LMFDB - Embedded newform 6005.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.97194 q^{2} +2.67165 q^{3} +1.88854 q^{4} +1.00000 q^{5} -5.26832 q^{6} -0.758910 q^{7} +0.219801 q^{8} +4.13769 q^{9} +O(q^{10})$	\(q-1.97194 q^{2} +2.67165 q^{3} +1.88854 q^{4} +1.00000 q^{5} -5.26832 q^{6} -0.758910 q^{7} +0.219801 q^{8} +4.13769 q^{9} -1.97194 q^{10} -4.86362 q^{11} +5.04550 q^{12} +5.71357 q^{13} +1.49652 q^{14} +2.67165 q^{15} -4.21050 q^{16} -2.56525 q^{17} -8.15926 q^{18} -6.14687 q^{19} +1.88854 q^{20} -2.02754 q^{21} +9.59074 q^{22} -3.97405 q^{23} +0.587231 q^{24} +1.00000 q^{25} -11.2668 q^{26} +3.03951 q^{27} -1.43323 q^{28} +4.75637 q^{29} -5.26832 q^{30} -7.52327 q^{31} +7.86325 q^{32} -12.9939 q^{33} +5.05852 q^{34} -0.758910 q^{35} +7.81417 q^{36} +8.83795 q^{37} +12.1212 q^{38} +15.2646 q^{39} +0.219801 q^{40} +1.57065 q^{41} +3.99818 q^{42} -2.18626 q^{43} -9.18511 q^{44} +4.13769 q^{45} +7.83658 q^{46} +1.33374 q^{47} -11.2490 q^{48} -6.42406 q^{49} -1.97194 q^{50} -6.85345 q^{51} +10.7903 q^{52} -0.843356 q^{53} -5.99371 q^{54} -4.86362 q^{55} -0.166809 q^{56} -16.4222 q^{57} -9.37927 q^{58} -2.08841 q^{59} +5.04550 q^{60} -7.91105 q^{61} +14.8354 q^{62} -3.14013 q^{63} -7.08482 q^{64} +5.71357 q^{65} +25.6231 q^{66} +4.54555 q^{67} -4.84457 q^{68} -10.6173 q^{69} +1.49652 q^{70} +2.60597 q^{71} +0.909470 q^{72} -4.53618 q^{73} -17.4279 q^{74} +2.67165 q^{75} -11.6086 q^{76} +3.69105 q^{77} -30.1009 q^{78} -14.8416 q^{79} -4.21050 q^{80} -4.29259 q^{81} -3.09722 q^{82} +7.11083 q^{83} -3.82908 q^{84} -2.56525 q^{85} +4.31117 q^{86} +12.7073 q^{87} -1.06903 q^{88} -7.00257 q^{89} -8.15926 q^{90} -4.33608 q^{91} -7.50514 q^{92} -20.0995 q^{93} -2.63005 q^{94} -6.14687 q^{95} +21.0078 q^{96} -0.518725 q^{97} +12.6678 q^{98} -20.1241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.97194	−1.39437	−0.697185	−	0.716891i	$-0.745564\pi$
$2$	−1.97194	−1.39437	−0.697185	+	0.716891i	$0.745564\pi$
$3$	2.67165	1.54248	0.771238	−	0.636547i	$-0.219638\pi$
$3$	2.67165	1.54248	0.771238	+	0.636547i	$0.219638\pi$
$4$	1.88854	0.944268
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.26832	−2.15078
$7$	−0.758910	−0.286841	−0.143421	−	0.989662i	$-0.545810\pi$
$7$	−0.758910	−0.286841	−0.143421	+	0.989662i	$0.545810\pi$
$8$	0.219801	0.0777115
$9$	4.13769	1.37923
$10$	−1.97194	−0.623581
$11$	−4.86362	−1.46644	−0.733218	−	0.679994i	$-0.761982\pi$
$11$	−4.86362	−1.46644	−0.733218	+	0.679994i	$0.761982\pi$
$12$	5.04550	1.45651
$13$	5.71357	1.58466	0.792329	−	0.610094i	$-0.208868\pi$
$13$	5.71357	1.58466	0.792329	+	0.610094i	$0.208868\pi$
$14$	1.49652	0.399963
$15$	2.67165	0.689816
$16$	−4.21050	−1.05263
$17$	−2.56525	−0.622165	−0.311083	−	0.950383i	$-0.600692\pi$
$17$	−2.56525	−0.622165	−0.311083	+	0.950383i	$0.600692\pi$
$18$	−8.15926	−1.92316
$19$	−6.14687	−1.41019	−0.705094	−	0.709114i	$-0.749095\pi$
$19$	−6.14687	−1.41019	−0.705094	+	0.709114i	$0.749095\pi$
$20$	1.88854	0.422289
$21$	−2.02754	−0.442445
$22$	9.59074	2.04475
$23$	−3.97405	−0.828647	−0.414324	−	0.910130i	$-0.635982\pi$
$23$	−3.97405	−0.828647	−0.414324	+	0.910130i	$0.635982\pi$
$24$	0.587231	0.119868
$25$	1.00000	0.200000
$26$	−11.2668	−2.20960
$27$	3.03951	0.584953
$28$	−1.43323	−0.270855
$29$	4.75637	0.883236	0.441618	−	0.897203i	$-0.354405\pi$
$29$	4.75637	0.883236	0.441618	+	0.897203i	$0.354405\pi$
$30$	−5.26832	−0.961859
$31$	−7.52327	−1.35122	−0.675610	−	0.737259i	$-0.736120\pi$
$31$	−7.52327	−1.35122	−0.675610	+	0.737259i	$0.736120\pi$
$32$	7.86325	1.39004
$33$	−12.9939	−2.26194
$34$	5.05852	0.867529
$35$	−0.758910	−0.128279
$36$	7.81417	1.30236
$37$	8.83795	1.45295	0.726475	−	0.687193i	$-0.241157\pi$
$37$	8.83795	1.45295	0.726475	+	0.687193i	$0.241157\pi$
$38$	12.1212	1.96632
$39$	15.2646	2.44430
$40$	0.219801	0.0347536
$41$	1.57065	0.245294	0.122647	−	0.992450i	$-0.460862\pi$
$41$	1.57065	0.245294	0.122647	+	0.992450i	$0.460862\pi$
$42$	3.99818	0.616932
$43$	−2.18626	−0.333401	−0.166701	−	0.986008i	$-0.553311\pi$
$43$	−2.18626	−0.333401	−0.166701	+	0.986008i	$0.553311\pi$
$44$	−9.18511	−1.38471
$45$	4.13769	0.616810
$46$	7.83658	1.15544
$47$	1.33374	0.194546	0.0972728	−	0.995258i	$-0.468988\pi$
$47$	1.33374	0.194546	0.0972728	+	0.995258i	$0.468988\pi$
$48$	−11.2490	−1.62365
$49$	−6.42406	−0.917722
$50$	−1.97194	−0.278874
$51$	−6.85345	−0.959675
$52$	10.7903	1.49634
$53$	−0.843356	−0.115844	−0.0579219	−	0.998321i	$-0.518447\pi$
$53$	−0.843356	−0.115844	−0.0579219	+	0.998321i	$0.518447\pi$
$54$	−5.99371	−0.815641
$55$	−4.86362	−0.655810
$56$	−0.166809	−0.0222908
$57$	−16.4222	−2.17518
$58$	−9.37927	−1.23156
$59$	−2.08841	−0.271888	−0.135944	−	0.990717i	$-0.543407\pi$
$59$	−2.08841	−0.271888	−0.135944	+	0.990717i	$0.543407\pi$
$60$	5.04550	0.651371
$61$	−7.91105	−1.01291	−0.506453	−	0.862268i	$-0.669044\pi$
$61$	−7.91105	−1.01291	−0.506453	+	0.862268i	$0.669044\pi$
$62$	14.8354	1.88410
$63$	−3.14013	−0.395620
$64$	−7.08482	−0.885602
$65$	5.71357	0.708681
$66$	25.6231	3.15398
$67$	4.54555	0.555328	0.277664	−	0.960678i	$-0.410440\pi$
$67$	4.54555	0.555328	0.277664	+	0.960678i	$0.410440\pi$
$68$	−4.84457	−0.587491
$69$	−10.6173	−1.27817
$70$	1.49652	0.178869
$71$	2.60597	0.309272	0.154636	−	0.987971i	$-0.450579\pi$
$71$	2.60597	0.309272	0.154636	+	0.987971i	$0.450579\pi$
$72$	0.909470	0.107182
$73$	−4.53618	−0.530920	−0.265460	−	0.964122i	$-0.585524\pi$
$73$	−4.53618	−0.530920	−0.265460	+	0.964122i	$0.585524\pi$
$74$	−17.4279	−2.02595
$75$	2.67165	0.308495
$76$	−11.6086	−1.33159
$77$	3.69105	0.420634
$78$	−30.1009	−3.40825
$79$	−14.8416	−1.66982	−0.834908	−	0.550390i	$-0.814479\pi$
$79$	−14.8416	−1.66982	−0.834908	+	0.550390i	$0.814479\pi$
$80$	−4.21050	−0.470749
$81$	−4.29259	−0.476954
$82$	−3.09722	−0.342031
$83$	7.11083	0.780515	0.390258	−	0.920706i	$-0.372386\pi$
$83$	7.11083	0.780515	0.390258	+	0.920706i	$0.372386\pi$
$84$	−3.82908	−0.417787
$85$	−2.56525	−0.278241
$86$	4.31117	0.464885
$87$	12.7073	1.36237
$88$	−1.06903	−0.113959
$89$	−7.00257	−0.742271	−0.371136	−	0.928579i	$-0.621032\pi$
$89$	−7.00257	−0.742271	−0.371136	+	0.928579i	$0.621032\pi$
$90$	−8.15926	−0.860062
$91$	−4.33608	−0.454545
$92$	−7.50514	−0.782465
$93$	−20.0995	−2.08422
$94$	−2.63005	−0.271269
$95$	−6.14687	−0.630655
$96$	21.0078	2.14410
$97$	−0.518725	−0.0526686	−0.0263343	−	0.999653i	$-0.508383\pi$
$97$	−0.518725	−0.0526686	−0.0263343	+	0.999653i	$0.508383\pi$
$98$	12.6678	1.27964
$99$	−20.1241	−2.02255
$100$	1.88854	0.188854
$101$	−17.8324	−1.77439	−0.887193	−	0.461398i	$-0.847348\pi$
$101$	−17.8324	−1.77439	−0.887193	+	0.461398i	$0.847348\pi$
$102$	13.5146	1.33814
$103$	0.376316	0.0370795	0.0185398	−	0.999828i	$-0.494098\pi$
$103$	0.376316	0.0370795	0.0185398	+	0.999828i	$0.494098\pi$
$104$	1.25585	0.123146
$105$	−2.02754	−0.197868
$106$	1.66305	0.161529
$107$	7.21720	0.697713	0.348857	−	0.937176i	$-0.386570\pi$
$107$	7.21720	0.697713	0.348857	+	0.937176i	$0.386570\pi$
$108$	5.74021	0.552352
$109$	−7.55044	−0.723201	−0.361601	−	0.932333i	$-0.617770\pi$
$109$	−7.55044	−0.723201	−0.361601	+	0.932333i	$0.617770\pi$
$110$	9.59074	0.914441
$111$	23.6119	2.24114
$112$	3.19539	0.301936
$113$	11.7524	1.10557	0.552787	−	0.833323i	$-0.313564\pi$
$113$	11.7524	1.10557	0.552787	+	0.833323i	$0.313564\pi$
$114$	32.3836	3.03301
$115$	−3.97405	−0.370582
$116$	8.98258	0.834012
$117$	23.6410	2.18561
$118$	4.11821	0.379112
$119$	1.94680	0.178463
$120$	0.587231	0.0536066
$121$	12.6548	1.15043
$122$	15.6001	1.41237
$123$	4.19622	0.378360
$124$	−14.2080	−1.27591
$125$	1.00000	0.0894427
$126$	6.19215	0.551640
$127$	−3.34177	−0.296534	−0.148267	−	0.988947i	$-0.547370\pi$
$127$	−3.34177	−0.296534	−0.148267	+	0.988947i	$0.547370\pi$
$128$	−1.75568	−0.155182
$129$	−5.84091	−0.514264
$130$	−11.2668	−0.988163
$131$	−0.893907	−0.0781010	−0.0390505	−	0.999237i	$-0.512433\pi$
$131$	−0.893907	−0.0781010	−0.0390505	+	0.999237i	$0.512433\pi$
$132$	−24.5394	−2.13588
$133$	4.66492	0.404500
$134$	−8.96355	−0.774333
$135$	3.03951	0.261599
$136$	−0.563846	−0.0483494
$137$	5.67981	0.485259	0.242629	−	0.970119i	$-0.421990\pi$
$137$	5.67981	0.485259	0.242629	+	0.970119i	$0.421990\pi$
$138$	20.9366	1.78224
$139$	13.7243	1.16408	0.582040	−	0.813160i	$-0.302255\pi$
$139$	13.7243	1.16408	0.582040	+	0.813160i	$0.302255\pi$
$140$	−1.43323	−0.121130
$141$	3.56328	0.300082
$142$	−5.13882	−0.431240
$143$	−27.7886	−2.32380
$144$	−17.4218	−1.45181
$145$	4.75637	0.394995
$146$	8.94506	0.740298
$147$	−17.1628	−1.41556
$148$	16.6908	1.37197
$149$	−12.2620	−1.00454	−0.502271	−	0.864710i	$-0.667502\pi$
$149$	−12.2620	−1.00454	−0.502271	+	0.864710i	$0.667502\pi$
$150$	−5.26832	−0.430156
$151$	−14.9553	−1.21704	−0.608522	−	0.793537i	$-0.708237\pi$
$151$	−14.9553	−1.21704	−0.608522	+	0.793537i	$0.708237\pi$
$152$	−1.35109	−0.109588
$153$	−10.6142	−0.858109
$154$	−7.27851	−0.586519
$155$	−7.52327	−0.604284
$156$	28.8278	2.30807
$157$	−12.9951	−1.03712	−0.518562	−	0.855040i	$-0.673532\pi$
$157$	−12.9951	−1.03712	−0.518562	+	0.855040i	$0.673532\pi$
$158$	29.2668	2.32834
$159$	−2.25315	−0.178686
$160$	7.86325	0.621644
$161$	3.01595	0.237690
$162$	8.46472	0.665051
$163$	−20.4811	−1.60420	−0.802101	−	0.597189i	$-0.796284\pi$
$163$	−20.4811	−1.60420	−0.802101	+	0.597189i	$0.796284\pi$
$164$	2.96622	0.231623
$165$	−12.9939	−1.01157
$166$	−14.0221	−1.08833
$167$	−0.844724	−0.0653667	−0.0326834	−	0.999466i	$-0.510405\pi$
$167$	−0.844724	−0.0653667	−0.0326834	+	0.999466i	$0.510405\pi$
$168$	−0.445656	−0.0343831
$169$	19.6448	1.51114
$170$	5.05852	0.387971
$171$	−25.4338	−1.94497
$172$	−4.12883	−0.314820
$173$	−6.52772	−0.496294	−0.248147	−	0.968722i	$-0.579822\pi$
$173$	−6.52772	−0.496294	−0.248147	+	0.968722i	$0.579822\pi$
$174$	−25.0581	−1.89965
$175$	−0.758910	−0.0573682
$176$	20.4783	1.54361
$177$	−5.57949	−0.419380
$178$	13.8086	1.03500
$179$	−19.6047	−1.46533	−0.732664	−	0.680591i	$-0.761723\pi$
$179$	−19.6047	−1.46533	−0.732664	+	0.680591i	$0.761723\pi$
$180$	7.81417	0.582434
$181$	−13.8791	−1.03162	−0.515812	−	0.856702i	$-0.672510\pi$
$181$	−13.8791	−1.03162	−0.515812	+	0.856702i	$0.672510\pi$
$182$	8.55048	0.633804
$183$	−21.1355	−1.56238
$184$	−0.873502	−0.0643954
$185$	8.83795	0.649779
$186$	39.6350	2.90618
$187$	12.4764	0.912365
$188$	2.51881	0.183703
$189$	−2.30671	−0.167789
$190$	12.1212	0.879366
$191$	−4.26043	−0.308274	−0.154137	−	0.988050i	$-0.549260\pi$
$191$	−4.26043	−0.308274	−0.154137	+	0.988050i	$0.549260\pi$
$192$	−18.9281	−1.36602
$193$	1.32192	0.0951542	0.0475771	−	0.998868i	$-0.484850\pi$
$193$	1.32192	0.0951542	0.0475771	+	0.998868i	$0.484850\pi$
$194$	1.02289	0.0734395
$195$	15.2646	1.09312
$196$	−12.1321	−0.866575
$197$	19.2577	1.37205	0.686026	−	0.727577i	$-0.259354\pi$
$197$	19.2577	1.37205	0.686026	+	0.727577i	$0.259354\pi$
$198$	39.6835	2.82019
$199$	5.60812	0.397549	0.198774	−	0.980045i	$-0.436304\pi$
$199$	5.60812	0.397549	0.198774	+	0.980045i	$0.436304\pi$
$200$	0.219801	0.0155423
$201$	12.1441	0.856580
$202$	35.1643	2.47415
$203$	−3.60966	−0.253348
$204$	−12.9430	−0.906190
$205$	1.57065	0.109699
$206$	−0.742072	−0.0517026
$207$	−16.4434	−1.14289
$208$	−24.0570	−1.66805
$209$	29.8960	2.06795
$210$	3.99818	0.275901
$211$	5.17817	0.356480	0.178240	−	0.983987i	$-0.442960\pi$
$211$	5.17817	0.356480	0.178240	+	0.983987i	$0.442960\pi$
$212$	−1.59271	−0.109388
$213$	6.96224	0.477045
$214$	−14.2319	−0.972870
$215$	−2.18626	−0.149102
$216$	0.668087	0.0454576
$217$	5.70949	0.387585
$218$	14.8890	1.00841
$219$	−12.1191	−0.818930
$220$	−9.18511	−0.619260
$221$	−14.6567	−0.985919
$222$	−46.5611	−3.12498
$223$	−11.1958	−0.749728	−0.374864	−	0.927080i	$-0.622311\pi$
$223$	−11.1958	−0.749728	−0.374864	+	0.927080i	$0.622311\pi$
$224$	−5.96750	−0.398720
$225$	4.13769	0.275846
$226$	−23.1750	−1.54158
$227$	8.47399	0.562438	0.281219	−	0.959644i	$-0.409261\pi$
$227$	8.47399	0.562438	0.281219	+	0.959644i	$0.409261\pi$
$228$	−31.0140	−2.05395
$229$	1.72991	0.114315	0.0571577	−	0.998365i	$-0.481796\pi$
$229$	1.72991	0.114315	0.0571577	+	0.998365i	$0.481796\pi$
$230$	7.83658	0.516729
$231$	9.86117	0.648817
$232$	1.04546	0.0686376
$233$	18.1162	1.18683	0.593415	−	0.804896i	$-0.297779\pi$
$233$	18.1162	1.18683	0.593415	+	0.804896i	$0.297779\pi$
$234$	−46.6185	−3.04755
$235$	1.33374	0.0870035
$236$	−3.94404	−0.256735
$237$	−39.6516	−2.57565
$238$	−3.83896	−0.248843
$239$	7.39650	0.478440	0.239220	−	0.970965i	$-0.423108\pi$
$239$	7.39650	0.478440	0.239220	+	0.970965i	$0.423108\pi$
$240$	−11.2490	−0.726118
$241$	−26.2240	−1.68924	−0.844618	−	0.535369i	$-0.820173\pi$
$241$	−26.2240	−1.68924	−0.844618	+	0.535369i	$0.820173\pi$
$242$	−24.9544	−1.60413
$243$	−20.5868	−1.32064
$244$	−14.9403	−0.956454
$245$	−6.42406	−0.410418
$246$	−8.27467	−0.527574
$247$	−35.1205	−2.23466
$248$	−1.65362	−0.105005
$249$	18.9976	1.20393
$250$	−1.97194	−0.124716
$251$	25.3522	1.60022	0.800109	−	0.599855i	$-0.204775\pi$
$251$	25.3522	1.60022	0.800109	+	0.599855i	$0.204775\pi$
$252$	−5.93026	−0.373571
$253$	19.3283	1.21516
$254$	6.58976	0.413478
$255$	−6.85345	−0.429180
$256$	17.6317	1.10198
$257$	−9.39152	−0.585827	−0.292913	−	0.956139i	$-0.594625\pi$
$257$	−9.39152	−0.585827	−0.292913	+	0.956139i	$0.594625\pi$
$258$	11.5179	0.717074
$259$	−6.70721	−0.416766
$260$	10.7903	0.669184
$261$	19.6804	1.21819
$262$	1.76273	0.108902
$263$	10.6421	0.656217	0.328109	−	0.944640i	$-0.393589\pi$
$263$	10.6421	0.656217	0.328109	+	0.944640i	$0.393589\pi$
$264$	−2.85607	−0.175779
$265$	−0.843356	−0.0518070
$266$	−9.19892	−0.564022
$267$	−18.7084	−1.14494
$268$	8.58444	0.524378
$269$	−15.4087	−0.939486	−0.469743	−	0.882803i	$-0.655654\pi$
$269$	−15.4087	−0.939486	−0.469743	+	0.882803i	$0.655654\pi$
$270$	−5.99371	−0.364766
$271$	−16.3167	−0.991168	−0.495584	−	0.868560i	$-0.665046\pi$
$271$	−16.3167	−0.991168	−0.495584	+	0.868560i	$0.665046\pi$
$272$	10.8010	0.654908
$273$	−11.5845	−0.701124
$274$	−11.2002	−0.676630
$275$	−4.86362	−0.293287
$276$	−20.0511	−1.20693
$277$	32.4204	1.94795	0.973975	−	0.226654i	$-0.0727787\pi$
$277$	32.4204	1.94795	0.973975	+	0.226654i	$0.0727787\pi$
$278$	−27.0635	−1.62316
$279$	−31.1290	−1.86364
$280$	−0.166809	−0.00996877
$281$	12.8482	0.766462	0.383231	−	0.923652i	$-0.374811\pi$
$281$	12.8482	0.766462	0.383231	+	0.923652i	$0.374811\pi$
$282$	−7.02655	−0.418425
$283$	−1.72443	−0.102507	−0.0512534	−	0.998686i	$-0.516322\pi$
$283$	−1.72443	−0.102507	−0.0512534	+	0.998686i	$0.516322\pi$
$284$	4.92147	0.292036
$285$	−16.4222	−0.972770
$286$	54.7973	3.24023
$287$	−1.19198	−0.0703604
$288$	32.5357	1.91718
$289$	−10.4195	−0.612910
$290$	−9.37927	−0.550770
$291$	−1.38585	−0.0812400
$292$	−8.56673	−0.501330
$293$	−14.9168	−0.871449	−0.435725	−	0.900080i	$-0.643508\pi$
$293$	−14.9168	−0.871449	−0.435725	+	0.900080i	$0.643508\pi$
$294$	33.8440	1.97382
$295$	−2.08841	−0.121592
$296$	1.94259	0.112911
$297$	−14.7830	−0.857796
$298$	24.1799	1.40070
$299$	−22.7060	−1.31312
$300$	5.04550	0.291302
$301$	1.65917	0.0956332
$302$	29.4909	1.69701
$303$	−47.6418	−2.73695
$304$	25.8814	1.48440
$305$	−7.91105	−0.452985
$306$	20.9306	1.19652
$307$	−30.6581	−1.74975	−0.874876	−	0.484346i	$-0.839057\pi$
$307$	−30.6581	−1.74975	−0.874876	+	0.484346i	$0.839057\pi$
$308$	6.97067	0.397191
$309$	1.00538	0.0571943
$310$	14.8354	0.842595
$311$	4.61820	0.261874	0.130937	−	0.991391i	$-0.458201\pi$
$311$	4.61820	0.261874	0.130937	+	0.991391i	$0.458201\pi$
$312$	3.35518	0.189950
$313$	−26.3711	−1.49058	−0.745292	−	0.666738i	$-0.767690\pi$
$313$	−26.3711	−1.49058	−0.745292	+	0.666738i	$0.767690\pi$
$314$	25.6256	1.44613
$315$	−3.14013	−0.176927
$316$	−28.0290	−1.57675
$317$	−20.3633	−1.14372	−0.571859	−	0.820352i	$-0.693777\pi$
$317$	−20.3633	−1.14372	−0.571859	+	0.820352i	$0.693777\pi$
$318$	4.44307	0.249155
$319$	−23.1332	−1.29521
$320$	−7.08482	−0.396053
$321$	19.2818	1.07621
$322$	−5.94726	−0.331428
$323$	15.7683	0.877370
$324$	−8.10671	−0.450373
$325$	5.71357	0.316932
$326$	40.3874	2.23685
$327$	−20.1721	−1.11552
$328$	0.345230	0.0190622
$329$	−1.01219	−0.0558037
$330$	25.6231	1.41050
$331$	23.8474	1.31077	0.655386	−	0.755294i	$-0.272506\pi$
$331$	23.8474	1.31077	0.655386	+	0.755294i	$0.272506\pi$
$332$	13.4291	0.737016
$333$	36.5687	2.00395
$334$	1.66574	0.0911454
$335$	4.54555	0.248350
$336$	8.53696	0.465729
$337$	18.1034	0.986157	0.493078	−	0.869985i	$-0.335872\pi$
$337$	18.1034	0.986157	0.493078	+	0.869985i	$0.335872\pi$
$338$	−38.7384	−2.10709
$339$	31.3983	1.70532
$340$	−4.84457	−0.262734
$341$	36.5903	1.98148
$342$	50.1539	2.71201
$343$	10.1877	0.550081
$344$	−0.480543	−0.0259091
$345$	−10.6173	−0.571614
$346$	12.8723	0.692017
$347$	−13.3798	−0.718267	−0.359133	−	0.933286i	$-0.616928\pi$
$347$	−13.3798	−0.718267	−0.359133	+	0.933286i	$0.616928\pi$
$348$	23.9983	1.28644
$349$	17.0630	0.913359	0.456680	−	0.889631i	$-0.349039\pi$
$349$	17.0630	0.913359	0.456680	+	0.889631i	$0.349039\pi$
$350$	1.49652	0.0799925
$351$	17.3664	0.926951
$352$	−38.2438	−2.03840
$353$	−15.0767	−0.802452	−0.401226	−	0.915979i	$-0.631416\pi$
$353$	−15.0767	−0.802452	−0.401226	+	0.915979i	$0.631416\pi$
$354$	11.0024	0.584771
$355$	2.60597	0.138311
$356$	−13.2246	−0.700903
$357$	5.20115	0.275274
$358$	38.6593	2.04321
$359$	−23.7538	−1.25368	−0.626839	−	0.779149i	$-0.715652\pi$
$359$	−23.7538	−1.25368	−0.626839	+	0.779149i	$0.715652\pi$
$360$	0.909470	0.0479333
$361$	18.7840	0.988629
$362$	27.3687	1.43846
$363$	33.8090	1.77451
$364$	−8.18884	−0.429212
$365$	−4.53618	−0.237434
$366$	41.6779	2.17854
$367$	−1.25028	−0.0652639	−0.0326320	−	0.999467i	$-0.510389\pi$
$367$	−1.25028	−0.0652639	−0.0326320	+	0.999467i	$0.510389\pi$
$368$	16.7328	0.872256
$369$	6.49886	0.338317
$370$	−17.4279	−0.906032
$371$	0.640031	0.0332288
$372$	−37.9586	−1.96806
$373$	15.5111	0.803134	0.401567	−	0.915830i	$-0.368466\pi$
$373$	15.5111	0.803134	0.401567	+	0.915830i	$0.368466\pi$
$374$	−24.6027	−1.27217
$375$	2.67165	0.137963
$376$	0.293157	0.0151184
$377$	27.1759	1.39963
$378$	4.54869	0.233959
$379$	22.7356	1.16785	0.583925	−	0.811807i	$-0.301516\pi$
$379$	22.7356	1.16785	0.583925	+	0.811807i	$0.301516\pi$
$380$	−11.6086	−0.595507
$381$	−8.92803	−0.457397
$382$	8.40129	0.429847
$383$	−3.21256	−0.164154	−0.0820770	−	0.996626i	$-0.526155\pi$
$383$	−3.21256	−0.164154	−0.0820770	+	0.996626i	$0.526155\pi$
$384$	−4.69055	−0.239364
$385$	3.69105	0.188113
$386$	−2.60675	−0.132680
$387$	−9.04607	−0.459837
$388$	−0.979631	−0.0497332
$389$	12.3152	0.624405	0.312202	−	0.950016i	$-0.398933\pi$
$389$	12.3152	0.624405	0.312202	+	0.950016i	$0.398933\pi$
$390$	−30.1009	−1.52422
$391$	10.1945	0.515556
$392$	−1.41202	−0.0713176
$393$	−2.38820	−0.120469
$394$	−37.9749	−1.91315
$395$	−14.8416	−0.746764
$396$	−38.0051	−1.90983
$397$	19.7555	0.991499	0.495749	−	0.868466i	$-0.334893\pi$
$397$	19.7555	0.991499	0.495749	+	0.868466i	$0.334893\pi$
$398$	−11.0589	−0.554330
$399$	12.4630	0.623931
$400$	−4.21050	−0.210525
$401$	15.1760	0.757854	0.378927	−	0.925427i	$-0.376293\pi$
$401$	15.1760	0.757854	0.378927	+	0.925427i	$0.376293\pi$
$402$	−23.9474	−1.19439
$403$	−42.9847	−2.14122
$404$	−33.6771	−1.67550
$405$	−4.29259	−0.213301
$406$	7.11802	0.353261
$407$	−42.9844	−2.13066
$408$	−1.50640	−0.0745778
$409$	22.9682	1.13570	0.567852	−	0.823131i	$-0.307775\pi$
$409$	22.9682	1.13570	0.567852	+	0.823131i	$0.307775\pi$
$410$	−3.09722	−0.152961
$411$	15.1744	0.748500
$412$	0.710687	0.0350130
$413$	1.58492	0.0779886
$414$	32.4253	1.59362
$415$	7.11083	0.349057
$416$	44.9272	2.20274
$417$	36.6665	1.79556
$418$	−58.9530	−2.88349
$419$	−32.4871	−1.58710	−0.793550	−	0.608505i	$-0.791769\pi$
$419$	−32.4871	−1.58710	−0.793550	+	0.608505i	$0.791769\pi$
$420$	−3.82908	−0.186840
$421$	12.3517	0.601985	0.300992	−	0.953627i	$-0.402682\pi$
$421$	12.3517	0.601985	0.300992	+	0.953627i	$0.402682\pi$
$422$	−10.2110	−0.497064
$423$	5.51859	0.268323
$424$	−0.185371	−0.00900240
$425$	−2.56525	−0.124433
$426$	−13.7291	−0.665177
$427$	6.00377	0.290543
$428$	13.6299	0.658828
$429$	−74.2413	−3.58440
$430$	4.31117	0.207903
$431$	14.6174	0.704095	0.352048	−	0.935982i	$-0.385486\pi$
$431$	14.6174	0.704095	0.352048	+	0.935982i	$0.385486\pi$
$432$	−12.7979	−0.615737
$433$	−15.9840	−0.768143	−0.384072	−	0.923303i	$-0.625478\pi$
$433$	−15.9840	−0.768143	−0.384072	+	0.923303i	$0.625478\pi$
$434$	−11.2587	−0.540437
$435$	12.7073	0.609271
$436$	−14.2593	−0.682896
$437$	24.4280	1.16855
$438$	23.8980	1.14189
$439$	33.9579	1.62072	0.810361	−	0.585931i	$-0.199271\pi$
$439$	33.9579	1.62072	0.810361	+	0.585931i	$0.199271\pi$
$440$	−1.06903	−0.0509639
$441$	−26.5808	−1.26575
$442$	28.9022	1.37474
$443$	27.1196	1.28849	0.644245	−	0.764819i	$-0.277172\pi$
$443$	27.1196	1.28849	0.644245	+	0.764819i	$0.277172\pi$
$444$	44.5918	2.11624
$445$	−7.00257	−0.331954
$446$	22.0775	1.04540
$447$	−32.7597	−1.54948
$448$	5.37674	0.254027
$449$	−6.02246	−0.284218	−0.142109	−	0.989851i	$-0.545388\pi$
$449$	−6.02246	−0.284218	−0.142109	+	0.989851i	$0.545388\pi$
$450$	−8.15926	−0.384631
$451$	−7.63903	−0.359708
$452$	22.1948	1.04396
$453$	−39.9552	−1.87726
$454$	−16.7102	−0.784247
$455$	−4.33608	−0.203279
$456$	−3.60963	−0.169036
$457$	11.6420	0.544591	0.272295	−	0.962214i	$-0.412217\pi$
$457$	11.6420	0.544591	0.272295	+	0.962214i	$0.412217\pi$
$458$	−3.41127	−0.159398
$459$	−7.79710	−0.363938
$460$	−7.50514	−0.349929
$461$	15.5795	0.725611	0.362805	−	0.931865i	$-0.381819\pi$
$461$	15.5795	0.725611	0.362805	+	0.931865i	$0.381819\pi$
$462$	−19.4456	−0.904691
$463$	−13.0699	−0.607410	−0.303705	−	0.952766i	$-0.598224\pi$
$463$	−13.0699	−0.607410	−0.303705	+	0.952766i	$0.598224\pi$
$464$	−20.0267	−0.929718
$465$	−20.0995	−0.932093
$466$	−35.7240	−1.65488
$467$	11.6093	0.537214	0.268607	−	0.963250i	$-0.413437\pi$
$467$	11.6093	0.537214	0.268607	+	0.963250i	$0.413437\pi$
$468$	44.6468	2.06380
$469$	−3.44967	−0.159291
$470$	−2.63005	−0.121315
$471$	−34.7184	−1.59974
$472$	−0.459035	−0.0211288
$473$	10.6331	0.488912
$474$	78.1905	3.59141
$475$	−6.14687	−0.282038
$476$	3.67659	0.168516
$477$	−3.48955	−0.159775
$478$	−14.5854	−0.667122
$479$	14.0731	0.643015	0.321507	−	0.946907i	$-0.395811\pi$
$479$	14.0731	0.643015	0.321507	+	0.946907i	$0.395811\pi$
$480$	21.0078	0.958871
$481$	50.4962	2.30243
$482$	51.7121	2.35542
$483$	8.05754	0.366631
$484$	23.8990	1.08632
$485$	−0.518725	−0.0235541
$486$	40.5959	1.84147
$487$	−26.8841	−1.21823	−0.609117	−	0.793080i	$-0.708476\pi$
$487$	−26.8841	−1.21823	−0.609117	+	0.793080i	$0.708476\pi$
$488$	−1.73886	−0.0787144
$489$	−54.7182	−2.47444
$490$	12.6678	0.572274
$491$	−9.88551	−0.446127	−0.223063	−	0.974804i	$-0.571606\pi$
$491$	−9.88551	−0.446127	−0.223063	+	0.974804i	$0.571606\pi$
$492$	7.92470	0.357273
$493$	−12.2013	−0.549519
$494$	69.2554	3.11595
$495$	−20.1241	−0.904513
$496$	31.6768	1.42233
$497$	−1.97770	−0.0887119
$498$	−37.4621	−1.67872
$499$	11.9210	0.533658	0.266829	−	0.963744i	$-0.414024\pi$
$499$	11.9210	0.533658	0.266829	+	0.963744i	$0.414024\pi$
$500$	1.88854	0.0844579
$501$	−2.25680	−0.100827
$502$	−49.9930	−2.23130
$503$	−43.5703	−1.94270	−0.971352	−	0.237646i	$-0.923624\pi$
$503$	−43.5703	−1.94270	−0.971352	+	0.237646i	$0.923624\pi$
$504$	−0.690206	−0.0307442
$505$	−17.8324	−0.793530
$506$	−38.1141	−1.69438
$507$	52.4840	2.33090
$508$	−6.31105	−0.280008
$509$	24.1971	1.07252	0.536259	−	0.844054i	$-0.319837\pi$
$509$	24.1971	1.07252	0.536259	+	0.844054i	$0.319837\pi$
$510$	13.5146	0.598435
$511$	3.44255	0.152290
$512$	−31.2573	−1.38139
$513$	−18.6834	−0.824894
$514$	18.5195	0.816859
$515$	0.376316	0.0165825
$516$	−11.0308	−0.485602
$517$	−6.48679	−0.285289
$518$	13.2262	0.581125
$519$	−17.4398	−0.765521
$520$	1.25585	0.0550726
$521$	−5.35357	−0.234544	−0.117272	−	0.993100i	$-0.537415\pi$
$521$	−5.35357	−0.234544	−0.117272	+	0.993100i	$0.537415\pi$
$522$	−38.8085	−1.69860
$523$	2.65532	0.116109	0.0580546	−	0.998313i	$-0.481510\pi$
$523$	2.65532	0.116109	0.0580546	+	0.998313i	$0.481510\pi$
$524$	−1.68817	−0.0737482
$525$	−2.02754	−0.0884890
$526$	−20.9855	−0.915010
$527$	19.2991	0.840682
$528$	54.7107	2.38098
$529$	−7.20691	−0.313344
$530$	1.66305	0.0722381
$531$	−8.64120	−0.374996
$532$	8.80986	0.381956
$533$	8.97400	0.388707
$534$	36.8918	1.59646
$535$	7.21720	0.312027
$536$	0.999119	0.0431554
$537$	−52.3769	−2.26023
$538$	30.3850	1.30999
$539$	31.2441	1.34578
$540$	5.74021	0.247019
$541$	−35.5989	−1.53051	−0.765257	−	0.643725i	$-0.777388\pi$
$541$	−35.5989	−1.53051	−0.765257	+	0.643725i	$0.777388\pi$
$542$	32.1755	1.38206
$543$	−37.0800	−1.59125
$544$	−20.1712	−0.864834
$545$	−7.55044	−0.323425
$546$	22.8439	0.977627
$547$	3.96384	0.169481	0.0847407	−	0.996403i	$-0.472994\pi$
$547$	3.96384	0.169481	0.0847407	+	0.996403i	$0.472994\pi$
$548$	10.7265	0.458214
$549$	−32.7335	−1.39703
$550$	9.59074	0.408951
$551$	−29.2368	−1.24553
$552$	−2.33369	−0.0993283
$553$	11.2635	0.478972
$554$	−63.9309	−2.71616
$555$	23.6119	1.00227
$556$	25.9188	1.09920
$557$	41.1213	1.74237	0.871183	−	0.490958i	$-0.163353\pi$
$557$	41.1213	1.74237	0.871183	+	0.490958i	$0.163353\pi$
$558$	61.3844	2.59861
$559$	−12.4913	−0.528327
$560$	3.19539	0.135030
$561$	33.3325	1.40730
$562$	−25.3359	−1.06873
$563$	18.2684	0.769920	0.384960	−	0.922933i	$-0.374215\pi$
$563$	18.2684	0.769920	0.384960	+	0.922933i	$0.374215\pi$
$564$	6.72937	0.283358
$565$	11.7524	0.494427
$566$	3.40047	0.142933
$567$	3.25769	0.136810
$568$	0.572796	0.0240340
$569$	−22.6301	−0.948705	−0.474353	−	0.880335i	$-0.657318\pi$
$569$	−22.6301	−0.948705	−0.474353	+	0.880335i	$0.657318\pi$
$570$	32.3836	1.35640
$571$	−23.0389	−0.964148	−0.482074	−	0.876131i	$-0.660116\pi$
$571$	−23.0389	−0.964148	−0.482074	+	0.876131i	$0.660116\pi$
$572$	−52.4797	−2.19429
$573$	−11.3823	−0.475504
$574$	2.35051	0.0981084
$575$	−3.97405	−0.165729
$576$	−29.3148	−1.22145
$577$	26.5535	1.10543	0.552717	−	0.833369i	$-0.313591\pi$
$577$	26.5535	1.10543	0.552717	+	0.833369i	$0.313591\pi$
$578$	20.5465	0.854624
$579$	3.53171	0.146773
$580$	8.98258	0.372981
$581$	−5.39648	−0.223884
$582$	2.73281	0.113279
$583$	4.10176	0.169878
$584$	−0.997058	−0.0412585
$585$	23.6410	0.977434
$586$	29.4150	1.21512
$587$	10.6810	0.440850	0.220425	−	0.975404i	$-0.429256\pi$
$587$	10.6810	0.440850	0.220425	+	0.975404i	$0.429256\pi$
$588$	−32.4126	−1.33667
$589$	46.2445	1.90547
$590$	4.11821	0.169544
$591$	51.4496	2.11636
$592$	−37.2122	−1.52941
$593$	18.1936	0.747122	0.373561	−	0.927606i	$-0.378137\pi$
$593$	18.1936	0.747122	0.373561	+	0.927606i	$0.378137\pi$
$594$	29.1511	1.19608
$595$	1.94680	0.0798109
$596$	−23.1572	−0.948557
$597$	14.9829	0.613209
$598$	44.7748	1.83098
$599$	32.8536	1.34236	0.671181	−	0.741294i	$-0.265787\pi$
$599$	32.8536	1.34236	0.671181	+	0.741294i	$0.265787\pi$
$600$	0.587231	0.0239736
$601$	23.4761	0.957611	0.478806	−	0.877921i	$-0.341070\pi$
$601$	23.4761	0.957611	0.478806	+	0.877921i	$0.341070\pi$
$602$	−3.27179	−0.133348
$603$	18.8081	0.765925
$604$	−28.2436	−1.14921
$605$	12.6548	0.514489
$606$	93.9466	3.81632
$607$	−4.97771	−0.202039	−0.101020	−	0.994884i	$-0.532210\pi$
$607$	−4.97771	−0.202039	−0.101020	+	0.994884i	$0.532210\pi$
$608$	−48.3343	−1.96022
$609$	−9.64373	−0.390784
$610$	15.6001	0.631629
$611$	7.62040	0.308288
$612$	−20.0453	−0.810285
$613$	−36.9284	−1.49153	−0.745763	−	0.666211i	$-0.767915\pi$
$613$	−36.9284	−1.49153	−0.745763	+	0.666211i	$0.767915\pi$
$614$	60.4559	2.43980
$615$	4.19622	0.169208
$616$	0.811297	0.0326881
$617$	12.6700	0.510075	0.255038	−	0.966931i	$-0.417912\pi$
$617$	12.6700	0.510075	0.255038	+	0.966931i	$0.417912\pi$
$618$	−1.98255	−0.0797500
$619$	−12.2945	−0.494158	−0.247079	−	0.968995i	$-0.579471\pi$
$619$	−12.2945	−0.494158	−0.247079	+	0.968995i	$0.579471\pi$
$620$	−14.2080	−0.570606
$621$	−12.0792	−0.484720
$622$	−9.10679	−0.365149
$623$	5.31432	0.212914
$624$	−64.2718	−2.57293
$625$	1.00000	0.0400000
$626$	52.0022	2.07843
$627$	79.8715	3.18976
$628$	−24.5417	−0.979322
$629$	−22.6716	−0.903975
$630$	6.19215	0.246701
$631$	−24.6606	−0.981723	−0.490862	−	0.871238i	$-0.663318\pi$
$631$	−24.6606	−0.981723	−0.490862	+	0.871238i	$0.663318\pi$
$632$	−3.26221	−0.129764
$633$	13.8342	0.549861
$634$	40.1552	1.59476
$635$	−3.34177	−0.132614
$636$	−4.25515	−0.168728
$637$	−36.7043	−1.45428
$638$	45.6172	1.80600
$639$	10.7827	0.426557
$640$	−1.75568	−0.0693993
$641$	−35.0858	−1.38581	−0.692904	−	0.721030i	$-0.743669\pi$
$641$	−35.0858	−1.38581	−0.692904	+	0.721030i	$0.743669\pi$
$642$	−38.0225	−1.50063
$643$	30.5513	1.20483	0.602414	−	0.798184i	$-0.294206\pi$
$643$	30.5513	1.20483	0.602414	+	0.798184i	$0.294206\pi$
$644$	5.69572	0.224443
$645$	−5.84091	−0.229986
$646$	−31.0940	−1.22338
$647$	−23.4545	−0.922092	−0.461046	−	0.887376i	$-0.652526\pi$
$647$	−23.4545	−0.922092	−0.461046	+	0.887376i	$0.652526\pi$
$648$	−0.943517	−0.0370648
$649$	10.1572	0.398706
$650$	−11.2668	−0.441920
$651$	15.2537	0.597841
$652$	−38.6792	−1.51480
$653$	9.47638	0.370839	0.185420	−	0.982659i	$-0.440636\pi$
$653$	9.47638	0.370839	0.185420	+	0.982659i	$0.440636\pi$
$654$	39.7781	1.55545
$655$	−0.893907	−0.0349278
$656$	−6.61322	−0.258203
$657$	−18.7693	−0.732260
$658$	1.99597	0.0778110
$659$	−34.8899	−1.35912	−0.679559	−	0.733621i	$-0.737829\pi$
$659$	−34.8899	−1.35912	−0.679559	+	0.733621i	$0.737829\pi$
$660$	−24.5394	−0.955193
$661$	−35.6680	−1.38733	−0.693663	−	0.720300i	$-0.744004\pi$
$661$	−35.6680	−1.38733	−0.693663	+	0.720300i	$0.744004\pi$
$662$	−47.0256	−1.82770
$663$	−39.1576	−1.52076
$664$	1.56297	0.0606550
$665$	4.66492	0.180898
$666$	−72.1112	−2.79425
$667$	−18.9021	−0.731891
$668$	−1.59529	−0.0617237
$669$	−29.9113	−1.15644
$670$	−8.96355	−0.346292
$671$	38.4763	1.48536
$672$	−15.9430	−0.615016
$673$	−29.9438	−1.15425	−0.577125	−	0.816656i	$-0.695825\pi$
$673$	−29.9438	−1.15425	−0.577125	+	0.816656i	$0.695825\pi$
$674$	−35.6988	−1.37507
$675$	3.03951	0.116991
$676$	37.1000	1.42692
$677$	20.1514	0.774483	0.387242	−	0.921978i	$-0.373428\pi$
$677$	20.1514	0.774483	0.387242	+	0.921978i	$0.373428\pi$
$678$	−61.9154	−2.37785
$679$	0.393666	0.0151075
$680$	−0.563846	−0.0216225
$681$	22.6395	0.867547
$682$	−72.1538	−2.76291
$683$	1.94739	0.0745150	0.0372575	−	0.999306i	$-0.488138\pi$
$683$	1.94739	0.0745150	0.0372575	+	0.999306i	$0.488138\pi$
$684$	−48.0327	−1.83658
$685$	5.67981	0.217014
$686$	−20.0894	−0.767017
$687$	4.62170	0.176329
$688$	9.20526	0.350947
$689$	−4.81857	−0.183573
$690$	20.9366	0.797041
$691$	−15.6527	−0.595459	−0.297729	−	0.954650i	$-0.596229\pi$
$691$	−15.6527	−0.595459	−0.297729	+	0.954650i	$0.596229\pi$
$692$	−12.3278	−0.468634
$693$	15.2724	0.580151
$694$	26.3842	1.00153
$695$	13.7243	0.520592
$696$	2.79309	0.105872
$697$	−4.02911	−0.152613
$698$	−33.6471	−1.27356
$699$	48.4000	1.83066
$700$	−1.43323	−0.0541709
$701$	25.7704	0.973333	0.486667	−	0.873588i	$-0.338213\pi$
$701$	25.7704	0.973333	0.486667	+	0.873588i	$0.338213\pi$
$702$	−34.2455	−1.29251
$703$	−54.3257	−2.04893
$704$	34.4578	1.29868
$705$	3.56328	0.134201
$706$	29.7303	1.11892
$707$	13.5332	0.508967
$708$	−10.5371	−0.396007
$709$	2.37271	0.0891090	0.0445545	−	0.999007i	$-0.485813\pi$
$709$	2.37271	0.0891090	0.0445545	+	0.999007i	$0.485813\pi$
$710$	−5.13882	−0.192856
$711$	−61.4101	−2.30306
$712$	−1.53917	−0.0576830
$713$	29.8979	1.11968
$714$	−10.2563	−0.383834
$715$	−27.7886	−1.03923
$716$	−37.0243	−1.38366
$717$	19.7608	0.737981
$718$	46.8410	1.74809
$719$	−7.85846	−0.293071	−0.146535	−	0.989205i	$-0.546812\pi$
$719$	−7.85846	−0.293071	−0.146535	+	0.989205i	$0.546812\pi$
$720$	−17.4218	−0.649271
$721$	−0.285590	−0.0106359
$722$	−37.0408	−1.37851
$723$	−70.0613	−2.60561
$724$	−26.2111	−0.974129
$725$	4.75637	0.176647
$726$	−66.6693	−2.47433
$727$	−48.8065	−1.81013	−0.905066	−	0.425271i	$-0.860179\pi$
$727$	−48.8065	−1.81013	−0.905066	+	0.425271i	$0.860179\pi$
$728$	−0.953076	−0.0353234
$729$	−42.1229	−1.56011
$730$	8.94506	0.331071
$731$	5.60831	0.207431
$732$	−39.9152	−1.47531
$733$	22.9573	0.847948	0.423974	−	0.905674i	$-0.360635\pi$
$733$	22.9573	0.847948	0.423974	+	0.905674i	$0.360635\pi$
$734$	2.46547	0.0910021
$735$	−17.1628	−0.633059
$736$	−31.2490	−1.15185
$737$	−22.1078	−0.814352
$738$	−12.8153	−0.471739
$739$	−12.3120	−0.452903	−0.226452	−	0.974022i	$-0.572713\pi$
$739$	−12.3120	−0.452903	−0.226452	+	0.974022i	$0.572713\pi$
$740$	16.6908	0.613565
$741$	−93.8296	−3.44692
$742$	−1.26210	−0.0463332
$743$	26.0325	0.955038	0.477519	−	0.878621i	$-0.341536\pi$
$743$	26.0325	0.955038	0.477519	+	0.878621i	$0.341536\pi$
$744$	−4.41790	−0.161968
$745$	−12.2620	−0.449245
$746$	−30.5869	−1.11987
$747$	29.4224	1.07651
$748$	23.5621	0.861517
$749$	−5.47721	−0.200133
$750$	−5.26832	−0.192372
$751$	−50.4439	−1.84072	−0.920362	−	0.391067i	$-0.872106\pi$
$751$	−50.4439	−1.84072	−0.920362	+	0.391067i	$0.872106\pi$
$752$	−5.61571	−0.204784
$753$	67.7321	2.46830
$754$	−53.5891	−1.95160
$755$	−14.9553	−0.544278
$756$	−4.35631	−0.158437
$757$	13.3240	0.484270	0.242135	−	0.970243i	$-0.422152\pi$
$757$	13.3240	0.484270	0.242135	+	0.970243i	$0.422152\pi$
$758$	−44.8332	−1.62842
$759$	51.6383	1.87435
$760$	−1.35109	−0.0490091
$761$	28.2974	1.02578	0.512890	−	0.858454i	$-0.328575\pi$
$761$	28.2974	1.02578	0.512890	+	0.858454i	$0.328575\pi$
$762$	17.6055	0.637780
$763$	5.73011	0.207444
$764$	−8.04596	−0.291093
$765$	−10.6142	−0.383758
$766$	6.33496	0.228891
$767$	−11.9323	−0.430849
$768$	47.1057	1.69978
$769$	−41.4339	−1.49414	−0.747071	−	0.664744i	$-0.768541\pi$
$769$	−41.4339	−1.49414	−0.747071	+	0.664744i	$0.768541\pi$
$770$	−7.27851	−0.262299
$771$	−25.0908	−0.903624
$772$	2.49650	0.0898510
$773$	−7.09112	−0.255050	−0.127525	−	0.991835i	$-0.540703\pi$
$773$	−7.09112	−0.255050	−0.127525	+	0.991835i	$0.540703\pi$
$774$	17.8383	0.641183
$775$	−7.52327	−0.270244
$776$	−0.114016	−0.00409295
$777$	−17.9193	−0.642851
$778$	−24.2848	−0.870652
$779$	−9.65456	−0.345911
$780$	28.8278	1.03220
$781$	−12.6745	−0.453528
$782$	−20.1028	−0.718875
$783$	14.4570	0.516652
$784$	27.0485	0.966018
$785$	−12.9951	−0.463816
$786$	4.70938	0.167978
$787$	38.8502	1.38486	0.692430	−	0.721485i	$-0.256540\pi$
$787$	38.8502	1.38486	0.692430	+	0.721485i	$0.256540\pi$
$788$	36.3688	1.29558
$789$	28.4318	1.01220
$790$	29.2668	1.04127
$791$	−8.91902	−0.317124
$792$	−4.42331	−0.157175
$793$	−45.2003	−1.60511
$794$	−38.9566	−1.38252
$795$	−2.25315	−0.0799110
$796$	10.5911	0.375393
$797$	−0.213706	−0.00756984	−0.00378492	−	0.999993i	$-0.501205\pi$
$797$	−0.213706	−0.00756984	−0.00378492	+	0.999993i	$0.501205\pi$
$798$	−24.5763	−0.869990
$799$	−3.42138	−0.121040
$800$	7.86325	0.278008
$801$	−28.9745	−1.02376
$802$	−29.9262	−1.05673
$803$	22.0622	0.778559
$804$	22.9346	0.808840
$805$	3.01595	0.106298
$806$	84.7631	2.98565
$807$	−41.1666	−1.44913
$808$	−3.91958	−0.137890
$809$	8.84575	0.311000	0.155500	−	0.987836i	$-0.450301\pi$
$809$	8.84575	0.311000	0.155500	+	0.987836i	$0.450301\pi$
$810$	8.46472	0.297420
$811$	−18.2881	−0.642180	−0.321090	−	0.947049i	$-0.604049\pi$
$811$	−18.2881	−0.642180	−0.321090	+	0.947049i	$0.604049\pi$
$812$	−6.81697	−0.239229
$813$	−43.5924	−1.52885
$814$	84.7625	2.97092
$815$	−20.4811	−0.717421
$816$	28.8565	1.01018
$817$	13.4386	0.470159
$818$	−45.2918	−1.58359
$819$	−17.9414	−0.626922
$820$	2.96622	0.103585
$821$	−45.0705	−1.57297	−0.786486	−	0.617609i	$-0.788102\pi$
$821$	−45.0705	−1.57297	−0.786486	+	0.617609i	$0.788102\pi$
$822$	−29.9230	−1.04369
$823$	−36.6412	−1.27723	−0.638616	−	0.769525i	$-0.720493\pi$
$823$	−36.6412	−1.27723	−0.638616	+	0.769525i	$0.720493\pi$
$824$	0.0827148	0.00288151
$825$	−12.9939	−0.452388
$826$	−3.12535	−0.108745
$827$	−27.0946	−0.942170	−0.471085	−	0.882088i	$-0.656138\pi$
$827$	−27.0946	−0.942170	−0.471085	+	0.882088i	$0.656138\pi$
$828$	−31.0539	−1.07920
$829$	−10.0859	−0.350296	−0.175148	−	0.984542i	$-0.556040\pi$
$829$	−10.0859	−0.350296	−0.175148	+	0.984542i	$0.556040\pi$
$830$	−14.0221	−0.486715
$831$	86.6157	3.00467
$832$	−40.4796	−1.40338
$833$	16.4793	0.570975
$834$	−72.3040	−2.50368
$835$	−0.844724	−0.0292329
$836$	56.4596	1.95270
$837$	−22.8670	−0.790400
$838$	64.0625	2.21300
$839$	47.2492	1.63122	0.815611	−	0.578601i	$-0.196401\pi$
$839$	47.2492	1.63122	0.815611	+	0.578601i	$0.196401\pi$
$840$	−0.445656	−0.0153766
$841$	−6.37691	−0.219893
$842$	−24.3568	−0.839390
$843$	34.3260	1.18225
$844$	9.77915	0.336612
$845$	19.6448	0.675803
$846$	−10.8823	−0.374142
$847$	−9.60382	−0.329991
$848$	3.55096	0.121940
$849$	−4.60707	−0.158114
$850$	5.05852	0.173506
$851$	−35.1225	−1.20398
$852$	13.1484	0.450458
$853$	51.0130	1.74665	0.873327	−	0.487135i	$-0.161958\pi$
$853$	51.0130	1.74665	0.873327	+	0.487135i	$0.161958\pi$
$854$	−11.8391	−0.405124
$855$	−25.4338	−0.869818
$856$	1.58635	0.0542203
$857$	17.0000	0.580710	0.290355	−	0.956919i	$-0.406227\pi$
$857$	17.0000	0.580710	0.290355	+	0.956919i	$0.406227\pi$
$858$	146.399	4.99798
$859$	32.3550	1.10394	0.551968	−	0.833865i	$-0.313877\pi$
$859$	32.3550	1.10394	0.551968	+	0.833865i	$0.313877\pi$
$860$	−4.12883	−0.140792
$861$	−3.18455	−0.108529
$862$	−28.8246	−0.981769
$863$	25.5724	0.870494	0.435247	−	0.900311i	$-0.356661\pi$
$863$	25.5724	0.870494	0.435247	+	0.900311i	$0.356661\pi$
$864$	23.9004	0.813108
$865$	−6.52772	−0.221949
$866$	31.5195	1.07108
$867$	−27.8371	−0.945399
$868$	10.7826	0.365984
$869$	72.1840	2.44868
$870$	−25.0581	−0.849549
$871$	25.9713	0.880005
$872$	−1.65960	−0.0562010
$873$	−2.14632	−0.0726421
$874$	−48.1704	−1.62939
$875$	−0.758910	−0.0256558
$876$	−22.8873	−0.773289
$877$	24.3685	0.822866	0.411433	−	0.911440i	$-0.365028\pi$
$877$	24.3685	0.822866	0.411433	+	0.911440i	$0.365028\pi$
$878$	−66.9628	−2.25988
$879$	−39.8524	−1.34419
$880$	20.4783	0.690323
$881$	−51.6198	−1.73912	−0.869558	−	0.493831i	$-0.835596\pi$
$881$	−51.6198	−1.73912	−0.869558	+	0.493831i	$0.835596\pi$
$882$	52.4156	1.76492
$883$	−35.8477	−1.20637	−0.603185	−	0.797601i	$-0.706102\pi$
$883$	−35.8477	−1.20637	−0.603185	+	0.797601i	$0.706102\pi$
$884$	−27.6798	−0.930972
$885$	−5.57949	−0.187553
$886$	−53.4781	−1.79663
$887$	33.8309	1.13593	0.567966	−	0.823052i	$-0.307730\pi$
$887$	33.8309	1.13593	0.567966	+	0.823052i	$0.307730\pi$
$888$	5.18992	0.174162
$889$	2.53610	0.0850582
$890$	13.8086	0.462866
$891$	20.8775	0.699423
$892$	−21.1437	−0.707944
$893$	−8.19831	−0.274346
$894$	64.6001	2.16055
$895$	−19.6047	−0.655314
$896$	1.33240	0.0445124
$897$	−60.6624	−2.02546
$898$	11.8759	0.396305
$899$	−35.7835	−1.19345
$900$	7.81417	0.260472
$901$	2.16342	0.0720741
$902$	15.0637	0.501566
$903$	4.43273	0.147512
$904$	2.58319	0.0859157
$905$	−13.8791	−0.461356
$906$	78.7891	2.61759
$907$	−54.9753	−1.82542	−0.912712	−	0.408604i	$-0.866016\pi$
$907$	−54.9753	−1.82542	−0.912712	+	0.408604i	$0.866016\pi$
$908$	16.0034	0.531092
$909$	−73.7848	−2.44729
$910$	8.55048	0.283446
$911$	−41.7412	−1.38295	−0.691474	−	0.722402i	$-0.743038\pi$
$911$	−41.7412	−1.38295	−0.691474	+	0.722402i	$0.743038\pi$
$912$	69.1459	2.28965
$913$	−34.5844	−1.14458
$914$	−22.9573	−0.759361
$915$	−21.1355	−0.698719
$916$	3.26699	0.107944
$917$	0.678395	0.0224026
$918$	15.3754	0.507464
$919$	−12.2698	−0.404743	−0.202371	−	0.979309i	$-0.564865\pi$
$919$	−12.2698	−0.404743	−0.202371	+	0.979309i	$0.564865\pi$
$920$	−0.873502	−0.0287985
$921$	−81.9077	−2.69895
$922$	−30.7218	−1.01177
$923$	14.8894	0.490091
$924$	18.6232	0.612657
$925$	8.83795	0.290590
$926$	25.7730	0.846954
$927$	1.55708	0.0511412
$928$	37.4005	1.22773
$929$	41.0325	1.34623	0.673116	−	0.739537i	$-0.264956\pi$
$929$	41.0325	1.34623	0.673116	+	0.739537i	$0.264956\pi$
$930$	39.6350	1.29968
$931$	39.4878	1.29416
$932$	34.2131	1.12069
$933$	12.3382	0.403934
$934$	−22.8928	−0.749075
$935$	12.4764	0.408022
$936$	5.19631	0.169847
$937$	−53.5341	−1.74888	−0.874442	−	0.485131i	$-0.838772\pi$
$937$	−53.5341	−1.74888	−0.874442	+	0.485131i	$0.838772\pi$
$938$	6.80253	0.222110
$939$	−70.4543	−2.29919
$940$	2.51881	0.0821546
$941$	49.4990	1.61362	0.806811	−	0.590810i	$-0.201192\pi$
$941$	49.4990	1.61362	0.806811	+	0.590810i	$0.201192\pi$
$942$	68.4624	2.23063
$943$	−6.24184	−0.203262
$944$	8.79326	0.286196
$945$	−2.30671	−0.0750373
$946$	−20.9679	−0.681724
$947$	−36.8294	−1.19680	−0.598398	−	0.801199i	$-0.704196\pi$
$947$	−36.8294	−1.19680	−0.598398	+	0.801199i	$0.704196\pi$
$948$	−74.8835	−2.43210
$949$	−25.9178	−0.841326
$950$	12.1212	0.393265
$951$	−54.4035	−1.76416
$952$	0.427908	0.0138686
$953$	57.3667	1.85829	0.929145	−	0.369716i	$-0.120545\pi$
$953$	57.3667	1.85829	0.929145	+	0.369716i	$0.120545\pi$
$954$	6.88117	0.222786
$955$	−4.26043	−0.137864
$956$	13.9685	0.451775
$957$	−61.8036	−1.99783
$958$	−27.7512	−0.896600
$959$	−4.31046	−0.139192
$960$	−18.9281	−0.610903
$961$	25.5996	0.825794
$962$	−99.5753	−3.21044
$963$	29.8625	0.962307
$964$	−49.5250	−1.59509
$965$	1.32192	0.0425542
$966$	−15.8890	−0.511219
$967$	−22.5891	−0.726416	−0.363208	−	0.931708i	$-0.618319\pi$
$967$	−22.5891	−0.726416	−0.363208	+	0.931708i	$0.618319\pi$
$968$	2.78153	0.0894018
$969$	42.1272	1.35332
$970$	1.02289	0.0328431
$971$	1.85943	0.0596718	0.0298359	−	0.999555i	$-0.490502\pi$
$971$	1.85943	0.0596718	0.0298359	+	0.999555i	$0.490502\pi$
$972$	−38.8789	−1.24704
$973$	−10.4155	−0.333906
$974$	53.0137	1.69867
$975$	15.2646	0.488859
$976$	33.3095	1.06621
$977$	−28.1503	−0.900609	−0.450304	−	0.892875i	$-0.648684\pi$
$977$	−28.1503	−0.900609	−0.450304	+	0.892875i	$0.648684\pi$
$978$	107.901	3.45029
$979$	34.0578	1.08849
$980$	−12.1321	−0.387544
$981$	−31.2414	−0.997461
$982$	19.4936	0.622066
$983$	−18.8234	−0.600373	−0.300186	−	0.953881i	$-0.597049\pi$
$983$	−18.8234	−0.600373	−0.300186	+	0.953881i	$0.597049\pi$
$984$	0.922333	0.0294029
$985$	19.2577	0.613600
$986$	24.0602	0.766233
$987$	−2.70421	−0.0860758
$988$	−66.3263	−2.11012
$989$	8.68831	0.276272
$990$	39.6835	1.26123
$991$	−13.5928	−0.431788	−0.215894	−	0.976417i	$-0.569267\pi$
$991$	−13.5928	−0.431788	−0.215894	+	0.976417i	$0.569267\pi$
$992$	−59.1574	−1.87825
$993$	63.7118	2.02183
$994$	3.89990	0.123697
$995$	5.60812	0.177789
$996$	35.8777	1.13683
$997$	−27.3863	−0.867334	−0.433667	−	0.901073i	$-0.642781\pi$
$997$	−27.3863	−0.867334	−0.433667	+	0.901073i	$0.642781\pi$
$998$	−23.5075	−0.744117
$999$	26.8630	0.849907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.17	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.17	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.97194 q^{2} +2.67165 q^{3} +1.88854 q^{4} +1.00000 q^{5} -5.26832 q^{6} -0.758910 q^{7} +0.219801 q^{8} +4.13769 q^{9} +O(q^{10})\)	\(q-1.97194 q^{2} +2.67165 q^{3} +1.88854 q^{4} +1.00000 q^{5} -5.26832 q^{6} -0.758910 q^{7} +0.219801 q^{8} +4.13769 q^{9} -1.97194 q^{10} -4.86362 q^{11} +5.04550 q^{12} +5.71357 q^{13} +1.49652 q^{14} +2.67165 q^{15} -4.21050 q^{16} -2.56525 q^{17} -8.15926 q^{18} -6.14687 q^{19} +1.88854 q^{20} -2.02754 q^{21} +9.59074 q^{22} -3.97405 q^{23} +0.587231 q^{24} +1.00000 q^{25} -11.2668 q^{26} +3.03951 q^{27} -1.43323 q^{28} +4.75637 q^{29} -5.26832 q^{30} -7.52327 q^{31} +7.86325 q^{32} -12.9939 q^{33} +5.05852 q^{34} -0.758910 q^{35} +7.81417 q^{36} +8.83795 q^{37} +12.1212 q^{38} +15.2646 q^{39} +0.219801 q^{40} +1.57065 q^{41} +3.99818 q^{42} -2.18626 q^{43} -9.18511 q^{44} +4.13769 q^{45} +7.83658 q^{46} +1.33374 q^{47} -11.2490 q^{48} -6.42406 q^{49} -1.97194 q^{50} -6.85345 q^{51} +10.7903 q^{52} -0.843356 q^{53} -5.99371 q^{54} -4.86362 q^{55} -0.166809 q^{56} -16.4222 q^{57} -9.37927 q^{58} -2.08841 q^{59} +5.04550 q^{60} -7.91105 q^{61} +14.8354 q^{62} -3.14013 q^{63} -7.08482 q^{64} +5.71357 q^{65} +25.6231 q^{66} +4.54555 q^{67} -4.84457 q^{68} -10.6173 q^{69} +1.49652 q^{70} +2.60597 q^{71} +0.909470 q^{72} -4.53618 q^{73} -17.4279 q^{74} +2.67165 q^{75} -11.6086 q^{76} +3.69105 q^{77} -30.1009 q^{78} -14.8416 q^{79} -4.21050 q^{80} -4.29259 q^{81} -3.09722 q^{82} +7.11083 q^{83} -3.82908 q^{84} -2.56525 q^{85} +4.31117 q^{86} +12.7073 q^{87} -1.06903 q^{88} -7.00257 q^{89} -8.15926 q^{90} -4.33608 q^{91} -7.50514 q^{92} -20.0995 q^{93} -2.63005 q^{94} -6.14687 q^{95} +21.0078 q^{96} -0.518725 q^{97} +12.6678 q^{98} -20.1241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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