LMFDB - Embedded newform 4030.2.a.m.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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 15x^{6} + 31x^{5} + 79x^{4} - 85x^{3} - 162x^{2} + 45x + 81 $ x^8 - 3x^7 - 15x^6 + 31x^5 + 79x^4 - 85x^3 - 162x^2 + 45*x + 81
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			$-1.77519$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.77519 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77519 q^{6} -3.40676 q^{7} -1.00000 q^{8} +4.70170 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.77519 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77519 q^{6} -3.40676 q^{7} -1.00000 q^{8} +4.70170 q^{9} -1.00000 q^{10} +2.66800 q^{11} +2.77519 q^{12} +1.00000 q^{13} +3.40676 q^{14} +2.77519 q^{15} +1.00000 q^{16} +3.25717 q^{17} -4.70170 q^{18} -1.99628 q^{19} +1.00000 q^{20} -9.45443 q^{21} -2.66800 q^{22} -1.57114 q^{23} -2.77519 q^{24} +1.00000 q^{25} -1.00000 q^{26} +4.72256 q^{27} -3.40676 q^{28} -0.00526255 q^{29} -2.77519 q^{30} +1.00000 q^{31} -1.00000 q^{32} +7.40423 q^{33} -3.25717 q^{34} -3.40676 q^{35} +4.70170 q^{36} +6.17978 q^{37} +1.99628 q^{38} +2.77519 q^{39} -1.00000 q^{40} +7.25327 q^{41} +9.45443 q^{42} +10.7864 q^{43} +2.66800 q^{44} +4.70170 q^{45} +1.57114 q^{46} -7.91638 q^{47} +2.77519 q^{48} +4.60603 q^{49} -1.00000 q^{50} +9.03928 q^{51} +1.00000 q^{52} +10.3864 q^{53} -4.72256 q^{54} +2.66800 q^{55} +3.40676 q^{56} -5.54007 q^{57} +0.00526255 q^{58} +3.16047 q^{59} +2.77519 q^{60} +2.33508 q^{61} -1.00000 q^{62} -16.0176 q^{63} +1.00000 q^{64} +1.00000 q^{65} -7.40423 q^{66} -11.4678 q^{67} +3.25717 q^{68} -4.36021 q^{69} +3.40676 q^{70} -15.8817 q^{71} -4.70170 q^{72} +8.38492 q^{73} -6.17978 q^{74} +2.77519 q^{75} -1.99628 q^{76} -9.08926 q^{77} -2.77519 q^{78} +13.0319 q^{79} +1.00000 q^{80} -0.999096 q^{81} -7.25327 q^{82} +10.2235 q^{83} -9.45443 q^{84} +3.25717 q^{85} -10.7864 q^{86} -0.0146046 q^{87} -2.66800 q^{88} -16.7243 q^{89} -4.70170 q^{90} -3.40676 q^{91} -1.57114 q^{92} +2.77519 q^{93} +7.91638 q^{94} -1.99628 q^{95} -2.77519 q^{96} +17.1489 q^{97} -4.60603 q^{98} +12.5442 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9} - 8 q^{10} + 4 q^{11} + 5 q^{12} + 8 q^{13} - 5 q^{14} + 5 q^{15} + 8 q^{16} + 19 q^{17} - 17 q^{18} - 14 q^{19} + 8 q^{20} + 3 q^{21} - 4 q^{22} + 8 q^{23} - 5 q^{24} + 8 q^{25} - 8 q^{26} + 17 q^{27} + 5 q^{28} + 21 q^{29} - 5 q^{30} + 8 q^{31} - 8 q^{32} + 4 q^{33} - 19 q^{34} + 5 q^{35} + 17 q^{36} - 3 q^{37} + 14 q^{38} + 5 q^{39} - 8 q^{40} - 8 q^{41} - 3 q^{42} + 25 q^{43} + 4 q^{44} + 17 q^{45} - 8 q^{46} + 11 q^{47} + 5 q^{48} + 15 q^{49} - 8 q^{50} + 7 q^{51} + 8 q^{52} + 2 q^{53} - 17 q^{54} + 4 q^{55} - 5 q^{56} + 9 q^{57} - 21 q^{58} - 22 q^{59} + 5 q^{60} - 2 q^{61} - 8 q^{62} + 30 q^{63} + 8 q^{64} + 8 q^{65} - 4 q^{66} - 14 q^{67} + 19 q^{68} + 36 q^{69} - 5 q^{70} + 4 q^{71} - 17 q^{72} + 17 q^{73} + 3 q^{74} + 5 q^{75} - 14 q^{76} + 17 q^{77} - 5 q^{78} - 12 q^{79} + 8 q^{80} + 40 q^{81} + 8 q^{82} + 21 q^{83} + 3 q^{84} + 19 q^{85} - 25 q^{86} + 25 q^{87} - 4 q^{88} - 25 q^{89} - 17 q^{90} + 5 q^{91} + 8 q^{92} + 5 q^{93} - 11 q^{94} - 14 q^{95} - 5 q^{96} + 8 q^{97} - 15 q^{98} - 57 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9 - 8 * q^10 + 4 * q^11 + 5 * q^12 + 8 * q^13 - 5 * q^14 + 5 * q^15 + 8 * q^16 + 19 * q^17 - 17 * q^18 - 14 * q^19 + 8 * q^20 + 3 * q^21 - 4 * q^22 + 8 * q^23 - 5 * q^24 + 8 * q^25 - 8 * q^26 + 17 * q^27 + 5 * q^28 + 21 * q^29 - 5 * q^30 + 8 * q^31 - 8 * q^32 + 4 * q^33 - 19 * q^34 + 5 * q^35 + 17 * q^36 - 3 * q^37 + 14 * q^38 + 5 * q^39 - 8 * q^40 - 8 * q^41 - 3 * q^42 + 25 * q^43 + 4 * q^44 + 17 * q^45 - 8 * q^46 + 11 * q^47 + 5 * q^48 + 15 * q^49 - 8 * q^50 + 7 * q^51 + 8 * q^52 + 2 * q^53 - 17 * q^54 + 4 * q^55 - 5 * q^56 + 9 * q^57 - 21 * q^58 - 22 * q^59 + 5 * q^60 - 2 * q^61 - 8 * q^62 + 30 * q^63 + 8 * q^64 + 8 * q^65 - 4 * q^66 - 14 * q^67 + 19 * q^68 + 36 * q^69 - 5 * q^70 + 4 * q^71 - 17 * q^72 + 17 * q^73 + 3 * q^74 + 5 * q^75 - 14 * q^76 + 17 * q^77 - 5 * q^78 - 12 * q^79 + 8 * q^80 + 40 * q^81 + 8 * q^82 + 21 * q^83 + 3 * q^84 + 19 * q^85 - 25 * q^86 + 25 * q^87 - 4 * q^88 - 25 * q^89 - 17 * q^90 + 5 * q^91 + 8 * q^92 + 5 * q^93 - 11 * q^94 - 14 * q^95 - 5 * q^96 + 8 * q^97 - 15 * q^98 - 57 * 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
$3$	2.77519	1.60226	0.801130	−	0.598491i	$-0.204233\pi$
$3$	2.77519	1.60226	0.801130	+	0.598491i	$0.204233\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.77519	−1.13297
$7$	−3.40676	−1.28764	−0.643818	−	0.765179i	$-0.722650\pi$
$7$	−3.40676	−1.28764	−0.643818	+	0.765179i	$0.722650\pi$
$8$	−1.00000	−0.353553
$9$	4.70170	1.56723
$10$	−1.00000	−0.316228
$11$	2.66800	0.804434	0.402217	−	0.915544i	$-0.368240\pi$
$11$	2.66800	0.804434	0.402217	+	0.915544i	$0.368240\pi$
$12$	2.77519	0.801130
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.40676	0.910496
$15$	2.77519	0.716552
$16$	1.00000	0.250000
$17$	3.25717	0.789980	0.394990	−	0.918685i	$-0.370748\pi$
$17$	3.25717	0.789980	0.394990	+	0.918685i	$0.370748\pi$
$18$	−4.70170	−1.10820
$19$	−1.99628	−0.457978	−0.228989	−	0.973429i	$-0.573542\pi$
$19$	−1.99628	−0.457978	−0.228989	+	0.973429i	$0.573542\pi$
$20$	1.00000	0.223607
$21$	−9.45443	−2.06313
$22$	−2.66800	−0.568821
$23$	−1.57114	−0.327605	−0.163802	−	0.986493i	$-0.552376\pi$
$23$	−1.57114	−0.327605	−0.163802	+	0.986493i	$0.552376\pi$
$24$	−2.77519	−0.566484
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	4.72256	0.908857
$28$	−3.40676	−0.643818
$29$	−0.00526255	−0.000977231 0	−0.000488615	−	1.00000i	$-0.500156\pi$
$29$	−0.00526255	−0.000977231 0	−0.000488615		1.00000i	$0.500156\pi$
$30$	−2.77519	−0.506679
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	7.40423	1.28891
$34$	−3.25717	−0.558600
$35$	−3.40676	−0.575848
$36$	4.70170	0.783617
$37$	6.17978	1.01595	0.507975	−	0.861372i	$-0.330394\pi$
$37$	6.17978	1.01595	0.507975	+	0.861372i	$0.330394\pi$
$38$	1.99628	0.323840
$39$	2.77519	0.444387
$40$	−1.00000	−0.158114
$41$	7.25327	1.13277	0.566385	−	0.824141i	$-0.308342\pi$
$41$	7.25327	1.13277	0.566385	+	0.824141i	$0.308342\pi$
$42$	9.45443	1.45885
$43$	10.7864	1.64491	0.822457	−	0.568827i	$-0.192603\pi$
$43$	10.7864	1.64491	0.822457	+	0.568827i	$0.192603\pi$
$44$	2.66800	0.402217
$45$	4.70170	0.700889
$46$	1.57114	0.231652
$47$	−7.91638	−1.15472	−0.577361	−	0.816489i	$-0.695918\pi$
$47$	−7.91638	−1.15472	−0.577361	+	0.816489i	$0.695918\pi$
$48$	2.77519	0.400565
$49$	4.60603	0.658005
$50$	−1.00000	−0.141421
$51$	9.03928	1.26575
$52$	1.00000	0.138675
$53$	10.3864	1.42669	0.713344	−	0.700814i	$-0.247180\pi$
$53$	10.3864	1.42669	0.713344	+	0.700814i	$0.247180\pi$
$54$	−4.72256	−0.642659
$55$	2.66800	0.359754
$56$	3.40676	0.455248
$57$	−5.54007	−0.733800
$58$	0.00526255	0.000691007 0
$59$	3.16047	0.411458	0.205729	−	0.978609i	$-0.434043\pi$
$59$	3.16047	0.411458	0.205729	+	0.978609i	$0.434043\pi$
$60$	2.77519	0.358276
$61$	2.33508	0.298976	0.149488	−	0.988764i	$-0.452237\pi$
$61$	2.33508	0.298976	0.149488	+	0.988764i	$0.452237\pi$
$62$	−1.00000	−0.127000
$63$	−16.0176	−2.01803
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−7.40423	−0.911398
$67$	−11.4678	−1.40101	−0.700505	−	0.713647i	$-0.747042\pi$
$67$	−11.4678	−1.40101	−0.700505	+	0.713647i	$0.747042\pi$
$68$	3.25717	0.394990
$69$	−4.36021	−0.524908
$70$	3.40676	0.407186
$71$	−15.8817	−1.88481	−0.942405	−	0.334474i	$-0.891441\pi$
$71$	−15.8817	−1.88481	−0.942405	+	0.334474i	$0.891441\pi$
$72$	−4.70170	−0.554101
$73$	8.38492	0.981381	0.490691	−	0.871334i	$-0.336745\pi$
$73$	8.38492	0.981381	0.490691	+	0.871334i	$0.336745\pi$
$74$	−6.17978	−0.718385
$75$	2.77519	0.320452
$76$	−1.99628	−0.228989
$77$	−9.08926	−1.03582
$78$	−2.77519	−0.314229
$79$	13.0319	1.46621	0.733103	−	0.680118i	$-0.238071\pi$
$79$	13.0319	1.46621	0.733103	+	0.680118i	$0.238071\pi$
$80$	1.00000	0.111803
$81$	−0.999096	−0.111011
$82$	−7.25327	−0.800989
$83$	10.2235	1.12218	0.561089	−	0.827755i	$-0.310382\pi$
$83$	10.2235	1.12218	0.561089	+	0.827755i	$0.310382\pi$
$84$	−9.45443	−1.03156
$85$	3.25717	0.353290
$86$	−10.7864	−1.16313
$87$	−0.0146046	−0.00156578
$88$	−2.66800	−0.284410
$89$	−16.7243	−1.77277	−0.886384	−	0.462950i	$-0.846791\pi$
$89$	−16.7243	−1.77277	−0.886384	+	0.462950i	$0.846791\pi$
$90$	−4.70170	−0.495603
$91$	−3.40676	−0.357126
$92$	−1.57114	−0.163802
$93$	2.77519	0.287774
$94$	7.91638	0.816512
$95$	−1.99628	−0.204814
$96$	−2.77519	−0.283242
$97$	17.1489	1.74121	0.870605	−	0.491984i	$-0.163728\pi$
$97$	17.1489	1.74121	0.870605	+	0.491984i	$0.163728\pi$
$98$	−4.60603	−0.465280
$99$	12.5442	1.26074
$100$	1.00000	0.100000
$101$	−13.0981	−1.30331	−0.651654	−	0.758516i	$-0.725925\pi$
$101$	−13.0981	−1.30331	−0.651654	+	0.758516i	$0.725925\pi$
$102$	−9.03928	−0.895022
$103$	2.57212	0.253438	0.126719	−	0.991939i	$-0.459555\pi$
$103$	2.57212	0.253438	0.126719	+	0.991939i	$0.459555\pi$
$104$	−1.00000	−0.0980581
$105$	−9.45443	−0.922658
$106$	−10.3864	−1.00882
$107$	8.25662	0.798198	0.399099	−	0.916908i	$-0.369323\pi$
$107$	8.25662	0.798198	0.399099	+	0.916908i	$0.369323\pi$
$108$	4.72256	0.454428
$109$	12.7984	1.22586	0.612932	−	0.790136i	$-0.289990\pi$
$109$	12.7984	1.22586	0.612932	+	0.790136i	$0.289990\pi$
$110$	−2.66800	−0.254384
$111$	17.1501	1.62781
$112$	−3.40676	−0.321909
$113$	4.80684	0.452190	0.226095	−	0.974105i	$-0.427404\pi$
$113$	4.80684	0.452190	0.226095	+	0.974105i	$0.427404\pi$
$114$	5.54007	0.518875
$115$	−1.57114	−0.146509
$116$	−0.00526255	−0.000488615 0
$117$	4.70170	0.434673
$118$	−3.16047	−0.290945
$119$	−11.0964	−1.01721
$120$	−2.77519	−0.253339
$121$	−3.88175	−0.352886
$122$	−2.33508	−0.211408
$123$	20.1292	1.81499
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	16.0176	1.42696
$127$	8.93532	0.792881	0.396441	−	0.918060i	$-0.370245\pi$
$127$	8.93532	0.792881	0.396441	+	0.918060i	$0.370245\pi$
$128$	−1.00000	−0.0883883
$129$	29.9344	2.63558
$130$	−1.00000	−0.0877058
$131$	13.0923	1.14388	0.571942	−	0.820294i	$-0.306190\pi$
$131$	13.0923	1.14388	0.571942	+	0.820294i	$0.306190\pi$
$132$	7.40423	0.644456
$133$	6.80086	0.589709
$134$	11.4678	0.990664
$135$	4.72256	0.406453
$136$	−3.25717	−0.279300
$137$	7.06798	0.603858	0.301929	−	0.953330i	$-0.402369\pi$
$137$	7.06798	0.603858	0.301929	+	0.953330i	$0.402369\pi$
$138$	4.36021	0.371166
$139$	−20.1664	−1.71049	−0.855246	−	0.518223i	$-0.826594\pi$
$139$	−20.1664	−1.71049	−0.855246	+	0.518223i	$0.826594\pi$
$140$	−3.40676	−0.287924
$141$	−21.9695	−1.85016
$142$	15.8817	1.33276
$143$	2.66800	0.223110
$144$	4.70170	0.391809
$145$	−0.00526255	−0.000437031 0
$146$	−8.38492	−0.693941
$147$	12.7826	1.05429
$148$	6.17978	0.507975
$149$	13.4372	1.10082	0.550409	−	0.834895i	$-0.314472\pi$
$149$	13.4372	1.10082	0.550409	+	0.834895i	$0.314472\pi$
$150$	−2.77519	−0.226594
$151$	−14.6284	−1.19044	−0.595222	−	0.803561i	$-0.702936\pi$
$151$	−14.6284	−1.19044	−0.595222	+	0.803561i	$0.702936\pi$
$152$	1.99628	0.161920
$153$	15.3142	1.23808
$154$	9.08926	0.732433
$155$	1.00000	0.0803219
$156$	2.77519	0.222193
$157$	6.89109	0.549969	0.274984	−	0.961449i	$-0.411327\pi$
$157$	6.89109	0.549969	0.274984	+	0.961449i	$0.411327\pi$
$158$	−13.0319	−1.03676
$159$	28.8244	2.28592
$160$	−1.00000	−0.0790569
$161$	5.35250	0.421836
$162$	0.999096	0.0784964
$163$	−18.0434	−1.41327	−0.706634	−	0.707580i	$-0.749787\pi$
$163$	−18.0434	−1.41327	−0.706634	+	0.707580i	$0.749787\pi$
$164$	7.25327	0.566385
$165$	7.40423	0.576419
$166$	−10.2235	−0.793500
$167$	−5.15459	−0.398874	−0.199437	−	0.979911i	$-0.563911\pi$
$167$	−5.15459	−0.398874	−0.199437	+	0.979911i	$0.563911\pi$
$168$	9.45443	0.729425
$169$	1.00000	0.0769231
$170$	−3.25717	−0.249814
$171$	−9.38592	−0.717759
$172$	10.7864	0.822457
$173$	5.68564	0.432272	0.216136	−	0.976363i	$-0.430655\pi$
$173$	5.68564	0.432272	0.216136	+	0.976363i	$0.430655\pi$
$174$	0.0146046	0.00110717
$175$	−3.40676	−0.257527
$176$	2.66800	0.201108
$177$	8.77092	0.659263
$178$	16.7243	1.25354
$179$	22.5474	1.68527	0.842637	−	0.538483i	$-0.181002\pi$
$179$	22.5474	1.68527	0.842637	+	0.538483i	$0.181002\pi$
$180$	4.70170	0.350444
$181$	8.03681	0.597371	0.298686	−	0.954352i	$-0.403452\pi$
$181$	8.03681	0.597371	0.298686	+	0.954352i	$0.403452\pi$
$182$	3.40676	0.252526
$183$	6.48030	0.479037
$184$	1.57114	0.115826
$185$	6.17978	0.454346
$186$	−2.77519	−0.203487
$187$	8.69015	0.635486
$188$	−7.91638	−0.577361
$189$	−16.0886	−1.17028
$190$	1.99628	0.144825
$191$	−18.3860	−1.33037	−0.665183	−	0.746680i	$-0.731647\pi$
$191$	−18.3860	−1.33037	−0.665183	+	0.746680i	$0.731647\pi$
$192$	2.77519	0.200282
$193$	−4.55627	−0.327967	−0.163984	−	0.986463i	$-0.552434\pi$
$193$	−4.55627	−0.327967	−0.163984	+	0.986463i	$0.552434\pi$
$194$	−17.1489	−1.23122
$195$	2.77519	0.198736
$196$	4.60603	0.329002
$197$	−17.5667	−1.25158	−0.625788	−	0.779993i	$-0.715223\pi$
$197$	−17.5667	−1.25158	−0.625788	+	0.779993i	$0.715223\pi$
$198$	−12.5442	−0.891475
$199$	−21.7608	−1.54258	−0.771292	−	0.636481i	$-0.780389\pi$
$199$	−21.7608	−1.54258	−0.771292	+	0.636481i	$0.780389\pi$
$200$	−1.00000	−0.0707107
$201$	−31.8253	−2.24478
$202$	13.0981	0.921578
$203$	0.0179283	0.00125832
$204$	9.03928	0.632876
$205$	7.25327	0.506590
$206$	−2.57212	−0.179208
$207$	−7.38703	−0.513434
$208$	1.00000	0.0693375
$209$	−5.32609	−0.368413
$210$	9.45443	0.652418
$211$	18.3686	1.26455	0.632275	−	0.774744i	$-0.282121\pi$
$211$	18.3686	1.26455	0.632275	+	0.774744i	$0.282121\pi$
$212$	10.3864	0.713344
$213$	−44.0748	−3.01995
$214$	−8.25662	−0.564411
$215$	10.7864	0.735628
$216$	−4.72256	−0.321329
$217$	−3.40676	−0.231266
$218$	−12.7984	−0.866817
$219$	23.2698	1.57243
$220$	2.66800	0.179877
$221$	3.25717	0.219101
$222$	−17.1501	−1.15104
$223$	15.7659	1.05576	0.527880	−	0.849319i	$-0.322987\pi$
$223$	15.7659	1.05576	0.527880	+	0.849319i	$0.322987\pi$
$224$	3.40676	0.227624
$225$	4.70170	0.313447
$226$	−4.80684	−0.319746
$227$	24.6834	1.63830	0.819149	−	0.573581i	$-0.194446\pi$
$227$	24.6834	1.63830	0.819149	+	0.573581i	$0.194446\pi$
$228$	−5.54007	−0.366900
$229$	−11.1572	−0.737289	−0.368645	−	0.929570i	$-0.620178\pi$
$229$	−11.1572	−0.737289	−0.368645	+	0.929570i	$0.620178\pi$
$230$	1.57114	0.103598
$231$	−25.2245	−1.65965
$232$	0.00526255	0.000345503 0
$233$	7.42398	0.486361	0.243180	−	0.969981i	$-0.421809\pi$
$233$	7.42398	0.486361	0.243180	+	0.969981i	$0.421809\pi$
$234$	−4.70170	−0.307360
$235$	−7.91638	−0.516408
$236$	3.16047	0.205729
$237$	36.1661	2.34924
$238$	11.0964	0.719273
$239$	8.32934	0.538780	0.269390	−	0.963031i	$-0.413178\pi$
$239$	8.32934	0.538780	0.269390	+	0.963031i	$0.413178\pi$
$240$	2.77519	0.179138
$241$	−11.2381	−0.723907	−0.361953	−	0.932196i	$-0.617890\pi$
$241$	−11.2381	−0.723907	−0.361953	+	0.932196i	$0.617890\pi$
$242$	3.88175	0.249528
$243$	−16.9404	−1.08672
$244$	2.33508	0.149488
$245$	4.60603	0.294269
$246$	−20.1292	−1.28339
$247$	−1.99628	−0.127020
$248$	−1.00000	−0.0635001
$249$	28.3723	1.79802
$250$	−1.00000	−0.0632456
$251$	−6.96565	−0.439668	−0.219834	−	0.975537i	$-0.570552\pi$
$251$	−6.96565	−0.439668	−0.219834	+	0.975537i	$0.570552\pi$
$252$	−16.0176	−1.00901
$253$	−4.19180	−0.263537
$254$	−8.93532	−0.560652
$255$	9.03928	0.566062
$256$	1.00000	0.0625000
$257$	21.5910	1.34681	0.673405	−	0.739274i	$-0.264831\pi$
$257$	21.5910	1.34681	0.673405	+	0.739274i	$0.264831\pi$
$258$	−29.9344	−1.86364
$259$	−21.0530	−1.30817
$260$	1.00000	0.0620174
$261$	−0.0247429	−0.00153155
$262$	−13.0923	−0.808848
$263$	−2.38550	−0.147096	−0.0735480	−	0.997292i	$-0.523432\pi$
$263$	−2.38550	−0.147096	−0.0735480	+	0.997292i	$0.523432\pi$
$264$	−7.40423	−0.455699
$265$	10.3864	0.638034
$266$	−6.80086	−0.416987
$267$	−46.4131	−2.84044
$268$	−11.4678	−0.700505
$269$	18.1685	1.10775	0.553876	−	0.832599i	$-0.313148\pi$
$269$	18.1685	1.10775	0.553876	+	0.832599i	$0.313148\pi$
$270$	−4.72256	−0.287406
$271$	−8.99893	−0.546646	−0.273323	−	0.961922i	$-0.588123\pi$
$271$	−8.99893	−0.546646	−0.273323	+	0.961922i	$0.588123\pi$
$272$	3.25717	0.197495
$273$	−9.45443	−0.572208
$274$	−7.06798	−0.426992
$275$	2.66800	0.160887
$276$	−4.36021	−0.262454
$277$	−19.4718	−1.16995	−0.584975	−	0.811052i	$-0.698896\pi$
$277$	−19.4718	−1.16995	−0.584975	+	0.811052i	$0.698896\pi$
$278$	20.1664	1.20950
$279$	4.70170	0.281484
$280$	3.40676	0.203593
$281$	5.75541	0.343339	0.171670	−	0.985155i	$-0.445084\pi$
$281$	5.75541	0.343339	0.171670	+	0.985155i	$0.445084\pi$
$282$	21.9695	1.30826
$283$	−21.8718	−1.30014	−0.650071	−	0.759873i	$-0.725261\pi$
$283$	−21.8718	−1.30014	−0.650071	+	0.759873i	$0.725261\pi$
$284$	−15.8817	−0.942405
$285$	−5.54007	−0.328165
$286$	−2.66800	−0.157762
$287$	−24.7102	−1.45859
$288$	−4.70170	−0.277051
$289$	−6.39084	−0.375932
$290$	0.00526255	0.000309028 0
$291$	47.5916	2.78987
$292$	8.38492	0.490691
$293$	−19.5390	−1.14148	−0.570739	−	0.821131i	$-0.693343\pi$
$293$	−19.5390	−1.14148	−0.570739	+	0.821131i	$0.693343\pi$
$294$	−12.7826	−0.745499
$295$	3.16047	0.184010
$296$	−6.17978	−0.359192
$297$	12.5998	0.731115
$298$	−13.4372	−0.778396
$299$	−1.57114	−0.0908613
$300$	2.77519	0.160226
$301$	−36.7468	−2.11805
$302$	14.6284	0.841771
$303$	−36.3497	−2.08824
$304$	−1.99628	−0.114495
$305$	2.33508	0.133706
$306$	−15.3142	−0.875457
$307$	−21.3001	−1.21566	−0.607832	−	0.794066i	$-0.707960\pi$
$307$	−21.3001	−1.21566	−0.607832	+	0.794066i	$0.707960\pi$
$308$	−9.08926	−0.517909
$309$	7.13812	0.406074
$310$	−1.00000	−0.0567962
$311$	−17.5746	−0.996564	−0.498282	−	0.867015i	$-0.666036\pi$
$311$	−17.5746	−0.996564	−0.498282	+	0.867015i	$0.666036\pi$
$312$	−2.77519	−0.157114
$313$	15.0753	0.852106	0.426053	−	0.904698i	$-0.359904\pi$
$313$	15.0753	0.852106	0.426053	+	0.904698i	$0.359904\pi$
$314$	−6.89109	−0.388887
$315$	−16.0176	−0.902489
$316$	13.0319	0.733103
$317$	0.747624	0.0419907	0.0209954	−	0.999780i	$-0.493316\pi$
$317$	0.747624	0.0419907	0.0209954	+	0.999780i	$0.493316\pi$
$318$	−28.8244	−1.61639
$319$	−0.0140405	−0.000786118 0
$320$	1.00000	0.0559017
$321$	22.9137	1.27892
$322$	−5.35250	−0.298283
$323$	−6.50223	−0.361794
$324$	−0.999096	−0.0555053
$325$	1.00000	0.0554700
$326$	18.0434	0.999331
$327$	35.5180	1.96415
$328$	−7.25327	−0.400495
$329$	26.9692	1.48686
$330$	−7.40423	−0.407590
$331$	14.5010	0.797047	0.398524	−	0.917158i	$-0.369523\pi$
$331$	14.5010	0.797047	0.398524	+	0.917158i	$0.369523\pi$
$332$	10.2235	0.561089
$333$	29.0555	1.59223
$334$	5.15459	0.282047
$335$	−11.4678	−0.626551
$336$	−9.45443	−0.515781
$337$	−2.60772	−0.142052	−0.0710258	−	0.997474i	$-0.522627\pi$
$337$	−2.60772	−0.142052	−0.0710258	+	0.997474i	$0.522627\pi$
$338$	−1.00000	−0.0543928
$339$	13.3399	0.724525
$340$	3.25717	0.176645
$341$	2.66800	0.144481
$342$	9.38592	0.507533
$343$	8.15568	0.440365
$344$	−10.7864	−0.581565
$345$	−4.36021	−0.234746
$346$	−5.68564	−0.305662
$347$	−23.9225	−1.28423	−0.642115	−	0.766609i	$-0.721943\pi$
$347$	−23.9225	−1.28423	−0.642115	+	0.766609i	$0.721943\pi$
$348$	−0.0146046	−0.000782889 0
$349$	16.3273	0.873979	0.436990	−	0.899467i	$-0.356045\pi$
$349$	16.3273	0.873979	0.436990	+	0.899467i	$0.356045\pi$
$350$	3.40676	0.182099
$351$	4.72256	0.252071
$352$	−2.66800	−0.142205
$353$	−10.0738	−0.536173	−0.268086	−	0.963395i	$-0.586391\pi$
$353$	−10.0738	−0.536173	−0.268086	+	0.963395i	$0.586391\pi$
$354$	−8.77092	−0.466169
$355$	−15.8817	−0.842913
$356$	−16.7243	−0.886384
$357$	−30.7947	−1.62983
$358$	−22.5474	−1.19167
$359$	−26.6503	−1.40655	−0.703276	−	0.710917i	$-0.748280\pi$
$359$	−26.6503	−1.40655	−0.703276	+	0.710917i	$0.748280\pi$
$360$	−4.70170	−0.247802
$361$	−15.0149	−0.790256
$362$	−8.03681	−0.422405
$363$	−10.7726	−0.565415
$364$	−3.40676	−0.178563
$365$	8.38492	0.438887
$366$	−6.48030	−0.338731
$367$	−15.6495	−0.816900	−0.408450	−	0.912781i	$-0.633931\pi$
$367$	−15.6495	−0.816900	−0.408450	+	0.912781i	$0.633931\pi$
$368$	−1.57114	−0.0819012
$369$	34.1027	1.77532
$370$	−6.17978	−0.321271
$371$	−35.3842	−1.83705
$372$	2.77519	0.143887
$373$	12.9179	0.668866	0.334433	−	0.942420i	$-0.391455\pi$
$373$	12.9179	0.668866	0.334433	+	0.942420i	$0.391455\pi$
$374$	−8.69015	−0.449357
$375$	2.77519	0.143310
$376$	7.91638	0.408256
$377$	−0.00526255	−0.000271035 0
$378$	16.0886	0.827510
$379$	7.98254	0.410035	0.205018	−	0.978758i	$-0.434275\pi$
$379$	7.98254	0.410035	0.205018	+	0.978758i	$0.434275\pi$
$380$	−1.99628	−0.102407
$381$	24.7972	1.27040
$382$	18.3860	0.940712
$383$	−14.9432	−0.763561	−0.381780	−	0.924253i	$-0.624689\pi$
$383$	−14.9432	−0.763561	−0.381780	+	0.924253i	$0.624689\pi$
$384$	−2.77519	−0.141621
$385$	−9.08926	−0.463232
$386$	4.55627	0.231908
$387$	50.7146	2.57797
$388$	17.1489	0.870605
$389$	16.0171	0.812098	0.406049	−	0.913851i	$-0.366906\pi$
$389$	16.0171	0.812098	0.406049	+	0.913851i	$0.366906\pi$
$390$	−2.77519	−0.140527
$391$	−5.11746	−0.258801
$392$	−4.60603	−0.232640
$393$	36.3338	1.83280
$394$	17.5667	0.884998
$395$	13.0319	0.655707
$396$	12.5442	0.630368
$397$	−34.9657	−1.75488	−0.877440	−	0.479687i	$-0.840750\pi$
$397$	−34.9657	−1.75488	−0.877440	+	0.479687i	$0.840750\pi$
$398$	21.7608	1.09077
$399$	18.8737	0.944867
$400$	1.00000	0.0500000
$401$	−16.9752	−0.847702	−0.423851	−	0.905732i	$-0.639322\pi$
$401$	−16.9752	−0.847702	−0.423851	+	0.905732i	$0.639322\pi$
$402$	31.8253	1.58730
$403$	1.00000	0.0498135
$404$	−13.0981	−0.651654
$405$	−0.999096	−0.0496455
$406$	−0.0179283	−0.000889765 0
$407$	16.4877	0.817264
$408$	−9.03928	−0.447511
$409$	36.9101	1.82509	0.912544	−	0.408978i	$-0.134115\pi$
$409$	36.9101	1.82509	0.912544	+	0.408978i	$0.134115\pi$
$410$	−7.25327	−0.358213
$411$	19.6150	0.967538
$412$	2.57212	0.126719
$413$	−10.7670	−0.529808
$414$	7.38703	0.363053
$415$	10.2235	0.501854
$416$	−1.00000	−0.0490290
$417$	−55.9657	−2.74065
$418$	5.32609	0.260508
$419$	9.18940	0.448932	0.224466	−	0.974482i	$-0.427936\pi$
$419$	9.18940	0.448932	0.224466	+	0.974482i	$0.427936\pi$
$420$	−9.45443	−0.461329
$421$	−17.6492	−0.860168	−0.430084	−	0.902789i	$-0.641516\pi$
$421$	−17.6492	−0.860168	−0.430084	+	0.902789i	$0.641516\pi$
$422$	−18.3686	−0.894172
$423$	−37.2205	−1.80972
$424$	−10.3864	−0.504410
$425$	3.25717	0.157996
$426$	44.0748	2.13543
$427$	−7.95506	−0.384972
$428$	8.25662	0.399099
$429$	7.40423	0.357480
$430$	−10.7864	−0.520168
$431$	22.5200	1.08475	0.542375	−	0.840137i	$-0.317525\pi$
$431$	22.5200	1.08475	0.542375	+	0.840137i	$0.317525\pi$
$432$	4.72256	0.227214
$433$	4.00011	0.192233	0.0961166	−	0.995370i	$-0.469358\pi$
$433$	4.00011	0.192233	0.0961166	+	0.995370i	$0.469358\pi$
$434$	3.40676	0.163530
$435$	−0.0146046	−0.000700237 0
$436$	12.7984	0.612932
$437$	3.13643	0.150036
$438$	−23.2698	−1.11187
$439$	−1.40765	−0.0671836	−0.0335918	−	0.999436i	$-0.510695\pi$
$439$	−1.40765	−0.0671836	−0.0335918	+	0.999436i	$0.510695\pi$
$440$	−2.66800	−0.127192
$441$	21.6562	1.03125
$442$	−3.25717	−0.154928
$443$	5.22257	0.248132	0.124066	−	0.992274i	$-0.460407\pi$
$443$	5.22257	0.248132	0.124066	+	0.992274i	$0.460407\pi$
$444$	17.1501	0.813907
$445$	−16.7243	−0.792806
$446$	−15.7659	−0.746536
$447$	37.2908	1.76380
$448$	−3.40676	−0.160954
$449$	11.9594	0.564400	0.282200	−	0.959356i	$-0.408936\pi$
$449$	11.9594	0.564400	0.282200	+	0.959356i	$0.408936\pi$
$450$	−4.70170	−0.221640
$451$	19.3517	0.911238
$452$	4.80684	0.226095
$453$	−40.5967	−1.90740
$454$	−24.6834	−1.15845
$455$	−3.40676	−0.159712
$456$	5.54007	0.259437
$457$	−32.3696	−1.51419	−0.757093	−	0.653307i	$-0.773381\pi$
$457$	−32.3696	−1.51419	−0.757093	+	0.653307i	$0.773381\pi$
$458$	11.1572	0.521342
$459$	15.3822	0.717978
$460$	−1.57114	−0.0732547
$461$	−23.2972	−1.08506	−0.542529	−	0.840037i	$-0.682533\pi$
$461$	−23.2972	−1.08506	−0.542529	+	0.840037i	$0.682533\pi$
$462$	25.2245	1.17355
$463$	42.7653	1.98747	0.993735	−	0.111759i	$-0.0356486\pi$
$463$	42.7653	1.98747	0.993735	+	0.111759i	$0.0356486\pi$
$464$	−0.00526255	−0.000244308 0
$465$	2.77519	0.128697
$466$	−7.42398	−0.343909
$467$	35.3276	1.63477	0.817384	−	0.576093i	$-0.195423\pi$
$467$	35.3276	1.63477	0.817384	+	0.576093i	$0.195423\pi$
$468$	4.70170	0.217336
$469$	39.0680	1.80399
$470$	7.91638	0.365155
$471$	19.1241	0.881193
$472$	−3.16047	−0.145472
$473$	28.7782	1.32322
$474$	−36.1661	−1.66116
$475$	−1.99628	−0.0915957
$476$	−11.0964	−0.508603
$477$	48.8340	2.23595
$478$	−8.32934	−0.380975
$479$	−28.3186	−1.29391	−0.646954	−	0.762529i	$-0.723958\pi$
$479$	−28.3186	−1.29391	−0.646954	+	0.762529i	$0.723958\pi$
$480$	−2.77519	−0.126670
$481$	6.17978	0.281774
$482$	11.2381	0.511879
$483$	14.8542	0.675890
$484$	−3.88175	−0.176443
$485$	17.1489	0.778692
$486$	16.9404	0.768430
$487$	−14.5727	−0.660354	−0.330177	−	0.943919i	$-0.607108\pi$
$487$	−14.5727	−0.660354	−0.330177	+	0.943919i	$0.607108\pi$
$488$	−2.33508	−0.105704
$489$	−50.0739	−2.26442
$490$	−4.60603	−0.208079
$491$	15.3933	0.694691	0.347345	−	0.937737i	$-0.387083\pi$
$491$	15.3933	0.694691	0.347345	+	0.937737i	$0.387083\pi$
$492$	20.1292	0.907495
$493$	−0.0171410	−0.000771993 0
$494$	1.99628	0.0898169
$495$	12.5442	0.563818
$496$	1.00000	0.0449013
$497$	54.1052	2.42695
$498$	−28.3723	−1.27139
$499$	−29.6506	−1.32735	−0.663673	−	0.748023i	$-0.731003\pi$
$499$	−29.6506	−1.32735	−0.663673	+	0.748023i	$0.731003\pi$
$500$	1.00000	0.0447214
$501$	−14.3050	−0.639100
$502$	6.96565	0.310892
$503$	−11.6270	−0.518422	−0.259211	−	0.965821i	$-0.583463\pi$
$503$	−11.6270	−0.518422	−0.259211	+	0.965821i	$0.583463\pi$
$504$	16.0176	0.713480
$505$	−13.0981	−0.582857
$506$	4.19180	0.186348
$507$	2.77519	0.123251
$508$	8.93532	0.396441
$509$	−0.768582	−0.0340668	−0.0170334	−	0.999855i	$-0.505422\pi$
$509$	−0.768582	−0.0340668	−0.0170334	+	0.999855i	$0.505422\pi$
$510$	−9.03928	−0.400266
$511$	−28.5654	−1.26366
$512$	−1.00000	−0.0441942
$513$	−9.42755	−0.416237
$514$	−21.5910	−0.952338
$515$	2.57212	0.113341
$516$	29.9344	1.31779
$517$	−21.1209	−0.928898
$518$	21.0530	0.925018
$519$	15.7788	0.692611
$520$	−1.00000	−0.0438529
$521$	−12.4878	−0.547102	−0.273551	−	0.961858i	$-0.588198\pi$
$521$	−12.4878	−0.547102	−0.273551	+	0.961858i	$0.588198\pi$
$522$	0.0247429	0.00108297
$523$	19.2210	0.840476	0.420238	−	0.907414i	$-0.361947\pi$
$523$	19.2210	0.840476	0.420238	+	0.907414i	$0.361947\pi$
$524$	13.0923	0.571942
$525$	−9.45443	−0.412625
$526$	2.38550	0.104013
$527$	3.25717	0.141885
$528$	7.40423	0.322228
$529$	−20.5315	−0.892675
$530$	−10.3864	−0.451158
$531$	14.8596	0.644852
$532$	6.80086	0.294855
$533$	7.25327	0.314174
$534$	46.4131	2.00849
$535$	8.25662	0.356965
$536$	11.4678	0.495332
$537$	62.5735	2.70024
$538$	−18.1685	−0.783299
$539$	12.2889	0.529321
$540$	4.72256	0.203227
$541$	−22.6849	−0.975298	−0.487649	−	0.873040i	$-0.662145\pi$
$541$	−22.6849	−0.975298	−0.487649	+	0.873040i	$0.662145\pi$
$542$	8.99893	0.386537
$543$	22.3037	0.957143
$544$	−3.25717	−0.139650
$545$	12.7984	0.548223
$546$	9.45443	0.404612
$547$	−28.4345	−1.21577	−0.607886	−	0.794024i	$-0.707982\pi$
$547$	−28.4345	−1.21577	−0.607886	+	0.794024i	$0.707982\pi$
$548$	7.06798	0.301929
$549$	10.9789	0.468566
$550$	−2.66800	−0.113764
$551$	0.0105055	0.000447551 0
$552$	4.36021	0.185583
$553$	−44.3967	−1.88794
$554$	19.4718	0.827279
$555$	17.1501	0.727981
$556$	−20.1664	−0.855246
$557$	43.2435	1.83228	0.916142	−	0.400853i	$-0.131286\pi$
$557$	43.2435	1.83228	0.916142	+	0.400853i	$0.131286\pi$
$558$	−4.70170	−0.199039
$559$	10.7864	0.456217
$560$	−3.40676	−0.143962
$561$	24.1168	1.01821
$562$	−5.75541	−0.242778
$563$	−8.13836	−0.342991	−0.171495	−	0.985185i	$-0.554860\pi$
$563$	−8.13836	−0.342991	−0.171495	+	0.985185i	$0.554860\pi$
$564$	−21.9695	−0.925082
$565$	4.80684	0.202225
$566$	21.8718	0.919339
$567$	3.40368	0.142941
$568$	15.8817	0.666381
$569$	−6.50407	−0.272665	−0.136332	−	0.990663i	$-0.543532\pi$
$569$	−6.50407	−0.272665	−0.136332	+	0.990663i	$0.543532\pi$
$570$	5.54007	0.232048
$571$	15.8836	0.664710	0.332355	−	0.943154i	$-0.392157\pi$
$571$	15.8836	0.664710	0.332355	+	0.943154i	$0.392157\pi$
$572$	2.66800	0.111555
$573$	−51.0248	−2.13159
$574$	24.7102	1.03138
$575$	−1.57114	−0.0655210
$576$	4.70170	0.195904
$577$	−22.9930	−0.957209	−0.478605	−	0.878031i	$-0.658857\pi$
$577$	−22.9930	−0.957209	−0.478605	+	0.878031i	$0.658857\pi$
$578$	6.39084	0.265824
$579$	−12.6445	−0.525489
$580$	−0.00526255	−0.000218515 0
$581$	−34.8292	−1.44496
$582$	−47.5916	−1.97273
$583$	27.7111	1.14768
$584$	−8.38492	−0.346971
$585$	4.70170	0.194392
$586$	19.5390	0.807147
$587$	6.73387	0.277937	0.138968	−	0.990297i	$-0.455621\pi$
$587$	6.73387	0.277937	0.138968	+	0.990297i	$0.455621\pi$
$588$	12.7826	0.527147
$589$	−1.99628	−0.0822553
$590$	−3.16047	−0.130115
$591$	−48.7511	−2.00535
$592$	6.17978	0.253987
$593$	−10.9485	−0.449601	−0.224801	−	0.974405i	$-0.572173\pi$
$593$	−10.9485	−0.449601	−0.224801	+	0.974405i	$0.572173\pi$
$594$	−12.5998	−0.516976
$595$	−11.0964	−0.454908
$596$	13.4372	0.550409
$597$	−60.3905	−2.47162
$598$	1.57114	0.0642486
$599$	−0.564336	−0.0230582	−0.0115291	−	0.999934i	$-0.503670\pi$
$599$	−0.564336	−0.0230582	−0.0115291	+	0.999934i	$0.503670\pi$
$600$	−2.77519	−0.113297
$601$	1.26557	0.0516237	0.0258119	−	0.999667i	$-0.491783\pi$
$601$	1.26557	0.0516237	0.0258119	+	0.999667i	$0.491783\pi$
$602$	36.7468	1.49769
$603$	−53.9180	−2.19571
$604$	−14.6284	−0.595222
$605$	−3.88175	−0.157816
$606$	36.3497	1.47661
$607$	8.93162	0.362523	0.181262	−	0.983435i	$-0.441982\pi$
$607$	8.93162	0.362523	0.181262	+	0.983435i	$0.441982\pi$
$608$	1.99628	0.0809599
$609$	0.0497544	0.00201615
$610$	−2.33508	−0.0945446
$611$	−7.91638	−0.320262
$612$	15.3142	0.619042
$613$	−18.6832	−0.754605	−0.377303	−	0.926090i	$-0.623148\pi$
$613$	−18.6832	−0.754605	−0.377303	+	0.926090i	$0.623148\pi$
$614$	21.3001	0.859604
$615$	20.1292	0.811689
$616$	9.08926	0.366217
$617$	17.3890	0.700056	0.350028	−	0.936739i	$-0.386172\pi$
$617$	17.3890	0.700056	0.350028	+	0.936739i	$0.386172\pi$
$618$	−7.13812	−0.287137
$619$	−46.5102	−1.86940	−0.934701	−	0.355435i	$-0.884333\pi$
$619$	−46.5102	−1.86940	−0.934701	+	0.355435i	$0.884333\pi$
$620$	1.00000	0.0401610
$621$	−7.41979	−0.297746
$622$	17.5746	0.704677
$623$	56.9756	2.28268
$624$	2.77519	0.111097
$625$	1.00000	0.0400000
$626$	−15.0753	−0.602530
$627$	−14.7809	−0.590294
$628$	6.89109	0.274984
$629$	20.1286	0.802580
$630$	16.0176	0.638156
$631$	−18.4684	−0.735214	−0.367607	−	0.929981i	$-0.619823\pi$
$631$	−18.4684	−0.735214	−0.367607	+	0.929981i	$0.619823\pi$
$632$	−13.0319	−0.518382
$633$	50.9766	2.02614
$634$	−0.747624	−0.0296919
$635$	8.93532	0.354587
$636$	28.8244	1.14296
$637$	4.60603	0.182498
$638$	0.0140405	0.000555869 0
$639$	−74.6710	−2.95394
$640$	−1.00000	−0.0395285
$641$	−32.1485	−1.26979	−0.634895	−	0.772599i	$-0.718956\pi$
$641$	−32.1485	−1.26979	−0.634895	+	0.772599i	$0.718956\pi$
$642$	−22.9137	−0.904333
$643$	−4.02424	−0.158700	−0.0793502	−	0.996847i	$-0.525285\pi$
$643$	−4.02424	−0.158700	−0.0793502	+	0.996847i	$0.525285\pi$
$644$	5.35250	0.210918
$645$	29.9344	1.17867
$646$	6.50223	0.255827
$647$	−10.8778	−0.427649	−0.213825	−	0.976872i	$-0.568592\pi$
$647$	−10.8778	−0.427649	−0.213825	+	0.976872i	$0.568592\pi$
$648$	0.999096	0.0392482
$649$	8.43215	0.330991
$650$	−1.00000	−0.0392232
$651$	−9.45443	−0.370548
$652$	−18.0434	−0.706634
$653$	−6.16371	−0.241204	−0.120602	−	0.992701i	$-0.538483\pi$
$653$	−6.16371	−0.241204	−0.120602	+	0.992701i	$0.538483\pi$
$654$	−35.5180	−1.38887
$655$	13.0923	0.511560
$656$	7.25327	0.283192
$657$	39.4234	1.53805
$658$	−26.9692	−1.05137
$659$	−22.3590	−0.870982	−0.435491	−	0.900193i	$-0.643425\pi$
$659$	−22.3590	−0.870982	−0.435491	+	0.900193i	$0.643425\pi$
$660$	7.40423	0.288209
$661$	−42.3202	−1.64606	−0.823032	−	0.567996i	$-0.807719\pi$
$661$	−42.3202	−1.64606	−0.823032	+	0.567996i	$0.807719\pi$
$662$	−14.5010	−0.563597
$663$	9.03928	0.351057
$664$	−10.2235	−0.396750
$665$	6.80086	0.263726
$666$	−29.0555	−1.12588
$667$	0.00826819	0.000320146 0
$668$	−5.15459	−0.199437
$669$	43.7533	1.69160
$670$	11.4678	0.443038
$671$	6.23000	0.240507
$672$	9.45443	0.364713
$673$	−21.2648	−0.819699	−0.409849	−	0.912153i	$-0.634419\pi$
$673$	−21.2648	−0.819699	−0.409849	+	0.912153i	$0.634419\pi$
$674$	2.60772	0.100446
$675$	4.72256	0.181771
$676$	1.00000	0.0384615
$677$	−29.9958	−1.15283	−0.576416	−	0.817156i	$-0.695549\pi$
$677$	−29.9958	−1.15283	−0.576416	+	0.817156i	$0.695549\pi$
$678$	−13.3399	−0.512317
$679$	−58.4223	−2.24204
$680$	−3.25717	−0.124907
$681$	68.5013	2.62498
$682$	−2.66800	−0.102163
$683$	36.5586	1.39887	0.699437	−	0.714694i	$-0.253434\pi$
$683$	36.5586	1.39887	0.699437	+	0.714694i	$0.253434\pi$
$684$	−9.38592	−0.358880
$685$	7.06798	0.270054
$686$	−8.15568	−0.311385
$687$	−30.9634	−1.18133
$688$	10.7864	0.411229
$689$	10.3864	0.395692
$690$	4.36021	0.165991
$691$	−1.20099	−0.0456877	−0.0228438	−	0.999739i	$-0.507272\pi$
$691$	−1.20099	−0.0456877	−0.0228438	+	0.999739i	$0.507272\pi$
$692$	5.68564	0.216136
$693$	−42.7350	−1.62337
$694$	23.9225	0.908087
$695$	−20.1664	−0.764955
$696$	0.0146046	0.000553586 0
$697$	23.6251	0.894865
$698$	−16.3273	−0.617997
$699$	20.6030	0.779276
$700$	−3.40676	−0.128764
$701$	31.4454	1.18767	0.593837	−	0.804585i	$-0.297612\pi$
$701$	31.4454	1.18767	0.593837	+	0.804585i	$0.297612\pi$
$702$	−4.72256	−0.178241
$703$	−12.3366	−0.465283
$704$	2.66800	0.100554
$705$	−21.9695	−0.827419
$706$	10.0738	0.379131
$707$	44.6221	1.67819
$708$	8.77092	0.329631
$709$	22.1278	0.831026	0.415513	−	0.909587i	$-0.363602\pi$
$709$	22.1278	0.831026	0.415513	+	0.909587i	$0.363602\pi$
$710$	15.8817	0.596029
$711$	61.2722	2.29789
$712$	16.7243	0.626768
$713$	−1.57114	−0.0588396
$714$	30.7947	1.15246
$715$	2.66800	0.0997777
$716$	22.5474	0.842637
$717$	23.1155	0.863266
$718$	26.6503	0.994582
$719$	14.9703	0.558299	0.279150	−	0.960248i	$-0.409947\pi$
$719$	14.9703	0.558299	0.279150	+	0.960248i	$0.409947\pi$
$720$	4.70170	0.175222
$721$	−8.76259	−0.326336
$722$	15.0149	0.558795
$723$	−31.1878	−1.15989
$724$	8.03681	0.298686
$725$	−0.00526255	−0.000195446 0
$726$	10.7726	0.399809
$727$	24.2862	0.900726	0.450363	−	0.892845i	$-0.351295\pi$
$727$	24.2862	0.900726	0.450363	+	0.892845i	$0.351295\pi$
$728$	3.40676	0.126263
$729$	−44.0155	−1.63020
$730$	−8.38492	−0.310340
$731$	35.1332	1.29945
$732$	6.48030	0.239519
$733$	−2.22305	−0.0821103	−0.0410552	−	0.999157i	$-0.513072\pi$
$733$	−2.22305	−0.0821103	−0.0410552	+	0.999157i	$0.513072\pi$
$734$	15.6495	0.577635
$735$	12.7826	0.471495
$736$	1.57114	0.0579129
$737$	−30.5961	−1.12702
$738$	−34.1027	−1.25534
$739$	19.2517	0.708185	0.354093	−	0.935210i	$-0.384790\pi$
$739$	19.2517	0.708185	0.354093	+	0.935210i	$0.384790\pi$
$740$	6.17978	0.227173
$741$	−5.54007	−0.203520
$742$	35.3842	1.29899
$743$	33.9700	1.24624	0.623119	−	0.782127i	$-0.285865\pi$
$743$	33.9700	1.24624	0.623119	+	0.782127i	$0.285865\pi$
$744$	−2.77519	−0.101744
$745$	13.4372	0.492301
$746$	−12.9179	−0.472959
$747$	48.0680	1.75872
$748$	8.69015	0.317743
$749$	−28.1284	−1.02779
$750$	−2.77519	−0.101336
$751$	16.5657	0.604489	0.302245	−	0.953230i	$-0.402264\pi$
$751$	16.5657	0.604489	0.302245	+	0.953230i	$0.402264\pi$
$752$	−7.91638	−0.288681
$753$	−19.3310	−0.704462
$754$	0.00526255	0.000191651 0
$755$	−14.6284	−0.532383
$756$	−16.0886	−0.585138
$757$	21.5746	0.784141	0.392071	−	0.919935i	$-0.371759\pi$
$757$	21.5746	0.784141	0.392071	+	0.919935i	$0.371759\pi$
$758$	−7.98254	−0.289939
$759$	−11.6331	−0.422254
$760$	1.99628	0.0724127
$761$	−32.5450	−1.17976	−0.589878	−	0.807493i	$-0.700824\pi$
$761$	−32.5450	−1.17976	−0.589878	+	0.807493i	$0.700824\pi$
$762$	−24.7972	−0.898310
$763$	−43.6011	−1.57847
$764$	−18.3860	−0.665183
$765$	15.3142	0.553688
$766$	14.9432	0.539919
$767$	3.16047	0.114118
$768$	2.77519	0.100141
$769$	28.1700	1.01583	0.507917	−	0.861406i	$-0.330416\pi$
$769$	28.1700	1.01583	0.507917	+	0.861406i	$0.330416\pi$
$770$	9.08926	0.327554
$771$	59.9192	2.15794
$772$	−4.55627	−0.163984
$773$	−27.1471	−0.976412	−0.488206	−	0.872728i	$-0.662349\pi$
$773$	−27.1471	−0.976412	−0.488206	+	0.872728i	$0.662349\pi$
$774$	−50.7146	−1.82290
$775$	1.00000	0.0359211
$776$	−17.1489	−0.615610
$777$	−58.4263	−2.09603
$778$	−16.0171	−0.574240
$779$	−14.4796	−0.518784
$780$	2.77519	0.0993679
$781$	−42.3724	−1.51620
$782$	5.11746	0.183000
$783$	−0.0248527	−0.000888163 0
$784$	4.60603	0.164501
$785$	6.89109	0.245954
$786$	−36.3338	−1.29598
$787$	36.8086	1.31208	0.656042	−	0.754724i	$-0.272229\pi$
$787$	36.8086	1.31208	0.656042	+	0.754724i	$0.272229\pi$
$788$	−17.5667	−0.625788
$789$	−6.62022	−0.235686
$790$	−13.0319	−0.463655
$791$	−16.3758	−0.582256
$792$	−12.5442	−0.445738
$793$	2.33508	0.0829211
$794$	34.9657	1.24089
$795$	28.8244	1.02230
$796$	−21.7608	−0.771292
$797$	28.3885	1.00557	0.502785	−	0.864411i	$-0.332309\pi$
$797$	28.3885	1.00557	0.502785	+	0.864411i	$0.332309\pi$
$798$	−18.8737	−0.668122
$799$	−25.7850	−0.912207
$800$	−1.00000	−0.0353553
$801$	−78.6325	−2.77834
$802$	16.9752	0.599416
$803$	22.3710	0.789456
$804$	−31.8253	−1.12239
$805$	5.35250	0.188651
$806$	−1.00000	−0.0352235
$807$	50.4211	1.77491
$808$	13.0981	0.460789
$809$	−7.12153	−0.250380	−0.125190	−	0.992133i	$-0.539954\pi$
$809$	−7.12153	−0.250380	−0.125190	+	0.992133i	$0.539954\pi$
$810$	0.999096	0.0351047
$811$	28.7659	1.01011	0.505054	−	0.863088i	$-0.331473\pi$
$811$	28.7659	1.01011	0.505054	+	0.863088i	$0.331473\pi$
$812$	0.0179283	0.000629159 0
$813$	−24.9738	−0.875869
$814$	−16.4877	−0.577893
$815$	−18.0434	−0.632032
$816$	9.03928	0.316438
$817$	−21.5327	−0.753335
$818$	−36.9101	−1.29053
$819$	−16.0176	−0.559700
$820$	7.25327	0.253295
$821$	31.7970	1.10972	0.554862	−	0.831943i	$-0.312771\pi$
$821$	31.7970	1.10972	0.554862	+	0.831943i	$0.312771\pi$
$822$	−19.6150	−0.684153
$823$	−31.7606	−1.10710	−0.553552	−	0.832815i	$-0.686728\pi$
$823$	−31.7606	−1.10710	−0.553552	+	0.832815i	$0.686728\pi$
$824$	−2.57212	−0.0896039
$825$	7.40423	0.257782
$826$	10.7670	0.374631
$827$	29.8289	1.03725	0.518626	−	0.855001i	$-0.326444\pi$
$827$	29.8289	1.03725	0.518626	+	0.855001i	$0.326444\pi$
$828$	−7.38703	−0.256717
$829$	−46.3734	−1.61062	−0.805308	−	0.592857i	$-0.798000\pi$
$829$	−46.3734	−1.61062	−0.805308	+	0.592857i	$0.798000\pi$
$830$	−10.2235	−0.354864
$831$	−54.0381	−1.87456
$832$	1.00000	0.0346688
$833$	15.0026	0.519810
$834$	55.9657	1.93793
$835$	−5.15459	−0.178382
$836$	−5.32609	−0.184207
$837$	4.72256	0.163235
$838$	−9.18940	−0.317443
$839$	−9.44171	−0.325964	−0.162982	−	0.986629i	$-0.552111\pi$
$839$	−9.44171	−0.325964	−0.162982	+	0.986629i	$0.552111\pi$
$840$	9.45443	0.326209
$841$	−29.0000	−0.999999
$842$	17.6492	0.608230
$843$	15.9724	0.550118
$844$	18.3686	0.632275
$845$	1.00000	0.0344010
$846$	37.2205	1.27967
$847$	13.2242	0.454389
$848$	10.3864	0.356672
$849$	−60.6984	−2.08316
$850$	−3.25717	−0.111720
$851$	−9.70929	−0.332830
$852$	−44.0748	−1.50998
$853$	37.3858	1.28007	0.640033	−	0.768347i	$-0.278921\pi$
$853$	37.3858	1.28007	0.640033	+	0.768347i	$0.278921\pi$
$854$	7.95506	0.272217
$855$	−9.38592	−0.320992
$856$	−8.25662	−0.282206
$857$	38.4279	1.31267	0.656337	−	0.754468i	$-0.272105\pi$
$857$	38.4279	1.31267	0.656337	+	0.754468i	$0.272105\pi$
$858$	−7.40423	−0.252776
$859$	−26.8859	−0.917336	−0.458668	−	0.888608i	$-0.651673\pi$
$859$	−26.8859	−0.917336	−0.458668	+	0.888608i	$0.651673\pi$
$860$	10.7864	0.367814
$861$	−68.5755	−2.33705
$862$	−22.5200	−0.767034
$863$	4.68300	0.159411	0.0797057	−	0.996818i	$-0.474602\pi$
$863$	4.68300	0.159411	0.0797057	+	0.996818i	$0.474602\pi$
$864$	−4.72256	−0.160665
$865$	5.68564	0.193318
$866$	−4.00011	−0.135929
$867$	−17.7358	−0.602340
$868$	−3.40676	−0.115633
$869$	34.7692	1.17947
$870$	0.0146046	0.000495142 0
$871$	−11.4678	−0.388570
$872$	−12.7984	−0.433408
$873$	80.6291	2.72888
$874$	−3.13643	−0.106091
$875$	−3.40676	−0.115170
$876$	23.2698	0.786213
$877$	−2.21680	−0.0748559	−0.0374279	−	0.999299i	$-0.511916\pi$
$877$	−2.21680	−0.0748559	−0.0374279	+	0.999299i	$0.511916\pi$
$878$	1.40765	0.0475060
$879$	−54.2244	−1.82895
$880$	2.66800	0.0899384
$881$	9.23628	0.311178	0.155589	−	0.987822i	$-0.450272\pi$
$881$	9.23628	0.311178	0.155589	+	0.987822i	$0.450272\pi$
$882$	−21.6562	−0.729202
$883$	−35.8255	−1.20562	−0.602812	−	0.797884i	$-0.705953\pi$
$883$	−35.8255	−1.20562	−0.602812	+	0.797884i	$0.705953\pi$
$884$	3.25717	0.109550
$885$	8.77092	0.294831
$886$	−5.22257	−0.175456
$887$	−20.4004	−0.684979	−0.342490	−	0.939522i	$-0.611270\pi$
$887$	−20.4004	−0.684979	−0.342490	+	0.939522i	$0.611270\pi$
$888$	−17.1501	−0.575519
$889$	−30.4405	−1.02094
$890$	16.7243	0.560599
$891$	−2.66559	−0.0893007
$892$	15.7659	0.527880
$893$	15.8033	0.528838
$894$	−37.2908	−1.24719
$895$	22.5474	0.753677
$896$	3.40676	0.113812
$897$	−4.36021	−0.145583
$898$	−11.9594	−0.399091
$899$	−0.00526255	−0.000175516 0
$900$	4.70170	0.156723
$901$	33.8304	1.12705
$902$	−19.3517	−0.644343
$903$	−101.979	−3.39366
$904$	−4.80684	−0.159873
$905$	8.03681	0.267153
$906$	40.5967	1.34874
$907$	−10.9601	−0.363923	−0.181961	−	0.983306i	$-0.558245\pi$
$907$	−10.9601	−0.363923	−0.181961	+	0.983306i	$0.558245\pi$
$908$	24.6834	0.819149
$909$	−61.5833	−2.04259
$910$	3.40676	0.112933
$911$	−31.0153	−1.02758	−0.513792	−	0.857915i	$-0.671760\pi$
$911$	−31.0153	−1.02758	−0.513792	+	0.857915i	$0.671760\pi$
$912$	−5.54007	−0.183450
$913$	27.2764	0.902718
$914$	32.3696	1.07069
$915$	6.48030	0.214232
$916$	−11.1572	−0.368645
$917$	−44.6025	−1.47290
$918$	−15.3822	−0.507687
$919$	−22.1468	−0.730556	−0.365278	−	0.930898i	$-0.619026\pi$
$919$	−22.1468	−0.730556	−0.365278	+	0.930898i	$0.619026\pi$
$920$	1.57114	0.0517989
$921$	−59.1120	−1.94781
$922$	23.2972	0.767251
$923$	−15.8817	−0.522752
$924$	−25.2245	−0.829824
$925$	6.17978	0.203190
$926$	−42.7653	−1.40535
$927$	12.0933	0.397197
$928$	0.00526255	0.000172752 0
$929$	−35.3127	−1.15857	−0.579286	−	0.815124i	$-0.696669\pi$
$929$	−35.3127	−1.15857	−0.579286	+	0.815124i	$0.696669\pi$
$930$	−2.77519	−0.0910022
$931$	−9.19494	−0.301352
$932$	7.42398	0.243180
$933$	−48.7729	−1.59675
$934$	−35.3276	−1.15596
$935$	8.69015	0.284198
$936$	−4.70170	−0.153680
$937$	3.29078	0.107505	0.0537526	−	0.998554i	$-0.482882\pi$
$937$	3.29078	0.107505	0.0537526	+	0.998554i	$0.482882\pi$
$938$	−39.0680	−1.27561
$939$	41.8369	1.36529
$940$	−7.91638	−0.258204
$941$	−3.06225	−0.0998264	−0.0499132	−	0.998754i	$-0.515894\pi$
$941$	−3.06225	−0.0998264	−0.0499132	+	0.998754i	$0.515894\pi$
$942$	−19.1241	−0.623097
$943$	−11.3959	−0.371101
$944$	3.16047	0.102865
$945$	−16.0886	−0.523363
$946$	−28.7782	−0.935661
$947$	−23.4241	−0.761180	−0.380590	−	0.924744i	$-0.624279\pi$
$947$	−23.4241	−0.761180	−0.380590	+	0.924744i	$0.624279\pi$
$948$	36.1661	1.17462
$949$	8.38492	0.272186
$950$	1.99628	0.0647679
$951$	2.07480	0.0672800
$952$	11.0964	0.359637
$953$	−34.4351	−1.11546	−0.557731	−	0.830022i	$-0.688328\pi$
$953$	−34.4351	−1.11546	−0.557731	+	0.830022i	$0.688328\pi$
$954$	−48.8340	−1.58106
$955$	−18.3860	−0.594958
$956$	8.32934	0.269390
$957$	−0.0389651	−0.00125956
$958$	28.3186	0.914931
$959$	−24.0789	−0.777550
$960$	2.77519	0.0895690
$961$	1.00000	0.0322581
$962$	−6.17978	−0.199244
$963$	38.8202	1.25096
$964$	−11.2381	−0.361953
$965$	−4.55627	−0.146672
$966$	−14.8542	−0.477927
$967$	20.9414	0.673432	0.336716	−	0.941606i	$-0.390684\pi$
$967$	20.9414	0.673432	0.336716	+	0.941606i	$0.390684\pi$
$968$	3.88175	0.124764
$969$	−18.0449	−0.579687
$970$	−17.1489	−0.550619
$971$	55.7549	1.78926	0.894629	−	0.446809i	$-0.147440\pi$
$971$	55.7549	1.78926	0.894629	+	0.446809i	$0.147440\pi$
$972$	−16.9404	−0.543362
$973$	68.7021	2.20249
$974$	14.5727	0.466941
$975$	2.77519	0.0888773
$976$	2.33508	0.0747441
$977$	−36.6923	−1.17389	−0.586946	−	0.809626i	$-0.699670\pi$
$977$	−36.6923	−1.17389	−0.586946	+	0.809626i	$0.699670\pi$
$978$	50.0739	1.60119
$979$	−44.6204	−1.42608
$980$	4.60603	0.147134
$981$	60.1743	1.92122
$982$	−15.3933	−0.491220
$983$	−51.7995	−1.65215	−0.826074	−	0.563562i	$-0.809431\pi$
$983$	−51.7995	−1.65215	−0.826074	+	0.563562i	$0.809431\pi$
$984$	−20.1292	−0.641696
$985$	−17.5667	−0.559722
$986$	0.0171410	0.000545881 0
$987$	74.8448	2.38234
$988$	−1.99628	−0.0635102
$989$	−16.9470	−0.538882
$990$	−12.5442	−0.398680
$991$	−43.9905	−1.39741	−0.698703	−	0.715412i	$-0.746239\pi$
$991$	−43.9905	−1.39741	−0.698703	+	0.715412i	$0.746239\pi$
$992$	−1.00000	−0.0317500
$993$	40.2431	1.27708
$994$	−54.1052	−1.71611
$995$	−21.7608	−0.689865
$996$	28.3723	0.899011
$997$	−41.8483	−1.32535	−0.662674	−	0.748908i	$-0.730578\pi$
$997$	−41.8483	−1.32535	−0.662674	+	0.748908i	$0.730578\pi$
$998$	29.6506	0.938575
$999$	29.1844	0.923352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.m.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.m.1.7	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.77519 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77519 q^{6} -3.40676 q^{7} -1.00000 q^{8} +4.70170 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.77519 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77519 q^{6} -3.40676 q^{7} -1.00000 q^{8} +4.70170 q^{9} -1.00000 q^{10} +2.66800 q^{11} +2.77519 q^{12} +1.00000 q^{13} +3.40676 q^{14} +2.77519 q^{15} +1.00000 q^{16} +3.25717 q^{17} -4.70170 q^{18} -1.99628 q^{19} +1.00000 q^{20} -9.45443 q^{21} -2.66800 q^{22} -1.57114 q^{23} -2.77519 q^{24} +1.00000 q^{25} -1.00000 q^{26} +4.72256 q^{27} -3.40676 q^{28} -0.00526255 q^{29} -2.77519 q^{30} +1.00000 q^{31} -1.00000 q^{32} +7.40423 q^{33} -3.25717 q^{34} -3.40676 q^{35} +4.70170 q^{36} +6.17978 q^{37} +1.99628 q^{38} +2.77519 q^{39} -1.00000 q^{40} +7.25327 q^{41} +9.45443 q^{42} +10.7864 q^{43} +2.66800 q^{44} +4.70170 q^{45} +1.57114 q^{46} -7.91638 q^{47} +2.77519 q^{48} +4.60603 q^{49} -1.00000 q^{50} +9.03928 q^{51} +1.00000 q^{52} +10.3864 q^{53} -4.72256 q^{54} +2.66800 q^{55} +3.40676 q^{56} -5.54007 q^{57} +0.00526255 q^{58} +3.16047 q^{59} +2.77519 q^{60} +2.33508 q^{61} -1.00000 q^{62} -16.0176 q^{63} +1.00000 q^{64} +1.00000 q^{65} -7.40423 q^{66} -11.4678 q^{67} +3.25717 q^{68} -4.36021 q^{69} +3.40676 q^{70} -15.8817 q^{71} -4.70170 q^{72} +8.38492 q^{73} -6.17978 q^{74} +2.77519 q^{75} -1.99628 q^{76} -9.08926 q^{77} -2.77519 q^{78} +13.0319 q^{79} +1.00000 q^{80} -0.999096 q^{81} -7.25327 q^{82} +10.2235 q^{83} -9.45443 q^{84} +3.25717 q^{85} -10.7864 q^{86} -0.0146046 q^{87} -2.66800 q^{88} -16.7243 q^{89} -4.70170 q^{90} -3.40676 q^{91} -1.57114 q^{92} +2.77519 q^{93} +7.91638 q^{94} -1.99628 q^{95} -2.77519 q^{96} +17.1489 q^{97} -4.60603 q^{98} +12.5442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9} - 8 q^{10} + 4 q^{11} + 5 q^{12} + 8 q^{13} - 5 q^{14} + 5 q^{15} + 8 q^{16} + 19 q^{17} - 17 q^{18} - 14 q^{19} + 8 q^{20} + 3 q^{21} - 4 q^{22} + 8 q^{23} - 5 q^{24} + 8 q^{25} - 8 q^{26} + 17 q^{27} + 5 q^{28} + 21 q^{29} - 5 q^{30} + 8 q^{31} - 8 q^{32} + 4 q^{33} - 19 q^{34} + 5 q^{35} + 17 q^{36} - 3 q^{37} + 14 q^{38} + 5 q^{39} - 8 q^{40} - 8 q^{41} - 3 q^{42} + 25 q^{43} + 4 q^{44} + 17 q^{45} - 8 q^{46} + 11 q^{47} + 5 q^{48} + 15 q^{49} - 8 q^{50} + 7 q^{51} + 8 q^{52} + 2 q^{53} - 17 q^{54} + 4 q^{55} - 5 q^{56} + 9 q^{57} - 21 q^{58} - 22 q^{59} + 5 q^{60} - 2 q^{61} - 8 q^{62} + 30 q^{63} + 8 q^{64} + 8 q^{65} - 4 q^{66} - 14 q^{67} + 19 q^{68} + 36 q^{69} - 5 q^{70} + 4 q^{71} - 17 q^{72} + 17 q^{73} + 3 q^{74} + 5 q^{75} - 14 q^{76} + 17 q^{77} - 5 q^{78} - 12 q^{79} + 8 q^{80} + 40 q^{81} + 8 q^{82} + 21 q^{83} + 3 q^{84} + 19 q^{85} - 25 q^{86} + 25 q^{87} - 4 q^{88} - 25 q^{89} - 17 q^{90} + 5 q^{91} + 8 q^{92} + 5 q^{93} - 11 q^{94} - 14 q^{95} - 5 q^{96} + 8 q^{97} - 15 q^{98} - 57 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9 - 8 * q^10 + 4 * q^11 + 5 * q^12 + 8 * q^13 - 5 * q^14 + 5 * q^15 + 8 * q^16 + 19 * q^17 - 17 * q^18 - 14 * q^19 + 8 * q^20 + 3 * q^21 - 4 * q^22 + 8 * q^23 - 5 * q^24 + 8 * q^25 - 8 * q^26 + 17 * q^27 + 5 * q^28 + 21 * q^29 - 5 * q^30 + 8 * q^31 - 8 * q^32 + 4 * q^33 - 19 * q^34 + 5 * q^35 + 17 * q^36 - 3 * q^37 + 14 * q^38 + 5 * q^39 - 8 * q^40 - 8 * q^41 - 3 * q^42 + 25 * q^43 + 4 * q^44 + 17 * q^45 - 8 * q^46 + 11 * q^47 + 5 * q^48 + 15 * q^49 - 8 * q^50 + 7 * q^51 + 8 * q^52 + 2 * q^53 - 17 * q^54 + 4 * q^55 - 5 * q^56 + 9 * q^57 - 21 * q^58 - 22 * q^59 + 5 * q^60 - 2 * q^61 - 8 * q^62 + 30 * q^63 + 8 * q^64 + 8 * q^65 - 4 * q^66 - 14 * q^67 + 19 * q^68 + 36 * q^69 - 5 * q^70 + 4 * q^71 - 17 * q^72 + 17 * q^73 + 3 * q^74 + 5 * q^75 - 14 * q^76 + 17 * q^77 - 5 * q^78 - 12 * q^79 + 8 * q^80 + 40 * q^81 + 8 * q^82 + 21 * q^83 + 3 * q^84 + 19 * q^85 - 25 * q^86 + 25 * q^87 - 4 * q^88 - 25 * q^89 - 17 * q^90 + 5 * q^91 + 8 * q^92 + 5 * q^93 - 11 * q^94 - 14 * q^95 - 5 * q^96 + 8 * q^97 - 15 * q^98 - 57 * q^99

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