LMFDB - Embedded newform 5290.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 12 $ x^3 - x^2 - 9*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.68740$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.68740 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.68740 q^{6} +4.59692 q^{7} +1.00000 q^{8} +4.22212 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.68740 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.68740 q^{6} +4.59692 q^{7} +1.00000 q^{8} +4.22212 q^{9} +1.00000 q^{10} -5.13163 q^{11} +2.68740 q^{12} -1.22212 q^{13} +4.59692 q^{14} +2.68740 q^{15} +1.00000 q^{16} +4.68740 q^{17} +4.22212 q^{18} +4.59692 q^{19} +1.00000 q^{20} +12.3537 q^{21} -5.13163 q^{22} +2.68740 q^{24} +1.00000 q^{25} -1.22212 q^{26} +3.28432 q^{27} +4.59692 q^{28} +3.37480 q^{29} +2.68740 q^{30} -0.777884 q^{31} +1.00000 q^{32} -13.7907 q^{33} +4.68740 q^{34} +4.59692 q^{35} +4.22212 q^{36} -5.81903 q^{37} +4.59692 q^{38} -3.28432 q^{39} +1.00000 q^{40} -8.50643 q^{41} +12.3537 q^{42} -8.00000 q^{43} -5.13163 q^{44} +4.22212 q^{45} -6.44423 q^{47} +2.68740 q^{48} +14.1316 q^{49} +1.00000 q^{50} +12.5969 q^{51} -1.22212 q^{52} +6.00000 q^{53} +3.28432 q^{54} -5.13163 q^{55} +4.59692 q^{56} +12.3537 q^{57} +3.37480 q^{58} +9.37480 q^{59} +2.68740 q^{60} -10.9507 q^{61} -0.777884 q^{62} +19.4087 q^{63} +1.00000 q^{64} -1.22212 q^{65} -13.7907 q^{66} -15.6381 q^{67} +4.68740 q^{68} +4.59692 q^{70} +1.31260 q^{71} +4.22212 q^{72} -4.44423 q^{73} -5.81903 q^{74} +2.68740 q^{75} +4.59692 q^{76} -23.5897 q^{77} -3.28432 q^{78} +4.88847 q^{79} +1.00000 q^{80} -3.84008 q^{81} -8.50643 q^{82} +3.81903 q^{83} +12.3537 q^{84} +4.68740 q^{85} -8.00000 q^{86} +9.06943 q^{87} -5.13163 q^{88} -8.93057 q^{89} +4.22212 q^{90} -5.61797 q^{91} -2.09048 q^{93} -6.44423 q^{94} +4.59692 q^{95} +2.68740 q^{96} +18.0622 q^{97} +14.1316 q^{98} -21.6663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - q^{13} - 3 q^{14} + q^{15} + 3 q^{16} + 7 q^{17} + 10 q^{18} - 3 q^{19} + 3 q^{20} + 22 q^{21} - 3 q^{22} + q^{24} + 3 q^{25} - q^{26} - 14 q^{27} - 3 q^{28} - 4 q^{29} + q^{30} - 5 q^{31} + 3 q^{32} + 9 q^{33} + 7 q^{34} - 3 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 14 q^{39} + 3 q^{40} + q^{41} + 22 q^{42} - 24 q^{43} - 3 q^{44} + 10 q^{45} - 14 q^{47} + q^{48} + 30 q^{49} + 3 q^{50} + 21 q^{51} - q^{52} + 18 q^{53} - 14 q^{54} - 3 q^{55} - 3 q^{56} + 22 q^{57} - 4 q^{58} + 14 q^{59} + q^{60} - q^{61} - 5 q^{62} - 8 q^{63} + 3 q^{64} - q^{65} + 9 q^{66} - 8 q^{67} + 7 q^{68} - 3 q^{70} + 11 q^{71} + 10 q^{72} - 8 q^{73} + 2 q^{74} + q^{75} - 3 q^{76} - 24 q^{77} + 14 q^{78} + 4 q^{79} + 3 q^{80} + 7 q^{81} + q^{82} - 8 q^{83} + 22 q^{84} + 7 q^{85} - 24 q^{86} + 36 q^{87} - 3 q^{88} - 18 q^{89} + 10 q^{90} - q^{91} - 16 q^{93} - 14 q^{94} - 3 q^{95} + q^{96} + 33 q^{97} + 30 q^{98} - 57 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9 + 3 * q^10 - 3 * q^11 + q^12 - q^13 - 3 * q^14 + q^15 + 3 * q^16 + 7 * q^17 + 10 * q^18 - 3 * q^19 + 3 * q^20 + 22 * q^21 - 3 * q^22 + q^24 + 3 * q^25 - q^26 - 14 * q^27 - 3 * q^28 - 4 * q^29 + q^30 - 5 * q^31 + 3 * q^32 + 9 * q^33 + 7 * q^34 - 3 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + 3 * q^40 + q^41 + 22 * q^42 - 24 * q^43 - 3 * q^44 + 10 * q^45 - 14 * q^47 + q^48 + 30 * q^49 + 3 * q^50 + 21 * q^51 - q^52 + 18 * q^53 - 14 * q^54 - 3 * q^55 - 3 * q^56 + 22 * q^57 - 4 * q^58 + 14 * q^59 + q^60 - q^61 - 5 * q^62 - 8 * q^63 + 3 * q^64 - q^65 + 9 * q^66 - 8 * q^67 + 7 * q^68 - 3 * q^70 + 11 * q^71 + 10 * q^72 - 8 * q^73 + 2 * q^74 + q^75 - 3 * q^76 - 24 * q^77 + 14 * q^78 + 4 * q^79 + 3 * q^80 + 7 * q^81 + q^82 - 8 * q^83 + 22 * q^84 + 7 * q^85 - 24 * q^86 + 36 * q^87 - 3 * q^88 - 18 * q^89 + 10 * q^90 - q^91 - 16 * q^93 - 14 * q^94 - 3 * q^95 + q^96 + 33 * q^97 + 30 * q^98 - 57 * 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
$3$	2.68740	1.55157	0.775785	−	0.630997i	$-0.217354\pi$
$3$	2.68740	1.55157	0.775785	+	0.630997i	$0.217354\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.68740	1.09713
$7$	4.59692	1.73747	0.868735	−	0.495277i	$-0.164933\pi$
$7$	4.59692	1.73747	0.868735	+	0.495277i	$0.164933\pi$
$8$	1.00000	0.353553
$9$	4.22212	1.40737
$10$	1.00000	0.316228
$11$	−5.13163	−1.54725	−0.773623	−	0.633647i	$-0.781557\pi$
$11$	−5.13163	−1.54725	−0.773623	+	0.633647i	$0.781557\pi$
$12$	2.68740	0.775785
$13$	−1.22212	−0.338954	−0.169477	−	0.985534i	$-0.554208\pi$
$13$	−1.22212	−0.338954	−0.169477	+	0.985534i	$0.554208\pi$
$14$	4.59692	1.22858
$15$	2.68740	0.693884
$16$	1.00000	0.250000
$17$	4.68740	1.13686	0.568431	−	0.822731i	$-0.307551\pi$
$17$	4.68740	1.13686	0.568431	+	0.822731i	$0.307551\pi$
$18$	4.22212	0.995162
$19$	4.59692	1.05460	0.527302	−	0.849678i	$-0.323204\pi$
$19$	4.59692	1.05460	0.527302	+	0.849678i	$0.323204\pi$
$20$	1.00000	0.223607
$21$	12.3537	2.69581
$22$	−5.13163	−1.09407
$23$	0	0
$23$	0	0
$24$	2.68740	0.548563
$25$	1.00000	0.200000
$26$	−1.22212	−0.239677
$27$	3.28432	0.632067
$28$	4.59692	0.868735
$29$	3.37480	0.626684	0.313342	−	0.949640i	$-0.398551\pi$
$29$	3.37480	0.626684	0.313342	+	0.949640i	$0.398551\pi$
$30$	2.68740	0.490650
$31$	−0.777884	−0.139712	−0.0698560	−	0.997557i	$-0.522254\pi$
$31$	−0.777884	−0.139712	−0.0698560	+	0.997557i	$0.522254\pi$
$32$	1.00000	0.176777
$33$	−13.7907	−2.40066
$34$	4.68740	0.803882
$35$	4.59692	0.777021
$36$	4.22212	0.703686
$37$	−5.81903	−0.956643	−0.478321	−	0.878185i	$-0.658755\pi$
$37$	−5.81903	−0.956643	−0.478321	+	0.878185i	$0.658755\pi$
$38$	4.59692	0.745718
$39$	−3.28432	−0.525911
$40$	1.00000	0.158114
$41$	−8.50643	−1.32848	−0.664241	−	0.747519i	$-0.731245\pi$
$41$	−8.50643	−1.32848	−0.664241	+	0.747519i	$0.731245\pi$
$42$	12.3537	1.90622
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−5.13163	−0.773623
$45$	4.22212	0.629396
$46$	0	0
$47$	−6.44423	−0.939988	−0.469994	−	0.882670i	$-0.655744\pi$
$47$	−6.44423	−0.939988	−0.469994	+	0.882670i	$0.655744\pi$
$48$	2.68740	0.387893
$49$	14.1316	2.01880
$50$	1.00000	0.141421
$51$	12.5969	1.76392
$52$	−1.22212	−0.169477
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	3.28432	0.446939
$55$	−5.13163	−0.691949
$56$	4.59692	0.614289
$57$	12.3537	1.63629
$58$	3.37480	0.443133
$59$	9.37480	1.22049	0.610247	−	0.792211i	$-0.291070\pi$
$59$	9.37480	1.22049	0.610247	+	0.792211i	$0.291070\pi$
$60$	2.68740	0.346942
$61$	−10.9507	−1.40209	−0.701044	−	0.713118i	$-0.747283\pi$
$61$	−10.9507	−1.40209	−0.701044	+	0.713118i	$0.747283\pi$
$62$	−0.777884	−0.0987913
$63$	19.4087	2.44527
$64$	1.00000	0.125000
$65$	−1.22212	−0.151585
$66$	−13.7907	−1.69752
$67$	−15.6381	−1.91049	−0.955247	−	0.295810i	$-0.904410\pi$
$67$	−15.6381	−1.91049	−0.955247	+	0.295810i	$0.904410\pi$
$68$	4.68740	0.568431
$69$	0	0
$70$	4.59692	0.549436
$71$	1.31260	0.155777	0.0778885	−	0.996962i	$-0.475182\pi$
$71$	1.31260	0.155777	0.0778885	+	0.996962i	$0.475182\pi$
$72$	4.22212	0.497581
$73$	−4.44423	−0.520158	−0.260079	−	0.965587i	$-0.583749\pi$
$73$	−4.44423	−0.520158	−0.260079	+	0.965587i	$0.583749\pi$
$74$	−5.81903	−0.676449
$75$	2.68740	0.310314
$76$	4.59692	0.527302
$77$	−23.5897	−2.68829
$78$	−3.28432	−0.371875
$79$	4.88847	0.549995	0.274998	−	0.961445i	$-0.411323\pi$
$79$	4.88847	0.549995	0.274998	+	0.961445i	$0.411323\pi$
$80$	1.00000	0.111803
$81$	−3.84008	−0.426676
$82$	−8.50643	−0.939378
$83$	3.81903	0.419193	0.209597	−	0.977788i	$-0.432785\pi$
$83$	3.81903	0.419193	0.209597	+	0.977788i	$0.432785\pi$
$84$	12.3537	1.34790
$85$	4.68740	0.508420
$86$	−8.00000	−0.862662
$87$	9.06943	0.972345
$88$	−5.13163	−0.547034
$89$	−8.93057	−0.946638	−0.473319	−	0.880891i	$-0.656944\pi$
$89$	−8.93057	−0.946638	−0.473319	+	0.880891i	$0.656944\pi$
$90$	4.22212	0.445050
$91$	−5.61797	−0.588923
$92$	0	0
$93$	−2.09048	−0.216773
$94$	−6.44423	−0.664672
$95$	4.59692	0.471634
$96$	2.68740	0.274282
$97$	18.0622	1.83394	0.916969	−	0.398958i	$-0.130628\pi$
$97$	18.0622	1.83394	0.916969	+	0.398958i	$0.130628\pi$
$98$	14.1316	1.42751
$99$	−21.6663	−2.17755
$100$	1.00000	0.100000
$101$	3.37480	0.335805	0.167903	−	0.985804i	$-0.446301\pi$
$101$	3.37480	0.335805	0.167903	+	0.985804i	$0.446301\pi$
$102$	12.5969	1.24728
$103$	−13.1316	−1.29390	−0.646949	−	0.762533i	$-0.723955\pi$
$103$	−13.1316	−1.29390	−0.646949	+	0.762533i	$0.723955\pi$
$104$	−1.22212	−0.119838
$105$	12.3537	1.20560
$106$	6.00000	0.582772
$107$	−12.3054	−1.18960	−0.594802	−	0.803872i	$-0.702770\pi$
$107$	−12.3054	−1.18960	−0.594802	+	0.803872i	$0.702770\pi$
$108$	3.28432	0.316033
$109$	10.5969	1.01500	0.507500	−	0.861652i	$-0.330570\pi$
$109$	10.5969	1.01500	0.507500	+	0.861652i	$0.330570\pi$
$110$	−5.13163	−0.489282
$111$	−15.6381	−1.48430
$112$	4.59692	0.434368
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	12.3537	1.15703
$115$	0	0
$116$	3.37480	0.313342
$117$	−5.15992	−0.477035
$118$	9.37480	0.863020
$119$	21.5476	1.97526
$120$	2.68740	0.245325
$121$	15.3337	1.39397
$122$	−10.9507	−0.991427
$123$	−22.8602	−2.06123
$124$	−0.777884	−0.0698560
$125$	1.00000	0.0894427
$126$	19.4087	1.72907
$127$	−2.26326	−0.200832	−0.100416	−	0.994946i	$-0.532017\pi$
$127$	−2.26326	−0.200832	−0.100416	+	0.994946i	$0.532017\pi$
$128$	1.00000	0.0883883
$129$	−21.4992	−1.89290
$130$	−1.22212	−0.107187
$131$	2.93057	0.256045	0.128022	−	0.991771i	$-0.459137\pi$
$131$	2.93057	0.256045	0.128022	+	0.991771i	$0.459137\pi$
$132$	−13.7907	−1.20033
$133$	21.1316	1.83234
$134$	−15.6381	−1.35092
$135$	3.28432	0.282669
$136$	4.68740	0.401941
$137$	19.7907	1.69084	0.845419	−	0.534104i	$-0.179351\pi$
$137$	19.7907	1.69084	0.845419	+	0.534104i	$0.179351\pi$
$138$	0	0
$139$	6.26326	0.531243	0.265622	−	0.964077i	$-0.414423\pi$
$139$	6.26326	0.531243	0.265622	+	0.964077i	$0.414423\pi$
$140$	4.59692	0.388510
$141$	−17.3182	−1.45846
$142$	1.31260	0.110151
$143$	6.27145	0.524445
$144$	4.22212	0.351843
$145$	3.37480	0.280262
$146$	−4.44423	−0.367807
$147$	37.9773	3.13232
$148$	−5.81903	−0.478321
$149$	19.7907	1.62132	0.810661	−	0.585516i	$-0.199108\pi$
$149$	19.7907	1.62132	0.810661	+	0.585516i	$0.199108\pi$
$150$	2.68740	0.219425
$151$	4.06220	0.330577	0.165289	−	0.986245i	$-0.447144\pi$
$151$	4.06220	0.330577	0.165289	+	0.986245i	$0.447144\pi$
$152$	4.59692	0.372859
$153$	19.7907	1.59999
$154$	−23.5897	−1.90091
$155$	−0.777884	−0.0624811
$156$	−3.28432	−0.262956
$157$	−4.62520	−0.369131	−0.184566	−	0.982820i	$-0.559088\pi$
$157$	−4.62520	−0.369131	−0.184566	+	0.982820i	$0.559088\pi$
$158$	4.88847	0.388905
$159$	16.1244	1.27875
$160$	1.00000	0.0790569
$161$	0	0
$162$	−3.84008	−0.301705
$163$	12.4159	0.972492	0.486246	−	0.873822i	$-0.338366\pi$
$163$	12.4159	0.972492	0.486246	+	0.873822i	$0.338366\pi$
$164$	−8.50643	−0.664241
$165$	−13.7907	−1.07361
$166$	3.81903	0.296414
$167$	12.8885	0.997339	0.498670	−	0.866792i	$-0.333822\pi$
$167$	12.8885	0.997339	0.498670	+	0.866792i	$0.333822\pi$
$168$	12.3537	0.953112
$169$	−11.5064	−0.885110
$170$	4.68740	0.359507
$171$	19.4087	1.48422
$172$	−8.00000	−0.609994
$173$	−10.2432	−0.778774	−0.389387	−	0.921074i	$-0.627313\pi$
$173$	−10.2432	−0.778774	−0.389387	+	0.921074i	$0.627313\pi$
$174$	9.06943	0.687552
$175$	4.59692	0.347494
$176$	−5.13163	−0.386811
$177$	25.1938	1.89368
$178$	−8.93057	−0.669374
$179$	−13.1938	−0.986153	−0.493077	−	0.869986i	$-0.664128\pi$
$179$	−13.1938	−0.986153	−0.493077	+	0.869986i	$0.664128\pi$
$180$	4.22212	0.314698
$181$	−15.7907	−1.17372	−0.586858	−	0.809690i	$-0.699636\pi$
$181$	−15.7907	−1.17372	−0.586858	+	0.809690i	$0.699636\pi$
$182$	−5.61797	−0.416431
$183$	−29.4288	−2.17544
$184$	0	0
$185$	−5.81903	−0.427824
$186$	−2.09048	−0.153282
$187$	−24.0540	−1.75900
$188$	−6.44423	−0.469994
$189$	15.0977	1.09820
$190$	4.59692	0.333495
$191$	−16.1244	−1.16672	−0.583360	−	0.812214i	$-0.698262\pi$
$191$	−16.1244	−1.16672	−0.583360	+	0.812214i	$0.698262\pi$
$192$	2.68740	0.193946
$193$	−17.9434	−1.29160	−0.645798	−	0.763508i	$-0.723475\pi$
$193$	−17.9434	−1.29160	−0.645798	+	0.763508i	$0.723475\pi$
$194$	18.0622	1.29679
$195$	−3.28432	−0.235195
$196$	14.1316	1.00940
$197$	5.88123	0.419020	0.209510	−	0.977806i	$-0.432813\pi$
$197$	5.88123	0.419020	0.209510	+	0.977806i	$0.432813\pi$
$198$	−21.6663	−1.53976
$199$	−6.56863	−0.465638	−0.232819	−	0.972520i	$-0.574795\pi$
$199$	−6.56863	−0.465638	−0.232819	+	0.972520i	$0.574795\pi$
$200$	1.00000	0.0707107
$201$	−42.0257	−2.96427
$202$	3.37480	0.237450
$203$	15.5137	1.08885
$204$	12.5969	0.881960
$205$	−8.50643	−0.594115
$206$	−13.1316	−0.914924
$207$	0	0
$208$	−1.22212	−0.0847385
$209$	−23.5897	−1.63173
$210$	12.3537	0.852490
$211$	−15.4571	−1.06411	−0.532055	−	0.846710i	$-0.678580\pi$
$211$	−15.4571	−1.06411	−0.532055	+	0.846710i	$0.678580\pi$
$212$	6.00000	0.412082
$213$	3.52748	0.241699
$214$	−12.3054	−0.841177
$215$	−8.00000	−0.545595
$216$	3.28432	0.223469
$217$	−3.57587	−0.242746
$218$	10.5969	0.717714
$219$	−11.9434	−0.807062
$220$	−5.13163	−0.345975
$221$	−5.72855	−0.385344
$222$	−15.6381	−1.04956
$223$	−10.7496	−0.719846	−0.359923	−	0.932982i	$-0.617197\pi$
$223$	−10.7496	−0.719846	−0.359923	+	0.932982i	$0.617197\pi$
$224$	4.59692	0.307144
$225$	4.22212	0.281474
$226$	6.00000	0.399114
$227$	12.3054	0.816736	0.408368	−	0.912817i	$-0.366098\pi$
$227$	12.3054	0.816736	0.408368	+	0.912817i	$0.366098\pi$
$228$	12.3537	0.818147
$229$	−9.63806	−0.636901	−0.318451	−	0.947939i	$-0.603162\pi$
$229$	−9.63806	−0.636901	−0.318451	+	0.947939i	$0.603162\pi$
$230$	0	0
$231$	−63.3949	−4.17108
$232$	3.37480	0.221566
$233$	13.9434	0.913464	0.456732	−	0.889604i	$-0.349020\pi$
$233$	13.9434	0.913464	0.456732	+	0.889604i	$0.349020\pi$
$234$	−5.15992	−0.337314
$235$	−6.44423	−0.420375
$236$	9.37480	0.610247
$237$	13.1373	0.853357
$238$	21.5476	1.39672
$239$	−26.3877	−1.70688	−0.853438	−	0.521194i	$-0.825487\pi$
$239$	−26.3877	−1.70688	−0.853438	+	0.521194i	$0.825487\pi$
$240$	2.68740	0.173471
$241$	7.06943	0.455382	0.227691	−	0.973733i	$-0.426882\pi$
$241$	7.06943	0.455382	0.227691	+	0.973733i	$0.426882\pi$
$242$	15.3337	0.985684
$243$	−20.1728	−1.29408
$244$	−10.9507	−0.701044
$245$	14.1316	0.902837
$246$	−22.8602	−1.45751
$247$	−5.61797	−0.357463
$248$	−0.777884	−0.0493957
$249$	10.2633	0.650408
$250$	1.00000	0.0632456
$251$	24.9023	1.57182	0.785909	−	0.618342i	$-0.212195\pi$
$251$	24.9023	1.57182	0.785909	+	0.618342i	$0.212195\pi$
$252$	19.4087	1.22263
$253$	0	0
$254$	−2.26326	−0.142010
$255$	12.5969	0.788849
$256$	1.00000	0.0625000
$257$	0.444233	0.0277105	0.0138552	−	0.999904i	$-0.495590\pi$
$257$	0.444233	0.0277105	0.0138552	+	0.999904i	$0.495590\pi$
$258$	−21.4992	−1.33848
$259$	−26.7496	−1.66214
$260$	−1.22212	−0.0757924
$261$	14.2488	0.881978
$262$	2.93057	0.181051
$263$	23.8812	1.47258	0.736290	−	0.676666i	$-0.236576\pi$
$263$	23.8812	1.47258	0.736290	+	0.676666i	$0.236576\pi$
$264$	−13.7907	−0.848762
$265$	6.00000	0.368577
$266$	21.1316	1.29566
$267$	−24.0000	−1.46878
$268$	−15.6381	−0.955247
$269$	16.2633	0.991589	0.495794	−	0.868440i	$-0.334877\pi$
$269$	16.2633	0.991589	0.495794	+	0.868440i	$0.334877\pi$
$270$	3.28432	0.199877
$271$	25.6098	1.55568	0.777842	−	0.628460i	$-0.216315\pi$
$271$	25.6098	1.55568	0.777842	+	0.628460i	$0.216315\pi$
$272$	4.68740	0.284215
$273$	−15.0977	−0.913756
$274$	19.7907	1.19560
$275$	−5.13163	−0.309449
$276$	0	0
$277$	2.88847	0.173551	0.0867755	−	0.996228i	$-0.472344\pi$
$277$	2.88847	0.173551	0.0867755	+	0.996228i	$0.472344\pi$
$278$	6.26326	0.375646
$279$	−3.28432	−0.196627
$280$	4.59692	0.274718
$281$	−4.26326	−0.254325	−0.127163	−	0.991882i	$-0.540587\pi$
$281$	−4.26326	−0.254325	−0.127163	+	0.991882i	$0.540587\pi$
$282$	−17.3182	−1.03129
$283$	−30.5686	−1.81712	−0.908558	−	0.417758i	$-0.862816\pi$
$283$	−30.5686	−1.81712	−0.908558	+	0.417758i	$0.862816\pi$
$284$	1.31260	0.0778885
$285$	12.3537	0.731773
$286$	6.27145	0.370839
$287$	−39.1033	−2.30820
$288$	4.22212	0.248791
$289$	4.97171	0.292454
$290$	3.37480	0.198175
$291$	48.5403	2.84549
$292$	−4.44423	−0.260079
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	37.9773	2.21488
$295$	9.37480	0.545822
$296$	−5.81903	−0.338224
$297$	−16.8539	−0.977962
$298$	19.7907	1.14645
$299$	0	0
$300$	2.68740	0.155157
$301$	−36.7753	−2.11969
$302$	4.06220	0.233753
$303$	9.06943	0.521025
$304$	4.59692	0.263651
$305$	−10.9507	−0.627033
$306$	19.7907	1.13136
$307$	−8.54853	−0.487891	−0.243945	−	0.969789i	$-0.578442\pi$
$307$	−8.54853	−0.487891	−0.243945	+	0.969789i	$0.578442\pi$
$308$	−23.5897	−1.34415
$309$	−35.2899	−2.00757
$310$	−0.777884	−0.0441808
$311$	−7.63806	−0.433115	−0.216557	−	0.976270i	$-0.569483\pi$
$311$	−7.63806	−0.433115	−0.216557	+	0.976270i	$0.569483\pi$
$312$	−3.28432	−0.185938
$313$	18.2350	1.03070	0.515351	−	0.856979i	$-0.327662\pi$
$313$	18.2350	1.03070	0.515351	+	0.856979i	$0.327662\pi$
$314$	−4.62520	−0.261015
$315$	19.4087	1.09356
$316$	4.88847	0.274998
$317$	−16.8602	−0.946962	−0.473481	−	0.880804i	$-0.657003\pi$
$317$	−16.8602	−0.946962	−0.473481	+	0.880804i	$0.657003\pi$
$318$	16.1244	0.904211
$319$	−17.3182	−0.969635
$320$	1.00000	0.0559017
$321$	−33.0694	−1.84576
$322$	0	0
$323$	21.5476	1.19894
$324$	−3.84008	−0.213338
$325$	−1.22212	−0.0677908
$326$	12.4159	0.687656
$327$	28.4781	1.57485
$328$	−8.50643	−0.469689
$329$	−29.6236	−1.63320
$330$	−13.7907	−0.759156
$331$	19.1517	1.05267	0.526337	−	0.850276i	$-0.323565\pi$
$331$	19.1517	1.05267	0.526337	+	0.850276i	$0.323565\pi$
$332$	3.81903	0.209597
$333$	−24.5686	−1.34635
$334$	12.8885	0.705225
$335$	−15.6381	−0.854399
$336$	12.3537	0.673952
$337$	−1.70845	−0.0930652	−0.0465326	−	0.998917i	$-0.514817\pi$
$337$	−1.70845	−0.0930652	−0.0465326	+	0.998917i	$0.514817\pi$
$338$	−11.5064	−0.625867
$339$	16.1244	0.875757
$340$	4.68740	0.254210
$341$	3.99181	0.216169
$342$	19.4087	1.04950
$343$	32.7835	1.77014
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−10.2432	−0.550676
$347$	10.6874	0.573730	0.286865	−	0.957971i	$-0.407387\pi$
$347$	10.6874	0.573730	0.286865	+	0.957971i	$0.407387\pi$
$348$	9.06943	0.486173
$349$	−12.3877	−0.663096	−0.331548	−	0.943438i	$-0.607571\pi$
$349$	−12.3877	−0.663096	−0.331548	+	0.943438i	$0.607571\pi$
$350$	4.59692	0.245715
$351$	−4.01382	−0.214242
$352$	−5.13163	−0.273517
$353$	5.45710	0.290452	0.145226	−	0.989399i	$-0.453609\pi$
$353$	5.45710	0.290452	0.145226	+	0.989399i	$0.453609\pi$
$354$	25.1938	1.33904
$355$	1.31260	0.0696656
$356$	−8.93057	−0.473319
$357$	57.9070	3.06476
$358$	−13.1938	−0.697316
$359$	−20.1810	−1.06511	−0.532555	−	0.846395i	$-0.678768\pi$
$359$	−20.1810	−1.06511	−0.532555	+	0.846395i	$0.678768\pi$
$360$	4.22212	0.222525
$361$	2.13163	0.112191
$362$	−15.7907	−0.829943
$363$	41.2076	2.16284
$364$	−5.61797	−0.294461
$365$	−4.44423	−0.232622
$366$	−29.4288	−1.53827
$367$	−2.74960	−0.143528	−0.0717639	−	0.997422i	$-0.522863\pi$
$367$	−2.74960	−0.143528	−0.0717639	+	0.997422i	$0.522863\pi$
$368$	0	0
$369$	−35.9151	−1.86967
$370$	−5.81903	−0.302517
$371$	27.5815	1.43196
$372$	−2.09048	−0.108387
$373$	12.0823	0.625598	0.312799	−	0.949819i	$-0.398733\pi$
$373$	12.0823	0.625598	0.312799	+	0.949819i	$0.398733\pi$
$374$	−24.0540	−1.24380
$375$	2.68740	0.138777
$376$	−6.44423	−0.332336
$377$	−4.12440	−0.212417
$378$	15.0977	0.776543
$379$	−5.25603	−0.269984	−0.134992	−	0.990847i	$-0.543101\pi$
$379$	−5.25603	−0.269984	−0.134992	+	0.990847i	$0.543101\pi$
$380$	4.59692	0.235817
$381$	−6.08230	−0.311605
$382$	−16.1244	−0.824996
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	2.68740	0.137141
$385$	−23.5897	−1.20224
$386$	−17.9434	−0.913297
$387$	−33.7769	−1.71698
$388$	18.0622	0.916969
$389$	−0.325463	−0.0165017	−0.00825083	−	0.999966i	$-0.502626\pi$
$389$	−0.325463	−0.0165017	−0.00825083	+	0.999966i	$0.502626\pi$
$390$	−3.28432	−0.166308
$391$	0	0
$392$	14.1316	0.713755
$393$	7.87560	0.397272
$394$	5.88123	0.296292
$395$	4.88847	0.245965
$396$	−21.6663	−1.08878
$397$	−17.7568	−0.891190	−0.445595	−	0.895235i	$-0.647008\pi$
$397$	−17.7568	−0.891190	−0.445595	+	0.895235i	$0.647008\pi$
$398$	−6.56863	−0.329256
$399$	56.7891	2.84301
$400$	1.00000	0.0500000
$401$	−3.91770	−0.195641	−0.0978204	−	0.995204i	$-0.531187\pi$
$401$	−3.91770	−0.195641	−0.0978204	+	0.995204i	$0.531187\pi$
$402$	−42.0257	−2.09605
$403$	0.950664	0.0473560
$404$	3.37480	0.167903
$405$	−3.84008	−0.190815
$406$	15.5137	0.769930
$407$	29.8611	1.48016
$408$	12.5969	0.623640
$409$	9.58405	0.473901	0.236950	−	0.971522i	$-0.423852\pi$
$409$	9.58405	0.473901	0.236950	+	0.971522i	$0.423852\pi$
$410$	−8.50643	−0.420103
$411$	53.1856	2.62345
$412$	−13.1316	−0.646949
$413$	43.0952	2.12057
$414$	0	0
$415$	3.81903	0.187469
$416$	−1.22212	−0.0599192
$417$	16.8319	0.824261
$418$	−23.5897	−1.15381
$419$	20.5265	1.00279	0.501393	−	0.865219i	$-0.332821\pi$
$419$	20.5265	1.00279	0.501393	+	0.865219i	$0.332821\pi$
$420$	12.3537	0.602801
$421$	−2.29155	−0.111683	−0.0558417	−	0.998440i	$-0.517784\pi$
$421$	−2.29155	−0.111683	−0.0558417	+	0.998440i	$0.517784\pi$
$422$	−15.4571	−0.752440
$423$	−27.2083	−1.32291
$424$	6.00000	0.291386
$425$	4.68740	0.227372
$426$	3.52748	0.170907
$427$	−50.3393	−2.43609
$428$	−12.3054	−0.594802
$429$	16.8539	0.813714
$430$	−8.00000	−0.385794
$431$	8.83189	0.425417	0.212709	−	0.977116i	$-0.431771\pi$
$431$	8.83189	0.425417	0.212709	+	0.977116i	$0.431771\pi$
$432$	3.28432	0.158017
$433$	−33.3465	−1.60253	−0.801266	−	0.598309i	$-0.795840\pi$
$433$	−33.3465	−1.60253	−0.801266	+	0.598309i	$0.795840\pi$
$434$	−3.57587	−0.171647
$435$	9.06943	0.434846
$436$	10.5969	0.507500
$437$	0	0
$438$	−11.9434	−0.570679
$439$	−6.02829	−0.287714	−0.143857	−	0.989598i	$-0.545951\pi$
$439$	−6.02829	−0.287714	−0.143857	+	0.989598i	$0.545951\pi$
$440$	−5.13163	−0.244641
$441$	59.6654	2.84121
$442$	−5.72855	−0.272479
$443$	−15.5275	−0.737733	−0.368866	−	0.929482i	$-0.620254\pi$
$443$	−15.5275	−0.737733	−0.368866	+	0.929482i	$0.620254\pi$
$444$	−15.6381	−0.742150
$445$	−8.93057	−0.423349
$446$	−10.7496	−0.509008
$447$	53.1856	2.51559
$448$	4.59692	0.217184
$449$	−18.3594	−0.866433	−0.433216	−	0.901290i	$-0.642621\pi$
$449$	−18.3594	−0.866433	−0.433216	+	0.901290i	$0.642621\pi$
$450$	4.22212	0.199032
$451$	43.6519	2.05549
$452$	6.00000	0.282216
$453$	10.9168	0.512914
$454$	12.3054	0.577519
$455$	−5.61797	−0.263374
$456$	12.3537	0.578517
$457$	11.4992	0.537910	0.268955	−	0.963153i	$-0.413322\pi$
$457$	11.4992	0.537910	0.268955	+	0.963153i	$0.413322\pi$
$458$	−9.63806	−0.450357
$459$	15.3949	0.718572
$460$	0	0
$461$	1.33270	0.0620700	0.0310350	−	0.999518i	$-0.490120\pi$
$461$	1.33270	0.0620700	0.0310350	+	0.999518i	$0.490120\pi$
$462$	−63.3949	−2.94940
$463$	35.8190	1.66465	0.832326	−	0.554287i	$-0.187009\pi$
$463$	35.8190	1.66465	0.832326	+	0.554287i	$0.187009\pi$
$464$	3.37480	0.156671
$465$	−2.09048	−0.0969439
$466$	13.9434	0.645917
$467$	23.7625	1.09960	0.549798	−	0.835298i	$-0.314705\pi$
$467$	23.7625	1.09960	0.549798	+	0.835298i	$0.314705\pi$
$468$	−5.15992	−0.238517
$469$	−71.8869	−3.31943
$470$	−6.44423	−0.297250
$471$	−12.4298	−0.572733
$472$	9.37480	0.431510
$473$	41.0531	1.88762
$474$	13.1373	0.603414
$475$	4.59692	0.210921
$476$	21.5476	0.987632
$477$	25.3327	1.15990
$478$	−26.3877	−1.20694
$479$	2.04210	0.0933060	0.0466530	−	0.998911i	$-0.485145\pi$
$479$	2.04210	0.0933060	0.0466530	+	0.998911i	$0.485145\pi$
$480$	2.68740	0.122662
$481$	7.11153	0.324258
$482$	7.06943	0.322004
$483$	0	0
$484$	15.3337	0.696984
$485$	18.0622	0.820162
$486$	−20.1728	−0.915056
$487$	−18.6252	−0.843988	−0.421994	−	0.906599i	$-0.638670\pi$
$487$	−18.6252	−0.843988	−0.421994	+	0.906599i	$0.638670\pi$
$488$	−10.9507	−0.495713
$489$	33.3666	1.50889
$490$	14.1316	0.638402
$491$	33.7204	1.52178	0.760889	−	0.648882i	$-0.224763\pi$
$491$	33.7204	1.52178	0.760889	+	0.648882i	$0.224763\pi$
$492$	−22.8602	−1.03062
$493$	15.8190	0.712453
$494$	−5.61797	−0.252764
$495$	−21.6663	−0.973830
$496$	−0.777884	−0.0349280
$497$	6.03391	0.270658
$498$	10.2633	0.459908
$499$	−16.8885	−0.756032	−0.378016	−	0.925799i	$-0.623393\pi$
$499$	−16.8885	−0.756032	−0.378016	+	0.925799i	$0.623393\pi$
$500$	1.00000	0.0447214
$501$	34.6365	1.54744
$502$	24.9023	1.11144
$503$	−11.4031	−0.508438	−0.254219	−	0.967147i	$-0.581818\pi$
$503$	−11.4031	−0.508438	−0.254219	+	0.967147i	$0.581818\pi$
$504$	19.4087	0.864533
$505$	3.37480	0.150177
$506$	0	0
$507$	−30.9224	−1.37331
$508$	−2.26326	−0.100416
$509$	−1.87560	−0.0831346	−0.0415673	−	0.999136i	$-0.513235\pi$
$509$	−1.87560	−0.0831346	−0.0415673	+	0.999136i	$0.513235\pi$
$510$	12.5969	0.557801
$511$	−20.4298	−0.903759
$512$	1.00000	0.0441942
$513$	15.0977	0.666581
$514$	0.444233	0.0195943
$515$	−13.1316	−0.578649
$516$	−21.4992	−0.946449
$517$	33.0694	1.45439
$518$	−26.7496	−1.17531
$519$	−27.5275	−1.20832
$520$	−1.22212	−0.0535933
$521$	−5.11153	−0.223940	−0.111970	−	0.993712i	$-0.535716\pi$
$521$	−5.11153	−0.223940	−0.111970	+	0.993712i	$0.535716\pi$
$522$	14.2488	0.623653
$523$	−19.4571	−0.850799	−0.425400	−	0.905006i	$-0.639866\pi$
$523$	−19.4571	−0.850799	−0.425400	+	0.905006i	$0.639866\pi$
$524$	2.93057	0.128022
$525$	12.3537	0.539162
$526$	23.8812	1.04127
$527$	−3.64625	−0.158833
$528$	−13.7907	−0.600165
$529$	0	0
$530$	6.00000	0.260623
$531$	39.5815	1.71769
$532$	21.1316	0.916172
$533$	10.3958	0.450294
$534$	−24.0000	−1.03858
$535$	−12.3054	−0.532007
$536$	−15.6381	−0.675461
$537$	−35.4571	−1.53009
$538$	16.2633	0.701159
$539$	−72.5183	−3.12359
$540$	3.28432	0.141334
$541$	−2.70750	−0.116404	−0.0582022	−	0.998305i	$-0.518537\pi$
$541$	−2.70750	−0.116404	−0.0582022	+	0.998305i	$0.518537\pi$
$542$	25.6098	1.10003
$543$	−42.4360	−1.82111
$544$	4.68740	0.200971
$545$	10.5969	0.453922
$546$	−15.0977	−0.646123
$547$	−1.66635	−0.0712479	−0.0356240	−	0.999365i	$-0.511342\pi$
$547$	−1.66635	−0.0712479	−0.0356240	+	0.999365i	$0.511342\pi$
$548$	19.7907	0.845419
$549$	−46.2350	−1.97326
$550$	−5.13163	−0.218814
$551$	15.5137	0.660904
$552$	0	0
$553$	22.4719	0.955601
$554$	2.88847	0.122719
$555$	−15.6381	−0.663799
$556$	6.26326	0.265622
$557$	20.9306	0.886857	0.443428	−	0.896310i	$-0.353762\pi$
$557$	20.9306	0.886857	0.443428	+	0.896310i	$0.353762\pi$
$558$	−3.28432	−0.139036
$559$	9.77693	0.413520
$560$	4.59692	0.194255
$561$	−64.6427	−2.72922
$562$	−4.26326	−0.179835
$563$	15.2761	0.643812	0.321906	−	0.946772i	$-0.395676\pi$
$563$	15.2761	0.643812	0.321906	+	0.946772i	$0.395676\pi$
$564$	−17.3182	−0.729229
$565$	6.00000	0.252422
$566$	−30.5686	−1.28490
$567$	−17.6525	−0.741337
$568$	1.31260	0.0550755
$569$	−20.3877	−0.854695	−0.427348	−	0.904087i	$-0.640552\pi$
$569$	−20.3877	−0.854695	−0.427348	+	0.904087i	$0.640552\pi$
$570$	12.3537	0.517442
$571$	−5.49357	−0.229899	−0.114949	−	0.993371i	$-0.536671\pi$
$571$	−5.49357	−0.229899	−0.114949	+	0.993371i	$0.536671\pi$
$572$	6.27145	0.262223
$573$	−43.3327	−1.81025
$574$	−39.1033	−1.63214
$575$	0	0
$576$	4.22212	0.175922
$577$	17.2761	0.719215	0.359607	−	0.933104i	$-0.382911\pi$
$577$	17.2761	0.719215	0.359607	+	0.933104i	$0.382911\pi$
$578$	4.97171	0.206796
$579$	−48.2212	−2.00400
$580$	3.37480	0.140131
$581$	17.5558	0.728336
$582$	48.5403	2.01206
$583$	−30.7898	−1.27518
$584$	−4.44423	−0.183904
$585$	−5.15992	−0.213336
$586$	6.00000	0.247858
$587$	31.8247	1.31354	0.656772	−	0.754089i	$-0.271921\pi$
$587$	31.8247	1.31354	0.656772	+	0.754089i	$0.271921\pi$
$588$	37.9773	1.56616
$589$	−3.57587	−0.147341
$590$	9.37480	0.385954
$591$	15.8052	0.650140
$592$	−5.81903	−0.239161
$593$	−12.4442	−0.511023	−0.255512	−	0.966806i	$-0.582244\pi$
$593$	−12.4442	−0.511023	−0.255512	+	0.966806i	$0.582244\pi$
$594$	−16.8539	−0.691524
$595$	21.5476	0.883365
$596$	19.7907	0.810661
$597$	−17.6525	−0.722470
$598$	0	0
$599$	17.4370	0.712456	0.356228	−	0.934399i	$-0.384063\pi$
$599$	17.4370	0.712456	0.356228	+	0.934399i	$0.384063\pi$
$600$	2.68740	0.109713
$601$	−0.916751	−0.0373951	−0.0186975	−	0.999825i	$-0.505952\pi$
$601$	−0.916751	−0.0373951	−0.0186975	+	0.999825i	$0.505952\pi$
$602$	−36.7753	−1.49885
$603$	−66.0257	−2.68878
$604$	4.06220	0.165289
$605$	15.3337	0.623402
$606$	9.06943	0.368421
$607$	36.7753	1.49266	0.746332	−	0.665574i	$-0.231813\pi$
$607$	36.7753	1.49266	0.746332	+	0.665574i	$0.231813\pi$
$608$	4.59692	0.186430
$609$	41.6914	1.68942
$610$	−10.9507	−0.443379
$611$	7.87560	0.318613
$612$	19.7907	0.799994
$613$	−4.38766	−0.177216	−0.0886080	−	0.996067i	$-0.528242\pi$
$613$	−4.38766	−0.177216	−0.0886080	+	0.996067i	$0.528242\pi$
$614$	−8.54853	−0.344991
$615$	−22.8602	−0.921811
$616$	−23.5897	−0.950455
$617$	−40.4499	−1.62845	−0.814225	−	0.580549i	$-0.802838\pi$
$617$	−40.4499	−1.62845	−0.814225	+	0.580549i	$0.802838\pi$
$618$	−35.2899	−1.41957
$619$	39.8165	1.60036	0.800180	−	0.599760i	$-0.204737\pi$
$619$	39.8165	1.60036	0.800180	+	0.599760i	$0.204737\pi$
$620$	−0.777884	−0.0312406
$621$	0	0
$622$	−7.63806	−0.306258
$623$	−41.0531	−1.64476
$624$	−3.28432	−0.131478
$625$	1.00000	0.0400000
$626$	18.2350	0.728816
$627$	−63.3949	−2.53175
$628$	−4.62520	−0.184566
$629$	−27.2761	−1.08757
$630$	19.4087	0.773262
$631$	−25.9013	−1.03112	−0.515558	−	0.856855i	$-0.672415\pi$
$631$	−25.9013	−1.03112	−0.515558	+	0.856855i	$0.672415\pi$
$632$	4.88847	0.194453
$633$	−41.5394	−1.65104
$634$	−16.8602	−0.669603
$635$	−2.26326	−0.0898149
$636$	16.1244	0.639374
$637$	−17.2705	−0.684282
$638$	−17.3182	−0.685635
$639$	5.54195	0.219236
$640$	1.00000	0.0395285
$641$	43.8448	1.73176	0.865882	−	0.500248i	$-0.166758\pi$
$641$	43.8448	1.73176	0.865882	+	0.500248i	$0.166758\pi$
$642$	−33.0694	−1.30515
$643$	−3.94343	−0.155514	−0.0777568	−	0.996972i	$-0.524776\pi$
$643$	−3.94343	−0.155514	−0.0777568	+	0.996972i	$0.524776\pi$
$644$	0	0
$645$	−21.4992	−0.846530
$646$	21.5476	0.847778
$647$	24.3456	0.957123	0.478561	−	0.878054i	$-0.341158\pi$
$647$	24.3456	0.957123	0.478561	+	0.878054i	$0.341158\pi$
$648$	−3.84008	−0.150853
$649$	−48.1080	−1.88841
$650$	−1.22212	−0.0479353
$651$	−9.60978	−0.376637
$652$	12.4159	0.486246
$653$	37.6921	1.47500	0.737502	−	0.675344i	$-0.236005\pi$
$653$	37.6921	1.47500	0.737502	+	0.675344i	$0.236005\pi$
$654$	28.4781	1.11358
$655$	2.93057	0.114507
$656$	−8.50643	−0.332120
$657$	−18.7641	−0.732056
$658$	−29.6236	−1.15485
$659$	−24.6107	−0.958698	−0.479349	−	0.877624i	$-0.659127\pi$
$659$	−24.6107	−0.958698	−0.479349	+	0.877624i	$0.659127\pi$
$660$	−13.7907	−0.536804
$661$	−27.3126	−1.06234	−0.531169	−	0.847266i	$-0.678247\pi$
$661$	−27.3126	−1.06234	−0.531169	+	0.847266i	$0.678247\pi$
$662$	19.1517	0.744353
$663$	−15.3949	−0.597888
$664$	3.81903	0.148207
$665$	21.1316	0.819450
$666$	−24.5686	−0.952015
$667$	0	0
$668$	12.8885	0.498670
$669$	−28.8885	−1.11689
$670$	−15.6381	−0.604151
$671$	56.1948	2.16938
$672$	12.3537	0.476556
$673$	22.5265	0.868334	0.434167	−	0.900832i	$-0.357043\pi$
$673$	22.5265	0.868334	0.434167	+	0.900832i	$0.357043\pi$
$674$	−1.70845	−0.0658070
$675$	3.28432	0.126413
$676$	−11.5064	−0.442555
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	16.1244	0.619254
$679$	83.0304	3.18641
$680$	4.68740	0.179754
$681$	33.0694	1.26722
$682$	3.99181	0.152854
$683$	−31.9974	−1.22435	−0.612174	−	0.790723i	$-0.709705\pi$
$683$	−31.9974	−1.22435	−0.612174	+	0.790723i	$0.709705\pi$
$684$	19.4087	0.742111
$685$	19.7907	0.756166
$686$	32.7835	1.25168
$687$	−25.9013	−0.988197
$688$	−8.00000	−0.304997
$689$	−7.33270	−0.279354
$690$	0	0
$691$	−2.80617	−0.106752	−0.0533758	−	0.998574i	$-0.516998\pi$
$691$	−2.80617	−0.106752	−0.0533758	+	0.998574i	$0.516998\pi$
$692$	−10.2432	−0.389387
$693$	−99.5984	−3.78343
$694$	10.6874	0.405688
$695$	6.26326	0.237579
$696$	9.06943	0.343776
$697$	−39.8730	−1.51030
$698$	−12.3877	−0.468880
$699$	37.4716	1.41730
$700$	4.59692	0.173747
$701$	−8.37385	−0.316276	−0.158138	−	0.987417i	$-0.550549\pi$
$701$	−8.37385	−0.316276	−0.158138	+	0.987417i	$0.550549\pi$
$702$	−4.01382	−0.151492
$703$	−26.7496	−1.00888
$704$	−5.13163	−0.193406
$705$	−17.3182	−0.652242
$706$	5.45710	0.205381
$707$	15.5137	0.583451
$708$	25.1938	0.946842
$709$	−21.2139	−0.796706	−0.398353	−	0.917232i	$-0.630418\pi$
$709$	−21.2139	−0.796706	−0.398353	+	0.917232i	$0.630418\pi$
$710$	1.31260	0.0492610
$711$	20.6397	0.774048
$712$	−8.93057	−0.334687
$713$	0	0
$714$	57.9070	2.16711
$715$	6.27145	0.234539
$716$	−13.1938	−0.493077
$717$	−70.9142	−2.64834
$718$	−20.1810	−0.753147
$719$	−28.1106	−1.04835	−0.524174	−	0.851611i	$-0.675626\pi$
$719$	−28.1106	−1.04835	−0.524174	+	0.851611i	$0.675626\pi$
$720$	4.22212	0.157349
$721$	−60.3650	−2.24811
$722$	2.13163	0.0793311
$723$	18.9984	0.706558
$724$	−15.7907	−0.586858
$725$	3.37480	0.125337
$726$	41.2076	1.52936
$727$	39.0330	1.44765	0.723826	−	0.689982i	$-0.242382\pi$
$727$	39.0330	1.44765	0.723826	+	0.689982i	$0.242382\pi$
$728$	−5.61797	−0.208216
$729$	−42.6921	−1.58119
$730$	−4.44423	−0.164488
$731$	−37.4992	−1.38696
$732$	−29.4288	−1.08772
$733$	−47.1373	−1.74105	−0.870527	−	0.492120i	$-0.836222\pi$
$733$	−47.1373	−1.74105	−0.870527	+	0.492120i	$0.836222\pi$
$734$	−2.74960	−0.101490
$735$	37.9773	1.40082
$736$	0	0
$737$	80.2488	2.95600
$738$	−35.9151	−1.32205
$739$	−24.5265	−0.902223	−0.451111	−	0.892468i	$-0.648972\pi$
$739$	−24.5265	−0.902223	−0.451111	+	0.892468i	$0.648972\pi$
$740$	−5.81903	−0.213912
$741$	−15.0977	−0.554629
$742$	27.5815	1.01255
$743$	7.34651	0.269517	0.134759	−	0.990878i	$-0.456974\pi$
$743$	7.34651	0.269517	0.134759	+	0.990878i	$0.456974\pi$
$744$	−2.09048	−0.0766409
$745$	19.7907	0.725077
$746$	12.0823	0.442364
$747$	16.1244	0.589961
$748$	−24.0540	−0.879502
$749$	−56.5667	−2.06690
$750$	2.68740	0.0981300
$751$	−11.2359	−0.410005	−0.205002	−	0.978761i	$-0.565720\pi$
$751$	−11.2359	−0.410005	−0.205002	+	0.978761i	$0.565720\pi$
$752$	−6.44423	−0.234997
$753$	66.9224	2.43879
$754$	−4.12440	−0.150202
$755$	4.06220	0.147839
$756$	15.0977	0.549099
$757$	−49.1794	−1.78745	−0.893727	−	0.448611i	$-0.851919\pi$
$757$	−49.1794	−1.78745	−0.893727	+	0.448611i	$0.851919\pi$
$758$	−5.25603	−0.190908
$759$	0	0
$760$	4.59692	0.166748
$761$	43.2478	1.56773	0.783867	−	0.620929i	$-0.213245\pi$
$761$	43.2478	1.56773	0.783867	+	0.620929i	$0.213245\pi$
$762$	−6.08230	−0.220338
$763$	48.7131	1.76353
$764$	−16.1244	−0.583360
$765$	19.7907	0.715536
$766$	0	0
$767$	−11.4571	−0.413692
$768$	2.68740	0.0969732
$769$	39.6638	1.43031	0.715156	−	0.698964i	$-0.246355\pi$
$769$	39.6638	1.43031	0.715156	+	0.698964i	$0.246355\pi$
$770$	−23.5897	−0.850113
$771$	1.19383	0.0429948
$772$	−17.9434	−0.645798
$773$	2.18097	0.0784440	0.0392220	−	0.999231i	$-0.487512\pi$
$773$	2.18097	0.0784440	0.0392220	+	0.999231i	$0.487512\pi$
$774$	−33.7769	−1.21409
$775$	−0.777884	−0.0279424
$776$	18.0622	0.648395
$777$	−71.8869	−2.57893
$778$	−0.325463	−0.0116684
$779$	−39.1033	−1.40102
$780$	−3.28432	−0.117597
$781$	−6.73578	−0.241025
$782$	0	0
$783$	11.0839	0.396106
$784$	14.1316	0.504701
$785$	−4.62520	−0.165080
$786$	7.87560	0.280913
$787$	−4.76407	−0.169821	−0.0849103	−	0.996389i	$-0.527060\pi$
$787$	−4.76407	−0.169821	−0.0849103	+	0.996389i	$0.527060\pi$
$788$	5.88123	0.209510
$789$	64.1784	2.28481
$790$	4.88847	0.173924
$791$	27.5815	0.980685
$792$	−21.6663	−0.769880
$793$	13.3830	0.475244
$794$	−17.7568	−0.630166
$795$	16.1244	0.571873
$796$	−6.56863	−0.232819
$797$	−39.7204	−1.40697	−0.703484	−	0.710711i	$-0.748373\pi$
$797$	−39.7204	−1.40697	−0.703484	+	0.710711i	$0.748373\pi$
$798$	56.7891	2.01031
$799$	−30.2067	−1.06864
$800$	1.00000	0.0353553
$801$	−37.7059	−1.33227
$802$	−3.91770	−0.138339
$803$	22.8062	0.804812
$804$	−42.0257	−1.48213
$805$	0	0
$806$	0.950664	0.0334857
$807$	43.7059	1.53852
$808$	3.37480	0.118725
$809$	46.8941	1.64871	0.824354	−	0.566074i	$-0.191538\pi$
$809$	46.8941	1.64871	0.824354	+	0.566074i	$0.191538\pi$
$810$	−3.84008	−0.134927
$811$	−36.8319	−1.29334	−0.646671	−	0.762769i	$-0.723839\pi$
$811$	−36.8319	−1.29334	−0.646671	+	0.762769i	$0.723839\pi$
$812$	15.5137	0.544423
$813$	68.8237	2.41375
$814$	29.8611	1.04663
$815$	12.4159	0.434912
$816$	12.5969	0.440980
$817$	−36.7753	−1.28661
$818$	9.58405	0.335099
$819$	−23.7197	−0.828834
$820$	−8.50643	−0.297057
$821$	−18.6107	−0.649519	−0.324759	−	0.945797i	$-0.605283\pi$
$821$	−18.6107	−0.649519	−0.324759	+	0.945797i	$0.605283\pi$
$822$	53.1856	1.85506
$823$	−9.31823	−0.324813	−0.162407	−	0.986724i	$-0.551926\pi$
$823$	−9.31823	−0.324813	−0.162407	+	0.986724i	$0.551926\pi$
$824$	−13.1316	−0.457462
$825$	−13.7907	−0.480132
$826$	43.0952	1.49947
$827$	−53.0129	−1.84344	−0.921719	−	0.387858i	$-0.873215\pi$
$827$	−53.0129	−1.84344	−0.921719	+	0.387858i	$0.873215\pi$
$828$	0	0
$829$	−25.2761	−0.877876	−0.438938	−	0.898517i	$-0.644645\pi$
$829$	−25.2761	−0.877876	−0.438938	+	0.898517i	$0.644645\pi$
$830$	3.81903	0.132561
$831$	7.76246	0.269277
$832$	−1.22212	−0.0423693
$833$	66.2406	2.29510
$834$	16.8319	0.582841
$835$	12.8885	0.446024
$836$	−23.5897	−0.815866
$837$	−2.55481	−0.0883073
$838$	20.5265	0.709077
$839$	−11.6946	−0.403744	−0.201872	−	0.979412i	$-0.564702\pi$
$839$	−11.6946	−0.403744	−0.201872	+	0.979412i	$0.564702\pi$
$840$	12.3537	0.426245
$841$	−17.6107	−0.607267
$842$	−2.29155	−0.0789720
$843$	−11.4571	−0.394603
$844$	−15.4571	−0.532055
$845$	−11.5064	−0.395833
$846$	−27.2083	−0.935441
$847$	70.4875	2.42198
$848$	6.00000	0.206041
$849$	−82.1501	−2.81938
$850$	4.68740	0.160776
$851$	0	0
$852$	3.52748	0.120850
$853$	38.6371	1.32291	0.661455	−	0.749985i	$-0.269939\pi$
$853$	38.6371	1.32291	0.661455	+	0.749985i	$0.269939\pi$
$854$	−50.3393	−1.72257
$855$	19.4087	0.663764
$856$	−12.3054	−0.420589
$857$	26.2488	0.896642	0.448321	−	0.893873i	$-0.352022\pi$
$857$	26.2488	0.896642	0.448321	+	0.893873i	$0.352022\pi$
$858$	16.8539	0.575383
$859$	37.5558	1.28139	0.640693	−	0.767797i	$-0.278647\pi$
$859$	37.5558	1.28139	0.640693	+	0.767797i	$0.278647\pi$
$860$	−8.00000	−0.272798
$861$	−105.086	−3.58133
$862$	8.83189	0.300816
$863$	−21.9855	−0.748396	−0.374198	−	0.927349i	$-0.622082\pi$
$863$	−21.9855	−0.748396	−0.374198	+	0.927349i	$0.622082\pi$
$864$	3.28432	0.111735
$865$	−10.2432	−0.348278
$866$	−33.3465	−1.13316
$867$	13.3610	0.453763
$868$	−3.57587	−0.121373
$869$	−25.0858	−0.850978
$870$	9.06943	0.307483
$871$	19.1115	0.647570
$872$	10.5969	0.358857
$873$	76.2607	2.58103
$874$	0	0
$875$	4.59692	0.155404
$876$	−11.9434	−0.403531
$877$	−36.5064	−1.23273	−0.616367	−	0.787459i	$-0.711396\pi$
$877$	−36.5064	−1.23273	−0.616367	+	0.787459i	$0.711396\pi$
$878$	−6.02829	−0.203445
$879$	16.1244	0.543862
$880$	−5.13163	−0.172987
$881$	17.4571	0.588145	0.294072	−	0.955783i	$-0.404989\pi$
$881$	17.4571	0.588145	0.294072	+	0.955783i	$0.404989\pi$
$882$	59.6654	2.00904
$883$	22.9444	0.772140	0.386070	−	0.922470i	$-0.373832\pi$
$883$	22.9444	0.772140	0.386070	+	0.922470i	$0.373832\pi$
$884$	−5.72855	−0.192672
$885$	25.1938	0.846881
$886$	−15.5275	−0.521656
$887$	−11.7223	−0.393595	−0.196798	−	0.980444i	$-0.563054\pi$
$887$	−11.7223	−0.393595	−0.196798	+	0.980444i	$0.563054\pi$
$888$	−15.6381	−0.524779
$889$	−10.4040	−0.348940
$890$	−8.93057	−0.299353
$891$	19.7059	0.660172
$892$	−10.7496	−0.359923
$893$	−29.6236	−0.991316
$894$	53.1856	1.77879
$895$	−13.1938	−0.441021
$896$	4.59692	0.153572
$897$	0	0
$898$	−18.3594	−0.612660
$899$	−2.62520	−0.0875554
$900$	4.22212	0.140737
$901$	28.1244	0.936960
$902$	43.6519	1.45345
$903$	−98.8300	−3.28886
$904$	6.00000	0.199557
$905$	−15.7907	−0.524902
$906$	10.9168	0.362685
$907$	1.91770	0.0636763	0.0318381	−	0.999493i	$-0.489864\pi$
$907$	1.91770	0.0636763	0.0318381	+	0.999493i	$0.489864\pi$
$908$	12.3054	0.408368
$909$	14.2488	0.472603
$910$	−5.61797	−0.186234
$911$	56.8319	1.88292	0.941462	−	0.337118i	$-0.109452\pi$
$911$	56.8319	1.88292	0.941462	+	0.337118i	$0.109452\pi$
$912$	12.3537	0.409073
$913$	−19.5979	−0.648595
$914$	11.4992	0.380360
$915$	−29.4288	−0.972886
$916$	−9.63806	−0.318451
$917$	13.4716	0.444870
$918$	15.3949	0.508107
$919$	26.0257	0.858509	0.429255	−	0.903183i	$-0.358776\pi$
$919$	26.0257	0.858509	0.429255	+	0.903183i	$0.358776\pi$
$920$	0	0
$921$	−22.9733	−0.756997
$922$	1.33270	0.0438901
$923$	−1.60415	−0.0528013
$924$	−63.3949	−2.08554
$925$	−5.81903	−0.191329
$926$	35.8190	1.17709
$927$	−55.4433	−1.82100
$928$	3.37480	0.110783
$929$	−17.1115	−0.561411	−0.280706	−	0.959794i	$-0.590568\pi$
$929$	−17.1115	−0.561411	−0.280706	+	0.959794i	$0.590568\pi$
$930$	−2.09048	−0.0685497
$931$	64.9619	2.12904
$932$	13.9434	0.456732
$933$	−20.5265	−0.672008
$934$	23.7625	0.777531
$935$	−24.0540	−0.786650
$936$	−5.15992	−0.168657
$937$	−16.3738	−0.534910	−0.267455	−	0.963570i	$-0.586183\pi$
$937$	−16.3738	−0.534910	−0.267455	+	0.963570i	$0.586183\pi$
$938$	−71.8869	−2.34719
$939$	49.0047	1.59921
$940$	−6.44423	−0.210188
$941$	16.4097	0.534940	0.267470	−	0.963566i	$-0.413812\pi$
$941$	16.4097	0.534940	0.267470	+	0.963566i	$0.413812\pi$
$942$	−12.4298	−0.404984
$943$	0	0
$944$	9.37480	0.305124
$945$	15.0977	0.491129
$946$	41.0531	1.33475
$947$	−21.3886	−0.695037	−0.347518	−	0.937673i	$-0.612976\pi$
$947$	−21.3886	−0.695037	−0.347518	+	0.937673i	$0.612976\pi$
$948$	13.1373	0.426678
$949$	5.43137	0.176310
$950$	4.59692	0.149144
$951$	−45.3100	−1.46928
$952$	21.5476	0.698361
$953$	16.7276	0.541860	0.270930	−	0.962599i	$-0.412669\pi$
$953$	16.7276	0.541860	0.270930	+	0.962599i	$0.412669\pi$
$954$	25.3327	0.820176
$955$	−16.1244	−0.521773
$956$	−26.3877	−0.853438
$957$	−46.5410	−1.50446
$958$	2.04210	0.0659773
$959$	90.9764	2.93778
$960$	2.68740	0.0867354
$961$	−30.3949	−0.980481
$962$	7.11153	0.229285
$963$	−51.9547	−1.67422
$964$	7.06943	0.227691
$965$	−17.9434	−0.577619
$966$	0	0
$967$	45.2617	1.45552	0.727758	−	0.685834i	$-0.240562\pi$
$967$	45.2617	1.45552	0.727758	+	0.685834i	$0.240562\pi$
$968$	15.3337	0.492842
$969$	57.9070	1.86024
$970$	18.0622	0.579942
$971$	−45.2560	−1.45234	−0.726168	−	0.687518i	$-0.758700\pi$
$971$	−45.2560	−1.45234	−0.726168	+	0.687518i	$0.758700\pi$
$972$	−20.1728	−0.647042
$973$	28.7917	0.923019
$974$	−18.6252	−0.596790
$975$	−3.28432	−0.105182
$976$	−10.9507	−0.350522
$977$	13.3465	0.426993	0.213496	−	0.976944i	$-0.431515\pi$
$977$	13.3465	0.426993	0.213496	+	0.976944i	$0.431515\pi$
$978$	33.3666	1.06695
$979$	45.8284	1.46468
$980$	14.1316	0.451418
$981$	44.7414	1.42848
$982$	33.7204	1.07606
$983$	−5.13163	−0.163674	−0.0818368	−	0.996646i	$-0.526079\pi$
$983$	−5.13163	−0.163674	−0.0818368	+	0.996646i	$0.526079\pi$
$984$	−22.8602	−0.728756
$985$	5.88123	0.187392
$986$	15.8190	0.503781
$987$	−79.6104	−2.53403
$988$	−5.61797	−0.178731
$989$	0	0
$990$	−21.6663	−0.688602
$991$	17.7989	0.565402	0.282701	−	0.959208i	$-0.408770\pi$
$991$	17.7989	0.565402	0.282701	+	0.959208i	$0.408770\pi$
$992$	−0.777884	−0.0246978
$993$	51.4684	1.63330
$994$	6.03391	0.191384
$995$	−6.56863	−0.208240
$996$	10.2633	0.325204
$997$	40.3877	1.27909	0.639545	−	0.768754i	$-0.279123\pi$
$997$	40.3877	1.27909	0.639545	+	0.768754i	$0.279123\pi$
$998$	−16.8885	−0.534595
$999$	−19.1115	−0.604662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.r.1.3		3
23.22	odd	2		230.2.a.d.1.3	✓	3
69.68	even	2		2070.2.a.z.1.1		3
92.91	even	2		1840.2.a.r.1.1		3
115.22	even	4		1150.2.b.j.599.4		6
115.68	even	4		1150.2.b.j.599.3		6
115.114	odd	2		1150.2.a.q.1.1		3
184.45	odd	2		7360.2.a.bz.1.1		3
184.91	even	2		7360.2.a.ce.1.3		3
460.459	even	2		9200.2.a.cf.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.d.1.3	✓	3	23.22	odd	2
1150.2.a.q.1.1		3	115.114	odd	2
1150.2.b.j.599.3		6	115.68	even	4
1150.2.b.j.599.4		6	115.22	even	4
1840.2.a.r.1.1		3	92.91	even	2
2070.2.a.z.1.1		3	69.68	even	2
5290.2.a.r.1.3		3	1.1	even	1	trivial
7360.2.a.bz.1.1		3	184.45	odd	2
7360.2.a.ce.1.3		3	184.91	even	2
9200.2.a.cf.1.3		3	460.459	even	2

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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.68740 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.68740 q^{6} +4.59692 q^{7} +1.00000 q^{8} +4.22212 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.68740 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.68740 q^{6} +4.59692 q^{7} +1.00000 q^{8} +4.22212 q^{9} +1.00000 q^{10} -5.13163 q^{11} +2.68740 q^{12} -1.22212 q^{13} +4.59692 q^{14} +2.68740 q^{15} +1.00000 q^{16} +4.68740 q^{17} +4.22212 q^{18} +4.59692 q^{19} +1.00000 q^{20} +12.3537 q^{21} -5.13163 q^{22} +2.68740 q^{24} +1.00000 q^{25} -1.22212 q^{26} +3.28432 q^{27} +4.59692 q^{28} +3.37480 q^{29} +2.68740 q^{30} -0.777884 q^{31} +1.00000 q^{32} -13.7907 q^{33} +4.68740 q^{34} +4.59692 q^{35} +4.22212 q^{36} -5.81903 q^{37} +4.59692 q^{38} -3.28432 q^{39} +1.00000 q^{40} -8.50643 q^{41} +12.3537 q^{42} -8.00000 q^{43} -5.13163 q^{44} +4.22212 q^{45} -6.44423 q^{47} +2.68740 q^{48} +14.1316 q^{49} +1.00000 q^{50} +12.5969 q^{51} -1.22212 q^{52} +6.00000 q^{53} +3.28432 q^{54} -5.13163 q^{55} +4.59692 q^{56} +12.3537 q^{57} +3.37480 q^{58} +9.37480 q^{59} +2.68740 q^{60} -10.9507 q^{61} -0.777884 q^{62} +19.4087 q^{63} +1.00000 q^{64} -1.22212 q^{65} -13.7907 q^{66} -15.6381 q^{67} +4.68740 q^{68} +4.59692 q^{70} +1.31260 q^{71} +4.22212 q^{72} -4.44423 q^{73} -5.81903 q^{74} +2.68740 q^{75} +4.59692 q^{76} -23.5897 q^{77} -3.28432 q^{78} +4.88847 q^{79} +1.00000 q^{80} -3.84008 q^{81} -8.50643 q^{82} +3.81903 q^{83} +12.3537 q^{84} +4.68740 q^{85} -8.00000 q^{86} +9.06943 q^{87} -5.13163 q^{88} -8.93057 q^{89} +4.22212 q^{90} -5.61797 q^{91} -2.09048 q^{93} -6.44423 q^{94} +4.59692 q^{95} +2.68740 q^{96} +18.0622 q^{97} +14.1316 q^{98} -21.6663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 10 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - q^{13} - 3 q^{14} + q^{15} + 3 q^{16} + 7 q^{17} + 10 q^{18} - 3 q^{19} + 3 q^{20} + 22 q^{21} - 3 q^{22} + q^{24} + 3 q^{25} - q^{26} - 14 q^{27} - 3 q^{28} - 4 q^{29} + q^{30} - 5 q^{31} + 3 q^{32} + 9 q^{33} + 7 q^{34} - 3 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 14 q^{39} + 3 q^{40} + q^{41} + 22 q^{42} - 24 q^{43} - 3 q^{44} + 10 q^{45} - 14 q^{47} + q^{48} + 30 q^{49} + 3 q^{50} + 21 q^{51} - q^{52} + 18 q^{53} - 14 q^{54} - 3 q^{55} - 3 q^{56} + 22 q^{57} - 4 q^{58} + 14 q^{59} + q^{60} - q^{61} - 5 q^{62} - 8 q^{63} + 3 q^{64} - q^{65} + 9 q^{66} - 8 q^{67} + 7 q^{68} - 3 q^{70} + 11 q^{71} + 10 q^{72} - 8 q^{73} + 2 q^{74} + q^{75} - 3 q^{76} - 24 q^{77} + 14 q^{78} + 4 q^{79} + 3 q^{80} + 7 q^{81} + q^{82} - 8 q^{83} + 22 q^{84} + 7 q^{85} - 24 q^{86} + 36 q^{87} - 3 q^{88} - 18 q^{89} + 10 q^{90} - q^{91} - 16 q^{93} - 14 q^{94} - 3 q^{95} + q^{96} + 33 q^{97} + 30 q^{98} - 57 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 10 * q^9 + 3 * q^10 - 3 * q^11 + q^12 - q^13 - 3 * q^14 + q^15 + 3 * q^16 + 7 * q^17 + 10 * q^18 - 3 * q^19 + 3 * q^20 + 22 * q^21 - 3 * q^22 + q^24 + 3 * q^25 - q^26 - 14 * q^27 - 3 * q^28 - 4 * q^29 + q^30 - 5 * q^31 + 3 * q^32 + 9 * q^33 + 7 * q^34 - 3 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + 3 * q^40 + q^41 + 22 * q^42 - 24 * q^43 - 3 * q^44 + 10 * q^45 - 14 * q^47 + q^48 + 30 * q^49 + 3 * q^50 + 21 * q^51 - q^52 + 18 * q^53 - 14 * q^54 - 3 * q^55 - 3 * q^56 + 22 * q^57 - 4 * q^58 + 14 * q^59 + q^60 - q^61 - 5 * q^62 - 8 * q^63 + 3 * q^64 - q^65 + 9 * q^66 - 8 * q^67 + 7 * q^68 - 3 * q^70 + 11 * q^71 + 10 * q^72 - 8 * q^73 + 2 * q^74 + q^75 - 3 * q^76 - 24 * q^77 + 14 * q^78 + 4 * q^79 + 3 * q^80 + 7 * q^81 + q^82 - 8 * q^83 + 22 * q^84 + 7 * q^85 - 24 * q^86 + 36 * q^87 - 3 * q^88 - 18 * q^89 + 10 * q^90 - q^91 - 16 * q^93 - 14 * q^94 - 3 * q^95 + q^96 + 33 * q^97 + 30 * q^98 - 57 * q^99

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