LMFDB - Embedded newform 4006.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, 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("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.91121 q^{3} +1.00000 q^{4} -1.39712 q^{5} +1.91121 q^{6} +3.46874 q^{7} -1.00000 q^{8} +0.652717 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.91121 q^{3} +1.00000 q^{4} -1.39712 q^{5} +1.91121 q^{6} +3.46874 q^{7} -1.00000 q^{8} +0.652717 q^{9} +1.39712 q^{10} -5.38542 q^{11} -1.91121 q^{12} +0.707447 q^{13} -3.46874 q^{14} +2.67020 q^{15} +1.00000 q^{16} +1.30288 q^{17} -0.652717 q^{18} +1.25277 q^{19} -1.39712 q^{20} -6.62949 q^{21} +5.38542 q^{22} -1.63099 q^{23} +1.91121 q^{24} -3.04804 q^{25} -0.707447 q^{26} +4.48615 q^{27} +3.46874 q^{28} +9.27361 q^{29} -2.67020 q^{30} +3.30654 q^{31} -1.00000 q^{32} +10.2927 q^{33} -1.30288 q^{34} -4.84626 q^{35} +0.652717 q^{36} -2.58531 q^{37} -1.25277 q^{38} -1.35208 q^{39} +1.39712 q^{40} -5.07679 q^{41} +6.62949 q^{42} +4.23096 q^{43} -5.38542 q^{44} -0.911927 q^{45} +1.63099 q^{46} -9.82173 q^{47} -1.91121 q^{48} +5.03217 q^{49} +3.04804 q^{50} -2.49007 q^{51} +0.707447 q^{52} +2.68330 q^{53} -4.48615 q^{54} +7.52410 q^{55} -3.46874 q^{56} -2.39431 q^{57} -9.27361 q^{58} -4.53284 q^{59} +2.67020 q^{60} -9.89612 q^{61} -3.30654 q^{62} +2.26411 q^{63} +1.00000 q^{64} -0.988392 q^{65} -10.2927 q^{66} -7.12165 q^{67} +1.30288 q^{68} +3.11715 q^{69} +4.84626 q^{70} +15.6360 q^{71} -0.652717 q^{72} +7.20729 q^{73} +2.58531 q^{74} +5.82545 q^{75} +1.25277 q^{76} -18.6806 q^{77} +1.35208 q^{78} +12.9876 q^{79} -1.39712 q^{80} -10.5321 q^{81} +5.07679 q^{82} +1.68735 q^{83} -6.62949 q^{84} -1.82028 q^{85} -4.23096 q^{86} -17.7238 q^{87} +5.38542 q^{88} +14.6065 q^{89} +0.911927 q^{90} +2.45395 q^{91} -1.63099 q^{92} -6.31948 q^{93} +9.82173 q^{94} -1.75028 q^{95} +1.91121 q^{96} -4.62606 q^{97} -5.03217 q^{98} -3.51515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.91121	−1.10344	−0.551718	−	0.834031i	$-0.686028\pi$
$3$	−1.91121	−1.10344	−0.551718	+	0.834031i	$0.686028\pi$
$4$	1.00000	0.500000
$5$	−1.39712	−0.624813	−0.312407	−	0.949949i	$-0.601135\pi$
$5$	−1.39712	−0.624813	−0.312407	+	0.949949i	$0.601135\pi$
$6$	1.91121	0.780248
$7$	3.46874	1.31106	0.655531	−	0.755169i	$-0.272445\pi$
$7$	3.46874	1.31106	0.655531	+	0.755169i	$0.272445\pi$
$8$	−1.00000	−0.353553
$9$	0.652717	0.217572
$10$	1.39712	0.441810
$11$	−5.38542	−1.62376	−0.811882	−	0.583821i	$-0.801557\pi$
$11$	−5.38542	−1.62376	−0.811882	+	0.583821i	$0.801557\pi$
$12$	−1.91121	−0.551718
$13$	0.707447	0.196211	0.0981053	−	0.995176i	$-0.468722\pi$
$13$	0.707447	0.196211	0.0981053	+	0.995176i	$0.468722\pi$
$14$	−3.46874	−0.927060
$15$	2.67020	0.689442
$16$	1.00000	0.250000
$17$	1.30288	0.315995	0.157997	−	0.987440i	$-0.449496\pi$
$17$	1.30288	0.315995	0.157997	+	0.987440i	$0.449496\pi$
$18$	−0.652717	−0.153847
$19$	1.25277	0.287406	0.143703	−	0.989621i	$-0.454099\pi$
$19$	1.25277	0.287406	0.143703	+	0.989621i	$0.454099\pi$
$20$	−1.39712	−0.312407
$21$	−6.62949	−1.44667
$22$	5.38542	1.14817
$23$	−1.63099	−0.340084	−0.170042	−	0.985437i	$-0.554390\pi$
$23$	−1.63099	−0.340084	−0.170042	+	0.985437i	$0.554390\pi$
$24$	1.91121	0.390124
$25$	−3.04804	−0.609609
$26$	−0.707447	−0.138742
$27$	4.48615	0.863359
$28$	3.46874	0.655531
$29$	9.27361	1.72207	0.861033	−	0.508549i	$-0.169818\pi$
$29$	9.27361	1.72207	0.861033	+	0.508549i	$0.169818\pi$
$30$	−2.67020	−0.487509
$31$	3.30654	0.593872	0.296936	−	0.954897i	$-0.404035\pi$
$31$	3.30654	0.593872	0.296936	+	0.954897i	$0.404035\pi$
$32$	−1.00000	−0.176777
$33$	10.2927	1.79172
$34$	−1.30288	−0.223442
$35$	−4.84626	−0.819168
$36$	0.652717	0.108786
$37$	−2.58531	−0.425022	−0.212511	−	0.977159i	$-0.568164\pi$
$37$	−2.58531	−0.425022	−0.212511	+	0.977159i	$0.568164\pi$
$38$	−1.25277	−0.203227
$39$	−1.35208	−0.216506
$40$	1.39712	0.220905
$41$	−5.07679	−0.792862	−0.396431	−	0.918065i	$-0.629751\pi$
$41$	−5.07679	−0.792862	−0.396431	+	0.918065i	$0.629751\pi$
$42$	6.62949	1.02295
$43$	4.23096	0.645215	0.322607	−	0.946533i	$-0.395441\pi$
$43$	4.23096	0.645215	0.322607	+	0.946533i	$0.395441\pi$
$44$	−5.38542	−0.811882
$45$	−0.911927	−0.135942
$46$	1.63099	0.240476
$47$	−9.82173	−1.43265	−0.716323	−	0.697769i	$-0.754176\pi$
$47$	−9.82173	−1.43265	−0.716323	+	0.697769i	$0.754176\pi$
$48$	−1.91121	−0.275859
$49$	5.03217	0.718881
$50$	3.04804	0.431058
$51$	−2.49007	−0.348680
$52$	0.707447	0.0981053
$53$	2.68330	0.368579	0.184290	−	0.982872i	$-0.441002\pi$
$53$	2.68330	0.368579	0.184290	+	0.982872i	$0.441002\pi$
$54$	−4.48615	−0.610487
$55$	7.52410	1.01455
$56$	−3.46874	−0.463530
$57$	−2.39431	−0.317134
$58$	−9.27361	−1.21768
$59$	−4.53284	−0.590125	−0.295062	−	0.955478i	$-0.595340\pi$
$59$	−4.53284	−0.590125	−0.295062	+	0.955478i	$0.595340\pi$
$60$	2.67020	0.344721
$61$	−9.89612	−1.26707	−0.633534	−	0.773715i	$-0.718396\pi$
$61$	−9.89612	−1.26707	−0.633534	+	0.773715i	$0.718396\pi$
$62$	−3.30654	−0.419931
$63$	2.26411	0.285251
$64$	1.00000	0.125000
$65$	−0.988392	−0.122595
$66$	−10.2927	−1.26694
$67$	−7.12165	−0.870049	−0.435024	−	0.900419i	$-0.643260\pi$
$67$	−7.12165	−0.870049	−0.435024	+	0.900419i	$0.643260\pi$
$68$	1.30288	0.157997
$69$	3.11715	0.375261
$70$	4.84626	0.579239
$71$	15.6360	1.85565	0.927825	−	0.373015i	$-0.121676\pi$
$71$	15.6360	1.85565	0.927825	+	0.373015i	$0.121676\pi$
$72$	−0.652717	−0.0769235
$73$	7.20729	0.843550	0.421775	−	0.906701i	$-0.361407\pi$
$73$	7.20729	0.843550	0.421775	+	0.906701i	$0.361407\pi$
$74$	2.58531	0.300536
$75$	5.82545	0.672665
$76$	1.25277	0.143703
$77$	−18.6806	−2.12885
$78$	1.35208	0.153093
$79$	12.9876	1.46122	0.730612	−	0.682793i	$-0.239235\pi$
$79$	12.9876	1.46122	0.730612	+	0.682793i	$0.239235\pi$
$80$	−1.39712	−0.156203
$81$	−10.5321	−1.17023
$82$	5.07679	0.560638
$83$	1.68735	0.185210	0.0926052	−	0.995703i	$-0.470481\pi$
$83$	1.68735	0.185210	0.0926052	+	0.995703i	$0.470481\pi$
$84$	−6.62949	−0.723336
$85$	−1.82028	−0.197438
$86$	−4.23096	−0.456236
$87$	−17.7238	−1.90019
$88$	5.38542	0.574087
$89$	14.6065	1.54829	0.774145	−	0.633009i	$-0.218180\pi$
$89$	14.6065	1.54829	0.774145	+	0.633009i	$0.218180\pi$
$90$	0.911927	0.0961256
$91$	2.45395	0.257244
$92$	−1.63099	−0.170042
$93$	−6.31948	−0.655300
$94$	9.82173	1.01303
$95$	−1.75028	−0.179575
$96$	1.91121	0.195062
$97$	−4.62606	−0.469705	−0.234853	−	0.972031i	$-0.575461\pi$
$97$	−4.62606	−0.469705	−0.234853	+	0.972031i	$0.575461\pi$
$98$	−5.03217	−0.508326
$99$	−3.51515	−0.353286
$100$	−3.04804	−0.304804
$101$	−18.7019	−1.86091	−0.930456	−	0.366405i	$-0.880589\pi$
$101$	−18.7019	−1.86091	−0.930456	+	0.366405i	$0.880589\pi$
$102$	2.49007	0.246554
$103$	2.87078	0.282866	0.141433	−	0.989948i	$-0.454829\pi$
$103$	2.87078	0.282866	0.141433	+	0.989948i	$0.454829\pi$
$104$	−0.707447	−0.0693709
$105$	9.26222	0.903900
$106$	−2.68330	−0.260625
$107$	−12.9417	−1.25113	−0.625563	−	0.780174i	$-0.715131\pi$
$107$	−12.9417	−1.25113	−0.625563	+	0.780174i	$0.715131\pi$
$108$	4.48615	0.431680
$109$	8.58800	0.822581	0.411290	−	0.911504i	$-0.365078\pi$
$109$	8.58800	0.822581	0.411290	+	0.911504i	$0.365078\pi$
$110$	−7.52410	−0.717394
$111$	4.94106	0.468985
$112$	3.46874	0.327765
$113$	6.36794	0.599045	0.299523	−	0.954089i	$-0.403173\pi$
$113$	6.36794	0.599045	0.299523	+	0.954089i	$0.403173\pi$
$114$	2.39431	0.224248
$115$	2.27869	0.212489
$116$	9.27361	0.861033
$117$	0.461763	0.0426900
$118$	4.53284	0.417281
$119$	4.51935	0.414288
$120$	−2.67020	−0.243754
$121$	18.0027	1.63661
$122$	9.89612	0.895953
$123$	9.70281	0.874873
$124$	3.30654	0.296936
$125$	11.2441	1.00570
$126$	−2.26411	−0.201703
$127$	11.5882	1.02829	0.514144	−	0.857704i	$-0.328110\pi$
$127$	11.5882	1.02829	0.514144	+	0.857704i	$0.328110\pi$
$128$	−1.00000	−0.0883883
$129$	−8.08624	−0.711954
$130$	0.988392	0.0866877
$131$	12.7769	1.11632	0.558159	−	0.829734i	$-0.311508\pi$
$131$	12.7769	1.11632	0.558159	+	0.829734i	$0.311508\pi$
$132$	10.2927	0.895860
$133$	4.34554	0.376806
$134$	7.12165	0.615217
$135$	−6.26770	−0.539438
$136$	−1.30288	−0.111721
$137$	−12.7306	−1.08765	−0.543825	−	0.839199i	$-0.683024\pi$
$137$	−12.7306	−1.08765	−0.543825	+	0.839199i	$0.683024\pi$
$138$	−3.11715	−0.265350
$139$	10.3838	0.880746	0.440373	−	0.897815i	$-0.354846\pi$
$139$	10.3838	0.880746	0.440373	+	0.897815i	$0.354846\pi$
$140$	−4.84626	−0.409584
$141$	18.7714	1.58083
$142$	−15.6360	−1.31214
$143$	−3.80990	−0.318600
$144$	0.652717	0.0543931
$145$	−12.9564	−1.07597
$146$	−7.20729	−0.596480
$147$	−9.61752	−0.793240
$148$	−2.58531	−0.212511
$149$	−12.1004	−0.991306	−0.495653	−	0.868521i	$-0.665071\pi$
$149$	−12.1004	−0.991306	−0.495653	+	0.868521i	$0.665071\pi$
$150$	−5.82545	−0.475646
$151$	2.15561	0.175421	0.0877105	−	0.996146i	$-0.472045\pi$
$151$	2.15561	0.175421	0.0877105	+	0.996146i	$0.472045\pi$
$152$	−1.25277	−0.101613
$153$	0.850412	0.0687517
$154$	18.6806	1.50533
$155$	−4.61964	−0.371059
$156$	−1.35208	−0.108253
$157$	6.01394	0.479965	0.239982	−	0.970777i	$-0.422858\pi$
$157$	6.01394	0.479965	0.239982	+	0.970777i	$0.422858\pi$
$158$	−12.9876	−1.03324
$159$	−5.12834	−0.406704
$160$	1.39712	0.110452
$161$	−5.65747	−0.445871
$162$	10.5321	0.827481
$163$	−19.3553	−1.51603	−0.758013	−	0.652239i	$-0.773830\pi$
$163$	−19.3553	−1.51603	−0.758013	+	0.652239i	$0.773830\pi$
$164$	−5.07679	−0.396431
$165$	−14.3801	−1.11949
$166$	−1.68735	−0.130964
$167$	17.6636	1.36685	0.683425	−	0.730021i	$-0.260490\pi$
$167$	17.6636	1.36685	0.683425	+	0.730021i	$0.260490\pi$
$168$	6.62949	0.511476
$169$	−12.4995	−0.961501
$170$	1.82028	0.139609
$171$	0.817706	0.0625316
$172$	4.23096	0.322607
$173$	−18.7071	−1.42228	−0.711139	−	0.703052i	$-0.751820\pi$
$173$	−18.7071	−1.42228	−0.711139	+	0.703052i	$0.751820\pi$
$174$	17.7238	1.34364
$175$	−10.5729	−0.799234
$176$	−5.38542	−0.405941
$177$	8.66319	0.651165
$178$	−14.6065	−1.09481
$179$	−23.0957	−1.72626	−0.863128	−	0.504985i	$-0.831498\pi$
$179$	−23.0957	−1.72626	−0.863128	+	0.504985i	$0.831498\pi$
$180$	−0.911927	−0.0679710
$181$	21.8782	1.62619	0.813096	−	0.582130i	$-0.197780\pi$
$181$	21.8782	1.62619	0.813096	+	0.582130i	$0.197780\pi$
$182$	−2.45395	−0.181899
$183$	18.9135	1.39813
$184$	1.63099	0.120238
$185$	3.61199	0.265559
$186$	6.31948	0.463367
$187$	−7.01655	−0.513101
$188$	−9.82173	−0.716323
$189$	15.5613	1.13192
$190$	1.75028	0.126979
$191$	−19.0384	−1.37757	−0.688787	−	0.724964i	$-0.741856\pi$
$191$	−19.0384	−1.37757	−0.688787	+	0.724964i	$0.741856\pi$
$192$	−1.91121	−0.137930
$193$	19.8450	1.42847	0.714237	−	0.699904i	$-0.246774\pi$
$193$	19.8450	1.42847	0.714237	+	0.699904i	$0.246774\pi$
$194$	4.62606	0.332132
$195$	1.88902	0.135276
$196$	5.03217	0.359441
$197$	−10.3872	−0.740054	−0.370027	−	0.929021i	$-0.620652\pi$
$197$	−10.3872	−0.740054	−0.370027	+	0.929021i	$0.620652\pi$
$198$	3.51515	0.249811
$199$	−28.0304	−1.98702	−0.993511	−	0.113735i	$-0.963719\pi$
$199$	−28.0304	−1.98702	−0.993511	+	0.113735i	$0.963719\pi$
$200$	3.04804	0.215529
$201$	13.6110	0.960043
$202$	18.7019	1.31586
$203$	32.1678	2.25773
$204$	−2.49007	−0.174340
$205$	7.09291	0.495390
$206$	−2.87078	−0.200017
$207$	−1.06457	−0.0739929
$208$	0.707447	0.0490526
$209$	−6.74670	−0.466679
$210$	−9.26222	−0.639154
$211$	−21.9817	−1.51328	−0.756642	−	0.653829i	$-0.773161\pi$
$211$	−21.9817	−1.51328	−0.756642	+	0.653829i	$0.773161\pi$
$212$	2.68330	0.184290
$213$	−29.8836	−2.04759
$214$	12.9417	0.884680
$215$	−5.91117	−0.403139
$216$	−4.48615	−0.305244
$217$	11.4695	0.778602
$218$	−8.58800	−0.581653
$219$	−13.7746	−0.930804
$220$	7.52410	0.507274
$221$	0.921719	0.0620015
$222$	−4.94106	−0.331622
$223$	−11.3740	−0.761661	−0.380830	−	0.924645i	$-0.624362\pi$
$223$	−11.3740	−0.761661	−0.380830	+	0.924645i	$0.624362\pi$
$224$	−3.46874	−0.231765
$225$	−1.98951	−0.132634
$226$	−6.36794	−0.423589
$227$	4.39704	0.291842	0.145921	−	0.989296i	$-0.453386\pi$
$227$	4.39704	0.291842	0.145921	+	0.989296i	$0.453386\pi$
$228$	−2.39431	−0.158567
$229$	0.737047	0.0487054	0.0243527	−	0.999703i	$-0.492248\pi$
$229$	0.737047	0.0487054	0.0243527	+	0.999703i	$0.492248\pi$
$230$	−2.27869	−0.150252
$231$	35.7026	2.34906
$232$	−9.27361	−0.608842
$233$	−29.1104	−1.90709	−0.953543	−	0.301257i	$-0.902594\pi$
$233$	−29.1104	−1.90709	−0.953543	+	0.301257i	$0.902594\pi$
$234$	−0.461763	−0.0301864
$235$	13.7222	0.895136
$236$	−4.53284	−0.295062
$237$	−24.8221	−1.61237
$238$	−4.51935	−0.292946
$239$	−13.9227	−0.900584	−0.450292	−	0.892881i	$-0.648680\pi$
$239$	−13.9227	−0.900584	−0.450292	+	0.892881i	$0.648680\pi$
$240$	2.67020	0.172360
$241$	15.9988	1.03057	0.515287	−	0.857018i	$-0.327685\pi$
$241$	15.9988	1.03057	0.515287	+	0.857018i	$0.327685\pi$
$242$	−18.0027	−1.15726
$243$	6.67062	0.427921
$244$	−9.89612	−0.633534
$245$	−7.03057	−0.449166
$246$	−9.70281	−0.618628
$247$	0.886271	0.0563920
$248$	−3.30654	−0.209965
$249$	−3.22487	−0.204368
$250$	−11.2441	−0.711140
$251$	−24.5132	−1.54726	−0.773629	−	0.633639i	$-0.781561\pi$
$251$	−24.5132	−1.54726	−0.773629	+	0.633639i	$0.781561\pi$
$252$	2.26411	0.142625
$253$	8.78354	0.552216
$254$	−11.5882	−0.727110
$255$	3.47894	0.217860
$256$	1.00000	0.0625000
$257$	−5.56235	−0.346970	−0.173485	−	0.984837i	$-0.555503\pi$
$257$	−5.56235	−0.346970	−0.173485	+	0.984837i	$0.555503\pi$
$258$	8.08624	0.503427
$259$	−8.96776	−0.557230
$260$	−0.988392	−0.0612975
$261$	6.05305	0.374674
$262$	−12.7769	−0.789357
$263$	29.4620	1.81670	0.908351	−	0.418208i	$-0.137342\pi$
$263$	29.4620	1.81670	0.908351	+	0.418208i	$0.137342\pi$
$264$	−10.2927	−0.633469
$265$	−3.74890	−0.230293
$266$	−4.34554	−0.266442
$267$	−27.9161	−1.70844
$268$	−7.12165	−0.435024
$269$	0.299339	0.0182510	0.00912551	−	0.999958i	$-0.497095\pi$
$269$	0.299339	0.0182510	0.00912551	+	0.999958i	$0.497095\pi$
$270$	6.26770	0.381440
$271$	29.9220	1.81763	0.908816	−	0.417198i	$-0.136988\pi$
$271$	29.9220	1.81763	0.908816	+	0.417198i	$0.136988\pi$
$272$	1.30288	0.0789987
$273$	−4.69001	−0.283853
$274$	12.7306	0.769085
$275$	16.4150	0.989861
$276$	3.11715	0.187631
$277$	−13.6109	−0.817802	−0.408901	−	0.912579i	$-0.634088\pi$
$277$	−13.6109	−0.817802	−0.408901	+	0.912579i	$0.634088\pi$
$278$	−10.3838	−0.622782
$279$	2.15823	0.129210
$280$	4.84626	0.289620
$281$	−20.9957	−1.25250	−0.626248	−	0.779624i	$-0.715410\pi$
$281$	−20.9957	−1.25250	−0.626248	+	0.779624i	$0.715410\pi$
$282$	−18.7714	−1.11782
$283$	−29.0276	−1.72551	−0.862755	−	0.505621i	$-0.831263\pi$
$283$	−29.0276	−1.72551	−0.862755	+	0.505621i	$0.831263\pi$
$284$	15.6360	0.927825
$285$	3.34515	0.198149
$286$	3.80990	0.225284
$287$	−17.6101	−1.03949
$288$	−0.652717	−0.0384617
$289$	−15.3025	−0.900147
$290$	12.9564	0.760825
$291$	8.84137	0.518290
$292$	7.20729	0.421775
$293$	−7.17957	−0.419435	−0.209717	−	0.977762i	$-0.567254\pi$
$293$	−7.17957	−0.419435	−0.209717	+	0.977762i	$0.567254\pi$
$294$	9.61752	0.560905
$295$	6.33294	0.368718
$296$	2.58531	0.150268
$297$	−24.1598	−1.40189
$298$	12.1004	0.700959
$299$	−1.15384	−0.0667281
$300$	5.82545	0.336332
$301$	14.6761	0.845916
$302$	−2.15561	−0.124041
$303$	35.7433	2.05340
$304$	1.25277	0.0718514
$305$	13.8261	0.791681
$306$	−0.850412	−0.0486148
$307$	−21.9860	−1.25481	−0.627404	−	0.778694i	$-0.715883\pi$
$307$	−21.9860	−1.25481	−0.627404	+	0.778694i	$0.715883\pi$
$308$	−18.6806	−1.06443
$309$	−5.48666	−0.312125
$310$	4.61964	0.262378
$311$	−6.43014	−0.364620	−0.182310	−	0.983241i	$-0.558357\pi$
$311$	−6.43014	−0.364620	−0.182310	+	0.983241i	$0.558357\pi$
$312$	1.35208	0.0765464
$313$	7.21113	0.407597	0.203799	−	0.979013i	$-0.434671\pi$
$313$	7.21113	0.407597	0.203799	+	0.979013i	$0.434671\pi$
$314$	−6.01394	−0.339386
$315$	−3.16324	−0.178228
$316$	12.9876	0.730612
$317$	−17.4497	−0.980071	−0.490035	−	0.871702i	$-0.663016\pi$
$317$	−17.4497	−0.980071	−0.490035	+	0.871702i	$0.663016\pi$
$318$	5.12834	0.287583
$319$	−49.9422	−2.79623
$320$	−1.39712	−0.0781016
$321$	24.7344	1.38054
$322$	5.65747	0.315278
$323$	1.63221	0.0908187
$324$	−10.5321	−0.585117
$325$	−2.15633	−0.119612
$326$	19.3553	1.07199
$327$	−16.4135	−0.907666
$328$	5.07679	0.280319
$329$	−34.0690	−1.87829
$330$	14.3801	0.791599
$331$	6.76232	0.371691	0.185845	−	0.982579i	$-0.440498\pi$
$331$	6.76232	0.371691	0.185845	+	0.982579i	$0.440498\pi$
$332$	1.68735	0.0926052
$333$	−1.68747	−0.0924730
$334$	−17.6636	−0.966508
$335$	9.94984	0.543618
$336$	−6.62949	−0.361668
$337$	3.88491	0.211625	0.105812	−	0.994386i	$-0.466256\pi$
$337$	3.88491	0.211625	0.105812	+	0.994386i	$0.466256\pi$
$338$	12.4995	0.679884
$339$	−12.1705	−0.661009
$340$	−1.82028	−0.0987188
$341$	−17.8071	−0.964308
$342$	−0.817706	−0.0442165
$343$	−6.82590	−0.368564
$344$	−4.23096	−0.228118
$345$	−4.35505	−0.234468
$346$	18.7071	1.00570
$347$	22.6570	1.21629	0.608146	−	0.793825i	$-0.291913\pi$
$347$	22.6570	1.21629	0.608146	+	0.793825i	$0.291913\pi$
$348$	−17.7238	−0.950095
$349$	−14.3862	−0.770074	−0.385037	−	0.922901i	$-0.625811\pi$
$349$	−14.3862	−0.770074	−0.385037	+	0.922901i	$0.625811\pi$
$350$	10.5729	0.565144
$351$	3.17371	0.169400
$352$	5.38542	0.287044
$353$	−31.0634	−1.65334	−0.826668	−	0.562689i	$-0.809767\pi$
$353$	−31.0634	−1.65334	−0.826668	+	0.562689i	$0.809767\pi$
$354$	−8.66319	−0.460444
$355$	−21.8454	−1.15943
$356$	14.6065	0.774145
$357$	−8.63743	−0.457141
$358$	23.0957	1.22065
$359$	−7.74628	−0.408833	−0.204417	−	0.978884i	$-0.565530\pi$
$359$	−7.74628	−0.408833	−0.204417	+	0.978884i	$0.565530\pi$
$360$	0.911927	0.0480628
$361$	−17.4306	−0.917398
$362$	−21.8782	−1.14989
$363$	−34.4069	−1.80590
$364$	2.45395	0.128622
$365$	−10.0695	−0.527061
$366$	−18.9135	−0.988627
$367$	3.81909	0.199355	0.0996774	−	0.995020i	$-0.468219\pi$
$367$	3.81909	0.199355	0.0996774	+	0.995020i	$0.468219\pi$
$368$	−1.63099	−0.0850210
$369$	−3.31371	−0.172505
$370$	−3.61199	−0.187779
$371$	9.30767	0.483230
$372$	−6.31948	−0.327650
$373$	26.7451	1.38481	0.692403	−	0.721510i	$-0.256552\pi$
$373$	26.7451	1.38481	0.692403	+	0.721510i	$0.256552\pi$
$374$	7.01655	0.362817
$375$	−21.4899	−1.10973
$376$	9.82173	0.506517
$377$	6.56059	0.337888
$378$	−15.5613	−0.800386
$379$	0.580027	0.0297940	0.0148970	−	0.999889i	$-0.495258\pi$
$379$	0.580027	0.0297940	0.0148970	+	0.999889i	$0.495258\pi$
$380$	−1.75028	−0.0897874
$381$	−22.1475	−1.13465
$382$	19.0384	0.974091
$383$	12.4377	0.635536	0.317768	−	0.948168i	$-0.397067\pi$
$383$	12.4377	0.635536	0.317768	+	0.948168i	$0.397067\pi$
$384$	1.91121	0.0975309
$385$	26.0991	1.33014
$386$	−19.8450	−1.01008
$387$	2.76162	0.140381
$388$	−4.62606	−0.234853
$389$	1.38667	0.0703070	0.0351535	−	0.999382i	$-0.488808\pi$
$389$	1.38667	0.0703070	0.0351535	+	0.999382i	$0.488808\pi$
$390$	−1.88902	−0.0956544
$391$	−2.12498	−0.107465
$392$	−5.03217	−0.254163
$393$	−24.4192	−1.23179
$394$	10.3872	0.523297
$395$	−18.1454	−0.912992
$396$	−3.51515	−0.176643
$397$	15.5049	0.778167	0.389084	−	0.921202i	$-0.372792\pi$
$397$	15.5049	0.778167	0.389084	+	0.921202i	$0.372792\pi$
$398$	28.0304	1.40504
$399$	−8.30524	−0.415782
$400$	−3.04804	−0.152402
$401$	−6.49569	−0.324379	−0.162190	−	0.986760i	$-0.551856\pi$
$401$	−6.49569	−0.324379	−0.162190	+	0.986760i	$0.551856\pi$
$402$	−13.6110	−0.678853
$403$	2.33920	0.116524
$404$	−18.7019	−0.930456
$405$	14.7147	0.731178
$406$	−32.1678	−1.59646
$407$	13.9230	0.690135
$408$	2.49007	0.123277
$409$	−22.7868	−1.12674	−0.563368	−	0.826206i	$-0.690495\pi$
$409$	−22.7868	−1.12674	−0.563368	+	0.826206i	$0.690495\pi$
$410$	−7.09291	−0.350294
$411$	24.3309	1.20015
$412$	2.87078	0.141433
$413$	−15.7232	−0.773690
$414$	1.06457	0.0523209
$415$	−2.35743	−0.115722
$416$	−0.707447	−0.0346855
$417$	−19.8457	−0.971848
$418$	6.74670	0.329992
$419$	−6.04978	−0.295551	−0.147776	−	0.989021i	$-0.547211\pi$
$419$	−6.04978	−0.295551	−0.147776	+	0.989021i	$0.547211\pi$
$420$	9.26222	0.451950
$421$	−33.3435	−1.62506	−0.812531	−	0.582917i	$-0.801911\pi$
$421$	−33.3435	−1.62506	−0.812531	+	0.582917i	$0.801911\pi$
$422$	21.9817	1.07005
$423$	−6.41081	−0.311704
$424$	−2.68330	−0.130313
$425$	−3.97123	−0.192633
$426$	29.8836	1.44787
$427$	−34.3271	−1.66120
$428$	−12.9417	−0.625563
$429$	7.28151	0.351555
$430$	5.91117	0.285062
$431$	−21.0016	−1.01161	−0.505807	−	0.862647i	$-0.668805\pi$
$431$	−21.0016	−1.01161	−0.505807	+	0.862647i	$0.668805\pi$
$432$	4.48615	0.215840
$433$	−16.0873	−0.773106	−0.386553	−	0.922267i	$-0.626334\pi$
$433$	−16.0873	−0.773106	−0.386553	+	0.922267i	$0.626334\pi$
$434$	−11.4695	−0.550555
$435$	24.7624	1.18726
$436$	8.58800	0.411290
$437$	−2.04325	−0.0977421
$438$	13.7746	0.658178
$439$	9.20885	0.439515	0.219757	−	0.975555i	$-0.429473\pi$
$439$	9.20885	0.439515	0.219757	+	0.975555i	$0.429473\pi$
$440$	−7.52410	−0.358697
$441$	3.28458	0.156409
$442$	−0.921719	−0.0438417
$443$	14.3123	0.679997	0.339999	−	0.940426i	$-0.389573\pi$
$443$	14.3123	0.679997	0.339999	+	0.940426i	$0.389573\pi$
$444$	4.94106	0.234492
$445$	−20.4071	−0.967391
$446$	11.3740	0.538576
$447$	23.1265	1.09384
$448$	3.46874	0.163883
$449$	−5.34142	−0.252077	−0.126039	−	0.992025i	$-0.540226\pi$
$449$	−5.34142	−0.252077	−0.126039	+	0.992025i	$0.540226\pi$
$450$	1.98951	0.0937864
$451$	27.3406	1.28742
$452$	6.36794	0.299523
$453$	−4.11982	−0.193566
$454$	−4.39704	−0.206363
$455$	−3.42848	−0.160729
$456$	2.39431	0.112124
$457$	−35.0989	−1.64186	−0.820928	−	0.571031i	$-0.806543\pi$
$457$	−35.0989	−1.64186	−0.820928	+	0.571031i	$0.806543\pi$
$458$	−0.737047	−0.0344400
$459$	5.84491	0.272817
$460$	2.27869	0.106245
$461$	−26.7673	−1.24668	−0.623339	−	0.781952i	$-0.714224\pi$
$461$	−26.7673	−1.24668	−0.623339	+	0.781952i	$0.714224\pi$
$462$	−35.7026	−1.66103
$463$	27.9389	1.29843	0.649216	−	0.760604i	$-0.275097\pi$
$463$	27.9389	1.29843	0.649216	+	0.760604i	$0.275097\pi$
$464$	9.27361	0.430516
$465$	8.82910	0.409440
$466$	29.1104	1.34851
$467$	14.7050	0.680467	0.340234	−	0.940341i	$-0.389494\pi$
$467$	14.7050	0.680467	0.340234	+	0.940341i	$0.389494\pi$
$468$	0.461763	0.0213450
$469$	−24.7032	−1.14069
$470$	−13.7222	−0.632957
$471$	−11.4939	−0.529611
$472$	4.53284	0.208641
$473$	−22.7855	−1.04768
$474$	24.8221	1.14012
$475$	−3.81850	−0.175205
$476$	4.51935	0.207144
$477$	1.75144	0.0801927
$478$	13.9227	0.636809
$479$	10.0084	0.457296	0.228648	−	0.973509i	$-0.426570\pi$
$479$	10.0084	0.457296	0.228648	+	0.973509i	$0.426570\pi$
$480$	−2.67020	−0.121877
$481$	−1.82897	−0.0833938
$482$	−15.9988	−0.728726
$483$	10.8126	0.491991
$484$	18.0027	0.818305
$485$	6.46318	0.293478
$486$	−6.67062	−0.302586
$487$	33.7144	1.52775	0.763873	−	0.645366i	$-0.223295\pi$
$487$	33.7144	1.52775	0.763873	+	0.645366i	$0.223295\pi$
$488$	9.89612	0.447976
$489$	36.9921	1.67284
$490$	7.03057	0.317609
$491$	−5.61119	−0.253230	−0.126615	−	0.991952i	$-0.540411\pi$
$491$	−5.61119	−0.253230	−0.126615	+	0.991952i	$0.540411\pi$
$492$	9.70281	0.437436
$493$	12.0824	0.544164
$494$	−0.886271	−0.0398752
$495$	4.91111	0.220738
$496$	3.30654	0.148468
$497$	54.2372	2.43287
$498$	3.22487	0.144510
$499$	−16.7330	−0.749072	−0.374536	−	0.927212i	$-0.622198\pi$
$499$	−16.7330	−0.749072	−0.374536	+	0.927212i	$0.622198\pi$
$500$	11.2441	0.502852
$501$	−33.7588	−1.50823
$502$	24.5132	1.09408
$503$	20.8072	0.927746	0.463873	−	0.885902i	$-0.346459\pi$
$503$	20.8072	0.927746	0.463873	+	0.885902i	$0.346459\pi$
$504$	−2.26411	−0.100851
$505$	26.1289	1.16272
$506$	−8.78354	−0.390476
$507$	23.8892	1.06096
$508$	11.5882	0.514144
$509$	−17.7056	−0.784786	−0.392393	−	0.919798i	$-0.628353\pi$
$509$	−17.7056	−0.784786	−0.392393	+	0.919798i	$0.628353\pi$
$510$	−3.47894	−0.154050
$511$	25.0002	1.10595
$512$	−1.00000	−0.0441942
$513$	5.62012	0.248134
$514$	5.56235	0.245345
$515$	−4.01084	−0.176739
$516$	−8.08624	−0.355977
$517$	52.8941	2.32628
$518$	8.96776	0.394021
$519$	35.7532	1.56939
$520$	0.988392	0.0433439
$521$	−2.08100	−0.0911702	−0.0455851	−	0.998960i	$-0.514515\pi$
$521$	−2.08100	−0.0911702	−0.0455851	+	0.998960i	$0.514515\pi$
$522$	−6.05305	−0.264935
$523$	25.0270	1.09436	0.547178	−	0.837016i	$-0.315702\pi$
$523$	25.0270	1.09436	0.547178	+	0.837016i	$0.315702\pi$
$524$	12.7769	0.558159
$525$	20.2070	0.881904
$526$	−29.4620	−1.28460
$527$	4.30802	0.187660
$528$	10.2927	0.447930
$529$	−20.3399	−0.884343
$530$	3.74890	0.162842
$531$	−2.95866	−0.128395
$532$	4.34554	0.188403
$533$	−3.59156	−0.155568
$534$	27.9161	1.20805
$535$	18.0812	0.781720
$536$	7.12165	0.307609
$537$	44.1408	1.90481
$538$	−0.299339	−0.0129054
$539$	−27.1003	−1.16729
$540$	−6.26770	−0.269719
$541$	−39.4401	−1.69566	−0.847831	−	0.530266i	$-0.822092\pi$
$541$	−39.4401	−1.69566	−0.847831	+	0.530266i	$0.822092\pi$
$542$	−29.9220	−1.28526
$543$	−41.8137	−1.79440
$544$	−1.30288	−0.0558605
$545$	−11.9985	−0.513959
$546$	4.69001	0.200714
$547$	7.09834	0.303503	0.151752	−	0.988419i	$-0.451509\pi$
$547$	7.09834	0.303503	0.151752	+	0.988419i	$0.451509\pi$
$548$	−12.7306	−0.543825
$549$	−6.45937	−0.275679
$550$	−16.4150	−0.699937
$551$	11.6177	0.494932
$552$	−3.11715	−0.132675
$553$	45.0508	1.91575
$554$	13.6109	0.578273
$555$	−6.90327	−0.293028
$556$	10.3838	0.440373
$557$	40.0389	1.69650	0.848251	−	0.529594i	$-0.177656\pi$
$557$	40.0389	1.69650	0.848251	+	0.529594i	$0.177656\pi$
$558$	−2.15823	−0.0913653
$559$	2.99318	0.126598
$560$	−4.84626	−0.204792
$561$	13.4101	0.566174
$562$	20.9957	0.885648
$563$	−3.48487	−0.146870	−0.0734348	−	0.997300i	$-0.523396\pi$
$563$	−3.48487	−0.146870	−0.0734348	+	0.997300i	$0.523396\pi$
$564$	18.7714	0.790417
$565$	−8.89681	−0.374291
$566$	29.0276	1.22012
$567$	−36.5332	−1.53425
$568$	−15.6360	−0.656072
$569$	−28.4361	−1.19210	−0.596052	−	0.802946i	$-0.703265\pi$
$569$	−28.4361	−1.19210	−0.596052	+	0.802946i	$0.703265\pi$
$570$	−3.34515	−0.140113
$571$	7.61716	0.318768	0.159384	−	0.987217i	$-0.449049\pi$
$571$	7.61716	0.318768	0.159384	+	0.987217i	$0.449049\pi$
$572$	−3.80990	−0.159300
$573$	36.3864	1.52006
$574$	17.6101	0.735030
$575$	4.97132	0.207318
$576$	0.652717	0.0271966
$577$	−24.5812	−1.02333	−0.511664	−	0.859185i	$-0.670971\pi$
$577$	−24.5812	−1.02333	−0.511664	+	0.859185i	$0.670971\pi$
$578$	15.3025	0.636500
$579$	−37.9279	−1.57623
$580$	−12.9564	−0.537985
$581$	5.85297	0.242822
$582$	−8.84137	−0.366487
$583$	−14.4507	−0.598486
$584$	−7.20729	−0.298240
$585$	−0.645140	−0.0266733
$586$	7.17957	0.296585
$587$	34.1297	1.40869	0.704343	−	0.709860i	$-0.251242\pi$
$587$	34.1297	1.40869	0.704343	+	0.709860i	$0.251242\pi$
$588$	−9.61752	−0.396620
$589$	4.14234	0.170682
$590$	−6.33294	−0.260723
$591$	19.8520	0.816603
$592$	−2.58531	−0.106255
$593$	−30.8247	−1.26582	−0.632909	−	0.774226i	$-0.718139\pi$
$593$	−30.8247	−1.26582	−0.632909	+	0.774226i	$0.718139\pi$
$594$	24.1598	0.991287
$595$	−6.31410	−0.258853
$596$	−12.1004	−0.495653
$597$	53.5719	2.19255
$598$	1.15384	0.0471839
$599$	40.4684	1.65349	0.826746	−	0.562575i	$-0.190189\pi$
$599$	40.4684	1.65349	0.826746	+	0.562575i	$0.190189\pi$
$600$	−5.82545	−0.237823
$601$	−34.6124	−1.41187	−0.705934	−	0.708277i	$-0.749473\pi$
$601$	−34.6124	−1.41187	−0.705934	+	0.708277i	$0.749473\pi$
$602$	−14.6761	−0.598153
$603$	−4.64843	−0.189299
$604$	2.15561	0.0877105
$605$	−25.1520	−1.02258
$606$	−35.7433	−1.45197
$607$	−11.4552	−0.464951	−0.232475	−	0.972602i	$-0.574683\pi$
$607$	−11.4552	−0.464951	−0.232475	+	0.972602i	$0.574683\pi$
$608$	−1.25277	−0.0508066
$609$	−61.4793	−2.49127
$610$	−13.8261	−0.559803
$611$	−6.94835	−0.281100
$612$	0.850412	0.0343759
$613$	22.3551	0.902912	0.451456	−	0.892293i	$-0.350905\pi$
$613$	22.3551	0.902912	0.451456	+	0.892293i	$0.350905\pi$
$614$	21.9860	0.887284
$615$	−13.5560	−0.546632
$616$	18.6806	0.752664
$617$	25.8788	1.04184	0.520921	−	0.853605i	$-0.325589\pi$
$617$	25.8788	1.04184	0.520921	+	0.853605i	$0.325589\pi$
$618$	5.48666	0.220706
$619$	−1.20842	−0.0485705	−0.0242853	−	0.999705i	$-0.507731\pi$
$619$	−1.20842	−0.0485705	−0.0242853	+	0.999705i	$0.507731\pi$
$620$	−4.61964	−0.185529
$621$	−7.31684	−0.293615
$622$	6.43014	0.257825
$623$	50.6663	2.02990
$624$	−1.35208	−0.0541265
$625$	−0.469214	−0.0187686
$626$	−7.21113	−0.288215
$627$	12.8944	0.514951
$628$	6.01394	0.239982
$629$	−3.36834	−0.134305
$630$	3.16324	0.126027
$631$	4.80816	0.191410	0.0957049	−	0.995410i	$-0.469489\pi$
$631$	4.80816	0.191410	0.0957049	+	0.995410i	$0.469489\pi$
$632$	−12.9876	−0.516621
$633$	42.0116	1.66981
$634$	17.4497	0.693015
$635$	−16.1902	−0.642488
$636$	−5.12834	−0.203352
$637$	3.55999	0.141052
$638$	49.9422	1.97723
$639$	10.2059	0.403739
$640$	1.39712	0.0552262
$641$	35.8358	1.41543	0.707715	−	0.706498i	$-0.249726\pi$
$641$	35.8358	1.41543	0.707715	+	0.706498i	$0.249726\pi$
$642$	−24.7344	−0.976188
$643$	−8.58870	−0.338705	−0.169353	−	0.985556i	$-0.554168\pi$
$643$	−8.58870	−0.338705	−0.169353	+	0.985556i	$0.554168\pi$
$644$	−5.65747	−0.222936
$645$	11.2975	0.444838
$646$	−1.63221	−0.0642185
$647$	−7.05683	−0.277433	−0.138716	−	0.990332i	$-0.544298\pi$
$647$	−7.05683	−0.277433	−0.138716	+	0.990332i	$0.544298\pi$
$648$	10.5321	0.413740
$649$	24.4112	0.958224
$650$	2.15633	0.0845782
$651$	−21.9207	−0.859138
$652$	−19.3553	−0.758013
$653$	−15.4677	−0.605296	−0.302648	−	0.953102i	$-0.597871\pi$
$653$	−15.4677	−0.605296	−0.302648	+	0.953102i	$0.597871\pi$
$654$	16.4135	0.641817
$655$	−17.8509	−0.697490
$656$	−5.07679	−0.198215
$657$	4.70433	0.183533
$658$	34.0690	1.32815
$659$	−9.78593	−0.381206	−0.190603	−	0.981667i	$-0.561044\pi$
$659$	−9.78593	−0.381206	−0.190603	+	0.981667i	$0.561044\pi$
$660$	−14.3801	−0.559745
$661$	−13.9810	−0.543799	−0.271899	−	0.962326i	$-0.587652\pi$
$661$	−13.9810	−0.543799	−0.271899	+	0.962326i	$0.587652\pi$
$662$	−6.76232	−0.262825
$663$	−1.76160	−0.0684147
$664$	−1.68735	−0.0654818
$665$	−6.07127	−0.235434
$666$	1.68747	0.0653883
$667$	−15.1251	−0.585647
$668$	17.6636	0.683425
$669$	21.7381	0.840445
$670$	−9.94984	−0.384396
$671$	53.2947	2.05742
$672$	6.62949	0.255738
$673$	18.4026	0.709369	0.354684	−	0.934986i	$-0.384588\pi$
$673$	18.4026	0.709369	0.354684	+	0.934986i	$0.384588\pi$
$674$	−3.88491	−0.149641
$675$	−13.6740	−0.526311
$676$	−12.4995	−0.480751
$677$	21.9176	0.842362	0.421181	−	0.906977i	$-0.361616\pi$
$677$	21.9176	0.842362	0.421181	+	0.906977i	$0.361616\pi$
$678$	12.1705	0.467404
$679$	−16.0466	−0.615813
$680$	1.82028	0.0698047
$681$	−8.40366	−0.322029
$682$	17.8071	0.681868
$683$	−44.9468	−1.71984	−0.859920	−	0.510429i	$-0.829487\pi$
$683$	−44.9468	−1.71984	−0.859920	+	0.510429i	$0.829487\pi$
$684$	0.817706	0.0312658
$685$	17.7863	0.679578
$686$	6.82590	0.260614
$687$	−1.40865	−0.0537434
$688$	4.23096	0.161304
$689$	1.89829	0.0723192
$690$	4.35505	0.165794
$691$	−40.4328	−1.53814	−0.769068	−	0.639166i	$-0.779279\pi$
$691$	−40.4328	−1.53814	−0.769068	+	0.639166i	$0.779279\pi$
$692$	−18.7071	−0.711139
$693$	−12.1932	−0.463180
$694$	−22.6570	−0.860048
$695$	−14.5075	−0.550302
$696$	17.7238	0.671819
$697$	−6.61445	−0.250540
$698$	14.3862	0.544525
$699$	55.6360	2.10435
$700$	−10.5729	−0.399617
$701$	−13.6798	−0.516681	−0.258340	−	0.966054i	$-0.583176\pi$
$701$	−13.6798	−0.516681	−0.258340	+	0.966054i	$0.583176\pi$
$702$	−3.17371	−0.119784
$703$	−3.23880	−0.122154
$704$	−5.38542	−0.202971
$705$	−26.2259	−0.987726
$706$	31.0634	1.16909
$707$	−64.8721	−2.43977
$708$	8.66319	0.325583
$709$	−9.89624	−0.371661	−0.185830	−	0.982582i	$-0.559498\pi$
$709$	−9.89624	−0.371661	−0.185830	+	0.982582i	$0.559498\pi$
$710$	21.8454	0.819844
$711$	8.47726	0.317922
$712$	−14.6065	−0.547403
$713$	−5.39292	−0.201966
$714$	8.63743	0.323248
$715$	5.32290	0.199065
$716$	−23.0957	−0.863128
$717$	26.6092	0.993738
$718$	7.74628	0.289089
$719$	16.1669	0.602925	0.301462	−	0.953478i	$-0.402525\pi$
$719$	16.1669	0.602925	0.301462	+	0.953478i	$0.402525\pi$
$720$	−0.911927	−0.0339855
$721$	9.95799	0.370855
$722$	17.4306	0.648698
$723$	−30.5771	−1.13717
$724$	21.8782	0.813096
$725$	−28.2664	−1.04979
$726$	34.4069	1.27696
$727$	10.9898	0.407588	0.203794	−	0.979014i	$-0.434673\pi$
$727$	10.9898	0.407588	0.203794	+	0.979014i	$0.434673\pi$
$728$	−2.45395	−0.0909495
$729$	18.8474	0.698051
$730$	10.0695	0.372688
$731$	5.51243	0.203884
$732$	18.9135	0.699065
$733$	−46.6820	−1.72424	−0.862120	−	0.506704i	$-0.830864\pi$
$733$	−46.6820	−1.72424	−0.862120	+	0.506704i	$0.830864\pi$
$734$	−3.81909	−0.140965
$735$	13.4369	0.495627
$736$	1.63099	0.0601190
$737$	38.3531	1.41275
$738$	3.31371	0.121979
$739$	−8.70226	−0.320118	−0.160059	−	0.987107i	$-0.551168\pi$
$739$	−8.70226	−0.320118	−0.160059	+	0.987107i	$0.551168\pi$
$740$	3.61199	0.132780
$741$	−1.69385	−0.0622250
$742$	−9.30767	−0.341695
$743$	−32.6614	−1.19823	−0.599115	−	0.800663i	$-0.704481\pi$
$743$	−32.6614	−1.19823	−0.599115	+	0.800663i	$0.704481\pi$
$744$	6.31948	0.231683
$745$	16.9058	0.619381
$746$	−26.7451	−0.979206
$747$	1.10136	0.0402967
$748$	−7.01655	−0.256550
$749$	−44.8916	−1.64030
$750$	21.4899	0.784698
$751$	−12.5661	−0.458544	−0.229272	−	0.973362i	$-0.573634\pi$
$751$	−12.5661	−0.458544	−0.229272	+	0.973362i	$0.573634\pi$
$752$	−9.82173	−0.358161
$753$	46.8498	1.70730
$754$	−6.56059	−0.238923
$755$	−3.01165	−0.109605
$756$	15.5613	0.565958
$757$	−27.4350	−0.997140	−0.498570	−	0.866849i	$-0.666141\pi$
$757$	−27.4350	−0.997140	−0.498570	+	0.866849i	$0.666141\pi$
$758$	−0.580027	−0.0210675
$759$	−16.7872	−0.609336
$760$	1.75028	0.0634893
$761$	2.93358	0.106342	0.0531712	−	0.998585i	$-0.483067\pi$
$761$	2.93358	0.106342	0.0531712	+	0.998585i	$0.483067\pi$
$762$	22.1475	0.802320
$763$	29.7895	1.07845
$764$	−19.0384	−0.688787
$765$	−1.18813	−0.0429570
$766$	−12.4377	−0.449392
$767$	−3.20674	−0.115789
$768$	−1.91121	−0.0689648
$769$	−45.4125	−1.63762	−0.818808	−	0.574067i	$-0.805365\pi$
$769$	−45.4125	−1.63762	−0.818808	+	0.574067i	$0.805365\pi$
$770$	−26.0991	−0.940548
$771$	10.6308	0.382859
$772$	19.8450	0.714237
$773$	16.9877	0.611004	0.305502	−	0.952191i	$-0.401176\pi$
$773$	16.9877	0.611004	0.305502	+	0.952191i	$0.401176\pi$
$774$	−2.76162	−0.0992643
$775$	−10.0785	−0.362029
$776$	4.62606	0.166066
$777$	17.1393	0.614867
$778$	−1.38667	−0.0497146
$779$	−6.36006	−0.227873
$780$	1.88902	0.0676379
$781$	−84.2063	−3.01314
$782$	2.12498	0.0759891
$783$	41.6028	1.48676
$784$	5.03217	0.179720
$785$	−8.40223	−0.299888
$786$	24.4192	0.871005
$787$	−46.6616	−1.66331	−0.831653	−	0.555295i	$-0.812605\pi$
$787$	−46.6616	−1.66331	−0.831653	+	0.555295i	$0.812605\pi$
$788$	−10.3872	−0.370027
$789$	−56.3080	−2.00462
$790$	18.1454	0.645583
$791$	22.0887	0.785385
$792$	3.51515	0.124906
$793$	−7.00098	−0.248612
$794$	−15.5049	−0.550247
$795$	7.16493	0.254114
$796$	−28.0304	−0.993511
$797$	23.4976	0.832329	0.416165	−	0.909289i	$-0.363374\pi$
$797$	23.4976	0.832329	0.416165	+	0.909289i	$0.363374\pi$
$798$	8.30524	0.294002
$799$	−12.7965	−0.452709
$800$	3.04804	0.107765
$801$	9.53394	0.336865
$802$	6.49569	0.229371
$803$	−38.8143	−1.36973
$804$	13.6110	0.480022
$805$	7.90419	0.278586
$806$	−2.33920	−0.0823948
$807$	−0.572099	−0.0201388
$808$	18.7019	0.657931
$809$	12.5746	0.442098	0.221049	−	0.975263i	$-0.429052\pi$
$809$	12.5746	0.442098	0.221049	+	0.975263i	$0.429052\pi$
$810$	−14.7147	−0.517021
$811$	−12.4741	−0.438025	−0.219013	−	0.975722i	$-0.570284\pi$
$811$	−12.4741	−0.438025	−0.219013	+	0.975722i	$0.570284\pi$
$812$	32.1678	1.12887
$813$	−57.1872	−2.00564
$814$	−13.9230	−0.487999
$815$	27.0418	0.947233
$816$	−2.49007	−0.0871700
$817$	5.30043	0.185438
$818$	22.7868	0.796723
$819$	1.60174	0.0559692
$820$	7.09291	0.247695
$821$	26.2145	0.914893	0.457446	−	0.889237i	$-0.348764\pi$
$821$	26.2145	0.914893	0.457446	+	0.889237i	$0.348764\pi$
$822$	−24.3309	−0.848636
$823$	−6.03310	−0.210301	−0.105150	−	0.994456i	$-0.533532\pi$
$823$	−6.03310	−0.210301	−0.105150	+	0.994456i	$0.533532\pi$
$824$	−2.87078	−0.100008
$825$	−31.3725	−1.09225
$826$	15.7232	0.547081
$827$	30.4989	1.06055	0.530276	−	0.847825i	$-0.322088\pi$
$827$	30.4989	1.06055	0.530276	+	0.847825i	$0.322088\pi$
$828$	−1.06457	−0.0369965
$829$	−39.5946	−1.37518	−0.687589	−	0.726100i	$-0.741331\pi$
$829$	−39.5946	−1.37518	−0.687589	+	0.726100i	$0.741331\pi$
$830$	2.35743	0.0818277
$831$	26.0133	0.902393
$832$	0.707447	0.0245263
$833$	6.55631	0.227163
$834$	19.8457	0.687200
$835$	−24.6782	−0.854025
$836$	−6.74670	−0.233340
$837$	14.8336	0.512725
$838$	6.04978	0.208986
$839$	37.2213	1.28502	0.642511	−	0.766276i	$-0.277893\pi$
$839$	37.2213	1.28502	0.642511	+	0.766276i	$0.277893\pi$
$840$	−9.26222	−0.319577
$841$	56.9998	1.96551
$842$	33.3435	1.14909
$843$	40.1271	1.38205
$844$	−21.9817	−0.756642
$845$	17.4634	0.600759
$846$	6.41081	0.220408
$847$	62.4467	2.14570
$848$	2.68330	0.0921449
$849$	55.4778	1.90399
$850$	3.97123	0.136212
$851$	4.21660	0.144543
$852$	−29.8836	−1.02380
$853$	−38.3368	−1.31263	−0.656314	−	0.754488i	$-0.727885\pi$
$853$	−38.3368	−1.31263	−0.656314	+	0.754488i	$0.727885\pi$
$854$	34.3271	1.17465
$855$	−1.14244	−0.0390705
$856$	12.9417	0.442340
$857$	−19.0032	−0.649138	−0.324569	−	0.945862i	$-0.605219\pi$
$857$	−19.0032	−0.649138	−0.324569	+	0.945862i	$0.605219\pi$
$858$	−7.28151	−0.248587
$859$	−38.9152	−1.32777	−0.663885	−	0.747835i	$-0.731093\pi$
$859$	−38.9152	−1.32777	−0.663885	+	0.747835i	$0.731093\pi$
$860$	−5.91117	−0.201569
$861$	33.6565	1.14701
$862$	21.0016	0.715319
$863$	43.3681	1.47627	0.738133	−	0.674655i	$-0.235708\pi$
$863$	43.3681	1.47627	0.738133	+	0.674655i	$0.235708\pi$
$864$	−4.48615	−0.152622
$865$	26.1362	0.888658
$866$	16.0873	0.546668
$867$	29.2463	0.993256
$868$	11.4695	0.389301
$869$	−69.9439	−2.37268
$870$	−24.7624	−0.839522
$871$	−5.03819	−0.170713
$872$	−8.58800	−0.290826
$873$	−3.01951	−0.102195
$874$	2.04325	0.0691141
$875$	39.0029	1.31854
$876$	−13.7746	−0.465402
$877$	−25.1145	−0.848055	−0.424028	−	0.905649i	$-0.639384\pi$
$877$	−25.1145	−0.848055	−0.424028	+	0.905649i	$0.639384\pi$
$878$	−9.20885	−0.310784
$879$	13.7216	0.462820
$880$	7.52410	0.253637
$881$	−6.81968	−0.229761	−0.114880	−	0.993379i	$-0.536648\pi$
$881$	−6.81968	−0.229761	−0.114880	+	0.993379i	$0.536648\pi$
$882$	−3.28458	−0.110598
$883$	33.9324	1.14192	0.570958	−	0.820979i	$-0.306572\pi$
$883$	33.9324	1.14192	0.570958	+	0.820979i	$0.306572\pi$
$884$	0.921719	0.0310008
$885$	−12.1036	−0.406857
$886$	−14.3123	−0.480831
$887$	−16.2336	−0.545073	−0.272536	−	0.962145i	$-0.587862\pi$
$887$	−16.2336	−0.545073	−0.272536	+	0.962145i	$0.587862\pi$
$888$	−4.94106	−0.165811
$889$	40.1966	1.34815
$890$	20.4071	0.684049
$891$	56.7198	1.90019
$892$	−11.3740	−0.380830
$893$	−12.3044	−0.411751
$894$	−23.1265	−0.773464
$895$	32.2676	1.07859
$896$	−3.46874	−0.115883
$897$	2.20522	0.0736302
$898$	5.34142	0.178246
$899$	30.6635	1.02269
$900$	−1.98951	−0.0663170
$901$	3.49602	0.116469
$902$	−27.3406	−0.910344
$903$	−28.0491	−0.933415
$904$	−6.36794	−0.211795
$905$	−30.5665	−1.01607
$906$	4.11982	0.136872
$907$	−49.3429	−1.63841	−0.819203	−	0.573504i	$-0.805584\pi$
$907$	−49.3429	−1.63841	−0.819203	+	0.573504i	$0.805584\pi$
$908$	4.39704	0.145921
$909$	−12.2071	−0.404883
$910$	3.42848	0.113653
$911$	42.7550	1.41654	0.708268	−	0.705944i	$-0.249477\pi$
$911$	42.7550	1.41654	0.708268	+	0.705944i	$0.249477\pi$
$912$	−2.39431	−0.0792835
$913$	−9.08706	−0.300738
$914$	35.0989	1.16097
$915$	−26.4246	−0.873570
$916$	0.737047	0.0243527
$917$	44.3196	1.46356
$918$	−5.84491	−0.192911
$919$	31.5375	1.04033	0.520164	−	0.854067i	$-0.325871\pi$
$919$	31.5375	1.04033	0.520164	+	0.854067i	$0.325871\pi$
$920$	−2.27869	−0.0751262
$921$	42.0199	1.38460
$922$	26.7673	0.881534
$923$	11.0616	0.364098
$924$	35.7026	1.17453
$925$	7.88013	0.259097
$926$	−27.9389	−0.918131
$927$	1.87381	0.0615439
$928$	−9.27361	−0.304421
$929$	23.1958	0.761030	0.380515	−	0.924775i	$-0.375747\pi$
$929$	23.1958	0.761030	0.380515	+	0.924775i	$0.375747\pi$
$930$	−8.82910	−0.289518
$931$	6.30416	0.206611
$932$	−29.1104	−0.953543
$933$	12.2893	0.402335
$934$	−14.7050	−0.481163
$935$	9.80299	0.320592
$936$	−0.461763	−0.0150932
$937$	−17.5749	−0.574148	−0.287074	−	0.957908i	$-0.592683\pi$
$937$	−17.5749	−0.574148	−0.287074	+	0.957908i	$0.592683\pi$
$938$	24.7032	0.806587
$939$	−13.7820	−0.449758
$940$	13.7222	0.447568
$941$	5.79800	0.189009	0.0945047	−	0.995524i	$-0.469873\pi$
$941$	5.79800	0.189009	0.0945047	+	0.995524i	$0.469873\pi$
$942$	11.4939	0.374491
$943$	8.28018	0.269640
$944$	−4.53284	−0.147531
$945$	−21.7410	−0.707236
$946$	22.7855	0.740819
$947$	−44.2098	−1.43662	−0.718312	−	0.695721i	$-0.755085\pi$
$947$	−44.2098	−1.43662	−0.718312	+	0.695721i	$0.755085\pi$
$948$	−24.8221	−0.806184
$949$	5.09878	0.165513
$950$	3.81850	0.123889
$951$	33.3499	1.08145
$952$	−4.51935	−0.146473
$953$	−23.0960	−0.748153	−0.374077	−	0.927398i	$-0.622040\pi$
$953$	−23.0960	−0.748153	−0.374077	+	0.927398i	$0.622040\pi$
$954$	−1.75144	−0.0567048
$955$	26.5991	0.860726
$956$	−13.9227	−0.450292
$957$	95.4500	3.08546
$958$	−10.0084	−0.323357
$959$	−44.1592	−1.42598
$960$	2.67020	0.0861802
$961$	−20.0668	−0.647316
$962$	1.82897	0.0589683
$963$	−8.44730	−0.272211
$964$	15.9988	0.515287
$965$	−27.7259	−0.892529
$966$	−10.8126	−0.347890
$967$	14.4469	0.464581	0.232291	−	0.972646i	$-0.425378\pi$
$967$	14.4469	0.464581	0.232291	+	0.972646i	$0.425378\pi$
$968$	−18.0027	−0.578629
$969$	−3.11950	−0.100213
$970$	−6.46318	−0.207520
$971$	32.0479	1.02847	0.514233	−	0.857650i	$-0.328077\pi$
$971$	32.0479	1.02847	0.514233	+	0.857650i	$0.328077\pi$
$972$	6.67062	0.213960
$973$	36.0189	1.15471
$974$	−33.7144	−1.08028
$975$	4.12120	0.131984
$976$	−9.89612	−0.316767
$977$	58.6860	1.87753	0.938766	−	0.344555i	$-0.111970\pi$
$977$	58.6860	1.87753	0.938766	+	0.344555i	$0.111970\pi$
$978$	−36.9921	−1.18288
$979$	−78.6623	−2.51406
$980$	−7.03057	−0.224583
$981$	5.60553	0.178971
$982$	5.61119	0.179060
$983$	11.6451	0.371421	0.185711	−	0.982604i	$-0.440541\pi$
$983$	11.6451	0.371421	0.185711	+	0.982604i	$0.440541\pi$
$984$	−9.70281	−0.309314
$985$	14.5121	0.462395
$986$	−12.0824	−0.384782
$987$	65.1130	2.07257
$988$	0.886271	0.0281960
$989$	−6.90063	−0.219427
$990$	−4.91111	−0.156085
$991$	−7.52094	−0.238910	−0.119455	−	0.992840i	$-0.538115\pi$
$991$	−7.52094	−0.238910	−0.119455	+	0.992840i	$0.538115\pi$
$992$	−3.30654	−0.104983
$993$	−12.9242	−0.410137
$994$	−54.2372	−1.72030
$995$	39.1620	1.24152
$996$	−3.22487	−0.102184
$997$	29.6352	0.938555	0.469277	−	0.883051i	$-0.344514\pi$
$997$	29.6352	0.938555	0.469277	+	0.883051i	$0.344514\pi$
$998$	16.7330	0.529674
$999$	−11.5981	−0.366946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.9	✓	40	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.91121 q^{3} +1.00000 q^{4} -1.39712 q^{5} +1.91121 q^{6} +3.46874 q^{7} -1.00000 q^{8} +0.652717 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.91121 q^{3} +1.00000 q^{4} -1.39712 q^{5} +1.91121 q^{6} +3.46874 q^{7} -1.00000 q^{8} +0.652717 q^{9} +1.39712 q^{10} -5.38542 q^{11} -1.91121 q^{12} +0.707447 q^{13} -3.46874 q^{14} +2.67020 q^{15} +1.00000 q^{16} +1.30288 q^{17} -0.652717 q^{18} +1.25277 q^{19} -1.39712 q^{20} -6.62949 q^{21} +5.38542 q^{22} -1.63099 q^{23} +1.91121 q^{24} -3.04804 q^{25} -0.707447 q^{26} +4.48615 q^{27} +3.46874 q^{28} +9.27361 q^{29} -2.67020 q^{30} +3.30654 q^{31} -1.00000 q^{32} +10.2927 q^{33} -1.30288 q^{34} -4.84626 q^{35} +0.652717 q^{36} -2.58531 q^{37} -1.25277 q^{38} -1.35208 q^{39} +1.39712 q^{40} -5.07679 q^{41} +6.62949 q^{42} +4.23096 q^{43} -5.38542 q^{44} -0.911927 q^{45} +1.63099 q^{46} -9.82173 q^{47} -1.91121 q^{48} +5.03217 q^{49} +3.04804 q^{50} -2.49007 q^{51} +0.707447 q^{52} +2.68330 q^{53} -4.48615 q^{54} +7.52410 q^{55} -3.46874 q^{56} -2.39431 q^{57} -9.27361 q^{58} -4.53284 q^{59} +2.67020 q^{60} -9.89612 q^{61} -3.30654 q^{62} +2.26411 q^{63} +1.00000 q^{64} -0.988392 q^{65} -10.2927 q^{66} -7.12165 q^{67} +1.30288 q^{68} +3.11715 q^{69} +4.84626 q^{70} +15.6360 q^{71} -0.652717 q^{72} +7.20729 q^{73} +2.58531 q^{74} +5.82545 q^{75} +1.25277 q^{76} -18.6806 q^{77} +1.35208 q^{78} +12.9876 q^{79} -1.39712 q^{80} -10.5321 q^{81} +5.07679 q^{82} +1.68735 q^{83} -6.62949 q^{84} -1.82028 q^{85} -4.23096 q^{86} -17.7238 q^{87} +5.38542 q^{88} +14.6065 q^{89} +0.911927 q^{90} +2.45395 q^{91} -1.63099 q^{92} -6.31948 q^{93} +9.82173 q^{94} -1.75028 q^{95} +1.91121 q^{96} -4.62606 q^{97} -5.03217 q^{98} -3.51515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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