LMFDB - Embedded newform 177.4.d.c.176.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.d (of order $2$, degree $1$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.6
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.72011 q^{2} +(-4.94573 + 1.59367i) q^{3} +14.2794 q^{4} -15.2708i q^{5} +(23.3444 - 7.52230i) q^{6} +9.03916 q^{7} -29.6395 q^{8} +(21.9204 - 15.7637i) q^{9} +O(q^{10})$	\(q-4.72011 q^{2} +(-4.94573 + 1.59367i) q^{3} +14.2794 q^{4} -15.2708i q^{5} +(23.3444 - 7.52230i) q^{6} +9.03916 q^{7} -29.6395 q^{8} +(21.9204 - 15.7637i) q^{9} +72.0799i q^{10} -12.9980 q^{11} +(-70.6221 + 22.7567i) q^{12} +55.4535i q^{13} -42.6658 q^{14} +(24.3366 + 75.5253i) q^{15} +25.6664 q^{16} -10.8602i q^{17} +(-103.467 + 74.4065i) q^{18} +126.731 q^{19} -218.058i q^{20} +(-44.7052 + 14.4054i) q^{21} +61.3519 q^{22} +21.4430 q^{23} +(146.589 - 47.2356i) q^{24} -108.198 q^{25} -261.746i q^{26} +(-83.2902 + 112.897i) q^{27} +129.074 q^{28} -6.52115i q^{29} +(-114.872 - 356.487i) q^{30} -223.822i q^{31} +115.968 q^{32} +(64.2845 - 20.7145i) q^{33} +51.2615i q^{34} -138.035i q^{35} +(313.011 - 225.097i) q^{36} -166.344i q^{37} -598.183 q^{38} +(-88.3746 - 274.258i) q^{39} +452.619i q^{40} -152.194i q^{41} +(211.013 - 67.9952i) q^{42} -122.150i q^{43} -185.604 q^{44} +(-240.725 - 334.743i) q^{45} -101.213 q^{46} +126.500 q^{47} +(-126.939 + 40.9038i) q^{48} -261.294 q^{49} +510.705 q^{50} +(17.3076 + 53.7117i) q^{51} +791.843i q^{52} +578.820i q^{53} +(393.139 - 532.886i) q^{54} +198.490i q^{55} -267.916 q^{56} +(-626.776 + 201.967i) q^{57} +30.7805i q^{58} +(183.057 - 414.571i) q^{59} +(347.513 + 1078.46i) q^{60} -272.491i q^{61} +1056.46i q^{62} +(198.142 - 142.491i) q^{63} -752.713 q^{64} +846.820 q^{65} +(-303.430 + 97.7748i) q^{66} -957.249i q^{67} -155.078i q^{68} +(-106.051 + 34.1731i) q^{69} +651.541i q^{70} -639.771i q^{71} +(-649.711 + 467.229i) q^{72} +869.650i q^{73} +785.164i q^{74} +(535.116 - 172.431i) q^{75} +1809.64 q^{76} -117.491 q^{77} +(417.138 + 1294.53i) q^{78} +668.109 q^{79} -391.947i q^{80} +(232.010 - 691.095i) q^{81} +718.373i q^{82} -1151.69 q^{83} +(-638.364 + 205.701i) q^{84} -165.845 q^{85} +576.561i q^{86} +(10.3926 + 32.2518i) q^{87} +385.254 q^{88} -505.096 q^{89} +(1136.25 + 1580.02i) q^{90} +501.253i q^{91} +306.194 q^{92} +(356.698 + 1106.96i) q^{93} -597.093 q^{94} -1935.28i q^{95} +(-573.546 + 184.815i) q^{96} -1503.21i q^{97} +1233.33 q^{98} +(-284.921 + 204.897i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.72011			−1.66881			−0.834405	−	0.551152i	$-0.814189\pi$
$2$	−4.72011			−1.66881			−0.834405	+	0.551152i	$0.814189\pi$
$3$	−4.94573	+	1.59367i	−0.951806	+	0.306702i
$3$	−4.94573	+	1.59367i	−0.951806	+	0.306702i
$4$	14.2794			1.78493
$5$		−	15.2708i		−	1.36586i	−0.730483	−	0.682931i	$-0.760705\pi$
$5$		−	15.2708i		−	1.36586i	0.730483	−	0.682931i	$-0.239295\pi$
$6$	23.3444	−	7.52230i	1.58838	−	0.511828i
$7$	9.03916			0.488069			0.244034	−	0.969767i	$-0.421529\pi$
$7$	9.03916			0.488069			0.244034	+	0.969767i	$0.421529\pi$
$8$	−29.6395			−1.30989
$9$	21.9204	−	15.7637i	0.811868	−	0.583842i
$10$			72.0799i			2.27937i
$11$	−12.9980			−0.356276			−0.178138	−	0.984005i	$-0.557007\pi$
$11$	−12.9980			−0.356276			−0.178138	+	0.984005i	$0.557007\pi$
$12$	−70.6221	+	22.7567i	−1.69890	+	0.547441i
$13$			55.4535i			1.18308i	0.806276	+	0.591540i	$0.201480\pi$
$13$			55.4535i			1.18308i	−0.806276	+	0.591540i	$0.798520\pi$
$14$	−42.6658			−0.814494
$15$	24.3366	+	75.5253i	0.418913	+	1.30004i
$16$	25.6664			0.401037
$17$		−	10.8602i		−	0.154941i	−0.996995	−	0.0774704i	$-0.975316\pi$
$17$		−	10.8602i		−	0.154941i	0.996995	−	0.0774704i	$-0.0246843\pi$
$18$	−103.467	+	74.4065i	−1.35485	+	0.974321i
$19$	126.731			1.53021			0.765106	−	0.643904i	$-0.222686\pi$
$19$	126.731			1.53021			0.765106	+	0.643904i	$0.222686\pi$
$20$		−	218.058i		−	2.43797i
$21$	−44.7052	+	14.4054i	−0.464546	+	0.149692i
$22$	61.3519			0.594558
$23$	21.4430			0.194399			0.0971996	−	0.995265i	$-0.469011\pi$
$23$	21.4430			0.194399			0.0971996	+	0.995265i	$0.469011\pi$
$24$	146.589	−	47.2356i	1.24676	−	0.401747i
$25$	−108.198			−0.865581
$26$		−	261.746i		−	1.97433i
$27$	−83.2902	+	112.897i	−0.593675	+	0.804705i
$28$	129.074			0.871167
$29$		−	6.52115i		−	0.0417568i	−0.999782	−	0.0208784i	$-0.993354\pi$
$29$		−	6.52115i		−	0.0417568i	0.999782	−	0.0208784i	$-0.00664628\pi$
$30$	−114.872	−	356.487i	−0.699086	−	2.16951i
$31$		−	223.822i		−	1.29676i	−0.761317	−	0.648380i	$-0.775447\pi$
$31$		−	223.822i		−	1.29676i	0.761317	−	0.648380i	$-0.224553\pi$
$32$	115.968			0.640639
$33$	64.2845	−	20.7145i	0.339106	−	0.109271i
$34$			51.2615i			0.258567i
$35$		−	138.035i		−	0.666635i
$36$	313.011	−	225.097i	1.44912	−	1.04211i
$37$		−	166.344i		−	0.739104i	−0.929210	−	0.369552i	$-0.879511\pi$
$37$		−	166.344i		−	0.739104i	0.929210	−	0.369552i	$-0.120489\pi$
$38$	−598.183			−2.55363
$39$	−88.3746	−	274.258i	−0.362853	−	1.12606i
$40$			452.619i			1.78914i
$41$		−	152.194i		−	0.579725i	−0.957068	−	0.289863i	$-0.906390\pi$
$41$		−	152.194i		−	0.579725i	0.957068	−	0.289863i	$-0.0936096\pi$
$42$	211.013	−	67.9952i	0.775240	−	0.249807i
$43$		−	122.150i		−	0.433202i	−0.976260	−	0.216601i	$-0.930503\pi$
$43$		−	122.150i		−	0.433202i	0.976260	−	0.216601i	$-0.0694971\pi$
$44$	−185.604			−0.635928
$45$	−240.725	−	334.743i	−0.797447	−	1.10890i
$46$	−101.213			−0.324415
$47$	126.500			0.392594			0.196297	−	0.980545i	$-0.437108\pi$
$47$	126.500			0.392594			0.196297	+	0.980545i	$0.437108\pi$
$48$	−126.939	+	40.9038i	−0.381710	+	0.122999i
$49$	−261.294			−0.761789
$50$	510.705			1.44449
$51$	17.3076	+	53.7117i	0.0475207	+	0.147473i
$52$			791.843i			2.11171i
$53$			578.820i			1.50013i	0.661363	+	0.750066i	$0.269978\pi$
$53$			578.820i			1.50013i	−0.661363	+	0.750066i	$0.730022\pi$
$54$	393.139	−	532.886i	0.990730	−	1.34290i
$55$			198.490i			0.486625i
$56$	−267.916			−0.639318
$57$	−626.776	+	201.967i	−1.45647	+	0.469320i
$58$			30.7805i			0.0696842i
$59$	183.057	−	414.571i	0.403932	−	0.914789i
$59$	183.057	−	414.571i	0.403932	−	0.914789i
$60$	347.513	+	1078.46i	0.747729	+	2.32047i
$61$		−	272.491i		−	0.571949i	−0.958237	−	0.285975i	$-0.907683\pi$
$61$		−	272.491i		−	0.571949i	0.958237	−	0.285975i	$-0.0923173\pi$
$62$			1056.46i			2.16404i
$63$	198.142	−	142.491i	0.396247	−	0.284955i
$64$	−752.713			−1.47014
$65$	846.820			1.61592
$66$	−303.430	+	97.7748i	−0.565903	+	0.182352i
$67$		−	957.249i		−	1.74547i	−0.488193	−	0.872736i	$-0.662344\pi$
$67$		−	957.249i		−	1.74547i	0.488193	−	0.872736i	$-0.337656\pi$
$68$		−	155.078i		−	0.276558i
$69$	−106.051	+	34.1731i	−0.185030	+	0.0596226i
$70$			651.541i			1.11249i
$71$		−	639.771i		−	1.06939i	−0.845044	−	0.534696i	$-0.820426\pi$
$71$		−	639.771i		−	1.06939i	0.845044	−	0.534696i	$-0.179574\pi$
$72$	−649.711	+	467.229i	−1.06346	+	0.764771i
$73$			869.650i			1.39431i	0.716919	+	0.697156i	$0.245552\pi$
$73$			869.650i			1.39431i	−0.716919	+	0.697156i	$0.754448\pi$
$74$			785.164i			1.23342i
$75$	535.116	−	172.431i	0.823865	−	0.265476i
$76$	1809.64			2.73132
$77$	−117.491			−0.173887
$78$	417.138	+	1294.53i	0.605532	+	1.87918i
$79$	668.109			0.951496			0.475748	−	0.879582i	$-0.342177\pi$
$79$	668.109			0.951496			0.475748	+	0.879582i	$0.342177\pi$
$80$		−	391.947i		−	0.547762i
$81$	232.010	−	691.095i	0.318258	−	0.948004i
$82$			718.373i			0.967452i
$83$	−1151.69			−1.52307			−0.761533	−	0.648126i	$-0.775553\pi$
$83$	−1151.69			−1.52307			−0.761533	+	0.648126i	$0.775553\pi$
$84$	−638.364	+	205.701i	−0.829182	+	0.267189i
$85$	−165.845			−0.211628
$86$			576.561i			0.722932i
$87$	10.3926	+	32.2518i	0.0128069	+	0.0397443i
$88$	385.254			0.466684
$89$	−505.096			−0.601573			−0.300787	−	0.953691i	$-0.597249\pi$
$89$	−505.096			−0.601573			−0.300787	+	0.953691i	$0.597249\pi$
$90$	1136.25	+	1580.02i	1.33079	+	1.85054i
$91$			501.253i			0.577424i
$92$	306.194			0.346988
$93$	356.698	+	1106.96i	0.397719	+	1.23426i
$94$	−597.093			−0.655164
$95$		−	1935.28i		−	2.09006i
$96$	−573.546	+	184.815i	−0.609764	+	0.196485i
$97$		−	1503.21i		−	1.57348i	−0.617282	−	0.786742i	$-0.711766\pi$
$97$		−	1503.21i		−	1.57348i	0.617282	−	0.786742i	$-0.288234\pi$
$98$	1233.33			1.27128
$99$	−284.921	+	204.897i	−0.289249	+	0.208009i
$100$	−1545.00			−1.54500
$101$	−1835.63			−1.80843			−0.904217	−	0.427074i	$-0.859544\pi$
$101$	−1835.63			−1.80843			−0.904217	+	0.427074i	$0.859544\pi$
$102$	−81.6939	−	253.525i	−0.0793030	−	0.246105i
$103$		−	348.680i		−	0.333558i	−0.985994	−	0.166779i	$-0.946663\pi$
$103$		−	348.680i		−	0.333558i	0.985994	−	0.166779i	$-0.0533367\pi$
$104$		−	1643.61i		−	1.54971i
$105$	219.983	+	682.685i	0.204458	+	0.634507i
$106$		−	2732.09i		−	2.50344i
$107$			519.223i			0.469114i	0.972102	+	0.234557i	$0.0753640\pi$
$107$			519.223i			0.469114i	−0.972102	+	0.234557i	$0.924636\pi$
$108$	−1189.34	+	1612.10i	−1.05967	+	1.43634i
$109$		−	1817.46i		−	1.59708i	−0.601944	−	0.798538i	$-0.705607\pi$
$109$		−	1817.46i		−	1.59708i	0.601944	−	0.798538i	$-0.294393\pi$
$110$		−	936.893i		−	0.812084i
$111$	265.098	+	822.694i	0.226685	+	0.703484i
$112$	232.003			0.195734
$113$	−1249.57			−1.04027			−0.520133	−	0.854085i	$-0.674118\pi$
$113$	−1249.57			−1.04027			−0.520133	+	0.854085i	$0.674118\pi$
$114$	2958.45	−	953.307i	2.43056	−	0.783205i
$115$		−	327.452i		−	0.265523i
$116$		−	93.1182i		−	0.0745328i
$117$	874.153	+	1215.56i	0.690731	+	0.960504i
$118$	−864.049	+	1956.82i	−0.674086	+	1.52661i
$119$		−	98.1674i		−	0.0756217i
$120$	−721.327	−	2238.53i	−0.548732	−	1.70291i
$121$	−1162.05			−0.873067
$122$			1286.19i			0.954475i
$123$	242.547	+	752.711i	0.177803	+	0.551786i
$124$		−	3196.04i		−	2.31462i
$125$		−	256.585i		−	0.183598i
$126$	−935.252	+	672.572i	−0.661261	+	0.475535i
$127$	1254.17			0.876294			0.438147	−	0.898903i	$-0.355635\pi$
$127$	1254.17			0.876294			0.438147	+	0.898903i	$0.355635\pi$
$128$	2625.14			1.81275
$129$	194.667	+	604.120i	0.132864	+	0.412324i
$130$	−3997.08			−2.69667
$131$	1262.94			0.842315			0.421157	−	0.906988i	$-0.361624\pi$
$131$	1262.94			0.842315			0.421157	+	0.906988i	$0.361624\pi$
$132$	917.945	−	295.791i	0.605279	−	0.195040i
$133$	1145.54			0.746849
$134$			4518.32i			2.91286i
$135$	1724.03	+	1271.91i	1.09912	+	0.810878i
$136$			321.892i			0.202956i
$137$		−	1067.52i		−	0.665724i	−0.942975	−	0.332862i	$-0.891986\pi$
$137$		−	1067.52i		−	0.665724i	0.942975	−	0.332862i	$-0.108014\pi$
$138$	500.574	−	161.301i	0.308780	−	0.0994988i
$139$	1083.44			0.661126			0.330563	−	0.943784i	$-0.392761\pi$
$139$	1083.44			0.661126			0.330563	+	0.943784i	$0.392761\pi$
$140$		−	1971.06i		−	1.18989i
$141$	−625.634	+	201.599i	−0.373673	+	0.120409i
$142$			3019.79i			1.78461i
$143$		−	720.784i		−	0.421503i
$144$	562.618	−	404.598i	0.325589	−	0.234142i
$145$	−99.5832			−0.0570341
$146$		−	4104.84i		−	2.32684i
$147$	1292.29	−	416.416i	0.725075	−	0.233642i
$148$		−	2375.30i		−	1.31925i
$149$	2330.79			1.28152			0.640758	−	0.767743i	$-0.278620\pi$
$149$	2330.79			1.28152			0.640758	+	0.767743i	$0.278620\pi$
$150$	−2525.81	+	813.895i	−1.37487	+	0.443028i
$151$		−	760.811i		−	0.410026i	−0.978759	−	0.205013i	$-0.934276\pi$
$151$		−	760.811i		−	0.410026i	0.978759	−	0.205013i	$-0.0657236\pi$
$152$	−3756.24			−2.00442
$153$	−171.198	−	238.061i	−0.0904609	−	0.125791i
$154$	554.570			0.290185
$155$	−3417.94			−1.77120
$156$	−1261.94	−	3916.24i	−0.647666	−	2.00994i
$157$			3112.47i			1.58218i	0.611701	+	0.791089i	$0.290485\pi$
$157$			3112.47i			1.58218i	−0.611701	+	0.791089i	$0.709515\pi$
$158$	−3153.55			−1.58787
$159$	−922.448	−	2862.68i	−0.460094	−	1.42783i
$160$		−	1770.93i		−	0.875025i
$161$	193.827			0.0948801
$162$	−1095.11	+	3262.04i	−0.531112	+	1.58204i
$163$	−3254.31			−1.56379			−0.781893	−	0.623413i	$-0.785746\pi$
$163$	−3254.31			−1.56379			−0.781893	+	0.623413i	$0.785746\pi$
$164$		−	2173.24i		−	1.03477i
$165$	−316.327	−	981.676i	−0.149249	−	0.463172i
$166$	5436.11			2.54171
$167$		−	1503.32i		−	0.696587i	−0.937385	−	0.348294i	$-0.886761\pi$
$167$		−	1503.32i		−	0.696587i	0.937385	−	0.348294i	$-0.113239\pi$
$168$	1325.04	−	426.970i	0.608507	−	0.196080i
$169$	−878.088			−0.399676
$170$	782.804			0.353167
$171$	2777.99	−	1997.75i	1.24233	−	0.893402i
$172$		−	1744.23i		−	0.773234i
$173$	4365.91			1.91870			0.959348	−	0.282227i	$-0.0910730\pi$
$173$	4365.91			1.91870			0.959348	+	0.282227i	$0.0910730\pi$
$174$	−49.0540	−	152.232i	−0.0213723	−	0.0663258i
$175$	−978.016			−0.422463
$176$	−333.612			−0.142880
$177$	−244.661	+	2342.09i	−0.103897	+	0.994588i
$178$	2384.11			1.00391
$179$	2897.20			1.20976			0.604880	−	0.796317i	$-0.293221\pi$
$179$	2897.20			1.20976			0.604880	+	0.796317i	$0.293221\pi$
$180$	−3437.41	−	4779.93i	−1.42339	−	1.97931i
$181$	1411.26			0.579549			0.289774	−	0.957095i	$-0.406420\pi$
$181$	1411.26			0.579549			0.289774	+	0.957095i	$0.406420\pi$
$182$		−	2365.97i		−	0.963611i
$183$	434.261	+	1347.67i	0.175418	+	0.544385i
$184$	−635.561			−0.254642
$185$	−2540.21			−1.00952
$186$	−1683.65	−	5224.97i	−0.663717	−	2.05975i
$187$			141.161i			0.0552018i
$188$	1806.34			0.700751
$189$	−752.874	+	1020.49i	−0.289754	+	0.392751i
$190$			9134.74i			3.48791i
$191$	−3909.32			−1.48099			−0.740493	−	0.672064i	$-0.765408\pi$
$191$	−3909.32			−1.48099			−0.740493	+	0.672064i	$0.765408\pi$
$192$	3722.71	−	1199.58i	1.39929	−	0.450896i
$193$	−318.770			−0.118889			−0.0594445	−	0.998232i	$-0.518933\pi$
$193$	−318.770			−0.118889			−0.0594445	+	0.998232i	$0.518933\pi$
$194$			7095.32i			2.62585i
$195$	−4188.14	+	1349.55i	−1.53805	+	0.495607i
$196$	−3731.12			−1.35974
$197$			5007.83i			1.81113i	0.424206	+	0.905566i	$0.360553\pi$
$197$			5007.83i			1.81113i	−0.424206	+	0.905566i	$0.639447\pi$
$198$	1344.86	−	967.134i	0.482702	−	0.347128i
$199$	−904.934			−0.322357			−0.161178	−	0.986925i	$-0.551529\pi$
$199$	−904.934			−0.322357			−0.161178	+	0.986925i	$0.551529\pi$
$200$	3206.93			1.13382
$201$	1525.54	+	4734.29i	0.535340	+	1.66135i
$202$	8664.36			3.01793
$203$		−	58.9457i		−	0.0203802i
$204$	247.143	+	766.972i	0.0848209	+	0.263229i
$205$	−2324.13			−0.791825
$206$			1645.81i			0.556645i
$207$	470.040	−	338.022i	0.157826	−	0.113498i
$208$			1423.29i			0.474459i
$209$	−1647.25			−0.545179
$210$	−1038.34	−	3222.35i	−0.341202	−	1.05887i
$211$			2400.18i			0.783106i	0.920156	+	0.391553i	$0.128062\pi$
$211$			2400.18i			0.783106i	−0.920156	+	0.391553i	$0.871938\pi$
$212$			8265.21i			2.67763i
$213$	1019.58	+	3164.13i	0.327985	+	1.01785i
$214$		−	2450.79i		−	0.782862i
$215$	−1865.33			−0.591695
$216$	2468.68	−	3346.21i	0.777651	−	1.05408i
$217$		−	2023.16i		−	0.632908i
$218$			8578.62i			2.66522i
$219$	−1385.94	−	4301.05i	−0.427639	−	1.32711i
$220$			2834.32i			0.868590i
$221$	602.238			0.183307
$222$	−1251.29	−	3883.21i	−0.378294	−	1.17398i
$223$	−1236.31			−0.371252			−0.185626	−	0.982620i	$-0.559431\pi$
$223$	−1236.31			−0.371252			−0.185626	+	0.982620i	$0.559431\pi$
$224$	1048.25			0.312676
$225$	−2371.74	+	1705.60i	−0.702737	+	0.505362i
$226$	5898.12			1.73601
$227$	1595.09			0.466388			0.233194	−	0.972430i	$-0.425082\pi$
$227$	1595.09			0.466388			0.233194	+	0.972430i	$0.425082\pi$
$228$	−8950.00	+	2883.97i	−2.59968	+	0.837701i
$229$			895.868i			0.258518i	0.991611	+	0.129259i	$0.0412599\pi$
$229$			895.868i			0.258518i	−0.991611	+	0.129259i	$0.958740\pi$
$230$			1545.61i			0.443107i
$231$	581.078	−	187.242i	0.165507	−	0.0533316i
$232$			193.284i			0.0546970i
$233$	4173.18			1.17336			0.586682	−	0.809817i	$-0.300434\pi$
$233$	4173.18			1.17336			0.586682	+	0.809817i	$0.300434\pi$
$234$	−4126.10	−	5737.59i	−1.15270	−	1.60290i
$235$		−	1931.75i		−	0.536229i
$236$	2613.95	−	5919.83i	0.720990	−	1.63283i
$237$	−3304.29	+	1064.75i	−0.905639	+	0.291826i
$238$			463.361i			0.126198i
$239$		−	4715.74i		−	1.27630i	−0.769911	−	0.638151i	$-0.779700\pi$
$239$		−	4715.74i		−	1.27630i	0.769911	−	0.638151i	$-0.220300\pi$
$240$	624.634	+	1938.46i	0.168000	+	0.521363i
$241$	111.516			0.0298066			0.0149033	−	0.999889i	$-0.495256\pi$
$241$	111.516			0.0298066			0.0149033	+	0.999889i	$0.495256\pi$
$242$	5485.01			1.45698
$243$	−46.0806	+	3787.71i	−0.0121649	+	0.999926i
$244$		−	3891.01i		−	1.02089i
$245$			3990.17i			1.04050i
$246$	−1144.85	−	3552.88i	−0.296719	−	0.920826i
$247$			7027.66i			1.81036i
$248$			6633.96i			1.69862i
$249$	5695.95	−	1835.42i	1.44966	−	0.467128i
$250$			1211.11i			0.306390i
$251$			504.008i			0.126744i	0.997990	+	0.0633719i	$0.0201854\pi$
$251$			504.008i			0.126744i	−0.997990	+	0.0633719i	$0.979815\pi$
$252$	2829.35	−	2034.69i	0.707272	−	0.508623i
$253$	−278.716			−0.0692598
$254$	−5919.80			−1.46237
$255$	820.222	−	264.302i	0.201429	−	0.0649067i
$256$	−6369.25			−1.55499
$257$		−	1386.31i		−	0.336480i	−0.985746	−	0.168240i	$-0.946192\pi$
$257$		−	1386.31i		−	0.336480i	0.985746	−	0.168240i	$-0.0538084\pi$
$258$	−918.848	−	2851.51i	−0.221725	−	0.688091i
$259$		−	1503.61i		−	0.360734i
$260$	12092.1			2.88431
$261$	−102.798	−	142.946i	−0.0243794	−	0.0339010i
$262$	−5961.19			−1.40566
$263$		−	7832.10i		−	1.83630i	−0.396228	−	0.918152i	$-0.629681\pi$
$263$		−	7832.10i		−	1.83630i	0.396228	−	0.918152i	$-0.370319\pi$
$264$	−1905.36	+	613.968i	−0.444193	+	0.143133i
$265$	8839.05			2.04897
$266$	−5407.07			−1.24635
$267$	2498.06	−	804.956i	0.572581	−	0.184504i
$268$		−	13669.0i		−	3.11554i
$269$	−711.848			−0.161346			−0.0806731	−	0.996741i	$-0.525707\pi$
$269$	−711.848			−0.161346			−0.0806731	+	0.996741i	$0.525707\pi$
$270$	−8137.60	−	6003.55i	−1.83422	−	1.35320i
$271$	−2607.47			−0.584474			−0.292237	−	0.956346i	$-0.594400\pi$
$271$	−2607.47			−0.584474			−0.292237	+	0.956346i	$0.594400\pi$
$272$		−	278.743i		−	0.0621371i
$273$	−798.832	−	2479.06i	−0.177097	−	0.549595i
$274$			5038.80i			1.11097i
$275$	1406.35			0.308386
$276$	−1514.35	+	487.972i	−0.330265	+	0.106422i
$277$	−5056.77			−1.09687			−0.548433	−	0.836195i	$-0.684775\pi$
$277$	−5056.77			−1.09687			−0.548433	+	0.836195i	$0.684775\pi$
$278$	−5113.98			−1.10329
$279$	−3528.26	−	4906.26i	−0.757102	−	1.05280i
$280$			4091.30i			0.873221i
$281$		−	559.120i		−	0.118699i	−0.998237	−	0.0593493i	$-0.981097\pi$
$281$		−	559.120i		−	0.118699i	0.998237	−	0.0593493i	$-0.0189026\pi$
$282$	2953.06	−	951.569i	0.623589	−	0.200940i
$283$		−	4024.72i		−	0.845387i	−0.906273	−	0.422693i	$-0.861085\pi$
$283$		−	4024.72i		−	0.845387i	0.906273	−	0.422693i	$-0.138915\pi$
$284$		−	9135.56i		−	1.90879i
$285$	3084.20	+	9571.38i	0.641026	+	1.98933i
$286$			3402.18i			0.703409i
$287$		−	1375.71i		−	0.282946i
$288$	2542.07	−	1828.09i	0.520114	−	0.374032i
$289$	4795.06			0.975993
$290$	470.044			0.0951790
$291$	2395.62	+	7434.47i	0.482591	+	1.49765i
$292$			12418.1i			2.48875i
$293$		−	736.817i		−	0.146912i	−0.997298	−	0.0734562i	$-0.976597\pi$
$293$		−	736.817i		−	0.146912i	0.997298	−	0.0734562i	$-0.0234029\pi$
$294$	−6099.73	+	1965.53i	−1.21001	+	0.389905i
$295$	−6330.83	−	2795.43i	−1.24948	−	0.551716i
$296$			4930.37i			0.968148i
$297$	1082.61	−	1467.43i	0.211512	−	0.286698i
$298$	−11001.6			−2.13861
$299$			1189.09i			0.229990i
$300$	7641.14	−	2462.22i	1.47054	−	0.473855i
$301$		−	1104.13i		−	0.211432i
$302$			3591.11i			0.684255i
$303$	9078.51	−	2925.39i	1.72128	−	0.554650i
$304$	3252.72			0.613673
$305$	−4161.16			−0.781204
$306$	808.072	+	1123.67i	0.150962	+	0.209922i
$307$	−452.628			−0.0841461			−0.0420730	−	0.999115i	$-0.513396\pi$
$307$	−452.628			−0.0841461			−0.0420730	+	0.999115i	$0.513396\pi$
$308$	−1677.70			−0.310376
$309$	555.682	+	1724.48i	0.102303	+	0.317483i
$310$	16133.0			2.95579
$311$			3689.41i			0.672692i	0.941738	+	0.336346i	$0.109191\pi$
$311$			3689.41i			0.672692i	−0.941738	+	0.336346i	$0.890809\pi$
$312$	2619.38	+	8128.87i	0.475299	+	1.47502i
$313$		−	10707.6i		−	1.93364i	−0.255450	−	0.966822i	$-0.582224\pi$
$313$		−	10707.6i		−	1.93364i	0.255450	−	0.966822i	$-0.417776\pi$
$314$		−	14691.2i		−	2.64035i
$315$	−2175.95	−	3025.79i	−0.389209	−	0.541219i
$316$	9540.21			1.69835
$317$			4660.59i			0.825756i	0.910786	+	0.412878i	$0.135476\pi$
$317$			4660.59i			0.825756i	−0.910786	+	0.412878i	$0.864524\pi$
$318$	4354.05	+	13512.2i	0.767809	+	2.38278i
$319$			84.7618i			0.0148770i
$320$			11494.5i			2.00801i
$321$	−827.471	−	2567.94i	−0.143878	−	0.446505i
$322$	−914.884			−0.158337
$323$		−	1376.33i		−	0.237092i
$324$	3312.97	−	9868.43i	0.568067	−	1.69212i
$325$		−	5999.94i		−	1.02405i
$326$	15360.7			2.60966
$327$	2896.44	+	8988.67i	0.489827	+	1.52011i
$328$			4510.96i			0.759379i
$329$	1143.45			0.191613
$330$	1493.10	+	4633.62i	0.249068	+	0.772946i
$331$	8908.61			1.47934			0.739670	−	0.672969i	$-0.234981\pi$
$331$	8908.61			1.47934			0.739670	+	0.672969i	$0.234981\pi$
$332$	−16445.5			−2.71856
$333$	−2622.21	−	3646.34i	−0.431520	−	0.600055i
$334$			7095.81i			1.16247i
$335$	−14618.0			−2.38407
$336$	−1147.42	+	369.736i	−0.186301	+	0.0600320i
$337$			3654.41i			0.590707i	0.955388	+	0.295354i	$0.0954375\pi$
$337$			3654.41i			0.590707i	−0.955388	+	0.295354i	$0.904563\pi$
$338$	4144.67			0.666983
$339$	6180.05	−	1991.41i	0.990131	−	0.319052i
$340$	−2368.16			−0.377740
$341$			2909.23i			0.462005i
$342$	−13112.4	+	9429.59i	−2.07321	+	1.49092i
$343$	−5462.31			−0.859874
$344$			3620.46i			0.567449i
$345$	521.851	+	1619.49i	0.0814363	+	0.252726i
$346$	−20607.6			−3.20194
$347$	3873.17			0.599200			0.299600	−	0.954065i	$-0.403147\pi$
$347$	3873.17			0.599200			0.299600	+	0.954065i	$0.403147\pi$
$348$	148.400	+	460.537i	0.0228594	+	0.0709408i
$349$			1703.25i			0.261241i	0.991432	+	0.130620i	$0.0416969\pi$
$349$			1703.25i			0.261241i	−0.991432	+	0.130620i	$0.958303\pi$
$350$	4616.34			0.705011
$351$	−6260.53	−	4618.73i	−0.952030	−	0.702364i
$352$	−1507.35			−0.228245
$353$	−853.113			−0.128631			−0.0643153	−	0.997930i	$-0.520486\pi$
$353$	−853.113			−0.128631			−0.0643153	+	0.997930i	$0.520486\pi$
$354$	1154.82	−	11054.9i	0.173385	−	1.65978i
$355$	−9769.82			−1.46064
$356$	−7212.47			−1.07376
$357$	156.446	+	485.509i	0.0231933	+	0.0719772i
$358$	−13675.1			−2.01886
$359$			6930.62i			1.01890i	0.860501	+	0.509448i	$0.170151\pi$
$359$			6930.62i			1.01890i	−0.860501	+	0.509448i	$0.829849\pi$
$360$	7134.97	+	9921.61i	1.04457	+	1.45254i
$361$	9201.70			1.34155
$362$	−6661.31			−0.967157
$363$	5747.19	−	1851.93i	0.830990	−	0.267772i
$364$			7157.60i			1.03066i
$365$	13280.3			1.90444
$366$	−2049.76	−	6361.13i	−0.292739	−	0.908474i
$367$		−	9975.19i		−	1.41880i	−0.704804	−	0.709402i	$-0.748965\pi$
$367$		−	9975.19i		−	1.41880i	0.704804	−	0.709402i	$-0.251035\pi$
$368$	550.365			0.0779613
$369$	−2399.15	−	3336.16i	−0.338468	−	0.470660i
$370$	11990.1			1.68469
$371$			5232.04i			0.732167i
$372$	5093.44	+	15806.7i	0.709899	+	2.20307i
$373$	−12889.7			−1.78928			−0.894642	−	0.446784i	$-0.852569\pi$
$373$	−12889.7			−1.78928			−0.894642	+	0.446784i	$0.852569\pi$
$374$		−	666.296i		−	0.0921212i
$375$	408.913	+	1269.00i	0.0563098	+	0.174749i
$376$	−3749.39			−0.514256
$377$	361.620			0.0494016
$378$	3553.65	−	4816.84i	0.483544	−	0.655427i
$379$	9726.01			1.31818			0.659092	−	0.752062i	$-0.270941\pi$
$379$	9726.01			1.31818			0.659092	+	0.752062i	$0.270941\pi$
$380$		−	27634.7i		−	3.73061i
$381$	−6202.77	+	1998.73i	−0.834061	+	0.268761i
$382$	18452.4			2.47148
$383$		−	6768.75i		−	0.903047i	−0.892259	−	0.451524i	$-0.850881\pi$
$383$		−	6768.75i		−	0.903047i	0.892259	−	0.451524i	$-0.149119\pi$
$384$	−12983.2	+	4183.61i	−1.72538	+	0.555974i
$385$			1794.18i			0.237506i
$386$	1504.63			0.198403
$387$	−1925.54	−	2677.58i	−0.252921	−	0.351703i
$388$		−	21465.0i		−	2.80855i
$389$		−	6858.16i		−	0.893888i	−0.894562	−	0.446944i	$-0.852512\pi$
$389$		−	6858.16i		−	0.893888i	0.894562	−	0.446944i	$-0.147488\pi$
$390$	19768.5	−	6370.03i	2.56671	−	0.827074i
$391$		−	232.876i		−	0.0301204i
$392$	7744.62			0.997863
$393$	−6246.14	+	2012.70i	−0.801720	+	0.258340i
$394$		−	23637.5i		−	3.02243i
$395$		−	10202.6i		−	1.29961i
$396$	−4068.51	+	2925.81i	−0.516289	+	0.371281i
$397$			7447.83i			0.941552i	0.882253	+	0.470776i	$0.156026\pi$
$397$			7447.83i			0.941552i	−0.882253	+	0.470776i	$0.843974\pi$
$398$	4271.38			0.537953
$399$	−5665.53	+	1825.61i	−0.710855	+	0.229060i
$400$	−2777.04			−0.347130
$401$	−4411.38			−0.549362			−0.274681	−	0.961535i	$-0.588572\pi$
$401$	−4411.38			−0.549362			−0.274681	+	0.961535i	$0.588572\pi$
$402$	−7200.71	−	22346.4i	−0.893380	−	2.77248i
$403$	12411.7			1.53417
$404$	−26211.7			−3.22792
$405$	−10553.6	−	3542.98i	−1.29484	−	0.434697i
$406$			278.230i			0.0340107i
$407$			2162.14i			0.263325i
$408$	−512.990	−	1591.99i	−0.0622470	−	0.193175i
$409$			669.354i			0.0809228i	0.999181	+	0.0404614i	$0.0128828\pi$
$409$			669.354i			0.0809228i	−0.999181	+	0.0404614i	$0.987117\pi$
$410$	10970.1			1.32141
$411$	1701.27	+	5279.65i	0.204179	+	0.633640i
$412$		−	4978.95i		−	0.595377i
$413$	1654.68	−	3747.37i	0.197147	−	0.446480i
$414$	−2218.64	+	1595.50i	−0.263382	+	0.189407i
$415$			17587.3i			2.08030i
$416$			6430.83i			0.757926i
$417$	−5358.42	+	1726.65i	−0.629264	+	0.202769i
$418$	7775.18			0.909800
$419$	616.743			0.0719090			0.0359545	−	0.999353i	$-0.488553\pi$
$419$	616.743			0.0719090			0.0359545	+	0.999353i	$0.488553\pi$
$420$	3141.23	+	9748.34i	0.364943	+	1.13255i
$421$			7169.53i			0.829979i	0.909826	+	0.414990i	$0.136215\pi$
$421$			7169.53i			0.829979i	−0.909826	+	0.414990i	$0.863785\pi$
$422$		−	11329.1i		−	1.30685i
$423$	2772.93	−	1994.11i	0.318734	−	0.229212i
$424$		−	17155.9i		−	1.96501i
$425$			1175.05i			0.134114i
$426$	−4812.55	−	14935.0i	−0.547344	−	1.69860i
$427$		−	2463.09i		−	0.279151i
$428$			7414.21i			0.837334i
$429$	1148.69	+	3564.80i	0.129276	+	0.401189i
$430$	8804.55			0.987426
$431$	13322.7			1.48894			0.744468	−	0.667659i	$-0.232703\pi$
$431$	13322.7			1.48894			0.744468	+	0.667659i	$0.232703\pi$
$432$	−2137.76	+	2897.66i	−0.238086	+	0.322717i
$433$	5914.82			0.656462			0.328231	−	0.944598i	$-0.393548\pi$
$433$	5914.82			0.656462			0.328231	+	0.944598i	$0.393548\pi$
$434$			9549.52i			1.05620i
$435$	492.511	−	158.703i	0.0542853	−	0.0174925i
$436$		−	25952.3i		−	2.85067i
$437$	2717.49			0.297472
$438$	6541.77	+	20301.4i	0.713648	+	2.21470i
$439$	−9240.25			−1.00459			−0.502293	−	0.864698i	$-0.667510\pi$
$439$	−9240.25			−1.00459			−0.502293	+	0.864698i	$0.667510\pi$
$440$		−	5883.14i		−	0.637427i
$441$	−5727.67	+	4118.96i	−0.618472	+	0.444764i
$442$	−2842.63			−0.305905
$443$	−8689.46			−0.931938			−0.465969	−	0.884801i	$-0.654294\pi$
$443$	−8689.46			−0.931938			−0.465969	+	0.884801i	$0.654294\pi$
$444$	3785.45	+	11747.6i	0.404616	+	1.25567i
$445$			7713.22i			0.821667i
$446$	5835.50			0.619550
$447$	−11527.5	+	3714.52i	−1.21975	+	0.393044i
$448$	−6803.89			−0.717530
$449$		−	952.486i		−	0.100113i	−0.998746	−	0.0500563i	$-0.984060\pi$
$449$		−	952.486i		−	0.100113i	0.998746	−	0.0500563i	$-0.0159401\pi$
$450$	11194.9	−	8050.61i	1.17274	−	0.843354i
$451$			1978.22i			0.206543i
$452$	−17843.2			−1.85680
$453$	1212.48	+	3762.76i	0.125756	+	0.390265i
$454$	−7529.01			−0.778313
$455$	7654.54			0.788682
$456$	18577.3	−	5986.21i	1.90781	−	0.614759i
$457$		−	10514.9i		−	1.07629i	−0.842852	−	0.538146i	$-0.819125\pi$
$457$		−	10514.9i		−	1.07629i	0.842852	−	0.538146i	$-0.180875\pi$
$458$		−	4228.60i		−	0.431418i
$459$	1226.09	+	904.551i	0.124682	+	0.0919844i
$460$		−	4675.83i		−	0.473938i
$461$		−	2406.90i		−	0.243168i	−0.992581	−	0.121584i	$-0.961203\pi$
$461$		−	2406.90i		−	0.243168i	0.992581	−	0.121584i	$-0.0387974\pi$
$462$	−2742.75	+	883.801i	−0.276200	+	0.0890004i
$463$			9106.31i			0.914052i	0.889453	+	0.457026i	$0.151085\pi$
$463$			9106.31i			0.914052i	−0.889453	+	0.457026i	$0.848915\pi$
$464$		−	167.374i		−	0.0167460i
$465$	16904.2	−	5447.07i	1.68583	−	0.543229i
$466$	−19697.8			−1.95812
$467$	−2006.05			−0.198777			−0.0993883	−	0.995049i	$-0.531689\pi$
$467$	−2006.05			−0.198777			−0.0993883	+	0.995049i	$0.531689\pi$
$468$	12482.4	+	17357.5i	1.23290	+	1.71443i
$469$		−	8652.72i		−	0.851910i
$470$			9118.09i			0.894864i
$471$	−4960.25	−	15393.4i	−0.485257	−	1.50593i
$472$	−5425.72	+	12287.7i	−0.529108	+	1.19828i
$473$			1587.70i			0.154340i
$474$	15596.6	−	5025.72i	1.51134	−	0.487002i
$475$	−13712.0			−1.32452
$476$		−	1401.77i		−	0.134979i
$477$	9124.35	+	12688.0i	0.875839	+	1.21791i
$478$			22258.8i			2.12991i
$479$		−	5805.96i		−	0.553822i	−0.960896	−	0.276911i	$-0.910689\pi$
$479$		−	5805.96i		−	0.553822i	0.960896	−	0.276911i	$-0.0893108\pi$
$480$	2822.27	+	8758.51i	0.268372	+	0.832853i
$481$	9224.38			0.874419
$482$	−526.369			−0.0497416
$483$	−958.615	+	308.896i	−0.0903074	+	0.0290999i
$484$	−16593.4			−1.55836
$485$	−22955.2			−2.14916
$486$	217.506	−	17878.4i	0.0203009	−	1.66869i
$487$	12433.3			1.15689			0.578444	−	0.815722i	$-0.303660\pi$
$487$	12433.3			1.15689			0.578444	+	0.815722i	$0.303660\pi$
$488$			8076.51i			0.749193i
$489$	16094.9	−	5186.30i	1.48842	−	0.479616i
$490$		−	18834.0i		−	1.73640i
$491$			15237.2i			1.40050i	0.713897	+	0.700251i	$0.246928\pi$
$491$			15237.2i			1.40050i	−0.713897	+	0.700251i	$0.753072\pi$
$492$	3463.44	+	10748.3i	0.317365	+	0.984897i
$493$	−70.8212			−0.00646983
$494$		−	33171.3i		−	3.02115i
$495$	3128.94	+	4350.98i	0.284112	+	0.395075i
$496$		−	5744.69i		−	0.520049i
$497$		−	5782.99i		−	0.521937i
$498$	−26885.5	+	8663.36i	−2.41921	+	0.779547i
$499$	341.264			0.0306154			0.0153077	−	0.999883i	$-0.495127\pi$
$499$	341.264			0.0306154			0.0153077	+	0.999883i	$0.495127\pi$
$500$		−	3663.89i		−	0.327708i
$501$	2395.79	+	7434.99i	0.213645	+	0.663016i
$502$		−	2378.97i		−	0.211511i
$503$	−1834.71			−0.162636			−0.0813179	−	0.996688i	$-0.525913\pi$
$503$	−1834.71			−0.162636			−0.0813179	+	0.996688i	$0.525913\pi$
$504$	−5872.84	+	4223.36i	−0.519042	+	0.373261i
$505$			28031.5i			2.47007i
$506$	1315.57			0.115582
$507$	4342.78	−	1399.38i	0.380414	−	0.122581i
$508$	17908.8			1.56412
$509$	12183.2			1.06093			0.530465	−	0.847707i	$-0.322018\pi$
$509$	12183.2			1.06093			0.530465	+	0.847707i	$0.322018\pi$
$510$	−3871.54	+	1247.53i	−0.336146	+	0.108317i
$511$			7860.90i			0.680520i
$512$	9062.40			0.782237
$513$	−10555.4	+	14307.5i	−0.908449	+	1.23137i
$514$			6543.52i			0.561522i
$515$	−5324.63			−0.455595
$516$	2779.73	+	8626.48i	0.237153	+	0.735968i
$517$	−1644.24			−0.139872
$518$			7097.22i			0.601996i
$519$	−21592.6	+	6957.83i	−1.82623	+	0.588468i
$520$	−25099.3			−2.11669
$521$			2837.05i			0.238567i	0.992860	+	0.119284i	$0.0380598\pi$
$521$			2837.05i			0.238567i	−0.992860	+	0.119284i	$0.961940\pi$
$522$	485.216	+	674.722i	0.0406845	+	0.0565743i
$523$	6034.65			0.504545			0.252272	−	0.967656i	$-0.418822\pi$
$523$	6034.65			0.504545			0.252272	+	0.967656i	$0.418822\pi$
$524$	18034.0			1.50347
$525$	4837.00	−	1558.64i	0.402103	−	0.129570i
$526$			36968.4i			3.06444i
$527$	−2430.75			−0.200921
$528$	1649.95	−	531.667i	0.135994	−	0.0438217i
$529$	−11707.2			−0.962209
$530$	−41721.2			−3.41935
$531$	−2522.49	−	11973.2i	−0.206152	−	0.978520i
$532$	16357.6			1.33307
$533$	8439.70			0.685861
$534$	−11791.1	+	3799.48i	−0.955528	+	0.307902i
$535$	7928.96			0.640746
$536$			28372.4i			2.28638i
$537$	−14328.8	+	4617.18i	−1.15146	+	0.371036i
$538$	3360.00			0.269256
$539$	3396.29			0.271407
$540$	24618.1	+	18162.1i	1.96184	+	1.44736i
$541$			16326.5i			1.29747i	0.761013	+	0.648736i	$0.224702\pi$
$541$			16326.5i			1.29747i	−0.761013	+	0.648736i	$0.775298\pi$
$542$	12307.5			0.975375
$543$	−6979.72	+	2249.09i	−0.551618	+	0.177749i
$544$		−	1259.44i		−	0.0992611i
$545$	−27754.1			−2.18139
$546$	3770.57	+	11701.4i	0.295541	+	0.917170i
$547$	16651.3			1.30157			0.650784	−	0.759263i	$-0.274440\pi$
$547$	16651.3			1.30157			0.650784	+	0.759263i	$0.274440\pi$
$548$		−	15243.5i		−	1.18827i
$549$	−4295.47	−	5973.12i	−0.333928	−	0.464347i
$550$	−6638.13			−0.514638
$551$		−	826.431i		−	0.0638968i
$552$	3143.31	−	1012.88i	0.242370	−	0.0780993i
$553$	6039.15			0.464395
$554$	23868.5			1.83046
$555$	12563.2	−	4048.27i	0.960862	−	0.309620i
$556$	15471.0			1.18006
$557$		−	16078.8i		−	1.22312i	−0.791197	−	0.611561i	$-0.790542\pi$
$557$		−	16078.8i		−	1.22312i	0.791197	−	0.611561i	$-0.209458\pi$
$558$	16653.8	+	23158.1i	1.26346	+	1.75692i
$559$	6773.64			0.512512
$560$		−	3542.87i		−	0.267346i
$561$	−224.964	−	698.145i	−0.0169305	−	0.0525413i
$562$			2639.11i			0.198086i
$563$	−8735.26			−0.653903			−0.326951	−	0.945041i	$-0.606021\pi$
$563$	−8735.26			−0.653903			−0.326951	+	0.945041i	$0.606021\pi$
$564$	−8933.68	+	2878.72i	−0.666979	+	0.214922i
$565$			19082.0i			1.42086i
$566$			18997.1i			1.41079i
$567$	2097.18	−	6246.92i	0.155332	−	0.462691i
$568$			18962.5i			1.40079i
$569$	14260.2			1.05064			0.525322	−	0.850903i	$-0.323945\pi$
$569$	14260.2			1.05064			0.525322	+	0.850903i	$0.323945\pi$
$570$	−14557.8	−	45177.9i	−1.06975	−	3.31982i
$571$			9210.71i			0.675055i	0.941316	+	0.337527i	$0.109591\pi$
$571$			9210.71i			0.675055i	−0.941316	+	0.337527i	$0.890409\pi$
$572$		−	10292.4i		−	0.752353i
$573$	19334.4	−	6230.17i	1.40961	−	0.454222i
$574$			6493.49i			0.472183i
$575$	−2320.09			−0.168268
$576$	−16499.8	+	11865.6i	−1.19356	+	0.858330i
$577$	−7145.53			−0.515550			−0.257775	−	0.966205i	$-0.582989\pi$
$577$	−7145.53			−0.515550			−0.257775	+	0.966205i	$0.582989\pi$
$578$	−22633.2			−1.62875
$579$	1576.55	−	508.015i	0.113159	−	0.0364635i
$580$	−1421.99			−0.101802
$581$	−10410.3			−0.743361
$582$	−11307.6	−	35091.5i	−0.805352	−	2.49929i
$583$		−	7523.49i		−	0.534462i
$584$		−	25776.0i		−	1.82640i
$585$	18562.6	−	13349.0i	1.31192	−	0.943443i
$586$			3477.86i			0.245169i
$587$	23849.3			1.67695			0.838473	−	0.544943i	$-0.183449\pi$
$587$	23849.3			1.67695			0.838473	+	0.544943i	$0.183449\pi$
$588$	18453.1	−	5946.18i	1.29421	−	0.417034i
$589$		−	28365.1i		−	1.98432i
$590$	29882.2	+	13194.7i	2.08514	+	0.920709i
$591$	−7980.83	−	24767.3i	−0.555478	−	1.72385i
$592$		−	4269.46i		−	0.296409i
$593$		−	22393.0i		−	1.55071i	−0.631526	−	0.775355i	$-0.717571\pi$
$593$		−	22393.0i		−	1.55071i	0.631526	−	0.775355i	$-0.282429\pi$
$594$	−5110.02	+	6926.45i	−0.352974	+	0.478444i
$595$	−1499.10			−0.103289
$596$	33282.3			2.28741
$597$	4475.55	−	1442.17i	0.306821	−	0.0988676i
$598$		−	5612.63i		−	0.383809i
$599$			1908.02i			0.130150i	0.997880	+	0.0650749i	$0.0207286\pi$
$599$			1908.02i			0.130150i	−0.997880	+	0.0650749i	$0.979271\pi$
$600$	−15860.6	+	5110.79i	−1.07918	+	0.347745i
$601$			3985.09i			0.270475i	0.990813	+	0.135237i	$0.0431797\pi$
$601$			3985.09i			0.270475i	−0.990813	+	0.135237i	$0.956820\pi$
$602$			5211.62i			0.352840i
$603$	−15089.8	−	20983.3i	−1.01908	−	1.41709i
$604$		−	10863.9i		−	0.731866i
$605$			17745.5i			1.19249i
$606$	−42851.6	+	13808.1i	−2.87248	+	0.925606i
$607$	−18670.7			−1.24847			−0.624235	−	0.781237i	$-0.714589\pi$
$607$	−18670.7			−1.24847			−0.624235	+	0.781237i	$0.714589\pi$
$608$	14696.7			0.980314
$609$	93.9400	+	291.529i	0.00625064	+	0.0193980i
$610$	19641.1			1.30368
$611$			7014.86i			0.464469i
$612$	−2444.60	−	3399.37i	−0.161466	−	0.224528i
$613$			9951.11i			0.655663i	0.944736	+	0.327832i	$0.106318\pi$
$613$			9951.11i			0.655663i	−0.944736	+	0.327832i	$0.893682\pi$
$614$	2136.45			0.140424
$615$	11494.5	−	3703.90i	0.753664	−	0.242855i
$616$	3482.37			0.227774
$617$			15527.0i			1.01311i	0.862206	+	0.506557i	$0.169082\pi$
$617$			15527.0i			1.01311i	−0.862206	+	0.506557i	$0.830918\pi$
$618$	−2622.88	−	8139.72i	−0.170724	−	0.529818i
$619$	9610.37			0.624028			0.312014	−	0.950077i	$-0.398996\pi$
$619$	9610.37			0.624028			0.312014	+	0.950077i	$0.398996\pi$
$620$	−48806.1			−3.16145
$621$	−1786.00	+	2420.85i	−0.115410	+	0.156434i
$622$		−	17414.4i		−	1.12260i
$623$	−4565.64			−0.293609
$624$	−2268.26	−	7039.21i	−0.145518	−	0.451593i
$625$	−17443.0			−1.11635
$626$			50541.1i			3.22689i
$627$	8146.83	−	2625.17i	0.518904	−	0.167208i
$628$			44444.2i			2.82407i
$629$	−1806.54			−0.114517
$630$	10270.7	+	14282.1i	0.649516	+	0.903192i
$631$	22899.0			1.44468			0.722342	−	0.691536i	$-0.243066\pi$
$631$	22899.0			1.44468			0.722342	+	0.691536i	$0.243066\pi$
$632$	−19802.4			−1.24636
$633$	−3825.10	−	11870.6i	−0.240180	−	0.745364i
$634$		−	21998.5i		−	1.37803i
$635$		−	19152.1i		−	1.19690i
$636$	−13172.0	−	40877.5i	−0.821234	−	2.54858i
$637$		−	14489.6i		−	0.901257i
$638$		−	400.085i		−	0.0248268i
$639$	−10085.2	−	14024.1i	−0.624356	−	0.868205i
$640$		−	40088.0i		−	2.47597i
$641$			15494.1i			0.954728i	0.878706	+	0.477364i	$0.158408\pi$
$641$			15494.1i			0.954728i	−0.878706	+	0.477364i	$0.841592\pi$
$642$	3905.75	+	12120.9i	0.240106	+	0.745133i
$643$	5728.58			0.351342			0.175671	−	0.984449i	$-0.443790\pi$
$643$	5728.58			0.351342			0.175671	+	0.984449i	$0.443790\pi$
$644$	2767.74			0.169354
$645$	9225.40	−	2972.72i	0.563178	−	0.181474i
$646$			6496.41i			0.395662i
$647$		−	25348.3i		−	1.54026i	−0.637889	−	0.770128i	$-0.720192\pi$
$647$		−	25348.3i		−	1.54026i	0.637889	−	0.770128i	$-0.279808\pi$
$648$	−6876.67	+	20483.7i	−0.416884	+	1.24178i
$649$	−2379.37	+	5388.59i	−0.143912	+	0.325918i
$650$			28320.3i			1.70895i
$651$	3224.25	+	10006.0i	0.194114	+	0.602405i
$652$	−46469.6			−2.79124
$653$			5226.26i			0.313199i	0.987662	+	0.156600i	$0.0500533\pi$
$653$			5226.26i			0.313199i	−0.987662	+	0.156600i	$0.949947\pi$
$654$	−13671.5	−	42427.5i	−0.817428	−	2.53677i
$655$		−	19286.1i		−	1.15049i
$656$		−	3906.28i		−	0.232492i
$657$	13708.9	+	19063.1i	0.814058	+	1.13200i
$658$	−5397.22			−0.319765
$659$	−11053.9			−0.653411			−0.326706	−	0.945126i	$-0.605939\pi$
$659$	−11053.9			−0.653411			−0.326706	+	0.945126i	$0.605939\pi$
$660$	−4516.97	−	14017.8i	−0.266398	−	0.826729i
$661$	−20881.3			−1.22873			−0.614365	−	0.789022i	$-0.710588\pi$
$661$	−20881.3			−1.22873			−0.614365	+	0.789022i	$0.710588\pi$
$662$	−42049.6			−2.46874
$663$	−2978.50	+	959.769i	−0.174473	+	0.0562207i
$664$	34135.6			1.99506
$665$		−	17493.3i		−	1.02009i
$666$	12377.1	+	17211.1i	0.720125	+	1.00138i
$667$		−	139.833i		−	0.00811748i
$668$		−	21466.5i		−	1.24336i
$669$	6114.44	−	1970.27i	0.353360	−	0.113864i
$670$	68998.4			3.97857
$671$			3541.84i			0.203772i
$672$	−5184.37	+	1670.57i	−0.297606	+	0.0958983i
$673$		−	5558.12i		−	0.318350i	−0.987250	−	0.159175i	$-0.949117\pi$
$673$		−	5558.12i		−	0.318350i	0.987250	−	0.159175i	$-0.0508834\pi$
$674$		−	17249.2i		−	0.985778i
$675$	9011.81	−	12215.2i	0.513874	−	0.696538i
$676$	−12538.6			−0.713393
$677$		−	442.874i		−	0.0251419i	−0.999921	−	0.0125709i	$-0.995998\pi$
$677$		−	442.874i		−	0.0251419i	0.999921	−	0.0125709i	$-0.00400156\pi$
$678$	−29170.5	+	9399.67i	−1.65234	+	0.532437i
$679$		−	13587.8i		−	0.767968i
$680$	4915.55			0.277210
$681$	−7888.90	+	2542.05i	−0.443911	+	0.143042i
$682$		−	13731.9i		−	0.770998i
$683$	13997.4			0.784180			0.392090	−	0.919927i	$-0.371752\pi$
$683$	13997.4			0.784180			0.392090	+	0.919927i	$0.371752\pi$
$684$	39668.1	−	28526.7i	2.21747	−	1.59466i
$685$	−16301.9			−0.909288
$686$	25782.7			1.43497
$687$	−1427.72	−	4430.72i	−0.0792881	−	0.246059i
$688$		−	3135.15i		−	0.173730i
$689$	−32097.6			−1.77477
$690$	−2463.19	−	7644.17i	−0.135902	−	0.421751i
$691$			14932.8i			0.822100i	0.911613	+	0.411050i	$0.134838\pi$
$691$			14932.8i			0.822100i	−0.911613	+	0.411050i	$0.865162\pi$
$692$	62342.7			3.42473
$693$	−2575.45	+	1852.09i	−0.141174	+	0.101523i
$694$	−18281.8			−0.999951
$695$		−	16545.1i		−	0.903008i
$696$	−308.031	−	955.929i	−0.0167757	−	0.0520609i
$697$	−1652.86			−0.0898231
$698$		−	8039.54i		−	0.435962i
$699$	−20639.4	+	6650.67i	−1.11681	+	0.359873i
$700$	−13965.5			−0.754066
$701$	−18225.0			−0.981952			−0.490976	−	0.871173i	$-0.663360\pi$
$701$	−18225.0			−0.981952			−0.490976	+	0.871173i	$0.663360\pi$
$702$	29550.4	+	21800.9i	1.58876	+	1.17211i
$703$		−	21081.0i		−	1.13099i
$704$	9783.75			0.523777
$705$	3078.58	+	9553.93i	0.164463	+	0.510386i
$706$	4026.78			0.214660
$707$	−16592.5			−0.882640
$708$	−3493.61	+	33443.6i	−0.185449	+	1.77527i
$709$	29479.6			1.56153			0.780767	−	0.624822i	$-0.214828\pi$
$709$	29479.6			1.56153			0.780767	+	0.624822i	$0.214828\pi$
$710$	46114.6			2.43754
$711$	14645.2	−	10531.9i	0.772489	−	0.555523i
$712$	14970.8			0.787997
$713$		−	4799.41i		−	0.252089i
$714$	−738.444	−	2291.65i	−0.0387053	−	0.120116i
$715$	−11007.0			−0.575716
$716$	41370.3			2.15933
$717$	7515.35	+	23322.8i	0.391445	+	1.21479i
$718$		−	32713.3i		−	1.70035i
$719$	17184.2			0.891325			0.445663	−	0.895201i	$-0.352968\pi$
$719$	17184.2			0.891325			0.445663	+	0.895201i	$0.352968\pi$
$720$	−6178.54	−	8591.64i	−0.319806	−	0.444710i
$721$		−	3151.78i		−	0.162799i
$722$	−43433.0			−2.23879
$723$	−551.529	+	177.720i	−0.0283701	+	0.00914175i
$724$	20152.0			1.03445
$725$			705.573i			0.0361439i
$726$	−27127.4	+	8741.30i	−1.38676	+	0.446860i
$727$	7341.84			0.374544			0.187272	−	0.982308i	$-0.440035\pi$
$727$	7341.84			0.374544			0.187272	+	0.982308i	$0.440035\pi$
$728$		−	14856.9i		−	0.756364i
$729$	−5808.47	−	18806.4i	−0.295101	−	0.955466i
$730$	−62684.3			−3.17815
$731$	−1326.58			−0.0671207
$732$	6201.00	+	19243.9i	0.313108	+	0.971687i
$733$	−24371.5			−1.22808			−0.614040	−	0.789275i	$-0.710457\pi$
$733$	−24371.5			−1.22808			−0.614040	+	0.789275i	$0.710457\pi$
$734$			47084.0i			2.36771i
$735$	−6359.01	−	19734.3i	−0.319123	−	0.990353i
$736$	2486.71			0.124540
$737$			12442.3i			0.621870i
$738$	11324.2	+	15747.0i	0.564838	+	0.785443i
$739$		−	24359.0i		−	1.21253i	−0.795262	−	0.606265i	$-0.792667\pi$
$739$		−	24359.0i		−	1.21253i	0.795262	−	0.606265i	$-0.207333\pi$
$740$	−36272.8			−1.80191
$741$	−11199.8	−	34756.9i	−0.555242	−	1.72311i
$742$		−	24695.8i		−	1.22185i
$743$			13871.0i			0.684895i	0.939537	+	0.342447i	$0.111256\pi$
$743$			13871.0i			0.684895i	−0.939537	+	0.342447i	$0.888744\pi$
$744$	−10572.4	−	32809.8i	−0.520969	−	1.61675i
$745$		−	35593.1i		−	1.75038i
$746$	60840.7			2.98597
$747$	−25245.6	+	18154.9i	−1.23653	+	0.889229i
$748$			2015.70i			0.0985311i
$749$			4693.34i			0.228960i
$750$	−1930.11	−	5989.82i	−0.0939703	−	0.291623i
$751$			36319.4i			1.76473i	0.470563	+	0.882366i	$0.344051\pi$
$751$			36319.4i			1.76473i	−0.470563	+	0.882366i	$0.655949\pi$
$752$	3246.79			0.157445
$753$	−803.223	−	2492.69i	−0.0388726	−	0.120635i
$754$	−1706.89			−0.0824419
$755$	−11618.2			−0.560039
$756$	−10750.6	+	14572.1i	−0.517190	+	0.701033i
$757$	−2905.61			−0.139506			−0.0697530	−	0.997564i	$-0.522221\pi$
$757$	−2905.61			−0.139506			−0.0697530	+	0.997564i	$0.522221\pi$
$758$	−45907.8			−2.19980
$759$	1378.45	−	444.182i	0.0659219	−	0.0212421i
$760$			57360.8i			2.73776i
$761$		−	30835.4i		−	1.46883i	−0.678699	−	0.734416i	$-0.737456\pi$
$761$		−	30835.4i		−	1.46883i	0.678699	−	0.734416i	$-0.262544\pi$
$762$	29277.7	−	9434.22i	1.39189	−	0.448511i
$763$		−	16428.3i		−	0.779483i
$764$	−55822.8			−2.64345
$765$	−3635.38	+	2614.33i	−0.171814	+	0.123557i
$766$			31949.2i			1.50701i
$767$	22989.4	+	10151.2i	1.08227	+	0.477884i
$768$	31500.5	−	10150.5i	1.48005	−	0.476919i
$769$			25096.4i			1.17685i	0.808551	+	0.588426i	$0.200252\pi$
$769$			25096.4i			1.17685i	−0.808551	+	0.588426i	$0.799748\pi$
$770$		−	8468.73i		−	0.396353i
$771$	2209.32	+	6856.30i	0.103199	+	0.320264i
$772$	−4551.86			−0.212208
$773$	33445.3			1.55620			0.778100	−	0.628140i	$-0.216183\pi$
$773$	33445.3			1.55620			0.778100	+	0.628140i	$0.216183\pi$
$774$	9088.74	+	12638.5i	0.422078	+	0.586925i
$775$			24217.0i			1.12245i
$776$			44554.4i			2.06110i
$777$	2396.27	+	7436.46i	0.110638	+	0.343348i
$778$			32371.3i			1.49173i
$779$		−	19287.7i		−	0.887103i
$780$	−59804.2	+	19270.8i	−2.74530	+	0.884623i
$781$			8315.74i			0.380999i
$782$			1099.20i			0.0502652i
$783$	736.218	+	543.148i	0.0336019	+	0.0247899i
$784$	−6706.47			−0.305506
$785$	47529.9			2.16104
$786$	29482.4	−	9500.18i	1.33792	−	0.431120i
$787$	−8933.60			−0.404636			−0.202318	−	0.979320i	$-0.564847\pi$
$787$	−8933.60			−0.404636			−0.202318	+	0.979320i	$0.564847\pi$
$788$			71508.9i			3.23274i
$789$	12481.8	+	38735.4i	0.563199	+	1.74780i
$790$			48157.2i			2.16881i
$791$	−11295.1			−0.507721
$792$	8444.94	−	6073.04i	0.378886	−	0.272470i
$793$	15110.6			0.676661
$794$		−	35154.6i		−	1.57127i
$795$	−43715.5	+	14086.5i	−1.95023	+	0.628425i
$796$	−12921.9			−0.575384
$797$	9071.76			0.403185			0.201592	−	0.979470i	$-0.435388\pi$
$797$	9071.76			0.403185			0.201592	+	0.979470i	$0.435388\pi$
$798$	26741.9	−	8617.09i	1.18628	−	0.382258i
$799$		−	1373.82i		−	0.0608288i
$800$	−12547.5			−0.554525
$801$	−11071.9	+	7962.19i	−0.488398	+	0.351223i
$802$	20822.2			0.916780
$803$		−	11303.7i		−	0.496761i
$804$	21783.8	+	67602.9i	0.955542	+	2.96539i
$805$		−	2959.89i		−	0.129593i
$806$	−58584.5			−2.56024
$807$	3520.61	−	1134.45i	0.153570	−	0.0494852i
$808$	54407.1			2.36886
$809$	1584.99			0.0688815			0.0344407	−	0.999407i	$-0.489035\pi$
$809$	1584.99			0.0688815			0.0344407	+	0.999407i	$0.489035\pi$
$810$	49814.0	+	16723.3i	2.16085	+	0.725426i
$811$		−	11234.9i		−	0.486449i	−0.969970	−	0.243225i	$-0.921795\pi$
$811$		−	11234.9i		−	0.486449i	0.969970	−	0.243225i	$-0.0782052\pi$
$812$		−	841.710i		−	0.0363771i
$813$	12895.8	−	4155.44i	0.556305	−	0.179259i
$814$		−	10205.6i		−	0.439440i
$815$			49695.9i			2.13592i
$816$	444.225	+	1378.59i	0.0190576	+	0.0591424i
$817$		−	15480.2i		−	0.662891i
$818$		−	3159.42i		−	0.135045i
$819$	7901.61	+	10987.7i	0.337124	+	0.468792i
$820$	−33187.2			−1.41335
$821$	5078.49			0.215884			0.107942	−	0.994157i	$-0.465574\pi$
$821$	5078.49			0.215884			0.107942	+	0.994157i	$0.465574\pi$
$822$	−8030.19	−	24920.5i	−0.340736	−	1.05743i
$823$		−	21231.6i		−	0.899255i	−0.893216	−	0.449627i	$-0.851557\pi$
$823$		−	21231.6i		−	0.899255i	0.893216	−	0.449627i	$-0.148443\pi$
$824$			10334.7i			0.436926i
$825$	−6955.43	+	2241.26i	−0.293524	+	0.0945827i
$826$	−7810.28	+	17688.0i	−0.329000	+	0.745090i
$827$			35632.1i			1.49825i	0.662431	+	0.749123i	$0.269525\pi$
$827$			35632.1i			1.49825i	−0.662431	+	0.749123i	$0.730475\pi$
$828$	6711.90	−	4826.76i	0.281709	−	0.202586i
$829$	−12717.0			−0.532787			−0.266393	−	0.963864i	$-0.585832\pi$
$829$	−12717.0			−0.532787			−0.266393	+	0.963864i	$0.585832\pi$
$830$		−	83013.7i		−	3.47163i
$831$	25009.4	−	8058.83i	1.04400	−	0.336411i
$832$		−	41740.5i		−	1.73929i
$833$			2837.71i			0.118032i
$834$	25292.3	−	8149.99i	1.05012	−	0.338383i
$835$	−22956.9			−0.951443
$836$	−23521.7			−0.973104
$837$	25268.8	+	18642.2i	1.04351	+	0.769853i
$838$	−2911.09			−0.120002
$839$	8378.65			0.344771			0.172386	−	0.985030i	$-0.444852\pi$
$839$	8378.65			0.344771			0.172386	+	0.985030i	$0.444852\pi$
$840$	−6520.18	−	20234.4i	−0.267819	−	0.831137i
$841$	24346.5			0.998256
$842$		−	33840.9i		−	1.38508i
$843$	891.054	+	2765.26i	0.0364051	+	0.112978i
$844$			34273.2i			1.39779i
$845$			13409.1i			0.545903i
$846$	−13088.5	+	9412.41i	−0.531906	+	0.382512i
$847$	−10504.0			−0.426117
$848$			14856.2i			0.601609i
$849$	6414.07	+	19905.1i	0.259282	+	0.804644i
$850$		−	5546.37i		−	0.223811i
$851$		−	3566.93i		−	0.143681i
$852$	14559.1	+	45182.0i	0.585429	+	1.81679i
$853$	−21970.7			−0.881904			−0.440952	−	0.897531i	$-0.645359\pi$
$853$	−21970.7			−0.881904			−0.440952	+	0.897531i	$0.645359\pi$
$854$			11626.1i			0.465849i
$855$	−30507.3	−	42422.2i	−1.22026	−	1.69685i
$856$		−	15389.5i		−	0.614490i
$857$	20745.2			0.826887			0.413444	−	0.910530i	$-0.364326\pi$
$857$	20745.2			0.826887			0.413444	+	0.910530i	$0.364326\pi$
$858$	−5421.95	−	16826.2i	−0.215737	−	0.669508i
$859$		−	34709.1i		−	1.37865i	−0.724453	−	0.689324i	$-0.757907\pi$
$859$		−	34709.1i		−	1.37865i	0.724453	−	0.689324i	$-0.242093\pi$
$860$	−26635.8			−1.05613
$861$	2192.42	+	6803.87i	0.0867801	+	0.269309i
$862$	−62884.5			−2.48475
$863$	−47925.2			−1.89038			−0.945188	−	0.326528i	$-0.894121\pi$
$863$	−47925.2			−1.89038			−0.945188	+	0.326528i	$0.894121\pi$
$864$	−9659.00	+	13092.4i	−0.380331	+	0.515525i
$865$		−	66671.1i		−	2.62067i
$866$	−27918.6			−1.09551
$867$	−23715.0	+	7641.74i	−0.928956	+	0.299339i
$868$		−	28889.5i		−	1.12969i
$869$	−8684.08			−0.338996
$870$	−2324.71	+	749.095i	−0.0905919	+	0.0291916i
$871$	53082.8			2.06503
$872$			53868.7i			2.09200i
$873$	−23696.2	−	32951.0i	−0.918665	−	1.27746i
$874$	−12826.9			−0.496424
$875$		−	2319.32i		−	0.0896082i
$876$	−19790.4	−	61416.5i	−0.763304	−	2.36880i
$877$	13299.1			0.512064			0.256032	−	0.966668i	$-0.417585\pi$
$877$	13299.1			0.512064			0.256032	+	0.966668i	$0.417585\pi$
$878$	43615.0			1.67646
$879$	1174.24	+	3644.10i	0.0450583	+	0.139832i
$880$			5094.52i			0.195155i
$881$	20829.3			0.796546			0.398273	−	0.917267i	$-0.369610\pi$
$881$	20829.3			0.796546			0.398273	+	0.917267i	$0.369610\pi$
$882$	27035.2	−	19441.9i	1.03211	−	0.742227i
$883$	14321.4			0.545815			0.272908	−	0.962040i	$-0.412015\pi$
$883$	14321.4			0.545815			0.272908	+	0.962040i	$0.412015\pi$
$884$	8599.60			0.327190
$885$	35765.6	+	3736.17i	1.35847	+	0.141909i
$886$	41015.2			1.55523
$887$	41356.9			1.56554			0.782768	−	0.622314i	$-0.213807\pi$
$887$	41356.9			1.56554			0.782768	+	0.622314i	$0.213807\pi$
$888$	−7857.39	−	24384.3i	−0.296933	−	0.921489i
$889$	11336.6			0.427691
$890$		−	36407.2i		−	1.37121i
$891$	−3015.67	+	8982.85i	−0.113388	+	0.337752i
$892$	−17653.7			−0.662658
$893$	16031.4			0.600752
$894$	54410.8	−	17532.9i	2.03554	−	0.655915i
$895$		−	44242.6i		−	1.65237i
$896$	23729.1			0.884746
$897$	−1895.02	−	5880.92i	−0.0705383	−	0.218905i
$898$			4495.84i			0.167069i
$899$	−1459.57			−0.0541485
$900$	−33867.0	+	24354.9i	−1.25433	+	0.902035i
$901$	6286.12			0.232432
$902$		−	9337.40i		−	0.344680i
$903$	1759.62	+	5460.74i	0.0648467	+	0.201242i
$904$	37036.8			1.36264
$905$		−	21551.1i		−	0.791584i
$906$	−5723.05	−	17760.6i	−0.209863	−	0.651278i
$907$	−47348.2			−1.73338			−0.866688	−	0.498850i	$-0.833756\pi$
$907$	−47348.2			−1.73338			−0.866688	+	0.498850i	$0.833756\pi$
$908$	22777.0			0.832469
$909$	−40237.7	+	28936.3i	−1.46821	+	1.05584i
$910$	−36130.2			−1.31616
$911$			15642.4i			0.568886i	0.958693	+	0.284443i	$0.0918086\pi$
$911$			15642.4i			0.568886i	−0.958693	+	0.284443i	$0.908191\pi$
$912$	−16087.1	+	5183.77i	−0.584097	+	0.188215i
$913$	14969.7			0.542633
$914$			49631.4i			1.79613i
$915$	20580.0	−	6631.52i	0.743555	−	0.239597i
$916$			12792.5i			0.461436i
$917$	11415.9			0.411107
$918$	−5787.27	−	4269.58i	−0.208070	−	0.153505i
$919$			44271.9i			1.58911i	0.607189	+	0.794557i	$0.292297\pi$
$919$			44271.9i			1.58911i	−0.607189	+	0.794557i	$0.707703\pi$
$920$			9705.53i			0.347806i
$921$	2238.57	−	721.340i	0.0800907	−	0.0258078i
$922$			11360.8i			0.405801i
$923$	35477.5			1.26518
$924$	8297.45	−	2673.70i	0.295418	−	0.0951931i
$925$			17998.1i			0.639755i
$926$		−	42982.8i		−	1.52538i
$927$	−5496.50	−	7643.22i	−0.194745	−	0.270805i
$928$		−	756.245i		−	0.0267510i
$929$	−26327.2			−0.929781			−0.464891	−	0.885368i	$-0.653906\pi$
$929$	−26327.2			−0.929781			−0.464891	+	0.885368i	$0.653906\pi$
$930$	−79789.5	+	25710.7i	−2.81334	+	0.906547i
$931$	−33114.0			−1.16570
$932$	59590.5			2.09437
$933$	−5879.71	−	18246.8i	−0.206316	−	0.640272i
$934$	9468.75			0.331721
$935$	2155.65			0.0753980
$936$	−25909.5	−	36028.7i	−0.904784	−	1.25816i
$937$		−	21202.5i		−	0.739226i	−0.929186	−	0.369613i	$-0.879490\pi$
$937$		−	21202.5i		−	0.739226i	0.929186	−	0.369613i	$-0.120510\pi$
$938$			40841.8i			1.42168i
$939$	17064.4	+	52957.0i	0.593053	+	1.84045i
$940$		−	27584.3i		−	0.957129i
$941$	−14857.3			−0.514700			−0.257350	−	0.966318i	$-0.582849\pi$
$941$	−14857.3			−0.514700			−0.257350	+	0.966318i	$0.582849\pi$
$942$	23412.9	+	72658.5i	0.809802	+	2.51310i
$943$		−	3263.50i		−	0.112698i
$944$	4698.42	−	10640.5i	0.161992	−	0.366865i
$945$	15583.8	+	11497.0i	0.536444	+	0.395764i
$946$		−	7494.13i		−	0.257564i
$947$			37914.2i			1.30100i	0.759507	+	0.650499i	$0.225440\pi$
$947$			37914.2i			1.30100i	−0.759507	+	0.650499i	$0.774560\pi$
$948$	−47183.3	+	15204.0i	−1.61650	+	0.520888i
$949$	−48225.1			−1.64958
$950$	64722.0			2.21038
$951$	−7427.45	−	23050.0i	−0.253261	−	0.785960i
$952$			2909.63i			0.0990565i
$953$			32091.4i			1.09081i	0.838172	+	0.545406i	$0.183624\pi$
$953$			32091.4i			1.09081i	−0.838172	+	0.545406i	$0.816376\pi$
$954$	−43067.9	−	59888.6i	−1.46161	−	2.03246i
$955$			59698.4i			2.02282i
$956$		−	67338.1i		−	2.27811i
$957$	−135.082	−	419.209i	−0.00456280	−	0.0141600i
$958$			27404.7i			0.924224i
$959$		−	9649.47i		−	0.324919i
$960$	−18318.5	−	56848.8i	−0.615862	−	1.91124i
$961$	−20305.1			−0.681584
$962$	−43540.1			−1.45924
$963$	8184.89	+	11381.6i	0.273888	+	0.380859i
$964$	1592.39			0.0532026
$965$			4867.88i			0.162386i
$966$	4524.77	−	1458.02i	0.150706	−	0.0485623i
$967$		−	38746.0i		−	1.28851i	−0.764812	−	0.644254i	$-0.777168\pi$
$967$		−	38746.0i		−	1.28851i	0.764812	−	0.644254i	$-0.222832\pi$
$968$	34442.7			1.14363
$969$	2193.41	+	6806.93i	0.0727167	+	0.225666i
$970$	108351.			3.58654
$971$			35781.2i			1.18257i	0.806463	+	0.591284i	$0.201379\pi$
$971$			35781.2i			1.18257i	−0.806463	+	0.591284i	$0.798621\pi$
$972$	−658.005	+	54086.4i	−0.0217135	+	1.78479i
$973$	9793.43			0.322675
$974$	−58686.3			−1.93063
$975$	9561.92	+	29674.0i	0.314079	+	0.974697i
$976$		−	6993.86i		−	0.229373i
$977$	−20376.5			−0.667250			−0.333625	−	0.942706i	$-0.608272\pi$
$977$	−20376.5			−0.667250			−0.333625	+	0.942706i	$0.608272\pi$
$978$	−75969.8	+	24479.9i	−2.48389	+	0.800389i
$979$	6565.23			0.214326
$980$			56977.2i			1.85722i
$981$	−28650.0	−	39839.6i	−0.932440	−	1.29661i
$982$		−	71921.3i		−	2.33717i
$983$	−47769.3			−1.54995			−0.774977	−	0.631990i	$-0.782239\pi$
$983$	−47769.3			−1.54995			−0.774977	+	0.631990i	$0.782239\pi$
$984$	−7188.99	−	22310.0i	−0.232903	−	0.722781i
$985$	76473.6			2.47376
$986$	334.284			0.0107969
$987$	−5655.20	+	1822.29i	−0.182378	+	0.0587680i
$988$			100351.i			3.23137i
$989$		−	2619.26i		−	0.0842141i
$990$	−14768.9	−	20537.1i	−0.474129	−	0.659305i
$991$		−	6620.75i		−	0.212225i	−0.994354	−	0.106113i	$-0.966160\pi$
$991$		−	6620.75i		−	0.212225i	0.994354	−	0.106113i	$-0.0338404\pi$
$992$		−	25956.1i		−	0.830754i
$993$	−44059.6	+	14197.4i	−1.40804	+	0.453717i
$994$			27296.3i			0.871013i
$995$			13819.1i			0.440295i
$996$	81334.8	−	26208.7i	2.58754	−	0.833789i
$997$	−49690.6			−1.57845			−0.789226	−	0.614102i	$-0.789518\pi$
$997$	−49690.6			−1.57845			−0.789226	+	0.614102i	$0.789518\pi$
$998$	−1610.80			−0.0510913
$999$	18779.8	+	13854.9i	0.594761	+	0.438788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.6	yes	52
3.2	odd	2	inner	177.4.d.c.176.47	yes	52
59.58	odd	2	inner	177.4.d.c.176.48	yes	52
177.176	even	2	inner	177.4.d.c.176.5	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.5	✓	52	177.176	even	2	inner
177.4.d.c.176.6	yes	52	1.1	even	1	trivial
177.4.d.c.176.47	yes	52	3.2	odd	2	inner
177.4.d.c.176.48	yes	52	59.58	odd	2	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.72011 q^{2} +(-4.94573 + 1.59367i) q^{3} +14.2794 q^{4} -15.2708i q^{5} +(23.3444 - 7.52230i) q^{6} +9.03916 q^{7} -29.6395 q^{8} +(21.9204 - 15.7637i) q^{9} +O(q^{10})\)	\(q-4.72011 q^{2} +(-4.94573 + 1.59367i) q^{3} +14.2794 q^{4} -15.2708i q^{5} +(23.3444 - 7.52230i) q^{6} +9.03916 q^{7} -29.6395 q^{8} +(21.9204 - 15.7637i) q^{9} +72.0799i q^{10} -12.9980 q^{11} +(-70.6221 + 22.7567i) q^{12} +55.4535i q^{13} -42.6658 q^{14} +(24.3366 + 75.5253i) q^{15} +25.6664 q^{16} -10.8602i q^{17} +(-103.467 + 74.4065i) q^{18} +126.731 q^{19} -218.058i q^{20} +(-44.7052 + 14.4054i) q^{21} +61.3519 q^{22} +21.4430 q^{23} +(146.589 - 47.2356i) q^{24} -108.198 q^{25} -261.746i q^{26} +(-83.2902 + 112.897i) q^{27} +129.074 q^{28} -6.52115i q^{29} +(-114.872 - 356.487i) q^{30} -223.822i q^{31} +115.968 q^{32} +(64.2845 - 20.7145i) q^{33} +51.2615i q^{34} -138.035i q^{35} +(313.011 - 225.097i) q^{36} -166.344i q^{37} -598.183 q^{38} +(-88.3746 - 274.258i) q^{39} +452.619i q^{40} -152.194i q^{41} +(211.013 - 67.9952i) q^{42} -122.150i q^{43} -185.604 q^{44} +(-240.725 - 334.743i) q^{45} -101.213 q^{46} +126.500 q^{47} +(-126.939 + 40.9038i) q^{48} -261.294 q^{49} +510.705 q^{50} +(17.3076 + 53.7117i) q^{51} +791.843i q^{52} +578.820i q^{53} +(393.139 - 532.886i) q^{54} +198.490i q^{55} -267.916 q^{56} +(-626.776 + 201.967i) q^{57} +30.7805i q^{58} +(183.057 - 414.571i) q^{59} +(347.513 + 1078.46i) q^{60} -272.491i q^{61} +1056.46i q^{62} +(198.142 - 142.491i) q^{63} -752.713 q^{64} +846.820 q^{65} +(-303.430 + 97.7748i) q^{66} -957.249i q^{67} -155.078i q^{68} +(-106.051 + 34.1731i) q^{69} +651.541i q^{70} -639.771i q^{71} +(-649.711 + 467.229i) q^{72} +869.650i q^{73} +785.164i q^{74} +(535.116 - 172.431i) q^{75} +1809.64 q^{76} -117.491 q^{77} +(417.138 + 1294.53i) q^{78} +668.109 q^{79} -391.947i q^{80} +(232.010 - 691.095i) q^{81} +718.373i q^{82} -1151.69 q^{83} +(-638.364 + 205.701i) q^{84} -165.845 q^{85} +576.561i q^{86} +(10.3926 + 32.2518i) q^{87} +385.254 q^{88} -505.096 q^{89} +(1136.25 + 1580.02i) q^{90} +501.253i q^{91} +306.194 q^{92} +(356.698 + 1106.96i) q^{93} -597.093 q^{94} -1935.28i q^{95} +(-573.546 + 184.815i) q^{96} -1503.21i q^{97} +1233.33 q^{98} +(-284.921 + 204.897i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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