LMFDB - Embedded newform 177.3.h.a.5.11

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			5.11
Character	$\chi$	$=$	177.5
Dual form			177.3.h.a.71.11

$q$-expansion

$f(q)$	$=$	$q+(-0.561287 + 1.66584i) q^{2} +(2.68858 - 1.33099i) q^{3} +(0.724387 + 0.550665i) q^{4} +(7.94437 + 3.16532i) q^{5} +(0.708151 + 5.22582i) q^{6} +(-11.0072 + 5.09247i) q^{7} +(-7.14376 + 4.84359i) q^{8} +(5.45694 - 7.15694i) q^{9} +O(q^{10})$	\(q+(-0.561287 + 1.66584i) q^{2} +(2.68858 - 1.33099i) q^{3} +(0.724387 + 0.550665i) q^{4} +(7.94437 + 3.16532i) q^{5} +(0.708151 + 5.22582i) q^{6} +(-11.0072 + 5.09247i) q^{7} +(-7.14376 + 4.84359i) q^{8} +(5.45694 - 7.15694i) q^{9} +(-9.73200 + 11.4574i) q^{10} +(5.78046 + 1.60494i) q^{11} +(2.68050 + 0.516355i) q^{12} +(3.73316 - 7.04149i) q^{13} +(-2.30505 - 21.1946i) q^{14} +(25.5721 - 2.06363i) q^{15} +(-3.08522 - 11.1120i) q^{16} +(5.02021 - 10.8510i) q^{17} +(8.85943 + 13.1075i) q^{18} +(-17.0313 + 3.74887i) q^{19} +(4.01176 + 6.66760i) q^{20} +(-22.8157 + 28.3420i) q^{21} +(-5.91807 + 8.72850i) q^{22} +(1.06856 + 0.175182i) q^{23} +(-12.7598 + 22.5306i) q^{24} +(34.9438 + 33.1005i) q^{25} +(9.63463 + 10.1712i) q^{26} +(5.14560 - 26.5051i) q^{27} +(-10.7777 - 2.37235i) q^{28} +(-11.2914 - 33.5116i) q^{29} +(-10.9156 + 43.7573i) q^{30} +(28.8402 + 6.34821i) q^{31} +(-14.2308 - 0.771569i) q^{32} +(17.6774 - 3.37873i) q^{33} +(15.2583 + 14.4534i) q^{34} +(-103.564 + 5.61510i) q^{35} +(7.89401 - 2.17946i) q^{36} +(-15.4779 + 22.8281i) q^{37} +(3.31443 - 30.4756i) q^{38} +(0.664760 - 23.9004i) q^{39} +(-72.0841 + 15.8669i) q^{40} +(64.5113 - 10.5761i) q^{41} +(-34.4071 - 53.9153i) q^{42} +(-1.67802 - 6.04366i) q^{43} +(3.30351 + 4.34569i) q^{44} +(66.0059 - 39.5844i) q^{45} +(-0.891595 + 1.68173i) q^{46} +(-28.3644 + 11.3014i) q^{47} +(-23.0848 - 25.7690i) q^{48} +(63.5031 - 74.7616i) q^{49} +(-74.7537 + 39.6319i) q^{50} +(-0.945332 - 35.8557i) q^{51} +(6.58175 - 3.04504i) q^{52} +(41.4105 - 35.1744i) q^{53} +(41.2652 + 23.4488i) q^{54} +(40.8419 + 31.0472i) q^{55} +(53.9669 - 89.6936i) q^{56} +(-40.8003 + 32.7476i) q^{57} +62.1626 q^{58} +(9.22505 + 58.2743i) q^{59} +(19.6605 + 12.5868i) q^{60} +(-35.2383 - 11.8732i) q^{61} +(-26.7628 + 44.4801i) q^{62} +(-23.6190 + 106.567i) q^{63} +(26.3471 - 66.1261i) q^{64} +(51.9462 - 44.1235i) q^{65} +(-4.29367 + 31.3442i) q^{66} +(-62.0406 - 91.5030i) q^{67} +(9.61185 - 5.09588i) q^{68} +(3.10608 - 0.951254i) q^{69} +(48.7756 - 175.674i) q^{70} +(-56.7190 + 22.5989i) q^{71} +(-4.31773 + 77.5586i) q^{72} +(-129.369 + 14.0698i) q^{73} +(-29.3405 - 38.5968i) q^{74} +(138.006 + 42.4836i) q^{75} +(-14.4016 - 6.66290i) q^{76} +(-71.7997 + 11.7710i) q^{77} +(39.4412 + 14.5224i) q^{78} +(74.7511 - 44.9762i) q^{79} +(10.6628 - 98.0433i) q^{80} +(-21.4437 - 78.1100i) q^{81} +(-18.5913 + 113.402i) q^{82} +(72.8133 - 3.94782i) q^{83} +(-32.1343 + 7.96676i) q^{84} +(74.2294 - 70.3138i) q^{85} +(11.0096 + 0.596925i) q^{86} +(-74.9613 - 75.0699i) q^{87} +(-49.0679 + 16.5329i) q^{88} +(-45.7688 - 135.837i) q^{89} +(28.8931 + 132.174i) q^{90} +(-5.23305 + 96.5180i) q^{91} +(0.677586 + 0.715319i) q^{92} +(85.9887 - 21.3183i) q^{93} +(-2.90578 - 53.5939i) q^{94} +(-147.169 - 24.1272i) q^{95} +(-39.2875 + 16.8666i) q^{96} +(-72.0110 - 7.83166i) q^{97} +(88.8976 + 147.749i) q^{98} +(43.0300 - 32.6124i) 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 $

$2$	−0.561287	+	1.66584i	−0.280644	+	0.832921i	0.710917	+	0.703276i	$0.248280\pi$
$2$	−0.561287	+	1.66584i	−0.280644	+	0.832921i	−0.991561	+	0.129645i	$0.958616\pi$
$3$	2.68858	−	1.33099i	0.896194	−	0.443663i
$3$	2.68858	−	1.33099i	0.896194	−	0.443663i
$4$	0.724387	+	0.550665i	0.181097	+	0.137666i
$5$	7.94437	+	3.16532i	1.58887	+	0.633065i	0.986294	−	0.164995i	$-0.0527606\pi$
$5$	7.94437	+	3.16532i	1.58887	+	0.633065i	0.602579	+	0.798059i	$0.294140\pi$
$6$	0.708151	+	5.22582i	0.118025	+	0.870970i
$7$	−11.0072	+	5.09247i	−1.57246	+	0.727496i	−0.995976	−	0.0896159i	$-0.971436\pi$
$7$	−11.0072	+	5.09247i	−1.57246	+	0.727496i	−0.576480	+	0.817112i	$0.695574\pi$
$8$	−7.14376	+	4.84359i	−0.892969	+	0.605448i
$9$	5.45694	−	7.15694i	0.606326	−	0.795216i
$10$	−9.73200	+	11.4574i	−0.973200	+	1.14574i
$11$	5.78046	+	1.60494i	0.525496	+	0.145903i	0.520138	−	0.854082i	$-0.325881\pi$
$11$	5.78046	+	1.60494i	0.525496	+	0.145903i	0.00535851	+	0.999986i	$0.498294\pi$
$12$	2.68050	+	0.516355i	0.223375	+	0.0430296i
$13$	3.73316	−	7.04149i	0.287166	−	0.541653i	−0.697396	−	0.716686i	$-0.745658\pi$
$13$	3.73316	−	7.04149i	0.287166	−	0.541653i	0.984563	+	0.175033i	$0.0560031\pi$
$14$	−2.30505	−	21.1946i	−0.164646	−	1.51390i
$15$	25.5721	−	2.06363i	1.70481	−	0.137576i
$16$	−3.08522	−	11.1120i	−0.192826	−	0.694498i
$17$	5.02021	−	10.8510i	0.295307	−	0.638295i	−0.701957	−	0.712219i	$-0.747690\pi$
$17$	5.02021	−	10.8510i	0.295307	−	0.638295i	0.997264	+	0.0739244i	$0.0235524\pi$
$18$	8.85943	+	13.1075i	0.492190	+	0.728194i
$19$	−17.0313	+	3.74887i	−0.896384	+	0.197309i	−0.639188	−	0.769050i	$-0.720730\pi$
$19$	−17.0313	+	3.74887i	−0.896384	+	0.197309i	−0.257196	+	0.966359i	$0.582798\pi$
$20$	4.01176	+	6.66760i	0.200588	+	0.333380i
$21$	−22.8157	+	28.3420i	−1.08646	+	1.34962i
$22$	−5.91807	+	8.72850i	−0.269003	+	0.396750i
$23$	1.06856	+	0.175182i	0.0464592	+	0.00761660i	0.184967	−	0.982745i	$-0.440782\pi$
$23$	1.06856	+	0.175182i	0.0464592	+	0.00761660i	−0.138508	+	0.990361i	$0.544231\pi$
$24$	−12.7598	+	22.5306i	−0.531659	+	0.938777i
$25$	34.9438	+	33.1005i	1.39775	+	1.32402i
$26$	9.63463	+	10.1712i	0.370563	+	0.391198i
$27$	5.14560	−	26.5051i	0.190578	−	0.981672i
$28$	−10.7777	−	2.37235i	−0.384918	−	0.0847269i
$29$	−11.2914	−	33.5116i	−0.389357	−	1.15557i	−0.945818	−	0.324697i	$-0.894738\pi$
$29$	−11.2914	−	33.5116i	−0.389357	−	1.15557i	0.556461	−	0.830874i	$-0.312159\pi$
$30$	−10.9156	+	43.7573i	−0.363853	+	1.45858i
$31$	28.8402	+	6.34821i	0.930330	+	0.204781i	0.654185	−	0.756335i	$-0.273012\pi$
$31$	28.8402	+	6.34821i	0.930330	+	0.204781i	0.276145	+	0.961116i	$0.410943\pi$
$32$	−14.2308	−	0.771569i	−0.444711	−	0.0241115i
$33$	17.6774	−	3.37873i	0.535679	−	0.102386i
$34$	15.2583	+	14.4534i	0.448773	+	0.425100i
$35$	−103.564	+	5.61510i	−2.95899	+	0.160432i
$36$	7.89401	−	2.17946i	0.219278	−	0.0605405i
$37$	−15.4779	+	22.8281i	−0.418321	+	0.616977i	−0.977212	−	0.212264i	$-0.931916\pi$
$37$	−15.4779	+	22.8281i	−0.418321	+	0.616977i	0.558892	+	0.829241i	$0.311227\pi$
$38$	3.31443	−	30.4756i	0.0872217	−	0.801990i
$39$	0.664760	−	23.9004i	0.0170451	−	0.612831i
$40$	−72.0841	+	15.8669i	−1.80210	+	0.396673i
$41$	64.5113	−	10.5761i	1.57345	−	0.257953i	0.689058	−	0.724706i	$-0.258024\pi$
$41$	64.5113	−	10.5761i	1.57345	−	0.257953i	0.884388	+	0.466753i	$0.154576\pi$
$42$	−34.4071	−	53.9153i	−0.819216	−	1.28370i
$43$	−1.67802	−	6.04366i	−0.0390236	−	0.140550i	0.941472	−	0.337091i	$-0.109443\pi$
$43$	−1.67802	−	6.04366i	−0.0390236	−	0.140550i	−0.980496	+	0.196541i	$0.937029\pi$
$44$	3.30351	+	4.34569i	0.0750798	+	0.0987657i
$45$	66.0059	−	39.5844i	1.46680	−	0.879654i
$46$	−0.891595	+	1.68173i	−0.0193825	+	0.0365593i
$47$	−28.3644	+	11.3014i	−0.603498	+	0.240455i	−0.651817	−	0.758377i	$-0.725993\pi$
$47$	−28.3644	+	11.3014i	−0.603498	+	0.240455i	0.0483191	+	0.998832i	$0.484614\pi$
$48$	−23.0848	−	25.7690i	−0.480933	−	0.536855i
$49$	63.5031	−	74.7616i	1.29598	−	1.52575i
$50$	−74.7537	+	39.6319i	−1.49507	+	0.792638i
$51$	−0.945332	−	35.8557i	−0.0185359	−	0.703052i
$52$	6.58175	−	3.04504i	0.126572	−	0.0585585i
$53$	41.4105	−	35.1744i	0.781331	−	0.663668i	−0.165208	−	0.986259i	$-0.552830\pi$
$53$	41.4105	−	35.1744i	0.781331	−	0.663668i	0.946539	+	0.322590i	$0.104554\pi$
$54$	41.2652	+	23.4488i	0.764171	+	0.434236i
$55$	40.8419	+	31.0472i	0.742581	+	0.564495i
$56$	53.9669	−	89.6936i	0.963694	−	1.60167i
$57$	−40.8003	+	32.7476i	−0.715795	+	0.574520i
$58$	62.1626			1.07177
$59$	9.22505	+	58.2743i	0.156357	+	0.987701i
$59$	9.22505	+	58.2743i	0.156357	+	0.987701i
$60$	19.6605	+	12.5868i	0.327674	+	0.209780i
$61$	−35.2383	−	11.8732i	−0.577677	−	0.194642i	0.0152704	−	0.999883i	$-0.495139\pi$
$61$	−35.2383	−	11.8732i	−0.577677	−	0.194642i	−0.592947	+	0.805241i	$0.702036\pi$
$62$	−26.7628	+	44.4801i	−0.431658	+	0.717421i
$63$	−23.6190	+	106.567i	−0.374905	+	1.69154i
$64$	26.3471	−	66.1261i	0.411673	−	1.03322i
$65$	51.9462	−	44.1235i	0.799172	−	0.678823i
$66$	−4.29367	+	31.3442i	−0.0650556	+	0.474912i
$67$	−62.0406	−	91.5030i	−0.925979	−	1.36572i	−0.930722	−	0.365728i	$-0.880820\pi$
$67$	−62.0406	−	91.5030i	−0.925979	−	1.36572i	0.00474326	−	0.999989i	$-0.498490\pi$
$68$	9.61185	−	5.09588i	0.141351	−	0.0749394i
$69$	3.10608	−	0.951254i	0.0450156	−	0.0137863i
$70$	48.7756	−	175.674i	0.696794	−	2.50962i
$71$	−56.7190	+	22.5989i	−0.798859	+	0.318294i	−0.733607	−	0.679574i	$-0.762164\pi$
$71$	−56.7190	+	22.5989i	−0.798859	+	0.318294i	−0.0652522	+	0.997869i	$0.520785\pi$
$72$	−4.31773	+	77.5586i	−0.0599685	+	1.07720i
$73$	−129.369	+	14.0698i	−1.77218	+	0.192737i	−0.935111	−	0.354354i	$-0.884701\pi$
$73$	−129.369	+	14.0698i	−1.77218	+	0.192737i	−0.837073	+	0.547091i	$0.815735\pi$
$74$	−29.3405	−	38.5968i	−0.396494	−	0.521579i
$75$	138.006	+	42.4836i	1.84007	+	0.566448i
$76$	−14.4016	−	6.66290i	−0.189495	−	0.0876698i
$77$	−71.7997	+	11.7710i	−0.932464	+	0.152870i
$78$	39.4412	+	14.5224i	0.505656	+	0.186184i
$79$	74.7511	−	44.9762i	0.946216	−	0.569319i	0.0432655	−	0.999064i	$-0.486224\pi$
$79$	74.7511	−	44.9762i	0.946216	−	0.569319i	0.902951	+	0.429744i	$0.141396\pi$
$80$	10.6628	−	98.0433i	0.133286	−	1.22554i
$81$	−21.4437	−	78.1100i	−0.264737	−	0.964321i
$82$	−18.5913	+	113.402i	−0.226723	+	1.38295i
$83$	72.8133	−	3.94782i	0.877269	−	0.0475641i	0.389999	−	0.920815i	$-0.372475\pi$
$83$	72.8133	−	3.94782i	0.877269	−	0.0475641i	0.487270	+	0.873251i	$0.337993\pi$
$84$	−32.1343	+	7.96676i	−0.382552	+	0.0948423i
$85$	74.2294	−	70.3138i	0.873287	−	0.827221i
$86$	11.0096	+	0.596925i	0.128019	+	0.00694099i
$87$	−74.9613	−	75.0699i	−0.861624	−	0.862872i
$88$	−49.0679	+	16.5329i	−0.557589	+	0.187874i
$89$	−45.7688	−	135.837i	−0.514257	−	1.52626i	−0.818982	−	0.573819i	$-0.805461\pi$
$89$	−45.7688	−	135.837i	−0.514257	−	1.52626i	0.304726	−	0.952440i	$-0.401435\pi$
$90$	28.8931	+	132.174i	0.321034	+	1.46860i
$91$	−5.23305	+	96.5180i	−0.0575061	+	1.06064i
$92$	0.677586	+	0.715319i	0.00736506	+	0.00777520i
$93$	85.9887	−	21.3183i	0.924610	−	0.229230i
$94$	−2.90578	−	53.5939i	−0.0309125	−	0.570148i
$95$	−147.169	−	24.1272i	−1.54915	−	0.253970i
$96$	−39.2875	+	16.8666i	−0.409245	+	0.175693i
$97$	−72.0110	−	7.83166i	−0.742381	−	0.0807388i	−0.270891	−	0.962610i	$-0.587318\pi$
$97$	−72.0110	−	7.83166i	−0.742381	−	0.0807388i	−0.471490	+	0.881871i	$0.656284\pi$
$98$	88.8976	+	147.749i	0.907118	+	1.50764i
$99$	43.0300	−	32.6124i	0.434647	−	0.329418i
$100$	7.08554	+	43.2199i	0.0708554	+	0.432199i
$101$	4.32263	−	9.34320i	0.0427983	−	0.0925070i	−0.884997	−	0.465597i	$-0.845840\pi$
$101$	4.32263	−	9.34320i	0.0427983	−	0.0925070i	0.927795	+	0.373090i	$0.121702\pi$
$102$	60.2605	+	18.5506i	0.590789	+	0.181868i
$103$	−46.3041	+	35.1995i	−0.449554	+	0.341742i	−0.805328	−	0.592830i	$-0.798011\pi$
$103$	−46.3041	+	35.1995i	−0.449554	+	0.341742i	0.355773	+	0.934572i	$0.384218\pi$
$104$	7.43727	+	68.3845i	0.0715122	+	0.657544i
$105$	−270.968	+	152.940i	−2.58065	+	1.45657i
$106$	35.3518	+	88.7263i	0.333508	+	0.837041i
$107$	19.4673	+	5.40507i	0.181937	+	0.0505147i	0.357302	−	0.933989i	$-0.383697\pi$
$107$	19.4673	+	5.40507i	0.181937	+	0.0505147i	−0.175365	+	0.984504i	$0.556110\pi$
$108$	18.3229	−	16.3665i	0.169656	−	0.151542i
$109$	88.8228	+	167.538i	0.814888	+	1.53704i	0.843298	+	0.537446i	$0.180611\pi$
$109$	88.8228	+	167.538i	0.814888	+	1.53704i	−0.0284095	+	0.999596i	$0.509044\pi$
$110$	−74.6439	+	50.6098i	−0.678581	+	0.460089i
$111$	−11.2295	+	81.9762i	−0.101166	+	0.738524i
$112$	90.5470	+	106.600i	0.808455	+	0.951787i
$113$	10.8543	+	4.32476i	0.0960560	+	0.0382722i	0.417671	−	0.908598i	$-0.362846\pi$
$113$	10.8543	+	4.32476i	0.0960560	+	0.0382722i	−0.321615	+	0.946870i	$0.604226\pi$
$114$	−31.6516	−	86.3477i	−0.277646	−	0.757436i
$115$	7.93454	+	4.77405i	0.0689960	+	0.0415135i
$116$	10.2743	−	30.4931i	0.0885717	−	0.262872i
$117$	−30.0239	−	65.1430i	−0.256615	−	0.556777i
$118$	−102.254	−	17.3412i	−0.866557	−	0.146959i
$119$			145.004i			1.21852i
$120$	−172.685	+	138.603i	−1.43904	+	1.15502i
$121$	−72.8418	−	43.8275i	−0.601998	−	0.362210i
$122$	39.5576	−	52.0371i	0.324243	−	0.426534i
$123$	159.367	−	114.299i	1.29567	−	0.929256i
$124$	17.3958	+	20.4799i	0.140288	+	0.165160i
$125$	83.0628	+	179.537i	0.664502	+	1.43630i
$126$	−164.267	−	99.1603i	−1.30371	−	0.786987i
$127$	87.5423	+	165.122i	0.689309	+	1.30018i	0.942969	+	0.332882i	$0.108021\pi$
$127$	87.5423	+	165.122i	0.689309	+	1.30018i	−0.253659	+	0.967294i	$0.581634\pi$
$128$	51.9191	+	44.1005i	0.405618	+	0.344535i
$129$	−12.5555	−	14.0155i	−0.0973297	−	0.108647i
$130$	44.3460	+	111.300i	0.341123	+	0.856154i
$131$	−35.9599	−	19.0647i	−0.274503	−	0.145532i	0.325470	−	0.945552i	$-0.394477\pi$
$131$	−35.9599	−	19.0647i	−0.274503	−	0.145532i	−0.599973	+	0.800020i	$0.704822\pi$
$132$	14.6658	+	7.28681i	0.111105	+	0.0552031i
$133$	168.376	−	127.996i	1.26598	−	0.962375i
$134$	187.252	−	51.9903i	1.39740	−	0.387987i
$135$	124.776	−	194.279i	0.924266	−	1.43910i
$136$	16.6946	+	101.833i	0.122755	+	0.748770i
$137$	12.8638	+	58.4407i	0.0938961	+	0.426574i	0.999994	+	0.00350583i	$0.00111594\pi$
$137$	12.8638	+	58.4407i	0.0938961	+	0.426574i	−0.906098	+	0.423068i	$0.860953\pi$
$138$	−0.158765	+	5.70816i	−0.00115047	+	0.0413635i
$139$	−49.8969	−	5.42662i	−0.358971	−	0.0390404i	−0.0731431	−	0.997321i	$-0.523303\pi$
$139$	−49.8969	−	5.42662i	−0.358971	−	0.0390404i	−0.285828	+	0.958281i	$0.592269\pi$
$140$	−78.1128	−	52.9618i	−0.557949	−	0.378299i
$141$	−61.2179	+	68.1374i	−0.434170	+	0.483244i
$142$	−5.81055	−	107.169i	−0.0409194	−	0.754714i
$143$	32.8805	−	34.7116i	0.229934	−	0.242738i
$144$	−96.3636	−	38.5565i	−0.669192	−	0.267754i
$145$	16.3723	−	301.969i	0.112912	−	2.08254i
$146$	49.1754	−	223.406i	0.336818	−	1.53018i
$147$	71.2263	−	285.525i	0.484533	−	1.94234i
$148$	−23.7826	+	8.01330i	−0.160693	+	0.0541439i
$149$	−46.0322	+	209.126i	−0.308941	+	1.40353i	0.524730	+	0.851269i	$0.324166\pi$
$149$	−46.0322	+	209.126i	−0.308941	+	1.40353i	−0.833670	+	0.552263i	$0.813765\pi$
$150$	−148.232	+	206.050i	−0.988212	+	1.37367i
$151$	−63.0343	+	59.7092i	−0.417446	+	0.395425i	−0.867388	−	0.497632i	$-0.834203\pi$
$151$	−63.0343	+	59.7092i	−0.417446	+	0.395425i	0.449943	+	0.893057i	$0.351444\pi$
$152$	103.509	−	109.274i	0.680983	−	0.718905i
$153$	−50.2651	−	95.1426i	−0.328530	−	0.621847i
$154$	20.6917	−	126.214i	0.134362	−	0.819571i
$155$	209.023	+	141.721i	1.34854	+	0.914331i
$156$	13.6427	−	16.9471i	0.0874529	−	0.108635i
$157$	−242.173	+	145.711i	−1.54250	+	0.928092i	−0.546625	+	0.837378i	$0.684088\pi$
$157$	−242.173	+	145.711i	−1.54250	+	0.928092i	−0.995877	+	0.0907148i	$0.971085\pi$
$158$	32.9664	+	149.768i	0.208648	+	0.947899i
$159$	64.5188	−	149.686i	0.405778	−	0.941423i
$160$	−110.612	−	51.1746i	−0.691326	−	0.319841i
$161$	−12.6540	+	3.51336i	−0.0785961	+	0.0218221i
$162$	142.155	+	8.12030i	0.877500	+	0.0501253i
$163$	26.7486	−	2.90909i	0.164102	−	0.0178472i	−0.0256992	−	0.999670i	$-0.508181\pi$
$163$	26.7486	−	2.90909i	0.164102	−	0.0178472i	0.189801	+	0.981823i	$0.439216\pi$
$164$	52.5550	+	27.8629i	0.320458	+	0.169896i
$165$	151.130	+	29.1128i	0.915942	+	0.176441i
$166$	−34.2928	+	123.511i	−0.206583	+	0.744044i
$167$	22.8997	+	19.4512i	0.137124	+	0.116474i	0.713323	−	0.700835i	$-0.247189\pi$
$167$	22.8997	+	19.4512i	0.137124	+	0.116474i	−0.576200	+	0.817309i	$0.695465\pi$
$168$	25.7130	−	312.978i	0.153054	−	1.86296i
$169$	59.1946	+	87.3054i	0.350264	+	0.516600i
$170$	75.4676	+	163.121i	0.443927	+	0.959533i
$171$	−66.1082	+	142.349i	−0.386598	+	0.832453i
$172$	2.11250	−	5.30198i	0.0122820	−	0.0308255i
$173$	56.0417	−	73.7215i	0.323940	−	0.426136i	−0.605080	−	0.796165i	$-0.706859\pi$
$173$	56.0417	−	73.7215i	0.323940	−	0.426136i	0.929020	+	0.370028i	$0.120652\pi$
$174$	167.129	−	82.7378i	0.960513	−	0.475505i
$175$	−553.196	−	186.394i	−3.16112	−	1.06511i
$176$		−	69.1839i		−	0.393090i
$177$	102.365	+	144.397i	0.578332	+	0.815801i
$178$	251.972			1.41558
$179$	11.9302	−	35.4075i	0.0666490	−	0.197807i	−0.909153	−	0.416461i	$-0.863270\pi$
$179$	11.9302	−	35.4075i	0.0666490	−	0.197807i	0.975802	+	0.218654i	$0.0701667\pi$
$180$	69.6116	+	7.67271i	0.386731	+	0.0426262i
$181$	−20.7741	−	15.7921i	−0.114774	−	0.0872490i	0.546213	−	0.837646i	$-0.316069\pi$
$181$	−20.7741	−	15.7921i	−0.114774	−	0.0872490i	−0.660987	+	0.750397i	$0.729862\pi$
$182$	−157.846	−	62.8918i	−0.867288	−	0.345559i
$183$	−110.544	+	14.9798i	−0.604066	+	0.0818569i
$184$	−8.48205	+	3.92421i	−0.0460981	+	0.0213273i
$185$	−195.220	+	132.363i	−1.05524	+	0.715474i
$186$	−12.7514	+	155.209i	−0.0685558	+	0.834458i
$187$	46.4343	−	54.6667i	0.248312	−	0.292335i
$188$	−26.7701	−	7.43268i	−0.142394	−	0.0395355i
$189$	78.3381	+	317.951i	0.414487	+	1.68228i
$190$	122.796	−	231.618i	0.646296	−	1.21904i
$191$	18.0271	+	165.757i	0.0943829	+	0.867837i	0.941633	+	0.336642i	$0.109291\pi$
$191$	18.0271	+	165.757i	0.0943829	+	0.867837i	−0.847250	+	0.531195i	$0.821743\pi$
$192$	−17.1770	−	212.853i	−0.0894634	−	1.10861i
$193$	−11.5839	−	41.7214i	−0.0600202	−	0.216173i	0.927458	−	0.373926i	$-0.121989\pi$
$193$	−11.5839	−	41.7214i	−0.0600202	−	0.216173i	−0.987479	+	0.157753i	$0.949575\pi$
$194$	53.4652	−	115.563i	0.275594	−	0.595686i
$195$	80.9336	−	187.769i	0.415044	−	0.962920i
$196$	87.1695	−	19.1874i	0.444742	−	0.0978951i
$197$	−100.464	−	166.973i	−0.509970	−	0.847577i	0.489735	−	0.871872i	$-0.337094\pi$
$197$	−100.464	−	166.973i	−0.509970	−	0.847577i	−0.999705	+	0.0242944i	$0.992266\pi$
$198$	30.1749	+	89.9862i	0.152398	+	0.454476i
$199$	−4.77992	+	7.04985i	−0.0240197	+	0.0354264i	−0.839509	−	0.543345i	$-0.817157\pi$
$199$	−4.77992	+	7.04985i	−0.0240197	+	0.0354264i	0.815490	+	0.578772i	$0.196468\pi$
$200$	−409.955	−	67.2087i	−2.04978	−	0.336044i
$201$	−288.591	−	163.438i	−1.43577	−	0.813124i
$202$	13.1381	+	12.4450i	0.0650399	+	0.0616091i
$203$	294.943	+	311.367i	1.45292	+	1.53383i
$204$	19.0597	−	26.4939i	0.0934297	−	0.129872i
$205$	545.978	+	120.179i	2.66331	+	0.586238i
$206$	−32.6468	−	96.8923i	−0.158480	−	0.470351i
$207$	7.08484	−	6.69168i	0.0342263	−	0.0323270i
$208$	−89.7624	−	19.7582i	−0.431550	−	0.0949913i
$209$	−104.465	−	5.66395i	−0.499835	−	0.0271002i
$210$	−102.683	−	537.233i	−0.488966	−	2.55825i
$211$	−15.8492	−	15.0131i	−0.0751146	−	0.0711523i	0.649221	−	0.760600i	$-0.275095\pi$
$211$	−15.8492	−	15.0131i	−0.0751146	−	0.0711523i	−0.724336	+	0.689447i	$0.757854\pi$
$212$	49.3666	−	2.67658i	0.232861	−	0.0126254i
$213$	−122.415	+	136.251i	−0.574717	+	0.639678i
$214$	−19.9307	+	29.3956i	−0.0931343	+	0.137363i
$215$	5.79939	−	53.3245i	0.0269739	−	0.248021i
$216$	91.6211	+	214.269i	0.424172	+	0.991988i
$217$	−349.778	+	76.9920i	−1.61188	+	0.354802i
$218$	−328.946	+	53.9280i	−1.50893	+	0.247376i
$219$	−329.094	+	210.017i	−1.50271	+	0.958982i
$220$	12.4888	+	44.9805i	0.0567671	+	0.204457i
$221$	−57.6660	−	75.8583i	−0.260932	−	0.343250i
$222$	−130.256	−	64.7187i	−0.586740	−	0.291526i
$223$	−110.142	+	207.750i	−0.493910	+	0.931613i	0.503790	+	0.863826i	$0.331939\pi$
$223$	−110.142	+	207.750i	−0.493910	+	0.931613i	−0.997700	+	0.0677870i	$0.978406\pi$
$224$	160.570	−	63.9769i	0.716830	−	0.285611i
$225$	427.584	−	69.4634i	1.90038	−	0.308726i
$226$	−13.2968	+	15.6542i	−0.0588352	+	0.0692662i
$227$	−266.470	+	141.274i	−1.17388	+	0.622351i	−0.937048	−	0.349200i	$-0.886453\pi$
$227$	−266.470	+	141.274i	−1.17388	+	0.622351i	−0.236830	+	0.971551i	$0.576108\pi$
$228$	−47.5882	+	1.25466i	−0.208720	+	0.00550289i
$229$	314.669	−	145.581i	1.37410	−	0.635727i	0.412697	−	0.910868i	$-0.364587\pi$
$229$	314.669	−	145.581i	1.37410	−	0.635727i	0.961404	+	0.275141i	$0.0887247\pi$
$230$	−12.4064	+	10.5381i	−0.0539407	+	0.0458177i
$231$	−177.372	+	127.212i	−0.767846	+	0.550701i
$232$	242.979	+	184.708i	1.04732	+	0.796154i
$233$	79.7126	−	132.483i	0.342114	−	0.568598i	−0.637261	−	0.770648i	$-0.719933\pi$
$233$	79.7126	−	132.483i	0.342114	−	0.568598i	0.979375	+	0.202050i	$0.0647603\pi$
$234$	125.370	−	13.4512i	0.535769	−	0.0574837i
$235$	−261.110			−1.11111
$236$	−25.4071	+	47.2931i	−0.107657	+	0.200395i
$237$	141.111	−	220.415i	0.595407	−	0.930022i
$238$	−241.554	−	81.3891i	−1.01493	−	0.341971i
$239$	31.2196	−	51.8874i	0.130626	−	0.217102i	−0.784641	−	0.619951i	$-0.787152\pi$
$239$	31.2196	−	51.8874i	0.130626	−	0.217102i	0.915266	+	0.402849i	$0.131980\pi$
$240$	−101.827	−	277.789i	−0.424277	−	1.15746i
$241$	−43.1503	+	108.299i	−0.179047	+	0.449373i	−0.990919	−	0.134462i	$-0.957069\pi$
$241$	−43.1503	+	108.299i	−0.179047	+	0.449373i	0.811872	+	0.583835i	$0.198449\pi$
$242$	113.895	−	96.7431i	0.470640	−	0.399765i
$243$	−161.617	−	181.464i	−0.665089	−	0.746764i
$244$	−18.9880	−	28.0052i	−0.0778198	−	0.114776i
$245$	741.137	−	392.926i	3.02505	−	1.60378i
$246$	100.952	+	329.635i	0.410376	+	1.33998i
$247$	−37.1829	+	133.921i	−0.150538	+	0.542189i
$248$	−236.776	+	94.3401i	−0.954741	+	0.380403i
$249$	190.510	−	107.528i	0.765100	−	0.431839i
$250$	−345.703	+	37.5974i	−1.38281	+	0.150390i
$251$	−20.0773	−	26.4113i	−0.0799894	−	0.105224i	0.754358	−	0.656463i	$-0.227948\pi$
$251$	−20.0773	−	26.4113i	−0.0799894	−	0.105224i	−0.834347	+	0.551239i	$0.814155\pi$
$252$	−75.7921	+	64.1897i	−0.300762	+	0.254721i
$253$	5.89562	+	2.72761i	0.0233029	+	0.0107810i
$254$	−324.204	+	53.1505i	−1.27639	+	0.209254i
$255$	105.985	−	287.843i	0.415626	−	1.12880i
$256$	141.364	−	85.0560i	0.552204	−	0.332250i
$257$	13.9939	−	128.672i	0.0544511	−	0.500670i	−0.934878	−	0.354970i	$-0.884491\pi$
$257$	13.9939	−	128.672i	0.0544511	−	0.500670i	0.989329	−	0.145700i	$-0.0465434\pi$
$258$	30.3948	−	13.0488i	0.117809	−	0.0505768i
$259$	54.1162	−	330.094i	0.208943	−	1.27450i
$260$	61.9264	−	3.35755i	0.238179	−	0.0129137i
$261$	−301.457	−	102.059i	−1.15501	−	0.391030i
$262$	51.9427	−	49.2027i	0.198254	−	0.187797i
$263$	87.1521	+	4.72525i	0.331377	+	0.0179667i	0.219077	−	0.975708i	$-0.429695\pi$
$263$	87.1521	+	4.72525i	0.331377	+	0.0179667i	0.112300	+	0.993674i	$0.464178\pi$
$264$	−109.918	+	109.759i	−0.416355	+	0.415753i
$265$	440.319	−	148.361i	1.66158	−	0.559852i
$266$	118.714	+	352.330i	0.446292	+	1.32455i
$267$	−303.851	−	304.291i	−1.13802	−	1.13967i
$268$	5.44609	−	100.447i	0.0203212	−	0.374803i
$269$	217.624	+	229.743i	0.809011	+	0.854063i	0.991629	−	0.129121i	$-0.0412157\pi$
$269$	217.624	+	229.743i	0.809011	+	0.854063i	−0.182618	+	0.983184i	$0.558457\pi$
$270$	253.603	+	316.903i	0.939271	+	1.17372i
$271$	−11.9069	−	219.610i	−0.0439369	−	0.810368i	−0.934599	−	0.355702i	$-0.884242\pi$
$271$	−11.9069	−	219.610i	−0.0439369	−	0.810368i	0.890662	−	0.454665i	$-0.150241\pi$
$272$	−136.064	−	22.3066i	−0.500237	−	0.0820097i
$273$	114.395	+	266.462i	0.419029	+	0.976050i
$274$	−104.573	−	11.3730i	−0.381654	−	0.0415074i
$275$	148.867	+	247.419i	0.541334	+	0.899705i
$276$	2.77383	+	1.02133i	0.0100501	+	0.00370048i
$277$	45.4924	+	277.491i	0.164232	+	1.00177i	0.932374	+	0.361494i	$0.117733\pi$
$277$	45.4924	+	277.491i	0.164232	+	1.00177i	−0.768142	+	0.640279i	$0.778819\pi$
$278$	37.0464	−	80.0745i	0.133260	−	0.288038i
$279$	202.813	−	171.766i	0.726929	−	0.615649i
$280$	712.642	−	541.736i	2.54515	−	1.93477i
$281$	−9.71145	−	89.2953i	−0.0345603	−	0.317777i	−0.998639	−	0.0521593i	$-0.983390\pi$
$281$	−9.71145	−	89.2953i	−0.0345603	−	0.317777i	0.964078	−	0.265618i	$-0.0855759\pi$
$282$	−79.1454	−	140.224i	−0.280657	−	0.497248i
$283$	157.799	+	396.046i	0.557594	+	1.39946i	0.889844	+	0.456265i	$0.150813\pi$
$283$	157.799	+	396.046i	0.557594	+	1.39946i	−0.332250	+	0.943191i	$0.607808\pi$
$284$	−53.5309	−	14.8628i	−0.188489	−	0.0523338i
$285$	−427.789	+	131.013i	−1.50102	+	0.459694i
$286$	39.3685	+	74.2569i	0.137652	+	0.259640i
$287$	−656.230	+	444.935i	−2.28651	+	1.55030i
$288$	−83.1784	+	97.6384i	−0.288814	+	0.339022i
$289$	94.5528	+	111.316i	0.327172	+	0.385177i
$290$	493.843	+	196.765i	1.70291	+	0.678500i
$291$	−204.031	+	74.7898i	−0.701138	+	0.257009i
$292$	−101.461	−	61.0473i	−0.347470	−	0.209066i
$293$	−149.326	+	443.182i	−0.509643	+	1.51257i	0.316213	+	0.948688i	$0.397588\pi$
$293$	−149.326	+	443.182i	−0.509643	+	1.51257i	−0.825857	+	0.563880i	$0.809308\pi$
$294$	435.660	+	278.913i	1.48184	+	0.948684i
$295$	−111.170	+	492.153i	−0.376847	+	1.66832i
$296$		−	238.047i		−	0.804213i
$297$	72.2830	−	144.954i	0.243377	−	0.488059i
$298$	−322.534	−	194.062i	−1.08233	−	0.651215i
$299$	5.22265	−	6.87028i	0.0174671	−	0.0229775i
$300$	76.5753	+	106.769i	0.255251	+	0.355898i
$301$	49.2474	+	57.9785i	0.163613	+	0.192620i
$302$	−64.0858	−	138.519i	−0.212205	−	0.458673i
$303$	−0.813973	−	30.8733i	−0.00268638	−	0.101892i
$304$	94.2027	+	177.685i	0.309877	+	0.584490i
$305$	−242.363	−	205.865i	−0.794634	−	0.674968i
$306$	186.706	−	30.3313i	0.610149	−	0.0991220i
$307$	−199.041	−	499.556i	−0.648343	−	1.62722i	−0.772544	−	0.634962i	$-0.781016\pi$
$307$	−199.041	−	499.556i	−0.648343	−	1.62722i	0.124200	−	0.992257i	$-0.460363\pi$
$308$	−58.4927	−	31.0109i	−0.189911	−	0.100685i
$309$	−77.6422	+	156.267i	−0.251269	+	0.505718i
$310$	−353.407	+	268.653i	−1.14002	+	0.866623i
$311$	61.9811	−	17.2090i	0.199296	−	0.0553343i	−0.166446	−	0.986051i	$-0.553229\pi$
$311$	61.9811	−	17.2090i	0.199296	−	0.0553343i	0.365742	+	0.930716i	$0.380815\pi$
$312$	111.015	+	173.958i	0.355817	+	0.557559i
$313$	1.19162	+	7.26855i	0.00380709	+	0.0232222i	0.988662	−	0.150160i	$-0.0479788\pi$
$313$	1.19162	+	7.26855i	0.00380709	+	0.0232222i	−0.984855	+	0.173382i	$0.944531\pi$
$314$	−106.802	−	485.207i	−0.340134	−	1.54525i
$315$	−524.958	+	771.847i	−1.66653	+	2.45031i
$316$	78.9156	+	8.58258i	0.249733	+	0.0271601i
$317$	440.856	+	298.908i	1.39071	+	0.942928i	0.999746	+	0.0225232i	$0.00716996\pi$
$317$	440.856	+	298.908i	1.39071	+	0.942928i	0.390968	+	0.920404i	$0.372140\pi$
$318$	213.140	+	191.495i	0.670252	+	0.602186i
$319$	−11.4853	−	211.834i	−0.0360041	−	0.664057i
$320$	418.621	−	441.933i	1.30819	−	1.38104i
$321$	59.5335	−	11.3788i	0.185463	−	0.0354480i
$322$	1.24982	−	23.0515i	0.00388142	−	0.0715885i
$323$	−44.8217	+	203.627i	−0.138767	+	0.630424i
$324$	27.4789	−	68.3902i	0.0848113	−	0.211081i
$325$	363.528	−	122.487i	1.11855	−	0.376882i
$326$	−10.1676	+	46.1918i	−0.0311889	+	0.141693i
$327$	461.798	+	332.216i	1.41223	+	1.01595i
$328$	−409.627	+	388.019i	−1.24886	+	1.18298i
$329$	254.660	−	268.842i	0.774043	−	0.817148i
$330$	−133.325	+	235.419i	−0.404015	+	0.713390i
$331$	35.3496	−	215.623i	0.106797	−	0.651430i	−0.878125	−	0.478430i	$-0.841206\pi$
$331$	35.3496	−	215.623i	0.106797	−	0.651430i	0.984922	−	0.172999i	$-0.0553459\pi$
$332$	54.9190	+	37.2360i	0.165419	+	0.112157i
$333$	78.9181	+	235.346i	0.236991	+	0.706745i
$334$	−45.2559	+	27.2296i	−0.135497	+	0.0815256i
$335$	−203.236	−	923.312i	−0.606676	−	2.75615i
$336$	385.327	+	166.086i	1.14681	+	0.494304i
$337$	91.5607	+	42.3605i	0.271693	+	0.125699i	0.551005	−	0.834502i	$-0.314244\pi$
$337$	91.5607	+	42.3605i	0.271693	+	0.125699i	−0.279312	+	0.960200i	$0.590106\pi$
$338$	−178.662	+	49.6053i	−0.528586	+	0.146761i
$339$	34.9390	−	2.81953i	0.103065	−	0.00831719i
$340$	92.4901	−	10.0589i	0.272030	−	0.0295850i
$341$	156.521	+	82.9824i	0.459007	+	0.243350i
$342$	−200.026	−	190.025i	−0.584871	−	0.555628i
$343$	−159.283	+	573.686i	−0.464383	+	1.67256i
$344$	41.2603	+	35.0468i	0.119943	+	0.101880i
$345$	27.6869	+	2.27464i	0.0802518	+	0.00659317i
$346$	91.3529	+	134.736i	0.264026	+	0.389409i
$347$	69.3001	+	149.790i	0.199712	+	0.431670i	0.981393	−	0.192007i	$-0.0614998\pi$
$347$	69.3001	+	149.790i	0.199712	+	0.431670i	−0.781681	+	0.623678i	$0.785638\pi$
$348$	−12.9626	−	95.6582i	−0.0372490	−	0.274880i
$349$	12.6591	−	31.7719i	0.0362725	−	0.0910370i	−0.909725	−	0.415212i	$-0.863707\pi$
$349$	12.6591	−	31.7719i	0.0362725	−	0.0910370i	0.945997	+	0.324175i	$0.105087\pi$
$350$	621.004	−	816.917i	1.77430	−	2.33405i
$351$	−167.426	−	135.181i	−0.476998	−	0.385130i
$352$	−81.0220	−	27.2995i	−0.230176	−	0.0775554i
$353$			130.788i			0.370503i	0.982691	+	0.185252i	$0.0593100\pi$
$353$			130.788i			0.370503i	−0.982691	+	0.185252i	$0.940690\pi$
$354$	−297.998	+	89.4755i	−0.841803	+	0.252756i
$355$	−522.129			−1.47079
$356$	41.6463	−	123.602i	0.116984	−	0.347196i
$357$	192.999	+	389.856i	0.540614	+	1.09203i
$358$	52.2870	+	39.7475i	0.146053	+	0.111027i
$359$	−498.105	−	198.463i	−1.38748	−	0.552822i	−0.447571	−	0.894248i	$-0.647711\pi$
$359$	−498.105	−	198.463i	−1.38748	−	0.552822i	−0.939909	+	0.341426i	$0.889090\pi$
$360$	−279.800	+	602.487i	−0.777222	+	1.67357i
$361$	−51.6238	+	23.8837i	−0.143002	+	0.0661598i
$362$	37.9673	−	25.7425i	0.104882	−	0.0711118i
$363$	−254.175	−	20.8820i	−0.700207	−	0.0575262i
$364$	−56.9398	+	67.0348i	−0.156428	+	0.184161i
$365$	−1072.29	−	297.721i	−2.93779	−	0.815674i
$366$	37.0929	−	192.557i	0.101347	−	0.526111i
$367$	−242.811	+	457.991i	−0.661611	+	1.24793i	0.294703	+	0.955589i	$0.404779\pi$
$367$	−242.811	+	457.991i	−0.661611	+	1.24793i	−0.956314	+	0.292342i	$0.905566\pi$
$368$	−1.35014	−	12.4143i	−0.00366885	−	0.0337345i
$369$	276.341	−	519.417i	0.748893	−	1.40763i
$370$	−110.921	−	399.500i	−0.299785	−	1.07973i
$371$	−276.689	+	598.053i	−0.745792	+	1.61200i
$372$	74.0284	+	31.9082i	0.199001	+	0.0857748i
$373$	683.324	−	150.411i	1.83197	−	0.403246i	0.841415	−	0.540389i	$-0.181723\pi$
$373$	683.324	−	150.411i	1.83197	−	0.403246i	0.990551	+	0.137143i	$0.0437919\pi$
$374$	65.0031	+	108.036i	0.173805	+	0.288866i
$375$	462.283	+	372.145i	1.23276	+	0.992386i
$376$	147.889	−	218.120i	0.393322	−	0.580106i
$377$	−278.124	−	45.5961i	−0.737728	−	0.120944i
$378$	−573.626	−	47.9630i	−1.51753	−	0.126886i
$379$	44.8714	+	42.5044i	0.118394	+	0.112149i	0.744607	−	0.667504i	$-0.232637\pi$
$379$	44.8714	+	42.5044i	0.118394	+	0.112149i	−0.626212	+	0.779652i	$0.715396\pi$
$380$	−93.3215	−	98.5184i	−0.245583	−	0.259259i
$381$	455.141	+	327.427i	1.19459	+	0.859388i
$382$	−286.243	−	63.0069i	−0.749327	−	0.164939i
$383$	−0.637992	−	1.89349i	−0.00166577	−	0.00494384i	0.946817	−	0.321772i	$-0.104279\pi$
$383$	−0.637992	−	1.89349i	−0.00166577	−	0.00494384i	−0.948483	+	0.316829i	$0.897382\pi$
$384$	198.286	+	49.4640i	0.516370	+	0.128812i
$385$	−607.662	−	133.757i	−1.57834	−	0.347420i
$386$	76.0032	+	4.12077i	0.196899	+	0.0106756i
$387$	−52.4110	−	20.9704i	−0.135429	−	0.0541871i
$388$	−47.8512	−	45.3271i	−0.123328	−	0.116822i
$389$	−245.959	+	13.3355i	−0.632285	+	0.0342815i	−0.367496	−	0.930025i	$-0.619785\pi$
$389$	−245.959	+	13.3355i	−0.632285	+	0.0342815i	−0.264789	+	0.964306i	$0.585302\pi$
$390$	267.367	+	240.215i	0.685556	+	0.615936i
$391$	7.26530	−	10.7155i	0.0185813	−	0.0274054i
$392$	−91.5362	+	841.662i	−0.233511	+	2.14710i
$393$	−122.056	−	3.39484i	−0.310575	−	0.00863826i
$394$	334.539	−	73.6377i	0.849085	−	0.186898i
$395$	736.214	−	120.696i	1.86383	−	0.305560i
$396$	49.1289	+	0.0711264i	0.124063	+	0.000179612i
$397$	−171.595	−	618.030i	−0.432229	−	1.55675i	−0.784059	−	0.620686i	$-0.786854\pi$
$397$	−171.595	−	618.030i	−0.432229	−	1.55675i	0.351830	−	0.936064i	$-0.385560\pi$
$398$	−9.06103	−	11.9196i	−0.0227664	−	0.0299487i
$399$	282.331	−	568.234i	0.707595	−	1.42414i
$400$	260.002	−	490.417i	0.650006	−	1.22604i
$401$	27.1042	−	10.7993i	0.0675916	−	0.0269310i	−0.336097	−	0.941827i	$-0.609107\pi$
$401$	27.1042	−	10.7993i	0.0675916	−	0.0269310i	0.403689	+	0.914896i	$0.367728\pi$
$402$	434.244	−	389.011i	1.08021	−	0.967688i
$403$	152.366	−	179.379i	0.378080	−	0.445110i
$404$	8.27623	−	4.38778i	0.0204857	−	0.0108608i
$405$	76.8867	−	688.411i	0.189844	−	1.69978i
$406$	−684.236	+	316.561i	−1.68531	+	0.779708i
$407$	−126.107	+	107.116i	−0.309845	+	0.263185i
$408$	180.423	+	251.565i	0.442214	+	0.616582i
$409$	493.546	+	375.184i	1.20671	+	0.917321i	0.998157	−	0.0606895i	$-0.0193299\pi$
$409$	493.546	+	375.184i	1.20671	+	0.917321i	0.208558	+	0.978010i	$0.433123\pi$
$410$	−506.650	+	842.058i	−1.23573	+	2.05380i
$411$	112.369	+	140.001i	0.273404	+	0.340635i
$412$	−52.9252			−0.128459
$413$	−398.302	−	594.459i	−0.964412	−	1.43937i
$414$	7.17065	+	15.5582i	0.0173204	+	0.0375801i
$415$	590.952	+	199.115i	1.42398	+	0.479795i
$416$	−58.5587	+	97.3253i	−0.140766	+	0.233955i
$417$	−141.375	+	51.8224i	−0.339028	+	0.124274i
$418$	68.0704	−	170.844i	0.162848	−	0.408717i
$419$	10.8902	−	9.25021i	0.0259909	−	0.0220769i	−0.634297	−	0.773090i	$-0.718710\pi$
$419$	10.8902	−	9.25021i	0.0259909	−	0.0220769i	0.660288	+	0.751013i	$0.270434\pi$
$420$	−280.504	−	38.4248i	−0.667867	−	0.0914876i
$421$	−130.102	−	191.886i	−0.309030	−	0.455785i	0.641182	−	0.767389i	$-0.278444\pi$
$421$	−130.102	−	191.886i	−0.309030	−	0.455785i	−0.950212	+	0.311603i	$0.899134\pi$
$422$	33.9054	−	17.9755i	0.0803447	−	0.0425960i
$423$	−73.8991	+	264.673i	−0.174702	+	0.625705i
$424$	−125.456	+	451.853i	−0.295888	+	1.06569i
$425$	534.599	−	213.004i	1.25788	−	0.501185i
$426$	−158.263	−	280.400i	−0.371510	−	0.658215i
$427$	448.338	−	48.7597i	1.04997	−	0.114191i
$428$	11.1255	+	14.6353i	0.0259941	+	0.0341947i
$429$	42.2013	−	137.088i	0.0983712	−	0.319553i
$430$	85.5751	+	39.5913i	0.199012	+	0.0920727i
$431$	163.055	−	26.7315i	0.378317	−	0.0620220i	0.0303767	−	0.999539i	$-0.490329\pi$
$431$	163.055	−	26.7315i	0.378317	−	0.0620220i	0.347941	+	0.937517i	$0.386881\pi$
$432$	−310.400	+	24.5966i	−0.718518	+	0.0569366i
$433$	−515.413	+	310.113i	−1.19033	+	0.716197i	−0.966057	−	0.258329i	$-0.916828\pi$
$433$	−515.413	+	310.113i	−1.19033	+	0.716197i	−0.224272	+	0.974526i	$0.572001\pi$
$434$	68.0696	−	625.889i	0.156842	−	1.44214i
$435$	−357.899	−	833.659i	−0.822757	−	1.91646i
$436$	−27.9150	+	170.274i	−0.0640252	+	0.390536i
$437$	−18.8557	+	1.02233i	−0.0431481	+	0.00233942i
$438$	−165.139	−	666.098i	−0.377030	−	1.52077i
$439$	275.538	−	261.003i	0.627649	−	0.594541i	−0.306305	−	0.951933i	$-0.599093\pi$
$439$	275.538	−	261.003i	0.627649	−	0.594541i	0.933954	+	0.357392i	$0.116334\pi$
$440$	−442.145	−	23.9724i	−1.00487	−	0.0544827i
$441$	−188.533	−	862.458i	−0.427512	−	1.95569i
$442$	158.735	−	53.4841i	0.359129	−	0.121005i
$443$	−152.890	−	453.763i	−0.345125	−	1.02429i	−0.969903	−	0.243492i	$-0.921707\pi$
$443$	−152.890	−	453.763i	−0.345125	−	1.02429i	0.624778	−	0.780803i	$-0.285190\pi$
$444$	−53.2759	+	53.1988i	−0.119991	+	0.119817i
$445$	66.3640	−	1224.01i	0.149133	−	2.75059i
$446$	−284.257	−	300.086i	−0.637347	−	0.672839i
$447$	154.584	+	623.521i	0.345825	+	1.39490i
$448$	46.7382	+	862.035i	0.104326	+	1.92418i
$449$	470.074	+	77.0647i	1.04693	+	0.171636i	0.660612	−	0.750728i	$-0.270297\pi$
$449$	470.074	+	77.0647i	1.04693	+	0.171636i	0.386323	+	0.922364i	$0.373745\pi$
$450$	−124.283	+	751.277i	−0.276184	+	1.66950i
$451$	389.879	+	42.4019i	0.864477	+	0.0940175i
$452$	5.48125	+	9.10990i	0.0121266	+	0.0201546i
$453$	−90.0004	+	244.431i	−0.198676	+	0.539583i
$454$	−85.7731	−	523.193i	−0.188927	−	1.15241i
$455$	−347.084	+	750.210i	−0.762822	+	1.64881i
$456$	132.852	−	431.561i	0.291341	−	0.946405i
$457$	−408.178	+	310.289i	−0.893168	+	0.678969i	−0.947569	−	0.319550i	$-0.896468\pi$
$457$	−408.178	+	310.289i	−0.893168	+	0.678969i	0.0544012	+	0.998519i	$0.482675\pi$
$458$	65.8958	+	605.902i	0.143877	+	1.32293i
$459$	−261.776	−	188.896i	−0.570317	−	0.411539i
$460$	3.11877	+	7.82753i	0.00677994	+	0.0170164i
$461$	509.960	+	141.590i	1.10620	+	0.307136i	0.772165	−	0.635423i	$-0.219174\pi$
$461$	509.960	+	141.590i	1.10620	+	0.307136i	0.334040	+	0.942559i	$0.391588\pi$
$462$	−112.358	−	366.877i	−0.243199	−	0.794105i
$463$	−273.772	−	516.388i	−0.591300	−	1.11531i	−0.980934	−	0.194340i	$-0.937744\pi$
$463$	−273.772	−	516.388i	−0.591300	−	1.11531i	0.389635	−	0.920970i	$-0.372601\pi$
$464$	−337.543	+	228.860i	−0.727463	+	0.493232i
$465$	750.605	+	102.821i	1.61420	+	0.221121i
$466$	175.955	+	207.150i	0.377585	+	0.444528i
$467$	117.344	+	46.7542i	0.251273	+	0.100116i	0.492374	−	0.870384i	$-0.336129\pi$
$467$	117.344	+	46.7542i	0.251273	+	0.100116i	−0.241101	+	0.970500i	$0.577509\pi$
$468$	14.1230	−	63.7219i	0.0301773	−	0.136158i
$469$	1148.87	+	691.251i	2.44961	+	1.47388i
$470$	146.558	−	434.967i	0.311825	−	0.925463i
$471$	−457.162	+	714.084i	−0.970620	+	1.51610i
$472$	−348.158	−	371.615i	−0.737624	−	0.787321i
$473$		−	37.6283i		−	0.0795524i
$474$	287.973	+	358.786i	0.607537	+	0.756932i
$475$	−719.227	−	432.745i	−1.51416	−	0.911042i
$476$	−79.8488	+	105.039i	−0.167750	+	0.220671i
$477$	−25.7668	−	488.317i	−0.0540185	−	1.02373i
$478$	68.9130	+	81.1306i	0.144169	+	0.169729i
$479$	−319.204	−	689.949i	−0.666398	−	1.44039i	−0.885475	−	0.464687i	$-0.846167\pi$
$479$	−319.204	−	689.949i	−0.666398	−	1.44039i	0.219077	−	0.975707i	$-0.429695\pi$
$480$	−365.502	+	9.63644i	−0.761463	+	0.0200759i
$481$	102.963	+	194.208i	0.214060	+	0.403759i
$482$	−156.189	−	132.668i	−0.324044	−	0.275246i
$483$	−29.3450	+	26.2882i	−0.0607557	+	0.0544270i
$484$	−28.6314	−	71.8595i	−0.0591559	−	0.148470i
$485$	−547.292	−	290.156i	−1.12844	−	0.598259i
$486$	393.003	−	167.375i	0.808648	−	0.344392i
$487$	−177.528	+	134.953i	−0.364533	+	0.277111i	−0.771366	−	0.636392i	$-0.780426\pi$
$487$	−177.528	+	134.953i	−0.364533	+	0.277111i	0.406833	+	0.913503i	$0.366633\pi$
$488$	309.242	−	85.8607i	0.633693	−	0.175944i
$489$	68.0439	−	43.4234i	0.139149	−	0.0888005i
$490$	238.562	+	1455.16i	0.486860	+	2.96972i
$491$	−30.2624	−	137.483i	−0.0616342	−	0.280007i	0.935716	−	0.352754i	$-0.114755\pi$
$491$	−30.2624	−	137.483i	−0.0616342	−	0.280007i	−0.997350	+	0.0727465i	$0.976824\pi$
$492$	178.384	+	4.96152i	0.362569	+	0.0100844i
$493$	−420.319	−	45.7125i	−0.852574	−	0.0927230i
$494$	−202.221	−	137.109i	−0.409353	−	0.277548i
$495$	445.075	−	122.881i	0.899142	−	0.248244i
$496$	−18.4374	−	340.057i	−0.0371721	−	0.685599i
$497$	509.232	−	537.590i	1.02461	−	1.08167i
$498$	72.1934	+	377.714i	0.144967	+	0.758461i
$499$	−1.28603	+	23.7195i	−0.00257722	+	0.0475341i	−0.999539	−	0.0303565i	$-0.990336\pi$
$499$	−1.28603	+	23.7195i	−0.00257722	+	0.0475341i	0.996962	+	0.0778906i	$0.0248185\pi$
$500$	−38.6953	+	175.794i	−0.0773905	+	0.351589i
$501$	87.4570	+	21.8168i	0.174565	+	0.0435465i
$502$	55.2662	−	18.6213i	0.110092	−	0.0370943i
$503$	180.837	−	821.549i	0.359516	−	1.63330i	−0.355846	−	0.934545i	$-0.615807\pi$
$503$	180.837	−	821.549i	0.359516	−	1.63330i	0.715362	−	0.698754i	$-0.246262\pi$
$504$	−347.439	−	875.690i	−0.689363	−	1.73748i
$505$	63.9148	−	60.5433i	0.126564	−	0.119888i
$506$	−7.85290	+	8.29020i	−0.0155196	+	0.0163838i
$507$	275.352	+	155.940i	0.543101	+	0.307575i
$508$	−27.5125	+	167.819i	−0.0541585	+	0.330352i
$509$	−411.700	−	279.140i	−0.808841	−	0.548408i	0.0852152	−	0.996363i	$-0.472842\pi$
$509$	−411.700	−	279.140i	−0.808841	−	0.548408i	−0.894056	+	0.447955i	$0.852153\pi$
$510$	420.013	+	338.116i	0.823554	+	0.662973i
$511$	1352.34	−	813.679i	2.64647	−	1.59233i
$512$	120.920	+	549.344i	0.236171	+	1.07294i
$513$	11.7282	+	470.707i	0.0228621	+	0.917558i
$514$	206.493	+	95.5337i	0.401737	+	0.185863i
$515$	−479.274	+	133.070i	−0.930630	+	0.258388i
$516$	−1.37725	−	17.0665i	−0.00266908	−	0.0330746i
$517$	−182.097	+	19.8043i	−0.352219	+	0.0383061i
$518$	519.510	+	275.427i	1.00292	+	0.531712i
$519$	52.5500	−	272.797i	0.101252	−	0.525621i
$520$	−157.375	+	566.813i	−0.302644	+	1.09003i
$521$	259.235	+	220.196i	0.497572	+	0.422642i	0.860711	−	0.509093i	$-0.170019\pi$
$521$	259.235	+	220.196i	0.497572	+	0.422642i	−0.363139	+	0.931735i	$0.618295\pi$
$522$	339.218	−	444.895i	0.649842	−	0.852289i
$523$	−325.255	−	479.715i	−0.621902	−	0.917236i	0.378062	−	0.925780i	$-0.376591\pi$
$523$	−325.255	−	479.715i	−0.621902	−	0.917236i	−0.999963	+	0.00854415i	$0.997280\pi$
$524$	−15.5506	−	33.6121i	−0.0296768	−	0.0641453i
$525$	−1735.40	+	235.164i	−3.30553	+	0.447932i
$526$	−56.7889	+	142.529i	−0.107964	+	0.270968i
$527$	213.669	−	281.076i	0.405443	−	0.533351i
$528$	−92.0830	−	186.006i	−0.174400	−	0.352285i
$529$	−500.197	−	168.536i	−0.945553	−	0.318594i
$530$			816.774i			1.54108i
$531$	467.407	+	251.976i	0.880239	+	0.474531i
$532$	192.452			0.361752
$533$	166.360	−	493.738i	0.312119	−	0.926337i
$534$	677.448	−	335.373i	1.26863	−	0.628039i
$535$	137.547	+	104.560i	0.257096	+	0.195440i
$536$	886.405	+	353.176i	1.65374	+	0.658911i
$537$	−15.0517	−	111.075i	−0.0280293	−	0.206843i
$538$	−504.865	+	233.575i	−0.938410	+	0.434155i
$539$	487.065	−	330.238i	0.903646	−	0.612687i
$540$	197.369	−	72.0236i	0.365498	−	0.133377i
$541$	−261.261	+	307.580i	−0.482922	+	0.568539i	−0.948625	−	0.316401i	$-0.897525\pi$
$541$	−261.261	+	307.580i	−0.482922	+	0.568539i	0.465704	+	0.884941i	$0.345801\pi$
$542$	372.518	+	103.429i	0.687303	+	0.190829i
$543$	−76.8719	−	14.8081i	−0.141569	−	0.0272710i
$544$	−79.8137	+	150.545i	−0.146716	+	0.276736i
$545$	175.330	+	1612.13i	0.321707	+	2.95804i
$546$	−508.091	+	41.0023i	−0.930570	+	0.0750958i
$547$	−13.0101	−	46.8581i	−0.0237844	−	0.0856638i	0.950705	−	0.310096i	$-0.100361\pi$
$547$	−13.0101	−	46.8581i	−0.0237844	−	0.0856638i	−0.974490	+	0.224432i	$0.927947\pi$
$548$	−22.8629	+	49.4173i	−0.0417206	+	0.0901775i
$549$	−277.268	+	187.407i	−0.505043	+	0.341361i
$550$	−495.718	+	109.116i	−0.901305	+	0.198392i
$551$	317.937	+	528.415i	0.577018	+	0.959012i
$552$	−17.5816	+	21.8401i	−0.0318507	+	0.0395654i
$553$	−593.759	+	875.730i	−1.07371	+	1.58360i
$554$	−487.791	−	79.9692i	−0.880489	−	0.144349i
$555$	−348.692	+	615.704i	−0.628274	+	1.10938i
$556$	−33.1565	−	31.4075i	−0.0596339	−	0.0564883i
$557$	270.337	+	285.391i	0.485345	+	0.512372i	0.921965	−	0.387274i	$-0.126583\pi$
$557$	270.337	+	285.391i	0.485345	+	0.512372i	−0.436620	+	0.899646i	$0.643825\pi$
$558$	172.299	+	434.265i	0.308779	+	0.778252i
$559$	−48.8207	−	10.7462i	−0.0873357	−	0.0192241i
$560$	381.914	+	1133.48i	0.681990	+	2.02407i
$561$	52.0816	−	208.779i	0.0928371	−	0.372156i
$562$	154.203	+	33.9426i	0.274382	+	0.0603961i
$563$	−499.591	−	27.0870i	−0.887372	−	0.0481119i	−0.395185	−	0.918601i	$-0.629320\pi$
$563$	−499.591	−	27.0870i	−0.887372	−	0.0481119i	−0.492187	+	0.870489i	$0.663802\pi$
$564$	−81.8664	+	15.6473i	−0.145153	+	0.0277435i
$565$	72.5415	+	68.7150i	0.128392	+	0.121619i
$566$	−748.321	+	40.5728i	−1.32212	+	0.0716833i
$567$	633.808	+	750.570i	1.11783	+	1.32376i
$568$	295.727	−	436.164i	0.520646	−	0.767895i
$569$	77.5598	−	713.150i	0.136309	−	1.25334i	−0.703594	−	0.710603i	$-0.748422\pi$
$569$	77.5598	−	713.150i	0.136309	−	1.25334i	0.839902	−	0.542737i	$-0.182612\pi$
$570$	21.8662	−	786.165i	0.0383617	−	1.37924i
$571$	534.301	−	117.609i	0.935729	−	0.205970i	0.279168	−	0.960242i	$-0.409941\pi$
$571$	534.301	−	117.609i	0.935729	−	0.205970i	0.656561	+	0.754273i	$0.272010\pi$
$572$	42.9327	−	7.03845i	0.0750571	−	0.0123050i
$573$	269.088	+	421.657i	0.469613	+	0.735876i
$574$	−372.857	−	1342.91i	−0.649577	−	2.33957i
$575$	31.5410	+	41.4914i	0.0548539	+	0.0721590i
$576$	−329.487	−	549.411i	−0.572026	−	0.953838i
$577$	−9.51001	+	17.9378i	−0.0164818	+	0.0310880i	−0.891616	−	0.452792i	$-0.850428\pi$
$577$	−9.51001	+	17.9378i	−0.0164818	+	0.0310880i	0.875134	+	0.483880i	$0.160773\pi$
$578$	−238.506	+	95.0296i	−0.412641	+	0.164411i
$579$	−86.6750	−	96.7534i	−0.149698	−	0.167104i
$580$	178.144	−	209.727i	0.307144	−	0.361598i
$581$	−781.366	+	414.254i	−1.34486	+	0.713002i
$582$	−10.0678	−	381.862i	−0.0172986	−	0.656121i
$583$	295.825	−	136.863i	0.507418	−	0.234757i
$584$	856.036	−	727.123i	1.46581	−	1.24507i
$585$	−32.3224	−	612.555i	−0.0552520	−	1.04710i
$586$	−654.457	−	497.505i	−1.11682	−	0.848985i
$587$	572.626	−	951.712i	0.975513	−	1.62131i	0.210198	−	0.977659i	$-0.432589\pi$
$587$	572.626	−	951.712i	0.975513	−	1.62131i	0.765315	−	0.643656i	$-0.222583\pi$
$588$	208.824	−	167.609i	0.355143	−	0.285049i
$589$	−514.985			−0.874338
$590$	−757.451	−	461.431i	−1.28381	−	0.782086i
$591$	−492.345	−	315.203i	−0.833071	−	0.533338i
$592$	301.418	+	101.560i	0.509152	+	0.171553i
$593$	180.260	−	299.594i	0.303979	−	0.505218i	−0.666786	−	0.745250i	$-0.732330\pi$
$593$	180.260	−	299.594i	0.303979	−	0.505218i	0.970765	+	0.240032i	$0.0771579\pi$
$594$	200.898	+	201.773i	0.338213	+	0.339685i
$595$	−458.986	+	1151.97i	−0.771405	+	1.93608i
$596$	−148.504	+	126.140i	−0.249167	+	0.211644i
$597$	−3.46792	+	25.3161i	−0.00580891	+	0.0424056i
$598$	8.51339	+	12.5563i	0.0142364	+	0.0209972i
$599$	−656.002	+	347.790i	−1.09516	+	0.580618i	−0.915177	−	0.403052i	$-0.867949\pi$
$599$	−656.002	+	347.790i	−1.09516	+	0.580618i	−0.179984	+	0.983670i	$0.557605\pi$
$600$	−1191.65	+	364.950i	−1.98609	+	0.608249i
$601$	−90.5556	+	326.152i	−0.150675	+	0.542682i	0.849218	+	0.528043i	$0.177074\pi$
$601$	−90.5556	+	326.152i	−0.150675	+	0.542682i	−0.999893	+	0.0146395i	$0.995340\pi$
$602$	−124.225	+	49.4958i	−0.206354	+	0.0822189i
$603$	−993.433	−	55.3050i	−1.64748	−	0.0917164i
$604$	−78.5410	+	8.54185i	−0.130035	+	0.0141421i
$605$	−439.954	−	578.749i	−0.727196	−	0.956611i
$606$	51.8870	+	15.9729i	0.0856220	+	0.0263579i
$607$	−140.467	−	64.9869i	−0.231412	−	0.107062i	0.300757	−	0.953701i	$-0.402761\pi$
$607$	−140.467	−	64.9869i	−0.231412	−	0.107062i	−0.532169	+	0.846638i	$0.678623\pi$
$608$	245.261	−	40.2085i	0.403389	−	0.0661323i
$609$	1207.40	+	444.570i	1.98260	+	0.730001i
$610$	478.974	−	288.189i	0.785204	−	0.472442i
$611$	−26.3101	+	241.917i	−0.0430607	+	0.395937i
$612$	15.9803	−	96.5993i	0.0261116	−	0.157842i
$613$	−60.1102	+	366.656i	−0.0980591	+	0.598134i	0.891388	+	0.453241i	$0.149732\pi$
$613$	−60.1102	+	366.656i	−0.0980591	+	0.598134i	−0.989447	+	0.144893i	$0.953716\pi$
$614$	943.901	−	51.1768i	1.53730	−	0.0833499i
$615$	1627.86	−	403.580i	2.64693	−	0.656228i
$616$	455.906	−	431.857i	0.740107	−	0.701067i
$617$	−33.8490	−	1.83524i	−0.0548606	−	0.00297445i	0.0266882	−	0.999644i	$-0.491504\pi$
$617$	−33.8490	−	1.83524i	−0.0548606	−	0.00297445i	−0.0815488	+	0.996669i	$0.525987\pi$
$618$	−216.736	−	217.050i	−0.350706	−	0.351214i
$619$	334.599	−	112.739i	0.540547	−	0.182132i	−0.0357663	−	0.999360i	$-0.511387\pi$
$619$	334.599	−	112.739i	0.540547	−	0.182132i	0.576314	+	0.817229i	$0.304491\pi$
$620$	73.3728	+	217.763i	0.118343	+	0.351230i
$621$	10.1416	−	27.4210i	0.0163311	−	0.0441561i
$622$	−6.12180	+	112.910i	−0.00984212	+	0.181527i
$623$	1195.53	+	1262.11i	1.91899	+	2.02586i
$624$	−267.631	+	66.3513i	−0.428897	+	0.106332i
$625$	26.4418	+	487.690i	0.0423068	+	0.780304i
$626$	−12.7771	−	2.09470i	−0.0204107	−	0.00334616i
$627$	−288.402	+	123.814i	−0.459972	+	0.197471i
$628$	−255.665	−	27.8052i	−0.407109	−	0.0442758i
$629$	170.006	+	282.553i	0.270280	+	0.449209i
$630$	−991.122	−	1307.72i	−1.57321	−	2.07575i
$631$	−18.0496	−	110.098i	−0.0286047	−	0.174481i	0.968660	−	0.248389i	$-0.0799012\pi$
$631$	−18.0496	−	110.098i	−0.0286047	−	0.174481i	−0.997265	+	0.0739079i	$0.976453\pi$
$632$	−316.157	+	683.363i	−0.500249	+	1.08127i
$633$	−62.5941	−	19.2689i	−0.0988848	−	0.0304407i
$634$	−745.381	+	566.624i	−1.17568	+	0.893728i
$635$	172.802	+	1588.89i	0.272130	+	2.50219i
$636$	129.164	−	72.9026i	0.203087	−	0.114627i
$637$	−289.366	−	726.253i	−0.454263	−	1.14012i
$638$	359.329	+	99.7671i	0.563211	+	0.156375i
$639$	−147.773	+	529.255i	−0.231256	+	0.828256i
$640$	272.872	+	514.691i	0.426363	+	0.804205i
$641$	−488.824	+	331.431i	−0.762596	+	0.517053i	−0.879389	−	0.476103i	$-0.842049\pi$
$641$	−488.824	+	331.431i	−0.762596	+	0.517053i	0.116793	+	0.993156i	$0.462738\pi$
$642$	−14.4601	+	105.560i	−0.0225236	+	0.164424i
$643$	−280.114	−	329.776i	−0.435636	−	0.512871i	0.499909	−	0.866078i	$-0.333367\pi$
$643$	−280.114	−	329.776i	−0.435636	−	0.512871i	−0.935545	+	0.353207i	$0.885091\pi$
$644$	−11.1011	−	4.42307i	−0.0172377	−	0.00686811i
$645$	−55.3823	−	151.086i	−0.0858640	−	0.234242i
$646$	−314.052	−	188.959i	−0.486149	−	0.292506i
$647$	100.218	−	297.437i	0.154897	−	0.459717i	−0.841905	−	0.539625i	$-0.818566\pi$
$647$	100.218	−	297.437i	0.154897	−	0.459717i	0.996802	+	0.0799077i	$0.0254625\pi$
$648$	531.521	+	454.134i	0.820249	+	0.700824i
$649$	−40.2016	+	351.658i	−0.0619439	+	0.541846i
$650$			674.330i			1.03743i
$651$	−837.931	+	672.550i	−1.28714	+	1.03310i
$652$	20.9783	+	12.6222i	0.0321753	+	0.0193592i
$653$	413.298	−	543.684i	0.632921	−	0.832594i	−0.362112	−	0.932135i	$-0.617944\pi$
$653$	413.298	−	543.684i	0.632921	−	0.832594i	0.995033	+	0.0995408i	$0.0317374\pi$
$654$	−812.621	+	582.814i	−1.24254	+	0.891153i
$655$	−225.333	−	265.282i	−0.344019	−	0.405011i
$656$	−316.553	−	684.218i	−0.482550	−	1.04301i
$657$	−605.264	+	1002.67i	−0.921254	+	1.52613i
$658$	304.910	+	575.121i	0.463389	+	0.874044i
$659$	−133.253	−	113.186i	−0.202204	−	0.171754i	0.540563	−	0.841304i	$-0.318211\pi$
$659$	−133.253	−	113.186i	−0.202204	−	0.171754i	−0.742767	+	0.669550i	$0.766487\pi$
$660$	93.4456	+	104.311i	0.141584	+	0.158047i
$661$	98.9884	+	248.442i	0.149756	+	0.375858i	0.984647	−	0.174556i	$-0.0558491\pi$
$661$	98.9884	+	248.442i	0.149756	+	0.375858i	−0.834892	+	0.550414i	$0.814470\pi$
$662$	339.353	+	179.914i	0.512618	+	0.271773i
$663$	−256.006	−	127.198i	−0.386133	−	0.191853i
$664$	−501.039	+	380.880i	−0.754577	+	0.573614i
$665$	1742.79	−	483.882i	2.62073	−	0.727643i
$666$	−436.345	−	0.631718i	−0.655172	−	0.000948525i
$667$	−6.19490	−	37.7872i	−0.00928770	−	0.0566525i
$668$	5.87717	+	26.7002i	0.00879816	+	0.0399704i
$669$	−19.6129	+	705.150i	−0.0293167	+	1.05404i
$670$	1652.17	+	179.684i	2.46592	+	0.268185i
$671$	−184.638	−	125.188i	−0.275168	−	0.186569i
$672$	346.553	−	385.724i	0.515703	−	0.573994i
$673$	−8.24370	−	152.046i	−0.0122492	−	0.225923i	−0.998248	−	0.0591701i	$-0.981155\pi$
$673$	−8.24370	−	152.046i	−0.0122492	−	0.225923i	0.985999	−	0.166753i	$-0.0533282\pi$
$674$	−121.958	+	128.749i	−0.180946	+	0.191022i
$675$	1057.14	−	755.868i	1.56613	−	1.11980i
$676$	−5.19626	+	95.8393i	−0.00768677	+	0.141774i
$677$	−259.883	+	1180.66i	−0.383874	+	1.74396i	0.247882	+	0.968790i	$0.420266\pi$
$677$	−259.883	+	1180.66i	−0.383874	+	1.74396i	−0.631756	+	0.775168i	$0.717665\pi$
$678$	−14.9139	+	59.7853i	−0.0219969	+	0.0881790i
$679$	832.521	−	280.509i	1.22610	−	0.413121i
$680$	−189.706	+	861.841i	−0.278979	+	1.26741i
$681$	−528.393	+	734.495i	−0.775908	+	1.07855i
$682$	−226.089	+	214.163i	−0.331509	+	0.314022i
$683$	−391.479	+	413.280i	−0.573176	+	0.605095i	−0.946538	−	0.322591i	$-0.895446\pi$
$683$	−391.479	+	413.280i	−0.573176	+	0.605095i	0.373362	+	0.927686i	$0.378205\pi$
$684$	−126.275	+	66.7126i	−0.184612	+	0.0975331i
$685$	−82.7892	+	504.992i	−0.120860	+	0.737215i
$686$	−866.267	−	587.344i	−1.26278	−	0.856186i
$687$	652.246	−	810.229i	0.949412	−	1.17937i
$688$	−61.9799	+	37.2921i	−0.0900871	+	0.0542036i
$689$	−93.0881	−	422.903i	−0.135106	−	0.613793i
$690$	−19.3295	+	44.8452i	−0.0280137	+	0.0649930i
$691$	858.959	+	397.397i	1.24307	+	0.575104i	0.927508	−	0.373802i	$-0.121946\pi$
$691$	858.959	+	397.397i	1.24307	+	0.575104i	0.315558	+	0.948906i	$0.397808\pi$
$692$	81.1917	−	22.5428i	0.117329	−	0.0325763i
$693$	−307.562	+	578.100i	−0.443813	+	0.834199i
$694$	−288.423	+	31.3679i	−0.415595	+	0.0451987i
$695$	−379.223	−	201.051i	−0.545644	−	0.289282i
$696$	899.112	+	173.199i	1.29183	+	0.248850i
$697$	209.099	−	753.107i	0.299999	−	1.08050i
$698$	45.8216	+	38.9212i	0.0656470	+	0.0557611i
$699$	37.9798	−	462.289i	0.0543345	−	0.661358i
$700$	−298.088	−	439.647i	−0.425840	−	0.628067i
$701$	−163.577	−	353.567i	−0.233349	−	0.504375i	0.755160	−	0.655541i	$-0.227559\pi$
$701$	−163.577	−	353.567i	−0.233349	−	0.504375i	−0.988508	+	0.151166i	$0.951697\pi$
$702$	319.164	−	203.031i	0.454649	−	0.289217i
$703$	178.028	−	446.817i	0.253241	−	0.635587i
$704$	258.426	−	339.954i	0.367083	−	0.482890i
$705$	−702.015	+	347.534i	−0.995765	+	0.492956i
$706$	−217.871	−	73.4095i	−0.308600	−	0.103979i
$707$			124.855i			0.176599i
$708$	−5.36249	+	160.968i	−0.00757414	+	0.227356i
$709$	−178.968			−0.252424			−0.126212	−	0.992003i	$-0.540282\pi$
$709$	−178.968			−0.252424			−0.126212	+	0.992003i	$0.540282\pi$
$710$	293.065	−	869.785i	0.412767	−	1.22505i
$711$	86.0194	−	780.422i	0.120984	−	1.09764i
$712$	984.900	+	748.701i	1.38329	+	1.05155i
$713$	29.7055	+	11.8357i	0.0416626	+	0.0165999i
$714$	−757.767	+	102.685i	−1.06130	+	0.143816i
$715$	371.088	−	171.684i	0.519005	−	0.240117i
$716$	28.1397	−	19.0792i	0.0393013	−	0.0266469i
$717$	14.8749	−	181.056i	0.0207460	−	0.252519i
$718$	610.189	−	718.370i	0.849845	−	1.00051i
$719$	253.219	+	70.3058i	0.352182	+	0.0977827i	0.439114	−	0.898432i	$-0.355293\pi$
$719$	253.219	+	70.3058i	0.352182	+	0.0977827i	−0.0869321	+	0.996214i	$0.527706\pi$
$720$	−643.504	−	611.329i	−0.893755	−	0.849068i
$721$	330.426	−	623.249i	0.458288	−	0.864424i
$722$	−10.8107	−	99.4026i	−0.0149733	−	0.137677i
$723$	28.1318	+	348.603i	0.0389099	+	0.482162i
$724$	−6.35236	−	22.8791i	−0.00877398	−	0.0316010i
$725$	714.687	−	1544.77i	0.985775	−	2.13072i
$726$	177.451	−	411.694i	0.244423	−	0.567072i
$727$	1005.08	−	221.235i	1.38250	−	0.304312i	0.539394	−	0.842053i	$-0.318653\pi$
$727$	1005.08	−	221.235i	1.38250	−	0.304312i	0.843110	+	0.537741i	$0.180722\pi$
$728$	−430.110	−	714.848i	−0.590810	−	0.981934i
$729$	−676.046	−	272.770i	−0.927360	−	0.374169i
$730$	1097.82	−	1619.16i	1.50386	−	2.21803i
$731$	−74.0038	−	12.1323i	−0.101236	−	0.0165969i
$732$	−88.3255	−	50.0215i	−0.120663	−	0.0683354i
$733$	205.380	+	194.547i	0.280192	+	0.265412i	0.814870	−	0.579644i	$-0.196808\pi$
$733$	205.380	+	194.547i	0.280192	+	0.265412i	−0.534678	+	0.845056i	$0.679567\pi$
$734$	−626.653	−	661.549i	−0.853750	−	0.901293i
$735$	1469.63	−	2042.86i	1.99949	−	2.77940i
$736$	−15.0713	−	3.31744i	−0.0204773	−	0.00450739i
$737$	−211.767	−	628.501i	−0.287336	−	0.852782i
$738$	710.159	+	751.883i	0.962275	+	1.01881i
$739$	−608.737	−	133.993i	−0.823731	−	0.181317i	−0.216947	−	0.976183i	$-0.569610\pi$
$739$	−608.737	−	133.993i	−0.823731	−	0.181317i	−0.606784	+	0.794866i	$0.707541\pi$
$740$	−214.303	−	11.6191i	−0.289598	−	0.0157016i
$741$	78.2778	+	409.547i	0.105638	+	0.552695i
$742$	−840.960	−	796.600i	−1.13337	−	1.07358i
$743$	1192.06	−	64.6318i	1.60439	−	0.0869876i	0.769957	−	0.638096i	$-0.220278\pi$
$743$	1192.06	−	64.6318i	1.60439	−	0.0869876i	0.834434	+	0.551108i	$0.185795\pi$
$744$	−511.025	+	568.787i	−0.686862	+	0.764498i
$745$	−1027.65	+	1515.67i	−1.37939	+	2.03445i
$746$	−132.980	+	1222.73i	−0.178258	+	1.63905i
$747$	369.083	−	542.664i	0.494087	−	0.726458i
$748$	63.7395	−	14.0301i	0.0852132	−	0.0187568i
$749$	−241.805	+	39.6420i	−0.322838	+	0.0529265i
$750$	−879.408	+	561.211i	−1.17254	+	0.748281i
$751$	−67.4237	−	242.838i	−0.0897785	−	0.323353i	0.905000	−	0.425412i	$-0.139871\pi$
$751$	−67.4237	−	242.838i	−0.0897785	−	0.323353i	−0.994778	+	0.102059i	$0.967457\pi$
$752$	213.091	+	280.317i	0.283366	+	0.372762i
$753$	−89.1327	−	44.2862i	−0.118370	−	0.0588130i
$754$	232.063	−	437.717i	0.307776	−	0.580527i
$755$	−689.767	+	274.828i	−0.913598	+	0.364011i
$756$	−118.337	+	273.458i	−0.156531	+	0.361717i
$757$	81.2662	−	95.6740i	0.107353	−	0.126386i	−0.705861	−	0.708350i	$-0.749440\pi$
$757$	81.2662	−	95.6740i	0.107353	−	0.126386i	0.813214	+	0.581964i	$0.197716\pi$
$758$	−95.9914	+	50.8914i	−0.126638	+	0.0671391i
$759$	19.4813	−	0.513622i	0.0256670	−	0.000676709i
$760$	1168.20	−	540.468i	1.53711	−	0.711143i
$761$	627.742	−	533.209i	0.824891	−	0.700669i	−0.131957	−	0.991255i	$-0.542126\pi$
$761$	627.742	−	533.209i	0.824891	−	0.700669i	0.956849	+	0.290586i	$0.0938503\pi$
$762$	−800.906	+	574.412i	−1.05106	+	0.753821i
$763$	−1830.87	−	1391.79i	−2.39957	−	1.82410i
$764$	−78.2178	+	129.999i	−0.102379	+	0.170156i
$765$	−98.1671	−	914.953i	−0.128323	−	1.19602i
$766$	3.51235			0.00458532
$767$	444.777	+	152.589i	0.579891	+	0.198943i
$768$	266.861	−	416.834i	0.347475	−	0.542753i
$769$	−514.385	−	173.317i	−0.668901	−	0.225379i	−0.0356957	−	0.999363i	$-0.511365\pi$
$769$	−514.385	−	173.317i	−0.668901	−	0.225379i	−0.633206	+	0.773984i	$0.718261\pi$
$770$	563.891	−	937.193i	0.732325	−	1.21713i
$771$	−133.637	−	364.571i	−0.173330	−	0.472855i
$772$	14.5833	−	36.6013i	0.0188903	−	0.0474110i
$773$	93.8036	−	79.6775i	0.121350	−	0.103076i	−0.584657	−	0.811281i	$-0.698771\pi$
$773$	93.8036	−	79.6775i	0.121350	−	0.103076i	0.706007	+	0.708205i

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)

\(f(q)\)	\(=\)	\(q+(-0.561287 + 1.66584i) q^{2} +(2.68858 - 1.33099i) q^{3} +(0.724387 + 0.550665i) q^{4} +(7.94437 + 3.16532i) q^{5} +(0.708151 + 5.22582i) q^{6} +(-11.0072 + 5.09247i) q^{7} +(-7.14376 + 4.84359i) q^{8} +(5.45694 - 7.15694i) q^{9} +O(q^{10})\)	\(q+(-0.561287 + 1.66584i) q^{2} +(2.68858 - 1.33099i) q^{3} +(0.724387 + 0.550665i) q^{4} +(7.94437 + 3.16532i) q^{5} +(0.708151 + 5.22582i) q^{6} +(-11.0072 + 5.09247i) q^{7} +(-7.14376 + 4.84359i) q^{8} +(5.45694 - 7.15694i) q^{9} +(-9.73200 + 11.4574i) q^{10} +(5.78046 + 1.60494i) q^{11} +(2.68050 + 0.516355i) q^{12} +(3.73316 - 7.04149i) q^{13} +(-2.30505 - 21.1946i) q^{14} +(25.5721 - 2.06363i) q^{15} +(-3.08522 - 11.1120i) q^{16} +(5.02021 - 10.8510i) q^{17} +(8.85943 + 13.1075i) q^{18} +(-17.0313 + 3.74887i) q^{19} +(4.01176 + 6.66760i) q^{20} +(-22.8157 + 28.3420i) q^{21} +(-5.91807 + 8.72850i) q^{22} +(1.06856 + 0.175182i) q^{23} +(-12.7598 + 22.5306i) q^{24} +(34.9438 + 33.1005i) q^{25} +(9.63463 + 10.1712i) q^{26} +(5.14560 - 26.5051i) q^{27} +(-10.7777 - 2.37235i) q^{28} +(-11.2914 - 33.5116i) q^{29} +(-10.9156 + 43.7573i) q^{30} +(28.8402 + 6.34821i) q^{31} +(-14.2308 - 0.771569i) q^{32} +(17.6774 - 3.37873i) q^{33} +(15.2583 + 14.4534i) q^{34} +(-103.564 + 5.61510i) q^{35} +(7.89401 - 2.17946i) q^{36} +(-15.4779 + 22.8281i) q^{37} +(3.31443 - 30.4756i) q^{38} +(0.664760 - 23.9004i) q^{39} +(-72.0841 + 15.8669i) q^{40} +(64.5113 - 10.5761i) q^{41} +(-34.4071 - 53.9153i) q^{42} +(-1.67802 - 6.04366i) q^{43} +(3.30351 + 4.34569i) q^{44} +(66.0059 - 39.5844i) q^{45} +(-0.891595 + 1.68173i) q^{46} +(-28.3644 + 11.3014i) q^{47} +(-23.0848 - 25.7690i) q^{48} +(63.5031 - 74.7616i) q^{49} +(-74.7537 + 39.6319i) q^{50} +(-0.945332 - 35.8557i) q^{51} +(6.58175 - 3.04504i) q^{52} +(41.4105 - 35.1744i) q^{53} +(41.2652 + 23.4488i) q^{54} +(40.8419 + 31.0472i) q^{55} +(53.9669 - 89.6936i) q^{56} +(-40.8003 + 32.7476i) q^{57} +62.1626 q^{58} +(9.22505 + 58.2743i) q^{59} +(19.6605 + 12.5868i) q^{60} +(-35.2383 - 11.8732i) q^{61} +(-26.7628 + 44.4801i) q^{62} +(-23.6190 + 106.567i) q^{63} +(26.3471 - 66.1261i) q^{64} +(51.9462 - 44.1235i) q^{65} +(-4.29367 + 31.3442i) q^{66} +(-62.0406 - 91.5030i) q^{67} +(9.61185 - 5.09588i) q^{68} +(3.10608 - 0.951254i) q^{69} +(48.7756 - 175.674i) q^{70} +(-56.7190 + 22.5989i) q^{71} +(-4.31773 + 77.5586i) q^{72} +(-129.369 + 14.0698i) q^{73} +(-29.3405 - 38.5968i) q^{74} +(138.006 + 42.4836i) q^{75} +(-14.4016 - 6.66290i) q^{76} +(-71.7997 + 11.7710i) q^{77} +(39.4412 + 14.5224i) q^{78} +(74.7511 - 44.9762i) q^{79} +(10.6628 - 98.0433i) q^{80} +(-21.4437 - 78.1100i) q^{81} +(-18.5913 + 113.402i) q^{82} +(72.8133 - 3.94782i) q^{83} +(-32.1343 + 7.96676i) q^{84} +(74.2294 - 70.3138i) q^{85} +(11.0096 + 0.596925i) q^{86} +(-74.9613 - 75.0699i) q^{87} +(-49.0679 + 16.5329i) q^{88} +(-45.7688 - 135.837i) q^{89} +(28.8931 + 132.174i) q^{90} +(-5.23305 + 96.5180i) q^{91} +(0.677586 + 0.715319i) q^{92} +(85.9887 - 21.3183i) q^{93} +(-2.90578 - 53.5939i) q^{94} +(-147.169 - 24.1272i) q^{95} +(-39.2875 + 16.8666i) q^{96} +(-72.0110 - 7.83166i) q^{97} +(88.8976 + 147.749i) q^{98} +(43.0300 - 32.6124i) 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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