LMFDB - Embedded newform 6023.2.a.c.1.86

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.86
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.811992 q^{2} +3.22771 q^{3} -1.34067 q^{4} -2.81140 q^{5} +2.62087 q^{6} -4.27963 q^{7} -2.71260 q^{8} +7.41810 q^{9} +O(q^{10})$	\(q+0.811992 q^{2} +3.22771 q^{3} -1.34067 q^{4} -2.81140 q^{5} +2.62087 q^{6} -4.27963 q^{7} -2.71260 q^{8} +7.41810 q^{9} -2.28283 q^{10} -3.91556 q^{11} -4.32729 q^{12} -4.55539 q^{13} -3.47502 q^{14} -9.07437 q^{15} +0.478731 q^{16} +5.72659 q^{17} +6.02344 q^{18} +1.00000 q^{19} +3.76915 q^{20} -13.8134 q^{21} -3.17940 q^{22} -7.01916 q^{23} -8.75547 q^{24} +2.90395 q^{25} -3.69894 q^{26} +14.2604 q^{27} +5.73756 q^{28} +6.70478 q^{29} -7.36831 q^{30} +2.60386 q^{31} +5.81392 q^{32} -12.6383 q^{33} +4.64994 q^{34} +12.0317 q^{35} -9.94522 q^{36} +7.92001 q^{37} +0.811992 q^{38} -14.7035 q^{39} +7.62618 q^{40} +3.56601 q^{41} -11.2164 q^{42} +3.55971 q^{43} +5.24946 q^{44} -20.8552 q^{45} -5.69950 q^{46} -7.98600 q^{47} +1.54520 q^{48} +11.3152 q^{49} +2.35798 q^{50} +18.4838 q^{51} +6.10727 q^{52} -6.44818 q^{53} +11.5793 q^{54} +11.0082 q^{55} +11.6089 q^{56} +3.22771 q^{57} +5.44422 q^{58} +8.87898 q^{59} +12.1657 q^{60} +13.4817 q^{61} +2.11431 q^{62} -31.7467 q^{63} +3.76339 q^{64} +12.8070 q^{65} -10.2622 q^{66} +12.6642 q^{67} -7.67746 q^{68} -22.6558 q^{69} +9.76966 q^{70} -15.7320 q^{71} -20.1223 q^{72} -4.41548 q^{73} +6.43098 q^{74} +9.37309 q^{75} -1.34067 q^{76} +16.7571 q^{77} -11.9391 q^{78} +1.14591 q^{79} -1.34590 q^{80} +23.7740 q^{81} +2.89557 q^{82} +3.10748 q^{83} +18.5192 q^{84} -16.0997 q^{85} +2.89045 q^{86} +21.6411 q^{87} +10.6213 q^{88} -10.5136 q^{89} -16.9343 q^{90} +19.4954 q^{91} +9.41036 q^{92} +8.40449 q^{93} -6.48457 q^{94} -2.81140 q^{95} +18.7656 q^{96} +0.00340543 q^{97} +9.18785 q^{98} -29.0460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	0.811992	0.574165	0.287083	−	0.957906i	$-0.407315\pi$
$2$	0.811992	0.574165	0.287083	+	0.957906i	$0.407315\pi$
$3$	3.22771	1.86352	0.931759	−	0.363077i	$-0.118274\pi$
$3$	3.22771	1.86352	0.931759	+	0.363077i	$0.118274\pi$
$4$	−1.34067	−0.670334
$5$	−2.81140	−1.25729	−0.628647	−	0.777691i	$-0.716391\pi$
$5$	−2.81140	−1.25729	−0.628647	+	0.777691i	$0.716391\pi$
$6$	2.62087	1.06997
$7$	−4.27963	−1.61755	−0.808773	−	0.588121i	$-0.799868\pi$
$7$	−4.27963	−1.61755	−0.808773	+	0.588121i	$0.799868\pi$
$8$	−2.71260	−0.959048
$9$	7.41810	2.47270
$10$	−2.28283	−0.721895
$11$	−3.91556	−1.18058	−0.590292	−	0.807190i	$-0.700987\pi$
$11$	−3.91556	−1.18058	−0.590292	+	0.807190i	$0.700987\pi$
$12$	−4.32729	−1.24918
$13$	−4.55539	−1.26344	−0.631719	−	0.775198i	$-0.717650\pi$
$13$	−4.55539	−1.26344	−0.631719	+	0.775198i	$0.717650\pi$
$14$	−3.47502	−0.928739
$15$	−9.07437	−2.34299
$16$	0.478731	0.119683
$17$	5.72659	1.38890	0.694451	−	0.719540i	$-0.255647\pi$
$17$	5.72659	1.38890	0.694451	+	0.719540i	$0.255647\pi$
$18$	6.02344	1.41974
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.76915	0.842808
$21$	−13.8134	−3.01433
$22$	−3.17940	−0.677850
$23$	−7.01916	−1.46360	−0.731798	−	0.681522i	$-0.761318\pi$
$23$	−7.01916	−1.46360	−0.731798	+	0.681522i	$0.761318\pi$
$24$	−8.75547	−1.78720
$25$	2.90395	0.580789
$26$	−3.69894	−0.725422
$27$	14.2604	2.74441
$28$	5.73756	1.08430
$29$	6.70478	1.24505	0.622523	−	0.782602i	$-0.286108\pi$
$29$	6.70478	1.24505	0.622523	+	0.782602i	$0.286108\pi$
$30$	−7.36831	−1.34526
$31$	2.60386	0.467666	0.233833	−	0.972277i	$-0.424873\pi$
$31$	2.60386	0.467666	0.233833	+	0.972277i	$0.424873\pi$
$32$	5.81392	1.02777
$33$	−12.6383	−2.20004
$34$	4.64994	0.797459
$35$	12.0317	2.03373
$36$	−9.94522	−1.65754
$37$	7.92001	1.30204	0.651021	−	0.759060i	$-0.274341\pi$
$37$	7.92001	1.30204	0.651021	+	0.759060i	$0.274341\pi$
$38$	0.811992	0.131723
$39$	−14.7035	−2.35444
$40$	7.62618	1.20581
$41$	3.56601	0.556918	0.278459	−	0.960448i	$-0.410176\pi$
$41$	3.56601	0.556918	0.278459	+	0.960448i	$0.410176\pi$
$42$	−11.2164	−1.73072
$43$	3.55971	0.542850	0.271425	−	0.962460i	$-0.412505\pi$
$43$	3.55971	0.542850	0.271425	+	0.962460i	$0.412505\pi$
$44$	5.24946	0.791386
$45$	−20.8552	−3.10891
$46$	−5.69950	−0.840345
$47$	−7.98600	−1.16488	−0.582439	−	0.812874i	$-0.697902\pi$
$47$	−7.98600	−1.16488	−0.582439	+	0.812874i	$0.697902\pi$
$48$	1.54520	0.223031
$49$	11.3152	1.61646
$50$	2.35798	0.333469
$51$	18.4838	2.58824
$52$	6.10727	0.846926
$53$	−6.44818	−0.885726	−0.442863	−	0.896589i	$-0.646037\pi$
$53$	−6.44818	−0.885726	−0.442863	+	0.896589i	$0.646037\pi$
$54$	11.5793	1.57574
$55$	11.0082	1.48434
$56$	11.6089	1.55130
$57$	3.22771	0.427520
$58$	5.44422	0.714862
$59$	8.87898	1.15594	0.577972	−	0.816056i	$-0.303844\pi$
$59$	8.87898	1.15594	0.577972	+	0.816056i	$0.303844\pi$
$60$	12.1657	1.57059
$61$	13.4817	1.72616	0.863080	−	0.505068i	$-0.168533\pi$
$61$	13.4817	1.72616	0.863080	+	0.505068i	$0.168533\pi$
$62$	2.11431	0.268518
$63$	−31.7467	−3.99971
$64$	3.76339	0.470424
$65$	12.8070	1.58851
$66$	−10.2622	−1.26319
$67$	12.6642	1.54718	0.773588	−	0.633689i	$-0.218460\pi$
$67$	12.6642	1.54718	0.773588	+	0.633689i	$0.218460\pi$
$68$	−7.67746	−0.931028
$69$	−22.6558	−2.72744
$70$	9.76966	1.16770
$71$	−15.7320	−1.86704	−0.933521	−	0.358522i	$-0.883281\pi$
$71$	−15.7320	−1.86704	−0.933521	+	0.358522i	$0.883281\pi$
$72$	−20.1223	−2.37144
$73$	−4.41548	−0.516793	−0.258397	−	0.966039i	$-0.583194\pi$
$73$	−4.41548	−0.516793	−0.258397	+	0.966039i	$0.583194\pi$
$74$	6.43098	0.747587
$75$	9.37309	1.08231
$76$	−1.34067	−0.153785
$77$	16.7571	1.90965
$78$	−11.9391	−1.35184
$79$	1.14591	0.128925	0.0644624	−	0.997920i	$-0.479467\pi$
$79$	1.14591	0.128925	0.0644624	+	0.997920i	$0.479467\pi$
$80$	−1.34590	−0.150476
$81$	23.7740	2.64155
$82$	2.89557	0.319763
$83$	3.10748	0.341090	0.170545	−	0.985350i	$-0.445447\pi$
$83$	3.10748	0.341090	0.170545	+	0.985350i	$0.445447\pi$
$84$	18.5192	2.02061
$85$	−16.0997	−1.74626
$86$	2.89045	0.311686
$87$	21.6411	2.32017
$88$	10.6213	1.13224
$89$	−10.5136	−1.11443	−0.557217	−	0.830367i	$-0.688131\pi$
$89$	−10.5136	−1.11443	−0.557217	+	0.830367i	$0.688131\pi$
$90$	−16.9343	−1.78503
$91$	19.4954	2.04367
$92$	9.41036	0.981098
$93$	8.40449	0.871505
$94$	−6.48457	−0.668832
$95$	−2.81140	−0.288443
$96$	18.7656	1.91526
$97$	0.00340543	0.000345770 0	0.000172885	−	1.00000i	$-0.499945\pi$
$97$	0.00340543	0.000345770 0	0.000172885		1.00000i	$0.499945\pi$
$98$	9.18785	0.928113
$99$	−29.0460	−2.91923
$100$	−3.89323	−0.389323
$101$	9.74041	0.969207	0.484604	−	0.874734i	$-0.338964\pi$
$101$	9.74041	0.969207	0.484604	+	0.874734i	$0.338964\pi$
$102$	15.0087	1.48608
$103$	−6.40849	−0.631448	−0.315724	−	0.948851i	$-0.602247\pi$
$103$	−6.40849	−0.631448	−0.315724	+	0.948851i	$0.602247\pi$
$104$	12.3569	1.21170
$105$	38.8349	3.78990
$106$	−5.23587	−0.508553
$107$	−9.16965	−0.886463	−0.443232	−	0.896407i	$-0.646168\pi$
$107$	−9.16965	−0.886463	−0.443232	+	0.896407i	$0.646168\pi$
$108$	−19.1184	−1.83967
$109$	−1.51047	−0.144677	−0.0723384	−	0.997380i	$-0.523046\pi$
$109$	−1.51047	−0.144677	−0.0723384	+	0.997380i	$0.523046\pi$
$110$	8.93855	0.852257
$111$	25.5635	2.42638
$112$	−2.04879	−0.193592
$113$	13.5480	1.27449	0.637244	−	0.770662i	$-0.280074\pi$
$113$	13.5480	1.27449	0.637244	+	0.770662i	$0.280074\pi$
$114$	2.62087	0.245467
$115$	19.7336	1.84017
$116$	−8.98888	−0.834597
$117$	−33.7924	−3.12410
$118$	7.20966	0.663703
$119$	−24.5076	−2.24661
$120$	24.6151	2.24704
$121$	4.33157	0.393779
$122$	10.9471	0.991100
$123$	11.5101	1.03783
$124$	−3.49091	−0.313493
$125$	5.89284	0.527071
$126$	−25.7781	−2.29649
$127$	10.8981	0.967049	0.483524	−	0.875331i	$-0.339356\pi$
$127$	10.8981	0.967049	0.483524	+	0.875331i	$0.339356\pi$
$128$	−8.57199	−0.757664
$129$	11.4897	1.01161
$130$	10.3992	0.912069
$131$	2.86764	0.250547	0.125273	−	0.992122i	$-0.460019\pi$
$131$	2.86764	0.250547	0.125273	+	0.992122i	$0.460019\pi$
$132$	16.9437	1.47476
$133$	−4.27963	−0.371091
$134$	10.2832	0.888335
$135$	−40.0915	−3.45053
$136$	−15.5339	−1.33202
$137$	−11.2449	−0.960718	−0.480359	−	0.877072i	$-0.659494\pi$
$137$	−11.2449	−0.960718	−0.480359	+	0.877072i	$0.659494\pi$
$138$	−18.3963	−1.56600
$139$	9.29335	0.788252	0.394126	−	0.919056i	$-0.371047\pi$
$139$	9.29335	0.788252	0.394126	+	0.919056i	$0.371047\pi$
$140$	−16.1306	−1.36328
$141$	−25.7765	−2.17077
$142$	−12.7742	−1.07199
$143$	17.8369	1.49159
$144$	3.55127	0.295940
$145$	−18.8498	−1.56539
$146$	−3.58534	−0.296725
$147$	36.5221	3.01230
$148$	−10.6181	−0.872803
$149$	−12.4579	−1.02059	−0.510294	−	0.860000i	$-0.670463\pi$
$149$	−12.4579	−1.02059	−0.510294	+	0.860000i	$0.670463\pi$
$150$	7.61088	0.621425
$151$	−4.31054	−0.350786	−0.175393	−	0.984498i	$-0.556120\pi$
$151$	−4.31054	−0.350786	−0.175393	+	0.984498i	$0.556120\pi$
$152$	−2.71260	−0.220021
$153$	42.4804	3.43434
$154$	13.6066	1.09645
$155$	−7.32047	−0.587994
$156$	19.7125	1.57826
$157$	6.35378	0.507087	0.253543	−	0.967324i	$-0.418404\pi$
$157$	6.35378	0.507087	0.253543	+	0.967324i	$0.418404\pi$
$158$	0.930468	0.0740241
$159$	−20.8128	−1.65057
$160$	−16.3452	−1.29220
$161$	30.0394	2.36743
$162$	19.3043	1.51669
$163$	−17.9526	−1.40616	−0.703078	−	0.711113i	$-0.748192\pi$
$163$	−17.9526	−1.40616	−0.703078	+	0.711113i	$0.748192\pi$
$164$	−4.78084	−0.373321
$165$	35.5312	2.76610
$166$	2.52325	0.195842
$167$	19.6339	1.51932	0.759660	−	0.650321i	$-0.225366\pi$
$167$	19.6339	1.51932	0.759660	+	0.650321i	$0.225366\pi$
$168$	37.4701	2.89088
$169$	7.75157	0.596275
$170$	−13.0728	−1.00264
$171$	7.41810	0.567277
$172$	−4.77239	−0.363891
$173$	11.5757	0.880087	0.440044	−	0.897976i	$-0.354963\pi$
$173$	11.5757	0.880087	0.440044	+	0.897976i	$0.354963\pi$
$174$	17.5724	1.33216
$175$	−12.4278	−0.939453
$176$	−1.87450	−0.141296
$177$	28.6588	2.15412
$178$	−8.53692	−0.639870
$179$	1.86730	0.139568	0.0697841	−	0.997562i	$-0.477769\pi$
$179$	1.86730	0.139568	0.0697841	+	0.997562i	$0.477769\pi$
$180$	27.9600	2.08401
$181$	−16.0962	−1.19642	−0.598209	−	0.801340i	$-0.704121\pi$
$181$	−16.0962	−1.19642	−0.598209	+	0.801340i	$0.704121\pi$
$182$	15.8301	1.17340
$183$	43.5151	3.21673
$184$	19.0401	1.40366
$185$	−22.2663	−1.63705
$186$	6.82438	0.500388
$187$	−22.4228	−1.63972
$188$	10.7066	0.780858
$189$	−61.0290	−4.43920
$190$	−2.28283	−0.165614
$191$	7.76912	0.562154	0.281077	−	0.959685i	$-0.409308\pi$
$191$	7.76912	0.562154	0.281077	+	0.959685i	$0.409308\pi$
$192$	12.1471	0.876644
$193$	−9.29246	−0.668886	−0.334443	−	0.942416i	$-0.608548\pi$
$193$	−9.29246	−0.668886	−0.334443	+	0.942416i	$0.608548\pi$
$194$	0.00276519	0.000198529 0
$195$	41.3373	2.96022
$196$	−15.1699	−1.08357
$197$	6.52293	0.464740	0.232370	−	0.972628i	$-0.425352\pi$
$197$	6.52293	0.464740	0.232370	+	0.972628i	$0.425352\pi$
$198$	−23.5851	−1.67612
$199$	−9.06205	−0.642392	−0.321196	−	0.947013i	$-0.604085\pi$
$199$	−9.06205	−0.642392	−0.321196	+	0.947013i	$0.604085\pi$
$200$	−7.87723	−0.557005
$201$	40.8763	2.88319
$202$	7.90914	0.556485
$203$	−28.6939	−2.01392
$204$	−24.7806	−1.73499
$205$	−10.0255	−0.700210
$206$	−5.20365	−0.362555
$207$	−52.0688	−3.61903
$208$	−2.18081	−0.151212
$209$	−3.91556	−0.270845
$210$	31.5336	2.17603
$211$	8.04146	0.553597	0.276798	−	0.960928i	$-0.410727\pi$
$211$	8.04146	0.553597	0.276798	+	0.960928i	$0.410727\pi$
$212$	8.64487	0.593732
$213$	−50.7783	−3.47927
$214$	−7.44568	−0.508976
$215$	−10.0077	−0.682523
$216$	−38.6826	−2.63202
$217$	−11.1435	−0.756472
$218$	−1.22649	−0.0830684
$219$	−14.2519	−0.963054
$220$	−14.7583	−0.995006
$221$	−26.0868	−1.75479
$222$	20.7573	1.39314
$223$	22.6010	1.51347	0.756737	−	0.653720i	$-0.226792\pi$
$223$	22.6010	1.51347	0.756737	+	0.653720i	$0.226792\pi$
$224$	−24.8814	−1.66246
$225$	21.5418	1.43612
$226$	11.0009	0.731767
$227$	2.65361	0.176127	0.0880633	−	0.996115i	$-0.471932\pi$
$227$	2.65361	0.176127	0.0880633	+	0.996115i	$0.471932\pi$
$228$	−4.32729	−0.286582
$229$	−8.80009	−0.581526	−0.290763	−	0.956795i	$-0.593909\pi$
$229$	−8.80009	−0.581526	−0.290763	+	0.956795i	$0.593909\pi$
$230$	16.0235	1.05656
$231$	54.0871	3.55867
$232$	−18.1874	−1.19406
$233$	20.9206	1.37055	0.685277	−	0.728283i	$-0.259681\pi$
$233$	20.9206	1.37055	0.685277	+	0.728283i	$0.259681\pi$
$234$	−27.4391	−1.79375
$235$	22.4518	1.46459
$236$	−11.9038	−0.774869
$237$	3.69866	0.240254
$238$	−19.9000	−1.28993
$239$	−11.9487	−0.772894	−0.386447	−	0.922312i	$-0.626298\pi$
$239$	−11.9487	−0.772894	−0.386447	+	0.922312i	$0.626298\pi$
$240$	−4.34418	−0.280416
$241$	−21.9124	−1.41150	−0.705752	−	0.708459i	$-0.749391\pi$
$241$	−21.9124	−1.41150	−0.705752	+	0.708459i	$0.749391\pi$
$242$	3.51720	0.226094
$243$	33.9544	2.17817
$244$	−18.0745	−1.15710
$245$	−31.8115	−2.03236
$246$	9.34607	0.595884
$247$	−4.55539	−0.289852
$248$	−7.06321	−0.448514
$249$	10.0300	0.635627
$250$	4.78494	0.302626
$251$	−2.38296	−0.150411	−0.0752055	−	0.997168i	$-0.523961\pi$
$251$	−2.38296	−0.150411	−0.0752055	+	0.997168i	$0.523961\pi$
$252$	42.5618	2.68114
$253$	27.4839	1.72790
$254$	8.84916	0.555246
$255$	−51.9652	−3.25418
$256$	−14.4872	−0.905449
$257$	−24.8042	−1.54724	−0.773622	−	0.633648i	$-0.781557\pi$
$257$	−24.8042	−1.54724	−0.773622	+	0.633648i	$0.781557\pi$
$258$	9.32955	0.580832
$259$	−33.8947	−2.10611
$260$	−17.1699	−1.06484
$261$	49.7367	3.07863
$262$	2.32850	0.143855
$263$	−2.95993	−0.182517	−0.0912584	−	0.995827i	$-0.529089\pi$
$263$	−2.95993	−0.182517	−0.0912584	+	0.995827i	$0.529089\pi$
$264$	34.2825	2.10994
$265$	18.1284	1.11362
$266$	−3.47502	−0.213067
$267$	−33.9347	−2.07677
$268$	−16.9785	−1.03713
$269$	28.9916	1.76765	0.883826	−	0.467817i	$-0.154959\pi$
$269$	28.9916	1.76765	0.883826	+	0.467817i	$0.154959\pi$
$270$	−32.5540	−1.98117
$271$	10.7558	0.653367	0.326684	−	0.945134i	$-0.394069\pi$
$271$	10.7558	0.653367	0.326684	+	0.945134i	$0.394069\pi$
$272$	2.74149	0.166227
$273$	62.9253	3.80842
$274$	−9.13078	−0.551611
$275$	−11.3706	−0.685671
$276$	30.3739	1.82829
$277$	30.7814	1.84948	0.924738	−	0.380605i	$-0.124284\pi$
$277$	30.7814	1.84948	0.924738	+	0.380605i	$0.124284\pi$
$278$	7.54613	0.452587
$279$	19.3157	1.15640
$280$	−32.6372	−1.95045
$281$	23.4395	1.39829	0.699143	−	0.714982i	$-0.253565\pi$
$281$	23.4395	1.39829	0.699143	+	0.714982i	$0.253565\pi$
$282$	−20.9303	−1.24638
$283$	−15.9257	−0.946684	−0.473342	−	0.880879i	$-0.656953\pi$
$283$	−15.9257	−0.946684	−0.473342	+	0.880879i	$0.656953\pi$
$284$	21.0914	1.25154
$285$	−9.07437	−0.537519
$286$	14.4834	0.856422
$287$	−15.2612	−0.900840
$288$	43.1283	2.54136
$289$	15.7938	0.929047
$290$	−15.3059	−0.898792
$291$	0.0109918	0.000644348 0
$292$	5.91970	0.346424
$293$	23.7071	1.38498	0.692492	−	0.721425i	$-0.256513\pi$
$293$	23.7071	1.38498	0.692492	+	0.721425i	$0.256513\pi$
$294$	29.6557	1.72956
$295$	−24.9623	−1.45336
$296$	−21.4838	−1.24872
$297$	−55.8372	−3.24000
$298$	−10.1157	−0.585986
$299$	31.9750	1.84916
$300$	−12.5662	−0.725511
$301$	−15.2342	−0.878086
$302$	−3.50012	−0.201409
$303$	31.4392	1.80614
$304$	0.478731	0.0274571
$305$	−37.9025	−2.17029
$306$	34.4938	1.97188
$307$	16.5153	0.942576	0.471288	−	0.881979i	$-0.343789\pi$
$307$	16.5153	0.942576	0.471288	+	0.881979i	$0.343789\pi$
$308$	−22.4657	−1.28010
$309$	−20.6848	−1.17671
$310$	−5.94416	−0.337606
$311$	1.33070	0.0754571	0.0377286	−	0.999288i	$-0.487988\pi$
$311$	1.33070	0.0754571	0.0377286	+	0.999288i	$0.487988\pi$
$312$	39.8846	2.25802
$313$	−12.2360	−0.691622	−0.345811	−	0.938304i	$-0.612396\pi$
$313$	−12.2360	−0.691622	−0.345811	+	0.938304i	$0.612396\pi$
$314$	5.15922	0.291151
$315$	89.2526	5.02881
$316$	−1.53628	−0.0864227
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−16.8999	−0.947698
$319$	−26.2529	−1.46988
$320$	−10.5804	−0.591462
$321$	−29.5970	−1.65194
$322$	24.3917	1.35930
$323$	5.72659	0.318636
$324$	−31.8730	−1.77072
$325$	−13.2286	−0.733791
$326$	−14.5774	−0.807366
$327$	−4.87536	−0.269608
$328$	−9.67316	−0.534111
$329$	34.1771	1.88424
$330$	28.8510	1.58820
$331$	19.2749	1.05945	0.529723	−	0.848171i	$-0.322296\pi$
$331$	19.2749	1.05945	0.529723	+	0.848171i	$0.322296\pi$
$332$	−4.16610	−0.228644
$333$	58.7514	3.21956
$334$	15.9426	0.872340
$335$	−35.6040	−1.94526
$336$	−6.61289	−0.360763
$337$	−23.0524	−1.25574	−0.627871	−	0.778318i	$-0.716073\pi$
$337$	−23.0524	−1.25574	−0.627871	+	0.778318i	$0.716073\pi$
$338$	6.29422	0.342360
$339$	43.7290	2.37503
$340$	21.5844	1.17058
$341$	−10.1955	−0.552119
$342$	6.02344	0.325710
$343$	−18.4674	−0.997146
$344$	−9.65605	−0.520619
$345$	63.6944	3.42919
$346$	9.39941	0.505315
$347$	−3.98200	−0.213765	−0.106882	−	0.994272i	$-0.534087\pi$
$347$	−3.98200	−0.213765	−0.106882	+	0.994272i	$0.534087\pi$
$348$	−29.0135	−1.55529
$349$	15.0782	0.807118	0.403559	−	0.914954i	$-0.367773\pi$
$349$	15.0782	0.807118	0.403559	+	0.914954i	$0.367773\pi$
$350$	−10.0913	−0.539401
$351$	−64.9615	−3.46739
$352$	−22.7647	−1.21336
$353$	18.3997	0.979317	0.489658	−	0.871914i	$-0.337121\pi$
$353$	18.3997	0.979317	0.489658	+	0.871914i	$0.337121\pi$
$354$	23.2707	1.23682
$355$	44.2288	2.34742
$356$	14.0952	0.747044
$357$	−79.1036	−4.18660
$358$	1.51623	0.0801352
$359$	14.0984	0.744084	0.372042	−	0.928216i	$-0.378658\pi$
$359$	14.0984	0.744084	0.372042	+	0.928216i	$0.378658\pi$
$360$	56.5718	2.98160
$361$	1.00000	0.0526316
$362$	−13.0699	−0.686941
$363$	13.9811	0.733815
$364$	−26.1368	−1.36994
$365$	12.4137	0.649761
$366$	35.3339	1.84693
$367$	−10.3052	−0.537927	−0.268963	−	0.963150i	$-0.586681\pi$
$367$	−10.3052	−0.537927	−0.268963	+	0.963150i	$0.586681\pi$
$368$	−3.36029	−0.175167
$369$	26.4531	1.37709
$370$	−18.0800	−0.939936
$371$	27.5958	1.43270
$372$	−11.2676	−0.584200
$373$	21.4189	1.10903	0.554514	−	0.832174i	$-0.312904\pi$
$373$	21.4189	1.10903	0.554514	+	0.832174i	$0.312904\pi$
$374$	−18.2071	−0.941467
$375$	19.0204	0.982207
$376$	21.6628	1.11717
$377$	−30.5429	−1.57304
$378$	−49.5550	−2.54884
$379$	20.0975	1.03234	0.516169	−	0.856487i	$-0.327358\pi$
$379$	20.0975	1.03234	0.516169	+	0.856487i	$0.327358\pi$
$380$	3.76915	0.193353
$381$	35.1759	1.80211
$382$	6.30847	0.322769
$383$	−5.64071	−0.288227	−0.144113	−	0.989561i	$-0.546033\pi$
$383$	−5.64071	−0.288227	−0.144113	+	0.989561i	$0.546033\pi$
$384$	−27.6679	−1.41192
$385$	−47.1109	−2.40099
$386$	−7.54540	−0.384051
$387$	26.4063	1.34231
$388$	−0.00456556	−0.000231781 0
$389$	22.2411	1.12767	0.563834	−	0.825888i	$-0.309326\pi$
$389$	22.2411	1.12767	0.563834	+	0.825888i	$0.309326\pi$
$390$	33.5655	1.69966
$391$	−40.1958	−2.03279
$392$	−30.6936	−1.55026
$393$	9.25590	0.466899
$394$	5.29657	0.266837
$395$	−3.22160	−0.162096
$396$	38.9411	1.95686
$397$	13.3577	0.670404	0.335202	−	0.942146i	$-0.391195\pi$
$397$	13.3577	0.670404	0.335202	+	0.942146i	$0.391195\pi$
$398$	−7.35831	−0.368839
$399$	−13.8134	−0.691534
$400$	1.39021	0.0695104
$401$	20.5999	1.02871	0.514354	−	0.857578i	$-0.328032\pi$
$401$	20.5999	1.02871	0.514354	+	0.857578i	$0.328032\pi$
$402$	33.1912	1.65543
$403$	−11.8616	−0.590867
$404$	−13.0587	−0.649693
$405$	−66.8380	−3.32121
$406$	−23.2992	−1.15632
$407$	−31.0112	−1.53717
$408$	−50.1390	−2.48225
$409$	−24.6061	−1.21669	−0.608346	−	0.793672i	$-0.708167\pi$
$409$	−24.6061	−1.21669	−0.608346	+	0.793672i	$0.708167\pi$
$410$	−8.14061	−0.402036
$411$	−36.2953	−1.79032
$412$	8.59167	0.423281
$413$	−37.9987	−1.86979
$414$	−42.2795	−2.07792
$415$	−8.73635	−0.428850
$416$	−26.4847	−1.29852
$417$	29.9962	1.46892
$418$	−3.17940	−0.155510
$419$	18.4583	0.901747	0.450874	−	0.892588i	$-0.351113\pi$
$419$	18.4583	0.901747	0.450874	+	0.892588i	$0.351113\pi$
$420$	−52.0647	−2.54050
$421$	37.3882	1.82219	0.911096	−	0.412195i	$-0.135238\pi$
$421$	37.3882	1.82219	0.911096	+	0.412195i	$0.135238\pi$
$422$	6.52960	0.317856
$423$	−59.2410	−2.88040
$424$	17.4913	0.849453
$425$	16.6297	0.806659
$426$	−41.2315	−1.99767
$427$	−57.6968	−2.79214
$428$	12.2935	0.594227
$429$	57.5723	2.77961
$430$	−8.12621	−0.391881
$431$	−20.7060	−0.997373	−0.498687	−	0.866782i	$-0.666184\pi$
$431$	−20.7060	−0.997373	−0.498687	+	0.866782i	$0.666184\pi$
$432$	6.82687	0.328458
$433$	35.2072	1.69195	0.845976	−	0.533222i	$-0.179019\pi$
$433$	35.2072	1.69195	0.845976	+	0.533222i	$0.179019\pi$
$434$	−9.04845	−0.434340
$435$	−60.8416	−2.91713
$436$	2.02504	0.0969818
$437$	−7.01916	−0.335772
$438$	−11.5724	−0.552952
$439$	−3.91206	−0.186713	−0.0933563	−	0.995633i	$-0.529760\pi$
$439$	−3.91206	−0.186713	−0.0933563	+	0.995633i	$0.529760\pi$
$440$	−29.8607	−1.42355
$441$	83.9373	3.99701
$442$	−21.1823	−1.00754
$443$	−11.2115	−0.532675	−0.266337	−	0.963880i	$-0.585814\pi$
$443$	−11.2115	−0.532675	−0.266337	+	0.963880i	$0.585814\pi$
$444$	−34.2722	−1.62648
$445$	29.5578	1.40117
$446$	18.3518	0.868984
$447$	−40.2103	−1.90188
$448$	−16.1059	−0.760933
$449$	−1.69587	−0.0800330	−0.0400165	−	0.999199i	$-0.512741\pi$
$449$	−1.69587	−0.0800330	−0.0400165	+	0.999199i	$0.512741\pi$
$450$	17.4917	0.824569
$451$	−13.9629	−0.657488
$452$	−18.1634	−0.854334
$453$	−13.9132	−0.653697
$454$	2.15471	0.101126
$455$	−54.8092	−2.56949
$456$	−8.75547	−0.410013
$457$	23.0237	1.07700	0.538501	−	0.842625i	$-0.318991\pi$
$457$	23.0237	1.07700	0.538501	+	0.842625i	$0.318991\pi$
$458$	−7.14560	−0.333892
$459$	81.6632	3.81171
$460$	−26.4563	−1.23353
$461$	25.3156	1.17907	0.589533	−	0.807744i	$-0.299312\pi$
$461$	25.3156	1.17907	0.589533	+	0.807744i	$0.299312\pi$
$462$	43.9183	2.04326
$463$	−16.8210	−0.781739	−0.390870	−	0.920446i	$-0.627826\pi$
$463$	−16.8210	−0.781739	−0.390870	+	0.920446i	$0.627826\pi$
$464$	3.20978	0.149010
$465$	−23.6283	−1.09574
$466$	16.9874	0.786924
$467$	38.7780	1.79443	0.897215	−	0.441594i	$-0.145587\pi$
$467$	38.7780	1.79443	0.897215	+	0.441594i	$0.145587\pi$
$468$	45.3044	2.09419
$469$	−54.1980	−2.50263
$470$	18.2307	0.840919
$471$	20.5081	0.944965
$472$	−24.0851	−1.10861
$473$	−13.9382	−0.640881
$474$	3.00328	0.137945
$475$	2.90395	0.133242
$476$	32.8566	1.50598
$477$	−47.8333	−2.19014
$478$	−9.70221	−0.443769
$479$	−28.8321	−1.31737	−0.658685	−	0.752418i	$-0.728887\pi$
$479$	−28.8321	−1.31737	−0.658685	+	0.752418i	$0.728887\pi$
$480$	−52.7576	−2.40805
$481$	−36.0787	−1.64505
$482$	−17.7927	−0.810437
$483$	96.9583	4.41176
$484$	−5.80721	−0.263964
$485$	−0.00957403	−0.000434734 0
$486$	27.5707	1.25063
$487$	11.3601	0.514778	0.257389	−	0.966308i	$-0.417138\pi$
$487$	11.3601	0.514778	0.257389	+	0.966308i	$0.417138\pi$
$488$	−36.5705	−1.65547
$489$	−57.9458	−2.62040
$490$	−25.8307	−1.16691
$491$	−34.5966	−1.56132	−0.780662	−	0.624954i	$-0.785118\pi$
$491$	−34.5966	−1.56132	−0.780662	+	0.624954i	$0.785118\pi$
$492$	−15.4312	−0.695691
$493$	38.3955	1.72925
$494$	−3.69894	−0.166423
$495$	81.6598	3.67033
$496$	1.24655	0.0559716
$497$	67.3270	3.02003
$498$	8.14430	0.364955
$499$	30.6493	1.37205	0.686026	−	0.727577i	$-0.259354\pi$
$499$	30.6493	1.37205	0.686026	+	0.727577i	$0.259354\pi$
$500$	−7.90034	−0.353314
$501$	63.3726	2.83128
$502$	−1.93494	−0.0863608
$503$	−18.1866	−0.810898	−0.405449	−	0.914118i	$-0.632885\pi$
$503$	−18.1866	−0.810898	−0.405449	+	0.914118i	$0.632885\pi$
$504$	86.1160	3.83591
$505$	−27.3842	−1.21858
$506$	22.3167	0.992099
$507$	25.0198	1.11117
$508$	−14.6107	−0.648246
$509$	9.33771	0.413887	0.206943	−	0.978353i	$-0.433648\pi$
$509$	9.33771	0.413887	0.206943	+	0.978353i	$0.433648\pi$
$510$	−42.1953	−1.86844
$511$	18.8966	0.835937
$512$	5.38051	0.237787
$513$	14.2604	0.629610
$514$	−20.1408	−0.888373
$515$	18.0168	0.793916
$516$	−15.4039	−0.678118
$517$	31.2696	1.37524
$518$	−27.5222	−1.20926
$519$	37.3631	1.64006
$520$	−34.7402	−1.52346
$521$	23.2393	1.01813	0.509067	−	0.860727i	$-0.329991\pi$
$521$	23.2393	1.01813	0.509067	+	0.860727i	$0.329991\pi$
$522$	40.3858	1.76764
$523$	28.2674	1.23605	0.618023	−	0.786160i	$-0.287934\pi$
$523$	28.2674	1.23605	0.618023	+	0.786160i	$0.287934\pi$
$524$	−3.84455	−0.167950
$525$	−40.1133	−1.75069
$526$	−2.40344	−0.104795
$527$	14.9112	0.649542
$528$	−6.05033	−0.263307
$529$	26.2686	1.14211
$530$	14.7201	0.639401
$531$	65.8652	2.85831
$532$	5.73756	0.248755
$533$	−16.2446	−0.703631
$534$	−27.5547	−1.19241
$535$	25.7795	1.11455
$536$	−34.3528	−1.48382
$537$	6.02709	0.260088
$538$	23.5410	1.01492
$539$	−44.3053	−1.90836
$540$	53.7494	2.31301
$541$	−24.5387	−1.05500	−0.527500	−	0.849555i	$-0.676870\pi$
$541$	−24.5387	−1.05500	−0.527500	+	0.849555i	$0.676870\pi$
$542$	8.73361	0.375141
$543$	−51.9537	−2.22955
$544$	33.2939	1.42746
$545$	4.24653	0.181901
$546$	51.0949	2.18666
$547$	8.66063	0.370302	0.185151	−	0.982710i	$-0.440723\pi$
$547$	8.66063	0.370302	0.185151	+	0.982710i	$0.440723\pi$
$548$	15.0757	0.644002
$549$	100.009	4.26828
$550$	−9.23281	−0.393688
$551$	6.70478	0.285633
$552$	61.4560	2.61574
$553$	−4.90406	−0.208542
$554$	24.9943	1.06190
$555$	−71.8690	−3.05067
$556$	−12.4593	−0.528392
$557$	−20.0865	−0.851091	−0.425545	−	0.904937i	$-0.639918\pi$
$557$	−20.0865	−0.851091	−0.425545	+	0.904937i	$0.639918\pi$
$558$	15.6842	0.663964
$559$	−16.2159	−0.685858
$560$	5.75995	0.243403
$561$	−72.3742	−3.05564
$562$	19.0327	0.802847
$563$	−27.1168	−1.14284	−0.571419	−	0.820659i	$-0.693607\pi$
$563$	−27.1168	−1.14284	−0.571419	+	0.820659i	$0.693607\pi$
$564$	34.5577	1.45514
$565$	−38.0888	−1.60241
$566$	−12.9315	−0.543553
$567$	−101.744	−4.27283
$568$	42.6745	1.79058
$569$	−7.87117	−0.329977	−0.164988	−	0.986296i	$-0.552759\pi$
$569$	−7.87117	−0.329977	−0.164988	+	0.986296i	$0.552759\pi$
$570$	−7.36831	−0.308625
$571$	−39.9501	−1.67186	−0.835931	−	0.548835i	$-0.815071\pi$
$571$	−39.9501	−1.67186	−0.835931	+	0.548835i	$0.815071\pi$
$572$	−23.9133	−0.999867
$573$	25.0765	1.04758
$574$	−12.3920	−0.517231
$575$	−20.3833	−0.850040
$576$	27.9173	1.16322
$577$	23.2282	0.967001	0.483501	−	0.875344i	$-0.339365\pi$
$577$	23.2282	0.967001	0.483501	+	0.875344i	$0.339365\pi$
$578$	12.8244	0.533426
$579$	−29.9933	−1.24648
$580$	25.2713	1.04933
$581$	−13.2988	−0.551729
$582$	0.00892522	0.000369962 0
$583$	25.2482	1.04567
$584$	11.9774	0.495629
$585$	95.0037	3.92792
$586$	19.2500	0.795210
$587$	11.2878	0.465898	0.232949	−	0.972489i	$-0.425163\pi$
$587$	11.2878	0.465898	0.232949	+	0.972489i	$0.425163\pi$
$588$	−48.9641	−2.01925
$589$	2.60386	0.107290
$590$	−20.2692	−0.834470
$591$	21.0541	0.866051
$592$	3.79155	0.155832
$593$	39.6699	1.62905	0.814524	−	0.580130i	$-0.196998\pi$
$593$	39.6699	1.62905	0.814524	+	0.580130i	$0.196998\pi$
$594$	−45.3394	−1.86030
$595$	68.9007	2.82465
$596$	16.7019	0.684135
$597$	−29.2497	−1.19711
$598$	25.9634	1.06172
$599$	−29.1390	−1.19059	−0.595294	−	0.803508i	$-0.702964\pi$
$599$	−29.1390	−1.19059	−0.595294	+	0.803508i	$0.702964\pi$
$600$	−25.4254	−1.03799
$601$	−11.4510	−0.467095	−0.233547	−	0.972345i	$-0.575033\pi$
$601$	−11.4510	−0.467095	−0.233547	+	0.972345i	$0.575033\pi$
$602$	−12.3701	−0.504166
$603$	93.9443	3.82571
$604$	5.77900	0.235144
$605$	−12.1778	−0.495097
$606$	25.5284	1.03702
$607$	12.1061	0.491372	0.245686	−	0.969349i	$-0.420987\pi$
$607$	12.1061	0.491372	0.245686	+	0.969349i	$0.420987\pi$
$608$	5.81392	0.235786
$609$	−92.6156	−3.75298
$610$	−30.7765	−1.24611
$611$	36.3794	1.47175
$612$	−56.9522	−2.30216
$613$	−10.7163	−0.432827	−0.216414	−	0.976302i	$-0.569436\pi$
$613$	−10.7163	−0.432827	−0.216414	+	0.976302i	$0.569436\pi$
$614$	13.4103	0.541194
$615$	−32.3593	−1.30485
$616$	−45.4553	−1.83145
$617$	−33.5138	−1.34921	−0.674607	−	0.738177i	$-0.735687\pi$
$617$	−33.5138	−1.34921	−0.674607	+	0.738177i	$0.735687\pi$
$618$	−16.7959	−0.675628
$619$	39.7982	1.59962	0.799812	−	0.600251i	$-0.204932\pi$
$619$	39.7982	1.59962	0.799812	+	0.600251i	$0.204932\pi$
$620$	9.81432	0.394153
$621$	−100.096	−4.01670
$622$	1.08052	0.0433249
$623$	44.9941	1.80265
$624$	−7.03900	−0.281786
$625$	−31.0868	−1.24347
$626$	−9.93557	−0.397105
$627$	−12.6383	−0.504724
$628$	−8.51831	−0.339918
$629$	45.3546	1.80841
$630$	72.4724	2.88737
$631$	−42.0968	−1.67585	−0.837923	−	0.545788i	$-0.816230\pi$
$631$	−42.0968	−1.67585	−0.837923	+	0.545788i	$0.816230\pi$
$632$	−3.10839	−0.123645
$633$	25.9555	1.03164
$634$	−0.811992	−0.0322483
$635$	−30.6388	−1.21587
$636$	27.9031	1.10643
$637$	−51.5451	−2.04229
$638$	−21.3172	−0.843955
$639$	−116.701	−4.61664
$640$	24.0993	0.952607
$641$	25.0465	0.989275	0.494638	−	0.869099i	$-0.335301\pi$
$641$	25.0465	0.989275	0.494638	+	0.869099i	$0.335301\pi$
$642$	−24.0325	−0.948487
$643$	−19.7061	−0.777135	−0.388567	−	0.921420i	$-0.627030\pi$
$643$	−19.7061	−0.777135	−0.388567	+	0.921420i	$0.627030\pi$
$644$	−40.2728	−1.58697
$645$	−32.3021	−1.27189
$646$	4.64994	0.182950
$647$	−8.26973	−0.325117	−0.162558	−	0.986699i	$-0.551975\pi$
$647$	−8.26973	−0.325117	−0.162558	+	0.986699i	$0.551975\pi$
$648$	−64.4892	−2.53337
$649$	−34.7661	−1.36469
$650$	−10.7415	−0.421317
$651$	−35.9681	−1.40970
$652$	24.0685	0.942595
$653$	6.90405	0.270176	0.135088	−	0.990834i	$-0.456868\pi$
$653$	6.90405	0.270176	0.135088	+	0.990834i	$0.456868\pi$
$654$	−3.95875	−0.154799
$655$	−8.06207	−0.315011
$656$	1.70716	0.0666534
$657$	−32.7545	−1.27788
$658$	27.7515	1.08187
$659$	−41.2378	−1.60640	−0.803198	−	0.595712i	$-0.796870\pi$
$659$	−41.2378	−1.60640	−0.803198	+	0.595712i	$0.796870\pi$
$660$	−47.6356	−1.85421
$661$	−35.5522	−1.38282	−0.691410	−	0.722463i	$-0.743010\pi$
$661$	−35.5522	−1.38282	−0.691410	+	0.722463i	$0.743010\pi$
$662$	15.6511	0.608297
$663$	−84.2007	−3.27008
$664$	−8.42933	−0.327121
$665$	12.0317	0.466570
$666$	47.7057	1.84856
$667$	−47.0619	−1.82224
$668$	−26.3226	−1.01845
$669$	72.9494	2.82039
$670$	−28.9102	−1.11690
$671$	−52.7885	−2.03788
$672$	−80.3099	−3.09802
$673$	46.2457	1.78264	0.891321	−	0.453374i	$-0.149780\pi$
$673$	46.2457	1.78264	0.891321	+	0.453374i	$0.149780\pi$
$674$	−18.7183	−0.721003
$675$	41.4113	1.59392
$676$	−10.3923	−0.399704
$677$	28.6929	1.10276	0.551379	−	0.834255i	$-0.314102\pi$
$677$	28.6929	1.10276	0.551379	+	0.834255i	$0.314102\pi$
$678$	35.5076	1.36366
$679$	−0.0145740	−0.000559298 0
$680$	43.6720	1.67474
$681$	8.56509	0.328215
$682$	−8.27870	−0.317008
$683$	−45.0490	−1.72375	−0.861876	−	0.507118i	$-0.830711\pi$
$683$	−45.0490	−1.72375	−0.861876	+	0.507118i	$0.830711\pi$
$684$	−9.94522	−0.380265
$685$	31.6139	1.20791
$686$	−14.9954	−0.572527
$687$	−28.4041	−1.08368
$688$	1.70414	0.0649698
$689$	29.3740	1.11906
$690$	51.7193	1.96892
$691$	−15.0187	−0.571340	−0.285670	−	0.958328i	$-0.592216\pi$
$691$	−15.0187	−0.571340	−0.285670	+	0.958328i	$0.592216\pi$
$692$	−15.5192	−0.589953
$693$	124.306	4.72199
$694$	−3.23335	−0.122736
$695$	−26.1273	−0.991064
$696$	−58.7035	−2.22515
$697$	20.4211	0.773504
$698$	12.2434	0.463419
$699$	67.5256	2.55405
$700$	16.6616	0.629748
$701$	−47.0048	−1.77535	−0.887674	−	0.460473i	$-0.847680\pi$
$701$	−47.0048	−1.77535	−0.887674	+	0.460473i	$0.847680\pi$
$702$	−52.7482	−1.99085
$703$	7.92001	0.298709
$704$	−14.7358	−0.555376
$705$	72.4679	2.72930
$706$	14.9404	0.562290
$707$	−41.6853	−1.56774
$708$	−38.4219	−1.44398
$709$	−29.0210	−1.08991	−0.544953	−	0.838467i	$-0.683452\pi$
$709$	−29.0210	−1.08991	−0.544953	+	0.838467i	$0.683452\pi$
$710$	35.9135	1.34781
$711$	8.50047	0.318792
$712$	28.5190	1.06880
$713$	−18.2769	−0.684474
$714$	−64.2315	−2.40380
$715$	−50.1465	−1.87537
$716$	−2.50343	−0.0935574
$717$	−38.5668	−1.44030
$718$	11.4478	0.427227
$719$	−9.13349	−0.340622	−0.170311	−	0.985390i	$-0.554477\pi$
$719$	−9.13349	−0.340622	−0.170311	+	0.985390i	$0.554477\pi$
$720$	−9.98404	−0.372083
$721$	27.4259	1.02140
$722$	0.811992	0.0302192
$723$	−70.7270	−2.63036
$724$	21.5796	0.802000
$725$	19.4703	0.723109
$726$	11.3525	0.421331
$727$	37.1619	1.37826	0.689129	−	0.724639i	$-0.257994\pi$
$727$	37.1619	1.37826	0.689129	+	0.724639i	$0.257994\pi$
$728$	−52.8830	−1.95998
$729$	38.2729	1.41751
$730$	10.0798	0.373070
$731$	20.3850	0.753966
$732$	−58.3394	−2.15628
$733$	−5.50492	−0.203329	−0.101664	−	0.994819i	$-0.532417\pi$
$733$	−5.50492	−0.203329	−0.101664	+	0.994819i	$0.532417\pi$
$734$	−8.36774	−0.308859
$735$	−102.678	−3.78734
$736$	−40.8088	−1.50423
$737$	−49.5873	−1.82657
$738$	21.4797	0.790678
$739$	−8.05256	−0.296218	−0.148109	−	0.988971i	$-0.547319\pi$
$739$	−8.05256	−0.296218	−0.148109	+	0.988971i	$0.547319\pi$
$740$	29.8517	1.09737
$741$	−14.7035	−0.540145
$742$	22.4076	0.822608
$743$	8.96268	0.328809	0.164404	−	0.986393i	$-0.447430\pi$
$743$	8.96268	0.328809	0.164404	+	0.986393i	$0.447430\pi$
$744$	−22.7980	−0.835815
$745$	35.0240	1.28318
$746$	17.3920	0.636765
$747$	23.0516	0.843413
$748$	30.0615	1.09916
$749$	39.2427	1.43390
$750$	15.4444	0.563949
$751$	23.9493	0.873921	0.436960	−	0.899481i	$-0.356055\pi$
$751$	23.9493	0.873921	0.436960	+	0.899481i	$0.356055\pi$
$752$	−3.82315	−0.139416
$753$	−7.69150	−0.280294
$754$	−24.8006	−0.903183
$755$	12.1186	0.441042
$756$	81.8196	2.97575
$757$	4.85471	0.176447	0.0882236	−	0.996101i	$-0.471881\pi$
$757$	4.85471	0.176447	0.0882236	+	0.996101i	$0.471881\pi$
$758$	16.3190	0.592732
$759$	88.7100	3.21997
$760$	7.62618	0.276631
$761$	−34.7766	−1.26065	−0.630325	−	0.776331i	$-0.717078\pi$
$761$	−34.7766	−1.26065	−0.630325	+	0.776331i	$0.717078\pi$
$762$	28.5625	1.03471
$763$	6.46425	0.234021
$764$	−10.4158	−0.376831
$765$	−119.429	−4.31797
$766$	−4.58021	−0.165490
$767$	−40.4472	−1.46046
$768$	−46.7604	−1.68732
$769$	−28.7586	−1.03706	−0.518530	−	0.855059i	$-0.673521\pi$
$769$	−28.7586	−1.03706	−0.518530	+	0.855059i	$0.673521\pi$
$770$	−38.2537	−1.37857
$771$	−80.0607	−2.88332
$772$	12.4581	0.448377
$773$	27.4523	0.987391	0.493696	−	0.869635i	$-0.335646\pi$
$773$	27.4523	0.987391	0.493696	+	0.869635i	$0.335646\pi$
$774$	21.4417	0.770706
$775$	7.56146	0.271615
$776$	−0.00923757	−0.000331609 0
$777$	−109.402	−3.92478
$778$	18.0596	0.647468
$779$	3.56601	0.127766
$780$	−55.4196	−1.98434
$781$	61.5995	2.20420
$782$	−32.6387	−1.16716
$783$	95.6125	3.41691
$784$	5.41693	0.193462
$785$	−17.8630	−0.637557
$786$	7.51572	0.268077
$787$	−28.1263	−1.00259	−0.501297	−	0.865275i	$-0.667144\pi$
$787$	−28.1263	−1.00259	−0.501297	+	0.865275i	$0.667144\pi$
$788$	−8.74509	−0.311531
$789$	−9.55378	−0.340124
$790$	−2.61591	−0.0930701
$791$	−57.9804	−2.06154
$792$	78.7901	2.79968
$793$	−61.4146	−2.18089
$794$	10.8464	0.384923
$795$	58.5132	2.07525
$796$	12.1492	0.430617
$797$	28.6211	1.01381	0.506905	−	0.862002i	$-0.330789\pi$
$797$	28.6211	1.01381	0.506905	+	0.862002i	$0.330789\pi$
$798$	−11.2164	−0.397055
$799$	−45.7325	−1.61790
$800$	16.8833	0.596915
$801$	−77.9907	−2.75566
$802$	16.7269	0.590649
$803$	17.2891	0.610118
$804$	−54.8016	−1.93270
$805$	−84.4525	−2.97656
$806$	−9.63151	−0.339255
$807$	93.5766	3.29405
$808$	−26.4218	−0.929516
$809$	19.1757	0.674181	0.337091	−	0.941472i	$-0.390557\pi$
$809$	19.1757	0.674181	0.337091	+	0.941472i	$0.390557\pi$
$810$	−54.2719	−1.90692
$811$	4.17962	0.146766	0.0733831	−	0.997304i	$-0.476620\pi$
$811$	4.17962	0.146766	0.0733831	+	0.997304i	$0.476620\pi$
$812$	38.4691	1.35000
$813$	34.7165	1.21756
$814$	−25.1809	−0.882589
$815$	50.4719	1.76795
$816$	8.84874	0.309768
$817$	3.55971	0.124538
$818$	−19.9799	−0.698582
$819$	144.619	5.05338
$820$	13.4408	0.469375
$821$	−9.84622	−0.343636	−0.171818	−	0.985129i	$-0.554964\pi$
$821$	−9.84622	−0.343636	−0.171818	+	0.985129i	$0.554964\pi$
$822$	−29.4715	−1.02794
$823$	24.9607	0.870077	0.435038	−	0.900412i	$-0.356735\pi$
$823$	24.9607	0.870077	0.435038	+	0.900412i	$0.356735\pi$
$824$	17.3837	0.605588
$825$	−36.7009	−1.27776
$826$	−30.8546	−1.07357
$827$	30.9555	1.07643	0.538215	−	0.842808i	$-0.319099\pi$
$827$	30.9555	1.07643	0.538215	+	0.842808i	$0.319099\pi$
$828$	69.8071	2.42596
$829$	21.7045	0.753828	0.376914	−	0.926248i	$-0.376985\pi$
$829$	21.7045	0.753828	0.376914	+	0.926248i	$0.376985\pi$
$830$	−7.09384	−0.246231
$831$	99.3534	3.44653
$832$	−17.1437	−0.594352
$833$	64.7974	2.24510
$834$	24.3567	0.843404
$835$	−55.1987	−1.91023
$836$	5.24946	0.181556
$837$	37.1319	1.28347
$838$	14.9880	0.517752
$839$	9.70991	0.335223	0.167612	−	0.985853i	$-0.446395\pi$
$839$	9.70991	0.335223	0.167612	+	0.985853i	$0.446395\pi$
$840$	−105.343	−3.63469
$841$	15.9540	0.550138
$842$	30.3590	1.04624
$843$	75.6560	2.60573
$844$	−10.7809	−0.371095
$845$	−21.7927	−0.749693
$846$	−48.1032	−1.65382
$847$	−18.5375	−0.636957
$848$	−3.08694	−0.106006
$849$	−51.4035	−1.76416
$850$	13.5032	0.463155
$851$	−55.5918	−1.90566
$852$	68.0768	2.33227
$853$	−7.90430	−0.270638	−0.135319	−	0.990802i	$-0.543206\pi$
$853$	−7.90430	−0.270638	−0.135319	+	0.990802i	$0.543206\pi$
$854$	−46.8493	−1.60315
$855$	−20.8552	−0.713234
$856$	24.8736	0.850161
$857$	−19.2493	−0.657544	−0.328772	−	0.944409i	$-0.606635\pi$
$857$	−19.2493	−0.657544	−0.328772	+	0.944409i	$0.606635\pi$
$858$	46.7482	1.59596
$859$	26.7489	0.912661	0.456330	−	0.889810i	$-0.349163\pi$
$859$	26.7489	0.912661	0.456330	+	0.889810i	$0.349163\pi$
$860$	13.4171	0.457519
$861$	−49.2587	−1.67873
$862$	−16.8131	−0.572657
$863$	−41.0085	−1.39595	−0.697973	−	0.716124i	$-0.745915\pi$
$863$	−41.0085	−1.39595	−0.697973	+	0.716124i	$0.745915\pi$
$864$	82.9085	2.82061
$865$	−32.5440	−1.10653
$866$	28.5880	0.971459
$867$	50.9778	1.73130
$868$	14.9398	0.507089
$869$	−4.48687	−0.152207
$870$	−49.4029	−1.67491
$871$	−57.6903	−1.95476
$872$	4.09730	0.138752
$873$	0.0252619	0.000854985 0
$874$	−5.69950	−0.192788
$875$	−25.2191	−0.852562
$876$	19.1071	0.645568
$877$	48.0854	1.62373	0.811865	−	0.583845i	$-0.198453\pi$
$877$	48.0854	1.62373	0.811865	+	0.583845i	$0.198453\pi$
$878$	−3.17656	−0.107204
$879$	76.5196	2.58094
$880$	5.26995	0.177650
$881$	41.7383	1.40620	0.703100	−	0.711091i	$-0.251799\pi$
$881$	41.7383	1.40620	0.703100	+	0.711091i	$0.251799\pi$
$882$	68.1564	2.29495
$883$	−20.5437	−0.691351	−0.345676	−	0.938354i	$-0.612350\pi$
$883$	−20.5437	−0.691351	−0.345676	+	0.938354i	$0.612350\pi$
$884$	34.9738	1.17630
$885$	−80.5711	−2.70837
$886$	−9.10366	−0.305843
$887$	21.6785	0.727894	0.363947	−	0.931420i	$-0.381429\pi$
$887$	21.6785	0.727894	0.363947	+	0.931420i	$0.381429\pi$
$888$	−69.3434	−2.32701
$889$	−46.6397	−1.56425
$890$	24.0007	0.804504
$891$	−93.0883	−3.11857
$892$	−30.3004	−1.01453
$893$	−7.98600	−0.267241
$894$	−32.6505	−1.09200
$895$	−5.24971	−0.175478
$896$	36.6849	1.22556
$897$	103.206	3.44595
$898$	−1.37703	−0.0459522
$899$	17.4583	0.582266
$900$	−28.8804	−0.962680
$901$	−36.9261	−1.23019
$902$	−11.3378	−0.377507
$903$	−49.1716	−1.63633
$904$	−36.7503	−1.22230
$905$	45.2527	1.50425
$906$	−11.2974	−0.375330
$907$	44.6051	1.48109	0.740545	−	0.672007i	$-0.234568\pi$
$907$	44.6051	1.48109	0.740545	+	0.672007i	$0.234568\pi$
$908$	−3.55762	−0.118064
$909$	72.2554	2.39656
$910$	−44.5046	−1.47531
$911$	7.59502	0.251634	0.125817	−	0.992053i	$-0.459845\pi$
$911$	7.59502	0.251634	0.125817	+	0.992053i	$0.459845\pi$
$912$	1.54520	0.0511668
$913$	−12.1675	−0.402685
$914$	18.6950	0.618376
$915$	−122.338	−4.04438
$916$	11.7980	0.389817
$917$	−12.2724	−0.405271
$918$	66.3098	2.18855
$919$	10.5876	0.349254	0.174627	−	0.984635i	$-0.444128\pi$
$919$	10.5876	0.349254	0.174627	+	0.984635i	$0.444128\pi$
$920$	−53.5294	−1.76481
$921$	53.3065	1.75651
$922$	20.5561	0.676978
$923$	71.6653	2.35889
$924$	−72.5129	−2.38550
$925$	22.9993	0.756211
$926$	−13.6585	−0.448848
$927$	−47.5389	−1.56138
$928$	38.9810	1.27961
$929$	1.78938	0.0587075	0.0293537	−	0.999569i	$-0.490655\pi$
$929$	1.78938	0.0587075	0.0293537	+	0.999569i	$0.490655\pi$
$930$	−19.1860	−0.629135
$931$	11.3152	0.370840
$932$	−28.0476	−0.918729
$933$	4.29512	0.140616
$934$	31.4874	1.03030
$935$	63.0393	2.06160
$936$	91.6650	2.99617
$937$	−51.2705	−1.67494	−0.837468	−	0.546487i	$-0.815965\pi$
$937$	−51.2705	−1.67494	−0.837468	+	0.546487i	$0.815965\pi$
$938$	−44.0083	−1.43692
$939$	−39.4944	−1.28885
$940$	−30.1004	−0.981768
$941$	−33.7601	−1.10055	−0.550274	−	0.834984i	$-0.685477\pi$
$941$	−33.7601	−1.10055	−0.550274	+	0.834984i	$0.685477\pi$
$942$	16.6524	0.542566
$943$	−25.0304	−0.815102
$944$	4.25064	0.138347
$945$	171.577	5.58139
$946$	−11.3177	−0.367971
$947$	16.0464	0.521438	0.260719	−	0.965415i	$-0.416040\pi$
$947$	16.0464	0.521438	0.260719	+	0.965415i	$0.416040\pi$
$948$	−4.95868	−0.161050
$949$	20.1142	0.652936
$950$	2.35798	0.0765030
$951$	−3.22771	−0.104666
$952$	66.4794	2.15461
$953$	−19.9007	−0.644646	−0.322323	−	0.946630i	$-0.604464\pi$
$953$	−19.9007	−0.644646	−0.322323	+	0.946630i	$0.604464\pi$
$954$	−38.8402	−1.25750
$955$	−21.8421	−0.706793
$956$	16.0192	0.518098
$957$	−84.7368	−2.73915
$958$	−23.4114	−0.756388
$959$	48.1240	1.55401
$960$	−34.1504	−1.10220
$961$	−24.2199	−0.781288
$962$	−29.2956	−0.944529
$963$	−68.0214	−2.19196
$964$	29.3773	0.946180
$965$	26.1248	0.840986
$966$	78.7294	2.53308
$967$	28.6977	0.922854	0.461427	−	0.887178i	$-0.347338\pi$
$967$	28.6977	0.922854	0.461427	+	0.887178i	$0.347338\pi$
$968$	−11.7498	−0.377653
$969$	18.4838	0.593784
$970$	−0.00777403	−0.000249609 0
$971$	−34.4980	−1.10710	−0.553548	−	0.832818i	$-0.686726\pi$
$971$	−34.4980	−1.10710	−0.553548	+	0.832818i	$0.686726\pi$
$972$	−45.5216	−1.46010
$973$	−39.7721	−1.27503
$974$	9.22435	0.295567
$975$	−42.6981	−1.36743
$976$	6.45412	0.206591
$977$	30.7320	0.983204	0.491602	−	0.870820i	$-0.336411\pi$
$977$	30.7320	0.983204	0.491602	+	0.870820i	$0.336411\pi$
$978$	−47.0515	−1.50454
$979$	41.1664	1.31568
$980$	42.6487	1.36236
$981$	−11.2048	−0.357742
$982$	−28.0922	−0.896458
$983$	6.42159	0.204817	0.102408	−	0.994742i	$-0.467345\pi$
$983$	6.42159	0.204817	0.102408	+	0.994742i	$0.467345\pi$
$984$	−31.2221	−0.995325
$985$	−18.3385	−0.584314
$986$	31.1768	0.992872
$987$	110.314	3.51132
$988$	6.10727	0.194298
$989$	−24.9861	−0.794513
$990$	66.3071	2.10738
$991$	25.1367	0.798495	0.399248	−	0.916843i	$-0.369271\pi$
$991$	25.1367	0.798495	0.399248	+	0.916843i	$0.369271\pi$
$992$	15.1386	0.480651
$993$	62.2139	1.97430
$994$	54.6690	1.73399
$995$	25.4770	0.807675
$996$	−13.4469	−0.426083
$997$	36.2863	1.14920	0.574599	−	0.818435i	$-0.305158\pi$
$997$	36.2863	1.14920	0.574599	+	0.818435i	$0.305158\pi$
$998$	24.8870	0.787784
$999$	112.942	3.57333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.86	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.86	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q+0.811992 q^{2} +3.22771 q^{3} -1.34067 q^{4} -2.81140 q^{5} +2.62087 q^{6} -4.27963 q^{7} -2.71260 q^{8} +7.41810 q^{9} +O(q^{10})\)	\(q+0.811992 q^{2} +3.22771 q^{3} -1.34067 q^{4} -2.81140 q^{5} +2.62087 q^{6} -4.27963 q^{7} -2.71260 q^{8} +7.41810 q^{9} -2.28283 q^{10} -3.91556 q^{11} -4.32729 q^{12} -4.55539 q^{13} -3.47502 q^{14} -9.07437 q^{15} +0.478731 q^{16} +5.72659 q^{17} +6.02344 q^{18} +1.00000 q^{19} +3.76915 q^{20} -13.8134 q^{21} -3.17940 q^{22} -7.01916 q^{23} -8.75547 q^{24} +2.90395 q^{25} -3.69894 q^{26} +14.2604 q^{27} +5.73756 q^{28} +6.70478 q^{29} -7.36831 q^{30} +2.60386 q^{31} +5.81392 q^{32} -12.6383 q^{33} +4.64994 q^{34} +12.0317 q^{35} -9.94522 q^{36} +7.92001 q^{37} +0.811992 q^{38} -14.7035 q^{39} +7.62618 q^{40} +3.56601 q^{41} -11.2164 q^{42} +3.55971 q^{43} +5.24946 q^{44} -20.8552 q^{45} -5.69950 q^{46} -7.98600 q^{47} +1.54520 q^{48} +11.3152 q^{49} +2.35798 q^{50} +18.4838 q^{51} +6.10727 q^{52} -6.44818 q^{53} +11.5793 q^{54} +11.0082 q^{55} +11.6089 q^{56} +3.22771 q^{57} +5.44422 q^{58} +8.87898 q^{59} +12.1657 q^{60} +13.4817 q^{61} +2.11431 q^{62} -31.7467 q^{63} +3.76339 q^{64} +12.8070 q^{65} -10.2622 q^{66} +12.6642 q^{67} -7.67746 q^{68} -22.6558 q^{69} +9.76966 q^{70} -15.7320 q^{71} -20.1223 q^{72} -4.41548 q^{73} +6.43098 q^{74} +9.37309 q^{75} -1.34067 q^{76} +16.7571 q^{77} -11.9391 q^{78} +1.14591 q^{79} -1.34590 q^{80} +23.7740 q^{81} +2.89557 q^{82} +3.10748 q^{83} +18.5192 q^{84} -16.0997 q^{85} +2.89045 q^{86} +21.6411 q^{87} +10.6213 q^{88} -10.5136 q^{89} -16.9343 q^{90} +19.4954 q^{91} +9.41036 q^{92} +8.40449 q^{93} -6.48457 q^{94} -2.81140 q^{95} +18.7656 q^{96} +0.00340543 q^{97} +9.18785 q^{98} -29.0460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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