LMFDB - Embedded newform 6026.2.a.k.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.711607 q^{3} +1.00000 q^{4} -3.74432 q^{5} -0.711607 q^{6} +2.05633 q^{7} +1.00000 q^{8} -2.49362 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.711607 q^{3} +1.00000 q^{4} -3.74432 q^{5} -0.711607 q^{6} +2.05633 q^{7} +1.00000 q^{8} -2.49362 q^{9} -3.74432 q^{10} -3.50585 q^{11} -0.711607 q^{12} -4.85256 q^{13} +2.05633 q^{14} +2.66448 q^{15} +1.00000 q^{16} -1.23768 q^{17} -2.49362 q^{18} -4.05710 q^{19} -3.74432 q^{20} -1.46330 q^{21} -3.50585 q^{22} -1.00000 q^{23} -0.711607 q^{24} +9.01995 q^{25} -4.85256 q^{26} +3.90929 q^{27} +2.05633 q^{28} +4.64524 q^{29} +2.66448 q^{30} -10.8281 q^{31} +1.00000 q^{32} +2.49479 q^{33} -1.23768 q^{34} -7.69955 q^{35} -2.49362 q^{36} +6.23895 q^{37} -4.05710 q^{38} +3.45311 q^{39} -3.74432 q^{40} +1.59949 q^{41} -1.46330 q^{42} -2.18745 q^{43} -3.50585 q^{44} +9.33690 q^{45} -1.00000 q^{46} -0.754851 q^{47} -0.711607 q^{48} -2.77152 q^{49} +9.01995 q^{50} +0.880745 q^{51} -4.85256 q^{52} -4.22918 q^{53} +3.90929 q^{54} +13.1270 q^{55} +2.05633 q^{56} +2.88706 q^{57} +4.64524 q^{58} -3.87405 q^{59} +2.66448 q^{60} +3.91639 q^{61} -10.8281 q^{62} -5.12769 q^{63} +1.00000 q^{64} +18.1695 q^{65} +2.49479 q^{66} +7.78783 q^{67} -1.23768 q^{68} +0.711607 q^{69} -7.69955 q^{70} +7.71925 q^{71} -2.49362 q^{72} +5.65260 q^{73} +6.23895 q^{74} -6.41865 q^{75} -4.05710 q^{76} -7.20917 q^{77} +3.45311 q^{78} +5.06056 q^{79} -3.74432 q^{80} +4.69897 q^{81} +1.59949 q^{82} -16.0117 q^{83} -1.46330 q^{84} +4.63429 q^{85} -2.18745 q^{86} -3.30559 q^{87} -3.50585 q^{88} -0.900612 q^{89} +9.33690 q^{90} -9.97844 q^{91} -1.00000 q^{92} +7.70532 q^{93} -0.754851 q^{94} +15.1911 q^{95} -0.711607 q^{96} +15.1866 q^{97} -2.77152 q^{98} +8.74224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.711607	−0.410846	−0.205423	−	0.978673i	$-0.565857\pi$
$3$	−0.711607	−0.410846	−0.205423	+	0.978673i	$0.565857\pi$
$4$	1.00000	0.500000
$5$	−3.74432	−1.67451	−0.837256	−	0.546811i	$-0.815841\pi$
$5$	−3.74432	−1.67451	−0.837256	+	0.546811i	$0.815841\pi$
$6$	−0.711607	−0.290512
$7$	2.05633	0.777218	0.388609	−	0.921403i	$-0.372956\pi$
$7$	2.05633	0.777218	0.388609	+	0.921403i	$0.372956\pi$
$8$	1.00000	0.353553
$9$	−2.49362	−0.831205
$10$	−3.74432	−1.18406
$11$	−3.50585	−1.05705	−0.528527	−	0.848917i	$-0.677255\pi$
$11$	−3.50585	−1.05705	−0.528527	+	0.848917i	$0.677255\pi$
$12$	−0.711607	−0.205423
$13$	−4.85256	−1.34586	−0.672929	−	0.739707i	$-0.734964\pi$
$13$	−4.85256	−1.34586	−0.672929	+	0.739707i	$0.734964\pi$
$14$	2.05633	0.549576
$15$	2.66448	0.687967
$16$	1.00000	0.250000
$17$	−1.23768	−0.300183	−0.150091	−	0.988672i	$-0.547957\pi$
$17$	−1.23768	−0.300183	−0.150091	+	0.988672i	$0.547957\pi$
$18$	−2.49362	−0.587751
$19$	−4.05710	−0.930763	−0.465381	−	0.885110i	$-0.654083\pi$
$19$	−4.05710	−0.930763	−0.465381	+	0.885110i	$0.654083\pi$
$20$	−3.74432	−0.837256
$21$	−1.46330	−0.319317
$22$	−3.50585	−0.747450
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.711607	−0.145256
$25$	9.01995	1.80399
$26$	−4.85256	−0.951665
$27$	3.90929	0.752344
$28$	2.05633	0.388609
$29$	4.64524	0.862600	0.431300	−	0.902209i	$-0.358055\pi$
$29$	4.64524	0.862600	0.431300	+	0.902209i	$0.358055\pi$
$30$	2.66448	0.486466
$31$	−10.8281	−1.94478	−0.972389	−	0.233367i	$-0.925026\pi$
$31$	−10.8281	−1.94478	−0.972389	+	0.233367i	$0.925026\pi$
$32$	1.00000	0.176777
$33$	2.49479	0.434286
$34$	−1.23768	−0.212261
$35$	−7.69955	−1.30146
$36$	−2.49362	−0.415603
$37$	6.23895	1.02568	0.512839	−	0.858485i	$-0.328594\pi$
$37$	6.23895	1.02568	0.512839	+	0.858485i	$0.328594\pi$
$38$	−4.05710	−0.658149
$39$	3.45311	0.552941
$40$	−3.74432	−0.592029
$41$	1.59949	0.249798	0.124899	−	0.992169i	$-0.460139\pi$
$41$	1.59949	0.249798	0.124899	+	0.992169i	$0.460139\pi$
$42$	−1.46330	−0.225791
$43$	−2.18745	−0.333582	−0.166791	−	0.985992i	$-0.553341\pi$
$43$	−2.18745	−0.333582	−0.166791	+	0.985992i	$0.553341\pi$
$44$	−3.50585	−0.528527
$45$	9.33690	1.39186
$46$	−1.00000	−0.147442
$47$	−0.754851	−0.110106	−0.0550532	−	0.998483i	$-0.517533\pi$
$47$	−0.754851	−0.110106	−0.0550532	+	0.998483i	$0.517533\pi$
$48$	−0.711607	−0.102712
$49$	−2.77152	−0.395932
$50$	9.01995	1.27561
$51$	0.880745	0.123329
$52$	−4.85256	−0.672929
$53$	−4.22918	−0.580923	−0.290462	−	0.956887i	$-0.593809\pi$
$53$	−4.22918	−0.580923	−0.290462	+	0.956887i	$0.593809\pi$
$54$	3.90929	0.531988
$55$	13.1270	1.77005
$56$	2.05633	0.274788
$57$	2.88706	0.382401
$58$	4.64524	0.609951
$59$	−3.87405	−0.504359	−0.252179	−	0.967681i	$-0.581147\pi$
$59$	−3.87405	−0.504359	−0.252179	+	0.967681i	$0.581147\pi$
$60$	2.66448	0.343983
$61$	3.91639	0.501442	0.250721	−	0.968059i	$-0.419332\pi$
$61$	3.91639	0.501442	0.250721	+	0.968059i	$0.419332\pi$
$62$	−10.8281	−1.37517
$63$	−5.12769	−0.646028
$64$	1.00000	0.125000
$65$	18.1695	2.25365
$66$	2.49479	0.307087
$67$	7.78783	0.951434	0.475717	−	0.879598i	$-0.342189\pi$
$67$	7.78783	0.951434	0.475717	+	0.879598i	$0.342189\pi$
$68$	−1.23768	−0.150091
$69$	0.711607	0.0856674
$70$	−7.69955	−0.920272
$71$	7.71925	0.916106	0.458053	−	0.888925i	$-0.348547\pi$
$71$	7.71925	0.916106	0.458053	+	0.888925i	$0.348547\pi$
$72$	−2.49362	−0.293875
$73$	5.65260	0.661587	0.330794	−	0.943703i	$-0.392684\pi$
$73$	5.65260	0.661587	0.330794	+	0.943703i	$0.392684\pi$
$74$	6.23895	0.725263
$75$	−6.41865	−0.741162
$76$	−4.05710	−0.465381
$77$	−7.20917	−0.821561
$78$	3.45311	0.390988
$79$	5.06056	0.569357	0.284679	−	0.958623i	$-0.408113\pi$
$79$	5.06056	0.569357	0.284679	+	0.958623i	$0.408113\pi$
$80$	−3.74432	−0.418628
$81$	4.69897	0.522108
$82$	1.59949	0.176634
$83$	−16.0117	−1.75751	−0.878754	−	0.477275i	$-0.841625\pi$
$83$	−16.0117	−1.75751	−0.878754	+	0.477275i	$0.841625\pi$
$84$	−1.46330	−0.159659
$85$	4.63429	0.502659
$86$	−2.18745	−0.235878
$87$	−3.30559	−0.354396
$88$	−3.50585	−0.373725
$89$	−0.900612	−0.0954647	−0.0477323	−	0.998860i	$-0.515199\pi$
$89$	−0.900612	−0.0954647	−0.0477323	+	0.998860i	$0.515199\pi$
$90$	9.33690	0.984196
$91$	−9.97844	−1.04602
$92$	−1.00000	−0.104257
$93$	7.70532	0.799005
$94$	−0.754851	−0.0778569
$95$	15.1911	1.55857
$96$	−0.711607	−0.0726281
$97$	15.1866	1.54197	0.770983	−	0.636856i	$-0.219765\pi$
$97$	15.1866	1.54197	0.770983	+	0.636856i	$0.219765\pi$
$98$	−2.77152	−0.279966
$99$	8.74224	0.878628
$100$	9.01995	0.901995
$101$	−5.31360	−0.528723	−0.264361	−	0.964424i	$-0.585161\pi$
$101$	−5.31360	−0.528723	−0.264361	+	0.964424i	$0.585161\pi$
$102$	0.880745	0.0872067
$103$	6.63108	0.653380	0.326690	−	0.945132i	$-0.394067\pi$
$103$	6.63108	0.653380	0.326690	+	0.945132i	$0.394067\pi$
$104$	−4.85256	−0.475832
$105$	5.47905	0.534700
$106$	−4.22918	−0.410775
$107$	15.1576	1.46534	0.732668	−	0.680586i	$-0.238275\pi$
$107$	15.1576	1.46534	0.732668	+	0.680586i	$0.238275\pi$
$108$	3.90929	0.376172
$109$	−12.3048	−1.17859	−0.589293	−	0.807919i	$-0.700594\pi$
$109$	−12.3048	−1.17859	−0.589293	+	0.807919i	$0.700594\pi$
$110$	13.1270	1.25161
$111$	−4.43968	−0.421396
$112$	2.05633	0.194305
$113$	−7.91136	−0.744239	−0.372119	−	0.928185i	$-0.621369\pi$
$113$	−7.91136	−0.744239	−0.372119	+	0.928185i	$0.621369\pi$
$114$	2.88706	0.270398
$115$	3.74432	0.349160
$116$	4.64524	0.431300
$117$	12.1004	1.11868
$118$	−3.87405	−0.356635
$119$	−2.54508	−0.233307
$120$	2.66448	0.243233
$121$	1.29098	0.117362
$122$	3.91639	0.354573
$123$	−1.13821	−0.102629
$124$	−10.8281	−0.972389
$125$	−15.0520	−1.34629
$126$	−5.12769	−0.456811
$127$	−0.0335384	−0.00297605	−0.00148802	−	0.999999i	$-0.500474\pi$
$127$	−0.0335384	−0.00297605	−0.00148802	+	0.999999i	$0.500474\pi$
$128$	1.00000	0.0883883
$129$	1.55660	0.137051
$130$	18.1695	1.59357
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	2.49479	0.217143
$133$	−8.34272	−0.723406
$134$	7.78783	0.672766
$135$	−14.6377	−1.25981
$136$	−1.23768	−0.106131
$137$	5.05460	0.431844	0.215922	−	0.976411i	$-0.430724\pi$
$137$	5.05460	0.431844	0.215922	+	0.976411i	$0.430724\pi$
$138$	0.711607	0.0605760
$139$	4.47552	0.379609	0.189805	−	0.981822i	$-0.439215\pi$
$139$	4.47552	0.379609	0.189805	+	0.981822i	$0.439215\pi$
$140$	−7.69955	−0.650730
$141$	0.537157	0.0452368
$142$	7.71925	0.647785
$143$	17.0123	1.42264
$144$	−2.49362	−0.207801
$145$	−17.3933	−1.44443
$146$	5.65260	0.467813
$147$	1.97223	0.162667
$148$	6.23895	0.512839
$149$	−1.73794	−0.142378	−0.0711889	−	0.997463i	$-0.522679\pi$
$149$	−1.73794	−0.142378	−0.0711889	+	0.997463i	$0.522679\pi$
$150$	−6.41865	−0.524081
$151$	21.1004	1.71713	0.858563	−	0.512708i	$-0.171358\pi$
$151$	21.1004	1.71713	0.858563	+	0.512708i	$0.171358\pi$
$152$	−4.05710	−0.329074
$153$	3.08631	0.249513
$154$	−7.20917	−0.580931
$155$	40.5437	3.25655
$156$	3.45311	0.276470
$157$	23.9220	1.90918	0.954591	−	0.297918i	$-0.0962924\pi$
$157$	23.9220	1.90918	0.954591	+	0.297918i	$0.0962924\pi$
$158$	5.06056	0.402597
$159$	3.00952	0.238670
$160$	−3.74432	−0.296015
$161$	−2.05633	−0.162061
$162$	4.69897	0.369186
$163$	6.27839	0.491761	0.245881	−	0.969300i	$-0.420923\pi$
$163$	6.27839	0.491761	0.245881	+	0.969300i	$0.420923\pi$
$164$	1.59949	0.124899
$165$	−9.34128	−0.727218
$166$	−16.0117	−1.24275
$167$	0.977046	0.0756061	0.0378030	−	0.999285i	$-0.487964\pi$
$167$	0.977046	0.0756061	0.0378030	+	0.999285i	$0.487964\pi$
$168$	−1.46330	−0.112896
$169$	10.5473	0.811333
$170$	4.63429	0.355434
$171$	10.1169	0.773655
$172$	−2.18745	−0.166791
$173$	−9.09576	−0.691538	−0.345769	−	0.938320i	$-0.612382\pi$
$173$	−9.09576	−0.691538	−0.345769	+	0.938320i	$0.612382\pi$
$174$	−3.30559	−0.250596
$175$	18.5479	1.40209
$176$	−3.50585	−0.264263
$177$	2.75680	0.207214
$178$	−0.900612	−0.0675037
$179$	−15.4217	−1.15267	−0.576334	−	0.817214i	$-0.695517\pi$
$179$	−15.4217	−1.15267	−0.576334	+	0.817214i	$0.695517\pi$
$180$	9.33690	0.695931
$181$	−17.0342	−1.26614	−0.633072	−	0.774093i	$-0.718206\pi$
$181$	−17.0342	−1.26614	−0.633072	+	0.774093i	$0.718206\pi$
$182$	−9.97844	−0.739651
$183$	−2.78693	−0.206016
$184$	−1.00000	−0.0737210
$185$	−23.3606	−1.71751
$186$	7.70532	0.564982
$187$	4.33914	0.317309
$188$	−0.754851	−0.0550532
$189$	8.03878	0.584735
$190$	15.1911	1.10208
$191$	14.5758	1.05467	0.527335	−	0.849657i	$-0.323191\pi$
$191$	14.5758	1.05467	0.527335	+	0.849657i	$0.323191\pi$
$192$	−0.711607	−0.0513558
$193$	12.3658	0.890107	0.445054	−	0.895504i	$-0.353185\pi$
$193$	12.3658	0.890107	0.445054	+	0.895504i	$0.353185\pi$
$194$	15.1866	1.09033
$195$	−12.9296	−0.925905
$196$	−2.77152	−0.197966
$197$	−11.2199	−0.799387	−0.399693	−	0.916649i	$-0.630883\pi$
$197$	−11.2199	−0.799387	−0.399693	+	0.916649i	$0.630883\pi$
$198$	8.74224	0.621284
$199$	−3.03021	−0.214806	−0.107403	−	0.994216i	$-0.534254\pi$
$199$	−3.03021	−0.214806	−0.107403	+	0.994216i	$0.534254\pi$
$200$	9.01995	0.637806
$201$	−5.54187	−0.390893
$202$	−5.31360	−0.373863
$203$	9.55214	0.670429
$204$	0.880745	0.0616645
$205$	−5.98901	−0.418290
$206$	6.63108	0.462009
$207$	2.49362	0.173318
$208$	−4.85256	−0.336464
$209$	14.2236	0.983866
$210$	5.47905	0.378090
$211$	1.79622	0.123657	0.0618284	−	0.998087i	$-0.480307\pi$
$211$	1.79622	0.123657	0.0618284	+	0.998087i	$0.480307\pi$
$212$	−4.22918	−0.290462
$213$	−5.49307	−0.376379
$214$	15.1576	1.03615
$215$	8.19050	0.558587
$216$	3.90929	0.265994
$217$	−22.2660	−1.51152
$218$	−12.3048	−0.833386
$219$	−4.02243	−0.271811
$220$	13.1270	0.885024
$221$	6.00594	0.404003
$222$	−4.43968	−0.297972
$223$	−18.2513	−1.22219	−0.611097	−	0.791555i	$-0.709272\pi$
$223$	−18.2513	−1.22219	−0.611097	+	0.791555i	$0.709272\pi$
$224$	2.05633	0.137394
$225$	−22.4923	−1.49949
$226$	−7.91136	−0.526256
$227$	−13.1854	−0.875145	−0.437573	−	0.899183i	$-0.644162\pi$
$227$	−13.1854	−0.875145	−0.437573	+	0.899183i	$0.644162\pi$
$228$	2.88706	0.191200
$229$	−29.9502	−1.97917	−0.989584	−	0.143956i	$-0.954018\pi$
$229$	−29.9502	−1.97917	−0.989584	+	0.143956i	$0.954018\pi$
$230$	3.74432	0.246893
$231$	5.13009	0.337535
$232$	4.64524	0.304975
$233$	−16.1270	−1.05652	−0.528258	−	0.849084i	$-0.677155\pi$
$233$	−16.1270	−1.05652	−0.528258	+	0.849084i	$0.677155\pi$
$234$	12.1004	0.791029
$235$	2.82641	0.184374
$236$	−3.87405	−0.252179
$237$	−3.60113	−0.233918
$238$	−2.54508	−0.164973
$239$	−6.14137	−0.397252	−0.198626	−	0.980075i	$-0.563648\pi$
$239$	−6.14137	−0.397252	−0.198626	+	0.980075i	$0.563648\pi$
$240$	2.66448	0.171992
$241$	3.28827	0.211816	0.105908	−	0.994376i	$-0.466225\pi$
$241$	3.28827	0.211816	0.105908	+	0.994376i	$0.466225\pi$
$242$	1.29098	0.0829872
$243$	−15.0717	−0.966850
$244$	3.91639	0.250721
$245$	10.3775	0.662993
$246$	−1.13821	−0.0725695
$247$	19.6873	1.25267
$248$	−10.8281	−0.687583
$249$	11.3940	0.722066
$250$	−15.0520	−0.951970
$251$	−16.1942	−1.02217	−0.511084	−	0.859531i	$-0.670756\pi$
$251$	−16.1942	−1.02217	−0.511084	+	0.859531i	$0.670756\pi$
$252$	−5.12769	−0.323014
$253$	3.50585	0.220411
$254$	−0.0335384	−0.00210438
$255$	−3.29779	−0.206516
$256$	1.00000	0.0625000
$257$	31.5273	1.96662	0.983310	−	0.181938i	$-0.0582370\pi$
$257$	31.5273	1.96662	0.983310	+	0.181938i	$0.0582370\pi$
$258$	1.55660	0.0969097
$259$	12.8293	0.797175
$260$	18.1695	1.12683
$261$	−11.5835	−0.716998
$262$	−1.00000	−0.0617802
$263$	−8.02776	−0.495013	−0.247507	−	0.968886i	$-0.579611\pi$
$263$	−8.02776	−0.495013	−0.247507	+	0.968886i	$0.579611\pi$
$264$	2.49479	0.153543
$265$	15.8354	0.972762
$266$	−8.34272	−0.511525
$267$	0.640882	0.0392213
$268$	7.78783	0.475717
$269$	−4.82132	−0.293961	−0.146981	−	0.989139i	$-0.546956\pi$
$269$	−4.82132	−0.293961	−0.146981	+	0.989139i	$0.546956\pi$
$270$	−14.6377	−0.890819
$271$	20.7183	1.25855	0.629274	−	0.777184i	$-0.283352\pi$
$271$	20.7183	1.25855	0.629274	+	0.777184i	$0.283352\pi$
$272$	−1.23768	−0.0750456
$273$	7.10073	0.429756
$274$	5.05460	0.305360
$275$	−31.6226	−1.90691
$276$	0.711607	0.0428337
$277$	4.37957	0.263143	0.131571	−	0.991307i	$-0.457998\pi$
$277$	4.37957	0.263143	0.131571	+	0.991307i	$0.457998\pi$
$278$	4.47552	0.268424
$279$	27.0010	1.61651
$280$	−7.69955	−0.460136
$281$	22.3742	1.33473	0.667366	−	0.744730i	$-0.267422\pi$
$281$	22.3742	1.33473	0.667366	+	0.744730i	$0.267422\pi$
$282$	0.537157	0.0319872
$283$	23.1995	1.37906	0.689532	−	0.724255i	$-0.257816\pi$
$283$	23.1995	1.37906	0.689532	+	0.724255i	$0.257816\pi$
$284$	7.71925	0.458053
$285$	−10.8101	−0.640334
$286$	17.0123	1.00596
$287$	3.28907	0.194148
$288$	−2.49362	−0.146938
$289$	−15.4681	−0.909890
$290$	−17.3933	−1.02137
$291$	−10.8069	−0.633511
$292$	5.65260	0.330794
$293$	21.5139	1.25686	0.628428	−	0.777868i	$-0.283699\pi$
$293$	21.5139	1.25686	0.628428	+	0.777868i	$0.283699\pi$
$294$	1.97223	0.115023
$295$	14.5057	0.844554
$296$	6.23895	0.362632
$297$	−13.7054	−0.795268
$298$	−1.73794	−0.100676
$299$	4.85256	0.280631
$300$	−6.41865	−0.370581
$301$	−4.49810	−0.259266
$302$	21.1004	1.21419
$303$	3.78119	0.217224
$304$	−4.05710	−0.232691
$305$	−14.6642	−0.839671
$306$	3.08631	0.176433
$307$	13.0864	0.746879	0.373439	−	0.927655i	$-0.378178\pi$
$307$	13.0864	0.746879	0.373439	+	0.927655i	$0.378178\pi$
$308$	−7.20917	−0.410781
$309$	−4.71872	−0.268439
$310$	40.5437	2.30273
$311$	13.7702	0.780835	0.390417	−	0.920638i	$-0.372331\pi$
$311$	13.7702	0.780835	0.390417	+	0.920638i	$0.372331\pi$
$312$	3.45311	0.195494
$313$	13.1690	0.744353	0.372177	−	0.928162i	$-0.378612\pi$
$313$	13.1690	0.744353	0.372177	+	0.928162i	$0.378612\pi$
$314$	23.9220	1.35000
$315$	19.1997	1.08178
$316$	5.06056	0.284679
$317$	25.2031	1.41555	0.707773	−	0.706440i	$-0.249700\pi$
$317$	25.2031	1.41555	0.707773	+	0.706440i	$0.249700\pi$
$318$	3.00952	0.168765
$319$	−16.2855	−0.911814
$320$	−3.74432	−0.209314
$321$	−10.7862	−0.602028
$322$	−2.05633	−0.114595
$323$	5.02141	0.279399
$324$	4.69897	0.261054
$325$	−43.7698	−2.42791
$326$	6.27839	0.347728
$327$	8.75618	0.484218
$328$	1.59949	0.0883171
$329$	−1.55222	−0.0855767
$330$	−9.34128	−0.514221
$331$	15.3843	0.845599	0.422800	−	0.906223i	$-0.361047\pi$
$331$	15.3843	0.845599	0.422800	+	0.906223i	$0.361047\pi$
$332$	−16.0117	−0.878754
$333$	−15.5576	−0.852549
$334$	0.977046	0.0534616
$335$	−29.1601	−1.59319
$336$	−1.46330	−0.0798293
$337$	16.5647	0.902337	0.451168	−	0.892439i	$-0.351007\pi$
$337$	16.5647	0.902337	0.451168	+	0.892439i	$0.351007\pi$
$338$	10.5473	0.573699
$339$	5.62978	0.305768
$340$	4.63429	0.251330
$341$	37.9616	2.05573
$342$	10.1169	0.547057
$343$	−20.0934	−1.08494
$344$	−2.18745	−0.117939
$345$	−2.66448	−0.143451
$346$	−9.09576	−0.488991
$347$	7.67594	0.412066	0.206033	−	0.978545i	$-0.433945\pi$
$347$	7.67594	0.412066	0.206033	+	0.978545i	$0.433945\pi$
$348$	−3.30559	−0.177198
$349$	10.7011	0.572819	0.286409	−	0.958107i	$-0.407538\pi$
$349$	10.7011	0.572819	0.286409	+	0.958107i	$0.407538\pi$
$350$	18.5479	0.991430
$351$	−18.9701	−1.01255
$352$	−3.50585	−0.186862
$353$	−28.4266	−1.51300	−0.756499	−	0.653995i	$-0.773092\pi$
$353$	−28.4266	−1.51300	−0.756499	+	0.653995i	$0.773092\pi$
$354$	2.75680	0.146522
$355$	−28.9033	−1.53403
$356$	−0.900612	−0.0477323
$357$	1.81110	0.0958535
$358$	−15.4217	−0.815060
$359$	−9.55656	−0.504376	−0.252188	−	0.967678i	$-0.581150\pi$
$359$	−9.55656	−0.504376	−0.252188	+	0.967678i	$0.581150\pi$
$360$	9.33690	0.492098
$361$	−2.53993	−0.133680
$362$	−17.0342	−0.895299
$363$	−0.918669	−0.0482176
$364$	−9.97844	−0.523012
$365$	−21.1652	−1.10784
$366$	−2.78693	−0.145675
$367$	12.5347	0.654308	0.327154	−	0.944971i	$-0.393910\pi$
$367$	12.5347	0.654308	0.327154	+	0.944971i	$0.393910\pi$
$368$	−1.00000	−0.0521286
$369$	−3.98851	−0.207634
$370$	−23.3606	−1.21446
$371$	−8.69658	−0.451504
$372$	7.70532	0.399502
$373$	−23.1684	−1.19962	−0.599808	−	0.800144i	$-0.704756\pi$
$373$	−23.1684	−1.19962	−0.599808	+	0.800144i	$0.704756\pi$
$374$	4.33914	0.224371
$375$	10.7111	0.553118
$376$	−0.754851	−0.0389285
$377$	−22.5413	−1.16094
$378$	8.03878	0.413470
$379$	21.4229	1.10042	0.550209	−	0.835027i	$-0.314548\pi$
$379$	21.4229	1.10042	0.550209	+	0.835027i	$0.314548\pi$
$380$	15.1911	0.779287
$381$	0.0238661	0.00122270
$382$	14.5758	0.745765
$383$	−0.861751	−0.0440334	−0.0220167	−	0.999758i	$-0.507009\pi$
$383$	−0.861751	−0.0440334	−0.0220167	+	0.999758i	$0.507009\pi$
$384$	−0.711607	−0.0363140
$385$	26.9934	1.37571
$386$	12.3658	0.629401
$387$	5.45465	0.277275
$388$	15.1866	0.770983
$389$	−0.701424	−0.0355636	−0.0177818	−	0.999842i	$-0.505660\pi$
$389$	−0.701424	−0.0355636	−0.0177818	+	0.999842i	$0.505660\pi$
$390$	−12.9296	−0.654714
$391$	1.23768	0.0625924
$392$	−2.77152	−0.139983
$393$	0.711607	0.0358958
$394$	−11.2199	−0.565252
$395$	−18.9484	−0.953396
$396$	8.74224	0.439314
$397$	−17.3568	−0.871112	−0.435556	−	0.900162i	$-0.643448\pi$
$397$	−17.3568	−0.871112	−0.435556	+	0.900162i	$0.643448\pi$
$398$	−3.03021	−0.151891
$399$	5.93674	0.297209
$400$	9.01995	0.450997
$401$	3.59906	0.179728	0.0898641	−	0.995954i	$-0.471357\pi$
$401$	3.59906	0.179728	0.0898641	+	0.995954i	$0.471357\pi$
$402$	−5.54187	−0.276403
$403$	52.5438	2.61739
$404$	−5.31360	−0.264361
$405$	−17.5944	−0.874275
$406$	9.55214	0.474065
$407$	−21.8728	−1.08420
$408$	0.880745	0.0436034
$409$	−12.4370	−0.614968	−0.307484	−	0.951553i	$-0.599487\pi$
$409$	−12.4370	−0.614968	−0.307484	+	0.951553i	$0.599487\pi$
$410$	−5.98901	−0.295776
$411$	−3.59689	−0.177421
$412$	6.63108	0.326690
$413$	−7.96631	−0.391997
$414$	2.49362	0.122555
$415$	59.9528	2.94297
$416$	−4.85256	−0.237916
$417$	−3.18481	−0.155961
$418$	14.2236	0.695698
$419$	11.9708	0.584812	0.292406	−	0.956294i	$-0.405544\pi$
$419$	11.9708	0.584812	0.292406	+	0.956294i	$0.405544\pi$
$420$	5.47905	0.267350
$421$	37.2324	1.81459	0.907297	−	0.420489i	$-0.138142\pi$
$421$	37.2324	1.81459	0.907297	+	0.420489i	$0.138142\pi$
$422$	1.79622	0.0874385
$423$	1.88231	0.0915210
$424$	−4.22918	−0.205387
$425$	−11.1638	−0.541526
$426$	−5.49307	−0.266140
$427$	8.05337	0.389730
$428$	15.1576	0.732668
$429$	−12.1061	−0.584488
$430$	8.19050	0.394981
$431$	6.37060	0.306861	0.153431	−	0.988159i	$-0.450968\pi$
$431$	6.37060	0.306861	0.153431	+	0.988159i	$0.450968\pi$
$432$	3.90929	0.188086
$433$	15.8899	0.763618	0.381809	−	0.924241i	$-0.375301\pi$
$433$	15.8899	0.763618	0.381809	+	0.924241i	$0.375301\pi$
$434$	−22.2660	−1.06880
$435$	12.3772	0.593440
$436$	−12.3048	−0.589293
$437$	4.05710	0.194077
$438$	−4.02243	−0.192199
$439$	−25.1636	−1.20099	−0.600496	−	0.799628i	$-0.705030\pi$
$439$	−25.1636	−1.20099	−0.600496	+	0.799628i	$0.705030\pi$
$440$	13.1270	0.625806
$441$	6.91111	0.329101
$442$	6.00594	0.285673
$443$	−27.7162	−1.31683	−0.658417	−	0.752653i	$-0.728774\pi$
$443$	−27.7162	−1.31683	−0.658417	+	0.752653i	$0.728774\pi$
$444$	−4.43968	−0.210698
$445$	3.37218	0.159857
$446$	−18.2513	−0.864222
$447$	1.23673	0.0584954
$448$	2.05633	0.0971523
$449$	28.6690	1.35297	0.676487	−	0.736455i	$-0.263502\pi$
$449$	28.6690	1.35297	0.676487	+	0.736455i	$0.263502\pi$
$450$	−22.4923	−1.06030
$451$	−5.60757	−0.264050
$452$	−7.91136	−0.372119
$453$	−15.0152	−0.705475
$454$	−13.1854	−0.618821
$455$	37.3625	1.75158
$456$	2.88706	0.135199
$457$	17.3659	0.812343	0.406172	−	0.913797i	$-0.366864\pi$
$457$	17.3659	0.812343	0.406172	+	0.913797i	$0.366864\pi$
$458$	−29.9502	−1.39948
$459$	−4.83847	−0.225841
$460$	3.74432	0.174580
$461$	−27.2163	−1.26759	−0.633794	−	0.773502i	$-0.718503\pi$
$461$	−27.2163	−1.26759	−0.633794	+	0.773502i	$0.718503\pi$
$462$	5.13009	0.238674
$463$	−5.01304	−0.232976	−0.116488	−	0.993192i	$-0.537164\pi$
$463$	−5.01304	−0.232976	−0.116488	+	0.993192i	$0.537164\pi$
$464$	4.64524	0.215650
$465$	−28.8512	−1.33794
$466$	−16.1270	−0.747070
$467$	33.2186	1.53717	0.768586	−	0.639746i	$-0.220961\pi$
$467$	33.2186	1.53717	0.768586	+	0.639746i	$0.220961\pi$
$468$	12.1004	0.559342
$469$	16.0143	0.739472
$470$	2.82641	0.130372
$471$	−17.0230	−0.784381
$472$	−3.87405	−0.178318
$473$	7.66885	0.352614
$474$	−3.60113	−0.165405
$475$	−36.5948	−1.67909
$476$	−2.54508	−0.116654
$477$	10.5460	0.482866
$478$	−6.14137	−0.280900
$479$	−4.97017	−0.227093	−0.113546	−	0.993533i	$-0.536221\pi$
$479$	−4.97017	−0.227093	−0.113546	+	0.993533i	$0.536221\pi$
$480$	2.66448	0.121617
$481$	−30.2749	−1.38042
$482$	3.28827	0.149776
$483$	1.46330	0.0665822
$484$	1.29098	0.0586808
$485$	−56.8635	−2.58204
$486$	−15.0717	−0.683666
$487$	25.4576	1.15359	0.576796	−	0.816888i	$-0.304303\pi$
$487$	25.4576	1.15359	0.576796	+	0.816888i	$0.304303\pi$
$488$	3.91639	0.177287
$489$	−4.46774	−0.202038
$490$	10.3775	0.468807
$491$	4.99312	0.225336	0.112668	−	0.993633i	$-0.464060\pi$
$491$	4.99312	0.225336	0.112668	+	0.993633i	$0.464060\pi$
$492$	−1.13821	−0.0513144
$493$	−5.74935	−0.258938
$494$	19.6873	0.885775
$495$	−32.7338	−1.47127
$496$	−10.8281	−0.486194
$497$	15.8733	0.712014
$498$	11.3940	0.510578
$499$	−28.5956	−1.28011	−0.640057	−	0.768327i	$-0.721089\pi$
$499$	−28.5956	−1.28011	−0.640057	+	0.768327i	$0.721089\pi$
$500$	−15.0520	−0.673145
$501$	−0.695272	−0.0310625
$502$	−16.1942	−0.722782
$503$	37.2376	1.66034	0.830170	−	0.557510i	$-0.188243\pi$
$503$	37.2376	1.66034	0.830170	+	0.557510i	$0.188243\pi$
$504$	−5.12769	−0.228405
$505$	19.8958	0.885352
$506$	3.50585	0.155854
$507$	−7.50555	−0.333333
$508$	−0.0335384	−0.00148802
$509$	38.3222	1.69860	0.849300	−	0.527910i	$-0.177024\pi$
$509$	38.3222	1.69860	0.849300	+	0.527910i	$0.177024\pi$
$510$	−3.29779	−0.146029
$511$	11.6236	0.514197
$512$	1.00000	0.0441942
$513$	−15.8604	−0.700254
$514$	31.5273	1.39061
$515$	−24.8289	−1.09409
$516$	1.55660	0.0685255
$517$	2.64639	0.116388
$518$	12.8293	0.563688
$519$	6.47260	0.284116
$520$	18.1695	0.796787
$521$	−5.11774	−0.224212	−0.112106	−	0.993696i	$-0.535760\pi$
$521$	−5.11774	−0.224212	−0.112106	+	0.993696i	$0.535760\pi$
$522$	−11.5835	−0.506994
$523$	13.8729	0.606618	0.303309	−	0.952892i	$-0.401909\pi$
$523$	13.8729	0.606618	0.303309	+	0.952892i	$0.401909\pi$
$524$	−1.00000	−0.0436852
$525$	−13.1988	−0.576045
$526$	−8.02776	−0.350027
$527$	13.4017	0.583788
$528$	2.49479	0.108572
$529$	1.00000	0.0434783
$530$	15.8354	0.687847
$531$	9.66040	0.419226
$532$	−8.34272	−0.361703
$533$	−7.76162	−0.336193
$534$	0.640882	0.0277337
$535$	−56.7548	−2.45372
$536$	7.78783	0.336383
$537$	10.9741	0.473570
$538$	−4.82132	−0.207862
$539$	9.71654	0.418521
$540$	−14.6377	−0.629904
$541$	−7.15776	−0.307736	−0.153868	−	0.988091i	$-0.549173\pi$
$541$	−7.15776	−0.307736	−0.153868	+	0.988091i	$0.549173\pi$
$542$	20.7183	0.889927
$543$	12.1217	0.520191
$544$	−1.23768	−0.0530653
$545$	46.0731	1.97356
$546$	7.10073	0.303883
$547$	−28.7249	−1.22819	−0.614093	−	0.789233i	$-0.710478\pi$
$547$	−28.7249	−1.22819	−0.614093	+	0.789233i	$0.710478\pi$
$548$	5.05460	0.215922
$549$	−9.76597	−0.416802
$550$	−31.6226	−1.34839
$551$	−18.8462	−0.802876
$552$	0.711607	0.0302880
$553$	10.4062	0.442515
$554$	4.37957	0.186070
$555$	16.6236	0.705632
$556$	4.47552	0.189805
$557$	−27.1462	−1.15022	−0.575110	−	0.818076i	$-0.695041\pi$
$557$	−27.1462	−1.15022	−0.575110	+	0.818076i	$0.695041\pi$
$558$	27.0010	1.14304
$559$	10.6147	0.448954
$560$	−7.69955	−0.325365
$561$	−3.08776	−0.130365
$562$	22.3742	0.943798
$563$	3.16452	0.133369	0.0666844	−	0.997774i	$-0.478758\pi$
$563$	3.16452	0.133369	0.0666844	+	0.997774i	$0.478758\pi$
$564$	0.537157	0.0226184
$565$	29.6227	1.24624
$566$	23.1995	0.975146
$567$	9.66261	0.405791
$568$	7.71925	0.323892
$569$	−31.0131	−1.30014	−0.650068	−	0.759876i	$-0.725260\pi$
$569$	−31.0131	−1.30014	−0.650068	+	0.759876i	$0.725260\pi$
$570$	−10.8101	−0.452785
$571$	−22.0312	−0.921976	−0.460988	−	0.887406i	$-0.652505\pi$
$571$	−22.0312	−0.921976	−0.460988	+	0.887406i	$0.652505\pi$
$572$	17.0123	0.711322
$573$	−10.3723	−0.433308
$574$	3.28907	0.137283
$575$	−9.01995	−0.376158
$576$	−2.49362	−0.103901
$577$	17.9107	0.745630	0.372815	−	0.927906i	$-0.378393\pi$
$577$	17.9107	0.745630	0.372815	+	0.927906i	$0.378393\pi$
$578$	−15.4681	−0.643390
$579$	−8.79956	−0.365697
$580$	−17.3933	−0.722217
$581$	−32.9252	−1.36597
$582$	−10.8069	−0.447960
$583$	14.8269	0.614067
$584$	5.65260	0.233906
$585$	−45.3079	−1.87325
$586$	21.5139	0.888731
$587$	−23.9757	−0.989582	−0.494791	−	0.869012i	$-0.664755\pi$
$587$	−23.9757	−0.989582	−0.494791	+	0.869012i	$0.664755\pi$
$588$	1.97223	0.0813336
$589$	43.9305	1.81013
$590$	14.5057	0.597190
$591$	7.98418	0.328425
$592$	6.23895	0.256419
$593$	−12.6870	−0.520991	−0.260496	−	0.965475i	$-0.583886\pi$
$593$	−12.6870	−0.520991	−0.260496	+	0.965475i	$0.583886\pi$
$594$	−13.7054	−0.562339
$595$	9.52961	0.390676
$596$	−1.73794	−0.0711889
$597$	2.15632	0.0882523
$598$	4.85256	0.198436
$599$	−43.9992	−1.79776	−0.898880	−	0.438196i	$-0.855618\pi$
$599$	−43.9992	−1.79776	−0.898880	+	0.438196i	$0.855618\pi$
$600$	−6.41865	−0.262040
$601$	−7.12799	−0.290757	−0.145378	−	0.989376i	$-0.546440\pi$
$601$	−7.12799	−0.290757	−0.145378	+	0.989376i	$0.546440\pi$
$602$	−4.49810	−0.183329
$603$	−19.4198	−0.790837
$604$	21.1004	0.858563
$605$	−4.83384	−0.196524
$606$	3.78119	0.153600
$607$	36.5021	1.48157	0.740786	−	0.671741i	$-0.234453\pi$
$607$	36.5021	1.48157	0.740786	+	0.671741i	$0.234453\pi$
$608$	−4.05710	−0.164537
$609$	−6.79737	−0.275443
$610$	−14.6642	−0.593737
$611$	3.66296	0.148187
$612$	3.08631	0.124757
$613$	14.4294	0.582798	0.291399	−	0.956602i	$-0.405879\pi$
$613$	14.4294	0.582798	0.291399	+	0.956602i	$0.405879\pi$
$614$	13.0864	0.528123
$615$	4.26182	0.171853
$616$	−7.20917	−0.290466
$617$	27.4190	1.10385	0.551924	−	0.833895i	$-0.313894\pi$
$617$	27.4190	1.10385	0.551924	+	0.833895i	$0.313894\pi$
$618$	−4.71872	−0.189815
$619$	−34.5365	−1.38814	−0.694070	−	0.719908i	$-0.744184\pi$
$619$	−34.5365	−1.38814	−0.694070	+	0.719908i	$0.744184\pi$
$620$	40.5437	1.62828
$621$	−3.90929	−0.156875
$622$	13.7702	0.552133
$623$	−1.85195	−0.0741969
$624$	3.45311	0.138235
$625$	11.2597	0.450387
$626$	13.1690	0.526337
$627$	−10.1216	−0.404218
$628$	23.9220	0.954591
$629$	−7.72185	−0.307891
$630$	19.1997	0.764935
$631$	11.5044	0.457982	0.228991	−	0.973429i	$-0.426457\pi$
$631$	11.5044	0.457982	0.228991	+	0.973429i	$0.426457\pi$
$632$	5.06056	0.201298
$633$	−1.27820	−0.0508039
$634$	25.2031	1.00094
$635$	0.125578	0.00498343
$636$	3.00952	0.119335
$637$	13.4490	0.532868
$638$	−16.2855	−0.644750
$639$	−19.2488	−0.761472
$640$	−3.74432	−0.148007
$641$	−22.8783	−0.903640	−0.451820	−	0.892109i	$-0.649225\pi$
$641$	−22.8783	−0.903640	−0.451820	+	0.892109i	$0.649225\pi$
$642$	−10.7862	−0.425698
$643$	24.2393	0.955903	0.477952	−	0.878386i	$-0.341379\pi$
$643$	24.2393	0.955903	0.477952	+	0.878386i	$0.341379\pi$
$644$	−2.05633	−0.0810306
$645$	−5.82841	−0.229494
$646$	5.02141	0.197565
$647$	−21.2515	−0.835482	−0.417741	−	0.908566i	$-0.637178\pi$
$647$	−21.2515	−0.835482	−0.417741	+	0.908566i	$0.637178\pi$
$648$	4.69897	0.184593
$649$	13.5818	0.533134
$650$	−43.7698	−1.71679
$651$	15.8447	0.621001
$652$	6.27839	0.245881
$653$	18.4016	0.720109	0.360054	−	0.932931i	$-0.382758\pi$
$653$	18.4016	0.720109	0.360054	+	0.932931i	$0.382758\pi$
$654$	8.75618	0.342394
$655$	3.74432	0.146303
$656$	1.59949	0.0624496
$657$	−14.0954	−0.549915
$658$	−1.55222	−0.0605118
$659$	−12.1042	−0.471513	−0.235756	−	0.971812i	$-0.575757\pi$
$659$	−12.1042	−0.471513	−0.235756	+	0.971812i	$0.575757\pi$
$660$	−9.34128	−0.363609
$661$	12.9536	0.503837	0.251918	−	0.967748i	$-0.418939\pi$
$661$	12.9536	0.503837	0.251918	+	0.967748i	$0.418939\pi$
$662$	15.3843	0.597929
$663$	−4.27386	−0.165983
$664$	−16.0117	−0.621373
$665$	31.2378	1.21135
$666$	−15.5576	−0.602843
$667$	−4.64524	−0.179865
$668$	0.977046	0.0378030
$669$	12.9877	0.502134
$670$	−29.1601	−1.12655
$671$	−13.7303	−0.530051
$672$	−1.46330	−0.0564478
$673$	1.19559	0.0460864	0.0230432	−	0.999734i	$-0.492664\pi$
$673$	1.19559	0.0460864	0.0230432	+	0.999734i	$0.492664\pi$
$674$	16.5647	0.638048
$675$	35.2616	1.35722
$676$	10.5473	0.405666
$677$	13.9923	0.537768	0.268884	−	0.963173i	$-0.413345\pi$
$677$	13.9923	0.537768	0.268884	+	0.963173i	$0.413345\pi$
$678$	5.62978	0.216210
$679$	31.2286	1.19844
$680$	4.63429	0.177717
$681$	9.38281	0.359550
$682$	37.9616	1.45362
$683$	−15.9334	−0.609676	−0.304838	−	0.952404i	$-0.598602\pi$
$683$	−15.9334	−0.609676	−0.304838	+	0.952404i	$0.598602\pi$
$684$	10.1169	0.386828
$685$	−18.9261	−0.723127
$686$	−20.0934	−0.767171
$687$	21.3128	0.813134
$688$	−2.18745	−0.0833956
$689$	20.5224	0.781840
$690$	−2.66448	−0.101435
$691$	−20.7810	−0.790547	−0.395274	−	0.918563i	$-0.629350\pi$
$691$	−20.7810	−0.790547	−0.395274	+	0.918563i	$0.629350\pi$
$692$	−9.09576	−0.345769
$693$	17.9769	0.682886
$694$	7.67594	0.291375
$695$	−16.7578	−0.635660
$696$	−3.30559	−0.125298
$697$	−1.97966	−0.0749851
$698$	10.7011	0.405044
$699$	11.4761	0.434066
$700$	18.5479	0.701047
$701$	−29.8537	−1.12756	−0.563780	−	0.825925i	$-0.690653\pi$
$701$	−29.8537	−1.12756	−0.563780	+	0.825925i	$0.690653\pi$
$702$	−18.9701	−0.715979
$703$	−25.3121	−0.954663
$704$	−3.50585	−0.132132
$705$	−2.01129	−0.0757495
$706$	−28.4266	−1.06985
$707$	−10.9265	−0.410933
$708$	2.75680	0.103607
$709$	42.1451	1.58279	0.791397	−	0.611303i	$-0.209354\pi$
$709$	42.1451	1.58279	0.791397	+	0.611303i	$0.209354\pi$
$710$	−28.9033	−1.08472
$711$	−12.6191	−0.473253
$712$	−0.900612	−0.0337519
$713$	10.8281	0.405514
$714$	1.81110	0.0677786
$715$	−63.6997	−2.38223
$716$	−15.4217	−0.576334
$717$	4.37024	0.163210
$718$	−9.55656	−0.356648
$719$	−6.24118	−0.232757	−0.116378	−	0.993205i	$-0.537128\pi$
$719$	−6.24118	−0.232757	−0.116378	+	0.993205i	$0.537128\pi$
$720$	9.33690	0.347966
$721$	13.6357	0.507819
$722$	−2.53993	−0.0945263
$723$	−2.33995	−0.0870238
$724$	−17.0342	−0.633072
$725$	41.8999	1.55612
$726$	−0.918669	−0.0340950
$727$	−22.3736	−0.829790	−0.414895	−	0.909869i	$-0.636182\pi$
$727$	−22.3736	−0.829790	−0.414895	+	0.909869i	$0.636182\pi$
$728$	−9.97844	−0.369826
$729$	−3.37178	−0.124881
$730$	−21.1652	−0.783358
$731$	2.70737	0.100136
$732$	−2.78693	−0.103008
$733$	−21.5836	−0.797208	−0.398604	−	0.917123i	$-0.630505\pi$
$733$	−21.5836	−0.797208	−0.398604	+	0.917123i	$0.630505\pi$
$734$	12.5347	0.462666
$735$	−7.38468	−0.272388
$736$	−1.00000	−0.0368605
$737$	−27.3029	−1.00572
$738$	−3.98851	−0.146819
$739$	−13.1162	−0.482489	−0.241244	−	0.970464i	$-0.577556\pi$
$739$	−13.1162	−0.482489	−0.241244	+	0.970464i	$0.577556\pi$
$740$	−23.3606	−0.858754
$741$	−14.0096	−0.514657
$742$	−8.69658	−0.319262
$743$	7.79608	0.286010	0.143005	−	0.989722i	$-0.454323\pi$
$743$	7.79608	0.286010	0.143005	+	0.989722i	$0.454323\pi$
$744$	7.70532	0.282491
$745$	6.50742	0.238413
$746$	−23.1684	−0.848257
$747$	39.9269	1.46085
$748$	4.33914	0.158655
$749$	31.1689	1.13889
$750$	10.7111	0.391113
$751$	−3.31131	−0.120831	−0.0604157	−	0.998173i	$-0.519243\pi$
$751$	−3.31131	−0.120831	−0.0604157	+	0.998173i	$0.519243\pi$
$752$	−0.754851	−0.0275266
$753$	11.5239	0.419954
$754$	−22.5413	−0.820907
$755$	−79.0067	−2.87535
$756$	8.03878	0.292368
$757$	−20.6945	−0.752153	−0.376076	−	0.926589i	$-0.622727\pi$
$757$	−20.6945	−0.752153	−0.376076	+	0.926589i	$0.622727\pi$
$758$	21.4229	0.778113
$759$	−2.49479	−0.0905550
$760$	15.1911	0.551039
$761$	−18.2826	−0.662745	−0.331373	−	0.943500i	$-0.607512\pi$
$761$	−18.2826	−0.662745	−0.331373	+	0.943500i	$0.607512\pi$
$762$	0.0238661	0.000864579 0
$763$	−25.3027	−0.916018
$764$	14.5758	0.527335
$765$	−11.5561	−0.417813
$766$	−0.861751	−0.0311363
$767$	18.7991	0.678795
$768$	−0.711607	−0.0256779
$769$	6.83092	0.246329	0.123165	−	0.992386i	$-0.460696\pi$
$769$	6.83092	0.246329	0.123165	+	0.992386i	$0.460696\pi$
$770$	26.9934	0.972776
$771$	−22.4350	−0.807979
$772$	12.3658	0.445054
$773$	29.7843	1.07127	0.535634	−	0.844450i	$-0.320073\pi$
$773$	29.7843	1.07127	0.535634	+	0.844450i	$0.320073\pi$
$774$	5.45465	0.196063
$775$	−97.6685	−3.50836
$776$	15.1866	0.545167
$777$	−9.12943	−0.327516
$778$	−0.701424	−0.0251473
$779$	−6.48929	−0.232503
$780$	−12.9296	−0.462953
$781$	−27.0625	−0.968373
$782$	1.23768	0.0442595
$783$	18.1596	0.648972
$784$	−2.77152	−0.0989830
$785$	−89.5716	−3.19695
$786$	0.711607	0.0253822
$787$	−14.3021	−0.509815	−0.254908	−	0.966965i	$-0.582045\pi$
$787$	−14.3021	−0.509815	−0.254908	+	0.966965i	$0.582045\pi$
$788$	−11.2199	−0.399693
$789$	5.71261	0.203374
$790$	−18.9484	−0.674153
$791$	−16.2683	−0.578436
$792$	8.74224	0.310642
$793$	−19.0045	−0.674870
$794$	−17.3568	−0.615969
$795$	−11.2686	−0.399656
$796$	−3.03021	−0.107403
$797$	0.212039	0.00751081	0.00375541	−	0.999993i	$-0.498805\pi$
$797$	0.212039	0.00751081	0.00375541	+	0.999993i	$0.498805\pi$
$798$	5.93674	0.210158
$799$	0.934268	0.0330520
$800$	9.01995	0.318903
$801$	2.24578	0.0793508
$802$	3.59906	0.127087
$803$	−19.8172	−0.699333
$804$	−5.54187	−0.195447
$805$	7.69955	0.271373
$806$	52.5438	1.85078
$807$	3.43089	0.120773
$808$	−5.31360	−0.186932
$809$	−37.5413	−1.31988	−0.659941	−	0.751318i	$-0.729419\pi$
$809$	−37.5413	−1.31988	−0.659941	+	0.751318i	$0.729419\pi$
$810$	−17.5944	−0.618206
$811$	10.5263	0.369628	0.184814	−	0.982773i	$-0.440832\pi$
$811$	10.5263	0.369628	0.184814	+	0.982773i	$0.440832\pi$
$812$	9.55214	0.335214
$813$	−14.7433	−0.517070
$814$	−21.8728	−0.766642
$815$	−23.5083	−0.823460
$816$	0.880745	0.0308322
$817$	8.87469	0.310486
$818$	−12.4370	−0.434848
$819$	24.8824	0.869461
$820$	−5.98901	−0.209145
$821$	−8.15442	−0.284591	−0.142296	−	0.989824i	$-0.545448\pi$
$821$	−8.15442	−0.284591	−0.142296	+	0.989824i	$0.545448\pi$
$822$	−3.59689	−0.125456
$823$	−2.15095	−0.0749773	−0.0374886	−	0.999297i	$-0.511936\pi$
$823$	−2.15095	−0.0749773	−0.0374886	+	0.999297i	$0.511936\pi$
$824$	6.63108	0.231005
$825$	22.5028	0.783448
$826$	−7.96631	−0.277184
$827$	−7.18791	−0.249948	−0.124974	−	0.992160i	$-0.539885\pi$
$827$	−7.18791	−0.249948	−0.124974	+	0.992160i	$0.539885\pi$
$828$	2.49362	0.0866591
$829$	10.5886	0.367758	0.183879	−	0.982949i	$-0.441134\pi$
$829$	10.5886	0.367758	0.183879	+	0.982949i	$0.441134\pi$
$830$	59.9528	2.08099
$831$	−3.11653	−0.108111
$832$	−4.85256	−0.168232
$833$	3.43027	0.118852
$834$	−3.18481	−0.110281
$835$	−3.65837	−0.126603
$836$	14.2236	0.491933
$837$	−42.3301	−1.46314
$838$	11.9708	0.413525
$839$	6.71941	0.231980	0.115990	−	0.993250i	$-0.462996\pi$
$839$	6.71941	0.231980	0.115990	+	0.993250i	$0.462996\pi$
$840$	5.47905	0.189045
$841$	−7.42170	−0.255921
$842$	37.2324	1.28311
$843$	−15.9216	−0.548369
$844$	1.79622	0.0618284
$845$	−39.4926	−1.35859
$846$	1.88231	0.0647151
$847$	2.65467	0.0912156
$848$	−4.22918	−0.145231
$849$	−16.5089	−0.566584
$850$	−11.1638	−0.382917
$851$	−6.23895	−0.213869
$852$	−5.49307	−0.188189
$853$	50.2770	1.72145	0.860726	−	0.509068i	$-0.170010\pi$
$853$	50.2770	1.72145	0.860726	+	0.509068i	$0.170010\pi$
$854$	8.05337	0.275581
$855$	−37.8808	−1.29549
$856$	15.1576	0.518075
$857$	−35.0194	−1.19624	−0.598120	−	0.801406i	$-0.704085\pi$
$857$	−35.0194	−1.19624	−0.598120	+	0.801406i	$0.704085\pi$
$858$	−12.1061	−0.413295
$859$	−14.4598	−0.493361	−0.246681	−	0.969097i	$-0.579340\pi$
$859$	−14.4598	−0.493361	−0.246681	+	0.969097i	$0.579340\pi$
$860$	8.19050	0.279294
$861$	−2.34053	−0.0797649
$862$	6.37060	0.216984
$863$	−42.9334	−1.46147	−0.730735	−	0.682661i	$-0.760823\pi$
$863$	−42.9334	−1.46147	−0.730735	+	0.682661i	$0.760823\pi$
$864$	3.90929	0.132997
$865$	34.0574	1.15799
$866$	15.8899	0.539960
$867$	11.0072	0.373825
$868$	−22.2660	−0.755758
$869$	−17.7416	−0.601841
$870$	12.3772	0.419626
$871$	−37.7909	−1.28050
$872$	−12.3048	−0.416693
$873$	−37.8695	−1.28169
$874$	4.05710	0.137234
$875$	−30.9518	−1.04636
$876$	−4.02243	−0.135905
$877$	13.7286	0.463582	0.231791	−	0.972766i	$-0.425541\pi$
$877$	13.7286	0.463582	0.231791	+	0.972766i	$0.425541\pi$
$878$	−25.1636	−0.849229
$879$	−15.3094	−0.516375
$880$	13.1270	0.442512
$881$	−28.6266	−0.964454	−0.482227	−	0.876046i	$-0.660172\pi$
$881$	−28.6266	−0.964454	−0.482227	+	0.876046i	$0.660172\pi$
$882$	6.91111	0.232709
$883$	−45.4776	−1.53044	−0.765222	−	0.643766i	$-0.777371\pi$
$883$	−45.4776	−1.53044	−0.765222	+	0.643766i	$0.777371\pi$
$884$	6.00594	0.202002
$885$	−10.3224	−0.346982
$886$	−27.7162	−0.931143
$887$	−15.7265	−0.528045	−0.264022	−	0.964517i	$-0.585049\pi$
$887$	−15.7265	−0.528045	−0.264022	+	0.964517i	$0.585049\pi$
$888$	−4.43968	−0.148986
$889$	−0.0689658	−0.00231304
$890$	3.37218	0.113036
$891$	−16.4739	−0.551896
$892$	−18.2513	−0.611097
$893$	3.06251	0.102483
$894$	1.23673	0.0413625
$895$	57.7436	1.93016
$896$	2.05633	0.0686970
$897$	−3.45311	−0.115296
$898$	28.6690	0.956697
$899$	−50.2990	−1.67757
$900$	−22.4923	−0.749743
$901$	5.23440	0.174383
$902$	−5.60757	−0.186712
$903$	3.20088	0.106519
$904$	−7.91136	−0.263128
$905$	63.7817	2.12017
$906$	−15.0152	−0.498846
$907$	12.7123	0.422106	0.211053	−	0.977475i	$-0.432311\pi$
$907$	12.7123	0.422106	0.211053	+	0.977475i	$0.432311\pi$
$908$	−13.1854	−0.437573
$909$	13.2501	0.439477
$910$	37.3625	1.23855
$911$	17.1172	0.567118	0.283559	−	0.958955i	$-0.408485\pi$
$911$	17.1172	0.567118	0.283559	+	0.958955i	$0.408485\pi$
$912$	2.88706	0.0956001
$913$	56.1345	1.85778
$914$	17.3659	0.574413
$915$	10.4352	0.344976
$916$	−29.9502	−0.989584
$917$	−2.05633	−0.0679059
$918$	−4.83847	−0.159693
$919$	−22.1535	−0.730776	−0.365388	−	0.930855i	$-0.619064\pi$
$919$	−22.1535	−0.730776	−0.365388	+	0.930855i	$0.619064\pi$
$920$	3.74432	0.123447
$921$	−9.31235	−0.306852
$922$	−27.2163	−0.896320
$923$	−37.4581	−1.23295
$924$	5.13009	0.168768
$925$	56.2750	1.85031
$926$	−5.01304	−0.164739
$927$	−16.5354	−0.543093
$928$	4.64524	0.152488
$929$	−6.77052	−0.222133	−0.111067	−	0.993813i	$-0.535427\pi$
$929$	−6.77052	−0.222133	−0.111067	+	0.993813i	$0.535427\pi$
$930$	−28.8512	−0.946068
$931$	11.2444	0.368519
$932$	−16.1270	−0.528258
$933$	−9.79894	−0.320803
$934$	33.2186	1.08694
$935$	−16.2471	−0.531338
$936$	12.1004	0.395514
$937$	19.2433	0.628652	0.314326	−	0.949315i	$-0.398221\pi$
$937$	19.2433	0.628652	0.314326	+	0.949315i	$0.398221\pi$
$938$	16.0143	0.522886
$939$	−9.37112	−0.305815
$940$	2.82641	0.0921872
$941$	−44.7308	−1.45818	−0.729091	−	0.684416i	$-0.760057\pi$
$941$	−44.7308	−1.45818	−0.729091	+	0.684416i	$0.760057\pi$
$942$	−17.0230	−0.554641
$943$	−1.59949	−0.0520866
$944$	−3.87405	−0.126090
$945$	−30.0998	−0.979146
$946$	7.66885	0.249336
$947$	−27.2433	−0.885288	−0.442644	−	0.896697i	$-0.645960\pi$
$947$	−27.2433	−0.885288	−0.442644	+	0.896697i	$0.645960\pi$
$948$	−3.60113	−0.116959
$949$	−27.4296	−0.890402
$950$	−36.5948	−1.18729
$951$	−17.9347	−0.581572
$952$	−2.54508	−0.0824866
$953$	−12.3841	−0.401159	−0.200579	−	0.979677i	$-0.564282\pi$
$953$	−12.3841	−0.401159	−0.200579	+	0.979677i	$0.564282\pi$
$954$	10.5460	0.341438
$955$	−54.5766	−1.76606
$956$	−6.14137	−0.198626
$957$	11.5889	0.374616
$958$	−4.97017	−0.160579
$959$	10.3939	0.335637
$960$	2.66448	0.0859959
$961$	86.2469	2.78216
$962$	−30.2749	−0.976101
$963$	−37.7971	−1.21800
$964$	3.28827	0.105908
$965$	−46.3014	−1.49049
$966$	1.46330	0.0470808
$967$	10.9214	0.351210	0.175605	−	0.984461i	$-0.443812\pi$
$967$	10.9214	0.351210	0.175605	+	0.984461i	$0.443812\pi$
$968$	1.29098	0.0414936
$969$	−3.57327	−0.114790
$970$	−56.8635	−1.82578
$971$	−2.89665	−0.0929578	−0.0464789	−	0.998919i	$-0.514800\pi$
$971$	−2.89665	−0.0929578	−0.0464789	+	0.998919i	$0.514800\pi$
$972$	−15.0717	−0.483425
$973$	9.20314	0.295039
$974$	25.4576	0.815713
$975$	31.1469	0.997499
$976$	3.91639	0.125361
$977$	0.404427	0.0129388	0.00646938	−	0.999979i	$-0.497941\pi$
$977$	0.404427	0.0129388	0.00646938	+	0.999979i	$0.497941\pi$
$978$	−4.46774	−0.142863
$979$	3.15741	0.100911
$980$	10.3775	0.331496
$981$	30.6834	0.979647
$982$	4.99312	0.159337
$983$	−27.8405	−0.887976	−0.443988	−	0.896033i	$-0.646437\pi$
$983$	−27.8405	−0.887976	−0.443988	+	0.896033i	$0.646437\pi$
$984$	−1.13821	−0.0362847
$985$	42.0110	1.33858
$986$	−5.74935	−0.183097
$987$	1.10457	0.0351589
$988$	19.6873	0.626337
$989$	2.18745	0.0695567
$990$	−32.7338	−1.04035
$991$	0.891321	0.0283137	0.0141569	−	0.999900i	$-0.495494\pi$
$991$	0.891321	0.0283137	0.0141569	+	0.999900i	$0.495494\pi$
$992$	−10.8281	−0.343791
$993$	−10.9476	−0.347411
$994$	15.8733	0.503470
$995$	11.3461	0.359695
$996$	11.3940	0.361033
$997$	5.60298	0.177448	0.0887241	−	0.996056i	$-0.471721\pi$
$997$	5.60298	0.177448	0.0887241	+	0.996056i	$0.471721\pi$
$998$	−28.5956	−0.905178
$999$	24.3899	0.771662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.16	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.16	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.711607 q^{3} +1.00000 q^{4} -3.74432 q^{5} -0.711607 q^{6} +2.05633 q^{7} +1.00000 q^{8} -2.49362 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.711607 q^{3} +1.00000 q^{4} -3.74432 q^{5} -0.711607 q^{6} +2.05633 q^{7} +1.00000 q^{8} -2.49362 q^{9} -3.74432 q^{10} -3.50585 q^{11} -0.711607 q^{12} -4.85256 q^{13} +2.05633 q^{14} +2.66448 q^{15} +1.00000 q^{16} -1.23768 q^{17} -2.49362 q^{18} -4.05710 q^{19} -3.74432 q^{20} -1.46330 q^{21} -3.50585 q^{22} -1.00000 q^{23} -0.711607 q^{24} +9.01995 q^{25} -4.85256 q^{26} +3.90929 q^{27} +2.05633 q^{28} +4.64524 q^{29} +2.66448 q^{30} -10.8281 q^{31} +1.00000 q^{32} +2.49479 q^{33} -1.23768 q^{34} -7.69955 q^{35} -2.49362 q^{36} +6.23895 q^{37} -4.05710 q^{38} +3.45311 q^{39} -3.74432 q^{40} +1.59949 q^{41} -1.46330 q^{42} -2.18745 q^{43} -3.50585 q^{44} +9.33690 q^{45} -1.00000 q^{46} -0.754851 q^{47} -0.711607 q^{48} -2.77152 q^{49} +9.01995 q^{50} +0.880745 q^{51} -4.85256 q^{52} -4.22918 q^{53} +3.90929 q^{54} +13.1270 q^{55} +2.05633 q^{56} +2.88706 q^{57} +4.64524 q^{58} -3.87405 q^{59} +2.66448 q^{60} +3.91639 q^{61} -10.8281 q^{62} -5.12769 q^{63} +1.00000 q^{64} +18.1695 q^{65} +2.49479 q^{66} +7.78783 q^{67} -1.23768 q^{68} +0.711607 q^{69} -7.69955 q^{70} +7.71925 q^{71} -2.49362 q^{72} +5.65260 q^{73} +6.23895 q^{74} -6.41865 q^{75} -4.05710 q^{76} -7.20917 q^{77} +3.45311 q^{78} +5.06056 q^{79} -3.74432 q^{80} +4.69897 q^{81} +1.59949 q^{82} -16.0117 q^{83} -1.46330 q^{84} +4.63429 q^{85} -2.18745 q^{86} -3.30559 q^{87} -3.50585 q^{88} -0.900612 q^{89} +9.33690 q^{90} -9.97844 q^{91} -1.00000 q^{92} +7.70532 q^{93} -0.754851 q^{94} +15.1911 q^{95} -0.711607 q^{96} +15.1866 q^{97} -2.77152 q^{98} +8.74224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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