LMFDB - Embedded newform 4030.2.a.p.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 46x^{6} + 80x^{5} - 212x^{4} - 133x^{3} + 294x^{2} + 52x - 112 $ x^9 - 3x^8 - 16x^7 + 46x^6 + 80x^5 - 212x^4 - 133x^3 + 294x^2 + 52x - 112
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.27856$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.27856 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.27856 q^{6} -0.354220 q^{7} -1.00000 q^{8} -1.36528 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.27856 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.27856 q^{6} -0.354220 q^{7} -1.00000 q^{8} -1.36528 q^{9} +1.00000 q^{10} +0.305890 q^{11} +1.27856 q^{12} -1.00000 q^{13} +0.354220 q^{14} -1.27856 q^{15} +1.00000 q^{16} -4.03548 q^{17} +1.36528 q^{18} -6.04444 q^{19} -1.00000 q^{20} -0.452892 q^{21} -0.305890 q^{22} -0.505848 q^{23} -1.27856 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.58128 q^{27} -0.354220 q^{28} +3.70225 q^{29} +1.27856 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.391098 q^{33} +4.03548 q^{34} +0.354220 q^{35} -1.36528 q^{36} +1.59130 q^{37} +6.04444 q^{38} -1.27856 q^{39} +1.00000 q^{40} +10.4532 q^{41} +0.452892 q^{42} +9.23118 q^{43} +0.305890 q^{44} +1.36528 q^{45} +0.505848 q^{46} +5.99825 q^{47} +1.27856 q^{48} -6.87453 q^{49} -1.00000 q^{50} -5.15961 q^{51} -1.00000 q^{52} +2.98625 q^{53} +5.58128 q^{54} -0.305890 q^{55} +0.354220 q^{56} -7.72818 q^{57} -3.70225 q^{58} +3.68788 q^{59} -1.27856 q^{60} +9.10400 q^{61} -1.00000 q^{62} +0.483611 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.391098 q^{66} +6.36478 q^{67} -4.03548 q^{68} -0.646757 q^{69} -0.354220 q^{70} +15.3505 q^{71} +1.36528 q^{72} +8.47357 q^{73} -1.59130 q^{74} +1.27856 q^{75} -6.04444 q^{76} -0.108352 q^{77} +1.27856 q^{78} +1.73554 q^{79} -1.00000 q^{80} -3.04014 q^{81} -10.4532 q^{82} -12.0848 q^{83} -0.452892 q^{84} +4.03548 q^{85} -9.23118 q^{86} +4.73355 q^{87} -0.305890 q^{88} -0.654341 q^{89} -1.36528 q^{90} +0.354220 q^{91} -0.505848 q^{92} +1.27856 q^{93} -5.99825 q^{94} +6.04444 q^{95} -1.27856 q^{96} +13.8925 q^{97} +6.87453 q^{98} -0.417626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} - 3 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 - 3 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} - 3 q^{7} - 9 q^{8} + 14 q^{9} + 9 q^{10} + 14 q^{11} - 3 q^{12} - 9 q^{13} + 3 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} - 14 q^{18} + 6 q^{19} - 9 q^{20} + q^{21} - 14 q^{22} - 4 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} - 15 q^{27} - 3 q^{28} + 15 q^{29} - 3 q^{30} + 9 q^{31} - 9 q^{32} + 14 q^{33} - q^{34} + 3 q^{35} + 14 q^{36} - 9 q^{37} - 6 q^{38} + 3 q^{39} + 9 q^{40} + 18 q^{41} - q^{42} - 23 q^{43} + 14 q^{44} - 14 q^{45} + 4 q^{46} + 3 q^{47} - 3 q^{48} + 12 q^{49} - 9 q^{50} - 11 q^{51} - 9 q^{52} - 6 q^{53} + 15 q^{54} - 14 q^{55} + 3 q^{56} + 17 q^{57} - 15 q^{58} + 28 q^{59} + 3 q^{60} - 9 q^{62} + 12 q^{63} + 9 q^{64} + 9 q^{65} - 14 q^{66} - 16 q^{67} + q^{68} - 6 q^{69} - 3 q^{70} + 32 q^{71} - 14 q^{72} - 11 q^{73} + 9 q^{74} - 3 q^{75} + 6 q^{76} - 29 q^{77} - 3 q^{78} - 8 q^{79} - 9 q^{80} + 9 q^{81} - 18 q^{82} + 15 q^{83} + q^{84} - q^{85} + 23 q^{86} - 19 q^{87} - 14 q^{88} + 51 q^{89} + 14 q^{90} + 3 q^{91} - 4 q^{92} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 3 q^{96} - 26 q^{97} - 12 q^{98} + 27 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 - 3 * q^7 - 9 * q^8 + 14 * q^9 + 9 * q^10 + 14 * q^11 - 3 * q^12 - 9 * q^13 + 3 * q^14 + 3 * q^15 + 9 * q^16 + q^17 - 14 * q^18 + 6 * q^19 - 9 * q^20 + q^21 - 14 * q^22 - 4 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 - 15 * q^27 - 3 * q^28 + 15 * q^29 - 3 * q^30 + 9 * q^31 - 9 * q^32 + 14 * q^33 - q^34 + 3 * q^35 + 14 * q^36 - 9 * q^37 - 6 * q^38 + 3 * q^39 + 9 * q^40 + 18 * q^41 - q^42 - 23 * q^43 + 14 * q^44 - 14 * q^45 + 4 * q^46 + 3 * q^47 - 3 * q^48 + 12 * q^49 - 9 * q^50 - 11 * q^51 - 9 * q^52 - 6 * q^53 + 15 * q^54 - 14 * q^55 + 3 * q^56 + 17 * q^57 - 15 * q^58 + 28 * q^59 + 3 * q^60 - 9 * q^62 + 12 * q^63 + 9 * q^64 + 9 * q^65 - 14 * q^66 - 16 * q^67 + q^68 - 6 * q^69 - 3 * q^70 + 32 * q^71 - 14 * q^72 - 11 * q^73 + 9 * q^74 - 3 * q^75 + 6 * q^76 - 29 * q^77 - 3 * q^78 - 8 * q^79 - 9 * q^80 + 9 * q^81 - 18 * q^82 + 15 * q^83 + q^84 - q^85 + 23 * q^86 - 19 * q^87 - 14 * q^88 + 51 * q^89 + 14 * q^90 + 3 * q^91 - 4 * q^92 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 3 * q^96 - 26 * q^97 - 12 * q^98 + 27 * 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
$3$	1.27856	0.738177	0.369088	−	0.929394i	$-0.379670\pi$
$3$	1.27856	0.738177	0.369088	+	0.929394i	$0.379670\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.27856	−0.521970
$7$	−0.354220	−0.133883	−0.0669413	−	0.997757i	$-0.521324\pi$
$7$	−0.354220	−0.133883	−0.0669413	+	0.997757i	$0.521324\pi$
$8$	−1.00000	−0.353553
$9$	−1.36528	−0.455095
$10$	1.00000	0.316228
$11$	0.305890	0.0922292	0.0461146	−	0.998936i	$-0.485316\pi$
$11$	0.305890	0.0922292	0.0461146	+	0.998936i	$0.485316\pi$
$12$	1.27856	0.369088
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.354220	0.0946693
$15$	−1.27856	−0.330123
$16$	1.00000	0.250000
$17$	−4.03548	−0.978748	−0.489374	−	0.872074i	$-0.662775\pi$
$17$	−4.03548	−0.978748	−0.489374	+	0.872074i	$0.662775\pi$
$18$	1.36528	0.321801
$19$	−6.04444	−1.38669	−0.693345	−	0.720606i	$-0.743864\pi$
$19$	−6.04444	−1.38669	−0.693345	+	0.720606i	$0.743864\pi$
$20$	−1.00000	−0.223607
$21$	−0.452892	−0.0988291
$22$	−0.305890	−0.0652159
$23$	−0.505848	−0.105477	−0.0527383	−	0.998608i	$-0.516795\pi$
$23$	−0.505848	−0.105477	−0.0527383	+	0.998608i	$0.516795\pi$
$24$	−1.27856	−0.260985
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−5.58128	−1.07412
$28$	−0.354220	−0.0669413
$29$	3.70225	0.687491	0.343746	−	0.939063i	$-0.388304\pi$
$29$	3.70225	0.687491	0.343746	+	0.939063i	$0.388304\pi$
$30$	1.27856	0.233432
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	0.391098	0.0680815
$34$	4.03548	0.692080
$35$	0.354220	0.0598741
$36$	−1.36528	−0.227547
$37$	1.59130	0.261608	0.130804	−	0.991408i	$-0.458244\pi$
$37$	1.59130	0.261608	0.130804	+	0.991408i	$0.458244\pi$
$38$	6.04444	0.980538
$39$	−1.27856	−0.204733
$40$	1.00000	0.158114
$41$	10.4532	1.63252	0.816261	−	0.577683i	$-0.196043\pi$
$41$	10.4532	1.63252	0.816261	+	0.577683i	$0.196043\pi$
$42$	0.452892	0.0698827
$43$	9.23118	1.40774	0.703871	−	0.710328i	$-0.251453\pi$
$43$	9.23118	1.40774	0.703871	+	0.710328i	$0.251453\pi$
$44$	0.305890	0.0461146
$45$	1.36528	0.203525
$46$	0.505848	0.0745832
$47$	5.99825	0.874935	0.437468	−	0.899234i	$-0.355875\pi$
$47$	5.99825	0.874935	0.437468	+	0.899234i	$0.355875\pi$
$48$	1.27856	0.184544
$49$	−6.87453	−0.982075
$50$	−1.00000	−0.141421
$51$	−5.15961	−0.722489
$52$	−1.00000	−0.138675
$53$	2.98625	0.410193	0.205097	−	0.978742i	$-0.434249\pi$
$53$	2.98625	0.410193	0.205097	+	0.978742i	$0.434249\pi$
$54$	5.58128	0.759516
$55$	−0.305890	−0.0412462
$56$	0.354220	0.0473347
$57$	−7.72818	−1.02362
$58$	−3.70225	−0.486130
$59$	3.68788	0.480121	0.240060	−	0.970758i	$-0.422833\pi$
$59$	3.68788	0.480121	0.240060	+	0.970758i	$0.422833\pi$
$60$	−1.27856	−0.165061
$61$	9.10400	1.16565	0.582824	−	0.812599i	$-0.301948\pi$
$61$	9.10400	1.16565	0.582824	+	0.812599i	$0.301948\pi$
$62$	−1.00000	−0.127000
$63$	0.483611	0.0609293
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−0.391098	−0.0481409
$67$	6.36478	0.777582	0.388791	−	0.921326i	$-0.372893\pi$
$67$	6.36478	0.777582	0.388791	+	0.921326i	$0.372893\pi$
$68$	−4.03548	−0.489374
$69$	−0.646757	−0.0778603
$70$	−0.354220	−0.0423374
$71$	15.3505	1.82177	0.910883	−	0.412665i	$-0.135402\pi$
$71$	15.3505	1.82177	0.910883	+	0.412665i	$0.135402\pi$
$72$	1.36528	0.160900
$73$	8.47357	0.991757	0.495878	−	0.868392i	$-0.334846\pi$
$73$	8.47357	0.991757	0.495878	+	0.868392i	$0.334846\pi$
$74$	−1.59130	−0.184985
$75$	1.27856	0.147635
$76$	−6.04444	−0.693345
$77$	−0.108352	−0.0123479
$78$	1.27856	0.144768
$79$	1.73554	0.195263	0.0976317	−	0.995223i	$-0.468873\pi$
$79$	1.73554	0.195263	0.0976317	+	0.995223i	$0.468873\pi$
$80$	−1.00000	−0.111803
$81$	−3.04014	−0.337794
$82$	−10.4532	−1.15437
$83$	−12.0848	−1.32648	−0.663238	−	0.748409i	$-0.730818\pi$
$83$	−12.0848	−1.32648	−0.663238	+	0.748409i	$0.730818\pi$
$84$	−0.452892	−0.0494145
$85$	4.03548	0.437710
$86$	−9.23118	−0.995423
$87$	4.73355	0.507490
$88$	−0.305890	−0.0326079
$89$	−0.654341	−0.0693601	−0.0346800	−	0.999398i	$-0.511041\pi$
$89$	−0.654341	−0.0693601	−0.0346800	+	0.999398i	$0.511041\pi$
$90$	−1.36528	−0.143914
$91$	0.354220	0.0371324
$92$	−0.505848	−0.0527383
$93$	1.27856	0.132580
$94$	−5.99825	−0.618673
$95$	6.04444	0.620146
$96$	−1.27856	−0.130492
$97$	13.8925	1.41057	0.705284	−	0.708925i	$-0.250819\pi$
$97$	13.8925	1.41057	0.705284	+	0.708925i	$0.250819\pi$
$98$	6.87453	0.694432
$99$	−0.417626	−0.0419730
$100$	1.00000	0.100000
$101$	−1.16228	−0.115652	−0.0578258	−	0.998327i	$-0.518417\pi$
$101$	−1.16228	−0.115652	−0.0578258	+	0.998327i	$0.518417\pi$
$102$	5.15961	0.510877
$103$	−14.1752	−1.39673	−0.698363	−	0.715743i	$-0.746088\pi$
$103$	−14.1752	−1.39673	−0.698363	+	0.715743i	$0.746088\pi$
$104$	1.00000	0.0980581
$105$	0.452892	0.0441977
$106$	−2.98625	−0.290051
$107$	−4.46117	−0.431277	−0.215639	−	0.976473i	$-0.569183\pi$
$107$	−4.46117	−0.431277	−0.215639	+	0.976473i	$0.569183\pi$
$108$	−5.58128	−0.537059
$109$	−0.197311	−0.0188989	−0.00944946	−	0.999955i	$-0.503008\pi$
$109$	−0.197311	−0.0188989	−0.00944946	+	0.999955i	$0.503008\pi$
$110$	0.305890	0.0291654
$111$	2.03457	0.193113
$112$	−0.354220	−0.0334707
$113$	−5.71203	−0.537342	−0.268671	−	0.963232i	$-0.586584\pi$
$113$	−5.71203	−0.537342	−0.268671	+	0.963232i	$0.586584\pi$
$114$	7.72818	0.723810
$115$	0.505848	0.0471705
$116$	3.70225	0.343746
$117$	1.36528	0.126221
$118$	−3.68788	−0.339497
$119$	1.42945	0.131037
$120$	1.27856	0.116716
$121$	−10.9064	−0.991494
$122$	−9.10400	−0.824237
$123$	13.3651	1.20509
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	−0.483611	−0.0430835
$127$	0.144472	0.0128199	0.00640993	−	0.999979i	$-0.497960\pi$
$127$	0.144472	0.0128199	0.00640993	+	0.999979i	$0.497960\pi$
$128$	−1.00000	−0.0883883
$129$	11.8026	1.03916
$130$	−1.00000	−0.0877058
$131$	6.96241	0.608308	0.304154	−	0.952623i	$-0.401626\pi$
$131$	6.96241	0.608308	0.304154	+	0.952623i	$0.401626\pi$
$132$	0.391098	0.0340407
$133$	2.14106	0.185654
$134$	−6.36478	−0.549834
$135$	5.58128	0.480360
$136$	4.03548	0.346040
$137$	17.4348	1.48956	0.744779	−	0.667311i	$-0.232555\pi$
$137$	17.4348	1.48956	0.744779	+	0.667311i	$0.232555\pi$
$138$	0.646757	0.0550556
$139$	3.90907	0.331563	0.165781	−	0.986163i	$-0.446985\pi$
$139$	3.90907	0.331563	0.165781	+	0.986163i	$0.446985\pi$
$140$	0.354220	0.0299371
$141$	7.66913	0.645857
$142$	−15.3505	−1.28818
$143$	−0.305890	−0.0255798
$144$	−1.36528	−0.113774
$145$	−3.70225	−0.307455
$146$	−8.47357	−0.701278
$147$	−8.78950	−0.724945
$148$	1.59130	0.130804
$149$	5.48686	0.449501	0.224750	−	0.974416i	$-0.427843\pi$
$149$	5.48686	0.449501	0.224750	+	0.974416i	$0.427843\pi$
$150$	−1.27856	−0.104394
$151$	8.16293	0.664290	0.332145	−	0.943228i	$-0.392228\pi$
$151$	8.16293	0.664290	0.332145	+	0.943228i	$0.392228\pi$
$152$	6.04444	0.490269
$153$	5.50958	0.445423
$154$	0.108352	0.00873128
$155$	−1.00000	−0.0803219
$156$	−1.27856	−0.102367
$157$	−7.93312	−0.633132	−0.316566	−	0.948570i	$-0.602530\pi$
$157$	−7.93312	−0.633132	−0.316566	+	0.948570i	$0.602530\pi$
$158$	−1.73554	−0.138072
$159$	3.81810	0.302795
$160$	1.00000	0.0790569
$161$	0.179181	0.0141215
$162$	3.04014	0.238856
$163$	5.25492	0.411597	0.205799	−	0.978594i	$-0.434021\pi$
$163$	5.25492	0.411597	0.205799	+	0.978594i	$0.434021\pi$
$164$	10.4532	0.816261
$165$	−0.391098	−0.0304470
$166$	12.0848	0.937960
$167$	12.8495	0.994322	0.497161	−	0.867658i	$-0.334376\pi$
$167$	12.8495	0.994322	0.497161	+	0.867658i	$0.334376\pi$
$168$	0.452892	0.0349414
$169$	1.00000	0.0769231
$170$	−4.03548	−0.309507
$171$	8.25238	0.631075
$172$	9.23118	0.703871
$173$	25.6872	1.95296	0.976481	−	0.215602i	$-0.0691714\pi$
$173$	25.6872	1.95296	0.976481	+	0.215602i	$0.0691714\pi$
$174$	−4.73355	−0.358850
$175$	−0.354220	−0.0267765
$176$	0.305890	0.0230573
$177$	4.71517	0.354414
$178$	0.654341	0.0490450
$179$	6.21304	0.464385	0.232192	−	0.972670i	$-0.425410\pi$
$179$	6.21304	0.464385	0.232192	+	0.972670i	$0.425410\pi$
$180$	1.36528	0.101762
$181$	−13.0891	−0.972904	−0.486452	−	0.873707i	$-0.661709\pi$
$181$	−13.0891	−0.972904	−0.486452	+	0.873707i	$0.661709\pi$
$182$	−0.354220	−0.0262565
$183$	11.6400	0.860454
$184$	0.505848	0.0372916
$185$	−1.59130	−0.116995
$186$	−1.27856	−0.0937486
$187$	−1.23441	−0.0902692
$188$	5.99825	0.437468
$189$	1.97700	0.143806
$190$	−6.04444	−0.438510
$191$	19.5353	1.41353	0.706763	−	0.707450i	$-0.250155\pi$
$191$	19.5353	1.41353	0.706763	+	0.707450i	$0.250155\pi$
$192$	1.27856	0.0922721
$193$	−16.7668	−1.20690	−0.603450	−	0.797401i	$-0.706208\pi$
$193$	−16.7668	−1.20690	−0.603450	+	0.797401i	$0.706208\pi$
$194$	−13.8925	−0.997422
$195$	1.27856	0.0915596
$196$	−6.87453	−0.491038
$197$	−7.20022	−0.512995	−0.256497	−	0.966545i	$-0.582568\pi$
$197$	−7.20022	−0.512995	−0.256497	+	0.966545i	$0.582568\pi$
$198$	0.417626	0.0296794
$199$	−18.7048	−1.32595	−0.662974	−	0.748642i	$-0.730706\pi$
$199$	−18.7048	−1.32595	−0.662974	+	0.748642i	$0.730706\pi$
$200$	−1.00000	−0.0707107
$201$	8.13776	0.573993
$202$	1.16228	0.0817780
$203$	−1.31141	−0.0920432
$204$	−5.15961	−0.361245
$205$	−10.4532	−0.730086
$206$	14.1752	0.987635
$207$	0.690626	0.0480018
$208$	−1.00000	−0.0693375
$209$	−1.84893	−0.127893
$210$	−0.452892	−0.0312525
$211$	2.30017	0.158350	0.0791752	−	0.996861i	$-0.474771\pi$
$211$	2.30017	0.158350	0.0791752	+	0.996861i	$0.474771\pi$
$212$	2.98625	0.205097
$213$	19.6265	1.34479
$214$	4.46117	0.304959
$215$	−9.23118	−0.629561
$216$	5.58128	0.379758
$217$	−0.354220	−0.0240460
$218$	0.197311	0.0133636
$219$	10.8340	0.732092
$220$	−0.305890	−0.0206231
$221$	4.03548	0.271456
$222$	−2.03457	−0.136552
$223$	−16.8137	−1.12593	−0.562964	−	0.826481i	$-0.690339\pi$
$223$	−16.8137	−1.12593	−0.562964	+	0.826481i	$0.690339\pi$
$224$	0.354220	0.0236673
$225$	−1.36528	−0.0910190
$226$	5.71203	0.379958
$227$	−24.1396	−1.60220	−0.801102	−	0.598528i	$-0.795752\pi$
$227$	−24.1396	−1.60220	−0.801102	+	0.598528i	$0.795752\pi$
$228$	−7.72818	−0.511811
$229$	−23.5859	−1.55860	−0.779302	−	0.626649i	$-0.784426\pi$
$229$	−23.5859	−1.55860	−0.779302	+	0.626649i	$0.784426\pi$
$230$	−0.505848	−0.0333546
$231$	−0.138535	−0.00911493
$232$	−3.70225	−0.243065
$233$	−26.8510	−1.75907	−0.879533	−	0.475837i	$-0.842145\pi$
$233$	−26.8510	−1.75907	−0.879533	+	0.475837i	$0.842145\pi$
$234$	−1.36528	−0.0892515
$235$	−5.99825	−0.391283
$236$	3.68788	0.240060
$237$	2.21899	0.144139
$238$	−1.42945	−0.0926575
$239$	22.8187	1.47602	0.738009	−	0.674790i	$-0.235766\pi$
$239$	22.8187	1.47602	0.738009	+	0.674790i	$0.235766\pi$
$240$	−1.27856	−0.0825307
$241$	7.32211	0.471659	0.235829	−	0.971794i	$-0.424219\pi$
$241$	7.32211	0.471659	0.235829	+	0.971794i	$0.424219\pi$
$242$	10.9064	0.701092
$243$	12.8568	0.824766
$244$	9.10400	0.582824
$245$	6.87453	0.439197
$246$	−13.3651	−0.852128
$247$	6.04444	0.384599
$248$	−1.00000	−0.0635001
$249$	−15.4511	−0.979173
$250$	1.00000	0.0632456
$251$	9.07896	0.573059	0.286530	−	0.958071i	$-0.407498\pi$
$251$	9.07896	0.573059	0.286530	+	0.958071i	$0.407498\pi$
$252$	0.483611	0.0304647
$253$	−0.154734	−0.00972802
$254$	−0.144472	−0.00906501
$255$	5.15961	0.323107
$256$	1.00000	0.0625000
$257$	−3.92798	−0.245020	−0.122510	−	0.992467i	$-0.539094\pi$
$257$	−3.92798	−0.245020	−0.122510	+	0.992467i	$0.539094\pi$
$258$	−11.8026	−0.734798
$259$	−0.563670	−0.0350248
$260$	1.00000	0.0620174
$261$	−5.05463	−0.312874
$262$	−6.96241	−0.430139
$263$	0.199205	0.0122835	0.00614177	−	0.999981i	$-0.498045\pi$
$263$	0.199205	0.0122835	0.00614177	+	0.999981i	$0.498045\pi$
$264$	−0.391098	−0.0240704
$265$	−2.98625	−0.183444
$266$	−2.14106	−0.131277
$267$	−0.836615	−0.0512000
$268$	6.36478	0.388791
$269$	6.25786	0.381549	0.190774	−	0.981634i	$-0.438900\pi$
$269$	6.25786	0.381549	0.190774	+	0.981634i	$0.438900\pi$
$270$	−5.58128	−0.339666
$271$	−9.38130	−0.569873	−0.284937	−	0.958546i	$-0.591973\pi$
$271$	−9.38130	−0.569873	−0.284937	+	0.958546i	$0.591973\pi$
$272$	−4.03548	−0.244687
$273$	0.452892	0.0274103
$274$	−17.4348	−1.05328
$275$	0.305890	0.0184458
$276$	−0.646757	−0.0389302
$277$	3.39227	0.203822	0.101911	−	0.994794i	$-0.467504\pi$
$277$	3.39227	0.203822	0.101911	+	0.994794i	$0.467504\pi$
$278$	−3.90907	−0.234450
$279$	−1.36528	−0.0817375
$280$	−0.354220	−0.0211687
$281$	2.17502	0.129751	0.0648755	−	0.997893i	$-0.479335\pi$
$281$	2.17502	0.129751	0.0648755	+	0.997893i	$0.479335\pi$
$282$	−7.66913	−0.456690
$283$	9.50795	0.565189	0.282595	−	0.959239i	$-0.408805\pi$
$283$	9.50795	0.565189	0.282595	+	0.959239i	$0.408805\pi$
$284$	15.3505	0.910883
$285$	7.72818	0.457778
$286$	0.305890	0.0180876
$287$	−3.70275	−0.218566
$288$	1.36528	0.0804502
$289$	−0.714879	−0.0420517
$290$	3.70225	0.217404
$291$	17.7624	1.04125
$292$	8.47357	0.495878
$293$	3.69141	0.215655	0.107827	−	0.994170i	$-0.465611\pi$
$293$	3.69141	0.215655	0.107827	+	0.994170i	$0.465611\pi$
$294$	8.78950	0.512614
$295$	−3.68788	−0.214717
$296$	−1.59130	−0.0924924
$297$	−1.70726	−0.0990650
$298$	−5.48686	−0.317845
$299$	0.505848	0.0292539
$300$	1.27856	0.0738177
$301$	−3.26987	−0.188472
$302$	−8.16293	−0.469724
$303$	−1.48605	−0.0853713
$304$	−6.04444	−0.346672
$305$	−9.10400	−0.521293
$306$	−5.50958	−0.314962
$307$	16.7593	0.956505	0.478253	−	0.878222i	$-0.341270\pi$
$307$	16.7593	0.956505	0.478253	+	0.878222i	$0.341270\pi$
$308$	−0.108352	−0.00617394
$309$	−18.1239	−1.03103
$310$	1.00000	0.0567962
$311$	18.1944	1.03171	0.515855	−	0.856676i	$-0.327474\pi$
$311$	18.1944	1.03171	0.515855	+	0.856676i	$0.327474\pi$
$312$	1.27856	0.0723842
$313$	21.6566	1.22410	0.612052	−	0.790818i	$-0.290344\pi$
$313$	21.6566	1.22410	0.612052	+	0.790818i	$0.290344\pi$
$314$	7.93312	0.447692
$315$	−0.483611	−0.0272484
$316$	1.73554	0.0976317
$317$	4.48216	0.251743	0.125872	−	0.992047i	$-0.459827\pi$
$317$	4.48216	0.251743	0.125872	+	0.992047i	$0.459827\pi$
$318$	−3.81810	−0.214109
$319$	1.13248	0.0634068
$320$	−1.00000	−0.0559017
$321$	−5.70387	−0.318359
$322$	−0.179181	−0.00998539
$323$	24.3922	1.35722
$324$	−3.04014	−0.168897
$325$	−1.00000	−0.0554700
$326$	−5.25492	−0.291043
$327$	−0.252273	−0.0139508
$328$	−10.4532	−0.577184
$329$	−2.12470	−0.117139
$330$	0.391098	0.0215292
$331$	26.2620	1.44349	0.721744	−	0.692160i	$-0.243341\pi$
$331$	26.2620	1.44349	0.721744	+	0.692160i	$0.243341\pi$
$332$	−12.0848	−0.663238
$333$	−2.17258	−0.119056
$334$	−12.8495	−0.703092
$335$	−6.36478	−0.347745
$336$	−0.452892	−0.0247073
$337$	0.275288	0.0149959	0.00749796	−	0.999972i	$-0.497613\pi$
$337$	0.275288	0.0149959	0.00749796	+	0.999972i	$0.497613\pi$
$338$	−1.00000	−0.0543928
$339$	−7.30317	−0.396654
$340$	4.03548	0.218855
$341$	0.305890	0.0165649
$342$	−8.25238	−0.446238
$343$	4.91464	0.265366
$344$	−9.23118	−0.497712
$345$	0.646757	0.0348202
$346$	−25.6872	−1.38095
$347$	−9.84915	−0.528730	−0.264365	−	0.964423i	$-0.585162\pi$
$347$	−9.84915	−0.528730	−0.264365	+	0.964423i	$0.585162\pi$
$348$	4.73355	0.253745
$349$	4.46153	0.238820	0.119410	−	0.992845i	$-0.461900\pi$
$349$	4.46153	0.238820	0.119410	+	0.992845i	$0.461900\pi$
$350$	0.354220	0.0189339
$351$	5.58128	0.297907
$352$	−0.305890	−0.0163040
$353$	−4.93007	−0.262401	−0.131201	−	0.991356i	$-0.541883\pi$
$353$	−4.93007	−0.262401	−0.131201	+	0.991356i	$0.541883\pi$
$354$	−4.71517	−0.250609
$355$	−15.3505	−0.814718
$356$	−0.654341	−0.0346800
$357$	1.82764	0.0967288
$358$	−6.21304	−0.328369
$359$	20.5295	1.08351	0.541753	−	0.840538i	$-0.317761\pi$
$359$	20.5295	1.08351	0.541753	+	0.840538i	$0.317761\pi$
$360$	−1.36528	−0.0719568
$361$	17.5353	0.922908
$362$	13.0891	0.687947
$363$	−13.9445	−0.731898
$364$	0.354220	0.0185662
$365$	−8.47357	−0.443527
$366$	−11.6400	−0.608433
$367$	−22.3284	−1.16553	−0.582767	−	0.812639i	$-0.698030\pi$
$367$	−22.3284	−1.16553	−0.582767	+	0.812639i	$0.698030\pi$
$368$	−0.505848	−0.0263691
$369$	−14.2717	−0.742953
$370$	1.59130	0.0827277
$371$	−1.05779	−0.0549178
$372$	1.27856	0.0662902
$373$	−34.0802	−1.76461	−0.882304	−	0.470680i	$-0.844009\pi$
$373$	−34.0802	−1.76461	−0.882304	+	0.470680i	$0.844009\pi$
$374$	1.23441	0.0638299
$375$	−1.27856	−0.0660245
$376$	−5.99825	−0.309336
$377$	−3.70225	−0.190676
$378$	−1.97700	−0.101686
$379$	−32.7293	−1.68119	−0.840596	−	0.541662i	$-0.817795\pi$
$379$	−32.7293	−1.68119	−0.840596	+	0.541662i	$0.817795\pi$
$380$	6.04444	0.310073
$381$	0.184717	0.00946332
$382$	−19.5353	−0.999514
$383$	−21.5392	−1.10060	−0.550301	−	0.834967i	$-0.685487\pi$
$383$	−21.5392	−1.10060	−0.550301	+	0.834967i	$0.685487\pi$
$384$	−1.27856	−0.0652462
$385$	0.108352	0.00552214
$386$	16.7668	0.853407
$387$	−12.6032	−0.640656
$388$	13.8925	0.705284
$389$	−3.52820	−0.178887	−0.0894435	−	0.995992i	$-0.528509\pi$
$389$	−3.52820	−0.178887	−0.0894435	+	0.995992i	$0.528509\pi$
$390$	−1.27856	−0.0647424
$391$	2.04134	0.103235
$392$	6.87453	0.347216
$393$	8.90185	0.449039
$394$	7.20022	0.362742
$395$	−1.73554	−0.0873245
$396$	−0.417626	−0.0209865
$397$	4.09690	0.205618	0.102809	−	0.994701i	$-0.467217\pi$
$397$	4.09690	0.205618	0.102809	+	0.994701i	$0.467217\pi$
$398$	18.7048	0.937587
$399$	2.73748	0.137045
$400$	1.00000	0.0500000
$401$	−2.37350	−0.118527	−0.0592636	−	0.998242i	$-0.518875\pi$
$401$	−2.37350	−0.118527	−0.0592636	+	0.998242i	$0.518875\pi$
$402$	−8.13776	−0.405874
$403$	−1.00000	−0.0498135
$404$	−1.16228	−0.0578258
$405$	3.04014	0.151066
$406$	1.31141	0.0650843
$407$	0.486762	0.0241279
$408$	5.15961	0.255439
$409$	25.0081	1.23657	0.618286	−	0.785953i	$-0.287827\pi$
$409$	25.0081	1.23657	0.618286	+	0.785953i	$0.287827\pi$
$410$	10.4532	0.516249
$411$	22.2915	1.09956
$412$	−14.1752	−0.698363
$413$	−1.30632	−0.0642798
$414$	−0.690626	−0.0339424
$415$	12.0848	0.593218
$416$	1.00000	0.0490290
$417$	4.99798	0.244752
$418$	1.84893	0.0904342
$419$	26.2949	1.28459	0.642294	−	0.766458i	$-0.277983\pi$
$419$	26.2949	1.28459	0.642294	+	0.766458i	$0.277983\pi$
$420$	0.452892	0.0220989
$421$	39.4981	1.92502	0.962510	−	0.271245i	$-0.0874355\pi$
$421$	39.4981	1.92502	0.962510	+	0.271245i	$0.0874355\pi$
$422$	−2.30017	−0.111971
$423$	−8.18932	−0.398179
$424$	−2.98625	−0.145025
$425$	−4.03548	−0.195750
$426$	−19.6265	−0.950907
$427$	−3.22482	−0.156060
$428$	−4.46117	−0.215639
$429$	−0.391098	−0.0188824
$430$	9.23118	0.445167
$431$	28.2755	1.36199	0.680993	−	0.732290i	$-0.261549\pi$
$431$	28.2755	1.36199	0.680993	+	0.732290i	$0.261549\pi$
$432$	−5.58128	−0.268529
$433$	23.4890	1.12881	0.564405	−	0.825498i	$-0.309106\pi$
$433$	23.4890	1.12881	0.564405	+	0.825498i	$0.309106\pi$
$434$	0.354220	0.0170031
$435$	−4.73355	−0.226957
$436$	−0.197311	−0.00944946
$437$	3.05757	0.146263
$438$	−10.8340	−0.517667
$439$	1.82431	0.0870697	0.0435349	−	0.999052i	$-0.486138\pi$
$439$	1.82431	0.0870697	0.0435349	+	0.999052i	$0.486138\pi$
$440$	0.305890	0.0145827
$441$	9.38569	0.446938
$442$	−4.03548	−0.191948
$443$	8.07473	0.383642	0.191821	−	0.981430i	$-0.438561\pi$
$443$	8.07473	0.383642	0.191821	+	0.981430i	$0.438561\pi$
$444$	2.03457	0.0965565
$445$	0.654341	0.0310188
$446$	16.8137	0.796152
$447$	7.01528	0.331811
$448$	−0.354220	−0.0167353
$449$	7.37436	0.348018	0.174009	−	0.984744i	$-0.444328\pi$
$449$	7.37436	0.348018	0.174009	+	0.984744i	$0.444328\pi$
$450$	1.36528	0.0643601
$451$	3.19754	0.150566
$452$	−5.71203	−0.268671
$453$	10.4368	0.490363
$454$	24.1396	1.13293
$455$	−0.354220	−0.0166061
$456$	7.72818	0.361905
$457$	−0.776664	−0.0363308	−0.0181654	−	0.999835i	$-0.505783\pi$
$457$	−0.776664	−0.0363308	−0.0181654	+	0.999835i	$0.505783\pi$
$458$	23.5859	1.10210
$459$	22.5232	1.05129
$460$	0.505848	0.0235853
$461$	10.3393	0.481550	0.240775	−	0.970581i	$-0.422598\pi$
$461$	10.3393	0.481550	0.240775	+	0.970581i	$0.422598\pi$
$462$	0.138535	0.00644523
$463$	8.13519	0.378074	0.189037	−	0.981970i	$-0.439463\pi$
$463$	8.13519	0.378074	0.189037	+	0.981970i	$0.439463\pi$
$464$	3.70225	0.171873
$465$	−1.27856	−0.0592918
$466$	26.8510	1.24385
$467$	−35.3349	−1.63510	−0.817551	−	0.575856i	$-0.804669\pi$
$467$	−35.3349	−1.63510	−0.817551	+	0.575856i	$0.804669\pi$
$468$	1.36528	0.0631103
$469$	−2.25453	−0.104105
$470$	5.99825	0.276679
$471$	−10.1430	−0.467363
$472$	−3.68788	−0.169748
$473$	2.82372	0.129835
$474$	−2.21899	−0.101922
$475$	−6.04444	−0.277338
$476$	1.42945	0.0655187
$477$	−4.07709	−0.186677
$478$	−22.8187	−1.04370
$479$	−4.36839	−0.199597	−0.0997984	−	0.995008i	$-0.531820\pi$
$479$	−4.36839	−0.199597	−0.0997984	+	0.995008i	$0.531820\pi$
$480$	1.27856	0.0583580
$481$	−1.59130	−0.0725570
$482$	−7.32211	−0.333513
$483$	0.229094	0.0104241
$484$	−10.9064	−0.495747
$485$	−13.8925	−0.630825
$486$	−12.8568	−0.583198
$487$	−34.3260	−1.55546	−0.777729	−	0.628600i	$-0.783628\pi$
$487$	−34.3260	−1.55546	−0.777729	+	0.628600i	$0.783628\pi$
$488$	−9.10400	−0.412119
$489$	6.71873	0.303832
$490$	−6.87453	−0.310560
$491$	−17.5968	−0.794131	−0.397065	−	0.917790i	$-0.629971\pi$
$491$	−17.5968	−0.794131	−0.397065	+	0.917790i	$0.629971\pi$
$492$	13.3651	0.602545
$493$	−14.9404	−0.672881
$494$	−6.04444	−0.271952
$495$	0.417626	0.0187709
$496$	1.00000	0.0449013
$497$	−5.43745	−0.243903
$498$	15.4511	0.692380
$499$	−12.0402	−0.538993	−0.269496	−	0.963001i	$-0.586857\pi$
$499$	−12.0402	−0.538993	−0.269496	+	0.963001i	$0.586857\pi$
$500$	−1.00000	−0.0447214
$501$	16.4288	0.733985
$502$	−9.07896	−0.405214
$503$	12.2855	0.547784	0.273892	−	0.961760i	$-0.411689\pi$
$503$	12.2855	0.547784	0.273892	+	0.961760i	$0.411689\pi$
$504$	−0.483611	−0.0215418
$505$	1.16228	0.0517209
$506$	0.154734	0.00687875
$507$	1.27856	0.0567828
$508$	0.144472	0.00640993
$509$	13.7003	0.607255	0.303628	−	0.952791i	$-0.401802\pi$
$509$	13.7003	0.607255	0.303628	+	0.952791i	$0.401802\pi$
$510$	−5.15961	−0.228471
$511$	−3.00151	−0.132779
$512$	−1.00000	−0.0441942
$513$	33.7357	1.48947
$514$	3.92798	0.173256
$515$	14.1752	0.624635
$516$	11.8026	0.519581
$517$	1.83480	0.0806946
$518$	0.563670	0.0247663
$519$	32.8426	1.44163
$520$	−1.00000	−0.0438529
$521$	15.6273	0.684645	0.342322	−	0.939583i	$-0.388786\pi$
$521$	15.6273	0.684645	0.342322	+	0.939583i	$0.388786\pi$
$522$	5.05463	0.221235
$523$	38.9318	1.70237	0.851183	−	0.524869i	$-0.175886\pi$
$523$	38.9318	1.70237	0.851183	+	0.524869i	$0.175886\pi$
$524$	6.96241	0.304154
$525$	−0.452892	−0.0197658
$526$	−0.199205	−0.00868577
$527$	−4.03548	−0.175788
$528$	0.391098	0.0170204
$529$	−22.7441	−0.988875
$530$	2.98625	0.129715
$531$	−5.03500	−0.218501
$532$	2.14106	0.0928268
$533$	−10.4532	−0.452780
$534$	0.836615	0.0362039
$535$	4.46117	0.192873
$536$	−6.36478	−0.274917
$537$	7.94375	0.342798
$538$	−6.25786	−0.269796
$539$	−2.10285	−0.0905760
$540$	5.58128	0.240180
$541$	17.2674	0.742382	0.371191	−	0.928557i	$-0.378950\pi$
$541$	17.2674	0.742382	0.371191	+	0.928557i	$0.378950\pi$
$542$	9.38130	0.402961
$543$	−16.7352	−0.718175
$544$	4.03548	0.173020
$545$	0.197311	0.00845186
$546$	−0.452892	−0.0193820
$547$	1.73673	0.0742573	0.0371287	−	0.999310i	$-0.488179\pi$
$547$	1.73673	0.0742573	0.0371287	+	0.999310i	$0.488179\pi$
$548$	17.4348	0.744779
$549$	−12.4296	−0.530480
$550$	−0.305890	−0.0130432
$551$	−22.3781	−0.953337
$552$	0.646757	0.0275278
$553$	−0.614763	−0.0261424
$554$	−3.39227	−0.144124
$555$	−2.03457	−0.0863628
$556$	3.90907	0.165781
$557$	−8.45258	−0.358147	−0.179074	−	0.983836i	$-0.557310\pi$
$557$	−8.45258	−0.358147	−0.179074	+	0.983836i	$0.557310\pi$
$558$	1.36528	0.0577971
$559$	−9.23118	−0.390437
$560$	0.354220	0.0149685
$561$	−1.57827	−0.0666346
$562$	−2.17502	−0.0917479
$563$	−7.34164	−0.309413	−0.154707	−	0.987960i	$-0.549443\pi$
$563$	−7.34164	−0.309413	−0.154707	+	0.987960i	$0.549443\pi$
$564$	7.66913	0.322928
$565$	5.71203	0.240307
$566$	−9.50795	−0.399649
$567$	1.07688	0.0452247
$568$	−15.3505	−0.644091
$569$	21.0020	0.880449	0.440225	−	0.897888i	$-0.354899\pi$
$569$	21.0020	0.880449	0.440225	+	0.897888i	$0.354899\pi$
$570$	−7.72818	−0.323698
$571$	−2.55298	−0.106839	−0.0534194	−	0.998572i	$-0.517012\pi$
$571$	−2.55298	−0.106839	−0.0534194	+	0.998572i	$0.517012\pi$
$572$	−0.305890	−0.0127899
$573$	24.9771	1.04343
$574$	3.70275	0.154550
$575$	−0.505848	−0.0210953
$576$	−1.36528	−0.0568869
$577$	−5.20952	−0.216875	−0.108438	−	0.994103i	$-0.534585\pi$
$577$	−5.20952	−0.216875	−0.108438	+	0.994103i	$0.534585\pi$
$578$	0.714879	0.0297350
$579$	−21.4373	−0.890906
$580$	−3.70225	−0.153728
$581$	4.28067	0.177592
$582$	−17.7624	−0.736274
$583$	0.913464	0.0378318
$584$	−8.47357	−0.350639
$585$	−1.36528	−0.0564476
$586$	−3.69141	−0.152491
$587$	11.8512	0.489152	0.244576	−	0.969630i	$-0.421351\pi$
$587$	11.8512	0.489152	0.244576	+	0.969630i	$0.421351\pi$
$588$	−8.78950	−0.362473
$589$	−6.04444	−0.249057
$590$	3.68788	0.151828
$591$	−9.20592	−0.378681
$592$	1.59130	0.0654020
$593$	37.8423	1.55400	0.776999	−	0.629501i	$-0.216741\pi$
$593$	37.8423	1.55400	0.776999	+	0.629501i	$0.216741\pi$
$594$	1.70726	0.0700495
$595$	−1.42945	−0.0586017
$596$	5.48686	0.224750
$597$	−23.9152	−0.978784
$598$	−0.505848	−0.0206857
$599$	21.7116	0.887111	0.443556	−	0.896247i	$-0.353717\pi$
$599$	21.7116	0.887111	0.443556	+	0.896247i	$0.353717\pi$
$600$	−1.27856	−0.0521970
$601$	0.695799	0.0283822	0.0141911	−	0.999899i	$-0.495483\pi$
$601$	0.695799	0.0283822	0.0141911	+	0.999899i	$0.495483\pi$
$602$	3.26987	0.133270
$603$	−8.68974	−0.353874
$604$	8.16293	0.332145
$605$	10.9064	0.443409
$606$	1.48605	0.0603666
$607$	−11.2309	−0.455848	−0.227924	−	0.973679i	$-0.573194\pi$
$607$	−11.2309	−0.455848	−0.227924	+	0.973679i	$0.573194\pi$
$608$	6.04444	0.245134
$609$	−1.67672	−0.0679441
$610$	9.10400	0.368610
$611$	−5.99825	−0.242663
$612$	5.50958	0.222712
$613$	−13.5569	−0.547559	−0.273779	−	0.961793i	$-0.588274\pi$
$613$	−13.5569	−0.547559	−0.273779	+	0.961793i	$0.588274\pi$
$614$	−16.7593	−0.676351
$615$	−13.3651	−0.538933
$616$	0.108352	0.00436564
$617$	45.7885	1.84337	0.921687	−	0.387933i	$-0.126811\pi$
$617$	45.7885	1.84337	0.921687	+	0.387933i	$0.126811\pi$
$618$	18.1239	0.729049
$619$	38.0461	1.52920	0.764600	−	0.644505i	$-0.222936\pi$
$619$	38.0461	1.52920	0.764600	+	0.644505i	$0.222936\pi$
$620$	−1.00000	−0.0401610
$621$	2.82328	0.113294
$622$	−18.1944	−0.729529
$623$	0.231781	0.00928611
$624$	−1.27856	−0.0511834
$625$	1.00000	0.0400000
$626$	−21.6566	−0.865572
$627$	−2.36397	−0.0944079
$628$	−7.93312	−0.316566
$629$	−6.42166	−0.256048
$630$	0.483611	0.0192675
$631$	−17.3261	−0.689742	−0.344871	−	0.938650i	$-0.612077\pi$
$631$	−17.3261	−0.689742	−0.344871	+	0.938650i	$0.612077\pi$
$632$	−1.73554	−0.0690361
$633$	2.94091	0.116891
$634$	−4.48216	−0.178009
$635$	−0.144472	−0.00573321
$636$	3.81810	0.151398
$637$	6.87453	0.272379
$638$	−1.13248	−0.0448354
$639$	−20.9578	−0.829076
$640$	1.00000	0.0395285
$641$	23.4844	0.927579	0.463789	−	0.885945i	$-0.346489\pi$
$641$	23.4844	0.927579	0.463789	+	0.885945i	$0.346489\pi$
$642$	5.70387	0.225114
$643$	−8.14473	−0.321197	−0.160598	−	0.987020i	$-0.551342\pi$
$643$	−8.14473	−0.321197	−0.160598	+	0.987020i	$0.551342\pi$
$644$	0.179181	0.00706074
$645$	−11.8026	−0.464727
$646$	−24.3922	−0.959700
$647$	−5.25274	−0.206506	−0.103253	−	0.994655i	$-0.532925\pi$
$647$	−5.25274	−0.206506	−0.103253	+	0.994655i	$0.532925\pi$
$648$	3.04014	0.119428
$649$	1.12808	0.0442812
$650$	1.00000	0.0392232
$651$	−0.452892	−0.0177502
$652$	5.25492	0.205799
$653$	0.955984	0.0374106	0.0187053	−	0.999825i	$-0.494046\pi$
$653$	0.955984	0.0374106	0.0187053	+	0.999825i	$0.494046\pi$
$654$	0.252273	0.00986467
$655$	−6.96241	−0.272044
$656$	10.4532	0.408131
$657$	−11.5688	−0.451343
$658$	2.12470	0.0828295
$659$	17.9978	0.701095	0.350547	−	0.936545i	$-0.385996\pi$
$659$	17.9978	0.701095	0.350547	+	0.936545i	$0.385996\pi$
$660$	−0.391098	−0.0152235
$661$	28.6663	1.11499	0.557494	−	0.830181i	$-0.311763\pi$
$661$	28.6663	1.11499	0.557494	+	0.830181i	$0.311763\pi$
$662$	−26.2620	−1.02070
$663$	5.15961	0.200382
$664$	12.0848	0.468980
$665$	−2.14106	−0.0830269
$666$	2.17258	0.0841857
$667$	−1.87278	−0.0725142
$668$	12.8495	0.497161
$669$	−21.4973	−0.831134
$670$	6.36478	0.245893
$671$	2.78482	0.107507
$672$	0.452892	0.0174707
$673$	19.0646	0.734885	0.367443	−	0.930046i	$-0.380233\pi$
$673$	19.0646	0.734885	0.367443	+	0.930046i	$0.380233\pi$
$674$	−0.275288	−0.0106037
$675$	−5.58128	−0.214823
$676$	1.00000	0.0384615
$677$	−36.7279	−1.41157	−0.705784	−	0.708427i	$-0.749405\pi$
$677$	−36.7279	−1.41157	−0.705784	+	0.708427i	$0.749405\pi$
$678$	7.30317	0.280476
$679$	−4.92100	−0.188851
$680$	−4.03548	−0.154754
$681$	−30.8640	−1.18271
$682$	−0.305890	−0.0117131
$683$	39.7439	1.52076	0.760378	−	0.649481i	$-0.225014\pi$
$683$	39.7439	1.52076	0.760378	+	0.649481i	$0.225014\pi$
$684$	8.25238	0.315538
$685$	−17.4348	−0.666151
$686$	−4.91464	−0.187642
$687$	−30.1560	−1.15052
$688$	9.23118	0.351935
$689$	−2.98625	−0.113767
$690$	−0.646757	−0.0246216
$691$	−41.1160	−1.56413	−0.782063	−	0.623199i	$-0.785833\pi$
$691$	−41.1160	−1.56413	−0.782063	+	0.623199i	$0.785833\pi$
$692$	25.6872	0.976481
$693$	0.147932	0.00561946
$694$	9.84915	0.373868
$695$	−3.90907	−0.148279
$696$	−4.73355	−0.179425
$697$	−42.1839	−1.59783
$698$	−4.46153	−0.168871
$699$	−34.3306	−1.29850
$700$	−0.354220	−0.0133883
$701$	10.2152	0.385823	0.192912	−	0.981216i	$-0.438207\pi$
$701$	10.2152	0.385823	0.192912	+	0.981216i	$0.438207\pi$
$702$	−5.58128	−0.210652
$703$	−9.61852	−0.362769
$704$	0.305890	0.0115286
$705$	−7.66913	−0.288836
$706$	4.93007	0.185546
$707$	0.411704	0.0154837
$708$	4.71517	0.177207
$709$	−14.0257	−0.526748	−0.263374	−	0.964694i	$-0.584835\pi$
$709$	−14.0257	−0.526748	−0.263374	+	0.964694i	$0.584835\pi$
$710$	15.3505	0.576093
$711$	−2.36951	−0.0888634
$712$	0.654341	0.0245225
$713$	−0.505848	−0.0189441
$714$	−1.82764	−0.0683976
$715$	0.305890	0.0114396
$716$	6.21304	0.232192
$717$	29.1751	1.08956
$718$	−20.5295	−0.766154
$719$	−9.45537	−0.352626	−0.176313	−	0.984334i	$-0.556417\pi$
$719$	−9.45537	−0.352626	−0.176313	+	0.984334i	$0.556417\pi$
$720$	1.36528	0.0508812
$721$	5.02115	0.186997
$722$	−17.5353	−0.652595
$723$	9.36176	0.348168
$724$	−13.0891	−0.486452
$725$	3.70225	0.137498
$726$	13.9445	0.517530
$727$	−44.6282	−1.65517	−0.827584	−	0.561342i	$-0.810285\pi$
$727$	−44.6282	−1.65517	−0.827584	+	0.561342i	$0.810285\pi$
$728$	−0.354220	−0.0131283
$729$	25.5587	0.946617
$730$	8.47357	0.313621
$731$	−37.2523	−1.37782
$732$	11.6400	0.430227
$733$	−16.4852	−0.608894	−0.304447	−	0.952529i	$-0.598472\pi$
$733$	−16.4852	−0.608894	−0.304447	+	0.952529i	$0.598472\pi$
$734$	22.3284	0.824157
$735$	8.78950	0.324205
$736$	0.505848	0.0186458
$737$	1.94692	0.0717158
$738$	14.2717	0.525347
$739$	54.1507	1.99197	0.995983	−	0.0895398i	$-0.0285396\pi$
$739$	54.1507	1.99197	0.995983	+	0.0895398i	$0.0285396\pi$
$740$	−1.59130	−0.0584973
$741$	7.72818	0.283902
$742$	1.05779	0.0388327
$743$	18.2371	0.669054	0.334527	−	0.942386i	$-0.391423\pi$
$743$	18.2371	0.669054	0.334527	+	0.942386i	$0.391423\pi$
$744$	−1.27856	−0.0468743
$745$	−5.48686	−0.201023
$746$	34.0802	1.24777
$747$	16.4991	0.603672
$748$	−1.23441	−0.0451346
$749$	1.58024	0.0577405
$750$	1.27856	0.0466864
$751$	15.3820	0.561297	0.280648	−	0.959811i	$-0.409451\pi$
$751$	15.3820	0.561297	0.280648	+	0.959811i	$0.409451\pi$
$752$	5.99825	0.218734
$753$	11.6080	0.423019
$754$	3.70225	0.134828
$755$	−8.16293	−0.297079
$756$	1.97700	0.0719028
$757$	26.5481	0.964908	0.482454	−	0.875921i	$-0.339745\pi$
$757$	26.5481	0.964908	0.482454	+	0.875921i	$0.339745\pi$
$758$	32.7293	1.18878
$759$	−0.197836	−0.00718100
$760$	−6.04444	−0.219255
$761$	−36.6320	−1.32791	−0.663954	−	0.747773i	$-0.731123\pi$
$761$	−36.6320	−1.32791	−0.663954	+	0.747773i	$0.731123\pi$
$762$	−0.184717	−0.00669158
$763$	0.0698914	0.00253024
$764$	19.5353	0.706763
$765$	−5.50958	−0.199199
$766$	21.5392	0.778243
$767$	−3.68788	−0.133162
$768$	1.27856	0.0461361
$769$	−28.5041	−1.02788	−0.513941	−	0.857825i	$-0.671815\pi$
$769$	−28.5041	−1.02788	−0.513941	+	0.857825i	$0.671815\pi$
$770$	−0.108352	−0.00390475
$771$	−5.02215	−0.180868
$772$	−16.7668	−0.603450
$773$	−6.41302	−0.230660	−0.115330	−	0.993327i	$-0.536793\pi$
$773$	−6.41302	−0.230660	−0.115330	+	0.993327i	$0.536793\pi$
$774$	12.6032	0.453012
$775$	1.00000	0.0359211
$776$	−13.8925	−0.498711
$777$	−0.720686	−0.0258545
$778$	3.52820	0.126492
$779$	−63.1840	−2.26380
$780$	1.27856	0.0457798
$781$	4.69555	0.168020
$782$	−2.04134	−0.0729982
$783$	−20.6633	−0.738446
$784$	−6.87453	−0.245519
$785$	7.93312	0.283145
$786$	−8.90185	−0.317519
$787$	−35.8662	−1.27849	−0.639246	−	0.769002i	$-0.720754\pi$
$787$	−35.8662	−1.27849	−0.639246	+	0.769002i	$0.720754\pi$
$788$	−7.20022	−0.256497
$789$	0.254696	0.00906742
$790$	1.73554	0.0617477
$791$	2.02331	0.0719408
$792$	0.417626	0.0148397
$793$	−9.10400	−0.323292
$794$	−4.09690	−0.145394
$795$	−3.81810	−0.135414
$796$	−18.7048	−0.662974
$797$	−34.9069	−1.23647	−0.618233	−	0.785995i	$-0.712151\pi$
$797$	−34.9069	−1.23647	−0.618233	+	0.785995i	$0.712151\pi$
$798$	−2.73748	−0.0969056
$799$	−24.2059	−0.856341
$800$	−1.00000	−0.0353553
$801$	0.893362	0.0315654
$802$	2.37350	0.0838114
$803$	2.59198	0.0914689
$804$	8.13776	0.286997
$805$	−0.179181	−0.00631532
$806$	1.00000	0.0352235
$807$	8.00105	0.281650
$808$	1.16228	0.0408890
$809$	21.7089	0.763243	0.381621	−	0.924319i	$-0.375366\pi$
$809$	21.7089	0.763243	0.381621	+	0.924319i	$0.375366\pi$
$810$	−3.04014	−0.106820
$811$	−8.59894	−0.301950	−0.150975	−	0.988538i	$-0.548241\pi$
$811$	−8.59894	−0.301950	−0.150975	+	0.988538i	$0.548241\pi$
$812$	−1.31141	−0.0460216
$813$	−11.9945	−0.420667
$814$	−0.486762	−0.0170610
$815$	−5.25492	−0.184072
$816$	−5.15961	−0.180622
$817$	−55.7973	−1.95210
$818$	−25.0081	−0.874388
$819$	−0.483611	−0.0168988
$820$	−10.4532	−0.365043
$821$	29.4342	1.02726	0.513630	−	0.858012i	$-0.328300\pi$
$821$	29.4342	1.02726	0.513630	+	0.858012i	$0.328300\pi$
$822$	−22.2915	−0.777505
$823$	29.8407	1.04018	0.520091	−	0.854111i	$-0.325898\pi$
$823$	29.8407	1.04018	0.520091	+	0.854111i	$0.325898\pi$
$824$	14.1752	0.493817
$825$	0.391098	0.0136163
$826$	1.30632	0.0454527
$827$	56.0721	1.94982	0.974909	−	0.222604i	$-0.0714557\pi$
$827$	56.0721	1.94982	0.974909	+	0.222604i	$0.0714557\pi$
$828$	0.690626	0.0240009
$829$	−4.03555	−0.140160	−0.0700802	−	0.997541i	$-0.522326\pi$
$829$	−4.03555	−0.140160	−0.0700802	+	0.997541i	$0.522326\pi$
$830$	−12.0848	−0.419468
$831$	4.33722	0.150456
$832$	−1.00000	−0.0346688
$833$	27.7420	0.961205
$834$	−4.99798	−0.173066
$835$	−12.8495	−0.444674
$836$	−1.84893	−0.0639466
$837$	−5.58128	−0.192917
$838$	−26.2949	−0.908341
$839$	24.8294	0.857205	0.428603	−	0.903493i	$-0.359006\pi$
$839$	24.8294	0.857205	0.428603	+	0.903493i	$0.359006\pi$
$840$	−0.452892	−0.0156262
$841$	−15.2933	−0.527356
$842$	−39.4981	−1.36120
$843$	2.78090	0.0957792
$844$	2.30017	0.0791752
$845$	−1.00000	−0.0344010
$846$	8.18932	0.281555
$847$	3.86328	0.132744
$848$	2.98625	0.102548
$849$	12.1565	0.417210
$850$	4.03548	0.138416
$851$	−0.804955	−0.0275935
$852$	19.6265	0.672393
$853$	10.5428	0.360977	0.180489	−	0.983577i	$-0.442232\pi$
$853$	10.5428	0.360977	0.180489	+	0.983577i	$0.442232\pi$
$854$	3.22482	0.110351
$855$	−8.25238	−0.282226
$856$	4.46117	0.152480
$857$	3.48104	0.118910	0.0594550	−	0.998231i	$-0.481064\pi$
$857$	3.48104	0.118910	0.0594550	+	0.998231i	$0.481064\pi$
$858$	0.391098	0.0133519
$859$	−1.56731	−0.0534759	−0.0267380	−	0.999642i	$-0.508512\pi$
$859$	−1.56731	−0.0534759	−0.0267380	+	0.999642i	$0.508512\pi$
$860$	−9.23118	−0.314781
$861$	−4.73419	−0.161341
$862$	−28.2755	−0.963069
$863$	−30.9882	−1.05485	−0.527426	−	0.849601i	$-0.676843\pi$
$863$	−30.9882	−1.05485	−0.527426	+	0.849601i	$0.676843\pi$
$864$	5.58128	0.189879
$865$	−25.6872	−0.873391
$866$	−23.4890	−0.798189
$867$	−0.914015	−0.0310416
$868$	−0.354220	−0.0120230
$869$	0.530884	0.0180090
$870$	4.73355	0.160482
$871$	−6.36478	−0.215662
$872$	0.197311	0.00668178
$873$	−18.9672	−0.641942
$874$	−3.05757	−0.103424
$875$	0.354220	0.0119748
$876$	10.8340	0.366046
$877$	39.6050	1.33737	0.668683	−	0.743548i	$-0.266859\pi$
$877$	39.6050	1.33737	0.668683	+	0.743548i	$0.266859\pi$
$878$	−1.82431	−0.0615676
$879$	4.71969	0.159191
$880$	−0.305890	−0.0103115
$881$	−16.2611	−0.547850	−0.273925	−	0.961751i	$-0.588322\pi$
$881$	−16.2611	−0.547850	−0.273925	+	0.961751i	$0.588322\pi$
$882$	−9.38569	−0.316033
$883$	−10.3012	−0.346664	−0.173332	−	0.984863i	$-0.555453\pi$
$883$	−10.3012	−0.346664	−0.173332	+	0.984863i	$0.555453\pi$
$884$	4.03548	0.135728
$885$	−4.71517	−0.158499
$886$	−8.07473	−0.271276
$887$	−7.64491	−0.256691	−0.128346	−	0.991730i	$-0.540967\pi$
$887$	−7.64491	−0.256691	−0.128346	+	0.991730i	$0.540967\pi$
$888$	−2.03457	−0.0682758
$889$	−0.0511751	−0.00171636
$890$	−0.654341	−0.0219336
$891$	−0.929948	−0.0311544
$892$	−16.8137	−0.562964
$893$	−36.2561	−1.21326
$894$	−7.01528	−0.234626
$895$	−6.21304	−0.207679
$896$	0.354220	0.0118337
$897$	0.646757	0.0215946
$898$	−7.37436	−0.246086
$899$	3.70225	0.123477
$900$	−1.36528	−0.0455095
$901$	−12.0510	−0.401476
$902$	−3.19754	−0.106466
$903$	−4.18072	−0.139126
$904$	5.71203	0.189979
$905$	13.0891	0.435096
$906$	−10.4368	−0.346739
$907$	−25.1462	−0.834966	−0.417483	−	0.908685i	$-0.637088\pi$
$907$	−25.1462	−0.834966	−0.417483	+	0.908685i	$0.637088\pi$
$908$	−24.1396	−0.801102
$909$	1.58685	0.0526324
$910$	0.354220	0.0117423
$911$	−2.38177	−0.0789114	−0.0394557	−	0.999221i	$-0.512562\pi$
$911$	−2.38177	−0.0789114	−0.0394557	+	0.999221i	$0.512562\pi$
$912$	−7.72818	−0.255906
$913$	−3.69660	−0.122340
$914$	0.776664	0.0256898
$915$	−11.6400	−0.384807
$916$	−23.5859	−0.779302
$917$	−2.46622	−0.0814419
$918$	−22.5232	−0.743375
$919$	−28.1455	−0.928436	−0.464218	−	0.885721i	$-0.653665\pi$
$919$	−28.1455	−0.928436	−0.464218	+	0.885721i	$0.653665\pi$
$920$	−0.505848	−0.0166773
$921$	21.4278	0.706070
$922$	−10.3393	−0.340508
$923$	−15.3505	−0.505267
$924$	−0.138535	−0.00455746
$925$	1.59130	0.0523216
$926$	−8.13519	−0.267339
$927$	19.3532	0.635643
$928$	−3.70225	−0.121532
$929$	51.0576	1.67515	0.837573	−	0.546325i	$-0.183974\pi$
$929$	51.0576	1.67515	0.837573	+	0.546325i	$0.183974\pi$
$930$	1.27856	0.0419256
$931$	41.5527	1.36183
$932$	−26.8510	−0.879533
$933$	23.2626	0.761585
$934$	35.3349	1.15619
$935$	1.23441	0.0403696
$936$	−1.36528	−0.0446257
$937$	−12.9950	−0.424527	−0.212263	−	0.977212i	$-0.568083\pi$
$937$	−12.9950	−0.424527	−0.212263	+	0.977212i	$0.568083\pi$
$938$	2.25453	0.0736132
$939$	27.6893	0.903605
$940$	−5.99825	−0.195641
$941$	−4.49051	−0.146386	−0.0731932	−	0.997318i	$-0.523319\pi$
$941$	−4.49051	−0.146386	−0.0731932	+	0.997318i	$0.523319\pi$
$942$	10.1430	0.330476
$943$	−5.28775	−0.172193
$944$	3.68788	0.120030
$945$	−1.97700	−0.0643119
$946$	−2.82372	−0.0918071
$947$	−46.1741	−1.50046	−0.750228	−	0.661179i	$-0.770056\pi$
$947$	−46.1741	−1.50046	−0.750228	+	0.661179i	$0.770056\pi$
$948$	2.21899	0.0720695
$949$	−8.47357	−0.275064
$950$	6.04444	0.196108
$951$	5.73071	0.185831
$952$	−1.42945	−0.0463287
$953$	−25.3289	−0.820484	−0.410242	−	0.911977i	$-0.634556\pi$
$953$	−25.3289	−0.820484	−0.410242	+	0.911977i	$0.634556\pi$
$954$	4.07709	0.132001
$955$	−19.5353	−0.632148
$956$	22.8187	0.738009
$957$	1.44795	0.0468054
$958$	4.36839	0.141136
$959$	−6.17577	−0.199426
$960$	−1.27856	−0.0412653
$961$	1.00000	0.0322581
$962$	1.59130	0.0513056
$963$	6.09076	0.196272
$964$	7.32211	0.235829
$965$	16.7668	0.539742
$966$	−0.229094	−0.00737099
$967$	16.2057	0.521139	0.260570	−	0.965455i	$-0.416090\pi$
$967$	16.2057	0.521139	0.260570	+	0.965455i	$0.416090\pi$
$968$	10.9064	0.350546
$969$	31.1869	1.00187
$970$	13.8925	0.446061
$971$	−1.74139	−0.0558838	−0.0279419	−	0.999610i	$-0.508895\pi$
$971$	−1.74139	−0.0558838	−0.0279419	+	0.999610i	$0.508895\pi$
$972$	12.8568	0.412383
$973$	−1.38467	−0.0443905
$974$	34.3260	1.09987
$975$	−1.27856	−0.0409467
$976$	9.10400	0.291412
$977$	−48.8452	−1.56270	−0.781349	−	0.624095i	$-0.785468\pi$
$977$	−48.8452	−1.56270	−0.781349	+	0.624095i	$0.785468\pi$
$978$	−6.71873	−0.214841
$979$	−0.200156	−0.00639702
$980$	6.87453	0.219599
$981$	0.269385	0.00860081
$982$	17.5968	0.561535
$983$	−20.3865	−0.650228	−0.325114	−	0.945675i	$-0.605403\pi$
$983$	−20.3865	−0.650228	−0.325114	+	0.945675i	$0.605403\pi$
$984$	−13.3651	−0.426064
$985$	7.20022	0.229418
$986$	14.9404	0.475799
$987$	−2.71656	−0.0864690
$988$	6.04444	0.192299
$989$	−4.66957	−0.148484
$990$	−0.417626	−0.0132730
$991$	39.0983	1.24200	0.620998	−	0.783812i	$-0.286727\pi$
$991$	39.0983	1.24200	0.620998	+	0.783812i	$0.286727\pi$
$992$	−1.00000	−0.0317500
$993$	33.5775	1.06555
$994$	5.43745	0.172465
$995$	18.7048	0.592982
$996$	−15.4511	−0.489587
$997$	21.0903	0.667936	0.333968	−	0.942584i	$-0.391612\pi$
$997$	21.0903	0.667936	0.333968	+	0.942584i	$0.391612\pi$
$998$	12.0402	0.381125
$999$	−8.88149	−0.280998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.p.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.p.1.7	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.27856 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.27856 q^{6} -0.354220 q^{7} -1.00000 q^{8} -1.36528 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.27856 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.27856 q^{6} -0.354220 q^{7} -1.00000 q^{8} -1.36528 q^{9} +1.00000 q^{10} +0.305890 q^{11} +1.27856 q^{12} -1.00000 q^{13} +0.354220 q^{14} -1.27856 q^{15} +1.00000 q^{16} -4.03548 q^{17} +1.36528 q^{18} -6.04444 q^{19} -1.00000 q^{20} -0.452892 q^{21} -0.305890 q^{22} -0.505848 q^{23} -1.27856 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.58128 q^{27} -0.354220 q^{28} +3.70225 q^{29} +1.27856 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.391098 q^{33} +4.03548 q^{34} +0.354220 q^{35} -1.36528 q^{36} +1.59130 q^{37} +6.04444 q^{38} -1.27856 q^{39} +1.00000 q^{40} +10.4532 q^{41} +0.452892 q^{42} +9.23118 q^{43} +0.305890 q^{44} +1.36528 q^{45} +0.505848 q^{46} +5.99825 q^{47} +1.27856 q^{48} -6.87453 q^{49} -1.00000 q^{50} -5.15961 q^{51} -1.00000 q^{52} +2.98625 q^{53} +5.58128 q^{54} -0.305890 q^{55} +0.354220 q^{56} -7.72818 q^{57} -3.70225 q^{58} +3.68788 q^{59} -1.27856 q^{60} +9.10400 q^{61} -1.00000 q^{62} +0.483611 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.391098 q^{66} +6.36478 q^{67} -4.03548 q^{68} -0.646757 q^{69} -0.354220 q^{70} +15.3505 q^{71} +1.36528 q^{72} +8.47357 q^{73} -1.59130 q^{74} +1.27856 q^{75} -6.04444 q^{76} -0.108352 q^{77} +1.27856 q^{78} +1.73554 q^{79} -1.00000 q^{80} -3.04014 q^{81} -10.4532 q^{82} -12.0848 q^{83} -0.452892 q^{84} +4.03548 q^{85} -9.23118 q^{86} +4.73355 q^{87} -0.305890 q^{88} -0.654341 q^{89} -1.36528 q^{90} +0.354220 q^{91} -0.505848 q^{92} +1.27856 q^{93} -5.99825 q^{94} +6.04444 q^{95} -1.27856 q^{96} +13.8925 q^{97} +6.87453 q^{98} -0.417626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} - 3 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 - 3 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} - 3 q^{7} - 9 q^{8} + 14 q^{9} + 9 q^{10} + 14 q^{11} - 3 q^{12} - 9 q^{13} + 3 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} - 14 q^{18} + 6 q^{19} - 9 q^{20} + q^{21} - 14 q^{22} - 4 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} - 15 q^{27} - 3 q^{28} + 15 q^{29} - 3 q^{30} + 9 q^{31} - 9 q^{32} + 14 q^{33} - q^{34} + 3 q^{35} + 14 q^{36} - 9 q^{37} - 6 q^{38} + 3 q^{39} + 9 q^{40} + 18 q^{41} - q^{42} - 23 q^{43} + 14 q^{44} - 14 q^{45} + 4 q^{46} + 3 q^{47} - 3 q^{48} + 12 q^{49} - 9 q^{50} - 11 q^{51} - 9 q^{52} - 6 q^{53} + 15 q^{54} - 14 q^{55} + 3 q^{56} + 17 q^{57} - 15 q^{58} + 28 q^{59} + 3 q^{60} - 9 q^{62} + 12 q^{63} + 9 q^{64} + 9 q^{65} - 14 q^{66} - 16 q^{67} + q^{68} - 6 q^{69} - 3 q^{70} + 32 q^{71} - 14 q^{72} - 11 q^{73} + 9 q^{74} - 3 q^{75} + 6 q^{76} - 29 q^{77} - 3 q^{78} - 8 q^{79} - 9 q^{80} + 9 q^{81} - 18 q^{82} + 15 q^{83} + q^{84} - q^{85} + 23 q^{86} - 19 q^{87} - 14 q^{88} + 51 q^{89} + 14 q^{90} + 3 q^{91} - 4 q^{92} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 3 q^{96} - 26 q^{97} - 12 q^{98} + 27 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 - 3 * q^7 - 9 * q^8 + 14 * q^9 + 9 * q^10 + 14 * q^11 - 3 * q^12 - 9 * q^13 + 3 * q^14 + 3 * q^15 + 9 * q^16 + q^17 - 14 * q^18 + 6 * q^19 - 9 * q^20 + q^21 - 14 * q^22 - 4 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 - 15 * q^27 - 3 * q^28 + 15 * q^29 - 3 * q^30 + 9 * q^31 - 9 * q^32 + 14 * q^33 - q^34 + 3 * q^35 + 14 * q^36 - 9 * q^37 - 6 * q^38 + 3 * q^39 + 9 * q^40 + 18 * q^41 - q^42 - 23 * q^43 + 14 * q^44 - 14 * q^45 + 4 * q^46 + 3 * q^47 - 3 * q^48 + 12 * q^49 - 9 * q^50 - 11 * q^51 - 9 * q^52 - 6 * q^53 + 15 * q^54 - 14 * q^55 + 3 * q^56 + 17 * q^57 - 15 * q^58 + 28 * q^59 + 3 * q^60 - 9 * q^62 + 12 * q^63 + 9 * q^64 + 9 * q^65 - 14 * q^66 - 16 * q^67 + q^68 - 6 * q^69 - 3 * q^70 + 32 * q^71 - 14 * q^72 - 11 * q^73 + 9 * q^74 - 3 * q^75 + 6 * q^76 - 29 * q^77 - 3 * q^78 - 8 * q^79 - 9 * q^80 + 9 * q^81 - 18 * q^82 + 15 * q^83 + q^84 - q^85 + 23 * q^86 - 19 * q^87 - 14 * q^88 + 51 * q^89 + 14 * q^90 + 3 * q^91 - 4 * q^92 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 3 * q^96 - 26 * q^97 - 12 * q^98 + 27 * q^99

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