LMFDB - Embedded newform 8018.2.a.j.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.316697 q^{3} +1.00000 q^{4} -0.633871 q^{5} -0.316697 q^{6} +1.30218 q^{7} +1.00000 q^{8} -2.89970 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.316697 q^{3} +1.00000 q^{4} -0.633871 q^{5} -0.316697 q^{6} +1.30218 q^{7} +1.00000 q^{8} -2.89970 q^{9} -0.633871 q^{10} -3.28199 q^{11} -0.316697 q^{12} +2.72112 q^{13} +1.30218 q^{14} +0.200745 q^{15} +1.00000 q^{16} +7.85122 q^{17} -2.89970 q^{18} -1.00000 q^{19} -0.633871 q^{20} -0.412396 q^{21} -3.28199 q^{22} +5.94658 q^{23} -0.316697 q^{24} -4.59821 q^{25} +2.72112 q^{26} +1.86842 q^{27} +1.30218 q^{28} +4.86917 q^{29} +0.200745 q^{30} -10.3129 q^{31} +1.00000 q^{32} +1.03940 q^{33} +7.85122 q^{34} -0.825413 q^{35} -2.89970 q^{36} +6.38504 q^{37} -1.00000 q^{38} -0.861770 q^{39} -0.633871 q^{40} +6.73152 q^{41} -0.412396 q^{42} -8.64507 q^{43} -3.28199 q^{44} +1.83804 q^{45} +5.94658 q^{46} -4.92688 q^{47} -0.316697 q^{48} -5.30433 q^{49} -4.59821 q^{50} -2.48646 q^{51} +2.72112 q^{52} +6.78791 q^{53} +1.86842 q^{54} +2.08036 q^{55} +1.30218 q^{56} +0.316697 q^{57} +4.86917 q^{58} +6.46212 q^{59} +0.200745 q^{60} +8.88569 q^{61} -10.3129 q^{62} -3.77593 q^{63} +1.00000 q^{64} -1.72484 q^{65} +1.03940 q^{66} -9.62712 q^{67} +7.85122 q^{68} -1.88326 q^{69} -0.825413 q^{70} -15.4994 q^{71} -2.89970 q^{72} +11.9836 q^{73} +6.38504 q^{74} +1.45624 q^{75} -1.00000 q^{76} -4.27374 q^{77} -0.861770 q^{78} -10.1395 q^{79} -0.633871 q^{80} +8.10739 q^{81} +6.73152 q^{82} +9.02471 q^{83} -0.412396 q^{84} -4.97666 q^{85} -8.64507 q^{86} -1.54205 q^{87} -3.28199 q^{88} +1.81210 q^{89} +1.83804 q^{90} +3.54339 q^{91} +5.94658 q^{92} +3.26607 q^{93} -4.92688 q^{94} +0.633871 q^{95} -0.316697 q^{96} +11.7199 q^{97} -5.30433 q^{98} +9.51681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.316697	−0.182845	−0.0914224	−	0.995812i	$-0.529141\pi$
$3$	−0.316697	−0.182845	−0.0914224	+	0.995812i	$0.529141\pi$
$4$	1.00000	0.500000
$5$	−0.633871	−0.283476	−0.141738	−	0.989904i	$-0.545269\pi$
$5$	−0.633871	−0.283476	−0.141738	+	0.989904i	$0.545269\pi$
$6$	−0.316697	−0.129291
$7$	1.30218	0.492177	0.246089	−	0.969247i	$-0.420855\pi$
$7$	1.30218	0.492177	0.246089	+	0.969247i	$0.420855\pi$
$8$	1.00000	0.353553
$9$	−2.89970	−0.966568
$10$	−0.633871	−0.200448
$11$	−3.28199	−0.989559	−0.494779	−	0.869019i	$-0.664751\pi$
$11$	−3.28199	−0.989559	−0.494779	+	0.869019i	$0.664751\pi$
$12$	−0.316697	−0.0914224
$13$	2.72112	0.754704	0.377352	−	0.926070i	$-0.376835\pi$
$13$	2.72112	0.754704	0.377352	+	0.926070i	$0.376835\pi$
$14$	1.30218	0.348022
$15$	0.200745	0.0518321
$16$	1.00000	0.250000
$17$	7.85122	1.90420	0.952101	−	0.305785i	$-0.0989187\pi$
$17$	7.85122	1.90420	0.952101	+	0.305785i	$0.0989187\pi$
$18$	−2.89970	−0.683467
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.633871	−0.141738
$21$	−0.412396	−0.0899921
$22$	−3.28199	−0.699724
$23$	5.94658	1.23995	0.619973	−	0.784623i	$-0.287143\pi$
$23$	5.94658	1.23995	0.619973	+	0.784623i	$0.287143\pi$
$24$	−0.316697	−0.0646454
$25$	−4.59821	−0.919642
$26$	2.72112	0.533656
$27$	1.86842	0.359577
$28$	1.30218	0.246089
$29$	4.86917	0.904182	0.452091	−	0.891972i	$-0.350678\pi$
$29$	4.86917	0.904182	0.452091	+	0.891972i	$0.350678\pi$
$30$	0.200745	0.0366508
$31$	−10.3129	−1.85225	−0.926127	−	0.377211i	$-0.876883\pi$
$31$	−10.3129	−1.85225	−0.926127	+	0.377211i	$0.876883\pi$
$32$	1.00000	0.176777
$33$	1.03940	0.180936
$34$	7.85122	1.34647
$35$	−0.825413	−0.139520
$36$	−2.89970	−0.483284
$37$	6.38504	1.04969	0.524847	−	0.851196i	$-0.324122\pi$
$37$	6.38504	1.04969	0.524847	+	0.851196i	$0.324122\pi$
$38$	−1.00000	−0.162221
$39$	−0.861770	−0.137994
$40$	−0.633871	−0.100224
$41$	6.73152	1.05129	0.525643	−	0.850705i	$-0.323825\pi$
$41$	6.73152	1.05129	0.525643	+	0.850705i	$0.323825\pi$
$42$	−0.412396	−0.0636340
$43$	−8.64507	−1.31836	−0.659180	−	0.751985i	$-0.729097\pi$
$43$	−8.64507	−1.31836	−0.659180	+	0.751985i	$0.729097\pi$
$44$	−3.28199	−0.494779
$45$	1.83804	0.273998
$46$	5.94658	0.876775
$47$	−4.92688	−0.718660	−0.359330	−	0.933211i	$-0.616995\pi$
$47$	−4.92688	−0.718660	−0.359330	+	0.933211i	$0.616995\pi$
$48$	−0.316697	−0.0457112
$49$	−5.30433	−0.757761
$50$	−4.59821	−0.650285
$51$	−2.48646	−0.348173
$52$	2.72112	0.377352
$53$	6.78791	0.932391	0.466195	−	0.884682i	$-0.345624\pi$
$53$	6.78791	0.932391	0.466195	+	0.884682i	$0.345624\pi$
$54$	1.86842	0.254259
$55$	2.08036	0.280516
$56$	1.30218	0.174011
$57$	0.316697	0.0419475
$58$	4.86917	0.639353
$59$	6.46212	0.841297	0.420648	−	0.907224i	$-0.361803\pi$
$59$	6.46212	0.841297	0.420648	+	0.907224i	$0.361803\pi$
$60$	0.200745	0.0259160
$61$	8.88569	1.13770	0.568848	−	0.822443i	$-0.307389\pi$
$61$	8.88569	1.13770	0.568848	+	0.822443i	$0.307389\pi$
$62$	−10.3129	−1.30974
$63$	−3.77593	−0.475723
$64$	1.00000	0.125000
$65$	−1.72484	−0.213940
$66$	1.03940	0.127941
$67$	−9.62712	−1.17614	−0.588070	−	0.808810i	$-0.700112\pi$
$67$	−9.62712	−1.17614	−0.588070	+	0.808810i	$0.700112\pi$
$68$	7.85122	0.952101
$69$	−1.88326	−0.226718
$70$	−0.825413	−0.0986558
$71$	−15.4994	−1.83944	−0.919721	−	0.392571i	$-0.871586\pi$
$71$	−15.4994	−1.83944	−0.919721	+	0.392571i	$0.871586\pi$
$72$	−2.89970	−0.341733
$73$	11.9836	1.40258	0.701290	−	0.712876i	$-0.252608\pi$
$73$	11.9836	1.40258	0.701290	+	0.712876i	$0.252608\pi$
$74$	6.38504	0.742246
$75$	1.45624	0.168152
$76$	−1.00000	−0.114708
$77$	−4.27374	−0.487038
$78$	−0.861770	−0.0975762
$79$	−10.1395	−1.14079	−0.570393	−	0.821372i	$-0.693209\pi$
$79$	−10.1395	−1.14079	−0.570393	+	0.821372i	$0.693209\pi$
$80$	−0.633871	−0.0708689
$81$	8.10739	0.900821
$82$	6.73152	0.743372
$83$	9.02471	0.990590	0.495295	−	0.868725i	$-0.335060\pi$
$83$	9.02471	0.990590	0.495295	+	0.868725i	$0.335060\pi$
$84$	−0.412396	−0.0449961
$85$	−4.97666	−0.539795
$86$	−8.64507	−0.932221
$87$	−1.54205	−0.165325
$88$	−3.28199	−0.349862
$89$	1.81210	0.192082	0.0960411	−	0.995377i	$-0.469382\pi$
$89$	1.81210	0.192082	0.0960411	+	0.995377i	$0.469382\pi$
$90$	1.83804	0.193746
$91$	3.54339	0.371448
$92$	5.94658	0.619973
$93$	3.26607	0.338675
$94$	−4.92688	−0.508169
$95$	0.633871	0.0650338
$96$	−0.316697	−0.0323227
$97$	11.7199	1.18998	0.594989	−	0.803734i	$-0.297156\pi$
$97$	11.7199	1.18998	0.594989	+	0.803734i	$0.297156\pi$
$98$	−5.30433	−0.535818
$99$	9.51681	0.956475
$100$	−4.59821	−0.459821
$101$	−8.56010	−0.851761	−0.425881	−	0.904779i	$-0.640036\pi$
$101$	−8.56010	−0.851761	−0.425881	+	0.904779i	$0.640036\pi$
$102$	−2.48646	−0.246196
$103$	14.5743	1.43605	0.718024	−	0.696018i	$-0.245047\pi$
$103$	14.5743	1.43605	0.718024	+	0.696018i	$0.245047\pi$
$104$	2.72112	0.266828
$105$	0.261406	0.0255106
$106$	6.78791	0.659300
$107$	0.0386434	0.00373580	0.00186790	−	0.999998i	$-0.499405\pi$
$107$	0.0386434	0.00373580	0.00186790	+	0.999998i	$0.499405\pi$
$108$	1.86842	0.179788
$109$	−10.5277	−1.00837	−0.504187	−	0.863594i	$-0.668208\pi$
$109$	−10.5277	−1.00837	−0.504187	+	0.863594i	$0.668208\pi$
$110$	2.08036	0.198355
$111$	−2.02212	−0.191931
$112$	1.30218	0.123044
$113$	9.61364	0.904375	0.452188	−	0.891923i	$-0.350644\pi$
$113$	9.61364	0.904375	0.452188	+	0.891923i	$0.350644\pi$
$114$	0.316697	0.0296613
$115$	−3.76936	−0.351495
$116$	4.86917	0.452091
$117$	−7.89045	−0.729472
$118$	6.46212	0.594887
$119$	10.2237	0.937205
$120$	0.200745	0.0183254
$121$	−0.228513	−0.0207739
$122$	8.88569	0.804473
$123$	−2.13185	−0.192222
$124$	−10.3129	−0.926127
$125$	6.08402	0.544172
$126$	−3.77593	−0.336387
$127$	−1.39508	−0.123793	−0.0618967	−	0.998083i	$-0.519715\pi$
$127$	−1.39508	−0.123793	−0.0618967	+	0.998083i	$0.519715\pi$
$128$	1.00000	0.0883883
$129$	2.73786	0.241055
$130$	−1.72484	−0.151278
$131$	−9.10667	−0.795653	−0.397827	−	0.917461i	$-0.630235\pi$
$131$	−9.10667	−0.795653	−0.397827	+	0.917461i	$0.630235\pi$
$132$	1.03940	0.0904678
$133$	−1.30218	−0.112913
$134$	−9.62712	−0.831656
$135$	−1.18433	−0.101931
$136$	7.85122	0.673237
$137$	22.7634	1.94481	0.972405	−	0.233298i	$-0.0749517\pi$
$137$	22.7634	1.94481	0.972405	+	0.233298i	$0.0749517\pi$
$138$	−1.88326	−0.160314
$139$	17.9297	1.52077	0.760387	−	0.649470i	$-0.225009\pi$
$139$	17.9297	1.52077	0.760387	+	0.649470i	$0.225009\pi$
$140$	−0.825413	−0.0697602
$141$	1.56033	0.131403
$142$	−15.4994	−1.30068
$143$	−8.93071	−0.746823
$144$	−2.89970	−0.241642
$145$	−3.08642	−0.256314
$146$	11.9836	0.991774
$147$	1.67986	0.138553
$148$	6.38504	0.524847
$149$	12.6405	1.03555	0.517775	−	0.855517i	$-0.326760\pi$
$149$	12.6405	1.03555	0.517775	+	0.855517i	$0.326760\pi$
$150$	1.45624	0.118901
$151$	21.7335	1.76865	0.884324	−	0.466875i	$-0.154620\pi$
$151$	21.7335	1.76865	0.884324	+	0.466875i	$0.154620\pi$
$152$	−1.00000	−0.0811107
$153$	−22.7662	−1.84054
$154$	−4.27374	−0.344388
$155$	6.53706	0.525069
$156$	−0.861770	−0.0689968
$157$	6.16246	0.491818	0.245909	−	0.969293i	$-0.420914\pi$
$157$	6.16246	0.491818	0.245909	+	0.969293i	$0.420914\pi$
$158$	−10.1395	−0.806658
$159$	−2.14971	−0.170483
$160$	−0.633871	−0.0501119
$161$	7.74351	0.610274
$162$	8.10739	0.636977
$163$	−11.7577	−0.920934	−0.460467	−	0.887677i	$-0.652318\pi$
$163$	−11.7577	−0.920934	−0.460467	+	0.887677i	$0.652318\pi$
$164$	6.73152	0.525643
$165$	−0.658843	−0.0512909
$166$	9.02471	0.700453
$167$	−5.50355	−0.425877	−0.212939	−	0.977066i	$-0.568303\pi$
$167$	−5.50355	−0.425877	−0.212939	+	0.977066i	$0.568303\pi$
$168$	−0.412396	−0.0318170
$169$	−5.59549	−0.430423
$170$	−4.97666	−0.381693
$171$	2.89970	0.221746
$172$	−8.64507	−0.659180
$173$	13.2067	1.00409	0.502044	−	0.864842i	$-0.332582\pi$
$173$	13.2067	1.00409	0.502044	+	0.864842i	$0.332582\pi$
$174$	−1.54205	−0.116902
$175$	−5.98769	−0.452627
$176$	−3.28199	−0.247390
$177$	−2.04653	−0.153827
$178$	1.81210	0.135823
$179$	22.4263	1.67622	0.838109	−	0.545503i	$-0.183661\pi$
$179$	22.4263	1.67622	0.838109	+	0.545503i	$0.183661\pi$
$180$	1.83804	0.136999
$181$	12.5002	0.929134	0.464567	−	0.885538i	$-0.346210\pi$
$181$	12.5002	0.929134	0.464567	+	0.885538i	$0.346210\pi$
$182$	3.54339	0.262653
$183$	−2.81407	−0.208022
$184$	5.94658	0.438387
$185$	−4.04729	−0.297563
$186$	3.26607	0.239480
$187$	−25.7677	−1.88432
$188$	−4.92688	−0.359330
$189$	2.43301	0.176976
$190$	0.633871	0.0459858
$191$	25.8064	1.86729	0.933644	−	0.358203i	$-0.116610\pi$
$191$	25.8064	1.86729	0.933644	+	0.358203i	$0.116610\pi$
$192$	−0.316697	−0.0228556
$193$	9.81184	0.706272	0.353136	−	0.935572i	$-0.385115\pi$
$193$	9.81184	0.706272	0.353136	+	0.935572i	$0.385115\pi$
$194$	11.7199	0.841442
$195$	0.546251	0.0391178
$196$	−5.30433	−0.378881
$197$	−9.53236	−0.679152	−0.339576	−	0.940579i	$-0.610284\pi$
$197$	−9.53236	−0.679152	−0.339576	+	0.940579i	$0.610284\pi$
$198$	9.51681	0.676330
$199$	16.1514	1.14494	0.572470	−	0.819926i	$-0.305985\pi$
$199$	16.1514	1.14494	0.572470	+	0.819926i	$0.305985\pi$
$200$	−4.59821	−0.325142
$201$	3.04887	0.215051
$202$	−8.56010	−0.602286
$203$	6.34053	0.445018
$204$	−2.48646	−0.174087
$205$	−4.26692	−0.298014
$206$	14.5743	1.01544
$207$	−17.2433	−1.19849
$208$	2.72112	0.188676
$209$	3.28199	0.227020
$210$	0.261406	0.0180387
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	6.78791	0.466195
$213$	4.90861	0.336333
$214$	0.0386434	0.00264161
$215$	5.47986	0.373723
$216$	1.86842	0.127130
$217$	−13.4293	−0.911638
$218$	−10.5277	−0.713029
$219$	−3.79518	−0.256454
$220$	2.08036	0.140258
$221$	21.3641	1.43711
$222$	−2.02212	−0.135716
$223$	6.01217	0.402604	0.201302	−	0.979529i	$-0.435483\pi$
$223$	6.01217	0.402604	0.201302	+	0.979529i	$0.435483\pi$
$224$	1.30218	0.0870055
$225$	13.3334	0.888896
$226$	9.61364	0.639490
$227$	0.456059	0.0302697	0.0151348	−	0.999885i	$-0.495182\pi$
$227$	0.456059	0.0302697	0.0151348	+	0.999885i	$0.495182\pi$
$228$	0.316697	0.0209737
$229$	6.93276	0.458129	0.229065	−	0.973411i	$-0.426433\pi$
$229$	6.93276	0.458129	0.229065	+	0.973411i	$0.426433\pi$
$230$	−3.76936	−0.248544
$231$	1.35348	0.0890525
$232$	4.86917	0.319677
$233$	8.39227	0.549796	0.274898	−	0.961473i	$-0.411356\pi$
$233$	8.39227	0.549796	0.274898	+	0.961473i	$0.411356\pi$
$234$	−7.89045	−0.515815
$235$	3.12301	0.203723
$236$	6.46212	0.420648
$237$	3.21115	0.208587
$238$	10.2237	0.662704
$239$	−2.25755	−0.146029	−0.0730143	−	0.997331i	$-0.523262\pi$
$239$	−2.25755	−0.146029	−0.0730143	+	0.997331i	$0.523262\pi$
$240$	0.200745	0.0129580
$241$	5.14424	0.331370	0.165685	−	0.986179i	$-0.447017\pi$
$241$	5.14424	0.331370	0.165685	+	0.986179i	$0.447017\pi$
$242$	−0.228513	−0.0146894
$243$	−8.17283	−0.524287
$244$	8.88569	0.568848
$245$	3.36226	0.214807
$246$	−2.13185	−0.135922
$247$	−2.72112	−0.173141
$248$	−10.3129	−0.654871
$249$	−2.85809	−0.181124
$250$	6.08402	0.384788
$251$	25.9841	1.64010	0.820052	−	0.572289i	$-0.193944\pi$
$251$	25.9841	1.64010	0.820052	+	0.572289i	$0.193944\pi$
$252$	−3.77593	−0.237861
$253$	−19.5166	−1.22700
$254$	−1.39508	−0.0875352
$255$	1.57609	0.0986987
$256$	1.00000	0.0625000
$257$	−18.5572	−1.15756	−0.578782	−	0.815482i	$-0.696472\pi$
$257$	−18.5572	−1.15756	−0.578782	+	0.815482i	$0.696472\pi$
$258$	2.73786	0.170452
$259$	8.31447	0.516636
$260$	−1.72484	−0.106970
$261$	−14.1191	−0.873953
$262$	−9.10667	−0.562612
$263$	−20.5112	−1.26477	−0.632386	−	0.774653i	$-0.717924\pi$
$263$	−20.5112	−1.26477	−0.632386	+	0.774653i	$0.717924\pi$
$264$	1.03940	0.0639704
$265$	−4.30266	−0.264310
$266$	−1.30218	−0.0798417
$267$	−0.573886	−0.0351212
$268$	−9.62712	−0.588070
$269$	−11.6832	−0.712339	−0.356170	−	0.934421i	$-0.615917\pi$
$269$	−11.6832	−0.712339	−0.356170	+	0.934421i	$0.615917\pi$
$270$	−1.18433	−0.0720763
$271$	16.9254	1.02814	0.514072	−	0.857747i	$-0.328136\pi$
$271$	16.9254	1.02814	0.514072	+	0.857747i	$0.328136\pi$
$272$	7.85122	0.476050
$273$	−1.12218	−0.0679174
$274$	22.7634	1.37519
$275$	15.0913	0.910039
$276$	−1.88326	−0.113359
$277$	−10.7834	−0.647910	−0.323955	−	0.946072i	$-0.605013\pi$
$277$	−10.7834	−0.647910	−0.323955	+	0.946072i	$0.605013\pi$
$278$	17.9297	1.07535
$279$	29.9044	1.79033
$280$	−0.825413	−0.0493279
$281$	0.140080	0.00835650	0.00417825	−	0.999991i	$-0.498670\pi$
$281$	0.140080	0.00835650	0.00417825	+	0.999991i	$0.498670\pi$
$282$	1.56033	0.0929161
$283$	15.7665	0.937221	0.468610	−	0.883405i	$-0.344755\pi$
$283$	15.7665	0.937221	0.468610	+	0.883405i	$0.344755\pi$
$284$	−15.4994	−0.919721
$285$	−0.200745	−0.0118911
$286$	−8.93071	−0.528084
$287$	8.76565	0.517420
$288$	−2.89970	−0.170867
$289$	44.6417	2.62598
$290$	−3.08642	−0.181241
$291$	−3.71166	−0.217581
$292$	11.9836	0.701290
$293$	−19.3202	−1.12870	−0.564349	−	0.825536i	$-0.690873\pi$
$293$	−19.3202	−1.12870	−0.564349	+	0.825536i	$0.690873\pi$
$294$	1.67986	0.0979716
$295$	−4.09615	−0.238487
$296$	6.38504	0.371123
$297$	−6.13213	−0.355822
$298$	12.6405	0.732245
$299$	16.1814	0.935792
$300$	1.45624	0.0840759
$301$	−11.2574	−0.648867
$302$	21.7335	1.25062
$303$	2.71095	0.155740
$304$	−1.00000	−0.0573539
$305$	−5.63238	−0.322509
$306$	−22.7662	−1.30146
$307$	−12.9088	−0.736745	−0.368372	−	0.929678i	$-0.620085\pi$
$307$	−12.9088	−0.736745	−0.368372	+	0.929678i	$0.620085\pi$
$308$	−4.27374	−0.243519
$309$	−4.61563	−0.262574
$310$	6.53706	0.371280
$311$	16.1837	0.917694	0.458847	−	0.888515i	$-0.348263\pi$
$311$	16.1837	0.917694	0.458847	+	0.888515i	$0.348263\pi$
$312$	−0.861770	−0.0487881
$313$	−30.7000	−1.73526	−0.867632	−	0.497206i	$-0.834359\pi$
$313$	−30.7000	−1.73526	−0.867632	+	0.497206i	$0.834359\pi$
$314$	6.16246	0.347768
$315$	2.39345	0.134856
$316$	−10.1395	−0.570393
$317$	13.8118	0.775748	0.387874	−	0.921712i	$-0.373210\pi$
$317$	13.8118	0.775748	0.387874	+	0.921712i	$0.373210\pi$
$318$	−2.14971	−0.120550
$319$	−15.9806	−0.894741
$320$	−0.633871	−0.0354345
$321$	−0.0122382	−0.000683071 0
$322$	7.74351	0.431529
$323$	−7.85122	−0.436854
$324$	8.10739	0.450411
$325$	−12.5123	−0.694057
$326$	−11.7577	−0.651199
$327$	3.33410	0.184376
$328$	6.73152	0.371686
$329$	−6.41569	−0.353708
$330$	−0.658843	−0.0362681
$331$	−13.2313	−0.727256	−0.363628	−	0.931544i	$-0.618462\pi$
$331$	−13.2313	−0.727256	−0.363628	+	0.931544i	$0.618462\pi$
$332$	9.02471	0.495295
$333$	−18.5147	−1.01460
$334$	−5.50355	−0.301141
$335$	6.10235	0.333407
$336$	−0.412396	−0.0224980
$337$	20.4876	1.11603	0.558016	−	0.829830i	$-0.311563\pi$
$337$	20.4876	1.11603	0.558016	+	0.829830i	$0.311563\pi$
$338$	−5.59549	−0.304355
$339$	−3.04461	−0.165360
$340$	−4.97666	−0.269897
$341$	33.8469	1.83291
$342$	2.89970	0.156798
$343$	−16.0224	−0.865130
$344$	−8.64507	−0.466111
$345$	1.19374	0.0642690
$346$	13.2067	0.709997
$347$	−23.1980	−1.24533	−0.622667	−	0.782487i	$-0.713951\pi$
$347$	−23.1980	−1.24533	−0.622667	+	0.782487i	$0.713951\pi$
$348$	−1.54205	−0.0826625
$349$	−2.16227	−0.115743	−0.0578717	−	0.998324i	$-0.518431\pi$
$349$	−2.16227	−0.115743	−0.0578717	+	0.998324i	$0.518431\pi$
$350$	−5.98769	−0.320055
$351$	5.08419	0.271374
$352$	−3.28199	−0.174931
$353$	−15.5308	−0.826623	−0.413311	−	0.910590i	$-0.635628\pi$
$353$	−15.5308	−0.826623	−0.413311	+	0.910590i	$0.635628\pi$
$354$	−2.04653	−0.108772
$355$	9.82463	0.521437
$356$	1.81210	0.0960411
$357$	−3.23781	−0.171363
$358$	22.4263	1.18526
$359$	−21.9983	−1.16102	−0.580512	−	0.814252i	$-0.697148\pi$
$359$	−21.9983	−1.16102	−0.580512	+	0.814252i	$0.697148\pi$
$360$	1.83804	0.0968731
$361$	1.00000	0.0526316
$362$	12.5002	0.656997
$363$	0.0723694	0.00379841
$364$	3.54339	0.185724
$365$	−7.59608	−0.397597
$366$	−2.81407	−0.147094
$367$	25.2122	1.31607	0.658033	−	0.752989i	$-0.271389\pi$
$367$	25.2122	1.31607	0.658033	+	0.752989i	$0.271389\pi$
$368$	5.94658	0.309987
$369$	−19.5194	−1.01614
$370$	−4.04729	−0.210409
$371$	8.83907	0.458902
$372$	3.26607	0.169338
$373$	22.5197	1.16603	0.583013	−	0.812463i	$-0.301873\pi$
$373$	22.5197	1.16603	0.583013	+	0.812463i	$0.301873\pi$
$374$	−25.7677	−1.33241
$375$	−1.92679	−0.0994990
$376$	−4.92688	−0.254085
$377$	13.2496	0.682389
$378$	2.43301	0.125141
$379$	−18.1362	−0.931594	−0.465797	−	0.884892i	$-0.654232\pi$
$379$	−18.1362	−0.931594	−0.465797	+	0.884892i	$0.654232\pi$
$380$	0.633871	0.0325169
$381$	0.441817	0.0226350
$382$	25.8064	1.32037
$383$	18.7929	0.960271	0.480135	−	0.877194i	$-0.340588\pi$
$383$	18.7929	0.960271	0.480135	+	0.877194i	$0.340588\pi$
$384$	−0.316697	−0.0161614
$385$	2.70900	0.138064
$386$	9.81184	0.499410
$387$	25.0681	1.27428
$388$	11.7199	0.594989
$389$	26.0243	1.31949	0.659743	−	0.751492i	$-0.270665\pi$
$389$	26.0243	1.31949	0.659743	+	0.751492i	$0.270665\pi$
$390$	0.546251	0.0276605
$391$	46.6879	2.36111
$392$	−5.30433	−0.267909
$393$	2.88405	0.145481
$394$	−9.53236	−0.480233
$395$	6.42715	0.323385
$396$	9.51681	0.478238
$397$	13.7105	0.688110	0.344055	−	0.938949i	$-0.388199\pi$
$397$	13.7105	0.688110	0.344055	+	0.938949i	$0.388199\pi$
$398$	16.1514	0.809594
$399$	0.412396	0.0206456
$400$	−4.59821	−0.229910
$401$	−37.7874	−1.88701	−0.943506	−	0.331355i	$-0.892494\pi$
$401$	−37.7874	−1.88701	−0.943506	+	0.331355i	$0.892494\pi$
$402$	3.04887	0.152064
$403$	−28.0627	−1.39790
$404$	−8.56010	−0.425881
$405$	−5.13904	−0.255361
$406$	6.34053	0.314675
$407$	−20.9557	−1.03873
$408$	−2.48646	−0.123098
$409$	−20.1267	−0.995199	−0.497599	−	0.867407i	$-0.665785\pi$
$409$	−20.1267	−0.995199	−0.497599	+	0.867407i	$0.665785\pi$
$410$	−4.26692	−0.210728
$411$	−7.20910	−0.355599
$412$	14.5743	0.718024
$413$	8.41484	0.414067
$414$	−17.2433	−0.847462
$415$	−5.72050	−0.280808
$416$	2.72112	0.133414
$417$	−5.67826	−0.278066
$418$	3.28199	0.160528
$419$	−29.3823	−1.43542	−0.717709	−	0.696343i	$-0.754809\pi$
$419$	−29.3823	−1.43542	−0.717709	+	0.696343i	$0.754809\pi$
$420$	0.261406	0.0127553
$421$	3.09990	0.151080	0.0755400	−	0.997143i	$-0.475932\pi$
$421$	3.09990	0.151080	0.0755400	+	0.997143i	$0.475932\pi$
$422$	−1.00000	−0.0486792
$423$	14.2865	0.694634
$424$	6.78791	0.329650
$425$	−36.1016	−1.75118
$426$	4.90861	0.237823
$427$	11.5708	0.559948
$428$	0.0386434	0.00186790
$429$	2.82832	0.136553
$430$	5.47986	0.264262
$431$	1.55279	0.0747953	0.0373977	−	0.999300i	$-0.488093\pi$
$431$	1.55279	0.0747953	0.0373977	+	0.999300i	$0.488093\pi$
$432$	1.86842	0.0898942
$433$	−9.38182	−0.450862	−0.225431	−	0.974259i	$-0.572379\pi$
$433$	−9.38182	−0.450862	−0.225431	+	0.974259i	$0.572379\pi$
$434$	−13.4293	−0.644625
$435$	0.977460	0.0468656
$436$	−10.5277	−0.504187
$437$	−5.94658	−0.284463
$438$	−3.79518	−0.181341
$439$	7.35006	0.350799	0.175400	−	0.984497i	$-0.443878\pi$
$439$	7.35006	0.350799	0.175400	+	0.984497i	$0.443878\pi$
$440$	2.08036	0.0991773
$441$	15.3810	0.732428
$442$	21.3641	1.01619
$443$	−19.9342	−0.947104	−0.473552	−	0.880766i	$-0.657028\pi$
$443$	−19.9342	−0.947104	−0.473552	+	0.880766i	$0.657028\pi$
$444$	−2.02212	−0.0959656
$445$	−1.14864	−0.0544507
$446$	6.01217	0.284684
$447$	−4.00321	−0.189345
$448$	1.30218	0.0615222
$449$	−14.5104	−0.684787	−0.342394	−	0.939557i	$-0.611238\pi$
$449$	−14.5104	−0.684787	−0.342394	+	0.939557i	$0.611238\pi$
$450$	13.3334	0.628544
$451$	−22.0928	−1.04031
$452$	9.61364	0.452188
$453$	−6.88292	−0.323388
$454$	0.456059	0.0214039
$455$	−2.24605	−0.105296
$456$	0.316697	0.0148307
$457$	9.65001	0.451409	0.225704	−	0.974196i	$-0.427532\pi$
$457$	9.65001	0.451409	0.225704	+	0.974196i	$0.427532\pi$
$458$	6.93276	0.323946
$459$	14.6693	0.684707
$460$	−3.76936	−0.175747
$461$	−3.51618	−0.163765	−0.0818824	−	0.996642i	$-0.526093\pi$
$461$	−3.51618	−0.163765	−0.0818824	+	0.996642i	$0.526093\pi$
$462$	1.35348	0.0629696
$463$	−14.2805	−0.663672	−0.331836	−	0.943337i	$-0.607668\pi$
$463$	−14.2805	−0.663672	−0.331836	+	0.943337i	$0.607668\pi$
$464$	4.86917	0.226045
$465$	−2.07026	−0.0960062
$466$	8.39227	0.388765
$467$	−7.93248	−0.367071	−0.183536	−	0.983013i	$-0.558754\pi$
$467$	−7.93248	−0.367071	−0.183536	+	0.983013i	$0.558754\pi$
$468$	−7.89045	−0.364736
$469$	−12.5362	−0.578869
$470$	3.12301	0.144054
$471$	−1.95163	−0.0899264
$472$	6.46212	0.297443
$473$	28.3731	1.30459
$474$	3.21115	0.147493
$475$	4.59821	0.210980
$476$	10.2237	0.468602
$477$	−19.6829	−0.901219
$478$	−2.25755	−0.103258
$479$	21.1612	0.966878	0.483439	−	0.875378i	$-0.339388\pi$
$479$	21.1612	0.966878	0.483439	+	0.875378i	$0.339388\pi$
$480$	0.200745	0.00916270
$481$	17.3745	0.792208
$482$	5.14424	0.234314
$483$	−2.45234	−0.111585
$484$	−0.228513	−0.0103870
$485$	−7.42892	−0.337330
$486$	−8.17283	−0.370727
$487$	−17.4317	−0.789908	−0.394954	−	0.918701i	$-0.629239\pi$
$487$	−17.4317	−0.789908	−0.394954	+	0.918701i	$0.629239\pi$
$488$	8.88569	0.402236
$489$	3.72362	0.168388
$490$	3.36226	0.151891
$491$	−40.2231	−1.81525	−0.907623	−	0.419787i	$-0.862105\pi$
$491$	−40.2231	−1.81525	−0.907623	+	0.419787i	$0.862105\pi$
$492$	−2.13185	−0.0961112
$493$	38.2289	1.72174
$494$	−2.72112	−0.122429
$495$	−6.03243	−0.271138
$496$	−10.3129	−0.463064
$497$	−20.1830	−0.905332
$498$	−2.85809	−0.128074
$499$	−18.6263	−0.833828	−0.416914	−	0.908946i	$-0.636888\pi$
$499$	−18.6263	−0.833828	−0.416914	+	0.908946i	$0.636888\pi$
$500$	6.08402	0.272086
$501$	1.74296	0.0778695
$502$	25.9841	1.15973
$503$	−1.00162	−0.0446601	−0.0223301	−	0.999751i	$-0.507108\pi$
$503$	−1.00162	−0.0446601	−0.0223301	+	0.999751i	$0.507108\pi$
$504$	−3.77593	−0.168193
$505$	5.42600	0.241454
$506$	−19.5166	−0.867620
$507$	1.77207	0.0787006
$508$	−1.39508	−0.0618967
$509$	−9.65915	−0.428134	−0.214067	−	0.976819i	$-0.568671\pi$
$509$	−9.65915	−0.428134	−0.214067	+	0.976819i	$0.568671\pi$
$510$	1.57609	0.0697905
$511$	15.6049	0.690318
$512$	1.00000	0.0441942
$513$	−1.86842	−0.0824926
$514$	−18.5572	−0.818522
$515$	−9.23822	−0.407085
$516$	2.73786	0.120528
$517$	16.1700	0.711156
$518$	8.31447	0.365317
$519$	−4.18252	−0.183592
$520$	−1.72484	−0.0756392
$521$	−39.0538	−1.71098	−0.855489	−	0.517822i	$-0.826743\pi$
$521$	−39.0538	−1.71098	−0.855489	+	0.517822i	$0.826743\pi$
$522$	−14.1191	−0.617978
$523$	41.0561	1.79526	0.897628	−	0.440754i	$-0.145289\pi$
$523$	41.0561	1.79526	0.897628	+	0.440754i	$0.145289\pi$
$524$	−9.10667	−0.397827
$525$	1.89628	0.0827605
$526$	−20.5112	−0.894329
$527$	−80.9690	−3.52707
$528$	1.03940	0.0452339
$529$	12.3618	0.537468
$530$	−4.30266	−0.186896
$531$	−18.7382	−0.813170
$532$	−1.30218	−0.0564566
$533$	18.3173	0.793410
$534$	−0.573886	−0.0248345
$535$	−0.0244949	−0.00105901
$536$	−9.62712	−0.415828
$537$	−7.10232	−0.306488
$538$	−11.6832	−0.503700
$539$	17.4088	0.749849
$540$	−1.18433	−0.0509656
$541$	−0.289335	−0.0124395	−0.00621973	−	0.999981i	$-0.501980\pi$
$541$	−0.289335	−0.0124395	−0.00621973	+	0.999981i	$0.501980\pi$
$542$	16.9254	0.727008
$543$	−3.95878	−0.169887
$544$	7.85122	0.336618
$545$	6.67323	0.285850
$546$	−1.12218	−0.0480248
$547$	−7.33466	−0.313607	−0.156804	−	0.987630i	$-0.550119\pi$
$547$	−7.33466	−0.313607	−0.156804	+	0.987630i	$0.550119\pi$
$548$	22.7634	0.972405
$549$	−25.7659	−1.09966
$550$	15.0913	0.643495
$551$	−4.86917	−0.207434
$552$	−1.88326	−0.0801569
$553$	−13.2035	−0.561469
$554$	−10.7834	−0.458142
$555$	1.28176	0.0544078
$556$	17.9297	0.760387
$557$	11.7624	0.498389	0.249195	−	0.968453i	$-0.419834\pi$
$557$	11.7624	0.498389	0.249195	+	0.968453i	$0.419834\pi$
$558$	29.9044	1.26595
$559$	−23.5243	−0.994971
$560$	−0.825413	−0.0348801
$561$	8.16053	0.344538
$562$	0.140080	0.00590894
$563$	−16.8546	−0.710337	−0.355169	−	0.934802i	$-0.615577\pi$
$563$	−16.8546	−0.710337	−0.355169	+	0.934802i	$0.615577\pi$
$564$	1.56033	0.0657016
$565$	−6.09381	−0.256368
$566$	15.7665	0.662715
$567$	10.5573	0.443364
$568$	−15.4994	−0.650341
$569$	−30.4909	−1.27824	−0.639122	−	0.769106i	$-0.720702\pi$
$569$	−30.4909	−1.27824	−0.639122	+	0.769106i	$0.720702\pi$
$570$	−0.200745	−0.00840827
$571$	−9.28553	−0.388588	−0.194294	−	0.980943i	$-0.562242\pi$
$571$	−9.28553	−0.388588	−0.194294	+	0.980943i	$0.562242\pi$
$572$	−8.93071	−0.373412
$573$	−8.17281	−0.341424
$574$	8.76565	0.365871
$575$	−27.3436	−1.14031
$576$	−2.89970	−0.120821
$577$	41.2739	1.71825	0.859127	−	0.511762i	$-0.171007\pi$
$577$	41.2739	1.71825	0.859127	+	0.511762i	$0.171007\pi$
$578$	44.6417	1.85685
$579$	−3.10738	−0.129138
$580$	−3.08642	−0.128157
$581$	11.7518	0.487546
$582$	−3.71166	−0.153853
$583$	−22.2779	−0.922655
$584$	11.9836	0.495887
$585$	5.00152	0.206788
$586$	−19.3202	−0.798111
$587$	−13.3476	−0.550915	−0.275457	−	0.961313i	$-0.588829\pi$
$587$	−13.3476	−0.550915	−0.275457	+	0.961313i	$0.588829\pi$
$588$	1.67986	0.0692764
$589$	10.3129	0.424936
$590$	−4.09615	−0.168636
$591$	3.01886	0.124179
$592$	6.38504	0.262424
$593$	−28.3630	−1.16473	−0.582364	−	0.812928i	$-0.697872\pi$
$593$	−28.3630	−1.16473	−0.582364	+	0.812928i	$0.697872\pi$
$594$	−6.13213	−0.251604
$595$	−6.48051	−0.265675
$596$	12.6405	0.517775
$597$	−5.11508	−0.209346
$598$	16.1814	0.661705
$599$	30.7521	1.25650	0.628248	−	0.778013i	$-0.283772\pi$
$599$	30.7521	1.25650	0.628248	+	0.778013i	$0.283772\pi$
$600$	1.45624	0.0594506
$601$	35.3404	1.44156	0.720782	−	0.693162i	$-0.243783\pi$
$601$	35.3404	1.44156	0.720782	+	0.693162i	$0.243783\pi$
$602$	−11.2574	−0.458818
$603$	27.9158	1.13682
$604$	21.7335	0.884324
$605$	0.144848	0.00588891
$606$	2.71095	0.110125
$607$	−30.2690	−1.22858	−0.614290	−	0.789080i	$-0.710557\pi$
$607$	−30.2690	−1.22858	−0.614290	+	0.789080i	$0.710557\pi$
$608$	−1.00000	−0.0405554
$609$	−2.00802	−0.0813692
$610$	−5.63238	−0.228048
$611$	−13.4067	−0.542375
$612$	−22.7662	−0.920270
$613$	−19.8122	−0.800207	−0.400103	−	0.916470i	$-0.631026\pi$
$613$	−19.8122	−0.800207	−0.400103	+	0.916470i	$0.631026\pi$
$614$	−12.9088	−0.520957
$615$	1.35132	0.0544904
$616$	−4.27374	−0.172194
$617$	3.39011	0.136481	0.0682403	−	0.997669i	$-0.478262\pi$
$617$	3.39011	0.136481	0.0682403	+	0.997669i	$0.478262\pi$
$618$	−4.61563	−0.185668
$619$	38.3541	1.54158	0.770791	−	0.637088i	$-0.219861\pi$
$619$	38.3541	1.54158	0.770791	+	0.637088i	$0.219861\pi$
$620$	6.53706	0.262535
$621$	11.1107	0.445856
$622$	16.1837	0.648908
$623$	2.35968	0.0945385
$624$	−0.861770	−0.0344984
$625$	19.1346	0.765382
$626$	−30.7000	−1.22702
$627$	−1.03940	−0.0415095
$628$	6.16246	0.245909
$629$	50.1304	1.99883
$630$	2.39345	0.0953575
$631$	33.9402	1.35114	0.675569	−	0.737297i	$-0.263898\pi$
$631$	33.9402	1.35114	0.675569	+	0.737297i	$0.263898\pi$
$632$	−10.1395	−0.403329
$633$	0.316697	0.0125876
$634$	13.8118	0.548537
$635$	0.884301	0.0350924
$636$	−2.14971	−0.0852414
$637$	−14.4337	−0.571885
$638$	−15.9806	−0.632677
$639$	44.9437	1.77795
$640$	−0.633871	−0.0250559
$641$	19.7731	0.780990	0.390495	−	0.920605i	$-0.372304\pi$
$641$	19.7731	0.780990	0.390495	+	0.920605i	$0.372304\pi$
$642$	−0.0122382	−0.000483004 0
$643$	−37.2279	−1.46813	−0.734063	−	0.679081i	$-0.762379\pi$
$643$	−37.2279	−1.46813	−0.734063	+	0.679081i	$0.762379\pi$
$644$	7.74351	0.305137
$645$	−1.73545	−0.0683333
$646$	−7.85122	−0.308902
$647$	39.8723	1.56754	0.783770	−	0.621051i	$-0.213294\pi$
$647$	39.8723	1.56754	0.783770	+	0.621051i	$0.213294\pi$
$648$	8.10739	0.318488
$649$	−21.2087	−0.832513
$650$	−12.5123	−0.490772
$651$	4.25300	0.166688
$652$	−11.7577	−0.460467
$653$	−15.0879	−0.590434	−0.295217	−	0.955430i	$-0.595392\pi$
$653$	−15.0879	−0.590434	−0.295217	+	0.955430i	$0.595392\pi$
$654$	3.33410	0.130374
$655$	5.77245	0.225548
$656$	6.73152	0.262822
$657$	−34.7490	−1.35569
$658$	−6.41569	−0.250109
$659$	−27.2238	−1.06049	−0.530245	−	0.847844i	$-0.677900\pi$
$659$	−27.2238	−1.06049	−0.530245	+	0.847844i	$0.677900\pi$
$660$	−0.658843	−0.0256454
$661$	8.89511	0.345980	0.172990	−	0.984924i	$-0.444657\pi$
$661$	8.89511	0.345980	0.172990	+	0.984924i	$0.444657\pi$
$662$	−13.2313	−0.514248
$663$	−6.76595	−0.262768
$664$	9.02471	0.350227
$665$	0.825413	0.0320082
$666$	−18.5147	−0.717431
$667$	28.9549	1.12114
$668$	−5.50355	−0.212939
$669$	−1.90403	−0.0736141
$670$	6.10235	0.235754
$671$	−29.1628	−1.12582
$672$	−0.412396	−0.0159085
$673$	−7.04337	−0.271502	−0.135751	−	0.990743i	$-0.543345\pi$
$673$	−7.04337	−0.271502	−0.135751	+	0.990743i	$0.543345\pi$
$674$	20.4876	0.789153
$675$	−8.59136	−0.330682
$676$	−5.59549	−0.215211
$677$	44.6504	1.71605	0.858027	−	0.513604i	$-0.171690\pi$
$677$	44.6504	1.71605	0.858027	+	0.513604i	$0.171690\pi$
$678$	−3.04461	−0.116927
$679$	15.2614	0.585680
$680$	−4.97666	−0.190846
$681$	−0.144432	−0.00553466
$682$	33.8469	1.29607
$683$	17.4383	0.667259	0.333629	−	0.942704i	$-0.391727\pi$
$683$	17.4383	0.667259	0.333629	+	0.942704i	$0.391727\pi$
$684$	2.89970	0.110873
$685$	−14.4291	−0.551307
$686$	−16.0224	−0.611740
$687$	−2.19558	−0.0837666
$688$	−8.64507	−0.329590
$689$	18.4707	0.703679
$690$	1.19374	0.0454451
$691$	43.9575	1.67222	0.836110	−	0.548561i	$-0.184824\pi$
$691$	43.9575	1.67222	0.836110	+	0.548561i	$0.184824\pi$
$692$	13.2067	0.502044
$693$	12.3926	0.470756
$694$	−23.1980	−0.880583
$695$	−11.3651	−0.431103
$696$	−1.54205	−0.0584512
$697$	52.8507	2.00186
$698$	−2.16227	−0.0818430
$699$	−2.65780	−0.100527
$700$	−5.98769	−0.226313
$701$	32.3793	1.22295	0.611475	−	0.791264i	$-0.290576\pi$
$701$	32.3793	1.22295	0.611475	+	0.791264i	$0.290576\pi$
$702$	5.08419	0.191890
$703$	−6.38504	−0.240816
$704$	−3.28199	−0.123695
$705$	−0.989046	−0.0372496
$706$	−15.5308	−0.584511
$707$	−11.1468	−0.419218
$708$	−2.04653	−0.0769134
$709$	−22.7288	−0.853596	−0.426798	−	0.904347i	$-0.640359\pi$
$709$	−22.7288	−0.853596	−0.426798	+	0.904347i	$0.640359\pi$
$710$	9.82463	0.368712
$711$	29.4016	1.10265
$712$	1.81210	0.0679113
$713$	−61.3266	−2.29670
$714$	−3.23781	−0.121172
$715$	5.66092	0.211706
$716$	22.4263	0.838109
$717$	0.714957	0.0267006
$718$	−21.9983	−0.820968
$719$	21.6467	0.807284	0.403642	−	0.914917i	$-0.367744\pi$
$719$	21.6467	0.807284	0.403642	+	0.914917i	$0.367744\pi$
$720$	1.83804	0.0684996
$721$	18.9783	0.706791
$722$	1.00000	0.0372161
$723$	−1.62916	−0.0605892
$724$	12.5002	0.464567
$725$	−22.3894	−0.831523
$726$	0.0723694	0.00268588
$727$	23.8204	0.883451	0.441726	−	0.897150i	$-0.354366\pi$
$727$	23.8204	0.883451	0.441726	+	0.897150i	$0.354366\pi$
$728$	3.54339	0.131327
$729$	−21.7339	−0.804958
$730$	−7.59608	−0.281144
$731$	−67.8743	−2.51042
$732$	−2.81407	−0.104011
$733$	16.1370	0.596032	0.298016	−	0.954561i	$-0.403675\pi$
$733$	16.1370	0.596032	0.298016	+	0.954561i	$0.403675\pi$
$734$	25.2122	0.930599
$735$	−1.06482	−0.0392763
$736$	5.94658	0.219194
$737$	31.5961	1.16386
$738$	−19.5194	−0.718520
$739$	52.5146	1.93178	0.965889	−	0.258955i	$-0.0833780\pi$
$739$	52.5146	1.93178	0.965889	+	0.258955i	$0.0833780\pi$
$740$	−4.04729	−0.148781
$741$	0.861770	0.0316579
$742$	8.83907	0.324493
$743$	−6.84173	−0.250999	−0.125499	−	0.992094i	$-0.540053\pi$
$743$	−6.84173	−0.250999	−0.125499	+	0.992094i	$0.540053\pi$
$744$	3.26607	0.119740
$745$	−8.01245	−0.293553
$746$	22.5197	0.824505
$747$	−26.1690	−0.957473
$748$	−25.7677	−0.942159
$749$	0.0503206	0.00183867
$750$	−1.92679	−0.0703564
$751$	7.49789	0.273602	0.136801	−	0.990599i	$-0.456318\pi$
$751$	7.49789	0.273602	0.136801	+	0.990599i	$0.456318\pi$
$752$	−4.92688	−0.179665
$753$	−8.22909	−0.299885
$754$	13.2496	0.482522
$755$	−13.7762	−0.501368
$756$	2.43301	0.0884878
$757$	1.81117	0.0658283	0.0329141	−	0.999458i	$-0.489521\pi$
$757$	1.81117	0.0658283	0.0329141	+	0.999458i	$0.489521\pi$
$758$	−18.1362	−0.658736
$759$	6.18085	0.224351
$760$	0.633871	0.0229929
$761$	−12.4752	−0.452226	−0.226113	−	0.974101i	$-0.572602\pi$
$761$	−12.4752	−0.452226	−0.226113	+	0.974101i	$0.572602\pi$
$762$	0.441817	0.0160054
$763$	−13.7090	−0.496299
$764$	25.8064	0.933644
$765$	14.4308	0.521748
$766$	18.7929	0.679014
$767$	17.5842	0.634930
$768$	−0.316697	−0.0114278
$769$	−4.38194	−0.158017	−0.0790084	−	0.996874i	$-0.525175\pi$
$769$	−4.38194	−0.158017	−0.0790084	+	0.996874i	$0.525175\pi$
$770$	2.70900	0.0976257
$771$	5.87699	0.211655
$772$	9.81184	0.353136
$773$	2.17024	0.0780582	0.0390291	−	0.999238i	$-0.487573\pi$
$773$	2.17024	0.0780582	0.0390291	+	0.999238i	$0.487573\pi$
$774$	25.0681	0.901055
$775$	47.4209	1.70341
$776$	11.7199	0.420721
$777$	−2.63316	−0.0944642
$778$	26.0243	0.933017
$779$	−6.73152	−0.241182
$780$	0.546251	0.0195589
$781$	50.8690	1.82024
$782$	46.6879	1.66956
$783$	9.09763	0.325123
$784$	−5.30433	−0.189440
$785$	−3.90620	−0.139418
$786$	2.88405	0.102871
$787$	24.3865	0.869283	0.434642	−	0.900603i	$-0.356875\pi$
$787$	24.3865	0.869283	0.434642	+	0.900603i	$0.356875\pi$
$788$	−9.53236	−0.339576
$789$	6.49581	0.231257
$790$	6.42715	0.228668
$791$	12.5187	0.445113
$792$	9.51681	0.338165
$793$	24.1790	0.858623
$794$	13.7105	0.486567
$795$	1.36264	0.0483277
$796$	16.1514	0.572470
$797$	−25.2277	−0.893610	−0.446805	−	0.894631i	$-0.647438\pi$
$797$	−25.2277	−0.893610	−0.446805	+	0.894631i	$0.647438\pi$
$798$	0.412396	0.0145986
$799$	−38.6821	−1.36847
$800$	−4.59821	−0.162571
$801$	−5.25455	−0.185661
$802$	−37.7874	−1.33432
$803$	−39.3303	−1.38793
$804$	3.04887	0.107526
$805$	−4.90838	−0.172998
$806$	−28.0627	−0.988467
$807$	3.70004	0.130248
$808$	−8.56010	−0.301143
$809$	−11.7622	−0.413537	−0.206768	−	0.978390i	$-0.566295\pi$
$809$	−11.7622	−0.413537	−0.206768	+	0.978390i	$0.566295\pi$
$810$	−5.13904	−0.180567
$811$	46.9368	1.64817	0.824087	−	0.566464i	$-0.191689\pi$
$811$	46.9368	1.64817	0.824087	+	0.566464i	$0.191689\pi$
$812$	6.34053	0.222509
$813$	−5.36021	−0.187991
$814$	−20.9557	−0.734496
$815$	7.45286	0.261062
$816$	−2.48646	−0.0870434
$817$	8.64507	0.302453
$818$	−20.1267	−0.703712
$819$	−10.2748	−0.359030
$820$	−4.26692	−0.149007
$821$	2.44949	0.0854878	0.0427439	−	0.999086i	$-0.486390\pi$
$821$	2.44949	0.0854878	0.0427439	+	0.999086i	$0.486390\pi$
$822$	−7.20910	−0.251446
$823$	−15.8230	−0.551554	−0.275777	−	0.961222i	$-0.588935\pi$
$823$	−15.8230	−0.551554	−0.275777	+	0.961222i	$0.588935\pi$
$824$	14.5743	0.507720
$825$	−4.77936	−0.166396
$826$	8.41484	0.292790
$827$	−29.8591	−1.03830	−0.519151	−	0.854683i	$-0.673752\pi$
$827$	−29.8591	−1.03830	−0.519151	+	0.854683i	$0.673752\pi$
$828$	−17.2433	−0.599246
$829$	−39.4678	−1.37078	−0.685388	−	0.728178i	$-0.740367\pi$
$829$	−39.4678	−1.37078	−0.685388	+	0.728178i	$0.740367\pi$
$830$	−5.72050	−0.198561
$831$	3.41506	0.118467
$832$	2.72112	0.0943379
$833$	−41.6455	−1.44293
$834$	−5.67826	−0.196622
$835$	3.48854	0.120726
$836$	3.28199	0.113510
$837$	−19.2688	−0.666028
$838$	−29.3823	−1.01499
$839$	−29.3345	−1.01274	−0.506370	−	0.862316i	$-0.669013\pi$
$839$	−29.3345	−1.01274	−0.506370	+	0.862316i	$0.669013\pi$
$840$	0.261406	0.00901935
$841$	−5.29120	−0.182455
$842$	3.09990	0.106830
$843$	−0.0443630	−0.00152794
$844$	−1.00000	−0.0344214
$845$	3.54682	0.122014
$846$	14.2865	0.491180
$847$	−0.297565	−0.0102245
$848$	6.78791	0.233098
$849$	−4.99319	−0.171366
$850$	−36.1016	−1.23827
$851$	37.9691	1.30157
$852$	4.90861	0.168166
$853$	20.6330	0.706461	0.353231	−	0.935536i	$-0.385083\pi$
$853$	20.6330	0.706461	0.353231	+	0.935536i	$0.385083\pi$
$854$	11.5708	0.395943
$855$	−1.83804	−0.0628596
$856$	0.0386434	0.00132080
$857$	11.7409	0.401063	0.200531	−	0.979687i	$-0.435733\pi$
$857$	11.7409	0.401063	0.200531	+	0.979687i	$0.435733\pi$
$858$	2.82832	0.0965574
$859$	−22.3891	−0.763906	−0.381953	−	0.924182i	$-0.624748\pi$
$859$	−22.3891	−0.763906	−0.381953	+	0.924182i	$0.624748\pi$
$860$	5.47986	0.186862
$861$	−2.77605	−0.0946075
$862$	1.55279	0.0528883
$863$	−37.9279	−1.29108	−0.645540	−	0.763727i	$-0.723368\pi$
$863$	−37.9279	−1.29108	−0.645540	+	0.763727i	$0.723368\pi$
$864$	1.86842	0.0635648
$865$	−8.37135	−0.284634
$866$	−9.38182	−0.318807
$867$	−14.1379	−0.480147
$868$	−13.4293	−0.455819
$869$	33.2779	1.12887
$870$	0.977460	0.0331390
$871$	−26.1966	−0.887636
$872$	−10.5277	−0.356514
$873$	−33.9843	−1.15019
$874$	−5.94658	−0.201146
$875$	7.92249	0.267829
$876$	−3.79518	−0.128227
$877$	30.0165	1.01358	0.506792	−	0.862068i	$-0.330831\pi$
$877$	30.0165	1.01358	0.506792	+	0.862068i	$0.330831\pi$
$878$	7.35006	0.248052
$879$	6.11864	0.206377
$880$	2.08036	0.0701289
$881$	−24.7663	−0.834399	−0.417199	−	0.908815i	$-0.636988\pi$
$881$	−24.7663	−0.834399	−0.417199	+	0.908815i	$0.636988\pi$
$882$	15.3810	0.517905
$883$	−13.1762	−0.443413	−0.221707	−	0.975113i	$-0.571163\pi$
$883$	−13.1762	−0.443413	−0.221707	+	0.975113i	$0.571163\pi$
$884$	21.3641	0.718554
$885$	1.29724	0.0436062
$886$	−19.9342	−0.669703
$887$	16.7332	0.561846	0.280923	−	0.959730i	$-0.409360\pi$
$887$	16.7332	0.561846	0.280923	+	0.959730i	$0.409360\pi$
$888$	−2.02212	−0.0678579
$889$	−1.81665	−0.0609283
$890$	−1.14864	−0.0385024
$891$	−26.6084	−0.891415
$892$	6.01217	0.201302
$893$	4.92688	0.164872
$894$	−4.00321	−0.133887
$895$	−14.2154	−0.475167
$896$	1.30218	0.0435027
$897$	−5.12458	−0.171105
$898$	−14.5104	−0.484218
$899$	−50.2153	−1.67478
$900$	13.3334	0.444448
$901$	53.2934	1.77546
$902$	−22.0928	−0.735610
$903$	3.56519	0.118642
$904$	9.61364	0.319745
$905$	−7.92353	−0.263387
$906$	−6.88292	−0.228670
$907$	56.2603	1.86809	0.934047	−	0.357151i	$-0.116252\pi$
$907$	56.2603	1.86809	0.934047	+	0.357151i	$0.116252\pi$
$908$	0.456059	0.0151348
$909$	24.8217	0.823285
$910$	−2.24605	−0.0744559
$911$	16.4810	0.546040	0.273020	−	0.962008i	$-0.411978\pi$
$911$	16.4810	0.546040	0.273020	+	0.962008i	$0.411978\pi$
$912$	0.316697	0.0104869
$913$	−29.6190	−0.980247
$914$	9.65001	0.319194
$915$	1.78376	0.0589691
$916$	6.93276	0.229065
$917$	−11.8585	−0.391603
$918$	14.6693	0.484161
$919$	−23.7440	−0.783243	−0.391621	−	0.920126i	$-0.628086\pi$
$919$	−23.7440	−0.783243	−0.391621	+	0.920126i	$0.628086\pi$
$920$	−3.76936	−0.124272
$921$	4.08818	0.134710
$922$	−3.51618	−0.115799
$923$	−42.1758	−1.38823
$924$	1.35348	0.0445262
$925$	−29.3597	−0.965343
$926$	−14.2805	−0.469287
$927$	−42.2611	−1.38804
$928$	4.86917	0.159838
$929$	16.3866	0.537629	0.268814	−	0.963192i	$-0.413368\pi$
$929$	16.3866	0.537629	0.268814	+	0.963192i	$0.413368\pi$
$930$	−2.07026	−0.0678866
$931$	5.30433	0.173842
$932$	8.39227	0.274898
$933$	−5.12533	−0.167796
$934$	−7.93248	−0.259559
$935$	16.3334	0.534159
$936$	−7.89045	−0.257907
$937$	−4.14264	−0.135334	−0.0676670	−	0.997708i	$-0.521556\pi$
$937$	−4.14264	−0.135334	−0.0676670	+	0.997708i	$0.521556\pi$
$938$	−12.5362	−0.409322
$939$	9.72258	0.317284
$940$	3.12301	0.101861
$941$	30.2726	0.986858	0.493429	−	0.869786i	$-0.335743\pi$
$941$	30.2726	0.986858	0.493429	+	0.869786i	$0.335743\pi$
$942$	−1.95163	−0.0635875
$943$	40.0295	1.30354
$944$	6.46212	0.210324
$945$	−1.54222	−0.0501683
$946$	28.3731	0.922488
$947$	−19.0803	−0.620028	−0.310014	−	0.950732i	$-0.600334\pi$
$947$	−19.0803	−0.620028	−0.310014	+	0.950732i	$0.600334\pi$
$948$	3.21115	0.104293
$949$	32.6090	1.05853
$950$	4.59821	0.149186
$951$	−4.37415	−0.141841
$952$	10.2237	0.331352
$953$	−9.67680	−0.313462	−0.156731	−	0.987641i	$-0.550096\pi$
$953$	−9.67680	−0.313462	−0.156731	+	0.987641i	$0.550096\pi$
$954$	−19.6829	−0.637258
$955$	−16.3579	−0.529331
$956$	−2.25755	−0.0730143
$957$	5.06100	0.163599
$958$	21.1612	0.683686
$959$	29.6421	0.957192
$960$	0.200745	0.00647901
$961$	75.3563	2.43085
$962$	17.3745	0.560176
$963$	−0.112054	−0.00361090
$964$	5.14424	0.165685
$965$	−6.21944	−0.200211
$966$	−2.45234	−0.0789028
$967$	−1.57849	−0.0507607	−0.0253804	−	0.999678i	$-0.508080\pi$
$967$	−1.57849	−0.0507607	−0.0253804	+	0.999678i	$0.508080\pi$
$968$	−0.228513	−0.00734470
$969$	2.48646	0.0798765
$970$	−7.42892	−0.238528
$971$	−15.3795	−0.493552	−0.246776	−	0.969073i	$-0.579371\pi$
$971$	−15.3795	−0.493552	−0.246776	+	0.969073i	$0.579371\pi$
$972$	−8.17283	−0.262144
$973$	23.3476	0.748491
$974$	−17.4317	−0.558549
$975$	3.96260	0.126905
$976$	8.88569	0.284424
$977$	−32.8029	−1.04946	−0.524729	−	0.851269i	$-0.675833\pi$
$977$	−32.8029	−1.04946	−0.524729	+	0.851269i	$0.675833\pi$
$978$	3.72362	0.119068
$979$	−5.94730	−0.190077
$980$	3.36226	0.107403
$981$	30.5273	0.974663
$982$	−40.2231	−1.28357
$983$	19.2148	0.612858	0.306429	−	0.951894i	$-0.400866\pi$
$983$	19.2148	0.612858	0.306429	+	0.951894i	$0.400866\pi$
$984$	−2.13185	−0.0679609
$985$	6.04228	0.192523
$986$	38.2289	1.21746
$987$	2.03183	0.0646737
$988$	−2.72112	−0.0865704
$989$	−51.4085	−1.63470
$990$	−6.03243	−0.191723
$991$	−12.3138	−0.391160	−0.195580	−	0.980688i	$-0.562659\pi$
$991$	−12.3138	−0.391160	−0.195580	+	0.980688i	$0.562659\pi$
$992$	−10.3129	−0.327436
$993$	4.19030	0.132975
$994$	−20.1830	−0.640167
$995$	−10.2379	−0.324563
$996$	−2.85809	−0.0905622
$997$	−46.7594	−1.48088	−0.740442	−	0.672121i	$-0.765384\pi$
$997$	−46.7594	−1.48088	−0.740442	+	0.672121i	$0.765384\pi$
$998$	−18.6263	−0.589606
$999$	11.9299	0.377446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.20	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.20	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.316697 q^{3} +1.00000 q^{4} -0.633871 q^{5} -0.316697 q^{6} +1.30218 q^{7} +1.00000 q^{8} -2.89970 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.316697 q^{3} +1.00000 q^{4} -0.633871 q^{5} -0.316697 q^{6} +1.30218 q^{7} +1.00000 q^{8} -2.89970 q^{9} -0.633871 q^{10} -3.28199 q^{11} -0.316697 q^{12} +2.72112 q^{13} +1.30218 q^{14} +0.200745 q^{15} +1.00000 q^{16} +7.85122 q^{17} -2.89970 q^{18} -1.00000 q^{19} -0.633871 q^{20} -0.412396 q^{21} -3.28199 q^{22} +5.94658 q^{23} -0.316697 q^{24} -4.59821 q^{25} +2.72112 q^{26} +1.86842 q^{27} +1.30218 q^{28} +4.86917 q^{29} +0.200745 q^{30} -10.3129 q^{31} +1.00000 q^{32} +1.03940 q^{33} +7.85122 q^{34} -0.825413 q^{35} -2.89970 q^{36} +6.38504 q^{37} -1.00000 q^{38} -0.861770 q^{39} -0.633871 q^{40} +6.73152 q^{41} -0.412396 q^{42} -8.64507 q^{43} -3.28199 q^{44} +1.83804 q^{45} +5.94658 q^{46} -4.92688 q^{47} -0.316697 q^{48} -5.30433 q^{49} -4.59821 q^{50} -2.48646 q^{51} +2.72112 q^{52} +6.78791 q^{53} +1.86842 q^{54} +2.08036 q^{55} +1.30218 q^{56} +0.316697 q^{57} +4.86917 q^{58} +6.46212 q^{59} +0.200745 q^{60} +8.88569 q^{61} -10.3129 q^{62} -3.77593 q^{63} +1.00000 q^{64} -1.72484 q^{65} +1.03940 q^{66} -9.62712 q^{67} +7.85122 q^{68} -1.88326 q^{69} -0.825413 q^{70} -15.4994 q^{71} -2.89970 q^{72} +11.9836 q^{73} +6.38504 q^{74} +1.45624 q^{75} -1.00000 q^{76} -4.27374 q^{77} -0.861770 q^{78} -10.1395 q^{79} -0.633871 q^{80} +8.10739 q^{81} +6.73152 q^{82} +9.02471 q^{83} -0.412396 q^{84} -4.97666 q^{85} -8.64507 q^{86} -1.54205 q^{87} -3.28199 q^{88} +1.81210 q^{89} +1.83804 q^{90} +3.54339 q^{91} +5.94658 q^{92} +3.26607 q^{93} -4.92688 q^{94} +0.633871 q^{95} -0.316697 q^{96} +11.7199 q^{97} -5.30433 q^{98} +9.51681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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