LMFDB - Embedded newform 187.2.g.f.86.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.8
Character	$\chi$	$=$	187.86
Dual form			187.2.g.f.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.648313 - 1.99530i) q^{2} +(-2.15638 + 1.56670i) q^{3} +(-1.94289 - 1.41159i) q^{4} +(1.10893 + 3.41293i) q^{5} +(1.72804 + 5.31835i) q^{6} +(0.243832 + 0.177154i) q^{7} +(-0.681533 + 0.495163i) q^{8} +(1.26837 - 3.90365i) q^{9} +O(q^{10})$	\(q+(0.648313 - 1.99530i) q^{2} +(-2.15638 + 1.56670i) q^{3} +(-1.94289 - 1.41159i) q^{4} +(1.10893 + 3.41293i) q^{5} +(1.72804 + 5.31835i) q^{6} +(0.243832 + 0.177154i) q^{7} +(-0.681533 + 0.495163i) q^{8} +(1.26837 - 3.90365i) q^{9} +7.52877 q^{10} +(3.21836 + 0.801361i) q^{11} +6.40114 q^{12} +(-1.93381 + 5.95165i) q^{13} +(0.511555 - 0.371666i) q^{14} +(-7.73833 - 5.62223i) q^{15} +(-0.938080 - 2.88711i) q^{16} +(0.309017 + 0.951057i) q^{17} +(-6.96666 - 5.06158i) q^{18} +(1.61571 - 1.17388i) q^{19} +(2.66314 - 8.19629i) q^{20} -0.803342 q^{21} +(3.68546 - 5.90206i) q^{22} -1.86690 q^{23} +(0.693872 - 2.13552i) q^{24} +(-6.37331 + 4.63048i) q^{25} +(10.6216 + 7.71707i) q^{26} +(0.909773 + 2.79999i) q^{27} +(-0.223668 - 0.688380i) q^{28} +(-2.05847 - 1.49557i) q^{29} +(-16.2349 + 11.7953i) q^{30} +(2.14084 - 6.58884i) q^{31} -8.05367 q^{32} +(-8.19550 + 3.31417i) q^{33} +2.09798 q^{34} +(-0.334223 + 1.02863i) q^{35} +(-7.97466 + 5.79393i) q^{36} +(8.01667 + 5.82445i) q^{37} +(-1.29477 - 3.98488i) q^{38} +(-5.15444 - 15.8637i) q^{39} +(-2.44573 - 1.77693i) q^{40} +(-3.24656 + 2.35876i) q^{41} +(-0.520817 + 1.60291i) q^{42} +3.66154 q^{43} +(-5.12170 - 6.09995i) q^{44} +14.7294 q^{45} +(-1.21033 + 3.72503i) q^{46} +(4.51530 - 3.28056i) q^{47} +(6.54611 + 4.75603i) q^{48} +(-2.13505 - 6.57100i) q^{49} +(5.10731 + 15.7187i) q^{50} +(-2.15638 - 1.56670i) q^{51} +(12.1585 - 8.83364i) q^{52} +(4.10427 - 12.6316i) q^{53} +6.17665 q^{54} +(0.833937 + 11.8727i) q^{55} -0.253899 q^{56} +(-1.64497 + 5.06269i) q^{57} +(-4.31864 + 3.13768i) q^{58} +(-5.89867 - 4.28563i) q^{59} +(7.09842 + 21.8467i) q^{60} +(0.823404 + 2.53418i) q^{61} +(-11.7588 - 8.54326i) q^{62} +(1.00082 - 0.727136i) q^{63} +(-3.34514 + 10.2953i) q^{64} -22.4571 q^{65} +(1.29952 + 18.5011i) q^{66} -0.815639 q^{67} +(0.742116 - 2.28400i) q^{68} +(4.02575 - 2.92488i) q^{69} +(1.83575 + 1.33375i) q^{70} +(-2.28220 - 7.02390i) q^{71} +(1.06850 + 3.28852i) q^{72} +(5.66806 + 4.11809i) q^{73} +(16.8188 - 12.2196i) q^{74} +(6.48870 - 19.9702i) q^{75} -4.79619 q^{76} +(0.642773 + 0.765542i) q^{77} -34.9947 q^{78} +(-0.496343 + 1.52759i) q^{79} +(8.81326 - 6.40321i) q^{80} +(3.61336 + 2.62526i) q^{81} +(2.60166 + 8.00708i) q^{82} +(-1.82421 - 5.61434i) q^{83} +(1.56080 + 1.13399i) q^{84} +(-2.90322 + 2.10931i) q^{85} +(2.37382 - 7.30587i) q^{86} +6.78196 q^{87} +(-2.59022 + 1.04746i) q^{88} -2.19294 q^{89} +(9.54929 - 29.3897i) q^{90} +(-1.52588 + 1.10862i) q^{91} +(3.62717 + 2.63529i) q^{92} +(5.70628 + 17.5621i) q^{93} +(-3.61837 - 11.1362i) q^{94} +(5.79810 + 4.21257i) q^{95} +(17.3668 - 12.6177i) q^{96} +(-2.10722 + 6.48535i) q^{97} -14.4953 q^{98} +(7.21032 - 11.5469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.648313	−	1.99530i	0.458426	−	1.41089i	−0.408639	−	0.912696i	$-0.633996\pi$
$2$	0.648313	−	1.99530i	0.458426	−	1.41089i	0.867065	−	0.498195i	$-0.166004\pi$
$3$	−2.15638	+	1.56670i	−1.24499	+	0.904537i	−0.997920	−	0.0644617i	$-0.979467\pi$
$3$	−2.15638	+	1.56670i	−1.24499	+	0.904537i	−0.247068	+	0.968998i	$0.579467\pi$
$4$	−1.94289	−	1.41159i	−0.971443	−	0.705794i
$5$	1.10893	+	3.41293i	0.495928	+	1.52631i	0.815505	+	0.578750i	$0.196459\pi$
$5$	1.10893	+	3.41293i	0.495928	+	1.52631i	−0.319576	+	0.947560i	$0.603541\pi$
$6$	1.72804	+	5.31835i	0.705468	+	2.17121i
$7$	0.243832	+	0.177154i	0.0921597	+	0.0669579i	0.632911	−	0.774225i	$-0.281860\pi$
$7$	0.243832	+	0.177154i	0.0921597	+	0.0669579i	−0.540751	+	0.841183i	$0.681860\pi$
$8$	−0.681533	+	0.495163i	−0.240958	+	0.175066i
$9$	1.26837	−	3.90365i	0.422791	−	1.30122i
$10$	7.52877			2.38081
$11$	3.21836	+	0.801361i	0.970371	+	0.241620i
$11$	3.21836	+	0.801361i	0.970371	+	0.241620i
$12$	6.40114			1.84785
$13$	−1.93381	+	5.95165i	−0.536342	+	1.65069i	0.204388	+	0.978890i	$0.434479\pi$
$13$	−1.93381	+	5.95165i	−0.536342	+	1.65069i	−0.740731	+	0.671802i	$0.765521\pi$
$14$	0.511555	−	0.371666i	0.136719	−	0.0993320i
$15$	−7.73833	−	5.62223i	−1.99803	−	1.45165i
$16$	−0.938080	−	2.88711i	−0.234520	−	0.721778i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−6.96666	−	5.06158i	−1.64206	−	1.19302i
$19$	1.61571	−	1.17388i	0.370670	−	0.269308i	−0.386819	−	0.922156i	$-0.626426\pi$
$19$	1.61571	−	1.17388i	0.370670	−	0.269308i	0.757489	+	0.652848i	$0.226426\pi$
$20$	2.66314	−	8.19629i	0.595496	−	1.83275i
$21$	−0.803342			−0.175304
$22$	3.68546	−	5.90206i	0.785743	−	1.25832i
$23$	−1.86690			−0.389275			−0.194638	−	0.980875i	$-0.562353\pi$
$23$	−1.86690			−0.389275			−0.194638	+	0.980875i	$0.562353\pi$
$24$	0.693872	−	2.13552i	0.141636	−	0.435911i
$25$	−6.37331	+	4.63048i	−1.27466	+	0.926096i
$26$	10.6216	+	7.71707i	2.08307	+	1.51344i
$27$	0.909773	+	2.79999i	0.175086	+	0.538859i
$28$	−0.223668	−	0.688380i	−0.0422693	−	0.130092i
$29$	−2.05847	−	1.49557i	−0.382249	−	0.277720i	0.380023	−	0.924977i	$-0.375916\pi$
$29$	−2.05847	−	1.49557i	−0.382249	−	0.277720i	−0.762272	+	0.647257i	$0.775916\pi$
$30$	−16.2349	+	11.7953i	−2.96407	+	2.15353i
$31$	2.14084	−	6.58884i	0.384507	−	1.18339i	−0.552331	−	0.833625i	$-0.686261\pi$
$31$	2.14084	−	6.58884i	0.384507	−	1.18339i	0.936837	−	0.349765i	$-0.113739\pi$
$32$	−8.05367			−1.42370
$33$	−8.19550	+	3.31417i	−1.42665	+	0.576923i
$34$	2.09798			0.359801
$35$	−0.334223	+	1.02863i	−0.0564940	+	0.173871i
$36$	−7.97466	+	5.79393i	−1.32911	+	0.965655i
$37$	8.01667	+	5.82445i	1.31793	+	0.957534i	0.999955	+	0.00943537i	$0.00300342\pi$
$37$	8.01667	+	5.82445i	1.31793	+	0.957534i	0.317977	+	0.948098i	$0.396997\pi$
$38$	−1.29477	−	3.98488i	−0.210039	−	0.646433i
$39$	−5.15444	−	15.8637i	−0.825372	−	2.54023i
$40$	−2.44573	−	1.77693i	−0.386704	−	0.280957i
$41$	−3.24656	+	2.35876i	−0.507027	+	0.368377i	−0.811695	−	0.584082i	$-0.801455\pi$
$41$	−3.24656	+	2.35876i	−0.507027	+	0.368377i	0.304668	+	0.952459i	$0.401455\pi$
$42$	−0.520817	+	1.60291i	−0.0803638	+	0.247334i
$43$	3.66154			0.558379			0.279189	−	0.960236i	$-0.409934\pi$
$43$	3.66154			0.558379			0.279189	+	0.960236i	$0.409934\pi$
$44$	−5.12170	−	6.09995i	−0.772126	−	0.919602i
$45$	14.7294			2.19574
$46$	−1.21033	+	3.72503i	−0.178454	+	0.549225i
$47$	4.51530	−	3.28056i	0.658624	−	0.478518i	−0.207574	−	0.978219i	$-0.566557\pi$
$47$	4.51530	−	3.28056i	0.658624	−	0.478518i	0.866198	+	0.499701i	$0.166557\pi$
$48$	6.54611	+	4.75603i	0.944849	+	0.686473i
$49$	−2.13505	−	6.57100i	−0.305007	−	0.938715i
$50$	5.10731	+	15.7187i	0.722283	+	2.22296i
$51$	−2.15638	−	1.56670i	−0.301954	−	0.219382i
$52$	12.1585	−	8.83364i	1.68607	−	1.22501i
$53$	4.10427	−	12.6316i	0.563765	−	1.73509i	−0.107829	−	0.994169i	$-0.534390\pi$
$53$	4.10427	−	12.6316i	0.563765	−	1.73509i	0.671594	−	0.740919i	$-0.265610\pi$
$54$	6.17665			0.840536
$55$	0.833937	+	11.8727i	0.112448	+	1.60091i
$56$	−0.253899			−0.0339287
$57$	−1.64497	+	5.06269i	−0.217881	+	0.670569i
$58$	−4.31864	+	3.13768i	−0.567066	+	0.411997i
$59$	−5.89867	−	4.28563i	−0.767941	−	0.557942i	0.133395	−	0.991063i	$-0.457412\pi$
$59$	−5.89867	−	4.28563i	−0.767941	−	0.557942i	−0.901336	+	0.433121i	$0.857412\pi$
$60$	7.09842	+	21.8467i	0.916402	+	2.82039i
$61$	0.823404	+	2.53418i	0.105426	+	0.324468i	0.989830	−	0.142254i	$-0.0454349\pi$
$61$	0.823404	+	2.53418i	0.105426	+	0.324468i	−0.884404	+	0.466722i	$0.845435\pi$
$62$	−11.7588	−	8.54326i	−1.49337	−	1.08499i
$63$	1.00082	−	0.727136i	0.126091	−	0.0916106i
$64$	−3.34514	+	10.2953i	−0.418142	+	1.28691i
$65$	−22.4571			−2.78546
$66$	1.29952	+	18.5011i	0.159959	+	2.27733i
$67$	−0.815639			−0.0996461			−0.0498231	−	0.998758i	$-0.515866\pi$
$67$	−0.815639			−0.0996461			−0.0498231	+	0.998758i	$0.515866\pi$
$68$	0.742116	−	2.28400i	0.0899948	−	0.276976i
$69$	4.02575	−	2.92488i	0.484643	−	0.352114i
$70$	1.83575	+	1.33375i	0.219414	+	0.159414i
$71$	−2.28220	−	7.02390i	−0.270848	−	0.833584i	−0.990288	−	0.139030i	$-0.955602\pi$
$71$	−2.28220	−	7.02390i	−0.270848	−	0.833584i	0.719440	−	0.694554i	$-0.244398\pi$
$72$	1.06850	+	3.28852i	0.125924	+	0.387556i
$73$	5.66806	+	4.11809i	0.663396	+	0.481986i	0.867808	−	0.496899i	$-0.165528\pi$
$73$	5.66806	+	4.11809i	0.663396	+	0.481986i	−0.204412	+	0.978885i	$0.565528\pi$
$74$	16.8188	−	12.2196i	1.95515	−	1.42050i
$75$	6.48870	−	19.9702i	0.749251	−	2.30596i
$76$	−4.79619			−0.550161
$77$	0.642773	+	0.765542i	0.0732507	+	0.0872416i
$78$	−34.9947			−3.96236
$79$	−0.496343	+	1.52759i	−0.0558430	+	0.171867i	−0.975088	−	0.221819i	$-0.928800\pi$
$79$	−0.496343	+	1.52759i	−0.0558430	+	0.171867i	0.919245	+	0.393686i	$0.128800\pi$
$80$	8.81326	−	6.40321i	0.985353	−	0.715901i
$81$	3.61336	+	2.62526i	0.401484	+	0.291695i
$82$	2.60166	+	8.00708i	0.287305	+	0.884234i
$83$	−1.82421	−	5.61434i	−0.200233	−	0.616254i	−0.999876	−	0.0157773i	$-0.994978\pi$
$83$	−1.82421	−	5.61434i	−0.200233	−	0.616254i	0.799643	−	0.600476i	$-0.205022\pi$
$84$	1.56080	+	1.13399i	0.170297	+	0.123728i
$85$	−2.90322	+	2.10931i	−0.314898	+	0.228787i
$86$	2.37382	−	7.30587i	0.255976	−	0.787812i
$87$	6.78196			0.727103
$88$	−2.59022	+	1.04746i	−0.276118	+	0.111659i
$89$	−2.19294			−0.232451			−0.116226	−	0.993223i	$-0.537080\pi$
$89$	−2.19294			−0.232451			−0.116226	+	0.993223i	$0.537080\pi$
$90$	9.54929	−	29.3897i	1.00658	−	3.09795i
$91$	−1.52588	+	1.10862i	−0.159956	+	0.116215i
$92$	3.62717	+	2.63529i	0.378159	+	0.274748i
$93$	5.70628	+	17.5621i	0.591714	+	1.82111i
$94$	−3.61837	−	11.1362i	−0.373207	−	1.14861i
$95$	5.79810	+	4.21257i	0.594873	+	0.432200i
$96$	17.3668	−	12.6177i	1.77249	−	1.28779i
$97$	−2.10722	+	6.48535i	−0.213956	+	0.658488i	0.785271	+	0.619153i	$0.212524\pi$
$97$	−2.10722	+	6.48535i	−0.213956	+	0.658488i	−0.999226	+	0.0393347i	$0.987476\pi$
$98$	−14.4953			−1.46425
$99$	7.21032	−	11.5469i	0.724664	−	1.16051i
$100$	18.9189			1.89189
$101$	3.49426	−	10.7542i	0.347692	−	1.07009i	−0.612434	−	0.790521i	$-0.709810\pi$
$101$	3.49426	−	10.7542i	0.347692	−	1.07009i	0.960127	−	0.279565i	$-0.0901904\pi$
$102$	−4.52406	+	3.28692i	−0.447948	+	0.325453i
$103$	1.15926	+	0.842254i	0.114226	+	0.0829897i	0.643432	−	0.765504i	$-0.277510\pi$
$103$	1.15926	+	0.842254i	0.114226	+	0.0829897i	−0.529206	+	0.848493i	$0.677510\pi$
$104$	−1.62908	−	5.01380i	−0.159745	−	0.491643i
$105$	−0.890850	−	2.74175i	−0.0869380	−	0.267568i
$106$	−22.5431	−	16.3785i	−2.18958	−	1.59082i
$107$	−11.4567	+	8.32382i	−1.10757	+	0.804694i	−0.982279	−	0.187427i	$-0.939985\pi$
$107$	−11.4567	+	8.32382i	−1.10757	+	0.804694i	−0.125287	+	0.992121i	$0.539985\pi$
$108$	2.18486	−	6.72429i	0.210238	−	0.647045i
$109$	6.22837			0.596569			0.298285	−	0.954477i	$-0.403586\pi$
$109$	6.22837			0.596569			0.298285	+	0.954477i	$0.403586\pi$
$110$	24.2303	+	6.03326i	2.31026	+	0.575249i
$111$	−26.4122			−2.50693
$112$	0.282730	−	0.870154i	0.0267155	−	0.0822218i
$113$	3.38576	−	2.45990i	0.318505	−	0.231408i	−0.417032	−	0.908892i	$-0.636930\pi$
$113$	3.38576	−	2.45990i	0.318505	−	0.231408i	0.735537	+	0.677484i	$0.236930\pi$
$114$	9.03514	+	6.56441i	0.846218	+	0.614813i
$115$	−2.07026	−	6.37160i	−0.193053	−	0.594155i
$116$	1.88825	+	5.81143i	0.175320	+	0.539578i
$117$	20.7804	+	15.0978i	1.92115	+	1.39580i
$118$	−12.3753	+	8.99119i	−1.13924	+	0.827706i
$119$	−0.0931354	+	0.286641i	−0.00853771	+	0.0262764i
$120$	8.05784			0.735577
$121$	9.71564	+	5.15813i	0.883240	+	0.468921i
$122$	5.59027			0.506119
$123$	3.30534	−	10.1728i	0.298032	−	0.917249i
$124$	−13.4601	+	9.77937i	−1.20876	+	0.878213i
$125$	−8.35501	−	6.07027i	−0.747295	−	0.542941i
$126$	−0.802014	−	2.46834i	−0.0714491	−	0.219898i
$127$	3.89031	+	11.9731i	0.345209	+	1.06244i	0.961472	+	0.274903i	$0.0886458\pi$
$127$	3.89031	+	11.9731i	0.345209	+	1.06244i	−0.616263	+	0.787540i	$0.711354\pi$
$128$	5.34238	+	3.88146i	0.472204	+	0.343076i
$129$	−7.89567	+	5.73654i	−0.695175	+	0.505074i
$130$	−14.5592	+	44.8086i	−1.27693	+	3.92998i
$131$	3.94812			0.344948			0.172474	−	0.985014i	$-0.444824\pi$
$131$	3.94812			0.344948			0.172474	+	0.985014i	$0.444824\pi$
$132$	20.6012	+	5.12963i	1.79310	+	0.446477i
$133$	0.601920			0.0521931
$134$	−0.528789	+	1.62745i	−0.0456804	+	0.140590i
$135$	−8.54732	+	6.20999i	−0.735636	+	0.534471i
$136$	−0.681533	−	0.495163i	−0.0584410	−	0.0424598i
$137$	−2.41983	−	7.44748i	−0.206740	−	0.636281i	−0.999637	−	0.0269257i	$-0.991428\pi$
$137$	−2.41983	−	7.44748i	−0.206740	−	0.636281i	0.792897	−	0.609355i	$-0.208572\pi$
$138$	−3.22607	−	9.92882i	−0.274621	−	0.845197i
$139$	15.4061	+	11.1932i	1.30673	+	0.949394i	0.999997	−	0.00240199i	$-0.000764579\pi$
$139$	15.4061	+	11.1932i	1.30673	+	0.949394i	0.306732	+	0.951796i	$0.400765\pi$
$140$	2.10136	−	1.52673i	0.177598	−	0.129032i
$141$	−4.59705	+	14.1483i	−0.387141	+	1.19150i
$142$	−15.4944			−1.30026
$143$	−10.9931	+	17.6049i	−0.919291	+	1.47219i
$144$	−12.4601			−1.03834
$145$	2.82157	−	8.68391i	0.234319	−	0.721159i
$146$	11.8915	−	8.63968i	0.984148	−	0.715025i
$147$	14.8988	+	10.8246i	1.22883	+	0.892799i
$148$	−7.35374	−	22.6325i	−0.604474	−	1.86038i
$149$	5.59667	+	17.2248i	0.458497	+	1.41111i	0.866980	+	0.498343i	$0.166058\pi$
$149$	5.59667	+	17.2248i	0.458497	+	1.41111i	−0.408483	+	0.912766i	$0.633942\pi$
$150$	−35.6398	−	25.8938i	−2.90998	−	2.11422i
$151$	16.2871	−	11.8333i	1.32542	−	0.962976i	0.325576	−	0.945516i	$-0.394442\pi$
$151$	16.2871	−	11.8333i	1.32542	−	0.962976i	0.999848	−	0.0174602i	$-0.00555805\pi$
$152$	−0.519898	+	1.60008i	−0.0421693	+	0.129784i
$153$	4.10454			0.331833
$154$	1.94421	−	0.786215i	0.156669	−	0.0633550i
$155$	24.8613			1.99691
$156$	−12.3786	+	38.0974i	−0.991081	+	3.05023i
$157$	−4.34770	+	3.15879i	−0.346984	+	0.252099i	−0.747603	−	0.664146i	$-0.768795\pi$
$157$	−4.34770	+	3.15879i	−0.346984	+	0.252099i	0.400619	+	0.916245i	$0.368795\pi$
$158$	2.72621	+	1.98071i	0.216886	+	0.157577i
$159$	10.9397	+	33.6688i	0.867571	+	2.67011i
$160$	−8.93096	−	27.4867i	−0.706054	−	2.17301i
$161$	−0.455209	−	0.330729i	−0.0358755	−	0.0260651i
$162$	7.58077	−	5.50775i	0.595601	−	0.432730i
$163$	0.997991	−	3.07150i	0.0781687	−	0.240579i	−0.904334	−	0.426825i	$-0.859632\pi$
$163$	0.997991	−	3.07150i	0.0781687	−	0.240579i	0.982503	+	0.186246i	$0.0596322\pi$
$164$	9.63729			0.752546
$165$	−20.3993	−	24.2955i	−1.58808	−	1.89140i
$166$	−12.3850			−0.961259
$167$	2.85083	−	8.77395i	0.220604	−	0.678949i	−0.778104	−	0.628135i	$-0.783819\pi$
$167$	2.85083	−	8.77395i	0.220604	−	0.678949i	0.998708	−	0.0508137i	$-0.0161815\pi$
$168$	0.547504	−	0.397785i	0.0422408	−	0.0306898i
$169$	−21.1654	−	15.3775i	−1.62810	−	1.18289i
$170$	2.32652	+	7.16028i	0.178436	+	0.549169i
$171$	−2.53311	−	7.79611i	−0.193712	−	0.596183i
$172$	−7.11394	−	5.16858i	−0.542433	−	0.394101i
$173$	−17.5779	+	12.7711i	−1.33642	+	0.970968i	−0.336856	+	0.941556i	$0.609364\pi$
$173$	−17.5779	+	12.7711i	−1.33642	+	0.970968i	−0.999567	+	0.0294121i	$0.990636\pi$
$174$	4.39683	−	13.5321i	0.333323	−	1.02586i
$175$	−2.37432			−0.179482
$176$	−0.705455	−	10.0435i	−0.0531757	−	0.757057i
$177$	19.4341			1.46076
$178$	−1.42171	+	4.37558i	−0.106562	+	0.327964i
$179$	−13.4245	+	9.75346i	−1.00339	+	0.729007i	−0.962813	−	0.270169i	$-0.912920\pi$
$179$	−13.4245	+	9.75346i	−1.00339	+	0.729007i	−0.0405797	+	0.999176i	$0.512920\pi$
$180$	−28.6176	−	20.7919i	−2.13303	−	1.54974i
$181$	−4.77274	−	14.6890i	−0.354755	−	1.09182i	−0.956151	−	0.292873i	$-0.905389\pi$
$181$	−4.77274	−	14.6890i	−0.354755	−	1.09182i	0.601396	−	0.798951i	$-0.294611\pi$
$182$	1.22278	+	3.76333i	0.0906385	+	0.278957i
$183$	−5.74588	−	4.17462i	−0.424747	−	0.308597i
$184$	1.27235	−	0.924419i	0.0937991	−	0.0681491i
$185$	−10.9885	+	33.8193i	−0.807894	+	2.48644i
$186$	38.7412			2.84064
$187$	0.232387	+	3.30847i	0.0169938	+	0.241940i
$188$	−13.4035			−0.977551
$189$	−0.274199	+	0.843897i	−0.0199450	+	0.0613845i
$190$	12.1643	−	8.83790i	0.882493	−	0.641169i
$191$	−11.9721	−	8.69824i	−0.866271	−	0.629382i	0.0633131	−	0.997994i	$-0.479833\pi$
$191$	−11.9721	−	8.69824i	−0.866271	−	0.629382i	−0.929584	+	0.368611i	$0.879833\pi$
$192$	−8.91625	−	27.4414i	−0.643475	−	1.98041i
$193$	−4.70687	−	14.4863i	−0.338808	−	1.04274i	−0.964816	−	0.262927i	$-0.915312\pi$
$193$	−4.70687	−	14.4863i	−0.338808	−	1.04274i	0.626008	−	0.779817i	$-0.284688\pi$
$194$	11.5741	+	8.40907i	0.830971	+	0.603736i
$195$	48.4260	−	35.1836i	3.46786	−	2.51955i
$196$	−5.12740	+	15.7805i	−0.366243	+	1.12718i
$197$	6.77377			0.482611			0.241306	−	0.970449i	$-0.422424\pi$
$197$	6.77377			0.482611			0.241306	+	0.970449i	$0.422424\pi$
$198$	−18.3651	−	21.8728i	−1.30515	−	1.55443i
$199$	−18.0827			−1.28185			−0.640924	−	0.767604i	$-0.721449\pi$
$199$	−18.0827			−1.28185			−0.640924	+	0.767604i	$0.721449\pi$
$200$	2.05078	−	6.31165i	0.145012	−	0.446301i
$201$	1.75883	−	1.27786i	0.124058	−	0.0901336i
$202$	−19.1926	−	13.9442i	−1.35039	−	0.981112i
$203$	−0.236975	−	0.729333i	−0.0166324	−	0.0511892i
$204$	1.97806	+	6.08785i	0.138492	+	0.426235i
$205$	−11.6505	−	8.46459i	−0.813707	−	0.591192i
$206$	2.43211	−	1.76703i	0.169453	−	0.123115i
$207$	−2.36793	+	7.28773i	−0.164582	+	0.506532i
$208$	18.9972			1.31722
$209$	6.14065	−	2.48321i	0.424758	−	0.171767i
$210$	−6.04817			−0.417364
$211$	−1.99445	+	6.13829i	−0.137304	+	0.422577i	−0.995941	−	0.0900060i	$-0.971311\pi$
$211$	−1.99445	+	6.13829i	−0.137304	+	0.422577i	0.858638	+	0.512583i	$0.171311\pi$
$212$	−25.8048	+	18.7483i	−1.77228	+	1.28764i
$213$	15.9257	+	11.5707i	1.09121	+	0.792810i
$214$	9.18097	+	28.2561i	0.627598	+	1.93155i
$215$	4.06039	+	12.4966i	0.276916	+	0.852260i
$216$	−2.00649	−	1.45780i	−0.136525	−	0.0991909i
$217$	1.68924	−	1.22731i	0.114673	−	0.0833151i
$218$	4.03793	−	12.4275i	0.273483	−	0.841695i
$219$	−18.6743			−1.26189
$220$	15.1391	−	24.2445i	1.02068	−	1.63456i
$221$	−6.25794			−0.420955
$222$	−17.1234	+	52.7003i	−1.14924	+	3.53701i
$223$	−18.9800	+	13.7897i	−1.27099	+	0.923430i	−0.999242	−	0.0389382i	$-0.987602\pi$
$223$	−18.9800	+	13.7897i	−1.27099	+	0.923430i	−0.271750	+	0.962368i	$0.587602\pi$
$224$	−1.96374	−	1.42674i	−0.131208	−	0.0953281i
$225$	9.99205	+	30.7524i	0.666137	+	2.05016i
$226$	−2.71321	−	8.35039i	−0.180480	−	0.555460i
$227$	−16.0653	−	11.6721i	−1.06629	−	0.774707i	−0.0910509	−	0.995846i	$-0.529023\pi$
$227$	−16.0653	−	11.6721i	−1.06629	−	0.774707i	−0.975242	+	0.221139i	$0.929023\pi$
$228$	10.3424	−	7.51420i	0.684943	−	0.497640i
$229$	6.89988	−	21.2356i	0.455957	−	1.40329i	−0.414052	−	0.910253i	$-0.635887\pi$
$229$	6.89988	−	21.2356i	0.455957	−	1.40329i	0.870008	−	0.493037i	$-0.164113\pi$
$230$	−14.0555			−0.926789
$231$	−2.58544	−	0.643767i	−0.170110	−	0.0423568i
$232$	2.14347			0.140725
$233$	−0.0190236	+	0.0585486i	−0.00124628	+	0.00383565i	−0.951678	−	0.307099i	$-0.900642\pi$
$233$	−0.0190236	+	0.0585486i	−0.00124628	+	0.00383565i	0.950431	+	0.310934i	$0.100642\pi$
$234$	43.5970	−	31.6750i	2.85002	−	2.07066i
$235$	16.2035	+	11.7725i	1.05700	+	0.767954i
$236$	5.41088	+	16.6530i	0.352218	+	1.08402i
$237$	−1.32297	−	4.07169i	−0.0859362	−	0.264484i
$238$	0.511555	+	0.371666i	0.0331592	+	0.0240916i
$239$	6.32509	−	4.59545i	0.409136	−	0.297255i	−0.364116	−	0.931354i	$-0.618629\pi$
$239$	6.32509	−	4.59545i	0.409136	−	0.297255i	0.773252	+	0.634099i	$0.218629\pi$
$240$	−8.97283	+	27.6155i	−0.579194	+	1.78258i
$241$	−15.4004			−0.992030			−0.496015	−	0.868314i	$-0.665204\pi$
$241$	−15.4004			−0.992030			−0.496015	+	0.868314i	$0.665204\pi$
$242$	16.5908	−	16.0415i	1.06650	−	1.03119i
$243$	−20.7370			−1.33028
$244$	1.97744	−	6.08592i	0.126592	−	0.389611i
$245$	20.0588	−	14.5736i	1.28151	−	0.931071i
$246$	−18.1549	−	13.1903i	−1.15751	−	0.840982i
$247$	3.86207	+	11.8862i	0.245738	+	0.756303i
$248$	1.80349	+	5.55058i	0.114522	+	0.352462i
$249$	12.7297	+	9.24866i	0.806711	+	0.586110i
$250$	−17.5287	+	12.7353i	−1.10861	+	0.805453i
$251$	5.74067	−	17.6680i	0.362348	−	1.11519i	−0.589277	−	0.807931i	$-0.700587\pi$
$251$	5.74067	−	17.6680i	0.362348	−	1.11519i	0.951625	−	0.307261i	$-0.0994125\pi$
$252$	−2.97089			−0.187149
$253$	−6.00835	−	1.49606i	−0.377742	−	0.0940566i
$254$	26.4121			1.65725
$255$	2.95578	−	9.09695i	0.185098	−	0.569673i
$256$	−6.30715	+	4.58242i	−0.394197	+	0.286401i
$257$	9.02322	+	6.55575i	0.562853	+	0.408937i	0.832502	−	0.554022i	$-0.186908\pi$
$257$	9.02322	+	6.55575i	0.562853	+	0.408937i	−0.269649	+	0.962959i	$0.586908\pi$
$258$	6.32726	+	19.4733i	0.393918	+	1.21236i
$259$	0.922892	+	2.84037i	0.0573457	+	0.176492i
$260$	43.6315	+	31.7001i	2.70591	+	1.96596i
$261$	−8.44909	+	6.13862i	−0.522985	+	0.379971i
$262$	2.55961	−	7.87768i	0.158133	−	0.486685i
$263$	−13.8303			−0.852812			−0.426406	−	0.904532i	$-0.640220\pi$
$263$	−13.8303			−0.852812			−0.426406	+	0.904532i	$0.640220\pi$
$264$	3.94445	−	6.31682i	0.242764	−	0.388773i
$265$	47.6623			2.92787
$266$	0.390233	−	1.20101i	0.0239267	−	0.0736388i
$267$	4.72882	−	3.43569i	0.289399	−	0.210261i
$268$	1.58469	+	1.15135i	0.0968005	+	0.0703297i
$269$	−0.497575	−	1.53138i	−0.0303377	−	0.0933698i	0.934741	−	0.355329i	$-0.115631\pi$
$269$	−0.497575	−	1.53138i	−0.0303377	−	0.0933698i	−0.965079	+	0.261960i	$0.915631\pi$
$270$	6.84947	+	21.0805i	0.416846	+	1.28292i
$271$	16.8507	+	12.2428i	1.02361	+	0.743696i	0.967020	−	0.254702i	$-0.0819774\pi$
$271$	16.8507	+	12.2428i	1.02361	+	0.743696i	0.0565895	+	0.998398i	$0.481977\pi$
$272$	2.45593	−	1.78433i	0.148912	−	0.108191i
$273$	1.55351	−	4.78121i	0.0940227	−	0.289372i
$274$	−16.4288			−0.992499
$275$	−24.2223	+	9.79522i	−1.46066	+	0.590674i
$276$	−11.9503			−0.719323
$277$	−0.673171	+	2.07181i	−0.0404469	+	0.124483i	−0.969241	−	0.246113i	$-0.920847\pi$
$277$	−0.673171	+	2.07181i	−0.0404469	+	0.124483i	0.928794	+	0.370596i	$0.120847\pi$
$278$	32.3218	−	23.4831i	1.93853	−	1.40843i
$279$	−23.0051	−	16.7142i	−1.37728	−	1.00065i
$280$	−0.281556	−	0.866542i	−0.0168262	−	0.0517858i
$281$	3.07212	+	9.45500i	0.183267	+	0.564038i	0.999914	−	0.0130992i	$-0.00416971\pi$
$281$	3.07212	+	9.45500i	0.183267	+	0.564038i	−0.816647	+	0.577137i	$0.804170\pi$
$282$	25.2497	+	18.3450i	1.50360	+	1.09243i
$283$	−14.6593	+	10.6506i	−0.871406	+	0.633114i	−0.930964	−	0.365111i	$-0.881031\pi$
$283$	−14.6593	+	10.6506i	−0.871406	+	0.633114i	0.0595578	+	0.998225i	$0.481031\pi$
$284$	−5.48080	+	16.8682i	−0.325226	+	1.00094i
$285$	−19.1028			−1.13155
$286$	28.0000	+	33.3480i	1.65568	+	1.97191i
$287$	−1.20948			−0.0713932
$288$	−10.2151	+	31.4387i	−0.601929	+	1.85255i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−15.4978	−	11.2598i	−0.910060	−	0.661197i
$291$	−5.61665	−	17.2863i	−0.329254	−	1.01334i
$292$	−5.19935	−	16.0019i	−0.304269	−	0.936443i
$293$	5.67189	+	4.12087i	0.331355	+	0.240744i	0.741006	−	0.671499i	$-0.234349\pi$
$293$	5.67189	+	4.12087i	0.331355	+	0.240744i	−0.409650	+	0.912243i	$0.634349\pi$
$294$	31.2574	−	22.7099i	1.82297	−	1.32447i
$295$	8.08538	−	24.8842i	0.470749	−	1.44882i
$296$	−8.34767			−0.485199
$297$	0.684168	+	9.74044i	0.0396994	+	0.565197i
$298$	37.9970			2.20111
$299$	3.61023	−	11.1111i	0.208785	−	0.642574i
$300$	−40.7965	+	29.6404i	−2.35539	+	1.71129i
$301$	0.892798	+	0.648656i	0.0514600	+	0.0373879i
$302$	−13.0518	−	40.1693i	−0.751046	−	2.31148i
$303$	9.31373	+	28.6647i	0.535060	+	1.64675i
$304$	−4.90481	−	3.56355i	−0.281310	−	0.204384i
$305$	−7.73588	+	5.62045i	−0.442955	+	0.321826i
$306$	2.66103	−	8.18980i	0.152121	−	0.468180i
$307$	−27.6818			−1.57988			−0.789941	−	0.613183i	$-0.789889\pi$
$307$	−27.6818			−1.57988			−0.789941	+	0.613183i	$0.789889\pi$
$308$	−0.168203	−	2.39469i	−0.00958425	−	0.136450i
$309$	−3.81937			−0.217277
$310$	16.1179	−	49.6058i	0.915436	−	2.81742i
$311$	−4.80583	+	3.49164i	−0.272514	+	0.197993i	−0.715646	−	0.698464i	$-0.753867\pi$
$311$	−4.80583	+	3.49164i	−0.272514	+	0.197993i	0.443132	+	0.896457i	$0.353867\pi$
$312$	11.3681	+	8.25938i	0.643590	+	0.467595i
$313$	3.53357	+	10.8752i	0.199729	+	0.614703i	0.999889	+	0.0149161i	$0.00474812\pi$
$313$	3.53357	+	10.8752i	0.199729	+	0.614703i	−0.800160	+	0.599787i	$0.795252\pi$
$314$	3.48407	+	10.7229i	0.196617	+	0.605126i
$315$	3.59151	+	2.60938i	0.202358	+	0.147022i
$316$	3.12066	−	2.26730i	0.175551	−	0.127545i
$317$	2.16876	−	6.67474i	0.121809	−	0.374891i	−0.871497	−	0.490401i	$-0.836850\pi$
$317$	2.16876	−	6.67474i	0.121809	−	0.374891i	0.993306	+	0.115510i	$0.0368503\pi$
$318$	74.2717			4.16495
$319$	−5.42641	−	6.46285i	−0.303821	−	0.361850i
$320$	−38.8466			−2.17159
$321$	11.6642	−	35.8987i	0.651031	−	2.00367i
$322$	−0.955022	+	0.693864i	−0.0532213	+	0.0386675i
$323$	1.61571	+	1.17388i	0.0899007	+	0.0653167i
$324$	−3.31455	−	10.2011i	−0.184142	−	0.566730i
$325$	−15.2343	−	46.8862i	−0.845045	−	2.60078i
$326$	−5.48156	−	3.98259i	−0.303596	−	0.220575i
$327$	−13.4307	+	9.75800i	−0.742722	+	0.539619i
$328$	1.04466	−	3.21515i	0.0576820	−	0.177527i
$329$	1.68214			0.0927391
$330$	−61.7020	+	24.9516i	−3.39658	+	1.37354i
$331$	6.55585			0.360342			0.180171	−	0.983635i	$-0.442335\pi$
$331$	6.55585			0.360342			0.180171	+	0.983635i	$0.442335\pi$
$332$	−4.38091	+	13.4830i	−0.240433	+	0.739978i
$333$	32.9048	−	23.9067i	1.80317	−	1.31008i
$334$	−15.6585	−	11.3765i	−0.856792	−	0.622496i
$335$	−0.904486	−	2.78372i	−0.0494173	−	0.152091i
$336$	0.753599	+	2.31934i	0.0411122	+	0.126530i
$337$	2.22882	+	1.61933i	0.121412	+	0.0882107i	0.646834	−	0.762631i	$-0.276093\pi$
$337$	2.22882	+	1.61933i	0.121412	+	0.0882107i	−0.525422	+	0.850842i	$0.676093\pi$
$338$	−44.4046	+	32.2618i	−2.41529	+	1.75481i
$339$	−3.44706	+	10.6090i	−0.187219	+	0.576199i
$340$	8.61809			0.467382
$341$	12.1700	−	19.4896i	0.659045	−	1.05542i
$342$	−17.1978			−0.929952
$343$	1.29544	−	3.98694i	0.0699469	−	0.215275i
$344$	−2.49546	+	1.81306i	−0.134546	+	0.0977534i
$345$	14.4467	+	10.4961i	0.777783	+	0.565093i
$346$	14.0862	+	43.3529i	0.757279	+	2.33067i
$347$	0.228155	+	0.702188i	0.0122480	+	0.0376954i	0.956994	−	0.290109i	$-0.0936914\pi$
$347$	0.228155	+	0.702188i	0.0122480	+	0.0376954i	−0.944746	+	0.327804i	$0.893691\pi$
$348$	−13.1766	−	9.57334i	−0.706339	−	0.513185i
$349$	7.55335	−	5.48783i	0.404322	−	0.293757i	−0.366977	−	0.930230i	$-0.619607\pi$
$349$	7.55335	−	5.48783i	0.404322	−	0.293757i	0.771299	+	0.636473i	$0.219607\pi$
$350$	−1.53930	+	4.73749i	−0.0822793	+	0.253230i
$351$	−18.4239			−0.983396
$352$	−25.9196	−	6.45390i	−1.38152	−	0.343994i
$353$	14.1491			0.753079			0.376540	−	0.926400i	$-0.377114\pi$
$353$	14.1491			0.753079			0.376540	+	0.926400i	$0.377114\pi$
$354$	12.5994	−	38.7769i	0.669649	−	2.06097i
$355$	21.4413	−	15.5780i	1.13799	−	0.826796i
$356$	4.26063	+	3.09553i	0.225813	+	0.164063i
$357$	−0.248246	−	0.764024i	−0.0131386	−	0.0404364i
$358$	10.7578	+	33.1092i	0.568569	+	1.74987i
$359$	−3.20675	−	2.32984i	−0.169246	−	0.122964i	0.499938	−	0.866061i	$-0.333356\pi$
$359$	−3.20675	−	2.32984i	−0.169246	−	0.122964i	−0.669184	+	0.743097i	$0.733356\pi$
$360$	−10.0386	+	7.29347i	−0.529081	+	0.384400i
$361$	−4.63880	+	14.2768i	−0.244147	+	0.751408i
$362$	−32.4032			−1.70307
$363$	−29.0319	+	4.09862i	−1.52378	+	0.215122i
$364$	4.52953			0.237412
$365$	−7.76928	+	23.9114i	−0.406663	+	1.25158i
$366$	−12.0548	+	8.75829i	−0.630112	+	0.457803i
$367$	−13.6819	−	9.94046i	−0.714188	−	0.518888i	0.170334	−	0.985386i	$-0.445515\pi$
$367$	−13.6819	−	9.94046i	−0.714188	−	0.518888i	−0.884522	+	0.466499i	$0.845515\pi$
$368$	1.75130	+	5.38995i	0.0912929	+	0.280971i
$369$	5.08994	+	15.6652i	0.264972	+	0.815499i
$370$	60.3556	+	43.8509i	3.13774	+	2.27970i
$371$	3.23850	−	2.35290i	0.168134	−	0.122157i
$372$	13.7038	−	42.1761i	0.710511	−	2.18673i
$373$	19.3218			1.00045			0.500224	−	0.865896i	$-0.333251\pi$
$373$	19.3218			1.00045			0.500224	+	0.865896i	$0.333251\pi$
$374$	6.75206	+	1.68124i	0.349141	+	0.0869350i
$375$	27.5269			1.42148
$376$	−1.45291	+	4.47161i	−0.0749284	+	0.230606i
$377$	12.8818	−	9.35917i	0.663446	−	0.482022i
$378$	1.50606	+	1.09422i	0.0774635	+	0.0562805i
$379$	0.535579	+	1.64834i	0.0275109	+	0.0846697i	0.963869	−	0.266376i	$-0.0858262\pi$
$379$	0.535579	+	1.64834i	0.0275109	+	0.0846697i	−0.936358	+	0.351046i	$0.885826\pi$
$380$	−5.31864	−	16.3691i	−0.272840	−	0.839716i
$381$	−27.1473	−	19.7237i	−1.39080	−	1.01048i
$382$	−25.1173	+	18.2488i	−1.28511	+	0.933688i
$383$	3.63429	−	11.1852i	0.185704	−	0.571537i	−0.814256	−	0.580506i	$-0.802855\pi$
$383$	3.63429	−	11.1852i	0.185704	−	0.571537i	0.999960	+	0.00896850i	$0.00285480\pi$
$384$	−17.6013			−0.898213
$385$	−1.89996	+	3.04267i	−0.0968307	+	0.155069i
$386$	−31.9560			−1.62652
$387$	4.64419	−	14.2934i	0.236078	−	0.726572i
$388$	13.2487	−	9.62577i	0.672602	−	0.488674i
$389$	17.8028	+	12.9345i	0.902637	+	0.655804i	0.939142	−	0.343530i	$-0.111623\pi$
$389$	17.8028	+	12.9345i	0.902637	+	0.655804i	−0.0365053	+	0.999333i	$0.511623\pi$
$390$	−38.8066	−	119.434i	−1.96505	−	6.04780i
$391$	−0.576904	−	1.77553i	−0.0291753	−	0.0897922i
$392$	4.70882	+	3.42116i	0.237831	+	0.172795i
$393$	−8.51365	+	6.18553i	−0.429457	+	0.312018i
$394$	4.39152	−	13.5157i	0.221242	−	0.680912i
$395$	−5.76397			−0.290017
$396$	−30.3083	+	12.2563i	−1.52305	+	0.615904i
$397$	7.02377			0.352513			0.176256	−	0.984344i	$-0.443601\pi$
$397$	7.02377			0.352513			0.176256	+	0.984344i	$0.443601\pi$
$398$	−11.7232	+	36.0804i	−0.587633	+	1.80855i
$399$	−1.29797	+	0.943031i	−0.0649798	+	0.0472106i
$400$	19.3474	+	14.0567i	0.967370	+	0.702836i
$401$	−9.95597	−	30.6413i	−0.497177	−	1.53015i	−0.813536	−	0.581515i	$-0.802460\pi$
$401$	−9.95597	−	30.6413i	−0.497177	−	1.53015i	0.316358	−	0.948640i	$-0.397540\pi$
$402$	−1.40945	−	4.33785i	−0.0702971	−	0.216352i
$403$	35.0745	+	25.4831i	1.74719	+	1.26940i
$404$	−21.9695	+	15.9618i	−1.09302	+	0.794129i
$405$	−4.95287	+	15.2434i	−0.246110	+	0.757449i
$406$	−1.60887			−0.0798471
$407$	21.1330	+	25.1694i	1.04752	+	1.24760i
$408$	2.24542			0.111165
$409$	−5.17694	+	15.9330i	−0.255983	+	0.787836i	0.737651	+	0.675182i	$0.235935\pi$
$409$	−5.17694	+	15.9330i	−0.255983	+	0.787836i	−0.993634	+	0.112654i	$0.964065\pi$
$410$	−24.4426	+	17.7586i	−1.20713	+	0.877033i
$411$	16.8861	+	12.2685i	0.832929	+	0.605158i
$412$	−1.06340	−	3.27280i	−0.0523899	−	0.161239i
$413$	−0.679064	−	2.08995i	−0.0334146	−	0.102839i
$414$	13.0061	+	9.44945i	0.639213	+	0.464415i
$415$	17.1384	−	12.4518i	0.841293	−	0.611235i
$416$	15.5743	−	47.9327i	0.763592	−	2.35009i
$417$	−50.7579			−2.48562
$418$	−0.973690	−	13.8623i	−0.0476247	−	0.678029i
$419$	−6.11025			−0.298505			−0.149253	−	0.988799i	$-0.547687\pi$
$419$	−6.11025			−0.298505			−0.149253	+	0.988799i	$0.547687\pi$
$420$	−2.13941	+	6.58443i	−0.104393	+	0.321287i
$421$	28.9555	−	21.0374i	1.41121	−	1.02530i	0.418061	−	0.908419i	$-0.362710\pi$
$421$	28.9555	−	21.0374i	1.41121	−	1.02530i	0.993146	−	0.116883i	$-0.0372901\pi$
$422$	10.9547	+	7.95906i	0.533267	+	0.387441i
$423$	−7.07906	−	21.7871i	−0.344196	−	1.05933i
$424$	3.45752	+	10.6412i	0.167912	+	0.516780i
$425$	−6.37331	−	4.63048i	−0.309151	−	0.224611i
$426$	33.4118	−	24.2751i	1.61881	−	1.17613i
$427$	−0.248168	+	0.763782i	−0.0120097	+	0.0369620i
$428$	34.0090			1.64388
$429$	−3.87624	−	55.1858i	−0.187147	−	2.66439i
$430$	27.5668			1.32939
$431$	7.27023	−	22.3755i	0.350195	−	1.07779i	−0.608549	−	0.793516i	$-0.708248\pi$
$431$	7.27023	−	22.3755i	0.350195	−	1.07779i	0.958744	−	0.284272i	$-0.0917519\pi$
$432$	7.23046	−	5.25324i	0.347876	−	0.252746i
$433$	−1.63766	−	1.18983i	−0.0787010	−	0.0571796i	0.547739	−	0.836649i	$-0.315489\pi$
$433$	−1.63766	−	1.18983i	−0.0787010	−	0.0571796i	−0.626440	+	0.779470i	$0.715489\pi$
$434$	−1.35369	−	4.16623i	−0.0649792	−	0.199986i
$435$	7.52072	+	23.1464i	0.360591	+	1.10978i
$436$	−12.1010	−	8.79189i	−0.579533	−	0.421055i
$437$	−3.01637	+	2.19152i	−0.144293	+	0.104835i
$438$	−12.1068	+	37.2609i	−0.578485	+	1.78040i
$439$	−0.252366			−0.0120448			−0.00602238	−	0.999982i	$-0.501917\pi$
$439$	−0.252366			−0.0120448			−0.00602238	+	0.999982i	$0.501917\pi$
$440$	−6.44727	−	7.67870i	−0.307362	−	0.366067i
$441$	−28.3590			−1.35043
$442$	−4.05710	+	12.4865i	−0.192977	+	0.593921i
$443$	−25.5481	+	18.5618i	−1.21383	+	0.881897i	−0.995573	−	0.0939947i	$-0.970036\pi$
$443$	−25.5481	+	18.5618i	−1.21383	+	0.881897i	−0.218255	+	0.975892i	$0.570036\pi$
$444$	51.3159	+	37.2831i	2.43534	+	1.76938i
$445$	−2.43182	−	7.48436i	−0.115279	−	0.354793i
$446$	15.2098	+	46.8108i	0.720203	+	2.21656i
$447$	−39.0547	−	28.3749i	−1.84722	−	1.34209i
$448$	−2.63950	+	1.91771i	−0.124705	+	0.0906033i
$449$	−8.24414	+	25.3729i	−0.389065	+	1.19742i	0.544423	+	0.838811i	$0.316749\pi$
$449$	−8.24414	+	25.3729i	−0.389065	+	1.19742i	−0.933488	+	0.358608i	$0.883251\pi$
$450$	67.8382			3.19793
$451$	−12.3388	+	4.98967i	−0.581012	+	0.234954i
$452$	−10.0505			−0.472736
$453$	−16.5820	+	51.0340i	−0.779088	+	2.39779i
$454$	−33.7048	+	24.4880i	−1.58184	+	1.14928i
$455$	−5.47574	−	3.97836i	−0.256707	−	0.186508i
$456$	−1.38575	−	4.26491i	−0.0648939	−	0.199723i
$457$	−11.4719	−	35.3068i	−0.536632	−	1.65158i	−0.740097	−	0.672500i	$-0.765221\pi$
$457$	−11.4719	−	35.3068i	−0.536632	−	1.65158i	0.203466	−	0.979082i	$-0.434779\pi$
$458$	−37.8982	−	27.5347i	−1.77087	−	1.28661i
$459$	−2.38182	+	1.73049i	−0.111174	+	0.0807724i
$460$	−4.97181	+	15.3017i	−0.231812	+	0.713443i
$461$	−28.0182			−1.30494			−0.652468	−	0.757816i	$-0.726266\pi$
$461$	−28.0182			−1.30494			−0.652468	+	0.757816i	$0.726266\pi$
$462$	−2.96068	+	4.74137i	−0.137744	+	0.220589i
$463$	13.9305			0.647404			0.323702	−	0.946159i	$-0.395072\pi$
$463$	13.9305			0.647404			0.323702	+	0.946159i	$0.395072\pi$
$464$	−2.38686	+	7.34600i	−0.110807	+	0.341030i
$465$	−53.6105	+	38.9503i	−2.48613	+	1.80628i
$466$	0.104489	+	0.0759156i	0.00484035	+	0.00351672i
$467$	6.33654	+	19.5019i	0.293220	+	0.902438i	0.983814	+	0.179195i	$0.0573493\pi$
$467$	6.33654	+	19.5019i	0.293220	+	0.902438i	−0.690594	+	0.723243i	$0.742651\pi$
$468$	−19.0620	−	58.6668i	−0.881141	−	2.71187i
$469$	−0.198879	−	0.144494i	−0.00918336	−	0.00667210i
$470$	33.9946	−	24.6985i	1.56805	−	1.13926i
$471$	4.42642	−	13.6231i	0.203959	−	0.627720i
$472$	6.14222			0.282719
$473$	11.7841	+	2.93421i	0.541835	+	0.134915i
$474$	−8.98194			−0.412554
$475$	−4.86179	+	14.9631i	−0.223074	+	0.686553i
$476$	0.585571	−	0.425442i	0.0268396	−	0.0195001i
$477$	−44.1038	−	32.0433i	−2.01937	−	1.46716i
$478$	−5.06867	−	15.5998i	−0.231835	−	0.713516i
$479$	3.37906	+	10.3997i	0.154393	+	0.475173i	0.998099	−	0.0616327i	$-0.0196307\pi$
$479$	3.37906	+	10.3997i	0.154393	+	0.475173i	−0.843706	+	0.536806i	$0.819631\pi$
$480$	62.3220	+	45.2796i	2.84460	+	2.06672i
$481$	−50.1678	+	36.4491i	−2.28746	+	1.66193i
$482$	−9.98430	+	30.7285i	−0.454773	+	1.39965i
$483$	1.49976			0.0682414
$484$	−11.5952	−	23.7361i	−0.527055	−	1.07892i
$485$	−24.4708			−1.11116
$486$	−13.4441	+	41.3767i	−0.609836	+	1.87688i
$487$	−3.13387	+	2.27689i	−0.142009	+	0.103176i	−0.656522	−	0.754307i	$-0.727973\pi$
$487$	−3.13387	+	2.27689i	−0.142009	+	0.103176i	0.514512	+	0.857483i	$0.327973\pi$
$488$	−1.81601	−	1.31941i	−0.0822067	−	0.0597267i
$489$	2.66008	+	8.18689i	0.120293	+	0.370224i
$490$	−16.0743	−	49.4716i	−0.726162	−	2.23490i
$491$	4.28402	+	3.11252i	0.193335	+	0.140466i	0.680242	−	0.732988i	$-0.261875\pi$
$491$	4.28402	+	3.11252i	0.193335	+	0.140466i	−0.486907	+	0.873454i	$0.661875\pi$
$492$	−20.7817	+	15.0988i	−0.936911	+	0.680705i
$493$	0.786266	−	2.41988i	0.0354117	−	0.108986i
$494$	26.2205			1.17971
$495$	47.4046	+	11.8036i	2.13068	+	0.530533i
$496$	−21.0310			−0.944320
$497$	0.687839	−	2.11695i	0.0308538	−	0.0949582i
$498$	26.7067	−	19.4035i	1.19676	−	0.869494i
$499$	32.3693	+	23.5177i	1.44905	+	1.05280i	0.986052	+	0.166438i	$0.0532265\pi$
$499$	32.3693	+	23.5177i	1.44905	+	1.05280i	0.462999	+	0.886359i	$0.346774\pi$
$500$	7.66410	+	23.5877i	0.342749	+	1.05487i
$501$	7.59870	+	23.3864i	0.339485	+	1.04483i
$502$	−31.5312	−	22.9087i	−1.40730	−	1.02247i
$503$	−20.8729	+	15.1651i	−0.930677	+	0.676177i	−0.946159	−	0.323704i	$-0.895072\pi$
$503$	−20.8729	+	15.1651i	−0.930677	+	0.676177i	0.0154813	+	0.999880i	$0.495072\pi$
$504$	−0.322039	+	0.991135i	−0.0143448	+	0.0441486i
$505$	40.5784			1.80572
$506$	−6.88038	+	11.0186i	−0.305870	+	0.489834i
$507$	69.7326			3.09693
$508$	9.34272	−	28.7539i	0.414516	−	1.27575i
$509$	0.531145	−	0.385899i	0.0235426	−	0.0171047i	−0.575952	−	0.817484i	$-0.695368\pi$
$509$	0.531145	−	0.385899i	0.0235426	−	0.0171047i	0.599494	+	0.800379i	$0.295368\pi$
$510$	−16.2349	−	11.7953i	−0.718893	−	0.522307i
$511$	0.652517	+	2.00824i	0.0288656	+	0.0888393i
$512$	9.13551	+	28.1162i	0.403736	+	1.24257i
$513$	4.75680	+	3.45602i	0.210018	+	0.152587i
$514$	18.9306	−	13.7539i	0.834992	−	0.606657i
$515$	−1.58902	+	4.89049i	−0.0700204	+	0.215501i
$516$	23.4380			1.03180
$517$	17.1607	−	6.93961i	0.754729	−	0.305204i
$518$	6.26572			0.275300
$519$	17.8962	−	55.0787i	0.785554	−	2.41769i
$520$	15.3052	−	11.1199i	0.671179	−	0.487640i
$521$	11.6266	+	8.44719i	0.509369	+	0.370078i	0.812584	−	0.582844i	$-0.198060\pi$
$521$	11.6266	+	8.44719i	0.509369	+	0.370078i	−0.303215	+	0.952922i	$0.598060\pi$
$522$	6.77075	+	20.8382i	0.296348	+	0.912064i
$523$	2.49117	+	7.66702i	0.108931	+	0.335255i	0.990633	−	0.136552i	$-0.0436019\pi$
$523$	2.49117	+	7.66702i	0.108931	+	0.335255i	−0.881702	+	0.471807i	$0.843602\pi$
$524$	−7.67073	−	5.57312i	−0.335098	−	0.243463i
$525$	5.11995	−	3.71986i	0.223453	−	0.162348i
$526$	−8.96635	+	27.5956i	−0.390951	+	1.20322i
$527$	6.92792			0.301785
$528$	17.2564	+	20.5524i	0.750989	+	0.894428i
$529$	−19.5147			−0.848465
$530$	30.9001	−	95.1007i	1.34221	−	4.13091i
$531$	−24.2113	+	17.5906i	−1.05068	+	0.763365i
$532$	−1.16946	−	0.849664i	−0.0507026	−	0.0368376i
$533$	−7.76031	−	23.8838i	−0.336136	−	1.03452i
$534$	−3.78948	−	11.6628i	−0.163987	−	0.504700i
$535$	−41.1134	−	29.8706i	−1.77749	−	1.29142i
$536$	0.555885	−	0.403874i	0.0240106	−	0.0174447i
$537$	13.6675	−	42.0644i	0.589798	−	1.81521i
$538$	−3.37815			−0.145642
$539$	−1.60560	−	22.8588i	−0.0691580	−	0.984597i
$540$	25.3724			1.09186
$541$	−9.53330	+	29.3405i	−0.409868	+	1.26145i	0.506892	+	0.862009i	$0.330794\pi$
$541$	−9.53330	+	29.3405i	−0.409868	+	1.26145i	−0.916761	+	0.399436i	$0.869206\pi$
$542$	35.3526	−	25.6851i	1.51852	−	1.10327i
$543$	33.3051	+	24.1976i	1.42926	+	1.03842i
$544$	−2.48872	−	7.65950i	−0.106703	−	0.328398i
$545$	6.90682	+	21.2570i	0.295856	+	0.910550i
$546$	−8.53280	−	6.19944i	−0.365170	−	0.265312i
$547$	2.01129	−	1.46129i	0.0859964	−	0.0624800i	−0.543956	−	0.839114i	$-0.683074\pi$
$547$	2.01129	−	1.46129i	0.0859964	−	0.0624800i	0.629953	+	0.776634i	$0.283074\pi$
$548$	−5.81132	+	17.8854i	−0.248247	+	0.764027i
$549$	10.9369			0.466777
$550$	3.84080	+	54.6811i	0.163772	+	2.33161i
$551$	−5.08153			−0.216480
$552$	−1.29539	+	3.98680i	−0.0551355	+	0.169689i
$553$	−0.391643	+	0.284545i	−0.0166543	+	0.0121001i
$554$	3.69746	+	2.68636i	0.157090	+	0.114132i
$555$	−29.2893	−	90.1431i	−1.24326	−	3.82636i
$556$	−14.1321	−	43.4942i	−0.599335	−	1.84456i
$557$	−19.2565	−	13.9907i	−0.815926	−	0.592805i	0.0996170	−	0.995026i	$-0.468238\pi$
$557$	−19.2565	−	13.9907i	−0.815926	−	0.592805i	−0.915542	+	0.402221i	$0.868238\pi$
$558$	−48.2644	+	35.0662i	−2.04320	+	1.48447i
$559$	−7.08071	+	21.7922i	−0.299482	+	0.921712i
$560$	3.28331			0.138745
$561$	−5.68451	−	6.77025i	−0.240000	−	0.285840i
$562$	20.8573			0.879811
$563$	7.60447	−	23.4041i	0.320490	−	0.986367i	−0.652945	−	0.757405i	$-0.726467\pi$
$563$	7.60447	−	23.4041i	0.320490	−	0.986367i	0.973435	−	0.228962i	$-0.0735331\pi$
$564$	28.9031	−	20.9993i	1.21704	−	0.884230i
$565$	12.1500	+	8.82752i	0.511156	+	0.371376i
$566$	11.7474	+	36.1547i	0.493779	+	1.51970i
$567$	0.415976	+	1.28024i	0.0174693	+	0.0537651i
$568$	5.03337	+	3.65696i	0.211196	+	0.153443i
$569$	4.95192	−	3.59778i	0.207595	−	0.150827i	−0.479130	−	0.877744i	$-0.659048\pi$
$569$	4.95192	−	3.59778i	0.207595	−	0.150827i	0.686725	+	0.726917i	$0.259048\pi$
$570$	−12.3846	+	38.1158i	−0.518733	+	1.59649i
$571$	−9.52171			−0.398471			−0.199236	−	0.979952i	$-0.563846\pi$
$571$	−9.52171			−0.398471			−0.199236	+	0.979952i	$0.563846\pi$
$572$	46.2092	−	18.6865i	1.93210	−	0.781321i
$573$	39.4440			1.64780
$574$	−0.784120	+	2.41327i	−0.0327285	+	0.100728i
$575$	11.8983	−	8.64464i	0.496195	−	0.360507i
$576$	35.9463	+	26.1165i	1.49776	+	1.08819i
$577$	−3.71457	−	11.4323i	−0.154639	−	0.475931i	0.843485	−	0.537153i	$-0.180500\pi$
$577$	−3.71457	−	11.4323i	−0.154639	−	0.475931i	−0.998124	+	0.0612219i	$0.980500\pi$
$578$	0.648313	+	1.99530i	0.0269663	+	0.0829936i
$579$	32.8455	+	23.8636i	1.36501	+	0.991739i
$580$	−17.7401	+	12.8889i	−0.736618	+	0.535184i
$581$	0.549803	−	1.69212i	0.0228097	−	0.0702009i
$582$	−38.1327			−1.58065
$583$	23.3315	−	37.3641i	0.966292	−	1.54746i
$584$	−5.90209			−0.244230
$585$	−28.4839	+	87.6646i	−1.17767	+	3.62448i
$586$	11.8995	−	8.64552i	0.491565	−	0.357143i
$587$	1.49260	+	1.08444i	0.0616064	+	0.0447596i	0.618162	−	0.786051i	$-0.287877\pi$
$587$	1.49260	+	1.08444i	0.0616064	+	0.0447596i	−0.556556	+	0.830810i	$0.687877\pi$
$588$	−13.6668	−	42.0619i	−0.563607	−	1.73461i
$589$	−4.27555	−	13.1588i	−0.176171	−	0.542198i
$590$	−44.4097	−	32.2655i	−1.82832	−	1.32835i
$591$	−14.6068	+	10.6125i	−0.600845	+	0.436540i
$592$	9.29557	−	28.6088i	0.382046	−	1.17582i
$593$	26.4831			1.08753			0.543765	−	0.839237i	$-0.316998\pi$
$593$	26.4831			1.08753			0.543765	+	0.839237i	$0.316998\pi$
$594$	19.8787	+	4.94973i	0.815632	+	0.203090i
$595$	−1.08157			−0.0443400
$596$	13.4406	−	41.3660i	0.550549	−	1.69442i
$597$	38.9932	−	28.3302i	1.59589	−	1.15948i
$598$	−19.8295	−	14.4070i	−0.810889	−	0.589146i
$599$	0.559073	+	1.72065i	0.0228431	+	0.0703039i	0.961828	−	0.273654i	$-0.0882323\pi$
$599$	0.559073	+	1.72065i	0.0228431	+	0.0703039i	−0.938985	+	0.343958i	$0.888232\pi$
$600$	5.46622	+	16.8233i	0.223157	+	0.686808i
$601$	−10.1488	−	7.37353i	−0.413978	−	0.300772i	0.361232	−	0.932476i	$-0.382356\pi$
$601$	−10.1488	−	7.37353i	−0.413978	−	0.300772i	−0.775210	+	0.631703i	$0.782356\pi$
$602$	1.87308	−	1.36087i	0.0763409	−	0.0554649i
$603$	−1.03453	+	3.18397i	−0.0421295	+	0.129661i
$604$	−48.3476			−1.96724
$605$	−6.83041	+	38.8788i	−0.277696	+	1.58065i
$606$	63.2330			2.56866
$607$	−3.41718	+	10.5170i	−0.138699	+	0.426872i	−0.996147	−	0.0876988i	$-0.972049\pi$
$607$	−3.41718	+	10.5170i	−0.138699	+	0.426872i	0.857448	+	0.514571i	$0.172049\pi$
$608$	−13.0124	+	9.45408i	−0.527724	+	0.383414i
$609$	1.65366	+	1.20145i	0.0670096	+	0.0486853i
$610$	6.19922	+	19.0792i	0.250999	+	0.772495i
$611$	10.7930	+	33.2175i	0.436638	+	1.34383i
$612$	−7.97466	−	5.79393i	−0.322356	−	0.234206i
$613$	−16.7664	+	12.1815i	−0.677190	+	0.492007i	−0.872424	−	0.488749i	$-0.837453\pi$
$613$	−16.7664	+	12.1815i	−0.677190	+	0.492007i	0.195234	+	0.980757i	$0.437453\pi$
$614$	−17.9464	+	55.2335i	−0.724259	+	2.22904i
$615$	38.3844			1.54781
$616$	−0.817139	−	0.203465i	−0.0329235	−	0.00819784i
$617$	4.49388			0.180917			0.0904584	−	0.995900i	$-0.471167\pi$
$617$	4.49388			0.180917			0.0904584	+	0.995900i	$0.471167\pi$
$618$	−2.47615	+	7.62080i	−0.0996053	+	0.306554i
$619$	13.1647	−	9.56469i	0.529133	−	0.384437i	−0.290900	−	0.956753i	$-0.593955\pi$
$619$	13.1647	−	9.56469i	0.529133	−	0.384437i	0.820033	+	0.572316i	$0.193955\pi$
$620$	−48.3027	−	35.0940i	−1.93988	−	1.40941i
$621$	−1.69846	−	5.22731i	−0.0681567	−	0.209765i
$622$	3.85120	+	11.8528i	0.154419	+	0.475253i
$623$	−0.534708	−	0.388488i	−0.0214226	−	0.0155645i
$624$	−40.9652	+	29.7629i	−1.63992	+	1.19147i
$625$	−0.719628	+	2.21479i	−0.0287851	+	0.0885915i
$626$	23.9902			0.958841
$627$	−9.35113	+	14.9753i	−0.373448	+	0.598057i
$628$	12.9060			0.515005
$629$	−3.06210	+	9.42416i	−0.122094	+	0.375766i
$630$	7.53492	−	5.47444i	0.300198	−	0.218107i
$631$	30.9648	+	22.4972i	1.23269	+	0.895600i	0.997089	−	0.0762501i	$-0.0242947\pi$
$631$	30.9648	+	22.4972i	1.23269	+	0.895600i	0.235599	+	0.971850i	$0.424295\pi$
$632$	−0.418130	−	1.28687i	−0.0166323	−	0.0511890i
$633$	−5.31608	−	16.3612i	−0.211295	−	0.650300i
$634$	−11.9121	−	8.65465i	−0.473090	−	0.343720i
$635$	−36.5494	+	26.5547i	−1.45042	+	1.05379i
$636$	26.2720	−	80.8569i	1.04175	−	3.20619i
$637$	43.2371			1.71312
$638$	−16.4133	+	6.63737i	−0.649811	+	0.262776i
$639$	−30.3136			−1.19919
$640$	−7.32286	+	22.5375i	−0.289462	+	0.890871i
$641$	−32.9688	+	23.9532i	−1.30219	+	0.946096i	−0.999974	−	0.00714353i	$-0.997726\pi$
$641$	−32.9688	+	23.9532i	−1.30219	+	0.946096i	−0.302215	+	0.953240i	$0.597726\pi$
$642$	−64.0666	−	46.5471i	−2.52851	−	1.83707i
$643$	−6.72736	−	20.7047i	−0.265301	−	0.816513i	−0.991624	−	0.129159i	$-0.958772\pi$
$643$	−6.72736	−	20.7047i	−0.265301	−	0.816513i	0.726323	−	0.687354i	$-0.241228\pi$
$644$	0.417566	+	1.28514i	0.0164544	+	0.0506415i
$645$	−28.3342	−	20.5860i	−1.11566	−	0.810572i
$646$	3.38974	−	2.46279i	0.133368	−	0.0968972i
$647$	7.58740	−	23.3516i	0.298292	−	0.918047i	−0.683804	−	0.729665i	$-0.739676\pi$
$647$	7.58740	−	23.3516i	0.298292	−	0.918047i	0.982096	−	0.188382i	$-0.0603242\pi$
$648$	−3.76255			−0.147807
$649$	−15.5497	−	18.5197i	−0.610378	−	0.726960i
$650$	−103.429			−4.05681
$651$	−1.71983	+	5.29309i	−0.0674054	+	0.207453i
$652$	−6.27468	+	4.55882i	−0.245735	+	0.178537i
$653$	−22.5406	−	16.3767i	−0.882082	−	0.640870i	0.0517194	−	0.998662i	$-0.483530\pi$
$653$	−22.5406	−	16.3767i	−0.882082	−	0.640870i	−0.933801	+	0.357792i	$0.883530\pi$
$654$	10.7628	+	33.1246i	0.420860	+	1.29527i
$655$	4.37818	+	13.4747i	0.171070	+	0.526498i
$656$	9.85554	+	7.16047i	0.384794	+	0.279569i
$657$	23.2648	−	16.9029i	0.907646	−	0.659444i
$658$	1.09055	−	3.35637i	0.0425141	−	0.130845i
$659$	−15.3193			−0.596756			−0.298378	−	0.954448i	$-0.596446\pi$
$659$	−15.3193			−0.596756			−0.298378	+	0.954448i	$0.596446\pi$
$660$	5.33815	+	75.9988i	0.207787	+	2.95825i
$661$	−22.0967			−0.859463			−0.429732	−	0.902957i	$-0.641392\pi$
$661$	−22.0967			−0.859463			−0.429732	+	0.902957i	$0.641392\pi$
$662$	4.25024	−	13.0809i	0.165190	−	0.508404i
$663$	13.4945	−	9.80434i	0.524083	−	0.380769i
$664$	4.02327	+	2.92308i	0.156133	+	0.113437i
$665$	0.667487	+	2.05432i	0.0258841	+	0.0796629i
$666$	−26.3685	−	81.1540i	−1.02176	−	3.14465i
$667$	3.84296	+	2.79207i	0.148800	+	0.108110i
$668$	−17.9240	+	13.0226i	−0.693502	+	0.503859i
$669$	19.3236	−	59.4719i	0.747093	−	2.29932i
$670$	−6.14075			−0.237238
$671$	0.619216	+	8.81573i	0.0239046	+	0.340327i
$672$	6.46985			0.249580
$673$	1.50273	−	4.62492i	0.0579259	−	0.178277i	−0.917907	−	0.396795i	$-0.870122\pi$
$673$	1.50273	−	4.62492i	0.0579259	−	0.178277i	0.975833	+	0.218518i	$0.0701222\pi$
$674$	4.67603	−	3.39733i	0.180114	−	0.130860i
$675$	−18.7636	−	13.6325i	−0.722211	−	0.524717i
$676$	19.4151	+	59.7535i	0.746735	+	2.29821i
$677$	−9.04508	−	27.8379i	−0.347631	−	1.06990i	−0.960160	−	0.279450i	$-0.909848\pi$
$677$	−9.04508	−	27.8379i	−0.347631	−	1.06990i	0.612530	−	0.790448i	$-0.290152\pi$
$678$	18.9333	+	13.7558i	0.727129	+	0.528290i
$679$	−1.66271	+	1.20803i	−0.0638090	+	0.0463600i
$680$	0.934186	−	2.87513i	0.0358244	−	0.110256i
$681$	52.9298			2.02827
$682$	−30.9977	−	36.9183i	−1.18696	−	1.41367i
$683$	−17.4193			−0.666531			−0.333265	−	0.942833i	$-0.608150\pi$
$683$	−17.4193			−0.666531			−0.333265	+	0.942833i	$0.608150\pi$
$684$	−6.08336	+	18.7227i	−0.232603	+	0.715879i
$685$	22.7343	−	16.5175i	0.868634	−	0.631100i
$686$	−7.11530	−	5.16957i	−0.271663	−	0.197375i
$687$	18.3912	+	56.6022i	0.701667	+	2.15951i
$688$	−3.43481	−	10.5713i	−0.130951	−	0.403026i
$689$	67.2423	+	48.8544i	2.56173	+	1.86120i
$690$	30.3089	−	22.0207i	1.15384	−	0.838314i
$691$	−2.83777	+	8.73376i	−0.107954	+	0.332248i	−0.990412	−	0.138142i	$-0.955887\pi$
$691$	−2.83777	+	8.73376i	−0.107954	+	0.332248i	0.882458	+	0.470390i	$0.155887\pi$
$692$	52.1794			1.98356
$693$	3.80369	−	1.53817i	0.144490	−	0.0584302i
$694$	1.54899			0.0587989
$695$	−21.1173	+	64.9925i	−0.801026	+	2.46531i
$696$	−4.62213	+	3.35817i	−0.175201	+	0.127291i
$697$	−3.24656	−	2.35876i	−0.122972	−	0.0893445i
$698$	−6.05295	−	18.6291i	−0.229107	−	0.705120i
$699$	−0.0507061	−	0.156057i	−0.00191788	−	0.00590263i
$700$	4.61304	+	3.35157i	0.174356	+	0.126677i
$701$	23.9347	−	17.3896i	0.904002	−	0.656796i	−0.0354889	−	0.999370i	$-0.511299\pi$
$701$	23.9347	−	17.3896i	0.904002	−	0.656796i	0.939491	+	0.342574i	$0.111299\pi$
$702$	−11.9445	+	36.7613i	−0.450815	+	1.38747i
$703$	19.7899			0.746389
$704$	−19.0161	+	30.4532i	−0.716696	+	1.14775i
$705$	−53.3849			−2.01059
$706$	9.17303	−	28.2317i	0.345231	−	1.06251i
$707$	2.75717	−	2.00320i	0.103694	−	0.0753381i
$708$	−37.7582	−	27.4329i	−1.41904	−	1.03099i
$709$	9.92298	+	30.5398i	0.372665	+	1.14695i	0.945040	+	0.326954i	$0.106022\pi$
$709$	9.92298	+	30.5398i	0.372665	+	1.14695i	−0.572375	+	0.819992i	$0.693978\pi$
$710$	−17.1822	−	52.8813i	−0.644836	−	1.98460i
$711$	5.33362	+	3.87510i	0.200026	+	0.145328i
$712$	1.49456	−	1.08586i	0.0560111	−	0.0406944i
$713$	−3.99674	+	12.3007i	−0.149679	+	0.460665i
$714$	−1.68540			−0.0630745
$715$	−72.2748	−	17.9962i	−2.70293	−	0.673021i
$716$	39.8501			1.48927
$717$	−6.43961	+	19.8191i	−0.240492	+	0.740157i
$718$	−6.72772	+	4.88798i	−0.251076	+	0.182418i
$719$	20.9595	+	15.2279i	0.781656	+	0.567907i	0.905476	−	0.424398i	$-0.139514\pi$
$719$	20.9595	+	15.2279i	0.781656	+	0.567907i	−0.123819	+	0.992305i	$0.539514\pi$
$720$	−13.8174	−	42.5256i	−0.514944	−	1.58483i
$721$	0.133456	+	0.410736i	0.00497017	+	0.0152966i
$722$	25.4790	+	18.5116i	0.948231	+	0.688930i
$723$	33.2092	−	24.1279i	1.23506	−	0.897327i
$724$	−11.4619	+	35.2762i	−0.425979	+	1.31103i
$725$	20.0445			0.744433
$726$	−10.6438	+	60.5846i	−0.395027	+	2.24850i
$727$	1.06987			0.0396792			0.0198396	−	0.999803i	$-0.493684\pi$
$727$	1.06987			0.0396792			0.0198396	+	0.999803i	$0.493684\pi$
$728$	0.490993	−	1.51112i	0.0181974	−	0.0560059i
$729$	33.8769	−	24.6130i	1.25470	−	0.911593i
$730$	42.6735	+	31.0041i	1.57942	+	1.14751i
$731$	1.13148	+	3.48233i	0.0418492	+	0.128799i
$732$	5.27073	+	16.2216i	0.194812	+	0.599569i
$733$	−18.9608	−	13.7758i	−0.700331	−	0.508820i	0.179709	−	0.983720i	$-0.442484\pi$
$733$	−18.9608	−	13.7758i	−0.700331	−	0.508820i	−0.880040	+	0.474899i	$0.842484\pi$
$734$	−28.7043	+	20.8549i	−1.05950	+	0.769770i
$735$	−20.4220	+	62.8523i	−0.753275	+	2.31834i
$736$	15.0354			0.554212
$737$	−2.62502	−	0.653621i	−0.0966937	−	0.0240765i
$738$	34.5567			1.27205
$739$	−4.96312	+	15.2749i	−0.182571	+	0.561897i	−0.999898	−	0.0142774i	$-0.995455\pi$
$739$	−4.96312	+	15.2749i	−0.182571	+	0.561897i	0.817327	+	0.576175i	$0.195455\pi$
$740$	69.0884	−	50.1957i	2.53974	−	1.84523i
$741$	−26.9503	−	19.5805i	−0.990045	−	0.719309i
$742$	−2.59520	−	7.98719i	−0.0952727	−	0.293219i
$743$	−7.76371	−	23.8942i	−0.284823	−	0.876595i	−0.986452	−	0.164052i	$-0.947543\pi$
$743$	−7.76371	−	23.8942i	−0.284823	−	0.876595i	0.701629	−	0.712543i	$-0.252457\pi$
$744$	−12.5851	−	9.14363i	−0.461393	−	0.335222i
$745$	−52.5807	+	38.2021i	−1.92641	+	1.39962i
$746$	12.5266	−	38.5529i	0.458631	−	1.41152i
$747$	−24.2302			−0.886537
$748$	4.21870	−	6.75602i	0.154251	−	0.247025i
$749$	−4.26812			−0.155954
$750$	17.8460	−	54.9245i	0.651645	−	2.00556i
$751$	−38.8456	+	28.2230i	−1.41750	+	1.02987i	−0.425318	+	0.905044i	$0.639838\pi$
$751$	−38.8456	+	28.2230i	−1.41750	+	1.02987i	−0.992178	+	0.124827i	$0.960162\pi$
$752$	−13.7070	−	9.95875i	−0.499844	−	0.363158i
$753$	15.3014	+	47.0928i	0.557613	+	1.71616i
$754$	−10.3229	−	31.7707i	−0.375939	−	1.15702i
$755$	58.4473	+	42.4645i	2.12712	+	1.54544i
$756$	1.72397	−	1.25254i	0.0627003	−	0.0455544i
$757$	6.02431	−	18.5409i	0.218957	−	0.673881i	−0.779892	−	0.625914i	$-0.784726\pi$
$757$	6.02431	−	18.5409i	0.218957	−	0.673881i	0.998849	−	0.0479665i	$-0.0152741\pi$
$758$	3.63617			0.132072
$759$	15.3002	−	6.18722i	0.555361	−	0.224582i
$760$	−6.03750			−0.219003
$761$	11.2164	−	34.5207i	0.406596	−	1.25137i	−0.512959	−	0.858413i	$-0.671451\pi$
$761$	11.2164	−	34.5207i	0.406596	−	1.25137i	0.919555	−	0.392961i	$-0.128549\pi$
$762$	−56.9547	+	41.3800i	−2.06325	+	1.49904i
$763$	1.51867	+	1.10338i	0.0549796	+	0.0399450i
$764$	10.9821	+	33.7994i	0.397318	+	1.22282i
$765$	4.55165	+	14.0085i	0.164565	+	0.506480i
$766$	−19.9617	−	14.5030i	−0.721246	−	0.524016i
$767$	36.9135	−	26.8192i	1.33287	−	0.968386i
$768$	6.42135	−	19.7629i	0.231710	−	0.713131i
$769$	−13.0406			−0.470258			−0.235129	−	0.971964i	$-0.575551\pi$
$769$	−13.0406			−0.470258			−0.235129	+	0.971964i	$0.575551\pi$
$770$	4.83929	+	5.76359i	0.174396	+	0.207705i
$771$	−29.7284			−1.07064
$772$	−11.3037	+	34.7893i	−0.406830	+	1.25209i
$773$	−20.2392	+	14.7047i	−0.727955	+	0.528890i	−0.888916	−	0.458071i	$-0.848541\pi$
$773$	−20.2392	+	14.7047i	−0.727955	+	0.528890i	0.160961	+	0.986961i	$0.448541\pi$
$774$	−25.5087	−	18.5331i	−0.916891	−	0.666160i
$775$	16.8652	+	51.9059i	0.605817	+	1.86451i
$776$	−1.77516	−	5.46339i	−0.0637247	−	0.196124i
$777$	−6.44013	−	4.67903i	−0.231038	−	0.167859i
$778$	37.3499	−	27.1363i	1.33906	−	0.972884i
$779$	−2.47659	+	7.62217i	−0.0887331	+	0.273093i
$780$	−143.751			−5.14711
$781$	−1.71626	−	24.4343i	−0.0614127	−	0.874328i
$782$	−3.91673			−0.140062
$783$	2.31484	−	7.12434i	0.0827255	−	0.254603i
$784$	−16.9684	+	12.3283i	−0.606014	+	0.440295i
$785$	−15.6020	−	11.3355i	−0.556860	−	0.404583i
$786$	6.82248	+	20.9974i	0.243350	+	0.748954i
$787$	4.05998	+	12.4953i	0.144723	+	0.445411i	0.996975	−	0.0777200i	$-0.0247640\pi$
$787$	4.05998	+	12.4953i	0.144723	+	0.445411i	−0.852253	+	0.523131i	$0.824764\pi$
$788$	−13.1607	−	9.56178i	−0.468829	−	0.340624i
$789$	29.8234	−	21.6679i	1.06174	−	0.771399i
$790$	−3.73685	+	11.5009i	−0.132951	+	0.409182i
$791$	1.26134			0.0448479
$792$	0.803537	+	11.4399i	0.0285524	+	0.406499i
$793$	−16.6748			−0.592141
$794$	4.55360	−	14.0145i	0.161601	−	0.497357i
$795$	−102.778	+	74.6727i	−3.64516	+	2.64837i
$796$	35.1326	+	25.5253i	1.24524	+	0.904721i
$797$	−1.07969	−	3.32296i	−0.0382447	−	0.117705i	0.930111	−	0.367277i	$-0.119710\pi$
$797$	−1.07969	−	3.32296i	−0.0382447	−	0.117705i	−0.968356	+	0.249572i	$0.919710\pi$
$798$	1.04014	+	3.20122i	0.0368206	+	0.113322i
$799$	4.51530	+	3.28056i	0.159740	+	0.116058i
$800$	51.3286	−	37.2924i	1.81474	−	1.31849i
$801$	−2.78147	+	8.56048i	−0.0982784	+	0.302470i
$802$	−67.5933			−2.38680
$803$	14.9418	+	17.7956i	0.527283	+	0.627994i
$804$	−5.22102			−0.184131
$805$	0.623961	−	1.92035i	0.0219917	−	0.0676836i
$806$	73.5858	−	53.4632i	2.59195	−	1.88316i
$807$	3.47218	+	2.52268i	0.122226	+	0.0888027i
$808$	2.94364	+	9.05960i	0.103557	+	0.318716i
$809$	−0.362243	−	1.11487i	−0.0127358	−	0.0391967i	0.944487	−	0.328550i	$-0.106560\pi$
$809$	−0.362243	−	1.11487i	−0.0127358	−	0.0391967i	−0.957222	+	0.289353i	$0.906560\pi$
$810$	27.2041	+	19.7650i	0.955855	+	0.694470i
$811$	21.9466	−	15.9451i	0.770648	−	0.559909i	−0.131509	−	0.991315i	$-0.541982\pi$
$811$	21.9466	−	15.9451i	0.770648	−	0.559909i	0.902158	+	0.431406i	$0.141982\pi$
$812$	−0.569104	+	1.75152i	−0.0199716	+	0.0614664i
$813$	−55.5174			−1.94708
$814$	63.9214	−	25.8491i	2.24044	−	0.906010i
$815$	11.5895			0.405964
$816$	−2.50039	+	7.69541i	−0.0875312	+	0.269393i
$817$	5.91599	−	4.29822i	0.206974	−	0.150376i
$818$	28.4349	+	20.6591i	0.994201	+	0.722329i
$819$	2.39227	+	7.36266i	0.0835928	+	0.257272i
$820$	10.6871	+	32.8914i	0.373209	+	1.14862i
$821$	−2.16066	−	1.56981i	−0.0754074	−	0.0547867i	0.549443	−	0.835531i	$-0.314840\pi$
$821$	−2.16066	−	1.56981i	−0.0754074	−	0.0547867i	−0.624850	+	0.780745i	$0.714840\pi$
$822$	35.4267	−	25.7390i	1.23565	−	0.897751i
$823$	11.5135	−	35.4350i	0.401336	−	1.23519i	−0.522579	−	0.852591i	$-0.675030\pi$
$823$	11.5135	−	35.4350i	0.401336	−	1.23519i	0.923916	−	0.382596i	$-0.124970\pi$
$824$	−1.20713			−0.0420523
$825$	36.8863	−	59.0714i	1.28422	−	2.05660i
$826$	−4.61032			−0.160413
$827$	0.807928	−	2.48655i	0.0280944	−	0.0864657i	−0.936026	−	0.351930i	$-0.885525\pi$
$827$	0.807928	−	2.48655i	0.0280944	−	0.0864657i	0.964121	+	0.265465i	$0.0855254\pi$
$828$	14.8879	−	10.8167i	0.517390	−	0.375906i
$829$	31.3678	+	22.7900i	1.08945	+	0.791531i	0.979306	−	0.202385i	$-0.0648691\pi$
$829$	31.3678	+	22.7900i	1.08945	+	0.791531i	0.110143	+	0.993916i	$0.464869\pi$
$830$	−13.7340	−	42.2690i	−0.476716	−	1.46718i
$831$	−1.79429	−	5.52227i	−0.0622434	−	0.191565i
$832$	−54.8051	−	39.8182i	−1.90002	−	1.38045i
$833$	5.58963	−	4.06110i	0.193669	−	0.140709i
$834$	−32.9070	+	101.277i	−1.13948	+	3.50694i
$835$	33.1063			1.14569
$836$	−15.4358	−	3.84348i	−0.533860	−	0.132930i
$837$	20.3964			0.705002
$838$	−3.96135	+	12.1918i	−0.136843	+	0.421158i
$839$	37.0244	−	26.8998i	1.27823	−	0.928685i	0.278727	−	0.960370i	$-0.410087\pi$
$839$	37.0244	−	26.8998i	1.27823	−	0.928685i	0.999498	+	0.0316853i	$0.0100874\pi$
$840$	1.96476	+	1.42748i	0.0677906	+	0.0492527i
$841$	−6.96091	−	21.4235i	−0.240031	−	0.738740i
$842$	−23.2038	−	71.4139i	−0.799655	−	2.46108i
$843$	−21.4378	−	15.5755i	−0.738359	−	0.536449i
$844$	12.5397	−	9.11065i	0.431635	−	0.313601i
$845$	29.0116	−	89.2886i	0.998030	−	3.07162i
$846$	−48.0613			−1.65238
$847$	1.45520	+	2.97888i	0.0500011	+	0.102356i
$848$	−40.3191			−1.38456
$849$	14.9247	−	45.9336i	0.512216	−	1.57644i
$850$	−13.3711	+	9.71468i	−0.458625	+	0.333211i
$851$	−14.9663	−	10.8737i	−0.513039	−	0.372744i
$852$	−14.6087	−	44.9610i	−0.500486	−	1.54034i
$853$	15.1725	+	46.6963i	0.519498	+	1.59885i	0.774947	+	0.632027i	$0.217777\pi$
$853$	15.1725	+	46.6963i	0.519498	+	1.59885i	−0.255449	+	0.966823i	$0.582223\pi$
$854$	1.36308	+	0.990339i	0.0466438	+	0.0338887i
$855$	23.7986	−	17.2907i	0.813894	−	0.591328i
$856$	3.68651	−	11.3459i	0.126002	−	0.387795i
$857$	3.28398			0.112179			0.0560893	−	0.998426i	$-0.482137\pi$
$857$	3.28398			0.112179			0.0560893	+	0.998426i	$0.482137\pi$
$858$	−112.625	−	28.0434i	−3.84496	−	0.957385i
$859$	−2.94664			−0.100538			−0.0502690	−	0.998736i	$-0.516008\pi$
$859$	−2.94664			−0.100538			−0.0502690	+	0.998736i	$0.516008\pi$
$860$	9.75117	−	30.0110i	0.332512	−	1.02337i
$861$	2.60810	−	1.89489i	0.0888837	−	0.0645778i
$862$	−39.9324	−	29.0126i	−1.36010	−	0.988173i
$863$	−14.1261	−	43.4756i	−0.480858	−	1.47993i	−0.837892	−	0.545837i	$-0.816212\pi$
$863$	−14.1261	−	43.4756i	−0.480858	−	1.47993i	0.357034	−	0.934091i	$-0.383788\pi$
$864$	−7.32702	−	22.5502i	−0.249270	−	0.767175i
$865$	−63.0796	−	45.8300i	−2.14477	−	1.55827i
$866$	−3.43579	+	2.49625i	−0.116753	+	0.0848259i
$867$	0.823665	−	2.53498i	0.0279731	−	0.0860924i
$868$	−5.01446			−0.170202
$869$	−2.82156	+	4.51857i	−0.0957149	+	0.153282i
$870$	51.0598			1.73109
$871$	1.57729	−	4.85440i	0.0534444	−	0.164485i
$872$	−4.24484	+	3.08405i	−0.143748	+	0.104439i
$873$	22.6438	+	16.4517i	0.766377	+	0.556805i
$874$	2.41720	+	7.43937i	0.0817629	+	0.251640i
$875$	−0.961843	−	2.96025i	−0.0325162	−	0.100075i
$876$	36.2821	+	26.3605i	1.22586	+	0.890638i
$877$	37.0044	−	26.8852i	1.24955	−	0.907850i	0.251353	−	0.967896i	$-0.419125\pi$
$877$	37.0044	−	26.8852i	1.24955	−	0.907850i	0.998196	+	0.0600456i	$0.0191246\pi$
$878$	−0.163612	+	0.503546i	−0.00552163	+	0.0169938i
$879$	−18.6869			−0.630295
$880$	33.4955	−	13.5452i	1.12913	−	0.456609i
$881$	23.6917			0.798193			0.399097	−	0.916909i	$-0.369324\pi$
$881$	23.6917			0.798193			0.399097	+	0.916909i	$0.369324\pi$
$882$	−18.3855	+	56.5847i	−0.619071	+	1.90531i
$883$	−9.32664	+	6.77620i	−0.313866	+	0.228037i	−0.733554	−	0.679632i	$-0.762140\pi$
$883$	−9.32664	+	6.77620i	−0.313866	+	0.228037i	0.419687	+	0.907669i	$0.362140\pi$
$884$	12.1585	+	8.83364i	0.408933	+	0.297107i
$885$	21.5510	+	66.3273i	0.724430	+	2.22957i
$886$	20.4732	+	63.0100i	0.687811	+	2.11686i
$887$	−4.54985	−	3.30566i	−0.152769	−	0.110993i	0.508775	−	0.860900i	$-0.330099\pi$
$887$	−4.54985	−	3.30566i	−0.152769	−	0.110993i	−0.661544	+	0.749906i	$0.730099\pi$
$888$	18.0008	−	13.0783i	0.604066	−	0.438880i
$889$	−1.17251	+	3.60861i	−0.0393247	+	0.121029i
$890$	−16.5101			−0.553421
$891$	9.52529	+	11.3446i	0.319109	+	0.380059i
$892$	56.3413			1.88645
$893$	3.44443	−	10.6009i	0.115264	−	0.354745i
$894$	−81.9361	+	59.5300i	−2.74035	+	1.99098i
$895$	−48.1747	−	35.0010i	−1.61030	−	1.16995i
$896$	0.615023	+	1.89285i	0.0205465	+	0.0632356i
$897$	9.62283	+	29.6160i	0.321297	+	0.988850i
$898$	45.2817	+	32.8991i	1.51107	+	1.09786i
$899$	−14.2609	+	10.3612i	−0.475628	+	0.345564i
$900$	23.9963	−	73.8530i	0.799877	−	2.46177i
$901$	13.2817			0.442477
$902$	1.95650	+	27.8545i	0.0651443	+	0.927453i
$903$	−2.94147			−0.0978858
$904$	−1.08946	+	3.35300i	−0.0362348	+	0.111519i
$905$	44.8399	−	32.5781i	1.49053	−	1.08293i
$906$	91.0780	+	66.1720i	3.02586	+	2.19842i
$907$	2.49162	+	7.66841i	0.0827328	+	0.254625i	0.983863	−	0.178923i	$-0.0572613\pi$
$907$	2.49162	+	7.66841i	0.0827328	+	0.254625i	−0.901130	+	0.433548i	$0.857261\pi$
$908$	14.7368	+	45.3553i	0.489059	+	1.50517i
$909$	−37.5488	−	27.2808i	−1.24541	−	0.904847i
$910$	−11.4880	+	8.34654i	−0.380824	+	0.276685i
$911$	−4.99555	+	15.3747i	−0.165510	+	0.509387i	−0.999074	−	0.0430363i	$-0.986297\pi$
$911$	−4.99555	+	15.3747i	−0.165510	+	0.509387i	0.833564	+	0.552424i	$0.186297\pi$
$912$	16.1597			0.535100
$913$	−1.37184	−	19.5308i	−0.0454013	−	0.646375i
$914$	−77.8851			−2.57621
$915$	7.87594	−	24.2397i	0.260371	−	0.801339i
$916$	−43.3817	+	31.5186i	−1.43337	+	1.04140i
$917$	0.962675	+	0.699425i	0.0317903	+	0.0230970i
$918$	1.90869	+	5.87434i	0.0629962	+	0.193882i
$919$	−7.63068	−	23.4848i	−0.251713	−	0.774692i	−0.994460	−	0.105120i	$-0.966477\pi$
$919$	−7.63068	−	23.4848i	−0.251713	−	0.774692i	0.742747	−	0.669572i	$-0.233523\pi$
$920$	4.56593	+	3.31734i	0.150534	+	0.109370i
$921$	59.6925	−	43.3691i	1.96693	−	1.42906i
$922$	−18.1645	+	55.9047i	−0.598217	+	1.84112i
$923$	46.2172			1.52126
$924$	4.11448	+	4.90035i	0.135356	+	0.161210i
$925$	−78.0627			−2.56669
$926$	9.03130	−	27.7955i	0.296787	−	0.913417i
$927$	4.75824	−	3.45707i	0.156281	−	0.113545i
$928$	16.5783	+	12.0448i	0.544208	+	0.395390i
$929$	1.94161	+	5.97566i	0.0637022	+	0.196055i	0.977842	−	0.209344i	$-0.0671327\pi$
$929$	1.94161	+	5.97566i	0.0637022	+	0.196055i	−0.914140	+	0.405399i	$0.867133\pi$
$930$	42.9612	+	132.221i	1.40875	+	4.33570i
$931$	−11.1632	−	8.11056i	−0.365860	−	0.265813i
$932$	0.119607	−	0.0868997i	0.00391786	−	0.00284649i
$933$	4.89285	−	15.0586i	0.160185	−	0.492997i
$934$	43.0201			1.40766
$935$	−11.0339	+	4.46199i	−0.360847	+	0.145923i
$936$	−21.6384			−0.707274
$937$	−9.58885	+	29.5114i	−0.313254	+	0.964097i	0.663213	+	0.748430i	$0.269192\pi$
$937$	−9.58885	+	29.5114i	−0.313254	+	0.964097i	−0.976467	+	0.215666i	$0.930808\pi$
$938$	−0.417244	+	0.303146i	−0.0136235	+	0.00989805i
$939$	−24.6580	−	17.9151i	−0.804682	−	0.584636i
$940$	−14.8635	−	45.7453i	−0.484795	−	1.49205i
$941$	10.4019	+	32.0136i	0.339091	+	1.04361i	0.964672	+	0.263455i	$0.0848620\pi$
$941$	10.4019	+	32.0136i	0.339091	+	1.04361i	−0.625581	+	0.780159i	$0.715138\pi$
$942$	−24.3125	−	17.6641i	−0.792144	−	0.575527i
$943$	6.06100	−	4.40357i	0.197373	−	0.143400i
$944$	−6.83968	+	21.0504i	−0.222613	+	0.685132i
$945$	−3.18423			−0.103583
$946$	13.4944	−	21.6106i	0.438742	−	0.702621i
$947$	12.5868			0.409016			0.204508	−	0.978865i	$-0.434441\pi$
$947$	12.5868			0.409016			0.204508	+	0.978865i	$0.434441\pi$
$948$	−3.17717	+	9.77831i	−0.103190	+	0.317585i
$949$	−35.4704	+	25.7707i	−1.15142	+	0.836554i
$950$	26.7039	+	19.4015i	0.866388	+	0.629468i
$951$	5.78068	+	17.7911i	0.187451	+	0.576916i
$952$	−0.0784592	−	0.241473i	−0.00254288	−	0.00782617i
$953$	9.99660	+	7.26296i	0.323822	+	0.235270i	0.737804	−	0.675014i	$-0.235863\pi$
$953$	9.99660	+	7.26296i	0.323822	+	0.235270i	−0.413983	+	0.910285i	$0.635863\pi$
$954$	−92.5290	+	67.2263i	−2.99574	+	2.17653i
$955$	16.4103	−	50.5057i	0.531025	−	1.63433i
$956$	−18.7758			−0.607253
$957$	21.8268	+	5.43480i	0.705560	+	0.175682i
$958$	22.9412			0.741196
$959$	0.729319	−	2.24461i	0.0235510	−	0.0724824i
$960$	83.7682	−	60.8612i	2.70361	−	1.96429i
$961$	−13.7501	−	9.99000i	−0.443550	−	0.322258i
$962$	40.2024	+	123.730i	1.29618	+	3.98923i
$963$	17.9618	+	55.2809i	0.578812	+	1.78140i
$964$	29.9213	+	21.7391i	0.963700	+	0.700169i
$965$	44.2211	−	32.1285i	1.42353	−	1.03425i
$966$	0.972313	−	2.99247i	0.0312836	−	0.0962812i
$967$	26.0540			0.837840			0.418920	−	0.908023i	$-0.362409\pi$
$967$	26.0540			0.837840			0.418920	+	0.908023i	$0.362409\pi$
$968$	−9.17564	+	1.29538i	−0.294916	+	0.0416352i
$969$	−5.32322			−0.171007
$970$	−15.8648	+	48.8267i	−0.509387	+	1.56773i
$971$	−8.04084	+	5.84201i	−0.258043	+	0.187479i	−0.709284	−	0.704923i	$-0.750981\pi$
$971$	−8.04084	+	5.84201i	−0.258043	+	0.187479i	0.451241	+	0.892402i	$0.350981\pi$
$972$	40.2897	+	29.2722i	1.29229	+	0.938905i
$973$	1.77358	+	5.45851i	0.0568583	+	0.174992i
$974$	2.51136	+	7.72916i	0.0804690	+	0.247658i
$975$	106.308	+	77.2370i	3.40457	+	2.47357i
$976$	6.54404	−	4.75452i	0.209469	−	0.152188i
$977$	−8.58026	+	26.4073i	−0.274507	+	0.844845i	0.714843	+	0.699285i	$0.246498\pi$
$977$	−8.58026	+	26.4073i	−0.274507	+	0.844845i	−0.989349	+	0.145560i	$0.953502\pi$
$978$	18.0599			0.577491
$979$	−7.05767	−	1.75734i	−0.225564	−	0.0561648i
$980$	−59.5438			−1.90206
$981$	7.89990	−	24.3134i	0.252224	−	0.776266i
$982$	8.98780	−	6.53002i	0.286812	−	0.208381i
$983$	−42.4094	−	30.8122i	−1.35265	−	0.982757i	−0.998875	−	0.0474267i	$-0.984898\pi$
$983$	−42.4094	−	30.8122i	−1.35265	−	0.982757i	−0.353775	−	0.935331i	$-0.615102\pi$
$984$	2.78449	+	8.56977i	0.0887662	+	0.273194i
$985$	7.51164	+	23.1184i	0.239341	+	0.736615i
$986$	−4.31864	−	3.13768i	−0.137534	−	0.0999240i
$987$	−3.62733	+	2.63541i	−0.115459	+	0.0838860i
$988$	9.27492	−	28.5453i	0.295074	−	0.908146i
$989$	−6.83572			−0.217363
$990$	54.2848	−	86.9341i	1.72528	−	2.76295i
$991$	−45.0898			−1.43232			−0.716162	−	0.697934i	$-0.754103\pi$
$991$	−45.0898			−1.43232			−0.716162	+	0.697934i	$0.754103\pi$
$992$	−17.2417	+	53.0644i	−0.547423	+	1.68479i
$993$	−14.1369	+	10.2711i	−0.448622	+	0.325943i
$994$	−3.77802	−	2.74489i	−0.119832	−	0.0870627i
$995$	−20.0524	−	61.7151i	−0.635705	−	1.95650i
$996$	−11.6770	−	35.9382i	−0.370001	−	1.13874i
$997$	28.8677	+	20.9736i	0.914248	+	0.664240i	0.942086	−	0.335372i	$-0.108862\pi$
$997$	28.8677	+	20.9736i	0.914248	+	0.664240i	−0.0278376	+	0.999612i	$0.508862\pi$
$998$	67.9104	−	49.3398i	2.14966	−	1.56182i
$999$	−9.01508	+	27.7456i	−0.285224	+	0.877831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.86.8	✓	36
11.4	even	5		2057.2.a.bd.1.15		18
11.5	even	5	inner	187.2.g.f.137.8	yes	36
11.7	odd	10		2057.2.a.be.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.86.8	✓	36	1.1	even	1	trivial
187.2.g.f.137.8	yes	36	11.5	even	5	inner
2057.2.a.bd.1.15		18	11.4	even	5
2057.2.a.be.1.4		18	11.7	odd	10

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.648313 - 1.99530i) q^{2} +(-2.15638 + 1.56670i) q^{3} +(-1.94289 - 1.41159i) q^{4} +(1.10893 + 3.41293i) q^{5} +(1.72804 + 5.31835i) q^{6} +(0.243832 + 0.177154i) q^{7} +(-0.681533 + 0.495163i) q^{8} +(1.26837 - 3.90365i) q^{9} +O(q^{10})\)	\(q+(0.648313 - 1.99530i) q^{2} +(-2.15638 + 1.56670i) q^{3} +(-1.94289 - 1.41159i) q^{4} +(1.10893 + 3.41293i) q^{5} +(1.72804 + 5.31835i) q^{6} +(0.243832 + 0.177154i) q^{7} +(-0.681533 + 0.495163i) q^{8} +(1.26837 - 3.90365i) q^{9} +7.52877 q^{10} +(3.21836 + 0.801361i) q^{11} +6.40114 q^{12} +(-1.93381 + 5.95165i) q^{13} +(0.511555 - 0.371666i) q^{14} +(-7.73833 - 5.62223i) q^{15} +(-0.938080 - 2.88711i) q^{16} +(0.309017 + 0.951057i) q^{17} +(-6.96666 - 5.06158i) q^{18} +(1.61571 - 1.17388i) q^{19} +(2.66314 - 8.19629i) q^{20} -0.803342 q^{21} +(3.68546 - 5.90206i) q^{22} -1.86690 q^{23} +(0.693872 - 2.13552i) q^{24} +(-6.37331 + 4.63048i) q^{25} +(10.6216 + 7.71707i) q^{26} +(0.909773 + 2.79999i) q^{27} +(-0.223668 - 0.688380i) q^{28} +(-2.05847 - 1.49557i) q^{29} +(-16.2349 + 11.7953i) q^{30} +(2.14084 - 6.58884i) q^{31} -8.05367 q^{32} +(-8.19550 + 3.31417i) q^{33} +2.09798 q^{34} +(-0.334223 + 1.02863i) q^{35} +(-7.97466 + 5.79393i) q^{36} +(8.01667 + 5.82445i) q^{37} +(-1.29477 - 3.98488i) q^{38} +(-5.15444 - 15.8637i) q^{39} +(-2.44573 - 1.77693i) q^{40} +(-3.24656 + 2.35876i) q^{41} +(-0.520817 + 1.60291i) q^{42} +3.66154 q^{43} +(-5.12170 - 6.09995i) q^{44} +14.7294 q^{45} +(-1.21033 + 3.72503i) q^{46} +(4.51530 - 3.28056i) q^{47} +(6.54611 + 4.75603i) q^{48} +(-2.13505 - 6.57100i) q^{49} +(5.10731 + 15.7187i) q^{50} +(-2.15638 - 1.56670i) q^{51} +(12.1585 - 8.83364i) q^{52} +(4.10427 - 12.6316i) q^{53} +6.17665 q^{54} +(0.833937 + 11.8727i) q^{55} -0.253899 q^{56} +(-1.64497 + 5.06269i) q^{57} +(-4.31864 + 3.13768i) q^{58} +(-5.89867 - 4.28563i) q^{59} +(7.09842 + 21.8467i) q^{60} +(0.823404 + 2.53418i) q^{61} +(-11.7588 - 8.54326i) q^{62} +(1.00082 - 0.727136i) q^{63} +(-3.34514 + 10.2953i) q^{64} -22.4571 q^{65} +(1.29952 + 18.5011i) q^{66} -0.815639 q^{67} +(0.742116 - 2.28400i) q^{68} +(4.02575 - 2.92488i) q^{69} +(1.83575 + 1.33375i) q^{70} +(-2.28220 - 7.02390i) q^{71} +(1.06850 + 3.28852i) q^{72} +(5.66806 + 4.11809i) q^{73} +(16.8188 - 12.2196i) q^{74} +(6.48870 - 19.9702i) q^{75} -4.79619 q^{76} +(0.642773 + 0.765542i) q^{77} -34.9947 q^{78} +(-0.496343 + 1.52759i) q^{79} +(8.81326 - 6.40321i) q^{80} +(3.61336 + 2.62526i) q^{81} +(2.60166 + 8.00708i) q^{82} +(-1.82421 - 5.61434i) q^{83} +(1.56080 + 1.13399i) q^{84} +(-2.90322 + 2.10931i) q^{85} +(2.37382 - 7.30587i) q^{86} +6.78196 q^{87} +(-2.59022 + 1.04746i) q^{88} -2.19294 q^{89} +(9.54929 - 29.3897i) q^{90} +(-1.52588 + 1.10862i) q^{91} +(3.62717 + 2.63529i) q^{92} +(5.70628 + 17.5621i) q^{93} +(-3.61837 - 11.1362i) q^{94} +(5.79810 + 4.21257i) q^{95} +(17.3668 - 12.6177i) q^{96} +(-2.10722 + 6.48535i) q^{97} -14.4953 q^{98} +(7.21032 - 11.5469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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