LMFDB - Embedded newform 177.3.g.a.10.6

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$560$
Relative dimension:	$20$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			10.6
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.6

$q$-expansion

$f(q)$	$=$	$q+(-2.06048 - 0.820970i) q^{2} +(1.72190 + 0.187268i) q^{3} +(0.667604 + 0.632388i) q^{4} +(4.71743 - 5.55378i) q^{5} +(-3.39419 - 1.79949i) q^{6} +(8.57272 + 5.15803i) q^{7} +(2.86886 + 6.20094i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(-2.06048 - 0.820970i) q^{2} +(1.72190 + 0.187268i) q^{3} +(0.667604 + 0.632388i) q^{4} +(4.71743 - 5.55378i) q^{5} +(-3.39419 - 1.79949i) q^{6} +(8.57272 + 5.15803i) q^{7} +(2.86886 + 6.20094i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-14.2797 + 7.57059i) q^{10} +(-9.85322 - 0.534226i) q^{11} +(1.03112 + 1.21393i) q^{12} +(0.252568 + 1.14743i) q^{13} +(-13.4293 - 17.6660i) q^{14} +(9.16297 - 8.67962i) q^{15} +(-1.01958 - 18.8051i) q^{16} +(21.8646 - 13.1555i) q^{17} +(-5.50747 - 3.73416i) q^{18} +(-5.87781 + 21.1699i) q^{19} +(6.66152 - 0.724484i) q^{20} +(13.7954 + 10.4870i) q^{21} +(19.8638 + 9.18996i) q^{22} +(29.3221 - 19.8809i) q^{23} +(3.77865 + 11.2146i) q^{24} +(-4.54585 - 27.7285i) q^{25} +(0.421593 - 2.57161i) q^{26} +(4.92415 + 1.65914i) q^{27} +(2.46130 + 8.86481i) q^{28} +(-15.5744 - 39.0887i) q^{29} +(-26.0058 + 10.3617i) q^{30} +(-16.5627 + 4.59860i) q^{31} +(-4.61115 + 13.6854i) q^{32} +(-16.8662 - 2.76507i) q^{33} +(-55.8518 + 9.15643i) q^{34} +(69.0877 - 23.2784i) q^{35} +(1.54815 + 2.28336i) q^{36} +(6.01201 - 12.9948i) q^{37} +(29.4910 - 38.7947i) q^{38} +(0.220020 + 2.02305i) q^{39} +(47.9723 + 13.3194i) q^{40} +(-6.55007 + 9.66063i) q^{41} +(-19.8156 - 32.9339i) q^{42} +(-28.9840 + 1.57147i) q^{43} +(-6.24021 - 6.58771i) q^{44} +(17.4031 - 13.2295i) q^{45} +(-76.7391 + 16.8916i) q^{46} +(-63.5192 + 53.9537i) q^{47} +(1.76596 - 32.5713i) q^{48} +(23.9341 + 45.1446i) q^{49} +(-13.3976 + 60.8659i) q^{50} +(40.1121 - 18.5579i) q^{51} +(-0.557005 + 0.925750i) q^{52} +(15.7517 - 29.7108i) q^{53} +(-8.78401 - 7.46121i) q^{54} +(-49.4488 + 52.2025i) q^{55} +(-7.39072 + 67.9566i) q^{56} +(-14.0854 + 35.3518i) q^{57} +93.3277i q^{58} +(-41.4288 + 42.0078i) q^{59} +11.6061 q^{60} +(64.7667 + 25.8054i) q^{61} +(37.9024 + 4.12213i) q^{62} +(21.7904 + 20.6410i) q^{63} +(-28.0316 + 33.0013i) q^{64} +(7.56404 + 4.01020i) q^{65} +(32.4824 + 19.5440i) q^{66} +(-19.5613 - 42.2811i) q^{67} +(22.9162 + 5.04425i) q^{68} +(54.2126 - 28.7417i) q^{69} +(-161.465 - 8.75437i) q^{70} +(-21.2533 - 25.0213i) q^{71} +(4.40631 + 20.0181i) q^{72} +(63.0095 + 82.8876i) q^{73} +(-23.0559 + 21.8397i) q^{74} +(-2.63484 - 48.5968i) q^{75} +(-17.3117 + 10.4161i) q^{76} +(-81.7133 - 55.4030i) q^{77} +(1.20752 - 4.34909i) q^{78} +(89.2685 - 9.70853i) q^{79} +(-109.249 - 83.0489i) q^{80} +(8.16818 + 3.77900i) q^{81} +(21.4274 - 14.5281i) q^{82} +(29.4391 + 87.3722i) q^{83} +(2.57802 + 15.7252i) q^{84} +(30.0818 - 183.491i) q^{85} +(61.0111 + 20.5570i) q^{86} +(-19.4974 - 70.2234i) q^{87} +(-24.9548 - 62.6318i) q^{88} +(-110.829 + 44.1584i) q^{89} +(-46.7198 + 12.9717i) q^{90} +(-3.75328 + 11.1393i) q^{91} +(32.1480 + 5.27039i) q^{92} +(-29.3804 + 4.81667i) q^{93} +(175.174 - 59.0232i) q^{94} +(89.8452 + 132.512i) q^{95} +(-10.5028 + 22.7013i) q^{96} +(-41.1357 + 54.1131i) q^{97} +(-12.2535 - 112.669i) q^{98} +(-28.5240 - 7.91966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) $	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{7}{58}\right)$	$1$

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 $

$2$	−2.06048	−	0.820970i	−1.03024	−	0.410485i	−0.207098	−	0.978320i	$-0.566402\pi$
$2$	−2.06048	−	0.820970i	−1.03024	−	0.410485i	−0.823142	+	0.567835i	$0.807781\pi$
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$4$	0.667604	+	0.632388i	0.166901	+	0.158097i
$5$	4.71743	−	5.55378i	0.943485	−	1.11076i	−0.0502209	−	0.998738i	$-0.515993\pi$
$5$	4.71743	−	5.55378i	0.943485	−	1.11076i	0.993706	−	0.112018i	$-0.0357316\pi$
$6$	−3.39419	−	1.79949i	−0.565699	−	0.299915i
$7$	8.57272	+	5.15803i	1.22467	+	0.736862i	0.972968	−	0.230942i	$-0.0741808\pi$
$7$	8.57272	+	5.15803i	1.22467	+	0.736862i	0.251706	+	0.967804i	$0.419008\pi$
$8$	2.86886	+	6.20094i	0.358608	+	0.775118i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	−14.2797	+	7.57059i	−1.42797	+	0.757059i
$11$	−9.85322	−	0.534226i	−0.895747	−	0.0485660i	−0.399486	−	0.916739i	$-0.630811\pi$
$11$	−9.85322	−	0.534226i	−0.895747	−	0.0485660i	−0.496261	+	0.868173i	$0.665294\pi$
$12$	1.03112	+	1.21393i	0.0859267	+	0.101161i
$13$	0.252568	+	1.14743i	0.0194283	+	0.0882638i	0.985337	−	0.170619i	$-0.0545767\pi$
$13$	0.252568	+	1.14743i	0.0194283	+	0.0882638i	−0.965909	+	0.258883i	$0.916646\pi$
$14$	−13.4293	−	17.6660i	−0.959237	−	1.26185i
$15$	9.16297	−	8.67962i	0.610864	−	0.578642i
$16$	−1.01958	−	18.8051i	−0.0637238	−	1.17532i
$17$	21.8646	−	13.1555i	1.28615	−	0.773852i	0.302364	−	0.953192i	$-0.402224\pi$
$17$	21.8646	−	13.1555i	1.28615	−	0.773852i	0.983787	+	0.179341i	$0.0573965\pi$
$18$	−5.50747	−	3.73416i	−0.305970	−	0.207453i
$19$	−5.87781	+	21.1699i	−0.309358	+	1.11421i	0.631491	+	0.775383i	$0.282443\pi$
$19$	−5.87781	+	21.1699i	−0.309358	+	1.11421i	−0.940850	+	0.338825i	$0.889971\pi$
$20$	6.66152	−	0.724484i	0.333076	−	0.0362242i
$21$	13.7954	+	10.4870i	0.656924	+	0.499381i
$22$	19.8638	+	9.18996i	0.902899	+	0.417725i
$23$	29.3221	−	19.8809i	1.27487	−	0.864385i	0.279469	−	0.960155i	$-0.409842\pi$
$23$	29.3221	−	19.8809i	1.27487	−	0.864385i	0.995404	+	0.0957695i	$0.0305312\pi$
$24$	3.77865	+	11.2146i	0.157444	+	0.467276i
$25$	−4.54585	−	27.7285i	−0.181834	−	1.10914i
$26$	0.421593	−	2.57161i	0.0162151	−	0.0989079i
$27$	4.92415	+	1.65914i	0.182376	+	0.0614496i
$28$	2.46130	+	8.86481i	0.0879036	+	0.316600i
$29$	−15.5744	−	39.0887i	−0.537048	−	1.34789i	−0.907896	−	0.419194i	$-0.862313\pi$
$29$	−15.5744	−	39.0887i	−0.537048	−	1.34789i	0.370849	−	0.928693i	$-0.379067\pi$
$30$	−26.0058	+	10.3617i	−0.866861	+	0.345389i
$31$	−16.5627	+	4.59860i	−0.534280	+	0.148342i	−0.524181	−	0.851607i	$-0.675628\pi$
$31$	−16.5627	+	4.59860i	−0.534280	+	0.148342i	−0.0100989	+	0.999949i	$0.503215\pi$
$32$	−4.61115	+	13.6854i	−0.144098	+	0.427669i
$33$	−16.8662	−	2.76507i	−0.511096	−	0.0837900i
$34$	−55.8518	+	9.15643i	−1.64270	+	0.269307i
$35$	69.0877	−	23.2784i	1.97394	−	0.665096i
$36$	1.54815	+	2.28336i	0.0430043	+	0.0634265i
$37$	6.01201	−	12.9948i	0.162487	−	0.351210i	−0.809181	−	0.587559i	$-0.800089\pi$
$37$	6.01201	−	12.9948i	0.162487	−	0.351210i	0.971668	+	0.236350i	$0.0759510\pi$
$38$	29.4910	−	38.7947i	0.776079	−	1.02091i
$39$	0.220020	+	2.02305i	0.00564155	+	0.0518732i
$40$	47.9723	+	13.3194i	1.19931	+	0.332986i
$41$	−6.55007	+	9.66063i	−0.159758	+	0.235625i	−0.899140	−	0.437660i	$-0.855807\pi$
$41$	−6.55007	+	9.66063i	−0.159758	+	0.235625i	0.739383	+	0.673286i	$0.235118\pi$
$42$	−19.8156	−	32.9339i	−0.471801	−	0.784140i
$43$	−28.9840	+	1.57147i	−0.674047	+	0.0365458i	−0.387985	−	0.921666i	$-0.626829\pi$
$43$	−28.9840	+	1.57147i	−0.674047	+	0.0365458i	−0.286061	+	0.958211i	$0.592346\pi$
$44$	−6.24021	−	6.58771i	−0.141823	−	0.149721i
$45$	17.4031	−	13.2295i	0.386736	−	0.293989i
$46$	−76.7391	+	16.8916i	−1.66824	+	0.367208i
$47$	−63.5192	+	53.9537i	−1.35147	+	1.14795i	−0.376302	+	0.926497i	$0.622804\pi$
$47$	−63.5192	+	53.9537i	−1.35147	+	1.14795i	−0.975171	+	0.221454i	$0.928920\pi$
$48$	1.76596	−	32.5713i	0.0367909	−	0.678569i
$49$	23.9341	+	45.1446i	0.488452	+	0.921318i
$50$	−13.3976	+	60.8659i	−0.267952	+	1.21732i
$51$	40.1121	−	18.5579i	0.786513	−	0.363880i
$52$	−0.557005	+	0.925750i	−0.0107116	+	0.0178029i
$53$	15.7517	−	29.7108i	0.297202	−	0.560582i	−0.689272	−	0.724503i	$-0.742069\pi$
$53$	15.7517	−	29.7108i	0.297202	−	0.560582i	0.986473	+	0.163921i	$0.0524142\pi$
$54$	−8.78401	−	7.46121i	−0.162667	−	0.138170i
$55$	−49.4488	+	52.2025i	−0.899069	+	0.949135i
$56$	−7.39072	+	67.9566i	−0.131977	+	1.21351i
$57$	−14.0854	+	35.3518i	−0.247113	+	0.620206i
$58$			93.3277i			1.60910i
$59$	−41.4288	+	42.0078i	−0.702183	+	0.711996i
$59$	−41.4288	+	42.0078i	−0.702183	+	0.711996i
$60$	11.6061			0.193435
$61$	64.7667	+	25.8054i	1.06175	+	0.423040i	0.834621	−	0.550825i	$-0.185687\pi$
$61$	64.7667	+	25.8054i	1.06175	+	0.423040i	0.227129	+	0.973865i	$0.427066\pi$
$62$	37.9024	+	4.12213i	0.611329	+	0.0664860i
$63$	21.7904	+	20.6410i	0.345879	+	0.327634i
$64$	−28.0316	+	33.0013i	−0.437993	+	0.515645i
$65$	7.56404	+	4.01020i	0.116370	+	0.0616954i
$66$	32.4824	+	19.5440i	0.492157	+	0.296121i
$67$	−19.5613	−	42.2811i	−0.291960	−	0.631060i	0.704981	−	0.709226i	$-0.250956\pi$
$67$	−19.5613	−	42.2811i	−0.291960	−	0.631060i	−0.996940	+	0.0781660i	$0.975094\pi$
$68$	22.9162	+	5.04425i	0.337004	+	0.0741801i
$69$	54.2126	−	28.7417i	0.785690	−	0.416547i
$70$	−161.465	−	8.75437i	−2.30664	−	0.125062i
$71$	−21.2533	−	25.0213i	−0.299342	−	0.352412i	0.591843	−	0.806054i	$-0.298401\pi$
$71$	−21.2533	−	25.0213i	−0.299342	−	0.352412i	−0.891184	+	0.453641i	$0.850125\pi$
$72$	4.40631	+	20.0181i	0.0611987	+	0.278029i
$73$	63.0095	+	82.8876i	0.863144	+	1.13545i	0.989653	+	0.143481i	$0.0458296\pi$
$73$	63.0095	+	82.8876i	0.863144	+	1.13545i	−0.126509	+	0.991965i	$0.540377\pi$
$74$	−23.0559	+	21.8397i	−0.311567	+	0.295132i
$75$	−2.63484	−	48.5968i	−0.0351313	−	0.647958i
$76$	−17.3117	+	10.4161i	−0.227785	+	0.137054i
$77$	−81.7133	−	55.4030i	−1.06121	−	0.719519i
$78$	1.20752	−	4.34909i	0.0154810	−	0.0557576i
$79$	89.2685	−	9.70853i	1.12998	−	0.122893i	0.476029	−	0.879429i	$-0.342076\pi$
$79$	89.2685	−	9.70853i	1.12998	−	0.122893i	0.653951	+	0.756537i	$0.273110\pi$
$80$	−109.249	−	83.0489i	−1.36561	−	1.03811i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	21.4274	−	14.5281i	0.261310	−	0.177172i
$83$	29.4391	+	87.3722i	0.354688	+	1.05268i	0.965389	+	0.260816i	$0.0839915\pi$
$83$	29.4391	+	87.3722i	0.354688	+	1.05268i	−0.610700	+	0.791862i	$0.709112\pi$
$84$	2.57802	+	15.7252i	0.0306907	+	0.187205i
$85$	30.0818	−	183.491i	0.353904	−	2.15872i
$86$	61.0111	+	20.5570i	0.709431	+	0.239035i
$87$	−19.4974	−	70.2234i	−0.224108	−	0.807165i
$88$	−24.9548	−	62.6318i	−0.283577	−	0.711725i
$89$	−110.829	+	44.1584i	−1.24527	+	0.496162i	−0.897333	−	0.441354i	$-0.854498\pi$
$89$	−110.829	+	44.1584i	−1.24527	+	0.496162i	−0.347940	+	0.937517i	$0.613119\pi$
$90$	−46.7198	+	12.9717i	−0.519109	+	0.144130i
$91$	−3.75328	+	11.1393i	−0.0412448	+	0.122410i
$92$	32.1480	+	5.27039i	0.349434	+	0.0572868i
$93$	−29.3804	+	4.81667i	−0.315918	+	0.0517922i
$94$	175.174	−	59.0232i	1.86356	−	0.627906i
$95$	89.8452	+	132.512i	0.945739	+	1.39486i
$96$	−10.5028	+	22.7013i	−0.109404	+	0.236472i
$97$	−41.1357	+	54.1131i	−0.424079	+	0.557867i	−0.957667	−	0.287878i	$-0.907050\pi$
$97$	−41.1357	+	54.1131i	−0.424079	+	0.557867i	0.533588	+	0.845745i	$0.320843\pi$
$98$	−12.2535	−	112.669i	−0.125035	−	1.14968i
$99$	−28.5240	−	7.91966i	−0.288122	−	0.0799965i
$100$	14.5003	−	21.3864i	0.145003	−	0.213864i
$101$	−80.6858	−	134.101i	−0.798869	−	1.32773i	−0.941179	−	0.337908i	$-0.890281\pi$
$101$	−80.6858	−	134.101i	−0.798869	−	1.32773i	0.142310	−	0.989822i	$-0.454547\pi$
$102$	−97.8857	+	5.30721i	−0.959664	+	0.0520315i
$103$	−24.3303	−	25.6852i	−0.236217	−	0.249371i	0.597100	−	0.802167i	$-0.296320\pi$
$103$	−24.3303	−	25.6852i	−0.236217	−	0.249371i	−0.833317	+	0.552796i	$0.813561\pi$
$104$	−6.39056	+	4.85798i	−0.0614477	+	0.0467113i
$105$	123.321	−	27.1451i	1.17449	−	0.258524i
$106$	−56.8478	+	48.2869i	−0.536300	+	0.455537i
$107$	−10.9872	+	202.647i	−0.102684	+	1.89389i	0.265456	+	0.964123i	$0.414477\pi$
$107$	−10.9872	+	202.647i	−0.102684	+	1.89389i	−0.368140	+	0.929770i	$0.620005\pi$
$108$	2.23816	+	4.22162i	0.0207237	+	0.0390891i
$109$	−3.18660	+	14.4769i	−0.0292349	+	0.132815i	−0.988978	−	0.148065i	$-0.952695\pi$
$109$	−3.18660	+	14.4769i	−0.0292349	+	0.132815i	0.959743	+	0.280881i	$0.0906265\pi$
$110$	144.745	−	66.9661i	1.31586	−	0.608783i
$111$	12.7856	−	21.2498i	0.115185	−	0.191439i
$112$	88.2565	−	166.469i	0.788004	−	1.48633i
$113$	55.0952	+	46.7983i	0.487568	+	0.414144i	0.857160	−	0.515050i	$-0.172227\pi$
$113$	55.0952	+	46.7983i	0.487568	+	0.414144i	−0.369592	+	0.929194i	$0.620503\pi$
$114$	58.0455	−	61.2779i	0.509171	−	0.537525i
$115$	27.9107	−	256.635i	0.242702	−	2.23161i
$116$	14.3217	−	35.9449i	0.123463	−	0.309869i
$117$			3.52469i			0.0301256i
$118$	119.850	−	52.5443i	1.01568	−	0.445291i
$119$	255.295			2.14534
$120$	80.1091	+	31.9184i	0.667576	+	0.265987i
$121$	−23.4902	−	2.55472i	−0.194134	−	0.0211134i
$122$	−112.265	−	106.343i	−0.920205	−	0.871665i
$123$	−13.0877	+	15.4080i	−0.106404	+	0.125268i
$124$	−13.9654	−	7.40399i	−0.112624	−	0.0597096i
$125$	−19.3472	−	11.6408i	−0.154777	−	0.0931264i
$126$	−27.9531	−	60.4196i	−0.221850	−	0.479520i
$127$	−92.7698	−	20.4202i	−0.730471	−	0.160789i	−0.165864	−	0.986149i	$-0.553041\pi$
$127$	−92.7698	−	20.4202i	−0.730471	−	0.160789i	−0.564607	+	0.825360i	$0.690972\pi$
$128$	135.888	−	72.0433i	1.06163	−	0.562838i
$129$	−50.2018	−	2.72186i	−0.389161	−	0.0210997i
$130$	−12.2933	−	14.4728i	−0.0945639	−	0.111329i
$131$	−25.8363	−	117.375i	−0.197224	−	0.895996i	−0.966417	−	0.256980i	$-0.917273\pi$
$131$	−25.8363	−	117.375i	−0.197224	−	0.895996i	0.769193	−	0.639016i	$-0.220658\pi$
$132$	−9.51134	−	12.5119i	−0.0720556	−	0.0947875i
$133$	−159.584	+	151.166i	−1.19988	+	1.13659i
$134$	5.59418	+	103.179i	0.0417476	+	0.769989i
$135$	32.4438	−	19.5208i	0.240325	−	0.144598i
$136$	144.303	+	97.8397i	1.06105	+	0.719410i
$137$	−11.6223	+	41.8596i	−0.0848341	+	0.305545i	−0.993779	−	0.111372i	$-0.964476\pi$
$137$	−11.6223	+	41.8596i	−0.0848341	+	0.305545i	0.908945	+	0.416917i	$0.136889\pi$
$138$	−135.300	+	14.7148i	−0.980436	+	0.106629i
$139$	142.841	+	108.585i	1.02763	+	0.781186i	0.976064	−	0.217483i	$-0.0697848\pi$
$139$	142.841	+	108.585i	1.02763	+	0.781186i	0.0515688	+	0.998669i	$0.483578\pi$
$140$	60.8442	+	28.1495i	0.434602	+	0.201068i
$141$	−119.477	+	81.0077i	−0.847357	+	0.574522i
$142$	23.2502	+	69.0042i	0.163734	+	0.485945i
$143$	−1.87562	−	11.4408i	−0.0131162	−	0.0800056i
$144$	9.14036	−	55.7537i	0.0634747	−	0.387179i
$145$	−290.561	−	97.9015i	−2.00387	−	0.675183i
$146$	−61.7816	−	222.517i	−0.423162	−	1.52409i
$147$	32.7580	+	82.2165i	0.222844	+	0.559296i
$148$	12.2314	−	4.87343i	0.0826444	−	0.0329286i
$149$	21.8734	−	6.07312i	0.146801	−	0.0407592i	−0.193350	−	0.981130i	$-0.561935\pi$
$149$	21.8734	−	6.07312i	0.146801	−	0.0407592i	0.340152	+	0.940371i	$0.389522\pi$
$150$	−34.4675	+	102.296i	−0.229784	+	0.681973i
$151$	−27.1339	−	4.44837i	−0.179694	−	0.0294594i	0.0712629	−	0.997458i	$-0.477297\pi$
$151$	−27.1339	−	4.44837i	−0.179694	−	0.0294594i	−0.250957	+	0.967998i	$0.580745\pi$
$152$	−148.136	+	24.2857i	−0.974580	+	0.159774i
$153$	72.5443	−	24.4430i	0.474146	−	0.159758i
$154$	122.884	+	181.241i	0.797950	+	1.17689i
$155$	−52.5935	+	113.679i	−0.339313	+	0.733413i
$156$	−1.13247	+	1.48974i	−0.00725941	+	0.00954960i
$157$	5.24500	+	48.2270i	0.0334076	+	0.307178i	0.998906	+	0.0467682i	$0.0148922\pi$
$157$	5.24500	+	48.2270i	0.0334076	+	0.307178i	−0.965498	+	0.260410i	$0.916142\pi$
$158$	−191.906	−	53.2825i	−1.21460	−	0.337231i
$159$	32.6867	−	48.2093i	0.205577	−	0.303203i
$160$	54.2530	+	90.1692i	0.339081	+	0.563558i
$161$	353.916	−	19.1888i	2.19824	−	0.119185i
$162$	−13.7279	−	14.4924i	−0.0847403	−	0.0894592i
$163$	−83.9828	+	63.8421i	−0.515232	+	0.391669i	−0.830228	−	0.557424i	$-0.811790\pi$
$163$	−83.9828	+	63.8421i	−0.515232	+	0.391669i	0.314996	+	0.949093i	$0.397997\pi$
$164$	−10.4821	+	2.30729i	−0.0639154	+	0.0140688i
$165$	−94.9216	+	80.6271i	−0.575282	+	0.488649i
$166$	11.0713	−	204.197i	0.0666943	−	1.23010i
$167$	−50.6574	−	95.5499i	−0.303337	−	0.572155i	0.684246	−	0.729251i	$-0.260132\pi$
$167$	−50.6574	−	95.5499i	−0.303337	−	0.572155i	−0.987583	+	0.157096i	$0.949787\pi$
$168$	−25.4521	+	115.630i	−0.151501	+	0.688275i
$169$	152.127	−	70.3816i	0.900162	−	0.416459i
$170$	−212.624	+	353.383i	−1.25073	+	2.07873i
$171$	−30.8739	+	58.2343i	−0.180549	+	0.340552i
$172$	−20.3436	−	17.2800i	−0.118277	−	0.100465i
$173$	−185.255	+	195.572i	−1.07084	+	1.13047i	−0.0798128	+	0.996810i	$0.525432\pi$
$173$	−185.255	+	195.572i	−1.07084	+	1.13047i	−0.991027	+	0.133662i	$0.957326\pi$
$174$	−17.4773	+	160.701i	−0.100444	+	0.923567i
$175$	104.054	−	261.156i	0.594594	−	1.49232i
$176$			185.835i			1.05588i
$177$	−79.2029	+	64.5748i	−0.447474	+	0.364829i
$178$	264.614			1.48660
$179$	−60.2208	−	23.9942i	−0.336429	−	0.134046i	0.195805	−	0.980643i	$-0.437268\pi$
$179$	−60.2208	−	23.9942i	−0.336429	−	0.134046i	−0.532234	+	0.846597i	$0.678647\pi$
$180$	19.9846	+	2.17345i	0.111025	+	0.0120747i
$181$	−120.242	−	113.899i	−0.664320	−	0.629278i	0.279340	−	0.960192i	$-0.409884\pi$
$181$	−120.242	−	113.899i	−0.664320	−	0.629278i	−0.943661	+	0.330914i	$0.892643\pi$
$182$	16.8786	−	19.8711i	0.0927397	−	0.109182i
$183$	106.689	+	56.5630i	0.583001	+	0.309087i
$184$	207.401	+	124.789i	1.12718	+	0.678201i
$185$	−43.8088	−	94.6912i	−0.236804	−	0.511844i
$186$	64.4921	+	14.1958i	0.346732	+	0.0763214i
$187$	−222.464	+	117.943i	−1.18965	+	0.630712i
$188$	−76.5254	−	4.14909i	−0.407050	−	0.0220696i
$189$	33.6554	+	39.6223i	0.178071	+	0.209642i
$190$	−76.3360	−	346.798i	−0.401768	−	1.82525i
$191$	9.48473	+	12.4770i	0.0496583	+	0.0653244i	0.820252	−	0.572002i	$-0.193833\pi$
$191$	9.48473	+	12.4770i	0.0496583	+	0.0653244i	−0.770594	+	0.637327i	$0.780040\pi$
$192$	−54.4475	+	51.5755i	−0.283581	+	0.268622i
$193$	−4.72485	−	87.1447i	−0.0244811	−	0.451527i	−0.984917	−	0.173027i	$-0.944645\pi$
$193$	−4.72485	−	87.1447i	−0.0244811	−	0.451527i	0.960436	−	0.278501i	$-0.0898374\pi$
$194$	129.184	−	77.7277i	0.665899	−	0.400658i
$195$	12.2735	+	8.32166i	0.0629412	+	0.0426752i
$196$	−12.5704	+	45.2744i	−0.0641346	+	0.230992i
$197$	−296.261	+	32.2203i	−1.50386	+	0.163555i	−0.822657	−	0.568538i	$-0.807509\pi$
$197$	−296.261	+	32.2203i	−1.50386	+	0.163555i	−0.681205	+	0.732093i	$0.738544\pi$
$198$	52.2714	+	39.7357i	0.263997	+	0.200685i
$199$	225.861	+	104.494i	1.13498	+	0.525098i	0.895171	−	0.445722i	$-0.147053\pi$
$199$	225.861	+	104.494i	1.13498	+	0.525098i	0.239809	+	0.970820i	$0.422915\pi$
$200$	158.901	−	107.738i	0.794506	−	0.538688i
$201$	−25.7647	−	76.4668i	−0.128182	−	0.380432i
$202$	56.1586	+	342.553i	0.278013	+	1.69580i
$203$	68.1063	−	415.430i	0.335499	−	2.04645i
$204$	38.5148	+	12.9771i	0.188798	+	0.0636135i
$205$	22.7536	+	81.9510i	0.110993	+	0.399761i
$206$	29.0454	+	72.8983i	0.140997	+	0.353875i
$207$	98.7310	−	39.3380i	0.476961	−	0.190039i
$208$	21.3200	−	5.91946i	0.102500	−	0.0284589i
$209$	69.2248	−	205.452i	0.331219	−	0.983024i
$210$	−276.386	−	45.3112i	−1.31613	−	0.215768i
$211$	−191.870	+	31.4554i	−0.909334	+	0.149078i	−0.598255	−	0.801306i	$-0.704139\pi$
$211$	−191.870	+	31.4554i	−0.909334	+	0.149078i	−0.311080	+	0.950384i	$0.600691\pi$
$212$	29.3047	−	9.87390i	0.138230	−	0.0465750i
$213$	−31.9103	−	47.0641i	−0.149813	−	0.220958i
$214$	189.006	−	408.529i	0.883204	−	1.90901i
$215$	−128.002	+	168.384i	−0.595360	+	0.783182i
$216$	3.83848	+	35.2942i	0.0177707	+	0.163399i
$217$	−165.707	−	46.0083i	−0.763626	−	0.212020i
$218$	18.4510	−	27.2132i	0.0846376	−	0.124831i
$219$	92.9738	+	154.524i	0.424538	+	0.705587i
$220$	−66.0244	+	3.57974i	−0.300111	+	0.0162715i
$221$	20.6173	+	21.7654i	0.0932908	+	0.0984859i
$222$	−43.7898	+	33.2882i	−0.197252	+	0.149947i
$223$	334.288	−	73.5823i	1.49905	−	0.329965i	0.611709	−	0.791083i	$-0.290482\pi$
$223$	334.288	−	73.5823i	1.49905	−	0.329965i	0.887339	+	0.461117i	$0.152551\pi$
$224$	−110.120	+	93.5366i	−0.491606	+	0.417574i
$225$	4.56368	−	84.1722i	0.0202830	−	0.374099i
$226$	−75.1025	−	141.658i	−0.332312	−	0.626807i
$227$	79.6539	−	361.871i	0.350898	−	1.59415i	−0.388876	−	0.921290i	$-0.627136\pi$
$227$	79.6539	−	361.871i	0.350898	−	1.59415i	0.739774	−	0.672856i	$-0.234933\pi$
$228$	−31.7595	+	14.6935i	−0.139296	+	0.0644453i
$229$	−55.7677	+	92.6866i	−0.243527	+	0.404745i	−0.954380	−	0.298596i	$-0.903482\pi$
$229$	−55.7677	+	92.6866i	−0.243527	+	0.404745i	0.710853	+	0.703341i	$0.248309\pi$
$230$	−268.199	+	505.877i	−1.16608	+	2.19947i
$231$	−130.327	−	110.700i	−0.564185	−	0.479223i
$232$	197.706	−	208.716i	0.852182	−	0.899638i
$233$	−11.7960	+	108.462i	−0.0506265	+	0.465503i	0.941194	+	0.337865i	$0.109705\pi$
$233$	−11.7960	+	108.462i	−0.0506265	+	0.465503i	−0.991821	+	0.127637i	$0.959261\pi$
$234$	2.89367	−	7.26256i	0.0123661	−	0.0310366i
$235$			607.295i			2.58423i
$236$	−54.2233	+	1.84546i	−0.229760	+	0.00781976i
$237$	155.529			0.656242
$238$	−526.031	−	209.590i	−2.21021	−	0.880629i
$239$	264.354	+	28.7502i	1.10608	+	0.120294i	0.642886	−	0.765962i	$-0.277737\pi$
$239$	264.354	+	28.7502i	1.10608	+	0.120294i	0.463196	+	0.886256i	$0.346702\pi$
$240$	−172.563	−	163.461i	−0.719013	−	0.681085i
$241$	−206.869	+	243.545i	−0.858378	+	1.01056i	0.141410	+	0.989951i	$0.454836\pi$
$241$	−206.869	+	243.545i	−0.858378	+	1.01056i	−0.999788	+	0.0206093i	$0.993439\pi$
$242$	46.3038	+	24.5487i	0.191338	+	0.101441i
$243$	13.3571	+	8.03669i	0.0549674	+	0.0330728i
$244$	26.9195	+	58.1855i	0.110326	+	0.238465i
$245$	363.631	+	80.0412i	1.48421	+	0.326699i
$246$	39.6164	−	21.0033i	0.161042	−	0.0853792i
$247$	−25.7756	−	1.39751i	−0.104354	−	0.00565794i
$248$	−76.0317	−	89.5114i	−0.306579	−	0.360933i
$249$	34.3292	+	155.959i	0.137868	+	0.626341i
$250$	30.3077	+	39.8691i	0.121231	+	0.159476i
$251$	−325.790	+	308.605i	−1.29797	+	1.22950i	−0.340743	+	0.940156i	$0.610679\pi$
$251$	−325.790	+	308.605i	−1.29797	+	1.22950i	−0.957225	+	0.289344i	$0.906563\pi$
$252$	1.49426	+	27.5600i	0.00592960	+	0.109365i
$253$	−299.538	+	180.226i	−1.18394	+	0.712355i
$254$	174.386	+	118.237i	0.686559	+	0.465498i
$255$	86.1598	−	310.319i	0.337881	−	1.21694i
$256$	−166.957	+	18.1577i	−0.652176	+	0.0709284i
$257$	−304.991	−	231.848i	−1.18674	−	0.902133i	−0.189915	−	0.981801i	$-0.560821\pi$
$257$	−304.991	−	231.848i	−1.18674	−	0.902133i	−0.996822	+	0.0796672i	$0.974614\pi$
$258$	101.205	+	46.8225i	0.392268	+	0.181483i
$259$	118.567	−	80.3902i	0.457786	−	0.310387i
$260$	2.51378	+	7.46064i	0.00966839	+	0.0286948i
$261$	−20.4220	−	124.569i	−0.0782452	−	0.477275i
$262$	−43.1266	+	263.061i	−0.164605	+	1.00405i
$263$	127.527	+	42.9687i	0.484892	+	0.163379i	0.551121	−	0.834425i	$-0.314200\pi$
$263$	127.527	+	42.9687i	0.484892	+	0.163379i	−0.0662290	+	0.997804i	$0.521097\pi$
$264$	−31.2407	−	112.519i	−0.118336	−	0.426208i
$265$	−90.7002	−	227.640i	−0.342265	−	0.859020i
$266$	452.923	−	180.461i	1.70272	−	0.678424i
$267$	−199.106	+	55.2816i	−0.745716	+	0.207047i
$268$	13.6788	−	40.5973i	0.0510404	−	0.151483i
$269$	164.442	+	26.9589i	0.611308	+	0.100219i	0.459480	−	0.888188i	$-0.348036\pi$
$269$	164.442	+	26.9589i	0.611308	+	0.100219i	0.151828	+	0.988407i	$0.451484\pi$
$270$	−82.8758	+	13.5868i	−0.306948	+	0.0503215i
$271$	−242.105	+	81.5745i	−0.893375	+	0.301013i	−0.728292	−	0.685267i	$-0.759686\pi$
$271$	−242.105	+	81.5745i	−0.893375	+	0.301013i	−0.165083	+	0.986280i	$0.552789\pi$
$272$	−269.682	−	397.751i	−0.991478	−	1.46232i
$273$	−8.54880	+	18.4779i	−0.0313143	+	0.0676847i
$274$	58.3130	−	76.7094i	0.212821	−	0.279961i
$275$	29.9780	+	275.643i	0.109011	+	1.00234i
$276$	54.3685	+	15.0953i	0.196987	+	0.0546933i
$277$	150.137	−	221.436i	0.542012	−	0.799408i	−0.453774	−	0.891117i	$-0.649923\pi$
$277$	150.137	−	221.436i	0.542012	−	0.799408i	0.995786	+	0.0917091i	$0.0292330\pi$
$278$	−205.176	−	341.005i	−0.738043	−	1.22664i
$279$	−51.4920	+	2.79182i	−0.184559	+	0.0100065i
$280$	342.551	+	361.627i	1.22340	+	1.29152i
$281$	80.9203	−	61.5140i	0.287973	−	0.218911i	−0.451207	−	0.892419i	$-0.649006\pi$
$281$	80.9203	−	61.5140i	0.287973	−	0.218911i	0.739180	+	0.673508i	$0.235213\pi$
$282$	312.686	−	68.8273i	1.10881	−	0.244068i
$283$	385.649	−	327.574i	1.36272	−	1.15750i	0.391264	−	0.920278i	$-0.372038\pi$
$283$	385.649	−	327.574i	1.36272	−	1.15750i	0.971455	−	0.237226i	$-0.0762381\pi$
$284$	1.63439	−	30.1446i	0.00575491	−	0.106143i
$285$	129.889	+	244.997i	0.455751	+	0.859637i
$286$	−5.52787	+	25.1134i	−0.0193282	+	0.0878090i
$287$	−105.982	+	49.0324i	−0.369274	+	0.170845i
$288$	−22.3359	+	37.1226i	−0.0775552	+	0.128898i
$289$	169.623	−	319.943i	0.586931	−	1.10707i
$290$	518.322	+	440.266i	1.78732	+	1.51816i
$291$	−80.9651	+	85.4738i	−0.278230	+	0.293724i
$292$	−10.3517	+	95.1826i	−0.0354511	+	0.325968i
$293$	−27.3550	+	68.6558i	−0.0933617	+	0.234320i	−0.968240	−	0.250023i	$-0.919562\pi$
$293$	−27.3550	+	68.6558i	−0.0933617	+	0.234320i	0.874878	+	0.484343i	$0.160941\pi$
$294$		−	196.299i		−	0.667683i
$295$	37.8647	+	428.255i	0.128355	+	1.45171i
$296$	97.8273			0.330498
$297$	−47.6324	−	18.9785i	−0.160378	−	0.0639006i
$298$	−50.0556	−	5.44387i	−0.167972	−	0.0182680i
$299$	30.2177	+	28.6237i	0.101063	+	0.0957315i
$300$	28.9730	−	34.1097i	0.0965768	−	0.113699i
$301$	−256.577	−	136.029i	−0.852416	−	0.451923i
$302$	52.2568	+	31.4419i	0.173036	+	0.104112i
$303$	−113.820	−	246.018i	−0.375643	−	0.811939i
$304$	404.095	+	88.9480i	1.32926	+	0.292592i
$305$	448.850	−	237.965i	1.47164	−	0.780214i
$306$	−169.543	−	9.19236i	−0.554062	−	0.0300404i
$307$	−222.511	−	261.960i	−0.724791	−	0.853290i	0.269162	−	0.963095i	$-0.413253\pi$
$307$	−222.511	−	261.960i	−0.724791	−	0.853290i	−0.993953	+	0.109805i	$0.964977\pi$
$308$	−19.5159	−	88.6618i	−0.0633634	−	0.287863i
$309$	−37.0843	−	48.7836i	−0.120014	−	0.157876i
$310$	201.695	−	191.056i	0.650629	−	0.616309i
$311$	1.99501	+	36.7958i	0.00641482	+	0.118314i	0.999987	+	0.00511343i	$0.00162766\pi$
$311$	1.99501	+	36.7958i	0.00641482	+	0.118314i	−0.993572	+	0.113201i	$0.963890\pi$
$312$	−11.9136	+	7.16819i	−0.0381847	+	0.0229750i
$313$	157.684	+	106.912i	0.503782	+	0.341572i	0.786459	−	0.617643i	$-0.211912\pi$
$313$	157.684	+	106.912i	0.503782	+	0.341572i	−0.282677	+	0.959215i	$0.591223\pi$
$314$	28.7857	−	103.677i	0.0916742	−	0.330181i
$315$	217.430	−	23.6469i	0.690254	−	0.0750696i
$316$	65.7356	+	49.9709i	0.208024	+	0.158136i
$317$	−544.085	−	251.721i	−1.71636	−	0.794072i	−0.994815	−	0.101702i	$-0.967571\pi$
$317$	−544.085	−	251.721i	−1.71636	−	0.794072i	−0.721543	−	0.692370i	$-0.756567\pi$
$318$	−106.929	+	72.4994i	−0.336254	+	0.227986i
$319$	132.575	+	393.470i	0.415597	+	1.23345i
$320$	51.0453	+	311.362i	0.159516	+	0.973007i
$321$	−56.8679	+	346.879i	−0.177159	+	1.08062i
$322$	−744.990	−	251.016i	−2.31363	−	0.779554i
$323$	149.985	+	540.197i	0.464350	+	1.67244i
$324$	3.06331	+	7.68834i	0.00945467	+	0.0237294i
$325$	30.6683	−	12.2194i	0.0943640	−	0.0375981i
$326$	225.457	−	62.5979i	0.691587	−	0.192018i
$327$	−8.19805	+	24.3309i	−0.0250705	+	0.0744065i
$328$	−78.6962	−	12.9016i	−0.239928	−	0.0393341i
$329$	−822.827	+	134.896i	−2.50099	+	0.410017i
$330$	261.776	−	88.2028i	0.793262	−	0.267281i
$331$	−19.1194	−	28.1991i	−0.0577627	−	0.0851936i	0.797711	−	0.603040i	$-0.206044\pi$
$331$	−19.1194	−	28.1991i	−0.0577627	−	0.0851936i	−0.855473	+	0.517847i	$0.826734\pi$
$332$	−35.5995	+	76.9470i	−0.107227	+	0.231768i
$333$	25.9948	−	34.1956i	0.0780626	−	0.102690i
$334$	25.9348	+	238.467i	0.0776492	+	0.713973i
$335$	−327.099	−	90.8185i	−0.976414	−	0.271100i
$336$	183.143	−	270.116i	0.545068	−	0.803916i
$337$	−149.173	−	247.927i	−0.442650	−	0.735690i	0.552558	−	0.833475i	$-0.313652\pi$
$337$	−149.173	−	247.927i	−0.442650	−	0.735690i	−0.995208	+	0.0977850i	$0.968824\pi$
$338$	−371.237	+	20.1279i	−1.09833	+	0.0595499i
$339$	86.1045	+	90.8994i	0.253995	+	0.268140i
$340$	136.120	−	103.476i	0.400354	−	0.304341i
$341$	165.652	−	36.4628i	0.485784	−	0.106929i
$342$	111.424	−	94.6442i	0.325800	−	0.276737i
$343$	−1.13571	+	20.9469i	−0.00331110	+	0.0610696i
$344$	−92.8957	−	175.220i	−0.270046	−	0.509360i
$345$	96.1188	−	436.672i	0.278605	−	1.26572i
$346$	542.273	−	250.882i	1.56726	−	0.725093i
$347$	181.164	−	301.096i	0.522085	−	0.867712i	−0.477857	−	0.878438i	$-0.658586\pi$
$347$	181.164	−	301.096i	0.522085	−	0.867712i	0.999942	+	0.0107251i	$0.00341397\pi$
$348$	31.3919	−	59.2114i	0.0902066	−	0.170148i
$349$	−485.213	−	412.143i	−1.39029	−	1.18093i	−0.960594	−	0.277956i	$-0.910343\pi$
$349$	−485.213	−	412.143i	−1.39029	−	1.18093i	−0.429701	−	0.902971i	$-0.641381\pi$
$350$	−428.802	+	452.681i	−1.22515	+	1.29337i
$351$	−0.660061	+	6.06916i	−0.00188052	+	0.0172911i
$352$	52.7458	−	132.382i	0.149846	−	0.376085i
$353$			62.0187i			0.175690i	0.996134	+	0.0878451i	$0.0279981\pi$
$353$			62.0187i			0.175690i	−0.996134	+	0.0878451i	$0.972002\pi$
$354$	216.210	−	68.0319i	0.610763	−	0.192180i
$355$	−239.224			−0.673869
$356$	−101.915	−	40.6068i	−0.286279	−	0.114064i
$357$	439.592	+	47.8085i	1.23135	+	0.133917i
$358$	104.385	+	98.8790i	0.291579	+	0.276198i
$359$	104.409	−	122.920i	0.290833	−	0.342396i	−0.597269	−	0.802041i	$-0.703748\pi$
$359$	104.409	−	122.920i	0.290833	−	0.342396i	0.888103	+	0.459645i	$0.152023\pi$
$360$	131.962	+	69.9620i	0.366562	+	0.194339i
$361$	−104.293	−	62.7508i	−0.288899	−	0.173825i
$362$	154.248	+	333.402i	0.426100	+	0.921001i
$363$	−39.9694	−	8.79792i	−0.110108	−	0.0242367i
$364$	−9.55009	+	5.06314i	−0.0262365	+	0.0139097i
$365$	757.582	+	41.0749i	2.07557	+	0.112534i
$366$	−173.394	−	204.136i	−0.473755	−	0.557747i
$367$	128.096	+	581.944i	0.349034	+	1.58568i	0.744774	+	0.667317i	$0.232557\pi$
$367$	128.096	+	581.944i	0.349034	+	1.58568i	−0.395739	+	0.918363i	$0.629512\pi$
$368$	−403.757	−	531.133i	−1.09717	−	1.44330i
$369$	−25.4211	+	24.0801i	−0.0688917	+	0.0652577i
$370$	12.5285	+	231.075i	0.0338609	+	0.624527i
$371$	288.284	−	173.455i	0.777047	−	0.467533i
$372$	−22.6605	−	15.3642i	−0.0609153	−	0.0413016i
$373$	65.5368	−	236.042i	0.175702	−	0.632821i	−0.822266	−	0.569103i	$-0.807291\pi$
$373$	65.5368	−	236.042i	0.175702	−	0.632821i	0.997968	−	0.0637176i	$-0.0202957\pi$
$374$	555.211	−	60.3829i	1.48452	−	0.161451i
$375$	−31.1339	−	23.6674i	−0.0830237	−	0.0631130i
$376$	−516.792	−	239.093i	−1.37445	−	0.635886i
$377$	40.9180	−	27.7431i	0.108536	−	0.0735891i
$378$	−36.8177	−	109.271i	−0.0974013	−	0.289077i
$379$	16.3282	+	99.5974i	0.0430822	+	0.262790i	0.999581	−	0.0289465i	$-0.00921525\pi$
$379$	16.3282	+	99.5974i	0.0430822	+	0.262790i	−0.956499	+	0.291736i	$0.905767\pi$
$380$	−23.8178	+	145.282i	−0.0626785	+	0.382322i
$381$	−155.916	−	52.5342i	−0.409228	−	0.137885i
$382$	−9.29990	−	33.4952i	−0.0243453	−	0.0876838i
$383$	36.9102	+	92.6375i	0.0963712	+	0.241873i	0.969257	−	0.246052i	$-0.0791333\pi$
$383$	36.9102	+	92.6375i	0.0963712	+	0.241873i	−0.872886	+	0.487925i	$0.837754\pi$
$384$	247.477	−	98.6037i	0.644470	−	0.256780i
$385$	−693.172	+	192.458i	−1.80045	+	0.499892i
$386$	−61.8078	+	183.439i	−0.160124	+	0.475230i
$387$	−85.9326	−	14.0879i	−0.222048	−	0.0364029i
$388$	−61.6828	+	10.1124i	−0.158976	+	0.0260629i
$389$	411.650	−	138.701i	1.05823	−	0.356558i	0.264216	−	0.964463i	$-0.414887\pi$
$389$	411.650	−	138.701i	1.05823	−	0.356558i	0.794009	+	0.607906i	$0.207990\pi$
$390$	−18.4575	−	27.2228i	−0.0473270	−	0.0698021i
$391$	379.572	−	820.432i	0.970773	−	2.09829i
$392$	−211.275	+	277.928i	−0.538967	+	0.708999i
$393$	−22.5068	−	206.947i	−0.0572693	−	0.526582i
$394$	636.891	+	176.832i	1.61648	+	0.448812i
$395$	367.198	−	541.577i	0.929616	−	1.37108i
$396$	−14.0345	−	23.3255i	−0.0354406	−	0.0589027i
$397$	195.507	−	10.6001i	0.492460	−	0.0267004i	0.193763	−	0.981048i	$-0.437931\pi$
$397$	195.507	−	10.6001i	0.492460	−	0.0267004i	0.298697	+	0.954348i	$0.403448\pi$
$398$	−379.595	−	400.734i	−0.953757	−	1.00687i
$399$	−303.096	+	230.407i	−0.759639	+	0.577462i
$400$	−516.800	+	113.756i	−1.29200	+	0.284391i
$401$	420.737	−	357.377i	1.04922	−	0.891215i	0.0549899	−	0.998487i	$-0.482487\pi$
$401$	420.737	−	357.377i	1.04922	−	0.891215i	0.994230	+	0.107272i	$0.0342115\pi$
$402$	−9.68940	+	178.710i	−0.0241030	+	0.444553i
$403$	−9.45978	−	17.8430i	−0.0234734	−	0.0442755i
$404$	30.9376	−	140.551i	0.0765782	−	0.347898i
$405$	59.5205	−	27.5371i	0.146964	−	0.0679929i
$406$	−481.387	+	800.072i	−1.18568	+	1.97062i
$407$	−66.1798	+	124.828i	−0.162604	+	0.306704i
$408$	230.152	+	195.493i	0.564099	+	0.479150i
$409$	−303.724	+	320.638i	−0.742602	+	0.783956i	−0.982384	−	0.186871i	$-0.940165\pi$
$409$	−303.724	+	320.638i	−0.742602	+	0.783956i	0.239782	+	0.970827i	$0.422924\pi$
$410$	20.3960	−	187.538i	0.0497464	−	0.457411i
$411$	−27.8513	+	69.9015i	−0.0677647	+	0.170077i
$412$		−	32.5338i		−	0.0789654i
$413$	−571.835	+	146.430i	−1.38459	+	0.354551i
$414$	−235.729			−0.569393
$415$	624.123	+	248.673i	1.50391	+	0.599213i
$416$	−16.8677	−	1.83447i	−0.0405473	−	0.00440978i
$417$	225.623	+	213.722i	0.541062	+	0.512522i
$418$	−311.306	+	366.498i	−0.744752	+	0.876790i
$419$	−274.480	−	145.520i	−0.655083	−	0.347303i	0.107489	−	0.994206i	$-0.465719\pi$
$419$	−274.480	−	145.520i	−0.655083	−	0.347303i	−0.762572	+	0.646903i	$0.776064\pi$
$420$	99.4960	+	59.8648i	0.236895	+	0.142535i
$421$	125.945	+	272.225i	0.299156	+	0.646616i	0.997614	−	0.0690355i	$-0.0219922\pi$
$421$	125.945	+	272.225i	0.299156	+	0.646616i	−0.698458	+	0.715651i	$0.746130\pi$
$422$	421.167	+	92.7059i	0.998027	+	0.219682i
$423$	−220.898	+	117.113i	−0.522217	+	0.276862i
$424$	229.425	+	12.4390i	0.541096	+	0.0293374i
$425$	−464.174	−	546.468i	−1.09217	−	1.28581i
$426$	27.1122	+	123.172i	0.0636437	+	0.289136i
$427$	422.121	+	555.291i	0.988575	+	1.30045i
$428$	−135.486	+	128.340i	−0.316557	+	0.299859i
$429$	−1.08714	−	20.0511i	−0.00253413	−	0.0467392i
$430$	401.985	−	241.866i	0.934848	−	0.562479i
$431$	−157.827	−	107.009i	−0.366188	−	0.248282i	0.364190	−	0.931325i	$-0.381346\pi$
$431$	−157.827	−	107.009i	−0.366188	−	0.248282i	−0.730378	+	0.683043i	$0.760656\pi$
$432$	26.1796	−	94.2905i	0.0606010	−	0.218265i
$433$	−455.601	+	49.5496i	−1.05220	+	0.114433i	−0.617837	−	0.786306i	$-0.711991\pi$
$433$	−455.601	+	49.5496i	−1.05220	+	0.114433i	−0.434360	+	0.900739i	$0.643025\pi$
$434$	303.664	+	230.840i	0.699687	+	0.531888i
$435$	−481.983	−	222.989i	−1.10801	−	0.512619i
$436$	−11.2824	+	7.64965i	−0.0258770	+	0.0175451i
$437$	248.527	+	737.603i	0.568712	+	1.68788i
$438$	−64.7113	−	394.721i	−0.147743	−	0.901191i
$439$	−101.136	+	616.900i	−0.230377	+	1.40524i	0.577742	+	0.816219i	$0.303934\pi$
$439$	−101.136	+	616.900i	−0.230377	+	1.40524i	−0.808119	+	0.589019i	$0.799514\pi$
$440$	−465.566	−	156.867i	−1.05810	−	0.356517i
$441$	41.0095	+	147.703i	0.0929920	+	0.334927i
$442$	−24.6127	−	61.7733i	−0.0556849	−	0.139759i
$443$	334.921	−	133.445i	0.756029	−	0.301230i	0.0399061	−	0.999203i	$-0.487294\pi$
$443$	334.921	−	133.445i	0.756029	−	0.301230i	0.716123	+	0.697974i	$0.245915\pi$
$444$	21.9738	−	6.10100i	0.0494906	−	0.0137410i
$445$	−277.583	+	823.836i	−0.623781	+	1.85132i
$446$	−749.202	−	122.825i	−1.67983	−	0.275393i
$447$	38.8010	−	6.36111i	0.0868032	−	0.0142307i
$448$	−410.528	+	138.323i	−0.916358	+	0.308757i
$449$	39.6661	+	58.5031i	0.0883431	+	0.130296i	0.869293	−	0.494298i	$-0.164575\pi$
$449$	39.6661	+	58.5031i	0.0883431	+	0.130296i	−0.780950	+	0.624594i	$0.785264\pi$
$450$	−78.5063	+	169.689i	−0.174458	+	0.377086i
$451$	69.7002	−	91.6891i	0.154546	−	0.203302i
$452$	7.18710	+	66.0843i	0.0159007	+	0.146204i
$453$	−45.8887	−	12.7409i	−0.101300	−	0.0281257i
$454$	−461.211	+	680.235i	−1.01588	+	1.49831i
$455$	44.1597	+	73.3939i	0.0970542	+	0.161305i
$456$	−259.623	+	14.0764i	−0.569349	+	0.0308692i
$457$	78.5063	+	82.8781i	0.171786	+	0.181352i	0.806204	−	0.591638i	$-0.201519\pi$
$457$	78.5063	+	82.8781i	0.171786	+	0.181352i	−0.634417	+	0.772991i	$0.718760\pi$
$458$	191.001	−	145.195i	0.417033	−	0.317020i
$459$	129.491	−	28.5032i	0.282116	−	0.0620984i
$460$	180.926	−	153.680i	0.393318	−	0.334087i
$461$	−10.6606	+	196.623i	−0.0231249	+	0.426514i	0.963933	+	0.266147i	$0.0857505\pi$
$461$	−10.6606	+	196.623i	−0.0231249	+	0.426514i	−0.987057	+	0.160367i	$0.948732\pi$
$462$	177.654	+	335.090i	0.384532	+	0.725304i
$463$	39.9925	−	181.688i	0.0863768	−	0.392414i	−0.913520	−	0.406794i	$-0.866647\pi$
$463$	39.9925	−	181.688i	0.0863768	−	0.392414i	0.999897	+	0.0143805i	$0.00457763\pi$
$464$	−719.187	+	332.731i	−1.54997	+	0.717093i
$465$	−111.849	+	185.895i	−0.240536	+	0.399773i
$466$	113.350	−	213.800i	0.243239	−	0.458798i
$467$	−198.641	−	168.727i	−0.425356	−	0.361301i	0.408993	−	0.912538i	$-0.365880\pi$
$467$	−198.641	−	168.727i	−0.425356	−	0.361301i	−0.834349	+	0.551237i	$0.814156\pi$
$468$	−2.22897	+	2.35310i	−0.00476277	+	0.00502799i
$469$	50.3936	−	463.361i	0.107449	−	0.987977i
$470$	498.571	−	1251.32i	1.06079	−	2.66238i
$471$			84.0241i			0.178395i
$472$	−379.341	−	136.383i	−0.803689	−	0.288947i
$473$	286.425			0.605550
$474$	−320.465	−	127.685i	−0.676086	−	0.269377i
$475$	613.730	+	66.7471i	1.29206	+	0.140520i
$476$	170.436	+	161.446i	0.358059	+	0.339172i
$477$	65.3112	−	76.8902i	0.136921	−	0.161195i
$478$	−521.092	−	276.266i	−1.09015	−	0.577962i
$479$	641.648	+	386.067i	1.33956	+	0.805984i	0.991326	−	0.131424i	$-0.0419551\pi$
$479$	641.648	+	386.067i	1.33956	+	0.805984i	0.348230	+	0.937409i	$0.386783\pi$
$480$	76.5324	+	165.422i	0.159442	+	0.344629i
$481$	16.4290	+	3.61630i	0.0341559	+	0.00751829i
$482$	626.193	−	331.986i	1.29916	−	0.688769i
$483$	613.000	+	33.2359i	1.26915	+	0.0688114i
$484$	−14.0666	−	16.5605i	−0.0290632	−	0.0342159i
$485$	106.478	+	483.733i	0.219542	+	0.997388i
$486$	−20.9241	−	27.5252i	−0.0430537	−	0.0566362i
$487$	20.7262	−	19.6329i	0.0425589	−	0.0403139i	−0.666125	−	0.745841i	$-0.732048\pi$
$487$	20.7262	−	19.6329i	0.0425589	−	0.0403139i	0.708683	+	0.705527i	$0.249289\pi$
$488$	25.7888	+	475.647i	0.0528459	+	0.974686i
$489$	−156.565	+	94.2023i	−0.320175	+	0.192643i
$490$	−683.543	−	463.453i	−1.39499	−	0.945823i
$491$	−199.835	+	719.742i	−0.406997	+	1.46587i	0.421990	+	0.906601i	$0.361332\pi$
$491$	−199.835	+	719.742i	−0.406997	+	1.46587i	−0.828987	+	0.559269i	$0.811082\pi$
$492$	−18.4812	+	2.00995i	−0.0375635	+	0.00408527i
$493$	−854.758	−	649.770i	−1.73379	−	1.31799i
$494$	51.9627	+	24.0405i	0.105188	+	0.0486650i
$495$	−178.544	+	121.056i	−0.360695	+	0.244557i
$496$	103.364	+	306.773i	0.208395	+	0.618495i
$497$	−53.1377	−	324.125i	−0.106917	−	0.652164i
$498$	57.3031	−	349.534i	0.115067	−	0.701875i
$499$	−438.165	−	147.635i	−0.878085	−	0.295861i	−0.156076	−	0.987745i	$-0.549885\pi$
$499$	−438.165	−	147.635i	−0.878085	−	0.295861i	−0.722009	+	0.691884i	$0.756781\pi$
$500$	−5.55474	−	20.0064i	−0.0111095	−	0.0400127i
$501$	−69.3334	−	174.014i	−0.138390	−	0.347333i
$502$	924.639	−	368.410i	1.84191	−	0.733884i
$503$	96.1431	−	26.6940i	0.191139	−	0.0530696i	−0.170639	−	0.985334i	$-0.554583\pi$
$503$	96.1431	−	26.6940i	0.191139	−	0.0530696i	0.361779	+	0.932264i	$0.382170\pi$
$504$	−65.4798	+	194.337i	−0.129920	+	0.385589i
$505$	−1125.40	−	184.499i	−2.22851	−	0.365345i
$506$	765.151	−	125.440i	1.51216	−	0.247905i
$507$	275.128	−	92.7014i	0.542659	−	0.182843i
$508$	−49.0200	−	72.2991i	−0.0964961	−	0.142321i
$509$	−43.3783	+	93.7606i	−0.0852225	+	0.184205i	−0.945501	−	0.325619i	$-0.894427\pi$
$509$	−43.3783	+	93.7606i	−0.0852225	+	0.184205i	0.860279	+	0.509824i	$0.170290\pi$
$510$	−432.294	+	568.673i	−0.847635	+	1.11504i
$511$	112.626	+	1035.58i	0.220403	+	2.02657i
$512$	−233.875	−	64.9349i	−0.456786	−	0.126826i
$513$	−64.0671	+	94.4919i	−0.124887	+	0.184195i
$514$	438.088	+	728.108i	0.852311	+	1.41655i
$515$	−257.427	+	13.9573i	−0.499857	+	0.0271015i
$516$	−31.7936	−	33.5641i	−0.0616156	−	0.0650468i
$517$	654.692	−	497.684i	1.26633	−	0.962638i
$518$	−310.302	+	68.3027i	−0.599039	+	0.131858i
$519$	−355.615	+	302.062i	−0.685192	+	0.582008i
$520$	−3.16684	+	58.4089i	−0.00609007	+	0.112325i
$521$	−101.628	−	191.691i	−0.195063	−	0.367929i	0.766616	−	0.642106i	$-0.221939\pi$
$521$	−101.628	−	191.691i	−0.195063	−	0.367929i	−0.961679	+	0.274178i	$0.911594\pi$
$522$	−60.1881	+	273.437i	−0.115303	+	0.523826i
$523$	200.437	−	92.7322i	0.383246	−	0.177308i	−0.218801	−	0.975770i	$-0.570214\pi$
$523$	200.437	−	92.7322i	0.383246	−	0.177308i	0.602046	+	0.798461i	$0.294352\pi$
$524$	56.9784	−	94.6989i	0.108737	−	0.180723i
$525$	228.076	−	430.198i	0.434431	−	0.819424i
$526$	−227.490	−	193.232i	−0.432491	−	0.367361i
$527$	−301.639	+	318.436i	−0.572370	+	0.604244i
$528$	−34.8009	+	319.989i	−0.0659107	+	0.606039i
$529$	268.732	−	674.467i	0.508001	−	1.27499i
$530$			543.510i			1.02549i
$531$	−148.472	+	96.3590i	−0.279608	+	0.181467i
$532$	−202.135			−0.379952
$533$	−12.7392	−	5.07577i	−0.0239010	−	0.00952303i
$534$	455.639	+	49.5537i	0.853256	+	0.0927972i
$535$	1073.62	+	1016.99i	2.00677	+	1.90092i
$536$	206.064	−	242.597i	0.384447	−	0.452606i
$537$	−99.2008	−	52.5929i	−0.184731	−	0.0979384i
$538$	−316.697	−	190.550i	−0.588656	−	0.354182i
$539$	−211.711	−	457.606i	−0.392785	−	0.848990i
$540$	34.0043	+	7.48492i	0.0629710	+	0.0138610i
$541$	395.847	−	209.865i	0.731696	−	0.387920i	−0.0605158	−	0.998167i	$-0.519275\pi$
$541$	395.847	−	209.865i	0.731696	−	0.387920i	0.792211	+	0.610247i	$0.208930\pi$
$542$	565.822	+	30.6780i	1.04395	+	0.0566014i
$543$	−185.715	−	218.640i	−0.342016	−	0.402652i
$544$	79.2172	+	359.887i	0.145620	+	0.661558i
$545$	65.3688	+	85.9912i	0.119943	+	0.157782i
$546$	32.7845	−	31.0551i	0.0600448	−	0.0568775i
$547$	−34.4276	−	634.980i	−0.0629390	−	1.16084i	−0.843985	−	0.536368i	$-0.819796\pi$
$547$	−34.4276	−	634.980i	−0.0629390	−	1.16084i	0.781046	−	0.624474i	$-0.214687\pi$
$548$	−34.2306	+	20.5959i	−0.0624646	+	0.0375837i
$549$	173.115	+	117.375i	0.315328	+	0.213798i
$550$	164.526	−	592.568i	0.299138	−	1.07740i
$551$	919.050	−	99.9527i	1.66797	−	0.181402i
$552$	333.754	+	253.713i	0.604627	+	0.459626i
$553$	815.350	+	377.221i	1.47441	+	0.682136i
$554$	−491.147	+	333.006i	−0.886547	+	0.601094i
$555$	−57.7017	−	171.253i	−0.103967	−	0.308563i
$556$	26.6934	+	162.823i	0.0480097	+	0.292847i
$557$	−73.5853	+	448.850i	−0.132110	+	0.805835i	0.834769	+	0.550600i	$0.185601\pi$
$557$	−73.5853	+	448.850i	−0.132110	+	0.805835i	−0.966879	+	0.255235i	$0.917847\pi$
$558$	108.390	+	36.5209i	0.194248	+	0.0654497i
$559$	−9.12359	−	32.8602i	−0.0163213	−	0.0587839i
$560$	−508.191	−	1275.46i	−0.907485	−	2.27762i
$561$	−405.148	+	161.426i	−0.722188	+	0.287746i
$562$	−217.236	+	60.3152i	−0.386541	+	0.107322i
$563$	233.098	−	691.809i	0.414028	−	1.22879i	−0.514488	−	0.857498i	$-0.672018\pi$
$563$	233.098	−	691.809i	0.414028	−	1.22879i	0.928516	−	0.371293i	$-0.121085\pi$
$564$	−130.992	−	21.4750i	−0.232255	−	0.0380763i
$565$	519.815	−	85.2193i	0.920026	−	0.150831i
$566$	−1063.55	+	358.352i	−1.87907	+	0.633131i
$567$	50.5313	+	74.5280i	0.0891204	+	0.131443i
$568$	94.1828	−	203.573i	0.165815	−	0.358403i
$569$	525.022	−	690.654i	0.922710	−	1.21380i	−0.0538483	−	0.998549i	$-0.517149\pi$
$569$	525.022	−	690.654i	0.922710	−	1.21380i	0.976558	−	0.215255i	$-0.0690582\pi$
$570$	−66.4987	−	611.446i	−0.116664	−	1.07271i
$571$	−268.593	−	74.5744i	−0.470390	−	0.130603i	0.0242412	−	0.999706i	$-0.492283\pi$
$571$	−268.593	−	74.5744i	−0.470390	−	0.130603i	−0.494631	+	0.869103i	$0.664697\pi$
$572$	5.98285	−	8.82404i	0.0104595	−	0.0154267i
$573$	13.9952	+	23.2602i	0.0244245	+	0.0405938i
$574$	258.627	−	14.0224i	0.450570	−	0.0244292i
$575$	−684.559	−	722.680i	−1.19054	−	1.25684i
$576$	−103.412	+	78.6114i	−0.179534	+	0.136478i
$577$	16.9818	−	3.73799i	0.0294313	−	0.00647831i	−0.200230	−	0.979749i	$-0.564169\pi$
$577$	16.9818	−	3.73799i	0.0294313	−	0.00647831i	0.229662	+	0.973271i	$0.426238\pi$
$578$	−612.168	+	519.980i	−1.05911	+	0.899620i
$579$	8.18368	−	150.939i	0.0141342	−	0.260689i
$580$	−132.068	−	249.107i	−0.227704	−	0.429495i
$581$	−198.295	+	900.865i	−0.341300	+	1.55054i
$582$	236.998	−	109.647i	0.407214	−	0.188397i
$583$	−171.077	+	284.332i	−0.293443	+	0.487706i
$584$	−333.216	+	628.511i	−0.570575	+	1.07622i
$585$	19.5754	+	16.6275i	0.0334622	+	0.0284230i
$586$	112.729	−	119.006i	0.192370	−	0.203083i
$587$	−16.4628	+	151.373i	−0.0280457	+	0.257876i	0.971718	+	0.236144i	$0.0758836\pi$
$587$	−16.4628	+	151.373i	−0.0280457	+	0.257876i	−0.999764	+	0.0217320i	$0.993082\pi$
$588$	−30.1233	+	75.6038i	−0.0512301	+	0.128578i
$589$		−	377.661i		−	0.641190i
$590$	273.565	−	913.497i	0.463670	−	1.54830i
$591$	−516.164			−0.873375
$592$	−250.497	−	99.8070i	−0.423136	−	0.168593i
$593$	610.274	+	66.3713i	1.02913	+	0.111925i	0.607074	−	0.794645i	$-0.292343\pi$
$593$	610.274	+	66.3713i	1.02913	+	0.111925i	0.422056	+	0.906570i	$0.361309\pi$
$594$	82.5648	+	78.2095i	0.138998	+	0.131666i
$595$	1204.34	−	1417.85i	2.02409	−	2.38295i
$596$	18.4433	+	9.77804i	0.0309452	+	0.0164061i
$597$	369.341	+	222.225i	0.618662	+	0.372236i
$598$	−38.7637	−	83.7865i	−0.0648223	−	0.140111i
$599$	−405.927	−	89.3514i	−0.677675	−	0.149168i	−0.137220	−	0.990541i	$-0.543817\pi$
$599$	−405.927	−	89.3514i	−0.677675	−	0.149168i	−0.540455	+	0.841373i	$0.681748\pi$
$600$	293.787	−	155.756i	0.489645	−	0.259594i
$601$	168.732	+	9.14838i	0.280752	+	0.0152219i	0.193977	−	0.981006i	$-0.437861\pi$
$601$	168.732	+	9.14838i	0.280752	+	0.0152219i	0.0867747	+	0.996228i	$0.472344\pi$
$602$	416.997	+	490.927i	0.692686	+	0.815493i
$603$	−30.0444	−	136.493i	−0.0498248	−	0.226356i
$604$	−15.3016	−	20.1289i	−0.0253337	−	0.0333260i
$605$	−125.002	+	118.408i	−0.206615	+	0.195716i
$606$	32.5504	+	600.357i	0.0537136	+	0.990688i
$607$	783.903	−	471.659i	1.29144	−	0.777033i	0.306823	−	0.951767i	$-0.400734\pi$
$607$	783.903	−	471.659i	1.29144	−	0.777033i	0.984616	+	0.174733i	$0.0559064\pi$
$608$	−262.616	−	178.058i	−0.431934	−	0.292859i
$609$	195.069	−	702.573i	0.320310	−	1.15365i
$610$	−1120.21	+	121.830i	−1.83641	+	0.199721i
$611$	−77.9510	−	59.2568i	−0.127579	−	0.0969833i
$612$	63.8883	+	29.5579i	0.104393	+	0.0482972i
$613$	−30.5880	+	20.7392i	−0.0498989	+	0.0338323i	−0.585882	−	0.810397i	$-0.699252\pi$
$613$	−30.5880	+	20.7392i	−0.0498989	+	0.0338323i	0.535983	+	0.844229i	$0.319941\pi$
$614$	243.418	+	722.438i	0.396446	+	1.17661i
$615$	23.8326	+	145.372i	0.0387521	+	0.236378i
$616$	109.127	−	665.642i	0.177153	−	1.08059i
$617$	−609.618	−	205.404i	−0.988036	−	0.332908i	−0.221536	−	0.975152i	$-0.571107\pi$
$617$	−609.618	−	205.404i	−0.988036	−	0.332908i	−0.766500	+	0.642244i	$0.778004\pi$
$618$	36.3616	+	130.963i	0.0588376	+	0.211914i
$619$	−327.284	−	821.422i	−0.528731	−	1.32701i	−0.914562	−	0.404445i	$-0.867465\pi$
$619$	−327.284	−	821.422i	−0.528731	−	1.32701i	0.385832	−	0.922569i	$-0.373915\pi$
$620$	−107.001	+	42.6331i	−0.172582	+	0.0687630i
$621$	177.371	−	49.2469i	0.285622	−	0.0793026i
$622$	26.0976	−	77.4549i	0.0419575	−	0.124526i
$623$	−1177.88	−	193.103i	−1.89066	−	0.309957i
$624$	37.8193	−	6.20016i	0.0606078	−	0.00993615i
$625$	509.774	−	171.763i	0.815639	−	0.274821i
$626$	−237.132	−	349.744i	−0.378806	−	0.558696i
$627$	157.673	−	340.804i	0.251471	−	0.543546i
$628$	−26.9966	+	35.5134i	−0.0429882	+	0.0565500i
$629$	−39.5021	−	363.216i	−0.0628014	−	0.577449i
$630$	−467.424	−	129.780i	−0.741942	−	0.205999i
$631$	142.276	−	209.842i	0.225478	−	0.332555i	−0.698076	−	0.716023i	$-0.745960\pi$
$631$	142.276	−	209.842i	0.225478	−	0.332555i	0.923554	+	0.383469i	$0.125271\pi$
$632$	316.301	+	525.696i	0.500476	+	0.831798i
$633$	−336.270	+	18.2320i	−0.531233	+	0.0288026i
$634$	914.422	+	965.343i	1.44231	+	1.52262i
$635$	−551.044	+	418.893i	−0.867786	+	0.659673i
$636$	52.3087	−	11.5140i	0.0822464	−	0.0181038i
$637$	−45.7552	+	38.8648i	−0.0718292	+	0.0610123i
$638$	49.8581	−	919.578i	0.0781474	−	1.44134i
$639$	−46.1326	−	87.0154i	−0.0721950	−	0.136174i
$640$	240.929	−	1094.55i	0.376452	−	1.71024i
$641$	545.320	−	252.292i	0.850733	−	0.393591i	0.0544507	−	0.998516i	$-0.482659\pi$
$641$	545.320	−	252.292i	0.850733	−	0.393591i	0.796282	+	0.604926i	$0.206797\pi$
$642$	401.953	−	668.051i	0.626095	−	1.04058i
$643$	−294.245	+	555.005i	−0.457613	+	0.863149i	0.542126	+	0.840297i	$0.317619\pi$
$643$	−294.245	+	555.005i	−0.457613	+	0.863149i	−0.999739	+	0.0228520i	$0.992725\pi$
$644$	248.410	+	211.002i	0.385731	+	0.327642i
$645$	−251.940	+	265.970i	−0.390604	+	0.412356i
$646$	134.445	−	1236.20i	0.208119	−	1.91362i
$647$	323.035	−	810.757i	0.499281	−	1.25310i	−0.436240	−	0.899830i	$-0.643690\pi$
$647$	323.035	−	810.757i	0.499281	−	1.25310i	0.935521	−	0.353271i	$-0.114931\pi$
$648$			61.4918i			0.0948948i
$649$	430.649	−	391.779i	0.663557	−	0.603666i
$650$	−73.2232			−0.112651
$651$	−276.714	−	110.253i	−0.425060	−	0.169360i
$652$	−96.4403	−	10.4885i	−0.147915	−	0.0160867i
$653$	609.916	+	577.743i	0.934021	+	0.884752i	0.993541	−	0.113475i	$-0.0361982\pi$
$653$	609.916	+	577.743i	0.934021	+	0.884752i	−0.0595196	+	0.998227i	$0.518957\pi$
$654$	36.8669	−	43.4031i	0.0563714	−	0.0663655i
$655$	−773.759	−	410.221i	−1.18131	−	0.626291i
$656$	188.347	+	113.325i	0.287114	+	0.172751i
$657$	131.154	+	283.485i	0.199626	+	0.431484i
$658$	1806.16	+	397.567i	2.74493	+	0.604205i
$659$	628.307	−	333.107i	0.953425	−	0.505474i	0.0823387	−	0.996604i	$-0.473761\pi$
$659$	628.307	−	333.107i	0.953425	−	0.505474i	0.871086	+	0.491131i	$0.163416\pi$
$660$	−114.358	−	6.20029i	−0.173269	−	0.00939438i
$661$	563.107	+	662.940i	0.851901	+	1.00294i	0.999903	+	0.0139482i	$0.00444000\pi$
$661$	563.107	+	662.940i	0.851901	+	1.00294i	−0.148002	+	0.988987i	$0.547284\pi$
$662$	16.2446	+	73.8001i	0.0245387	+	0.111481i
$663$	31.4249	+	41.3387i	0.0473980	+	0.0623510i
$664$	−457.333	+	433.209i	−0.688755	+	0.652423i
$665$	86.7175	+	1599.41i	0.130402	+	2.40513i
$666$	−81.6354	+	49.1184i	−0.122576	+	0.0737514i
$667$	−1233.79	−	836.531i	−1.84976	−	1.25417i
$668$	26.6056	−	95.8246i	0.0398287	−	0.143450i
$669$	589.389	−	64.0999i	0.881000	−	0.0958145i
$670$	599.421	+	455.668i	0.894658	+	0.680102i
$671$	−624.374	−	288.866i	−0.930513	−	0.430501i
$672$	−207.131	+	140.439i	−0.308231	+	0.208986i
$673$	252.411	+	749.128i	0.375053	+	1.11312i	0.954526	+	0.298126i	$0.0963616\pi$
$673$	252.411	+	749.128i	0.375053	+	1.11312i	−0.579474	+	0.814991i	$0.696742\pi$
$674$	103.827	+	633.316i	0.154046	+	0.939638i
$675$	23.6209	−	144.081i	0.0349940	−	0.213454i
$676$	146.069	+	49.2165i	0.216079	+	0.0728055i
$677$	318.725	+	1147.94i	0.470790	+	1.69563i	0.693255	+	0.720692i	$0.256176\pi$
$677$	318.725	+	1147.94i	0.470790	+	1.69563i	−0.222465	+	0.974941i	$0.571410\pi$
$678$	−102.791	−	257.986i	−0.151609	−	0.380510i
$679$	−631.762	+	251.717i	−0.930429	+	0.370717i
$680$	1224.12	−	339.875i	1.80017	−	0.499816i
$681$	204.923	−	608.188i	0.300914	−	0.893081i
$682$	−371.258	−	60.8647i	−0.544367	−	0.0892444i
$683$	−1146.84	+	188.014i	−1.67912	+	0.275277i	−0.924582	−	0.380983i	$-0.875585\pi$
$683$	−1146.84	+	188.014i	−1.67912	+	0.275277i	−0.754534	+	0.656261i	$0.772137\pi$
$684$	−57.4383	+	19.3532i	−0.0839741	+	0.0282942i
$685$	177.652	+	262.017i	0.259346	+	0.382507i
$686$	19.5369	−	42.2283i	0.0284794	−	0.0615572i
$687$	−113.383	+	149.153i	−0.165041	+	0.217108i
$688$	59.1031	+	543.444i	0.0859056	+	0.789889i
$689$	38.0695	+	10.5699i	0.0552532	+	0.0153410i
$690$	−556.546	+	820.844i	−0.806588	+	1.18963i
$691$	−113.643	−	188.876i	−0.164462	−	0.273338i	0.763657	−	0.645623i	$-0.223402\pi$
$691$	−113.643	−	188.876i	−0.164462	−	0.273338i	−0.928119	+	0.372285i	$0.878574\pi$
$692$	−247.354	+	13.4112i	−0.357449	+	0.0193803i
$693$	−203.679	−	215.021i	−0.293908	−	0.310275i
$694$	−620.475	+	471.673i	−0.894056	+	0.679644i
$695$	1276.90	−	281.067i	1.83726	−	0.404412i
$696$	379.516	−	322.363i	0.545281	−	0.463166i
$697$	−16.1243	+	297.395i	−0.0231338	+	0.426678i
$698$	661.414	+	1247.56i	0.947584	+	1.78733i
$699$	−40.6229	+	184.552i	−0.0581157	+	0.264022i
$700$	234.619	−	108.546i	0.335170	−	0.155066i
$701$	−236.167	+	392.512i	−0.336900	+	0.559932i	−0.978279	−	0.207292i	$-0.933535\pi$
$701$	−236.167	+	392.512i	−0.336900	+	0.559932i	0.641379	+	0.767224i	$0.278362\pi$
$702$	6.34264	−	11.9635i	0.00903510	−	0.0170420i
$703$	239.761	+	203.655i	0.341054	+	0.289694i
$704$	293.831	−	310.194i	0.417374	−	0.440616i
$705$	−113.727	+	1045.70i	−0.161314	+	1.48326i
$706$	50.9155	−	127.788i	0.0721182	−	0.181003i
$707$		−	1565.79i		−	2.21469i
$708$	−93.7125	−	6.97656i	−0.132362	−	0.00985390i
$709$	6.99813			0.00987043			0.00493521	−	0.999988i	$-0.498429\pi$
$709$	6.99813			0.00987043			0.00493521	+	0.999988i	$0.498429\pi$
$710$	492.915	+	196.395i	0.694247	+	0.276613i
$711$	267.805	+	29.1256i	0.376660	+	0.0409643i
$712$	−591.778	−	560.562i	−0.831148	−	0.787306i
$713$	−394.228	+	464.121i	−0.552914	+	0.650941i
$714$	−866.521	−	459.401i	−1.21362	−	0.643418i
$715$	−72.3878	−	43.5543i	−0.101242	−	0.0609151i
$716$	−25.0300	−	54.1016i	−0.0349582	−	0.0755608i
$717$	449.806	+	99.0098i	0.627344	+	0.138089i
$718$	−316.047	+	167.557i	−0.440177	+	0.233367i
$719$	−1042.19	−	56.5061i	−1.44951	−	0.0785899i	−0.687511	−	0.726174i	$-0.741297\pi$
$719$	−1042.19	−	56.5061i	−1.44951	−	0.0785899i	−0.761994	+	0.647584i	$0.775780\pi$
$720$	−266.525	−	313.778i	−0.370174	−	0.435802i
$721$	−76.0918	−	345.689i	−0.105536	−	0.479457i
$722$	163.376	+	214.918i	0.226283	+	0.297670i
$723$	−401.815	+	380.620i	−0.555761	+	0.526445i
$724$	−8.24550	−	152.079i	−0.0113888	−	0.210054i
$725$	−1013.07	+	609.545i	−1.39734	+	0.840752i
$726$	75.1332	+	50.9416i	0.103489	+	0.0701675i
$727$	−210.985	+	759.898i	−0.290213	+	1.04525i	0.664394	+	0.747382i	$0.268690\pi$
$727$	−210.985	+	759.898i	−0.290213	+	1.04525i	−0.954607	+	0.297869i	$0.903724\pi$
$728$	−79.8420	+	8.68334i	−0.109673	+	0.0119277i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	−1527.26	−	706.587i	−2.09214	−	0.967927i
$731$	−613.050	+	415.658i	−0.838645	+	0.568616i
$732$	35.4563	+	105.231i	0.0484376	+	0.143758i
$733$	−167.037	−	1018.88i	−0.227881	−	1.39001i	−0.814506	−	0.580155i	$-0.802992\pi$
$733$	−167.037	−	1018.88i	−0.227881	−	1.39001i	0.586625	−	0.809859i	$-0.300456\pi$
$734$	213.821	−	1304.25i	0.291309	−	1.77690i
$735$	611.146	+	205.919i	0.831491	+	0.280162i
$736$	136.869	+	492.958i	0.185964	+	0.669780i
$737$	170.154	+	427.054i	0.230874	+	0.579450i
$738$	72.1486	−	28.7466i	0.0977624	−	0.0389521i
$739$	948.634	−	263.387i	1.28367	−	0.356410i	0.442301	−	0.896867i	$-0.354162\pi$
$739$	948.634	−	263.387i	1.28367	−	0.356410i	0.841372	+	0.540457i	$0.181748\pi$
$740$	30.6347	−	90.9204i	0.0413982	−	0.122865i
$741$	−44.1212	−	7.23330i	−0.0595427	−	0.00976154i
$742$	−736.405	+	120.728i	−0.992460	+	0.162706i
$743$	−1078.00	+	363.221i	−1.45088	+	0.488857i	−0.930884	−	0.365315i	$-0.880961\pi$
$743$	−1078.00	+	363.221i	−1.45088	+	0.488857i	−0.519991	+	0.854172i	$0.674065\pi$
$744$	−114.156	−	168.368i	−0.153436	−	0.226301i
$745$	69.4573	−	150.130i	0.0932313	−	0.201516i
$746$	−328.821	+	432.556i	−0.440779	+	0.579834i
$747$	29.9052	+	274.974i	0.0400338	+	0.368105i
$748$	−223.104	−	61.9445i	−0.298267	−	0.0828135i
$749$	−1139.45	+	1680.56i	−1.52129	+	2.24374i
$750$	44.7206	+	74.3262i	0.0596274	+	0.0991015i
$751$	719.248	−	38.9965i	0.957720	−	0.0519261i	0.431353	−	0.902183i	$-0.358036\pi$
$751$	719.248	−	38.9965i	0.957720	−	0.0519261i	0.526367	+	0.850257i	$0.323554\pi$
$752$	1079.37	+	1139.47i	1.43533	+	1.51526i
$753$	−618.769	+	470.376i	−0.821738	+	0.624669i
$754$	−107.087	+	23.5716i	−0.142025	+	0.0312621i
$755$	−152.707	+	129.711i	−0.202261	+	0.171802i
$756$	−2.58813	+	47.7353i	−0.00342346	+	0.0631419i
$757$	−65.9803	−	124.452i	−0.0871602	−	0.164402i	0.836100	−	0.548577i	$-0.184830\pi$
$757$	−65.9803	−	124.452i	−0.0871602	−	0.164402i	−0.923260	+	0.384176i	$0.874486\pi$
$758$	48.1226	−	218.623i	0.0634863	−	0.288421i
$759$	−549.523	+	254.237i	−0.724010	+	0.334963i
$760$	−563.944	+	937.282i	−0.742032	+	1.23327i
$761$	561.578	−	1059.25i	0.737947	−	1.39192i	−0.175303	−	0.984515i	$-0.556090\pi$
$761$	561.578	−	1059.25i	0.737947	−	1.39192i	0.913249	−	0.407401i	$-0.133565\pi$
$762$	278.133	+	236.248i	0.365004	+	0.310037i
$763$	−101.990	+	107.669i	−0.133670	+	0.141113i
$764$	−1.55823	+	14.3277i	−0.00203957	+	0.0187535i
$765$	206.471	−	518.203i	0.269897	−	0.677390i
$766$		−	221.180i		−	0.288747i
$767$	−58.6645	−	36.9268i	−0.0764857	−	0.0481445i
$768$	−290.883			−0.378754
$769$	1037.96	+	413.563i	1.34976	+	0.537793i	0.929235	−	0.369488i	$-0.120467\pi$
$769$	1037.96	+	413.563i	1.34976	+	0.537793i	0.420524	+	0.907281i	$0.361846\pi$
$770$	1586.27	+	172.517i	2.06009	+	0.224048i
$771$	−481.746	−	456.334i	−0.624833	−	0.591873i
$772$	51.9550	−	61.1661i	0.0672992	−	0.0792307i
$773$	304.659	+	161.520i	0.394126	+	0.208952i	0.653671	−	0.756779i	$-0.273228\pi$
$773$	304.659	+	161.520i	0.394126	+	0.208952i	−0.259546	+	0.965731i	$0.583573\pi$

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.g (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06048 - 0.820970i) q^{2} +(1.72190 + 0.187268i) q^{3} +(0.667604 + 0.632388i) q^{4} +(4.71743 - 5.55378i) q^{5} +(-3.39419 - 1.79949i) q^{6} +(8.57272 + 5.15803i) q^{7} +(2.86886 + 6.20094i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(-2.06048 - 0.820970i) q^{2} +(1.72190 + 0.187268i) q^{3} +(0.667604 + 0.632388i) q^{4} +(4.71743 - 5.55378i) q^{5} +(-3.39419 - 1.79949i) q^{6} +(8.57272 + 5.15803i) q^{7} +(2.86886 + 6.20094i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-14.2797 + 7.57059i) q^{10} +(-9.85322 - 0.534226i) q^{11} +(1.03112 + 1.21393i) q^{12} +(0.252568 + 1.14743i) q^{13} +(-13.4293 - 17.6660i) q^{14} +(9.16297 - 8.67962i) q^{15} +(-1.01958 - 18.8051i) q^{16} +(21.8646 - 13.1555i) q^{17} +(-5.50747 - 3.73416i) q^{18} +(-5.87781 + 21.1699i) q^{19} +(6.66152 - 0.724484i) q^{20} +(13.7954 + 10.4870i) q^{21} +(19.8638 + 9.18996i) q^{22} +(29.3221 - 19.8809i) q^{23} +(3.77865 + 11.2146i) q^{24} +(-4.54585 - 27.7285i) q^{25} +(0.421593 - 2.57161i) q^{26} +(4.92415 + 1.65914i) q^{27} +(2.46130 + 8.86481i) q^{28} +(-15.5744 - 39.0887i) q^{29} +(-26.0058 + 10.3617i) q^{30} +(-16.5627 + 4.59860i) q^{31} +(-4.61115 + 13.6854i) q^{32} +(-16.8662 - 2.76507i) q^{33} +(-55.8518 + 9.15643i) q^{34} +(69.0877 - 23.2784i) q^{35} +(1.54815 + 2.28336i) q^{36} +(6.01201 - 12.9948i) q^{37} +(29.4910 - 38.7947i) q^{38} +(0.220020 + 2.02305i) q^{39} +(47.9723 + 13.3194i) q^{40} +(-6.55007 + 9.66063i) q^{41} +(-19.8156 - 32.9339i) q^{42} +(-28.9840 + 1.57147i) q^{43} +(-6.24021 - 6.58771i) q^{44} +(17.4031 - 13.2295i) q^{45} +(-76.7391 + 16.8916i) q^{46} +(-63.5192 + 53.9537i) q^{47} +(1.76596 - 32.5713i) q^{48} +(23.9341 + 45.1446i) q^{49} +(-13.3976 + 60.8659i) q^{50} +(40.1121 - 18.5579i) q^{51} +(-0.557005 + 0.925750i) q^{52} +(15.7517 - 29.7108i) q^{53} +(-8.78401 - 7.46121i) q^{54} +(-49.4488 + 52.2025i) q^{55} +(-7.39072 + 67.9566i) q^{56} +(-14.0854 + 35.3518i) q^{57} +93.3277i q^{58} +(-41.4288 + 42.0078i) q^{59} +11.6061 q^{60} +(64.7667 + 25.8054i) q^{61} +(37.9024 + 4.12213i) q^{62} +(21.7904 + 20.6410i) q^{63} +(-28.0316 + 33.0013i) q^{64} +(7.56404 + 4.01020i) q^{65} +(32.4824 + 19.5440i) q^{66} +(-19.5613 - 42.2811i) q^{67} +(22.9162 + 5.04425i) q^{68} +(54.2126 - 28.7417i) q^{69} +(-161.465 - 8.75437i) q^{70} +(-21.2533 - 25.0213i) q^{71} +(4.40631 + 20.0181i) q^{72} +(63.0095 + 82.8876i) q^{73} +(-23.0559 + 21.8397i) q^{74} +(-2.63484 - 48.5968i) q^{75} +(-17.3117 + 10.4161i) q^{76} +(-81.7133 - 55.4030i) q^{77} +(1.20752 - 4.34909i) q^{78} +(89.2685 - 9.70853i) q^{79} +(-109.249 - 83.0489i) q^{80} +(8.16818 + 3.77900i) q^{81} +(21.4274 - 14.5281i) q^{82} +(29.4391 + 87.3722i) q^{83} +(2.57802 + 15.7252i) q^{84} +(30.0818 - 183.491i) q^{85} +(61.0111 + 20.5570i) q^{86} +(-19.4974 - 70.2234i) q^{87} +(-24.9548 - 62.6318i) q^{88} +(-110.829 + 44.1584i) q^{89} +(-46.7198 + 12.9717i) q^{90} +(-3.75328 + 11.1393i) q^{91} +(32.1480 + 5.27039i) q^{92} +(-29.3804 + 4.81667i) q^{93} +(175.174 - 59.0232i) q^{94} +(89.8452 + 132.512i) q^{95} +(-10.5028 + 22.7013i) q^{96} +(-41.1357 + 54.1131i) q^{97} +(-12.2535 - 112.669i) q^{98} +(-28.5240 - 7.91966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) \)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) \)

Introduction

L-functions

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