LMFDB - Embedded newform 209.2.f.b.58.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(20,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("209.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.5
Character	$\chi$	$=$	209.58
Dual form			209.2.f.b.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.507210 - 0.368509i) q^{2} +(-0.519183 - 1.59788i) q^{3} +(-0.496571 + 1.52829i) q^{4} +(3.26196 + 2.36995i) q^{5} +(-0.852170 - 0.619138i) q^{6} +(-1.09252 + 3.36244i) q^{7} +(0.698797 + 2.15068i) q^{8} +(0.143374 - 0.104168i) q^{9} +2.52785 q^{10} +(-3.06597 - 1.26484i) q^{11} +2.69984 q^{12} +(3.90297 - 2.83568i) q^{13} +(0.684954 + 2.10807i) q^{14} +(2.09335 - 6.44267i) q^{15} +(-1.45310 - 1.05574i) q^{16} +(-4.26899 - 3.10160i) q^{17} +(0.0343341 - 0.105670i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-5.24177 + 3.80837i) q^{20} +5.94001 q^{21} +(-2.02120 + 0.488299i) q^{22} +5.36251 q^{23} +(3.07372 - 2.23319i) q^{24} +(3.47862 + 10.7061i) q^{25} +(0.934652 - 2.87656i) q^{26} +(-4.31860 - 3.13765i) q^{27} +(-4.59627 - 3.33939i) q^{28} +(0.271458 - 0.835461i) q^{29} +(-1.31242 - 4.03920i) q^{30} +(3.35526 - 2.43774i) q^{31} -5.64879 q^{32} +(-0.429267 + 5.55575i) q^{33} -3.30824 q^{34} +(-11.5326 + 8.37893i) q^{35} +(0.0880026 + 0.270844i) q^{36} +(-0.430857 + 1.32604i) q^{37} +(-0.507210 - 0.368509i) q^{38} +(-6.55743 - 4.76425i) q^{39} +(-2.81755 + 8.67154i) q^{40} +(-0.963944 - 2.96671i) q^{41} +(3.01283 - 2.18895i) q^{42} -0.442465 q^{43} +(3.45552 - 4.05761i) q^{44} +0.714554 q^{45} +(2.71992 - 1.97614i) q^{46} +(-0.403816 - 1.24282i) q^{47} +(-0.932521 + 2.87001i) q^{48} +(-4.44931 - 3.23261i) q^{49} +(5.70969 + 4.14833i) q^{50} +(-2.73961 + 8.43165i) q^{51} +(2.39563 + 7.37299i) q^{52} +(2.36780 - 1.72031i) q^{53} -3.34669 q^{54} +(-7.00346 - 11.3921i) q^{55} -7.99498 q^{56} +(-1.35924 + 0.987546i) q^{57} +(-0.170189 - 0.523789i) q^{58} +(1.88167 - 5.79117i) q^{59} +(8.80677 + 6.39849i) q^{60} +(-0.604838 - 0.439441i) q^{61} +(0.803492 - 2.47289i) q^{62} +(0.193618 + 0.595894i) q^{63} +(0.0410809 - 0.0298470i) q^{64} +19.4518 q^{65} +(1.82962 + 2.97612i) q^{66} -12.0633 q^{67} +(6.86001 - 4.98409i) q^{68} +(-2.78413 - 8.56866i) q^{69} +(-2.76174 + 8.49975i) q^{70} +(7.69395 + 5.58998i) q^{71} +(0.324220 + 0.235560i) q^{72} +(0.826895 - 2.54492i) q^{73} +(0.270124 + 0.831356i) q^{74} +(15.3010 - 11.1169i) q^{75} +1.60694 q^{76} +(7.60261 - 8.92729i) q^{77} -5.08167 q^{78} +(-8.64630 + 6.28190i) q^{79} +(-2.23790 - 6.88756i) q^{80} +(-2.60716 + 8.02400i) q^{81} +(-1.58218 - 1.14952i) q^{82} +(-9.50216 - 6.90373i) q^{83} +(-2.94964 + 9.07806i) q^{84} +(-6.57462 - 20.2346i) q^{85} +(-0.224423 + 0.163053i) q^{86} -1.47590 q^{87} +(0.577774 - 7.47778i) q^{88} +16.6193 q^{89} +(0.362429 - 0.263320i) q^{90} +(5.27071 + 16.2216i) q^{91} +(-2.66287 + 8.19547i) q^{92} +(-5.63722 - 4.09568i) q^{93} +(-0.662809 - 0.481559i) q^{94} +(1.24596 - 3.83466i) q^{95} +(2.93276 + 9.02610i) q^{96} +(-13.1346 + 9.54282i) q^{97} -3.44798 q^{98} +(-0.571337 + 0.138029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.507210	−	0.368509i	0.358651	−	0.260576i	−0.393838	−	0.919180i	$-0.628853\pi$
$2$	0.507210	−	0.368509i	0.358651	−	0.260576i	0.752489	+	0.658604i	$0.228853\pi$
$3$	−0.519183	−	1.59788i	−0.299751	−	0.922538i	−0.981584	−	0.191030i	$-0.938817\pi$
$3$	−0.519183	−	1.59788i	−0.299751	−	0.922538i	0.681833	−	0.731507i	$-0.261183\pi$
$4$	−0.496571	+	1.52829i	−0.248286	+	0.764145i
$5$	3.26196	+	2.36995i	1.45879	+	1.05987i	0.983675	+	0.179952i	$0.0575944\pi$
$5$	3.26196	+	2.36995i	1.45879	+	1.05987i	0.475117	+	0.879922i	$0.342406\pi$
$6$	−0.852170	−	0.619138i	−0.347897	−	0.252762i
$7$	−1.09252	+	3.36244i	−0.412935	+	1.27088i	0.501149	+	0.865361i	$0.332911\pi$
$7$	−1.09252	+	3.36244i	−0.412935	+	1.27088i	−0.914085	+	0.405524i	$0.867089\pi$
$8$	0.698797	+	2.15068i	0.247062	+	0.760379i
$9$	0.143374	−	0.104168i	0.0477915	−	0.0347225i
$10$	2.52785			0.799376
$11$	−3.06597	−	1.26484i	−0.924425	−	0.381364i
$11$	−3.06597	−	1.26484i	−0.924425	−	0.381364i
$12$	2.69984			0.779376
$13$	3.90297	−	2.83568i	1.08249	−	0.786475i	0.104374	−	0.994538i	$-0.466716\pi$
$13$	3.90297	−	2.83568i	1.08249	−	0.786475i	0.978115	+	0.208063i	$0.0667160\pi$
$14$	0.684954	+	2.10807i	0.183062	+	0.563406i
$15$	2.09335	−	6.44267i	0.540501	−	1.66349i
$16$	−1.45310	−	1.05574i	−0.363275	−	0.263935i
$17$	−4.26899	−	3.10160i	−1.03538	−	0.752249i	−0.0660036	−	0.997819i	$-0.521025\pi$
$17$	−4.26899	−	3.10160i	−1.03538	−	0.752249i	−0.969379	+	0.245570i	$0.921025\pi$
$18$	0.0343341	−	0.105670i	0.00809264	−	0.0249066i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−5.24177	+	3.80837i	−1.17210	+	0.851577i
$21$	5.94001			1.29622
$22$	−2.02120	+	0.488299i	−0.430921	+	0.104106i
$23$	5.36251			1.11816			0.559080	−	0.829114i	$-0.311154\pi$
$23$	5.36251			1.11816			0.559080	+	0.829114i	$0.311154\pi$
$24$	3.07372	−	2.23319i	0.627421	−	0.455848i
$25$	3.47862	+	10.7061i	0.695724	+	2.14122i
$26$	0.934652	−	2.87656i	0.183300	−	0.564141i
$27$	−4.31860	−	3.13765i	−0.831116	−	0.603841i
$28$	−4.59627	−	3.33939i	−0.868614	−	0.631085i
$29$	0.271458	−	0.835461i	0.0504084	−	0.155141i	−0.922684	−	0.385558i	$-0.874009\pi$
$29$	0.271458	−	0.835461i	0.0504084	−	0.155141i	0.973092	+	0.230417i	$0.0740090\pi$
$30$	−1.31242	−	4.03920i	−0.239613	−	0.737454i
$31$	3.35526	−	2.43774i	0.602623	−	0.437831i	−0.244186	−	0.969728i	$-0.578521\pi$
$31$	3.35526	−	2.43774i	0.602623	−	0.437831i	0.846809	+	0.531897i	$0.178521\pi$
$32$	−5.64879			−0.998574
$33$	−0.429267	+	5.55575i	−0.0747258	+	0.967131i
$34$	−3.30824			−0.567359
$35$	−11.5326	+	8.37893i	−1.94937	+	1.41630i
$36$	0.0880026	+	0.270844i	0.0146671	+	0.0451407i
$37$	−0.430857	+	1.32604i	−0.0708324	+	0.218000i	−0.980206	−	0.197981i	$-0.936562\pi$
$37$	−0.430857	+	1.32604i	−0.0708324	+	0.218000i	0.909373	+	0.415981i	$0.136562\pi$
$38$	−0.507210	−	0.368509i	−0.0822803	−	0.0597801i
$39$	−6.55743	−	4.76425i	−1.05003	−	0.762891i
$40$	−2.81755	+	8.67154i	−0.445494	+	1.37109i
$41$	−0.963944	−	2.96671i	−0.150543	−	0.463323i	0.847139	−	0.531371i	$-0.178323\pi$
$41$	−0.963944	−	2.96671i	−0.150543	−	0.463323i	−0.997682	+	0.0680480i	$0.978323\pi$
$42$	3.01283	−	2.18895i	0.464890	−	0.337762i
$43$	−0.442465			−0.0674754			−0.0337377	−	0.999431i	$-0.510741\pi$
$43$	−0.442465			−0.0674754			−0.0337377	+	0.999431i	$0.510741\pi$
$44$	3.45552	−	4.05761i	0.520939	−	0.611707i
$45$	0.714554			0.106519
$46$	2.71992	−	1.97614i	0.401030	−	0.291365i
$47$	−0.403816	−	1.24282i	−0.0589026	−	0.181283i	0.917276	−	0.398252i	$-0.130383\pi$
$47$	−0.403816	−	1.24282i	−0.0589026	−	0.181283i	−0.976179	+	0.216969i	$0.930383\pi$
$48$	−0.932521	+	2.87001i	−0.134598	+	0.414250i
$49$	−4.44931	−	3.23261i	−0.635615	−	0.461802i
$50$	5.70969	+	4.14833i	0.807472	+	0.586663i
$51$	−2.73961	+	8.43165i	−0.383622	+	1.18067i
$52$	2.39563	+	7.37299i	0.332214	+	1.02245i
$53$	2.36780	−	1.72031i	0.325243	−	0.236303i	−0.413167	−	0.910655i	$-0.635577\pi$
$53$	2.36780	−	1.72031i	0.325243	−	0.236303i	0.738409	+	0.674353i	$0.235577\pi$
$54$	−3.34669			−0.455427
$55$	−7.00346	−	11.3921i	−0.944346	−	1.53611i
$56$	−7.99498			−1.06837
$57$	−1.35924	+	0.987546i	−0.180036	+	0.130804i
$58$	−0.170189	−	0.523789i	−0.0223469	−	0.0687768i
$59$	1.88167	−	5.79117i	0.244972	−	0.753946i	−0.750669	−	0.660678i	$-0.770269\pi$
$59$	1.88167	−	5.79117i	0.244972	−	0.753946i	0.995641	−	0.0932678i	$-0.0297313\pi$
$60$	8.80677	+	6.39849i	1.13695	+	0.826041i
$61$	−0.604838	−	0.439441i	−0.0774416	−	0.0562646i	0.548391	−	0.836222i	$-0.315241\pi$
$61$	−0.604838	−	0.439441i	−0.0774416	−	0.0562646i	−0.625832	+	0.779958i	$0.715241\pi$
$62$	0.803492	−	2.47289i	0.102044	−	0.314058i
$63$	0.193618	+	0.595894i	0.0243935	+	0.0750756i
$64$	0.0410809	−	0.0298470i	0.00513511	−	0.00373087i
$65$	19.4518			2.41269
$66$	1.82962	+	2.97612i	0.225210	+	0.366335i
$67$	−12.0633			−1.47376			−0.736880	−	0.676023i	$-0.763702\pi$
$67$	−12.0633			−1.47376			−0.736880	+	0.676023i	$0.763702\pi$
$68$	6.86001	−	4.98409i	0.831898	−	0.604409i
$69$	−2.78413	−	8.56866i	−0.335169	−	1.03155i
$70$	−2.76174	+	8.49975i	−0.330091	+	1.01591i
$71$	7.69395	+	5.58998i	0.913104	+	0.663409i	0.941798	−	0.336179i	$-0.109135\pi$
$71$	7.69395	+	5.58998i	0.913104	+	0.663409i	−0.0286940	+	0.999588i	$0.509135\pi$
$72$	0.324220	+	0.235560i	0.0382097	+	0.0277610i
$73$	0.826895	−	2.54492i	0.0967807	−	0.297860i	−0.890933	−	0.454135i	$-0.849948\pi$
$73$	0.826895	−	2.54492i	0.0967807	−	0.297860i	0.987714	+	0.156274i	$0.0499484\pi$
$74$	0.270124	+	0.831356i	0.0314013	+	0.0966432i
$75$	15.3010	−	11.1169i	1.76681	−	1.28366i
$76$	1.60694			0.184329
$77$	7.60261	−	8.92729i	0.866398	−	1.01736i
$78$	−5.08167			−0.575386
$79$	−8.64630	+	6.28190i	−0.972784	+	0.706769i	−0.956084	−	0.293091i	$-0.905316\pi$
$79$	−8.64630	+	6.28190i	−0.972784	+	0.706769i	−0.0166998	+	0.999861i	$0.505316\pi$
$80$	−2.23790	−	6.88756i	−0.250205	−	0.770052i
$81$	−2.60716	+	8.02400i	−0.289684	+	0.891555i
$82$	−1.58218	−	1.14952i	−0.174723	−	0.126944i
$83$	−9.50216	−	6.90373i	−1.04300	−	0.757782i	−0.0721294	−	0.997395i	$-0.522979\pi$
$83$	−9.50216	−	6.90373i	−1.04300	−	0.757782i	−0.970869	+	0.239613i	$0.922979\pi$
$84$	−2.94964	+	9.07806i	−0.321832	+	0.990498i
$85$	−6.57462	−	20.2346i	−0.713118	−	2.19475i
$86$	−0.224423	+	0.163053i	−0.0242001	+	0.0175824i
$87$	−1.47590			−0.158234
$88$	0.577774	−	7.47778i	0.0615909	−	0.797134i
$89$	16.6193			1.76164			0.880820	−	0.473452i	$-0.156992\pi$
$89$	16.6193			1.76164			0.880820	+	0.473452i	$0.156992\pi$
$90$	0.362429	−	0.263320i	0.0382033	−	0.0277563i
$91$	5.27071	+	16.2216i	0.552520	+	1.70048i
$92$	−2.66287	+	8.19547i	−0.277623	+	0.854437i
$93$	−5.63722	−	4.09568i	−0.584553	−	0.424702i
$94$	−0.662809	−	0.481559i	−0.0683635	−	0.0496690i
$95$	1.24596	−	3.83466i	0.127833	−	0.393428i
$96$	2.93276	+	9.02610i	0.299323	+	0.921222i
$97$	−13.1346	+	9.54282i	−1.33361	+	0.968926i	−0.333959	+	0.942588i	$0.608385\pi$
$97$	−13.1346	+	9.54282i	−1.33361	+	0.968926i	−0.999653	+	0.0263386i	$0.991615\pi$
$98$	−3.44798			−0.348299
$99$	−0.571337	+	0.138029i	−0.0574215	+	0.0138724i
$100$	−18.0894			−1.80894
$101$	−6.72386	+	4.88517i	−0.669049	+	0.486092i	−0.869707	−	0.493569i	$-0.835692\pi$
$101$	−6.72386	+	4.88517i	−0.669049	+	0.486092i	0.200658	+	0.979661i	$0.435692\pi$
$102$	1.71759	+	5.28619i	0.170066	+	0.523410i
$103$	−0.593962	+	1.82803i	−0.0585248	+	0.180121i	−0.976045	−	0.217568i	$-0.930188\pi$
$103$	−0.593962	+	1.82803i	−0.0585248	+	0.180121i	0.917520	+	0.397689i	$0.130188\pi$
$104$	8.82601	+	6.41247i	0.865461	+	0.628794i
$105$	19.3761	+	14.0775i	1.89091	+	1.37383i
$106$	0.567022	−	1.74511i	0.0550741	−	0.169501i
$107$	0.0348647	+	0.107302i	0.00337049	+	0.0103733i	0.952728	−	0.303826i	$-0.0982641\pi$
$107$	0.0348647	+	0.107302i	0.00337049	+	0.0103733i	−0.949357	+	0.314199i	$0.898264\pi$
$108$	6.93973	−	5.04201i	0.667776	−	0.485168i
$109$	−1.10098			−0.105455			−0.0527275	−	0.998609i	$-0.516791\pi$
$109$	−1.10098			−0.105455			−0.0527275	+	0.998609i	$0.516791\pi$
$110$	−7.75031	−	3.19733i	−0.738963	−	0.304853i
$111$	2.34255			0.222345
$112$	5.13741	−	3.73255i	0.485440	−	0.352693i
$113$	−3.84720	−	11.8405i	−0.361914	−	1.11386i	−0.951891	−	0.306437i	$-0.900863\pi$
$113$	−3.84720	−	11.8405i	−0.361914	−	1.11386i	0.589976	−	0.807420i	$-0.299137\pi$
$114$	−0.325500	+	1.00179i	−0.0304859	+	0.0938258i
$115$	17.4923	+	12.7089i	1.63116	+	1.18511i
$116$	1.14203	+	0.829732i	0.106035	+	0.0770387i
$117$	0.264201	−	0.813126i	0.0244254	−	0.0751736i
$118$	−1.17970	−	3.63075i	−0.108600	−	0.334238i
$119$	15.0929	−	10.9657i	1.38357	−	1.00522i
$120$	15.3189			1.39842
$121$	7.80035	+	7.75593i	0.709123	+	0.705085i
$122$	−0.468718			−0.0424357
$123$	−4.24000	+	3.08054i	−0.382307	+	0.277763i
$124$	2.05945	+	6.33833i	0.184944	+	0.569199i
$125$	−7.79602	+	23.9937i	−0.697298	+	2.14606i
$126$	0.317797	+	0.230893i	0.0283116	+	0.0205696i
$127$	1.03501	+	0.751979i	0.0918423	+	0.0667273i	0.632759	−	0.774349i	$-0.281922\pi$
$127$	1.03501	+	0.751979i	0.0918423	+	0.0667273i	−0.540916	+	0.841076i	$0.681922\pi$
$128$	3.50098	−	10.7749i	0.309446	−	0.952376i
$129$	0.229721	+	0.707008i	0.0202258	+	0.0622486i
$130$	9.86612	−	7.16816i	0.865316	−	0.628689i
$131$	9.67185			0.845034			0.422517	−	0.906355i	$-0.361147\pi$
$131$	9.67185			0.845034			0.422517	+	0.906355i	$0.361147\pi$
$132$	−8.27763	−	3.41487i	−0.720475	−	0.297226i
$133$	3.53548			0.306565
$134$	−6.11860	+	4.44542i	−0.528566	+	0.384026i
$135$	−6.65103	−	20.4698i	−0.572430	−	1.76176i
$136$	3.68739	−	11.3486i	0.316191	−	0.973135i
$137$	3.92430	+	2.85117i	0.335275	+	0.243592i	0.742666	−	0.669662i	$-0.233561\pi$
$137$	3.92430	+	2.85117i	0.335275	+	0.243592i	−0.407390	+	0.913254i	$0.633561\pi$
$138$	−4.56977	−	3.32013i	−0.389004	−	0.282628i
$139$	−3.05595	+	9.40525i	−0.259202	+	0.797743i	0.733770	+	0.679398i	$0.237759\pi$
$139$	−3.05595	+	9.40525i	−0.259202	+	0.797743i	−0.992973	+	0.118345i	$0.962241\pi$
$140$	−7.07867	−	21.7859i	−0.598257	−	1.84124i
$141$	−1.77622	+	1.29050i	−0.149585	+	0.108680i
$142$	5.96241			0.500354
$143$	−15.5531	+	3.75746i	−1.30061	+	0.314214i
$144$	−0.318311			−0.0265259
$145$	2.86549	−	2.08190i	0.237966	−	0.172892i
$146$	−0.518418	−	1.59553i	−0.0429046	−	0.132047i
$147$	−2.85533	+	8.78779i	−0.235503	+	0.724804i
$148$	−1.81262	−	1.31695i	−0.148997	−	0.108253i
$149$	4.72071	+	3.42980i	0.386736	+	0.280980i	0.764116	−	0.645078i	$-0.223175\pi$
$149$	4.72071	+	3.42980i	0.386736	+	0.280980i	−0.377381	+	0.926058i	$0.623175\pi$
$150$	3.66417	−	11.2772i	0.299178	−	0.920776i
$151$	0.490244	+	1.50882i	0.0398955	+	0.122786i	0.969021	−	0.246980i	$-0.0794381\pi$
$151$	0.490244	+	1.50882i	0.0398955	+	0.122786i	−0.929125	+	0.369765i	$0.879438\pi$
$152$	1.82947	−	1.32919i	0.148390	−	0.107812i
$153$	−0.935151			−0.0756024
$154$	0.566328	−	7.32964i	0.0456360	−	0.590639i
$155$	16.7221			1.34315
$156$	10.5374	−	7.65587i	0.843667	−	0.612960i
$157$	−2.02240	−	6.22432i	−0.161405	−	0.496754i	0.837348	−	0.546670i	$-0.184105\pi$
$157$	−2.02240	−	6.22432i	−0.161405	−	0.496754i	−0.998753	+	0.0499155i	$0.984105\pi$
$158$	−2.07055	+	6.37248i	−0.164724	+	0.506968i
$159$	−3.97817	−	2.89031i	−0.315490	−	0.229217i
$160$	−18.4261	−	13.3874i	−1.45671	−	1.05836i
$161$	−5.85867	+	18.0311i	−0.461728	+	1.42105i
$162$	1.63454	+	5.03061i	0.128422	+	0.395242i
$163$	−3.52243	+	2.55919i	−0.275898	+	0.200451i	−0.717126	−	0.696943i	$-0.754543\pi$
$163$	−3.52243	+	2.55919i	−0.275898	+	0.200451i	0.441228	+	0.897395i	$0.354543\pi$
$164$	5.01266			0.391423
$165$	−14.5671	+	17.1053i	−1.13405	+	1.33164i
$166$	−7.36368			−0.571532
$167$	2.45901	−	1.78657i	0.190284	−	0.138249i	−0.488565	−	0.872528i	$-0.662479\pi$
$167$	2.45901	−	1.78657i	0.190284	−	0.138249i	0.678848	+	0.734278i	$0.262479\pi$
$168$	4.15086	+	12.7750i	0.320246	+	0.985616i
$169$	3.17492	−	9.77139i	0.244224	−	0.751645i
$170$	−10.7914	−	7.84038i	−0.827659	−	0.601330i
$171$	−0.143374	−	0.104168i	−0.0109641	−	0.00796589i
$172$	0.219716	−	0.676215i	0.0167532	−	0.0515609i
$173$	3.17436	+	9.76968i	0.241342	+	0.742775i	0.996217	+	0.0869056i	$0.0276978\pi$
$173$	3.17436	+	9.76968i	0.241342	+	0.742775i	−0.754874	+	0.655869i	$0.772302\pi$
$174$	−0.748593	+	0.543885i	−0.0567507	+	0.0412318i
$175$	−39.7991			−3.00853
$176$	3.11982	+	5.07481i	0.235165	+	0.382528i
$177$	−10.2305			−0.768974
$178$	8.42946	−	6.12436i	0.631815	−	0.459040i
$179$	−4.60444	−	14.1710i	−0.344152	−	1.05919i	−0.962036	−	0.272922i	$-0.912010\pi$
$179$	−4.60444	−	14.1710i	−0.344152	−	1.05919i	0.617884	−	0.786269i	$-0.287990\pi$
$180$	−0.354827	+	1.09205i	−0.0264472	+	0.0813962i
$181$	12.5055	+	9.08576i	0.929525	+	0.675339i	0.945876	−	0.324527i	$-0.105205\pi$
$181$	12.5055	+	9.08576i	0.929525	+	0.675339i	−0.0163518	+	0.999866i	$0.505205\pi$
$182$	8.65116	+	6.28543i	0.641267	+	0.465907i
$183$	−0.388152	+	1.19461i	−0.0286930	+	0.0883081i
$184$	3.74731	+	11.5330i	0.276255	+	0.850226i
$185$	−4.54809	+	3.30438i	−0.334382	+	0.242943i
$186$	−4.36855			−0.320318
$187$	9.16556	+	14.9090i	0.670252	+	1.09026i
$188$	2.09991			0.153152
$189$	15.2684	−	11.0931i	1.11061	−	0.806905i
$190$	−0.781148	−	2.40413i	−0.0566704	−	0.174414i
$191$	−2.11530	+	6.51022i	−0.153058	+	0.471063i	−0.997959	−	0.0638594i	$-0.979659\pi$
$191$	−2.11530	+	6.51022i	−0.153058	+	0.471063i	0.844901	+	0.534922i	$0.179659\pi$
$192$	−0.0690205	−	0.0501463i	−0.00498113	−	0.00361900i
$193$	−18.9931	−	13.7993i	−1.36715	−	0.993296i	−0.997953	−	0.0639466i	$-0.979631\pi$
$193$	−18.9931	−	13.7993i	−1.36715	−	0.993296i	−0.369201	−	0.929349i	$-0.620369\pi$
$194$	−3.14536	+	9.68042i	−0.225824	+	0.695014i
$195$	−10.0990	−	31.0816i	−0.723206	−	2.22580i
$196$	7.14977	−	5.19461i	0.510698	−	0.371043i
$197$	−26.5527			−1.89180			−0.945902	−	0.324454i	$-0.894820\pi$
$197$	−26.5527			−1.89180			−0.945902	+	0.324454i	$0.894820\pi$
$198$	−0.238923	+	0.280553i	−0.0169795	+	0.0199380i
$199$	23.9852			1.70027			0.850134	−	0.526566i	$-0.176521\pi$
$199$	23.9852			1.70027			0.850134	+	0.526566i	$0.176521\pi$
$200$	−20.5945	+	14.9628i	−1.45625	+	1.05803i
$201$	6.26304	+	19.2757i	0.441761	+	1.35960i
$202$	−1.61018	+	4.95561i	−0.113292	+	0.348675i
$203$	2.51262	+	1.82552i	0.176351	+	0.128127i
$204$	−11.5256	−	8.37383i	−0.806953	−	0.586285i
$205$	3.88662	−	11.9618i	0.271454	−	0.835448i
$206$	0.372382	+	1.14607i	0.0259451	+	0.0798508i
$207$	0.768846	−	0.558600i	0.0534385	−	0.0388254i
$208$	−8.66514			−0.600820
$209$	−0.255499	+	3.30677i	−0.0176732	+	0.228734i
$210$	15.0154			1.03616
$211$	−1.96542	+	1.42796i	−0.135305	+	0.0983048i	−0.653379	−	0.757031i	$-0.726649\pi$
$211$	−1.96542	+	1.42796i	−0.135305	+	0.0983048i	0.518074	+	0.855336i	$0.326649\pi$
$212$	1.45335	+	4.47294i	0.0998163	+	0.307203i
$213$	4.93756	−	15.1963i	0.338316	−	1.04123i
$214$	0.0572256	+	0.0415769i	0.00391186	+	0.00284214i
$215$	−1.44330	−	1.04862i	−0.0984326	−	0.0715154i
$216$	3.73024	−	11.4805i	0.253811	−	0.781149i
$217$	4.53107	+	13.9452i	0.307589	+	0.946661i
$218$	−0.558429	+	0.405723i	−0.0378216	+	0.0274790i
$219$	−4.49579			−0.303798
$220$	20.8881	−	5.04634i	1.40828	−	0.340224i
$221$	−25.4569			−1.71242
$222$	1.18817	−	0.863253i	0.0797444	−	0.0579377i
$223$	6.32938	+	19.4798i	0.423847	+	1.30447i	0.904094	+	0.427333i	$0.140547\pi$
$223$	6.32938	+	19.4798i	0.423847	+	1.30447i	−0.480248	+	0.877133i	$0.659453\pi$
$224$	6.17144	−	18.9937i	0.412347	−	1.26907i
$225$	1.61397	+	1.17262i	0.107598	+	0.0781747i
$226$	−6.31466	−	4.58787i	−0.420045	−	0.305181i
$227$	6.15289	−	18.9366i	0.408381	−	1.25687i	−0.509657	−	0.860378i	$-0.670228\pi$
$227$	6.15289	−	18.9366i	0.408381	−	1.25687i	0.918039	−	0.396491i	$-0.129772\pi$
$228$	−0.834296	−	2.56770i	−0.0552526	−	0.170050i
$229$	−15.5529	+	11.2999i	−1.02777	+	0.746717i	−0.967861	−	0.251487i	$-0.919080\pi$
$229$	−15.5529	+	11.2999i	−1.02777	+	0.746717i	−0.0599068	+	0.998204i	$0.519080\pi$
$230$	13.5556			0.893830
$231$	−18.2119	−	7.51317i	−1.19826	−	0.494331i
$232$	1.98650			0.130420
$233$	−14.9596	+	10.8688i	−0.980039	+	0.712040i	−0.957717	−	0.287711i	$-0.907106\pi$
$233$	−14.9596	+	10.8688i	−0.980039	+	0.712040i	−0.0223214	+	0.999751i	$0.507106\pi$
$234$	−0.165640	−	0.509786i	−0.0108282	−	0.0333258i
$235$	1.62819	−	5.01104i	0.106211	−	0.326884i
$236$	7.91620	+	5.75146i	0.515301	+	0.374388i
$237$	14.5268	+	10.5543i	0.943614	+	0.685576i
$238$	3.61434	−	11.1238i	0.234283	−	0.721048i
$239$	−3.25331	−	10.0127i	−0.210439	−	0.647666i	−0.999446	−	0.0332812i	$-0.989404\pi$
$239$	−3.25331	−	10.0127i	−0.210439	−	0.647666i	0.789007	−	0.614385i	$-0.210596\pi$
$240$	−9.84362	+	7.15181i	−0.635403	+	0.461647i
$241$	−16.8152			−1.08316			−0.541581	−	0.840648i	$-0.682174\pi$
$241$	−16.8152			−1.08316			−0.541581	+	0.840648i	$0.682174\pi$
$242$	6.81455	+	1.05938i	0.438056	+	0.0680997i
$243$	−1.83927			−0.117989
$244$	0.971938	−	0.706154i	0.0622219	−	0.0452069i
$245$	−6.85233	−	21.0893i	−0.437779	−	1.34735i
$246$	−1.01536	+	3.12496i	−0.0647370	+	0.199240i
$247$	−3.90297	−	2.83568i	−0.248340	−	0.180430i
$248$	7.58744	+	5.51260i	0.481803	+	0.350050i
$249$	−6.09798	+	18.7676i	−0.386444	+	1.18935i
$250$	4.88768	+	15.0427i	0.309124	+	0.951387i
$251$	12.8890	−	9.36444i	0.813549	−	0.591078i	−0.101308	−	0.994855i	$-0.532303\pi$
$251$	12.8890	−	9.36444i	0.813549	−	0.591078i	0.914857	+	0.403777i	$0.132303\pi$
$252$	−1.00684			−0.0634252
$253$	−16.4413	−	6.78272i	−1.03366	−	0.426426i
$254$	0.802078			0.0503269
$255$	−28.9191	+	21.0110i	−1.81098	+	1.31576i
$256$	−2.16354	−	6.65870i	−0.135221	−	0.416169i
$257$	−0.453448	+	1.39557i	−0.0282853	+	0.0870533i	−0.964203	−	0.265167i	$-0.914573\pi$
$257$	−0.453448	+	1.39557i	−0.0282853	+	0.0870533i	0.935917	+	0.352220i	$0.114573\pi$
$258$	0.377056	+	0.273947i	0.0234745	+	0.0170552i
$259$	−3.98802	−	2.89747i	−0.247803	−	0.180040i
$260$	−9.65919	+	29.7279i	−0.599037	+	1.84365i
$261$	−0.0481079	−	0.148061i	−0.00297780	−	0.00916473i
$262$	4.90566	−	3.56417i	0.303073	−	0.220195i
$263$	16.3858			1.01039			0.505195	−	0.863005i	$-0.331421\pi$
$263$	16.3858			1.01039			0.505195	+	0.863005i	$0.331421\pi$
$264$	−12.2486	+	2.95912i	−0.753848	+	0.182122i
$265$	11.8007			0.724913
$266$	1.79323	−	1.30286i	0.109950	−	0.0798834i
$267$	−8.62845	−	26.5556i	−0.528053	−	1.62518i
$268$	5.99027	−	18.4361i	0.365914	−	1.12617i
$269$	14.7445	+	10.7125i	0.898991	+	0.653155i	0.938207	−	0.346076i	$-0.112486\pi$
$269$	14.7445	+	10.7125i	0.898991	+	0.653155i	−0.0392158	+	0.999231i	$0.512486\pi$
$270$	−10.9168	−	7.93150i	−0.664374	−	0.482696i
$271$	−0.384815	+	1.18434i	−0.0233759	+	0.0719435i	−0.962064	−	0.272824i	$-0.912042\pi$
$271$	−0.384815	+	1.18434i	−0.0233759	+	0.0719435i	0.938688	+	0.344768i	$0.112042\pi$
$272$	2.92879	+	9.01388i	0.177584	+	0.546547i
$273$	23.1837	−	16.8439i	1.40314	−	1.01944i
$274$	3.04113			0.183721
$275$	2.87616	−	37.2245i	0.173439	−	2.24472i
$276$	14.4779			0.871468
$277$	14.4236	−	10.4794i	0.866630	−	0.629643i	−0.0630507	−	0.998010i	$-0.520083\pi$
$277$	14.4236	−	10.4794i	0.866630	−	0.629643i	0.929681	+	0.368367i	$0.120083\pi$
$278$	1.91592	+	5.89658i	0.114909	+	0.353654i
$279$	0.227125	−	0.699020i	0.0135976	−	0.0418492i
$280$	−26.0793	−	18.9477i	−1.55854	−	1.13234i
$281$	6.83916	+	4.96894i	0.407990	+	0.296422i	0.772788	−	0.634665i	$-0.218862\pi$
$281$	6.83916	+	4.96894i	0.407990	+	0.296422i	−0.364797	+	0.931087i	$0.618862\pi$
$282$	−0.425355	+	1.30911i	−0.0253295	+	0.0779563i
$283$	7.97647	+	24.5490i	0.474152	+	1.45929i	0.847098	+	0.531436i	$0.178347\pi$
$283$	7.97647	+	24.5490i	0.474152	+	1.45929i	−0.372947	+	0.927853i	$0.621653\pi$
$284$	−12.3637	+	8.98276i	−0.733651	+	0.533029i
$285$	−6.77422			−0.401270
$286$	−6.50402	+	7.63727i	−0.384590	+	0.451602i
$287$	11.0285			0.650994
$288$	−0.809891	+	0.588421i	−0.0477233	+	0.0346730i
$289$	3.35105	+	10.3135i	0.197121	+	0.606675i
$290$	0.686204	−	2.11192i	0.0402953	−	0.124016i
$291$	22.0675	+	16.0330i	1.29362	+	0.939872i
$292$	3.47876	+	2.52747i	0.203579	+	0.147909i
$293$	6.12581	−	18.8533i	0.357874	−	1.10142i	−0.596451	−	0.802650i	$-0.703423\pi$
$293$	6.12581	−	18.8533i	0.357874	−	1.10142i	0.954324	−	0.298772i	$-0.0965771\pi$
$294$	1.79013	+	5.50947i	0.104403	+	0.321319i
$295$	19.8627	−	14.4311i	1.15645	−	0.840211i
$296$	−3.15297			−0.183263
$297$	9.27209	+	15.0823i	0.538021	+	0.875163i
$298$	3.65830			0.211920
$299$	20.9297	−	15.2063i	1.21040	−	0.879405i
$300$	9.39172	+	28.9047i	0.542231	+	1.66882i
$301$	0.483404	−	1.48777i	0.0278630	−	0.0857534i
$302$	0.804670	+	0.584627i	0.0463036	+	0.0336415i
$303$	11.2968	+	8.20763i	0.648986	+	0.471516i
$304$	−0.555035	+	1.70822i	−0.0318334	+	0.0979733i
$305$	−0.931504	−	2.86687i	−0.0533378	−	0.164157i
$306$	−0.474317	+	0.344612i	−0.0271149	+	0.0197001i
$307$	19.6632			1.12224			0.561120	−	0.827735i	$-0.310371\pi$
$307$	19.6632			1.12224			0.561120	+	0.827735i	$0.310371\pi$
$308$	9.86824	+	16.0520i	0.562295	+	0.914649i
$309$	3.22935			0.183711
$310$	8.48160	−	6.16224i	0.481722	−	0.349992i
$311$	7.45658	+	22.9490i	0.422824	+	1.30132i	0.905063	+	0.425278i	$0.139824\pi$
$311$	7.45658	+	22.9490i	0.422824	+	1.30132i	−0.482239	+	0.876040i	$0.660176\pi$
$312$	5.66405	−	17.4322i	0.320664	−	0.986902i
$313$	−23.1203	−	16.7978i	−1.30683	−	0.949470i	−0.306836	−	0.951762i	$-0.599270\pi$
$313$	−23.1203	−	16.7978i	−1.30683	−	0.949470i	−0.999997	+	0.00229189i	$0.999270\pi$
$314$	−3.31950	−	2.41176i	−0.187330	−	0.136103i
$315$	−0.780667	+	2.40265i	−0.0439856	+	0.135374i
$316$	−5.30706	−	16.3335i	−0.298546	−	0.918829i
$317$	7.45766	−	5.41830i	0.418864	−	0.304322i	−0.358317	−	0.933600i	$-0.616649\pi$
$317$	7.45766	−	5.41830i	0.418864	−	0.304322i	0.777180	+	0.629278i	$0.216649\pi$
$318$	−3.08288			−0.172879
$319$	−1.88901	+	2.21815i	−0.105764	+	0.124192i
$320$	0.204740			0.0114453
$321$	0.153355	−	0.111419i	0.00855947	−	0.00621882i
$322$	3.67307	+	11.3045i	0.204692	+	0.629978i
$323$	−1.63061	+	5.01850i	−0.0907295	+	0.279237i
$324$	−10.9684	−	7.96898i	−0.609353	−	0.442721i
$325$	43.9360	+	31.9213i	2.43713	+	1.77068i
$326$	−0.843523	+	2.59610i	−0.0467184	+	0.143784i
$327$	0.571612	+	1.75924i	0.0316102	+	0.0972863i
$328$	5.70684	−	4.14626i	0.315107	−	0.228939i
$329$	4.62008			0.254713
$330$	−1.08512	+	14.0441i	−0.0597340	+	0.773101i
$331$	−19.8090			−1.08880			−0.544402	−	0.838825i	$-0.683243\pi$
$331$	−19.8090			−1.08880			−0.544402	+	0.838825i	$0.683243\pi$
$332$	15.2694	−	11.0939i	0.838017	−	0.608855i
$333$	0.0763567	+	0.235002i	0.00418432	+	0.0128780i
$334$	0.588864	−	1.81234i	0.0322212	−	0.0991666i
$335$	−39.3498	−	28.5893i	−2.14991	−	1.56200i
$336$	−8.63143	−	6.27110i	−0.470883	−	0.342117i
$337$	−10.3733	+	31.9256i	−0.565068	+	1.73910i	0.102681	+	0.994714i	$0.467258\pi$
$337$	−10.3733	+	31.9256i	−0.565068	+	1.73910i	−0.667749	+	0.744386i	$0.732742\pi$
$338$	−1.99050	−	6.12613i	−0.108269	−	0.333218i
$339$	−16.9223	+	12.2948i	−0.919092	+	0.667759i
$340$	34.1891			1.85417
$341$	−13.3705	+	3.23017i	−0.724053	+	0.174923i
$342$	−0.111108			−0.00600801
$343$	−4.29141	+	3.11789i	−0.231714	+	0.168350i
$344$	−0.309194	−	0.951600i	−0.0166706	−	0.0513068i
$345$	11.2256	−	34.5489i	0.604366	−	1.86005i
$346$	5.21029	+	3.78550i	0.280107	+	0.203509i
$347$	6.30380	+	4.57998i	0.338406	+	0.245866i	0.743989	−	0.668192i	$-0.232932\pi$
$347$	6.30380	+	4.57998i	0.338406	+	0.245866i	−0.405583	+	0.914058i	$0.632932\pi$
$348$	0.732892	−	2.25561i	0.0392871	−	0.120913i
$349$	3.67330	+	11.3053i	0.196627	+	0.605157i	0.999954	+	0.00961799i	$0.00306155\pi$
$349$	3.67330	+	11.3053i	0.196627	+	0.605157i	−0.803326	+	0.595539i	$0.796938\pi$
$350$	−20.1865	+	14.6664i	−1.07901	+	0.783950i
$351$	−25.7528			−1.37458
$352$	17.3190	+	7.14482i	0.923107	+	0.380820i
$353$	−22.9951			−1.22390			−0.611952	−	0.790895i	$-0.709615\pi$
$353$	−22.9951			−1.22390			−0.611952	+	0.790895i	$0.709615\pi$
$354$	−5.18903	+	3.77005i	−0.275794	+	0.200376i
$355$	11.8494	+	36.4686i	0.628899	+	1.93555i
$356$	−8.25266	+	25.3991i	−0.437390	+	1.34615i
$357$	−25.3579	−	18.4236i	−1.34208	−	0.975078i
$358$	−7.55757	−	5.49090i	−0.399430	−	0.290203i
$359$	−2.74063	+	8.43480i	−0.144645	+	0.445172i	−0.996965	−	0.0778487i	$-0.975195\pi$
$359$	−2.74063	+	8.43480i	−0.144645	+	0.445172i	0.852320	+	0.523020i	$0.175195\pi$
$360$	0.499328	+	1.53677i	0.0263169	+	0.0809951i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	9.69109			0.509352
$363$	8.34326	−	16.4908i	0.437907	−	0.865542i
$364$	−27.4085			−1.43660
$365$	8.72864	−	6.34173i	0.456878	−	0.331941i
$366$	0.243350	+	0.748956i	0.0127201	+	0.0391485i
$367$	−8.06912	+	24.8342i	−0.421205	+	1.29634i	0.485377	+	0.874305i	$0.338682\pi$
$367$	−8.06912	+	24.8342i	−0.421205	+	1.29634i	−0.906582	+	0.422030i	$0.861318\pi$
$368$	−7.79226	−	5.66141i	−0.406200	−	0.295121i
$369$	−0.447240	−	0.324939i	−0.0232824	−	0.0169156i
$370$	−1.08914	+	3.35203i	−0.0566217	+	0.174264i
$371$	3.19756	+	9.84108i	0.166009	+	0.510924i
$372$	9.05867	−	6.58151i	0.469670	−	0.341235i
$373$	28.1780			1.45900			0.729501	−	0.683980i	$-0.239753\pi$
$373$	28.1780			1.45900			0.729501	+	0.683980i	$0.239753\pi$
$374$	10.1430	+	4.18441i	0.524481	+	0.216370i
$375$	42.3867			2.18884
$376$	2.39071	−	1.73695i	0.123292	−	0.0895766i
$377$	−1.30960	−	4.03055i	−0.0674480	−	0.207584i
$378$	3.65634	−	11.2531i	0.188062	−	0.578795i
$379$	−0.874167	−	0.635119i	−0.0449029	−	0.0326239i	0.565107	−	0.825017i	$-0.308835\pi$
$379$	−0.874167	−	0.635119i	−0.0449029	−	0.0326239i	−0.610010	+	0.792393i	$0.708835\pi$
$380$	5.24177	+	3.80837i	0.268897	+	0.195365i
$381$	0.664214	−	2.04424i	0.0340287	−	0.104730i
$382$	1.32618	+	4.08155i	0.0678531	+	0.208830i
$383$	−12.7587	+	9.26972i	−0.651938	+	0.473660i	−0.863931	−	0.503611i	$-0.832005\pi$
$383$	−12.7587	+	9.26972i	−0.651938	+	0.473660i	0.211993	+	0.977271i	$0.432005\pi$
$384$	−19.0347			−0.971360
$385$	45.9566	−	11.1026i	2.34217	−	0.565842i
$386$	−14.7187			−0.749161
$387$	−0.0634382	+	0.0460906i	−0.00322475	+	0.00234291i
$388$	−8.06194	−	24.8121i	−0.409283	−	1.25964i
$389$	−8.16329	+	25.1240i	−0.413895	+	1.27384i	0.499340	+	0.866406i	$0.333576\pi$
$389$	−8.16329	+	25.1240i	−0.413895	+	1.27384i	−0.913235	+	0.407432i	$0.866424\pi$
$390$	−16.5762	−	12.0433i	−0.839368	−	0.609837i
$391$	−22.8925	−	16.6324i	−1.15772	−	0.841135i
$392$	3.84314	−	11.8280i	0.194108	−	0.597402i
$393$	−5.02147	−	15.4545i	−0.253299	−	0.779575i
$394$	−13.4678	+	9.78493i	−0.678498	+	0.492958i
$395$	−43.0917			−2.16818
$396$	0.0727616	−	0.941710i	0.00365641	−	0.0473227i
$397$	9.42172			0.472863			0.236431	−	0.971648i	$-0.424022\pi$
$397$	9.42172			0.472863			0.236431	+	0.971648i	$0.424022\pi$
$398$	12.1655	−	8.83879i	0.609804	−	0.443048i
$399$	−1.83556	−	5.64929i	−0.0918932	−	0.282818i
$400$	6.24806	−	19.2295i	0.312403	−	0.961477i
$401$	1.95006	+	1.41680i	0.0973812	+	0.0707516i	0.635410	−	0.772175i	$-0.280831\pi$
$401$	1.95006	+	1.41680i	0.0973812	+	0.0707516i	−0.538029	+	0.842926i	$0.680831\pi$
$402$	10.2799	+	7.46881i	0.512717	+	0.372510i
$403$	6.18286	−	19.0289i	0.307990	−	0.947896i
$404$	−4.12708	−	12.7018i	−0.205330	−	0.631940i
$405$	−27.5209	+	19.9951i	−1.36753	+	0.993566i
$406$	1.94715			0.0966352
$407$	2.99823	−	3.52064i	0.148617	−	0.174512i
$408$	−20.0482			−0.992533
$409$	6.69638	−	4.86520i	0.331115	−	0.240569i	−0.409789	−	0.912180i	$-0.634398\pi$
$409$	6.69638	−	4.86520i	0.331115	−	0.240569i	0.740903	+	0.671612i	$0.234398\pi$
$410$	−2.43670	−	7.49940i	−0.120340	−	0.370369i
$411$	2.51840	−	7.75085i	0.124224	−	0.382321i
$412$	−2.49881	−	1.81549i	−0.123108	−	0.0894429i
$413$	17.4167	+	12.6540i	0.857021	+	0.622662i
$414$	0.184117	−	0.566654i	0.00904886	−	0.0278495i
$415$	−14.6342	−	45.0393i	−0.718363	−	2.21089i
$416$	−22.0471	+	16.0181i	−1.08095	+	0.785353i
$417$	16.6151			0.813644
$418$	1.08898	+	1.77138i	0.0532640	+	0.0866410i
$419$	−13.1197			−0.640939			−0.320469	−	0.947259i	$-0.603841\pi$
$419$	−13.1197			−0.640939			−0.320469	+	0.947259i	$0.603841\pi$
$420$	−31.1362	+	22.6218i	−1.51929	+	1.10383i
$421$	−9.06930	−	27.9124i	−0.442011	−	1.36037i	−0.885729	−	0.464202i	$-0.846341\pi$
$421$	−9.06930	−	27.9124i	−0.442011	−	1.36037i	0.443719	−	0.896166i	$-0.353659\pi$
$422$	−0.470663	+	1.44855i	−0.0229115	+	0.0705143i
$423$	−0.187358	−	0.136124i	−0.00910966	−	0.00661856i
$424$	5.35444	+	3.89023i	0.260035	+	0.188926i
$425$	18.3559	−	56.4935i	0.890390	−	2.74034i
$426$	−3.09558	−	9.52723i	−0.149982	−	0.461596i
$427$	2.13839	−	1.55363i	0.103484	−	0.0751857i
$428$	−0.181302			−0.00876356
$429$	14.0789	+	22.9012i	0.679734	+	1.10568i
$430$	−1.11849			−0.0539382
$431$	13.6897	−	9.94616i	0.659411	−	0.479090i	−0.207053	−	0.978330i	$-0.566387\pi$
$431$	13.6897	−	9.94616i	0.659411	−	0.479090i	0.866464	+	0.499240i	$0.166387\pi$
$432$	2.96283	+	9.11864i	0.142549	+	0.438721i
$433$	3.57415	−	11.0001i	0.171762	−	0.528630i	−0.827708	−	0.561159i	$-0.810356\pi$
$433$	3.57415	−	11.0001i	0.171762	−	0.528630i	0.999471	+	0.0325280i	$0.0103558\pi$
$434$	7.43713	+	5.40339i	0.356994	+	0.259371i
$435$	−4.81434	−	3.49782i	−0.230830	−	0.167708i
$436$	0.546717	−	1.68262i	0.0261830	−	0.0805829i
$437$	−1.65711	−	5.10005i	−0.0792701	−	0.243968i
$438$	−2.28031	+	1.65674i	−0.108957	+	0.0791622i
$439$	−8.57822			−0.409416			−0.204708	−	0.978823i	$-0.565625\pi$
$439$	−8.57822			−0.409416			−0.204708	+	0.978823i	$0.565625\pi$
$440$	19.6067	−	23.0229i	0.934711	−	1.09757i
$441$	−0.974650			−0.0464119
$442$	−12.9120	+	9.38111i	−0.614161	+	0.446214i
$443$	−7.87768	−	24.2450i	−0.374280	−	1.15192i	−0.943963	−	0.330051i	$-0.892934\pi$
$443$	−7.87768	−	24.2450i	−0.374280	−	1.15192i	0.569683	−	0.821864i	$-0.307066\pi$
$444$	−1.16324	+	3.58010i	−0.0552051	+	0.169904i
$445$	54.2114	+	39.3869i	2.56987	+	1.86712i
$446$	10.3888	+	7.54792i	0.491925	+	0.357405i
$447$	3.02950	−	9.32383i	0.143290	−	0.441002i
$448$	0.0554770	+	0.170741i	0.00262104	+	0.00806674i
$449$	−3.86783	+	2.81014i	−0.182534	+	0.132619i	−0.675300	−	0.737543i	$-0.735986\pi$
$449$	−3.86783	+	2.81014i	−0.182534	+	0.132619i	0.492766	+	0.870162i	$0.335986\pi$
$450$	1.25074			0.0589607
$451$	−0.797000	+	10.3151i	−0.0375293	+	0.485719i
$452$	20.0061			0.941007
$453$	2.15638	−	1.56671i	0.101316	−	0.0736102i
$454$	−3.85753	−	11.8722i	−0.181043	−	0.557192i
$455$	−21.2515	+	65.4054i	−0.996287	+	3.06625i
$456$	−3.07372	−	2.23319i	−0.143940	−	0.104579i
$457$	−18.9537	−	13.7707i	−0.886616	−	0.644164i	0.0483778	−	0.998829i	$-0.484595\pi$
$457$	−18.9537	−	13.7707i	−0.886616	−	0.644164i	−0.934993	+	0.354665i	$0.884595\pi$
$458$	−3.72449	+	11.4628i	−0.174034	+	0.535622i
$459$	8.70434	+	26.7892i	0.406284	+	1.25041i
$460$	−28.1090	+	20.4224i	−1.31059	+	0.952200i
$461$	13.8382			0.644509			0.322255	−	0.946653i	$-0.395559\pi$
$461$	13.8382			0.644509			0.322255	+	0.946653i	$0.395559\pi$
$462$	−12.0059	+	2.90050i	−0.558566	+	0.134944i
$463$	−5.00021			−0.232380			−0.116190	−	0.993227i	$-0.537068\pi$
$463$	−5.00021			−0.232380			−0.116190	+	0.993227i	$0.537068\pi$
$464$	−1.27648	+	0.927420i	−0.0592593	+	0.0430544i
$465$	−8.68182	−	26.7199i	−0.402610	−	1.23911i
$466$	−3.58241	+	11.0255i	−0.165952	+	0.510748i
$467$	−6.18477	−	4.49350i	−0.286197	−	0.207934i	0.435419	−	0.900228i	$-0.356600\pi$
$467$	−6.18477	−	4.49350i	−0.286197	−	0.207934i	−0.721616	+	0.692294i	$0.756600\pi$
$468$	1.11150	+	0.807551i	0.0513790	+	0.0373290i
$469$	13.1794	−	40.5620i	0.608568	−	1.87298i
$470$	−1.02078	−	3.14165i	−0.0470853	−	0.144914i
$471$	−8.89573	+	6.46312i	−0.409893	+	0.297805i
$472$	13.7698			0.633808
$473$	1.35659	+	0.559649i	0.0623759	+	0.0257327i
$474$	11.2575			0.517073
$475$	9.10715	−	6.61673i	0.417865	−	0.303596i
$476$	9.26399	+	28.5116i	0.424614	+	1.30683i
$477$	0.160282	−	0.493296i	0.00733880	−	0.0225865i
$478$	−5.33988	−	3.87965i	−0.244240	−	0.177451i
$479$	17.6713	+	12.8389i	0.807421	+	0.586625i	0.913082	−	0.407777i	$-0.133696\pi$
$479$	17.6713	+	12.8389i	0.807421	+	0.586625i	−0.105661	+	0.994402i	$0.533696\pi$
$480$	−11.8249	+	36.3933i	−0.539730	+	1.66112i
$481$	2.07860	+	6.39727i	0.0947760	+	0.291691i
$482$	−8.52884	+	6.19656i	−0.388478	+	0.282246i
$483$	31.8534			1.44938
$484$	−15.7267	+	8.06982i	−0.714852	+	0.366810i
$485$	−65.4604			−2.97240
$486$	−0.932896	+	0.677788i	−0.0423170	+	0.0307451i
$487$	−3.68517	−	11.3418i	−0.166991	−	0.513945i	0.832186	−	0.554496i	$-0.187089\pi$
$487$	−3.68517	−	11.3418i	−0.166991	−	0.513945i	−0.999177	+	0.0405504i	$0.987089\pi$
$488$	0.522435	−	1.60789i	0.0236495	−	0.0727858i
$489$	5.91808	+	4.29973i	0.267625	+	0.194441i
$490$	−11.2472	−	8.17155i	−0.508095	−	0.369153i
$491$	12.3477	−	38.0025i	0.557246	−	1.71503i	−0.132691	−	0.991157i	$-0.542362\pi$
$491$	12.3477	−	38.0025i	0.557246	−	1.71503i	0.689937	−	0.723869i	$-0.257638\pi$
$492$	−2.60249	−	8.00965i	−0.117329	−	0.361103i
$493$	−3.75012	+	2.72462i	−0.168897	+	0.122711i
$494$	−3.02460			−0.136083
$495$	−2.19080	−	0.903797i	−0.0984692	−	0.0406227i
$496$	−7.44916			−0.334477
$497$	−27.2018	+	19.7633i	−1.22017	+	0.886505i
$498$	3.82310	+	11.7663i	0.171317	+	0.527260i
$499$	7.04830	−	21.6924i	0.315525	−	0.971087i	−0.660013	−	0.751255i	$-0.729449\pi$
$499$	7.04830	−	21.6924i	0.315525	−	0.971087i	0.975538	−	0.219832i	$-0.0705510\pi$
$500$	−32.7980	−	23.8292i	−1.46677	−	1.06567i
$501$	−4.13141	−	3.00165i	−0.184578	−	0.134104i
$502$	3.08656	−	9.49947i	0.137760	−	0.423982i
$503$	5.21397	+	16.0470i	0.232479	+	0.715498i	0.997446	+	0.0714279i	$0.0227556\pi$
$503$	5.21397	+	16.0470i	0.232479	+	0.715498i	−0.764966	+	0.644070i	$0.777244\pi$
$504$	−1.14628	+	0.832818i	−0.0510592	+	0.0370967i
$505$	−33.5106			−1.49120
$506$	−10.8387	+	2.61851i	−0.481838	+	0.116407i
$507$	−17.2619			−0.766628
$508$	−1.66320	+	1.20838i	−0.0737925	+	0.0536134i
$509$	−9.80279	−	30.1699i	−0.434501	−	1.33726i	−0.893597	−	0.448870i	$-0.851827\pi$
$509$	−9.80279	−	30.1699i	−0.434501	−	1.33726i	0.459096	−	0.888387i	$-0.348173\pi$
$510$	−6.92531	+	21.3139i	−0.306658	+	0.943796i
$511$	7.65375	+	5.56078i	0.338582	+	0.245994i
$512$	14.7802	+	10.7384i	0.653199	+	0.474577i
$513$	−1.64956	+	5.07682i	−0.0728299	+	0.224147i
$514$	0.284287	+	0.874947i	0.0125394	+	0.0385923i
$515$	−6.26982	+	4.55529i	−0.276281	+	0.200730i
$516$	−1.19459			−0.0525887
$517$	−0.333880	+	4.32120i	−0.0146840	+	0.190046i
$518$	−3.09051			−0.135789
$519$	13.9627	−	10.1445i	0.612896	−	0.445295i
$520$	13.5928	+	41.8344i	0.596085	+	1.83456i
$521$	0.702944	−	2.16344i	0.0307965	−	0.0947820i	−0.934477	−	0.356024i	$-0.884132\pi$
$521$	0.702944	−	2.16344i	0.0307965	−	0.0947820i	0.965273	+	0.261242i	$0.0841321\pi$
$522$	−0.0789626	−	0.0573697i	−0.00345610	−	0.00251100i
$523$	8.65238	+	6.28632i	0.378342	+	0.274882i	0.760662	−	0.649148i	$-0.224875\pi$
$523$	8.65238	+	6.28632i	0.378342	+	0.274882i	−0.382319	+	0.924030i	$0.624875\pi$
$524$	−4.80277	+	14.7814i	−0.209810	+	0.645728i
$525$	20.6631	+	63.5943i	0.901809	+	2.77548i
$526$	8.31102	−	6.03831i	0.362378	−	0.263283i
$527$	−21.8845			−0.953304
$528$	6.48919	−	7.61986i	0.282406	−	0.331612i
$529$	5.75650			0.250283
$530$	5.98544	−	4.34868i	0.259991	−	0.188895i
$531$	−0.333470	−	1.02631i	−0.0144713	−	0.0445382i
$532$	−1.75562	+	5.40324i	−0.0761158	+	0.234260i
$533$	−12.1749	−	8.84557i	−0.527353	−	0.383144i
$534$	−14.1624	−	10.2896i	−0.612869	−	0.445275i
$535$	−0.140574	+	0.432644i	−0.00607756	+	0.0187048i
$536$	−8.42977	−	25.9441i	−0.364110	−	1.12062i
$537$	−20.2531	+	14.7147i	−0.873985	+	0.634987i
$538$	11.4263			0.492621
$539$	9.55270	+	15.5388i	0.411464	+	0.669302i
$540$	34.5865			1.48836
$541$	−22.7096	+	16.4995i	−0.976363	+	0.709369i	−0.956893	−	0.290442i	$-0.906198\pi$
$541$	−22.7096	+	16.4995i	−0.976363	+	0.709369i	−0.0194698	+	0.999810i	$0.506198\pi$
$542$	0.241258	+	0.742517i	0.0103629	+	0.0318938i
$543$	8.02534	−	24.6995i	0.344400	−	1.05996i
$544$	24.1146	+	17.5203i	1.03391	+	0.751177i
$545$	−3.59136	−	2.60928i	−0.153837	−	0.111769i
$546$	5.55185	−	17.0868i	0.237597	−	0.731249i
$547$	7.94547	+	24.4536i	0.339724	+	1.04556i	0.964348	+	0.264637i	$0.0852520\pi$
$547$	7.94547	+	24.4536i	0.339724	+	1.04556i	−0.624625	+	0.780925i	$0.714748\pi$
$548$	−6.30611	+	4.58166i	−0.269384	+	0.195719i
$549$	−0.132494			−0.00565469
$550$	−12.2588	−	19.9405i	−0.522715	−	0.850266i
$551$	−0.878455			−0.0374235
$552$	16.4829	−	11.9755i	0.701558	−	0.509711i
$553$	−11.6763	−	35.9358i	−0.496525	−	1.52815i
$554$	3.45405	−	10.6305i	0.146748	−	0.451645i
$555$	7.64131	+	5.55174i	0.324356	+	0.235658i
$556$	−12.8565	−	9.34076i	−0.545235	−	0.396137i
$557$	6.68268	−	20.5672i	0.283154	−	0.871460i	−0.703791	−	0.710407i	$-0.748511\pi$
$557$	6.68268	−	20.5672i	0.283154	−	0.871460i	0.986946	−	0.161053i	$-0.0514890\pi$
$558$	−0.142395	−	0.438247i	−0.00602807	−	0.0185525i
$559$	−1.72693	+	1.25469i	−0.0730414	+	0.0530677i
$560$	25.6040			1.08197
$561$	19.0643	−	22.3860i	0.804894	−	0.945138i
$562$	5.29999			0.223567
$563$	11.5439	−	8.38712i	0.486516	−	0.353475i	−0.317327	−	0.948316i	$-0.602785\pi$
$563$	11.5439	−	8.38712i	0.486516	−	0.353475i	0.803843	+	0.594841i	$0.202785\pi$
$564$	−1.09024	−	3.35541i	−0.0459073	−	0.141288i
$565$	15.5119	−	47.7408i	0.652592	−	2.00847i
$566$	13.0923	+	9.51211i	0.550310	+	0.399824i
$567$	−24.1319	−	17.5328i	−1.01344	−	0.736310i
$568$	−6.64573	+	20.4535i	−0.278849	+	0.858208i
$569$	−0.347328	−	1.06897i	−0.0145607	−	0.0448134i	0.943512	−	0.331338i	$-0.107500\pi$
$569$	−0.347328	−	1.06897i	−0.0145607	−	0.0448134i	−0.958073	+	0.286525i	$0.907500\pi$
$570$	−3.43595	+	2.49636i	−0.143916	+	0.104561i
$571$	30.2840			1.26734			0.633672	−	0.773602i	$-0.281547\pi$
$571$	30.2840			1.26734			0.633672	+	0.773602i	$0.281547\pi$
$572$	1.98073	−	25.6355i	0.0828187	−	1.07187i
$573$	11.5008			0.480452
$574$	5.59378	−	4.06412i	0.233480	−	0.169633i
$575$	18.6541	+	57.4115i	0.777931	+	2.39423i
$576$	0.00278085	−	0.00855859i	0.000115869	−	0.000356608i
$577$	−0.0356774	−	0.0259211i	−0.00148527	−	0.00107911i	0.587042	−	0.809556i	$-0.300292\pi$
$577$	−0.0356774	−	0.0259211i	−0.00148527	−	0.00107911i	−0.588528	+	0.808477i	$0.700292\pi$
$578$	5.50030	+	3.99620i	0.228782	+	0.166220i
$579$	−12.1888	+	37.5131i	−0.506548	+	1.55899i
$580$	1.75882	+	5.41310i	0.0730312	+	0.224767i
$581$	33.5947	−	24.4080i	1.39374	−	1.01261i
$582$	17.1012			0.708867
$583$	−9.43553	+	2.27952i	−0.390780	+	0.0944081i
$584$	6.05113			0.250398
$585$	2.78888	−	2.02624i	0.115306	−	0.0837748i
$586$	−3.84055	−	11.8200i	−0.158652	−	0.488280i
$587$	3.85787	−	11.8733i	0.159231	−	0.490064i	−0.839334	−	0.543617i	$-0.817055\pi$
$587$	3.85787	−	11.8733i	0.159231	−	0.490064i	0.998565	+	0.0535528i	$0.0170545\pi$
$588$	−12.0124	−	8.72753i	−0.495384	−	0.359917i
$589$	−3.35526	−	2.43774i	−0.138251	−	0.100445i
$590$	4.75656	−	14.6392i	0.195825	−	0.602686i
$591$	13.7857	+	42.4281i	0.567069	+	1.74526i
$592$	2.02603	−	1.47200i	0.0832694	−	0.0604988i
$593$	−0.838916			−0.0344501			−0.0172251	−	0.999852i	$-0.505483\pi$
$593$	−0.838916			−0.0344501			−0.0172251	+	0.999852i	$0.505483\pi$
$594$	10.2609	+	4.23304i	0.421008	+	0.173684i
$595$	75.2207			3.08375
$596$	−7.58589	+	5.51147i	−0.310730	+	0.225759i
$597$	−12.4527	−	38.3256i	−0.509657	−	1.56856i
$598$	5.01208	−	15.4256i	0.204959	−	0.630800i
$599$	−1.74527	−	1.26801i	−0.0713097	−	0.0518095i	0.551559	−	0.834136i	$-0.314033\pi$
$599$	−1.74527	−	1.26801i	−0.0713097	−	0.0518095i	−0.622869	+	0.782326i	$0.714033\pi$
$600$	34.6011	+	25.1392i	1.41258	+	1.02630i
$601$	9.32064	−	28.6860i	0.380197	−	1.17013i	−0.559709	−	0.828690i	$-0.689087\pi$
$601$	9.32064	−	28.6860i	0.380197	−	1.17013i	0.939905	−	0.341436i	$-0.110913\pi$
$602$	−0.303068	−	0.932749i	−0.0123521	−	0.0380160i
$603$	−1.72956	+	1.25660i	−0.0704332	+	0.0511727i
$604$	−2.54935			−0.103732
$605$	7.06323	+	43.7860i	0.287161	+	1.78015i
$606$	8.75446			0.355625
$607$	−17.3074	+	12.5746i	−0.702488	+	0.510387i	−0.880741	−	0.473597i	$-0.842955\pi$
$607$	−17.3074	+	12.5746i	−0.702488	+	0.510387i	0.178254	+	0.983985i	$0.442955\pi$
$608$	1.74557	+	5.37232i	0.0707923	+	0.217876i
$609$	1.61246	−	4.96265i	0.0653403	−	0.201097i
$610$	−1.52894	−	1.11084i	−0.0619049	−	0.0449765i
$611$	−5.10031	−	3.70559i	−0.206336	−	0.149912i
$612$	0.464369	−	1.42918i	0.0187710	−	0.0577712i
$613$	−0.377597	−	1.16212i	−0.0152510	−	0.0469378i	0.943141	−	0.332392i	$-0.107856\pi$
$613$	−0.377597	−	1.16212i	−0.0152510	−	0.0469378i	−0.958392	+	0.285454i	$0.907856\pi$
$614$	9.97338	−	7.24609i	0.402493	−	0.292428i
$615$	−21.1314			−0.852101
$616$	24.5124	+	10.1124i	0.987632	+	0.407440i
$617$	−30.7139			−1.23649			−0.618247	−	0.785984i	$-0.712157\pi$
$617$	−30.7139			−1.23649			−0.618247	+	0.785984i	$0.712157\pi$
$618$	1.63796	−	1.19005i	0.0658883	−	0.0478706i
$619$	−12.7902	−	39.3642i	−0.514081	−	1.58218i	−0.784947	−	0.619562i	$-0.787310\pi$
$619$	−12.7902	−	39.3642i	−0.514081	−	1.58218i	0.270866	−	0.962617i	$-0.412690\pi$
$620$	−8.30370	+	25.5562i	−0.333485	+	1.02636i
$621$	−23.1586	−	16.8257i	−0.929321	−	0.675191i
$622$	12.2390	+	8.89213i	0.490738	+	0.356542i
$623$	−18.1570	+	55.8814i	−0.727443	+	2.23884i
$624$	4.49880	+	13.8459i	0.180096	+	0.554279i
$625$	−36.7585	+	26.7066i	−1.47034	+	1.06826i
$626$	−17.9170			−0.716107
$627$	5.41648	−	1.30856i	0.216313	−	0.0522590i
$628$	10.5168			0.419667
$629$	5.95218	−	4.32451i	0.237329	−	0.172430i
$630$	0.489436	+	1.50633i	0.0194996	+	0.0600136i
$631$	−5.66999	+	17.4504i	−0.225719	+	0.694691i	0.772499	+	0.635016i	$0.219006\pi$
$631$	−5.66999	+	17.4504i	−0.225719	+	0.694691i	−0.998218	+	0.0596750i	$0.980994\pi$
$632$	−19.5523	−	14.2056i	−0.777751	−	0.565069i
$633$	3.30212	+	2.39913i	0.131248	+	0.0953570i
$634$	1.78590	−	5.49643i	0.0709271	−	0.218291i
$635$	1.59401	+	4.90585i	0.0632562	+	0.194683i
$636$	6.39268	−	4.64456i	0.253486	−	0.184169i
$637$	−26.5322			−1.05124
$638$	−0.140714	+	1.82118i	−0.00557094	+	0.0721013i
$639$	1.68541			0.0666738
$640$	36.9561	−	26.8502i	1.46082	−	1.06135i
$641$	−10.6594	−	32.8062i	−0.421021	−	1.29577i	−0.906753	−	0.421661i	$-0.861447\pi$
$641$	−10.6594	−	32.8062i	−0.421021	−	1.29577i	0.485733	−	0.874107i	$-0.338553\pi$
$642$	0.0367243	−	0.113026i	0.00144939	−	0.00446078i
$643$	19.1350	+	13.9024i	0.754610	+	0.548257i	0.897252	−	0.441518i	$-0.145560\pi$
$643$	19.1350	+	13.9024i	0.754610	+	0.548257i	−0.142642	+	0.989774i	$0.545560\pi$
$644$	−24.6476	−	17.9075i	−0.971250	−	0.705654i
$645$	−0.926235	+	2.85066i	−0.0364705	+	0.112245i
$646$	1.02230	+	3.14633i	0.0402220	+	0.123791i
$647$	−33.2480	+	24.1561i	−1.30711	+	0.949673i	−0.999998	−	0.00199922i	$-0.999364\pi$
$647$	−33.2480	+	24.1561i	−1.30711	+	0.949673i	−0.307115	+	0.951672i	$0.599364\pi$
$648$	−19.0789			−0.749490
$649$	−13.0940	+	15.3755i	−0.513986	+	0.603543i
$650$	34.0481			1.33548
$651$	19.9303	−	14.4802i	0.781130	−	0.567524i
$652$	−2.16205	−	6.65411i	−0.0846725	−	0.260595i
$653$	−2.55392	+	7.86015i	−0.0999426	+	0.307592i	−0.988510	−	0.151154i	$-0.951701\pi$
$653$	−2.55392	+	7.86015i	−0.0999426	+	0.307592i	0.888568	+	0.458746i	$0.151701\pi$
$654$	0.938224	+	0.681660i	0.0366875	+	0.0266550i
$655$	31.5492	+	22.9218i	1.23273	+	0.895630i
$656$	−1.73137	+	5.32861i	−0.0675986	+	0.208047i
$657$	−0.146543	−	0.451012i	−0.00571718	−	0.0175957i
$658$	2.34335	−	1.70254i	0.0913533	−	0.0663721i
$659$	−7.25500			−0.282615			−0.141307	−	0.989966i	$-0.545131\pi$
$659$	−7.25500			−0.282615			−0.141307	+	0.989966i	$0.545131\pi$
$660$	−18.9082	−	30.7567i	−0.736001	−	1.19720i
$661$	−19.7407			−0.767824			−0.383912	−	0.923370i	$-0.625423\pi$
$661$	−19.7407			−0.767824			−0.383912	+	0.923370i	$0.625423\pi$
$662$	−10.0473	+	7.29982i	−0.390501	+	0.283716i
$663$	13.2168	+	40.6771i	0.513298	+	1.57977i
$664$	8.20760	−	25.2604i	0.318517	−	0.980293i
$665$	11.5326	+	8.37893i	0.447215	+	0.324921i
$666$	0.125329	+	0.0910570i	0.00485641	+	0.00352839i
$667$	1.45569	−	4.48017i	0.0563647	−	0.173473i
$668$	1.50933	+	4.64524i	0.0583977	+	0.179730i
$669$	27.8404	−	20.2272i	1.07637	−	0.782029i
$670$	−30.4941			−1.17809
$671$	1.29859	+	2.11234i	0.0501316	+	0.0815458i
$672$	−33.5539			−1.29437
$673$	−17.8696	+	12.9830i	−0.688821	+	0.500458i	−0.876272	−	0.481816i	$-0.839977\pi$
$673$	−17.8696	+	12.9830i	−0.688821	+	0.500458i	0.187451	+	0.982274i	$0.439977\pi$
$674$	6.50348	+	20.0156i	0.250505	+	0.770974i
$675$	18.5692	−	57.1501i	0.714728	−	2.19971i
$676$	13.3569	+	9.70438i	0.513728	+	0.373246i
$677$	32.5219	+	23.6285i	1.24992	+	0.908119i	0.998217	−	0.0596861i	$-0.0190100\pi$
$677$	32.5219	+	23.6285i	1.24992	+	0.908119i	0.251701	+	0.967805i	$0.419010\pi$
$678$	−4.05241	+	12.4720i	−0.155632	+	0.478986i
$679$	−17.7374	−	54.5900i	−0.680698	−	2.09497i
$680$	38.9238	−	28.2798i	1.49266	−	1.08448i
$681$	−33.4530			−1.28192
$682$	−5.59130	+	6.56553i	−0.214102	+	0.251407i
$683$	16.5356			0.632717			0.316359	−	0.948640i	$-0.397540\pi$
$683$	16.5356			0.632717			0.316359	+	0.948640i	$0.397540\pi$
$684$	0.230394	−	0.167391i	0.00880933	−	0.00640035i
$685$	6.04377	+	18.6008i	0.230920	+	0.710700i
$686$	−1.02767	+	3.16285i	−0.0392367	+	0.120758i
$687$	26.1307	+	18.9851i	0.996948	+	0.724325i
$688$	0.642947	+	0.467128i	0.0245121	+	0.0178091i
$689$	4.36323	−	13.4286i	0.166226	−	0.511590i
$690$	−7.03785	−	21.6603i	−0.267926	−	0.824592i
$691$	39.3266	−	28.5724i	1.49605	−	1.08695i	0.524134	−	0.851636i	$-0.324389\pi$
$691$	39.3266	−	28.5724i	1.49605	−	1.08695i	0.971920	−	0.235311i	$-0.0756109\pi$
$692$	−16.5072			−0.627510
$693$	0.160085	−	2.07189i	0.00608114	−	0.0787046i
$694$	4.88511			0.185436
$695$	−32.2584	+	23.4371i	−1.22363	+	0.889020i
$696$	−1.03136	−	3.17419i	−0.0390935	−	0.120317i
$697$	−5.08650	+	15.6546i	−0.192665	+	0.592962i
$698$	6.02923	+	4.38050i	0.228210	+	0.165804i
$699$	25.1339	+	18.2608i	0.950651	+	0.690688i
$700$	19.7631	−	60.8246i	0.746975	−	2.29895i
$701$	1.62328	+	4.99595i	0.0613105	+	0.188694i	0.977020	−	0.213145i	$-0.0683708\pi$
$701$	1.62328	+	4.99595i	0.0613105	+	0.188694i	−0.915710	+	0.401840i	$0.868371\pi$
$702$	−13.0620	+	9.49013i	−0.492995	+	0.358182i
$703$	1.39428			0.0525864
$704$	−0.163704	+	0.0395492i	−0.00616984	+	0.00149057i
$705$	−8.85238			−0.333400
$706$	−11.6633	+	8.47390i	−0.438955	+	0.318920i
$707$	−9.08013	−	27.9458i	−0.341493	−	1.05101i
$708$	5.08019	−	15.6352i	0.190925	−	0.587608i
$709$	−8.27518	−	6.01227i	−0.310781	−	0.225796i	0.421451	−	0.906851i	$-0.361521\pi$
$709$	−8.27518	−	6.01227i	−0.310781	−	0.225796i	−0.732231	+	0.681056i	$0.761521\pi$
$710$	19.4491	+	14.1306i	0.729913	+	0.530313i
$711$	−0.585287	+	1.80133i	−0.0219500	+	0.0675551i
$712$	11.6135	+	35.7427i	0.435234	+	1.33951i
$713$	17.9926	−	13.0724i	0.673829	−	0.489566i
$714$	−19.6510			−0.735421
$715$	−59.6385	−	24.6034i	−2.23035	−	0.920114i
$716$	23.9439			0.894824
$717$	−14.3100	+	10.3968i	−0.534417	+	0.388277i
$718$	1.71823	+	5.28816i	0.0641237	+	0.197352i
$719$	8.03773	−	24.7376i	0.299757	−	0.922557i	−0.681825	−	0.731515i	$-0.738813\pi$
$719$	8.03773	−	24.7376i	0.299757	−	0.922557i	0.981582	−	0.191042i	$-0.0611865\pi$
$720$	−1.03832	−	0.754382i	−0.0386958	−	0.0281142i
$721$	−5.49772	−	3.99433i	−0.204746	−	0.148757i
$722$	−0.193737	+	0.596261i	−0.00721014	+	0.0221905i
$723$	8.73018	+	26.8687i	0.324679	+	0.999259i
$724$	−20.0955	+	14.6003i	−0.746845	+	0.542614i
$725$	9.88882			0.367262
$726$	−1.84523	−	11.4389i	−0.0684830	−	0.424536i
$727$	8.38603			0.311021			0.155510	−	0.987834i	$-0.450298\pi$
$727$	8.38603			0.311021			0.155510	+	0.987834i	$0.450298\pi$
$728$	−31.2042	+	22.6712i	−1.15650	+	0.840250i
$729$	8.77638	+	27.0109i	0.325051	+	1.00040i
$730$	2.09026	−	6.43317i	0.0773642	−	0.238102i
$731$	1.88888	+	1.37235i	0.0698628	+	0.0507583i
$732$	−1.63297	−	1.18642i	−0.0603561	−	0.0438513i
$733$	−6.22111	+	19.1466i	−0.229782	+	0.707196i	0.767989	+	0.640463i	$0.221258\pi$
$733$	−6.22111	+	19.1466i	−0.229782	+	0.707196i	−0.997771	+	0.0667331i	$0.978742\pi$
$734$	5.05890	+	15.5697i	0.186727	+	0.574688i
$735$	−30.1406	+	21.8984i	−1.11175	+	0.807735i
$736$	−30.2917			−1.11657
$737$	36.9856	+	15.2581i	1.36238	+	0.562039i
$738$	−0.346588			−0.0127581
$739$	−1.00031	+	0.726766i	−0.0367969	+	0.0267345i	−0.606032	−	0.795441i	$-0.707240\pi$
$739$	−1.00031	+	0.726766i	−0.0367969	+	0.0267345i	0.569235	+	0.822175i	$0.307240\pi$
$740$	−2.79160	−	8.59167i	−0.102621	−	0.315836i
$741$	−2.50472	+	7.70873i	−0.0920131	+	0.283187i
$742$	5.24837	+	3.81316i	0.192674	+	0.139986i
$743$	−11.9203	−	8.66063i	−0.437315	−	0.317728i	0.347252	−	0.937772i	$-0.387115\pi$
$743$	−11.9203	−	8.66063i	−0.437315	−	0.317728i	−0.784567	+	0.620044i	$0.787115\pi$
$744$	4.86921	−	14.9859i	0.178514	−	0.549410i
$745$	7.27031	+	22.3757i	0.266364	+	0.819783i
$746$	14.2922	−	10.3839i	0.523273	−	0.380180i
$747$	−2.08151			−0.0761585
$748$	−27.3367	+	6.60424i	−0.999527	+	0.241475i
$749$	−0.398889			−0.0145751
$750$	21.4989	−	15.6199i	0.785030	−	0.570358i
$751$	10.3976	+	32.0005i	0.379414	+	1.16772i	0.940452	+	0.339926i	$0.110402\pi$
$751$	10.3976	+	32.0005i	0.379414	+	1.16772i	−0.561039	+	0.827790i	$0.689598\pi$
$752$	−0.725306	+	2.23226i	−0.0264492	+	0.0814022i
$753$	−21.6550	−	15.7333i	−0.789154	−	0.573354i
$754$	−2.14954	−	1.56173i	−0.0782816	−	0.0568749i
$755$	−1.97667	+	6.08355i	−0.0719383	+	0.221403i
$756$	9.37166	+	28.8430i	0.340844	+	1.04901i
$757$	−13.9726	+	10.1517i	−0.507842	+	0.368969i	−0.812004	−	0.583652i	$-0.801623\pi$
$757$	−13.9726	+	10.1517i	−0.507842	+	0.368969i	0.304163	+	0.952620i	$0.401623\pi$
$758$	−0.677433			−0.0246055
$759$	−2.30195	+	29.7927i	−0.0835554	+	1.08141i
$760$	9.11779			0.330737
$761$	25.6568	−	18.6408i	0.930059	−	0.675727i	−0.0159485	−	0.999873i	$-0.505077\pi$
$761$	25.6568	−	18.6408i	0.930059	−	0.675727i	0.946007	+	0.324146i	$0.105077\pi$
$762$	−0.416426	−	1.28163i	−0.0150855	−	0.0464284i
$763$	1.20285	−	3.70199i	0.0435461	−	0.134021i
$764$	−8.89910	−	6.46558i	−0.321958	−	0.233916i
$765$	−3.05042	−	2.21626i	−0.110288	−	0.0801291i
$766$	−3.05534	+	9.40338i	−0.110394	+	0.339758i
$767$	−9.07779	−	27.9386i	−0.327780	−	1.00880i
$768$	−9.51654	+	6.91417i	−0.343399	+	0.249494i
$769$	−35.0768			−1.26490			−0.632451	−	0.774601i	$-0.717951\pi$
$769$	−35.0768			−1.26490			−0.632451	+	0.774601i	$0.717951\pi$
$770$	19.2182	−	22.5668i	0.692577	−	0.813252i
$771$	2.46538			0.0887885
$772$	30.5208	−	22.1746i	1.09847	−	0.798083i
$773$	−11.5512	−	35.5509i	−0.415467	−	1.27868i	−0.911832	−	0.410563i	$-0.865332\pi$
$773$	−11.5512	−	35.5509i	−0.415467	−	1.27868i	0.496365	−	0.868114i	$-0.334668\pi$
$774$	−0.0151917	+	0.0467552i	−0.000546053	+	0.00168058i
$775$	37.7704	+	27.4418i	1.35675	+	0.985738i
$776$	−29.7019	−	21.5797i	−1.06624	−	0.774666i
$777$	−2.55930	+	7.87670i	−0.0918142	+	0.282575i
$778$	5.11794	+	15.7514i	0.183487	+	0.564715i
$779$	−2.52364	+	1.83353i	−0.0904187	+	0.0656930i
$780$	52.5166			1.88040
$781$	−16.5190	−	26.8704i	−0.591096	−	0.961497i
$782$	−17.7405			−0.634399
$783$	−3.79370	+	2.75629i	−0.135576	+	0.0985016i
$784$	3.05250	+	9.39462i	0.109018	+	0.335522i
$785$	8.15434	−	25.0965i	0.291041	−	0.895731i
$786$	−8.24206	−	5.98821i	−0.293985	−	0.213592i
$787$	18.9053	+	13.7355i	0.673902	+	0.489619i	0.871329	−	0.490699i	$-0.163258\pi$
$787$	18.9053	+	13.7355i	0.673902	+	0.489619i	−0.197427	+	0.980318i	$0.563258\pi$
$788$	13.1853	−	40.5803i	0.469708	−	1.44561i
$789$	−8.50721	−	26.1825i	−0.302865	−	0.932122i
$790$	−21.8565	+	15.8797i	−0.777620	+	0.564974i
$791$	44.0161			1.56503
$792$	−0.696104	−	1.13231i	−0.0247350	−	0.0402348i
$793$	−3.60678			−0.128080
$794$	4.77879	−	3.47199i	0.169593	−	0.123216i
$795$	−6.12674	−	18.8562i	−0.217293	−	0.668759i
$796$	−11.9104	+	36.6564i	−0.422152	+	1.29925i
$797$	−15.4614	−	11.2333i	−0.547670	−	0.397905i	0.279256	−	0.960217i	$-0.409912\pi$
$797$	−15.4614	−	11.2333i	−0.547670	−	0.397905i	−0.826926	+	0.562311i	$0.809912\pi$
$798$	−3.01283	−	2.18895i	−0.106653	−	0.0774880i
$799$	−2.13084	+	6.55805i	−0.0753837	+	0.232007i
$800$	−19.6500	−	60.4764i	−0.694732	−	2.13817i
$801$	2.38278	−	1.73119i	0.0841913	−	0.0611686i
$802$	1.51119			0.0533620
$803$	−5.75416	+	6.75676i	−0.203060	+	0.238441i
$804$	−32.5688			−1.14861
$805$	−61.8437	+	44.9321i	−2.17970	+	1.58365i
$806$	−3.87632	−	11.9301i	−0.136537	−	0.420219i
$807$	9.46225	−	29.1218i	0.333087	−	1.02514i
$808$	−15.2050	−	11.0471i	−0.534911	−	0.388636i
$809$	22.9931	+	16.7055i	0.808396	+	0.587334i	0.913365	−	0.407141i	$-0.133474\pi$
$809$	22.9931	+	16.7055i	0.808396	+	0.587334i	−0.104969	+	0.994475i	$0.533474\pi$
$810$	−6.59049	+	20.2834i	−0.231566	+	0.712688i
$811$	5.66530	+	17.4360i	0.198936	+	0.612261i	0.999908	+	0.0135598i	$0.00431636\pi$
$811$	5.66530	+	17.4360i	0.198936	+	0.612261i	−0.800972	+	0.598701i	$0.795684\pi$
$812$	−4.03762	+	2.93350i	−0.141693	+	0.102946i
$813$	2.09223			0.0733776
$814$	0.223342	−	2.89058i	0.00782812	−	0.101315i
$815$	−17.5552			−0.614931
$816$	12.8825	−	9.35972i	0.450979	−	0.327656i
$817$	0.136729	+	0.420810i	0.00478355	+	0.0147223i
$818$	1.60360	−	4.93536i	0.0560684	−	0.172561i
$819$	2.44545	+	1.77672i	0.0854508	+	0.0620837i
$820$	16.3511	+	11.8798i	0.571005	+	0.414860i
$821$	−13.3925	+	41.2179i	−0.467401	+	1.43851i	0.388536	+	0.921434i	$0.372981\pi$
$821$	−13.3925	+	41.2179i	−0.467401	+	1.43851i	−0.855937	+	0.517080i	$0.827019\pi$
$822$	−1.57890	−	4.85936i	−0.0550705	−	0.169490i
$823$	14.0877	−	10.2353i	0.491067	−	0.356781i	−0.314528	−	0.949248i	$-0.601846\pi$
$823$	14.0877	−	10.2353i	0.491067	−	0.356781i	0.805594	+	0.592468i	$0.201846\pi$
$824$	−4.34655			−0.151419
$825$	−60.9736	+	14.7306i	−2.12283	+	0.512852i
$826$	13.4970			0.469622
$827$	−3.00213	+	2.18117i	−0.104394	+	0.0758468i	−0.638758	−	0.769408i	$-0.720551\pi$
$827$	−3.00213	+	2.18117i	−0.104394	+	0.0758468i	0.534364	+	0.845255i	$0.320551\pi$
$828$	0.471915	+	1.45240i	0.0164002	+	0.0504746i
$829$	−9.28017	+	28.5614i	−0.322313	+	0.991979i	0.650325	+	0.759656i	$0.274633\pi$
$829$	−9.28017	+	28.5614i	−0.322313	+	0.991979i	−0.972639	+	0.232323i	$0.925367\pi$
$830$	−24.0200	−	17.4516i	−0.833747	−	0.605753i
$831$	−24.2333	−	17.6065i	−0.840643	−	0.610763i
$832$	0.0757011	−	0.232984i	0.00262446	−	0.00807727i
$833$	8.96778	+	27.6000i	0.310715	+	0.956282i
$834$	8.42734	−	6.12282i	0.291815	−	0.212016i
$835$	12.2553			0.424112
$836$	−4.92683	−	2.03252i	−0.170398	−	0.0702963i
$837$	−22.1388			−0.765230
$838$	−6.65443	+	4.83473i	−0.229874	+	0.167013i
$839$	9.64095	+	29.6718i	0.332842	+	1.02438i	0.967775	+	0.251816i	$0.0810278\pi$
$839$	9.64095	+	29.6718i	0.332842	+	1.02438i	−0.634933	+	0.772568i	$0.718972\pi$
$840$	−16.7363	+	51.5090i	−0.577457	+	1.77723i
$841$	22.8372	+	16.5922i	0.787489	+	0.572144i
$842$	−14.8860	−	10.8153i	−0.513006	−	0.372721i
$843$	4.38900	−	13.5080i	0.151165	−	0.465239i
$844$	−1.20637	−	3.71281i	−0.0415248	−	0.127800i
$845$	33.5142	−	24.3495i	1.15292	−	0.837647i
$846$	−0.145193			−0.00499183
$847$	−34.6010	+	17.7547i	−1.18890	+	0.610059i
$848$	−5.25685			−0.180521
$849$	35.0852	−	25.4909i	1.20412	−	0.874846i
$850$	−11.5081	−	35.4184i	−0.394726	−	1.21484i
$851$	−2.31047	+	7.11091i	−0.0792020	+	0.243759i
$852$	20.7724	+	15.0921i	0.711652	+	0.517045i
$853$	11.1844	+	8.12593i	0.382946	+	0.278226i	0.762559	−	0.646919i	$-0.223943\pi$
$853$	11.1844	+	8.12593i	0.382946	+	0.278226i	−0.379613	+	0.925145i	$0.623943\pi$
$854$	0.512086	−	1.57604i	0.0175232	−	0.0539309i
$855$	−0.220809	−	0.679581i	−0.00755152	−	0.0232412i
$856$	−0.206409	+	0.149965i	−0.00705493	+	0.00512571i
$857$	40.4572			1.38199			0.690996	−	0.722859i	$-0.257172\pi$
$857$	40.4572			1.38199			0.690996	+	0.722859i	$0.257172\pi$
$858$	15.5802	+	6.42750i	0.531901	+	0.219431i
$859$	25.9611			0.885780			0.442890	−	0.896576i	$-0.353953\pi$
$859$	25.9611			0.885780			0.442890	+	0.896576i	$0.353953\pi$
$860$	2.31930	−	1.68507i	0.0790876	−	0.0574605i
$861$	−5.72584	−	17.6223i	−0.195136	−	0.600567i
$862$	3.27830	−	10.0896i	0.111659	−	0.343653i
$863$	−36.2507	−	26.3376i	−1.23399	−	0.896544i	−0.236804	−	0.971557i	$-0.576100\pi$
$863$	−36.2507	−	26.3376i	−1.23399	−	0.896544i	−0.997183	+	0.0750137i	$0.976100\pi$
$864$	24.3949	+	17.7239i	0.829931	+	0.602980i
$865$	−12.7990	+	39.3914i	−0.435180	+	1.33935i
$866$	−2.24080	−	6.89646i	−0.0761453	−	0.234351i
$867$	14.7399	−	10.7092i	0.500594	−	0.363703i
$868$	−23.5623			−0.799756
$869$	34.4549	−	8.32393i	1.16880	−	0.282370i
$870$	−3.73086			−0.126488
$871$	−47.0825	+	34.2075i	−1.59533	+	1.15908i
$872$	−0.769364	−	2.36786i	−0.0260539	−	0.0801858i
$873$	−0.889107	+	2.73639i	−0.0300917	+	0.0926128i
$874$	−2.71992	−	1.97614i	−0.0920026	−	0.0668438i
$875$	−72.1601	−	52.4274i	−2.43946	−	1.77237i
$876$	2.23248	−	6.87088i	0.0754286	−	0.232145i
$877$	−14.3496	−	44.1636i	−0.484553	−	1.49130i	−0.832628	−	0.553833i	$-0.813165\pi$
$877$	−14.3496	−	44.1636i	−0.484553	−	1.49130i	0.348075	−	0.937467i	$-0.386835\pi$
$878$	−4.35096	+	3.16116i	−0.146838	+	0.106684i
$879$	−33.3058			−1.12338
$880$	−1.85032	+	23.9476i	−0.0623744	+	0.807275i
$881$	−8.00306			−0.269630			−0.134815	−	0.990871i	$-0.543044\pi$
$881$	−8.00306			−0.269630			−0.134815	+	0.990871i	$0.543044\pi$
$882$	−0.494352	+	0.359168i	−0.0166457	+	0.0120938i
$883$	−0.305601	−	0.940544i	−0.0102843	−	0.0316518i	0.945783	−	0.324800i	$-0.105297\pi$
$883$	−0.305601	−	0.940544i	−0.0102843	−	0.0316518i	−0.956067	+	0.293148i	$0.905297\pi$
$884$	12.6412	−	38.9055i	0.425168	−	1.30853i
$885$	−33.3716	−	24.2459i	−1.12177	−	0.815017i
$886$	−12.9302	−	9.39431i	−0.434397	−	0.315608i
$887$	16.1496	−	49.7032i	0.542249	−	1.66887i	−0.185192	−	0.982702i	$-0.559291\pi$
$887$	16.1496	−	49.7032i	0.542249	−	1.66887i	0.727442	−	0.686169i	$-0.240709\pi$
$888$	1.63697	+	5.03807i	0.0549331	+	0.169067i
$889$	−3.65926	+	2.65861i	−0.122728	+	0.0891669i
$890$	42.0110			1.40821
$891$	18.1425	−	21.3037i	0.607798	−	0.713701i
$892$	−32.9138			−1.10204
$893$	−1.05720	+	0.768103i	−0.0353780	+	0.0257036i
$894$	−1.89933	−	5.84554i	−0.0635231	−	0.195504i
$895$	18.5651	−	57.1376i	0.620564	−	1.90990i
$896$	32.4051	+	23.5437i	1.08258	+	0.786540i
$897$	−35.1643	−	25.5484i	−1.17410	−	0.853035i
$898$	−0.926237	+	2.85066i	−0.0309089	+	0.0951279i
$899$	−1.12583	−	3.46494i	−0.0375484	−	0.115562i
$900$	−2.59356	+	1.88433i	−0.0864519	+	0.0628110i
$901$	−15.4438			−0.514509
$902$	3.39696	+	5.52562i	0.113106	+	0.183983i
$903$	−2.62825			−0.0874627
$904$	22.7766	−	16.5482i	0.757539	−	0.550384i
$905$	19.2595	+	59.2748i	0.640209	+	1.97036i
$906$	0.516394	−	1.58930i	0.0171560	−	0.0528008i
$907$	−14.5087	−	10.5412i	−0.481755	−	0.350016i	0.320250	−	0.947333i	$-0.396233\pi$
$907$	−14.5087	−	10.5412i	−0.481755	−	0.350016i	−0.802005	+	0.597318i	$0.796233\pi$
$908$	25.8853	+	18.8068i	0.859035	+	0.624125i
$909$	−0.455153	+	1.40082i	−0.0150965	+	0.0464621i
$910$	13.3235	+	41.0057i	0.441671	+	1.35932i
$911$	0.355792	−	0.258498i	0.0117879	−	0.00856442i	−0.581876	−	0.813278i	$-0.697681\pi$
$911$	0.355792	−	0.258498i	0.0117879	−	0.00856442i	0.593664	+	0.804713i	$0.297681\pi$
$912$	3.01770			0.0999261
$913$	20.4012	+	33.1854i	0.675182	+	1.09827i
$914$	−14.6881			−0.485839
$915$	−4.09731	+	2.97687i	−0.135453	+	0.0984122i
$916$	−9.54634	−	29.3806i	−0.315420	−	0.970762i
$917$	−10.5667	+	32.5211i	−0.348944	+	1.07394i
$918$	14.2870	+	10.3801i	0.471541	+	0.342595i
$919$	26.0396	+	18.9189i	0.858969	+	0.624077i	0.927604	−	0.373564i	$-0.121865\pi$
$919$	26.0396	+	18.9189i	0.858969	+	0.624077i	−0.0686355	+	0.997642i	$0.521865\pi$
$920$	−15.1092	+	46.5012i	−0.498134	+	1.53310i
$921$	−10.2088	−	31.4195i	−0.336392	−	1.03531i
$922$	7.01887	−	5.09951i	0.231154	−	0.167943i
$923$	45.8806			1.51018
$924$	20.5258	−	24.1022i	0.675250	−	0.792905i
$925$	−15.6955			−0.516065
$926$	−2.53616	+	1.84263i	−0.0833433	+	0.0605524i
$927$	0.105262	+	0.323964i	0.00345727	+	0.0106404i
$928$	−1.53341	+	4.71934i	−0.0503365	+	0.154920i
$929$	5.51055	+	4.00365i	0.180795	+	0.131355i	0.674502	−	0.738273i	$-0.264358\pi$
$929$	5.51055	+	4.00365i	0.180795	+	0.131355i	−0.493707	+	0.869628i	$0.664358\pi$
$930$	−14.2500	−	10.3533i	−0.467277	−	0.339497i
$931$	−1.69948	+	5.23047i	−0.0556983	+	0.171422i
$932$	−9.18217	−	28.2598i	−0.300772	−	0.925681i
$933$	32.7985	−	23.8295i	1.07377	−	0.780142i
$934$	−4.79287			−0.156828
$935$	−5.43598	+	70.3546i	−0.177775	+	2.30084i
$936$	1.93339			0.0631950
$937$	27.3459	−	19.8680i	0.893353	−	0.649059i	−0.0433971	−	0.999058i	$-0.513818\pi$
$937$	27.3459	−	19.8680i	0.893353	−	0.649059i	0.936750	+	0.349999i	$0.113818\pi$
$938$	−8.26277	−	25.4302i	−0.269789	−	0.830325i
$939$	−14.8373	+	45.6646i	−0.484198	+	1.49021i
$940$	6.84981	+	4.97668i	0.223416	+	0.162321i
$941$	44.9420	+	32.6523i	1.46507	+	1.06443i	0.982006	+	0.188848i	$0.0604755\pi$
$941$	44.9420	+	32.6523i	1.46507	+	1.06443i	0.483062	+	0.875586i	$0.339524\pi$
$942$	−2.13028	+	6.55632i	−0.0694082	+	0.213616i
$943$	−5.16916	−	15.9090i	−0.168331	−	0.518069i
$944$	−8.84821	+	6.42860i	−0.287985	+	0.209233i
$945$	76.0949			2.47537
$946$	0.894310	−	0.216056i	0.0290765	−	0.00702457i
$947$	16.1934			0.526214			0.263107	−	0.964767i	$-0.415253\pi$
$947$	16.1934			0.526214			0.263107	+	0.964767i	$0.415253\pi$
$948$	−23.3436	+	16.9601i	−0.758165	+	0.550839i
$949$	−3.98922	−	12.2776i	−0.129496	−	0.398547i
$950$	2.18091	−	6.71214i	0.0707580	−	0.217771i
$951$	−12.5297	−	9.10336i	−0.406304	−	0.295197i
$952$	34.1305	+	24.7973i	1.10618	+	0.803684i
$953$	−13.9557	+	42.9512i	−0.452069	+	1.39133i	0.422472	+	0.906376i	$0.361162\pi$
$953$	−13.9557	+	42.9512i	−0.452069	+	1.39133i	−0.874542	+	0.484951i	$0.838838\pi$
$954$	−0.100488	−	0.309270i	−0.00325342	−	0.0100130i
$955$	−22.3289	+	16.2229i	−0.722547	+	0.524961i
$956$	16.9178			0.547160
$957$	4.52508	+	1.86679i	0.146275	+	0.0603446i
$958$	13.6943			0.442443
$959$	−13.8743	+	10.0803i	−0.448024	+	0.325509i
$960$	−0.106298	−	0.327151i	−0.00343074	−	0.0105587i
$961$	−4.26432	+	13.1242i	−0.137559	+	0.423362i
$962$	3.41174	+	2.47878i	0.109999	+	0.0799189i
$963$	0.0161761	+	0.0117526i	0.000521269	+	0.000378724i
$964$	8.34995	−	25.6985i	0.268934	−	0.827693i
$965$	−29.2511	−	90.0256i	−0.941626	−	2.89803i
$966$	16.1563	−	11.7383i	0.519822	−	0.377673i
$967$	13.7686			0.442769			0.221385	−	0.975187i	$-0.428942\pi$
$967$	13.7686			0.442769			0.221385	+	0.975187i	$0.428942\pi$
$968$	−11.2296	+	22.1959i	−0.360934	+	0.713402i
$969$	8.86556			0.284803
$970$	−33.2022	+	24.1228i	−1.06606	+	0.774536i
$971$	8.96721	+	27.5982i	0.287771	+	0.885669i	0.985554	+	0.169360i	$0.0541701\pi$
$971$	8.96721	+	27.5982i	0.287771	+	0.885669i	−0.697783	+	0.716309i	$0.745830\pi$
$972$	0.913329	−	2.81094i	0.0292950	−	0.0901609i
$973$	−28.2859	−	20.5509i	−0.906806	−	0.658833i
$974$	−6.04871	−	4.39465i	−0.193813	−	0.140814i
$975$	28.1957	−	86.7775i	0.902986	−	2.77911i
$976$	0.414956	+	1.27710i	0.0132824	+	0.0408791i
$977$	28.7435	−	20.8834i	0.919586	−	0.668119i	−0.0238346	−	0.999716i	$-0.507588\pi$
$977$	28.7435	−	20.8834i	0.919586	−	0.668119i	0.943421	+	0.331597i	$0.107588\pi$
$978$	4.58620			0.146650
$979$	−50.9542	−	21.0207i	−1.62850	−	0.671826i
$980$	35.6332			1.13826
$981$	−0.157853	+	0.114687i	−0.00503985	+	0.00366167i
$982$	−7.74137	−	23.8255i	−0.247037	−	0.760302i
$983$	−5.76635	+	17.7470i	−0.183918	+	0.566041i	−0.999928	−	0.0119963i	$-0.996181\pi$
$983$	−5.76635	+	17.7470i	−0.183918	+	0.566041i	0.816010	+	0.578038i	$0.196181\pi$
$984$	−9.58813	−	6.96619i	−0.305659	−	0.222074i
$985$	−86.6139	−	62.9287i	−2.75975	−	2.00507i
$986$	−0.898048	+	2.76391i	−0.0285997	+	0.0880208i
$987$	−2.39867	−	7.38235i	−0.0763505	−	0.234983i
$988$	6.27184	−	4.55676i	0.199534	−	0.144970i
$989$	−2.37273			−0.0754483
$990$	−1.44425	+	0.348916i	−0.0459014	+	0.0110893i
$991$	−1.39512			−0.0443175			−0.0221588	−	0.999754i	$-0.507054\pi$
$991$	−1.39512			−0.0443175			−0.0221588	+	0.999754i	$0.507054\pi$
$992$	−18.9532	+	13.7703i	−0.601764	+	0.437207i
$993$	10.2845	+	31.6525i	0.326370	+	1.00446i
$994$	−6.51408	+	20.0483i	−0.206614	+	0.635893i
$995$	78.2389	+	56.8439i	2.48034	+	1.80207i
$996$	−25.6543	−	18.6389i	−0.812888	−	0.590598i
$997$	−3.25314	+	10.0121i	−0.103028	+	0.317088i	−0.989263	−	0.146149i	$-0.953312\pi$
$997$	−3.25314	+	10.0121i	−0.103028	+	0.317088i	0.886235	+	0.463237i	$0.153312\pi$
$998$	−4.41890	−	13.6000i	−0.139878	−	0.430500i
$999$	6.02135	−	4.37477i	0.190507	−	0.138412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.b.58.5	✓	28
11.2	odd	10		2299.2.a.u.1.9		14
11.4	even	5	inner	209.2.f.b.191.5	yes	28
11.9	even	5		2299.2.a.t.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.b.58.5	✓	28	1.1	even	1	trivial
209.2.f.b.191.5	yes	28	11.4	even	5	inner
2299.2.a.t.1.6		14	11.9	even	5
2299.2.a.u.1.9		14	11.2	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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.507210 - 0.368509i) q^{2} +(-0.519183 - 1.59788i) q^{3} +(-0.496571 + 1.52829i) q^{4} +(3.26196 + 2.36995i) q^{5} +(-0.852170 - 0.619138i) q^{6} +(-1.09252 + 3.36244i) q^{7} +(0.698797 + 2.15068i) q^{8} +(0.143374 - 0.104168i) q^{9} +2.52785 q^{10} +(-3.06597 - 1.26484i) q^{11} +2.69984 q^{12} +(3.90297 - 2.83568i) q^{13} +(0.684954 + 2.10807i) q^{14} +(2.09335 - 6.44267i) q^{15} +(-1.45310 - 1.05574i) q^{16} +(-4.26899 - 3.10160i) q^{17} +(0.0343341 - 0.105670i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-5.24177 + 3.80837i) q^{20} +5.94001 q^{21} +(-2.02120 + 0.488299i) q^{22} +5.36251 q^{23} +(3.07372 - 2.23319i) q^{24} +(3.47862 + 10.7061i) q^{25} +(0.934652 - 2.87656i) q^{26} +(-4.31860 - 3.13765i) q^{27} +(-4.59627 - 3.33939i) q^{28} +(0.271458 - 0.835461i) q^{29} +(-1.31242 - 4.03920i) q^{30} +(3.35526 - 2.43774i) q^{31} -5.64879 q^{32} +(-0.429267 + 5.55575i) q^{33} -3.30824 q^{34} +(-11.5326 + 8.37893i) q^{35} +(0.0880026 + 0.270844i) q^{36} +(-0.430857 + 1.32604i) q^{37} +(-0.507210 - 0.368509i) q^{38} +(-6.55743 - 4.76425i) q^{39} +(-2.81755 + 8.67154i) q^{40} +(-0.963944 - 2.96671i) q^{41} +(3.01283 - 2.18895i) q^{42} -0.442465 q^{43} +(3.45552 - 4.05761i) q^{44} +0.714554 q^{45} +(2.71992 - 1.97614i) q^{46} +(-0.403816 - 1.24282i) q^{47} +(-0.932521 + 2.87001i) q^{48} +(-4.44931 - 3.23261i) q^{49} +(5.70969 + 4.14833i) q^{50} +(-2.73961 + 8.43165i) q^{51} +(2.39563 + 7.37299i) q^{52} +(2.36780 - 1.72031i) q^{53} -3.34669 q^{54} +(-7.00346 - 11.3921i) q^{55} -7.99498 q^{56} +(-1.35924 + 0.987546i) q^{57} +(-0.170189 - 0.523789i) q^{58} +(1.88167 - 5.79117i) q^{59} +(8.80677 + 6.39849i) q^{60} +(-0.604838 - 0.439441i) q^{61} +(0.803492 - 2.47289i) q^{62} +(0.193618 + 0.595894i) q^{63} +(0.0410809 - 0.0298470i) q^{64} +19.4518 q^{65} +(1.82962 + 2.97612i) q^{66} -12.0633 q^{67} +(6.86001 - 4.98409i) q^{68} +(-2.78413 - 8.56866i) q^{69} +(-2.76174 + 8.49975i) q^{70} +(7.69395 + 5.58998i) q^{71} +(0.324220 + 0.235560i) q^{72} +(0.826895 - 2.54492i) q^{73} +(0.270124 + 0.831356i) q^{74} +(15.3010 - 11.1169i) q^{75} +1.60694 q^{76} +(7.60261 - 8.92729i) q^{77} -5.08167 q^{78} +(-8.64630 + 6.28190i) q^{79} +(-2.23790 - 6.88756i) q^{80} +(-2.60716 + 8.02400i) q^{81} +(-1.58218 - 1.14952i) q^{82} +(-9.50216 - 6.90373i) q^{83} +(-2.94964 + 9.07806i) q^{84} +(-6.57462 - 20.2346i) q^{85} +(-0.224423 + 0.163053i) q^{86} -1.47590 q^{87} +(0.577774 - 7.47778i) q^{88} +16.6193 q^{89} +(0.362429 - 0.263320i) q^{90} +(5.27071 + 16.2216i) q^{91} +(-2.66287 + 8.19547i) q^{92} +(-5.63722 - 4.09568i) q^{93} +(-0.662809 - 0.481559i) q^{94} +(1.24596 - 3.83466i) q^{95} +(2.93276 + 9.02610i) q^{96} +(-13.1346 + 9.54282i) q^{97} -3.44798 q^{98} +(-0.571337 + 0.138029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

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