LMFDB - Embedded newform 177.3.h.a.5.19

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.h (of order $58$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$1064$
Relative dimension:	$38$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			5.19
Character	$\chi$	$=$	177.5
Dual form			177.3.h.a.71.19

$q$-expansion

$f(q)$	$=$	$q+(-0.0718854 + 0.213348i) q^{2} +(2.81983 - 1.02398i) q^{3} +(3.14402 + 2.39002i) q^{4} +(-7.60675 - 3.03081i) q^{5} +(0.0157589 + 0.675216i) q^{6} +(4.35627 - 2.01543i) q^{7} +(-1.48128 + 1.00433i) q^{8} +(6.90294 - 5.77490i) q^{9} +O(q^{10})$	\(q+(-0.0718854 + 0.213348i) q^{2} +(2.81983 - 1.02398i) q^{3} +(3.14402 + 2.39002i) q^{4} +(-7.60675 - 3.03081i) q^{5} +(0.0157589 + 0.675216i) q^{6} +(4.35627 - 2.01543i) q^{7} +(-1.48128 + 1.00433i) q^{8} +(6.90294 - 5.77490i) q^{9} +(1.19343 - 1.40502i) q^{10} +(20.3175 + 5.64112i) q^{11} +(11.3130 + 3.52006i) q^{12} +(10.6705 - 20.1268i) q^{13} +(0.116835 + 1.07428i) q^{14} +(-24.5533 - 0.757230i) q^{15} +(4.11842 + 14.8332i) q^{16} +(-6.72609 + 14.5382i) q^{17} +(0.735844 + 1.88786i) q^{18} +(-20.7890 + 4.57601i) q^{19} +(-16.6721 - 27.7092i) q^{20} +(10.2202 - 10.1439i) q^{21} +(-2.66405 + 3.92918i) q^{22} +(-3.12206 - 0.511835i) q^{23} +(-3.14855 + 4.34884i) q^{24} +(30.5270 + 28.9167i) q^{25} +(3.52696 + 3.72336i) q^{26} +(13.5518 - 23.3527i) q^{27} +(18.5131 + 4.07505i) q^{28} +(0.204099 + 0.605744i) q^{29} +(1.92657 - 5.18396i) q^{30} +(-39.7784 - 8.75589i) q^{31} +(-10.6088 - 0.575193i) q^{32} +(63.0683 - 4.89762i) q^{33} +(-2.61819 - 2.48008i) q^{34} +(-39.2455 + 2.12783i) q^{35} +(35.5051 - 1.65822i) q^{36} +(-15.8511 + 23.3786i) q^{37} +(0.518144 - 4.76425i) q^{38} +(9.47980 - 67.6806i) q^{39} +(14.3116 - 3.15023i) q^{40} +(-13.9739 + 2.29091i) q^{41} +(1.42950 + 2.90966i) q^{42} +(-3.08193 - 11.1001i) q^{43} +(50.3962 + 66.2951i) q^{44} +(-70.0115 + 23.0067i) q^{45} +(0.333629 - 0.629292i) q^{46} +(-11.3922 + 4.53905i) q^{47} +(26.8022 + 37.6101i) q^{48} +(-16.8068 + 19.7864i) q^{49} +(-8.36378 + 4.43419i) q^{50} +(-4.07966 + 47.8827i) q^{51} +(81.6519 - 37.7762i) q^{52} +(35.8230 - 30.4284i) q^{53} +(4.00808 + 4.56997i) q^{54} +(-137.453 - 104.489i) q^{55} +(-4.42869 + 7.36055i) q^{56} +(-53.9359 + 34.1911i) q^{57} -0.143906 q^{58} +(-58.4198 + 8.25420i) q^{59} +(-75.3862 - 61.0636i) q^{60} +(14.2552 + 4.80312i) q^{61} +(4.72754 - 7.85723i) q^{62} +(18.4322 - 39.0694i) q^{63} +(-21.9068 + 54.9819i) q^{64} +(-142.169 + 120.759i) q^{65} +(-3.48879 + 13.8076i) q^{66} +(29.3943 + 43.3533i) q^{67} +(-55.8936 + 29.6329i) q^{68} +(-9.32779 + 1.75363i) q^{69} +(2.36721 - 8.52591i) q^{70} +(-32.2100 + 12.8336i) q^{71} +(-4.42526 + 15.4871i) q^{72} +(-58.7889 + 6.39367i) q^{73} +(-3.84832 - 5.06238i) q^{74} +(115.691 + 50.2814i) q^{75} +(-76.2980 - 35.2992i) q^{76} +(99.8777 - 16.3741i) q^{77} +(13.7581 + 6.88775i) q^{78} +(40.6892 - 24.4819i) q^{79} +(13.6288 - 125.315i) q^{80} +(14.3011 - 79.7275i) q^{81} +(0.515759 - 3.14599i) q^{82} +(15.8720 - 0.860557i) q^{83} +(56.3767 - 7.46607i) q^{84} +(95.2262 - 90.2030i) q^{85} +(2.58973 + 0.140411i) q^{86} +(1.19579 + 1.49911i) q^{87} +(-35.7614 + 12.0494i) q^{88} +(6.15329 + 18.2623i) q^{89} +(0.124360 - 16.5907i) q^{90} +(5.91976 - 109.183i) q^{91} +(-8.59252 - 9.07101i) q^{92} +(-121.134 + 16.0420i) q^{93} +(-0.149469 - 2.75679i) q^{94} +(172.006 + 28.1990i) q^{95} +(-30.5041 + 9.24124i) q^{96} +(147.069 + 15.9947i) q^{97} +(-3.01324 - 5.00805i) q^{98} +(172.827 - 78.3910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} + O(q^{10}) $	$ 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} - 94q^{10} - 29q^{12} - 54q^{13} - 12q^{15} - 158q^{16} - 27q^{18} - 30q^{19} - 18q^{21} - 142q^{22} - 23q^{24} + 108q^{25} - 32q^{27} - 70q^{28} - 131q^{30} - 18q^{31} + 17q^{33} + 90q^{34} + 67q^{36} - 170q^{37} - 91q^{39} - 2q^{40} - 43q^{42} - 222q^{43} - 461q^{45} - 54q^{46} - 1645q^{48} - 300q^{49} - 893q^{51} - 66q^{52} - 859q^{54} + 170q^{55} - 27q^{57} - 36q^{58} + 510q^{60} - 70q^{61} + 610q^{63} - 106q^{64} + 1619q^{66} - 182q^{67} + 1487q^{69} - 206q^{70} + 2241q^{72} + 134q^{73} + 542q^{75} + 246q^{76} - 273q^{78} - 122q^{79} + 127q^{81} + 122q^{82} - 329q^{84} - 6q^{85} + 54q^{87} + 38q^{88} + 347q^{90} + 274q^{91} - 483q^{93} - 826q^{94} + 693q^{96} - 474q^{97} - 523q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{3}{29}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.0718854	+	0.213348i	−0.0359427	+	0.106674i	−0.964122	−	0.265458i	$-0.914477\pi$
$2$	−0.0718854	+	0.213348i	−0.0359427	+	0.106674i	0.928180	+	0.372132i	$0.121373\pi$
$3$	2.81983	−	1.02398i	0.939945	−	0.341326i
$3$	2.81983	−	1.02398i	0.939945	−	0.341326i
$4$	3.14402	+	2.39002i	0.786006	+	0.597506i
$5$	−7.60675	−	3.03081i	−1.52135	−	0.606161i	−0.548203	−	0.836345i	$-0.684688\pi$
$5$	−7.60675	−	3.03081i	−1.52135	−	0.606161i	−0.973147	+	0.230184i	$0.926067\pi$
$6$	0.0157589	+	0.675216i	0.00262649	+	0.112536i
$7$	4.35627	−	2.01543i	0.622325	−	0.287918i	−0.0832773	−	0.996526i	$-0.526539\pi$
$7$	4.35627	−	2.01543i	0.622325	−	0.287918i	0.705602	+	0.708608i	$0.250677\pi$
$8$	−1.48128	+	1.00433i	−0.185160	+	0.125541i
$9$	6.90294	−	5.77490i	0.766993	−	0.641655i
$10$	1.19343	−	1.40502i	0.119343	−	0.140502i
$11$	20.3175	+	5.64112i	1.84704	+	0.512829i	0.999830	−	0.0184237i	$-0.00586479\pi$
$11$	20.3175	+	5.64112i	1.84704	+	0.512829i	0.847213	+	0.531253i	$0.178279\pi$
$12$	11.3130	+	3.52006i	0.942746	+	0.293339i
$13$	10.6705	−	20.1268i	0.820811	−	1.54821i	−0.0154480	−	0.999881i	$-0.504917\pi$
$13$	10.6705	−	20.1268i	0.820811	−	1.54821i	0.836259	−	0.548334i	$-0.184738\pi$
$14$	0.116835	+	1.07428i	0.00834538	+	0.0767345i
$15$	−24.5533	−	0.757230i	−1.63688	−	0.0504820i
$16$	4.11842	+	14.8332i	0.257402	+	0.927077i
$17$	−6.72609	+	14.5382i	−0.395652	+	0.855188i	0.602709	+	0.797961i	$0.294088\pi$
$17$	−6.72609	+	14.5382i	−0.395652	+	0.855188i	−0.998361	+	0.0572271i	$0.981774\pi$
$18$	0.735844	+	1.88786i	0.0408802	+	0.104881i
$19$	−20.7890	+	4.57601i	−1.09416	+	0.240843i	−0.725156	−	0.688585i	$-0.758232\pi$
$19$	−20.7890	+	4.57601i	−1.09416	+	0.240843i	−0.369004	+	0.929428i	$0.620301\pi$
$20$	−16.6721	−	27.7092i	−0.833605	−	1.38546i
$21$	10.2202	−	10.1439i	0.486677	−	0.483043i
$22$	−2.66405	+	3.92918i	−0.121093	+	0.178599i
$23$	−3.12206	−	0.511835i	−0.135742	−	0.0222537i	0.0935281	−	0.995617i	$-0.470186\pi$
$23$	−3.12206	−	0.511835i	−0.135742	−	0.0222537i	−0.229270	+	0.973363i	$0.573634\pi$
$24$	−3.14855	+	4.34884i	−0.131189	+	0.181202i
$25$	30.5270	+	28.9167i	1.22108	+	1.15667i
$26$	3.52696	+	3.72336i	0.135652	+	0.143206i
$27$	13.5518	−	23.3527i	0.501918	−	0.864915i
$28$	18.5131	+	4.07505i	0.661183	+	0.145537i
$29$	0.204099	+	0.605744i	0.00703789	+	0.0208877i	0.951115	−	0.308838i	$-0.0999402\pi$
$29$	0.204099	+	0.605744i	0.00703789	+	0.0208877i	−0.944077	+	0.329726i	$0.893044\pi$
$30$	1.92657	−	5.18396i	0.0642192	−	0.172799i
$31$	−39.7784	−	8.75589i	−1.28317	−	0.282448i	−0.479513	−	0.877535i	$-0.659187\pi$
$31$	−39.7784	−	8.75589i	−1.28317	−	0.282448i	−0.803662	+	0.595087i	$0.797118\pi$
$32$	−10.6088	−	0.575193i	−0.331526	−	0.0179748i
$33$	63.0683	−	4.89762i	1.91116	−	0.148413i
$34$	−2.61819	−	2.48008i	−0.0770056	−	0.0729436i
$35$	−39.2455	+	2.12783i	−1.12130	+	0.0607951i
$36$	35.5051	−	1.65822i	0.986254	−	0.0460617i
$37$	−15.8511	+	23.3786i	−0.428407	+	0.631854i	−0.979226	−	0.202771i	$-0.935005\pi$
$37$	−15.8511	+	23.3786i	−0.428407	+	0.631854i	0.550819	+	0.834625i	$0.314316\pi$
$38$	0.518144	−	4.76425i	0.0136354	−	0.125375i
$39$	9.47980	−	67.6806i	0.243072	−	1.73540i
$40$	14.3116	−	3.15023i	0.357791	−	0.0787558i
$41$	−13.9739	+	2.29091i	−0.340827	+	0.0558758i	−0.329765	−	0.944063i	$-0.606970\pi$
$41$	−13.9739	+	2.29091i	−0.340827	+	0.0558758i	−0.0110621	+	0.999939i	$0.503521\pi$
$42$	1.42950	+	2.90966i	0.0340357	+	0.0692777i
$43$	−3.08193	−	11.1001i	−0.0716728	−	0.258142i	0.919030	−	0.394188i	$-0.128974\pi$
$43$	−3.08193	−	11.1001i	−0.0716728	−	0.258142i	−0.990702	+	0.136046i	$0.956560\pi$
$44$	50.3962	+	66.2951i	1.14537	+	1.50671i
$45$	−70.0115	+	23.0067i	−1.55581	+	0.511261i
$46$	0.333629	−	0.629292i	0.00725281	−	0.0136803i
$47$	−11.3922	+	4.53905i	−0.242386	+	0.0965755i	−0.488168	−	0.872750i	$-0.662335\pi$
$47$	−11.3922	+	4.53905i	−0.242386	+	0.0965755i	0.245782	+	0.969325i	$0.420955\pi$
$48$	26.8022	+	37.6101i	0.558379	+	0.783543i
$49$	−16.8068	+	19.7864i	−0.342995	+	0.403805i
$50$	−8.36378	+	4.43419i	−0.167276	+	0.0886839i
$51$	−4.07966	+	47.8827i	−0.0799934	+	0.938876i
$52$	81.6519	−	37.7762i	1.57023	−	0.726466i
$53$	35.8230	−	30.4284i	0.675906	−	0.574120i	−0.242310	−	0.970199i	$-0.577905\pi$
$53$	35.8230	−	30.4284i	0.675906	−	0.574120i	0.918217	+	0.396079i	$0.129629\pi$
$54$	4.00808	+	4.56997i	0.0742238	+	0.0846290i
$55$	−137.453	−	104.489i	−2.49914	−	1.89980i
$56$	−4.42869	+	7.36055i	−0.0790838	+	0.131438i
$57$	−53.9359	+	34.1911i	−0.946245	+	0.599844i
$58$	−0.143906			−0.00248114
$59$	−58.4198	+	8.25420i	−0.990165	+	0.139902i
$59$	−58.4198	+	8.25420i	−0.990165	+	0.139902i
$60$	−75.3862	−	61.0636i	−1.25644	−	1.01773i
$61$	14.2552	+	4.80312i	0.233691	+	0.0787397i	0.433711	−	0.901052i	$-0.357204\pi$
$61$	14.2552	+	4.80312i	0.233691	+	0.0787397i	−0.200020	+	0.979792i	$0.564101\pi$
$62$	4.72754	−	7.85723i	0.0762506	−	0.126730i
$63$	18.4322	−	39.0694i	0.292575	−	0.620149i
$64$	−21.9068	+	54.9819i	−0.342294	+	0.859093i
$65$	−142.169	+	120.759i	−2.18721	+	1.85783i
$66$	−3.48879	+	13.8076i	−0.0528605	+	0.209206i
$67$	29.3943	+	43.3533i	0.438720	+	0.647064i	0.981197	−	0.193007i	$-0.0618239\pi$
$67$	29.3943	+	43.3533i	0.438720	+	0.647064i	−0.542477	+	0.840071i	$0.682514\pi$
$68$	−55.8936	+	29.6329i	−0.821965	+	0.435778i
$69$	−9.32779	+	1.75363i	−0.135185	+	0.0254149i
$70$	2.36721	−	8.52591i	0.0338172	−	0.121799i
$71$	−32.2100	+	12.8336i	−0.453662	+	0.180755i	−0.585766	−	0.810480i	$-0.699206\pi$
$71$	−32.2100	+	12.8336i	−0.453662	+	0.180755i	0.132104	+	0.991236i	$0.457827\pi$
$72$	−4.42526	+	15.4871i	−0.0614619	+	0.215098i
$73$	−58.7889	+	6.39367i	−0.805327	+	0.0875846i	−0.501517	−	0.865148i	$-0.667224\pi$
$73$	−58.7889	+	6.39367i	−0.805327	+	0.0875846i	−0.303810	+	0.952733i	$0.598259\pi$
$74$	−3.84832	−	5.06238i	−0.0520043	−	0.0684105i
$75$	115.691	+	50.2814i	1.54255	+	0.670419i
$76$	−76.2980	−	35.2992i	−1.00392	−	0.464463i
$77$	99.8777	−	16.3741i	1.29711	−	0.212651i
$78$	13.7581	+	6.88775i	0.176386	+	0.0883044i
$79$	40.6892	−	24.4819i	0.515053	−	0.309897i	−0.234192	−	0.972190i	$-0.575244\pi$
$79$	40.6892	−	24.4819i	0.515053	−	0.309897i	0.749245	+	0.662293i	$0.230417\pi$
$80$	13.6288	−	125.315i	0.170360	−	1.56644i
$81$	14.3011	−	79.7275i	0.176557	−	0.984290i
$82$	0.515759	−	3.14599i	0.00628975	−	0.0383658i
$83$	15.8720	−	0.860557i	0.191229	−	0.0103682i	0.0417246	−	0.999129i	$-0.486715\pi$
$83$	15.8720	−	0.860557i	0.191229	−	0.0103682i	0.149505	+	0.988761i	$0.452232\pi$
$84$	56.3767	−	7.46607i	0.671152	−	0.0888818i
$85$	95.2262	−	90.2030i	1.12031	−	1.06121i
$86$	2.58973	+	0.140411i	0.0301132	+	0.00163269i
$87$	1.19579	+	1.49911i	0.0137448	+	0.0172311i
$88$	−35.7614	+	12.0494i	−0.406379	+	0.136925i
$89$	6.15329	+	18.2623i	0.0691381	+	0.205195i	0.976652	−	0.214827i	$-0.0689189\pi$
$89$	6.15329	+	18.2623i	0.0691381	+	0.205195i	−0.907514	+	0.420022i	$0.862022\pi$
$90$	0.124360	−	16.5907i	0.00138178	−	0.184341i
$91$	5.91976	−	109.183i	0.0650523	−	1.19982i
$92$	−8.59252	−	9.07101i	−0.0933969	−	0.0985979i
$93$	−121.134	+	16.0420i	−1.30252	+	0.172495i
$94$	−0.149469	−	2.75679i	−0.00159009	−	0.0293275i
$95$	172.006	+	28.1990i	1.81059	+	0.296831i
$96$	−30.5041	+	9.24124i	−0.317751	+	0.0962630i
$97$	147.069	+	15.9947i	1.51618	+	0.164894i	0.828033	−	0.560680i	$-0.189460\pi$
$97$	147.069	+	15.9947i	1.51618	+	0.164894i	0.688144	+	0.725574i	$0.258426\pi$
$98$	−3.01324	−	5.00805i	−0.0307474	−	0.0511025i
$99$	172.827	−	78.3910i	1.74573	−	0.791829i
$100$	26.8660	+	163.875i	0.268660	+	1.63875i
$101$	−31.4151	+	67.9026i	−0.311040	+	0.672303i	−0.998548	−	0.0538747i	$-0.982843\pi$
$101$	−31.4151	+	67.9026i	−0.311040	+	0.672303i	0.687507	+	0.726177i	$0.258705\pi$
$102$	−9.92242	−	4.31245i	−0.0972786	−	0.0422790i
$103$	−114.541	+	87.0717i	−1.11205	+	0.845356i	−0.989127	−	0.147061i	$-0.953019\pi$
$103$	−114.541	+	87.0717i	−1.11205	+	0.845356i	−0.122919	+	0.992417i	$0.539226\pi$
$104$	4.40792	+	40.5301i	0.0423838	+	0.389713i
$105$	−108.487	+	46.1866i	−1.03321	+	0.439872i
$106$	3.91668	+	9.83014i	0.0369499	+	0.0927371i
$107$	−51.4407	−	14.2824i	−0.480754	−	0.133481i	0.0186926	−	0.999825i	$-0.494050\pi$
$107$	−51.4407	−	14.2824i	−0.480754	−	0.133481i	−0.499447	+	0.866345i	$0.666463\pi$
$108$	98.4206	−	41.0324i	0.911302	−	0.379929i
$109$	−12.9038	−	24.3392i	−0.118384	−	0.223296i	0.817237	−	0.576301i	$-0.195505\pi$
$109$	−12.9038	−	24.3392i	−0.118384	−	0.223296i	−0.935621	+	0.353005i	$0.885160\pi$
$110$	32.1734	−	21.8141i	0.292485	−	0.198310i
$111$	−20.7583	+	82.1549i	−0.187011	+	0.740134i
$112$	47.8363	+	56.3172i	0.427109	+	0.502832i
$113$	28.7673	+	11.4619i	0.254577	+	0.101433i	0.493936	−	0.869498i	$-0.335558\pi$
$113$	28.7673	+	11.4619i	0.254577	+	0.101433i	−0.239358	+	0.970931i	$0.576937\pi$
$114$	−3.41741	−	13.9650i	−0.0299773	−	0.122500i
$115$	22.1974	+	13.3558i	0.193021	+	0.116137i
$116$	−0.806051	+	2.39227i	−0.00694871	+	0.0206230i
$117$	−42.5720	−	200.555i	−0.363863	−	1.71415i
$118$	2.43851	−	13.0571i	0.0206653	−	0.110653i
$119$			76.8883i			0.646120i
$120$	37.1307	−	23.5379i	0.309423	−	0.196150i
$121$	277.298	+	166.845i	2.29172	+	1.37888i
$122$	−2.04947	+	2.69604i	−0.0167990	+	0.0220987i
$123$	−37.0583	+	20.7690i	−0.301287	+	0.168853i
$124$	−104.137	−	122.600i	−0.839818	−	0.988710i
$125$	−58.6158	−	126.696i	−0.468926	−	1.01357i
$126$	7.01038	+	6.74100i	0.0556379	+	0.0535000i
$127$	12.9731	+	24.4698i	0.102150	+	0.192676i	0.929319	−	0.369278i	$-0.120395\pi$
$127$	12.9731	+	24.4698i	0.102150	+	0.192676i	−0.827169	+	0.561953i	$0.810050\pi$
$128$	−42.5456	−	36.1385i	−0.332387	−	0.282332i
$129$	−20.0568	−	28.1446i	−0.155479	−	0.218175i
$130$	−15.5439	−	39.0122i	−0.119568	−	0.300094i
$131$	40.7018	+	21.5787i	0.310701	+	0.164723i	0.616461	−	0.787385i	$-0.288566\pi$
$131$	40.7018	+	21.5787i	0.310701	+	0.164723i	−0.305760	+	0.952109i	$0.598911\pi$
$132$	209.994	+	135.337i	1.59086	+	1.02528i
$133$	−81.3401	+	61.8332i	−0.611580	+	0.464911i
$134$	−11.3624	+	3.15474i	−0.0847938	+	0.0235429i
$135$	−173.863	+	136.565i	−1.28787	+	1.01160i
$136$	−4.63796	−	28.2903i	−0.0341027	−	0.208017i
$137$	−44.5880	−	202.565i	−0.325460	−	1.47858i	−0.800882	−	0.598822i	$-0.795636\pi$
$137$	−44.5880	−	202.565i	−0.325460	−	1.47858i	0.475423	−	0.879758i	$-0.342295\pi$
$138$	0.296399	−	2.11613i	0.00214782	−	0.0153343i
$139$	−6.68380	−	0.726907i	−0.0480849	−	0.00522955i	0.0840449	−	0.996462i	$-0.473216\pi$
$139$	−6.68380	−	0.726907i	−0.0480849	−	0.00522955i	−0.132130	+	0.991232i	$0.542182\pi$
$140$	−128.474	−	87.1076i	−0.917673	−	0.622197i
$141$	−27.4761	+	24.4647i	−0.194866	+	0.173508i
$142$	−0.422605	−	7.79449i	−0.00297609	−	0.0548908i
$143$	330.336	−	348.732i	2.31004	−	2.43868i
$144$	114.090	+	78.6094i	0.792289	+	0.545898i
$145$	0.283363	−	5.22633i	0.00195423	−	0.0360436i
$146$	2.86198	−	13.0021i	0.0196026	−	0.0890556i
$147$	−27.1314	+	73.0043i	−0.184567	+	0.496628i
$148$	−105.712	+	35.6184i	−0.714267	+	0.240665i
$149$	13.7893	−	62.6455i	0.0925457	−	0.420440i	−0.907454	−	0.420151i	$-0.861977\pi$
$149$	13.7893	−	62.6455i	0.0925457	−	0.420440i	1.00000		0.000288584i	$-9.18593e-5\pi$
$150$	−19.0440	+	21.0680i	−0.126960	+	0.140453i
$151$	−122.587	+	116.120i	−0.811833	+	0.769009i	−0.976080	−	0.217410i	$-0.930239\pi$
$151$	−122.587	+	116.120i	−0.811833	+	0.769009i	0.164247	+	0.986419i	$0.447480\pi$
$152$	26.1985	−	27.6574i	0.172359	−	0.181957i
$153$	37.5268	+	139.199i	0.245273	+	0.909796i
$154$	−3.68636	+	22.4858i	−0.0239374	+	0.146012i
$155$	276.047	+	187.165i	1.78095	+	1.20751i
$156$	191.563	−	190.132i	1.22797	−	1.21880i
$157$	216.406	−	130.207i	1.37838	−	0.829344i	0.382853	−	0.923809i	$-0.374942\pi$
$157$	216.406	−	130.207i	1.37838	−	0.829344i	0.995528	+	0.0944652i	$0.0301141\pi$
$158$	2.29821	+	10.4409i	0.0145456	+	0.0660814i
$159$	69.8571	−	122.485i	0.439353	−	0.770346i
$160$	78.9554	+	36.5286i	0.493471	+	0.228304i
$161$	−14.6321	+	4.06258i	−0.0908826	+	0.0252334i
$162$	15.9817	+	8.78236i	0.0986524	+	0.0542121i
$163$	−93.6563	+	10.1857i	−0.574578	+	0.0624892i	−0.390795	−	0.920478i	$-0.627800\pi$
$163$	−93.6563	+	10.1857i	−0.574578	+	0.0624892i	−0.183783	+	0.982967i	$0.558834\pi$
$164$	−49.4096	−	26.1953i	−0.301278	−	0.159728i
$165$	−494.589	−	153.893i	−2.99751	−	0.932684i
$166$	−0.957370	+	3.44813i	−0.00576729	+	0.0207719i
$167$	−60.0295	−	50.9895i	−0.359458	−	0.305327i	0.449400	−	0.893331i	$-0.351638\pi$
$167$	−60.0295	−	50.9895i	−0.359458	−	0.305327i	−0.808858	+	0.588004i	$0.799914\pi$
$168$	−4.95115	+	25.2904i	−0.0294711	+	0.150538i
$169$	−196.386	−	289.648i	−1.16205	−	1.71390i
$170$	12.3993	+	26.8006i	0.0729370	+	0.157651i
$171$	−117.079	+	151.643i	−0.684675	+	0.886799i
$172$	16.8399	−	42.2649i	0.0979061	−	0.245726i
$173$	64.5385	−	84.8990i	0.373055	−	0.490746i	−0.570807	−	0.821084i	$-0.693370\pi$
$173$	64.5385	−	84.8990i	0.373055	−	0.490746i	0.943863	+	0.330338i	$0.107163\pi$
$174$	−0.405791	+	0.147357i	−0.00233213	+	0.000846877i
$175$	191.263	+	64.4442i	1.09293	+	0.368252i
$176$			324.606i			1.84435i
$177$	−156.282	+	83.0960i	−0.882949	+	0.469469i
$178$	−4.33857			−0.0243740
$179$	−41.6980	+	123.755i	−0.232950	+	0.691370i	0.765879	+	0.642985i	$0.222304\pi$
$179$	−41.6980	+	123.755i	−0.232950	+	0.691370i	−0.998829	+	0.0483855i	$0.984592\pi$
$180$	−275.105	−	94.9956i	−1.52836	−	0.527753i
$181$	−4.44746	−	3.38087i	−0.0245716	−	0.0186788i	0.592816	−	0.805338i	$-0.298016\pi$
$181$	−4.44746	−	3.38087i	−0.0245716	−	0.0186788i	−0.617388	+	0.786659i	$0.711809\pi$
$182$	22.8686	+	9.11167i	0.125651	+	0.0500641i
$183$	45.1155	−	1.05295i	0.246533	−	0.00575385i
$184$	5.13869	−	2.37741i	0.0279276	−	0.0129207i
$185$	191.431	−	129.794i	1.03476	−	0.701587i
$186$	5.28525	−	26.9970i	0.0284153	−	0.145145i
$187$	−218.669	+	257.437i	−1.16935	+	1.37667i
$188$	−46.6656	−	12.9566i	−0.248221	−	0.0689183i
$189$	11.9696	−	129.043i	0.0633311	−	0.682769i
$190$	−18.3809	+	34.6701i	−0.0967417	+	0.182474i
$191$	−26.3720	−	242.487i	−0.138073	−	1.26956i	−0.834126	−	0.551574i	$-0.814028\pi$
$191$	−26.3720	−	242.487i	−0.138073	−	1.26956i	0.696053	−	0.717991i	$-0.254938\pi$
$192$	−5.47329	+	177.472i	−0.0285067	+	0.924334i
$193$	−53.5044	−	192.706i	−0.277225	−	0.998475i	−0.962743	−	0.270419i	$-0.912838\pi$
$193$	−53.5044	−	192.706i	−0.277225	−	0.998475i	0.685518	−	0.728056i	$-0.259576\pi$
$194$	−13.9846	+	30.2272i	−0.0720854	+	0.155810i
$195$	−277.237	+	486.098i	−1.42173	+	2.49281i
$196$	−100.131	+	22.0405i	−0.510872	+	0.112451i
$197$	173.228	+	287.907i	0.879329	+	1.46146i	0.887147	+	0.461486i	$0.152684\pi$
$197$	173.228	+	287.907i	0.879329	+	1.46146i	−0.00781861	+	0.999969i	$0.502489\pi$
$198$	4.30084	+	42.5075i	0.0217214	+	0.214685i
$199$	102.329	−	150.924i	0.514217	−	0.758413i	−0.478603	−	0.878031i	$-0.658857\pi$
$199$	102.329	−	150.924i	0.514217	−	0.758413i	0.992820	+	0.119618i	$0.0381671\pi$
$200$	−74.2609	−	12.1745i	−0.371305	−	0.0608723i
$201$	127.280	+	92.1500i	0.633233	+	0.458458i
$202$	−12.2286	−	11.5836i	−0.0605377	−	0.0573443i
$203$	2.10994	+	2.22744i	0.0103938	+	0.0109726i
$204$	−127.267	+	140.794i	−0.623859	+	0.690165i
$205$	113.239	+	24.9259i	0.552387	+	0.121590i
$206$	−10.3428	−	30.6963i	−0.0502076	−	0.149011i
$207$	−24.5072	+	14.4964i	−0.118392	+	0.0700309i
$208$	342.491	+	75.3880i	1.64659	+	0.362442i
$209$	−448.195	−	24.3004i	−2.14447	−	0.116270i
$210$	−2.05521	−	26.4656i	−0.00978671	−	0.126027i
$211$	109.503	+	103.727i	0.518972	+	0.491596i	0.901758	−	0.432241i	$-0.142277\pi$
$211$	109.503	+	103.727i	0.518972	+	0.491596i	−0.382787	+	0.923837i	$0.625036\pi$
$212$	185.353	−	10.0495i	0.874306	−	0.0474035i
$213$	−77.6855	+	69.1710i	−0.364721	+	0.324747i
$214$	6.74497	−	9.94808i	0.0315185	−	0.0464864i
$215$	−10.1988	+	93.7765i	−0.0474363	+	0.436170i
$216$	3.37991	+	48.2023i	0.0156477	+	0.223159i
$217$	−190.932	+	42.0274i	−0.879873	+	0.193675i
$218$	6.12033	−	1.00338i	0.0280749	−	0.00460265i
$219$	−159.228	+	78.2276i	−0.727068	+	0.357204i
$220$	−182.424	−	657.031i	−0.829199	−	2.98651i
$221$	220.836	+	290.505i	0.999259	+	1.31450i
$222$	−16.0354	−	10.3345i	−0.0722315	−	0.0465517i
$223$	166.253	−	313.586i	0.745528	−	1.40622i	−0.162243	−	0.986751i	$-0.551873\pi$
$223$	166.253	−	313.586i	0.745528	−	1.40622i	0.907772	−	0.419465i	$-0.137782\pi$
$224$	−47.3742	+	18.8756i	−0.211492	+	0.0842660i
$225$	377.717	+	23.3200i	1.67874	+	0.103644i
$226$	−4.51333	+	5.31350i	−0.0199705	+	0.0235110i
$227$	−127.516	+	67.6046i	−0.561744	+	0.297818i	−0.724981	−	0.688769i	$-0.758151\pi$
$227$	−127.516	+	67.6046i	−0.561744	+	0.297818i	0.163237	+	0.986587i	$0.447807\pi$
$228$	−251.293	−	21.4105i	−1.10216	−	0.0939057i
$229$	−272.468	+	126.057i	−1.18982	+	0.550468i	−0.912010	−	0.410169i	$-0.865470\pi$
$229$	−272.468	+	126.057i	−1.18982	+	0.550468i	−0.277807	+	0.960637i	$0.589608\pi$
$230$	−4.44510	+	3.77570i	−0.0193265	+	0.0164161i
$231$	264.872	−	148.445i	1.14663	−	0.642619i
$232$	−0.910695	−	0.692292i	−0.00392541	−	0.00298402i
$233$	−51.1532	+	85.0172i	−0.219542	+	0.364881i	−0.946980	−	0.321292i	$-0.895883\pi$
$233$	−51.1532	+	85.0172i	−0.219542	+	0.364881i	0.727439	+	0.686173i	$0.240711\pi$
$234$	45.8484	+	5.33434i	0.195933	+	0.0227963i
$235$	100.414			0.427295
$236$	−203.401	−	113.673i	−0.861868	−	0.481666i
$237$	89.6679	−	110.700i	0.378346	−	0.467087i
$238$	−16.4040	−	5.52714i	−0.0689243	−	0.0232233i
$239$	222.181	−	369.267i	0.929626	−	1.54505i	0.0941266	−	0.995560i	$-0.469994\pi$
$239$	222.181	−	369.267i	0.929626	−	1.54505i	0.835500	−	0.549491i	$-0.185178\pi$
$240$	−89.8886	−	367.323i	−0.374536	−	1.53051i
$241$	21.0227	−	52.7630i	0.0872312	−	0.218934i	−0.878889	−	0.477026i	$-0.841715\pi$
$241$	21.0227	−	52.7630i	0.0872312	−	0.218934i	0.966120	+	0.258093i	$0.0830939\pi$
$242$	−55.5297	+	47.1673i	−0.229462	+	0.194906i
$243$	−41.3124	−	239.462i	−0.170010	−	0.985442i
$244$	33.3389	+	49.1713i	0.136635	+	0.201522i
$245$	187.814	−	99.5726i	0.766587	−	0.406419i
$246$	−1.76707	−	9.39930i	−0.00718321	−	0.0382086i
$247$	−129.730	+	467.245i	−0.525223	+	1.89168i
$248$	67.7167	−	26.9808i	0.273051	−	0.108794i
$249$	43.8754	−	18.6793i	0.176206	−	0.0750171i
$250$	31.2440	−	3.39799i	0.124976	−	0.0135920i
$251$	198.001	+	260.466i	0.788848	+	1.03771i	0.998206	+	0.0598726i	$0.0190694\pi$
$251$	198.001	+	260.466i	0.788848	+	1.03771i	−0.209358	+	0.977839i	$0.567137\pi$
$252$	151.328	−	78.7816i	0.600508	−	0.312626i
$253$	−60.5450	−	28.0111i	−0.239308	−	0.110716i
$254$	−6.15316	+	1.00876i	−0.0242250	+	0.00397149i
$255$	176.156	−	351.867i	0.690808	−	1.37987i
$256$	−192.086	+	115.574i	−0.750334	+	0.451461i
$257$	−3.08343	+	28.3517i	−0.0119978	+	0.110318i	−0.998605	−	0.0527936i	$-0.983187\pi$
$257$	−3.08343	+	28.3517i	−0.0119978	+	0.110318i	0.986608	+	0.163111i	$0.0521530\pi$
$258$	7.44640	−	2.25589i	0.0288620	−	0.00874377i
$259$	−21.9338	+	133.790i	−0.0846864	+	0.516564i
$260$	−735.599	+	39.8830i	−2.82923	+	0.153396i
$261$	4.90699	+	3.00276i	0.0188007	+	0.0115048i
$262$	−7.52965	+	7.13246i	−0.0287391	+	0.0272231i
$263$	391.353	+	21.2185i	1.48803	+	0.0806788i	0.780124	−	0.625625i	$-0.215156\pi$
$263$	391.353	+	21.2185i	1.48803	+	0.0806788i	0.707909	+	0.706304i	$0.249639\pi$
$264$	−88.5029	+	70.5962i	−0.335238	+	0.267410i
$265$	−364.719	+	122.888i	−1.37630	+	0.463729i
$266$	−7.34483	−	21.7987i	−0.0276121	−	0.0819499i
$267$	36.0515	+	45.1959i	0.135024	+	0.169273i
$268$	−11.1992	+	206.557i	−0.0417880	+	0.770734i
$269$	−279.276	−	294.828i	−1.03820	−	1.09601i	−0.995291	−	0.0969349i	$-0.969096\pi$
$269$	−279.276	−	294.828i	−1.03820	−	1.09601i	−0.0429088	−	0.999079i	$-0.513662\pi$
$270$	−16.6378	−	46.9103i	−0.0616216	−	0.173742i
$271$	18.0811	+	333.486i	0.0667198	+	1.23057i	0.819802	+	0.572648i	$0.194084\pi$
$271$	18.0811	+	333.486i	0.0667198	+	1.23057i	−0.753082	+	0.657927i	$0.771434\pi$
$272$	−243.349	−	39.8951i	−0.894666	−	0.146673i
$273$	−95.1087	−	313.941i	−0.348384	−	1.14997i
$274$	46.4222	+	5.04872i	0.169424	+	0.0184260i
$275$	457.109	+	759.721i	1.66222	+	2.76262i
$276$	−33.5180	−	16.7802i	−0.121442	−	0.0607978i
$277$	−40.9715	−	249.915i	−0.147911	−	0.902220i	−0.951638	−	0.307221i	$-0.900601\pi$
$277$	−40.9715	−	249.915i	−0.147911	−	0.902220i	0.803727	−	0.594999i	$-0.202847\pi$
$278$	0.635552	−	1.37372i	0.00228616	−	0.00494145i
$279$	−325.152	+	169.275i	−1.16542	+	0.606720i
$280$	55.9964	−	42.5673i	0.199987	−	0.152026i
$281$	−49.9715	−	459.481i	−0.177835	−	1.63516i	−0.654489	−	0.756072i	$-0.727116\pi$
$281$	−49.9715	−	459.481i	−0.177835	−	1.63516i	0.476654	−	0.879091i	$-0.341850\pi$
$282$	−3.24437	−	7.62063i	−0.0115048	−	0.0270235i
$283$	92.5286	+	232.229i	0.326956	+	0.820598i	0.996936	+	0.0782188i	$0.0249233\pi$
$283$	92.5286	+	232.229i	0.326956	+	0.820598i	−0.669980	+	0.742379i	$0.733697\pi$
$284$	−131.942	−	36.6334i	−0.464583	−	0.128991i
$285$	513.904	−	96.6140i	1.80317	−	0.338997i
$286$	50.6550	+	95.5454i	0.177115	+	0.334075i
$287$	−56.2570	+	38.1432i	−0.196017	+	0.132903i
$288$	−76.5537	+	57.2943i	−0.265811	+	0.198939i
$289$	20.9757	+	24.6945i	0.0725802	+	0.0854480i
$290$	1.09466	+	0.436152i	0.00377468	+	0.00150397i
$291$	431.089	−	105.493i	1.48141	−	0.362519i
$292$	−200.115	−	120.405i	−0.685324	−	0.412346i
$293$	−32.5154	+	96.5023i	−0.110974	+	0.329359i	−0.988722	−	0.149764i	$-0.952149\pi$
$293$	−32.5154	+	96.5023i	−0.110974	+	0.329359i	0.877748	+	0.479123i	$0.159045\pi$
$294$	−13.6250	−	11.0364i	−0.0463435	−	0.0375387i
$295$	469.402	+	114.271i	1.59119	+	0.387361i
$296$		−	50.5499i		−	0.170777i
$297$	407.073	−	398.021i	1.37062	−	1.34014i
$298$	12.3741	+	7.44522i	0.0415237	+	0.0249840i
$299$	−43.6157	+	57.3754i	−0.145872	+	0.191891i
$300$	243.562	+	434.591i	0.811873	+	1.44864i
$301$	−35.7972	−	42.1437i	−0.118927	−	0.140012i
$302$	−15.9619	−	34.5010i	−0.0528539	−	0.114242i
$303$	−19.0546	+	223.642i	−0.0628865	+	0.738094i
$304$	−153.495	−	289.523i	−0.504918	−	0.952377i
$305$	−93.8781	−	79.7408i	−0.307797	−	0.261445i
$306$	−32.3954	−	2.00007i	−0.105867	−	0.00653618i
$307$	−129.122	−	324.071i	−0.420592	−	1.05561i	−0.974771	−	0.223209i	$-0.928347\pi$
$307$	−129.122	−	324.071i	−0.420592	−	1.05561i	0.554178	−	0.832398i	$-0.313033\pi$
$308$	353.152	+	187.230i	1.14660	+	0.607888i
$309$	−233.827	+	362.815i	−0.756721	+	1.17416i
$310$	−59.7750	+	45.4398i	−0.192823	+	0.146580i
$311$	−3.90249	+	1.08352i	−0.0125482	+	0.00348399i	−0.273797	−	0.961788i	$-0.588280\pi$
$311$	−3.90249	+	1.08352i	−0.0125482	+	0.00348399i	0.261249	+	0.965272i	$0.415866\pi$
$312$	53.9316	+	109.775i	0.172858	+	0.351842i
$313$	46.4396	+	283.269i	0.148369	+	0.905013i	0.951148	+	0.308736i	$0.0999059\pi$
$313$	46.4396	+	283.269i	0.148369	+	0.905013i	−0.802778	+	0.596277i	$0.796646\pi$
$314$	12.2230	+	55.5298i	0.0389268	+	0.176846i
$315$	−258.621	+	241.327i	−0.821019	+	0.766117i
$316$	186.440	+	20.2766i	0.590000	+	0.0641664i
$317$	−120.017	−	81.3738i	−0.378604	−	0.256700i	0.357011	−	0.934100i	$-0.383796\pi$
$317$	−120.017	−	81.3738i	−0.378604	−	0.256700i	−0.735614	+	0.677401i	$0.763106\pi$
$318$	21.1102	+	23.7088i	0.0663844	+	0.0745559i
$319$	0.729701	+	13.4585i	0.00228746	+	0.0421898i
$320$	333.279	−	351.839i	1.04150	−	1.09950i
$321$	−159.679	+	12.4000i	−0.497443	+	0.0386293i
$322$	0.185089	−	3.41377i	0.000574812	−	0.0106018i
$323$	73.3019	−	333.014i	0.226941	−	1.03100i
$324$	235.514	−	216.485i	0.726894	−	0.668164i
$325$	907.741	−	305.853i	2.79305	−	0.941087i
$326$	4.55941	−	20.7136i	0.0139859	−	0.0635387i
$327$	−61.3096	−	55.4194i	−0.187491	−	0.169478i
$328$	18.3984	−	17.4279i	0.0560927	−	0.0531339i
$329$	−40.4792	+	42.7334i	−0.123037	+	0.129889i
$330$	68.3865	−	94.4570i	0.207232	−	0.286233i
$331$	30.9230	−	188.622i	0.0934230	−	0.569855i	−0.898086	−	0.439819i	$-0.855043\pi$
$331$	30.9230	−	188.622i	0.0934230	−	0.569855i	0.991509	−	0.130036i	$-0.0415092\pi$
$332$	51.9588	+	35.2290i	0.156502	+	0.106111i
$333$	25.5899	+	252.919i	0.0768467	+	0.759517i
$334$	15.1938	−	9.14179i	0.0454903	−	0.0273706i
$335$	−92.1994	−	418.866i	−0.275222	−	1.25035i
$336$	192.558	+	109.822i	0.573089	+	0.326851i
$337$	−50.2255	−	23.2368i	−0.149037	−	0.0689520i	0.343953	−	0.938987i	$-0.388234\pi$
$337$	−50.2255	−	23.2368i	−0.149037	−	0.0689520i	−0.492990	+	0.870035i	$0.664096\pi$
$338$	75.9133	−	21.0772i	0.224595	−	0.0623586i
$339$	92.8557	+	2.86370i	0.273910	+	0.00844748i
$340$	514.980	−	56.0075i	1.51465	−	0.164728i
$341$	−758.804	−	402.292i	−2.22523	−	1.17974i
$342$	−23.9364	−	35.8796i	−0.0699894	−	0.104911i
$343$	−96.2581	+	346.690i	−0.280636	+	1.01076i
$344$	15.7134	+	13.3471i	0.0456784	+	0.0387996i
$345$	76.2691	+	14.9313i	0.221070	+	0.0432792i
$346$	13.4737	+	19.8722i	0.0389412	+	0.0574340i
$347$	170.650	+	368.855i	0.491788	+	1.06298i	0.981564	+	0.191134i	$0.0612165\pi$
$347$	170.650	+	368.855i	0.491788	+	1.06298i	−0.489776	+	0.871848i	$0.662921\pi$
$348$	0.176705	+	7.57119i	0.000507773	+	0.0217563i
$349$	70.8924	−	177.927i	0.203130	−	0.509818i	−0.791754	−	0.610840i	$-0.790832\pi$
$349$	70.8924	−	177.927i	0.203130	−	0.509818i	0.994884	+	0.101022i	$0.0322112\pi$
$350$	−27.4981	+	36.1731i	−0.0785660	+	0.103352i
$351$	−325.410	−	521.940i	−0.927095	−	1.48701i
$352$	−212.300	−	71.5321i	−0.603124	−	0.203216i
$353$			467.922i			1.32556i	0.748815	+	0.662779i	$0.230623\pi$
$353$			467.922i			1.32556i	−0.748815	+	0.662779i	$0.769377\pi$
$354$	−6.49400	−	39.3159i	−0.0183446	−	0.111062i
$355$	283.910			0.799746
$356$	−24.3013	+	72.1237i	−0.0682621	+	0.202595i
$357$	78.7319	+	216.812i	0.220538	+	0.607317i
$358$	−23.4055	−	17.7924i	−0.0653785	−	0.0496994i
$359$	−465.018	−	185.280i	−1.29531	−	0.516100i	−0.382304	−	0.924037i	$-0.624869\pi$
$359$	−465.018	−	185.280i	−1.29531	−	0.516100i	−0.913010	+	0.407936i	$0.866249\pi$
$360$	80.6002	−	104.394i	0.223889	−	0.289984i
$361$	83.6098	−	38.6820i	0.231606	−	0.107152i
$362$	1.04101	−	0.705822i	0.00287572	−	0.00194978i
$363$	952.780	+	186.527i	2.62474	+	0.513850i
$364$	279.563	−	329.127i	0.768030	−	0.904195i
$365$	466.570	+	129.543i	1.27828	+	0.354911i
$366$	−3.01850	+	9.70099i	−0.00824726	+	0.0265055i
$367$	−53.9214	+	101.707i	−0.146925	+	0.277130i	−0.946041	−	0.324047i	$-0.894956\pi$
$367$	−53.9214	+	101.707i	−0.146925	+	0.277130i	0.799116	+	0.601177i	$0.205301\pi$
$368$	−5.26579	−	48.4181i	−0.0143092	−	0.131571i
$369$	−83.2313	+	96.5119i	−0.225559	+	0.261550i
$370$	13.9301	+	50.1718i	0.0376490	+	0.135599i
$371$	94.7288	−	204.753i	0.255334	−	0.551895i
$372$	−419.190	−	239.078i	−1.12686	−	0.642681i
$373$	226.641	−	49.8875i	0.607617	−	0.133747i	0.0995041	−	0.995037i	$-0.468274\pi$
$373$	226.641	−	49.8875i	0.607617	−	0.133747i	0.508113	+	0.861291i	$0.330343\pi$
$374$	−39.2046	−	65.1586i	−0.104825	−	0.174221i
$375$	−295.021	−	297.240i	−0.786722	−	0.792641i
$376$	12.3162	−	18.1651i	0.0327559	−	0.0483114i
$377$	14.3695	+	2.35576i	0.0381155	+	0.00624871i
$378$	26.6707	+	11.8300i	0.0705575	+	0.0312964i
$379$	−335.467	−	317.771i	−0.885136	−	0.838446i	0.102577	−	0.994725i	$-0.467291\pi$
$379$	−335.467	−	317.771i	−0.885136	−	0.838446i	−0.987713	+	0.156279i	$0.950050\pi$
$380$	473.395	+	499.757i	1.24578	+	1.31515i
$381$	61.6384	+	55.7166i	0.161781	+	0.146238i
$382$	53.6299	+	11.8048i	0.140392	+	0.0309027i
$383$	41.4497	+	123.018i	0.108224	+	0.321197i	0.988058	−	0.154084i	$-0.0492428\pi$
$383$	41.4497	+	123.018i	0.108224	+	0.321197i	−0.879834	+	0.475281i	$0.842346\pi$
$384$	−156.977	−	58.3390i	−0.408793	−	0.151924i
$385$	−809.372	−	178.156i	−2.10227	−	0.462744i
$386$	44.9596	+	2.43764i	0.116476	+	0.00631512i
$387$	−85.3763	−	58.8255i	−0.220611	−	0.152004i
$388$	424.161	+	401.787i	1.09320	+	1.03553i
$389$	−452.549	+	24.5365i	−1.16337	+	0.0630758i	−0.625687	−	0.780074i	$-0.715181\pi$
$389$	−452.549	+	24.5365i	−1.16337	+	0.0630758i	−0.537678	+	0.843150i	$0.680699\pi$
$390$	−83.7789	−	94.0915i	−0.214818	−	0.241260i
$391$	28.4404	−	41.9464i	0.0727376	−	0.107280i
$392$	5.02333	−	46.1888i	0.0128146	−	0.117829i
$393$	136.868	+	19.1707i	0.348266	+	0.0487804i
$394$	−73.8769	+	16.2615i	−0.187505	+	0.0412730i
$395$	−383.712	+	62.9065i	−0.971424	+	0.159257i
$396$	730.729	+	166.598i	1.84528	+	0.420702i
$397$	25.3272	+	91.2205i	0.0637966	+	0.229774i	0.988575	−	0.150733i	$-0.0481632\pi$
$397$	25.3272	+	91.2205i	0.0637966	+	0.229774i	−0.924778	+	0.380507i	$0.875749\pi$
$398$	24.8434	+	32.6810i	0.0624207	+	0.0821130i
$399$	−166.050	+	257.650i	−0.416165	+	0.645739i
$400$	−303.205	+	571.905i	−0.758012	+	1.42976i
$401$	318.379	−	126.854i	0.793964	−	0.316344i	0.0623420	−	0.998055i	$-0.480143\pi$
$401$	318.379	−	126.854i	0.793964	−	0.316344i	0.731622	+	0.681711i	$0.238764\pi$
$402$	−28.8096	+	20.5307i	−0.0716657	+	0.0510713i
$403$	−600.685	+	707.182i	−1.49053	+	1.75479i
$404$	−261.058	+	138.404i	−0.646184	+	0.342585i
$405$	−350.424	+	563.124i	−0.865244	+	1.39043i
$406$	−0.626894	+	0.290032i	−0.00154407	+	0.000714365i
$407$	−453.935	+	385.576i	−1.11532	+	0.947362i
$408$	−42.0470	−	75.0249i	−0.103056	−	0.183885i
$409$	−523.154	−	397.691i	−1.27910	−	0.972350i	−0.999927	−	0.0121103i	$-0.996145\pi$
$409$	−523.154	−	397.691i	−1.27910	−	0.972350i	−0.279178	−	0.960239i	$-0.590062\pi$
$410$	−13.4581	+	22.3676i	−0.0328247	+	0.0545552i
$411$	−333.153	−	525.544i	−0.810592	−	1.27870i
$412$	−568.222			−1.37918
$413$	−237.857	+	153.698i	−0.575924	+	0.372151i
$414$	−1.33107	−	6.27064i	−0.00321515	−	0.0151465i
$415$	−123.343	−	41.5591i	−0.297212	−	0.100142i
$416$	−124.779	+	207.384i	−0.299949	+	0.498519i
$417$	−19.5916	+	4.79431i	−0.0469821	+	0.0114971i
$418$	37.4031	−	93.8747i	0.0894811	−	0.224581i
$419$	−321.424	+	273.020i	−0.767122	+	0.651600i	−0.942993	−	0.332814i	$-0.892002\pi$
$419$	−321.424	+	273.020i	−0.767122	+	0.651600i	0.175870	+	0.984413i	$0.443726\pi$
$420$	−451.472	−	114.074i	−1.07493	−	0.271606i
$421$	−115.024	−	169.648i	−0.273217	−	0.402965i	0.666183	−	0.745789i	$-0.267927\pi$
$421$	−115.024	−	169.648i	−0.273217	−	0.402965i	−0.939400	+	0.342823i	$0.888617\pi$
$422$	−30.0016	+	15.9058i	−0.0710938	+	0.0376916i
$423$	−52.4268	+	97.1213i	−0.123940	+	0.229601i
$424$	−22.5037	+	81.0511i	−0.0530748	+	0.191158i
$425$	−625.724	+	249.311i	−1.47229	+	0.586615i
$426$	−9.17307	−	21.5465i	−0.0215330	−	0.0505785i
$427$	71.7797	−	7.80651i	0.168102	−	0.0182822i
$428$	−127.595	−	167.849i	−0.298120	−	0.392170i
$429$	574.400	−	1321.62i	1.33893	−	3.08071i
$430$	−19.2739	−	8.91705i	−0.0448230	−	0.0207373i
$431$	280.961	−	46.0612i	0.651881	−	0.106871i	0.173238	−	0.984880i	$-0.444577\pi$
$431$	280.961	−	46.0612i	0.651881	−	0.106871i	0.478643	+	0.878009i	$0.341129\pi$
$432$	402.208	+	104.840i	0.931037	+	0.242686i
$433$	157.937	−	95.0278i	0.364752	−	0.219464i	−0.321365	−	0.946955i	$-0.604142\pi$
$433$	157.937	−	95.0278i	0.364752	−	0.219464i	0.686117	+	0.727492i	$0.259314\pi$
$434$	4.75878	−	43.7563i	0.0109649	−	0.100821i
$435$	−4.55261	−	15.0275i	−0.0104658	−	0.0345461i
$436$	17.6014	−	107.364i	0.0403701	−	0.246247i
$437$	67.2467	−	3.64601i	0.153883	−	0.00834328i
$438$	−5.24356	−	39.5944i	−0.0119716	−	0.0903982i
$439$	262.057	−	248.234i	0.596942	−	0.565453i	−0.328423	−	0.944531i	$-0.606517\pi$
$439$	262.057	−	248.234i	0.596942	−	0.565453i	0.925365	+	0.379077i	$0.123759\pi$
$440$	308.547	+	16.7290i	0.701244	+	0.0380204i
$441$	−1.75133	+	233.642i	−0.00397127	+	0.529800i
$442$	−77.8536	+	26.2319i	−0.176139	+	0.0593483i
$443$	−163.776	−	486.069i	−0.369697	−	1.09722i	−0.957554	−	0.288255i	$-0.906925\pi$
$443$	−163.776	−	486.069i	−0.369697	−	1.09722i	0.587857	−	0.808965i	$-0.299972\pi$
$444$	−261.617	+	208.684i	−0.589227	+	0.470009i
$445$	8.54300	−	157.566i	0.0191978	−	0.354082i
$446$	54.9519	+	58.0120i	0.123210	+	0.130072i
$447$	−25.2640	−	190.770i	−0.0565190	−	0.426778i
$448$	15.3800	+	283.668i	0.0343304	+	0.633187i
$449$	122.750	+	20.1239i	0.273386	+	0.0448194i	0.296915	−	0.954904i	$-0.404042\pi$
$449$	122.750	+	20.1239i	0.273386	+	0.0448194i	−0.0235294	+	0.999723i	$0.507490\pi$
$450$	−32.1276	+	78.9089i	−0.0713947	+	0.175353i
$451$	−296.838	−	32.2831i	−0.658177	−	0.0715811i
$452$	63.0506	+	104.791i	0.139493	+	0.231838i
$453$	−226.770	+	452.966i	−0.500596	+	0.999926i
$454$	−5.25680	−	32.0651i	−0.0115789	−	0.0706279i
$455$	−375.944	+	812.590i	−0.826251	+	1.78591i
$456$	45.5549	−	104.816i	0.0999011	−	0.229860i
$457$	520.040	−	395.324i	1.13794	−	0.865042i	0.145697	−	0.989329i	$-0.453458\pi$
$457$	520.040	−	395.324i	1.13794	−	0.865042i	0.992246	+	0.124287i	$0.0396645\pi$
$458$	−7.30760	−	67.1922i	−0.0159555	−	0.146708i
$459$	248.356	+	354.091i	0.541080	+	0.771440i
$460$	37.8687	+	95.0432i	0.0823232	+	0.206616i
$461$	793.293	+	220.257i	1.72081	+	0.477780i	0.980833	−	0.194853i	$-0.0624228\pi$
$461$	793.293	+	220.257i	1.72081	+	0.477780i	0.739976	+	0.672633i	$0.234837\pi$
$462$	12.6300	+	67.1810i	0.0273377	+	0.145413i
$463$	−118.008	−	222.587i	−0.254877	−	0.480749i	0.722746	−	0.691114i	$-0.242880\pi$
$463$	−118.008	−	222.587i	−0.254877	−	0.480749i	−0.977623	+	0.210365i	$0.932535\pi$
$464$	−8.14457	+	5.52216i	−0.0175530	+	0.0119012i
$465$	970.060	+	245.107i	2.08615	+	0.527112i
$466$	−14.4611	−	17.0249i	−0.0310324	−	0.0365342i
$467$	378.869	+	150.955i	0.811283	+	0.323245i	0.738629	−	0.674112i	$-0.235474\pi$
$467$	378.869	+	150.955i	0.811283	+	0.323245i	0.0726546	+	0.997357i	$0.476853\pi$
$468$	345.485	−	732.298i	0.738215	−	1.56474i
$469$	215.425	+	129.617i	0.459328	+	0.276368i
$470$	−7.21832	+	21.4232i	−0.0153581	+	0.0455813i
$471$	476.899	−	588.757i	1.01253	−	1.25002i
$472$	78.2459	−	70.8996i	0.165775	−	0.150211i
$473$		−	242.912i		−	0.513555i
$474$	17.1718	+	27.0882i	0.0362274	+	0.0571481i
$475$	−766.951	−	461.459i	−1.61463	−	0.971492i
$476$	−183.765	+	241.739i	−0.386061	+	0.507854i
$477$	71.5636	−	416.919i	0.150028	−	0.874045i
$478$	62.8110	+	73.9468i	0.131404	+	0.154700i
$479$	201.609	+	435.771i	0.420896	+	0.909751i	0.995802	+	0.0915318i	$0.0291763\pi$
$479$	201.609	+	435.771i	0.420896	+	0.909751i	−0.574907	+	0.818219i	$0.694962\pi$
$480$	260.046	+	22.1562i	0.541762	+	0.0461587i
$481$	301.396	+	568.494i	0.626603	+	1.18190i
$482$	9.74567	+	8.27805i	0.0202192	+	0.0171744i
$483$	−37.1001	+	26.4388i	−0.0768118	+	0.0547386i
$484$	473.068	+	1187.31i	0.977414	+	2.45312i
$485$	−1070.24	−	567.406i	−2.20668	−	1.16991i
$486$	54.0587	+	8.39992i	0.111232	+	0.0172838i
$487$	21.5082	−	16.3501i	0.0441646	−	0.0335731i	−0.582859	−	0.812573i	$-0.698066\pi$
$487$	21.5082	−	16.3501i	0.0441646	−	0.0335731i	0.627024	+	0.779000i	$0.284273\pi$
$488$	−25.9398	+	7.20214i	−0.0531552	+	0.0147585i
$489$	−253.665	+	124.624i	−0.518743	+	0.254855i
$490$	7.74256	+	47.2275i	0.0158011	+	0.0963827i
$491$	60.2978	+	273.935i	0.122806	+	0.557913i	0.997336	+	0.0729422i	$0.0232389\pi$
$491$	60.2978	+	273.935i	0.122806	+	0.557913i	−0.874530	+	0.484971i	$0.838830\pi$
$492$	−166.150	−	23.2721i	−0.337704	−	0.0473011i
$493$	−10.1792	−	1.10706i	−0.0206475	−	0.00224555i
$494$	−90.3603	−	61.2658i	−0.182916	−	0.124020i
$495$	−1552.24	+	72.4954i	−3.13584	+	0.146455i
$496$	−33.9463	−	626.103i	−0.0684401	−	1.26230i
$497$	−114.450	+	120.824i	−0.230282	+	0.243106i
$498$	0.831189	+	10.7035i	0.00166905	+	0.0214930i
$499$	26.9489	−	497.043i	0.0540058	−	0.996078i	−0.838460	−	0.544963i	$-0.816544\pi$
$499$	26.9489	−	497.043i	0.0540058	−	0.996078i	0.892466	−	0.451115i	$-0.148974\pi$
$500$	118.517	−	538.428i	0.237034	−	1.07686i
$501$	−221.486	−	82.3132i	−0.442087	−	0.164298i
$502$	−69.8032	+	23.5194i	−0.139050	+	0.0468515i
$503$	−6.50433	+	29.5495i	−0.0129311	+	0.0587465i	−0.982644	−	0.185500i	$-0.940610\pi$
$503$	−6.50433	+	29.5495i	−0.0129311	+	0.0587465i	0.969713	+	0.244246i	$0.0785406\pi$
$504$	11.9354	+	76.3847i	0.0236813	+	0.151557i
$505$	444.766	−	421.305i	0.880725	−	0.834267i
$506$	10.3284	−	10.9036i	0.0204119	−	0.0215486i
$507$	−850.371	−	615.665i	−1.67726	−	1.21433i
$508$	−17.6958	+	107.939i	−0.0348342	+	0.212479i
$509$	556.394	+	377.244i	1.09311	+	0.741148i	0.967989	−	0.250993i	$-0.0807571\pi$
$509$	556.394	+	377.244i	1.09311	+	0.741148i	0.125123	+	0.992141i	$0.460067\pi$
$510$	62.4072	+	62.8767i	0.122367	+	0.123288i
$511$	−243.214	+	146.337i	−0.475958	+	0.286374i
$512$	−58.8499	−	267.358i	−0.114941	−	0.522183i
$513$	−174.866	+	547.494i	−0.340870	+	1.06724i
$514$	−5.82712	−	2.69591i	−0.0113368	−	0.00524497i
$515$	1135.18	−	315.181i	2.20424	−	0.612003i
$516$	4.20734	−	136.424i	0.00815376	−	0.264387i
$517$	−257.065	+	27.9575i	−0.497225	+	0.0540764i
$518$	−26.9672	−	14.2971i	−0.0520602	−	0.0276006i
$519$	95.0533	−	305.487i	0.183147	−	0.588607i
$520$	89.3091	−	321.662i	0.171748	−	0.618581i
$521$	−692.483	−	588.201i	−1.32914	−	1.12898i	−0.981522	−	0.191349i	$-0.938714\pi$
$521$	−692.483	−	588.201i	−1.32914	−	1.12898i	−0.347620	−	0.937635i	$-0.613010\pi$
$522$	−0.993375	+	0.831043i	−0.00190302	+	0.00159204i
$523$	455.148	+	671.294i	0.870265	+	1.28354i	0.957815	+	0.287384i	$0.0927857\pi$
$523$	455.148	+	671.294i	0.870265	+	1.28354i	−0.0875505	+	0.996160i	$0.527904\pi$
$524$	76.3937	+	165.122i	0.145789	+	0.315119i
$525$	605.321	−	14.1277i	1.15299	−	0.0269098i
$526$	−32.6595	+	81.9691i	−0.0620903	+	0.155835i
$527$	394.848	−	519.414i	0.749237	−	0.985604i
$528$	332.390	+	915.336i	0.629526	+	1.73359i
$529$	−491.823	−	165.715i	−0.929723	−	0.313260i
$530$		−	86.6461i		−	0.163483i
$531$	−355.601	+	394.346i	−0.669681	+	0.742648i
$532$	−403.518			−0.758492
$533$	−103.001	+	305.695i	−0.193247	+	0.573537i
$534$	−12.2340	+	4.44260i	−0.0229102	+	0.00831947i
$535$	348.009	+	264.550i	0.650485	+	0.494486i
$536$	−87.0821	−	34.6967i	−0.162467	−	0.0647326i
$537$	9.14117	+	391.667i	0.0170227	+	0.729362i
$538$	82.9768	−	38.3892i	0.154232	−	0.0713553i
$539$	−453.089	+	307.202i	−0.840610	+	0.569948i
$540$	−873.023	+	13.8292i	−1.61671	+	0.0256096i
$541$	−613.695	+	722.498i	−1.13437	+	1.33549i	−0.199748	+	0.979847i	$0.564012\pi$
$541$	−613.695	+	722.498i	−1.13437	+	1.33549i	−0.934624	+	0.355638i	$0.884264\pi$
$542$	−72.4483	−	20.1152i	−0.133669	−	0.0371129i
$543$	−16.0030	−	4.97939i	−0.0294715	−	0.00917015i
$544$	79.7181	−	150.364i	0.146541	−	0.276405i
$545$	24.3888	+	224.252i	0.0447502	+	0.411471i
$546$	73.8157	+	2.27650i	0.135194	+	0.00416941i
$547$	107.001	+	385.383i	0.195615	+	0.704540i	0.994654	+	0.103262i	$0.0329279\pi$
$547$	107.001	+	385.383i	0.195615	+	0.704540i	−0.799040	+	0.601278i	$0.794658\pi$
$548$	343.950	−	743.436i	0.627646	−	1.35664i
$549$	126.140	−	49.1664i	0.229763	−	0.0895563i
$550$	−194.945	+	42.9106i	−0.354445	+	0.0780192i
$551$	−7.01491	−	11.6589i	−0.0127312	−	0.0211595i
$552$	12.0558	−	11.9658i	0.0218403	−	0.0216772i
$553$	127.912	−	188.656i	0.231305	−	0.341150i
$554$	56.2641	+	9.22404i	0.101560	+	0.0166499i
$555$	406.899	−	562.018i	0.733151	−	1.01264i
$556$	−19.2767	−	18.2599i	−0.0346703	−	0.0328415i
$557$	310.975	+	328.293i	0.558304	+	0.589395i	0.942645	−	0.333797i	$-0.108330\pi$
$557$	310.975	+	328.293i	0.558304	+	0.589395i	−0.384341	+	0.923191i	$0.625571\pi$
$558$	−12.7408	−	81.5391i	−0.0228330	−	0.146127i
$559$	−256.295	−	56.4149i	−0.458489	−	0.100921i
$560$	−193.192	−	573.373i	−0.344986	−	1.02388i
$561$	−353.000	+	949.842i	−0.629234	+	1.69312i
$562$	101.622	+	22.3686i	0.180821	+	0.0398018i
$563$	283.512	+	15.3716i	0.503574	+	0.0273030i	0.304176	−	0.952616i	$-0.401619\pi$
$563$	283.512	+	15.3716i	0.503574	+	0.0273030i	0.199397	+	0.979919i	$0.436102\pi$
$564$	−144.857	+	11.2490i	−0.256838	+	0.0199450i
$565$	−184.086	−	174.376i	−0.325817	−	0.308630i
$566$	−56.1971	+	3.04692i	−0.0992882	+	0.00538325i
$567$	−98.3854	−	376.138i	−0.173519	−	0.663382i
$568$	34.8227	−	51.3597i	0.0613076	−	0.0904220i
$569$	−8.51787	+	78.3206i	−0.0149699	+	0.137646i	−0.999238	−	0.0390366i	$-0.987571\pi$
$569$	−8.51787	+	78.3206i	−0.0149699	+	0.137646i	0.984268	+	0.176683i	$0.0565366\pi$
$570$	−16.3298	+	116.586i	−0.0286487	+	0.204536i
$571$	342.747	−	75.4443i	0.600257	−	0.132127i	0.0955609	−	0.995424i	$-0.469536\pi$
$571$	342.747	−	75.4443i	0.600257	−	0.132127i	0.504696	+	0.863297i	$0.331604\pi$
$572$	1872.06	−	306.909i	3.27284	−	0.536554i
$573$	−322.666	−	656.768i	−0.563117	−	1.14619i
$574$	−4.09373	−	14.7443i	−0.00713193	−	0.0256869i
$575$	−80.5064	−	105.904i	−0.140011	−	0.184182i
$576$	166.294	+	506.047i	0.288704	+	0.878553i
$577$	−272.487	+	513.965i	−0.472248	+	0.890754i	0.526918	+	0.849916i	$0.323348\pi$
$577$	−272.487	+	513.965i	−0.472248	+	0.890754i	−0.999166	+	0.0408381i	$0.986997\pi$
$578$	−6.77636	+	2.69995i	−0.0117238	+	0.00467119i
$579$	−348.200	−	488.611i	−0.601382	−	0.843887i
$580$	13.3819	−	15.7544i	0.0230723	−	0.0271628i
$581$	67.4086	−	35.7378i	0.116022	−	0.0615108i
$582$	−8.48225	+	99.5555i	−0.0145743	+	0.171058i
$583$	899.484	−	416.146i	1.54285	−	0.713800i
$584$	80.6613	−	68.5143i	0.138119	−	0.117319i
$585$	−284.010	+	1654.60i	−0.485487	+	2.82838i
$586$	−18.2512	−	13.8742i	−0.0311454	−	0.0236761i
$587$	473.499	−	786.962i	0.806642	−	1.34065i	−0.130410	−	0.991460i	$-0.541629\pi$
$587$	473.499	−	786.962i	0.806642	−	1.34065i	0.937052	−	0.349190i	$-0.113543\pi$
$588$	−259.784	+	164.682i	−0.441809	+	0.280072i
$589$	867.022			1.47202
$590$	−58.1227	+	91.9315i	−0.0985131	+	0.155816i
$591$	783.284	+	634.468i	1.32535	+	1.07355i
$592$	−412.061	−	138.840i	−0.696050	−	0.234526i
$593$	132.236	−	219.778i	0.222995	−	0.370621i	−0.725081	−	0.688663i	$-0.758198\pi$
$593$	132.236	−	219.778i	0.222995	−	0.370621i	0.948077	+	0.318042i	$0.103025\pi$
$594$	55.6544	+	115.460i	0.0936944	+	0.194378i
$595$	233.034	−	584.870i	0.391653	−	0.982975i
$596$	193.078	−	164.002i	0.323957	−	0.275171i
$597$	134.008	−	530.364i	0.224469	−	0.888382i
$598$	−9.10561	−	13.4298i	−0.0152268	−	0.0224578i
$599$	−754.242	+	399.874i	−1.25917	+	0.667569i	−0.958209	−	0.286068i	$-0.907652\pi$
$599$	−754.242	+	399.874i	−1.25917	+	0.667569i	−0.300959	+	0.953637i	$0.597307\pi$
$600$	−221.870	+	41.7116i	−0.369783	+	0.0695193i
$601$	162.019	−	583.539i	0.269582	−	0.970947i	−0.697521	−	0.716564i	$-0.745714\pi$
$601$	162.019	−	583.539i	0.269582	−	0.970947i	0.967103	−	0.254383i	$-0.0818725\pi$
$602$	11.5646	−	4.60775i	0.0192103	−	0.00765406i
$603$	453.267	+	129.516i	0.751687	+	0.214786i
$604$	−662.946	+	72.0997i	−1.09759	+	0.119370i
$605$	−1603.66	−	2109.58i	−2.65068	−	3.48691i
$606$	−46.3440	−	20.1419i	−0.0764752	−	0.0332374i
$607$	622.077	+	287.803i	1.02484	+	0.474141i	0.858980	−	0.512009i	$-0.171099\pi$
$607$	622.077	+	287.803i	1.02484	+	0.474141i	0.165858	+	0.986150i	$0.446961\pi$
$608$	223.179	−	36.5884i	0.367071	−	0.0601783i
$609$	8.23054	+	4.12048i	0.0135148	+	0.00676597i
$610$	23.7610	−	14.2965i	0.0389525	−	0.0234369i
$611$	−30.2040	+	277.722i	−0.0494338	+	0.454536i
$612$	−214.703	+	527.334i	−0.350822	+	0.861657i
$613$	35.9401	−	219.225i	0.0586299	−	0.357626i	−0.941176	−	0.337917i	$-0.890278\pi$
$613$	35.9401	−	219.225i	0.0586299	−	0.357626i	0.999806	−	0.0197092i	$-0.00627405\pi$
$614$	78.4220	−	4.25192i	0.127723	−	0.00692495i
$615$	344.840	−	45.6678i	0.560715	−	0.0742565i
$616$	−131.502	+	124.565i	−0.213477	+	0.202216i
$617$	554.868	+	30.0841i	0.899300	+	0.0487586i	0.497989	−	0.867183i	$-0.334072\pi$
$617$	554.868	+	30.0841i	0.899300	+	0.0487586i	0.401311	+	0.915942i	$0.368555\pi$
$618$	−60.5972	−	75.9676i	−0.0980537	−	0.122925i
$619$	1022.99	−	344.684i	1.65264	−	0.556841i	0.670003	−	0.742358i	$-0.266293\pi$
$619$	1022.99	−	344.684i	1.65264	−	0.556841i	0.982641	+	0.185517i	$0.0593961\pi$
$620$	420.571	+	1248.21i	0.678340	+	2.01324i
$621$	−54.2622	+	65.9722i	−0.0873787	+	0.106235i
$622$	0.0493648	−	0.910479i	7.93646e−5	−	0.00146379i
$623$	63.6118	+	67.1542i	0.102106	+	0.107792i
$624$	1042.96	−	138.122i	1.67142	−	0.221349i
$625$	4.97334	+	91.7279i	0.00795735	+	0.146765i
$626$	−63.7733	−	10.4551i	−0.101874	−	0.0167014i
$627$	−1288.72	+	390.418i	−2.05537	+	0.622677i
$628$	991.583	+	107.841i	1.57895	+	0.171721i
$629$	−233.267	−	387.692i	−0.370853	−	0.616363i
$630$	−32.8956	−	72.5242i	−0.0522152	−	0.115118i
$631$	−152.522	−	930.341i	−0.241714	−	1.47439i	−0.776882	−	0.629646i	$-0.783200\pi$
$631$	−152.522	−	930.341i	−0.241714	−	1.47439i	0.535168	−	0.844746i	$-0.320248\pi$
$632$	−35.6841	+	77.1299i	−0.0564622	+	0.122041i
$633$	414.994	+	180.364i	0.655599	+	0.284935i
$634$	25.9885	−	19.7559i	0.0409912	−	0.0311607i
$635$	−24.5197	−	225.455i	−0.0386136	−	0.355046i
$636$	512.374	−	218.135i	0.805620	−	0.342980i
$637$	218.900	+	549.398i	0.343643	+	0.862478i
$638$	−2.92381	−	0.811792i	−0.00458277	−	0.00127240i
$639$	−148.231	+	274.599i	−0.231973	+	0.429733i
$640$	214.105	+	403.844i	0.334539	+	0.631007i
$641$	202.709	−	137.440i	0.316239	−	0.214416i	−0.392732	−	0.919653i	$-0.628470\pi$
$641$	202.709	−	137.440i	0.316239	−	0.214416i	0.708971	+	0.705237i	$0.249160\pi$
$642$	8.83308	−	34.9587i	0.0137587	−	0.0544527i
$643$	135.968	+	160.074i	0.211459	+	0.248949i	0.857658	−	0.514220i	$-0.171918\pi$
$643$	135.968	+	160.074i	0.211459	+	0.248949i	−0.646200	+	0.763169i	$0.723643\pi$
$644$	−55.7133	−	22.1982i	−0.0865113	−	0.0344693i
$645$	67.2661	+	274.878i	0.104288	+	0.426167i
$646$	65.7786	+	39.5777i	0.101824	+	0.0612657i
$647$	38.6526	−	114.717i	0.0597413	−	0.177306i	−0.913627	−	0.406554i	$-0.866730\pi$
$647$	38.6526	−	114.717i	0.0597413	−	0.177306i	0.973368	+	0.229248i	$0.0736268\pi$
$648$	58.8889	+	132.462i	0.0908779	+	0.204416i
$649$	−1233.51	−	161.848i	−1.90062	−	0.249381i
$650$			215.651i			0.331771i
$651$	−495.363	+	314.021i	−0.760926	+	0.482367i
$652$	−318.802	−	191.817i	−0.488959	−	0.294197i
$653$	−5.43581	+	7.15068i	−0.00832436	+	0.0109505i	−0.800236	−	0.599685i	$-0.795293\pi$
$653$	−5.43581	+	7.15068i	−0.00832436	+	0.0109505i	0.791912	+	0.610635i	$0.209086\pi$
$654$	16.2309	−	9.09644i	0.0248179	−	0.0139089i
$655$	−244.208	−	287.503i	−0.372836	−	0.438936i
$656$	−91.5320	−	197.843i	−0.139531	−	0.301590i
$657$	−368.893	+	383.635i	−0.561481	+	0.583919i
$658$	−6.20723	−	11.7081i	−0.00943348	−	0.0177934i
$659$	436.633	+	370.879i	0.662568	+	0.562791i	0.914316	−	0.405002i	$-0.132729\pi$
$659$	436.633	+	370.879i	0.662568	+	0.562791i	−0.251747	+	0.967793i	$0.581005\pi$
$660$	−1187.19	−	1665.92i	−1.79877	−	2.52412i
$661$	279.204	+	700.748i	0.422396	+	1.06013i	0.974105	+	0.226097i	$0.0725967\pi$
$661$	279.204	+	700.748i	0.422396	+	1.06013i	−0.551709	+	0.834037i	$0.686024\pi$
$662$	38.0192	+	20.1565i	0.0574309	+	0.0304479i
$663$	920.193	+	593.045i	1.38792	+	0.894487i
$664$	−22.6466	+	17.2155i	−0.0341064	+	0.0259270i
$665$	806.139	−	223.823i	1.21224	−	0.336576i
$666$	−55.7994	−	12.7216i	−0.0837829	−	0.0191015i
$667$	−0.327167	−	1.99563i	−0.000490506	−	0.00299195i
$668$	−66.8680	−	303.784i	−0.100102	−	0.454767i
$669$	147.700	−	1054.50i	0.220778	−	1.57623i
$670$	95.9921	+	10.4398i	0.143272	+	0.0155817i
$671$	262.534	+	178.002i	0.391257	+	0.265279i
$672$	−114.259	+	101.736i	−0.170028	+	0.151393i
$673$	49.0927	+	905.461i	0.0729460	+	1.34541i	0.774401	+	0.632696i	$0.218052\pi$
$673$	49.0927	+	905.461i	0.0729460	+	1.34541i	−0.701455	+	0.712714i	$0.747466\pi$
$674$	8.56802	−	9.04514i	0.0127122	−	0.0134201i
$675$	1088.98	−	321.015i	1.61330	−	0.475578i
$676$	74.8230	−	1380.03i	0.110685	−	2.04146i
$677$	172.335	−	782.927i	0.254557	−	1.15647i	−0.659763	−	0.751474i	$-0.729343\pi$
$677$	172.335	−	782.927i	0.254557	−	1.15647i	0.914320	−	0.404992i	$-0.132726\pi$
$678$	−7.28593	+	19.6047i	−0.0107462	+	0.0289155i
$679$	672.910	−	226.730i	0.991030	−	0.333917i
$680$	−50.4627	+	229.254i	−0.0742098	+	0.337139i
$681$	−290.348	+	321.207i	−0.426356	+	0.471670i
$682$	140.375	−	132.971i	0.205829	−	0.194971i
$683$	−298.019	+	314.615i	−0.436338	+	0.460636i	−0.906662	−	0.421857i	$-0.861378\pi$
$683$	−298.019	+	314.615i	−0.436338	+	0.460636i	0.470324	+	0.882494i	$0.344137\pi$
$684$	−730.530	+	196.945i	−1.06803	+	0.287931i
$685$	−274.767	+	1676.00i	−0.401119	+	2.44672i
$686$	−67.0462	−	45.4585i	−0.0977350	−	0.0662660i
$687$	−639.235	+	634.462i	−0.930473	+	0.923525i
$688$	151.958	−	91.4299i	0.220869	−	0.132892i
$689$	−230.174	−	1045.69i	−0.334069	−	1.51769i
$690$	−8.66821	+	15.1985i	−0.0125626	+	0.0220269i
$691$	294.806	+	136.392i	0.426637	+	0.197383i	0.621444	−	0.783458i	$-0.286546\pi$
$691$	294.806	+	136.392i	0.426637	+	0.197383i	−0.194808	+	0.980841i	$0.562408\pi$
$692$	405.821	−	112.676i	0.586447	−	0.162826i
$693$	594.891	−	689.813i	0.858429	−	0.995402i
$694$	−90.9618	+	9.89269i	−0.131069	+	0.0142546i
$695$	48.6389	+	25.7867i	0.0699840	+	0.0371032i
$696$	−3.27690	−	1.01962i	−0.00470819	−	0.00146497i
$697$	60.6841	−	218.564i	0.0870647	−	0.313579i
$698$	32.8642	+	27.9151i	0.0470834	+	0.0399930i
$699$	−57.1877	+	292.114i	−0.0818137	+	0.417903i
$700$	447.314	+	659.738i	0.639019	+	0.942483i
$701$	342.393	+	740.070i	0.488435	+	1.05574i	0.982492	+	0.186306i	$0.0596515\pi$
$701$	342.393	+	740.070i	0.488435	+	1.05574i	−0.494057	+	0.869430i	$0.664486\pi$
$702$	134.747	−	31.9058i	0.191948	−	0.0454499i
$703$	222.548	−	558.553i	0.316569	−	0.794528i
$704$	−755.251	+	993.516i	−1.07280	+	1.41124i
$705$	283.152	−	102.822i	0.401634	−	0.145847i
$706$	−99.8303	−	33.6367i	−0.141403	−	0.0476441i
$707$			359.117i			0.507945i
$708$	−689.955	−	112.262i	−0.974513	−	0.158562i
$709$	−31.5779			−0.0445386			−0.0222693	−	0.999752i	$-0.507089\pi$
$709$	−31.5779			−0.0445386			−0.0222693	+	0.999752i	$0.507089\pi$
$710$	−20.4090	+	60.5716i	−0.0287450	+	0.0853122i
$711$	139.495	−	403.973i	0.196195	−	0.568176i
$712$	−27.4562	−	20.8716i	−0.0385620	−	0.0293141i
$713$	119.709	+	47.6964i	0.167895	+	0.0668953i
$714$	−51.9162	+	1.21168i	−0.0727118	+	0.00169703i
$715$	−3569.73	+	1651.53i	−4.99262	+	2.30983i
$716$	−426.877	+	289.430i	−0.596198	+	0.404232i
$717$	248.391	−	1268.78i	0.346432	−	1.76957i
$718$	72.9572	−	85.8918i	0.101612	−	0.119626i
$719$	−608.473	−	168.942i	−0.846277	−	0.234968i	−0.182787	−	0.983153i	$-0.558512\pi$
$719$	−608.473	−	168.942i	−0.846277	−	0.234968i	−0.663490	+	0.748185i	$0.730926\pi$
$720$	−629.601	−	943.746i	−0.874446	−	1.31076i
$721$	−323.484	+	610.156i	−0.448661	+	0.846264i
$722$	2.24241	+	20.6187i	0.00310584	+	0.0285577i
$723$	5.25240	−	170.310i	0.00726474	−	0.235560i
$724$	−5.90255	−	21.2590i	−0.00815269	−	0.0293633i
$725$	−11.2856	+	24.3934i	−0.0155663	+	0.0336461i
$726$	−108.286	+	189.865i	−0.149155	+	0.261522i
$727$	177.460	−	39.0619i	0.244099	−	0.0537302i	−0.0912357	−	0.995829i	$-0.529082\pi$
$727$	177.460	−	39.0619i	0.244099	−	0.0537302i	0.335335	+	0.942099i	$0.391151\pi$
$728$	100.888	+	167.676i	0.138582	+	0.230325i
$729$	−361.698	−	632.942i	−0.496157	−	0.868233i
$730$	−61.1773	+	90.2297i	−0.0838045	+	0.123602i
$731$	182.105	+	29.8546i	0.249117	+	0.0408407i
$732$	144.361	+	104.516i	0.197214	+	0.142782i
$733$	−917.565	−	869.164i	−1.25179	−	1.18576i	−0.974354	−	0.225020i	$-0.927755\pi$
$733$	−917.565	−	869.164i	−1.25179	−	1.18576i	−0.277440	−	0.960743i	$-0.589486\pi$
$734$	−17.8228	−	18.8153i	−0.0242817	−	0.0256339i
$735$	427.644	−	473.095i	0.581828	−	0.643667i
$736$	32.8269	+	7.22575i	0.0446018	+	0.00981760i
$737$	352.656	+	1046.65i	0.478502	+	1.42014i
$738$	−14.6075	−	24.6950i	−0.0197934	−	0.0334621i
$739$	317.371	+	69.8587i	0.429460	+	0.0945314i	0.424440	−	0.905456i	$-0.360471\pi$
$739$	317.371	+	69.8587i	0.429460	+	0.0945314i	0.00502028	+	0.999987i	$0.498402\pi$
$740$	912.074	+	49.4512i	1.23253	+	0.0668259i
$741$	112.632	+	1450.40i	0.151999	+	1.95735i
$742$	36.8741	+	34.9290i	0.0496955	+	0.0470741i
$743$	−578.111	+	31.3443i	−0.778076	+	0.0421861i	−0.438899	−	0.898536i	$-0.644631\pi$
$743$	−578.111	+	31.3443i	−0.778076	+	0.0421861i	−0.339177	+	0.940722i	$0.610149\pi$
$744$	163.322	−	145.422i	0.219519	−	0.195459i
$745$	−294.758	+	434.736i	−0.395649	+	0.583538i
$746$	−5.64878	+	51.9397i	−0.00757209	+	0.0696242i
$747$	104.594	−	97.5998i	0.140019	−	0.130656i
$748$	−1302.78	+	286.764i	−1.74168	+	0.383374i
$749$	−252.875	+	41.4567i	−0.337617	+	0.0553495i
$750$	84.6234	−	41.5749i	0.112831	−	0.0554332i
$751$	−77.6407	−	279.637i	−0.103383	−	0.372352i	0.893701	−	0.448663i	$-0.148100\pi$
$751$	−77.6407	−	279.637i	−0.103383	−	0.372352i	−0.997084	+	0.0763108i	$0.975686\pi$
$752$	−114.246	−	150.289i	−0.151923	−	0.199852i
$753$	825.041	+	531.722i	1.09567	+	0.706138i
$754$	−1.53556	+	2.89637i	−0.00203655	+	0.00384134i
$755$	1284.43	−	511.762i	1.70123	−	0.677830i
$756$	346.049	−	377.108i	0.457737	−	0.498820i
$757$	583.174	−	686.565i	0.770375	−	0.906955i	−0.227388	−	0.973804i	$-0.573019\pi$
$757$	583.174	−	686.565i	0.770375	−	0.906955i	0.997763	+	0.0668488i	$0.0212945\pi$
$758$	91.9110	−	48.7281i	0.121255	−	0.0642851i
$759$	−199.410	−	16.9899i	−0.262727	−	0.0223846i
$760$	−283.110	+	130.981i	−0.372513	+	0.172343i
$761$	−95.3373	+	80.9802i	−0.125279	+	0.106413i	−0.707836	−	0.706377i	$-0.750328\pi$
$761$	−95.3373	+	80.9802i	−0.125279	+	0.106413i	0.582557	+	0.812790i	$0.302052\pi$
$762$	−16.3179	+	9.14524i	−0.0214146	+	0.0120016i
$763$	−105.267	−	80.0216i	−0.137964	−	0.104878i
$764$	496.635	−	825.414i	0.650046	−	1.08038i
$765$	136.427	−	1172.59i	0.178336	−	1.53279i
$766$	−29.2254			−0.0381533
$767$	−457.240	+	1263.88i	−0.596141	+	1.64782i
$768$	−423.304	+	522.591i	−0.551177	+	0.680457i
$769$	31.8997	+	10.7483i	0.0414821	+	0.0139769i	0.339966	−	0.940438i	$-0.389584\pi$
$769$	31.8997	+	10.7483i	0.0414821	+	0.0139769i	−0.298484	+	0.954415i	$0.596481\pi$
$770$	96.1914	−	159.871i	0.124924	−	0.207625i
$771$	20.3367	+	83.1044i	0.0263771	+	0.107788i
$772$	292.352	−	733.748i	0.378694	−	0.950450i
$773$	151.053	−	128.306i	0.195412	−	0.165984i	−0.544339	−	0.838866i	$-0.683219\pi$

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.h (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0718854 + 0.213348i) q^{2} +(2.81983 - 1.02398i) q^{3} +(3.14402 + 2.39002i) q^{4} +(-7.60675 - 3.03081i) q^{5} +(0.0157589 + 0.675216i) q^{6} +(4.35627 - 2.01543i) q^{7} +(-1.48128 + 1.00433i) q^{8} +(6.90294 - 5.77490i) q^{9} +O(q^{10})\)	\(q+(-0.0718854 + 0.213348i) q^{2} +(2.81983 - 1.02398i) q^{3} +(3.14402 + 2.39002i) q^{4} +(-7.60675 - 3.03081i) q^{5} +(0.0157589 + 0.675216i) q^{6} +(4.35627 - 2.01543i) q^{7} +(-1.48128 + 1.00433i) q^{8} +(6.90294 - 5.77490i) q^{9} +(1.19343 - 1.40502i) q^{10} +(20.3175 + 5.64112i) q^{11} +(11.3130 + 3.52006i) q^{12} +(10.6705 - 20.1268i) q^{13} +(0.116835 + 1.07428i) q^{14} +(-24.5533 - 0.757230i) q^{15} +(4.11842 + 14.8332i) q^{16} +(-6.72609 + 14.5382i) q^{17} +(0.735844 + 1.88786i) q^{18} +(-20.7890 + 4.57601i) q^{19} +(-16.6721 - 27.7092i) q^{20} +(10.2202 - 10.1439i) q^{21} +(-2.66405 + 3.92918i) q^{22} +(-3.12206 - 0.511835i) q^{23} +(-3.14855 + 4.34884i) q^{24} +(30.5270 + 28.9167i) q^{25} +(3.52696 + 3.72336i) q^{26} +(13.5518 - 23.3527i) q^{27} +(18.5131 + 4.07505i) q^{28} +(0.204099 + 0.605744i) q^{29} +(1.92657 - 5.18396i) q^{30} +(-39.7784 - 8.75589i) q^{31} +(-10.6088 - 0.575193i) q^{32} +(63.0683 - 4.89762i) q^{33} +(-2.61819 - 2.48008i) q^{34} +(-39.2455 + 2.12783i) q^{35} +(35.5051 - 1.65822i) q^{36} +(-15.8511 + 23.3786i) q^{37} +(0.518144 - 4.76425i) q^{38} +(9.47980 - 67.6806i) q^{39} +(14.3116 - 3.15023i) q^{40} +(-13.9739 + 2.29091i) q^{41} +(1.42950 + 2.90966i) q^{42} +(-3.08193 - 11.1001i) q^{43} +(50.3962 + 66.2951i) q^{44} +(-70.0115 + 23.0067i) q^{45} +(0.333629 - 0.629292i) q^{46} +(-11.3922 + 4.53905i) q^{47} +(26.8022 + 37.6101i) q^{48} +(-16.8068 + 19.7864i) q^{49} +(-8.36378 + 4.43419i) q^{50} +(-4.07966 + 47.8827i) q^{51} +(81.6519 - 37.7762i) q^{52} +(35.8230 - 30.4284i) q^{53} +(4.00808 + 4.56997i) q^{54} +(-137.453 - 104.489i) q^{55} +(-4.42869 + 7.36055i) q^{56} +(-53.9359 + 34.1911i) q^{57} -0.143906 q^{58} +(-58.4198 + 8.25420i) q^{59} +(-75.3862 - 61.0636i) q^{60} +(14.2552 + 4.80312i) q^{61} +(4.72754 - 7.85723i) q^{62} +(18.4322 - 39.0694i) q^{63} +(-21.9068 + 54.9819i) q^{64} +(-142.169 + 120.759i) q^{65} +(-3.48879 + 13.8076i) q^{66} +(29.3943 + 43.3533i) q^{67} +(-55.8936 + 29.6329i) q^{68} +(-9.32779 + 1.75363i) q^{69} +(2.36721 - 8.52591i) q^{70} +(-32.2100 + 12.8336i) q^{71} +(-4.42526 + 15.4871i) q^{72} +(-58.7889 + 6.39367i) q^{73} +(-3.84832 - 5.06238i) q^{74} +(115.691 + 50.2814i) q^{75} +(-76.2980 - 35.2992i) q^{76} +(99.8777 - 16.3741i) q^{77} +(13.7581 + 6.88775i) q^{78} +(40.6892 - 24.4819i) q^{79} +(13.6288 - 125.315i) q^{80} +(14.3011 - 79.7275i) q^{81} +(0.515759 - 3.14599i) q^{82} +(15.8720 - 0.860557i) q^{83} +(56.3767 - 7.46607i) q^{84} +(95.2262 - 90.2030i) q^{85} +(2.58973 + 0.140411i) q^{86} +(1.19579 + 1.49911i) q^{87} +(-35.7614 + 12.0494i) q^{88} +(6.15329 + 18.2623i) q^{89} +(0.124360 - 16.5907i) q^{90} +(5.91976 - 109.183i) q^{91} +(-8.59252 - 9.07101i) q^{92} +(-121.134 + 16.0420i) q^{93} +(-0.149469 - 2.75679i) q^{94} +(172.006 + 28.1990i) q^{95} +(-30.5041 + 9.24124i) q^{96} +(147.069 + 15.9947i) q^{97} +(-3.01324 - 5.00805i) q^{98} +(172.827 - 78.3910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} + O(q^{10}) \)	\( 1064q - 29q^{3} + 18q^{4} - 21q^{6} - 46q^{7} - 49q^{9} - 94q^{10} - 29q^{12} - 54q^{13} - 12q^{15} - 158q^{16} - 27q^{18} - 30q^{19} - 18q^{21} - 142q^{22} - 23q^{24} + 108q^{25} - 32q^{27} - 70q^{28} - 131q^{30} - 18q^{31} + 17q^{33} + 90q^{34} + 67q^{36} - 170q^{37} - 91q^{39} - 2q^{40} - 43q^{42} - 222q^{43} - 461q^{45} - 54q^{46} - 1645q^{48} - 300q^{49} - 893q^{51} - 66q^{52} - 859q^{54} + 170q^{55} - 27q^{57} - 36q^{58} + 510q^{60} - 70q^{61} + 610q^{63} - 106q^{64} + 1619q^{66} - 182q^{67} + 1487q^{69} - 206q^{70} + 2241q^{72} + 134q^{73} + 542q^{75} + 246q^{76} - 273q^{78} - 122q^{79} + 127q^{81} + 122q^{82} - 329q^{84} - 6q^{85} + 54q^{87} + 38q^{88} + 347q^{90} + 274q^{91} - 483q^{93} - 826q^{94} + 693q^{96} - 474q^{97} - 523q^{99} + O(q^{100}) \)

Introduction

L-functions

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