LMFDB - Embedded newform 4030.2.a.j.1.3

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:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 20x^{4} + 9x^{3} - 37x^{2} - 3x + 20 $ x^7 - 3x^6 - 6x^5 + 20x^4 + 9x^3 - 37x^2 - 3x + 20
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.30511$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.69801 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.69801 q^{6} +4.41789 q^{7} +1.00000 q^{8} -0.116762 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.69801 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.69801 q^{6} +4.41789 q^{7} +1.00000 q^{8} -0.116762 q^{9} -1.00000 q^{10} -5.34924 q^{11} -1.69801 q^{12} -1.00000 q^{13} +4.41789 q^{14} +1.69801 q^{15} +1.00000 q^{16} -5.12392 q^{17} -0.116762 q^{18} +7.74667 q^{19} -1.00000 q^{20} -7.50162 q^{21} -5.34924 q^{22} +3.66021 q^{23} -1.69801 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.29229 q^{27} +4.41789 q^{28} -3.96049 q^{29} +1.69801 q^{30} +1.00000 q^{31} +1.00000 q^{32} +9.08306 q^{33} -5.12392 q^{34} -4.41789 q^{35} -0.116762 q^{36} -3.45749 q^{37} +7.74667 q^{38} +1.69801 q^{39} -1.00000 q^{40} -11.5734 q^{41} -7.50162 q^{42} -6.03489 q^{43} -5.34924 q^{44} +0.116762 q^{45} +3.66021 q^{46} -9.45970 q^{47} -1.69801 q^{48} +12.5178 q^{49} +1.00000 q^{50} +8.70046 q^{51} -1.00000 q^{52} -7.79976 q^{53} +5.29229 q^{54} +5.34924 q^{55} +4.41789 q^{56} -13.1539 q^{57} -3.96049 q^{58} +2.68431 q^{59} +1.69801 q^{60} -7.65180 q^{61} +1.00000 q^{62} -0.515840 q^{63} +1.00000 q^{64} +1.00000 q^{65} +9.08306 q^{66} +9.27554 q^{67} -5.12392 q^{68} -6.21507 q^{69} -4.41789 q^{70} +4.68621 q^{71} -0.116762 q^{72} +11.1318 q^{73} -3.45749 q^{74} -1.69801 q^{75} +7.74667 q^{76} -23.6323 q^{77} +1.69801 q^{78} +10.3829 q^{79} -1.00000 q^{80} -8.63608 q^{81} -11.5734 q^{82} -9.54435 q^{83} -7.50162 q^{84} +5.12392 q^{85} -6.03489 q^{86} +6.72494 q^{87} -5.34924 q^{88} +7.99993 q^{89} +0.116762 q^{90} -4.41789 q^{91} +3.66021 q^{92} -1.69801 q^{93} -9.45970 q^{94} -7.74667 q^{95} -1.69801 q^{96} -14.2148 q^{97} +12.5178 q^{98} +0.624586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 10 q^{11} - 3 q^{12} - 7 q^{13} + 4 q^{14} + 3 q^{15} + 7 q^{16} - 6 q^{17} + 4 q^{18} - 5 q^{19} - 7 q^{20} - 15 q^{21} - 10 q^{22} - 11 q^{23} - 3 q^{24} + 7 q^{25} - 7 q^{26} - 21 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 7 q^{31} + 7 q^{32} + 4 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + 3 q^{39} - 7 q^{40} - 12 q^{41} - 15 q^{42} - 5 q^{43} - 10 q^{44} - 4 q^{45} - 11 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 7 q^{50} - 29 q^{51} - 7 q^{52} - 18 q^{53} - 21 q^{54} + 10 q^{55} + 4 q^{56} + 13 q^{57} - 18 q^{58} - 11 q^{59} + 3 q^{60} - 25 q^{61} + 7 q^{62} + 17 q^{63} + 7 q^{64} + 7 q^{65} + 4 q^{66} - 22 q^{67} - 6 q^{68} - 18 q^{69} - 4 q^{70} - 22 q^{71} + 4 q^{72} + 19 q^{73} - 8 q^{74} - 3 q^{75} - 5 q^{76} - 47 q^{77} + 3 q^{78} - 20 q^{79} - 7 q^{80} + 7 q^{81} - 12 q^{82} - 8 q^{83} - 15 q^{84} + 6 q^{85} - 5 q^{86} + 29 q^{87} - 10 q^{88} - 4 q^{89} - 4 q^{90} - 4 q^{91} - 11 q^{92} - 3 q^{93} - 10 q^{94} + 5 q^{95} - 3 q^{96} + 13 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 10 * q^11 - 3 * q^12 - 7 * q^13 + 4 * q^14 + 3 * q^15 + 7 * q^16 - 6 * q^17 + 4 * q^18 - 5 * q^19 - 7 * q^20 - 15 * q^21 - 10 * q^22 - 11 * q^23 - 3 * q^24 + 7 * q^25 - 7 * q^26 - 21 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 7 * q^31 + 7 * q^32 + 4 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + 3 * q^39 - 7 * q^40 - 12 * q^41 - 15 * q^42 - 5 * q^43 - 10 * q^44 - 4 * q^45 - 11 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 7 * q^50 - 29 * q^51 - 7 * q^52 - 18 * q^53 - 21 * q^54 + 10 * q^55 + 4 * q^56 + 13 * q^57 - 18 * q^58 - 11 * q^59 + 3 * q^60 - 25 * q^61 + 7 * q^62 + 17 * q^63 + 7 * q^64 + 7 * q^65 + 4 * q^66 - 22 * q^67 - 6 * q^68 - 18 * q^69 - 4 * q^70 - 22 * q^71 + 4 * q^72 + 19 * q^73 - 8 * q^74 - 3 * q^75 - 5 * q^76 - 47 * q^77 + 3 * q^78 - 20 * q^79 - 7 * q^80 + 7 * q^81 - 12 * q^82 - 8 * q^83 - 15 * q^84 + 6 * q^85 - 5 * q^86 + 29 * q^87 - 10 * q^88 - 4 * q^89 - 4 * q^90 - 4 * q^91 - 11 * q^92 - 3 * q^93 - 10 * q^94 + 5 * q^95 - 3 * q^96 + 13 * q^97 + 7 * 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
$3$	−1.69801	−0.980347	−0.490173	−	0.871625i	$-0.663067\pi$
$3$	−1.69801	−0.980347	−0.490173	+	0.871625i	$0.663067\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.69801	−0.693210
$7$	4.41789	1.66981	0.834903	−	0.550397i	$-0.185524\pi$
$7$	4.41789	1.66981	0.834903	+	0.550397i	$0.185524\pi$
$8$	1.00000	0.353553
$9$	−0.116762	−0.0389206
$10$	−1.00000	−0.316228
$11$	−5.34924	−1.61286	−0.806428	−	0.591332i	$-0.798602\pi$
$11$	−5.34924	−1.61286	−0.806428	+	0.591332i	$0.798602\pi$
$12$	−1.69801	−0.490173
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.41789	1.18073
$15$	1.69801	0.438424
$16$	1.00000	0.250000
$17$	−5.12392	−1.24273	−0.621366	−	0.783520i	$-0.713422\pi$
$17$	−5.12392	−1.24273	−0.621366	+	0.783520i	$0.713422\pi$
$18$	−0.116762	−0.0275210
$19$	7.74667	1.77721	0.888604	−	0.458675i	$-0.151676\pi$
$19$	7.74667	1.77721	0.888604	+	0.458675i	$0.151676\pi$
$20$	−1.00000	−0.223607
$21$	−7.50162	−1.63699
$22$	−5.34924	−1.14046
$23$	3.66021	0.763207	0.381603	−	0.924326i	$-0.375372\pi$
$23$	3.66021	0.763207	0.381603	+	0.924326i	$0.375372\pi$
$24$	−1.69801	−0.346605
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	5.29229	1.01850
$28$	4.41789	0.834903
$29$	−3.96049	−0.735444	−0.367722	−	0.929936i	$-0.619862\pi$
$29$	−3.96049	−0.735444	−0.367722	+	0.929936i	$0.619862\pi$
$30$	1.69801	0.310013
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	9.08306	1.58116
$34$	−5.12392	−0.878745
$35$	−4.41789	−0.746760
$36$	−0.116762	−0.0194603
$37$	−3.45749	−0.568408	−0.284204	−	0.958764i	$-0.591729\pi$
$37$	−3.45749	−0.568408	−0.284204	+	0.958764i	$0.591729\pi$
$38$	7.74667	1.25668
$39$	1.69801	0.271899
$40$	−1.00000	−0.158114
$41$	−11.5734	−1.80746	−0.903731	−	0.428101i	$-0.859183\pi$
$41$	−11.5734	−1.80746	−0.903731	+	0.428101i	$0.859183\pi$
$42$	−7.50162	−1.15753
$43$	−6.03489	−0.920313	−0.460156	−	0.887838i	$-0.652207\pi$
$43$	−6.03489	−0.920313	−0.460156	+	0.887838i	$0.652207\pi$
$44$	−5.34924	−0.806428
$45$	0.116762	0.0174058
$46$	3.66021	0.539669
$47$	−9.45970	−1.37984	−0.689919	−	0.723886i	$-0.742354\pi$
$47$	−9.45970	−1.37984	−0.689919	+	0.723886i	$0.742354\pi$
$48$	−1.69801	−0.245087
$49$	12.5178	1.78825
$50$	1.00000	0.141421
$51$	8.70046	1.21831
$52$	−1.00000	−0.138675
$53$	−7.79976	−1.07138	−0.535690	−	0.844415i	$-0.679948\pi$
$53$	−7.79976	−1.07138	−0.535690	+	0.844415i	$0.679948\pi$
$54$	5.29229	0.720190
$55$	5.34924	0.721291
$56$	4.41789	0.590366
$57$	−13.1539	−1.74228
$58$	−3.96049	−0.520037
$59$	2.68431	0.349468	0.174734	−	0.984616i	$-0.444093\pi$
$59$	2.68431	0.349468	0.174734	+	0.984616i	$0.444093\pi$
$60$	1.69801	0.219212
$61$	−7.65180	−0.979712	−0.489856	−	0.871803i	$-0.662951\pi$
$61$	−7.65180	−0.979712	−0.489856	+	0.871803i	$0.662951\pi$
$62$	1.00000	0.127000
$63$	−0.515840	−0.0649898
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	9.08306	1.11805
$67$	9.27554	1.13319	0.566594	−	0.823997i	$-0.308261\pi$
$67$	9.27554	1.13319	0.566594	+	0.823997i	$0.308261\pi$
$68$	−5.12392	−0.621366
$69$	−6.21507	−0.748207
$70$	−4.41789	−0.528039
$71$	4.68621	0.556151	0.278075	−	0.960559i	$-0.410304\pi$
$71$	4.68621	0.556151	0.278075	+	0.960559i	$0.410304\pi$
$72$	−0.116762	−0.0137605
$73$	11.1318	1.30287	0.651437	−	0.758703i	$-0.274166\pi$
$73$	11.1318	1.30287	0.651437	+	0.758703i	$0.274166\pi$
$74$	−3.45749	−0.401925
$75$	−1.69801	−0.196069
$76$	7.74667	0.888604
$77$	−23.6323	−2.69316
$78$	1.69801	0.192262
$79$	10.3829	1.16817	0.584083	−	0.811694i	$-0.301454\pi$
$79$	10.3829	1.16817	0.584083	+	0.811694i	$0.301454\pi$
$80$	−1.00000	−0.111803
$81$	−8.63608	−0.959565
$82$	−11.5734	−1.27807
$83$	−9.54435	−1.04763	−0.523814	−	0.851832i	$-0.675491\pi$
$83$	−9.54435	−1.04763	−0.523814	+	0.851832i	$0.675491\pi$
$84$	−7.50162	−0.818494
$85$	5.12392	0.555767
$86$	−6.03489	−0.650759
$87$	6.72494	0.720990
$88$	−5.34924	−0.570231
$89$	7.99993	0.847991	0.423996	−	0.905664i	$-0.360627\pi$
$89$	7.99993	0.847991	0.423996	+	0.905664i	$0.360627\pi$
$90$	0.116762	0.0123078
$91$	−4.41789	−0.463121
$92$	3.66021	0.381603
$93$	−1.69801	−0.176075
$94$	−9.45970	−0.975693
$95$	−7.74667	−0.794791
$96$	−1.69801	−0.173302
$97$	−14.2148	−1.44329	−0.721646	−	0.692262i	$-0.756614\pi$
$97$	−14.2148	−1.44329	−0.721646	+	0.692262i	$0.756614\pi$
$98$	12.5178	1.26449
$99$	0.624586	0.0627733
$100$	1.00000	0.100000
$101$	1.05000	0.104479	0.0522394	−	0.998635i	$-0.483364\pi$
$101$	1.05000	0.104479	0.0522394	+	0.998635i	$0.483364\pi$
$102$	8.70046	0.861474
$103$	−17.5157	−1.72587	−0.862936	−	0.505313i	$-0.831377\pi$
$103$	−17.5157	−1.72587	−0.862936	+	0.505313i	$0.831377\pi$
$104$	−1.00000	−0.0980581
$105$	7.50162	0.732084
$106$	−7.79976	−0.757580
$107$	−11.1582	−1.07871	−0.539353	−	0.842080i	$-0.681331\pi$
$107$	−11.1582	−1.07871	−0.539353	+	0.842080i	$0.681331\pi$
$108$	5.29229	0.509251
$109$	−9.48278	−0.908285	−0.454143	−	0.890929i	$-0.650054\pi$
$109$	−9.48278	−0.908285	−0.454143	+	0.890929i	$0.650054\pi$
$110$	5.34924	0.510030
$111$	5.87086	0.557237
$112$	4.41789	0.417451
$113$	3.15963	0.297233	0.148616	−	0.988895i	$-0.452518\pi$
$113$	3.15963	0.297233	0.148616	+	0.988895i	$0.452518\pi$
$114$	−13.1539	−1.23198
$115$	−3.66021	−0.341316
$116$	−3.96049	−0.367722
$117$	0.116762	0.0107946
$118$	2.68431	0.247111
$119$	−22.6369	−2.07512
$120$	1.69801	0.155006
$121$	17.6143	1.60130
$122$	−7.65180	−0.692761
$123$	19.6518	1.77194
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	−0.515840	−0.0459547
$127$	9.51337	0.844175	0.422088	−	0.906555i	$-0.361297\pi$
$127$	9.51337	0.844175	0.422088	+	0.906555i	$0.361297\pi$
$128$	1.00000	0.0883883
$129$	10.2473	0.902225
$130$	1.00000	0.0877058
$131$	19.5734	1.71013	0.855067	−	0.518518i	$-0.173516\pi$
$131$	19.5734	1.71013	0.855067	+	0.518518i	$0.173516\pi$
$132$	9.08306	0.790579
$133$	34.2239	2.96759
$134$	9.27554	0.801285
$135$	−5.29229	−0.455488
$136$	−5.12392	−0.439372
$137$	−5.11164	−0.436717	−0.218358	−	0.975869i	$-0.570070\pi$
$137$	−5.11164	−0.436717	−0.218358	+	0.975869i	$0.570070\pi$
$138$	−6.21507	−0.529062
$139$	−21.1693	−1.79555	−0.897777	−	0.440451i	$-0.854819\pi$
$139$	−21.1693	−1.79555	−0.897777	+	0.440451i	$0.854819\pi$
$140$	−4.41789	−0.373380
$141$	16.0627	1.35272
$142$	4.68621	0.393258
$143$	5.34924	0.447326
$144$	−0.116762	−0.00973014
$145$	3.96049	0.328900
$146$	11.1318	0.921271
$147$	−21.2553	−1.75311
$148$	−3.45749	−0.284204
$149$	−20.4796	−1.67776	−0.838878	−	0.544319i	$-0.816788\pi$
$149$	−20.4796	−1.67776	−0.838878	+	0.544319i	$0.816788\pi$
$150$	−1.69801	−0.138642
$151$	−23.3305	−1.89861	−0.949305	−	0.314357i	$-0.898211\pi$
$151$	−23.3305	−1.89861	−0.949305	+	0.314357i	$0.898211\pi$
$152$	7.74667	0.628338
$153$	0.598277	0.0483679
$154$	−23.6323	−1.90435
$155$	−1.00000	−0.0803219
$156$	1.69801	0.135950
$157$	−11.0264	−0.880006	−0.440003	−	0.897996i	$-0.645023\pi$
$157$	−11.0264	−0.880006	−0.440003	+	0.897996i	$0.645023\pi$
$158$	10.3829	0.826018
$159$	13.2441	1.05032
$160$	−1.00000	−0.0790569
$161$	16.1704	1.27441
$162$	−8.63608	−0.678515
$163$	−0.993605	−0.0778251	−0.0389126	−	0.999243i	$-0.512389\pi$
$163$	−0.993605	−0.0778251	−0.0389126	+	0.999243i	$0.512389\pi$
$164$	−11.5734	−0.903731
$165$	−9.08306	−0.707115
$166$	−9.54435	−0.740785
$167$	6.37441	0.493267	0.246633	−	0.969109i	$-0.420676\pi$
$167$	6.37441	0.493267	0.246633	+	0.969109i	$0.420676\pi$
$168$	−7.50162	−0.578763
$169$	1.00000	0.0769231
$170$	5.12392	0.392987
$171$	−0.904514	−0.0691699
$172$	−6.03489	−0.460156
$173$	−9.95613	−0.756951	−0.378475	−	0.925611i	$-0.623551\pi$
$173$	−9.95613	−0.756951	−0.378475	+	0.925611i	$0.623551\pi$
$174$	6.72494	0.509817
$175$	4.41789	0.333961
$176$	−5.34924	−0.403214
$177$	−4.55799	−0.342600
$178$	7.99993	0.599620
$179$	−13.7383	−1.02685	−0.513425	−	0.858134i	$-0.671624\pi$
$179$	−13.7383	−1.02685	−0.513425	+	0.858134i	$0.671624\pi$
$180$	0.116762	0.00870290
$181$	−8.93369	−0.664036	−0.332018	−	0.943273i	$-0.607729\pi$
$181$	−8.93369	−0.664036	−0.332018	+	0.943273i	$0.607729\pi$
$182$	−4.41789	−0.327476
$183$	12.9928	0.960457
$184$	3.66021	0.269834
$185$	3.45749	0.254200
$186$	−1.69801	−0.124504
$187$	27.4091	2.00435
$188$	−9.45970	−0.689919
$189$	23.3808	1.70070
$190$	−7.74667	−0.562002
$191$	4.86720	0.352178	0.176089	−	0.984374i	$-0.443655\pi$
$191$	4.86720	0.352178	0.176089	+	0.984374i	$0.443655\pi$
$192$	−1.69801	−0.122543
$193$	17.3631	1.24982	0.624910	−	0.780697i	$-0.285136\pi$
$193$	17.3631	1.24982	0.624910	+	0.780697i	$0.285136\pi$
$194$	−14.2148	−1.02056
$195$	−1.69801	−0.121597
$196$	12.5178	0.894126
$197$	−6.12574	−0.436441	−0.218220	−	0.975900i	$-0.570025\pi$
$197$	−6.12574	−0.436441	−0.218220	+	0.975900i	$0.570025\pi$
$198$	0.624586	0.0443874
$199$	−7.79330	−0.552453	−0.276226	−	0.961093i	$-0.589084\pi$
$199$	−7.79330	−0.552453	−0.276226	+	0.961093i	$0.589084\pi$
$200$	1.00000	0.0707107
$201$	−15.7500	−1.11092
$202$	1.05000	0.0738777
$203$	−17.4970	−1.22805
$204$	8.70046	0.609154
$205$	11.5734	0.808322
$206$	−17.5157	−1.22038
$207$	−0.427372	−0.0297044
$208$	−1.00000	−0.0693375
$209$	−41.4388	−2.86638
$210$	7.50162	0.517661
$211$	−22.6247	−1.55755	−0.778775	−	0.627303i	$-0.784159\pi$
$211$	−22.6247	−1.55755	−0.778775	+	0.627303i	$0.784159\pi$
$212$	−7.79976	−0.535690
$213$	−7.95723	−0.545220
$214$	−11.1582	−0.762760
$215$	6.03489	0.411576
$216$	5.29229	0.360095
$217$	4.41789	0.299906
$218$	−9.48278	−0.642255
$219$	−18.9018	−1.27727
$220$	5.34924	0.360646
$221$	5.12392	0.344672
$222$	5.87086	0.394026
$223$	9.37795	0.627994	0.313997	−	0.949424i	$-0.398332\pi$
$223$	9.37795	0.627994	0.313997	+	0.949424i	$0.398332\pi$
$224$	4.41789	0.295183
$225$	−0.116762	−0.00778411
$226$	3.15963	0.210175
$227$	25.1599	1.66992	0.834960	−	0.550310i	$-0.185491\pi$
$227$	25.1599	1.66992	0.834960	+	0.550310i	$0.185491\pi$
$228$	−13.1539	−0.871140
$229$	−24.1463	−1.59563	−0.797816	−	0.602901i	$-0.794011\pi$
$229$	−24.1463	−1.59563	−0.797816	+	0.602901i	$0.794011\pi$
$230$	−3.66021	−0.241347
$231$	40.1280	2.64023
$232$	−3.96049	−0.260019
$233$	−25.4212	−1.66540	−0.832699	−	0.553726i	$-0.813205\pi$
$233$	−25.4212	−1.66540	−0.832699	+	0.553726i	$0.813205\pi$
$234$	0.116762	0.00763295
$235$	9.45970	0.617083
$236$	2.68431	0.174734
$237$	−17.6302	−1.14521
$238$	−22.6369	−1.46733
$239$	−13.2128	−0.854663	−0.427331	−	0.904095i	$-0.640546\pi$
$239$	−13.2128	−0.854663	−0.427331	+	0.904095i	$0.640546\pi$
$240$	1.69801	0.109606
$241$	−10.7886	−0.694957	−0.347478	−	0.937688i	$-0.612962\pi$
$241$	−10.7886	−0.694957	−0.347478	+	0.937688i	$0.612962\pi$
$242$	17.6143	1.13229
$243$	−1.21272	−0.0777963
$244$	−7.65180	−0.489856
$245$	−12.5178	−0.799731
$246$	19.6518	1.25295
$247$	−7.74667	−0.492909
$248$	1.00000	0.0635001
$249$	16.2064	1.02704
$250$	−1.00000	−0.0632456
$251$	−2.56592	−0.161959	−0.0809796	−	0.996716i	$-0.525805\pi$
$251$	−2.56592	−0.161959	−0.0809796	+	0.996716i	$0.525805\pi$
$252$	−0.515840	−0.0324949
$253$	−19.5793	−1.23094
$254$	9.51337	0.596922
$255$	−8.70046	−0.544844
$256$	1.00000	0.0625000
$257$	4.10397	0.255998	0.127999	−	0.991774i	$-0.459144\pi$
$257$	4.10397	0.255998	0.127999	+	0.991774i	$0.459144\pi$
$258$	10.2473	0.637970
$259$	−15.2748	−0.949131
$260$	1.00000	0.0620174
$261$	0.462433	0.0286239
$262$	19.5734	1.20925
$263$	−7.63525	−0.470809	−0.235405	−	0.971897i	$-0.575642\pi$
$263$	−7.63525	−0.470809	−0.235405	+	0.971897i	$0.575642\pi$
$264$	9.08306	0.559024
$265$	7.79976	0.479136
$266$	34.2239	2.09840
$267$	−13.5840	−0.831325
$268$	9.27554	0.566594
$269$	18.5129	1.12875	0.564374	−	0.825519i	$-0.309117\pi$
$269$	18.5129	1.12875	0.564374	+	0.825519i	$0.309117\pi$
$270$	−5.29229	−0.322079
$271$	19.7829	1.20172	0.600861	−	0.799353i	$-0.294824\pi$
$271$	19.7829	1.20172	0.600861	+	0.799353i	$0.294824\pi$
$272$	−5.12392	−0.310683
$273$	7.50162	0.454019
$274$	−5.11164	−0.308805
$275$	−5.34924	−0.322571
$276$	−6.21507	−0.374104
$277$	20.2107	1.21434	0.607170	−	0.794572i	$-0.292305\pi$
$277$	20.2107	1.21434	0.607170	+	0.794572i	$0.292305\pi$
$278$	−21.1693	−1.26965
$279$	−0.116762	−0.00699034
$280$	−4.41789	−0.264019
$281$	19.3429	1.15390	0.576949	−	0.816780i	$-0.304243\pi$
$281$	19.3429	1.15390	0.576949	+	0.816780i	$0.304243\pi$
$282$	16.0627	0.956518
$283$	16.4191	0.976014	0.488007	−	0.872840i	$-0.337724\pi$
$283$	16.4191	0.976014	0.488007	+	0.872840i	$0.337724\pi$
$284$	4.68621	0.278075
$285$	13.1539	0.779171
$286$	5.34924	0.316307
$287$	−51.1300	−3.01811
$288$	−0.116762	−0.00688025
$289$	9.25453	0.544384
$290$	3.96049	0.232568
$291$	24.1368	1.41493
$292$	11.1318	0.651437
$293$	3.77817	0.220723	0.110361	−	0.993892i	$-0.464799\pi$
$293$	3.77817	0.220723	0.110361	+	0.993892i	$0.464799\pi$
$294$	−21.2553	−1.23963
$295$	−2.68431	−0.156287
$296$	−3.45749	−0.200963
$297$	−28.3097	−1.64270
$298$	−20.4796	−1.18635
$299$	−3.66021	−0.211675
$300$	−1.69801	−0.0980347
$301$	−26.6615	−1.53674
$302$	−23.3305	−1.34252
$303$	−1.78291	−0.102425
$304$	7.74667	0.444302
$305$	7.65180	0.438141
$306$	0.598277	0.0342012
$307$	−15.5810	−0.889253	−0.444626	−	0.895716i	$-0.646664\pi$
$307$	−15.5810	−0.889253	−0.444626	+	0.895716i	$0.646664\pi$
$308$	−23.6323	−1.34658
$309$	29.7418	1.69195
$310$	−1.00000	−0.0567962
$311$	−15.3073	−0.867998	−0.433999	−	0.900913i	$-0.642898\pi$
$311$	−15.3073	−0.867998	−0.433999	+	0.900913i	$0.642898\pi$
$312$	1.69801	0.0961309
$313$	10.2328	0.578394	0.289197	−	0.957270i	$-0.406612\pi$
$313$	10.2328	0.578394	0.289197	+	0.957270i	$0.406612\pi$
$314$	−11.0264	−0.622258
$315$	0.515840	0.0290643
$316$	10.3829	0.584083
$317$	18.6830	1.04934	0.524670	−	0.851306i	$-0.324189\pi$
$317$	18.6830	1.04934	0.524670	+	0.851306i	$0.324189\pi$
$318$	13.2441	0.742691
$319$	21.1856	1.18616
$320$	−1.00000	−0.0559017
$321$	18.9468	1.05751
$322$	16.1704	0.901142
$323$	−39.6933	−2.20859
$324$	−8.63608	−0.479782
$325$	−1.00000	−0.0554700
$326$	−0.993605	−0.0550307
$327$	16.1019	0.890435
$328$	−11.5734	−0.639034
$329$	−41.7919	−2.30406
$330$	−9.08306	−0.500006
$331$	−21.3013	−1.17082	−0.585411	−	0.810736i	$-0.699067\pi$
$331$	−21.3013	−1.17082	−0.585411	+	0.810736i	$0.699067\pi$
$332$	−9.54435	−0.523814
$333$	0.403703	0.0221228
$334$	6.37441	0.348792
$335$	−9.27554	−0.506777
$336$	−7.50162	−0.409247
$337$	−25.6632	−1.39796	−0.698981	−	0.715140i	$-0.746363\pi$
$337$	−25.6632	−1.39796	−0.698981	+	0.715140i	$0.746363\pi$
$338$	1.00000	0.0543928
$339$	−5.36508	−0.291391
$340$	5.12392	0.277883
$341$	−5.34924	−0.289677
$342$	−0.904514	−0.0489105
$343$	24.3769	1.31623
$344$	−6.03489	−0.325380
$345$	6.21507	0.334608
$346$	−9.95613	−0.535245
$347$	−14.2512	−0.765045	−0.382522	−	0.923946i	$-0.624945\pi$
$347$	−14.2512	−0.765045	−0.382522	+	0.923946i	$0.624945\pi$
$348$	6.72494	0.360495
$349$	10.2684	0.549657	0.274828	−	0.961493i	$-0.411379\pi$
$349$	10.2684	0.549657	0.274828	+	0.961493i	$0.411379\pi$
$350$	4.41789	0.236146
$351$	−5.29229	−0.282482
$352$	−5.34924	−0.285115
$353$	29.2527	1.55696	0.778482	−	0.627667i	$-0.215990\pi$
$353$	29.2527	1.55696	0.778482	+	0.627667i	$0.215990\pi$
$354$	−4.55799	−0.242255
$355$	−4.68621	−0.248718
$356$	7.99993	0.423996
$357$	38.4377	2.03434
$358$	−13.7383	−0.726093
$359$	12.0054	0.633622	0.316811	−	0.948489i	$-0.397388\pi$
$359$	12.0054	0.633622	0.316811	+	0.948489i	$0.397388\pi$
$360$	0.116762	0.00615388
$361$	41.0109	2.15847
$362$	−8.93369	−0.469544
$363$	−29.9093	−1.56983
$364$	−4.41789	−0.231560
$365$	−11.1318	−0.582663
$366$	12.9928	0.679146
$367$	0.898580	0.0469055	0.0234527	−	0.999725i	$-0.492534\pi$
$367$	0.898580	0.0469055	0.0234527	+	0.999725i	$0.492534\pi$
$368$	3.66021	0.190802
$369$	1.35133	0.0703474
$370$	3.45749	0.179746
$371$	−34.4585	−1.78900
$372$	−1.69801	−0.0880377
$373$	−24.5817	−1.27279	−0.636395	−	0.771363i	$-0.719575\pi$
$373$	−24.5817	−1.27279	−0.636395	+	0.771363i	$0.719575\pi$
$374$	27.4091	1.41729
$375$	1.69801	0.0876849
$376$	−9.45970	−0.487847
$377$	3.96049	0.203975
$378$	23.3808	1.20258
$379$	−5.57190	−0.286209	−0.143105	−	0.989708i	$-0.545709\pi$
$379$	−5.57190	−0.286209	−0.143105	+	0.989708i	$0.545709\pi$
$380$	−7.74667	−0.397396
$381$	−16.1538	−0.827584
$382$	4.86720	0.249028
$383$	−15.0710	−0.770090	−0.385045	−	0.922898i	$-0.625814\pi$
$383$	−15.0710	−0.770090	−0.385045	+	0.922898i	$0.625814\pi$
$384$	−1.69801	−0.0866512
$385$	23.6323	1.20442
$386$	17.3631	0.883756
$387$	0.704644	0.0358191
$388$	−14.2148	−0.721646
$389$	−12.6790	−0.642853	−0.321426	−	0.946935i	$-0.604162\pi$
$389$	−12.6790	−0.642853	−0.321426	+	0.946935i	$0.604162\pi$
$390$	−1.69801	−0.0859821
$391$	−18.7546	−0.948462
$392$	12.5178	0.632243
$393$	−33.2358	−1.67652
$394$	−6.12574	−0.308610
$395$	−10.3829	−0.522419
$396$	0.624586	0.0313866
$397$	8.38112	0.420636	0.210318	−	0.977633i	$-0.432550\pi$
$397$	8.38112	0.420636	0.210318	+	0.977633i	$0.432550\pi$
$398$	−7.79330	−0.390643
$399$	−58.1126	−2.90927
$400$	1.00000	0.0500000
$401$	18.5548	0.926585	0.463292	−	0.886206i	$-0.346668\pi$
$401$	18.5548	0.926585	0.463292	+	0.886206i	$0.346668\pi$
$402$	−15.7500	−0.785537
$403$	−1.00000	−0.0498135
$404$	1.05000	0.0522394
$405$	8.63608	0.429130
$406$	−17.4970	−0.868361
$407$	18.4949	0.916760
$408$	8.70046	0.430737
$409$	−20.7879	−1.02789	−0.513947	−	0.857822i	$-0.671817\pi$
$409$	−20.7879	−1.02789	−0.513947	+	0.857822i	$0.671817\pi$
$410$	11.5734	0.571570
$411$	8.67961	0.428134
$412$	−17.5157	−0.862936
$413$	11.8590	0.583544
$414$	−0.427372	−0.0210042
$415$	9.54435	0.468514
$416$	−1.00000	−0.0490290
$417$	35.9456	1.76026
$418$	−41.4388	−2.02684
$419$	10.4541	0.510717	0.255359	−	0.966846i	$-0.417807\pi$
$419$	10.4541	0.510717	0.255359	+	0.966846i	$0.417807\pi$
$420$	7.50162	0.366042
$421$	6.63046	0.323149	0.161574	−	0.986861i	$-0.448343\pi$
$421$	6.63046	0.323149	0.161574	+	0.986861i	$0.448343\pi$
$422$	−22.6247	−1.10135
$423$	1.10453	0.0537041
$424$	−7.79976	−0.378790
$425$	−5.12392	−0.248547
$426$	−7.95723	−0.385529
$427$	−33.8048	−1.63593
$428$	−11.1582	−0.539353
$429$	−9.08306	−0.438534
$430$	6.03489	0.291028
$431$	−6.88837	−0.331801	−0.165901	−	0.986142i	$-0.553053\pi$
$431$	−6.88837	−0.331801	−0.165901	+	0.986142i	$0.553053\pi$
$432$	5.29229	0.254626
$433$	22.3060	1.07196	0.535978	−	0.844232i	$-0.319943\pi$
$433$	22.3060	1.07196	0.535978	+	0.844232i	$0.319943\pi$
$434$	4.41789	0.212066
$435$	−6.72494	−0.322436
$436$	−9.48278	−0.454143
$437$	28.3544	1.35638
$438$	−18.9018	−0.903165
$439$	−34.6820	−1.65528	−0.827640	−	0.561259i	$-0.810317\pi$
$439$	−34.6820	−1.65528	−0.827640	+	0.561259i	$0.810317\pi$
$440$	5.34924	0.255015
$441$	−1.46160	−0.0695998
$442$	5.12392	0.243720
$443$	16.0306	0.761638	0.380819	−	0.924650i	$-0.375642\pi$
$443$	16.0306	0.761638	0.380819	+	0.924650i	$0.375642\pi$
$444$	5.87086	0.278619
$445$	−7.99993	−0.379233
$446$	9.37795	0.444059
$447$	34.7746	1.64478
$448$	4.41789	0.208726
$449$	−6.85005	−0.323274	−0.161637	−	0.986850i	$-0.551677\pi$
$449$	−6.85005	−0.323274	−0.161637	+	0.986850i	$0.551677\pi$
$450$	−0.116762	−0.00550420
$451$	61.9089	2.91518
$452$	3.15963	0.148616
$453$	39.6154	1.86130
$454$	25.1599	1.18081
$455$	4.41789	0.207114
$456$	−13.1539	−0.615989
$457$	−13.5158	−0.632244	−0.316122	−	0.948718i	$-0.602381\pi$
$457$	−13.5158	−0.632244	−0.316122	+	0.948718i	$0.602381\pi$
$458$	−24.1463	−1.12828
$459$	−27.1173	−1.26573
$460$	−3.66021	−0.170658
$461$	17.6240	0.820833	0.410416	−	0.911898i	$-0.365383\pi$
$461$	17.6240	0.820833	0.410416	+	0.911898i	$0.365383\pi$
$462$	40.1280	1.86692
$463$	−0.887077	−0.0412260	−0.0206130	−	0.999788i	$-0.506562\pi$
$463$	−0.887077	−0.0412260	−0.0206130	+	0.999788i	$0.506562\pi$
$464$	−3.96049	−0.183861
$465$	1.69801	0.0787433
$466$	−25.4212	−1.17761
$467$	2.90810	0.134571	0.0672854	−	0.997734i	$-0.478566\pi$
$467$	2.90810	0.134571	0.0672854	+	0.997734i	$0.478566\pi$
$468$	0.116762	0.00539731
$469$	40.9783	1.89220
$470$	9.45970	0.436343
$471$	18.7230	0.862711
$472$	2.68431	0.123556
$473$	32.2821	1.48433
$474$	−17.6302	−0.809784
$475$	7.74667	0.355442
$476$	−22.6369	−1.03756
$477$	0.910713	0.0416987
$478$	−13.2128	−0.604338
$479$	37.4240	1.70994	0.854972	−	0.518674i	$-0.173574\pi$
$479$	37.4240	1.70994	0.854972	+	0.518674i	$0.173574\pi$
$480$	1.69801	0.0775032
$481$	3.45749	0.157648
$482$	−10.7886	−0.491408
$483$	−27.4575	−1.24936
$484$	17.6143	0.800652
$485$	14.2148	0.645460
$486$	−1.21272	−0.0550103
$487$	32.2287	1.46042	0.730211	−	0.683221i	$-0.239422\pi$
$487$	32.2287	1.46042	0.730211	+	0.683221i	$0.239422\pi$
$488$	−7.65180	−0.346381
$489$	1.68715	0.0762956
$490$	−12.5178	−0.565495
$491$	11.1151	0.501618	0.250809	−	0.968037i	$-0.419303\pi$
$491$	11.1151	0.501618	0.250809	+	0.968037i	$0.419303\pi$
$492$	19.6518	0.885970
$493$	20.2932	0.913960
$494$	−7.74667	−0.348539
$495$	−0.624586	−0.0280731
$496$	1.00000	0.0449013
$497$	20.7032	0.928663
$498$	16.2064	0.726226
$499$	−0.554375	−0.0248172	−0.0124086	−	0.999923i	$-0.503950\pi$
$499$	−0.554375	−0.0248172	−0.0124086	+	0.999923i	$0.503950\pi$
$500$	−1.00000	−0.0447214
$501$	−10.8238	−0.483572
$502$	−2.56592	−0.114522
$503$	14.9297	0.665684	0.332842	−	0.942983i	$-0.391992\pi$
$503$	14.9297	0.665684	0.332842	+	0.942983i	$0.391992\pi$
$504$	−0.515840	−0.0229774
$505$	−1.05000	−0.0467244
$506$	−19.5793	−0.870408
$507$	−1.69801	−0.0754113
$508$	9.51337	0.422088
$509$	1.24960	0.0553876	0.0276938	−	0.999616i	$-0.491184\pi$
$509$	1.24960	0.0553876	0.0276938	+	0.999616i	$0.491184\pi$
$510$	−8.70046	−0.385263
$511$	49.1789	2.17555
$512$	1.00000	0.0441942
$513$	40.9976	1.81009
$514$	4.10397	0.181018
$515$	17.5157	0.771833
$516$	10.2473	0.451113
$517$	50.6022	2.22548
$518$	−15.2748	−0.671137
$519$	16.9056	0.742074
$520$	1.00000	0.0438529
$521$	22.6507	0.992345	0.496173	−	0.868224i	$-0.334738\pi$
$521$	22.6507	0.992345	0.496173	+	0.868224i	$0.334738\pi$
$522$	0.462433	0.0202401
$523$	36.2912	1.58690	0.793452	−	0.608633i	$-0.208282\pi$
$523$	36.2912	1.58690	0.793452	+	0.608633i	$0.208282\pi$
$524$	19.5734	0.855067
$525$	−7.50162	−0.327398
$526$	−7.63525	−0.332913
$527$	−5.12392	−0.223201
$528$	9.08306	0.395289
$529$	−9.60286	−0.417516
$530$	7.79976	0.338800
$531$	−0.313425	−0.0136015
$532$	34.2239	1.48380
$533$	11.5734	0.501300
$534$	−13.5840	−0.587836
$535$	11.1582	0.482412
$536$	9.27554	0.400642
$537$	23.3278	1.00667
$538$	18.5129	0.798146
$539$	−66.9605	−2.88419
$540$	−5.29229	−0.227744
$541$	−28.6889	−1.23343	−0.616716	−	0.787186i	$-0.711537\pi$
$541$	−28.6889	−1.23343	−0.616716	+	0.787186i	$0.711537\pi$
$542$	19.7829	0.849746
$543$	15.1695	0.650986
$544$	−5.12392	−0.219686
$545$	9.48278	0.406198
$546$	7.50162	0.321040
$547$	−41.4732	−1.77327	−0.886634	−	0.462473i	$-0.846962\pi$
$547$	−41.4732	−1.77327	−0.886634	+	0.462473i	$0.846962\pi$
$548$	−5.11164	−0.218358
$549$	0.893437	0.0381309
$550$	−5.34924	−0.228092
$551$	−30.6806	−1.30704
$552$	−6.21507	−0.264531
$553$	45.8704	1.95061
$554$	20.2107	0.858669
$555$	−5.87086	−0.249204
$556$	−21.1693	−0.897777
$557$	25.7058	1.08919	0.544595	−	0.838699i	$-0.316683\pi$
$557$	25.7058	1.08919	0.544595	+	0.838699i	$0.316683\pi$
$558$	−0.116762	−0.00494292
$559$	6.03489	0.255249
$560$	−4.41789	−0.186690
$561$	−46.5408	−1.96496
$562$	19.3429	0.815930
$563$	31.7336	1.33741	0.668707	−	0.743526i	$-0.266848\pi$
$563$	31.7336	1.33741	0.668707	+	0.743526i	$0.266848\pi$
$564$	16.0627	0.676360
$565$	−3.15963	−0.132927
$566$	16.4191	0.690146
$567$	−38.1533	−1.60229
$568$	4.68621	0.196629
$569$	11.7847	0.494039	0.247020	−	0.969010i	$-0.420549\pi$
$569$	11.7847	0.494039	0.247020	+	0.969010i	$0.420549\pi$
$570$	13.1539	0.550957
$571$	17.0445	0.713289	0.356644	−	0.934240i	$-0.383921\pi$
$571$	17.0445	0.713289	0.356644	+	0.934240i	$0.383921\pi$
$572$	5.34924	0.223663
$573$	−8.26456	−0.345257
$574$	−51.1300	−2.13413
$575$	3.66021	0.152641
$576$	−0.116762	−0.00486507
$577$	−25.7425	−1.07167	−0.535837	−	0.844321i	$-0.680004\pi$
$577$	−25.7425	−1.07167	−0.535837	+	0.844321i	$0.680004\pi$
$578$	9.25453	0.384938
$579$	−29.4826	−1.22526
$580$	3.96049	0.164450
$581$	−42.1659	−1.74934
$582$	24.1368	1.00050
$583$	41.7228	1.72798
$584$	11.1318	0.460636
$585$	−0.116762	−0.00482750
$586$	3.77817	0.156075
$587$	−6.68952	−0.276106	−0.138053	−	0.990425i	$-0.544084\pi$
$587$	−6.68952	−0.276106	−0.138053	+	0.990425i	$0.544084\pi$
$588$	−21.2553	−0.876553
$589$	7.74667	0.319196
$590$	−2.68431	−0.110511
$591$	10.4016	0.427863
$592$	−3.45749	−0.142102
$593$	−24.2258	−0.994835	−0.497418	−	0.867511i	$-0.665718\pi$
$593$	−24.2258	−0.994835	−0.497418	+	0.867511i	$0.665718\pi$
$594$	−28.3097	−1.16156
$595$	22.6369	0.928023
$596$	−20.4796	−0.838878
$597$	13.2331	0.541595
$598$	−3.66021	−0.149677
$599$	−32.4789	−1.32705	−0.663526	−	0.748153i	$-0.730941\pi$
$599$	−32.4789	−1.32705	−0.663526	+	0.748153i	$0.730941\pi$
$600$	−1.69801	−0.0693210
$601$	−32.5443	−1.32751	−0.663756	−	0.747949i	$-0.731039\pi$
$601$	−32.5443	−1.32751	−0.663756	+	0.747949i	$0.731039\pi$
$602$	−26.6615	−1.08664
$603$	−1.08303	−0.0441043
$604$	−23.3305	−0.949305
$605$	−17.6143	−0.716125
$606$	−1.78291	−0.0724258
$607$	29.7253	1.20651	0.603257	−	0.797547i	$-0.293869\pi$
$607$	29.7253	1.20651	0.603257	+	0.797547i	$0.293869\pi$
$608$	7.74667	0.314169
$609$	29.7101	1.20391
$610$	7.65180	0.309812
$611$	9.45970	0.382698
$612$	0.598277	0.0241839
$613$	45.9816	1.85718	0.928590	−	0.371108i	$-0.121022\pi$
$613$	45.9816	1.85718	0.928590	+	0.371108i	$0.121022\pi$
$614$	−15.5810	−0.628797
$615$	−19.6518	−0.792435
$616$	−23.6323	−0.952175
$617$	47.4223	1.90915	0.954574	−	0.297973i	$-0.0963104\pi$
$617$	47.4223	1.90915	0.954574	+	0.297973i	$0.0963104\pi$
$618$	29.7418	1.19639
$619$	19.5305	0.784999	0.392499	−	0.919752i	$-0.371611\pi$
$619$	19.5305	0.784999	0.392499	+	0.919752i	$0.371611\pi$
$620$	−1.00000	−0.0401610
$621$	19.3709	0.777328
$622$	−15.3073	−0.613768
$623$	35.3428	1.41598
$624$	1.69801	0.0679748
$625$	1.00000	0.0400000
$626$	10.2328	0.408987
$627$	70.3635	2.81005
$628$	−11.0264	−0.440003
$629$	17.7159	0.706379
$630$	0.515840	0.0205516
$631$	5.48336	0.218289	0.109145	−	0.994026i	$-0.465189\pi$
$631$	5.48336	0.218289	0.109145	+	0.994026i	$0.465189\pi$
$632$	10.3829	0.413009
$633$	38.4170	1.52694
$634$	18.6830	0.741995
$635$	−9.51337	−0.377527
$636$	13.2441	0.525162
$637$	−12.5178	−0.495972
$638$	21.1856	0.838745
$639$	−0.547170	−0.0216457
$640$	−1.00000	−0.0395285
$641$	25.8904	1.02261	0.511305	−	0.859399i	$-0.329162\pi$
$641$	25.8904	1.02261	0.511305	+	0.859399i	$0.329162\pi$
$642$	18.9468	0.747769
$643$	33.2719	1.31211	0.656057	−	0.754711i	$-0.272223\pi$
$643$	33.2719	1.31211	0.656057	+	0.754711i	$0.272223\pi$
$644$	16.1704	0.637204
$645$	−10.2473	−0.403487
$646$	−39.6933	−1.56171
$647$	9.39477	0.369347	0.184673	−	0.982800i	$-0.440877\pi$
$647$	9.39477	0.369347	0.184673	+	0.982800i	$0.440877\pi$
$648$	−8.63608	−0.339257
$649$	−14.3590	−0.563641
$650$	−1.00000	−0.0392232
$651$	−7.50162	−0.294012
$652$	−0.993605	−0.0389126
$653$	0.995184	0.0389446	0.0194723	−	0.999810i	$-0.493801\pi$
$653$	0.995184	0.0389446	0.0194723	+	0.999810i	$0.493801\pi$
$654$	16.1019	0.629632
$655$	−19.5734	−0.764795
$656$	−11.5734	−0.451866
$657$	−1.29976	−0.0507086
$658$	−41.7919	−1.62922
$659$	1.32086	0.0514535	0.0257268	−	0.999669i	$-0.491810\pi$
$659$	1.32086	0.0514535	0.0257268	+	0.999669i	$0.491810\pi$
$660$	−9.08306	−0.353558
$661$	−19.2181	−0.747499	−0.373750	−	0.927530i	$-0.621928\pi$
$661$	−19.2181	−0.747499	−0.373750	+	0.927530i	$0.621928\pi$
$662$	−21.3013	−0.827897
$663$	−8.70046	−0.337898
$664$	−9.54435	−0.370393
$665$	−34.2239	−1.32715
$666$	0.403703	0.0156432
$667$	−14.4962	−0.561295
$668$	6.37441	0.246633
$669$	−15.9239	−0.615652
$670$	−9.27554	−0.358345
$671$	40.9313	1.58013
$672$	−7.50162	−0.289381
$673$	7.13366	0.274982	0.137491	−	0.990503i	$-0.456096\pi$
$673$	7.13366	0.274982	0.137491	+	0.990503i	$0.456096\pi$
$674$	−25.6632	−0.988509
$675$	5.29229	0.203700
$676$	1.00000	0.0384615
$677$	−3.10348	−0.119276	−0.0596381	−	0.998220i	$-0.518995\pi$
$677$	−3.10348	−0.119276	−0.0596381	+	0.998220i	$0.518995\pi$
$678$	−5.36508	−0.206045
$679$	−62.7993	−2.41002
$680$	5.12392	0.196493
$681$	−42.7217	−1.63710
$682$	−5.34924	−0.204833
$683$	−3.07849	−0.117795	−0.0588975	−	0.998264i	$-0.518759\pi$
$683$	−3.07849	−0.117795	−0.0588975	+	0.998264i	$0.518759\pi$
$684$	−0.904514	−0.0345850
$685$	5.11164	0.195306
$686$	24.3769	0.930713
$687$	41.0006	1.56427
$688$	−6.03489	−0.230078
$689$	7.79976	0.297147
$690$	6.21507	0.236604
$691$	−23.6224	−0.898639	−0.449320	−	0.893371i	$-0.648334\pi$
$691$	−23.6224	−0.898639	−0.449320	+	0.893371i	$0.648334\pi$
$692$	−9.95613	−0.378475
$693$	2.75935	0.104819
$694$	−14.2512	−0.540968
$695$	21.1693	0.802996
$696$	6.72494	0.254908
$697$	59.3012	2.24619
$698$	10.2684	0.388666
$699$	43.1654	1.63267
$700$	4.41789	0.166981
$701$	−24.9578	−0.942644	−0.471322	−	0.881961i	$-0.656223\pi$
$701$	−24.9578	−0.942644	−0.471322	+	0.881961i	$0.656223\pi$
$702$	−5.29229	−0.199745
$703$	−26.7840	−1.01018
$704$	−5.34924	−0.201607
$705$	−16.0627	−0.604955
$706$	29.2527	1.10094
$707$	4.63878	0.174459
$708$	−4.55799	−0.171300
$709$	15.2846	0.574025	0.287012	−	0.957927i	$-0.407338\pi$
$709$	15.2846	0.574025	0.287012	+	0.957927i	$0.407338\pi$
$710$	−4.68621	−0.175870
$711$	−1.21232	−0.0454657
$712$	7.99993	0.299810
$713$	3.66021	0.137076
$714$	38.4377	1.43849
$715$	−5.34924	−0.200050
$716$	−13.7383	−0.513425
$717$	22.4354	0.837866
$718$	12.0054	0.448039
$719$	21.5569	0.803937	0.401968	−	0.915654i	$-0.368326\pi$
$719$	21.5569	0.803937	0.401968	+	0.915654i	$0.368326\pi$
$720$	0.116762	0.00435145
$721$	−77.3824	−2.88187
$722$	41.0109	1.52627
$723$	18.3192	0.681298
$724$	−8.93369	−0.332018
$725$	−3.96049	−0.147089
$726$	−29.9093	−1.11004
$727$	0.662021	0.0245530	0.0122765	−	0.999925i	$-0.496092\pi$
$727$	0.662021	0.0245530	0.0122765	+	0.999925i	$0.496092\pi$
$728$	−4.41789	−0.163738
$729$	27.9675	1.03583
$730$	−11.1318	−0.412005
$731$	30.9223	1.14370
$732$	12.9928	0.480229
$733$	−48.5511	−1.79328	−0.896639	−	0.442763i	$-0.853998\pi$
$733$	−48.5511	−1.79328	−0.896639	+	0.442763i	$0.853998\pi$
$734$	0.898580	0.0331672
$735$	21.2553	0.784013
$736$	3.66021	0.134917
$737$	−49.6171	−1.82767
$738$	1.35133	0.0497432
$739$	−14.1133	−0.519165	−0.259583	−	0.965721i	$-0.583585\pi$
$739$	−14.1133	−0.519165	−0.259583	+	0.965721i	$0.583585\pi$
$740$	3.45749	0.127100
$741$	13.1539	0.483221
$742$	−34.4585	−1.26501
$743$	35.3634	1.29736	0.648679	−	0.761062i	$-0.275322\pi$
$743$	35.3634	1.29736	0.648679	+	0.761062i	$0.275322\pi$
$744$	−1.69801	−0.0622521
$745$	20.4796	0.750316
$746$	−24.5817	−0.899999
$747$	1.11441	0.0407743
$748$	27.4091	1.00217
$749$	−49.2958	−1.80123
$750$	1.69801	0.0620026
$751$	27.6231	1.00798	0.503990	−	0.863710i	$-0.331865\pi$
$751$	27.6231	1.00798	0.503990	+	0.863710i	$0.331865\pi$
$752$	−9.45970	−0.344960
$753$	4.35695	0.158776
$754$	3.96049	0.144232
$755$	23.3305	0.849084
$756$	23.3808	0.850351
$757$	3.35207	0.121833	0.0609166	−	0.998143i	$-0.480598\pi$
$757$	3.35207	0.121833	0.0609166	+	0.998143i	$0.480598\pi$
$758$	−5.57190	−0.202381
$759$	33.2459	1.20675
$760$	−7.74667	−0.281001
$761$	−27.6480	−1.00224	−0.501120	−	0.865378i	$-0.667079\pi$
$761$	−27.6480	−1.00224	−0.501120	+	0.865378i	$0.667079\pi$
$762$	−16.1538	−0.585190
$763$	−41.8939	−1.51666
$764$	4.86720	0.176089
$765$	−0.598277	−0.0216308
$766$	−15.0710	−0.544536
$767$	−2.68431	−0.0969249
$768$	−1.69801	−0.0612717
$769$	37.4294	1.34974	0.674870	−	0.737937i	$-0.264200\pi$
$769$	37.4294	1.34974	0.674870	+	0.737937i	$0.264200\pi$
$770$	23.6323	0.851651
$771$	−6.96858	−0.250967
$772$	17.3631	0.624910
$773$	44.3635	1.59564	0.797821	−	0.602894i	$-0.205986\pi$
$773$	44.3635	1.59564	0.797821	+	0.602894i	$0.205986\pi$
$774$	0.704644	0.0253279
$775$	1.00000	0.0359211
$776$	−14.2148	−0.510281
$777$	25.9368	0.930478
$778$	−12.6790	−0.454565
$779$	−89.6553	−3.21224
$780$	−1.69801	−0.0607985
$781$	−25.0676	−0.896991
$782$	−18.7546	−0.670664
$783$	−20.9600	−0.749051
$784$	12.5178	0.447063
$785$	11.0264	0.393551
$786$	−33.2358	−1.18548
$787$	5.25921	0.187471	0.0937354	−	0.995597i	$-0.470119\pi$
$787$	5.25921	0.187471	0.0937354	+	0.995597i	$0.470119\pi$
$788$	−6.12574	−0.218220
$789$	12.9647	0.461556
$790$	−10.3829	−0.369406
$791$	13.9589	0.496321
$792$	0.624586	0.0221937
$793$	7.65180	0.271723
$794$	8.38112	0.297435
$795$	−13.2441	−0.469719
$796$	−7.79330	−0.276226
$797$	36.7625	1.30219	0.651097	−	0.758994i	$-0.274309\pi$
$797$	36.7625	1.30219	0.651097	+	0.758994i	$0.274309\pi$
$798$	−58.1126	−2.05716
$799$	48.4707	1.71477
$800$	1.00000	0.0353553
$801$	−0.934086	−0.0330043
$802$	18.5548	0.655194
$803$	−59.5464	−2.10135
$804$	−15.7500	−0.555458
$805$	−16.1704	−0.569932
$806$	−1.00000	−0.0352235
$807$	−31.4350	−1.10657
$808$	1.05000	0.0369389
$809$	−23.6840	−0.832685	−0.416343	−	0.909208i	$-0.636688\pi$
$809$	−23.6840	−0.832685	−0.416343	+	0.909208i	$0.636688\pi$
$810$	8.63608	0.303441
$811$	2.04711	0.0718838	0.0359419	−	0.999354i	$-0.488557\pi$
$811$	2.04711	0.0718838	0.0359419	+	0.999354i	$0.488557\pi$
$812$	−17.4970	−0.614024
$813$	−33.5915	−1.17810
$814$	18.4949	0.648248
$815$	0.993605	0.0348045
$816$	8.70046	0.304577
$817$	−46.7503	−1.63559
$818$	−20.7879	−0.726831
$819$	0.515840	0.0180249
$820$	11.5734	0.404161
$821$	19.8054	0.691213	0.345606	−	0.938380i	$-0.387673\pi$
$821$	19.8054	0.691213	0.345606	+	0.938380i	$0.387673\pi$
$822$	8.67961	0.302736
$823$	−20.8202	−0.725745	−0.362872	−	0.931839i	$-0.618204\pi$
$823$	−20.8202	−0.725745	−0.362872	+	0.931839i	$0.618204\pi$
$824$	−17.5157	−0.610188
$825$	9.08306	0.316232
$826$	11.8590	0.412628
$827$	−53.3696	−1.85584	−0.927921	−	0.372776i	$-0.878406\pi$
$827$	−53.3696	−1.85584	−0.927921	+	0.372776i	$0.878406\pi$
$828$	−0.427372	−0.0148522
$829$	−36.0783	−1.25305	−0.626526	−	0.779401i	$-0.715524\pi$
$829$	−36.0783	−1.25305	−0.626526	+	0.779401i	$0.715524\pi$
$830$	9.54435	0.331289
$831$	−34.3179	−1.19047
$832$	−1.00000	−0.0346688
$833$	−64.1400	−2.22232
$834$	35.9456	1.24470
$835$	−6.37441	−0.220596
$836$	−41.4388	−1.43319
$837$	5.29229	0.182928
$838$	10.4541	0.361131
$839$	26.3086	0.908274	0.454137	−	0.890932i	$-0.349948\pi$
$839$	26.3086	0.908274	0.454137	+	0.890932i	$0.349948\pi$
$840$	7.50162	0.258831
$841$	−13.3146	−0.459123
$842$	6.63046	0.228501
$843$	−32.8444	−1.13122
$844$	−22.6247	−0.778775
$845$	−1.00000	−0.0344010
$846$	1.10453	0.0379745
$847$	77.8183	2.67387
$848$	−7.79976	−0.267845
$849$	−27.8798	−0.956832
$850$	−5.12392	−0.175749
$851$	−12.6551	−0.433813
$852$	−7.95723	−0.272610
$853$	40.4047	1.38343	0.691716	−	0.722170i	$-0.256855\pi$
$853$	40.4047	1.38343	0.691716	+	0.722170i	$0.256855\pi$
$854$	−33.8048	−1.15678
$855$	0.904514	0.0309337
$856$	−11.1582	−0.381380
$857$	3.69266	0.126139	0.0630694	−	0.998009i	$-0.479911\pi$
$857$	3.69266	0.126139	0.0630694	+	0.998009i	$0.479911\pi$
$858$	−9.08306	−0.310091
$859$	11.7012	0.399238	0.199619	−	0.979874i	$-0.436029\pi$
$859$	11.7012	0.399238	0.199619	+	0.979874i	$0.436029\pi$
$860$	6.03489	0.205788
$861$	86.8193	2.95879
$862$	−6.88837	−0.234619
$863$	13.4457	0.457698	0.228849	−	0.973462i	$-0.426504\pi$
$863$	13.4457	0.457698	0.228849	+	0.973462i	$0.426504\pi$
$864$	5.29229	0.180047
$865$	9.95613	0.338519
$866$	22.3060	0.757988
$867$	−15.7143	−0.533685
$868$	4.41789	0.149953
$869$	−55.5405	−1.88408
$870$	−6.72494	−0.227997
$871$	−9.27554	−0.314290
$872$	−9.48278	−0.321127
$873$	1.65974	0.0561737
$874$	28.3544	0.959103
$875$	−4.41789	−0.149352
$876$	−18.9018	−0.638634
$877$	−26.1319	−0.882413	−0.441206	−	0.897406i	$-0.645449\pi$
$877$	−26.1319	−0.882413	−0.441206	+	0.897406i	$0.645449\pi$
$878$	−34.6820	−1.17046
$879$	−6.41536	−0.216385
$880$	5.34924	0.180323
$881$	26.3136	0.886528	0.443264	−	0.896391i	$-0.353821\pi$
$881$	26.3136	0.886528	0.443264	+	0.896391i	$0.353821\pi$
$882$	−1.46160	−0.0492145
$883$	−37.3859	−1.25814	−0.629068	−	0.777350i	$-0.716563\pi$
$883$	−37.3859	−1.25814	−0.629068	+	0.777350i	$0.716563\pi$
$884$	5.12392	0.172336
$885$	4.55799	0.153215
$886$	16.0306	0.538559
$887$	19.9998	0.671529	0.335764	−	0.941946i	$-0.391005\pi$
$887$	19.9998	0.671529	0.335764	+	0.941946i	$0.391005\pi$
$888$	5.87086	0.197013
$889$	42.0290	1.40961
$890$	−7.99993	−0.268158
$891$	46.1965	1.54764
$892$	9.37795	0.313997
$893$	−73.2812	−2.45226
$894$	34.7746	1.16304
$895$	13.7383	0.459222
$896$	4.41789	0.147591
$897$	6.21507	0.207515
$898$	−6.85005	−0.228589
$899$	−3.96049	−0.132090
$900$	−0.116762	−0.00389206
$901$	39.9653	1.33144
$902$	61.9089	2.06134
$903$	45.2715	1.50654
$904$	3.15963	0.105088
$905$	8.93369	0.296966
$906$	39.6154	1.31613
$907$	−39.2057	−1.30180	−0.650902	−	0.759162i	$-0.725609\pi$
$907$	−39.2057	−1.30180	−0.650902	+	0.759162i	$0.725609\pi$
$908$	25.1599	0.834960
$909$	−0.122600	−0.00406638
$910$	4.41789	0.146452
$911$	−5.74958	−0.190492	−0.0952461	−	0.995454i	$-0.530364\pi$
$911$	−5.74958	−0.190492	−0.0952461	+	0.995454i	$0.530364\pi$
$912$	−13.1539	−0.435570
$913$	51.0550	1.68967
$914$	−13.5158	−0.447064
$915$	−12.9928	−0.429530
$916$	−24.1463	−0.797816
$917$	86.4730	2.85559
$918$	−27.1173	−0.895003
$919$	−25.2249	−0.832093	−0.416047	−	0.909343i	$-0.636585\pi$
$919$	−25.2249	−0.832093	−0.416047	+	0.909343i	$0.636585\pi$
$920$	−3.66021	−0.120674
$921$	26.4566	0.871776
$922$	17.6240	0.580417
$923$	−4.68621	−0.154248
$924$	40.1280	1.32011
$925$	−3.45749	−0.113682
$926$	−0.887077	−0.0291512
$927$	2.04516	0.0671719
$928$	−3.96049	−0.130009
$929$	−2.81606	−0.0923921	−0.0461960	−	0.998932i	$-0.514710\pi$
$929$	−2.81606	−0.0923921	−0.0461960	+	0.998932i	$0.514710\pi$
$930$	1.69801	0.0556799
$931$	96.9710	3.17810
$932$	−25.4212	−0.832699
$933$	25.9920	0.850939
$934$	2.90810	0.0951559
$935$	−27.4091	−0.896372
$936$	0.116762	0.00381648
$937$	0.121207	0.00395965	0.00197983	−	0.999998i	$-0.499370\pi$
$937$	0.121207	0.00395965	0.00197983	+	0.999998i	$0.499370\pi$
$938$	40.9783	1.33799
$939$	−17.3755	−0.567027
$940$	9.45970	0.308541
$941$	7.73567	0.252176	0.126088	−	0.992019i	$-0.459758\pi$
$941$	7.73567	0.252176	0.126088	+	0.992019i	$0.459758\pi$
$942$	18.7230	0.610029
$943$	−42.3611	−1.37947
$944$	2.68431	0.0873670
$945$	−23.3808	−0.760577
$946$	32.2821	1.04958
$947$	11.6185	0.377551	0.188776	−	0.982020i	$-0.439548\pi$
$947$	11.6185	0.377551	0.188776	+	0.982020i	$0.439548\pi$
$948$	−17.6302	−0.572604
$949$	−11.1318	−0.361352
$950$	7.74667	0.251335
$951$	−31.7238	−1.02872
$952$	−22.6369	−0.733666
$953$	−46.4344	−1.50416	−0.752079	−	0.659073i	$-0.770949\pi$
$953$	−46.4344	−1.50416	−0.752079	+	0.659073i	$0.770949\pi$
$954$	0.910713	0.0294854
$955$	−4.86720	−0.157499
$956$	−13.2128	−0.427331
$957$	−35.9733	−1.16285
$958$	37.4240	1.20911
$959$	−22.5827	−0.729232
$960$	1.69801	0.0548030
$961$	1.00000	0.0322581
$962$	3.45749	0.111474
$963$	1.30285	0.0419838
$964$	−10.7886	−0.347478
$965$	−17.3631	−0.558937
$966$	−27.4575	−0.883431
$967$	33.4999	1.07728	0.538642	−	0.842535i	$-0.318937\pi$
$967$	33.4999	1.07728	0.538642	+	0.842535i	$0.318937\pi$
$968$	17.6143	0.566146
$969$	67.3996	2.16519
$970$	14.2148	0.456409
$971$	31.0777	0.997330	0.498665	−	0.866795i	$-0.333824\pi$
$971$	31.0777	0.997330	0.498665	+	0.866795i	$0.333824\pi$
$972$	−1.21272	−0.0388982
$973$	−93.5235	−2.99823
$974$	32.2287	1.03267
$975$	1.69801	0.0543798
$976$	−7.65180	−0.244928
$977$	−20.5274	−0.656729	−0.328364	−	0.944551i	$-0.606497\pi$
$977$	−20.5274	−0.656729	−0.328364	+	0.944551i	$0.606497\pi$
$978$	1.68715	0.0539491
$979$	−42.7935	−1.36769
$980$	−12.5178	−0.399865
$981$	1.10723	0.0353510
$982$	11.1151	0.354698
$983$	3.48119	0.111033	0.0555164	−	0.998458i	$-0.482319\pi$
$983$	3.48119	0.111033	0.0555164	+	0.998458i	$0.482319\pi$
$984$	19.6518	0.626475
$985$	6.12574	0.195182
$986$	20.2932	0.646267
$987$	70.9631	2.25878
$988$	−7.74667	−0.246454
$989$	−22.0890	−0.702389
$990$	−0.624586	−0.0198506
$991$	45.0313	1.43047	0.715234	−	0.698886i	$-0.246320\pi$
$991$	45.0313	1.43047	0.715234	+	0.698886i	$0.246320\pi$
$992$	1.00000	0.0317500
$993$	36.1697	1.14781
$994$	20.7032	0.656664
$995$	7.79330	0.247064
$996$	16.2064	0.513520
$997$	2.76026	0.0874183	0.0437091	−	0.999044i	$-0.486083\pi$
$997$	2.76026	0.0874183	0.0437091	+	0.999044i	$0.486083\pi$
$998$	−0.554375	−0.0175484
$999$	−18.2981	−0.578925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.j.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.j.1.3	✓	7	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.69801 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.69801 q^{6} +4.41789 q^{7} +1.00000 q^{8} -0.116762 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.69801 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.69801 q^{6} +4.41789 q^{7} +1.00000 q^{8} -0.116762 q^{9} -1.00000 q^{10} -5.34924 q^{11} -1.69801 q^{12} -1.00000 q^{13} +4.41789 q^{14} +1.69801 q^{15} +1.00000 q^{16} -5.12392 q^{17} -0.116762 q^{18} +7.74667 q^{19} -1.00000 q^{20} -7.50162 q^{21} -5.34924 q^{22} +3.66021 q^{23} -1.69801 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.29229 q^{27} +4.41789 q^{28} -3.96049 q^{29} +1.69801 q^{30} +1.00000 q^{31} +1.00000 q^{32} +9.08306 q^{33} -5.12392 q^{34} -4.41789 q^{35} -0.116762 q^{36} -3.45749 q^{37} +7.74667 q^{38} +1.69801 q^{39} -1.00000 q^{40} -11.5734 q^{41} -7.50162 q^{42} -6.03489 q^{43} -5.34924 q^{44} +0.116762 q^{45} +3.66021 q^{46} -9.45970 q^{47} -1.69801 q^{48} +12.5178 q^{49} +1.00000 q^{50} +8.70046 q^{51} -1.00000 q^{52} -7.79976 q^{53} +5.29229 q^{54} +5.34924 q^{55} +4.41789 q^{56} -13.1539 q^{57} -3.96049 q^{58} +2.68431 q^{59} +1.69801 q^{60} -7.65180 q^{61} +1.00000 q^{62} -0.515840 q^{63} +1.00000 q^{64} +1.00000 q^{65} +9.08306 q^{66} +9.27554 q^{67} -5.12392 q^{68} -6.21507 q^{69} -4.41789 q^{70} +4.68621 q^{71} -0.116762 q^{72} +11.1318 q^{73} -3.45749 q^{74} -1.69801 q^{75} +7.74667 q^{76} -23.6323 q^{77} +1.69801 q^{78} +10.3829 q^{79} -1.00000 q^{80} -8.63608 q^{81} -11.5734 q^{82} -9.54435 q^{83} -7.50162 q^{84} +5.12392 q^{85} -6.03489 q^{86} +6.72494 q^{87} -5.34924 q^{88} +7.99993 q^{89} +0.116762 q^{90} -4.41789 q^{91} +3.66021 q^{92} -1.69801 q^{93} -9.45970 q^{94} -7.74667 q^{95} -1.69801 q^{96} -14.2148 q^{97} +12.5178 q^{98} +0.624586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 10 q^{11} - 3 q^{12} - 7 q^{13} + 4 q^{14} + 3 q^{15} + 7 q^{16} - 6 q^{17} + 4 q^{18} - 5 q^{19} - 7 q^{20} - 15 q^{21} - 10 q^{22} - 11 q^{23} - 3 q^{24} + 7 q^{25} - 7 q^{26} - 21 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 7 q^{31} + 7 q^{32} + 4 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + 3 q^{39} - 7 q^{40} - 12 q^{41} - 15 q^{42} - 5 q^{43} - 10 q^{44} - 4 q^{45} - 11 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 7 q^{50} - 29 q^{51} - 7 q^{52} - 18 q^{53} - 21 q^{54} + 10 q^{55} + 4 q^{56} + 13 q^{57} - 18 q^{58} - 11 q^{59} + 3 q^{60} - 25 q^{61} + 7 q^{62} + 17 q^{63} + 7 q^{64} + 7 q^{65} + 4 q^{66} - 22 q^{67} - 6 q^{68} - 18 q^{69} - 4 q^{70} - 22 q^{71} + 4 q^{72} + 19 q^{73} - 8 q^{74} - 3 q^{75} - 5 q^{76} - 47 q^{77} + 3 q^{78} - 20 q^{79} - 7 q^{80} + 7 q^{81} - 12 q^{82} - 8 q^{83} - 15 q^{84} + 6 q^{85} - 5 q^{86} + 29 q^{87} - 10 q^{88} - 4 q^{89} - 4 q^{90} - 4 q^{91} - 11 q^{92} - 3 q^{93} - 10 q^{94} + 5 q^{95} - 3 q^{96} + 13 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 10 * q^11 - 3 * q^12 - 7 * q^13 + 4 * q^14 + 3 * q^15 + 7 * q^16 - 6 * q^17 + 4 * q^18 - 5 * q^19 - 7 * q^20 - 15 * q^21 - 10 * q^22 - 11 * q^23 - 3 * q^24 + 7 * q^25 - 7 * q^26 - 21 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 7 * q^31 + 7 * q^32 + 4 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + 3 * q^39 - 7 * q^40 - 12 * q^41 - 15 * q^42 - 5 * q^43 - 10 * q^44 - 4 * q^45 - 11 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 7 * q^50 - 29 * q^51 - 7 * q^52 - 18 * q^53 - 21 * q^54 + 10 * q^55 + 4 * q^56 + 13 * q^57 - 18 * q^58 - 11 * q^59 + 3 * q^60 - 25 * q^61 + 7 * q^62 + 17 * q^63 + 7 * q^64 + 7 * q^65 + 4 * q^66 - 22 * q^67 - 6 * q^68 - 18 * q^69 - 4 * q^70 - 22 * q^71 + 4 * q^72 + 19 * q^73 - 8 * q^74 - 3 * q^75 - 5 * q^76 - 47 * q^77 + 3 * q^78 - 20 * q^79 - 7 * q^80 + 7 * q^81 - 12 * q^82 - 8 * q^83 - 15 * q^84 + 6 * q^85 - 5 * q^86 + 29 * q^87 - 10 * q^88 - 4 * q^89 - 4 * q^90 - 4 * q^91 - 11 * q^92 - 3 * q^93 - 10 * q^94 + 5 * q^95 - 3 * q^96 + 13 * q^97 + 7 * q^98 - 27 * q^99

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