LMFDB - Embedded newform 8027.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34386 q^{2} +0.672591 q^{3} +3.49366 q^{4} +0.169027 q^{5} -1.57646 q^{6} +4.26981 q^{7} -3.50093 q^{8} -2.54762 q^{9} +O(q^{10})$	\(q-2.34386 q^{2} +0.672591 q^{3} +3.49366 q^{4} +0.169027 q^{5} -1.57646 q^{6} +4.26981 q^{7} -3.50093 q^{8} -2.54762 q^{9} -0.396175 q^{10} +0.147008 q^{11} +2.34980 q^{12} -2.50657 q^{13} -10.0078 q^{14} +0.113686 q^{15} +1.21835 q^{16} -2.95147 q^{17} +5.97126 q^{18} -0.457223 q^{19} +0.590523 q^{20} +2.87183 q^{21} -0.344566 q^{22} -1.00000 q^{23} -2.35469 q^{24} -4.97143 q^{25} +5.87505 q^{26} -3.73128 q^{27} +14.9173 q^{28} +5.18134 q^{29} -0.266464 q^{30} +9.24201 q^{31} +4.14622 q^{32} +0.0988763 q^{33} +6.91783 q^{34} +0.721713 q^{35} -8.90053 q^{36} -11.5666 q^{37} +1.07166 q^{38} -1.68590 q^{39} -0.591752 q^{40} +0.989258 q^{41} -6.73117 q^{42} -12.1102 q^{43} +0.513597 q^{44} -0.430617 q^{45} +2.34386 q^{46} -7.05564 q^{47} +0.819452 q^{48} +11.2313 q^{49} +11.6523 q^{50} -1.98513 q^{51} -8.75712 q^{52} +10.6719 q^{53} +8.74558 q^{54} +0.0248483 q^{55} -14.9483 q^{56} -0.307524 q^{57} -12.1443 q^{58} +13.8068 q^{59} +0.397180 q^{60} +10.5654 q^{61} -21.6620 q^{62} -10.8779 q^{63} -12.1548 q^{64} -0.423679 q^{65} -0.231752 q^{66} +13.6670 q^{67} -10.3115 q^{68} -0.672591 q^{69} -1.69159 q^{70} -1.28142 q^{71} +8.91905 q^{72} -11.0364 q^{73} +27.1104 q^{74} -3.34374 q^{75} -1.59738 q^{76} +0.627697 q^{77} +3.95150 q^{78} +5.46466 q^{79} +0.205934 q^{80} +5.13324 q^{81} -2.31868 q^{82} +12.6422 q^{83} +10.0332 q^{84} -0.498879 q^{85} +28.3845 q^{86} +3.48492 q^{87} -0.514665 q^{88} +0.837415 q^{89} +1.00930 q^{90} -10.7026 q^{91} -3.49366 q^{92} +6.21609 q^{93} +16.5374 q^{94} -0.0772830 q^{95} +2.78871 q^{96} +5.54532 q^{97} -26.3245 q^{98} -0.374521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.34386	−1.65736	−0.828678	−	0.559725i	$-0.810907\pi$
$2$	−2.34386	−1.65736	−0.828678	+	0.559725i	$0.810907\pi$
$3$	0.672591	0.388320	0.194160	−	0.980970i	$-0.437802\pi$
$3$	0.672591	0.388320	0.194160	+	0.980970i	$0.437802\pi$
$4$	3.49366	1.74683
$5$	0.169027	0.0755912	0.0377956	−	0.999285i	$-0.487966\pi$
$5$	0.169027	0.0755912	0.0377956	+	0.999285i	$0.487966\pi$
$6$	−1.57646	−0.643585
$7$	4.26981	1.61384	0.806919	−	0.590663i	$-0.201134\pi$
$7$	4.26981	1.61384	0.806919	+	0.590663i	$0.201134\pi$
$8$	−3.50093	−1.23777
$9$	−2.54762	−0.849207
$10$	−0.396175	−0.125282
$11$	0.147008	0.0443246	0.0221623	−	0.999754i	$-0.492945\pi$
$11$	0.147008	0.0443246	0.0221623	+	0.999754i	$0.492945\pi$
$12$	2.34980	0.678330
$13$	−2.50657	−0.695198	−0.347599	−	0.937643i	$-0.613003\pi$
$13$	−2.50657	−0.695198	−0.347599	+	0.937643i	$0.613003\pi$
$14$	−10.0078	−2.67470
$15$	0.113686	0.0293536
$16$	1.21835	0.304588
$17$	−2.95147	−0.715837	−0.357919	−	0.933753i	$-0.616514\pi$
$17$	−2.95147	−0.715837	−0.357919	+	0.933753i	$0.616514\pi$
$18$	5.97126	1.40744
$19$	−0.457223	−0.104894	−0.0524470	−	0.998624i	$-0.516702\pi$
$19$	−0.457223	−0.104894	−0.0524470	+	0.998624i	$0.516702\pi$
$20$	0.590523	0.132045
$21$	2.87183	0.626686
$22$	−0.344566	−0.0734617
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.35469	−0.480650
$25$	−4.97143	−0.994286
$26$	5.87505	1.15219
$27$	−3.73128	−0.718085
$28$	14.9173	2.81910
$29$	5.18134	0.962151	0.481075	−	0.876679i	$-0.340246\pi$
$29$	5.18134	0.962151	0.481075	+	0.876679i	$0.340246\pi$
$30$	−0.266464	−0.0486494
$31$	9.24201	1.65991	0.829957	−	0.557827i	$-0.188365\pi$
$31$	9.24201	1.65991	0.829957	+	0.557827i	$0.188365\pi$
$32$	4.14622	0.732955
$33$	0.0988763	0.0172122
$34$	6.91783	1.18640
$35$	0.721713	0.121992
$36$	−8.90053	−1.48342
$37$	−11.5666	−1.90153	−0.950767	−	0.309907i	$-0.899702\pi$
$37$	−11.5666	−1.90153	−0.950767	+	0.309907i	$0.899702\pi$
$38$	1.07166	0.173847
$39$	−1.68590	−0.269960
$40$	−0.591752	−0.0935641
$41$	0.989258	0.154496	0.0772481	−	0.997012i	$-0.475387\pi$
$41$	0.989258	0.154496	0.0772481	+	0.997012i	$0.475387\pi$
$42$	−6.73117	−1.03864
$43$	−12.1102	−1.84678	−0.923392	−	0.383859i	$-0.874595\pi$
$43$	−12.1102	−1.84678	−0.923392	+	0.383859i	$0.874595\pi$
$44$	0.513597	0.0774276
$45$	−0.430617	−0.0641926
$46$	2.34386	0.345583
$47$	−7.05564	−1.02917	−0.514585	−	0.857439i	$-0.672054\pi$
$47$	−7.05564	−1.02917	−0.514585	+	0.857439i	$0.672054\pi$
$48$	0.819452	0.118278
$49$	11.2313	1.60447
$50$	11.6523	1.64789
$51$	−1.98513	−0.277974
$52$	−8.75712	−1.21439
$53$	10.6719	1.46589	0.732947	−	0.680286i	$-0.238144\pi$
$53$	10.6719	1.46589	0.732947	+	0.680286i	$0.238144\pi$
$54$	8.74558	1.19012
$55$	0.0248483	0.00335055
$56$	−14.9483	−1.99755
$57$	−0.307524	−0.0407325
$58$	−12.1443	−1.59463
$59$	13.8068	1.79750	0.898748	−	0.438466i	$-0.144478\pi$
$59$	13.8068	1.79750	0.898748	+	0.438466i	$0.144478\pi$
$60$	0.397180	0.0512758
$61$	10.5654	1.35276	0.676380	−	0.736553i	$-0.263548\pi$
$61$	10.5654	1.35276	0.676380	+	0.736553i	$0.263548\pi$
$62$	−21.6620	−2.75107
$63$	−10.8779	−1.37048
$64$	−12.1548	−1.51936
$65$	−0.423679	−0.0525509
$66$	−0.231752	−0.0285267
$67$	13.6670	1.66969	0.834844	−	0.550486i	$-0.185558\pi$
$67$	13.6670	1.66969	0.834844	+	0.550486i	$0.185558\pi$
$68$	−10.3115	−1.25045
$69$	−0.672591	−0.0809704
$70$	−1.69159	−0.202184
$71$	−1.28142	−0.152077	−0.0760384	−	0.997105i	$-0.524227\pi$
$71$	−1.28142	−0.152077	−0.0760384	+	0.997105i	$0.524227\pi$
$72$	8.91905	1.05112
$73$	−11.0364	−1.29172	−0.645858	−	0.763457i	$-0.723500\pi$
$73$	−11.0364	−1.29172	−0.645858	+	0.763457i	$0.723500\pi$
$74$	27.1104	3.15152
$75$	−3.34374	−0.386101
$76$	−1.59738	−0.183232
$77$	0.627697	0.0715327
$78$	3.95150	0.447419
$79$	5.46466	0.614823	0.307411	−	0.951577i	$-0.400537\pi$
$79$	5.46466	0.614823	0.307411	+	0.951577i	$0.400537\pi$
$80$	0.205934	0.0230242
$81$	5.13324	0.570360
$82$	−2.31868	−0.256055
$83$	12.6422	1.38766	0.693829	−	0.720140i	$-0.255922\pi$
$83$	12.6422	1.38766	0.693829	+	0.720140i	$0.255922\pi$
$84$	10.0332	1.09471
$85$	−0.498879	−0.0541110
$86$	28.3845	3.06078
$87$	3.48492	0.373623
$88$	−0.514665	−0.0548635
$89$	0.837415	0.0887658	0.0443829	−	0.999015i	$-0.485868\pi$
$89$	0.837415	0.0887658	0.0443829	+	0.999015i	$0.485868\pi$
$90$	1.00930	0.106390
$91$	−10.7026	−1.12194
$92$	−3.49366	−0.364239
$93$	6.21609	0.644579
$94$	16.5374	1.70570
$95$	−0.0772830	−0.00792906
$96$	2.78871	0.284621
$97$	5.54532	0.563042	0.281521	−	0.959555i	$-0.409161\pi$
$97$	5.54532	0.563042	0.281521	+	0.959555i	$0.409161\pi$
$98$	−26.3245	−2.65918
$99$	−0.374521	−0.0376408
$100$	−17.3685	−1.73685
$101$	2.77910	0.276530	0.138265	−	0.990395i	$-0.455847\pi$
$101$	2.77910	0.276530	0.138265	+	0.990395i	$0.455847\pi$
$102$	4.65287	0.460702
$103$	−15.5309	−1.53030	−0.765151	−	0.643851i	$-0.777336\pi$
$103$	−15.5309	−1.53030	−0.765151	+	0.643851i	$0.777336\pi$
$104$	8.77534	0.860493
$105$	0.485418	0.0473719
$106$	−25.0133	−2.42951
$107$	−0.766199	−0.0740712	−0.0370356	−	0.999314i	$-0.511791\pi$
$107$	−0.766199	−0.0740712	−0.0370356	+	0.999314i	$0.511791\pi$
$108$	−13.0358	−1.25437
$109$	−15.7135	−1.50508	−0.752539	−	0.658548i	$-0.771171\pi$
$109$	−15.7135	−1.50508	−0.752539	+	0.658548i	$0.771171\pi$
$110$	−0.0582409	−0.00555306
$111$	−7.77957	−0.738404
$112$	5.20213	0.491555
$113$	−1.05541	−0.0992842	−0.0496421	−	0.998767i	$-0.515808\pi$
$113$	−1.05541	−0.0992842	−0.0496421	+	0.998767i	$0.515808\pi$
$114$	0.720791	0.0675083
$115$	−0.169027	−0.0157618
$116$	18.1019	1.68071
$117$	6.38580	0.590368
$118$	−32.3612	−2.97909
$119$	−12.6022	−1.15524
$120$	−0.398007	−0.0363329
$121$	−10.9784	−0.998035
$122$	−24.7638	−2.24201
$123$	0.665366	0.0599940
$124$	32.2885	2.89959
$125$	−1.68544	−0.150750
$126$	25.4962	2.27138
$127$	−21.8832	−1.94182	−0.970909	−	0.239449i	$-0.923033\pi$
$127$	−21.8832	−1.94182	−0.970909	+	0.239449i	$0.923033\pi$
$128$	20.1968	1.78516
$129$	−8.14519	−0.717144
$130$	0.993042	0.0870955
$131$	5.97595	0.522121	0.261060	−	0.965322i	$-0.415928\pi$
$131$	5.97595	0.522121	0.261060	+	0.965322i	$0.415928\pi$
$132$	0.345440	0.0300667
$133$	−1.95225	−0.169282
$134$	−32.0335	−2.76727
$135$	−0.630687	−0.0542809
$136$	10.3329	0.886039
$137$	−22.6396	−1.93423	−0.967116	−	0.254336i	$-0.918143\pi$
$137$	−22.6396	−1.93423	−0.967116	+	0.254336i	$0.918143\pi$
$138$	1.57646	0.134197
$139$	−0.112378	−0.00953181	−0.00476591	−	0.999989i	$-0.501517\pi$
$139$	−0.112378	−0.00953181	−0.00476591	+	0.999989i	$0.501517\pi$
$140$	2.52142	0.213099
$141$	−4.74556	−0.399648
$142$	3.00347	0.252046
$143$	−0.368487	−0.0308144
$144$	−3.10390	−0.258658
$145$	0.875786	0.0727301
$146$	25.8678	2.14084
$147$	7.55406	0.623048
$148$	−40.4097	−3.32166
$149$	−13.8486	−1.13452	−0.567260	−	0.823539i	$-0.691996\pi$
$149$	−13.8486	−1.13452	−0.567260	+	0.823539i	$0.691996\pi$
$150$	7.83724	0.639908
$151$	23.7661	1.93406	0.967031	−	0.254660i	$-0.0819635\pi$
$151$	23.7661	1.93406	0.967031	+	0.254660i	$0.0819635\pi$
$152$	1.60070	0.129834
$153$	7.51924	0.607894
$154$	−1.47123	−0.118555
$155$	1.56215	0.125475
$156$	−5.88996	−0.471574
$157$	−19.2678	−1.53774	−0.768870	−	0.639405i	$-0.779181\pi$
$157$	−19.2678	−1.53774	−0.768870	+	0.639405i	$0.779181\pi$
$158$	−12.8084	−1.01898
$159$	7.17779	0.569236
$160$	0.700823	0.0554049
$161$	−4.26981	−0.336508
$162$	−12.0316	−0.945291
$163$	1.74465	0.136652	0.0683258	−	0.997663i	$-0.478234\pi$
$163$	1.74465	0.136652	0.0683258	+	0.997663i	$0.478234\pi$
$164$	3.45613	0.269879
$165$	0.0167128	0.00130109
$166$	−29.6314	−2.29984
$167$	−11.6932	−0.904850	−0.452425	−	0.891802i	$-0.649441\pi$
$167$	−11.6932	−0.904850	−0.452425	+	0.891802i	$0.649441\pi$
$168$	−10.0541	−0.775690
$169$	−6.71709	−0.516699
$170$	1.16930	0.0896812
$171$	1.16483	0.0890768
$172$	−42.3088	−3.22602
$173$	18.4014	1.39903	0.699515	−	0.714618i	$-0.253399\pi$
$173$	18.4014	1.39903	0.699515	+	0.714618i	$0.253399\pi$
$174$	−8.16815	−0.619226
$175$	−21.2271	−1.60462
$176$	0.179108	0.0135007
$177$	9.28634	0.698004
$178$	−1.96278	−0.147117
$179$	−4.17872	−0.312332	−0.156166	−	0.987731i	$-0.549913\pi$
$179$	−4.17872	−0.312332	−0.156166	+	0.987731i	$0.549913\pi$
$180$	−1.50443	−0.112134
$181$	−13.5327	−1.00588	−0.502938	−	0.864323i	$-0.667748\pi$
$181$	−13.5327	−1.00588	−0.502938	+	0.864323i	$0.667748\pi$
$182$	25.0853	1.85945
$183$	7.10618	0.525304
$184$	3.50093	0.258092
$185$	−1.95506	−0.143739
$186$	−14.5696	−1.06830
$187$	−0.433891	−0.0317292
$188$	−24.6500	−1.79779
$189$	−15.9319	−1.15887
$190$	0.181140	0.0131413
$191$	2.78998	0.201876	0.100938	−	0.994893i	$-0.467816\pi$
$191$	2.78998	0.201876	0.100938	+	0.994893i	$0.467816\pi$
$192$	−8.17523	−0.589997
$193$	10.6533	0.766840	0.383420	−	0.923574i	$-0.374746\pi$
$193$	10.6533	0.766840	0.383420	+	0.923574i	$0.374746\pi$
$194$	−12.9974	−0.933161
$195$	−0.284962	−0.0204066
$196$	39.2383	2.80274
$197$	−1.55515	−0.110800	−0.0554000	−	0.998464i	$-0.517643\pi$
$197$	−1.55515	−0.110800	−0.0554000	+	0.998464i	$0.517643\pi$
$198$	0.877824	0.0623842
$199$	−11.9104	−0.844307	−0.422153	−	0.906524i	$-0.638726\pi$
$199$	−11.9104	−0.844307	−0.422153	+	0.906524i	$0.638726\pi$
$200$	17.4046	1.23069
$201$	9.19229	0.648374
$202$	−6.51380	−0.458310
$203$	22.1233	1.55275
$204$	−6.93538	−0.485574
$205$	0.167211	0.0116785
$206$	36.4021	2.53626
$207$	2.54762	0.177072
$208$	−3.05389	−0.211749
$209$	−0.0672155	−0.00464939
$210$	−1.13775	−0.0785121
$211$	−17.3760	−1.19621	−0.598105	−	0.801418i	$-0.704080\pi$
$211$	−17.3760	−1.19621	−0.598105	+	0.801418i	$0.704080\pi$
$212$	37.2839	2.56067
$213$	−0.861872	−0.0590545
$214$	1.79586	0.122762
$215$	−2.04695	−0.139601
$216$	13.0629	0.888821
$217$	39.4617	2.67883
$218$	36.8301	2.49445
$219$	−7.42300	−0.501600
$220$	0.0868117	0.00585284
$221$	7.39808	0.497649
$222$	18.2342	1.22380
$223$	0.846145	0.0566621	0.0283310	−	0.999599i	$-0.490981\pi$
$223$	0.846145	0.0566621	0.0283310	+	0.999599i	$0.490981\pi$
$224$	17.7036	1.18287
$225$	12.6653	0.844355
$226$	2.47372	0.164549
$227$	−16.9652	−1.12602	−0.563011	−	0.826449i	$-0.690357\pi$
$227$	−16.9652	−1.12602	−0.563011	+	0.826449i	$0.690357\pi$
$228$	−1.07438	−0.0711528
$229$	−8.89060	−0.587507	−0.293754	−	0.955881i	$-0.594904\pi$
$229$	−8.89060	−0.587507	−0.293754	+	0.955881i	$0.594904\pi$
$230$	0.396175	0.0261230
$231$	0.422183	0.0277776
$232$	−18.1395	−1.19092
$233$	−21.8350	−1.43046	−0.715228	−	0.698892i	$-0.753677\pi$
$233$	−21.8350	−1.43046	−0.715228	+	0.698892i	$0.753677\pi$
$234$	−14.9674	−0.978450
$235$	−1.19259	−0.0777962
$236$	48.2364	3.13992
$237$	3.67548	0.238748
$238$	29.5378	1.91465
$239$	−3.57589	−0.231305	−0.115653	−	0.993290i	$-0.536896\pi$
$239$	−3.57589	−0.231305	−0.115653	+	0.993290i	$0.536896\pi$
$240$	0.138509	0.00894075
$241$	−18.4106	−1.18593	−0.592964	−	0.805229i	$-0.702043\pi$
$241$	−18.4106	−1.18593	−0.592964	+	0.805229i	$0.702043\pi$
$242$	25.7318	1.65410
$243$	14.6464	0.939567
$244$	36.9119	2.36304
$245$	1.89839	0.121284
$246$	−1.55952	−0.0994315
$247$	1.14606	0.0729222
$248$	−32.3556	−2.05459
$249$	8.50300	0.538856
$250$	3.95043	0.249847
$251$	−24.6267	−1.55442	−0.777211	−	0.629240i	$-0.783366\pi$
$251$	−24.6267	−1.55442	−0.777211	+	0.629240i	$0.783366\pi$
$252$	−38.0036	−2.39400
$253$	−0.147008	−0.00924232
$254$	51.2910	3.21828
$255$	−0.335541	−0.0210124
$256$	−23.0286	−1.43929
$257$	−22.3362	−1.39330	−0.696648	−	0.717413i	$-0.745326\pi$
$257$	−22.3362	−1.39330	−0.696648	+	0.717413i	$0.745326\pi$
$258$	19.0911	1.18856
$259$	−49.3871	−3.06877
$260$	−1.48019	−0.0917975
$261$	−13.2001	−0.817065
$262$	−14.0068	−0.865341
$263$	−7.39866	−0.456221	−0.228110	−	0.973635i	$-0.573255\pi$
$263$	−7.39866	−0.456221	−0.228110	+	0.973635i	$0.573255\pi$
$264$	−0.346159	−0.0213046
$265$	1.80383	0.110809
$266$	4.57580	0.280561
$267$	0.563237	0.0344696
$268$	47.7479	2.91666
$269$	22.2268	1.35519	0.677595	−	0.735435i	$-0.263022\pi$
$269$	22.2268	1.35519	0.677595	+	0.735435i	$0.263022\pi$
$270$	1.47824	0.0899628
$271$	−24.3196	−1.47731	−0.738656	−	0.674083i	$-0.764539\pi$
$271$	−24.3196	−1.47731	−0.738656	+	0.674083i	$0.764539\pi$
$272$	−3.59593	−0.218035
$273$	−7.19847	−0.435671
$274$	53.0640	3.20571
$275$	−0.730841	−0.0440714
$276$	−2.34980	−0.141442
$277$	12.3621	0.742769	0.371384	−	0.928479i	$-0.378883\pi$
$277$	12.3621	0.742769	0.371384	+	0.928479i	$0.378883\pi$
$278$	0.263399	0.0157976
$279$	−23.5452	−1.40961
$280$	−2.52667	−0.150997
$281$	−13.9805	−0.834004	−0.417002	−	0.908905i	$-0.636919\pi$
$281$	−13.9805	−0.834004	−0.417002	+	0.908905i	$0.636919\pi$
$282$	11.1229	0.662359
$283$	−16.8670	−1.00264	−0.501320	−	0.865262i	$-0.667152\pi$
$283$	−16.8670	−1.00264	−0.501320	+	0.865262i	$0.667152\pi$
$284$	−4.47686	−0.265653
$285$	−0.0519798	−0.00307902
$286$	0.863680	0.0510705
$287$	4.22395	0.249332
$288$	−10.5630	−0.622431
$289$	−8.28881	−0.487577
$290$	−2.05272	−0.120540
$291$	3.72973	0.218640
$292$	−38.5576	−2.25641
$293$	12.0183	0.702116	0.351058	−	0.936354i	$-0.385822\pi$
$293$	12.0183	0.702116	0.351058	+	0.936354i	$0.385822\pi$
$294$	−17.7056	−1.03261
$295$	2.33373	0.135875
$296$	40.4938	2.35365
$297$	−0.548528	−0.0318288
$298$	32.4591	1.88030
$299$	2.50657	0.144959
$300$	−11.6819	−0.674454
$301$	−51.7081	−2.98041
$302$	−55.7044	−3.20543
$303$	1.86919	0.107382
$304$	−0.557058	−0.0319495
$305$	1.78584	0.102257
$306$	−17.6240	−1.00750
$307$	20.4035	1.16449	0.582244	−	0.813014i	$-0.302175\pi$
$307$	20.4035	1.16449	0.582244	+	0.813014i	$0.302175\pi$
$308$	2.19296	0.124956
$309$	−10.4459	−0.594247
$310$	−3.66145	−0.207957
$311$	6.10693	0.346292	0.173146	−	0.984896i	$-0.444607\pi$
$311$	6.10693	0.346292	0.173146	+	0.984896i	$0.444607\pi$
$312$	5.90221	0.334147
$313$	15.5071	0.876510	0.438255	−	0.898851i	$-0.355597\pi$
$313$	15.5071	0.876510	0.438255	+	0.898851i	$0.355597\pi$
$314$	45.1610	2.54859
$315$	−1.83865	−0.103596
$316$	19.0917	1.07399
$317$	30.7837	1.72898	0.864491	−	0.502648i	$-0.167641\pi$
$317$	30.7837	1.72898	0.864491	+	0.502648i	$0.167641\pi$
$318$	−16.8237	−0.943427
$319$	0.761699	0.0426470
$320$	−2.05450	−0.114850
$321$	−0.515338	−0.0287634
$322$	10.0078	0.557714
$323$	1.34948	0.0750871
$324$	17.9338	0.996323
$325$	12.4613	0.691226
$326$	−4.08921	−0.226480
$327$	−10.5687	−0.584452
$328$	−3.46332	−0.191230
$329$	−30.1263	−1.66091
$330$	−0.0391723	−0.00215636
$331$	17.7847	0.977535	0.488768	−	0.872414i	$-0.337447\pi$
$331$	17.7847	0.977535	0.488768	+	0.872414i	$0.337447\pi$
$332$	44.1674	2.42400
$333$	29.4673	1.61480
$334$	27.4073	1.49966
$335$	2.31009	0.126214
$336$	3.49890	0.190881
$337$	6.95462	0.378842	0.189421	−	0.981896i	$-0.439339\pi$
$337$	6.95462	0.378842	0.189421	+	0.981896i	$0.439339\pi$
$338$	15.7439	0.856355
$339$	−0.709855	−0.0385541
$340$	−1.74291	−0.0945227
$341$	1.35865	0.0735751
$342$	−2.73020	−0.147632
$343$	18.0668	0.975516
$344$	42.3969	2.28589
$345$	−0.113686	−0.00612065
$346$	−43.1302	−2.31869
$347$	−10.2677	−0.551198	−0.275599	−	0.961273i	$-0.588876\pi$
$347$	−10.2677	−0.551198	−0.275599	+	0.961273i	$0.588876\pi$
$348$	12.1751	0.652656
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	49.7532	2.65942
$351$	9.35272	0.499211
$352$	0.609528	0.0324879
$353$	16.9029	0.899649	0.449824	−	0.893117i	$-0.351487\pi$
$353$	16.9029	0.899649	0.449824	+	0.893117i	$0.351487\pi$
$354$	−21.7658	−1.15684
$355$	−0.216595	−0.0114957
$356$	2.92564	0.155059
$357$	−8.47614	−0.448605
$358$	9.79431	0.517645
$359$	−1.21861	−0.0643158	−0.0321579	−	0.999483i	$-0.510238\pi$
$359$	−1.21861	−0.0643158	−0.0321579	+	0.999483i	$0.510238\pi$
$360$	1.50756	0.0794554
$361$	−18.7909	−0.988997
$362$	31.7186	1.66710
$363$	−7.38396	−0.387557
$364$	−37.3913	−1.95983
$365$	−1.86545	−0.0976424
$366$	−16.6559	−0.870616
$367$	−31.0037	−1.61838	−0.809189	−	0.587549i	$-0.800093\pi$
$367$	−31.0037	−1.61838	−0.809189	+	0.587549i	$0.800093\pi$
$368$	−1.21835	−0.0635110
$369$	−2.52026	−0.131199
$370$	4.58239	0.238227
$371$	45.5668	2.36571
$372$	21.7169	1.12597
$373$	−4.95615	−0.256620	−0.128310	−	0.991734i	$-0.540955\pi$
$373$	−4.95615	−0.256620	−0.128310	+	0.991734i	$0.540955\pi$
$374$	1.01698	0.0525866
$375$	−1.13361	−0.0585394
$376$	24.7013	1.27387
$377$	−12.9874	−0.668886
$378$	37.3420	1.92066
$379$	3.87546	0.199069	0.0995345	−	0.995034i	$-0.468265\pi$
$379$	3.87546	0.199069	0.0995345	+	0.995034i	$0.468265\pi$
$380$	−0.270001	−0.0138507
$381$	−14.7184	−0.754047
$382$	−6.53932	−0.334581
$383$	−2.68710	−0.137304	−0.0686521	−	0.997641i	$-0.521870\pi$
$383$	−2.68710	−0.137304	−0.0686521	+	0.997641i	$0.521870\pi$
$384$	13.5842	0.693214
$385$	0.106098	0.00540724
$386$	−24.9698	−1.27093
$387$	30.8521	1.56830
$388$	19.3735	0.983539
$389$	−10.0109	−0.507575	−0.253787	−	0.967260i	$-0.581676\pi$
$389$	−10.0109	−0.507575	−0.253787	+	0.967260i	$0.581676\pi$
$390$	0.667910	0.0338210
$391$	2.95147	0.149262
$392$	−39.3200	−1.98596
$393$	4.01937	0.202750
$394$	3.64505	0.183635
$395$	0.923675	0.0464752
$396$	−1.30845	−0.0657521
$397$	8.37094	0.420125	0.210063	−	0.977688i	$-0.432633\pi$
$397$	8.37094	0.420125	0.210063	+	0.977688i	$0.432633\pi$
$398$	27.9163	1.39932
$399$	−1.31307	−0.0657356
$400$	−6.05695	−0.302847
$401$	20.1903	1.00826	0.504129	−	0.863629i	$-0.331814\pi$
$401$	20.1903	1.00826	0.504129	+	0.863629i	$0.331814\pi$
$402$	−21.5454	−1.07459
$403$	−23.1658	−1.15397
$404$	9.70923	0.483052
$405$	0.867657	0.0431142
$406$	−51.8539	−2.57347
$407$	−1.70038	−0.0842848
$408$	6.94981	0.344067
$409$	1.81380	0.0896864	0.0448432	−	0.998994i	$-0.485721\pi$
$409$	1.81380	0.0896864	0.0448432	+	0.998994i	$0.485721\pi$
$410$	−0.391919	−0.0193555
$411$	−15.2272	−0.751102
$412$	−54.2596	−2.67318
$413$	58.9525	2.90086
$414$	−5.97126	−0.293471
$415$	2.13687	0.104895
$416$	−10.3928	−0.509549
$417$	−0.0755847	−0.00370140
$418$	0.157543	0.00770570
$419$	−31.2551	−1.52691	−0.763455	−	0.645861i	$-0.776499\pi$
$419$	−31.2551	−1.52691	−0.763455	+	0.645861i	$0.776499\pi$
$420$	1.69589	0.0827507
$421$	13.5787	0.661786	0.330893	−	0.943668i	$-0.392650\pi$
$421$	13.5787	0.661786	0.330893	+	0.943668i	$0.392650\pi$
$422$	40.7268	1.98255
$423$	17.9751	0.873980
$424$	−37.3614	−1.81443
$425$	14.6730	0.711747
$426$	2.02011	0.0978744
$427$	45.1122	2.18313
$428$	−2.67684	−0.129390
$429$	−0.247841	−0.0119659
$430$	4.79775	0.231368
$431$	−0.993230	−0.0478422	−0.0239211	−	0.999714i	$-0.507615\pi$
$431$	−0.993230	−0.0478422	−0.0239211	+	0.999714i	$0.507615\pi$
$432$	−4.54601	−0.218720
$433$	−21.4580	−1.03121	−0.515603	−	0.856828i	$-0.672432\pi$
$433$	−21.4580	−1.03121	−0.515603	+	0.856828i	$0.672432\pi$
$434$	−92.4925	−4.43978
$435$	0.589046	0.0282426
$436$	−54.8976	−2.62912
$437$	0.457223	0.0218719
$438$	17.3984	0.831330
$439$	−19.3145	−0.921831	−0.460916	−	0.887444i	$-0.652479\pi$
$439$	−19.3145	−0.921831	−0.460916	+	0.887444i	$0.652479\pi$
$440$	−0.0869923	−0.00414720
$441$	−28.6131	−1.36253
$442$	−17.3400	−0.824782
$443$	−40.9461	−1.94541	−0.972703	−	0.232054i	$-0.925456\pi$
$443$	−40.9461	−1.94541	−0.972703	+	0.232054i	$0.925456\pi$
$444$	−27.1792	−1.28987
$445$	0.141546	0.00670991
$446$	−1.98324	−0.0939093
$447$	−9.31442	−0.440557
$448$	−51.8989	−2.45199
$449$	16.2926	0.768895	0.384448	−	0.923147i	$-0.374392\pi$
$449$	16.2926	0.768895	0.384448	+	0.923147i	$0.374392\pi$
$450$	−29.6857	−1.39940
$451$	0.145429	0.00684798
$452$	−3.68723	−0.173433
$453$	15.9849	0.751035
$454$	39.7641	1.86622
$455$	−1.80903	−0.0848085
$456$	1.07662	0.0504173
$457$	34.9335	1.63412	0.817060	−	0.576553i	$-0.195603\pi$
$457$	34.9335	1.63412	0.817060	+	0.576553i	$0.195603\pi$
$458$	20.8383	0.973709
$459$	11.0128	0.514032
$460$	−0.590523	−0.0275333
$461$	−18.3737	−0.855747	−0.427874	−	0.903839i	$-0.640737\pi$
$461$	−18.3737	−0.855747	−0.427874	+	0.903839i	$0.640737\pi$
$462$	−0.989537	−0.0460374
$463$	2.25876	0.104973	0.0524867	−	0.998622i	$-0.483285\pi$
$463$	2.25876	0.104973	0.0524867	+	0.998622i	$0.483285\pi$
$464$	6.31269	0.293059
$465$	1.05069	0.0487245
$466$	51.1780	2.37077
$467$	−29.0630	−1.34488	−0.672438	−	0.740154i	$-0.734753\pi$
$467$	−29.0630	−1.34488	−0.672438	+	0.740154i	$0.734753\pi$
$468$	22.3098	1.03127
$469$	58.3555	2.69461
$470$	2.79527	0.128936
$471$	−12.9594	−0.597136
$472$	−48.3367	−2.22488
$473$	−1.78029	−0.0818580
$474$	−8.61480	−0.395691
$475$	2.27305	0.104295
$476$	−44.0280	−2.01802
$477$	−27.1879	−1.24485
$478$	8.38137	0.383355
$479$	36.5644	1.67067	0.835335	−	0.549742i	$-0.185274\pi$
$479$	36.5644	1.67067	0.835335	+	0.549742i	$0.185274\pi$
$480$	0.471367	0.0215149
$481$	28.9925	1.32194
$482$	43.1517	1.96551
$483$	−2.87183	−0.130673
$484$	−38.3548	−1.74340
$485$	0.937308	0.0425610
$486$	−34.3291	−1.55720
$487$	−35.1958	−1.59488	−0.797438	−	0.603401i	$-0.793812\pi$
$487$	−35.1958	−1.59488	−0.797438	+	0.603401i	$0.793812\pi$
$488$	−36.9887	−1.67440
$489$	1.17344	0.0530646
$490$	−4.44956	−0.201010
$491$	−27.0115	−1.21901	−0.609505	−	0.792782i	$-0.708632\pi$
$491$	−27.0115	−1.21901	−0.609505	+	0.792782i	$0.708632\pi$
$492$	2.32456	0.104799
$493$	−15.2926	−0.688743
$494$	−2.68621	−0.120858
$495$	−0.0633042	−0.00284531
$496$	11.2600	0.505590
$497$	−5.47143	−0.245427
$498$	−19.9298	−0.893076
$499$	−9.87164	−0.441915	−0.220958	−	0.975283i	$-0.570918\pi$
$499$	−9.87164	−0.441915	−0.220958	+	0.975283i	$0.570918\pi$
$500$	−5.88836	−0.263335
$501$	−7.86477	−0.351372
$502$	57.7214	2.57623
$503$	−20.5870	−0.917929	−0.458964	−	0.888455i	$-0.651779\pi$
$503$	−20.5870	−0.917929	−0.458964	+	0.888455i	$0.651779\pi$
$504$	38.0826	1.69634
$505$	0.469742	0.0209033
$506$	0.344566	0.0153178
$507$	−4.51785	−0.200645
$508$	−76.4524	−3.39203
$509$	41.5899	1.84344	0.921720	−	0.387857i	$-0.126785\pi$
$509$	41.5899	1.84344	0.921720	+	0.387857i	$0.126785\pi$
$510$	0.786460	0.0348250
$511$	−47.1235	−2.08462
$512$	13.5823	0.600258
$513$	1.70602	0.0753228
$514$	52.3529	2.30919
$515$	−2.62514	−0.115677
$516$	−28.4565	−1.25273
$517$	−1.03724	−0.0456176
$518$	115.756	5.08604
$519$	12.3766	0.543272
$520$	1.48327	0.0650456
$521$	−3.26750	−0.143152	−0.0715758	−	0.997435i	$-0.522803\pi$
$521$	−3.26750	−0.143152	−0.0715758	+	0.997435i	$0.522803\pi$
$522$	30.9391	1.35417
$523$	−41.3539	−1.80828	−0.904139	−	0.427238i	$-0.859487\pi$
$523$	−41.3539	−1.80828	−0.904139	+	0.427238i	$0.859487\pi$
$524$	20.8779	0.912057
$525$	−14.2771	−0.623105
$526$	17.3414	0.756121
$527$	−27.2776	−1.18823
$528$	0.120466	0.00524261
$529$	1.00000	0.0434783
$530$	−4.22793	−0.183649
$531$	−35.1746	−1.52645
$532$	−6.82052	−0.295707
$533$	−2.47965	−0.107405
$534$	−1.32015	−0.0571284
$535$	−0.129508	−0.00559913
$536$	−47.8472	−2.06668
$537$	−2.81057	−0.121285
$538$	−52.0964	−2.24603
$539$	1.65109	0.0711175
$540$	−2.20341	−0.0948195
$541$	26.9133	1.15709	0.578546	−	0.815650i	$-0.303620\pi$
$541$	26.9133	1.15709	0.578546	+	0.815650i	$0.303620\pi$
$542$	57.0017	2.44843
$543$	−9.10195	−0.390602
$544$	−12.2375	−0.524676
$545$	−2.65600	−0.113771
$546$	16.8722	0.722062
$547$	9.33581	0.399170	0.199585	−	0.979880i	$-0.436041\pi$
$547$	9.33581	0.399170	0.199585	+	0.979880i	$0.436041\pi$
$548$	−79.0951	−3.37878
$549$	−26.9166	−1.14877
$550$	1.71299	0.0730419
$551$	−2.36903	−0.100924
$552$	2.35469	0.100222
$553$	23.3331	0.992223
$554$	−28.9751	−1.23103
$555$	−1.31496	−0.0558168
$556$	−0.392612	−0.0166505
$557$	21.3025	0.902614	0.451307	−	0.892369i	$-0.350958\pi$
$557$	21.3025	0.902614	0.451307	+	0.892369i	$0.350958\pi$
$558$	55.1865	2.33623
$559$	30.3550	1.28388
$560$	0.879301	0.0371572
$561$	−0.291831	−0.0123211
$562$	32.7682	1.38224
$563$	−20.5828	−0.867463	−0.433731	−	0.901042i	$-0.642803\pi$
$563$	−20.5828	−0.867463	−0.433731	+	0.901042i	$0.642803\pi$
$564$	−16.5794	−0.698118
$565$	−0.178392	−0.00750501
$566$	39.5339	1.66173
$567$	21.9180	0.920469
$568$	4.48617	0.188235
$569$	19.6744	0.824793	0.412397	−	0.911004i	$-0.364692\pi$
$569$	19.6744	0.824793	0.412397	+	0.911004i	$0.364692\pi$
$570$	0.121833	0.00510303
$571$	−12.7107	−0.531925	−0.265963	−	0.963983i	$-0.585690\pi$
$571$	−12.7107	−0.531925	−0.265963	+	0.963983i	$0.585690\pi$
$572$	−1.28737	−0.0538276
$573$	1.87652	0.0783926
$574$	−9.90032	−0.413231
$575$	4.97143	0.207323
$576$	30.9659	1.29025
$577$	1.46512	0.0609939	0.0304969	−	0.999535i	$-0.490291\pi$
$577$	1.46512	0.0609939	0.0304969	+	0.999535i	$0.490291\pi$
$578$	19.4278	0.808089
$579$	7.16529	0.297779
$580$	3.05970	0.127047
$581$	53.9797	2.23945
$582$	−8.74194	−0.362365
$583$	1.56885	0.0649752
$584$	38.6378	1.59884
$585$	1.07937	0.0446266
$586$	−28.1691	−1.16366
$587$	−2.78093	−0.114781	−0.0573905	−	0.998352i	$-0.518278\pi$
$587$	−2.78093	−0.114781	−0.0573905	+	0.998352i	$0.518278\pi$
$588$	26.3913	1.08836
$589$	−4.22566	−0.174115
$590$	−5.46992	−0.225193
$591$	−1.04598	−0.0430259
$592$	−14.0922	−0.579184
$593$	−34.6229	−1.42179	−0.710897	−	0.703296i	$-0.751711\pi$
$593$	−34.6229	−1.42179	−0.710897	+	0.703296i	$0.751711\pi$
$594$	1.28567	0.0527517
$595$	−2.13012	−0.0873263
$596$	−48.3823	−1.98181
$597$	−8.01083	−0.327861
$598$	−5.87505	−0.240249
$599$	44.1942	1.80573	0.902864	−	0.429927i	$-0.141461\pi$
$599$	44.1942	1.80573	0.902864	+	0.429927i	$0.141461\pi$
$600$	11.7062	0.477903
$601$	23.2378	0.947889	0.473945	−	0.880555i	$-0.342830\pi$
$601$	23.2378	0.947889	0.473945	+	0.880555i	$0.342830\pi$
$602$	121.196	4.93960
$603$	−34.8183	−1.41791
$604$	83.0309	3.37848
$605$	−1.85564	−0.0754427
$606$	−4.38112	−0.177971
$607$	7.05630	0.286407	0.143203	−	0.989693i	$-0.454260\pi$
$607$	7.05630	0.286407	0.143203	+	0.989693i	$0.454260\pi$
$608$	−1.89574	−0.0768826
$609$	14.8800	0.602966
$610$	−4.18574	−0.169476
$611$	17.6855	0.715478
$612$	26.2697	1.06189
$613$	34.0112	1.37370	0.686849	−	0.726800i	$-0.258993\pi$
$613$	34.0112	1.37370	0.686849	+	0.726800i	$0.258993\pi$
$614$	−47.8228	−1.92997
$615$	0.112465	0.00453502
$616$	−2.19752	−0.0885407
$617$	10.6736	0.429703	0.214852	−	0.976647i	$-0.431073\pi$
$617$	10.6736	0.429703	0.214852	+	0.976647i	$0.431073\pi$
$618$	24.4837	0.984880
$619$	21.3816	0.859397	0.429699	−	0.902972i	$-0.358620\pi$
$619$	21.3816	0.859397	0.429699	+	0.902972i	$0.358620\pi$
$620$	5.45762	0.219183
$621$	3.73128	0.149731
$622$	−14.3138	−0.573930
$623$	3.57560	0.143254
$624$	−2.05402	−0.0822265
$625$	24.5723	0.982891
$626$	−36.3463	−1.45269
$627$	−0.0452085	−0.00180545
$628$	−67.3153	−2.68617
$629$	34.1384	1.36119
$630$	4.30954	0.171696
$631$	−19.7156	−0.784867	−0.392434	−	0.919780i	$-0.628367\pi$
$631$	−19.7156	−0.784867	−0.392434	+	0.919780i	$0.628367\pi$
$632$	−19.1314	−0.761006
$633$	−11.6869	−0.464513
$634$	−72.1525	−2.86554
$635$	−3.69885	−0.146784
$636$	25.0768	0.994359
$637$	−28.1521	−1.11543
$638$	−1.78531	−0.0706812
$639$	3.26458	0.129145
$640$	3.41380	0.134942
$641$	−0.516345	−0.0203944	−0.0101972	−	0.999948i	$-0.503246\pi$
$641$	−0.516345	−0.0203944	−0.0101972	+	0.999948i	$0.503246\pi$
$642$	1.20788	0.0476711
$643$	33.9388	1.33842	0.669208	−	0.743075i	$-0.266634\pi$
$643$	33.9388	1.33842	0.669208	+	0.743075i	$0.266634\pi$
$644$	−14.9173	−0.587823
$645$	−1.37676	−0.0542097
$646$	−3.16299	−0.124446
$647$	5.62305	0.221065	0.110532	−	0.993873i	$-0.464744\pi$
$647$	5.62305	0.221065	0.110532	+	0.993873i	$0.464744\pi$
$648$	−17.9711	−0.705972
$649$	2.02972	0.0796733
$650$	−29.2074	−1.14561
$651$	26.5415	1.04025
$652$	6.09522	0.238707
$653$	20.7090	0.810404	0.405202	−	0.914227i	$-0.367201\pi$
$653$	20.7090	0.810404	0.405202	+	0.914227i	$0.367201\pi$
$654$	24.7716	0.968646
$655$	1.01010	0.0394677
$656$	1.20526	0.0470577
$657$	28.1167	1.09694
$658$	70.6116	2.75273
$659$	−24.7412	−0.963781	−0.481890	−	0.876232i	$-0.660050\pi$
$659$	−24.7412	−0.963781	−0.481890	+	0.876232i	$0.660050\pi$
$660$	0.0583887	0.00227278
$661$	−19.6791	−0.765429	−0.382715	−	0.923867i	$-0.625011\pi$
$661$	−19.6791	−0.765429	−0.382715	+	0.923867i	$0.625011\pi$
$662$	−41.6848	−1.62012
$663$	4.97588	0.193247
$664$	−44.2593	−1.71759
$665$	−0.329984	−0.0127962
$666$	−69.0670	−2.67629
$667$	−5.18134	−0.200622
$668$	−40.8522	−1.58062
$669$	0.569109	0.0220030
$670$	−5.41452	−0.209181
$671$	1.55320	0.0599606
$672$	11.9073	0.459332
$673$	−13.9653	−0.538321	−0.269161	−	0.963095i	$-0.586746\pi$
$673$	−13.9653	−0.538321	−0.269161	+	0.963095i	$0.586746\pi$
$674$	−16.3006	−0.627876
$675$	18.5498	0.713982
$676$	−23.4672	−0.902586
$677$	−15.2395	−0.585700	−0.292850	−	0.956158i	$-0.594604\pi$
$677$	−15.2395	−0.585700	−0.292850	+	0.956158i	$0.594604\pi$
$678$	1.66380	0.0638978
$679$	23.6775	0.908657
$680$	1.74654	0.0669767
$681$	−11.4107	−0.437257
$682$	−3.18448	−0.121940
$683$	−48.1541	−1.84257	−0.921283	−	0.388893i	$-0.872857\pi$
$683$	−48.1541	−1.84257	−0.921283	+	0.388893i	$0.872857\pi$
$684$	4.06952	0.155602
$685$	−3.82670	−0.146211
$686$	−42.3460	−1.61678
$687$	−5.97973	−0.228141
$688$	−14.7544	−0.562508
$689$	−26.7498	−1.01909
$690$	0.266464	0.0101441
$691$	−11.5029	−0.437590	−0.218795	−	0.975771i	$-0.570213\pi$
$691$	−11.5029	−0.437590	−0.218795	+	0.975771i	$0.570213\pi$
$692$	64.2882	2.44387
$693$	−1.59913	−0.0607461
$694$	24.0660	0.913532
$695$	−0.0189950	−0.000720521 0
$696$	−12.2005	−0.462457
$697$	−2.91977	−0.110594
$698$	2.34386	0.0887163
$699$	−14.6860	−0.555475
$700$	−74.1602	−2.80299
$701$	19.2562	0.727298	0.363649	−	0.931536i	$-0.381531\pi$
$701$	19.2562	0.727298	0.363649	+	0.931536i	$0.381531\pi$
$702$	−21.9214	−0.827371
$703$	5.28850	0.199460
$704$	−1.78686	−0.0673449
$705$	−0.802127	−0.0302099
$706$	−39.6179	−1.49104
$707$	11.8662	0.446275
$708$	32.4433	1.21930
$709$	−43.0762	−1.61776	−0.808881	−	0.587973i	$-0.799926\pi$
$709$	−43.0762	−1.61776	−0.808881	+	0.587973i	$0.799926\pi$
$710$	0.507667	0.0190524
$711$	−13.9219	−0.522112
$712$	−2.93173	−0.109871
$713$	−9.24201	−0.346116
$714$	19.8669	0.743499
$715$	−0.0622842	−0.00232930
$716$	−14.5990	−0.545591
$717$	−2.40511	−0.0898204
$718$	2.85625	0.106594
$719$	−4.52661	−0.168814	−0.0844071	−	0.996431i	$-0.526900\pi$
$719$	−4.52661	−0.168814	−0.0844071	+	0.996431i	$0.526900\pi$
$720$	−0.524643	−0.0195523
$721$	−66.3139	−2.46966
$722$	44.0433	1.63912
$723$	−12.3828	−0.460520
$724$	−47.2786	−1.75710
$725$	−25.7587	−0.956653
$726$	17.3069	0.642321
$727$	19.1416	0.709923	0.354962	−	0.934881i	$-0.384494\pi$
$727$	19.1416	0.709923	0.354962	+	0.934881i	$0.384494\pi$
$728$	37.4690	1.38870
$729$	−5.54870	−0.205507
$730$	4.37236	0.161828
$731$	35.7428	1.32200
$732$	24.8266	0.917618
$733$	−26.7839	−0.989286	−0.494643	−	0.869096i	$-0.664701\pi$
$733$	−26.7839	−0.989286	−0.494643	+	0.869096i	$0.664701\pi$
$734$	72.6681	2.68223
$735$	1.27684	0.0470970
$736$	−4.14622	−0.152832
$737$	2.00916	0.0740083
$738$	5.90712	0.217444
$739$	26.0524	0.958351	0.479176	−	0.877719i	$-0.340936\pi$
$739$	26.0524	0.958351	0.479176	+	0.877719i	$0.340936\pi$
$740$	−6.83033	−0.251088
$741$	0.770831	0.0283172
$742$	−106.802	−3.92083
$743$	−11.9317	−0.437731	−0.218865	−	0.975755i	$-0.570236\pi$
$743$	−11.9317	−0.437731	−0.218865	+	0.975755i	$0.570236\pi$
$744$	−21.7621	−0.797837
$745$	−2.34078	−0.0857597
$746$	11.6165	0.425311
$747$	−32.2075	−1.17841
$748$	−1.51587	−0.0554256
$749$	−3.27152	−0.119539
$750$	2.65702	0.0970207
$751$	−3.59503	−0.131184	−0.0655922	−	0.997847i	$-0.520894\pi$
$751$	−3.59503	−0.131184	−0.0655922	+	0.997847i	$0.520894\pi$
$752$	−8.59625	−0.313473
$753$	−16.5637	−0.603614
$754$	30.4406	1.10858
$755$	4.01712	0.146198
$756$	−55.6605	−2.02435
$757$	14.2312	0.517240	0.258620	−	0.965979i	$-0.416732\pi$
$757$	14.2312	0.517240	0.258620	+	0.965979i	$0.416732\pi$
$758$	−9.08352	−0.329928
$759$	−0.0988763	−0.00358898
$760$	0.270562	0.00981432
$761$	−14.2643	−0.517081	−0.258541	−	0.966000i	$-0.583242\pi$
$761$	−14.2643	−0.517081	−0.258541	+	0.966000i	$0.583242\pi$
$762$	34.4979	1.24973
$763$	−67.0936	−2.42895
$764$	9.74726	0.352644
$765$	1.27095	0.0459514
$766$	6.29817	0.227562
$767$	−34.6078	−1.24962
$768$	−15.4888	−0.558906
$769$	−3.84184	−0.138540	−0.0692702	−	0.997598i	$-0.522067\pi$
$769$	−3.84184	−0.138540	−0.0692702	+	0.997598i	$0.522067\pi$
$770$	−0.248678	−0.00896173
$771$	−15.0231	−0.541045
$772$	37.2190	1.33954
$773$	19.2708	0.693124	0.346562	−	0.938027i	$-0.387349\pi$
$773$	19.2708	0.693124	0.346562	+	0.938027i	$0.387349\pi$
$774$	−72.3130	−2.59924
$775$	−45.9460	−1.65043
$776$	−19.4138	−0.696913
$777$	−33.2173	−1.19166
$778$	23.4642	0.841233
$779$	−0.452311	−0.0162057
$780$	−0.995562	−0.0356468
$781$	−0.188380	−0.00674075
$782$	−6.91783	−0.247381
$783$	−19.3330	−0.690906
$784$	13.6837	0.488702
$785$	−3.25678	−0.116240
$786$	−9.42082	−0.336029
$787$	−28.8159	−1.02718	−0.513588	−	0.858037i	$-0.671684\pi$
$787$	−28.8159	−1.02718	−0.513588	+	0.858037i	$0.671684\pi$
$788$	−5.43317	−0.193549
$789$	−4.97627	−0.177160
$790$	−2.16496	−0.0770259
$791$	−4.50638	−0.160228
$792$	1.31117	0.0465905
$793$	−26.4829	−0.940437
$794$	−19.6203	−0.696298
$795$	1.21324	0.0430292
$796$	−41.6109	−1.47486
$797$	−27.1891	−0.963089	−0.481544	−	0.876422i	$-0.659924\pi$
$797$	−27.1891	−0.963089	−0.481544	+	0.876422i	$0.659924\pi$
$798$	3.07764	0.108947
$799$	20.8245	0.736719
$800$	−20.6126	−0.728767
$801$	−2.13342	−0.0753806
$802$	−47.3232	−1.67104
$803$	−1.62245	−0.0572548
$804$	32.1148	1.13260
$805$	−0.721713	−0.0254371
$806$	54.2973	1.91254
$807$	14.9495	0.526248
$808$	−9.72942	−0.342280
$809$	−9.60474	−0.337685	−0.168842	−	0.985643i	$-0.554003\pi$
$809$	−9.60474	−0.337685	−0.168842	+	0.985643i	$0.554003\pi$
$810$	−2.03366	−0.0714556
$811$	−48.0869	−1.68856	−0.844280	−	0.535903i	$-0.819971\pi$
$811$	−48.0869	−1.68856	−0.844280	+	0.535903i	$0.819971\pi$
$812$	77.2915	2.71240
$813$	−16.3571	−0.573670
$814$	3.98545	0.139690
$815$	0.294893	0.0103297
$816$	−2.41859	−0.0846676
$817$	5.53704	0.193717
$818$	−4.25128	−0.148642
$819$	27.2662	0.952757
$820$	0.584180	0.0204004
$821$	−16.5466	−0.577480	−0.288740	−	0.957407i	$-0.593236\pi$
$821$	−16.5466	−0.577480	−0.288740	+	0.957407i	$0.593236\pi$
$822$	35.6903	1.24484
$823$	33.8280	1.17917	0.589584	−	0.807707i	$-0.299292\pi$
$823$	33.8280	1.17917	0.589584	+	0.807707i	$0.299292\pi$
$824$	54.3725	1.89416
$825$	−0.491557	−0.0171138
$826$	−138.176	−4.80777
$827$	4.98815	0.173455	0.0867275	−	0.996232i	$-0.472359\pi$
$827$	4.98815	0.173455	0.0867275	+	0.996232i	$0.472359\pi$
$828$	8.90053	0.309315
$829$	42.2570	1.46765	0.733823	−	0.679341i	$-0.237734\pi$
$829$	42.2570	1.46765	0.733823	+	0.679341i	$0.237734\pi$
$830$	−5.00851	−0.173848
$831$	8.31466	0.288432
$832$	30.4670	1.05625
$833$	−33.1489	−1.14854
$834$	0.177160	0.00613453
$835$	−1.97647	−0.0683987
$836$	−0.234828	−0.00812170
$837$	−34.4845	−1.19196
$838$	73.2574	2.53064
$839$	54.4704	1.88053	0.940263	−	0.340448i	$-0.110579\pi$
$839$	54.4704	1.88053	0.940263	+	0.340448i	$0.110579\pi$
$840$	−1.69941	−0.0586353
$841$	−2.15372	−0.0742662
$842$	−31.8266	−1.09682
$843$	−9.40313	−0.323861
$844$	−60.7057	−2.08958
$845$	−1.13537	−0.0390579
$846$	−42.1311	−1.44850
$847$	−46.8757	−1.61067
$848$	13.0021	0.446493
$849$	−11.3446	−0.389346
$850$	−34.3915	−1.17962
$851$	11.5666	0.396497
$852$	−3.01109	−0.103158
$853$	14.7107	0.503684	0.251842	−	0.967768i	$-0.418964\pi$
$853$	14.7107	0.503684	0.251842	+	0.967768i	$0.418964\pi$
$854$	−105.737	−3.61823
$855$	0.196888	0.00673342
$856$	2.68241	0.0916828
$857$	−28.9624	−0.989336	−0.494668	−	0.869082i	$-0.664710\pi$
$857$	−28.9624	−0.989336	−0.494668	+	0.869082i	$0.664710\pi$
$858$	0.580903	0.0198317
$859$	23.5150	0.802321	0.401160	−	0.916008i	$-0.368607\pi$
$859$	23.5150	0.802321	0.401160	+	0.916008i	$0.368607\pi$
$860$	−7.15134	−0.243859
$861$	2.84099	0.0968206
$862$	2.32799	0.0792916
$863$	43.1118	1.46754	0.733771	−	0.679397i	$-0.237758\pi$
$863$	43.1118	1.46754	0.733771	+	0.679397i	$0.237758\pi$
$864$	−15.4707	−0.526324
$865$	3.11033	0.105754
$866$	50.2945	1.70908
$867$	−5.57497	−0.189336
$868$	137.866	4.67947
$869$	0.803350	0.0272518
$870$	−1.38064	−0.0468080
$871$	−34.2573	−1.16077
$872$	55.0118	1.86293
$873$	−14.1274	−0.478139
$874$	−1.07166	−0.0362496
$875$	−7.19651	−0.243287
$876$	−25.9335	−0.876210
$877$	−42.4415	−1.43315	−0.716574	−	0.697512i	$-0.754291\pi$
$877$	−42.4415	−1.43315	−0.716574	+	0.697512i	$0.754291\pi$
$878$	45.2704	1.52780
$879$	8.08339	0.272646
$880$	0.0302740	0.00102054
$881$	30.6638	1.03309	0.516545	−	0.856260i	$-0.327218\pi$
$881$	30.6638	1.03309	0.516545	+	0.856260i	$0.327218\pi$
$882$	67.0650	2.25819
$883$	−39.3457	−1.32409	−0.662043	−	0.749466i	$-0.730311\pi$
$883$	−39.3457	−1.32409	−0.662043	+	0.749466i	$0.730311\pi$
$884$	25.8464	0.869309
$885$	1.56964	0.0527629
$886$	95.9717	3.22423
$887$	−19.0081	−0.638228	−0.319114	−	0.947716i	$-0.603385\pi$
$887$	−19.0081	−0.638228	−0.319114	+	0.947716i	$0.603385\pi$
$888$	27.2357	0.913971
$889$	−93.4370	−3.13378
$890$	−0.331763	−0.0111207
$891$	0.754629	0.0252810
$892$	2.95615	0.0989791
$893$	3.22600	0.107954
$894$	21.8317	0.730160
$895$	−0.706316	−0.0236095
$896$	86.2364	2.88096
$897$	1.68590	0.0562905
$898$	−38.1875	−1.27433
$899$	47.8860	1.59709
$900$	44.2484	1.47495
$901$	−31.4977	−1.04934
$902$	−0.340865	−0.0113496
$903$	−34.7784	−1.15735
$904$	3.69490	0.122891
$905$	−2.28739	−0.0760353
$906$	−37.4663	−1.24473
$907$	4.84475	0.160867	0.0804336	−	0.996760i	$-0.474369\pi$
$907$	4.84475	0.160867	0.0804336	+	0.996760i	$0.474369\pi$
$908$	−59.2708	−1.96697
$909$	−7.08009	−0.234832
$910$	4.24010	0.140558
$911$	−5.51050	−0.182571	−0.0912855	−	0.995825i	$-0.529098\pi$
$911$	−5.51050	−0.182571	−0.0912855	+	0.995825i	$0.529098\pi$
$912$	−0.374672	−0.0124066
$913$	1.85850	0.0615074
$914$	−81.8791	−2.70832
$915$	1.20114	0.0397084
$916$	−31.0607	−1.02628
$917$	25.5162	0.842618
$918$	−25.8123	−0.851934
$919$	−52.7737	−1.74084	−0.870422	−	0.492307i	$-0.836154\pi$
$919$	−52.7737	−1.74084	−0.870422	+	0.492307i	$0.836154\pi$
$920$	0.591752	0.0195095
$921$	13.7232	0.452194
$922$	43.0653	1.41828
$923$	3.21198	0.105724
$924$	1.47497	0.0485228
$925$	57.5024	1.89067
$926$	−5.29421	−0.173978
$927$	39.5668	1.29954
$928$	21.4830	0.705213
$929$	−18.2297	−0.598097	−0.299049	−	0.954238i	$-0.596669\pi$
$929$	−18.2297	−0.598097	−0.299049	+	0.954238i	$0.596669\pi$
$930$	−2.46266	−0.0807538
$931$	−5.13520	−0.168299
$932$	−76.2839	−2.49876
$933$	4.10747	0.134472
$934$	68.1195	2.22894
$935$	−0.0733392	−0.00239845
$936$	−22.3562	−0.730737
$937$	−28.2363	−0.922440	−0.461220	−	0.887286i	$-0.652588\pi$
$937$	−28.2363	−0.922440	−0.461220	+	0.887286i	$0.652588\pi$
$938$	−136.777	−4.46592
$939$	10.4299	0.340367
$940$	−4.16652	−0.135897
$941$	−15.6969	−0.511704	−0.255852	−	0.966716i	$-0.582356\pi$
$941$	−15.6969	−0.511704	−0.255852	+	0.966716i	$0.582356\pi$
$942$	30.3749	0.989667
$943$	−0.989258	−0.0322147
$944$	16.8216	0.547495
$945$	−2.69291	−0.0876005
$946$	4.17275	0.135668
$947$	−35.6970	−1.16000	−0.579999	−	0.814617i	$-0.696947\pi$
$947$	−35.6970	−1.16000	−0.579999	+	0.814617i	$0.696947\pi$
$948$	12.8409	0.417053
$949$	27.6636	0.897999
$950$	−5.32770	−0.172854
$951$	20.7048	0.671399
$952$	44.1195	1.42992
$953$	−21.4418	−0.694568	−0.347284	−	0.937760i	$-0.612896\pi$
$953$	−21.4418	−0.694568	−0.347284	+	0.937760i	$0.612896\pi$
$954$	63.7245	2.06316
$955$	0.471583	0.0152601
$956$	−12.4929	−0.404051
$957$	0.512312	0.0165607
$958$	−85.7017	−2.76890
$959$	−96.6668	−3.12154
$960$	−1.38183	−0.0445985
$961$	54.4148	1.75532
$962$	−67.9542	−2.19093
$963$	1.95198	0.0629018
$964$	−64.3203	−2.07162
$965$	1.80069	0.0579663
$966$	6.73117	0.216572
$967$	23.6614	0.760900	0.380450	−	0.924801i	$-0.375769\pi$
$967$	23.6614	0.760900	0.380450	+	0.924801i	$0.375769\pi$
$968$	38.4346	1.23533
$969$	0.907648	0.0291578
$970$	−2.19692	−0.0705387
$971$	13.3106	0.427158	0.213579	−	0.976926i	$-0.431488\pi$
$971$	13.3106	0.427158	0.213579	+	0.976926i	$0.431488\pi$
$972$	51.1696	1.64127
$973$	−0.479835	−0.0153828
$974$	82.4940	2.64328
$975$	8.38132	0.268417
$976$	12.8724	0.412034
$977$	34.2917	1.09709	0.548545	−	0.836121i	$-0.315182\pi$
$977$	34.2917	1.09709	0.548545	+	0.836121i	$0.315182\pi$
$978$	−2.75036	−0.0879469
$979$	0.123107	0.00393451
$980$	6.63234	0.211862
$981$	40.0320	1.27812
$982$	63.3110	2.02034
$983$	27.4092	0.874217	0.437108	−	0.899409i	$-0.356003\pi$
$983$	27.4092	0.874217	0.437108	+	0.899409i	$0.356003\pi$
$984$	−2.32940	−0.0742585
$985$	−0.262863	−0.00837550
$986$	35.8436	1.14149
$987$	−20.2626	−0.644967
$988$	4.00395	0.127383
$989$	12.1102	0.385081
$990$	0.148376	0.00471570
$991$	10.2592	0.325894	0.162947	−	0.986635i	$-0.447900\pi$
$991$	10.2592	0.325894	0.162947	+	0.986635i	$0.447900\pi$
$992$	38.3194	1.21664
$993$	11.9618	0.379597
$994$	12.8242	0.406760
$995$	−2.01318	−0.0638221
$996$	29.7066	0.941290
$997$	−28.6822	−0.908375	−0.454188	−	0.890906i	$-0.650070\pi$
$997$	−28.6822	−0.908375	−0.454188	+	0.890906i	$0.650070\pi$
$998$	23.1377	0.732411
$999$	43.1581	1.36546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.13	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.13	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34386 q^{2} +0.672591 q^{3} +3.49366 q^{4} +0.169027 q^{5} -1.57646 q^{6} +4.26981 q^{7} -3.50093 q^{8} -2.54762 q^{9} +O(q^{10})\)	\(q-2.34386 q^{2} +0.672591 q^{3} +3.49366 q^{4} +0.169027 q^{5} -1.57646 q^{6} +4.26981 q^{7} -3.50093 q^{8} -2.54762 q^{9} -0.396175 q^{10} +0.147008 q^{11} +2.34980 q^{12} -2.50657 q^{13} -10.0078 q^{14} +0.113686 q^{15} +1.21835 q^{16} -2.95147 q^{17} +5.97126 q^{18} -0.457223 q^{19} +0.590523 q^{20} +2.87183 q^{21} -0.344566 q^{22} -1.00000 q^{23} -2.35469 q^{24} -4.97143 q^{25} +5.87505 q^{26} -3.73128 q^{27} +14.9173 q^{28} +5.18134 q^{29} -0.266464 q^{30} +9.24201 q^{31} +4.14622 q^{32} +0.0988763 q^{33} +6.91783 q^{34} +0.721713 q^{35} -8.90053 q^{36} -11.5666 q^{37} +1.07166 q^{38} -1.68590 q^{39} -0.591752 q^{40} +0.989258 q^{41} -6.73117 q^{42} -12.1102 q^{43} +0.513597 q^{44} -0.430617 q^{45} +2.34386 q^{46} -7.05564 q^{47} +0.819452 q^{48} +11.2313 q^{49} +11.6523 q^{50} -1.98513 q^{51} -8.75712 q^{52} +10.6719 q^{53} +8.74558 q^{54} +0.0248483 q^{55} -14.9483 q^{56} -0.307524 q^{57} -12.1443 q^{58} +13.8068 q^{59} +0.397180 q^{60} +10.5654 q^{61} -21.6620 q^{62} -10.8779 q^{63} -12.1548 q^{64} -0.423679 q^{65} -0.231752 q^{66} +13.6670 q^{67} -10.3115 q^{68} -0.672591 q^{69} -1.69159 q^{70} -1.28142 q^{71} +8.91905 q^{72} -11.0364 q^{73} +27.1104 q^{74} -3.34374 q^{75} -1.59738 q^{76} +0.627697 q^{77} +3.95150 q^{78} +5.46466 q^{79} +0.205934 q^{80} +5.13324 q^{81} -2.31868 q^{82} +12.6422 q^{83} +10.0332 q^{84} -0.498879 q^{85} +28.3845 q^{86} +3.48492 q^{87} -0.514665 q^{88} +0.837415 q^{89} +1.00930 q^{90} -10.7026 q^{91} -3.49366 q^{92} +6.21609 q^{93} +16.5374 q^{94} -0.0772830 q^{95} +2.78871 q^{96} +5.54532 q^{97} -26.3245 q^{98} -0.374521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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