LMFDB - Embedded newform 4030.2.a.c.1.1

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:	$6$
Coefficient field:	6.6.3081125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 10x - 5 $ x^6 - x^5 - 8x^4 + 6x^3 + 16x^2 - 10x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.71605$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.52877 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.52877 q^{6} +2.66088 q^{7} -1.00000 q^{8} +3.39466 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.52877 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.52877 q^{6} +2.66088 q^{7} -1.00000 q^{8} +3.39466 q^{9} +1.00000 q^{10} +0.213764 q^{11} -2.52877 q^{12} +1.00000 q^{13} -2.66088 q^{14} +2.52877 q^{15} +1.00000 q^{16} -0.744740 q^{17} -3.39466 q^{18} -2.06933 q^{19} -1.00000 q^{20} -6.72875 q^{21} -0.213764 q^{22} +1.27351 q^{23} +2.52877 q^{24} +1.00000 q^{25} -1.00000 q^{26} -0.998009 q^{27} +2.66088 q^{28} -7.66900 q^{29} -2.52877 q^{30} +1.00000 q^{31} -1.00000 q^{32} -0.540560 q^{33} +0.744740 q^{34} -2.66088 q^{35} +3.39466 q^{36} +6.35516 q^{37} +2.06933 q^{38} -2.52877 q^{39} +1.00000 q^{40} -2.70408 q^{41} +6.72875 q^{42} -0.538569 q^{43} +0.213764 q^{44} -3.39466 q^{45} -1.27351 q^{46} -12.5290 q^{47} -2.52877 q^{48} +0.0802857 q^{49} -1.00000 q^{50} +1.88327 q^{51} +1.00000 q^{52} -2.24210 q^{53} +0.998009 q^{54} -0.213764 q^{55} -2.66088 q^{56} +5.23285 q^{57} +7.66900 q^{58} -6.20197 q^{59} +2.52877 q^{60} +9.65364 q^{61} -1.00000 q^{62} +9.03279 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.540560 q^{66} +8.67775 q^{67} -0.744740 q^{68} -3.22040 q^{69} +2.66088 q^{70} -7.36180 q^{71} -3.39466 q^{72} +4.07808 q^{73} -6.35516 q^{74} -2.52877 q^{75} -2.06933 q^{76} +0.568802 q^{77} +2.52877 q^{78} -11.1226 q^{79} -1.00000 q^{80} -7.66025 q^{81} +2.70408 q^{82} +17.0160 q^{83} -6.72875 q^{84} +0.744740 q^{85} +0.538569 q^{86} +19.3931 q^{87} -0.213764 q^{88} +3.82418 q^{89} +3.39466 q^{90} +2.66088 q^{91} +1.27351 q^{92} -2.52877 q^{93} +12.5290 q^{94} +2.06933 q^{95} +2.52877 q^{96} -10.3458 q^{97} -0.0802857 q^{98} +0.725658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9} + 6 q^{10} - 6 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} + q^{18} + 3 q^{19} - 6 q^{20} - q^{21} + 6 q^{22} - 7 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - q^{27} + 4 q^{28} - 14 q^{29} - q^{30} + 6 q^{31} - 6 q^{32} - 2 q^{33} + 4 q^{34} - 4 q^{35} - q^{36} + 14 q^{37} - 3 q^{38} - q^{39} + 6 q^{40} - 12 q^{41} + q^{42} + 3 q^{43} - 6 q^{44} + q^{45} + 7 q^{46} - 2 q^{47} - q^{48} - 6 q^{49} - 6 q^{50} - 7 q^{51} + 6 q^{52} - 4 q^{53} + q^{54} + 6 q^{55} - 4 q^{56} + 13 q^{57} + 14 q^{58} - 17 q^{59} + q^{60} - 5 q^{61} - 6 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + 2 q^{66} + 8 q^{67} - 4 q^{68} - 8 q^{69} + 4 q^{70} - 16 q^{71} + q^{72} + 11 q^{73} - 14 q^{74} - q^{75} + 3 q^{76} - 15 q^{77} + q^{78} - 2 q^{79} - 6 q^{80} - 26 q^{81} + 12 q^{82} + 4 q^{83} - q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 6 q^{88} - 8 q^{89} - q^{90} + 4 q^{91} - 7 q^{92} - q^{93} + 2 q^{94} - 3 q^{95} + q^{96} + 5 q^{97} + 6 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9 + 6 * q^10 - 6 * q^11 - q^12 + 6 * q^13 - 4 * q^14 + q^15 + 6 * q^16 - 4 * q^17 + q^18 + 3 * q^19 - 6 * q^20 - q^21 + 6 * q^22 - 7 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - q^27 + 4 * q^28 - 14 * q^29 - q^30 + 6 * q^31 - 6 * q^32 - 2 * q^33 + 4 * q^34 - 4 * q^35 - q^36 + 14 * q^37 - 3 * q^38 - q^39 + 6 * q^40 - 12 * q^41 + q^42 + 3 * q^43 - 6 * q^44 + q^45 + 7 * q^46 - 2 * q^47 - q^48 - 6 * q^49 - 6 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + q^54 + 6 * q^55 - 4 * q^56 + 13 * q^57 + 14 * q^58 - 17 * q^59 + q^60 - 5 * q^61 - 6 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + 2 * q^66 + 8 * q^67 - 4 * q^68 - 8 * q^69 + 4 * q^70 - 16 * q^71 + q^72 + 11 * q^73 - 14 * q^74 - q^75 + 3 * q^76 - 15 * q^77 + q^78 - 2 * q^79 - 6 * q^80 - 26 * q^81 + 12 * q^82 + 4 * q^83 - q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 6 * q^88 - 8 * q^89 - q^90 + 4 * q^91 - 7 * q^92 - q^93 + 2 * q^94 - 3 * q^95 + q^96 + 5 * q^97 + 6 * q^98 + 15 * 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
$3$	−2.52877	−1.45998	−0.729992	−	0.683456i	$-0.760476\pi$
$3$	−2.52877	−1.45998	−0.729992	+	0.683456i	$0.760476\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.52877	1.03236
$7$	2.66088	1.00572	0.502859	−	0.864368i	$-0.332281\pi$
$7$	2.66088	1.00572	0.502859	+	0.864368i	$0.332281\pi$
$8$	−1.00000	−0.353553
$9$	3.39466	1.13155
$10$	1.00000	0.316228
$11$	0.213764	0.0644524	0.0322262	−	0.999481i	$-0.489740\pi$
$11$	0.213764	0.0644524	0.0322262	+	0.999481i	$0.489740\pi$
$12$	−2.52877	−0.729992
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.66088	−0.711150
$15$	2.52877	0.652925
$16$	1.00000	0.250000
$17$	−0.744740	−0.180626	−0.0903130	−	0.995913i	$-0.528787\pi$
$17$	−0.744740	−0.180626	−0.0903130	+	0.995913i	$0.528787\pi$
$18$	−3.39466	−0.800130
$19$	−2.06933	−0.474736	−0.237368	−	0.971420i	$-0.576285\pi$
$19$	−2.06933	−0.474736	−0.237368	+	0.971420i	$0.576285\pi$
$20$	−1.00000	−0.223607
$21$	−6.72875	−1.46833
$22$	−0.213764	−0.0455747
$23$	1.27351	0.265545	0.132772	−	0.991147i	$-0.457612\pi$
$23$	1.27351	0.265545	0.132772	+	0.991147i	$0.457612\pi$
$24$	2.52877	0.516182
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−0.998009	−0.192067
$28$	2.66088	0.502859
$29$	−7.66900	−1.42410	−0.712049	−	0.702130i	$-0.752233\pi$
$29$	−7.66900	−1.42410	−0.712049	+	0.702130i	$0.752233\pi$
$30$	−2.52877	−0.461688
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−0.540560	−0.0940995
$34$	0.744740	0.127722
$35$	−2.66088	−0.449771
$36$	3.39466	0.565777
$37$	6.35516	1.04478	0.522391	−	0.852706i	$-0.325040\pi$
$37$	6.35516	1.04478	0.522391	+	0.852706i	$0.325040\pi$
$38$	2.06933	0.335689
$39$	−2.52877	−0.404927
$40$	1.00000	0.158114
$41$	−2.70408	−0.422306	−0.211153	−	0.977453i	$-0.567722\pi$
$41$	−2.70408	−0.422306	−0.211153	+	0.977453i	$0.567722\pi$
$42$	6.72875	1.03827
$43$	−0.538569	−0.0821311	−0.0410655	−	0.999156i	$-0.513075\pi$
$43$	−0.538569	−0.0821311	−0.0410655	+	0.999156i	$0.513075\pi$
$44$	0.213764	0.0322262
$45$	−3.39466	−0.506046
$46$	−1.27351	−0.187768
$47$	−12.5290	−1.82755	−0.913773	−	0.406224i	$-0.866845\pi$
$47$	−12.5290	−1.82755	−0.913773	+	0.406224i	$0.866845\pi$
$48$	−2.52877	−0.364996
$49$	0.0802857	0.0114694
$50$	−1.00000	−0.141421
$51$	1.88327	0.263711
$52$	1.00000	0.138675
$53$	−2.24210	−0.307976	−0.153988	−	0.988073i	$-0.549212\pi$
$53$	−2.24210	−0.307976	−0.153988	+	0.988073i	$0.549212\pi$
$54$	0.998009	0.135812
$55$	−0.213764	−0.0288240
$56$	−2.66088	−0.355575
$57$	5.23285	0.693107
$58$	7.66900	1.00699
$59$	−6.20197	−0.807428	−0.403714	−	0.914885i	$-0.632281\pi$
$59$	−6.20197	−0.807428	−0.403714	+	0.914885i	$0.632281\pi$
$60$	2.52877	0.326462
$61$	9.65364	1.23602	0.618011	−	0.786170i	$-0.287939\pi$
$61$	9.65364	1.23602	0.618011	+	0.786170i	$0.287939\pi$
$62$	−1.00000	−0.127000
$63$	9.03279	1.13802
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	0.540560	0.0665384
$67$	8.67775	1.06016	0.530078	−	0.847949i	$-0.322163\pi$
$67$	8.67775	1.06016	0.530078	+	0.847949i	$0.322163\pi$
$68$	−0.744740	−0.0903130
$69$	−3.22040	−0.387691
$70$	2.66088	0.318036
$71$	−7.36180	−0.873684	−0.436842	−	0.899538i	$-0.643903\pi$
$71$	−7.36180	−0.873684	−0.436842	+	0.899538i	$0.643903\pi$
$72$	−3.39466	−0.400065
$73$	4.07808	0.477303	0.238651	−	0.971105i	$-0.423295\pi$
$73$	4.07808	0.477303	0.238651	+	0.971105i	$0.423295\pi$
$74$	−6.35516	−0.738772
$75$	−2.52877	−0.291997
$76$	−2.06933	−0.237368
$77$	0.568802	0.0648210
$78$	2.52877	0.286326
$79$	−11.1226	−1.25139	−0.625694	−	0.780069i	$-0.715184\pi$
$79$	−11.1226	−1.25139	−0.625694	+	0.780069i	$0.715184\pi$
$80$	−1.00000	−0.111803
$81$	−7.66025	−0.851139
$82$	2.70408	0.298616
$83$	17.0160	1.86774	0.933872	−	0.357607i	$-0.116407\pi$
$83$	17.0160	1.86774	0.933872	+	0.357607i	$0.116407\pi$
$84$	−6.72875	−0.734166
$85$	0.744740	0.0807784
$86$	0.538569	0.0580754
$87$	19.3931	2.07916
$88$	−0.213764	−0.0227874
$89$	3.82418	0.405362	0.202681	−	0.979245i	$-0.435034\pi$
$89$	3.82418	0.405362	0.202681	+	0.979245i	$0.435034\pi$
$90$	3.39466	0.357829
$91$	2.66088	0.278936
$92$	1.27351	0.132772
$93$	−2.52877	−0.262221
$94$	12.5290	1.29227
$95$	2.06933	0.212309
$96$	2.52877	0.258091
$97$	−10.3458	−1.05046	−0.525229	−	0.850961i	$-0.676020\pi$
$97$	−10.3458	−1.05046	−0.525229	+	0.850961i	$0.676020\pi$
$98$	−0.0802857	−0.00811008
$99$	0.725658	0.0729314
$100$	1.00000	0.100000
$101$	17.5439	1.74568	0.872842	−	0.488002i	$-0.162274\pi$
$101$	17.5439	1.74568	0.872842	+	0.488002i	$0.162274\pi$
$102$	−1.88327	−0.186472
$103$	5.58776	0.550579	0.275289	−	0.961361i	$-0.411226\pi$
$103$	5.58776	0.550579	0.275289	+	0.961361i	$0.411226\pi$
$104$	−1.00000	−0.0980581
$105$	6.72875	0.656658
$106$	2.24210	0.217772
$107$	16.1912	1.56526	0.782629	−	0.622488i	$-0.213878\pi$
$107$	16.1912	1.56526	0.782629	+	0.622488i	$0.213878\pi$
$108$	−0.998009	−0.0960335
$109$	10.1510	0.972289	0.486145	−	0.873878i	$-0.338403\pi$
$109$	10.1510	0.972289	0.486145	+	0.873878i	$0.338403\pi$
$110$	0.213764	0.0203816
$111$	−16.0707	−1.52536
$112$	2.66088	0.251430
$113$	−0.909261	−0.0855361	−0.0427681	−	0.999085i	$-0.513618\pi$
$113$	−0.909261	−0.0855361	−0.0427681	+	0.999085i	$0.513618\pi$
$114$	−5.23285	−0.490101
$115$	−1.27351	−0.118755
$116$	−7.66900	−0.712049
$117$	3.39466	0.313837
$118$	6.20197	0.570938
$119$	−1.98166	−0.181659
$120$	−2.52877	−0.230844
$121$	−10.9543	−0.995846
$122$	−9.65364	−0.873999
$123$	6.83799	0.616561
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	−9.03279	−0.804705
$127$	1.80268	0.159962	0.0799811	−	0.996796i	$-0.474514\pi$
$127$	1.80268	0.159962	0.0799811	+	0.996796i	$0.474514\pi$
$128$	−1.00000	−0.0883883
$129$	1.36192	0.119910
$130$	1.00000	0.0877058
$131$	11.3910	0.995237	0.497619	−	0.867396i	$-0.334208\pi$
$131$	11.3910	0.995237	0.497619	+	0.867396i	$0.334208\pi$
$132$	−0.540560	−0.0470497
$133$	−5.50623	−0.477451
$134$	−8.67775	−0.749644
$135$	0.998009	0.0858949
$136$	0.744740	0.0638609
$137$	−13.2132	−1.12888	−0.564438	−	0.825475i	$-0.690907\pi$
$137$	−13.2132	−1.12888	−0.564438	+	0.825475i	$0.690907\pi$
$138$	3.22040	0.274139
$139$	−18.8299	−1.59713	−0.798566	−	0.601907i	$-0.794408\pi$
$139$	−18.8299	−1.59713	−0.798566	+	0.601907i	$0.794408\pi$
$140$	−2.66088	−0.224885
$141$	31.6830	2.66819
$142$	7.36180	0.617788
$143$	0.213764	0.0178759
$144$	3.39466	0.282889
$145$	7.66900	0.636876
$146$	−4.07808	−0.337504
$147$	−0.203024	−0.0167451
$148$	6.35516	0.522391
$149$	−11.6157	−0.951596	−0.475798	−	0.879554i	$-0.657841\pi$
$149$	−11.6157	−0.951596	−0.475798	+	0.879554i	$0.657841\pi$
$150$	2.52877	0.206473
$151$	15.0258	1.22278	0.611390	−	0.791330i	$-0.290611\pi$
$151$	15.0258	1.22278	0.611390	+	0.791330i	$0.290611\pi$
$152$	2.06933	0.167845
$153$	−2.52814	−0.204388
$154$	−0.568802	−0.0458353
$155$	−1.00000	−0.0803219
$156$	−2.52877	−0.202463
$157$	−0.878749	−0.0701318	−0.0350659	−	0.999385i	$-0.511164\pi$
$157$	−0.878749	−0.0701318	−0.0350659	+	0.999385i	$0.511164\pi$
$158$	11.1226	0.884864
$159$	5.66975	0.449641
$160$	1.00000	0.0790569
$161$	3.38865	0.267063
$162$	7.66025	0.601846
$163$	−2.93691	−0.230036	−0.115018	−	0.993363i	$-0.536693\pi$
$163$	−2.93691	−0.230036	−0.115018	+	0.993363i	$0.536693\pi$
$164$	−2.70408	−0.211153
$165$	0.540560	0.0420826
$166$	−17.0160	−1.32069
$167$	10.5402	0.815624	0.407812	−	0.913066i	$-0.366292\pi$
$167$	10.5402	0.815624	0.407812	+	0.913066i	$0.366292\pi$
$168$	6.72875	0.519134
$169$	1.00000	0.0769231
$170$	−0.744740	−0.0571190
$171$	−7.02467	−0.537190
$172$	−0.538569	−0.0410655
$173$	20.2839	1.54216	0.771078	−	0.636740i	$-0.219718\pi$
$173$	20.2839	1.54216	0.771078	+	0.636740i	$0.219718\pi$
$174$	−19.3931	−1.47019
$175$	2.66088	0.201144
$176$	0.213764	0.0161131
$177$	15.6833	1.17883
$178$	−3.82418	−0.286635
$179$	−25.1050	−1.87644	−0.938218	−	0.346045i	$-0.887524\pi$
$179$	−25.1050	−1.87644	−0.938218	+	0.346045i	$0.887524\pi$
$180$	−3.39466	−0.253023
$181$	−20.9349	−1.55608	−0.778038	−	0.628217i	$-0.783785\pi$
$181$	−20.9349	−1.55608	−0.778038	+	0.628217i	$0.783785\pi$
$182$	−2.66088	−0.197238
$183$	−24.4118	−1.80457
$184$	−1.27351	−0.0938842
$185$	−6.35516	−0.467240
$186$	2.52877	0.185418
$187$	−0.159199	−0.0116418
$188$	−12.5290	−0.913773
$189$	−2.65558	−0.193165
$190$	−2.06933	−0.150125
$191$	−8.25432	−0.597262	−0.298631	−	0.954369i	$-0.596530\pi$
$191$	−8.25432	−0.597262	−0.298631	+	0.954369i	$0.596530\pi$
$192$	−2.52877	−0.182498
$193$	−16.8137	−1.21028	−0.605138	−	0.796120i	$-0.706882\pi$
$193$	−16.8137	−1.21028	−0.605138	+	0.796120i	$0.706882\pi$
$194$	10.3458	0.742785
$195$	2.52877	0.181089
$196$	0.0802857	0.00573469
$197$	−8.56451	−0.610196	−0.305098	−	0.952321i	$-0.598689\pi$
$197$	−8.56451	−0.610196	−0.305098	+	0.952321i	$0.598689\pi$
$198$	−0.725658	−0.0515703
$199$	−6.95810	−0.493246	−0.246623	−	0.969111i	$-0.579321\pi$
$199$	−6.95810	−0.493246	−0.246623	+	0.969111i	$0.579321\pi$
$200$	−1.00000	−0.0707107
$201$	−21.9440	−1.54781
$202$	−17.5439	−1.23439
$203$	−20.4063	−1.43224
$204$	1.88327	0.131856
$205$	2.70408	0.188861
$206$	−5.58776	−0.389318
$207$	4.32313	0.300478
$208$	1.00000	0.0693375
$209$	−0.442349	−0.0305979
$210$	−6.72875	−0.464328
$211$	16.0060	1.10190	0.550951	−	0.834538i	$-0.314265\pi$
$211$	16.0060	1.10190	0.550951	+	0.834538i	$0.314265\pi$
$212$	−2.24210	−0.153988
$213$	18.6163	1.27557
$214$	−16.1912	−1.10680
$215$	0.538569	0.0367301
$216$	0.998009	0.0679059
$217$	2.66088	0.180632
$218$	−10.1510	−0.687512
$219$	−10.3125	−0.696855
$220$	−0.213764	−0.0144120
$221$	−0.744740	−0.0500966
$222$	16.0707	1.07860
$223$	12.4591	0.834321	0.417161	−	0.908833i	$-0.363025\pi$
$223$	12.4591	0.834321	0.417161	+	0.908833i	$0.363025\pi$
$224$	−2.66088	−0.177788
$225$	3.39466	0.226311
$226$	0.909261	0.0604832
$227$	−12.8779	−0.854733	−0.427367	−	0.904078i	$-0.640559\pi$
$227$	−12.8779	−0.854733	−0.427367	+	0.904078i	$0.640559\pi$
$228$	5.23285	0.346554
$229$	−29.2969	−1.93599	−0.967996	−	0.250967i	$-0.919252\pi$
$229$	−29.2969	−1.93599	−0.967996	+	0.250967i	$0.919252\pi$
$230$	1.27351	0.0839726
$231$	−1.43837	−0.0946376
$232$	7.66900	0.503495
$233$	−6.32322	−0.414248	−0.207124	−	0.978315i	$-0.566410\pi$
$233$	−6.32322	−0.414248	−0.207124	+	0.978315i	$0.566410\pi$
$234$	−3.39466	−0.221916
$235$	12.5290	0.817304
$236$	−6.20197	−0.403714
$237$	28.1264	1.82701
$238$	1.98166	0.128452
$239$	−7.19504	−0.465409	−0.232704	−	0.972548i	$-0.574757\pi$
$239$	−7.19504	−0.465409	−0.232704	+	0.972548i	$0.574757\pi$
$240$	2.52877	0.163231
$241$	−15.1442	−0.975526	−0.487763	−	0.872976i	$-0.662187\pi$
$241$	−15.1442	−0.975526	−0.487763	+	0.872976i	$0.662187\pi$
$242$	10.9543	0.704169
$243$	22.3650	1.43472
$244$	9.65364	0.618011
$245$	−0.0802857	−0.00512926
$246$	−6.83799	−0.435974
$247$	−2.06933	−0.131668
$248$	−1.00000	−0.0635001
$249$	−43.0294	−2.72688
$250$	1.00000	0.0632456
$251$	5.00498	0.315912	0.157956	−	0.987446i	$-0.449510\pi$
$251$	5.00498	0.315912	0.157956	+	0.987446i	$0.449510\pi$
$252$	9.03279	0.569012
$253$	0.272230	0.0171150
$254$	−1.80268	−0.113110
$255$	−1.88327	−0.117935
$256$	1.00000	0.0625000
$257$	2.49245	0.155475	0.0777373	−	0.996974i	$-0.475230\pi$
$257$	2.49245	0.155475	0.0777373	+	0.996974i	$0.475230\pi$
$258$	−1.36192	−0.0847892
$259$	16.9103	1.05076
$260$	−1.00000	−0.0620174
$261$	−26.0337	−1.61144
$262$	−11.3910	−0.703739
$263$	−0.762506	−0.0470182	−0.0235091	−	0.999724i	$-0.507484\pi$
$263$	−0.762506	−0.0470182	−0.0235091	+	0.999724i	$0.507484\pi$
$264$	0.540560	0.0332692
$265$	2.24210	0.137731
$266$	5.50623	0.337609
$267$	−9.67047	−0.591823
$268$	8.67775	0.530078
$269$	−18.7362	−1.14237	−0.571183	−	0.820823i	$-0.693515\pi$
$269$	−18.7362	−1.14237	−0.571183	+	0.820823i	$0.693515\pi$
$270$	−0.998009	−0.0607369
$271$	4.09369	0.248674	0.124337	−	0.992240i	$-0.460320\pi$
$271$	4.09369	0.248674	0.124337	+	0.992240i	$0.460320\pi$
$272$	−0.744740	−0.0451565
$273$	−6.72875	−0.407242
$274$	13.2132	0.798236
$275$	0.213764	0.0128905
$276$	−3.22040	−0.193845
$277$	−4.16910	−0.250497	−0.125249	−	0.992125i	$-0.539973\pi$
$277$	−4.16910	−0.250497	−0.125249	+	0.992125i	$0.539973\pi$
$278$	18.8299	1.12934
$279$	3.39466	0.203233
$280$	2.66088	0.159018
$281$	−4.10052	−0.244616	−0.122308	−	0.992492i	$-0.539030\pi$
$281$	−4.10052	−0.244616	−0.122308	+	0.992492i	$0.539030\pi$
$282$	−31.6830	−1.88670
$283$	−4.14456	−0.246368	−0.123184	−	0.992384i	$-0.539311\pi$
$283$	−4.14456	−0.246368	−0.123184	+	0.992384i	$0.539311\pi$
$284$	−7.36180	−0.436842
$285$	−5.23285	−0.309967
$286$	−0.213764	−0.0126402
$287$	−7.19523	−0.424721
$288$	−3.39466	−0.200032
$289$	−16.4454	−0.967374
$290$	−7.66900	−0.450339
$291$	26.1621	1.53365
$292$	4.07808	0.238651
$293$	2.86033	0.167102	0.0835512	−	0.996503i	$-0.473374\pi$
$293$	2.86033	0.167102	0.0835512	+	0.996503i	$0.473374\pi$
$294$	0.203024	0.0118406
$295$	6.20197	0.361093
$296$	−6.35516	−0.369386
$297$	−0.213339	−0.0123792
$298$	11.6157	0.672880
$299$	1.27351	0.0736488
$300$	−2.52877	−0.145998
$301$	−1.43307	−0.0826007
$302$	−15.0258	−0.864636
$303$	−44.3645	−2.54867
$304$	−2.06933	−0.118684
$305$	−9.65364	−0.552766
$306$	2.52814	0.144524
$307$	21.6329	1.23466	0.617328	−	0.786706i	$-0.288215\pi$
$307$	21.6329	1.23466	0.617328	+	0.786706i	$0.288215\pi$
$308$	0.568802	0.0324105
$309$	−14.1301	−0.803836
$310$	1.00000	0.0567962
$311$	−2.52050	−0.142925	−0.0714623	−	0.997443i	$-0.522767\pi$
$311$	−2.52050	−0.142925	−0.0714623	+	0.997443i	$0.522767\pi$
$312$	2.52877	0.143163
$313$	−12.1390	−0.686137	−0.343068	−	0.939310i	$-0.611466\pi$
$313$	−12.1390	−0.686137	−0.343068	+	0.939310i	$0.611466\pi$
$314$	0.878749	0.0495907
$315$	−9.03279	−0.508940
$316$	−11.1226	−0.625694
$317$	−18.9374	−1.06363	−0.531815	−	0.846860i	$-0.678490\pi$
$317$	−18.9374	−1.06363	−0.531815	+	0.846860i	$0.678490\pi$
$318$	−5.66975	−0.317944
$319$	−1.63936	−0.0917865
$320$	−1.00000	−0.0559017
$321$	−40.9437	−2.28525
$322$	−3.38865	−0.188842
$323$	1.54111	0.0857497
$324$	−7.66025	−0.425570
$325$	1.00000	0.0554700
$326$	2.93691	0.162660
$327$	−25.6695	−1.41953
$328$	2.70408	0.149308
$329$	−33.3383	−1.83800
$330$	−0.540560	−0.0297569
$331$	22.8808	1.25764	0.628822	−	0.777549i	$-0.283537\pi$
$331$	22.8808	1.25764	0.628822	+	0.777549i	$0.283537\pi$
$332$	17.0160	0.933872
$333$	21.5736	1.18223
$334$	−10.5402	−0.576733
$335$	−8.67775	−0.474116
$336$	−6.72875	−0.367083
$337$	18.7432	1.02101	0.510504	−	0.859875i	$-0.329459\pi$
$337$	18.7432	1.02101	0.510504	+	0.859875i	$0.329459\pi$
$338$	−1.00000	−0.0543928
$339$	2.29931	0.124881
$340$	0.744740	0.0403892
$341$	0.213764	0.0115760
$342$	7.02467	0.379851
$343$	−18.4125	−0.994183
$344$	0.538569	0.0290377
$345$	3.22040	0.173381
$346$	−20.2839	−1.09047
$347$	−17.6990	−0.950130	−0.475065	−	0.879951i	$-0.657575\pi$
$347$	−17.6990	−0.950130	−0.475065	+	0.879951i	$0.657575\pi$
$348$	19.3931	1.03958
$349$	3.46650	0.185558	0.0927789	−	0.995687i	$-0.470425\pi$
$349$	3.46650	0.185558	0.0927789	+	0.995687i	$0.470425\pi$
$350$	−2.66088	−0.142230
$351$	−0.998009	−0.0532698
$352$	−0.213764	−0.0113937
$353$	−27.3627	−1.45637	−0.728184	−	0.685382i	$-0.759635\pi$
$353$	−27.3627	−1.45637	−0.728184	+	0.685382i	$0.759635\pi$
$354$	−15.6833	−0.833560
$355$	7.36180	0.390724
$356$	3.82418	0.202681
$357$	5.01117	0.265219
$358$	25.1050	1.32684
$359$	−23.2916	−1.22928	−0.614642	−	0.788806i	$-0.710700\pi$
$359$	−23.2916	−1.22928	−0.614642	+	0.788806i	$0.710700\pi$
$360$	3.39466	0.178914
$361$	−14.7179	−0.774625
$362$	20.9349	1.10031
$363$	27.7009	1.45392
$364$	2.66088	0.139468
$365$	−4.07808	−0.213456
$366$	24.4118	1.27603
$367$	−17.0141	−0.888127	−0.444063	−	0.895995i	$-0.646464\pi$
$367$	−17.0141	−0.888127	−0.444063	+	0.895995i	$0.646464\pi$
$368$	1.27351	0.0663861
$369$	−9.17944	−0.477862
$370$	6.35516	0.330389
$371$	−5.96596	−0.309737
$372$	−2.52877	−0.131110
$373$	−8.05647	−0.417148	−0.208574	−	0.978007i	$-0.566882\pi$
$373$	−8.05647	−0.417148	−0.208574	+	0.978007i	$0.566882\pi$
$374$	0.159199	0.00823198
$375$	2.52877	0.130585
$376$	12.5290	0.646135
$377$	−7.66900	−0.394974
$378$	2.65558	0.136588
$379$	32.1182	1.64980	0.824901	−	0.565277i	$-0.191231\pi$
$379$	32.1182	1.64980	0.824901	+	0.565277i	$0.191231\pi$
$380$	2.06933	0.106154
$381$	−4.55857	−0.233542
$382$	8.25432	0.422328
$383$	−35.1019	−1.79362	−0.896811	−	0.442414i	$-0.854122\pi$
$383$	−35.1019	−1.79362	−0.896811	+	0.442414i	$0.854122\pi$
$384$	2.52877	0.129046
$385$	−0.568802	−0.0289888
$386$	16.8137	0.855795
$387$	−1.82826	−0.0929357
$388$	−10.3458	−0.525229
$389$	1.41513	0.0717499	0.0358750	−	0.999356i	$-0.488578\pi$
$389$	1.41513	0.0717499	0.0358750	+	0.999356i	$0.488578\pi$
$390$	−2.52877	−0.128049
$391$	−0.948432	−0.0479643
$392$	−0.0802857	−0.00405504
$393$	−28.8052	−1.45303
$394$	8.56451	0.431474
$395$	11.1226	0.559637
$396$	0.725658	0.0364657
$397$	−18.2010	−0.913481	−0.456740	−	0.889600i	$-0.650983\pi$
$397$	−18.2010	−0.913481	−0.456740	+	0.889600i	$0.650983\pi$
$398$	6.95810	0.348778
$399$	13.9240	0.697071
$400$	1.00000	0.0500000
$401$	−30.0933	−1.50279	−0.751394	−	0.659854i	$-0.770618\pi$
$401$	−30.0933	−1.50279	−0.751394	+	0.659854i	$0.770618\pi$
$402$	21.9440	1.09447
$403$	1.00000	0.0498135
$404$	17.5439	0.872842
$405$	7.66025	0.380641
$406$	20.4063	1.01275
$407$	1.35851	0.0673387
$408$	−1.88327	−0.0932360
$409$	25.6205	1.26685	0.633427	−	0.773802i	$-0.281648\pi$
$409$	25.6205	1.26685	0.633427	+	0.773802i	$0.281648\pi$
$410$	−2.70408	−0.133545
$411$	33.4130	1.64814
$412$	5.58776	0.275289
$413$	−16.5027	−0.812045
$414$	−4.32313	−0.212470
$415$	−17.0160	−0.835281
$416$	−1.00000	−0.0490290
$417$	47.6165	2.33179
$418$	0.442349	0.0216360
$419$	8.66847	0.423483	0.211741	−	0.977326i	$-0.432087\pi$
$419$	8.66847	0.423483	0.211741	+	0.977326i	$0.432087\pi$
$420$	6.72875	0.328329
$421$	33.5781	1.63650	0.818249	−	0.574864i	$-0.194945\pi$
$421$	33.5781	1.63650	0.818249	+	0.574864i	$0.194945\pi$
$422$	−16.0060	−0.779162
$423$	−42.5318	−2.06797
$424$	2.24210	0.108886
$425$	−0.744740	−0.0361252
$426$	−18.6163	−0.901961
$427$	25.6872	1.24309
$428$	16.1912	0.782629
$429$	−0.540560	−0.0260985
$430$	−0.538569	−0.0259721
$431$	−6.11900	−0.294742	−0.147371	−	0.989081i	$-0.547081\pi$
$431$	−6.11900	−0.294742	−0.147371	+	0.989081i	$0.547081\pi$
$432$	−0.998009	−0.0480167
$433$	−28.7821	−1.38318	−0.691590	−	0.722290i	$-0.743089\pi$
$433$	−28.7821	−1.38318	−0.691590	+	0.722290i	$0.743089\pi$
$434$	−2.66088	−0.127726
$435$	−19.3931	−0.929829
$436$	10.1510	0.486145
$437$	−2.63530	−0.126064
$438$	10.3125	0.492751
$439$	−2.94685	−0.140646	−0.0703228	−	0.997524i	$-0.522403\pi$
$439$	−2.94685	−0.140646	−0.0703228	+	0.997524i	$0.522403\pi$
$440$	0.213764	0.0101908
$441$	0.272543	0.0129782
$442$	0.744740	0.0354237
$443$	−6.37020	−0.302657	−0.151329	−	0.988483i	$-0.548355\pi$
$443$	−6.37020	−0.302657	−0.151329	+	0.988483i	$0.548355\pi$
$444$	−16.0707	−0.762682
$445$	−3.82418	−0.181284
$446$	−12.4591	−0.589954
$447$	29.3734	1.38932
$448$	2.66088	0.125715
$449$	−16.9648	−0.800619	−0.400310	−	0.916380i	$-0.631097\pi$
$449$	−16.9648	−0.800619	−0.400310	+	0.916380i	$0.631097\pi$
$450$	−3.39466	−0.160026
$451$	−0.578036	−0.0272186
$452$	−0.909261	−0.0427681
$453$	−37.9967	−1.78524
$454$	12.8779	0.604388
$455$	−2.66088	−0.124744
$456$	−5.23285	−0.245050
$457$	−18.9108	−0.884612	−0.442306	−	0.896864i	$-0.645839\pi$
$457$	−18.9108	−0.884612	−0.442306	+	0.896864i	$0.645839\pi$
$458$	29.2969	1.36895
$459$	0.743257	0.0346923
$460$	−1.27351	−0.0593776
$461$	−12.9343	−0.602409	−0.301205	−	0.953559i	$-0.597389\pi$
$461$	−12.9343	−0.602409	−0.301205	+	0.953559i	$0.597389\pi$
$462$	1.43837	0.0669189
$463$	19.9494	0.927125	0.463563	−	0.886064i	$-0.346571\pi$
$463$	19.9494	0.927125	0.463563	+	0.886064i	$0.346571\pi$
$464$	−7.66900	−0.356025
$465$	2.52877	0.117269
$466$	6.32322	0.292918
$467$	6.99307	0.323601	0.161800	−	0.986824i	$-0.448270\pi$
$467$	6.99307	0.323601	0.161800	+	0.986824i	$0.448270\pi$
$468$	3.39466	0.156918
$469$	23.0905	1.06622
$470$	−12.5290	−0.577921
$471$	2.22215	0.102391
$472$	6.20197	0.285469
$473$	−0.115127	−0.00529354
$474$	−28.1264	−1.29189
$475$	−2.06933	−0.0949472
$476$	−1.98166	−0.0908294
$477$	−7.61118	−0.348492
$478$	7.19504	0.329094
$479$	35.4289	1.61879	0.809394	−	0.587266i	$-0.199796\pi$
$479$	35.4289	1.61879	0.809394	+	0.587266i	$0.199796\pi$
$480$	−2.52877	−0.115422
$481$	6.35516	0.289770
$482$	15.1442	0.689801
$483$	−8.56911	−0.389908
$484$	−10.9543	−0.497923
$485$	10.3458	0.469779
$486$	−22.3650	−1.01450
$487$	−20.7243	−0.939107	−0.469553	−	0.882904i	$-0.655585\pi$
$487$	−20.7243	−0.939107	−0.469553	+	0.882904i	$0.655585\pi$
$488$	−9.65364	−0.437000
$489$	7.42676	0.335850
$490$	0.0802857	0.00362694
$491$	−24.5167	−1.10642	−0.553212	−	0.833040i	$-0.686598\pi$
$491$	−24.5167	−1.10642	−0.553212	+	0.833040i	$0.686598\pi$
$492$	6.83799	0.308280
$493$	5.71141	0.257229
$494$	2.06933	0.0931034
$495$	−0.725658	−0.0326159
$496$	1.00000	0.0449013
$497$	−19.5889	−0.878680
$498$	43.0294	1.92819
$499$	−6.72974	−0.301265	−0.150632	−	0.988590i	$-0.548131\pi$
$499$	−6.72974	−0.301265	−0.150632	+	0.988590i	$0.548131\pi$
$500$	−1.00000	−0.0447214
$501$	−26.6537	−1.19080
$502$	−5.00498	−0.223383
$503$	12.2684	0.547021	0.273510	−	0.961869i	$-0.411815\pi$
$503$	12.2684	0.547021	0.273510	+	0.961869i	$0.411815\pi$
$504$	−9.03279	−0.402352
$505$	−17.5439	−0.780694
$506$	−0.272230	−0.0121021
$507$	−2.52877	−0.112306
$508$	1.80268	0.0799811
$509$	−9.03222	−0.400346	−0.200173	−	0.979761i	$-0.564150\pi$
$509$	−9.03222	−0.400346	−0.200173	+	0.979761i	$0.564150\pi$
$510$	1.88327	0.0833928
$511$	10.8513	0.480032
$512$	−1.00000	−0.0441942
$513$	2.06521	0.0911811
$514$	−2.49245	−0.109937
$515$	−5.58776	−0.246226
$516$	1.36192	0.0599550
$517$	−2.67826	−0.117790
$518$	−16.9103	−0.742997
$519$	−51.2933	−2.25152
$520$	1.00000	0.0438529
$521$	22.1212	0.969148	0.484574	−	0.874750i	$-0.338975\pi$
$521$	22.1212	0.969148	0.484574	+	0.874750i	$0.338975\pi$
$522$	26.0337	1.13946
$523$	24.3905	1.06652	0.533262	−	0.845950i	$-0.320966\pi$
$523$	24.3905	1.06652	0.533262	+	0.845950i	$0.320966\pi$
$524$	11.3910	0.497619
$525$	−6.72875	−0.293667
$526$	0.762506	0.0332469
$527$	−0.744740	−0.0324414
$528$	−0.540560	−0.0235249
$529$	−21.3782	−0.929486
$530$	−2.24210	−0.0973907
$531$	−21.0536	−0.913648
$532$	−5.50623	−0.238725
$533$	−2.70408	−0.117127
$534$	9.67047	0.418482
$535$	−16.1912	−0.700005
$536$	−8.67775	−0.374822
$537$	63.4847	2.73957
$538$	18.7362	0.807775
$539$	0.0171622	0.000739229 0
$540$	0.998009	0.0429475
$541$	−29.5713	−1.27137	−0.635685	−	0.771948i	$-0.719282\pi$
$541$	−29.5713	−1.27137	−0.635685	+	0.771948i	$0.719282\pi$
$542$	−4.09369	−0.175839
$543$	52.9394	2.27185
$544$	0.744740	0.0319305
$545$	−10.1510	−0.434821
$546$	6.72875	0.287964
$547$	10.4557	0.447054	0.223527	−	0.974698i	$-0.428243\pi$
$547$	10.4557	0.447054	0.223527	+	0.974698i	$0.428243\pi$
$548$	−13.2132	−0.564438
$549$	32.7708	1.39863
$550$	−0.213764	−0.00911494
$551$	15.8697	0.676071
$552$	3.22040	0.137069
$553$	−29.5958	−1.25854
$554$	4.16910	0.177128
$555$	16.0707	0.682164
$556$	−18.8299	−0.798566
$557$	13.3105	0.563984	0.281992	−	0.959417i	$-0.409005\pi$
$557$	13.3105	0.563984	0.281992	+	0.959417i	$0.409005\pi$
$558$	−3.39466	−0.143708
$559$	−0.538569	−0.0227791
$560$	−2.66088	−0.112443
$561$	0.402577	0.0169968
$562$	4.10052	0.172970
$563$	21.1152	0.889901	0.444950	−	0.895555i	$-0.353221\pi$
$563$	21.1152	0.889901	0.444950	+	0.895555i	$0.353221\pi$
$564$	31.6830	1.33409
$565$	0.909261	0.0382529
$566$	4.14456	0.174209
$567$	−20.3830	−0.856007
$568$	7.36180	0.308894
$569$	−13.1216	−0.550088	−0.275044	−	0.961432i	$-0.588692\pi$
$569$	−13.1216	−0.550088	−0.275044	+	0.961432i	$0.588692\pi$
$570$	5.23285	0.219180
$571$	−29.5048	−1.23474	−0.617369	−	0.786674i	$-0.711801\pi$
$571$	−29.5048	−1.23474	−0.617369	+	0.786674i	$0.711801\pi$
$572$	0.213764	0.00893794
$573$	20.8733	0.871993
$574$	7.19523	0.300323
$575$	1.27351	0.0531089
$576$	3.39466	0.141444
$577$	27.9675	1.16430	0.582150	−	0.813081i	$-0.302211\pi$
$577$	27.9675	1.16430	0.582150	+	0.813081i	$0.302211\pi$
$578$	16.4454	0.684037
$579$	42.5179	1.76699
$580$	7.66900	0.318438
$581$	45.2774	1.87842
$582$	−26.1621	−1.08445
$583$	−0.479281	−0.0198498
$584$	−4.07808	−0.168752
$585$	−3.39466	−0.140352
$586$	−2.86033	−0.118159
$587$	−36.2609	−1.49665	−0.748324	−	0.663333i	$-0.769141\pi$
$587$	−36.2609	−1.49665	−0.748324	+	0.663333i	$0.769141\pi$
$588$	−0.203024	−0.00837256
$589$	−2.06933	−0.0852651
$590$	−6.20197	−0.255331
$591$	21.6577	0.890877
$592$	6.35516	0.261195
$593$	9.62434	0.395224	0.197612	−	0.980280i	$-0.436681\pi$
$593$	9.62434	0.395224	0.197612	+	0.980280i	$0.436681\pi$
$594$	0.213339	0.00875340
$595$	1.98166	0.0812403
$596$	−11.6157	−0.475798
$597$	17.5954	0.720132
$598$	−1.27351	−0.0520776
$599$	10.0016	0.408655	0.204327	−	0.978903i	$-0.434499\pi$
$599$	10.0016	0.408655	0.204327	+	0.978903i	$0.434499\pi$
$600$	2.52877	0.103236
$601$	−7.81548	−0.318800	−0.159400	−	0.987214i	$-0.550956\pi$
$601$	−7.81548	−0.318800	−0.159400	+	0.987214i	$0.550956\pi$
$602$	1.43307	0.0584075
$603$	29.4580	1.19962
$604$	15.0258	0.611390
$605$	10.9543	0.445356
$606$	44.3645	1.80218
$607$	33.4344	1.35706	0.678531	−	0.734572i	$-0.262617\pi$
$607$	33.4344	1.35706	0.678531	+	0.734572i	$0.262617\pi$
$608$	2.06933	0.0839223
$609$	51.6028	2.09105
$610$	9.65364	0.390864
$611$	−12.5290	−0.506870
$612$	−2.52814	−0.102194
$613$	−45.3122	−1.83014	−0.915071	−	0.403293i	$-0.867866\pi$
$613$	−45.3122	−1.83014	−0.915071	+	0.403293i	$0.867866\pi$
$614$	−21.6329	−0.873034
$615$	−6.83799	−0.275734
$616$	−0.568802	−0.0229177
$617$	23.8073	0.958446	0.479223	−	0.877693i	$-0.340919\pi$
$617$	23.8073	0.958446	0.479223	+	0.877693i	$0.340919\pi$
$618$	14.1301	0.568398
$619$	−11.6039	−0.466399	−0.233199	−	0.972429i	$-0.574919\pi$
$619$	−11.6039	−0.466399	−0.233199	+	0.972429i	$0.574919\pi$
$620$	−1.00000	−0.0401610
$621$	−1.27097	−0.0510023
$622$	2.52050	0.101063
$623$	10.1757	0.407680
$624$	−2.52877	−0.101232
$625$	1.00000	0.0400000
$626$	12.1390	0.485172
$627$	1.11860	0.0446724
$628$	−0.878749	−0.0350659
$629$	−4.73294	−0.188715
$630$	9.03279	0.359875
$631$	−3.62114	−0.144155	−0.0720777	−	0.997399i	$-0.522963\pi$
$631$	−3.62114	−0.144155	−0.0720777	+	0.997399i	$0.522963\pi$
$632$	11.1226	0.442432
$633$	−40.4755	−1.60876
$634$	18.9374	0.752100
$635$	−1.80268	−0.0715373
$636$	5.66975	0.224820
$637$	0.0802857	0.00318103
$638$	1.63936	0.0649029
$639$	−24.9908	−0.988621
$640$	1.00000	0.0395285
$641$	10.4811	0.413978	0.206989	−	0.978343i	$-0.433634\pi$
$641$	10.4811	0.413978	0.206989	+	0.978343i	$0.433634\pi$
$642$	40.9437	1.61592
$643$	−3.88538	−0.153225	−0.0766123	−	0.997061i	$-0.524410\pi$
$643$	−3.88538	−0.153225	−0.0766123	+	0.997061i	$0.524410\pi$
$644$	3.38865	0.133532
$645$	−1.36192	−0.0536254
$646$	−1.54111	−0.0606342
$647$	−12.1965	−0.479495	−0.239748	−	0.970835i	$-0.577065\pi$
$647$	−12.1965	−0.479495	−0.239748	+	0.970835i	$0.577065\pi$
$648$	7.66025	0.300923
$649$	−1.32576	−0.0520407
$650$	−1.00000	−0.0392232
$651$	−6.72875	−0.263720
$652$	−2.93691	−0.115018
$653$	−18.7434	−0.733484	−0.366742	−	0.930323i	$-0.619527\pi$
$653$	−18.7434	−0.733484	−0.366742	+	0.930323i	$0.619527\pi$
$654$	25.6695	1.00376
$655$	−11.3910	−0.445084
$656$	−2.70408	−0.105577
$657$	13.8437	0.540094
$658$	33.3383	1.29966
$659$	0.779368	0.0303599	0.0151799	−	0.999885i	$-0.495168\pi$
$659$	0.779368	0.0303599	0.0151799	+	0.999885i	$0.495168\pi$
$660$	0.540560	0.0210413
$661$	49.6609	1.93159	0.965793	−	0.259314i	$-0.0834963\pi$
$661$	49.6609	1.93159	0.965793	+	0.259314i	$0.0834963\pi$
$662$	−22.8808	−0.889288
$663$	1.88327	0.0731403
$664$	−17.0160	−0.660347
$665$	5.50623	0.213523
$666$	−21.5736	−0.835961
$667$	−9.76653	−0.378162
$668$	10.5402	0.407812
$669$	−31.5061	−1.21810
$670$	8.67775	0.335251
$671$	2.06360	0.0796645
$672$	6.72875	0.259567
$673$	−20.5879	−0.793607	−0.396803	−	0.917904i	$-0.629880\pi$
$673$	−20.5879	−0.793607	−0.396803	+	0.917904i	$0.629880\pi$
$674$	−18.7432	−0.721962
$675$	−0.998009	−0.0384134
$676$	1.00000	0.0384615
$677$	13.4808	0.518109	0.259055	−	0.965863i	$-0.416589\pi$
$677$	13.4808	0.518109	0.259055	+	0.965863i	$0.416589\pi$
$678$	−2.29931	−0.0883045
$679$	−27.5289	−1.05646
$680$	−0.744740	−0.0285595
$681$	32.5651	1.24790
$682$	−0.213764	−0.00818546
$683$	−16.9208	−0.647456	−0.323728	−	0.946150i	$-0.604936\pi$
$683$	−16.9208	−0.647456	−0.323728	+	0.946150i	$0.604936\pi$
$684$	−7.02467	−0.268595
$685$	13.2132	0.504849
$686$	18.4125	0.702994
$687$	74.0850	2.82652
$688$	−0.538569	−0.0205328
$689$	−2.24210	−0.0854173
$690$	−3.22040	−0.122599
$691$	−11.1451	−0.423979	−0.211990	−	0.977272i	$-0.567994\pi$
$691$	−11.1451	−0.423979	−0.211990	+	0.977272i	$0.567994\pi$
$692$	20.2839	0.771078
$693$	1.93089	0.0733484
$694$	17.6990	0.671843
$695$	18.8299	0.714259
$696$	−19.3931	−0.735094
$697$	2.01384	0.0762795
$698$	−3.46650	−0.131209
$699$	15.9900	0.604796
$700$	2.66088	0.100572
$701$	−14.5324	−0.548880	−0.274440	−	0.961604i	$-0.588493\pi$
$701$	−14.5324	−0.548880	−0.274440	+	0.961604i	$0.588493\pi$
$702$	0.998009	0.0376674
$703$	−13.1509	−0.495996
$704$	0.213764	0.00805655
$705$	−31.6830	−1.19325
$706$	27.3627	1.02981
$707$	46.6823	1.75567
$708$	15.6833	0.589416
$709$	−22.8618	−0.858591	−0.429296	−	0.903164i	$-0.641238\pi$
$709$	−22.8618	−0.858591	−0.429296	+	0.903164i	$0.641238\pi$
$710$	−7.36180	−0.276283
$711$	−37.7574	−1.41601
$712$	−3.82418	−0.143317
$713$	1.27351	0.0476932
$714$	−5.01117	−0.187538
$715$	−0.213764	−0.00799434
$716$	−25.1050	−0.938218
$717$	18.1946	0.679489
$718$	23.2916	0.869236
$719$	18.6974	0.697294	0.348647	−	0.937254i	$-0.386641\pi$
$719$	18.6974	0.697294	0.348647	+	0.937254i	$0.386641\pi$
$720$	−3.39466	−0.126512
$721$	14.8684	0.553727
$722$	14.7179	0.547743
$723$	38.2963	1.42425
$724$	−20.9349	−0.778038
$725$	−7.66900	−0.284820
$726$	−27.7009	−1.02808
$727$	−20.6957	−0.767559	−0.383780	−	0.923425i	$-0.625378\pi$
$727$	−20.6957	−0.767559	−0.383780	+	0.923425i	$0.625378\pi$
$728$	−2.66088	−0.0986188
$729$	−33.5752	−1.24352
$730$	4.07808	0.150936
$731$	0.401094	0.0148350
$732$	−24.4118	−0.902286
$733$	−11.0047	−0.406467	−0.203233	−	0.979130i	$-0.565145\pi$
$733$	−11.0047	−0.406467	−0.203233	+	0.979130i	$0.565145\pi$
$734$	17.0141	0.628001
$735$	0.203024	0.00748864
$736$	−1.27351	−0.0469421
$737$	1.85499	0.0683296
$738$	9.17944	0.337900
$739$	−0.207106	−0.00761852	−0.00380926	−	0.999993i	$-0.501213\pi$
$739$	−0.207106	−0.00761852	−0.00380926	+	0.999993i	$0.501213\pi$
$740$	−6.35516	−0.233620
$741$	5.23285	0.192233
$742$	5.96596	0.219017
$743$	−0.704667	−0.0258517	−0.0129259	−	0.999916i	$-0.504115\pi$
$743$	−0.704667	−0.0258517	−0.0129259	+	0.999916i	$0.504115\pi$
$744$	2.52877	0.0927091
$745$	11.6157	0.425567
$746$	8.05647	0.294968
$747$	57.7634	2.11345
$748$	−0.159199	−0.00582089
$749$	43.0827	1.57421
$750$	−2.52877	−0.0923375
$751$	−49.7426	−1.81513	−0.907567	−	0.419907i	$-0.862063\pi$
$751$	−49.7426	−1.81513	−0.907567	+	0.419907i	$0.862063\pi$
$752$	−12.5290	−0.456887
$753$	−12.6564	−0.461226
$754$	7.66900	0.279289
$755$	−15.0258	−0.546844
$756$	−2.65558	−0.0965826
$757$	52.7324	1.91659	0.958296	−	0.285779i	$-0.0922522\pi$
$757$	52.7324	1.91659	0.958296	+	0.285779i	$0.0922522\pi$
$758$	−32.1182	−1.16659
$759$	−0.688407	−0.0249876
$760$	−2.06933	−0.0750624
$761$	−48.0671	−1.74243	−0.871216	−	0.490900i	$-0.836668\pi$
$761$	−48.0671	−1.74243	−0.871216	+	0.490900i	$0.836668\pi$
$762$	4.55857	0.165139
$763$	27.0106	0.977849
$764$	−8.25432	−0.298631
$765$	2.52814	0.0914051
$766$	35.1019	1.26828
$767$	−6.20197	−0.223940
$768$	−2.52877	−0.0912490
$769$	50.8401	1.83334	0.916670	−	0.399645i	$-0.130866\pi$
$769$	50.8401	1.83334	0.916670	+	0.399645i	$0.130866\pi$
$770$	0.568802	0.0204982
$771$	−6.30282	−0.226991
$772$	−16.8137	−0.605138
$773$	−24.2457	−0.872059	−0.436029	−	0.899932i	$-0.643616\pi$
$773$	−24.2457	−0.872059	−0.436029	+	0.899932i	$0.643616\pi$
$774$	1.82826	0.0657155
$775$	1.00000	0.0359211
$776$	10.3458	0.371393
$777$	−42.7622	−1.53409
$778$	−1.41513	−0.0507349
$779$	5.59563	0.200484
$780$	2.52877	0.0905444
$781$	−1.57369	−0.0563111
$782$	0.948432	0.0339158
$783$	7.65374	0.273522
$784$	0.0802857	0.00286735
$785$	0.878749	0.0313639
$786$	28.8052	1.02745
$787$	−1.50276	−0.0535677	−0.0267838	−	0.999641i	$-0.508527\pi$
$787$	−1.50276	−0.0535677	−0.0267838	+	0.999641i	$0.508527\pi$
$788$	−8.56451	−0.305098
$789$	1.92820	0.0686458
$790$	−11.1226	−0.395723
$791$	−2.41944	−0.0860252
$792$	−0.725658	−0.0257851
$793$	9.65364	0.342811
$794$	18.2010	0.645928
$795$	−5.66975	−0.201085
$796$	−6.95810	−0.246623
$797$	−30.9603	−1.09667	−0.548336	−	0.836258i	$-0.684738\pi$
$797$	−30.9603	−1.09667	−0.548336	+	0.836258i	$0.684738\pi$
$798$	−13.9240	−0.492904
$799$	9.33087	0.330102
$800$	−1.00000	−0.0353553
$801$	12.9818	0.458690
$802$	30.0933	1.06263
$803$	0.871748	0.0307633
$804$	−21.9440	−0.773906
$805$	−3.38865	−0.119434
$806$	−1.00000	−0.0352235
$807$	47.3795	1.66784
$808$	−17.5439	−0.617193
$809$	−0.896974	−0.0315359	−0.0157680	−	0.999876i	$-0.505019\pi$
$809$	−0.896974	−0.0315359	−0.0157680	+	0.999876i	$0.505019\pi$
$810$	−7.66025	−0.269154
$811$	20.5557	0.721808	0.360904	−	0.932603i	$-0.382468\pi$
$811$	20.5557	0.721808	0.360904	+	0.932603i	$0.382468\pi$
$812$	−20.4063	−0.716121
$813$	−10.3520	−0.363060
$814$	−1.35851	−0.0476156
$815$	2.93691	0.102875
$816$	1.88327	0.0659278
$817$	1.11448	0.0389906
$818$	−25.6205	−0.895801
$819$	9.03279	0.315631
$820$	2.70408	0.0944306
$821$	−32.1364	−1.12157	−0.560784	−	0.827962i	$-0.689500\pi$
$821$	−32.1364	−1.12157	−0.560784	+	0.827962i	$0.689500\pi$
$822$	−33.4130	−1.16541
$823$	−17.5149	−0.610531	−0.305266	−	0.952267i	$-0.598745\pi$
$823$	−17.5149	−0.610531	−0.305266	+	0.952267i	$0.598745\pi$
$824$	−5.58776	−0.194659
$825$	−0.540560	−0.0188199
$826$	16.5027	0.574203
$827$	−36.1862	−1.25832	−0.629159	−	0.777277i	$-0.716601\pi$
$827$	−36.1862	−1.25832	−0.629159	+	0.777277i	$0.716601\pi$
$828$	4.32313	0.150239
$829$	1.71663	0.0596210	0.0298105	−	0.999556i	$-0.490510\pi$
$829$	1.71663	0.0596210	0.0298105	+	0.999556i	$0.490510\pi$
$830$	17.0160	0.590633
$831$	10.5427	0.365722
$832$	1.00000	0.0346688
$833$	−0.0597920	−0.00207167
$834$	−47.6165	−1.64882
$835$	−10.5402	−0.364758
$836$	−0.442349	−0.0152989
$837$	−0.998009	−0.0344962
$838$	−8.66847	−0.299447
$839$	44.2843	1.52886	0.764431	−	0.644705i	$-0.223020\pi$
$839$	44.2843	1.52886	0.764431	+	0.644705i	$0.223020\pi$
$840$	−6.72875	−0.232164
$841$	29.8136	1.02806
$842$	−33.5781	−1.15718
$843$	10.3692	0.357136
$844$	16.0060	0.550951
$845$	−1.00000	−0.0344010
$846$	42.5318	1.46227
$847$	−29.1481	−1.00154
$848$	−2.24210	−0.0769941
$849$	10.4806	0.359694
$850$	0.744740	0.0255444
$851$	8.09334	0.277436
$852$	18.6163	0.637783
$853$	−40.9208	−1.40110	−0.700551	−	0.713602i	$-0.747062\pi$
$853$	−40.9208	−1.40110	−0.700551	+	0.713602i	$0.747062\pi$
$854$	−25.6872	−0.878997
$855$	7.02467	0.240239
$856$	−16.1912	−0.553402
$857$	−36.6848	−1.25313	−0.626565	−	0.779369i	$-0.715540\pi$
$857$	−36.6848	−1.25313	−0.626565	+	0.779369i	$0.715540\pi$
$858$	0.540560	0.0184544
$859$	48.5064	1.65502	0.827509	−	0.561453i	$-0.189757\pi$
$859$	48.5064	1.65502	0.827509	+	0.561453i	$0.189757\pi$
$860$	0.538569	0.0183651
$861$	18.1951	0.620086
$862$	6.11900	0.208414
$863$	17.6911	0.602213	0.301106	−	0.953591i	$-0.402644\pi$
$863$	17.6911	0.602213	0.301106	+	0.953591i	$0.402644\pi$
$864$	0.998009	0.0339530
$865$	−20.2839	−0.689673
$866$	28.7821	0.978056
$867$	41.5865	1.41235
$868$	2.66088	0.0903162
$869$	−2.37761	−0.0806549
$870$	19.3931	0.657489
$871$	8.67775	0.294034
$872$	−10.1510	−0.343756
$873$	−35.1205	−1.18865
$874$	2.63530	0.0891404
$875$	−2.66088	−0.0899542
$876$	−10.3125	−0.348427
$877$	34.6225	1.16912	0.584560	−	0.811351i	$-0.301267\pi$
$877$	34.6225	1.16912	0.584560	+	0.811351i	$0.301267\pi$
$878$	2.94685	0.0994515
$879$	−7.23311	−0.243967
$880$	−0.213764	−0.00720600
$881$	16.9273	0.570296	0.285148	−	0.958483i	$-0.407957\pi$
$881$	16.9273	0.570296	0.285148	+	0.958483i	$0.407957\pi$
$882$	−0.272543	−0.00917699
$883$	−24.0325	−0.808757	−0.404379	−	0.914592i	$-0.632512\pi$
$883$	−24.0325	−0.808757	−0.404379	+	0.914592i	$0.632512\pi$
$884$	−0.744740	−0.0250483
$885$	−15.6833	−0.527190
$886$	6.37020	0.214011
$887$	−24.8230	−0.833475	−0.416738	−	0.909027i	$-0.636827\pi$
$887$	−24.8230	−0.833475	−0.416738	+	0.909027i	$0.636827\pi$
$888$	16.0707	0.539298
$889$	4.79673	0.160877
$890$	3.82418	0.128187
$891$	−1.63749	−0.0548580
$892$	12.4591	0.417161
$893$	25.9267	0.867603
$894$	−29.3734	−0.982395
$895$	25.1050	0.839168
$896$	−2.66088	−0.0888938
$897$	−3.22040	−0.107526
$898$	16.9648	0.566123
$899$	−7.66900	−0.255776
$900$	3.39466	0.113155
$901$	1.66978	0.0556285
$902$	0.578036	0.0192465
$903$	3.62390	0.120596
$904$	0.909261	0.0302416
$905$	20.9349	0.695898
$906$	37.9967	1.26235
$907$	−43.2492	−1.43607	−0.718033	−	0.696009i	$-0.754958\pi$
$907$	−43.2492	−1.43607	−0.718033	+	0.696009i	$0.754958\pi$
$908$	−12.8779	−0.427367
$909$	59.5557	1.97534
$910$	2.66088	0.0882073
$911$	−14.6924	−0.486781	−0.243391	−	0.969928i	$-0.578260\pi$
$911$	−14.6924	−0.486781	−0.243391	+	0.969928i	$0.578260\pi$
$912$	5.23285	0.173277
$913$	3.63741	0.120381
$914$	18.9108	0.625515
$915$	24.4118	0.807029
$916$	−29.2969	−0.967996
$917$	30.3101	1.00093
$918$	−0.743257	−0.0245311
$919$	33.2347	1.09631	0.548156	−	0.836376i	$-0.315330\pi$
$919$	33.2347	1.09631	0.548156	+	0.836376i	$0.315330\pi$
$920$	1.27351	0.0419863
$921$	−54.7046	−1.80258
$922$	12.9343	0.425968
$923$	−7.36180	−0.242316
$924$	−1.43837	−0.0473188
$925$	6.35516	0.208956
$926$	−19.9494	−0.655577
$927$	18.9686	0.623009
$928$	7.66900	0.251747
$929$	−12.8147	−0.420438	−0.210219	−	0.977654i	$-0.567418\pi$
$929$	−12.8147	−0.420438	−0.210219	+	0.977654i	$0.567418\pi$
$930$	−2.52877	−0.0829215
$931$	−0.166137	−0.00544493
$932$	−6.32322	−0.207124
$933$	6.37376	0.208668
$934$	−6.99307	−0.228820
$935$	0.159199	0.00520636
$936$	−3.39466	−0.110958
$937$	28.4554	0.929598	0.464799	−	0.885416i	$-0.346127\pi$
$937$	28.4554	0.929598	0.464799	+	0.885416i	$0.346127\pi$
$938$	−23.0905	−0.753930
$939$	30.6967	1.00175
$940$	12.5290	0.408652
$941$	19.7138	0.642652	0.321326	−	0.946969i	$-0.395872\pi$
$941$	19.7138	0.642652	0.321326	+	0.946969i	$0.395872\pi$
$942$	−2.22215	−0.0724016
$943$	−3.44366	−0.112141
$944$	−6.20197	−0.201857
$945$	2.65558	0.0863861
$946$	0.115127	0.00374310
$947$	53.2093	1.72907	0.864535	−	0.502572i	$-0.167613\pi$
$947$	53.2093	1.72907	0.864535	+	0.502572i	$0.167613\pi$
$948$	28.1264	0.913503
$949$	4.07808	0.132380
$950$	2.06933	0.0671378
$951$	47.8883	1.55288
$952$	1.98166	0.0642261
$953$	19.6934	0.637933	0.318966	−	0.947766i	$-0.396664\pi$
$953$	19.6934	0.637933	0.318966	+	0.947766i	$0.396664\pi$
$954$	7.61118	0.246421
$955$	8.25432	0.267104
$956$	−7.19504	−0.232704
$957$	4.14556	0.134007
$958$	−35.4289	−1.14466
$959$	−35.1586	−1.13533
$960$	2.52877	0.0816156
$961$	1.00000	0.0322581
$962$	−6.35516	−0.204899
$963$	54.9635	1.77117
$964$	−15.1442	−0.487763
$965$	16.8137	0.541252
$966$	8.56911	0.275706
$967$	53.4207	1.71790	0.858948	−	0.512064i	$-0.171119\pi$
$967$	53.4207	1.71790	0.858948	+	0.512064i	$0.171119\pi$
$968$	10.9543	0.352085
$969$	−3.89711	−0.125193
$970$	−10.3458	−0.332184
$971$	−5.72239	−0.183640	−0.0918201	−	0.995776i	$-0.529268\pi$
$971$	−5.72239	−0.183640	−0.0918201	+	0.995776i	$0.529268\pi$
$972$	22.3650	0.717359
$973$	−50.1041	−1.60627
$974$	20.7243	0.664049
$975$	−2.52877	−0.0809854
$976$	9.65364	0.309005
$977$	44.3273	1.41816	0.709078	−	0.705130i	$-0.249111\pi$
$977$	44.3273	1.41816	0.709078	+	0.705130i	$0.249111\pi$
$978$	−7.42676	−0.237482
$979$	0.817474	0.0261266
$980$	−0.0802857	−0.00256463
$981$	34.4592	1.10020
$982$	24.5167	0.782360
$983$	25.2726	0.806071	0.403036	−	0.915184i	$-0.367955\pi$
$983$	25.2726	0.806071	0.403036	+	0.915184i	$0.367955\pi$
$984$	−6.83799	−0.217987
$985$	8.56451	0.272888
$986$	−5.71141	−0.181889
$987$	84.3047	2.68345
$988$	−2.06933	−0.0658341
$989$	−0.685872	−0.0218095
$990$	0.725658	0.0230629
$991$	−5.24526	−0.166621	−0.0833106	−	0.996524i	$-0.526549\pi$
$991$	−5.24526	−0.166621	−0.0833106	+	0.996524i	$0.526549\pi$
$992$	−1.00000	−0.0317500
$993$	−57.8603	−1.83614
$994$	19.5889	0.621321
$995$	6.95810	0.220586
$996$	−43.0294	−1.36344
$997$	−21.8140	−0.690856	−0.345428	−	0.938445i	$-0.612266\pi$
$997$	−21.8140	−0.690856	−0.345428	+	0.938445i	$0.612266\pi$
$998$	6.72974	0.213026
$999$	−6.34250	−0.200668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.c.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.c.1.1	✓	6	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.52877 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.52877 q^{6} +2.66088 q^{7} -1.00000 q^{8} +3.39466 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.52877 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.52877 q^{6} +2.66088 q^{7} -1.00000 q^{8} +3.39466 q^{9} +1.00000 q^{10} +0.213764 q^{11} -2.52877 q^{12} +1.00000 q^{13} -2.66088 q^{14} +2.52877 q^{15} +1.00000 q^{16} -0.744740 q^{17} -3.39466 q^{18} -2.06933 q^{19} -1.00000 q^{20} -6.72875 q^{21} -0.213764 q^{22} +1.27351 q^{23} +2.52877 q^{24} +1.00000 q^{25} -1.00000 q^{26} -0.998009 q^{27} +2.66088 q^{28} -7.66900 q^{29} -2.52877 q^{30} +1.00000 q^{31} -1.00000 q^{32} -0.540560 q^{33} +0.744740 q^{34} -2.66088 q^{35} +3.39466 q^{36} +6.35516 q^{37} +2.06933 q^{38} -2.52877 q^{39} +1.00000 q^{40} -2.70408 q^{41} +6.72875 q^{42} -0.538569 q^{43} +0.213764 q^{44} -3.39466 q^{45} -1.27351 q^{46} -12.5290 q^{47} -2.52877 q^{48} +0.0802857 q^{49} -1.00000 q^{50} +1.88327 q^{51} +1.00000 q^{52} -2.24210 q^{53} +0.998009 q^{54} -0.213764 q^{55} -2.66088 q^{56} +5.23285 q^{57} +7.66900 q^{58} -6.20197 q^{59} +2.52877 q^{60} +9.65364 q^{61} -1.00000 q^{62} +9.03279 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.540560 q^{66} +8.67775 q^{67} -0.744740 q^{68} -3.22040 q^{69} +2.66088 q^{70} -7.36180 q^{71} -3.39466 q^{72} +4.07808 q^{73} -6.35516 q^{74} -2.52877 q^{75} -2.06933 q^{76} +0.568802 q^{77} +2.52877 q^{78} -11.1226 q^{79} -1.00000 q^{80} -7.66025 q^{81} +2.70408 q^{82} +17.0160 q^{83} -6.72875 q^{84} +0.744740 q^{85} +0.538569 q^{86} +19.3931 q^{87} -0.213764 q^{88} +3.82418 q^{89} +3.39466 q^{90} +2.66088 q^{91} +1.27351 q^{92} -2.52877 q^{93} +12.5290 q^{94} +2.06933 q^{95} +2.52877 q^{96} -10.3458 q^{97} -0.0802857 q^{98} +0.725658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9} + 6 q^{10} - 6 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} + q^{18} + 3 q^{19} - 6 q^{20} - q^{21} + 6 q^{22} - 7 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - q^{27} + 4 q^{28} - 14 q^{29} - q^{30} + 6 q^{31} - 6 q^{32} - 2 q^{33} + 4 q^{34} - 4 q^{35} - q^{36} + 14 q^{37} - 3 q^{38} - q^{39} + 6 q^{40} - 12 q^{41} + q^{42} + 3 q^{43} - 6 q^{44} + q^{45} + 7 q^{46} - 2 q^{47} - q^{48} - 6 q^{49} - 6 q^{50} - 7 q^{51} + 6 q^{52} - 4 q^{53} + q^{54} + 6 q^{55} - 4 q^{56} + 13 q^{57} + 14 q^{58} - 17 q^{59} + q^{60} - 5 q^{61} - 6 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + 2 q^{66} + 8 q^{67} - 4 q^{68} - 8 q^{69} + 4 q^{70} - 16 q^{71} + q^{72} + 11 q^{73} - 14 q^{74} - q^{75} + 3 q^{76} - 15 q^{77} + q^{78} - 2 q^{79} - 6 q^{80} - 26 q^{81} + 12 q^{82} + 4 q^{83} - q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 6 q^{88} - 8 q^{89} - q^{90} + 4 q^{91} - 7 q^{92} - q^{93} + 2 q^{94} - 3 q^{95} + q^{96} + 5 q^{97} + 6 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9 + 6 * q^10 - 6 * q^11 - q^12 + 6 * q^13 - 4 * q^14 + q^15 + 6 * q^16 - 4 * q^17 + q^18 + 3 * q^19 - 6 * q^20 - q^21 + 6 * q^22 - 7 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - q^27 + 4 * q^28 - 14 * q^29 - q^30 + 6 * q^31 - 6 * q^32 - 2 * q^33 + 4 * q^34 - 4 * q^35 - q^36 + 14 * q^37 - 3 * q^38 - q^39 + 6 * q^40 - 12 * q^41 + q^42 + 3 * q^43 - 6 * q^44 + q^45 + 7 * q^46 - 2 * q^47 - q^48 - 6 * q^49 - 6 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + q^54 + 6 * q^55 - 4 * q^56 + 13 * q^57 + 14 * q^58 - 17 * q^59 + q^60 - 5 * q^61 - 6 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + 2 * q^66 + 8 * q^67 - 4 * q^68 - 8 * q^69 + 4 * q^70 - 16 * q^71 + q^72 + 11 * q^73 - 14 * q^74 - q^75 + 3 * q^76 - 15 * q^77 + q^78 - 2 * q^79 - 6 * q^80 - 26 * q^81 + 12 * q^82 + 4 * q^83 - q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 6 * q^88 - 8 * q^89 - q^90 + 4 * q^91 - 7 * q^92 - q^93 + 2 * q^94 - 3 * q^95 + q^96 + 5 * q^97 + 6 * q^98 + 15 * q^99

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