LMFDB - Embedded newform 115.2.l.a.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$115 = 5 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	115.l (of order $44$ , degree $20$ , 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	115.103
Dual form			115.2.l.a.67.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.579415 + 2.66353i) q^{2} +(-2.04324 + 1.52955i) q^{3} +(-4.93941 - 2.25575i) q^{4} +(2.12059 + 0.709280i) q^{5} +(-2.89012 - 6.32847i) q^{6} +(-0.134338 + 1.87829i) q^{7} +(5.60318 - 7.48497i) q^{8} +(0.990105 - 3.37199i) q^{9} +(-3.11789 + 5.23730i) q^{10} +(-0.338516 + 0.526741i) q^{11} +(13.5427 - 2.94603i) q^{12} +(-2.62317 + 0.187613i) q^{13} +(-4.92504 - 1.44612i) q^{14} +(-5.41776 + 1.79432i) q^{15} +(9.57793 + 11.0535i) q^{16} +(0.245364 - 0.657846i) q^{17} +(8.40771 + 4.59096i) q^{18} +(-0.374105 + 0.819175i) q^{19} +(-8.87452 - 8.28696i) q^{20} +(-2.59845 - 4.04326i) q^{21} +(-1.20685 - 1.20685i) q^{22} +(-3.33880 + 3.44274i) q^{23} +23.8639i q^{24} +(3.99384 + 3.00819i) q^{25} +(1.02019 - 7.09560i) q^{26} +(0.458767 + 1.23000i) q^{27} +(4.90050 - 8.97459i) q^{28} +(-0.285445 + 0.130359i) q^{29} +(-1.64010 - 15.4700i) q^{30} +(0.816998 + 5.68235i) q^{31} +(-18.5786 + 10.1447i) q^{32} +(-0.114008 - 1.59403i) q^{33} +(1.61002 + 1.03470i) q^{34} +(-1.61711 + 3.88780i) q^{35} +(-12.4969 + 14.4222i) q^{36} +(0.127765 + 0.233984i) q^{37} +(-1.96514 - 1.47108i) q^{38} +(5.07280 - 4.39561i) q^{39} +(17.1910 - 11.8984i) q^{40} +(6.57092 - 1.92940i) q^{41} +(12.2749 - 4.57831i) q^{42} +(6.98343 + 9.32877i) q^{43} +(2.86026 - 1.83818i) q^{44} +(4.49130 - 6.44836i) q^{45} +(-7.23528 - 10.8878i) q^{46} +(3.96485 - 3.96485i) q^{47} +(-36.4769 - 7.93507i) q^{48} +(3.41883 + 0.491554i) q^{49} +(-10.3265 + 8.89473i) q^{50} +(0.504871 + 1.71943i) q^{51} +(13.3801 + 4.99052i) q^{52} +(6.60144 + 0.472144i) q^{53} +(-3.54196 + 0.509257i) q^{54} +(-1.09146 + 0.876901i) q^{55} +(13.3062 + 11.5299i) q^{56} +(-0.488583 - 2.24598i) q^{57} +(-0.181822 - 0.835824i) q^{58} +(-2.23622 - 1.93770i) q^{59} +(30.8081 + 3.35822i) q^{60} +(-9.02346 + 1.29738i) q^{61} +(-15.6085 - 1.11634i) q^{62} +(6.20055 + 2.31269i) q^{63} +(-8.01475 - 27.2957i) q^{64} +(-5.69575 - 1.46271i) q^{65} +(4.31181 + 0.619945i) q^{66} +(-13.7837 - 2.99845i) q^{67} +(-2.69589 + 2.69589i) q^{68} +(1.55612 - 12.1412i) q^{69} +(-9.41830 - 6.55987i) q^{70} +(5.95122 - 3.82461i) q^{71} +(-19.6915 - 26.3048i) q^{72} +(-6.69927 + 2.49870i) q^{73} +(-0.697253 + 0.204732i) q^{74} +(-12.7616 - 0.0376761i) q^{75} +(3.69571 - 3.20235i) q^{76} +(-0.943895 - 0.706591i) q^{77} +(8.76857 + 16.0584i) q^{78} +(6.21028 - 7.16705i) q^{79} +(12.4709 + 30.2335i) q^{80} +(6.05065 + 3.88851i) q^{81} +(1.33171 + 18.6198i) q^{82} +(-0.0389168 + 0.0212502i) q^{83} +(3.71419 + 25.8328i) q^{84} +(0.986914 - 1.22099i) q^{85} +(-28.8938 + 13.1953i) q^{86} +(0.383843 - 0.702956i) q^{87} +(2.04587 + 5.48520i) q^{88} +(-0.678818 + 4.72128i) q^{89} +(14.5731 + 15.6990i) q^{90} -4.95227i q^{91} +(24.2576 - 9.47358i) q^{92} +(-10.3608 - 10.3608i) q^{93} +(8.26321 + 12.8578i) q^{94} +(-1.37435 + 1.47179i) q^{95} +(22.4437 - 49.1449i) q^{96} +(9.14950 + 4.99601i) q^{97} +(-3.29020 + 8.82136i) q^{98} +(1.44100 + 1.66300i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100})$ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$ .

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.579415	+	2.66353i	−0.409709	+	1.88340i	0.0559464	+	0.998434i	$0.482182\pi$
$2$	−0.579415	+	2.66353i	−0.409709	+	1.88340i	−0.465655	+	0.884966i	$0.654181\pi$
$3$	−2.04324	+	1.52955i	−1.17966	+	0.883086i	−0.995016	−	0.0997190i	$-0.968206\pi$
$3$	−2.04324	+	1.52955i	−1.17966	+	0.883086i	−0.184649	+	0.982805i	$0.559115\pi$
$4$	−4.93941	−	2.25575i	−2.46970	−	1.12788i
$5$	2.12059	+	0.709280i	0.948359	+	0.317200i
$5$	2.12059	+	0.709280i	0.948359	+	0.317200i
$6$	−2.89012	−	6.32847i	−1.17988	−	2.58359i
$7$	−0.134338	+	1.87829i	−0.0507749	+	0.709926i	0.906767	+	0.421632i	$0.138543\pi$
$7$	−0.134338	+	1.87829i	−0.0507749	+	0.709926i	−0.957542	+	0.288294i	$0.906912\pi$
$8$	5.60318	−	7.48497i	1.98102	−	2.64634i
$9$	0.990105	−	3.37199i	0.330035	−	1.12400i
$10$	−3.11789	+	5.23730i	−0.985965	+	1.65618i
$11$	−0.338516	+	0.526741i	−0.102066	+	0.158818i	−0.888530	−	0.458818i	$-0.848273\pi$
$11$	−0.338516	+	0.526741i	−0.102066	+	0.158818i	0.786464	+	0.617636i	$0.211909\pi$
$12$	13.5427	−	2.94603i	3.90943	−	0.850445i
$13$	−2.62317	+	0.187613i	−0.727537	+	0.0520345i	−0.430194	−	0.902736i	$-0.641555\pi$
$13$	−2.62317	+	0.187613i	−0.727537	+	0.0520345i	−0.297343	+	0.954771i	$0.596100\pi$
$14$	−4.92504	−	1.44612i	−1.31627	−	0.386492i
$15$	−5.41776	+	1.79432i	−1.39886	+	0.463293i
$16$	9.57793	+	11.0535i	2.39448	+	2.76338i
$17$	0.245364	−	0.657846i	0.0595094	−	0.159551i	−0.903793	−	0.427971i	$-0.859229\pi$
$17$	0.245364	−	0.657846i	0.0595094	−	0.159551i	0.963302	+	0.268420i	$0.0865014\pi$
$18$	8.40771	+	4.59096i	1.98172	+	1.08210i
$19$	−0.374105	+	0.819175i	−0.0858255	+	0.187932i	−0.947678	−	0.319227i	$-0.896577\pi$
$19$	−0.374105	+	0.819175i	−0.0858255	+	0.187932i	0.861853	+	0.507158i	$0.169304\pi$
$20$	−8.87452	−	8.28696i	−1.98440	−	1.85302i
$21$	−2.59845	−	4.04326i	−0.567028	−	0.882313i
$22$	−1.20685	−	1.20685i	−0.257301	−	0.257301i
$23$	−3.33880	+	3.44274i	−0.696187	+	0.717860i
$23$	−3.33880	+	3.44274i	−0.696187	+	0.717860i
$24$			23.8639i			4.87120i
$25$	3.99384	+	3.00819i	0.798769	+	0.601638i
$26$	1.02019	−	7.09560i	0.200076	−	1.39156i
$27$	0.458767	+	1.23000i	0.0882897	+	0.236714i
$28$	4.90050	−	8.97459i	0.926107	−	1.69604i
$29$	−0.285445	+	0.130359i	−0.0530059	+	0.0242070i	−0.441742	−	0.897142i	$-0.645639\pi$
$29$	−0.285445	+	0.130359i	−0.0530059	+	0.0242070i	0.388736	+	0.921349i	$0.372912\pi$
$30$	−1.64010	−	15.4700i	−0.299441	−	2.82443i
$31$	0.816998	+	5.68235i	0.146737	+	1.02058i	0.921514	+	0.388345i	$0.126953\pi$
$31$	0.816998	+	5.68235i	0.146737	+	1.02058i	−0.774777	+	0.632235i	$0.782138\pi$
$32$	−18.5786	+	10.1447i	−3.28426	+	1.79334i
$33$	−0.114008	−	1.59403i	−0.0198462	−	0.277486i
$34$	1.61002	+	1.03470i	0.276117	+	0.177449i
$35$	−1.61711	+	3.88780i	−0.273341	+	0.657158i
$36$	−12.4969	+	14.4222i	−2.08282	+	2.40370i
$37$	0.127765	+	0.233984i	0.0210044	+	0.0384668i	0.887970	−	0.459901i	$-0.152115\pi$
$37$	0.127765	+	0.233984i	0.0210044	+	0.0384668i	−0.866966	+	0.498367i	$0.833933\pi$
$38$	−1.96514	−	1.47108i	−0.318787	−	0.238641i
$39$	5.07280	−	4.39561i	0.812298	−	0.703860i
$40$	17.1910	−	11.8984i	2.71814	−	1.88130i
$41$	6.57092	−	1.92940i	1.02621	−	0.301321i	0.275039	−	0.961433i	$-0.411309\pi$
$41$	6.57092	−	1.92940i	1.02621	−	0.301321i	0.751167	+	0.660112i	$0.229491\pi$
$42$	12.2749	−	4.57831i	1.89406	−	0.706449i
$43$	6.98343	+	9.32877i	1.06496	+	1.42262i	0.899771	+	0.436362i	$0.143733\pi$
$43$	6.98343	+	9.32877i	1.06496	+	1.42262i	0.165192	+	0.986261i	$0.447176\pi$
$44$	2.86026	−	1.83818i	0.431201	−	0.277116i
$45$	4.49130	−	6.44836i	0.669523	−	0.961265i
$46$	−7.23528	−	10.8878i	−1.06678	−	1.60531i
$47$	3.96485	−	3.96485i	0.578333	−	0.578333i	−0.356111	−	0.934444i	$-0.615897\pi$
$47$	3.96485	−	3.96485i	0.578333	−	0.578333i	0.934444	+	0.356111i	$0.115897\pi$
$48$	−36.4769	−	7.93507i	−5.26499	−	1.14533i
$49$	3.41883	+	0.491554i	0.488405	+	0.0702220i
$50$	−10.3265	+	8.89473i	−1.46039	+	1.25790i
$51$	0.504871	+	1.71943i	0.0706960	+	0.240769i
$52$	13.3801	+	4.99052i	1.85549	+	0.692061i
$53$	6.60144	+	0.472144i	0.906777	+	0.0648540i	0.516932	−	0.856026i	$-0.327074\pi$
$53$	6.60144	+	0.472144i	0.906777	+	0.0648540i	0.389845	+	0.920880i	$0.372528\pi$
$54$	−3.54196	+	0.509257i	−0.482000	+	0.0693011i
$55$	−1.09146	+	0.876901i	−0.147173	+	0.118241i
$56$	13.3062	+	11.5299i	1.77812	+	1.54075i
$57$	−0.488583	−	2.24598i	−0.0647145	−	0.297488i
$58$	−0.181822	−	0.835824i	−0.0238745	−	0.109749i
$59$	−2.23622	−	1.93770i	−0.291132	−	0.252267i	0.497033	−	0.867732i	$-0.334423\pi$
$59$	−2.23622	−	1.93770i	−0.291132	−	0.252267i	−0.788164	+	0.615465i	$0.788968\pi$
$60$	30.8081	+	3.35822i	3.97730	+	0.433544i
$61$	−9.02346	+	1.29738i	−1.15534	+	0.166112i	−0.693232	−	0.720714i	$-0.743814\pi$
$61$	−9.02346	+	1.29738i	−1.15534	+	0.166112i	−0.462103	+	0.886826i	$0.652905\pi$
$62$	−15.6085	−	1.11634i	−1.98228	−	0.141775i
$63$	6.20055	+	2.31269i	0.781196	+	0.291371i
$64$	−8.01475	−	27.2957i	−1.00184	−	3.41197i
$65$	−5.69575	−	1.46271i	−0.706471	−	0.181427i
$66$	4.31181	+	0.619945i	0.530748	+	0.0763100i
$67$	−13.7837	−	2.99845i	−1.68394	−	0.366319i	−0.734099	−	0.679042i	$-0.762395\pi$
$67$	−13.7837	−	2.99845i	−1.68394	−	0.366319i	−0.949844	+	0.312723i	$0.898759\pi$
$68$	−2.69589	+	2.69589i	−0.326924	+	0.326924i
$69$	1.55612	−	12.1412i	0.187335	−	1.46163i
$70$	−9.41830	−	6.55987i	−1.12570	−	0.784054i
$71$	5.95122	−	3.82461i	0.706279	−	0.453898i	−0.137560	−	0.990493i	$-0.543926\pi$
$71$	5.95122	−	3.82461i	0.706279	−	0.453898i	0.843840	+	0.536595i	$0.180290\pi$
$72$	−19.6915	−	26.3048i	−2.32067	−	3.10005i
$73$	−6.69927	+	2.49870i	−0.784091	+	0.292451i	−0.709446	−	0.704759i	$-0.751055\pi$
$73$	−6.69927	+	2.49870i	−0.784091	+	0.292451i	−0.0746444	+	0.997210i	$0.523782\pi$
$74$	−0.697253	+	0.204732i	−0.0810540	+	0.0237996i
$75$	−12.7616	−	0.0376761i	−1.47358	−	0.00435046i
$76$	3.69571	−	3.20235i	0.423927	−	0.367335i
$77$	−0.943895	−	0.706591i	−0.107567	−	0.0805235i
$78$	8.76857	+	16.0584i	0.992845	+	1.81826i
$79$	6.21028	−	7.16705i	0.698712	−	0.806356i	−0.289866	−	0.957067i	$-0.593611\pi$
$79$	6.21028	−	7.16705i	0.698712	−	0.806356i	0.988578	+	0.150711i	$0.0481563\pi$
$80$	12.4709	+	30.2335i	1.39429	+	3.38021i
$81$	6.05065	+	3.88851i	0.672294	+	0.432057i
$82$	1.33171	+	18.6198i	0.147063	+	2.05621i
$83$	−0.0389168	+	0.0212502i	−0.00427168	+	0.00233251i	−0.481383	−	0.876510i	$-0.659866\pi$
$83$	−0.0389168	+	0.0212502i	−0.00427168	+	0.00233251i	0.477112	+	0.878843i	$0.341684\pi$
$84$	3.71419	+	25.8328i	0.405252	+	2.81859i
$85$	0.986914	−	1.22099i	0.107046	−	0.132435i
$86$	−28.8938	+	13.1953i	−3.11569	+	1.42289i
$87$	0.383843	−	0.702956i	0.0411523	−	0.0753648i
$88$	2.04587	+	5.48520i	0.218091	+	0.584725i
$89$	−0.678818	+	4.72128i	−0.0719545	+	0.500455i	0.921693	+	0.387920i	$0.126806\pi$
$89$	−0.678818	+	4.72128i	−0.0719545	+	0.500455i	−0.993648	+	0.112535i	$0.964103\pi$
$90$	14.5731	+	15.6990i	1.53614	+	1.65482i
$91$		−	4.95227i		−	0.519139i
$92$	24.2576	−	9.47358i	2.52903	−	0.987689i
$93$	−10.3608	−	10.3608i	−1.07436	−	1.07436i
$94$	8.26321	+	12.8578i	0.852285	+	1.32618i
$95$	−1.37435	+	1.47179i	−0.141005	+	0.151003i
$96$	22.4437	−	49.1449i	2.29065	−	5.01583i
$97$	9.14950	+	4.99601i	0.928991	+	0.507267i	0.871127	−	0.491057i	$-0.163389\pi$
$97$	9.14950	+	4.99601i	0.928991	+	0.507267i	0.0578636	+	0.998325i	$0.481571\pi$
$98$	−3.29020	+	8.82136i	−0.332360	+	0.891091i
$99$	1.44100	+	1.66300i	0.144826	+	0.167138i
$100$	−12.9415	−	23.8678i	−1.29415	−	2.38678i
$101$	−1.17854	−	0.346050i	−0.117269	−	0.0344332i	0.222572	−	0.974916i	$-0.428555\pi$
$101$	−1.17854	−	0.346050i	−0.117269	−	0.0344332i	−0.339840	+	0.940483i	$0.610373\pi$
$102$	−4.87229	+	0.348473i	−0.482428	+	0.0345039i
$103$	2.69152	−	0.585505i	0.265204	−	0.0576916i	−0.0779971	−	0.996954i	$-0.524852\pi$
$103$	2.69152	−	0.585505i	0.265204	−	0.0576916i	0.343201	+	0.939262i	$0.388489\pi$
$104$	−13.2938	+	20.6856i	−1.30357	+	2.02839i
$105$	−2.64245	−	10.4172i	−0.257876	−	1.01661i
$106$	−5.08255	+	17.3096i	−0.493661	+	1.68125i
$107$	9.18388	−	12.2682i	0.887839	−	1.18601i	−0.0938620	−	0.995585i	$-0.529921\pi$
$107$	9.18388	−	12.2682i	0.887839	−	1.18601i	0.981701	−	0.190429i	$-0.0609879\pi$
$108$	0.508541	−	7.11034i	0.0489344	−	0.684193i
$109$	2.70126	+	5.91493i	0.258734	+	0.566548i	0.993766	−	0.111484i	$-0.0355604\pi$
$109$	2.70126	+	5.91493i	0.258734	+	0.566548i	−0.735032	+	0.678032i	$0.762833\pi$
$110$	−1.70324	−	3.41523i	−0.162398	−	0.325630i
$111$	−0.618945	−	0.282663i	−0.0587476	−	0.0268291i
$112$	−22.0484	+	16.5052i	−2.08338	+	1.55960i
$113$	4.09881	−	18.8419i	0.385584	−	1.77250i	−0.218761	−	0.975778i	$-0.570202\pi$
$113$	4.09881	−	18.8419i	0.385584	−	1.77250i	0.604345	−	0.796722i	$-0.293435\pi$
$114$	6.26533			0.586802
$115$	−9.52210	+	4.93251i	−0.887940	+	0.459959i
$116$	1.70399			0.158211
$117$	−1.96459	+	9.03106i	−0.181626	+	0.834922i
$118$	6.45682	−	4.83352i	0.594399	−	0.444961i
$119$	1.20266	+	0.549237i	0.110248	+	0.0503485i
$120$	−16.9262	+	50.6057i	−1.54514	+	4.61965i
$121$	4.40670	+	9.64933i	0.400609	+	0.877212i
$122$	1.77273	−	24.7860i	0.160495	−	2.24402i
$123$	−10.4749	+	13.9928i	−0.944486	+	1.26169i
$124$	8.78247	−	29.9104i	0.788689	−	2.68603i
$125$	6.33567	+	9.21191i	0.566679	+	0.823938i
$126$	−9.75261	+	15.1754i	−0.868831	+	1.35193i
$127$	2.49018	−	0.541705i	0.220967	−	0.0480685i	−0.100718	−	0.994915i	$-0.532114\pi$
$127$	2.49018	−	0.541705i	0.220967	−	0.0480685i	0.321686	+	0.946846i	$0.395750\pi$
$128$	35.1190	−	2.51176i	3.10411	−	0.222010i
$129$	−28.5376	−	8.37940i	−2.51260	−	0.737765i
$130$	7.19619	−	14.3233i	0.631147	−	1.25624i
$131$	−7.52420	−	8.68339i	−0.657392	−	0.758671i	0.324957	−	0.945729i	$-0.394650\pi$
$131$	−7.52420	−	8.68339i	−0.657392	−	0.758671i	−0.982349	+	0.187058i	$0.940105\pi$
$132$	−3.03261	+	8.13075i	−0.263955	+	0.707691i
$133$	−1.48839	−	0.812722i	−0.129060	−	0.0704720i
$134$	15.9729	−	34.9759i	1.37985	−	3.02145i
$135$	0.100442	+	2.93373i	0.00864471	+	0.252495i
$136$	−3.54914	−	5.52257i	−0.304336	−	0.473556i
$137$	5.48458	+	5.48458i	0.468579	+	0.468579i	0.901454	−	0.432875i	$-0.142501\pi$
$137$	5.48458	+	5.48458i	0.468579	+	0.468579i	−0.432875	+	0.901454i	$0.642501\pi$
$138$	31.4368	+	11.1796i	2.67608	+	0.951668i
$139$			6.48562i			0.550103i	0.961429	+	0.275052i	$0.0886949\pi$
$139$			6.48562i			0.550103i	−0.961429	+	0.275052i	$0.911305\pi$
$140$	16.7575	−	15.5556i	1.41626	−	1.31469i
$141$	−2.03670	+	14.1656i	−0.171521	+	1.19296i
$142$	6.73875	+	18.0673i	0.565503	+	1.51617i
$143$	0.789162	−	1.44524i	0.0659930	−	0.120857i
$144$	46.7555	−	21.3525i	3.89629	−	1.77938i
$145$	−0.697775	+	0.0739768i	−0.0579470	+	0.00614344i
$146$	−2.77370	−	19.2915i	−0.229553	−	1.59658i
$147$	−7.73735	+	4.22491i	−0.638166	+	0.348465i
$148$	−0.103273	−	1.44395i	−0.00848901	−	0.118692i
$149$	9.69019	+	6.22751i	0.793852	+	0.510177i	0.873604	−	0.486637i	$-0.161777\pi$
$149$	9.69019	+	6.22751i	0.793852	+	0.510177i	−0.0797526	+	0.996815i	$0.525413\pi$
$150$	7.49459	−	33.9689i	0.611931	−	2.77355i
$151$	12.3540	−	14.2573i	1.00536	−	1.16024i	0.0183059	−	0.999832i	$-0.494173\pi$
$151$	12.3540	−	14.2573i	1.00536	−	1.16024i	0.987050	−	0.160411i	$-0.0512818\pi$
$152$	4.03533	+	7.39015i	0.327308	+	0.599420i
$153$	−1.97531	−	1.47870i	−0.159695	−	0.119546i
$154$	2.42893	−	2.10468i	0.195729	−	0.169600i
$155$	−2.29786	+	12.6294i	−0.184568	+	1.01442i
$156$	−34.9720	+	10.2687i	−2.80000	+	0.822155i
$157$	−15.5457	+	5.79824i	−1.24068	+	0.462750i	−0.882239	−	0.470802i	$-0.843965\pi$
$157$	−15.5457	+	5.79824i	−1.24068	+	0.462750i	−0.358442	+	0.933552i	$0.616692\pi$
$158$	15.4913	+	20.6940i	1.23242	+	1.64632i
$159$	−14.2105	+	9.13252i	−1.12696	+	0.724256i
$160$	−46.5931	+	8.33532i	−3.68351	+	0.658965i
$161$	−6.01792	−	6.73371i	−0.474279	−	0.530690i
$162$	−13.8630	+	13.8630i	−1.08918	+	1.08918i
$163$	6.93880	+	1.50944i	0.543489	+	0.118229i	0.475924	−	0.879486i	$-0.342114\pi$
$163$	6.93880	+	1.50944i	0.543489	+	0.118229i	0.0675644	+	0.997715i	$0.478477\pi$
$164$	−36.8087	−	5.29229i	−2.87428	−	0.413259i
$165$	0.888853	−	3.46116i	0.0691971	−	0.269451i
$166$	−0.0340515	−	0.115969i	−0.00264291	−	0.00900093i
$167$	4.51969	+	1.68576i	0.349744	+	0.130448i	0.518196	−	0.855262i	$-0.326604\pi$
$167$	4.51969	+	1.68576i	0.349744	+	0.130448i	−0.168452	+	0.985710i	$0.553877\pi$
$168$	−44.8233	−	3.20582i	−3.45819	−	0.247335i
$169$	−6.02185	+	0.865811i	−0.463219	+	0.0666009i
$170$	2.68032	+	3.33614i	0.205571	+	0.255870i
$171$	2.39185	+	2.07255i	0.182909	+	0.158492i
$172$	−13.4506	−	61.8314i	−1.02560	−	4.71460i
$173$	−3.43070	−	15.7707i	−0.260831	−	1.19902i	−0.902039	−	0.431654i	$-0.857930\pi$
$173$	−3.43070	−	15.7707i	−0.260831	−	1.19902i	0.641208	−	0.767367i	$-0.278434\pi$
$174$	1.64994	+	1.42968i	0.125082	+	0.108384i
$175$	−6.18677	+	7.09747i	−0.467676	+	0.536518i
$176$	−9.06463	+	1.30330i	−0.683272	+	0.0982397i
$177$	7.53295	+	0.538767i	0.566211	+	0.0404962i
$178$	−12.1820	−	4.54363i	−0.913076	−	0.340560i
$179$	2.20385	+	7.50562i	0.164723	+	0.560996i	0.999939	+	0.0110732i	$0.00352479\pi$
$179$	2.20385	+	7.50562i	0.164723	+	0.560996i	−0.835215	+	0.549923i	$0.814657\pi$
$180$	−36.7302	+	21.7198i	−2.73771	+	1.61890i
$181$	−0.718152	−	0.103255i	−0.0533798	−	0.00767486i	0.115573	−	0.993299i	$-0.463130\pi$
$181$	−0.718152	−	0.103255i	−0.0533798	−	0.00767486i	−0.168953	+	0.985624i	$0.554039\pi$
$182$	13.1905	+	2.86942i	0.977747	+	0.212696i
$183$	16.4527	−	16.4527i	1.21622	−	1.21622i
$184$	7.06091	+	44.2811i	0.520537	+	3.26444i
$185$	0.104977	+	0.586807i	0.00771809	+	0.0431429i
$186$	33.5993	−	21.5930i	2.46362	−	1.58327i
$187$	0.263455	+	0.351934i	0.0192657	+	0.0257360i
$188$	−28.5277	+	10.6403i	−2.08060	+	0.776023i
$189$	−2.37193	+	0.696460i	−0.172532	+	0.0506600i
$190$	−3.12385	−	4.51340i	−0.226628	−	0.327437i
$191$	−0.881798	+	0.764082i	−0.0638046	+	0.0552870i	−0.686179	−	0.727432i	$-0.740713\pi$
$191$	−0.881798	+	0.764082i	−0.0638046	+	0.0552870i	0.622375	+	0.782719i	$0.286168\pi$
$192$	58.1262	+	43.5127i	4.19490	+	3.14026i
$193$	−9.44775	−	17.3023i	−0.680064	−	1.24544i	−0.958528	−	0.284998i	$-0.908007\pi$
$193$	−9.44775	−	17.3023i	−0.680064	−	1.24544i	0.278464	−	0.960447i	$-0.410175\pi$
$194$	−18.6084	+	21.4752i	−1.33600	+	1.54183i
$195$	13.8751	−	5.72326i	0.993615	−	0.409851i
$196$	−15.7782	−	10.1400i	−1.12701	−	0.724288i
$197$	0.404464	+	5.65515i	0.0288169	+	0.402912i	0.991305	+	0.131587i	$0.0420073\pi$
$197$	0.404464	+	5.65515i	0.0288169	+	0.402912i	−0.962488	+	0.271325i	$0.912538\pi$
$198$	−5.26439	+	2.87457i	−0.374124	+	0.204287i
$199$	−1.95540	−	13.6001i	−0.138614	−	0.964085i	−0.933820	−	0.357744i	$-0.883546\pi$
$199$	−1.95540	−	13.6001i	−0.138614	−	0.964085i	0.795205	−	0.606341i	$-0.207363\pi$
$200$	44.8944	−	13.0384i	3.17452	−	0.921951i
$201$	32.7496	−	14.9562i	2.30998	−	1.05493i
$202$	1.60458	−	2.93856i	0.112898	−	0.206757i
$203$	−0.206505	−	0.553661i	−0.0144938	−	0.0388593i
$204$	1.38485	−	9.63183i	0.0969588	−	0.674363i
$205$	15.3027	+	0.569158i	1.06879	+	0.0397517i
$206$			7.50821i			0.523122i
$207$	8.30311	+	14.6671i	0.577106	+	1.01943i
$208$	−27.1983	−	27.1983i	−1.88587	−	1.88587i
$209$	−0.304853	−	0.474360i	−0.0210871	−	0.0328122i
$210$	29.2775	−	1.00238i	2.02034	−	0.0691706i
$211$	6.80328	−	14.8971i	0.468357	−	1.02556i	−0.517146	−	0.855897i	$-0.673005\pi$
$211$	6.80328	−	14.8971i	0.468357	−	1.02556i	0.985502	−	0.169661i	$-0.0542673\pi$
$212$	−31.5421	−	17.2233i	−2.16632	−	1.18290i
$213$	−6.30982	+	16.9173i	−0.432342	+	1.15915i
$214$	27.3555	+	31.5699i	1.86998	+	2.15808i
$215$	8.19231	+	24.7357i	0.558711	+	1.68696i
$216$	11.7771	+	3.45806i	0.801328	+	0.235291i
$217$	−10.7828	+	0.771203i	−0.731986	+	0.0523527i
$218$	−17.3198	+	3.76768i	−1.17304	+	0.255180i
$219$	9.86633	−	15.3523i	0.666705	−	1.03741i
$220$	7.36924	−	1.86930i	0.496834	−	0.126028i
$221$	−0.520211	+	1.77167i	−0.0349932	+	0.119176i
$222$	1.11151	−	1.48480i	0.0745994	−	0.0996532i
$223$	−1.34761	+	18.8420i	−0.0902426	+	1.26176i	0.727474	+	0.686135i	$0.240694\pi$
$223$	−1.34761	+	18.8420i	−0.0902426	+	1.26176i	−0.817717	+	0.575621i	$0.804760\pi$
$224$	−16.5588	−	36.2588i	−1.10638	−	2.42264i
$225$	14.0979	−	10.4888i	0.939861	−	0.699251i
$226$	47.8112	+	21.8346i	3.18035	+	1.45242i
$227$	11.0056	−	8.23865i	0.730464	−	0.546819i	−0.168042	−	0.985780i	$-0.553744\pi$
$227$	11.0056	−	8.23865i	0.730464	−	0.546819i	0.898506	+	0.438961i	$0.144653\pi$
$228$	−2.65306	+	12.1959i	−0.175703	+	0.807696i
$229$	−8.81270			−0.582360			−0.291180	−	0.956668i	$-0.594048\pi$
$229$	−8.81270			−0.582360			−0.291180	+	0.956668i	$0.594048\pi$
$230$	−7.62063	−	28.2204i	−0.502489	−	1.86080i
$231$	3.00937			0.198002
$232$	−0.623672	+	2.86697i	−0.0409461	+	0.188226i
$233$	4.44241	−	3.32554i	0.291032	−	0.217864i	−0.443778	−	0.896137i	$-0.646362\pi$
$233$	4.44241	−	3.32554i	0.291032	−	0.217864i	0.734810	+	0.678273i	$0.237271\pi$
$234$	−22.9162	−	10.4655i	−1.49808	−	0.684149i
$235$	11.2200	−	5.59565i	0.731914	−	0.365020i
$236$	6.67465	+	14.6154i	0.434483	+	0.951385i
$237$	−1.72674	+	24.1429i	−0.112164	+	1.56825i
$238$	−2.15975	+	2.88509i	−0.139996	+	0.187012i
$239$	−1.21124	+	4.12509i	−0.0783483	+	0.266830i	−0.989346	−	0.145581i	$-0.953495\pi$
$239$	−1.21124	+	4.12509i	−0.0783483	+	0.266830i	0.910998	+	0.412411i	$0.135313\pi$
$240$	−71.7246	−	42.6994i	−4.62980	−	2.75624i
$241$	0.0866550	−	0.134838i	0.00558194	−	0.00868567i	−0.838451	−	0.544976i	$-0.816539\pi$
$241$	0.0866550	−	0.134838i	0.00558194	−	0.00868567i	0.844033	+	0.536291i	$0.180175\pi$
$242$	−28.2546	+	6.14641i	−1.81627	+	0.395106i
$243$	−22.2389	+	1.59056i	−1.42662	+	0.102034i
$244$	47.4971	+	13.9464i	3.04069	+	0.892827i
$245$	6.90131	+	3.46730i	0.440909	+	0.221518i
$246$	−31.2009	−	36.0077i	−1.98929	−	2.29577i
$247$	0.827653	−	2.21902i	0.0526623	−	0.141193i
$248$	47.1100	+	25.7240i	2.99149	+	1.63348i
$249$	0.0470132	−	0.102944i	0.00297934	−	0.00652384i
$250$	−28.2072	+	11.5377i	−1.78398	+	0.729709i
$251$	7.73871	+	12.0417i	0.488463	+	0.760063i	0.994754	−	0.102300i	$-0.0326201\pi$
$251$	7.73871	+	12.0417i	0.488463	+	0.760063i	−0.506291	+	0.862363i	$0.668984\pi$
$252$	−25.4102	−	25.4102i	−1.60069	−	1.60069i
$253$	−0.683195	−	2.92410i	−0.0429521	−	0.183837i
$254$			6.94653i			0.435864i
$255$	−0.148933	+	4.00431i	−0.00932656	+	0.250760i
$256$	−5.56117	+	38.6788i	−0.347573	+	2.41742i
$257$	−7.61089	−	20.4056i	−0.474754	−	1.27287i	−0.925002	−	0.379962i	$-0.875937\pi$
$257$	−7.61089	−	20.4056i	−0.474754	−	1.27287i	0.450248	−	0.892904i	$-0.351336\pi$
$258$	38.8539	−	71.1556i	2.41894	−	4.42996i
$259$	−0.456653	+	0.208547i	−0.0283750	+	0.0129584i
$260$	24.8341	+	20.0731i	1.54015	+	1.24488i
$261$	0.156947	+	1.09159i	0.00971475	+	0.0675676i
$262$	27.4881	−	15.0096i	1.69822	−	0.927299i
$263$	−1.68880	−	23.6124i	−0.104136	−	1.45601i	−0.733920	−	0.679236i	$-0.762311\pi$
$263$	−1.68880	−	23.6124i	−0.104136	−	1.45601i	0.629784	−	0.776770i	$-0.283143\pi$
$264$	−12.5701	−	8.07831i	−0.773636	−	0.497186i
$265$	13.6641	+	5.68350i	0.839379	+	0.349135i
$266$	3.02711	−	3.49347i	0.185604	−	0.214198i
$267$	−5.83444	−	10.6850i	−0.357062	−	0.653911i
$268$	61.3194	+	45.9031i	3.74568	+	2.80398i
$269$	−12.9397	+	11.2123i	−0.788945	+	0.683624i	−0.953048	−	0.302819i	$-0.902072\pi$
$269$	−12.9397	+	11.2123i	−0.788945	+	0.683624i	0.164104	+	0.986443i	$0.447527\pi$
$270$	−7.87227	−	1.43232i	−0.479091	−	0.0871680i
$271$	−15.5892	+	4.57742i	−0.946979	+	0.278058i	−0.718529	−	0.695497i	$-0.755184\pi$
$271$	−15.5892	+	4.57742i	−0.946979	+	0.278058i	−0.228451	+	0.973556i	$0.573366\pi$
$272$	9.62159	−	3.58867i	0.583395	−	0.217595i
$273$	7.57474	+	10.1187i	0.458444	+	0.612410i
$274$	−17.7862	+	11.4305i	−1.07450	+	0.690541i
$275$	−2.93652	+	1.08540i	−0.177079	+	0.0654520i
$276$	−35.0738	+	56.4600i	−2.11119	+	3.39849i
$277$	2.00389	−	2.00389i	0.120402	−	0.120402i	−0.644338	−	0.764741i	$-0.722867\pi$
$277$	2.00389	−	2.00389i	0.120402	−	0.120402i	0.764741	+	0.644338i	$0.222867\pi$
$278$	−17.2746	−	3.75787i	−1.03606	−	0.225382i
$279$	19.9697	+	2.87121i	1.19556	+	0.171895i
$280$	20.0391	+	33.8880i	1.19757	+	2.02520i
$281$	−0.703529	−	2.39600i	−0.0419690	−	0.142933i	0.935843	−	0.352417i	$-0.114640\pi$
$281$	−0.703529	−	2.39600i	−0.0419690	−	0.142933i	−0.977812	+	0.209483i	$0.932822\pi$
$282$	−36.5503	−	13.6326i	−2.17654	−	0.811808i
$283$	−32.7258	−	2.34060i	−1.94535	−	0.139134i	−0.956873	−	0.290507i	$-0.906176\pi$
$283$	−32.7258	−	2.34060i	−1.94535	−	0.139134i	−0.988477	+	0.151373i	$0.951631\pi$
$284$	−38.0228	+	5.46686i	−2.25624	+	0.324398i
$285$	0.556944	−	5.10936i	0.0329905	−	0.302652i
$286$	3.39219	+	2.93935i	0.200584	+	0.173807i
$287$	2.74124	+	12.6013i	0.161810	+	0.743829i
$288$	15.8130	+	72.6911i	0.931789	+	4.28337i
$289$	12.4752	+	10.8098i	0.733834	+	0.635871i
$290$	0.207262	−	1.90141i	0.0121709	−	0.111654i
$291$	−26.3362	+	3.78658i	−1.54386	+	0.221973i
$292$	38.7269	+	2.76980i	2.26632	+	0.162090i
$293$	18.2521	+	6.80768i	1.06630	+	0.397709i	0.820520	−	0.571618i	$-0.193684\pi$
$293$	18.2521	+	6.80768i	1.06630	+	0.397709i	0.245778	+	0.969326i	$0.420957\pi$
$294$	−6.77004	−	23.0566i	−0.394837	−	1.34469i
$295$	−3.36775	−	5.69519i	−0.196078	−	0.331587i
$296$	2.46725	+	0.354738i	0.143406	+	0.0206187i
$297$	−0.803192	−	0.174724i	−0.0466059	−	0.0101385i
$298$	−22.2018	+	22.2018i	−1.28612	+	1.28612i
$299$	8.11233	−	9.65729i	0.469148	−	0.558496i
$300$	62.9495	+	28.9730i	3.63439	+	1.67276i
$301$	−18.4602	+	11.8637i	−1.06403	+	0.683811i
$302$	30.8166	+	41.1662i	1.77330	+	2.36885i
$303$	2.93733	−	1.09557i	0.168745	−	0.0629388i
$304$	−12.6379	+	3.71083i	−0.724835	+	0.212831i
$305$	−20.0553	−	3.64895i	−1.14836	−	0.208938i
$306$	5.08309	−	4.40452i	0.290581	−	0.251790i
$307$	−23.0608	−	17.2631i	−1.31615	−	0.985257i	−0.999324	−	0.0367733i	$-0.988292\pi$
$307$	−23.0608	−	17.2631i	−1.31615	−	0.985257i	−0.316826	−	0.948484i	$-0.602617\pi$
$308$	3.06839	+	5.61933i	0.174838	+	0.320191i
$309$	−4.60387	+	5.31315i	−0.261905	+	0.302254i
$310$	−32.3075	−	13.4381i	−1.83494	−	0.763233i
$311$	−5.35705	−	3.44277i	−0.303771	−	0.195222i	0.379871	−	0.925040i	$-0.375968\pi$
$311$	−5.35705	−	3.44277i	−0.303771	−	0.195222i	−0.683642	+	0.729818i	$0.739605\pi$
$312$	−4.47718	−	62.5991i	−0.253470	−	3.54398i
$313$	29.1856	−	15.9366i	1.64967	−	0.900788i	0.661053	−	0.750340i	$-0.270110\pi$
$313$	29.1856	−	15.9366i	1.64967	−	0.900788i	0.988618	−	0.150449i	$-0.0480718\pi$
$314$	−6.43638	−	44.7660i	−0.363226	−	2.52629i
$315$	11.5085	+	9.30220i	0.648431	+	0.524120i
$316$	−46.8422	+	21.3921i	−2.63508	+	1.20340i
$317$	−10.4419	+	19.1230i	−0.586477	+	1.07405i	0.400968	+	0.916092i	$0.368674\pi$
$317$	−10.4419	+	19.1230i	−0.586477	+	1.07405i	−0.987445	+	0.157961i	$0.949508\pi$
$318$	−16.0910	−	43.1416i	−0.902337	−	2.41926i
$319$	0.0279626	−	0.194484i	0.00156561	−	0.0108890i
$320$	2.36429	−	63.5679i	0.132168	−	3.55355i
$321$			39.1141i			2.18314i
$322$	21.4223	−	12.1273i	1.19382	−	0.675828i
$323$	0.447099	+	0.447099i	0.0248773	+	0.0248773i
$324$	−21.1151	−	32.8557i	−1.17306	−	1.82532i
$325$	−11.0409	−	7.14171i	−0.612439	−	0.396151i
$326$	−8.04090	+	17.6071i	−0.445344	+	0.975168i
$327$	−14.5665	−	7.95391i	−0.805529	−	0.439852i
$328$	22.3766	−	59.9939i	1.23554	−	3.31261i
$329$	6.91450	+	7.97976i	0.381209	+	0.439938i
$330$	8.70390	+	4.37294i	0.479134	+	0.240722i
$331$	8.25389	+	2.42356i	0.453675	+	0.133211i	0.500584	−	0.865688i	$-0.333119\pi$
$331$	8.25389	+	2.42356i	0.453675	+	0.133211i	−0.0469087	+	0.998899i	$0.514937\pi$
$332$	0.240161	−	0.0171767i	0.0131806	−	0.000942692i
$333$	0.915493	−	0.199153i	0.0501687	−	0.0109135i
$334$	−7.10884	+	11.0616i	−0.388978	+	0.605262i
$335$	−27.1028	−	16.1350i	−1.48079	−	0.881549i
$336$	19.8046	−	67.4481i	1.08043	−	3.67960i
$337$	3.96712	−	5.29945i	0.216103	−	0.288680i	−0.679370	−	0.733796i	$-0.737747\pi$
$337$	3.96712	−	5.29945i	0.216103	−	0.288680i	0.895473	+	0.445116i	$0.146838\pi$
$338$	1.18304	−	16.5410i	0.0643488	−	0.899714i
$339$	20.4448	+	44.7679i	1.11041	+	2.43146i
$340$	−7.62902	+	3.80474i	−0.413742	+	0.206341i
$341$	−3.26969	−	1.49322i	−0.177064	−	0.0808623i
$342$	−6.90616	+	5.16989i	−0.373443	+	0.279556i
$343$	−4.18451	+	19.2359i	−0.225942	+	1.03864i
$344$	108.955			5.87446
$345$	11.9114	−	24.6428i	0.641289	−	1.32672i
$346$	43.9934			2.36510
$347$	−2.03584	+	9.35860i	−0.109289	+	0.502396i	0.889662	+	0.456619i	$0.150940\pi$
$347$	−2.03584	+	9.35860i	−0.109289	+	0.502396i	−0.998952	+	0.0457765i	$0.985424\pi$
$348$	−3.48165	+	2.60633i	−0.186636	+	0.139714i
$349$	−15.9385	−	7.27885i	−0.853167	−	0.389628i	−0.0596813	−	0.998217i	$-0.519008\pi$
$349$	−15.9385	−	7.27885i	−0.853167	−	0.389628i	−0.793485	+	0.608589i	$0.791736\pi$
$350$	−15.3196	−	20.5910i	−0.818867	−	1.10064i
$351$	−1.43419	−	3.14043i	−0.0765513	−	0.167624i
$352$	0.945531	−	13.2202i	0.0503970	−	0.704641i
$353$	−1.33702	+	1.78605i	−0.0711622	+	0.0950616i	−0.834710	−	0.550690i	$-0.814365\pi$
$353$	−1.33702	+	1.78605i	−0.0711622	+	0.0950616i	0.763548	+	0.645751i	$0.223456\pi$
$354$	−5.79973	+	19.7521i	−0.308252	+	1.04981i
$355$	15.3328	−	3.88937i	0.813783	−	0.206427i
$356$	14.0030	−	21.7891i	0.742157	−	1.15482i
$357$	−3.29741	+	0.717307i	−0.174517	+	0.0379639i
$358$	−21.2684	+	1.52114i	−1.12407	+	0.0803950i
$359$	−4.20106	−	1.23354i	−0.221723	−	0.0651038i	0.168984	−	0.985619i	$-0.445951\pi$
$359$	−4.20106	−	1.23354i	−0.221723	−	0.0651038i	−0.390707	+	0.920515i	$0.627770\pi$
$360$	−23.1002	−	69.7485i	−1.21749	−	3.67607i
$361$	11.9113	+	13.7463i	0.626908	+	0.723491i
$362$	0.691131	−	1.85299i	0.0363250	−	0.0973912i
$363$	−23.7631	−	12.9756i	−1.24724	−	0.681043i
$364$	−11.1711	+	24.4613i	−0.585524	+	1.28212i
$365$	−15.9787	+	0.547066i	−0.836365	+	0.0286347i
$366$	34.2892	+	53.3551i	1.79233	+	2.78892i
$367$	−14.2775	−	14.2775i	−0.745280	−	0.745280i	0.228309	−	0.973589i	$-0.426680\pi$
$367$	−14.2775	−	14.2775i	−0.745280	−	0.745280i	−0.973589	+	0.228309i	$0.926680\pi$
$368$	−70.0332	−	3.93116i	−3.65073	−	0.204926i
$369$		−	24.0674i		−	1.25290i
$370$	−1.62380	−	0.0603945i	−0.0844175	−	0.00313976i
$371$	−1.77364	+	12.3360i	−0.0920830	+	0.640452i
$372$	27.8047	+	74.5472i	1.44161	+	3.86509i
$373$	−7.86310	+	14.4002i	−0.407136	+	0.745614i	−0.998134	−	0.0610591i	$-0.980552\pi$
$373$	−7.86310	+	14.4002i	−0.407136	+	0.745614i	0.590998	+	0.806673i	$0.298734\pi$
$374$	−1.09004	+	0.497803i	−0.0563645	+	0.0257408i
$375$	−27.0354	−	9.13141i	−1.39610	−	0.471544i
$376$	−7.46102	−	51.8926i	−0.384773	−	2.67615i
$377$	0.724315	−	0.395506i	0.0373041	−	0.0203696i
$378$	−0.480712	−	6.72123i	−0.0247252	−	0.345703i
$379$	−4.03462	−	2.59289i	−0.207244	−	0.133188i	0.432902	−	0.901441i	$-0.357490\pi$
$379$	−4.03462	−	2.59289i	−0.207244	−	0.133188i	−0.640146	+	0.768253i	$0.721126\pi$
$380$	10.1085	−	4.16959i	0.518554	−	0.213896i
$381$	−4.25946	+	4.91568i	−0.218219	+	0.251838i
$382$	−1.52423	−	2.79142i	−0.0779863	−	0.142821i
$383$	10.6001	+	7.93517i	0.541642	+	0.405468i	0.834765	−	0.550607i	$-0.185604\pi$
$383$	10.6001	+	7.93517i	0.541642	+	0.405468i	−0.293123	+	0.956075i	$0.594694\pi$
$384$	−67.9146	+	58.8484i	−3.46575	+	3.00309i
$385$	−1.50045	−	2.16788i	−0.0764699	−	0.110485i
$386$	51.5593	−	15.1392i	2.62430	−	0.770564i
$387$	38.3708	−	14.3116i	1.95050	−	0.727498i
$388$	−33.9233	−	45.3163i	−1.72220	−	2.30059i
$389$	−11.1062	+	7.13754i	−0.563108	+	0.361888i	−0.791016	−	0.611795i	$-0.790448\pi$
$389$	−11.1062	+	7.13754i	−0.563108	+	0.361888i	0.227908	+	0.973683i	$0.426811\pi$
$390$	7.20465	+	40.2728i	0.364822	+	2.03929i
$391$	1.44557	+	3.04114i	0.0731056	+	0.153797i
$392$	22.8356	−	22.8356i	1.15337	−	1.15337i
$393$	28.6554	+	6.23360i	1.44547	+	0.314444i
$394$	−15.2970	−	2.19938i	−0.770652	−	0.110803i
$395$	18.2529	−	10.7936i	0.918405	−	0.543084i
$396$	−3.36636	−	11.4648i	−0.169166	−	0.576126i
$397$	13.6063	+	5.07488i	0.682879	+	0.254701i	0.666873	−	0.745171i	$-0.267632\pi$
$397$	13.6063	+	5.07488i	0.682879	+	0.254701i	0.0160058	+	0.999872i	$0.494905\pi$
$398$	37.3572	+	2.67184i	1.87255	+	0.133927i
$399$	4.28423	−	0.615980i	0.214480	−	0.0308376i
$400$	5.00163	+	72.9583i	0.250081	+	3.64792i
$401$	−12.3145	−	10.6706i	−0.614955	−	0.532862i	0.290734	−	0.956804i	$-0.406101\pi$
$401$	−12.3145	−	10.6706i	−0.614955	−	0.532862i	−0.905689	+	0.423942i	$0.860646\pi$
$402$	20.8608	+	95.8954i	1.04044	+	4.78283i
$403$	−3.20921	−	14.7525i	−0.159862	−	0.734874i
$404$	5.04067	+	4.36777i	0.250783	+	0.217305i
$405$	10.0729	+	12.5376i	0.500527	+	0.622997i
$406$	1.59434	−	0.229232i	0.0791259	−	0.0113766i
$407$	−0.166500	−	0.0119083i	−0.00825308	−	0.000590272i
$408$	15.6988	+	5.85534i	0.777205	+	0.289882i
$409$	1.62410	+	5.53116i	0.0803064	+	0.273498i	0.989851	−	0.142107i	$-0.0453878\pi$
$409$	1.62410	+	5.53116i	0.0803064	+	0.273498i	−0.909545	+	0.415606i	$0.863570\pi$
$410$	−10.3826	+	40.4295i	−0.512761	+	1.99667i
$411$	−19.5952	−	2.81737i	−0.966562	−	0.138971i
$412$	−14.6153	−	3.17936i	−0.720043	−	0.156636i
$413$	3.93997	−	3.93997i	0.193873	−	0.193873i
$414$	−43.8771	+	13.6173i	−2.15644	+	0.669252i
$415$	−0.0975992	+	0.0174601i	−0.00479096	+	0.000857083i
$416$	46.8316	−	30.0968i	2.29611	−	1.47562i
$417$	−9.92008	−	13.2517i	−0.485788	−	0.648937i
$418$	1.44011	−	0.537133i	0.0704380	−	0.0262720i
$419$	29.0927	−	8.54240i	1.42127	−	0.417324i	0.521339	−	0.853349i	$-0.325433\pi$
$419$	29.0927	−	8.54240i	1.42127	−	0.417324i	0.899934	+	0.436026i	$0.143614\pi$
$420$	−10.4464	+	57.4152i	−0.509731	+	2.80158i
$421$	12.6074	−	10.9244i	0.614448	−	0.532422i	−0.291085	−	0.956697i	$-0.594016\pi$
$421$	12.6074	−	10.9244i	0.614448	−	0.532422i	0.905533	+	0.424275i	$0.139471\pi$
$422$	35.7369	+	26.7523i	1.73965	+	1.30228i
$423$	−9.44382	−	17.2951i	−0.459174	−	0.840914i
$424$	40.5230	−	46.7661i	1.96797	−	2.27116i
$425$	2.95887	−	1.88923i	0.143526	−	0.0916411i
$426$	−41.4037	−	26.6085i	−2.00601	−	1.28919i
$427$	−1.22466	−	17.1229i	−0.0592652	−	0.828636i
$428$	−73.0370	+	39.8812i	−3.53037	+	1.92773i
$429$	0.598123	+	4.16003i	0.0288776	+	0.200848i
$430$	−70.6311	+	7.48818i	−3.40614	+	0.361112i
$431$	20.1413	−	9.19824i	0.970174	−	0.443063i	0.133671	−	0.991026i	$-0.457324\pi$
$431$	20.1413	−	9.19824i	0.970174	−	0.443063i	0.836503	+	0.547962i	$0.184596\pi$
$432$	−9.20181	+	16.8519i	−0.442722	+	0.810786i
$433$	7.90994	+	21.2074i	0.380128	+	1.01916i	0.976322	+	0.216321i	$0.0694059\pi$
$433$	7.90994	+	21.2074i	0.380128	+	1.01916i	−0.596195	+	0.802840i	$0.703321\pi$
$434$	4.19362	−	29.1672i	0.201300	−	1.40007i
$435$	1.31257	−	1.21843i	0.0629329	−	0.0584194i
$436$		−	35.3096i		−	1.69102i
$437$	−1.57115	−	4.02300i	−0.0751581	−	0.192446i
$438$	35.1746	+	35.1746i	1.68071	+	1.68071i
$439$	−14.4740	−	22.5219i	−0.690805	−	1.07491i	−0.992587	−	0.121536i	$-0.961218\pi$
$439$	−14.4740	−	22.5219i	−0.690805	−	1.07491i	0.301782	−	0.953377i	$-0.402418\pi$
$440$	0.447924	+	13.0830i	0.0213539	+	0.623707i
$441$	5.04252	−	11.0416i	0.240120	−	0.525790i
$442$	−4.41749	−	2.41213i	−0.210119	−	0.114733i
$443$	5.72218	−	15.3418i	0.271869	−	0.728909i	−0.727227	−	0.686397i	$-0.759191\pi$
$443$	5.72218	−	15.3418i	0.271869	−	0.728909i	0.999096	−	0.0425117i	$-0.0135360\pi$
$444$	2.41960	+	2.79237i	0.114829	+	0.132520i
$445$	−4.78821	+	9.53045i	−0.226983	+	0.451787i
$446$	−49.4055	−	14.5068i	−2.33942	−	0.686915i
$447$	−29.3247	+	2.09734i	−1.38701	+	0.0992008i
$448$	52.3459	−	11.3872i	2.47311	−	0.537993i
$449$	−7.17802	+	11.1692i	−0.338752	+	0.527108i	−0.968279	−	0.249870i	$-0.919612\pi$
$449$	−7.17802	+	11.1692i	−0.338752	+	0.527108i	0.629527	+	0.776978i	$0.283249\pi$
$450$	19.7686	+	43.6276i	0.931900	+	2.05662i
$451$	−1.20807	+	4.11431i	−0.0568857	+	0.193735i
$452$	−62.7484	+	83.8221i	−2.95144	+	3.94266i
$453$	−3.43497	+	48.0272i	−0.161389	+	2.25651i
$454$	15.5671	+	34.0872i	0.730601	+	1.59979i
$455$	3.51255	−	10.5018i	0.164671	−	0.492330i
$456$	−19.5487	−	8.92760i	−0.915453	−	0.418073i
$457$	4.57417	−	3.42418i	0.213970	−	0.160176i	−0.486917	−	0.873448i	$-0.661879\pi$
$457$	4.57417	−	3.42418i	0.213970	−	0.160176i	0.700887	+	0.713272i	$0.252788\pi$
$458$	5.10622	−	23.4729i	0.238598	−	1.09682i
$459$	0.921716			0.0430220
$460$	58.1600	−	2.88417i	2.71172	−	0.134475i
$461$	−40.1698			−1.87090			−0.935448	−	0.353465i	$-0.885003\pi$
$461$	−40.1698			−1.87090			−0.935448	+	0.353465i	$0.885003\pi$
$462$	−1.74367	+	8.01554i	−0.0811231	+	0.372917i
$463$	14.4235	−	10.7973i	0.670318	−	0.501793i	−0.209070	−	0.977901i	$-0.567044\pi$
$463$	14.4235	−	10.7973i	0.670318	−	0.501793i	0.879387	+	0.476107i	$0.157953\pi$
$464$	−4.17490	−	1.90661i	−0.193815	−	0.0885123i
$465$	−14.6223	−	29.3196i	−0.678092	−	1.35967i
$466$	6.28369	+	13.7594i	0.291086	+	0.637390i
$467$	1.64520	−	23.0029i	0.0761306	−	1.06445i	−0.805528	−	0.592558i	$-0.798118\pi$
$467$	1.64520	−	23.0029i	0.0761306	−	1.06445i	0.881659	−	0.471888i	$-0.156427\pi$
$468$	30.0757	−	40.1764i	1.39025	−	1.85716i
$469$	7.48362	−	25.4869i	0.345562	−	1.17687i
$470$	8.40312	+	33.1271i	0.387607	+	1.52804i
$471$	22.8949	−	35.6251i	1.05494	−	1.64152i
$472$	−27.0336	+	5.88080i	−1.24432	+	0.270686i
$473$	−7.27784	+	0.520522i	−0.334636	+	0.0239336i
$474$	−63.3049	−	18.5880i	−2.90769	−	0.853775i
$475$	−3.95835	+	2.14628i	−0.181622	+	0.0984780i
$476$	−4.70149	−	5.42581i	−0.215492	−	0.248691i
$477$	8.12818	−	21.7925i	0.372164	−	0.997810i
$478$	−10.2855	−	5.61630i	−0.470447	−	0.256884i
$479$	−13.1399	+	28.7724i	−0.600378	+	1.31464i	0.328586	+	0.944474i	$0.393428\pi$
$479$	−13.1399	+	28.7724i	−0.600378	+	1.31464i	−0.928964	+	0.370170i	$0.879300\pi$
$480$	82.4516	−	88.2975i	3.76338	−	4.03021i
$481$	−0.379048	−	0.589810i	−0.0172831	−	0.0268930i
$482$	0.308935	+	0.308935i	0.0140716	+	0.0140716i
$483$	22.5956	+	4.55386i	1.02813	+	0.207208i
$484$		−	57.6024i		−	2.61829i
$485$	15.8588	+	17.0841i	0.720112	+	0.775747i
$486$	8.64905	−	60.1555i	0.392329	−	2.72871i
$487$	4.55136	+	12.2027i	0.206242	+	0.552955i	0.998350	−	0.0574256i	$-0.0182892\pi$
$487$	4.55136	+	12.2027i	0.206242	+	0.552955i	−0.792108	+	0.610381i	$0.791016\pi$
$488$	−40.8492	+	74.8097i	−1.84916	+	3.38648i
$489$	−16.4864	+	7.52908i	−0.745541	+	0.340477i
$490$	−13.2340	+	16.3728i	−0.597851	+	0.739650i
$491$	1.56156	+	10.8609i	0.0704723	+	0.490145i	0.994239	+	0.107189i	$0.0341850\pi$
$491$	1.56156	+	10.8609i	0.0704723	+	0.490145i	−0.923766	+	0.382956i	$0.874906\pi$
$492$	83.3038	−	45.4873i	3.75562	−	2.05073i
$493$	0.0157179	+	0.219764i	0.000707896	+	0.00989769i
$494$	5.43088	+	3.49022i	0.244347	+	0.157032i
$495$	1.87624	+	4.54862i	0.0843307	+	0.204445i
$496$	−54.9848	+	63.4559i	−2.46889	+	2.84925i
$497$	6.38425	+	11.6919i	0.286373	+	0.524452i
$498$	0.246956	+	0.184869i	0.0110663	+	0.00828416i
$499$	26.0855	−	22.6032i	1.16775	−	1.01186i	0.168086	−	0.985772i	$-0.446241\pi$
$499$	26.0855	−	22.6032i	1.16775	−	1.01186i	0.999660	−	0.0260851i	$-0.00830409\pi$
$500$	−10.5147	−	59.7931i	−0.470230	−	2.67403i
$501$	−11.8132	+	3.46868i	−0.527777	+	0.154969i
$502$	−36.5573	+	13.6352i	−1.63163	+	0.608567i
$503$	8.26553	+	11.0415i	0.368542	+	0.492314i	0.946027	−	0.324087i	$-0.105057\pi$
$503$	8.26553	+	11.0415i	0.368542	+	0.492314i	−0.577486	+	0.816401i	$0.695966\pi$
$504$	52.0532	−	33.4526i	2.31863	−	1.49010i
$505$	−2.25375	−	1.56974i	−0.100291	−	0.0698527i
$506$	8.18429	−	0.125441i	0.363836	−	0.00557654i
$507$	10.9798	−	10.9798i	0.487629	−	0.487629i
$508$	−13.5219	−	2.94152i	−0.599939	−	0.130509i
$509$	−22.1258	−	3.18121i	−0.980709	−	0.141005i	−0.366730	−	0.930327i	$-0.619523\pi$
$509$	−22.1258	−	3.18121i	−0.980709	−	0.141005i	−0.613979	+	0.789323i	$0.710432\pi$
$510$	−10.5793	−	2.71685i	−0.468460	−	0.120304i
$511$	−3.79331	−	12.9188i	−0.167806	−	0.571495i
$512$	−33.8223	−	12.6151i	−1.49475	−	0.557513i
$513$	−1.17921	−	0.0843390i	−0.0520635	−	0.00372366i
$514$	58.7608	−	8.44852i	2.59183	−	0.372648i
$515$	6.12292	+	0.667426i	0.269808	+	0.0294103i
$516$	122.057	+	105.763i	5.37326	+	4.65596i
$517$	0.746285	+	3.43061i	0.0328216	+	0.150878i
$518$	−0.290878	−	1.33714i	−0.0127804	−	0.0587508i
$519$	31.1317	+	26.9758i	1.36653	+	1.18411i
$520$	−42.8627	+	34.4367i	−1.87965	+	1.51015i
$521$	26.3748	−	3.79213i	1.15550	−	0.166136i	0.462195	−	0.886779i	$-0.347062\pi$
$521$	26.3748	−	3.79213i	1.15550	−	0.166136i	0.693307	+	0.720643i	$0.256153\pi$
$522$	−2.99841	−	0.214451i	−0.131237	−	0.00938625i
$523$	10.4950	+	3.91444i	0.458915	+	0.171166i	0.568280	−	0.822835i	$-0.307609\pi$
$523$	10.4950	+	3.91444i	0.458915	+	0.171166i	−0.109365	+	0.994002i	$0.534882\pi$
$524$	17.5775	+	59.8635i	0.767877	+	2.61515i
$525$	1.78512	−	23.9648i	0.0779092	−	1.04591i
$526$	63.8710	+	9.18326i	2.78491	+	0.400409i
$527$	3.93857	+	0.856783i	0.171567	+	0.0373221i
$528$	16.5277	−	16.5277i	0.719277	−	0.719277i
$529$	−0.704880	−	22.9892i	−0.0306470	−	0.999530i
$530$	−23.0554	+	33.1016i	−1.00146	+	1.43784i
$531$	−8.74800	+	5.62200i	−0.379631	+	0.243974i
$532$	5.51846	+	7.37180i	0.239256	+	0.319608i
$533$	−16.8747	+	6.29393i	−0.730923	+	0.272620i
$534$	31.8404	−	9.34917i	1.37787	−	0.404578i
$535$	28.1769	−	19.5020i	1.21819	−	0.843144i
$536$	−99.6757	+	86.3695i	−4.30533	+	3.73059i
$537$	−15.9832	−	11.9649i	−0.689726	−	0.516322i
$538$	−22.3668	−	40.9617i	−0.964301	−	1.76598i
$539$	−1.41625	+	1.63444i	−0.0610023	+	0.0704004i
$540$	6.12163	−	14.7174i	0.263433	−	0.633338i
$541$	−19.0798	−	12.2618i	−0.820305	−	0.527178i	0.0618788	−	0.998084i	$-0.480291\pi$
$541$	−19.0798	−	12.2618i	−0.820305	−	0.527178i	−0.882183	+	0.470906i	$0.843927\pi$
$542$	−3.15943	−	44.1747i	−0.135709	−	1.89746i
$543$	1.62529	−	0.887475i	0.0697479	−	0.0380852i
$544$	2.11512	+	14.7110i	0.0906851	+	0.630728i
$545$	1.53293	+	14.4591i	0.0656635	+	0.619361i
$546$	−31.3403	+	14.3126i	−1.34124	+	0.612524i
$547$	−6.24748	+	11.4414i	−0.267123	+	0.489199i	−0.976468	−	0.215662i	$-0.930809\pi$
$547$	−6.24748	+	11.4414i	−0.267123	+	0.489199i	0.709345	+	0.704861i	$0.248991\pi$
$548$	−14.7187	−	39.4624i	−0.628753	−	1.68575i
$549$	−4.55943	+	31.7115i	−0.194592	+	1.35342i
$550$	−1.18953	−	8.45040i	−0.0507218	−	0.360326i
$551$		−	0.282598i		−	0.0120391i
$552$	−82.1572	−	79.6767i	−3.49684	−	3.39127i
$553$	12.6275	+	12.6275i	0.536976	+	0.536976i
$554$	4.17634	+	6.49851i	0.177436	+	0.276095i
$555$	−1.11204	−	1.03842i	−0.0472036	−	0.0440784i
$556$	14.6299	−	32.0351i	0.620448	−	1.35859i
$557$	39.4102	+	21.5196i	1.66986	+	0.911814i	0.982676	+	0.185332i	$0.0593361\pi$
$557$	39.4102	+	21.5196i	1.66986	+	0.911814i	0.687186	+	0.726482i	$0.258846\pi$
$558$	−19.2183	+	51.5263i	−0.813577	+	2.18128i
$559$	−20.0689	−	23.1608i	−0.848825	−	0.979596i
$560$	−58.4625	+	19.3624i	−2.47049	+	0.818209i
$561$	−1.07660	−	0.316119i	−0.0454541	−	0.0133465i
$562$	6.78945	−	0.485591i	0.286396	−	0.0204834i
$563$	5.17637	−	1.12605i	0.218158	−	0.0474573i	−0.102158	−	0.994768i	$-0.532575\pi$
$563$	5.17637	−	1.12605i	0.218158	−	0.0474573i	0.320316	+	0.947311i	$0.396211\pi$
$564$	42.0141	−	65.3752i	1.76911	−	2.75279i
$565$	22.0561	−	37.0489i	0.927909	−	1.55866i
$566$	25.1961	−	85.8101i	1.05907	−	3.60687i
$567$	−8.11658	+	10.8425i	−0.340864	+	0.455341i
$568$	4.71860	−	65.9747i	0.197988	−	2.76823i
$569$	−12.6740	−	27.7522i	−0.531321	−	1.16343i	−0.964973	−	0.262350i	$-0.915502\pi$
$569$	−12.6740	−	27.7522i	−0.531321	−	1.16343i	0.433651	−	0.901081i	$-0.357225\pi$
$570$	13.2862	+	4.44388i	0.556499	+	0.186134i
$571$	1.89474	+	0.865299i	0.0792924	+	0.0362116i	0.454666	−	0.890662i	$-0.349758\pi$
$571$	1.89474	+	0.865299i	0.0792924	+	0.0362116i	−0.375374	+	0.926873i	$0.622486\pi$
$572$	−7.15809	+	5.35848i	−0.299295	+	0.224049i
$573$	0.633022	−	2.90995i	0.0264449	−	0.121565i
$574$	−35.1522			−1.46722
$575$	−23.6910	+	3.70601i	−0.987985	+	0.154551i
$576$	−99.9764			−4.16568
$577$	0.0288762	−	0.132742i	0.00120213	−	0.00552612i	−0.976542	−	0.215327i	$-0.930918\pi$
$577$	0.0288762	−	0.132742i	0.00120213	−	0.00552612i	0.977744	+	0.209801i	$0.0672817\pi$
$578$	−36.0206	+	26.9647i	−1.49826	+	1.12158i
$579$	45.7687	+	20.9019i	1.90208	+	0.868652i
$580$	3.61347	+	1.20860i	0.150041	+	0.0501846i
$581$	−0.0346860	−	0.0759517i	−0.00143902	−	0.00315101i
$582$	5.17396	−	72.3414i	0.214467	−	2.99865i
$583$	−2.48339	+	3.31742i	−0.102851	+	0.137393i
$584$	−18.8345	+	64.1445i	−0.779378	+	2.65432i
$585$	−10.5716	+	17.7578i	−0.437084	+	0.734194i
$586$	−28.7080	+	44.6705i	−1.18592	+	1.84532i
$587$	19.0839	−	4.15144i	0.787676	−	0.171348i	0.199303	−	0.979938i	$-0.436132\pi$
$587$	19.0839	−	4.15144i	0.787676	−	0.171348i	0.588373	+	0.808590i	$0.299769\pi$
$588$	47.7483	−	3.41502i	1.96911	−	0.140833i
$589$	−4.96048	−	1.45653i	−0.204393	−	0.0600152i
$590$	17.1206	−	5.67023i	0.704845	−	0.233440i
$591$	−9.47624	−	10.9362i	−0.389800	−	0.449854i
$592$	−1.36263	+	3.65334i	−0.0560036	+	0.150151i
$593$	−16.1268	−	8.80591i	−0.662249	−	0.361616i	0.112709	−	0.993628i	$-0.464047\pi$
$593$	−16.1268	−	8.80591i	−0.662249	−	0.361616i	−0.774958	+	0.632012i	$0.782229\pi$
$594$	0.930763	−	2.03809i	0.0381897	−	0.0836237i
$595$	2.16079	+	2.01773i	0.0885839	+	0.0827190i
$596$	−33.8161	−	52.6189i	−1.38516	−	2.15535i
$597$	24.7974	+	24.7974i	1.01489	+	1.01489i
$598$	21.0221	+	27.2030i	0.859656	+	1.11241i
$599$			30.0593i			1.22819i	0.789232	+	0.614095i	$0.210479\pi$
$599$			30.0593i			1.22819i	−0.789232	+	0.614095i	$0.789521\pi$
$600$	−71.7872	+	95.3087i	−2.93070	+	3.89096i
$601$	−1.70361	+	11.8489i	−0.0694919	+	0.483327i	0.925121	+	0.379671i	$0.123963\pi$
$601$	−1.70361	+	11.8489i	−0.0694919	+	0.483327i	−0.994613	+	0.103655i	$0.966946\pi$
$602$	−20.9031	−	56.0434i	−0.851947	−	2.28416i
$603$	−23.7580	+	43.5096i	−0.967502	+	1.77185i
$604$	−93.1825	+	42.5550i	−3.79154	+	1.73154i
$605$	2.50075	+	23.5879i	0.101670	+	0.958985i
$606$	1.21614	+	8.45846i	0.0494025	+	0.343602i
$607$	−30.8683	+	16.8553i	−1.25290	+	0.684137i	−0.962113	−	0.272649i	$-0.912100\pi$
$607$	−30.8683	+	16.8553i	−1.25290	+	0.684137i	−0.290791	+	0.956787i	$0.593918\pi$
$608$	−1.35993	−	19.0143i	−0.0551524	−	0.771132i
$609$	1.26879	+	0.815401i	0.0514139	+	0.0330417i
$610$	21.3394	−	51.3036i	0.864008	−	2.07722i
$611$	−9.65663	+	11.1443i	−0.390665	+	0.450852i
$612$	6.42129	+	11.7597i	0.259565	+	0.475358i
$613$	2.21490	+	1.65805i	0.0894588	+	0.0669680i	0.643071	−	0.765807i	$-0.277660\pi$
$613$	2.21490	+	1.65805i	0.0894588	+	0.0669680i	−0.553612	+	0.832775i	$0.686751\pi$
$614$	59.3426	−	51.4206i	2.39487	−	2.07517i
$615$	−32.1377	+	22.2434i	−1.29592	+	0.896940i
$616$	−10.5776	+	3.10587i	−0.426185	+	0.125139i
$617$	35.7466	−	13.3328i	1.43910	−	0.536758i	0.495727	−	0.868479i	$-0.334902\pi$
$617$	35.7466	−	13.3328i	1.43910	−	0.536758i	0.943378	+	0.331720i	$0.107629\pi$
$618$	−11.4842	−	15.3411i	−0.461961	−	0.617108i
$619$	−18.7737	+	12.0651i	−0.754577	+	0.484937i	−0.860508	−	0.509436i	$-0.829854\pi$
$619$	−18.7737	+	12.0651i	−0.754577	+	0.484937i	0.105931	+	0.994373i	$0.466218\pi$
$620$	39.8389	−	57.1985i	1.59997	−	2.29715i
$621$	−5.76630	−	2.52731i	−0.231394	−	0.101417i
$622$	12.2739	−	12.2739i	0.492138	−	0.492138i
$623$	−8.77673	−	1.90926i	−0.351632	−	0.0764929i
$624$	97.1739	+	13.9715i	3.89007	+	0.559308i
$625$	6.90156	+	24.0285i	0.276062	+	0.961140i
$626$	25.5369	+	86.9707i	1.02066	+	3.47605i
$627$	1.34844	+	0.502944i	0.0538517	+	0.0200856i
$628$	89.8658	+	6.42733i	3.58604	+	0.256478i
$629$	0.185274	−	0.0266384i	0.00738737	−	0.00106214i
$630$	−31.4449	+	25.2634i	−1.25280	+	1.00652i
$631$	6.26642	+	5.42988i	0.249462	+	0.216160i	0.770611	−	0.637305i	$-0.219951\pi$
$631$	6.26642	+	5.42988i	0.249462	+	0.216160i	−0.521149	+	0.853466i	$0.674496\pi$
$632$	−18.8478	−	86.6420i	−0.749726	−	3.44644i
$633$	8.88513	+	40.8443i	0.353152	+	1.62341i
$634$	−44.8844	−	38.8925i	−1.78259	−	1.54462i
$635$	5.66488	+	0.617497i	0.224804	+	0.0245046i
$636$	90.7920	−	13.0539i	3.60014	−	0.517622i
$637$	−9.06041	−	0.648013i	−0.358987	−	0.0256752i
$638$	0.501813	+	0.187166i	0.0198669	+	0.00740999i
$639$	−7.00423	−	23.8542i	−0.277083	−	0.943658i
$640$	76.2547	+	19.5828i	3.01423	+	0.774078i
$641$	−35.5107	−	5.10566i	−1.40259	−	0.201662i	−0.600861	−	0.799353i	$-0.705176\pi$
$641$	−35.5107	−	5.10566i	−1.40259	−	0.201662i	−0.801726	+	0.597692i	$0.796085\pi$
$642$	−104.182	−	22.6633i	−4.11172	−	0.894450i
$643$	23.2345	−	23.2345i	0.916279	−	0.916279i	−0.0804779	−	0.996756i	$-0.525645\pi$
$643$	23.2345	−	23.2345i	0.916279	−	0.916279i	0.996756	+	0.0804779i	$0.0256446\pi$
$644$	14.5354	+	46.8354i	0.572775	+	1.84557i
$645$	−54.5734	−	38.0105i	−2.14882	−	1.49666i
$646$	−1.44992	+	0.931806i	−0.0570463	+	0.0366614i
$647$	16.1914	+	21.6292i	0.636551	+	0.850333i	0.996582	−	0.0826075i	$-0.0263248\pi$
$647$	16.1914	+	21.6292i	0.636551	+	0.850333i	−0.360031	+	0.932940i	$0.617234\pi$
$648$	63.0083	−	23.5009i	2.47520	−	0.923201i
$649$	1.77766	−	0.521969i	0.0697794	−	0.0204891i
$650$	25.4194	−	25.2698i	0.997032	−	0.991162i
$651$	20.8523	−	18.0686i	0.817266	−	0.708165i
$652$	−30.8686	−	23.1080i	−1.20891	−	0.904978i
$653$	11.1705	+	20.4573i	0.437136	+	0.800555i	0.999656	−	0.0262286i	$-0.00834978\pi$
$653$	11.1705	+	20.4573i	0.437136	+	0.800555i	−0.562520	+	0.826784i	$0.690168\pi$
$654$	29.6255	−	34.1897i	1.15845	−	1.33692i
$655$	−9.79682	−	23.7507i	−0.382793	−	0.928017i
$656$	84.2625	+	54.1522i	3.28990	+	2.11429i
$657$	1.79260	+	25.0639i	0.0699361	+	0.977834i
$658$	−25.2607	+	13.7934i	−0.984764	+	0.537722i
$659$	−3.25005	−	22.6046i	−0.126604	−	0.880550i	−0.949814	−	0.312814i	$-0.898728\pi$
$659$	−3.25005	−	22.6046i	−0.126604	−	0.880550i	0.823211	−	0.567736i	$-0.192181\pi$
$660$	−12.1979	+	15.0911i	−0.474804	+	0.587418i
$661$	−8.22561	+	3.75651i	−0.319939	+	0.146111i	−0.568910	−	0.822400i	$-0.692635\pi$
$661$	−8.22561	+	3.75651i	−0.319939	+	0.146111i	0.248971	+	0.968511i	$0.419908\pi$
$662$	−11.2377	+	20.5802i	−0.436764	+	0.799874i
$663$	−1.64695	−	4.41564i	−0.0639622	−	0.171489i
$664$	−0.0590009	+	0.410360i	−0.00228968	+	0.0159251i
$665$	−2.57982	−	2.77914i	−0.100041	−	0.107770i
$666$			2.55384i			0.0989591i
$667$	0.504254	−	1.41795i	0.0195248	−	0.0549034i
$668$	−18.5219	−	18.5219i	−0.716635	−	0.716635i
$669$	−26.0663	−	40.5600i	−1.00778	−	1.56814i
$670$	58.6798	−	62.8403i	2.26700	−	2.42773i
$671$	2.37120	−	5.19221i	0.0915392	−	0.200443i
$672$	89.2932	+	48.7578i	3.44456	+	1.88087i
$673$	−5.49127	+	14.7227i	−0.211673	+	0.567517i	−0.998784	−	0.0492939i	$-0.984303\pi$
$673$	−5.49127	+	14.7227i	−0.211673	+	0.567517i	0.787111	+	0.616811i	$0.211576\pi$
$674$	11.8166	+	13.6371i	0.455160	+	0.525283i
$675$	−1.86784	+	6.29249i	−0.0718931	+	0.242198i
$676$	31.6974	+	9.30720i	1.21913	+	0.357969i
$677$	−6.69166	+	0.478597i	−0.257181	+	0.0183940i	−0.199335	−	0.979931i	$-0.563878\pi$
$677$	−6.69166	+	0.478597i	−0.257181	+	0.0183940i	−0.0578469	+	0.998325i	$0.518424\pi$
$678$	−131.087	+	28.5162i	−5.03436	+	1.09516i
$679$	−10.6131	+	16.5142i	−0.407292	+	0.633758i
$680$	−3.60923	−	14.2285i	−0.138408	−	0.545636i
$681$	−9.88554	+	33.6671i	−0.378815	+	1.29013i
$682$	5.87174	−	7.84373i	0.224841	−	0.300352i
$683$	0.355542	−	4.97112i	0.0136044	−	0.190215i	−0.986105	−	0.166122i	$-0.946876\pi$
$683$	0.355542	−	4.97112i	0.0136044	−	0.190215i	0.999710	−	0.0240933i	$-0.00766986\pi$
$684$	−7.13915	−	15.6326i	−0.272972	−	0.597726i
$685$	7.74047	+	15.5207i	0.295748	+	0.593015i
$686$	−48.8108	−	22.2911i	−1.86360	−	0.851079i
$687$	18.0064	−	13.4795i	0.686989	−	0.514273i
$688$	−36.2290	+	166.542i	−1.38122	+	6.34935i
$689$	−17.4053			−0.663089
$690$	58.7352	+	46.0048i	2.23601	+	1.75137i
$691$	−24.3053			−0.924617			−0.462308	−	0.886719i	$-0.652979\pi$
$691$	−24.3053			−0.924617			−0.462308	+	0.886719i	$0.652979\pi$
$692$	−18.6291	+	85.6365i	−0.708171	+	3.25541i
$693$	−3.31717	+	2.48320i	−0.126009	+	0.0943291i
$694$	−23.7473	−	10.8450i	−0.901435	−	0.411672i
$695$	−4.60012	+	13.7534i	−0.174493	+	0.521695i
$696$	−3.11087	−	6.81185i	−0.117917	−	0.258202i
$697$	0.343021	−	4.79606i	0.0129928	−	0.181664i
$698$	28.6224	−	38.2351i	1.08338	−	1.44722i
$699$	−3.99031	+	13.5898i	−0.150928	+	0.514012i
$700$	46.5691	−	21.1015i	1.76015	−	0.797560i
$701$	11.0877	−	17.2529i	0.418778	−	0.651632i	−0.566208	−	0.824262i	$-0.691590\pi$
$701$	11.0877	−	17.2529i	0.418778	−	0.651632i	0.984987	+	0.172630i	$0.0552266\pi$
$702$	9.19563	−	2.00039i	0.347067	−	0.0754997i
$703$	−0.239472	+	0.0171273i	−0.00903184	+	0.000645970i
$704$	17.0909	+	5.01834i	0.644138	+	0.189136i
$705$	−14.3664	+	28.5948i	−0.541069	+	1.07694i
$706$	−3.98250	−	4.59605i	−0.149883	−	0.172975i
$707$	0.808303	−	2.16714i	0.0303994	−	0.0815038i
$708$	−35.9930	−	19.6536i	−1.35270	−	0.738629i
$709$	4.12217	−	9.02630i	0.154811	−	0.338990i	−0.816295	−	0.577635i	$-0.803976\pi$
$709$	4.12217	−	9.02630i	0.154811	−	0.338990i	0.971107	+	0.238645i	$0.0767032\pi$
$710$	1.47538	+	43.0930i	0.0553701	+	1.61725i
$711$	−18.0184	−	28.0371i	−0.675742	−	1.05147i
$712$	31.5351	+	31.5351i	1.18183	+	1.18183i
$713$	−22.2906	−	16.1595i	−0.834790	−	0.605178i
$714$		−	9.19836i		−	0.344240i
$715$	2.69857	−	2.50503i	0.100921	−	0.0936830i
$716$	6.04510	−	42.0446i	0.225916	−	1.57128i
$717$	−3.83468	−	10.2812i	−0.143209	−	0.383958i
$718$	5.71973	−	10.4749i	0.213459	−	0.390920i
$719$	9.55228	−	4.36238i	0.356240	−	0.162689i	−0.229253	−	0.973367i	$-0.573628\pi$
$719$	9.55228	−	4.36238i	0.356240	−	0.162689i	0.585493	+	0.810678i	$0.300901\pi$
$720$	114.294	−	12.1173i	4.25950	−	0.451585i
$721$	0.738174	+	5.13411i	0.0274910	+	0.191204i
$722$	−43.5153	+	23.7612i	−1.61947	+	0.884299i
$723$	0.0291842	+	0.408049i	0.00108537	+	0.0151755i
$724$	3.31433	+	2.12999i	0.123176	+	0.0791605i
$725$	−1.53217	−	0.338043i	−0.0569033	−	0.0125546i
$726$	48.3296	−	55.7754i	1.79368	−	2.07002i
$727$	10.9624	+	20.0762i	0.406575	+	0.744586i	0.998094	−	0.0617047i	$-0.0196537\pi$
$727$	10.9624	+	20.0762i	0.406575	+	0.744586i	−0.591520	+	0.806290i	$0.701472\pi$
$728$	−37.0676	−	27.7485i	−1.37382	−	1.02843i
$729$	26.6995	−	23.1352i	0.988870	−	0.856860i
$730$	7.80119	−	42.8768i	0.288735	−	1.58694i
$731$	7.85037	−	2.30508i	0.290356	−	0.0852563i
$732$	−118.380	+	44.1533i	−4.37543	+	1.63195i
$733$	−4.02395	−	5.37537i	−0.148628	−	0.198544i	0.720048	−	0.693924i	$-0.244120\pi$
$733$	−4.02395	−	5.37537i	−0.148628	−	0.198544i	−0.868676	+	0.495380i	$0.835029\pi$
$734$	46.3012	−	29.7560i	1.70901	−	1.09831i
$735$	−19.4044	+	3.47138i	−0.715743	+	0.128044i
$736$	27.1047	−	97.8323i	0.999092	−	3.60615i
$737$	6.24540	−	6.24540i	0.230052	−	0.230052i
$738$	64.1042	+	13.9450i	2.35971	+	0.513323i
$739$	−3.53564	−	0.508349i	−0.130061	−	0.0186999i	0.0769770	−	0.997033i	$-0.475473\pi$
$739$	−3.53564	−	0.508349i	−0.130061	−	0.0186999i	−0.207038	+	0.978333i	$0.566382\pi$
$740$	0.805164	−	3.13528i	0.0295984	−	0.115255i
$741$	1.70301	+	5.79993i	0.0625618	+	0.213066i
$742$	−31.8295	−	11.8718i	−1.16850	−	0.435828i
$743$	−21.4165	−	1.53174i	−0.785696	−	0.0561941i	−0.327275	−	0.944929i	$-0.606130\pi$
$743$	−21.4165	−	1.53174i	−0.785696	−	0.0561941i	−0.458421	+	0.888735i	$0.651585\pi$
$744$	−135.603	+	19.4968i	−4.97145	+	0.714786i
$745$	16.1319	+	20.0791i	0.591028	+	0.735641i
$746$	−33.7993	−	29.2873i	−1.23748	−	1.07228i
$747$	0.0331237	+	0.152267i	0.00121193	+	0.00557116i
$748$	−0.507433	−	2.33263i	−0.0185536	−	0.0852895i
$749$	21.8095	+	18.8980i	0.796902	+	0.690520i
$750$	39.9865	−	66.7186i	1.46010	−	2.43622i
$751$	−34.8402	+	5.00927i	−1.27134	+	0.182791i	−0.744758	−	0.667334i	$-0.767435\pi$
$751$	−34.8402	+	5.00927i	−1.27134	+	0.182791i	−0.526580	+	0.850125i	$0.676526\pi$
$752$	81.8007	+	5.85050i	2.98296	+	0.213346i
$753$	−34.2303	−	12.7673i	−1.24742	−	0.465265i
$754$	0.633763	+	2.15840i	0.0230803	+	0.0786042i
$755$	36.3103	−	21.4715i	1.32147	−	0.781428i
$756$	13.2869	+	1.91037i	0.483241	+	0.0694796i
$757$	46.2968	+	10.0712i	1.68268	+	0.366046i	0.949447	−	0.313927i	$-0.101645\pi$
$757$	46.2968	+	10.0712i	1.68268	+	0.366046i	0.733237	+	0.679973i	$0.238008\pi$
$758$	9.24397	−	9.24397i	0.335756	−	0.335756i
$759$	5.86849	+	4.92966i	0.213013	+	0.178935i
$760$	3.31560	+	18.5337i	0.120270	+	0.672287i
$761$	−21.3031	+	13.6907i	−0.772237	+	0.496286i	−0.866449	−	0.499266i	$-0.833603\pi$
$761$	−21.3031	+	13.6907i	−0.772237	+	0.496286i	0.0942122	+	0.995552i	$0.469967\pi$
$762$	−10.6251	−	14.1934i	−0.384905	−	0.514174i
$763$	−11.4728	+	4.27914i	−0.415344	+	0.154915i
$764$	6.07913	−	1.78500i	0.219935	−	0.0645789i
$765$	−3.14002	−	4.53677i	−0.113528	−	0.164027i
$766$	−27.2775	+	23.6360i	−0.985574	+	0.854005i
$767$	6.22954	+	4.66337i	0.224936	+	0.168385i
$768$	−47.7983	−	87.5361i	−1.72477	−	3.15869i
$769$	22.6888	−	26.1843i	0.818179	−	0.944228i	−0.181051	−	0.983474i	$-0.557950\pi$
$769$	22.6888	−	26.1843i	0.818179	−	0.944228i	0.999230	+	0.0392453i	$0.0124954\pi$
$770$	6.64359	−	2.74038i	0.239418	−	0.0987566i
$771$	46.7622	+	30.0523i	1.68410	+	1.08231i
$772$	7.63668	+	106.775i	0.274850	+	3.84291i
$773$	30.0247	−	16.3948i	1.07992	−	0.589678i	0.162136	−	0.986768i	$-0.448162\pi$
$773$	30.0247	−	16.3948i	1.07992	−	0.589678i	0.917780	+	0.397090i	$0.129980\pi$
$774$	15.8867	+	110.494i	0.571034	+	3.97163i
$775$	−13.8306	+	25.1521i	−0.496811	+	0.903490i
$776$	88.6612	−	40.4902i	3.18275	−	1.45351i
$777$	0.614069	−	1.12458i	0.0220296	−	0.0403442i
$778$	−12.5759	−	33.7174i	−0.450869	−	1.20883i
$779$	−0.877700	+	6.10453i	−0.0314469	+	0.218718i
$780$	−81.4449	−	3.02920i	−2.91619	−	0.108463i
$781$			4.42944i			0.158498i
$782$	−8.93774	+	2.08824i	−0.319613	+	0.0746753i
$783$	−0.291294	−	0.291294i	−0.0104100	−	0.0104100i
$784$	27.3120	+	42.4983i	0.975427	+	1.51779i
$785$	−37.0787	+	1.26947i	−1.32339	+	0.0453092i
$786$	−33.2068	+	72.7127i	−1.18445	+	2.59358i
$787$	22.5883	+	12.3341i	0.805185	+	0.439664i	0.828449	−	0.560065i	$-0.189224\pi$
$787$	22.5883	+	12.3341i	0.805185	+	0.439664i	−0.0232634	+	0.999729i	$0.507406\pi$
$788$	10.7588	−	28.8454i	0.383266	−	1.02758i
$789$	39.5670	+	45.6628i	1.40862	+	1.62564i
$790$	18.1730	+	54.8712i	0.646565	+	1.95223i
$791$	34.8399	+	10.2299i	1.23877	+	0.363734i
$792$	20.5217	−	1.46774i	0.729206	−	0.0521538i
$793$	23.4267	−	5.09616i	0.831905	−	0.180970i
$794$	−21.4008	+	33.3002i	−0.759485	+	1.18178i
$795$	−36.6122	+	9.28716i	−1.29850	+	0.329382i
$796$	−21.0199	+	71.5873i	−0.745031	+	2.53734i
$797$	22.9720	−	30.6870i	0.813711	−	1.08699i	−0.180920	−	0.983498i	$-0.557907\pi$
$797$	22.9720	−	30.6870i	0.813711	−	1.08699i	0.994630	−	0.103492i	$-0.0330017\pi$
$798$	−0.841671	+	11.7681i	−0.0297948	+	0.416586i
$799$	−1.63543	−	3.58109i	−0.0578573	−	0.126690i
$800$	−104.717	−	15.3717i	−3.70231	−	0.543473i
$801$	15.2480	+	6.96353i	0.538762	+	0.246044i
$802$	35.5565	−	26.6173i	1.25554	−	0.939889i
$803$	0.951643	−	4.37463i	0.0335827	−	0.154377i
$804$	−195.501			−6.89479
$805$	−7.98549	−	18.5479i	−0.281451	−	0.653726i
$806$	41.1532			1.44956
$807$	9.28907	−	42.7012i	0.326991	−	1.50315i
$808$	−9.19373	+	6.88234i	−0.323434	+	0.242120i
$809$	−22.1760	−	10.1275i	−0.779668	−	0.356062i	−0.0145015	−	0.999895i	$-0.504616\pi$
$809$	−22.1760	−	10.1275i	−0.779668	−	0.356062i	−0.765167	+	0.643832i	$0.777343\pi$
$810$	−39.2306	+	19.5651i	−1.37842	+	0.687446i
$811$	−1.71142	−	3.74749i	−0.0600961	−	0.131592i	0.877201	−	0.480123i	$-0.159408\pi$
$811$	−1.71142	−	3.74749i	−0.0600961	−	0.131592i	−0.937297	+	0.348531i	$0.886681\pi$
$812$	−0.228910	+	3.20058i	−0.00803316	+	0.112318i
$813$	24.8512	−	33.1973i	0.871568	−	1.16428i
$814$	0.128190	−	0.436577i	0.00449307	−	0.0153020i
$815$	13.6438	+	8.12247i	0.477920	+	0.284518i
$816$	−14.1702	+	22.0492i	−0.496055	+	0.771876i
$817$	−10.2544	+	2.23071i	−0.358757	+	0.0780428i
$818$	−15.6734	+	1.12099i	−0.548009	+	0.0391944i
$819$	−16.6990	−	4.90327i	−0.583510	−	0.171334i
$820$	−74.3026	−	37.3305i	−2.59476	−	1.30364i
$821$	−30.6809	−	35.4076i	−1.07077	−	1.23573i	−0.970583	−	0.240766i	$-0.922601\pi$
$821$	−30.6809	−	35.4076i	−1.07077	−	1.23573i	−0.100187	−	0.994969i	$-0.531944\pi$
$822$	18.8579	−	50.5601i	0.657746	−	1.76349i
$823$	16.8502	+	9.20092i	0.587362	+	0.320724i	0.745304	−	0.666724i	$-0.232304\pi$
$823$	16.8502	+	9.20092i	0.587362	+	0.320724i	−0.157942	+	0.987448i	$0.550486\pi$
$824$	10.6986	−	23.4267i	0.372703	−	0.816107i
$825$	4.33983	−	6.70928i	0.151094	−	0.233587i
$826$	8.21134	+	12.7771i	0.285709	+	0.444572i
$827$	−37.9205	−	37.9205i	−1.31862	−	1.31862i	−0.914865	−	0.403760i	$-0.867703\pi$
$827$	−37.9205	−	37.9205i	−1.31862	−	1.31862i	−0.403760	−	0.914865i	$-0.632297\pi$
$828$	−7.92721	−	91.1763i	−0.275490	−	3.16859i
$829$			43.7742i			1.52034i	0.649723	+	0.760171i	$0.274885\pi$
$829$			43.7742i			1.52034i	−0.649723	+	0.760171i	$0.725115\pi$
$830$	0.0100450	−	0.270075i	0.000348666	−	0.00937444i
$831$	−1.02938	+	7.15948i	−0.0357087	+	0.248360i
$832$	26.1451	+	70.0977i	0.906418	+	2.43020i
$833$	1.16222	−	2.12846i	0.0402687	−	0.0737466i
$834$	41.0441	−	18.7442i	1.42124	−	0.649059i
$835$	8.38875	+	6.78053i	0.290305	+	0.234650i
$836$	0.435753	+	3.03073i	0.0150708	+	0.104820i
$837$	−6.61448	+	3.61178i	−0.228630	+	0.124841i
$838$	5.89615	+	82.4390i	0.203679	+	2.84781i
$839$	−9.16913	−	5.89264i	−0.316553	−	0.203436i	0.372709	−	0.927948i	$-0.378429\pi$
$839$	−9.16913	−	5.89264i	−0.316553	−	0.203436i	−0.689262	+	0.724512i	$0.742065\pi$
$840$	−92.7782	−	38.5905i	−3.20115	−	1.33150i
$841$	−18.9265	+	21.8423i	−0.652637	+	0.753183i
$842$	21.7925	+	39.9100i	0.751019	+	1.37539i
$843$	5.10227	+	3.81951i	0.175732	+	0.131551i
$844$	−67.2083	+	58.2363i	−2.31340	+	2.00458i
$845$	−13.3840	−	2.43515i	−0.460424	−	0.0837716i
$846$	51.5378	−	15.1329i	1.77191	−	0.520278i
$847$	−18.7162	+	6.98078i	−0.643096	+	0.239862i
$848$	58.0093	+	77.4913i	1.99205	+	2.66106i
$849$	70.4468	−	45.2734i	2.41773	−	1.55378i
$850$	3.31761	+	8.97569i	0.113793	+	0.307864i
$851$	−1.23213	−	0.341364i	−0.0422368	−	0.0117018i
$852$	69.3279	−	69.3279i	2.37513	−	2.37513i
$853$	45.1692	+	9.82595i	1.54656	+	0.336434i	0.903232	−	0.429153i	$-0.141188\pi$
$853$	45.1692	+	9.82595i	1.54656	+	0.336434i	0.643332	+	0.765588i	$0.277552\pi$
$854$	46.3170	+	6.65938i	1.58494	+	0.227879i
$855$	3.60212	+	6.09152i	0.123190	+	0.208326i
$856$	−40.3684	−	137.482i	−1.37976	−	4.69904i
$857$	−35.6548	−	13.2985i	−1.21794	−	0.454269i	−0.343387	−	0.939194i	$-0.611574\pi$
$857$	−35.6548	−	13.2985i	−1.21794	−	0.454269i	−0.874556	+	0.484924i	$0.838847\pi$
$858$	−11.4269	−	0.817271i	−0.390109	−	0.0279012i
$859$	15.3761	−	2.21075i	0.524626	−	0.0754298i	0.125087	−	0.992146i	$-0.460079\pi$
$859$	15.3761	−	2.21075i	0.524626	−	0.0754298i	0.399539	+	0.916716i	$0.369170\pi$
$860$	15.3325	−	140.660i	0.522836	−	4.79645i
$861$	−24.8753	−	21.5545i	−0.847747	−	0.734577i
$862$	12.8296	+	58.9766i	0.436977	+	2.00875i
$863$	6.27524	+	28.8468i	0.213612	+	0.981957i	0.951647	+	0.307194i	$0.0993902\pi$
$863$	6.27524	+	28.8468i	0.213612	+	0.981957i	−0.738035	+	0.674762i	$0.764246\pi$
$864$	−21.0012	−	18.1977i	−0.714476	−	0.619097i
$865$	3.91070	−	35.8765i	0.132968	−	1.21984i
$866$	−61.0696	+	8.78048i	−2.07523	+	0.298373i
$867$	−42.0239	−	3.00561i	−1.42721	−	0.102076i
$868$	55.0004	+	20.5141i	1.86684	+	0.696294i
$869$	1.67290	+	5.69737i	0.0567492	+	0.193270i
$870$	2.48481	+	4.20205i	0.0842430	+	0.142463i
$871$	36.7195	+	5.27946i	1.24419	+	0.178888i
$872$	59.4087	+	12.9236i	2.01183	+	0.437648i
$873$	25.9054	−	25.9054i	0.876766	−	0.876766i
$874$	11.6257	−	1.85380i	0.393246	−	0.0627058i
$875$	−18.1537	+	10.6627i	−0.613708	+	0.360465i
$876$	−83.3648	+	53.5753i	−2.81664	+	1.81014i
$877$	−7.15587	−	9.55912i	−0.241636	−	0.322788i	0.663285	−	0.748367i	$-0.269162\pi$
$877$	−7.15587	−	9.55912i	−0.241636	−	0.322788i	−0.904922	+	0.425578i	$0.860071\pi$
$878$	68.3743	−	25.5023i	2.30752	−	0.860660i
$879$	−47.7060	+	14.0078i	−1.60908	+	0.472470i
$880$	−20.1468	−	3.66560i	−0.679148	−	0.123567i
$881$	21.0560	−	18.2451i	0.709394	−	0.614693i	−0.223559	−	0.974690i	$-0.571768\pi$
$881$	21.0560	−	18.2451i	0.709394	−	0.614693i	0.932954	+	0.359997i	$0.117222\pi$
$882$	26.4879	+	19.8286i	0.891893	+	0.667663i
$883$	0.776599	+	1.42224i	0.0261347	+	0.0478620i	0.890420	−	0.455140i	$-0.150411\pi$
$883$	0.776599	+	1.42224i	0.0261347	+	0.0478620i	−0.864285	+	0.503002i	$0.832229\pi$
$884$	6.56599	−	7.57756i	0.220838	−	0.254861i
$885$	15.5922	+	6.48548i	0.524126	+	0.218007i
$886$	37.5477	+	24.1304i	1.26144	+	0.810678i
$887$	2.45854	+	34.3749i	0.0825498	+	1.15420i	0.854828	+	0.518912i	$0.173663\pi$
$887$	2.45854	+	34.3749i	0.0825498	+	1.15420i	−0.772278	+	0.635285i	$0.780883\pi$
$888$	−5.58378	+	3.04897i	−0.187379	+	0.102317i
$889$	0.682952	+	4.75004i	0.0229055	+	0.159311i
$890$	−22.6103	−	18.2756i	−0.757898	−	0.612600i
$891$	−4.09648	+	1.87080i	−0.137237	+	0.0626741i
$892$	49.1593	−	90.0286i	1.64598	−	3.01438i
$893$	1.76464	+	4.73118i	0.0590514	+	0.158323i
$894$	11.4048	−	79.3223i	0.381435	−	2.65294i
$895$	−0.650119	+	17.4795i	−0.0217311	+	0.584276i
$896$			66.3010i			2.21496i
$897$	−1.80413	+	32.1404i	−0.0602381	+	1.07314i
$898$	−25.5905	−	25.5905i	−0.853966	−	0.853966i
$899$	−0.973951	−	1.51550i	−0.0324831	−	0.0505447i
$900$	−93.2954	+	20.0069i	−3.10985	+	0.666896i
$901$	1.93035	−	4.22688i	0.0643093	−	0.140818i
$902$	−10.2586	−	5.60162i	−0.341574	−	0.186514i
$903$	19.5726	−	52.4762i	0.651335	−	1.74630i
$904$	−118.065	−	136.254i	−3.92678	−	4.53175i
$905$	−1.44967	−	0.728333i	−0.0481888	−	0.0242106i
$906$	−125.932	−	36.9768i	−4.18379	−	1.22847i
$907$	−30.5895	+	2.18781i	−1.01571	+	0.0726449i	−0.569254	−	0.822162i	$-0.692768\pi$
$907$	−30.5895	+	2.18781i	−1.01571	+	0.0726449i	−0.446454	+	0.894806i	$0.647313\pi$
$908$	−72.9452	+	15.8683i	−2.42077	+	0.526607i
$909$	−2.33375	+	3.63139i	−0.0774057	+	0.120446i
$910$	25.9365	+	15.4407i	0.859788	+	0.511853i
$911$	−10.1960	+	34.7242i	−0.337807	+	1.15047i	0.599038	+	0.800721i	$0.295550\pi$
$911$	−10.1960	+	34.7242i	−0.337807	+	1.15047i	−0.936845	+	0.349745i	$0.886268\pi$
$912$	20.1464	−	26.9124i	0.667114	−	0.891160i
$913$	0.00198062	−	0.0276926i	6.55488e−5	−	0.000916492i
$914$	6.47006	+	14.1674i	0.214010	+	0.468617i
$915$	46.5590	−	23.2199i	1.53919	−	0.767626i
$916$	43.5295	+	19.8793i	1.43826	+	0.656829i
$917$	17.3207	−	12.9661i	0.571979	−	0.428178i
$918$	−0.534056	+	2.45502i	−0.0176265	+	0.0810276i
$919$	28.2597			0.932202			0.466101	−	0.884732i	$-0.345658\pi$
$919$	28.2597			0.932202			0.466101	+	0.884732i	$0.345658\pi$
$920$	−16.4344	+	98.9103i	−0.541824	+	3.26098i
$921$	73.5235			2.42268
$922$	23.2750	−	106.994i	0.766522	−	3.52364i
$923$	−14.8935	+	11.1491i	−0.490226	+	0.366978i
$924$	−14.8645	−	6.78839i	−0.489006	−	0.223321i
$925$	−0.193596	+	1.31884i	−0.00636540	+	0.0433631i
$926$	20.4017	+	44.6736i	0.670443	+	1.46807i
$927$	0.690575	−	9.65550i	0.0226815	−	0.317128i
$928$	3.98073	−	5.31763i	0.130674	−	0.174560i
$929$	3.41489	−	11.6300i	0.112039	−	0.381570i	−0.884314	−	0.466892i	$-0.845374\pi$
$929$	3.41489	−	11.6300i	0.112039	−	0.381570i	0.996353	+	0.0853222i	$0.0271920\pi$
$930$	86.5661	−	21.9586i	2.83861	−	0.720051i
$931$	−1.68167	+	2.61673i	−0.0551146	+	0.0857599i
$932$	−29.4445	+	6.40525i	−0.964485	+	0.209811i
$933$	16.2116	−	1.15948i	0.530745	−	0.0379596i
$934$	60.3156	+	17.7102i	1.97359	+	0.579497i
$935$	0.309060	+	0.933173i	0.0101074	+	0.0305180i
$936$	56.5893	+	65.3075i	1.84968	+	2.13464i
$937$	−1.86625	+	5.00361i	−0.0609677	+	0.163461i	−0.963862	−	0.266402i	$-0.914165\pi$
$937$	−1.86625	+	5.00361i	−0.0609677	+	0.163461i	0.902894	+	0.429862i	$0.141438\pi$
$938$	63.5489	+	34.7004i	2.07495	+	1.13301i
$939$	−35.2575	+	77.2031i	−1.15058	+	2.51943i
$940$	−68.0427	+	2.32959i	−2.21931	+	0.0759827i
$941$	−14.6570	−	22.8067i	−0.477803	−	0.743476i	0.515763	−	0.856731i	$-0.327509\pi$
$941$	−14.6570	−	22.8067i	−0.477803	−	0.743476i	−0.993566	+	0.113255i	$0.963872\pi$
$942$	81.6229	+	81.6229i	2.65942	+	2.65942i
$943$	−15.2966	+	29.0638i	−0.498125	+	0.946448i
$944$		−	43.2773i		−	1.40856i
$945$	−5.52388	−	0.205451i	−0.179692	−	0.00668331i
$946$	2.83047	−	19.6864i	0.0920265	−	0.640059i
$947$	8.27712	+	22.1918i	0.268970	+	0.721137i	0.999277	+	0.0380178i	$0.0121044\pi$
$947$	8.27712	+	22.1918i	0.268970	+	0.721137i	−0.730307	+	0.683119i	$0.760623\pi$
$948$	62.9895	−	115.357i	2.04580	−	3.74661i
$949$	17.1046	−	7.81139i	0.555237	−	0.253568i
$950$	−3.42314	−	11.7868i	−0.111061	−	0.382414i
$951$	−7.91416	−	55.0442i	−0.256634	−	1.78493i
$952$	10.8497	−	5.92441i	0.351642	−	0.192011i
$953$	−1.26091	−	17.6298i	−0.0408448	−	0.571085i	−0.976130	−	0.217189i	$-0.930311\pi$
$953$	−1.26091	−	17.6298i	−0.0408448	−	0.571085i	0.935285	−	0.353896i	$-0.115143\pi$
$954$	53.3354	+	34.2766i	1.72680	+	1.10975i
$955$	−2.41188	+	0.994866i	−0.0780467	+	0.0321931i
$956$	15.2880	−	17.6432i	0.494448	−	0.570623i
$957$	0.240339	+	0.440148i	0.00776905	+	0.0142280i
$958$	−69.0226	−	51.6697i	−2.23002	−	1.66937i
$959$	−11.0384	+	9.56483i	−0.356449	+	0.308864i
$960$	92.3994	+	133.501i	2.98218	+	4.30872i
$961$	−1.87729	+	0.551223i	−0.0605579	+	0.0177814i
$962$	1.79060	−	0.667861i	0.0577314	−	0.0215327i
$963$	−32.2753	−	43.1148i	−1.04006	−	1.38935i
$964$	−0.732185	+	0.470547i	−0.0235821	+	0.0151553i
$965$	−7.76269	−	43.3922i	−0.249890	−	1.39684i
$966$	−25.2216	+	57.5454i	−0.811491	+	1.85149i
$967$	−35.9237	+	35.9237i	−1.15523	+	1.15523i	−0.169739	+	0.985489i	$0.554292\pi$
$967$	−35.9237	+	35.9237i	−1.15523	+	1.15523i	−0.985489	+	0.169739i	$0.945708\pi$
$968$	96.9165	+	21.0829i	3.11501	+	0.677630i
$969$	−1.59739	−	0.229670i	−0.0513156	−	0.00737806i
$970$	−54.6928	+	32.3416i	−1.75608	+	1.03843i
$971$	1.34882	+	4.59367i	0.0432858	+	0.147418i	0.978300	−	0.207191i	$-0.0664322\pi$
$971$	1.34882	+	4.59367i	0.0432858	+	0.147418i	−0.935015	+	0.354609i	$0.884614\pi$
$972$	113.435	+	42.3090i	3.63842	+	1.35706i
$973$	−12.1819	−	0.871264i	−0.390532	−	0.0279314i
$974$	−35.1393	+	5.05226i	−1.12593	+	0.161885i
$975$	33.4828	−	2.29540i	1.07231	−	0.0735117i
$976$	−100.767	−	87.3148i	−3.22546	−	2.79488i
$977$	−1.48156	−	6.81062i	−0.0473993	−	0.217891i	0.947355	−	0.320186i	$-0.103745\pi$
$977$	−1.48156	−	6.81062i	−0.0473993	−	0.217891i	−0.994754	+	0.102294i	$0.967382\pi$
$978$	−10.5015	−	48.2745i	−0.335800	−	1.54365i
$979$	−2.25710	−	1.95579i	−0.0721373	−	0.0625073i
$980$	−26.2670	−	32.6940i	−0.839069	−	1.04437i
$981$	22.6196	−	3.25221i	0.722189	−	0.103835i
$982$	−29.8331	−	2.13371i	−0.952013	−	0.0680893i
$983$	−22.3640	−	8.34134i	−0.713301	−	0.266047i	−0.0334941	−	0.999439i	$-0.510664\pi$
$983$	−22.3640	−	8.34134i	−0.713301	−	0.266047i	−0.679806	+	0.733392i	$0.737936\pi$
$984$	46.0430	+	156.808i	1.46780	+	4.99885i
$985$	−3.15338	+	12.2791i	−0.100475	+	0.391246i
$986$	−0.594456	−	0.0854699i	−0.0189313	−	0.00272191i
$987$	−26.3334	−	5.72848i	−0.838202	−	0.182340i
$988$	−9.09368	+	9.09368i	−0.289308	+	0.289308i
$989$	−55.4327	−	7.10475i	−1.76266	−	0.225918i
$990$	−13.2025	+	2.36188i	−0.419603	+	0.0750654i
$991$	11.9433	−	7.67552i	0.379393	−	0.243821i	−0.337020	−	0.941497i	$-0.609419\pi$
$991$	11.9433	−	7.67552i	0.379393	−	0.243821i	0.716413	+	0.697676i	$0.245783\pi$
$992$	−72.8243	−	97.2819i	−2.31217	−	3.08870i
$993$	−20.5716	+	7.67282i	−0.652821	+	0.243490i
$994$	−34.8408	+	10.2302i	−1.10508	+	0.324482i
$995$	5.49967	−	30.2272i	0.174351	−	0.958267i
$996$	−0.464434	+	0.402435i	−0.0147162	+	0.0127516i
$997$	−17.8053	−	13.3288i	−0.563898	−	0.422129i	0.278930	−	0.960311i	$-0.410020\pi$
$997$	−17.8053	−	13.3288i	−0.563898	−	0.422129i	−0.842828	+	0.538183i	$0.819111\pi$
$998$	45.0899	+	82.5760i	1.42730	+	2.61390i
$999$	−0.229187	+	0.264495i	−0.00725114	+	0.00836826i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.103.1	yes	200
5.2	odd	4	inner	115.2.l.a.57.1	✓	200
5.3	odd	4		575.2.r.b.57.10		200
5.4	even	2		575.2.r.b.218.10		200
23.21	odd	22	inner	115.2.l.a.113.1	yes	200
115.44	odd	22		575.2.r.b.343.10		200
115.67	even	44	inner	115.2.l.a.67.1	yes	200
115.113	even	44		575.2.r.b.182.10		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.57.1	✓	200	5.2	odd	4	inner
115.2.l.a.67.1	yes	200	115.67	even	44	inner
115.2.l.a.103.1	yes	200	1.1	even	1	trivial
115.2.l.a.113.1	yes	200	23.21	odd	22	inner
575.2.r.b.57.10		200	5.3	odd	4
575.2.r.b.182.10		200	115.113	even	44
575.2.r.b.218.10		200	5.4	even	2
575.2.r.b.343.10		200	115.44	odd	22

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	115.2.l.a.103.1

Level	$115$
Weight	$2$
Character	115.103
Analytic conductor	$0.918$
Analytic rank	$0$
Dimension	$200$
Inner twists	$4$