LMFDB - Embedded newform 575.2.g.c.116.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(116,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("575.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			116.3
Character	$\chi$	$=$	575.116
Dual form			575.2.g.c.461.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95531 - 1.42062i) q^{2} +(0.481235 + 1.48109i) q^{3} +(1.18705 + 3.65338i) q^{4} +(-1.37069 + 1.76669i) q^{5} +(1.16310 - 3.57964i) q^{6} -4.40282 q^{7} +(1.37526 - 4.23262i) q^{8} +(0.465011 - 0.337850i) q^{9} +O(q^{10})$	\(q+(-1.95531 - 1.42062i) q^{2} +(0.481235 + 1.48109i) q^{3} +(1.18705 + 3.65338i) q^{4} +(-1.37069 + 1.76669i) q^{5} +(1.16310 - 3.57964i) q^{6} -4.40282 q^{7} +(1.37526 - 4.23262i) q^{8} +(0.465011 - 0.337850i) q^{9} +(5.18992 - 1.50721i) q^{10} +(-1.84394 - 1.33970i) q^{11} +(-4.83973 + 3.51627i) q^{12} +(-0.533615 + 0.387694i) q^{13} +(8.60889 + 6.25472i) q^{14} +(-3.27626 - 1.17992i) q^{15} +(-2.48650 + 1.80655i) q^{16} +(-1.40599 + 4.32720i) q^{17} -1.38920 q^{18} +(0.821028 - 2.52686i) q^{19} +(-8.08148 - 2.91048i) q^{20} +(-2.11879 - 6.52098i) q^{21} +(1.70228 + 5.23907i) q^{22} +(0.809017 + 0.587785i) q^{23} +6.93072 q^{24} +(-1.24242 - 4.84318i) q^{25} +1.59415 q^{26} +(4.50384 + 3.27223i) q^{27} +(-5.22639 - 16.0852i) q^{28} +(-0.476377 - 1.46614i) q^{29} +(4.72989 + 6.96141i) q^{30} +(1.79684 - 5.53011i) q^{31} -1.47259 q^{32} +(1.09685 - 3.37576i) q^{33} +(8.89644 - 6.46364i) q^{34} +(6.03490 - 7.77845i) q^{35} +(1.78629 + 1.29781i) q^{36} +(9.29763 - 6.75512i) q^{37} +(-5.19507 + 3.77444i) q^{38} +(-0.831005 - 0.603760i) q^{39} +(5.59270 + 8.23128i) q^{40} +(0.342907 - 0.249136i) q^{41} +(-5.12091 + 15.7605i) q^{42} +0.493278 q^{43} +(2.70558 - 8.32691i) q^{44} +(-0.0405073 + 1.28462i) q^{45} +(-0.746862 - 2.29861i) q^{46} +(-3.45622 - 10.6371i) q^{47} +(-3.87225 - 2.81336i) q^{48} +12.3849 q^{49} +(-4.45098 + 11.2349i) q^{50} -7.08558 q^{51} +(-2.04982 - 1.48928i) q^{52} +(-1.16159 - 3.57500i) q^{53} +(-4.15782 - 12.7964i) q^{54} +(4.89432 - 1.42137i) q^{55} +(-6.05504 + 18.6355i) q^{56} +4.13762 q^{57} +(-1.15135 + 3.54351i) q^{58} +(-10.5513 + 7.66600i) q^{59} +(0.421591 - 13.3700i) q^{60} +(-2.85521 - 2.07443i) q^{61} +(-11.3696 + 8.26047i) q^{62} +(-2.04736 + 1.48749i) q^{63} +(7.85238 + 5.70509i) q^{64} +(0.0464835 - 1.47414i) q^{65} +(-6.94033 + 5.04245i) q^{66} +(-0.839650 + 2.58418i) q^{67} -17.4779 q^{68} +(-0.481235 + 1.48109i) q^{69} +(-22.8503 + 6.63599i) q^{70} +(-4.29490 - 13.2183i) q^{71} +(-0.790480 - 2.43285i) q^{72} +(-5.49660 - 3.99352i) q^{73} -27.7762 q^{74} +(6.57529 - 4.17085i) q^{75} +10.2062 q^{76} +(8.11855 + 5.89847i) q^{77} +(0.767161 + 2.36108i) q^{78} +(0.715350 + 2.20162i) q^{79} +(0.216600 - 6.86911i) q^{80} +(-2.14621 + 6.60534i) q^{81} -1.02442 q^{82} +(-2.15449 + 6.63084i) q^{83} +(21.3085 - 15.4815i) q^{84} +(-5.71766 - 8.41520i) q^{85} +(-0.964512 - 0.700759i) q^{86} +(1.94223 - 1.41112i) q^{87} +(-8.20636 + 5.96227i) q^{88} +(9.64085 + 7.00449i) q^{89} +(1.90416 - 2.45428i) q^{90} +(2.34941 - 1.70695i) q^{91} +(-1.18705 + 3.65338i) q^{92} +9.05530 q^{93} +(-8.35332 + 25.7089i) q^{94} +(3.33882 + 4.91405i) q^{95} +(-0.708664 - 2.18104i) q^{96} +(-0.835568 - 2.57161i) q^{97} +(-24.2162 - 17.5941i) q^{98} -1.31007 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + q^{2} + 4 q^{3} - 29 q^{4} - 2 q^{5} - 2 q^{6} - 36 q^{7} + 12 q^{8} - 22 q^{9}+O(q^{10}) $ 112 * q + q^2 + 4 * q^3 - 29 * q^4 - 2 * q^5 - 2 * q^6 - 36 * q^7 + 12 * q^8 - 22 * q^9	\( 112 q + q^{2} + 4 q^{3} - 29 q^{4} - 2 q^{5} - 2 q^{6} - 36 q^{7} + 12 q^{8} - 22 q^{9} - 5 q^{10} + 4 q^{12} + 8 q^{13} + 18 q^{14} - 25 q^{15} - 19 q^{16} - 34 q^{18} + 6 q^{19} + 24 q^{20} - 6 q^{21} + 2 q^{22} + 28 q^{23} - 198 q^{24} - 6 q^{25} + 26 q^{26} + 13 q^{27} + 36 q^{28} - 6 q^{29} - 36 q^{30} - 18 q^{31} - 60 q^{32} + 15 q^{33} + 45 q^{34} + q^{35} + 27 q^{36} + 43 q^{37} + 14 q^{38} + 6 q^{39} - 30 q^{40} - 41 q^{41} + 20 q^{42} - 88 q^{43} + 91 q^{44} + 60 q^{45} - q^{46} + 11 q^{47} - 2 q^{48} + 36 q^{49} + 36 q^{50} + 26 q^{51} + 10 q^{52} + 14 q^{53} + 56 q^{54} - 51 q^{55} - 75 q^{56} - 72 q^{57} + 43 q^{58} - 2 q^{59} + 131 q^{60} - 3 q^{61} - q^{63} + 22 q^{64} - 13 q^{65} - 5 q^{66} + 40 q^{67} - 70 q^{68} - 4 q^{69} + 50 q^{70} + 57 q^{71} + 52 q^{72} - 4 q^{73} - 274 q^{74} + 4 q^{75} + 52 q^{76} + 18 q^{77} - 36 q^{78} + 2 q^{79} + 30 q^{80} - 128 q^{81} - 148 q^{82} + 22 q^{83} + 112 q^{84} + 77 q^{85} - 5 q^{86} + 33 q^{87} + 121 q^{88} + 69 q^{89} - 167 q^{90} - 64 q^{91} + 29 q^{92} - 92 q^{93} + 64 q^{94} + 6 q^{95} + 172 q^{96} + 68 q^{97} + 28 q^{98} - 168 q^{99}+O(q^{100}) \) 112 * q + q^2 + 4 * q^3 - 29 * q^4 - 2 * q^5 - 2 * q^6 - 36 * q^7 + 12 * q^8 - 22 * q^9 - 5 * q^10 + 4 * q^12 + 8 * q^13 + 18 * q^14 - 25 * q^15 - 19 * q^16 - 34 * q^18 + 6 * q^19 + 24 * q^20 - 6 * q^21 + 2 * q^22 + 28 * q^23 - 198 * q^24 - 6 * q^25 + 26 * q^26 + 13 * q^27 + 36 * q^28 - 6 * q^29 - 36 * q^30 - 18 * q^31 - 60 * q^32 + 15 * q^33 + 45 * q^34 + q^35 + 27 * q^36 + 43 * q^37 + 14 * q^38 + 6 * q^39 - 30 * q^40 - 41 * q^41 + 20 * q^42 - 88 * q^43 + 91 * q^44 + 60 * q^45 - q^46 + 11 * q^47 - 2 * q^48 + 36 * q^49 + 36 * q^50 + 26 * q^51 + 10 * q^52 + 14 * q^53 + 56 * q^54 - 51 * q^55 - 75 * q^56 - 72 * q^57 + 43 * q^58 - 2 * q^59 + 131 * q^60 - 3 * q^61 - q^63 + 22 * q^64 - 13 * q^65 - 5 * q^66 + 40 * q^67 - 70 * q^68 - 4 * q^69 + 50 * q^70 + 57 * q^71 + 52 * q^72 - 4 * q^73 - 274 * q^74 + 4 * q^75 + 52 * q^76 + 18 * q^77 - 36 * q^78 + 2 * q^79 + 30 * q^80 - 128 * q^81 - 148 * q^82 + 22 * q^83 + 112 * q^84 + 77 * q^85 - 5 * q^86 + 33 * q^87 + 121 * q^88 + 69 * q^89 - 167 * q^90 - 64 * q^91 + 29 * q^92 - 92 * q^93 + 64 * q^94 + 6 * q^95 + 172 * q^96 + 68 * q^97 + 28 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.95531	−	1.42062i	−1.38261	−	1.00453i	−0.996631	−	0.0820211i	$-0.973863\pi$
$2$	−1.95531	−	1.42062i	−1.38261	−	1.00453i	−0.385983	−	0.922506i	$-0.626137\pi$
$3$	0.481235	+	1.48109i	0.277841	+	0.855108i	0.988454	+	0.151524i	$0.0484180\pi$
$3$	0.481235	+	1.48109i	0.277841	+	0.855108i	−0.710612	+	0.703584i	$0.751582\pi$
$4$	1.18705	+	3.65338i	0.593527	+	1.82669i
$5$	−1.37069	+	1.76669i	−0.612991	+	0.790090i
$5$	−1.37069	+	1.76669i	−0.612991	+	0.790090i
$6$	1.16310	−	3.57964i	0.474832	−	1.46138i
$7$	−4.40282			−1.66411			−0.832055	−	0.554693i	$-0.812836\pi$
$7$	−4.40282			−1.66411			−0.832055	+	0.554693i	$0.812836\pi$
$8$	1.37526	−	4.23262i	0.486229	−	1.49646i
$9$	0.465011	−	0.337850i	0.155004	−	0.112617i
$10$	5.18992	−	1.50721i	1.64120	−	0.476623i
$11$	−1.84394	−	1.33970i	−0.555969	−	0.403935i	0.274012	−	0.961726i	$-0.411649\pi$
$11$	−1.84394	−	1.33970i	−0.555969	−	0.403935i	−0.829982	+	0.557791i	$0.811649\pi$
$12$	−4.83973	+	3.51627i	−1.39711	+	1.01506i
$13$	−0.533615	+	0.387694i	−0.147998	+	0.107527i	−0.659320	−	0.751862i	$-0.729156\pi$
$13$	−0.533615	+	0.387694i	−0.147998	+	0.107527i	0.511322	+	0.859389i	$0.329156\pi$
$14$	8.60889	+	6.25472i	2.30082	+	1.67164i
$15$	−3.27626	−	1.17992i	−0.845926	−	0.304654i
$16$	−2.48650	+	1.80655i	−0.621625	+	0.451637i
$17$	−1.40599	+	4.32720i	−0.341003	+	1.04950i	0.622686	+	0.782472i	$0.286041\pi$
$17$	−1.40599	+	4.32720i	−0.341003	+	1.04950i	−0.963689	+	0.267028i	$0.913959\pi$
$18$	−1.38920			−0.327437
$19$	0.821028	−	2.52686i	0.188357	−	0.579702i	−0.811633	−	0.584167i	$-0.801421\pi$
$19$	0.821028	−	2.52686i	0.188357	−	0.579702i	0.999990	+	0.00446485i	$0.00142121\pi$
$20$	−8.08148	−	2.91048i	−1.80707	−	0.650804i
$21$	−2.11879	−	6.52098i	−0.462359	−	1.42299i
$22$	1.70228	+	5.23907i	0.362926	+	1.11697i
$23$	0.809017	+	0.587785i	0.168692	+	0.122562i
$23$	0.809017	+	0.587785i	0.168692	+	0.122562i
$24$	6.93072			1.41473
$25$	−1.24242	−	4.84318i	−0.248484	−	0.968636i
$26$	1.59415			0.312638
$27$	4.50384	+	3.27223i	0.866764	+	0.629741i
$28$	−5.22639	−	16.0852i	−0.987695	−	3.03981i
$29$	−0.476377	−	1.46614i	−0.0884611	−	0.272255i	0.897033	−	0.441963i	$-0.145718\pi$
$29$	−0.476377	−	1.46614i	−0.0884611	−	0.272255i	−0.985494	+	0.169708i	$0.945718\pi$
$30$	4.72989	+	6.96141i	0.863556	+	1.27097i
$31$	1.79684	−	5.53011i	0.322723	−	0.993238i	−0.649736	−	0.760160i	$-0.725120\pi$
$31$	1.79684	−	5.53011i	0.322723	−	0.993238i	0.972458	−	0.233078i	$-0.0748796\pi$
$32$	−1.47259			−0.260320
$33$	1.09685	−	3.37576i	0.190937	−	0.587644i
$34$	8.89644	−	6.46364i	1.52573	−	1.10850i
$35$	6.03490	−	7.77845i	1.02008	−	1.31480i
$36$	1.78629	+	1.29781i	0.297714	+	0.216302i
$37$	9.29763	−	6.75512i	1.52852	−	1.11054i	0.571467	−	0.820625i	$-0.306375\pi$
$37$	9.29763	−	6.75512i	1.52852	−	1.11054i	0.957054	−	0.289910i	$-0.0936255\pi$
$38$	−5.19507	+	3.77444i	−0.842751	+	0.612295i
$39$	−0.831005	−	0.603760i	−0.133067	−	0.0966790i
$40$	5.59270	+	8.23128i	0.884283	+	1.30148i
$41$	0.342907	−	0.249136i	0.0535531	−	0.0389086i	−0.560687	−	0.828028i	$-0.689463\pi$
$41$	0.342907	−	0.249136i	0.0535531	−	0.0389086i	0.614240	+	0.789119i	$0.289463\pi$
$42$	−5.12091	+	15.7605i	−0.790173	+	2.43190i
$43$	0.493278			0.0752242			0.0376121	−	0.999292i	$-0.488025\pi$
$43$	0.493278			0.0752242			0.0376121	+	0.999292i	$0.488025\pi$
$44$	2.70558	−	8.32691i	0.407881	−	1.25533i
$45$	−0.0405073	+	1.28462i	−0.00603847	+	0.191500i
$46$	−0.746862	−	2.29861i	−0.110119	−	0.338911i
$47$	−3.45622	−	10.6371i	−0.504141	−	1.55159i	−0.802210	−	0.597043i	$-0.796342\pi$
$47$	−3.45622	−	10.6371i	−0.504141	−	1.55159i	0.298068	−	0.954545i	$-0.403658\pi$
$48$	−3.87225	−	2.81336i	−0.558912	−	0.406073i
$49$	12.3849			1.76926
$50$	−4.45098	+	11.2349i	−0.629464	+	1.58886i
$51$	−7.08558			−0.992180
$52$	−2.04982	−	1.48928i	−0.284259	−	0.206527i
$53$	−1.16159	−	3.57500i	−0.159556	−	0.491064i	0.839038	−	0.544073i	$-0.183119\pi$
$53$	−1.16159	−	3.57500i	−0.159556	−	0.491064i	−0.998594	+	0.0530094i	$0.983119\pi$
$54$	−4.15782	−	12.7964i	−0.565807	−	1.74138i
$55$	4.89432	−	1.42137i	0.659949	−	0.191657i
$56$	−6.05504	+	18.6355i	−0.809139	+	2.49027i
$57$	4.13762			0.548041
$58$	−1.15135	+	3.54351i	−0.151180	+	0.465285i
$59$	−10.5513	+	7.66600i	−1.37367	+	0.998029i	−0.376228	+	0.926527i	$0.622779\pi$
$59$	−10.5513	+	7.66600i	−1.37367	+	0.998029i	−0.997441	+	0.0715014i	$0.977221\pi$
$60$	0.421591	−	13.3700i	0.0544271	−	1.72606i
$61$	−2.85521	−	2.07443i	−0.365573	−	0.265604i	0.389800	−	0.920900i	$-0.372544\pi$
$61$	−2.85521	−	2.07443i	−0.365573	−	0.265604i	−0.755373	+	0.655295i	$0.772544\pi$
$62$	−11.3696	+	8.26047i	−1.44393	+	1.04908i
$63$	−2.04736	+	1.48749i	−0.257943	+	0.187407i
$64$	7.85238	+	5.70509i	0.981547	+	0.713136i
$65$	0.0464835	−	1.47414i	0.00576556	−	0.182845i
$66$	−6.94033	+	5.04245i	−0.854296	+	0.620682i
$67$	−0.839650	+	2.58418i	−0.102580	+	0.315707i	−0.989155	−	0.146877i	$-0.953078\pi$
$67$	−0.839650	+	2.58418i	−0.102580	+	0.315707i	0.886575	+	0.462585i	$0.153078\pi$
$68$	−17.4779			−2.11950
$69$	−0.481235	+	1.48109i	−0.0579339	+	0.178302i
$70$	−22.8503	+	6.63599i	−2.73113	+	0.793153i
$71$	−4.29490	−	13.2183i	−0.509711	−	1.56873i	−0.792704	−	0.609607i	$-0.791327\pi$
$71$	−4.29490	−	13.2183i	−0.509711	−	1.56873i	0.282993	−	0.959122i	$-0.408673\pi$
$72$	−0.790480	−	2.43285i	−0.0931590	−	0.286714i
$73$	−5.49660	−	3.99352i	−0.643329	−	0.467406i	0.217663	−	0.976024i	$-0.430157\pi$
$73$	−5.49660	−	3.99352i	−0.643329	−	0.467406i	−0.860992	+	0.508618i	$0.830157\pi$
$74$	−27.7762			−3.22892
$75$	6.57529	−	4.17085i	0.759249	−	0.481608i
$76$	10.2062			1.17073
$77$	8.11855	+	5.89847i	0.925195	+	0.672193i
$78$	0.767161	+	2.36108i	0.0868638	+	0.267339i
$79$	0.715350	+	2.20162i	0.0804832	+	0.247702i	0.983199	−	0.182535i	$-0.0584302\pi$
$79$	0.715350	+	2.20162i	0.0804832	+	0.247702i	−0.902716	+	0.430236i	$0.858430\pi$
$80$	0.216600	−	6.86911i	0.0242166	−	0.767990i
$81$	−2.14621	+	6.60534i	−0.238467	+	0.733927i
$82$	−1.02442			−0.113128
$83$	−2.15449	+	6.63084i	−0.236486	+	0.727829i	0.760435	+	0.649414i	$0.224986\pi$
$83$	−2.15449	+	6.63084i	−0.236486	+	0.727829i	−0.996921	+	0.0784147i	$0.975014\pi$
$84$	21.3085	−	15.4815i	2.32494	−	1.68917i
$85$	−5.71766	−	8.41520i	−0.620167	−	0.912757i
$86$	−0.964512	−	0.700759i	−0.104006	−	0.0755648i
$87$	1.94223	−	1.41112i	0.208229	−	0.151287i
$88$	−8.20636	+	5.96227i	−0.874801	+	0.635580i
$89$	9.64085	+	7.00449i	1.02193	+	0.742474i	0.966677	−	0.255998i	$-0.0824041\pi$
$89$	9.64085	+	7.00449i	1.02193	+	0.742474i	0.0552510	+	0.998472i	$0.482404\pi$
$90$	1.90416	−	2.45428i	0.200716	−	0.258704i
$91$	2.34941	−	1.70695i	0.246286	−	0.178937i
$92$	−1.18705	+	3.65338i	−0.123759	+	0.380891i
$93$	9.05530			0.938991
$94$	−8.35332	+	25.7089i	−0.861579	+	2.65167i
$95$	3.33882	+	4.91405i	0.342556	+	0.504171i
$96$	−0.708664	−	2.18104i	−0.0723277	−	0.222602i
$97$	−0.835568	−	2.57161i	−0.0848391	−	0.261108i	0.899634	−	0.436646i	$-0.143834\pi$
$97$	−0.835568	−	2.57161i	−0.0848391	−	0.261108i	−0.984473	+	0.175538i	$0.943834\pi$
$98$	−24.2162	−	17.5941i	−2.44621	−	1.77727i
$99$	−1.31007			−0.131667
$100$	16.2191	−	10.2881i	1.62191	−	1.02881i
$101$	8.69086			0.864773			0.432386	−	0.901688i	$-0.357672\pi$
$101$	8.69086			0.864773			0.432386	+	0.901688i	$0.357672\pi$
$102$	13.8545	+	10.0659i	1.37180	+	0.996672i
$103$	−5.24742	−	16.1499i	−0.517044	−	1.59130i	−0.779533	−	0.626361i	$-0.784543\pi$
$103$	−5.24742	−	16.1499i	−0.517044	−	1.59130i	0.262489	−	0.964935i	$-0.415457\pi$
$104$	0.907103	+	2.79177i	0.0889487	+	0.273756i
$105$	14.4248	+	5.19497i	1.40772	+	0.506977i
$106$	−2.80744	+	8.64040i	−0.272682	+	0.839230i
$107$	−13.6548			−1.32005			−0.660027	−	0.751242i	$-0.729455\pi$
$107$	−13.6548			−1.32005			−0.660027	+	0.751242i	$0.729455\pi$
$108$	−6.60839	+	20.3385i	−0.635892	+	1.95708i
$109$	−5.25412	+	3.81734i	−0.503254	+	0.365635i	−0.810258	−	0.586073i	$-0.800673\pi$
$109$	−5.25412	+	3.81734i	−0.503254	+	0.365635i	0.307005	+	0.951708i	$0.400673\pi$
$110$	−11.5891	−	4.17373i	−1.10498	−	0.397950i
$111$	14.4793	+	10.5198i	1.37431	+	0.998497i
$112$	10.9476	−	7.95392i	1.03445	−	0.751574i
$113$	−4.92111	+	3.57539i	−0.462939	+	0.336345i	−0.794683	−	0.607025i	$-0.792363\pi$
$113$	−4.92111	+	3.57539i	−0.462939	+	0.336345i	0.331744	+	0.943369i	$0.392363\pi$
$114$	−8.09033	−	5.87797i	−0.757729	−	0.550522i
$115$	−2.14735	+	0.623615i	−0.200241	+	0.0581524i
$116$	4.79087	−	3.48077i	0.444821	−	0.323182i
$117$	−0.117154	+	0.360564i	−0.0108309	+	0.0333342i
$118$	31.5216			2.90180
$119$	6.19033	−	19.0519i	0.567467	−	1.74648i
$120$	−9.49987	+	12.2445i	−0.867215	+	1.11776i
$121$	−1.79387	−	5.52096i	−0.163079	−	0.501905i
$122$	2.63585	+	8.11232i	0.238639	+	0.734455i
$123$	0.534012	+	0.387983i	0.0481503	+	0.0349832i
$124$	22.3365			2.00588
$125$	10.2594	+	4.44352i	0.917628	+	0.397440i
$126$	6.11638			0.544891
$127$	−3.71102	−	2.69622i	−0.329300	−	0.239251i	0.410833	−	0.911710i	$-0.365238\pi$
$127$	−3.71102	−	2.69622i	−0.329300	−	0.239251i	−0.740134	+	0.672460i	$0.765238\pi$
$128$	−6.33899	−	19.5094i	−0.560292	−	1.72440i
$129$	0.237383	+	0.730590i	0.0209004	+	0.0643248i
$130$	−2.18508	+	2.81637i	−0.191644	+	0.247012i
$131$	−2.47499	+	7.61723i	−0.216241	+	0.665521i	0.782822	+	0.622245i	$0.213779\pi$
$131$	−2.47499	+	7.61723i	−0.216241	+	0.665521i	−0.999063	+	0.0432754i	$0.986221\pi$
$132$	13.6349			1.18677
$133$	−3.61484	+	11.1253i	−0.313446	+	0.964689i
$134$	5.31290	−	3.86005i	0.458965	−	0.333457i
$135$	−11.9544	+	3.47170i	−1.02887	+	0.298796i
$136$	16.3818	+	11.9021i	1.40473	+	1.02059i
$137$	2.24990	−	1.63465i	0.192222	−	0.139657i	−0.487512	−	0.873116i	$-0.662095\pi$
$137$	2.24990	−	1.63465i	0.192222	−	0.139657i	0.679734	+	0.733459i	$0.262095\pi$
$138$	3.04502	−	2.21234i	0.259210	−	0.188327i
$139$	3.22399	+	2.34237i	0.273456	+	0.198677i	0.716058	−	0.698041i	$-0.245945\pi$
$139$	3.22399	+	2.34237i	0.273456	+	0.198677i	−0.442602	+	0.896718i	$0.645945\pi$
$140$	35.5813	+	12.8143i	3.00717	+	1.08301i
$141$	14.0913	−	10.2379i	1.18670	−	0.862190i
$142$	−10.3803	+	31.9474i	−0.871098	+	2.68096i
$143$	1.50335			0.125717
$144$	−0.545907	+	1.68013i	−0.0454923	+	0.140011i
$145$	3.24319	+	1.16801i	0.269332	+	0.0969977i
$146$	5.07431	+	15.6171i	0.419953	+	1.29248i
$147$	5.96003	+	18.3431i	0.491575	+	1.51291i
$148$	35.7158	+	25.9490i	2.93582	+	2.13300i
$149$	−14.0352			−1.14981			−0.574903	−	0.818221i	$-0.694960\pi$
$149$	−14.0352			−1.14981			−0.574903	+	0.818221i	$0.694960\pi$
$150$	−18.7819	−	1.18566i	−1.53354	−	0.0968087i
$151$	23.5381			1.91550			0.957751	−	0.287599i	$-0.0928571\pi$
$151$	23.5381			1.91550			0.957751	+	0.287599i	$0.0928571\pi$
$152$	−9.56614	−	6.95020i	−0.775916	−	0.563736i
$153$	0.808143	+	2.48721i	0.0653345	+	0.201079i
$154$	−7.49482	−	23.0667i	−0.603950	−	1.85877i
$155$	7.30711	+	10.7545i	0.586921	+	0.863826i
$156$	1.21932	−	3.75267i	0.0976234	−	0.300454i
$157$	−9.15012			−0.730259			−0.365129	−	0.930957i	$-0.618975\pi$
$157$	−9.15012			−0.730259			−0.365129	+	0.930957i	$0.618975\pi$
$158$	1.72893	−	5.32109i	0.137546	−	0.423323i
$159$	4.73590	−	3.44083i	0.375581	−	0.272876i
$160$	2.01847	−	2.60162i	0.159574	−	0.205676i
$161$	−3.56196	−	2.58791i	−0.280722	−	0.203956i
$162$	13.5802	−	9.86656i	1.06696	−	0.775190i
$163$	20.0797	−	14.5887i	1.57276	−	1.14268i	0.648312	−	0.761374i	$-0.275475\pi$
$163$	20.0797	−	14.5887i	1.57276	−	1.14268i	0.924450	−	0.381304i	$-0.124525\pi$
$164$	1.31724	+	0.957030i	0.102859	+	0.0747315i
$165$	4.46049	+	6.56491i	0.347249	+	0.511078i
$166$	13.6326	−	9.90464i	1.05809	−	0.768749i
$167$	6.16486	−	18.9735i	0.477051	−	1.46821i	−0.366121	−	0.930567i	$-0.619314\pi$
$167$	6.16486	−	18.9735i	0.477051	−	1.46821i	0.843172	−	0.537645i	$-0.180686\pi$
$168$	−30.5147			−2.35426
$169$	−3.88278	+	11.9500i	−0.298676	+	0.919229i
$170$	−0.774972	+	24.5769i	−0.0594377	+	1.88496i
$171$	−0.471914	−	1.45240i	−0.0360882	−	0.111068i
$172$	0.585548	+	1.80213i	0.0446476	+	0.137411i
$173$	−0.862612	−	0.626724i	−0.0655832	−	0.0476490i	0.554511	−	0.832177i	$-0.312905\pi$
$173$	−0.862612	−	0.626724i	−0.0655832	−	0.0476490i	−0.620094	+	0.784528i	$0.712905\pi$
$174$	−5.80232			−0.439873
$175$	5.47016	+	21.3237i	0.413505	+	1.61192i
$176$	7.00520			0.528037
$177$	−16.4317	−	11.9383i	−1.23508	−	0.897341i
$178$	−8.90017	−	27.3919i	−0.667096	−	2.05311i
$179$	−4.16746	−	12.8261i	−0.311491	−	0.958669i	−0.977175	−	0.212436i	$-0.931860\pi$
$179$	−4.16746	−	12.8261i	−0.311491	−	0.958669i	0.665684	−	0.746233i	$-0.268140\pi$
$180$	−4.74128	+	1.37692i	−0.353394	+	0.102630i
$181$	0.173897	−	0.535201i	0.0129257	−	0.0397812i	−0.944386	−	0.328840i	$-0.893342\pi$
$181$	0.173897	−	0.535201i	0.0129257	−	0.0397812i	0.957311	+	0.289059i	$0.0933423\pi$
$182$	−7.01875			−0.520265
$183$	1.69839	−	5.22712i	0.125549	−	0.386400i
$184$	3.60048	−	2.61591i	0.265431	−	0.192847i
$185$	−0.809920	+	25.6852i	−0.0595465	+	1.88842i
$186$	−17.7059	−	12.8641i	−1.29826	−	0.943242i
$187$	8.38972	−	6.09549i	0.613517	−	0.445746i
$188$	34.7588	−	25.2537i	2.53504	−	1.84182i
$189$	−19.8296	−	14.4070i	−1.44239	−	1.04796i
$190$	0.452545	−	14.3517i	0.0328310	−	1.04118i
$191$	−18.6194	+	13.5278i	−1.34725	+	0.978837i	−0.348111	+	0.937453i	$0.613177\pi$
$191$	−18.6194	+	13.5278i	−1.34725	+	0.978837i	−0.999143	+	0.0413838i	$0.986823\pi$
$192$	−4.67091	+	14.3756i	−0.337094	+	1.03747i
$193$	−23.5877			−1.69788			−0.848940	−	0.528489i	$-0.822759\pi$
$193$	−23.5877			−1.69788			−0.848940	+	0.528489i	$0.822759\pi$
$194$	−2.01948	+	6.21532i	−0.144990	+	0.446234i
$195$	2.20571	−	0.640564i	0.157954	−	0.0458717i
$196$	14.7015	+	45.2465i	1.05011	+	3.23190i
$197$	1.61375	+	4.96660i	0.114975	+	0.353855i	0.991942	−	0.126695i	$-0.0404369\pi$
$197$	1.61375	+	4.96660i	0.114975	+	0.353855i	−0.876967	+	0.480550i	$0.840437\pi$
$198$	2.56160	+	1.86111i	0.182045	+	0.132263i
$199$	−12.8140			−0.908361			−0.454180	−	0.890910i	$-0.650068\pi$
$199$	−12.8140			−0.908361			−0.454180	+	0.890910i	$0.650068\pi$
$200$	−22.2080	−	1.40194i	−1.57034	−	0.0991323i
$201$	−4.23147			−0.298465
$202$	−16.9933	−	12.3464i	−1.19565	−	0.868688i
$203$	2.09741	+	6.45515i	0.147209	+	0.453063i
$204$	−8.41097	−	25.8863i	−0.588886	−	1.81240i
$205$	−0.0298708	+	0.947300i	−0.00208626	+	0.0661623i
$206$	−12.6825	+	39.0326i	−0.883629	+	2.71953i
$207$	0.574785			0.0399503
$208$	0.626447	−	1.92801i	0.0434363	−	0.133683i
$209$	−4.89917	+	3.55946i	−0.338883	+	0.246213i
$210$	−20.8249	−	30.6499i	−1.43705	−	2.11504i
$211$	−8.17486	−	5.93938i	−0.562781	−	0.408884i	0.269695	−	0.962946i	$-0.413077\pi$
$211$	−8.17486	−	5.93938i	−0.562781	−	0.408884i	−0.832476	+	0.554062i	$0.813077\pi$
$212$	11.6820	−	8.48743i	0.802320	−	0.582919i
$213$	17.5107	−	12.7223i	1.19981	−	0.871715i
$214$	26.6993	+	19.3982i	1.82512	+	1.32603i
$215$	−0.676131	+	0.871472i	−0.0461118	+	0.0594339i
$216$	20.0441	−	14.5629i	1.36383	−	0.990878i
$217$	−7.91118	+	24.3481i	−0.537046	+	1.65286i
$218$	15.6964			1.06310
$219$	3.26960	−	10.0628i	0.220939	−	0.679980i
$220$	11.0026	+	16.1935i	0.741796	+	1.09177i
$221$	−0.927371	−	2.85415i	−0.0623817	−	0.191991i
$222$	−13.3669	−	41.1390i	−0.897126	−	2.76107i
$223$	−0.875166	−	0.635846i	−0.0586055	−	0.0425794i	0.558097	−	0.829776i	$-0.311532\pi$
$223$	−0.875166	−	0.635846i	−0.0586055	−	0.0425794i	−0.616702	+	0.787196i	$0.711532\pi$
$224$	6.48356			0.433201
$225$	−2.21401	−	1.83238i	−0.147601	−	0.122159i
$226$	14.7016			0.977933
$227$	−7.85791	−	5.70911i	−0.521548	−	0.378927i	0.295639	−	0.955300i	$-0.404468\pi$
$227$	−7.85791	−	5.70911i	−0.521548	−	0.378927i	−0.817187	+	0.576373i	$0.804468\pi$
$228$	4.91158	+	15.1163i	0.325277	+	1.00110i
$229$	4.48749	+	13.8111i	0.296542	+	0.912662i	0.982699	+	0.185209i	$0.0592962\pi$
$229$	4.48749	+	13.8111i	0.296542	+	0.912662i	−0.686157	+	0.727453i	$0.740704\pi$
$230$	5.08465	+	1.83120i	0.335272	+	0.120745i
$231$	−4.82923	+	14.8629i	−0.317740	+	0.977904i
$232$	−6.86076			−0.450431
$233$	2.02087	−	6.21961i	0.132392	−	0.407460i	−0.862783	−	0.505574i	$-0.831281\pi$
$233$	2.02087	−	6.21961i	0.132392	−	0.407460i	0.995175	+	0.0981136i	$0.0312809\pi$
$234$	0.741296	−	0.538583i	0.0484601	−	0.0352083i
$235$	23.5300	+	8.47414i	1.53493	+	0.552792i
$236$	−40.5318	−	29.4481i	−2.63840	−	1.91691i
$237$	−2.91655	+	2.11900i	−0.189450	+	0.137644i
$238$	−39.1694	+	28.4583i	−2.53898	+	1.84468i
$239$	−19.6484	−	14.2754i	−1.27095	−	0.923400i	−0.271712	−	0.962379i	$-0.587590\pi$
$239$	−19.6484	−	14.2754i	−1.27095	−	0.923400i	−0.999240	+	0.0389782i	$0.987590\pi$
$240$	10.2780	−	2.98485i	0.663442	−	0.192671i
$241$	−4.47653	+	3.25239i	−0.288359	+	0.209505i	−0.722555	−	0.691313i	$-0.757032\pi$
$241$	−4.47653	+	3.25239i	−0.288359	+	0.209505i	0.434196	+	0.900818i	$0.357032\pi$
$242$	−4.33559	+	13.3436i	−0.278702	+	0.857758i
$243$	5.88521			0.377536
$244$	4.18940	−	12.8936i	0.268199	−	0.825431i
$245$	−16.9758	+	21.8803i	−1.08454	+	1.39788i
$246$	−0.492985	−	1.51725i	−0.0314316	−	0.0967365i
$247$	0.541538	+	1.66668i	0.0344572	+	0.106048i
$248$	−20.9358	−	15.2107i	−1.32942	−	0.965882i
$249$	−10.8577			−0.688078
$250$	−13.7478	−	23.2631i	−0.869485	−	1.47129i
$251$	−3.60183			−0.227346			−0.113673	−	0.993518i	$-0.536262\pi$
$251$	−3.60183			−0.227346			−0.113673	+	0.993518i	$0.536262\pi$
$252$	−7.86471	−	5.71404i	−0.495430	−	0.359951i
$253$	−0.704323	−	2.16768i	−0.0442804	−	0.136281i
$254$	3.42591	+	10.5439i	0.214961	+	0.661582i
$255$	9.71213	−	12.5181i	0.608197	−	0.783911i
$256$	−9.32199	+	28.6901i	−0.582624	+	1.79313i
$257$	29.0638			1.81295			0.906475	−	0.422260i	$-0.138763\pi$
$257$	29.0638			1.81295			0.906475	+	0.422260i	$0.138763\pi$
$258$	0.573730	−	1.76576i	0.0357189	−	0.109931i
$259$	−40.9358	+	29.7416i	−2.54363	+	1.84805i
$260$	5.44078	−	1.58007i	0.337423	−	0.0979916i
$261$	−0.716856	−	0.520826i	−0.0443723	−	0.0322383i
$262$	15.6605	−	11.3780i	0.967511	−	0.702938i
$263$	2.84390	−	2.06621i	0.175362	−	0.127408i	−0.496642	−	0.867956i	$-0.665434\pi$
$263$	2.84390	−	2.06621i	0.175362	−	0.127408i	0.672004	+	0.740547i	$0.265434\pi$
$264$	−12.7798	−	9.28510i	−0.786545	−	0.571459i
$265$	7.90811	+	2.84804i	0.485791	+	0.174954i
$266$	22.8730	−	16.6182i	1.40243	−	1.01893i
$267$	−5.73476	+	17.6498i	−0.350962	+	1.08015i
$268$	−10.4377			−0.637583
$269$	5.16954	−	15.9102i	0.315192	−	0.970062i	−0.660483	−	0.750841i	$-0.729648\pi$
$269$	5.16954	−	15.9102i	0.315192	−	0.970062i	0.975675	−	0.219221i	$-0.0703516\pi$
$270$	28.3065	+	10.1944i	1.72268	+	0.620409i
$271$	−3.26069	−	10.0354i	−0.198073	−	0.609606i	−0.999927	−	0.0120858i	$-0.996153\pi$
$271$	−3.26069	−	10.0354i	−0.198073	−	0.609606i	0.801854	−	0.597520i	$-0.203847\pi$
$272$	−4.32129	−	13.2996i	−0.262017	−	0.806405i
$273$	3.65877	+	2.65825i	0.221439	+	0.160885i
$274$	−6.72145			−0.406058
$275$	−4.19747	+	10.5950i	−0.253117	+	0.638903i
$276$	−5.98223			−0.360088
$277$	−4.88424	−	3.54861i	−0.293465	−	0.213215i	0.431304	−	0.902207i	$-0.358054\pi$
$277$	−4.88424	−	3.54861i	−0.293465	−	0.213215i	−0.724769	+	0.688992i	$0.758054\pi$
$278$	−2.97630	−	9.16012i	−0.178507	−	0.549387i
$279$	−1.03280	−	3.17863i	−0.0618320	−	0.190299i
$280$	−24.6237	−	36.2409i	−1.47154	−	2.16581i
$281$	−4.86420	+	14.9705i	−0.290174	+	0.893064i	0.694626	+	0.719371i	$0.255570\pi$
$281$	−4.86420	+	14.9705i	−0.290174	+	0.893064i	−0.984800	+	0.173693i	$0.944430\pi$
$282$	−42.0971			−2.50684
$283$	0.359284	−	1.10576i	0.0213572	−	0.0657308i	−0.939810	−	0.341698i	$-0.888998\pi$
$283$	0.359284	−	1.10576i	0.0213572	−	0.0657308i	0.961167	+	0.275967i	$0.0889981\pi$
$284$	43.1933	−	31.3818i	2.56305	−	1.86217i
$285$	−5.67139	+	7.30991i	−0.335944	+	0.433002i
$286$	−2.93952	−	2.13568i	−0.173817	−	0.126286i
$287$	−1.50976	+	1.09690i	−0.0891182	+	0.0647482i
$288$	−0.684771	+	0.497516i	−0.0403505	+	0.0293164i
$289$	−2.99454	−	2.17566i	−0.176149	−	0.127980i
$290$	−4.68214	−	6.89114i	−0.274945	−	0.404662i
$291$	3.40669	−	2.47510i	0.199703	−	0.145093i
$292$	8.06505	−	24.8217i	0.471972	−	1.45258i
$293$	28.1109			1.64226			0.821130	−	0.570742i	$-0.193344\pi$
$293$	28.1109			1.64226			0.821130	+	0.570742i	$0.193344\pi$
$294$	14.4048	−	44.3333i	0.840103	−	2.58557i
$295$	0.919132	−	29.1487i	0.0535140	−	1.69710i
$296$	−15.8052	−	48.6434i	−0.918659	−	2.82734i
$297$	−3.92100	−	12.0676i	−0.227520	−	0.700233i
$298$	27.4431	+	19.9386i	1.58974	+	1.15501i
$299$	−0.659585			−0.0381448
$300$	23.0429	+	19.0710i	1.33038	+	1.10106i
$301$	−2.17182			−0.125181
$302$	−46.0242	−	33.4386i	−2.64840	−	1.92417i
$303$	4.18235	+	12.8719i	0.240270	+	0.739474i
$304$	2.52342	+	7.76628i	0.144728	+	0.445427i
$305$	7.57850	−	2.20089i	0.433944	−	0.126022i
$306$	1.95320	−	6.01132i	0.111657	−	0.343645i
$307$	−25.0427			−1.42927			−0.714633	−	0.699500i	$-0.753406\pi$
$307$	−25.0427			−1.42927			−0.714633	+	0.699500i	$0.753406\pi$
$308$	−11.9122	+	36.6619i	−0.678760	+	2.08901i
$309$	21.3942	−	15.5438i	1.21707	−	0.884256i
$310$	0.990407	−	31.4091i	0.0562513	−	1.78392i
$311$	18.0447	+	13.1102i	1.02322	+	0.743414i	0.966941	−	0.255001i	$-0.0820758\pi$
$311$	18.0447	+	13.1102i	1.02322	+	0.743414i	0.0562809	+	0.998415i	$0.482076\pi$
$312$	−3.69834	+	2.68700i	−0.209377	+	0.152121i
$313$	−11.2506	+	8.17404i	−0.635921	+	0.462024i	−0.858447	−	0.512903i	$-0.828570\pi$
$313$	−11.2506	+	8.17404i	−0.635921	+	0.462024i	0.222525	+	0.974927i	$0.428570\pi$
$314$	17.8913	+	12.9988i	1.00967	+	0.733565i
$315$	0.178346	−	5.65595i	0.0100487	−	0.318677i
$316$	−7.19419	+	5.22689i	−0.404705	+	0.294035i
$317$	3.34877	−	10.3064i	0.188085	−	0.578868i	−0.811902	−	0.583793i	$-0.801568\pi$
$317$	3.34877	−	10.3064i	0.188085	−	0.578868i	0.999988	+	0.00492566i	$0.00156789\pi$
$318$	−14.1483			−0.793394
$319$	−1.08578	+	3.34168i	−0.0607918	+	0.187098i
$320$	−20.8423	+	6.05285i	−1.16512	+	0.338365i
$321$	−6.57115	−	20.2239i	−0.366766	−	1.12879i
$322$	3.28830	+	10.1204i	0.183250	+	0.563985i
$323$	9.77988	+	7.10550i	0.544167	+	0.395361i
$324$	−26.6795			−1.48219
$325$	2.54065	+	2.10272i	0.140930	+	0.116638i
$326$	−59.9870			−3.32237
$327$	−8.18230	−	5.94479i	−0.452482	−	0.328747i
$328$	−0.582914	−	1.79402i	−0.0321860	−	0.0990584i
$329$	15.2171	+	46.8335i	0.838947	+	2.58201i
$330$	0.604575	−	19.1731i	0.0332808	−	1.05544i
$331$	7.57894	−	23.3256i	0.416576	−	1.28209i	−0.494258	−	0.869315i	$-0.664560\pi$
$331$	7.57894	−	23.3256i	0.416576	−	1.28209i	0.910834	−	0.412774i	$-0.135440\pi$
$332$	−26.7824			−1.46988
$333$	2.04128	−	6.28241i	0.111861	−	0.344274i
$334$	−39.0082	+	28.3411i	−2.13444	+	1.55076i
$335$	−3.41455	−	5.02551i	−0.186557	−	0.274573i
$336$	17.0489	+	12.3867i	0.930091	+	0.675751i
$337$	15.0670	−	10.9468i	0.820750	−	0.596309i	−0.0961776	−	0.995364i	$-0.530662\pi$
$337$	15.0670	−	10.9468i	0.820750	−	0.596309i	0.916927	+	0.399055i	$0.130662\pi$
$338$	24.5684	−	17.8500i	1.33634	−	0.970910i
$339$	−7.66369	−	5.56800i	−0.416235	−	0.302412i
$340$	23.9567	−	30.8781i	1.29924	−	1.67460i
$341$	−10.7220	+	7.78997i	−0.580628	+	0.421851i
$342$	−1.14057	+	3.51031i	−0.0616749	+	0.189816i
$343$	−23.7086			−1.28014
$344$	0.678387	−	2.08786i	0.0365762	−	0.112570i
$345$	−1.95701	−	2.88031i	−0.105362	−	0.155071i
$346$	0.796339	+	2.45088i	0.0428115	+	0.131760i
$347$	0.451409	+	1.38929i	0.0242329	+	0.0745812i	0.962442	−	0.271489i	$-0.0875160\pi$
$347$	0.451409	+	1.38929i	0.0242329	+	0.0745812i	−0.938209	+	0.346070i	$0.887516\pi$
$348$	7.46087	+	5.42064i	0.399945	+	0.290577i
$349$	24.2123			1.29606			0.648028	−	0.761617i	$-0.275594\pi$
$349$	24.2123			1.29606			0.648028	+	0.761617i	$0.275594\pi$
$350$	19.5969	−	49.4654i	1.04750	−	2.64404i
$351$	−3.67194			−0.195994
$352$	2.71537	+	1.97284i	0.144730	+	0.105152i
$353$	2.98661	+	9.19185i	0.158961	+	0.489233i	0.998541	−	0.0540042i	$-0.0171985\pi$
$353$	2.98661	+	9.19185i	0.158961	+	0.489233i	−0.839579	+	0.543237i	$0.817198\pi$
$354$	15.1693	+	46.6863i	0.806240	+	2.48135i
$355$	29.2398	+	10.5305i	1.55189	+	0.558899i
$356$	−14.1458	+	43.5364i	−0.749727	+	2.30742i
$357$	31.1966			1.65110
$358$	−10.0723	+	30.9994i	−0.532339	+	1.63837i
$359$	−17.9809	+	13.0639i	−0.948997	+	0.689487i	−0.950569	−	0.310512i	$-0.899500\pi$
$359$	−17.9809	+	13.0639i	−0.948997	+	0.689487i	0.00157227	+	0.999999i	$0.499500\pi$
$360$	5.38160	+	1.93814i	0.283635	+	0.102149i
$361$	9.66037	+	7.01867i	0.508440	+	0.369404i
$362$	−1.10034	+	0.799443i	−0.0578325	+	0.0420178i
$363$	7.31376	−	5.31376i	0.383873	−	0.278900i
$364$	9.02501	+	6.55706i	0.473039	+	0.343683i
$365$	14.5895	−	4.23695i	0.763647	−	0.221772i
$366$	−10.7466	+	7.80787i	−0.561735	+	0.408124i
$367$	−1.88978	+	5.81616i	−0.0986460	+	0.303601i	−0.988187	−	0.153255i	$-0.951024\pi$
$367$	−1.88978	+	5.81616i	−0.0986460	+	0.303601i	0.889541	+	0.456856i	$0.151024\pi$
$368$	−3.07348			−0.160216
$369$	0.0752846	−	0.231702i	0.00391916	−	0.0120619i
$370$	38.0725	−	49.0720i	1.97930	−	2.55113i
$371$	5.11426	+	15.7401i	0.265519	+	0.817185i
$372$	10.7491	+	33.0824i	0.557317	+	1.71524i
$373$	−13.5827	−	9.86842i	−0.703287	−	0.510968i	0.177714	−	0.984082i	$-0.443130\pi$
$373$	−13.5827	−	9.86842i	−0.703287	−	0.510968i	−0.881001	+	0.473115i	$0.843130\pi$
$374$	−25.0639			−1.29602
$375$	−1.64406	+	17.3335i	−0.0848991	+	0.895096i
$376$	−49.7762			−2.56701
$377$	0.822616	+	0.597666i	0.0423669	+	0.0307813i
$378$	18.3061	+	56.3405i	0.941566	+	2.89784i
$379$	−3.59784	−	11.0730i	−0.184809	−	0.568783i	0.815136	−	0.579269i	$-0.196662\pi$
$379$	−3.59784	−	11.0730i	−0.184809	−	0.568783i	−0.999945	+	0.0104862i	$0.996662\pi$
$380$	−13.9895	+	18.0312i	−0.717647	+	0.924982i
$381$	2.20746	−	6.79387i	0.113092	−	0.348061i
$382$	55.6246			2.84600
$383$	−8.65685	+	26.6430i	−0.442344	+	1.36140i	0.443026	+	0.896509i	$0.353905\pi$
$383$	−8.65685	+	26.6430i	−0.442344	+	1.36140i	−0.885370	+	0.464887i	$0.846095\pi$
$384$	25.8446	−	18.7772i	1.31888	−	0.958221i
$385$	−21.5488	+	6.25803i	−1.09823	+	0.318939i
$386$	46.1213	+	33.5091i	2.34751	+	1.70557i
$387$	0.229380	−	0.166654i	0.0116600	−	0.00847150i
$388$	8.40321	−	6.10529i	0.426608	−	0.309949i
$389$	−11.4398	−	8.31151i	−0.580021	−	0.421410i	0.258711	−	0.965955i	$-0.416702\pi$
$389$	−11.4398	−	8.31151i	−0.580021	−	0.421410i	−0.838732	+	0.544545i	$0.816702\pi$
$390$	−5.22284	−	1.88097i	−0.264469	−	0.0952464i
$391$	−3.68093	+	2.67436i	−0.186153	+	0.135248i
$392$	17.0324	−	52.4204i	0.860267	−	2.64763i
$393$	−12.4729			−0.629172
$394$	3.90025	−	12.0038i	0.196492	−	0.604740i
$395$	−4.87012	−	1.75393i	−0.245042	−	0.0882500i
$396$	−1.55513	−	4.78618i	−0.0781480	−	0.240515i
$397$	3.08622	+	9.49842i	0.154893	+	0.476712i	0.998150	−	0.0607986i	$-0.0193647\pi$
$397$	3.08622	+	9.49842i	0.154893	+	0.476712i	−0.843257	+	0.537511i	$0.819365\pi$
$398$	25.0554	+	18.2038i	1.25591	+	0.912473i
$399$	−18.2172			−0.912001
$400$	11.8387	+	9.79808i	0.591936	+	0.489904i
$401$	−24.9690			−1.24689			−0.623447	−	0.781866i	$-0.714268\pi$
$401$	−24.9690			−1.24689			−0.623447	+	0.781866i	$0.714268\pi$
$402$	8.27383	+	6.01129i	0.412661	+	0.299816i
$403$	1.18517	+	3.64758i	0.0590376	+	0.181699i
$404$	10.3165	+	31.7510i	0.513266	+	1.57967i
$405$	−8.72784	−	12.8456i	−0.433690	−	0.638301i
$406$	5.06921	−	15.6014i	0.251581	−	0.774286i
$407$	−26.1941			−1.29840
$408$	−9.74454	+	29.9906i	−0.482426	+	1.48476i
$409$	−10.7777	+	7.83049i	−0.532925	+	0.387193i	−0.821451	−	0.570279i	$-0.806835\pi$
$409$	−10.7777	+	7.83049i	−0.532925	+	0.387193i	0.288526	+	0.957472i	$0.406835\pi$
$410$	1.40416	−	1.80983i	0.0693464	−	0.0893812i
$411$	3.50379	+	2.54565i	0.172829	+	0.125568i
$412$	52.7727	−	38.3416i	2.59992	−	1.88895i
$413$	46.4557	−	33.7521i	2.28594	−	1.66083i
$414$	−1.12388	−	0.816549i	−0.0552358	−	0.0401312i
$415$	−8.76153	−	12.8951i	−0.430087	−	0.632998i
$416$	0.785798	−	0.570916i	0.0385269	−	0.0279915i
$417$	−1.91776	+	5.90226i	−0.0939131	+	0.289035i
$418$	14.6360			0.715871
$419$	5.06571	−	15.5907i	0.247476	−	0.761654i	−0.747743	−	0.663988i	$-0.768862\pi$
$419$	5.06571	−	15.5907i	0.247476	−	0.761654i	0.995219	−	0.0976655i	$-0.0311375\pi$
$420$	−1.85619	+	58.8659i	−0.0905728	+	2.87236i
$421$	−3.77700	−	11.6244i	−0.184080	−	0.566540i	0.815851	−	0.578262i	$-0.196269\pi$
$421$	−3.77700	−	11.6244i	−0.184080	−	0.566540i	−0.999931	+	0.0117220i	$0.996269\pi$
$422$	7.54681	+	23.2267i	0.367373	+	1.13066i
$423$	−5.20094	−	3.77870i	−0.252878	−	0.183727i
$424$	−16.7291			−0.812438
$425$	22.7042	+	1.43327i	1.10132	+	0.0695237i
$426$	−52.3123			−2.53454
$427$	12.5710	+	9.13337i	0.608353	+	0.441995i
$428$	−16.2089	−	49.8860i	−0.783488	−	2.41133i
$429$	0.723466	+	2.22660i	0.0349292	+	0.107501i
$430$	2.56007	−	0.743476i	0.123458	−	0.0358536i
$431$	10.4172	−	32.0609i	0.501779	−	1.54432i	−0.304340	−	0.952563i	$-0.598436\pi$
$431$	10.4172	−	32.0609i	0.501779	−	1.54432i	0.806119	−	0.591753i	$-0.201564\pi$
$432$	−17.1102			−0.823217
$433$	1.25703	−	3.86874i	0.0604090	−	0.185920i	−0.916298	−	0.400497i	$-0.868837\pi$
$433$	1.25703	−	3.86874i	0.0604090	−	0.185920i	0.976707	+	0.214577i	$0.0688374\pi$
$434$	50.0581	−	36.3694i	2.40287	−	1.74579i
$435$	−0.169189	+	5.36554i	−0.00811198	+	0.257258i
$436$	−20.1831	−	14.6639i	−0.966596	−	0.702273i
$437$	2.14948	−	1.56169i	0.102824	−	0.0747057i
$438$	−20.6884	+	15.0310i	−0.988532	+	0.718210i
$439$	−8.15787	−	5.92704i	−0.389354	−	0.282882i	0.375837	−	0.926686i	$-0.377355\pi$
$439$	−8.15787	−	5.92704i	−0.389354	−	0.282882i	−0.765191	+	0.643804i	$0.777355\pi$
$440$	0.714859	−	22.6705i	0.0340796	−	1.08078i
$441$	5.75909	−	4.18422i	0.274242	−	0.199249i
$442$	−2.24136	+	6.89820i	−0.106611	+	0.328114i
$443$	28.5905			1.35837			0.679187	−	0.733966i	$-0.262333\pi$
$443$	28.5905			1.35837			0.679187	+	0.733966i	$0.262333\pi$
$444$	−21.2452	+	65.3859i	−1.00825	+	3.10308i
$445$	−25.5894	+	7.43147i	−1.21305	+	0.352285i
$446$	0.807929	+	2.48655i	0.0382566	+	0.117742i
$447$	−6.75422	−	20.7874i	−0.319464	−	0.983208i
$448$	−34.5726	−	25.1185i	−1.63340	−	1.18674i
$449$	−30.2241			−1.42636			−0.713181	−	0.700980i	$-0.752746\pi$
$449$	−30.2241			−1.42636			−0.713181	+	0.700980i	$0.752746\pi$
$450$	1.72597	+	6.72812i	0.0813628	+	0.317167i
$451$	−0.966069			−0.0454904
$452$	−18.9039	−	13.7345i	−0.889164	−	0.646015i
$453$	11.3274	+	34.8620i	0.532206	+	1.63796i
$454$	7.25421	+	22.3262i	0.340457	+	1.04782i
$455$	−0.204659	+	6.49040i	−0.00959454	+	0.304274i
$456$	5.69032	−	17.5130i	0.266473	−	0.820121i
$457$	−2.97328			−0.139084			−0.0695421	−	0.997579i	$-0.522154\pi$
$457$	−2.97328			−0.139084			−0.0695421	+	0.997579i	$0.522154\pi$
$458$	10.8458	−	33.3800i	0.506791	−	1.55974i
$459$	−20.4919	+	14.8883i	−0.956482	+	0.694925i
$460$	−4.82732	−	7.10481i	−0.225075	−	0.331263i
$461$	31.0933	+	22.5906i	1.44816	+	1.05215i	0.986257	+	0.165217i	$0.0528324\pi$
$461$	31.0933	+	22.5906i	1.44816	+	1.05215i	0.461901	+	0.886932i	$0.347168\pi$
$462$	30.5571	−	22.2010i	1.42164	−	1.03288i
$463$	−19.8136	+	14.3954i	−0.920817	+	0.669012i	−0.943727	−	0.330725i	$-0.892707\pi$
$463$	−19.8136	+	14.3954i	−0.920817	+	0.669012i	0.0229106	+	0.999738i	$0.492707\pi$
$464$	3.83317	+	2.78496i	0.177950	+	0.129288i
$465$	−12.4120	+	15.9980i	−0.575593	+	0.741887i
$466$	−12.7871	+	9.29038i	−0.592351	+	0.430368i
$467$	6.67838	−	20.5539i	0.309039	−	0.951123i	−0.669101	−	0.743172i	$-0.733320\pi$
$467$	6.67838	−	20.5539i	0.309039	−	0.951123i	0.978139	−	0.207951i	$-0.0666796\pi$
$468$	−1.45635			−0.0673196
$469$	3.69683	−	11.3777i	0.170704	−	0.525372i
$470$	−33.9699	−	49.9967i	−1.56692	−	2.30617i
$471$	−4.40336	−	13.5521i	−0.202896	−	0.624450i
$472$	17.9364	+	55.2026i	0.825591	+	2.54091i
$473$	−0.909576	−	0.660846i	−0.0418224	−	0.0303857i
$474$	8.71303			0.400203
$475$	−13.2581	−	0.836956i	−0.608324	−	0.0384022i
$476$	76.9520			3.52709
$477$	−1.74796	−	1.26997i	−0.0800338	−	0.0581480i
$478$	18.1389	+	55.8258i	0.829654	+	2.55341i
$479$	−8.95683	−	27.5663i	−0.409248	−	1.25954i	−0.917296	−	0.398207i	$-0.869633\pi$
$479$	−8.95683	−	27.5663i	−0.409248	−	1.25954i	0.508047	−	0.861329i	$-0.330367\pi$
$480$	4.82459	+	1.73754i	0.220212	+	0.0793074i
$481$	−2.34244	+	7.20928i	−0.106806	+	0.328715i
$482$	13.3734			0.609142
$483$	2.11879	−	6.52098i	0.0964085	−	0.296715i
$484$	18.0407	−	13.1073i	0.820033	−	0.595789i
$485$	5.68856	+	2.04869i	0.258304	+	0.0930262i
$486$	−11.5074	−	8.36063i	−0.521987	−	0.379246i
$487$	−1.01479	+	0.737291i	−0.0459847	+	0.0334098i	−0.610540	−	0.791985i	$-0.709048\pi$
$487$	−1.01479	+	0.737291i	−0.0459847	+	0.0334098i	0.564555	+	0.825395i	$0.309048\pi$
$488$	−12.7070	+	9.23215i	−0.575217	+	0.417920i
$489$	31.2703	+	22.7192i	1.41409	+	1.02740i
$490$	64.2764	−	18.6666i	2.90371	−	0.843272i
$491$	10.3397	−	7.51220i	0.466622	−	0.339021i	−0.329501	−	0.944155i	$-0.606881\pi$
$491$	10.3397	−	7.51220i	0.466622	−	0.339021i	0.796124	+	0.605134i	$0.206881\pi$
$492$	−0.783545	+	2.41150i	−0.0353250	+	0.108719i
$493$	7.01406			0.315897
$494$	1.30884	−	4.02820i	0.0588875	−	0.181237i
$495$	1.79570	−	2.31450i	0.0807107	−	0.104029i
$496$	5.52257	+	16.9967i	0.247971	+	0.763175i
$497$	18.9097	+	58.1980i	0.848215	+	2.61054i
$498$	21.2301	+	15.4246i	0.951345	+	0.691193i
$499$	−33.6568			−1.50669			−0.753343	−	0.657627i	$-0.771560\pi$
$499$	−33.6568			−1.50669			−0.753343	+	0.657627i	$0.771560\pi$
$500$	−4.05538	+	42.7561i	−0.181362	+	1.91211i
$501$	31.0682			1.38802
$502$	7.04270	+	5.11682i	0.314331	+	0.228375i
$503$	2.43841	+	7.50464i	0.108723	+	0.334616i	0.990586	−	0.136890i	$-0.0437107\pi$
$503$	2.43841	+	7.50464i	0.108723	+	0.334616i	−0.881863	+	0.471506i	$0.843711\pi$
$504$	3.48035	+	10.7114i	0.155027	+	0.477124i
$505$	−11.9125	+	15.3541i	−0.530098	+	0.683248i
$506$	−1.70228	+	5.23907i	−0.0756754	+	0.232905i
$507$	−19.5675			−0.869024
$508$	5.44511	−	16.7583i	0.241588	−	0.743530i
$509$	−17.8086	+	12.9387i	−0.789353	+	0.573499i	−0.907771	−	0.419465i	$-0.862218\pi$
$509$	−17.8086	+	12.9387i	−0.789353	+	0.573499i	0.118418	+	0.992964i	$0.462218\pi$
$510$	−36.7736	+	10.6795i	−1.62836	+	0.472895i
$511$	24.2006	+	17.5827i	1.07057	+	0.777815i
$512$	25.7937	−	18.7402i	1.13993	−	0.828208i
$513$	11.9663	−	8.69399i	0.528323	−	0.383849i
$514$	−56.8287	−	41.2885i	−2.50661	−	1.82116i
$515$	35.7245	+	12.8659i	1.57421	+	0.566939i
$516$	−2.38733	+	1.73450i	−0.105096	+	0.0763570i
$517$	−7.87754	+	24.2446i	−0.346454	+	1.06628i
$518$	122.294			5.37327
$519$	0.513116	−	1.57921i	0.0225233	−	0.0693195i
$520$	−6.17557	−	2.22408i	−0.270817	−	0.0975325i
$521$	−11.5658	−	35.5959i	−0.506707	−	1.55948i	−0.797881	−	0.602814i	$-0.794046\pi$
$521$	−11.5658	−	35.5959i	−0.506707	−	1.55948i	0.291174	−	0.956670i	$-0.405954\pi$
$522$	0.661781	+	2.03675i	0.0289654	+	0.0891463i
$523$	−29.8872	−	21.7143i	−1.30687	−	0.949500i	−0.306877	−	0.951749i	$-0.599284\pi$
$523$	−29.8872	−	21.7143i	−1.30687	−	0.949500i	−0.999997	+	0.00224936i	$0.999284\pi$
$524$	−30.7666			−1.34404
$525$	−28.9498	+	18.3635i	−1.26347	+	0.801449i
$526$	−8.49599			−0.370443
$527$	21.4036	+	15.5506i	0.932353	+	0.677394i
$528$	3.37115	+	10.3753i	0.146710	+	0.451528i
$529$	0.309017	+	0.951057i	0.0134355	+	0.0413503i
$530$	−11.4168	−	16.8032i	−0.495915	−	0.729884i
$531$	−2.31653	+	7.12955i	−0.100529	+	0.309396i
$532$	−44.9361			−1.94823
$533$	−0.0863916	+	0.265886i	−0.00374204	+	0.0115168i
$534$	36.2868	−	26.3639i	1.57028	−	1.14088i
$535$	18.7164	−	24.1238i	0.809181	−	1.04296i
$536$	9.78311	+	7.10785i	0.422566	+	0.307012i
$537$	16.9911	−	12.3448i	0.733221	−	0.532716i
$538$	−32.7103	+	23.7655i	−1.41024	+	1.02460i
$539$	−22.8369	−	16.5920i	−0.983657	−	0.714669i
$540$	−26.8739	−	39.5528i	−1.15647	−	1.70208i
$541$	4.35351	−	3.16301i	0.187172	−	0.135989i	−0.490253	−	0.871580i	$-0.663096\pi$
$541$	4.35351	−	3.16301i	0.187172	−	0.135989i	0.677425	+	0.735592i	$0.263096\pi$
$542$	−7.88075	+	24.2545i	−0.338507	+	1.04182i
$543$	0.876367			0.0376085
$544$	2.07045	−	6.37220i	0.0887699	−	0.273206i
$545$	0.457689	−	14.5148i	0.0196052	−	0.621747i
$546$	−3.37767	−	10.3954i	−0.144551	−	0.444882i
$547$	10.3125	+	31.7386i	0.440930	+	1.35704i	0.886886	+	0.461988i	$0.152864\pi$
$547$	10.3125	+	31.7386i	0.440930	+	1.35704i	−0.445956	+	0.895055i	$0.647136\pi$
$548$	8.64273	+	6.27931i	0.369199	+	0.268239i
$549$	−2.02855			−0.0865765
$550$	23.2588	−	14.7536i	0.991758	−	0.629094i
$551$	−4.09585			−0.174489
$552$	5.60707	+	4.07378i	0.238653	+	0.173391i
$553$	−3.14956	−	9.69335i	−0.133933	−	0.412203i
$554$	4.50899	+	13.8772i	0.191569	+	0.589588i
$555$	−38.4319	+	11.1611i	−1.63134	+	0.473762i
$556$	−4.73050	+	14.5590i	−0.200618	+	0.617439i
$557$	25.5294			1.08172			0.540859	−	0.841113i	$-0.318099\pi$
$557$	25.5294			1.08172			0.540859	+	0.841113i	$0.318099\pi$
$558$	−2.49617	+	7.68241i	−0.105671	+	0.325222i
$559$	−0.263221	+	0.191241i	−0.0111331	+	0.00808864i
$560$	−0.953652	+	30.2435i	−0.0402992	+	1.27802i
$561$	13.0654	+	9.49257i	0.551622	+	0.400777i
$562$	30.7783	−	22.3618i	1.29831	−	0.943274i
$563$	8.88658	−	6.45648i	0.374525	−	0.272108i	−0.384560	−	0.923100i	$-0.625647\pi$
$563$	8.88658	−	6.45648i	0.374525	−	0.272108i	0.759085	+	0.650992i	$0.225647\pi$
$564$	54.1302	+	39.3279i	2.27929	+	1.65600i
$565$	0.428680	−	13.5948i	0.0180347	−	0.571940i
$566$	−2.27338	+	1.65170i	−0.0955571	+	0.0694263i
$567$	9.44936	−	29.0822i	0.396836	−	1.22134i
$568$	−61.8549			−2.59537
$569$	5.03071	−	15.4829i	0.210899	−	0.649079i	−0.788521	−	0.615008i	$-0.789153\pi$
$569$	5.03071	−	15.4829i	0.210899	−	0.649079i	0.999419	−	0.0340710i	$-0.0108472\pi$
$570$	21.4739	−	6.23628i	0.899443	−	0.261209i
$571$	−10.2766	−	31.6282i	−0.430063	−	1.32360i	−0.898062	−	0.439870i	$-0.855025\pi$
$571$	−10.2766	−	31.6282i	−0.430063	−	1.32360i	0.467998	−	0.883729i	$-0.344975\pi$
$572$	1.78456	+	5.49231i	0.0746162	+	0.229645i
$573$	−28.9962	−	21.0670i	−1.21133	−	0.880086i
$574$	4.51032			0.188257
$575$	1.84161	−	4.64849i	0.0768004	−	0.193856i
$576$	5.57890			0.232454
$577$	0.161998	+	0.117698i	0.00674405	+	0.00489984i	0.591152	−	0.806560i	$-0.298673\pi$
$577$	0.161998	+	0.117698i	0.00674405	+	0.00489984i	−0.584408	+	0.811460i	$0.698673\pi$
$578$	2.76447	+	8.50817i	0.114987	+	0.353893i
$579$	−11.3512	−	34.9355i	−0.471741	−	1.45187i
$580$	−0.417335	+	13.2351i	−0.0173289	+	0.549556i
$581$	9.48584	−	29.1944i	0.393539	−	1.21119i
$582$	−10.1773			−0.421863
$583$	−2.64753	+	8.14827i	−0.109650	+	0.337467i
$584$	−24.4623	+	17.7729i	−1.01226	+	0.735449i
$585$	−0.476424	−	0.701197i	−0.0196977	−	0.0289909i
$586$	−54.9656	−	39.9349i	−2.27061	−	1.64969i
$587$	−12.9787	+	9.42954i	−0.535686	+	0.389199i	−0.822480	−	0.568793i	$-0.807410\pi$
$587$	−12.9787	+	9.42954i	−0.535686	+	0.389199i	0.286794	+	0.957992i	$0.407410\pi$
$588$	−59.9393	+	43.5485i	−2.47186	+	1.79591i
$589$	−12.4986	−	9.08076i	−0.514995	−	0.374166i
$590$	−43.2063	+	55.6891i	−1.77878	+	2.29268i
$591$	−6.57939	+	4.78020i	−0.270640	+	0.196631i
$592$	−10.9151	+	33.5932i	−0.448608	+	1.38067i
$593$	−16.1053			−0.661367			−0.330683	−	0.943742i	$-0.607279\pi$
$593$	−16.1053			−0.661367			−0.330683	+	0.943742i	$0.607279\pi$
$594$	−9.47665	+	29.1661i	−0.388832	+	1.19670i
$595$	25.1738	+	37.0506i	1.03203	+	1.51893i
$596$	−16.6605	−	51.2758i	−0.682441	−	2.10034i
$597$	−6.16655	−	18.9787i	−0.252380	−	0.776746i
$598$	1.28969	+	0.937017i	0.0527395	+	0.0383175i
$599$	2.28193			0.0932371			0.0466185	−	0.998913i	$-0.485155\pi$
$599$	2.28193			0.0932371			0.0466185	+	0.998913i	$0.485155\pi$
$600$	−8.61088	−	33.5667i	−0.351538	−	1.37036i
$601$	11.1455			0.454633			0.227316	−	0.973821i	$-0.427005\pi$
$601$	11.1455			0.454633			0.227316	+	0.973821i	$0.427005\pi$
$602$	4.24658	+	3.08532i	0.173078	+	0.125748i
$603$	0.482618	+	1.48535i	0.0196537	+	0.0604880i
$604$	27.9410	+	85.9935i	1.13690	+	3.49902i
$605$	12.2127	+	4.39830i	0.496516	+	0.178816i
$606$	10.1083	−	31.1102i	0.410622	−	1.26376i
$607$	−27.9204			−1.13325			−0.566627	−	0.823974i	$-0.691752\pi$
$607$	−27.9204			−1.13325			−0.566627	+	0.823974i	$0.691752\pi$
$608$	−1.20904	+	3.72104i	−0.0490330	+	0.150908i
$609$	−8.55131	+	6.21289i	−0.346517	+	0.251759i
$610$	−17.9449	−	6.46273i	−0.726569	−	0.261668i
$611$	5.96825	+	4.33619i	0.241450	+	0.175423i
$612$	−8.12740	+	5.90490i	−0.328531	+	0.238691i
$613$	−8.41754	+	6.11570i	−0.339981	+	0.247011i	−0.744654	−	0.667451i	$-0.767385\pi$
$613$	−8.41754	+	6.11570i	−0.339981	+	0.247011i	0.404673	+	0.914462i	$0.367385\pi$
$614$	48.9663	+	35.5761i	1.97612	+	1.43574i
$615$	−1.41741	+	0.411633i	−0.0571556	+	0.0165986i
$616$	36.1311	−	26.2508i	1.45577	−	1.05768i
$617$	7.52420	−	23.1571i	0.302913	−	0.932270i	−0.677535	−	0.735491i	$-0.736952\pi$
$617$	7.52420	−	23.1571i	0.302913	−	0.932270i	0.980448	−	0.196780i	$-0.0630483\pi$
$618$	−63.9141			−2.57100
$619$	−11.9428	+	36.7561i	−0.480021	+	1.47735i	0.359043	+	0.933321i	$0.383103\pi$
$619$	−11.9428	+	36.7561i	−0.480021	+	1.47735i	−0.839064	+	0.544032i	$0.816897\pi$
$620$	−30.6165	+	39.4619i	−1.22959	+	1.58483i
$621$	1.72031	+	5.29458i	0.0690338	+	0.212464i
$622$	−16.6584	−	51.2692i	−0.667940	−	2.05571i
$623$	−42.4470	−	30.8395i	−1.70060	−	1.23556i
$624$	3.15702			0.126382
$625$	−21.9128	+	12.0345i	−0.876511	+	0.481382i
$626$	33.6106			1.34335
$627$	−7.62953	−	5.54318i	−0.304694	−	0.221373i
$628$	−10.8617	−	33.4288i	−0.433428	−	1.33396i
$629$	16.1584	+	49.7303i	0.644276	+	1.98288i
$630$	−8.38366	+	10.8058i	−0.334013	+	0.430513i
$631$	−2.75952	+	8.49292i	−0.109855	+	0.338098i	−0.990839	−	0.135047i	$-0.956881\pi$
$631$	−2.75952	+	8.49292i	−0.109855	+	0.338098i	0.880985	+	0.473145i	$0.156881\pi$
$632$	10.3024			0.409809
$633$	4.86273	−	14.9659i	0.193276	−	0.594843i
$634$	−21.1894	+	15.3950i	−0.841538	+	0.611413i
$635$	9.85005	−	2.86057i	0.390887	−	0.113518i
$636$	18.1924	+	13.2176i	0.721376	+	0.524111i
$637$	−6.60875	+	4.80154i	−0.261848	+	0.190244i
$638$	6.87027	−	4.99155i	0.271997	−	0.197617i
$639$	−6.46299	−	4.69564i	−0.255672	−	0.185757i
$640$	43.1559	+	15.5423i	1.70589	+	0.614362i
$641$	−4.24932	+	3.08731i	−0.167838	+	0.121941i	−0.668533	−	0.743682i	$-0.733078\pi$
$641$	−4.24932	+	3.08731i	−0.167838	+	0.121941i	0.500695	+	0.865623i	$0.333078\pi$
$642$	−15.8818	+	48.8791i	−0.626804	+	1.92910i
$643$	19.0025			0.749386			0.374693	−	0.927149i	$-0.377748\pi$
$643$	19.0025			0.749386			0.374693	+	0.927149i	$0.377748\pi$
$644$	5.22639	−	16.0852i	0.205949	−	0.633845i
$645$	−1.61611	−	0.582028i	−0.0636341	−	0.0229173i
$646$	−9.02852	−	27.7869i	−0.355222	−	1.09326i
$647$	−10.0142	−	30.8204i	−0.393698	−	1.21168i	−0.929971	−	0.367632i	$-0.880168\pi$
$647$	−10.0142	−	30.8204i	−0.393698	−	1.21168i	0.536274	−	0.844044i	$-0.319832\pi$
$648$	25.0063	+	18.1682i	0.982341	+	0.713713i
$649$	29.7262			1.16686
$650$	−1.98060	−	7.72075i	−0.0776857	−	0.302833i
$651$	−39.8689			−1.56259
$652$	77.1338	+	56.0410i	3.02079	+	2.19474i
$653$	−4.27825	−	13.1671i	−0.167421	−	0.515268i	0.831786	−	0.555097i	$-0.187319\pi$
$653$	−4.27825	−	13.1671i	−0.167421	−	0.515268i	−0.999207	+	0.0398288i	$0.987319\pi$
$654$	7.55367	+	23.2478i	0.295372	+	0.909061i
$655$	−10.0649	−	14.8134i	−0.393268	−	0.578808i
$656$	−0.402561	+	1.23896i	−0.0157174	+	0.0483731i
$657$	−3.90519			−0.152356
$658$	36.7782	−	113.192i	1.43376	−	4.41267i
$659$	39.3157	−	28.5645i	1.53152	−	1.11271i	0.576134	−	0.817355i	$-0.304560\pi$
$659$	39.3157	−	28.5645i	1.53152	−	1.11271i	0.955386	−	0.295360i	$-0.0954395\pi$
$660$	−18.6893	+	24.0888i	−0.727478	+	0.937654i
$661$	12.4037	+	9.01178i	0.482446	+	0.350518i	0.802272	−	0.596959i	$-0.203624\pi$
$661$	12.4037	+	9.01178i	0.482446	+	0.350518i	−0.319826	+	0.947476i	$0.603624\pi$
$662$	−47.9558	+	34.8420i	−1.86386	+	1.35417i
$663$	3.78098	−	2.74704i	0.146841	−	0.106686i
$664$	25.1028	+	18.2383i	0.974179	+	0.707783i
$665$	−14.7003	−	21.6357i	−0.570051	−	0.838997i
$666$	−12.9162	+	9.38419i	−0.500494	+	0.363630i
$667$	0.476377	−	1.46614i	0.0184454	−	0.0567691i
$668$	76.6353			2.96511
$669$	0.520584	−	1.60219i	0.0201269	−	0.0619443i
$670$	−0.462809	+	14.6772i	−0.0178799	+	0.567030i
$671$	2.48572	+	7.65027i	0.0959603	+	0.295335i
$672$	3.12012	+	9.60274i	0.120361	+	0.370434i
$673$	−14.0841	−	10.2327i	−0.542904	−	0.394443i	0.282259	−	0.959338i	$-0.408916\pi$
$673$	−14.0841	−	10.2327i	−0.542904	−	0.394443i	−0.825162	+	0.564896i	$0.808916\pi$
$674$	−45.0118			−1.73379
$675$	10.2523	−	25.8784i	0.394612	−	0.996059i
$676$	−48.2668			−1.85642
$677$	−22.3079	−	16.2076i	−0.857363	−	0.622911i	0.0698034	−	0.997561i	$-0.477763\pi$
$677$	−22.3079	−	16.2076i	−0.857363	−	0.622911i	−0.927166	+	0.374650i	$0.877763\pi$
$678$	7.07491	+	21.7743i	0.271710	+	0.836238i
$679$	3.67886	+	11.3224i	0.141182	+	0.434512i
$680$	−43.4817	+	12.6276i	−1.66745	+	0.484246i
$681$	4.67420	−	14.3857i	0.179116	−	0.551261i
$682$	32.0314			1.22654
$683$	4.84259	−	14.9040i	0.185297	−	0.570284i	−0.814657	−	0.579943i	$-0.803075\pi$
$683$	4.84259	−	14.9040i	0.185297	−	0.570284i	0.999953	+	0.00965927i	$0.00307469\pi$
$684$	4.74599	−	3.44816i	0.181467	−	0.131844i
$685$	−0.195990	+	6.21547i	−0.00748837	+	0.237481i
$686$	46.3576	+	33.6808i	1.76994	+	1.28594i
$687$	−18.2959	+	13.2928i	−0.698033	+	0.507151i
$688$	−1.22654	+	0.891131i	−0.0467613	+	0.0339741i
$689$	2.00585	+	1.45733i	0.0764167	+	0.0555200i
$690$	−0.265253	+	8.41206i	−0.0100980	+	0.320242i
$691$	−23.2110	+	16.8638i	−0.882988	+	0.641529i	−0.934040	−	0.357167i	$-0.883743\pi$
$691$	−23.2110	+	16.8638i	−0.882988	+	0.641529i	0.0510520	+	0.998696i	$0.483743\pi$
$692$	1.26569	−	3.89540i	0.0481144	−	0.148081i
$693$	5.76801			0.219109
$694$	1.09101	−	3.35778i	0.0414141	−	0.127460i
$695$	−8.55735	+	2.48515i	−0.324599	+	0.0942673i
$696$	−3.30164	−	10.1614i	−0.125148	−	0.385167i
$697$	0.595938	+	1.83411i	0.0225728	+	0.0694718i
$698$	−47.3426	−	34.3964i	−1.79194	−	1.30192i
$699$	10.1843			0.385206
$700$	−71.4100	+	45.2969i	−2.69904	+	1.71206i
$701$	−35.6169			−1.34523			−0.672616	−	0.739991i	$-0.734830\pi$
$701$	−35.6169			−1.34523			−0.672616	+	0.739991i	$0.734830\pi$
$702$	7.17979	+	5.21642i	0.270984	+	0.196881i
$703$	−9.43566	−	29.0400i	−0.355873	−	1.09526i
$704$	−6.83621	−	21.0397i	−0.257649	−	0.792963i
$705$	−1.22750	+	38.9281i	−0.0462303	+	1.46612i
$706$	7.21834	−	22.2158i	0.271666	−	0.836101i
$707$	−38.2643			−1.43908
$708$	24.1099	−	74.2027i	0.906107	−	2.78871i
$709$	21.0191	−	15.2713i	0.789389	−	0.573525i	−0.118393	−	0.992967i	$-0.537774\pi$
$709$	21.0191	−	15.2713i	0.789389	−	0.573525i	0.907782	+	0.419442i	$0.137774\pi$
$710$	−42.2130	−	62.1288i	−1.58423	−	2.33165i
$711$	1.07646	+	0.782097i	0.0403705	+	0.0293309i
$712$	42.9061	−	31.1731i	1.60797	−	1.16826i
$713$	4.70420	−	3.41780i	0.176174	−	0.127998i
$714$	−60.9990	−	44.3183i	−2.28283	−	1.65857i
$715$	−2.06063	+	2.65596i	−0.0770631	+	0.0993274i
$716$	41.9117	−	30.4506i	1.56631	−	1.13799i
$717$	11.6877	−	35.9709i	0.436484	−	1.34336i
$718$	53.7171			2.00470
$719$	−5.03881	+	15.5079i	−0.187916	+	0.578345i	−0.999986	−	0.00521377i	$-0.998340\pi$
$719$	−5.03881	+	15.5079i	−0.187916	+	0.578345i	0.812071	+	0.583559i	$0.198340\pi$
$720$	−2.22001	−	3.26739i	−0.0827348	−	0.121768i
$721$	23.1035	+	71.1051i	0.860418	+	2.64809i
$722$	−8.91818	−	27.4473i	−0.331900	−	1.02148i
$723$	−6.97135	−	5.06498i	−0.259267	−	0.188369i
$724$	2.16172			0.0803396
$725$	−6.50891	+	4.12874i	−0.241735	+	0.153338i
$726$	−21.8495			−0.810910
$727$	35.4669	+	25.7682i	1.31540	+	0.955691i	0.999977	+	0.00673802i	$0.00214479\pi$
$727$	35.4669	+	25.7682i	1.31540	+	0.955691i	0.315418	+	0.948953i	$0.397855\pi$
$728$	−3.99381	−	12.2917i	−0.148021	−	0.455560i
$729$	9.27079	+	28.5326i	0.343363	+	1.05676i
$730$	−34.5460	−	12.4415i	−1.27860	−	0.460479i
$731$	−0.693545	+	2.13451i	−0.0256517	+	0.0789478i
$732$	21.1127			0.780349
$733$	16.1591	−	49.7325i	0.596849	−	1.83691i	0.0515483	−	0.998671i	$-0.483584\pi$
$733$	16.1591	−	49.7325i	0.596849	−	1.83691i	0.545300	−	0.838241i	$-0.316416\pi$
$734$	11.9576	−	8.68774i	0.441365	−	0.320670i
$735$	−40.5760	−	14.6131i	−1.49667	−	0.539013i
$736$	−1.19135	−	0.865568i	−0.0439138	−	0.0319053i
$737$	5.01029	−	3.64019i	0.184557	−	0.134088i
$738$	−0.476365	+	0.346099i	−0.0175352	+	0.0127401i
$739$	2.72584	+	1.98044i	0.100271	+	0.0728515i	0.636791	−	0.771036i	$-0.280261\pi$
$739$	2.72584	+	1.98044i	0.100271	+	0.0728515i	−0.536520	+	0.843888i	$0.680261\pi$
$740$	−94.7993	+	27.5308i	−3.48489	+	1.01205i
$741$	−2.20790	+	1.60413i	−0.0811092	+	0.0589293i
$742$	12.3606	−	38.0422i	0.453774	−	1.39657i
$743$	−53.6642			−1.96875			−0.984374	−	0.176088i	$-0.943656\pi$
$743$	−53.6642			−1.96875			−0.984374	+	0.176088i	$0.943656\pi$
$744$	12.4534	−	38.3277i	0.456564	−	1.40516i
$745$	19.2379	−	24.7959i	0.704821	−	0.908451i
$746$	12.5392	+	38.5917i	0.459092	+	1.41294i
$747$	1.23837	+	3.81131i	0.0453095	+	0.139448i
$748$	32.2282	+	23.4151i	1.17838	+	0.856142i
$749$	60.1195			2.19672
$750$	27.8388	−	31.5567i	1.01653	−	1.15229i
$751$	8.61078			0.314212			0.157106	−	0.987582i	$-0.449784\pi$
$751$	8.61078			0.314212			0.157106	+	0.987582i	$0.449784\pi$
$752$	27.8104	+	20.2055i	1.01414	+	0.736817i
$753$	−1.73333	−	5.33464i	−0.0631660	−	0.194405i
$754$	−0.759416	−	2.33724i	−0.0276563	−	0.0851174i
$755$	−32.2634	+	41.5846i	−1.17419	+	1.51342i
$756$	29.0956	−	89.5470i	1.05820	−	3.25679i
$757$	7.85546			0.285512			0.142756	−	0.989758i	$-0.454404\pi$
$757$	7.85546			0.285512			0.142756	+	0.989758i	$0.454404\pi$
$758$	−8.69562	+	26.7624i	−0.315839	+	0.972053i
$759$	2.87159	−	2.08633i	0.104232	−	0.0757290i
$760$	25.3911	−	7.37387i	0.921032	−	0.267478i
$761$	−0.197573	−	0.143545i	−0.00716203	−	0.00520352i	0.584198	−	0.811611i	$-0.301409\pi$
$761$	−0.197573	−	0.143545i	−0.00716203	−	0.00520352i	−0.591361	+	0.806407i	$0.701409\pi$
$762$	−13.9678	+	10.1482i	−0.505999	+	0.367630i
$763$	23.1330	−	16.8071i	0.837470	−	0.608457i
$764$	−71.5244	−	51.9655i	−2.58766	−	1.88005i
$765$	−5.50185	−	1.98145i	−0.198920	−	0.0716394i
$766$	54.7764	−	39.7974i	1.97915	−	1.43794i
$767$	2.65830	−	8.18140i	0.0959855	−	0.295413i
$768$	−46.9787			−1.69520
$769$	−12.0179	+	36.9873i	−0.433377	+	1.33380i	0.461364	+	0.887211i	$0.347360\pi$
$769$	−12.0179	+	36.9873i	−0.433377	+	1.33380i	−0.894741	+	0.446586i	$0.852640\pi$
$770$	51.0249	+	18.3762i	1.83881	+	0.662232i
$771$	13.9865	+	43.0461i	0.503712	+	1.55027i
$772$	−27.9999	−	86.1748i	−1.00774	−	3.10150i
$773$	−2.24509	−	1.63115i	−0.0807503	−	0.0586685i	0.546678	−	0.837343i	$-0.315892\pi$
$773$	−2.24509	−	1.63115i	−0.0807503	−	0.0586685i	−0.627428	+	0.778675i	$0.715892\pi$
$774$	−0.685260			−0.0246312
$775$	−29.0158	−	1.83170i	−1.04228	−	0.0657967i
$776$	−12.0338			−0.431988
$777$	−63.7498	−	46.3169i	−2.28701	−	1.66161i
$778$	10.5609	+	32.5031i	0.378627	+	1.16529i
$779$	−0.347998	−	1.07103i	−0.0124683	−	0.0383735i
$780$	4.95852	+	7.29791i	0.177543	+	0.261307i
$781$	−9.78910	+	30.1277i	−0.350281	+	1.07806i
$782$	10.9966			0.393238
$783$	2.65202	−	8.16207i	0.0947753	−	0.291688i
$784$	−30.7950	+	22.3738i	−1.09982	+	0.799066i
$785$	12.5420	−	16.1655i	0.447642	−	0.576970i
$786$	24.3883	+	17.7191i	0.869902	+	0.632021i
$787$	34.5929	−	25.1332i	1.23310	−	0.895902i	0.235985	−	0.971757i	$-0.424168\pi$
$787$	34.5929	−	25.1332i	1.23310	−	0.895902i	0.997119	+	0.0758545i	$0.0241685\pi$
$788$	−16.2292	+	11.7912i	−0.578143	+	0.420046i
$789$	4.42883	+	3.21773i	0.157671	+	0.114554i
$790$	7.03092	+	10.3480i	0.250149	+	0.368167i
$791$	21.6668	−	15.7418i	0.770381	−	0.559715i
$792$	−1.80169	+	5.54504i	−0.0640203	+	0.197034i
$793$	2.32783			0.0826638
$794$	7.45909	−	22.9567i	0.264713	−	0.814703i
$795$	−0.412546	+	13.0832i	−0.0146315	+	0.464013i
$796$	−15.2109	−	46.8144i	−0.539137	−	1.65929i
$797$	10.2635	+	31.5878i	0.363552	+	1.11890i	0.950883	+	0.309551i	$0.100179\pi$
$797$	10.2635	+	31.5878i	0.363552	+	1.11890i	−0.587331	+	0.809347i	$0.699821\pi$
$798$	35.6203	+	25.8797i	1.26095	+	0.916130i
$799$	50.8884			1.80030
$800$	1.82958	+	7.13203i	0.0646854	+	0.252155i
$801$	6.84957			0.242018
$802$	48.8222	+	35.4714i	1.72397	+	1.25254i
$803$	4.78529	+	14.7276i	0.168869	+	0.519727i
$804$	−5.02298	−	15.4591i	−0.177147	−	0.545202i
$805$	9.45439	−	2.74567i	0.333224	−	0.0967721i
$806$	2.86444	−	8.81582i	0.100895	−	0.310524i
$807$	26.0522			0.917081
$808$	11.9522	−	36.7851i	0.420478	−	1.29410i
$809$	37.6005	−	27.3183i	1.32196	−	0.960461i	0.322056	−	0.946721i	$-0.395626\pi$
$809$	37.6005	−	27.3183i	1.32196	−	0.960461i	0.999906	−	0.0137407i	$-0.00437393\pi$
$810$	−1.18297	+	37.5160i	−0.0415654	+	1.31818i
$811$	22.1882	+	16.1207i	0.779132	+	0.566073i	0.904718	−	0.426010i	$-0.140081\pi$
$811$	22.1882	+	16.1207i	0.779132	+	0.566073i	−0.125586	+	0.992083i	$0.540081\pi$
$812$	−21.0934	+	15.3252i	−0.740232	+	0.537810i
$813$	13.2941	−	9.65875i	0.466246	−	0.338747i
$814$	51.2177	+	37.2118i	1.79518	+	1.30427i
$815$	−1.74915	+	55.4713i	−0.0612700	+	1.94308i
$816$	17.6183	−	12.8005i	0.616764	−	0.448105i
$817$	0.404995	−	1.24645i	0.0141690	−	0.0436077i
$818$	32.1980			1.12578
$819$	0.515810	−	1.58750i	0.0180239	−	0.0554717i
$820$	−3.49630	+	1.01537i	−0.122096	+	0.0354582i
$821$	10.0536	+	30.9418i	0.350873	+	1.07988i	0.958364	+	0.285549i	$0.0921759\pi$
$821$	10.0536	+	30.9418i	0.350873	+	1.07988i	−0.607491	+	0.794326i	$0.707824\pi$
$822$	−3.23460	−	9.95508i	−0.112820	−	0.347223i
$823$	4.33547	+	3.14990i	0.151125	+	0.109799i	0.660778	−	0.750581i	$-0.270226\pi$
$823$	4.33547	+	3.14990i	0.151125	+	0.109799i	−0.509653	+	0.860380i	$0.670226\pi$
$824$	−75.5730			−2.63271
$825$	−17.7121	−	1.11813i	−0.616658	−	0.0389282i
$826$	−138.784			−4.82891
$827$	34.5724	+	25.1183i	1.20220	+	0.873449i	0.994499	−	0.104744i	$-0.0334023\pi$
$827$	34.5724	+	25.1183i	1.20220	+	0.873449i	0.207700	+	0.978193i	$0.433402\pi$
$828$	0.682301	+	2.09991i	0.0237116	+	0.0729768i
$829$	7.17962	+	22.0966i	0.249358	+	0.767446i	0.994889	+	0.100975i	$0.0321962\pi$
$829$	7.17962	+	22.0966i	0.249358	+	0.767446i	−0.745530	+	0.666472i	$0.767804\pi$
$830$	−1.18754	+	37.6608i	−0.0412201	+	1.30722i
$831$	2.90534	−	8.94171i	0.100785	−	0.310184i
$832$	−6.40198			−0.221949
$833$	−17.4130	+	53.5917i	−0.603325	+	1.85684i
$834$	12.1347	−	8.81634i	0.420189	−	0.305285i
$835$	25.0702	+	36.8982i	0.867592	+	1.27691i
$836$	−18.8196	−	13.6733i	−0.650890	−	0.472899i
$837$	26.1885	−	19.0271i	0.905207	−	0.657671i
$838$	−32.0534	+	23.2881i	−1.10727	+	0.804476i
$839$	−8.96331	−	6.51222i	−0.309448	−	0.224827i	0.422212	−	0.906497i	$-0.361254\pi$
$839$	−8.96331	−	6.51222i	−0.309448	−	0.224827i	−0.731659	+	0.681670i	$0.761254\pi$
$840$	41.8262	−	53.9102i	1.44314	−	1.86008i
$841$	21.5389	−	15.6489i	0.742719	−	0.539617i
$842$	−9.12863	+	28.0950i	−0.314593	+	0.968218i
$843$	−24.5135			−0.844288
$844$	11.9948	−	36.9162i	0.412878	−	1.27071i
$845$	−15.7899	−	23.2394i	−0.543188	−	0.799460i
$846$	4.80136	+	14.7771i	0.165074	+	0.508046i
$847$	7.89808	+	24.3078i	0.271381	+	0.835226i
$848$	9.34670	+	6.79078i	0.320967	+	0.233196i
$849$	1.81063			0.0621408
$850$	−42.3577	−	35.0565i	−1.45286	−	1.20243i
$851$	11.4925			0.393958
$852$	67.2654	+	48.8712i	2.30447	+	1.67430i
$853$	−0.905639	−	2.78727i	−0.0310085	−	0.0954344i	0.934354	−	0.356345i	$-0.115977\pi$
$853$	−0.905639	−	2.78727i	−0.0310085	−	0.0954344i	−0.965363	+	0.260911i	$0.915977\pi$
$854$	−11.6052	−	35.7171i	−0.397122	−	1.22222i
$855$	3.21280	+	1.15707i	0.109876	+	0.0395708i
$856$	−18.7789	+	57.7954i	−0.641849	+	1.97541i
$857$	52.8434			1.80510			0.902548	−	0.430590i	$-0.141694\pi$
$857$	52.8434			1.80510			0.902548	+	0.430590i	$0.141694\pi$
$858$	1.74854	−	5.38146i	0.0596942	−	0.183720i
$859$	13.4254	−	9.75410i	0.458067	−	0.332805i	−0.334705	−	0.942323i	$-0.608637\pi$
$859$	13.4254	−	9.75410i	0.458067	−	0.332805i	0.792773	+	0.609517i	$0.208637\pi$
$860$	−3.98642	−	1.43568i	−0.135936	−	0.0489562i
$861$	−2.35116	−	1.70822i	−0.0801274	−	0.0582160i
$862$	−65.9150	+	47.8901i	−2.24507	+	1.63114i
$863$	−44.1667	+	32.0890i	−1.50345	+	1.09232i	−0.534472	+	0.845186i	$0.679489\pi$
$863$	−44.1667	+	32.0890i	−1.50345	+	1.09232i	−0.968981	+	0.247136i	$0.920511\pi$
$864$	−6.63232	−	4.81866i	−0.225636	−	0.163934i
$865$	2.28960	−	0.664928i	0.0778489	−	0.0226082i
$866$	−7.95388	+	5.77883i	−0.270284	+	0.196373i
$867$	1.78127	−	5.48218i	0.0604951	−	0.186185i
$868$	−98.3439			−3.33801
$869$	1.63045	−	5.01802i	0.0553093	−	0.170225i
$870$	7.95318	−	10.2509i	0.269638	−	0.347539i
$871$	−0.553821	−	1.70448i	−0.0187655	−	0.0577543i
$872$	8.93158	+	27.4886i	0.302461	+	0.930880i
$873$	−1.25737	−	0.913531i	−0.0425555	−	0.0309184i
$874$	−6.42146			−0.217209
$875$	−45.1703	−	19.5640i	−1.52703	−	0.661384i
$876$	40.6443			1.37324
$877$	−33.2940	−	24.1895i	−1.12426	−	0.816822i	−0.139410	−	0.990235i	$-0.544520\pi$
$877$	−33.2940	−	24.1895i	−1.12426	−	0.816822i	−0.984849	+	0.173413i	$0.944520\pi$
$878$	7.53112	+	23.1784i	0.254163	+	0.782233i
$879$	13.5280	+	41.6348i	0.456287	+	1.40431i
$880$	−9.60196	+	12.3761i	−0.323682	+	0.417197i
$881$	−3.07902	+	9.47624i	−0.103735	+	0.319263i	−0.989431	−	0.145002i	$-0.953681\pi$
$881$	−3.07902	+	9.47624i	−0.103735	+	0.319263i	0.885697	+	0.464264i	$0.153681\pi$
$882$	−17.2050			−0.579322
$883$	−12.0465	+	37.0753i	−0.405397	+	1.24768i	0.515166	+	0.857090i	$0.327730\pi$
$883$	−12.0465	+	37.0753i	−0.405397	+	1.24768i	−0.920563	+	0.390594i	$0.872270\pi$
$884$	9.32646	−	6.77607i	0.313683	−	0.227904i
$885$	43.6142	−	12.6661i	1.46608	−	0.425765i
$886$	−55.9032	−	40.6161i	−1.87810	−	1.36452i
$887$	−13.0922	+	9.51207i	−0.439594	+	0.319384i	−0.785474	−	0.618895i	$-0.787581\pi$
$887$	−13.0922	+	9.51207i	−0.439594	+	0.319384i	0.345879	+	0.938279i	$0.387581\pi$
$888$	64.4393	−	46.8179i	2.16244	−	1.57110i
$889$	16.3390	+	11.8710i	0.547992	+	0.398139i
$890$	60.5925	+	21.8219i	2.03106	+	0.731472i
$891$	12.8067	−	9.30459i	0.429040	−	0.311715i
$892$	1.28411	−	3.95210i	0.0429953	−	0.132326i
$893$	−29.7163			−0.994417
$894$	−16.3243	+	50.2409i	−0.545965	+	1.68031i
$895$	28.3721	+	10.2180i	0.948376	+	0.341550i
$896$	27.9094	+	85.8964i	0.932389	+	2.86960i
$897$	−0.317416	−	0.976905i	−0.0105982	−	0.0326179i
$898$	59.0974	+	42.9368i	1.97211	+	1.43282i
$899$	−8.96389			−0.298963
$900$	4.06622	−	10.2637i	0.135541	−	0.342125i
$901$	17.1029			0.569781
$902$	1.88896	+	1.37241i	0.0628956	+	0.0456964i
$903$	−1.04516	−	3.21666i	−0.0347806	−	0.107044i
$904$	8.36548	+	25.7463i	0.278232	+	0.856309i
$905$	0.707178	+	1.04082i	0.0235074	+	0.0345980i
$906$	27.3770	−	84.2579i	0.909541	−	2.79928i
$907$	46.1780			1.53331			0.766657	−	0.642057i	$-0.221919\pi$
$907$	46.1780			1.53331			0.766657	+	0.642057i	$0.221919\pi$
$908$	11.5298	−	35.4849i	0.382628	−	1.17761i
$909$	4.04134	−	2.93621i	0.134043	−	0.0973879i
$910$	9.62053	−	12.4000i	0.318918	−	0.411056i
$911$	−36.6595	−	26.6347i	−1.21458	−	0.882446i	−0.218944	−	0.975737i	$-0.570261\pi$
$911$	−36.6595	−	26.6347i	−1.21458	−	0.882446i	−0.995639	+	0.0932912i	$0.970261\pi$
$912$	−10.2882	+	7.47482i	−0.340676	+	0.247516i
$913$	12.8561	−	9.34050i	0.425475	−	0.309126i
$914$	5.81369	+	4.22389i	0.192300	+	0.139714i
$915$	6.90675	+	10.1653i	0.228330	+	0.336054i
$916$	−45.1302	+	32.7890i	−1.49114	+	1.08338i
$917$	10.8969	−	33.5373i	0.359849	−	1.10750i
$918$	61.2186			2.02052
$919$	−1.43991	+	4.43159i	−0.0474983	+	0.146185i	−0.971993	−	0.235011i	$-0.924488\pi$
$919$	−1.43991	+	4.43159i	−0.0474983	+	0.146185i	0.924494	+	0.381195i	$0.124488\pi$
$920$	−0.313640	+	9.94655i	−0.0103404	+	0.327928i
$921$	−12.0515	−	37.0906i	−0.397109	−	1.22218i
$922$	−28.7044	−	88.3432i	−0.945331	−	2.90943i
$923$	7.41650	+	5.38840i	0.244117	+	0.177361i
$924$	−60.0322			−1.97491
$925$	−44.2678	−	36.6374i	−1.45552	−	1.20463i
$926$	59.1921			1.94517
$927$	−7.89635	−	5.73703i	−0.259350	−	0.188429i
$928$	0.701510	+	2.15903i	0.0230282	+	0.0708735i
$929$	−1.72035	−	5.29468i	−0.0564427	−	0.173713i	0.918861	−	0.394582i	$-0.129111\pi$
$929$	−1.72035	−	5.29468i	−0.0564427	−	0.173713i	−0.975303	+	0.220869i	$0.929111\pi$
$930$	46.9963	−	13.6483i	1.54107	−	0.447544i
$931$	10.1683	−	31.2948i	0.333253	−	1.02565i
$932$	25.1215			0.822881
$933$	−10.7337	+	33.0350i	−0.351406	+	1.08152i
$934$	−42.2576	+	30.7019i	−1.38271	+	1.00460i
$935$	−0.730832	+	23.1771i	−0.0239008	+	0.757972i
$936$	1.36501	+	0.991741i	0.0446169	+	0.0324161i
$937$	19.9772	−	14.5143i	0.652627	−	0.474161i	−0.211538	−	0.977370i	$-0.567847\pi$
$937$	19.9772	−	14.5143i	0.652627	−	0.474161i	0.864165	+	0.503208i	$0.167847\pi$
$938$	−23.3918	+	16.9951i	−0.763768	+	0.554910i
$939$	−17.5207	−	12.7295i	−0.571765	−	0.415412i
$940$	−3.02785	+	96.0232i	−0.0987576	+	3.13193i
$941$	5.89920	−	4.28602i	0.192308	−	0.139720i	−0.487465	−	0.873143i	$-0.662078\pi$
$941$	5.89920	−	4.28602i	0.192308	−	0.139720i	0.679773	+	0.733422i	$0.262078\pi$
$942$	−10.6425	+	32.7541i	−0.346750	+	1.06719i
$943$	0.423856			0.0138027
$944$	12.3869	−	38.1231i	0.403160	−	1.24080i
$945$	52.6331	−	15.2853i	1.71215	−	0.497230i
$946$	0.839696	+	2.58432i	0.0273009	+	0.0840234i
$947$	−9.79202	−	30.1367i	−0.318198	−	0.979312i	−0.974418	−	0.224743i	$-0.927846\pi$
$947$	−9.79202	−	30.1367i	−0.318198	−	0.979312i	0.656220	−	0.754569i	$-0.272154\pi$
$948$	−11.2036	−	8.13989i	−0.363876	−	0.264371i
$949$	4.48134			0.145470
$950$	24.7347	+	20.4712i	0.802501	+	0.664174i
$951$	16.8763			0.547252
$952$	−72.1261	−	52.4027i	−2.33762	−	1.69838i
$953$	1.37973	+	4.24636i	0.0446937	+	0.137553i	0.970913	−	0.239431i	$-0.0769610\pi$
$953$	1.37973	+	4.24636i	0.0446937	+	0.137553i	−0.926220	+	0.376984i	$0.876961\pi$
$954$	1.61367	+	4.96637i	0.0522446	+	0.160792i
$955$	1.62195	−	51.4372i	0.0524849	−	1.66447i
$956$	28.8298	−	88.7288i	0.932421	−	2.86970i
$957$	−5.47184			−0.176879
$958$	−21.6477	+	66.6249i	−0.699407	+	2.15255i
$959$	−9.90590	+	7.19706i	−0.319878	+	0.232405i
$960$	−18.9949	−	27.9565i	−0.613057	−	0.902292i
$961$	−2.27400	−	1.65215i	−0.0733547	−	0.0532953i
$962$	14.8218	−	10.7687i	0.477874	−	0.347196i
$963$	−6.34961	+	4.61326i	−0.204613	+	0.148660i
$964$	−17.1961	−	12.4937i	−0.553849	−	0.402395i
$965$	32.3314	−	41.6723i	1.04078	−	1.34148i
$966$	−13.4067	+	9.74054i	−0.431354	+	0.313397i
$967$	−14.8167	+	45.6010i	−0.476471	+	1.46643i	0.367492	+	0.930027i	$0.380217\pi$
$967$	−14.8167	+	45.6010i	−0.476471	+	1.46643i	−0.843963	+	0.536401i	$0.819783\pi$
$968$	−25.8352			−0.830374
$969$	−5.81746	+	17.9043i	−0.186884	+	0.575169i
$970$	−8.21250	−	12.0871i	−0.263687	−	0.388093i
$971$	−2.91551	−	8.97303i	−0.0935633	−	0.287958i	0.893313	−	0.449434i	$-0.148374\pi$
$971$	−2.91551	−	8.97303i	−0.0935633	−	0.287958i	−0.986877	+	0.161476i	$0.948374\pi$
$972$	6.98606	+	21.5009i	0.224078	+	0.689642i
$973$	−14.1947	−	10.3130i	−0.455060	−	0.330621i
$974$	3.03164			0.0971402
$975$	−1.89166	+	4.77483i	−0.0605817	+	0.152917i
$976$	10.8471			0.347206
$977$	36.1798	+	26.2862i	1.15749	+	0.840969i	0.989459	−	0.144812i	$-0.0462577\pi$
$977$	36.1798	+	26.2862i	1.15749	+	0.840969i	0.168035	+	0.985781i	$0.446258\pi$
$978$	−28.8679	−	88.8462i	−0.923093	−	2.84099i
$979$	−8.39324	−	25.8317i	−0.268249	−	0.825586i
$980$	−100.088	−	36.0459i	−3.19719	−	1.15144i
$981$	−1.15353	+	3.55021i	−0.0368295	+	0.113350i
$982$	−30.8892			−0.985714
$983$	−16.2327	+	49.9590i	−0.517741	+	1.59344i	0.260497	+	0.965475i	$0.416114\pi$
$983$	−16.2327	+	49.9590i	−0.517741	+	1.59344i	−0.778238	+	0.627969i	$0.783886\pi$
$984$	2.37659	−	1.72670i	0.0757630	−	0.0550450i
$985$	−10.9864	−	3.95667i	−0.350056	−	0.126070i
$986$	−13.7147	−	9.96428i	−0.436764	−	0.317327i
$987$	−62.0416	+	45.0758i	−1.97481	+	1.43478i
$988$	−5.44618	+	3.95688i	−0.173266	+	0.125885i
$989$	0.399070	+	0.289942i	0.0126897	+	0.00921961i
$990$	−6.79916	+	1.97456i	−0.216092	+	0.0627555i
$991$	−29.6353	+	21.5313i	−0.941397	+	0.683965i	−0.948757	−	0.316008i	$-0.897657\pi$
$991$	−29.6353	+	21.5313i	−0.941397	+	0.683965i	0.00735921	+	0.999973i	$0.497657\pi$
$992$	−2.64602	+	8.14361i	−0.0840112	+	0.258560i
$993$	38.1945			1.21207
$994$	45.7028	−	140.659i	1.44960	−	4.46142i
$995$	17.5640	−	22.6384i	0.556817	−	0.717687i
$996$	−12.8887	−	39.6672i	−0.408393	−	1.25690i
$997$	0.366933	+	1.12930i	0.0116209	+	0.0357654i	0.956699	−	0.291080i	$-0.0940145\pi$
$997$	0.366933	+	1.12930i	0.0116209	+	0.0357654i	−0.945078	+	0.326845i	$0.894014\pi$
$998$	65.8096	+	47.8134i	2.08317	+	1.51351i
$999$	63.9793			2.02422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.g.c.116.3	✓	112
25.11	even	5	inner	575.2.g.c.461.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.g.c.116.3	✓	112	1.1	even	1	trivial
575.2.g.c.461.3	yes	112	25.11	even	5	inner

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95531 - 1.42062i) q^{2} +(0.481235 + 1.48109i) q^{3} +(1.18705 + 3.65338i) q^{4} +(-1.37069 + 1.76669i) q^{5} +(1.16310 - 3.57964i) q^{6} -4.40282 q^{7} +(1.37526 - 4.23262i) q^{8} +(0.465011 - 0.337850i) q^{9} +O(q^{10})\)	\(q+(-1.95531 - 1.42062i) q^{2} +(0.481235 + 1.48109i) q^{3} +(1.18705 + 3.65338i) q^{4} +(-1.37069 + 1.76669i) q^{5} +(1.16310 - 3.57964i) q^{6} -4.40282 q^{7} +(1.37526 - 4.23262i) q^{8} +(0.465011 - 0.337850i) q^{9} +(5.18992 - 1.50721i) q^{10} +(-1.84394 - 1.33970i) q^{11} +(-4.83973 + 3.51627i) q^{12} +(-0.533615 + 0.387694i) q^{13} +(8.60889 + 6.25472i) q^{14} +(-3.27626 - 1.17992i) q^{15} +(-2.48650 + 1.80655i) q^{16} +(-1.40599 + 4.32720i) q^{17} -1.38920 q^{18} +(0.821028 - 2.52686i) q^{19} +(-8.08148 - 2.91048i) q^{20} +(-2.11879 - 6.52098i) q^{21} +(1.70228 + 5.23907i) q^{22} +(0.809017 + 0.587785i) q^{23} +6.93072 q^{24} +(-1.24242 - 4.84318i) q^{25} +1.59415 q^{26} +(4.50384 + 3.27223i) q^{27} +(-5.22639 - 16.0852i) q^{28} +(-0.476377 - 1.46614i) q^{29} +(4.72989 + 6.96141i) q^{30} +(1.79684 - 5.53011i) q^{31} -1.47259 q^{32} +(1.09685 - 3.37576i) q^{33} +(8.89644 - 6.46364i) q^{34} +(6.03490 - 7.77845i) q^{35} +(1.78629 + 1.29781i) q^{36} +(9.29763 - 6.75512i) q^{37} +(-5.19507 + 3.77444i) q^{38} +(-0.831005 - 0.603760i) q^{39} +(5.59270 + 8.23128i) q^{40} +(0.342907 - 0.249136i) q^{41} +(-5.12091 + 15.7605i) q^{42} +0.493278 q^{43} +(2.70558 - 8.32691i) q^{44} +(-0.0405073 + 1.28462i) q^{45} +(-0.746862 - 2.29861i) q^{46} +(-3.45622 - 10.6371i) q^{47} +(-3.87225 - 2.81336i) q^{48} +12.3849 q^{49} +(-4.45098 + 11.2349i) q^{50} -7.08558 q^{51} +(-2.04982 - 1.48928i) q^{52} +(-1.16159 - 3.57500i) q^{53} +(-4.15782 - 12.7964i) q^{54} +(4.89432 - 1.42137i) q^{55} +(-6.05504 + 18.6355i) q^{56} +4.13762 q^{57} +(-1.15135 + 3.54351i) q^{58} +(-10.5513 + 7.66600i) q^{59} +(0.421591 - 13.3700i) q^{60} +(-2.85521 - 2.07443i) q^{61} +(-11.3696 + 8.26047i) q^{62} +(-2.04736 + 1.48749i) q^{63} +(7.85238 + 5.70509i) q^{64} +(0.0464835 - 1.47414i) q^{65} +(-6.94033 + 5.04245i) q^{66} +(-0.839650 + 2.58418i) q^{67} -17.4779 q^{68} +(-0.481235 + 1.48109i) q^{69} +(-22.8503 + 6.63599i) q^{70} +(-4.29490 - 13.2183i) q^{71} +(-0.790480 - 2.43285i) q^{72} +(-5.49660 - 3.99352i) q^{73} -27.7762 q^{74} +(6.57529 - 4.17085i) q^{75} +10.2062 q^{76} +(8.11855 + 5.89847i) q^{77} +(0.767161 + 2.36108i) q^{78} +(0.715350 + 2.20162i) q^{79} +(0.216600 - 6.86911i) q^{80} +(-2.14621 + 6.60534i) q^{81} -1.02442 q^{82} +(-2.15449 + 6.63084i) q^{83} +(21.3085 - 15.4815i) q^{84} +(-5.71766 - 8.41520i) q^{85} +(-0.964512 - 0.700759i) q^{86} +(1.94223 - 1.41112i) q^{87} +(-8.20636 + 5.96227i) q^{88} +(9.64085 + 7.00449i) q^{89} +(1.90416 - 2.45428i) q^{90} +(2.34941 - 1.70695i) q^{91} +(-1.18705 + 3.65338i) q^{92} +9.05530 q^{93} +(-8.35332 + 25.7089i) q^{94} +(3.33882 + 4.91405i) q^{95} +(-0.708664 - 2.18104i) q^{96} +(-0.835568 - 2.57161i) q^{97} +(-24.2162 - 17.5941i) q^{98} -1.31007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + q^{2} + 4 q^{3} - 29 q^{4} - 2 q^{5} - 2 q^{6} - 36 q^{7} + 12 q^{8} - 22 q^{9}+O(q^{10}) \) 112 * q + q^2 + 4 * q^3 - 29 * q^4 - 2 * q^5 - 2 * q^6 - 36 * q^7 + 12 * q^8 - 22 * q^9	\( 112 q + q^{2} + 4 q^{3} - 29 q^{4} - 2 q^{5} - 2 q^{6} - 36 q^{7} + 12 q^{8} - 22 q^{9} - 5 q^{10} + 4 q^{12} + 8 q^{13} + 18 q^{14} - 25 q^{15} - 19 q^{16} - 34 q^{18} + 6 q^{19} + 24 q^{20} - 6 q^{21} + 2 q^{22} + 28 q^{23} - 198 q^{24} - 6 q^{25} + 26 q^{26} + 13 q^{27} + 36 q^{28} - 6 q^{29} - 36 q^{30} - 18 q^{31} - 60 q^{32} + 15 q^{33} + 45 q^{34} + q^{35} + 27 q^{36} + 43 q^{37} + 14 q^{38} + 6 q^{39} - 30 q^{40} - 41 q^{41} + 20 q^{42} - 88 q^{43} + 91 q^{44} + 60 q^{45} - q^{46} + 11 q^{47} - 2 q^{48} + 36 q^{49} + 36 q^{50} + 26 q^{51} + 10 q^{52} + 14 q^{53} + 56 q^{54} - 51 q^{55} - 75 q^{56} - 72 q^{57} + 43 q^{58} - 2 q^{59} + 131 q^{60} - 3 q^{61} - q^{63} + 22 q^{64} - 13 q^{65} - 5 q^{66} + 40 q^{67} - 70 q^{68} - 4 q^{69} + 50 q^{70} + 57 q^{71} + 52 q^{72} - 4 q^{73} - 274 q^{74} + 4 q^{75} + 52 q^{76} + 18 q^{77} - 36 q^{78} + 2 q^{79} + 30 q^{80} - 128 q^{81} - 148 q^{82} + 22 q^{83} + 112 q^{84} + 77 q^{85} - 5 q^{86} + 33 q^{87} + 121 q^{88} + 69 q^{89} - 167 q^{90} - 64 q^{91} + 29 q^{92} - 92 q^{93} + 64 q^{94} + 6 q^{95} + 172 q^{96} + 68 q^{97} + 28 q^{98} - 168 q^{99}+O(q^{100}) \) 112 * q + q^2 + 4 * q^3 - 29 * q^4 - 2 * q^5 - 2 * q^6 - 36 * q^7 + 12 * q^8 - 22 * q^9 - 5 * q^10 + 4 * q^12 + 8 * q^13 + 18 * q^14 - 25 * q^15 - 19 * q^16 - 34 * q^18 + 6 * q^19 + 24 * q^20 - 6 * q^21 + 2 * q^22 + 28 * q^23 - 198 * q^24 - 6 * q^25 + 26 * q^26 + 13 * q^27 + 36 * q^28 - 6 * q^29 - 36 * q^30 - 18 * q^31 - 60 * q^32 + 15 * q^33 + 45 * q^34 + q^35 + 27 * q^36 + 43 * q^37 + 14 * q^38 + 6 * q^39 - 30 * q^40 - 41 * q^41 + 20 * q^42 - 88 * q^43 + 91 * q^44 + 60 * q^45 - q^46 + 11 * q^47 - 2 * q^48 + 36 * q^49 + 36 * q^50 + 26 * q^51 + 10 * q^52 + 14 * q^53 + 56 * q^54 - 51 * q^55 - 75 * q^56 - 72 * q^57 + 43 * q^58 - 2 * q^59 + 131 * q^60 - 3 * q^61 - q^63 + 22 * q^64 - 13 * q^65 - 5 * q^66 + 40 * q^67 - 70 * q^68 - 4 * q^69 + 50 * q^70 + 57 * q^71 + 52 * q^72 - 4 * q^73 - 274 * q^74 + 4 * q^75 + 52 * q^76 + 18 * q^77 - 36 * q^78 + 2 * q^79 + 30 * q^80 - 128 * q^81 - 148 * q^82 + 22 * q^83 + 112 * q^84 + 77 * q^85 - 5 * q^86 + 33 * q^87 + 121 * q^88 + 69 * q^89 - 167 * q^90 - 64 * q^91 + 29 * q^92 - 92 * q^93 + 64 * q^94 + 6 * q^95 + 172 * q^96 + 68 * q^97 + 28 * q^98 - 168 * q^99

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