LMFDB - Embedded newform 147.3.h.f.116.1

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			116.1
Root			$1.71271 + 1.80533i$ of defining polynomial
Character	$\chi$	$=$	147.116
Dual form			147.3.h.f.128.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.92214 + 1.68710i) q^{2} +(-1.08438 + 2.79716i) q^{3} +(3.69258 - 6.39574i) q^{4} +(-4.92837 + 2.84540i) q^{5} +(-1.55039 - 10.0031i) q^{6} +11.4222i q^{8} +(-6.64826 - 6.06636i) q^{9} +O(q^{10})$	\(q+(-2.92214 + 1.68710i) q^{2} +(-1.08438 + 2.79716i) q^{3} +(3.69258 - 6.39574i) q^{4} +(-4.92837 + 2.84540i) q^{5} +(-1.55039 - 10.0031i) q^{6} +11.4222i q^{8} +(-6.64826 - 6.06636i) q^{9} +(9.60092 - 16.6293i) q^{10} +(-9.43753 - 5.44876i) q^{11} +(13.8858 + 17.2641i) q^{12} -1.14186 q^{13} +(-2.61484 - 16.8710i) q^{15} +(-4.50000 - 7.79423i) q^{16} +(13.9893 + 8.07671i) q^{17} +(29.6616 + 6.51047i) q^{18} +(-1.00568 - 1.74190i) q^{19} +42.0275i q^{20} +36.7703 q^{22} +(32.5979 - 18.8204i) q^{23} +(-31.9497 - 12.3860i) q^{24} +(3.69258 - 6.39574i) q^{25} +(3.33667 - 1.92643i) q^{26} +(24.1778 - 12.0181i) q^{27} -17.3956i q^{29} +(36.1038 + 44.8877i) q^{30} +(-13.8173 + 23.9323i) q^{31} +(-13.2684 - 7.66053i) q^{32} +(25.4749 - 20.4898i) q^{33} -54.5047 q^{34} +(-63.3481 + 20.1200i) q^{36} +(-22.5777 - 39.1058i) q^{37} +(5.87749 + 3.39337i) q^{38} +(1.23821 - 3.19397i) q^{39} +(-32.5007 - 56.2928i) q^{40} -39.2706i q^{41} -28.6962 q^{43} +(-69.6977 + 40.2400i) q^{44} +(50.0263 + 10.9803i) q^{45} +(-63.5036 + 109.991i) q^{46} +(-33.3667 + 19.2643i) q^{47} +(26.6814 - 4.13536i) q^{48} +24.9190i q^{50} +(-37.7615 + 30.3721i) q^{51} +(-4.21642 + 7.30305i) q^{52} +(1.34226 + 0.774952i) q^{53} +(-50.3752 + 75.9087i) q^{54} +62.0156 q^{55} +(5.96291 - 0.924194i) q^{57} +(29.3481 + 50.8324i) q^{58} +(-73.2830 - 42.3100i) q^{59} +(-117.558 - 45.5736i) q^{60} +(-47.4599 - 82.2029i) q^{61} -93.2446i q^{62} +87.6962 q^{64} +(5.62752 - 3.24905i) q^{65} +(-39.8729 + 102.853i) q^{66} +(48.5407 - 84.0749i) q^{67} +(103.313 - 59.6478i) q^{68} +(17.2954 + 111.590i) q^{69} +17.3956i q^{71} +(69.2911 - 75.9377i) q^{72} +(34.5433 - 59.8308i) q^{73} +(131.950 + 76.1816i) q^{74} +(13.8858 + 17.2641i) q^{75} -14.8543 q^{76} +(1.77033 + 11.4222i) q^{78} +(6.77033 + 11.7266i) q^{79} +(44.3554 + 25.6086i) q^{80} +(7.39864 + 80.6614i) q^{81} +(66.2532 + 114.754i) q^{82} +61.5028i q^{83} -91.9258 q^{85} +(83.8540 - 48.4132i) q^{86} +(48.6584 + 18.8634i) q^{87} +(62.2368 - 107.797i) q^{88} +(26.0508 - 15.0404i) q^{89} +(-164.708 + 52.3131i) q^{90} -277.983i q^{92} +(-51.9595 - 64.6010i) q^{93} +(65.0014 - 112.586i) q^{94} +(9.91278 + 5.72315i) q^{95} +(35.8157 - 28.8071i) 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	−0.999061	−	0.0433287i	$-0.986204\pi$
$2$	−2.92214	+	1.68710i	−1.46107	+	0.843548i	−0.462007	+	0.886876i	$0.652870\pi$
$3$	−1.08438	+	2.79716i	−0.361459	+	0.932388i
$3$	−1.08438	+	2.79716i	−0.361459	+	0.932388i
$4$	3.69258	−	6.39574i	0.923146	−	1.59894i
$5$	−4.92837	+	2.84540i	−0.985675	+	0.569080i	−0.903979	−	0.427578i	$-0.859367\pi$
$5$	−4.92837	+	2.84540i	−0.985675	+	0.569080i	−0.0816962	+	0.996657i	$0.526034\pi$
$6$	−1.55039	−	10.0031i	−0.258398	−	1.66719i
$7$		0			0
$7$		0			0
$8$			11.4222i			1.42777i
$9$	−6.64826	−	6.06636i	−0.738695	−	0.674040i
$10$	9.60092	−	16.6293i	0.960092	−	1.66293i
$11$	−9.43753	−	5.44876i	−0.857958	−	0.495342i	0.00537023	−	0.999986i	$-0.498291\pi$
$11$	−9.43753	−	5.44876i	−0.857958	−	0.495342i	−0.863328	+	0.504644i	$0.831624\pi$
$12$	13.8858	+	17.2641i	1.15715	+	1.43868i
$13$	−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	0.851415	−	0.524493i	$-0.175745\pi$
$17$	13.9893	+	8.07671i	0.822898	+	0.475101i	−0.0285166	+	0.999593i	$0.509078\pi$
$18$	29.6616	+	6.51047i	1.64787	+	0.361693i
$19$	−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	0.421238	−	0.906950i	$-0.361596\pi$
$23$	32.5979	−	18.8204i	1.41730	−	0.818278i	0.996061	+	0.0886728i	$0.0282625\pi$
$24$	−31.9497	−	12.3860i	−1.33124	−	0.516081i
$25$	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	$-0.903038\pi$
$29$		−	17.3956i		−	0.599849i	0.953963	−	0.299925i	$-0.0969615\pi$
$30$	36.1038	+	44.8877i	1.20346	+	1.49626i
$31$	−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
$33$	25.4749	−	20.4898i	0.771967	−	0.620904i
$34$	−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
$39$	1.23821	−	3.19397i	0.0317489	−	0.0818967i
$40$	−32.5007	−	56.2928i	−0.812517	−	1.40732i
$41$		−	39.2706i		−	0.957819i	−0.877864	−	0.478909i	$-0.841032\pi$
$41$		−	39.2706i		−	0.957819i	0.877864	−	0.478909i	$-0.158968\pi$
$42$		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
$45$	50.0263	+	10.9803i	1.11170	+	0.244007i
$46$	−63.5036	+	109.991i	−1.38051	+	2.39112i
$47$	−33.3667	+	19.2643i	−0.709930	+	0.409878i	−0.811035	−	0.584997i	$-0.801096\pi$
$47$	−33.3667	+	19.2643i	−0.709930	+	0.409878i	0.101105	+	0.994876i	$0.467762\pi$
$48$	26.6814	−	4.13536i	0.555863	−	0.0861534i
$49$		0			0
$50$			24.9190i			0.498379i
$51$	−37.7615	+	30.3721i	−0.740422	+	0.595531i
$52$	−4.21642	+	7.30305i	−0.0810849	+	0.140443i
$53$	1.34226	+	0.774952i	0.0253256	+	0.0146217i	0.512609	−	0.858622i	$-0.328679\pi$
$53$	1.34226	+	0.774952i	0.0253256	+	0.0146217i	−0.487284	+	0.873244i	$0.662012\pi$
$54$	−50.3752	+	75.9087i	−0.932874	+	1.40572i
$55$	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	−0.272567	−	0.962137i	$-0.587873\pi$
$59$	−73.2830	−	42.3100i	−1.24209	−	0.717118i	−0.969518	+	0.245019i	$0.921206\pi$
$60$	−117.558	−	45.5736i	−1.95930	−	0.759560i
$61$	−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
$66$	−39.8729	+	102.853i	−0.604134	+	1.55837i
$67$	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	$0.0390926\pi$
$71$			17.3956i			0.245009i	−0.992468	+	0.122504i	$0.960907\pi$
$72$	69.2911	−	75.9377i	0.962376	−	1.05469i
$73$	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
$75$	13.8858	+	17.2641i	0.185144	+	0.230189i
$76$	−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
$81$	7.39864	+	80.6614i	0.0913412	+	0.995820i
$82$	66.2532	+	114.754i	0.807966	+	1.39944i
$83$			61.5028i			0.740998i	0.928833	+	0.370499i	$0.120813\pi$
$83$			61.5028i			0.740998i	−0.928833	+	0.370499i	$0.879187\pi$
$84$		0			0
$85$	−91.9258			−1.08148
$86$	83.8540	−	48.4132i	0.975047	−	0.562944i
$87$	48.6584	+	18.8634i	0.559292	+	0.216821i
$88$	62.2368	−	107.797i	0.707237	−	1.22497i
$89$	26.0508	−	15.0404i	0.292706	−	0.168994i	−0.346456	−	0.938066i	$-0.612615\pi$
$89$	26.0508	−	15.0404i	0.292706	−	0.168994i	0.639161	+	0.769073i	$0.279282\pi$
$90$	−164.708	+	52.3131i	−1.83009	+	0.581257i
$91$		0			0
$92$		−	277.983i		−	3.02156i
$93$	−51.9595	−	64.6010i	−0.558704	−	0.694634i
$94$	65.0014	−	112.586i	0.691504	−	1.19772i
$95$	9.91278	+	5.72315i	0.104345	+	0.0602436i
$96$	35.8157	−	28.8071i	0.373080	−	0.300074i
$97$	−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	−0.331133	−	0.943584i	$-0.607431\pi$
$101$	−132.701	−	76.6147i	−1.31387	−	0.758561i	−0.982734	+	0.185023i	$0.940764\pi$
$102$	59.1036	−	152.459i	0.579447	−	1.49469i
$103$	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	−0.321256	−	0.946992i	$-0.604105\pi$
$107$	36.1911	−	20.8950i	0.338235	−	0.195280i	0.659491	+	0.751712i	$0.270772\pi$
$108$	12.4142	−	199.013i	0.114946	−	1.84271i
$109$	−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	$0.283497\pi$
$113$			175.708i			1.55494i	−0.628920	+	0.777470i	$0.716503\pi$
$114$	−15.8652	+	12.7606i	−0.139169	+	0.111935i
$115$	−107.103	+	185.508i	−0.931330	+	1.61311i
$116$	−111.258	−	64.2348i	−0.959120	−	0.553748i
$117$	7.59138	+	6.92694i	0.0648836	+	0.0592046i
$118$	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
$123$	109.846	+	42.5841i	0.893059	+	0.346212i
$124$	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
$129$	31.1174	−	80.2679i	0.241220	−	0.622231i
$130$	−10.9629	+	18.9883i	−0.0843301	+	0.146064i
$131$	66.6097	−	38.4571i	0.508471	−	0.293566i	−0.223734	−	0.974650i	$-0.571825\pi$
$131$	66.6097	−	38.4571i	0.508471	−	0.293566i	0.732205	+	0.681084i	$0.238491\pi$
$132$	−36.9794	−	238.591i	−0.280147	−	1.80751i
$133$		0			0
$134$			327.571i			2.44456i
$135$	−84.9611	+	128.025i	−0.629342	+	0.948333i
$136$	−92.2537	+	159.788i	−0.678336	+	1.17491i
$137$	−140.738	−	81.2550i	−1.02728	−	0.593102i	−0.111078	−	0.993812i	$-0.535430\pi$
$137$	−140.738	−	81.2550i	−1.02728	−	0.593102i	−0.916205	+	0.400710i	$0.868764\pi$
$138$	−238.802	−	296.902i	−1.73045	−	2.15146i
$139$	−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
$144$	−17.3654	+	79.1166i	−0.120593	+	0.549421i
$145$	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	−0.546183	−	0.837666i	$-0.683920\pi$
$149$	−13.9813	+	8.07210i	−0.0938342	+	0.0541752i	0.452349	+	0.891841i	$0.350586\pi$
$150$	−69.7024	−	27.0215i	−0.464683	−	0.180143i
$151$	−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
$156$	−15.8556	−	19.7133i	−0.101639	−	0.126367i
$157$	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
$159$	−3.62318	+	2.91417i	−0.0227873	+	0.0183281i
$160$	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
$165$	−67.2482	+	173.468i	−0.407565	+	1.05132i
$166$	−103.761	−	179.720i	−0.625067	−	1.08265i
$167$			110.140i			0.659521i	0.944065	+	0.329761i	$0.106968\pi$
$167$			110.140i			0.659521i	−0.944065	+	0.329761i	$0.893032\pi$
$168$		0			0
$169$	−167.696			−0.992285
$170$	268.620	−	155.088i	1.58012	−	0.912280i
$171$	−3.88092	+	17.6814i	−0.0226954	+	0.103400i
$172$	−105.963	+	183.533i	−0.616063	+	1.06705i
$173$	−256.676	+	148.192i	−1.48368	+	0.856602i	−0.999828	−	0.0185494i	$-0.994095\pi$
$173$	−256.676	+	148.192i	−1.48368	+	0.856602i	−0.483850	+	0.875151i	$0.660762\pi$
$174$	−174.011	+	26.9700i	−1.00006	+	0.155000i
$175$		0			0
$176$			98.0777i			0.557260i
$177$	197.814	−	159.105i	1.11760	−	0.898897i
$178$	−50.7493	+	87.9003i	−0.285108	+	0.493822i
$179$	41.5601	+	23.9948i	0.232180	+	0.134049i	0.611577	−	0.791185i	$-0.290535\pi$
$179$	41.5601	+	23.9948i	0.232180	+	0.134049i	−0.379398	+	0.925234i	$0.623869\pi$
$180$	254.954	−	279.409i	1.41641	−	1.55227i
$181$	−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
$186$	260.821	+	101.112i	1.40226	+	0.543614i
$187$	−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	−0.543544	−	0.839381i	$-0.682918\pi$
$191$	−16.8826	+	9.74715i	−0.0883903	+	0.0510322i	0.455153	+	0.890413i	$0.349584\pi$
$192$	−95.0956	+	245.301i	−0.495290	+	1.27761i
$193$	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	$-0.756803\pi$
$197$		−	272.583i		−	1.38367i	0.722056	−	0.691834i	$-0.243197\pi$
$198$	−244.459	−	223.062i	−1.23464	−	1.12658i
$199$	−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
$201$	182.535	+	226.945i	0.908134	+	1.12908i
$202$	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
$207$	−330.890	−	72.6275i	−1.59850	−	0.350857i
$208$	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
$213$	−48.6584	−	18.8634i	−0.228443	−	0.0885606i
$214$	−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
$219$	129.899	+	161.502i	0.593144	+	0.737454i
$220$	228.998	−	396.636i	1.04090	−	1.80289i
$221$	−15.9738	−	9.22248i	−0.0722797	−	0.0417307i
$222$	−356.176	+	286.478i	−1.60440	+	1.29044i
$223$	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	0.957922	−	0.287029i	$-0.0926677\pi$
$227$	269.746	+	155.738i	1.18831	+	0.686070i	0.230386	+	0.973099i	$0.426001\pi$
$228$	16.1076	−	41.5499i	0.0706475	−	0.182236i
$229$	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	−0.612041	−	0.790826i	$-0.709651\pi$
$233$	−54.3324	+	31.3689i	−0.233186	+	0.134630i	0.378855	+	0.925456i	$0.376318\pi$
$234$	−33.8695	−	7.43405i	−0.144741	−	0.0317694i
$235$	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	$0.167581\pi$
$239$			240.189i			1.00497i	−0.864585	+	0.502487i	$0.832419\pi$
$240$	−119.729	+	96.2999i	−0.498872	+	0.401250i
$241$	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
$243$	−233.646	−	66.7721i	−0.961506	−	0.274782i
$244$	−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
$249$	−172.033	−	66.6922i	−0.690898	−	0.267840i
$250$	169.119	+	292.922i	0.676474	+	1.17169i
$251$		−	429.607i		−	1.71158i	−0.517321	−	0.855791i	$-0.673071\pi$
$251$		−	429.607i		−	1.71158i	0.517321	−	0.855791i	$-0.326929\pi$
$252$		0			0
$253$	−410.191			−1.62131
$254$	−364.638	+	210.524i	−1.43558	+	0.828833i
$255$	99.6822	−	257.132i	0.390910	−	1.00836i
$256$	220.433	−	381.801i	0.861066	−	1.49141i
$257$	181.436	−	104.752i	0.705976	−	0.407596i	−0.103593	−	0.994620i	$-0.533034\pi$
$257$	181.436	−	104.752i	0.705976	−	0.407596i	0.809569	+	0.587024i	$0.199701\pi$
$258$	44.4902	+	287.052i	0.172443	+	1.11260i
$259$		0			0
$260$		−	47.9895i		−	0.184575i
$261$	−105.528	+	115.651i	−0.404322	+	0.443106i
$262$	−129.762	+	224.754i	−0.495274	+	0.857839i
$263$	223.725	+	129.168i	0.850664	+	0.491131i	0.860875	−	0.508816i	$-0.169917\pi$
$263$	223.725	+	129.168i	0.850664	+	0.491131i	−0.0102105	+	0.999948i	$0.503250\pi$
$264$	234.039	+	290.979i	0.886510	+	1.10219i
$265$	−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	0.683528	−	0.729924i	$-0.260445\pi$
$269$	105.760	+	61.0604i	0.393159	+	0.226990i	−0.290369	+	0.956915i	$0.593778\pi$
$270$	32.2776	−	517.444i	0.119547	−	1.91646i
$271$	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
$276$	777.565	+	301.438i	2.81726	+	1.09217i
$277$	−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	$-0.948616\pi$
$281$		−	90.3282i		−	0.321453i	0.986999	−	0.160726i	$-0.0513837\pi$
$282$	244.435	+	303.905i	0.866790	+	1.07768i
$283$	−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
$285$	−26.7578	+	21.5216i	−0.0938869	+	0.0755145i
$286$	−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
$291$	136.258	−	351.478i	0.468239	−	1.20783i
$292$	−255.108	−	441.860i	−0.873658	−	1.51322i
$293$			265.983i			0.907793i	0.891054	+	0.453897i	$0.149966\pi$
$293$			265.983i			0.907793i	−0.891054	+	0.453897i	$0.850034\pi$
$294$		0			0
$295$	481.555			1.63239
$296$	446.674	−	257.887i	1.50903	−	0.871241i
$297$	−293.662	−	18.3183i	−0.988762	−	0.0616779i
$298$	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
$303$	358.201	−	288.106i	1.18218	−	0.950845i
$304$	−9.05116	+	15.6771i	−0.0297736	+	0.0515693i
$305$	467.800	+	270.085i	1.53377	+	0.885523i
$306$	362.361	+	330.645i	1.18419	+	1.08054i
$307$	−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	−0.262152	−	0.965026i	$-0.584432\pi$
$311$	−382.208	−	220.668i	−1.22897	−	0.709544i	−0.966814	+	0.255483i	$0.917766\pi$
$312$	36.4822	+	14.1430i	0.116930	+	0.0453302i
$313$	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	−0.787165	−	0.616742i	$-0.788452\pi$
$317$	−204.983	+	118.347i	−0.646634	+	0.373334i	0.140531	+	0.990076i	$0.455119\pi$
$318$	5.67093	−	14.6282i	0.0178331	−	0.0460008i
$319$	−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
$324$	543.209	+	250.529i	1.67657	+	0.773238i
$325$	−4.21642	+	7.30305i	−0.0129736	+	0.0224709i
$326$	−349.572	−	201.826i	−1.07231	−	0.619097i
$327$	−69.5818	−	86.5108i	−0.212789	−	0.264559i
$328$	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
$333$	−87.1271	+	396.950i	−0.261643	+	1.19204i
$334$	−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
$339$	−491.485	−	190.534i	−1.44981	−	0.562047i
$340$	−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
$345$	−402.756	−	500.745i	−1.16741	−	1.45143i
$346$	500.028	−	866.075i	1.44517	−	2.50311i
$347$	−137.144	−	79.1804i	−0.395229	−	0.228186i	0.289194	−	0.957270i	$-0.406613\pi$
$347$	−137.144	−	79.1804i	−0.395229	−	0.228186i	−0.684423	+	0.729085i	$0.739946\pi$
$348$	300.321	−	241.552i	0.862990	−	0.694115i
$349$	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	0.678609	−	0.734500i	$-0.262583\pi$
$353$	134.782	+	77.8162i	0.381817	+	0.220442i	−0.296791	+	0.954942i	$0.595917\pi$
$354$	−309.615	+	798.657i	−0.874619	+	2.25609i
$355$	−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	−0.801574	−	0.597896i	$-0.796004\pi$
$359$	−245.760	+	141.889i	−0.684567	+	0.395235i	0.117006	+	0.993131i	$0.462670\pi$
$360$	−125.420	+	571.410i	−0.348388	+	1.58725i
$361$	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
$366$	−748.706	+	602.194i	−2.04564	+	1.64534i
$367$	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
$369$	−238.229	+	261.081i	−0.645608	+	0.707536i
$370$	−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
$375$	280.395	+	108.701i	0.747719	+	0.289868i
$376$	−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
$381$	−135.313	+	349.043i	−0.355153	+	0.916124i
$382$	32.8887	−	56.9650i	0.0860962	−	0.149123i
$383$	−249.732	+	144.183i	−0.652041	+	0.376456i	−0.789238	−	0.614088i	$-0.789524\pi$
$383$	−249.732	+	144.183i	−0.652041	+	0.376456i	0.137197	+	0.990544i	$0.456191\pi$
$384$	−107.804	−	695.553i	−0.280740	−	1.81134i
$385$		0			0
$386$			441.995i			1.14506i
$387$	190.779	+	174.081i	0.492970	+	0.449822i
$388$	−463.992	+	803.658i	−1.19586	+	2.07128i
$389$	−386.064	−	222.894i	−0.992452	−	0.572992i	−0.0864456	−	0.996257i	$-0.527551\pi$
$389$	−386.064	−	222.894i	−0.992452	−	0.572992i	−0.906006	+	0.423264i	$0.860884\pi$
$390$	−41.2255	−	51.2555i	−0.105706	−	0.131424i
$391$	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
$396$	707.479	+	155.285i	1.78656	+	0.392135i
$397$	−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	−0.497951	−	0.867205i	$-0.665914\pi$
$401$	1.64249	−	0.948294i	0.00409599	−	0.00236482i	0.502047	+	0.864841i	$0.332581\pi$
$402$	−916.270	−	355.210i	−2.27928	−	0.883607i
$403$	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
$408$	−346.916	−	431.319i	−0.850284	−	1.05716i
$409$	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
$411$	379.896	−	305.556i	0.924321	−	0.743444i
$412$	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
$417$	149.060	−	384.501i	0.357457	−	0.922066i
$418$	−36.9794	−	64.0501i	−0.0884674	−	0.153230i
$419$			178.858i			0.426869i	0.976957	+	0.213435i	$0.0684651\pi$
$419$			178.858i			0.426869i	−0.976957	+	0.213435i	$0.931535\pi$
$420$		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
$423$	338.695	+	74.3405i	0.800696	+	0.175746i
$424$	−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
$429$	−29.0888	+	23.3965i	−0.0678061	+	0.0545374i
$430$	−275.509	+	477.196i	−0.640720	+	1.10976i
$431$	−264.985	−	152.989i	−0.614814	−	0.354963i	0.160033	−	0.987112i	$-0.448840\pi$
$431$	−264.985	−	152.989i	−0.614814	−	0.354963i	−0.774847	+	0.632149i	$0.782173\pi$
$432$	−202.472	−	134.366i	−0.468684	−	0.311033i
$433$	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
$438$	−652.051	−	252.781i	−1.48870	−	0.577125i
$439$	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	−0.242352	−	0.970188i	$-0.577919\pi$
$443$	211.169	−	121.919i	0.476680	−	0.275211i	0.719032	+	0.694977i	$0.244586\pi$
$444$	361.619	−	932.801i	0.814456	−	2.10090i
$445$	−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	$-0.737332\pi$
$449$		−	659.743i		−	1.46936i	0.678413	−	0.734681i	$-0.262668\pi$
$450$	151.167	−	165.668i	0.335927	−	0.368150i
$451$	−213.976	+	370.617i	−0.474448	+	0.821768i
$452$	1123.78	+	648.817i	2.48625	+	1.43544i
$453$	−38.1893	−	47.4806i	−0.0843030	−	0.104814i
$454$	−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
$459$	435.296	+	27.1533i	0.948358	+	0.0591575i
$460$	790.973	+	1370.01i	1.71951	+	2.97827i
$461$			106.424i			0.230854i	0.993316	+	0.115427i	$0.0368236\pi$
$461$			106.424i			0.230854i	−0.993316	+	0.115427i	$0.963176\pi$
$462$		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
$465$	439.891	+	170.533i	0.946003	+	0.366737i
$466$	105.845	−	183.328i	0.227134	−	0.393408i
$467$	63.6738	−	36.7621i	0.136346	−	0.0787196i	−0.430275	−	0.902698i	$-0.641583\pi$
$467$	63.6738	−	36.7621i	0.136346	−	0.0787196i	0.566622	+	0.823978i	$0.308250\pi$
$468$	72.3347	−	22.9742i	0.154561	−	0.0490903i
$469$		0			0
$470$			739.819i			1.57408i
$471$	268.051	+	333.267i	0.569111	+	0.707573i
$472$	483.273	−	837.053i	1.02388	−	1.77342i
$473$	270.821	+	156.359i	0.572560	+	0.330568i
$474$	106.806	−	85.9053i	0.225328	−	0.181235i
$475$	−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	0.915271	−	0.402838i	$-0.131976\pi$
$479$	490.515	+	283.199i	1.02404	+	0.591229i	0.108768	+	0.994067i	$0.465310\pi$
$480$	−94.5457	+	243.882i	−0.196970	+	0.508087i
$481$	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
$486$	795.396	−	199.066i	1.63662	−	0.409601i
$487$	−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	$-0.724999\pi$
$491$		−	746.721i		−	1.52082i	0.649445	−	0.760409i	$-0.275001\pi$
$492$	677.973	−	545.303i	1.37799	−	1.10834i
$493$	140.499	−	243.352i	0.284989	−	0.493615i
$494$	−6.71128	−	3.87476i	−0.0135856	−	0.00784364i
$495$	−412.296	−	376.209i	−0.832920	−	0.760018i
$496$	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
$501$	−308.080	−	119.433i	−0.614930	−	0.238390i
$502$	724.789	+	1255.37i	1.44380	+	2.50074i
$503$		−	987.870i		−	1.96396i	−0.188993	−	0.981978i	$-0.560522\pi$
$503$		−	987.870i		−	1.96396i	0.188993	−	0.981978i	$-0.439478\pi$
$504$		0			0
$505$	871.997			1.72673
$506$	1198.63	−	692.032i	2.36884	−	1.36765i
$507$	181.846	−	469.074i	0.358670	−	0.925195i
$508$	460.777	−	798.090i	0.907042	−	1.57104i
$509$	87.5198	−	50.5296i	0.171945	−	0.0992723i	−0.411558	−	0.911384i	$-0.635015\pi$
$509$	87.5198	−	50.5296i	0.171945	−	0.0992723i	0.583502	+	0.812111i	$0.301682\pi$
$510$	142.521	+	919.547i	0.279453	+	1.80303i
$511$		0			0
$512$			549.088i			1.07244i
$513$	−45.2495	−	30.0289i	−0.0882056	−	0.0585358i
$514$	−353.454	+	612.199i	−0.687653	+	1.19105i
$515$	−292.214	−	168.710i	−0.567405	−	0.327591i
$516$	−398.469	−	495.415i	−0.772226	−	0.960106i
$517$	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	$-0.970893\pi$
$521$	−819.436	−	473.102i	−1.57281	−	0.908065i	−0.576992	−	0.816750i	$-0.695774\pi$
$522$	113.254	−	515.982i	0.216961	−	0.988472i
$523$	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
$528$	−274.340	−	106.353i	−0.519582	−	0.201426i
$529$	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
$534$	−190.840	−	237.271i	−0.357379	−	0.444328i
$535$	−118.909	+	205.956i	−0.222260	+	0.384965i
$536$	960.320	+	554.441i	1.79164	+	1.03440i
$537$	−112.184	+	90.2312i	−0.208909	+	0.168028i
$538$	−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
$543$	177.129	−	456.908i	0.326205	−	0.841450i
$544$	−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
$549$	−183.147	+	834.415i	−0.333601	+	1.51988i
$550$	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
$555$	−600.715	+	483.163i	−1.08237	+	0.870565i
$556$	−507.587	+	879.166i	−0.912926	+	1.58123i
$557$	310.096	+	179.034i	0.556726	+	0.321426i	0.751830	−	0.659357i	$-0.229171\pi$
$557$	310.096	+	179.034i	0.556726	+	0.321426i	−0.195104	+	0.980782i	$0.562505\pi$
$558$	−565.655	+	619.914i	−1.01372	+	1.11096i
$559$	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	0.874458	−	0.485102i	$-0.161217\pi$
$563$	501.957	+	289.805i	0.891576	+	0.514752i	0.0171184	+	0.999853i	$0.494551\pi$
$564$	−795.905	−	308.548i	−1.41118	−	0.547071i
$565$	−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	0.0304622	−	0.999536i	$-0.490302\pi$
$569$	518.539	−	299.379i	0.911317	−	0.526149i	0.880855	+	0.473387i	$0.156969\pi$
$570$	41.8807	−	108.032i	0.0734750	−	0.189530i
$571$	−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
$576$	−583.027	−	531.996i	−1.01220	−	0.923604i
$577$	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
$579$	246.296	+	306.219i	0.425382	+	0.528876i
$580$	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
$585$	−57.1231	−	12.5380i	−0.0976463	−	0.0214325i
$586$	−448.739	−	777.240i	−0.765767	−	1.32635i
$587$		−	430.520i		−	0.733424i	−0.930335	−	0.366712i	$-0.880483\pi$
$587$		−	430.520i		−	0.733424i	0.930335	−	0.366712i	$-0.119517\pi$
$588$		0			0
$589$	55.5835			0.0943693
$590$	−1407.17	+	812.429i	−2.38503	+	1.37700i
$591$	762.459	+	295.582i	1.29012	+	0.500139i
$592$	−203.200	+	351.952i	−0.343243	+	0.594514i
$593$	−887.325	+	512.298i	−1.49633	+	0.863908i	−0.999991	−	0.00421907i	$-0.998657\pi$
$593$	−887.325	+	512.298i	−1.49633	+	0.863908i	−0.496342	+	0.868127i	$0.665324\pi$
$594$	889.026	−	441.908i	1.49668	−	0.743953i
$595$		0			0
$596$			119.228i			0.200046i
$597$	−372.660	−	463.327i	−0.624222	−	0.776093i
$598$	72.5122	−	125.595i	0.121258	−	0.210025i
$599$	−127.615	−	73.6788i	−0.213047	−	0.123003i	0.389679	−	0.920951i	$-0.372586\pi$
$599$	−127.615	−	73.6788i	−0.213047	−	0.123003i	−0.602727	+	0.797948i	$0.705919\pi$
$600$	−197.194	+	158.606i	−0.328657	+	0.264344i
$601$	−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
$606$	−560.650	+	1446.20i	−0.925165	+	2.38648i
$607$	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
$612$	−1048.70	−	230.180i	−1.71356	−	0.376111i
$613$	−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	$0.0885344\pi$
$617$			338.815i			0.549133i	−0.961568	+	0.274567i	$0.911466\pi$
$618$	467.683	−	376.163i	0.756768	−	0.608679i
$619$	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
$621$	561.960	−	846.799i	0.904928	−	1.36360i
$622$	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
$627$	−61.3109	−	23.7684i	−0.0977845	−	0.0379081i
$628$	−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
$633$	−292.973	+	755.729i	−0.462833	+	1.19389i
$634$	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
$639$	105.528	−	115.651i	0.165146	−	0.180987i
$640$	667.586	−	1156.29i	1.04310	−	1.80671i
$641$	−1016.56	−	586.912i	−1.58590	−	0.915619i	−0.993973	−	0.109627i	$-0.965035\pi$
$641$	−1016.56	−	586.912i	−1.58590	−	0.915619i	−0.591926	−	0.805992i	$-0.701632\pi$
$642$	−265.125	−	329.629i	−0.412968	−	0.513442i
$643$	−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	−0.400518	−	0.916289i	$-0.631170\pi$
$647$	−902.116	−	520.837i	−1.39431	−	0.805003i	−0.993788	+	0.111286i	$0.964503\pi$
$648$	−921.330	+	84.5087i	−1.42181	+	0.130415i
$649$	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	−0.159133	−	0.987257i	$-0.550870\pi$
$653$	402.437	−	232.347i	0.616290	−	0.355815i	0.775423	+	0.631442i	$0.217537\pi$
$654$	349.280	+	135.405i	0.534067	+	0.207041i
$655$	−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	$0.301221\pi$
$659$			1069.25i			1.62253i	−0.584678	+	0.811265i	$0.698779\pi$
$660$	861.135	+	1070.65i	1.30475	+	1.62219i
$661$	−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
$663$	43.1184	−	34.6807i	0.0650353	−	0.0523088i
$664$	−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
$669$	−45.4374	+	117.207i	−0.0679184	+	0.175197i
$670$	−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
$675$	12.4142	−	199.013i	0.0183914	−	0.294834i
$676$	−619.232	+	1072.54i	−0.916023	+	1.58660i
$677$	755.020	−	435.911i	1.11524	−	0.643886i	0.175061	−	0.984558i	$-0.443988\pi$
$677$	755.020	−	435.911i	1.11524	−	0.643886i	0.940182	+	0.340671i	$0.110654\pi$
$678$	1757.63	−	272.416i	2.59238	−	0.401794i
$679$		0			0
$680$		−	1049.99i		−	1.54411i
$681$	−728.130	+	585.645i	−1.06921	+	0.859978i
$682$	−508.068	+	879.999i	−0.744968	+	1.29032i
$683$	954.567	+	551.119i	1.39761	+	0.806910i	0.994142	−	0.108084i	$-0.0344717\pi$
$683$	954.567	+	551.119i	1.39761	+	0.806910i	0.403467	+	0.914994i	$0.367805\pi$
$684$	98.7552	+	90.1114i	0.144379	+	0.131742i
$685$	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
$690$	2021.71	+	783.756i	2.93002	+	1.13588i
$691$	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
$696$	−215.461	+	555.786i	−0.309571	+	0.798543i
$697$	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	$0.0710658\pi$
$701$			310.416i			0.442819i	−0.975181	+	0.221410i	$0.928934\pi$
$702$	57.5215	−	86.6771i	0.0819394	−	0.123472i
$703$	−45.4122	+	78.6562i	−0.0645977	+	0.111887i
$704$	−827.635	−	477.836i	−1.17562	−	0.678744i
$705$	412.255	+	512.555i	0.584759	+	0.727029i
$706$	−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
$711$	26.1266	−	119.032i	0.0367462	−	0.167415i
$712$	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
$717$	−671.847	−	260.455i	−0.937025	−	0.363256i
$718$	478.762	−	829.240i	0.666799	−	1.15493i
$719$	523.881	−	302.463i	0.728625	−	0.420672i	−0.0892940	−	0.996005i	$-0.528461\pi$
$719$	523.881	−	302.463i	0.728625	−	0.420672i	0.817919	+	0.575334i	$0.195128\pi$
$720$	−139.535	−	439.328i	−0.193799	−	0.610178i
$721$		0			0
$722$			1204.43i			1.66819i
$723$	590.956	+	734.734i	0.817367	+	1.01623i
$724$	−603.171	+	1044.72i	−0.833109	+	1.44299i
$725$	−111.258	−	64.2348i	−0.153459	−	0.0885997i
$726$	−17.6998	+	14.2362i	−0.0243799	+	0.0196091i
$727$	−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
$732$	760.146	−	1960.81i	1.03845	−	2.67870i
$733$	−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
$738$	255.670	−	1164.83i	0.346436	−	1.57836i
$739$	−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	$-0.992171\pi$
$743$		−	36.5432i		−	0.0491834i	0.999698	−	0.0245917i	$-0.00782856\pi$
$744$	737.885	−	593.491i	0.991781	−	0.797703i
$745$	45.9367	−	79.5647i	0.0616600	−	0.106798i
$746$	−508.368	−	293.506i	−0.681458	−	0.393440i
$747$	373.098	−	408.887i	0.499462	−	0.547371i
$748$	−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
$753$	1201.68	+	465.856i	1.59586	+	0.618667i
$754$	−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
$759$	444.802	−	1147.37i	0.586036	−	1.51169i
$760$	−65.3709	+	113.226i	−0.0860143	+	0.148981i
$761$	−974.503	+	562.630i	−1.28056	+	0.739330i	−0.976950	−	0.213468i	$-0.931524\pi$
$761$	−974.503	+	562.630i	−1.28056	+	0.739330i	−0.303606	+	0.952798i	$0.598191\pi$
$762$	−193.465	−	1248.24i	−0.253891	−	1.63811i
$763$		0			0
$764$			143.969i			0.188441i
$765$	611.146	+	557.655i	0.798884	+	0.728961i
$766$	486.500	−	842.642i	0.635117	−	1.10005i
$767$	83.6790	+	48.3121i	0.109099	+	0.0629884i
$768$	828.928	+	1030.60i	1.07933	+	1.34193i
$769$	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	0.476559	−	0.879142i	$-0.341884\pi$
$773$	−35.9609	−	20.7620i	−0.0465212	−	0.0268590i	−0.523080	+	0.852283i	$0.675217\pi$
$774$	−851.175	−	186.825i	−1.09971	−	0.241377i
$775$	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
$780$	134.235	+	52.0387i	0.172096	+	0.0667163i
$781$	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
$786$	−487.963	−	606.682i	−0.620818	−	0.771861i
$787$	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
$789$	−603.905	+	485.729i	−0.765405	+	0.615626i
$790$	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
$795$	9.56440	−	24.6715i	0.0120307	−	0.0310333i
$796$	731.869	+	1267.63i	0.919433	+	1.59250i
$797$			138.675i			0.173997i	0.996208	+	0.0869983i	$0.0277275\pi$
$797$			138.675i			0.173997i	−0.996208	+	0.0869983i	$0.972273\pi$
$798$		0			0
$799$	−622.368			−0.778934
$800$	−97.9895	+	56.5742i	−0.122487	+	0.0707178i
$801$	−264.433	−	58.0407i	−0.330129	−	0.0724603i
$802$	−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
$807$	−285.479	+	229.615i	−0.353754	+	0.284529i
$808$	875.108	−	1515.73i	1.08305	−	1.87590i
$809$	795.371	+	459.208i	0.983154	+	0.567624i	0.903221	−	0.429176i	$-0.141196\pi$
$809$	795.371	+	459.208i	0.983154	+	0.567624i	0.0799330	+	0.996800i	$0.474529\pi$
$810$	1412.37	+	651.389i	1.74367	+	0.804184i
$811$	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
$816$	406.654	+	157.647i	0.498350	+	0.193195i
$817$	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	$0.686069\pi$
$821$	−1272.53	+	734.693i	−1.54997	+	0.894876i	−0.998143	+	0.0609175i	$0.980597\pi$
$822$	−594.606	+	1533.80i	−0.723365	+	1.86593i
$823$	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	$-0.809865\pi$
$827$		−	930.266i		−	1.12487i	0.826842	−	0.562434i	$-0.190135\pi$
$828$	−1686.35	+	1848.10i	−2.03665	+	2.23201i
$829$	−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
$831$	−522.145	−	649.181i	−0.628334	−	0.781205i
$832$	−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
$837$	−46.4528	+	744.689i	−0.0554992	+	0.889712i
$838$	−301.751	−	522.648i	−0.360085	−	0.623685i
$839$		−	451.383i		−	0.538002i	−0.963140	−	0.269001i	$-0.913307\pi$
$839$		−	451.383i		−	0.538002i	0.963140	−	0.269001i	$-0.0866934\pi$
$840$		0			0
$841$	538.392			0.640181
$842$	−430.700	+	248.665i	−0.511520	+	0.295326i
$843$	252.663	+	97.9497i	0.299719	+	0.116192i
$844$	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
$849$	−545.278	−	677.943i	−0.642260	−	0.798519i
$850$	−201.263	+	348.598i	−0.236780	+	0.410115i
$851$	−1471.97	−	849.844i	−1.72970	−	0.998641i
$852$	−300.321	+	241.552i	−0.352489	+	0.283512i
$853$	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	0.815483	−	0.578781i	$-0.196472\pi$
$857$	618.741	+	357.230i	0.721985	+	0.416838i	−0.0934980	+	0.995619i	$0.529805\pi$
$858$	45.5293	−	117.443i	0.0530644	−	0.136880i
$859$	−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	−0.597197	−	0.802095i	$-0.703719\pi$
$863$	−173.602	+	100.229i	−0.201161	+	0.116140i	0.396036	+	0.918235i	$0.370386\pi$
$864$	−412.866	−	25.7541i	−0.477854	−	0.0298080i
$865$	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
$870$	780.850	−	628.048i	0.897529	−	0.721895i
$871$	−55.4267	+	96.0018i	−0.0636357	+	0.110220i
$872$	−366.071	−	211.351i	−0.419807	−	0.242375i
$873$	835.388	+	762.269i	0.956916	+	0.873161i
$874$	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
$879$	−743.999	−	288.426i	−0.846416	−	0.328130i
$880$	−279.070	−	483.364i	−0.317125	−	0.549277i
$881$		−	436.714i		−	0.495703i	−0.968798	−	0.247851i	$-0.920276\pi$
$881$		−	436.714i		−	0.495703i	0.968798	−	0.247851i	$-0.0797244\pi$
$882$		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
$885$	−522.187	+	1346.99i	−0.590041	+	1.52202i
$886$	−411.377	+	712.525i	−0.464308	+	0.804205i
$887$	770.548	−	444.876i	0.868712	−	0.501551i	0.00179198	−	0.999998i	$-0.499430\pi$
$887$	770.548	−	444.876i	0.868712	−	0.501551i	0.866920	+	0.498447i	$0.166096\pi$
$888$	236.991	+	1529.07i	0.266881	+	1.72192i
$889$		0			0
$890$		−	577.608i		−	0.648997i
$891$	369.680	−	801.558i	0.414904	−	0.899616i
$892$	154.726	−	267.994i	0.173460	−	0.300441i
$893$	67.1128	+	38.7476i	0.0751543	+	0.0433904i
$894$	102.423	+	127.342i	0.114567	+	0.142441i
$895$	−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
$900$	−105.236	+	479.453i	−0.116929	+	0.532725i
$901$	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
$906$	191.698	+	74.3157i	0.211588	+	0.0820262i
$907$	−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	$0.0383172\pi$
$911$			218.798i			0.240173i	−0.992763	+	0.120087i	$0.961683\pi$
$912$	−34.0365	−	42.3174i	−0.0373207	−	0.0464007i
$913$	335.114	−	580.435i	0.367047	−	0.635745i
$914$	1781.07	+	1028.30i	1.94865	+	1.12506i
$915$	−1262.74	+	1015.64i	−1.38005	+	1.10999i
$916$	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
$921$	324.951	−	838.215i	0.352824	−	0.910114i
$922$	−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
$927$	114.403	−	521.221i	0.123413	−	0.562266i
$928$	−133.260	+	230.812i	−0.143599	+	0.248720i
$929$	801.244	−	462.598i	0.862480	−	0.497953i	−0.00236194	−	0.999997i	$-0.500752\pi$
$929$	801.244	−	462.598i	0.862480	−	0.497953i	0.864842	+	0.502044i	$0.167418\pi$
$930$	−1573.13	+	243.819i	−1.69153	+	0.262171i
$931$		0			0
$932$			463.328i			0.497133i
$933$	1031.70	−	829.813i	1.10579	−	0.889403i
$934$	−124.042	+	214.848i	−0.132808	+	0.230029i
$935$	867.553	+	500.882i	0.927864	+	0.535703i
$936$	−79.1208	+	86.7103i	−0.0845308	+	0.0926392i
$937$	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	0.930420	−	0.366495i	$-0.119442\pi$
$941$	1014.62	+	585.791i	1.07824	+	0.622520i	0.147816	+	0.989015i	$0.452776\pi$
$942$	−1345.54	−	521.623i	−1.42838	−	0.553740i
$943$	−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	0.0789497	−	0.996879i	$-0.474843\pi$
$947$	929.714	−	536.771i	0.981747	−	0.566812i	0.902797	+	0.430067i	$0.141510\pi$
$948$	−108.438	+	279.716i	−0.114386	+	0.295060i
$949$	−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	$-0.900916\pi$
$953$		−	583.768i		−	0.612559i	0.951942	−	0.306279i	$-0.0990842\pi$
$954$	34.7682	+	31.7250i	0.0364446	+	0.0332548i
$955$	55.4690	−	96.0752i	0.0580828	−	0.100602i
$956$	1536.18	+	886.916i	1.60689	+	0.927737i
$957$	−356.433	−	443.152i	−0.372449	−	0.463064i
$958$	−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
$963$	−367.364	−	80.6332i	−0.381479	−	0.0837313i
$964$	−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
$969$	90.8812	+	35.2319i	0.0937887	+	0.0363590i
$970$	−1206.41	+	2089.56i	−1.24372	+	2.15418i
$971$	1531.78	−	884.371i	1.57752	−	0.910784i	0.582320	−	0.812960i	$-0.302145\pi$
$971$	1531.78	−	884.371i	1.57752	−	0.910784i	0.995204	−	0.0978237i	$-0.0311881\pi$
$972$	−1289.81	+	1247.78i	−1.32697	+	1.28372i
$973$		0			0
$974$		−	1638.26i		−	1.68199i
$975$	−15.8556	−	19.7133i	−0.0162622	−	0.0202187i
$976$	−427.139	+	739.826i	−0.437642	+	0.758019i
$977$	−305.761	−	176.531i	−0.312959	−	0.180687i	0.335291	−	0.942115i	$-0.391165\pi$
$977$	−305.761	−	176.531i	−0.312959	−	0.180687i	−0.648250	+	0.761428i	$0.724499\pi$
$978$	943.608	−	758.957i	0.964834	−	0.776029i
$979$	−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	0.926453	−	0.376410i	$-0.122841\pi$
$983$	1045.62	+	603.687i	1.06370	+	0.614127i	0.137246	+	0.990537i	$0.456175\pi$
$984$	−486.403	+	1254.68i	−0.494312	+	1.27509i
$985$	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
$990$	1839.48	+	403.751i	1.85806	+	0.407829i
$991$	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
$996$	−1061.79	+	854.015i	−1.06606	+	0.857445i
$997$	−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
$999$	−1015.86	−	674.152i	−1.01687	−	0.674827i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-2.92214 + 1.68710i) q^{2} +(-1.08438 + 2.79716i) q^{3} +(3.69258 - 6.39574i) q^{4} +(-4.92837 + 2.84540i) q^{5} +(-1.55039 - 10.0031i) q^{6} +11.4222i q^{8} +(-6.64826 - 6.06636i) q^{9} +O(q^{10})\)	\(q+(-2.92214 + 1.68710i) q^{2} +(-1.08438 + 2.79716i) q^{3} +(3.69258 - 6.39574i) q^{4} +(-4.92837 + 2.84540i) q^{5} +(-1.55039 - 10.0031i) q^{6} +11.4222i q^{8} +(-6.64826 - 6.06636i) q^{9} +(9.60092 - 16.6293i) q^{10} +(-9.43753 - 5.44876i) q^{11} +(13.8858 + 17.2641i) q^{12} -1.14186 q^{13} +(-2.61484 - 16.8710i) q^{15} +(-4.50000 - 7.79423i) q^{16} +(13.9893 + 8.07671i) q^{17} +(29.6616 + 6.51047i) q^{18} +(-1.00568 - 1.74190i) q^{19} +42.0275i q^{20} +36.7703 q^{22} +(32.5979 - 18.8204i) q^{23} +(-31.9497 - 12.3860i) q^{24} +(3.69258 - 6.39574i) q^{25} +(3.33667 - 1.92643i) q^{26} +(24.1778 - 12.0181i) q^{27} -17.3956i q^{29} +(36.1038 + 44.8877i) q^{30} +(-13.8173 + 23.9323i) q^{31} +(-13.2684 - 7.66053i) q^{32} +(25.4749 - 20.4898i) q^{33} -54.5047 q^{34} +(-63.3481 + 20.1200i) q^{36} +(-22.5777 - 39.1058i) q^{37} +(5.87749 + 3.39337i) q^{38} +(1.23821 - 3.19397i) q^{39} +(-32.5007 - 56.2928i) q^{40} -39.2706i q^{41} -28.6962 q^{43} +(-69.6977 + 40.2400i) q^{44} +(50.0263 + 10.9803i) q^{45} +(-63.5036 + 109.991i) q^{46} +(-33.3667 + 19.2643i) q^{47} +(26.6814 - 4.13536i) q^{48} +24.9190i q^{50} +(-37.7615 + 30.3721i) q^{51} +(-4.21642 + 7.30305i) q^{52} +(1.34226 + 0.774952i) q^{53} +(-50.3752 + 75.9087i) q^{54} +62.0156 q^{55} +(5.96291 - 0.924194i) q^{57} +(29.3481 + 50.8324i) q^{58} +(-73.2830 - 42.3100i) q^{59} +(-117.558 - 45.5736i) q^{60} +(-47.4599 - 82.2029i) q^{61} -93.2446i q^{62} +87.6962 q^{64} +(5.62752 - 3.24905i) q^{65} +(-39.8729 + 102.853i) q^{66} +(48.5407 - 84.0749i) q^{67} +(103.313 - 59.6478i) q^{68} +(17.2954 + 111.590i) q^{69} +17.3956i q^{71} +(69.2911 - 75.9377i) q^{72} +(34.5433 - 59.8308i) q^{73} +(131.950 + 76.1816i) q^{74} +(13.8858 + 17.2641i) q^{75} -14.8543 q^{76} +(1.77033 + 11.4222i) q^{78} +(6.77033 + 11.7266i) q^{79} +(44.3554 + 25.6086i) q^{80} +(7.39864 + 80.6614i) q^{81} +(66.2532 + 114.754i) q^{82} +61.5028i q^{83} -91.9258 q^{85} +(83.8540 - 48.4132i) q^{86} +(48.6584 + 18.8634i) q^{87} +(62.2368 - 107.797i) q^{88} +(26.0508 - 15.0404i) q^{89} +(-164.708 + 52.3131i) q^{90} -277.983i q^{92} +(-51.9595 - 64.6010i) q^{93} +(65.0014 - 112.586i) q^{94} +(9.91278 + 5.72315i) q^{95} +(35.8157 - 28.8071i) 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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