LMFDB - Embedded newform 4034.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.27997 q^{3} +1.00000 q^{4} +2.11941 q^{5} +3.27997 q^{6} -0.124927 q^{7} -1.00000 q^{8} +7.75819 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.27997 q^{3} +1.00000 q^{4} +2.11941 q^{5} +3.27997 q^{6} -0.124927 q^{7} -1.00000 q^{8} +7.75819 q^{9} -2.11941 q^{10} -5.51208 q^{11} -3.27997 q^{12} +4.44243 q^{13} +0.124927 q^{14} -6.95161 q^{15} +1.00000 q^{16} -0.642423 q^{17} -7.75819 q^{18} +0.147395 q^{19} +2.11941 q^{20} +0.409757 q^{21} +5.51208 q^{22} +3.37688 q^{23} +3.27997 q^{24} -0.508082 q^{25} -4.44243 q^{26} -15.6067 q^{27} -0.124927 q^{28} +2.66664 q^{29} +6.95161 q^{30} +5.69698 q^{31} -1.00000 q^{32} +18.0794 q^{33} +0.642423 q^{34} -0.264772 q^{35} +7.75819 q^{36} -7.36167 q^{37} -0.147395 q^{38} -14.5710 q^{39} -2.11941 q^{40} -6.82637 q^{41} -0.409757 q^{42} -8.47080 q^{43} -5.51208 q^{44} +16.4428 q^{45} -3.37688 q^{46} -2.64489 q^{47} -3.27997 q^{48} -6.98439 q^{49} +0.508082 q^{50} +2.10713 q^{51} +4.44243 q^{52} +10.3326 q^{53} +15.6067 q^{54} -11.6824 q^{55} +0.124927 q^{56} -0.483450 q^{57} -2.66664 q^{58} +4.76410 q^{59} -6.95161 q^{60} -9.35674 q^{61} -5.69698 q^{62} -0.969208 q^{63} +1.00000 q^{64} +9.41535 q^{65} -18.0794 q^{66} +12.4058 q^{67} -0.642423 q^{68} -11.0761 q^{69} +0.264772 q^{70} -13.3767 q^{71} -7.75819 q^{72} +1.77853 q^{73} +7.36167 q^{74} +1.66649 q^{75} +0.147395 q^{76} +0.688607 q^{77} +14.5710 q^{78} -16.4199 q^{79} +2.11941 q^{80} +27.9150 q^{81} +6.82637 q^{82} +8.04537 q^{83} +0.409757 q^{84} -1.36156 q^{85} +8.47080 q^{86} -8.74650 q^{87} +5.51208 q^{88} +14.9530 q^{89} -16.4428 q^{90} -0.554979 q^{91} +3.37688 q^{92} -18.6859 q^{93} +2.64489 q^{94} +0.312390 q^{95} +3.27997 q^{96} -5.37623 q^{97} +6.98439 q^{98} -42.7638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	−3.27997	−1.89369	−0.946845	−	0.321689i	$-0.895749\pi$
$3$	−3.27997	−1.89369	−0.946845	+	0.321689i	$0.895749\pi$
$4$	1.00000	0.500000
$5$	2.11941	0.947831	0.473916	−	0.880570i	$-0.342840\pi$
$5$	2.11941	0.947831	0.473916	+	0.880570i	$0.342840\pi$
$6$	3.27997	1.33904
$7$	−0.124927	−0.0472180	−0.0236090	−	0.999721i	$-0.507516\pi$
$7$	−0.124927	−0.0472180	−0.0236090	+	0.999721i	$0.507516\pi$
$8$	−1.00000	−0.353553
$9$	7.75819	2.58606
$10$	−2.11941	−0.670218
$11$	−5.51208	−1.66195	−0.830977	−	0.556307i	$-0.812218\pi$
$11$	−5.51208	−1.66195	−0.830977	+	0.556307i	$0.812218\pi$
$12$	−3.27997	−0.946845
$13$	4.44243	1.23211	0.616054	−	0.787704i	$-0.288730\pi$
$13$	4.44243	1.23211	0.616054	+	0.787704i	$0.288730\pi$
$14$	0.124927	0.0333881
$15$	−6.95161	−1.79490
$16$	1.00000	0.250000
$17$	−0.642423	−0.155810	−0.0779052	−	0.996961i	$-0.524823\pi$
$17$	−0.642423	−0.155810	−0.0779052	+	0.996961i	$0.524823\pi$
$18$	−7.75819	−1.82862
$19$	0.147395	0.0338147	0.0169073	−	0.999857i	$-0.494618\pi$
$19$	0.147395	0.0338147	0.0169073	+	0.999857i	$0.494618\pi$
$20$	2.11941	0.473916
$21$	0.409757	0.0894162
$22$	5.51208	1.17518
$23$	3.37688	0.704129	0.352064	−	0.935976i	$-0.385480\pi$
$23$	3.37688	0.704129	0.352064	+	0.935976i	$0.385480\pi$
$24$	3.27997	0.669521
$25$	−0.508082	−0.101616
$26$	−4.44243	−0.871232
$27$	−15.6067	−3.00352
$28$	−0.124927	−0.0236090
$29$	2.66664	0.495183	0.247591	−	0.968865i	$-0.420361\pi$
$29$	2.66664	0.495183	0.247591	+	0.968865i	$0.420361\pi$
$30$	6.95161	1.26919
$31$	5.69698	1.02321	0.511604	−	0.859221i	$-0.329052\pi$
$31$	5.69698	1.02321	0.511604	+	0.859221i	$0.329052\pi$
$32$	−1.00000	−0.176777
$33$	18.0794	3.14723
$34$	0.642423	0.110175
$35$	−0.264772	−0.0447546
$36$	7.75819	1.29303
$37$	−7.36167	−1.21025	−0.605126	−	0.796130i	$-0.706877\pi$
$37$	−7.36167	−1.21025	−0.605126	+	0.796130i	$0.706877\pi$
$38$	−0.147395	−0.0239106
$39$	−14.5710	−2.33323
$40$	−2.11941	−0.335109
$41$	−6.82637	−1.06610	−0.533050	−	0.846084i	$-0.678954\pi$
$41$	−6.82637	−1.06610	−0.533050	+	0.846084i	$0.678954\pi$
$42$	−0.409757	−0.0632268
$43$	−8.47080	−1.29178	−0.645892	−	0.763429i	$-0.723514\pi$
$43$	−8.47080	−1.29178	−0.645892	+	0.763429i	$0.723514\pi$
$44$	−5.51208	−0.830977
$45$	16.4428	2.45115
$46$	−3.37688	−0.497894
$47$	−2.64489	−0.385797	−0.192898	−	0.981219i	$-0.561789\pi$
$47$	−2.64489	−0.385797	−0.192898	+	0.981219i	$0.561789\pi$
$48$	−3.27997	−0.473423
$49$	−6.98439	−0.997770
$50$	0.508082	0.0718536
$51$	2.10713	0.295057
$52$	4.44243	0.616054
$53$	10.3326	1.41929	0.709647	−	0.704558i	$-0.248854\pi$
$53$	10.3326	1.41929	0.709647	+	0.704558i	$0.248854\pi$
$54$	15.6067	2.12381
$55$	−11.6824	−1.57525
$56$	0.124927	0.0166941
$57$	−0.483450	−0.0640345
$58$	−2.66664	−0.350147
$59$	4.76410	0.620233	0.310117	−	0.950699i	$-0.399632\pi$
$59$	4.76410	0.620233	0.310117	+	0.950699i	$0.399632\pi$
$60$	−6.95161	−0.897449
$61$	−9.35674	−1.19801	−0.599004	−	0.800746i	$-0.704437\pi$
$61$	−9.35674	−1.19801	−0.599004	+	0.800746i	$0.704437\pi$
$62$	−5.69698	−0.723517
$63$	−0.969208	−0.122109
$64$	1.00000	0.125000
$65$	9.41535	1.16783
$66$	−18.0794	−2.22543
$67$	12.4058	1.51561	0.757805	−	0.652481i	$-0.226272\pi$
$67$	12.4058	1.51561	0.757805	+	0.652481i	$0.226272\pi$
$68$	−0.642423	−0.0779052
$69$	−11.0761	−1.33340
$70$	0.264772	0.0316463
$71$	−13.3767	−1.58752	−0.793762	−	0.608228i	$-0.791881\pi$
$71$	−13.3767	−1.58752	−0.793762	+	0.608228i	$0.791881\pi$
$72$	−7.75819	−0.914312
$73$	1.77853	0.208161	0.104081	−	0.994569i	$-0.466810\pi$
$73$	1.77853	0.208161	0.104081	+	0.994569i	$0.466810\pi$
$74$	7.36167	0.855777
$75$	1.66649	0.192430
$76$	0.147395	0.0169073
$77$	0.688607	0.0784741
$78$	14.5710	1.64984
$79$	−16.4199	−1.84738	−0.923691	−	0.383137i	$-0.874844\pi$
$79$	−16.4199	−1.84738	−0.923691	+	0.383137i	$0.874844\pi$
$80$	2.11941	0.236958
$81$	27.9150	3.10167
$82$	6.82637	0.753846
$83$	8.04537	0.883094	0.441547	−	0.897238i	$-0.354430\pi$
$83$	8.04537	0.883094	0.441547	+	0.897238i	$0.354430\pi$
$84$	0.409757	0.0447081
$85$	−1.36156	−0.147682
$86$	8.47080	0.913429
$87$	−8.74650	−0.937723
$88$	5.51208	0.587590
$89$	14.9530	1.58502	0.792508	−	0.609861i	$-0.208775\pi$
$89$	14.9530	1.58502	0.792508	+	0.609861i	$0.208775\pi$
$90$	−16.4428	−1.73323
$91$	−0.554979	−0.0581776
$92$	3.37688	0.352064
$93$	−18.6859	−1.93764
$94$	2.64489	0.272799
$95$	0.312390	0.0320506
$96$	3.27997	0.334760
$97$	−5.37623	−0.545873	−0.272937	−	0.962032i	$-0.587995\pi$
$97$	−5.37623	−0.545873	−0.272937	+	0.962032i	$0.587995\pi$
$98$	6.98439	0.705530
$99$	−42.7638	−4.29792
$100$	−0.508082	−0.0508082
$101$	12.4065	1.23449	0.617244	−	0.786772i	$-0.288249\pi$
$101$	12.4065	1.23449	0.617244	+	0.786772i	$0.288249\pi$
$102$	−2.10713	−0.208637
$103$	−5.06543	−0.499112	−0.249556	−	0.968360i	$-0.580285\pi$
$103$	−5.06543	−0.499112	−0.249556	+	0.968360i	$0.580285\pi$
$104$	−4.44243	−0.435616
$105$	0.868444	0.0847515
$106$	−10.3326	−1.00359
$107$	17.3656	1.67879	0.839396	−	0.543521i	$-0.182909\pi$
$107$	17.3656	1.67879	0.839396	+	0.543521i	$0.182909\pi$
$108$	−15.6067	−1.50176
$109$	1.47093	0.140890	0.0704448	−	0.997516i	$-0.477558\pi$
$109$	1.47093	0.140890	0.0704448	+	0.997516i	$0.477558\pi$
$110$	11.6824	1.11387
$111$	24.1461	2.29184
$112$	−0.124927	−0.0118045
$113$	2.11168	0.198650	0.0993250	−	0.995055i	$-0.468332\pi$
$113$	2.11168	0.198650	0.0993250	+	0.995055i	$0.468332\pi$
$114$	0.483450	0.0452792
$115$	7.15701	0.667395
$116$	2.66664	0.247591
$117$	34.4652	3.18631
$118$	−4.76410	−0.438571
$119$	0.0802559	0.00735705
$120$	6.95161	0.634593
$121$	19.3830	1.76209
$122$	9.35674	0.847120
$123$	22.3903	2.01886
$124$	5.69698	0.511604
$125$	−11.6739	−1.04415
$126$	0.969208	0.0863439
$127$	−8.39616	−0.745038	−0.372519	−	0.928024i	$-0.621506\pi$
$127$	−8.39616	−0.745038	−0.372519	+	0.928024i	$0.621506\pi$
$128$	−1.00000	−0.0883883
$129$	27.7839	2.44624
$130$	−9.41535	−0.825781
$131$	12.4631	1.08891	0.544455	−	0.838790i	$-0.316736\pi$
$131$	12.4631	1.08891	0.544455	+	0.838790i	$0.316736\pi$
$132$	18.0794	1.57361
$133$	−0.0184136	−0.00159666
$134$	−12.4058	−1.07170
$135$	−33.0771	−2.84683
$136$	0.642423	0.0550873
$137$	1.04990	0.0896989	0.0448494	−	0.998994i	$-0.485719\pi$
$137$	1.04990	0.0896989	0.0448494	+	0.998994i	$0.485719\pi$
$138$	11.0761	0.942858
$139$	−22.8656	−1.93943	−0.969717	−	0.244233i	$-0.921464\pi$
$139$	−22.8656	−1.93943	−0.969717	+	0.244233i	$0.921464\pi$
$140$	−0.264772	−0.0223773
$141$	8.67515	0.730579
$142$	13.3767	1.12255
$143$	−24.4870	−2.04771
$144$	7.75819	0.646516
$145$	5.65172	0.469349
$146$	−1.77853	−0.147192
$147$	22.9086	1.88947
$148$	−7.36167	−0.605126
$149$	−10.5722	−0.866111	−0.433055	−	0.901367i	$-0.642565\pi$
$149$	−10.5722	−0.866111	−0.433055	+	0.901367i	$0.642565\pi$
$150$	−1.66649	−0.136068
$151$	17.0348	1.38627	0.693137	−	0.720806i	$-0.256228\pi$
$151$	17.0348	1.38627	0.693137	+	0.720806i	$0.256228\pi$
$152$	−0.147395	−0.0119553
$153$	−4.98404	−0.402936
$154$	−0.688607	−0.0554896
$155$	12.0743	0.969828
$156$	−14.5710	−1.16662
$157$	13.6817	1.09191	0.545957	−	0.837813i	$-0.316166\pi$
$157$	13.6817	1.09191	0.545957	+	0.837813i	$0.316166\pi$
$158$	16.4199	1.30630
$159$	−33.8907	−2.68770
$160$	−2.11941	−0.167554
$161$	−0.421864	−0.0332475
$162$	−27.9150	−2.19321
$163$	−8.40791	−0.658558	−0.329279	−	0.944233i	$-0.606806\pi$
$163$	−8.40791	−0.658558	−0.329279	+	0.944233i	$0.606806\pi$
$164$	−6.82637	−0.533050
$165$	38.3178	2.98304
$166$	−8.04537	−0.624442
$167$	13.5011	1.04475	0.522373	−	0.852717i	$-0.325047\pi$
$167$	13.5011	1.04475	0.522373	+	0.852717i	$0.325047\pi$
$168$	−0.409757	−0.0316134
$169$	6.73518	0.518091
$170$	1.36156	0.104427
$171$	1.14352	0.0874469
$172$	−8.47080	−0.645892
$173$	−5.74465	−0.436758	−0.218379	−	0.975864i	$-0.570077\pi$
$173$	−5.74465	−0.436758	−0.218379	+	0.975864i	$0.570077\pi$
$174$	8.74650	0.663070
$175$	0.0634731	0.00479811
$176$	−5.51208	−0.415489
$177$	−15.6261	−1.17453
$178$	−14.9530	−1.12078
$179$	−8.34388	−0.623651	−0.311825	−	0.950139i	$-0.600940\pi$
$179$	−8.34388	−0.623651	−0.311825	+	0.950139i	$0.600940\pi$
$180$	16.4428	1.22558
$181$	1.57657	0.117186	0.0585929	−	0.998282i	$-0.481339\pi$
$181$	1.57657	0.117186	0.0585929	+	0.998282i	$0.481339\pi$
$182$	0.554979	0.0411378
$183$	30.6898	2.26866
$184$	−3.37688	−0.248947
$185$	−15.6024	−1.14711
$186$	18.6859	1.37012
$187$	3.54108	0.258950
$188$	−2.64489	−0.192898
$189$	1.94970	0.141820
$190$	−0.312390	−0.0226632
$191$	−0.616314	−0.0445949	−0.0222975	−	0.999751i	$-0.507098\pi$
$191$	−0.616314	−0.0445949	−0.0222975	+	0.999751i	$0.507098\pi$
$192$	−3.27997	−0.236711
$193$	−14.5294	−1.04585	−0.522925	−	0.852379i	$-0.675159\pi$
$193$	−14.5294	−1.04585	−0.522925	+	0.852379i	$0.675159\pi$
$194$	5.37623	0.385991
$195$	−30.8821	−2.21151
$196$	−6.98439	−0.498885
$197$	23.4259	1.66902	0.834512	−	0.550990i	$-0.185750\pi$
$197$	23.4259	1.66902	0.834512	+	0.550990i	$0.185750\pi$
$198$	42.7638	3.03909
$199$	−17.3046	−1.22669	−0.613347	−	0.789814i	$-0.710177\pi$
$199$	−17.3046	−1.22669	−0.613347	+	0.789814i	$0.710177\pi$
$200$	0.508082	0.0359268
$201$	−40.6906	−2.87010
$202$	−12.4065	−0.872915
$203$	−0.333135	−0.0233815
$204$	2.10713	0.147528
$205$	−14.4679	−1.01048
$206$	5.06543	0.352926
$207$	26.1985	1.82092
$208$	4.44243	0.308027
$209$	−0.812451	−0.0561984
$210$	−0.868444	−0.0599283
$211$	−12.5945	−0.867038	−0.433519	−	0.901144i	$-0.642728\pi$
$211$	−12.5945	−0.867038	−0.433519	+	0.901144i	$0.642728\pi$
$212$	10.3326	0.709647
$213$	43.8752	3.00628
$214$	−17.3656	−1.18708
$215$	−17.9531	−1.22439
$216$	15.6067	1.06190
$217$	−0.711706	−0.0483138
$218$	−1.47093	−0.0996240
$219$	−5.83352	−0.394193
$220$	−11.6824	−0.787626
$221$	−2.85392	−0.191975
$222$	−24.1461	−1.62058
$223$	−0.560737	−0.0375497	−0.0187749	−	0.999824i	$-0.505977\pi$
$223$	−0.560737	−0.0375497	−0.0187749	+	0.999824i	$0.505977\pi$
$224$	0.124927	0.00834703
$225$	−3.94180	−0.262786
$226$	−2.11168	−0.140467
$227$	−23.7376	−1.57552	−0.787761	−	0.615981i	$-0.788760\pi$
$227$	−23.7376	−1.57552	−0.787761	+	0.615981i	$0.788760\pi$
$228$	−0.483450	−0.0320172
$229$	12.9244	0.854070	0.427035	−	0.904235i	$-0.359558\pi$
$229$	12.9244	0.854070	0.427035	+	0.904235i	$0.359558\pi$
$230$	−7.15701	−0.471919
$231$	−2.25861	−0.148606
$232$	−2.66664	−0.175074
$233$	−14.1092	−0.924322	−0.462161	−	0.886796i	$-0.652926\pi$
$233$	−14.1092	−0.924322	−0.462161	+	0.886796i	$0.652926\pi$
$234$	−34.4652	−2.25306
$235$	−5.60561	−0.365670
$236$	4.76410	0.310117
$237$	53.8567	3.49837
$238$	−0.0802559	−0.00520222
$239$	−20.9473	−1.35497	−0.677484	−	0.735538i	$-0.736930\pi$
$239$	−20.9473	−1.35497	−0.677484	+	0.735538i	$0.736930\pi$
$240$	−6.95161	−0.448725
$241$	−4.84493	−0.312089	−0.156045	−	0.987750i	$-0.549874\pi$
$241$	−4.84493	−0.312089	−0.156045	+	0.987750i	$0.549874\pi$
$242$	−19.3830	−1.24599
$243$	−44.7401	−2.87008
$244$	−9.35674	−0.599004
$245$	−14.8028	−0.945718
$246$	−22.3903	−1.42755
$247$	0.654790	0.0416633
$248$	−5.69698	−0.361759
$249$	−26.3886	−1.67231
$250$	11.6739	0.738323
$251$	18.1904	1.14817	0.574083	−	0.818797i	$-0.305359\pi$
$251$	18.1904	1.14817	0.574083	+	0.818797i	$0.305359\pi$
$252$	−0.969208	−0.0610543
$253$	−18.6136	−1.17023
$254$	8.39616	0.526822
$255$	4.46587	0.279664
$256$	1.00000	0.0625000
$257$	−30.0950	−1.87727	−0.938636	−	0.344909i	$-0.887910\pi$
$257$	−30.0950	−1.87727	−0.938636	+	0.344909i	$0.887910\pi$
$258$	−27.7839	−1.72975
$259$	0.919671	0.0571456
$260$	9.41535	0.583915
$261$	20.6883	1.28057
$262$	−12.4631	−0.769976
$263$	−11.0541	−0.681624	−0.340812	−	0.940131i	$-0.610702\pi$
$263$	−11.0541	−0.681624	−0.340812	+	0.940131i	$0.610702\pi$
$264$	−18.0794	−1.11271
$265$	21.8991	1.34525
$266$	0.0184136	0.00112901
$267$	−49.0454	−3.00153
$268$	12.4058	0.757805
$269$	−26.2364	−1.59966	−0.799831	−	0.600226i	$-0.795077\pi$
$269$	−26.2364	−1.59966	−0.799831	+	0.600226i	$0.795077\pi$
$270$	33.0771	2.01301
$271$	3.85353	0.234085	0.117043	−	0.993127i	$-0.462659\pi$
$271$	3.85353	0.234085	0.117043	+	0.993127i	$0.462659\pi$
$272$	−0.642423	−0.0389526
$273$	1.82031	0.110170
$274$	−1.04990	−0.0634267
$275$	2.80059	0.168882
$276$	−11.0761	−0.666701
$277$	−19.7055	−1.18399	−0.591995	−	0.805941i	$-0.701660\pi$
$277$	−19.7055	−1.18399	−0.591995	+	0.805941i	$0.701660\pi$
$278$	22.8656	1.37139
$279$	44.1983	2.64608
$280$	0.264772	0.0158232
$281$	−7.69389	−0.458979	−0.229490	−	0.973311i	$-0.573706\pi$
$281$	−7.69389	−0.458979	−0.229490	+	0.973311i	$0.573706\pi$
$282$	−8.67515	−0.516598
$283$	25.9840	1.54459	0.772293	−	0.635266i	$-0.219110\pi$
$283$	25.9840	1.54459	0.772293	+	0.635266i	$0.219110\pi$
$284$	−13.3767	−0.793762
$285$	−1.02463	−0.0606939
$286$	24.4870	1.44795
$287$	0.852797	0.0503390
$288$	−7.75819	−0.457156
$289$	−16.5873	−0.975723
$290$	−5.65172	−0.331880
$291$	17.6339	1.03372
$292$	1.77853	0.104081
$293$	12.6443	0.738687	0.369344	−	0.929293i	$-0.379583\pi$
$293$	12.6443	0.738687	0.369344	+	0.929293i	$0.379583\pi$
$294$	−22.9086	−1.33606
$295$	10.0971	0.587876
$296$	7.36167	0.427889
$297$	86.0255	4.99171
$298$	10.5722	0.612433
$299$	15.0016	0.867563
$300$	1.66649	0.0962149
$301$	1.05823	0.0609954
$302$	−17.0348	−0.980244
$303$	−40.6928	−2.33774
$304$	0.147395	0.00845366
$305$	−19.8308	−1.13551
$306$	4.98404	0.284919
$307$	12.2461	0.698922	0.349461	−	0.936951i	$-0.386365\pi$
$307$	12.2461	0.698922	0.349461	+	0.936951i	$0.386365\pi$
$308$	0.688607	0.0392370
$309$	16.6145	0.945164
$310$	−12.0743	−0.685772
$311$	−21.3382	−1.20998	−0.604990	−	0.796233i	$-0.706823\pi$
$311$	−21.3382	−1.20998	−0.604990	+	0.796233i	$0.706823\pi$
$312$	14.5710	0.824922
$313$	11.3563	0.641895	0.320947	−	0.947097i	$-0.395999\pi$
$313$	11.3563	0.641895	0.320947	+	0.947097i	$0.395999\pi$
$314$	−13.6817	−0.772100
$315$	−2.05415	−0.115738
$316$	−16.4199	−0.923691
$317$	13.9434	0.783137	0.391568	−	0.920149i	$-0.371933\pi$
$317$	13.9434	0.783137	0.391568	+	0.920149i	$0.371933\pi$
$318$	33.8907	1.90049
$319$	−14.6987	−0.822971
$320$	2.11941	0.118479
$321$	−56.9585	−3.17911
$322$	0.421864	0.0235095
$323$	−0.0946897	−0.00526867
$324$	27.9150	1.55083
$325$	−2.25712	−0.125202
$326$	8.40791	0.465671
$327$	−4.82461	−0.266801
$328$	6.82637	0.376923
$329$	0.330418	0.0182165
$330$	−38.3178	−2.10933
$331$	−32.8780	−1.80714	−0.903570	−	0.428440i	$-0.859063\pi$
$331$	−32.8780	−1.80714	−0.903570	+	0.428440i	$0.859063\pi$
$332$	8.04537	0.441547
$333$	−57.1133	−3.12979
$334$	−13.5011	−0.738747
$335$	26.2930	1.43654
$336$	0.409757	0.0223541
$337$	16.6292	0.905848	0.452924	−	0.891549i	$-0.350381\pi$
$337$	16.6292	0.905848	0.452924	+	0.891549i	$0.350381\pi$
$338$	−6.73518	−0.366345
$339$	−6.92624	−0.376182
$340$	−1.36156	−0.0738409
$341$	−31.4022	−1.70052
$342$	−1.14352	−0.0618343
$343$	1.74703	0.0943306
$344$	8.47080	0.456715
$345$	−23.4748	−1.26384
$346$	5.74465	0.308834
$347$	−6.86139	−0.368339	−0.184169	−	0.982895i	$-0.558959\pi$
$347$	−6.86139	−0.368339	−0.184169	+	0.982895i	$0.558959\pi$
$348$	−8.74650	−0.468861
$349$	−15.2994	−0.818958	−0.409479	−	0.912319i	$-0.634290\pi$
$349$	−15.2994	−0.818958	−0.409479	+	0.912319i	$0.634290\pi$
$350$	−0.0634731	−0.00339278
$351$	−69.3318	−3.70066
$352$	5.51208	0.293795
$353$	12.2185	0.650323	0.325161	−	0.945659i	$-0.394581\pi$
$353$	12.2185	0.650323	0.325161	+	0.945659i	$0.394581\pi$
$354$	15.6261	0.830518
$355$	−28.3508	−1.50471
$356$	14.9530	0.792508
$357$	−0.263237	−0.0139320
$358$	8.34388	0.440988
$359$	−0.106054	−0.00559731	−0.00279866	−	0.999996i	$-0.500891\pi$
$359$	−0.106054	−0.00559731	−0.00279866	+	0.999996i	$0.500891\pi$
$360$	−16.4428	−0.866613
$361$	−18.9783	−0.998857
$362$	−1.57657	−0.0828629
$363$	−63.5757	−3.33686
$364$	−0.554979	−0.0290888
$365$	3.76944	0.197302
$366$	−30.6898	−1.60418
$367$	−26.5399	−1.38537	−0.692686	−	0.721239i	$-0.743573\pi$
$367$	−26.5399	−1.38537	−0.692686	+	0.721239i	$0.743573\pi$
$368$	3.37688	0.176032
$369$	−52.9603	−2.75700
$370$	15.6024	0.811132
$371$	−1.29082	−0.0670161
$372$	−18.6859	−0.968820
$373$	4.68815	0.242743	0.121372	−	0.992607i	$-0.461271\pi$
$373$	4.68815	0.242743	0.121372	+	0.992607i	$0.461271\pi$
$374$	−3.54108	−0.183105
$375$	38.2901	1.97729
$376$	2.64489	0.136400
$377$	11.8464	0.610119
$378$	−1.94970	−0.100282
$379$	−30.3530	−1.55913	−0.779565	−	0.626321i	$-0.784560\pi$
$379$	−30.3530	−1.55913	−0.779565	+	0.626321i	$0.784560\pi$
$380$	0.312390	0.0160253
$381$	27.5391	1.41087
$382$	0.616314	0.0315334
$383$	−14.4631	−0.739032	−0.369516	−	0.929224i	$-0.620477\pi$
$383$	−14.4631	−0.739032	−0.369516	+	0.929224i	$0.620477\pi$
$384$	3.27997	0.167380
$385$	1.45944	0.0743802
$386$	14.5294	0.739528
$387$	−65.7181	−3.34064
$388$	−5.37623	−0.272937
$389$	21.0751	1.06855	0.534275	−	0.845310i	$-0.320585\pi$
$389$	21.0751	1.06855	0.534275	+	0.845310i	$0.320585\pi$
$390$	30.8821	1.56377
$391$	−2.16939	−0.109711
$392$	6.98439	0.352765
$393$	−40.8787	−2.06206
$394$	−23.4259	−1.18018
$395$	−34.8006	−1.75101
$396$	−42.7638	−2.14896
$397$	−15.1136	−0.758532	−0.379266	−	0.925288i	$-0.623823\pi$
$397$	−15.1136	−0.758532	−0.379266	+	0.925288i	$0.623823\pi$
$398$	17.3046	0.867403
$399$	0.0603959	0.00302358
$400$	−0.508082	−0.0254041
$401$	−36.3919	−1.81733	−0.908663	−	0.417530i	$-0.862896\pi$
$401$	−36.3919	−1.81733	−0.908663	+	0.417530i	$0.862896\pi$
$402$	40.6906	2.02946
$403$	25.3084	1.26070
$404$	12.4065	0.617244
$405$	59.1635	2.93986
$406$	0.333135	0.0165332
$407$	40.5781	2.01138
$408$	−2.10713	−0.104318
$409$	−3.54414	−0.175246	−0.0876231	−	0.996154i	$-0.527927\pi$
$409$	−3.54414	−0.175246	−0.0876231	+	0.996154i	$0.527927\pi$
$410$	14.4679	0.714519
$411$	−3.44363	−0.169862
$412$	−5.06543	−0.249556
$413$	−0.595165	−0.0292861
$414$	−26.1985	−1.28759
$415$	17.0515	0.837024
$416$	−4.44243	−0.217808
$417$	74.9984	3.67269
$418$	0.812451	0.0397383
$419$	27.0996	1.32390	0.661951	−	0.749547i	$-0.269729\pi$
$419$	27.0996	1.32390	0.661951	+	0.749547i	$0.269729\pi$
$420$	0.868444	0.0423757
$421$	0.275602	0.0134320	0.00671602	−	0.999977i	$-0.497862\pi$
$421$	0.275602	0.0134320	0.00671602	+	0.999977i	$0.497862\pi$
$422$	12.5945	0.613088
$423$	−20.5196	−0.997695
$424$	−10.3326	−0.501796
$425$	0.326403	0.0158329
$426$	−43.8752	−2.12576
$427$	1.16891	0.0565675
$428$	17.3656	0.839396
$429$	80.3167	3.87772
$430$	17.9531	0.865777
$431$	3.70754	0.178586	0.0892930	−	0.996005i	$-0.471539\pi$
$431$	3.70754	0.178586	0.0892930	+	0.996005i	$0.471539\pi$
$432$	−15.6067	−0.750879
$433$	7.69534	0.369815	0.184907	−	0.982756i	$-0.440802\pi$
$433$	7.69534	0.369815	0.184907	+	0.982756i	$0.440802\pi$
$434$	0.711706	0.0341630
$435$	−18.5375	−0.888803
$436$	1.47093	0.0704448
$437$	0.497734	0.0238099
$438$	5.83352	0.278737
$439$	25.4517	1.21474	0.607371	−	0.794419i	$-0.292224\pi$
$439$	25.4517	1.21474	0.607371	+	0.794419i	$0.292224\pi$
$440$	11.6824	0.556936
$441$	−54.1863	−2.58030
$442$	2.85392	0.135747
$443$	15.6290	0.742555	0.371277	−	0.928522i	$-0.378920\pi$
$443$	15.6290	0.742555	0.371277	+	0.928522i	$0.378920\pi$
$444$	24.1461	1.14592
$445$	31.6916	1.50233
$446$	0.560737	0.0265517
$447$	34.6766	1.64015
$448$	−0.124927	−0.00590224
$449$	−28.3718	−1.33895	−0.669473	−	0.742836i	$-0.733480\pi$
$449$	−28.3718	−1.33895	−0.669473	+	0.742836i	$0.733480\pi$
$450$	3.94180	0.185818
$451$	37.6275	1.77181
$452$	2.11168	0.0993250
$453$	−55.8737	−2.62517
$454$	23.7376	1.11406
$455$	−1.17623	−0.0551426
$456$	0.483450	0.0226396
$457$	4.07478	0.190610	0.0953050	−	0.995448i	$-0.469617\pi$
$457$	4.07478	0.190610	0.0953050	+	0.995448i	$0.469617\pi$
$458$	−12.9244	−0.603919
$459$	10.0261	0.467979
$460$	7.15701	0.333697
$461$	23.3364	1.08688	0.543442	−	0.839447i	$-0.317121\pi$
$461$	23.3364	1.08688	0.543442	+	0.839447i	$0.317121\pi$
$462$	2.25861	0.105080
$463$	14.9702	0.695725	0.347862	−	0.937546i	$-0.386908\pi$
$463$	14.9702	0.695725	0.347862	+	0.937546i	$0.386908\pi$
$464$	2.66664	0.123796
$465$	−39.6032	−1.83655
$466$	14.1092	0.653594
$467$	−34.9382	−1.61675	−0.808373	−	0.588671i	$-0.799651\pi$
$467$	−34.9382	−1.61675	−0.808373	+	0.588671i	$0.799651\pi$
$468$	34.4652	1.59316
$469$	−1.54982	−0.0715640
$470$	5.60561	0.258568
$471$	−44.8754	−2.06775
$472$	−4.76410	−0.219286
$473$	46.6917	2.14689
$474$	−53.8567	−2.47372
$475$	−0.0748885	−0.00343612
$476$	0.0802559	0.00367852
$477$	80.1624	3.67039
$478$	20.9473	0.958107
$479$	6.08023	0.277813	0.138906	−	0.990306i	$-0.455641\pi$
$479$	6.08023	0.277813	0.138906	+	0.990306i	$0.455641\pi$
$480$	6.95161	0.317296
$481$	−32.7037	−1.49116
$482$	4.84493	0.220680
$483$	1.38370	0.0629605
$484$	19.3830	0.881046
$485$	−11.3945	−0.517396
$486$	44.7401	2.02945
$487$	−24.0940	−1.09181	−0.545903	−	0.837849i	$-0.683813\pi$
$487$	−24.0940	−1.09181	−0.545903	+	0.837849i	$0.683813\pi$
$488$	9.35674	0.423560
$489$	27.5777	1.24711
$490$	14.8028	0.668723
$491$	2.55977	0.115521	0.0577605	−	0.998330i	$-0.481604\pi$
$491$	2.55977	0.115521	0.0577605	+	0.998330i	$0.481604\pi$
$492$	22.3903	1.00943
$493$	−1.71311	−0.0771546
$494$	−0.654790	−0.0294604
$495$	−90.6342	−4.07370
$496$	5.69698	0.255802
$497$	1.67111	0.0749597
$498$	26.3886	1.18250
$499$	−40.5673	−1.81604	−0.908021	−	0.418924i	$-0.862407\pi$
$499$	−40.5673	−1.81604	−0.908021	+	0.418924i	$0.862407\pi$
$500$	−11.6739	−0.522073
$501$	−44.2832	−1.97843
$502$	−18.1904	−0.811876
$503$	14.0379	0.625918	0.312959	−	0.949767i	$-0.398680\pi$
$503$	14.0379	0.625918	0.312959	+	0.949767i	$0.398680\pi$
$504$	0.969208	0.0431719
$505$	26.2944	1.17009
$506$	18.6136	0.827477
$507$	−22.0912	−0.981104
$508$	−8.39616	−0.372519
$509$	−33.1918	−1.47120	−0.735601	−	0.677415i	$-0.763100\pi$
$509$	−33.1918	−1.47120	−0.735601	+	0.677415i	$0.763100\pi$
$510$	−4.46587	−0.197752
$511$	−0.222186	−0.00982895
$512$	−1.00000	−0.0441942
$513$	−2.30035	−0.101563
$514$	30.0950	1.32743
$515$	−10.7358	−0.473074
$516$	27.7839	1.22312
$517$	14.5788	0.641176
$518$	−0.919671	−0.0404080
$519$	18.8423	0.827084
$520$	−9.41535	−0.412890
$521$	−37.6748	−1.65056	−0.825282	−	0.564720i	$-0.808984\pi$
$521$	−37.6748	−1.65056	−0.825282	+	0.564720i	$0.808984\pi$
$522$	−20.6883	−0.905503
$523$	−18.1465	−0.793492	−0.396746	−	0.917928i	$-0.629861\pi$
$523$	−18.1465	−0.793492	−0.396746	+	0.917928i	$0.629861\pi$
$524$	12.4631	0.544455
$525$	−0.208190	−0.00908615
$526$	11.0541	0.481981
$527$	−3.65987	−0.159426
$528$	18.0794	0.786807
$529$	−11.5967	−0.504203
$530$	−21.8991	−0.951236
$531$	36.9608	1.60396
$532$	−0.0184136	−0.000798329 0
$533$	−30.3256	−1.31355
$534$	49.0454	2.12240
$535$	36.8048	1.59121
$536$	−12.4058	−0.535849
$537$	27.3677	1.18100
$538$	26.2364	1.13113
$539$	38.4985	1.65825
$540$	−33.0771	−1.42341
$541$	20.4836	0.880658	0.440329	−	0.897837i	$-0.354862\pi$
$541$	20.4836	0.880658	0.440329	+	0.897837i	$0.354862\pi$
$542$	−3.85353	−0.165523
$543$	−5.17111	−0.221914
$544$	0.642423	0.0275436
$545$	3.11751	0.133540
$546$	−1.82031	−0.0779023
$547$	26.1981	1.12015	0.560076	−	0.828441i	$-0.310772\pi$
$547$	26.1981	1.12015	0.560076	+	0.828441i	$0.310772\pi$
$548$	1.04990	0.0448494
$549$	−72.5914	−3.09813
$550$	−2.80059	−0.119417
$551$	0.393049	0.0167444
$552$	11.0761	0.471429
$553$	2.05129	0.0872296
$554$	19.7055	0.837208
$555$	51.1755	2.17228
$556$	−22.8656	−0.969717
$557$	−24.7814	−1.05002	−0.525010	−	0.851096i	$-0.675938\pi$
$557$	−24.7814	−1.05002	−0.525010	+	0.851096i	$0.675938\pi$
$558$	−44.1983	−1.87106
$559$	−37.6309	−1.59162
$560$	−0.264772	−0.0111887
$561$	−11.6146	−0.490371
$562$	7.69389	0.324547
$563$	38.9662	1.64223	0.821114	−	0.570764i	$-0.193353\pi$
$563$	38.9662	1.64223	0.821114	+	0.570764i	$0.193353\pi$
$564$	8.67515	0.365290
$565$	4.47552	0.188287
$566$	−25.9840	−1.09219
$567$	−3.48734	−0.146454
$568$	13.3767	0.561275
$569$	−20.1024	−0.842734	−0.421367	−	0.906890i	$-0.638450\pi$
$569$	−20.1024	−0.842734	−0.421367	+	0.906890i	$0.638450\pi$
$570$	1.02463	0.0429171
$571$	4.57235	0.191347	0.0956735	−	0.995413i	$-0.469500\pi$
$571$	4.57235	0.191347	0.0956735	+	0.995413i	$0.469500\pi$
$572$	−24.4870	−1.02385
$573$	2.02149	0.0844490
$574$	−0.852797	−0.0355951
$575$	−1.71573	−0.0715510
$576$	7.75819	0.323258
$577$	23.1901	0.965414	0.482707	−	0.875782i	$-0.339654\pi$
$577$	23.1901	0.965414	0.482707	+	0.875782i	$0.339654\pi$
$578$	16.5873	0.689940
$579$	47.6560	1.98052
$580$	5.65172	0.234675
$581$	−1.00508	−0.0416979
$582$	−17.6339	−0.730947
$583$	−56.9542	−2.35880
$584$	−1.77853	−0.0735961
$585$	73.0461	3.02009
$586$	−12.6443	−0.522331
$587$	−40.0454	−1.65285	−0.826425	−	0.563047i	$-0.809629\pi$
$587$	−40.0454	−1.65285	−0.826425	+	0.563047i	$0.809629\pi$
$588$	22.9086	0.944734
$589$	0.839705	0.0345994
$590$	−10.0971	−0.415691
$591$	−76.8361	−3.16061
$592$	−7.36167	−0.302563
$593$	−37.3216	−1.53262	−0.766308	−	0.642474i	$-0.777908\pi$
$593$	−37.3216	−1.53262	−0.766308	+	0.642474i	$0.777908\pi$
$594$	−86.0255	−3.52967
$595$	0.170096	0.00697324
$596$	−10.5722	−0.433055
$597$	56.7587	2.32298
$598$	−15.0016	−0.613459
$599$	−1.15388	−0.0471461	−0.0235731	−	0.999722i	$-0.507504\pi$
$599$	−1.15388	−0.0471461	−0.0235731	+	0.999722i	$0.507504\pi$
$600$	−1.66649	−0.0680342
$601$	−29.5283	−1.20448	−0.602242	−	0.798314i	$-0.705726\pi$
$601$	−29.5283	−1.20448	−0.602242	+	0.798314i	$0.705726\pi$
$602$	−1.05823	−0.0431303
$603$	96.2466	3.91946
$604$	17.0348	0.693137
$605$	41.0806	1.67017
$606$	40.6928	1.65303
$607$	−21.8382	−0.886384	−0.443192	−	0.896427i	$-0.646154\pi$
$607$	−21.8382	−0.886384	−0.443192	+	0.896427i	$0.646154\pi$
$608$	−0.147395	−0.00597764
$609$	1.09267	0.0442774
$610$	19.8308	0.802926
$611$	−11.7497	−0.475343
$612$	−4.98404	−0.201468
$613$	−13.2960	−0.537022	−0.268511	−	0.963277i	$-0.586532\pi$
$613$	−13.2960	−0.537022	−0.268511	+	0.963277i	$0.586532\pi$
$614$	−12.2461	−0.494212
$615$	47.4543	1.91354
$616$	−0.688607	−0.0277448
$617$	−11.9157	−0.479708	−0.239854	−	0.970809i	$-0.577099\pi$
$617$	−11.9157	−0.479708	−0.239854	+	0.970809i	$0.577099\pi$
$618$	−16.6145	−0.668332
$619$	−13.3658	−0.537219	−0.268609	−	0.963249i	$-0.586564\pi$
$619$	−13.3658	−0.537219	−0.268609	+	0.963249i	$0.586564\pi$
$620$	12.0743	0.484914
$621$	−52.7021	−2.11486
$622$	21.3382	0.855586
$623$	−1.86804	−0.0748413
$624$	−14.5710	−0.583308
$625$	−22.2014	−0.888058
$626$	−11.3563	−0.453888
$627$	2.66481	0.106422
$628$	13.6817	0.545957
$629$	4.72930	0.188570
$630$	2.05415	0.0818394
$631$	−7.57087	−0.301392	−0.150696	−	0.988580i	$-0.548151\pi$
$631$	−7.57087	−0.301392	−0.150696	+	0.988580i	$0.548151\pi$
$632$	16.4199	0.653148
$633$	41.3094	1.64190
$634$	−13.9434	−0.553761
$635$	−17.7949	−0.706171
$636$	−33.8907	−1.34385
$637$	−31.0277	−1.22936
$638$	14.6987	0.581928
$639$	−103.779	−4.10544
$640$	−2.11941	−0.0837772
$641$	−14.3448	−0.566585	−0.283292	−	0.959034i	$-0.591427\pi$
$641$	−14.3448	−0.566585	−0.283292	+	0.959034i	$0.591427\pi$
$642$	56.9585	2.24797
$643$	−5.16013	−0.203496	−0.101748	−	0.994810i	$-0.532443\pi$
$643$	−5.16013	−0.203496	−0.101748	+	0.994810i	$0.532443\pi$
$644$	−0.421864	−0.0166238
$645$	58.8857	2.31862
$646$	0.0946897	0.00372551
$647$	28.1932	1.10839	0.554195	−	0.832387i	$-0.313026\pi$
$647$	28.1932	1.10839	0.554195	+	0.832387i	$0.313026\pi$
$648$	−27.9150	−1.09660
$649$	−26.2601	−1.03080
$650$	2.25712	0.0885314
$651$	2.33438	0.0914914
$652$	−8.40791	−0.329279
$653$	25.0747	0.981249	0.490624	−	0.871371i	$-0.336769\pi$
$653$	25.0747	0.981249	0.490624	+	0.871371i	$0.336769\pi$
$654$	4.82461	0.188657
$655$	26.4146	1.03210
$656$	−6.82637	−0.266525
$657$	13.7982	0.538318
$658$	−0.330418	−0.0128810
$659$	44.3489	1.72759	0.863794	−	0.503846i	$-0.168082\pi$
$659$	44.3489	1.72759	0.863794	+	0.503846i	$0.168082\pi$
$660$	38.3178	1.49152
$661$	−33.9943	−1.32223	−0.661113	−	0.750286i	$-0.729916\pi$
$661$	−33.9943	−1.32223	−0.661113	+	0.750286i	$0.729916\pi$
$662$	32.8780	1.27784
$663$	9.36076	0.363542
$664$	−8.04537	−0.312221
$665$	−0.0390260	−0.00151336
$666$	57.1133	2.21310
$667$	9.00493	0.348672
$668$	13.5011	0.522373
$669$	1.83920	0.0711076
$670$	−26.2930	−1.01579
$671$	51.5751	1.99103
$672$	−0.409757	−0.0158067
$673$	14.2134	0.547885	0.273942	−	0.961746i	$-0.411672\pi$
$673$	14.2134	0.547885	0.273942	+	0.961746i	$0.411672\pi$
$674$	−16.6292	−0.640531
$675$	7.92949	0.305206
$676$	6.73518	0.259045
$677$	−0.699321	−0.0268771	−0.0134385	−	0.999910i	$-0.504278\pi$
$677$	−0.699321	−0.0268771	−0.0134385	+	0.999910i	$0.504278\pi$
$678$	6.92624	0.266001
$679$	0.671636	0.0257750
$680$	1.36156	0.0522134
$681$	77.8587	2.98355
$682$	31.4022	1.20245
$683$	−0.167537	−0.00641063	−0.00320531	−	0.999995i	$-0.501020\pi$
$683$	−0.167537	−0.00641063	−0.00320531	+	0.999995i	$0.501020\pi$
$684$	1.14352	0.0437234
$685$	2.22517	0.0850194
$686$	−1.74703	−0.0667018
$687$	−42.3917	−1.61735
$688$	−8.47080	−0.322946
$689$	45.9019	1.74872
$690$	23.4748	0.893670
$691$	32.3265	1.22976	0.614879	−	0.788621i	$-0.289205\pi$
$691$	32.3265	1.22976	0.614879	+	0.788621i	$0.289205\pi$
$692$	−5.74465	−0.218379
$693$	5.34235	0.202939
$694$	6.86139	0.260455
$695$	−48.4616	−1.83825
$696$	8.74650	0.331535
$697$	4.38541	0.166109
$698$	15.2994	0.579091
$699$	46.2776	1.75038
$700$	0.0634731	0.00239906
$701$	−5.98230	−0.225948	−0.112974	−	0.993598i	$-0.536038\pi$
$701$	−5.98230	−0.225948	−0.112974	+	0.993598i	$0.536038\pi$
$702$	69.3318	2.61676
$703$	−1.08507	−0.0409242
$704$	−5.51208	−0.207744
$705$	18.3862	0.692466
$706$	−12.2185	−0.459848
$707$	−1.54990	−0.0582900
$708$	−15.6261	−0.587265
$709$	−27.5092	−1.03313	−0.516565	−	0.856248i	$-0.672790\pi$
$709$	−27.5092	−1.03313	−0.516565	+	0.856248i	$0.672790\pi$
$710$	28.3508	1.06399
$711$	−127.389	−4.77745
$712$	−14.9530	−0.560388
$713$	19.2380	0.720470
$714$	0.263237	0.00985139
$715$	−51.8982	−1.94088
$716$	−8.34388	−0.311825
$717$	68.7065	2.56589
$718$	0.106054	0.00395790
$719$	45.7938	1.70782	0.853910	−	0.520420i	$-0.174225\pi$
$719$	45.7938	1.70782	0.853910	+	0.520420i	$0.174225\pi$
$720$	16.4428	0.612788
$721$	0.632809	0.0235670
$722$	18.9783	0.706298
$723$	15.8912	0.591000
$724$	1.57657	0.0585929
$725$	−1.35487	−0.0503186
$726$	63.5757	2.35951
$727$	34.4892	1.27913	0.639566	−	0.768736i	$-0.279114\pi$
$727$	34.4892	1.27913	0.639566	+	0.768736i	$0.279114\pi$
$728$	0.554979	0.0205689
$729$	63.0013	2.33338
$730$	−3.76944	−0.139513
$731$	5.44183	0.201273
$732$	30.6898	1.13433
$733$	−13.5846	−0.501758	−0.250879	−	0.968018i	$-0.580720\pi$
$733$	−13.5846	−0.501758	−0.250879	+	0.968018i	$0.580720\pi$
$734$	26.5399	0.979606
$735$	48.5528	1.79090
$736$	−3.37688	−0.124474
$737$	−68.3817	−2.51887
$738$	52.9603	1.94949
$739$	4.74965	0.174719	0.0873593	−	0.996177i	$-0.472157\pi$
$739$	4.74965	0.174719	0.0873593	+	0.996177i	$0.472157\pi$
$740$	−15.6024	−0.573557
$741$	−2.14769	−0.0788974
$742$	1.29082	0.0473876
$743$	−29.3941	−1.07836	−0.539182	−	0.842189i	$-0.681266\pi$
$743$	−29.3941	−1.07836	−0.539182	+	0.842189i	$0.681266\pi$
$744$	18.6859	0.685059
$745$	−22.4069	−0.820927
$746$	−4.68815	−0.171646
$747$	62.4176	2.28374
$748$	3.54108	0.129475
$749$	−2.16943	−0.0792691
$750$	−38.2901	−1.39816
$751$	51.3359	1.87327	0.936637	−	0.350302i	$-0.113921\pi$
$751$	51.3359	1.87327	0.936637	+	0.350302i	$0.113921\pi$
$752$	−2.64489	−0.0964491
$753$	−59.6639	−2.17427
$754$	−11.8464	−0.431419
$755$	36.1038	1.31395
$756$	1.94970	0.0709100
$757$	−36.4109	−1.32338	−0.661688	−	0.749779i	$-0.730160\pi$
$757$	−36.4109	−1.32338	−0.661688	+	0.749779i	$0.730160\pi$
$758$	30.3530	1.10247
$759$	61.0522	2.21605
$760$	−0.312390	−0.0113316
$761$	3.46376	0.125561	0.0627806	−	0.998027i	$-0.480003\pi$
$761$	3.46376	0.125561	0.0627806	+	0.998027i	$0.480003\pi$
$762$	−27.5391	−0.997637
$763$	−0.183759	−0.00665252
$764$	−0.616314	−0.0222975
$765$	−10.5632	−0.381915
$766$	14.4631	0.522575
$767$	21.1642	0.764194
$768$	−3.27997	−0.118356
$769$	−30.8481	−1.11241	−0.556206	−	0.831045i	$-0.687743\pi$
$769$	−30.8481	−1.11241	−0.556206	+	0.831045i	$0.687743\pi$
$770$	−1.45944	−0.0525947
$771$	98.7105	3.55497
$772$	−14.5294	−0.522925
$773$	−12.4336	−0.447205	−0.223602	−	0.974680i	$-0.571782\pi$
$773$	−12.4336	−0.447205	−0.223602	+	0.974680i	$0.571782\pi$
$774$	65.7181	2.36219
$775$	−2.89453	−0.103975
$776$	5.37623	0.192995
$777$	−3.01649	−0.108216
$778$	−21.0751	−0.755580
$779$	−1.00617	−0.0360498
$780$	−30.8821	−1.10575
$781$	73.7335	2.63839
$782$	2.16939	0.0775771
$783$	−41.6175	−1.48729
$784$	−6.98439	−0.249443
$785$	28.9971	1.03495
$786$	40.8787	1.45810
$787$	5.00597	0.178443	0.0892217	−	0.996012i	$-0.471562\pi$
$787$	5.00597	0.178443	0.0892217	+	0.996012i	$0.471562\pi$
$788$	23.4259	0.834512
$789$	36.2571	1.29079
$790$	34.8006	1.23815
$791$	−0.263806	−0.00937985
$792$	42.7638	1.51954
$793$	−41.5667	−1.47608
$794$	15.1136	0.536363
$795$	−71.8283	−2.54749
$796$	−17.3046	−0.613347
$797$	−14.4217	−0.510842	−0.255421	−	0.966830i	$-0.582214\pi$
$797$	−14.4217	−0.510842	−0.255421	+	0.966830i	$0.582214\pi$
$798$	−0.0603959	−0.00213799
$799$	1.69914	0.0601111
$800$	0.508082	0.0179634
$801$	116.008	4.09896
$802$	36.3919	1.28504
$803$	−9.80340	−0.345954
$804$	−40.6906	−1.43505
$805$	−0.894104	−0.0315130
$806$	−25.3084	−0.891452
$807$	86.0546	3.02926
$808$	−12.4065	−0.436458
$809$	1.60988	0.0566002	0.0283001	−	0.999599i	$-0.490991\pi$
$809$	1.60988	0.0566002	0.0283001	+	0.999599i	$0.490991\pi$
$810$	−59.1635	−2.07879
$811$	−25.9240	−0.910316	−0.455158	−	0.890411i	$-0.650417\pi$
$811$	−25.9240	−0.910316	−0.455158	+	0.890411i	$0.650417\pi$
$812$	−0.333135	−0.0116908
$813$	−12.6395	−0.443285
$814$	−40.5781	−1.42226
$815$	−17.8198	−0.624202
$816$	2.10713	0.0737642
$817$	−1.24855	−0.0436812
$818$	3.54414	0.123918
$819$	−4.30564	−0.150451
$820$	−14.4679	−0.505241
$821$	25.1841	0.878930	0.439465	−	0.898260i	$-0.355168\pi$
$821$	25.1841	0.878930	0.439465	+	0.898260i	$0.355168\pi$
$822$	3.44363	0.120110
$823$	31.9046	1.11212	0.556062	−	0.831141i	$-0.312312\pi$
$823$	31.9046	1.11212	0.556062	+	0.831141i	$0.312312\pi$
$824$	5.06543	0.176463
$825$	−9.18583	−0.319810
$826$	0.595165	0.0207084
$827$	34.4033	1.19632	0.598159	−	0.801377i	$-0.295899\pi$
$827$	34.4033	1.19632	0.598159	+	0.801377i	$0.295899\pi$
$828$	26.1985	0.910461
$829$	0.702094	0.0243847	0.0121924	−	0.999926i	$-0.496119\pi$
$829$	0.702094	0.0243847	0.0121924	+	0.999926i	$0.496119\pi$
$830$	−17.0515	−0.591865
$831$	64.6335	2.24211
$832$	4.44243	0.154014
$833$	4.48693	0.155463
$834$	−74.9984	−2.59698
$835$	28.6144	0.990243
$836$	−0.812451	−0.0280992
$837$	−88.9112	−3.07322
$838$	−27.0996	−0.936140
$839$	−13.9298	−0.480911	−0.240455	−	0.970660i	$-0.577297\pi$
$839$	−13.9298	−0.480911	−0.240455	+	0.970660i	$0.577297\pi$
$840$	−0.868444	−0.0299642
$841$	−21.8890	−0.754794
$842$	−0.275602	−0.00949788
$843$	25.2357	0.869165
$844$	−12.5945	−0.433519
$845$	14.2746	0.491063
$846$	20.5196	0.705477
$847$	−2.42146	−0.0832024
$848$	10.3326	0.354823
$849$	−85.2266	−2.92497
$850$	−0.326403	−0.0111955
$851$	−24.8595	−0.852173
$852$	43.8752	1.50314
$853$	−2.71254	−0.0928756	−0.0464378	−	0.998921i	$-0.514787\pi$
$853$	−2.71254	−0.0928756	−0.0464378	+	0.998921i	$0.514787\pi$
$854$	−1.16891	−0.0399993
$855$	2.42359	0.0828849
$856$	−17.3656	−0.593542
$857$	16.7729	0.572953	0.286476	−	0.958087i	$-0.407516\pi$
$857$	16.7729	0.572953	0.286476	+	0.958087i	$0.407516\pi$
$858$	−80.3167	−2.74197
$859$	12.6024	0.429988	0.214994	−	0.976615i	$-0.431027\pi$
$859$	12.6024	0.429988	0.214994	+	0.976615i	$0.431027\pi$
$860$	−17.9531	−0.612197
$861$	−2.79715	−0.0953265
$862$	−3.70754	−0.126279
$863$	29.7952	1.01424	0.507120	−	0.861875i	$-0.330710\pi$
$863$	29.7952	1.01424	0.507120	+	0.861875i	$0.330710\pi$
$864$	15.6067	0.530952
$865$	−12.1753	−0.413972
$866$	−7.69534	−0.261498
$867$	54.4058	1.84772
$868$	−0.711706	−0.0241569
$869$	90.5078	3.07027
$870$	18.5375	0.628478
$871$	55.1119	1.86740
$872$	−1.47093	−0.0498120
$873$	−41.7098	−1.41166
$874$	−0.497734	−0.0168361
$875$	1.45839	0.0493024
$876$	−5.83352	−0.197097
$877$	−41.9087	−1.41516	−0.707578	−	0.706636i	$-0.750212\pi$
$877$	−41.9087	−1.41516	−0.707578	+	0.706636i	$0.750212\pi$
$878$	−25.4517	−0.858952
$879$	−41.4729	−1.39885
$880$	−11.6824	−0.393813
$881$	−35.3786	−1.19193	−0.595967	−	0.803009i	$-0.703231\pi$
$881$	−35.3786	−1.19193	−0.595967	+	0.803009i	$0.703231\pi$
$882$	54.1863	1.82455
$883$	−6.86613	−0.231064	−0.115532	−	0.993304i	$-0.536857\pi$
$883$	−6.86613	−0.231064	−0.115532	+	0.993304i	$0.536857\pi$
$884$	−2.85392	−0.0959876
$885$	−33.1182	−1.11326
$886$	−15.6290	−0.525066
$887$	3.94660	0.132514	0.0662569	−	0.997803i	$-0.478894\pi$
$887$	3.94660	0.132514	0.0662569	+	0.997803i	$0.478894\pi$
$888$	−24.1461	−0.810289
$889$	1.04891	0.0351792
$890$	−31.6916	−1.06231
$891$	−153.870	−5.15483
$892$	−0.560737	−0.0187749
$893$	−0.389842	−0.0130456
$894$	−34.6766	−1.15976
$895$	−17.6841	−0.591115
$896$	0.124927	0.00417352
$897$	−49.2047	−1.64290
$898$	28.3718	0.946778
$899$	15.1918	0.506675
$900$	−3.94180	−0.131393
$901$	−6.63790	−0.221141
$902$	−37.6275	−1.25286
$903$	−3.47096	−0.115506
$904$	−2.11168	−0.0702334
$905$	3.34141	0.111072
$906$	55.8737	1.85628
$907$	31.0937	1.03245	0.516225	−	0.856453i	$-0.327337\pi$
$907$	31.0937	1.03245	0.516225	+	0.856453i	$0.327337\pi$
$908$	−23.7376	−0.787761
$909$	96.2517	3.19247
$910$	1.17623	0.0389917
$911$	−6.62680	−0.219556	−0.109778	−	0.993956i	$-0.535014\pi$
$911$	−6.62680	−0.219556	−0.109778	+	0.993956i	$0.535014\pi$
$912$	−0.483450	−0.0160086
$913$	−44.3467	−1.46766
$914$	−4.07478	−0.134782
$915$	65.0445	2.15030
$916$	12.9244	0.427035
$917$	−1.55698	−0.0514161
$918$	−10.0261	−0.330911
$919$	27.6324	0.911508	0.455754	−	0.890106i	$-0.349370\pi$
$919$	27.6324	0.911508	0.455754	+	0.890106i	$0.349370\pi$
$920$	−7.15701	−0.235960
$921$	−40.1668	−1.32354
$922$	−23.3364	−0.768542
$923$	−59.4251	−1.95600
$924$	−2.25861	−0.0743028
$925$	3.74033	0.122981
$926$	−14.9702	−0.491952
$927$	−39.2986	−1.29074
$928$	−2.66664	−0.0875368
$929$	52.0749	1.70852	0.854261	−	0.519845i	$-0.174010\pi$
$929$	52.0749	1.70852	0.854261	+	0.519845i	$0.174010\pi$
$930$	39.6032	1.29864
$931$	−1.02946	−0.0337393
$932$	−14.1092	−0.462161
$933$	69.9888	2.29133
$934$	34.9382	1.14321
$935$	7.50502	0.245441
$936$	−34.4652	−1.12653
$937$	−26.2058	−0.856105	−0.428052	−	0.903754i	$-0.640800\pi$
$937$	−26.2058	−0.856105	−0.428052	+	0.903754i	$0.640800\pi$
$938$	1.54982	0.0506034
$939$	−37.2482	−1.21555
$940$	−5.60561	−0.182835
$941$	3.87379	0.126282	0.0631410	−	0.998005i	$-0.479888\pi$
$941$	3.87379	0.126282	0.0631410	+	0.998005i	$0.479888\pi$
$942$	44.8754	1.46212
$943$	−23.0518	−0.750671
$944$	4.76410	0.155058
$945$	4.13223	0.134421
$946$	−46.6917	−1.51808
$947$	19.1716	0.622992	0.311496	−	0.950247i	$-0.399170\pi$
$947$	19.1716	0.622992	0.311496	+	0.950247i	$0.399170\pi$
$948$	53.8567	1.74919
$949$	7.90100	0.256477
$950$	0.0748885	0.00242970
$951$	−45.7338	−1.48302
$952$	−0.0802559	−0.00260111
$953$	−28.8862	−0.935716	−0.467858	−	0.883804i	$-0.654974\pi$
$953$	−28.8862	−0.935716	−0.467858	+	0.883804i	$0.654974\pi$
$954$	−80.1624	−2.59535
$955$	−1.30622	−0.0422684
$956$	−20.9473	−0.677484
$957$	48.2114	1.55845
$958$	−6.08023	−0.196443
$959$	−0.131161	−0.00423540
$960$	−6.95161	−0.224362
$961$	1.45559	0.0469545
$962$	32.7037	1.05441
$963$	134.725	4.34146
$964$	−4.84493	−0.156045
$965$	−30.7939	−0.991290
$966$	−1.38370	−0.0445198
$967$	22.7331	0.731048	0.365524	−	0.930802i	$-0.380890\pi$
$967$	22.7331	0.731048	0.365524	+	0.930802i	$0.380890\pi$
$968$	−19.3830	−0.622994
$969$	0.310579	0.00997724
$970$	11.3945	0.365854
$971$	−5.55701	−0.178333	−0.0891664	−	0.996017i	$-0.528420\pi$
$971$	−5.55701	−0.178333	−0.0891664	+	0.996017i	$0.528420\pi$
$972$	−44.7401	−1.43504
$973$	2.85653	0.0915761
$974$	24.0940	0.772023
$975$	7.40327	0.237094
$976$	−9.35674	−0.299502
$977$	17.2703	0.552527	0.276264	−	0.961082i	$-0.410904\pi$
$977$	17.2703	0.552527	0.276264	+	0.961082i	$0.410904\pi$
$978$	−27.5777	−0.881837
$979$	−82.4222	−2.63423
$980$	−14.8028	−0.472859
$981$	11.4118	0.364350
$982$	−2.55977	−0.0816857
$983$	−13.7470	−0.438461	−0.219230	−	0.975673i	$-0.570355\pi$
$983$	−13.7470	−0.438461	−0.219230	+	0.975673i	$0.570355\pi$
$984$	−22.3903	−0.713776
$985$	49.6491	1.58195
$986$	1.71311	0.0545565
$987$	−1.08376	−0.0344965
$988$	0.654790	0.0208317
$989$	−28.6049	−0.909582
$990$	90.6342	2.88054
$991$	11.6672	0.370620	0.185310	−	0.982680i	$-0.440671\pi$
$991$	11.6672	0.370620	0.185310	+	0.982680i	$0.440671\pi$
$992$	−5.69698	−0.180879
$993$	107.839	3.42216
$994$	−1.67111	−0.0530045
$995$	−36.6757	−1.16270
$996$	−26.3886	−0.836154
$997$	51.2640	1.62355	0.811774	−	0.583972i	$-0.198502\pi$
$997$	51.2640	1.62355	0.811774	+	0.583972i	$0.198502\pi$
$998$	40.5673	1.28414
$999$	114.892	3.63501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.1	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.1	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.27997 q^{3} +1.00000 q^{4} +2.11941 q^{5} +3.27997 q^{6} -0.124927 q^{7} -1.00000 q^{8} +7.75819 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.27997 q^{3} +1.00000 q^{4} +2.11941 q^{5} +3.27997 q^{6} -0.124927 q^{7} -1.00000 q^{8} +7.75819 q^{9} -2.11941 q^{10} -5.51208 q^{11} -3.27997 q^{12} +4.44243 q^{13} +0.124927 q^{14} -6.95161 q^{15} +1.00000 q^{16} -0.642423 q^{17} -7.75819 q^{18} +0.147395 q^{19} +2.11941 q^{20} +0.409757 q^{21} +5.51208 q^{22} +3.37688 q^{23} +3.27997 q^{24} -0.508082 q^{25} -4.44243 q^{26} -15.6067 q^{27} -0.124927 q^{28} +2.66664 q^{29} +6.95161 q^{30} +5.69698 q^{31} -1.00000 q^{32} +18.0794 q^{33} +0.642423 q^{34} -0.264772 q^{35} +7.75819 q^{36} -7.36167 q^{37} -0.147395 q^{38} -14.5710 q^{39} -2.11941 q^{40} -6.82637 q^{41} -0.409757 q^{42} -8.47080 q^{43} -5.51208 q^{44} +16.4428 q^{45} -3.37688 q^{46} -2.64489 q^{47} -3.27997 q^{48} -6.98439 q^{49} +0.508082 q^{50} +2.10713 q^{51} +4.44243 q^{52} +10.3326 q^{53} +15.6067 q^{54} -11.6824 q^{55} +0.124927 q^{56} -0.483450 q^{57} -2.66664 q^{58} +4.76410 q^{59} -6.95161 q^{60} -9.35674 q^{61} -5.69698 q^{62} -0.969208 q^{63} +1.00000 q^{64} +9.41535 q^{65} -18.0794 q^{66} +12.4058 q^{67} -0.642423 q^{68} -11.0761 q^{69} +0.264772 q^{70} -13.3767 q^{71} -7.75819 q^{72} +1.77853 q^{73} +7.36167 q^{74} +1.66649 q^{75} +0.147395 q^{76} +0.688607 q^{77} +14.5710 q^{78} -16.4199 q^{79} +2.11941 q^{80} +27.9150 q^{81} +6.82637 q^{82} +8.04537 q^{83} +0.409757 q^{84} -1.36156 q^{85} +8.47080 q^{86} -8.74650 q^{87} +5.51208 q^{88} +14.9530 q^{89} -16.4428 q^{90} -0.554979 q^{91} +3.37688 q^{92} -18.6859 q^{93} +2.64489 q^{94} +0.312390 q^{95} +3.27997 q^{96} -5.37623 q^{97} +6.98439 q^{98} -42.7638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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