LMFDB - Embedded newform 177.4.f.a.2.14

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.f (of order $58$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$1624$
Relative dimension:	$58$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			2.14
Character	$\chi$	$=$	177.2
Dual form			177.4.f.a.89.14

$q$-expansion

$f(q)$	$=$	$q+(-0.191601 + 3.53386i) q^{2} +(-0.887175 + 5.11986i) q^{3} +(-4.49838 - 0.489228i) q^{4} +(2.01755 - 5.98787i) q^{5} +(-17.9229 - 4.11612i) q^{6} +(16.3407 + 24.1007i) q^{7} +(-1.98968 + 12.1365i) q^{8} +(-25.4258 - 9.08442i) q^{9} +O(q^{10})$	\(q+(-0.191601 + 3.53386i) q^{2} +(-0.887175 + 5.11986i) q^{3} +(-4.49838 - 0.489228i) q^{4} +(2.01755 - 5.98787i) q^{5} +(-17.9229 - 4.11612i) q^{6} +(16.3407 + 24.1007i) q^{7} +(-1.98968 + 12.1365i) q^{8} +(-25.4258 - 9.08442i) q^{9} +(20.7738 + 8.27702i) q^{10} +(-40.8859 + 8.99967i) q^{11} +(6.49563 - 22.5970i) q^{12} +(8.51733 - 7.23469i) q^{13} +(-88.2996 + 53.1281i) q^{14} +(28.8671 + 15.6418i) q^{15} +(-77.8606 - 17.1384i) q^{16} +(-23.1396 - 15.6890i) q^{17} +(36.9747 - 88.1109i) q^{18} +(-26.4317 + 49.8555i) q^{19} +(-12.0051 + 25.9487i) q^{20} +(-137.889 + 62.2805i) q^{21} +(-23.9698 - 146.210i) q^{22} +(54.6255 - 51.7441i) q^{23} +(-60.3721 - 20.9541i) q^{24} +(67.7275 + 51.4851i) q^{25} +(23.9345 + 31.4853i) q^{26} +(69.0681 - 122.117i) q^{27} +(-61.7159 - 116.409i) q^{28} +(-29.1882 + 1.58254i) q^{29} +(-60.8071 + 99.0155i) q^{30} +(152.028 - 80.5999i) q^{31} +(49.1612 - 177.063i) q^{32} +(-9.80405 - 217.314i) q^{33} +(59.8765 - 78.7661i) q^{34} +(177.280 - 49.2216i) q^{35} +(109.931 + 53.3042i) q^{36} +(139.695 - 22.9018i) q^{37} +(-171.118 - 102.958i) q^{38} +(29.4842 + 50.0260i) q^{39} +(68.6577 + 36.4000i) q^{40} +(-214.851 + 226.815i) q^{41} +(-193.671 - 499.215i) q^{42} +(6.71486 - 30.5059i) q^{43} +(188.323 - 20.4814i) q^{44} +(-105.694 + 133.918i) q^{45} +(172.390 + 202.953i) q^{46} +(-242.442 + 81.6882i) q^{47} +(156.822 - 383.430i) q^{48} +(-186.870 + 469.007i) q^{49} +(-194.918 + 229.475i) q^{50} +(100.854 - 104.552i) q^{51} +(-41.8536 + 28.3775i) q^{52} +(-344.447 + 137.240i) q^{53} +(418.312 + 267.475i) q^{54} +(-28.6005 + 262.977i) q^{55} +(-325.012 + 150.367i) q^{56} +(-231.803 - 179.557i) q^{57} -103.450i q^{58} +(433.081 - 133.491i) q^{59} +(-122.203 - 84.4856i) q^{60} +(-392.130 - 21.2606i) q^{61} +(255.701 + 552.688i) q^{62} +(-196.535 - 761.227i) q^{63} +(11.8871 + 4.00523i) q^{64} +(-26.1362 - 65.5970i) q^{65} +(769.838 + 6.99134i) q^{66} +(308.653 + 50.6011i) q^{67} +(96.4151 + 81.8958i) q^{68} +(216.460 + 325.581i) q^{69} +(139.976 + 635.915i) q^{70} +(55.9132 + 165.944i) q^{71} +(160.843 - 290.507i) q^{72} +(452.410 + 751.911i) q^{73} +(54.1663 + 498.051i) q^{74} +(-323.683 + 301.079i) q^{75} +(143.290 - 211.338i) q^{76} +(-885.004 - 838.320i) q^{77} +(-182.434 + 94.6081i) q^{78} +(720.120 + 333.163i) q^{79} +(-259.710 + 431.641i) q^{80} +(563.947 + 461.958i) q^{81} +(-760.368 - 802.711i) q^{82} +(-55.4155 - 199.589i) q^{83} +(650.748 - 212.702i) q^{84} +(-140.629 + 106.904i) q^{85} +(106.517 + 29.5743i) q^{86} +(17.7927 - 150.843i) q^{87} +(-27.8748 - 514.120i) q^{88} +(25.0337 + 461.720i) q^{89} +(-452.998 - 399.168i) q^{90} +(313.541 + 87.0541i) q^{91} +(-271.041 + 206.040i) q^{92} +(277.785 + 849.866i) q^{93} +(-242.223 - 872.408i) q^{94} +(245.201 + 258.855i) q^{95} +(862.921 + 408.784i) q^{96} +(-732.057 + 1216.69i) q^{97} +(-1621.60 - 750.234i) q^{98} +(1121.32 + 142.600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} + O(q^{10}) $	$ 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} - 58q^{10} - 57q^{12} - 58q^{13} - 11q^{15} - 926q^{16} - 29q^{18} + 126q^{19} + 159q^{21} + 2q^{22} - 29q^{24} + 656q^{25} - 99q^{27} - 54q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} + 859q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} + 1703q^{45} + 602q^{46} + 9507q^{48} - 1192q^{49} + 1511q^{51} - 58q^{52} - 7743q^{54} - 58q^{55} - 7441q^{57} - 18722q^{60} - 58q^{61} - 3251q^{63} - 4634q^{64} - 1751q^{66} - 58q^{67} + 6003q^{69} - 58q^{70} + 21547q^{72} - 58q^{73} + 3869q^{75} + 5622q^{76} - 3253q^{78} + 1446q^{79} + 247q^{81} - 58q^{82} + 3303q^{84} + 790q^{85} - 2199q^{87} - 5818q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 946q^{94} - 29q^{96} - 58q^{97} - 29q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{1}{58}\right)$	$-1$

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 $

$2$	−0.191601	+	3.53386i	−0.0677410	+	1.24941i	0.745111	+	0.666940i	$0.232396\pi$
$2$	−0.191601	+	3.53386i	−0.0677410	+	1.24941i	−0.812852	+	0.582470i	$0.802087\pi$
$3$	−0.887175	+	5.11986i	−0.170737	+	0.985317i
$3$	−0.887175	+	5.11986i	−0.170737	+	0.985317i
$4$	−4.49838	−	0.489228i	−0.562297	−	0.0611535i
$5$	2.01755	−	5.98787i	0.180455	−	0.535571i	−0.818803	−	0.574074i	$-0.805362\pi$
$5$	2.01755	−	5.98787i	0.180455	−	0.535571i	0.999259	+	0.0385025i	$0.0122587\pi$
$6$	−17.9229	−	4.11612i	−1.21950	−	0.280067i
$7$	16.3407	+	24.1007i	0.882315	+	1.30132i	0.952736	+	0.303800i	$0.0982556\pi$
$7$	16.3407	+	24.1007i	0.882315	+	1.30132i	−0.0704204	+	0.997517i	$0.522434\pi$
$8$	−1.98968	+	12.1365i	−0.0879324	+	0.536364i
$9$	−25.4258	−	9.08442i	−0.941698	−	0.336460i
$10$	20.7738	+	8.27702i	0.656924	+	0.261742i
$11$	−40.8859	+	8.99967i	−1.12069	+	0.246682i	−0.736410	−	0.676535i	$-0.763481\pi$
$11$	−40.8859	+	8.99967i	−1.12069	+	0.246682i	−0.384278	+	0.923217i	$0.625550\pi$
$12$	6.49563	−	22.5970i	0.156261	−	0.543600i
$13$	8.51733	−	7.23469i	0.181714	−	0.154349i	−0.551913	−	0.833902i	$-0.686102\pi$
$13$	8.51733	−	7.23469i	0.181714	−	0.154349i	0.733627	+	0.679552i	$0.237826\pi$
$14$	−88.2996	+	53.1281i	−1.68565	+	1.01422i
$15$	28.8671	+	15.6418i	0.496897	+	0.269247i
$16$	−77.8606	−	17.1384i	−1.21657	−	0.267788i
$17$	−23.1396	−	15.6890i	−0.330128	−	0.223832i	0.384850	−	0.922979i	$-0.374253\pi$
$17$	−23.1396	−	15.6890i	−0.330128	−	0.223832i	−0.714978	+	0.699147i	$0.753563\pi$
$18$	36.9747	−	88.1109i	0.484168	−	1.15377i
$19$	−26.4317	+	49.8555i	−0.319150	+	0.601980i	−0.990236	−	0.139399i	$-0.955483\pi$
$19$	−26.4317	+	49.8555i	−0.319150	+	0.601980i	0.671087	+	0.741379i	$0.265828\pi$
$20$	−12.0051	+	25.9487i	−0.134221	+	0.290115i
$21$	−137.889	+	62.2805i	−1.43285	+	0.647177i
$22$	−23.9698	−	146.210i	−0.232290	−	1.41691i
$23$	54.6255	−	51.7441i	0.495227	−	0.469103i	−0.398851	−	0.917016i	$-0.630591\pi$
$23$	54.6255	−	51.7441i	0.495227	−	0.469103i	0.894078	+	0.447912i	$0.147832\pi$
$24$	−60.3721	−	20.9541i	−0.513475	−	0.178218i
$25$	67.7275	+	51.4851i	0.541820	+	0.411881i
$26$	23.9345	+	31.4853i	0.180536	+	0.237491i
$27$	69.0681	−	122.117i	0.492302	−	0.870424i
$28$	−61.7159	−	116.409i	−0.416543	−	0.785684i
$29$	−29.1882	+	1.58254i	−0.186900	+	0.0101334i	−0.147351	−	0.989084i	$-0.547075\pi$
$29$	−29.1882	+	1.58254i	−0.186900	+	0.0101334i	−0.0395488	+	0.999218i	$0.512592\pi$
$30$	−60.8071	+	99.0155i	−0.370060	+	0.602589i
$31$	152.028	−	80.5999i	0.880805	−	0.466973i	0.0343357	−	0.999410i	$-0.489068\pi$
$31$	152.028	−	80.5999i	0.880805	−	0.466973i	0.846470	+	0.532437i	$0.178724\pi$
$32$	49.1612	−	177.063i	0.271580	−	0.978143i
$33$	−9.80405	−	217.314i	−0.0517172	−	1.14635i
$34$	59.8765	−	78.7661i	0.302021	−	0.397302i
$35$	177.280	−	49.2216i	0.856167	−	0.237714i
$36$	109.931	+	53.3042i	0.508939	+	0.246779i
$37$	139.695	−	22.9018i	0.620694	−	0.101758i	0.156774	−	0.987635i	$-0.449891\pi$
$37$	139.695	−	22.9018i	0.620694	−	0.101758i	0.463920	+	0.885877i	$0.346442\pi$
$38$	−171.118	−	102.958i	−0.730501	−	0.439528i
$39$	29.4842	+	50.0260i	0.121058	+	0.205399i
$40$	68.6577	+	36.4000i	0.271394	+	0.143884i
$41$	−214.851	+	226.815i	−0.818391	+	0.863965i	−0.992686	−	0.120729i	$-0.961477\pi$
$41$	−214.851	+	226.815i	−0.818391	+	0.863965i	0.174294	+	0.984694i	$0.444236\pi$
$42$	−193.671	−	499.215i	−0.711526	−	1.83406i
$43$	6.71486	−	30.5059i	0.0238141	−	0.108189i	−0.963214	−	0.268735i	$-0.913395\pi$
$43$	6.71486	−	30.5059i	0.0238141	−	0.108189i	0.987028	+	0.160546i	$0.0513255\pi$
$44$	188.323	−	20.4814i	0.645245	−	0.0701747i
$45$	−105.694	+	133.918i	−0.350132	+	0.443631i
$46$	172.390	+	202.953i	0.552555	+	0.650518i
$47$	−242.442	+	81.6882i	−0.752421	+	0.253520i	−0.669272	−	0.743017i	$-0.733394\pi$
$47$	−242.442	+	81.6882i	−0.752421	+	0.253520i	−0.0831483	+	0.996537i	$0.526498\pi$
$48$	156.822	−	383.430i	0.471569	−	1.15299i
$49$	−186.870	+	469.007i	−0.544809	+	1.36737i
$50$	−194.918	+	229.475i	−0.551312	+	0.649054i
$51$	100.854	−	104.552i	0.276911	−	0.287064i
$52$	−41.8536	+	28.3775i	−0.111616	+	0.0756778i
$53$	−344.447	+	137.240i	−0.892706	+	0.355687i	−0.770967	−	0.636875i	$-0.780227\pi$
$53$	−344.447	+	137.240i	−0.892706	+	0.355687i	−0.121740	+	0.992562i	$0.538847\pi$
$54$	418.312	+	267.475i	1.05417	+	0.674050i
$55$	−28.6005	+	262.977i	−0.0701179	+	0.644724i
$56$	−325.012	+	150.367i	−0.775564	+	0.358814i
$57$	−231.803	−	179.557i	−0.538651	−	0.417244i
$58$		−	103.450i		−	0.234201i
$59$	433.081	−	133.491i	0.955633	−	0.294560i
$59$	433.081	−	133.491i	0.955633	−	0.294560i
$60$	−122.203	−	84.4856i	−0.262939	−	0.181784i
$61$	−392.130	−	21.2606i	−0.823066	−	0.0446254i	−0.362206	−	0.932098i	$-0.617976\pi$
$61$	−392.130	−	21.2606i	−0.823066	−	0.0446254i	−0.460860	+	0.887473i	$0.652459\pi$
$62$	255.701	+	552.688i	0.523774	+	1.13212i
$63$	−196.535	−	761.227i	−0.393033	−	1.52231i
$64$	11.8871	+	4.00523i	0.0232170	+	0.00782271i
$65$	−26.1362	−	65.5970i	−0.0498739	−	0.125174i
$66$	769.838	+	6.99134i	1.43576	+	0.0130390i
$67$	308.653	+	50.6011i	0.562806	+	0.0922673i	0.436468	−	0.899720i	$-0.356229\pi$
$67$	308.653	+	50.6011i	0.562806	+	0.0922673i	0.126338	+	0.991987i	$0.459678\pi$
$68$	96.4151	+	81.8958i	0.171942	+	0.146049i
$69$	216.460	+	325.581i	0.377662	+	0.568048i
$70$	139.976	+	635.915i	0.239004	+	1.08581i
$71$	55.9132	+	165.944i	0.0934602	+	0.277380i	0.984180	−	0.177173i	$-0.0566954\pi$
$71$	55.9132	+	165.944i	0.0934602	+	0.277380i	−0.890719	+	0.454554i	$0.849799\pi$
$72$	160.843	−	290.507i	0.263271	−	0.475507i
$73$	452.410	+	751.911i	0.725350	+	1.20554i	0.971668	+	0.236352i	$0.0759518\pi$
$73$	452.410	+	751.911i	0.725350	+	1.20554i	−0.246318	+	0.969189i	$0.579221\pi$
$74$	54.1663	+	498.051i	0.0850905	+	0.782395i
$75$	−323.683	+	301.079i	−0.498342	+	0.463541i
$76$	143.290	−	211.338i	0.216270	−	0.318975i
$77$	−885.004	−	838.320i	−1.30981	−	1.24072i
$78$	−182.434	+	94.6081i	−0.264828	+	0.137337i
$79$	720.120	+	333.163i	1.02557	+	0.474478i	0.859229	−	0.511591i	$-0.170944\pi$
$79$	720.120	+	333.163i	1.02557	+	0.474478i	0.166338	+	0.986069i	$0.446806\pi$
$80$	−259.710	+	431.641i	−0.362956	+	0.603237i
$81$	563.947	+	461.958i	0.773590	+	0.633687i
$82$	−760.368	−	802.711i	−1.02401	−	1.08103i
$83$	−55.4155	−	199.589i	−0.0732848	−	0.263948i	0.917827	−	0.396981i	$-0.129942\pi$
$83$	−55.4155	−	199.589i	−0.0732848	−	0.263948i	−0.991112	+	0.133033i	$0.957528\pi$
$84$	650.748	−	212.702i	0.845267	−	0.276282i
$85$	−140.629	+	106.904i	−0.179451	+	0.136415i
$86$	106.517	+	29.5743i	0.133559	+	0.0370824i
$87$	17.7927	−	150.843i	0.0219261	−	0.185886i
$88$	−27.8748	−	514.120i	−0.0337666	−	0.622788i
$89$	25.0337	+	461.720i	0.0298154	+	0.549913i	0.974839	+	0.222911i	$0.0715558\pi$
$89$	25.0337	+	461.720i	0.0298154	+	0.549913i	−0.945023	+	0.327002i	$0.893961\pi$
$90$	−452.998	−	399.168i	−0.530558	−	0.467511i
$91$	313.541	+	87.0541i	0.361187	+	0.100283i
$92$	−271.041	+	206.040i	−0.307152	+	0.233491i
$93$	277.785	+	849.866i	0.309731	+	0.947602i
$94$	−242.223	−	872.408i	−0.265781	−	0.957255i
$95$	245.201	+	258.855i	0.264811	+	0.279558i
$96$	862.921	+	408.784i	0.917412	+	0.434597i
$97$	−732.057	+	1216.69i	−0.766279	+	1.27357i	0.190194	+	0.981747i	$0.439088\pi$
$97$	−732.057	+	1216.69i	−0.766279	+	1.27357i	−0.956473	+	0.291820i	$0.905739\pi$
$98$	−1621.60	−	750.234i	−1.67150	−	0.773317i
$99$	1121.32	+	142.600i	1.13835	+	0.144767i
$100$	−279.476	−	264.734i	−0.279476	−	0.264734i
$101$	743.848	−	1097.09i	0.732828	−	1.08084i	−0.260495	−	0.965475i	$-0.583886\pi$
$101$	743.848	−	1097.09i	0.732828	−	1.08084i	0.993323	−	0.115365i	$-0.0368038\pi$
$102$	350.150	+	376.438i	0.339902	+	0.365421i
$103$	179.639	+	1651.75i	0.171848	+	1.58011i	0.689348	+	0.724430i	$0.257897\pi$
$103$	179.639	+	1651.75i	0.171848	+	1.58011i	−0.517500	+	0.855683i	$0.673137\pi$
$104$	70.8573	+	117.766i	0.0668089	+	0.111037i
$105$	94.7290	+	951.318i	0.0880438	+	0.884182i
$106$	−418.992	−	1243.52i	−0.383926	−	1.13945i
$107$	366.612	+	1665.53i	0.331231	+	1.50480i	0.788259	+	0.615344i	$0.210983\pi$
$107$	366.612	+	1665.53i	0.331231	+	1.50480i	−0.457028	+	0.889452i	$0.651086\pi$
$108$	−370.438	+	515.539i	−0.330050	+	0.459331i
$109$	−322.859	−	274.239i	−0.283709	−	0.240985i	0.494220	−	0.869337i	$-0.335454\pi$
$109$	−322.859	−	274.239i	−0.283709	−	0.240985i	−0.777929	+	0.628352i	$0.783730\pi$
$110$	−923.845	−	151.457i	−0.800774	−	0.131280i
$111$	−6.67982	+	735.535i	−0.00571190	+	0.628954i
$112$	−859.248	−	2156.55i	−0.724923	−	1.81942i
$113$	2021.19	+	681.017i	1.68263	+	0.566944i	0.988275	−	0.152688i	$-0.0487928\pi$
$113$	2021.19	+	681.017i	1.68263	+	0.566944i	0.694356	+	0.719632i	$0.255689\pi$
$114$	678.944	−	784.758i	0.557797	−	0.644731i
$115$	−199.627	−	431.487i	−0.161872	−	0.349881i
$116$	132.074	+	7.16083i	0.105713	+	0.00573160i
$117$	−282.283	+	106.573i	−0.223052	+	0.0842110i
$118$	388.760	+	1556.03i	0.303290	+	1.21393i
$119$		−	814.051i		−	0.627092i
$120$	−247.274	+	319.224i	−0.188108	+	0.242842i
$121$	382.681	−	177.047i	0.287514	−	0.133018i
$122$	150.264	−	1381.66i	0.111511	−	1.02532i
$123$	−970.650	−	1301.23i	−0.711550	−	0.953885i
$124$	−723.310	+	288.193i	−0.523832	+	0.208714i
$125$	1098.66	−	744.912i	0.786139	−	0.533015i
$126$	2727.73	−	548.677i	1.92862	−	0.387937i
$127$	1634.84	−	1924.69i	1.14228	−	1.34479i	0.212284	−	0.977208i	$-0.431910\pi$
$127$	1634.84	−	1924.69i	1.14228	−	1.34479i	0.929991	−	0.367583i	$-0.119814\pi$
$128$	527.704	−	1324.44i	0.364397	−	0.914568i
$129$	150.229	+	61.4432i	0.102534	+	0.0419362i
$130$	236.819	−	79.7935i	0.159772	−	0.0538335i
$131$	753.367	+	886.932i	0.502458	+	0.591539i	0.953661	−	0.300882i	$-0.0972810\pi$
$131$	753.367	+	886.932i	0.502458	+	0.591539i	−0.451203	+	0.892421i	$0.649005\pi$
$132$	−62.2139	+	982.358i	−0.0410229	+	0.647753i
$133$	−1633.47	+	177.650i	−1.06496	+	0.115821i
$134$	−237.955	+	1081.04i	−0.153405	+	0.696924i
$135$	−591.874	−	659.948i	−0.377336	−	0.420735i
$136$	236.451	−	249.618i	0.149085	−	0.157387i
$137$	−1986.10	−	1052.96i	−1.23857	−	0.656649i	−0.285205	−	0.958466i	$-0.592062\pi$
$137$	−1986.10	−	1052.96i	−1.23857	−	0.656649i	−0.953366	+	0.301818i	$0.902407\pi$
$138$	−1192.03	+	702.558i	−0.735308	+	0.433374i
$139$	−1516.36	−	912.361i	−0.925292	−	0.556730i	−0.0287004	−	0.999588i	$-0.509137\pi$
$139$	−1516.36	−	912.361i	−0.925292	−	0.556730i	−0.896592	+	0.442858i	$0.853964\pi$
$140$	−821.555	+	134.687i	−0.495957	+	0.0813081i
$141$	−203.143	−	1313.74i	−0.121332	−	0.784658i
$142$	−597.138	+	165.795i	−0.352892	+	0.0979801i
$143$	−283.129	+	372.450i	−0.165570	+	0.217803i
$144$	1823.98	+	1143.08i	1.05554	+	0.661502i
$145$	−49.4125	+	177.968i	−0.0282999	+	0.101927i
$146$	−2743.83	+	1454.69i	−1.55535	+	0.824595i
$147$	−2235.46	−	1372.84i	−1.25427	−	0.770270i
$148$	−639.605	+	34.6784i	−0.355238	+	0.0192604i
$149$	420.706	+	793.536i	0.231313	+	0.436302i	0.971813	−	0.235754i	$-0.0757561\pi$
$149$	420.706	+	793.536i	0.231313	+	0.436302i	−0.740500	+	0.672056i	$0.765411\pi$
$150$	−1001.95	−	1201.54i	−0.545395	−	0.654034i
$151$	−1110.53	−	1460.87i	−0.598499	−	0.787312i	0.392703	−	0.919665i	$-0.371540\pi$
$151$	−1110.53	−	1460.87i	−0.598499	−	0.787312i	−0.991203	+	0.132353i	$0.957747\pi$
$152$	−552.482	−	419.986i	−0.294817	−	0.224114i
$153$	445.818	+	609.117i	0.235570	+	0.321857i
$154$	3132.08	−	2966.86i	1.63890	−	1.55244i
$155$	−175.899	−	1072.94i	−0.0911519	−	0.556002i
$156$	−108.157	−	239.460i	−0.0555095	−	0.122898i
$157$	−424.979	+	918.577i	−0.216032	+	0.466946i	−0.985047	−	0.172285i	$-0.944885\pi$
$157$	−424.979	+	918.577i	−0.216032	+	0.466946i	0.769015	+	0.639231i	$0.220747\pi$
$158$	−1315.33	+	2480.97i	−0.662290	+	1.24921i
$159$	−397.065	−	1885.28i	−0.198046	−	0.940327i
$160$	−961.044	−	651.604i	−0.474857	−	0.321961i
$161$	2139.69	+	470.981i	1.04740	+	0.230550i
$162$	−1740.55	+	1904.40i	−0.844138	+	0.923604i
$163$	3367.87	−	2026.38i	1.61836	−	0.973733i	0.639599	−	0.768709i	$-0.279100\pi$
$163$	3367.87	−	2026.38i	1.61836	−	0.973733i	0.978757	−	0.205024i	$-0.0657273\pi$
$164$	1077.44	−	915.189i	0.513014	−	0.435758i
$165$	−1321.03	−	379.737i	−0.623285	−	0.179166i
$166$	715.936	−	157.590i	0.334744	−	0.0736826i
$167$	−784.324	−	312.503i	−0.363430	−	0.144804i	0.181273	−	0.983433i	$-0.441978\pi$
$167$	−784.324	−	312.503i	−0.363430	−	0.144804i	−0.544703	+	0.838629i	$0.683358\pi$
$168$	−481.513	−	1797.42i	−0.221128	−	0.825439i
$169$	−335.231	+	2044.82i	−0.152586	+	0.930732i
$170$	−350.838	−	517.447i	−0.158283	−	0.233449i
$171$	1124.96	−	1027.50i	0.503085	−	0.459503i
$172$	−45.1303	+	133.942i	−0.0200067	+	0.0593778i
$173$	−521.948	−	56.7653i	−0.229381	−	0.0249467i	−0.00729356	−	0.999973i	$-0.502322\pi$
$173$	−521.948	−	56.7653i	−0.229381	−	0.0249467i	−0.222088	+	0.975027i	$0.571287\pi$
$174$	529.650	+	91.7785i	0.230763	+	0.0399868i
$175$	−134.114	+	2473.59i	−0.0579318	+	1.06849i
$176$	3337.64			1.42946
$177$	299.235	+	2335.74i	0.127073	+	0.991893i
$178$	−1636.45			−0.689086
$179$	−240.031	+	4427.10i	−0.100228	+	1.84859i	0.327709	+	0.944779i	$0.393724\pi$
$179$	−240.031	+	4427.10i	−0.100228	+	1.84859i	−0.427936	+	0.903809i	$0.640759\pi$
$180$	540.969	−	550.707i	0.224008	−	0.228041i
$181$	−1020.94	−	111.034i	−0.419257	−	0.0455970i	−0.103941	−	0.994583i	$-0.533145\pi$
$181$	−1020.94	−	111.034i	−0.419257	−	0.0455970i	−0.315317	+	0.948986i	$0.602111\pi$
$182$	−367.712	+	1091.33i	−0.149762	+	0.444477i
$183$	456.739	−	1988.78i	0.184498	−	0.803362i
$184$	519.306	+	765.919i	0.208064	+	0.306871i
$185$	144.708	−	882.680i	0.0575089	−	0.350789i
$186$	−3056.53	+	818.820i	−1.20492	+	0.322789i
$187$	1087.28	+	433.212i	0.425186	+	0.169410i
$188$	1130.56	−	248.855i	0.438588	−	0.0965405i
$189$	4071.74	−	330.889i	1.56706	−	0.127347i
$190$	−961.740	+	816.910i	−0.367221	+	0.311920i
$191$	627.656	−	377.648i	0.237778	−	0.143066i	−0.391678	−	0.920102i	$-0.628105\pi$
$191$	627.656	−	377.648i	0.237778	−	0.143066i	0.629456	+	0.777036i	$0.283278\pi$
$192$	−31.0521	+	57.3069i	−0.0116718	+	0.0215405i
$193$	1370.33	+	301.632i	0.511080	+	0.112497i	0.463021	−	0.886347i	$-0.346765\pi$
$193$	1370.33	+	301.632i	0.511080	+	0.112497i	0.0480591	+	0.998844i	$0.484696\pi$
$194$	−4159.35	−	2820.11i	−1.53930	−	1.04367i
$195$	359.035	−	75.6178i	0.131851	−	0.0277697i
$196$	1070.06	−	2018.35i	0.389964	−	0.735551i
$197$	276.393	−	597.413i	0.0999603	−	0.216061i	−0.851143	−	0.524934i	$-0.824090\pi$
$197$	276.393	−	597.413i	0.0999603	−	0.216061i	0.951103	+	0.308874i	$0.0999520\pi$
$198$	−718.775	+	3935.25i	−0.257986	+	1.41246i
$199$	−578.415	−	3528.18i	−0.206044	−	1.25681i	−0.863898	−	0.503668i	$-0.831984\pi$
$199$	−578.415	−	3528.18i	−0.206044	−	1.25681i	0.657853	−	0.753146i	$-0.271465\pi$
$200$	−759.608	+	719.539i	−0.268562	+	0.254395i
$201$	−532.900	+	1535.37i	−0.187004	+	0.538788i
$202$	3734.46	+	2838.86i	1.30077	+	0.988819i
$203$	−515.096	−	677.597i	−0.178092	−	0.234276i
$204$	−504.832	+	420.976i	−0.173261	+	0.144481i
$205$	924.668	+	1744.11i	0.315032	+	0.594214i
$206$	−5871.48	+	318.342i	−1.98585	+	0.107670i
$207$	−1858.96	+	819.395i	−0.624188	+	0.275130i
$208$	−787.155	+	417.323i	−0.262401	+	0.139116i
$209$	632.001	−	2276.26i	0.209170	−	0.753361i
$210$	−3379.98	+	152.486i	−1.11067	+	0.0501074i
$211$	−1279.67	+	1683.38i	−0.417518	+	0.549236i	−0.955987	−	0.293410i	$-0.905210\pi$
$211$	−1279.67	+	1683.38i	−0.417518	+	0.549236i	0.538469	+	0.842646i	$0.319003\pi$
$212$	1616.60	−	448.845i	0.523718	−	0.145410i
$213$	−899.216	+	139.046i	−0.289264	+	0.0447289i
$214$	−5956.01	+	976.438i	−1.90254	+	0.311906i
$215$	−169.118	−	101.755i	−0.0536453	−	0.0322773i
$216$	1344.66	+	1081.22i	0.423575	+	0.340592i
$217$	4426.76	+	2346.92i	1.38483	+	0.734190i
$218$	1030.98	−	1088.40i	0.320308	−	0.338145i
$219$	−4251.04	+	1649.20i	−1.31168	+	0.508869i
$220$	257.311	−	1168.98i	0.0788542	−	0.358238i
$221$	−310.593	+	33.7790i	−0.0945373	+	0.0102815i
$222$	−2598.00	−	164.535i	−0.785434	−	0.0497425i
$223$	−4191.91	−	4935.10i	−1.25880	−	1.48197i	−0.807817	−	0.589433i	$-0.799351\pi$
$223$	−4191.91	−	4935.10i	−1.25880	−	1.48197i	−0.450978	−	0.892535i	$-0.648925\pi$
$224$	5070.67	−	1708.51i	1.51249	−	0.509618i
$225$	−1254.32	−	1924.32i	−0.371650	−	0.570168i
$226$	−2793.88	+	7012.11i	−0.822329	+	2.06389i
$227$	3208.21	−	3777.00i	0.938046	−	1.10435i	−0.0563265	−	0.998412i	$-0.517939\pi$
$227$	3208.21	−	3777.00i	0.938046	−	1.10435i	0.994372	−	0.105941i	$-0.0337854\pi$
$228$	954.895	+	921.120i	0.277366	+	0.267556i
$229$	1851.14	−	1255.10i	0.534178	−	0.362182i	−0.264076	−	0.964502i	$-0.585067\pi$
$229$	1851.14	−	1255.10i	0.534178	−	0.362182i	0.798255	+	0.602320i	$0.205757\pi$
$230$	1563.06	−	622.782i	0.448110	−	0.178544i
$231$	5077.23	−	3787.35i	1.44614	−	1.07874i
$232$	38.8687	−	357.392i	0.0109994	−	0.101138i
$233$	3252.90	−	1504.95i	0.914611	−	0.423144i	0.0946156	−	0.995514i	$-0.469838\pi$
$233$	3252.90	−	1504.95i	0.914611	−	0.423144i	0.819996	+	0.572370i	$0.193976\pi$
$234$	−322.529	−	1017.97i	−0.0901042	−	0.284388i
$235$			1616.52i			0.448724i
$236$	−2013.47	+	388.617i	−0.555363	+	0.107190i
$237$	−2344.62	+	3391.34i	−0.642613	+	0.929498i
$238$	2876.75	+	155.973i	0.783495	+	0.0424799i
$239$	−1819.84	−	3933.51i	−0.492533	−	1.06459i	−0.981354	−	0.192209i	$-0.938435\pi$
$239$	−1819.84	−	3933.51i	−0.492533	−	1.06459i	0.488821	−	0.872384i	$-0.337427\pi$
$240$	−1979.53	−	1712.62i	−0.532410	−	0.460621i
$241$	2439.07	+	821.819i	0.651927	+	0.219660i	0.625782	−	0.779998i	$-0.284780\pi$
$241$	2439.07	+	821.819i	0.651927	+	0.219660i	0.0261457	+	0.999658i	$0.491677\pi$
$242$	552.339	+	1386.27i	0.146718	+	0.368234i
$243$	−2865.48	+	2477.49i	−0.756463	+	0.654037i
$244$	1753.55	+	287.479i	0.460079	+	0.0754261i
$245$	2431.34	+	2065.20i	0.634010	+	0.538533i
$246$	4784.34	−	3180.83i	1.23999	−	0.824400i
$247$	135.561	+	615.861i	0.0349213	+	0.158649i
$248$	675.717	+	2005.46i	0.173016	+	0.513495i
$249$	1071.03	−	106.649i	0.272585	−	0.0271431i
$250$	2421.91	+	4025.25i	0.612701	+	1.01832i
$251$	424.675	+	3904.82i	0.106794	+	0.981953i	0.917835	+	0.396963i	$0.129936\pi$
$251$	424.675	+	3904.82i	0.106794	+	0.981953i	−0.811041	+	0.584990i	$0.801099\pi$
$252$	511.676	+	3520.44i	0.127907	+	0.880027i
$253$	−1767.74	+	2607.21i	−0.439275	+	0.647882i
$254$	6488.35	+	6146.09i	1.60282	+	1.51827i
$255$	−422.568	−	814.843i	−0.103773	−	0.200108i
$256$	4670.34	+	2160.73i	1.14022	+	0.527522i
$257$	3694.88	−	6140.93i	0.896810	−	1.49051i	0.0255582	−	0.999673i	$-0.491864\pi$
$257$	3694.88	−	6140.93i	0.896810	−	1.49051i	0.871252	−	0.490836i	$-0.163309\pi$
$258$	−245.916	+	519.115i	−0.0593413	+	0.125266i
$259$	2834.66	+	2992.52i	0.680067	+	0.717938i
$260$	85.4788	+	307.867i	0.0203891	+	0.0734350i
$261$	756.510	+	224.920i	0.179413	+	0.0533418i
$262$	−3278.64	+	2492.36i	−0.773112	+	0.587704i
$263$	5921.89	+	1644.20i	1.38844	+	0.385498i	0.879743	−	0.475449i	$-0.157714\pi$
$263$	5921.89	+	1644.20i	1.38844	+	0.385498i	0.508695	+	0.860947i	$0.330128\pi$
$264$	2656.95	+	313.400i	0.619409	+	0.0730622i
$265$	126.838	+	2339.39i	0.0294023	+	0.542293i
$266$	−314.818	−	5806.49i	−0.0725668	−	1.33842i
$267$	−2386.15	−	281.458i	−0.546929	−	0.0645128i
$268$	−1363.68	−	378.625i	−0.310822	−	0.0862992i
$269$	4632.23	−	3521.33i	1.04993	−	0.798139i	0.0700174	−	0.997546i	$-0.477695\pi$
$269$	4632.23	−	3521.33i	1.04993	−	0.798139i	0.979917	+	0.199406i	$0.0639014\pi$
$270$	2445.57	−	1965.15i	0.551232	−	0.442946i
$271$	176.376	+	635.249i	0.0395354	+	0.142393i	0.980684	−	0.195600i	$-0.0626655\pi$
$271$	176.376	+	635.249i	0.0395354	+	0.142393i	−0.941148	+	0.337994i	$0.890252\pi$
$272$	1532.78	+	1618.13i	0.341685	+	0.360712i
$273$	−723.870	+	1528.05i	−0.160478	+	0.338761i
$274$	4101.57	−	6816.87i	0.904325	−	1.50300i
$275$	−3232.45	−	1495.49i	−0.708815	−	0.327933i
$276$	−814.434	−	1570.48i	−0.177620	−	0.342507i
$277$	−6103.22	−	5781.28i	−1.32385	−	1.25402i	−0.944397	−	0.328809i	$-0.893353\pi$
$277$	−6103.22	−	5781.28i	−1.32385	−	1.25402i	−0.379455	−	0.925210i	$-0.623888\pi$
$278$	3514.69	−	5183.78i	0.758264	−	1.11836i
$279$	−4597.63	+	668.239i	−0.986570	+	0.143392i
$280$	244.648	+	2249.50i	0.0522162	+	0.480120i
$281$	1448.14	+	2406.82i	0.307433	+	0.510957i	0.971601	−	0.236626i	$-0.0760416\pi$
$281$	1448.14	+	2406.82i	0.307433	+	0.510957i	−0.664168	+	0.747583i	$0.731214\pi$
$282$	4681.50	−	466.168i	0.988578	−	0.0984393i
$283$	1263.69	+	3750.49i	0.265436	+	0.787785i	0.994632	+	0.103480i	$0.0329978\pi$
$283$	1263.69	+	3750.49i	0.265436	+	0.787785i	−0.729196	+	0.684305i	$0.760106\pi$
$284$	−170.334	−	773.835i	−0.0355897	−	0.161686i
$285$	−1542.84	+	1025.74i	−0.320666	+	0.213192i
$286$	−1261.94	−	1071.90i	−0.260909	−	0.221618i
$287$	−8977.22	−	1471.74i	−1.84637	−	0.302697i
$288$	−2858.48	+	4055.37i	−0.584852	+	0.829739i
$289$	−1529.19	−	3837.99i	−0.311255	−	0.781190i
$290$	−619.447	−	208.716i	−0.125432	−	0.0422628i
$291$	−5579.80	−	4827.44i	−1.12403	−	0.972473i
$292$	−1667.25	−	3603.71i	−0.334139	−	0.722230i
$293$	2854.05	+	154.742i	0.569063	+	0.0308537i	0.336426	−	0.941710i	$-0.390782\pi$
$293$	2854.05	+	154.742i	0.569063	+	0.0308537i	0.232637	+	0.972564i	$0.425265\pi$
$294$	5279.73	−	7636.79i	1.04735	−	1.51492i
$295$	74.4362	−	2862.56i	0.0146910	−	0.564965i
$296$			1740.98i			0.341866i
$297$	−1724.90	+	5614.46i	−0.336999	+	1.09692i
$298$	−2884.85	+	1334.68i	−0.560789	+	0.259449i
$299$	90.9118	−	835.920i	0.0175838	−	0.161681i
$300$	1603.34	−	1196.01i	0.308564	−	0.230173i
$301$	844.941	−	336.655i	0.161799	−	0.0644667i
$302$	5375.30	−	3644.55i	1.02422	−	0.694437i
$303$	4957.04	+	4781.71i	0.939849	+	0.906607i
$304$	2912.43	−	3428.78i	0.549471	−	0.646888i
$305$	−918.446	+	2305.13i	−0.172427	+	0.432758i
$306$	−2237.95	+	1458.75i	−0.418089	+	0.272521i
$307$	8395.26	−	2828.69i	1.56072	−	0.525869i	0.599203	−	0.800597i	$-0.295484\pi$
$307$	8395.26	−	2828.69i	1.56072	−	0.525869i	0.961522	+	0.274728i	$0.0885877\pi$
$308$	3570.95	+	4204.05i	0.660629	+	0.777753i
$309$	−8616.09	−	545.667i	−1.58625	−	0.100459i
$310$	3825.31	−	416.028i	0.700849	−	0.0762219i
$311$	−1403.39	+	6375.64i	−0.255880	+	1.16247i	0.656886	+	0.753990i	$0.271873\pi$
$311$	−1403.39	+	6375.64i	−0.255880	+	1.16247i	−0.912765	+	0.408484i	$0.866058\pi$
$312$	−665.806	+	258.300i	−0.120814	+	0.0468698i
$313$	−6415.28	+	6772.53i	−1.15851	+	1.22302i	−0.187944	+	0.982180i	$0.560182\pi$
$313$	−6415.28	+	6772.53i	−1.15851	+	1.22302i	−0.970564	+	0.240843i	$0.922576\pi$
$314$	−3164.70	−	1677.82i	−0.568772	−	0.301544i
$315$	−4954.65	−	358.986i	−0.886232	−	0.0642114i
$316$	−3076.38	−	1851.00i	−0.547658	−	0.329515i
$317$	−9935.50	+	1628.84i	−1.76036	+	0.288596i	−0.953333	−	0.301922i	$-0.902372\pi$
$317$	−9935.50	+	1628.84i	−1.76036	+	0.288596i	−0.807025	+	0.590518i	$0.798924\pi$
$318$	6738.38	−	1041.96i	1.18827	−	0.183742i
$319$	1179.14	−	327.387i	0.206957	−	0.0574614i
$320$	47.9656	−	63.0976i	0.00837924	−	0.0110227i
$321$	−8852.54	+	399.379i	−1.53925	+	0.0694429i
$322$	−2074.35	+	7471.13i	−0.359003	+	1.29301i
$323$	1393.80	−	738.947i	0.240103	−	0.127295i
$324$	−2310.84	−	2353.96i	−0.396235	−	0.403628i
$325$	949.337	−	51.4716i	0.162030	−	0.00878501i
$326$	6515.67	+	12289.9i	1.10696	+	2.08795i
$327$	1690.50	−	1409.70i	0.285886	−	0.238399i
$328$	−2325.26	−	3058.83i	−0.391437	−	0.514926i
$329$	−5930.42	−	4508.18i	−0.993782	−	0.755454i
$330$	1595.05	−	4595.58i	0.266074	−	0.766601i
$331$	2440.08	−	2311.37i	0.405193	−	0.383819i	−0.457783	−	0.889064i	$-0.651356\pi$
$331$	2440.08	−	2311.37i	0.405193	−	0.383819i	0.862976	+	0.505245i	$0.168598\pi$
$332$	151.636	+	924.936i	0.0250665	+	0.152899i
$333$	−3759.91	−	686.748i	−0.618744	−	0.113014i
$334$	1254.62	−	2711.82i	0.205538	−	0.444264i
$335$	925.715	−	1746.08i	0.150977	−	0.284772i
$336$	11803.5	−	2485.99i	1.91647	−	0.403636i
$337$	3926.08	+	2661.95i	0.634621	+	0.430284i	0.835620	−	0.549307i	$-0.185108\pi$
$337$	3926.08	+	2661.95i	0.634621	+	0.430284i	−0.200999	+	0.979591i	$0.564419\pi$
$338$	−7161.88	−	1576.45i	−1.15253	−	0.253691i
$339$	−5279.85	+	9744.00i	−0.845907	+	1.56113i
$340$	684.904	−	412.093i	0.109247	−	0.0657320i
$341$	−5490.42	+	4663.60i	−0.871914	+	0.740610i
$342$	3415.51	+	4172.31i	0.540027	+	0.659686i
$343$	−4603.00	+	1013.20i	−0.724602	+	0.159497i
$344$	356.876	+	142.192i	0.0559344	+	0.0222863i
$345$	2386.25	−	639.257i	0.372381	−	0.0997578i
$346$	300.606	−	1833.62i	0.0467072	−	0.284901i
$347$	−3075.15	−	4535.51i	−0.475743	−	0.701668i	0.511785	−	0.859114i	$-0.328985\pi$
$347$	−3075.15	−	4535.51i	−0.475743	−	0.701668i	−0.987528	+	0.157445i	$0.949674\pi$
$348$	−153.835	+	669.845i	−0.0236966	+	0.103182i
$349$	3139.33	−	9317.20i	0.481503	−	1.42905i	−0.381744	−	0.924268i	$-0.624676\pi$
$349$	3139.33	−	9317.20i	0.481503	−	1.42905i	0.863247	−	0.504782i	$-0.168427\pi$
$350$	−8715.62	−	947.881i	−1.33106	−	0.144761i
$351$	−295.204	−	1539.80i	−0.0448912	−	0.234155i
$352$	−416.496	+	7681.81i	−0.0630662	+	1.16319i
$353$	−4452.86			−0.671393			−0.335697	−	0.941970i	$-0.608972\pi$
$353$	−4452.86			−0.671393			−0.335697	+	0.941970i	$0.608972\pi$
$354$	−8311.53	+	609.927i	−1.24789	+	0.0915741i
$355$	1106.46			0.165422
$356$	113.275	−	2089.24i	0.0168640	−	0.311038i
$357$	4167.82	+	722.206i	0.617884	+	0.107068i
$358$	−15598.8	−	1696.47i	−2.30285	−	0.250450i
$359$	59.9581	−	177.949i	0.00881467	−	0.0261610i	−0.943156	−	0.332352i	$-0.892158\pi$
$359$	59.9581	−	177.949i	0.00881467	−	0.0261610i	0.951970	+	0.306191i	$0.0990545\pi$
$360$	−1415.01	−	1549.22i	−0.207160	−	0.226808i
$361$	2062.25	+	3041.59i	0.300663	+	0.443445i
$362$	587.989	−	3586.58i	0.0853702	−	0.520735i
$363$	566.951	+	2116.35i	0.0819758	+	0.306004i
$364$	−1367.84	−	544.995i	−0.196962	−	0.0784767i
$365$	5415.10	−	1191.95i	0.776546	−	0.170931i
$366$	6940.58	+	1995.11i	0.991230	+	0.284934i
$367$	−6816.32	+	5789.83i	−0.969506	+	0.823506i	−0.984321	−	0.176384i	$-0.943560\pi$
$367$	−6816.32	+	5789.83i	−0.969506	+	0.823506i	0.0148151	+	0.999890i	$0.495284\pi$
$368$	−5139.98	+	3092.63i	−0.728098	+	0.438082i
$369$	7523.24	−	3815.17i	1.06137	−	0.538238i
$370$	3091.55	+	680.501i	0.434383	+	0.0956150i
$371$	−8936.10	−	6058.83i	−1.25051	−	0.847867i
$372$	−833.804	−	3958.92i	−0.116212	−	0.551775i
$373$	2663.53	−	5023.94i	0.369738	−	0.697399i	−0.626921	−	0.779083i	$-0.715685\pi$
$373$	2663.53	−	5023.94i	0.369738	−	0.697399i	0.996658	+	0.0816840i	$0.0260298\pi$
$374$	−1739.23	+	3759.29i	−0.240464	+	0.519755i
$375$	2839.13	+	6285.86i	0.390966	+	0.865601i
$376$	−509.029	−	3104.94i	−0.0698169	−	0.425864i
$377$	−237.156	+	224.646i	−0.0323983	+	0.0306893i
$378$	389.172	+	14452.4i	0.0529546	+	1.96653i
$379$	−9628.43	−	7319.34i	−1.30496	−	0.992003i	−0.999204	−	0.0398925i	$-0.987298\pi$
$379$	−9628.43	−	7319.34i	−1.30496	−	0.992003i	−0.305754	−	0.952111i	$-0.598908\pi$
$380$	−976.367	−	1284.39i	−0.131807	−	0.173389i
$381$	8403.73	+	10077.7i	1.13002	+	1.35511i
$382$	1214.30	+	2290.41i	0.162641	+	0.306773i
$383$	7197.43	−	390.233i	0.960238	−	0.0520626i	0.432649	−	0.901562i	$-0.357579\pi$
$383$	7197.43	−	390.233i	0.960238	−	0.0520626i	0.527589	+	0.849500i	$0.323096\pi$
$384$	6312.76	+	3876.77i	0.838923	+	0.515197i
$385$	−6805.29	+	3607.94i	−0.900856	+	0.477604i
$386$	−1328.48	+	4784.77i	−0.175176	+	0.630928i
$387$	−447.859	+	714.638i	−0.0588268	+	0.0938684i
$388$	3888.31	−	5114.98i	0.508760	−	0.669262i
$389$	1944.95	−	540.012i	0.253503	−	0.0703848i	−0.138452	−	0.990369i	$-0.544213\pi$
$389$	1944.95	−	540.012i	0.253503	−	0.0703848i	0.391955	+	0.919984i	$0.371799\pi$
$390$	198.432	+	1283.27i	0.0257640	+	0.166617i
$391$	−2075.83	+	340.315i	−0.268489	+	0.0440165i
$392$	−5320.31	−	3201.13i	−0.685501	−	0.412452i
$393$	−5209.33	+	3070.27i	−0.668642	+	0.394083i
$394$	2058.22	+	1091.20i	0.263177	+	0.139527i
$395$	3447.81	−	3639.81i	0.439186	−	0.463643i
$396$	−4974.34	−	1190.05i	−0.631237	−	0.151016i
$397$	474.240	−	2154.50i	0.0599533	−	0.272370i	−0.937102	−	0.349055i	$-0.886503\pi$
$397$	474.240	−	2154.50i	0.0599533	−	0.272370i	0.997055	+	0.0766849i	$0.0244336\pi$
$398$	12578.9	−	1368.04i	1.58423	−	0.172296i
$399$	539.627	−	8520.72i	0.0677071	−	1.06910i
$400$	−4390.93	−	5169.40i	−0.548866	−	0.646175i
$401$	−2574.72	+	867.525i	−0.320637	+	0.108035i	−0.475018	−	0.879976i	$-0.657558\pi$
$401$	−2574.72	+	867.525i	−0.320637	+	0.108035i	0.154381	+	0.988011i	$0.450662\pi$
$402$	−5323.67	−	2177.37i	−0.660499	−	0.270143i
$403$	711.755	−	1786.37i	0.0879777	−	0.220807i
$404$	−3882.84	+	4571.23i	−0.478164	+	0.562939i
$405$	3903.93	−	2444.82i	0.478983	−	0.299960i
$406$	2493.23	−	1690.45i	0.304770	−	0.206639i
$407$	−5505.44	+	2193.57i	−0.670503	+	0.267153i
$408$	1068.24	+	1432.05i	0.129622	+	0.173767i
$409$	1463.32	−	13455.0i	0.176910	−	1.62666i	−0.483210	−	0.875505i	$-0.660529\pi$
$409$	1463.32	−	13455.0i	0.176910	−	1.62666i	0.660120	−	0.751160i	$-0.270505\pi$
$410$	−6340.61	+	2933.48i	−0.763757	+	0.353352i
$411$	7153.05	−	9234.39i	0.858477	−	1.10827i
$412$		−	7518.08i		−	0.899003i
$413$	10294.1	+	8256.24i	1.22649	+	0.983688i
$414$	−2539.45	−	6726.32i	−0.301467	−	0.798504i
$415$	−1306.91	−	70.8588i	−0.154588	−	0.00838150i
$416$	−862.271	−	1863.77i	−0.101626	−	0.219661i
$417$	6016.43	−	6954.10i	0.706537	−	0.816651i
$418$	7922.91	+	2669.54i	0.927087	+	0.312372i
$419$	−1666.57	−	4182.77i	−0.194313	−	0.487690i	0.799246	−	0.601004i	$-0.205233\pi$
$419$	−1666.57	−	4182.77i	−0.194313	−	0.487690i	−0.993559	+	0.113315i	$0.963853\pi$
$420$	39.2845	−	4325.73i	0.00456402	−	0.502557i
$421$	−7458.54	−	1222.77i	−0.863437	−	0.141553i	−0.286240	−	0.958158i	$-0.592405\pi$
$421$	−7458.54	−	1222.77i	−0.863437	−	0.141553i	−0.577197	+	0.816605i	$0.695854\pi$
$422$	−5703.66	−	4844.73i	−0.657937	−	0.558857i
$423$	6906.38	+	125.452i	0.793852	+	0.0144201i
$424$	−980.280	−	4453.46i	−0.112280	−	0.510092i
$425$	−759.436	−	2253.92i	−0.0866777	−	0.257250i
$426$	−319.078	−	3204.35i	−0.0362897	−	0.364440i
$427$	−5895.28	−	9798.03i	−0.668132	−	1.11044i
$428$	−834.332	−	7671.56i	−0.0942265	−	0.866399i
$429$	−1655.71	−	1780.01i	−0.186336	−	0.200326i
$430$	391.991	−	578.143i	0.0439616	−	0.0648385i
$431$	9799.08	+	9282.19i	1.09514	+	1.03737i	0.999118	+	0.0419924i	$0.0133705\pi$
$431$	9799.08	+	9282.19i	1.09514	+	1.03737i	0.0960219	+	0.995379i	$0.469388\pi$
$432$	−7470.57	+	8324.39i	−0.832009	+	0.927101i
$433$	−6807.90	−	3149.67i	−0.755581	−	0.349569i	0.00399116	−	0.999992i	$-0.498730\pi$
$433$	−6807.90	−	3149.67i	−0.755581	−	0.349569i	−0.759572	+	0.650423i	$0.774592\pi$
$434$	−9141.86	+	15193.9i	−1.01111	+	1.68048i
$435$	−867.332	−	410.874i	−0.0955986	−	0.0452871i
$436$	1318.18	+	1391.58i	0.144792	+	0.152855i
$437$	1135.88	+	4091.06i	0.124340	+	0.447831i
$438$	−5013.53	−	15338.6i	−0.546931	−	1.67330i
$439$	4394.51	−	3340.62i	0.477764	−	0.363187i	−0.338404	−	0.941001i	$-0.609887\pi$
$439$	4394.51	−	3340.62i	0.477764	−	0.363187i	0.816169	+	0.577814i	$0.196094\pi$
$440$	−3134.72	−	870.351i	−0.339641	−	0.0943009i
$441$	9011.97	−	10227.3i	0.973110	−	1.10434i
$442$	−59.8607	−	1104.07i	−0.00644181	−	0.118812i
$443$	487.415	+	8989.83i	0.0522749	+	0.964153i	0.900592	+	0.434665i	$0.143133\pi$
$443$	487.415	+	8989.83i	0.0522749	+	0.964153i	−0.848317	+	0.529488i	$0.822384\pi$
$444$	389.893	−	3305.45i	0.0416746	−	0.353310i
$445$	2815.23	+	781.644i	0.299898	+	0.0832663i
$446$	18243.2	−	13868.1i	1.93686	−	1.47236i
$447$	−4436.03	+	1449.95i	−0.469389	+	0.153423i
$448$	97.7146	+	351.936i	0.0103049	+	0.0371148i
$449$	4904.03	+	5177.12i	0.515446	+	0.544150i	0.930809	−	0.365506i	$-0.119104\pi$
$449$	4904.03	+	5177.12i	0.515446	+	0.544150i	−0.415363	+	0.909656i	$0.636345\pi$
$450$	7040.61	−	4063.89i	0.737550	−	0.425719i
$451$	6743.11	−	11207.1i	0.704036	−	1.17012i
$452$	−8758.89	−	4052.29i	−0.911468	−	0.421690i
$453$	8464.69	−	4389.69i	0.877938	−	0.455288i
$454$	12732.7	+	12061.1i	1.31625	+	1.24681i
$455$	1153.85	−	1701.80i	0.118887	−	0.175345i
$456$	2640.42	−	2456.03i	0.271160	−	0.252224i
$457$	868.718	+	7987.73i	0.0889211	+	0.817616i	0.950654	+	0.310253i	$0.100414\pi$
$457$	868.718	+	7987.73i	0.0889211	+	0.817616i	−0.861733	+	0.507362i	$0.830621\pi$
$458$	4080.69	+	6782.16i	0.416328	+	0.691942i
$459$	−3514.11	+	1742.13i	−0.357352	+	0.177158i
$460$	686.903	+	2038.65i	0.0696239	+	0.206636i
$461$	1816.78	+	8253.73i	0.183549	+	0.833871i	0.974924	+	0.222540i	$0.0714347\pi$
$461$	1816.78	+	8253.73i	0.183549	+	0.833871i	−0.791375	+	0.611331i	$0.790634\pi$
$462$	12411.2	+	18667.9i	1.24983	+	1.87989i
$463$	−4945.01	−	4200.33i	−0.496359	−	0.421611i	0.363923	−	0.931429i	$-0.381437\pi$
$463$	−4945.01	−	4200.33i	−0.496359	−	0.421611i	−0.860283	+	0.509818i	$0.829713\pi$
$464$	2299.73	+	377.022i	0.230091	+	0.0377215i
$465$	5649.33	+	51.3049i	0.563401	+	0.00511657i
$466$	4695.03	+	11783.6i	0.466724	+	1.17139i
$467$	−1325.79	−	446.709i	−0.131371	−	0.0442639i	0.252848	−	0.967506i	$-0.418633\pi$
$467$	−1325.79	−	446.709i	−0.131371	−	0.0442639i	−0.384219	+	0.923242i	$0.625529\pi$
$468$	1321.96	−	341.305i	0.130571	−	0.0337112i
$469$	3824.09	+	8265.63i	0.376503	+	0.813798i
$470$	−5712.56	−	309.726i	−0.560640	−	0.0303970i
$471$	−4325.95	−	2990.77i	−0.423205	−	0.292585i
$472$	758.422	+	5521.71i	0.0739602	+	0.538469i
$473$			1307.69i			0.127120i
$474$	−11535.3	−	8935.34i	−1.11779	−	0.865852i
$475$	−4356.97	+	2015.75i	−0.420866	+	0.194713i
$476$	−398.257	+	3661.91i	−0.0383489	+	0.352612i
$477$	10004.6	−	360.349i	0.960334	−	0.0345896i
$478$	14249.2	−	5677.39i	1.36348	−	0.543259i
$479$	8248.16	−	5592.39i	0.786781	−	0.533451i	−0.100359	−	0.994951i	$-0.531999\pi$
$479$	8248.16	−	5592.39i	0.786781	−	0.533451i	0.887140	+	0.461500i	$0.152689\pi$
$480$	4188.73	−	4342.32i	0.398309	−	0.412914i
$481$	1024.14	−	1205.71i	0.0970827	−	0.114295i
$482$	−3371.53	+	8461.89i	−0.318607	+	0.799644i
$483$	−4309.64	+	10537.1i	−0.405994	+	0.992656i
$484$	−1808.06	+	609.207i	−0.169803	+	0.0572133i
$485$	5808.41	+	6838.19i	0.543807	+	0.640219i
$486$	−8206.08	−	10600.9i	−0.765916	−	0.989437i
$487$	−1428.86	+	155.398i	−0.132953	+	0.0144595i	−0.174353	−	0.984683i	$-0.555784\pi$
$487$	−1428.86	+	155.398i	−0.132953	+	0.0144595i	0.0414006	+	0.999143i	$0.486818\pi$
$488$	1038.24	−	4716.79i	0.0963097	−	0.437539i
$489$	7386.89	+	19040.8i	0.683122	+	1.76085i
$490$	−7763.97	+	8196.32i	−0.715796	+	0.755657i
$491$	−12053.1	−	6390.14i	−1.10784	−	0.587338i	−0.189001	−	0.981977i	$-0.560525\pi$
$491$	−12053.1	−	6390.14i	−1.10784	−	0.587338i	−0.918837	+	0.394638i	$0.870870\pi$
$492$	3729.76	+	6328.29i	0.341769	+	0.579881i
$493$	700.231	+	421.315i	0.0639692	+	0.0384890i
$494$	−2202.34	+	361.056i	−0.200583	+	0.0328839i
$495$	3116.18	−	6426.59i	0.282953	−	0.583543i
$496$	−13218.3	+	3670.05i	−1.19661	+	0.332238i
$497$	−3085.72	+	4059.20i	−0.278498	+	0.366358i
$498$	171.675	+	3805.30i	0.0154476	+	0.342409i
$499$	2170.49	−	7817.39i	0.194718	−	0.701312i	−0.800120	−	0.599840i	$-0.795231\pi$
$499$	2170.49	−	7817.39i	0.194718	−	0.701312i	0.994838	−	0.101472i	$-0.0323552\pi$
$500$	−5306.63	+	2813.40i	−0.474640	+	0.251638i
$501$	2295.80	−	3738.38i	0.204728	−	0.333370i
$502$	−13880.5	+	752.577i	−1.23410	+	0.0669107i
$503$	−1484.75	−	2800.54i	−0.131614	−	0.248250i	0.808942	−	0.587888i	$-0.200040\pi$
$503$	−1484.75	−	2800.54i	−0.131614	−	0.248250i	−0.940556	+	0.339638i	$0.889696\pi$
$504$	9629.71	−	870.653i	0.851074	−	0.0769484i
$505$	−5068.50	−	6667.50i	−0.446625	−	0.587525i
$506$	−8874.84	−	6746.48i	−0.779713	−	0.592723i
$507$	−10171.8	−	3530.44i	−0.891013	−	0.309255i
$508$	−8295.76	+	7858.16i	−0.724537	+	0.686318i
$509$	−1852.47	−	11299.6i	−0.161315	−	0.983977i	−0.936095	−	0.351746i	$-0.885588\pi$
$509$	−1852.47	−	11299.6i	−0.161315	−	0.983977i	0.774781	−	0.632230i	$-0.217860\pi$
$510$	2960.51	−	1337.17i	0.257046	−	0.116100i
$511$	−10728.9	+	23190.2i	−0.928804	+	2.00758i
$512$	−3188.11	+	6013.42i	−0.275188	+	0.519059i
$513$	4262.62	+	6671.18i	0.366860	+	0.574152i
$514$	20993.3	+	14233.8i	1.80151	+	1.22145i
$515$	10252.9	+	2256.83i	0.877274	+	0.193103i
$516$	−645.726	−	349.891i	−0.0550901	−	0.0298509i
$517$	9177.29	−	5521.79i	0.780690	−	0.469726i
$518$	−11118.3	+	9443.94i	−0.943067	+	0.801048i
$519$	753.689	−	2621.94i	0.0637443	−	0.221754i
$520$	848.124	−	186.686i	0.0715244	−	0.0157437i
$521$	8909.54	+	3549.88i	0.749201	+	0.298509i	0.713312	−	0.700847i	$-0.247194\pi$
$521$	8909.54	+	3549.88i	0.749201	+	0.298509i	0.0358893	+	0.999356i	$0.488574\pi$
$522$	−939.785	+	2630.31i	−0.0787994	+	0.220547i
$523$	−1570.45	+	9579.30i	−0.131302	+	0.800906i	0.836272	+	0.548316i	$0.184731\pi$
$523$	−1570.45	+	9579.30i	−0.131302	+	0.800906i	−0.967573	+	0.252590i	$0.918718\pi$
$524$	−2955.02	−	4358.33i	−0.246356	−	0.363348i
$525$	−12545.4	−	2881.15i	−1.04291	−	0.239512i
$526$	−6945.03	+	20612.1i	−0.575699	+	1.70861i
$527$	−4782.39	−	520.117i	−0.395302	−	0.0429917i
$528$	−2961.07	+	17088.2i	−0.244061	+	1.40847i
$529$	−352.206	+	6496.06i	−0.0289477	+	0.533908i
$530$	−8291.40			−0.679538
$531$	−12224.1	−	540.171i	−0.999025	−	0.0441458i
$532$	7434.86			0.605906
$533$	−189.018	+	3486.24i	−0.0153608	+	0.283313i
$534$	1451.82	−	8378.40i	0.117652	−	0.678968i
$535$	10712.7	+	1165.07i	0.865698	+	0.0941503i
$536$	−1228.24	+	3645.30i	−0.0989777	+	0.293755i
$537$	−22453.2	−	5156.54i	−1.80433	−	0.414378i
$538$	11556.4	+	17044.4i	0.926079	+	1.36586i
$539$	3419.42	−	20857.6i	0.273256	−	1.66679i
$540$	2339.61	+	3258.26i	0.186446	+	0.259654i
$541$	14903.6	+	5938.12i	1.18439	+	0.471904i	0.877377	−	0.479802i	$-0.159292\pi$
$541$	14903.6	+	5938.12i	1.18439	+	0.471904i	0.307012	+	0.951706i	$0.400671\pi$
$542$	−2278.68	+	501.575i	−0.180586	+	0.0397500i
$543$	1474.22	−	5128.54i	0.116510	−	0.405316i
$544$	−3915.51	+	3325.87i	−0.308596	+	0.262124i
$545$	−2293.49	+	1379.95i	−0.180261	+	0.108460i
$546$	−5261.23	−	2850.83i	−0.412381	−	0.223451i
$547$	−14726.2	−	3241.49i	−1.15109	−	0.253375i	−0.401872	−	0.915696i	$-0.631640\pi$
$547$	−14726.2	−	3241.49i	−1.15109	−	0.253375i	−0.749220	+	0.662321i	$0.769571\pi$
$548$	8419.10	+	5708.29i	0.656289	+	0.444975i
$549$	9777.08	+	4102.84i	0.760065	+	0.318952i
$550$	5904.20	−	11136.5i	0.457738	−	0.863386i
$551$	692.595	−	1497.02i	0.0535491	−	0.115744i
$552$	−4382.11	+	1979.27i	−0.337889	+	0.152615i
$553$	3737.80	+	22799.5i	0.287427	+	1.75323i
$554$	21599.6	−	20460.2i	1.65646	−	1.56908i
$555$	4390.81	+	1523.98i	0.335819	+	0.116557i
$556$	6374.79	+	4845.99i	0.486243	+	0.369633i
$557$	−1426.09	−	1875.99i	−0.108484	−	0.142708i	0.738647	−	0.674092i	$-0.235465\pi$
$557$	−1426.09	−	1875.99i	−0.108484	−	0.142708i	−0.847131	+	0.531385i	$0.821672\pi$
$558$	−1480.56	−	16375.4i	−0.112324	−	1.24234i
$559$	−163.508	−	308.409i	−0.0123715	−	0.0233351i
$560$	−14646.7	+	794.122i	−1.10524	+	0.0599246i
$561$	−3182.59	+	5182.38i	−0.239517	+	0.390018i
$562$	−8782.85	+	4656.37i	−0.659221	+	0.349497i
$563$	3695.42	−	13309.7i	0.276631	−	0.996336i	−0.686462	−	0.727166i	$-0.740837\pi$
$563$	3695.42	−	13309.7i	0.276631	−	0.996336i	0.963093	−	0.269170i	$-0.0867492\pi$
$564$	271.097	+	6009.08i	0.0202398	+	0.448631i
$565$	8155.68	−	10728.6i	0.607278	−	0.798861i
$566$	−13495.8	+	3747.10i	−1.00225	+	0.278273i
$567$	−1918.24	+	21140.3i	−0.142078	+	1.56580i
$568$	−2125.24	+	348.416i	−0.156995	+	0.0257380i
$569$	6153.69	+	3702.55i	0.453385	+	0.272793i	0.723876	−	0.689930i	$-0.242359\pi$
$569$	6153.69	+	3702.55i	0.453385	+	0.272793i	−0.270491	+	0.962722i	$0.587186\pi$
$570$	−3329.23	−	5648.71i	−0.244642	−	0.415085i
$571$	14983.0	+	7943.46i	1.09810	+	0.582178i	0.916031	−	0.401107i	$-0.131375\pi$
$571$	14983.0	+	7943.46i	1.09810	+	0.582178i	0.182073	+	0.983285i	$0.441719\pi$
$572$	1455.84	−	1536.91i	0.106419	−	0.112345i
$573$	1376.66	+	3548.55i	0.100368	+	0.258713i
$574$	6920.97	−	31442.3i	0.503268	−	2.28637i
$575$	6363.70	−	692.094i	0.461539	−	0.0501954i
$576$	−265.854	−	209.824i	−0.0192314	−	0.0151782i
$577$	875.635	+	1030.88i	0.0631770	+	0.0743777i	0.792843	−	0.609426i	$-0.208600\pi$
$577$	875.635	+	1030.88i	0.0631770	+	0.0743777i	−0.729666	+	0.683804i	$0.760324\pi$
$578$	13855.9	−	4668.60i	0.997111	−	0.335966i
$579$	−2760.04	+	6748.29i	−0.198106	+	0.484369i
$580$	309.343	−	776.393i	0.0221462	−	0.0555827i
$581$	3904.70	−	4596.97i	0.278820	−	0.328252i
$582$	18128.6	−	18793.3i	1.29116	−	1.33850i
$583$	12847.9	−	8711.10i	0.912704	−	0.618829i
$584$	−10025.7	+	3994.62i	−0.710391	+	0.283046i
$585$	68.6254	+	1905.29i	0.00485010	+	0.134657i
$586$	−1093.68	+	10056.2i	−0.0770978	+	0.708903i
$587$	−13247.4	+	6128.90i	−0.931480	+	0.430949i	−0.826126	−	0.563486i	$-0.809460\pi$
$587$	−13247.4	+	6128.90i	−0.931480	+	0.430949i	−0.105355	+	0.994435i	$0.533598\pi$
$588$	9384.33	+	7269.19i	0.658169	+	0.509824i
$589$			9709.80i			0.679262i
$590$	10101.6	+	811.515i	0.704877	+	0.0566263i
$591$	2813.46	+	1945.10i	0.195821	+	0.135382i
$592$	−11269.2	−	610.999i	−0.782368	−	0.0424188i
$593$	−3170.20	−	6852.29i	−0.219536	−	0.474519i	0.766246	−	0.642547i	$-0.222122\pi$
$593$	−3170.20	−	6852.29i	−0.219536	−	0.474519i	−0.985782	+	0.168028i	$0.946260\pi$
$594$	−19510.3	−	7171.28i	−1.34767	−	0.495356i
$595$	−4874.43	−	1642.39i	−0.335853	−	0.113162i
$596$	−1504.27	−	3775.45i	−0.103385	−	0.259477i
$597$	18576.9	+	168.708i	1.27354	+	0.0115657i
$598$	2936.61	+	481.433i	0.200814	+	0.0329218i
$599$	17359.9	+	14745.6i	1.18415	+	1.00583i	0.999736	+	0.0229764i	$0.00731426\pi$
$599$	17359.9	+	14745.6i	1.18415	+	1.00583i	0.184413	+	0.982849i	$0.440962\pi$
$600$	−3010.03	−	4527.44i	−0.204807	−	0.308053i
$601$	−541.277	−	2459.04i	−0.0367373	−	0.166899i	0.954680	−	0.297634i	$-0.0961975\pi$
$601$	−541.277	−	2459.04i	−0.0367373	−	0.166899i	−0.991417	+	0.130735i	$0.958266\pi$
$602$	1027.80	+	3050.41i	0.0695849	+	0.206521i
$603$	−7388.08	−	4090.51i	−0.498949	−	0.276249i
$604$	4280.87	+	7114.86i	0.288388	+	0.479304i
$605$	−288.058	−	2648.65i	−0.0193574	−	0.177988i
$606$	−17847.7	+	16601.3i	−1.19639	+	1.11284i
$607$	12478.5	−	18404.4i	0.834407	−	1.23066i	−0.136366	−	0.990659i	$-0.543542\pi$
$607$	12478.5	−	18404.4i	0.834407	−	1.23066i	0.970773	−	0.240000i	$-0.0771475\pi$
$608$	7528.13	+	7131.02i	0.502148	+	0.475660i
$609$	3926.18	−	2036.07i	0.261243	−	0.135477i
$610$	−7970.03	−	3687.33i	−0.529012	−	0.244747i
$611$	−1473.97	+	2449.76i	−0.0975948	+	0.162204i
$612$	−1707.46	−	2958.14i	−0.112778	−	0.195385i
$613$	10947.9	+	11557.5i	0.721338	+	0.761507i	0.978808	−	0.204779i	$-0.0656476\pi$
$613$	10947.9	+	11557.5i	0.721338	+	0.761507i	−0.257470	+	0.966286i	$0.582889\pi$
$614$	8387.67	+	30209.7i	0.551301	+	1.98561i
$615$	−9749.93	+	3186.84i	−0.639276	+	0.208952i
$616$	11935.2	−	9072.89i	0.780653	−	0.593437i
$617$	4268.12	+	1185.04i	0.278490	+	0.0773222i	0.403965	−	0.914774i	$-0.367632\pi$
$617$	4268.12	+	1185.04i	0.278490	+	0.0773222i	−0.125475	+	0.992097i	$0.540046\pi$
$618$	3579.16	−	30343.5i	0.232969	−	1.97507i
$619$	−1277.27	−	23557.8i	−0.0829365	−	1.52967i	−0.683414	−	0.730031i	$-0.739505\pi$
$619$	−1277.27	−	23557.8i	−0.0829365	−	1.52967i	0.600477	−	0.799642i	$-0.294977\pi$
$620$	266.350	+	4912.53i	0.0172530	+	0.318213i
$621$	−2545.96	−	10244.6i	−0.164518	−	0.661998i
$622$	−22261.8	−	6180.95i	−1.43507	−	0.398446i
$623$	−10718.7	+	8148.17i	−0.689305	+	0.523996i
$624$	−1438.29	−	4400.36i	−0.0922720	−	0.282300i
$625$	601.163	+	2165.19i	0.0384745	+	0.138572i
$626$	−22704.0	−	23968.4i	−1.44958	−	1.53030i
$627$	11093.4	+	5255.20i	0.706586	+	0.334725i
$628$	2361.11	−	3924.20i	0.150030	−	0.249351i
$629$	−3591.79	−	1661.74i	−0.227685	−	0.105338i
$630$	2217.92	−	17440.3i	0.140261	−	1.10292i
$631$	−12919.5	−	12238.0i	−0.815080	−	0.772085i	0.161584	−	0.986859i	$-0.448340\pi$
$631$	−12919.5	−	12238.0i	−0.815080	−	0.772085i	−0.976664	+	0.214774i	$0.931098\pi$
$632$	−5476.26	+	8076.87i	−0.344674	+	0.508356i
$633$	−7483.38	−	8045.20i	−0.469885	−	0.505163i
$634$	−3852.46	−	35422.8i	−0.241326	−	2.21896i
$635$	−8226.40	−	13672.4i	−0.514102	−	0.854444i
$636$	863.821	+	8674.94i	0.0538565	+	0.540855i
$637$	1801.49	+	5346.64i	0.112053	+	0.332561i
$638$	931.018	+	4229.66i	0.0577733	+	0.262467i
$639$	85.8683	−	4727.22i	0.00531596	−	0.292654i
$640$	−6865.89	−	5831.94i	−0.424059	−	0.360199i
$641$	−8259.17	−	1354.02i	−0.508920	−	0.0834332i	−0.0981488	−	0.995172i	$-0.531292\pi$
$641$	−8259.17	−	1354.02i	−0.508920	−	0.0834332i	−0.410771	+	0.911739i	$0.634740\pi$
$642$	284.800	−	31360.2i	0.0175080	−	1.92786i
$643$	−1485.95	−	3729.45i	−0.0911354	−	0.228733i	0.876342	−	0.481689i	$-0.159976\pi$
$643$	−1485.95	−	3729.45i	−0.0911354	−	0.228733i	−0.967478	+	0.252956i	$0.918597\pi$
$644$	−9394.72	−	3165.45i	−0.574851	−	0.193690i
$645$	671.007	−	775.585i	0.0409626	−	0.0473467i
$646$	2344.29	+	5067.09i	0.142778	+	0.308610i
$647$	−4395.66	−	238.326i	−0.267096	−	0.0144815i	−0.0798956	−	0.996803i	$-0.525459\pi$
$647$	−4395.66	−	238.326i	−0.267096	−	0.0144815i	−0.187201	+	0.982322i	$0.559941\pi$
$648$	−6728.64	+	5925.21i	−0.407911	+	0.359204i
$649$	−16505.5	+	9355.48i	−0.998304	+	0.565847i
$650$			3364.69i			0.203037i
$651$	−15943.2	+	20582.2i	−0.959851	+	1.23914i
$652$	−16141.3	+	7467.77i	−0.969545	+	0.448559i
$653$	−1245.69	+	11453.9i	−0.0746515	+	0.686409i	0.895691	+	0.444676i	$0.146681\pi$
$653$	−1245.69	+	11453.9i	−0.0746515	+	0.686409i	−0.970343	+	0.241733i	$0.922284\pi$
$654$	4657.77	+	6244.09i	0.278491	+	0.373338i
$655$	6830.79	−	2721.64i	0.407483	−	0.162356i
$656$	20615.6	−	13977.8i	1.22699	−	0.831920i
$657$	−4672.23	−	23227.8i	−0.277444	−	1.37931i
$658$	17067.6	−	20093.5i	1.01119	−	1.19047i
$659$	3265.55	−	8195.91i	0.193031	−	0.484472i	−0.800323	−	0.599569i	$-0.795339\pi$
$659$	3265.55	−	8195.91i	0.193031	−	0.484472i	0.993354	+	0.115097i	$0.0367179\pi$
$660$	5756.72	+	2354.48i	0.339515	+	0.138861i
$661$	−14034.4	+	4728.75i	−0.825834	+	0.278256i	−0.700314	−	0.713835i	$-0.746956\pi$
$661$	−14034.4	+	4728.75i	−0.825834	+	0.278256i	−0.125520	+	0.992091i	$0.540060\pi$
$662$	7700.53	+	9065.77i	0.452099	+	0.532252i
$663$	102.607	−	1620.16i	0.00601042	−	0.0949046i
$664$	2532.57	−	275.434i	0.148016	−	0.0160978i
$665$	−2231.85	+	10139.4i	−0.130147	+	0.591262i
$666$	3147.28	−	13155.4i	0.183115	−	0.765409i
$667$	−1512.53	+	1596.76i	−0.0878043	+	0.0926939i
$668$	3375.30	+	1789.47i	0.195500	+	0.103648i
$669$	28986.0	−	17083.7i	1.67513	−	0.987285i
$670$	5993.06	+	3605.90i	0.345570	+	0.207923i
$671$	16223.9	−	2659.78i	0.933409	−	0.153025i
$672$	4248.74	+	27476.9i	0.243897	+	1.57730i
$673$	−11798.9	+	3275.94i	−0.675799	+	0.187635i	−0.588438	−	0.808542i	$-0.700257\pi$
$673$	−11798.9	+	3275.94i	−0.675799	+	0.187635i	−0.0873608	+	0.996177i	$0.527843\pi$
$674$	−10159.2	+	13364.2i	−0.580591	+	0.763754i
$675$	10965.0	−	4714.72i	0.625251	−	0.268844i
$676$	2508.38	−	9034.36i	0.142716	−	0.514017i
$677$	14605.5	−	7743.37i	0.829153	−	0.439589i	0.000938053	−	1.00000i	$-0.499701\pi$
$677$	14605.5	−	7743.37i	0.829153	−	0.439589i	0.828215	+	0.560410i	$0.189357\pi$
$678$	−33422.4	−	20525.2i	−1.89318	−	1.16264i
$679$	−41285.4	+	2238.43i	−2.33341	+	0.126514i
$680$	−1017.63	−	1919.46i	−0.0573888	−	0.108247i
$681$	16491.4	+	19776.4i	0.927978	+	1.11283i
$682$	−15428.6	−	20295.9i	−0.866261	−	1.13955i
$683$	−4287.09	−	3258.96i	−0.240177	−	0.182578i	0.478161	−	0.878272i	$-0.341304\pi$
$683$	−4287.09	−	3258.96i	−0.240177	−	0.182578i	−0.718338	+	0.695694i	$0.755097\pi$
$684$	−5563.16	+	4071.73i	−0.310984	+	0.227612i
$685$	−10312.1	+	9768.12i	−0.575189	+	0.544848i
$686$	−2698.56	−	16460.5i	−0.150192	−	0.916129i
$687$	4783.67	+	10591.1i	0.265660	+	0.588173i
$688$	−1045.65	+	2260.13i	−0.0579431	+	0.125242i
$689$	−1940.88	+	3660.89i	−0.107317	+	0.202422i
$690$	1801.84	+	8555.18i	0.0994129	+	0.472015i
$691$	26772.4	+	18152.1i	1.47391	+	0.999335i	0.992421	+	0.122881i	$0.0392134\pi$
$691$	26772.4	+	18152.1i	1.47391	+	0.999335i	0.481487	+	0.876453i	$0.340097\pi$
$692$	2320.15	+	510.703i	0.127455	+	0.0280550i
$693$	14886.3	+	29354.7i	0.815995	+	1.60908i
$694$	16617.1	−	9998.16i	0.908898	−	0.546866i
$695$	−8522.42	+	7239.01i	−0.465142	+	0.395095i
$696$	1795.31	+	516.072i	0.0977746	+	0.0281058i
$697$	8530.07	−	1877.61i	0.463557	−	0.102037i
$698$	32324.2	+	12879.1i	1.75285	+	0.698400i
$699$	4819.24	+	17989.5i	0.260773	+	0.973428i
$700$	1813.44	−	11061.5i	0.0979168	−	0.597266i
$701$	−14503.1	−	21390.5i	−0.781420	−	1.15251i	−0.984848	−	0.173419i	$-0.944519\pi$
$701$	−14503.1	−	21390.5i	−0.781420	−	1.15251i	0.203428	−	0.979090i	$-0.434792\pi$
$702$	5498.00	−	748.184i	0.295596	−	0.0402256i
$703$	−2550.59	+	7569.88i	−0.136838	+	0.406122i
$704$	−522.061	−	56.7775i	−0.0279487	−	0.00303961i
$705$	−8276.35	−	1434.14i	−0.442135	−	0.0766137i
$706$	853.170	−	15735.8i	0.0454809	−	0.838845i
$707$	38595.8			2.05310
$708$	−203.362	−	10653.4i	−0.0107949	−	0.565510i
$709$	16348.6			0.865985			0.432992	−	0.901398i	$-0.357458\pi$
$709$	16348.6			0.865985			0.432992	+	0.901398i	$0.357458\pi$
$710$	−211.999	+	3910.08i	−0.0112059	+	0.206680i
$711$	−15283.1	−	15012.8i	−0.806132	−	0.791877i
$712$	−5653.49	−	614.855i	−0.297575	−	0.0323633i
$713$	4134.02	−	12269.3i	0.217139	−	0.644447i
$714$	−3350.73	+	14590.2i	−0.175628	+	0.764738i
$715$	1658.96	+	2446.78i	0.0867712	+	0.127978i
$716$	3245.61	−	19797.4i	0.169405	−	1.03333i
$717$	21753.5	−	5827.58i	1.13305	−	0.303536i
$718$	617.361	+	245.979i	0.0320887	+	0.0127853i
$719$	12192.4	−	2683.75i	0.632405	−	0.139203i	0.112811	−	0.993616i	$-0.464014\pi$
$719$	12192.4	−	2683.75i	0.632405	−	0.139203i	0.519594	+	0.854414i	$0.326083\pi$
$720$	10524.6	−	8615.53i	0.544760	−	0.445947i
$721$	−36873.0	+	31320.2i	−1.90461	+	1.61779i
$722$	−11143.7	+	6704.94i	−0.574412	+	0.345612i
$723$	−6371.48	+	11758.6i	−0.327743	+	0.604851i
$724$	4538.24	+	998.942i	0.232959	+	0.0512781i
$725$	−2058.32	−	1395.58i	−0.105440	−	0.0714902i
$726$	−7587.50	+	1598.03i	−0.387877	+	0.0816923i
$727$	8883.88	−	16756.8i	0.453211	−	0.854847i	−0.546636	−	0.837370i	$-0.684092\pi$
$727$	8883.88	−	16756.8i	0.453211	−	0.854847i	0.999847	−	0.0174770i	$-0.00556339\pi$
$728$	−1680.38	+	3632.09i	−0.0855482	+	0.184909i
$729$	−10142.2	−	16868.8i	−0.515277	−	0.857023i
$730$	3174.67	+	19364.6i	0.160959	+	0.981803i
$731$	−633.987	+	600.545i	−0.0320778	+	0.0303857i
$732$	−3027.55	+	8722.86i	−0.152871	+	0.440446i
$733$	−22716.2	−	17268.4i	−1.14467	−	0.870153i	−0.151686	−	0.988429i	$-0.548470\pi$
$733$	−22716.2	−	17268.4i	−1.14467	−	0.870153i	−0.992981	+	0.118275i	$0.962263\pi$
$734$	−19154.5	−	25197.3i	−0.963221	−	1.26710i
$735$	−12730.5	+	10615.9i	−0.638874	+	0.532753i
$736$	−6476.49	−	12215.9i	−0.324357	−	0.611801i
$737$	−13075.0	+	708.904i	−0.653490	+	0.0354312i
$738$	12040.8	+	27317.1i	0.600582	+	1.36254i
$739$	−9675.69	+	5129.73i	−0.481632	+	0.255345i	−0.691489	−	0.722387i	$-0.743045\pi$
$739$	−9675.69	+	5129.73i	−0.481632	+	0.255345i	0.209857	+	0.977732i	$0.432700\pi$
$740$	−1082.78	+	3899.83i	−0.0537891	+	0.193731i
$741$	−3273.38	+	147.678i	−0.162282	+	0.00732128i
$742$	23123.2	−	30418.1i	1.14404	−	1.50496i
$743$	−13637.4	+	3786.40i	−0.673361	+	0.186958i	−0.587346	−	0.809336i	$-0.699827\pi$
$743$	−13637.4	+	3786.40i	−0.673361	+	0.186958i	−0.0860151	+	0.996294i	$0.527413\pi$
$744$	−10867.1	+	1680.38i	−0.535495	+	0.0828035i
$745$	5600.38	−	918.136i	0.275412	−	0.0451516i
$746$	17243.6	+	10375.1i	0.846291	+	0.509196i
$747$	−404.160	+	5578.12i	−0.0197958	+	0.273217i
$748$	−4679.06	−	2480.68i	−0.228721	−	0.121260i
$749$	−34149.9	+	36051.6i	−1.66597	+	1.75874i
$750$	−22757.4	+	8828.74i	−1.10797	+	0.429840i
$751$	−6226.00	+	28285.0i	−0.302517	+	1.37435i	0.542701	+	0.839926i	$0.317402\pi$
$751$	−6226.00	+	28285.0i	−0.302517	+	1.37435i	−0.845218	+	0.534422i	$0.820529\pi$
$752$	20276.7	−	2205.22i	0.983263	−	0.106936i
$753$	−20368.9	−	1289.99i	−0.985768	−	0.0624298i
$754$	−748.430	−	881.120i	−0.0361488	−	0.0425577i
$755$	−10988.1	+	3702.31i	−0.529664	+	0.178465i
$756$	−18478.1	−	503.542i	−0.888944	−	0.0242244i
$757$	5436.58	−	13644.8i	0.261025	−	0.655123i	−0.738798	−	0.673926i	$-0.764606\pi$
$757$	5436.58	−	13644.8i	0.261025	−	0.655123i	0.999823	+	0.0188037i	$0.00598577\pi$
$758$	27710.4	−	32623.2i	1.32782	−	1.56323i
$759$	−11780.3	−	11363.6i	−0.563369	−	0.543442i
$760$	−3629.48	+	2460.85i	−0.173230	+	0.117453i
$761$	−9862.61	+	3929.62i	−0.469802	+	0.187186i	−0.593011	−	0.805195i	$-0.702061\pi$
$761$	−9862.61	+	3929.62i	−0.469802	+	0.187186i	0.123209	+	0.992381i	$0.460682\pi$
$762$	−37223.4	+	27766.7i	−1.76963	+	1.32006i
$763$	1333.62	−	12262.4i	0.0632768	−	0.581821i
$764$	−3008.19	+	1391.74i	−0.142451	+	0.0659048i
$765$	4546.77	−	1440.58i	0.214887	−	0.0680839i
$766$			25509.5i			1.20326i
$767$	2722.93	−	4270.19i	0.128187	−	0.201027i
$768$	−15206.0	+	21994.5i	−0.714454	+	1.03341i
$769$	−1997.69	−	108.311i	−0.0936780	−	0.00507907i	0.00724030	−	0.999974i	$-0.497695\pi$
$769$	−1997.69	−	108.311i	−0.0936780	−	0.00507907i	−0.100918	+	0.994895i	$0.532178\pi$
$770$	−11446.1	−	24740.2i	−0.535698	−	1.15789i
$771$	28162.7	+	24365.3i	1.31551	+	1.13813i
$772$	−6016.70	−	2027.26i	−0.280500	−	0.0945113i
$773$	−3209.26	−	8054.63i	−0.149326	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.f (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.191601 + 3.53386i) q^{2} +(-0.887175 + 5.11986i) q^{3} +(-4.49838 - 0.489228i) q^{4} +(2.01755 - 5.98787i) q^{5} +(-17.9229 - 4.11612i) q^{6} +(16.3407 + 24.1007i) q^{7} +(-1.98968 + 12.1365i) q^{8} +(-25.4258 - 9.08442i) q^{9} +O(q^{10})\)	\(q+(-0.191601 + 3.53386i) q^{2} +(-0.887175 + 5.11986i) q^{3} +(-4.49838 - 0.489228i) q^{4} +(2.01755 - 5.98787i) q^{5} +(-17.9229 - 4.11612i) q^{6} +(16.3407 + 24.1007i) q^{7} +(-1.98968 + 12.1365i) q^{8} +(-25.4258 - 9.08442i) q^{9} +(20.7738 + 8.27702i) q^{10} +(-40.8859 + 8.99967i) q^{11} +(6.49563 - 22.5970i) q^{12} +(8.51733 - 7.23469i) q^{13} +(-88.2996 + 53.1281i) q^{14} +(28.8671 + 15.6418i) q^{15} +(-77.8606 - 17.1384i) q^{16} +(-23.1396 - 15.6890i) q^{17} +(36.9747 - 88.1109i) q^{18} +(-26.4317 + 49.8555i) q^{19} +(-12.0051 + 25.9487i) q^{20} +(-137.889 + 62.2805i) q^{21} +(-23.9698 - 146.210i) q^{22} +(54.6255 - 51.7441i) q^{23} +(-60.3721 - 20.9541i) q^{24} +(67.7275 + 51.4851i) q^{25} +(23.9345 + 31.4853i) q^{26} +(69.0681 - 122.117i) q^{27} +(-61.7159 - 116.409i) q^{28} +(-29.1882 + 1.58254i) q^{29} +(-60.8071 + 99.0155i) q^{30} +(152.028 - 80.5999i) q^{31} +(49.1612 - 177.063i) q^{32} +(-9.80405 - 217.314i) q^{33} +(59.8765 - 78.7661i) q^{34} +(177.280 - 49.2216i) q^{35} +(109.931 + 53.3042i) q^{36} +(139.695 - 22.9018i) q^{37} +(-171.118 - 102.958i) q^{38} +(29.4842 + 50.0260i) q^{39} +(68.6577 + 36.4000i) q^{40} +(-214.851 + 226.815i) q^{41} +(-193.671 - 499.215i) q^{42} +(6.71486 - 30.5059i) q^{43} +(188.323 - 20.4814i) q^{44} +(-105.694 + 133.918i) q^{45} +(172.390 + 202.953i) q^{46} +(-242.442 + 81.6882i) q^{47} +(156.822 - 383.430i) q^{48} +(-186.870 + 469.007i) q^{49} +(-194.918 + 229.475i) q^{50} +(100.854 - 104.552i) q^{51} +(-41.8536 + 28.3775i) q^{52} +(-344.447 + 137.240i) q^{53} +(418.312 + 267.475i) q^{54} +(-28.6005 + 262.977i) q^{55} +(-325.012 + 150.367i) q^{56} +(-231.803 - 179.557i) q^{57} -103.450i q^{58} +(433.081 - 133.491i) q^{59} +(-122.203 - 84.4856i) q^{60} +(-392.130 - 21.2606i) q^{61} +(255.701 + 552.688i) q^{62} +(-196.535 - 761.227i) q^{63} +(11.8871 + 4.00523i) q^{64} +(-26.1362 - 65.5970i) q^{65} +(769.838 + 6.99134i) q^{66} +(308.653 + 50.6011i) q^{67} +(96.4151 + 81.8958i) q^{68} +(216.460 + 325.581i) q^{69} +(139.976 + 635.915i) q^{70} +(55.9132 + 165.944i) q^{71} +(160.843 - 290.507i) q^{72} +(452.410 + 751.911i) q^{73} +(54.1663 + 498.051i) q^{74} +(-323.683 + 301.079i) q^{75} +(143.290 - 211.338i) q^{76} +(-885.004 - 838.320i) q^{77} +(-182.434 + 94.6081i) q^{78} +(720.120 + 333.163i) q^{79} +(-259.710 + 431.641i) q^{80} +(563.947 + 461.958i) q^{81} +(-760.368 - 802.711i) q^{82} +(-55.4155 - 199.589i) q^{83} +(650.748 - 212.702i) q^{84} +(-140.629 + 106.904i) q^{85} +(106.517 + 29.5743i) q^{86} +(17.7927 - 150.843i) q^{87} +(-27.8748 - 514.120i) q^{88} +(25.0337 + 461.720i) q^{89} +(-452.998 - 399.168i) q^{90} +(313.541 + 87.0541i) q^{91} +(-271.041 + 206.040i) q^{92} +(277.785 + 849.866i) q^{93} +(-242.223 - 872.408i) q^{94} +(245.201 + 258.855i) q^{95} +(862.921 + 408.784i) q^{96} +(-732.057 + 1216.69i) q^{97} +(-1621.60 - 750.234i) q^{98} +(1121.32 + 142.600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} + O(q^{10}) \)	\( 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} - 58q^{10} - 57q^{12} - 58q^{13} - 11q^{15} - 926q^{16} - 29q^{18} + 126q^{19} + 159q^{21} + 2q^{22} - 29q^{24} + 656q^{25} - 99q^{27} - 54q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} + 859q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} + 1703q^{45} + 602q^{46} + 9507q^{48} - 1192q^{49} + 1511q^{51} - 58q^{52} - 7743q^{54} - 58q^{55} - 7441q^{57} - 18722q^{60} - 58q^{61} - 3251q^{63} - 4634q^{64} - 1751q^{66} - 58q^{67} + 6003q^{69} - 58q^{70} + 21547q^{72} - 58q^{73} + 3869q^{75} + 5622q^{76} - 3253q^{78} + 1446q^{79} + 247q^{81} - 58q^{82} + 3303q^{84} + 790q^{85} - 2199q^{87} - 5818q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 946q^{94} - 29q^{96} - 58q^{97} - 29q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about