LMFDB - Embedded newform 4006.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.941592 q^{3} +1.00000 q^{4} -0.129713 q^{5} +0.941592 q^{6} +0.350515 q^{7} -1.00000 q^{8} -2.11340 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.941592 q^{3} +1.00000 q^{4} -0.129713 q^{5} +0.941592 q^{6} +0.350515 q^{7} -1.00000 q^{8} -2.11340 q^{9} +0.129713 q^{10} +3.66879 q^{11} -0.941592 q^{12} -0.342580 q^{13} -0.350515 q^{14} +0.122137 q^{15} +1.00000 q^{16} -0.324847 q^{17} +2.11340 q^{18} -0.916569 q^{19} -0.129713 q^{20} -0.330042 q^{21} -3.66879 q^{22} +1.25046 q^{23} +0.941592 q^{24} -4.98317 q^{25} +0.342580 q^{26} +4.81474 q^{27} +0.350515 q^{28} +2.88923 q^{29} -0.122137 q^{30} -8.36762 q^{31} -1.00000 q^{32} -3.45450 q^{33} +0.324847 q^{34} -0.0454664 q^{35} -2.11340 q^{36} +10.3336 q^{37} +0.916569 q^{38} +0.322571 q^{39} +0.129713 q^{40} -1.92216 q^{41} +0.330042 q^{42} -8.00424 q^{43} +3.66879 q^{44} +0.274136 q^{45} -1.25046 q^{46} -2.84720 q^{47} -0.941592 q^{48} -6.87714 q^{49} +4.98317 q^{50} +0.305874 q^{51} -0.342580 q^{52} +7.31739 q^{53} -4.81474 q^{54} -0.475890 q^{55} -0.350515 q^{56} +0.863034 q^{57} -2.88923 q^{58} +3.01002 q^{59} +0.122137 q^{60} +10.1935 q^{61} +8.36762 q^{62} -0.740780 q^{63} +1.00000 q^{64} +0.0444371 q^{65} +3.45450 q^{66} +2.69312 q^{67} -0.324847 q^{68} -1.17742 q^{69} +0.0454664 q^{70} +5.69491 q^{71} +2.11340 q^{72} -10.4653 q^{73} -10.3336 q^{74} +4.69212 q^{75} -0.916569 q^{76} +1.28597 q^{77} -0.322571 q^{78} +1.47461 q^{79} -0.129713 q^{80} +1.80669 q^{81} +1.92216 q^{82} -10.6060 q^{83} -0.330042 q^{84} +0.0421370 q^{85} +8.00424 q^{86} -2.72047 q^{87} -3.66879 q^{88} -17.5017 q^{89} -0.274136 q^{90} -0.120080 q^{91} +1.25046 q^{92} +7.87888 q^{93} +2.84720 q^{94} +0.118891 q^{95} +0.941592 q^{96} -15.5913 q^{97} +6.87714 q^{98} -7.75363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.941592	−0.543629	−0.271814	−	0.962350i	$-0.587624\pi$
$3$	−0.941592	−0.543629	−0.271814	+	0.962350i	$0.587624\pi$
$4$	1.00000	0.500000
$5$	−0.129713	−0.0580095	−0.0290047	−	0.999579i	$-0.509234\pi$
$5$	−0.129713	−0.0580095	−0.0290047	+	0.999579i	$0.509234\pi$
$6$	0.941592	0.384403
$7$	0.350515	0.132482	0.0662411	−	0.997804i	$-0.478899\pi$
$7$	0.350515	0.132482	0.0662411	+	0.997804i	$0.478899\pi$
$8$	−1.00000	−0.353553
$9$	−2.11340	−0.704468
$10$	0.129713	0.0410189
$11$	3.66879	1.10618	0.553091	−	0.833121i	$-0.313448\pi$
$11$	3.66879	1.10618	0.553091	+	0.833121i	$0.313448\pi$
$12$	−0.941592	−0.271814
$13$	−0.342580	−0.0950146	−0.0475073	−	0.998871i	$-0.515128\pi$
$13$	−0.342580	−0.0950146	−0.0475073	+	0.998871i	$0.515128\pi$
$14$	−0.350515	−0.0936791
$15$	0.122137	0.0315356
$16$	1.00000	0.250000
$17$	−0.324847	−0.0787871	−0.0393935	−	0.999224i	$-0.512543\pi$
$17$	−0.324847	−0.0787871	−0.0393935	+	0.999224i	$0.512543\pi$
$18$	2.11340	0.498134
$19$	−0.916569	−0.210275	−0.105138	−	0.994458i	$-0.533528\pi$
$19$	−0.916569	−0.210275	−0.105138	+	0.994458i	$0.533528\pi$
$20$	−0.129713	−0.0290047
$21$	−0.330042	−0.0720212
$22$	−3.66879	−0.782189
$23$	1.25046	0.260739	0.130369	−	0.991466i	$-0.458384\pi$
$23$	1.25046	0.260739	0.130369	+	0.991466i	$0.458384\pi$
$24$	0.941592	0.192202
$25$	−4.98317	−0.996635
$26$	0.342580	0.0671855
$27$	4.81474	0.926598
$28$	0.350515	0.0662411
$29$	2.88923	0.536516	0.268258	−	0.963347i	$-0.413552\pi$
$29$	2.88923	0.536516	0.268258	+	0.963347i	$0.413552\pi$
$30$	−0.122137	−0.0222990
$31$	−8.36762	−1.50287	−0.751434	−	0.659808i	$-0.770638\pi$
$31$	−8.36762	−1.50287	−0.751434	+	0.659808i	$0.770638\pi$
$32$	−1.00000	−0.176777
$33$	−3.45450	−0.601352
$34$	0.324847	0.0557109
$35$	−0.0454664	−0.00768523
$36$	−2.11340	−0.352234
$37$	10.3336	1.69884	0.849419	−	0.527719i	$-0.176953\pi$
$37$	10.3336	1.69884	0.849419	+	0.527719i	$0.176953\pi$
$38$	0.916569	0.148687
$39$	0.322571	0.0516527
$40$	0.129713	0.0205094
$41$	−1.92216	−0.300190	−0.150095	−	0.988672i	$-0.547958\pi$
$41$	−1.92216	−0.300190	−0.150095	+	0.988672i	$0.547958\pi$
$42$	0.330042	0.0509266
$43$	−8.00424	−1.22063	−0.610317	−	0.792157i	$-0.708958\pi$
$43$	−8.00424	−1.22063	−0.610317	+	0.792157i	$0.708958\pi$
$44$	3.66879	0.553091
$45$	0.274136	0.0408658
$46$	−1.25046	−0.184370
$47$	−2.84720	−0.415306	−0.207653	−	0.978203i	$-0.566583\pi$
$47$	−2.84720	−0.415306	−0.207653	+	0.978203i	$0.566583\pi$
$48$	−0.941592	−0.135907
$49$	−6.87714	−0.982448
$50$	4.98317	0.704727
$51$	0.305874	0.0428309
$52$	−0.342580	−0.0475073
$53$	7.31739	1.00512	0.502560	−	0.864542i	$-0.332391\pi$
$53$	7.31739	1.00512	0.502560	+	0.864542i	$0.332391\pi$
$54$	−4.81474	−0.655203
$55$	−0.475890	−0.0641690
$56$	−0.350515	−0.0468396
$57$	0.863034	0.114312
$58$	−2.88923	−0.379374
$59$	3.01002	0.391871	0.195935	−	0.980617i	$-0.437226\pi$
$59$	3.01002	0.391871	0.195935	+	0.980617i	$0.437226\pi$
$60$	0.122137	0.0157678
$61$	10.1935	1.30515	0.652574	−	0.757725i	$-0.273689\pi$
$61$	10.1935	1.30515	0.652574	+	0.757725i	$0.273689\pi$
$62$	8.36762	1.06269
$63$	−0.740780	−0.0933295
$64$	1.00000	0.125000
$65$	0.0444371	0.00551175
$66$	3.45450	0.425220
$67$	2.69312	0.329017	0.164508	−	0.986376i	$-0.447396\pi$
$67$	2.69312	0.329017	0.164508	+	0.986376i	$0.447396\pi$
$68$	−0.324847	−0.0393935
$69$	−1.17742	−0.141745
$70$	0.0454664	0.00543428
$71$	5.69491	0.675862	0.337931	−	0.941171i	$-0.390273\pi$
$71$	5.69491	0.675862	0.337931	+	0.941171i	$0.390273\pi$
$72$	2.11340	0.249067
$73$	−10.4653	−1.22487	−0.612436	−	0.790520i	$-0.709810\pi$
$73$	−10.4653	−1.22487	−0.612436	+	0.790520i	$0.709810\pi$
$74$	−10.3336	−1.20126
$75$	4.69212	0.541799
$76$	−0.916569	−0.105138
$77$	1.28597	0.146549
$78$	−0.322571	−0.0365239
$79$	1.47461	0.165907	0.0829535	−	0.996553i	$-0.473565\pi$
$79$	1.47461	0.165907	0.0829535	+	0.996553i	$0.473565\pi$
$80$	−0.129713	−0.0145024
$81$	1.80669	0.200743
$82$	1.92216	0.212267
$83$	−10.6060	−1.16416	−0.582078	−	0.813133i	$-0.697760\pi$
$83$	−10.6060	−1.16416	−0.582078	+	0.813133i	$0.697760\pi$
$84$	−0.330042	−0.0360106
$85$	0.0421370	0.00457040
$86$	8.00424	0.863119
$87$	−2.72047	−0.291665
$88$	−3.66879	−0.391094
$89$	−17.5017	−1.85518	−0.927588	−	0.373604i	$-0.878122\pi$
$89$	−17.5017	−1.85518	−0.927588	+	0.373604i	$0.878122\pi$
$90$	−0.274136	−0.0288965
$91$	−0.120080	−0.0125878
$92$	1.25046	0.130369
$93$	7.87888	0.817002
$94$	2.84720	0.293666
$95$	0.118891	0.0121980
$96$	0.941592	0.0961009
$97$	−15.5913	−1.58306	−0.791530	−	0.611130i	$-0.790715\pi$
$97$	−15.5913	−1.58306	−0.791530	+	0.611130i	$0.790715\pi$
$98$	6.87714	0.694696
$99$	−7.75363	−0.779270
$100$	−4.98317	−0.498317
$101$	6.78412	0.675046	0.337523	−	0.941317i	$-0.390411\pi$
$101$	6.78412	0.675046	0.337523	+	0.941317i	$0.390411\pi$
$102$	−0.305874	−0.0302860
$103$	11.3369	1.11706	0.558528	−	0.829485i	$-0.311366\pi$
$103$	11.3369	1.11706	0.558528	+	0.829485i	$0.311366\pi$
$104$	0.342580	0.0335927
$105$	0.0428108	0.00417791
$106$	−7.31739	−0.710728
$107$	−11.4350	−1.10547	−0.552733	−	0.833358i	$-0.686415\pi$
$107$	−11.4350	−1.10547	−0.552733	+	0.833358i	$0.686415\pi$
$108$	4.81474	0.463299
$109$	18.1642	1.73982	0.869909	−	0.493212i	$-0.164177\pi$
$109$	18.1642	1.73982	0.869909	+	0.493212i	$0.164177\pi$
$110$	0.475890	0.0453743
$111$	−9.73007	−0.923537
$112$	0.350515	0.0331206
$113$	−1.75797	−0.165376	−0.0826881	−	0.996575i	$-0.526351\pi$
$113$	−1.75797	−0.165376	−0.0826881	+	0.996575i	$0.526351\pi$
$114$	−0.863034	−0.0808306
$115$	−0.162201	−0.0151253
$116$	2.88923	0.268258
$117$	0.724010	0.0669348
$118$	−3.01002	−0.277094
$119$	−0.113864	−0.0104379
$120$	−0.122137	−0.0111495
$121$	2.46002	0.223638
$122$	−10.1935	−0.922879
$123$	1.80989	0.163192
$124$	−8.36762	−0.751434
$125$	1.29495	0.115824
$126$	0.740780	0.0659939
$127$	19.0525	1.69064	0.845320	−	0.534261i	$-0.179410\pi$
$127$	19.0525	1.69064	0.845320	+	0.534261i	$0.179410\pi$
$128$	−1.00000	−0.0883883
$129$	7.53673	0.663572
$130$	−0.0444371	−0.00389739
$131$	−12.1222	−1.05912	−0.529562	−	0.848271i	$-0.677644\pi$
$131$	−12.1222	−1.05912	−0.529562	+	0.848271i	$0.677644\pi$
$132$	−3.45450	−0.300676
$133$	−0.321271	−0.0278578
$134$	−2.69312	−0.232650
$135$	−0.624535	−0.0537514
$136$	0.324847	0.0278554
$137$	−9.76659	−0.834416	−0.417208	−	0.908811i	$-0.636991\pi$
$137$	−9.76659	−0.834416	−0.417208	+	0.908811i	$0.636991\pi$
$138$	1.17742	0.100229
$139$	−0.211615	−0.0179490	−0.00897448	−	0.999960i	$-0.502857\pi$
$139$	−0.211615	−0.0179490	−0.00897448	+	0.999960i	$0.502857\pi$
$140$	−0.0454664	−0.00384261
$141$	2.68090	0.225772
$142$	−5.69491	−0.477907
$143$	−1.25685	−0.105103
$144$	−2.11340	−0.176117
$145$	−0.374771	−0.0311230
$146$	10.4653	0.866116
$147$	6.47546	0.534087
$148$	10.3336	0.849419
$149$	−0.581612	−0.0476475	−0.0238238	−	0.999716i	$-0.507584\pi$
$149$	−0.581612	−0.0476475	−0.0238238	+	0.999716i	$0.507584\pi$
$150$	−4.69212	−0.383110
$151$	−2.43880	−0.198466	−0.0992332	−	0.995064i	$-0.531639\pi$
$151$	−2.43880	−0.198466	−0.0992332	+	0.995064i	$0.531639\pi$
$152$	0.916569	0.0743436
$153$	0.686534	0.0555030
$154$	−1.28597	−0.103626
$155$	1.08539	0.0871806
$156$	0.322571	0.0258263
$157$	20.0875	1.60315	0.801577	−	0.597891i	$-0.203994\pi$
$157$	20.0875	1.60315	0.801577	+	0.597891i	$0.203994\pi$
$158$	−1.47461	−0.117314
$159$	−6.89000	−0.546412
$160$	0.129713	0.0102547
$161$	0.438304	0.0345432
$162$	−1.80669	−0.141947
$163$	6.78425	0.531384	0.265692	−	0.964058i	$-0.414400\pi$
$163$	6.78425	0.531384	0.265692	+	0.964058i	$0.414400\pi$
$164$	−1.92216	−0.150095
$165$	0.448095	0.0348841
$166$	10.6060	0.823182
$167$	−18.7317	−1.44950	−0.724752	−	0.689009i	$-0.758046\pi$
$167$	−18.7317	−1.44950	−0.724752	+	0.689009i	$0.758046\pi$
$168$	0.330042	0.0254633
$169$	−12.8826	−0.990972
$170$	−0.0421370	−0.00323176
$171$	1.93708	0.148132
$172$	−8.00424	−0.610317
$173$	−25.2897	−1.92274	−0.961370	−	0.275258i	$-0.911237\pi$
$173$	−25.2897	−1.92274	−0.961370	+	0.275258i	$0.911237\pi$
$174$	2.72047	0.206239
$175$	−1.74668	−0.132036
$176$	3.66879	0.276545
$177$	−2.83421	−0.213032
$178$	17.5017	1.31181
$179$	−14.2700	−1.06659	−0.533296	−	0.845929i	$-0.679047\pi$
$179$	−14.2700	−1.06659	−0.533296	+	0.845929i	$0.679047\pi$
$180$	0.274136	0.0204329
$181$	−1.28838	−0.0957645	−0.0478823	−	0.998853i	$-0.515247\pi$
$181$	−1.28838	−0.0957645	−0.0478823	+	0.998853i	$0.515247\pi$
$182$	0.120080	0.00890089
$183$	−9.59815	−0.709516
$184$	−1.25046	−0.0921850
$185$	−1.34041	−0.0985487
$186$	−7.87888	−0.577708
$187$	−1.19180	−0.0871528
$188$	−2.84720	−0.207653
$189$	1.68764	0.122758
$190$	−0.118891	−0.00862526
$191$	−7.65560	−0.553940	−0.276970	−	0.960879i	$-0.589330\pi$
$191$	−7.65560	−0.553940	−0.276970	+	0.960879i	$0.589330\pi$
$192$	−0.941592	−0.0679536
$193$	15.6131	1.12386	0.561930	−	0.827185i	$-0.310059\pi$
$193$	15.6131	1.12386	0.561930	+	0.827185i	$0.310059\pi$
$194$	15.5913	1.11939
$195$	−0.0418417	−0.00299634
$196$	−6.87714	−0.491224
$197$	−2.44421	−0.174142	−0.0870712	−	0.996202i	$-0.527751\pi$
$197$	−2.44421	−0.174142	−0.0870712	+	0.996202i	$0.527751\pi$
$198$	7.75363	0.551027
$199$	−27.3011	−1.93532	−0.967661	−	0.252255i	$-0.918828\pi$
$199$	−27.3011	−1.93532	−0.967661	+	0.252255i	$0.918828\pi$
$200$	4.98317	0.352364
$201$	−2.53582	−0.178863
$202$	−6.78412	−0.477329
$203$	1.01272	0.0710788
$204$	0.305874	0.0214155
$205$	0.249329	0.0174139
$206$	−11.3369	−0.789878
$207$	−2.64272	−0.183682
$208$	−0.342580	−0.0237537
$209$	−3.36270	−0.232603
$210$	−0.0428108	−0.00295423
$211$	4.19124	0.288537	0.144269	−	0.989539i	$-0.453917\pi$
$211$	4.19124	0.288537	0.144269	+	0.989539i	$0.453917\pi$
$212$	7.31739	0.502560
$213$	−5.36229	−0.367418
$214$	11.4350	0.781683
$215$	1.03825	0.0708084
$216$	−4.81474	−0.327602
$217$	−2.93298	−0.199103
$218$	−18.1642	−1.23024
$219$	9.85406	0.665876
$220$	−0.475890	−0.0320845
$221$	0.111286	0.00748592
$222$	9.73007	0.653039
$223$	4.63209	0.310188	0.155094	−	0.987900i	$-0.450432\pi$
$223$	4.63209	0.310188	0.155094	+	0.987900i	$0.450432\pi$
$224$	−0.350515	−0.0234198
$225$	10.5315	0.702097
$226$	1.75797	0.116939
$227$	10.4114	0.691027	0.345513	−	0.938414i	$-0.387705\pi$
$227$	10.4114	0.691027	0.345513	+	0.938414i	$0.387705\pi$
$228$	0.863034	0.0571558
$229$	−8.95876	−0.592012	−0.296006	−	0.955186i	$-0.595655\pi$
$229$	−8.95876	−0.592012	−0.296006	+	0.955186i	$0.595655\pi$
$230$	0.162201	0.0106952
$231$	−1.21086	−0.0796685
$232$	−2.88923	−0.189687
$233$	21.0993	1.38226	0.691132	−	0.722729i	$-0.257113\pi$
$233$	21.0993	1.38226	0.691132	+	0.722729i	$0.257113\pi$
$234$	−0.724010	−0.0473300
$235$	0.369319	0.0240917
$236$	3.01002	0.195935
$237$	−1.38849	−0.0901918
$238$	0.113864	0.00738070
$239$	4.13040	0.267174	0.133587	−	0.991037i	$-0.457350\pi$
$239$	4.13040	0.267174	0.133587	+	0.991037i	$0.457350\pi$
$240$	0.122137	0.00788390
$241$	−13.0441	−0.840242	−0.420121	−	0.907468i	$-0.638012\pi$
$241$	−13.0441	−0.840242	−0.420121	+	0.907468i	$0.638012\pi$
$242$	−2.46002	−0.158136
$243$	−16.1454	−1.03573
$244$	10.1935	0.652574
$245$	0.892055	0.0569913
$246$	−1.80989	−0.115394
$247$	0.313998	0.0199792
$248$	8.36762	0.531344
$249$	9.98649	0.632868
$250$	−1.29495	−0.0818998
$251$	20.2778	1.27992	0.639962	−	0.768406i	$-0.278950\pi$
$251$	20.2778	1.27992	0.639962	+	0.768406i	$0.278950\pi$
$252$	−0.740780	−0.0466648
$253$	4.58767	0.288424
$254$	−19.0525	−1.19546
$255$	−0.0396759	−0.00248460
$256$	1.00000	0.0625000
$257$	−0.336181	−0.0209704	−0.0104852	−	0.999945i	$-0.503338\pi$
$257$	−0.336181	−0.0209704	−0.0104852	+	0.999945i	$0.503338\pi$
$258$	−7.53673	−0.469216
$259$	3.62209	0.225066
$260$	0.0444371	0.00275587
$261$	−6.10610	−0.377958
$262$	12.1222	0.748914
$263$	−24.0852	−1.48516	−0.742578	−	0.669759i	$-0.766397\pi$
$263$	−24.0852	−1.48516	−0.742578	+	0.669759i	$0.766397\pi$
$264$	3.45450	0.212610
$265$	−0.949161	−0.0583065
$266$	0.321271	0.0196984
$267$	16.4795	1.00853
$268$	2.69312	0.164508
$269$	−8.89648	−0.542428	−0.271214	−	0.962519i	$-0.587425\pi$
$269$	−8.89648	−0.542428	−0.271214	+	0.962519i	$0.587425\pi$
$270$	0.624535	0.0380080
$271$	−15.9456	−0.968624	−0.484312	−	0.874895i	$-0.660930\pi$
$271$	−15.9456	−0.968624	−0.484312	+	0.874895i	$0.660930\pi$
$272$	−0.324847	−0.0196968
$273$	0.113066	0.00684306
$274$	9.76659	0.590021
$275$	−18.2822	−1.10246
$276$	−1.17742	−0.0708725
$277$	−24.6530	−1.48125	−0.740626	−	0.671917i	$-0.765471\pi$
$277$	−24.6530	−1.48125	−0.740626	+	0.671917i	$0.765471\pi$
$278$	0.211615	0.0126918
$279$	17.6842	1.05872
$280$	0.0454664	0.00271714
$281$	−12.2409	−0.730233	−0.365116	−	0.930962i	$-0.618971\pi$
$281$	−12.2409	−0.730233	−0.365116	+	0.930962i	$0.618971\pi$
$282$	−2.68090	−0.159645
$283$	21.5413	1.28050	0.640249	−	0.768168i	$-0.278831\pi$
$283$	21.5413	1.28050	0.640249	+	0.768168i	$0.278831\pi$
$284$	5.69491	0.337931
$285$	−0.111947	−0.00663116
$286$	1.25685	0.0743193
$287$	−0.673745	−0.0397699
$288$	2.11340	0.124534
$289$	−16.8945	−0.993793
$290$	0.374771	0.0220073
$291$	14.6807	0.860597
$292$	−10.4653	−0.612436
$293$	−22.8468	−1.33473	−0.667363	−	0.744733i	$-0.732577\pi$
$293$	−22.8468	−1.33473	−0.667363	+	0.744733i	$0.732577\pi$
$294$	−6.47546	−0.377657
$295$	−0.390439	−0.0227322
$296$	−10.3336	−0.600630
$297$	17.6643	1.02499
$298$	0.581612	0.0336919
$299$	−0.428382	−0.0247740
$300$	4.69212	0.270900
$301$	−2.80561	−0.161712
$302$	2.43880	0.140337
$303$	−6.38788	−0.366974
$304$	−0.916569	−0.0525688
$305$	−1.32223	−0.0757109
$306$	−0.686534	−0.0392465
$307$	−9.56090	−0.545670	−0.272835	−	0.962061i	$-0.587961\pi$
$307$	−9.56090	−0.545670	−0.272835	+	0.962061i	$0.587961\pi$
$308$	1.28597	0.0732747
$309$	−10.6747	−0.607264
$310$	−1.08539	−0.0616460
$311$	−10.2196	−0.579501	−0.289750	−	0.957102i	$-0.593572\pi$
$311$	−10.2196	−0.579501	−0.289750	+	0.957102i	$0.593572\pi$
$312$	−0.322571	−0.0182620
$313$	−10.7607	−0.608229	−0.304114	−	0.952636i	$-0.598360\pi$
$313$	−10.7607	−0.608229	−0.304114	+	0.952636i	$0.598360\pi$
$314$	−20.0875	−1.13360
$315$	0.0960889	0.00541400
$316$	1.47461	0.0829535
$317$	14.7775	0.829985	0.414993	−	0.909825i	$-0.363784\pi$
$317$	14.7775	0.829985	0.414993	+	0.909825i	$0.363784\pi$
$318$	6.89000	0.386372
$319$	10.6000	0.593484
$320$	−0.129713	−0.00725118
$321$	10.7671	0.600963
$322$	−0.438304	−0.0244258
$323$	0.297745	0.0165670
$324$	1.80669	0.100372
$325$	1.70714	0.0946949
$326$	−6.78425	−0.375745
$327$	−17.1033	−0.945815
$328$	1.92216	0.106133
$329$	−0.997985	−0.0550207
$330$	−0.448095	−0.0246668
$331$	4.76669	0.262001	0.131000	−	0.991382i	$-0.458181\pi$
$331$	4.76669	0.262001	0.131000	+	0.991382i	$0.458181\pi$
$332$	−10.6060	−0.582078
$333$	−21.8391	−1.19678
$334$	18.7317	1.02495
$335$	−0.349333	−0.0190861
$336$	−0.330042	−0.0180053
$337$	−0.980382	−0.0534048	−0.0267024	−	0.999643i	$-0.508501\pi$
$337$	−0.980382	−0.0534048	−0.0267024	+	0.999643i	$0.508501\pi$
$338$	12.8826	0.700723
$339$	1.65529	0.0899033
$340$	0.0421370	0.00228520
$341$	−30.6990	−1.66245
$342$	−1.93708	−0.104745
$343$	−4.86415	−0.262639
$344$	8.00424	0.431560
$345$	0.152727	0.00822255
$346$	25.2897	1.35958
$347$	−23.2784	−1.24965	−0.624826	−	0.780764i	$-0.714830\pi$
$347$	−23.2784	−1.24965	−0.624826	+	0.780764i	$0.714830\pi$
$348$	−2.72047	−0.145833
$349$	5.88858	0.315208	0.157604	−	0.987502i	$-0.449623\pi$
$349$	5.88858	0.315208	0.157604	+	0.987502i	$0.449623\pi$
$350$	1.74668	0.0933639
$351$	−1.64943	−0.0880403
$352$	−3.66879	−0.195547
$353$	−17.0303	−0.906434	−0.453217	−	0.891400i	$-0.649724\pi$
$353$	−17.0303	−0.906434	−0.453217	+	0.891400i	$0.649724\pi$
$354$	2.83421	0.150636
$355$	−0.738705	−0.0392064
$356$	−17.5017	−0.927588
$357$	0.107213	0.00567434
$358$	14.2700	0.754195
$359$	−15.5151	−0.818855	−0.409428	−	0.912343i	$-0.634272\pi$
$359$	−15.5151	−0.818855	−0.409428	+	0.912343i	$0.634272\pi$
$360$	−0.274136	−0.0144482
$361$	−18.1599	−0.955784
$362$	1.28838	0.0677158
$363$	−2.31633	−0.121576
$364$	−0.120080	−0.00629388
$365$	1.35749	0.0710542
$366$	9.59815	0.501703
$367$	26.9568	1.40714	0.703568	−	0.710628i	$-0.251589\pi$
$367$	26.9568	1.40714	0.703568	+	0.710628i	$0.251589\pi$
$368$	1.25046	0.0651846
$369$	4.06229	0.211474
$370$	1.34041	0.0696845
$371$	2.56486	0.133161
$372$	7.87888	0.408501
$373$	−5.36389	−0.277732	−0.138866	−	0.990311i	$-0.544346\pi$
$373$	−5.36389	−0.277732	−0.138866	+	0.990311i	$0.544346\pi$
$374$	1.19180	0.0616263
$375$	−1.21931	−0.0629651
$376$	2.84720	0.146833
$377$	−0.989791	−0.0509768
$378$	−1.68764	−0.0868028
$379$	−13.8038	−0.709056	−0.354528	−	0.935045i	$-0.615358\pi$
$379$	−13.8038	−0.709056	−0.354528	+	0.935045i	$0.615358\pi$
$380$	0.118891	0.00609898
$381$	−17.9397	−0.919080
$382$	7.65560	0.391694
$383$	−23.4129	−1.19634	−0.598171	−	0.801369i	$-0.704105\pi$
$383$	−23.4129	−1.19634	−0.598171	+	0.801369i	$0.704105\pi$
$384$	0.941592	0.0480504
$385$	−0.166807	−0.00850126
$386$	−15.6131	−0.794688
$387$	16.9162	0.859898
$388$	−15.5913	−0.791530
$389$	−23.9313	−1.21336	−0.606682	−	0.794945i	$-0.707500\pi$
$389$	−23.9313	−1.21336	−0.606682	+	0.794945i	$0.707500\pi$
$390$	0.0418417	0.00211874
$391$	−0.406208	−0.0205428
$392$	6.87714	0.347348
$393$	11.4142	0.575770
$394$	2.44421	0.123137
$395$	−0.191277	−0.00962418
$396$	−7.75363	−0.389635
$397$	−4.43559	−0.222616	−0.111308	−	0.993786i	$-0.535504\pi$
$397$	−4.43559	−0.222616	−0.111308	+	0.993786i	$0.535504\pi$
$398$	27.3011	1.36848
$399$	0.302507	0.0151443
$400$	−4.98317	−0.249159
$401$	−6.81431	−0.340290	−0.170145	−	0.985419i	$-0.554424\pi$
$401$	−6.81431	−0.340290	−0.170145	+	0.985419i	$0.554424\pi$
$402$	2.53582	0.126475
$403$	2.86658	0.142794
$404$	6.78412	0.337523
$405$	−0.234351	−0.0116450
$406$	−1.01272	−0.0502603
$407$	37.9119	1.87922
$408$	−0.305874	−0.0151430
$409$	−24.3559	−1.20432	−0.602161	−	0.798375i	$-0.705693\pi$
$409$	−24.3559	−1.20432	−0.602161	+	0.798375i	$0.705693\pi$
$410$	−0.249329	−0.0123135
$411$	9.19615	0.453612
$412$	11.3369	0.558528
$413$	1.05506	0.0519159
$414$	2.64272	0.129883
$415$	1.37573	0.0675320
$416$	0.342580	0.0167964
$417$	0.199255	0.00975757
$418$	3.36270	0.164475
$419$	29.0451	1.41894	0.709472	−	0.704734i	$-0.248933\pi$
$419$	29.0451	1.41894	0.709472	+	0.704734i	$0.248933\pi$
$420$	0.0428108	0.00208895
$421$	−14.3006	−0.696968	−0.348484	−	0.937315i	$-0.613303\pi$
$421$	−14.3006	−0.696968	−0.348484	+	0.937315i	$0.613303\pi$
$422$	−4.19124	−0.204027
$423$	6.01727	0.292570
$424$	−7.31739	−0.355364
$425$	1.61877	0.0785219
$426$	5.36229	0.259804
$427$	3.57299	0.172909
$428$	−11.4350	−0.552733
$429$	1.18344	0.0571372
$430$	−1.03825	−0.0500691
$431$	−22.7210	−1.09443	−0.547217	−	0.836991i	$-0.684313\pi$
$431$	−22.7210	−1.09443	−0.547217	+	0.836991i	$0.684313\pi$
$432$	4.81474	0.231649
$433$	−35.0246	−1.68317	−0.841587	−	0.540121i	$-0.818378\pi$
$433$	−35.0246	−1.68317	−0.841587	+	0.540121i	$0.818378\pi$
$434$	2.93298	0.140787
$435$	0.352881	0.0169194
$436$	18.1642	0.869909
$437$	−1.14613	−0.0548269
$438$	−9.85406	−0.470845
$439$	3.41021	0.162761	0.0813803	−	0.996683i	$-0.474067\pi$
$439$	3.41021	0.162761	0.0813803	+	0.996683i	$0.474067\pi$
$440$	0.475890	0.0226872
$441$	14.5342	0.692103
$442$	−0.111286	−0.00529335
$443$	−2.49849	−0.118707	−0.0593535	−	0.998237i	$-0.518904\pi$
$443$	−2.49849	−0.118707	−0.0593535	+	0.998237i	$0.518904\pi$
$444$	−9.73007	−0.461768
$445$	2.27020	0.107618
$446$	−4.63209	−0.219336
$447$	0.547642	0.0259026
$448$	0.350515	0.0165603
$449$	−16.2151	−0.765237	−0.382619	−	0.923906i	$-0.624978\pi$
$449$	−16.2151	−0.765237	−0.382619	+	0.923906i	$0.624978\pi$
$450$	−10.5315	−0.496458
$451$	−7.05199	−0.332065
$452$	−1.75797	−0.0826881
$453$	2.29635	0.107892
$454$	−10.4114	−0.488630
$455$	0.0155759	0.000730209 0
$456$	−0.863034	−0.0404153
$457$	13.4972	0.631372	0.315686	−	0.948864i	$-0.397765\pi$
$457$	13.4972	0.631372	0.315686	+	0.948864i	$0.397765\pi$
$458$	8.95876	0.418615
$459$	−1.56406	−0.0730039
$460$	−0.162201	−0.00756265
$461$	−37.6469	−1.75339	−0.876696	−	0.481046i	$-0.840257\pi$
$461$	−37.6469	−1.75339	−0.876696	+	0.481046i	$0.840257\pi$
$462$	1.21086	0.0563341
$463$	31.4858	1.46327	0.731635	−	0.681697i	$-0.238758\pi$
$463$	31.4858	1.46327	0.731635	+	0.681697i	$0.238758\pi$
$464$	2.88923	0.134129
$465$	−1.02199	−0.0473939
$466$	−21.0993	−0.977408
$467$	6.12073	0.283233	0.141617	−	0.989922i	$-0.454770\pi$
$467$	6.12073	0.283233	0.141617	+	0.989922i	$0.454770\pi$
$468$	0.724010	0.0334674
$469$	0.943979	0.0435889
$470$	−0.369319	−0.0170354
$471$	−18.9142	−0.871521
$472$	−3.01002	−0.138547
$473$	−29.3659	−1.35024
$474$	1.38849	0.0637753
$475$	4.56742	0.209568
$476$	−0.113864	−0.00521895
$477$	−15.4646	−0.708075
$478$	−4.13040	−0.188920
$479$	17.8974	0.817752	0.408876	−	0.912590i	$-0.365921\pi$
$479$	17.8974	0.817752	0.408876	+	0.912590i	$0.365921\pi$
$480$	−0.122137	−0.00557476
$481$	−3.54010	−0.161414
$482$	13.0441	0.594141
$483$	−0.412704	−0.0187787
$484$	2.46002	0.111819
$485$	2.02240	0.0918325
$486$	16.1454	0.732370
$487$	−0.111862	−0.00506897	−0.00253448	−	0.999997i	$-0.500807\pi$
$487$	−0.111862	−0.00506897	−0.00253448	+	0.999997i	$0.500807\pi$
$488$	−10.1935	−0.461439
$489$	−6.38800	−0.288875
$490$	−0.892055	−0.0402989
$491$	−23.4744	−1.05939	−0.529693	−	0.848189i	$-0.677693\pi$
$491$	−23.4744	−1.05939	−0.529693	+	0.848189i	$0.677693\pi$
$492$	1.80989	0.0815960
$493$	−0.938558	−0.0422705
$494$	−0.313998	−0.0141274
$495$	1.00575	0.0452050
$496$	−8.36762	−0.375717
$497$	1.99615	0.0895397
$498$	−9.98649	−0.447505
$499$	−5.14322	−0.230242	−0.115121	−	0.993351i	$-0.536726\pi$
$499$	−5.14322	−0.230242	−0.115121	+	0.993351i	$0.536726\pi$
$500$	1.29495	0.0579119
$501$	17.6377	0.787992
$502$	−20.2778	−0.905044
$503$	−9.95795	−0.444003	−0.222002	−	0.975046i	$-0.571259\pi$
$503$	−9.95795	−0.444003	−0.222002	+	0.975046i	$0.571259\pi$
$504$	0.740780	0.0329970
$505$	−0.879990	−0.0391590
$506$	−4.58767	−0.203947
$507$	12.1302	0.538721
$508$	19.0525	0.845320
$509$	−16.0954	−0.713416	−0.356708	−	0.934216i	$-0.616101\pi$
$509$	−16.0954	−0.713416	−0.356708	+	0.934216i	$0.616101\pi$
$510$	0.0396759	0.00175688
$511$	−3.66825	−0.162274
$512$	−1.00000	−0.0441942
$513$	−4.41304	−0.194841
$514$	0.336181	0.0148283
$515$	−1.47054	−0.0647999
$516$	7.53673	0.331786
$517$	−10.4458	−0.459404
$518$	−3.62209	−0.159146
$519$	23.8126	1.04526
$520$	−0.0444371	−0.00194870
$521$	12.6857	0.555769	0.277884	−	0.960615i	$-0.410367\pi$
$521$	12.6857	0.555769	0.277884	+	0.960615i	$0.410367\pi$
$522$	6.10610	0.267257
$523$	29.4170	1.28632	0.643159	−	0.765733i	$-0.277624\pi$
$523$	29.4170	1.28632	0.643159	+	0.765733i	$0.277624\pi$
$524$	−12.1222	−0.529562
$525$	1.64466	0.0717788
$526$	24.0852	1.05016
$527$	2.71820	0.118407
$528$	−3.45450	−0.150338
$529$	−21.4364	−0.932015
$530$	0.949161	0.0412289
$531$	−6.36138	−0.276060
$532$	−0.321271	−0.0139289
$533$	0.658492	0.0285225
$534$	−16.4795	−0.713136
$535$	1.48327	0.0641276
$536$	−2.69312	−0.116325
$537$	13.4366	0.579830
$538$	8.89648	0.383555
$539$	−25.2308	−1.08677
$540$	−0.624535	−0.0268757
$541$	8.95639	0.385065	0.192533	−	0.981291i	$-0.438330\pi$
$541$	8.95639	0.385065	0.192533	+	0.981291i	$0.438330\pi$
$542$	15.9456	0.684921
$543$	1.21313	0.0520603
$544$	0.324847	0.0139277
$545$	−2.35614	−0.100926
$546$	−0.113066	−0.00483878
$547$	40.1406	1.71629	0.858145	−	0.513407i	$-0.171617\pi$
$547$	40.1406	1.71629	0.858145	+	0.513407i	$0.171617\pi$
$548$	−9.76659	−0.417208
$549$	−21.5430	−0.919435
$550$	18.2822	0.779556
$551$	−2.64817	−0.112816
$552$	1.17742	0.0501144
$553$	0.516875	0.0219797
$554$	24.6530	1.04740
$555$	1.26212	0.0535739
$556$	−0.211615	−0.00897448
$557$	26.0020	1.10174	0.550870	−	0.834591i	$-0.314296\pi$
$557$	26.0020	1.10174	0.550870	+	0.834591i	$0.314296\pi$
$558$	−17.6842	−0.748630
$559$	2.74209	0.115978
$560$	−0.0454664	−0.00192131
$561$	1.12219	0.0473788
$562$	12.2409	0.516352
$563$	−16.9325	−0.713621	−0.356811	−	0.934177i	$-0.616136\pi$
$563$	−16.9325	−0.713621	−0.356811	+	0.934177i	$0.616136\pi$
$564$	2.68090	0.112886
$565$	0.228032	0.00959339
$566$	−21.5413	−0.905449
$567$	0.633271	0.0265949
$568$	−5.69491	−0.238953
$569$	4.85638	0.203590	0.101795	−	0.994805i	$-0.467541\pi$
$569$	4.85638	0.203590	0.101795	+	0.994805i	$0.467541\pi$
$570$	0.111947	0.00468894
$571$	−28.5545	−1.19497	−0.597485	−	0.801880i	$-0.703833\pi$
$571$	−28.5545	−1.19497	−0.597485	+	0.801880i	$0.703833\pi$
$572$	−1.25685	−0.0525517
$573$	7.20845	0.301137
$574$	0.673745	0.0281216
$575$	−6.23125	−0.259861
$576$	−2.11340	−0.0880585
$577$	−24.5989	−1.02406	−0.512032	−	0.858967i	$-0.671107\pi$
$577$	−24.5989	−1.02406	−0.512032	+	0.858967i	$0.671107\pi$
$578$	16.8945	0.702717
$579$	−14.7012	−0.610962
$580$	−0.374771	−0.0155615
$581$	−3.71755	−0.154230
$582$	−14.6807	−0.608534
$583$	26.8460	1.11185
$584$	10.4653	0.433058
$585$	−0.0939136	−0.00388285
$586$	22.8468	0.943794
$587$	−14.0595	−0.580296	−0.290148	−	0.956982i	$-0.593705\pi$
$587$	−14.0595	−0.580296	−0.290148	+	0.956982i	$0.593705\pi$
$588$	6.47546	0.267044
$589$	7.66950	0.316016
$590$	0.390439	0.0160741
$591$	2.30145	0.0946688
$592$	10.3336	0.424710
$593$	−12.9160	−0.530395	−0.265197	−	0.964194i	$-0.585437\pi$
$593$	−12.9160	−0.530395	−0.265197	+	0.964194i	$0.585437\pi$
$594$	−17.6643	−0.724774
$595$	0.0147696	0.000605497 0
$596$	−0.581612	−0.0238238
$597$	25.7065	1.05210
$598$	0.428382	0.0175178
$599$	25.1142	1.02614	0.513070	−	0.858347i	$-0.328508\pi$
$599$	25.1142	1.02614	0.513070	+	0.858347i	$0.328508\pi$
$600$	−4.69212	−0.191555
$601$	25.2372	1.02944	0.514722	−	0.857357i	$-0.327895\pi$
$601$	25.2372	1.02944	0.514722	+	0.857357i	$0.327895\pi$
$602$	2.80561	0.114348
$603$	−5.69165	−0.231782
$604$	−2.43880	−0.0992332
$605$	−0.319096	−0.0129731
$606$	6.38788	0.259490
$607$	47.4054	1.92413	0.962063	−	0.272827i	$-0.0879587\pi$
$607$	47.4054	1.92413	0.962063	+	0.272827i	$0.0879587\pi$
$608$	0.916569	0.0371718
$609$	−0.953567	−0.0386405
$610$	1.32223	0.0535357
$611$	0.975392	0.0394602
$612$	0.686534	0.0277515
$613$	−18.9950	−0.767200	−0.383600	−	0.923499i	$-0.625316\pi$
$613$	−18.9950	−0.767200	−0.383600	+	0.923499i	$0.625316\pi$
$614$	9.56090	0.385847
$615$	−0.234766	−0.00946668
$616$	−1.28597	−0.0518131
$617$	44.5007	1.79153	0.895766	−	0.444525i	$-0.146628\pi$
$617$	44.5007	1.79153	0.895766	+	0.444525i	$0.146628\pi$
$618$	10.6747	0.429400
$619$	−23.2897	−0.936091	−0.468045	−	0.883704i	$-0.655042\pi$
$619$	−23.2897	−0.936091	−0.468045	+	0.883704i	$0.655042\pi$
$620$	1.08539	0.0435903
$621$	6.02063	0.241600
$622$	10.2196	0.409769
$623$	−6.13461	−0.245778
$624$	0.322571	0.0129132
$625$	24.7479	0.989916
$626$	10.7607	0.430083
$627$	3.16629	0.126449
$628$	20.0875	0.801577
$629$	−3.35685	−0.133846
$630$	−0.0960889	−0.00382827
$631$	−19.2637	−0.766874	−0.383437	−	0.923567i	$-0.625260\pi$
$631$	−19.2637	−0.766874	−0.383437	+	0.923567i	$0.625260\pi$
$632$	−1.47461	−0.0586570
$633$	−3.94644	−0.156857
$634$	−14.7775	−0.586888
$635$	−2.47136	−0.0980731
$636$	−6.89000	−0.273206
$637$	2.35597	0.0933470
$638$	−10.6000	−0.419657
$639$	−12.0357	−0.476123
$640$	0.129713	0.00512736
$641$	3.98859	0.157540	0.0787699	−	0.996893i	$-0.474901\pi$
$641$	3.98859	0.157540	0.0787699	+	0.996893i	$0.474901\pi$
$642$	−10.7671	−0.424945
$643$	39.6773	1.56472	0.782360	−	0.622827i	$-0.214016\pi$
$643$	39.6773	1.56472	0.782360	+	0.622827i	$0.214016\pi$
$644$	0.438304	0.0172716
$645$	−0.977613	−0.0384935
$646$	−0.297745	−0.0117146
$647$	39.8399	1.56627	0.783135	−	0.621852i	$-0.213619\pi$
$647$	39.8399	1.56627	0.783135	+	0.621852i	$0.213619\pi$
$648$	−1.80669	−0.0709734
$649$	11.0431	0.433480
$650$	−1.70714	−0.0669594
$651$	2.76167	0.108238
$652$	6.78425	0.265692
$653$	−14.6957	−0.575088	−0.287544	−	0.957768i	$-0.592839\pi$
$653$	−14.6957	−0.575088	−0.287544	+	0.957768i	$0.592839\pi$
$654$	17.1033	0.668792
$655$	1.57241	0.0614392
$656$	−1.92216	−0.0750476
$657$	22.1174	0.862884
$658$	0.997985	0.0389055
$659$	−18.1529	−0.707137	−0.353569	−	0.935409i	$-0.615032\pi$
$659$	−18.1529	−0.707137	−0.353569	+	0.935409i	$0.615032\pi$
$660$	0.448095	0.0174421
$661$	−8.74244	−0.340042	−0.170021	−	0.985440i	$-0.554383\pi$
$661$	−8.74244	−0.340042	−0.170021	+	0.985440i	$0.554383\pi$
$662$	−4.76669	−0.185263
$663$	−0.104786	−0.00406956
$664$	10.6060	0.411591
$665$	0.0416731	0.00161601
$666$	21.8391	0.846249
$667$	3.61286	0.139890
$668$	−18.7317	−0.724752
$669$	−4.36154	−0.168627
$670$	0.349333	0.0134959
$671$	37.3979	1.44373
$672$	0.330042	0.0127317
$673$	6.40280	0.246810	0.123405	−	0.992356i	$-0.460619\pi$
$673$	6.40280	0.246810	0.123405	+	0.992356i	$0.460619\pi$
$674$	0.980382	0.0377629
$675$	−23.9927	−0.923479
$676$	−12.8826	−0.495486
$677$	−16.2493	−0.624510	−0.312255	−	0.949998i	$-0.601084\pi$
$677$	−16.2493	−0.624510	−0.312255	+	0.949998i	$0.601084\pi$
$678$	−1.65529	−0.0635712
$679$	−5.46500	−0.209727
$680$	−0.0421370	−0.00161588
$681$	−9.80326	−0.375662
$682$	30.6990	1.17553
$683$	19.7004	0.753815	0.376908	−	0.926251i	$-0.376987\pi$
$683$	19.7004	0.753815	0.376908	+	0.926251i	$0.376987\pi$
$684$	1.93708	0.0740661
$685$	1.26686	0.0484040
$686$	4.86415	0.185714
$687$	8.43550	0.321834
$688$	−8.00424	−0.305159
$689$	−2.50679	−0.0955012
$690$	−0.152727	−0.00581422
$691$	−16.9280	−0.643971	−0.321986	−	0.946745i	$-0.604350\pi$
$691$	−16.9280	−0.643971	−0.321986	+	0.946745i	$0.604350\pi$
$692$	−25.2897	−0.961370
$693$	−2.71777	−0.103239
$694$	23.2784	0.883637
$695$	0.0274493	0.00104121
$696$	2.72047	0.103119
$697$	0.624407	0.0236511
$698$	−5.88858	−0.222886
$699$	−19.8670	−0.751438
$700$	−1.74668	−0.0660182
$701$	14.6088	0.551768	0.275884	−	0.961191i	$-0.411029\pi$
$701$	14.6088	0.551768	0.275884	+	0.961191i	$0.411029\pi$
$702$	1.64943	0.0622539
$703$	−9.47148	−0.357224
$704$	3.66879	0.138273
$705$	−0.347748	−0.0130969
$706$	17.0303	0.640945
$707$	2.37794	0.0894316
$708$	−2.83421	−0.106516
$709$	−24.6702	−0.926507	−0.463254	−	0.886226i	$-0.653318\pi$
$709$	−24.6702	−0.926507	−0.463254	+	0.886226i	$0.653318\pi$
$710$	0.738705	0.0277231
$711$	−3.11646	−0.116876
$712$	17.5017	0.655904
$713$	−10.4634	−0.391856
$714$	−0.107213	−0.00401236
$715$	0.163030	0.00609699
$716$	−14.2700	−0.533296
$717$	−3.88916	−0.145243
$718$	15.5151	0.579018
$719$	13.8705	0.517283	0.258642	−	0.965973i	$-0.416725\pi$
$719$	13.8705	0.517283	0.258642	+	0.965973i	$0.416725\pi$
$720$	0.274136	0.0102165
$721$	3.97375	0.147990
$722$	18.1599	0.675842
$723$	12.2822	0.456780
$724$	−1.28838	−0.0478823
$725$	−14.3975	−0.534710
$726$	2.31633	0.0859672
$727$	−7.88316	−0.292370	−0.146185	−	0.989257i	$-0.546699\pi$
$727$	−7.88316	−0.292370	−0.146185	+	0.989257i	$0.546699\pi$
$728$	0.120080	0.00445044
$729$	9.78231	0.362308
$730$	−1.35749	−0.0502429
$731$	2.60016	0.0961703
$732$	−9.59815	−0.354758
$733$	37.1659	1.37275	0.686377	−	0.727246i	$-0.259200\pi$
$733$	37.1659	1.37275	0.686377	+	0.727246i	$0.259200\pi$
$734$	−26.9568	−0.994995
$735$	−0.839952	−0.0309821
$736$	−1.25046	−0.0460925
$737$	9.88048	0.363952
$738$	−4.06229	−0.149535
$739$	32.2183	1.18517	0.592585	−	0.805508i	$-0.298108\pi$
$739$	32.2183	1.18517	0.592585	+	0.805508i	$0.298108\pi$
$740$	−1.34041	−0.0492744
$741$	−0.295658	−0.0108613
$742$	−2.56486	−0.0941588
$743$	−37.0544	−1.35939	−0.679697	−	0.733493i	$-0.737889\pi$
$743$	−37.0544	−1.35939	−0.679697	+	0.733493i	$0.737889\pi$
$744$	−7.87888	−0.288854
$745$	0.0754427	0.00276401
$746$	5.36389	0.196386
$747$	22.4147	0.820110
$748$	−1.19180	−0.0435764
$749$	−4.00815	−0.146455
$750$	1.21931	0.0445230
$751$	49.6468	1.81164	0.905818	−	0.423667i	$-0.139257\pi$
$751$	49.6468	1.81164	0.905818	+	0.423667i	$0.139257\pi$
$752$	−2.84720	−0.103827
$753$	−19.0934	−0.695804
$754$	0.989791	0.0360461
$755$	0.316344	0.0115129
$756$	1.68764	0.0613789
$757$	−48.3117	−1.75592	−0.877958	−	0.478737i	$-0.841095\pi$
$757$	−48.3117	−1.75592	−0.877958	+	0.478737i	$0.841095\pi$
$758$	13.8038	0.501378
$759$	−4.31971	−0.156796
$760$	−0.118891	−0.00431263
$761$	4.36062	0.158072	0.0790362	−	0.996872i	$-0.474816\pi$
$761$	4.36062	0.158072	0.0790362	+	0.996872i	$0.474816\pi$
$762$	17.9397	0.649888
$763$	6.36684	0.230495
$764$	−7.65560	−0.276970
$765$	−0.0890524	−0.00321970
$766$	23.4129	0.845941
$767$	−1.03117	−0.0372334
$768$	−0.941592	−0.0339768
$769$	−15.4316	−0.556478	−0.278239	−	0.960512i	$-0.589751\pi$
$769$	−15.4316	−0.556478	−0.278239	+	0.960512i	$0.589751\pi$
$770$	0.166807	0.00601130
$771$	0.316546	0.0114001
$772$	15.6131	0.561930
$773$	34.7219	1.24886	0.624430	−	0.781081i	$-0.285331\pi$
$773$	34.7219	1.24886	0.624430	+	0.781081i	$0.285331\pi$
$774$	−16.9162	−0.608040
$775$	41.6973	1.49781
$776$	15.5913	0.559696
$777$	−3.41054	−0.122352
$778$	23.9313	0.857978
$779$	1.76179	0.0631226
$780$	−0.0418417	−0.00149817
$781$	20.8934	0.747626
$782$	0.406208	0.0145260
$783$	13.9109	0.497134
$784$	−6.87714	−0.245612
$785$	−2.60561	−0.0929982
$786$	−11.4142	−0.407131
$787$	13.5974	0.484696	0.242348	−	0.970189i	$-0.422082\pi$
$787$	13.5974	0.484696	0.242348	+	0.970189i	$0.422082\pi$
$788$	−2.44421	−0.0870712
$789$	22.6784	0.807374
$790$	0.191277	0.00680532
$791$	−0.616197	−0.0219094
$792$	7.75363	0.275513
$793$	−3.49210	−0.124008
$794$	4.43559	0.157413
$795$	0.893723	0.0316971
$796$	−27.3011	−0.967661
$797$	46.3988	1.64353	0.821765	−	0.569826i	$-0.192989\pi$
$797$	46.3988	1.64353	0.821765	+	0.569826i	$0.192989\pi$
$798$	−0.302507	−0.0107086
$799$	0.924904	0.0327208
$800$	4.98317	0.176182
$801$	36.9882	1.30691
$802$	6.81431	0.240622
$803$	−38.3951	−1.35493
$804$	−2.53582	−0.0894315
$805$	−0.0568538	−0.00200383
$806$	−2.86658	−0.100971
$807$	8.37686	0.294879
$808$	−6.78412	−0.238665
$809$	−26.6972	−0.938625	−0.469313	−	0.883032i	$-0.655498\pi$
$809$	−26.6972	−0.938625	−0.469313	+	0.883032i	$0.655498\pi$
$810$	0.234351	0.00823426
$811$	−6.42122	−0.225480	−0.112740	−	0.993625i	$-0.535963\pi$
$811$	−6.42122	−0.225480	−0.112740	+	0.993625i	$0.535963\pi$
$812$	1.01272	0.0355394
$813$	15.0142	0.526572
$814$	−37.9119	−1.32881
$815$	−0.880007	−0.0308253
$816$	0.305874	0.0107077
$817$	7.33644	0.256669
$818$	24.3559	0.851584
$819$	0.253776	0.00886767
$820$	0.249329	0.00870694
$821$	10.7889	0.376536	0.188268	−	0.982118i	$-0.439713\pi$
$821$	10.7889	0.376536	0.188268	+	0.982118i	$0.439713\pi$
$822$	−9.19615	−0.320752
$823$	−27.6366	−0.963351	−0.481676	−	0.876350i	$-0.659972\pi$
$823$	−27.6366	−0.963351	−0.481676	+	0.876350i	$0.659972\pi$
$824$	−11.3369	−0.394939
$825$	17.2144	0.599328
$826$	−1.05506	−0.0367101
$827$	43.2078	1.50248	0.751242	−	0.660027i	$-0.229455\pi$
$827$	43.2078	1.50248	0.751242	+	0.660027i	$0.229455\pi$
$828$	−2.64272	−0.0918410
$829$	−31.9777	−1.11063	−0.555316	−	0.831639i	$-0.687403\pi$
$829$	−31.9777	−1.11063	−0.555316	+	0.831639i	$0.687403\pi$
$830$	−1.37573	−0.0477524
$831$	23.2130	0.805251
$832$	−0.342580	−0.0118768
$833$	2.23402	0.0774042
$834$	−0.199255	−0.00689964
$835$	2.42975	0.0840850
$836$	−3.36270	−0.116301
$837$	−40.2879	−1.39255
$838$	−29.0451	−1.00334
$839$	6.33484	0.218703	0.109351	−	0.994003i	$-0.465123\pi$
$839$	6.33484	0.218703	0.109351	+	0.994003i	$0.465123\pi$
$840$	−0.0428108	−0.00147711
$841$	−20.6524	−0.712151
$842$	14.3006	0.492831
$843$	11.5260	0.396975
$844$	4.19124	0.144269
$845$	1.67105	0.0574858
$846$	−6.01727	−0.206878
$847$	0.862273	0.0296281
$848$	7.31739	0.251280
$849$	−20.2831	−0.696115
$850$	−1.61877	−0.0555234
$851$	12.9218	0.442953
$852$	−5.36229	−0.183709
$853$	28.2288	0.966534	0.483267	−	0.875473i	$-0.339450\pi$
$853$	28.2288	0.966534	0.483267	+	0.875473i	$0.339450\pi$
$854$	−3.57299	−0.122265
$855$	−0.251265	−0.00859307
$856$	11.4350	0.390842
$857$	−31.8090	−1.08657	−0.543287	−	0.839547i	$-0.682821\pi$
$857$	−31.8090	−1.08657	−0.543287	+	0.839547i	$0.682821\pi$
$858$	−1.18344	−0.0404021
$859$	41.2690	1.40808	0.704041	−	0.710160i	$-0.251377\pi$
$859$	41.2690	1.40808	0.704041	+	0.710160i	$0.251377\pi$
$860$	1.03825	0.0354042
$861$	0.634393	0.0216201
$862$	22.7210	0.773881
$863$	−40.4998	−1.37863	−0.689314	−	0.724463i	$-0.742088\pi$
$863$	−40.4998	−1.37863	−0.689314	+	0.724463i	$0.742088\pi$
$864$	−4.81474	−0.163801
$865$	3.28041	0.111537
$866$	35.0246	1.19018
$867$	15.9077	0.540254
$868$	−2.93298	−0.0995517
$869$	5.41005	0.183523
$870$	−0.352881	−0.0119638
$871$	−0.922609	−0.0312614
$872$	−18.1642	−0.615119
$873$	32.9508	1.11522
$874$	1.14613	0.0387685
$875$	0.453899	0.0153446
$876$	9.85406	0.332938
$877$	32.1167	1.08450	0.542252	−	0.840216i	$-0.317572\pi$
$877$	32.1167	1.08450	0.542252	+	0.840216i	$0.317572\pi$
$878$	−3.41021	−0.115089
$879$	21.5124	0.725595
$880$	−0.475890	−0.0160423
$881$	14.5979	0.491815	0.245908	−	0.969293i	$-0.420914\pi$
$881$	14.5979	0.491815	0.245908	+	0.969293i	$0.420914\pi$
$882$	−14.5342	−0.489391
$883$	13.3780	0.450206	0.225103	−	0.974335i	$-0.427728\pi$
$883$	13.3780	0.450206	0.225103	+	0.974335i	$0.427728\pi$
$884$	0.111286	0.00374296
$885$	0.367634	0.0123579
$886$	2.49849	0.0839385
$887$	45.1662	1.51653	0.758266	−	0.651945i	$-0.226047\pi$
$887$	45.1662	1.51653	0.758266	+	0.651945i	$0.226047\pi$
$888$	9.73007	0.326520
$889$	6.67820	0.223980
$890$	−2.27020	−0.0760973
$891$	6.62836	0.222058
$892$	4.63209	0.155094
$893$	2.60965	0.0873286
$894$	−0.547642	−0.0183159
$895$	1.85101	0.0618725
$896$	−0.350515	−0.0117099
$897$	0.403361	0.0134678
$898$	16.2151	0.541105
$899$	−24.1759	−0.806313
$900$	10.5315	0.351049
$901$	−2.37703	−0.0791905
$902$	7.05199	0.234805
$903$	2.64174	0.0879115
$904$	1.75797	0.0584693
$905$	0.167120	0.00555525
$906$	−2.29635	−0.0762911
$907$	10.5519	0.350370	0.175185	−	0.984536i	$-0.443948\pi$
$907$	10.5519	0.350370	0.175185	+	0.984536i	$0.443948\pi$
$908$	10.4114	0.345513
$909$	−14.3376	−0.475548
$910$	−0.0155759	−0.000516336 0
$911$	36.4848	1.20880	0.604398	−	0.796683i	$-0.293414\pi$
$911$	36.4848	1.20880	0.604398	+	0.796683i	$0.293414\pi$
$912$	0.863034	0.0285779
$913$	−38.9110	−1.28777
$914$	−13.4972	−0.446447
$915$	1.24501	0.0411586
$916$	−8.95876	−0.296006
$917$	−4.24903	−0.140315
$918$	1.56406	0.0516216
$919$	19.5171	0.643810	0.321905	−	0.946772i	$-0.395677\pi$
$919$	19.5171	0.643810	0.321905	+	0.946772i	$0.395677\pi$
$920$	0.162201	0.00534760
$921$	9.00247	0.296642
$922$	37.6469	1.23983
$923$	−1.95096	−0.0642168
$924$	−1.21086	−0.0398342
$925$	−51.4943	−1.69312
$926$	−31.4858	−1.03469
$927$	−23.9594	−0.786931
$928$	−2.88923	−0.0948435
$929$	8.12380	0.266533	0.133267	−	0.991080i	$-0.457453\pi$
$929$	8.12380	0.266533	0.133267	+	0.991080i	$0.457453\pi$
$930$	1.02199	0.0335125
$931$	6.30337	0.206585
$932$	21.0993	0.691132
$933$	9.62271	0.315033
$934$	−6.12073	−0.200276
$935$	0.154592	0.00505569
$936$	−0.724010	−0.0236650
$937$	45.0973	1.47326	0.736632	−	0.676294i	$-0.236415\pi$
$937$	45.0973	1.47326	0.736632	+	0.676294i	$0.236415\pi$
$938$	−0.943979	−0.0308220
$939$	10.1322	0.330651
$940$	0.369319	0.0120458
$941$	−31.8845	−1.03940	−0.519702	−	0.854348i	$-0.673957\pi$
$941$	−31.8845	−1.03940	−0.519702	+	0.854348i	$0.673957\pi$
$942$	18.9142	0.616258
$943$	−2.40358	−0.0782712
$944$	3.01002	0.0979677
$945$	−0.218909	−0.00712111
$946$	29.3659	0.954767
$947$	59.1408	1.92182	0.960909	−	0.276866i	$-0.0892957\pi$
$947$	59.1408	1.92182	0.960909	+	0.276866i	$0.0892957\pi$
$948$	−1.38849	−0.0450959
$949$	3.58521	0.116381
$950$	−4.56742	−0.148187
$951$	−13.9144	−0.451204
$952$	0.113864	0.00369035
$953$	23.1786	0.750830	0.375415	−	0.926857i	$-0.377500\pi$
$953$	23.1786	0.750830	0.375415	+	0.926857i	$0.377500\pi$
$954$	15.4646	0.500685
$955$	0.993032	0.0321337
$956$	4.13040	0.133587
$957$	−9.98084	−0.322635
$958$	−17.8974	−0.578238
$959$	−3.42334	−0.110545
$960$	0.122137	0.00394195
$961$	39.0170	1.25861
$962$	3.54010	0.114137
$963$	24.1669	0.778766
$964$	−13.0441	−0.420121
$965$	−2.02523	−0.0651945
$966$	0.412704	0.0132785
$967$	30.2130	0.971586	0.485793	−	0.874074i	$-0.338531\pi$
$967$	30.2130	0.971586	0.485793	+	0.874074i	$0.338531\pi$
$968$	−2.46002	−0.0790679
$969$	−0.280354	−0.00900628
$970$	−2.02240	−0.0649354
$971$	−13.9789	−0.448603	−0.224302	−	0.974520i	$-0.572010\pi$
$971$	−13.9789	−0.448603	−0.224302	+	0.974520i	$0.572010\pi$
$972$	−16.1454	−0.517864
$973$	−0.0741743	−0.00237792
$974$	0.111862	0.00358430
$975$	−1.60743	−0.0514788
$976$	10.1935	0.326287
$977$	30.2608	0.968129	0.484064	−	0.875032i	$-0.339160\pi$
$977$	30.2608	0.968129	0.484064	+	0.875032i	$0.339160\pi$
$978$	6.38800	0.204266
$979$	−64.2101	−2.05216
$980$	0.892055	0.0284957
$981$	−38.3884	−1.22565
$982$	23.4744	0.749099
$983$	28.7492	0.916956	0.458478	−	0.888706i	$-0.348395\pi$
$983$	28.7492	0.916956	0.458478	+	0.888706i	$0.348395\pi$
$984$	−1.80989	−0.0576971
$985$	0.317046	0.0101019
$986$	0.938558	0.0298898
$987$	0.939695	0.0299108
$988$	0.313998	0.00998962
$989$	−10.0090	−0.318267
$990$	−1.00575	−0.0319648
$991$	37.4492	1.18961	0.594806	−	0.803869i	$-0.297229\pi$
$991$	37.4492	1.18961	0.594806	+	0.803869i	$0.297229\pi$
$992$	8.36762	0.265672
$993$	−4.48828	−0.142431
$994$	−1.99615	−0.0633141
$995$	3.54131	0.112267
$996$	9.98649	0.316434
$997$	−53.8516	−1.70550	−0.852748	−	0.522322i	$-0.825066\pi$
$997$	−53.8516	−1.70550	−0.852748	+	0.522322i	$0.825066\pi$
$998$	5.14322	0.162806
$999$	49.7538	1.57414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.15	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.15	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.941592 q^{3} +1.00000 q^{4} -0.129713 q^{5} +0.941592 q^{6} +0.350515 q^{7} -1.00000 q^{8} -2.11340 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.941592 q^{3} +1.00000 q^{4} -0.129713 q^{5} +0.941592 q^{6} +0.350515 q^{7} -1.00000 q^{8} -2.11340 q^{9} +0.129713 q^{10} +3.66879 q^{11} -0.941592 q^{12} -0.342580 q^{13} -0.350515 q^{14} +0.122137 q^{15} +1.00000 q^{16} -0.324847 q^{17} +2.11340 q^{18} -0.916569 q^{19} -0.129713 q^{20} -0.330042 q^{21} -3.66879 q^{22} +1.25046 q^{23} +0.941592 q^{24} -4.98317 q^{25} +0.342580 q^{26} +4.81474 q^{27} +0.350515 q^{28} +2.88923 q^{29} -0.122137 q^{30} -8.36762 q^{31} -1.00000 q^{32} -3.45450 q^{33} +0.324847 q^{34} -0.0454664 q^{35} -2.11340 q^{36} +10.3336 q^{37} +0.916569 q^{38} +0.322571 q^{39} +0.129713 q^{40} -1.92216 q^{41} +0.330042 q^{42} -8.00424 q^{43} +3.66879 q^{44} +0.274136 q^{45} -1.25046 q^{46} -2.84720 q^{47} -0.941592 q^{48} -6.87714 q^{49} +4.98317 q^{50} +0.305874 q^{51} -0.342580 q^{52} +7.31739 q^{53} -4.81474 q^{54} -0.475890 q^{55} -0.350515 q^{56} +0.863034 q^{57} -2.88923 q^{58} +3.01002 q^{59} +0.122137 q^{60} +10.1935 q^{61} +8.36762 q^{62} -0.740780 q^{63} +1.00000 q^{64} +0.0444371 q^{65} +3.45450 q^{66} +2.69312 q^{67} -0.324847 q^{68} -1.17742 q^{69} +0.0454664 q^{70} +5.69491 q^{71} +2.11340 q^{72} -10.4653 q^{73} -10.3336 q^{74} +4.69212 q^{75} -0.916569 q^{76} +1.28597 q^{77} -0.322571 q^{78} +1.47461 q^{79} -0.129713 q^{80} +1.80669 q^{81} +1.92216 q^{82} -10.6060 q^{83} -0.330042 q^{84} +0.0421370 q^{85} +8.00424 q^{86} -2.72047 q^{87} -3.66879 q^{88} -17.5017 q^{89} -0.274136 q^{90} -0.120080 q^{91} +1.25046 q^{92} +7.87888 q^{93} +2.84720 q^{94} +0.118891 q^{95} +0.941592 q^{96} -15.5913 q^{97} +6.87714 q^{98} -7.75363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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