LMFDB - Embedded newform 4007.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42814 q^{2} -1.84708 q^{3} +3.89588 q^{4} -2.88367 q^{5} +4.48497 q^{6} -1.14516 q^{7} -4.60348 q^{8} +0.411691 q^{9} +O(q^{10})$	\(q-2.42814 q^{2} -1.84708 q^{3} +3.89588 q^{4} -2.88367 q^{5} +4.48497 q^{6} -1.14516 q^{7} -4.60348 q^{8} +0.411691 q^{9} +7.00198 q^{10} +2.52423 q^{11} -7.19600 q^{12} -2.67680 q^{13} +2.78062 q^{14} +5.32636 q^{15} +3.38615 q^{16} -2.29587 q^{17} -0.999644 q^{18} -1.73521 q^{19} -11.2345 q^{20} +2.11520 q^{21} -6.12920 q^{22} +2.51661 q^{23} +8.50298 q^{24} +3.31557 q^{25} +6.49966 q^{26} +4.78080 q^{27} -4.46142 q^{28} -4.01813 q^{29} -12.9332 q^{30} -1.64057 q^{31} +0.984905 q^{32} -4.66245 q^{33} +5.57470 q^{34} +3.30227 q^{35} +1.60390 q^{36} -5.96423 q^{37} +4.21335 q^{38} +4.94425 q^{39} +13.2749 q^{40} +7.55411 q^{41} -5.13601 q^{42} +1.27008 q^{43} +9.83411 q^{44} -1.18718 q^{45} -6.11070 q^{46} -10.5000 q^{47} -6.25448 q^{48} -5.68861 q^{49} -8.05069 q^{50} +4.24064 q^{51} -10.4285 q^{52} +9.64112 q^{53} -11.6085 q^{54} -7.27906 q^{55} +5.27173 q^{56} +3.20507 q^{57} +9.75659 q^{58} +2.58180 q^{59} +20.7509 q^{60} +7.41138 q^{61} +3.98354 q^{62} -0.471452 q^{63} -9.16379 q^{64} +7.71902 q^{65} +11.3211 q^{66} -14.5029 q^{67} -8.94443 q^{68} -4.64838 q^{69} -8.01839 q^{70} +4.02257 q^{71} -1.89521 q^{72} +11.4803 q^{73} +14.4820 q^{74} -6.12412 q^{75} -6.76019 q^{76} -2.89065 q^{77} -12.0054 q^{78} +10.1796 q^{79} -9.76455 q^{80} -10.0656 q^{81} -18.3425 q^{82} +3.09449 q^{83} +8.24058 q^{84} +6.62053 q^{85} -3.08395 q^{86} +7.42179 q^{87} -11.6203 q^{88} +7.92520 q^{89} +2.88265 q^{90} +3.06537 q^{91} +9.80444 q^{92} +3.03026 q^{93} +25.4956 q^{94} +5.00379 q^{95} -1.81919 q^{96} +4.68181 q^{97} +13.8128 q^{98} +1.03920 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.42814	−1.71696	−0.858479	−	0.512849i	$-0.828590\pi$
$2$	−2.42814	−1.71696	−0.858479	+	0.512849i	$0.828590\pi$
$3$	−1.84708	−1.06641	−0.533205	−	0.845986i	$-0.679013\pi$
$3$	−1.84708	−1.06641	−0.533205	+	0.845986i	$0.679013\pi$
$4$	3.89588	1.94794
$5$	−2.88367	−1.28962	−0.644809	−	0.764344i	$-0.723063\pi$
$5$	−2.88367	−1.28962	−0.644809	+	0.764344i	$0.723063\pi$
$6$	4.48497	1.83098
$7$	−1.14516	−0.432830	−0.216415	−	0.976301i	$-0.569436\pi$
$7$	−1.14516	−0.432830	−0.216415	+	0.976301i	$0.569436\pi$
$8$	−4.60348	−1.62758
$9$	0.411691	0.137230
$10$	7.00198	2.21422
$11$	2.52423	0.761084	0.380542	−	0.924764i	$-0.375737\pi$
$11$	2.52423	0.761084	0.380542	+	0.924764i	$0.375737\pi$
$12$	−7.19600	−2.07731
$13$	−2.67680	−0.742411	−0.371205	−	0.928551i	$-0.621055\pi$
$13$	−2.67680	−0.742411	−0.371205	+	0.928551i	$0.621055\pi$
$14$	2.78062	0.743151
$15$	5.32636	1.37526
$16$	3.38615	0.846537
$17$	−2.29587	−0.556829	−0.278415	−	0.960461i	$-0.589809\pi$
$17$	−2.29587	−0.556829	−0.278415	+	0.960461i	$0.589809\pi$
$18$	−0.999644	−0.235618
$19$	−1.73521	−0.398085	−0.199043	−	0.979991i	$-0.563783\pi$
$19$	−1.73521	−0.398085	−0.199043	+	0.979991i	$0.563783\pi$
$20$	−11.2345	−2.51210
$21$	2.11520	0.461575
$22$	−6.12920	−1.30675
$23$	2.51661	0.524750	0.262375	−	0.964966i	$-0.415494\pi$
$23$	2.51661	0.524750	0.262375	+	0.964966i	$0.415494\pi$
$24$	8.50298	1.73566
$25$	3.31557	0.663114
$26$	6.49966	1.27469
$27$	4.78080	0.920066
$28$	−4.46142	−0.843129
$29$	−4.01813	−0.746147	−0.373074	−	0.927802i	$-0.621696\pi$
$29$	−4.01813	−0.746147	−0.373074	+	0.927802i	$0.621696\pi$
$30$	−12.9332	−2.36127
$31$	−1.64057	−0.294655	−0.147328	−	0.989088i	$-0.547067\pi$
$31$	−1.64057	−0.294655	−0.147328	+	0.989088i	$0.547067\pi$
$32$	0.984905	0.174108
$33$	−4.66245	−0.811628
$34$	5.57470	0.956052
$35$	3.30227	0.558186
$36$	1.60390	0.267317
$37$	−5.96423	−0.980514	−0.490257	−	0.871578i	$-0.663097\pi$
$37$	−5.96423	−0.980514	−0.490257	+	0.871578i	$0.663097\pi$
$38$	4.21335	0.683496
$39$	4.94425	0.791714
$40$	13.2749	2.09895
$41$	7.55411	1.17975	0.589877	−	0.807493i	$-0.299176\pi$
$41$	7.55411	1.17975	0.589877	+	0.807493i	$0.299176\pi$
$42$	−5.13601	−0.792504
$43$	1.27008	0.193686	0.0968431	−	0.995300i	$-0.469126\pi$
$43$	1.27008	0.193686	0.0968431	+	0.995300i	$0.469126\pi$
$44$	9.83411	1.48255
$45$	−1.18718	−0.176975
$46$	−6.11070	−0.900974
$47$	−10.5000	−1.53159	−0.765794	−	0.643086i	$-0.777654\pi$
$47$	−10.5000	−1.53159	−0.765794	+	0.643086i	$0.777654\pi$
$48$	−6.25448	−0.902756
$49$	−5.68861	−0.812658
$50$	−8.05069	−1.13854
$51$	4.24064	0.593808
$52$	−10.4285	−1.44617
$53$	9.64112	1.32431	0.662155	−	0.749367i	$-0.269642\pi$
$53$	9.64112	1.32431	0.662155	+	0.749367i	$0.269642\pi$
$54$	−11.6085	−1.57971
$55$	−7.27906	−0.981508
$56$	5.27173	0.704465
$57$	3.20507	0.424522
$58$	9.75659	1.28110
$59$	2.58180	0.336122	0.168061	−	0.985777i	$-0.446250\pi$
$59$	2.58180	0.336122	0.168061	+	0.985777i	$0.446250\pi$
$60$	20.7509	2.67893
$61$	7.41138	0.948930	0.474465	−	0.880274i	$-0.342642\pi$
$61$	7.41138	0.948930	0.474465	+	0.880274i	$0.342642\pi$
$62$	3.98354	0.505910
$63$	−0.471452	−0.0593974
$64$	−9.16379	−1.14547
$65$	7.71902	0.957426
$66$	11.3211	1.39353
$67$	−14.5029	−1.77181	−0.885904	−	0.463869i	$-0.846461\pi$
$67$	−14.5029	−1.77181	−0.885904	+	0.463869i	$0.846461\pi$
$68$	−8.94443	−1.08467
$69$	−4.64838	−0.559599
$70$	−8.01839	−0.958381
$71$	4.02257	0.477391	0.238696	−	0.971094i	$-0.423280\pi$
$71$	4.02257	0.477391	0.238696	+	0.971094i	$0.423280\pi$
$72$	−1.89521	−0.223353
$73$	11.4803	1.34367	0.671836	−	0.740700i	$-0.265506\pi$
$73$	11.4803	1.34367	0.671836	+	0.740700i	$0.265506\pi$
$74$	14.4820	1.68350
$75$	−6.12412	−0.707152
$76$	−6.76019	−0.775447
$77$	−2.89065	−0.329420
$78$	−12.0054	−1.35934
$79$	10.1796	1.14529	0.572647	−	0.819802i	$-0.305916\pi$
$79$	10.1796	1.14529	0.572647	+	0.819802i	$0.305916\pi$
$80$	−9.76455	−1.09171
$81$	−10.0656	−1.11840
$82$	−18.3425	−2.02559
$83$	3.09449	0.339665	0.169832	−	0.985473i	$-0.445677\pi$
$83$	3.09449	0.339665	0.169832	+	0.985473i	$0.445677\pi$
$84$	8.24058	0.899121
$85$	6.62053	0.718097
$86$	−3.08395	−0.332551
$87$	7.42179	0.795699
$88$	−11.6203	−1.23872
$89$	7.92520	0.840070	0.420035	−	0.907508i	$-0.362018\pi$
$89$	7.92520	0.840070	0.420035	+	0.907508i	$0.362018\pi$
$90$	2.88265	0.303858
$91$	3.06537	0.321338
$92$	9.80444	1.02218
$93$	3.03026	0.314223
$94$	25.4956	2.62967
$95$	5.00379	0.513378
$96$	−1.81919	−0.185671
$97$	4.68181	0.475366	0.237683	−	0.971343i	$-0.423612\pi$
$97$	4.68181	0.475366	0.237683	+	0.971343i	$0.423612\pi$
$98$	13.8128	1.39530
$99$	1.03920	0.104444
$100$	12.9171	1.29171
$101$	13.6678	1.36000	0.680000	−	0.733212i	$-0.261980\pi$
$101$	13.6678	1.36000	0.680000	+	0.733212i	$0.261980\pi$
$102$	−10.2969	−1.01954
$103$	−14.8430	−1.46252	−0.731261	−	0.682097i	$-0.761068\pi$
$103$	−14.8430	−1.46252	−0.731261	+	0.682097i	$0.761068\pi$
$104$	12.3226	1.20833
$105$	−6.09955	−0.595255
$106$	−23.4100	−2.27378
$107$	0.838025	0.0810150	0.0405075	−	0.999179i	$-0.487103\pi$
$107$	0.838025	0.0810150	0.0405075	+	0.999179i	$0.487103\pi$
$108$	18.6255	1.79224
$109$	6.53992	0.626411	0.313205	−	0.949685i	$-0.398597\pi$
$109$	6.53992	0.626411	0.313205	+	0.949685i	$0.398597\pi$
$110$	17.6746	1.68521
$111$	11.0164	1.04563
$112$	−3.87769	−0.366407
$113$	12.7665	1.20097	0.600487	−	0.799635i	$-0.294974\pi$
$113$	12.7665	1.20097	0.600487	+	0.799635i	$0.294974\pi$
$114$	−7.78238	−0.728887
$115$	−7.25710	−0.676728
$116$	−15.6542	−1.45345
$117$	−1.10201	−0.101881
$118$	−6.26898	−0.577106
$119$	2.62914	0.241013
$120$	−24.5198	−2.23834
$121$	−4.62826	−0.420751
$122$	−17.9959	−1.62927
$123$	−13.9530	−1.25810
$124$	−6.39147	−0.573971
$125$	4.85734	0.434454
$126$	1.14475	0.101983
$127$	−15.8783	−1.40897	−0.704487	−	0.709717i	$-0.748823\pi$
$127$	−15.8783	−1.40897	−0.704487	+	0.709717i	$0.748823\pi$
$128$	20.2812	1.79262
$129$	−2.34594	−0.206549
$130$	−18.7429	−1.64386
$131$	−11.3517	−0.991804	−0.495902	−	0.868379i	$-0.665162\pi$
$131$	−11.3517	−0.991804	−0.495902	+	0.868379i	$0.665162\pi$
$132$	−18.1644	−1.58100
$133$	1.98710	0.172303
$134$	35.2151	3.04212
$135$	−13.7863	−1.18653
$136$	10.5690	0.906283
$137$	−11.3190	−0.967045	−0.483522	−	0.875332i	$-0.660643\pi$
$137$	−11.3190	−0.967045	−0.483522	+	0.875332i	$0.660643\pi$
$138$	11.2869	0.960808
$139$	20.2733	1.71956	0.859778	−	0.510668i	$-0.170602\pi$
$139$	20.2733	1.71956	0.859778	+	0.510668i	$0.170602\pi$
$140$	12.8653	1.08731
$141$	19.3944	1.63330
$142$	−9.76738	−0.819661
$143$	−6.75686	−0.565037
$144$	1.39405	0.116171
$145$	11.5870	0.962245
$146$	−27.8759	−2.30703
$147$	10.5073	0.866626
$148$	−23.2360	−1.90998
$149$	17.0700	1.39843	0.699214	−	0.714913i	$-0.253534\pi$
$149$	17.0700	1.39843	0.699214	+	0.714913i	$0.253534\pi$
$150$	14.8702	1.21415
$151$	22.8054	1.85588	0.927940	−	0.372731i	$-0.121578\pi$
$151$	22.8054	1.85588	0.927940	+	0.372731i	$0.121578\pi$
$152$	7.98803	0.647915
$153$	−0.945187	−0.0764138
$154$	7.01892	0.565601
$155$	4.73087	0.379992
$156$	19.2622	1.54221
$157$	−8.40771	−0.671008	−0.335504	−	0.942039i	$-0.608907\pi$
$157$	−8.40771	−0.671008	−0.335504	+	0.942039i	$0.608907\pi$
$158$	−24.7175	−1.96642
$159$	−17.8079	−1.41226
$160$	−2.84014	−0.224533
$161$	−2.88193	−0.227128
$162$	24.4407	1.92024
$163$	−12.6427	−0.990256	−0.495128	−	0.868820i	$-0.664879\pi$
$163$	−12.6427	−0.990256	−0.495128	+	0.868820i	$0.664879\pi$
$164$	29.4300	2.29809
$165$	13.4450	1.04669
$166$	−7.51387	−0.583190
$167$	21.3286	1.65046	0.825230	−	0.564797i	$-0.191046\pi$
$167$	21.3286	1.65046	0.825230	+	0.564797i	$0.191046\pi$
$168$	−9.73729	−0.751248
$169$	−5.83474	−0.448826
$170$	−16.0756	−1.23294
$171$	−0.714371	−0.0546294
$172$	4.94810	0.377289
$173$	15.3945	1.17042	0.585212	−	0.810880i	$-0.301011\pi$
$173$	15.3945	1.17042	0.585212	+	0.810880i	$0.301011\pi$
$174$	−18.0212	−1.36618
$175$	−3.79687	−0.287016
$176$	8.54742	0.644286
$177$	−4.76878	−0.358443
$178$	−19.2435	−1.44236
$179$	1.49512	0.111750	0.0558751	−	0.998438i	$-0.482205\pi$
$179$	1.49512	0.111750	0.0558751	+	0.998438i	$0.482205\pi$
$180$	−4.62512	−0.344736
$181$	0.534041	0.0396950	0.0198475	−	0.999803i	$-0.493682\pi$
$181$	0.534041	0.0396950	0.0198475	+	0.999803i	$0.493682\pi$
$182$	−7.44316	−0.551724
$183$	−13.6894	−1.01195
$184$	−11.5852	−0.854072
$185$	17.1989	1.26449
$186$	−7.35790	−0.539508
$187$	−5.79530	−0.423794
$188$	−40.9070	−2.98345
$189$	−5.47479	−0.398233
$190$	−12.1499	−0.881448
$191$	−12.0009	−0.868357	−0.434179	−	0.900827i	$-0.642961\pi$
$191$	−12.0009	−0.868357	−0.434179	+	0.900827i	$0.642961\pi$
$192$	16.9262	1.22154
$193$	22.2816	1.60387	0.801934	−	0.597413i	$-0.203805\pi$
$193$	22.2816	1.60387	0.801934	+	0.597413i	$0.203805\pi$
$194$	−11.3681	−0.816182
$195$	−14.2576	−1.02101
$196$	−22.1622	−1.58301
$197$	−15.5200	−1.10575	−0.552875	−	0.833264i	$-0.686469\pi$
$197$	−15.5200	−1.10575	−0.552875	+	0.833264i	$0.686469\pi$
$198$	−2.52333	−0.179325
$199$	16.0675	1.13899	0.569497	−	0.821994i	$-0.307138\pi$
$199$	16.0675	1.13899	0.569497	+	0.821994i	$0.307138\pi$
$200$	−15.2632	−1.07927
$201$	26.7879	1.88947
$202$	−33.1875	−2.33506
$203$	4.60140	0.322955
$204$	16.5210	1.15670
$205$	−21.7836	−1.52143
$206$	36.0409	2.51109
$207$	1.03607	0.0720116
$208$	−9.06405	−0.628479
$209$	−4.38008	−0.302977
$210$	14.8106	1.02203
$211$	12.3985	0.853550	0.426775	−	0.904358i	$-0.359650\pi$
$211$	12.3985	0.853550	0.426775	+	0.904358i	$0.359650\pi$
$212$	37.5607	2.57968
$213$	−7.43000	−0.509095
$214$	−2.03485	−0.139099
$215$	−3.66251	−0.249781
$216$	−22.0083	−1.49748
$217$	1.87872	0.127536
$218$	−15.8799	−1.07552
$219$	−21.2051	−1.43291
$220$	−28.3584	−1.91192
$221$	6.14558	0.413396
$222$	−26.7494	−1.79530
$223$	−4.99754	−0.334660	−0.167330	−	0.985901i	$-0.553514\pi$
$223$	−4.99754	−0.334660	−0.167330	+	0.985901i	$0.553514\pi$
$224$	−1.12788	−0.0753593
$225$	1.36499	0.0909993
$226$	−30.9990	−2.06202
$227$	17.7200	1.17612	0.588060	−	0.808817i	$-0.299892\pi$
$227$	17.7200	1.17612	0.588060	+	0.808817i	$0.299892\pi$
$228$	12.4866	0.826945
$229$	12.6766	0.837691	0.418846	−	0.908057i	$-0.362435\pi$
$229$	12.6766	0.837691	0.418846	+	0.908057i	$0.362435\pi$
$230$	17.6213	1.16191
$231$	5.33925	0.351297
$232$	18.4974	1.21441
$233$	−2.08028	−0.136284	−0.0681420	−	0.997676i	$-0.521707\pi$
$233$	−2.08028	−0.136284	−0.0681420	+	0.997676i	$0.521707\pi$
$234$	2.67585	0.174926
$235$	30.2787	1.97516
$236$	10.0584	0.654745
$237$	−18.8025	−1.22135
$238$	−6.38393	−0.413808
$239$	−4.45428	−0.288123	−0.144062	−	0.989569i	$-0.546016\pi$
$239$	−4.45428	−0.288123	−0.144062	+	0.989569i	$0.546016\pi$
$240$	18.0359	1.16421
$241$	−6.34816	−0.408921	−0.204460	−	0.978875i	$-0.565544\pi$
$241$	−6.34816	−0.408921	−0.204460	+	0.978875i	$0.565544\pi$
$242$	11.2381	0.722411
$243$	4.24948	0.272605
$244$	28.8739	1.84846
$245$	16.4041	1.04802
$246$	33.8800	2.16011
$247$	4.64482	0.295543
$248$	7.55233	0.479574
$249$	−5.71576	−0.362222
$250$	−11.7943	−0.745938
$251$	15.0519	0.950065	0.475033	−	0.879968i	$-0.342436\pi$
$251$	15.0519	0.950065	0.475033	+	0.879968i	$0.342436\pi$
$252$	−1.83672	−0.115703
$253$	6.35252	0.399379
$254$	38.5549	2.41915
$255$	−12.2286	−0.765786
$256$	−30.9181	−1.93238
$257$	−12.5560	−0.783224	−0.391612	−	0.920131i	$-0.628082\pi$
$257$	−12.5560	−0.783224	−0.391612	+	0.920131i	$0.628082\pi$
$258$	5.69629	0.354635
$259$	6.83001	0.424396
$260$	30.0724	1.86501
$261$	−1.65423	−0.102394
$262$	27.5636	1.70288
$263$	−10.4663	−0.645381	−0.322690	−	0.946505i	$-0.604587\pi$
$263$	−10.4663	−0.645381	−0.322690	+	0.946505i	$0.604587\pi$
$264$	21.4635	1.32099
$265$	−27.8018	−1.70785
$266$	−4.82497	−0.295838
$267$	−14.6384	−0.895858
$268$	−56.5015	−3.45138
$269$	−2.89802	−0.176695	−0.0883475	−	0.996090i	$-0.528159\pi$
$269$	−2.89802	−0.176695	−0.0883475	+	0.996090i	$0.528159\pi$
$270$	33.4751	2.03723
$271$	3.09761	0.188167	0.0940833	−	0.995564i	$-0.470008\pi$
$271$	3.09761	0.188167	0.0940833	+	0.995564i	$0.470008\pi$
$272$	−7.77415	−0.471377
$273$	−5.66197	−0.342678
$274$	27.4841	1.66037
$275$	8.36927	0.504686
$276$	−18.1096	−1.09007
$277$	8.85247	0.531893	0.265947	−	0.963988i	$-0.414316\pi$
$277$	8.85247	0.531893	0.265947	+	0.963988i	$0.414316\pi$
$278$	−49.2264	−2.95240
$279$	−0.675407	−0.0404356
$280$	−15.2019	−0.908490
$281$	−10.4612	−0.624063	−0.312031	−	0.950072i	$-0.601009\pi$
$281$	−10.4612	−0.624063	−0.312031	+	0.950072i	$0.601009\pi$
$282$	−47.0924	−2.80431
$283$	−18.2566	−1.08524	−0.542622	−	0.839977i	$-0.682568\pi$
$283$	−18.2566	−1.08524	−0.542622	+	0.839977i	$0.682568\pi$
$284$	15.6715	0.929931
$285$	−9.24238	−0.547472
$286$	16.4066	0.970145
$287$	−8.65068	−0.510634
$288$	0.405476	0.0238929
$289$	−11.7290	−0.689941
$290$	−28.1348	−1.65213
$291$	−8.64766	−0.506935
$292$	44.7261	2.61740
$293$	−13.6784	−0.799100	−0.399550	−	0.916711i	$-0.630834\pi$
$293$	−13.6784	−0.799100	−0.399550	+	0.916711i	$0.630834\pi$
$294$	−25.5132	−1.48796
$295$	−7.44506	−0.433468
$296$	27.4562	1.59586
$297$	12.0679	0.700248
$298$	−41.4484	−2.40104
$299$	−6.73648	−0.389580
$300$	−23.8588	−1.37749
$301$	−1.45445	−0.0838332
$302$	−55.3749	−3.18647
$303$	−25.2455	−1.45032
$304$	−5.87569	−0.336994
$305$	−21.3720	−1.22376
$306$	2.29505	0.131199
$307$	0.687181	0.0392195	0.0196097	−	0.999808i	$-0.493758\pi$
$307$	0.687181	0.0392195	0.0196097	+	0.999808i	$0.493758\pi$
$308$	−11.2616	−0.641692
$309$	27.4161	1.55965
$310$	−11.4872	−0.652431
$311$	34.7326	1.96951	0.984753	−	0.173959i	$-0.0556562\pi$
$311$	34.7326	1.96951	0.984753	+	0.173959i	$0.0556562\pi$
$312$	−22.7608	−1.28858
$313$	−5.26300	−0.297482	−0.148741	−	0.988876i	$-0.547522\pi$
$313$	−5.26300	−0.297482	−0.148741	+	0.988876i	$0.547522\pi$
$314$	20.4151	1.15209
$315$	1.35951	0.0766000
$316$	39.6586	2.23097
$317$	8.27032	0.464507	0.232254	−	0.972655i	$-0.425390\pi$
$317$	8.27032	0.464507	0.232254	+	0.972655i	$0.425390\pi$
$318$	43.2401	2.42478
$319$	−10.1427	−0.567881
$320$	26.4254	1.47722
$321$	−1.54790	−0.0863952
$322$	6.99774	0.389969
$323$	3.98382	0.221666
$324$	−39.2144	−2.17858
$325$	−8.87513	−0.492303
$326$	30.6984	1.70023
$327$	−12.0797	−0.668011
$328$	−34.7752	−1.92014
$329$	12.0242	0.662918
$330$	−32.6463	−1.79712
$331$	−26.9318	−1.48031	−0.740153	−	0.672438i	$-0.765247\pi$
$331$	−26.9318	−1.48031	−0.740153	+	0.672438i	$0.765247\pi$
$332$	12.0558	0.661647
$333$	−2.45542	−0.134556
$334$	−51.7890	−2.83377
$335$	41.8215	2.28496
$336$	7.16238	0.390740
$337$	−33.8709	−1.84507	−0.922534	−	0.385917i	$-0.873885\pi$
$337$	−33.8709	−1.84507	−0.922534	+	0.385917i	$0.873885\pi$
$338$	14.1676	0.770615
$339$	−23.5807	−1.28073
$340$	25.7928	1.39881
$341$	−4.14118	−0.224257
$342$	1.73460	0.0937963
$343$	14.5305	0.784573
$344$	−5.84681	−0.315239
$345$	13.4044	0.721669
$346$	−37.3801	−2.00957
$347$	−24.7532	−1.32882	−0.664411	−	0.747367i	$-0.731318\pi$
$347$	−24.7532	−1.32882	−0.664411	+	0.747367i	$0.731318\pi$
$348$	28.9144	1.54998
$349$	−4.73422	−0.253417	−0.126709	−	0.991940i	$-0.540441\pi$
$349$	−4.73422	−0.253417	−0.126709	+	0.991940i	$0.540441\pi$
$350$	9.21934	0.492794
$351$	−12.7973	−0.683067
$352$	2.48613	0.132511
$353$	3.55719	0.189330	0.0946650	−	0.995509i	$-0.469822\pi$
$353$	3.55719	0.189330	0.0946650	+	0.995509i	$0.469822\pi$
$354$	11.5793	0.615432
$355$	−11.5998	−0.615652
$356$	30.8757	1.63641
$357$	−4.85622	−0.257018
$358$	−3.63036	−0.191870
$359$	−18.5122	−0.977037	−0.488519	−	0.872553i	$-0.662463\pi$
$359$	−18.5122	−0.977037	−0.488519	+	0.872553i	$0.662463\pi$
$360$	5.46517	0.288040
$361$	−15.9890	−0.841528
$362$	−1.29673	−0.0681546
$363$	8.54875	0.448693
$364$	11.9423	0.625948
$365$	−33.1056	−1.73282
$366$	33.2398	1.73747
$367$	3.83631	0.200254	0.100127	−	0.994975i	$-0.468075\pi$
$367$	3.83631	0.200254	0.100127	+	0.994975i	$0.468075\pi$
$368$	8.52163	0.444221
$369$	3.10996	0.161898
$370$	−41.7614	−2.17107
$371$	−11.0406	−0.573201
$372$	11.8055	0.612088
$373$	−11.3632	−0.588363	−0.294181	−	0.955750i	$-0.595047\pi$
$373$	−11.3632	−0.588363	−0.294181	+	0.955750i	$0.595047\pi$
$374$	14.0718	0.727636
$375$	−8.97188	−0.463306
$376$	48.3368	2.49278
$377$	10.7557	0.553948
$378$	13.2936	0.683748
$379$	19.9139	1.02291	0.511454	−	0.859311i	$-0.329107\pi$
$379$	19.9139	1.02291	0.511454	+	0.859311i	$0.329107\pi$
$380$	19.4942	1.00003
$381$	29.3285	1.50254
$382$	29.1400	1.49093
$383$	8.35177	0.426756	0.213378	−	0.976970i	$-0.431553\pi$
$383$	8.35177	0.426756	0.213378	+	0.976970i	$0.431553\pi$
$384$	−37.4609	−1.91167
$385$	8.33570	0.424826
$386$	−54.1030	−2.75377
$387$	0.522882	0.0265796
$388$	18.2398	0.925985
$389$	24.4519	1.23976	0.619880	−	0.784697i	$-0.287181\pi$
$389$	24.4519	1.23976	0.619880	+	0.784697i	$0.287181\pi$
$390$	34.6195	1.75303
$391$	−5.77781	−0.292196
$392$	26.1874	1.32266
$393$	20.9675	1.05767
$394$	37.6847	1.89853
$395$	−29.3546	−1.47699
$396$	4.04861	0.203450
$397$	5.18866	0.260411	0.130206	−	0.991487i	$-0.458436\pi$
$397$	5.18866	0.260411	0.130206	+	0.991487i	$0.458436\pi$
$398$	−39.0142	−1.95560
$399$	−3.67033	−0.183746
$400$	11.2270	0.561351
$401$	−18.2677	−0.912245	−0.456122	−	0.889917i	$-0.650762\pi$
$401$	−18.2677	−0.912245	−0.456122	+	0.889917i	$0.650762\pi$
$402$	−65.0449	−3.24415
$403$	4.39148	0.218755
$404$	53.2483	2.64920
$405$	29.0259	1.44231
$406$	−11.1729	−0.554500
$407$	−15.0551	−0.746254
$408$	−19.5217	−0.966469
$409$	−30.3070	−1.49859	−0.749293	−	0.662239i	$-0.769606\pi$
$409$	−30.3070	−1.49859	−0.749293	+	0.662239i	$0.769606\pi$
$410$	52.8937	2.61223
$411$	20.9070	1.03127
$412$	−57.8266	−2.84891
$413$	−2.95658	−0.145484
$414$	−2.51572	−0.123641
$415$	−8.92350	−0.438037
$416$	−2.63639	−0.129260
$417$	−37.4463	−1.83375
$418$	10.6355	0.520198
$419$	20.6622	1.00941	0.504707	−	0.863291i	$-0.331601\pi$
$419$	20.6622	1.00941	0.504707	+	0.863291i	$0.331601\pi$
$420$	−23.7631	−1.15952
$421$	−19.9528	−0.972441	−0.486220	−	0.873836i	$-0.661625\pi$
$421$	−19.9528	−0.972441	−0.486220	+	0.873836i	$0.661625\pi$
$422$	−30.1054	−1.46551
$423$	−4.32277	−0.210180
$424$	−44.3827	−2.15541
$425$	−7.61211	−0.369242
$426$	18.0411	0.874094
$427$	−8.48722	−0.410726
$428$	3.26485	0.157812
$429$	12.4804	0.602561
$430$	8.89310	0.428863
$431$	−19.9253	−0.959770	−0.479885	−	0.877331i	$-0.659322\pi$
$431$	−19.9253	−0.959770	−0.479885	+	0.877331i	$0.659322\pi$
$432$	16.1885	0.778870
$433$	−24.2744	−1.16655	−0.583276	−	0.812274i	$-0.698229\pi$
$433$	−24.2744	−1.16655	−0.583276	+	0.812274i	$0.698229\pi$
$434$	−4.56180	−0.218973
$435$	−21.4020	−1.02615
$436$	25.4788	1.22021
$437$	−4.36687	−0.208896
$438$	51.4890	2.46024
$439$	−0.944408	−0.0450742	−0.0225371	−	0.999746i	$-0.507174\pi$
$439$	−0.944408	−0.0450742	−0.0225371	+	0.999746i	$0.507174\pi$
$440$	33.5090	1.59748
$441$	−2.34195	−0.111521
$442$	−14.9223	−0.709784
$443$	1.64830	0.0783132	0.0391566	−	0.999233i	$-0.487533\pi$
$443$	1.64830	0.0783132	0.0391566	+	0.999233i	$0.487533\pi$
$444$	42.9186	2.03683
$445$	−22.8537	−1.08337
$446$	12.1347	0.574596
$447$	−31.5296	−1.49130
$448$	10.4940	0.495796
$449$	−41.6911	−1.96753	−0.983763	−	0.179475i	$-0.942560\pi$
$449$	−41.6911	−1.96753	−0.983763	+	0.179475i	$0.942560\pi$
$450$	−3.31439	−0.156242
$451$	19.0683	0.897892
$452$	49.7369	2.33943
$453$	−42.1234	−1.97913
$454$	−43.0268	−2.01935
$455$	−8.83952	−0.414403
$456$	−14.7545	−0.690943
$457$	−11.9153	−0.557372	−0.278686	−	0.960382i	$-0.589899\pi$
$457$	−11.9153	−0.557372	−0.278686	+	0.960382i	$0.589899\pi$
$458$	−30.7805	−1.43828
$459$	−10.9761	−0.512320
$460$	−28.2728	−1.31823
$461$	−23.9456	−1.11526	−0.557630	−	0.830090i	$-0.688289\pi$
$461$	−23.9456	−1.11526	−0.557630	+	0.830090i	$0.688289\pi$
$462$	−12.9645	−0.603162
$463$	−15.7032	−0.729788	−0.364894	−	0.931049i	$-0.618895\pi$
$463$	−15.7032	−0.729788	−0.364894	+	0.931049i	$0.618895\pi$
$464$	−13.6060	−0.631642
$465$	−8.73827	−0.405228
$466$	5.05123	0.233994
$467$	−31.6984	−1.46683	−0.733415	−	0.679782i	$-0.762075\pi$
$467$	−31.6984	−1.46683	−0.733415	+	0.679782i	$0.762075\pi$
$468$	−4.29332	−0.198459
$469$	16.6081	0.766892
$470$	−73.5210	−3.39127
$471$	15.5297	0.715570
$472$	−11.8853	−0.547064
$473$	3.20599	0.147411
$474$	45.6552	2.09701
$475$	−5.75323	−0.263976
$476$	10.2428	0.469479
$477$	3.96916	0.181735
$478$	10.8156	0.494695
$479$	23.4175	1.06997	0.534987	−	0.844860i	$-0.320316\pi$
$479$	23.4175	1.06997	0.534987	+	0.844860i	$0.320316\pi$
$480$	5.24596	0.239444
$481$	15.9651	0.727944
$482$	15.4142	0.702099
$483$	5.32314	0.242211
$484$	−18.0312	−0.819598
$485$	−13.5008	−0.613040
$486$	−10.3184	−0.468050
$487$	12.6026	0.571080	0.285540	−	0.958367i	$-0.407827\pi$
$487$	12.6026	0.571080	0.285540	+	0.958367i	$0.407827\pi$
$488$	−34.1181	−1.54446
$489$	23.3521	1.05602
$490$	−39.8315	−1.79940
$491$	−33.8029	−1.52550	−0.762752	−	0.646691i	$-0.776152\pi$
$491$	−33.8029	−1.52550	−0.762752	+	0.646691i	$0.776152\pi$
$492$	−54.3594	−2.45071
$493$	9.22508	0.415477
$494$	−11.2783	−0.507435
$495$	−2.99672	−0.134693
$496$	−5.55521	−0.249436
$497$	−4.60649	−0.206629
$498$	13.8787	0.621919
$499$	26.5690	1.18939	0.594697	−	0.803950i	$-0.297272\pi$
$499$	26.5690	1.18939	0.594697	+	0.803950i	$0.297272\pi$
$500$	18.9236	0.846291
$501$	−39.3956	−1.76007
$502$	−36.5481	−1.63122
$503$	−1.87531	−0.0836161	−0.0418081	−	0.999126i	$-0.513312\pi$
$503$	−1.87531	−0.0836161	−0.0418081	+	0.999126i	$0.513312\pi$
$504$	2.17032	0.0966738
$505$	−39.4136	−1.75388
$506$	−15.4248	−0.685717
$507$	10.7772	0.478633
$508$	−61.8602	−2.74460
$509$	19.3604	0.858134	0.429067	−	0.903273i	$-0.358842\pi$
$509$	19.3604	0.858134	0.429067	+	0.903273i	$0.358842\pi$
$510$	29.6929	1.31482
$511$	−13.1469	−0.581582
$512$	34.5112	1.52519
$513$	−8.29572	−0.366265
$514$	30.4879	1.34476
$515$	42.8023	1.88610
$516$	−9.13953	−0.402345
$517$	−26.5045	−1.16567
$518$	−16.5843	−0.728670
$519$	−28.4349	−1.24815
$520$	−35.5344	−1.55828
$521$	−38.1522	−1.67148	−0.835740	−	0.549126i	$-0.814961\pi$
$521$	−38.1522	−1.67148	−0.835740	+	0.549126i	$0.814961\pi$
$522$	4.01670	0.175806
$523$	−22.6162	−0.988939	−0.494470	−	0.869195i	$-0.664638\pi$
$523$	−22.6162	−0.988939	−0.494470	+	0.869195i	$0.664638\pi$
$524$	−44.2250	−1.93198
$525$	7.01310	0.306077
$526$	25.4137	1.10809
$527$	3.76653	0.164073
$528$	−15.7877	−0.687073
$529$	−16.6667	−0.724637
$530$	67.5069	2.93231
$531$	1.06290	0.0461260
$532$	7.74151	0.335637
$533$	−20.2209	−0.875862
$534$	35.5443	1.53815
$535$	−2.41659	−0.104478
$536$	66.7637	2.88375
$537$	−2.76159	−0.119172
$538$	7.03680	0.303378
$539$	−14.3594	−0.618501
$540$	−53.7098	−2.31130
$541$	−9.96578	−0.428462	−0.214231	−	0.976783i	$-0.568725\pi$
$541$	−9.96578	−0.428462	−0.214231	+	0.976783i	$0.568725\pi$
$542$	−7.52145	−0.323074
$543$	−0.986415	−0.0423311
$544$	−2.26121	−0.0969486
$545$	−18.8590	−0.807830
$546$	13.7481	0.588363
$547$	11.7745	0.503440	0.251720	−	0.967800i	$-0.419004\pi$
$547$	11.7745	0.503440	0.251720	+	0.967800i	$0.419004\pi$
$548$	−44.0974	−1.88375
$549$	3.05120	0.130222
$550$	−20.3218	−0.866524
$551$	6.97231	0.297030
$552$	21.3987	0.910790
$553$	−11.6573	−0.495718
$554$	−21.4951	−0.913238
$555$	−31.7677	−1.34846
$556$	78.9823	3.34960
$557$	−38.8085	−1.64437	−0.822185	−	0.569221i	$-0.807245\pi$
$557$	−38.8085	−1.64437	−0.822185	+	0.569221i	$0.807245\pi$
$558$	1.63999	0.0694262
$559$	−3.39976	−0.143795
$560$	11.1820	0.472525
$561$	10.7044	0.451938
$562$	25.4013	1.07149
$563$	−10.9222	−0.460314	−0.230157	−	0.973153i	$-0.573924\pi$
$563$	−10.9222	−0.460314	−0.230157	+	0.973153i	$0.573924\pi$
$564$	75.5583	3.18158
$565$	−36.8145	−1.54880
$566$	44.3297	1.86332
$567$	11.5267	0.484077
$568$	−18.5178	−0.776991
$569$	13.6593	0.572630	0.286315	−	0.958136i	$-0.407570\pi$
$569$	13.6593	0.572630	0.286315	+	0.958136i	$0.407570\pi$
$570$	22.4418	0.939985
$571$	27.4068	1.14694	0.573469	−	0.819227i	$-0.305597\pi$
$571$	27.4068	1.14694	0.573469	+	0.819227i	$0.305597\pi$
$572$	−26.3240	−1.10066
$573$	22.1666	0.926025
$574$	21.0051	0.876736
$575$	8.34402	0.347970
$576$	−3.77265	−0.157194
$577$	26.8128	1.11623	0.558116	−	0.829763i	$-0.311525\pi$
$577$	26.8128	1.11623	0.558116	+	0.829763i	$0.311525\pi$
$578$	28.4797	1.18460
$579$	−41.1559	−1.71038
$580$	45.1415	1.87440
$581$	−3.54369	−0.147017
$582$	20.9978	0.870385
$583$	24.3364	1.00791
$584$	−52.8496	−2.18693
$585$	3.17785	0.131388
$586$	33.2131	1.37202
$587$	20.8300	0.859748	0.429874	−	0.902889i	$-0.358558\pi$
$587$	20.8300	0.859748	0.429874	+	0.902889i	$0.358558\pi$
$588$	40.9352	1.68814
$589$	2.84674	0.117298
$590$	18.0777	0.744247
$591$	28.6665	1.17918
$592$	−20.1958	−0.830042
$593$	28.1152	1.15455	0.577276	−	0.816549i	$-0.304116\pi$
$593$	28.1152	1.15455	0.577276	+	0.816549i	$0.304116\pi$
$594$	−29.3025	−1.20230
$595$	−7.58157	−0.310814
$596$	66.5027	2.72406
$597$	−29.6779	−1.21463
$598$	16.3571	0.668893
$599$	−9.28256	−0.379275	−0.189638	−	0.981854i	$-0.560731\pi$
$599$	−9.28256	−0.379275	−0.189638	+	0.981854i	$0.560731\pi$
$600$	28.1923	1.15094
$601$	−2.15094	−0.0877386	−0.0438693	−	0.999037i	$-0.513969\pi$
$601$	−2.15094	−0.0877386	−0.0438693	+	0.999037i	$0.513969\pi$
$602$	3.53162	0.143938
$603$	−5.97070	−0.243146
$604$	88.8473	3.61515
$605$	13.3464	0.542608
$606$	61.2998	2.49013
$607$	−12.0030	−0.487186	−0.243593	−	0.969878i	$-0.578326\pi$
$607$	−12.0030	−0.487186	−0.243593	+	0.969878i	$0.578326\pi$
$608$	−1.70902	−0.0693100
$609$	−8.49914	−0.344403
$610$	51.8943	2.10114
$611$	28.1065	1.13707
$612$	−3.68234	−0.148850
$613$	4.35188	0.175771	0.0878855	−	0.996131i	$-0.471989\pi$
$613$	4.35188	0.175771	0.0878855	+	0.996131i	$0.471989\pi$
$614$	−1.66857	−0.0673382
$615$	40.2360	1.62247
$616$	13.3071	0.536157
$617$	31.3747	1.26310	0.631549	−	0.775336i	$-0.282420\pi$
$617$	31.3747	1.26310	0.631549	+	0.775336i	$0.282420\pi$
$618$	−66.5703	−2.67785
$619$	14.4439	0.580549	0.290275	−	0.956943i	$-0.406253\pi$
$619$	14.4439	0.580549	0.290275	+	0.956943i	$0.406253\pi$
$620$	18.4309	0.740203
$621$	12.0314	0.482805
$622$	−84.3358	−3.38156
$623$	−9.07563	−0.363608
$624$	16.7420	0.670216
$625$	−30.5848	−1.22339
$626$	12.7793	0.510765
$627$	8.09034	0.323097
$628$	−32.7555	−1.30709
$629$	13.6931	0.545979
$630$	−3.30110	−0.131519
$631$	41.6024	1.65617	0.828084	−	0.560605i	$-0.189431\pi$
$631$	41.6024	1.65617	0.828084	+	0.560605i	$0.189431\pi$
$632$	−46.8616	−1.86405
$633$	−22.9010	−0.910234
$634$	−20.0815	−0.797539
$635$	45.7879	1.81704
$636$	−69.3774	−2.75099
$637$	15.2273	0.603326
$638$	24.6279	0.975027
$639$	1.65605	0.0655125
$640$	−58.4843	−2.31180
$641$	−17.8175	−0.703749	−0.351874	−	0.936047i	$-0.614456\pi$
$641$	−17.8175	−0.703749	−0.351874	+	0.936047i	$0.614456\pi$
$642$	3.75852	0.148337
$643$	−36.3975	−1.43538	−0.717688	−	0.696365i	$-0.754800\pi$
$643$	−36.3975	−1.43538	−0.717688	+	0.696365i	$0.754800\pi$
$644$	−11.2277	−0.442432
$645$	6.76493	0.266369
$646$	−9.67329	−0.380590
$647$	43.0506	1.69249	0.846247	−	0.532791i	$-0.178857\pi$
$647$	43.0506	1.69249	0.846247	+	0.532791i	$0.178857\pi$
$648$	46.3367	1.82028
$649$	6.51706	0.255817
$650$	21.5501	0.845264
$651$	−3.47013	−0.136005
$652$	−49.2547	−1.92896
$653$	26.6677	1.04359	0.521795	−	0.853071i	$-0.325263\pi$
$653$	26.6677	1.04359	0.521795	+	0.853071i	$0.325263\pi$
$654$	29.3313	1.14695
$655$	32.7346	1.27905
$656$	25.5794	0.998706
$657$	4.72635	0.184393
$658$	−29.1966	−1.13820
$659$	−27.3408	−1.06505	−0.532523	−	0.846415i	$-0.678756\pi$
$659$	−27.3408	−1.06505	−0.532523	+	0.846415i	$0.678756\pi$
$660$	52.3801	2.03889
$661$	−48.7156	−1.89482	−0.947409	−	0.320026i	$-0.896308\pi$
$661$	−48.7156	−1.89482	−0.947409	+	0.320026i	$0.896308\pi$
$662$	65.3943	2.54162
$663$	−11.3513	−0.440850
$664$	−14.2454	−0.552830
$665$	−5.73015	−0.222206
$666$	5.96211	0.231027
$667$	−10.1121	−0.391541
$668$	83.0939	3.21500
$669$	9.23083	0.356884
$670$	−101.549	−3.92317
$671$	18.7080	0.722215
$672$	2.08327	0.0803639
$673$	13.1696	0.507649	0.253825	−	0.967250i	$-0.418311\pi$
$673$	13.1696	0.507649	0.253825	+	0.967250i	$0.418311\pi$
$674$	82.2435	3.16790
$675$	15.8511	0.610109
$676$	−22.7315	−0.874287
$677$	9.36087	0.359767	0.179884	−	0.983688i	$-0.442428\pi$
$677$	9.36087	0.359767	0.179884	+	0.983688i	$0.442428\pi$
$678$	57.2574	2.19896
$679$	−5.36143	−0.205753
$680$	−30.4775	−1.16876
$681$	−32.7302	−1.25423
$682$	10.0554	0.385040
$683$	15.6947	0.600540	0.300270	−	0.953854i	$-0.402923\pi$
$683$	15.6947	0.600540	0.300270	+	0.953854i	$0.402923\pi$
$684$	−2.78311	−0.106415
$685$	32.6402	1.24712
$686$	−35.2822	−1.34708
$687$	−23.4146	−0.893322
$688$	4.30070	0.163963
$689$	−25.8073	−0.983182
$690$	−32.5478	−1.23907
$691$	−2.74087	−0.104268	−0.0521338	−	0.998640i	$-0.516602\pi$
$691$	−2.74087	−0.104268	−0.0521338	+	0.998640i	$0.516602\pi$
$692$	59.9753	2.27992
$693$	−1.19005	−0.0452064
$694$	60.1044	2.28153
$695$	−58.4615	−2.21757
$696$	−34.1661	−1.29506
$697$	−17.3432	−0.656922
$698$	11.4954	0.435106
$699$	3.84244	0.145335
$700$	−14.7922	−0.559091
$701$	9.40836	0.355349	0.177674	−	0.984089i	$-0.443143\pi$
$701$	9.40836	0.355349	0.177674	+	0.984089i	$0.443143\pi$
$702$	31.0736	1.17280
$703$	10.3492	0.390328
$704$	−23.1315	−0.871802
$705$	−55.9271	−2.10633
$706$	−8.63736	−0.325071
$707$	−15.6519	−0.588650
$708$	−18.5786	−0.698227
$709$	3.03647	0.114037	0.0570185	−	0.998373i	$-0.481841\pi$
$709$	3.03647	0.114037	0.0570185	+	0.998373i	$0.481841\pi$
$710$	28.1659	1.05705
$711$	4.19085	0.157169
$712$	−36.4835	−1.36728
$713$	−4.12868	−0.154620
$714$	11.7916	0.441289
$715$	19.4846	0.728682
$716$	5.82480	0.217683
$717$	8.22739	0.307258
$718$	44.9503	1.67753
$719$	8.81789	0.328852	0.164426	−	0.986389i	$-0.447423\pi$
$719$	8.81789	0.328852	0.164426	+	0.986389i	$0.447423\pi$
$720$	−4.01997	−0.149816
$721$	16.9976	0.633024
$722$	38.8237	1.44487
$723$	11.7255	0.436077
$724$	2.08056	0.0773235
$725$	−13.3224	−0.494781
$726$	−20.7576	−0.770386
$727$	−3.42236	−0.126928	−0.0634641	−	0.997984i	$-0.520215\pi$
$727$	−3.42236	−0.126928	−0.0634641	+	0.997984i	$0.520215\pi$
$728$	−14.1114	−0.523002
$729$	22.3476	0.827690
$730$	80.3851	2.97519
$731$	−2.91595	−0.107850
$732$	−53.3323	−1.97122
$733$	28.9048	1.06762	0.533812	−	0.845603i	$-0.320759\pi$
$733$	28.9048	1.06762	0.533812	+	0.845603i	$0.320759\pi$
$734$	−9.31513	−0.343828
$735$	−30.2996	−1.11762
$736$	2.47863	0.0913634
$737$	−36.6086	−1.34850
$738$	−7.55143	−0.277972
$739$	−20.9329	−0.770029	−0.385015	−	0.922910i	$-0.625804\pi$
$739$	−20.9329	−0.770029	−0.385015	+	0.922910i	$0.625804\pi$
$740$	67.0049	2.46315
$741$	−8.57934	−0.315170
$742$	26.8083	0.984162
$743$	−18.6421	−0.683911	−0.341956	−	0.939716i	$-0.611089\pi$
$743$	−18.6421	−0.683911	−0.341956	+	0.939716i	$0.611089\pi$
$744$	−13.9497	−0.511422
$745$	−49.2242	−1.80344
$746$	27.5914	1.01019
$747$	1.27397	0.0466122
$748$	−22.5778	−0.825527
$749$	−0.959674	−0.0350657
$750$	21.7850	0.795476
$751$	1.09348	0.0399018	0.0199509	−	0.999801i	$-0.493649\pi$
$751$	1.09348	0.0399018	0.0199509	+	0.999801i	$0.493649\pi$
$752$	−35.5547	−1.29655
$753$	−27.8019	−1.01316
$754$	−26.1164	−0.951105
$755$	−65.7634	−2.39338
$756$	−21.3292	−0.775734
$757$	52.5830	1.91116	0.955581	−	0.294728i	$-0.0952291\pi$
$757$	52.5830	1.91116	0.955581	+	0.294728i	$0.0952291\pi$
$758$	−48.3538	−1.75629
$759$	−11.7336	−0.425902
$760$	−23.0349	−0.835562
$761$	−14.6068	−0.529494	−0.264747	−	0.964318i	$-0.585288\pi$
$761$	−14.6068	−0.529494	−0.264747	+	0.964318i	$0.585288\pi$
$762$	−71.2138	−2.57980
$763$	−7.48926	−0.271130
$764$	−46.7543	−1.69151
$765$	2.72561	0.0985446
$766$	−20.2793	−0.732721
$767$	−6.91096	−0.249540
$768$	57.1081	2.06071
$769$	−26.3598	−0.950559	−0.475279	−	0.879835i	$-0.657653\pi$
$769$	−26.3598	−0.950559	−0.475279	+	0.879835i	$0.657653\pi$
$770$	−20.2403	−0.729409
$771$	23.1919	0.835237
$772$	86.8067	3.12424
$773$	13.2602	0.476935	0.238467	−	0.971151i	$-0.423355\pi$
$773$	13.2602	0.476935	0.238467	+	0.971151i	$0.423355\pi$
$774$	−1.26963	−0.0456360
$775$	−5.43943	−0.195390
$776$	−21.5526	−0.773694
$777$	−12.6156	−0.452580
$778$	−59.3727	−2.12862
$779$	−13.1080	−0.469643
$780$	−55.5460	−1.98887
$781$	10.1539	0.363335
$782$	14.0294	0.501689
$783$	−19.2099	−0.686505
$784$	−19.2625	−0.687945
$785$	24.2451	0.865344
$786$	−50.9121	−1.81597
$787$	39.2156	1.39789	0.698943	−	0.715178i	$-0.253654\pi$
$787$	39.2156	1.39789	0.698943	+	0.715178i	$0.253654\pi$
$788$	−60.4640	−2.15394
$789$	19.3321	0.688241
$790$	71.2773	2.53593
$791$	−14.6197	−0.519818
$792$	−4.78395	−0.169990
$793$	−19.8388	−0.704496
$794$	−12.5988	−0.447115
$795$	51.3521	1.82127
$796$	62.5970	2.21869
$797$	−24.6409	−0.872825	−0.436413	−	0.899747i	$-0.643751\pi$
$797$	−24.6409	−0.872825	−0.436413	+	0.899747i	$0.643751\pi$
$798$	8.91208	0.315484
$799$	24.1067	0.852834
$800$	3.26552	0.115454
$801$	3.26273	0.115283
$802$	44.3566	1.56629
$803$	28.9790	1.02265
$804$	104.363	3.68059
$805$	8.31055	0.292908
$806$	−10.6631	−0.375593
$807$	5.35285	0.188429
$808$	−62.9196	−2.21351
$809$	−15.8094	−0.555828	−0.277914	−	0.960606i	$-0.589643\pi$
$809$	−15.8094	−0.555828	−0.277914	+	0.960606i	$0.589643\pi$
$810$	−70.4790	−2.47638
$811$	47.5467	1.66959	0.834795	−	0.550560i	$-0.185586\pi$
$811$	47.5467	1.66959	0.834795	+	0.550560i	$0.185586\pi$
$812$	17.9265	0.629098
$813$	−5.72153	−0.200663
$814$	36.5560	1.28129
$815$	36.4575	1.27705
$816$	14.3594	0.502681
$817$	−2.20387	−0.0771036
$818$	73.5898	2.57301
$819$	1.26198	0.0440973
$820$	−84.8664	−2.96366
$821$	−22.3949	−0.781586	−0.390793	−	0.920478i	$-0.627799\pi$
$821$	−22.3949	−0.781586	−0.390793	+	0.920478i	$0.627799\pi$
$822$	−50.7652	−1.77064
$823$	12.2166	0.425844	0.212922	−	0.977069i	$-0.431702\pi$
$823$	12.2166	0.425844	0.212922	+	0.977069i	$0.431702\pi$
$824$	68.3294	2.38037
$825$	−15.4587	−0.538202
$826$	7.17899	0.249789
$827$	35.0846	1.22001	0.610005	−	0.792398i	$-0.291167\pi$
$827$	35.0846	1.22001	0.610005	+	0.792398i	$0.291167\pi$
$828$	4.03640	0.140274
$829$	37.4004	1.29897	0.649484	−	0.760375i	$-0.274985\pi$
$829$	37.4004	1.29897	0.649484	+	0.760375i	$0.274985\pi$
$830$	21.6676	0.752092
$831$	−16.3512	−0.567216
$832$	24.5296	0.850412
$833$	13.0603	0.452512
$834$	90.9249	3.14847
$835$	−61.5048	−2.12846
$836$	−17.0643	−0.590181
$837$	−7.84324	−0.271102
$838$	−50.1707	−1.73312
$839$	−13.7998	−0.476421	−0.238210	−	0.971214i	$-0.576561\pi$
$839$	−13.7998	−0.476421	−0.238210	+	0.971214i	$0.576561\pi$
$840$	28.0792	0.968823
$841$	−12.8547	−0.443264
$842$	48.4483	1.66964
$843$	19.3226	0.665507
$844$	48.3032	1.66267
$845$	16.8255	0.578814
$846$	10.4963	0.360871
$847$	5.30010	0.182114
$848$	32.6463	1.12108
$849$	33.7214	1.15732
$850$	18.4833	0.633972
$851$	−15.0097	−0.514525
$852$	−28.9464	−0.991688
$853$	−13.6721	−0.468123	−0.234061	−	0.972222i	$-0.575202\pi$
$853$	−13.6721	−0.468123	−0.234061	+	0.972222i	$0.575202\pi$
$854$	20.6082	0.705198
$855$	2.06001	0.0704510
$856$	−3.85783	−0.131858
$857$	54.9627	1.87749	0.938746	−	0.344610i	$-0.111989\pi$
$857$	54.9627	1.87749	0.938746	+	0.344610i	$0.111989\pi$
$858$	−30.3043	−1.03457
$859$	−17.3275	−0.591205	−0.295603	−	0.955311i	$-0.595520\pi$
$859$	−17.3275	−0.591205	−0.295603	+	0.955311i	$0.595520\pi$
$860$	−14.2687	−0.486559
$861$	15.9785	0.544545
$862$	48.3816	1.64788
$863$	29.8033	1.01452	0.507258	−	0.861794i	$-0.330659\pi$
$863$	29.8033	1.01452	0.507258	+	0.861794i	$0.330659\pi$
$864$	4.70864	0.160191
$865$	−44.3928	−1.50940
$866$	58.9417	2.00292
$867$	21.6644	0.735760
$868$	7.31927	0.248432
$869$	25.6957	0.871666
$870$	51.9672	1.76185
$871$	38.8213	1.31541
$872$	−30.1064	−1.01953
$873$	1.92746	0.0652345
$874$	10.6034	0.358665
$875$	−5.56244	−0.188045
$876$	−82.6125	−2.79122
$877$	−2.59545	−0.0876420	−0.0438210	−	0.999039i	$-0.513953\pi$
$877$	−2.59545	−0.0876420	−0.0438210	+	0.999039i	$0.513953\pi$
$878$	2.29316	0.0773904
$879$	25.2650	0.852168
$880$	−24.6480	−0.830883
$881$	−13.9622	−0.470398	−0.235199	−	0.971947i	$-0.575574\pi$
$881$	−13.9622	−0.470398	−0.235199	+	0.971947i	$0.575574\pi$
$882$	5.68658	0.191477
$883$	−54.3256	−1.82820	−0.914101	−	0.405486i	$-0.867102\pi$
$883$	−54.3256	−1.82820	−0.914101	+	0.405486i	$0.867102\pi$
$884$	23.9425	0.805272
$885$	13.7516	0.462255
$886$	−4.00232	−0.134460
$887$	−45.8552	−1.53967	−0.769833	−	0.638245i	$-0.779661\pi$
$887$	−45.8552	−1.53967	−0.769833	+	0.638245i	$0.779661\pi$
$888$	−50.7138	−1.70184
$889$	18.1833	0.609847
$890$	55.4921	1.86010
$891$	−25.4079	−0.851195
$892$	−19.4698	−0.651898
$893$	18.2198	0.609703
$894$	76.5583	2.56049
$895$	−4.31143	−0.144115
$896$	−23.2252	−0.775901
$897$	12.4428	0.415452
$898$	101.232	3.37816
$899$	6.59202	0.219856
$900$	5.31784	0.177261
$901$	−22.1347	−0.737414
$902$	−46.3007	−1.54164
$903$	2.68648	0.0894006
$904$	−58.7705	−1.95468
$905$	−1.54000	−0.0511914
$906$	102.282	3.39808
$907$	−12.2518	−0.406814	−0.203407	−	0.979094i	$-0.565201\pi$
$907$	−12.2518	−0.406814	−0.203407	+	0.979094i	$0.565201\pi$
$908$	69.0352	2.29101
$909$	5.62692	0.186633
$910$	21.4636	0.711513
$911$	24.7342	0.819482	0.409741	−	0.912202i	$-0.365619\pi$
$911$	24.7342	0.819482	0.409741	+	0.912202i	$0.365619\pi$
$912$	10.8529	0.359374
$913$	7.81121	0.258513
$914$	28.9320	0.956984
$915$	39.4757	1.30503
$916$	49.3865	1.63177
$917$	12.9995	0.429283
$918$	26.6515	0.879632
$919$	32.6889	1.07831	0.539154	−	0.842207i	$-0.318744\pi$
$919$	32.6889	1.07831	0.539154	+	0.842207i	$0.318744\pi$
$920$	33.4079	1.10143
$921$	−1.26928	−0.0418240
$922$	58.1434	1.91485
$923$	−10.7676	−0.354421
$924$	20.8011	0.684307
$925$	−19.7748	−0.650193
$926$	38.1296	1.25302
$927$	−6.11072	−0.200702
$928$	−3.95747	−0.129910
$929$	−27.0712	−0.888176	−0.444088	−	0.895983i	$-0.646472\pi$
$929$	−27.0712	−0.888176	−0.444088	+	0.895983i	$0.646472\pi$
$930$	21.2178	0.695759
$931$	9.87095	0.323507
$932$	−8.10455	−0.265473
$933$	−64.1538	−2.10030
$934$	76.9684	2.51848
$935$	16.7117	0.546532
$936$	5.07310	0.165819
$937$	11.2798	0.368494	0.184247	−	0.982880i	$-0.441015\pi$
$937$	11.2798	0.368494	0.184247	+	0.982880i	$0.441015\pi$
$938$	−40.3269	−1.31672
$939$	9.72116	0.317238
$940$	117.962	3.84751
$941$	−38.3561	−1.25037	−0.625187	−	0.780475i	$-0.714977\pi$
$941$	−38.3561	−1.25037	−0.625187	+	0.780475i	$0.714977\pi$
$942$	−37.7083	−1.22860
$943$	19.0108	0.619077
$944$	8.74236	0.284539
$945$	15.7875	0.513568
$946$	−7.78460	−0.253099
$947$	−18.2182	−0.592012	−0.296006	−	0.955186i	$-0.595655\pi$
$947$	−18.2182	−0.592012	−0.296006	+	0.955186i	$0.595655\pi$
$948$	−73.2524	−2.37913
$949$	−30.7306	−0.997557
$950$	13.9697	0.453236
$951$	−15.2759	−0.495355
$952$	−12.1032	−0.392267
$953$	17.4611	0.565621	0.282811	−	0.959176i	$-0.408733\pi$
$953$	17.4611	0.565621	0.282811	+	0.959176i	$0.408733\pi$
$954$	−9.63769	−0.312032
$955$	34.6068	1.11985
$956$	−17.3534	−0.561248
$957$	18.7343	0.605594
$958$	−56.8611	−1.83710
$959$	12.9620	0.418566
$960$	−48.8097	−1.57533
$961$	−28.3085	−0.913178
$962$	−38.7655	−1.24985
$963$	0.345007	0.0111177
$964$	−24.7317	−0.796554
$965$	−64.2530	−2.06838
$966$	−12.9254	−0.415867
$967$	−18.8093	−0.604866	−0.302433	−	0.953171i	$-0.597799\pi$
$967$	−18.8093	−0.604866	−0.302433	+	0.953171i	$0.597799\pi$
$968$	21.3061	0.684804
$969$	−7.35842	−0.236386
$970$	32.7819	1.05256
$971$	20.4459	0.656140	0.328070	−	0.944653i	$-0.393602\pi$
$971$	20.4459	0.656140	0.328070	+	0.944653i	$0.393602\pi$
$972$	16.5555	0.531018
$973$	−23.2162	−0.744276
$974$	−30.6010	−0.980520
$975$	16.3930	0.524997
$976$	25.0960	0.803304
$977$	38.6208	1.23559	0.617795	−	0.786339i	$-0.288026\pi$
$977$	38.6208	1.23559	0.617795	+	0.786339i	$0.288026\pi$
$978$	−56.7023	−1.81314
$979$	20.0050	0.639364
$980$	63.9084	2.04148
$981$	2.69242	0.0859625
$982$	82.0783	2.61922
$983$	−10.4865	−0.334466	−0.167233	−	0.985917i	$-0.553483\pi$
$983$	−10.4865	−0.334466	−0.167233	+	0.985917i	$0.553483\pi$
$984$	64.2325	2.04766
$985$	44.7545	1.42600
$986$	−22.3998	−0.713356
$987$	−22.2097	−0.706942
$988$	18.0957	0.575701
$989$	3.19631	0.101637
$990$	7.27647	0.231261
$991$	−46.8036	−1.48677	−0.743383	−	0.668866i	$-0.766780\pi$
$991$	−46.8036	−1.48677	−0.743383	+	0.668866i	$0.766780\pi$
$992$	−1.61581	−0.0513019
$993$	49.7451	1.57861
$994$	11.1852	0.354774
$995$	−46.3334	−1.46887
$996$	−22.2679	−0.705587
$997$	49.2323	1.55920	0.779601	−	0.626277i	$-0.215422\pi$
$997$	49.2323	1.55920	0.779601	+	0.626277i	$0.215422\pi$
$998$	−64.5135	−2.04214
$999$	−28.5138	−0.902138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.12	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.12	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42814 q^{2} -1.84708 q^{3} +3.89588 q^{4} -2.88367 q^{5} +4.48497 q^{6} -1.14516 q^{7} -4.60348 q^{8} +0.411691 q^{9} +O(q^{10})\)	\(q-2.42814 q^{2} -1.84708 q^{3} +3.89588 q^{4} -2.88367 q^{5} +4.48497 q^{6} -1.14516 q^{7} -4.60348 q^{8} +0.411691 q^{9} +7.00198 q^{10} +2.52423 q^{11} -7.19600 q^{12} -2.67680 q^{13} +2.78062 q^{14} +5.32636 q^{15} +3.38615 q^{16} -2.29587 q^{17} -0.999644 q^{18} -1.73521 q^{19} -11.2345 q^{20} +2.11520 q^{21} -6.12920 q^{22} +2.51661 q^{23} +8.50298 q^{24} +3.31557 q^{25} +6.49966 q^{26} +4.78080 q^{27} -4.46142 q^{28} -4.01813 q^{29} -12.9332 q^{30} -1.64057 q^{31} +0.984905 q^{32} -4.66245 q^{33} +5.57470 q^{34} +3.30227 q^{35} +1.60390 q^{36} -5.96423 q^{37} +4.21335 q^{38} +4.94425 q^{39} +13.2749 q^{40} +7.55411 q^{41} -5.13601 q^{42} +1.27008 q^{43} +9.83411 q^{44} -1.18718 q^{45} -6.11070 q^{46} -10.5000 q^{47} -6.25448 q^{48} -5.68861 q^{49} -8.05069 q^{50} +4.24064 q^{51} -10.4285 q^{52} +9.64112 q^{53} -11.6085 q^{54} -7.27906 q^{55} +5.27173 q^{56} +3.20507 q^{57} +9.75659 q^{58} +2.58180 q^{59} +20.7509 q^{60} +7.41138 q^{61} +3.98354 q^{62} -0.471452 q^{63} -9.16379 q^{64} +7.71902 q^{65} +11.3211 q^{66} -14.5029 q^{67} -8.94443 q^{68} -4.64838 q^{69} -8.01839 q^{70} +4.02257 q^{71} -1.89521 q^{72} +11.4803 q^{73} +14.4820 q^{74} -6.12412 q^{75} -6.76019 q^{76} -2.89065 q^{77} -12.0054 q^{78} +10.1796 q^{79} -9.76455 q^{80} -10.0656 q^{81} -18.3425 q^{82} +3.09449 q^{83} +8.24058 q^{84} +6.62053 q^{85} -3.08395 q^{86} +7.42179 q^{87} -11.6203 q^{88} +7.92520 q^{89} +2.88265 q^{90} +3.06537 q^{91} +9.80444 q^{92} +3.03026 q^{93} +25.4956 q^{94} +5.00379 q^{95} -1.81919 q^{96} +4.68181 q^{97} +13.8128 q^{98} +1.03920 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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