LMFDB - Embedded newform 1155.2.a.w.1.4

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:	$5$
Coefficient field:	5.5.352076.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 3x^{2} + 8x - 4 $ x^5 - x^4 - 8x^3 + 3x^2 + 8*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.27097$ 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)

$f(q)$	$=$	$q+1.88068 q^{2} +1.00000 q^{3} +1.53695 q^{4} -1.00000 q^{5} +1.88068 q^{6} +1.00000 q^{7} -0.870842 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.88068 q^{2} +1.00000 q^{3} +1.53695 q^{4} -1.00000 q^{5} +1.88068 q^{6} +1.00000 q^{7} -0.870842 q^{8} +1.00000 q^{9} -1.88068 q^{10} +1.00000 q^{11} +1.53695 q^{12} +4.75152 q^{13} +1.88068 q^{14} -1.00000 q^{15} -4.71168 q^{16} +6.78559 q^{17} +1.88068 q^{18} +1.46305 q^{19} -1.53695 q^{20} +1.00000 q^{21} +1.88068 q^{22} +3.22440 q^{23} -0.870842 q^{24} +1.00000 q^{25} +8.93609 q^{26} +1.00000 q^{27} +1.53695 q^{28} -2.96016 q^{29} -1.88068 q^{30} -4.51288 q^{31} -7.11948 q^{32} +1.00000 q^{33} +12.7615 q^{34} -1.00000 q^{35} +1.53695 q^{36} +11.0002 q^{37} +2.75152 q^{38} +4.75152 q^{39} +0.870842 q^{40} -7.25847 q^{41} +1.88068 q^{42} -2.36238 q^{43} +1.53695 q^{44} -1.00000 q^{45} +6.06407 q^{46} -10.0741 q^{47} -4.71168 q^{48} +1.00000 q^{49} +1.88068 q^{50} +6.78559 q^{51} +7.30287 q^{52} +5.71168 q^{53} +1.88068 q^{54} -1.00000 q^{55} -0.870842 q^{56} +1.46305 q^{57} -5.56711 q^{58} -7.79543 q^{59} -1.53695 q^{60} -6.72745 q^{61} -8.48728 q^{62} +1.00000 q^{63} -3.96609 q^{64} -4.75152 q^{65} +1.88068 q^{66} -0.487276 q^{67} +10.4291 q^{68} +3.22440 q^{69} -1.88068 q^{70} -4.02560 q^{71} -0.870842 q^{72} -12.8453 q^{73} +20.6878 q^{74} +1.00000 q^{75} +2.24863 q^{76} +1.00000 q^{77} +8.93609 q^{78} +5.24848 q^{79} +4.71168 q^{80} +1.00000 q^{81} -13.6509 q^{82} -10.9661 q^{83} +1.53695 q^{84} -6.78559 q^{85} -4.44288 q^{86} -2.96016 q^{87} -0.870842 q^{88} +8.66338 q^{89} -1.88068 q^{90} +4.75152 q^{91} +4.95576 q^{92} -4.51288 q^{93} -18.9461 q^{94} -1.46305 q^{95} -7.11948 q^{96} +1.43629 q^{97} +1.88068 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + q^98 + 5 * 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 $

$2$	1.88068	1.32984	0.664920	−	0.746914i	$-0.268465\pi$
$2$	1.88068	1.32984	0.664920	+	0.746914i	$0.268465\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.53695	0.768477
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.88068	0.767784
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.870842	−0.307889
$9$	1.00000	0.333333
$10$	−1.88068	−0.594723
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.53695	0.443680
$13$	4.75152	1.31783	0.658917	−	0.752215i	$-0.271015\pi$
$13$	4.75152	1.31783	0.658917	+	0.752215i	$0.271015\pi$
$14$	1.88068	0.502633
$15$	−1.00000	−0.258199
$16$	−4.71168	−1.17792
$17$	6.78559	1.64575	0.822873	−	0.568225i	$-0.192370\pi$
$17$	6.78559	1.64575	0.822873	+	0.568225i	$0.192370\pi$
$18$	1.88068	0.443280
$19$	1.46305	0.335646	0.167823	−	0.985817i	$-0.446326\pi$
$19$	1.46305	0.335646	0.167823	+	0.985817i	$0.446326\pi$
$20$	−1.53695	−0.343673
$21$	1.00000	0.218218
$22$	1.88068	0.400962
$23$	3.22440	0.672335	0.336167	−	0.941802i	$-0.390869\pi$
$23$	3.22440	0.672335	0.336167	+	0.941802i	$0.390869\pi$
$24$	−0.870842	−0.177760
$25$	1.00000	0.200000
$26$	8.93609	1.75251
$27$	1.00000	0.192450
$28$	1.53695	0.290457
$29$	−2.96016	−0.549688	−0.274844	−	0.961489i	$-0.588626\pi$
$29$	−2.96016	−0.549688	−0.274844	+	0.961489i	$0.588626\pi$
$30$	−1.88068	−0.343363
$31$	−4.51288	−0.810537	−0.405268	−	0.914198i	$-0.632822\pi$
$31$	−4.51288	−0.810537	−0.405268	+	0.914198i	$0.632822\pi$
$32$	−7.11948	−1.25856
$33$	1.00000	0.174078
$34$	12.7615	2.18858
$35$	−1.00000	−0.169031
$36$	1.53695	0.256159
$37$	11.0002	1.80841	0.904207	−	0.427094i	$-0.140463\pi$
$37$	11.0002	1.80841	0.904207	+	0.427094i	$0.140463\pi$
$38$	2.75152	0.446356
$39$	4.75152	0.760852
$40$	0.870842	0.137692
$41$	−7.25847	−1.13358	−0.566791	−	0.823861i	$-0.691815\pi$
$41$	−7.25847	−1.13358	−0.566791	+	0.823861i	$0.691815\pi$
$42$	1.88068	0.290195
$43$	−2.36238	−0.360260	−0.180130	−	0.983643i	$-0.557652\pi$
$43$	−2.36238	−0.360260	−0.180130	+	0.983643i	$0.557652\pi$
$44$	1.53695	0.231704
$45$	−1.00000	−0.149071
$46$	6.06407	0.894098
$47$	−10.0741	−1.46945	−0.734727	−	0.678363i	$-0.762690\pi$
$47$	−10.0741	−1.46945	−0.734727	+	0.678363i	$0.762690\pi$
$48$	−4.71168	−0.680073
$49$	1.00000	0.142857
$50$	1.88068	0.265968
$51$	6.78559	0.950172
$52$	7.30287	1.01273
$53$	5.71168	0.784560	0.392280	−	0.919846i	$-0.371686\pi$
$53$	5.71168	0.784560	0.392280	+	0.919846i	$0.371686\pi$
$54$	1.88068	0.255928
$55$	−1.00000	−0.134840
$56$	−0.870842	−0.116371
$57$	1.46305	0.193785
$58$	−5.56711	−0.730998
$59$	−7.79543	−1.01488	−0.507439	−	0.861688i	$-0.669408\pi$
$59$	−7.79543	−1.01488	−0.507439	+	0.861688i	$0.669408\pi$
$60$	−1.53695	−0.198420
$61$	−6.72745	−0.861361	−0.430681	−	0.902504i	$-0.641726\pi$
$61$	−6.72745	−0.861361	−0.430681	+	0.902504i	$0.641726\pi$
$62$	−8.48728	−1.07789
$63$	1.00000	0.125988
$64$	−3.96609	−0.495761
$65$	−4.75152	−0.589354
$66$	1.88068	0.231496
$67$	−0.487276	−0.0595303	−0.0297651	−	0.999557i	$-0.509476\pi$
$67$	−0.487276	−0.0595303	−0.0297651	+	0.999557i	$0.509476\pi$
$68$	10.4291	1.26472
$69$	3.22440	0.388173
$70$	−1.88068	−0.224784
$71$	−4.02560	−0.477751	−0.238876	−	0.971050i	$-0.576779\pi$
$71$	−4.02560	−0.477751	−0.238876	+	0.971050i	$0.576779\pi$
$72$	−0.870842	−0.102630
$73$	−12.8453	−1.50342	−0.751712	−	0.659492i	$-0.770772\pi$
$73$	−12.8453	−1.50342	−0.751712	+	0.659492i	$0.770772\pi$
$74$	20.6878	2.40490
$75$	1.00000	0.115470
$76$	2.24863	0.257936
$77$	1.00000	0.113961
$78$	8.93609	1.01181
$79$	5.24848	0.590500	0.295250	−	0.955420i	$-0.404597\pi$
$79$	5.24848	0.590500	0.295250	+	0.955420i	$0.404597\pi$
$80$	4.71168	0.526782
$81$	1.00000	0.111111
$82$	−13.6509	−1.50748
$83$	−10.9661	−1.20368	−0.601842	−	0.798615i	$-0.705566\pi$
$83$	−10.9661	−1.20368	−0.601842	+	0.798615i	$0.705566\pi$
$84$	1.53695	0.167695
$85$	−6.78559	−0.736000
$86$	−4.44288	−0.479088
$87$	−2.96016	−0.317362
$88$	−0.870842	−0.0928320
$89$	8.66338	0.918316	0.459158	−	0.888355i	$-0.348151\pi$
$89$	8.66338	0.918316	0.459158	+	0.888355i	$0.348151\pi$
$90$	−1.88068	−0.198241
$91$	4.75152	0.498095
$92$	4.95576	0.516674
$93$	−4.51288	−0.467964
$94$	−18.9461	−1.95414
$95$	−1.46305	−0.150105
$96$	−7.11948	−0.726628
$97$	1.43629	0.145833	0.0729165	−	0.997338i	$-0.476769\pi$
$97$	1.43629	0.145833	0.0729165	+	0.997338i	$0.476769\pi$
$98$	1.88068	0.189977
$99$	1.00000	0.100504
$100$	1.53695	0.153695
$101$	−15.7132	−1.56352	−0.781761	−	0.623578i	$-0.785678\pi$
$101$	−15.7132	−1.56352	−0.781761	+	0.623578i	$0.785678\pi$
$102$	12.7615	1.26358
$103$	4.21457	0.415274	0.207637	−	0.978206i	$-0.433423\pi$
$103$	4.21457	0.415274	0.207637	+	0.978206i	$0.433423\pi$
$104$	−4.13782	−0.405747
$105$	−1.00000	−0.0975900
$106$	10.7418	1.04334
$107$	−9.20033	−0.889429	−0.444715	−	0.895672i	$-0.646695\pi$
$107$	−9.20033	−0.889429	−0.444715	+	0.895672i	$0.646695\pi$
$108$	1.53695	0.147893
$109$	−0.00592754	−0.000567755 0	−0.000283878	−	1.00000i	$-0.500090\pi$
$109$	−0.00592754	−0.000567755 0	−0.000283878		1.00000i	$0.500090\pi$
$110$	−1.88068	−0.179316
$111$	11.0002	1.04409
$112$	−4.71168	−0.445212
$113$	12.2886	1.15602	0.578009	−	0.816031i	$-0.303830\pi$
$113$	12.2886	1.15602	0.578009	+	0.816031i	$0.303830\pi$
$114$	2.75152	0.257704
$115$	−3.22440	−0.300677
$116$	−4.54963	−0.422422
$117$	4.75152	0.439278
$118$	−14.6607	−1.34963
$119$	6.78559	0.622034
$120$	0.870842	0.0794966
$121$	1.00000	0.0909091
$122$	−12.6522	−1.14547
$123$	−7.25847	−0.654474
$124$	−6.93609	−0.622879
$125$	−1.00000	−0.0894427
$126$	1.88068	0.167544
$127$	−2.77966	−0.246655	−0.123327	−	0.992366i	$-0.539357\pi$
$127$	−2.77966	−0.246655	−0.123327	+	0.992366i	$0.539357\pi$
$128$	6.78001	0.599274
$129$	−2.36238	−0.207996
$130$	−8.93609	−0.783747
$131$	−2.95170	−0.257891	−0.128945	−	0.991652i	$-0.541159\pi$
$131$	−2.95170	−0.257891	−0.128945	+	0.991652i	$0.541159\pi$
$132$	1.53695	0.133775
$133$	1.46305	0.126862
$134$	−0.916410	−0.0791658
$135$	−1.00000	−0.0860663
$136$	−5.90917	−0.506707
$137$	0.576949	0.0492920	0.0246460	−	0.999696i	$-0.492154\pi$
$137$	0.576949	0.0492920	0.0246460	+	0.999696i	$0.492154\pi$
$138$	6.06407	0.516208
$139$	10.8453	0.919883	0.459941	−	0.887949i	$-0.347870\pi$
$139$	10.8453	0.919883	0.459941	+	0.887949i	$0.347870\pi$
$140$	−1.53695	−0.129896
$141$	−10.0741	−0.848389
$142$	−7.57087	−0.635333
$143$	4.75152	0.397342
$144$	−4.71168	−0.392640
$145$	2.96016	0.245828
$146$	−24.1578	−1.99931
$147$	1.00000	0.0824786
$148$	16.9067	1.38972
$149$	4.72592	0.387162	0.193581	−	0.981084i	$-0.437990\pi$
$149$	4.72592	0.387162	0.193581	+	0.981084i	$0.437990\pi$
$150$	1.88068	0.153557
$151$	7.67169	0.624313	0.312156	−	0.950031i	$-0.398949\pi$
$151$	7.67169	0.624313	0.312156	+	0.950031i	$0.398949\pi$
$152$	−1.27408	−0.103342
$153$	6.78559	0.548582
$154$	1.88068	0.151549
$155$	4.51288	0.362483
$156$	7.30287	0.584697
$157$	−0.294247	−0.0234834	−0.0117417	−	0.999931i	$-0.503738\pi$
$157$	−0.294247	−0.0234834	−0.0117417	+	0.999931i	$0.503738\pi$
$158$	9.87071	0.785271
$159$	5.71168	0.452966
$160$	7.11948	0.562844
$161$	3.22440	0.254119
$162$	1.88068	0.147760
$163$	−2.36506	−0.185246	−0.0926231	−	0.995701i	$-0.529525\pi$
$163$	−2.36506	−0.185246	−0.0926231	+	0.995701i	$0.529525\pi$
$164$	−11.1559	−0.871132
$165$	−1.00000	−0.0778499
$166$	−20.6237	−1.60071
$167$	19.8198	1.53370	0.766851	−	0.641825i	$-0.221822\pi$
$167$	19.8198	1.53370	0.766851	+	0.641825i	$0.221822\pi$
$168$	−0.870842	−0.0671869
$169$	9.57695	0.736688
$170$	−12.7615	−0.978763
$171$	1.46305	0.111882
$172$	−3.63087	−0.276851
$173$	−2.06813	−0.157237	−0.0786187	−	0.996905i	$-0.525051\pi$
$173$	−2.06813	−0.157237	−0.0786187	+	0.996905i	$0.525051\pi$
$174$	−5.56711	−0.422042
$175$	1.00000	0.0755929
$176$	−4.71168	−0.355156
$177$	−7.79543	−0.585940
$178$	16.2930	1.22121
$179$	−21.4974	−1.60679	−0.803396	−	0.595444i	$-0.796976\pi$
$179$	−21.4974	−1.60679	−0.803396	+	0.595444i	$0.796976\pi$
$180$	−1.53695	−0.114558
$181$	−20.1678	−1.49906	−0.749530	−	0.661970i	$-0.769721\pi$
$181$	−20.1678	−1.49906	−0.749530	+	0.661970i	$0.769721\pi$
$182$	8.93609	0.662387
$183$	−6.72745	−0.497307
$184$	−2.80795	−0.207004
$185$	−11.0002	−0.808747
$186$	−8.48728	−0.622317
$187$	6.78559	0.496211
$188$	−15.4834	−1.12924
$189$	1.00000	0.0727393
$190$	−2.75152	−0.199616
$191$	−27.5427	−1.99292	−0.996460	−	0.0840688i	$-0.973208\pi$
$191$	−27.5427	−1.99292	−0.996460	+	0.0840688i	$0.973208\pi$
$192$	−3.96609	−0.286228
$193$	−6.68745	−0.481373	−0.240687	−	0.970603i	$-0.577373\pi$
$193$	−6.68745	−0.481373	−0.240687	+	0.970603i	$0.577373\pi$
$194$	2.70120	0.193935
$195$	−4.75152	−0.340263
$196$	1.53695	0.109782
$197$	6.65477	0.474132	0.237066	−	0.971493i	$-0.423814\pi$
$197$	6.65477	0.474132	0.237066	+	0.971493i	$0.423814\pi$
$198$	1.88068	0.133654
$199$	5.56118	0.394222	0.197111	−	0.980381i	$-0.436844\pi$
$199$	5.56118	0.394222	0.197111	+	0.980381i	$0.436844\pi$
$200$	−0.870842	−0.0615778
$201$	−0.487276	−0.0343698
$202$	−29.5515	−2.07924
$203$	−2.96016	−0.207763
$204$	10.4291	0.730185
$205$	7.25847	0.506954
$206$	7.92625	0.552248
$207$	3.22440	0.224112
$208$	−22.3876	−1.55230
$209$	1.46305	0.101201
$210$	−1.88068	−0.129779
$211$	18.5496	1.27701	0.638505	−	0.769618i	$-0.279553\pi$
$211$	18.5496	1.27701	0.638505	+	0.769618i	$0.279553\pi$
$212$	8.77859	0.602916
$213$	−4.02560	−0.275830
$214$	−17.3029	−1.18280
$215$	2.36238	0.161113
$216$	−0.870842	−0.0592533
$217$	−4.51288	−0.306354
$218$	−0.0111478	−0.000755024 0
$219$	−12.8453	−0.868002
$220$	−1.53695	−0.103621
$221$	32.2419	2.16882
$222$	20.6878	1.38847
$223$	0.313922	0.0210217	0.0105109	−	0.999945i	$-0.496654\pi$
$223$	0.313922	0.0210217	0.0105109	+	0.999945i	$0.496654\pi$
$224$	−7.11948	−0.475690
$225$	1.00000	0.0666667
$226$	23.1110	1.53732
$227$	21.1339	1.40271	0.701353	−	0.712814i	$-0.252580\pi$
$227$	21.1339	1.40271	0.701353	+	0.712814i	$0.252580\pi$
$228$	2.24863	0.148919
$229$	28.1934	1.86307	0.931536	−	0.363649i	$-0.118469\pi$
$229$	28.1934	1.86307	0.931536	+	0.363649i	$0.118469\pi$
$230$	−6.06407	−0.399853
$231$	1.00000	0.0657952
$232$	2.57783	0.169243
$233$	−13.6352	−0.893275	−0.446637	−	0.894715i	$-0.647379\pi$
$233$	−13.6352	−0.893275	−0.446637	+	0.894715i	$0.647379\pi$
$234$	8.93609	0.584170
$235$	10.0741	0.657159
$236$	−11.9812	−0.779910
$237$	5.24848	0.340925
$238$	12.7615	0.827206
$239$	17.8851	1.15689	0.578445	−	0.815721i	$-0.303660\pi$
$239$	17.8851	1.15689	0.578445	+	0.815721i	$0.303660\pi$
$240$	4.71168	0.304138
$241$	−3.00391	−0.193499	−0.0967494	−	0.995309i	$-0.530845\pi$
$241$	−3.00391	−0.193499	−0.0967494	+	0.995309i	$0.530845\pi$
$242$	1.88068	0.120895
$243$	1.00000	0.0641500
$244$	−10.3398	−0.661936
$245$	−1.00000	−0.0638877
$246$	−13.6509	−0.870347
$247$	6.95170	0.442326
$248$	3.93000	0.249555
$249$	−10.9661	−0.694948
$250$	−1.88068	−0.118945
$251$	−21.5612	−1.36093	−0.680465	−	0.732781i	$-0.738222\pi$
$251$	−21.5612	−1.36093	−0.680465	+	0.732781i	$0.738222\pi$
$252$	1.53695	0.0968190
$253$	3.22440	0.202717
$254$	−5.22765	−0.328012
$255$	−6.78559	−0.424930
$256$	20.6832	1.29270
$257$	−15.5456	−0.969706	−0.484853	−	0.874596i	$-0.661127\pi$
$257$	−15.5456	−0.969706	−0.484853	+	0.874596i	$0.661127\pi$
$258$	−4.44288	−0.276602
$259$	11.0002	0.683516
$260$	−7.30287	−0.452905
$261$	−2.96016	−0.183229
$262$	−5.55119	−0.342954
$263$	6.24863	0.385307	0.192654	−	0.981267i	$-0.438291\pi$
$263$	6.24863	0.385307	0.192654	+	0.981267i	$0.438291\pi$
$264$	−0.870842	−0.0535966
$265$	−5.71168	−0.350866
$266$	2.75152	0.168707
$267$	8.66338	0.530190
$268$	−0.748921	−0.0457476
$269$	−18.6437	−1.13673	−0.568363	−	0.822778i	$-0.692423\pi$
$269$	−18.6437	−1.13673	−0.568363	+	0.822778i	$0.692423\pi$
$270$	−1.88068	−0.114454
$271$	−11.1624	−0.678065	−0.339033	−	0.940775i	$-0.610100\pi$
$271$	−11.1624	−0.678065	−0.339033	+	0.940775i	$0.610100\pi$
$272$	−31.9715	−1.93856
$273$	4.75152	0.287575
$274$	1.08506	0.0655506
$275$	1.00000	0.0603023
$276$	4.95576	0.298302
$277$	0.289847	0.0174152	0.00870760	−	0.999962i	$-0.497228\pi$
$277$	0.289847	0.0174152	0.00870760	+	0.999962i	$0.497228\pi$
$278$	20.3964	1.22330
$279$	−4.51288	−0.270179
$280$	0.870842	0.0520427
$281$	−3.34222	−0.199380	−0.0996900	−	0.995019i	$-0.531785\pi$
$281$	−3.34222	−0.199380	−0.0996900	+	0.995019i	$0.531785\pi$
$282$	−18.9461	−1.12822
$283$	0.752676	0.0447419	0.0223710	−	0.999750i	$-0.492879\pi$
$283$	0.752676	0.0447419	0.0223710	+	0.999750i	$0.492879\pi$
$284$	−6.18716	−0.367141
$285$	−1.46305	−0.0866634
$286$	8.93609	0.528402
$287$	−7.25847	−0.428454
$288$	−7.11948	−0.419519
$289$	29.0442	1.70848
$290$	5.56711	0.326912
$291$	1.43629	0.0841967
$292$	−19.7426	−1.15535
$293$	28.4080	1.65961	0.829806	−	0.558053i	$-0.188451\pi$
$293$	28.4080	1.65961	0.829806	+	0.558053i	$0.188451\pi$
$294$	1.88068	0.109683
$295$	7.79543	0.453867
$296$	−9.57939	−0.556791
$297$	1.00000	0.0580259
$298$	8.88794	0.514864
$299$	15.3208	0.886026
$300$	1.53695	0.0887361
$301$	−2.36238	−0.136165
$302$	14.4280	0.830237
$303$	−15.7132	−0.902700
$304$	−6.89341	−0.395364
$305$	6.72745	0.385212
$306$	12.7615	0.729527
$307$	−0.249790	−0.0142563	−0.00712813	−	0.999975i	$-0.502269\pi$
$307$	−0.249790	−0.0142563	−0.00712813	+	0.999975i	$0.502269\pi$
$308$	1.53695	0.0875761
$309$	4.21457	0.239758
$310$	8.48728	0.482045
$311$	−19.9419	−1.13080	−0.565400	−	0.824817i	$-0.691278\pi$
$311$	−19.9419	−1.13080	−0.565400	+	0.824817i	$0.691278\pi$
$312$	−4.13782	−0.234258
$313$	0.779661	0.0440690	0.0220345	−	0.999757i	$-0.492986\pi$
$313$	0.779661	0.0440690	0.0220345	+	0.999757i	$0.492986\pi$
$314$	−0.553384	−0.0312292
$315$	−1.00000	−0.0563436
$316$	8.06667	0.453786
$317$	−27.4942	−1.54423	−0.772115	−	0.635483i	$-0.780801\pi$
$317$	−27.4942	−1.54423	−0.772115	+	0.635483i	$0.780801\pi$
$318$	10.7418	0.602372
$319$	−2.96016	−0.165737
$320$	3.96609	0.221711
$321$	−9.20033	−0.513512
$322$	6.06407	0.337937
$323$	9.92763	0.552388
$324$	1.53695	0.0853863
$325$	4.75152	0.263567
$326$	−4.44793	−0.246348
$327$	−0.00592754	−0.000327794 0
$328$	6.32098	0.349018
$329$	−10.0741	−0.555401
$330$	−1.88068	−0.103528
$331$	23.9592	1.31691	0.658457	−	0.752618i	$-0.271209\pi$
$331$	23.9592	1.31691	0.658457	+	0.752618i	$0.271209\pi$
$332$	−16.8544	−0.925004
$333$	11.0002	0.602805
$334$	37.2747	2.03958
$335$	0.487276	0.0266228
$336$	−4.71168	−0.257043
$337$	−13.4278	−0.731457	−0.365728	−	0.930722i	$-0.619180\pi$
$337$	−13.4278	−0.731457	−0.365728	+	0.930722i	$0.619180\pi$
$338$	18.0112	0.979678
$339$	12.2886	0.667427
$340$	−10.4291	−0.565599
$341$	−4.51288	−0.244386
$342$	2.75152	0.148785
$343$	1.00000	0.0539949
$344$	2.05726	0.110920
$345$	−3.22440	−0.173596
$346$	−3.88950	−0.209101
$347$	−29.0731	−1.56072	−0.780362	−	0.625328i	$-0.784965\pi$
$347$	−29.0731	−1.56072	−0.780362	+	0.625328i	$0.784965\pi$
$348$	−4.54963	−0.243886
$349$	24.7471	1.32468	0.662341	−	0.749202i	$-0.269563\pi$
$349$	24.7471	1.32468	0.662341	+	0.749202i	$0.269563\pi$
$350$	1.88068	0.100527
$351$	4.75152	0.253617
$352$	−7.11948	−0.379469
$353$	−33.8525	−1.80179	−0.900893	−	0.434041i	$-0.857087\pi$
$353$	−33.8525	−1.80179	−0.900893	+	0.434041i	$0.857087\pi$
$354$	−14.6607	−0.779207
$355$	4.02560	0.213657
$356$	13.3152	0.705705
$357$	6.78559	0.359131
$358$	−40.4298	−2.13678
$359$	34.6834	1.83052	0.915259	−	0.402866i	$-0.131986\pi$
$359$	34.6834	1.83052	0.915259	+	0.402866i	$0.131986\pi$
$360$	0.870842	0.0458974
$361$	−16.8595	−0.887342
$362$	−37.9292	−1.99351
$363$	1.00000	0.0524864
$364$	7.30287	0.382774
$365$	12.8453	0.672352
$366$	−12.6522	−0.661339
$367$	−30.6152	−1.59810	−0.799051	−	0.601263i	$-0.794664\pi$
$367$	−30.6152	−1.59810	−0.799051	+	0.601263i	$0.794664\pi$
$368$	−15.1924	−0.791957
$369$	−7.25847	−0.377861
$370$	−20.6878	−1.07551
$371$	5.71168	0.296536
$372$	−6.93609	−0.359619
$373$	9.00168	0.466089	0.233045	−	0.972466i	$-0.425131\pi$
$373$	9.00168	0.466089	0.233045	+	0.972466i	$0.425131\pi$
$374$	12.7615	0.659882
$375$	−1.00000	−0.0516398
$376$	8.77291	0.452428
$377$	−14.0653	−0.724398
$378$	1.88068	0.0967317
$379$	7.71168	0.396122	0.198061	−	0.980190i	$-0.436536\pi$
$379$	7.71168	0.396122	0.198061	+	0.980190i	$0.436536\pi$
$380$	−2.24863	−0.115353
$381$	−2.77966	−0.142406
$382$	−51.7990	−2.65027
$383$	29.6768	1.51641	0.758206	−	0.652015i	$-0.226076\pi$
$383$	29.6768	1.51641	0.758206	+	0.652015i	$0.226076\pi$
$384$	6.78001	0.345991
$385$	−1.00000	−0.0509647
$386$	−12.5769	−0.640150
$387$	−2.36238	−0.120087
$388$	2.20751	0.112069
$389$	−5.67646	−0.287808	−0.143904	−	0.989592i	$-0.545966\pi$
$389$	−5.67646	−0.287808	−0.143904	+	0.989592i	$0.545966\pi$
$390$	−8.93609	−0.452496
$391$	21.8795	1.10649
$392$	−0.870842	−0.0439841
$393$	−2.95170	−0.148893
$394$	12.5155	0.630521
$395$	−5.24848	−0.264080
$396$	1.53695	0.0772348
$397$	24.5851	1.23389	0.616945	−	0.787006i	$-0.288370\pi$
$397$	24.5851	1.23389	0.616945	+	0.787006i	$0.288370\pi$
$398$	10.4588	0.524252
$399$	1.46305	0.0732439
$400$	−4.71168	−0.235584
$401$	3.04830	0.152225	0.0761125	−	0.997099i	$-0.475749\pi$
$401$	3.04830	0.152225	0.0761125	+	0.997099i	$0.475749\pi$
$402$	−0.916410	−0.0457064
$403$	−21.4430	−1.06815
$404$	−24.1505	−1.20153
$405$	−1.00000	−0.0496904
$406$	−5.56711	−0.276291
$407$	11.0002	0.545257
$408$	−5.90917	−0.292548
$409$	−10.3710	−0.512813	−0.256406	−	0.966569i	$-0.582538\pi$
$409$	−10.3710	−0.512813	−0.256406	+	0.966569i	$0.582538\pi$
$410$	13.6509	0.674168
$411$	0.576949	0.0284588
$412$	6.47759	0.319128
$413$	−7.79543	−0.383588
$414$	6.06407	0.298033
$415$	10.9661	0.538304
$416$	−33.8283	−1.65857
$417$	10.8453	0.531095
$418$	2.75152	0.134581
$419$	−22.6222	−1.10517	−0.552583	−	0.833458i	$-0.686358\pi$
$419$	−22.6222	−1.10517	−0.552583	+	0.833458i	$0.686358\pi$
$420$	−1.53695	−0.0749957
$421$	38.6093	1.88170	0.940851	−	0.338820i	$-0.110028\pi$
$421$	38.6093	1.88170	0.940851	+	0.338820i	$0.110028\pi$
$422$	34.8859	1.69822
$423$	−10.0741	−0.489818
$424$	−4.97397	−0.241557
$425$	6.78559	0.329149
$426$	−7.57087	−0.366810
$427$	−6.72745	−0.325564
$428$	−14.1405	−0.683506
$429$	4.75152	0.229406
$430$	4.44288	0.214255
$431$	−2.51694	−0.121237	−0.0606185	−	0.998161i	$-0.519307\pi$
$431$	−2.51694	−0.121237	−0.0606185	+	0.998161i	$0.519307\pi$
$432$	−4.71168	−0.226691
$433$	31.1620	1.49755	0.748776	−	0.662823i	$-0.230642\pi$
$433$	31.1620	1.49755	0.748776	+	0.662823i	$0.230642\pi$
$434$	−8.48728	−0.407402
$435$	2.96016	0.141929
$436$	−0.00911035	−0.000436307 0
$437$	4.71745	0.225666
$438$	−24.1578	−1.15430
$439$	−8.35792	−0.398902	−0.199451	−	0.979908i	$-0.563916\pi$
$439$	−8.35792	−0.398902	−0.199451	+	0.979908i	$0.563916\pi$
$440$	0.870842	0.0415157
$441$	1.00000	0.0476190
$442$	60.6366	2.88419
$443$	−9.01576	−0.428352	−0.214176	−	0.976795i	$-0.568707\pi$
$443$	−9.01576	−0.428352	−0.214176	+	0.976795i	$0.568707\pi$
$444$	16.9067	0.802358
$445$	−8.66338	−0.410683
$446$	0.590386	0.0279556
$447$	4.72592	0.223528
$448$	−3.96609	−0.187380
$449$	8.29507	0.391468	0.195734	−	0.980657i	$-0.437291\pi$
$449$	8.29507	0.391468	0.195734	+	0.980657i	$0.437291\pi$
$450$	1.88068	0.0886561
$451$	−7.25847	−0.341788
$452$	18.8871	0.888372
$453$	7.67169	0.360447
$454$	39.7461	1.86537
$455$	−4.75152	−0.222755
$456$	−1.27408	−0.0596643
$457$	−26.9820	−1.26217	−0.631083	−	0.775716i	$-0.717389\pi$
$457$	−26.9820	−1.26217	−0.631083	+	0.775716i	$0.717389\pi$
$458$	53.0227	2.47759
$459$	6.78559	0.316724
$460$	−4.95576	−0.231064
$461$	−29.2362	−1.36167	−0.680834	−	0.732438i	$-0.738382\pi$
$461$	−29.2362	−1.36167	−0.680834	+	0.732438i	$0.738382\pi$
$462$	1.88068	0.0874971
$463$	−6.98424	−0.324585	−0.162292	−	0.986743i	$-0.551889\pi$
$463$	−6.98424	−0.324585	−0.162292	+	0.986743i	$0.551889\pi$
$464$	13.9473	0.647489
$465$	4.51288	0.209280
$466$	−25.6435	−1.18791
$467$	−13.0258	−0.602760	−0.301380	−	0.953504i	$-0.597447\pi$
$467$	−13.0258	−0.602760	−0.301380	+	0.953504i	$0.597447\pi$
$468$	7.30287	0.337575
$469$	−0.487276	−0.0225003
$470$	18.9461	0.873917
$471$	−0.294247	−0.0135582
$472$	6.78858	0.312470
$473$	−2.36238	−0.108622
$474$	9.87071	0.453376
$475$	1.46305	0.0671292
$476$	10.4291	0.478019
$477$	5.71168	0.261520
$478$	33.6361	1.53848
$479$	−29.5968	−1.35231	−0.676156	−	0.736759i	$-0.736355\pi$
$479$	−29.5968	−1.35231	−0.676156	+	0.736759i	$0.736355\pi$
$480$	7.11948	0.324958
$481$	52.2675	2.38319
$482$	−5.64939	−0.257323
$483$	3.22440	0.146715
$484$	1.53695	0.0698615
$485$	−1.43629	−0.0652185
$486$	1.88068	0.0853093
$487$	35.3852	1.60346	0.801728	−	0.597689i	$-0.203914\pi$
$487$	35.3852	1.60346	0.801728	+	0.597689i	$0.203914\pi$
$488$	5.85854	0.265204
$489$	−2.36506	−0.106952
$490$	−1.88068	−0.0849604
$491$	−0.163362	−0.00737244	−0.00368622	−	0.999993i	$-0.501173\pi$
$491$	−0.163362	−0.00737244	−0.00368622	+	0.999993i	$0.501173\pi$
$492$	−11.1559	−0.502948
$493$	−20.0864	−0.904647
$494$	13.0739	0.588223
$495$	−1.00000	−0.0449467
$496$	21.2632	0.954748
$497$	−4.02560	−0.180573
$498$	−20.6237	−0.924170
$499$	9.49573	0.425087	0.212544	−	0.977152i	$-0.431825\pi$
$499$	9.49573	0.425087	0.212544	+	0.977152i	$0.431825\pi$
$500$	−1.53695	−0.0687347
$501$	19.8198	0.885484
$502$	−40.5497	−1.80982
$503$	−30.6169	−1.36514	−0.682571	−	0.730819i	$-0.739138\pi$
$503$	−30.6169	−1.36514	−0.682571	+	0.730819i	$0.739138\pi$
$504$	−0.870842	−0.0387904
$505$	15.7132	0.699229
$506$	6.06407	0.269581
$507$	9.57695	0.425327
$508$	−4.27221	−0.189549
$509$	31.4078	1.39213	0.696063	−	0.717980i	$-0.254933\pi$
$509$	31.4078	1.39213	0.696063	+	0.717980i	$0.254933\pi$
$510$	−12.7615	−0.565089
$511$	−12.8453	−0.568241
$512$	25.3384	1.11981
$513$	1.46305	0.0645951
$514$	−29.2362	−1.28956
$515$	−4.21457	−0.185716
$516$	−3.63087	−0.159840
$517$	−10.0741	−0.443057
$518$	20.6878	0.908968
$519$	−2.06813	−0.0907810
$520$	4.13782	0.181455
$521$	−10.8593	−0.475756	−0.237878	−	0.971295i	$-0.576452\pi$
$521$	−10.8593	−0.475756	−0.237878	+	0.971295i	$0.576452\pi$
$522$	−5.56711	−0.243666
$523$	−31.1736	−1.36313	−0.681563	−	0.731760i	$-0.738699\pi$
$523$	−31.1736	−1.36313	−0.681563	+	0.731760i	$0.738699\pi$
$524$	−4.53662	−0.198183
$525$	1.00000	0.0436436
$526$	11.7517	0.512397
$527$	−30.6225	−1.33394
$528$	−4.71168	−0.205050
$529$	−12.6032	−0.547966
$530$	−10.7418	−0.466596
$531$	−7.79543	−0.338293
$532$	2.24863	0.0974907
$533$	−34.4888	−1.49387
$534$	16.2930	0.705068
$535$	9.20033	0.397765
$536$	0.424341	0.0183287
$537$	−21.4974	−0.927682
$538$	−35.0628	−1.51167
$539$	1.00000	0.0430730
$540$	−1.53695	−0.0661400
$541$	29.0317	1.24817	0.624085	−	0.781357i	$-0.285472\pi$
$541$	29.0317	1.24817	0.624085	+	0.781357i	$0.285472\pi$
$542$	−20.9928	−0.901719
$543$	−20.1678	−0.865483
$544$	−48.3098	−2.07127
$545$	0.00592754	0.000253908 0
$546$	8.93609	0.382429
$547$	33.5529	1.43462	0.717309	−	0.696755i	$-0.245374\pi$
$547$	33.5529	1.43462	0.717309	+	0.696755i	$0.245374\pi$
$548$	0.886743	0.0378798
$549$	−6.72745	−0.287120
$550$	1.88068	0.0801924
$551$	−4.33085	−0.184500
$552$	−2.80795	−0.119514
$553$	5.24848	0.223188
$554$	0.545108	0.0231594
$555$	−11.0002	−0.466931
$556$	16.6687	0.706909
$557$	26.4391	1.12026	0.560131	−	0.828404i	$-0.310751\pi$
$557$	26.4391	1.12026	0.560131	+	0.828404i	$0.310751\pi$
$558$	−8.48728	−0.359295
$559$	−11.2249	−0.474763
$560$	4.71168	0.199105
$561$	6.78559	0.286488
$562$	−6.28564	−0.265144
$563$	42.1042	1.77448	0.887240	−	0.461308i	$-0.152620\pi$
$563$	42.1042	1.77448	0.887240	+	0.461308i	$0.152620\pi$
$564$	−15.4834	−0.651967
$565$	−12.2886	−0.516987
$566$	1.41554	0.0594997
$567$	1.00000	0.0419961
$568$	3.50566	0.147094
$569$	23.9741	1.00504	0.502522	−	0.864564i	$-0.332405\pi$
$569$	23.9741	1.00504	0.502522	+	0.864564i	$0.332405\pi$
$570$	−2.75152	−0.115249
$571$	20.4221	0.854636	0.427318	−	0.904101i	$-0.359458\pi$
$571$	20.4221	0.854636	0.427318	+	0.904101i	$0.359458\pi$
$572$	7.30287	0.305348
$573$	−27.5427	−1.15061
$574$	−13.6509	−0.569776
$575$	3.22440	0.134467
$576$	−3.96609	−0.165254
$577$	3.73590	0.155528	0.0777638	−	0.996972i	$-0.475222\pi$
$577$	3.73590	0.155528	0.0777638	+	0.996972i	$0.475222\pi$
$578$	54.6228	2.27201
$579$	−6.68745	−0.277921
$580$	4.54963	0.188913
$581$	−10.9661	−0.454950
$582$	2.70120	0.111968
$583$	5.71168	0.236554
$584$	11.1862	0.462888
$585$	−4.75152	−0.196451
$586$	53.4263	2.20702
$587$	−10.8917	−0.449548	−0.224774	−	0.974411i	$-0.572164\pi$
$587$	−10.8917	−0.449548	−0.224774	+	0.974411i	$0.572164\pi$
$588$	1.53695	0.0633829
$589$	−6.60255	−0.272053
$590$	14.6607	0.603571
$591$	6.65477	0.273740
$592$	−51.8292	−2.13017
$593$	22.3979	0.919772	0.459886	−	0.887978i	$-0.347890\pi$
$593$	22.3979	0.919772	0.459886	+	0.887978i	$0.347890\pi$
$594$	1.88068	0.0771652
$595$	−6.78559	−0.278182
$596$	7.26352	0.297525
$597$	5.56118	0.227604
$598$	28.8136	1.17827
$599$	18.4806	0.755099	0.377549	−	0.925989i	$-0.376767\pi$
$599$	18.4806	0.755099	0.377549	+	0.925989i	$0.376767\pi$
$600$	−0.870842	−0.0355520
$601$	34.1027	1.39108	0.695538	−	0.718489i	$-0.255166\pi$
$601$	34.1027	1.39108	0.695538	+	0.718489i	$0.255166\pi$
$602$	−4.44288	−0.181078
$603$	−0.487276	−0.0198434
$604$	11.7910	0.479770
$605$	−1.00000	−0.0406558
$606$	−29.5515	−1.20045
$607$	−2.89487	−0.117499	−0.0587496	−	0.998273i	$-0.518711\pi$
$607$	−2.89487	−0.117499	−0.0587496	+	0.998273i	$0.518711\pi$
$608$	−10.4161	−0.422430
$609$	−2.96016	−0.119952
$610$	12.6522	0.512271
$611$	−47.8671	−1.93650
$612$	10.4291	0.421573
$613$	−31.3722	−1.26711	−0.633555	−	0.773697i	$-0.718405\pi$
$613$	−31.3722	−1.26711	−0.633555	+	0.773697i	$0.718405\pi$
$614$	−0.469774	−0.0189585
$615$	7.25847	0.292690
$616$	−0.870842	−0.0350872
$617$	7.57118	0.304804	0.152402	−	0.988319i	$-0.451299\pi$
$617$	7.57118	0.304804	0.152402	+	0.988319i	$0.451299\pi$
$618$	7.92625	0.318840
$619$	−18.0215	−0.724347	−0.362173	−	0.932111i	$-0.617965\pi$
$619$	−18.0215	−0.724347	−0.362173	+	0.932111i	$0.617965\pi$
$620$	6.93609	0.278560
$621$	3.22440	0.129391
$622$	−37.5042	−1.50378
$623$	8.66338	0.347091
$624$	−22.3876	−0.896223
$625$	1.00000	0.0400000
$626$	1.46629	0.0586048
$627$	1.46305	0.0584284
$628$	−0.452244	−0.0180465
$629$	74.6425	2.97619
$630$	−1.88068	−0.0749280
$631$	−43.8316	−1.74491	−0.872455	−	0.488694i	$-0.837473\pi$
$631$	−43.8316	−1.74491	−0.872455	+	0.488694i	$0.837473\pi$
$632$	−4.57059	−0.181808
$633$	18.5496	0.737282
$634$	−51.7078	−2.05358
$635$	2.77966	0.110307
$636$	8.77859	0.348094
$637$	4.75152	0.188262
$638$	−5.56711	−0.220404
$639$	−4.02560	−0.159250
$640$	−6.78001	−0.268004
$641$	42.9945	1.69818	0.849091	−	0.528246i	$-0.177150\pi$
$641$	42.9945	1.69818	0.849091	+	0.528246i	$0.177150\pi$
$642$	−17.3029	−0.682890
$643$	−41.4078	−1.63296	−0.816482	−	0.577370i	$-0.804079\pi$
$643$	−41.4078	−1.63296	−0.816482	+	0.577370i	$0.804079\pi$
$644$	4.95576	0.195284
$645$	2.36238	0.0930187
$646$	18.6707	0.734588
$647$	−24.6254	−0.968125	−0.484062	−	0.875034i	$-0.660839\pi$
$647$	−24.6254	−0.968125	−0.484062	+	0.875034i	$0.660839\pi$
$648$	−0.870842	−0.0342099
$649$	−7.79543	−0.305997
$650$	8.93609	0.350502
$651$	−4.51288	−0.176874
$652$	−3.63499	−0.142357
$653$	12.9988	0.508681	0.254341	−	0.967115i	$-0.418142\pi$
$653$	12.9988	0.508681	0.254341	+	0.967115i	$0.418142\pi$
$654$	−0.0111478	−0.000435913 0
$655$	2.95170	0.115332
$656$	34.1996	1.33527
$657$	−12.8453	−0.501141
$658$	−18.9461	−0.738595
$659$	−21.1868	−0.825321	−0.412660	−	0.910885i	$-0.635400\pi$
$659$	−21.1868	−0.825321	−0.412660	+	0.910885i	$0.635400\pi$
$660$	−1.53695	−0.0598258
$661$	−16.9805	−0.660464	−0.330232	−	0.943900i	$-0.607127\pi$
$661$	−16.9805	−0.660464	−0.330232	+	0.943900i	$0.607127\pi$
$662$	45.0595	1.75129
$663$	32.2419	1.25217
$664$	9.54973	0.370601
$665$	−1.46305	−0.0567345
$666$	20.6878	0.801634
$667$	−9.54475	−0.369574
$668$	30.4621	1.17862
$669$	0.313922	0.0121369
$670$	0.916410	0.0354040
$671$	−6.72745	−0.259710
$672$	−7.11948	−0.274640
$673$	−18.1237	−0.698619	−0.349309	−	0.937007i	$-0.613584\pi$
$673$	−18.1237	−0.698619	−0.349309	+	0.937007i	$0.613584\pi$
$674$	−25.2533	−0.972721
$675$	1.00000	0.0384900
$676$	14.7193	0.566128
$677$	18.9672	0.728970	0.364485	−	0.931209i	$-0.381245\pi$
$677$	18.9672	0.728970	0.364485	+	0.931209i	$0.381245\pi$
$678$	23.1110	0.887571
$679$	1.43629	0.0551197
$680$	5.90917	0.226606
$681$	21.1339	0.809852
$682$	−8.48728	−0.324995
$683$	−33.4649	−1.28050	−0.640249	−	0.768167i	$-0.721169\pi$
$683$	−33.4649	−1.28050	−0.640249	+	0.768167i	$0.721169\pi$
$684$	2.24863	0.0859787
$685$	−0.576949	−0.0220441
$686$	1.88068	0.0718047
$687$	28.1934	1.07565
$688$	11.1308	0.424357
$689$	27.1392	1.03392
$690$	−6.06407	−0.230855
$691$	42.8544	1.63026	0.815129	−	0.579279i	$-0.196666\pi$
$691$	42.8544	1.63026	0.815129	+	0.579279i	$0.196666\pi$
$692$	−3.17863	−0.120833
$693$	1.00000	0.0379869
$694$	−54.6771	−2.07551
$695$	−10.8453	−0.411384
$696$	2.57783	0.0977124
$697$	−49.2530	−1.86559
$698$	46.5414	1.76162
$699$	−13.6352	−0.515732
$700$	1.53695	0.0580914
$701$	45.0510	1.70155	0.850777	−	0.525527i	$-0.176132\pi$
$701$	45.0510	1.70155	0.850777	+	0.525527i	$0.176132\pi$
$702$	8.93609	0.337271
$703$	16.0937	0.606987
$704$	−3.96609	−0.149478
$705$	10.0741	0.379411
$706$	−63.6657	−2.39609
$707$	−15.7132	−0.590956
$708$	−11.9812	−0.450281
$709$	35.3341	1.32700	0.663499	−	0.748177i	$-0.269071\pi$
$709$	35.3341	1.32700	0.663499	+	0.748177i	$0.269071\pi$
$710$	7.57087	0.284130
$711$	5.24848	0.196833
$712$	−7.54443	−0.282739
$713$	−14.5513	−0.544952
$714$	12.7615	0.477588
$715$	−4.75152	−0.177697
$716$	−33.0405	−1.23478
$717$	17.8851	0.667931
$718$	65.2283	2.43430
$719$	48.4439	1.80665	0.903326	−	0.428955i	$-0.141118\pi$
$719$	48.4439	1.80665	0.903326	+	0.428955i	$0.141118\pi$
$720$	4.71168	0.175594
$721$	4.21457	0.156959
$722$	−31.7073	−1.18002
$723$	−3.00391	−0.111717
$724$	−30.9970	−1.15199
$725$	−2.96016	−0.109938
$726$	1.88068	0.0697985
$727$	14.8478	0.550674	0.275337	−	0.961348i	$-0.411211\pi$
$727$	14.8478	0.550674	0.275337	+	0.961348i	$0.411211\pi$
$728$	−4.13782	−0.153358
$729$	1.00000	0.0370370
$730$	24.1578	0.894121
$731$	−16.0301	−0.592896
$732$	−10.3398	−0.382169
$733$	−26.8168	−0.990500	−0.495250	−	0.868750i	$-0.664924\pi$
$733$	−26.8168	−0.990500	−0.495250	+	0.868750i	$0.664924\pi$
$734$	−57.5774	−2.12522
$735$	−1.00000	−0.0368856
$736$	−22.9561	−0.846172
$737$	−0.487276	−0.0179491
$738$	−13.6509	−0.502495
$739$	19.6405	0.722486	0.361243	−	0.932472i	$-0.382352\pi$
$739$	19.6405	0.722486	0.361243	+	0.932472i	$0.382352\pi$
$740$	−16.9067	−0.621504
$741$	6.95170	0.255377
$742$	10.7418	0.394345
$743$	−32.8768	−1.20613	−0.603066	−	0.797691i	$-0.706055\pi$
$743$	−32.8768	−1.20613	−0.603066	+	0.797691i	$0.706055\pi$
$744$	3.93000	0.144081
$745$	−4.72592	−0.173144
$746$	16.9293	0.619825
$747$	−10.9661	−0.401228
$748$	10.4291	0.381327
$749$	−9.20033	−0.336173
$750$	−1.88068	−0.0686727
$751$	24.8568	0.907037	0.453518	−	0.891247i	$-0.350169\pi$
$751$	24.8568	0.907037	0.453518	+	0.891247i	$0.350169\pi$
$752$	47.4658	1.73090
$753$	−21.5612	−0.785733
$754$	−26.4522	−0.963334
$755$	−7.67169	−0.279201
$756$	1.53695	0.0558985
$757$	45.5546	1.65571	0.827854	−	0.560943i	$-0.189561\pi$
$757$	45.5546	1.65571	0.827854	+	0.560943i	$0.189561\pi$
$758$	14.5032	0.526780
$759$	3.22440	0.117038
$760$	1.27408	0.0462158
$761$	33.0881	1.19944	0.599722	−	0.800209i	$-0.295278\pi$
$761$	33.0881	1.19944	0.599722	+	0.800209i	$0.295278\pi$
$762$	−5.22765	−0.189378
$763$	−0.00592754	−0.000214591 0
$764$	−42.3319	−1.53151
$765$	−6.78559	−0.245333
$766$	55.8125	2.01659
$767$	−37.0401	−1.33744
$768$	20.6832	0.746341
$769$	46.2583	1.66812	0.834058	−	0.551676i	$-0.186012\pi$
$769$	46.2583	1.66812	0.834058	+	0.551676i	$0.186012\pi$
$770$	−1.88068	−0.0677750
$771$	−15.5456	−0.559860
$772$	−10.2783	−0.369924
$773$	−21.8525	−0.785980	−0.392990	−	0.919543i	$-0.628559\pi$
$773$	−21.8525	−0.785980	−0.392990	+	0.919543i	$0.628559\pi$
$774$	−4.44288	−0.159696
$775$	−4.51288	−0.162107
$776$	−1.25078	−0.0449004
$777$	11.0002	0.394628
$778$	−10.6756	−0.382739
$779$	−10.6195	−0.380482
$780$	−7.30287	−0.261485
$781$	−4.02560	−0.144047
$782$	41.1483	1.47146
$783$	−2.96016	−0.105787
$784$	−4.71168	−0.168274
$785$	0.294247	0.0105021
$786$	−5.55119	−0.198004
$787$	23.7990	0.848342	0.424171	−	0.905582i	$-0.360566\pi$
$787$	23.7990	0.848342	0.424171	+	0.905582i	$0.360566\pi$
$788$	10.2281	0.364360
$789$	6.24863	0.222457
$790$	−9.87071	−0.351184
$791$	12.2886	0.436933
$792$	−0.870842	−0.0309440
$793$	−31.9656	−1.13513
$794$	46.2366	1.64088
$795$	−5.71168	−0.202572
$796$	8.54728	0.302950
$797$	−2.14812	−0.0760905	−0.0380452	−	0.999276i	$-0.512113\pi$
$797$	−2.14812	−0.0760905	−0.0380452	+	0.999276i	$0.512113\pi$
$798$	2.75152	0.0974028
$799$	−68.3584	−2.41835
$800$	−7.11948	−0.251711
$801$	8.66338	0.306105
$802$	5.73288	0.202435
$803$	−12.8453	−0.453299
$804$	−0.748921	−0.0264124
$805$	−3.22440	−0.113645
$806$	−40.3275	−1.42047
$807$	−18.6437	−0.656289
$808$	13.6837	0.481391
$809$	−39.1978	−1.37812	−0.689060	−	0.724704i	$-0.741976\pi$
$809$	−39.1978	−1.37812	−0.689060	+	0.724704i	$0.741976\pi$
$810$	−1.88068	−0.0660803
$811$	12.2290	0.429417	0.214708	−	0.976678i	$-0.431120\pi$
$811$	12.2290	0.429417	0.214708	+	0.976678i	$0.431120\pi$
$812$	−4.54963	−0.159661
$813$	−11.1624	−0.391481
$814$	20.6878	0.725106
$815$	2.36506	0.0828446
$816$	−31.9715	−1.11923
$817$	−3.45627	−0.120920
$818$	−19.5045	−0.681959
$819$	4.75152	0.166032
$820$	11.1559	0.389582
$821$	44.3615	1.54823	0.774114	−	0.633046i	$-0.218196\pi$
$821$	44.3615	1.54823	0.774114	+	0.633046i	$0.218196\pi$
$822$	1.08506	0.0378456
$823$	−35.3139	−1.23096	−0.615482	−	0.788151i	$-0.711039\pi$
$823$	−35.3139	−1.23096	−0.615482	+	0.788151i	$0.711039\pi$
$824$	−3.67022	−0.127858
$825$	1.00000	0.0348155
$826$	−14.6607	−0.510111
$827$	−10.5666	−0.367435	−0.183718	−	0.982979i	$-0.558813\pi$
$827$	−10.5666	−0.367435	−0.183718	+	0.982979i	$0.558813\pi$
$828$	4.95576	0.172225
$829$	−12.3353	−0.428422	−0.214211	−	0.976787i	$-0.568718\pi$
$829$	−12.3353	−0.428422	−0.214211	+	0.976787i	$0.568718\pi$
$830$	20.6237	0.715859
$831$	0.289847	0.0100547
$832$	−18.8449	−0.653331
$833$	6.78559	0.235107
$834$	20.3964	0.706271
$835$	−19.8198	−0.685893
$836$	2.24863	0.0777706
$837$	−4.51288	−0.155988
$838$	−42.5450	−1.46969
$839$	7.89235	0.272474	0.136237	−	0.990676i	$-0.456499\pi$
$839$	7.89235	0.272474	0.136237	+	0.990676i	$0.456499\pi$
$840$	0.870842	0.0300469
$841$	−20.2375	−0.697843
$842$	72.6117	2.50236
$843$	−3.34222	−0.115112
$844$	28.5099	0.981352
$845$	−9.57695	−0.329457
$846$	−18.9461	−0.651380
$847$	1.00000	0.0343604
$848$	−26.9116	−0.924149
$849$	0.752676	0.0258318
$850$	12.7615	0.437716
$851$	35.4689	1.21586
$852$	−6.18716	−0.211969
$853$	41.5475	1.42256	0.711279	−	0.702910i	$-0.248116\pi$
$853$	41.5475	1.42256	0.711279	+	0.702910i	$0.248116\pi$
$854$	−12.6522	−0.432948
$855$	−1.46305	−0.0500351
$856$	8.01203	0.273846
$857$	30.7166	1.04926	0.524629	−	0.851331i	$-0.324204\pi$
$857$	30.7166	1.04926	0.524629	+	0.851331i	$0.324204\pi$
$858$	8.93609	0.305073
$859$	−34.6948	−1.18377	−0.591886	−	0.806021i	$-0.701617\pi$
$859$	−34.6948	−1.18377	−0.591886	+	0.806021i	$0.701617\pi$
$860$	3.63087	0.123812
$861$	−7.25847	−0.247368
$862$	−4.73356	−0.161226
$863$	43.6006	1.48418	0.742092	−	0.670299i	$-0.233834\pi$
$863$	43.6006	1.48418	0.742092	+	0.670299i	$0.233834\pi$
$864$	−7.11948	−0.242209
$865$	2.06813	0.0703187
$866$	58.6058	1.99151
$867$	29.0442	0.986393
$868$	−6.93609	−0.235426
$869$	5.24848	0.178042
$870$	5.56711	0.188743
$871$	−2.31530	−0.0784511
$872$	0.00516195	0.000174806 0
$873$	1.43629	0.0486110
$874$	8.87202	0.300100
$875$	−1.00000	−0.0338062
$876$	−19.7426	−0.667039
$877$	6.08439	0.205455	0.102728	−	0.994710i	$-0.467243\pi$
$877$	6.08439	0.205455	0.102728	+	0.994710i	$0.467243\pi$
$878$	−15.7186	−0.530476
$879$	28.4080	0.958177
$880$	4.71168	0.158831
$881$	37.5844	1.26625	0.633126	−	0.774049i	$-0.281772\pi$
$881$	37.5844	1.26625	0.633126	+	0.774049i	$0.281772\pi$
$882$	1.88068	0.0633258
$883$	23.5615	0.792907	0.396454	−	0.918055i	$-0.370241\pi$
$883$	23.5615	0.792907	0.396454	+	0.918055i	$0.370241\pi$
$884$	49.5542	1.66669
$885$	7.79543	0.262040
$886$	−16.9558	−0.569640
$887$	−11.8583	−0.398164	−0.199082	−	0.979983i	$-0.563796\pi$
$887$	−11.8583	−0.398164	−0.199082	+	0.979983i	$0.563796\pi$
$888$	−9.57939	−0.321463
$889$	−2.77966	−0.0932268
$890$	−16.2930	−0.546144
$891$	1.00000	0.0335013
$892$	0.482483	0.0161547
$893$	−14.7388	−0.493216
$894$	8.88794	0.297257
$895$	21.4974	0.718580
$896$	6.78001	0.226504
$897$	15.3208	0.511547
$898$	15.6004	0.520591
$899$	13.3588	0.445542
$900$	1.53695	0.0512318
$901$	38.7571	1.29119
$902$	−13.6509	−0.454524
$903$	−2.36238	−0.0786151
$904$	−10.7014	−0.355925
$905$	20.1678	0.670400
$906$	14.4280	0.479337
$907$	45.0420	1.49559	0.747797	−	0.663927i	$-0.231111\pi$
$907$	45.0420	1.49559	0.747797	+	0.663927i	$0.231111\pi$
$908$	32.4818	1.07795
$909$	−15.7132	−0.521174
$910$	−8.93609	−0.296228
$911$	13.7793	0.456529	0.228264	−	0.973599i	$-0.426695\pi$
$911$	13.7793	0.456529	0.228264	+	0.973599i	$0.426695\pi$
$912$	−6.89341	−0.228264
$913$	−10.9661	−0.362925
$914$	−50.7445	−1.67848
$915$	6.72745	0.222402
$916$	43.3320	1.43173
$917$	−2.95170	−0.0974736
$918$	12.7615	0.421193
$919$	−44.0527	−1.45316	−0.726582	−	0.687080i	$-0.758892\pi$
$919$	−44.0527	−1.45316	−0.726582	+	0.687080i	$0.758892\pi$
$920$	2.80795	0.0925752
$921$	−0.249790	−0.00823085
$922$	−54.9840	−1.81080
$923$	−19.1277	−0.629597
$924$	1.53695	0.0505621
$925$	11.0002	0.361683
$926$	−13.1351	−0.431646
$927$	4.21457	0.138425
$928$	21.0748	0.691814
$929$	−19.3525	−0.634934	−0.317467	−	0.948269i	$-0.602832\pi$
$929$	−19.3525	−0.634934	−0.317467	+	0.948269i	$0.602832\pi$
$930$	8.48728	0.278309
$931$	1.46305	0.0479494
$932$	−20.9567	−0.686461
$933$	−19.9419	−0.652867
$934$	−24.4973	−0.801575
$935$	−6.78559	−0.221912
$936$	−4.13782	−0.135249
$937$	25.5356	0.834212	0.417106	−	0.908858i	$-0.363044\pi$
$937$	25.5356	0.834212	0.417106	+	0.908858i	$0.363044\pi$
$938$	−0.916410	−0.0299219
$939$	0.779661	0.0254433
$940$	15.4834	0.505012
$941$	47.1910	1.53838	0.769191	−	0.639019i	$-0.220660\pi$
$941$	47.1910	1.53838	0.769191	+	0.639019i	$0.220660\pi$
$942$	−0.553384	−0.0180302
$943$	−23.4042	−0.762147
$944$	36.7296	1.19545
$945$	−1.00000	−0.0325300
$946$	−4.44288	−0.144451
$947$	−12.3495	−0.401305	−0.200653	−	0.979662i	$-0.564306\pi$
$947$	−12.3495	−0.401305	−0.200653	+	0.979662i	$0.564306\pi$
$948$	8.06667	0.261993
$949$	−61.0345	−1.98126
$950$	2.75152	0.0892711
$951$	−27.4942	−0.891562
$952$	−5.90917	−0.191517
$953$	14.6266	0.473802	0.236901	−	0.971534i	$-0.423868\pi$
$953$	14.6266	0.473802	0.236901	+	0.971534i	$0.423868\pi$
$954$	10.7418	0.347780
$955$	27.5427	0.891261
$956$	27.4886	0.889044
$957$	−2.96016	−0.0956884
$958$	−55.6620	−1.79836
$959$	0.576949	0.0186306
$960$	3.96609	0.128005
$961$	−10.6339	−0.343030
$962$	98.2983	3.16927
$963$	−9.20033	−0.296476
$964$	−4.61687	−0.148699
$965$	6.68745	0.215277
$966$	6.06407	0.195108
$967$	15.5098	0.498761	0.249381	−	0.968406i	$-0.419773\pi$
$967$	15.5098	0.498761	0.249381	+	0.968406i	$0.419773\pi$
$968$	−0.870842	−0.0279899
$969$	9.92763	0.318921
$970$	−2.70120	−0.0867302
$971$	−42.1395	−1.35232	−0.676161	−	0.736754i	$-0.736357\pi$
$971$	−42.1395	−1.35232	−0.676161	+	0.736754i	$0.736357\pi$
$972$	1.53695	0.0492978
$973$	10.8453	0.347683
$974$	66.5482	2.13234
$975$	4.75152	0.152170
$976$	31.6976	1.01461
$977$	2.40997	0.0771017	0.0385509	−	0.999257i	$-0.487726\pi$
$977$	2.40997	0.0771017	0.0385509	+	0.999257i	$0.487726\pi$
$978$	−4.44793	−0.142229
$979$	8.66338	0.276883
$980$	−1.53695	−0.0490962
$981$	−0.00592754	−0.000189252 0
$982$	−0.307232	−0.00980417
$983$	−14.0997	−0.449709	−0.224855	−	0.974392i	$-0.572191\pi$
$983$	−14.0997	−0.449709	−0.224855	+	0.974392i	$0.572191\pi$
$984$	6.32098	0.201505
$985$	−6.65477	−0.212038
$986$	−37.7761	−1.20304
$987$	−10.0741	−0.320661
$988$	10.6844	0.339917
$989$	−7.61727	−0.242215
$990$	−1.88068	−0.0597719
$991$	−21.3853	−0.679325	−0.339663	−	0.940547i	$-0.610313\pi$
$991$	−21.3853	−0.679325	−0.339663	+	0.940547i	$0.610313\pi$
$992$	32.1293	1.02011
$993$	23.9592	0.760321
$994$	−7.57087	−0.240133
$995$	−5.56118	−0.176301
$996$	−16.8544	−0.534051
$997$	−47.1466	−1.49315	−0.746573	−	0.665303i	$-0.768302\pi$
$997$	−47.1466	−1.49315	−0.746573	+	0.665303i	$0.768302\pi$
$998$	17.8584	0.565299
$999$	11.0002	0.348030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.w.1.4	✓	5
3.2	odd	2		3465.2.a.bm.1.2		5
5.4	even	2		5775.2.a.cg.1.2		5
7.6	odd	2		8085.2.a.bv.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.w.1.4	✓	5	1.1	even	1	trivial
3465.2.a.bm.1.2		5	3.2	odd	2
5775.2.a.cg.1.2		5	5.4	even	2
8085.2.a.bv.1.4		5	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)

\(f(q)\)	\(=\)	\(q+1.88068 q^{2} +1.00000 q^{3} +1.53695 q^{4} -1.00000 q^{5} +1.88068 q^{6} +1.00000 q^{7} -0.870842 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.88068 q^{2} +1.00000 q^{3} +1.53695 q^{4} -1.00000 q^{5} +1.88068 q^{6} +1.00000 q^{7} -0.870842 q^{8} +1.00000 q^{9} -1.88068 q^{10} +1.00000 q^{11} +1.53695 q^{12} +4.75152 q^{13} +1.88068 q^{14} -1.00000 q^{15} -4.71168 q^{16} +6.78559 q^{17} +1.88068 q^{18} +1.46305 q^{19} -1.53695 q^{20} +1.00000 q^{21} +1.88068 q^{22} +3.22440 q^{23} -0.870842 q^{24} +1.00000 q^{25} +8.93609 q^{26} +1.00000 q^{27} +1.53695 q^{28} -2.96016 q^{29} -1.88068 q^{30} -4.51288 q^{31} -7.11948 q^{32} +1.00000 q^{33} +12.7615 q^{34} -1.00000 q^{35} +1.53695 q^{36} +11.0002 q^{37} +2.75152 q^{38} +4.75152 q^{39} +0.870842 q^{40} -7.25847 q^{41} +1.88068 q^{42} -2.36238 q^{43} +1.53695 q^{44} -1.00000 q^{45} +6.06407 q^{46} -10.0741 q^{47} -4.71168 q^{48} +1.00000 q^{49} +1.88068 q^{50} +6.78559 q^{51} +7.30287 q^{52} +5.71168 q^{53} +1.88068 q^{54} -1.00000 q^{55} -0.870842 q^{56} +1.46305 q^{57} -5.56711 q^{58} -7.79543 q^{59} -1.53695 q^{60} -6.72745 q^{61} -8.48728 q^{62} +1.00000 q^{63} -3.96609 q^{64} -4.75152 q^{65} +1.88068 q^{66} -0.487276 q^{67} +10.4291 q^{68} +3.22440 q^{69} -1.88068 q^{70} -4.02560 q^{71} -0.870842 q^{72} -12.8453 q^{73} +20.6878 q^{74} +1.00000 q^{75} +2.24863 q^{76} +1.00000 q^{77} +8.93609 q^{78} +5.24848 q^{79} +4.71168 q^{80} +1.00000 q^{81} -13.6509 q^{82} -10.9661 q^{83} +1.53695 q^{84} -6.78559 q^{85} -4.44288 q^{86} -2.96016 q^{87} -0.870842 q^{88} +8.66338 q^{89} -1.88068 q^{90} +4.75152 q^{91} +4.95576 q^{92} -4.51288 q^{93} -18.9461 q^{94} -1.46305 q^{95} -7.11948 q^{96} +1.43629 q^{97} +1.88068 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + q^98 + 5 * q^99

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