LMFDB - Embedded newform 177.3.h.a.5.5

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			5.5
Character	$\chi$	$=$	177.5
Dual form			177.3.h.a.71.5

$q$-expansion

$f(q)$	$=$	$q+(-0.999960 + 2.96778i) q^{2} +(-1.56678 - 2.55836i) q^{3} +(-4.62340 - 3.51462i) q^{4} +(4.69371 + 1.87015i) q^{5} +(9.15935 - 2.09161i) q^{6} +(-2.98209 + 1.37966i) q^{7} +(4.68548 - 3.17683i) q^{8} +(-4.09038 + 8.01678i) q^{9} +O(q^{10})$	\(q+(-0.999960 + 2.96778i) q^{2} +(-1.56678 - 2.55836i) q^{3} +(-4.62340 - 3.51462i) q^{4} +(4.69371 + 1.87015i) q^{5} +(9.15935 - 2.09161i) q^{6} +(-2.98209 + 1.37966i) q^{7} +(4.68548 - 3.17683i) q^{8} +(-4.09038 + 8.01678i) q^{9} +(-10.2437 + 12.0598i) q^{10} +(-5.12806 - 1.42380i) q^{11} +(-1.74778 + 17.3350i) q^{12} +(-7.65201 + 14.4332i) q^{13} +(-1.11256 - 10.2298i) q^{14} +(-2.56953 - 14.9383i) q^{15} +(-1.47196 - 5.30154i) q^{16} +(2.37465 - 5.13272i) q^{17} +(-19.7018 - 20.1558i) q^{18} +(-29.6004 + 6.51555i) q^{19} +(-15.1281 - 25.1430i) q^{20} +(8.20195 + 5.46762i) q^{21} +(9.35336 - 13.7952i) q^{22} +(-6.42262 - 1.05293i) q^{23} +(-15.4686 - 7.00972i) q^{24} +(0.383589 + 0.363355i) q^{25} +(-35.1829 - 37.1421i) q^{26} +(26.9185 - 2.09592i) q^{27} +(18.6364 + 4.10218i) q^{28} +(13.1216 + 38.9436i) q^{29} +(46.9029 + 7.31191i) q^{30} +(-38.3739 - 8.44674i) q^{31} +(39.8161 + 2.15877i) q^{32} +(4.39197 + 15.3502i) q^{33} +(12.8582 + 12.1799i) q^{34} +(-16.5772 + 0.898791i) q^{35} +(47.0874 - 22.6887i) q^{36} +(12.2214 - 18.0252i) q^{37} +(10.2626 - 94.3627i) q^{38} +(48.9144 - 3.03716i) q^{39} +(27.9334 - 6.14861i) q^{40} +(-12.2769 + 2.01269i) q^{41} +(-24.4283 + 18.8742i) q^{42} +(7.49855 + 27.0073i) q^{43} +(18.7049 + 24.6059i) q^{44} +(-34.1916 + 29.9789i) q^{45} +(9.54723 - 18.0080i) q^{46} +(-42.0041 + 16.7360i) q^{47} +(-11.2570 + 12.0722i) q^{48} +(-24.7325 + 29.1174i) q^{49} +(-1.46193 + 0.775066i) q^{50} +(-16.8519 + 1.96666i) q^{51} +(86.1056 - 39.8367i) q^{52} +(8.72926 - 7.41470i) q^{53} +(-20.6972 + 81.9840i) q^{54} +(-21.4069 - 16.2731i) q^{55} +(-9.58956 + 15.9380i) q^{56} +(63.0465 + 65.5200i) q^{57} -128.697 q^{58} +(38.0637 + 45.0795i) q^{59} +(-40.6224 + 78.0966i) q^{60} +(46.0786 + 15.5257i) q^{61} +(63.4404 - 105.439i) q^{62} +(1.13743 - 29.5501i) q^{63} +(-38.0752 + 95.5615i) q^{64} +(-62.9086 + 53.4350i) q^{65} +(-49.9477 - 2.31518i) q^{66} +(-31.2284 - 46.0585i) q^{67} +(-29.0185 + 15.3846i) q^{68} +(7.36907 + 18.0811i) q^{69} +(13.9092 - 50.0962i) q^{70} +(75.0351 - 29.8967i) q^{71} +(6.30260 + 50.5569i) q^{72} +(28.1527 - 3.06179i) q^{73} +(41.2738 + 54.2947i) q^{74} +(0.328590 - 1.55066i) q^{75} +(159.754 + 73.9102i) q^{76} +(17.2567 - 2.82909i) q^{77} +(-39.8988 + 148.204i) q^{78} +(-14.6892 + 8.83819i) q^{79} +(3.00567 - 27.6367i) q^{80} +(-47.5376 - 65.5834i) q^{81} +(6.30317 - 38.4476i) q^{82} +(144.486 - 7.83379i) q^{83} +(-18.7043 - 54.1057i) q^{84} +(20.7448 - 19.6506i) q^{85} +(-87.6500 - 4.75224i) q^{86} +(79.0728 - 94.5859i) q^{87} +(-28.5506 + 9.61981i) q^{88} +(28.9065 + 85.7915i) q^{89} +(-54.7803 - 131.451i) q^{90} +(2.90602 - 53.5983i) q^{91} +(25.9937 + 27.4412i) q^{92} +(38.5139 + 111.408i) q^{93} +(-7.66616 - 141.394i) q^{94} +(-151.121 - 24.7750i) q^{95} +(-56.8604 - 105.246i) q^{96} +(132.380 + 14.3972i) q^{97} +(-61.6824 - 102.517i) q^{98} +(32.3900 - 35.2866i) 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 $

$2$	−0.999960	+	2.96778i	−0.499980	+	1.48389i	0.339557	+	0.940585i	$0.389723\pi$
$2$	−0.999960	+	2.96778i	−0.499980	+	1.48389i	−0.839537	+	0.543302i	$0.817174\pi$
$3$	−1.56678	−	2.55836i	−0.522261	−	0.852786i
$3$	−1.56678	−	2.55836i	−0.522261	−	0.852786i
$4$	−4.62340	−	3.51462i	−1.15585	−	0.878654i
$5$	4.69371	+	1.87015i	0.938742	+	0.374029i	0.788789	−	0.614664i	$-0.210708\pi$
$5$	4.69371	+	1.87015i	0.938742	+	0.374029i	0.149953	+	0.988693i	$0.452088\pi$
$6$	9.15935	−	2.09161i	1.52656	−	0.348601i
$7$	−2.98209	+	1.37966i	−0.426013	+	0.197094i	−0.621167	−	0.783678i	$-0.713341\pi$
$7$	−2.98209	+	1.37966i	−0.426013	+	0.197094i	0.195155	+	0.980773i	$0.437479\pi$
$8$	4.68548	−	3.17683i	0.585685	−	0.397104i
$9$	−4.09038	+	8.01678i	−0.454486	+	0.890754i
$10$	−10.2437	+	12.0598i	−1.02437	+	1.20598i
$11$	−5.12806	−	1.42380i	−0.466187	−	0.129436i	0.0264889	−	0.999649i	$-0.491567\pi$
$11$	−5.12806	−	1.42380i	−0.466187	−	0.129436i	−0.492676	+	0.870213i	$0.663981\pi$
$12$	−1.74778	+	17.3350i	−0.145648	+	1.44458i
$13$	−7.65201	+	14.4332i	−0.588616	+	1.11025i	0.393028	+	0.919527i	$0.371428\pi$
$13$	−7.65201	+	14.4332i	−0.588616	+	1.11025i	−0.981644	+	0.190722i	$0.938917\pi$
$14$	−1.11256	−	10.2298i	−0.0794682	−	0.730698i
$15$	−2.56953	−	14.9383i	−0.171302	−	0.995887i
$16$	−1.47196	−	5.30154i	−0.0919978	−	0.331346i
$17$	2.37465	−	5.13272i	0.139685	−	0.301925i	−0.825090	−	0.565002i	$-0.808875\pi$
$17$	2.37465	−	5.13272i	0.139685	−	0.301925i	0.964775	+	0.263077i	$0.0847374\pi$
$18$	−19.7018	−	20.1558i	−1.09454	−	1.11977i
$19$	−29.6004	+	6.51555i	−1.55792	+	0.342923i	−0.908624	−	0.417615i	$-0.862866\pi$
$19$	−29.6004	+	6.51555i	−1.55792	+	0.342923i	−0.649293	+	0.760538i	$0.724935\pi$
$20$	−15.1281	−	25.1430i	−0.756403	−	1.25715i
$21$	8.20195	+	5.46762i	0.390569	+	0.260363i
$22$	9.35336	−	13.7952i	0.425153	−	0.627054i
$23$	−6.42262	−	1.05293i	−0.279244	−	0.0457798i	0.0205324	−	0.999789i	$-0.493464\pi$
$23$	−6.42262	−	1.05293i	−0.279244	−	0.0457798i	−0.299777	+	0.954009i	$0.596912\pi$
$24$	−15.4686	−	7.00972i	−0.644525	−	0.292072i
$25$	0.383589	+	0.363355i	0.0153436	+	0.0145342i
$26$	−35.1829	−	37.1421i	−1.35319	−	1.42854i
$27$	26.9185	−	2.09592i	0.996983	−	0.0776265i
$28$	18.6364	+	4.10218i	0.665585	+	0.146506i
$29$	13.1216	+	38.9436i	0.452469	+	1.34288i	0.894975	+	0.446116i	$0.147193\pi$
$29$	13.1216	+	38.9436i	0.452469	+	1.34288i	−0.442506	+	0.896766i	$0.645910\pi$
$30$	46.9029	+	7.31191i	1.56343	+	0.243730i
$31$	−38.3739	−	8.44674i	−1.23787	−	0.272475i	−0.452646	−	0.891690i	$-0.649520\pi$
$31$	−38.3739	−	8.44674i	−1.23787	−	0.272475i	−0.785222	+	0.619215i	$0.787451\pi$
$32$	39.8161	+	2.15877i	1.24425	+	0.0674615i
$33$	4.39197	+	15.3502i	0.133090	+	0.465157i
$34$	12.8582	+	12.1799i	0.378183	+	0.358234i
$35$	−16.5772	+	0.898791i	−0.473635	+	0.0256797i
$36$	47.0874	−	22.6887i	1.30798	−	0.630241i
$37$	12.2214	−	18.0252i	0.330307	−	0.487167i	−0.625881	−	0.779918i	$-0.715261\pi$
$37$	12.2214	−	18.0252i	0.330307	−	0.487167i	0.956189	+	0.292752i	$0.0945709\pi$
$38$	10.2626	−	94.3627i	0.270067	−	2.48323i
$39$	48.9144	−	3.03716i	1.25422	−	0.0778760i
$40$	27.9334	−	6.14861i	0.698336	−	0.153715i
$41$	−12.2769	+	2.01269i	−0.299436	+	0.0490900i	−0.309627	−	0.950858i	$-0.600204\pi$
$41$	−12.2769	+	2.01269i	−0.299436	+	0.0490900i	0.0101913	+	0.999948i	$0.496756\pi$
$42$	−24.4283	+	18.8742i	−0.581626	+	0.449385i
$43$	7.49855	+	27.0073i	0.174385	+	0.628078i	0.998131	+	0.0611182i	$0.0194667\pi$
$43$	7.49855	+	27.0073i	0.174385	+	0.628078i	−0.823746	+	0.566960i	$0.808120\pi$
$44$	18.7049	+	24.6059i	0.425112	+	0.559226i
$45$	−34.1916	+	29.9789i	−0.759813	+	0.666197i
$46$	9.54723	−	18.0080i	0.207549	−	0.391478i
$47$	−42.0041	+	16.7360i	−0.893704	+	0.356084i	−0.771357	−	0.636403i	$-0.780421\pi$
$47$	−42.0041	+	16.7360i	−0.893704	+	0.356084i	−0.122347	+	0.992487i	$0.539042\pi$
$48$	−11.2570	+	12.0722i	−0.234520	+	0.251503i
$49$	−24.7325	+	29.1174i	−0.504746	+	0.594233i
$50$	−1.46193	+	0.775066i	−0.0292386	+	0.0155013i
$51$	−16.8519	+	1.96666i	−0.330429	+	0.0385620i
$52$	86.1056	−	39.8367i	1.65588	−	0.766090i
$53$	8.72926	−	7.41470i	0.164703	−	0.139900i	−0.561245	−	0.827650i	$-0.689677\pi$
$53$	8.72926	−	7.41470i	0.164703	−	0.139900i	0.725948	+	0.687750i	$0.241401\pi$
$54$	−20.6972	+	81.9840i	−0.383282	+	1.51822i
$55$	−21.4069	−	16.2731i	−0.389216	−	0.295875i
$56$	−9.58956	+	15.9380i	−0.171242	+	0.284607i
$57$	63.0465	+	65.5200i	1.10608	+	1.14947i
$58$	−128.697			−2.21891
$59$	38.0637	+	45.0795i	0.645147	+	0.764059i
$59$	38.0637	+	45.0795i	0.645147	+	0.764059i
$60$	−40.6224	+	78.0966i	−0.677041	+	1.30161i
$61$	46.0786	+	15.5257i	0.755387	+	0.254520i	0.670539	−	0.741874i	$-0.266063\pi$
$61$	46.0786	+	15.5257i	0.755387	+	0.254520i	0.0848482	+	0.996394i	$0.472959\pi$
$62$	63.4404	−	105.439i	1.02323	−	1.70063i
$63$	1.13743	−	29.5501i	0.0180544	−	0.469049i
$64$	−38.0752	+	95.5615i	−0.594924	+	1.49315i
$65$	−62.9086	+	53.4350i	−0.967824	+	0.822077i
$66$	−49.9477	−	2.31518i	−0.756783	−	0.0350785i
$67$	−31.2284	−	46.0585i	−0.466096	−	0.687440i	0.519897	−	0.854229i	$-0.325970\pi$
$67$	−31.2284	−	46.0585i	−0.466096	−	0.687440i	−0.985993	+	0.166789i	$0.946660\pi$
$68$	−29.0185	+	15.3846i	−0.426743	+	0.226245i
$69$	7.36907	+	18.0811i	0.106798	+	0.262044i
$70$	13.9092	−	50.0962i	0.198702	−	0.715661i
$71$	75.0351	−	29.8967i	1.05683	−	0.421081i	0.223991	−	0.974591i	$-0.428091\pi$
$71$	75.0351	−	29.8967i	1.05683	−	0.421081i	0.832842	+	0.553511i	$0.186712\pi$
$72$	6.30260	+	50.5569i	0.0875362	+	0.702180i
$73$	28.1527	−	3.06179i	0.385653	−	0.0419423i	0.0867609	−	0.996229i	$-0.472348\pi$
$73$	28.1527	−	3.06179i	0.385653	−	0.0419423i	0.298892	+	0.954287i	$0.403383\pi$
$74$	41.2738	+	54.2947i	0.557754	+	0.733713i
$75$	0.328590	−	1.55066i	0.00438120	−	0.0206754i
$76$	159.754	+	73.9102i	2.10203	+	0.972502i
$77$	17.2567	−	2.82909i	0.224113	−	0.0367414i
$78$	−39.8988	+	148.204i	−0.511523	+	1.90005i
$79$	−14.6892	+	8.83819i	−0.185939	+	0.111876i	−0.605480	−	0.795861i	$-0.707019\pi$
$79$	−14.6892	+	8.83819i	−0.185939	+	0.111876i	0.419541	+	0.907737i	$0.362191\pi$
$80$	3.00567	−	27.6367i	0.0375708	−	0.345458i
$81$	−47.5376	−	65.5834i	−0.586884	−	0.809671i
$82$	6.30317	−	38.4476i	0.0768679	−	0.468873i
$83$	144.486	−	7.83379i	1.74079	−	0.0943830i	0.843863	−	0.536558i	$-0.180276\pi$
$83$	144.486	−	7.83379i	1.74079	−	0.0943830i	0.896929	+	0.442175i	$0.145793\pi$
$84$	−18.7043	−	54.1057i	−0.222671	−	0.644116i
$85$	20.7448	−	19.6506i	0.244057	−	0.231183i
$86$	−87.6500	−	4.75224i	−1.01919	−	0.0552587i
$87$	79.0728	−	94.5859i	0.908883	−	1.08719i
$88$	−28.5506	+	9.61981i	−0.324438	+	0.109316i
$89$	28.9065	+	85.7915i	0.324792	+	0.963950i	0.978329	+	0.207055i	$0.0663879\pi$
$89$	28.9065	+	85.7915i	0.324792	+	0.963950i	−0.653537	+	0.756895i	$0.726716\pi$
$90$	−54.7803	−	131.451i	−0.608670	−	1.46056i
$91$	2.90602	−	53.5983i	0.0319343	−	0.588993i
$92$	25.9937	+	27.4412i	0.282540	+	0.298274i
$93$	38.5139	+	111.408i	0.414127	+	1.19794i
$94$	−7.66616	−	141.394i	−0.0815549	−	1.50419i
$95$	−151.121	−	24.7750i	−1.59075	−	0.260790i
$96$	−56.8604	−	105.246i	−0.592296	−	1.09631i
$97$	132.380	+	14.3972i	1.36474	+	0.148424i	0.760998	−	0.648755i	$-0.224710\pi$
$97$	132.380	+	14.3972i	1.36474	+	0.148424i	0.603743	+	0.797179i	$0.293675\pi$
$98$	−61.6824	−	102.517i	−0.629412	−	1.04609i
$99$	32.3900	−	35.2866i	0.327171	−	0.356431i
$100$	−0.496432	−	3.02810i	−0.00496432	−	0.0302810i
$101$	−27.0739	+	58.5192i	−0.268058	+	0.579398i	−0.994127	−	0.108224i	$-0.965484\pi$
$101$	−27.0739	+	58.5192i	−0.268058	+	0.579398i	0.726068	+	0.687623i	$0.241346\pi$
$102$	11.0146	−	51.9792i	0.107986	−	0.509600i
$103$	144.159	−	109.587i	1.39960	−	1.06395i	0.411287	−	0.911506i	$-0.365080\pi$
$103$	144.159	−	109.587i	1.39960	−	1.06395i	0.988313	−	0.152441i	$-0.0487135\pi$
$104$	9.99862	+	91.9358i	0.0961406	+	0.883998i
$105$	28.2724	+	41.0023i	0.269261	+	0.390498i
$106$	13.2763	+	33.3209i	0.125248	+	0.314348i
$107$	−51.2007	−	14.2158i	−0.478511	−	0.132858i	0.0198943	−	0.999802i	$-0.493667\pi$
$107$	−51.2007	−	14.2158i	−0.478511	−	0.132858i	−0.498405	+	0.866944i	$0.666081\pi$
$108$	−131.821	−	84.9181i	−1.22057	−	0.786278i
$109$	−7.62691	−	14.3859i	−0.0699716	−	0.131981i	0.846058	−	0.533090i	$-0.178969\pi$
$109$	−7.62691	−	14.3859i	−0.0699716	−	0.131981i	−0.916030	+	0.401110i	$0.868625\pi$
$110$	69.7010	−	47.2584i	0.633645	−	0.429622i
$111$	−65.2631	−	3.02508i	−0.587956	−	0.0272530i
$112$	11.7038	+	13.7788i	0.104499	+	0.123025i
$113$	−125.523	−	50.0129i	−1.11082	−	0.442592i	−0.258713	−	0.965954i	$-0.583298\pi$
$113$	−125.523	−	50.0129i	−1.11082	−	0.442592i	−0.852111	+	0.523362i	$0.824678\pi$
$114$	−257.493	+	121.591i	−2.25871	+	1.06658i
$115$	−28.1768	−	16.9534i	−0.245015	−	0.147421i
$116$	76.2052	−	226.169i	0.656942	−	1.94973i
$117$	−84.4084	−	120.382i	−0.721439	−	1.02891i
$118$	−171.848	+	67.8867i	−1.45634	+	0.575311i
$119$			18.5824i			0.156155i
$120$	−59.4960	−	61.8301i	−0.495800	−	0.515251i
$121$	−79.4100	−	47.7794i	−0.656281	−	0.394871i
$122$	−92.1536	+	121.226i	−0.755357	+	0.993655i
$123$	24.3844	+	28.2552i	0.198247	+	0.229717i
$124$	147.731	+	173.922i	1.19138	+	1.40260i
$125$	−51.9169	−	112.217i	−0.415336	−	0.897733i
$126$	86.5607	+	32.9245i	0.686989	+	0.261306i
$127$	68.1391	+	128.524i	0.536529	+	1.01200i	0.992528	+	0.122020i	$0.0389373\pi$
$127$	68.1391	+	128.524i	0.536529	+	1.01200i	−0.455999	+	0.889980i	$0.650718\pi$
$128$	−123.968	−	105.299i	−0.968497	−	0.822649i
$129$	57.3458	−	61.4986i	0.444541	−	0.476734i
$130$	−95.6771	−	240.131i	−0.735978	−	1.84716i
$131$	47.8339	+	25.3599i	0.365144	+	0.193587i	0.640871	−	0.767649i	$-0.278573\pi$
$131$	47.8339	+	25.3599i	0.365144	+	0.193587i	−0.275726	+	0.961236i	$0.588918\pi$
$132$	33.6442	−	86.4061i	0.254880	−	0.654592i
$133$	79.2818	−	60.2685i	0.596104	−	0.453146i
$134$	167.918	−	46.6223i	1.25312	−	0.347928i
$135$	130.267	+	40.5039i	0.964944	+	0.300029i
$136$	−5.17943	−	31.5931i	−0.0380840	−	0.232302i
$137$	55.2346	+	250.933i	0.403172	+	1.83163i	0.540806	+	0.841147i	$0.318119\pi$
$137$	55.2346	+	250.933i	0.403172	+	1.83163i	−0.137634	+	0.990483i	$0.543950\pi$
$138$	−61.0293	+	3.78940i	−0.442241	+	0.0274594i
$139$	−258.835	−	28.1501i	−1.86213	−	0.202518i	−0.893164	−	0.449731i	$-0.851520\pi$
$139$	−258.835	−	28.1501i	−1.86213	−	0.202518i	−0.968961	+	0.247212i	$0.920485\pi$
$140$	79.8021	+	54.1071i	0.570015	+	0.386480i
$141$	108.628	+	81.2398i	0.770410	+	0.576169i
$142$	13.6947	+	252.583i	0.0964412	+	1.77875i
$143$	59.7899	−	63.1195i	0.418111	−	0.441395i
$144$	48.5221	+	9.88487i	0.336959	+	0.0686449i
$145$	−11.2411	+	207.329i	−0.0775245	+	1.42986i
$146$	−19.0649	+	86.6125i	−0.130581	+	0.593237i
$147$	113.243	+	17.6540i	0.770362	+	0.120095i
$148$	−119.856	+	40.3842i	−0.809837	+	0.272866i
$149$	−13.4429	+	61.0716i	−0.0902206	+	0.409876i	−0.999986	−	0.00524598i	$-0.998330\pi$
$149$	−13.4429	+	61.0716i	−0.0902206	+	0.409876i	0.909766	+	0.415122i	$0.136261\pi$
$150$	4.27342	+	2.52578i	0.0284895	+	0.0168385i
$151$	−65.7849	+	62.3148i	−0.435662	+	0.412681i	−0.873845	−	0.486205i	$-0.838381\pi$
$151$	−65.7849	+	62.3148i	−0.435662	+	0.412681i	0.438183	+	0.898886i	$0.355622\pi$
$152$	−117.993	+	124.564i	−0.776272	+	0.819501i
$153$	31.4347	+	40.0318i	0.205455	+	0.261646i
$154$	−8.85989	+	54.0429i	−0.0575317	+	0.350928i
$155$	−164.319	−	111.411i	−1.06013	−	0.718783i
$156$	−236.825	−	157.873i	−1.51811	−	1.01201i
$157$	181.669	−	109.307i	1.15713	−	0.696220i	0.198281	−	0.980145i	$-0.436464\pi$
$157$	181.669	−	109.307i	1.15713	−	0.696220i	0.958847	+	0.283925i	$0.0916366\pi$
$158$	−11.5412	−	52.4320i	−0.0730453	−	0.331848i
$159$	−32.6463	−	10.7153i	−0.205323	−	0.0673920i
$160$	182.848	+	84.5946i	1.14280	+	0.528716i
$161$	20.6055	−	5.72109i	0.127985	−	0.0355347i
$162$	242.172	−	75.5002i	1.49489	−	0.466051i
$163$	−301.686	+	32.8103i	−1.85083	+	0.201290i	−0.964917	−	0.262557i	$-0.915434\pi$
$163$	−301.686	+	32.8103i	−1.85083	+	0.201290i	−0.885915	+	0.463847i	$0.846469\pi$
$164$	63.8347	+	33.8430i	0.389236	+	0.206360i
$165$	−8.09242	+	80.2629i	−0.0490450	+	0.486442i
$166$	−121.231	+	436.635i	−0.730307	+	2.63033i
$167$	−99.7994	−	84.7704i	−0.597601	−	0.507607i	0.296760	−	0.954952i	$-0.404094\pi$
$167$	−99.7994	−	84.7704i	−0.597601	−	0.507607i	−0.894362	+	0.447345i	$0.852370\pi$
$168$	55.7998	−	0.437838i	0.332142	−	0.00260618i
$169$	−54.9241	−	81.0071i	−0.324995	−	0.479332i
$170$	37.5744	+	81.2158i	0.221026	+	0.477740i
$171$	68.8432	−	263.951i	0.402592	−	1.54357i
$172$	60.2517	−	151.220i	0.350300	−	0.879188i
$173$	−56.1834	+	73.9080i	−0.324759	+	0.427214i	−0.929280	−	0.369376i	$-0.879572\pi$
$173$	−56.1834	+	73.9080i	−0.324759	+	0.427214i	0.604521	+	0.796589i	$0.293365\pi$
$174$	201.640	+	329.252i	1.15885	+	1.89226i
$175$	−1.64520	−	0.554333i	−0.00940116	−	0.00316762i
$176$			29.2823i			0.166377i
$177$	55.6918	−	168.010i	0.314643	−	0.949210i
$178$	−283.515			−1.59278
$179$	−1.21641	+	3.61016i	−0.00679556	+	0.0201685i	−0.950997	−	0.309199i	$-0.899939\pi$
$179$	−1.21641	+	3.61016i	−0.00679556	+	0.0201685i	0.944202	+	0.329368i	$0.106836\pi$
$180$	263.446	−	18.4339i	1.46359	−	0.102410i
$181$	−239.854	−	182.333i	−1.32516	−	1.00736i	−0.998053	−	0.0623761i	$-0.980132\pi$
$181$	−239.854	−	182.333i	−1.32516	−	1.00736i	−0.327110	−	0.944986i	$-0.606075\pi$
$182$	156.162	+	62.2206i	0.858033	+	0.341872i
$183$	−32.4750	−	142.211i	−0.177459	−	0.777109i
$184$	−33.4380	+	15.4701i	−0.181729	+	0.0840766i
$185$	91.0733	−	61.7492i	0.492288	−	0.333780i
$186$	−369.147	+	2.89655i	−1.98466	+	0.0155728i
$187$	−19.4853	+	22.9399i	−0.104199	+	0.122673i
$188$	253.022	+	70.2512i	1.34586	+	0.373677i
$189$	−77.3818	+	43.3887i	−0.409427	+	0.229570i
$190$	224.641	−	423.719i	1.18232	−	2.23010i
$191$	6.06415	+	55.7590i	0.0317495	+	0.291932i	0.999238	+	0.0390187i	$0.0124232\pi$
$191$	6.06415	+	55.7590i	0.0317495	+	0.291932i	−0.967489	+	0.252913i	$0.918611\pi$
$192$	304.136	−	52.3143i	1.58404	−	0.272470i
$193$	−18.5902	−	66.9557i	−0.0963221	−	0.346921i	0.899647	−	0.436618i	$-0.143824\pi$
$193$	−18.5902	−	66.9557i	−0.0963221	−	0.346921i	−0.995969	+	0.0896972i	$0.971410\pi$
$194$	−175.102	+	378.477i	−0.902588	+	1.95091i
$195$	235.270	+	77.2214i	1.20651	+	0.396007i
$196$	216.685	−	47.6960i	1.10554	−	0.243347i
$197$	−127.062	−	211.178i	−0.644983	−	1.07197i	−0.991015	−	0.133748i	$-0.957299\pi$
$197$	−127.062	−	211.178i	−0.644983	−	1.07197i	0.346032	−	0.938223i	$-0.387529\pi$
$198$	72.3341	+	131.411i	0.365324	+	0.663694i
$199$	−110.501	+	162.977i	−0.555281	+	0.818978i	−0.996937	−	0.0782064i	$-0.975081\pi$
$199$	−110.501	+	162.977i	−0.555281	+	0.818978i	0.441656	+	0.897184i	$0.354391\pi$
$200$	2.95162	+	0.483893i	0.0147581	+	0.00241947i
$201$	−68.9058	+	152.057i	−0.342815	+	0.756503i
$202$	−146.599	−	138.866i	−0.725739	−	0.687456i
$203$	−92.8587	−	98.0298i	−0.457432	−	0.482905i
$204$	84.8251	+	50.1353i	0.415809	+	0.245761i
$205$	−61.3881	−	13.5125i	−0.299454	−	0.0659148i
$206$	181.075	+	537.413i	0.879007	+	2.60880i
$207$	34.7121	−	47.1818i	0.167691	−	0.227932i
$208$	87.7818	+	19.3222i	0.422028	+	0.0928953i
$209$	161.069	+	8.73293i	0.770667	+	0.0417844i
$210$	−149.957	+	42.9054i	−0.714080	+	0.204311i
$211$	180.529	+	171.007i	0.855590	+	0.810457i	0.983421	−	0.181338i	$-0.0580430\pi$
$211$	180.529	+	171.007i	0.855590	+	0.810457i	−0.127831	+	0.991796i	$0.540802\pi$
$212$	−66.4187	+	3.60112i	−0.313296	+	0.0169864i
$213$	−194.050	−	145.125i	−0.911034	−	0.681338i
$214$	93.3879	−	137.737i	0.436392	−	0.643630i
$215$	−15.3116	+	140.788i	−0.0712169	+	0.654828i
$216$	119.468	−	95.3361i	0.553092	−	0.441371i
$217$	126.088	−	27.7541i	0.581051	−	0.127899i
$218$	50.3207	−	8.24965i	0.230829	−	0.0378424i
$219$	−51.9423	−	67.2275i	−0.237180	−	0.306975i
$220$	41.7789	+	150.474i	0.189904	+	0.683973i
$221$	55.9109	+	73.5495i	0.252990	+	0.332803i
$222$	74.2382	−	190.661i	0.334406	−	0.858834i
$223$	52.8889	−	99.7590i	0.237170	−	0.447350i	−0.736145	−	0.676824i	$-0.763356\pi$
$223$	52.8889	−	99.7590i	0.237170	−	0.447350i	0.973315	+	0.229474i	$0.0737006\pi$
$224$	−121.714	+	48.4951i	−0.543364	+	0.216496i
$225$	−4.48196	+	1.58889i	−0.0199198	+	0.00706174i
$226$	273.945	−	322.513i	1.21215	−	1.42705i
$227$	163.972	−	86.9327i	0.722346	−	0.382963i	−0.0663096	−	0.997799i	$-0.521122\pi$
$227$	163.972	−	86.9327i	0.722346	−	0.382963i	0.788655	+	0.614836i	$0.210778\pi$
$228$	−61.2117	−	524.510i	−0.268472	−	2.30048i
$229$	−14.8233	+	6.85800i	−0.0647307	+	0.0299476i	−0.451987	−	0.892024i	$-0.649285\pi$
$229$	−14.8233	+	6.85800i	−0.0647307	+	0.0299476i	0.387257	+	0.921972i	$0.373423\pi$
$230$	78.4895	−	66.6696i	0.341259	−	0.289868i
$231$	−34.2753	−	39.7162i	−0.148378	−	0.171931i
$232$	185.198	+	140.784i	0.798269	+	0.606828i
$233$	−51.5725	+	85.7142i	−0.221341	+	0.367872i	−0.947553	−	0.319599i	$-0.896452\pi$
$233$	−51.5725	+	85.7142i	−0.221341	+	0.367872i	0.726211	+	0.687471i	$0.241279\pi$
$234$	441.671	−	130.128i	1.88749	−	0.556103i
$235$	−228.454			−0.972143
$236$	−17.5464	−	342.200i	−0.0743493	−	1.45000i
$237$	45.6260	+	23.7326i	0.192515	+	0.100138i
$238$	−55.1485	−	18.5817i	−0.231716	−	0.0780743i
$239$	51.5949	−	85.7514i	0.215878	−	0.358793i	−0.729928	−	0.683524i	$-0.760446\pi$
$239$	51.5949	−	85.7514i	0.215878	−	0.358793i	0.945806	+	0.324732i	$0.105274\pi$
$240$	−75.4137	+	35.6111i	−0.314224	+	0.148380i
$241$	−60.0809	+	150.792i	−0.249298	+	0.625692i	−0.999364	−	0.0356721i	$-0.988643\pi$
$241$	−60.0809	+	150.792i	−0.249298	+	0.625692i	0.750065	+	0.661364i	$0.230022\pi$
$242$	221.205	−	187.893i	0.914072	−	0.776419i
$243$	−93.3045	+	224.373i	−0.383969	+	0.923346i
$244$	−158.473	−	233.730i	−0.649480	−	0.957911i
$245$	−170.541	+	90.4152i	−0.696086	+	0.369042i
$246$	−108.238	+	44.1133i	−0.439993	+	0.179322i
$247$	132.462	−	477.087i	0.536285	−	1.93152i
$248$	−206.634	+	82.3306i	−0.833202	+	0.331978i
$249$	−246.419	−	357.372i	−0.989636	−	1.43523i
$250$	384.949	−	41.8657i	1.53979	−	0.167463i
$251$	131.796	+	173.374i	0.525082	+	0.690734i	0.979818	−	0.199893i	$-0.0640593\pi$
$251$	131.796	+	173.374i	0.525082	+	0.690734i	−0.454736	+	0.890627i	$0.650266\pi$
$252$	−109.116	+	132.624i	−0.433000	+	0.526287i
$253$	31.4364	+	14.5440i	0.124254	+	0.0574862i
$254$	−449.567	+	73.7028i	−1.76995	+	0.290168i
$255$	−82.7758	−	22.2845i	−0.324611	−	0.0873903i
$256$	83.8958	−	50.4784i	0.327718	−	0.197181i
$257$	−45.7784	+	420.926i	−0.178126	+	1.63784i	0.474566	+	0.880220i	$0.342605\pi$
$257$	−45.7784	+	420.926i	−0.178126	+	1.63784i	−0.652692	+	0.757623i	$0.726361\pi$
$258$	125.171	+	231.686i	0.485158	+	0.898007i
$259$	−11.5766	+	70.6140i	−0.0446972	+	0.272641i
$260$	478.655	−	25.9519i	1.84098	−	0.0998151i
$261$	−365.874	−	54.1008i	−1.40182	−	0.207283i
$262$	−123.095	+	116.601i	−0.469827	+	0.445044i
$263$	389.077	+	21.0951i	1.47938	+	0.0802096i	0.776058	−	0.630662i	$-0.217216\pi$
$263$	389.077	+	21.0951i	1.47938	+	0.0802096i	0.703322	+	0.710871i	$0.251699\pi$
$264$	69.3435	+	57.9704i	0.262665	+	0.219585i
$265$	54.8392	−	18.4775i	0.206940	−	0.0697263i
$266$	99.5847	+	295.557i	0.374378	+	1.11112i
$267$	174.195	−	208.370i	0.652416	−	0.780412i
$268$	−17.4964	+	322.703i	−0.0652852	+	1.20411i
$269$	−218.327	−	230.485i	−0.811625	−	0.856822i	0.180305	−	0.983611i	$-0.442292\pi$
$269$	−218.327	−	230.485i	−0.811625	−	0.856822i	−0.991930	+	0.126789i	$0.959533\pi$
$270$	−250.469	+	346.102i	−0.927662	+	1.28186i
$271$	14.0786	+	259.664i	0.0519505	+	0.958170i	0.902073	+	0.431584i	$0.142045\pi$
$271$	14.0786	+	259.664i	0.0519505	+	0.958170i	−0.850122	+	0.526585i	$0.823472\pi$
$272$	−30.7067	−	5.03411i	−0.112892	−	0.0185077i
$273$	−141.677	+	76.5424i	−0.518963	+	0.280375i
$274$	−799.946	−	86.9994i	−2.91951	−	0.317516i
$275$	−1.44972	−	2.40946i	−0.00527172	−	0.00876166i
$276$	29.4779	−	109.495i	0.106804	−	0.396723i
$277$	67.3911	+	411.067i	0.243289	+	1.48400i	0.772232	+	0.635341i	$0.219140\pi$
$277$	67.3911	+	411.067i	0.243289	+	1.48400i	−0.528943	+	0.848657i	$0.677411\pi$
$278$	342.368	−	740.017i	1.23154	−	2.66193i
$279$	224.679	−	273.085i	0.805303	−	0.978799i
$280$	−74.8170	+	56.8744i	−0.267203	+	0.203123i
$281$	27.6770	+	254.486i	0.0984946	+	0.905643i	0.934269	+	0.356570i	$0.116054\pi$
$281$	27.6770	+	254.486i	0.0984946	+	0.905643i	−0.835774	+	0.549074i	$0.814981\pi$
$282$	−349.725	+	241.146i	−1.24016	+	0.855129i
$283$	152.134	+	381.827i	0.537575	+	1.34921i	0.907462	+	0.420135i	$0.138017\pi$
$283$	152.134	+	381.827i	0.537575	+	1.34921i	−0.369887	+	0.929077i	$0.620603\pi$
$284$	−451.993	−	125.495i	−1.59152	−	0.441885i
$285$	173.390	+	425.438i	0.608387	+	1.49277i
$286$	127.537	+	240.560i	0.445933	+	0.841119i
$287$	33.8339	−	22.9399i	0.117888	−	0.0799301i
$288$	−180.169	+	310.367i	−0.625588	+	1.07766i
$289$	166.389	+	195.888i	0.575740	+	0.677813i
$290$	−604.066	−	240.682i	−2.08299	−	0.829937i
$291$	−170.577	−	361.232i	−0.586177	−	1.24135i
$292$	−140.922	−	84.7901i	−0.482610	−	0.290377i
$293$	106.688	−	316.637i	0.364121	−	1.08067i	−0.596452	−	0.802648i	$-0.703424\pi$
$293$	106.688	−	316.637i	0.364121	−	1.08067i	0.960574	−	0.278025i	$-0.0896799\pi$
$294$	−165.632	+	318.427i	−0.563374	+	1.08309i
$295$	94.3546	+	282.775i	0.319846	+	0.958558i
$296$		−	123.282i		−	0.416493i
$297$	−141.024	−	27.5786i	−0.474828	−	0.0928571i
$298$	−167.804	−	100.965i	−0.563102	−	0.338807i
$299$	64.3432	−	84.6420i	0.215195	−	0.283084i
$300$	−6.96917	+	6.01443i	−0.0232306	+	0.0200481i
$301$	−59.6223	−	70.1928i	−0.198081	−	0.233199i
$302$	−119.154	−	257.547i	−0.394550	−	0.852805i
$303$	192.132	−	22.4223i	0.634099	−	0.0740011i
$304$	78.1132	+	147.337i	0.256951	+	0.484661i
$305$	187.244	+	159.047i	0.613916	+	0.521465i
$306$	−150.239	+	53.2609i	−0.490977	+	0.174055i
$307$	−189.507	−	475.627i	−0.617287	−	1.54927i	−0.821416	−	0.570330i	$-0.806815\pi$
$307$	−189.507	−	475.627i	−0.617287	−	1.54927i	0.204129	−	0.978944i	$-0.434564\pi$
$308$	−89.7277	−	47.5706i	−0.291324	−	0.154450i
$309$	−506.227	−	197.111i	−1.63828	−	0.637899i
$310$	494.957	−	376.256i	1.59663	−	1.21373i
$311$	−353.231	+	98.0742i	−1.13579	+	0.315351i	−0.784021	−	0.620735i	$-0.786834\pi$
$311$	−353.231	+	98.0742i	−1.13579	+	0.315351i	−0.351771	+	0.936086i	$0.614421\pi$
$312$	219.539	−	169.624i	0.703650	−	0.543665i
$313$	58.5910	+	357.389i	0.187192	+	1.14182i	0.898511	+	0.438950i	$0.144650\pi$
$313$	58.5910	+	357.389i	0.187192	+	1.14182i	−0.711320	+	0.702869i	$0.751902\pi$
$314$	142.736	+	648.455i	0.454572	+	2.06514i
$315$	60.6017	−	136.572i	0.192386	−	0.433563i
$316$	98.9768	+	10.7644i	0.313218	+	0.0340645i
$317$	−42.0242	−	28.4931i	−0.132568	−	0.0898836i	0.493100	−	0.869972i	$-0.335864\pi$
$317$	−42.0242	−	28.4931i	−0.132568	−	0.0898836i	−0.625669	+	0.780089i	$0.715174\pi$
$318$	64.4457	−	86.1720i	0.202659	−	0.270981i
$319$	−11.8406	−	218.387i	−0.0371179	−	0.684600i
$320$	−357.428	+	377.332i	−1.11696	+	1.17916i
$321$	43.8513	+	153.263i	0.136608	+	0.477454i
$322$	−3.62577	+	66.8734i	−0.0112602	+	0.207681i
$323$	−36.8481	+	167.403i	−0.114081	+	0.518275i
$324$	−10.7150	+	470.295i	−0.0330710	+	1.45153i
$325$	−8.17961	+	2.75603i	−0.0251680	+	0.00848010i
$326$	204.300	−	928.144i	0.626687	−	2.84707i
$327$	−24.8545	+	42.0519i	−0.0760076	+	0.128599i
$328$	−51.1291	+	48.4320i	−0.155881	+	0.147659i
$329$	102.170	−	107.859i	0.310547	−	0.327840i
$330$	−230.110	−	104.276i	−0.697304	−	0.315988i
$331$	44.4240	−	270.974i	0.134211	−	0.818653i	−0.830824	−	0.556535i	$-0.812131\pi$
$331$	44.4240	−	270.974i	0.134211	−	0.818653i	0.965036	−	0.262118i	$-0.0844211\pi$
$332$	−695.548	−	471.593i	−2.09502	−	1.42046i
$333$	94.5139	+	171.706i	0.283825	+	0.515633i
$334$	351.375	−	211.415i	1.05202	−	0.632980i
$335$	−60.4411	−	274.587i	−0.180421	−	0.819662i
$336$	16.9138	−	51.5311i	0.0503386	−	0.153366i
$337$	−300.133	−	138.857i	−0.890604	−	0.412037i	−0.0794286	−	0.996841i	$-0.525310\pi$
$337$	−300.133	−	138.857i	−0.890604	−	0.412037i	−0.811175	+	0.584803i	$0.801172\pi$
$338$	295.333	−	81.9987i	0.873765	−	0.242600i
$339$	68.7165	+	399.492i	0.202703	+	1.17844i
$340$	−164.976	+	17.9422i	−0.485223	+	0.0527712i
$341$	184.757	+	97.9520i	0.541810	+	0.287249i
$342$	714.507	+	468.252i	2.08920	+	1.36916i
$343$	76.6553	−	276.088i	0.223485	−	0.804920i
$344$	120.932	+	102.721i	0.351547	+	0.298607i
$345$	0.774055	+	98.6485i	0.00224364	+	0.285938i
$346$	−163.161	−	240.645i	−0.471564	−	0.695505i
$347$	−69.1009	−	149.359i	−0.199138	−	0.430430i	0.782120	−	0.623128i	$-0.214138\pi$
$347$	−69.1009	−	149.359i	−0.199138	−	0.430430i	−0.981258	+	0.192698i	$0.938276\pi$
$348$	−698.018	+	159.398i	−2.00580	+	0.458040i
$349$	85.6053	−	214.853i	0.245288	−	0.615625i	−0.753854	−	0.657041i	$-0.771808\pi$
$349$	85.6053	−	214.853i	0.245288	−	0.615625i	0.999142	+	0.0414162i	$0.0131870\pi$
$350$	3.29027	−	4.32828i	0.00940078	−	0.0123665i
$351$	−175.730	+	404.559i	−0.500656	+	1.15259i
$352$	−201.106	−	67.7604i	−0.571323	−	0.192501i
$353$		−	474.482i		−	1.34414i	−0.740487	−	0.672071i	$-0.765405\pi$
$353$		−	474.482i		−	1.34414i	0.740487	−	0.672071i	$-0.234595\pi$
$354$	442.927	+	333.284i	1.25121	+	0.941481i
$355$	408.104			1.14959
$356$	167.878	−	498.244i	0.471567	−	1.39956i
$357$	47.5405	−	29.1147i	0.133167	−	0.0815537i
$358$	−9.49780	−	7.22004i	−0.0265302	−	0.0201677i
$359$	−546.213	−	217.631i	−1.52149	−	0.606215i	−0.548310	−	0.836275i	$-0.684728\pi$
$359$	−546.213	−	217.631i	−1.52149	−	0.606215i	−0.973176	+	0.230060i	$0.926108\pi$
$360$	−64.9662	+	249.086i	−0.180462	+	0.691907i
$361$	506.098	−	234.146i	1.40193	−	0.648603i
$362$	780.967	−	529.509i	2.15737	−	1.46273i
$363$	2.18150	+	278.019i	0.00600965	+	0.765893i
$364$	−201.813	+	237.593i	−0.554432	+	0.652728i
$365$	137.867	+	38.2785i	0.377717	+	0.104873i
$366$	454.524	+	45.8269i	1.24187	+	0.125210i
$367$	123.409	−	232.773i	0.336263	−	0.634259i	−0.656503	−	0.754323i	$-0.727965\pi$
$367$	123.409	−	232.773i	0.336263	−	0.634259i	0.992766	+	0.120064i	$0.0383100\pi$
$368$	3.87169	+	35.5996i	0.0105209	+	0.0967381i
$369$	34.0817	−	106.654i	0.0923624	−	0.289034i
$370$	92.1882	+	332.032i	0.249157	+	0.897383i
$371$	−15.8017	+	34.1547i	−0.0425921	+	0.0920612i
$372$	213.493	−	650.447i	0.573906	−	1.74851i
$373$	−317.909	+	69.9770i	−0.852302	+	0.187606i	−0.619576	−	0.784936i	$-0.712696\pi$
$373$	−317.909	+	69.9770i	−0.852302	+	0.187606i	−0.232726	+	0.972542i	$0.574765\pi$
$374$	−48.5958	−	80.7669i	−0.129935	−	0.215954i
$375$	−205.748	+	308.641i	−0.548660	+	0.823043i
$376$	−143.642	+	211.856i	−0.382026	+	0.563447i
$377$	−662.488	−	108.609i	−1.75726	−	0.288089i
$378$	−51.3891	−	273.039i	−0.135950	−	0.722325i
$379$	241.489	+	228.750i	0.637173	+	0.603563i	0.936534	−	0.350578i	$-0.114015\pi$
$379$	241.489	+	228.750i	0.637173	+	0.603563i	−0.299360	+	0.954140i	$0.596773\pi$
$380$	611.617	+	645.677i	1.60952	+	1.69915i
$381$	222.051	−	375.694i	0.582811	−	0.986073i
$382$	−171.544	−	37.7597i	−0.449068	−	0.0988474i
$383$	56.2264	+	166.874i	0.146805	+	0.435702i	0.995676	−	0.0928987i	$-0.0296133\pi$
$383$	56.2264	+	166.874i	0.146805	+	0.435702i	−0.848870	+	0.528601i	$0.822717\pi$
$384$	−75.1621	+	482.134i	−0.195735	+	1.25556i
$385$	86.2886	+	18.9936i	0.224126	+	0.0493339i
$386$	217.299	+	11.7816i	0.562951	+	0.0305223i
$387$	−247.184	−	50.3560i	−0.638718	−	0.130119i
$388$	−561.444	−	531.828i	−1.44702	−	1.37069i
$389$	460.349	−	24.9594i	1.18342	−	0.0641629i	0.548098	−	0.836414i	$-0.315352\pi$
$389$	460.349	−	24.9594i	1.18342	−	0.0641629i	0.635317	+	0.772251i	$0.280869\pi$
$390$	−464.436	+	621.010i	−1.19086	+	1.59233i
$391$	−20.6559	+	30.4651i	−0.0528283	+	0.0779160i
$392$	−23.3827	+	215.000i	−0.0596497	+	0.548470i
$393$	−10.0656	−	162.110i	−0.0256123	−	0.412493i
$394$	753.786	−	165.921i	1.91316	−	0.421119i
$395$	−85.4755	+	14.0130i	−0.216394	+	0.0354759i
$396$	−273.771	+	49.3059i	−0.691340	+	0.124510i
$397$	118.593	+	427.134i	0.298724	+	1.07590i	0.948759	+	0.316001i	$0.102340\pi$
$397$	118.593	+	427.134i	0.298724	+	1.07590i	−0.650035	+	0.759904i	$0.725246\pi$
$398$	−373.182	−	490.912i	−0.937642	−	1.23345i
$399$	−278.406	−	108.404i	−0.697759	−	0.271688i
$400$	1.36171	−	2.56846i	0.00340427	−	0.00642114i
$401$	−448.965	+	178.884i	−1.11961	+	0.446094i	−0.855191	−	0.518313i	$-0.826560\pi$
$401$	−448.965	+	178.884i	−1.11961	+	0.446094i	−0.264421	+	0.964407i	$0.585181\pi$
$402$	−382.368	−	356.548i	−0.951165	−	0.886935i
$403$	415.551	−	489.225i	1.03114	−	1.21396i
$404$	330.846	−	175.404i	0.818926	−	0.434167i
$405$	−100.477	−	396.731i	−0.248092	−	0.979584i
$406$	383.785	−	177.558i	0.945284	−	0.437335i
$407$	−88.3361	+	75.0333i	−0.217042	+	0.184357i
$408$	−72.7114	+	62.7504i	−0.178214	+	0.153800i
$409$	132.357	+	100.615i	0.323610	+	0.246002i	0.754348	−	0.656475i	$-0.227953\pi$
$409$	132.357	+	100.615i	0.323610	+	0.246002i	−0.430737	+	0.902477i	$0.641746\pi$
$410$	101.488	−	168.674i	0.247531	−	0.411400i
$411$	555.436	−	534.468i	1.35143	−	1.30041i
$412$	−1051.66			−2.55257
$413$	−175.704	−	81.9160i	−0.425432	−	0.198344i
$414$	105.314	+	150.198i	0.254383	+	0.362796i
$415$	692.824	+	233.440i	1.66946	+	0.562505i
$416$	−335.832	+	558.157i	−0.807288	+	1.34172i
$417$	333.521	+	706.298i	0.799811	+	1.69376i
$418$	−186.980	+	469.285i	−0.447321	+	1.12269i
$419$	−314.783	+	267.379i	−0.751272	+	0.638136i	−0.938934	−	0.344098i	$-0.888185\pi$
$419$	−314.783	+	267.379i	−0.751272	+	0.638136i	0.187662	+	0.982234i	$0.439909\pi$
$420$	13.3928	−	288.936i	0.0318876	−	0.687944i
$421$	−356.990	−	526.520i	−0.847956	−	1.25064i	−0.966235	−	0.257662i	$-0.917048\pi$
$421$	−356.990	−	526.520i	−0.847956	−	1.25064i	0.118279	−	0.992980i	$-0.462262\pi$
$422$	−688.031	+	364.771i	−1.63041	+	0.864386i
$423$	37.6441	−	405.194i	0.0889931	−	0.957905i
$424$	17.3455	−	62.4729i	0.0409092	−	0.147342i
$425$	2.77589	−	1.10601i	0.00653150	−	0.00260239i
$426$	624.741	−	430.779i	1.46653	−	1.01122i
$427$	−158.831	+	17.2739i	−0.371969	+	0.0404541i
$428$	186.758	+	245.676i	0.436351	+	0.574009i
$429$	−255.160	−	54.0694i	−0.594779	−	0.126036i
$430$	−402.516	−	186.224i	−0.936085	−	0.433079i
$431$	−329.819	+	54.0711i	−0.765242	+	0.125455i	−0.531747	−	0.846903i	$-0.678464\pi$
$431$	−329.819	+	54.0711i	−0.765242	+	0.125455i	−0.233494	+	0.972358i	$0.575016\pi$
$432$	−50.7347	−	139.624i	−0.117441	−	0.323205i
$433$	−286.823	+	172.576i	−0.662409	+	0.398558i	−0.806687	−	0.590979i	$-0.798742\pi$
$433$	−286.823	+	172.576i	−0.662409	+	0.398558i	0.144278	+	0.989537i	$0.453914\pi$
$434$	−43.7151	+	401.954i	−0.100726	+	0.926161i
$435$	548.034	−	296.081i	1.25985	−	0.680646i
$436$	−15.2986	+	93.3173i	−0.0350885	+	0.214031i
$437$	196.973	−	10.6795i	0.450738	−	0.0244383i
$438$	251.456	−	86.9284i	0.574101	−	0.198467i
$439$	−214.146	+	202.850i	−0.487804	+	0.462072i	−0.891631	−	0.452763i	$-0.850438\pi$
$439$	−214.146	+	202.850i	−0.487804	+	0.462072i	0.403827	+	0.914835i	$0.367680\pi$
$440$	−151.999	−	8.24112i	−0.345451	−	0.0187298i
$441$	−132.262	−	317.377i	−0.299915	−	0.719675i
$442$	−274.187	+	92.3844i	−0.620333	+	0.209014i
$443$	−197.821	−	587.111i	−0.446548	−	1.32531i	−0.900723	−	0.434395i	$-0.856962\pi$
$443$	−197.821	−	587.111i	−0.446548	−	1.32531i	0.454174	−	0.890913i	$-0.349934\pi$
$444$	291.105	+	243.361i	0.655643	+	0.548110i
$445$	−24.7637	+	456.740i	−0.0556488	+	1.02638i
$446$	243.176	+	256.717i	0.545237	+	0.575600i
$447$	177.305	−	61.2943i	0.396655	−	0.137124i
$448$	−18.2989	−	337.504i	−0.0408458	−	0.753356i
$449$	104.863	+	17.1914i	0.233548	+	0.0382882i	0.277419	−	0.960749i	$-0.410521\pi$
$449$	104.863	+	17.1914i	0.233548	+	0.0382882i	−0.0438713	+	0.999037i	$0.513969\pi$
$450$	−0.233690	−	14.8903i	−0.000519312	−	0.0330895i
$451$	65.8221	+	7.15859i	0.145947	+	0.0158727i
$452$	404.567	+	672.395i	0.895059	+	1.48760i
$453$	262.494	+	70.6675i	0.579458	+	0.155999i
$454$	94.0308	+	573.563i	0.207116	+	1.26335i
$455$	113.877	−	246.140i	0.250278	−	0.540968i
$456$	503.550	+	106.704i	1.10428	+	0.234000i
$457$	78.0417	−	59.3257i	0.170770	−	0.129816i	−0.516299	−	0.856409i	$-0.672691\pi$
$457$	78.0417	−	59.3257i	0.170770	−	0.129816i	0.687068	+	0.726593i	$0.258897\pi$
$458$	−5.53027	−	50.8500i	−0.0120748	−	0.111026i
$459$	53.1643	−	143.142i	0.115826	−	0.311857i
$460$	70.6878	+	177.413i	0.153669	+	0.385680i
$461$	723.528	+	200.887i	1.56948	+	0.435763i	0.939977	−	0.341238i	$-0.110846\pi$
$461$	723.528	+	200.887i	1.56948	+	0.435763i	0.629499	+	0.777001i	$0.283260\pi$
$462$	152.143	−	62.0068i	0.329313	−	0.134214i
$463$	−18.3423	−	34.5972i	−0.0396161	−	0.0747239i	0.862914	−	0.505351i	$-0.168637\pi$
$463$	−18.3423	−	34.5972i	−0.0396161	−	0.0747239i	−0.902530	+	0.430627i	$0.858292\pi$
$464$	187.146	−	126.888i	0.403332	−	0.273466i
$465$	−27.5770	+	594.945i	−0.0593053	+	1.27945i
$466$	−202.810	−	238.767i	−0.435215	−	0.512375i
$467$	830.570	+	330.929i	1.77852	+	0.708628i	0.996330	+	0.0855912i	$0.0272779\pi$
$467$	830.570	+	330.929i	1.77852	+	0.708628i	0.782192	+	0.623037i	$0.214101\pi$
$468$	−32.8424	+	853.237i	−0.0701760	+	1.82316i
$469$	156.671	+	94.2658i	0.334053	+	0.200993i
$470$	228.445	−	677.999i	0.486052	−	1.44255i
$471$	−564.281	−	293.514i	−1.19805	−	0.623173i
$472$	321.557	+	90.2970i	0.681264	+	0.191307i
$473$		−	149.172i		−	0.315373i
$474$	−116.057	+	111.676i	−0.244847	+	0.235603i
$475$	−13.7218	−	8.25616i	−0.0288881	−	0.0173814i
$476$	65.3101	−	85.9140i	0.137206	−	0.180492i
$477$	23.7361	+	100.310i	0.0497611	+	0.210292i
$478$	202.898	+	238.870i	0.424473	+	0.499728i
$479$	161.489	+	349.053i	0.337138	+	0.728712i	0.999796	−	0.0202106i	$-0.00643367\pi$
$479$	161.489	+	349.053i	0.337138	+	0.728712i	−0.662658	+	0.748922i	$0.730572\pi$
$480$	−70.0604	−	600.332i	−0.145959	−	1.25069i
$481$	166.643	+	314.323i	0.346452	+	0.653478i
$482$	−387.437	−	329.092i	−0.803812	−	0.682764i
$483$	−46.9210	−	43.7525i	−0.0971448	−	0.0905849i
$484$	199.218	+	499.999i	0.411607	+	1.03306i
$485$	594.428	+	315.146i	1.22562	+	0.649785i
$486$	−572.588	−	501.271i	−1.17817	−	1.03142i
$487$	−476.636	+	362.329i	−0.978719	+	0.744003i	−0.966697	−	0.255925i	$-0.917620\pi$
$487$	−476.636	+	362.329i	−0.978719	+	0.744003i	−0.0120222	+	0.999928i	$0.503827\pi$
$488$	265.223	−	73.6388i	0.543490	−	0.150899i
$489$	556.616	+	720.413i	1.13828	+	1.47324i
$490$	−97.7977	−	596.539i	−0.199587	−	1.21743i
$491$	133.828	+	607.985i	0.272561	+	1.23826i	0.891573	+	0.452877i	$0.149602\pi$
$491$	133.828	+	607.985i	0.272561	+	1.23826i	−0.619012	+	0.785382i	$0.712467\pi$
$492$	−13.4327	−	216.337i	−0.0273021	−	0.439709i
$493$	231.046	+	25.1277i	0.468652	+	0.0509690i
$494$	1283.43	+	870.186i	2.59803	+	1.76151i
$495$	218.020	−	105.051i	0.440445	−	0.212225i
$496$	11.7043	+	215.874i	0.0235975	+	0.435230i
$497$	−182.514	+	192.678i	−0.367232	+	0.387682i
$498$	1307.01	−	373.960i	2.62452	−	0.750923i
$499$	17.5992	−	324.599i	0.0352690	−	0.650499i	−0.926443	−	0.376436i	$-0.877150\pi$
$499$	17.5992	−	324.599i	0.0352690	−	0.650499i	0.961712	−	0.274063i	$-0.0883677\pi$
$500$	−154.366	+	701.291i	−0.308731	+	1.40258i
$501$	−60.5088	+	388.139i	−0.120776	+	0.774729i
$502$	−646.326	+	217.773i	−1.28750	+	0.433810i
$503$	−125.783	+	571.438i	−0.250066	+	1.13606i	0.669404	+	0.742899i	$0.266550\pi$
$503$	−125.783	+	571.438i	−0.250066	+	1.13606i	−0.919469	+	0.393161i	$0.871381\pi$
$504$	−88.5464	−	142.070i	−0.175687	−	0.281885i
$505$	−236.516	+	224.040i	−0.468349	+	0.443644i
$506$	−74.5985	+	78.7527i	−0.147428	+	0.155638i
$507$	−121.191	+	267.436i	−0.239035	+	0.527487i
$508$	136.678	−	833.701i	0.269052	−	1.64114i
$509$	−445.577	−	302.109i	−0.875397	−	0.593534i	0.0386000	−	0.999255i	$-0.487710\pi$
$509$	−445.577	−	302.109i	−0.875397	−	0.593534i	−0.913997	+	0.405721i	$0.867021\pi$
$510$	148.908	−	223.376i	0.291977	−	0.437993i
$511$	−79.7296	+	47.9717i	−0.156027	+	0.0938781i
$512$	−73.9458	−	335.939i	−0.144425	−	0.656131i
$513$	−783.144	+	237.429i	−1.52660	+	0.462824i
$514$	−1203.44	−	556.769i	−2.34132	−	1.08321i
$515$	881.582	−	244.770i	1.71181	−	0.475282i
$516$	−481.277	+	82.7842i	−0.932707	+	0.160435i
$517$	239.228	−	26.0176i	0.462723	−	0.0503242i
$518$	−197.990	−	104.968i	−0.382221	−	0.202641i
$519$	277.110	+	27.9393i	0.533931	+	0.0538330i
$520$	−125.003	+	450.219i	−0.240390	+	0.865806i
$521$	−117.386	−	99.7088i	−0.225310	−	0.191380i	0.527621	−	0.849480i	$-0.323084\pi$
$521$	−117.386	−	99.7088i	−0.225310	−	0.191380i	−0.752930	+	0.658101i	$0.771360\pi$
$522$	526.419	−	1031.73i	1.00847	−	1.97650i
$523$	117.121	+	172.740i	0.223940	+	0.330287i	0.923017	−	0.384760i	$-0.125716\pi$
$523$	117.121	+	172.740i	0.223940	+	0.330287i	−0.699077	+	0.715047i	$0.746405\pi$
$524$	−132.025	−	285.367i	−0.251956	−	0.544594i
$525$	1.15949	+	5.07754i	0.00220856	+	0.00967150i
$526$	−451.667	+	1133.60i	−0.858682	+	2.15513i
$527$	−134.479	+	176.904i	−0.255179	+	0.335682i
$528$	74.9147	−	45.8791i	0.141884	−	0.0868922i
$529$	−461.167	−	155.385i	−0.871772	−	0.293734i
$530$			181.227i			0.341938i
$531$	−517.087	+	120.756i	−0.973799	+	0.227412i
$532$	−578.372			−1.08717
$533$	64.8931	−	192.596i	0.121751	−	0.361343i
$534$	444.207	+	725.334i	0.831849	+	1.35830i
$535$	−213.736	−	162.478i	−0.399506	−	0.303696i
$536$	−292.640	−	116.599i	−0.545971	−	0.217535i
$537$	11.1419	−	2.54434i	0.0207485	−	0.00473807i
$538$	902.346	−	417.470i	1.67722	−	0.775966i
$539$	168.287	−	114.101i	0.312221	−	0.211691i
$540$	−459.923	−	645.106i	−0.851709	−	1.19464i
$541$	639.160	−	752.477i	1.18144	−	1.39090i	0.278887	−	0.960324i	$-0.410034\pi$
$541$	639.160	−	752.477i	1.18144	−	1.39090i	0.902554	−	0.430576i	$-0.141690\pi$
$542$	−784.702	−	217.872i	−1.44779	−	0.401977i
$543$	−90.6719	+	899.309i	−0.166983	+	1.65619i
$544$	105.630	−	199.239i	0.194172	−	0.366248i
$545$	−8.89482	−	81.7866i	−0.0163208	−	0.150067i
$546$	−85.4895	−	497.004i	−0.156574	−	0.910264i
$547$	−22.3176	−	80.3808i	−0.0408001	−	0.146949i	0.940345	−	0.340224i	$-0.110503\pi$
$547$	−22.3176	−	80.3808i	−0.0408001	−	0.146949i	−0.981145	+	0.193275i	$0.938089\pi$
$548$	626.563	−	1354.29i	1.14336	−	2.47134i
$549$	−312.945	+	305.896i	−0.570028	+	0.557188i
$550$	8.60039	−	1.89309i	0.0156371	−	0.00344198i
$551$	−642.144	−	1067.25i	−1.16542	−	1.93694i
$552$	91.9682	+	61.3082i	0.166609	+	0.111066i
$553$	31.6107	−	46.6223i	0.0571623	−	0.0843080i
$554$	−1287.34	−	211.049i	−2.32373	−	0.380956i
$555$	−300.669	−	136.250i	−0.541745	−	0.245496i
$556$	1097.76	+	1039.86i	1.97439	+	1.87025i
$557$	29.4298	+	31.0686i	0.0528362	+	0.0557785i	0.751878	−	0.659303i	$-0.229148\pi$
$557$	29.4298	+	31.0686i	0.0528362	+	0.0557785i	−0.699041	+	0.715081i	$0.746390\pi$
$558$	585.784	+	939.872i	1.04979	+	1.68436i
$559$	−447.182	−	98.4322i	−0.799968	−	0.176086i
$560$	29.1661	+	86.5618i	0.0520822	+	0.154575i
$561$	89.2175	+	13.9085i	0.159033	+	0.0247924i
$562$	−782.933	−	172.336i	−1.39312	−	0.306649i
$563$	652.449	+	35.3748i	1.15888	+	0.0628326i	0.623531	−	0.781799i	$-0.285697\pi$
$563$	652.449	+	35.3748i	1.15888	+	0.0628326i	0.535349	+	0.844631i	$0.320180\pi$
$564$	−216.703	−	757.389i	−0.384225	−	1.34289i
$565$	−495.637	−	469.493i	−0.877234	−	0.830960i
$566$	−1285.30	+	69.6872i	−2.27086	+	0.123122i
$567$	232.244	+	129.990i	0.409602	+	0.229259i
$568$	256.599	−	378.455i	0.451758	−	0.666294i
$569$	−86.9800	+	799.768i	−0.152865	+	1.40557i	0.626707	+	0.779255i	$0.284402\pi$
$569$	−86.9800	+	799.768i	−0.152865	+	1.40557i	−0.779572	+	0.626313i	$0.784563\pi$
$570$	−1435.99	+	89.1626i	−2.51928	+	0.156426i
$571$	−544.764	+	119.912i	−0.954053	+	0.210003i	−0.664608	−	0.747192i	$-0.731402\pi$
$571$	−544.764	+	119.912i	−0.954053	+	0.210003i	−0.289444	+	0.957195i	$0.593471\pi$
$572$	−498.274	+	81.6878i	−0.871108	+	0.142811i
$573$	133.150	−	102.877i	0.232374	−	0.179540i
$574$	34.2481	+	123.350i	0.0596656	+	0.214896i
$575$	−2.08106	−	2.73758i	−0.00361923	−	0.00476101i
$576$	−610.354	−	696.123i	−1.05964	−	1.20855i
$577$	−279.531	+	527.252i	−0.484456	+	0.913781i	0.513976	+	0.857805i	$0.328172\pi$
$577$	−279.531	+	527.252i	−0.484456	+	0.913781i	−0.998432	+	0.0559767i	$0.982173\pi$
$578$	−747.734	+	297.924i	−1.29366	+	0.515440i
$579$	−142.170	+	152.465i	−0.245544	+	0.263325i
$580$	780.654	−	919.057i	1.34596	−	1.58458i
$581$	−420.061	+	222.702i	−0.722997	+	0.383309i
$582$	1242.63	−	145.018i	2.13510	−	0.249172i
$583$	−55.3212	+	25.5943i	−0.0948905	+	0.0439010i
$584$	122.182	−	103.782i	0.209216	−	0.177710i
$585$	−171.057	−	722.894i	−0.292405	−	1.23572i
$586$	833.025	+	633.249i	1.42155	+	1.08063i
$587$	−295.273	+	490.748i	−0.503021	+	0.836027i	−0.999487	−	0.0320292i	$-0.989803\pi$
$587$	−295.273	+	490.748i	−0.503021	+	0.836027i	0.496466	+	0.868056i	$0.334631\pi$
$588$	−461.522	−	479.628i	−0.784901	−	0.815694i
$589$	1190.92			2.02193
$590$	−933.562	−	2.73985i	−1.58231	−	0.00464382i
$591$	−341.191	+	655.940i	−0.577311	+	1.10988i
$592$	−113.551	−	38.2596i	−0.191808	−	0.0646277i
$593$	449.780	−	747.540i	0.758482	−	1.26061i	−0.201208	−	0.979549i	$-0.564487\pi$
$593$	449.780	−	747.540i	0.758482	−	1.26061i	0.959690	−	0.281059i	$-0.0906857\pi$
$594$	222.865	−	390.950i	0.375194	−	0.658165i
$595$	−34.7519	+	87.2206i	−0.0584065	+	0.146589i
$596$	276.795	−	235.112i	0.464421	−	0.394483i
$597$	590.083	+	27.3516i	0.988414	+	0.0458151i
$598$	186.858	+	275.595i	0.312471	+	0.460861i
$599$	−337.984	+	179.188i	−0.564246	+	0.299144i	−0.726009	−	0.687685i	$-0.758627\pi$
$599$	−337.984	+	179.188i	−0.564246	+	0.299144i	0.161763	+	0.986830i	$0.448282\pi$
$600$	−3.38657	−	8.30944i	−0.00564429	−	0.0138491i
$601$	1.01753	−	3.66483i	0.00169307	−	0.00609788i	−0.962699	−	0.270576i	$-0.912786\pi$
$601$	1.01753	−	3.66483i	0.00169307	−	0.00609788i	0.964392	+	0.264478i	$0.0851997\pi$
$602$	267.937	−	106.756i	0.445077	−	0.177335i
$603$	496.977	−	61.9549i	0.824174	−	0.102744i
$604$	523.163	−	56.8974i	0.866164	−	0.0942010i
$605$	−283.373	−	372.771i	−0.468385	−	0.616150i
$606$	−125.580	+	592.626i	−0.207228	+	0.977931i
$607$	−72.0821	−	33.3487i	−0.118751	−	0.0549402i	0.359614	−	0.933101i	$-0.382908\pi$
$607$	−72.0821	−	33.3487i	−0.118751	−	0.0549402i	−0.478365	+	0.878161i	$0.658770\pi$
$608$	−1192.64	+	195.523i	−1.96158	+	0.321585i
$609$	−105.306	+	391.157i	−0.172916	+	0.642294i
$610$	−659.252	+	396.659i	−1.08074	+	0.650261i
$611$	79.8619	−	734.318i	0.130707	−	1.20183i
$612$	−4.63863	−	295.564i	−0.00757945	−	0.482948i
$613$	−55.6727	+	339.589i	−0.0908201	+	0.553978i	0.901745	+	0.432267i	$0.142286\pi$
$613$	−55.6727	+	339.589i	−0.0908201	+	0.553978i	−0.992566	+	0.121711i	$0.961162\pi$
$614$	1601.05	−	86.8066i	2.60758	−	0.141379i
$615$	61.6120	+	178.224i	0.100182	+	0.289795i
$616$	71.8683	−	68.0772i	0.116669	−	0.110515i
$617$	497.118	+	26.9530i	0.805702	+	0.0436839i	0.452388	−	0.891821i	$-0.350572\pi$
$617$	497.118	+	26.9530i	0.805702	+	0.0436839i	0.353314	+	0.935505i	$0.385055\pi$
$618$	1091.19	−	1305.27i	1.76568	−	2.11208i
$619$	903.361	−	304.378i	1.45939	−	0.491725i	0.525966	−	0.850505i	$-0.323704\pi$
$619$	903.361	−	304.378i	1.45939	−	0.491725i	0.933422	+	0.358780i	$0.116807\pi$
$620$	368.146	+	1092.62i	0.593784	+	1.76229i
$621$	−175.094	−	14.8822i	−0.281955	−	0.0239649i
$622$	62.1550	−	1146.38i	0.0999277	−	1.84306i
$623$	−204.565	−	215.957i	−0.328355	−	0.346640i
$624$	−88.1019	−	254.851i	−0.141189	−	0.408415i
$625$	−34.5368	−	636.994i	−0.0552589	−	1.01919i
$626$	−1119.24	−	183.490i	−1.78792	−	0.293115i
$627$	−230.019	−	425.756i	−0.366856	−	0.679036i
$628$	−1224.10	−	133.129i	−1.94920	−	0.211989i
$629$	−63.4967	−	105.532i	−0.100949	−	0.167778i
$630$	344.717	+	316.419i	0.547170	+	0.502253i
$631$	94.5480	+	576.717i	0.149838	+	0.913973i	0.949556	+	0.313597i	$0.101534\pi$
$631$	94.5480	+	576.717i	0.149838	+	0.913973i	−0.799718	+	0.600376i	$0.795018\pi$
$632$	−40.7484	+	88.0763i	−0.0644753	+	0.139361i
$633$	154.645	−	729.789i	0.244305	−	1.15290i
$634$	126.584	−	96.2264i	0.199659	−	0.151777i
$635$	79.4668	+	730.685i	0.125145	+	1.15068i
$636$	113.277	+	164.281i	0.178108	+	0.258303i
$637$	−231.004	−	579.777i	−0.362644	−	0.910168i
$638$	659.964	+	183.238i	1.03443	+	0.287207i
$639$	−67.2465	+	723.829i	−0.105237	+	1.13275i
$640$	−384.944	−	726.081i	−0.601474	−	1.13450i
$641$	562.171	−	381.161i	0.877021	−	0.594635i	−0.0374444	−	0.999299i	$-0.511922\pi$
$641$	562.171	−	381.161i	0.877021	−	0.594635i	0.914466	+	0.404664i	$0.132611\pi$
$642$	−498.699	−	23.1157i	−0.776789	−	0.0360058i
$643$	−138.601	−	163.173i	−0.215553	−	0.253769i	0.643750	−	0.765236i	$-0.277378\pi$
$643$	−138.601	−	163.173i	−0.215553	−	0.253769i	−0.859303	+	0.511468i	$0.829102\pi$
$644$	−115.375	−	45.9696i	−0.179154	−	0.0713813i
$645$	384.176	−	181.412i	0.595622	−	0.281259i
$646$	−459.967	−	276.753i	−0.712024	−	0.428410i
$647$	−366.899	+	1088.92i	−0.567077	+	1.68302i	0.152241	+	0.988343i	$0.451351\pi$
$647$	−366.899	+	1088.92i	−0.567077	+	1.68302i	−0.719318	+	0.694681i	$0.755546\pi$
$648$	−431.084	−	156.270i	−0.665253	−	0.241158i
$649$	−131.008	−	285.365i	−0.201862	−	0.439699i
$650$		−	27.0312i		−	0.0415864i
$651$	−268.558	−	279.094i	−0.412531	−	0.428715i
$652$	1510.13	+	908.614i	2.31615	+	1.39358i
$653$	229.922	−	302.457i	0.352101	−	0.463181i	−0.585612	−	0.810592i	$-0.699146\pi$
$653$	229.922	−	302.457i	0.352101	−	0.463181i	0.937713	+	0.347410i	$0.112939\pi$
$654$	−99.9471	−	115.813i	−0.152824	−	0.177084i
$655$	177.092	+	208.489i	0.270369	+	0.318303i
$656$	28.7415	+	62.1237i	0.0438132	+	0.0947007i
$657$	−90.6095	+	238.218i	−0.137914	+	0.362584i
$658$	217.937	+	411.073i	0.331211	+	0.624730i
$659$	−84.6825	−	71.9299i	−0.128501	−	0.109150i	0.580831	−	0.814024i	$-0.302728\pi$
$659$	−84.6825	−	71.9299i	−0.128501	−	0.109150i	−0.709333	+	0.704874i	$0.751004\pi$
$660$	319.508	−	342.646i	0.484103	−	0.519160i
$661$	−152.967	−	383.918i	−0.231418	−	0.580815i	0.766709	−	0.641995i	$-0.221893\pi$
$661$	−152.967	−	383.918i	−0.231418	−	0.580815i	−0.998127	+	0.0611801i	$0.980514\pi$
$662$	759.768	+	402.804i	1.14769	+	0.608465i
$663$	100.566	−	258.276i	0.151683	−	0.389557i
$664$	652.098	−	495.712i	0.982076	−	0.746555i
$665$	484.837	−	134.614i	0.729078	−	0.202427i
$666$	−604.095	+	108.797i	−0.907049	+	0.163359i
$667$	−43.2701	−	263.936i	−0.0648727	−	0.395706i
$668$	163.477	+	742.684i	0.244726	+	1.11180i
$669$	−338.085	+	20.9922i	−0.505358	+	0.0313784i
$670$	875.351	+	95.2001i	1.30649	+	0.142090i
$671$	−214.188	−	145.223i	−0.319208	−	0.216428i
$672$	314.767	+	235.406i	0.468403	+	0.350306i
$673$	−57.8718	−	1067.38i	−0.0859908	−	1.58601i	−0.649802	−	0.760104i	$-0.725148\pi$
$673$	−57.8718	−	1067.38i	−0.0859908	−	1.58601i	0.563811	−	0.825904i	$-0.309335\pi$
$674$	712.216	−	751.878i	1.05670	−	1.11555i
$675$	11.0872	+	8.97700i	0.0164255	+	0.0132993i
$676$	−30.7725	+	567.565i	−0.0455214	+	0.839594i
$677$	−148.594	+	675.068i	−0.219488	+	0.997146i	0.730025	+	0.683420i	$0.239508\pi$
$677$	−148.594	+	675.068i	−0.219488	+	0.997146i	−0.949514	+	0.313726i	$0.898423\pi$
$678$	−1254.32	−	195.541i	−1.85002	−	0.288409i
$679$	−414.632	+	139.706i	−0.610650	+	0.205752i
$680$	34.7730	−	157.975i	0.0511367	−	0.232317i
$681$	−479.314	−	283.295i	−0.703839	−	0.415999i
$682$	−475.449	+	450.370i	−0.697140	+	0.660366i
$683$	314.703	−	332.228i	0.460765	−	0.486424i	−0.453662	−	0.891174i	$-0.649883\pi$
$683$	314.703	−	332.228i	0.460765	−	0.486424i	0.914427	+	0.404750i	$0.132641\pi$
$684$	−1245.98	+	978.394i	−1.82160	+	1.43040i
$685$	−210.027	+	1281.11i	−0.306608	+	1.87023i
$686$	742.714	+	503.572i	1.08267	+	0.734071i
$687$	40.7702	+	27.1784i	0.0593452	+	0.0395609i
$688$	132.143	−	79.5077i	0.192068	−	0.115564i
$689$	40.2216	+	182.729i	0.0583768	+	0.265209i
$690$	−293.541	−	96.3474i	−0.425421	−	0.139634i
$691$	−1009.39	−	466.994i	−1.46077	−	0.675823i	−0.481140	−	0.876644i	$-0.659777\pi$
$691$	−1009.39	−	466.994i	−1.46077	−	0.675823i	−0.979628	+	0.200821i	$0.935639\pi$
$692$	519.516	−	144.243i	0.750746	−	0.208444i
$693$	−47.9061	+	149.915i	−0.0691286	+	0.216328i
$694$	512.362	−	55.7228i	0.738274	−	0.0802922i
$695$	−1162.25	−	616.188i	−1.67231	−	0.886602i
$696$	70.0103	−	694.382i	0.100589	−	0.997675i
$697$	−18.8227	+	67.7932i	−0.0270053	+	0.0972642i
$698$	552.034	+	468.902i	0.790880	+	0.671779i
$699$	300.091	−	2.35469i	0.429314	−	0.00336865i
$700$	5.65816	+	8.34516i	0.00808309	+	0.0119217i
$701$	79.5559	+	171.957i	0.113489	+	0.245303i	0.955994	−	0.293386i	$-0.0947820\pi$
$701$	79.5559	+	171.957i	0.113489	+	0.245303i	−0.842505	+	0.538689i	$0.818920\pi$
$702$	−1024.92	−	926.071i	−1.46000	−	1.31919i
$703$	−244.314	+	613.182i	−0.347530	+	0.872236i
$704$	331.312	−	435.833i	0.470613	−	0.619081i
$705$	357.937	+	584.466i	0.507713	+	0.829030i
$706$	1408.16	+	474.463i	1.99456	+	0.672044i
$707$		−	211.862i		−	0.299664i
$708$	−847.977	+	581.043i	−1.19771	+	0.820682i
$709$	−1257.20			−1.77320			−0.886602	−	0.462533i	$-0.846940\pi$
$709$	−1257.20			−1.77320			−0.886602	+	0.462533i	$0.846940\pi$
$710$	−408.088	+	1211.16i	−0.574772	+	1.70586i
$711$	−10.7695	−	153.911i	−0.0151470	−	0.216472i
$712$	407.987	+	310.143i	0.573015	+	0.435595i
$713$	237.567	+	94.6554i	0.333194	+	0.132756i
$714$	38.8672	+	170.203i	0.0544358	+	0.238380i
$715$	398.679	−	184.449i	0.557593	−	0.257970i
$716$	18.3123	−	12.4160i	0.0255758	−	0.0173408i
$717$	−300.221	+	2.35571i	−0.418718	+	0.00328551i
$718$	1192.07	−	1403.42i	1.66027	−	1.95462i
$719$	−187.369	−	52.0227i	−0.260596	−	0.0723542i	0.134773	−	0.990877i	$-0.456970\pi$
$719$	−187.369	−	52.0227i	−0.260596	−	0.0723542i	−0.395369	+	0.918522i	$0.629383\pi$
$720$	209.263	+	137.140i	0.290643	+	0.190472i
$721$	−278.702	+	525.687i	−0.386549	+	0.729108i
$722$	188.815	+	1736.12i	0.261516	+	2.40460i
$723$	479.913	−	82.5496i	0.663780	−	0.114176i
$724$	468.114	+	1685.99i	0.646566	+	2.32872i
$725$	−9.11702	+	19.7061i	−0.0125752	+	0.0271809i
$726$	−827.279	−	271.534i	−1.13950	−	0.374013i
$727$	−438.268	+	96.4701i	−0.602845	+	0.132696i	−0.505898	−	0.862593i	$-0.668839\pi$
$727$	−438.268	+	96.4701i	−0.602845	+	0.132696i	−0.0969470	+	0.995290i	$0.530908\pi$
$728$	−156.657	−	260.366i	−0.215188	−	0.357646i
$729$	720.214	−	112.838i	0.987948	−	0.154785i
$730$	−251.463	+	370.880i	−0.344470	+	0.508055i
$731$	156.428	+	25.6450i	0.213991	+	0.0350821i
$732$	−349.672	+	771.635i	−0.477694	+	1.05415i
$733$	563.134	+	533.429i	0.768259	+	0.727734i	0.967680	−	0.252180i	$-0.0811475\pi$
$733$	563.134	+	533.429i	0.768259	+	0.727734i	−0.199421	+	0.979914i	$0.563906\pi$
$734$	567.415	+	599.013i	0.773045	+	0.816094i
$735$	498.515	+	294.644i	0.678252	+	0.400876i
$736$	−253.451	−	55.7887i	−0.344362	−	0.0757999i
$737$	94.5631	+	280.653i	0.128308	+	0.380805i
$738$	282.444	+	207.796i	0.382715	+	0.281567i
$739$	260.657	+	57.3749i	0.352715	+	0.0776385i	0.387794	−	0.921746i	$-0.373237\pi$
$739$	260.657	+	57.3749i	0.352715	+	0.0776385i	−0.0350788	+	0.999385i	$0.511168\pi$
$740$	−638.093	−	34.5964i	−0.862288	−	0.0467519i
$741$	−1428.10	+	408.605i	−1.92726	+	0.551424i
$742$	−85.5625	−	81.0491i	−0.115313	−	0.109231i
$743$	−96.7047	+	5.24318i	−0.130154	+	0.00705677i	−0.119101	−	0.992882i	$-0.538001\pi$
$743$	−96.7047	+	5.24318i	−0.130154	+	0.00705677i	−0.0110534	+	0.999939i	$0.503518\pi$
$744$	534.382	+	399.650i	0.718255	+	0.537164i
$745$	−177.310	+	261.512i	−0.237999	+	0.351023i
$746$	110.220	−	1013.46i	0.147748	−	1.35852i
$747$	−528.199	+	1190.35i	−0.707094	+	1.59351i
$748$	170.713	−	37.5768i	0.228226	−	0.0502363i
$749$	172.298	−	28.2468i	0.230037	−	0.0377127i
$750$	−710.239	−	919.242i	−0.946985	−	1.22566i
$751$	−37.6538	−	135.617i	−0.0501382	−	0.180581i	0.934241	−	0.356642i	$-0.116078\pi$
$751$	−37.6538	−	135.617i	−0.0501382	−	0.180581i	−0.984379	+	0.176060i	$0.943665\pi$
$752$	150.555	+	198.051i	0.200206	+	0.263366i
$753$	237.058	−	608.820i	0.314818	−	0.808526i
$754$	984.790	−	1857.51i	1.30609	−	2.46354i
$755$	−425.313	+	169.460i	−0.563329	+	0.224451i
$756$	510.261	+	71.3643i	0.674949	+	0.0943972i
$757$	366.018	−	430.910i	0.483511	−	0.569233i	−0.465269	−	0.885169i	$-0.654043\pi$
$757$	366.018	−	430.910i	0.483511	−	0.569233i	0.948781	+	0.315936i	$0.102318\pi$
$758$	−920.358	+	487.943i	−1.21419	+	0.643724i
$759$	−12.0452	−	103.213i	−0.0158698	−	0.135985i
$760$	−786.780	+	364.003i	−1.03524	+	0.478951i
$761$	996.070	−	846.069i	1.30890	−	1.11179i	0.322647	−	0.946519i	$-0.395427\pi$
$761$	996.070	−	846.069i	1.30890	−	1.11179i	0.986249	−	0.165267i	$-0.0528486\pi$
$762$	892.932	+	1034.68i	1.17183	+	1.35784i
$763$	42.5918	+	32.3774i	0.0558214	+	0.0424343i
$764$	167.934	−	279.109i	0.219809	−	0.365326i
$765$	72.6800	+	246.685i	0.0950065	+	0.322464i
$766$	−551.469			−0.719933
$767$	−941.906	+	204.433i	−1.22804	+	0.266536i
$768$	−260.588	−	135.547i	−0.339308	−	0.176493i
$769$	606.872	+	204.479i	0.789171	+	0.265903i	0.684891	−	0.728645i	$-0.259850\pi$
$769$	606.872	+	204.479i	0.789171	+	0.265903i	0.104280	+	0.994548i	$0.466746\pi$
$770$	−142.654	+	237.093i	−0.185265	+	0.307912i
$771$	1148.60	−	542.382i	1.48976	−	0.703478i
$772$	−149.374	+	374.900i	−0.193490	+	0.485622i
$773$	164.956	−	140.115i	0.213397	−	0.181261i	−0.534312	−	0.845287i	$-0.679429\pi$
$773$	164.956	−	140.115i	0.213397	−	0.181261i	0.747710	+	0.664026i	$0.231154\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.999960 + 2.96778i) q^{2} +(-1.56678 - 2.55836i) q^{3} +(-4.62340 - 3.51462i) q^{4} +(4.69371 + 1.87015i) q^{5} +(9.15935 - 2.09161i) q^{6} +(-2.98209 + 1.37966i) q^{7} +(4.68548 - 3.17683i) q^{8} +(-4.09038 + 8.01678i) q^{9} +O(q^{10})\)	\(q+(-0.999960 + 2.96778i) q^{2} +(-1.56678 - 2.55836i) q^{3} +(-4.62340 - 3.51462i) q^{4} +(4.69371 + 1.87015i) q^{5} +(9.15935 - 2.09161i) q^{6} +(-2.98209 + 1.37966i) q^{7} +(4.68548 - 3.17683i) q^{8} +(-4.09038 + 8.01678i) q^{9} +(-10.2437 + 12.0598i) q^{10} +(-5.12806 - 1.42380i) q^{11} +(-1.74778 + 17.3350i) q^{12} +(-7.65201 + 14.4332i) q^{13} +(-1.11256 - 10.2298i) q^{14} +(-2.56953 - 14.9383i) q^{15} +(-1.47196 - 5.30154i) q^{16} +(2.37465 - 5.13272i) q^{17} +(-19.7018 - 20.1558i) q^{18} +(-29.6004 + 6.51555i) q^{19} +(-15.1281 - 25.1430i) q^{20} +(8.20195 + 5.46762i) q^{21} +(9.35336 - 13.7952i) q^{22} +(-6.42262 - 1.05293i) q^{23} +(-15.4686 - 7.00972i) q^{24} +(0.383589 + 0.363355i) q^{25} +(-35.1829 - 37.1421i) q^{26} +(26.9185 - 2.09592i) q^{27} +(18.6364 + 4.10218i) q^{28} +(13.1216 + 38.9436i) q^{29} +(46.9029 + 7.31191i) q^{30} +(-38.3739 - 8.44674i) q^{31} +(39.8161 + 2.15877i) q^{32} +(4.39197 + 15.3502i) q^{33} +(12.8582 + 12.1799i) q^{34} +(-16.5772 + 0.898791i) q^{35} +(47.0874 - 22.6887i) q^{36} +(12.2214 - 18.0252i) q^{37} +(10.2626 - 94.3627i) q^{38} +(48.9144 - 3.03716i) q^{39} +(27.9334 - 6.14861i) q^{40} +(-12.2769 + 2.01269i) q^{41} +(-24.4283 + 18.8742i) q^{42} +(7.49855 + 27.0073i) q^{43} +(18.7049 + 24.6059i) q^{44} +(-34.1916 + 29.9789i) q^{45} +(9.54723 - 18.0080i) q^{46} +(-42.0041 + 16.7360i) q^{47} +(-11.2570 + 12.0722i) q^{48} +(-24.7325 + 29.1174i) q^{49} +(-1.46193 + 0.775066i) q^{50} +(-16.8519 + 1.96666i) q^{51} +(86.1056 - 39.8367i) q^{52} +(8.72926 - 7.41470i) q^{53} +(-20.6972 + 81.9840i) q^{54} +(-21.4069 - 16.2731i) q^{55} +(-9.58956 + 15.9380i) q^{56} +(63.0465 + 65.5200i) q^{57} -128.697 q^{58} +(38.0637 + 45.0795i) q^{59} +(-40.6224 + 78.0966i) q^{60} +(46.0786 + 15.5257i) q^{61} +(63.4404 - 105.439i) q^{62} +(1.13743 - 29.5501i) q^{63} +(-38.0752 + 95.5615i) q^{64} +(-62.9086 + 53.4350i) q^{65} +(-49.9477 - 2.31518i) q^{66} +(-31.2284 - 46.0585i) q^{67} +(-29.0185 + 15.3846i) q^{68} +(7.36907 + 18.0811i) q^{69} +(13.9092 - 50.0962i) q^{70} +(75.0351 - 29.8967i) q^{71} +(6.30260 + 50.5569i) q^{72} +(28.1527 - 3.06179i) q^{73} +(41.2738 + 54.2947i) q^{74} +(0.328590 - 1.55066i) q^{75} +(159.754 + 73.9102i) q^{76} +(17.2567 - 2.82909i) q^{77} +(-39.8988 + 148.204i) q^{78} +(-14.6892 + 8.83819i) q^{79} +(3.00567 - 27.6367i) q^{80} +(-47.5376 - 65.5834i) q^{81} +(6.30317 - 38.4476i) q^{82} +(144.486 - 7.83379i) q^{83} +(-18.7043 - 54.1057i) q^{84} +(20.7448 - 19.6506i) q^{85} +(-87.6500 - 4.75224i) q^{86} +(79.0728 - 94.5859i) q^{87} +(-28.5506 + 9.61981i) q^{88} +(28.9065 + 85.7915i) q^{89} +(-54.7803 - 131.451i) q^{90} +(2.90602 - 53.5983i) q^{91} +(25.9937 + 27.4412i) q^{92} +(38.5139 + 111.408i) q^{93} +(-7.66616 - 141.394i) q^{94} +(-151.121 - 24.7750i) q^{95} +(-56.8604 - 105.246i) q^{96} +(132.380 + 14.3972i) q^{97} +(-61.6824 - 102.517i) q^{98} +(32.3900 - 35.2866i) 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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