LMFDB - Embedded newform 1155.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} +1.00000 q^{5} -2.34292 q^{6} -1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} +1.00000 q^{5} -2.34292 q^{6} -1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} +2.34292 q^{10} -1.00000 q^{11} -3.48929 q^{12} +3.14637 q^{13} -2.34292 q^{14} -1.00000 q^{15} +1.19656 q^{16} +6.48929 q^{17} +2.34292 q^{18} +7.17513 q^{19} +3.48929 q^{20} +1.00000 q^{21} -2.34292 q^{22} +2.19656 q^{23} -3.48929 q^{24} +1.00000 q^{25} +7.37169 q^{26} -1.00000 q^{27} -3.48929 q^{28} +0.949808 q^{29} -2.34292 q^{30} -6.12494 q^{31} -4.17513 q^{32} +1.00000 q^{33} +15.2039 q^{34} -1.00000 q^{35} +3.48929 q^{36} +0.853635 q^{37} +16.8108 q^{38} -3.14637 q^{39} +3.48929 q^{40} +3.53948 q^{41} +2.34292 q^{42} -5.63565 q^{43} -3.48929 q^{44} +1.00000 q^{45} +5.14637 q^{46} -1.53948 q^{47} -1.19656 q^{48} +1.00000 q^{49} +2.34292 q^{50} -6.48929 q^{51} +10.9786 q^{52} -6.15371 q^{53} -2.34292 q^{54} -1.00000 q^{55} -3.48929 q^{56} -7.17513 q^{57} +2.22533 q^{58} -5.63565 q^{59} -3.48929 q^{60} +4.58967 q^{61} -14.3503 q^{62} -1.00000 q^{63} -12.1751 q^{64} +3.14637 q^{65} +2.34292 q^{66} -10.3503 q^{67} +22.6430 q^{68} -2.19656 q^{69} -2.34292 q^{70} -8.22533 q^{71} +3.48929 q^{72} -4.68585 q^{73} +2.00000 q^{74} -1.00000 q^{75} +25.0361 q^{76} +1.00000 q^{77} -7.37169 q^{78} +2.51806 q^{79} +1.19656 q^{80} +1.00000 q^{81} +8.29273 q^{82} +13.8610 q^{83} +3.48929 q^{84} +6.48929 q^{85} -13.2039 q^{86} -0.949808 q^{87} -3.48929 q^{88} -18.3790 q^{89} +2.34292 q^{90} -3.14637 q^{91} +7.66442 q^{92} +6.12494 q^{93} -3.60688 q^{94} +7.17513 q^{95} +4.17513 q^{96} -5.00735 q^{97} +2.34292 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 8 q^{13} - q^{14} - 3 q^{15} - q^{16} + 12 q^{17} + q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - q^{22} + 2 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} + 6 q^{29} - q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} + 4 q^{37} + 22 q^{38} - 8 q^{39} + 3 q^{40} + q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 14 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} + q^{50} - 12 q^{51} + 18 q^{52} + 16 q^{53} - q^{54} - 3 q^{55} - 3 q^{56} - 2 q^{57} - 16 q^{58} - 8 q^{59} - 3 q^{60} - 4 q^{62} - 3 q^{63} - 17 q^{64} + 8 q^{65} + q^{66} + 8 q^{67} + 26 q^{68} - 2 q^{69} - q^{70} - 2 q^{71} + 3 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} + 24 q^{76} + 3 q^{77} + 2 q^{78} - 18 q^{79} - q^{80} + 3 q^{81} + 22 q^{82} + 10 q^{83} + 3 q^{84} + 12 q^{85} - 2 q^{86} - 6 q^{87} - 3 q^{88} + 2 q^{89} + q^{90} - 8 q^{91} - 4 q^{92} + 2 q^{93} - 20 q^{94} + 2 q^{95} - 7 q^{96} + 18 q^{97} + q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 8 * q^13 - q^14 - 3 * q^15 - q^16 + 12 * q^17 + q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - q^22 + 2 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 + 6 * q^29 - q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 + 4 * q^37 + 22 * q^38 - 8 * q^39 + 3 * q^40 + q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 14 * q^46 + 6 * q^47 + q^48 + 3 * q^49 + q^50 - 12 * q^51 + 18 * q^52 + 16 * q^53 - q^54 - 3 * q^55 - 3 * q^56 - 2 * q^57 - 16 * q^58 - 8 * q^59 - 3 * q^60 - 4 * q^62 - 3 * q^63 - 17 * q^64 + 8 * q^65 + q^66 + 8 * q^67 + 26 * q^68 - 2 * q^69 - q^70 - 2 * q^71 + 3 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 + 24 * q^76 + 3 * q^77 + 2 * q^78 - 18 * q^79 - q^80 + 3 * q^81 + 22 * q^82 + 10 * q^83 + 3 * q^84 + 12 * q^85 - 2 * q^86 - 6 * q^87 - 3 * q^88 + 2 * q^89 + q^90 - 8 * q^91 - 4 * q^92 + 2 * q^93 - 20 * q^94 + 2 * q^95 - 7 * q^96 + 18 * q^97 + q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.34292	1.65670	0.828348	−	0.560213i	$-0.189281\pi$
$2$	2.34292	1.65670	0.828348	+	0.560213i	$0.189281\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.48929	1.74464
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.34292	−0.956494
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.48929	1.23365
$9$	1.00000	0.333333
$10$	2.34292	0.740897
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.48929	−1.00727
$13$	3.14637	0.872645	0.436322	−	0.899790i	$-0.356281\pi$
$13$	3.14637	0.872645	0.436322	+	0.899790i	$0.356281\pi$
$14$	−2.34292	−0.626173
$15$	−1.00000	−0.258199
$16$	1.19656	0.299139
$17$	6.48929	1.57388	0.786942	−	0.617027i	$-0.211663\pi$
$17$	6.48929	1.57388	0.786942	+	0.617027i	$0.211663\pi$
$18$	2.34292	0.552232
$19$	7.17513	1.64609	0.823044	−	0.567977i	$-0.192274\pi$
$19$	7.17513	1.64609	0.823044	+	0.567977i	$0.192274\pi$
$20$	3.48929	0.780229
$21$	1.00000	0.218218
$22$	−2.34292	−0.499513
$23$	2.19656	0.458014	0.229007	−	0.973425i	$-0.426452\pi$
$23$	2.19656	0.458014	0.229007	+	0.973425i	$0.426452\pi$
$24$	−3.48929	−0.712248
$25$	1.00000	0.200000
$26$	7.37169	1.44571
$27$	−1.00000	−0.192450
$28$	−3.48929	−0.659414
$29$	0.949808	0.176375	0.0881874	−	0.996104i	$-0.471893\pi$
$29$	0.949808	0.176375	0.0881874	+	0.996104i	$0.471893\pi$
$30$	−2.34292	−0.427757
$31$	−6.12494	−1.10007	−0.550036	−	0.835141i	$-0.685386\pi$
$31$	−6.12494	−1.10007	−0.550036	+	0.835141i	$0.685386\pi$
$32$	−4.17513	−0.738067
$33$	1.00000	0.174078
$34$	15.2039	2.60745
$35$	−1.00000	−0.169031
$36$	3.48929	0.581548
$37$	0.853635	0.140337	0.0701683	−	0.997535i	$-0.477646\pi$
$37$	0.853635	0.140337	0.0701683	+	0.997535i	$0.477646\pi$
$38$	16.8108	2.72707
$39$	−3.14637	−0.503822
$40$	3.48929	0.551705
$41$	3.53948	0.552774	0.276387	−	0.961046i	$-0.410863\pi$
$41$	3.53948	0.552774	0.276387	+	0.961046i	$0.410863\pi$
$42$	2.34292	0.361521
$43$	−5.63565	−0.859429	−0.429715	−	0.902965i	$-0.641386\pi$
$43$	−5.63565	−0.859429	−0.429715	+	0.902965i	$0.641386\pi$
$44$	−3.48929	−0.526030
$45$	1.00000	0.149071
$46$	5.14637	0.758790
$47$	−1.53948	−0.224556	−0.112278	−	0.993677i	$-0.535815\pi$
$47$	−1.53948	−0.224556	−0.112278	+	0.993677i	$0.535815\pi$
$48$	−1.19656	−0.172708
$49$	1.00000	0.142857
$50$	2.34292	0.331339
$51$	−6.48929	−0.908682
$52$	10.9786	1.52245
$53$	−6.15371	−0.845277	−0.422639	−	0.906298i	$-0.638896\pi$
$53$	−6.15371	−0.845277	−0.422639	+	0.906298i	$0.638896\pi$
$54$	−2.34292	−0.318831
$55$	−1.00000	−0.134840
$56$	−3.48929	−0.466276
$57$	−7.17513	−0.950370
$58$	2.22533	0.292200
$59$	−5.63565	−0.733700	−0.366850	−	0.930280i	$-0.619564\pi$
$59$	−5.63565	−0.733700	−0.366850	+	0.930280i	$0.619564\pi$
$60$	−3.48929	−0.450465
$61$	4.58967	0.587647	0.293824	−	0.955860i	$-0.405072\pi$
$61$	4.58967	0.587647	0.293824	+	0.955860i	$0.405072\pi$
$62$	−14.3503	−1.82249
$63$	−1.00000	−0.125988
$64$	−12.1751	−1.52189
$65$	3.14637	0.390259
$66$	2.34292	0.288394
$67$	−10.3503	−1.26449	−0.632243	−	0.774770i	$-0.717866\pi$
$67$	−10.3503	−1.26449	−0.632243	+	0.774770i	$0.717866\pi$
$68$	22.6430	2.74587
$69$	−2.19656	−0.264434
$70$	−2.34292	−0.280033
$71$	−8.22533	−0.976167	−0.488083	−	0.872797i	$-0.662304\pi$
$71$	−8.22533	−0.976167	−0.488083	+	0.872797i	$0.662304\pi$
$72$	3.48929	0.411217
$73$	−4.68585	−0.548437	−0.274218	−	0.961667i	$-0.588419\pi$
$73$	−4.68585	−0.548437	−0.274218	+	0.961667i	$0.588419\pi$
$74$	2.00000	0.232495
$75$	−1.00000	−0.115470
$76$	25.0361	2.87184
$77$	1.00000	0.113961
$78$	−7.37169	−0.834680
$79$	2.51806	0.283304	0.141652	−	0.989917i	$-0.454759\pi$
$79$	2.51806	0.283304	0.141652	+	0.989917i	$0.454759\pi$
$80$	1.19656	0.133779
$81$	1.00000	0.111111
$82$	8.29273	0.915779
$83$	13.8610	1.52144	0.760720	−	0.649080i	$-0.224846\pi$
$83$	13.8610	1.52144	0.760720	+	0.649080i	$0.224846\pi$
$84$	3.48929	0.380713
$85$	6.48929	0.703862
$86$	−13.2039	−1.42381
$87$	−0.949808	−0.101830
$88$	−3.48929	−0.371959
$89$	−18.3790	−1.94817	−0.974087	−	0.226173i	$-0.927378\pi$
$89$	−18.3790	−1.94817	−0.974087	+	0.226173i	$0.927378\pi$
$90$	2.34292	0.246966
$91$	−3.14637	−0.329829
$92$	7.66442	0.799071
$93$	6.12494	0.635127
$94$	−3.60688	−0.372022
$95$	7.17513	0.736153
$96$	4.17513	0.426123
$97$	−5.00735	−0.508419	−0.254209	−	0.967149i	$-0.581815\pi$
$97$	−5.00735	−0.508419	−0.254209	+	0.967149i	$0.581815\pi$
$98$	2.34292	0.236671
$99$	−1.00000	−0.100504
$100$	3.48929	0.348929
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−15.2039	−1.50541
$103$	11.9284	1.17534	0.587669	−	0.809101i	$-0.300046\pi$
$103$	11.9284	1.17534	0.587669	+	0.809101i	$0.300046\pi$
$104$	10.9786	1.07654
$105$	1.00000	0.0975900
$106$	−14.4177	−1.40037
$107$	−5.20390	−0.503080	−0.251540	−	0.967847i	$-0.580937\pi$
$107$	−5.20390	−0.503080	−0.251540	+	0.967847i	$0.580937\pi$
$108$	−3.48929	−0.335757
$109$	−10.2253	−0.979409	−0.489704	−	0.871889i	$-0.662895\pi$
$109$	−10.2253	−0.979409	−0.489704	+	0.871889i	$0.662895\pi$
$110$	−2.34292	−0.223389
$111$	−0.853635	−0.0810234
$112$	−1.19656	−0.113064
$113$	11.0748	1.04182	0.520912	−	0.853610i	$-0.325592\pi$
$113$	11.0748	1.04182	0.520912	+	0.853610i	$0.325592\pi$
$114$	−16.8108	−1.57447
$115$	2.19656	0.204830
$116$	3.31415	0.307711
$117$	3.14637	0.290882
$118$	−13.2039	−1.21552
$119$	−6.48929	−0.594872
$120$	−3.48929	−0.318527
$121$	1.00000	0.0909091
$122$	10.7533	0.973554
$123$	−3.53948	−0.319144
$124$	−21.3717	−1.91923
$125$	1.00000	0.0894427
$126$	−2.34292	−0.208724
$127$	−8.65708	−0.768191	−0.384096	−	0.923293i	$-0.625487\pi$
$127$	−8.65708	−0.768191	−0.384096	+	0.923293i	$0.625487\pi$
$128$	−20.1751	−1.78325
$129$	5.63565	0.496192
$130$	7.37169	0.646540
$131$	4.75325	0.415293	0.207647	−	0.978204i	$-0.433420\pi$
$131$	4.75325	0.415293	0.207647	+	0.978204i	$0.433420\pi$
$132$	3.48929	0.303704
$133$	−7.17513	−0.622163
$134$	−24.2499	−2.09487
$135$	−1.00000	−0.0860663
$136$	22.6430	1.94162
$137$	12.1004	1.03381	0.516903	−	0.856044i	$-0.327085\pi$
$137$	12.1004	1.03381	0.516903	+	0.856044i	$0.327085\pi$
$138$	−5.14637	−0.438088
$139$	−21.4292	−1.81760	−0.908802	−	0.417228i	$-0.863002\pi$
$139$	−21.4292	−1.81760	−0.908802	+	0.417228i	$0.863002\pi$
$140$	−3.48929	−0.294899
$141$	1.53948	0.129648
$142$	−19.2713	−1.61721
$143$	−3.14637	−0.263112
$144$	1.19656	0.0997131
$145$	0.949808	0.0788773
$146$	−10.9786	−0.908594
$147$	−1.00000	−0.0824786
$148$	2.97858	0.244838
$149$	−8.87819	−0.727330	−0.363665	−	0.931530i	$-0.618475\pi$
$149$	−8.87819	−0.727330	−0.363665	+	0.931530i	$0.618475\pi$
$150$	−2.34292	−0.191299
$151$	18.9357	1.54097	0.770484	−	0.637459i	$-0.220015\pi$
$151$	18.9357	1.54097	0.770484	+	0.637459i	$0.220015\pi$
$152$	25.0361	2.03070
$153$	6.48929	0.524628
$154$	2.34292	0.188798
$155$	−6.12494	−0.491967
$156$	−10.9786	−0.878990
$157$	10.7146	0.855119	0.427560	−	0.903987i	$-0.359373\pi$
$157$	10.7146	0.855119	0.427560	+	0.903987i	$0.359373\pi$
$158$	5.89962	0.469348
$159$	6.15371	0.488021
$160$	−4.17513	−0.330073
$161$	−2.19656	−0.173113
$162$	2.34292	0.184077
$163$	12.0821	0.946343	0.473171	−	0.880970i	$-0.343109\pi$
$163$	12.0821	0.946343	0.473171	+	0.880970i	$0.343109\pi$
$164$	12.3503	0.964394
$165$	1.00000	0.0778499
$166$	32.4752	2.52057
$167$	−17.4292	−1.34871	−0.674357	−	0.738405i	$-0.735579\pi$
$167$	−17.4292	−1.34871	−0.674357	+	0.738405i	$0.735579\pi$
$168$	3.48929	0.269204
$169$	−3.10038	−0.238491
$170$	15.2039	1.16609
$171$	7.17513	0.548696
$172$	−19.6644	−1.49940
$173$	13.4721	1.02426	0.512132	−	0.858907i	$-0.328856\pi$
$173$	13.4721	1.02426	0.512132	+	0.858907i	$0.328856\pi$
$174$	−2.22533	−0.168702
$175$	−1.00000	−0.0755929
$176$	−1.19656	−0.0901939
$177$	5.63565	0.423602
$178$	−43.0607	−3.22753
$179$	−12.2253	−0.913764	−0.456882	−	0.889527i	$-0.651034\pi$
$179$	−12.2253	−0.913764	−0.456882	+	0.889527i	$0.651034\pi$
$180$	3.48929	0.260076
$181$	−11.9572	−0.888768	−0.444384	−	0.895836i	$-0.646577\pi$
$181$	−11.9572	−0.888768	−0.444384	+	0.895836i	$0.646577\pi$
$182$	−7.37169	−0.546426
$183$	−4.58967	−0.339278
$184$	7.66442	0.565029
$185$	0.853635	0.0627605
$186$	14.3503	1.05221
$187$	−6.48929	−0.474544
$188$	−5.37169	−0.391771
$189$	1.00000	0.0727393
$190$	16.8108	1.21958
$191$	5.37169	0.388682	0.194341	−	0.980934i	$-0.437743\pi$
$191$	5.37169	0.388682	0.194341	+	0.980934i	$0.437743\pi$
$192$	12.1751	0.878665
$193$	−2.92104	−0.210261	−0.105130	−	0.994458i	$-0.533526\pi$
$193$	−2.92104	−0.210261	−0.105130	+	0.994458i	$0.533526\pi$
$194$	−11.7318	−0.842296
$195$	−3.14637	−0.225316
$196$	3.48929	0.249235
$197$	9.27131	0.660553	0.330277	−	0.943884i	$-0.392858\pi$
$197$	9.27131	0.660553	0.330277	+	0.943884i	$0.392858\pi$
$198$	−2.34292	−0.166504
$199$	−8.78623	−0.622839	−0.311420	−	0.950272i	$-0.600804\pi$
$199$	−8.78623	−0.622839	−0.311420	+	0.950272i	$0.600804\pi$
$200$	3.48929	0.246730
$201$	10.3503	0.730052
$202$	14.0575	0.989085
$203$	−0.949808	−0.0666634
$204$	−22.6430	−1.58533
$205$	3.53948	0.247208
$206$	27.9473	1.94718
$207$	2.19656	0.152671
$208$	3.76481	0.261042
$209$	−7.17513	−0.496314
$210$	2.34292	0.161677
$211$	−24.0575	−1.65619	−0.828095	−	0.560588i	$-0.810575\pi$
$211$	−24.0575	−1.65619	−0.828095	+	0.560588i	$0.810575\pi$
$212$	−21.4721	−1.47471
$213$	8.22533	0.563590
$214$	−12.1923	−0.833452
$215$	−5.63565	−0.384348
$216$	−3.48929	−0.237416
$217$	6.12494	0.415788
$218$	−23.9572	−1.62258
$219$	4.68585	0.316640
$220$	−3.48929	−0.235248
$221$	20.4177	1.37344
$222$	−2.00000	−0.134231
$223$	8.32150	0.557249	0.278624	−	0.960400i	$-0.410122\pi$
$223$	8.32150	0.557249	0.278624	+	0.960400i	$0.410122\pi$
$224$	4.17513	0.278963
$225$	1.00000	0.0666667
$226$	25.9473	1.72599
$227$	7.51071	0.498503	0.249252	−	0.968439i	$-0.419815\pi$
$227$	7.51071	0.498503	0.249252	+	0.968439i	$0.419815\pi$
$228$	−25.0361	−1.65806
$229$	17.6890	1.16892	0.584460	−	0.811422i	$-0.301306\pi$
$229$	17.6890	1.16892	0.584460	+	0.811422i	$0.301306\pi$
$230$	5.14637	0.339341
$231$	−1.00000	−0.0657952
$232$	3.31415	0.217585
$233$	−6.75325	−0.442420	−0.221210	−	0.975226i	$-0.571001\pi$
$233$	−6.75325	−0.442420	−0.221210	+	0.975226i	$0.571001\pi$
$234$	7.37169	0.481903
$235$	−1.53948	−0.100425
$236$	−19.6644	−1.28004
$237$	−2.51806	−0.163565
$238$	−15.2039	−0.985523
$239$	−12.5223	−0.809998	−0.404999	−	0.914317i	$-0.632728\pi$
$239$	−12.5223	−0.809998	−0.404999	+	0.914317i	$0.632728\pi$
$240$	−1.19656	−0.0772375
$241$	−8.93573	−0.575601	−0.287801	−	0.957690i	$-0.592924\pi$
$241$	−8.93573	−0.575601	−0.287801	+	0.957690i	$0.592924\pi$
$242$	2.34292	0.150609
$243$	−1.00000	−0.0641500
$244$	16.0147	1.02524
$245$	1.00000	0.0638877
$246$	−8.29273	−0.528725
$247$	22.5756	1.43645
$248$	−21.3717	−1.35710
$249$	−13.8610	−0.878404
$250$	2.34292	0.148179
$251$	−28.4998	−1.79889	−0.899445	−	0.437034i	$-0.856029\pi$
$251$	−28.4998	−1.79889	−0.899445	+	0.437034i	$0.856029\pi$
$252$	−3.48929	−0.219805
$253$	−2.19656	−0.138096
$254$	−20.2829	−1.27266
$255$	−6.48929	−0.406375
$256$	−22.9185	−1.43241
$257$	−19.7894	−1.23443	−0.617213	−	0.786796i	$-0.711738\pi$
$257$	−19.7894	−1.23443	−0.617213	+	0.786796i	$0.711738\pi$
$258$	13.2039	0.822039
$259$	−0.853635	−0.0530423
$260$	10.9786	0.680862
$261$	0.949808	0.0587916
$262$	11.1365	0.688015
$263$	24.4507	1.50769	0.753846	−	0.657051i	$-0.228196\pi$
$263$	24.4507	1.50769	0.753846	+	0.657051i	$0.228196\pi$
$264$	3.48929	0.214751
$265$	−6.15371	−0.378020
$266$	−16.8108	−1.03074
$267$	18.3790	1.12478
$268$	−36.1151	−2.20608
$269$	16.0863	0.980799	0.490400	−	0.871498i	$-0.336851\pi$
$269$	16.0863	0.980799	0.490400	+	0.871498i	$0.336851\pi$
$270$	−2.34292	−0.142586
$271$	−31.2327	−1.89725	−0.948625	−	0.316403i	$-0.897525\pi$
$271$	−31.2327	−1.89725	−0.948625	+	0.316403i	$0.897525\pi$
$272$	7.76481	0.470811
$273$	3.14637	0.190427
$274$	28.3503	1.71270
$275$	−1.00000	−0.0603023
$276$	−7.66442	−0.461344
$277$	−19.7648	−1.18755	−0.593776	−	0.804630i	$-0.702364\pi$
$277$	−19.7648	−1.18755	−0.593776	+	0.804630i	$0.702364\pi$
$278$	−50.2070	−3.01122
$279$	−6.12494	−0.366691
$280$	−3.48929	−0.208525
$281$	0.350269	0.0208953	0.0104477	−	0.999945i	$-0.496674\pi$
$281$	0.350269	0.0208953	0.0104477	+	0.999945i	$0.496674\pi$
$282$	3.60688	0.214787
$283$	−14.3748	−0.854495	−0.427247	−	0.904135i	$-0.640517\pi$
$283$	−14.3748	−0.854495	−0.427247	+	0.904135i	$0.640517\pi$
$284$	−28.7005	−1.70306
$285$	−7.17513	−0.425018
$286$	−7.37169	−0.435897
$287$	−3.53948	−0.208929
$288$	−4.17513	−0.246022
$289$	25.1109	1.47711
$290$	2.22533	0.130676
$291$	5.00735	0.293536
$292$	−16.3503	−0.956827
$293$	22.5468	1.31720	0.658600	−	0.752493i	$-0.271149\pi$
$293$	22.5468	1.31720	0.658600	+	0.752493i	$0.271149\pi$
$294$	−2.34292	−0.136642
$295$	−5.63565	−0.328120
$296$	2.97858	0.173126
$297$	1.00000	0.0580259
$298$	−20.8009	−1.20497
$299$	6.91117	0.399683
$300$	−3.48929	−0.201454
$301$	5.63565	0.324834
$302$	44.3650	2.55292
$303$	−6.00000	−0.344691
$304$	8.58546	0.492410
$305$	4.58967	0.262804
$306$	15.2039	0.869149
$307$	9.89962	0.565001	0.282500	−	0.959267i	$-0.408836\pi$
$307$	9.89962	0.565001	0.282500	+	0.959267i	$0.408836\pi$
$308$	3.48929	0.198821
$309$	−11.9284	−0.678582
$310$	−14.3503	−0.815041
$311$	13.0361	0.739210	0.369605	−	0.929189i	$-0.379493\pi$
$311$	13.0361	0.739210	0.369605	+	0.929189i	$0.379493\pi$
$312$	−10.9786	−0.621540
$313$	−23.7507	−1.34247	−0.671235	−	0.741244i	$-0.734236\pi$
$313$	−23.7507	−1.34247	−0.671235	+	0.741244i	$0.734236\pi$
$314$	25.1035	1.41667
$315$	−1.00000	−0.0563436
$316$	8.78623	0.494264
$317$	13.0214	0.731356	0.365678	−	0.930741i	$-0.380837\pi$
$317$	13.0214	0.731356	0.365678	+	0.930741i	$0.380837\pi$
$318$	14.4177	0.808503
$319$	−0.949808	−0.0531790
$320$	−12.1751	−0.680611
$321$	5.20390	0.290454
$322$	−5.14637	−0.286796
$323$	46.5615	2.59075
$324$	3.48929	0.193849
$325$	3.14637	0.174529
$326$	28.3074	1.56780
$327$	10.2253	0.565462
$328$	12.3503	0.681930
$329$	1.53948	0.0848743
$330$	2.34292	0.128974
$331$	19.2327	1.05712	0.528562	−	0.848895i	$-0.322732\pi$
$331$	19.2327	1.05712	0.528562	+	0.848895i	$0.322732\pi$
$332$	48.3650	2.65437
$333$	0.853635	0.0467789
$334$	−40.8353	−2.23441
$335$	−10.3503	−0.565496
$336$	1.19656	0.0652776
$337$	−24.2787	−1.32254	−0.661271	−	0.750147i	$-0.729983\pi$
$337$	−24.2787	−1.32254	−0.661271	+	0.750147i	$0.729983\pi$
$338$	−7.26396	−0.395107
$339$	−11.0748	−0.601498
$340$	22.6430	1.22799
$341$	6.12494	0.331684
$342$	16.8108	0.909023
$343$	−1.00000	−0.0539949
$344$	−19.6644	−1.06023
$345$	−2.19656	−0.118259
$346$	31.5640	1.69689
$347$	10.4935	0.563321	0.281660	−	0.959514i	$-0.409115\pi$
$347$	10.4935	0.563321	0.281660	+	0.959514i	$0.409115\pi$
$348$	−3.31415	−0.177657
$349$	3.94667	0.211261	0.105630	−	0.994405i	$-0.466314\pi$
$349$	3.94667	0.211261	0.105630	+	0.994405i	$0.466314\pi$
$350$	−2.34292	−0.125235
$351$	−3.14637	−0.167941
$352$	4.17513	0.222535
$353$	18.4507	0.982029	0.491015	−	0.871151i	$-0.336626\pi$
$353$	18.4507	0.982029	0.491015	+	0.871151i	$0.336626\pi$
$354$	13.2039	0.701780
$355$	−8.22533	−0.436555
$356$	−64.1298	−3.39887
$357$	6.48929	0.343450
$358$	−28.6430	−1.51383
$359$	35.4005	1.86836	0.934182	−	0.356796i	$-0.116131\pi$
$359$	35.4005	1.86836	0.934182	+	0.356796i	$0.116131\pi$
$360$	3.48929	0.183902
$361$	32.4826	1.70961
$362$	−28.0147	−1.47242
$363$	−1.00000	−0.0524864
$364$	−10.9786	−0.575434
$365$	−4.68585	−0.245268
$366$	−10.7533	−0.562081
$367$	10.9498	0.571575	0.285788	−	0.958293i	$-0.407745\pi$
$367$	10.9498	0.571575	0.285788	+	0.958293i	$0.407745\pi$
$368$	2.62831	0.137010
$369$	3.53948	0.184258
$370$	2.00000	0.103975
$371$	6.15371	0.319485
$372$	21.3717	1.10807
$373$	−2.51385	−0.130162	−0.0650810	−	0.997880i	$-0.520731\pi$
$373$	−2.51385	−0.130162	−0.0650810	+	0.997880i	$0.520731\pi$
$374$	−15.2039	−0.786175
$375$	−1.00000	−0.0516398
$376$	−5.37169	−0.277024
$377$	2.98844	0.153913
$378$	2.34292	0.120507
$379$	−34.8971	−1.79254	−0.896272	−	0.443505i	$-0.853735\pi$
$379$	−34.8971	−1.79254	−0.896272	+	0.443505i	$0.853735\pi$
$380$	25.0361	1.28433
$381$	8.65708	0.443515
$382$	12.5855	0.643928
$383$	24.5609	1.25500	0.627502	−	0.778615i	$-0.284078\pi$
$383$	24.5609	1.25500	0.627502	+	0.778615i	$0.284078\pi$
$384$	20.1751	1.02956
$385$	1.00000	0.0509647
$386$	−6.84377	−0.348339
$387$	−5.63565	−0.286476
$388$	−17.4721	−0.887010
$389$	14.2253	0.721253	0.360626	−	0.932710i	$-0.382563\pi$
$389$	14.2253	0.721253	0.360626	+	0.932710i	$0.382563\pi$
$390$	−7.37169	−0.373280
$391$	14.2541	0.720861
$392$	3.48929	0.176236
$393$	−4.75325	−0.239770
$394$	21.7220	1.09434
$395$	2.51806	0.126697
$396$	−3.48929	−0.175343
$397$	−18.9786	−0.952507	−0.476254	−	0.879308i	$-0.658006\pi$
$397$	−18.9786	−0.952507	−0.476254	+	0.879308i	$0.658006\pi$
$398$	−20.5855	−1.03186
$399$	7.17513	0.359206
$400$	1.19656	0.0598279
$401$	4.71040	0.235226	0.117613	−	0.993059i	$-0.462476\pi$
$401$	4.71040	0.235226	0.117613	+	0.993059i	$0.462476\pi$
$402$	24.2499	1.20947
$403$	−19.2713	−0.959972
$404$	20.9357	1.04159
$405$	1.00000	0.0496904
$406$	−2.22533	−0.110441
$407$	−0.853635	−0.0423131
$408$	−22.6430	−1.12100
$409$	30.1067	1.48868	0.744339	−	0.667802i	$-0.232765\pi$
$409$	30.1067	1.48868	0.744339	+	0.667802i	$0.232765\pi$
$410$	8.29273	0.409549
$411$	−12.1004	−0.596868
$412$	41.6216	2.05055
$413$	5.63565	0.277312
$414$	5.14637	0.252930
$415$	13.8610	0.680409
$416$	−13.1365	−0.644070
$417$	21.4292	1.04939
$418$	−16.8108	−0.822243
$419$	35.6503	1.74163	0.870817	−	0.491608i	$-0.163591\pi$
$419$	35.6503	1.74163	0.870817	+	0.491608i	$0.163591\pi$
$420$	3.48929	0.170260
$421$	−23.3246	−1.13677	−0.568387	−	0.822762i	$-0.692432\pi$
$421$	−23.3246	−1.13677	−0.568387	+	0.822762i	$0.692432\pi$
$422$	−56.3650	−2.74380
$423$	−1.53948	−0.0748521
$424$	−21.4721	−1.04278
$425$	6.48929	0.314777
$426$	19.2713	0.933698
$427$	−4.58967	−0.222110
$428$	−18.1579	−0.877696
$429$	3.14637	0.151908
$430$	−13.2039	−0.636749
$431$	4.24989	0.204710	0.102355	−	0.994748i	$-0.467362\pi$
$431$	4.24989	0.204710	0.102355	+	0.994748i	$0.467362\pi$
$432$	−1.19656	−0.0575694
$433$	31.0361	1.49150	0.745750	−	0.666226i	$-0.232091\pi$
$433$	31.0361	1.49150	0.745750	+	0.666226i	$0.232091\pi$
$434$	14.3503	0.688835
$435$	−0.949808	−0.0455398
$436$	−35.6791	−1.70872
$437$	15.7606	0.753932
$438$	10.9786	0.524577
$439$	−19.0319	−0.908343	−0.454172	−	0.890914i	$-0.650065\pi$
$439$	−19.0319	−0.908343	−0.454172	+	0.890914i	$0.650065\pi$
$440$	−3.48929	−0.166345
$441$	1.00000	0.0476190
$442$	47.8370	2.27538
$443$	34.3994	1.63436	0.817182	−	0.576380i	$-0.195535\pi$
$443$	34.3994	1.63436	0.817182	+	0.576380i	$0.195535\pi$
$444$	−2.97858	−0.141357
$445$	−18.3790	−0.871250
$446$	19.4966	0.923192
$447$	8.87819	0.419924
$448$	12.1751	0.575221
$449$	25.7465	1.21505	0.607527	−	0.794299i	$-0.292162\pi$
$449$	25.7465	1.21505	0.607527	+	0.794299i	$0.292162\pi$
$450$	2.34292	0.110446
$451$	−3.53948	−0.166668
$452$	38.6430	1.81761
$453$	−18.9357	−0.889678
$454$	17.5970	0.825869
$455$	−3.14637	−0.147504
$456$	−25.0361	−1.17242
$457$	3.63565	0.170069	0.0850344	−	0.996378i	$-0.472900\pi$
$457$	3.63565	0.170069	0.0850344	+	0.996378i	$0.472900\pi$
$458$	41.4439	1.93655
$459$	−6.48929	−0.302894
$460$	7.66442	0.357356
$461$	30.8353	1.43615	0.718073	−	0.695968i	$-0.245025\pi$
$461$	30.8353	1.43615	0.718073	+	0.695968i	$0.245025\pi$
$462$	−2.34292	−0.109003
$463$	−22.0147	−1.02311	−0.511555	−	0.859251i	$-0.670930\pi$
$463$	−22.0147	−1.02311	−0.511555	+	0.859251i	$0.670930\pi$
$464$	1.13650	0.0527607
$465$	6.12494	0.284037
$466$	−15.8223	−0.732956
$467$	8.92104	0.412816	0.206408	−	0.978466i	$-0.433823\pi$
$467$	8.92104	0.412816	0.206408	+	0.978466i	$0.433823\pi$
$468$	10.9786	0.507485
$469$	10.3503	0.477931
$470$	−3.60688	−0.166373
$471$	−10.7146	−0.493703
$472$	−19.6644	−0.905128
$473$	5.63565	0.259128
$474$	−5.89962	−0.270978
$475$	7.17513	0.329218
$476$	−22.6430	−1.03784
$477$	−6.15371	−0.281759
$478$	−29.3387	−1.34192
$479$	26.8255	1.22569	0.612844	−	0.790204i	$-0.290025\pi$
$479$	26.8255	1.22569	0.612844	+	0.790204i	$0.290025\pi$
$480$	4.17513	0.190568
$481$	2.68585	0.122464
$482$	−20.9357	−0.953596
$483$	2.19656	0.0999468
$484$	3.48929	0.158604
$485$	−5.00735	−0.227372
$486$	−2.34292	−0.106277
$487$	−19.2713	−0.873266	−0.436633	−	0.899640i	$-0.643829\pi$
$487$	−19.2713	−0.873266	−0.436633	+	0.899640i	$0.643829\pi$
$488$	16.0147	0.724951
$489$	−12.0821	−0.546371
$490$	2.34292	0.105842
$491$	−34.6718	−1.56472	−0.782358	−	0.622830i	$-0.785983\pi$
$491$	−34.6718	−1.56472	−0.782358	+	0.622830i	$0.785983\pi$
$492$	−12.3503	−0.556793
$493$	6.16358	0.277594
$494$	52.8929	2.37976
$495$	−1.00000	−0.0449467
$496$	−7.32885	−0.329075
$497$	8.22533	0.368956
$498$	−32.4752	−1.45525
$499$	9.94667	0.445274	0.222637	−	0.974901i	$-0.428533\pi$
$499$	9.94667	0.445274	0.222637	+	0.974901i	$0.428533\pi$
$500$	3.48929	0.156046
$501$	17.4292	0.778681
$502$	−66.7728	−2.98021
$503$	−12.3461	−0.550484	−0.275242	−	0.961375i	$-0.588758\pi$
$503$	−12.3461	−0.550484	−0.275242	+	0.961375i	$0.588758\pi$
$504$	−3.48929	−0.155425
$505$	6.00000	0.266996
$506$	−5.14637	−0.228784
$507$	3.10038	0.137693
$508$	−30.2070	−1.34022
$509$	−39.3576	−1.74450	−0.872248	−	0.489064i	$-0.837338\pi$
$509$	−39.3576	−1.74450	−0.872248	+	0.489064i	$0.837338\pi$
$510$	−15.2039	−0.673240
$511$	4.68585	0.207290
$512$	−13.3461	−0.589818
$513$	−7.17513	−0.316790
$514$	−46.3650	−2.04507
$515$	11.9284	0.525627
$516$	19.6644	0.865678
$517$	1.53948	0.0677063
$518$	−2.00000	−0.0878750
$519$	−13.4721	−0.591359
$520$	10.9786	0.481442
$521$	−38.2933	−1.67766	−0.838831	−	0.544392i	$-0.816760\pi$
$521$	−38.2933	−1.67766	−0.838831	+	0.544392i	$0.816760\pi$
$522$	2.22533	0.0973999
$523$	28.1642	1.23153	0.615767	−	0.787928i	$-0.288846\pi$
$523$	28.1642	1.23153	0.615767	+	0.787928i	$0.288846\pi$
$524$	16.5855	0.724539
$525$	1.00000	0.0436436
$526$	57.2860	2.49779
$527$	−39.7465	−1.73139
$528$	1.19656	0.0520735
$529$	−18.1751	−0.790223
$530$	−14.4177	−0.626264
$531$	−5.63565	−0.244567
$532$	−25.0361	−1.08545
$533$	11.1365	0.482375
$534$	43.0607	1.86342
$535$	−5.20390	−0.224984
$536$	−36.1151	−1.55993
$537$	12.2253	0.527562
$538$	37.6890	1.62489
$539$	−1.00000	−0.0430730
$540$	−3.48929	−0.150155
$541$	−32.3832	−1.39226	−0.696132	−	0.717913i	$-0.745097\pi$
$541$	−32.3832	−1.39226	−0.696132	+	0.717913i	$0.745097\pi$
$542$	−73.1758	−3.14317
$543$	11.9572	0.513131
$544$	−27.0937	−1.16163
$545$	−10.2253	−0.438005
$546$	7.37169	0.315479
$547$	3.65035	0.156078	0.0780388	−	0.996950i	$-0.475134\pi$
$547$	3.65035	0.156078	0.0780388	+	0.996950i	$0.475134\pi$
$548$	42.2217	1.80362
$549$	4.58967	0.195882
$550$	−2.34292	−0.0999026
$551$	6.81500	0.290329
$552$	−7.66442	−0.326220
$553$	−2.51806	−0.107079
$554$	−46.3074	−1.96741
$555$	−0.853635	−0.0362348
$556$	−74.7728	−3.17107
$557$	17.0790	0.723659	0.361829	−	0.932244i	$-0.382152\pi$
$557$	17.0790	0.723659	0.361829	+	0.932244i	$0.382152\pi$
$558$	−14.3503	−0.607495
$559$	−17.7318	−0.749976
$560$	−1.19656	−0.0505638
$561$	6.48929	0.273978
$562$	0.820654	0.0346172
$563$	17.5640	0.740236	0.370118	−	0.928985i	$-0.379317\pi$
$563$	17.5640	0.740236	0.370118	+	0.928985i	$0.379317\pi$
$564$	5.37169	0.226189
$565$	11.0748	0.465918
$566$	−33.6791	−1.41564
$567$	−1.00000	−0.0419961
$568$	−28.7005	−1.20425
$569$	−23.6075	−0.989678	−0.494839	−	0.868985i	$-0.664773\pi$
$569$	−23.6075	−0.989678	−0.494839	+	0.868985i	$0.664773\pi$
$570$	−16.8108	−0.704126
$571$	35.5542	1.48790	0.743948	−	0.668238i	$-0.232951\pi$
$571$	35.5542	1.48790	0.743948	+	0.668238i	$0.232951\pi$
$572$	−10.9786	−0.459037
$573$	−5.37169	−0.224406
$574$	−8.29273	−0.346132
$575$	2.19656	0.0916028
$576$	−12.1751	−0.507297
$577$	45.5296	1.89542	0.947711	−	0.319129i	$-0.103390\pi$
$577$	45.5296	1.89542	0.947711	+	0.319129i	$0.103390\pi$
$578$	58.8328	2.44712
$579$	2.92104	0.121394
$580$	3.31415	0.137613
$581$	−13.8610	−0.575050
$582$	11.7318	0.486300
$583$	6.15371	0.254861
$584$	−16.3503	−0.676579
$585$	3.14637	0.130086
$586$	52.8255	2.18220
$587$	29.5113	1.21806	0.609031	−	0.793146i	$-0.291558\pi$
$587$	29.5113	1.21806	0.609031	+	0.793146i	$0.291558\pi$
$588$	−3.48929	−0.143896
$589$	−43.9473	−1.81082
$590$	−13.2039	−0.543596
$591$	−9.27131	−0.381371
$592$	1.02142	0.0419802
$593$	−16.9357	−0.695467	−0.347734	−	0.937593i	$-0.613049\pi$
$593$	−16.9357	−0.695467	−0.347734	+	0.937593i	$0.613049\pi$
$594$	2.34292	0.0961313
$595$	−6.48929	−0.266035
$596$	−30.9786	−1.26893
$597$	8.78623	0.359596
$598$	16.1923	0.662154
$599$	1.31415	0.0536949	0.0268474	−	0.999640i	$-0.491453\pi$
$599$	1.31415	0.0536949	0.0268474	+	0.999640i	$0.491453\pi$
$600$	−3.48929	−0.142450
$601$	−16.0533	−0.654829	−0.327414	−	0.944881i	$-0.606177\pi$
$601$	−16.0533	−0.654829	−0.327414	+	0.944881i	$0.606177\pi$
$602$	13.2039	0.538151
$603$	−10.3503	−0.421496
$604$	66.0722	2.68844
$605$	1.00000	0.0406558
$606$	−14.0575	−0.571048
$607$	−39.8568	−1.61774	−0.808868	−	0.587990i	$-0.799919\pi$
$607$	−39.8568	−1.61774	−0.808868	+	0.587990i	$0.799919\pi$
$608$	−29.9572	−1.21492
$609$	0.949808	0.0384882
$610$	10.7533	0.435386
$611$	−4.84377	−0.195958
$612$	22.6430	0.915289
$613$	−39.4868	−1.59486	−0.797428	−	0.603414i	$-0.793807\pi$
$613$	−39.4868	−1.59486	−0.797428	+	0.603414i	$0.793807\pi$
$614$	23.1940	0.936035
$615$	−3.53948	−0.142726
$616$	3.48929	0.140587
$617$	−2.77781	−0.111830	−0.0559152	−	0.998436i	$-0.517808\pi$
$617$	−2.77781	−0.111830	−0.0559152	+	0.998436i	$0.517808\pi$
$618$	−27.9473	−1.12420
$619$	−31.7220	−1.27501	−0.637507	−	0.770445i	$-0.720034\pi$
$619$	−31.7220	−1.27501	−0.637507	+	0.770445i	$0.720034\pi$
$620$	−21.3717	−0.858308
$621$	−2.19656	−0.0881448
$622$	30.5426	1.22465
$623$	18.3790	0.736341
$624$	−3.76481	−0.150713
$625$	1.00000	0.0400000
$626$	−55.6461	−2.22407
$627$	7.17513	0.286547
$628$	37.3864	1.49188
$629$	5.53948	0.220874
$630$	−2.34292	−0.0933443
$631$	−5.99579	−0.238689	−0.119344	−	0.992853i	$-0.538079\pi$
$631$	−5.99579	−0.238689	−0.119344	+	0.992853i	$0.538079\pi$
$632$	8.78623	0.349497
$633$	24.0575	0.956201
$634$	30.5082	1.21164
$635$	−8.65708	−0.343546
$636$	21.4721	0.851423
$637$	3.14637	0.124664
$638$	−2.22533	−0.0881015
$639$	−8.22533	−0.325389
$640$	−20.1751	−0.797492
$641$	−20.5426	−0.811385	−0.405692	−	0.914010i	$-0.632970\pi$
$641$	−20.5426	−0.811385	−0.405692	+	0.914010i	$0.632970\pi$
$642$	12.1923	0.481194
$643$	−4.51385	−0.178009	−0.0890044	−	0.996031i	$-0.528369\pi$
$643$	−4.51385	−0.178009	−0.0890044	+	0.996031i	$0.528369\pi$
$644$	−7.66442	−0.302021
$645$	5.63565	0.221904
$646$	109.090	4.29209
$647$	−19.0790	−0.750071	−0.375036	−	0.927010i	$-0.622370\pi$
$647$	−19.0790	−0.750071	−0.375036	+	0.927010i	$0.622370\pi$
$648$	3.48929	0.137072
$649$	5.63565	0.221219
$650$	7.37169	0.289142
$651$	−6.12494	−0.240055
$652$	42.1579	1.65103
$653$	30.7392	1.20292	0.601458	−	0.798904i	$-0.294587\pi$
$653$	30.7392	1.20292	0.601458	+	0.798904i	$0.294587\pi$
$654$	23.9572	0.936799
$655$	4.75325	0.185725
$656$	4.23519	0.165356
$657$	−4.68585	−0.182812
$658$	3.60688	0.140611
$659$	−31.7079	−1.23516	−0.617582	−	0.786507i	$-0.711888\pi$
$659$	−31.7079	−1.23516	−0.617582	+	0.786507i	$0.711888\pi$
$660$	3.48929	0.135820
$661$	33.6890	1.31035	0.655175	−	0.755477i	$-0.272595\pi$
$661$	33.6890	1.31035	0.655175	+	0.755477i	$0.272595\pi$
$662$	45.0607	1.75133
$663$	−20.4177	−0.792957
$664$	48.3650	1.87692
$665$	−7.17513	−0.278240
$666$	2.00000	0.0774984
$667$	2.08631	0.0807822
$668$	−60.8156	−2.35303
$669$	−8.32150	−0.321728
$670$	−24.2499	−0.936855
$671$	−4.58967	−0.177182
$672$	−4.17513	−0.161059
$673$	6.37904	0.245894	0.122947	−	0.992413i	$-0.460766\pi$
$673$	6.37904	0.245894	0.122947	+	0.992413i	$0.460766\pi$
$674$	−56.8830	−2.19105
$675$	−1.00000	−0.0384900
$676$	−10.8181	−0.416082
$677$	−13.6258	−0.523682	−0.261841	−	0.965111i	$-0.584330\pi$
$677$	−13.6258	−0.523682	−0.261841	+	0.965111i	$0.584330\pi$
$678$	−25.9473	−0.996500
$679$	5.00735	0.192164
$680$	22.6430	0.868319
$681$	−7.51071	−0.287811
$682$	14.3503	0.549500
$683$	−26.6577	−1.02003	−0.510014	−	0.860166i	$-0.670360\pi$
$683$	−26.6577	−1.02003	−0.510014	+	0.860166i	$0.670360\pi$
$684$	25.0361	0.957280
$685$	12.1004	0.462332
$686$	−2.34292	−0.0894532
$687$	−17.6890	−0.674877
$688$	−6.74338	−0.257089
$689$	−19.3618	−0.737627
$690$	−5.14637	−0.195919
$691$	−41.0080	−1.56002	−0.780008	−	0.625769i	$-0.784785\pi$
$691$	−41.0080	−1.56002	−0.780008	+	0.625769i	$0.784785\pi$
$692$	47.0080	1.78697
$693$	1.00000	0.0379869
$694$	24.5855	0.933251
$695$	−21.4292	−0.812857
$696$	−3.31415	−0.125623
$697$	22.9687	0.870002
$698$	9.24675	0.349995
$699$	6.75325	0.255431
$700$	−3.48929	−0.131883
$701$	−1.03550	−0.0391103	−0.0195551	−	0.999809i	$-0.506225\pi$
$701$	−1.03550	−0.0391103	−0.0195551	+	0.999809i	$0.506225\pi$
$702$	−7.37169	−0.278227
$703$	6.12494	0.231007
$704$	12.1751	0.458868
$705$	1.53948	0.0579802
$706$	43.2285	1.62692
$707$	−6.00000	−0.225653
$708$	19.6644	0.739034
$709$	38.6901	1.45304	0.726518	−	0.687148i	$-0.241137\pi$
$709$	38.6901	1.45304	0.726518	+	0.687148i	$0.241137\pi$
$710$	−19.2713	−0.723239
$711$	2.51806	0.0944345
$712$	−64.1298	−2.40336
$713$	−13.4538	−0.503848
$714$	15.2039	0.568992
$715$	−3.14637	−0.117667
$716$	−42.6577	−1.59419
$717$	12.5223	0.467653
$718$	82.9406	3.09531
$719$	27.7360	1.03438	0.517190	−	0.855871i	$-0.326978\pi$
$719$	27.7360	1.03438	0.517190	+	0.855871i	$0.326978\pi$
$720$	1.19656	0.0445931
$721$	−11.9284	−0.444236
$722$	76.1041	2.83230
$723$	8.93573	0.332323
$724$	−41.7220	−1.55058
$725$	0.949808	0.0352750
$726$	−2.34292	−0.0869540
$727$	26.8066	0.994201	0.497100	−	0.867693i	$-0.334398\pi$
$727$	26.8066	0.994201	0.497100	+	0.867693i	$0.334398\pi$
$728$	−10.9786	−0.406893
$729$	1.00000	0.0370370
$730$	−10.9786	−0.406335
$731$	−36.5714	−1.35264
$732$	−16.0147	−0.591920
$733$	32.7925	1.21122	0.605609	−	0.795762i	$-0.292929\pi$
$733$	32.7925	1.21122	0.605609	+	0.795762i	$0.292929\pi$
$734$	25.6546	0.946927
$735$	−1.00000	−0.0368856
$736$	−9.17092	−0.338045
$737$	10.3503	0.381257
$738$	8.29273	0.305260
$739$	−29.3142	−1.07834	−0.539169	−	0.842197i	$-0.681262\pi$
$739$	−29.3142	−1.07834	−0.539169	+	0.842197i	$0.681262\pi$
$740$	2.97858	0.109495
$741$	−22.5756	−0.829335
$742$	14.4177	0.529289
$743$	2.10038	0.0770556	0.0385278	−	0.999258i	$-0.487733\pi$
$743$	2.10038	0.0770556	0.0385278	+	0.999258i	$0.487733\pi$
$744$	21.3717	0.783524
$745$	−8.87819	−0.325272
$746$	−5.88975	−0.215639
$747$	13.8610	0.507147
$748$	−22.6430	−0.827910
$749$	5.20390	0.190147
$750$	−2.34292	−0.0855515
$751$	−26.0533	−0.950699	−0.475350	−	0.879797i	$-0.657678\pi$
$751$	−26.0533	−0.950699	−0.475350	+	0.879797i	$0.657678\pi$
$752$	−1.84208	−0.0671736
$753$	28.4998	1.03859
$754$	7.00169	0.254987
$755$	18.9357	0.689142
$756$	3.48929	0.126904
$757$	30.9504	1.12491	0.562456	−	0.826827i	$-0.309857\pi$
$757$	30.9504	1.12491	0.562456	+	0.826827i	$0.309857\pi$
$758$	−81.7612	−2.96970
$759$	2.19656	0.0797300
$760$	25.0361	0.908155
$761$	0.542616	0.0196698	0.00983491	−	0.999952i	$-0.496869\pi$
$761$	0.542616	0.0196698	0.00983491	+	0.999952i	$0.496869\pi$
$762$	20.2829	0.734771
$763$	10.2253	0.370182
$764$	18.7434	0.678112
$765$	6.48929	0.234621
$766$	57.5443	2.07916
$767$	−17.7318	−0.640259
$768$	22.9185	0.827001
$769$	21.3184	0.768760	0.384380	−	0.923175i	$-0.374415\pi$
$769$	21.3184	0.768760	0.384380	+	0.923175i	$0.374415\pi$
$770$	2.34292	0.0844331
$771$	19.7894	0.712697
$772$	−10.1923	−0.366831
$773$	17.5787	0.632263	0.316132	−	0.948715i	$-0.397616\pi$
$773$	17.5787	0.632263	0.316132	+	0.948715i	$0.397616\pi$
$774$	−13.2039	−0.474605
$775$	−6.12494	−0.220014
$776$	−17.4721	−0.627211
$777$	0.853635	0.0306240
$778$	33.3288	1.19490
$779$	25.3963	0.909915
$780$	−10.9786	−0.393096
$781$	8.22533	0.294325
$782$	33.3963	1.19425
$783$	−0.949808	−0.0339434
$784$	1.19656	0.0427342
$785$	10.7146	0.382421
$786$	−11.1365	−0.397226
$787$	41.2003	1.46863	0.734316	−	0.678808i	$-0.237503\pi$
$787$	41.2003	1.46863	0.734316	+	0.678808i	$0.237503\pi$
$788$	32.3503	1.15243
$789$	−24.4507	−0.870466
$790$	5.89962	0.209899
$791$	−11.0748	−0.393773
$792$	−3.48929	−0.123986
$793$	14.4408	0.512807
$794$	−44.4653	−1.57802
$795$	6.15371	0.218250
$796$	−30.6577	−1.08663
$797$	−40.9933	−1.45206	−0.726028	−	0.687665i	$-0.758636\pi$
$797$	−40.9933	−1.45206	−0.726028	+	0.687665i	$0.758636\pi$
$798$	16.8108	0.595095
$799$	−9.99013	−0.353426
$800$	−4.17513	−0.147613
$801$	−18.3790	−0.649391
$802$	11.0361	0.389699
$803$	4.68585	0.165360
$804$	36.1151	1.27368
$805$	−2.19656	−0.0774185
$806$	−45.1512	−1.59038
$807$	−16.0863	−0.566265
$808$	20.9357	0.736516
$809$	25.7795	0.906359	0.453179	−	0.891419i	$-0.350290\pi$
$809$	25.7795	0.906359	0.453179	+	0.891419i	$0.350290\pi$
$810$	2.34292	0.0823219
$811$	−31.9143	−1.12066	−0.560331	−	0.828268i	$-0.689326\pi$
$811$	−31.9143	−1.12066	−0.560331	+	0.828268i	$0.689326\pi$
$812$	−3.31415	−0.116304
$813$	31.2327	1.09538
$814$	−2.00000	−0.0701000
$815$	12.0821	0.423217
$816$	−7.76481	−0.271823
$817$	−40.4366	−1.41470
$818$	70.5376	2.46629
$819$	−3.14637	−0.109943
$820$	12.3503	0.431290
$821$	52.5945	1.83556	0.917780	−	0.397088i	$-0.129979\pi$
$821$	52.5945	1.83556	0.917780	+	0.397088i	$0.129979\pi$
$822$	−28.3503	−0.988829
$823$	1.87506	0.0653604	0.0326802	−	0.999466i	$-0.489596\pi$
$823$	1.87506	0.0653604	0.0326802	+	0.999466i	$0.489596\pi$
$824$	41.6216	1.44996
$825$	1.00000	0.0348155
$826$	13.2039	0.459423
$827$	25.1512	0.874593	0.437296	−	0.899317i	$-0.355936\pi$
$827$	25.1512	0.874593	0.437296	+	0.899317i	$0.355936\pi$
$828$	7.66442	0.266357
$829$	−11.6216	−0.403634	−0.201817	−	0.979423i	$-0.564685\pi$
$829$	−11.6216	−0.403634	−0.201817	+	0.979423i	$0.564685\pi$
$830$	32.4752	1.12723
$831$	19.7648	0.685634
$832$	−38.3074	−1.32807
$833$	6.48929	0.224841
$834$	50.2070	1.73853
$835$	−17.4292	−0.603163
$836$	−25.0361	−0.865892
$837$	6.12494	0.211709
$838$	83.5260	2.88536
$839$	−46.8641	−1.61793	−0.808964	−	0.587858i	$-0.799972\pi$
$839$	−46.8641	−1.61793	−0.808964	+	0.587858i	$0.799972\pi$
$840$	3.48929	0.120392
$841$	−28.0979	−0.968892
$842$	−54.6478	−1.88329
$843$	−0.350269	−0.0120639
$844$	−83.9437	−2.88946
$845$	−3.10038	−0.106656
$846$	−3.60688	−0.124007
$847$	−1.00000	−0.0343604
$848$	−7.36327	−0.252856
$849$	14.3748	0.493343
$850$	15.2039	0.521490
$851$	1.87506	0.0642761
$852$	28.7005	0.983264
$853$	48.1543	1.64877	0.824386	−	0.566027i	$-0.191520\pi$
$853$	48.1543	1.64877	0.824386	+	0.566027i	$0.191520\pi$
$854$	−10.7533	−0.367969
$855$	7.17513	0.245384
$856$	−18.1579	−0.620625
$857$	−44.2730	−1.51234	−0.756168	−	0.654377i	$-0.772931\pi$
$857$	−44.2730	−1.51234	−0.756168	+	0.654377i	$0.772931\pi$
$858$	7.37169	0.251665
$859$	12.8683	0.439062	0.219531	−	0.975606i	$-0.429547\pi$
$859$	12.8683	0.439062	0.219531	+	0.975606i	$0.429547\pi$
$860$	−19.6644	−0.670551
$861$	3.53948	0.120625
$862$	9.95715	0.339142
$863$	−10.1966	−0.347095	−0.173547	−	0.984826i	$-0.555523\pi$
$863$	−10.1966	−0.347095	−0.173547	+	0.984826i	$0.555523\pi$
$864$	4.17513	0.142041
$865$	13.4721	0.458064
$866$	72.7152	2.47096
$867$	−25.1109	−0.852810
$868$	21.3717	0.725403
$869$	−2.51806	−0.0854193
$870$	−2.22533	−0.0754456
$871$	−32.5657	−1.10345
$872$	−35.6791	−1.20825
$873$	−5.00735	−0.169473
$874$	36.9259	1.24904
$875$	−1.00000	−0.0338062
$876$	16.3503	0.552424
$877$	32.3937	1.09386	0.546929	−	0.837179i	$-0.315797\pi$
$877$	32.3937	1.09386	0.546929	+	0.837179i	$0.315797\pi$
$878$	−44.5903	−1.50485
$879$	−22.5468	−0.760486
$880$	−1.19656	−0.0403359
$881$	−53.3429	−1.79717	−0.898584	−	0.438801i	$-0.855403\pi$
$881$	−53.3429	−1.79717	−0.898584	+	0.438801i	$0.855403\pi$
$882$	2.34292	0.0788903
$883$	8.92104	0.300217	0.150108	−	0.988670i	$-0.452038\pi$
$883$	8.92104	0.300217	0.150108	+	0.988670i	$0.452038\pi$
$884$	71.2432	2.39617
$885$	5.63565	0.189440
$886$	80.5951	2.70765
$887$	−44.6044	−1.49767	−0.748834	−	0.662758i	$-0.769386\pi$
$887$	−44.6044	−1.49767	−0.748834	+	0.662758i	$0.769386\pi$
$888$	−2.97858	−0.0999545
$889$	8.65708	0.290349
$890$	−43.0607	−1.44340
$891$	−1.00000	−0.0335013
$892$	29.0361	0.972201
$893$	−11.0460	−0.369640
$894$	20.8009	0.695687
$895$	−12.2253	−0.408648
$896$	20.1751	0.674004
$897$	−6.91117	−0.230757
$898$	60.3221	2.01298
$899$	−5.81752	−0.194025
$900$	3.48929	0.116310
$901$	−39.9332	−1.33037
$902$	−8.29273	−0.276118
$903$	−5.63565	−0.187543
$904$	38.6430	1.28525
$905$	−11.9572	−0.397469
$906$	−44.3650	−1.47393
$907$	−18.1741	−0.603460	−0.301730	−	0.953393i	$-0.597564\pi$
$907$	−18.1741	−0.603460	−0.301730	+	0.953393i	$0.597564\pi$
$908$	26.2070	0.869711
$909$	6.00000	0.199007
$910$	−7.37169	−0.244369
$911$	11.4637	0.379808	0.189904	−	0.981803i	$-0.439182\pi$
$911$	11.4637	0.379808	0.189904	+	0.981803i	$0.439182\pi$
$912$	−8.58546	−0.284293
$913$	−13.8610	−0.458732
$914$	8.51806	0.281752
$915$	−4.58967	−0.151730
$916$	61.7220	2.03935
$917$	−4.75325	−0.156966
$918$	−15.2039	−0.501804
$919$	−57.4783	−1.89604	−0.948018	−	0.318217i	$-0.896916\pi$
$919$	−57.4783	−1.89604	−0.948018	+	0.318217i	$0.896916\pi$
$920$	7.66442	0.252689
$921$	−9.89962	−0.326203
$922$	72.2448	2.37926
$923$	−25.8799	−0.851847
$924$	−3.48929	−0.114789
$925$	0.853635	0.0280673
$926$	−51.5787	−1.69498
$927$	11.9284	0.391780
$928$	−3.96558	−0.130176
$929$	37.4355	1.22822	0.614109	−	0.789221i	$-0.289515\pi$
$929$	37.4355	1.22822	0.614109	+	0.789221i	$0.289515\pi$
$930$	14.3503	0.470564
$931$	7.17513	0.235156
$932$	−23.5640	−0.771866
$933$	−13.0361	−0.426783
$934$	20.9013	0.683912
$935$	−6.48929	−0.212222
$936$	10.9786	0.358846
$937$	33.0754	1.08053	0.540263	−	0.841496i	$-0.318325\pi$
$937$	33.0754	1.08053	0.540263	+	0.841496i	$0.318325\pi$
$938$	24.2499	0.791787
$939$	23.7507	0.775076
$940$	−5.37169	−0.175205
$941$	19.1464	0.624154	0.312077	−	0.950057i	$-0.398975\pi$
$941$	19.1464	0.624154	0.312077	+	0.950057i	$0.398975\pi$
$942$	−25.1035	−0.817917
$943$	7.77467	0.253178
$944$	−6.74338	−0.219478
$945$	1.00000	0.0325300
$946$	13.2039	0.429296
$947$	11.1176	0.361273	0.180637	−	0.983550i	$-0.442184\pi$
$947$	11.1176	0.361273	0.180637	+	0.983550i	$0.442184\pi$
$948$	−8.78623	−0.285363
$949$	−14.7434	−0.478591
$950$	16.8108	0.545414
$951$	−13.0214	−0.422249
$952$	−22.6430	−0.733864
$953$	−10.2008	−0.330435	−0.165218	−	0.986257i	$-0.552833\pi$
$953$	−10.2008	−0.330435	−0.165218	+	0.986257i	$0.552833\pi$
$954$	−14.4177	−0.466789
$955$	5.37169	0.173824
$956$	−43.6938	−1.41316
$957$	0.949808	0.0307029
$958$	62.8500	2.03059
$959$	−12.1004	−0.390742
$960$	12.1751	0.392951
$961$	6.51492	0.210159
$962$	6.29273	0.202886
$963$	−5.20390	−0.167693
$964$	−31.1793	−1.00422
$965$	−2.92104	−0.0940316
$966$	5.14637	0.165582
$967$	0.436577	0.0140394	0.00701969	−	0.999975i	$-0.497766\pi$
$967$	0.436577	0.0140394	0.00701969	+	0.999975i	$0.497766\pi$
$968$	3.48929	0.112150
$969$	−46.5615	−1.49577
$970$	−11.7318	−0.376686
$971$	18.6718	0.599206	0.299603	−	0.954064i	$-0.403146\pi$
$971$	18.6718	0.599206	0.299603	+	0.954064i	$0.403146\pi$
$972$	−3.48929	−0.111919
$973$	21.4292	0.686990
$974$	−45.1512	−1.44674
$975$	−3.14637	−0.100764
$976$	5.49181	0.175788
$977$	−19.3246	−0.618250	−0.309125	−	0.951021i	$-0.600036\pi$
$977$	−19.3246	−0.618250	−0.309125	+	0.951021i	$0.600036\pi$
$978$	−28.3074	−0.905172
$979$	18.3790	0.587397
$980$	3.48929	0.111461
$981$	−10.2253	−0.326470
$982$	−81.2333	−2.59226
$983$	48.2583	1.53920	0.769600	−	0.638526i	$-0.220455\pi$
$983$	48.2583	1.53920	0.769600	+	0.638526i	$0.220455\pi$
$984$	−12.3503	−0.393712
$985$	9.27131	0.295408
$986$	14.4408	0.459888
$987$	−1.53948	−0.0490022
$988$	78.7728	2.50610
$989$	−12.3790	−0.393631
$990$	−2.34292	−0.0744630
$991$	33.7178	1.07108	0.535540	−	0.844510i	$-0.320108\pi$
$991$	33.7178	1.07108	0.535540	+	0.844510i	$0.320108\pi$
$992$	25.5725	0.811926
$993$	−19.2327	−0.610330
$994$	19.2713	0.611249
$995$	−8.78623	−0.278542
$996$	−48.3650	−1.53250
$997$	−33.8286	−1.07136	−0.535682	−	0.844420i	$-0.679945\pi$
$997$	−33.8286	−1.07136	−0.535682	+	0.844420i	$0.679945\pi$
$998$	23.3043	0.737684
$999$	−0.853635	−0.0270078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.s.1.3	✓	3
3.2	odd	2		3465.2.a.bc.1.1		3
5.4	even	2		5775.2.a.br.1.1		3
7.6	odd	2		8085.2.a.bm.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.s.1.3	✓	3	1.1	even	1	trivial
3465.2.a.bc.1.1		3	3.2	odd	2
5775.2.a.br.1.1		3	5.4	even	2
8085.2.a.bm.1.3		3	7.6	odd	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} +1.00000 q^{5} -2.34292 q^{6} -1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} +1.00000 q^{5} -2.34292 q^{6} -1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} +2.34292 q^{10} -1.00000 q^{11} -3.48929 q^{12} +3.14637 q^{13} -2.34292 q^{14} -1.00000 q^{15} +1.19656 q^{16} +6.48929 q^{17} +2.34292 q^{18} +7.17513 q^{19} +3.48929 q^{20} +1.00000 q^{21} -2.34292 q^{22} +2.19656 q^{23} -3.48929 q^{24} +1.00000 q^{25} +7.37169 q^{26} -1.00000 q^{27} -3.48929 q^{28} +0.949808 q^{29} -2.34292 q^{30} -6.12494 q^{31} -4.17513 q^{32} +1.00000 q^{33} +15.2039 q^{34} -1.00000 q^{35} +3.48929 q^{36} +0.853635 q^{37} +16.8108 q^{38} -3.14637 q^{39} +3.48929 q^{40} +3.53948 q^{41} +2.34292 q^{42} -5.63565 q^{43} -3.48929 q^{44} +1.00000 q^{45} +5.14637 q^{46} -1.53948 q^{47} -1.19656 q^{48} +1.00000 q^{49} +2.34292 q^{50} -6.48929 q^{51} +10.9786 q^{52} -6.15371 q^{53} -2.34292 q^{54} -1.00000 q^{55} -3.48929 q^{56} -7.17513 q^{57} +2.22533 q^{58} -5.63565 q^{59} -3.48929 q^{60} +4.58967 q^{61} -14.3503 q^{62} -1.00000 q^{63} -12.1751 q^{64} +3.14637 q^{65} +2.34292 q^{66} -10.3503 q^{67} +22.6430 q^{68} -2.19656 q^{69} -2.34292 q^{70} -8.22533 q^{71} +3.48929 q^{72} -4.68585 q^{73} +2.00000 q^{74} -1.00000 q^{75} +25.0361 q^{76} +1.00000 q^{77} -7.37169 q^{78} +2.51806 q^{79} +1.19656 q^{80} +1.00000 q^{81} +8.29273 q^{82} +13.8610 q^{83} +3.48929 q^{84} +6.48929 q^{85} -13.2039 q^{86} -0.949808 q^{87} -3.48929 q^{88} -18.3790 q^{89} +2.34292 q^{90} -3.14637 q^{91} +7.66442 q^{92} +6.12494 q^{93} -3.60688 q^{94} +7.17513 q^{95} +4.17513 q^{96} -5.00735 q^{97} +2.34292 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 8 q^{13} - q^{14} - 3 q^{15} - q^{16} + 12 q^{17} + q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - q^{22} + 2 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} + 6 q^{29} - q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} + 4 q^{37} + 22 q^{38} - 8 q^{39} + 3 q^{40} + q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 14 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} + q^{50} - 12 q^{51} + 18 q^{52} + 16 q^{53} - q^{54} - 3 q^{55} - 3 q^{56} - 2 q^{57} - 16 q^{58} - 8 q^{59} - 3 q^{60} - 4 q^{62} - 3 q^{63} - 17 q^{64} + 8 q^{65} + q^{66} + 8 q^{67} + 26 q^{68} - 2 q^{69} - q^{70} - 2 q^{71} + 3 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} + 24 q^{76} + 3 q^{77} + 2 q^{78} - 18 q^{79} - q^{80} + 3 q^{81} + 22 q^{82} + 10 q^{83} + 3 q^{84} + 12 q^{85} - 2 q^{86} - 6 q^{87} - 3 q^{88} + 2 q^{89} + q^{90} - 8 q^{91} - 4 q^{92} + 2 q^{93} - 20 q^{94} + 2 q^{95} - 7 q^{96} + 18 q^{97} + q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 8 * q^13 - q^14 - 3 * q^15 - q^16 + 12 * q^17 + q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - q^22 + 2 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 + 6 * q^29 - q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 + 4 * q^37 + 22 * q^38 - 8 * q^39 + 3 * q^40 + q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 14 * q^46 + 6 * q^47 + q^48 + 3 * q^49 + q^50 - 12 * q^51 + 18 * q^52 + 16 * q^53 - q^54 - 3 * q^55 - 3 * q^56 - 2 * q^57 - 16 * q^58 - 8 * q^59 - 3 * q^60 - 4 * q^62 - 3 * q^63 - 17 * q^64 + 8 * q^65 + q^66 + 8 * q^67 + 26 * q^68 - 2 * q^69 - q^70 - 2 * q^71 + 3 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 + 24 * q^76 + 3 * q^77 + 2 * q^78 - 18 * q^79 - q^80 + 3 * q^81 + 22 * q^82 + 10 * q^83 + 3 * q^84 + 12 * q^85 - 2 * q^86 - 6 * q^87 - 3 * q^88 + 2 * q^89 + q^90 - 8 * q^91 - 4 * q^92 + 2 * q^93 - 20 * q^94 + 2 * q^95 - 7 * q^96 + 18 * q^97 + q^98 - 3 * q^99

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