LMFDB - Embedded newform 1155.2.a.o.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
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			1.1
Root			$2.56155$ 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)

$f(q)$	$=$	$q-2.56155 q^{2} -1.00000 q^{3} +4.56155 q^{4} +1.00000 q^{5} +2.56155 q^{6} -1.00000 q^{7} -6.56155 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.56155 q^{2} -1.00000 q^{3} +4.56155 q^{4} +1.00000 q^{5} +2.56155 q^{6} -1.00000 q^{7} -6.56155 q^{8} +1.00000 q^{9} -2.56155 q^{10} +1.00000 q^{11} -4.56155 q^{12} +1.12311 q^{13} +2.56155 q^{14} -1.00000 q^{15} +7.68466 q^{16} -3.56155 q^{17} -2.56155 q^{18} +1.56155 q^{19} +4.56155 q^{20} +1.00000 q^{21} -2.56155 q^{22} -5.56155 q^{23} +6.56155 q^{24} +1.00000 q^{25} -2.87689 q^{26} -1.00000 q^{27} -4.56155 q^{28} -10.6847 q^{29} +2.56155 q^{30} +3.12311 q^{31} -6.56155 q^{32} -1.00000 q^{33} +9.12311 q^{34} -1.00000 q^{35} +4.56155 q^{36} +1.12311 q^{37} -4.00000 q^{38} -1.12311 q^{39} -6.56155 q^{40} +2.00000 q^{41} -2.56155 q^{42} -1.56155 q^{43} +4.56155 q^{44} +1.00000 q^{45} +14.2462 q^{46} +3.12311 q^{47} -7.68466 q^{48} +1.00000 q^{49} -2.56155 q^{50} +3.56155 q^{51} +5.12311 q^{52} -1.31534 q^{53} +2.56155 q^{54} +1.00000 q^{55} +6.56155 q^{56} -1.56155 q^{57} +27.3693 q^{58} +6.43845 q^{59} -4.56155 q^{60} -7.56155 q^{61} -8.00000 q^{62} -1.00000 q^{63} +1.43845 q^{64} +1.12311 q^{65} +2.56155 q^{66} +15.1231 q^{67} -16.2462 q^{68} +5.56155 q^{69} +2.56155 q^{70} -3.12311 q^{71} -6.56155 q^{72} -2.87689 q^{73} -2.87689 q^{74} -1.00000 q^{75} +7.12311 q^{76} -1.00000 q^{77} +2.87689 q^{78} +6.24621 q^{79} +7.68466 q^{80} +1.00000 q^{81} -5.12311 q^{82} -9.56155 q^{83} +4.56155 q^{84} -3.56155 q^{85} +4.00000 q^{86} +10.6847 q^{87} -6.56155 q^{88} -14.6847 q^{89} -2.56155 q^{90} -1.12311 q^{91} -25.3693 q^{92} -3.12311 q^{93} -8.00000 q^{94} +1.56155 q^{95} +6.56155 q^{96} -17.8078 q^{97} -2.56155 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} + 5 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 + 5 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} + 5 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 2 q^{11} - 5 q^{12} - 6 q^{13} + q^{14} - 2 q^{15} + 3 q^{16} - 3 q^{17} - q^{18} - q^{19} + 5 q^{20} + 2 q^{21} - q^{22} - 7 q^{23} + 9 q^{24} + 2 q^{25} - 14 q^{26} - 2 q^{27} - 5 q^{28} - 9 q^{29} + q^{30} - 2 q^{31} - 9 q^{32} - 2 q^{33} + 10 q^{34} - 2 q^{35} + 5 q^{36} - 6 q^{37} - 8 q^{38} + 6 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + q^{43} + 5 q^{44} + 2 q^{45} + 12 q^{46} - 2 q^{47} - 3 q^{48} + 2 q^{49} - q^{50} + 3 q^{51} + 2 q^{52} - 15 q^{53} + q^{54} + 2 q^{55} + 9 q^{56} + q^{57} + 30 q^{58} + 17 q^{59} - 5 q^{60} - 11 q^{61} - 16 q^{62} - 2 q^{63} + 7 q^{64} - 6 q^{65} + q^{66} + 22 q^{67} - 16 q^{68} + 7 q^{69} + q^{70} + 2 q^{71} - 9 q^{72} - 14 q^{73} - 14 q^{74} - 2 q^{75} + 6 q^{76} - 2 q^{77} + 14 q^{78} - 4 q^{79} + 3 q^{80} + 2 q^{81} - 2 q^{82} - 15 q^{83} + 5 q^{84} - 3 q^{85} + 8 q^{86} + 9 q^{87} - 9 q^{88} - 17 q^{89} - q^{90} + 6 q^{91} - 26 q^{92} + 2 q^{93} - 16 q^{94} - q^{95} + 9 q^{96} - 15 q^{97} - q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 + 5 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9 - q^10 + 2 * q^11 - 5 * q^12 - 6 * q^13 + q^14 - 2 * q^15 + 3 * q^16 - 3 * q^17 - q^18 - q^19 + 5 * q^20 + 2 * q^21 - q^22 - 7 * q^23 + 9 * q^24 + 2 * q^25 - 14 * q^26 - 2 * q^27 - 5 * q^28 - 9 * q^29 + q^30 - 2 * q^31 - 9 * q^32 - 2 * q^33 + 10 * q^34 - 2 * q^35 + 5 * q^36 - 6 * q^37 - 8 * q^38 + 6 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + q^43 + 5 * q^44 + 2 * q^45 + 12 * q^46 - 2 * q^47 - 3 * q^48 + 2 * q^49 - q^50 + 3 * q^51 + 2 * q^52 - 15 * q^53 + q^54 + 2 * q^55 + 9 * q^56 + q^57 + 30 * q^58 + 17 * q^59 - 5 * q^60 - 11 * q^61 - 16 * q^62 - 2 * q^63 + 7 * q^64 - 6 * q^65 + q^66 + 22 * q^67 - 16 * q^68 + 7 * q^69 + q^70 + 2 * q^71 - 9 * q^72 - 14 * q^73 - 14 * q^74 - 2 * q^75 + 6 * q^76 - 2 * q^77 + 14 * q^78 - 4 * q^79 + 3 * q^80 + 2 * q^81 - 2 * q^82 - 15 * q^83 + 5 * q^84 - 3 * q^85 + 8 * q^86 + 9 * q^87 - 9 * q^88 - 17 * q^89 - q^90 + 6 * q^91 - 26 * q^92 + 2 * q^93 - 16 * q^94 - q^95 + 9 * q^96 - 15 * q^97 - q^98 + 2 * 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 $

$2$	−2.56155	−1.81129	−0.905646	−	0.424035i	$-0.860613\pi$
$2$	−2.56155	−1.81129	−0.905646	+	0.424035i	$0.860613\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.56155	2.28078
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.56155	1.04575
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.56155	−2.31986
$9$	1.00000	0.333333
$10$	−2.56155	−0.810034
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.56155	−1.31681
$13$	1.12311	0.311493	0.155747	−	0.987797i	$-0.450222\pi$
$13$	1.12311	0.311493	0.155747	+	0.987797i	$0.450222\pi$
$14$	2.56155	0.684604
$15$	−1.00000	−0.258199
$16$	7.68466	1.92116
$17$	−3.56155	−0.863803	−0.431902	−	0.901921i	$-0.642157\pi$
$17$	−3.56155	−0.863803	−0.431902	+	0.901921i	$0.642157\pi$
$18$	−2.56155	−0.603764
$19$	1.56155	0.358245	0.179122	−	0.983827i	$-0.442674\pi$
$19$	1.56155	0.358245	0.179122	+	0.983827i	$0.442674\pi$
$20$	4.56155	1.01999
$21$	1.00000	0.218218
$22$	−2.56155	−0.546125
$23$	−5.56155	−1.15966	−0.579832	−	0.814736i	$-0.696882\pi$
$23$	−5.56155	−1.15966	−0.579832	+	0.814736i	$0.696882\pi$
$24$	6.56155	1.33937
$25$	1.00000	0.200000
$26$	−2.87689	−0.564205
$27$	−1.00000	−0.192450
$28$	−4.56155	−0.862052
$29$	−10.6847	−1.98409	−0.992046	−	0.125879i	$-0.959825\pi$
$29$	−10.6847	−1.98409	−0.992046	+	0.125879i	$0.959825\pi$
$30$	2.56155	0.467673
$31$	3.12311	0.560926	0.280463	−	0.959865i	$-0.409512\pi$
$31$	3.12311	0.560926	0.280463	+	0.959865i	$0.409512\pi$
$32$	−6.56155	−1.15993
$33$	−1.00000	−0.174078
$34$	9.12311	1.56460
$35$	−1.00000	−0.169031
$36$	4.56155	0.760259
$37$	1.12311	0.184637	0.0923187	−	0.995730i	$-0.470572\pi$
$37$	1.12311	0.184637	0.0923187	+	0.995730i	$0.470572\pi$
$38$	−4.00000	−0.648886
$39$	−1.12311	−0.179841
$40$	−6.56155	−1.03747
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−2.56155	−0.395256
$43$	−1.56155	−0.238135	−0.119067	−	0.992886i	$-0.537990\pi$
$43$	−1.56155	−0.238135	−0.119067	+	0.992886i	$0.537990\pi$
$44$	4.56155	0.687680
$45$	1.00000	0.149071
$46$	14.2462	2.10049
$47$	3.12311	0.455552	0.227776	−	0.973714i	$-0.426855\pi$
$47$	3.12311	0.455552	0.227776	+	0.973714i	$0.426855\pi$
$48$	−7.68466	−1.10918
$49$	1.00000	0.142857
$50$	−2.56155	−0.362258
$51$	3.56155	0.498717
$52$	5.12311	0.710447
$53$	−1.31534	−0.180676	−0.0903380	−	0.995911i	$-0.528795\pi$
$53$	−1.31534	−0.180676	−0.0903380	+	0.995911i	$0.528795\pi$
$54$	2.56155	0.348583
$55$	1.00000	0.134840
$56$	6.56155	0.876824
$57$	−1.56155	−0.206833
$58$	27.3693	3.59377
$59$	6.43845	0.838214	0.419107	−	0.907937i	$-0.362343\pi$
$59$	6.43845	0.838214	0.419107	+	0.907937i	$0.362343\pi$
$60$	−4.56155	−0.588894
$61$	−7.56155	−0.968158	−0.484079	−	0.875024i	$-0.660845\pi$
$61$	−7.56155	−0.968158	−0.484079	+	0.875024i	$0.660845\pi$
$62$	−8.00000	−1.01600
$63$	−1.00000	−0.125988
$64$	1.43845	0.179806
$65$	1.12311	0.139304
$66$	2.56155	0.315305
$67$	15.1231	1.84758	0.923791	−	0.382898i	$-0.125074\pi$
$67$	15.1231	1.84758	0.923791	+	0.382898i	$0.125074\pi$
$68$	−16.2462	−1.97014
$69$	5.56155	0.669532
$70$	2.56155	0.306164
$71$	−3.12311	−0.370644	−0.185322	−	0.982678i	$-0.559333\pi$
$71$	−3.12311	−0.370644	−0.185322	+	0.982678i	$0.559333\pi$
$72$	−6.56155	−0.773286
$73$	−2.87689	−0.336715	−0.168358	−	0.985726i	$-0.553846\pi$
$73$	−2.87689	−0.336715	−0.168358	+	0.985726i	$0.553846\pi$
$74$	−2.87689	−0.334432
$75$	−1.00000	−0.115470
$76$	7.12311	0.817076
$77$	−1.00000	−0.113961
$78$	2.87689	0.325744
$79$	6.24621	0.702754	0.351377	−	0.936234i	$-0.385714\pi$
$79$	6.24621	0.702754	0.351377	+	0.936234i	$0.385714\pi$
$80$	7.68466	0.859171
$81$	1.00000	0.111111
$82$	−5.12311	−0.565752
$83$	−9.56155	−1.04952	−0.524758	−	0.851251i	$-0.675844\pi$
$83$	−9.56155	−1.04952	−0.524758	+	0.851251i	$0.675844\pi$
$84$	4.56155	0.497706
$85$	−3.56155	−0.386305
$86$	4.00000	0.431331
$87$	10.6847	1.14552
$88$	−6.56155	−0.699464
$89$	−14.6847	−1.55657	−0.778285	−	0.627911i	$-0.783910\pi$
$89$	−14.6847	−1.55657	−0.778285	+	0.627911i	$0.783910\pi$
$90$	−2.56155	−0.270011
$91$	−1.12311	−0.117733
$92$	−25.3693	−2.64493
$93$	−3.12311	−0.323851
$94$	−8.00000	−0.825137
$95$	1.56155	0.160212
$96$	6.56155	0.669686
$97$	−17.8078	−1.80810	−0.904052	−	0.427422i	$-0.859422\pi$
$97$	−17.8078	−1.80810	−0.904052	+	0.427422i	$0.859422\pi$
$98$	−2.56155	−0.258756
$99$	1.00000	0.100504
$100$	4.56155	0.456155
$101$	4.24621	0.422514	0.211257	−	0.977431i	$-0.432244\pi$
$101$	4.24621	0.422514	0.211257	+	0.977431i	$0.432244\pi$
$102$	−9.12311	−0.903322
$103$	−8.68466	−0.855725	−0.427862	−	0.903844i	$-0.640733\pi$
$103$	−8.68466	−0.855725	−0.427862	+	0.903844i	$0.640733\pi$
$104$	−7.36932	−0.722621
$105$	1.00000	0.0975900
$106$	3.36932	0.327257
$107$	−5.36932	−0.519071	−0.259536	−	0.965734i	$-0.583570\pi$
$107$	−5.36932	−0.519071	−0.259536	+	0.965734i	$0.583570\pi$
$108$	−4.56155	−0.438936
$109$	−14.4924	−1.38812	−0.694061	−	0.719916i	$-0.744180\pi$
$109$	−14.4924	−1.38812	−0.694061	+	0.719916i	$0.744180\pi$
$110$	−2.56155	−0.244234
$111$	−1.12311	−0.106600
$112$	−7.68466	−0.726132
$113$	4.43845	0.417534	0.208767	−	0.977965i	$-0.433055\pi$
$113$	4.43845	0.417534	0.208767	+	0.977965i	$0.433055\pi$
$114$	4.00000	0.374634
$115$	−5.56155	−0.518617
$116$	−48.7386	−4.52527
$117$	1.12311	0.103831
$118$	−16.4924	−1.51825
$119$	3.56155	0.326487
$120$	6.56155	0.598985
$121$	1.00000	0.0909091
$122$	19.3693	1.75362
$123$	−2.00000	−0.180334
$124$	14.2462	1.27935
$125$	1.00000	0.0894427
$126$	2.56155	0.228201
$127$	−19.8078	−1.75765	−0.878827	−	0.477140i	$-0.841674\pi$
$127$	−19.8078	−1.75765	−0.878827	+	0.477140i	$0.841674\pi$
$128$	9.43845	0.834249
$129$	1.56155	0.137487
$130$	−2.87689	−0.252320
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	−4.56155	−0.397032
$133$	−1.56155	−0.135404
$134$	−38.7386	−3.34651
$135$	−1.00000	−0.0860663
$136$	23.3693	2.00390
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	−14.2462	−1.21272
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	−4.56155	−0.385522
$141$	−3.12311	−0.263013
$142$	8.00000	0.671345
$143$	1.12311	0.0939188
$144$	7.68466	0.640388
$145$	−10.6847	−0.887313
$146$	7.36932	0.609889
$147$	−1.00000	−0.0824786
$148$	5.12311	0.421117
$149$	−16.2462	−1.33094	−0.665471	−	0.746424i	$-0.731769\pi$
$149$	−16.2462	−1.33094	−0.665471	+	0.746424i	$0.731769\pi$
$150$	2.56155	0.209150
$151$	−3.12311	−0.254155	−0.127077	−	0.991893i	$-0.540560\pi$
$151$	−3.12311	−0.254155	−0.127077	+	0.991893i	$0.540560\pi$
$152$	−10.2462	−0.831077
$153$	−3.56155	−0.287934
$154$	2.56155	0.206416
$155$	3.12311	0.250854
$156$	−5.12311	−0.410177
$157$	−15.5616	−1.24195	−0.620974	−	0.783832i	$-0.713263\pi$
$157$	−15.5616	−1.24195	−0.620974	+	0.783832i	$0.713263\pi$
$158$	−16.0000	−1.27289
$159$	1.31534	0.104313
$160$	−6.56155	−0.518736
$161$	5.56155	0.438312
$162$	−2.56155	−0.201255
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	9.12311	0.712395
$165$	−1.00000	−0.0778499
$166$	24.4924	1.90098
$167$	−14.2462	−1.10240	−0.551202	−	0.834372i	$-0.685831\pi$
$167$	−14.2462	−1.10240	−0.551202	+	0.834372i	$0.685831\pi$
$168$	−6.56155	−0.506235
$169$	−11.7386	−0.902972
$170$	9.12311	0.699710
$171$	1.56155	0.119415
$172$	−7.12311	−0.543132
$173$	12.2462	0.931062	0.465531	−	0.885032i	$-0.345863\pi$
$173$	12.2462	0.931062	0.465531	+	0.885032i	$0.345863\pi$
$174$	−27.3693	−2.07486
$175$	−1.00000	−0.0755929
$176$	7.68466	0.579253
$177$	−6.43845	−0.483943
$178$	37.6155	2.81940
$179$	5.36932	0.401322	0.200661	−	0.979661i	$-0.435691\pi$
$179$	5.36932	0.401322	0.200661	+	0.979661i	$0.435691\pi$
$180$	4.56155	0.339998
$181$	−3.75379	−0.279017	−0.139508	−	0.990221i	$-0.544552\pi$
$181$	−3.75379	−0.279017	−0.139508	+	0.990221i	$0.544552\pi$
$182$	2.87689	0.213250
$183$	7.56155	0.558966
$184$	36.4924	2.69026
$185$	1.12311	0.0825724
$186$	8.00000	0.586588
$187$	−3.56155	−0.260447
$188$	14.2462	1.03901
$189$	1.00000	0.0727393
$190$	−4.00000	−0.290191
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.43845	−0.103811
$193$	−10.4924	−0.755261	−0.377631	−	0.925956i	$-0.623261\pi$
$193$	−10.4924	−0.755261	−0.377631	+	0.925956i	$0.623261\pi$
$194$	45.6155	3.27500
$195$	−1.12311	−0.0804273
$196$	4.56155	0.325825
$197$	−14.8769	−1.05993	−0.529967	−	0.848018i	$-0.677796\pi$
$197$	−14.8769	−1.05993	−0.529967	+	0.848018i	$0.677796\pi$
$198$	−2.56155	−0.182042
$199$	−12.4924	−0.885564	−0.442782	−	0.896629i	$-0.646009\pi$
$199$	−12.4924	−0.885564	−0.442782	+	0.896629i	$0.646009\pi$
$200$	−6.56155	−0.463972
$201$	−15.1231	−1.06670
$202$	−10.8769	−0.765296
$203$	10.6847	0.749916
$204$	16.2462	1.13746
$205$	2.00000	0.139686
$206$	22.2462	1.54997
$207$	−5.56155	−0.386555
$208$	8.63068	0.598430
$209$	1.56155	0.108015
$210$	−2.56155	−0.176764
$211$	21.3693	1.47112	0.735562	−	0.677457i	$-0.236918\pi$
$211$	21.3693	1.47112	0.735562	+	0.677457i	$0.236918\pi$
$212$	−6.00000	−0.412082
$213$	3.12311	0.213992
$214$	13.7538	0.940190
$215$	−1.56155	−0.106497
$216$	6.56155	0.446457
$217$	−3.12311	−0.212010
$218$	37.1231	2.51429
$219$	2.87689	0.194403
$220$	4.56155	0.307540
$221$	−4.00000	−0.269069
$222$	2.87689	0.193085
$223$	10.4384	0.699010	0.349505	−	0.936934i	$-0.386350\pi$
$223$	10.4384	0.699010	0.349505	+	0.936934i	$0.386350\pi$
$224$	6.56155	0.438412
$225$	1.00000	0.0666667
$226$	−11.3693	−0.756276
$227$	2.93087	0.194529	0.0972643	−	0.995259i	$-0.468991\pi$
$227$	2.93087	0.194529	0.0972643	+	0.995259i	$0.468991\pi$
$228$	−7.12311	−0.471739
$229$	−22.4924	−1.48634	−0.743171	−	0.669102i	$-0.766679\pi$
$229$	−22.4924	−1.48634	−0.743171	+	0.669102i	$0.766679\pi$
$230$	14.2462	0.939367
$231$	1.00000	0.0657952
$232$	70.1080	4.60281
$233$	17.6155	1.15403	0.577016	−	0.816733i	$-0.304217\pi$
$233$	17.6155	1.15403	0.577016	+	0.816733i	$0.304217\pi$
$234$	−2.87689	−0.188068
$235$	3.12311	0.203729
$236$	29.3693	1.91178
$237$	−6.24621	−0.405735
$238$	−9.12311	−0.591363
$239$	7.31534	0.473190	0.236595	−	0.971608i	$-0.423969\pi$
$239$	7.31534	0.473190	0.236595	+	0.971608i	$0.423969\pi$
$240$	−7.68466	−0.496043
$241$	16.2462	1.04651	0.523255	−	0.852176i	$-0.324717\pi$
$241$	16.2462	1.04651	0.523255	+	0.852176i	$0.324717\pi$
$242$	−2.56155	−0.164663
$243$	−1.00000	−0.0641500
$244$	−34.4924	−2.20815
$245$	1.00000	0.0638877
$246$	5.12311	0.326637
$247$	1.75379	0.111591
$248$	−20.4924	−1.30127
$249$	9.56155	0.605939
$250$	−2.56155	−0.162007
$251$	−8.49242	−0.536037	−0.268018	−	0.963414i	$-0.586369\pi$
$251$	−8.49242	−0.536037	−0.268018	+	0.963414i	$0.586369\pi$
$252$	−4.56155	−0.287351
$253$	−5.56155	−0.349652
$254$	50.7386	3.18363
$255$	3.56155	0.223033
$256$	−27.0540	−1.69087
$257$	−15.3693	−0.958712	−0.479356	−	0.877621i	$-0.659130\pi$
$257$	−15.3693	−0.958712	−0.479356	+	0.877621i	$0.659130\pi$
$258$	−4.00000	−0.249029
$259$	−1.12311	−0.0697864
$260$	5.12311	0.317722
$261$	−10.6847	−0.661364
$262$	−10.2462	−0.633013
$263$	−1.75379	−0.108143	−0.0540716	−	0.998537i	$-0.517220\pi$
$263$	−1.75379	−0.108143	−0.0540716	+	0.998537i	$0.517220\pi$
$264$	6.56155	0.403836
$265$	−1.31534	−0.0808008
$266$	4.00000	0.245256
$267$	14.6847	0.898687
$268$	68.9848	4.21392
$269$	−10.6847	−0.651455	−0.325728	−	0.945464i	$-0.605609\pi$
$269$	−10.6847	−0.651455	−0.325728	+	0.945464i	$0.605609\pi$
$270$	2.56155	0.155891
$271$	14.9309	0.906986	0.453493	−	0.891260i	$-0.350178\pi$
$271$	14.9309	0.906986	0.453493	+	0.891260i	$0.350178\pi$
$272$	−27.3693	−1.65951
$273$	1.12311	0.0679734
$274$	−25.6155	−1.54749
$275$	1.00000	0.0603023
$276$	25.3693	1.52705
$277$	24.7386	1.48640	0.743200	−	0.669069i	$-0.233307\pi$
$277$	24.7386	1.48640	0.743200	+	0.669069i	$0.233307\pi$
$278$	51.2311	3.07263
$279$	3.12311	0.186975
$280$	6.56155	0.392128
$281$	−18.4924	−1.10317	−0.551583	−	0.834120i	$-0.685976\pi$
$281$	−18.4924	−1.10317	−0.551583	+	0.834120i	$0.685976\pi$
$282$	8.00000	0.476393
$283$	−10.2462	−0.609074	−0.304537	−	0.952501i	$-0.598502\pi$
$283$	−10.2462	−0.609074	−0.304537	+	0.952501i	$0.598502\pi$
$284$	−14.2462	−0.845357
$285$	−1.56155	−0.0924984
$286$	−2.87689	−0.170114
$287$	−2.00000	−0.118056
$288$	−6.56155	−0.386643
$289$	−4.31534	−0.253844
$290$	27.3693	1.60718
$291$	17.8078	1.04391
$292$	−13.1231	−0.767972
$293$	19.1771	1.12034	0.560169	−	0.828379i	$-0.310736\pi$
$293$	19.1771	1.12034	0.560169	+	0.828379i	$0.310736\pi$
$294$	2.56155	0.149393
$295$	6.43845	0.374861
$296$	−7.36932	−0.428333
$297$	−1.00000	−0.0580259
$298$	41.6155	2.41072
$299$	−6.24621	−0.361228
$300$	−4.56155	−0.263361
$301$	1.56155	0.0900064
$302$	8.00000	0.460348
$303$	−4.24621	−0.243938
$304$	12.0000	0.688247
$305$	−7.56155	−0.432973
$306$	9.12311	0.521533
$307$	−13.3693	−0.763027	−0.381514	−	0.924363i	$-0.624597\pi$
$307$	−13.3693	−0.763027	−0.381514	+	0.924363i	$0.624597\pi$
$308$	−4.56155	−0.259919
$309$	8.68466	0.494053
$310$	−8.00000	−0.454369
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	7.36932	0.417205
$313$	−14.6847	−0.830026	−0.415013	−	0.909815i	$-0.636223\pi$
$313$	−14.6847	−0.830026	−0.415013	+	0.909815i	$0.636223\pi$
$314$	39.8617	2.24953
$315$	−1.00000	−0.0563436
$316$	28.4924	1.60282
$317$	10.4924	0.589313	0.294657	−	0.955603i	$-0.404795\pi$
$317$	10.4924	0.589313	0.294657	+	0.955603i	$0.404795\pi$
$318$	−3.36932	−0.188942
$319$	−10.6847	−0.598226
$320$	1.43845	0.0804116
$321$	5.36932	0.299686
$322$	−14.2462	−0.793910
$323$	−5.56155	−0.309453
$324$	4.56155	0.253420
$325$	1.12311	0.0622987
$326$	−51.2311	−2.83743
$327$	14.4924	0.801433
$328$	−13.1231	−0.724602
$329$	−3.12311	−0.172182
$330$	2.56155	0.141009
$331$	−11.3153	−0.621947	−0.310974	−	0.950419i	$-0.600655\pi$
$331$	−11.3153	−0.621947	−0.310974	+	0.950419i	$0.600655\pi$
$332$	−43.6155	−2.39371
$333$	1.12311	0.0615458
$334$	36.4924	1.99678
$335$	15.1231	0.826264
$336$	7.68466	0.419232
$337$	28.0540	1.52820	0.764099	−	0.645099i	$-0.223184\pi$
$337$	28.0540	1.52820	0.764099	+	0.645099i	$0.223184\pi$
$338$	30.0691	1.63555
$339$	−4.43845	−0.241063
$340$	−16.2462	−0.881075
$341$	3.12311	0.169126
$342$	−4.00000	−0.216295
$343$	−1.00000	−0.0539949
$344$	10.2462	0.552439
$345$	5.56155	0.299424
$346$	−31.3693	−1.68642
$347$	2.24621	0.120583	0.0602915	−	0.998181i	$-0.480797\pi$
$347$	2.24621	0.120583	0.0602915	+	0.998181i	$0.480797\pi$
$348$	48.7386	2.61267
$349$	−29.8078	−1.59557	−0.797787	−	0.602940i	$-0.793996\pi$
$349$	−29.8078	−1.59557	−0.797787	+	0.602940i	$0.793996\pi$
$350$	2.56155	0.136921
$351$	−1.12311	−0.0599469
$352$	−6.56155	−0.349732
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	16.4924	0.876562
$355$	−3.12311	−0.165757
$356$	−66.9848	−3.55019
$357$	−3.56155	−0.188497
$358$	−13.7538	−0.726910
$359$	−16.6847	−0.880583	−0.440291	−	0.897855i	$-0.645125\pi$
$359$	−16.6847	−0.880583	−0.440291	+	0.897855i	$0.645125\pi$
$360$	−6.56155	−0.345824
$361$	−16.5616	−0.871661
$362$	9.61553	0.505381
$363$	−1.00000	−0.0524864
$364$	−5.12311	−0.268524
$365$	−2.87689	−0.150584
$366$	−19.3693	−1.01245
$367$	21.5616	1.12550	0.562752	−	0.826626i	$-0.309743\pi$
$367$	21.5616	1.12550	0.562752	+	0.826626i	$0.309743\pi$
$368$	−42.7386	−2.22791
$369$	2.00000	0.104116
$370$	−2.87689	−0.149563
$371$	1.31534	0.0682891
$372$	−14.2462	−0.738632
$373$	3.56155	0.184410	0.0922051	−	0.995740i	$-0.470608\pi$
$373$	3.56155	0.184410	0.0922051	+	0.995740i	$0.470608\pi$
$374$	9.12311	0.471745
$375$	−1.00000	−0.0516398
$376$	−20.4924	−1.05682
$377$	−12.0000	−0.618031
$378$	−2.56155	−0.131752
$379$	−14.0540	−0.721904	−0.360952	−	0.932584i	$-0.617548\pi$
$379$	−14.0540	−0.721904	−0.360952	+	0.932584i	$0.617548\pi$
$380$	7.12311	0.365408
$381$	19.8078	1.01478
$382$	0	0
$383$	20.4924	1.04711	0.523557	−	0.851991i	$-0.324605\pi$
$383$	20.4924	1.04711	0.523557	+	0.851991i	$0.324605\pi$
$384$	−9.43845	−0.481654
$385$	−1.00000	−0.0509647
$386$	26.8769	1.36800
$387$	−1.56155	−0.0793782
$388$	−81.2311	−4.12388
$389$	35.8617	1.81826	0.909131	−	0.416510i	$-0.136747\pi$
$389$	35.8617	1.81826	0.909131	+	0.416510i	$0.136747\pi$
$390$	2.87689	0.145677
$391$	19.8078	1.00172
$392$	−6.56155	−0.331408
$393$	−4.00000	−0.201773
$394$	38.1080	1.91985
$395$	6.24621	0.314281
$396$	4.56155	0.229227
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	32.0000	1.60402
$399$	1.56155	0.0781754
$400$	7.68466	0.384233
$401$	−1.50758	−0.0752848	−0.0376424	−	0.999291i	$-0.511985\pi$
$401$	−1.50758	−0.0752848	−0.0376424	+	0.999291i	$0.511985\pi$
$402$	38.7386	1.93211
$403$	3.50758	0.174725
$404$	19.3693	0.963660
$405$	1.00000	0.0496904
$406$	−27.3693	−1.35832
$407$	1.12311	0.0556703
$408$	−23.3693	−1.15695
$409$	8.24621	0.407749	0.203874	−	0.978997i	$-0.434647\pi$
$409$	8.24621	0.407749	0.203874	+	0.978997i	$0.434647\pi$
$410$	−5.12311	−0.253012
$411$	−10.0000	−0.493264
$412$	−39.6155	−1.95172
$413$	−6.43845	−0.316815
$414$	14.2462	0.700163
$415$	−9.56155	−0.469358
$416$	−7.36932	−0.361310
$417$	20.0000	0.979404
$418$	−4.00000	−0.195646
$419$	31.8078	1.55391	0.776955	−	0.629556i	$-0.216763\pi$
$419$	31.8078	1.55391	0.776955	+	0.629556i	$0.216763\pi$
$420$	4.56155	0.222581
$421$	−15.1771	−0.739686	−0.369843	−	0.929094i	$-0.620588\pi$
$421$	−15.1771	−0.739686	−0.369843	+	0.929094i	$0.620588\pi$
$422$	−54.7386	−2.66463
$423$	3.12311	0.151851
$424$	8.63068	0.419143
$425$	−3.56155	−0.172761
$426$	−8.00000	−0.387601
$427$	7.56155	0.365929
$428$	−24.4924	−1.18389
$429$	−1.12311	−0.0542241
$430$	4.00000	0.192897
$431$	34.7386	1.67330	0.836651	−	0.547737i	$-0.184511\pi$
$431$	34.7386	1.67330	0.836651	+	0.547737i	$0.184511\pi$
$432$	−7.68466	−0.369728
$433$	36.7386	1.76555	0.882773	−	0.469800i	$-0.155674\pi$
$433$	36.7386	1.76555	0.882773	+	0.469800i	$0.155674\pi$
$434$	8.00000	0.384012
$435$	10.6847	0.512290
$436$	−66.1080	−3.16600
$437$	−8.68466	−0.415444
$438$	−7.36932	−0.352120
$439$	−6.93087	−0.330792	−0.165396	−	0.986227i	$-0.552890\pi$
$439$	−6.93087	−0.330792	−0.165396	+	0.986227i	$0.552890\pi$
$440$	−6.56155	−0.312810
$441$	1.00000	0.0476190
$442$	10.2462	0.487363
$443$	30.7386	1.46044	0.730218	−	0.683214i	$-0.239418\pi$
$443$	30.7386	1.46044	0.730218	+	0.683214i	$0.239418\pi$
$444$	−5.12311	−0.243132
$445$	−14.6847	−0.696120
$446$	−26.7386	−1.26611
$447$	16.2462	0.768419
$448$	−1.43845	−0.0679602
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	−2.56155	−0.120753
$451$	2.00000	0.0941763
$452$	20.2462	0.952302
$453$	3.12311	0.146736
$454$	−7.50758	−0.352348
$455$	−1.12311	−0.0526520
$456$	10.2462	0.479823
$457$	−30.6847	−1.43537	−0.717684	−	0.696369i	$-0.754798\pi$
$457$	−30.6847	−1.43537	−0.717684	+	0.696369i	$0.754798\pi$
$458$	57.6155	2.69220
$459$	3.56155	0.166239
$460$	−25.3693	−1.18285
$461$	15.7538	0.733727	0.366864	−	0.930275i	$-0.380432\pi$
$461$	15.7538	0.733727	0.366864	+	0.930275i	$0.380432\pi$
$462$	−2.56155	−0.119174
$463$	−29.8617	−1.38779	−0.693896	−	0.720075i	$-0.744107\pi$
$463$	−29.8617	−1.38779	−0.693896	+	0.720075i	$0.744107\pi$
$464$	−82.1080	−3.81177
$465$	−3.12311	−0.144831
$466$	−45.1231	−2.09029
$467$	−16.4924	−0.763178	−0.381589	−	0.924332i	$-0.624623\pi$
$467$	−16.4924	−0.763178	−0.381589	+	0.924332i	$0.624623\pi$
$468$	5.12311	0.236816
$469$	−15.1231	−0.698320
$470$	−8.00000	−0.369012
$471$	15.5616	0.717039
$472$	−42.2462	−1.94454
$473$	−1.56155	−0.0718003
$474$	16.0000	0.734904
$475$	1.56155	0.0716490
$476$	16.2462	0.744644
$477$	−1.31534	−0.0602254
$478$	−18.7386	−0.857085
$479$	−3.50758	−0.160265	−0.0801327	−	0.996784i	$-0.525534\pi$
$479$	−3.50758	−0.160265	−0.0801327	+	0.996784i	$0.525534\pi$
$480$	6.56155	0.299493
$481$	1.26137	0.0575134
$482$	−41.6155	−1.89554
$483$	−5.56155	−0.253059
$484$	4.56155	0.207343
$485$	−17.8078	−0.808609
$486$	2.56155	0.116194
$487$	31.6155	1.43264	0.716318	−	0.697774i	$-0.245826\pi$
$487$	31.6155	1.43264	0.716318	+	0.697774i	$0.245826\pi$
$488$	49.6155	2.24599
$489$	−20.0000	−0.904431
$490$	−2.56155	−0.115719
$491$	−20.3002	−0.916135	−0.458067	−	0.888918i	$-0.651458\pi$
$491$	−20.3002	−0.916135	−0.458067	+	0.888918i	$0.651458\pi$
$492$	−9.12311	−0.411301
$493$	38.0540	1.71386
$494$	−4.49242	−0.202124
$495$	1.00000	0.0449467
$496$	24.0000	1.07763
$497$	3.12311	0.140090
$498$	−24.4924	−1.09753
$499$	30.0540	1.34540	0.672700	−	0.739915i	$-0.265134\pi$
$499$	30.0540	1.34540	0.672700	+	0.739915i	$0.265134\pi$
$500$	4.56155	0.203999
$501$	14.2462	0.636474
$502$	21.7538	0.970919
$503$	−20.1922	−0.900327	−0.450164	−	0.892946i	$-0.648634\pi$
$503$	−20.1922	−0.900327	−0.450164	+	0.892946i	$0.648634\pi$
$504$	6.56155	0.292275
$505$	4.24621	0.188954
$506$	14.2462	0.633321
$507$	11.7386	0.521331
$508$	−90.3542	−4.00882
$509$	−21.8078	−0.966612	−0.483306	−	0.875451i	$-0.660564\pi$
$509$	−21.8078	−0.966612	−0.483306	+	0.875451i	$0.660564\pi$
$510$	−9.12311	−0.403978
$511$	2.87689	0.127266
$512$	50.4233	2.22842
$513$	−1.56155	−0.0689442
$514$	39.3693	1.73651
$515$	−8.68466	−0.382692
$516$	7.12311	0.313577
$517$	3.12311	0.137354
$518$	2.87689	0.126403
$519$	−12.2462	−0.537549
$520$	−7.36932	−0.323166
$521$	24.9309	1.09224	0.546121	−	0.837707i	$-0.316104\pi$
$521$	24.9309	1.09224	0.546121	+	0.837707i	$0.316104\pi$
$522$	27.3693	1.19792
$523$	−13.7538	−0.601411	−0.300706	−	0.953717i	$-0.597222\pi$
$523$	−13.7538	−0.601411	−0.300706	+	0.953717i	$0.597222\pi$
$524$	18.2462	0.797089
$525$	1.00000	0.0436436
$526$	4.49242	0.195879
$527$	−11.1231	−0.484530
$528$	−7.68466	−0.334432
$529$	7.93087	0.344820
$530$	3.36932	0.146354
$531$	6.43845	0.279405
$532$	−7.12311	−0.308826
$533$	2.24621	0.0972942
$534$	−37.6155	−1.62778
$535$	−5.36932	−0.232136
$536$	−99.2311	−4.28613
$537$	−5.36932	−0.231703
$538$	27.3693	1.17998
$539$	1.00000	0.0430730
$540$	−4.56155	−0.196298
$541$	10.4924	0.451104	0.225552	−	0.974231i	$-0.427581\pi$
$541$	10.4924	0.451104	0.225552	+	0.974231i	$0.427581\pi$
$542$	−38.2462	−1.64282
$543$	3.75379	0.161090
$544$	23.3693	1.00195
$545$	−14.4924	−0.620787
$546$	−2.87689	−0.123120
$547$	14.0540	0.600905	0.300452	−	0.953797i	$-0.402862\pi$
$547$	14.0540	0.600905	0.300452	+	0.953797i	$0.402862\pi$
$548$	45.6155	1.94860
$549$	−7.56155	−0.322719
$550$	−2.56155	−0.109225
$551$	−16.6847	−0.710790
$552$	−36.4924	−1.55322
$553$	−6.24621	−0.265616
$554$	−63.3693	−2.69230
$555$	−1.12311	−0.0476732
$556$	−91.2311	−3.86906
$557$	−14.4924	−0.614064	−0.307032	−	0.951699i	$-0.599336\pi$
$557$	−14.4924	−0.614064	−0.307032	+	0.951699i	$0.599336\pi$
$558$	−8.00000	−0.338667
$559$	−1.75379	−0.0741774
$560$	−7.68466	−0.324736
$561$	3.56155	0.150369
$562$	47.3693	1.99815
$563$	−8.49242	−0.357913	−0.178956	−	0.983857i	$-0.557272\pi$
$563$	−8.49242	−0.357913	−0.178956	+	0.983857i	$0.557272\pi$
$564$	−14.2462	−0.599874
$565$	4.43845	0.186727
$566$	26.2462	1.10321
$567$	−1.00000	−0.0419961
$568$	20.4924	0.859843
$569$	−2.19224	−0.0919033	−0.0459517	−	0.998944i	$-0.514632\pi$
$569$	−2.19224	−0.0919033	−0.0459517	+	0.998944i	$0.514632\pi$
$570$	4.00000	0.167542
$571$	2.24621	0.0940010	0.0470005	−	0.998895i	$-0.485034\pi$
$571$	2.24621	0.0940010	0.0470005	+	0.998895i	$0.485034\pi$
$572$	5.12311	0.214208
$573$	0	0
$574$	5.12311	0.213834
$575$	−5.56155	−0.231933
$576$	1.43845	0.0599353
$577$	−38.9848	−1.62296	−0.811480	−	0.584380i	$-0.801338\pi$
$577$	−38.9848	−1.62296	−0.811480	+	0.584380i	$0.801338\pi$
$578$	11.0540	0.459785
$579$	10.4924	0.436050
$580$	−48.7386	−2.02376
$581$	9.56155	0.396680
$582$	−45.6155	−1.89082
$583$	−1.31534	−0.0544759
$584$	18.8769	0.781131
$585$	1.12311	0.0464347
$586$	−49.1231	−2.02926
$587$	−36.9848	−1.52653	−0.763264	−	0.646087i	$-0.776404\pi$
$587$	−36.9848	−1.52653	−0.763264	+	0.646087i	$0.776404\pi$
$588$	−4.56155	−0.188115
$589$	4.87689	0.200949
$590$	−16.4924	−0.678982
$591$	14.8769	0.611954
$592$	8.63068	0.354719
$593$	16.2462	0.667152	0.333576	−	0.942723i	$-0.391745\pi$
$593$	16.2462	0.667152	0.333576	+	0.942723i	$0.391745\pi$
$594$	2.56155	0.105102
$595$	3.56155	0.146009
$596$	−74.1080	−3.03558
$597$	12.4924	0.511281
$598$	16.0000	0.654289
$599$	25.3693	1.03656	0.518281	−	0.855210i	$-0.326572\pi$
$599$	25.3693	1.03656	0.518281	+	0.855210i	$0.326572\pi$
$600$	6.56155	0.267874
$601$	28.0540	1.14435	0.572173	−	0.820133i	$-0.306101\pi$
$601$	28.0540	1.14435	0.572173	+	0.820133i	$0.306101\pi$
$602$	−4.00000	−0.163028
$603$	15.1231	0.615860
$604$	−14.2462	−0.579670
$605$	1.00000	0.0406558
$606$	10.8769	0.441844
$607$	−1.36932	−0.0555789	−0.0277894	−	0.999614i	$-0.508847\pi$
$607$	−1.36932	−0.0555789	−0.0277894	+	0.999614i	$0.508847\pi$
$608$	−10.2462	−0.415539
$609$	−10.6847	−0.432964
$610$	19.3693	0.784241
$611$	3.50758	0.141901
$612$	−16.2462	−0.656714
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	34.2462	1.38206
$615$	−2.00000	−0.0806478
$616$	6.56155	0.264372
$617$	−12.2462	−0.493014	−0.246507	−	0.969141i	$-0.579283\pi$
$617$	−12.2462	−0.493014	−0.246507	+	0.969141i	$0.579283\pi$
$618$	−22.2462	−0.894874
$619$	−7.12311	−0.286302	−0.143151	−	0.989701i	$-0.545723\pi$
$619$	−7.12311	−0.286302	−0.143151	+	0.989701i	$0.545723\pi$
$620$	14.2462	0.572142
$621$	5.56155	0.223177
$622$	40.9848	1.64334
$623$	14.6847	0.588328
$624$	−8.63068	−0.345504
$625$	1.00000	0.0400000
$626$	37.6155	1.50342
$627$	−1.56155	−0.0623624
$628$	−70.9848	−2.83260
$629$	−4.00000	−0.159490
$630$	2.56155	0.102055
$631$	−24.3002	−0.967375	−0.483688	−	0.875241i	$-0.660703\pi$
$631$	−24.3002	−0.967375	−0.483688	+	0.875241i	$0.660703\pi$
$632$	−40.9848	−1.63029
$633$	−21.3693	−0.849354
$634$	−26.8769	−1.06742
$635$	−19.8078	−0.786047
$636$	6.00000	0.237915
$637$	1.12311	0.0444991
$638$	27.3693	1.08356
$639$	−3.12311	−0.123548
$640$	9.43845	0.373087
$641$	36.7386	1.45109	0.725544	−	0.688175i	$-0.241588\pi$
$641$	36.7386	1.45109	0.725544	+	0.688175i	$0.241588\pi$
$642$	−13.7538	−0.542819
$643$	28.3002	1.11605	0.558025	−	0.829824i	$-0.311559\pi$
$643$	28.3002	1.11605	0.558025	+	0.829824i	$0.311559\pi$
$644$	25.3693	0.999691
$645$	1.56155	0.0614861
$646$	14.2462	0.560510
$647$	6.24621	0.245564	0.122782	−	0.992434i	$-0.460818\pi$
$647$	6.24621	0.245564	0.122782	+	0.992434i	$0.460818\pi$
$648$	−6.56155	−0.257762
$649$	6.43845	0.252731
$650$	−2.87689	−0.112841
$651$	3.12311	0.122404
$652$	91.2311	3.57288
$653$	−39.1771	−1.53312	−0.766559	−	0.642174i	$-0.778033\pi$
$653$	−39.1771	−1.53312	−0.766559	+	0.642174i	$0.778033\pi$
$654$	−37.1231	−1.45163
$655$	4.00000	0.156293
$656$	15.3693	0.600071
$657$	−2.87689	−0.112238
$658$	8.00000	0.311872
$659$	12.6847	0.494124	0.247062	−	0.969000i	$-0.420535\pi$
$659$	12.6847	0.494124	0.247062	+	0.969000i	$0.420535\pi$
$660$	−4.56155	−0.177558
$661$	−22.4924	−0.874854	−0.437427	−	0.899254i	$-0.644110\pi$
$661$	−22.4924	−0.874854	−0.437427	+	0.899254i	$0.644110\pi$
$662$	28.9848	1.12653
$663$	4.00000	0.155347
$664$	62.7386	2.43473
$665$	−1.56155	−0.0605544
$666$	−2.87689	−0.111477
$667$	59.4233	2.30088
$668$	−64.9848	−2.51434
$669$	−10.4384	−0.403574
$670$	−38.7386	−1.49660
$671$	−7.56155	−0.291911
$672$	−6.56155	−0.253117
$673$	4.43845	0.171090	0.0855448	−	0.996334i	$-0.472737\pi$
$673$	4.43845	0.171090	0.0855448	+	0.996334i	$0.472737\pi$
$674$	−71.8617	−2.76801
$675$	−1.00000	−0.0384900
$676$	−53.5464	−2.05948
$677$	44.9309	1.72683	0.863417	−	0.504491i	$-0.168320\pi$
$677$	44.9309	1.72683	0.863417	+	0.504491i	$0.168320\pi$
$678$	11.3693	0.436636
$679$	17.8078	0.683399
$680$	23.3693	0.896172
$681$	−2.93087	−0.112311
$682$	−8.00000	−0.306336
$683$	−7.50758	−0.287269	−0.143635	−	0.989631i	$-0.545879\pi$
$683$	−7.50758	−0.287269	−0.143635	+	0.989631i	$0.545879\pi$
$684$	7.12311	0.272359
$685$	10.0000	0.382080
$686$	2.56155	0.0978005
$687$	22.4924	0.858139
$688$	−12.0000	−0.457496
$689$	−1.47727	−0.0562794
$690$	−14.2462	−0.542344
$691$	39.1231	1.48831	0.744157	−	0.668005i	$-0.232852\pi$
$691$	39.1231	1.48831	0.744157	+	0.668005i	$0.232852\pi$
$692$	55.8617	2.12354
$693$	−1.00000	−0.0379869
$694$	−5.75379	−0.218411
$695$	−20.0000	−0.758643
$696$	−70.1080	−2.65744
$697$	−7.12311	−0.269807
$698$	76.3542	2.89005
$699$	−17.6155	−0.666280
$700$	−4.56155	−0.172410
$701$	38.6847	1.46110	0.730550	−	0.682860i	$-0.239264\pi$
$701$	38.6847	1.46110	0.730550	+	0.682860i	$0.239264\pi$
$702$	2.87689	0.108581
$703$	1.75379	0.0661454
$704$	1.43845	0.0542135
$705$	−3.12311	−0.117623
$706$	76.8466	2.89216
$707$	−4.24621	−0.159695
$708$	−29.3693	−1.10377
$709$	−22.1922	−0.833447	−0.416723	−	0.909033i	$-0.636822\pi$
$709$	−22.1922	−0.833447	−0.416723	+	0.909033i	$0.636822\pi$
$710$	8.00000	0.300235
$711$	6.24621	0.234251
$712$	96.3542	3.61102
$713$	−17.3693	−0.650486
$714$	9.12311	0.341424
$715$	1.12311	0.0420018
$716$	24.4924	0.915325
$717$	−7.31534	−0.273196
$718$	42.7386	1.59499
$719$	−46.5464	−1.73589	−0.867944	−	0.496662i	$-0.834559\pi$
$719$	−46.5464	−1.73589	−0.867944	+	0.496662i	$0.834559\pi$
$720$	7.68466	0.286390
$721$	8.68466	0.323434
$722$	42.4233	1.57883
$723$	−16.2462	−0.604203
$724$	−17.1231	−0.636375
$725$	−10.6847	−0.396818
$726$	2.56155	0.0950681
$727$	18.4384	0.683844	0.341922	−	0.939728i	$-0.388922\pi$
$727$	18.4384	0.683844	0.341922	+	0.939728i	$0.388922\pi$
$728$	7.36932	0.273125
$729$	1.00000	0.0370370
$730$	7.36932	0.272751
$731$	5.56155	0.205701
$732$	34.4924	1.27488
$733$	−35.7538	−1.32060	−0.660298	−	0.751004i	$-0.729570\pi$
$733$	−35.7538	−1.32060	−0.660298	+	0.751004i	$0.729570\pi$
$734$	−55.2311	−2.03862
$735$	−1.00000	−0.0368856
$736$	36.4924	1.34513
$737$	15.1231	0.557067
$738$	−5.12311	−0.188584
$739$	−29.3693	−1.08037	−0.540184	−	0.841547i	$-0.681645\pi$
$739$	−29.3693	−1.08037	−0.540184	+	0.841547i	$0.681645\pi$
$740$	5.12311	0.188329
$741$	−1.75379	−0.0644270
$742$	−3.36932	−0.123692
$743$	47.6155	1.74684	0.873422	−	0.486964i	$-0.161896\pi$
$743$	47.6155	1.74684	0.873422	+	0.486964i	$0.161896\pi$
$744$	20.4924	0.751289
$745$	−16.2462	−0.595215
$746$	−9.12311	−0.334021
$747$	−9.56155	−0.349839
$748$	−16.2462	−0.594020
$749$	5.36932	0.196191
$750$	2.56155	0.0935347
$751$	8.68466	0.316908	0.158454	−	0.987366i	$-0.449349\pi$
$751$	8.68466	0.316908	0.158454	+	0.987366i	$0.449349\pi$
$752$	24.0000	0.875190
$753$	8.49242	0.309481
$754$	30.7386	1.11944
$755$	−3.12311	−0.113661
$756$	4.56155	0.165902
$757$	34.4924	1.25365	0.626824	−	0.779161i	$-0.284354\pi$
$757$	34.4924	1.25365	0.626824	+	0.779161i	$0.284354\pi$
$758$	36.0000	1.30758
$759$	5.56155	0.201872
$760$	−10.2462	−0.371669
$761$	−20.2462	−0.733925	−0.366962	−	0.930236i	$-0.619602\pi$
$761$	−20.2462	−0.733925	−0.366962	+	0.930236i	$0.619602\pi$
$762$	−50.7386	−1.83807
$763$	14.4924	0.524661
$764$	0	0
$765$	−3.56155	−0.128768
$766$	−52.4924	−1.89663
$767$	7.23106	0.261098
$768$	27.0540	0.976226
$769$	47.1771	1.70125	0.850625	−	0.525774i	$-0.176224\pi$
$769$	47.1771	1.70125	0.850625	+	0.525774i	$0.176224\pi$
$770$	2.56155	0.0923120
$771$	15.3693	0.553512
$772$	−47.8617	−1.72258
$773$	24.7386	0.889787	0.444893	−	0.895584i	$-0.353242\pi$
$773$	24.7386	0.889787	0.444893	+	0.895584i	$0.353242\pi$
$774$	4.00000	0.143777
$775$	3.12311	0.112185
$776$	116.847	4.19455
$777$	1.12311	0.0402912
$778$	−91.8617	−3.29340
$779$	3.12311	0.111897
$780$	−5.12311	−0.183437
$781$	−3.12311	−0.111754
$782$	−50.7386	−1.81441
$783$	10.6847	0.381839
$784$	7.68466	0.274452
$785$	−15.5616	−0.555416
$786$	10.2462	0.365470
$787$	0.492423	0.0175530	0.00877648	−	0.999961i	$-0.497206\pi$
$787$	0.492423	0.0175530	0.00877648	+	0.999961i	$0.497206\pi$
$788$	−67.8617	−2.41747
$789$	1.75379	0.0624365
$790$	−16.0000	−0.569254
$791$	−4.43845	−0.157813
$792$	−6.56155	−0.233155
$793$	−8.49242	−0.301575
$794$	−35.8617	−1.27269
$795$	1.31534	0.0466504
$796$	−56.9848	−2.01977
$797$	−36.7386	−1.30135	−0.650675	−	0.759357i	$-0.725514\pi$
$797$	−36.7386	−1.30135	−0.650675	+	0.759357i	$0.725514\pi$
$798$	−4.00000	−0.141598
$799$	−11.1231	−0.393507
$800$	−6.56155	−0.231986
$801$	−14.6847	−0.518857
$802$	3.86174	0.136363
$803$	−2.87689	−0.101523
$804$	−68.9848	−2.43291
$805$	5.56155	0.196019
$806$	−8.98485	−0.316478
$807$	10.6847	0.376118
$808$	−27.8617	−0.980173
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	−2.56155	−0.0900038
$811$	−4.00000	−0.140459	−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000	−0.140459	−0.0702295	+	0.997531i	$0.522373\pi$
$812$	48.7386	1.71039
$813$	−14.9309	−0.523648
$814$	−2.87689	−0.100835
$815$	20.0000	0.700569
$816$	27.3693	0.958118
$817$	−2.43845	−0.0853105
$818$	−21.1231	−0.738552
$819$	−1.12311	−0.0392445
$820$	9.12311	0.318593
$821$	−32.5464	−1.13588	−0.567939	−	0.823071i	$-0.692259\pi$
$821$	−32.5464	−1.13588	−0.567939	+	0.823071i	$0.692259\pi$
$822$	25.6155	0.893444
$823$	26.7386	0.932050	0.466025	−	0.884772i	$-0.345686\pi$
$823$	26.7386	0.932050	0.466025	+	0.884772i	$0.345686\pi$
$824$	56.9848	1.98516
$825$	−1.00000	−0.0348155
$826$	16.4924	0.573845
$827$	46.7386	1.62526	0.812631	−	0.582779i	$-0.198035\pi$
$827$	46.7386	1.62526	0.812631	+	0.582779i	$0.198035\pi$
$828$	−25.3693	−0.881645
$829$	−49.2311	−1.70987	−0.854933	−	0.518739i	$-0.826402\pi$
$829$	−49.2311	−1.70987	−0.854933	+	0.518739i	$0.826402\pi$
$830$	24.4924	0.850144
$831$	−24.7386	−0.858174
$832$	1.61553	0.0560084
$833$	−3.56155	−0.123400
$834$	−51.2311	−1.77399
$835$	−14.2462	−0.493010
$836$	7.12311	0.246358
$837$	−3.12311	−0.107950
$838$	−81.4773	−2.81459
$839$	27.4233	0.946757	0.473379	−	0.880859i	$-0.343034\pi$
$839$	27.4233	0.946757	0.473379	+	0.880859i	$0.343034\pi$
$840$	−6.56155	−0.226395
$841$	85.1619	2.93662
$842$	38.8769	1.33979
$843$	18.4924	0.636913
$844$	97.4773	3.35531
$845$	−11.7386	−0.403821
$846$	−8.00000	−0.275046
$847$	−1.00000	−0.0343604
$848$	−10.1080	−0.347108
$849$	10.2462	0.351649
$850$	9.12311	0.312920
$851$	−6.24621	−0.214117
$852$	14.2462	0.488067
$853$	−30.4924	−1.04404	−0.522020	−	0.852933i	$-0.674821\pi$
$853$	−30.4924	−1.04404	−0.522020	+	0.852933i	$0.674821\pi$
$854$	−19.3693	−0.662804
$855$	1.56155	0.0534040
$856$	35.2311	1.20417
$857$	46.4924	1.58815	0.794075	−	0.607819i	$-0.207955\pi$
$857$	46.4924	1.58815	0.794075	+	0.607819i	$0.207955\pi$
$858$	2.87689	0.0982156
$859$	−32.8769	−1.12175	−0.560873	−	0.827902i	$-0.689534\pi$
$859$	−32.8769	−1.12175	−0.560873	+	0.827902i	$0.689534\pi$
$860$	−7.12311	−0.242896
$861$	2.00000	0.0681598
$862$	−88.9848	−3.03084
$863$	−38.5464	−1.31213	−0.656067	−	0.754702i	$-0.727781\pi$
$863$	−38.5464	−1.31213	−0.656067	+	0.754702i	$0.727781\pi$
$864$	6.56155	0.223229
$865$	12.2462	0.416384
$866$	−94.1080	−3.19792
$867$	4.31534	0.146557
$868$	−14.2462	−0.483548
$869$	6.24621	0.211888
$870$	−27.3693	−0.927907
$871$	16.9848	0.575510
$872$	95.0928	3.22025
$873$	−17.8078	−0.602701
$874$	22.2462	0.752489
$875$	−1.00000	−0.0338062
$876$	13.1231	0.443389
$877$	31.6695	1.06940	0.534702	−	0.845041i	$-0.320424\pi$
$877$	31.6695	1.06940	0.534702	+	0.845041i	$0.320424\pi$
$878$	17.7538	0.599161
$879$	−19.1771	−0.646827
$880$	7.68466	0.259050
$881$	3.06913	0.103402	0.0517008	−	0.998663i	$-0.483536\pi$
$881$	3.06913	0.103402	0.0517008	+	0.998663i	$0.483536\pi$
$882$	−2.56155	−0.0862520
$883$	−44.0000	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$884$	−18.2462	−0.613686
$885$	−6.43845	−0.216426
$886$	−78.7386	−2.64528
$887$	−37.5616	−1.26119	−0.630597	−	0.776111i	$-0.717190\pi$
$887$	−37.5616	−1.26119	−0.630597	+	0.776111i	$0.717190\pi$
$888$	7.36932	0.247298
$889$	19.8078	0.664331
$890$	37.6155	1.26088
$891$	1.00000	0.0335013
$892$	47.6155	1.59429
$893$	4.87689	0.163199
$894$	−41.6155	−1.39183
$895$	5.36932	0.179476
$896$	−9.43845	−0.315316
$897$	6.24621	0.208555
$898$	−5.12311	−0.170960
$899$	−33.3693	−1.11293
$900$	4.56155	0.152052
$901$	4.68466	0.156069
$902$	−5.12311	−0.170581
$903$	−1.56155	−0.0519652
$904$	−29.1231	−0.968620
$905$	−3.75379	−0.124780
$906$	−8.00000	−0.265782
$907$	−41.4773	−1.37723	−0.688615	−	0.725127i	$-0.741781\pi$
$907$	−41.4773	−1.37723	−0.688615	+	0.725127i	$0.741781\pi$
$908$	13.3693	0.443676
$909$	4.24621	0.140838
$910$	2.87689	0.0953681
$911$	−12.4924	−0.413892	−0.206946	−	0.978352i	$-0.566353\pi$
$911$	−12.4924	−0.413892	−0.206946	+	0.978352i	$0.566353\pi$
$912$	−12.0000	−0.397360
$913$	−9.56155	−0.316441
$914$	78.6004	2.59987
$915$	7.56155	0.249977
$916$	−102.600	−3.39001
$917$	−4.00000	−0.132092
$918$	−9.12311	−0.301107
$919$	37.8617	1.24894	0.624472	−	0.781047i	$-0.285314\pi$
$919$	37.8617	1.24894	0.624472	+	0.781047i	$0.285314\pi$
$920$	36.4924	1.20312
$921$	13.3693	0.440534
$922$	−40.3542	−1.32899
$923$	−3.50758	−0.115453
$924$	4.56155	0.150064
$925$	1.12311	0.0369275
$926$	76.4924	2.51370
$927$	−8.68466	−0.285242
$928$	70.1080	2.30141
$929$	42.9848	1.41029	0.705144	−	0.709065i	$-0.250883\pi$
$929$	42.9848	1.41029	0.705144	+	0.709065i	$0.250883\pi$
$930$	8.00000	0.262330
$931$	1.56155	0.0511778
$932$	80.3542	2.63209
$933$	16.0000	0.523816
$934$	42.2462	1.38234
$935$	−3.56155	−0.116475
$936$	−7.36932	−0.240874
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	38.7386	1.26486
$939$	14.6847	0.479216
$940$	14.2462	0.464660
$941$	−33.6155	−1.09583	−0.547917	−	0.836532i	$-0.684579\pi$
$941$	−33.6155	−1.09583	−0.547917	+	0.836532i	$0.684579\pi$
$942$	−39.8617	−1.29877
$943$	−11.1231	−0.362218
$944$	49.4773	1.61035
$945$	1.00000	0.0325300
$946$	4.00000	0.130051
$947$	−6.05398	−0.196728	−0.0983639	−	0.995151i	$-0.531361\pi$
$947$	−6.05398	−0.196728	−0.0983639	+	0.995151i	$0.531361\pi$
$948$	−28.4924	−0.925391
$949$	−3.23106	−0.104885
$950$	−4.00000	−0.129777
$951$	−10.4924	−0.340240
$952$	−23.3693	−0.757404
$953$	32.2462	1.04456	0.522279	−	0.852775i	$-0.325082\pi$
$953$	32.2462	1.04456	0.522279	+	0.852775i	$0.325082\pi$
$954$	3.36932	0.109086
$955$	0	0
$956$	33.3693	1.07924
$957$	10.6847	0.345386
$958$	8.98485	0.290287
$959$	−10.0000	−0.322917
$960$	−1.43845	−0.0464257
$961$	−21.2462	−0.685362
$962$	−3.23106	−0.104173
$963$	−5.36932	−0.173024
$964$	74.1080	2.38686
$965$	−10.4924	−0.337763
$966$	14.2462	0.458364
$967$	26.4384	0.850203	0.425102	−	0.905146i	$-0.360238\pi$
$967$	26.4384	0.850203	0.425102	+	0.905146i	$0.360238\pi$
$968$	−6.56155	−0.210896
$969$	5.56155	0.178663
$970$	45.6155	1.46463
$971$	−15.8078	−0.507295	−0.253648	−	0.967297i	$-0.581630\pi$
$971$	−15.8078	−0.507295	−0.253648	+	0.967297i	$0.581630\pi$
$972$	−4.56155	−0.146312
$973$	20.0000	0.641171
$974$	−80.9848	−2.59492
$975$	−1.12311	−0.0359682
$976$	−58.1080	−1.85999
$977$	39.1771	1.25339	0.626693	−	0.779266i	$-0.284408\pi$
$977$	39.1771	1.25339	0.626693	+	0.779266i	$0.284408\pi$
$978$	51.2311	1.63819
$979$	−14.6847	−0.469324
$980$	4.56155	0.145713
$981$	−14.4924	−0.462707
$982$	52.0000	1.65939
$983$	8.38447	0.267423	0.133712	−	0.991020i	$-0.457310\pi$
$983$	8.38447	0.267423	0.133712	+	0.991020i	$0.457310\pi$
$984$	13.1231	0.418349
$985$	−14.8769	−0.474017
$986$	−97.4773	−3.10431
$987$	3.12311	0.0994095
$988$	8.00000	0.254514
$989$	8.68466	0.276156
$990$	−2.56155	−0.0814115
$991$	61.5616	1.95557	0.977784	−	0.209617i	$-0.0672217\pi$
$991$	61.5616	1.95557	0.977784	+	0.209617i	$0.0672217\pi$
$992$	−20.4924	−0.650635
$993$	11.3153	0.359082
$994$	−8.00000	−0.253745
$995$	−12.4924	−0.396036
$996$	43.6155	1.38201
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	−76.9848	−2.43691
$999$	−1.12311	−0.0355335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.o.1.1	✓	2
3.2	odd	2		3465.2.a.z.1.2		2
5.4	even	2		5775.2.a.bm.1.2		2
7.6	odd	2		8085.2.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.o.1.1	✓	2	1.1	even	1	trivial
3465.2.a.z.1.2		2	3.2	odd	2
5775.2.a.bm.1.2		2	5.4	even	2
8085.2.a.bb.1.1		2	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)

\(f(q)\)	\(=\)	\(q-2.56155 q^{2} -1.00000 q^{3} +4.56155 q^{4} +1.00000 q^{5} +2.56155 q^{6} -1.00000 q^{7} -6.56155 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.56155 q^{2} -1.00000 q^{3} +4.56155 q^{4} +1.00000 q^{5} +2.56155 q^{6} -1.00000 q^{7} -6.56155 q^{8} +1.00000 q^{9} -2.56155 q^{10} +1.00000 q^{11} -4.56155 q^{12} +1.12311 q^{13} +2.56155 q^{14} -1.00000 q^{15} +7.68466 q^{16} -3.56155 q^{17} -2.56155 q^{18} +1.56155 q^{19} +4.56155 q^{20} +1.00000 q^{21} -2.56155 q^{22} -5.56155 q^{23} +6.56155 q^{24} +1.00000 q^{25} -2.87689 q^{26} -1.00000 q^{27} -4.56155 q^{28} -10.6847 q^{29} +2.56155 q^{30} +3.12311 q^{31} -6.56155 q^{32} -1.00000 q^{33} +9.12311 q^{34} -1.00000 q^{35} +4.56155 q^{36} +1.12311 q^{37} -4.00000 q^{38} -1.12311 q^{39} -6.56155 q^{40} +2.00000 q^{41} -2.56155 q^{42} -1.56155 q^{43} +4.56155 q^{44} +1.00000 q^{45} +14.2462 q^{46} +3.12311 q^{47} -7.68466 q^{48} +1.00000 q^{49} -2.56155 q^{50} +3.56155 q^{51} +5.12311 q^{52} -1.31534 q^{53} +2.56155 q^{54} +1.00000 q^{55} +6.56155 q^{56} -1.56155 q^{57} +27.3693 q^{58} +6.43845 q^{59} -4.56155 q^{60} -7.56155 q^{61} -8.00000 q^{62} -1.00000 q^{63} +1.43845 q^{64} +1.12311 q^{65} +2.56155 q^{66} +15.1231 q^{67} -16.2462 q^{68} +5.56155 q^{69} +2.56155 q^{70} -3.12311 q^{71} -6.56155 q^{72} -2.87689 q^{73} -2.87689 q^{74} -1.00000 q^{75} +7.12311 q^{76} -1.00000 q^{77} +2.87689 q^{78} +6.24621 q^{79} +7.68466 q^{80} +1.00000 q^{81} -5.12311 q^{82} -9.56155 q^{83} +4.56155 q^{84} -3.56155 q^{85} +4.00000 q^{86} +10.6847 q^{87} -6.56155 q^{88} -14.6847 q^{89} -2.56155 q^{90} -1.12311 q^{91} -25.3693 q^{92} -3.12311 q^{93} -8.00000 q^{94} +1.56155 q^{95} +6.56155 q^{96} -17.8078 q^{97} -2.56155 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} + 5 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 + 5 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} + 5 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 2 q^{11} - 5 q^{12} - 6 q^{13} + q^{14} - 2 q^{15} + 3 q^{16} - 3 q^{17} - q^{18} - q^{19} + 5 q^{20} + 2 q^{21} - q^{22} - 7 q^{23} + 9 q^{24} + 2 q^{25} - 14 q^{26} - 2 q^{27} - 5 q^{28} - 9 q^{29} + q^{30} - 2 q^{31} - 9 q^{32} - 2 q^{33} + 10 q^{34} - 2 q^{35} + 5 q^{36} - 6 q^{37} - 8 q^{38} + 6 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + q^{43} + 5 q^{44} + 2 q^{45} + 12 q^{46} - 2 q^{47} - 3 q^{48} + 2 q^{49} - q^{50} + 3 q^{51} + 2 q^{52} - 15 q^{53} + q^{54} + 2 q^{55} + 9 q^{56} + q^{57} + 30 q^{58} + 17 q^{59} - 5 q^{60} - 11 q^{61} - 16 q^{62} - 2 q^{63} + 7 q^{64} - 6 q^{65} + q^{66} + 22 q^{67} - 16 q^{68} + 7 q^{69} + q^{70} + 2 q^{71} - 9 q^{72} - 14 q^{73} - 14 q^{74} - 2 q^{75} + 6 q^{76} - 2 q^{77} + 14 q^{78} - 4 q^{79} + 3 q^{80} + 2 q^{81} - 2 q^{82} - 15 q^{83} + 5 q^{84} - 3 q^{85} + 8 q^{86} + 9 q^{87} - 9 q^{88} - 17 q^{89} - q^{90} + 6 q^{91} - 26 q^{92} + 2 q^{93} - 16 q^{94} - q^{95} + 9 q^{96} - 15 q^{97} - q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 + 5 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9 - q^10 + 2 * q^11 - 5 * q^12 - 6 * q^13 + q^14 - 2 * q^15 + 3 * q^16 - 3 * q^17 - q^18 - q^19 + 5 * q^20 + 2 * q^21 - q^22 - 7 * q^23 + 9 * q^24 + 2 * q^25 - 14 * q^26 - 2 * q^27 - 5 * q^28 - 9 * q^29 + q^30 - 2 * q^31 - 9 * q^32 - 2 * q^33 + 10 * q^34 - 2 * q^35 + 5 * q^36 - 6 * q^37 - 8 * q^38 + 6 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + q^43 + 5 * q^44 + 2 * q^45 + 12 * q^46 - 2 * q^47 - 3 * q^48 + 2 * q^49 - q^50 + 3 * q^51 + 2 * q^52 - 15 * q^53 + q^54 + 2 * q^55 + 9 * q^56 + q^57 + 30 * q^58 + 17 * q^59 - 5 * q^60 - 11 * q^61 - 16 * q^62 - 2 * q^63 + 7 * q^64 - 6 * q^65 + q^66 + 22 * q^67 - 16 * q^68 + 7 * q^69 + q^70 + 2 * q^71 - 9 * q^72 - 14 * q^73 - 14 * q^74 - 2 * q^75 + 6 * q^76 - 2 * q^77 + 14 * q^78 - 4 * q^79 + 3 * q^80 + 2 * q^81 - 2 * q^82 - 15 * q^83 + 5 * q^84 - 3 * q^85 + 8 * q^86 + 9 * q^87 - 9 * q^88 - 17 * q^89 - q^90 + 6 * q^91 - 26 * q^92 + 2 * q^93 - 16 * q^94 - q^95 + 9 * q^96 - 15 * q^97 - q^98 + 2 * q^99

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