LMFDB - Embedded newform 4006.2.a.g.1.3

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			1.3
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.96542 q^{3} +1.00000 q^{4} +0.539090 q^{5} +2.96542 q^{6} -0.220082 q^{7} -1.00000 q^{8} +5.79371 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.96542 q^{3} +1.00000 q^{4} +0.539090 q^{5} +2.96542 q^{6} -0.220082 q^{7} -1.00000 q^{8} +5.79371 q^{9} -0.539090 q^{10} +5.11019 q^{11} -2.96542 q^{12} -1.83998 q^{13} +0.220082 q^{14} -1.59863 q^{15} +1.00000 q^{16} +4.75454 q^{17} -5.79371 q^{18} -4.79891 q^{19} +0.539090 q^{20} +0.652635 q^{21} -5.11019 q^{22} +2.67550 q^{23} +2.96542 q^{24} -4.70938 q^{25} +1.83998 q^{26} -8.28451 q^{27} -0.220082 q^{28} -5.41969 q^{29} +1.59863 q^{30} -6.62830 q^{31} -1.00000 q^{32} -15.1538 q^{33} -4.75454 q^{34} -0.118644 q^{35} +5.79371 q^{36} -1.59451 q^{37} +4.79891 q^{38} +5.45632 q^{39} -0.539090 q^{40} -4.76330 q^{41} -0.652635 q^{42} +10.8795 q^{43} +5.11019 q^{44} +3.12333 q^{45} -2.67550 q^{46} +2.31041 q^{47} -2.96542 q^{48} -6.95156 q^{49} +4.70938 q^{50} -14.0992 q^{51} -1.83998 q^{52} +2.96006 q^{53} +8.28451 q^{54} +2.75485 q^{55} +0.220082 q^{56} +14.2308 q^{57} +5.41969 q^{58} -4.09203 q^{59} -1.59863 q^{60} -2.30748 q^{61} +6.62830 q^{62} -1.27509 q^{63} +1.00000 q^{64} -0.991915 q^{65} +15.1538 q^{66} +4.94120 q^{67} +4.75454 q^{68} -7.93397 q^{69} +0.118644 q^{70} +5.87372 q^{71} -5.79371 q^{72} -4.62683 q^{73} +1.59451 q^{74} +13.9653 q^{75} -4.79891 q^{76} -1.12466 q^{77} -5.45632 q^{78} -9.45252 q^{79} +0.539090 q^{80} +7.18592 q^{81} +4.76330 q^{82} +7.62420 q^{83} +0.652635 q^{84} +2.56313 q^{85} -10.8795 q^{86} +16.0716 q^{87} -5.11019 q^{88} +9.82531 q^{89} -3.12333 q^{90} +0.404946 q^{91} +2.67550 q^{92} +19.6557 q^{93} -2.31041 q^{94} -2.58704 q^{95} +2.96542 q^{96} -3.10555 q^{97} +6.95156 q^{98} +29.6069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.96542	−1.71209	−0.856043	−	0.516905i	$-0.827084\pi$
$3$	−2.96542	−1.71209	−0.856043	+	0.516905i	$0.827084\pi$
$4$	1.00000	0.500000
$5$	0.539090	0.241088	0.120544	−	0.992708i	$-0.461536\pi$
$5$	0.539090	0.241088	0.120544	+	0.992708i	$0.461536\pi$
$6$	2.96542	1.21063
$7$	−0.220082	−0.0831831	−0.0415915	−	0.999135i	$-0.513243\pi$
$7$	−0.220082	−0.0831831	−0.0415915	+	0.999135i	$0.513243\pi$
$8$	−1.00000	−0.353553
$9$	5.79371	1.93124
$10$	−0.539090	−0.170475
$11$	5.11019	1.54078	0.770390	−	0.637573i	$-0.220062\pi$
$11$	5.11019	1.54078	0.770390	+	0.637573i	$0.220062\pi$
$12$	−2.96542	−0.856043
$13$	−1.83998	−0.510319	−0.255160	−	0.966899i	$-0.582128\pi$
$13$	−1.83998	−0.510319	−0.255160	+	0.966899i	$0.582128\pi$
$14$	0.220082	0.0588193
$15$	−1.59863	−0.412764
$16$	1.00000	0.250000
$17$	4.75454	1.15315	0.576573	−	0.817046i	$-0.304390\pi$
$17$	4.75454	1.15315	0.576573	+	0.817046i	$0.304390\pi$
$18$	−5.79371	−1.36559
$19$	−4.79891	−1.10095	−0.550473	−	0.834853i	$-0.685552\pi$
$19$	−4.79891	−1.10095	−0.550473	+	0.834853i	$0.685552\pi$
$20$	0.539090	0.120544
$21$	0.652635	0.142417
$22$	−5.11019	−1.08950
$23$	2.67550	0.557880	0.278940	−	0.960309i	$-0.410017\pi$
$23$	2.67550	0.557880	0.278940	+	0.960309i	$0.410017\pi$
$24$	2.96542	0.605314
$25$	−4.70938	−0.941876
$26$	1.83998	0.360850
$27$	−8.28451	−1.59435
$28$	−0.220082	−0.0415915
$29$	−5.41969	−1.00641	−0.503206	−	0.864167i	$-0.667846\pi$
$29$	−5.41969	−1.00641	−0.503206	+	0.864167i	$0.667846\pi$
$30$	1.59863	0.291868
$31$	−6.62830	−1.19048	−0.595239	−	0.803549i	$-0.702943\pi$
$31$	−6.62830	−1.19048	−0.595239	+	0.803549i	$0.702943\pi$
$32$	−1.00000	−0.176777
$33$	−15.1538	−2.63795
$34$	−4.75454	−0.815398
$35$	−0.118644	−0.0200545
$36$	5.79371	0.965618
$37$	−1.59451	−0.262136	−0.131068	−	0.991373i	$-0.541841\pi$
$37$	−1.59451	−0.262136	−0.131068	+	0.991373i	$0.541841\pi$
$38$	4.79891	0.778486
$39$	5.45632	0.873710
$40$	−0.539090	−0.0852376
$41$	−4.76330	−0.743902	−0.371951	−	0.928252i	$-0.621311\pi$
$41$	−4.76330	−0.743902	−0.371951	+	0.928252i	$0.621311\pi$
$42$	−0.652635	−0.100704
$43$	10.8795	1.65911	0.829553	−	0.558429i	$-0.188596\pi$
$43$	10.8795	1.65911	0.829553	+	0.558429i	$0.188596\pi$
$44$	5.11019	0.770390
$45$	3.12333	0.465598
$46$	−2.67550	−0.394481
$47$	2.31041	0.337008	0.168504	−	0.985701i	$-0.446106\pi$
$47$	2.31041	0.337008	0.168504	+	0.985701i	$0.446106\pi$
$48$	−2.96542	−0.428021
$49$	−6.95156	−0.993081
$50$	4.70938	0.666007
$51$	−14.0992	−1.97428
$52$	−1.83998	−0.255160
$53$	2.96006	0.406596	0.203298	−	0.979117i	$-0.434834\pi$
$53$	2.96006	0.406596	0.203298	+	0.979117i	$0.434834\pi$
$54$	8.28451	1.12738
$55$	2.75485	0.371464
$56$	0.220082	0.0294097
$57$	14.2308	1.88491
$58$	5.41969	0.711640
$59$	−4.09203	−0.532737	−0.266369	−	0.963871i	$-0.585824\pi$
$59$	−4.09203	−0.532737	−0.266369	+	0.963871i	$0.585824\pi$
$60$	−1.59863	−0.206382
$61$	−2.30748	−0.295442	−0.147721	−	0.989029i	$-0.547194\pi$
$61$	−2.30748	−0.295442	−0.147721	+	0.989029i	$0.547194\pi$
$62$	6.62830	0.841795
$63$	−1.27509	−0.160646
$64$	1.00000	0.125000
$65$	−0.991915	−0.123032
$66$	15.1538	1.86531
$67$	4.94120	0.603664	0.301832	−	0.953361i	$-0.402402\pi$
$67$	4.94120	0.603664	0.301832	+	0.953361i	$0.402402\pi$
$68$	4.75454	0.576573
$69$	−7.93397	−0.955138
$70$	0.118644	0.0141806
$71$	5.87372	0.697082	0.348541	−	0.937293i	$-0.386677\pi$
$71$	5.87372	0.697082	0.348541	+	0.937293i	$0.386677\pi$
$72$	−5.79371	−0.682795
$73$	−4.62683	−0.541529	−0.270765	−	0.962646i	$-0.587276\pi$
$73$	−4.62683	−0.541529	−0.270765	+	0.962646i	$0.587276\pi$
$74$	1.59451	0.185358
$75$	13.9653	1.61257
$76$	−4.79891	−0.550473
$77$	−1.12466	−0.128167
$78$	−5.45632	−0.617806
$79$	−9.45252	−1.06349	−0.531746	−	0.846904i	$-0.678464\pi$
$79$	−9.45252	−1.06349	−0.531746	+	0.846904i	$0.678464\pi$
$80$	0.539090	0.0602721
$81$	7.18592	0.798435
$82$	4.76330	0.526018
$83$	7.62420	0.836865	0.418433	−	0.908248i	$-0.362580\pi$
$83$	7.62420	0.836865	0.418433	+	0.908248i	$0.362580\pi$
$84$	0.652635	0.0712083
$85$	2.56313	0.278010
$86$	−10.8795	−1.17316
$87$	16.0716	1.72306
$88$	−5.11019	−0.544748
$89$	9.82531	1.04148	0.520740	−	0.853715i	$-0.325656\pi$
$89$	9.82531	1.04148	0.520740	+	0.853715i	$0.325656\pi$
$90$	−3.12333	−0.329228
$91$	0.404946	0.0424499
$92$	2.67550	0.278940
$93$	19.6557	2.03820
$94$	−2.31041	−0.238301
$95$	−2.58704	−0.265425
$96$	2.96542	0.302657
$97$	−3.10555	−0.315321	−0.157660	−	0.987493i	$-0.550395\pi$
$97$	−3.10555	−0.315321	−0.157660	+	0.987493i	$0.550395\pi$
$98$	6.95156	0.702214
$99$	29.6069	2.97561
$100$	−4.70938	−0.470938
$101$	−7.86660	−0.782756	−0.391378	−	0.920230i	$-0.628002\pi$
$101$	−7.86660	−0.782756	−0.391378	+	0.920230i	$0.628002\pi$
$102$	14.0992	1.39603
$103$	9.82927	0.968507	0.484253	−	0.874928i	$-0.339091\pi$
$103$	9.82927	0.968507	0.484253	+	0.874928i	$0.339091\pi$
$104$	1.83998	0.180425
$105$	0.351829	0.0343350
$106$	−2.96006	−0.287507
$107$	−9.15461	−0.885009	−0.442505	−	0.896766i	$-0.645910\pi$
$107$	−9.15461	−0.885009	−0.442505	+	0.896766i	$0.645910\pi$
$108$	−8.28451	−0.797177
$109$	−5.20154	−0.498217	−0.249108	−	0.968476i	$-0.580138\pi$
$109$	−5.20154	−0.498217	−0.249108	+	0.968476i	$0.580138\pi$
$110$	−2.75485	−0.262665
$111$	4.72839	0.448799
$112$	−0.220082	−0.0207958
$113$	−10.1470	−0.954554	−0.477277	−	0.878753i	$-0.658376\pi$
$113$	−10.1470	−0.954554	−0.477277	+	0.878753i	$0.658376\pi$
$114$	−14.2308	−1.33283
$115$	1.44233	0.134498
$116$	−5.41969	−0.503206
$117$	−10.6603	−0.985547
$118$	4.09203	0.376702
$119$	−1.04639	−0.0959223
$120$	1.59863	0.145934
$121$	15.1140	1.37400
$122$	2.30748	0.208909
$123$	14.1252	1.27362
$124$	−6.62830	−0.595239
$125$	−5.23423	−0.468164
$126$	1.27509	0.113594
$127$	−8.05548	−0.714808	−0.357404	−	0.933950i	$-0.616338\pi$
$127$	−8.05548	−0.714808	−0.357404	+	0.933950i	$0.616338\pi$
$128$	−1.00000	−0.0883883
$129$	−32.2622	−2.84053
$130$	0.991915	0.0869967
$131$	5.25397	0.459041	0.229521	−	0.973304i	$-0.426284\pi$
$131$	5.25397	0.459041	0.229521	+	0.973304i	$0.426284\pi$
$132$	−15.1538	−1.31897
$133$	1.05615	0.0915800
$134$	−4.94120	−0.426855
$135$	−4.46609	−0.384380
$136$	−4.75454	−0.407699
$137$	4.67123	0.399090	0.199545	−	0.979889i	$-0.436054\pi$
$137$	4.67123	0.399090	0.199545	+	0.979889i	$0.436054\pi$
$138$	7.93397	0.675384
$139$	−11.9008	−1.00941	−0.504706	−	0.863291i	$-0.668399\pi$
$139$	−11.9008	−1.00941	−0.504706	+	0.863291i	$0.668399\pi$
$140$	−0.118644	−0.0100272
$141$	−6.85134	−0.576987
$142$	−5.87372	−0.492912
$143$	−9.40265	−0.786289
$144$	5.79371	0.482809
$145$	−2.92170	−0.242634
$146$	4.62683	0.382919
$147$	20.6143	1.70024
$148$	−1.59451	−0.131068
$149$	15.6554	1.28254	0.641272	−	0.767314i	$-0.278407\pi$
$149$	15.6554	1.28254	0.641272	+	0.767314i	$0.278407\pi$
$150$	−13.9653	−1.14026
$151$	16.0723	1.30795	0.653975	−	0.756517i	$-0.273100\pi$
$151$	16.0723	1.30795	0.653975	+	0.756517i	$0.273100\pi$
$152$	4.79891	0.389243
$153$	27.5464	2.22700
$154$	1.12466	0.0906276
$155$	−3.57325	−0.287010
$156$	5.45632	0.436855
$157$	11.3185	0.903314	0.451657	−	0.892192i	$-0.350833\pi$
$157$	11.3185	0.903314	0.451657	+	0.892192i	$0.350833\pi$
$158$	9.45252	0.752002
$159$	−8.77782	−0.696127
$160$	−0.539090	−0.0426188
$161$	−0.588828	−0.0464062
$162$	−7.18592	−0.564579
$163$	10.8088	0.846612	0.423306	−	0.905987i	$-0.360870\pi$
$163$	10.8088	0.846612	0.423306	+	0.905987i	$0.360870\pi$
$164$	−4.76330	−0.371951
$165$	−8.16928	−0.635978
$166$	−7.62420	−0.591753
$167$	23.4075	1.81133	0.905663	−	0.423999i	$-0.139374\pi$
$167$	23.4075	1.81133	0.905663	+	0.423999i	$0.139374\pi$
$168$	−0.652635	−0.0503518
$169$	−9.61447	−0.739574
$170$	−2.56313	−0.196583
$171$	−27.8035	−2.12618
$172$	10.8795	0.829553
$173$	−7.35810	−0.559426	−0.279713	−	0.960084i	$-0.590239\pi$
$173$	−7.35810	−0.559426	−0.279713	+	0.960084i	$0.590239\pi$
$174$	−16.0716	−1.21839
$175$	1.03645	0.0783482
$176$	5.11019	0.385195
$177$	12.1346	0.912092
$178$	−9.82531	−0.736438
$179$	−13.1350	−0.981759	−0.490879	−	0.871228i	$-0.663324\pi$
$179$	−13.1350	−0.981759	−0.490879	+	0.871228i	$0.663324\pi$
$180$	3.12333	0.232799
$181$	−12.5443	−0.932413	−0.466206	−	0.884676i	$-0.654380\pi$
$181$	−12.5443	−0.932413	−0.466206	+	0.884676i	$0.654380\pi$
$182$	−0.404946	−0.0300166
$183$	6.84264	0.505822
$184$	−2.67550	−0.197240
$185$	−0.859583	−0.0631978
$186$	−19.6557	−1.44123
$187$	24.2966	1.77674
$188$	2.31041	0.168504
$189$	1.82327	0.132623
$190$	2.58704	0.187684
$191$	6.85138	0.495749	0.247874	−	0.968792i	$-0.420268\pi$
$191$	6.85138	0.495749	0.247874	+	0.968792i	$0.420268\pi$
$192$	−2.96542	−0.214011
$193$	7.46745	0.537519	0.268760	−	0.963207i	$-0.413386\pi$
$193$	7.46745	0.537519	0.268760	+	0.963207i	$0.413386\pi$
$194$	3.10555	0.222965
$195$	2.94144	0.210641
$196$	−6.95156	−0.496540
$197$	−11.3676	−0.809905	−0.404953	−	0.914338i	$-0.632712\pi$
$197$	−11.3676	−0.809905	−0.404953	+	0.914338i	$0.632712\pi$
$198$	−29.6069	−2.10407
$199$	6.57036	0.465760	0.232880	−	0.972505i	$-0.425185\pi$
$199$	6.57036	0.465760	0.232880	+	0.972505i	$0.425185\pi$
$200$	4.70938	0.333004
$201$	−14.6527	−1.03352
$202$	7.86660	0.553492
$203$	1.19277	0.0837164
$204$	−14.0992	−0.987142
$205$	−2.56785	−0.179346
$206$	−9.82927	−0.684838
$207$	15.5010	1.07740
$208$	−1.83998	−0.127580
$209$	−24.5233	−1.69631
$210$	−0.351829	−0.0242785
$211$	−12.4627	−0.857970	−0.428985	−	0.903312i	$-0.641129\pi$
$211$	−12.4627	−0.857970	−0.428985	+	0.903312i	$0.641129\pi$
$212$	2.96006	0.203298
$213$	−17.4180	−1.19346
$214$	9.15461	0.625796
$215$	5.86502	0.399991
$216$	8.28451	0.563690
$217$	1.45877	0.0990277
$218$	5.20154	0.352293
$219$	13.7205	0.927144
$220$	2.75485	0.185732
$221$	−8.74828	−0.588473
$222$	−4.72839	−0.317348
$223$	−13.6367	−0.913179	−0.456589	−	0.889678i	$-0.650929\pi$
$223$	−13.6367	−0.913179	−0.456589	+	0.889678i	$0.650929\pi$
$224$	0.220082	0.0147048
$225$	−27.2848	−1.81899
$226$	10.1470	0.674971
$227$	−28.8214	−1.91294	−0.956471	−	0.291829i	$-0.905736\pi$
$227$	−28.8214	−1.91294	−0.956471	+	0.291829i	$0.905736\pi$
$228$	14.2308	0.942456
$229$	−17.4261	−1.15155	−0.575775	−	0.817608i	$-0.695299\pi$
$229$	−17.4261	−1.15155	−0.575775	+	0.817608i	$0.695299\pi$
$230$	−1.44233	−0.0951046
$231$	3.33509	0.219433
$232$	5.41969	0.355820
$233$	2.26966	0.148690	0.0743452	−	0.997233i	$-0.476313\pi$
$233$	2.26966	0.148690	0.0743452	+	0.997233i	$0.476313\pi$
$234$	10.6603	0.696887
$235$	1.24552	0.0812487
$236$	−4.09203	−0.266369
$237$	28.0307	1.82079
$238$	1.04639	0.0678273
$239$	23.3995	1.51359	0.756793	−	0.653654i	$-0.226765\pi$
$239$	23.3995	1.51359	0.756793	+	0.653654i	$0.226765\pi$
$240$	−1.59863	−0.103191
$241$	13.4798	0.868308	0.434154	−	0.900839i	$-0.357047\pi$
$241$	13.4798	0.868308	0.434154	+	0.900839i	$0.357047\pi$
$242$	−15.1140	−0.971566
$243$	3.54427	0.227365
$244$	−2.30748	−0.147721
$245$	−3.74752	−0.239420
$246$	−14.1252	−0.900588
$247$	8.82990	0.561833
$248$	6.62830	0.420898
$249$	−22.6090	−1.43278
$250$	5.23423	0.331042
$251$	−31.0300	−1.95860	−0.979299	−	0.202421i	$-0.935119\pi$
$251$	−31.0300	−1.95860	−0.979299	+	0.202421i	$0.935119\pi$
$252$	−1.27509	−0.0803231
$253$	13.6723	0.859570
$254$	8.05548	0.505445
$255$	−7.60074	−0.475977
$256$	1.00000	0.0625000
$257$	−28.0792	−1.75153	−0.875765	−	0.482737i	$-0.839643\pi$
$257$	−28.0792	−1.75153	−0.875765	+	0.482737i	$0.839643\pi$
$258$	32.2622	2.00856
$259$	0.350922	0.0218053
$260$	−0.991915	−0.0615160
$261$	−31.4001	−1.94362
$262$	−5.25397	−0.324591
$263$	−0.786856	−0.0485197	−0.0242598	−	0.999706i	$-0.507723\pi$
$263$	−0.786856	−0.0485197	−0.0242598	+	0.999706i	$0.507723\pi$
$264$	15.1538	0.932655
$265$	1.59574	0.0980255
$266$	−1.05615	−0.0647568
$267$	−29.1361	−1.78310
$268$	4.94120	0.301832
$269$	−17.0961	−1.04237	−0.521184	−	0.853444i	$-0.674510\pi$
$269$	−17.0961	−1.04237	−0.521184	+	0.853444i	$0.674510\pi$
$270$	4.46609	0.271798
$271$	−4.65637	−0.282855	−0.141427	−	0.989949i	$-0.545169\pi$
$271$	−4.65637	−0.282855	−0.141427	+	0.989949i	$0.545169\pi$
$272$	4.75454	0.288287
$273$	−1.20084	−0.0726779
$274$	−4.67123	−0.282199
$275$	−24.0658	−1.45122
$276$	−7.93397	−0.477569
$277$	−20.2844	−1.21877	−0.609385	−	0.792874i	$-0.708584\pi$
$277$	−20.2844	−1.21877	−0.609385	+	0.792874i	$0.708584\pi$
$278$	11.9008	0.713762
$279$	−38.4024	−2.29909
$280$	0.118644	0.00709032
$281$	1.65735	0.0988694	0.0494347	−	0.998777i	$-0.484258\pi$
$281$	1.65735	0.0988694	0.0494347	+	0.998777i	$0.484258\pi$
$282$	6.85134	0.407991
$283$	−27.8194	−1.65369	−0.826846	−	0.562428i	$-0.809867\pi$
$283$	−27.8194	−1.65369	−0.826846	+	0.562428i	$0.809867\pi$
$284$	5.87372	0.348541
$285$	7.67166	0.454430
$286$	9.40265	0.555991
$287$	1.04832	0.0618801
$288$	−5.79371	−0.341397
$289$	5.60569	0.329746
$290$	2.92170	0.171568
$291$	9.20925	0.539856
$292$	−4.62683	−0.270765
$293$	−0.258205	−0.0150845	−0.00754226	−	0.999972i	$-0.502401\pi$
$293$	−0.258205	−0.0150845	−0.00754226	+	0.999972i	$0.502401\pi$
$294$	−20.6143	−1.20225
$295$	−2.20597	−0.128437
$296$	1.59451	0.0926789
$297$	−42.3354	−2.45655
$298$	−15.6554	−0.906895
$299$	−4.92287	−0.284697
$300$	13.9653	0.806286
$301$	−2.39438	−0.138010
$302$	−16.0723	−0.924860
$303$	23.3278	1.34015
$304$	−4.79891	−0.275236
$305$	−1.24394	−0.0712277
$306$	−27.5464	−1.57472
$307$	31.9661	1.82440	0.912201	−	0.409744i	$-0.134382\pi$
$307$	31.9661	1.82440	0.912201	+	0.409744i	$0.134382\pi$
$308$	−1.12466	−0.0640834
$309$	−29.1479	−1.65817
$310$	3.57325	0.202947
$311$	2.69476	0.152806	0.0764029	−	0.997077i	$-0.475656\pi$
$311$	2.69476	0.152806	0.0764029	+	0.997077i	$0.475656\pi$
$312$	−5.45632	−0.308903
$313$	−11.7999	−0.666970	−0.333485	−	0.942755i	$-0.608225\pi$
$313$	−11.7999	−0.666970	−0.333485	+	0.942755i	$0.608225\pi$
$314$	−11.3185	−0.638739
$315$	−0.687388	−0.0387299
$316$	−9.45252	−0.531746
$317$	−20.0170	−1.12427	−0.562133	−	0.827047i	$-0.690019\pi$
$317$	−20.0170	−1.12427	−0.562133	+	0.827047i	$0.690019\pi$
$318$	8.77782	0.492236
$319$	−27.6956	−1.55066
$320$	0.539090	0.0301360
$321$	27.1472	1.51521
$322$	0.588828	0.0328141
$323$	−22.8166	−1.26955
$324$	7.18592	0.399218
$325$	8.66518	0.480658
$326$	−10.8088	−0.598645
$327$	15.4247	0.852990
$328$	4.76330	0.263009
$329$	−0.508480	−0.0280334
$330$	8.16928	0.449704
$331$	6.57648	0.361476	0.180738	−	0.983531i	$-0.442151\pi$
$331$	6.57648	0.361476	0.180738	+	0.983531i	$0.442151\pi$
$332$	7.62420	0.418433
$333$	−9.23812	−0.506246
$334$	−23.4075	−1.28080
$335$	2.66375	0.145536
$336$	0.652635	0.0356041
$337$	−8.95217	−0.487656	−0.243828	−	0.969818i	$-0.578403\pi$
$337$	−8.95217	−0.487656	−0.243828	+	0.969818i	$0.578403\pi$
$338$	9.61447	0.522958
$339$	30.0902	1.63428
$340$	2.56313	0.139005
$341$	−33.8719	−1.83426
$342$	27.8035	1.50344
$343$	3.07048	0.165791
$344$	−10.8795	−0.586582
$345$	−4.27712	−0.230272
$346$	7.35810	0.395574
$347$	15.9803	0.857867	0.428934	−	0.903336i	$-0.358889\pi$
$347$	15.9803	0.857867	0.428934	+	0.903336i	$0.358889\pi$
$348$	16.0716	0.861531
$349$	−28.3421	−1.51712	−0.758560	−	0.651603i	$-0.774097\pi$
$349$	−28.3421	−1.51712	−0.758560	+	0.651603i	$0.774097\pi$
$350$	−1.03645	−0.0554005
$351$	15.2433	0.813630
$352$	−5.11019	−0.272374
$353$	2.23439	0.118924	0.0594622	−	0.998231i	$-0.481061\pi$
$353$	2.23439	0.118924	0.0594622	+	0.998231i	$0.481061\pi$
$354$	−12.1346	−0.644946
$355$	3.16646	0.168058
$356$	9.82531	0.520740
$357$	3.10298	0.164227
$358$	13.1350	0.694208
$359$	4.83027	0.254932	0.127466	−	0.991843i	$-0.459316\pi$
$359$	4.83027	0.254932	0.127466	+	0.991843i	$0.459316\pi$
$360$	−3.12333	−0.164614
$361$	4.02952	0.212080
$362$	12.5443	0.659316
$363$	−44.8194	−2.35241
$364$	0.404946	0.0212250
$365$	−2.49427	−0.130556
$366$	−6.84264	−0.357670
$367$	30.9066	1.61331	0.806655	−	0.591023i	$-0.201276\pi$
$367$	30.9066	1.61331	0.806655	+	0.591023i	$0.201276\pi$
$368$	2.67550	0.139470
$369$	−27.5972	−1.43665
$370$	0.859583	0.0446876
$371$	−0.651456	−0.0338219
$372$	19.6557	1.01910
$373$	0.175729	0.00909892	0.00454946	−	0.999990i	$-0.498552\pi$
$373$	0.175729	0.00909892	0.00454946	+	0.999990i	$0.498552\pi$
$374$	−24.2966	−1.25635
$375$	15.5217	0.801536
$376$	−2.31041	−0.119150
$377$	9.97213	0.513591
$378$	−1.82327	−0.0937789
$379$	−20.4684	−1.05139	−0.525696	−	0.850673i	$-0.676195\pi$
$379$	−20.4684	−1.05139	−0.525696	+	0.850673i	$0.676195\pi$
$380$	−2.58704	−0.132712
$381$	23.8879	1.22381
$382$	−6.85138	−0.350547
$383$	−23.6401	−1.20795	−0.603976	−	0.797002i	$-0.706418\pi$
$383$	−23.6401	−1.20795	−0.603976	+	0.797002i	$0.706418\pi$
$384$	2.96542	0.151328
$385$	−0.606292	−0.0308995
$386$	−7.46745	−0.380083
$387$	63.0325	3.20412
$388$	−3.10555	−0.157660
$389$	−11.5581	−0.586019	−0.293010	−	0.956109i	$-0.594657\pi$
$389$	−11.5581	−0.586019	−0.293010	+	0.956109i	$0.594657\pi$
$390$	−2.94144	−0.148946
$391$	12.7208	0.643317
$392$	6.95156	0.351107
$393$	−15.5802	−0.785918
$394$	11.3676	0.572689
$395$	−5.09576	−0.256395
$396$	29.6069	1.48780
$397$	8.09403	0.406227	0.203114	−	0.979155i	$-0.434894\pi$
$397$	8.09403	0.406227	0.203114	+	0.979155i	$0.434894\pi$
$398$	−6.57036	−0.329342
$399$	−3.13193	−0.156793
$400$	−4.70938	−0.235469
$401$	11.8819	0.593355	0.296677	−	0.954978i	$-0.404121\pi$
$401$	11.8819	0.593355	0.296677	+	0.954978i	$0.404121\pi$
$402$	14.6527	0.730812
$403$	12.1960	0.607524
$404$	−7.86660	−0.391378
$405$	3.87386	0.192493
$406$	−1.19277	−0.0591964
$407$	−8.14824	−0.403893
$408$	14.0992	0.698015
$409$	39.2750	1.94203	0.971013	−	0.239027i	$-0.0768286\pi$
$409$	39.2750	1.94203	0.971013	+	0.239027i	$0.0768286\pi$
$410$	2.56785	0.126817
$411$	−13.8521	−0.683276
$412$	9.82927	0.484253
$413$	0.900582	0.0443147
$414$	−15.5010	−0.761835
$415$	4.11013	0.201758
$416$	1.83998	0.0902125
$417$	35.2908	1.72820
$418$	24.5233	1.19948
$419$	−27.0626	−1.32210	−0.661048	−	0.750344i	$-0.729888\pi$
$419$	−27.0626	−1.32210	−0.661048	+	0.750344i	$0.729888\pi$
$420$	0.351829	0.0171675
$421$	21.1878	1.03263	0.516316	−	0.856398i	$-0.327303\pi$
$421$	21.1878	1.03263	0.516316	+	0.856398i	$0.327303\pi$
$422$	12.4627	0.606676
$423$	13.3859	0.650842
$424$	−2.96006	−0.143753
$425$	−22.3910	−1.08612
$426$	17.4180	0.843907
$427$	0.507834	0.0245758
$428$	−9.15461	−0.442505
$429$	27.8828	1.34619
$430$	−5.86502	−0.282836
$431$	−19.4929	−0.938939	−0.469470	−	0.882949i	$-0.655555\pi$
$431$	−19.4929	−0.938939	−0.469470	+	0.882949i	$0.655555\pi$
$432$	−8.28451	−0.398589
$433$	16.8948	0.811913	0.405957	−	0.913892i	$-0.366938\pi$
$433$	16.8948	0.811913	0.405957	+	0.913892i	$0.366938\pi$
$434$	−1.45877	−0.0700231
$435$	8.66406	0.415410
$436$	−5.20154	−0.249108
$437$	−12.8395	−0.614195
$438$	−13.7205	−0.655590
$439$	−33.8285	−1.61455	−0.807273	−	0.590178i	$-0.799058\pi$
$439$	−33.8285	−1.61455	−0.807273	+	0.590178i	$0.799058\pi$
$440$	−2.75485	−0.131332
$441$	−40.2753	−1.91787
$442$	8.74828	0.416113
$443$	−21.2006	−1.00727	−0.503635	−	0.863916i	$-0.668004\pi$
$443$	−21.2006	−1.00727	−0.503635	+	0.863916i	$0.668004\pi$
$444$	4.72839	0.224399
$445$	5.29672	0.251089
$446$	13.6367	0.645715
$447$	−46.4249	−2.19582
$448$	−0.220082	−0.0103979
$449$	−11.5835	−0.546660	−0.273330	−	0.961920i	$-0.588125\pi$
$449$	−11.5835	−0.546660	−0.273330	+	0.961920i	$0.588125\pi$
$450$	27.2848	1.28622
$451$	−24.3414	−1.14619
$452$	−10.1470	−0.477277
$453$	−47.6612	−2.23932
$454$	28.8214	1.35265
$455$	0.218303	0.0102342
$456$	−14.2308	−0.666417
$457$	12.3740	0.578830	0.289415	−	0.957204i	$-0.406539\pi$
$457$	12.3740	0.578830	0.289415	+	0.957204i	$0.406539\pi$
$458$	17.4261	0.814268
$459$	−39.3891	−1.83852
$460$	1.44233	0.0672491
$461$	−26.7956	−1.24799	−0.623997	−	0.781426i	$-0.714492\pi$
$461$	−26.7956	−1.24799	−0.623997	+	0.781426i	$0.714492\pi$
$462$	−3.33509	−0.155162
$463$	−1.70450	−0.0792147	−0.0396073	−	0.999215i	$-0.512611\pi$
$463$	−1.70450	−0.0792147	−0.0396073	+	0.999215i	$0.512611\pi$
$464$	−5.41969	−0.251603
$465$	10.5962	0.491386
$466$	−2.26966	−0.105140
$467$	−22.2192	−1.02818	−0.514091	−	0.857736i	$-0.671871\pi$
$467$	−22.2192	−1.02818	−0.514091	+	0.857736i	$0.671871\pi$
$468$	−10.6603	−0.492773
$469$	−1.08747	−0.0502146
$470$	−1.24552	−0.0574515
$471$	−33.5641	−1.54655
$472$	4.09203	0.188351
$473$	55.5962	2.55632
$474$	−28.0307	−1.28749
$475$	22.5999	1.03695
$476$	−1.04639	−0.0479611
$477$	17.1497	0.785232
$478$	−23.3995	−1.07027
$479$	−31.3616	−1.43295	−0.716473	−	0.697615i	$-0.754245\pi$
$479$	−31.3616	−1.43295	−0.716473	+	0.697615i	$0.754245\pi$
$480$	1.59863	0.0729670
$481$	2.93387	0.133773
$482$	−13.4798	−0.613987
$483$	1.74612	0.0794513
$484$	15.1140	0.687001
$485$	−1.67417	−0.0760201
$486$	−3.54427	−0.160771
$487$	7.48526	0.339190	0.169595	−	0.985514i	$-0.445754\pi$
$487$	7.48526	0.339190	0.169595	+	0.985514i	$0.445754\pi$
$488$	2.30748	0.104455
$489$	−32.0527	−1.44947
$490$	3.74752	0.169296
$491$	37.2492	1.68103	0.840516	−	0.541786i	$-0.182252\pi$
$491$	37.2492	1.68103	0.840516	+	0.541786i	$0.182252\pi$
$492$	14.1252	0.636812
$493$	−25.7682	−1.16054
$494$	−8.82990	−0.397276
$495$	15.9608	0.717384
$496$	−6.62830	−0.297620
$497$	−1.29270	−0.0579855
$498$	22.6090	1.01313
$499$	21.4802	0.961585	0.480792	−	0.876835i	$-0.340349\pi$
$499$	21.4802	0.961585	0.480792	+	0.876835i	$0.340349\pi$
$500$	−5.23423	−0.234082
$501$	−69.4130	−3.10114
$502$	31.0300	1.38494
$503$	−42.8529	−1.91072	−0.955359	−	0.295447i	$-0.904532\pi$
$503$	−42.8529	−1.91072	−0.955359	+	0.295447i	$0.904532\pi$
$504$	1.27509	0.0567970
$505$	−4.24081	−0.188713
$506$	−13.6723	−0.607808
$507$	28.5109	1.26621
$508$	−8.05548	−0.357404
$509$	0.0331688	0.00147018	0.000735090	−	1.00000i	$-0.499766\pi$
$509$	0.0331688	0.00147018	0.000735090		1.00000i	$0.499766\pi$
$510$	7.60074	0.336566
$511$	1.01828	0.0450461
$512$	−1.00000	−0.0441942
$513$	39.7566	1.75530
$514$	28.0792	1.23852
$515$	5.29886	0.233496
$516$	−32.2622	−1.42026
$517$	11.8066	0.519255
$518$	−0.350922	−0.0154186
$519$	21.8198	0.957785
$520$	0.991915	0.0434984
$521$	20.8175	0.912029	0.456015	−	0.889972i	$-0.349276\pi$
$521$	20.8175	0.912029	0.456015	+	0.889972i	$0.349276\pi$
$522$	31.4001	1.37434
$523$	8.83260	0.386222	0.193111	−	0.981177i	$-0.438142\pi$
$523$	8.83260	0.386222	0.193111	+	0.981177i	$0.438142\pi$
$524$	5.25397	0.229521
$525$	−3.07351	−0.134139
$526$	0.786856	0.0343086
$527$	−31.5146	−1.37280
$528$	−15.1538	−0.659487
$529$	−15.8417	−0.688770
$530$	−1.59574	−0.0693145
$531$	−23.7080	−1.02884
$532$	1.05615	0.0457900
$533$	8.76438	0.379628
$534$	29.1361	1.26084
$535$	−4.93515	−0.213365
$536$	−4.94120	−0.213427
$537$	38.9509	1.68085
$538$	17.0961	0.737066
$539$	−35.5238	−1.53012
$540$	−4.46609	−0.192190
$541$	−9.64488	−0.414666	−0.207333	−	0.978270i	$-0.566478\pi$
$541$	−9.64488	−0.414666	−0.207333	+	0.978270i	$0.566478\pi$
$542$	4.65637	0.200008
$543$	37.1992	1.59637
$544$	−4.75454	−0.203849
$545$	−2.80410	−0.120114
$546$	1.20084	0.0513910
$547$	4.51428	0.193017	0.0965083	−	0.995332i	$-0.469233\pi$
$547$	4.51428	0.193017	0.0965083	+	0.995332i	$0.469233\pi$
$548$	4.67123	0.199545
$549$	−13.3689	−0.570569
$550$	24.0658	1.02617
$551$	26.0086	1.10800
$552$	7.93397	0.337692
$553$	2.08033	0.0884645
$554$	20.2844	0.861801
$555$	2.54902	0.108200
$556$	−11.9008	−0.504706
$557$	−12.2984	−0.521101	−0.260551	−	0.965460i	$-0.583904\pi$
$557$	−12.2984	−0.521101	−0.260551	+	0.965460i	$0.583904\pi$
$558$	38.4024	1.62570
$559$	−20.0180	−0.846673
$560$	−0.118644	−0.00501362
$561$	−72.0496	−3.04194
$562$	−1.65735	−0.0699112
$563$	8.74121	0.368398	0.184199	−	0.982889i	$-0.441031\pi$
$563$	8.74121	0.368398	0.184199	+	0.982889i	$0.441031\pi$
$564$	−6.85134	−0.288493
$565$	−5.47017	−0.230132
$566$	27.8194	1.16934
$567$	−1.58149	−0.0664163
$568$	−5.87372	−0.246456
$569$	−11.2391	−0.471169	−0.235585	−	0.971854i	$-0.575701\pi$
$569$	−11.2391	−0.471169	−0.235585	+	0.971854i	$0.575701\pi$
$570$	−7.67166	−0.321331
$571$	9.65898	0.404216	0.202108	−	0.979363i	$-0.435221\pi$
$571$	9.65898	0.404216	0.202108	+	0.979363i	$0.435221\pi$
$572$	−9.40265	−0.393145
$573$	−20.3172	−0.848764
$574$	−1.04832	−0.0437558
$575$	−12.5999	−0.525454
$576$	5.79371	0.241404
$577$	0.979135	0.0407619	0.0203810	−	0.999792i	$-0.493512\pi$
$577$	0.979135	0.0407619	0.0203810	+	0.999792i	$0.493512\pi$
$578$	−5.60569	−0.233166
$579$	−22.1441	−0.920279
$580$	−2.92170	−0.121317
$581$	−1.67795	−0.0696130
$582$	−9.20925	−0.381736
$583$	15.1265	0.626474
$584$	4.62683	0.191459
$585$	−5.74687	−0.237604
$586$	0.258205	0.0106664
$587$	26.5042	1.09395	0.546973	−	0.837150i	$-0.315780\pi$
$587$	26.5042	1.09395	0.546973	+	0.837150i	$0.315780\pi$
$588$	20.6143	0.850119
$589$	31.8086	1.31065
$590$	2.20597	0.0908185
$591$	33.7096	1.38663
$592$	−1.59451	−0.0655339
$593$	−2.78421	−0.114334	−0.0571669	−	0.998365i	$-0.518207\pi$
$593$	−2.78421	−0.114334	−0.0571669	+	0.998365i	$0.518207\pi$
$594$	42.3354	1.73704
$595$	−0.564097	−0.0231257
$596$	15.6554	0.641272
$597$	−19.4839	−0.797421
$598$	4.92287	0.201311
$599$	−8.26439	−0.337674	−0.168837	−	0.985644i	$-0.554001\pi$
$599$	−8.26439	−0.337674	−0.168837	+	0.985644i	$0.554001\pi$
$600$	−13.9653	−0.570131
$601$	−11.5506	−0.471160	−0.235580	−	0.971855i	$-0.575699\pi$
$601$	−11.5506	−0.471160	−0.235580	+	0.971855i	$0.575699\pi$
$602$	2.39438	0.0975875
$603$	28.6279	1.16582
$604$	16.0723	0.653975
$605$	8.14782	0.331256
$606$	−23.3278	−0.947626
$607$	−1.08893	−0.0441983	−0.0220992	−	0.999756i	$-0.507035\pi$
$607$	−1.08893	−0.0441983	−0.0220992	+	0.999756i	$0.507035\pi$
$608$	4.79891	0.194621
$609$	−3.53708	−0.143330
$610$	1.24394	0.0503656
$611$	−4.25112	−0.171982
$612$	27.5464	1.11350
$613$	−33.0129	−1.33338	−0.666690	−	0.745335i	$-0.732289\pi$
$613$	−33.0129	−1.33338	−0.666690	+	0.745335i	$0.732289\pi$
$614$	−31.9661	−1.29005
$615$	7.61474	0.307056
$616$	1.12466	0.0453138
$617$	−16.1373	−0.649663	−0.324831	−	0.945772i	$-0.605308\pi$
$617$	−16.1373	−0.649663	−0.324831	+	0.945772i	$0.605308\pi$
$618$	29.1479	1.17250
$619$	17.3721	0.698245	0.349122	−	0.937077i	$-0.386480\pi$
$619$	17.3721	0.698245	0.349122	+	0.937077i	$0.386480\pi$
$620$	−3.57325	−0.143505
$621$	−22.1652	−0.889458
$622$	−2.69476	−0.108050
$623$	−2.16237	−0.0866336
$624$	5.45632	0.218427
$625$	20.7252	0.829008
$626$	11.7999	0.471619
$627$	72.7219	2.90423
$628$	11.3185	0.451657
$629$	−7.58116	−0.302281
$630$	0.687388	0.0273862
$631$	−6.58014	−0.261951	−0.130976	−	0.991386i	$-0.541811\pi$
$631$	−6.58014	−0.261951	−0.130976	+	0.991386i	$0.541811\pi$
$632$	9.45252	0.376001
$633$	36.9572	1.46892
$634$	20.0170	0.794976
$635$	−4.34262	−0.172332
$636$	−8.77782	−0.348063
$637$	12.7908	0.506788
$638$	27.6956	1.09648
$639$	34.0306	1.34623
$640$	−0.539090	−0.0213094
$641$	37.3463	1.47509	0.737545	−	0.675298i	$-0.235985\pi$
$641$	37.3463	1.47509	0.737545	+	0.675298i	$0.235985\pi$
$642$	−27.1472	−1.07142
$643$	34.0081	1.34115	0.670573	−	0.741843i	$-0.266048\pi$
$643$	34.0081	1.34115	0.670573	+	0.741843i	$0.266048\pi$
$644$	−0.588828	−0.0232031
$645$	−17.3922	−0.684818
$646$	22.8166	0.897708
$647$	16.1058	0.633183	0.316592	−	0.948562i	$-0.397462\pi$
$647$	16.1058	0.633183	0.316592	+	0.948562i	$0.397462\pi$
$648$	−7.18592	−0.282290
$649$	−20.9111	−0.820831
$650$	−8.66518	−0.339876
$651$	−4.32586	−0.169544
$652$	10.8088	0.423306
$653$	28.2006	1.10357	0.551787	−	0.833985i	$-0.313946\pi$
$653$	28.2006	1.10357	0.551787	+	0.833985i	$0.313946\pi$
$654$	−15.4247	−0.603155
$655$	2.83236	0.110669
$656$	−4.76330	−0.185976
$657$	−26.8065	−1.04582
$658$	0.508480	0.0198226
$659$	5.64841	0.220031	0.110015	−	0.993930i	$-0.464910\pi$
$659$	5.64841	0.220031	0.110015	+	0.993930i	$0.464910\pi$
$660$	−8.16928	−0.317989
$661$	10.7607	0.418543	0.209272	−	0.977858i	$-0.432891\pi$
$661$	10.7607	0.418543	0.209272	+	0.977858i	$0.432891\pi$
$662$	−6.57648	−0.255602
$663$	25.9423	1.00752
$664$	−7.62420	−0.295876
$665$	0.569361	0.0220789
$666$	9.23812	0.357970
$667$	−14.5004	−0.561456
$668$	23.4075	0.905663
$669$	40.4384	1.56344
$670$	−2.66375	−0.102910
$671$	−11.7916	−0.455212
$672$	−0.652635	−0.0251759
$673$	9.75137	0.375888	0.187944	−	0.982180i	$-0.439818\pi$
$673$	9.75137	0.375888	0.187944	+	0.982180i	$0.439818\pi$
$674$	8.95217	0.344825
$675$	39.0149	1.50169
$676$	−9.61447	−0.369787
$677$	−31.3089	−1.20330	−0.601648	−	0.798761i	$-0.705489\pi$
$677$	−31.3089	−1.20330	−0.601648	+	0.798761i	$0.705489\pi$
$678$	−30.0902	−1.15561
$679$	0.683474	0.0262293
$680$	−2.56313	−0.0982914
$681$	85.4674	3.27512
$682$	33.8719	1.29702
$683$	−34.6757	−1.32683	−0.663414	−	0.748253i	$-0.730893\pi$
$683$	−34.6757	−1.32683	−0.663414	+	0.748253i	$0.730893\pi$
$684$	−27.8035	−1.06309
$685$	2.51821	0.0962159
$686$	−3.07048	−0.117232
$687$	51.6757	1.97155
$688$	10.8795	0.414776
$689$	−5.44646	−0.207494
$690$	4.27712	0.162827
$691$	−21.4456	−0.815827	−0.407914	−	0.913020i	$-0.633744\pi$
$691$	−21.4456	−0.815827	−0.407914	+	0.913020i	$0.633744\pi$
$692$	−7.35810	−0.279713
$693$	−6.51595	−0.247520
$694$	−15.9803	−0.606604
$695$	−6.41559	−0.243357
$696$	−16.0716	−0.609194
$697$	−22.6473	−0.857828
$698$	28.3421	1.07277
$699$	−6.73049	−0.254570
$700$	1.03645	0.0391741
$701$	17.7909	0.671952	0.335976	−	0.941871i	$-0.390934\pi$
$701$	17.7909	0.671952	0.335976	+	0.941871i	$0.390934\pi$
$702$	−15.2433	−0.575323
$703$	7.65190	0.288597
$704$	5.11019	0.192597
$705$	−3.69349	−0.139105
$706$	−2.23439	−0.0840922
$707$	1.73130	0.0651121
$708$	12.1346	0.456046
$709$	13.7638	0.516909	0.258455	−	0.966023i	$-0.416787\pi$
$709$	13.7638	0.516909	0.258455	+	0.966023i	$0.416787\pi$
$710$	−3.16646	−0.118835
$711$	−54.7651	−2.05385
$712$	−9.82531	−0.368219
$713$	−17.7340	−0.664144
$714$	−3.10298	−0.116126
$715$	−5.06887	−0.189565
$716$	−13.1350	−0.490879
$717$	−69.3893	−2.59139
$718$	−4.83027	−0.180264
$719$	−4.58682	−0.171060	−0.0855298	−	0.996336i	$-0.527258\pi$
$719$	−4.58682	−0.171060	−0.0855298	+	0.996336i	$0.527258\pi$
$720$	3.12333	0.116400
$721$	−2.16324	−0.0805634
$722$	−4.02952	−0.149963
$723$	−39.9732	−1.48662
$724$	−12.5443	−0.466206
$725$	25.5234	0.947915
$726$	44.8194	1.66340
$727$	−11.2167	−0.416004	−0.208002	−	0.978128i	$-0.566696\pi$
$727$	−11.2167	−0.416004	−0.208002	+	0.978128i	$0.566696\pi$
$728$	−0.404946	−0.0150083
$729$	−32.0680	−1.18770
$730$	2.49427	0.0923173
$731$	51.7270	1.91319
$732$	6.84264	0.252911
$733$	−36.0414	−1.33122	−0.665609	−	0.746300i	$-0.731828\pi$
$733$	−36.0414	−1.33122	−0.665609	+	0.746300i	$0.731828\pi$
$734$	−30.9066	−1.14078
$735$	11.1130	0.409908
$736$	−2.67550	−0.0986201
$737$	25.2505	0.930113
$738$	27.5972	1.01587
$739$	−26.3421	−0.969010	−0.484505	−	0.874789i	$-0.661000\pi$
$739$	−26.3421	−0.969010	−0.484505	+	0.874789i	$0.661000\pi$
$740$	−0.859583	−0.0315989
$741$	−26.1844	−0.961907
$742$	0.651456	0.0239157
$743$	−11.1231	−0.408068	−0.204034	−	0.978964i	$-0.565405\pi$
$743$	−11.1231	−0.408068	−0.204034	+	0.978964i	$0.565405\pi$
$744$	−19.6557	−0.720613
$745$	8.43969	0.309206
$746$	−0.175729	−0.00643391
$747$	44.1724	1.61618
$748$	24.2966	0.888372
$749$	2.01476	0.0736178
$750$	−15.5217	−0.566772
$751$	−5.39268	−0.196782	−0.0983909	−	0.995148i	$-0.531370\pi$
$751$	−5.39268	−0.196782	−0.0983909	+	0.995148i	$0.531370\pi$
$752$	2.31041	0.0842521
$753$	92.0170	3.35329
$754$	−9.97213	−0.363164
$755$	8.66444	0.315331
$756$	1.82327	0.0663117
$757$	−28.1986	−1.02489	−0.512447	−	0.858719i	$-0.671261\pi$
$757$	−28.1986	−1.02489	−0.512447	+	0.858719i	$0.671261\pi$
$758$	20.4684	0.743446
$759$	−40.5441	−1.47166
$760$	2.58704	0.0938419
$761$	−42.0164	−1.52309	−0.761546	−	0.648111i	$-0.775559\pi$
$761$	−42.0164	−1.52309	−0.761546	+	0.648111i	$0.775559\pi$
$762$	−23.8879	−0.865366
$763$	1.14476	0.0414432
$764$	6.85138	0.247874
$765$	14.8500	0.536903
$766$	23.6401	0.854151
$767$	7.52927	0.271866
$768$	−2.96542	−0.107005
$769$	9.93916	0.358415	0.179208	−	0.983811i	$-0.442647\pi$
$769$	9.93916	0.358415	0.179208	+	0.983811i	$0.442647\pi$
$770$	0.606292	0.0218493
$771$	83.2665	2.99877
$772$	7.46745	0.268760
$773$	−6.95910	−0.250301	−0.125151	−	0.992138i	$-0.539941\pi$
$773$	−6.95910	−0.250301	−0.125151	+	0.992138i	$0.539941\pi$
$774$	−63.0325	−2.26566
$775$	31.2152	1.12128
$776$	3.10555	0.111483
$777$	−1.04063	−0.0373325
$778$	11.5581	0.414378
$779$	22.8586	0.818995
$780$	2.94144	0.105321
$781$	30.0158	1.07405
$782$	−12.7208	−0.454894
$783$	44.8995	1.60458
$784$	−6.95156	−0.248270
$785$	6.10168	0.217778
$786$	15.5802	0.555728
$787$	6.10260	0.217534	0.108767	−	0.994067i	$-0.465310\pi$
$787$	6.10260	0.217534	0.108767	+	0.994067i	$0.465310\pi$
$788$	−11.3676	−0.404953
$789$	2.33336	0.0830698
$790$	5.09576	0.181299
$791$	2.23318	0.0794027
$792$	−29.6069	−1.05204
$793$	4.24572	0.150770
$794$	−8.09403	−0.287246
$795$	−4.73203	−0.167828
$796$	6.57036	0.232880
$797$	−11.7296	−0.415485	−0.207742	−	0.978184i	$-0.566612\pi$
$797$	−11.7296	−0.415485	−0.207742	+	0.978184i	$0.566612\pi$
$798$	3.13193	0.110869
$799$	10.9850	0.388620
$800$	4.70938	0.166502
$801$	56.9250	2.01134
$802$	−11.8819	−0.419565
$803$	−23.6440	−0.834377
$804$	−14.6527	−0.516762
$805$	−0.317431	−0.0111880
$806$	−12.1960	−0.429584
$807$	50.6971	1.78462
$808$	7.86660	0.276746
$809$	20.6454	0.725853	0.362926	−	0.931818i	$-0.381778\pi$
$809$	20.6454	0.725853	0.362926	+	0.931818i	$0.381778\pi$
$810$	−3.87386	−0.136113
$811$	41.4740	1.45635	0.728175	−	0.685391i	$-0.240369\pi$
$811$	41.4740	1.45635	0.728175	+	0.685391i	$0.240369\pi$
$812$	1.19277	0.0418582
$813$	13.8081	0.484271
$814$	8.14824	0.285596
$815$	5.82692	0.204108
$816$	−14.0992	−0.493571
$817$	−52.2096	−1.82658
$818$	−39.2750	−1.37322
$819$	2.34614	0.0819808
$820$	−2.56785	−0.0896730
$821$	13.8087	0.481927	0.240964	−	0.970534i	$-0.422537\pi$
$821$	13.8087	0.481927	0.240964	+	0.970534i	$0.422537\pi$
$822$	13.8521	0.483149
$823$	12.6286	0.440206	0.220103	−	0.975477i	$-0.429361\pi$
$823$	12.6286	0.440206	0.220103	+	0.975477i	$0.429361\pi$
$824$	−9.82927	−0.342419
$825$	71.3653	2.48462
$826$	−0.900582	−0.0313353
$827$	49.3348	1.71554	0.857770	−	0.514034i	$-0.171849\pi$
$827$	49.3348	1.71554	0.857770	+	0.514034i	$0.171849\pi$
$828$	15.5010	0.538699
$829$	−28.0521	−0.974289	−0.487145	−	0.873321i	$-0.661962\pi$
$829$	−28.0521	−0.974289	−0.487145	+	0.873321i	$0.661962\pi$
$830$	−4.11013	−0.142665
$831$	60.1517	2.08664
$832$	−1.83998	−0.0637899
$833$	−33.0515	−1.14517
$834$	−35.2908	−1.22202
$835$	12.6187	0.436689
$836$	−24.5233	−0.848157
$837$	54.9122	1.89804
$838$	27.0626	0.934863
$839$	17.5700	0.606584	0.303292	−	0.952898i	$-0.401914\pi$
$839$	17.5700	0.606584	0.303292	+	0.952898i	$0.401914\pi$
$840$	−0.351829	−0.0121392
$841$	0.373036	0.0128633
$842$	−21.1878	−0.730181
$843$	−4.91474	−0.169273
$844$	−12.4627	−0.428985
$845$	−5.18306	−0.178303
$846$	−13.3859	−0.460215
$847$	−3.32632	−0.114294
$848$	2.96006	0.101649
$849$	82.4962	2.83126
$850$	22.3910	0.768004
$851$	−4.26610	−0.146240
$852$	−17.4180	−0.596732
$853$	−11.0901	−0.379717	−0.189858	−	0.981811i	$-0.560803\pi$
$853$	−11.0901	−0.379717	−0.189858	+	0.981811i	$0.560803\pi$
$854$	−0.507834	−0.0173777
$855$	−14.9886	−0.512598
$856$	9.15461	0.312898
$857$	−9.82809	−0.335721	−0.167861	−	0.985811i	$-0.553686\pi$
$857$	−9.82809	−0.335721	−0.167861	+	0.985811i	$0.553686\pi$
$858$	−27.8828	−0.951903
$859$	0.914828	0.0312135	0.0156068	−	0.999878i	$-0.495032\pi$
$859$	0.914828	0.0312135	0.0156068	+	0.999878i	$0.495032\pi$
$860$	5.86502	0.199995
$861$	−3.10869	−0.105944
$862$	19.4929	0.663930
$863$	49.6226	1.68917	0.844586	−	0.535420i	$-0.179847\pi$
$863$	49.6226	1.68917	0.844586	+	0.535420i	$0.179847\pi$
$864$	8.28451	0.281845
$865$	−3.96667	−0.134871
$866$	−16.8948	−0.574109
$867$	−16.6232	−0.564554
$868$	1.45877	0.0495138
$869$	−48.3042	−1.63861
$870$	−8.66406	−0.293739
$871$	−9.09172	−0.308061
$872$	5.20154	0.176146
$873$	−17.9926	−0.608958
$874$	12.8395	0.434301
$875$	1.15196	0.0389433
$876$	13.7205	0.463572
$877$	−43.6707	−1.47465	−0.737327	−	0.675536i	$-0.763912\pi$
$877$	−43.6707	−1.47465	−0.737327	+	0.675536i	$0.763912\pi$
$878$	33.8285	1.14166
$879$	0.765687	0.0258260
$880$	2.75485	0.0928660
$881$	33.0418	1.11321	0.556604	−	0.830778i	$-0.312104\pi$
$881$	33.0418	1.11321	0.556604	+	0.830778i	$0.312104\pi$
$882$	40.2753	1.35614
$883$	−9.37760	−0.315581	−0.157791	−	0.987473i	$-0.550437\pi$
$883$	−9.37760	−0.315581	−0.157791	+	0.987473i	$0.550437\pi$
$884$	−8.74828	−0.294236
$885$	6.54163	0.219895
$886$	21.2006	0.712248
$887$	−19.9083	−0.668454	−0.334227	−	0.942493i	$-0.608475\pi$
$887$	−19.9083	−0.668454	−0.334227	+	0.942493i	$0.608475\pi$
$888$	−4.72839	−0.158674
$889$	1.77286	0.0594599
$890$	−5.29672	−0.177547
$891$	36.7214	1.23021
$892$	−13.6367	−0.456589
$893$	−11.0875	−0.371028
$894$	46.4249	1.55268
$895$	−7.08096	−0.236691
$896$	0.220082	0.00735242
$897$	14.5984	0.487425
$898$	11.5835	0.386547
$899$	35.9233	1.19811
$900$	−27.2848	−0.909493
$901$	14.0737	0.468864
$902$	24.3414	0.810478
$903$	7.10033	0.236284
$904$	10.1470	0.337486
$905$	−6.76252	−0.224794
$906$	47.6612	1.58344
$907$	−29.9600	−0.994805	−0.497402	−	0.867520i	$-0.665713\pi$
$907$	−29.9600	−0.994805	−0.497402	+	0.867520i	$0.665713\pi$
$908$	−28.8214	−0.956471
$909$	−45.5768	−1.51169
$910$	−0.218303	−0.00723666
$911$	35.2589	1.16818	0.584089	−	0.811690i	$-0.301452\pi$
$911$	35.2589	1.16818	0.584089	+	0.811690i	$0.301452\pi$
$912$	14.2308	0.471228
$913$	38.9611	1.28942
$914$	−12.3740	−0.409295
$915$	3.68880	0.121948
$916$	−17.4261	−0.575775
$917$	−1.15630	−0.0381845
$918$	39.3891	1.30003
$919$	−30.6263	−1.01027	−0.505135	−	0.863041i	$-0.668557\pi$
$919$	−30.6263	−1.01027	−0.505135	+	0.863041i	$0.668557\pi$
$920$	−1.44233	−0.0475523
$921$	−94.7929	−3.12353
$922$	26.7956	0.882466
$923$	−10.8075	−0.355735
$924$	3.33509	0.109716
$925$	7.50915	0.246899
$926$	1.70450	0.0560132
$927$	56.9479	1.87041
$928$	5.41969	0.177910
$929$	−3.02603	−0.0992809	−0.0496405	−	0.998767i	$-0.515808\pi$
$929$	−3.02603	−0.0992809	−0.0496405	+	0.998767i	$0.515808\pi$
$930$	−10.5962	−0.347462
$931$	33.3599	1.09333
$932$	2.26966	0.0743452
$933$	−7.99109	−0.261616
$934$	22.2192	0.727034
$935$	13.0981	0.428352
$936$	10.6603	0.348443
$937$	−40.6266	−1.32721	−0.663607	−	0.748081i	$-0.730975\pi$
$937$	−40.6266	−1.32721	−0.663607	+	0.748081i	$0.730975\pi$
$938$	1.08747	0.0355071
$939$	34.9917	1.14191
$940$	1.24552	0.0406244
$941$	−0.630592	−0.0205567	−0.0102784	−	0.999947i	$-0.503272\pi$
$941$	−0.630592	−0.0205567	−0.0102784	+	0.999947i	$0.503272\pi$
$942$	33.5641	1.09358
$943$	−12.7442	−0.415008
$944$	−4.09203	−0.133184
$945$	0.982906	0.0319739
$946$	−55.5962	−1.80759
$947$	−47.9657	−1.55868	−0.779338	−	0.626604i	$-0.784444\pi$
$947$	−47.9657	−1.55868	−0.779338	+	0.626604i	$0.784444\pi$
$948$	28.0307	0.910394
$949$	8.51328	0.276353
$950$	−22.5999	−0.733237
$951$	59.3587	1.92484
$952$	1.04639	0.0339136
$953$	28.3270	0.917602	0.458801	−	0.888539i	$-0.348279\pi$
$953$	28.3270	0.917602	0.458801	+	0.888539i	$0.348279\pi$
$954$	−17.1497	−0.555243
$955$	3.69351	0.119519
$956$	23.3995	0.756793
$957$	82.1291	2.65486
$958$	31.3616	1.01325
$959$	−1.02805	−0.0331975
$960$	−1.59863	−0.0515955
$961$	12.9344	0.417238
$962$	−2.93387	−0.0945917
$963$	−53.0391	−1.70916
$964$	13.4798	0.434154
$965$	4.02563	0.129590
$966$	−1.74612	−0.0561806
$967$	7.77713	0.250096	0.125048	−	0.992151i	$-0.460092\pi$
$967$	7.77713	0.250096	0.125048	+	0.992151i	$0.460092\pi$
$968$	−15.1140	−0.485783
$969$	67.6608	2.17358
$970$	1.67417	0.0537543
$971$	−10.9041	−0.349930	−0.174965	−	0.984575i	$-0.555981\pi$
$971$	−10.9041	−0.349930	−0.174965	+	0.984575i	$0.555981\pi$
$972$	3.54427	0.113683
$973$	2.61915	0.0839660
$974$	−7.48526	−0.239843
$975$	−25.6959	−0.822927
$976$	−2.30748	−0.0738606
$977$	−51.5261	−1.64847	−0.824233	−	0.566251i	$-0.808393\pi$
$977$	−51.5261	−1.64847	−0.824233	+	0.566251i	$0.808393\pi$
$978$	32.0527	1.02493
$979$	50.2092	1.60469
$980$	−3.74752	−0.119710
$981$	−30.1362	−0.962174
$982$	−37.2492	−1.18867
$983$	−49.3988	−1.57558	−0.787789	−	0.615945i	$-0.788774\pi$
$983$	−49.3988	−1.57558	−0.787789	+	0.615945i	$0.788774\pi$
$984$	−14.1252	−0.450294
$985$	−6.12814	−0.195259
$986$	25.7682	0.820625
$987$	1.50785	0.0479955
$988$	8.82990	0.280917
$989$	29.1080	0.925581
$990$	−15.9608	−0.507267
$991$	43.5919	1.38474	0.692371	−	0.721542i	$-0.256566\pi$
$991$	43.5919	1.38474	0.692371	+	0.721542i	$0.256566\pi$
$992$	6.62830	0.210449
$993$	−19.5020	−0.618878
$994$	1.29270	0.0410019
$995$	3.54201	0.112289
$996$	−22.6090	−0.716392
$997$	19.2513	0.609693	0.304847	−	0.952401i	$-0.401395\pi$
$997$	19.2513	0.609693	0.304847	+	0.952401i	$0.401395\pi$
$998$	−21.4802	−0.679943
$999$	13.2097	0.417937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.96542 q^{3} +1.00000 q^{4} +0.539090 q^{5} +2.96542 q^{6} -0.220082 q^{7} -1.00000 q^{8} +5.79371 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.96542 q^{3} +1.00000 q^{4} +0.539090 q^{5} +2.96542 q^{6} -0.220082 q^{7} -1.00000 q^{8} +5.79371 q^{9} -0.539090 q^{10} +5.11019 q^{11} -2.96542 q^{12} -1.83998 q^{13} +0.220082 q^{14} -1.59863 q^{15} +1.00000 q^{16} +4.75454 q^{17} -5.79371 q^{18} -4.79891 q^{19} +0.539090 q^{20} +0.652635 q^{21} -5.11019 q^{22} +2.67550 q^{23} +2.96542 q^{24} -4.70938 q^{25} +1.83998 q^{26} -8.28451 q^{27} -0.220082 q^{28} -5.41969 q^{29} +1.59863 q^{30} -6.62830 q^{31} -1.00000 q^{32} -15.1538 q^{33} -4.75454 q^{34} -0.118644 q^{35} +5.79371 q^{36} -1.59451 q^{37} +4.79891 q^{38} +5.45632 q^{39} -0.539090 q^{40} -4.76330 q^{41} -0.652635 q^{42} +10.8795 q^{43} +5.11019 q^{44} +3.12333 q^{45} -2.67550 q^{46} +2.31041 q^{47} -2.96542 q^{48} -6.95156 q^{49} +4.70938 q^{50} -14.0992 q^{51} -1.83998 q^{52} +2.96006 q^{53} +8.28451 q^{54} +2.75485 q^{55} +0.220082 q^{56} +14.2308 q^{57} +5.41969 q^{58} -4.09203 q^{59} -1.59863 q^{60} -2.30748 q^{61} +6.62830 q^{62} -1.27509 q^{63} +1.00000 q^{64} -0.991915 q^{65} +15.1538 q^{66} +4.94120 q^{67} +4.75454 q^{68} -7.93397 q^{69} +0.118644 q^{70} +5.87372 q^{71} -5.79371 q^{72} -4.62683 q^{73} +1.59451 q^{74} +13.9653 q^{75} -4.79891 q^{76} -1.12466 q^{77} -5.45632 q^{78} -9.45252 q^{79} +0.539090 q^{80} +7.18592 q^{81} +4.76330 q^{82} +7.62420 q^{83} +0.652635 q^{84} +2.56313 q^{85} -10.8795 q^{86} +16.0716 q^{87} -5.11019 q^{88} +9.82531 q^{89} -3.12333 q^{90} +0.404946 q^{91} +2.67550 q^{92} +19.6557 q^{93} -2.31041 q^{94} -2.58704 q^{95} +2.96542 q^{96} -3.10555 q^{97} +6.95156 q^{98} +29.6069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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