LMFDB - Embedded newform 4017.2.a.k.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21491 q^{2} +1.00000 q^{3} +2.90581 q^{4} +3.81514 q^{5} -2.21491 q^{6} +4.67656 q^{7} -2.00629 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.21491 q^{2} +1.00000 q^{3} +2.90581 q^{4} +3.81514 q^{5} -2.21491 q^{6} +4.67656 q^{7} -2.00629 q^{8} +1.00000 q^{9} -8.45019 q^{10} +1.01146 q^{11} +2.90581 q^{12} +1.00000 q^{13} -10.3582 q^{14} +3.81514 q^{15} -1.36787 q^{16} +1.06731 q^{17} -2.21491 q^{18} +4.69990 q^{19} +11.0861 q^{20} +4.67656 q^{21} -2.24030 q^{22} -0.133501 q^{23} -2.00629 q^{24} +9.55532 q^{25} -2.21491 q^{26} +1.00000 q^{27} +13.5892 q^{28} -4.34373 q^{29} -8.45019 q^{30} -9.18856 q^{31} +7.04230 q^{32} +1.01146 q^{33} -2.36399 q^{34} +17.8418 q^{35} +2.90581 q^{36} -9.96627 q^{37} -10.4098 q^{38} +1.00000 q^{39} -7.65430 q^{40} -7.56657 q^{41} -10.3582 q^{42} +8.27342 q^{43} +2.93913 q^{44} +3.81514 q^{45} +0.295692 q^{46} -4.98464 q^{47} -1.36787 q^{48} +14.8703 q^{49} -21.1641 q^{50} +1.06731 q^{51} +2.90581 q^{52} -5.95354 q^{53} -2.21491 q^{54} +3.85888 q^{55} -9.38257 q^{56} +4.69990 q^{57} +9.62096 q^{58} +3.35004 q^{59} +11.0861 q^{60} +7.55884 q^{61} +20.3518 q^{62} +4.67656 q^{63} -12.8623 q^{64} +3.81514 q^{65} -2.24030 q^{66} -3.22008 q^{67} +3.10140 q^{68} -0.133501 q^{69} -39.5179 q^{70} +7.00567 q^{71} -2.00629 q^{72} +11.5377 q^{73} +22.0744 q^{74} +9.55532 q^{75} +13.6570 q^{76} +4.73018 q^{77} -2.21491 q^{78} +6.15889 q^{79} -5.21863 q^{80} +1.00000 q^{81} +16.7592 q^{82} -12.0154 q^{83} +13.5892 q^{84} +4.07193 q^{85} -18.3249 q^{86} -4.34373 q^{87} -2.02930 q^{88} +13.0067 q^{89} -8.45019 q^{90} +4.67656 q^{91} -0.387928 q^{92} -9.18856 q^{93} +11.0405 q^{94} +17.9308 q^{95} +7.04230 q^{96} +6.38621 q^{97} -32.9362 q^{98} +1.01146 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	−2.21491	−1.56618	−0.783088	−	0.621911i	$-0.786357\pi$
$2$	−2.21491	−1.56618	−0.783088	+	0.621911i	$0.786357\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.90581	1.45291
$5$	3.81514	1.70618	0.853092	−	0.521761i	$-0.174725\pi$
$5$	3.81514	1.70618	0.853092	+	0.521761i	$0.174725\pi$
$6$	−2.21491	−0.904232
$7$	4.67656	1.76758	0.883788	−	0.467888i	$-0.154985\pi$
$7$	4.67656	1.76758	0.883788	+	0.467888i	$0.154985\pi$
$8$	−2.00629	−0.709332
$9$	1.00000	0.333333
$10$	−8.45019	−2.67218
$11$	1.01146	0.304968	0.152484	−	0.988306i	$-0.451273\pi$
$11$	1.01146	0.304968	0.152484	+	0.988306i	$0.451273\pi$
$12$	2.90581	0.838836
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−10.3582	−2.76833
$15$	3.81514	0.985066
$16$	−1.36787	−0.341968
$17$	1.06731	0.258860	0.129430	−	0.991589i	$-0.458685\pi$
$17$	1.06731	0.258860	0.129430	+	0.991589i	$0.458685\pi$
$18$	−2.21491	−0.522059
$19$	4.69990	1.07823	0.539116	−	0.842232i	$-0.318758\pi$
$19$	4.69990	1.07823	0.539116	+	0.842232i	$0.318758\pi$
$20$	11.0861	2.47893
$21$	4.67656	1.02051
$22$	−2.24030	−0.477634
$23$	−0.133501	−0.0278368	−0.0139184	−	0.999903i	$-0.504431\pi$
$23$	−0.133501	−0.0278368	−0.0139184	+	0.999903i	$0.504431\pi$
$24$	−2.00629	−0.409533
$25$	9.55532	1.91106
$26$	−2.21491	−0.434379
$27$	1.00000	0.192450
$28$	13.5892	2.56812
$29$	−4.34373	−0.806610	−0.403305	−	0.915066i	$-0.632139\pi$
$29$	−4.34373	−0.806610	−0.403305	+	0.915066i	$0.632139\pi$
$30$	−8.45019	−1.54279
$31$	−9.18856	−1.65031	−0.825157	−	0.564904i	$-0.808913\pi$
$31$	−9.18856	−1.65031	−0.825157	+	0.564904i	$0.808913\pi$
$32$	7.04230	1.24491
$33$	1.01146	0.176073
$34$	−2.36399	−0.405421
$35$	17.8418	3.01581
$36$	2.90581	0.484302
$37$	−9.96627	−1.63845	−0.819223	−	0.573475i	$-0.805595\pi$
$37$	−9.96627	−1.63845	−0.819223	+	0.573475i	$0.805595\pi$
$38$	−10.4098	−1.68870
$39$	1.00000	0.160128
$40$	−7.65430	−1.21025
$41$	−7.56657	−1.18170	−0.590850	−	0.806782i	$-0.701207\pi$
$41$	−7.56657	−1.18170	−0.590850	+	0.806782i	$0.701207\pi$
$42$	−10.3582	−1.59830
$43$	8.27342	1.26168	0.630842	−	0.775911i	$-0.282709\pi$
$43$	8.27342	1.26168	0.630842	+	0.775911i	$0.282709\pi$
$44$	2.93913	0.443090
$45$	3.81514	0.568728
$46$	0.295692	0.0435973
$47$	−4.98464	−0.727085	−0.363542	−	0.931578i	$-0.618433\pi$
$47$	−4.98464	−0.727085	−0.363542	+	0.931578i	$0.618433\pi$
$48$	−1.36787	−0.197435
$49$	14.8703	2.12432
$50$	−21.1641	−2.99306
$51$	1.06731	0.149453
$52$	2.90581	0.402964
$53$	−5.95354	−0.817781	−0.408891	−	0.912583i	$-0.634084\pi$
$53$	−5.95354	−0.817781	−0.408891	+	0.912583i	$0.634084\pi$
$54$	−2.21491	−0.301411
$55$	3.85888	0.520331
$56$	−9.38257	−1.25380
$57$	4.69990	0.622517
$58$	9.62096	1.26329
$59$	3.35004	0.436139	0.218069	−	0.975933i	$-0.430024\pi$
$59$	3.35004	0.436139	0.218069	+	0.975933i	$0.430024\pi$
$60$	11.0861	1.43121
$61$	7.55884	0.967810	0.483905	−	0.875121i	$-0.339218\pi$
$61$	7.55884	0.967810	0.483905	+	0.875121i	$0.339218\pi$
$62$	20.3518	2.58468
$63$	4.67656	0.589192
$64$	−12.8623	−1.60779
$65$	3.81514	0.473210
$66$	−2.24030	−0.275762
$67$	−3.22008	−0.393396	−0.196698	−	0.980464i	$-0.563022\pi$
$67$	−3.22008	−0.393396	−0.196698	+	0.980464i	$0.563022\pi$
$68$	3.10140	0.376100
$69$	−0.133501	−0.0160716
$70$	−39.5179	−4.72329
$71$	7.00567	0.831420	0.415710	−	0.909497i	$-0.363533\pi$
$71$	7.00567	0.831420	0.415710	+	0.909497i	$0.363533\pi$
$72$	−2.00629	−0.236444
$73$	11.5377	1.35039	0.675193	−	0.737641i	$-0.264060\pi$
$73$	11.5377	1.35039	0.675193	+	0.737641i	$0.264060\pi$
$74$	22.0744	2.56609
$75$	9.55532	1.10335
$76$	13.6570	1.56657
$77$	4.73018	0.539054
$78$	−2.21491	−0.250789
$79$	6.15889	0.692929	0.346464	−	0.938063i	$-0.387382\pi$
$79$	6.15889	0.692929	0.346464	+	0.938063i	$0.387382\pi$
$80$	−5.21863	−0.583460
$81$	1.00000	0.111111
$82$	16.7592	1.85075
$83$	−12.0154	−1.31886	−0.659430	−	0.751766i	$-0.729202\pi$
$83$	−12.0154	−1.31886	−0.659430	+	0.751766i	$0.729202\pi$
$84$	13.5892	1.48271
$85$	4.07193	0.441663
$86$	−18.3249	−1.97602
$87$	−4.34373	−0.465697
$88$	−2.02930	−0.216324
$89$	13.0067	1.37871	0.689356	−	0.724422i	$-0.257893\pi$
$89$	13.0067	1.37871	0.689356	+	0.724422i	$0.257893\pi$
$90$	−8.45019	−0.890728
$91$	4.67656	0.490237
$92$	−0.387928	−0.0404443
$93$	−9.18856	−0.952809
$94$	11.0405	1.13874
$95$	17.9308	1.83966
$96$	7.04230	0.718752
$97$	6.38621	0.648421	0.324211	−	0.945985i	$-0.394901\pi$
$97$	6.38621	0.648421	0.324211	+	0.945985i	$0.394901\pi$
$98$	−32.9362	−3.32706
$99$	1.01146	0.101656
$100$	27.7660	2.77660
$101$	3.38994	0.337311	0.168656	−	0.985675i	$-0.446057\pi$
$101$	3.38994	0.337311	0.168656	+	0.985675i	$0.446057\pi$
$102$	−2.36399	−0.234070
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.00629	−0.196733
$105$	17.8418	1.74118
$106$	13.1865	1.28079
$107$	−11.0650	−1.06969	−0.534847	−	0.844949i	$-0.679631\pi$
$107$	−11.0650	−1.06969	−0.534847	+	0.844949i	$0.679631\pi$
$108$	2.90581	0.279612
$109$	18.2350	1.74660	0.873299	−	0.487185i	$-0.161976\pi$
$109$	18.2350	1.74660	0.873299	+	0.487185i	$0.161976\pi$
$110$	−8.54707	−0.814931
$111$	−9.96627	−0.945957
$112$	−6.39694	−0.604454
$113$	3.15367	0.296672	0.148336	−	0.988937i	$-0.452608\pi$
$113$	3.15367	0.296672	0.148336	+	0.988937i	$0.452608\pi$
$114$	−10.4098	−0.974972
$115$	−0.509324	−0.0474947
$116$	−12.6221	−1.17193
$117$	1.00000	0.0924500
$118$	−7.42004	−0.683070
$119$	4.99134	0.457555
$120$	−7.65430	−0.698739
$121$	−9.97694	−0.906995
$122$	−16.7421	−1.51576
$123$	−7.56657	−0.682254
$124$	−26.7002	−2.39775
$125$	17.3792	1.55444
$126$	−10.3582	−0.922778
$127$	2.75290	0.244280	0.122140	−	0.992513i	$-0.461024\pi$
$127$	2.75290	0.244280	0.122140	+	0.992513i	$0.461024\pi$
$128$	14.4042	1.27316
$129$	8.27342	0.728434
$130$	−8.45019	−0.741131
$131$	8.52327	0.744681	0.372341	−	0.928096i	$-0.378555\pi$
$131$	8.52327	0.744681	0.372341	+	0.928096i	$0.378555\pi$
$132$	2.93913	0.255818
$133$	21.9794	1.90586
$134$	7.13219	0.616127
$135$	3.81514	0.328355
$136$	−2.14134	−0.183618
$137$	−17.2656	−1.47510	−0.737551	−	0.675292i	$-0.764018\pi$
$137$	−17.2656	−1.47510	−0.737551	+	0.675292i	$0.764018\pi$
$138$	0.295692	0.0251709
$139$	−19.9290	−1.69036	−0.845179	−	0.534483i	$-0.820506\pi$
$139$	−19.9290	−1.69036	−0.845179	+	0.534483i	$0.820506\pi$
$140$	51.8449	4.38169
$141$	−4.98464	−0.419783
$142$	−15.5169	−1.30215
$143$	1.01146	0.0845829
$144$	−1.36787	−0.113989
$145$	−16.5719	−1.37623
$146$	−25.5549	−2.11494
$147$	14.8703	1.22648
$148$	−28.9601	−2.38051
$149$	−19.9534	−1.63465	−0.817323	−	0.576180i	$-0.804543\pi$
$149$	−19.9534	−1.63465	−0.817323	+	0.576180i	$0.804543\pi$
$150$	−21.1641	−1.72804
$151$	−18.2069	−1.48166	−0.740828	−	0.671695i	$-0.765567\pi$
$151$	−18.2069	−1.48166	−0.740828	+	0.671695i	$0.765567\pi$
$152$	−9.42939	−0.764825
$153$	1.06731	0.0862868
$154$	−10.4769	−0.844253
$155$	−35.0557	−2.81574
$156$	2.90581	0.232651
$157$	4.47640	0.357256	0.178628	−	0.983917i	$-0.442834\pi$
$157$	4.47640	0.357256	0.178628	+	0.983917i	$0.442834\pi$
$158$	−13.6414	−1.08525
$159$	−5.95354	−0.472146
$160$	26.8674	2.12405
$161$	−0.624324	−0.0492037
$162$	−2.21491	−0.174020
$163$	−10.5618	−0.827265	−0.413632	−	0.910444i	$-0.635740\pi$
$163$	−10.5618	−0.827265	−0.413632	+	0.910444i	$0.635740\pi$
$164$	−21.9870	−1.71690
$165$	3.85888	0.300414
$166$	26.6129	2.06557
$167$	−6.56255	−0.507826	−0.253913	−	0.967227i	$-0.581718\pi$
$167$	−6.56255	−0.507826	−0.253913	+	0.967227i	$0.581718\pi$
$168$	−9.38257	−0.723881
$169$	1.00000	0.0769231
$170$	−9.01896	−0.691723
$171$	4.69990	0.359411
$172$	24.0410	1.83311
$173$	−3.67950	−0.279747	−0.139874	−	0.990169i	$-0.544670\pi$
$173$	−3.67950	−0.279747	−0.139874	+	0.990169i	$0.544670\pi$
$174$	9.62096	0.729363
$175$	44.6861	3.37795
$176$	−1.38355	−0.104289
$177$	3.35004	0.251805
$178$	−28.8087	−2.15931
$179$	−10.8825	−0.813398	−0.406699	−	0.913562i	$-0.633320\pi$
$179$	−10.8825	−0.813398	−0.406699	+	0.913562i	$0.633320\pi$
$180$	11.0861	0.826309
$181$	13.7817	1.02438	0.512192	−	0.858871i	$-0.328834\pi$
$181$	13.7817	1.02438	0.512192	+	0.858871i	$0.328834\pi$
$182$	−10.3582	−0.767798
$183$	7.55884	0.558765
$184$	0.267842	0.0197456
$185$	−38.0228	−2.79549
$186$	20.3518	1.49227
$187$	1.07954	0.0789441
$188$	−14.4844	−1.05639
$189$	4.67656	0.340170
$190$	−39.7151	−2.88123
$191$	15.8344	1.14574	0.572870	−	0.819646i	$-0.305830\pi$
$191$	15.8344	1.14574	0.572870	+	0.819646i	$0.305830\pi$
$192$	−12.8623	−0.928256
$193$	25.2229	1.81559	0.907794	−	0.419417i	$-0.137765\pi$
$193$	25.2229	1.81559	0.907794	+	0.419417i	$0.137765\pi$
$194$	−14.1449	−1.01554
$195$	3.81514	0.273208
$196$	43.2102	3.08644
$197$	−3.04893	−0.217227	−0.108614	−	0.994084i	$-0.534641\pi$
$197$	−3.04893	−0.217227	−0.108614	+	0.994084i	$0.534641\pi$
$198$	−2.24030	−0.159211
$199$	−20.6185	−1.46161	−0.730803	−	0.682588i	$-0.760854\pi$
$199$	−20.6185	−1.46161	−0.730803	+	0.682588i	$0.760854\pi$
$200$	−19.1708	−1.35558
$201$	−3.22008	−0.227127
$202$	−7.50839	−0.528289
$203$	−20.3137	−1.42574
$204$	3.10140	0.217141
$205$	−28.8675	−2.01620
$206$	−2.21491	−0.154320
$207$	−0.133501	−0.00927894
$208$	−1.36787	−0.0948448
$209$	4.75379	0.328826
$210$	−39.5179	−2.72699
$211$	−3.35855	−0.231212	−0.115606	−	0.993295i	$-0.536881\pi$
$211$	−3.35855	−0.231212	−0.115606	+	0.993295i	$0.536881\pi$
$212$	−17.2999	−1.18816
$213$	7.00567	0.480020
$214$	24.5080	1.67533
$215$	31.5643	2.15267
$216$	−2.00629	−0.136511
$217$	−42.9709	−2.91705
$218$	−40.3889	−2.73548
$219$	11.5377	0.779646
$220$	11.2132	0.755993
$221$	1.06731	0.0717949
$222$	22.0744	1.48154
$223$	21.9650	1.47088	0.735442	−	0.677588i	$-0.236974\pi$
$223$	21.9650	1.47088	0.735442	+	0.677588i	$0.236974\pi$
$224$	32.9338	2.20048
$225$	9.55532	0.637021
$226$	−6.98508	−0.464641
$227$	−4.30748	−0.285897	−0.142949	−	0.989730i	$-0.545658\pi$
$227$	−4.30748	−0.285897	−0.142949	+	0.989730i	$0.545658\pi$
$228$	13.6570	0.904460
$229$	15.3707	1.01572	0.507862	−	0.861439i	$-0.330436\pi$
$229$	15.3707	1.01572	0.507862	+	0.861439i	$0.330436\pi$
$230$	1.12811	0.0743851
$231$	4.73018	0.311223
$232$	8.71480	0.572155
$233$	6.97957	0.457247	0.228623	−	0.973515i	$-0.426578\pi$
$233$	6.97957	0.457247	0.228623	+	0.973515i	$0.426578\pi$
$234$	−2.21491	−0.144793
$235$	−19.0171	−1.24054
$236$	9.73461	0.633669
$237$	6.15889	0.400063
$238$	−11.0554	−0.716612
$239$	28.1310	1.81965	0.909823	−	0.414997i	$-0.136217\pi$
$239$	28.1310	1.81965	0.909823	+	0.414997i	$0.136217\pi$
$240$	−5.21863	−0.336861
$241$	6.08071	0.391693	0.195846	−	0.980635i	$-0.437255\pi$
$241$	6.08071	0.391693	0.195846	+	0.980635i	$0.437255\pi$
$242$	22.0980	1.42051
$243$	1.00000	0.0641500
$244$	21.9646	1.40614
$245$	56.7322	3.62448
$246$	16.7592	1.06853
$247$	4.69990	0.299048
$248$	18.4350	1.17062
$249$	−12.0154	−0.761444
$250$	−38.4933	−2.43453
$251$	−7.19234	−0.453977	−0.226988	−	0.973897i	$-0.572888\pi$
$251$	−7.19234	−0.453977	−0.226988	+	0.973897i	$0.572888\pi$
$252$	13.5892	0.856041
$253$	−0.135031	−0.00848934
$254$	−6.09741	−0.382586
$255$	4.07193	0.254994
$256$	−6.17937	−0.386210
$257$	−12.8672	−0.802635	−0.401318	−	0.915939i	$-0.631448\pi$
$257$	−12.8672	−0.802635	−0.401318	+	0.915939i	$0.631448\pi$
$258$	−18.3249	−1.14086
$259$	−46.6079	−2.89608
$260$	11.0861	0.687531
$261$	−4.34373	−0.268870
$262$	−18.8782	−1.16630
$263$	−21.0240	−1.29640	−0.648198	−	0.761472i	$-0.724477\pi$
$263$	−21.0240	−1.29640	−0.648198	+	0.761472i	$0.724477\pi$
$264$	−2.02930	−0.124895
$265$	−22.7136	−1.39528
$266$	−48.6823	−2.98491
$267$	13.0067	0.796000
$268$	−9.35697	−0.571568
$269$	−21.4723	−1.30919	−0.654595	−	0.755980i	$-0.727161\pi$
$269$	−21.4723	−1.30919	−0.654595	+	0.755980i	$0.727161\pi$
$270$	−8.45019	−0.514262
$271$	−3.95231	−0.240086	−0.120043	−	0.992769i	$-0.538303\pi$
$271$	−3.95231	−0.240086	−0.120043	+	0.992769i	$0.538303\pi$
$272$	−1.45994	−0.0885219
$273$	4.67656	0.283039
$274$	38.2417	2.31027
$275$	9.66486	0.582813
$276$	−0.387928	−0.0233505
$277$	−17.3952	−1.04518	−0.522589	−	0.852585i	$-0.675034\pi$
$277$	−17.3952	−1.04518	−0.522589	+	0.852585i	$0.675034\pi$
$278$	44.1410	2.64740
$279$	−9.18856	−0.550104
$280$	−35.7958	−2.13921
$281$	−17.1929	−1.02564	−0.512822	−	0.858495i	$-0.671400\pi$
$281$	−17.1929	−1.02564	−0.512822	+	0.858495i	$0.671400\pi$
$282$	11.0405	0.657453
$283$	13.6531	0.811595	0.405797	−	0.913963i	$-0.366994\pi$
$283$	13.6531	0.811595	0.405797	+	0.913963i	$0.366994\pi$
$284$	20.3572	1.20798
$285$	17.9308	1.06213
$286$	−2.24030	−0.132472
$287$	−35.3855	−2.08874
$288$	7.04230	0.414971
$289$	−15.8609	−0.932991
$290$	36.7053	2.15541
$291$	6.38621	0.374366
$292$	33.5264	1.96199
$293$	−33.5872	−1.96218	−0.981092	−	0.193543i	$-0.938002\pi$
$293$	−33.5872	−1.96218	−0.981092	+	0.193543i	$0.938002\pi$
$294$	−32.9362	−1.92088
$295$	12.7809	0.744133
$296$	19.9953	1.16220
$297$	1.01146	0.0586911
$298$	44.1949	2.56014
$299$	−0.133501	−0.00772054
$300$	27.7660	1.60307
$301$	38.6912	2.23012
$302$	40.3266	2.32053
$303$	3.38994	0.194747
$304$	−6.42886	−0.368721
$305$	28.8380	1.65126
$306$	−2.36399	−0.135140
$307$	−10.4550	−0.596698	−0.298349	−	0.954457i	$-0.596436\pi$
$307$	−10.4550	−0.596698	−0.298349	+	0.954457i	$0.596436\pi$
$308$	13.7450	0.783195
$309$	1.00000	0.0568880
$310$	77.6450	4.40994
$311$	7.15347	0.405636	0.202818	−	0.979216i	$-0.434990\pi$
$311$	7.15347	0.405636	0.202818	+	0.979216i	$0.434990\pi$
$312$	−2.00629	−0.113584
$313$	13.5027	0.763220	0.381610	−	0.924323i	$-0.375370\pi$
$313$	13.5027	0.763220	0.381610	+	0.924323i	$0.375370\pi$
$314$	−9.91481	−0.559525
$315$	17.8418	1.00527
$316$	17.8966	1.00676
$317$	−17.9165	−1.00629	−0.503145	−	0.864202i	$-0.667824\pi$
$317$	−17.9165	−1.00629	−0.503145	+	0.864202i	$0.667824\pi$
$318$	13.1865	0.739464
$319$	−4.39353	−0.245990
$320$	−49.0715	−2.74318
$321$	−11.0650	−0.617589
$322$	1.38282	0.0770616
$323$	5.01625	0.279111
$324$	2.90581	0.161434
$325$	9.55532	0.530034
$326$	23.3934	1.29564
$327$	18.2350	1.00840
$328$	15.1808	0.838217
$329$	−23.3110	−1.28518
$330$	−8.54707	−0.470500
$331$	18.3721	1.00982	0.504910	−	0.863172i	$-0.331526\pi$
$331$	18.3721	1.00982	0.504910	+	0.863172i	$0.331526\pi$
$332$	−34.9145	−1.91618
$333$	−9.96627	−0.546148
$334$	14.5354	0.795344
$335$	−12.2851	−0.671206
$336$	−6.39694	−0.348982
$337$	−30.3885	−1.65537	−0.827685	−	0.561193i	$-0.810342\pi$
$337$	−30.3885	−1.65537	−0.827685	+	0.561193i	$0.810342\pi$
$338$	−2.21491	−0.120475
$339$	3.15367	0.171284
$340$	11.8323	0.641696
$341$	−9.29390	−0.503293
$342$	−10.4098	−0.562900
$343$	36.8058	1.98732
$344$	−16.5989	−0.894954
$345$	−0.509324	−0.0274211
$346$	8.14975	0.438133
$347$	36.3417	1.95093	0.975463	−	0.220163i	$-0.0706588\pi$
$347$	36.3417	1.95093	0.975463	+	0.220163i	$0.0706588\pi$
$348$	−12.6221	−0.676614
$349$	8.30048	0.444314	0.222157	−	0.975011i	$-0.428690\pi$
$349$	8.30048	0.444314	0.222157	+	0.975011i	$0.428690\pi$
$350$	−98.9755	−5.29046
$351$	1.00000	0.0533761
$352$	7.12303	0.379659
$353$	−30.5674	−1.62694	−0.813470	−	0.581607i	$-0.802424\pi$
$353$	−30.5674	−1.62694	−0.813470	+	0.581607i	$0.802424\pi$
$354$	−7.42004	−0.394371
$355$	26.7276	1.41856
$356$	37.7952	2.00314
$357$	4.99134	0.264170
$358$	24.1038	1.27392
$359$	−22.0921	−1.16598	−0.582988	−	0.812481i	$-0.698117\pi$
$359$	−22.0921	−1.16598	−0.582988	+	0.812481i	$0.698117\pi$
$360$	−7.65430	−0.403417
$361$	3.08909	0.162584
$362$	−30.5252	−1.60437
$363$	−9.97694	−0.523654
$364$	13.5892	0.712269
$365$	44.0180	2.30401
$366$	−16.7421	−0.875125
$367$	32.1363	1.67750	0.838750	−	0.544517i	$-0.183287\pi$
$367$	32.1363	1.67750	0.838750	+	0.544517i	$0.183287\pi$
$368$	0.182612	0.00951930
$369$	−7.56657	−0.393900
$370$	84.2169	4.37823
$371$	−27.8421	−1.44549
$372$	−26.7002	−1.38434
$373$	20.3842	1.05545	0.527727	−	0.849414i	$-0.323044\pi$
$373$	20.3842	1.05545	0.527727	+	0.849414i	$0.323044\pi$
$374$	−2.39109	−0.123640
$375$	17.3792	0.897457
$376$	10.0007	0.515745
$377$	−4.34373	−0.223713
$378$	−10.3582	−0.532766
$379$	−14.8723	−0.763936	−0.381968	−	0.924175i	$-0.624754\pi$
$379$	−14.8723	−0.763936	−0.381968	+	0.924175i	$0.624754\pi$
$380$	52.1036	2.67286
$381$	2.75290	0.141035
$382$	−35.0718	−1.79443
$383$	12.5371	0.640617	0.320308	−	0.947313i	$-0.396213\pi$
$383$	12.5371	0.640617	0.320308	+	0.947313i	$0.396213\pi$
$384$	14.4042	0.735061
$385$	18.0463	0.919725
$386$	−55.8665	−2.84353
$387$	8.27342	0.420562
$388$	18.5571	0.942096
$389$	−22.5241	−1.14202	−0.571008	−	0.820944i	$-0.693448\pi$
$389$	−22.5241	−1.14202	−0.571008	+	0.820944i	$0.693448\pi$
$390$	−8.45019	−0.427892
$391$	−0.142486	−0.00720585
$392$	−29.8341	−1.50685
$393$	8.52327	0.429942
$394$	6.75310	0.340216
$395$	23.4970	1.18226
$396$	2.93913	0.147697
$397$	11.0075	0.552450	0.276225	−	0.961093i	$-0.410916\pi$
$397$	11.0075	0.552450	0.276225	+	0.961093i	$0.410916\pi$
$398$	45.6680	2.28913
$399$	21.9794	1.10035
$400$	−13.0704	−0.653522
$401$	−27.9974	−1.39813	−0.699063	−	0.715060i	$-0.746399\pi$
$401$	−27.9974	−1.39813	−0.699063	+	0.715060i	$0.746399\pi$
$402$	7.13219	0.355721
$403$	−9.18856	−0.457715
$404$	9.85052	0.490082
$405$	3.81514	0.189576
$406$	44.9930	2.23297
$407$	−10.0805	−0.499673
$408$	−2.14134	−0.106012
$409$	0.0528989	0.00261568	0.00130784	−	0.999999i	$-0.499584\pi$
$409$	0.0528989	0.00261568	0.00130784	+	0.999999i	$0.499584\pi$
$410$	63.9389	3.15772
$411$	−17.2656	−0.851650
$412$	2.90581	0.143159
$413$	15.6667	0.770908
$414$	0.295692	0.0145324
$415$	−45.8404	−2.25022
$416$	7.04230	0.345277
$417$	−19.9290	−0.975929
$418$	−10.5292	−0.515000
$419$	17.4381	0.851908	0.425954	−	0.904745i	$-0.359938\pi$
$419$	17.4381	0.851908	0.425954	+	0.904745i	$0.359938\pi$
$420$	51.8449	2.52977
$421$	6.11957	0.298250	0.149125	−	0.988818i	$-0.452354\pi$
$421$	6.11957	0.298250	0.149125	+	0.988818i	$0.452354\pi$
$422$	7.43888	0.362119
$423$	−4.98464	−0.242362
$424$	11.9445	0.580079
$425$	10.1985	0.494699
$426$	−15.5169	−0.751797
$427$	35.3494	1.71068
$428$	−32.1529	−1.55417
$429$	1.01146	0.0488340
$430$	−69.9120	−3.37145
$431$	4.54899	0.219117	0.109558	−	0.993980i	$-0.465056\pi$
$431$	4.54899	0.219117	0.109558	+	0.993980i	$0.465056\pi$
$432$	−1.36787	−0.0658118
$433$	−25.4079	−1.22103	−0.610514	−	0.792006i	$-0.709037\pi$
$433$	−25.4079	−1.22103	−0.610514	+	0.792006i	$0.709037\pi$
$434$	95.1765	4.56862
$435$	−16.5719	−0.794564
$436$	52.9876	2.53764
$437$	−0.627440	−0.0300145
$438$	−25.5549	−1.22106
$439$	6.32547	0.301898	0.150949	−	0.988542i	$-0.451767\pi$
$439$	6.32547	0.301898	0.150949	+	0.988542i	$0.451767\pi$
$440$	−7.74205	−0.369088
$441$	14.8703	0.708108
$442$	−2.36399	−0.112444
$443$	1.19468	0.0567609	0.0283804	−	0.999597i	$-0.490965\pi$
$443$	1.19468	0.0567609	0.0283804	+	0.999597i	$0.490965\pi$
$444$	−28.9601	−1.37439
$445$	49.6226	2.35234
$446$	−48.6504	−2.30366
$447$	−19.9534	−0.943763
$448$	−60.1514	−2.84188
$449$	21.1957	1.00029	0.500144	−	0.865942i	$-0.333280\pi$
$449$	21.1957	1.00029	0.500144	+	0.865942i	$0.333280\pi$
$450$	−21.1641	−0.997687
$451$	−7.65331	−0.360380
$452$	9.16397	0.431037
$453$	−18.2069	−0.855434
$454$	9.54066	0.447765
$455$	17.8418	0.836435
$456$	−9.42939	−0.441572
$457$	6.90517	0.323010	0.161505	−	0.986872i	$-0.448365\pi$
$457$	6.90517	0.323010	0.161505	+	0.986872i	$0.448365\pi$
$458$	−34.0446	−1.59080
$459$	1.06731	0.0498177
$460$	−1.48000	−0.0690054
$461$	32.3430	1.50637	0.753183	−	0.657811i	$-0.228518\pi$
$461$	32.3430	1.50637	0.753183	+	0.657811i	$0.228518\pi$
$462$	−10.4769	−0.487430
$463$	9.16618	0.425988	0.212994	−	0.977053i	$-0.431678\pi$
$463$	9.16618	0.425988	0.212994	+	0.977053i	$0.431678\pi$
$464$	5.94166	0.275835
$465$	−35.0557	−1.62567
$466$	−15.4591	−0.716129
$467$	−2.77334	−0.128335	−0.0641675	−	0.997939i	$-0.520439\pi$
$467$	−2.77334	−0.128335	−0.0641675	+	0.997939i	$0.520439\pi$
$468$	2.90581	0.134321
$469$	−15.0589	−0.695357
$470$	42.1212	1.94290
$471$	4.47640	0.206262
$472$	−6.72118	−0.309367
$473$	8.36827	0.384774
$474$	−13.6414	−0.626568
$475$	44.9091	2.06057
$476$	14.5039	0.664785
$477$	−5.95354	−0.272594
$478$	−62.3077	−2.84989
$479$	−11.5607	−0.528224	−0.264112	−	0.964492i	$-0.585079\pi$
$479$	−11.5607	−0.528224	−0.264112	+	0.964492i	$0.585079\pi$
$480$	26.8674	1.22632
$481$	−9.96627	−0.454423
$482$	−13.4682	−0.613460
$483$	−0.624324	−0.0284077
$484$	−28.9911	−1.31778
$485$	24.3643	1.10633
$486$	−2.21491	−0.100470
$487$	37.9308	1.71881	0.859404	−	0.511296i	$-0.170835\pi$
$487$	37.9308	1.71881	0.859404	+	0.511296i	$0.170835\pi$
$488$	−15.1653	−0.686499
$489$	−10.5618	−0.477621
$490$	−125.656	−5.67658
$491$	9.30864	0.420093	0.210047	−	0.977691i	$-0.432638\pi$
$491$	9.30864	0.420093	0.210047	+	0.977691i	$0.432638\pi$
$492$	−21.9870	−0.991252
$493$	−4.63610	−0.208799
$494$	−10.4098	−0.468361
$495$	3.85888	0.173444
$496$	12.5688	0.564354
$497$	32.7625	1.46960
$498$	26.6129	1.19255
$499$	−24.9124	−1.11523	−0.557617	−	0.830098i	$-0.688284\pi$
$499$	−24.9124	−1.11523	−0.557617	+	0.830098i	$0.688284\pi$
$500$	50.5007	2.25846
$501$	−6.56255	−0.293193
$502$	15.9304	0.711007
$503$	−15.2546	−0.680170	−0.340085	−	0.940395i	$-0.610456\pi$
$503$	−15.2546	−0.680170	−0.340085	+	0.940395i	$0.610456\pi$
$504$	−9.38257	−0.417933
$505$	12.9331	0.575515
$506$	0.299082	0.0132958
$507$	1.00000	0.0444116
$508$	7.99941	0.354916
$509$	20.5236	0.909693	0.454847	−	0.890570i	$-0.349694\pi$
$509$	20.5236	0.909693	0.454847	+	0.890570i	$0.349694\pi$
$510$	−9.01896	−0.399366
$511$	53.9568	2.38691
$512$	−15.1217	−0.668290
$513$	4.69990	0.207506
$514$	28.4997	1.25707
$515$	3.81514	0.168115
$516$	24.0410	1.05835
$517$	−5.04179	−0.221738
$518$	103.232	4.53576
$519$	−3.67950	−0.161512
$520$	−7.65430	−0.335663
$521$	−31.5384	−1.38172	−0.690861	−	0.722988i	$-0.742768\pi$
$521$	−31.5384	−1.38172	−0.690861	+	0.722988i	$0.742768\pi$
$522$	9.62096	0.421098
$523$	−31.8328	−1.39195	−0.695977	−	0.718064i	$-0.745028\pi$
$523$	−31.8328	−1.39195	−0.695977	+	0.718064i	$0.745028\pi$
$524$	24.7670	1.08195
$525$	44.6861	1.95026
$526$	46.5662	2.03038
$527$	−9.80703	−0.427201
$528$	−1.38355	−0.0602114
$529$	−22.9822	−0.999225
$530$	50.3085	2.18526
$531$	3.35004	0.145380
$532$	63.8681	2.76903
$533$	−7.56657	−0.327744
$534$	−28.8087	−1.24668
$535$	−42.2146	−1.82510
$536$	6.46044	0.279048
$537$	−10.8825	−0.469616
$538$	47.5592	2.05042
$539$	15.0407	0.647850
$540$	11.0861	0.477070
$541$	0.463456	0.0199255	0.00996276	−	0.999950i	$-0.496829\pi$
$541$	0.463456	0.0199255	0.00996276	+	0.999950i	$0.496829\pi$
$542$	8.75400	0.376016
$543$	13.7817	0.591429
$544$	7.51631	0.322259
$545$	69.5692	2.98002
$546$	−10.3582	−0.443288
$547$	0.734700	0.0314135	0.0157067	−	0.999877i	$-0.495000\pi$
$547$	0.734700	0.0314135	0.0157067	+	0.999877i	$0.495000\pi$
$548$	−50.1707	−2.14319
$549$	7.55884	0.322603
$550$	−21.4068	−0.912788
$551$	−20.4151	−0.869713
$552$	0.267842	0.0114001
$553$	28.8024	1.22480
$554$	38.5288	1.63693
$555$	−38.0228	−1.61398
$556$	−57.9101	−2.45593
$557$	4.97512	0.210803	0.105401	−	0.994430i	$-0.466387\pi$
$557$	4.97512	0.210803	0.105401	+	0.994430i	$0.466387\pi$
$558$	20.3518	0.861560
$559$	8.27342	0.349928
$560$	−24.4052	−1.03131
$561$	1.07954	0.0455784
$562$	38.0807	1.60634
$563$	−5.46044	−0.230130	−0.115065	−	0.993358i	$-0.536708\pi$
$563$	−5.46044	−0.230130	−0.115065	+	0.993358i	$0.536708\pi$
$564$	−14.4844	−0.609905
$565$	12.0317	0.506177
$566$	−30.2404	−1.27110
$567$	4.67656	0.196397
$568$	−14.0554	−0.589753
$569$	35.0262	1.46838	0.734188	−	0.678946i	$-0.237563\pi$
$569$	35.0262	1.46838	0.734188	+	0.678946i	$0.237563\pi$
$570$	−39.7151	−1.66348
$571$	−27.2567	−1.14066	−0.570329	−	0.821417i	$-0.693184\pi$
$571$	−27.2567	−1.14066	−0.570329	+	0.821417i	$0.693184\pi$
$572$	2.93913	0.122891
$573$	15.8344	0.661493
$574$	78.3757	3.27134
$575$	−1.27564	−0.0531979
$576$	−12.8623	−0.535929
$577$	−20.4814	−0.852651	−0.426326	−	0.904570i	$-0.640192\pi$
$577$	−20.4814	−0.852651	−0.426326	+	0.904570i	$0.640192\pi$
$578$	35.1303	1.46123
$579$	25.2229	1.04823
$580$	−48.1550	−1.99953
$581$	−56.1907	−2.33118
$582$	−14.1449	−0.586323
$583$	−6.02179	−0.249397
$584$	−23.1480	−0.957873
$585$	3.81514	0.157737
$586$	74.3925	3.07312
$587$	30.6609	1.26551	0.632756	−	0.774351i	$-0.281924\pi$
$587$	30.6609	1.26551	0.632756	+	0.774351i	$0.281924\pi$
$588$	43.2102	1.78196
$589$	−43.1853	−1.77942
$590$	−28.3085	−1.16544
$591$	−3.04893	−0.125416
$592$	13.6326	0.560296
$593$	21.7160	0.891770	0.445885	−	0.895090i	$-0.352889\pi$
$593$	21.7160	0.891770	0.445885	+	0.895090i	$0.352889\pi$
$594$	−2.24030	−0.0919206
$595$	19.0427	0.780673
$596$	−57.9809	−2.37499
$597$	−20.6185	−0.843859
$598$	0.295692	0.0120917
$599$	4.38303	0.179086	0.0895428	−	0.995983i	$-0.471459\pi$
$599$	4.38303	0.179086	0.0895428	+	0.995983i	$0.471459\pi$
$600$	−19.1708	−0.782644
$601$	17.9118	0.730638	0.365319	−	0.930882i	$-0.380960\pi$
$601$	17.9118	0.730638	0.365319	+	0.930882i	$0.380960\pi$
$602$	−85.6974	−3.49276
$603$	−3.22008	−0.131132
$604$	−52.9059	−2.15271
$605$	−38.0635	−1.54750
$606$	−7.50839	−0.305008
$607$	−42.1209	−1.70963	−0.854816	−	0.518931i	$-0.826330\pi$
$607$	−42.1209	−1.70963	−0.854816	+	0.518931i	$0.826330\pi$
$608$	33.0981	1.34231
$609$	−20.3137	−0.823154
$610$	−63.8736	−2.58617
$611$	−4.98464	−0.201657
$612$	3.10140	0.125367
$613$	11.0562	0.446557	0.223278	−	0.974755i	$-0.428324\pi$
$613$	11.0562	0.446557	0.223278	+	0.974755i	$0.428324\pi$
$614$	23.1569	0.934535
$615$	−28.8675	−1.16405
$616$	−9.49013	−0.382368
$617$	29.2185	1.17629	0.588146	−	0.808755i	$-0.299858\pi$
$617$	29.2185	1.17629	0.588146	+	0.808755i	$0.299858\pi$
$618$	−2.21491	−0.0890966
$619$	31.4316	1.26334	0.631672	−	0.775236i	$-0.282369\pi$
$619$	31.4316	1.26334	0.631672	+	0.775236i	$0.282369\pi$
$620$	−101.865	−4.09101
$621$	−0.133501	−0.00535720
$622$	−15.8443	−0.635297
$623$	60.8269	2.43698
$624$	−1.36787	−0.0547587
$625$	18.5275	0.741100
$626$	−29.9073	−1.19534
$627$	4.75379	0.189848
$628$	13.0076	0.519059
$629$	−10.6371	−0.424129
$630$	−39.5179	−1.57443
$631$	−26.1364	−1.04048	−0.520238	−	0.854022i	$-0.674157\pi$
$631$	−26.1364	−1.04048	−0.520238	+	0.854022i	$0.674157\pi$
$632$	−12.3565	−0.491517
$633$	−3.35855	−0.133490
$634$	39.6834	1.57603
$635$	10.5027	0.416787
$636$	−17.2999	−0.685984
$637$	14.8703	0.589181
$638$	9.73126	0.385264
$639$	7.00567	0.277140
$640$	54.9541	2.17225
$641$	−0.976749	−0.0385793	−0.0192896	−	0.999814i	$-0.506140\pi$
$641$	−0.976749	−0.0385793	−0.0192896	+	0.999814i	$0.506140\pi$
$642$	24.5080	0.967252
$643$	22.7319	0.896458	0.448229	−	0.893919i	$-0.352055\pi$
$643$	22.7319	0.896458	0.448229	+	0.893919i	$0.352055\pi$
$644$	−1.81417	−0.0714884
$645$	31.5643	1.24284
$646$	−11.1105	−0.437138
$647$	17.1593	0.674602	0.337301	−	0.941397i	$-0.390486\pi$
$647$	17.1593	0.674602	0.337301	+	0.941397i	$0.390486\pi$
$648$	−2.00629	−0.0788147
$649$	3.38845	0.133008
$650$	−21.1641	−0.830126
$651$	−42.9709	−1.68416
$652$	−30.6907	−1.20194
$653$	27.0986	1.06045	0.530224	−	0.847857i	$-0.322108\pi$
$653$	27.0986	1.06045	0.530224	+	0.847857i	$0.322108\pi$
$654$	−40.3889	−1.57933
$655$	32.5175	1.27056
$656$	10.3501	0.404103
$657$	11.5377	0.450129
$658$	51.6317	2.01281
$659$	17.6160	0.686222	0.343111	−	0.939295i	$-0.388519\pi$
$659$	17.6160	0.686222	0.343111	+	0.939295i	$0.388519\pi$
$660$	11.2132	0.436473
$661$	−19.1574	−0.745136	−0.372568	−	0.928005i	$-0.621523\pi$
$661$	−19.1574	−0.745136	−0.372568	+	0.928005i	$0.621523\pi$
$662$	−40.6924	−1.58156
$663$	1.06731	0.0414508
$664$	24.1064	0.935509
$665$	83.8546	3.25174
$666$	22.0744	0.855365
$667$	0.579891	0.0224535
$668$	−19.0696	−0.737824
$669$	21.9650	0.849215
$670$	27.2103	1.05123
$671$	7.64549	0.295151
$672$	32.9338	1.27045
$673$	−24.8667	−0.958540	−0.479270	−	0.877668i	$-0.659099\pi$
$673$	−24.8667	−0.958540	−0.479270	+	0.877668i	$0.659099\pi$
$674$	67.3078	2.59260
$675$	9.55532	0.367784
$676$	2.90581	0.111762
$677$	−0.810466	−0.0311487	−0.0155744	−	0.999879i	$-0.504958\pi$
$677$	−0.810466	−0.0311487	−0.0155744	+	0.999879i	$0.504958\pi$
$678$	−6.98508	−0.268260
$679$	29.8655	1.14613
$680$	−8.16950	−0.313286
$681$	−4.30748	−0.165063
$682$	20.5851	0.788245
$683$	−9.85014	−0.376905	−0.188453	−	0.982082i	$-0.560347\pi$
$683$	−9.85014	−0.376905	−0.188453	+	0.982082i	$0.560347\pi$
$684$	13.6570	0.522190
$685$	−65.8708	−2.51679
$686$	−81.5214	−3.11250
$687$	15.3707	0.586428
$688$	−11.3170	−0.431456
$689$	−5.95354	−0.226812
$690$	1.12811	0.0429463
$691$	−34.0813	−1.29651	−0.648257	−	0.761422i	$-0.724502\pi$
$691$	−34.0813	−1.29651	−0.648257	+	0.761422i	$0.724502\pi$
$692$	−10.6919	−0.406447
$693$	4.73018	0.179685
$694$	−80.4936	−3.05549
$695$	−76.0321	−2.88406
$696$	8.71480	0.330334
$697$	−8.07586	−0.305895
$698$	−18.3848	−0.695875
$699$	6.97957	0.263991
$700$	129.849	4.90785
$701$	25.4936	0.962878	0.481439	−	0.876479i	$-0.340114\pi$
$701$	25.4936	0.962878	0.481439	+	0.876479i	$0.340114\pi$
$702$	−2.21491	−0.0835963
$703$	−46.8405	−1.76662
$704$	−13.0098	−0.490324
$705$	−19.0171	−0.716226
$706$	67.7040	2.54807
$707$	15.8533	0.596223
$708$	9.73461	0.365849
$709$	−5.29427	−0.198830	−0.0994152	−	0.995046i	$-0.531697\pi$
$709$	−5.29427	−0.198830	−0.0994152	+	0.995046i	$0.531697\pi$
$710$	−59.1992	−2.22171
$711$	6.15889	0.230976
$712$	−26.0954	−0.977966
$713$	1.22668	0.0459395
$714$	−11.0554	−0.413736
$715$	3.85888	0.144314
$716$	−31.6226	−1.18179
$717$	28.1310	1.05057
$718$	48.9320	1.82612
$719$	18.5964	0.693529	0.346764	−	0.937952i	$-0.387280\pi$
$719$	18.5964	0.693529	0.346764	+	0.937952i	$0.387280\pi$
$720$	−5.21863	−0.194487
$721$	4.67656	0.174164
$722$	−6.84205	−0.254635
$723$	6.08071	0.226144
$724$	40.0470	1.48834
$725$	−41.5057	−1.54148
$726$	22.0980	0.820134
$727$	37.8562	1.40401	0.702005	−	0.712172i	$-0.252288\pi$
$727$	37.8562	1.40401	0.702005	+	0.712172i	$0.252288\pi$
$728$	−9.38257	−0.347741
$729$	1.00000	0.0370370
$730$	−97.4958	−3.60848
$731$	8.83029	0.326600
$732$	21.9646	0.811834
$733$	−35.7747	−1.32137	−0.660685	−	0.750664i	$-0.729734\pi$
$733$	−35.7747	−1.32137	−0.660685	+	0.750664i	$0.729734\pi$
$734$	−71.1789	−2.62726
$735$	56.7322	2.09260
$736$	−0.940152	−0.0346544
$737$	−3.25700	−0.119973
$738$	16.7592	0.616916
$739$	−1.56105	−0.0574241	−0.0287120	−	0.999588i	$-0.509141\pi$
$739$	−1.56105	−0.0574241	−0.0287120	+	0.999588i	$0.509141\pi$
$740$	−110.487	−4.06159
$741$	4.69990	0.172655
$742$	61.6677	2.26389
$743$	24.4125	0.895606	0.447803	−	0.894132i	$-0.352207\pi$
$743$	24.4125	0.895606	0.447803	+	0.894132i	$0.352207\pi$
$744$	18.4350	0.675858
$745$	−76.1251	−2.78901
$746$	−45.1491	−1.65303
$747$	−12.0154	−0.439620
$748$	3.13696	0.114698
$749$	−51.7462	−1.89077
$750$	−38.4933	−1.40558
$751$	−40.1788	−1.46615	−0.733073	−	0.680150i	$-0.761915\pi$
$751$	−40.1788	−1.46615	−0.733073	+	0.680150i	$0.761915\pi$
$752$	6.81835	0.248640
$753$	−7.19234	−0.262104
$754$	9.62096	0.350375
$755$	−69.4619	−2.52798
$756$	13.5892	0.494235
$757$	6.71364	0.244011	0.122006	−	0.992529i	$-0.461067\pi$
$757$	6.71364	0.244011	0.122006	+	0.992529i	$0.461067\pi$
$758$	32.9407	1.19646
$759$	−0.135031	−0.00490132
$760$	−35.9745	−1.30493
$761$	−32.7956	−1.18884	−0.594420	−	0.804154i	$-0.702619\pi$
$761$	−32.7956	−1.18884	−0.594420	+	0.804154i	$0.702619\pi$
$762$	−6.09741	−0.220886
$763$	85.2772	3.08724
$764$	46.0119	1.66465
$765$	4.07193	0.147221
$766$	−27.7686	−1.00332
$767$	3.35004	0.120963
$768$	−6.17937	−0.222979
$769$	−16.6093	−0.598947	−0.299474	−	0.954105i	$-0.596811\pi$
$769$	−16.6093	−0.598947	−0.299474	+	0.954105i	$0.596811\pi$
$770$	−39.9709	−1.44045
$771$	−12.8672	−0.463402
$772$	73.2932	2.63788
$773$	34.0523	1.22478	0.612389	−	0.790557i	$-0.290209\pi$
$773$	34.0523	1.22478	0.612389	+	0.790557i	$0.290209\pi$
$774$	−18.3249	−0.658673
$775$	−87.7996	−3.15385
$776$	−12.8126	−0.459946
$777$	−46.6079	−1.67205
$778$	49.8888	1.78860
$779$	−35.5621	−1.27415
$780$	11.0861	0.396946
$781$	7.08598	0.253556
$782$	0.315594	0.0112856
$783$	−4.34373	−0.155232
$784$	−20.3406	−0.726450
$785$	17.0781	0.609544
$786$	−18.8782	−0.673365
$787$	0.621832	0.0221659	0.0110830	−	0.999939i	$-0.496472\pi$
$787$	0.621832	0.0221659	0.0110830	+	0.999939i	$0.496472\pi$
$788$	−8.85963	−0.315611
$789$	−21.0240	−0.748475
$790$	−52.0437	−1.85163
$791$	14.7483	0.524390
$792$	−2.02930	−0.0721079
$793$	7.55884	0.268422
$794$	−24.3806	−0.865234
$795$	−22.7136	−0.805568
$796$	−59.9135	−2.12358
$797$	−24.8916	−0.881705	−0.440853	−	0.897580i	$-0.645324\pi$
$797$	−24.8916	−0.881705	−0.440853	+	0.897580i	$0.645324\pi$
$798$	−48.6823	−1.72334
$799$	−5.32015	−0.188213
$800$	67.2914	2.37911
$801$	13.0067	0.459571
$802$	62.0117	2.18971
$803$	11.6700	0.411825
$804$	−9.35697	−0.329995
$805$	−2.38189	−0.0839505
$806$	20.3518	0.716862
$807$	−21.4723	−0.755861
$808$	−6.80121	−0.239266
$809$	−36.3222	−1.27702	−0.638510	−	0.769613i	$-0.720449\pi$
$809$	−36.3222	−1.27702	−0.638510	+	0.769613i	$0.720449\pi$
$810$	−8.45019	−0.296909
$811$	−6.38770	−0.224303	−0.112151	−	0.993691i	$-0.535774\pi$
$811$	−6.38770	−0.224303	−0.112151	+	0.993691i	$0.535774\pi$
$812$	−59.0279	−2.07147
$813$	−3.95231	−0.138614
$814$	22.3274	0.782577
$815$	−40.2948	−1.41147
$816$	−1.45994	−0.0511082
$817$	38.8843	1.36039
$818$	−0.117166	−0.00409662
$819$	4.67656	0.163412
$820$	−83.8837	−2.92935
$821$	9.65131	0.336833	0.168416	−	0.985716i	$-0.446135\pi$
$821$	9.65131	0.336833	0.168416	+	0.985716i	$0.446135\pi$
$822$	38.2417	1.33383
$823$	25.0364	0.872713	0.436356	−	0.899774i	$-0.356269\pi$
$823$	25.0364	0.872713	0.436356	+	0.899774i	$0.356269\pi$
$824$	−2.00629	−0.0698926
$825$	9.66486	0.336487
$826$	−34.7003	−1.20738
$827$	27.1153	0.942891	0.471445	−	0.881895i	$-0.343732\pi$
$827$	27.1153	0.942891	0.471445	+	0.881895i	$0.343732\pi$
$828$	−0.387928	−0.0134814
$829$	−33.2513	−1.15486	−0.577432	−	0.816439i	$-0.695945\pi$
$829$	−33.2513	−1.15486	−0.577432	+	0.816439i	$0.695945\pi$
$830$	101.532	3.52423
$831$	−17.3952	−0.603434
$832$	−12.8623	−0.445920
$833$	15.8712	0.549903
$834$	44.1410	1.52848
$835$	−25.0371	−0.866444
$836$	13.8136	0.477754
$837$	−9.18856	−0.317603
$838$	−38.6238	−1.33424
$839$	−20.7743	−0.717209	−0.358605	−	0.933490i	$-0.616747\pi$
$839$	−20.7743	−0.717209	−0.358605	+	0.933490i	$0.616747\pi$
$840$	−35.7958	−1.23507
$841$	−10.1320	−0.349380
$842$	−13.5543	−0.467112
$843$	−17.1929	−0.592156
$844$	−9.75933	−0.335930
$845$	3.81514	0.131245
$846$	11.0405	0.379581
$847$	−46.6578	−1.60318
$848$	8.14367	0.279655
$849$	13.6531	0.468575
$850$	−22.5887	−0.774785
$851$	1.33050	0.0456091
$852$	20.3572	0.697425
$853$	−17.5085	−0.599478	−0.299739	−	0.954021i	$-0.596900\pi$
$853$	−17.5085	−0.599478	−0.299739	+	0.954021i	$0.596900\pi$
$854$	−78.2956	−2.67922
$855$	17.9308	0.613221
$856$	22.1997	0.758769
$857$	−15.0258	−0.513273	−0.256636	−	0.966508i	$-0.582614\pi$
$857$	−15.0258	−0.513273	−0.256636	+	0.966508i	$0.582614\pi$
$858$	−2.24030	−0.0764826
$859$	47.8056	1.63111	0.815553	−	0.578682i	$-0.196433\pi$
$859$	47.8056	1.63111	0.815553	+	0.578682i	$0.196433\pi$
$860$	91.7199	3.12762
$861$	−35.3855	−1.20594
$862$	−10.0756	−0.343176
$863$	−21.1797	−0.720967	−0.360483	−	0.932766i	$-0.617388\pi$
$863$	−21.1797	−0.720967	−0.360483	+	0.932766i	$0.617388\pi$
$864$	7.04230	0.239584
$865$	−14.0378	−0.477300
$866$	56.2762	1.91234
$867$	−15.8609	−0.538663
$868$	−124.865	−4.23821
$869$	6.22949	0.211321
$870$	36.7053	1.24443
$871$	−3.22008	−0.109108
$872$	−36.5848	−1.23892
$873$	6.38621	0.216140
$874$	1.38972	0.0470080
$875$	81.2749	2.74759
$876$	33.5264	1.13275
$877$	25.9961	0.877824	0.438912	−	0.898530i	$-0.355364\pi$
$877$	25.9961	0.877824	0.438912	+	0.898530i	$0.355364\pi$
$878$	−14.0103	−0.472826
$879$	−33.5872	−1.13287
$880$	−5.27845	−0.177937
$881$	7.71713	0.259997	0.129998	−	0.991514i	$-0.458503\pi$
$881$	7.71713	0.259997	0.129998	+	0.991514i	$0.458503\pi$
$882$	−32.9362	−1.10902
$883$	−12.4713	−0.419692	−0.209846	−	0.977734i	$-0.567296\pi$
$883$	−12.4713	−0.419692	−0.209846	+	0.977734i	$0.567296\pi$
$884$	3.10140	0.104311
$885$	12.7809	0.429625
$886$	−2.64610	−0.0888975
$887$	−10.8597	−0.364632	−0.182316	−	0.983240i	$-0.558359\pi$
$887$	−10.8597	−0.364632	−0.182316	+	0.983240i	$0.558359\pi$
$888$	19.9953	0.670998
$889$	12.8741	0.431783
$890$	−109.909	−3.68417
$891$	1.01146	0.0338853
$892$	63.8262	2.13706
$893$	−23.4273	−0.783966
$894$	44.1949	1.47810
$895$	−41.5184	−1.38781
$896$	67.3621	2.25041
$897$	−0.133501	−0.00445746
$898$	−46.9466	−1.56663
$899$	39.9126	1.33116
$900$	27.7660	0.925533
$901$	−6.35426	−0.211691
$902$	16.9514	0.564419
$903$	38.6912	1.28756
$904$	−6.32719	−0.210439
$905$	52.5791	1.74779
$906$	40.3266	1.33976
$907$	−48.4401	−1.60843	−0.804214	−	0.594340i	$-0.797413\pi$
$907$	−48.4401	−1.60843	−0.804214	+	0.594340i	$0.797413\pi$
$908$	−12.5167	−0.415382
$909$	3.38994	0.112437
$910$	−39.5179	−1.31000
$911$	29.4081	0.974332	0.487166	−	0.873309i	$-0.338031\pi$
$911$	29.4081	0.974332	0.487166	+	0.873309i	$0.338031\pi$
$912$	−6.42886	−0.212881
$913$	−12.1531	−0.402210
$914$	−15.2943	−0.505891
$915$	28.8380	0.953356
$916$	44.6644	1.47575
$917$	39.8596	1.31628
$918$	−2.36399	−0.0780233
$919$	−17.8326	−0.588242	−0.294121	−	0.955768i	$-0.595027\pi$
$919$	−17.8326	−0.588242	−0.294121	+	0.955768i	$0.595027\pi$
$920$	1.02185	0.0336895
$921$	−10.4550	−0.344504
$922$	−71.6368	−2.35923
$923$	7.00567	0.230594
$924$	13.7450	0.452178
$925$	−95.2309	−3.13117
$926$	−20.3022	−0.667173
$927$	1.00000	0.0328443
$928$	−30.5898	−1.00416
$929$	56.4100	1.85075	0.925376	−	0.379050i	$-0.123749\pi$
$929$	56.4100	1.85075	0.925376	+	0.379050i	$0.123749\pi$
$930$	77.6450	2.54608
$931$	69.8888	2.29051
$932$	20.2813	0.664337
$933$	7.15347	0.234194
$934$	6.14269	0.200995
$935$	4.11862	0.134693
$936$	−2.00629	−0.0655778
$937$	−25.8004	−0.842862	−0.421431	−	0.906861i	$-0.638472\pi$
$937$	−25.8004	−0.842862	−0.421431	+	0.906861i	$0.638472\pi$
$938$	33.3541	1.08905
$939$	13.5027	0.440646
$940$	−55.2602	−1.80239
$941$	−15.8249	−0.515877	−0.257939	−	0.966161i	$-0.583043\pi$
$941$	−15.8249	−0.515877	−0.257939	+	0.966161i	$0.583043\pi$
$942$	−9.91481	−0.323042
$943$	1.01014	0.0328947
$944$	−4.58243	−0.149145
$945$	17.8418	0.580393
$946$	−18.5349	−0.602623
$947$	47.5804	1.54615	0.773077	−	0.634312i	$-0.218717\pi$
$947$	47.5804	1.54615	0.773077	+	0.634312i	$0.218717\pi$
$948$	17.8966	0.581254
$949$	11.5377	0.374530
$950$	−99.4694	−3.22721
$951$	−17.9165	−0.580982
$952$	−10.0141	−0.324559
$953$	1.35842	0.0440035	0.0220018	−	0.999758i	$-0.492996\pi$
$953$	1.35842	0.0440035	0.0220018	+	0.999758i	$0.492996\pi$
$954$	13.1865	0.426930
$955$	60.4107	1.95484
$956$	81.7436	2.64378
$957$	−4.39353	−0.142023
$958$	25.6060	0.827292
$959$	−80.7438	−2.60735
$960$	−49.0715	−1.58378
$961$	53.4296	1.72353
$962$	22.0744	0.711706
$963$	−11.0650	−0.356565
$964$	17.6694	0.569094
$965$	96.2291	3.09773
$966$	1.38282	0.0444915
$967$	2.58504	0.0831292	0.0415646	−	0.999136i	$-0.486766\pi$
$967$	2.58504	0.0831292	0.0415646	+	0.999136i	$0.486766\pi$
$968$	20.0167	0.643361
$969$	5.01625	0.161145
$970$	−53.9646	−1.73270
$971$	−27.0002	−0.866476	−0.433238	−	0.901279i	$-0.642629\pi$
$971$	−27.0002	−0.866476	−0.433238	+	0.901279i	$0.642629\pi$
$972$	2.90581	0.0932040
$973$	−93.1994	−2.98784
$974$	−84.0132	−2.69196
$975$	9.55532	0.306015
$976$	−10.3395	−0.330960
$977$	42.3292	1.35423	0.677116	−	0.735876i	$-0.263230\pi$
$977$	42.3292	1.35423	0.677116	+	0.735876i	$0.263230\pi$
$978$	23.3934	0.748039
$979$	13.1559	0.420463
$980$	164.853	5.26604
$981$	18.2350	0.582199
$982$	−20.6178	−0.657940
$983$	27.4987	0.877071	0.438535	−	0.898714i	$-0.355497\pi$
$983$	27.4987	0.877071	0.438535	+	0.898714i	$0.355497\pi$
$984$	15.1808	0.483945
$985$	−11.6321	−0.370630
$986$	10.2685	0.327017
$987$	−23.3110	−0.741997
$988$	13.6570	0.434489
$989$	−1.10451	−0.0351213
$990$	−8.54707	−0.271644
$991$	41.7300	1.32560	0.662799	−	0.748798i	$-0.269369\pi$
$991$	41.7300	1.32560	0.662799	+	0.748798i	$0.269369\pi$
$992$	−64.7086	−2.05450
$993$	18.3721	0.583020
$994$	−72.5658	−2.30165
$995$	−78.6625	−2.49377
$996$	−34.9145	−1.10631
$997$	50.5163	1.59987	0.799934	−	0.600088i	$-0.204868\pi$
$997$	50.5163	1.59987	0.799934	+	0.600088i	$0.204868\pi$
$998$	55.1788	1.74665
$999$	−9.96627	−0.315319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.5	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21491 q^{2} +1.00000 q^{3} +2.90581 q^{4} +3.81514 q^{5} -2.21491 q^{6} +4.67656 q^{7} -2.00629 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.21491 q^{2} +1.00000 q^{3} +2.90581 q^{4} +3.81514 q^{5} -2.21491 q^{6} +4.67656 q^{7} -2.00629 q^{8} +1.00000 q^{9} -8.45019 q^{10} +1.01146 q^{11} +2.90581 q^{12} +1.00000 q^{13} -10.3582 q^{14} +3.81514 q^{15} -1.36787 q^{16} +1.06731 q^{17} -2.21491 q^{18} +4.69990 q^{19} +11.0861 q^{20} +4.67656 q^{21} -2.24030 q^{22} -0.133501 q^{23} -2.00629 q^{24} +9.55532 q^{25} -2.21491 q^{26} +1.00000 q^{27} +13.5892 q^{28} -4.34373 q^{29} -8.45019 q^{30} -9.18856 q^{31} +7.04230 q^{32} +1.01146 q^{33} -2.36399 q^{34} +17.8418 q^{35} +2.90581 q^{36} -9.96627 q^{37} -10.4098 q^{38} +1.00000 q^{39} -7.65430 q^{40} -7.56657 q^{41} -10.3582 q^{42} +8.27342 q^{43} +2.93913 q^{44} +3.81514 q^{45} +0.295692 q^{46} -4.98464 q^{47} -1.36787 q^{48} +14.8703 q^{49} -21.1641 q^{50} +1.06731 q^{51} +2.90581 q^{52} -5.95354 q^{53} -2.21491 q^{54} +3.85888 q^{55} -9.38257 q^{56} +4.69990 q^{57} +9.62096 q^{58} +3.35004 q^{59} +11.0861 q^{60} +7.55884 q^{61} +20.3518 q^{62} +4.67656 q^{63} -12.8623 q^{64} +3.81514 q^{65} -2.24030 q^{66} -3.22008 q^{67} +3.10140 q^{68} -0.133501 q^{69} -39.5179 q^{70} +7.00567 q^{71} -2.00629 q^{72} +11.5377 q^{73} +22.0744 q^{74} +9.55532 q^{75} +13.6570 q^{76} +4.73018 q^{77} -2.21491 q^{78} +6.15889 q^{79} -5.21863 q^{80} +1.00000 q^{81} +16.7592 q^{82} -12.0154 q^{83} +13.5892 q^{84} +4.07193 q^{85} -18.3249 q^{86} -4.34373 q^{87} -2.02930 q^{88} +13.0067 q^{89} -8.45019 q^{90} +4.67656 q^{91} -0.387928 q^{92} -9.18856 q^{93} +11.0405 q^{94} +17.9308 q^{95} +7.04230 q^{96} +6.38621 q^{97} -32.9362 q^{98} +1.01146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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