LMFDB - Embedded newform 447.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [447,2,Mod(1,447)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(447, 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("447.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 447 = 3 \cdot 149 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	447.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:	$3.56931297035$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 12x^{8} + 37x^{7} + 44x^{6} - 142x^{5} - 50x^{4} + 181x^{3} - 5x^{2} - 30x + 1 $ x^10 - 3x^9 - 12x^8 + 37x^7 + 44x^6 - 142x^5 - 50x^4 + 181x^3 - 5x^2 - 30*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.41389$ of defining polynomial
Character	$\chi$	$=$	447.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41389 q^{2} -1.00000 q^{3} -0.000922380 q^{4} +3.18405 q^{5} -1.41389 q^{6} +4.73714 q^{7} -2.82908 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.41389 q^{2} -1.00000 q^{3} -0.000922380 q^{4} +3.18405 q^{5} -1.41389 q^{6} +4.73714 q^{7} -2.82908 q^{8} +1.00000 q^{9} +4.50188 q^{10} -5.19316 q^{11} +0.000922380 q^{12} -1.23507 q^{13} +6.69778 q^{14} -3.18405 q^{15} -3.99815 q^{16} +6.28281 q^{17} +1.41389 q^{18} +6.58961 q^{19} -0.00293690 q^{20} -4.73714 q^{21} -7.34254 q^{22} +2.49398 q^{23} +2.82908 q^{24} +5.13815 q^{25} -1.74625 q^{26} -1.00000 q^{27} -0.00436944 q^{28} -4.54091 q^{29} -4.50188 q^{30} -1.69003 q^{31} +0.00521777 q^{32} +5.19316 q^{33} +8.88319 q^{34} +15.0833 q^{35} -0.000922380 q^{36} -3.71429 q^{37} +9.31696 q^{38} +1.23507 q^{39} -9.00792 q^{40} +1.75395 q^{41} -6.69778 q^{42} -10.4820 q^{43} +0.00479006 q^{44} +3.18405 q^{45} +3.52621 q^{46} -9.53857 q^{47} +3.99815 q^{48} +15.4405 q^{49} +7.26476 q^{50} -6.28281 q^{51} +0.00113920 q^{52} -8.13686 q^{53} -1.41389 q^{54} -16.5352 q^{55} -13.4017 q^{56} -6.58961 q^{57} -6.42033 q^{58} +1.85642 q^{59} +0.00293690 q^{60} +9.90116 q^{61} -2.38952 q^{62} +4.73714 q^{63} +8.00369 q^{64} -3.93252 q^{65} +7.34254 q^{66} -12.1542 q^{67} -0.00579514 q^{68} -2.49398 q^{69} +21.3260 q^{70} -12.3113 q^{71} -2.82908 q^{72} +8.10393 q^{73} -5.25159 q^{74} -5.13815 q^{75} -0.00607812 q^{76} -24.6007 q^{77} +1.74625 q^{78} -5.50748 q^{79} -12.7303 q^{80} +1.00000 q^{81} +2.47989 q^{82} -10.7628 q^{83} +0.00436944 q^{84} +20.0048 q^{85} -14.8204 q^{86} +4.54091 q^{87} +14.6918 q^{88} -6.37036 q^{89} +4.50188 q^{90} -5.85069 q^{91} -0.00230040 q^{92} +1.69003 q^{93} -13.4865 q^{94} +20.9816 q^{95} -0.00521777 q^{96} +6.63646 q^{97} +21.8311 q^{98} -5.19316 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 13 q^{4} + 4 q^{5} - 3 q^{6} + 9 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 13 * q^4 + 4 * q^5 - 3 * q^6 + 9 * q^7 + 12 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 13 q^{4} + 4 q^{5} - 3 q^{6} + 9 q^{7} + 12 q^{8} + 10 q^{9} + 8 q^{10} - 7 q^{11} - 13 q^{12} + 4 q^{13} - q^{14} - 4 q^{15} + 23 q^{16} + 10 q^{17} + 3 q^{18} + 9 q^{19} + 6 q^{20} - 9 q^{21} + 12 q^{22} + 9 q^{23} - 12 q^{24} + 34 q^{25} - 12 q^{26} - 10 q^{27} + 30 q^{28} + 8 q^{29} - 8 q^{30} + 15 q^{31} + 32 q^{32} + 7 q^{33} + 12 q^{34} - 16 q^{35} + 13 q^{36} + 31 q^{37} - q^{38} - 4 q^{39} + 2 q^{40} - 5 q^{41} + q^{42} + 8 q^{43} - 9 q^{44} + 4 q^{45} - 11 q^{46} + 2 q^{47} - 23 q^{48} + 29 q^{49} - 7 q^{50} - 10 q^{51} - 40 q^{52} + 4 q^{53} - 3 q^{54} - 2 q^{55} - 48 q^{56} - 9 q^{57} - 8 q^{58} - 59 q^{59} - 6 q^{60} + q^{61} - 14 q^{62} + 9 q^{63} + 24 q^{64} + 12 q^{65} - 12 q^{66} + 5 q^{67} - 12 q^{68} - 9 q^{69} - 34 q^{70} - 11 q^{71} + 12 q^{72} + 51 q^{73} - 23 q^{74} - 34 q^{75} - 27 q^{76} + 4 q^{77} + 12 q^{78} - 6 q^{79} + 10 q^{80} + 10 q^{81} - 40 q^{82} - 21 q^{83} - 30 q^{84} + 32 q^{85} - 44 q^{86} - 8 q^{87} - 29 q^{88} - 5 q^{89} + 8 q^{90} - 6 q^{91} - 14 q^{92} - 15 q^{93} - 42 q^{94} - 24 q^{95} - 32 q^{96} + 32 q^{97} + 14 q^{98} - 7 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 13 * q^4 + 4 * q^5 - 3 * q^6 + 9 * q^7 + 12 * q^8 + 10 * q^9 + 8 * q^10 - 7 * q^11 - 13 * q^12 + 4 * q^13 - q^14 - 4 * q^15 + 23 * q^16 + 10 * q^17 + 3 * q^18 + 9 * q^19 + 6 * q^20 - 9 * q^21 + 12 * q^22 + 9 * q^23 - 12 * q^24 + 34 * q^25 - 12 * q^26 - 10 * q^27 + 30 * q^28 + 8 * q^29 - 8 * q^30 + 15 * q^31 + 32 * q^32 + 7 * q^33 + 12 * q^34 - 16 * q^35 + 13 * q^36 + 31 * q^37 - q^38 - 4 * q^39 + 2 * q^40 - 5 * q^41 + q^42 + 8 * q^43 - 9 * q^44 + 4 * q^45 - 11 * q^46 + 2 * q^47 - 23 * q^48 + 29 * q^49 - 7 * q^50 - 10 * q^51 - 40 * q^52 + 4 * q^53 - 3 * q^54 - 2 * q^55 - 48 * q^56 - 9 * q^57 - 8 * q^58 - 59 * q^59 - 6 * q^60 + q^61 - 14 * q^62 + 9 * q^63 + 24 * q^64 + 12 * q^65 - 12 * q^66 + 5 * q^67 - 12 * q^68 - 9 * q^69 - 34 * q^70 - 11 * q^71 + 12 * q^72 + 51 * q^73 - 23 * q^74 - 34 * q^75 - 27 * q^76 + 4 * q^77 + 12 * q^78 - 6 * q^79 + 10 * q^80 + 10 * q^81 - 40 * q^82 - 21 * q^83 - 30 * q^84 + 32 * q^85 - 44 * q^86 - 8 * q^87 - 29 * q^88 - 5 * q^89 + 8 * q^90 - 6 * q^91 - 14 * q^92 - 15 * q^93 - 42 * q^94 - 24 * q^95 - 32 * q^96 + 32 * q^97 + 14 * q^98 - 7 * 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 $

$2$	1.41389	0.999769	0.499885	−	0.866092i	$-0.333376\pi$
$2$	1.41389	0.999769	0.499885	+	0.866092i	$0.333376\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.000922380 0	−0.000461190 0
$5$	3.18405	1.42395	0.711974	−	0.702206i	$-0.247801\pi$
$5$	3.18405	1.42395	0.711974	+	0.702206i	$0.247801\pi$
$6$	−1.41389	−0.577217
$7$	4.73714	1.79047	0.895235	−	0.445594i	$-0.147008\pi$
$7$	4.73714	1.79047	0.895235	+	0.445594i	$0.147008\pi$
$8$	−2.82908	−1.00023
$9$	1.00000	0.333333
$10$	4.50188	1.42362
$11$	−5.19316	−1.56580	−0.782898	−	0.622150i	$-0.786259\pi$
$11$	−5.19316	−1.56580	−0.782898	+	0.622150i	$0.786259\pi$
$12$	0.000922380 0	0.000266268 0
$13$	−1.23507	−0.342547	−0.171273	−	0.985224i	$-0.554788\pi$
$13$	−1.23507	−0.342547	−0.171273	+	0.985224i	$0.554788\pi$
$14$	6.69778	1.79006
$15$	−3.18405	−0.822117
$16$	−3.99815	−0.999539
$17$	6.28281	1.52381	0.761903	−	0.647691i	$-0.224265\pi$
$17$	6.28281	1.52381	0.761903	+	0.647691i	$0.224265\pi$
$18$	1.41389	0.333256
$19$	6.58961	1.51176	0.755880	−	0.654710i	$-0.227209\pi$
$19$	6.58961	1.51176	0.755880	+	0.654710i	$0.227209\pi$
$20$	−0.00293690	−0.000656711 0
$21$	−4.73714	−1.03373
$22$	−7.34254	−1.56543
$23$	2.49398	0.520031	0.260015	−	0.965604i	$-0.416272\pi$
$23$	2.49398	0.520031	0.260015	+	0.965604i	$0.416272\pi$
$24$	2.82908	0.577483
$25$	5.13815	1.02763
$26$	−1.74625	−0.342468
$27$	−1.00000	−0.192450
$28$	−0.00436944	−0.000825747 0
$29$	−4.54091	−0.843225	−0.421613	−	0.906776i	$-0.638536\pi$
$29$	−4.54091	−0.843225	−0.421613	+	0.906776i	$0.638536\pi$
$30$	−4.50188	−0.821928
$31$	−1.69003	−0.303539	−0.151769	−	0.988416i	$-0.548497\pi$
$31$	−1.69003	−0.303539	−0.151769	+	0.988416i	$0.548497\pi$
$32$	0.00521777	0.000922380 0
$33$	5.19316	0.904012
$34$	8.88319	1.52345
$35$	15.0833	2.54954
$36$	−0.000922380 0	−0.000153730 0
$37$	−3.71429	−0.610625	−0.305313	−	0.952252i	$-0.598761\pi$
$37$	−3.71429	−0.610625	−0.305313	+	0.952252i	$0.598761\pi$
$38$	9.31696	1.51141
$39$	1.23507	0.197769
$40$	−9.00792	−1.42428
$41$	1.75395	0.273921	0.136961	−	0.990576i	$-0.456267\pi$
$41$	1.75395	0.273921	0.136961	+	0.990576i	$0.456267\pi$
$42$	−6.69778	−1.03349
$43$	−10.4820	−1.59849	−0.799244	−	0.601006i	$-0.794767\pi$
$43$	−10.4820	−1.59849	−0.799244	+	0.601006i	$0.794767\pi$
$44$	0.00479006	0.000722129 0
$45$	3.18405	0.474650
$46$	3.52621	0.519911
$47$	−9.53857	−1.39134	−0.695672	−	0.718360i	$-0.744893\pi$
$47$	−9.53857	−1.39134	−0.695672	+	0.718360i	$0.744893\pi$
$48$	3.99815	0.577084
$49$	15.4405	2.20578
$50$	7.26476	1.02739
$51$	−6.28281	−0.879770
$52$	0.00113920	0.000157979 0
$53$	−8.13686	−1.11768	−0.558842	−	0.829274i	$-0.688754\pi$
$53$	−8.13686	−1.11768	−0.558842	+	0.829274i	$0.688754\pi$
$54$	−1.41389	−0.192406
$55$	−16.5352	−2.22961
$56$	−13.4017	−1.79088
$57$	−6.58961	−0.872815
$58$	−6.42033	−0.843031
$59$	1.85642	0.241685	0.120843	−	0.992672i	$-0.461440\pi$
$59$	1.85642	0.241685	0.120843	+	0.992672i	$0.461440\pi$
$60$	0.00293690	0.000379152 0
$61$	9.90116	1.26771	0.633857	−	0.773450i	$-0.281471\pi$
$61$	9.90116	1.26771	0.633857	+	0.773450i	$0.281471\pi$
$62$	−2.38952	−0.303469
$63$	4.73714	0.596823
$64$	8.00369	1.00046
$65$	−3.93252	−0.487769
$66$	7.34254	0.903804
$67$	−12.1542	−1.48487	−0.742435	−	0.669918i	$-0.766329\pi$
$67$	−12.1542	−1.48487	−0.742435	+	0.669918i	$0.766329\pi$
$68$	−0.00579514	−0.000702764 0
$69$	−2.49398	−0.300240
$70$	21.3260	2.54895
$71$	−12.3113	−1.46108	−0.730542	−	0.682868i	$-0.760732\pi$
$71$	−12.3113	−1.46108	−0.730542	+	0.682868i	$0.760732\pi$
$72$	−2.82908	−0.333410
$73$	8.10393	0.948493	0.474246	−	0.880392i	$-0.342721\pi$
$73$	8.10393	0.948493	0.474246	+	0.880392i	$0.342721\pi$
$74$	−5.25159	−0.610485
$75$	−5.13815	−0.593302
$76$	−0.00607812	−0.000697209 0
$77$	−24.6007	−2.80351
$78$	1.74625	0.197724
$79$	−5.50748	−0.619640	−0.309820	−	0.950795i	$-0.600269\pi$
$79$	−5.50748	−0.619640	−0.309820	+	0.950795i	$0.600269\pi$
$80$	−12.7303	−1.42329
$81$	1.00000	0.111111
$82$	2.47989	0.273858
$83$	−10.7628	−1.18137	−0.590686	−	0.806902i	$-0.701143\pi$
$83$	−10.7628	−1.18137	−0.590686	+	0.806902i	$0.701143\pi$
$84$	0.00436944	0.000476745 0
$85$	20.0048	2.16982
$86$	−14.8204	−1.59812
$87$	4.54091	0.486836
$88$	14.6918	1.56616
$89$	−6.37036	−0.675257	−0.337628	−	0.941279i	$-0.609625\pi$
$89$	−6.37036	−0.675257	−0.337628	+	0.941279i	$0.609625\pi$
$90$	4.50188	0.474540
$91$	−5.85069	−0.613319
$92$	−0.00230040	−0.000239833 0
$93$	1.69003	0.175248
$94$	−13.4865	−1.39102
$95$	20.9816	2.15267
$96$	−0.00521777	−0.000532536 0
$97$	6.63646	0.673831	0.336915	−	0.941535i	$-0.390616\pi$
$97$	6.63646	0.673831	0.336915	+	0.941535i	$0.390616\pi$
$98$	21.8311	2.20527
$99$	−5.19316	−0.521932
$100$	−0.00473933	−0.000473933 0
$101$	7.49014	0.745297	0.372649	−	0.927973i	$-0.378450\pi$
$101$	7.49014	0.745297	0.372649	+	0.927973i	$0.378450\pi$
$102$	−8.88319	−0.879567
$103$	1.52145	0.149913	0.0749563	−	0.997187i	$-0.476118\pi$
$103$	1.52145	0.149913	0.0749563	+	0.997187i	$0.476118\pi$
$104$	3.49411	0.342626
$105$	−15.0833	−1.47198
$106$	−11.5046	−1.11743
$107$	1.87556	0.181317	0.0906585	−	0.995882i	$-0.471103\pi$
$107$	1.87556	0.181317	0.0906585	+	0.995882i	$0.471103\pi$
$108$	0.000922380 0	8.87561e−5 0
$109$	−12.3123	−1.17931	−0.589653	−	0.807657i	$-0.700735\pi$
$109$	−12.3123	−1.17931	−0.589653	+	0.807657i	$0.700735\pi$
$110$	−23.3790	−2.22910
$111$	3.71429	0.352545
$112$	−18.9398	−1.78964
$113$	−12.3443	−1.16125	−0.580625	−	0.814171i	$-0.697192\pi$
$113$	−12.3443	−1.16125	−0.580625	+	0.814171i	$0.697192\pi$
$114$	−9.31696	−0.872614
$115$	7.94095	0.740497
$116$	0.00418844	0.000388887 0
$117$	−1.23507	−0.114182
$118$	2.62477	0.241630
$119$	29.7626	2.72833
$120$	9.00792	0.822307
$121$	15.9689	1.45172
$122$	13.9991	1.26742
$123$	−1.75395	−0.158149
$124$	0.00155885	0.000139989 0
$125$	0.439869	0.0393431
$126$	6.69778	0.596686
$127$	11.2947	1.00224	0.501120	−	0.865378i	$-0.332921\pi$
$127$	11.2947	1.00224	0.501120	+	0.865378i	$0.332921\pi$
$128$	11.3059	0.999308
$129$	10.4820	0.922888
$130$	−5.56014	−0.487656
$131$	−3.67755	−0.321309	−0.160654	−	0.987011i	$-0.551360\pi$
$131$	−3.67755	−0.321309	−0.160654	+	0.987011i	$0.551360\pi$
$132$	−0.00479006	−0.000416922 0
$133$	31.2159	2.70676
$134$	−17.1846	−1.48453
$135$	−3.18405	−0.274039
$136$	−17.7746	−1.52416
$137$	20.3101	1.73521	0.867605	−	0.497253i	$-0.165658\pi$
$137$	20.3101	1.73521	0.867605	+	0.497253i	$0.165658\pi$
$138$	−3.52621	−0.300171
$139$	14.1983	1.20428	0.602142	−	0.798389i	$-0.294314\pi$
$139$	14.1983	1.20428	0.602142	+	0.798389i	$0.294314\pi$
$140$	−0.0139125	−0.00117582
$141$	9.53857	0.803293
$142$	−17.4068	−1.46075
$143$	6.41391	0.536358
$144$	−3.99815	−0.333180
$145$	−14.4585	−1.20071
$146$	11.4580	0.948274
$147$	−15.4405	−1.27351
$148$	0.00342599	0.000281614 0
$149$	1.00000	0.0819232
$149$	1.00000	0.0819232
$150$	−7.26476	−0.593165
$151$	4.58370	0.373016	0.186508	−	0.982453i	$-0.440283\pi$
$151$	4.58370	0.373016	0.186508	+	0.982453i	$0.440283\pi$
$152$	−18.6425	−1.51211
$153$	6.28281	0.507935
$154$	−34.7826	−2.80286
$155$	−5.38114	−0.432224
$156$	−0.00113920	−9.12093e−5 0
$157$	6.90631	0.551184	0.275592	−	0.961275i	$-0.411126\pi$
$157$	6.90631	0.551184	0.275592	+	0.961275i	$0.411126\pi$
$158$	−7.78696	−0.619497
$159$	8.13686	0.645295
$160$	0.0166136	0.00131342
$161$	11.8143	0.931100
$162$	1.41389	0.111085
$163$	7.98777	0.625650	0.312825	−	0.949811i	$-0.398725\pi$
$163$	7.98777	0.625650	0.312825	+	0.949811i	$0.398725\pi$
$164$	−0.00161781	−0.000126330 0
$165$	16.5352	1.28727
$166$	−15.2174	−1.18110
$167$	1.65974	0.128435	0.0642173	−	0.997936i	$-0.479545\pi$
$167$	1.65974	0.128435	0.0642173	+	0.997936i	$0.479545\pi$
$168$	13.4017	1.03397
$169$	−11.4746	−0.882662
$170$	28.2845	2.16932
$171$	6.58961	0.503920
$172$	0.00966838	0.000737207 0
$173$	−15.1471	−1.15161	−0.575806	−	0.817587i	$-0.695311\pi$
$173$	−15.1471	−1.15161	−0.575806	+	0.817587i	$0.695311\pi$
$174$	6.42033	0.486724
$175$	24.3401	1.83994
$176$	20.7630	1.56507
$177$	−1.85642	−0.139537
$178$	−9.00697	−0.675101
$179$	−19.0319	−1.42251	−0.711254	−	0.702935i	$-0.751872\pi$
$179$	−19.0319	−1.42251	−0.711254	+	0.702935i	$0.751872\pi$
$180$	−0.00293690	−0.000218904 0
$181$	7.17236	0.533117	0.266559	−	0.963819i	$-0.414113\pi$
$181$	7.17236	0.533117	0.266559	+	0.963819i	$0.414113\pi$
$182$	−8.27222	−0.613178
$183$	−9.90116	−0.731915
$184$	−7.05567	−0.520151
$185$	−11.8265	−0.869499
$186$	2.38952	0.175208
$187$	−32.6276	−2.38597
$188$	0.00879819	0.000641674 0
$189$	−4.73714	−0.344576
$190$	29.6656	2.15217
$191$	14.5269	1.05113	0.525567	−	0.850752i	$-0.323853\pi$
$191$	14.5269	1.05113	0.525567	+	0.850752i	$0.323853\pi$
$192$	−8.00369	−0.577616
$193$	4.95722	0.356829	0.178414	−	0.983955i	$-0.442903\pi$
$193$	4.95722	0.356829	0.178414	+	0.983955i	$0.442903\pi$
$194$	9.38321	0.673675
$195$	3.93252	0.281613
$196$	−0.0142420	−0.00101729
$197$	9.53711	0.679491	0.339745	−	0.940517i	$-0.389659\pi$
$197$	9.53711	0.679491	0.339745	+	0.940517i	$0.389659\pi$
$198$	−7.34254	−0.521811
$199$	−12.7043	−0.900586	−0.450293	−	0.892881i	$-0.648681\pi$
$199$	−12.7043	−0.900586	−0.450293	+	0.892881i	$0.648681\pi$
$200$	−14.5362	−1.02787
$201$	12.1542	0.857290
$202$	10.5902	0.745125
$203$	−21.5109	−1.50977
$204$	0.00579514	0.000405741 0
$205$	5.58467	0.390050
$206$	2.15115	0.149878
$207$	2.49398	0.173344
$208$	4.93800	0.342389
$209$	−34.2209	−2.36711
$210$	−21.3260	−1.47164
$211$	11.1150	0.765186	0.382593	−	0.923917i	$-0.375031\pi$
$211$	11.1150	0.765186	0.382593	+	0.923917i	$0.375031\pi$
$212$	0.00750528	0.000515465 0
$213$	12.3113	0.843557
$214$	2.65183	0.181275
$215$	−33.3751	−2.27617
$216$	2.82908	0.192494
$217$	−8.00592	−0.543477
$218$	−17.4082	−1.17903
$219$	−8.10393	−0.547613
$220$	0.0152518	0.00102828
$221$	−7.75971	−0.521974
$222$	5.25159	0.352463
$223$	−6.51895	−0.436541	−0.218271	−	0.975888i	$-0.570042\pi$
$223$	−6.51895	−0.436541	−0.218271	+	0.975888i	$0.570042\pi$
$224$	0.0247173	0.00165149
$225$	5.13815	0.342543
$226$	−17.4534	−1.16098
$227$	6.13420	0.407141	0.203571	−	0.979060i	$-0.434745\pi$
$227$	6.13420	0.407141	0.203571	+	0.979060i	$0.434745\pi$
$228$	0.00607812	0.000402534 0
$229$	13.8881	0.917750	0.458875	−	0.888501i	$-0.348253\pi$
$229$	13.8881	0.917750	0.458875	+	0.888501i	$0.348253\pi$
$230$	11.2276	0.740326
$231$	24.6007	1.61861
$232$	12.8466	0.843420
$233$	−4.64848	−0.304532	−0.152266	−	0.988340i	$-0.548657\pi$
$233$	−4.64848	−0.304532	−0.152266	+	0.988340i	$0.548657\pi$
$234$	−1.74625	−0.114156
$235$	−30.3713	−1.98120
$236$	−0.00171233	−0.000111463 0
$237$	5.50748	0.357749
$238$	42.0809	2.72770
$239$	12.8310	0.829966	0.414983	−	0.909829i	$-0.363788\pi$
$239$	12.8310	0.829966	0.414983	+	0.909829i	$0.363788\pi$
$240$	12.7303	0.821738
$241$	6.02191	0.387905	0.193953	−	0.981011i	$-0.437869\pi$
$241$	6.02191	0.387905	0.193953	+	0.981011i	$0.437869\pi$
$242$	22.5782	1.45138
$243$	−1.00000	−0.0641500
$244$	−0.00913264	−0.000584657 0
$245$	49.1632	3.14092
$246$	−2.47989	−0.158112
$247$	−8.13862	−0.517848
$248$	4.78124	0.303609
$249$	10.7628	0.682065
$250$	0.621926	0.0393340
$251$	−17.4583	−1.10196	−0.550980	−	0.834518i	$-0.685746\pi$
$251$	−17.4583	−1.10196	−0.550980	+	0.834518i	$0.685746\pi$
$252$	−0.00436944	−0.000275249 0
$253$	−12.9516	−0.814262
$254$	15.9694	1.00201
$255$	−20.0048	−1.25275
$256$	−0.0221371	−0.00138357
$257$	13.9080	0.867556	0.433778	−	0.901020i	$-0.357180\pi$
$257$	13.9080	0.867556	0.433778	+	0.901020i	$0.357180\pi$
$258$	14.8204	0.922675
$259$	−17.5951	−1.09331
$260$	0.00362728	0.000224954 0
$261$	−4.54091	−0.281075
$262$	−5.19964	−0.321235
$263$	−7.98710	−0.492505	−0.246253	−	0.969206i	$-0.579199\pi$
$263$	−7.98710	−0.492505	−0.246253	+	0.969206i	$0.579199\pi$
$264$	−14.6918	−0.904221
$265$	−25.9081	−1.59152
$266$	44.1357	2.70614
$267$	6.37036	0.389860
$268$	0.0112108	0.000684807 0
$269$	−3.66194	−0.223272	−0.111636	−	0.993749i	$-0.535609\pi$
$269$	−3.66194	−0.223272	−0.111636	+	0.993749i	$0.535609\pi$
$270$	−4.50188	−0.273976
$271$	−2.86563	−0.174075	−0.0870373	−	0.996205i	$-0.527740\pi$
$271$	−2.86563	−0.174075	−0.0870373	+	0.996205i	$0.527740\pi$
$272$	−25.1197	−1.52310
$273$	5.85069	0.354100
$274$	28.7162	1.73481
$275$	−26.6832	−1.60906
$276$	0.00230040	0.000138468 0
$277$	3.87069	0.232567	0.116284	−	0.993216i	$-0.462902\pi$
$277$	3.87069	0.232567	0.116284	+	0.993216i	$0.462902\pi$
$278$	20.0748	1.20401
$279$	−1.69003	−0.101180
$280$	−42.6718	−2.55012
$281$	−12.6892	−0.756976	−0.378488	−	0.925606i	$-0.623556\pi$
$281$	−12.6892	−0.756976	−0.378488	+	0.925606i	$0.623556\pi$
$282$	13.4865	0.803108
$283$	22.9691	1.36537	0.682685	−	0.730712i	$-0.260812\pi$
$283$	22.9691	1.36537	0.682685	+	0.730712i	$0.260812\pi$
$284$	0.0113557	0.000673837 0
$285$	−20.9816	−1.24284
$286$	9.06854	0.536234
$287$	8.30872	0.490448
$288$	0.00521777	0.000307460 0
$289$	22.4737	1.32198
$290$	−20.4426	−1.20043
$291$	−6.63646	−0.389036
$292$	−0.00747490	−0.000437436 0
$293$	28.4476	1.66192	0.830962	−	0.556329i	$-0.187790\pi$
$293$	28.4476	1.66192	0.830962	+	0.556329i	$0.187790\pi$
$294$	−21.8311	−1.27322
$295$	5.91093	0.344148
$296$	10.5080	0.610766
$297$	5.19316	0.301337
$298$	1.41389	0.0819043
$299$	−3.08024	−0.178135
$300$	0.00473933	0.000273625 0
$301$	−49.6547	−2.86205
$302$	6.48084	0.372930
$303$	−7.49014	−0.430297
$304$	−26.3463	−1.51106
$305$	31.5258	1.80516
$306$	8.88319	0.507818
$307$	24.4357	1.39462	0.697308	−	0.716771i	$-0.254381\pi$
$307$	24.4357	1.39462	0.697308	+	0.716771i	$0.254381\pi$
$308$	0.0226912	0.00129295
$309$	−1.52145	−0.0865521
$310$	−7.60833	−0.432124
$311$	−15.7799	−0.894797	−0.447398	−	0.894335i	$-0.647649\pi$
$311$	−15.7799	−0.894797	−0.447398	+	0.894335i	$0.647649\pi$
$312$	−3.49411	−0.197815
$313$	−9.72844	−0.549884	−0.274942	−	0.961461i	$-0.588659\pi$
$313$	−9.72844	−0.549884	−0.274942	+	0.961461i	$0.588659\pi$
$314$	9.76475	0.551057
$315$	15.0833	0.849846
$316$	0.00507999	0.000285772 0
$317$	10.1962	0.572676	0.286338	−	0.958129i	$-0.407562\pi$
$317$	10.1962	0.572676	0.286338	+	0.958129i	$0.407562\pi$
$318$	11.5046	0.645146
$319$	23.5816	1.32032
$320$	25.4841	1.42460
$321$	−1.87556	−0.104683
$322$	16.7041	0.930885
$323$	41.4013	2.30363
$324$	−0.000922380 0	−5.12433e−5 0
$325$	−6.34597	−0.352011
$326$	11.2938	0.625506
$327$	12.3123	0.680872
$328$	−4.96207	−0.273985
$329$	−45.1855	−2.49116
$330$	23.3790	1.28697
$331$	11.5187	0.633124	0.316562	−	0.948572i	$-0.397471\pi$
$331$	11.5187	0.633124	0.316562	+	0.948572i	$0.397471\pi$
$332$	0.00992740	0.000544837 0
$333$	−3.71429	−0.203542
$334$	2.34669	0.128405
$335$	−38.6995	−2.11438
$336$	18.9398	1.03325
$337$	5.05544	0.275388	0.137694	−	0.990475i	$-0.456031\pi$
$337$	5.05544	0.275388	0.137694	+	0.990475i	$0.456031\pi$
$338$	−16.2238	−0.882458
$339$	12.3443	0.670448
$340$	−0.0184520	−0.00100070
$341$	8.77660	0.475280
$342$	9.31696	0.503804
$343$	39.9837	2.15892
$344$	29.6544	1.59886
$345$	−7.94095	−0.427526
$346$	−21.4163	−1.15135
$347$	−5.64505	−0.303042	−0.151521	−	0.988454i	$-0.548417\pi$
$347$	−5.64505	−0.303042	−0.151521	+	0.988454i	$0.548417\pi$
$348$	−0.00418844	−0.000224524 0
$349$	33.3651	1.78600	0.892998	−	0.450061i	$-0.148598\pi$
$349$	33.3651	1.78600	0.892998	+	0.450061i	$0.148598\pi$
$350$	34.4142	1.83952
$351$	1.23507	0.0659231
$352$	−0.0270967	−0.00144426
$353$	−5.25617	−0.279758	−0.139879	−	0.990169i	$-0.544671\pi$
$353$	−5.25617	−0.279758	−0.139879	+	0.990169i	$0.544671\pi$
$354$	−2.62477	−0.139505
$355$	−39.1998	−2.08051
$356$	0.00587590	0.000311422 0
$357$	−29.7626	−1.57520
$358$	−26.9089	−1.42218
$359$	26.3796	1.39226	0.696131	−	0.717915i	$-0.254903\pi$
$359$	26.3796	1.39226	0.696131	+	0.717915i	$0.254903\pi$
$360$	−9.00792	−0.474759
$361$	24.4229	1.28542
$362$	10.1409	0.532994
$363$	−15.9689	−0.838148
$364$	0.00539657	0.000282857 0
$365$	25.8033	1.35060
$366$	−13.9991	−0.731746
$367$	−37.6533	−1.96549	−0.982744	−	0.184970i	$-0.940781\pi$
$367$	−37.6533	−1.96549	−0.982744	+	0.184970i	$0.940781\pi$
$368$	−9.97132	−0.519791
$369$	1.75395	0.0913071
$370$	−16.7213	−0.869299
$371$	−38.5455	−2.00118
$372$	−0.00155885	−8.08227e−5 0
$373$	0.528983	0.0273897	0.0136948	−	0.999906i	$-0.495641\pi$
$373$	0.528983	0.0273897	0.0136948	+	0.999906i	$0.495641\pi$
$374$	−46.1318	−2.38542
$375$	−0.439869	−0.0227147
$376$	26.9854	1.39166
$377$	5.60833	0.288844
$378$	−6.69778	−0.344497
$379$	−21.4126	−1.09989	−0.549945	−	0.835201i	$-0.685351\pi$
$379$	−21.4126	−1.09989	−0.549945	+	0.835201i	$0.685351\pi$
$380$	−0.0193530	−0.000992789 0
$381$	−11.2947	−0.578644
$382$	20.5395	1.05089
$383$	4.37324	0.223462	0.111731	−	0.993738i	$-0.464360\pi$
$383$	4.37324	0.223462	0.111731	+	0.993738i	$0.464360\pi$
$384$	−11.3059	−0.576951
$385$	−78.3298	−3.99205
$386$	7.00895	0.356746
$387$	−10.4820	−0.532830
$388$	−0.00612134	−0.000310764 0
$389$	18.3909	0.932456	0.466228	−	0.884665i	$-0.345613\pi$
$389$	18.3909	0.932456	0.466228	+	0.884665i	$0.345613\pi$
$390$	5.56014	0.281548
$391$	15.6692	0.792426
$392$	−43.6823	−2.20629
$393$	3.67755	0.185508
$394$	13.4844	0.679334
$395$	−17.5361	−0.882336
$396$	0.00479006	0.000240710 0
$397$	−15.3913	−0.772467	−0.386233	−	0.922401i	$-0.626224\pi$
$397$	−15.3913	−0.772467	−0.386233	+	0.922401i	$0.626224\pi$
$398$	−17.9625	−0.900379
$399$	−31.2159	−1.56275
$400$	−20.5431	−1.02716
$401$	−19.2369	−0.960647	−0.480324	−	0.877091i	$-0.659481\pi$
$401$	−19.2369	−0.960647	−0.480324	+	0.877091i	$0.659481\pi$
$402$	17.1846	0.857092
$403$	2.08731	0.103976
$404$	−0.00690876	−0.000343724 0
$405$	3.18405	0.158217
$406$	−30.4140	−1.50942
$407$	19.2889	0.956114
$408$	17.7746	0.879972
$409$	14.7110	0.727412	0.363706	−	0.931514i	$-0.381511\pi$
$409$	14.7110	0.727412	0.363706	+	0.931514i	$0.381511\pi$
$410$	7.89609	0.389960
$411$	−20.3101	−1.00182
$412$	−0.00140335	−6.91382e−5 0
$413$	8.79412	0.432730
$414$	3.52621	0.173304
$415$	−34.2693	−1.68221
$416$	−0.00644431	−0.000315958 0
$417$	−14.1983	−0.695294
$418$	−48.3844	−2.36656
$419$	−29.5587	−1.44404	−0.722018	−	0.691874i	$-0.756785\pi$
$419$	−29.5587	−1.44404	−0.722018	+	0.691874i	$0.756785\pi$
$420$	0.0139125	0.000678861 0
$421$	0.171619	0.00836417	0.00418209	−	0.999991i	$-0.498669\pi$
$421$	0.171619	0.00836417	0.00418209	+	0.999991i	$0.498669\pi$
$422$	15.7153	0.765010
$423$	−9.53857	−0.463781
$424$	23.0198	1.11794
$425$	32.2820	1.56591
$426$	17.4068	0.843362
$427$	46.9032	2.26980
$428$	−0.00172998	−8.36216e−5 0
$429$	−6.41391	−0.309666
$430$	−47.1887	−2.27564
$431$	32.4822	1.56461	0.782306	−	0.622894i	$-0.214043\pi$
$431$	32.4822	1.56461	0.782306	+	0.622894i	$0.214043\pi$
$432$	3.99815	0.192361
$433$	13.8698	0.666539	0.333270	−	0.942832i	$-0.391848\pi$
$433$	13.8698	0.666539	0.333270	+	0.942832i	$0.391848\pi$
$434$	−11.3195	−0.543352
$435$	14.4585	0.693230
$436$	0.0113566	0.000543884 0
$437$	16.4344	0.786162
$438$	−11.4580	−0.547486
$439$	−25.0794	−1.19698	−0.598488	−	0.801132i	$-0.704232\pi$
$439$	−25.0794	−1.19698	−0.598488	+	0.801132i	$0.704232\pi$
$440$	46.7795	2.23013
$441$	15.4405	0.735261
$442$	−10.9714	−0.521854
$443$	9.85547	0.468248	0.234124	−	0.972207i	$-0.424778\pi$
$443$	9.85547	0.468248	0.234124	+	0.972207i	$0.424778\pi$
$444$	−0.00342599	−0.000162590 0
$445$	−20.2835	−0.961531
$446$	−9.21706	−0.436440
$447$	−1.00000	−0.0472984
$448$	37.9146	1.79130
$449$	−6.79110	−0.320492	−0.160246	−	0.987077i	$-0.551229\pi$
$449$	−6.79110	−0.320492	−0.160246	+	0.987077i	$0.551229\pi$
$450$	7.26476	0.342464
$451$	−9.10855	−0.428905
$452$	0.0113861	0.000535557 0
$453$	−4.58370	−0.215361
$454$	8.67307	0.407048
$455$	−18.6289	−0.873335
$456$	18.6425	0.873016
$457$	−40.3668	−1.88828	−0.944139	−	0.329548i	$-0.893104\pi$
$457$	−40.3668	−1.88828	−0.944139	+	0.329548i	$0.893104\pi$
$458$	19.6362	0.917538
$459$	−6.28281	−0.293257
$460$	−0.00732457	−0.000341510 0
$461$	−33.1331	−1.54316	−0.771580	−	0.636132i	$-0.780533\pi$
$461$	−33.1331	−1.54316	−0.771580	+	0.636132i	$0.780533\pi$
$462$	34.7826	1.61823
$463$	−5.13312	−0.238556	−0.119278	−	0.992861i	$-0.538058\pi$
$463$	−5.13312	−0.238556	−0.119278	+	0.992861i	$0.538058\pi$
$464$	18.1552	0.842836
$465$	5.38114	0.249544
$466$	−6.57242	−0.304462
$467$	27.3483	1.26553	0.632764	−	0.774344i	$-0.281920\pi$
$467$	27.3483	1.26553	0.632764	+	0.774344i	$0.281920\pi$
$468$	0.00113920	5.26597e−5 0
$469$	−57.5760	−2.65861
$470$	−42.9415	−1.98075
$471$	−6.90631	−0.318226
$472$	−5.25196	−0.241741
$473$	54.4346	2.50291
$474$	7.78696	0.357667
$475$	33.8584	1.55353
$476$	−0.0274524	−0.00125828
$477$	−8.13686	−0.372561
$478$	18.1415	0.829775
$479$	9.23953	0.422165	0.211082	−	0.977468i	$-0.432301\pi$
$479$	9.23953	0.422165	0.211082	+	0.977468i	$0.432301\pi$
$480$	−0.0166136	−0.000758305 0
$481$	4.58740	0.209168
$482$	8.51430	0.387816
$483$	−11.8143	−0.537571
$484$	−0.0147294	−0.000669517 0
$485$	21.1308	0.959500
$486$	−1.41389	−0.0641352
$487$	−0.242639	−0.0109950	−0.00549751	−	0.999985i	$-0.501750\pi$
$487$	−0.242639	−0.0109950	−0.00549751	+	0.999985i	$0.501750\pi$
$488$	−28.0112	−1.26801
$489$	−7.98777	−0.361219
$490$	69.5112	3.14020
$491$	−20.0726	−0.905865	−0.452933	−	0.891545i	$-0.649622\pi$
$491$	−20.0726	−0.905865	−0.452933	+	0.891545i	$0.649622\pi$
$492$	0.00161781	7.29366e−5 0
$493$	−28.5297	−1.28491
$494$	−11.5071	−0.517729
$495$	−16.5352	−0.743204
$496$	6.75701	0.303399
$497$	−58.3204	−2.61603
$498$	15.2174	0.681908
$499$	11.9748	0.536064	0.268032	−	0.963410i	$-0.413627\pi$
$499$	11.9748	0.536064	0.268032	+	0.963410i	$0.413627\pi$
$500$	−0.000405727 0	−1.81446e−5 0
$501$	−1.65974	−0.0741517
$502$	−24.6841	−1.10171
$503$	8.51322	0.379586	0.189793	−	0.981824i	$-0.439218\pi$
$503$	8.51322	0.379586	0.189793	+	0.981824i	$0.439218\pi$
$504$	−13.4017	−0.596961
$505$	23.8490	1.06126
$506$	−18.3121	−0.814074
$507$	11.4746	0.509605
$508$	−0.0104180	−0.000462223 0
$509$	0.450336	0.0199608	0.00998040	−	0.999950i	$-0.496823\pi$
$509$	0.450336	0.0199608	0.00998040	+	0.999950i	$0.496823\pi$
$510$	−28.2845	−1.25246
$511$	38.3894	1.69825
$512$	−22.6431	−1.00069
$513$	−6.58961	−0.290938
$514$	19.6643	0.867356
$515$	4.84435	0.213468
$516$	−0.00966838	−0.000425627 0
$517$	49.5353	2.17856
$518$	−24.8775	−1.09305
$519$	15.1471	0.664883
$520$	11.1254	0.487881
$521$	25.6001	1.12156	0.560779	−	0.827965i	$-0.310502\pi$
$521$	25.6001	1.12156	0.560779	+	0.827965i	$0.310502\pi$
$522$	−6.42033	−0.281010
$523$	6.81241	0.297886	0.148943	−	0.988846i	$-0.452413\pi$
$523$	6.81241	0.297886	0.148943	+	0.988846i	$0.452413\pi$
$524$	0.00339210	0.000148184 0
$525$	−24.3401	−1.06229
$526$	−11.2929	−0.492392
$527$	−10.6182	−0.462534
$528$	−20.7630	−0.903595
$529$	−16.7801	−0.729568
$530$	−36.6312	−1.59116
$531$	1.85642	0.0805618
$532$	−0.0287929	−0.00124833
$533$	−2.16625	−0.0938308
$534$	9.00697	0.389770
$535$	5.97186	0.258186
$536$	34.3851	1.48521
$537$	19.0319	0.821285
$538$	−5.17757	−0.223221
$539$	−80.1848	−3.45381
$540$	0.00293690	0.000126384 0
$541$	3.52115	0.151386	0.0756931	−	0.997131i	$-0.475883\pi$
$541$	3.52115	0.151386	0.0756931	+	0.997131i	$0.475883\pi$
$542$	−4.05168	−0.174034
$543$	−7.17236	−0.307795
$544$	0.0327823	0.00140553
$545$	−39.2030	−1.67927
$546$	8.27222	0.354018
$547$	−1.26215	−0.0539657	−0.0269829	−	0.999636i	$-0.508590\pi$
$547$	−1.26215	−0.0539657	−0.0269829	+	0.999636i	$0.508590\pi$
$548$	−0.0187337	−0.000800262 0
$549$	9.90116	0.422571
$550$	−37.7270	−1.60869
$551$	−29.9228	−1.27475
$552$	7.05567	0.300309
$553$	−26.0897	−1.10945
$554$	5.47272	0.232514
$555$	11.8265	0.502006
$556$	−0.0130962	−0.000555404 0
$557$	−36.0028	−1.52549	−0.762744	−	0.646701i	$-0.776148\pi$
$557$	−36.0028	−1.52549	−0.762744	+	0.646701i	$0.776148\pi$
$558$	−2.38952	−0.101156
$559$	12.9460	0.547557
$560$	−60.3052	−2.54836
$561$	32.6276	1.37754
$562$	−17.9411	−0.756801
$563$	36.9421	1.55692	0.778462	−	0.627692i	$-0.216000\pi$
$563$	36.9421	1.55692	0.778462	+	0.627692i	$0.216000\pi$
$564$	−0.00879819	−0.000370471 0
$565$	−39.3047	−1.65356
$566$	32.4757	1.36506
$567$	4.73714	0.198941
$568$	34.8297	1.46142
$569$	−15.8679	−0.665218	−0.332609	−	0.943065i	$-0.607929\pi$
$569$	−15.8679	−0.665218	−0.332609	+	0.943065i	$0.607929\pi$
$570$	−29.6656	−1.24256
$571$	−20.2570	−0.847731	−0.423865	−	0.905725i	$-0.639327\pi$
$571$	−20.2570	−0.847731	−0.423865	+	0.905725i	$0.639327\pi$
$572$	−0.00591606	−0.000247363 0
$573$	−14.5269	−0.606872
$574$	11.7476	0.490335
$575$	12.8144	0.534399
$576$	8.00369	0.333487
$577$	27.3927	1.14037	0.570186	−	0.821515i	$-0.306871\pi$
$577$	27.3927	1.14037	0.570186	+	0.821515i	$0.306871\pi$
$578$	31.7753	1.32168
$579$	−4.95722	−0.206015
$580$	0.0133362	0.000553755 0
$581$	−50.9849	−2.11521
$582$	−9.38321	−0.388947
$583$	42.2560	1.75006
$584$	−22.9266	−0.948711
$585$	−3.93252	−0.162590
$586$	40.2217	1.66154
$587$	−9.12074	−0.376453	−0.188227	−	0.982126i	$-0.560274\pi$
$587$	−9.12074	−0.376453	−0.188227	+	0.982126i	$0.560274\pi$
$588$	0.0142420	0.000587330 0
$589$	−11.1367	−0.458878
$590$	8.35739	0.344068
$591$	−9.53711	−0.392304
$592$	14.8503	0.610344
$593$	−30.6053	−1.25681	−0.628404	−	0.777887i	$-0.716292\pi$
$593$	−30.6053	−1.25681	−0.628404	+	0.777887i	$0.716292\pi$
$594$	7.34254	0.301268
$595$	94.7653	3.88500
$596$	−0.000922380 0	−3.77822e−5 0
$597$	12.7043	0.519954
$598$	−4.35511	−0.178094
$599$	43.0131	1.75747	0.878734	−	0.477312i	$-0.158389\pi$
$599$	43.0131	1.75747	0.878734	+	0.477312i	$0.158389\pi$
$600$	14.5362	0.593439
$601$	0.229079	0.00934434	0.00467217	−	0.999989i	$-0.498513\pi$
$601$	0.229079	0.00934434	0.00467217	+	0.999989i	$0.498513\pi$
$602$	−70.2061	−2.86139
$603$	−12.1542	−0.494957
$604$	−0.00422792	−0.000172031 0
$605$	50.8456	2.06717
$606$	−10.5902	−0.430198
$607$	1.43211	0.0581276	0.0290638	−	0.999578i	$-0.490747\pi$
$607$	1.43211	0.0581276	0.0290638	+	0.999578i	$0.490747\pi$
$608$	0.0343831	0.00139442
$609$	21.5109	0.871666
$610$	44.5739	1.80474
$611$	11.7808	0.476600
$612$	−0.00579514	−0.000234255 0
$613$	23.2193	0.937820	0.468910	−	0.883246i	$-0.344647\pi$
$613$	23.2193	0.937820	0.468910	+	0.883246i	$0.344647\pi$
$614$	34.5493	1.39430
$615$	−5.58467	−0.225195
$616$	69.5973	2.80416
$617$	30.1574	1.21409	0.607046	−	0.794667i	$-0.292354\pi$
$617$	30.1574	1.21409	0.607046	+	0.794667i	$0.292354\pi$
$618$	−2.15115	−0.0865321
$619$	2.01707	0.0810729	0.0405365	−	0.999178i	$-0.487093\pi$
$619$	2.01707	0.0810729	0.0405365	+	0.999178i	$0.487093\pi$
$620$	0.00496346	0.000199337 0
$621$	−2.49398	−0.100080
$622$	−22.3110	−0.894590
$623$	−30.1773	−1.20903
$624$	−4.93800	−0.197678
$625$	−24.2902	−0.971607
$626$	−13.7549	−0.549757
$627$	34.2209	1.36665
$628$	−0.00637025	−0.000254200 0
$629$	−23.3362	−0.930474
$630$	21.3260	0.849650
$631$	−41.9603	−1.67041	−0.835207	−	0.549936i	$-0.814652\pi$
$631$	−41.9603	−1.67041	−0.835207	+	0.549936i	$0.814652\pi$
$632$	15.5811	0.619783
$633$	−11.1150	−0.441781
$634$	14.4163	0.572544
$635$	35.9628	1.42714
$636$	−0.00750528	−0.000297604 0
$637$	−19.0701	−0.755584
$638$	33.3418	1.32001
$639$	−12.3113	−0.487028
$640$	35.9984	1.42296
$641$	−12.1926	−0.481577	−0.240788	−	0.970578i	$-0.577406\pi$
$641$	−12.1926	−0.481577	−0.240788	+	0.970578i	$0.577406\pi$
$642$	−2.65183	−0.104659
$643$	26.6880	1.05247	0.526236	−	0.850338i	$-0.323603\pi$
$643$	26.6880	1.05247	0.526236	+	0.850338i	$0.323603\pi$
$644$	−0.0108973	−0.000429414 0
$645$	33.3751	1.31415
$646$	58.5367	2.30310
$647$	−4.14614	−0.163002	−0.0815008	−	0.996673i	$-0.525971\pi$
$647$	−4.14614	−0.163002	−0.0815008	+	0.996673i	$0.525971\pi$
$648$	−2.82908	−0.111137
$649$	−9.64068	−0.378430
$650$	−8.97248	−0.351930
$651$	8.00592	0.313777
$652$	−0.00736776	−0.000288544 0
$653$	16.5711	0.648478	0.324239	−	0.945975i	$-0.394892\pi$
$653$	16.5711	0.648478	0.324239	+	0.945975i	$0.394892\pi$
$654$	17.4082	0.680715
$655$	−11.7095	−0.457527
$656$	−7.01257	−0.273795
$657$	8.10393	0.316164
$658$	−63.8873	−2.49059
$659$	34.9082	1.35983	0.679916	−	0.733290i	$-0.262016\pi$
$659$	34.9082	1.35983	0.679916	+	0.733290i	$0.262016\pi$
$660$	−0.0152518	−0.000593675 0
$661$	−1.61494	−0.0628140	−0.0314070	−	0.999507i	$-0.509999\pi$
$661$	−1.61494	−0.0628140	−0.0314070	+	0.999507i	$0.509999\pi$
$662$	16.2861	0.632978
$663$	7.75971	0.301362
$664$	30.4488	1.18164
$665$	99.3928	3.85429
$666$	−5.25159	−0.203495
$667$	−11.3249	−0.438503
$668$	−0.00153091	−5.92328e−5 0
$669$	6.51895	0.252037
$670$	−54.7167	−2.11389
$671$	−51.4183	−1.98498
$672$	−0.0247173	−0.000953491 0
$673$	49.5787	1.91112	0.955559	−	0.294799i	$-0.0952528\pi$
$673$	49.5787	1.91112	0.955559	+	0.294799i	$0.0952528\pi$
$674$	7.14783	0.275324
$675$	−5.13815	−0.197767
$676$	0.0105839	0.000407075 0
$677$	−17.4605	−0.671063	−0.335531	−	0.942029i	$-0.608916\pi$
$677$	−17.4605	−0.671063	−0.335531	+	0.942029i	$0.608916\pi$
$678$	17.4534	0.670293
$679$	31.4379	1.20647
$680$	−56.5950	−2.17032
$681$	−6.13420	−0.235063
$682$	12.4091	0.475170
$683$	−0.548006	−0.0209689	−0.0104844	−	0.999945i	$-0.503337\pi$
$683$	−0.548006	−0.0209689	−0.0104844	+	0.999945i	$0.503337\pi$
$684$	−0.00607812	−0.000232403 0
$685$	64.6684	2.47085
$686$	56.5325	2.15842
$687$	−13.8881	−0.529863
$688$	41.9086	1.59775
$689$	10.0496	0.382859
$690$	−11.2276	−0.427428
$691$	49.5894	1.88647	0.943235	−	0.332125i	$-0.107766\pi$
$691$	49.5894	1.88647	0.943235	+	0.332125i	$0.107766\pi$
$692$	0.0139714	0.000531112 0
$693$	−24.6007	−0.934503
$694$	−7.98147	−0.302972
$695$	45.2080	1.71484
$696$	−12.8466	−0.486948
$697$	11.0198	0.417403
$698$	47.1746	1.78558
$699$	4.64848	0.175822
$700$	−0.0224508	−0.000848562 0
$701$	−21.7718	−0.822308	−0.411154	−	0.911566i	$-0.634874\pi$
$701$	−21.7718	−0.822308	−0.411154	+	0.911566i	$0.634874\pi$
$702$	1.74625	0.0659079
$703$	−24.4757	−0.923119
$704$	−41.5644	−1.56652
$705$	30.3713	1.14385
$706$	−7.43163	−0.279693
$707$	35.4818	1.33443
$708$	0.00171233	6.43532e−5 0
$709$	−30.9681	−1.16303	−0.581516	−	0.813535i	$-0.697540\pi$
$709$	−30.9681	−1.16303	−0.581516	+	0.813535i	$0.697540\pi$
$710$	−55.4241	−2.08003
$711$	−5.50748	−0.206547
$712$	18.0223	0.675413
$713$	−4.21491	−0.157850
$714$	−42.0809	−1.57484
$715$	20.4222	0.763746
$716$	0.0175546	0.000656047 0
$717$	−12.8310	−0.479181
$718$	37.2978	1.39194
$719$	14.8030	0.552058	0.276029	−	0.961149i	$-0.410981\pi$
$719$	14.8030	0.552058	0.276029	+	0.961149i	$0.410981\pi$
$720$	−12.7303	−0.474431
$721$	7.20730	0.268414
$722$	34.5313	1.28512
$723$	−6.02191	−0.223957
$724$	−0.00661564	−0.000245868 0
$725$	−23.3318	−0.866523
$726$	−22.5782	−0.837955
$727$	−19.1677	−0.710891	−0.355446	−	0.934697i	$-0.615671\pi$
$727$	−19.1677	−0.710891	−0.355446	+	0.934697i	$0.615671\pi$
$728$	16.5521	0.613461
$729$	1.00000	0.0370370
$730$	36.4829	1.35029
$731$	−65.8564	−2.43579
$732$	0.00913264	0.000337552 0
$733$	16.8186	0.621211	0.310605	−	0.950539i	$-0.399468\pi$
$733$	16.8186	0.621211	0.310605	+	0.950539i	$0.399468\pi$
$734$	−53.2376	−1.96504
$735$	−49.1632	−1.81341
$736$	0.0130130	0.000479666 0
$737$	63.1186	2.32500
$738$	2.47989	0.0912861
$739$	−47.0127	−1.72939	−0.864695	−	0.502297i	$-0.832488\pi$
$739$	−47.0127	−1.72939	−0.864695	+	0.502297i	$0.832488\pi$
$740$	0.0109085	0.000401004 0
$741$	8.13862	0.298980
$742$	−54.4989	−2.00072
$743$	−5.35405	−0.196421	−0.0982104	−	0.995166i	$-0.531312\pi$
$743$	−5.35405	−0.196421	−0.0982104	+	0.995166i	$0.531312\pi$
$744$	−4.78124	−0.175289
$745$	3.18405	0.116654
$746$	0.747922	0.0273834
$747$	−10.7628	−0.393790
$748$	0.0300951	0.00110038
$749$	8.88477	0.324643
$750$	−0.621926	−0.0227095
$751$	14.8659	0.542464	0.271232	−	0.962514i	$-0.412569\pi$
$751$	14.8659	0.542464	0.271232	+	0.962514i	$0.412569\pi$
$752$	38.1367	1.39070
$753$	17.4583	0.636217
$754$	7.92955	0.288777
$755$	14.5947	0.531156
$756$	0.00436944	0.000158915 0
$757$	−20.9145	−0.760152	−0.380076	−	0.924955i	$-0.624102\pi$
$757$	−20.9145	−0.760152	−0.380076	+	0.924955i	$0.624102\pi$
$758$	−30.2750	−1.09964
$759$	12.9516	0.470114
$760$	−59.3586	−2.15316
$761$	46.1180	1.67178	0.835888	−	0.548900i	$-0.184953\pi$
$761$	46.1180	1.67178	0.835888	+	0.548900i	$0.184953\pi$
$762$	−15.9694	−0.578510
$763$	−58.3251	−2.11151
$764$	−0.0133994	−0.000484772 0
$765$	20.0048	0.723274
$766$	6.18327	0.223411
$767$	−2.29281	−0.0827885
$768$	0.0221371	0.000798805 0
$769$	−26.1977	−0.944712	−0.472356	−	0.881408i	$-0.656596\pi$
$769$	−26.1977	−0.944712	−0.472356	+	0.881408i	$0.656596\pi$
$770$	−110.749	−3.99113
$771$	−13.9080	−0.500883
$772$	−0.00457244	−0.000164566 0
$773$	−5.89126	−0.211894	−0.105947	−	0.994372i	$-0.533787\pi$
$773$	−5.89126	−0.211894	−0.105947	+	0.994372i	$0.533787\pi$
$774$	−14.8204	−0.532707
$775$	−8.68364	−0.311925
$776$	−18.7751	−0.673986
$777$	17.5951	0.631221
$778$	26.0027	0.932241
$779$	11.5579	0.414103
$780$	−0.00362728	−0.000129877 0
$781$	63.9345	2.28776
$782$	22.1545	0.792243
$783$	4.54091	0.162279
$784$	−61.7334	−2.20477
$785$	21.9900	0.784857
$786$	5.19964	0.185465
$787$	−31.4176	−1.11992	−0.559959	−	0.828520i	$-0.689183\pi$
$787$	−31.4176	−1.11992	−0.559959	+	0.828520i	$0.689183\pi$
$788$	−0.00879684	−0.000313374 0
$789$	7.98710	0.284348
$790$	−24.7940	−0.882132
$791$	−58.4764	−2.07918
$792$	14.6918	0.522052
$793$	−12.2286	−0.434251
$794$	−21.7616	−0.772289
$795$	25.9081	0.918867
$796$	0.0117182	0.000415342 0
$797$	36.7374	1.30130	0.650652	−	0.759376i	$-0.274496\pi$
$797$	36.7374	1.30130	0.650652	+	0.759376i	$0.274496\pi$
$798$	−44.1357	−1.56239
$799$	−59.9291	−2.12014
$800$	0.0268097	0.000947865 0
$801$	−6.37036	−0.225086
$802$	−27.1989	−0.960426
$803$	−42.0850	−1.48515
$804$	−0.0112108	−0.000395374 0
$805$	37.6174	1.32584
$806$	2.95122	0.103952
$807$	3.66194	0.128906
$808$	−21.1902	−0.745469
$809$	−20.9708	−0.737295	−0.368647	−	0.929569i	$-0.620179\pi$
$809$	−20.9708	−0.737295	−0.368647	+	0.929569i	$0.620179\pi$
$810$	4.50188	0.158180
$811$	28.1115	0.987127	0.493563	−	0.869710i	$-0.335694\pi$
$811$	28.1115	0.987127	0.493563	+	0.869710i	$0.335694\pi$
$812$	0.0198412	0.000696291 0
$813$	2.86563	0.100502
$814$	27.2723	0.955894
$815$	25.4334	0.890894
$816$	25.1197	0.879364
$817$	−69.0722	−2.41653
$818$	20.7997	0.727245
$819$	−5.85069	−0.204440
$820$	−0.00515119	−0.000179887 0
$821$	−4.10216	−0.143166	−0.0715831	−	0.997435i	$-0.522805\pi$
$821$	−4.10216	−0.143166	−0.0715831	+	0.997435i	$0.522805\pi$
$822$	−28.7162	−1.00159
$823$	−48.0931	−1.67642	−0.838210	−	0.545347i	$-0.816398\pi$
$823$	−48.0931	−1.67642	−0.838210	+	0.545347i	$0.816398\pi$
$824$	−4.30429	−0.149947
$825$	26.6832	0.928990
$826$	12.4339	0.432631
$827$	−0.620244	−0.0215680	−0.0107840	−	0.999942i	$-0.503433\pi$
$827$	−0.620244	−0.0215680	−0.0107840	+	0.999942i	$0.503433\pi$
$828$	−0.00230040	−7.99444e−5 0
$829$	−26.5797	−0.923150	−0.461575	−	0.887101i	$-0.652715\pi$
$829$	−26.5797	−0.923150	−0.461575	+	0.887101i	$0.652715\pi$
$830$	−48.4529	−1.68182
$831$	−3.87069	−0.134273
$832$	−9.88511	−0.342704
$833$	97.0097	3.36119
$834$	−20.0748	−0.695133
$835$	5.28469	0.182884
$836$	0.0315646	0.00109169
$837$	1.69003	0.0584161
$838$	−41.7926	−1.44370
$839$	7.85037	0.271025	0.135512	−	0.990776i	$-0.456732\pi$
$839$	7.85037	0.271025	0.135512	+	0.990776i	$0.456732\pi$
$840$	42.6718	1.47232
$841$	−8.38017	−0.288971
$842$	0.242649	0.00836225
$843$	12.6892	0.437040
$844$	−0.0102522	−0.000352896 0
$845$	−36.5357	−1.25687
$846$	−13.4865	−0.463674
$847$	75.6468	2.59925
$848$	32.5324	1.11717
$849$	−22.9691	−0.788297
$850$	45.6431	1.56555
$851$	−9.26336	−0.317544
$852$	−0.0113557	−0.000389040 0
$853$	−31.2490	−1.06995	−0.534973	−	0.844869i	$-0.679678\pi$
$853$	−31.2490	−1.06995	−0.534973	+	0.844869i	$0.679678\pi$
$854$	66.3158	2.26928
$855$	20.9816	0.717556
$856$	−5.30610	−0.181359
$857$	−7.09062	−0.242211	−0.121106	−	0.992640i	$-0.538644\pi$
$857$	−7.09062	−0.242211	−0.121106	+	0.992640i	$0.538644\pi$
$858$	−9.06854	−0.309595
$859$	40.4642	1.38062	0.690311	−	0.723513i	$-0.257474\pi$
$859$	40.4642	1.38062	0.690311	+	0.723513i	$0.257474\pi$
$860$	0.0307846	0.00104975
$861$	−8.30872	−0.283160
$862$	45.9262	1.56425
$863$	12.9147	0.439622	0.219811	−	0.975543i	$-0.429456\pi$
$863$	12.9147	0.439622	0.219811	+	0.975543i	$0.429456\pi$
$864$	−0.00521777	−0.000177512 0
$865$	−48.2290	−1.63984
$866$	19.6103	0.666386
$867$	−22.4737	−0.763248
$868$	0.00738450	0.000250646 0
$869$	28.6012	0.970230
$870$	20.4426	0.693070
$871$	15.0113	0.508637
$872$	34.8325	1.17958
$873$	6.63646	0.224610
$874$	23.2363	0.785980
$875$	2.08372	0.0704426
$876$	0.00747490	0.000252554 0
$877$	−15.9970	−0.540182	−0.270091	−	0.962835i	$-0.587054\pi$
$877$	−15.9970	−0.540182	−0.270091	+	0.962835i	$0.587054\pi$
$878$	−35.4595	−1.19670
$879$	−28.4476	−0.959513
$880$	66.1105	2.22858
$881$	16.9769	0.571967	0.285983	−	0.958235i	$-0.407680\pi$
$881$	16.9769	0.571967	0.285983	+	0.958235i	$0.407680\pi$
$882$	21.8311	0.735092
$883$	1.49704	0.0503794	0.0251897	−	0.999683i	$-0.491981\pi$
$883$	1.49704	0.0503794	0.0251897	+	0.999683i	$0.491981\pi$
$884$	0.00715740	0.000240729 0
$885$	−5.91093	−0.198694
$886$	13.9345	0.468140
$887$	−3.58193	−0.120270	−0.0601348	−	0.998190i	$-0.519153\pi$
$887$	−3.58193	−0.120270	−0.0601348	+	0.998190i	$0.519153\pi$
$888$	−10.5080	−0.352626
$889$	53.5045	1.79448
$890$	−28.6786	−0.961309
$891$	−5.19316	−0.173977
$892$	0.00601295	0.000201328 0
$893$	−62.8555	−2.10338
$894$	−1.41389	−0.0472875
$895$	−60.5983	−2.02558
$896$	53.5575	1.78923
$897$	3.08024	0.102846
$898$	−9.60185	−0.320418
$899$	7.67428	0.255952
$900$	−0.00473933	−0.000157978 0
$901$	−51.1224	−1.70313
$902$	−12.8785	−0.428806
$903$	49.6547	1.65240
$904$	34.9229	1.16152
$905$	22.8371	0.759132
$906$	−6.48084	−0.215311
$907$	−55.8917	−1.85585	−0.927927	−	0.372761i	$-0.878411\pi$
$907$	−55.8917	−1.85585	−0.927927	+	0.372761i	$0.878411\pi$
$908$	−0.00565807	−0.000187770 0
$909$	7.49014	0.248432
$910$	−26.3391	−0.873134
$911$	−48.2092	−1.59724	−0.798621	−	0.601834i	$-0.794437\pi$
$911$	−48.2092	−1.59724	−0.798621	+	0.601834i	$0.794437\pi$
$912$	26.3463	0.872412
$913$	55.8929	1.84979
$914$	−57.0741	−1.88784
$915$	−31.5258	−1.04221
$916$	−0.0128101	−0.000423257 0
$917$	−17.4210	−0.575294
$918$	−8.88319	−0.293189
$919$	11.8112	0.389616	0.194808	−	0.980841i	$-0.437592\pi$
$919$	11.8112	0.389616	0.194808	+	0.980841i	$0.437592\pi$
$920$	−22.4656	−0.740668
$921$	−24.4357	−0.805182
$922$	−46.8464	−1.54280
$923$	15.2053	0.500489
$924$	−0.0226912	−0.000746486 0
$925$	−19.0846	−0.627497
$926$	−7.25765	−0.238501
$927$	1.52145	0.0499709
$928$	−0.0236934	−0.000777774 0
$929$	−31.5820	−1.03617	−0.518086	−	0.855328i	$-0.673355\pi$
$929$	−31.5820	−1.03617	−0.518086	+	0.855328i	$0.673355\pi$
$930$	7.60833	0.249487
$931$	101.747	3.33461
$932$	0.00428766	0.000140447 0
$933$	15.7799	0.516611
$934$	38.6674	1.26524
$935$	−103.888	−3.39750
$936$	3.49411	0.114209
$937$	−13.0323	−0.425747	−0.212873	−	0.977080i	$-0.568282\pi$
$937$	−13.0323	−0.425747	−0.212873	+	0.977080i	$0.568282\pi$
$938$	−81.4060	−2.65800
$939$	9.72844	0.317476
$940$	0.0280138	0.000913711 0
$941$	7.03399	0.229301	0.114651	−	0.993406i	$-0.463425\pi$
$941$	7.03399	0.229301	0.114651	+	0.993406i	$0.463425\pi$
$942$	−9.76475	−0.318153
$943$	4.37432	0.142448
$944$	−7.42226	−0.241574
$945$	−15.0833	−0.490659
$946$	76.9644	2.50233
$947$	22.7176	0.738223	0.369112	−	0.929385i	$-0.379662\pi$
$947$	22.7176	0.738223	0.369112	+	0.929385i	$0.379662\pi$
$948$	−0.00507999	−0.000164990 0
$949$	−10.0089	−0.324903
$950$	47.8719	1.55317
$951$	−10.1962	−0.330634
$952$	−84.2006	−2.72896
$953$	−4.95223	−0.160418	−0.0802092	−	0.996778i	$-0.525559\pi$
$953$	−4.95223	−0.160418	−0.0802092	+	0.996778i	$0.525559\pi$
$954$	−11.5046	−0.372475
$955$	46.2545	1.49676
$956$	−0.0118350	−0.000382772 0
$957$	−23.5816	−0.762286
$958$	13.0637	0.422067
$959$	96.2119	3.10684
$960$	−25.4841	−0.822496
$961$	−28.1438	−0.907864
$962$	6.48607	0.209119
$963$	1.87556	0.0604390
$964$	−0.00555449	−0.000178898 0
$965$	15.7840	0.508106
$966$	−16.7041	−0.537447
$967$	−40.6599	−1.30753	−0.653767	−	0.756696i	$-0.726813\pi$
$967$	−40.6599	−1.30753	−0.653767	+	0.756696i	$0.726813\pi$
$968$	−45.1772	−1.45205
$969$	−41.4013	−1.33000
$970$	29.8766	0.959279
$971$	−41.2832	−1.32484	−0.662421	−	0.749132i	$-0.730471\pi$
$971$	−41.2832	−1.32484	−0.662421	+	0.749132i	$0.730471\pi$
$972$	0.000922380 0	2.95854e−5 0
$973$	67.2593	2.15623
$974$	−0.343064	−0.0109925
$975$	6.34597	0.203234
$976$	−39.5864	−1.26713
$977$	−5.40511	−0.172925	−0.0864624	−	0.996255i	$-0.527556\pi$
$977$	−5.40511	−0.172925	−0.0864624	+	0.996255i	$0.527556\pi$
$978$	−11.2938	−0.361136
$979$	33.0823	1.05731
$980$	−0.0453472	−0.00144856
$981$	−12.3123	−0.393102
$982$	−28.3804	−0.905656
$983$	59.3207	1.89204	0.946019	−	0.324112i	$-0.105065\pi$
$983$	59.3207	1.89204	0.946019	+	0.324112i	$0.105065\pi$
$984$	4.96207	0.158185
$985$	30.3666	0.967560
$986$	−40.3377	−1.28462
$987$	45.1855	1.43827
$988$	0.00750690	0.000238826 0
$989$	−26.1419	−0.831263
$990$	−23.3790	−0.743033
$991$	−30.1076	−0.956400	−0.478200	−	0.878251i	$-0.658711\pi$
$991$	−30.1076	−0.956400	−0.478200	+	0.878251i	$0.658711\pi$
$992$	−0.00881820	−0.000279978 0
$993$	−11.5187	−0.365534
$994$	−82.4584	−2.61542
$995$	−40.4512	−1.28239
$996$	−0.00992740	−0.000314562 0
$997$	54.3695	1.72190	0.860950	−	0.508690i	$-0.169870\pi$
$997$	54.3695	1.72190	0.860950	+	0.508690i	$0.169870\pi$
$998$	16.9310	0.535940
$999$	3.71429	0.117515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	447.2.a.d.1.7	✓	10
3.2	odd	2		1341.2.a.f.1.4		10
4.3	odd	2		7152.2.a.bc.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
447.2.a.d.1.7	✓	10	1.1	even	1	trivial
1341.2.a.f.1.4		10	3.2	odd	2
7152.2.a.bc.1.8		10	4.3	odd	2

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:	\( N \)	\(=\)	\( 447 = 3 \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	447.a (trivial)

\(f(q)\)	\(=\)	\(q+1.41389 q^{2} -1.00000 q^{3} -0.000922380 q^{4} +3.18405 q^{5} -1.41389 q^{6} +4.73714 q^{7} -2.82908 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.41389 q^{2} -1.00000 q^{3} -0.000922380 q^{4} +3.18405 q^{5} -1.41389 q^{6} +4.73714 q^{7} -2.82908 q^{8} +1.00000 q^{9} +4.50188 q^{10} -5.19316 q^{11} +0.000922380 q^{12} -1.23507 q^{13} +6.69778 q^{14} -3.18405 q^{15} -3.99815 q^{16} +6.28281 q^{17} +1.41389 q^{18} +6.58961 q^{19} -0.00293690 q^{20} -4.73714 q^{21} -7.34254 q^{22} +2.49398 q^{23} +2.82908 q^{24} +5.13815 q^{25} -1.74625 q^{26} -1.00000 q^{27} -0.00436944 q^{28} -4.54091 q^{29} -4.50188 q^{30} -1.69003 q^{31} +0.00521777 q^{32} +5.19316 q^{33} +8.88319 q^{34} +15.0833 q^{35} -0.000922380 q^{36} -3.71429 q^{37} +9.31696 q^{38} +1.23507 q^{39} -9.00792 q^{40} +1.75395 q^{41} -6.69778 q^{42} -10.4820 q^{43} +0.00479006 q^{44} +3.18405 q^{45} +3.52621 q^{46} -9.53857 q^{47} +3.99815 q^{48} +15.4405 q^{49} +7.26476 q^{50} -6.28281 q^{51} +0.00113920 q^{52} -8.13686 q^{53} -1.41389 q^{54} -16.5352 q^{55} -13.4017 q^{56} -6.58961 q^{57} -6.42033 q^{58} +1.85642 q^{59} +0.00293690 q^{60} +9.90116 q^{61} -2.38952 q^{62} +4.73714 q^{63} +8.00369 q^{64} -3.93252 q^{65} +7.34254 q^{66} -12.1542 q^{67} -0.00579514 q^{68} -2.49398 q^{69} +21.3260 q^{70} -12.3113 q^{71} -2.82908 q^{72} +8.10393 q^{73} -5.25159 q^{74} -5.13815 q^{75} -0.00607812 q^{76} -24.6007 q^{77} +1.74625 q^{78} -5.50748 q^{79} -12.7303 q^{80} +1.00000 q^{81} +2.47989 q^{82} -10.7628 q^{83} +0.00436944 q^{84} +20.0048 q^{85} -14.8204 q^{86} +4.54091 q^{87} +14.6918 q^{88} -6.37036 q^{89} +4.50188 q^{90} -5.85069 q^{91} -0.00230040 q^{92} +1.69003 q^{93} -13.4865 q^{94} +20.9816 q^{95} -0.00521777 q^{96} +6.63646 q^{97} +21.8311 q^{98} -5.19316 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 13 q^{4} + 4 q^{5} - 3 q^{6} + 9 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 13 * q^4 + 4 * q^5 - 3 * q^6 + 9 * q^7 + 12 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 13 q^{4} + 4 q^{5} - 3 q^{6} + 9 q^{7} + 12 q^{8} + 10 q^{9} + 8 q^{10} - 7 q^{11} - 13 q^{12} + 4 q^{13} - q^{14} - 4 q^{15} + 23 q^{16} + 10 q^{17} + 3 q^{18} + 9 q^{19} + 6 q^{20} - 9 q^{21} + 12 q^{22} + 9 q^{23} - 12 q^{24} + 34 q^{25} - 12 q^{26} - 10 q^{27} + 30 q^{28} + 8 q^{29} - 8 q^{30} + 15 q^{31} + 32 q^{32} + 7 q^{33} + 12 q^{34} - 16 q^{35} + 13 q^{36} + 31 q^{37} - q^{38} - 4 q^{39} + 2 q^{40} - 5 q^{41} + q^{42} + 8 q^{43} - 9 q^{44} + 4 q^{45} - 11 q^{46} + 2 q^{47} - 23 q^{48} + 29 q^{49} - 7 q^{50} - 10 q^{51} - 40 q^{52} + 4 q^{53} - 3 q^{54} - 2 q^{55} - 48 q^{56} - 9 q^{57} - 8 q^{58} - 59 q^{59} - 6 q^{60} + q^{61} - 14 q^{62} + 9 q^{63} + 24 q^{64} + 12 q^{65} - 12 q^{66} + 5 q^{67} - 12 q^{68} - 9 q^{69} - 34 q^{70} - 11 q^{71} + 12 q^{72} + 51 q^{73} - 23 q^{74} - 34 q^{75} - 27 q^{76} + 4 q^{77} + 12 q^{78} - 6 q^{79} + 10 q^{80} + 10 q^{81} - 40 q^{82} - 21 q^{83} - 30 q^{84} + 32 q^{85} - 44 q^{86} - 8 q^{87} - 29 q^{88} - 5 q^{89} + 8 q^{90} - 6 q^{91} - 14 q^{92} - 15 q^{93} - 42 q^{94} - 24 q^{95} - 32 q^{96} + 32 q^{97} + 14 q^{98} - 7 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 13 * q^4 + 4 * q^5 - 3 * q^6 + 9 * q^7 + 12 * q^8 + 10 * q^9 + 8 * q^10 - 7 * q^11 - 13 * q^12 + 4 * q^13 - q^14 - 4 * q^15 + 23 * q^16 + 10 * q^17 + 3 * q^18 + 9 * q^19 + 6 * q^20 - 9 * q^21 + 12 * q^22 + 9 * q^23 - 12 * q^24 + 34 * q^25 - 12 * q^26 - 10 * q^27 + 30 * q^28 + 8 * q^29 - 8 * q^30 + 15 * q^31 + 32 * q^32 + 7 * q^33 + 12 * q^34 - 16 * q^35 + 13 * q^36 + 31 * q^37 - q^38 - 4 * q^39 + 2 * q^40 - 5 * q^41 + q^42 + 8 * q^43 - 9 * q^44 + 4 * q^45 - 11 * q^46 + 2 * q^47 - 23 * q^48 + 29 * q^49 - 7 * q^50 - 10 * q^51 - 40 * q^52 + 4 * q^53 - 3 * q^54 - 2 * q^55 - 48 * q^56 - 9 * q^57 - 8 * q^58 - 59 * q^59 - 6 * q^60 + q^61 - 14 * q^62 + 9 * q^63 + 24 * q^64 + 12 * q^65 - 12 * q^66 + 5 * q^67 - 12 * q^68 - 9 * q^69 - 34 * q^70 - 11 * q^71 + 12 * q^72 + 51 * q^73 - 23 * q^74 - 34 * q^75 - 27 * q^76 + 4 * q^77 + 12 * q^78 - 6 * q^79 + 10 * q^80 + 10 * q^81 - 40 * q^82 - 21 * q^83 - 30 * q^84 + 32 * q^85 - 44 * q^86 - 8 * q^87 - 29 * q^88 - 5 * q^89 + 8 * q^90 - 6 * q^91 - 14 * q^92 - 15 * q^93 - 42 * q^94 - 24 * q^95 - 32 * q^96 + 32 * q^97 + 14 * q^98 - 7 * q^99

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