LMFDB - Embedded newform 8041.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38493 q^{2} -1.31374 q^{3} +3.68787 q^{4} +1.21176 q^{5} +3.13318 q^{6} -4.42296 q^{7} -4.02545 q^{8} -1.27408 q^{9} +O(q^{10})$	\(q-2.38493 q^{2} -1.31374 q^{3} +3.68787 q^{4} +1.21176 q^{5} +3.13318 q^{6} -4.42296 q^{7} -4.02545 q^{8} -1.27408 q^{9} -2.88995 q^{10} -1.00000 q^{11} -4.84491 q^{12} -0.688674 q^{13} +10.5484 q^{14} -1.59194 q^{15} +2.22466 q^{16} -1.00000 q^{17} +3.03859 q^{18} +1.77230 q^{19} +4.46881 q^{20} +5.81063 q^{21} +2.38493 q^{22} -5.23888 q^{23} +5.28841 q^{24} -3.53164 q^{25} +1.64244 q^{26} +5.61504 q^{27} -16.3113 q^{28} +2.58803 q^{29} +3.79665 q^{30} +5.45240 q^{31} +2.74525 q^{32} +1.31374 q^{33} +2.38493 q^{34} -5.35956 q^{35} -4.69865 q^{36} -3.52914 q^{37} -4.22681 q^{38} +0.904740 q^{39} -4.87787 q^{40} +1.76224 q^{41} -13.8579 q^{42} +1.00000 q^{43} -3.68787 q^{44} -1.54388 q^{45} +12.4943 q^{46} -6.41983 q^{47} -2.92264 q^{48} +12.5626 q^{49} +8.42271 q^{50} +1.31374 q^{51} -2.53974 q^{52} -4.25956 q^{53} -13.3915 q^{54} -1.21176 q^{55} +17.8044 q^{56} -2.32835 q^{57} -6.17226 q^{58} +7.36311 q^{59} -5.87086 q^{60} -6.67715 q^{61} -13.0036 q^{62} +5.63521 q^{63} -10.9965 q^{64} -0.834506 q^{65} -3.13318 q^{66} -1.93528 q^{67} -3.68787 q^{68} +6.88253 q^{69} +12.7821 q^{70} -14.9763 q^{71} +5.12876 q^{72} -4.56799 q^{73} +8.41674 q^{74} +4.63967 q^{75} +6.53602 q^{76} +4.42296 q^{77} -2.15774 q^{78} +1.14484 q^{79} +2.69575 q^{80} -3.55447 q^{81} -4.20281 q^{82} -6.75242 q^{83} +21.4289 q^{84} -1.21176 q^{85} -2.38493 q^{86} -3.40000 q^{87} +4.02545 q^{88} -8.00812 q^{89} +3.68204 q^{90} +3.04598 q^{91} -19.3203 q^{92} -7.16304 q^{93} +15.3108 q^{94} +2.14760 q^{95} -3.60655 q^{96} -8.91740 q^{97} -29.9608 q^{98} +1.27408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	−2.38493	−1.68640	−0.843199	−	0.537602i	$-0.819330\pi$
$2$	−2.38493	−1.68640	−0.843199	+	0.537602i	$0.819330\pi$
$3$	−1.31374	−0.758489	−0.379245	−	0.925296i	$-0.623816\pi$
$3$	−1.31374	−0.758489	−0.379245	+	0.925296i	$0.623816\pi$
$4$	3.68787	1.84394
$5$	1.21176	0.541914	0.270957	−	0.962591i	$-0.412660\pi$
$5$	1.21176	0.541914	0.270957	+	0.962591i	$0.412660\pi$
$6$	3.13318	1.27911
$7$	−4.42296	−1.67172	−0.835861	−	0.548941i	$-0.815031\pi$
$7$	−4.42296	−1.67172	−0.835861	+	0.548941i	$0.815031\pi$
$8$	−4.02545	−1.42321
$9$	−1.27408	−0.424694
$10$	−2.88995	−0.913883
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.84491	−1.39861
$13$	−0.688674	−0.191004	−0.0955019	−	0.995429i	$-0.530446\pi$
$13$	−0.688674	−0.191004	−0.0955019	+	0.995429i	$0.530446\pi$
$14$	10.5484	2.81919
$15$	−1.59194	−0.411036
$16$	2.22466	0.556166
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.03859	0.716203
$19$	1.77230	0.406594	0.203297	−	0.979117i	$-0.434834\pi$
$19$	1.77230	0.406594	0.203297	+	0.979117i	$0.434834\pi$
$20$	4.46881	0.999256
$21$	5.81063	1.26798
$22$	2.38493	0.508468
$23$	−5.23888	−1.09238	−0.546191	−	0.837661i	$-0.683923\pi$
$23$	−5.23888	−1.09238	−0.546191	+	0.837661i	$0.683923\pi$
$24$	5.28841	1.07949
$25$	−3.53164	−0.706329
$26$	1.64244	0.322108
$27$	5.61504	1.08062
$28$	−16.3113	−3.08255
$29$	2.58803	0.480585	0.240292	−	0.970701i	$-0.422757\pi$
$29$	2.58803	0.480585	0.240292	+	0.970701i	$0.422757\pi$
$30$	3.79665	0.693171
$31$	5.45240	0.979279	0.489640	−	0.871925i	$-0.337128\pi$
$31$	5.45240	0.979279	0.489640	+	0.871925i	$0.337128\pi$
$32$	2.74525	0.485296
$33$	1.31374	0.228693
$34$	2.38493	0.409011
$35$	−5.35956	−0.905930
$36$	−4.69865	−0.783109
$37$	−3.52914	−0.580187	−0.290094	−	0.956998i	$-0.593686\pi$
$37$	−3.52914	−0.580187	−0.290094	+	0.956998i	$0.593686\pi$
$38$	−4.22681	−0.685678
$39$	0.904740	0.144874
$40$	−4.87787	−0.771260
$41$	1.76224	0.275215	0.137608	−	0.990487i	$-0.456059\pi$
$41$	1.76224	0.275215	0.137608	+	0.990487i	$0.456059\pi$
$42$	−13.8579	−2.13832
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−3.68787	−0.555968
$45$	−1.54388	−0.230148
$46$	12.4943	1.84219
$47$	−6.41983	−0.936428	−0.468214	−	0.883615i	$-0.655102\pi$
$47$	−6.41983	−0.936428	−0.468214	+	0.883615i	$0.655102\pi$
$48$	−2.92264	−0.421846
$49$	12.5626	1.79465
$50$	8.42271	1.19115
$51$	1.31374	0.183961
$52$	−2.53974	−0.352199
$53$	−4.25956	−0.585095	−0.292548	−	0.956251i	$-0.594503\pi$
$53$	−4.25956	−0.585095	−0.292548	+	0.956251i	$0.594503\pi$
$54$	−13.3915	−1.82235
$55$	−1.21176	−0.163393
$56$	17.8044	2.37922
$57$	−2.32835	−0.308397
$58$	−6.17226	−0.810457
$59$	7.36311	0.958596	0.479298	−	0.877652i	$-0.340891\pi$
$59$	7.36311	0.958596	0.479298	+	0.877652i	$0.340891\pi$
$60$	−5.87086	−0.757925
$61$	−6.67715	−0.854922	−0.427461	−	0.904034i	$-0.640592\pi$
$61$	−6.67715	−0.854922	−0.427461	+	0.904034i	$0.640592\pi$
$62$	−13.0036	−1.65145
$63$	5.63521	0.709970
$64$	−10.9965	−1.37457
$65$	−0.834506	−0.103508
$66$	−3.13318	−0.385668
$67$	−1.93528	−0.236432	−0.118216	−	0.992988i	$-0.537718\pi$
$67$	−1.93528	−0.236432	−0.118216	+	0.992988i	$0.537718\pi$
$68$	−3.68787	−0.447220
$69$	6.88253	0.828559
$70$	12.7821	1.52776
$71$	−14.9763	−1.77736	−0.888679	−	0.458531i	$-0.848376\pi$
$71$	−14.9763	−1.77736	−0.888679	+	0.458531i	$0.848376\pi$
$72$	5.12876	0.604430
$73$	−4.56799	−0.534642	−0.267321	−	0.963607i	$-0.586138\pi$
$73$	−4.56799	−0.534642	−0.267321	+	0.963607i	$0.586138\pi$
$74$	8.41674	0.978426
$75$	4.63967	0.535743
$76$	6.53602	0.749733
$77$	4.42296	0.504043
$78$	−2.15774	−0.244316
$79$	1.14484	0.128804	0.0644021	−	0.997924i	$-0.479486\pi$
$79$	1.14484	0.128804	0.0644021	+	0.997924i	$0.479486\pi$
$80$	2.69575	0.301394
$81$	−3.55447	−0.394941
$82$	−4.20281	−0.464122
$83$	−6.75242	−0.741174	−0.370587	−	0.928798i	$-0.620843\pi$
$83$	−6.75242	−0.741174	−0.370587	+	0.928798i	$0.620843\pi$
$84$	21.4289	2.33808
$85$	−1.21176	−0.131434
$86$	−2.38493	−0.257173
$87$	−3.40000	−0.364519
$88$	4.02545	0.429115
$89$	−8.00812	−0.848859	−0.424429	−	0.905461i	$-0.639525\pi$
$89$	−8.00812	−0.848859	−0.424429	+	0.905461i	$0.639525\pi$
$90$	3.68204	0.388121
$91$	3.04598	0.319305
$92$	−19.3203	−2.01428
$93$	−7.16304	−0.742773
$94$	15.3108	1.57919
$95$	2.14760	0.220339
$96$	−3.60655	−0.368092
$97$	−8.91740	−0.905424	−0.452712	−	0.891657i	$-0.649543\pi$
$97$	−8.91740	−0.905424	−0.452712	+	0.891657i	$0.649543\pi$
$98$	−29.9608	−3.02650
$99$	1.27408	0.128050
$100$	−13.0243	−1.30243
$101$	−8.94542	−0.890102	−0.445051	−	0.895505i	$-0.646815\pi$
$101$	−8.94542	−0.890102	−0.445051	+	0.895505i	$0.646815\pi$
$102$	−3.13318	−0.310231
$103$	−14.7751	−1.45583	−0.727916	−	0.685666i	$-0.759511\pi$
$103$	−14.7751	−1.45583	−0.727916	+	0.685666i	$0.759511\pi$
$104$	2.77222	0.271839
$105$	7.04107	0.687138
$106$	10.1587	0.986703
$107$	−8.55714	−0.827250	−0.413625	−	0.910447i	$-0.635737\pi$
$107$	−8.55714	−0.827250	−0.413625	+	0.910447i	$0.635737\pi$
$108$	20.7076	1.99259
$109$	−14.1844	−1.35862	−0.679308	−	0.733854i	$-0.737720\pi$
$109$	−14.1844	−1.35862	−0.679308	+	0.733854i	$0.737720\pi$
$110$	2.88995	0.275546
$111$	4.63638	0.440066
$112$	−9.83960	−0.929755
$113$	−2.98855	−0.281140	−0.140570	−	0.990071i	$-0.544893\pi$
$113$	−2.98855	−0.281140	−0.140570	+	0.990071i	$0.544893\pi$
$114$	5.55293	0.520080
$115$	−6.34825	−0.591977
$116$	9.54432	0.886168
$117$	0.877427	0.0811181
$118$	−17.5605	−1.61657
$119$	4.42296	0.405452
$120$	6.40827	0.584992
$121$	1.00000	0.0909091
$122$	15.9245	1.44174
$123$	−2.31513	−0.208748
$124$	20.1078	1.80573
$125$	−10.3383	−0.924684
$126$	−13.4396	−1.19729
$127$	5.75436	0.510617	0.255308	−	0.966860i	$-0.417823\pi$
$127$	5.75436	0.510617	0.255308	+	0.966860i	$0.417823\pi$
$128$	20.7354	1.83277
$129$	−1.31374	−0.115669
$130$	1.99023	0.174555
$131$	−6.61612	−0.578053	−0.289027	−	0.957321i	$-0.593332\pi$
$131$	−6.61612	−0.578053	−0.289027	+	0.957321i	$0.593332\pi$
$132$	4.84491	0.421696
$133$	−7.83881	−0.679711
$134$	4.61550	0.398719
$135$	6.80407	0.585601
$136$	4.02545	0.345180
$137$	0.169189	0.0144548	0.00722741	−	0.999974i	$-0.497699\pi$
$137$	0.169189	0.0144548	0.00722741	+	0.999974i	$0.497699\pi$
$138$	−16.4143	−1.39728
$139$	16.4754	1.39742	0.698712	−	0.715403i	$-0.253757\pi$
$139$	16.4754	1.39742	0.698712	+	0.715403i	$0.253757\pi$
$140$	−19.7654	−1.67048
$141$	8.43400	0.710271
$142$	35.7173	2.99733
$143$	0.688674	0.0575898
$144$	−2.83440	−0.236200
$145$	3.13606	0.260436
$146$	10.8943	0.901619
$147$	−16.5040	−1.36123
$148$	−13.0150	−1.06983
$149$	−2.99293	−0.245190	−0.122595	−	0.992457i	$-0.539122\pi$
$149$	−2.99293	−0.245190	−0.122595	+	0.992457i	$0.539122\pi$
$150$	−11.0653	−0.903475
$151$	2.94382	0.239564	0.119782	−	0.992800i	$-0.461780\pi$
$151$	2.94382	0.239564	0.119782	+	0.992800i	$0.461780\pi$
$152$	−7.13431	−0.578669
$153$	1.27408	0.103003
$154$	−10.5484	−0.850017
$155$	6.60698	0.530686
$156$	3.33657	0.267139
$157$	−10.8955	−0.869555	−0.434778	−	0.900538i	$-0.643173\pi$
$157$	−10.8955	−0.869555	−0.434778	+	0.900538i	$0.643173\pi$
$158$	−2.73035	−0.217215
$159$	5.59596	0.443789
$160$	3.32657	0.262989
$161$	23.1713	1.82616
$162$	8.47715	0.666028
$163$	7.51917	0.588946	0.294473	−	0.955660i	$-0.404856\pi$
$163$	7.51917	0.588946	0.294473	+	0.955660i	$0.404856\pi$
$164$	6.49891	0.507480
$165$	1.59194	0.123932
$166$	16.1040	1.24991
$167$	5.35668	0.414512	0.207256	−	0.978287i	$-0.433547\pi$
$167$	5.35668	0.414512	0.207256	+	0.978287i	$0.433547\pi$
$168$	−23.3904	−1.80461
$169$	−12.5257	−0.963518
$170$	2.88995	0.221649
$171$	−2.25806	−0.172678
$172$	3.68787	0.281198
$173$	6.31435	0.480071	0.240035	−	0.970764i	$-0.422841\pi$
$173$	6.31435	0.480071	0.240035	+	0.970764i	$0.422841\pi$
$174$	8.10875	0.614723
$175$	15.6203	1.18079
$176$	−2.22466	−0.167690
$177$	−9.67323	−0.727085
$178$	19.0988	1.43151
$179$	13.2023	0.986788	0.493394	−	0.869806i	$-0.335756\pi$
$179$	13.2023	0.986788	0.493394	+	0.869806i	$0.335756\pi$
$180$	−5.69363	−0.424378
$181$	3.95376	0.293881	0.146940	−	0.989145i	$-0.453057\pi$
$181$	3.95376	0.293881	0.146940	+	0.989145i	$0.453057\pi$
$182$	−7.26443	−0.538475
$183$	8.77206	0.648449
$184$	21.0889	1.55469
$185$	−4.27646	−0.314412
$186$	17.0833	1.25261
$187$	1.00000	0.0731272
$188$	−23.6755	−1.72671
$189$	−24.8351	−1.80649
$190$	−5.12186	−0.371579
$191$	−7.28341	−0.527009	−0.263504	−	0.964658i	$-0.584878\pi$
$191$	−7.28341	−0.527009	−0.263504	+	0.964658i	$0.584878\pi$
$192$	14.4466	1.04259
$193$	−5.20599	−0.374736	−0.187368	−	0.982290i	$-0.559996\pi$
$193$	−5.20599	−0.374736	−0.187368	+	0.982290i	$0.559996\pi$
$194$	21.2673	1.52691
$195$	1.09632	0.0785095
$196$	46.3292	3.30923
$197$	2.76172	0.196764	0.0983820	−	0.995149i	$-0.468633\pi$
$197$	2.76172	0.196764	0.0983820	+	0.995149i	$0.468633\pi$
$198$	−3.03859	−0.215943
$199$	8.12473	0.575947	0.287973	−	0.957638i	$-0.407019\pi$
$199$	8.12473	0.575947	0.287973	+	0.957638i	$0.407019\pi$
$200$	14.2165	1.00526
$201$	2.54246	0.179331
$202$	21.3342	1.50107
$203$	−11.4468	−0.803404
$204$	4.84491	0.339212
$205$	2.13540	0.149143
$206$	35.2375	2.45511
$207$	6.67476	0.463928
$208$	−1.53207	−0.106230
$209$	−1.77230	−0.122593
$210$	−16.7924	−1.15879
$211$	−7.90279	−0.544050	−0.272025	−	0.962290i	$-0.587693\pi$
$211$	−7.90279	−0.544050	−0.272025	+	0.962290i	$0.587693\pi$
$212$	−15.7087	−1.07888
$213$	19.6750	1.34811
$214$	20.4081	1.39507
$215$	1.21176	0.0826412
$216$	−22.6031	−1.53795
$217$	−24.1157	−1.63708
$218$	33.8287	2.29117
$219$	6.00115	0.405520
$220$	−4.46881	−0.301287
$221$	0.688674	0.0463252
$222$	−11.0574	−0.742126
$223$	−6.37200	−0.426701	−0.213350	−	0.976976i	$-0.568438\pi$
$223$	−6.37200	−0.426701	−0.213350	+	0.976976i	$0.568438\pi$
$224$	−12.1421	−0.811280
$225$	4.49960	0.299974
$226$	7.12748	0.474113
$227$	8.21359	0.545155	0.272578	−	0.962134i	$-0.412124\pi$
$227$	8.21359	0.545155	0.272578	+	0.962134i	$0.412124\pi$
$228$	−8.58664	−0.568664
$229$	−14.7970	−0.977812	−0.488906	−	0.872336i	$-0.662604\pi$
$229$	−14.7970	−0.977812	−0.488906	+	0.872336i	$0.662604\pi$
$230$	15.1401	0.998309
$231$	−5.81063	−0.382311
$232$	−10.4180	−0.683975
$233$	−12.1727	−0.797463	−0.398732	−	0.917068i	$-0.630550\pi$
$233$	−12.1727	−0.797463	−0.398732	+	0.917068i	$0.630550\pi$
$234$	−2.09260	−0.136797
$235$	−7.77927	−0.507464
$236$	27.1542	1.76759
$237$	−1.50402	−0.0976967
$238$	−10.5484	−0.683754
$239$	9.95660	0.644039	0.322019	−	0.946733i	$-0.395638\pi$
$239$	9.95660	0.644039	0.322019	+	0.946733i	$0.395638\pi$
$240$	−3.54152	−0.228604
$241$	−20.2548	−1.30473	−0.652364	−	0.757906i	$-0.726222\pi$
$241$	−20.2548	−1.30473	−0.652364	+	0.757906i	$0.726222\pi$
$242$	−2.38493	−0.153309
$243$	−12.1755	−0.781057
$244$	−24.6245	−1.57642
$245$	15.2228	0.972549
$246$	5.52140	0.352032
$247$	−1.22054	−0.0776609
$248$	−21.9484	−1.39372
$249$	8.87093	0.562173
$250$	24.6560	1.55939
$251$	11.2973	0.713081	0.356540	−	0.934280i	$-0.383956\pi$
$251$	11.2973	0.713081	0.356540	+	0.934280i	$0.383956\pi$
$252$	20.7820	1.30914
$253$	5.23888	0.329365
$254$	−13.7237	−0.861103
$255$	1.59194	0.0996909
$256$	−27.4594	−1.71621
$257$	−28.5478	−1.78076	−0.890380	−	0.455217i	$-0.849562\pi$
$257$	−28.5478	−1.78076	−0.890380	+	0.455217i	$0.849562\pi$
$258$	3.13318	0.195063
$259$	15.6093	0.969912
$260$	−3.07755	−0.190862
$261$	−3.29736	−0.204101
$262$	15.7790	0.974827
$263$	−17.5812	−1.08411	−0.542053	−	0.840344i	$-0.682353\pi$
$263$	−17.5812	−1.08411	−0.542053	+	0.840344i	$0.682353\pi$
$264$	−5.28841	−0.325479
$265$	−5.16155	−0.317072
$266$	18.6950	1.14626
$267$	10.5206	0.643850
$268$	−7.13707	−0.435966
$269$	3.36673	0.205273	0.102637	−	0.994719i	$-0.467272\pi$
$269$	3.36673	0.205273	0.102637	+	0.994719i	$0.467272\pi$
$270$	−16.2272	−0.987556
$271$	7.09089	0.430741	0.215371	−	0.976532i	$-0.430904\pi$
$271$	7.09089	0.430741	0.215371	+	0.976532i	$0.430904\pi$
$272$	−2.22466	−0.134890
$273$	−4.00163	−0.242190
$274$	−0.403504	−0.0243766
$275$	3.53164	0.212966
$276$	25.3819	1.52781
$277$	28.4038	1.70662	0.853310	−	0.521404i	$-0.174591\pi$
$277$	28.4038	1.70662	0.853310	+	0.521404i	$0.174591\pi$
$278$	−39.2926	−2.35661
$279$	−6.94680	−0.415894
$280$	21.5746	1.28933
$281$	7.87391	0.469718	0.234859	−	0.972029i	$-0.424537\pi$
$281$	7.87391	0.469718	0.234859	+	0.972029i	$0.424537\pi$
$282$	−20.1145	−1.19780
$283$	28.6160	1.70105	0.850523	−	0.525938i	$-0.176286\pi$
$283$	28.6160	1.70105	0.850523	+	0.525938i	$0.176286\pi$
$284$	−55.2306	−3.27733
$285$	−2.82139	−0.167125
$286$	−1.64244	−0.0971193
$287$	−7.79431	−0.460084
$288$	−3.49767	−0.206102
$289$	1.00000	0.0588235
$290$	−7.47928	−0.439198
$291$	11.7152	0.686755
$292$	−16.8462	−0.985847
$293$	20.3485	1.18877	0.594387	−	0.804179i	$-0.297395\pi$
$293$	20.3485	1.18877	0.594387	+	0.804179i	$0.297395\pi$
$294$	39.3608	2.29557
$295$	8.92231	0.519477
$296$	14.2064	0.825730
$297$	−5.61504	−0.325818
$298$	7.13792	0.413488
$299$	3.60788	0.208649
$300$	17.1105	0.987876
$301$	−4.42296	−0.254935
$302$	−7.02079	−0.404001
$303$	11.7520	0.675133
$304$	3.94277	0.226134
$305$	−8.09109	−0.463294
$306$	−3.03859	−0.173705
$307$	−15.6090	−0.890853	−0.445427	−	0.895318i	$-0.646948\pi$
$307$	−15.6090	−0.890853	−0.445427	+	0.895318i	$0.646948\pi$
$308$	16.3113	0.929424
$309$	19.4106	1.10423
$310$	−15.7572	−0.894947
$311$	16.2681	0.922478	0.461239	−	0.887276i	$-0.347405\pi$
$311$	16.2681	0.922478	0.461239	+	0.887276i	$0.347405\pi$
$312$	−3.64199	−0.206187
$313$	−12.4971	−0.706379	−0.353190	−	0.935552i	$-0.614903\pi$
$313$	−12.4971	−0.706379	−0.353190	+	0.935552i	$0.614903\pi$
$314$	25.9849	1.46642
$315$	6.82851	0.384743
$316$	4.22202	0.237507
$317$	26.7792	1.50407	0.752035	−	0.659123i	$-0.229072\pi$
$317$	26.7792	1.50407	0.752035	+	0.659123i	$0.229072\pi$
$318$	−13.3460	−0.748404
$319$	−2.58803	−0.144902
$320$	−13.3251	−0.744898
$321$	11.2419	0.627460
$322$	−55.2619	−3.07963
$323$	−1.77230	−0.0986134
$324$	−13.1084	−0.728246
$325$	2.43215	0.134911
$326$	−17.9327	−0.993198
$327$	18.6346	1.03050
$328$	−7.09381	−0.391690
$329$	28.3946	1.56545
$330$	−3.79665	−0.208999
$331$	−7.31868	−0.402271	−0.201135	−	0.979563i	$-0.564463\pi$
$331$	−7.31868	−0.402271	−0.201135	+	0.979563i	$0.564463\pi$
$332$	−24.9021	−1.36668
$333$	4.49641	0.246402
$334$	−12.7753	−0.699033
$335$	−2.34509	−0.128126
$336$	12.9267	0.705209
$337$	−10.9930	−0.598825	−0.299412	−	0.954124i	$-0.596791\pi$
$337$	−10.9930	−0.598825	−0.299412	+	0.954124i	$0.596791\pi$
$338$	29.8729	1.62487
$339$	3.92619	0.213241
$340$	−4.46881	−0.242355
$341$	−5.45240	−0.295264
$342$	5.38530	0.291203
$343$	−24.6031	−1.32844
$344$	−4.02545	−0.217038
$345$	8.33996	0.449008
$346$	−15.0593	−0.809590
$347$	−33.2700	−1.78603	−0.893013	−	0.450031i	$-0.851413\pi$
$347$	−33.2700	−1.78603	−0.893013	+	0.450031i	$0.851413\pi$
$348$	−12.5388	−0.672149
$349$	4.51865	0.241878	0.120939	−	0.992660i	$-0.461410\pi$
$349$	4.51865	0.241878	0.120939	+	0.992660i	$0.461410\pi$
$350$	−37.2533	−1.99127
$351$	−3.86693	−0.206402
$352$	−2.74525	−0.146322
$353$	−4.18440	−0.222713	−0.111356	−	0.993781i	$-0.535520\pi$
$353$	−4.18440	−0.222713	−0.111356	+	0.993781i	$0.535520\pi$
$354$	23.0699	1.22615
$355$	−18.1476	−0.963175
$356$	−29.5329	−1.56524
$357$	−5.81063	−0.307531
$358$	−31.4866	−1.66412
$359$	1.08226	0.0571193	0.0285597	−	0.999592i	$-0.490908\pi$
$359$	1.08226	0.0571193	0.0285597	+	0.999592i	$0.490908\pi$
$360$	6.21481	0.327549
$361$	−15.8590	−0.834682
$362$	−9.42943	−0.495600
$363$	−1.31374	−0.0689536
$364$	11.2332	0.588779
$365$	−5.53529	−0.289730
$366$	−20.9207	−1.09354
$367$	17.5041	0.913706	0.456853	−	0.889542i	$-0.348977\pi$
$367$	17.5041	0.913706	0.456853	+	0.889542i	$0.348977\pi$
$368$	−11.6547	−0.607545
$369$	−2.24524	−0.116882
$370$	10.1990	0.530223
$371$	18.8399	0.978117
$372$	−26.4164	−1.36963
$373$	−27.6810	−1.43327	−0.716634	−	0.697449i	$-0.754318\pi$
$373$	−27.6810	−1.43327	−0.716634	+	0.697449i	$0.754318\pi$
$374$	−2.38493	−0.123322
$375$	13.5818	0.701363
$376$	25.8427	1.33274
$377$	−1.78231	−0.0917935
$378$	59.2299	3.04646
$379$	−35.3720	−1.81694	−0.908469	−	0.417952i	$-0.862748\pi$
$379$	−35.3720	−1.81694	−0.908469	+	0.417952i	$0.862748\pi$
$380$	7.92007	0.406291
$381$	−7.55974	−0.387297
$382$	17.3704	0.888746
$383$	−13.0095	−0.664752	−0.332376	−	0.943147i	$-0.607850\pi$
$383$	−13.0095	−0.664752	−0.332376	+	0.943147i	$0.607850\pi$
$384$	−27.2410	−1.39014
$385$	5.35956	0.273148
$386$	12.4159	0.631953
$387$	−1.27408	−0.0647652
$388$	−32.8862	−1.66955
$389$	23.6782	1.20053	0.600266	−	0.799800i	$-0.295061\pi$
$389$	23.6782	1.20053	0.600266	+	0.799800i	$0.295061\pi$
$390$	−2.61465	−0.132398
$391$	5.23888	0.264941
$392$	−50.5701	−2.55418
$393$	8.69188	0.438447
$394$	−6.58649	−0.331822
$395$	1.38727	0.0698009
$396$	4.69865	0.236116
$397$	−1.00843	−0.0506118	−0.0253059	−	0.999680i	$-0.508056\pi$
$397$	−1.00843	−0.0506118	−0.0253059	+	0.999680i	$0.508056\pi$
$398$	−19.3769	−0.971276
$399$	10.2982	0.515554
$400$	−7.85672	−0.392836
$401$	−28.6142	−1.42892	−0.714462	−	0.699674i	$-0.753329\pi$
$401$	−28.6142	−1.42892	−0.714462	+	0.699674i	$0.753329\pi$
$402$	−6.06358	−0.302424
$403$	−3.75492	−0.187046
$404$	−32.9896	−1.64129
$405$	−4.30715	−0.214024
$406$	27.2997	1.35486
$407$	3.52914	0.174933
$408$	−5.28841	−0.261815
$409$	9.62819	0.476083	0.238042	−	0.971255i	$-0.423495\pi$
$409$	9.62819	0.476083	0.238042	+	0.971255i	$0.423495\pi$
$410$	−5.09278	−0.251515
$411$	−0.222271	−0.0109638
$412$	−54.4886	−2.68446
$413$	−32.5668	−1.60251
$414$	−15.9188	−0.782366
$415$	−8.18229	−0.401653
$416$	−1.89058	−0.0926933
$417$	−21.6444	−1.05993
$418$	4.22681	0.206740
$419$	−23.1982	−1.13331	−0.566653	−	0.823956i	$-0.691762\pi$
$419$	−23.1982	−1.13331	−0.566653	+	0.823956i	$0.691762\pi$
$420$	25.9666	1.26704
$421$	−27.8901	−1.35928	−0.679640	−	0.733546i	$-0.737864\pi$
$421$	−27.8901	−1.35928	−0.679640	+	0.733546i	$0.737864\pi$
$422$	18.8476	0.917485
$423$	8.17939	0.397695
$424$	17.1467	0.832715
$425$	3.53164	0.171310
$426$	−46.9233	−2.27344
$427$	29.5328	1.42919
$428$	−31.5576	−1.52540
$429$	−0.904740	−0.0436812
$430$	−2.88995	−0.139366
$431$	8.41348	0.405263	0.202631	−	0.979255i	$-0.435051\pi$
$431$	8.41348	0.405263	0.202631	+	0.979255i	$0.435051\pi$
$432$	12.4916	0.601002
$433$	−24.0775	−1.15709	−0.578545	−	0.815650i	$-0.696379\pi$
$433$	−24.0775	−1.15709	−0.578545	+	0.815650i	$0.696379\pi$
$434$	57.5143	2.76077
$435$	−4.11998	−0.197538
$436$	−52.3101	−2.50520
$437$	−9.28486	−0.444155
$438$	−14.3123	−0.683869
$439$	22.5553	1.07651	0.538253	−	0.842783i	$-0.319085\pi$
$439$	22.5553	1.07651	0.538253	+	0.842783i	$0.319085\pi$
$440$	4.87787	0.232544
$441$	−16.0058	−0.762179
$442$	−1.64244	−0.0781227
$443$	25.6133	1.21692	0.608462	−	0.793583i	$-0.291787\pi$
$443$	25.6133	1.21692	0.608462	+	0.793583i	$0.291787\pi$
$444$	17.0984	0.811453
$445$	−9.70389	−0.460009
$446$	15.1968	0.719587
$447$	3.93194	0.185974
$448$	48.6373	2.29790
$449$	22.1517	1.04540	0.522701	−	0.852516i	$-0.324925\pi$
$449$	22.1517	1.04540	0.522701	+	0.852516i	$0.324925\pi$
$450$	−10.7312	−0.505875
$451$	−1.76224	−0.0829805
$452$	−11.0214	−0.518404
$453$	−3.86742	−0.181707
$454$	−19.5888	−0.919348
$455$	3.69099	0.173036
$456$	9.37265	0.438914
$457$	0.640899	0.0299800	0.0149900	−	0.999888i	$-0.495228\pi$
$457$	0.640899	0.0299800	0.0149900	+	0.999888i	$0.495228\pi$
$458$	35.2897	1.64898
$459$	−5.61504	−0.262088
$460$	−23.4115	−1.09157
$461$	35.0275	1.63139	0.815696	−	0.578481i	$-0.196354\pi$
$461$	35.0275	1.63139	0.815696	+	0.578481i	$0.196354\pi$
$462$	13.8579	0.644729
$463$	−21.4294	−0.995909	−0.497954	−	0.867203i	$-0.665915\pi$
$463$	−21.4294	−0.995909	−0.497954	+	0.867203i	$0.665915\pi$
$464$	5.75750	0.267285
$465$	−8.67987	−0.402519
$466$	29.0311	1.34484
$467$	−37.6573	−1.74257	−0.871285	−	0.490777i	$-0.836713\pi$
$467$	−37.6573	−1.74257	−0.871285	+	0.490777i	$0.836713\pi$
$468$	3.23584	0.149577
$469$	8.55967	0.395249
$470$	18.5530	0.855786
$471$	14.3139	0.659548
$472$	−29.6399	−1.36429
$473$	−1.00000	−0.0459800
$474$	3.58698	0.164755
$475$	−6.25913	−0.287189
$476$	16.3113	0.747628
$477$	5.42703	0.248486
$478$	−23.7458	−1.08611
$479$	0.770389	0.0352000	0.0176000	−	0.999845i	$-0.494397\pi$
$479$	0.770389	0.0352000	0.0176000	+	0.999845i	$0.494397\pi$
$480$	−4.37026	−0.199474
$481$	2.43043	0.110818
$482$	48.3062	2.20029
$483$	−30.4412	−1.38512
$484$	3.68787	0.167631
$485$	−10.8057	−0.490662
$486$	29.0376	1.31717
$487$	−1.82062	−0.0825000	−0.0412500	−	0.999149i	$-0.513134\pi$
$487$	−1.82062	−0.0825000	−0.0412500	+	0.999149i	$0.513134\pi$
$488$	26.8786	1.21674
$489$	−9.87824	−0.446710
$490$	−36.3053	−1.64010
$491$	24.0192	1.08397	0.541985	−	0.840388i	$-0.317673\pi$
$491$	24.0192	1.08397	0.541985	+	0.840388i	$0.317673\pi$
$492$	−8.53789	−0.384918
$493$	−2.58803	−0.116559
$494$	2.91089	0.130967
$495$	1.54388	0.0693922
$496$	12.1298	0.544642
$497$	66.2395	2.97125
$498$	−21.1565	−0.948047
$499$	3.38052	0.151333	0.0756665	−	0.997133i	$-0.475892\pi$
$499$	3.38052	0.151333	0.0756665	+	0.997133i	$0.475892\pi$
$500$	−38.1263	−1.70506
$501$	−7.03730	−0.314403
$502$	−26.9433	−1.20254
$503$	22.8523	1.01893	0.509467	−	0.860490i	$-0.329843\pi$
$503$	22.8523	1.01893	0.509467	+	0.860490i	$0.329843\pi$
$504$	−22.6843	−1.01044
$505$	−10.8397	−0.482359
$506$	−12.4943	−0.555441
$507$	16.4556	0.730818
$508$	21.2214	0.941545
$509$	28.3374	1.25603	0.628016	−	0.778200i	$-0.283867\pi$
$509$	28.3374	1.25603	0.628016	+	0.778200i	$0.283867\pi$
$510$	−3.79665	−0.168119
$511$	20.2040	0.893773
$512$	24.0178	1.06145
$513$	9.95154	0.439371
$514$	68.0843	3.00307
$515$	−17.9038	−0.788936
$516$	−4.84491	−0.213285
$517$	6.41983	0.282344
$518$	−37.2269	−1.63566
$519$	−8.29542	−0.364129
$520$	3.35926	0.147313
$521$	−2.71719	−0.119042	−0.0595210	−	0.998227i	$-0.518957\pi$
$521$	−2.71719	−0.119042	−0.0595210	+	0.998227i	$0.518957\pi$
$522$	7.86396	0.344196
$523$	13.7182	0.599854	0.299927	−	0.953962i	$-0.403038\pi$
$523$	13.7182	0.599854	0.299927	+	0.953962i	$0.403038\pi$
$524$	−24.3994	−1.06589
$525$	−20.5211	−0.895613
$526$	41.9300	1.82823
$527$	−5.45240	−0.237510
$528$	2.92264	0.127191
$529$	4.44582	0.193297
$530$	12.3099	0.534709
$531$	−9.38121	−0.407110
$532$	−28.9086	−1.25334
$533$	−1.21361	−0.0525672
$534$	−25.0909	−1.08579
$535$	−10.3692	−0.448299
$536$	7.79038	0.336493
$537$	−17.3445	−0.748468
$538$	−8.02941	−0.346172
$539$	−12.5626	−0.541109
$540$	25.0925	1.07981
$541$	−7.09321	−0.304961	−0.152480	−	0.988306i	$-0.548726\pi$
$541$	−7.09321	−0.304961	−0.152480	+	0.988306i	$0.548726\pi$
$542$	−16.9113	−0.726401
$543$	−5.19422	−0.222906
$544$	−2.74525	−0.117702
$545$	−17.1880	−0.736253
$546$	9.54359	0.408428
$547$	15.1589	0.648150	0.324075	−	0.946031i	$-0.394947\pi$
$547$	15.1589	0.648150	0.324075	+	0.946031i	$0.394947\pi$
$548$	0.623949	0.0266538
$549$	8.50724	0.363080
$550$	−8.42271	−0.359146
$551$	4.58676	0.195403
$552$	−27.7053	−1.17922
$553$	−5.06357	−0.215325
$554$	−67.7410	−2.87804
$555$	5.61817	0.238478
$556$	60.7591	2.57676
$557$	6.34852	0.268995	0.134498	−	0.990914i	$-0.457058\pi$
$557$	6.34852	0.268995	0.134498	+	0.990914i	$0.457058\pi$
$558$	16.5676	0.701363
$559$	−0.688674	−0.0291278
$560$	−11.9232	−0.503848
$561$	−1.31374	−0.0554662
$562$	−18.7787	−0.792131
$563$	27.2129	1.14689	0.573443	−	0.819245i	$-0.305607\pi$
$563$	27.2129	1.14689	0.573443	+	0.819245i	$0.305607\pi$
$564$	31.1035	1.30969
$565$	−3.62140	−0.152354
$566$	−68.2471	−2.86864
$567$	15.7213	0.660232
$568$	60.2863	2.52956
$569$	14.7119	0.616753	0.308376	−	0.951264i	$-0.400214\pi$
$569$	14.7119	0.616753	0.308376	+	0.951264i	$0.400214\pi$
$570$	6.72881	0.281839
$571$	21.8312	0.913608	0.456804	−	0.889567i	$-0.348994\pi$
$571$	21.8312	0.913608	0.456804	+	0.889567i	$0.348994\pi$
$572$	2.53974	0.106192
$573$	9.56852	0.399730
$574$	18.5889	0.775884
$575$	18.5018	0.771580
$576$	14.0105	0.583771
$577$	−29.7790	−1.23972	−0.619859	−	0.784713i	$-0.712810\pi$
$577$	−29.7790	−1.23972	−0.619859	+	0.784713i	$0.712810\pi$
$578$	−2.38493	−0.0991999
$579$	6.83933	0.284233
$580$	11.5654	0.480227
$581$	29.8657	1.23904
$582$	−27.9398	−1.15814
$583$	4.25956	0.176413
$584$	18.3882	0.760910
$585$	1.06323	0.0439591
$586$	−48.5298	−2.00475
$587$	29.1178	1.20182	0.600911	−	0.799316i	$-0.294805\pi$
$587$	29.1178	1.20182	0.600911	+	0.799316i	$0.294805\pi$
$588$	−60.8646	−2.51002
$589$	9.66328	0.398169
$590$	−21.2790	−0.876045
$591$	−3.62818	−0.149243
$592$	−7.85115	−0.322680
$593$	32.8387	1.34852	0.674262	−	0.738492i	$-0.264462\pi$
$593$	32.8387	1.34852	0.674262	+	0.738492i	$0.264462\pi$
$594$	13.3915	0.549458
$595$	5.35956	0.219720
$596$	−11.0375	−0.452115
$597$	−10.6738	−0.436850
$598$	−8.60452	−0.351865
$599$	−27.4124	−1.12004	−0.560021	−	0.828479i	$-0.689207\pi$
$599$	−27.4124	−1.12004	−0.560021	+	0.828479i	$0.689207\pi$
$600$	−18.6768	−0.762476
$601$	−28.0723	−1.14509	−0.572547	−	0.819872i	$-0.694045\pi$
$601$	−28.0723	−1.14509	−0.572547	+	0.819872i	$0.694045\pi$
$602$	10.5484	0.429922
$603$	2.46571	0.100411
$604$	10.8564	0.441742
$605$	1.21176	0.0492649
$606$	−28.0276	−1.13854
$607$	−29.7530	−1.20764	−0.603819	−	0.797122i	$-0.706355\pi$
$607$	−29.7530	−1.20764	−0.603819	+	0.797122i	$0.706355\pi$
$608$	4.86540	0.197318
$609$	15.0381	0.609374
$610$	19.2967	0.781299
$611$	4.42117	0.178861
$612$	4.69865	0.189932
$613$	6.98822	0.282252	0.141126	−	0.989992i	$-0.454928\pi$
$613$	6.98822	0.282252	0.141126	+	0.989992i	$0.454928\pi$
$614$	37.2263	1.50233
$615$	−2.80537	−0.113123
$616$	−17.8044	−0.717361
$617$	−22.0753	−0.888718	−0.444359	−	0.895849i	$-0.646569\pi$
$617$	−22.0753	−0.888718	−0.444359	+	0.895849i	$0.646569\pi$
$618$	−46.2930	−1.86218
$619$	18.2196	0.732307	0.366154	−	0.930554i	$-0.380674\pi$
$619$	18.2196	0.732307	0.366154	+	0.930554i	$0.380674\pi$
$620$	24.3657	0.978551
$621$	−29.4165	−1.18044
$622$	−38.7982	−1.55566
$623$	35.4196	1.41906
$624$	2.01274	0.0805742
$625$	5.13073	0.205229
$626$	29.8047	1.19124
$627$	2.32835	0.0929851
$628$	−40.1812	−1.60340
$629$	3.52914	0.140716
$630$	−16.2855	−0.648830
$631$	−15.3175	−0.609779	−0.304890	−	0.952388i	$-0.598620\pi$
$631$	−15.3175	−0.609779	−0.304890	+	0.952388i	$0.598620\pi$
$632$	−4.60849	−0.183316
$633$	10.3822	0.412656
$634$	−63.8665	−2.53646
$635$	6.97289	0.276711
$636$	20.6372	0.818318
$637$	−8.65152	−0.342786
$638$	6.17226	0.244362
$639$	19.0810	0.754833
$640$	25.1263	0.993205
$641$	−13.4162	−0.529908	−0.264954	−	0.964261i	$-0.585357\pi$
$641$	−13.4162	−0.529908	−0.264954	+	0.964261i	$0.585357\pi$
$642$	−26.8110	−1.05815
$643$	−23.3860	−0.922252	−0.461126	−	0.887335i	$-0.652554\pi$
$643$	−23.3860	−0.922252	−0.461126	+	0.887335i	$0.652554\pi$
$644$	85.4530	3.36732
$645$	−1.59194	−0.0626824
$646$	4.22681	0.166301
$647$	40.1384	1.57800	0.789002	−	0.614391i	$-0.210598\pi$
$647$	40.1384	1.57800	0.789002	+	0.614391i	$0.210598\pi$
$648$	14.3084	0.562085
$649$	−7.36311	−0.289028
$650$	−5.80050	−0.227514
$651$	31.6819	1.24171
$652$	27.7297	1.08598
$653$	6.33149	0.247771	0.123885	−	0.992297i	$-0.460465\pi$
$653$	6.33149	0.247771	0.123885	+	0.992297i	$0.460465\pi$
$654$	−44.4421	−1.73782
$655$	−8.01713	−0.313255
$656$	3.92039	0.153065
$657$	5.81999	0.227059
$658$	−67.7191	−2.63997
$659$	−16.8519	−0.656457	−0.328229	−	0.944598i	$-0.606452\pi$
$659$	−16.8519	−0.656457	−0.328229	+	0.944598i	$0.606452\pi$
$660$	5.87086	0.228523
$661$	11.9880	0.466278	0.233139	−	0.972443i	$-0.425100\pi$
$661$	11.9880	0.466278	0.233139	+	0.972443i	$0.425100\pi$
$662$	17.4545	0.678389
$663$	−0.904740	−0.0351372
$664$	27.1815	1.05485
$665$	−9.49874	−0.368345
$666$	−10.7236	−0.415532
$667$	−13.5584	−0.524982
$668$	19.7548	0.764335
$669$	8.37116	0.323648
$670$	5.59287	0.216071
$671$	6.67715	0.257769
$672$	15.9516	0.615347
$673$	−22.7707	−0.877745	−0.438872	−	0.898549i	$-0.644622\pi$
$673$	−22.7707	−0.877745	−0.438872	+	0.898549i	$0.644622\pi$
$674$	26.2174	1.00986
$675$	−19.8303	−0.763270
$676$	−46.1933	−1.77667
$677$	23.5727	0.905972	0.452986	−	0.891518i	$-0.350359\pi$
$677$	23.5727	0.905972	0.452986	+	0.891518i	$0.350359\pi$
$678$	−9.36367	−0.359610
$679$	39.4413	1.51362
$680$	4.87787	0.187058
$681$	−10.7905	−0.413494
$682$	13.0036	0.497932
$683$	20.2229	0.773809	0.386905	−	0.922120i	$-0.373544\pi$
$683$	20.2229	0.773809	0.386905	+	0.922120i	$0.373544\pi$
$684$	−8.32742	−0.318407
$685$	0.205017	0.00783328
$686$	58.6766	2.24028
$687$	19.4394	0.741660
$688$	2.22466	0.0848145
$689$	2.93345	0.111755
$690$	−19.8902	−0.757206
$691$	25.9115	0.985718	0.492859	−	0.870109i	$-0.335952\pi$
$691$	25.9115	0.985718	0.492859	+	0.870109i	$0.335952\pi$
$692$	23.2865	0.885220
$693$	−5.63521	−0.214064
$694$	79.3464	3.01195
$695$	19.9642	0.757284
$696$	13.6866	0.518787
$697$	−1.76224	−0.0667495
$698$	−10.7766	−0.407902
$699$	15.9919	0.604867
$700$	57.6058	2.17729
$701$	−30.0787	−1.13606	−0.568029	−	0.823008i	$-0.692294\pi$
$701$	−30.0787	−1.13606	−0.568029	+	0.823008i	$0.692294\pi$
$702$	9.22235	0.348075
$703$	−6.25470	−0.235900
$704$	10.9965	0.414448
$705$	10.2200	0.384906
$706$	9.97948	0.375583
$707$	39.5652	1.48800
$708$	−35.6737	−1.34070
$709$	2.72612	0.102382	0.0511908	−	0.998689i	$-0.483698\pi$
$709$	2.72612	0.102382	0.0511908	+	0.998689i	$0.483698\pi$
$710$	43.2807	1.62430
$711$	−1.45862	−0.0547024
$712$	32.2363	1.20811
$713$	−28.5644	−1.06975
$714$	13.8579	0.518620
$715$	0.834506	0.0312087
$716$	48.6885	1.81958
$717$	−13.0804	−0.488497
$718$	−2.58110	−0.0963259
$719$	18.5197	0.690669	0.345334	−	0.938480i	$-0.387766\pi$
$719$	18.5197	0.690669	0.345334	+	0.938480i	$0.387766\pi$
$720$	−3.43461	−0.128000
$721$	65.3496	2.43375
$722$	37.8224	1.40761
$723$	26.6096	0.989622
$724$	14.5810	0.541898
$725$	−9.14000	−0.339451
$726$	3.13318	0.116283
$727$	−3.28156	−0.121706	−0.0608531	−	0.998147i	$-0.519382\pi$
$727$	−3.28156	−0.121706	−0.0608531	+	0.998147i	$0.519382\pi$
$728$	−12.2614	−0.454439
$729$	26.6588	0.987364
$730$	13.2013	0.488601
$731$	−1.00000	−0.0369863
$732$	32.3502	1.19570
$733$	33.5009	1.23738	0.618692	−	0.785634i	$-0.287663\pi$
$733$	33.5009	1.23738	0.618692	+	0.785634i	$0.287663\pi$
$734$	−41.7460	−1.54087
$735$	−19.9988	−0.737668
$736$	−14.3820	−0.530128
$737$	1.93528	0.0712870
$738$	5.35472	0.197110
$739$	−43.8162	−1.61181	−0.805903	−	0.592048i	$-0.798320\pi$
$739$	−43.8162	−1.61181	−0.805903	+	0.592048i	$0.798320\pi$
$740$	−15.7711	−0.579755
$741$	1.60347	0.0589050
$742$	−44.9317	−1.64949
$743$	26.4791	0.971424	0.485712	−	0.874119i	$-0.338560\pi$
$743$	26.4791	0.971424	0.485712	+	0.874119i	$0.338560\pi$
$744$	28.8345	1.05712
$745$	−3.62670	−0.132872
$746$	66.0172	2.41706
$747$	8.60313	0.314772
$748$	3.68787	0.134842
$749$	37.8479	1.38293
$750$	−32.3917	−1.18278
$751$	11.1688	0.407554	0.203777	−	0.979017i	$-0.434678\pi$
$751$	11.1688	0.407554	0.203777	+	0.979017i	$0.434678\pi$
$752$	−14.2820	−0.520810
$753$	−14.8418	−0.540864
$754$	4.25067	0.154800
$755$	3.56719	0.129823
$756$	−91.5887	−3.33105
$757$	16.5179	0.600352	0.300176	−	0.953884i	$-0.402955\pi$
$757$	16.5179	0.600352	0.300176	+	0.953884i	$0.402955\pi$
$758$	84.3596	3.06408
$759$	−6.88253	−0.249820
$760$	−8.64506	−0.313589
$761$	38.8910	1.40980	0.704899	−	0.709308i	$-0.250992\pi$
$761$	38.8910	1.40980	0.704899	+	0.709308i	$0.250992\pi$
$762$	18.0294	0.653138
$763$	62.7369	2.27123
$764$	−26.8603	−0.971771
$765$	1.54388	0.0558190
$766$	31.0266	1.12104
$767$	−5.07078	−0.183095
$768$	36.0746	1.30173
$769$	23.6295	0.852103	0.426051	−	0.904699i	$-0.359904\pi$
$769$	23.6295	0.852103	0.426051	+	0.904699i	$0.359904\pi$
$770$	−12.7821	−0.460637
$771$	37.5044	1.35069
$772$	−19.1990	−0.690989
$773$	−15.5145	−0.558019	−0.279009	−	0.960288i	$-0.590006\pi$
$773$	−15.5145	−0.558019	−0.279009	+	0.960288i	$0.590006\pi$
$774$	3.03859	0.109220
$775$	−19.2559	−0.691693
$776$	35.8966	1.28861
$777$	−20.5065	−0.735668
$778$	−56.4708	−2.02457
$779$	3.12321	0.111901
$780$	4.04311	0.144766
$781$	14.9763	0.535893
$782$	−12.4943	−0.446796
$783$	14.5319	0.519327
$784$	27.9475	0.998126
$785$	−13.2027	−0.471224
$786$	−20.7295	−0.739396
$787$	−15.0220	−0.535475	−0.267737	−	0.963492i	$-0.586276\pi$
$787$	−15.0220	−0.535475	−0.267737	+	0.963492i	$0.586276\pi$
$788$	10.1849	0.362821
$789$	23.0972	0.822283
$790$	−3.30852	−0.117712
$791$	13.2183	0.469987
$792$	−5.12876	−0.182242
$793$	4.59838	0.163293
$794$	2.40504	0.0853515
$795$	6.78095	0.240495
$796$	29.9630	1.06201
$797$	−22.2147	−0.786885	−0.393443	−	0.919349i	$-0.628716\pi$
$797$	−22.2147	−0.786885	−0.393443	+	0.919349i	$0.628716\pi$
$798$	−24.5604	−0.869429
$799$	6.41983	0.227117
$800$	−9.69524	−0.342778
$801$	10.2030	0.360505
$802$	68.2428	2.40974
$803$	4.56799	0.161201
$804$	9.37627	0.330675
$805$	28.0780	0.989621
$806$	8.95521	0.315434
$807$	−4.42302	−0.155698
$808$	36.0094	1.26681
$809$	−54.0235	−1.89937	−0.949683	−	0.313213i	$-0.898595\pi$
$809$	−54.0235	−1.89937	−0.949683	+	0.313213i	$0.898595\pi$
$810$	10.2722	0.360930
$811$	25.4420	0.893389	0.446695	−	0.894687i	$-0.352601\pi$
$811$	25.4420	0.893389	0.446695	+	0.894687i	$0.352601\pi$
$812$	−42.2142	−1.48143
$813$	−9.31561	−0.326713
$814$	−8.41674	−0.295007
$815$	9.11140	0.319159
$816$	2.92264	0.102313
$817$	1.77230	0.0620049
$818$	−22.9625	−0.802866
$819$	−3.88082	−0.135607
$820$	7.87510	0.275011
$821$	45.4279	1.58545	0.792723	−	0.609582i	$-0.208663\pi$
$821$	45.4279	1.58545	0.792723	+	0.609582i	$0.208663\pi$
$822$	0.530101	0.0184894
$823$	14.2983	0.498408	0.249204	−	0.968451i	$-0.419831\pi$
$823$	14.2983	0.498408	0.249204	+	0.968451i	$0.419831\pi$
$824$	59.4764	2.07196
$825$	−4.63967	−0.161533
$826$	77.6693	2.70246
$827$	−5.81655	−0.202261	−0.101131	−	0.994873i	$-0.532246\pi$
$827$	−5.81655	−0.202261	−0.101131	+	0.994873i	$0.532246\pi$
$828$	24.6157	0.855453
$829$	30.6413	1.06422	0.532109	−	0.846676i	$-0.321400\pi$
$829$	30.6413	1.06422	0.532109	+	0.846676i	$0.321400\pi$
$830$	19.5142	0.677346
$831$	−37.3153	−1.29445
$832$	7.57303	0.262548
$833$	−12.5626	−0.435268
$834$	51.6203	1.78746
$835$	6.49100	0.224630
$836$	−6.53602	−0.226053
$837$	30.6154	1.05822
$838$	55.3260	1.91120
$839$	36.0085	1.24315	0.621575	−	0.783354i	$-0.286493\pi$
$839$	36.0085	1.24315	0.621575	+	0.783354i	$0.286493\pi$
$840$	−28.3435	−0.977944
$841$	−22.3021	−0.769038
$842$	66.5158	2.29229
$843$	−10.3443	−0.356276
$844$	−29.1445	−1.00319
$845$	−15.1781	−0.522144
$846$	−19.5072	−0.670673
$847$	−4.42296	−0.151975
$848$	−9.47609	−0.325410
$849$	−37.5941	−1.29023
$850$	−8.42271	−0.288897
$851$	18.4887	0.633785
$852$	72.5588	2.48582
$853$	−32.7469	−1.12123	−0.560616	−	0.828076i	$-0.689436\pi$
$853$	−32.7469	−1.12123	−0.560616	+	0.828076i	$0.689436\pi$
$854$	−70.4335	−2.41019
$855$	−2.73622	−0.0935766
$856$	34.4464	1.17735
$857$	42.7402	1.45998	0.729989	−	0.683458i	$-0.239525\pi$
$857$	42.7402	1.45998	0.729989	+	0.683458i	$0.239525\pi$
$858$	2.15774	0.0736639
$859$	10.6913	0.364781	0.182391	−	0.983226i	$-0.441616\pi$
$859$	10.6913	0.364781	0.182391	+	0.983226i	$0.441616\pi$
$860$	4.46881	0.152385
$861$	10.2397	0.348968
$862$	−20.0655	−0.683434
$863$	−33.0347	−1.12451	−0.562257	−	0.826963i	$-0.690067\pi$
$863$	−33.0347	−1.12451	−0.562257	+	0.826963i	$0.690067\pi$
$864$	15.4147	0.524418
$865$	7.65146	0.260157
$866$	57.4230	1.95131
$867$	−1.31374	−0.0446170
$868$	−88.9358	−3.01868
$869$	−1.14484	−0.0388359
$870$	9.82584	0.333127
$871$	1.33278	0.0451594
$872$	57.0985	1.93360
$873$	11.3615	0.384528
$874$	22.1437	0.749022
$875$	45.7258	1.54581
$876$	22.1315	0.747754
$877$	2.36857	0.0799810	0.0399905	−	0.999200i	$-0.487267\pi$
$877$	2.36857	0.0799810	0.0399905	+	0.999200i	$0.487267\pi$
$878$	−53.7927	−1.81542
$879$	−26.7327	−0.901673
$880$	−2.69575	−0.0908738
$881$	38.7361	1.30505	0.652526	−	0.757767i	$-0.273709\pi$
$881$	38.7361	1.30505	0.652526	+	0.757767i	$0.273709\pi$
$882$	38.1726	1.28534
$883$	−19.1039	−0.642896	−0.321448	−	0.946927i	$-0.604170\pi$
$883$	−19.1039	−0.642896	−0.321448	+	0.946927i	$0.604170\pi$
$884$	2.53974	0.0854208
$885$	−11.7216	−0.394018
$886$	−61.0858	−2.05222
$887$	7.72486	0.259375	0.129688	−	0.991555i	$-0.458603\pi$
$887$	7.72486	0.259375	0.129688	+	0.991555i	$0.458603\pi$
$888$	−18.6635	−0.626307
$889$	−25.4513	−0.853610
$890$	23.1431	0.775757
$891$	3.55447	0.119079
$892$	−23.4991	−0.786809
$893$	−11.3779	−0.380746
$894$	−9.37738	−0.313627
$895$	15.9980	0.534755
$896$	−91.7121	−3.06389
$897$	−4.73982	−0.158258
$898$	−52.8301	−1.76296
$899$	14.1110	0.470627
$900$	16.5940	0.553132
$901$	4.25956	0.141906
$902$	4.20281	0.139938
$903$	5.81063	0.193366
$904$	12.0303	0.400121
$905$	4.79100	0.159258
$906$	9.22350	0.306430
$907$	39.3876	1.30784	0.653922	−	0.756562i	$-0.273122\pi$
$907$	39.3876	1.30784	0.653922	+	0.756562i	$0.273122\pi$
$908$	30.2907	1.00523
$909$	11.3972	0.378021
$910$	−8.80273	−0.291808
$911$	−46.7024	−1.54732	−0.773660	−	0.633601i	$-0.781576\pi$
$911$	−46.7024	−1.54732	−0.773660	+	0.633601i	$0.781576\pi$
$912$	−5.17979	−0.171520
$913$	6.75242	0.223472
$914$	−1.52850	−0.0505582
$915$	10.6296	0.351404
$916$	−54.5694	−1.80302
$917$	29.2628	0.966344
$918$	13.3915	0.441984
$919$	−9.22209	−0.304209	−0.152104	−	0.988364i	$-0.548605\pi$
$919$	−9.22209	−0.304209	−0.152104	+	0.988364i	$0.548605\pi$
$920$	25.5546	0.842509
$921$	20.5062	0.675703
$922$	−83.5379	−2.75117
$923$	10.3138	0.339482
$924$	−21.4289	−0.704958
$925$	12.4637	0.409803
$926$	51.1075	1.67950
$927$	18.8247	0.618283
$928$	7.10478	0.233226
$929$	−28.8174	−0.945468	−0.472734	−	0.881205i	$-0.656733\pi$
$929$	−28.8174	−0.945468	−0.472734	+	0.881205i	$0.656733\pi$
$930$	20.7009	0.678808
$931$	22.2647	0.729695
$932$	−44.8916	−1.47047
$933$	−21.3721	−0.699690
$934$	89.8098	2.93867
$935$	1.21176	0.0396287
$936$	−3.53204	−0.115448
$937$	25.1213	0.820678	0.410339	−	0.911933i	$-0.365410\pi$
$937$	25.1213	0.820678	0.410339	+	0.911933i	$0.365410\pi$
$938$	−20.4142	−0.666547
$939$	16.4180	0.535781
$940$	−28.6890	−0.935731
$941$	38.2151	1.24578	0.622888	−	0.782311i	$-0.285959\pi$
$941$	38.2151	1.24578	0.622888	+	0.782311i	$0.285959\pi$
$942$	−34.1375	−1.11226
$943$	−9.23215	−0.300640
$944$	16.3805	0.533139
$945$	−30.0941	−0.978962
$946$	2.38493	0.0775406
$947$	26.1811	0.850772	0.425386	−	0.905012i	$-0.360138\pi$
$947$	26.1811	0.850772	0.425386	+	0.905012i	$0.360138\pi$
$948$	−5.54664	−0.180146
$949$	3.14585	0.102119
$950$	14.9276	0.484314
$951$	−35.1810	−1.14082
$952$	−17.8044	−0.577045
$953$	−18.9561	−0.614049	−0.307024	−	0.951702i	$-0.599333\pi$
$953$	−18.9561	−0.614049	−0.307024	+	0.951702i	$0.599333\pi$
$954$	−12.9431	−0.419047
$955$	−8.82572	−0.285594
$956$	36.7187	1.18757
$957$	3.40000	0.109906
$958$	−1.83732	−0.0593612
$959$	−0.748318	−0.0241645
$960$	17.5058	0.564997
$961$	−1.27137	−0.0410119
$962$	−5.79639	−0.186883
$963$	10.9025	0.351328
$964$	−74.6972	−2.40583
$965$	−6.30840	−0.203075
$966$	72.5999	2.33586
$967$	31.9624	1.02784	0.513921	−	0.857838i	$-0.328193\pi$
$967$	31.9624	1.02784	0.513921	+	0.857838i	$0.328193\pi$
$968$	−4.02545	−0.129383
$969$	2.32835	0.0747972
$970$	25.7708	0.827452
$971$	−0.364484	−0.0116968	−0.00584842	−	0.999983i	$-0.501862\pi$
$971$	−0.364484	−0.0116968	−0.00584842	+	0.999983i	$0.501862\pi$
$972$	−44.9016	−1.44022
$973$	−72.8700	−2.33610
$974$	4.34204	0.139128
$975$	−3.19522	−0.102329
$976$	−14.8544	−0.475479
$977$	11.8101	0.377839	0.188919	−	0.981993i	$-0.439502\pi$
$977$	11.8101	0.377839	0.188919	+	0.981993i	$0.439502\pi$
$978$	23.5589	0.753330
$979$	8.00812	0.255940
$980$	56.1398	1.79332
$981$	18.0720	0.576996
$982$	−57.2840	−1.82801
$983$	−19.0193	−0.606620	−0.303310	−	0.952892i	$-0.598092\pi$
$983$	−19.0193	−0.606620	−0.303310	+	0.952892i	$0.598092\pi$
$984$	9.31943	0.297093
$985$	3.34653	0.106629
$986$	6.17226	0.196565
$987$	−37.3032	−1.18738
$988$	−4.50118	−0.143202
$989$	−5.23888	−0.166587
$990$	−3.68204	−0.117023
$991$	52.3015	1.66141	0.830705	−	0.556713i	$-0.187938\pi$
$991$	52.3015	1.66141	0.830705	+	0.556713i	$0.187938\pi$
$992$	14.9682	0.475240
$993$	9.61485	0.305118
$994$	−157.976	−5.01070
$995$	9.84520	0.312114
$996$	32.7149	1.03661
$997$	−3.80083	−0.120373	−0.0601867	−	0.998187i	$-0.519170\pi$
$997$	−3.80083	−0.120373	−0.0601867	+	0.998187i	$0.519170\pi$
$998$	−8.06230	−0.255208
$999$	−19.8163	−0.626959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.8	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.8	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38493 q^{2} -1.31374 q^{3} +3.68787 q^{4} +1.21176 q^{5} +3.13318 q^{6} -4.42296 q^{7} -4.02545 q^{8} -1.27408 q^{9} +O(q^{10})\)	\(q-2.38493 q^{2} -1.31374 q^{3} +3.68787 q^{4} +1.21176 q^{5} +3.13318 q^{6} -4.42296 q^{7} -4.02545 q^{8} -1.27408 q^{9} -2.88995 q^{10} -1.00000 q^{11} -4.84491 q^{12} -0.688674 q^{13} +10.5484 q^{14} -1.59194 q^{15} +2.22466 q^{16} -1.00000 q^{17} +3.03859 q^{18} +1.77230 q^{19} +4.46881 q^{20} +5.81063 q^{21} +2.38493 q^{22} -5.23888 q^{23} +5.28841 q^{24} -3.53164 q^{25} +1.64244 q^{26} +5.61504 q^{27} -16.3113 q^{28} +2.58803 q^{29} +3.79665 q^{30} +5.45240 q^{31} +2.74525 q^{32} +1.31374 q^{33} +2.38493 q^{34} -5.35956 q^{35} -4.69865 q^{36} -3.52914 q^{37} -4.22681 q^{38} +0.904740 q^{39} -4.87787 q^{40} +1.76224 q^{41} -13.8579 q^{42} +1.00000 q^{43} -3.68787 q^{44} -1.54388 q^{45} +12.4943 q^{46} -6.41983 q^{47} -2.92264 q^{48} +12.5626 q^{49} +8.42271 q^{50} +1.31374 q^{51} -2.53974 q^{52} -4.25956 q^{53} -13.3915 q^{54} -1.21176 q^{55} +17.8044 q^{56} -2.32835 q^{57} -6.17226 q^{58} +7.36311 q^{59} -5.87086 q^{60} -6.67715 q^{61} -13.0036 q^{62} +5.63521 q^{63} -10.9965 q^{64} -0.834506 q^{65} -3.13318 q^{66} -1.93528 q^{67} -3.68787 q^{68} +6.88253 q^{69} +12.7821 q^{70} -14.9763 q^{71} +5.12876 q^{72} -4.56799 q^{73} +8.41674 q^{74} +4.63967 q^{75} +6.53602 q^{76} +4.42296 q^{77} -2.15774 q^{78} +1.14484 q^{79} +2.69575 q^{80} -3.55447 q^{81} -4.20281 q^{82} -6.75242 q^{83} +21.4289 q^{84} -1.21176 q^{85} -2.38493 q^{86} -3.40000 q^{87} +4.02545 q^{88} -8.00812 q^{89} +3.68204 q^{90} +3.04598 q^{91} -19.3203 q^{92} -7.16304 q^{93} +15.3108 q^{94} +2.14760 q^{95} -3.60655 q^{96} -8.91740 q^{97} -29.9608 q^{98} +1.27408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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