LMFDB - Embedded newform 4006.2.a.h.1.18

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:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.388226 q^{3} +1.00000 q^{4} +3.10956 q^{5} +0.388226 q^{6} +1.22808 q^{7} -1.00000 q^{8} -2.84928 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.388226 q^{3} +1.00000 q^{4} +3.10956 q^{5} +0.388226 q^{6} +1.22808 q^{7} -1.00000 q^{8} -2.84928 q^{9} -3.10956 q^{10} -0.937511 q^{11} -0.388226 q^{12} +0.868041 q^{13} -1.22808 q^{14} -1.20721 q^{15} +1.00000 q^{16} -6.91455 q^{17} +2.84928 q^{18} +5.26872 q^{19} +3.10956 q^{20} -0.476774 q^{21} +0.937511 q^{22} -8.57710 q^{23} +0.388226 q^{24} +4.66934 q^{25} -0.868041 q^{26} +2.27084 q^{27} +1.22808 q^{28} +6.65681 q^{29} +1.20721 q^{30} -1.73144 q^{31} -1.00000 q^{32} +0.363966 q^{33} +6.91455 q^{34} +3.81879 q^{35} -2.84928 q^{36} -8.37805 q^{37} -5.26872 q^{38} -0.336996 q^{39} -3.10956 q^{40} +9.92201 q^{41} +0.476774 q^{42} -3.11520 q^{43} -0.937511 q^{44} -8.86000 q^{45} +8.57710 q^{46} +11.7602 q^{47} -0.388226 q^{48} -5.49181 q^{49} -4.66934 q^{50} +2.68441 q^{51} +0.868041 q^{52} +10.5347 q^{53} -2.27084 q^{54} -2.91524 q^{55} -1.22808 q^{56} -2.04545 q^{57} -6.65681 q^{58} +3.57540 q^{59} -1.20721 q^{60} +14.2792 q^{61} +1.73144 q^{62} -3.49915 q^{63} +1.00000 q^{64} +2.69922 q^{65} -0.363966 q^{66} -8.57238 q^{67} -6.91455 q^{68} +3.32986 q^{69} -3.81879 q^{70} +12.7650 q^{71} +2.84928 q^{72} +15.6687 q^{73} +8.37805 q^{74} -1.81276 q^{75} +5.26872 q^{76} -1.15134 q^{77} +0.336996 q^{78} +13.9939 q^{79} +3.10956 q^{80} +7.66624 q^{81} -9.92201 q^{82} +16.4809 q^{83} -0.476774 q^{84} -21.5012 q^{85} +3.11520 q^{86} -2.58435 q^{87} +0.937511 q^{88} +9.23480 q^{89} +8.86000 q^{90} +1.06603 q^{91} -8.57710 q^{92} +0.672189 q^{93} -11.7602 q^{94} +16.3834 q^{95} +0.388226 q^{96} -3.58018 q^{97} +5.49181 q^{98} +2.67123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * 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
$3$	−0.388226	−0.224142	−0.112071	−	0.993700i	$-0.535748\pi$
$3$	−0.388226	−0.224142	−0.112071	+	0.993700i	$0.535748\pi$
$4$	1.00000	0.500000
$5$	3.10956	1.39064	0.695318	−	0.718702i	$-0.255264\pi$
$5$	3.10956	1.39064	0.695318	+	0.718702i	$0.255264\pi$
$6$	0.388226	0.158493
$7$	1.22808	0.464171	0.232086	−	0.972695i	$-0.425445\pi$
$7$	1.22808	0.464171	0.232086	+	0.972695i	$0.425445\pi$
$8$	−1.00000	−0.353553
$9$	−2.84928	−0.949760
$10$	−3.10956	−0.983328
$11$	−0.937511	−0.282670	−0.141335	−	0.989962i	$-0.545139\pi$
$11$	−0.937511	−0.282670	−0.141335	+	0.989962i	$0.545139\pi$
$12$	−0.388226	−0.112071
$13$	0.868041	0.240751	0.120376	−	0.992728i	$-0.461590\pi$
$13$	0.868041	0.240751	0.120376	+	0.992728i	$0.461590\pi$
$14$	−1.22808	−0.328219
$15$	−1.20721	−0.311701
$16$	1.00000	0.250000
$17$	−6.91455	−1.67703	−0.838513	−	0.544882i	$-0.816574\pi$
$17$	−6.91455	−1.67703	−0.838513	+	0.544882i	$0.816574\pi$
$18$	2.84928	0.671582
$19$	5.26872	1.20873	0.604364	−	0.796709i	$-0.293427\pi$
$19$	5.26872	1.20873	0.604364	+	0.796709i	$0.293427\pi$
$20$	3.10956	0.695318
$21$	−0.476774	−0.104041
$22$	0.937511	0.199878
$23$	−8.57710	−1.78845	−0.894225	−	0.447618i	$-0.852272\pi$
$23$	−8.57710	−1.78845	−0.894225	+	0.447618i	$0.852272\pi$
$24$	0.388226	0.0792463
$25$	4.66934	0.933869
$26$	−0.868041	−0.170237
$27$	2.27084	0.437024
$28$	1.22808	0.232086
$29$	6.65681	1.23614	0.618069	−	0.786124i	$-0.287915\pi$
$29$	6.65681	1.23614	0.618069	+	0.786124i	$0.287915\pi$
$30$	1.20721	0.220406
$31$	−1.73144	−0.310975	−0.155488	−	0.987838i	$-0.549695\pi$
$31$	−1.73144	−0.310975	−0.155488	+	0.987838i	$0.549695\pi$
$32$	−1.00000	−0.176777
$33$	0.363966	0.0633584
$34$	6.91455	1.18584
$35$	3.81879	0.645494
$36$	−2.84928	−0.474880
$37$	−8.37805	−1.37734	−0.688672	−	0.725073i	$-0.741806\pi$
$37$	−8.37805	−1.37734	−0.688672	+	0.725073i	$0.741806\pi$
$38$	−5.26872	−0.854699
$39$	−0.336996	−0.0539626
$40$	−3.10956	−0.491664
$41$	9.92201	1.54956	0.774779	−	0.632232i	$-0.217861\pi$
$41$	9.92201	1.54956	0.774779	+	0.632232i	$0.217861\pi$
$42$	0.476774	0.0735678
$43$	−3.11520	−0.475064	−0.237532	−	0.971380i	$-0.576338\pi$
$43$	−3.11520	−0.475064	−0.237532	+	0.971380i	$0.576338\pi$
$44$	−0.937511	−0.141335
$45$	−8.86000	−1.32077
$46$	8.57710	1.26462
$47$	11.7602	1.71540	0.857701	−	0.514149i	$-0.171892\pi$
$47$	11.7602	1.71540	0.857701	+	0.514149i	$0.171892\pi$
$48$	−0.388226	−0.0560356
$49$	−5.49181	−0.784545
$50$	−4.66934	−0.660345
$51$	2.68441	0.375893
$52$	0.868041	0.120376
$53$	10.5347	1.44706	0.723528	−	0.690295i	$-0.242519\pi$
$53$	10.5347	1.44706	0.723528	+	0.690295i	$0.242519\pi$
$54$	−2.27084	−0.309023
$55$	−2.91524	−0.393091
$56$	−1.22808	−0.164109
$57$	−2.04545	−0.270927
$58$	−6.65681	−0.874082
$59$	3.57540	0.465478	0.232739	−	0.972539i	$-0.425231\pi$
$59$	3.57540	0.465478	0.232739	+	0.972539i	$0.425231\pi$
$60$	−1.20721	−0.155850
$61$	14.2792	1.82826	0.914131	−	0.405419i	$-0.132874\pi$
$61$	14.2792	1.82826	0.914131	+	0.405419i	$0.132874\pi$
$62$	1.73144	0.219893
$63$	−3.49915	−0.440852
$64$	1.00000	0.125000
$65$	2.69922	0.334797
$66$	−0.363966	−0.0448011
$67$	−8.57238	−1.04728	−0.523641	−	0.851939i	$-0.675427\pi$
$67$	−8.57238	−1.04728	−0.523641	+	0.851939i	$0.675427\pi$
$68$	−6.91455	−0.838513
$69$	3.32986	0.400867
$70$	−3.81879	−0.456433
$71$	12.7650	1.51492	0.757462	−	0.652879i	$-0.226439\pi$
$71$	12.7650	1.51492	0.757462	+	0.652879i	$0.226439\pi$
$72$	2.84928	0.335791
$73$	15.6687	1.83388	0.916939	−	0.399027i	$-0.130652\pi$
$73$	15.6687	1.83388	0.916939	+	0.399027i	$0.130652\pi$
$74$	8.37805	0.973929
$75$	−1.81276	−0.209320
$76$	5.26872	0.604364
$77$	−1.15134	−0.131207
$78$	0.336996	0.0381573
$79$	13.9939	1.57444	0.787218	−	0.616674i	$-0.211520\pi$
$79$	13.9939	1.57444	0.787218	+	0.616674i	$0.211520\pi$
$80$	3.10956	0.347659
$81$	7.66624	0.851805
$82$	−9.92201	−1.09570
$83$	16.4809	1.80901	0.904504	−	0.426465i	$-0.140241\pi$
$83$	16.4809	1.80901	0.904504	+	0.426465i	$0.140241\pi$
$84$	−0.476774	−0.0520203
$85$	−21.5012	−2.33213
$86$	3.11520	0.335921
$87$	−2.58435	−0.277071
$88$	0.937511	0.0999390
$89$	9.23480	0.978887	0.489443	−	0.872035i	$-0.337200\pi$
$89$	9.23480	0.978887	0.489443	+	0.872035i	$0.337200\pi$
$90$	8.86000	0.933926
$91$	1.06603	0.111750
$92$	−8.57710	−0.894225
$93$	0.672189	0.0697027
$94$	−11.7602	−1.21297
$95$	16.3834	1.68090
$96$	0.388226	0.0396232
$97$	−3.58018	−0.363512	−0.181756	−	0.983344i	$-0.558178\pi$
$97$	−3.58018	−0.363512	−0.181756	+	0.983344i	$0.558178\pi$
$98$	5.49181	0.554757
$99$	2.67123	0.268469
$100$	4.66934	0.466934
$101$	2.83678	0.282271	0.141135	−	0.989990i	$-0.454925\pi$
$101$	2.83678	0.282271	0.141135	+	0.989990i	$0.454925\pi$
$102$	−2.68441	−0.265796
$103$	−18.6753	−1.84013	−0.920064	−	0.391769i	$-0.871863\pi$
$103$	−18.6753	−1.84013	−0.920064	+	0.391769i	$0.871863\pi$
$104$	−0.868041	−0.0851184
$105$	−1.48255	−0.144682
$106$	−10.5347	−1.02322
$107$	3.01532	0.291502	0.145751	−	0.989321i	$-0.453440\pi$
$107$	3.01532	0.291502	0.145751	+	0.989321i	$0.453440\pi$
$108$	2.27084	0.218512
$109$	17.4585	1.67222	0.836112	−	0.548559i	$-0.184823\pi$
$109$	17.4585	1.67222	0.836112	+	0.548559i	$0.184823\pi$
$110$	2.91524	0.277957
$111$	3.25258	0.308721
$112$	1.22808	0.116043
$113$	−15.9178	−1.49742	−0.748712	−	0.662895i	$-0.769327\pi$
$113$	−15.9178	−1.49742	−0.748712	+	0.662895i	$0.769327\pi$
$114$	2.04545	0.191574
$115$	−26.6710	−2.48708
$116$	6.65681	0.618069
$117$	−2.47329	−0.228656
$118$	−3.57540	−0.329143
$119$	−8.49164	−0.778427
$120$	1.20721	0.110203
$121$	−10.1211	−0.920098
$122$	−14.2792	−1.29278
$123$	−3.85198	−0.347322
$124$	−1.73144	−0.155488
$125$	−1.02820	−0.0919646
$126$	3.49915	0.311729
$127$	4.11695	0.365321	0.182660	−	0.983176i	$-0.441529\pi$
$127$	4.11695	0.365321	0.182660	+	0.983176i	$0.441529\pi$
$128$	−1.00000	−0.0883883
$129$	1.20940	0.106482
$130$	−2.69922	−0.236738
$131$	8.83379	0.771812	0.385906	−	0.922538i	$-0.373889\pi$
$131$	8.83379	0.771812	0.385906	+	0.922538i	$0.373889\pi$
$132$	0.363966	0.0316792
$133$	6.47042	0.561057
$134$	8.57238	0.740541
$135$	7.06132	0.607741
$136$	6.91455	0.592918
$137$	19.2042	1.64072	0.820361	−	0.571846i	$-0.193772\pi$
$137$	19.2042	1.64072	0.820361	+	0.571846i	$0.193772\pi$
$138$	−3.32986	−0.283456
$139$	−7.02689	−0.596013	−0.298006	−	0.954564i	$-0.596322\pi$
$139$	−7.02689	−0.596013	−0.298006	+	0.954564i	$0.596322\pi$
$140$	3.81879	0.322747
$141$	−4.56562	−0.384494
$142$	−12.7650	−1.07121
$143$	−0.813798	−0.0680532
$144$	−2.84928	−0.237440
$145$	20.6997	1.71902
$146$	−15.6687	−1.29675
$147$	2.13207	0.175850
$148$	−8.37805	−0.688672
$149$	−1.95768	−0.160379	−0.0801897	−	0.996780i	$-0.525553\pi$
$149$	−1.95768	−0.160379	−0.0801897	+	0.996780i	$0.525553\pi$
$150$	1.81276	0.148011
$151$	1.98527	0.161559	0.0807793	−	0.996732i	$-0.474259\pi$
$151$	1.98527	0.161559	0.0807793	+	0.996732i	$0.474259\pi$
$152$	−5.26872	−0.427350
$153$	19.7015	1.59277
$154$	1.15134	0.0927776
$155$	−5.38400	−0.432453
$156$	−0.336996	−0.0269813
$157$	8.17510	0.652444	0.326222	−	0.945293i	$-0.394224\pi$
$157$	8.17510	0.652444	0.326222	+	0.945293i	$0.394224\pi$
$158$	−13.9939	−1.11330
$159$	−4.08986	−0.324347
$160$	−3.10956	−0.245832
$161$	−10.5334	−0.830147
$162$	−7.66624	−0.602317
$163$	6.33468	0.496170	0.248085	−	0.968738i	$-0.420199\pi$
$163$	6.33468	0.496170	0.248085	+	0.968738i	$0.420199\pi$
$164$	9.92201	0.774779
$165$	1.13177	0.0881084
$166$	−16.4809	−1.27916
$167$	−5.78990	−0.448036	−0.224018	−	0.974585i	$-0.571917\pi$
$167$	−5.78990	−0.448036	−0.224018	+	0.974585i	$0.571917\pi$
$168$	0.476774	0.0367839
$169$	−12.2465	−0.942039
$170$	21.5012	1.64907
$171$	−15.0121	−1.14800
$172$	−3.11520	−0.237532
$173$	−13.2572	−1.00792	−0.503961	−	0.863726i	$-0.668125\pi$
$173$	−13.2572	−1.00792	−0.503961	+	0.863726i	$0.668125\pi$
$174$	2.58435	0.195919
$175$	5.73434	0.433475
$176$	−0.937511	−0.0706675
$177$	−1.38806	−0.104333
$178$	−9.23480	−0.692177
$179$	−15.1205	−1.13016	−0.565079	−	0.825037i	$-0.691154\pi$
$179$	−15.1205	−1.13016	−0.565079	+	0.825037i	$0.691154\pi$
$180$	−8.86000	−0.660385
$181$	0.353991	0.0263119	0.0131560	−	0.999913i	$-0.495812\pi$
$181$	0.353991	0.0263119	0.0131560	+	0.999913i	$0.495812\pi$
$182$	−1.06603	−0.0790191
$183$	−5.54355	−0.409791
$184$	8.57710	0.632312
$185$	−26.0520	−1.91538
$186$	−0.672189	−0.0492873
$187$	6.48247	0.474045
$188$	11.7602	0.857701
$189$	2.78878	0.202854
$190$	−16.3834	−1.18858
$191$	17.9374	1.29790	0.648951	−	0.760830i	$-0.275208\pi$
$191$	17.9374	1.29790	0.648951	+	0.760830i	$0.275208\pi$
$192$	−0.388226	−0.0280178
$193$	0.744531	0.0535925	0.0267962	−	0.999641i	$-0.491469\pi$
$193$	0.744531	0.0535925	0.0267962	+	0.999641i	$0.491469\pi$
$194$	3.58018	0.257042
$195$	−1.04791	−0.0750423
$196$	−5.49181	−0.392272
$197$	−6.12284	−0.436235	−0.218117	−	0.975923i	$-0.569992\pi$
$197$	−6.12284	−0.436235	−0.218117	+	0.975923i	$0.569992\pi$
$198$	−2.67123	−0.189836
$199$	−1.73145	−0.122739	−0.0613697	−	0.998115i	$-0.519547\pi$
$199$	−1.73145	−0.122739	−0.0613697	+	0.998115i	$0.519547\pi$
$200$	−4.66934	−0.330172
$201$	3.32802	0.234740
$202$	−2.83678	−0.199595
$203$	8.17511	0.573780
$204$	2.68441	0.187946
$205$	30.8531	2.15487
$206$	18.6753	1.30117
$207$	24.4386	1.69860
$208$	0.868041	0.0601878
$209$	−4.93948	−0.341671
$210$	1.48255	0.102306
$211$	−6.78471	−0.467079	−0.233539	−	0.972347i	$-0.575031\pi$
$211$	−6.78471	−0.467079	−0.233539	+	0.972347i	$0.575031\pi$
$212$	10.5347	0.723528
$213$	−4.95570	−0.339559
$214$	−3.01532	−0.206123
$215$	−9.68689	−0.660641
$216$	−2.27084	−0.154511
$217$	−2.12635	−0.144346
$218$	−17.4585	−1.18244
$219$	−6.08298	−0.411050
$220$	−2.91524	−0.196546
$221$	−6.00212	−0.403746
$222$	−3.25258	−0.218299
$223$	−16.2890	−1.09079	−0.545396	−	0.838179i	$-0.683621\pi$
$223$	−16.2890	−1.09079	−0.545396	+	0.838179i	$0.683621\pi$
$224$	−1.22808	−0.0820547
$225$	−13.3043	−0.886951
$226$	15.9178	1.05884
$227$	−7.71676	−0.512180	−0.256090	−	0.966653i	$-0.582434\pi$
$227$	−7.71676	−0.512180	−0.256090	+	0.966653i	$0.582434\pi$
$228$	−2.04545	−0.135464
$229$	−24.4802	−1.61770	−0.808848	−	0.588018i	$-0.799909\pi$
$229$	−24.4802	−1.61770	−0.808848	+	0.588018i	$0.799909\pi$
$230$	26.6710	1.75863
$231$	0.446980	0.0294091
$232$	−6.65681	−0.437041
$233$	20.4741	1.34131	0.670653	−	0.741771i	$-0.266014\pi$
$233$	20.4741	1.34131	0.670653	+	0.741771i	$0.266014\pi$
$234$	2.47329	0.161684
$235$	36.5690	2.38550
$236$	3.57540	0.232739
$237$	−5.43280	−0.352898
$238$	8.49164	0.550431
$239$	12.9208	0.835780	0.417890	−	0.908498i	$-0.362770\pi$
$239$	12.9208	0.835780	0.417890	+	0.908498i	$0.362770\pi$
$240$	−1.20721	−0.0779251
$241$	−2.80175	−0.180476	−0.0902382	−	0.995920i	$-0.528763\pi$
$241$	−2.80175	−0.180476	−0.0902382	+	0.995920i	$0.528763\pi$
$242$	10.1211	0.650607
$243$	−9.78876	−0.627950
$244$	14.2792	0.914131
$245$	−17.0771	−1.09102
$246$	3.85198	0.245594
$247$	4.57347	0.291003
$248$	1.73144	0.109946
$249$	−6.39830	−0.405476
$250$	1.02820	0.0650288
$251$	−23.7546	−1.49938	−0.749690	−	0.661789i	$-0.769797\pi$
$251$	−23.7546	−1.49938	−0.749690	+	0.661789i	$0.769797\pi$
$252$	−3.49915	−0.220426
$253$	8.04112	0.505541
$254$	−4.11695	−0.258321
$255$	8.34732	0.522730
$256$	1.00000	0.0625000
$257$	10.8602	0.677439	0.338720	−	0.940887i	$-0.390006\pi$
$257$	10.8602	0.677439	0.338720	+	0.940887i	$0.390006\pi$
$258$	−1.20940	−0.0752941
$259$	−10.2889	−0.639323
$260$	2.69922	0.167399
$261$	−18.9671	−1.17404
$262$	−8.83379	−0.545754
$263$	−3.52190	−0.217170	−0.108585	−	0.994087i	$-0.534632\pi$
$263$	−3.52190	−0.217170	−0.108585	+	0.994087i	$0.534632\pi$
$264$	−0.363966	−0.0224006
$265$	32.7584	2.01233
$266$	−6.47042	−0.396727
$267$	−3.58519	−0.219410
$268$	−8.57238	−0.523641
$269$	8.38444	0.511208	0.255604	−	0.966782i	$-0.417726\pi$
$269$	8.38444	0.511208	0.255604	+	0.966782i	$0.417726\pi$
$270$	−7.06132	−0.429738
$271$	2.12691	0.129201	0.0646004	−	0.997911i	$-0.479423\pi$
$271$	2.12691	0.129201	0.0646004	+	0.997911i	$0.479423\pi$
$272$	−6.91455	−0.419256
$273$	−0.413859	−0.0250479
$274$	−19.2042	−1.16017
$275$	−4.37756	−0.263977
$276$	3.32986	0.200434
$277$	20.5887	1.23705	0.618527	−	0.785764i	$-0.287730\pi$
$277$	20.5887	1.23705	0.618527	+	0.785764i	$0.287730\pi$
$278$	7.02689	0.421445
$279$	4.93335	0.295352
$280$	−3.81879	−0.228216
$281$	6.16965	0.368051	0.184025	−	0.982921i	$-0.441087\pi$
$281$	6.16965	0.368051	0.184025	+	0.982921i	$0.441087\pi$
$282$	4.56562	0.271878
$283$	22.7173	1.35041	0.675203	−	0.737632i	$-0.264056\pi$
$283$	22.7173	1.35041	0.675203	+	0.737632i	$0.264056\pi$
$284$	12.7650	0.757462
$285$	−6.36046	−0.376761
$286$	0.813798	0.0481209
$287$	12.1850	0.719261
$288$	2.84928	0.167895
$289$	30.8110	1.81241
$290$	−20.6997	−1.21553
$291$	1.38992	0.0814784
$292$	15.6687	0.916939
$293$	−17.2280	−1.00647	−0.503236	−	0.864149i	$-0.667858\pi$
$293$	−17.2280	−1.00647	−0.503236	+	0.864149i	$0.667858\pi$
$294$	−2.13207	−0.124345
$295$	11.1179	0.647310
$296$	8.37805	0.486964
$297$	−2.12894	−0.123534
$298$	1.95768	0.113405
$299$	−7.44528	−0.430572
$300$	−1.81276	−0.104660
$301$	−3.82572	−0.220511
$302$	−1.98527	−0.114239
$303$	−1.10131	−0.0632688
$304$	5.26872	0.302182
$305$	44.4019	2.54245
$306$	−19.7015	−1.12626
$307$	0.946070	0.0539951	0.0269975	−	0.999636i	$-0.491405\pi$
$307$	0.946070	0.0539951	0.0269975	+	0.999636i	$0.491405\pi$
$308$	−1.15134	−0.0656037
$309$	7.25022	0.412451
$310$	5.38400	0.305791
$311$	−9.24769	−0.524389	−0.262194	−	0.965015i	$-0.584446\pi$
$311$	−9.24769	−0.524389	−0.262194	+	0.965015i	$0.584446\pi$
$312$	0.336996	0.0190787
$313$	−2.81729	−0.159243	−0.0796214	−	0.996825i	$-0.525371\pi$
$313$	−2.81729	−0.159243	−0.0796214	+	0.996825i	$0.525371\pi$
$314$	−8.17510	−0.461348
$315$	−10.8808	−0.613064
$316$	13.9939	0.787218
$317$	7.31654	0.410938	0.205469	−	0.978664i	$-0.434128\pi$
$317$	7.31654	0.410938	0.205469	+	0.978664i	$0.434128\pi$
$318$	4.08986	0.229348
$319$	−6.24083	−0.349419
$320$	3.10956	0.173830
$321$	−1.17063	−0.0653380
$322$	10.5334	0.587003
$323$	−36.4308	−2.02707
$324$	7.66624	0.425902
$325$	4.05318	0.224830
$326$	−6.33468	−0.350845
$327$	−6.77786	−0.374816
$328$	−9.92201	−0.547851
$329$	14.4425	0.796240
$330$	−1.13177	−0.0623021
$331$	−16.5804	−0.911342	−0.455671	−	0.890148i	$-0.650601\pi$
$331$	−16.5804	−0.911342	−0.455671	+	0.890148i	$0.650601\pi$
$332$	16.4809	0.904504
$333$	23.8714	1.30815
$334$	5.78990	0.316809
$335$	−26.6563	−1.45639
$336$	−0.476774	−0.0260101
$337$	−26.3531	−1.43555	−0.717773	−	0.696277i	$-0.754838\pi$
$337$	−26.3531	−1.43555	−0.717773	+	0.696277i	$0.754838\pi$
$338$	12.2465	0.666122
$339$	6.17972	0.335636
$340$	−21.5012	−1.16607
$341$	1.62324	0.0879033
$342$	15.0121	0.811759
$343$	−15.3410	−0.828335
$344$	3.11520	0.167960
$345$	10.3544	0.557461
$346$	13.2572	0.712709
$347$	−4.66615	−0.250492	−0.125246	−	0.992126i	$-0.539972\pi$
$347$	−4.66615	−0.250492	−0.125246	+	0.992126i	$0.539972\pi$
$348$	−2.58435	−0.138536
$349$	−19.3119	−1.03374	−0.516871	−	0.856064i	$-0.672903\pi$
$349$	−19.3119	−1.03374	−0.516871	+	0.856064i	$0.672903\pi$
$350$	−5.73434	−0.306513
$351$	1.97119	0.105214
$352$	0.937511	0.0499695
$353$	32.5192	1.73082	0.865412	−	0.501061i	$-0.167057\pi$
$353$	32.5192	1.73082	0.865412	+	0.501061i	$0.167057\pi$
$354$	1.38806	0.0737748
$355$	39.6934	2.10671
$356$	9.23480	0.489443
$357$	3.29668	0.174479
$358$	15.1205	0.799142
$359$	−12.7127	−0.670951	−0.335476	−	0.942049i	$-0.608897\pi$
$359$	−12.7127	−0.670951	−0.335476	+	0.942049i	$0.608897\pi$
$360$	8.86000	0.466963
$361$	8.75941	0.461021
$362$	−0.353991	−0.0186053
$363$	3.92926	0.206233
$364$	1.06603	0.0558749
$365$	48.7226	2.55026
$366$	5.54355	0.289766
$367$	8.81749	0.460269	0.230135	−	0.973159i	$-0.426083\pi$
$367$	8.81749	0.460269	0.230135	+	0.973159i	$0.426083\pi$
$368$	−8.57710	−0.447112
$369$	−28.2706	−1.47171
$370$	26.0520	1.35438
$371$	12.9375	0.671683
$372$	0.672189	0.0348514
$373$	−22.6576	−1.17317	−0.586584	−	0.809888i	$-0.699528\pi$
$373$	−22.6576	−1.17317	−0.586584	+	0.809888i	$0.699528\pi$
$374$	−6.48247	−0.335200
$375$	0.399173	0.0206132
$376$	−11.7602	−0.606486
$377$	5.77838	0.297602
$378$	−2.78878	−0.143439
$379$	−28.9932	−1.48928	−0.744639	−	0.667467i	$-0.767378\pi$
$379$	−28.9932	−1.48928	−0.744639	+	0.667467i	$0.767378\pi$
$380$	16.3834	0.840450
$381$	−1.59831	−0.0818838
$382$	−17.9374	−0.917756
$383$	21.3885	1.09290	0.546452	−	0.837491i	$-0.315978\pi$
$383$	21.3885	1.09290	0.546452	+	0.837491i	$0.315978\pi$
$384$	0.388226	0.0198116
$385$	−3.58016	−0.182462
$386$	−0.744531	−0.0378956
$387$	8.87608	0.451196
$388$	−3.58018	−0.181756
$389$	35.8000	1.81513	0.907566	−	0.419909i	$-0.137938\pi$
$389$	35.8000	1.81513	0.907566	+	0.419909i	$0.137938\pi$
$390$	1.04791	0.0530629
$391$	59.3068	2.99928
$392$	5.49181	0.277378
$393$	−3.42951	−0.172996
$394$	6.12284	0.308464
$395$	43.5148	2.18947
$396$	2.67123	0.134234
$397$	9.11396	0.457417	0.228708	−	0.973495i	$-0.426550\pi$
$397$	9.11396	0.457417	0.228708	+	0.973495i	$0.426550\pi$
$398$	1.73145	0.0867899
$399$	−2.51199	−0.125757
$400$	4.66934	0.233467
$401$	6.07800	0.303521	0.151760	−	0.988417i	$-0.451506\pi$
$401$	6.07800	0.303521	0.151760	+	0.988417i	$0.451506\pi$
$402$	−3.32802	−0.165987
$403$	−1.50296	−0.0748677
$404$	2.83678	0.141135
$405$	23.8386	1.18455
$406$	−8.17511	−0.405724
$407$	7.85451	0.389334
$408$	−2.68441	−0.132898
$409$	38.2776	1.89271	0.946354	−	0.323133i	$-0.104736\pi$
$409$	38.2776	1.89271	0.946354	+	0.323133i	$0.104736\pi$
$410$	−30.8531	−1.52372
$411$	−7.45556	−0.367756
$412$	−18.6753	−0.920064
$413$	4.39089	0.216062
$414$	−24.4386	−1.20109
$415$	51.2481	2.51567
$416$	−0.868041	−0.0425592
$417$	2.72802	0.133592
$418$	4.93948	0.241598
$419$	−14.1534	−0.691441	−0.345720	−	0.938338i	$-0.612365\pi$
$419$	−14.1534	−0.691441	−0.345720	+	0.938338i	$0.612365\pi$
$420$	−1.48255	−0.0723412
$421$	1.16939	0.0569924	0.0284962	−	0.999594i	$-0.490928\pi$
$421$	1.16939	0.0569924	0.0284962	+	0.999594i	$0.490928\pi$
$422$	6.78471	0.330275
$423$	−33.5081	−1.62922
$424$	−10.5347	−0.511612
$425$	−32.2864	−1.56612
$426$	4.95570	0.240104
$427$	17.5360	0.848627
$428$	3.01532	0.145751
$429$	0.315938	0.0152536
$430$	9.68689	0.467143
$431$	−5.83747	−0.281181	−0.140591	−	0.990068i	$-0.544900\pi$
$431$	−5.83747	−0.281181	−0.140591	+	0.990068i	$0.544900\pi$
$432$	2.27084	0.109256
$433$	12.0995	0.581466	0.290733	−	0.956804i	$-0.406101\pi$
$433$	12.0995	0.581466	0.290733	+	0.956804i	$0.406101\pi$
$434$	2.12635	0.102068
$435$	−8.03617	−0.385305
$436$	17.4585	0.836112
$437$	−45.1904	−2.16175
$438$	6.08298	0.290656
$439$	8.88512	0.424063	0.212032	−	0.977263i	$-0.431992\pi$
$439$	8.88512	0.424063	0.212032	+	0.977263i	$0.431992\pi$
$440$	2.91524	0.138979
$441$	15.6477	0.745129
$442$	6.00212	0.285492
$443$	34.5283	1.64049	0.820246	−	0.572012i	$-0.193837\pi$
$443$	34.5283	1.64049	0.820246	+	0.572012i	$0.193837\pi$
$444$	3.25258	0.154361
$445$	28.7161	1.36128
$446$	16.2890	0.771306
$447$	0.760022	0.0359478
$448$	1.22808	0.0580214
$449$	27.7902	1.31150	0.655751	−	0.754977i	$-0.272352\pi$
$449$	27.7902	1.31150	0.655751	+	0.754977i	$0.272352\pi$
$450$	13.3043	0.627169
$451$	−9.30199	−0.438014
$452$	−15.9178	−0.748712
$453$	−0.770732	−0.0362121
$454$	7.71676	0.362166
$455$	3.31487	0.155403
$456$	2.04545	0.0957872
$457$	20.3555	0.952191	0.476096	−	0.879394i	$-0.342052\pi$
$457$	20.3555	0.952191	0.476096	+	0.879394i	$0.342052\pi$
$458$	24.4802	1.14388
$459$	−15.7019	−0.732900
$460$	−26.6710	−1.24354
$461$	7.62631	0.355193	0.177596	−	0.984103i	$-0.443168\pi$
$461$	7.62631	0.355193	0.177596	+	0.984103i	$0.443168\pi$
$462$	−0.446980	−0.0207954
$463$	−20.8218	−0.967669	−0.483835	−	0.875159i	$-0.660756\pi$
$463$	−20.8218	−0.967669	−0.483835	+	0.875159i	$0.660756\pi$
$464$	6.65681	0.309035
$465$	2.09021	0.0969311
$466$	−20.4741	−0.948447
$467$	−16.3101	−0.754742	−0.377371	−	0.926062i	$-0.623172\pi$
$467$	−16.3101	−0.754742	−0.377371	+	0.926062i	$0.623172\pi$
$468$	−2.47329	−0.114328
$469$	−10.5276	−0.486119
$470$	−36.5690	−1.68680
$471$	−3.17379	−0.146240
$472$	−3.57540	−0.164571
$473$	2.92053	0.134286
$474$	5.43280	0.249537
$475$	24.6015	1.12879
$476$	−8.49164	−0.389214
$477$	−30.0164	−1.37436
$478$	−12.9208	−0.590986
$479$	−23.4269	−1.07040	−0.535200	−	0.844725i	$-0.679764\pi$
$479$	−23.4269	−1.07040	−0.535200	+	0.844725i	$0.679764\pi$
$480$	1.20721	0.0551014
$481$	−7.27250	−0.331597
$482$	2.80175	0.127616
$483$	4.08934	0.186071
$484$	−10.1211	−0.460049
$485$	−11.1328	−0.505513
$486$	9.78876	0.444027
$487$	1.11759	0.0506428	0.0253214	−	0.999679i	$-0.491939\pi$
$487$	1.11759	0.0506428	0.0253214	+	0.999679i	$0.491939\pi$
$488$	−14.2792	−0.646388
$489$	−2.45929	−0.111213
$490$	17.0771	0.771465
$491$	−37.1004	−1.67432	−0.837160	−	0.546958i	$-0.815786\pi$
$491$	−37.1004	−1.67432	−0.837160	+	0.546958i	$0.815786\pi$
$492$	−3.85198	−0.173661
$493$	−46.0289	−2.07304
$494$	−4.57347	−0.205770
$495$	8.30634	0.373342
$496$	−1.73144	−0.0777438
$497$	15.6765	0.703185
$498$	6.39830	0.286715
$499$	−9.42876	−0.422089	−0.211045	−	0.977476i	$-0.567687\pi$
$499$	−9.42876	−0.422089	−0.211045	+	0.977476i	$0.567687\pi$
$500$	−1.02820	−0.0459823
$501$	2.24779	0.100424
$502$	23.7546	1.06022
$503$	−42.3308	−1.88744	−0.943718	−	0.330751i	$-0.892698\pi$
$503$	−42.3308	−1.88744	−0.943718	+	0.330751i	$0.892698\pi$
$504$	3.49915	0.155865
$505$	8.82114	0.392536
$506$	−8.04112	−0.357472
$507$	4.75441	0.211151
$508$	4.11695	0.182660
$509$	0.230046	0.0101966	0.00509830	−	0.999987i	$-0.498377\pi$
$509$	0.230046	0.0101966	0.00509830	+	0.999987i	$0.498377\pi$
$510$	−8.34732	−0.369626
$511$	19.2424	0.851234
$512$	−1.00000	−0.0441942
$513$	11.9644	0.528243
$514$	−10.8602	−0.479022
$515$	−58.0718	−2.55895
$516$	1.20940	0.0532410
$517$	−11.0253	−0.484893
$518$	10.2889	0.452070
$519$	5.14677	0.225918
$520$	−2.69922	−0.118369
$521$	−11.2626	−0.493424	−0.246712	−	0.969089i	$-0.579350\pi$
$521$	−11.2626	−0.493424	−0.246712	+	0.969089i	$0.579350\pi$
$522$	18.9671	0.830168
$523$	26.0805	1.14042	0.570210	−	0.821499i	$-0.306862\pi$
$523$	26.0805	1.14042	0.570210	+	0.821499i	$0.306862\pi$
$524$	8.83379	0.385906
$525$	−2.22622	−0.0971602
$526$	3.52190	0.153562
$527$	11.9721	0.521513
$528$	0.363966	0.0158396
$529$	50.5667	2.19855
$530$	−32.7584	−1.42293
$531$	−10.1873	−0.442092
$532$	6.47042	0.280528
$533$	8.61272	0.373058
$534$	3.58519	0.155146
$535$	9.37631	0.405373
$536$	8.57238	0.370270
$537$	5.87017	0.253316
$538$	−8.38444	−0.361479
$539$	5.14863	0.221767
$540$	7.06132	0.303871
$541$	8.22020	0.353414	0.176707	−	0.984264i	$-0.443456\pi$
$541$	8.22020	0.353414	0.176707	+	0.984264i	$0.443456\pi$
$542$	−2.12691	−0.0913587
$543$	−0.137428	−0.00589762
$544$	6.91455	0.296459
$545$	54.2883	2.32546
$546$	0.413859	0.0177115
$547$	−14.5976	−0.624150	−0.312075	−	0.950057i	$-0.601024\pi$
$547$	−14.5976	−0.624150	−0.312075	+	0.950057i	$0.601024\pi$
$548$	19.2042	0.820361
$549$	−40.6854	−1.73641
$550$	4.37756	0.186660
$551$	35.0729	1.49415
$552$	−3.32986	−0.141728
$553$	17.1857	0.730809
$554$	−20.5887	−0.874729
$555$	10.1141	0.429319
$556$	−7.02689	−0.298006
$557$	−10.2181	−0.432957	−0.216478	−	0.976287i	$-0.569457\pi$
$557$	−10.2181	−0.432957	−0.216478	+	0.976287i	$0.569457\pi$
$558$	−4.93335	−0.208845
$559$	−2.70412	−0.114372
$560$	3.81879	0.161373
$561$	−2.51666	−0.106254
$562$	−6.16965	−0.260251
$563$	4.61038	0.194304	0.0971521	−	0.995270i	$-0.469027\pi$
$563$	4.61038	0.194304	0.0971521	+	0.995270i	$0.469027\pi$
$564$	−4.56562	−0.192247
$565$	−49.4974	−2.08237
$566$	−22.7173	−0.954881
$567$	9.41477	0.395383
$568$	−12.7650	−0.535607
$569$	22.3499	0.936957	0.468478	−	0.883475i	$-0.344802\pi$
$569$	22.3499	0.936957	0.468478	+	0.883475i	$0.344802\pi$
$570$	6.36046	0.266410
$571$	13.1554	0.550538	0.275269	−	0.961367i	$-0.411233\pi$
$571$	13.1554	0.550538	0.275269	+	0.961367i	$0.411233\pi$
$572$	−0.813798	−0.0340266
$573$	−6.96376	−0.290915
$574$	−12.1850	−0.508594
$575$	−40.0494	−1.67018
$576$	−2.84928	−0.118720
$577$	−15.0501	−0.626543	−0.313272	−	0.949664i	$-0.601425\pi$
$577$	−15.0501	−0.626543	−0.313272	+	0.949664i	$0.601425\pi$
$578$	−30.8110	−1.28157
$579$	−0.289046	−0.0120124
$580$	20.6997	0.859509
$581$	20.2398	0.839690
$582$	−1.38992	−0.0576139
$583$	−9.87642	−0.409040
$584$	−15.6687	−0.648374
$585$	−7.69084	−0.317977
$586$	17.2280	0.711684
$587$	−2.05706	−0.0849039	−0.0424519	−	0.999099i	$-0.513517\pi$
$587$	−2.05706	−0.0849039	−0.0424519	+	0.999099i	$0.513517\pi$
$588$	2.13207	0.0879249
$589$	−9.12245	−0.375884
$590$	−11.1179	−0.457717
$591$	2.37705	0.0977787
$592$	−8.37805	−0.344336
$593$	25.3568	1.04128	0.520640	−	0.853776i	$-0.325693\pi$
$593$	25.3568	1.04128	0.520640	+	0.853776i	$0.325693\pi$
$594$	2.12894	0.0873514
$595$	−26.4052	−1.08251
$596$	−1.95768	−0.0801897
$597$	0.672195	0.0275111
$598$	7.44528	0.304460
$599$	5.72822	0.234049	0.117024	−	0.993129i	$-0.462664\pi$
$599$	5.72822	0.234049	0.117024	+	0.993129i	$0.462664\pi$
$600$	1.81276	0.0740057
$601$	−20.0521	−0.817942	−0.408971	−	0.912547i	$-0.634112\pi$
$601$	−20.0521	−0.817942	−0.408971	+	0.912547i	$0.634112\pi$
$602$	3.82572	0.155925
$603$	24.4251	0.994667
$604$	1.98527	0.0807793
$605$	−31.4721	−1.27952
$606$	1.10131	0.0447378
$607$	−41.9055	−1.70089	−0.850446	−	0.526063i	$-0.823668\pi$
$607$	−41.9055	−1.70089	−0.850446	+	0.526063i	$0.823668\pi$
$608$	−5.26872	−0.213675
$609$	−3.17379	−0.128608
$610$	−44.4019	−1.79778
$611$	10.2083	0.412985
$612$	19.7015	0.796386
$613$	13.7419	0.555032	0.277516	−	0.960721i	$-0.410489\pi$
$613$	13.7419	0.555032	0.277516	+	0.960721i	$0.410489\pi$
$614$	−0.946070	−0.0381803
$615$	−11.9780	−0.482998
$616$	1.15134	0.0463888
$617$	10.3091	0.415027	0.207514	−	0.978232i	$-0.433463\pi$
$617$	10.3091	0.415027	0.207514	+	0.978232i	$0.433463\pi$
$618$	−7.25022	−0.291647
$619$	−47.5154	−1.90980	−0.954902	−	0.296920i	$-0.904041\pi$
$619$	−47.5154	−1.90980	−0.954902	+	0.296920i	$0.904041\pi$
$620$	−5.38400	−0.216227
$621$	−19.4773	−0.781595
$622$	9.24769	0.370799
$623$	11.3411	0.454371
$624$	−0.336996	−0.0134906
$625$	−26.5439	−1.06176
$626$	2.81729	0.112602
$627$	1.91764	0.0765830
$628$	8.17510	0.326222
$629$	57.9305	2.30984
$630$	10.8808	0.433502
$631$	0.357038	0.0142134	0.00710672	−	0.999975i	$-0.497738\pi$
$631$	0.357038	0.0142134	0.00710672	+	0.999975i	$0.497738\pi$
$632$	−13.9939	−0.556648
$633$	2.63400	0.104692
$634$	−7.31654	−0.290577
$635$	12.8019	0.508028
$636$	−4.08986	−0.162173
$637$	−4.76712	−0.188880
$638$	6.24083	0.247077
$639$	−36.3710	−1.43882
$640$	−3.10956	−0.122916
$641$	−12.1672	−0.480576	−0.240288	−	0.970702i	$-0.577242\pi$
$641$	−12.1672	−0.480576	−0.240288	+	0.970702i	$0.577242\pi$
$642$	1.17063	0.0462009
$643$	3.07951	0.121444	0.0607221	−	0.998155i	$-0.480660\pi$
$643$	3.07951	0.121444	0.0607221	+	0.998155i	$0.480660\pi$
$644$	−10.5334	−0.415074
$645$	3.76070	0.148078
$646$	36.4308	1.43335
$647$	−18.5081	−0.727627	−0.363814	−	0.931472i	$-0.618526\pi$
$647$	−18.5081	−0.727627	−0.363814	+	0.931472i	$0.618526\pi$
$648$	−7.66624	−0.301158
$649$	−3.35198	−0.131577
$650$	−4.05318	−0.158979
$651$	0.825503	0.0323540
$652$	6.33468	0.248085
$653$	7.26449	0.284282	0.142141	−	0.989846i	$-0.454601\pi$
$653$	7.26449	0.284282	0.142141	+	0.989846i	$0.454601\pi$
$654$	6.77786	0.265035
$655$	27.4692	1.07331
$656$	9.92201	0.387389
$657$	−44.6444	−1.74174
$658$	−14.4425	−0.563027
$659$	7.46156	0.290661	0.145330	−	0.989383i	$-0.453575\pi$
$659$	7.46156	0.290661	0.145330	+	0.989383i	$0.453575\pi$
$660$	1.13177	0.0440542
$661$	44.2188	1.71991	0.859956	−	0.510368i	$-0.170491\pi$
$661$	44.2188	1.71991	0.859956	+	0.510368i	$0.170491\pi$
$662$	16.5804	0.644416
$663$	2.33018	0.0904966
$664$	−16.4809	−0.639581
$665$	20.1201	0.780226
$666$	−23.8714	−0.924999
$667$	−57.0961	−2.21077
$668$	−5.78990	−0.224018
$669$	6.32381	0.244493
$670$	26.6563	1.02982
$671$	−13.3869	−0.516795
$672$	0.476774	0.0183919
$673$	29.8470	1.15052	0.575259	−	0.817971i	$-0.304901\pi$
$673$	29.8470	1.15052	0.575259	+	0.817971i	$0.304901\pi$
$674$	26.3531	1.01508
$675$	10.6033	0.408123
$676$	−12.2465	−0.471019
$677$	21.7870	0.837343	0.418671	−	0.908138i	$-0.362496\pi$
$677$	21.7870	0.837343	0.418671	+	0.908138i	$0.362496\pi$
$678$	−6.17972	−0.237331
$679$	−4.39675	−0.168732
$680$	21.5012	0.824533
$681$	2.99585	0.114801
$682$	−1.62324	−0.0621570
$683$	−43.4538	−1.66271	−0.831356	−	0.555740i	$-0.812435\pi$
$683$	−43.4538	−1.66271	−0.831356	+	0.555740i	$0.812435\pi$
$684$	−15.0121	−0.574000
$685$	59.7164	2.28165
$686$	15.3410	0.585721
$687$	9.50385	0.362594
$688$	−3.11520	−0.118766
$689$	9.14458	0.348381
$690$	−10.3544	−0.394184
$691$	20.5552	0.781958	0.390979	−	0.920400i	$-0.372136\pi$
$691$	20.5552	0.781958	0.390979	+	0.920400i	$0.372136\pi$
$692$	−13.2572	−0.503961
$693$	3.28049	0.124616
$694$	4.66615	0.177124
$695$	−21.8505	−0.828837
$696$	2.58435	0.0979594
$697$	−68.6063	−2.59865
$698$	19.3119	0.730965
$699$	−7.94860	−0.300644
$700$	5.73434	0.216738
$701$	−4.80715	−0.181563	−0.0907817	−	0.995871i	$-0.528937\pi$
$701$	−4.80715	−0.181563	−0.0907817	+	0.995871i	$0.528937\pi$
$702$	−1.97119	−0.0743976
$703$	−44.1416	−1.66483
$704$	−0.937511	−0.0353338
$705$	−14.1970	−0.534692
$706$	−32.5192	−1.22388
$707$	3.48380	0.131022
$708$	−1.38806	−0.0521667
$709$	2.55177	0.0958339	0.0479170	−	0.998851i	$-0.484742\pi$
$709$	2.55177	0.0958339	0.0479170	+	0.998851i	$0.484742\pi$
$710$	−39.6934	−1.48967
$711$	−39.8726	−1.49534
$712$	−9.23480	−0.346089
$713$	14.8507	0.556163
$714$	−3.29668	−0.123375
$715$	−2.53055	−0.0946372
$716$	−15.1205	−0.565079
$717$	−5.01621	−0.187334
$718$	12.7127	0.474434
$719$	34.2056	1.27565	0.637826	−	0.770180i	$-0.279834\pi$
$719$	34.2056	1.27565	0.637826	+	0.770180i	$0.279834\pi$
$720$	−8.86000	−0.330193
$721$	−22.9347	−0.854135
$722$	−8.75941	−0.325991
$723$	1.08771	0.0404524
$724$	0.353991	0.0131560
$725$	31.0829	1.15439
$726$	−3.92926	−0.145829
$727$	−49.8070	−1.84724	−0.923620	−	0.383309i	$-0.874784\pi$
$727$	−49.8070	−1.84724	−0.923620	+	0.383309i	$0.874784\pi$
$728$	−1.06603	−0.0395096
$729$	−19.1985	−0.711054
$730$	−48.7226	−1.80330
$731$	21.5402	0.796694
$732$	−5.54355	−0.204896
$733$	12.3016	0.454369	0.227185	−	0.973852i	$-0.427048\pi$
$733$	12.3016	0.454369	0.227185	+	0.973852i	$0.427048\pi$
$734$	−8.81749	−0.325460
$735$	6.62978	0.244543
$736$	8.57710	0.316156
$737$	8.03669	0.296035
$738$	28.2706	1.04066
$739$	−12.0435	−0.443026	−0.221513	−	0.975157i	$-0.571100\pi$
$739$	−12.0435	−0.443026	−0.221513	+	0.975157i	$0.571100\pi$
$740$	−26.0520	−0.957692
$741$	−1.77554	−0.0652260
$742$	−12.9375	−0.474951
$743$	−43.9171	−1.61116	−0.805582	−	0.592485i	$-0.798147\pi$
$743$	−43.9171	−1.61116	−0.805582	+	0.592485i	$0.798147\pi$
$744$	−0.672189	−0.0246436
$745$	−6.08752	−0.223029
$746$	22.6576	0.829555
$747$	−46.9586	−1.71812
$748$	6.48247	0.237022
$749$	3.70306	0.135307
$750$	−0.399173	−0.0145757
$751$	1.74592	0.0637097	0.0318548	−	0.999493i	$-0.489859\pi$
$751$	1.74592	0.0637097	0.0318548	+	0.999493i	$0.489859\pi$
$752$	11.7602	0.428850
$753$	9.22217	0.336075
$754$	−5.77838	−0.210436
$755$	6.17329	0.224669
$756$	2.78878	0.101427
$757$	−0.816941	−0.0296922	−0.0148461	−	0.999890i	$-0.504726\pi$
$757$	−0.816941	−0.0296922	−0.0148461	+	0.999890i	$0.504726\pi$
$758$	28.9932	1.05308
$759$	−3.12177	−0.113313
$760$	−16.3834	−0.594288
$761$	−13.1559	−0.476903	−0.238451	−	0.971154i	$-0.576640\pi$
$761$	−13.1559	−0.476903	−0.238451	+	0.971154i	$0.576640\pi$
$762$	1.59831	0.0579006
$763$	21.4405	0.776199
$764$	17.9374	0.648951
$765$	61.2629	2.21497
$766$	−21.3885	−0.772799
$767$	3.10360	0.112064
$768$	−0.388226	−0.0140089
$769$	18.8808	0.680858	0.340429	−	0.940270i	$-0.389428\pi$
$769$	18.8808	0.680858	0.340429	+	0.940270i	$0.389428\pi$
$770$	3.58016	0.129020
$771$	−4.21620	−0.151843
$772$	0.744531	0.0267962
$773$	−12.1297	−0.436275	−0.218137	−	0.975918i	$-0.569998\pi$
$773$	−12.1297	−0.436275	−0.218137	+	0.975918i	$0.569998\pi$
$774$	−8.87608	−0.319044
$775$	−8.08467	−0.290410
$776$	3.58018	0.128521
$777$	3.99443	0.143300
$778$	−35.8000	−1.28349
$779$	52.2763	1.87299
$780$	−1.04791	−0.0375212
$781$	−11.9673	−0.428224
$782$	−59.3068	−2.12081
$783$	15.1166	0.540222
$784$	−5.49181	−0.196136
$785$	25.4209	0.907313
$786$	3.42951	0.122327
$787$	−9.03018	−0.321891	−0.160946	−	0.986963i	$-0.551454\pi$
$787$	−9.03018	−0.321891	−0.160946	+	0.986963i	$0.551454\pi$
$788$	−6.12284	−0.218117
$789$	1.36729	0.0486770
$790$	−43.5148	−1.54819
$791$	−19.5484	−0.695062
$792$	−2.67123	−0.0949180
$793$	12.3949	0.440157
$794$	−9.11396	−0.323443
$795$	−12.7176	−0.451048
$796$	−1.73145	−0.0613697
$797$	11.2239	0.397572	0.198786	−	0.980043i	$-0.436300\pi$
$797$	11.2239	0.397572	0.198786	+	0.980043i	$0.436300\pi$
$798$	2.51199	0.0889233
$799$	−81.3165	−2.87677
$800$	−4.66934	−0.165086
$801$	−26.3125	−0.929708
$802$	−6.07800	−0.214622
$803$	−14.6895	−0.518382
$804$	3.32802	0.117370
$805$	−32.7542	−1.15443
$806$	1.50296	0.0529394
$807$	−3.25506	−0.114584
$808$	−2.83678	−0.0997977
$809$	−10.0724	−0.354125	−0.177063	−	0.984200i	$-0.556660\pi$
$809$	−10.0724	−0.354125	−0.177063	+	0.984200i	$0.556660\pi$
$810$	−23.8386	−0.837603
$811$	−42.4328	−1.49002	−0.745008	−	0.667055i	$-0.767555\pi$
$811$	−42.4328	−1.49002	−0.745008	+	0.667055i	$0.767555\pi$
$812$	8.17511	0.286890
$813$	−0.825723	−0.0289594
$814$	−7.85451	−0.275301
$815$	19.6980	0.689992
$816$	2.68441	0.0939731
$817$	−16.4131	−0.574222
$818$	−38.2776	−1.33835
$819$	−3.03741	−0.106136
$820$	30.8531	1.07744
$821$	−42.6442	−1.48829	−0.744146	−	0.668017i	$-0.767143\pi$
$821$	−42.6442	−1.48829	−0.744146	+	0.668017i	$0.767143\pi$
$822$	7.45556	0.260042
$823$	14.5116	0.505843	0.252922	−	0.967487i	$-0.418609\pi$
$823$	14.5116	0.505843	0.252922	+	0.967487i	$0.418609\pi$
$824$	18.6753	0.650583
$825$	1.69948	0.0591684
$826$	−4.39089	−0.152779
$827$	−32.2423	−1.12117	−0.560587	−	0.828096i	$-0.689424\pi$
$827$	−32.2423	−1.12117	−0.560587	+	0.828096i	$0.689424\pi$
$828$	24.4386	0.849299
$829$	−44.7505	−1.55425	−0.777124	−	0.629348i	$-0.783322\pi$
$829$	−44.7505	−1.55425	−0.777124	+	0.629348i	$0.783322\pi$
$830$	−51.2481	−1.77885
$831$	−7.99306	−0.277276
$832$	0.868041	0.0300939
$833$	37.9734	1.31570
$834$	−2.72802	−0.0944636
$835$	−18.0040	−0.623055
$836$	−4.93948	−0.170835
$837$	−3.93182	−0.135904
$838$	14.1534	0.488922
$839$	28.3006	0.977046	0.488523	−	0.872551i	$-0.337536\pi$
$839$	28.3006	0.977046	0.488523	+	0.872551i	$0.337536\pi$
$840$	1.48255	0.0511530
$841$	15.3131	0.528038
$842$	−1.16939	−0.0402997
$843$	−2.39522	−0.0824958
$844$	−6.78471	−0.233539
$845$	−38.0812	−1.31003
$846$	33.5081	1.15203
$847$	−12.4295	−0.427083
$848$	10.5347	0.361764
$849$	−8.81946	−0.302683
$850$	32.2864	1.10741
$851$	71.8594	2.46331
$852$	−4.95570	−0.169779
$853$	9.54760	0.326904	0.163452	−	0.986551i	$-0.447737\pi$
$853$	9.54760	0.326904	0.163452	+	0.986551i	$0.447737\pi$
$854$	−17.5360	−0.600070
$855$	−46.6809	−1.59645
$856$	−3.01532	−0.103062
$857$	47.8762	1.63542	0.817709	−	0.575631i	$-0.195244\pi$
$857$	47.8762	1.63542	0.817709	+	0.575631i	$0.195244\pi$
$858$	−0.315938	−0.0107859
$859$	32.9207	1.12324	0.561620	−	0.827395i	$-0.310178\pi$
$859$	32.9207	1.12324	0.561620	+	0.827395i	$0.310178\pi$
$860$	−9.68689	−0.330320
$861$	−4.73055	−0.161217
$862$	5.83747	0.198825
$863$	44.8025	1.52509	0.762547	−	0.646933i	$-0.223949\pi$
$863$	44.8025	1.52509	0.762547	+	0.646933i	$0.223949\pi$
$864$	−2.27084	−0.0772557
$865$	−41.2239	−1.40165
$866$	−12.0995	−0.411159
$867$	−11.9616	−0.406239
$868$	−2.12635	−0.0721729
$869$	−13.1194	−0.445046
$870$	8.03617	0.272452
$871$	−7.44118	−0.252135
$872$	−17.4585	−0.591221
$873$	10.2009	0.345249
$874$	45.1904	1.52859
$875$	−1.26271	−0.0426874
$876$	−6.08298	−0.205525
$877$	−2.07335	−0.0700121	−0.0350060	−	0.999387i	$-0.511145\pi$
$877$	−2.07335	−0.0700121	−0.0350060	+	0.999387i	$0.511145\pi$
$878$	−8.88512	−0.299858
$879$	6.68838	0.225593
$880$	−2.91524	−0.0982728
$881$	43.7172	1.47287	0.736436	−	0.676508i	$-0.236507\pi$
$881$	43.7172	1.47287	0.736436	+	0.676508i	$0.236507\pi$
$882$	−15.6477	−0.526886
$883$	32.7682	1.10274	0.551369	−	0.834262i	$-0.314106\pi$
$883$	32.7682	1.10274	0.551369	+	0.834262i	$0.314106\pi$
$884$	−6.00212	−0.201873
$885$	−4.31627	−0.145090
$886$	−34.5283	−1.16000
$887$	−29.6144	−0.994354	−0.497177	−	0.867649i	$-0.665630\pi$
$887$	−29.6144	−0.994354	−0.497177	+	0.867649i	$0.665630\pi$
$888$	−3.25258	−0.109149
$889$	5.05596	0.169571
$890$	−28.7161	−0.962567
$891$	−7.18718	−0.240780
$892$	−16.2890	−0.545396
$893$	61.9612	2.07345
$894$	−0.760022	−0.0254190
$895$	−47.0180	−1.57164
$896$	−1.22808	−0.0410273
$897$	2.89045	0.0965094
$898$	−27.7902	−0.927372
$899$	−11.5258	−0.384408
$900$	−13.3043	−0.443476
$901$	−72.8430	−2.42675
$902$	9.30199	0.309722
$903$	1.48525	0.0494259
$904$	15.9178	0.529419
$905$	1.10075	0.0365903
$906$	0.770732	0.0256058
$907$	51.1099	1.69708	0.848539	−	0.529133i	$-0.177483\pi$
$907$	51.1099	1.69708	0.848539	+	0.529133i	$0.177483\pi$
$908$	−7.71676	−0.256090
$909$	−8.08279	−0.268089
$910$	−3.31487	−0.109887
$911$	10.8082	0.358092	0.179046	−	0.983841i	$-0.442699\pi$
$911$	10.8082	0.358092	0.179046	+	0.983841i	$0.442699\pi$
$912$	−2.04545	−0.0677318
$913$	−15.4510	−0.511352
$914$	−20.3555	−0.673301
$915$	−17.2380	−0.569870
$916$	−24.4802	−0.808848
$917$	10.8486	0.358253
$918$	15.7019	0.518239
$919$	−7.82361	−0.258077	−0.129039	−	0.991640i	$-0.541189\pi$
$919$	−7.82361	−0.258077	−0.129039	+	0.991640i	$0.541189\pi$
$920$	26.6710	0.879317
$921$	−0.367289	−0.0121026
$922$	−7.62631	−0.251159
$923$	11.0805	0.364720
$924$	0.446980	0.0147046
$925$	−39.1200	−1.28626
$926$	20.8218	0.684245
$927$	53.2110	1.74768
$928$	−6.65681	−0.218520
$929$	49.1719	1.61328	0.806639	−	0.591045i	$-0.201284\pi$
$929$	49.1719	1.61328	0.806639	+	0.591045i	$0.201284\pi$
$930$	−2.09021	−0.0685406
$931$	−28.9348	−0.948301
$932$	20.4741	0.670653
$933$	3.59020	0.117538
$934$	16.3101	0.533683
$935$	20.1576	0.659224
$936$	2.47329	0.0808421
$937$	−34.8787	−1.13944	−0.569719	−	0.821839i	$-0.692948\pi$
$937$	−34.8787	−1.13944	−0.569719	+	0.821839i	$0.692948\pi$
$938$	10.5276	0.343738
$939$	1.09375	0.0356931
$940$	36.5690	1.19275
$941$	12.9154	0.421031	0.210515	−	0.977591i	$-0.432486\pi$
$941$	12.9154	0.421031	0.210515	+	0.977591i	$0.432486\pi$
$942$	3.17379	0.103408
$943$	−85.1021	−2.77131
$944$	3.57540	0.116369
$945$	8.67188	0.282096
$946$	−2.92053	−0.0949547
$947$	6.53925	0.212497	0.106249	−	0.994340i	$-0.466116\pi$
$947$	6.53925	0.212497	0.106249	+	0.994340i	$0.466116\pi$
$948$	−5.43280	−0.176449
$949$	13.6010	0.441509
$950$	−24.6015	−0.798177
$951$	−2.84047	−0.0921086
$952$	8.49164	0.275216
$953$	11.1855	0.362333	0.181167	−	0.983452i	$-0.442013\pi$
$953$	11.1855	0.362333	0.181167	+	0.983452i	$0.442013\pi$
$954$	30.0164	0.971817
$955$	55.7773	1.80491
$956$	12.9208	0.417890
$957$	2.42285	0.0783197
$958$	23.4269	0.756887
$959$	23.5843	0.761577
$960$	−1.20721	−0.0389626
$961$	−28.0021	−0.903295
$962$	7.27250	0.234475
$963$	−8.59149	−0.276857
$964$	−2.80175	−0.0902382
$965$	2.31516	0.0745277
$966$	−4.08934	−0.131572
$967$	28.3543	0.911813	0.455907	−	0.890028i	$-0.349315\pi$
$967$	28.3543	0.911813	0.455907	+	0.890028i	$0.349315\pi$
$968$	10.1211	0.325304
$969$	14.1434	0.454351
$970$	11.1328	0.357451
$971$	34.8551	1.11855	0.559276	−	0.828981i	$-0.311079\pi$
$971$	34.8551	1.11855	0.559276	+	0.828981i	$0.311079\pi$
$972$	−9.78876	−0.313975
$973$	−8.62959	−0.276652
$974$	−1.11759	−0.0358099
$975$	−1.57355	−0.0503940
$976$	14.2792	0.457066
$977$	8.45261	0.270423	0.135211	−	0.990817i	$-0.456829\pi$
$977$	8.45261	0.270423	0.135211	+	0.990817i	$0.456829\pi$
$978$	2.45929	0.0786394
$979$	−8.65772	−0.276702
$980$	−17.0771	−0.545508
$981$	−49.7443	−1.58821
$982$	37.1004	1.18392
$983$	6.98981	0.222940	0.111470	−	0.993768i	$-0.464444\pi$
$983$	6.98981	0.222940	0.111470	+	0.993768i	$0.464444\pi$
$984$	3.85198	0.122797
$985$	−19.0393	−0.606644
$986$	46.0289	1.46586
$987$	−5.60695	−0.178471
$988$	4.57347	0.145501
$989$	26.7194	0.849627
$990$	−8.30634	−0.263993
$991$	−19.6648	−0.624672	−0.312336	−	0.949972i	$-0.601112\pi$
$991$	−19.6648	−0.624672	−0.312336	+	0.949972i	$0.601112\pi$
$992$	1.73144	0.0549731
$993$	6.43695	0.204270
$994$	−15.6765	−0.497227
$995$	−5.38405	−0.170686
$996$	−6.39830	−0.202738
$997$	−55.1483	−1.74656	−0.873282	−	0.487215i	$-0.838013\pi$
$997$	−55.1483	−1.74656	−0.873282	+	0.487215i	$0.838013\pi$
$998$	9.42876	0.298462
$999$	−19.0252	−0.601932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.18	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.18	✓	42	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.388226 q^{3} +1.00000 q^{4} +3.10956 q^{5} +0.388226 q^{6} +1.22808 q^{7} -1.00000 q^{8} -2.84928 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.388226 q^{3} +1.00000 q^{4} +3.10956 q^{5} +0.388226 q^{6} +1.22808 q^{7} -1.00000 q^{8} -2.84928 q^{9} -3.10956 q^{10} -0.937511 q^{11} -0.388226 q^{12} +0.868041 q^{13} -1.22808 q^{14} -1.20721 q^{15} +1.00000 q^{16} -6.91455 q^{17} +2.84928 q^{18} +5.26872 q^{19} +3.10956 q^{20} -0.476774 q^{21} +0.937511 q^{22} -8.57710 q^{23} +0.388226 q^{24} +4.66934 q^{25} -0.868041 q^{26} +2.27084 q^{27} +1.22808 q^{28} +6.65681 q^{29} +1.20721 q^{30} -1.73144 q^{31} -1.00000 q^{32} +0.363966 q^{33} +6.91455 q^{34} +3.81879 q^{35} -2.84928 q^{36} -8.37805 q^{37} -5.26872 q^{38} -0.336996 q^{39} -3.10956 q^{40} +9.92201 q^{41} +0.476774 q^{42} -3.11520 q^{43} -0.937511 q^{44} -8.86000 q^{45} +8.57710 q^{46} +11.7602 q^{47} -0.388226 q^{48} -5.49181 q^{49} -4.66934 q^{50} +2.68441 q^{51} +0.868041 q^{52} +10.5347 q^{53} -2.27084 q^{54} -2.91524 q^{55} -1.22808 q^{56} -2.04545 q^{57} -6.65681 q^{58} +3.57540 q^{59} -1.20721 q^{60} +14.2792 q^{61} +1.73144 q^{62} -3.49915 q^{63} +1.00000 q^{64} +2.69922 q^{65} -0.363966 q^{66} -8.57238 q^{67} -6.91455 q^{68} +3.32986 q^{69} -3.81879 q^{70} +12.7650 q^{71} +2.84928 q^{72} +15.6687 q^{73} +8.37805 q^{74} -1.81276 q^{75} +5.26872 q^{76} -1.15134 q^{77} +0.336996 q^{78} +13.9939 q^{79} +3.10956 q^{80} +7.66624 q^{81} -9.92201 q^{82} +16.4809 q^{83} -0.476774 q^{84} -21.5012 q^{85} +3.11520 q^{86} -2.58435 q^{87} +0.937511 q^{88} +9.23480 q^{89} +8.86000 q^{90} +1.06603 q^{91} -8.57710 q^{92} +0.672189 q^{93} -11.7602 q^{94} +16.3834 q^{95} +0.388226 q^{96} -3.58018 q^{97} +5.49181 q^{98} +2.67123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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