LMFDB - Embedded newform 8049.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00502 q^{2} -1.00000 q^{3} +2.02010 q^{4} -0.637068 q^{5} +2.00502 q^{6} -2.14824 q^{7} -0.0403022 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.00502 q^{2} -1.00000 q^{3} +2.02010 q^{4} -0.637068 q^{5} +2.00502 q^{6} -2.14824 q^{7} -0.0403022 q^{8} +1.00000 q^{9} +1.27733 q^{10} -4.24482 q^{11} -2.02010 q^{12} -3.63635 q^{13} +4.30725 q^{14} +0.637068 q^{15} -3.95939 q^{16} -2.68150 q^{17} -2.00502 q^{18} +4.74611 q^{19} -1.28694 q^{20} +2.14824 q^{21} +8.51095 q^{22} -6.93512 q^{23} +0.0403022 q^{24} -4.59414 q^{25} +7.29095 q^{26} -1.00000 q^{27} -4.33965 q^{28} -0.543472 q^{29} -1.27733 q^{30} +1.31925 q^{31} +8.01927 q^{32} +4.24482 q^{33} +5.37646 q^{34} +1.36857 q^{35} +2.02010 q^{36} +5.53186 q^{37} -9.51604 q^{38} +3.63635 q^{39} +0.0256752 q^{40} +3.48832 q^{41} -4.30725 q^{42} +10.6067 q^{43} -8.57497 q^{44} -0.637068 q^{45} +13.9050 q^{46} +9.37028 q^{47} +3.95939 q^{48} -2.38509 q^{49} +9.21135 q^{50} +2.68150 q^{51} -7.34579 q^{52} +4.43034 q^{53} +2.00502 q^{54} +2.70424 q^{55} +0.0865786 q^{56} -4.74611 q^{57} +1.08967 q^{58} +11.1709 q^{59} +1.28694 q^{60} -6.83482 q^{61} -2.64513 q^{62} -2.14824 q^{63} -8.15999 q^{64} +2.31660 q^{65} -8.51095 q^{66} -9.13398 q^{67} -5.41690 q^{68} +6.93512 q^{69} -2.74401 q^{70} -14.4281 q^{71} -0.0403022 q^{72} +13.1651 q^{73} -11.0915 q^{74} +4.59414 q^{75} +9.58762 q^{76} +9.11888 q^{77} -7.29095 q^{78} +9.58517 q^{79} +2.52240 q^{80} +1.00000 q^{81} -6.99415 q^{82} -4.96673 q^{83} +4.33965 q^{84} +1.70830 q^{85} -21.2667 q^{86} +0.543472 q^{87} +0.171076 q^{88} +6.84521 q^{89} +1.27733 q^{90} +7.81173 q^{91} -14.0096 q^{92} -1.31925 q^{93} -18.7876 q^{94} -3.02360 q^{95} -8.01927 q^{96} +17.1704 q^{97} +4.78214 q^{98} -4.24482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) $ 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * 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 $

$2$	−2.00502	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$2$	−2.00502	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.02010	1.01005
$5$	−0.637068	−0.284905	−0.142453	−	0.989802i	$-0.545499\pi$
$5$	−0.637068	−0.284905	−0.142453	+	0.989802i	$0.545499\pi$
$6$	2.00502	0.818546
$7$	−2.14824	−0.811957	−0.405978	−	0.913883i	$-0.633069\pi$
$7$	−2.14824	−0.811957	−0.405978	+	0.913883i	$0.633069\pi$
$8$	−0.0403022	−0.0142490
$9$	1.00000	0.333333
$10$	1.27733	0.403928
$11$	−4.24482	−1.27986	−0.639931	−	0.768432i	$-0.721037\pi$
$11$	−4.24482	−1.27986	−0.639931	+	0.768432i	$0.721037\pi$
$12$	−2.02010	−0.583153
$13$	−3.63635	−1.00854	−0.504271	−	0.863546i	$-0.668239\pi$
$13$	−3.63635	−1.00854	−0.504271	+	0.863546i	$0.668239\pi$
$14$	4.30725	1.15116
$15$	0.637068	0.164490
$16$	−3.95939	−0.989849
$17$	−2.68150	−0.650360	−0.325180	−	0.945652i	$-0.605425\pi$
$17$	−2.68150	−0.650360	−0.325180	+	0.945652i	$0.605425\pi$
$18$	−2.00502	−0.472587
$19$	4.74611	1.08883	0.544416	−	0.838815i	$-0.316751\pi$
$19$	4.74611	1.08883	0.544416	+	0.838815i	$0.316751\pi$
$20$	−1.28694	−0.287769
$21$	2.14824	0.468783
$22$	8.51095	1.81454
$23$	−6.93512	−1.44607	−0.723036	−	0.690811i	$-0.757254\pi$
$23$	−6.93512	−1.44607	−0.723036	+	0.690811i	$0.757254\pi$
$24$	0.0403022	0.00822665
$25$	−4.59414	−0.918829
$26$	7.29095	1.42987
$27$	−1.00000	−0.192450
$28$	−4.33965	−0.820117
$29$	−0.543472	−0.100920	−0.0504601	−	0.998726i	$-0.516069\pi$
$29$	−0.543472	−0.100920	−0.0504601	+	0.998726i	$0.516069\pi$
$30$	−1.27733	−0.233208
$31$	1.31925	0.236945	0.118472	−	0.992957i	$-0.462200\pi$
$31$	1.31925	0.236945	0.118472	+	0.992957i	$0.462200\pi$
$32$	8.01927	1.41762
$33$	4.24482	0.738929
$34$	5.37646	0.922056
$35$	1.36857	0.231331
$36$	2.02010	0.336683
$37$	5.53186	0.909432	0.454716	−	0.890637i	$-0.349741\pi$
$37$	5.53186	0.909432	0.454716	+	0.890637i	$0.349741\pi$
$38$	−9.51604	−1.54371
$39$	3.63635	0.582282
$40$	0.0256752	0.00405961
$41$	3.48832	0.544784	0.272392	−	0.962186i	$-0.412185\pi$
$41$	3.48832	0.544784	0.272392	+	0.962186i	$0.412185\pi$
$42$	−4.30725	−0.664623
$43$	10.6067	1.61751	0.808754	−	0.588147i	$-0.200142\pi$
$43$	10.6067	1.61751	0.808754	+	0.588147i	$0.200142\pi$
$44$	−8.57497	−1.29273
$45$	−0.637068	−0.0949685
$46$	13.9050	2.05019
$47$	9.37028	1.36680	0.683398	−	0.730046i	$-0.260502\pi$
$47$	9.37028	1.36680	0.683398	+	0.730046i	$0.260502\pi$
$48$	3.95939	0.571489
$49$	−2.38509	−0.340726
$50$	9.21135	1.30268
$51$	2.68150	0.375485
$52$	−7.34579	−1.01868
$53$	4.43034	0.608555	0.304277	−	0.952583i	$-0.401585\pi$
$53$	4.43034	0.608555	0.304277	+	0.952583i	$0.401585\pi$
$54$	2.00502	0.272849
$55$	2.70424	0.364640
$56$	0.0865786	0.0115696
$57$	−4.74611	−0.628638
$58$	1.08967	0.143081
$59$	11.1709	1.45433	0.727166	−	0.686462i	$-0.240837\pi$
$59$	11.1709	1.45433	0.727166	+	0.686462i	$0.240837\pi$
$60$	1.28694	0.166143
$61$	−6.83482	−0.875110	−0.437555	−	0.899192i	$-0.644155\pi$
$61$	−6.83482	−0.875110	−0.437555	+	0.899192i	$0.644155\pi$
$62$	−2.64513	−0.335931
$63$	−2.14824	−0.270652
$64$	−8.15999	−1.02000
$65$	2.31660	0.287339
$66$	−8.51095	−1.04763
$67$	−9.13398	−1.11589	−0.557947	−	0.829877i	$-0.688411\pi$
$67$	−9.13398	−1.11589	−0.557947	+	0.829877i	$0.688411\pi$
$68$	−5.41690	−0.656896
$69$	6.93512	0.834890
$70$	−2.74401	−0.327972
$71$	−14.4281	−1.71230	−0.856150	−	0.516728i	$-0.827150\pi$
$71$	−14.4281	−1.71230	−0.856150	+	0.516728i	$0.827150\pi$
$72$	−0.0403022	−0.00474966
$73$	13.1651	1.54086	0.770431	−	0.637524i	$-0.220041\pi$
$73$	13.1651	1.54086	0.770431	+	0.637524i	$0.220041\pi$
$74$	−11.0915	−1.28936
$75$	4.59414	0.530486
$76$	9.58762	1.09978
$77$	9.11888	1.03919
$78$	−7.29095	−0.825537
$79$	9.58517	1.07842	0.539208	−	0.842172i	$-0.318724\pi$
$79$	9.58517	1.07842	0.539208	+	0.842172i	$0.318724\pi$
$80$	2.52240	0.282013
$81$	1.00000	0.111111
$82$	−6.99415	−0.772375
$83$	−4.96673	−0.545169	−0.272585	−	0.962132i	$-0.587878\pi$
$83$	−4.96673	−0.545169	−0.272585	+	0.962132i	$0.587878\pi$
$84$	4.33965	0.473495
$85$	1.70830	0.185291
$86$	−21.2667	−2.29324
$87$	0.543472	0.0582663
$88$	0.171076	0.0182367
$89$	6.84521	0.725590	0.362795	−	0.931869i	$-0.381822\pi$
$89$	6.84521	0.725590	0.362795	+	0.931869i	$0.381822\pi$
$90$	1.27733	0.134643
$91$	7.81173	0.818892
$92$	−14.0096	−1.46060
$93$	−1.31925	−0.136800
$94$	−18.7876	−1.93779
$95$	−3.02360	−0.310214
$96$	−8.01927	−0.818463
$97$	17.1704	1.74339	0.871696	−	0.490048i	$-0.163021\pi$
$97$	17.1704	1.74339	0.871696	+	0.490048i	$0.163021\pi$
$98$	4.78214	0.483069
$99$	−4.24482	−0.426621
$100$	−9.28063	−0.928063
$101$	−13.2277	−1.31621	−0.658104	−	0.752927i	$-0.728641\pi$
$101$	−13.2277	−1.31621	−0.658104	+	0.752927i	$0.728641\pi$
$102$	−5.37646	−0.532349
$103$	1.19087	0.117340	0.0586699	−	0.998277i	$-0.481314\pi$
$103$	1.19087	0.117340	0.0586699	+	0.998277i	$0.481314\pi$
$104$	0.146553	0.0143707
$105$	−1.36857	−0.133559
$106$	−8.88292	−0.862786
$107$	3.99027	0.385754	0.192877	−	0.981223i	$-0.438218\pi$
$107$	3.99027	0.385754	0.192877	+	0.981223i	$0.438218\pi$
$108$	−2.02010	−0.194384
$109$	6.64792	0.636755	0.318378	−	0.947964i	$-0.396862\pi$
$109$	6.64792	0.636755	0.318378	+	0.947964i	$0.396862\pi$
$110$	−5.42205	−0.516972
$111$	−5.53186	−0.525061
$112$	8.50571	0.803714
$113$	−0.409937	−0.0385637	−0.0192818	−	0.999814i	$-0.506138\pi$
$113$	−0.409937	−0.0385637	−0.0192818	+	0.999814i	$0.506138\pi$
$114$	9.51604	0.891259
$115$	4.41814	0.411994
$116$	−1.09787	−0.101935
$117$	−3.63635	−0.336180
$118$	−22.3979	−2.06190
$119$	5.76050	0.528064
$120$	−0.0256752	−0.00234382
$121$	7.01852	0.638047
$122$	13.7040	1.24070
$123$	−3.48832	−0.314531
$124$	2.66502	0.239326
$125$	6.11212	0.546685
$126$	4.30725	0.383721
$127$	−14.9783	−1.32911	−0.664555	−	0.747240i	$-0.731379\pi$
$127$	−14.9783	−1.32911	−0.664555	+	0.747240i	$0.731379\pi$
$128$	0.322401	0.0284965
$129$	−10.6067	−0.933869
$130$	−4.64483	−0.407378
$131$	−18.8618	−1.64796	−0.823982	−	0.566616i	$-0.808252\pi$
$131$	−18.8618	−1.64796	−0.823982	+	0.566616i	$0.808252\pi$
$132$	8.57497	0.746355
$133$	−10.1958	−0.884085
$134$	18.3138	1.58207
$135$	0.637068	0.0548301
$136$	0.108070	0.00926696
$137$	20.3027	1.73458	0.867288	−	0.497807i	$-0.165861\pi$
$137$	20.3027	1.73458	0.867288	+	0.497807i	$0.165861\pi$
$138$	−13.9050	−1.18368
$139$	8.50089	0.721036	0.360518	−	0.932752i	$-0.382600\pi$
$139$	8.50089	0.721036	0.360518	+	0.932752i	$0.382600\pi$
$140$	2.76465	0.233656
$141$	−9.37028	−0.789120
$142$	28.9286	2.42763
$143$	15.4357	1.29079
$144$	−3.95939	−0.329950
$145$	0.346229	0.0287527
$146$	−26.3963	−2.18457
$147$	2.38509	0.196719
$148$	11.1749	0.918572
$149$	−7.03955	−0.576702	−0.288351	−	0.957525i	$-0.593107\pi$
$149$	−7.03955	−0.576702	−0.288351	+	0.957525i	$0.593107\pi$
$150$	−9.21135	−0.752103
$151$	6.54833	0.532896	0.266448	−	0.963849i	$-0.414150\pi$
$151$	6.54833	0.532896	0.266448	+	0.963849i	$0.414150\pi$
$152$	−0.191279	−0.0155148
$153$	−2.68150	−0.216787
$154$	−18.2835	−1.47333
$155$	−0.840454	−0.0675069
$156$	7.34579	0.588134
$157$	8.05939	0.643209	0.321605	−	0.946874i	$-0.395778\pi$
$157$	8.05939	0.643209	0.321605	+	0.946874i	$0.395778\pi$
$158$	−19.2185	−1.52894
$159$	−4.43034	−0.351349
$160$	−5.10882	−0.403887
$161$	14.8983	1.17415
$162$	−2.00502	−0.157529
$163$	11.8354	0.927018	0.463509	−	0.886092i	$-0.346590\pi$
$163$	11.8354	0.927018	0.463509	+	0.886092i	$0.346590\pi$
$164$	7.04676	0.550260
$165$	−2.70424	−0.210525
$166$	9.95838	0.772920
$167$	−0.571621	−0.0442334	−0.0221167	−	0.999755i	$-0.507041\pi$
$167$	−0.571621	−0.0442334	−0.0221167	+	0.999755i	$0.507041\pi$
$168$	−0.0865786	−0.00667968
$169$	0.223027	0.0171560
$170$	−3.42517	−0.262699
$171$	4.74611	0.362944
$172$	21.4266	1.63376
$173$	−23.8311	−1.81184	−0.905922	−	0.423444i	$-0.860821\pi$
$173$	−23.8311	−1.81184	−0.905922	+	0.423444i	$0.860821\pi$
$174$	−1.08967	−0.0826078
$175$	9.86930	0.746049
$176$	16.8069	1.26687
$177$	−11.1709	−0.839659
$178$	−13.7248	−1.02871
$179$	2.41911	0.180813	0.0904063	−	0.995905i	$-0.471183\pi$
$179$	2.41911	0.180813	0.0904063	+	0.995905i	$0.471183\pi$
$180$	−1.28694	−0.0959229
$181$	−13.2778	−0.986932	−0.493466	−	0.869765i	$-0.664270\pi$
$181$	−13.2778	−0.986932	−0.493466	+	0.869765i	$0.664270\pi$
$182$	−15.6627	−1.16099
$183$	6.83482	0.505245
$184$	0.279500	0.0206050
$185$	−3.52417	−0.259102
$186$	2.64513	0.193950
$187$	11.3825	0.832371
$188$	18.9289	1.38053
$189$	2.14824	0.156261
$190$	6.06237	0.439810
$191$	−15.3635	−1.11166	−0.555831	−	0.831295i	$-0.687600\pi$
$191$	−15.3635	−1.11166	−0.555831	+	0.831295i	$0.687600\pi$
$192$	8.15999	0.588896
$193$	1.76635	0.127145	0.0635723	−	0.997977i	$-0.479751\pi$
$193$	1.76635	0.127145	0.0635723	+	0.997977i	$0.479751\pi$
$194$	−34.4270	−2.47171
$195$	−2.31660	−0.165895
$196$	−4.81811	−0.344151
$197$	18.6132	1.32613	0.663066	−	0.748561i	$-0.269255\pi$
$197$	18.6132	1.32613	0.663066	+	0.748561i	$0.269255\pi$
$198$	8.51095	0.604847
$199$	9.84842	0.698136	0.349068	−	0.937097i	$-0.386498\pi$
$199$	9.84842	0.698136	0.349068	+	0.937097i	$0.386498\pi$
$200$	0.185154	0.0130924
$201$	9.13398	0.644261
$202$	26.5218	1.86607
$203$	1.16751	0.0819429
$204$	5.41690	0.379259
$205$	−2.22230	−0.155212
$206$	−2.38772	−0.166360
$207$	−6.93512	−0.482024
$208$	14.3977	0.998303
$209$	−20.1464	−1.39356
$210$	2.74401	0.189355
$211$	−1.90113	−0.130879	−0.0654397	−	0.997857i	$-0.520845\pi$
$211$	−1.90113	−0.130879	−0.0654397	+	0.997857i	$0.520845\pi$
$212$	8.94974	0.614671
$213$	14.4281	0.988597
$214$	−8.00056	−0.546907
$215$	−6.75720	−0.460837
$216$	0.0403022	0.00274222
$217$	−2.83407	−0.192389
$218$	−13.3292	−0.902768
$219$	−13.1651	−0.889617
$220$	5.46284	0.368304
$221$	9.75087	0.655915
$222$	11.0915	0.744411
$223$	13.4713	0.902106	0.451053	−	0.892497i	$-0.351049\pi$
$223$	13.4713	0.902106	0.451053	+	0.892497i	$0.351049\pi$
$224$	−17.2273	−1.15105
$225$	−4.59414	−0.306276
$226$	0.821932	0.0546741
$227$	15.1089	1.00281	0.501407	−	0.865211i	$-0.332816\pi$
$227$	15.1089	1.00281	0.501407	+	0.865211i	$0.332816\pi$
$228$	−9.58762	−0.634956
$229$	−25.3015	−1.67197	−0.835986	−	0.548750i	$-0.815104\pi$
$229$	−25.3015	−1.67197	−0.835986	+	0.548750i	$0.815104\pi$
$230$	−8.85845	−0.584109
$231$	−9.11888	−0.599978
$232$	0.0219031	0.00143801
$233$	20.6827	1.35497	0.677484	−	0.735538i	$-0.263071\pi$
$233$	20.6827	1.35497	0.677484	+	0.735538i	$0.263071\pi$
$234$	7.29095	0.476624
$235$	−5.96950	−0.389407
$236$	22.5664	1.46895
$237$	−9.58517	−0.622624
$238$	−11.5499	−0.748669
$239$	−5.99755	−0.387950	−0.193975	−	0.981007i	$-0.562138\pi$
$239$	−5.99755	−0.387950	−0.193975	+	0.981007i	$0.562138\pi$
$240$	−2.52240	−0.162820
$241$	6.56221	0.422709	0.211355	−	0.977409i	$-0.432213\pi$
$241$	6.56221	0.422709	0.211355	+	0.977409i	$0.432213\pi$
$242$	−14.0723	−0.904599
$243$	−1.00000	−0.0641500
$244$	−13.8070	−0.883905
$245$	1.51946	0.0970748
$246$	6.99415	0.445931
$247$	−17.2585	−1.09813
$248$	−0.0531688	−0.00337622
$249$	4.96673	0.314754
$250$	−12.2549	−0.775069
$251$	−8.27847	−0.522533	−0.261266	−	0.965267i	$-0.584140\pi$
$251$	−8.27847	−0.522533	−0.261266	+	0.965267i	$0.584140\pi$
$252$	−4.33965	−0.273372
$253$	29.4383	1.85077
$254$	30.0318	1.88436
$255$	−1.70830	−0.106978
$256$	15.6736	0.979597
$257$	−18.9160	−1.17995	−0.589975	−	0.807422i	$-0.700862\pi$
$257$	−18.9160	−1.17995	−0.589975	+	0.807422i	$0.700862\pi$
$258$	21.2667	1.32400
$259$	−11.8837	−0.738419
$260$	4.67977	0.290227
$261$	−0.543472	−0.0336401
$262$	37.8183	2.33642
$263$	−4.83308	−0.298020	−0.149010	−	0.988836i	$-0.547609\pi$
$263$	−4.83308	−0.298020	−0.149010	+	0.988836i	$0.547609\pi$
$264$	−0.171076	−0.0105290
$265$	−2.82243	−0.173381
$266$	20.4427	1.25342
$267$	−6.84521	−0.418920
$268$	−18.4516	−1.12711
$269$	17.6338	1.07515	0.537576	−	0.843215i	$-0.319340\pi$
$269$	17.6338	1.07515	0.537576	+	0.843215i	$0.319340\pi$
$270$	−1.27733	−0.0777360
$271$	−0.548011	−0.0332893	−0.0166447	−	0.999861i	$-0.505298\pi$
$271$	−0.548011	−0.0332893	−0.0166447	+	0.999861i	$0.505298\pi$
$272$	10.6171	0.643758
$273$	−7.81173	−0.472787
$274$	−40.7073	−2.45922
$275$	19.5013	1.17597
$276$	14.0096	0.843281
$277$	17.8998	1.07550	0.537748	−	0.843106i	$-0.319275\pi$
$277$	17.8998	1.07550	0.537748	+	0.843106i	$0.319275\pi$
$278$	−17.0444	−1.02226
$279$	1.31925	0.0789816
$280$	−0.0551564	−0.00329623
$281$	−23.6337	−1.40987	−0.704935	−	0.709272i	$-0.749024\pi$
$281$	−23.6337	−1.40987	−0.704935	+	0.709272i	$0.749024\pi$
$282$	18.7876	1.11878
$283$	11.9505	0.710383	0.355192	−	0.934794i	$-0.384416\pi$
$283$	11.9505	0.710383	0.355192	+	0.934794i	$0.384416\pi$
$284$	−29.1462	−1.72951
$285$	3.02360	0.179102
$286$	−30.9488	−1.83004
$287$	−7.49373	−0.442341
$288$	8.01927	0.472540
$289$	−9.80955	−0.577032
$290$	−0.694195	−0.0407645
$291$	−17.1704	−1.00655
$292$	26.5949	1.55635
$293$	−10.6567	−0.622572	−0.311286	−	0.950316i	$-0.600760\pi$
$293$	−10.6567	−0.622572	−0.311286	+	0.950316i	$0.600760\pi$
$294$	−4.78214	−0.278900
$295$	−7.11664	−0.414347
$296$	−0.222946	−0.0129585
$297$	4.24482	0.246310
$298$	14.1144	0.817627
$299$	25.2185	1.45842
$300$	9.28063	0.535818
$301$	−22.7857	−1.31335
$302$	−13.1295	−0.755520
$303$	13.2277	0.759913
$304$	−18.7917	−1.07778
$305$	4.35425	0.249323
$306$	5.37646	0.307352
$307$	−10.9034	−0.622291	−0.311146	−	0.950362i	$-0.600713\pi$
$307$	−10.9034	−0.622291	−0.311146	+	0.950362i	$0.600713\pi$
$308$	18.4211	1.04964
$309$	−1.19087	−0.0677462
$310$	1.68513	0.0957087
$311$	−27.1096	−1.53725	−0.768623	−	0.639702i	$-0.779058\pi$
$311$	−27.1096	−1.53725	−0.768623	+	0.639702i	$0.779058\pi$
$312$	−0.146553	−0.00829692
$313$	−11.4177	−0.645368	−0.322684	−	0.946507i	$-0.604585\pi$
$313$	−11.4177	−0.645368	−0.322684	+	0.946507i	$0.604585\pi$
$314$	−16.1592	−0.911918
$315$	1.36857	0.0771103
$316$	19.3630	1.08925
$317$	1.68826	0.0948219	0.0474110	−	0.998875i	$-0.484903\pi$
$317$	1.68826	0.0948219	0.0474110	+	0.998875i	$0.484903\pi$
$318$	8.88292	0.498130
$319$	2.30694	0.129164
$320$	5.19847	0.290603
$321$	−3.99027	−0.222715
$322$	−29.8713	−1.66466
$323$	−12.7267	−0.708133
$324$	2.02010	0.112228
$325$	16.7059	0.926677
$326$	−23.7301	−1.31429
$327$	−6.64792	−0.367631
$328$	−0.140587	−0.00776262
$329$	−20.1296	−1.10978
$330$	5.42205	0.298474
$331$	35.1381	1.93137	0.965683	−	0.259723i	$-0.0836312\pi$
$331$	35.1381	1.93137	0.965683	+	0.259723i	$0.0836312\pi$
$332$	−10.0333	−0.550648
$333$	5.53186	0.303144
$334$	1.14611	0.0627124
$335$	5.81896	0.317924
$336$	−8.50571	−0.464025
$337$	24.4168	1.33007	0.665033	−	0.746814i	$-0.268417\pi$
$337$	24.4168	1.33007	0.665033	+	0.746814i	$0.268417\pi$
$338$	−0.447174	−0.0243231
$339$	0.409937	0.0222647
$340$	3.45093	0.187153
$341$	−5.60000	−0.303257
$342$	−9.51604	−0.514569
$343$	20.1614	1.08861
$344$	−0.427474	−0.0230478
$345$	−4.41814	−0.237865
$346$	47.7818	2.56876
$347$	−0.787047	−0.0422509	−0.0211254	−	0.999777i	$-0.506725\pi$
$347$	−0.787047	−0.0422509	−0.0211254	+	0.999777i	$0.506725\pi$
$348$	1.09787	0.0588519
$349$	4.96819	0.265941	0.132971	−	0.991120i	$-0.457548\pi$
$349$	4.96819	0.265941	0.132971	+	0.991120i	$0.457548\pi$
$350$	−19.7881	−1.05772
$351$	3.63635	0.194094
$352$	−34.0404	−1.81436
$353$	17.0345	0.906655	0.453327	−	0.891344i	$-0.350237\pi$
$353$	17.0345	0.906655	0.453327	+	0.891344i	$0.350237\pi$
$354$	22.3979	1.19044
$355$	9.19167	0.487843
$356$	13.8280	0.732883
$357$	−5.76050	−0.304878
$358$	−4.85036	−0.256349
$359$	26.2848	1.38726	0.693629	−	0.720332i	$-0.256011\pi$
$359$	26.2848	1.38726	0.693629	+	0.720332i	$0.256011\pi$
$360$	0.0256752	0.00135320
$361$	3.52558	0.185557
$362$	26.6223	1.39923
$363$	−7.01852	−0.368377
$364$	15.7805	0.827122
$365$	−8.38708	−0.439000
$366$	−13.7040	−0.716317
$367$	−13.2344	−0.690832	−0.345416	−	0.938450i	$-0.612262\pi$
$367$	−13.2344	−0.690832	−0.345416	+	0.938450i	$0.612262\pi$
$368$	27.4589	1.43139
$369$	3.48832	0.181595
$370$	7.06603	0.367345
$371$	−9.51742	−0.494120
$372$	−2.66502	−0.138175
$373$	0.0394669	0.00204352	0.00102176	−	0.999999i	$-0.499675\pi$
$373$	0.0394669	0.00204352	0.00102176	+	0.999999i	$0.499675\pi$
$374$	−22.8221	−1.18010
$375$	−6.11212	−0.315629
$376$	−0.377643	−0.0194754
$377$	1.97625	0.101782
$378$	−4.30725	−0.221541
$379$	30.6249	1.57310	0.786549	−	0.617528i	$-0.211866\pi$
$379$	30.6249	1.57310	0.786549	+	0.617528i	$0.211866\pi$
$380$	−6.10797	−0.313332
$381$	14.9783	0.767362
$382$	30.8040	1.57607
$383$	−12.8130	−0.654713	−0.327357	−	0.944901i	$-0.606158\pi$
$383$	−12.8130	−0.654713	−0.327357	+	0.944901i	$0.606158\pi$
$384$	−0.322401	−0.0164525
$385$	−5.80934	−0.296072
$386$	−3.54156	−0.180261
$387$	10.6067	0.539169
$388$	34.6860	1.76091
$389$	−9.92016	−0.502972	−0.251486	−	0.967861i	$-0.580919\pi$
$389$	−9.92016	−0.502972	−0.251486	+	0.967861i	$0.580919\pi$
$390$	4.64483	0.235200
$391$	18.5965	0.940467
$392$	0.0961242	0.00485500
$393$	18.8618	0.951452
$394$	−37.3197	−1.88014
$395$	−6.10641	−0.307247
$396$	−8.57497	−0.430908
$397$	16.4112	0.823653	0.411827	−	0.911262i	$-0.364891\pi$
$397$	16.4112	0.823653	0.411827	+	0.911262i	$0.364891\pi$
$398$	−19.7463	−0.989791
$399$	10.1958	0.510427
$400$	18.1900	0.909502
$401$	−0.790242	−0.0394628	−0.0197314	−	0.999805i	$-0.506281\pi$
$401$	−0.790242	−0.0394628	−0.0197314	+	0.999805i	$0.506281\pi$
$402$	−18.3138	−0.913409
$403$	−4.79726	−0.238969
$404$	−26.7213	−1.32944
$405$	−0.637068	−0.0316562
$406$	−2.34087	−0.116176
$407$	−23.4818	−1.16395
$408$	−0.108070	−0.00535028
$409$	29.1435	1.44105	0.720526	−	0.693428i	$-0.243900\pi$
$409$	29.1435	1.44105	0.720526	+	0.693428i	$0.243900\pi$
$410$	4.45575	0.220054
$411$	−20.3027	−1.00146
$412$	2.40568	0.118519
$413$	−23.9978	−1.18085
$414$	13.9050	0.683395
$415$	3.16414	0.155322
$416$	−29.1608	−1.42973
$417$	−8.50089	−0.416290
$418$	40.3939	1.97573
$419$	−2.30659	−0.112684	−0.0563422	−	0.998412i	$-0.517944\pi$
$419$	−2.30659	−0.112684	−0.0563422	+	0.998412i	$0.517944\pi$
$420$	−2.76465	−0.134901
$421$	−18.7112	−0.911927	−0.455963	−	0.889999i	$-0.650705\pi$
$421$	−18.7112	−0.911927	−0.455963	+	0.889999i	$0.650705\pi$
$422$	3.81181	0.185556
$423$	9.37028	0.455598
$424$	−0.178553	−0.00867128
$425$	12.3192	0.597569
$426$	−28.9286	−1.40160
$427$	14.6828	0.710551
$428$	8.06074	0.389631
$429$	−15.4357	−0.745240
$430$	13.5483	0.653357
$431$	−27.2716	−1.31363	−0.656814	−	0.754053i	$-0.728096\pi$
$431$	−27.2716	−1.31363	−0.656814	+	0.754053i	$0.728096\pi$
$432$	3.95939	0.190496
$433$	−18.3118	−0.880007	−0.440004	−	0.897996i	$-0.645023\pi$
$433$	−18.3118	−0.880007	−0.440004	+	0.897996i	$0.645023\pi$
$434$	5.68236	0.272762
$435$	−0.346229	−0.0166004
$436$	13.4295	0.643155
$437$	−32.9148	−1.57453
$438$	26.3963	1.26126
$439$	19.9061	0.950066	0.475033	−	0.879968i	$-0.342436\pi$
$439$	19.9061	0.950066	0.475033	+	0.879968i	$0.342436\pi$
$440$	−0.108987	−0.00519574
$441$	−2.38509	−0.113575
$442$	−19.5507	−0.929931
$443$	−3.58655	−0.170402	−0.0852011	−	0.996364i	$-0.527153\pi$
$443$	−3.58655	−0.170402	−0.0852011	+	0.996364i	$0.527153\pi$
$444$	−11.1749	−0.530338
$445$	−4.36086	−0.206725
$446$	−27.0102	−1.27897
$447$	7.03955	0.332959
$448$	17.5296	0.828195
$449$	26.9616	1.27239	0.636197	−	0.771527i	$-0.280506\pi$
$449$	26.9616	1.27239	0.636197	+	0.771527i	$0.280506\pi$
$450$	9.21135	0.434227
$451$	−14.8073	−0.697249
$452$	−0.828115	−0.0389512
$453$	−6.54833	−0.307668
$454$	−30.2937	−1.42175
$455$	−4.97660	−0.233307
$456$	0.191279	0.00895745
$457$	−6.07148	−0.284012	−0.142006	−	0.989866i	$-0.545355\pi$
$457$	−6.07148	−0.284012	−0.142006	+	0.989866i	$0.545355\pi$
$458$	50.7301	2.37046
$459$	2.68150	0.125162
$460$	8.92509	0.416134
$461$	11.2583	0.524353	0.262177	−	0.965020i	$-0.415560\pi$
$461$	11.2583	0.524353	0.262177	+	0.965020i	$0.415560\pi$
$462$	18.2835	0.850626
$463$	31.0606	1.44351	0.721753	−	0.692151i	$-0.243337\pi$
$463$	31.0606	1.44351	0.721753	+	0.692151i	$0.243337\pi$
$464$	2.15182	0.0998958
$465$	0.840454	0.0389751
$466$	−41.4692	−1.92102
$467$	−40.3337	−1.86642	−0.933211	−	0.359329i	$-0.883005\pi$
$467$	−40.3337	−1.86642	−0.933211	+	0.359329i	$0.883005\pi$
$468$	−7.34579	−0.339559
$469$	19.6219	0.906057
$470$	11.9690	0.552087
$471$	−8.05939	−0.371357
$472$	−0.450213	−0.0207227
$473$	−45.0236	−2.07019
$474$	19.2185	0.882733
$475$	−21.8043	−1.00045
$476$	11.6368	0.533371
$477$	4.43034	0.202852
$478$	12.0252	0.550020
$479$	−30.3772	−1.38797	−0.693986	−	0.719989i	$-0.744147\pi$
$479$	−30.3772	−1.38797	−0.693986	+	0.719989i	$0.744147\pi$
$480$	5.10882	0.233184
$481$	−20.1158	−0.917200
$482$	−13.1574	−0.599301
$483$	−14.8983	−0.677894
$484$	14.1781	0.644460
$485$	−10.9387	−0.496702
$486$	2.00502	0.0909495
$487$	−40.4721	−1.83397	−0.916983	−	0.398926i	$-0.869383\pi$
$487$	−40.4721	−1.83397	−0.916983	+	0.398926i	$0.869383\pi$
$488$	0.275458	0.0124694
$489$	−11.8354	−0.535214
$490$	−3.04655	−0.137629
$491$	2.41904	0.109170	0.0545850	−	0.998509i	$-0.482616\pi$
$491$	2.41904	0.109170	0.0545850	+	0.998509i	$0.482616\pi$
$492$	−7.04676	−0.317692
$493$	1.45732	0.0656345
$494$	34.6036	1.55689
$495$	2.70424	0.121547
$496$	−5.22344	−0.234540
$497$	30.9949	1.39031
$498$	−9.95838	−0.446246
$499$	20.3604	0.911458	0.455729	−	0.890118i	$-0.349379\pi$
$499$	20.3604	0.911458	0.455729	+	0.890118i	$0.349379\pi$
$500$	12.3471	0.552179
$501$	0.571621	0.0255382
$502$	16.5985	0.740827
$503$	−37.4253	−1.66871	−0.834356	−	0.551227i	$-0.814160\pi$
$503$	−37.4253	−1.66871	−0.834356	+	0.551227i	$0.814160\pi$
$504$	0.0865786	0.00385652
$505$	8.42695	0.374995
$506$	−59.0244	−2.62396
$507$	−0.223027	−0.00990499
$508$	−30.2577	−1.34247
$509$	−5.31957	−0.235786	−0.117893	−	0.993026i	$-0.537614\pi$
$509$	−5.31957	−0.235786	−0.117893	+	0.993026i	$0.537614\pi$
$510$	3.42517	0.151669
$511$	−28.2818	−1.25111
$512$	−32.0706	−1.41733
$513$	−4.74611	−0.209546
$514$	37.9270	1.67289
$515$	−0.758665	−0.0334308
$516$	−21.4266	−0.943255
$517$	−39.7752	−1.74931
$518$	23.8271	1.04690
$519$	23.8311	1.04607
$520$	−0.0933641	−0.00409429
$521$	31.0635	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$521$	31.0635	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$522$	1.08967	0.0476936
$523$	5.70041	0.249261	0.124631	−	0.992203i	$-0.460225\pi$
$523$	5.70041	0.249261	0.124631	+	0.992203i	$0.460225\pi$
$524$	−38.1028	−1.66453
$525$	−9.86930	−0.430732
$526$	9.69041	0.422522
$527$	−3.53758	−0.154099
$528$	−16.8069	−0.731428
$529$	25.0958	1.09112
$530$	5.65903	0.245812
$531$	11.1709	0.484777
$532$	−20.5965	−0.892970
$533$	−12.6848	−0.549438
$534$	13.7248	0.593929
$535$	−2.54207	−0.109903
$536$	0.368119	0.0159003
$537$	−2.41911	−0.104392
$538$	−35.3561	−1.52431
$539$	10.1243	0.436083
$540$	1.28694	0.0553811
$541$	−0.339986	−0.0146171	−0.00730856	−	0.999973i	$-0.502326\pi$
$541$	−0.339986	−0.0146171	−0.00730856	+	0.999973i	$0.502326\pi$
$542$	1.09877	0.0471963
$543$	13.2778	0.569805
$544$	−21.5037	−0.921962
$545$	−4.23518	−0.181415
$546$	15.6627	0.670300
$547$	18.7110	0.800025	0.400013	−	0.916510i	$-0.369006\pi$
$547$	18.7110	0.800025	0.400013	+	0.916510i	$0.369006\pi$
$548$	41.0135	1.75201
$549$	−6.83482	−0.291703
$550$	−39.1005	−1.66725
$551$	−2.57938	−0.109885
$552$	−0.279500	−0.0118963
$553$	−20.5912	−0.875627
$554$	−35.8895	−1.52480
$555$	3.52417	0.149593
$556$	17.1727	0.728283
$557$	10.7940	0.457356	0.228678	−	0.973502i	$-0.426560\pi$
$557$	10.7940	0.457356	0.228678	+	0.973502i	$0.426560\pi$
$558$	−2.64513	−0.111977
$559$	−38.5697	−1.63132
$560$	−5.41872	−0.228983
$561$	−11.3825	−0.480569
$562$	47.3861	1.99886
$563$	−36.9435	−1.55698	−0.778492	−	0.627655i	$-0.784015\pi$
$563$	−36.9435	−1.55698	−0.778492	+	0.627655i	$0.784015\pi$
$564$	−18.9289	−0.797051
$565$	0.261158	0.0109870
$566$	−23.9610	−1.00715
$567$	−2.14824	−0.0902174
$568$	0.581484	0.0243985
$569$	−35.1708	−1.47444	−0.737219	−	0.675654i	$-0.763861\pi$
$569$	−35.1708	−1.47444	−0.737219	+	0.675654i	$0.763861\pi$
$570$	−6.06237	−0.253925
$571$	−19.8608	−0.831147	−0.415574	−	0.909560i	$-0.636419\pi$
$571$	−19.8608	−0.831147	−0.415574	+	0.909560i	$0.636419\pi$
$572$	31.1816	1.30377
$573$	15.3635	0.641818
$574$	15.0251	0.627135
$575$	31.8609	1.32869
$576$	−8.15999	−0.340000
$577$	37.8594	1.57611	0.788053	−	0.615607i	$-0.211089\pi$
$577$	37.8594	1.57611	0.788053	+	0.615607i	$0.211089\pi$
$578$	19.6683	0.818095
$579$	−1.76635	−0.0734069
$580$	0.699417	0.0290417
$581$	10.6697	0.442654
$582$	34.4270	1.42705
$583$	−18.8060	−0.778866
$584$	−0.530583	−0.0219557
$585$	2.31660	0.0957796
$586$	21.3669	0.882659
$587$	−29.9342	−1.23552	−0.617758	−	0.786368i	$-0.711959\pi$
$587$	−29.9342	−1.23552	−0.617758	+	0.786368i	$0.711959\pi$
$588$	4.81811	0.198696
$589$	6.26132	0.257993
$590$	14.2690	0.587446
$591$	−18.6132	−0.765643
$592$	−21.9028	−0.900200
$593$	−30.6088	−1.25695	−0.628476	−	0.777829i	$-0.716321\pi$
$593$	−30.6088	−1.25695	−0.628476	+	0.777829i	$0.716321\pi$
$594$	−8.51095	−0.349208
$595$	−3.66983	−0.150448
$596$	−14.2206	−0.582498
$597$	−9.84842	−0.403069
$598$	−50.5636	−2.06770
$599$	25.9367	1.05974	0.529872	−	0.848077i	$-0.322240\pi$
$599$	25.9367	1.05974	0.529872	+	0.848077i	$0.322240\pi$
$600$	−0.185154	−0.00755889
$601$	−41.9305	−1.71038	−0.855190	−	0.518314i	$-0.826560\pi$
$601$	−41.9305	−1.71038	−0.855190	+	0.518314i	$0.826560\pi$
$602$	45.6858	1.86201
$603$	−9.13398	−0.371964
$604$	13.2283	0.538252
$605$	−4.47127	−0.181783
$606$	−26.5218	−1.07738
$607$	21.6024	0.876814	0.438407	−	0.898777i	$-0.355543\pi$
$607$	21.6024	0.876814	0.438407	+	0.898777i	$0.355543\pi$
$608$	38.0603	1.54355
$609$	−1.16751	−0.0473097
$610$	−8.73035	−0.353481
$611$	−34.0736	−1.37847
$612$	−5.41690	−0.218965
$613$	20.3094	0.820287	0.410144	−	0.912021i	$-0.365479\pi$
$613$	20.3094	0.820287	0.410144	+	0.912021i	$0.365479\pi$
$614$	21.8616	0.882261
$615$	2.22230	0.0896117
$616$	−0.367511	−0.0148074
$617$	48.6980	1.96051	0.980253	−	0.197746i	$-0.0633621\pi$
$617$	48.6980	1.96051	0.980253	+	0.197746i	$0.0633621\pi$
$618$	2.38772	0.0960480
$619$	−3.78274	−0.152041	−0.0760206	−	0.997106i	$-0.524221\pi$
$619$	−3.78274	−0.152041	−0.0760206	+	0.997106i	$0.524221\pi$
$620$	−1.69780	−0.0681853
$621$	6.93512	0.278297
$622$	54.3553	2.17945
$623$	−14.7051	−0.589148
$624$	−14.3977	−0.576371
$625$	19.0769	0.763075
$626$	22.8928	0.914978
$627$	20.1464	0.804570
$628$	16.2808	0.649674
$629$	−14.8337	−0.591458
$630$	−2.74401	−0.109324
$631$	−41.5788	−1.65523	−0.827613	−	0.561299i	$-0.810302\pi$
$631$	−41.5788	−1.65523	−0.827613	+	0.561299i	$0.810302\pi$
$632$	−0.386304	−0.0153663
$633$	1.90113	0.0755633
$634$	−3.38499	−0.134435
$635$	9.54220	0.378671
$636$	−8.94974	−0.354880
$637$	8.67300	0.343637
$638$	−4.62546	−0.183124
$639$	−14.4281	−0.570767
$640$	−0.205392	−0.00811881
$641$	33.7501	1.33305	0.666524	−	0.745484i	$-0.267782\pi$
$641$	33.7501	1.33305	0.666524	+	0.745484i	$0.267782\pi$
$642$	8.00056	0.315757
$643$	−29.7765	−1.17427	−0.587135	−	0.809489i	$-0.699744\pi$
$643$	−29.7765	−1.17427	−0.587135	+	0.809489i	$0.699744\pi$
$644$	30.0960	1.18595
$645$	6.75720	0.266064
$646$	25.5173	1.00396
$647$	−27.1535	−1.06751	−0.533757	−	0.845638i	$-0.679220\pi$
$647$	−27.1535	−1.06751	−0.533757	+	0.845638i	$0.679220\pi$
$648$	−0.0403022	−0.00158322
$649$	−47.4186	−1.86134
$650$	−33.4957	−1.31381
$651$	2.83407	0.111076
$652$	23.9086	0.936335
$653$	0.971734	0.0380269	0.0190134	−	0.999819i	$-0.493947\pi$
$653$	0.971734	0.0380269	0.0190134	+	0.999819i	$0.493947\pi$
$654$	13.3292	0.521213
$655$	12.0163	0.469514
$656$	−13.8116	−0.539254
$657$	13.1651	0.513620
$658$	40.3601	1.57340
$659$	−19.4643	−0.758221	−0.379110	−	0.925351i	$-0.623770\pi$
$659$	−19.4643	−0.758221	−0.379110	+	0.925351i	$0.623770\pi$
$660$	−5.46284	−0.212641
$661$	40.7436	1.58474	0.792371	−	0.610039i	$-0.208846\pi$
$661$	40.7436	1.58474	0.792371	+	0.610039i	$0.208846\pi$
$662$	−70.4526	−2.73822
$663$	−9.75087	−0.378693
$664$	0.200170	0.00776811
$665$	6.49539	0.251881
$666$	−11.0915	−0.429786
$667$	3.76904	0.145938
$668$	−1.15473	−0.0446779
$669$	−13.4713	−0.520831
$670$	−11.6671	−0.450741
$671$	29.0126	1.12002
$672$	17.2273	0.664556
$673$	11.0086	0.424352	0.212176	−	0.977231i	$-0.431945\pi$
$673$	11.0086	0.424352	0.212176	+	0.977231i	$0.431945\pi$
$674$	−48.9561	−1.88572
$675$	4.59414	0.176829
$676$	0.450538	0.0173284
$677$	−34.7465	−1.33542	−0.667708	−	0.744424i	$-0.732724\pi$
$677$	−34.7465	−1.33542	−0.667708	+	0.744424i	$0.732724\pi$
$678$	−0.821932	−0.0315661
$679$	−36.8861	−1.41556
$680$	−0.0688482	−0.00264021
$681$	−15.1089	−0.578975
$682$	11.2281	0.429946
$683$	−0.448196	−0.0171497	−0.00857487	−	0.999963i	$-0.502729\pi$
$683$	−0.448196	−0.0171497	−0.00857487	+	0.999963i	$0.502729\pi$
$684$	9.58762	0.366592
$685$	−12.9342	−0.494190
$686$	−40.4239	−1.54339
$687$	25.3015	0.965314
$688$	−41.9962	−1.60109
$689$	−16.1103	−0.613753
$690$	8.85845	0.337236
$691$	−40.5058	−1.54091	−0.770457	−	0.637492i	$-0.779972\pi$
$691$	−40.5058	−1.54091	−0.770457	+	0.637492i	$0.779972\pi$
$692$	−48.1412	−1.83005
$693$	9.11888	0.346398
$694$	1.57804	0.0599017
$695$	−5.41564	−0.205427
$696$	−0.0219031	−0.000830236 0
$697$	−9.35394	−0.354306
$698$	−9.96131	−0.377041
$699$	−20.6827	−0.782291
$700$	19.9370	0.753547
$701$	40.5999	1.53344	0.766718	−	0.641984i	$-0.221888\pi$
$701$	40.5999	1.53344	0.766718	+	0.641984i	$0.221888\pi$
$702$	−7.29095	−0.275179
$703$	26.2548	0.990219
$704$	34.6377	1.30546
$705$	5.96950	0.224824
$706$	−34.1545	−1.28542
$707$	28.4162	1.06870
$708$	−22.5664	−0.848098
$709$	−34.4074	−1.29220	−0.646099	−	0.763254i	$-0.723601\pi$
$709$	−34.4074	−1.29220	−0.646099	+	0.763254i	$0.723601\pi$
$710$	−18.4295	−0.691646
$711$	9.58517	0.359472
$712$	−0.275877	−0.0103389
$713$	−9.14917	−0.342639
$714$	11.5499	0.432244
$715$	−9.83356	−0.367754
$716$	4.88684	0.182630
$717$	5.99755	0.223983
$718$	−52.7015	−1.96680
$719$	17.3816	0.648226	0.324113	−	0.946018i	$-0.394934\pi$
$719$	17.3816	0.648226	0.324113	+	0.946018i	$0.394934\pi$
$720$	2.52240	0.0940044
$721$	−2.55827	−0.0952749
$722$	−7.06885	−0.263075
$723$	−6.56221	−0.244051
$724$	−26.8225	−0.996850
$725$	2.49679	0.0927284
$726$	14.0723	0.522271
$727$	30.7016	1.13866	0.569329	−	0.822110i	$-0.307203\pi$
$727$	30.7016	1.13866	0.569329	+	0.822110i	$0.307203\pi$
$728$	−0.314830	−0.0116684
$729$	1.00000	0.0370370
$730$	16.8162	0.622397
$731$	−28.4419	−1.05196
$732$	13.8070	0.510323
$733$	−25.9896	−0.959950	−0.479975	−	0.877282i	$-0.659354\pi$
$733$	−25.9896	−0.959950	−0.479975	+	0.877282i	$0.659354\pi$
$734$	26.5353	0.979436
$735$	−1.51946	−0.0560462
$736$	−55.6145	−2.04998
$737$	38.7721	1.42819
$738$	−6.99415	−0.257458
$739$	−20.7013	−0.761509	−0.380755	−	0.924676i	$-0.624336\pi$
$739$	−20.7013	−0.761509	−0.380755	+	0.924676i	$0.624336\pi$
$740$	−7.11918	−0.261706
$741$	17.2585	0.634007
$742$	19.0826	0.700545
$743$	−31.5243	−1.15652	−0.578258	−	0.815854i	$-0.696267\pi$
$743$	−31.5243	−1.15652	−0.578258	+	0.815854i	$0.696267\pi$
$744$	0.0531688	0.00194926
$745$	4.48467	0.164306
$746$	−0.0791320	−0.00289723
$747$	−4.96673	−0.181723
$748$	22.9938	0.840736
$749$	−8.57203	−0.313215
$750$	12.2549	0.447486
$751$	−22.7415	−0.829850	−0.414925	−	0.909856i	$-0.636192\pi$
$751$	−22.7415	−0.829850	−0.414925	+	0.909856i	$0.636192\pi$
$752$	−37.1006	−1.35292
$753$	8.27847	0.301684
$754$	−3.96243	−0.144303
$755$	−4.17173	−0.151825
$756$	4.33965	0.157832
$757$	22.9150	0.832860	0.416430	−	0.909168i	$-0.363281\pi$
$757$	22.9150	0.832860	0.416430	+	0.909168i	$0.363281\pi$
$758$	−61.4036	−2.23028
$759$	−29.4383	−1.06854
$760$	0.121858	0.00442024
$761$	−23.0226	−0.834570	−0.417285	−	0.908776i	$-0.637018\pi$
$761$	−23.0226	−0.834570	−0.417285	+	0.908776i	$0.637018\pi$
$762$	−30.0318	−1.08794
$763$	−14.2813	−0.517018
$764$	−31.0358	−1.12283
$765$	1.70830	0.0617637
$766$	25.6903	0.928228
$767$	−40.6214	−1.46675
$768$	−15.6736	−0.565571
$769$	−19.3475	−0.697688	−0.348844	−	0.937181i	$-0.613426\pi$
$769$	−19.3475	−0.697688	−0.348844	+	0.937181i	$0.613426\pi$
$770$	11.6478	0.419759
$771$	18.9160	0.681244
$772$	3.56820	0.128422
$773$	35.5482	1.27858	0.639289	−	0.768966i	$-0.279229\pi$
$773$	35.5482	1.27858	0.639289	+	0.768966i	$0.279229\pi$
$774$	−21.2667	−0.764414
$775$	−6.06084	−0.217712
$776$	−0.692005	−0.0248415
$777$	11.8837	0.426327
$778$	19.8901	0.713095
$779$	16.5560	0.593179
$780$	−4.67977	−0.167563
$781$	61.2447	2.19151
$782$	−37.2864	−1.33336
$783$	0.543472	0.0194221
$784$	9.44349	0.337268
$785$	−5.13438	−0.183254
$786$	−37.8183	−1.34893
$787$	22.1244	0.788650	0.394325	−	0.918971i	$-0.370978\pi$
$787$	22.1244	0.788650	0.394325	+	0.918971i	$0.370978\pi$
$788$	37.6005	1.33946
$789$	4.83308	0.172062
$790$	12.2435	0.435603
$791$	0.880642	0.0313120
$792$	0.171076	0.00607891
$793$	24.8538	0.882584
$794$	−32.9047	−1.16774
$795$	2.82243	0.100101
$796$	19.8948	0.705152
$797$	−0.542985	−0.0192335	−0.00961675	−	0.999954i	$-0.503061\pi$
$797$	−0.542985	−0.0192335	−0.00961675	+	0.999954i	$0.503061\pi$
$798$	−20.4427	−0.723664
$799$	−25.1264	−0.888909
$800$	−36.8417	−1.30255
$801$	6.84521	0.241863
$802$	1.58445	0.0559489
$803$	−55.8836	−1.97209
$804$	18.4516	0.650736
$805$	−9.49120	−0.334521
$806$	9.61860	0.338801
$807$	−17.6338	−0.620739
$808$	0.533106	0.0187546
$809$	23.9511	0.842077	0.421039	−	0.907043i	$-0.361666\pi$
$809$	23.9511	0.842077	0.421039	+	0.907043i	$0.361666\pi$
$810$	1.27733	0.0448809
$811$	−23.0494	−0.809373	−0.404687	−	0.914455i	$-0.632619\pi$
$811$	−23.0494	−0.809373	−0.404687	+	0.914455i	$0.632619\pi$
$812$	2.35848	0.0827664
$813$	0.548011	0.0192196
$814$	47.0814	1.65020
$815$	−7.53993	−0.264112
$816$	−10.6171	−0.371674
$817$	50.3406	1.76120
$818$	−58.4332	−2.04307
$819$	7.81173	0.272964
$820$	−4.48926	−0.156772
$821$	1.09799	0.0383203	0.0191601	−	0.999816i	$-0.493901\pi$
$821$	1.09799	0.0383203	0.0191601	+	0.999816i	$0.493901\pi$
$822$	40.7073	1.41983
$823$	−18.4634	−0.643595	−0.321797	−	0.946809i	$-0.604287\pi$
$823$	−18.4634	−0.643595	−0.321797	+	0.946809i	$0.604287\pi$
$824$	−0.0479947	−0.00167197
$825$	−19.5013	−0.678949
$826$	48.1160	1.67417
$827$	−4.35627	−0.151482	−0.0757411	−	0.997128i	$-0.524132\pi$
$827$	−4.35627	−0.151482	−0.0757411	+	0.997128i	$0.524132\pi$
$828$	−14.0096	−0.486868
$829$	4.54614	0.157894	0.0789470	−	0.996879i	$-0.474844\pi$
$829$	4.54614	0.157894	0.0789470	+	0.996879i	$0.474844\pi$
$830$	−6.34417	−0.220209
$831$	−17.8998	−0.620938
$832$	29.6726	1.02871
$833$	6.39561	0.221595
$834$	17.0444	0.590201
$835$	0.364162	0.0126023
$836$	−40.6978	−1.40756
$837$	−1.31925	−0.0456001
$838$	4.62476	0.159760
$839$	−48.0029	−1.65724	−0.828622	−	0.559808i	$-0.810875\pi$
$839$	−48.0029	−1.65724	−0.828622	+	0.559808i	$0.810875\pi$
$840$	0.0551564	0.00190308
$841$	−28.7046	−0.989815
$842$	37.5163	1.29290
$843$	23.6337	0.813989
$844$	−3.84048	−0.132195
$845$	−0.142084	−0.00488782
$846$	−18.7876	−0.645930
$847$	−15.0774	−0.518067
$848$	−17.5415	−0.602377
$849$	−11.9505	−0.410140
$850$	−24.7002	−0.847211
$851$	−38.3641	−1.31510
$852$	29.1462	0.998532
$853$	−4.10478	−0.140545	−0.0702725	−	0.997528i	$-0.522387\pi$
$853$	−4.10478	−0.140545	−0.0702725	+	0.997528i	$0.522387\pi$
$854$	−29.4393	−1.00739
$855$	−3.02360	−0.103405
$856$	−0.160817	−0.00549660
$857$	−22.0617	−0.753612	−0.376806	−	0.926292i	$-0.622978\pi$
$857$	−22.0617	−0.753612	−0.376806	+	0.926292i	$0.622978\pi$
$858$	30.9488	1.05657
$859$	−39.0808	−1.33342	−0.666710	−	0.745317i	$-0.732298\pi$
$859$	−39.0808	−1.33342	−0.666710	+	0.745317i	$0.732298\pi$
$860$	−13.6502	−0.465468
$861$	7.49373	0.255386
$862$	54.6801	1.86241
$863$	29.0629	0.989312	0.494656	−	0.869089i	$-0.335294\pi$
$863$	29.0629	0.989312	0.494656	+	0.869089i	$0.335294\pi$
$864$	−8.01927	−0.272821
$865$	15.1820	0.516204
$866$	36.7154	1.24764
$867$	9.80955	0.333150
$868$	−5.72510	−0.194323
$869$	−40.6874	−1.38022
$870$	0.694195	0.0235354
$871$	33.2143	1.12542
$872$	−0.267926	−0.00907311
$873$	17.1704	0.581130
$874$	65.9949	2.23231
$875$	−13.1303	−0.443884
$876$	−26.5949	−0.898557
$877$	−54.7236	−1.84788	−0.923942	−	0.382532i	$-0.875052\pi$
$877$	−54.7236	−1.84788	−0.923942	+	0.382532i	$0.875052\pi$
$878$	−39.9121	−1.34697
$879$	10.6567	0.359442
$880$	−10.7072	−0.360938
$881$	34.2924	1.15534	0.577671	−	0.816270i	$-0.303962\pi$
$881$	34.2924	1.15534	0.577671	+	0.816270i	$0.303962\pi$
$882$	4.78214	0.161023
$883$	18.7945	0.632487	0.316243	−	0.948678i	$-0.397578\pi$
$883$	18.7945	0.632487	0.316243	+	0.948678i	$0.397578\pi$
$884$	19.6977	0.662507
$885$	7.11664	0.239223
$886$	7.19111	0.241590
$887$	28.3706	0.952592	0.476296	−	0.879285i	$-0.341979\pi$
$887$	28.3706	0.952592	0.476296	+	0.879285i	$0.341979\pi$
$888$	0.222946	0.00748158
$889$	32.1769	1.07918
$890$	8.74361	0.293086
$891$	−4.24482	−0.142207
$892$	27.2134	0.911173
$893$	44.4724	1.48821
$894$	−14.1144	−0.472057
$895$	−1.54114	−0.0515145
$896$	−0.692594	−0.0231379
$897$	−25.2185	−0.842021
$898$	−54.0584	−1.80395
$899$	−0.716977	−0.0239125
$900$	−9.28063	−0.309354
$901$	−11.8800	−0.395779
$902$	29.6889	0.988533
$903$	22.7857	0.758261
$904$	0.0165214	0.000549493 0
$905$	8.45886	0.281182
$906$	13.1295	0.436200
$907$	−28.2123	−0.936773	−0.468386	−	0.883524i	$-0.655164\pi$
$907$	−28.2123	−0.936773	−0.468386	+	0.883524i	$0.655164\pi$
$908$	30.5216	1.01289
$909$	−13.2277	−0.438736
$910$	9.97818	0.330774
$911$	9.53216	0.315815	0.157907	−	0.987454i	$-0.449525\pi$
$911$	9.53216	0.315815	0.157907	+	0.987454i	$0.449525\pi$
$912$	18.7917	0.622256
$913$	21.0829	0.697741
$914$	12.1734	0.402661
$915$	−4.35425	−0.143947
$916$	−51.1117	−1.68878
$917$	40.5196	1.33808
$918$	−5.37646	−0.177450
$919$	34.2954	1.13130	0.565651	−	0.824645i	$-0.308625\pi$
$919$	34.2954	1.13130	0.565651	+	0.824645i	$0.308625\pi$
$920$	−0.178061	−0.00587049
$921$	10.9034	0.359280
$922$	−22.5732	−0.743408
$923$	52.4656	1.72693
$924$	−18.4211	−0.606008
$925$	−25.4142	−0.835612
$926$	−62.2770	−2.04655
$927$	1.19087	0.0391133
$928$	−4.35825	−0.143066
$929$	6.03384	0.197964	0.0989819	−	0.995089i	$-0.468441\pi$
$929$	6.03384	0.197964	0.0989819	+	0.995089i	$0.468441\pi$
$930$	−1.68513	−0.0552574
$931$	−11.3199	−0.370994
$932$	41.7811	1.36858
$933$	27.1096	0.887529
$934$	80.8699	2.64614
$935$	−7.25142	−0.237147
$936$	0.146553	0.00479023
$937$	22.5086	0.735325	0.367663	−	0.929959i	$-0.380158\pi$
$937$	22.5086	0.735325	0.367663	+	0.929959i	$0.380158\pi$
$938$	−39.3424	−1.28457
$939$	11.4177	0.372603
$940$	−12.0590	−0.393321
$941$	−32.3647	−1.05506	−0.527529	−	0.849537i	$-0.676881\pi$
$941$	−32.3647	−1.05506	−0.527529	+	0.849537i	$0.676881\pi$
$942$	16.1592	0.526496
$943$	−24.1919	−0.787797
$944$	−44.2301	−1.43957
$945$	−1.36857	−0.0445196
$946$	90.2732	2.93503
$947$	−35.9826	−1.16928	−0.584639	−	0.811294i	$-0.698764\pi$
$947$	−35.9826	−1.16928	−0.584639	+	0.811294i	$0.698764\pi$
$948$	−19.3630	−0.628882
$949$	−47.8730	−1.55402
$950$	43.7181	1.41840
$951$	−1.68826	−0.0547455
$952$	−0.232161	−0.00752437
$953$	50.4508	1.63426	0.817131	−	0.576452i	$-0.195563\pi$
$953$	50.4508	1.63426	0.817131	+	0.576452i	$0.195563\pi$
$954$	−8.88292	−0.287595
$955$	9.78757	0.316718
$956$	−12.1157	−0.391849
$957$	−2.30694	−0.0745729
$958$	60.9069	1.96781
$959$	−43.6150	−1.40840
$960$	−5.19847	−0.167780
$961$	−29.2596	−0.943857
$962$	40.3325	1.30037
$963$	3.99027	0.128585
$964$	13.2563	0.426957
$965$	−1.12528	−0.0362242
$966$	29.8713	0.961093
$967$	28.1277	0.904525	0.452262	−	0.891885i	$-0.350617\pi$
$967$	28.1277	0.904525	0.452262	+	0.891885i	$0.350617\pi$
$968$	−0.282862	−0.00909152
$969$	12.7267	0.408841
$970$	21.9323	0.704205
$971$	−23.0603	−0.740041	−0.370021	−	0.929024i	$-0.620649\pi$
$971$	−23.0603	−0.740041	−0.370021	+	0.929024i	$0.620649\pi$
$972$	−2.02010	−0.0647948
$973$	−18.2619	−0.585450
$974$	81.1473	2.60013
$975$	−16.7059	−0.535017
$976$	27.0618	0.866226
$977$	−8.40538	−0.268912	−0.134456	−	0.990920i	$-0.542929\pi$
$977$	−8.40538	−0.268912	−0.134456	+	0.990920i	$0.542929\pi$
$978$	23.7301	0.758806
$979$	−29.0567	−0.928656
$980$	3.06946	0.0980504
$981$	6.64792	0.212252
$982$	−4.85023	−0.154777
$983$	11.4091	0.363895	0.181947	−	0.983308i	$-0.441760\pi$
$983$	11.4091	0.363895	0.181947	+	0.983308i	$0.441760\pi$
$984$	0.140587	0.00448175
$985$	−11.8578	−0.377822
$986$	−2.92196	−0.0930541
$987$	20.1296	0.640731
$988$	−34.8639	−1.10917
$989$	−73.5588	−2.33903
$990$	−5.42205	−0.172324
$991$	27.6878	0.879531	0.439765	−	0.898113i	$-0.355062\pi$
$991$	27.6878	0.879531	0.439765	+	0.898113i	$0.355062\pi$
$992$	10.5794	0.335898
$993$	−35.1381	−1.11507
$994$	−62.1454	−1.97113
$995$	−6.27411	−0.198903
$996$	10.0333	0.317917
$997$	25.0174	0.792310	0.396155	−	0.918184i	$-0.370344\pi$
$997$	25.0174	0.792310	0.396155	+	0.918184i	$0.370344\pi$
$998$	−40.8231	−1.29223
$999$	−5.53186	−0.175020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.b.1.18	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.b.1.18	✓	104	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00502 q^{2} -1.00000 q^{3} +2.02010 q^{4} -0.637068 q^{5} +2.00502 q^{6} -2.14824 q^{7} -0.0403022 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.00502 q^{2} -1.00000 q^{3} +2.02010 q^{4} -0.637068 q^{5} +2.00502 q^{6} -2.14824 q^{7} -0.0403022 q^{8} +1.00000 q^{9} +1.27733 q^{10} -4.24482 q^{11} -2.02010 q^{12} -3.63635 q^{13} +4.30725 q^{14} +0.637068 q^{15} -3.95939 q^{16} -2.68150 q^{17} -2.00502 q^{18} +4.74611 q^{19} -1.28694 q^{20} +2.14824 q^{21} +8.51095 q^{22} -6.93512 q^{23} +0.0403022 q^{24} -4.59414 q^{25} +7.29095 q^{26} -1.00000 q^{27} -4.33965 q^{28} -0.543472 q^{29} -1.27733 q^{30} +1.31925 q^{31} +8.01927 q^{32} +4.24482 q^{33} +5.37646 q^{34} +1.36857 q^{35} +2.02010 q^{36} +5.53186 q^{37} -9.51604 q^{38} +3.63635 q^{39} +0.0256752 q^{40} +3.48832 q^{41} -4.30725 q^{42} +10.6067 q^{43} -8.57497 q^{44} -0.637068 q^{45} +13.9050 q^{46} +9.37028 q^{47} +3.95939 q^{48} -2.38509 q^{49} +9.21135 q^{50} +2.68150 q^{51} -7.34579 q^{52} +4.43034 q^{53} +2.00502 q^{54} +2.70424 q^{55} +0.0865786 q^{56} -4.74611 q^{57} +1.08967 q^{58} +11.1709 q^{59} +1.28694 q^{60} -6.83482 q^{61} -2.64513 q^{62} -2.14824 q^{63} -8.15999 q^{64} +2.31660 q^{65} -8.51095 q^{66} -9.13398 q^{67} -5.41690 q^{68} +6.93512 q^{69} -2.74401 q^{70} -14.4281 q^{71} -0.0403022 q^{72} +13.1651 q^{73} -11.0915 q^{74} +4.59414 q^{75} +9.58762 q^{76} +9.11888 q^{77} -7.29095 q^{78} +9.58517 q^{79} +2.52240 q^{80} +1.00000 q^{81} -6.99415 q^{82} -4.96673 q^{83} +4.33965 q^{84} +1.70830 q^{85} -21.2667 q^{86} +0.543472 q^{87} +0.171076 q^{88} +6.84521 q^{89} +1.27733 q^{90} +7.81173 q^{91} -14.0096 q^{92} -1.31925 q^{93} -18.7876 q^{94} -3.02360 q^{95} -8.01927 q^{96} +17.1704 q^{97} +4.78214 q^{98} -4.24482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * q^99

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