.0376404	+	0.999291i	$0.511984\pi$
$828$	12.1030	0.420609
$829$	4.26087	0.147986	0.0739931	−	0.997259i	$-0.476426\pi$
$829$	4.26087	0.147986	0.0739931	+	0.997259i	$0.476426\pi$
$830$	−1.36511	−0.0473838
$831$	−5.78625	−0.200723
$832$	−18.9701	−0.657670
$833$	−3.04555	−0.105522
$834$	5.91671	0.204879
$835$	−53.4635	−1.85018
$836$	−10.1018	−0.349376
$837$	25.9589	0.897269
$838$	0.362696	0.0125291
$839$	−30.0242	−1.03655	−0.518275	−	0.855214i	$-0.673426\pi$
$839$	−30.0242	−1.03655	−0.518275	+	0.855214i	$0.673426\pi$
$840$	−0.0856903	−0.00295660
$841$	−28.9965	−0.999881
$842$	5.96544	0.205583
$843$	−9.58312	−0.330060
$844$	34.3303	1.18170
$845$	−15.5477	−0.534857
$846$	2.73075	0.0938852
$847$	−0.248543	−0.00854004
$848$	23.0953	0.793097
$849$	2.61701	0.0898154
$850$	−0.535345	−0.0183622
$851$	−14.2134	−0.487231
$852$	−8.47083	−0.290206
$853$	44.7535	1.53233	0.766166	−	0.642643i	$-0.222162\pi$
$853$	44.7535	1.53233	0.766166	+	0.642643i	$0.222162\pi$
$854$	0.0296940	0.00101611
$855$	−4.19230	−0.143374
$856$	1.80990	0.0618611
$857$	39.1704	1.33804	0.669018	−	0.743246i	$-0.266715\pi$
$857$	39.1704	1.33804	0.669018	+	0.743246i	$0.266715\pi$
$858$	−4.34928	−0.148482
$859$	−1.75524	−0.0598881	−0.0299440	−	0.999552i	$-0.509533\pi$
$859$	−1.75524	−0.0598881	−0.0299440	+	0.999552i	$0.509533\pi$
$860$	−7.02533	−0.239562
$861$	0.181405	0.00618225
$862$	4.89546	0.166740
$863$	18.2170	0.620113	0.310056	−	0.950718i	$-0.399652\pi$
$863$	18.2170	0.620113	0.310056	+	0.950718i	$0.399652\pi$
$864$	15.5651	0.529536
$865$	−8.65626	−0.294322
$866$	−2.91041	−0.0988997
$867$	−22.5190	−0.764785
$868$	−0.190576	−0.00646857
$869$	32.5049	1.10265
$870$	−0.0600503	−0.00203590
$871$	22.1151	0.749341
$872$	6.45938	0.218742
$873$	−22.5367	−0.762753
$874$	−1.35042	−0.0456787
$875$	−0.00957939	−0.000323843 0
$876$	11.9553	0.403934
$877$	−22.0566	−0.744800	−0.372400	−	0.928072i	$-0.621465\pi$
$877$	−22.0566	−0.744800	−0.372400	+	0.928072i	$0.621465\pi$
$878$	1.56572	0.0528405
$879$	7.28860	0.245838
$880$	55.4954	1.87075
$881$	−1.83846	−0.0619393	−0.0309697	−	0.999520i	$-0.509860\pi$
$881$	−1.83846	−0.0619393	−0.0309697	+	0.999520i	$0.509860\pi$
$882$	−2.01942	−0.0679975
$883$	7.17740	0.241539	0.120769	−	0.992681i	$-0.461464\pi$
$883$	7.17740	0.241539	0.120769	+	0.992681i	$0.461464\pi$
$884$	−2.40838	−0.0810027
$885$	−35.7239	−1.20085
$886$	5.69061	0.191180
$887$	−33.6487	−1.12981	−0.564906	−	0.825155i	$-0.691088\pi$
$887$	−33.6487	−1.12981	−0.564906	+	0.825155i	$0.691088\pi$
$888$	−3.47645	−0.116662
$889$	−0.00187338	−6.28310e−5 0
$890$	10.0751	0.337719
$891$	−18.7134	−0.626921
$892$	−7.36752	−0.246683
$893$	10.3357	0.345870
$894$	0.459675	0.0153738
$895$	−50.6021	−1.69144
$896$	−0.151561	−0.00506329
$897$	19.7229	0.658528
$898$	−8.89764	−0.296918
$899$	−0.271042	−0.00903976
$900$	12.0414	0.401380
$901$	2.74587	0.0914781
$902$	7.24873	0.241356
$903$	−0.0323840	−0.00107767
$904$	6.06858	0.201838
$905$	30.4037	1.01065
$906$	−7.35198	−0.244253
$907$	40.5410	1.34614	0.673071	−	0.739578i	$-0.264975\pi$
$907$	40.5410	1.34614	0.673071	+	0.739578i	$0.264975\pi$
$908$	1.12706	0.0374029
$909$	−10.4808	−0.347627
$910$	0.0462263	0.00153239
$911$	−49.7821	−1.64935	−0.824677	−	0.565604i	$-0.808643\pi$
$911$	−49.7821	−1.64935	−0.824677	+	0.565604i	$0.808643\pi$
$912$	5.35326	0.177264
$913$	8.52956	0.282287
$914$	2.66899	0.0882823
$915$	24.8630	0.821946
$916$	−31.3260	−1.03504
$917$	0.107205	0.00354023
$918$	0.586610	0.0193610
$919$	−39.3831	−1.29913	−0.649564	−	0.760307i	$-0.725049\pi$
$919$	−39.3831	−1.29913	−0.649564	+	0.760307i	$0.725049\pi$
$920$	15.5274	0.511923
$921$	7.10424	0.234093
$922$	−3.19832	−0.105331
$923$	9.27402	0.305258
$924$	0.263818	0.00867898
$925$	−14.1411	−0.464956
$926$	3.82569	0.125720
$927$	−2.19181	−0.0719885
$928$	−0.162519	−0.00533494
$929$	−12.5423	−0.411501	−0.205750	−	0.978605i	$-0.565963\pi$
$929$	−12.5423	−0.411501	−0.205750	+	0.978605i	$0.565963\pi$
$930$	4.70406	0.154252
$931$	−7.64336	−0.250501
$932$	−9.73550	−0.318897
$933$	0.413011	0.0135214
$934$	2.51668	0.0823484
$935$	6.59800	0.215778
$936$	−3.24095	−0.105934
$937$	21.4452	0.700583	0.350292	−	0.936641i	$-0.386082\pi$
$937$	21.4452	0.700583	0.350292	+	0.936641i	$0.386082\pi$
$938$	0.0395453	0.00129120
$939$	22.0186	0.718549
$940$	−58.5577	−1.90994
$941$	−15.8038	−0.515189	−0.257595	−	0.966253i	$-0.582930\pi$
$941$	−15.8038	−0.515189	−0.257595	+	0.966253i	$0.582930\pi$
$942$	3.09435	0.100819
$943$	−32.8712	−1.07043
$944$	−30.6471	−0.997478
$945$	0.381939	0.0124245
$946$	−1.29403	−0.0420725
$947$	−45.0015	−1.46235	−0.731176	−	0.682188i	$-0.761028\pi$
$947$	−45.0015	−1.46235	−0.731176	+	0.682188i	$0.761028\pi$
$948$	−17.7645	−0.576965
$949$	−13.0889	−0.424885
$950$	−1.34355	−0.0435904
$951$	−2.69034	−0.0872403
$952$	−0.00874011	−0.000283268 0
$953$	36.3716	1.17819	0.589095	−	0.808064i	$-0.299484\pi$
$953$	36.3716	1.17819	0.589095	+	0.808064i	$0.299484\pi$
$954$	1.82071	0.0589478
$955$	0.279872	0.00905645
$956$	−8.08792	−0.261582
$957$	0.375209	0.0121288
$958$	0.909710	0.0293914
$959$	0.0596731	0.00192694
$960$	−28.4028	−0.916698
$961$	−9.76781	−0.315091
$962$	1.87540	0.0604653
$963$	−2.31251	−0.0745196
$964$	−40.7711	−1.31315
$965$	11.7795	0.379195
$966$	0.0352677	0.00113472
$967$	−10.2899	−0.330901	−0.165451	−	0.986218i	$-0.552908\pi$
$967$	−10.2899	−0.330901	−0.165451	+	0.986218i	$0.552908\pi$
$968$	11.0155	0.354053
$969$	0.636463	0.0204461
$970$	−14.2466	−0.457431
$971$	23.9304	0.767963	0.383982	−	0.923341i	$-0.374553\pi$
$971$	23.9304	0.767963	0.383982	+	0.923341i	$0.374553\pi$
$972$	−22.6066	−0.725108
$973$	0.392925	0.0125966
$974$	−5.75586	−0.184430
$975$	19.6225	0.628423
$976$	21.3297	0.682746
$977$	22.7905	0.729134	0.364567	−	0.931177i	$-0.381217\pi$
$977$	22.7905	0.729134	0.364567	+	0.931177i	$0.381217\pi$
$978$	−3.45847	−0.110590
$979$	−62.9517	−2.01195
$980$	43.3041	1.38330
$981$	−8.25315	−0.263503
$982$	5.19632	0.165821
$983$	−37.6036	−1.19937	−0.599685	−	0.800236i	$-0.704707\pi$
$983$	−37.6036	−1.19937	−0.599685	+	0.800236i	$0.704707\pi$
$984$	−8.03993	−0.256304
$985$	−12.7891	−0.407495
$986$	−0.00612492	−0.000195057 0
$987$	−0.269927	−0.00859188
$988$	−6.04428	−0.192294
$989$	5.86810	0.186595
$990$	4.37496	0.139045
$991$	25.7914	0.819291	0.409645	−	0.912245i	$-0.365652\pi$
$991$	25.7914	0.819291	0.409645	+	0.912245i	$0.365652\pi$
$992$	12.7310	0.404209
$993$	−25.2306	−0.800669
$994$	0.0165834	0.000525994 0
$995$	20.9086	0.662847
$996$	−4.66157	−0.147708
$997$	9.51627	0.301383	0.150692	−	0.988581i	$-0.451850\pi$
$997$	9.51627	0.301383	0.150692	+	0.988581i	$0.451850\pi$
$998$	−9.47869	−0.300043
$999$	15.4952	0.490248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.55	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.55	✓	122	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-0.239313 q^{2} +1.33956 q^{3} -1.94273 q^{4} +3.18454 q^{5} -0.320575 q^{6} -0.0212892 q^{7} +0.943545 q^{8} -1.20557 q^{9} +O(q^{10})\)	\(q-0.239313 q^{2} +1.33956 q^{3} -1.94273 q^{4} +3.18454 q^{5} -0.320575 q^{6} -0.0212892 q^{7} +0.943545 q^{8} -1.20557 q^{9} -0.762101 q^{10} +4.76179 q^{11} -2.60241 q^{12} +2.84917 q^{13} +0.00509477 q^{14} +4.26590 q^{15} +3.65966 q^{16} +0.435106 q^{17} +0.288508 q^{18} +1.09198 q^{19} -6.18670 q^{20} -0.0285182 q^{21} -1.13956 q^{22} +5.16760 q^{23} +1.26394 q^{24} +5.14130 q^{25} -0.681842 q^{26} -5.63363 q^{27} +0.0413591 q^{28} +0.0588219 q^{29} -1.02088 q^{30} -4.60784 q^{31} -2.76289 q^{32} +6.37872 q^{33} -0.104126 q^{34} -0.0677962 q^{35} +2.34209 q^{36} -2.75049 q^{37} -0.261324 q^{38} +3.81664 q^{39} +3.00476 q^{40} -6.36101 q^{41} +0.00682477 q^{42} +1.13555 q^{43} -9.25087 q^{44} -3.83918 q^{45} -1.23667 q^{46} +9.46509 q^{47} +4.90234 q^{48} -6.99955 q^{49} -1.23038 q^{50} +0.582853 q^{51} -5.53516 q^{52} +6.31080 q^{53} +1.34820 q^{54} +15.1641 q^{55} -0.0200873 q^{56} +1.46278 q^{57} -0.0140768 q^{58} -8.37431 q^{59} -8.28748 q^{60} +5.82832 q^{61} +1.10271 q^{62} +0.0256655 q^{63} -6.65812 q^{64} +9.07329 q^{65} -1.52651 q^{66} +7.76195 q^{67} -0.845294 q^{68} +6.92234 q^{69} +0.0162245 q^{70} +3.25499 q^{71} -1.13751 q^{72} -4.59395 q^{73} +0.658227 q^{74} +6.88710 q^{75} -2.12142 q^{76} -0.101374 q^{77} -0.913371 q^{78} +6.82619 q^{79} +11.6543 q^{80} -3.92990 q^{81} +1.52227 q^{82} +1.79125 q^{83} +0.0554031 q^{84} +1.38561 q^{85} -0.271753 q^{86} +0.0787957 q^{87} +4.49296 q^{88} -13.2202 q^{89} +0.918764 q^{90} -0.0606564 q^{91} -10.0393 q^{92} -6.17250 q^{93} -2.26512 q^{94} +3.47745 q^{95} -3.70107 q^{96} +18.6939 q^{97} +1.67508 q^{98} -5.74066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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