LMFDB - Embedded newform 147.3.h.f.116.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,3,Mod(116,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("147.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	147.h (of order $6$, degree $2$, not minimal)

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:	no
Analytic conductor:	$4.00545988610$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 10x^{14} + 65x^{12} - 366x^{10} + 1280x^{8} + 780x^{6} - 811x^{4} + 200x^{2} + 625 $ x^16 - 10x^14 + 65x^12 - 366x^10 + 1280x^8 + 780x^6 - 811x^4 + 200*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.7
Root			$-2.41981 - 0.580584i$ of defining polynomial
Character	$\chi$	$=$	147.116
Dual form			147.3.h.f.128.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.92214 - 1.68710i) q^{2} +(-1.88023 + 2.33768i) q^{3} +(3.69258 - 6.39574i) q^{4} +(4.92837 - 2.84540i) q^{5} +(-1.55039 + 10.0031i) q^{6} -11.4222i q^{8} +(-1.92949 - 8.79074i) q^{9} +O(q^{10})$	\(q+(2.92214 - 1.68710i) q^{2} +(-1.88023 + 2.33768i) q^{3} +(3.69258 - 6.39574i) q^{4} +(4.92837 - 2.84540i) q^{5} +(-1.55039 + 10.0031i) q^{6} -11.4222i q^{8} +(-1.92949 - 8.79074i) q^{9} +(9.60092 - 16.6293i) q^{10} +(9.43753 + 5.44876i) q^{11} +(8.00830 + 20.6575i) q^{12} -1.14186 q^{13} +(-2.61484 + 16.8710i) q^{15} +(-4.50000 - 7.79423i) q^{16} +(-13.9893 - 8.07671i) q^{17} +(-20.4690 - 22.4325i) q^{18} +(-1.00568 - 1.74190i) q^{19} -42.0275i q^{20} +36.7703 q^{22} +(-32.5979 + 18.8204i) q^{23} +(26.7014 + 21.4763i) q^{24} +(3.69258 - 6.39574i) q^{25} +(-3.33667 + 1.92643i) q^{26} +(24.1778 + 12.0181i) q^{27} +17.3956i q^{29} +(20.8220 + 53.7107i) q^{30} +(-13.8173 + 23.9323i) q^{31} +(13.2684 + 7.66053i) q^{32} +(-30.4822 + 11.8170i) q^{33} -54.5047 q^{34} +(-63.3481 - 20.1200i) q^{36} +(-22.5777 - 39.1058i) q^{37} +(-5.87749 - 3.39337i) q^{38} +(2.14696 - 2.66930i) q^{39} +(-32.5007 - 56.2928i) q^{40} +39.2706i q^{41} -28.6962 q^{43} +(69.6977 - 40.2400i) q^{44} +(-34.5224 - 37.8339i) q^{45} +(-63.5036 + 109.991i) q^{46} +(33.3667 - 19.2643i) q^{47} +(26.6814 + 4.13536i) q^{48} -24.9190i q^{50} +(45.1838 - 17.5164i) q^{51} +(-4.21642 + 7.30305i) q^{52} +(-1.34226 - 0.774952i) q^{53} +(90.9264 - 5.67189i) q^{54} +62.0156 q^{55} +(5.96291 + 0.924194i) q^{57} +(29.3481 + 50.8324i) q^{58} +(73.2830 + 42.3100i) q^{59} +(98.2468 + 79.0212i) q^{60} +(-47.4599 - 82.2029i) q^{61} +93.2446i q^{62} +87.6962 q^{64} +(-5.62752 + 3.24905i) q^{65} +(-69.1366 + 85.9572i) q^{66} +(48.5407 - 84.0749i) q^{67} +(-103.313 + 59.6478i) q^{68} +(17.2954 - 111.590i) q^{69} -17.3956i q^{71} +(-100.409 + 22.0390i) q^{72} +(34.5433 - 59.8308i) q^{73} +(-131.950 - 76.1816i) q^{74} +(8.00830 + 20.6575i) q^{75} -14.8543 q^{76} +(1.77033 - 11.4222i) q^{78} +(6.77033 + 11.7266i) q^{79} +(-44.3554 - 25.6086i) q^{80} +(-73.5541 + 33.9233i) q^{81} +(66.2532 + 114.754i) q^{82} -61.5028i q^{83} -91.9258 q^{85} +(-83.8540 + 48.4132i) q^{86} +(-40.6654 - 32.7077i) q^{87} +(62.2368 - 107.797i) q^{88} +(-26.0508 + 15.0404i) q^{89} +(-164.708 - 52.3131i) q^{90} +277.983i q^{92} +(-29.9664 - 77.2987i) q^{93} +(65.0014 - 112.586i) q^{94} +(-9.91278 - 5.72315i) q^{95} +(-42.8555 + 16.6138i) q^{96} -125.655 q^{97} +(29.6890 - 93.4762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 4 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 4 * q^9	$ 16 q + 16 q^{4} - 4 q^{9} - 128 q^{15} - 72 q^{16} + 52 q^{18} + 416 q^{22} + 16 q^{25} + 240 q^{30} - 712 q^{36} - 232 q^{37} - 16 q^{39} + 144 q^{43} - 456 q^{46} + 124 q^{51} - 120 q^{57} + 168 q^{58} + 104 q^{60} + 800 q^{64} + 432 q^{67} - 12 q^{72} - 144 q^{78} - 64 q^{79} - 400 q^{81} - 1040 q^{85} + 48 q^{88} - 440 q^{93} + 992 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 4 * q^9 - 128 * q^15 - 72 * q^16 + 52 * q^18 + 416 * q^22 + 16 * q^25 + 240 * q^30 - 712 * q^36 - 232 * q^37 - 16 * q^39 + 144 * q^43 - 456 * q^46 + 124 * q^51 - 120 * q^57 + 168 * q^58 + 104 * q^60 + 800 * q^64 + 432 * q^67 - 12 * q^72 - 144 * q^78 - 64 * q^79 - 400 * q^81 - 1040 * q^85 + 48 * q^88 - 440 * q^93 + 992 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.92214	−	1.68710i	1.46107	−	0.843548i	0.462007	−	0.886876i	$-0.347130\pi$
$2$	2.92214	−	1.68710i	1.46107	−	0.843548i	0.999061	+	0.0433287i	$0.0137963\pi$
$3$	−1.88023	+	2.33768i	−0.626742	+	0.779226i
$3$	−1.88023	+	2.33768i	−0.626742	+	0.779226i
$4$	3.69258	−	6.39574i	0.923146	−	1.59894i
$5$	4.92837	−	2.84540i	0.985675	−	0.569080i	0.0816962	−	0.996657i	$-0.473966\pi$
$5$	4.92837	−	2.84540i	0.985675	−	0.569080i	0.903979	+	0.427578i	$0.140633\pi$
$6$	−1.55039	+	10.0031i	−0.258398	+	1.66719i
$7$		0			0
$7$		0			0
$8$		−	11.4222i		−	1.42777i
$9$	−1.92949	−	8.79074i	−0.214388	−	0.976749i
$10$	9.60092	−	16.6293i	0.960092	−	1.66293i
$11$	9.43753	+	5.44876i	0.857958	+	0.495342i	0.863328	−	0.504644i	$-0.168376\pi$
$11$	9.43753	+	5.44876i	0.857958	+	0.495342i	−0.00537023	+	0.999986i	$0.501709\pi$
$12$	8.00830	+	20.6575i	0.667358	+	1.72146i
$13$	−1.14186			−0.0878355			−0.0439177	−	0.999035i	$-0.513984\pi$
$13$	−1.14186			−0.0878355			−0.0439177	+	0.999035i	$0.513984\pi$
$14$		0			0
$15$	−2.61484	+	16.8710i	−0.174322	+	1.12473i
$16$	−4.50000	−	7.79423i	−0.281250	−	0.487139i
$17$	−13.9893	−	8.07671i	−0.822898	−	0.475101i	0.0285166	−	0.999593i	$-0.490922\pi$
$17$	−13.9893	−	8.07671i	−0.822898	−	0.475101i	−0.851415	+	0.524493i	$0.824255\pi$
$18$	−20.4690	−	22.4325i	−1.13717	−	1.24625i
$19$	−1.00568	−	1.74190i	−0.0529308	−	0.0916788i	0.838346	−	0.545138i	$-0.183523\pi$
$19$	−1.00568	−	1.74190i	−0.0529308	−	0.0916788i	−0.891277	+	0.453460i	$0.850190\pi$
$20$		−	42.0275i		−	2.10137i
$21$		0			0
$22$	36.7703			1.67138
$23$	−32.5979	+	18.8204i	−1.41730	+	0.818278i	−0.996061	−	0.0886728i	$-0.971737\pi$
$23$	−32.5979	+	18.8204i	−1.41730	+	0.818278i	−0.421238	+	0.906950i	$0.638404\pi$
$24$	26.7014	+	21.4763i	1.11256	+	0.894847i
$25$	3.69258	−	6.39574i	0.147703	−	0.255830i
$26$	−3.33667	+	1.92643i	−0.128334	+	0.0740934i
$27$	24.1778	+	12.0181i	0.895474	+	0.445113i
$28$		0			0
$29$			17.3956i			0.599849i	0.953963	+	0.299925i	$0.0969615\pi$
$29$			17.3956i			0.599849i	−0.953963	+	0.299925i	$0.903038\pi$
$30$	20.8220	+	53.7107i	0.694067	+	1.79036i
$31$	−13.8173	+	23.9323i	−0.445720	+	0.772010i	−0.998102	−	0.0615809i	$-0.980386\pi$
$31$	−13.8173	+	23.9323i	−0.445720	+	0.772010i	0.552382	+	0.833591i	$0.313719\pi$
$32$	13.2684	+	7.66053i	0.414638	+	0.239391i
$33$	−30.4822	+	11.8170i	−0.923702	+	0.358091i
$34$	−54.5047			−1.60308
$35$		0			0
$36$	−63.3481	−	20.1200i	−1.75967	−	0.558889i
$37$	−22.5777	−	39.1058i	−0.610209	−	1.05691i	−0.991205	−	0.132337i	$-0.957752\pi$
$37$	−22.5777	−	39.1058i	−0.610209	−	1.05691i	0.380995	−	0.924577i	$-0.375581\pi$
$38$	−5.87749	−	3.39337i	−0.154671	−	0.0892993i
$39$	2.14696	−	2.66930i	0.0550502	−	0.0684437i
$40$	−32.5007	−	56.2928i	−0.812517	−	1.40732i
$41$			39.2706i			0.957819i	0.877864	+	0.478909i	$0.158968\pi$
$41$			39.2706i			0.957819i	−0.877864	+	0.478909i	$0.841032\pi$
$42$		0			0
$43$	−28.6962			−0.667352			−0.333676	−	0.942688i	$-0.608289\pi$
$43$	−28.6962			−0.667352			−0.333676	+	0.942688i	$0.608289\pi$
$44$	69.6977	−	40.2400i	1.58404	−	0.914546i
$45$	−34.5224	−	37.8339i	−0.767164	−	0.840753i
$46$	−63.5036	+	109.991i	−1.38051	+	2.39112i
$47$	33.3667	−	19.2643i	0.709930	−	0.409878i	−0.101105	−	0.994876i	$-0.532238\pi$
$47$	33.3667	−	19.2643i	0.709930	−	0.409878i	0.811035	+	0.584997i	$0.198904\pi$
$48$	26.6814	+	4.13536i	0.555863	+	0.0861534i
$49$		0			0
$50$		−	24.9190i		−	0.498379i
$51$	45.1838	−	17.5164i	0.885956	−	0.343458i
$52$	−4.21642	+	7.30305i	−0.0810849	+	0.140443i
$53$	−1.34226	−	0.774952i	−0.0253256	−	0.0146217i	0.487284	−	0.873244i	$-0.337988\pi$
$53$	−1.34226	−	0.774952i	−0.0253256	−	0.0146217i	−0.512609	+	0.858622i	$0.671321\pi$
$54$	90.9264	−	5.67189i	1.68382	−	0.105035i
$55$	62.0156			1.12756
$56$		0			0
$57$	5.96291	+	0.924194i	0.104612	+	0.0162139i
$58$	29.3481	+	50.8324i	0.506001	+	0.876420i
$59$	73.2830	+	42.3100i	1.24209	+	0.717118i	0.969518	−	0.245019i	$-0.0787941\pi$
$59$	73.2830	+	42.3100i	1.24209	+	0.717118i	0.272567	+	0.962137i	$0.412127\pi$
$60$	98.2468	+	79.0212i	1.63745	+	1.31702i
$61$	−47.4599	−	82.2029i	−0.778031	−	1.34759i	−0.933075	−	0.359681i	$-0.882885\pi$
$61$	−47.4599	−	82.2029i	−0.778031	−	1.34759i	0.155044	−	0.987908i	$-0.450448\pi$
$62$			93.2446i			1.50395i
$63$		0			0
$64$	87.6962			1.37025
$65$	−5.62752	+	3.24905i	−0.0865772	+	0.0499854i
$66$	−69.1366	+	85.9572i	−1.04752	+	1.30238i
$67$	48.5407	−	84.0749i	0.724487	−	1.25485i	−0.234697	−	0.972069i	$-0.575410\pi$
$67$	48.5407	−	84.0749i	0.724487	−	1.25485i	0.959185	−	0.282781i	$-0.0912568\pi$
$68$	−103.313	+	59.6478i	−1.51931	+	0.877174i
$69$	17.2954	−	111.590i	0.250657	−	1.61725i
$70$		0			0
$71$		−	17.3956i		−	0.245009i	−0.992468	−	0.122504i	$-0.960907\pi$
$71$		−	17.3956i		−	0.245009i	0.992468	−	0.122504i	$-0.0390926\pi$
$72$	−100.409	+	22.0390i	−1.39458	+	0.306097i
$73$	34.5433	−	59.8308i	0.473196	−	0.819600i	−0.526333	−	0.850279i	$-0.676433\pi$
$73$	34.5433	−	59.8308i	0.473196	−	0.819600i	0.999529	+	0.0306785i	$0.00976679\pi$
$74$	−131.950	−	76.1816i	−1.78311	−	1.02948i
$75$	8.00830	+	20.6575i	0.106777	+	0.275434i
$76$	−14.8543			−0.195451
$77$		0			0
$78$	1.77033	−	11.4222i	0.0226965	−	0.146438i
$79$	6.77033	+	11.7266i	0.0857004	+	0.148437i	0.905689	−	0.423942i	$-0.139354\pi$
$79$	6.77033	+	11.7266i	0.0857004	+	0.148437i	−0.819989	+	0.572379i	$0.806021\pi$
$80$	−44.3554	−	25.6086i	−0.554442	−	0.320107i
$81$	−73.5541	+	33.9233i	−0.908076	+	0.418806i
$82$	66.2532	+	114.754i	0.807966	+	1.39944i
$83$		−	61.5028i		−	0.740998i	−0.928833	−	0.370499i	$-0.879187\pi$
$83$		−	61.5028i		−	0.740998i	0.928833	−	0.370499i	$-0.120813\pi$
$84$		0			0
$85$	−91.9258			−1.08148
$86$	−83.8540	+	48.4132i	−0.975047	+	0.562944i
$87$	−40.6654	−	32.7077i	−0.467418	−	0.375951i
$88$	62.2368	−	107.797i	0.707237	−	1.22497i
$89$	−26.0508	+	15.0404i	−0.292706	+	0.168994i	−0.639161	−	0.769073i	$-0.720718\pi$
$89$	−26.0508	+	15.0404i	−0.292706	+	0.168994i	0.346456	+	0.938066i	$0.387385\pi$
$90$	−164.708	−	52.3131i	−1.83009	−	0.581257i
$91$		0			0
$92$			277.983i			3.02156i
$93$	−29.9664	−	77.2987i	−0.322219	−	0.831169i
$94$	65.0014	−	112.586i	0.691504	−	1.19772i
$95$	−9.91278	−	5.72315i	−0.104345	−	0.0602436i
$96$	−42.8555	+	16.6138i	−0.446411	+	0.173060i
$97$	−125.655			−1.29541			−0.647707	−	0.761889i	$-0.724272\pi$
$97$	−125.655			−1.29541			−0.647707	+	0.761889i	$0.724272\pi$
$98$		0			0
$99$	29.6890	−	93.4762i	0.299889	−	0.944204i
$100$	−27.2703	−	47.2336i	−0.272703	−	0.472336i
$101$	132.701	+	76.6147i	1.31387	+	0.758561i	0.982734	−	0.185023i	$-0.0592359\pi$
$101$	132.701	+	76.6147i	1.31387	+	0.758561i	0.331133	+	0.943584i	$0.392569\pi$
$102$	102.481	−	127.415i	1.00472	−	1.24916i
$103$	29.6460	+	51.3484i	0.287826	+	0.498529i	0.973290	−	0.229577i	$-0.0737343\pi$
$103$	29.6460	+	51.3484i	0.287826	+	0.498529i	−0.685465	+	0.728106i	$0.740401\pi$
$104$			13.0426i			0.125409i
$105$		0			0
$106$	−5.22967			−0.0493365
$107$	−36.1911	+	20.8950i	−0.338235	+	0.195280i	−0.659491	−	0.751712i	$-0.729228\pi$
$107$	−36.1911	+	20.8950i	−0.338235	+	0.195280i	0.321256	+	0.946992i	$0.395895\pi$
$108$	166.143	−	110.257i	1.53836	−	1.02090i
$109$	−18.5036	+	32.0491i	−0.169758	+	0.294029i	−0.938335	−	0.345729i	$-0.887632\pi$
$109$	−18.5036	+	32.0491i	−0.169758	+	0.294029i	0.768577	+	0.639757i	$0.220965\pi$
$110$	181.218	−	104.626i	1.64744	−	0.951148i
$111$	133.868	+	20.7483i	1.20602	+	0.186921i
$112$		0			0
$113$		−	175.708i		−	1.55494i	−0.628920	−	0.777470i	$-0.716503\pi$
$113$		−	175.708i		−	1.55494i	0.628920	−	0.777470i	$-0.283497\pi$
$114$	18.9836	−	7.35938i	0.166523	−	0.0645560i
$115$	−107.103	+	185.508i	−0.931330	+	1.61311i
$116$	111.258	+	64.2348i	0.959120	+	0.553748i
$117$	2.20321	+	10.0378i	0.0188309	+	0.0857932i
$118$	285.524			2.41969
$119$		0			0
$120$	192.703	+	29.8672i	1.60586	+	0.248893i
$121$	−1.12198	−	1.94332i	−0.00927254	−	0.0160605i
$122$	−277.368	−	160.139i	−2.27351	−	1.31261i
$123$	−91.8020	−	73.8376i	−0.746358	−	0.600306i
$124$	102.043	+	176.744i	0.822930	+	1.42536i
$125$			100.242i			0.801940i
$126$		0			0
$127$	124.785			0.982556			0.491278	−	0.871003i	$-0.336530\pi$
$127$	124.785			0.982556			0.491278	+	0.871003i	$0.336530\pi$
$128$	203.186	−	117.310i	1.58739	−	0.916482i
$129$	53.9553	−	67.0824i	0.418258	−	0.520019i
$130$	−10.9629	+	18.9883i	−0.0843301	+	0.146064i
$131$	−66.6097	+	38.4571i	−0.508471	+	0.293566i	−0.732205	−	0.681084i	$-0.761509\pi$
$131$	−66.6097	+	38.4571i	−0.508471	+	0.293566i	0.223734	+	0.974650i	$0.428175\pi$
$132$	−36.9794	+	238.591i	−0.280147	+	1.80751i
$133$		0			0
$134$		−	327.571i		−	2.44456i
$135$	153.353	−	9.56601i	1.13595	−	0.0708594i
$136$	−92.2537	+	159.788i	−0.678336	+	1.17491i
$137$	140.738	+	81.2550i	1.02728	+	0.593102i	0.916205	−	0.400710i	$-0.131236\pi$
$137$	140.738	+	81.2550i	1.02728	+	0.593102i	0.111078	+	0.993812i	$0.464570\pi$
$138$	−137.724	−	355.260i	−0.997996	−	2.57435i
$139$	−137.461			−0.988929			−0.494465	−	0.869198i	$-0.664636\pi$
$139$	−137.461			−0.988929			−0.494465	+	0.869198i	$0.664636\pi$
$140$		0			0
$141$	−17.7033	+	114.222i	−0.125555	+	0.810085i
$142$	−29.3481	−	50.8324i	−0.206677	−	0.357974i
$143$	−10.7764	−	6.22173i	−0.0753591	−	0.0435086i
$144$	−59.8343	+	54.5972i	−0.415516	+	0.379147i
$145$	49.4975	+	85.7321i	0.341362	+	0.591256i
$146$		−	233.112i		−	1.59665i
$147$		0			0
$148$	−333.481			−2.25325
$149$	13.9813	−	8.07210i	0.0938342	−	0.0541752i	−0.452349	−	0.891841i	$-0.649414\pi$
$149$	13.9813	−	8.07210i	0.0938342	−	0.0541752i	0.546183	+	0.837666i	$0.316080\pi$
$150$	58.2525	+	46.8533i	0.388350	+	0.312355i
$151$	−10.1555	+	17.5898i	−0.0672549	+	0.116489i	−0.897692	−	0.440623i	$-0.854757\pi$
$151$	−10.1555	+	17.5898i	−0.0672549	+	0.116489i	0.830437	+	0.557112i	$0.188091\pi$
$152$	−19.8963	+	11.4871i	−0.130897	+	0.0755732i
$153$	−44.0081	+	138.560i	−0.287634	+	0.905621i
$154$		0			0
$155$			157.263i			1.01460i
$156$	−9.14436	−	23.5880i	−0.0586177	−	0.151205i
$157$	71.2816	−	123.463i	0.454023	−	0.786391i	−0.544608	−	0.838690i	$-0.683322\pi$
$157$	71.2816	−	123.463i	0.454023	−	0.786391i	0.998631	+	0.0522995i	$0.0166551\pi$
$158$	39.5676	+	22.8444i	0.250428	+	0.144585i
$159$	4.33533	−	1.68068i	0.0272663	−	0.0105703i
$160$	87.1890			0.544931
$161$		0			0
$162$	−157.703	+	223.221i	−0.973477	+	1.37791i
$163$	59.8146	+	103.602i	0.366960	+	0.635594i	0.989089	−	0.147321i	$-0.0470651\pi$
$163$	59.8146	+	103.602i	0.366960	+	0.635594i	−0.622128	+	0.782915i	$0.713732\pi$
$164$	251.164	+	145.010i	1.53149	+	0.884206i
$165$	−116.603	+	144.973i	−0.706687	+	0.878622i
$166$	−103.761	−	179.720i	−0.625067	−	1.08265i
$167$		−	110.140i		−	0.659521i	−0.944065	−	0.329761i	$-0.893032\pi$
$167$		−	110.140i		−	0.659521i	0.944065	−	0.329761i	$-0.106968\pi$
$168$		0			0
$169$	−167.696			−0.992285
$170$	−268.620	+	155.088i	−1.58012	+	0.912280i
$171$	−13.3721	+	12.2017i	−0.0781994	+	0.0713549i
$172$	−105.963	+	183.533i	−0.616063	+	1.06705i
$173$	256.676	−	148.192i	1.48368	−	0.856602i	0.483850	−	0.875151i	$-0.339238\pi$
$173$	256.676	−	148.192i	1.48368	−	0.856602i	0.999828	+	0.0185494i	$0.00590480\pi$
$174$	−174.011	−	26.9700i	−1.00006	−	0.155000i
$175$		0			0
$176$		−	98.0777i		−	0.557260i
$177$	−236.696	+	91.7599i	−1.33727	+	0.518417i
$178$	−50.7493	+	87.9003i	−0.285108	+	0.493822i
$179$	−41.5601	−	23.9948i	−0.232180	−	0.134049i	0.379398	−	0.925234i	$-0.376131\pi$
$179$	−41.5601	−	23.9948i	−0.232180	−	0.134049i	−0.611577	+	0.791185i	$0.709465\pi$
$180$	−369.452	+	81.0916i	−2.05251	+	0.450509i
$181$	−163.347			−0.902468			−0.451234	−	0.892406i	$-0.649016\pi$
$181$	−163.347			−0.902468			−0.451234	+	0.892406i	$0.649016\pi$
$182$		0			0
$183$	281.399	+	43.6142i	1.53770	+	0.238329i
$184$	214.970	+	372.339i	1.16832	+	2.02358i
$185$	−222.543	−	128.485i	−1.20294	−	0.694515i
$186$	−217.976	−	175.321i	−1.17191	−	0.942587i
$187$	−88.0161	−	152.448i	−0.470675	−	0.815232i
$188$		−	284.540i		−	1.51351i
$189$		0			0
$190$	−38.6220			−0.203274
$191$	16.8826	−	9.74715i	0.0883903	−	0.0510322i	−0.455153	−	0.890413i	$-0.650416\pi$
$191$	16.8826	−	9.74715i	0.0883903	−	0.0510322i	0.543544	+	0.839381i	$0.317082\pi$
$192$	−164.889	+	205.005i	−0.858795	+	1.06774i
$193$	65.4964	−	113.443i	0.339360	−	0.587788i	−0.644953	−	0.764222i	$-0.723123\pi$
$193$	65.4964	−	113.443i	0.339360	−	0.587788i	0.984312	+	0.176434i	$0.0564563\pi$
$194$	−367.181	+	211.992i	−1.89269	+	1.09274i
$195$	2.98578	−	19.2643i	0.0153117	−	0.0987912i
$196$		0			0
$197$			272.583i			1.38367i	0.722056	+	0.691834i	$0.243197\pi$
$197$			272.583i			1.38367i	−0.722056	+	0.691834i	$0.756803\pi$
$198$	−70.9480	−	323.238i	−0.358323	−	1.63252i
$199$	−99.0999	+	171.646i	−0.497989	+	0.862543i	−0.999997	−	0.00232032i	$-0.999261\pi$
$199$	−99.0999	+	171.646i	−0.497989	+	0.862543i	0.502008	+	0.864863i	$0.332595\pi$
$200$	−73.0534	−	42.1774i	−0.365267	−	0.210887i
$201$	105.273	+	271.552i	0.523745	+	1.35101i
$202$	517.025			2.55953
$203$		0			0
$204$	54.8146	−	353.664i	0.268699	−	1.73365i
$205$	111.740	+	193.540i	0.545075	+	0.944098i
$206$	173.259	+	100.031i	0.841065	+	0.485589i
$207$	228.342	+	250.246i	1.10310	+	1.20892i
$208$	5.13837	+	8.89993i	0.0247037	+	0.0427881i
$209$		−	21.9189i		−	0.104875i
$210$		0			0
$211$	270.177			1.28046			0.640230	−	0.768184i	$-0.278839\pi$
$211$	270.177			1.28046			0.640230	+	0.768184i	$0.278839\pi$
$212$	−9.91278	+	5.72315i	−0.0467584	+	0.0269960i
$213$	40.6654	+	32.7077i	0.190917	+	0.153557i
$214$	−70.5036	+	122.116i	−0.329456	+	0.570634i
$215$	−141.425	+	81.6520i	−0.657792	+	0.379777i
$216$	137.273	−	276.164i	0.635521	−	1.27854i
$217$		0			0
$218$			124.869i			0.572794i
$219$	74.9159	+	193.247i	0.342082	+	0.882405i
$220$	228.998	−	396.636i	1.04090	−	1.80289i
$221$	15.9738	+	9.22248i	0.0722797	+	0.0417307i
$222$	426.185	−	165.219i	1.91975	−	0.744230i
$223$	41.9019			0.187901			0.0939505	−	0.995577i	$-0.470050\pi$
$223$	41.9019			0.187901			0.0939505	+	0.995577i	$0.470050\pi$
$224$		0			0
$225$	−63.3481	−	20.1200i	−0.281547	−	0.0894222i
$226$	−296.437	−	513.443i	−1.31167	−	2.27187i
$227$	−269.746	−	155.738i	−1.18831	−	0.686070i	−0.230386	−	0.973099i	$-0.573999\pi$
$227$	−269.746	−	155.738i	−1.18831	−	0.686070i	−0.957922	+	0.287029i	$0.907332\pi$
$228$	27.9294	−	34.7246i	0.122498	−	0.152301i
$229$	11.5699	+	20.0397i	0.0505237	+	0.0875097i	0.890181	−	0.455607i	$-0.150578\pi$
$229$	11.5699	+	20.0397i	0.0505237	+	0.0875097i	−0.839657	+	0.543116i	$0.817244\pi$
$230$			722.772i			3.14249i
$231$		0			0
$232$	198.696			0.856449
$233$	54.3324	−	31.3689i	0.233186	−	0.134630i	−0.378855	−	0.925456i	$-0.623682\pi$
$233$	54.3324	−	31.3689i	0.233186	−	0.134630i	0.612041	+	0.790826i	$0.290349\pi$
$234$	23.3728	+	25.6148i	0.0998838	+	0.109465i
$235$	109.629	−	189.883i	0.466507	−	0.808014i
$236$	541.207	−	312.466i	2.29325	−	1.32401i
$237$	−40.1427	−	6.22173i	−0.169378	−	0.0262520i
$238$		0			0
$239$		−	240.189i		−	1.00497i	−0.864585	−	0.502487i	$-0.832419\pi$
$239$		−	240.189i		−	1.00497i	0.864585	−	0.502487i	$-0.167581\pi$
$240$	143.263	−	55.5387i	0.596928	−	0.231411i
$241$	157.150	−	272.192i	0.652076	−	1.12943i	−0.330543	−	0.943791i	$-0.607232\pi$
$241$	157.150	−	272.192i	0.652076	−	1.12943i	0.982618	−	0.185637i	$-0.0594348\pi$
$242$	−6.55714	−	3.78577i	−0.0270956	−	0.0156437i
$243$	58.9967	−	235.729i	0.242785	−	0.970080i
$244$	−700.998			−2.87294
$245$		0			0
$246$	−392.829	−	60.8847i	−1.59687	−	0.247499i
$247$	1.14835	+	1.98900i	0.00464920	+	0.00805265i
$248$	273.360	+	157.824i	1.10226	+	0.636388i
$249$	143.774	+	115.639i	0.577405	+	0.464415i
$250$	169.119	+	292.922i	0.676474	+	1.17169i
$251$			429.607i			1.71158i	0.517321	+	0.855791i	$0.326929\pi$
$251$			429.607i			1.71158i	−0.517321	+	0.855791i	$0.673071\pi$
$252$		0			0
$253$	−410.191			−1.62131
$254$	364.638	−	210.524i	1.43558	−	0.828833i
$255$	172.841	−	214.893i	0.677810	−	0.842718i
$256$	220.433	−	381.801i	0.861066	−	1.49141i
$257$	−181.436	+	104.752i	−0.705976	+	0.407596i	−0.809569	−	0.587024i	$-0.800299\pi$
$257$	−181.436	+	104.752i	−0.705976	+	0.407596i	0.103593	+	0.994620i	$0.466966\pi$
$258$	44.4902	−	287.052i	0.172443	−	1.11260i
$259$		0			0
$260$			47.9895i			0.184575i
$261$	152.920	−	33.5647i	0.585902	−	0.128600i
$262$	−129.762	+	224.754i	−0.495274	+	0.857839i
$263$	−223.725	−	129.168i	−0.850664	−	0.491131i	0.0102105	−	0.999948i	$-0.496750\pi$
$263$	−223.725	−	129.168i	−0.850664	−	0.491131i	−0.860875	+	0.508816i	$0.830083\pi$
$264$	134.976	+	348.173i	0.511274	+	1.31884i
$265$	−8.82019			−0.0332837
$266$		0			0
$267$	13.8217	−	89.1778i	0.0517667	−	0.333999i
$268$	−358.481	−	620.907i	−1.33761	−	2.31682i
$269$	−105.760	−	61.0604i	−0.393159	−	0.226990i	0.290369	−	0.956915i	$-0.406222\pi$
$269$	−105.760	−	61.0604i	−0.393159	−	0.226990i	−0.683528	+	0.729924i	$0.739555\pi$
$270$	431.981	−	286.675i	1.59993	−	1.06176i
$271$	27.7396	+	48.0463i	0.102360	+	0.177293i	0.912657	−	0.408727i	$-0.134027\pi$
$271$	27.7396	+	48.0463i	0.102360	+	0.177293i	−0.810297	+	0.586020i	$0.800694\pi$
$272$			145.381i			0.534488i
$273$		0			0
$274$	548.340			2.00124
$275$	69.6977	−	40.2400i	0.253446	−	0.146327i
$276$	−649.836	−	522.672i	−2.35448	−	1.89374i
$277$	−138.852	+	240.498i	−0.501269	+	0.868224i	0.498729	+	0.866758i	$0.333800\pi$
$277$	−138.852	+	240.498i	−0.501269	+	0.868224i	−0.999999	+	0.00146650i	$0.999533\pi$
$278$	−401.680	+	231.910i	−1.44489	+	0.834209i
$279$	237.043	+	75.2874i	0.849617	+	0.269847i
$280$		0			0
$281$			90.3282i			0.321453i	0.986999	+	0.160726i	$0.0513837\pi$
$281$			90.3282i			0.321453i	−0.986999	+	0.160726i	$0.948616\pi$
$282$	140.972	+	363.639i	0.499900	+	1.28950i
$283$	−145.003	+	251.153i	−0.512379	+	0.887467i	0.487518	+	0.873113i	$0.337902\pi$
$283$	−145.003	+	251.153i	−0.512379	+	0.887467i	−0.999897	+	0.0143538i	$0.995431\pi$
$284$	−111.258	−	64.2348i	−0.391753	−	0.226179i
$285$	32.0172	−	12.4121i	0.112341	−	0.0435512i
$286$	−41.9866			−0.146806
$287$		0			0
$288$	41.7404	−	131.420i	0.144932	−	0.456320i
$289$	−14.0335	−	24.3068i	−0.0485589	−	0.0841064i
$290$	289.277	+	167.014i	0.997506	+	0.575910i
$291$	236.260	−	293.742i	0.811891	−	1.00942i
$292$	−255.108	−	441.860i	−0.873658	−	1.51322i
$293$		−	265.983i		−	0.907793i	−0.891054	−	0.453897i	$-0.850034\pi$
$293$		−	265.983i		−	0.907793i	0.891054	−	0.453897i	$-0.149966\pi$
$294$		0			0
$295$	481.555			1.63239
$296$	−446.674	+	257.887i	−1.50903	+	0.871241i
$297$	162.695	+	245.160i	0.547796	+	0.825454i
$298$	27.2368	−	47.1755i	0.0913987	−	0.158307i
$299$	37.2222	−	21.4903i	0.124489	−	0.0718738i
$300$	161.691	+	25.0606i	0.538971	+	0.0835354i
$301$		0			0
$302$			68.5332i			0.226931i
$303$	−428.608	+	166.158i	−1.41455	+	0.548377i
$304$	−9.05116	+	15.6771i	−0.0297736	+	0.0515693i
$305$	−467.800	−	270.085i	−1.53377	−	0.885523i
$306$	105.166	+	479.137i	0.343681	+	1.56581i
$307$	−299.666			−0.976111			−0.488055	−	0.872813i	$-0.662294\pi$
$307$	−299.666			−0.976111			−0.488055	+	0.872813i	$0.662294\pi$
$308$		0			0
$309$	−175.777	−	27.2438i	−0.568859	−	0.0881677i
$310$	265.318	+	459.544i	0.855865	+	1.48240i
$311$	382.208	+	220.668i	1.22897	+	0.709544i	0.966814	−	0.255483i	$-0.0822344\pi$
$311$	382.208	+	220.668i	1.22897	+	0.709544i	0.262152	+	0.965026i	$0.415568\pi$
$312$	−30.4893	−	24.5230i	−0.0977222	−	0.0785993i
$313$	63.9271	+	110.725i	0.204240	+	0.353754i	0.949890	−	0.312583i	$-0.101194\pi$
$313$	63.9271	+	110.725i	0.204240	+	0.353754i	−0.745650	+	0.666337i	$0.767861\pi$
$314$		−	481.036i		−	1.53196i
$315$		0			0
$316$	100.000			0.316456
$317$	204.983	−	118.347i	0.646634	−	0.373334i	−0.140531	−	0.990076i	$-0.544881\pi$
$317$	204.983	−	118.347i	0.646634	−	0.373334i	0.787165	+	0.616742i	$0.211548\pi$
$318$	9.83297	−	12.2253i	0.0309213	−	0.0384443i
$319$	−94.7846	+	164.172i	−0.297130	+	0.514645i
$320$	432.199	−	249.530i	1.35062	−	0.779783i
$321$	19.2018	−	123.891i	0.0598188	−	0.385952i
$322$		0			0
$323$			32.4905i			0.100590i
$324$	−54.6402	+	595.698i	−0.168643	+	1.83857i
$325$	−4.21642	+	7.30305i	−0.0129736	+	0.0224709i
$326$	349.572	+	201.826i	1.07231	+	0.619097i
$327$	−40.1297	−	103.515i	−0.122721	−	0.316560i
$328$	448.556			1.36755
$329$		0			0
$330$	−96.1484	+	620.351i	−0.291359	+	1.87985i
$331$	−211.578	−	366.463i	−0.639208	−	1.10714i	−0.985607	−	0.169053i	$-0.945929\pi$
$331$	−211.578	−	366.463i	−0.639208	−	1.10714i	0.346399	−	0.938087i	$-0.387404\pi$
$332$	−393.356	−	227.104i	−1.18481	−	0.684049i
$333$	−300.205	+	273.929i	−0.901518	+	0.822611i
$334$	−185.817	−	321.844i	−0.556338	−	0.963605i
$335$		−	552.470i		−	1.64916i
$336$		0			0
$337$	−263.481			−0.781842			−0.390921	−	0.920424i	$-0.627843\pi$
$337$	−263.481			−0.781842			−0.390921	+	0.920424i	$0.627843\pi$
$338$	−490.031	+	282.919i	−1.44980	+	0.837040i
$339$	410.749	+	330.371i	1.21165	+	0.974547i
$340$	−339.444	+	587.934i	−0.998364	+	1.72922i
$341$	−260.803	+	150.575i	−0.764818	+	0.441568i
$342$	−18.4897	+	58.2150i	−0.0540634	+	0.170219i
$343$		0			0
$344$			327.773i			0.952828i
$345$	−232.280	−	599.169i	−0.673275	−	1.73672i
$346$	500.028	−	866.075i	1.44517	−	2.50311i
$347$	137.144	+	79.1804i	0.395229	+	0.228186i	0.684423	−	0.729085i	$-0.260054\pi$
$347$	137.144	+	79.1804i	0.395229	+	0.228186i	−0.289194	+	0.957270i	$0.593387\pi$
$348$	−359.350	+	139.309i	−1.03262	+	0.400314i
$349$	152.703			0.437544			0.218772	−	0.975776i	$-0.429795\pi$
$349$	152.703			0.437544			0.218772	+	0.975776i	$0.429795\pi$
$350$		0			0
$351$	−27.6077	−	13.7229i	−0.0786544	−	0.0390967i
$352$	83.4808	+	144.593i	0.237161	+	0.410775i
$353$	−134.782	−	77.8162i	−0.381817	−	0.220442i	0.296791	−	0.954942i	$-0.404083\pi$
$353$	−134.782	−	77.8162i	−0.381817	−	0.220442i	−0.678609	+	0.734500i	$0.737417\pi$
$354$	−536.850	+	667.463i	−1.51652	+	1.88549i
$355$	−49.4975	−	85.7321i	−0.139430	−	0.241499i
$356$			222.152i			0.624023i
$357$		0			0
$358$	−161.926			−0.452307
$359$	245.760	−	141.889i	0.684567	−	0.395235i	−0.117006	−	0.993131i	$-0.537330\pi$
$359$	245.760	−	141.889i	0.684567	−	0.395235i	0.801574	+	0.597896i	$0.203996\pi$
$360$	−432.146	+	394.321i	−1.20041	+	1.09534i
$361$	178.477	−	309.132i	0.494397	−	0.856320i
$362$	−477.321	+	275.582i	−1.31857	+	0.761275i
$363$	6.65244	+	1.03106i	0.0183263	+	0.00284040i
$364$		0			0
$365$		−	393.158i		−	1.07715i
$366$	895.869	−	347.301i	2.44773	−	0.948910i
$367$	1.80157	−	3.12041i	0.00490890	−	0.00850247i	−0.863561	−	0.504245i	$-0.831771\pi$
$367$	1.80157	−	3.12041i	0.00490890	−	0.00850247i	0.868469	+	0.495743i	$0.165104\pi$
$368$	293.381	+	169.383i	0.797230	+	0.460281i
$369$	345.217	−	75.7722i	0.935548	−	0.205345i
$370$	−867.068			−2.34343
$371$		0			0
$372$	−605.036	−	93.7747i	−1.62644	−	0.252083i
$373$	86.9857	+	150.664i	0.233206	+	0.403924i	0.958750	−	0.284252i	$-0.0917451\pi$
$373$	86.9857	+	150.664i	0.233206	+	0.403924i	−0.725544	+	0.688176i	$0.758412\pi$
$374$	−514.390	−	296.983i	−1.37537	−	0.794073i
$375$	−234.335	−	188.479i	−0.624893	−	0.502610i
$376$	−220.040	−	381.121i	−0.585214	−	1.01362i
$377$		−	19.8634i		−	0.0526880i
$378$		0			0
$379$	−240.873			−0.635549			−0.317775	−	0.948166i	$-0.602935\pi$
$379$	−240.873			−0.635549			−0.317775	+	0.948166i	$0.602935\pi$
$380$	−73.2075	+	42.2664i	−0.192651	+	0.111227i
$381$	−234.623	+	291.706i	−0.615810	+	0.765634i
$382$	32.8887	−	56.9650i	0.0860962	−	0.149123i
$383$	249.732	−	144.183i	0.652041	−	0.376456i	−0.137197	−	0.990544i	$-0.543809\pi$
$383$	249.732	−	144.183i	0.652041	−	0.376456i	0.789238	+	0.614088i	$0.210476\pi$
$384$	−107.804	+	695.553i	−0.280740	+	1.81134i
$385$		0			0
$386$		−	441.995i		−	1.14506i
$387$	55.3690	+	252.260i	0.143072	+	0.651836i
$388$	−463.992	+	803.658i	−1.19586	+	2.07128i
$389$	386.064	+	222.894i	0.992452	+	0.572992i	0.906006	−	0.423264i	$-0.139116\pi$
$389$	386.064	+	222.894i	0.992452	+	0.572992i	0.0864456	+	0.996257i	$0.472449\pi$
$390$	−23.7758	−	61.3301i	−0.0609637	−	0.157257i
$391$	608.027			1.55506
$392$		0			0
$393$	35.3409	−	228.020i	0.0899260	−	0.580204i
$394$	459.873	+	796.524i	1.16719	+	2.02163i
$395$	66.7334	+	38.5286i	0.168945	+	0.0975407i
$396$	−488.220	−	535.052i	−1.23288	−	1.35114i
$397$	−274.414	−	475.299i	−0.691219	−	1.19723i	−0.971439	−	0.237291i	$-0.923741\pi$
$397$	−274.414	−	475.299i	−0.691219	−	1.19723i	0.280220	−	0.959936i	$-0.409593\pi$
$398$			668.764i			1.68031i
$399$		0			0
$400$	−66.4665			−0.166166
$401$	−1.64249	+	0.948294i	−0.00409599	+	0.00236482i	−0.502047	−	0.864841i	$-0.667419\pi$
$401$	−1.64249	+	0.948294i	−0.00409599	+	0.00236482i	0.497951	+	0.867205i	$0.334086\pi$
$402$	765.756	+	615.908i	1.90487	+	1.53211i
$403$	15.7775	−	27.3274i	0.0391501	−	0.0678099i
$404$	980.015	−	565.812i	2.42578	−	1.40053i
$405$	−265.977	+	376.477i	−0.656733	+	0.929574i
$406$		0			0
$407$		−	492.083i		−	1.20905i
$408$	−200.075	−	516.098i	−0.490381	−	1.26495i
$409$	197.115	−	341.414i	0.481945	−	0.834753i	−0.517841	−	0.855477i	$-0.673264\pi$
$409$	197.115	−	341.414i	0.481945	−	0.834753i	0.999785	+	0.0207246i	$0.00659731\pi$
$410$	653.041	+	377.033i	1.59278	+	0.919594i
$411$	−454.567	+	176.222i	−1.10600	+	0.428764i
$412$	437.882			1.06282
$413$		0			0
$414$	1089.44	+	346.016i	2.63149	+	0.835787i
$415$	−175.000	−	303.109i	−0.421687	−	0.730383i
$416$	−15.1507	−	8.74725i	−0.0364199	−	0.0210271i
$417$	258.458	−	321.340i	0.619804	−	0.770600i
$418$	−36.9794	−	64.0501i	−0.0884674	−	0.153230i
$419$		−	178.858i		−	0.426869i	−0.976957	−	0.213435i	$-0.931535\pi$
$419$		−	178.858i		−	0.426869i	0.976957	−	0.213435i	$-0.0684651\pi$
$420$		0			0
$421$	147.392			0.350100			0.175050	−	0.984560i	$-0.443991\pi$
$421$	147.392			0.350100			0.175050	+	0.984560i	$0.443991\pi$
$422$	789.493	−	455.814i	1.87084	−	1.08013i
$423$	−233.728	−	256.148i	−0.552549	−	0.605550i
$424$	−8.85165	+	15.3315i	−0.0208765	+	0.0361592i
$425$	−103.313	+	59.6478i	−0.243090	+	0.140348i
$426$	174.011	+	26.9700i	0.408476	+	0.0633099i
$427$		0			0
$428$			308.625i			0.721087i
$429$	34.8064	−	13.4934i	0.0811338	−	0.0314531i
$430$	−275.509	+	477.196i	−0.640720	+	1.10976i
$431$	264.985	+	152.989i	0.614814	+	0.354963i	0.774847	−	0.632149i	$-0.217827\pi$
$431$	264.985	+	152.989i	0.614814	+	0.354963i	−0.160033	+	0.987112i	$0.551160\pi$
$432$	−15.1287	−	242.529i	−0.0350200	−	0.561409i
$433$	487.379			1.12559			0.562794	−	0.826598i	$-0.309727\pi$
$433$	487.379			1.12559			0.562794	+	0.826598i	$0.309727\pi$
$434$		0			0
$435$	−293.481	−	45.4867i	−0.674668	−	0.104567i
$436$	136.652	+	236.688i	0.313422	+	0.542863i
$437$	65.5663	+	37.8547i	0.150037	+	0.0866241i
$438$	544.940	+	438.303i	1.24416	+	1.00069i
$439$	180.045	+	311.847i	0.410125	+	0.710358i	0.994903	−	0.100836i	$-0.0321517\pi$
$439$	180.045	+	311.847i	0.410125	+	0.710358i	−0.584778	+	0.811193i	$0.698818\pi$
$440$		−	708.354i		−	1.60990i
$441$		0			0
$442$	62.2368			0.140807
$443$	−211.169	+	121.919i	−0.476680	+	0.275211i	−0.719032	−	0.694977i	$-0.755414\pi$
$443$	−211.169	+	121.919i	−0.476680	+	0.275211i	0.242352	+	0.970188i	$0.422081\pi$
$444$	627.020	−	779.571i	1.41221	−	1.75579i
$445$	−85.5920	+	148.250i	−0.192342	+	0.333146i
$446$	122.443	−	70.6925i	0.274536	−	0.158503i
$447$	−7.41802	+	47.8612i	−0.0165951	+	0.107072i
$448$		0			0
$449$			659.743i			1.46936i	0.678413	+	0.734681i	$0.262668\pi$
$449$			659.743i			1.46936i	−0.678413	+	0.734681i	$0.737332\pi$
$450$	−219.056	+	48.0809i	−0.486791	+	0.106846i
$451$	−213.976	+	370.617i	−0.474448	+	0.821768i
$452$	−1123.78	−	648.817i	−2.48625	−	1.43544i
$453$	−22.0248	−	56.8132i	−0.0486198	−	0.125415i
$454$	−1050.98			−2.31493
$455$		0			0
$456$	10.5563	−	68.1095i	0.0231498	−	0.149363i
$457$	−304.755	−	527.851i	−0.666859	−	1.15503i	−0.978778	−	0.204925i	$-0.934305\pi$
$457$	−304.755	−	527.851i	−0.666859	−	1.15503i	0.311918	−	0.950109i	$-0.399028\pi$
$458$	67.6178	+	39.0392i	0.147637	+	0.0852384i
$459$	−241.164	−	363.401i	−0.525411	−	0.791723i
$460$	790.973	+	1370.01i	1.71951	+	2.97827i
$461$		−	106.424i		−	0.230854i	−0.993316	−	0.115427i	$-0.963176\pi$
$461$		−	106.424i		−	0.230854i	0.993316	−	0.115427i	$-0.0368236\pi$
$462$		0			0
$463$	−577.392			−1.24707			−0.623534	−	0.781796i	$-0.714304\pi$
$463$	−577.392			−1.24707			−0.623534	+	0.781796i	$0.714304\pi$
$464$	135.585	−	78.2803i	0.292210	−	0.168708i
$465$	−367.631	−	295.691i	−0.790604	−	0.635894i
$466$	105.845	−	183.328i	0.227134	−	0.393408i
$467$	−63.6738	+	36.7621i	−0.136346	+	0.0787196i	−0.566622	−	0.823978i	$-0.691750\pi$
$467$	−63.6738	+	36.7621i	−0.136346	+	0.0787196i	0.430275	+	0.902698i	$0.358417\pi$
$468$	72.3347	+	22.9742i	0.154561	+	0.0490903i
$469$		0			0
$470$		−	739.819i		−	1.57408i
$471$	154.592	+	398.773i	0.328221	+	0.846651i
$472$	483.273	−	837.053i	1.02388	−	1.77342i
$473$	−270.821	−	156.359i	−0.572560	−	0.330568i
$474$	−127.799	+	49.5438i	−0.269618	+	0.104523i
$475$	−14.8543			−0.0312722
$476$		0			0
$477$	−4.22253	+	13.2947i	−0.00885226	+	0.0278714i
$478$	−405.221	−	701.864i	−0.847743	−	1.46833i
$479$	−490.515	−	283.199i	−1.02404	−	0.591229i	−0.108768	−	0.994067i	$-0.534690\pi$
$479$	−490.515	−	283.199i	−1.02404	−	0.591229i	−0.915271	+	0.402838i	$0.868024\pi$
$480$	−163.935	+	203.820i	−0.341531	+	0.424625i
$481$	25.7806	+	44.6534i	0.0535980	+	0.0928345i
$482$		−	1060.51i		−	2.20023i
$483$		0			0
$484$	−16.5720			−0.0342396
$485$	−619.276	+	357.539i	−1.27686	+	0.737194i
$486$	−225.302	−	788.366i	−0.463584	−	1.62215i
$487$	−242.763	+	420.478i	−0.498487	+	0.863405i	−0.999998	−	0.00174614i	$-0.999444\pi$
$487$	−242.763	+	420.478i	−0.498487	+	0.863405i	0.501511	+	0.865151i	$0.332778\pi$
$488$	−938.938	+	542.096i	−1.92405	+	1.11085i
$489$	−354.653	−	54.9678i	−0.725262	−	0.112409i
$490$		0			0
$491$			746.721i			1.52082i	0.649445	+	0.760409i	$0.275001\pi$
$491$			746.721i			1.52082i	−0.649445	+	0.760409i	$0.724999\pi$
$492$	−811.232	+	314.490i	−1.64885	+	0.639208i
$493$	140.499	−	243.352i	0.284989	−	0.493615i
$494$	6.71128	+	3.87476i	0.0135856	+	0.00784364i
$495$	−119.658	−	545.163i	−0.241734	−	1.10134i
$496$	248.712			0.501435
$497$		0			0
$498$	615.221	+	95.3533i	1.23538	+	0.191473i
$499$	−16.9258	−	29.3164i	−0.0339195	−	0.0587503i	0.848567	−	0.529087i	$-0.177466\pi$
$499$	−16.9258	−	29.3164i	−0.0339195	−	0.0587503i	−0.882487	+	0.470337i	$0.844132\pi$
$500$	641.125	+	370.153i	1.28225	+	0.740307i
$501$	257.472	+	207.088i	0.513916	+	0.413350i
$502$	724.789	+	1255.37i	1.44380	+	2.50074i
$503$			987.870i			1.96396i	0.188993	+	0.981978i	$0.439478\pi$
$503$			987.870i			1.96396i	−0.188993	+	0.981978i	$0.560522\pi$
$504$		0			0
$505$	871.997			1.72673
$506$	−1198.63	+	692.032i	−2.36884	+	1.36765i
$507$	315.307	−	392.020i	0.621907	−	0.773215i
$508$	460.777	−	798.090i	0.907042	−	1.57104i
$509$	−87.5198	+	50.5296i	−0.171945	+	0.0992723i	−0.583502	−	0.812111i	$-0.698318\pi$
$509$	−87.5198	+	50.5296i	−0.171945	+	0.0992723i	0.411558	+	0.911384i	$0.364985\pi$
$510$	142.521	−	919.547i	0.279453	−	1.80303i
$511$		0			0
$512$		−	549.088i		−	1.07244i
$513$	−3.38104	−	54.2016i	−0.00659071	−	0.105656i
$514$	−353.454	+	612.199i	−0.687653	+	1.19105i
$515$	292.214	+	168.710i	0.567405	+	0.327591i
$516$	−229.807	−	592.791i	−0.445363	−	1.14882i
$517$	419.866			0.812120
$518$		0			0
$519$	−136.184	+	878.662i	−0.262397	+	1.69299i
$520$	37.1113	+	64.2786i	0.0713678	+	0.123613i
$521$	819.436	+	473.102i	1.57281	+	0.908065i	0.995822	+	0.0913150i	$0.0291070\pi$
$521$	819.436	+	473.102i	1.57281	+	0.908065i	0.576992	+	0.816750i	$0.304226\pi$
$522$	390.227	−	356.072i	0.747562	−	0.682130i
$523$	173.372	+	300.290i	0.331496	+	0.574168i	0.982805	−	0.184645i	$-0.0591134\pi$
$523$	173.372	+	300.290i	0.331496	+	0.574168i	−0.651310	+	0.758812i	$0.725780\pi$
$524$			568.024i			1.08402i
$525$		0			0
$526$	−871.672			−1.65717
$527$	386.589	−	223.197i	0.733565	−	0.423524i
$528$	229.274	+	184.408i	0.434232	+	0.349258i
$529$	443.914	−	768.881i	0.839156	−	1.45346i
$530$	−25.7738	+	14.8805i	−0.0486298	+	0.0280764i
$531$	230.537	−	725.849i	0.434156	−	1.36695i
$532$		0			0
$533$		−	44.8415i		−	0.0841304i
$534$	−110.063	−	283.908i	−0.206110	−	0.531663i
$535$	−118.909	+	205.956i	−0.222260	+	0.384965i
$536$	−960.320	−	554.441i	−1.79164	−	1.03440i
$537$	134.235	−	52.0387i	0.249971	−	0.0969063i
$538$	−412.059			−0.765908
$539$		0			0
$540$	505.088	−	1016.13i	0.935349	−	1.88173i
$541$	475.251	+	823.159i	0.878468	+	1.52155i	0.853022	+	0.521875i	$0.174767\pi$
$541$	475.251	+	823.159i	0.878468	+	1.52155i	0.0254457	+	0.999676i	$0.491900\pi$
$542$	162.118	+	93.5986i	0.299110	+	0.172691i
$543$	307.129	−	381.852i	0.565615	−	0.703227i
$544$	−123.744	−	214.330i	−0.227470	−	0.393990i
$545$			210.600i			0.386422i
$546$		0			0
$547$	201.735			0.368802			0.184401	−	0.982851i	$-0.440966\pi$
$547$	201.735			0.368802			0.184401	+	0.982851i	$0.440966\pi$
$548$	1039.37	−	600.081i	1.89666	−	1.09504i
$549$	−631.051	+	575.817i	−1.14946	+	1.04885i
$550$	135.777	−	235.173i	0.246868	−	0.427588i
$551$	30.3014	−	17.4945i	0.0549934	−	0.0317505i
$552$	−1274.60	−	197.551i	−2.30906	−	0.357882i
$553$		0			0
$554$			937.024i			1.69138i
$555$	718.789	−	278.653i	1.29512	−	0.502077i
$556$	−507.587	+	879.166i	−0.912926	+	1.58123i
$557$	−310.096	−	179.034i	−0.556726	−	0.321426i	0.195104	−	0.980782i	$-0.437495\pi$
$557$	−310.096	−	179.034i	−0.556726	−	0.321426i	−0.751830	+	0.659357i	$0.770829\pi$
$558$	819.689	−	179.915i	1.46898	−	0.322428i
$559$	32.7670			0.0586172
$560$		0			0
$561$	521.866	+	80.8842i	0.930242	+	0.144179i
$562$	152.392	+	263.951i	0.271161	+	0.469664i
$563$	−501.957	−	289.805i	−0.891576	−	0.514752i	−0.0171184	−	0.999853i	$-0.505449\pi$
$563$	−501.957	−	289.805i	−0.891576	−	0.514752i	−0.874458	+	0.485102i	$0.838783\pi$
$564$	665.163	+	535.000i	1.17937	+	0.948581i
$565$	−499.960	−	865.956i	−0.884885	−	1.53267i
$566$			978.538i			1.72887i
$567$		0			0
$568$	−198.696			−0.349817
$569$	−518.539	+	299.379i	−0.911317	+	0.526149i	−0.880855	−	0.473387i	$-0.843031\pi$
$569$	−518.539	+	299.379i	−0.911317	+	0.526149i	−0.0304622	+	0.999536i	$0.509698\pi$
$570$	72.6181	−	90.2858i	0.127400	−	0.158396i
$571$	−263.504	+	456.402i	−0.461477	+	0.799302i	−0.999035	−	0.0439249i	$-0.986014\pi$
$571$	−263.504	+	456.402i	−0.461477	+	0.799302i	0.537557	+	0.843227i	$0.319347\pi$
$572$	−79.5851	+	45.9485i	−0.139135	+	0.0803295i
$573$	−8.95733	+	57.7929i	−0.0156323	+	0.100860i
$574$		0			0
$575$			277.983i			0.483449i
$576$	−169.209	−	770.914i	−0.293765	−	1.33839i
$577$	440.055	−	762.198i	0.762661	−	1.32097i	−0.178813	−	0.983883i	$-0.557226\pi$
$577$	440.055	−	762.198i	0.762661	−	1.32097i	0.941474	−	0.337085i	$-0.109441\pi$
$578$	−82.0157	−	47.3518i	−0.141896	−	0.0819235i
$579$	142.046	+	366.409i	0.245329	+	0.632830i
$580$	731.094			1.26051
$581$		0			0
$582$	194.815	−	1256.95i	0.334733	−	2.15970i
$583$	−8.44506	−	14.6273i	−0.0144855	−	0.0250896i
$584$	−683.399	−	394.561i	−1.17020	−	0.675617i
$585$	39.4198	+	43.2010i	0.0673842	+	0.0738479i
$586$	−448.739	−	777.240i	−0.765767	−	1.32635i
$587$			430.520i			0.733424i	0.930335	+	0.366712i	$0.119517\pi$
$587$			430.520i			0.733424i	−0.930335	+	0.366712i	$0.880483\pi$
$588$		0			0
$589$	55.5835			0.0943693
$590$	1407.17	−	812.429i	2.38503	−	1.37700i
$591$	−637.211	−	512.517i	−1.07819	−	0.867204i
$592$	−203.200	+	351.952i	−0.343243	+	0.594514i
$593$	887.325	−	512.298i	1.49633	−	0.863908i	0.496342	−	0.868127i	$-0.334676\pi$
$593$	887.325	−	512.298i	1.49633	−	0.863908i	0.999991	+	0.00421907i	$0.00134298\pi$
$594$	889.026	+	441.908i	1.49668	+	0.743953i
$595$		0			0
$596$		−	119.228i		−	0.200046i
$597$	−214.923	−	554.397i	−0.360005	−	0.928638i
$598$	72.5122	−	125.595i	0.121258	−	0.210025i
$599$	127.615	+	73.6788i	0.213047	+	0.123003i	0.602727	−	0.797948i	$-0.294081\pi$
$599$	127.615	+	73.6788i	0.213047	+	0.123003i	−0.389679	+	0.920951i	$0.627414\pi$
$600$	235.954	−	91.4723i	0.393257	−	0.152454i
$601$	−394.481			−0.656374			−0.328187	−	0.944613i	$-0.606438\pi$
$601$	−394.481			−0.656374			−0.328187	+	0.944613i	$0.606438\pi$
$602$		0			0
$603$	−832.739	−	264.487i	−1.38099	−	0.438618i
$604$	75.0000	+	129.904i	0.124172	+	0.215073i
$605$	−11.0591	−	6.38495i	−0.0182794	−	0.0105536i
$606$	−972.125	+	1208.64i	−1.60417	+	1.99445i
$607$	542.146	+	939.025i	0.893157	+	1.54699i	0.836069	+	0.548624i	$0.184848\pi$
$607$	542.146	+	939.025i	0.893157	+	1.54699i	0.0570874	+	0.998369i	$0.481819\pi$
$608$		−	30.8163i		−	0.0506847i
$609$		0			0
$610$	−1822.63			−2.98792
$611$	−38.1002	+	21.9971i	−0.0623570	+	0.0360019i
$612$	723.690	+	793.108i	1.18250	+	1.29593i
$613$	−510.161	+	883.625i	−0.832237	+	1.44148i	0.0640234	+	0.997948i	$0.479607\pi$
$613$	−510.161	+	883.625i	−0.832237	+	1.44148i	−0.896260	+	0.443528i	$0.853727\pi$
$614$	−875.665	+	505.565i	−1.42616	+	0.823396i
$615$	−662.532	−	102.686i	−1.07729	−	0.166969i
$616$		0			0
$617$		−	338.815i		−	0.549133i	−0.961568	−	0.274567i	$-0.911466\pi$
$617$		−	338.815i		−	0.549133i	0.961568	−	0.274567i	$-0.0885344\pi$
$618$	−559.608	+	216.943i	−0.905515	+	0.351041i
$619$	269.674	−	467.089i	0.435661	−	0.754587i	−0.561689	−	0.827349i	$-0.689848\pi$
$619$	269.674	−	467.089i	0.435661	−	0.754587i	0.997349	+	0.0727622i	$0.0231814\pi$
$620$	1005.81	+	580.708i	1.62228	+	0.936625i
$621$	−1014.33	+	63.2727i	−1.63338	+	0.101888i
$622$	1489.15			2.39414
$623$		0			0
$624$	−30.4665	−	4.72201i	−0.0488245	−	0.00756733i
$625$	377.544	+	653.926i	0.604071	+	1.04628i
$626$	373.607	+	215.702i	0.596817	+	0.344572i
$627$	51.2395	+	41.2126i	0.0817216	+	0.0657298i
$628$	−526.426	−	911.797i	−0.838259	−	1.45191i
$629$			729.416i			1.15964i
$630$		0			0
$631$	−297.392			−0.471303			−0.235652	−	0.971838i	$-0.575722\pi$
$631$	−297.392			−0.471303			−0.235652	+	0.971838i	$0.575722\pi$
$632$	133.943	−	77.3320i	0.211935	−	0.122361i
$633$	−507.994	+	631.587i	−0.802518	+	0.997768i
$634$	399.325	−	691.652i	0.629851	−	1.09093i
$635$	614.985	−	355.062i	0.968481	−	0.559153i
$636$	5.25940	−	33.9337i	0.00826950	−	0.0533549i
$637$		0			0
$638$			639.643i			1.00257i
$639$	−152.920	+	33.5647i	−0.239312	+	0.0525269i
$640$	667.586	−	1156.29i	1.04310	−	1.80671i
$641$	1016.56	+	586.912i	1.58590	+	0.915619i	0.993973	+	0.109627i	$0.0349655\pi$
$641$	1016.56	+	586.912i	1.58590	+	0.915619i	0.591926	+	0.805992i	$0.298368\pi$
$642$	−152.905	−	394.420i	−0.238169	−	0.614362i
$643$	−580.665			−0.903056			−0.451528	−	0.892257i	$-0.649121\pi$
$643$	−580.665			−0.903056			−0.451528	+	0.892257i	$0.649121\pi$
$644$		0			0
$645$	75.0357	−	484.132i	0.116334	−	0.750591i
$646$	54.8146	+	94.9416i	0.0848523	+	0.146968i
$647$	902.116	+	520.837i	1.39431	+	0.805003i	0.993788	−	0.111286i	$-0.0354969\pi$
$647$	902.116	+	520.837i	1.39431	+	0.805003i	0.400518	+	0.916289i	$0.368830\pi$
$648$	387.478	+	840.149i	0.597960	+	1.29653i
$649$	461.074	+	798.604i	0.710438	+	1.23051i
$650$			28.4540i			0.0437754i
$651$		0			0
$652$	883.481			1.35503
$653$	−402.437	+	232.347i	−0.616290	+	0.355815i	−0.775423	−	0.631442i	$-0.782463\pi$
$653$	−402.437	+	232.347i	−0.616290	+	0.355815i	0.159133	+	0.987257i	$0.449130\pi$
$654$	−291.904	−	234.782i	−0.446337	−	0.358995i
$655$	−218.852	+	379.062i	−0.334125	+	0.578721i
$656$	306.084	−	176.718i	0.466591	−	0.269386i
$657$	−592.608	−	188.218i	−0.901991	−	0.286482i
$658$		0			0
$659$		−	1069.25i		−	1.62253i	−0.584678	−	0.811265i	$-0.698779\pi$
$659$		−	1069.25i		−	1.62253i	0.584678	−	0.811265i	$-0.301221\pi$
$660$	496.639	+	1281.09i	0.752484	+	1.94104i
$661$	−566.904	+	981.907i	−0.857646	+	1.48549i	0.0165223	+	0.999863i	$0.494741\pi$
$661$	−566.904	+	981.907i	−0.857646	+	1.48549i	−0.874168	+	0.485623i	$0.838593\pi$
$662$	−1236.52	−	713.904i	−1.86785	−	1.07840i
$663$	−51.5936	+	20.0013i	−0.0778184	+	0.0301678i
$664$	−702.497			−1.05798
$665$		0			0
$666$	−415.096	+	1306.93i	−0.623267	+	1.96236i
$667$	−327.392	−	567.060i	−0.490843	−	0.850165i
$668$	−704.427	−	406.701i	−1.05453	−	0.608834i
$669$	−78.7851	+	97.9532i	−0.117765	+	0.146417i
$670$	−932.070	−	1614.39i	−1.39115	−	2.40954i
$671$		−	1034.39i		−	1.54157i
$672$		0			0
$673$	1246.96			1.85284			0.926420	−	0.376491i	$-0.122870\pi$
$673$	1246.96			1.85284			0.926420	+	0.376491i	$0.122870\pi$
$674$	−769.926	+	444.517i	−1.14232	+	0.659521i
$675$	166.143	−	110.257i	0.246138	−	0.163344i
$676$	−619.232	+	1072.54i	−0.916023	+	1.58660i
$677$	−755.020	+	435.911i	−1.11524	+	0.643886i	−0.940182	−	0.340671i	$-0.889346\pi$
$677$	−755.020	+	435.911i	−1.11524	+	0.643886i	−0.175061	+	0.984558i	$0.556012\pi$
$678$	1757.63	+	272.416i	2.59238	+	0.401794i
$679$		0			0
$680$			1049.99i			1.54411i
$681$	871.249	−	337.757i	1.27937	−	0.495972i
$682$	−508.068	+	879.999i	−0.744968	+	1.29032i
$683$	−954.567	−	551.119i	−1.39761	−	0.806910i	−0.403467	−	0.914994i	$-0.632195\pi$
$683$	−954.567	−	551.119i	−1.39761	−	0.806910i	−0.994142	+	0.108084i	$0.965528\pi$
$684$	28.6612	+	130.580i	0.0419024	+	0.190907i
$685$	924.811			1.35009
$686$		0			0
$687$	−68.6006	−	10.6324i	−0.0998552	−	0.0154766i
$688$	129.133	+	223.664i	0.187693	+	0.325094i
$689$	1.53267	+	0.884887i	0.00222448	+	0.00128431i
$690$	−1689.61	−	1358.98i	−2.44871	−	1.96953i
$691$	101.068	+	175.055i	0.146263	+	0.253335i	0.929844	−	0.367955i	$-0.119942\pi$
$691$	101.068	+	175.055i	0.146263	+	0.253335i	−0.783580	+	0.621291i	$0.786609\pi$
$692$		−	2188.85i		−	3.16307i
$693$		0			0
$694$	534.340			0.769942
$695$	−677.460	+	391.132i	−0.974763	+	0.562780i
$696$	−373.594	+	464.488i	−0.536773	+	0.667368i
$697$	317.177	−	549.367i	0.455060	−	0.788187i
$698$	446.218	−	257.624i	0.639281	−	0.369089i
$699$	−28.8270	+	185.992i	−0.0412404	+	0.266084i
$700$		0			0
$701$		−	310.416i		−	0.442819i	−0.975181	−	0.221410i	$-0.928934\pi$
$701$		−	310.416i		−	0.442819i	0.975181	−	0.221410i	$-0.0710658\pi$
$702$	−103.825	+	6.47651i	−0.147899	+	0.00922579i
$703$	−45.4122	+	78.6562i	−0.0645977	+	0.111887i
$704$	827.635	+	477.836i	1.17562	+	0.678744i
$705$	237.758	+	613.301i	0.337246	+	0.869931i
$706$	−525.133			−0.743815
$707$		0			0
$708$	−287.147	+	1852.68i	−0.405575	+	2.61677i
$709$	200.903	+	347.974i	0.283361	+	0.490796i	0.972210	−	0.234109i	$-0.0752172\pi$
$709$	200.903	+	347.974i	0.283361	+	0.490796i	−0.688849	+	0.724905i	$0.741884\pi$
$710$	−289.277	−	167.014i	−0.407432	−	0.235231i
$711$	90.0218	−	82.1425i	0.126613	−	0.115531i
$712$	171.795	+	297.557i	0.241285	+	0.417917i
$713$		−	1040.19i		−	1.45889i
$714$		0			0
$715$	−70.8132			−0.0990394
$716$	−306.929	+	177.205i	−0.428671	+	0.247493i
$717$	561.484	+	451.609i	0.783102	+	0.629859i
$718$	478.762	−	829.240i	0.666799	−	1.15493i
$719$	−523.881	+	302.463i	−0.728625	+	0.420672i	−0.817919	−	0.575334i	$-0.804872\pi$
$719$	−523.881	+	302.463i	−0.728625	+	0.420672i	0.0892940	+	0.996005i	$0.471539\pi$
$720$	−139.535	+	439.328i	−0.193799	+	0.610178i
$721$		0			0
$722$		−	1204.43i		−	1.66819i
$723$	340.820	+	879.150i	0.471397	+	1.21597i
$724$	−603.171	+	1044.72i	−0.833109	+	1.44299i
$725$	111.258	+	64.2348i	0.153459	+	0.0885997i
$726$	21.1788	−	8.21039i	0.0291719	−	0.0113091i
$727$	−1225.37			−1.68552			−0.842761	−	0.538288i	$-0.819071\pi$
$727$	−1225.37			−1.68552			−0.842761	+	0.538288i	$0.819071\pi$
$728$		0			0
$729$	440.133	+	581.140i	0.603749	+	0.797175i
$730$	−663.295	−	1148.86i	−0.908624	−	1.57378i
$731$	401.438	+	231.771i	0.549163	+	0.317060i
$732$	1318.04	−	1638.71i	1.80060	−	2.23867i
$733$	−355.884	−	616.408i	−0.485516	−	0.840939i	0.514345	−	0.857583i	$-0.328035\pi$
$733$	−355.884	−	616.408i	−0.485516	−	0.840939i	−0.999861	+	0.0166442i	$0.994702\pi$
$734$		−	12.1577i		−	0.0165636i
$735$		0			0
$736$	−576.696			−0.783555
$737$	916.208	−	528.973i	1.24316	−	0.717738i
$738$	880.936	−	803.831i	1.19368	−	1.08920i
$739$	−531.161	+	919.998i	−0.718757	+	1.24492i	0.242736	+	0.970092i	$0.421955\pi$
$739$	−531.161	+	919.998i	−0.718757	+	1.24492i	−0.961493	+	0.274831i	$0.911378\pi$
$740$	−1643.52	+	948.886i	−2.22097	+	1.28228i
$741$	−6.80882	−	1.05530i	−0.00918869	−	0.00142416i
$742$		0			0
$743$			36.5432i			0.0491834i	0.999698	+	0.0245917i	$0.00782856\pi$
$743$			36.5432i			0.0491834i	−0.999698	+	0.0245917i	$0.992171\pi$
$744$	−882.921	+	342.282i	−1.18672	+	0.460056i
$745$	45.9367	−	79.5647i	0.0616600	−	0.106798i
$746$	508.368	+	293.506i	0.681458	+	0.393440i
$747$	−540.655	+	118.669i	−0.723769	+	0.158861i
$748$	−1300.03			−1.73800
$749$		0			0
$750$	−1002.74	−	155.415i	−1.33699	−	0.207220i
$751$	−190.318	−	329.641i	−0.253420	−	0.438936i	0.711045	−	0.703146i	$-0.248222\pi$
$751$	−190.318	−	329.641i	−0.253420	−	0.438936i	−0.964465	+	0.264210i	$0.914889\pi$
$752$	−300.300	−	173.379i	−0.399336	−	0.230557i
$753$	−1004.28	−	807.759i	−1.33371	−	1.07272i
$754$	−33.5114	−	58.0435i	−0.0444449	−	0.0769807i
$755$			115.586i			0.153094i
$756$		0			0
$757$	−265.658			−0.350935			−0.175467	−	0.984485i	$-0.556144\pi$
$757$	−265.658			−0.350935			−0.175467	+	0.984485i	$0.556144\pi$
$758$	−703.864	+	406.376i	−0.928580	+	0.536116i
$759$	771.253	−	958.896i	1.01614	−	1.26337i
$760$	−65.3709	+	113.226i	−0.0860143	+	0.148981i
$761$	974.503	−	562.630i	1.28056	−	0.739330i	0.303606	−	0.952798i	$-0.401809\pi$
$761$	974.503	−	562.630i	1.28056	−	0.739330i	0.976950	+	0.213468i	$0.0684759\pi$
$762$	−193.465	+	1248.24i	−0.253891	+	1.63811i
$763$		0			0
$764$		−	143.969i		−	0.188441i
$765$	177.370	+	808.096i	0.231856	+	1.05633i
$766$	486.500	−	842.642i	0.635117	−	1.10005i
$767$	−83.6790	−	48.3121i	−0.109099	−	0.0629884i
$768$	478.064	+	1233.17i	0.622480	+	1.60570i
$769$	189.660			0.246632			0.123316	−	0.992367i	$-0.460647\pi$
$769$	189.660			0.246632			0.123316	+	0.992367i	$0.460647\pi$
$770$		0			0
$771$	96.2640	−	621.097i	0.124856	−	0.805573i
$772$	−483.702	−	837.796i	−0.626557	−	1.08523i
$773$	35.9609	+	20.7620i	0.0465212	+	0.0268590i	0.523080	−	0.852283i	$-0.324783\pi$
$773$	35.9609	+	20.7620i	0.0465212	+	0.0268590i	−0.476559	+	0.879142i	$0.658116\pi$
$774$	587.383	+	643.726i	0.758893	+	0.831688i
$775$	102.043	+	176.744i	0.131669	+	0.228057i
$776$			1435.26i			1.84956i
$777$		0			0
$778$	1504.17			1.93339
$779$	68.4053	−	39.4938i	0.0878116	−	0.0506981i
$780$	−112.184	−	90.2312i	−0.143826	−	0.115681i
$781$	94.7846	−	164.172i	0.121363	−	0.210207i
$782$	1776.74	−	1025.80i	2.27204	−	1.31176i
$783$	−209.062	+	420.588i	−0.267001	+	0.537149i
$784$		0			0
$785$		−	811.298i		−	1.03350i
$786$	−281.421	−	725.929i	−0.358042	−	0.923574i
$787$	479.103	−	829.830i	0.608771	−	1.05442i	−0.382672	−	0.923884i	$-0.624996\pi$
$787$	479.103	−	829.830i	0.608771	−	1.05442i	0.991443	−	0.130538i	$-0.0416705\pi$
$788$	1743.37	+	1006.53i	2.21240	+	1.27733i
$789$	722.606	−	280.132i	0.915850	−	0.355047i
$790$	260.005			0.329121
$791$		0			0
$792$	−1067.70	−	339.114i	−1.34811	−	0.428174i
$793$	54.1926	+	93.8643i	0.0683387	+	0.118366i
$794$	−1603.75	−	925.925i	−2.01984	−	1.16615i
$795$	16.5840	−	20.6188i	0.0208603	−	0.0259356i
$796$	731.869	+	1267.63i	0.919433	+	1.59250i
$797$		−	138.675i		−	0.173997i	−0.996208	−	0.0869983i	$-0.972273\pi$
$797$		−	138.675i		−	0.173997i	0.996208	−	0.0869983i	$-0.0277275\pi$
$798$		0			0
$799$	−622.368			−0.778934
$800$	97.9895	−	56.5742i	0.122487	−	0.0707178i
$801$	182.481	+	199.985i	0.227817	+	0.249670i
$802$	−3.19972	+	5.54209i	−0.00398968	+	0.00691033i
$803$	652.008	−	376.437i	0.811965	−	0.468788i
$804$	2125.51	+	329.433i	2.64366	+	0.409743i
$805$		0			0
$806$		−	106.472i		−	0.132100i
$807$	341.592	−	132.425i	0.423286	−	0.164095i
$808$	875.108	−	1515.73i	1.08305	−	1.87590i
$809$	−795.371	−	459.208i	−0.983154	−	0.567624i	−0.0799330	−	0.996800i	$-0.525471\pi$
$809$	−795.371	−	459.208i	−0.983154	−	0.567624i	−0.903221	+	0.429176i	$0.858804\pi$
$810$	−142.067	+	1548.85i	−0.175392	+	1.91216i
$811$	264.676			0.326357			0.163179	−	0.986597i	$-0.447825\pi$
$811$	264.676			0.326357			0.163179	+	0.986597i	$0.447825\pi$
$812$		0			0
$813$	−164.474	−	25.4918i	−0.202305	−	0.0313553i
$814$	−830.191	−	1437.93i	−1.01989	−	1.76650i
$815$	589.577	+	340.392i	0.723407	+	0.417659i
$816$	−339.854	−	273.349i	−0.416487	−	0.334986i
$817$	28.8593	+	49.9857i	0.0353235	+	0.0611821i
$818$		−	1330.21i		−	1.62617i
$819$		0			0
$820$	1650.44			2.01273
$821$	1272.53	−	734.693i	1.54997	−	0.894876i	0.551827	−	0.833958i	$-0.313931\pi$
$821$	1272.53	−	734.693i	1.54997	−	0.894876i	0.998143	−	0.0609175i	$-0.0194026\pi$
$822$	−1031.00	+	1281.84i	−1.25426	+	1.55942i
$823$	97.0214	−	168.046i	0.117888	−	0.204187i	−0.801043	−	0.598607i	$-0.795721\pi$
$823$	97.0214	−	168.046i	0.117888	−	0.204187i	0.918930	+	0.394420i	$0.129054\pi$
$824$	586.512	−	338.623i	0.711786	−	0.410950i
$825$	−36.9794	+	238.591i	−0.0448235	+	0.289202i
$826$		0			0
$827$			930.266i			1.12487i	0.826842	+	0.562434i	$0.190135\pi$
$827$			930.266i			1.12487i	−0.826842	+	0.562434i	$0.809865\pi$
$828$	2443.68	−	536.366i	2.95130	−	0.647785i
$829$	−59.3183	+	102.742i	−0.0715540	+	0.123935i	−0.899583	−	0.436751i	$-0.856129\pi$
$829$	−59.3183	+	102.742i	−0.0715540	+	0.123935i	0.828029	+	0.560686i	$0.189463\pi$
$830$	−1022.75	−	590.483i	−1.23223	−	0.711426i
$831$	−301.135	−	776.782i	−0.362376	−	0.934755i
$832$	−100.137			−0.120357
$833$		0			0
$834$	213.118	−	1375.04i	0.255538	−	1.64873i
$835$	−313.392	−	542.811i	−0.375320	−	0.650074i
$836$	−140.188	−	80.9375i	−0.167689	−	0.0968152i
$837$	−621.693	+	412.574i	−0.742763	+	0.492919i
$838$	−301.751	−	522.648i	−0.360085	−	0.623685i
$839$			451.383i			0.538002i	0.963140	+	0.269001i	$0.0866934\pi$
$839$			451.383i			0.538002i	−0.963140	+	0.269001i	$0.913307\pi$
$840$		0			0
$841$	538.392			0.640181
$842$	430.700	−	248.665i	0.511520	−	0.295326i
$843$	−211.158	−	169.838i	−0.250484	−	0.201468i
$844$	997.651	−	1727.98i	1.18205	−	2.04737i
$845$	−826.469	+	477.162i	−0.978070	+	0.564689i
$846$	−1115.13	−	354.177i	−1.31812	−	0.418649i
$847$		0			0
$848$			13.9491i			0.0164494i
$849$	−314.476	−	811.196i	−0.370408	−	0.955473i
$850$	−201.263	+	348.598i	−0.236780	+	0.410115i
$851$	1471.97	+	849.844i	1.72970	+	0.998641i
$852$	359.350	−	139.309i	0.421773	−	0.163509i
$853$	535.041			0.627246			0.313623	−	0.949548i	$-0.398457\pi$
$853$	535.041			0.627246			0.313623	+	0.949548i	$0.398457\pi$
$854$		0			0
$855$	−31.1841	+	98.1834i	−0.0364726	+	0.114834i
$856$	238.666	+	413.382i	0.278816	+	0.482923i
$857$	−618.741	−	357.230i	−0.721985	−	0.416838i	0.0934980	−	0.995619i	$-0.470195\pi$
$857$	−618.741	−	357.230i	−0.721985	−	0.416838i	−0.815483	+	0.578781i	$0.803528\pi$
$858$	78.9444	−	98.1512i	0.0920097	−	0.114395i
$859$	−222.240	−	384.932i	−0.258720	−	0.448116i	0.707179	−	0.707034i	$-0.249967\pi$
$859$	−222.240	−	384.932i	−0.258720	−	0.448116i	−0.965899	+	0.258918i	$0.916634\pi$
$860$			1206.03i			1.40236i
$861$		0			0
$862$	1032.43			1.19771
$863$	173.602	−	100.229i	0.201161	−	0.116140i	−0.396036	−	0.918235i	$-0.629614\pi$
$863$	173.602	−	100.229i	0.201161	−	0.116140i	0.597197	+	0.802095i	$0.296281\pi$
$864$	228.737	+	344.675i	0.264742	+	0.398930i
$865$	843.331	−	1460.69i	0.974949	−	1.68866i
$866$	1424.19	−	822.255i	1.64456	−	0.949486i
$867$	83.2076	+	12.8964i	0.0959719	+	0.0148747i
$868$		0			0
$869$			147.560i			0.169804i
$870$	−934.331	+	362.212i	−1.07394	+	0.416335i
$871$	−55.4267	+	96.0018i	−0.0636357	+	0.110220i
$872$	366.071	+	211.351i	0.419807	+	0.242375i
$873$	242.451	+	1104.60i	0.277721	+	1.26529i
$874$	255.458			0.292286
$875$		0			0
$876$	1512.59	+	234.437i	1.72670	+	0.267622i
$877$	625.257	+	1082.98i	0.712950	+	1.23487i	0.963745	+	0.266825i	$0.0859745\pi$
$877$	625.257	+	1082.98i	0.712950	+	1.23487i	−0.250795	+	0.968040i	$0.580692\pi$
$878$	1052.23	+	607.506i	1.19844	+	0.691920i
$879$	621.784	+	500.109i	0.707377	+	0.568953i
$880$	−279.070	−	483.364i	−0.317125	−	0.549277i
$881$			436.714i			0.495703i	0.968798	+	0.247851i	$0.0797244\pi$
$881$			436.714i			0.495703i	−0.968798	+	0.247851i	$0.920276\pi$
$882$		0			0
$883$	269.138			0.304800			0.152400	−	0.988319i	$-0.451300\pi$
$883$	269.138			0.304800			0.152400	+	0.988319i	$0.451300\pi$
$884$	117.969	−	68.1095i	0.133449	−	0.0770470i
$885$	−905.433	+	1125.72i	−1.02309	+	1.27200i
$886$	−411.377	+	712.525i	−0.464308	+	0.804205i
$887$	−770.548	+	444.876i	−0.868712	+	0.501551i	−0.866920	−	0.498447i	$-0.833904\pi$
$887$	−770.548	+	444.876i	−0.868712	+	0.501551i	−0.00179198	+	0.999998i	$0.500570\pi$
$888$	236.991	−	1529.07i	0.266881	−	1.72192i
$889$		0			0
$890$			577.608i			0.648997i
$891$	−879.010	−	80.6269i	−0.986543	−	0.0904903i
$892$	154.726	−	267.994i	0.173460	−	0.300441i
$893$	−67.1128	−	38.7476i	−0.0751543	−	0.0433904i
$894$	59.0699	+	152.372i	0.0660737	+	0.170438i
$895$	−273.099			−0.305138
$896$		0			0
$897$	−19.7489	+	127.420i	−0.0220166	+	0.142052i
$898$	1113.05	+	1927.86i	1.23948	+	2.14684i
$899$	−416.318	−	240.361i	−0.463090	−	0.267365i
$900$	−362.600	+	330.863i	−0.402889	+	0.367626i
$901$	12.5181	+	21.6820i	0.0138936	+	0.0240644i
$902$			1443.99i			1.60088i
$903$		0			0
$904$	−2006.97			−2.22010
$905$	−805.034	+	464.786i	−0.889540	+	0.513576i
$906$	−160.209	−	128.858i	−0.176831	−	0.142227i
$907$	−642.332	+	1112.55i	−0.708195	+	1.22663i	0.257332	+	0.966323i	$0.417157\pi$
$907$	−642.332	+	1112.55i	−0.708195	+	1.22663i	−0.965526	+	0.260306i	$0.916177\pi$
$908$	−1992.12	+	1150.15i	−2.19396	+	1.26668i
$909$	417.455	−	1314.36i	0.459247	−	1.44594i
$910$		0			0
$911$		−	218.798i		−	0.240173i	−0.992763	−	0.120087i	$-0.961683\pi$
$911$		−	218.798i		−	0.240173i	0.992763	−	0.120087i	$-0.0383172\pi$
$912$	−19.6297	−	50.6352i	−0.0215238	−	0.0555210i
$913$	335.114	−	580.435i	0.367047	−	0.635745i
$914$	−1781.07	−	1028.30i	−1.94865	−	1.12506i
$915$	1510.94	−	585.746i	1.65130	−	0.640160i
$916$	170.892			0.186563
$917$		0			0
$918$	−1317.80	−	655.041i	−1.43552	−	0.713552i
$919$	166.682	+	288.701i	0.181373	+	0.314147i	0.942348	−	0.334633i	$-0.108613\pi$
$919$	166.682	+	288.701i	0.181373	+	0.314147i	−0.760975	+	0.648781i	$0.775279\pi$
$920$	2118.91	+	1223.35i	2.30316	+	1.32973i
$921$	563.440	−	700.523i	0.611770	−	0.760611i
$922$	−179.547	−	310.984i	−0.194736	−	0.337293i
$923$			19.8634i			0.0215205i
$924$		0			0
$925$	−333.481			−0.360520
$926$	−1687.22	+	974.116i	−1.82205	+	1.05196i
$927$	394.189	−	359.687i	0.425231	−	0.388012i
$928$	−133.260	+	230.812i	−0.143599	+	0.248720i
$929$	−801.244	+	462.598i	−0.862480	+	0.497953i	−0.864842	−	0.502044i	$-0.832582\pi$
$929$	−801.244	+	462.598i	−0.862480	+	0.497953i	0.00236194	+	0.999997i	$0.499248\pi$
$930$	−1573.13	−	243.819i	−1.69153	−	0.262171i
$931$		0			0
$932$		−	463.328i		−	0.497133i
$933$	−1234.49	+	478.575i	−1.32314	+	0.512942i
$934$	−124.042	+	214.848i	−0.132808	+	0.230029i
$935$	−867.553	−	500.882i	−0.927864	−	0.535703i
$936$	114.654	−	25.1655i	0.122493	−	0.0268862i
$937$	433.264			0.462395			0.231197	−	0.972907i	$-0.425736\pi$
$937$	433.264			0.462395			0.231197	+	0.972907i	$0.425736\pi$
$938$		0			0
$939$	−379.037	−	58.7471i	−0.403660	−	0.0625635i
$940$	−809.629	−	1402.32i	−0.861308	−	1.49183i
$941$	−1014.62	−	585.791i	−1.07824	−	0.622520i	−0.147816	−	0.989015i	$-0.547224\pi$
$941$	−1014.62	−	585.791i	−1.07824	−	0.622520i	−0.930420	+	0.366495i	$0.880558\pi$
$942$	1124.51	+	904.456i	1.19374	+	0.960145i
$943$	−739.087	−	1280.14i	−0.783761	−	1.35751i
$944$		−	761.580i		−	0.806758i
$945$		0			0
$946$	−1055.17			−1.11540
$947$	−929.714	+	536.771i	−0.981747	+	0.566812i	−0.902797	−	0.430067i	$-0.858490\pi$
$947$	−929.714	+	536.771i	−0.981747	+	0.566812i	−0.0789497	+	0.996879i	$0.525157\pi$
$948$	−188.023	+	233.768i	−0.198336	+	0.246591i
$949$	−39.4437	+	68.3185i	−0.0415634	+	0.0719899i
$950$	−43.4063	+	25.0606i	−0.0456908	+	0.0263796i
$951$	−108.757	+	701.704i	−0.114361	+	0.737859i
$952$		0			0
$953$			583.768i			0.612559i	0.951942	+	0.306279i	$0.0990842\pi$
$953$			583.768i			0.612559i	−0.951942	+	0.306279i	$0.900916\pi$
$954$	10.0906	+	45.9727i	0.0105771	+	0.0481894i
$955$	55.4690	−	96.0752i	0.0580828	−	0.100602i
$956$	−1536.18	−	886.916i	−1.60689	−	0.927737i
$957$	−205.564	−	530.256i	−0.214801	−	0.554082i
$958$	−1911.13			−1.99492
$959$		0			0
$960$	−229.311	+	1479.52i	−0.238866	+	1.54116i
$961$	98.6626	+	170.889i	0.102667	+	0.177824i
$962$	150.669	+	86.9888i	0.156621	+	0.0904250i
$963$	253.512	+	277.830i	0.263253	+	0.288505i
$964$	−1160.58	−	2010.18i	−1.20392	−	2.08525i
$965$		−	745.454i		−	0.772491i
$966$		0			0
$967$	−1116.96			−1.15508			−0.577540	−	0.816363i	$-0.695987\pi$
$967$	−1116.96			−1.15508			−0.577540	+	0.816363i	$0.695987\pi$
$968$	−22.1970	+	12.8154i	−0.0229308	+	0.0132391i
$969$	−75.9524	−	61.0895i	−0.0783822	−	0.0630439i
$970$	−1206.41	+	2089.56i	−1.24372	+	2.15418i
$971$	−1531.78	+	884.371i	−1.57752	+	0.910784i	−0.582320	+	0.812960i	$0.697855\pi$
$971$	−1531.78	+	884.371i	−1.57752	+	0.910784i	−0.995204	+	0.0978237i	$0.968812\pi$
$972$	−1289.81	−	1247.78i	−1.32697	−	1.28372i
$973$		0			0
$974$			1638.26i			1.68199i
$975$	−9.14436	−	23.5880i	−0.00937883	−	0.0241928i
$976$	−427.139	+	739.826i	−0.437642	+	0.758019i
$977$	305.761	+	176.531i	0.312959	+	0.180687i	0.648250	−	0.761428i	$-0.275501\pi$
$977$	305.761	+	176.531i	0.312959	+	0.180687i	−0.335291	+	0.942115i	$0.608835\pi$
$978$	−1129.08	+	437.710i	−1.15448	+	0.447556i
$979$	−327.807			−0.334839
$980$		0			0
$981$	317.438	+	100.822i	0.323586	+	0.102774i
$982$	1259.79	+	2182.02i	1.28288	+	2.22202i
$983$	−1045.62	−	603.687i	−1.06370	−	0.614127i	−0.137246	−	0.990537i	$-0.543825\pi$
$983$	−1045.62	−	603.687i	−1.06370	−	0.614127i	−0.926453	+	0.376410i	$0.877159\pi$
$984$	−843.387	+	1048.58i	−0.857101	+	1.06563i
$985$	775.606	+	1343.39i	0.787418	+	1.36385i
$986$		−	948.144i		−	0.961606i
$987$		0			0
$988$	16.9615			0.0171675
$989$	935.433	−	540.073i	0.945837	−	0.546080i
$990$	−1269.40	−	1391.16i	−1.28222	−	1.40522i
$991$	844.933	−	1463.47i	0.852606	−	1.47676i	−0.0262415	−	0.999656i	$-0.508354\pi$
$991$	844.933	−	1463.47i	0.852606	−	1.47676i	0.878848	−	0.477102i	$-0.158313\pi$
$992$	−366.668	+	211.696i	−0.369625	+	0.213403i
$993$	1254.49	+	194.434i	1.26333	+	0.195804i
$994$		0			0
$995$			1127.91i			1.13358i
$996$	1270.50	−	492.533i	1.27560	−	0.494511i
$997$	−512.859	+	888.298i	−0.514403	+	0.890971i	0.485458	+	0.874260i	$0.338653\pi$
$997$	−512.859	+	888.298i	−0.514403	+	0.890971i	−0.999860	+	0.0167112i	$0.994680\pi$
$998$	−98.9191	−	57.1110i	−0.0991173	−	0.0572254i
$999$	−75.9047	−	1216.83i	−0.0759807	−	1.21805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.3.h.f.116.7		16
3.2	odd	2	inner	147.3.h.f.116.1		16
7.2	even	3	inner	147.3.h.f.128.1		16
7.3	odd	6		147.3.b.g.50.7	yes	8
7.4	even	3		147.3.b.g.50.8	yes	8
7.5	odd	6	inner	147.3.h.f.128.2		16
7.6	odd	2	inner	147.3.h.f.116.8		16
21.2	odd	6	inner	147.3.h.f.128.7		16
21.5	even	6	inner	147.3.h.f.128.8		16
21.11	odd	6		147.3.b.g.50.2	yes	8
21.17	even	6		147.3.b.g.50.1	✓	8
21.20	even	2	inner	147.3.h.f.116.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.3.b.g.50.1	✓	8	21.17	even	6
147.3.b.g.50.2	yes	8	21.11	odd	6
147.3.b.g.50.7	yes	8	7.3	odd	6
147.3.b.g.50.8	yes	8	7.4	even	3
147.3.h.f.116.1		16	3.2	odd	2	inner
147.3.h.f.116.2		16	21.20	even	2	inner
147.3.h.f.116.7		16	1.1	even	1	trivial
147.3.h.f.116.8		16	7.6	odd	2	inner
147.3.h.f.128.1		16	7.2	even	3	inner
147.3.h.f.128.2		16	7.5	odd	6	inner
147.3.h.f.128.7		16	21.2	odd	6	inner
147.3.h.f.128.8		16	21.5	even	6	inner

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	147.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.92214 - 1.68710i) q^{2} +(-1.88023 + 2.33768i) q^{3} +(3.69258 - 6.39574i) q^{4} +(4.92837 - 2.84540i) q^{5} +(-1.55039 + 10.0031i) q^{6} -11.4222i q^{8} +(-1.92949 - 8.79074i) q^{9} +O(q^{10})\)	\(q+(2.92214 - 1.68710i) q^{2} +(-1.88023 + 2.33768i) q^{3} +(3.69258 - 6.39574i) q^{4} +(4.92837 - 2.84540i) q^{5} +(-1.55039 + 10.0031i) q^{6} -11.4222i q^{8} +(-1.92949 - 8.79074i) q^{9} +(9.60092 - 16.6293i) q^{10} +(9.43753 + 5.44876i) q^{11} +(8.00830 + 20.6575i) q^{12} -1.14186 q^{13} +(-2.61484 + 16.8710i) q^{15} +(-4.50000 - 7.79423i) q^{16} +(-13.9893 - 8.07671i) q^{17} +(-20.4690 - 22.4325i) q^{18} +(-1.00568 - 1.74190i) q^{19} -42.0275i q^{20} +36.7703 q^{22} +(-32.5979 + 18.8204i) q^{23} +(26.7014 + 21.4763i) q^{24} +(3.69258 - 6.39574i) q^{25} +(-3.33667 + 1.92643i) q^{26} +(24.1778 + 12.0181i) q^{27} +17.3956i q^{29} +(20.8220 + 53.7107i) q^{30} +(-13.8173 + 23.9323i) q^{31} +(13.2684 + 7.66053i) q^{32} +(-30.4822 + 11.8170i) q^{33} -54.5047 q^{34} +(-63.3481 - 20.1200i) q^{36} +(-22.5777 - 39.1058i) q^{37} +(-5.87749 - 3.39337i) q^{38} +(2.14696 - 2.66930i) q^{39} +(-32.5007 - 56.2928i) q^{40} +39.2706i q^{41} -28.6962 q^{43} +(69.6977 - 40.2400i) q^{44} +(-34.5224 - 37.8339i) q^{45} +(-63.5036 + 109.991i) q^{46} +(33.3667 - 19.2643i) q^{47} +(26.6814 + 4.13536i) q^{48} -24.9190i q^{50} +(45.1838 - 17.5164i) q^{51} +(-4.21642 + 7.30305i) q^{52} +(-1.34226 - 0.774952i) q^{53} +(90.9264 - 5.67189i) q^{54} +62.0156 q^{55} +(5.96291 + 0.924194i) q^{57} +(29.3481 + 50.8324i) q^{58} +(73.2830 + 42.3100i) q^{59} +(98.2468 + 79.0212i) q^{60} +(-47.4599 - 82.2029i) q^{61} +93.2446i q^{62} +87.6962 q^{64} +(-5.62752 + 3.24905i) q^{65} +(-69.1366 + 85.9572i) q^{66} +(48.5407 - 84.0749i) q^{67} +(-103.313 + 59.6478i) q^{68} +(17.2954 - 111.590i) q^{69} -17.3956i q^{71} +(-100.409 + 22.0390i) q^{72} +(34.5433 - 59.8308i) q^{73} +(-131.950 - 76.1816i) q^{74} +(8.00830 + 20.6575i) q^{75} -14.8543 q^{76} +(1.77033 - 11.4222i) q^{78} +(6.77033 + 11.7266i) q^{79} +(-44.3554 - 25.6086i) q^{80} +(-73.5541 + 33.9233i) q^{81} +(66.2532 + 114.754i) q^{82} -61.5028i q^{83} -91.9258 q^{85} +(-83.8540 + 48.4132i) q^{86} +(-40.6654 - 32.7077i) q^{87} +(62.2368 - 107.797i) q^{88} +(-26.0508 + 15.0404i) q^{89} +(-164.708 - 52.3131i) q^{90} +277.983i q^{92} +(-29.9664 - 77.2987i) q^{93} +(65.0014 - 112.586i) q^{94} +(-9.91278 - 5.72315i) q^{95} +(-42.8555 + 16.6138i) q^{96} -125.655 q^{97} +(29.6890 - 93.4762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 4 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 4 * q^9	\( 16 q + 16 q^{4} - 4 q^{9} - 128 q^{15} - 72 q^{16} + 52 q^{18} + 416 q^{22} + 16 q^{25} + 240 q^{30} - 712 q^{36} - 232 q^{37} - 16 q^{39} + 144 q^{43} - 456 q^{46} + 124 q^{51} - 120 q^{57} + 168 q^{58} + 104 q^{60} + 800 q^{64} + 432 q^{67} - 12 q^{72} - 144 q^{78} - 64 q^{79} - 400 q^{81} - 1040 q^{85} + 48 q^{88} - 440 q^{93} + 992 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 4 * q^9 - 128 * q^15 - 72 * q^16 + 52 * q^18 + 416 * q^22 + 16 * q^25 + 240 * q^30 - 712 * q^36 - 232 * q^37 - 16 * q^39 + 144 * q^43 - 456 * q^46 + 124 * q^51 - 120 * q^57 + 168 * q^58 + 104 * q^60 + 800 * q^64 + 432 * q^67 - 12 * q^72 - 144 * q^78 - 64 * q^79 - 400 * q^81 - 1040 * q^85 + 48 * q^88 - 440 * q^93 + 992 * q^99

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