LMFDB - Embedded newform 4033.2.a.d.1.58

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.58
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.32967 q^{2} +3.41937 q^{3} -0.231965 q^{4} -0.655569 q^{5} +4.54664 q^{6} -4.44023 q^{7} -2.96779 q^{8} +8.69206 q^{9} +O(q^{10})$	\(q+1.32967 q^{2} +3.41937 q^{3} -0.231965 q^{4} -0.655569 q^{5} +4.54664 q^{6} -4.44023 q^{7} -2.96779 q^{8} +8.69206 q^{9} -0.871694 q^{10} +2.16016 q^{11} -0.793173 q^{12} -3.88207 q^{13} -5.90406 q^{14} -2.24163 q^{15} -3.48226 q^{16} -3.69280 q^{17} +11.5576 q^{18} -4.89968 q^{19} +0.152069 q^{20} -15.1828 q^{21} +2.87231 q^{22} -5.52199 q^{23} -10.1480 q^{24} -4.57023 q^{25} -5.16189 q^{26} +19.4632 q^{27} +1.02998 q^{28} -1.09894 q^{29} -2.98064 q^{30} -2.60426 q^{31} +1.30530 q^{32} +7.38639 q^{33} -4.91022 q^{34} +2.91088 q^{35} -2.01625 q^{36} -1.00000 q^{37} -6.51499 q^{38} -13.2742 q^{39} +1.94559 q^{40} +8.57080 q^{41} -20.1882 q^{42} +8.44155 q^{43} -0.501082 q^{44} -5.69825 q^{45} -7.34246 q^{46} -7.56721 q^{47} -11.9071 q^{48} +12.7157 q^{49} -6.07692 q^{50} -12.6270 q^{51} +0.900505 q^{52} +4.49353 q^{53} +25.8798 q^{54} -1.41614 q^{55} +13.1777 q^{56} -16.7538 q^{57} -1.46124 q^{58} -10.7107 q^{59} +0.519980 q^{60} -5.55252 q^{61} -3.46282 q^{62} -38.5948 q^{63} +8.70015 q^{64} +2.54497 q^{65} +9.82149 q^{66} -11.1936 q^{67} +0.856600 q^{68} -18.8817 q^{69} +3.87052 q^{70} +0.747775 q^{71} -25.7962 q^{72} +2.67858 q^{73} -1.32967 q^{74} -15.6273 q^{75} +1.13656 q^{76} -9.59162 q^{77} -17.6504 q^{78} +2.41113 q^{79} +2.28286 q^{80} +40.4758 q^{81} +11.3964 q^{82} +5.61579 q^{83} +3.52187 q^{84} +2.42089 q^{85} +11.2245 q^{86} -3.75769 q^{87} -6.41090 q^{88} -7.69105 q^{89} -7.57682 q^{90} +17.2373 q^{91} +1.28091 q^{92} -8.90492 q^{93} -10.0619 q^{94} +3.21208 q^{95} +4.46329 q^{96} +14.8725 q^{97} +16.9077 q^{98} +18.7763 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	1.32967	0.940222	0.470111	−	0.882607i	$-0.344214\pi$
$2$	1.32967	0.940222	0.470111	+	0.882607i	$0.344214\pi$
$3$	3.41937	1.97417	0.987086	−	0.160192i	$-0.0512114\pi$
$3$	3.41937	1.97417	0.987086	+	0.160192i	$0.0512114\pi$
$4$	−0.231965	−0.115983
$5$	−0.655569	−0.293179	−0.146590	−	0.989197i	$-0.546830\pi$
$5$	−0.655569	−0.293179	−0.146590	+	0.989197i	$0.546830\pi$
$6$	4.54664	1.85616
$7$	−4.44023	−1.67825	−0.839125	−	0.543939i	$-0.816932\pi$
$7$	−4.44023	−1.67825	−0.839125	+	0.543939i	$0.816932\pi$
$8$	−2.96779	−1.04927
$9$	8.69206	2.89735
$10$	−0.871694	−0.275654
$11$	2.16016	0.651314	0.325657	−	0.945488i	$-0.394415\pi$
$11$	2.16016	0.651314	0.325657	+	0.945488i	$0.394415\pi$
$12$	−0.793173	−0.228969
$13$	−3.88207	−1.07669	−0.538347	−	0.842724i	$-0.680951\pi$
$13$	−3.88207	−1.07669	−0.538347	+	0.842724i	$0.680951\pi$
$14$	−5.90406	−1.57793
$15$	−2.24163	−0.578787
$16$	−3.48226	−0.870566
$17$	−3.69280	−0.895635	−0.447818	−	0.894125i	$-0.647799\pi$
$17$	−3.69280	−0.895635	−0.447818	+	0.894125i	$0.647799\pi$
$18$	11.5576	2.72416
$19$	−4.89968	−1.12406	−0.562032	−	0.827115i	$-0.689980\pi$
$19$	−4.89968	−1.12406	−0.562032	+	0.827115i	$0.689980\pi$
$20$	0.152069	0.0340037
$21$	−15.1828	−3.31315
$22$	2.87231	0.612379
$23$	−5.52199	−1.15142	−0.575708	−	0.817656i	$-0.695273\pi$
$23$	−5.52199	−1.15142	−0.575708	+	0.817656i	$0.695273\pi$
$24$	−10.1480	−2.07144
$25$	−4.57023	−0.914046
$26$	−5.16189	−1.01233
$27$	19.4632	3.74570
$28$	1.02998	0.194648
$29$	−1.09894	−0.204069	−0.102034	−	0.994781i	$-0.532535\pi$
$29$	−1.09894	−0.204069	−0.102034	+	0.994781i	$0.532535\pi$
$30$	−2.98064	−0.544188
$31$	−2.60426	−0.467739	−0.233869	−	0.972268i	$-0.575139\pi$
$31$	−2.60426	−0.467739	−0.233869	+	0.972268i	$0.575139\pi$
$32$	1.30530	0.230746
$33$	7.38639	1.28580
$34$	−4.91022	−0.842096
$35$	2.91088	0.492028
$36$	−2.01625	−0.336042
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−6.51499	−1.05687
$39$	−13.2742	−2.12558
$40$	1.94559	0.307625
$41$	8.57080	1.33853	0.669267	−	0.743022i	$-0.266608\pi$
$41$	8.57080	1.33853	0.669267	+	0.743022i	$0.266608\pi$
$42$	−20.1882	−3.11510
$43$	8.44155	1.28732	0.643662	−	0.765310i	$-0.277414\pi$
$43$	8.44155	1.28732	0.643662	+	0.765310i	$0.277414\pi$
$44$	−0.501082	−0.0755410
$45$	−5.69825	−0.849445
$46$	−7.34246	−1.08259
$47$	−7.56721	−1.10379	−0.551895	−	0.833913i	$-0.686095\pi$
$47$	−7.56721	−1.10379	−0.551895	+	0.833913i	$0.686095\pi$
$48$	−11.9071	−1.71865
$49$	12.7157	1.81652
$50$	−6.07692	−0.859406
$51$	−12.6270	−1.76814
$52$	0.900505	0.124878
$53$	4.49353	0.617234	0.308617	−	0.951186i	$-0.400134\pi$
$53$	4.49353	0.617234	0.308617	+	0.951186i	$0.400134\pi$
$54$	25.8798	3.52179
$55$	−1.41614	−0.190952
$56$	13.1777	1.76094
$57$	−16.7538	−2.21910
$58$	−1.46124	−0.191870
$59$	−10.7107	−1.39441	−0.697206	−	0.716871i	$-0.745574\pi$
$59$	−10.7107	−1.39441	−0.697206	+	0.716871i	$0.745574\pi$
$60$	0.519980	0.0671291
$61$	−5.55252	−0.710927	−0.355463	−	0.934690i	$-0.615677\pi$
$61$	−5.55252	−0.710927	−0.355463	+	0.934690i	$0.615677\pi$
$62$	−3.46282	−0.439778
$63$	−38.5948	−4.86248
$64$	8.70015	1.08752
$65$	2.54497	0.315664
$66$	9.82149	1.20894
$67$	−11.1936	−1.36751	−0.683755	−	0.729711i	$-0.739654\pi$
$67$	−11.1936	−1.36751	−0.683755	+	0.729711i	$0.739654\pi$
$68$	0.856600	0.103878
$69$	−18.8817	−2.27309
$70$	3.87052	0.462616
$71$	0.747775	0.0887445	0.0443723	−	0.999015i	$-0.485871\pi$
$71$	0.747775	0.0887445	0.0443723	+	0.999015i	$0.485871\pi$
$72$	−25.7962	−3.04011
$73$	2.67858	0.313504	0.156752	−	0.987638i	$-0.449898\pi$
$73$	2.67858	0.313504	0.156752	+	0.987638i	$0.449898\pi$
$74$	−1.32967	−0.154572
$75$	−15.6273	−1.80448
$76$	1.13656	0.130372
$77$	−9.59162	−1.09307
$78$	−17.6504	−1.99851
$79$	2.41113	0.271273	0.135637	−	0.990759i	$-0.456692\pi$
$79$	2.41113	0.271273	0.135637	+	0.990759i	$0.456692\pi$
$80$	2.28286	0.255232
$81$	40.4758	4.49731
$82$	11.3964	1.25852
$83$	5.61579	0.616413	0.308207	−	0.951319i	$-0.400271\pi$
$83$	5.61579	0.616413	0.308207	+	0.951319i	$0.400271\pi$
$84$	3.52187	0.384268
$85$	2.42089	0.262582
$86$	11.2245	1.21037
$87$	−3.75769	−0.402866
$88$	−6.41090	−0.683405
$89$	−7.69105	−0.815250	−0.407625	−	0.913149i	$-0.633643\pi$
$89$	−7.69105	−0.815250	−0.407625	+	0.913149i	$0.633643\pi$
$90$	−7.57682	−0.798666
$91$	17.2373	1.80696
$92$	1.28091	0.133544
$93$	−8.90492	−0.923397
$94$	−10.0619	−1.03781
$95$	3.21208	0.329553
$96$	4.46329	0.455533
$97$	14.8725	1.51008	0.755039	−	0.655680i	$-0.227618\pi$
$97$	14.8725	1.51008	0.755039	+	0.655680i	$0.227618\pi$
$98$	16.9077	1.70793
$99$	18.7763	1.88709
$100$	1.06013	0.106013
$101$	14.7292	1.46561	0.732804	−	0.680440i	$-0.238211\pi$
$101$	14.7292	1.46561	0.732804	+	0.680440i	$0.238211\pi$
$102$	−16.7898	−1.66244
$103$	−18.9077	−1.86303	−0.931514	−	0.363706i	$-0.881511\pi$
$103$	−18.9077	−1.86303	−0.931514	+	0.363706i	$0.881511\pi$
$104$	11.5212	1.12974
$105$	9.95336	0.971348
$106$	5.97494	0.580337
$107$	−0.0606969	−0.00586779	−0.00293390	−	0.999996i	$-0.500934\pi$
$107$	−0.0606969	−0.00586779	−0.00293390	+	0.999996i	$0.500934\pi$
$108$	−4.51479	−0.434436
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−1.88300	−0.179537
$111$	−3.41937	−0.324552
$112$	15.4621	1.46103
$113$	−19.4601	−1.83065	−0.915327	−	0.402711i	$-0.868068\pi$
$113$	−19.4601	−1.83065	−0.915327	+	0.402711i	$0.868068\pi$
$114$	−22.2771	−2.08644
$115$	3.62005	0.337571
$116$	0.254916	0.0236684
$117$	−33.7432	−3.11956
$118$	−14.2417	−1.31106
$119$	16.3969	1.50310
$120$	6.65268	0.607304
$121$	−6.33370	−0.575791
$122$	−7.38304	−0.668429
$123$	29.3067	2.64250
$124$	0.604097	0.0542495
$125$	6.27395	0.561159
$126$	−51.3185	−4.57181
$127$	−16.6109	−1.47398	−0.736988	−	0.675906i	$-0.763752\pi$
$127$	−16.6109	−1.47398	−0.736988	+	0.675906i	$0.763752\pi$
$128$	8.95777	0.791762
$129$	28.8648	2.54140
$130$	3.38398	0.296794
$131$	20.9345	1.82905	0.914526	−	0.404528i	$-0.132564\pi$
$131$	20.9345	1.82905	0.914526	+	0.404528i	$0.132564\pi$
$132$	−1.71338	−0.149131
$133$	21.7557	1.88646
$134$	−14.8838	−1.28576
$135$	−12.7595	−1.09816
$136$	10.9594	0.939765
$137$	21.2443	1.81503	0.907513	−	0.420024i	$-0.137978\pi$
$137$	21.2443	1.81503	0.907513	+	0.420024i	$0.137978\pi$
$138$	−25.1065	−2.13721
$139$	−9.05839	−0.768323	−0.384161	−	0.923266i	$-0.625509\pi$
$139$	−9.05839	−0.768323	−0.384161	+	0.923266i	$0.625509\pi$
$140$	−0.675222	−0.0570667
$141$	−25.8750	−2.17907
$142$	0.994297	0.0834396
$143$	−8.38591	−0.701265
$144$	−30.2680	−2.52234
$145$	0.720433	0.0598287
$146$	3.56164	0.294764
$147$	43.4795	3.58613
$148$	0.231965	0.0190674
$149$	1.82136	0.149211	0.0746057	−	0.997213i	$-0.476230\pi$
$149$	1.82136	0.149211	0.0746057	+	0.997213i	$0.476230\pi$
$150$	−20.7792	−1.69662
$151$	15.2700	1.24265	0.621327	−	0.783551i	$-0.286594\pi$
$151$	15.2700	1.24265	0.621327	+	0.783551i	$0.286594\pi$
$152$	14.5412	1.17945
$153$	−32.0980	−2.59497
$154$	−12.7537	−1.02773
$155$	1.70727	0.137131
$156$	3.07916	0.246530
$157$	−2.41163	−0.192469	−0.0962347	−	0.995359i	$-0.530680\pi$
$157$	−2.41163	−0.192469	−0.0962347	+	0.995359i	$0.530680\pi$
$158$	3.20602	0.255057
$159$	15.3650	1.21853
$160$	−0.855714	−0.0676501
$161$	24.5189	1.93236
$162$	53.8196	4.22847
$163$	−13.7048	−1.07344	−0.536721	−	0.843760i	$-0.680337\pi$
$163$	−13.7048	−1.07344	−0.536721	+	0.843760i	$0.680337\pi$
$164$	−1.98813	−0.155247
$165$	−4.84229	−0.376972
$166$	7.46718	0.579565
$167$	22.9477	1.77575	0.887873	−	0.460088i	$-0.152182\pi$
$167$	22.9477	1.77575	0.887873	+	0.460088i	$0.152182\pi$
$168$	45.0593	3.47640
$169$	2.07049	0.159268
$170$	3.21899	0.246885
$171$	−42.5884	−3.25681
$172$	−1.95814	−0.149307
$173$	−20.4932	−1.55807	−0.779036	−	0.626979i	$-0.784291\pi$
$173$	−20.4932	−1.55807	−0.779036	+	0.626979i	$0.784291\pi$
$174$	−4.99650	−0.378784
$175$	20.2929	1.53400
$176$	−7.52225	−0.567011
$177$	−36.6237	−2.75281
$178$	−10.2266	−0.766516
$179$	−8.19711	−0.612681	−0.306340	−	0.951922i	$-0.599105\pi$
$179$	−8.19711	−0.612681	−0.306340	+	0.951922i	$0.599105\pi$
$180$	1.32179	0.0985207
$181$	−5.45550	−0.405504	−0.202752	−	0.979230i	$-0.564989\pi$
$181$	−5.45550	−0.405504	−0.202752	+	0.979230i	$0.564989\pi$
$182$	22.9200	1.69894
$183$	−18.9861	−1.40349
$184$	16.3881	1.20815
$185$	0.655569	0.0481984
$186$	−11.8406	−0.868198
$187$	−7.97705	−0.583340
$188$	1.75533	0.128020
$189$	−86.4213	−6.28622
$190$	4.27102	0.309853
$191$	−11.9777	−0.866676	−0.433338	−	0.901232i	$-0.642664\pi$
$191$	−11.9777	−0.866676	−0.433338	+	0.901232i	$0.642664\pi$
$192$	29.7490	2.14695
$193$	0.391461	0.0281780	0.0140890	−	0.999901i	$-0.495515\pi$
$193$	0.391461	0.0281780	0.0140890	+	0.999901i	$0.495515\pi$
$194$	19.7756	1.41981
$195$	8.70217	0.623175
$196$	−2.94959	−0.210685
$197$	24.7271	1.76173	0.880867	−	0.473364i	$-0.156960\pi$
$197$	24.7271	1.76173	0.880867	+	0.473364i	$0.156960\pi$
$198$	24.9663	1.77428
$199$	7.68336	0.544659	0.272329	−	0.962204i	$-0.412206\pi$
$199$	7.68336	0.544659	0.272329	+	0.962204i	$0.412206\pi$
$200$	13.5635	0.959082
$201$	−38.2749	−2.69970
$202$	19.5850	1.37800
$203$	4.87956	0.342478
$204$	2.92903	0.205073
$205$	−5.61875	−0.392431
$206$	−25.1410	−1.75166
$207$	−47.9975	−3.33606
$208$	13.5184	0.937332
$209$	−10.5841	−0.732119
$210$	13.2347	0.913283
$211$	−8.12568	−0.559395	−0.279697	−	0.960088i	$-0.590234\pi$
$211$	−8.12568	−0.559395	−0.279697	+	0.960088i	$0.590234\pi$
$212$	−1.04234	−0.0715884
$213$	2.55692	0.175197
$214$	−0.0807071	−0.00551703
$215$	−5.53402	−0.377417
$216$	−57.7628	−3.93026
$217$	11.5635	0.784983
$218$	−1.32967	−0.0900569
$219$	9.15905	0.618912
$220$	0.328494	0.0221471
$221$	14.3357	0.964325
$222$	−4.54664	−0.305151
$223$	−11.8637	−0.794452	−0.397226	−	0.917721i	$-0.630027\pi$
$223$	−11.8637	−0.794452	−0.397226	+	0.917721i	$0.630027\pi$
$224$	−5.79583	−0.387250
$225$	−39.7247	−2.64831
$226$	−25.8756	−1.72122
$227$	23.2466	1.54293	0.771466	−	0.636270i	$-0.219524\pi$
$227$	23.2466	1.54293	0.771466	+	0.636270i	$0.219524\pi$
$228$	3.88630	0.257376
$229$	5.21934	0.344904	0.172452	−	0.985018i	$-0.444831\pi$
$229$	5.21934	0.344904	0.172452	+	0.985018i	$0.444831\pi$
$230$	4.81349	0.317392
$231$	−32.7973	−2.15790
$232$	3.26143	0.214123
$233$	−23.7251	−1.55428	−0.777141	−	0.629326i	$-0.783331\pi$
$233$	−23.7251	−1.55428	−0.777141	+	0.629326i	$0.783331\pi$
$234$	−44.8675	−2.93308
$235$	4.96083	0.323609
$236$	2.48450	0.161727
$237$	8.24454	0.535540
$238$	21.8025	1.41325
$239$	−16.1884	−1.04714	−0.523572	−	0.851982i	$-0.675401\pi$
$239$	−16.1884	−1.04714	−0.523572	+	0.851982i	$0.675401\pi$
$240$	7.80595	0.503872
$241$	−24.3954	−1.57145	−0.785724	−	0.618577i	$-0.787709\pi$
$241$	−24.3954	−1.57145	−0.785724	+	0.618577i	$0.787709\pi$
$242$	−8.42176	−0.541371
$243$	80.0117	5.13275
$244$	1.28799	0.0824551
$245$	−8.33599	−0.532567
$246$	38.9684	2.48453
$247$	19.0209	1.21027
$248$	7.72889	0.490785
$249$	19.2025	1.21691
$250$	8.34231	0.527614
$251$	−23.0279	−1.45351	−0.726754	−	0.686897i	$-0.758972\pi$
$251$	−23.0279	−1.45351	−0.726754	+	0.686897i	$0.758972\pi$
$252$	8.95264	0.563963
$253$	−11.9284	−0.749933
$254$	−22.0870	−1.38586
$255$	8.27789	0.518382
$256$	−5.48938	−0.343086
$257$	5.90345	0.368247	0.184123	−	0.982903i	$-0.441055\pi$
$257$	5.90345	0.368247	0.184123	+	0.982903i	$0.441055\pi$
$258$	38.3807	2.38948
$259$	4.44023	0.275903
$260$	−0.590343	−0.0366115
$261$	−9.55208	−0.591259
$262$	27.8360	1.71971
$263$	3.07305	0.189492	0.0947461	−	0.995501i	$-0.469796\pi$
$263$	3.07305	0.189492	0.0947461	+	0.995501i	$0.469796\pi$
$264$	−21.9212	−1.34916
$265$	−2.94582	−0.180960
$266$	28.9281	1.77369
$267$	−26.2985	−1.60944
$268$	2.59651	0.158607
$269$	5.32935	0.324936	0.162468	−	0.986714i	$-0.448055\pi$
$269$	5.32935	0.324936	0.162468	+	0.986714i	$0.448055\pi$
$270$	−16.9660	−1.03252
$271$	22.8167	1.38602	0.693008	−	0.720929i	$-0.256285\pi$
$271$	22.8167	1.38602	0.693008	+	0.720929i	$0.256285\pi$
$272$	12.8593	0.779709
$273$	58.9406	3.56725
$274$	28.2481	1.70653
$275$	−9.87244	−0.595330
$276$	4.37990	0.263639
$277$	−3.37995	−0.203081	−0.101541	−	0.994831i	$-0.532377\pi$
$277$	−3.37995	−0.203081	−0.101541	+	0.994831i	$0.532377\pi$
$278$	−12.0447	−0.722394
$279$	−22.6364	−1.35521
$280$	−8.63887	−0.516271
$281$	24.1851	1.44276	0.721380	−	0.692539i	$-0.243508\pi$
$281$	24.1851	1.44276	0.721380	+	0.692539i	$0.243508\pi$
$282$	−34.4054	−2.04881
$283$	−26.3032	−1.56356	−0.781781	−	0.623553i	$-0.785689\pi$
$283$	−26.3032	−1.56356	−0.781781	+	0.623553i	$0.785689\pi$
$284$	−0.173458	−0.0102928
$285$	10.9833	0.650593
$286$	−11.1505	−0.659345
$287$	−38.0563	−2.24639
$288$	11.3457	0.668554
$289$	−3.36323	−0.197837
$290$	0.957942	0.0562523
$291$	50.8547	2.98115
$292$	−0.621337	−0.0363610
$293$	−1.77288	−0.103573	−0.0517864	−	0.998658i	$-0.516491\pi$
$293$	−1.77288	−0.103573	−0.0517864	+	0.998658i	$0.516491\pi$
$294$	57.8136	3.37176
$295$	7.02159	0.408813
$296$	2.96779	0.172499
$297$	42.0438	2.43963
$298$	2.42181	0.140292
$299$	21.4368	1.23972
$300$	3.62498	0.209289
$301$	−37.4825	−2.16045
$302$	20.3041	1.16837
$303$	50.3645	2.89336
$304$	17.0620	0.978572
$305$	3.64006	0.208429
$306$	−42.6800	−2.43985
$307$	9.90447	0.565278	0.282639	−	0.959226i	$-0.408790\pi$
$307$	9.90447	0.565278	0.282639	+	0.959226i	$0.408790\pi$
$308$	2.22492	0.126777
$309$	−64.6522	−3.67794
$310$	2.27012	0.128934
$311$	4.74913	0.269299	0.134649	−	0.990893i	$-0.457009\pi$
$311$	4.74913	0.269299	0.134649	+	0.990893i	$0.457009\pi$
$312$	39.3951	2.23031
$313$	−7.67700	−0.433930	−0.216965	−	0.976179i	$-0.569616\pi$
$313$	−7.67700	−0.433930	−0.216965	+	0.976179i	$0.569616\pi$
$314$	−3.20669	−0.180964
$315$	25.3015	1.42558
$316$	−0.559298	−0.0314630
$317$	4.56712	0.256515	0.128258	−	0.991741i	$-0.459062\pi$
$317$	4.56712	0.256515	0.128258	+	0.991741i	$0.459062\pi$
$318$	20.4305	1.14569
$319$	−2.37390	−0.132913
$320$	−5.70355	−0.318838
$321$	−0.207545	−0.0115840
$322$	32.6022	1.81685
$323$	18.0936	1.00675
$324$	−9.38896	−0.521609
$325$	17.7420	0.984147
$326$	−18.2229	−1.00927
$327$	−3.41937	−0.189091
$328$	−25.4363	−1.40449
$329$	33.6001	1.85244
$330$	−6.43867	−0.354437
$331$	−9.33484	−0.513089	−0.256545	−	0.966532i	$-0.582584\pi$
$331$	−9.33484	−0.513089	−0.256545	+	0.966532i	$0.582584\pi$
$332$	−1.30267	−0.0714932
$333$	−8.69206	−0.476322
$334$	30.5130	1.66960
$335$	7.33815	0.400926
$336$	52.8704	2.88432
$337$	−15.3424	−0.835753	−0.417877	−	0.908504i	$-0.637226\pi$
$337$	−15.3424	−0.835753	−0.417877	+	0.908504i	$0.637226\pi$
$338$	2.75307	0.149747
$339$	−66.5413	−3.61403
$340$	−0.561561	−0.0304549
$341$	−5.62563	−0.304645
$342$	−56.6287	−3.06213
$343$	−25.3789	−1.37033
$344$	−25.0527	−1.35075
$345$	12.3783	0.666424
$346$	−27.2493	−1.46493
$347$	17.6749	0.948839	0.474420	−	0.880299i	$-0.342658\pi$
$347$	17.6749	0.948839	0.474420	+	0.880299i	$0.342658\pi$
$348$	0.871652	0.0467255
$349$	−24.3318	−1.30245	−0.651225	−	0.758885i	$-0.725744\pi$
$349$	−24.3318	−1.30245	−0.651225	+	0.758885i	$0.725744\pi$
$350$	26.9829	1.44230
$351$	−75.5577	−4.03297
$352$	2.81966	0.150288
$353$	13.2367	0.704519	0.352259	−	0.935902i	$-0.385414\pi$
$353$	13.2367	0.704519	0.352259	+	0.935902i	$0.385414\pi$
$354$	−48.6977	−2.58825
$355$	−0.490218	−0.0260181
$356$	1.78406	0.0945547
$357$	56.0670	2.96738
$358$	−10.8995	−0.576056
$359$	−5.82617	−0.307493	−0.153747	−	0.988110i	$-0.549134\pi$
$359$	−5.82617	−0.307493	−0.153747	+	0.988110i	$0.549134\pi$
$360$	16.9112	0.891298
$361$	5.00691	0.263521
$362$	−7.25404	−0.381264
$363$	−21.6572	−1.13671
$364$	−3.99845	−0.209576
$365$	−1.75600	−0.0919130
$366$	−25.2453	−1.31959
$367$	−11.8016	−0.616039	−0.308019	−	0.951380i	$-0.599666\pi$
$367$	−11.8016	−0.616039	−0.308019	+	0.951380i	$0.599666\pi$
$368$	19.2290	1.00238
$369$	74.4979	3.87821
$370$	0.871694	0.0453172
$371$	−19.9523	−1.03587
$372$	2.06563	0.107098
$373$	25.7036	1.33088	0.665441	−	0.746450i	$-0.268243\pi$
$373$	25.7036	1.33088	0.665441	+	0.746450i	$0.268243\pi$
$374$	−10.6069	−0.548469
$375$	21.4529	1.10782
$376$	22.4579	1.15818
$377$	4.26618	0.219719
$378$	−114.912	−5.91045
$379$	15.3282	0.787357	0.393679	−	0.919248i	$-0.371202\pi$
$379$	15.3282	0.787357	0.393679	+	0.919248i	$0.371202\pi$
$380$	−0.745091	−0.0382223
$381$	−56.7986	−2.90988
$382$	−15.9264	−0.814868
$383$	−14.0179	−0.716283	−0.358142	−	0.933667i	$-0.616590\pi$
$383$	−14.0179	−0.716283	−0.358142	+	0.933667i	$0.616590\pi$
$384$	30.6299	1.56307
$385$	6.28797	0.320465
$386$	0.520516	0.0264936
$387$	73.3745	3.72984
$388$	−3.44991	−0.175143
$389$	4.86461	0.246646	0.123323	−	0.992367i	$-0.460645\pi$
$389$	4.86461	0.246646	0.123323	+	0.992367i	$0.460645\pi$
$390$	11.5711	0.585923
$391$	20.3916	1.03125
$392$	−37.7374	−1.90603
$393$	71.5825	3.61086
$394$	32.8790	1.65642
$395$	−1.58066	−0.0795318
$396$	−4.35544	−0.218869
$397$	−37.8347	−1.89887	−0.949433	−	0.313969i	$-0.898341\pi$
$397$	−37.8347	−1.89887	−0.949433	+	0.313969i	$0.898341\pi$
$398$	10.2164	0.512100
$399$	74.3908	3.72420
$400$	15.9147	0.795737
$401$	−0.324542	−0.0162069	−0.00810343	−	0.999967i	$-0.502579\pi$
$401$	−0.324542	−0.0162069	−0.00810343	+	0.999967i	$0.502579\pi$
$402$	−50.8931	−2.53832
$403$	10.1099	0.503611
$404$	−3.41666	−0.169985
$405$	−26.5347	−1.31852
$406$	6.48823	0.322005
$407$	−2.16016	−0.107075
$408$	37.4743	1.85526
$409$	34.6496	1.71331	0.856657	−	0.515887i	$-0.172538\pi$
$409$	34.6496	1.71331	0.856657	+	0.515887i	$0.172538\pi$
$410$	−7.47111	−0.368972
$411$	72.6422	3.58317
$412$	4.38592	0.216079
$413$	47.5579	2.34017
$414$	−63.8211	−3.13664
$415$	−3.68154	−0.180720
$416$	−5.06726	−0.248443
$417$	−30.9740	−1.51680
$418$	−14.0734	−0.688354
$419$	−12.4081	−0.606177	−0.303089	−	0.952962i	$-0.598018\pi$
$419$	−12.4081	−0.606177	−0.303089	+	0.952962i	$0.598018\pi$
$420$	−2.30883	−0.112659
$421$	−21.6135	−1.05338	−0.526688	−	0.850059i	$-0.676566\pi$
$421$	−21.6135	−1.05338	−0.526688	+	0.850059i	$0.676566\pi$
$422$	−10.8045	−0.525955
$423$	−65.7746	−3.19807
$424$	−13.3359	−0.647646
$425$	16.8769	0.818652
$426$	3.39987	0.164724
$427$	24.6545	1.19311
$428$	0.0140796	0.000680561 0
$429$	−28.6745	−1.38442
$430$	−7.35845	−0.354856
$431$	13.9466	0.671785	0.335892	−	0.941900i	$-0.390962\pi$
$431$	13.9466	0.671785	0.335892	+	0.941900i	$0.390962\pi$
$432$	−67.7761	−3.26088
$433$	−9.27765	−0.445856	−0.222928	−	0.974835i	$-0.571561\pi$
$433$	−9.27765	−0.445856	−0.222928	+	0.974835i	$0.571561\pi$
$434$	15.3757	0.738058
$435$	2.46342	0.118112
$436$	0.231965	0.0111091
$437$	27.0560	1.29427
$438$	12.1786	0.581914
$439$	−0.108083	−0.00515853	−0.00257927	−	0.999997i	$-0.500821\pi$
$439$	−0.108083	−0.00515853	−0.00257927	+	0.999997i	$0.500821\pi$
$440$	4.20279	0.200360
$441$	110.525	5.26311
$442$	19.0618	0.906679
$443$	0.450636	0.0214104	0.0107052	−	0.999943i	$-0.496592\pi$
$443$	0.450636	0.0214104	0.0107052	+	0.999943i	$0.496592\pi$
$444$	0.793173	0.0376423
$445$	5.04202	0.239015
$446$	−15.7749	−0.746961
$447$	6.22788	0.294569
$448$	−38.6307	−1.82513
$449$	7.41594	0.349980	0.174990	−	0.984570i	$-0.444011\pi$
$449$	7.41594	0.349980	0.174990	+	0.984570i	$0.444011\pi$
$450$	−52.8209	−2.49000
$451$	18.5143	0.871805
$452$	4.51407	0.212324
$453$	52.2137	2.45321
$454$	30.9104	1.45070
$455$	−11.3002	−0.529764
$456$	49.7218	2.32843
$457$	11.1399	0.521103	0.260552	−	0.965460i	$-0.416096\pi$
$457$	11.1399	0.521103	0.260552	+	0.965460i	$0.416096\pi$
$458$	6.94003	0.324286
$459$	−71.8738	−3.35478
$460$	−0.839725	−0.0391524
$461$	−1.31747	−0.0613607	−0.0306804	−	0.999529i	$-0.509767\pi$
$461$	−1.31747	−0.0613607	−0.0306804	+	0.999529i	$0.509767\pi$
$462$	−43.6097	−2.02891
$463$	−21.8538	−1.01563	−0.507817	−	0.861465i	$-0.669547\pi$
$463$	−21.8538	−1.01563	−0.507817	+	0.861465i	$0.669547\pi$
$464$	3.82681	0.177655
$465$	5.83779	0.270721
$466$	−31.5467	−1.46137
$467$	−33.3792	−1.54460	−0.772302	−	0.635255i	$-0.780895\pi$
$467$	−33.3792	−1.54460	−0.772302	+	0.635255i	$0.780895\pi$
$468$	7.82724	0.361815
$469$	49.7020	2.29502
$470$	6.59629	0.304264
$471$	−8.24626	−0.379968
$472$	31.7870	1.46312
$473$	18.2351	0.838452
$474$	10.9626	0.503527
$475$	22.3927	1.02745
$476$	−3.80350	−0.174333
$477$	39.0581	1.78835
$478$	−21.5254	−0.984547
$479$	−7.33513	−0.335150	−0.167575	−	0.985859i	$-0.553594\pi$
$479$	−7.33513	−0.335150	−0.167575	+	0.985859i	$0.553594\pi$
$480$	−2.92600	−0.133553
$481$	3.88207	0.177007
$482$	−32.4380	−1.47751
$483$	83.8392	3.81482
$484$	1.46920	0.0667816
$485$	−9.74998	−0.442724
$486$	106.390	4.82593
$487$	29.6168	1.34207	0.671033	−	0.741427i	$-0.265851\pi$
$487$	29.6168	1.34207	0.671033	+	0.741427i	$0.265851\pi$
$488$	16.4787	0.745955
$489$	−46.8617	−2.11916
$490$	−11.0842	−0.500731
$491$	35.8847	1.61945	0.809726	−	0.586808i	$-0.199616\pi$
$491$	35.8847	1.61945	0.809726	+	0.586808i	$0.199616\pi$
$492$	−6.79813	−0.306483
$493$	4.05818	0.182771
$494$	25.2916	1.13793
$495$	−12.3091	−0.553255
$496$	9.06872	0.407197
$497$	−3.32029	−0.148935
$498$	25.5330	1.14416
$499$	−4.88950	−0.218884	−0.109442	−	0.993993i	$-0.534906\pi$
$499$	−4.88950	−0.218884	−0.109442	+	0.993993i	$0.534906\pi$
$500$	−1.45534	−0.0650846
$501$	78.4666	3.50563
$502$	−30.6196	−1.36662
$503$	−14.6191	−0.651832	−0.325916	−	0.945399i	$-0.605673\pi$
$503$	−14.6191	−0.651832	−0.325916	+	0.945399i	$0.605673\pi$
$504$	114.541	5.10207
$505$	−9.65600	−0.429686
$506$	−15.8609	−0.705103
$507$	7.07975	0.314423
$508$	3.85314	0.170955
$509$	32.2659	1.43016	0.715079	−	0.699043i	$-0.246391\pi$
$509$	32.2659	1.43016	0.715079	+	0.699043i	$0.246391\pi$
$510$	11.0069	0.487394
$511$	−11.8935	−0.526139
$512$	−25.2146	−1.11434
$513$	−95.3637	−4.21041
$514$	7.84966	0.346234
$515$	12.3953	0.546201
$516$	−6.69561	−0.294758
$517$	−16.3464	−0.718914
$518$	5.90406	0.259410
$519$	−70.0739	−3.07590
$520$	−7.55292	−0.331217
$521$	−20.0902	−0.880168	−0.440084	−	0.897957i	$-0.645051\pi$
$521$	−20.0902	−0.880168	−0.440084	+	0.897957i	$0.645051\pi$
$522$	−12.7012	−0.555915
$523$	−13.4054	−0.586176	−0.293088	−	0.956085i	$-0.594683\pi$
$523$	−13.4054	−0.586176	−0.293088	+	0.956085i	$0.594683\pi$
$524$	−4.85606	−0.212138
$525$	69.3888	3.02837
$526$	4.08615	0.178165
$527$	9.61701	0.418924
$528$	−25.7213	−1.11938
$529$	7.49242	0.325758
$530$	−3.91699	−0.170143
$531$	−93.0979	−4.04011
$532$	−5.04657	−0.218797
$533$	−33.2725	−1.44119
$534$	−34.9685	−1.51323
$535$	0.0397910	0.00172032
$536$	33.2201	1.43489
$537$	−28.0289	−1.20954
$538$	7.08630	0.305512
$539$	27.4679	1.18313
$540$	2.95976	0.127368
$541$	−8.47836	−0.364513	−0.182257	−	0.983251i	$-0.558340\pi$
$541$	−8.47836	−0.364513	−0.182257	+	0.983251i	$0.558340\pi$
$542$	30.3388	1.30316
$543$	−18.6543	−0.800534
$544$	−4.82021	−0.206665
$545$	0.655569	0.0280815
$546$	78.3719	3.35401
$547$	−24.1000	−1.03044	−0.515221	−	0.857058i	$-0.672290\pi$
$547$	−24.1000	−1.03044	−0.515221	+	0.857058i	$0.672290\pi$
$548$	−4.92794	−0.210511
$549$	−48.2628	−2.05981
$550$	−13.1271	−0.559743
$551$	5.38447	0.229386
$552$	56.0369	2.38509
$553$	−10.7060	−0.455264
$554$	−4.49423	−0.190942
$555$	2.24163	0.0951519
$556$	2.10123	0.0891120
$557$	3.33989	0.141516	0.0707579	−	0.997494i	$-0.477458\pi$
$557$	3.33989	0.141516	0.0707579	+	0.997494i	$0.477458\pi$
$558$	−30.0990	−1.27419
$559$	−32.7707	−1.38605
$560$	−10.1364	−0.428343
$561$	−27.2764	−1.15161
$562$	32.1583	1.35652
$563$	−44.7041	−1.88405	−0.942026	−	0.335539i	$-0.891081\pi$
$563$	−44.7041	−1.88405	−0.942026	+	0.335539i	$0.891081\pi$
$564$	6.00210	0.252734
$565$	12.7575	0.536710
$566$	−34.9747	−1.47010
$567$	−179.722	−7.54760
$568$	−2.21924	−0.0931171
$569$	−29.0067	−1.21603	−0.608013	−	0.793927i	$-0.708033\pi$
$569$	−29.0067	−1.21603	−0.608013	+	0.793927i	$0.708033\pi$
$570$	14.6042	0.611702
$571$	−16.0278	−0.670744	−0.335372	−	0.942086i	$-0.608862\pi$
$571$	−16.0278	−0.670744	−0.335372	+	0.942086i	$0.608862\pi$
$572$	1.94524	0.0813345
$573$	−40.9561	−1.71097
$574$	−50.6026	−2.11211
$575$	25.2368	1.05245
$576$	75.6222	3.15093
$577$	13.7692	0.573221	0.286610	−	0.958047i	$-0.407471\pi$
$577$	13.7692	0.573221	0.286610	+	0.958047i	$0.407471\pi$
$578$	−4.47200	−0.186011
$579$	1.33855	0.0556282
$580$	−0.167115	−0.00693908
$581$	−24.9354	−1.03450
$582$	67.6201	2.80295
$583$	9.70677	0.402013
$584$	−7.94946	−0.328951
$585$	22.1210	0.914591
$586$	−2.35735	−0.0973814
$587$	14.6811	0.605952	0.302976	−	0.952998i	$-0.402020\pi$
$587$	14.6811	0.605952	0.302976	+	0.952998i	$0.402020\pi$
$588$	−10.0857	−0.415928
$589$	12.7601	0.525769
$590$	9.33644	0.384375
$591$	84.5511	3.47797
$592$	3.48226	0.143120
$593$	25.3702	1.04183	0.520915	−	0.853608i	$-0.325591\pi$
$593$	25.3702	1.04183	0.520915	+	0.853608i	$0.325591\pi$
$594$	55.9045	2.29379
$595$	−10.7493	−0.440678
$596$	−0.422491	−0.0173059
$597$	26.2722	1.07525
$598$	28.5039	1.16561
$599$	−15.3476	−0.627087	−0.313543	−	0.949574i	$-0.601516\pi$
$599$	−15.3476	−0.627087	−0.313543	+	0.949574i	$0.601516\pi$
$600$	46.3785	1.89339
$601$	−9.95406	−0.406035	−0.203017	−	0.979175i	$-0.565075\pi$
$601$	−9.95406	−0.406035	−0.203017	+	0.979175i	$0.565075\pi$
$602$	−49.8395	−2.03131
$603$	−97.2951	−3.96216
$604$	−3.54210	−0.144126
$605$	4.15218	0.168810
$606$	66.9684	2.72040
$607$	−22.1057	−0.897242	−0.448621	−	0.893722i	$-0.648085\pi$
$607$	−22.1057	−0.897242	−0.448621	+	0.893722i	$0.648085\pi$
$608$	−6.39555	−0.259374
$609$	16.6850	0.676111
$610$	4.84009	0.195970
$611$	29.3764	1.18844
$612$	7.44562	0.300971
$613$	10.1396	0.409534	0.204767	−	0.978811i	$-0.434356\pi$
$613$	10.1396	0.409534	0.204767	+	0.978811i	$0.434356\pi$
$614$	13.1697	0.531487
$615$	−19.2126	−0.774725
$616$	28.4659	1.14692
$617$	33.6227	1.35360	0.676799	−	0.736168i	$-0.263367\pi$
$617$	33.6227	1.35360	0.676799	+	0.736168i	$0.263367\pi$
$618$	−85.9664	−3.45808
$619$	−8.82680	−0.354779	−0.177390	−	0.984141i	$-0.556765\pi$
$619$	−8.82680	−0.354779	−0.177390	+	0.984141i	$0.556765\pi$
$620$	−0.396027	−0.0159048
$621$	−107.476	−4.31286
$622$	6.31480	0.253200
$623$	34.1501	1.36819
$624$	46.2243	1.85045
$625$	18.7381	0.749526
$626$	−10.2079	−0.407990
$627$	−36.1910	−1.44533
$628$	0.559415	0.0223231
$629$	3.69280	0.147242
$630$	33.6428	1.34036
$631$	24.9790	0.994400	0.497200	−	0.867636i	$-0.334361\pi$
$631$	24.9790	0.994400	0.497200	+	0.867636i	$0.334361\pi$
$632$	−7.15572	−0.284639
$633$	−27.7847	−1.10434
$634$	6.07278	0.241181
$635$	10.8896	0.432139
$636$	−3.56415	−0.141328
$637$	−49.3631	−1.95584
$638$	−3.15651	−0.124967
$639$	6.49970	0.257124
$640$	−5.87244	−0.232128
$641$	11.6852	0.461537	0.230769	−	0.973009i	$-0.425876\pi$
$641$	11.6852	0.461537	0.230769	+	0.973009i	$0.425876\pi$
$642$	−0.275967	−0.0108916
$643$	−9.28196	−0.366045	−0.183022	−	0.983109i	$-0.558588\pi$
$643$	−9.28196	−0.366045	−0.183022	+	0.983109i	$0.558588\pi$
$644$	−5.68754	−0.224120
$645$	−18.9228	−0.745086
$646$	24.0585	0.946571
$647$	−3.70405	−0.145621	−0.0728106	−	0.997346i	$-0.523197\pi$
$647$	−3.70405	−0.145621	−0.0728106	+	0.997346i	$0.523197\pi$
$648$	−120.123	−4.71889
$649$	−23.1368	−0.908200
$650$	23.5910	0.925317
$651$	39.5399	1.54969
$652$	3.17903	0.124500
$653$	15.6186	0.611204	0.305602	−	0.952159i	$-0.401142\pi$
$653$	15.6186	0.611204	0.305602	+	0.952159i	$0.401142\pi$
$654$	−4.54664	−0.177788
$655$	−13.7240	−0.536240
$656$	−29.8458	−1.16528
$657$	23.2824	0.908333
$658$	44.6773	1.74170
$659$	−7.89711	−0.307628	−0.153814	−	0.988100i	$-0.549156\pi$
$659$	−7.89711	−0.307628	−0.153814	+	0.988100i	$0.549156\pi$
$660$	1.12324	0.0437221
$661$	32.0202	1.24544	0.622721	−	0.782444i	$-0.286027\pi$
$661$	32.0202	1.24544	0.622721	+	0.782444i	$0.286027\pi$
$662$	−12.4123	−0.482418
$663$	49.0191	1.90374
$664$	−16.6665	−0.646785
$665$	−14.2624	−0.553072
$666$	−11.5576	−0.447848
$667$	6.06836	0.234968
$668$	−5.32306	−0.205956
$669$	−40.5663	−1.56838
$670$	9.75735	0.376959
$671$	−11.9943	−0.463036
$672$	−19.8181	−0.764498
$673$	12.4890	0.481415	0.240707	−	0.970598i	$-0.422621\pi$
$673$	12.4890	0.481415	0.240707	+	0.970598i	$0.422621\pi$
$674$	−20.4004	−0.785794
$675$	−88.9515	−3.42374
$676$	−0.480280	−0.0184723
$677$	14.6914	0.564635	0.282318	−	0.959321i	$-0.408897\pi$
$677$	14.6914	0.564635	0.282318	+	0.959321i	$0.408897\pi$
$678$	−88.4782	−3.39799
$679$	−66.0375	−2.53429
$680$	−7.18467	−0.275520
$681$	79.4887	3.04601
$682$	−7.48025	−0.286434
$683$	7.97708	0.305234	0.152617	−	0.988285i	$-0.451230\pi$
$683$	7.97708	0.305234	0.152617	+	0.988285i	$0.451230\pi$
$684$	9.87901	0.377733
$685$	−13.9271	−0.532128
$686$	−33.7456	−1.28841
$687$	17.8468	0.680900
$688$	−29.3957	−1.12070
$689$	−17.4442	−0.664572
$690$	16.4591	0.626586
$691$	13.8148	0.525541	0.262770	−	0.964858i	$-0.415364\pi$
$691$	13.8148	0.525541	0.262770	+	0.964858i	$0.415364\pi$
$692$	4.75371	0.180709
$693$	−83.3710	−3.16700
$694$	23.5019	0.892119
$695$	5.93840	0.225256
$696$	11.1520	0.422716
$697$	−31.6502	−1.19884
$698$	−32.3533	−1.22459
$699$	−81.1248	−3.06842
$700$	−4.70724	−0.177917
$701$	23.0187	0.869405	0.434703	−	0.900574i	$-0.356853\pi$
$701$	23.0187	0.869405	0.434703	+	0.900574i	$0.356853\pi$
$702$	−100.467	−3.79189
$703$	4.89968	0.184795
$704$	18.7937	0.708316
$705$	16.9629	0.638859
$706$	17.6005	0.662404
$707$	−65.4010	−2.45966
$708$	8.49543	0.319278
$709$	−42.9222	−1.61198	−0.805989	−	0.591931i	$-0.798366\pi$
$709$	−42.9222	−1.61198	−0.805989	+	0.591931i	$0.798366\pi$
$710$	−0.651830	−0.0244628
$711$	20.9577	0.785975
$712$	22.8254	0.855419
$713$	14.3807	0.538562
$714$	74.5508	2.78999
$715$	5.49754	0.205596
$716$	1.90144	0.0710603
$717$	−55.3542	−2.06724
$718$	−7.74691	−0.289112
$719$	9.58411	0.357427	0.178714	−	0.983901i	$-0.442806\pi$
$719$	9.58411	0.357427	0.178714	+	0.983901i	$0.442806\pi$
$720$	19.8428	0.739497
$721$	83.9544	3.12663
$722$	6.65756	0.247769
$723$	−83.4169	−3.10231
$724$	1.26548	0.0470314
$725$	5.02242	0.186528
$726$	−28.7971	−1.06876
$727$	18.7984	0.697194	0.348597	−	0.937273i	$-0.386658\pi$
$727$	18.7984	0.697194	0.348597	+	0.937273i	$0.386658\pi$
$728$	−51.1566	−1.89599
$729$	152.162	5.63563
$730$	−2.33490	−0.0864187
$731$	−31.1730	−1.15297
$732$	4.40411	0.162780
$733$	5.16806	0.190887	0.0954434	−	0.995435i	$-0.469573\pi$
$733$	5.16806	0.190887	0.0954434	+	0.995435i	$0.469573\pi$
$734$	−15.6923	−0.579213
$735$	−28.5038	−1.05138
$736$	−7.20785	−0.265685
$737$	−24.1799	−0.890678
$738$	99.0580	3.64638
$739$	39.3951	1.44917	0.724585	−	0.689185i	$-0.242031\pi$
$739$	39.3951	1.44917	0.724585	+	0.689185i	$0.242031\pi$
$740$	−0.152069	−0.00559017
$741$	65.0395	2.38929
$742$	−26.5301	−0.973951
$743$	−36.8813	−1.35304	−0.676521	−	0.736423i	$-0.736513\pi$
$743$	−36.8813	−1.35304	−0.676521	+	0.736423i	$0.736513\pi$
$744$	26.4279	0.968894
$745$	−1.19403	−0.0437457
$746$	34.1775	1.25133
$747$	48.8128	1.78597
$748$	1.85040	0.0676572
$749$	0.269508	0.00984762
$750$	28.5254	1.04160
$751$	0.0709160	0.00258776	0.00129388	−	0.999999i	$-0.499588\pi$
$751$	0.0709160	0.00258776	0.00129388	+	0.999999i	$0.499588\pi$
$752$	26.3510	0.960922
$753$	−78.7408	−2.86948
$754$	5.67263	0.206585
$755$	−10.0105	−0.364321
$756$	20.0467	0.729092
$757$	10.0128	0.363921	0.181961	−	0.983306i	$-0.441756\pi$
$757$	10.0128	0.363921	0.181961	+	0.983306i	$0.441756\pi$
$758$	20.3815	0.740291
$759$	−40.7876	−1.48050
$760$	−9.53278	−0.345790
$761$	−26.7176	−0.968511	−0.484255	−	0.874927i	$-0.660909\pi$
$761$	−26.7176	−0.968511	−0.484255	+	0.874927i	$0.660909\pi$
$762$	−75.5236	−2.73593
$763$	4.44023	0.160747
$764$	2.77841	0.100519
$765$	21.0425	0.760793
$766$	−18.6393	−0.673466
$767$	41.5796	1.50135
$768$	−18.7702	−0.677311
$769$	−0.242221	−0.00873470	−0.00436735	−	0.999990i	$-0.501390\pi$
$769$	−0.242221	−0.00873470	−0.00436735	+	0.999990i	$0.501390\pi$
$770$	8.36096	0.301308
$771$	20.1860	0.726983
$772$	−0.0908053	−0.00326815
$773$	−23.1451	−0.832471	−0.416235	−	0.909257i	$-0.636651\pi$
$773$	−23.1451	−0.832471	−0.416235	+	0.909257i	$0.636651\pi$
$774$	97.5642	3.50687
$775$	11.9021	0.427535
$776$	−44.1385	−1.58448
$777$	15.1828	0.544679
$778$	6.46835	0.231902
$779$	−41.9942	−1.50460
$780$	−2.01860	−0.0722775
$781$	1.61532	0.0578005
$782$	27.1142	0.969603
$783$	−21.3890	−0.764380
$784$	−44.2793	−1.58140
$785$	1.58099	0.0564281
$786$	95.1815	3.39501
$787$	−47.1003	−1.67894	−0.839472	−	0.543403i	$-0.817136\pi$
$787$	−47.1003	−1.67894	−0.839472	+	0.543403i	$0.817136\pi$
$788$	−5.73583	−0.204330
$789$	10.5079	0.374090
$790$	−2.10177	−0.0747775
$791$	86.4074	3.07229
$792$	−55.7240	−1.98007
$793$	21.5553	0.765450
$794$	−50.3078	−1.78536
$795$	−10.0728	−0.357247
$796$	−1.78227	−0.0631709
$797$	8.04217	0.284868	0.142434	−	0.989804i	$-0.454507\pi$
$797$	8.04217	0.284868	0.142434	+	0.989804i	$0.454507\pi$
$798$	98.9156	3.50157
$799$	27.9442	0.988594
$800$	−5.96552	−0.210913
$801$	−66.8511	−2.36207
$802$	−0.431535	−0.0152380
$803$	5.78618	0.204190
$804$	8.87843	0.313118
$805$	−16.0739	−0.566529
$806$	13.4429	0.473506
$807$	18.2230	0.641480
$808$	−43.7131	−1.53782
$809$	−26.1347	−0.918846	−0.459423	−	0.888218i	$-0.651944\pi$
$809$	−26.1347	−0.918846	−0.459423	+	0.888218i	$0.651944\pi$
$810$	−35.2825	−1.23970
$811$	−50.0728	−1.75829	−0.879147	−	0.476551i	$-0.841887\pi$
$811$	−50.0728	−1.75829	−0.879147	+	0.476551i	$0.841887\pi$
$812$	−1.13189	−0.0397215
$813$	78.0187	2.73624
$814$	−2.87231	−0.100675
$815$	8.98444	0.314711
$816$	43.9706	1.53928
$817$	−41.3609	−1.44704
$818$	46.0727	1.61089
$819$	149.828	5.23540
$820$	1.30335	0.0455151
$821$	−18.5015	−0.645707	−0.322853	−	0.946449i	$-0.604642\pi$
$821$	−18.5015	−0.645707	−0.322853	+	0.946449i	$0.604642\pi$
$822$	96.5904	3.36898
$823$	20.8200	0.725738	0.362869	−	0.931840i	$-0.381797\pi$
$823$	20.8200	0.725738	0.362869	+	0.931840i	$0.381797\pi$
$824$	56.1139	1.95482
$825$	−33.7575	−1.17528
$826$	63.2366	2.20028
$827$	31.9993	1.11272	0.556362	−	0.830940i	$-0.312197\pi$
$827$	31.9993	1.11272	0.556362	+	0.830940i	$0.312197\pi$
$828$	11.1337	0.386924
$829$	55.5055	1.92779	0.963894	−	0.266287i	$-0.0857970\pi$
$829$	55.5055	1.92779	0.963894	+	0.266287i	$0.0857970\pi$
$830$	−4.89525	−0.169917
$831$	−11.5573	−0.400918
$832$	−33.7746	−1.17092
$833$	−46.9564	−1.62694
$834$	−41.1853	−1.42613
$835$	−15.0438	−0.520612
$836$	2.45514	0.0849130
$837$	−50.6873	−1.75201
$838$	−16.4988	−0.569941
$839$	18.9441	0.654022	0.327011	−	0.945020i	$-0.393959\pi$
$839$	18.9441	0.654022	0.327011	+	0.945020i	$0.393959\pi$
$840$	−29.5395	−1.01921
$841$	−27.7923	−0.958356
$842$	−28.7389	−0.990407
$843$	82.6976	2.84826
$844$	1.88487	0.0648800
$845$	−1.35735	−0.0466941
$846$	−87.4589	−3.00690
$847$	28.1231	0.966320
$848$	−15.6477	−0.537343
$849$	−89.9402	−3.08674
$850$	22.4408	0.769715
$851$	5.52199	0.189292
$852$	−0.593115	−0.0203198
$853$	−22.7479	−0.778873	−0.389437	−	0.921053i	$-0.627330\pi$
$853$	−22.7479	−0.778873	−0.389437	+	0.921053i	$0.627330\pi$
$854$	32.7824	1.12179
$855$	27.9196	0.954831
$856$	0.180136	0.00615691
$857$	3.31159	0.113122	0.0565609	−	0.998399i	$-0.481986\pi$
$857$	3.31159	0.113122	0.0565609	+	0.998399i	$0.481986\pi$
$858$	−38.1277	−1.30166
$859$	−17.2983	−0.590211	−0.295105	−	0.955465i	$-0.595355\pi$
$859$	−17.2983	−0.590211	−0.295105	+	0.955465i	$0.595355\pi$
$860$	1.28370	0.0437738
$861$	−130.129	−4.43477
$862$	18.5445	0.631627
$863$	−6.31574	−0.214990	−0.107495	−	0.994206i	$-0.534283\pi$
$863$	−6.31574	−0.214990	−0.107495	+	0.994206i	$0.534283\pi$
$864$	25.4053	0.864307
$865$	13.4347	0.456795
$866$	−12.3363	−0.419203
$867$	−11.5001	−0.390564
$868$	−2.68233	−0.0910443
$869$	5.20843	0.176684
$870$	3.27555	0.111052
$871$	43.4542	1.47239
$872$	2.96779	0.100502
$873$	129.273	4.37523
$874$	35.9757	1.21690
$875$	−27.8578	−0.941765
$876$	−2.12458	−0.0717829
$877$	−38.1953	−1.28976	−0.644881	−	0.764283i	$-0.723093\pi$
$877$	−38.1953	−1.28976	−0.644881	+	0.764283i	$0.723093\pi$
$878$	−0.143716	−0.00485017
$879$	−6.06213	−0.204470
$880$	4.93136	0.166236
$881$	−16.3737	−0.551646	−0.275823	−	0.961209i	$-0.588950\pi$
$881$	−16.3737	−0.551646	−0.275823	+	0.961209i	$0.588950\pi$
$882$	146.963	4.94849
$883$	26.7681	0.900817	0.450408	−	0.892823i	$-0.351278\pi$
$883$	26.7681	0.900817	0.450408	+	0.892823i	$0.351278\pi$
$884$	−3.32538	−0.111845
$885$	24.0094	0.807067
$886$	0.599200	0.0201305
$887$	−17.5144	−0.588077	−0.294039	−	0.955794i	$-0.594999\pi$
$887$	−17.5144	−0.588077	−0.294039	+	0.955794i	$0.594999\pi$
$888$	10.1480	0.340543
$889$	73.7560	2.47370
$890$	6.70424	0.224727
$891$	87.4342	2.92916
$892$	2.75196	0.0921425
$893$	37.0769	1.24073
$894$	8.28106	0.276960
$895$	5.37377	0.179625
$896$	−39.7746	−1.32878
$897$	73.3002	2.44742
$898$	9.86078	0.329059
$899$	2.86193	0.0954508
$900$	9.21474	0.307158
$901$	−16.5937	−0.552817
$902$	24.6180	0.819691
$903$	−128.166	−4.26510
$904$	57.7535	1.92085
$905$	3.57646	0.118885
$906$	69.4272	2.30657
$907$	−6.95578	−0.230963	−0.115481	−	0.993310i	$-0.536841\pi$
$907$	−6.95578	−0.230963	−0.115481	+	0.993310i	$0.536841\pi$
$908$	−5.39240	−0.178953
$909$	128.027	4.24639
$910$	−15.0256	−0.498095
$911$	54.7770	1.81484	0.907422	−	0.420221i	$-0.138048\pi$
$911$	54.7770	1.81484	0.907422	+	0.420221i	$0.138048\pi$
$912$	58.3412	1.93187
$913$	12.1310	0.401478
$914$	14.8125	0.489953
$915$	12.4467	0.411475
$916$	−1.21070	−0.0400028
$917$	−92.9538	−3.06961
$918$	−95.5688	−3.15424
$919$	8.67128	0.286039	0.143020	−	0.989720i	$-0.454319\pi$
$919$	8.67128	0.286039	0.143020	+	0.989720i	$0.454319\pi$
$920$	−10.7435	−0.354204
$921$	33.8670	1.11596
$922$	−1.75181	−0.0576927
$923$	−2.90292	−0.0955506
$924$	7.60782	0.250279
$925$	4.57023	0.150268
$926$	−29.0585	−0.954922
$927$	−164.347	−5.39785
$928$	−1.43445	−0.0470881
$929$	−24.1684	−0.792940	−0.396470	−	0.918048i	$-0.629765\pi$
$929$	−24.1684	−0.792940	−0.396470	+	0.918048i	$0.629765\pi$
$930$	7.76236	0.254538
$931$	−62.3027	−2.04189
$932$	5.50339	0.180270
$933$	16.2390	0.531642
$934$	−44.3835	−1.45227
$935$	5.22951	0.171023
$936$	100.143	3.27327
$937$	12.9778	0.423967	0.211984	−	0.977273i	$-0.432008\pi$
$937$	12.9778	0.423967	0.211984	+	0.977273i	$0.432008\pi$
$938$	66.0875	2.15783
$939$	−26.2505	−0.856652
$940$	−1.15074	−0.0375329
$941$	−35.4700	−1.15629	−0.578145	−	0.815934i	$-0.696223\pi$
$941$	−35.4700	−1.15629	−0.578145	+	0.815934i	$0.696223\pi$
$942$	−10.9648	−0.357254
$943$	−47.3279	−1.54121
$944$	37.2974	1.21393
$945$	56.6551	1.84299
$946$	24.2468	0.788331
$947$	−16.1584	−0.525078	−0.262539	−	0.964921i	$-0.584560\pi$
$947$	−16.1584	−0.525078	−0.262539	+	0.964921i	$0.584560\pi$
$948$	−1.91244	−0.0621133
$949$	−10.3985	−0.337548
$950$	29.7750	0.966028
$951$	15.6167	0.506405
$952$	−48.6625	−1.57716
$953$	5.87916	0.190445	0.0952223	−	0.995456i	$-0.469644\pi$
$953$	5.87916	0.190445	0.0952223	+	0.995456i	$0.469644\pi$
$954$	51.9345	1.68144
$955$	7.85221	0.254091
$956$	3.75515	0.121450
$957$	−8.11722	−0.262392
$958$	−9.75333	−0.315116
$959$	−94.3298	−3.04607
$960$	−19.5025	−0.629441
$961$	−24.2178	−0.781220
$962$	5.16189	0.166426
$963$	−0.527581	−0.0170011
$964$	5.65889	0.182261
$965$	−0.256630	−0.00826121
$966$	111.479	3.58677
$967$	4.48062	0.144087	0.0720436	−	0.997401i	$-0.477048\pi$
$967$	4.48062	0.144087	0.0720436	+	0.997401i	$0.477048\pi$
$968$	18.7971	0.604161
$969$	61.8685	1.98750
$970$	−12.9643	−0.416259
$971$	−7.33267	−0.235317	−0.117658	−	0.993054i	$-0.537539\pi$
$971$	−7.33267	−0.235317	−0.117658	+	0.993054i	$0.537539\pi$
$972$	−18.5599	−0.595309
$973$	40.2214	1.28944
$974$	39.3807	1.26184
$975$	60.6662	1.94287
$976$	19.3353	0.618908
$977$	−12.2679	−0.392486	−0.196243	−	0.980555i	$-0.562874\pi$
$977$	−12.2679	−0.392486	−0.196243	+	0.980555i	$0.562874\pi$
$978$	−62.3108	−1.99248
$979$	−16.6139	−0.530983
$980$	1.93366	0.0617685
$981$	−8.69206	−0.277516
$982$	47.7149	1.52265
$983$	15.1092	0.481907	0.240954	−	0.970537i	$-0.422540\pi$
$983$	15.1092	0.481907	0.240954	+	0.970537i	$0.422540\pi$
$984$	−86.9761	−2.77270
$985$	−16.2103	−0.516504
$986$	5.39605	0.171845
$987$	114.891	3.65703
$988$	−4.41219	−0.140370
$989$	−46.6142	−1.48225
$990$	−16.3672	−0.520182
$991$	−1.57775	−0.0501188	−0.0250594	−	0.999686i	$-0.507977\pi$
$991$	−1.57775	−0.0501188	−0.0250594	+	0.999686i	$0.507977\pi$
$992$	−3.39934	−0.107929
$993$	−31.9192	−1.01293
$994$	−4.41491	−0.140032
$995$	−5.03697	−0.159683
$996$	−4.45430	−0.141140
$997$	32.0606	1.01537	0.507684	−	0.861543i	$-0.330502\pi$
$997$	32.0606	1.01537	0.507684	+	0.861543i	$0.330502\pi$
$998$	−6.50145	−0.205800
$999$	−19.4632	−0.615790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.58	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.58	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+1.32967 q^{2} +3.41937 q^{3} -0.231965 q^{4} -0.655569 q^{5} +4.54664 q^{6} -4.44023 q^{7} -2.96779 q^{8} +8.69206 q^{9} +O(q^{10})\)	\(q+1.32967 q^{2} +3.41937 q^{3} -0.231965 q^{4} -0.655569 q^{5} +4.54664 q^{6} -4.44023 q^{7} -2.96779 q^{8} +8.69206 q^{9} -0.871694 q^{10} +2.16016 q^{11} -0.793173 q^{12} -3.88207 q^{13} -5.90406 q^{14} -2.24163 q^{15} -3.48226 q^{16} -3.69280 q^{17} +11.5576 q^{18} -4.89968 q^{19} +0.152069 q^{20} -15.1828 q^{21} +2.87231 q^{22} -5.52199 q^{23} -10.1480 q^{24} -4.57023 q^{25} -5.16189 q^{26} +19.4632 q^{27} +1.02998 q^{28} -1.09894 q^{29} -2.98064 q^{30} -2.60426 q^{31} +1.30530 q^{32} +7.38639 q^{33} -4.91022 q^{34} +2.91088 q^{35} -2.01625 q^{36} -1.00000 q^{37} -6.51499 q^{38} -13.2742 q^{39} +1.94559 q^{40} +8.57080 q^{41} -20.1882 q^{42} +8.44155 q^{43} -0.501082 q^{44} -5.69825 q^{45} -7.34246 q^{46} -7.56721 q^{47} -11.9071 q^{48} +12.7157 q^{49} -6.07692 q^{50} -12.6270 q^{51} +0.900505 q^{52} +4.49353 q^{53} +25.8798 q^{54} -1.41614 q^{55} +13.1777 q^{56} -16.7538 q^{57} -1.46124 q^{58} -10.7107 q^{59} +0.519980 q^{60} -5.55252 q^{61} -3.46282 q^{62} -38.5948 q^{63} +8.70015 q^{64} +2.54497 q^{65} +9.82149 q^{66} -11.1936 q^{67} +0.856600 q^{68} -18.8817 q^{69} +3.87052 q^{70} +0.747775 q^{71} -25.7962 q^{72} +2.67858 q^{73} -1.32967 q^{74} -15.6273 q^{75} +1.13656 q^{76} -9.59162 q^{77} -17.6504 q^{78} +2.41113 q^{79} +2.28286 q^{80} +40.4758 q^{81} +11.3964 q^{82} +5.61579 q^{83} +3.52187 q^{84} +2.42089 q^{85} +11.2245 q^{86} -3.75769 q^{87} -6.41090 q^{88} -7.69105 q^{89} -7.57682 q^{90} +17.2373 q^{91} +1.28091 q^{92} -8.90492 q^{93} -10.0619 q^{94} +3.21208 q^{95} +4.46329 q^{96} +14.8725 q^{97} +16.9077 q^{98} +18.7763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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