LMFDB - Embedded newform 185.2.e.b.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(26,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("185.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, degree $2$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 13 x^{12} - 16 x^{11} + 98 x^{10} - 116 x^{9} + 378 x^{8} - 264 x^{7} + 795 x^{6} + \cdots + 9 $ x^14 - 2x^13 + 13x^12 - 16x^11 + 98x^10 - 116x^9 + 378x^8 - 264x^7 + 795x^6 - 520x^5 + 927x^4 - 71x^3 + 94x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$-0.155125 - 0.268684i$ of defining polynomial
Character	$\chi$	$=$	185.121
Dual form			185.2.e.b.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.155125 + 0.268684i) q^{2} +(-1.03095 - 1.78566i) q^{3} +(0.951873 + 1.64869i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.639704 q^{6} +(1.06035 + 1.83659i) q^{7} -1.21113 q^{8} +(-0.625722 + 1.08378i) q^{9} +O(q^{10})$	\(q+(-0.155125 + 0.268684i) q^{2} +(-1.03095 - 1.78566i) q^{3} +(0.951873 + 1.64869i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.639704 q^{6} +(1.06035 + 1.83659i) q^{7} -1.21113 q^{8} +(-0.625722 + 1.08378i) q^{9} -0.310249 q^{10} +5.48703 q^{11} +(1.96267 - 3.39944i) q^{12} +(-0.826151 - 1.43093i) q^{13} -0.657948 q^{14} +(1.03095 - 1.78566i) q^{15} +(-1.71587 + 2.97197i) q^{16} +(1.42247 - 2.46379i) q^{17} +(-0.194130 - 0.336243i) q^{18} +(1.19568 + 2.07098i) q^{19} +(-0.951873 + 1.64869i) q^{20} +(2.18635 - 3.78686i) q^{21} +(-0.851174 + 1.47428i) q^{22} +1.29182 q^{23} +(1.24862 + 2.16267i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.512625 q^{26} -3.60535 q^{27} +(-2.01864 + 3.49639i) q^{28} -0.459480 q^{29} +(0.319852 + 0.554000i) q^{30} -7.00913 q^{31} +(-1.74348 - 3.01980i) q^{32} +(-5.65686 - 9.79798i) q^{33} +(0.441320 + 0.764389i) q^{34} +(-1.06035 + 1.83659i) q^{35} -2.38243 q^{36} +(-2.41356 + 5.58343i) q^{37} -0.741917 q^{38} +(-1.70344 + 2.95045i) q^{39} +(-0.605567 - 1.04887i) q^{40} +(-3.63843 - 6.30194i) q^{41} +(0.678313 + 1.17487i) q^{42} -4.39190 q^{43} +(5.22296 + 9.04642i) q^{44} -1.25144 q^{45} +(-0.200394 + 0.347092i) q^{46} -0.310249 q^{47} +7.07591 q^{48} +(1.25130 - 2.16731i) q^{49} +(-0.155125 - 0.268684i) q^{50} -5.86599 q^{51} +(1.57278 - 2.72414i) q^{52} +(6.00746 - 10.4052i) q^{53} +(0.559279 - 0.968700i) q^{54} +(2.74352 + 4.75191i) q^{55} +(-1.28423 - 2.22435i) q^{56} +(2.46537 - 4.27015i) q^{57} +(0.0712767 - 0.123455i) q^{58} +(-4.14947 + 7.18709i) q^{59} +3.92534 q^{60} +(-5.10365 - 8.83978i) q^{61} +(1.08729 - 1.88324i) q^{62} -2.65395 q^{63} -5.78165 q^{64} +(0.826151 - 1.43093i) q^{65} +3.51008 q^{66} +(-0.664518 - 1.15098i) q^{67} +5.41604 q^{68} +(-1.33181 - 2.30676i) q^{69} +(-0.328974 - 0.569800i) q^{70} +(-0.293650 - 0.508617i) q^{71} +(0.757834 - 1.31261i) q^{72} +10.8030 q^{73} +(-1.12578 - 1.51461i) q^{74} +2.06190 q^{75} +(-2.27627 + 3.94261i) q^{76} +(5.81820 + 10.0774i) q^{77} +(-0.528492 - 0.915375i) q^{78} +(1.41967 + 2.45893i) q^{79} -3.43174 q^{80} +(5.59411 + 9.68928i) q^{81} +2.25764 q^{82} +(-5.91099 + 10.2381i) q^{83} +8.32450 q^{84} +2.84494 q^{85} +(0.681292 - 1.18003i) q^{86} +(0.473702 + 0.820476i) q^{87} -6.64553 q^{88} +(8.40980 - 14.5662i) q^{89} +(0.194130 - 0.336243i) q^{90} +(1.75202 - 3.03459i) q^{91} +(1.22965 + 2.12982i) q^{92} +(7.22607 + 12.5159i) q^{93} +(0.0481273 - 0.0833590i) q^{94} +(-1.19568 + 2.07098i) q^{95} +(-3.59489 + 6.22653i) q^{96} -18.5979 q^{97} +(0.388215 + 0.672407i) q^{98} +(-3.43336 + 5.94675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.155125	+	0.268684i	−0.109690	+	0.189988i	−0.915645	−	0.401989i	$-0.868319\pi$
$2$	−0.155125	+	0.268684i	−0.109690	+	0.189988i	0.805955	+	0.591977i	$0.201652\pi$
$3$	−1.03095	−	1.78566i	−0.595220	−	1.03095i	−0.993516	−	0.113694i	$-0.963732\pi$
$3$	−1.03095	−	1.78566i	−0.595220	−	1.03095i	0.398296	−	0.917257i	$-0.369602\pi$
$4$	0.951873	+	1.64869i	0.475936	+	0.824346i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.639704			0.261158
$7$	1.06035	+	1.83659i	0.400776	+	0.694165i	0.993820	−	0.111006i	$-0.0354072\pi$
$7$	1.06035	+	1.83659i	0.400776	+	0.694165i	−0.593044	+	0.805170i	$0.702074\pi$
$8$	−1.21113			−0.428201
$9$	−0.625722	+	1.08378i	−0.208574	+	0.361261i
$10$	−0.310249			−0.0981094
$11$	5.48703			1.65440			0.827201	−	0.561906i	$-0.189932\pi$
$11$	5.48703			1.65440			0.827201	+	0.561906i	$0.189932\pi$
$12$	1.96267	−	3.39944i	0.566574	−	0.981335i
$13$	−0.826151	−	1.43093i	−0.229133	−	0.396870i	0.728418	−	0.685133i	$-0.240256\pi$
$13$	−0.826151	−	1.43093i	−0.229133	−	0.396870i	−0.957551	+	0.288263i	$0.906922\pi$
$14$	−0.657948			−0.175844
$15$	1.03095	−	1.78566i	0.266191	−	0.461056i
$16$	−1.71587	+	2.97197i	−0.428967	+	0.742993i
$17$	1.42247	−	2.46379i	0.345000	−	0.597557i	−0.640354	−	0.768080i	$-0.721212\pi$
$17$	1.42247	−	2.46379i	0.345000	−	0.597557i	0.985354	+	0.170523i	$0.0545457\pi$
$18$	−0.194130	−	0.336243i	−0.0457568	−	0.0792532i
$19$	1.19568	+	2.07098i	0.274308	+	0.475115i	0.969960	−	0.243264i	$-0.0782180\pi$
$19$	1.19568	+	2.07098i	0.274308	+	0.475115i	−0.695653	+	0.718378i	$0.744885\pi$
$20$	−0.951873	+	1.64869i	−0.212845	+	0.368659i
$21$	2.18635	−	3.78686i	0.477100	−	0.826362i
$22$	−0.851174	+	1.47428i	−0.181471	+	0.314317i
$23$	1.29182			0.269364			0.134682	−	0.990889i	$-0.456999\pi$
$23$	1.29182			0.269364			0.134682	+	0.990889i	$0.456999\pi$
$24$	1.24862	+	2.16267i	0.254874	+	0.441454i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.512625			0.100534
$27$	−3.60535			−0.693850
$28$	−2.01864	+	3.49639i	−0.381488	+	0.660756i
$29$	−0.459480			−0.0853234			−0.0426617	−	0.999090i	$-0.513584\pi$
$29$	−0.459480			−0.0853234			−0.0426617	+	0.999090i	$0.513584\pi$
$30$	0.319852	+	0.554000i	0.0583967	+	0.101146i
$31$	−7.00913			−1.25888			−0.629438	−	0.777051i	$-0.716715\pi$
$31$	−7.00913			−1.25888			−0.629438	+	0.777051i	$0.716715\pi$
$32$	−1.74348	−	3.01980i	−0.308207	−	0.533830i
$33$	−5.65686	−	9.79798i	−0.984734	−	1.70561i
$34$	0.441320	+	0.764389i	0.0756858	+	0.131092i
$35$	−1.06035	+	1.83659i	−0.179233	+	0.310440i
$36$	−2.38243			−0.397072
$37$	−2.41356	+	5.58343i	−0.396786	+	0.917911i
$37$	−2.41356	+	5.58343i	−0.396786	+	0.917911i
$38$	−0.741917			−0.120355
$39$	−1.70344	+	2.95045i	−0.272769	+	0.472450i
$40$	−0.605567	−	1.04887i	−0.0957486	−	0.165841i
$41$	−3.63843	−	6.30194i	−0.568227	−	0.984198i	−0.996741	−	0.0806634i	$-0.974296\pi$
$41$	−3.63843	−	6.30194i	−0.568227	−	0.984198i	0.428514	−	0.903535i	$-0.359037\pi$
$42$	0.678313	+	1.17487i	0.104666	+	0.181287i
$43$	−4.39190			−0.669758			−0.334879	−	0.942261i	$-0.608696\pi$
$43$	−4.39190			−0.669758			−0.334879	+	0.942261i	$0.608696\pi$
$44$	5.22296	+	9.04642i	0.787390	+	1.36380i
$45$	−1.25144			−0.186554
$46$	−0.200394	+	0.347092i	−0.0295464	+	0.0511759i
$47$	−0.310249			−0.0452545			−0.0226273	−	0.999744i	$-0.507203\pi$
$47$	−0.310249			−0.0452545			−0.0226273	+	0.999744i	$0.507203\pi$
$48$	7.07591			1.02132
$49$	1.25130	−	2.16731i	0.178757	−	0.309616i
$50$	−0.155125	−	0.268684i	−0.0219379	−	0.0379976i
$51$	−5.86599			−0.821403
$52$	1.57278	−	2.72414i	0.218105	−	0.377770i
$53$	6.00746	−	10.4052i	0.825188	−	1.42927i	−0.0765878	−	0.997063i	$-0.524403\pi$
$53$	6.00746	−	10.4052i	0.825188	−	1.42927i	0.901776	−	0.432204i	$-0.142264\pi$
$54$	0.559279	−	0.968700i	0.0761082	−	0.131823i
$55$	2.74352	+	4.75191i	0.369936	+	0.640747i
$56$	−1.28423	−	2.22435i	−0.171613	−	0.297242i
$57$	2.46537	−	4.27015i	0.326547	−	0.565596i
$58$	0.0712767	−	0.123455i	0.00935910	−	0.0162104i
$59$	−4.14947	+	7.18709i	−0.540215	+	0.935680i	0.458676	+	0.888603i	$0.348324\pi$
$59$	−4.14947	+	7.18709i	−0.540215	+	0.935680i	−0.998891	+	0.0470765i	$0.985010\pi$
$60$	3.92534			0.506759
$61$	−5.10365	−	8.83978i	−0.653456	−	1.13182i	−0.982279	−	0.187427i	$-0.939985\pi$
$61$	−5.10365	−	8.83978i	−0.653456	−	1.13182i	0.328823	−	0.944392i	$-0.393348\pi$
$62$	1.08729	−	1.88324i	0.138086	−	0.239172i
$63$	−2.65395			−0.334366
$64$	−5.78165			−0.722706
$65$	0.826151	−	1.43093i	0.102471	−	0.177486i
$66$	3.51008			0.432061
$67$	−0.664518	−	1.15098i	−0.0811838	−	0.140614i	0.822575	−	0.568657i	$-0.192537\pi$
$67$	−0.664518	−	1.15098i	−0.0811838	−	0.140614i	−0.903759	+	0.428042i	$0.859203\pi$
$68$	5.41604			0.656792
$69$	−1.33181	−	2.30676i	−0.160331	−	0.277701i
$70$	−0.328974	−	0.569800i	−0.0393199	−	0.0681041i
$71$	−0.293650	−	0.508617i	−0.0348498	−	0.0603617i	0.848074	−	0.529877i	$-0.177762\pi$
$71$	−0.293650	−	0.508617i	−0.0348498	−	0.0603617i	−0.882924	+	0.469515i	$0.844429\pi$
$72$	0.757834	−	1.31261i	0.0893115	−	0.154692i
$73$	10.8030			1.26439			0.632197	−	0.774808i	$-0.282153\pi$
$73$	10.8030			1.26439			0.632197	+	0.774808i	$0.282153\pi$
$74$	−1.12578	−	1.51461i	−0.130869	−	0.176070i
$75$	2.06190			0.238088
$76$	−2.27627	+	3.94261i	−0.261106	+	0.452249i
$77$	5.81820	+	10.0774i	0.663045	+	1.14843i
$78$	−0.528492	−	0.915375i	−0.0598399	−	0.103646i
$79$	1.41967	+	2.45893i	0.159725	+	0.276652i	0.934769	−	0.355255i	$-0.115606\pi$
$79$	1.41967	+	2.45893i	0.159725	+	0.276652i	−0.775045	+	0.631907i	$0.782273\pi$
$80$	−3.43174			−0.383680
$81$	5.59411	+	9.68928i	0.621568	+	1.07659i
$82$	2.25764			0.249315
$83$	−5.91099	+	10.2381i	−0.648815	+	1.12378i	0.334591	+	0.942363i	$0.391402\pi$
$83$	−5.91099	+	10.2381i	−0.648815	+	1.12378i	−0.983406	+	0.181417i	$0.941932\pi$
$84$	8.32450			0.908277
$85$	2.84494			0.308577
$86$	0.681292	−	1.18003i	0.0734656	−	0.127246i
$87$	0.473702	+	0.820476i	0.0507862	+	0.0879643i
$88$	−6.64553			−0.708416
$89$	8.40980	−	14.5662i	0.891437	−	1.54401i	0.0532843	−	0.998579i	$-0.483031\pi$
$89$	8.40980	−	14.5662i	0.891437	−	1.54401i	0.838153	−	0.545435i	$-0.183636\pi$
$90$	0.194130	−	0.336243i	0.0204631	−	0.0354431i
$91$	1.75202	−	3.03459i	0.183662	−	0.318112i
$92$	1.22965	+	2.12982i	0.128200	+	0.222049i
$93$	7.22607	+	12.5159i	0.749308	+	1.29784i
$94$	0.0481273	−	0.0833590i	0.00496395	−	0.00859782i
$95$	−1.19568	+	2.07098i	−0.122674	+	0.212478i
$96$	−3.59489	+	6.22653i	−0.366902	+	0.635493i
$97$	−18.5979			−1.88833			−0.944165	−	0.329472i	$-0.893129\pi$
$97$	−18.5979			−1.88833			−0.944165	+	0.329472i	$0.893129\pi$
$98$	0.388215	+	0.672407i	0.0392156	+	0.0679234i
$99$	−3.43336	+	5.94675i	−0.345065	+	0.597671i
$100$	−1.90375			−0.190375
$101$	−8.79352			−0.874988			−0.437494	−	0.899221i	$-0.644134\pi$
$101$	−8.79352			−0.874988			−0.437494	+	0.899221i	$0.644134\pi$
$102$	0.909960	−	1.57610i	0.0900994	−	0.156057i
$103$	5.36532			0.528660			0.264330	−	0.964432i	$-0.414849\pi$
$103$	5.36532			0.528660			0.264330	+	0.964432i	$0.414849\pi$
$104$	1.00058	+	1.73305i	0.0981149	+	0.169940i
$105$	4.37269			0.426731
$106$	1.86381	+	3.22821i	0.181029	+	0.313552i
$107$	1.42697	+	2.47158i	0.137950	+	0.238937i	0.926721	−	0.375751i	$-0.122615\pi$
$107$	1.42697	+	2.47158i	0.137950	+	0.238937i	−0.788770	+	0.614688i	$0.789282\pi$
$108$	−3.43184	−	5.94412i	−0.330229	−	0.571973i
$109$	−4.37956	+	7.58562i	−0.419486	+	0.726571i	−0.995888	−	0.0905956i	$-0.971123\pi$
$109$	−4.37956	+	7.58562i	−0.419486	+	0.726571i	0.576402	+	0.817166i	$0.304456\pi$
$110$	−1.70235			−0.162312
$111$	12.4584	−	1.44646i	1.18250	−	0.137292i
$112$	−7.27771			−0.687679
$113$	7.88239	−	13.6527i	0.741513	−	1.28434i	−0.210294	−	0.977638i	$-0.567442\pi$
$113$	7.88239	−	13.6527i	0.741513	−	1.28434i	0.951806	−	0.306699i	$-0.0992246\pi$
$114$	0.764881	+	1.32481i	0.0716376	+	0.124080i
$115$	0.645912	+	1.11875i	0.0602316	+	0.104324i
$116$	−0.437367	−	0.757542i	−0.0406085	−	0.0703360i
$117$	2.06776			0.191165
$118$	−1.28737	−	2.22979i	−0.118512	−	0.205269i
$119$	6.03329			0.553071
$120$	−1.24862	+	2.16267i	−0.113983	+	0.197424i
$121$	19.1075			1.73705
$122$	3.16681			0.286709
$123$	−7.50209	+	12.9940i	−0.676441	+	1.17163i
$124$	−6.67180	−	11.5559i	−0.599145	−	1.03775i
$125$	−1.00000			−0.0894427
$126$	0.411693	−	0.713073i	0.0366765	−	0.0635256i
$127$	−2.00325	+	3.46973i	−0.177760	+	0.307889i	−0.941113	−	0.338093i	$-0.890218\pi$
$127$	−2.00325	+	3.46973i	−0.177760	+	0.307889i	0.763353	+	0.645981i	$0.223552\pi$
$128$	4.38384	−	7.59303i	0.387480	−	0.671135i
$129$	4.52784	+	7.84244i	0.398654	+	0.690489i
$130$	0.256313	+	0.443946i	0.0224801	+	0.0389367i
$131$	10.2080	−	17.6807i	0.891873	−	1.54477i	0.0542464	−	0.998528i	$-0.482724\pi$
$131$	10.2080	−	17.6807i	0.891873	−	1.54477i	0.837627	−	0.546243i	$-0.183942\pi$
$132$	10.7692	−	18.6529i	0.937341	−	1.62352i
$133$	−2.53569	+	4.39194i	−0.219872	+	0.380829i
$134$	0.412332			0.0356201
$135$	−1.80268	−	3.12233i	−0.155150	−	0.268727i
$136$	−1.72280	+	2.98398i	−0.147729	+	0.255874i
$137$	−5.52931			−0.472401			−0.236200	−	0.971704i	$-0.575902\pi$
$137$	−5.52931			−0.472401			−0.236200	+	0.971704i	$0.575902\pi$
$138$	0.826385			0.0703465
$139$	10.4632	−	18.1228i	0.887477	−	1.53716i	0.0446295	−	0.999004i	$-0.485789\pi$
$139$	10.4632	−	18.1228i	0.887477	−	1.53716i	0.842848	−	0.538152i	$-0.180877\pi$
$140$	−4.03729			−0.341213
$141$	0.319852	+	0.554000i	0.0269364	+	0.0466552i
$142$	0.182209			0.0152907
$143$	−4.53311	−	7.85158i	−0.379078	−	0.656582i
$144$	−2.14731	−	3.71926i	−0.178943	−	0.309938i
$145$	−0.229740	−	0.397922i	−0.0190789	−	0.0330456i
$146$	−1.67581	+	2.90259i	−0.138691	+	0.240220i
$147$	−5.16011			−0.425599
$148$	−11.5028	+	1.33551i	−0.945521	+	0.109778i
$149$	−4.87785			−0.399609			−0.199804	−	0.979836i	$-0.564031\pi$
$149$	−4.87785			−0.399609			−0.199804	+	0.979836i	$0.564031\pi$
$150$	−0.319852	+	0.554000i	−0.0261158	+	0.0452339i
$151$	11.8485	+	20.5222i	0.964216	+	1.67007i	0.711708	+	0.702475i	$0.247922\pi$
$151$	11.8485	+	20.5222i	0.964216	+	1.67007i	0.252507	+	0.967595i	$0.418745\pi$
$152$	−1.44813	−	2.50823i	−0.117459	−	0.203444i
$153$	1.78014	+	3.08330i	0.143916	+	0.249270i
$154$	−3.61018			−0.290917
$155$	−3.50456	−	6.07008i	−0.281493	−	0.487561i
$156$	−6.48584			−0.519283
$157$	−10.5385	+	18.2533i	−0.841067	+	1.45677i	0.0479266	+	0.998851i	$0.484739\pi$
$157$	−10.5385	+	18.2533i	−0.841067	+	1.45677i	−0.888994	+	0.457920i	$0.848595\pi$
$158$	−0.880901			−0.0700807
$159$	−24.7736			−1.96467
$160$	1.74348	−	3.01980i	0.137834	−	0.238736i
$161$	1.36979	+	2.37255i	0.107955	+	0.186983i
$162$	−3.47114			−0.272718
$163$	−2.60566	+	4.51313i	−0.204091	+	0.353496i	−0.949843	−	0.312728i	$-0.898757\pi$
$163$	−2.60566	+	4.51313i	−0.204091	+	0.353496i	0.745752	+	0.666224i	$0.232090\pi$
$164$	6.92664	−	11.9973i	0.540880	−	0.936832i
$165$	5.65686	−	9.79798i	0.440386	−	0.762771i
$166$	−1.83388	−	3.17637i	−0.142337	−	0.246534i
$167$	5.28579	+	9.15526i	0.409027	+	0.708455i	0.994781	−	0.102034i	$-0.0325349\pi$
$167$	5.28579	+	9.15526i	0.409027	+	0.708455i	−0.585754	+	0.810489i	$0.699202\pi$
$168$	−2.64796	+	4.58640i	−0.204295	+	0.353849i
$169$	5.13495	−	8.89400i	0.394996	−	0.684153i
$170$	−0.441320	+	0.764389i	−0.0338477	+	0.0586260i
$171$	−2.99265			−0.228854
$172$	−4.18053	−	7.24089i	−0.318762	−	0.552113i
$173$	−6.76942	+	11.7250i	−0.514670	+	0.891434i	0.485185	+	0.874411i	$0.338752\pi$
$173$	−6.76942	+	11.7250i	−0.514670	+	0.891434i	−0.999855	+	0.0170229i	$0.994581\pi$
$174$	−0.293931			−0.0222829
$175$	−2.12071			−0.160310
$176$	−9.41503	+	16.3073i	−0.709684	+	1.22921i
$177$	17.1116			1.28619
$178$	2.60914	+	4.51915i	0.195563	+	0.338725i
$179$	−14.8133			−1.10720			−0.553599	−	0.832783i	$-0.686746\pi$
$179$	−14.8133			−1.10720			−0.553599	+	0.832783i	$0.686746\pi$
$180$	−1.19122	−	2.06325i	−0.0887880	−	0.153785i
$181$	−2.30881	−	3.99897i	−0.171612	−	0.297241i	0.767371	−	0.641203i	$-0.221564\pi$
$181$	−2.30881	−	3.99897i	−0.171612	−	0.297241i	−0.938984	+	0.343962i	$0.888231\pi$
$182$	0.543564	+	0.941481i	0.0402917	+	0.0697872i
$183$	−10.5232	+	18.2268i	−0.777900	+	1.34736i
$184$	−1.56457			−0.115342
$185$	−6.04217	+	0.701515i	−0.444230	+	0.0515764i
$186$	−4.48377			−0.328766
$187$	7.80514	−	13.5189i	0.570768	−	0.988600i
$188$	−0.295318	−	0.511505i	−0.0215383	−	0.0373054i
$189$	−3.82295	−	6.62154i	−0.278079	−	0.481646i
$190$	−0.370959	−	0.642519i	−0.0269122	−	0.0466132i
$191$	−11.6768			−0.844902			−0.422451	−	0.906386i	$-0.638830\pi$
$191$	−11.6768			−0.844902			−0.422451	+	0.906386i	$0.638830\pi$
$192$	5.96060	+	10.3241i	0.430169	+	0.745075i
$193$	−15.2222			−1.09572			−0.547859	−	0.836570i	$-0.684557\pi$
$193$	−15.2222			−1.09572			−0.547859	+	0.836570i	$0.684557\pi$
$194$	2.88499	−	4.99695i	0.207130	−	0.358760i
$195$	−3.40688			−0.243972
$196$	4.76431			0.340308
$197$	−5.34376	+	9.25567i	−0.380727	+	0.659439i	−0.991166	−	0.132624i	$-0.957660\pi$
$197$	−5.34376	+	9.25567i	−0.380727	+	0.659439i	0.610439	+	0.792063i	$0.290993\pi$
$198$	−1.06520	−	1.84497i	−0.0757002	−	0.131117i
$199$	−3.95137			−0.280105			−0.140052	−	0.990144i	$-0.544727\pi$
$199$	−3.95137			−0.280105			−0.140052	+	0.990144i	$0.544727\pi$
$200$	0.605567	−	1.04887i	0.0428201	−	0.0741665i
$201$	−1.37017	+	2.37321i	−0.0966444	+	0.167393i
$202$	1.36409	−	2.36268i	0.0959771	−	0.166237i
$203$	−0.487212	−	0.843876i	−0.0341956	−	0.0592285i
$204$	−5.58368	−	9.67121i	−0.390936	−	0.677120i
$205$	3.63843	−	6.30194i	0.254119	−	0.440147i
$206$	−0.832293	+	1.44157i	−0.0579886	+	0.100439i
$207$	−0.808323	+	1.40006i	−0.0561823	+	0.0973106i
$208$	5.67026			0.393162
$209$	6.56073	+	11.3635i	0.453815	+	0.786031i
$210$	−0.678313	+	1.17487i	−0.0468080	+	0.0810739i
$211$	8.40966			0.578945			0.289472	−	0.957186i	$-0.406520\pi$
$211$	8.40966			0.578945			0.289472	+	0.957186i	$0.406520\pi$
$212$	22.8733			1.57095
$213$	−0.605478	+	1.04872i	−0.0414867	+	0.0718570i
$214$	−0.885432			−0.0605269
$215$	−2.19595	−	3.80350i	−0.149763	−	0.259396i
$216$	4.36657			0.297107
$217$	−7.43216	−	12.8729i	−0.504528	−	0.873867i
$218$	−1.35876	−	2.35343i	−0.0920265	−	0.159395i
$219$	−11.1374	−	19.2905i	−0.752593	−	1.30353i
$220$	−5.22296	+	9.04642i	−0.352132	+	0.609910i
$221$	−4.70070			−0.316203
$222$	−1.54396	+	3.57175i	−0.103624	+	0.239720i
$223$	16.4686			1.10282			0.551411	−	0.834234i	$-0.314090\pi$
$223$	16.4686			1.10282			0.551411	+	0.834234i	$0.314090\pi$
$224$	3.69741	−	6.40411i	0.247044	−	0.427893i
$225$	−0.625722	−	1.08378i	−0.0417148	−	0.0722522i
$226$	2.44551	+	4.23574i	0.162673	+	0.281757i
$227$	6.79120	+	11.7627i	0.450748	+	0.780719i	0.998433	−	0.0559663i	$-0.0178239\pi$
$227$	6.79120	+	11.7627i	0.450748	+	0.780719i	−0.547685	+	0.836685i	$0.684491\pi$
$228$	9.38689			0.621662
$229$	10.9009	+	18.8809i	0.720351	+	1.24768i	0.960859	+	0.277037i	$0.0893524\pi$
$229$	10.9009	+	18.8809i	0.720351	+	1.24768i	−0.240509	+	0.970647i	$0.577314\pi$
$230$	−0.400787			−0.0264271
$231$	11.9966	−	20.7786i	0.789316	−	1.36713i
$232$	0.556493			0.0365355
$233$	13.2237			0.866313			0.433156	−	0.901319i	$-0.357400\pi$
$233$	13.2237			0.866313			0.433156	+	0.901319i	$0.357400\pi$
$234$	−0.320761	+	0.555574i	−0.0209688	+	0.0363190i
$235$	−0.155125	−	0.268684i	−0.0101192	−	0.0175270i
$236$	−15.7991			−1.02843
$237$	2.92721	−	5.07008i	0.190143	−	0.329337i
$238$	−0.935912	+	1.62105i	−0.0606661	+	0.105077i
$239$	−6.04811	+	10.4756i	−0.391220	+	0.677613i	−0.992611	−	0.121342i	$-0.961280\pi$
$239$	−6.04811	+	10.4756i	−0.391220	+	0.677613i	0.601391	+	0.798955i	$0.294613\pi$
$240$	3.53795	+	6.12792i	0.228374	+	0.395555i
$241$	7.34971	+	12.7301i	0.473436	+	0.820016i	0.999538	−	0.0304061i	$-0.00968004\pi$
$241$	7.34971	+	12.7301i	0.473436	+	0.820016i	−0.526101	+	0.850422i	$0.676347\pi$
$242$	−2.96405	+	5.13388i	−0.190536	+	0.330018i
$243$	6.12648	−	10.6114i	0.393014	−	0.680720i
$244$	9.71605	−	16.8287i	0.622007	−	1.07735i
$245$	2.50260			0.159885
$246$	−2.32752	−	4.03138i	−0.148397	−	0.257031i
$247$	1.97562	−	3.42188i	0.125706	−	0.217729i
$248$	8.48899			0.539052
$249$	24.3758			1.54475
$250$	0.155125	−	0.268684i	0.00981094	−	0.0169931i
$251$	−27.4854			−1.73486			−0.867430	−	0.497559i	$-0.834230\pi$
$251$	−27.4854			−1.73486			−0.867430	+	0.497559i	$0.834230\pi$
$252$	−2.52622	−	4.37554i	−0.159137	−	0.275633i
$253$	7.08828			0.445636
$254$	−0.621507	−	1.07648i	−0.0389968	−	0.0675445i
$255$	−2.93300	−	5.08010i	−0.183671	−	0.318128i
$256$	−4.42156	−	7.65837i	−0.276348	−	0.478648i
$257$	11.8389	−	20.5056i	0.738491	−	1.27910i	−0.214683	−	0.976684i	$-0.568872\pi$
$257$	11.8389	−	20.5056i	0.738491	−	1.27910i	0.953174	−	0.302421i	$-0.0977948\pi$
$258$	−2.80952			−0.174913
$259$	−12.8137	+	1.48771i	−0.796204	+	0.0924417i
$260$	3.14556			0.195079
$261$	0.287507	−	0.497977i	0.0177962	−	0.0308240i
$262$	3.16701	+	5.48543i	0.195659	+	0.338891i
$263$	9.38548	+	16.2561i	0.578733	+	1.00240i	0.995625	+	0.0934393i	$0.0297861\pi$
$263$	9.38548	+	16.2561i	0.578733	+	1.00240i	−0.416892	+	0.908956i	$0.636881\pi$
$264$	6.85122	+	11.8667i	0.421664	+	0.730343i
$265$	12.0149			0.738070
$266$	−0.786695	−	1.36260i	−0.0482354	−	0.0835461i
$267$	−34.6804			−2.12241
$268$	1.26507	−	2.19117i	0.0772766	−	0.133847i
$269$	2.86020			0.174389			0.0871947	−	0.996191i	$-0.472210\pi$
$269$	2.86020			0.174389			0.0871947	+	0.996191i	$0.472210\pi$
$270$	1.11856			0.0680733
$271$	11.3218	−	19.6099i	0.687750	−	1.19122i	−0.284814	−	0.958583i	$-0.591932\pi$
$271$	11.3218	−	19.6099i	0.687750	−	1.19122i	0.972564	−	0.232635i	$-0.0747349\pi$
$272$	4.88154	+	8.45508i	0.295987	+	0.512665i
$273$	−7.22501			−0.437277
$274$	0.857732	−	1.48564i	0.0518175	−	0.0897506i
$275$	−2.74352	+	4.75191i	−0.165440	+	0.286551i
$276$	2.53542	−	4.39148i	0.152615	−	0.264336i
$277$	−0.0821921	−	0.142361i	−0.00493844	−	0.00855364i	0.863546	−	0.504271i	$-0.168239\pi$
$277$	−0.0821921	−	0.142361i	−0.00493844	−	0.00855364i	−0.868484	+	0.495717i	$0.834905\pi$
$278$	3.24620	+	5.62259i	0.194694	+	0.337220i
$279$	4.38577	−	7.59637i	0.262569	−	0.454783i
$280$	1.28423	−	2.22435i	0.0767475	−	0.132931i
$281$	−12.2966	+	21.2983i	−0.733554	+	1.27055i	0.221801	+	0.975092i	$0.428807\pi$
$281$	−12.2966	+	21.2983i	−0.733554	+	1.27055i	−0.955355	+	0.295461i	$0.904527\pi$
$282$	−0.198468			−0.0118186
$283$	10.4090	+	18.0290i	0.618752	+	1.07171i	0.989714	+	0.143062i	$0.0456948\pi$
$283$	10.4090	+	18.0290i	0.618752	+	1.07171i	−0.370962	+	0.928648i	$0.620972\pi$
$284$	0.559035	−	0.968277i	0.0331726	−	0.0574567i
$285$	4.93075			0.292072
$286$	2.81279			0.166324
$287$	7.71605	−	13.3646i	0.455464	−	0.788887i
$288$	4.36374			0.257136
$289$	4.45316	+	7.71309i	0.261950	+	0.453711i
$290$	0.142553			0.00837103
$291$	19.1735	+	33.2095i	1.12397	+	1.94678i
$292$	10.2831	+	17.8108i	0.601771	+	1.04230i
$293$	−5.83149	−	10.1004i	−0.340679	−	0.590074i	0.643880	−	0.765127i	$-0.277324\pi$
$293$	−5.83149	−	10.1004i	−0.340679	−	0.590074i	−0.984559	+	0.175053i	$0.943990\pi$
$294$	0.800461	−	1.38644i	0.0466838	−	0.0808587i
$295$	−8.29894			−0.483183
$296$	2.92314	−	6.76229i	0.169904	−	0.393050i
$297$	−19.7827			−1.14791
$298$	0.756674	−	1.31060i	0.0438330	−	0.0759209i
$299$	−1.06724	−	1.84852i	−0.0617201	−	0.106902i
$300$	1.96267	+	3.39944i	0.113315	+	0.196267i
$301$	−4.65697	−	8.06611i	−0.268423	−	0.464923i
$302$	−7.35196			−0.423058
$303$	9.06569	+	15.7022i	0.520810	+	0.902070i
$304$	−8.20651			−0.470676
$305$	5.10365	−	8.83978i	0.292234	−	0.506165i
$306$	−1.10458			−0.0631444
$307$	−13.5798			−0.775039			−0.387520	−	0.921861i	$-0.626668\pi$
$307$	−13.5798			−0.775039			−0.387520	+	0.921861i	$0.626668\pi$
$308$	−11.0764	+	19.1848i	−0.631134	+	1.09316i
$309$	−5.53138	−	9.58063i	−0.314669	−	0.545023i
$310$	2.17458			0.123508
$311$	1.32600	−	2.29670i	0.0751907	−	0.130234i	−0.825978	−	0.563702i	$-0.809377\pi$
$311$	1.32600	−	2.29670i	0.0751907	−	0.130234i	0.901169	+	0.433468i	$0.142710\pi$
$312$	2.06310	−	3.57339i	0.116800	−	0.202303i
$313$	0.296906	−	0.514255i	0.0167821	−	0.0290674i	−0.857512	−	0.514463i	$-0.827991\pi$
$313$	0.296906	−	0.514255i	0.0167821	−	0.0290674i	0.874294	+	0.485396i	$0.161325\pi$
$314$	−3.26957	−	5.66307i	−0.184513	−	0.319585i
$315$	−1.32697	−	2.29839i	−0.0747665	−	0.129499i
$316$	−2.70268	+	4.68118i	−0.152038	+	0.263337i
$317$	3.38803	−	5.86825i	0.190291	−	0.329594i	−0.755056	−	0.655661i	$-0.772390\pi$
$317$	3.38803	−	5.86825i	0.190291	−	0.329594i	0.945347	+	0.326067i	$0.105724\pi$
$318$	3.84299	−	6.65626i	0.215504	−	0.373265i
$319$	−2.52118			−0.141159
$320$	−2.89082	−	5.00705i	−0.161602	−	0.279903i
$321$	2.94227	−	5.09616i	0.164221	−	0.284440i
$322$	−0.849953			−0.0473660
$323$	6.80327			0.378544
$324$	−10.6498	+	18.4459i	−0.591653	+	1.02477i
$325$	1.65230			0.0916532
$326$	−0.808404	−	1.40020i	−0.0447733	−	0.0775497i
$327$	18.0605			0.998746
$328$	4.40663	+	7.63250i	0.243315	+	0.421434i
$329$	−0.328974	−	0.569800i	−0.0181369	−	0.0314141i
$330$	1.75504	+	3.03982i	0.0966117	+	0.167336i
$331$	1.40790	−	2.43855i	0.0773850	−	0.134035i	−0.824736	−	0.565518i	$-0.808676\pi$
$331$	1.40790	−	2.43855i	0.0773850	−	0.134035i	0.902121	+	0.431483i	$0.142010\pi$
$332$	−22.5060			−1.23518
$333$	−4.54101	−	6.10945i	−0.248846	−	0.334796i
$334$	−3.27983			−0.179464
$335$	0.664518	−	1.15098i	0.0363065	−	0.0628847i
$336$	7.50297	+	12.9955i	0.409321	+	0.708964i
$337$	12.3263	+	21.3498i	0.671457	+	1.16300i	0.977491	+	0.210976i	$0.0676643\pi$
$337$	12.3263	+	21.3498i	0.671457	+	1.16300i	−0.306035	+	0.952020i	$0.599002\pi$
$338$	1.59311	+	2.75936i	0.0866540	+	0.150089i
$339$	−32.5054			−1.76545
$340$	2.70802	+	4.69043i	0.146863	+	0.254374i
$341$	−38.4593			−2.08269
$342$	0.464234	−	0.804077i	0.0251029	−	0.0434795i
$343$	20.1522			1.08812
$344$	5.31918			0.286791
$345$	1.33181	−	2.30676i	0.0717021	−	0.124192i
$346$	−2.10021	−	3.63767i	−0.112908	−	0.195562i
$347$	8.80294			0.472566			0.236283	−	0.971684i	$-0.424071\pi$
$347$	8.80294			0.472566			0.236283	+	0.971684i	$0.424071\pi$
$348$	−0.901808	+	1.56198i	−0.0483420	+	0.0837308i
$349$	1.42867	−	2.47454i	0.0764752	−	0.132459i	−0.825252	−	0.564765i	$-0.808967\pi$
$349$	1.42867	−	2.47454i	0.0764752	−	0.132459i	0.901727	+	0.432306i	$0.142300\pi$
$350$	0.328974	−	0.569800i	0.0175844	−	0.0304571i
$351$	2.97856	+	5.15902i	0.158984	+	0.275368i
$352$	−9.56654	−	16.5697i	−0.509898	−	0.883170i
$353$	6.20795	−	10.7525i	0.330416	−	0.572297i	−0.652177	−	0.758066i	$-0.726144\pi$
$353$	6.20795	−	10.7525i	0.330416	−	0.572297i	0.982593	+	0.185769i	$0.0594776\pi$
$354$	−2.65443	+	4.59761i	−0.141082	+	0.244360i
$355$	0.293650	−	0.508617i	0.0155853	−	0.0269946i
$356$	32.0202			1.69707
$357$	−6.22003	−	10.7734i	−0.329199	−	0.570189i
$358$	2.29791	−	3.98010i	0.121448	−	0.210355i
$359$	21.7819			1.14961			0.574803	−	0.818292i	$-0.305079\pi$
$359$	21.7819			1.14961			0.574803	+	0.818292i	$0.305079\pi$
$360$	1.51567			0.0798827
$361$	6.64070	−	11.5020i	0.349511	−	0.605370i
$362$	1.43261			0.0752964
$363$	−19.6989	−	34.1195i	−1.03393	−	1.79081i
$364$	6.67082			0.349646
$365$	5.40149	+	9.35566i	0.282727	+	0.489698i
$366$	−3.26483	−	5.65484i	−0.170655	−	0.295583i
$367$	−11.6653	−	20.2050i	−0.608926	−	1.05469i	−0.991418	−	0.130732i	$-0.958267\pi$
$367$	−11.6653	−	20.2050i	−0.608926	−	1.05469i	0.382492	−	0.923959i	$-0.375066\pi$
$368$	−2.21660	+	3.83926i	−0.115548	+	0.200135i
$369$	9.10658			0.474070
$370$	0.748805	−	1.73226i	0.0389285	−	0.0900557i
$371$	25.4801			1.32286
$372$	−13.7566	+	23.8271i	−0.713246	+	1.23538i
$373$	−14.4904	−	25.0981i	−0.750283	−	1.29953i	−0.947685	−	0.319206i	$-0.896584\pi$
$373$	−14.4904	−	25.0981i	−0.750283	−	1.29953i	0.197402	−	0.980323i	$-0.436749\pi$
$374$	2.42154	+	4.19423i	0.125215	+	0.216878i
$375$	1.03095	+	1.78566i	0.0532381	+	0.0922111i
$376$	0.375754			0.0193780
$377$	0.379600	+	0.657487i	0.0195504	+	0.0338623i
$378$	2.37214			0.122009
$379$	8.18583	−	14.1783i	0.420478	−	0.728289i	−0.575509	−	0.817796i	$-0.695196\pi$
$379$	8.18583	−	14.1783i	0.420478	−	0.728289i	0.995986	+	0.0895072i	$0.0285292\pi$
$380$	−4.55254			−0.233540
$381$	8.26102			0.423225
$382$	1.81136	−	3.13736i	0.0926770	−	0.160521i
$383$	2.00449	+	3.47188i	0.102425	+	0.177405i	0.912683	−	0.408668i	$-0.134007\pi$
$383$	2.00449	+	3.47188i	0.102425	+	0.177405i	−0.810258	+	0.586073i	$0.800673\pi$
$384$	−18.0781			−0.922544
$385$	−5.81820	+	10.0774i	−0.296523	+	0.513592i
$386$	2.36134	−	4.08996i	0.120189	−	0.208174i
$387$	2.74811	−	4.75986i	0.139694	−	0.241958i
$388$	−17.7028	−	30.6622i	−0.898725	−	1.55664i
$389$	9.11602	+	15.7894i	0.462200	+	0.800555i	0.999070	−	0.0431105i	$-0.0137267\pi$
$389$	9.11602	+	15.7894i	0.462200	+	0.800555i	−0.536870	+	0.843665i	$0.680393\pi$
$390$	0.528492	−	0.915375i	0.0267612	−	0.0463518i
$391$	1.83758	−	3.18278i	0.0929305	−	0.160960i
$392$	−1.51549	+	2.62491i	−0.0765438	+	0.132578i
$393$	−42.0956			−2.12344
$394$	−1.65790	−	2.87156i	−0.0835237	−	0.144667i
$395$	−1.41967	+	2.45893i	−0.0714311	+	0.123722i
$396$	−13.0725			−0.656917
$397$	25.9749			1.30364			0.651822	−	0.758372i	$-0.274005\pi$
$397$	25.9749			1.30364			0.651822	+	0.758372i	$0.274005\pi$
$398$	0.612954	−	1.06167i	0.0307246	−	0.0532166i
$399$	10.4567			0.523489
$400$	−1.71587	−	2.97197i	−0.0857934	−	0.148599i
$401$	−16.7311			−0.835510			−0.417755	−	0.908560i	$-0.637183\pi$
$401$	−16.7311			−0.835510			−0.417755	+	0.908560i	$0.637183\pi$
$402$	−0.425095	−	0.736286i	−0.0212018	−	0.0367226i
$403$	5.79059	+	10.0296i	0.288450	+	0.499610i
$404$	−8.37031	−	14.4978i	−0.416439	−	0.721293i
$405$	−5.59411	+	9.68928i	−0.277974	+	0.481464i
$406$	0.302314			0.0150036
$407$	−13.2433	+	30.6365i	−0.656444	+	1.51859i
$408$	7.10450			0.351725
$409$	−0.181239	+	0.313915i	−0.00896170	+	0.0155221i	−0.870471	−	0.492219i	$-0.836186\pi$
$409$	−0.181239	+	0.313915i	−0.00896170	+	0.0155221i	0.861510	+	0.507741i	$0.169519\pi$
$410$	1.12882	+	1.95517i	0.0557485	+	0.0965592i
$411$	5.70045	+	9.87347i	0.281183	+	0.487022i
$412$	5.10710	+	8.84575i	0.251609	+	0.435799i
$413$	−17.5996			−0.866021
$414$	−0.250782	−	0.434366i	−0.0123252	−	0.0213479i
$415$	−11.8220			−0.580318
$416$	−2.88076	+	4.98962i	−0.141241	+	0.244636i
$417$	−43.1482			−2.11298
$418$	−4.07092			−0.199115
$419$	−8.20109	+	14.2047i	−0.400649	+	0.693945i	−0.993804	−	0.111143i	$-0.964549\pi$
$419$	−8.20109	+	14.2047i	−0.400649	+	0.693945i	0.593155	+	0.805088i	$0.297882\pi$
$420$	4.16225	+	7.20923i	0.203097	+	0.351774i
$421$	−5.36363			−0.261407			−0.130704	−	0.991421i	$-0.541724\pi$
$421$	−5.36363			−0.261407			−0.130704	+	0.991421i	$0.541724\pi$
$422$	−1.30455	+	2.25954i	−0.0635043	+	0.109993i
$423$	0.194130	−	0.336243i	0.00943892	−	0.0163487i
$424$	−7.27584	+	12.6021i	−0.353346	+	0.612013i
$425$	1.42247	+	2.46379i	0.0689999	+	0.119511i
$426$	−0.187849	−	0.325364i	−0.00910132	−	0.0157639i
$427$	10.8234	−	18.7466i	0.523779	−	0.907212i
$428$	−2.71658	+	4.70526i	−0.131311	+	0.227437i
$429$	−9.34684	+	16.1892i	−0.451270	+	0.781622i
$430$	1.36258			0.0657096
$431$	−20.0498	−	34.7272i	−0.965763	−	1.67275i	−0.707551	−	0.706662i	$-0.750200\pi$
$431$	−20.0498	−	34.7272i	−0.965763	−	1.67275i	−0.258212	−	0.966088i	$-0.583133\pi$
$432$	6.18631	−	10.7150i	0.297639	−	0.515526i
$433$	8.94867			0.430046			0.215023	−	0.976609i	$-0.431017\pi$
$433$	8.94867			0.430046			0.215023	+	0.976609i	$0.431017\pi$
$434$	4.61164			0.221366
$435$	−0.473702	+	0.820476i	−0.0227123	+	0.0393388i
$436$	−16.6751			−0.798594
$437$	1.54461	+	2.67534i	0.0738885	+	0.127979i
$438$	6.91071			0.330207
$439$	11.9458	+	20.6906i	0.570140	+	0.987511i	0.996551	+	0.0829815i	$0.0264442\pi$
$439$	11.9458	+	20.6906i	0.570140	+	0.987511i	−0.426411	+	0.904529i	$0.640222\pi$
$440$	−3.32277	−	5.75520i	−0.158407	−	0.274368i
$441$	1.56593	+	2.71227i	0.0745681	+	0.129156i
$442$	0.729194	−	1.26300i	0.0346842	−	0.0600748i
$443$	−40.0576			−1.90320			−0.951598	−	0.307346i	$-0.900559\pi$
$443$	−40.0576			−1.90320			−0.951598	+	0.307346i	$0.900559\pi$
$444$	14.2436	+	19.1632i	0.675969	+	0.909445i
$445$	16.8196			0.797326
$446$	−2.55469	+	4.42486i	−0.120968	+	0.209523i
$447$	5.02882	+	8.71018i	0.237855	+	0.411977i
$448$	−6.13059	−	10.6185i	−0.289643	−	0.501677i
$449$	3.83167	+	6.63665i	0.180828	+	0.313203i	0.942163	−	0.335156i	$-0.108789\pi$
$449$	3.83167	+	6.63665i	0.180828	+	0.313203i	−0.761335	+	0.648359i	$0.775456\pi$
$450$	0.388260			0.0183027
$451$	−19.9642	−	34.5790i	−0.940076	−	1.62826i
$452$	30.0121			1.41165
$453$	24.4304	−	42.3147i	1.14784	−	1.98812i
$454$	−4.21393			−0.197770
$455$	3.50405			0.164272
$456$	−2.98590	+	5.17173i	−0.139828	+	0.242188i
$457$	−16.9554	−	29.3676i	−0.793141	−	1.37376i	−0.924013	−	0.382361i	$-0.875111\pi$
$457$	−16.9554	−	29.3676i	−0.793141	−	1.37376i	0.130872	−	0.991399i	$-0.458222\pi$
$458$	−6.76398			−0.316060
$459$	−5.12851	+	8.88283i	−0.239378	+	0.414615i
$460$	−1.22965	+	2.12982i	−0.0573328	+	0.0993033i
$461$	−7.29012	+	12.6269i	−0.339535	+	0.588091i	−0.984345	−	0.176251i	$-0.943603\pi$
$461$	−7.29012	+	12.6269i	−0.339535	+	0.588091i	0.644811	+	0.764342i	$0.276936\pi$
$462$	3.72192	+	6.44656i	0.173160	+	0.299921i
$463$	−1.99424	−	3.45413i	−0.0926802	−	0.160527i	0.815958	−	0.578111i	$-0.196210\pi$
$463$	−1.99424	−	3.45413i	−0.0926802	−	0.160527i	−0.908638	+	0.417585i	$0.862877\pi$
$464$	0.788408	−	1.36556i	0.0366009	−	0.0633947i
$465$	−7.22607	+	12.5159i	−0.335101	+	0.580412i
$466$	−2.05132	+	3.55299i	−0.0950256	+	0.164589i
$467$	14.7664			0.683307			0.341653	−	0.939826i	$-0.389013\pi$
$467$	14.7664			0.683307			0.341653	+	0.939826i	$0.389013\pi$
$468$	1.96825	+	3.40910i	0.0909822	+	0.157586i
$469$	1.40925	−	2.44089i	0.0650730	−	0.112710i
$470$	0.0962546			0.00443989
$471$	43.4589			2.00248
$472$	5.02557	−	8.70454i	0.231320	−	0.400659i
$473$	−24.0985			−1.10805
$474$	0.908166	+	1.57299i	0.0417134	+	0.0722498i
$475$	−2.39136			−0.109723
$476$	5.74292	+	9.94703i	0.263226	+	0.455922i
$477$	7.51800	+	13.0216i	0.344226	+	0.596216i
$478$	−1.87642	−	3.25006i	−0.0858256	−	0.148654i
$479$	−7.80662	+	13.5215i	−0.356693	+	0.617811i	−0.987406	−	0.158205i	$-0.949429\pi$
$479$	−7.80662	+	13.5215i	−0.356693	+	0.617811i	0.630713	+	0.776016i	$0.282763\pi$
$480$	−7.18978			−0.328167
$481$	9.98349	−	1.15911i	0.455208	−	0.0528511i
$482$	−4.56048			−0.207724
$483$	2.82438	−	4.89196i	0.128514	−	0.222592i
$484$	18.1879	+	31.5024i	0.826724	+	1.43193i
$485$	−9.29895	−	16.1063i	−0.422244	−	0.731347i
$486$	1.90074	+	3.29217i	0.0862192	+	0.149336i
$487$	35.6982			1.61764			0.808820	−	0.588056i	$-0.200107\pi$
$487$	35.6982			1.61764			0.808820	+	0.588056i	$0.200107\pi$
$488$	6.18121	+	10.7062i	0.279810	+	0.484645i
$489$	10.7452			0.485916
$490$	−0.388215	+	0.672407i	−0.0175377	+	0.0303763i
$491$	−0.411627			−0.0185765			−0.00928823	−	0.999957i	$-0.502957\pi$
$491$	−0.411627			−0.0185765			−0.00928823	+	0.999957i	$0.502957\pi$
$492$	−28.5641			−1.28777
$493$	−0.653597	+	1.13206i	−0.0294365	+	0.0509856i
$494$	0.612935	+	1.06163i	0.0275773	+	0.0477652i
$495$	−6.86671			−0.308636
$496$	12.0267	−	20.8309i	0.540017	−	0.935336i
$497$	0.622746	−	1.07863i	0.0279340	−	0.0483831i
$498$	−3.78128	+	6.54937i	−0.169443	+	0.293484i
$499$	−19.0374	−	32.9738i	−0.852232	−	1.47611i	−0.879190	−	0.476472i	$-0.841915\pi$
$499$	−19.0374	−	32.9738i	−0.852232	−	1.47611i	0.0269579	−	0.999637i	$-0.491418\pi$
$500$	−0.951873	−	1.64869i	−0.0425690	−	0.0737317i
$501$	10.8988	−	18.8773i	0.486922	−	0.843374i
$502$	4.26366	−	7.38487i	0.190296	−	0.329603i
$503$	7.75338	−	13.4292i	0.345706	−	0.598780i	−0.639776	−	0.768562i	$-0.720973\pi$
$503$	7.75338	−	13.4292i	0.345706	−	0.598780i	0.985482	+	0.169781i	$0.0543061\pi$
$504$	3.21429			0.143176
$505$	−4.39676	−	7.61541i	−0.195653	−	0.338881i
$506$	−1.09957	+	1.90451i	−0.0488817	+	0.0846656i
$507$	−21.1755			−0.940439
$508$	−7.62736			−0.338409
$509$	−2.99718	+	5.19127i	−0.132848	+	0.230099i	−0.924773	−	0.380519i	$-0.875745\pi$
$509$	−2.99718	+	5.19127i	−0.132848	+	0.230099i	0.791926	+	0.610618i	$0.209079\pi$
$510$	1.81992			0.0805874
$511$	11.4550	+	19.8406i	0.506739	+	0.877698i
$512$	20.2789			0.896210
$513$	−4.31084	−	7.46660i	−0.190328	−	0.329658i
$514$	3.67302	+	6.36185i	0.162010	+	0.280609i
$515$	2.68266	+	4.64650i	0.118212	+	0.204749i
$516$	−8.61985	+	14.9300i	−0.379468	+	0.657257i
$517$	−1.70235			−0.0748692
$518$	1.58800	−	3.67361i	0.0697725	−	0.161409i
$519$	27.9158			1.22537
$520$	−1.00058	+	1.73305i	−0.0438783	+	0.0759994i
$521$	−8.46908	−	14.6689i	−0.371037	−	0.642655i	0.618688	−	0.785637i	$-0.287664\pi$
$521$	−8.46908	−	14.6689i	−0.371037	−	0.642655i	−0.989725	+	0.142982i	$0.954331\pi$
$522$	0.0891989	+	0.154497i	0.00390413	+	0.00676215i
$523$	1.72028	+	2.97961i	0.0752226	+	0.130289i	0.901183	−	0.433439i	$-0.142700\pi$
$523$	1.72028	+	2.97961i	0.0752226	+	0.130289i	−0.825960	+	0.563728i	$0.809367\pi$
$524$	38.8667			1.69790
$525$	2.18635	+	3.78686i	0.0954200	+	0.165272i
$526$	−5.82368			−0.253924
$527$	−9.97027	+	17.2690i	−0.434312	+	0.752250i
$528$	38.8257			1.68967
$529$	−21.3312			−0.927443
$530$	−1.86381	+	3.22821i	−0.0809587	+	0.140225i
$531$	−5.19283	−	8.99425i	−0.225350	−	0.390317i
$532$	−9.65460			−0.418580
$533$	−6.01178	+	10.4127i	−0.260399	+	0.451025i
$534$	5.37978	−	9.31806i	0.232806	−	0.403232i
$535$	−1.42697	+	2.47158i	−0.0616932	+	0.106856i
$536$	0.804820	+	1.39399i	0.0347629	+	0.0602112i
$537$	15.2718	+	26.4515i	0.659027	+	1.14147i
$538$	−0.443687	+	0.768489i	−0.0191287	+	0.0331319i
$539$	6.86592	−	11.8921i	0.295736	−	0.512230i
$540$	3.43184	−	5.94412i	0.147683	−	0.255794i
$541$	26.7548			1.15028			0.575140	−	0.818055i	$-0.304948\pi$
$541$	26.7548			1.15028			0.575140	+	0.818055i	$0.304948\pi$
$542$	3.51258	+	6.08397i	0.150878	+	0.261329i
$543$	−4.76054	+	8.24549i	−0.204294	+	0.353848i
$544$	−9.92020			−0.425325
$545$	−8.75912			−0.375200
$546$	1.12078	−	1.94124i	0.0479648	−	0.0830775i
$547$	10.5797			0.452357			0.226178	−	0.974086i	$-0.427377\pi$
$547$	10.5797			0.452357			0.226178	+	0.974086i	$0.427377\pi$
$548$	−5.26320	−	9.11613i	−0.224833	−	0.389422i
$549$	12.7739			0.545175
$550$	−0.851174	−	1.47428i	−0.0362942	−	0.0628634i
$551$	−0.549391	−	0.951573i	−0.0234048	−	0.0405384i
$552$	1.61300	+	2.79379i	0.0686537	+	0.118912i
$553$	−3.01070	+	5.21468i	−0.128028	+	0.221751i
$554$	0.0510001			0.00216679
$555$	7.48186	+	10.0660i	0.317587	+	0.427280i
$556$	39.8385			1.68953
$557$	21.0151	−	36.3993i	0.890440	−	1.54229i	0.0510917	−	0.998694i	$-0.483730\pi$
$557$	21.0151	−	36.3993i	0.890440	−	1.54229i	0.839349	−	0.543594i	$-0.182937\pi$
$558$	1.36068	+	2.35677i	0.0576022	+	0.0997699i
$559$	3.62837	+	6.28452i	0.153464	+	0.265807i
$560$	−3.63886	−	6.30268i	−0.153770	−	0.266337i
$561$	−32.1869			−1.35893
$562$	−3.81501	−	6.60780i	−0.160927	−	0.278733i
$563$	15.1171			0.637108			0.318554	−	0.947905i	$-0.396803\pi$
$563$	15.1171			0.637108			0.318554	+	0.947905i	$0.396803\pi$
$564$	−0.608917	+	1.05467i	−0.0256400	+	0.0444098i
$565$	15.7648			0.663229
$566$	−6.45878			−0.271483
$567$	−11.8635	+	20.5481i	−0.498219	+	0.862941i
$568$	0.355650	+	0.616003i	0.0149227	+	0.0258469i
$569$	29.9574			1.25588			0.627940	−	0.778262i	$-0.283898\pi$
$569$	29.9574			1.25588			0.627940	+	0.778262i	$0.283898\pi$
$570$	−0.764881	+	1.32481i	−0.0320373	+	0.0554903i
$571$	−15.6228	+	27.0594i	−0.653792	+	1.13240i	0.328403	+	0.944538i	$0.393490\pi$
$571$	−15.6228	+	27.0594i	−0.653792	+	1.13240i	−0.982195	+	0.187863i	$0.939844\pi$
$572$	8.62990	−	14.9474i	0.360834	−	0.624983i
$573$	12.0382	+	20.8507i	0.502902	+	0.871053i
$574$	2.39390	+	4.14635i	0.0999194	+	0.173065i
$575$	−0.645912	+	1.11875i	−0.0269364	+	0.0466552i
$576$	3.61770	−	6.26605i	0.150738	−	0.261085i
$577$	−14.3757	+	24.8994i	−0.598467	+	1.03658i	0.394581	+	0.918861i	$0.370890\pi$
$577$	−14.3757	+	24.8994i	−0.598467	+	1.03658i	−0.993048	+	0.117714i	$0.962443\pi$
$578$	−2.76318			−0.114933
$579$	15.6934	+	27.1817i	0.652194	+	1.12963i
$580$	0.437367	−	0.757542i	0.0181607	−	0.0314552i
$581$	−25.0710			−1.04012
$582$	−11.8971			−0.493153
$583$	32.9631	−	57.0938i	1.36519	−	2.36458i
$584$	−13.0839			−0.541414
$585$	1.03388	+	1.79074i	0.0427457	+	0.0740378i
$586$	3.61843			0.149476
$587$	7.05861	+	12.2259i	0.291340	+	0.504616i	0.974127	−	0.226002i	$-0.0725656\pi$
$587$	7.05861	+	12.2259i	0.291340	+	0.504616i	−0.682787	+	0.730618i	$0.739232\pi$
$588$	−4.91177	−	8.50744i	−0.202558	−	0.350841i
$589$	−8.38066	−	14.5157i	−0.345319	−	0.598110i
$590$	1.28737	−	2.22979i	0.0530002	−	0.0917990i
$591$	22.0366			0.906466
$592$	−12.4525	−	16.7535i	−0.511793	−	0.688563i
$593$	−5.88296			−0.241584			−0.120792	−	0.992678i	$-0.538543\pi$
$593$	−5.88296			−0.241584			−0.120792	+	0.992678i	$0.538543\pi$
$594$	3.06878	−	5.31529i	0.125914	−	0.218089i
$595$	3.01664	+	5.22498i	0.123670	+	0.214203i
$596$	−4.64309	−	8.04207i	−0.190188	−	0.329416i
$597$	4.07367	+	7.05580i	0.166724	+	0.288775i
$598$	0.662221			0.0270802
$599$	−7.85750	−	13.6096i	−0.321049	−	0.556073i	0.659656	−	0.751568i	$-0.270702\pi$
$599$	−7.85750	−	13.6096i	−0.321049	−	0.556073i	−0.980705	+	0.195495i	$0.937369\pi$
$600$	−2.49724			−0.101949
$601$	−7.77357	+	13.4642i	−0.317090	+	0.549217i	−0.979880	−	0.199589i	$-0.936039\pi$
$601$	−7.77357	+	13.4642i	−0.317090	+	0.549217i	0.662789	+	0.748806i	$0.269373\pi$
$602$	2.88964			0.117773
$603$	1.66321			0.0677313
$604$	−22.5565	+	39.0690i	−0.917810	+	1.58969i
$605$	9.55376	+	16.5476i	0.388416	+	0.672756i
$606$	−5.62525			−0.228510
$607$	−10.9690	+	18.9989i	−0.445219	+	0.771141i	−0.998067	−	0.0621402i	$-0.980207\pi$
$607$	−10.9690	+	18.9989i	−0.445219	+	0.771141i	0.552849	+	0.833282i	$0.313541\pi$
$608$	4.16929	−	7.22142i	0.169087	−	0.292867i
$609$	−1.00458	+	1.73999i	−0.0407078	+	0.0705080i
$610$	1.58340	+	2.74254i	0.0641102	+	0.111042i
$611$	0.256313	+	0.443946i	0.0103693	+	0.0179602i
$612$	−3.38894	+	5.86981i	−0.136990	+	0.237273i
$613$	−14.2377	+	24.6605i	−0.575057	+	0.996027i	0.420979	+	0.907070i	$0.361687\pi$
$613$	−14.2377	+	24.6605i	−0.575057	+	0.996027i	−0.996035	+	0.0889567i	$0.971647\pi$
$614$	2.10656	−	3.64867i	0.0850138	−	0.147248i
$615$	−15.0042			−0.605027
$616$	−7.04662	−	12.2051i	−0.283916	−	0.491757i
$617$	17.7869	−	30.8078i	0.716072	−	1.24027i	−0.246472	−	0.969150i	$-0.579271\pi$
$617$	17.7869	−	30.8078i	0.716072	−	1.24027i	0.962545	−	0.271124i	$-0.0873953\pi$
$618$	3.43221			0.138064
$619$	−9.30332			−0.373932			−0.186966	−	0.982366i	$-0.559865\pi$
$619$	−9.30332			−0.373932			−0.186966	+	0.982366i	$0.559865\pi$
$620$	6.67180	−	11.5559i	0.267946	−	0.464096i
$621$	−4.65748			−0.186898
$622$	0.411391	+	0.712551i	0.0164953	+	0.0285707i
$623$	35.6695			1.42907
$624$	−5.84577	−	10.1252i	−0.234018	−	0.405331i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.0921147	+	0.159547i	0.00368164	+	0.00637680i
$627$	13.5276	−	23.4305i	0.540240	−	0.935723i
$628$	−40.1254			−1.60118
$629$	10.3232	+	13.8888i	0.411613	+	0.553782i
$630$	0.823386			0.0328045
$631$	−11.6294	+	20.1428i	−0.462961	+	0.801872i	−0.999107	−	0.0422534i	$-0.986546\pi$
$631$	−11.6294	+	20.1428i	−0.462961	+	0.801872i	0.536146	+	0.844125i	$0.319880\pi$
$632$	−1.71941	−	2.97810i	−0.0683943	−	0.118462i
$633$	−8.66995	−	15.0168i	−0.344600	−	0.596864i
$634$	1.05114	+	1.82062i	0.0417459	+	0.0723060i
$635$	−4.00650			−0.158993
$636$	−23.5813	−	40.8440i	−0.935060	−	1.61957i
$637$	−4.13504			−0.163836
$638$	0.391098	−	0.677401i	0.0154837	−	0.0268186i
$639$	0.734973			0.0290751
$640$	8.76768			0.346573
$641$	4.09344	−	7.09004i	0.161681	−	0.280040i	−0.773791	−	0.633441i	$-0.781642\pi$
$641$	4.09344	−	7.09004i	0.161681	−	0.280040i	0.935472	+	0.353402i	$0.114975\pi$
$642$	0.912837	+	1.58108i	0.0360268	+	0.0624003i
$643$	11.4564			0.451796			0.225898	−	0.974151i	$-0.427468\pi$
$643$	11.4564			0.451796			0.225898	+	0.974151i	$0.427468\pi$
$644$	−2.60773	+	4.51672i	−0.102759	+	0.177984i
$645$	−4.52784	+	7.84244i	−0.178283	+	0.308796i
$646$	−1.05535	+	1.82793i	−0.0415224	+	0.0719189i
$647$	−7.96151	−	13.7897i	−0.312999	−	0.542130i	0.666011	−	0.745942i	$-0.268000\pi$
$647$	−7.96151	−	13.7897i	−0.312999	−	0.542130i	−0.979010	+	0.203812i	$0.934667\pi$
$648$	−6.77522	−	11.7350i	−0.266156	−	0.460995i
$649$	−22.7683	+	39.4358i	−0.893733	+	1.54799i
$650$	−0.256313	+	0.443946i	−0.0100534	+	0.0174130i
$651$	−15.3244	+	26.5426i	−0.600610	+	1.04029i
$652$	−9.92102			−0.388537
$653$	10.4891	+	18.1677i	0.410471	+	0.710957i	0.994941	−	0.100458i	$-0.0320310\pi$
$653$	10.4891	+	18.1677i	0.410471	+	0.710957i	−0.584470	+	0.811415i	$0.698698\pi$
$654$	−2.80162	+	4.85255i	−0.109552	+	0.189750i
$655$	20.4159			0.797716
$656$	24.9723			0.975003
$657$	−6.75967	+	11.7081i	−0.263720	+	0.456776i
$658$	0.204128			0.00795774
$659$	0.598998	+	1.03749i	0.0233336	+	0.0404151i	0.877456	−	0.479656i	$-0.159239\pi$
$659$	0.598998	+	1.03749i	0.0233336	+	0.0404151i	−0.854123	+	0.520071i	$0.825905\pi$
$660$	21.5385			0.838383
$661$	16.1732	+	28.0129i	0.629066	+	1.08957i	0.987740	+	0.156111i	$0.0498958\pi$
$661$	16.1732	+	28.0129i	0.629066	+	1.08957i	−0.358674	+	0.933463i	$0.616771\pi$
$662$	0.436799	+	0.756558i	0.0169767	+	0.0294045i
$663$	4.84619	+	8.39385i	0.188210	+	0.325990i
$664$	7.15900	−	12.3997i	0.277823	−	0.481204i
$665$	−5.07137			−0.196659
$666$	2.34593	−	0.272370i	0.0909031	−	0.0105541i
$667$	−0.593568			−0.0229830
$668$	−10.0628	+	17.4293i	−0.389341	+	0.674359i
$669$	−16.9784	−	29.4074i	−0.656422	−	1.13696i
$670$	0.206166	+	0.357090i	0.00796489	+	0.0137956i
$671$	−28.0039	−	48.5042i	−1.08108	−	1.87248i
$672$	−15.2474			−0.588182
$673$	18.5482	+	32.1264i	0.714981	+	1.23838i	0.962967	+	0.269620i	$0.0868979\pi$
$673$	18.5482	+	32.1264i	0.714981	+	1.23838i	−0.247986	+	0.968764i	$0.579769\pi$
$674$	−7.64845			−0.294607
$675$	1.80268	−	3.12233i	0.0693850	−	0.120178i
$676$	19.5513			0.751972
$677$	6.39266			0.245690			0.122845	−	0.992426i	$-0.460798\pi$
$677$	6.39266			0.245690			0.122845	+	0.992426i	$0.460798\pi$
$678$	5.04239	−	8.73368i	0.193652	−	0.335415i
$679$	−19.7204	−	34.1567i	−0.756798	−	1.31081i
$680$	−3.44560			−0.132133
$681$	14.0028	−	24.2536i	0.536589	−	0.929399i
$682$	5.96599	−	10.3334i	0.228449	−	0.395686i
$683$	−7.57751	+	13.1246i	−0.289945	+	0.502200i	−0.973796	−	0.227421i	$-0.926970\pi$
$683$	−7.57751	+	13.1246i	−0.289945	+	0.502200i	0.683851	+	0.729622i	$0.260304\pi$
$684$	−2.84862	−	4.93396i	−0.108920	−	0.188655i
$685$	−2.76466	−	4.78852i	−0.105632	−	0.182960i
$686$	−3.12611	+	5.41458i	−0.119355	+	0.206730i
$687$	22.4766	−	38.9306i	0.857534	−	1.48529i
$688$	7.53592	−	13.0526i	0.287304	−	0.497626i
$689$	−19.8523			−0.756311
$690$	0.413192	+	0.715670i	0.0157300	+	0.0272451i
$691$	−19.1544	+	33.1764i	−0.728668	+	1.26209i	0.228779	+	0.973478i	$0.426527\pi$
$691$	−19.1544	+	33.1764i	−0.728668	+	1.26209i	−0.957447	+	0.288611i	$0.906807\pi$
$692$	−25.7745			−0.979800
$693$	−14.5623			−0.553176
$694$	−1.36555	+	2.36521i	−0.0518357	+	0.0897820i
$695$	20.9264			0.793784
$696$	−0.573717	−	0.993707i	−0.0217467	−	0.0376664i
$697$	−20.7022			−0.784153
$698$	0.443245	+	0.767723i	0.0167771	+	0.0290587i
$699$	−13.6330	−	23.6130i	−0.515647	−	0.893126i
$700$	−2.01864	−	3.49639i	−0.0762976	−	0.132151i
$701$	−7.37527	+	12.7743i	−0.278560	+	0.482480i	−0.971027	−	0.238969i	$-0.923191\pi$
$701$	−7.37527	+	12.7743i	−0.278560	+	0.482480i	0.692467	+	0.721450i	$0.256524\pi$
$702$	−1.84819			−0.0697556
$703$	−14.4490	+	1.67757i	−0.544954	+	0.0632709i
$704$	−31.7241			−1.19565
$705$	−0.319852	+	0.554000i	−0.0120463	+	0.0208648i
$706$	1.92601	+	3.33595i	0.0724865	+	0.125550i
$707$	−9.32424	−	16.1501i	−0.350674	−	0.607386i
$708$	16.2881	+	28.2118i	0.612143	+	1.06026i
$709$	−15.3282			−0.575664			−0.287832	−	0.957681i	$-0.592935\pi$
$709$	−15.3282			−0.575664			−0.287832	+	0.957681i	$0.592935\pi$
$710$	0.0911047	+	0.157798i	0.00341910	+	0.00592205i
$711$	−3.55327			−0.133258
$712$	−10.1854	+	17.6416i	−0.381714	+	0.661148i
$713$	−9.05456			−0.339096
$714$	3.85952			0.144439
$715$	4.53311	−	7.85158i	0.169529	−	0.293633i
$716$	−14.1004	−	24.4226i	−0.526956	−	0.912715i
$717$	24.9412			0.931448
$718$	−3.37891	+	5.85245i	−0.126100	+	0.218411i
$719$	2.50682	−	4.34194i	0.0934885	−	0.161927i	−0.815488	−	0.578774i	$-0.803531\pi$
$719$	2.50682	−	4.34194i	0.0934885	−	0.161927i	0.908977	+	0.416847i	$0.136865\pi$
$720$	2.14731	−	3.71926i	0.0800257	−	0.138609i
$721$	5.68913	+	9.85387i	0.211874	+	0.366977i
$722$	2.06027	+	3.56850i	0.0766755	+	0.132806i
$723$	15.1544	−	26.2482i	0.563598	−	0.976180i
$724$	4.39538	−	7.61302i	0.163353	−	0.282936i
$725$	0.229740	−	0.397922i	0.00853234	−	0.0147784i
$726$	12.2232			0.453644
$727$	15.2817	+	26.4687i	0.566767	+	0.981670i	0.996883	+	0.0788961i	$0.0251395\pi$
$727$	15.2817	+	26.4687i	0.566767	+	0.981670i	−0.430115	+	0.902774i	$0.641527\pi$
$728$	−2.12194	+	3.67530i	−0.0786442	+	0.136216i
$729$	8.30023			0.307416
$730$	−3.35162			−0.124049
$731$	−6.24735	+	10.8207i	−0.231066	+	0.400219i
$732$	−40.0671			−1.48092
$733$	0.0641308	+	0.111078i	0.00236872	+	0.00410275i	0.867207	−	0.497947i	$-0.165913\pi$
$733$	0.0641308	+	0.111078i	0.00236872	+	0.00410275i	−0.864839	+	0.502050i	$0.832579\pi$
$734$	7.23833			0.267172
$735$	−2.58006	−	4.46879i	−0.0951668	−	0.164834i
$736$	−2.25227	−	3.90105i	−0.0830198	−	0.143794i
$737$	−3.64623	−	6.31546i	−0.134311	−	0.232633i
$738$	−1.41266	+	2.44679i	−0.0520006	+	0.0900676i
$739$	3.03253			0.111553			0.0557767	−	0.998443i	$-0.482237\pi$
$739$	3.03253			0.111553			0.0557767	+	0.998443i	$0.482237\pi$
$740$	−6.90796	−	9.29393i	−0.253942	−	0.341652i
$741$	−8.14708			−0.299290
$742$	−3.95260	+	6.84610i	−0.145104	+	0.251328i
$743$	−0.962952	−	1.66788i	−0.0353273	−	0.0611886i	0.847821	−	0.530282i	$-0.177914\pi$
$743$	−0.962952	−	1.66788i	−0.0353273	−	0.0611886i	−0.883148	+	0.469094i	$0.844581\pi$
$744$	−8.75174	−	15.1585i	−0.320854	−	0.555736i
$745$	−2.43892	−	4.22434i	−0.0893553	−	0.154768i
$746$	8.99126			0.329193
$747$	−7.39727	−	12.8124i	−0.270652	−	0.468783i
$748$	29.7180			1.08660
$749$	−3.02618	+	5.24150i	−0.110574	+	0.191520i
$750$	−0.639704			−0.0233587
$751$	11.6540			0.425261			0.212630	−	0.977133i	$-0.431797\pi$
$751$	11.6540			0.425261			0.212630	+	0.977133i	$0.431797\pi$
$752$	0.532347	−	0.922052i	0.0194127	−	0.0336238i
$753$	28.3361	+	49.0795i	1.03262	+	1.78856i
$754$	−0.235541			−0.00857791
$755$	−11.8485	+	20.5222i	−0.431210	+	0.746878i
$756$	7.27792	−	12.6057i	0.264696	−	0.458466i
$757$	−2.32020	+	4.01870i	−0.0843290	+	0.146062i	−0.905105	−	0.425188i	$-0.860208\pi$
$757$	−2.32020	+	4.01870i	−0.0843290	+	0.146062i	0.820776	+	0.571250i	$0.193541\pi$
$758$	2.53965	+	4.39880i	0.0922441	+	0.159771i
$759$	−7.30767	−	12.6573i	−0.265252	−	0.459429i
$760$	1.44813	−	2.50823i	0.0525291	−	0.0909831i
$761$	−6.38323	+	11.0561i	−0.231392	+	0.400782i	−0.958218	−	0.286039i	$-0.907661\pi$
$761$	−6.38323	+	11.0561i	−0.231392	+	0.400782i	0.726826	+	0.686822i	$0.240995\pi$
$762$	−1.28149	+	2.21960i	−0.0464234	+	0.0804077i
$763$	−18.5755			−0.672480
$764$	−11.1148	−	19.2514i	−0.402119	−	0.696491i
$765$	−1.78014	+	3.08330i	−0.0643612	+	0.111477i
$766$	−1.24379			−0.0449398
$767$	13.7124			0.495124
$768$	−9.11684	+	15.7908i	−0.328975	+	0.569802i
$769$	37.0113			1.33466			0.667330	−	0.744762i	$-0.267437\pi$
$769$	37.0113			1.33466			0.667330	+	0.744762i	$0.267437\pi$
$770$	−1.80509	−	3.12651i	−0.0650510	−	0.112672i
$771$	−48.8214			−1.75826
$772$	−14.4896	−	25.0967i	−0.521492	−	0.903251i
$773$	−21.9124	−	37.9535i	−0.788136	−	1.36509i	−0.927108	−	0.374795i	$-0.877713\pi$
$773$	−21.9124	−	37.9535i	−0.788136	−	1.36509i	0.138972	−	0.990296i	$-0.455620\pi$
$774$	0.852599	+	1.47674i	0.0306460	+	0.0530805i
$775$	3.50456	−	6.07008i	0.125888	−	0.218044i
$776$	22.5246			0.808584
$777$	15.8668	+	21.3471i	0.569220	+	0.765824i
$778$	−5.65648			−0.202794
$779$	8.70079	−	15.0702i	0.311738	−	0.539946i
$780$	−3.24292	−	5.61690i	−0.116115	−	0.201117i
$781$	−1.61127	−	2.79080i	−0.0576557	−	0.0998625i
$782$	0.570108	+	0.987456i	0.0203870	+	0.0353114i
$783$	1.65659			0.0592017
$784$	4.29413	+	7.43765i	0.153362	+	0.265630i
$785$	−21.0771			−0.752273
$786$	6.53007	−	11.3104i	0.232920	−	0.403429i
$787$	−19.9883			−0.712506			−0.356253	−	0.934389i	$-0.615946\pi$
$787$	−19.9883			−0.712506			−0.356253	+	0.934389i	$0.615946\pi$
$788$	−20.3463			−0.724808
$789$	19.3519	−	33.5186i	0.688947	−	1.19329i
$790$	−0.440450	−	0.762882i	−0.0156705	−	0.0271421i
$791$	33.4325			1.18872
$792$	4.15826	−	7.20231i	0.147757	−	0.255923i
$793$	−8.43277	+	14.6060i	−0.299456	+	0.518674i
$794$	−4.02935	+	6.97904i	−0.142996	+	0.247677i
$795$	−12.3868	−	21.4546i	−0.439314	−	0.760915i
$796$	−3.76120	−	6.51459i	−0.133312	−	0.230903i
$797$	−20.4059	+	35.3441i	−0.722814	+	1.25195i	0.237053	+	0.971497i	$0.423818\pi$
$797$	−20.4059	+	35.3441i	−0.722814	+	1.25195i	−0.959867	+	0.280454i	$0.909515\pi$
$798$	−1.62209	+	2.80954i	−0.0574213	+	0.0994566i
$799$	−0.441320	+	0.764389i	−0.0156128	+	0.0270421i
$800$	3.48696			0.123283
$801$	10.5244	+	18.2288i	0.371861	+	0.644083i
$802$	2.59540	−	4.49537i	0.0916468	−	0.158737i
$803$	59.2763			2.09182
$804$	−5.21691			−0.183986
$805$	−1.36979	+	2.37255i	−0.0482788	+	0.0836213i
$806$	−3.59305			−0.126560
$807$	−2.94873	−	5.10734i	−0.103800	−	0.179787i
$808$	10.6501			0.374670
$809$	−1.45711	−	2.52378i	−0.0512292	−	0.0887315i	0.839274	−	0.543709i	$-0.182981\pi$
$809$	−1.45711	−	2.52378i	−0.0512292	−	0.0887315i	−0.890503	+	0.454978i	$0.849647\pi$
$810$	−1.73557	−	3.00609i	−0.0609817	−	0.105623i
$811$	13.8960	+	24.0686i	0.487956	+	0.845164i	0.999904	−	0.0138524i	$-0.00440949\pi$
$811$	13.8960	+	24.0686i	0.487956	+	0.845164i	−0.511949	+	0.859016i	$0.671076\pi$
$812$	0.927528	−	1.60652i	0.0325498	−	0.0563780i
$813$	−46.6889			−1.63745
$814$	−6.17717	−	8.31072i	−0.216510	−	0.291291i
$815$	−5.21132			−0.182544
$816$	10.0653	−	17.4336i	0.352355	−	0.610297i
$817$	−5.25130	−	9.09552i	−0.183720	−	0.318212i
$818$	−0.0562293	−	0.0973920i	−0.00196601	−	0.00340523i
$819$	2.19256	+	3.79763i	0.0766143	+	0.132700i
$820$	13.8533			0.483778
$821$	20.8119	+	36.0473i	0.726342	+	1.25806i	0.958419	+	0.285364i	$0.0921144\pi$
$821$	20.8119	+	36.0473i	0.726342	+	1.25806i	−0.232077	+	0.972697i	$0.574552\pi$
$822$	−3.53712			−0.123371
$823$	−11.8160	+	20.4659i	−0.411880	+	0.713398i	−0.995095	−	0.0989202i	$-0.968461\pi$
$823$	−11.8160	+	20.4659i	−0.411880	+	0.713398i	0.583215	+	0.812318i	$0.301794\pi$
$824$	−6.49812			−0.226373
$825$	11.3137			0.393893
$826$	2.73014	−	4.72874i	0.0949936	−	0.164534i
$827$	6.09101	+	10.5499i	0.211805	+	0.366857i	0.952279	−	0.305227i	$-0.0987325\pi$
$827$	6.09101	+	10.5499i	0.211805	+	0.366857i	−0.740474	+	0.672085i	$0.765399\pi$
$828$	−3.07768			−0.106957
$829$	3.01060	−	5.21452i	0.104563	−	0.181108i	−0.808997	−	0.587813i	$-0.799989\pi$
$829$	3.01060	−	5.21452i	0.104563	−	0.181108i	0.913559	+	0.406705i	$0.133322\pi$
$830$	1.83388	−	3.17637i	0.0636549	−	0.110253i
$831$	−0.169472	+	0.293534i	−0.00587892	+	0.0101826i
$832$	4.77651	+	8.27316i	0.165596	+	0.286820i
$833$	−3.55987	−	6.16588i	−0.123342	−	0.213635i
$834$	6.69335	−	11.5932i	0.231772	−	0.401441i
$835$	−5.28579	+	9.15526i	−0.182922	+	0.316831i
$836$	−12.4900	+	21.6332i	−0.431974	+	0.748201i
$837$	25.2704			0.873472
$838$	−2.54438	−	4.40700i	−0.0878942	−	0.152237i
$839$	4.03238	−	6.98429i	0.139213	−	0.241124i	−0.787986	−	0.615693i	$-0.788876\pi$
$839$	4.03238	−	6.98429i	0.139213	−	0.241124i	0.927199	+	0.374569i	$0.122209\pi$
$840$	−5.29592			−0.182727
$841$	−28.7889			−0.992720
$842$	0.832031	−	1.44112i	0.0286737	−	0.0496643i
$843$	50.7088			1.74650
$844$	8.00493	+	13.8649i	0.275541	+	0.477251i
$845$	10.2699			0.353295
$846$	0.0602287	+	0.104319i	0.00207070	+	0.00358656i
$847$	20.2607	+	35.0926i	0.696167	+	1.20580i
$848$	20.6160	+	35.7080i	0.707957	+	1.22622i
$849$	21.4624	−	37.1740i	0.736587	−	1.27581i
$850$	−0.882641			−0.0302743
$851$	−3.11789	+	7.21281i	−0.106880	+	0.247252i
$852$	−2.30535			−0.0789800
$853$	−21.5722	+	37.3642i	−0.738619	+	1.27933i	0.214498	+	0.976724i	$0.431188\pi$
$853$	−21.5722	+	37.3642i	−0.738619	+	1.27933i	−0.953117	+	0.302602i	$0.902145\pi$
$854$	3.35794	+	5.81612i	0.114906	+	0.199024i
$855$	−1.49633	−	2.59171i	−0.0511733	−	0.0886347i
$856$	−1.72825	−	2.99342i	−0.0590704	−	0.102313i
$857$	−33.4524			−1.14271			−0.571356	−	0.820703i	$-0.693582\pi$
$857$	−33.4524			−1.14271			−0.571356	+	0.820703i	$0.693582\pi$
$858$	−2.89985	−	5.02269i	−0.0989993	−	0.171472i
$859$	7.52085			0.256608			0.128304	−	0.991735i	$-0.459047\pi$
$859$	7.52085			0.256608			0.128304	+	0.991735i	$0.459047\pi$
$860$	4.18053	−	7.24089i	0.142555	−	0.246912i
$861$	−31.8195			−1.08441
$862$	12.4408			0.423737
$863$	11.5106	−	19.9370i	0.391827	−	0.678664i	−0.600864	−	0.799351i	$-0.705177\pi$
$863$	11.5106	−	19.9370i	0.391827	−	0.678664i	0.992691	+	0.120688i	$0.0385100\pi$
$864$	6.28586	+	10.8874i	0.213849	+	0.370398i
$865$	−13.5388			−0.460335
$866$	−1.38816	+	2.40436i	−0.0471716	+	0.0817036i
$867$	9.18198	−	15.9037i	0.311836	−	0.540116i
$868$	14.1489	−	24.5067i	0.480246	−	0.831810i
$869$	7.78975	+	13.4922i	0.264249	+	0.457693i
$870$	−0.146966	−	0.254552i	−0.00498261	−	0.00863013i
$871$	−1.09798	+	1.90176i	−0.0372038	+	0.0644388i
$872$	5.30424	−	9.18721i	0.179624	−	0.311118i
$873$	11.6371	−	20.1561i	0.393857	−	0.682180i
$874$	−0.958426			−0.0324192
$875$	−1.06035	−	1.83659i	−0.0358465	−	0.0620880i
$876$	21.2027	−	36.7241i	0.716373	−	1.24079i
$877$	12.6479			0.427089			0.213545	−	0.976933i	$-0.431499\pi$
$877$	12.6479			0.427089			0.213545	+	0.976933i	$0.431499\pi$
$878$	−7.41232			−0.250154
$879$	−12.0240	+	20.8261i	−0.405558	+	0.702448i
$880$	−18.8301			−0.634761
$881$	−2.42275	−	4.19633i	−0.0816247	−	0.141378i	0.822323	−	0.569021i	$-0.192678\pi$
$881$	−2.42275	−	4.19633i	−0.0816247	−	0.141378i	−0.903948	+	0.427643i	$0.859344\pi$
$882$	−0.971658			−0.0327174
$883$	−22.8338	−	39.5494i	−0.768420	−	1.33094i	−0.938419	−	0.345498i	$-0.887710\pi$
$883$	−22.8338	−	39.5494i	−0.768420	−	1.33094i	0.169999	−	0.985444i	$-0.445623\pi$
$884$	−4.47447	−	7.75000i	−0.150493	−	0.260661i
$885$	8.55581	+	14.8191i	0.287600	+	0.498138i
$886$	6.21393	−	10.7628i	0.208761	−	0.361585i
$887$	48.0641			1.61383			0.806917	−	0.590665i	$-0.201134\pi$
$887$	48.0641			1.61383			0.806917	+	0.590665i	$0.201134\pi$
$888$	−15.0888	+	1.75185i	−0.506346	+	0.0587883i
$889$	−8.49662			−0.284967
$890$	−2.60914	+	4.51915i	−0.0874584	+	0.151482i
$891$	30.6951	+	53.1654i	1.02832	+	1.78111i
$892$	15.6761	+	27.1517i	0.524873	+	0.909107i
$893$	−0.370959	−	0.642519i	−0.0124137	−	0.0215011i
$894$	−3.12038			−0.104361
$895$	−7.40665	−	12.8287i	−0.247577	−	0.428816i
$896$	18.5937			0.621171
$897$	−2.20055	+	3.81146i	−0.0734741	+	0.127261i
$898$	−2.37755			−0.0793398
$899$	3.22056			0.107412
$900$	1.19122	−	2.06325i	0.0397072	−	0.0687749i
$901$	−17.0909	−	29.6022i	−0.569379	−	0.986194i
$902$	12.3877			0.412467
$903$	−9.60222	+	16.6315i	−0.319542	+	0.553463i
$904$	−9.54663	+	16.5352i	−0.317516	+	0.549954i
$905$	2.30881	−	3.99897i	0.0767474	−	0.132930i
$906$	7.57952	+	13.1281i	0.251813	+	0.436152i
$907$	−23.2510	−	40.2719i	−0.772036	−	1.33721i	−0.936446	−	0.350813i	$-0.885905\pi$
$907$	−23.2510	−	40.2719i	−0.772036	−	1.33721i	0.164410	−	0.986392i	$-0.447428\pi$
$908$	−12.9287	+	22.3932i	−0.429055	+	0.743145i
$909$	5.50230	−	9.53026i	0.182500	−	0.316099i
$910$	−0.543564	+	0.941481i	−0.0180190	+	0.0312098i
$911$	14.3173			0.474353			0.237177	−	0.971467i	$-0.423778\pi$
$911$	14.3173			0.474353			0.237177	+	0.971467i	$0.423778\pi$
$912$	8.46052	+	14.6540i	0.280156	+	0.485244i
$913$	−32.4338	+	56.1769i	−1.07340	+	1.85919i
$914$	10.5208			0.347997
$915$	−21.0465			−0.695775
$916$	−20.7525	+	35.9444i	−0.685682	+	1.18764i
$917$	43.2962			1.42977
$918$	−1.59112	−	2.75589i	−0.0525146	−	0.0909580i
$919$	−43.3839			−1.43110			−0.715552	−	0.698559i	$-0.753825\pi$
$919$	−43.3839			−1.43110			−0.715552	+	0.698559i	$0.753825\pi$
$920$	−0.782286	−	1.35496i	−0.0257912	−	0.0446717i
$921$	14.0001	+	24.2489i	0.461319	+	0.799028i
$922$	−2.26175	−	3.91747i	−0.0744869	−	0.129015i
$923$	−0.485198	+	0.840388i	−0.0159705	+	0.0276617i
$924$	45.6768			1.50266
$925$	−3.62862	−	4.88192i	−0.119308	−	0.160517i
$926$	1.23742			0.0406643
$927$	−3.35720	+	5.81484i	−0.110265	+	0.190984i
$928$	0.801096	+	1.38754i	0.0262973	+	0.0455482i
$929$	14.8015	+	25.6370i	0.485623	+	0.841124i	0.999863	−	0.0165222i	$-0.00525942\pi$
$929$	14.8015	+	25.6370i	0.485623	+	0.841124i	−0.514240	+	0.857646i	$0.671926\pi$
$930$	−2.24188	−	3.88306i	−0.0735142	−	0.127330i
$931$	5.98461			0.196138
$932$	12.5873	+	21.8018i	0.412310	+	0.714141i
$933$	−5.46818			−0.179020
$934$	−2.29063	+	3.96749i	−0.0749517	+	0.129820i
$935$	15.6103			0.510511
$936$	−2.50434			−0.0818569
$937$	−5.69829	+	9.86973i	−0.186155	+	0.322430i	−0.943965	−	0.330045i	$-0.892936\pi$
$937$	−5.69829	+	9.86973i	−0.186155	+	0.322430i	0.757810	+	0.652475i	$0.226269\pi$
$938$	0.437218	+	0.757284i	0.0142757	+	0.0247262i
$939$	−1.22438			−0.0399562
$940$	0.295318	−	0.511505i	0.00963221	−	0.0166835i
$941$	12.7126	−	22.0189i	0.414419	−	0.717795i	−0.580948	−	0.813940i	$-0.697318\pi$
$941$	12.7126	−	22.0189i	0.414419	−	0.717795i	0.995367	+	0.0961458i	$0.0306515\pi$
$942$	−6.74154	+	11.6767i	−0.219651	+	0.380447i
$943$	−4.70021	−	8.14100i	−0.153060	−	0.265107i
$944$	−14.2399	−	24.6642i	−0.463469	−	0.802752i
$945$	3.82295	−	6.62154i	0.124361	−	0.215399i
$946$	3.73827	−	6.47487i	0.121542	−	0.210516i
$947$	8.09396	−	14.0192i	0.263018	−	0.455561i	−0.704024	−	0.710176i	$-0.748615\pi$
$947$	8.09396	−	14.0192i	0.263018	−	0.455561i	0.967043	+	0.254615i	$0.0819486\pi$
$948$	11.1453			0.361984
$949$	−8.92489	−	15.4584i	−0.289714	−	0.501800i
$950$	0.370959	−	0.642519i	0.0120355	−	0.0208461i
$951$	−13.9716			−0.453060
$952$	−7.30712			−0.236825
$953$	9.72346	−	16.8415i	0.314974	−	0.545550i	−0.664458	−	0.747325i	$-0.731338\pi$
$953$	9.72346	−	16.8415i	0.314974	−	0.545550i	0.979432	+	0.201775i	$0.0646710\pi$
$954$	−4.66491			−0.151032
$955$	−5.83839	−	10.1124i	−0.188926	−	0.327229i
$956$	−23.0281			−0.744783
$957$	2.59922	+	4.50198i	0.0840208	+	0.145528i
$958$	−2.42200	−	4.19502i	−0.0782512	−	0.135535i
$959$	−5.86303	−	10.1551i	−0.189327	−	0.327924i
$960$	−5.96060	+	10.3241i	−0.192377	+	0.333208i
$961$	18.1278			0.584769
$962$	−1.23725	+	2.86221i	−0.0398906	+	0.0922813i
$963$	−3.57154			−0.115091
$964$	−13.9920	+	24.2348i	−0.450651	+	0.780551i
$965$	−7.61111	−	13.1828i	−0.245010	−	0.424370i
$966$	0.876260	+	1.51773i	0.0281932	+	0.0488321i
$967$	−0.352631	−	0.610774i	−0.0113398	−	0.0196412i	0.860300	−	0.509788i	$-0.170276\pi$
$967$	−0.352631	−	0.610774i	−0.0113398	−	0.0196412i	−0.871640	+	0.490147i	$0.836943\pi$
$968$	−23.1418			−0.743805
$969$	−7.01384	−	12.1483i	−0.225317	−	0.390261i
$970$	5.76998			0.185263
$971$	−5.02834	+	8.70933i	−0.161367	+	0.279496i	−0.935359	−	0.353699i	$-0.884924\pi$
$971$	−5.02834	+	8.70933i	−0.161367	+	0.279496i	0.773992	+	0.633195i	$0.218257\pi$
$972$	23.3265			0.748199
$973$	44.3788			1.42272
$974$	−5.53767	+	9.59153i	−0.177438	+	0.307332i
$975$	−1.70344	−	2.95045i	−0.0545538	−	0.0944900i
$976$	35.0288			1.12124
$977$	21.8771	−	37.8923i	0.699911	−	1.21228i	−0.268586	−	0.963256i	$-0.586556\pi$
$977$	21.8771	−	37.8923i	0.699911	−	1.21228i	0.968497	−	0.249025i	$-0.0801103\pi$
$978$	−1.66685	+	2.88707i	−0.0533000	+	0.0923183i
$979$	46.1449	−	79.9252i	1.47480	−	2.55442i
$980$	2.38215	+	4.12601i	0.0760951	+	0.131801i
$981$	−5.48078	−	9.49298i	−0.174988	−	0.303088i
$982$	0.0638534	−	0.110597i	0.00203765	−	0.00352931i
$983$	−6.04809	+	10.4756i	−0.192904	+	0.334119i	−0.946211	−	0.323549i	$-0.895124\pi$
$983$	−6.04809	+	10.4756i	−0.192904	+	0.334119i	0.753307	+	0.657669i	$0.228457\pi$
$984$	9.08604	−	15.7375i	0.289652	−	0.501692i
$985$	−10.6875			−0.340533
$986$	−0.202778	−	0.351222i	−0.00645777	−	0.0111852i
$987$	−0.678313	+	1.17487i	−0.0215909	+	0.0373966i
$988$	7.52216			0.239312
$989$	−5.67356			−0.180409
$990$	1.06520	−	1.84497i	0.0338542	−	0.0586371i
$991$	−37.4383			−1.18927			−0.594633	−	0.803997i	$-0.702703\pi$
$991$	−37.4383			−1.18927			−0.594633	+	0.803997i	$0.702703\pi$
$992$	12.2203	+	21.1661i	0.387994	+	0.672026i
$993$	−5.80589			−0.184244
$994$	0.193206	+	0.334643i	0.00612814	+	0.0106142i
$995$	−1.97568	−	3.42198i	−0.0626334	−	0.108484i
$996$	23.2026	+	40.1881i	0.735203	+	1.27341i
$997$	15.4743	−	26.8024i	0.490078	−	0.848839i	−0.509857	−	0.860259i	$-0.670302\pi$
$997$	15.4743	−	26.8024i	0.490078	−	0.848839i	0.999935	+	0.0114198i	$0.00363511\pi$
$998$	11.8127			0.373924
$999$	8.70173	−	20.1302i	0.275310	−	0.636893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.b.121.3	yes	14
5.2	odd	4		925.2.o.c.824.7		28
5.3	odd	4		925.2.o.c.824.8		28
5.4	even	2		925.2.e.b.676.5		14
37.10	even	3		6845.2.a.j.1.5		7
37.26	even	3	inner	185.2.e.b.26.3	✓	14
37.27	even	6		6845.2.a.m.1.3		7
185.63	odd	12		925.2.o.c.174.7		28
185.137	odd	12		925.2.o.c.174.8		28
185.174	even	6		925.2.e.b.26.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.b.26.3	✓	14	37.26	even	3	inner
185.2.e.b.121.3	yes	14	1.1	even	1	trivial
925.2.e.b.26.5		14	185.174	even	6
925.2.e.b.676.5		14	5.4	even	2
925.2.o.c.174.7		28	185.63	odd	12
925.2.o.c.174.8		28	185.137	odd	12
925.2.o.c.824.7		28	5.2	odd	4
925.2.o.c.824.8		28	5.3	odd	4
6845.2.a.j.1.5		7	37.10	even	3
6845.2.a.m.1.3		7	37.27	even	6

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.155125 + 0.268684i) q^{2} +(-1.03095 - 1.78566i) q^{3} +(0.951873 + 1.64869i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.639704 q^{6} +(1.06035 + 1.83659i) q^{7} -1.21113 q^{8} +(-0.625722 + 1.08378i) q^{9} +O(q^{10})\)	\(q+(-0.155125 + 0.268684i) q^{2} +(-1.03095 - 1.78566i) q^{3} +(0.951873 + 1.64869i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.639704 q^{6} +(1.06035 + 1.83659i) q^{7} -1.21113 q^{8} +(-0.625722 + 1.08378i) q^{9} -0.310249 q^{10} +5.48703 q^{11} +(1.96267 - 3.39944i) q^{12} +(-0.826151 - 1.43093i) q^{13} -0.657948 q^{14} +(1.03095 - 1.78566i) q^{15} +(-1.71587 + 2.97197i) q^{16} +(1.42247 - 2.46379i) q^{17} +(-0.194130 - 0.336243i) q^{18} +(1.19568 + 2.07098i) q^{19} +(-0.951873 + 1.64869i) q^{20} +(2.18635 - 3.78686i) q^{21} +(-0.851174 + 1.47428i) q^{22} +1.29182 q^{23} +(1.24862 + 2.16267i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.512625 q^{26} -3.60535 q^{27} +(-2.01864 + 3.49639i) q^{28} -0.459480 q^{29} +(0.319852 + 0.554000i) q^{30} -7.00913 q^{31} +(-1.74348 - 3.01980i) q^{32} +(-5.65686 - 9.79798i) q^{33} +(0.441320 + 0.764389i) q^{34} +(-1.06035 + 1.83659i) q^{35} -2.38243 q^{36} +(-2.41356 + 5.58343i) q^{37} -0.741917 q^{38} +(-1.70344 + 2.95045i) q^{39} +(-0.605567 - 1.04887i) q^{40} +(-3.63843 - 6.30194i) q^{41} +(0.678313 + 1.17487i) q^{42} -4.39190 q^{43} +(5.22296 + 9.04642i) q^{44} -1.25144 q^{45} +(-0.200394 + 0.347092i) q^{46} -0.310249 q^{47} +7.07591 q^{48} +(1.25130 - 2.16731i) q^{49} +(-0.155125 - 0.268684i) q^{50} -5.86599 q^{51} +(1.57278 - 2.72414i) q^{52} +(6.00746 - 10.4052i) q^{53} +(0.559279 - 0.968700i) q^{54} +(2.74352 + 4.75191i) q^{55} +(-1.28423 - 2.22435i) q^{56} +(2.46537 - 4.27015i) q^{57} +(0.0712767 - 0.123455i) q^{58} +(-4.14947 + 7.18709i) q^{59} +3.92534 q^{60} +(-5.10365 - 8.83978i) q^{61} +(1.08729 - 1.88324i) q^{62} -2.65395 q^{63} -5.78165 q^{64} +(0.826151 - 1.43093i) q^{65} +3.51008 q^{66} +(-0.664518 - 1.15098i) q^{67} +5.41604 q^{68} +(-1.33181 - 2.30676i) q^{69} +(-0.328974 - 0.569800i) q^{70} +(-0.293650 - 0.508617i) q^{71} +(0.757834 - 1.31261i) q^{72} +10.8030 q^{73} +(-1.12578 - 1.51461i) q^{74} +2.06190 q^{75} +(-2.27627 + 3.94261i) q^{76} +(5.81820 + 10.0774i) q^{77} +(-0.528492 - 0.915375i) q^{78} +(1.41967 + 2.45893i) q^{79} -3.43174 q^{80} +(5.59411 + 9.68928i) q^{81} +2.25764 q^{82} +(-5.91099 + 10.2381i) q^{83} +8.32450 q^{84} +2.84494 q^{85} +(0.681292 - 1.18003i) q^{86} +(0.473702 + 0.820476i) q^{87} -6.64553 q^{88} +(8.40980 - 14.5662i) q^{89} +(0.194130 - 0.336243i) q^{90} +(1.75202 - 3.03459i) q^{91} +(1.22965 + 2.12982i) q^{92} +(7.22607 + 12.5159i) q^{93} +(0.0481273 - 0.0833590i) q^{94} +(-1.19568 + 2.07098i) q^{95} +(-3.59489 + 6.22653i) q^{96} -18.5979 q^{97} +(0.388215 + 0.672407i) q^{98} +(-3.43336 + 5.94675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

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