LMFDB - Embedded newform 966.2.s.a.727.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			727.3
Character	$\chi$	$=$	966.727
Dual form			966.2.s.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.288108 - 2.00384i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.63618 - 0.224848i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.288108 - 2.00384i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.63618 - 0.224848i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +(0.840984 + 1.84150i) q^{10} +(1.41556 - 4.82096i) q^{11} +(-0.281733 + 0.959493i) q^{12} +(2.71849 - 1.24149i) q^{13} +(-2.46605 + 0.958437i) q^{14} +(1.52997 + 1.32573i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-2.66541 - 1.71295i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-5.50906 + 3.54046i) q^{19} +(-1.32573 - 1.52997i) q^{20} +(-1.84505 + 1.89626i) q^{21} +5.02449i q^{22} +(1.21115 + 4.64038i) q^{23} -1.00000i q^{24} +(0.865112 - 0.254020i) q^{25} +(-2.25860 + 1.95709i) q^{26} +(0.540641 + 0.841254i) q^{27} +(2.09613 - 1.61438i) q^{28} +(-7.83543 - 5.03553i) q^{29} +(-1.84150 - 0.840984i) q^{30} +(-6.73891 - 5.83930i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(2.08725 + 4.57044i) q^{33} +(3.04004 + 0.892635i) q^{34} +(-1.21006 - 5.21769i) q^{35} +(-0.415415 - 0.909632i) q^{36} +(8.87698 + 1.27632i) q^{37} +(4.28844 - 4.94913i) q^{38} +(-1.24149 + 2.71849i) q^{39} +(1.70307 + 1.09450i) q^{40} +(3.87631 - 0.557329i) q^{41} +(1.23607 - 2.33926i) q^{42} +(-6.98924 + 6.05621i) q^{43} +(-1.41556 - 4.82096i) q^{44} -2.02444 q^{45} +(-2.46943 - 4.11119i) q^{46} -8.39447i q^{47} +(0.281733 + 0.959493i) q^{48} +(6.89889 - 1.18548i) q^{49} +(-0.758504 + 0.487461i) q^{50} +(3.13613 - 0.450907i) q^{51} +(1.61574 - 2.51413i) q^{52} +(-3.30382 - 1.50881i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-10.0683 - 1.44760i) q^{55} +(-1.55640 + 2.13954i) q^{56} +(1.84496 - 6.28337i) q^{57} +(8.93671 + 2.62406i) q^{58} +(-0.0236635 + 0.0108068i) q^{59} +(2.00384 + 0.288108i) q^{60} +(-5.64895 + 6.51924i) q^{61} +(8.11105 + 3.70419i) q^{62} +(0.152608 - 2.64135i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.27096 - 5.08972i) q^{65} +(-3.29034 - 3.79726i) q^{66} +(-0.852984 - 2.90500i) q^{67} -3.16838 q^{68} +(-3.95413 - 2.71383i) q^{69} +(2.63104 + 4.66542i) q^{70} +(7.65856 - 2.24876i) q^{71} +(0.654861 + 0.755750i) q^{72} +(-6.38080 - 9.92872i) q^{73} +(-8.87698 + 1.27632i) q^{74} +(-0.487461 + 0.758504i) q^{75} +(-2.72040 + 5.95685i) q^{76} +(2.64770 - 13.0272i) q^{77} +(0.425316 - 2.95814i) q^{78} +(8.35048 - 3.81354i) q^{79} +(-1.94244 - 0.570351i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-3.56227 + 1.62683i) q^{82} +(0.168430 - 1.17146i) q^{83} +(-0.526958 + 2.59274i) q^{84} +(-2.66455 + 5.83456i) q^{85} +(4.99990 - 7.77999i) q^{86} +(9.21919 - 1.32552i) q^{87} +(2.71645 + 4.22687i) q^{88} +(0.733224 + 0.846186i) q^{89} +(1.94244 - 0.570351i) q^{90} +(6.88728 - 3.88404i) q^{91} +(3.52766 + 3.24894i) q^{92} +8.91685 q^{93} +(2.36499 + 8.05443i) q^{94} +(8.68170 + 10.0192i) q^{95} +(-0.540641 - 0.841254i) q^{96} +(-1.87253 - 13.0238i) q^{97} +(-6.28545 + 3.08110i) q^{98} +(-4.57044 - 2.08725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.288108	−	2.00384i	−0.128846	−	0.896143i	−0.947021	−	0.321173i	$-0.895923\pi$
$5$	−0.288108	−	2.00384i	−0.128846	−	0.896143i	0.818175	−	0.574970i	$-0.194986\pi$
$6$	0.540641	−	0.841254i	0.220716	−	0.343440i
$7$	2.63618	−	0.224848i	0.996382	−	0.0849845i
$7$	2.63618	−	0.224848i	0.996382	−	0.0849845i
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	0.840984	+	1.84150i	0.265942	+	0.582333i
$11$	1.41556	−	4.82096i	0.426808	−	1.45358i	−0.413019	−	0.910722i	$-0.635526\pi$
$11$	1.41556	−	4.82096i	0.426808	−	1.45358i	0.839828	−	0.542853i	$-0.182656\pi$
$12$	−0.281733	+	0.959493i	−0.0813292	+	0.276982i
$13$	2.71849	−	1.24149i	0.753973	−	0.344328i	−0.00107335	−	0.999999i	$-0.500342\pi$
$13$	2.71849	−	1.24149i	0.753973	−	0.344328i	0.755046	+	0.655672i	$0.227614\pi$
$14$	−2.46605	+	0.958437i	−0.659079	+	0.256153i
$15$	1.52997	+	1.32573i	0.395037	+	0.342301i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−2.66541	−	1.71295i	−0.646457	−	0.415452i	0.175913	−	0.984406i	$-0.443712\pi$
$17$	−2.66541	−	1.71295i	−0.646457	−	0.415452i	−0.822370	+	0.568953i	$0.807349\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	−5.50906	+	3.54046i	−1.26387	+	0.812237i	−0.988808	−	0.149191i	$-0.952333\pi$
$19$	−5.50906	+	3.54046i	−1.26387	+	0.812237i	−0.275057	+	0.961428i	$0.588697\pi$
$20$	−1.32573	−	1.52997i	−0.296442	−	0.342112i
$21$	−1.84505	+	1.89626i	−0.402622	+	0.413798i
$22$			5.02449i			1.07123i
$23$	1.21115	+	4.64038i	0.252542	+	0.967586i
$23$	1.21115	+	4.64038i	0.252542	+	0.967586i
$24$		−	1.00000i		−	0.204124i
$25$	0.865112	−	0.254020i	0.173022	−	0.0508040i
$26$	−2.25860	+	1.95709i	−0.442948	+	0.383817i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	2.09613	−	1.61438i	0.396132	−	0.305089i
$29$	−7.83543	−	5.03553i	−1.45500	−	0.935074i	−0.998982	−	0.0451046i	$-0.985638\pi$
$29$	−7.83543	−	5.03553i	−1.45500	−	0.935074i	−0.456021	−	0.889969i	$-0.650726\pi$
$30$	−1.84150	−	0.840984i	−0.336210	−	0.153542i
$31$	−6.73891	−	5.83930i	−1.21034	−	1.04877i	−0.997426	−	0.0716984i	$-0.977158\pi$
$31$	−6.73891	−	5.83930i	−1.21034	−	1.04877i	−0.212917	−	0.977070i	$-0.568296\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	2.08725	+	4.57044i	0.363343	+	0.795611i
$34$	3.04004	+	0.892635i	0.521362	+	0.153086i
$35$	−1.21006	−	5.21769i	−0.204538	−	0.881951i
$36$	−0.415415	−	0.909632i	−0.0692358	−	0.151605i
$37$	8.87698	+	1.27632i	1.45937	+	0.209825i	0.825844	−	0.563899i	$-0.190699\pi$
$37$	8.87698	+	1.27632i	1.45937	+	0.209825i	0.633522	+	0.773724i	$0.281608\pi$
$38$	4.28844	−	4.94913i	0.695677	−	0.802854i
$39$	−1.24149	+	2.71849i	−0.198798	+	0.435306i
$40$	1.70307	+	1.09450i	0.269279	+	0.173055i
$41$	3.87631	−	0.557329i	0.605377	−	0.0870401i	0.167191	−	0.985924i	$-0.446530\pi$
$41$	3.87631	−	0.557329i	0.605377	−	0.0870401i	0.438186	+	0.898884i	$0.355621\pi$
$42$	1.23607	−	2.33926i	0.190730	−	0.360955i
$43$	−6.98924	+	6.05621i	−1.06585	+	0.923564i	−0.997252	−	0.0740805i	$-0.976398\pi$
$43$	−6.98924	+	6.05621i	−1.06585	+	0.923564i	−0.0685974	+	0.997644i	$0.521852\pi$
$44$	−1.41556	−	4.82096i	−0.213404	−	0.726788i
$45$	−2.02444			−0.301786
$46$	−2.46943	−	4.11119i	−0.364098	−	0.606162i
$47$		−	8.39447i		−	1.22446i	−0.790680	−	0.612230i	$-0.790273\pi$
$47$		−	8.39447i		−	1.22446i	0.790680	−	0.612230i	$-0.209727\pi$
$48$	0.281733	+	0.959493i	0.0406646	+	0.138491i
$49$	6.89889	−	1.18548i	0.985555	−	0.169354i
$50$	−0.758504	+	0.487461i	−0.107269	+	0.0689373i
$51$	3.13613	−	0.450907i	0.439146	−	0.0631396i
$52$	1.61574	−	2.51413i	0.224062	−	0.348648i
$53$	−3.30382	−	1.50881i	−0.453815	−	0.207250i	0.175375	−	0.984502i	$-0.443886\pi$
$53$	−3.30382	−	1.50881i	−0.453815	−	0.207250i	−0.629190	+	0.777251i	$0.716613\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	−10.0683	−	1.44760i	−1.35760	−	0.195194i
$56$	−1.55640	+	2.13954i	−0.207983	+	0.285907i
$57$	1.84496	−	6.28337i	0.244371	−	0.832252i
$58$	8.93671	+	2.62406i	1.17345	+	0.344555i
$59$	−0.0236635	+	0.0108068i	−0.00308073	+	0.00140692i	−0.416955	−	0.908927i	$-0.636903\pi$
$59$	−0.0236635	+	0.0108068i	−0.00308073	+	0.00140692i	0.413874	+	0.910334i	$0.364175\pi$
$60$	2.00384	+	0.288108i	0.258694	+	0.0371946i
$61$	−5.64895	+	6.51924i	−0.723274	+	0.834703i	−0.991697	−	0.128598i	$-0.958952\pi$
$61$	−5.64895	+	6.51924i	−0.723274	+	0.834703i	0.268422	+	0.963301i	$0.413498\pi$
$62$	8.11105	+	3.70419i	1.03010	+	0.470433i
$63$	0.152608	−	2.64135i	0.0192268	−	0.332778i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−3.27096	−	5.08972i	−0.405713	−	0.631302i
$66$	−3.29034	−	3.79726i	−0.405013	−	0.467410i
$67$	−0.852984	−	2.90500i	−0.104209	−	0.354902i	0.890837	−	0.454323i	$-0.150119\pi$
$67$	−0.852984	−	2.90500i	−0.104209	−	0.354902i	−0.995045	+	0.0994216i	$0.968301\pi$
$68$	−3.16838			−0.384222
$69$	−3.95413	−	2.71383i	−0.476021	−	0.326707i
$70$	2.63104	+	4.66542i	0.314469	+	0.557625i
$71$	7.65856	−	2.24876i	0.908904	−	0.266878i	0.206324	−	0.978484i	$-0.433850\pi$
$71$	7.65856	−	2.24876i	0.908904	−	0.266878i	0.702579	+	0.711605i	$0.252032\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	−6.38080	−	9.92872i	−0.746816	−	1.16207i	−0.981772	−	0.190063i	$-0.939131\pi$
$73$	−6.38080	−	9.92872i	−0.746816	−	1.16207i	0.234956	−	0.972006i	$-0.424505\pi$
$74$	−8.87698	+	1.27632i	−1.03193	+	0.148369i
$75$	−0.487461	+	0.758504i	−0.0562871	+	0.0875844i
$76$	−2.72040	+	5.95685i	−0.312051	+	0.683297i
$77$	2.64770	−	13.0272i	0.301733	−	1.48459i
$78$	0.425316	−	2.95814i	0.0481576	−	0.334943i
$79$	8.35048	−	3.81354i	0.939503	−	0.429056i	0.114016	−	0.993479i	$-0.463628\pi$
$79$	8.35048	−	3.81354i	0.939503	−	0.429056i	0.825486	+	0.564422i	$0.190901\pi$
$80$	−1.94244	−	0.570351i	−0.217171	−	0.0637672i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−3.56227	+	1.62683i	−0.393387	+	0.179654i
$83$	0.168430	−	1.17146i	0.0184876	−	0.128584i	−0.978487	−	0.206306i	$-0.933856\pi$
$83$	0.168430	−	1.17146i	0.0184876	−	0.128584i	0.996975	+	0.0777223i	$0.0247648\pi$
$84$	−0.526958	+	2.59274i	−0.0574958	+	0.282891i
$85$	−2.66455	+	5.83456i	−0.289011	+	0.632847i
$86$	4.99990	−	7.77999i	0.539153	−	0.838938i
$87$	9.21919	−	1.32552i	0.988401	−	0.142111i
$88$	2.71645	+	4.22687i	0.289574	+	0.450586i
$89$	0.733224	+	0.846186i	0.0777216	+	0.0896955i	0.793279	−	0.608859i	$-0.208372\pi$
$89$	0.733224	+	0.846186i	0.0777216	+	0.0896955i	−0.715557	+	0.698554i	$0.753827\pi$
$90$	1.94244	−	0.570351i	0.204751	−	0.0601203i
$91$	6.88728	−	3.88404i	0.721983	−	0.407158i
$92$	3.52766	+	3.24894i	0.367784	+	0.338725i
$93$	8.91685			0.924635
$94$	2.36499	+	8.05443i	0.243931	+	0.830751i
$95$	8.68170	+	10.0192i	0.890724	+	1.02795i
$96$	−0.540641	−	0.841254i	−0.0551789	−	0.0858601i
$97$	−1.87253	−	13.0238i	−0.190127	−	1.32236i	−0.831668	−	0.555273i	$-0.812614\pi$
$97$	−1.87253	−	13.0238i	−0.190127	−	1.32236i	0.641541	−	0.767089i	$-0.278295\pi$
$98$	−6.28545	+	3.08110i	−0.634926	+	0.311238i
$99$	−4.57044	−	2.08725i	−0.459346	−	0.209776i
$100$	0.590445	−	0.681410i	0.0590445	−	0.0681410i
$101$	1.06230	+	0.152735i	0.105703	+	0.0151977i	0.194963	−	0.980811i	$-0.437541\pi$
$101$	1.06230	+	0.152735i	0.105703	+	0.0151977i	−0.0892605	+	0.996008i	$0.528450\pi$
$102$	−2.88206	+	1.31619i	−0.285366	+	0.130322i
$103$	14.7740	+	4.33804i	1.45572	+	0.427439i	0.911430	−	0.411455i	$-0.134979\pi$
$103$	14.7740	+	4.33804i	1.45572	+	0.427439i	0.544295	+	0.838894i	$0.316797\pi$
$104$	−0.841974	+	2.86750i	−0.0825624	+	0.281182i
$105$	4.33137	+	3.15085i	0.422698	+	0.307491i
$106$	3.59508	+	0.516894i	0.349185	+	0.0502052i
$107$	−6.71216	−	5.81612i	−0.648889	−	0.562266i	0.267000	−	0.963696i	$-0.413968\pi$
$107$	−6.71216	−	5.81612i	−0.648889	−	0.562266i	−0.915889	+	0.401431i	$0.868513\pi$
$108$	0.909632	+	0.415415i	0.0875294	+	0.0399733i
$109$	7.38075	−	11.4847i	0.706947	−	1.10003i	−0.283072	−	0.959099i	$-0.591353\pi$
$109$	7.38075	−	11.4847i	0.706947	−	1.10003i	0.990019	−	0.140933i	$-0.0450101\pi$
$110$	10.0683	−	1.44760i	0.959971	−	0.138023i
$111$	−7.54458	+	4.84861i	−0.716100	+	0.460209i
$112$	0.890580	−	2.49136i	0.0841519	−	0.235411i
$113$	−0.771575	−	2.62774i	−0.0725836	−	0.247197i	0.915207	−	0.402984i	$-0.132027\pi$
$113$	−0.771575	−	2.62774i	−0.0725836	−	0.247197i	−0.987791	+	0.155787i	$0.950209\pi$
$114$			6.54863i			0.613336i
$115$	8.94962	−	3.76387i	0.834556	−	0.350983i
$116$	−9.31400			−0.864783
$117$	−0.841974	−	2.86750i	−0.0778405	−	0.265101i
$118$	0.0196604	−	0.0170358i	0.00180988	−	0.00156827i
$119$	−7.41165	−	3.91634i	−0.679425	−	0.359011i
$120$	−2.00384	+	0.288108i	−0.182924	+	0.0263006i
$121$	−11.9841	−	7.70171i	−1.08946	−	0.700155i
$122$	3.58345	−	7.84666i	0.324430	−	0.710403i
$123$	−2.56454	+	2.95964i	−0.231237	+	0.266862i
$124$	−8.82609	−	1.26900i	−0.792606	−	0.113960i
$125$	−4.96318	−	10.8678i	−0.443920	−	0.972050i
$126$	0.597727	+	2.57735i	0.0532497	+	0.229608i
$127$	7.65856	+	2.24876i	0.679588	+	0.199545i	0.603268	−	0.797538i	$-0.293865\pi$
$127$	7.65856	+	2.24876i	0.679588	+	0.199545i	0.0763196	+	0.997083i	$0.475683\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	1.31614	−	9.15396i	0.115880	−	0.805961i
$130$	4.57241	+	3.96201i	0.401027	+	0.347492i
$131$	1.70730	+	0.779698i	0.149168	+	0.0681225i	0.488600	−	0.872508i	$-0.337508\pi$
$131$	1.70730	+	0.779698i	0.149168	+	0.0681225i	−0.339433	+	0.940630i	$0.610235\pi$
$132$	4.22687	+	2.71645i	0.367902	+	0.236436i
$133$	−13.7268	+	10.5720i	−1.19027	+	0.916707i
$134$	1.63686	+	2.54701i	0.141404	+	0.220028i
$135$	1.52997	−	1.32573i	0.131679	−	0.114100i
$136$	3.04004	−	0.892635i	0.260681	−	0.0765428i
$137$		−	8.00531i		−	0.683940i	−0.939711	−	0.341970i	$-0.888906\pi$
$137$		−	8.00531i		−	0.683940i	0.939711	−	0.341970i	$-0.111094\pi$
$138$	4.55853	+	1.48990i	0.388048	+	0.126828i
$139$			17.6167i			1.49423i	0.664697	+	0.747113i	$0.268561\pi$
$139$			17.6167i			1.49423i	−0.664697	+	0.747113i	$0.731439\pi$
$140$	−3.83887	−	3.73519i	−0.324443	−	0.315681i
$141$	5.49721	+	6.34412i	0.462948	+	0.534271i
$142$	−6.71479	+	4.31533i	−0.563492	+	0.362135i
$143$	−2.13700	−	14.8631i	−0.178705	−	1.24292i
$144$	−0.841254	−	0.540641i	−0.0701045	−	0.0450534i
$145$	−7.83292	+	17.1517i	−0.650488	+	1.42437i
$146$	8.91958	+	7.72886i	0.738189	+	0.639645i
$147$	−4.43751	+	5.41373i	−0.365999	+	0.446517i
$148$	8.15782	−	3.72555i	0.670568	−	0.306238i
$149$	−3.00377	+	10.2299i	−0.246079	+	0.838067i	0.740116	+	0.672479i	$0.234770\pi$
$149$	−3.00377	+	10.2299i	−0.246079	+	0.838067i	−0.986195	+	0.165588i	$0.947048\pi$
$150$	0.254020	−	0.865112i	0.0207406	−	0.0706361i
$151$	−1.26402	−	2.76782i	−0.102864	−	0.225242i	0.851201	−	0.524840i	$-0.175875\pi$
$151$	−1.26402	−	2.76782i	−0.102864	−	0.225242i	−0.954066	+	0.299598i	$0.903147\pi$
$152$	0.931968	−	6.48198i	0.0755926	−	0.525758i
$153$	−2.07485	+	2.39450i	−0.167741	+	0.193584i
$154$	1.12975	+	13.2455i	0.0910375	+	1.06735i
$155$	−9.75946	+	15.1860i	−0.783899	+	1.21977i
$156$	0.425316	+	2.95814i	0.0340525	+	0.236841i
$157$	9.21062	−	5.91930i	0.735087	−	0.472412i	−0.118768	−	0.992922i	$-0.537895\pi$
$157$	9.21062	−	5.91930i	0.735087	−	0.472412i	0.853856	+	0.520510i	$0.174258\pi$
$158$	−6.93783	+	6.01166i	−0.551944	+	0.478262i
$159$	3.48492	−	1.02327i	0.276372	−	0.0811502i
$160$	2.02444			0.160046
$161$	4.23618	+	11.9606i	0.333858	+	0.942623i
$162$	1.00000			0.0785674
$163$	−13.5895	+	3.99024i	−1.06441	+	0.312540i	−0.766627	−	0.642093i	$-0.778066\pi$
$163$	−13.5895	+	3.99024i	−1.06441	+	0.312540i	−0.297785	+	0.954633i	$0.596248\pi$
$164$	2.95964	−	2.56454i	0.231109	−	0.200257i
$165$	8.55706	−	5.49929i	0.666166	−	0.428119i
$166$	0.168430	+	1.17146i	0.0130727	+	0.0909226i
$167$	−8.00526	+	12.4564i	−0.619466	+	0.963908i	0.379780	+	0.925077i	$0.376000\pi$
$167$	−8.00526	+	12.4564i	−0.619466	+	0.963908i	−0.999246	+	0.0388307i	$0.987637\pi$
$168$	−0.224848	−	2.63618i	−0.0173474	−	0.203386i
$169$	−2.66431	+	3.07478i	−0.204947	+	0.236522i
$170$	0.912835	−	6.34891i	0.0700113	−	0.486939i
$171$	2.72040	+	5.95685i	0.208034	+	0.455531i
$172$	−2.60549	+	8.87348i	−0.198667	+	0.676597i
$173$	−3.14475	+	10.7100i	−0.239091	+	0.814269i	0.749286	+	0.662246i	$0.230397\pi$
$173$	−3.14475	+	10.7100i	−0.239091	+	0.814269i	−0.988377	+	0.152022i	$0.951421\pi$
$174$	−8.47231	+	3.86917i	−0.642284	+	0.293321i
$175$	2.22348	−	0.864161i	0.168079	−	0.0653244i
$176$	−3.79726	−	3.29034i	−0.286229	−	0.248019i
$177$	0.0108068	−	0.0236635i	0.000812287	−	0.00177866i
$178$	−0.941921	−	0.605336i	−0.0706000	−	0.0453719i
$179$	1.33075	+	9.25558i	0.0994651	+	0.691795i	0.977149	+	0.212555i	$0.0681785\pi$
$179$	1.33075	+	9.25558i	0.0994651	+	0.691795i	−0.877684	+	0.479240i	$0.840912\pi$
$180$	−1.70307	+	1.09450i	−0.126939	+	0.0815789i
$181$	8.32934	+	9.61258i	0.619115	+	0.714497i	0.975539	−	0.219827i	$-0.0705494\pi$
$181$	8.32934	+	9.61258i	0.619115	+	0.714497i	−0.356423	+	0.934325i	$0.616004\pi$
$182$	−5.51403	+	5.66708i	−0.408727	+	0.420072i
$183$		−	8.62619i		−	0.637666i
$184$	−4.30010	−	2.12348i	−0.317007	−	0.156545i
$185$		−	18.1557i		−	1.33484i
$186$	−8.55566	+	2.51217i	−0.627331	+	0.184201i
$187$	−12.0311	+	10.4250i	−0.879805	+	0.762355i
$188$	−4.53839	−	7.06188i	−0.330996	−	0.515040i
$189$	1.61438	+	2.09613i	0.117429	+	0.152471i
$190$	−11.1528	−	7.16745i	−0.809107	−	0.519982i
$191$	3.72300	+	1.70024i	0.269387	+	0.123025i	0.545529	−	0.838092i	$-0.316329\pi$
$191$	3.72300	+	1.70024i	0.269387	+	0.123025i	−0.276142	+	0.961117i	$0.589056\pi$
$192$	0.755750	+	0.654861i	0.0545415	+	0.0472605i
$193$	2.56259	−	17.8232i	0.184459	−	1.28294i	−0.661601	−	0.749856i	$-0.730123\pi$
$193$	2.56259	−	17.8232i	0.184459	−	1.28294i	0.846061	−	0.533087i	$-0.178968\pi$
$194$	5.46590	+	11.9686i	0.392429	+	0.859299i
$195$	5.80509	+	1.70453i	0.415711	+	0.122064i
$196$	5.16280	−	4.72711i	0.368771	−	0.337651i
$197$	−11.4795	−	25.1365i	−0.817879	−	1.79090i	−0.568926	−	0.822389i	$-0.692641\pi$
$197$	−11.4795	−	25.1365i	−0.817879	−	1.79090i	−0.248953	−	0.968516i	$-0.580086\pi$
$198$	4.97335	+	0.715060i	0.353441	+	0.0508171i
$199$	1.23881	−	1.42966i	0.0878166	−	0.101346i	−0.710141	−	0.704060i	$-0.751369\pi$
$199$	1.23881	−	1.42966i	0.0878166	−	0.101346i	0.797957	+	0.602714i	$0.205914\pi$
$200$	−0.374553	+	0.820156i	−0.0264849	+	0.0579938i
$201$	2.54701	+	1.63686i	0.179652	+	0.115455i
$202$	−1.06230	+	0.152735i	−0.0747430	+	0.0107464i
$203$	−21.7878	−	11.5128i	−1.52921	−	0.808038i
$204$	2.39450	−	2.07485i	0.167649	−	0.145268i
$205$	−2.23359	−	7.60691i	−0.156001	−	0.531290i
$206$	−15.3977			−1.07281
$207$	4.76551	−	0.538425i	0.331226	−	0.0374231i
$208$		−	2.98856i		−	0.207219i
$209$	9.27000	+	31.5707i	0.641220	+	2.18379i
$210$	−5.04361	−	1.80293i	−0.348042	−	0.124414i
$211$	−10.2078	+	6.56018i	−0.702737	+	0.451621i	−0.842593	−	0.538550i	$-0.818972\pi$
$211$	−10.2078	+	6.56018i	−0.702737	+	0.451621i	0.139857	+	0.990172i	$0.455336\pi$
$212$	−3.59508	+	0.516894i	−0.246911	+	0.0355004i
$213$	−4.31533	+	6.71479i	−0.295682	+	0.460090i
$214$	8.07886	+	3.68949i	0.552260	+	0.252209i
$215$	14.1493	+	12.2605i	0.964975	+	0.836156i
$216$	−0.989821	−	0.142315i	−0.0673488	−	0.00968330i
$217$	−19.0779	−	13.8782i	−1.29509	−	0.942114i
$218$	−3.84617	+	13.0989i	−0.260496	+	0.887166i
$219$	11.3242	+	3.32509i	0.765219	+	0.224689i
$220$	−9.25259	+	4.22552i	−0.623809	+	0.284884i
$221$	−9.37250	−	1.34756i	−0.630463	−	0.0906469i
$222$	5.87296	−	6.77776i	0.394167	−	0.454893i
$223$	26.1294	+	11.9329i	1.74976	+	0.799087i	0.988609	+	0.150506i	$0.0480904\pi$
$223$	26.1294	+	11.9329i	1.74976	+	0.799087i	0.761146	+	0.648580i	$0.224637\pi$
$224$	−0.152608	+	2.64135i	−0.0101966	+	0.176482i
$225$	−0.128316	−	0.892458i	−0.00855440	−	0.0594972i
$226$	1.48064	+	2.30392i	0.0984908	+	0.153255i
$227$	7.95194	+	9.17703i	0.527789	+	0.609101i	0.955564	−	0.294784i	$-0.0952478\pi$
$227$	7.95194	+	9.17703i	0.527789	+	0.609101i	−0.427775	+	0.903885i	$0.640702\pi$
$228$	−1.84496	−	6.28337i	−0.122186	−	0.416126i
$229$	−8.68759			−0.574092			−0.287046	−	0.957917i	$-0.592673\pi$
$229$	−8.68759			−0.574092			−0.287046	+	0.957917i	$0.592673\pi$
$230$	−7.52669	+	6.13281i	−0.496295	+	0.404385i
$231$	6.53002	+	11.5792i	0.429644	+	0.761854i
$232$	8.93671	−	2.62406i	0.586724	−	0.172278i
$233$	−5.84151	−	6.74146i	−0.382690	−	0.441648i	0.531424	−	0.847106i	$-0.321657\pi$
$233$	−5.84151	−	6.74146i	−0.382690	−	0.441648i	−0.914113	+	0.405459i	$0.867112\pi$
$234$	1.61574	+	2.51413i	0.105624	+	0.164354i
$235$	−16.8211	+	2.41851i	−1.09729	+	0.157766i
$236$	−0.0140644	+	0.0218847i	−0.000915517	+	0.00142457i
$237$	−3.81354	+	8.35048i	−0.247716	+	0.542422i
$238$	8.21479	+	1.66960i	0.532486	+	0.108224i
$239$	−3.77053	+	26.2246i	−0.243896	+	1.69633i	0.388309	+	0.921529i	$0.373059\pi$
$239$	−3.77053	+	26.2246i	−0.243896	+	1.69633i	−0.632204	+	0.774802i	$0.717850\pi$
$240$	1.84150	−	0.840984i	0.118868	−	0.0542853i
$241$	−8.41629	−	2.47125i	−0.542141	−	0.159187i	−0.000814869	−	1.00000i	$-0.500259\pi$
$241$	−8.41629	−	2.47125i	−0.542141	−	0.159187i	−0.541326	+	0.840813i	$0.682078\pi$
$242$	13.6685	+	4.01343i	0.878643	+	0.257993i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	−1.22763	+	8.53839i	−0.0785913	+	0.546614i
$245$	−4.36313	−	13.4827i	−0.278750	−	0.861378i
$246$	1.62683	−	3.56227i	0.103723	−	0.227122i
$247$	−10.5809	+	16.4641i	−0.673244	+	1.04759i
$248$	8.82609	−	1.26900i	0.560457	−	0.0805816i
$249$	0.639850	+	0.995625i	0.0405488	+	0.0630952i
$250$	7.82396	+	9.02933i	0.494831	+	0.571065i
$251$	18.3859	−	5.39859i	1.16051	−	0.340756i	0.355878	−	0.934533i	$-0.384182\pi$
$251$	18.3859	−	5.39859i	1.16051	−	0.340756i	0.804630	+	0.593777i	$0.202364\pi$
$252$	−1.29964	−	2.30455i	−0.0818695	−	0.145173i
$253$	24.0856	+	0.729850i	1.51425	+	0.0458853i
$254$	−7.98189			−0.500828
$255$	−1.80709	−	6.15438i	−0.113164	−	0.385402i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	9.79388	+	15.2396i	0.610925	+	0.950618i	0.999573	+	0.0292316i	$0.00930603\pi$
$257$	9.79388	+	15.2396i	0.610925	+	0.950618i	−0.388648	+	0.921387i	$0.627058\pi$
$258$	1.31614	+	9.15396i	0.0819394	+	0.569901i
$259$	23.6883	+	1.36863i	1.47192	+	0.0850426i
$260$	−5.50342	−	2.51333i	−0.341308	−	0.155870i
$261$	−6.09937	+	7.03905i	−0.377542	+	0.435706i
$262$	−1.85781	−	0.267113i	−0.114776	−	0.0165023i
$263$	6.89832	−	3.15036i	0.425369	−	0.194259i	−0.191216	−	0.981548i	$-0.561243\pi$
$263$	6.89832	−	3.15036i	0.425369	−	0.194259i	0.616585	+	0.787289i	$0.288516\pi$
$264$	−4.82096	−	1.41556i	−0.296710	−	0.0871219i
$265$	−2.07154	+	7.05502i	−0.127254	+	0.433386i
$266$	10.1923	−	14.0110i	0.624930	−	0.859072i
$267$	−1.10827	−	0.159345i	−0.0678249	−	0.00975175i
$268$	−2.28814	−	1.98268i	−0.139770	−	0.121111i
$269$	4.04364	+	1.84667i	0.246545	+	0.112593i	0.534855	−	0.844944i	$-0.320366\pi$
$269$	4.04364	+	1.84667i	0.246545	+	0.112593i	−0.288310	+	0.957537i	$0.593093\pi$
$270$	−1.09450	+	1.70307i	−0.0666089	+	0.103645i
$271$	15.8140	−	2.27371i	0.960634	−	0.138118i	0.355881	−	0.934531i	$-0.384181\pi$
$271$	15.8140	−	2.27371i	0.960634	−	0.138118i	0.604753	+	0.796413i	$0.293272\pi$
$272$	−2.66541	+	1.71295i	−0.161614	+	0.103863i
$273$	−2.66155	+	7.44557i	−0.161084	+	0.450626i
$274$	2.25536	+	7.68104i	0.136251	+	0.464028i
$275$		−	4.53026i		−	0.273185i
$276$	−4.79363	−	0.145258i	−0.288543	−	0.00874353i
$277$	4.95418			0.297668			0.148834	−	0.988862i	$-0.452448\pi$
$277$	4.95418			0.297668			0.148834	+	0.988862i	$0.452448\pi$
$278$	−4.96319	−	16.9031i	−0.297672	−	1.01378i
$279$	−6.73891	+	5.83930i	−0.403448	+	0.349590i
$280$	4.73569	+	2.50236i	0.283012	+	0.149544i
$281$	10.5222	−	1.51286i	0.627702	−	0.0902499i	0.178879	−	0.983871i	$-0.442753\pi$
$281$	10.5222	−	1.51286i	0.627702	−	0.0902499i	0.448822	+	0.893621i	$0.351844\pi$
$282$	−7.06188	−	4.53839i	−0.420529	−	0.270257i
$283$	10.9754	−	24.0329i	0.652422	−	1.42861i	−0.236995	−	0.971511i	$-0.576163\pi$
$283$	10.9754	−	24.0329i	0.652422	−	1.42861i	0.889418	−	0.457095i	$-0.151110\pi$
$284$	5.22702	−	6.03230i	0.310167	−	0.357951i
$285$	−13.1224	−	1.88671i	−0.777303	−	0.111759i
$286$	6.23787	+	13.6590i	0.368853	+	0.807675i
$287$	10.0933	−	2.34080i	0.595790	−	0.138173i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	−2.89186	−	6.33229i	−0.170110	−	0.372488i
$290$	2.68344	−	18.6637i	0.157577	−	1.09597i
$291$	9.94391	+	8.61645i	0.582922	+	0.505105i
$292$	−10.7357	−	4.90285i	−0.628262	−	0.286918i
$293$	−17.9533	−	11.5379i	−1.04884	−	0.674051i	−0.101685	−	0.994817i	$-0.532423\pi$
$293$	−17.9533	−	11.5379i	−1.04884	−	0.674051i	−0.947158	+	0.320766i	$0.896060\pi$
$294$	2.73253	−	6.44463i	0.159365	−	0.375859i
$295$	0.0284727	+	0.0443043i	0.00165774	+	0.00257950i
$296$	−6.77776	+	5.87296i	−0.393949	+	0.341359i
$297$	4.82096	−	1.41556i	0.279741	−	0.0821393i
$298$		−	10.6618i		−	0.617621i
$299$	9.05348	+	11.1112i	0.523576	+	0.642576i
$300$			0.901635i			0.0520559i
$301$	−17.0632	+	17.5368i	−0.983505	+	1.01080i
$302$	1.99260	+	2.29959i	0.114661	+	0.132326i
$303$	−0.902852	+	0.580228i	−0.0518675	+	0.0333332i
$304$	0.931968	+	6.48198i	0.0534520	+	0.371767i
$305$	14.6910	+	9.44133i	0.841204	+	0.540609i
$306$	1.31619	−	2.88206i	0.0752417	−	0.164756i
$307$	13.6861	+	11.8591i	0.781109	+	0.676834i	0.951194	−	0.308595i	$-0.0998587\pi$
$307$	13.6861	+	11.8591i	0.781109	+	0.676834i	−0.170085	+	0.985429i	$0.554404\pi$
$308$	−4.81566	−	12.3906i	−0.274398	−	0.706022i
$309$	−14.0062	+	6.39644i	−0.796788	+	0.363881i
$310$	5.08574	−	17.3204i	0.288850	−	0.983734i
$311$	−4.64621	+	15.8235i	−0.263462	+	0.897270i	0.716416	+	0.697674i	$0.245781\pi$
$311$	−4.64621	+	15.8235i	−0.263462	+	0.897270i	−0.979878	+	0.199597i	$0.936037\pi$
$312$	−1.24149	−	2.71849i	−0.0702856	−	0.153904i
$313$	−3.66602	+	25.4977i	−0.207216	+	1.44122i	0.574972	+	0.818173i	$0.305013\pi$
$313$	−3.66602	+	25.4977i	−0.207216	+	1.44122i	−0.782188	+	0.623043i	$0.785896\pi$
$314$	−7.16986	+	8.27446i	−0.404619	+	0.466955i
$315$	−5.33679	+	0.455191i	−0.300694	+	0.0256471i
$316$	4.96312	−	7.72276i	0.279197	−	0.434439i
$317$	1.84890	+	12.8594i	0.103845	+	0.722256i	0.973515	+	0.228623i	$0.0734223\pi$
$317$	1.84890	+	12.8594i	0.103845	+	0.722256i	−0.869670	+	0.493633i	$0.835669\pi$
$318$	−3.05547	+	1.96363i	−0.171342	+	0.110115i
$319$	−35.3676	+	30.6462i	−1.98021	+	1.71586i
$320$	−1.94244	+	0.570351i	−0.108586	+	0.0318836i
$321$	8.88146			0.495715
$322$	−7.43426	−	10.2826i	−0.414295	−	0.573027i
$323$	20.7485			1.15448
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	2.03643	−	1.76458i	0.112961	−	0.0978813i
$326$	11.9149	−	7.65721i	0.659903	−	0.424094i
$327$	1.94286	+	13.5129i	0.107440	+	0.747265i
$328$	−2.11724	+	3.29449i	−0.116905	+	0.181908i
$329$	−1.88748	−	22.1293i	−0.104060	−	1.22003i
$330$	−6.66111	+	7.68733i	−0.366682	+	0.423173i
$331$	2.79698	−	19.4534i	0.153736	−	1.06926i	−0.756151	−	0.654398i	$-0.772922\pi$
$331$	2.79698	−	19.4534i	0.153736	−	1.06926i	0.909886	−	0.414858i	$-0.136169\pi$
$332$	−0.491645	−	1.07655i	−0.0269825	−	0.0590834i
$333$	2.52665	−	8.60498i	0.138460	−	0.471550i
$334$	4.17161	−	14.2072i	0.228260	−	0.777383i
$335$	−5.57539	+	2.54619i	−0.304616	+	0.139113i
$336$	0.958437	+	2.46605i	0.0522871	+	0.134534i
$337$	−3.86724	−	3.35099i	−0.210662	−	0.182540i	0.543138	−	0.839643i	$-0.317236\pi$
$337$	−3.86724	−	3.35099i	−0.210662	−	0.182540i	−0.753800	+	0.657103i	$0.771781\pi$
$338$	1.69012	−	3.70086i	0.0919307	−	0.201300i
$339$	2.30392	+	1.48064i	0.125132	+	0.0804174i
$340$	0.912835	+	6.34891i	0.0495055	+	0.344318i
$341$	−37.6904	+	24.2221i	−2.04105	+	1.31170i
$342$	−4.28844	−	4.94913i	−0.231892	−	0.267618i
$343$	17.9202	−	4.67633i	0.967597	−	0.252498i
$344$		−	9.24809i		−	0.498624i
$345$	−4.29886	+	8.70530i	−0.231443	+	0.468678i
$346$		−	11.1622i		−	0.600082i
$347$	16.3137	−	4.79013i	0.875764	−	0.257148i	0.187199	−	0.982322i	$-0.440059\pi$
$347$	16.3137	−	4.79013i	0.875764	−	0.257148i	0.688565	+	0.725174i	$0.258241\pi$
$348$	7.03905	−	6.09937i	0.377333	−	0.326961i
$349$	−15.7535	−	24.5129i	−0.843263	−	1.31214i	−0.948203	−	0.317664i	$-0.897101\pi$
$349$	−15.7535	−	24.5129i	−0.843263	−	1.31214i	0.104940	−	0.994479i	$-0.466535\pi$
$350$	−1.88995	+	1.45558i	−0.101022	+	0.0778041i
$351$	2.51413	+	1.61574i	0.134195	+	0.0862416i
$352$	4.57044	+	2.08725i	0.243605	+	0.111251i
$353$	18.5822	+	16.1016i	0.989033	+	0.857002i	0.989723	−	0.142998i	$-0.0456742\pi$
$353$	18.5822	+	16.1016i	0.989033	+	0.857002i	−0.000690163		1.00000i	$0.500220\pi$
$354$	−0.00370224	+	0.0257496i	−0.000196772	+	0.00136858i
$355$	−6.71263	−	14.6986i	−0.356269	−	0.780121i
$356$	1.07431	+	0.315446i	0.0569383	+	0.0167186i
$357$	8.16601	−	1.89382i	0.432191	−	0.100232i
$358$	−3.88445	−	8.50575i	−0.205299	−	0.449543i
$359$	−15.4652	−	2.22357i	−0.816224	−	0.117355i	−0.278457	−	0.960449i	$-0.589823\pi$
$359$	−15.4652	−	2.22357i	−0.816224	−	0.117355i	−0.537767	+	0.843093i	$0.680732\pi$
$360$	1.32573	−	1.52997i	0.0698720	−	0.0806366i
$361$	9.92202	−	21.7262i	0.522212	−	1.14348i
$362$	−10.7001	−	6.87655i	−0.562386	−	0.361424i
$363$	14.1005	−	2.02735i	0.740085	−	0.106408i
$364$	3.69407	−	6.99101i	0.193622	−	0.366428i
$365$	−18.0572	+	15.6466i	−0.945155	+	0.818982i
$366$	2.43028	+	8.27677i	0.127033	+	0.432634i
$367$	−9.15015			−0.477634			−0.238817	−	0.971065i	$-0.576760\pi$
$367$	−9.15015			−0.477634			−0.238817	+	0.971065i	$0.576760\pi$
$368$	4.72417	+	0.825985i	0.246264	+	0.0430574i
$369$		−	3.91617i		−	0.203868i
$370$	5.11506	+	17.4203i	0.265919	+	0.905638i
$371$	−9.04872	−	3.23463i	−0.469786	−	0.167933i
$372$	7.50133	−	4.82081i	0.388926	−	0.249948i
$373$	−0.178738	+	0.0256987i	−0.00925472	+	0.00133063i	−0.146941	−	0.989145i	$-0.546943\pi$
$373$	−0.178738	+	0.0256987i	−0.00925472	+	0.00133063i	0.137686	+	0.990476i	$0.456034\pi$
$374$	8.60673	−	13.3923i	0.445043	−	0.692501i
$375$	10.8678	+	4.96318i	0.561213	+	0.256297i
$376$	6.34412	+	5.49721i	0.327173	+	0.283497i
$377$	−27.5521	−	3.96139i	−1.41900	−	0.204022i
$378$	−2.13954	−	1.55640i	−0.110046	−	0.0800527i
$379$	7.30503	−	24.8787i	0.375234	−	1.27793i	−0.528169	−	0.849139i	$-0.677121\pi$
$379$	7.30503	−	24.8787i	0.375234	−	1.27793i	0.903404	−	0.428791i	$-0.141060\pi$
$380$	12.7203	+	3.73502i	0.652538	+	0.191603i
$381$	−7.26058	+	3.31580i	−0.371971	+	0.169873i
$382$	−4.05120	−	0.582475i	−0.207277	−	0.0298020i
$383$	11.8738	−	13.7031i	0.606721	−	0.700194i	−0.366408	−	0.930454i	$-0.619412\pi$
$383$	11.8738	−	13.7031i	0.606721	−	0.700194i	0.973129	+	0.230261i	$0.0739579\pi$
$384$	−0.909632	−	0.415415i	−0.0464195	−	0.0211991i
$385$	−26.8672	−	1.55230i	−1.36928	−	0.0791126i
$386$	2.56259	+	17.8232i	0.130432	+	0.907177i
$387$	4.99990	+	7.77999i	0.254159	+	0.395479i
$388$	−8.61645	−	9.94391i	−0.437434	−	0.504825i
$389$	9.49221	+	32.3275i	0.481274	+	1.63907i	0.739625	+	0.673019i	$0.235003\pi$
$389$	9.49221	+	32.3275i	0.481274	+	1.63907i	−0.258351	+	0.966051i	$0.583179\pi$
$390$	−6.05016			−0.306362
$391$	4.72056	−	14.4432i	0.238729	−	0.730422i
$392$	−3.62189	+	5.99015i	−0.182933	+	0.302548i
$393$	−1.80088	+	0.528788i	−0.0908426	+	0.0266738i
$394$	18.0963	+	20.8842i	0.911676	+	1.05213i
$395$	−10.0475	−	15.6343i	−0.505547	−	0.786646i
$396$	−4.97335	+	0.715060i	−0.249920	+	0.0359331i
$397$	14.5674	−	22.6674i	0.731118	−	1.13764i	−0.254239	−	0.967141i	$-0.581825\pi$
$397$	14.5674	−	22.6674i	0.731118	−	1.13764i	0.985358	−	0.170501i	$-0.0545385\pi$
$398$	−0.785844	+	1.72076i	−0.0393908	+	0.0862539i
$399$	3.45085	−	16.9789i	0.172759	−	0.850009i
$400$	0.128316	−	0.892458i	0.00641580	−	0.0446229i
$401$	−3.56735	+	1.62915i	−0.178145	+	0.0813561i	−0.502491	−	0.864582i	$-0.667583\pi$
$401$	−3.56735	+	1.62915i	−0.178145	+	0.0813561i	0.324346	+	0.945938i	$0.394856\pi$
$402$	−2.90500	−	0.852984i	−0.144888	−	0.0425430i
$403$	−25.5691	−	7.50776i	−1.27369	−	0.373988i
$404$	0.976237	−	0.445832i	0.0485696	−	0.0221810i
$405$	−0.288108	+	2.00384i	−0.0143162	+	0.0995714i
$406$	24.1488	+	4.90808i	1.19848	+	0.243584i
$407$	18.7190	−	40.9889i	0.927866	−	2.03174i
$408$	−1.71295	+	2.66541i	−0.0848039	+	0.131957i
$409$	1.59002	−	0.228610i	0.0786214	−	0.0113040i	−0.102892	−	0.994693i	$-0.532810\pi$
$409$	1.59002	−	0.228610i	0.0786214	−	0.0113040i	0.181513	+	0.983389i	$0.441900\pi$
$410$	4.28623	+	6.66950i	0.211682	+	0.329383i
$411$	5.24236	+	6.05001i	0.258587	+	0.298425i
$412$	14.7740	−	4.33804i	0.727862	−	0.213720i
$413$	−0.0599514	+	0.0338093i	−0.00295002	+	0.00166365i
$414$	−4.42078	+	1.85921i	−0.217270	+	0.0913754i
$415$	−2.39593			−0.117612
$416$	0.841974	+	2.86750i	0.0412812	+	0.140591i
$417$	−11.5365	−	13.3138i	−0.564943	−	0.651979i
$418$	−17.7890	−	27.6802i	−0.870089	−	1.35388i
$419$	1.01595	+	7.06612i	0.0496326	+	0.345202i	0.999473	+	0.0324668i	$0.0103363\pi$
$419$	1.01595	+	7.06612i	0.0496326	+	0.345202i	−0.949840	+	0.312736i	$0.898755\pi$
$420$	5.34725	+	0.308947i	0.260919	+	0.0150751i
$421$	−28.7826	−	13.1446i	−1.40278	−	0.640627i	−0.436872	−	0.899524i	$-0.643914\pi$
$421$	−28.7826	−	13.1446i	−1.40278	−	0.640627i	−0.965905	+	0.258897i	$0.916641\pi$
$422$	7.94613	−	9.17033i	0.386812	−	0.446405i
$423$	−8.30902	−	1.19466i	−0.403999	−	0.0580862i
$424$	3.30382	−	1.50881i	0.160448	−	0.0732741i
$425$	−2.74100	−	0.804831i	−0.132958	−	0.0390400i
$426$	2.24876	−	7.65856i	0.108953	−	0.371058i
$427$	−13.4258	+	18.4560i	−0.649721	+	0.893150i
$428$	−8.79106	−	1.26396i	−0.424932	−	0.0610960i
$429$	11.3483	+	9.83338i	0.547902	+	0.474760i
$430$	−17.0303	−	7.77750i	−0.821276	−	0.375064i
$431$	0.175765	−	0.273496i	0.00846633	−	0.0131739i	−0.836995	−	0.547211i	$-0.815689\pi$
$431$	0.175765	−	0.273496i	0.00846633	−	0.0131739i	0.845461	+	0.534037i	$0.179326\pi$
$432$	0.989821	−	0.142315i	0.0476228	−	0.00684713i
$433$	18.9368	−	12.1699i	0.910042	−	0.584849i	0.000289984	−	1.00000i	$-0.499908\pi$
$433$	18.9368	−	12.1699i	0.910042	−	0.584849i	0.909752	+	0.415151i	$0.136271\pi$
$434$	22.2151	+	7.94117i	1.06636	+	0.381188i
$435$	−5.31225	−	18.0919i	−0.254703	−	0.867438i
$436$		−	13.6518i		−	0.653805i
$437$	−23.1014	−	21.2761i	−1.10509	−	1.01777i
$438$	−11.8023			−0.563935
$439$	−2.17082	−	7.39314i	−0.103608	−	0.352856i	0.891329	−	0.453357i	$-0.149774\pi$
$439$	−2.17082	−	7.39314i	−0.103608	−	0.352856i	−0.994937	+	0.100501i	$0.967955\pi$
$440$	7.68733	−	6.66111i	0.366479	−	0.317556i
$441$	−0.191598	−	6.99738i	−0.00912369	−	0.333208i
$442$	9.37250	−	1.34756i	0.445804	−	0.0640970i
$443$	17.2158	+	11.0639i	0.817945	+	0.525661i	0.881426	−	0.472322i	$-0.156584\pi$
$443$	17.2158	+	11.0639i	0.817945	+	0.525661i	−0.0634812	+	0.997983i	$0.520220\pi$
$444$	−3.72555	+	8.15782i	−0.176807	+	0.387153i
$445$	1.48437	−	1.71305i	0.0703659	−	0.0812065i
$446$	−28.4329	−	4.08803i	−1.34634	−	0.193574i
$447$	−4.42907	−	9.69831i	−0.209488	−	0.458714i
$448$	−0.597727	−	2.57735i	−0.0282399	−	0.121768i
$449$	39.4617	+	11.5870i	1.86231	+	0.546825i	0.999119	+	0.0419551i	$0.0133586\pi$
$449$	39.4617	+	11.5870i	1.86231	+	0.546825i	0.863195	+	0.504870i	$0.168460\pi$
$450$	0.374553	+	0.820156i	0.0176566	+	0.0386625i
$451$	2.80029	−	19.4765i	0.131861	−	0.917111i
$452$	−2.06975	−	1.79345i	−0.0973531	−	0.0843569i
$453$	2.76782	+	1.26402i	0.130043	+	0.0593888i
$454$	−10.2153	−	6.56498i	−0.479428	−	0.308110i
$455$	−9.76726	−	12.6819i	−0.457896	−	0.594539i
$456$	3.54046	+	5.50906i	0.165797	+	0.257985i
$457$	20.6494	−	17.8928i	0.965938	−	0.836990i	−0.0207215	−	0.999785i	$-0.506596\pi$
$457$	20.6494	−	17.8928i	0.965938	−	0.836990i	0.986660	+	0.162795i	$0.0520509\pi$
$458$	8.33568	−	2.44758i	0.389501	−	0.114368i
$459$		−	3.16838i		−	0.147887i
$460$	5.49400	−	8.00490i	0.256159	−	0.373230i
$461$			32.2910i			1.50394i	0.659197	+	0.751970i	$0.270896\pi$
$461$			32.2910i			1.50394i	−0.659197	+	0.751970i	$0.729104\pi$
$462$	−9.52774	−	9.27043i	−0.443271	−	0.431299i
$463$	6.18922	+	7.14274i	0.287637	+	0.331951i	0.881117	−	0.472898i	$-0.156792\pi$
$463$	6.18922	+	7.14274i	0.287637	+	0.331951i	−0.593480	+	0.804849i	$0.702246\pi$
$464$	−7.83543	+	5.03553i	−0.363751	+	0.233768i
$465$	−2.56902	−	17.8679i	−0.119135	−	0.828605i
$466$	7.50417	+	4.82264i	0.347624	+	0.223404i
$467$	3.24072	−	7.09618i	0.149963	−	0.328372i	−0.819710	−	0.572778i	$-0.805866\pi$
$467$	3.24072	−	7.09618i	0.149963	−	0.328372i	0.969673	+	0.244406i	$0.0785929\pi$
$468$	−2.25860	−	1.95709i	−0.104404	−	0.0904665i
$469$	−2.90180	−	7.46630i	−0.133993	−	0.344762i
$470$	15.4584	−	7.05961i	0.713042	−	0.325636i
$471$	−3.08460	+	10.5052i	−0.142131	+	0.484053i
$472$	0.00732910	−	0.0249606i	0.000337349	−	0.00114891i
$473$	19.3031	+	42.2678i	0.887557	+	1.94348i
$474$	1.30646	−	9.08663i	0.0600077	−	0.417363i
$475$	−3.86661	+	4.46231i	−0.177412	+	0.204745i
$476$	−8.35241	+	0.712403i	−0.382832	+	0.0326529i
$477$	−1.96363	+	3.05547i	−0.0899085	+	0.139900i
$478$	−3.77053	−	26.2246i	−0.172460	−	1.19949i
$479$	12.6092	−	8.10345i	0.576130	−	0.370256i	−0.219892	−	0.975524i	$-0.570570\pi$
$479$	12.6092	−	8.10345i	0.576130	−	0.370256i	0.796022	+	0.605268i	$0.206934\pi$
$480$	−1.52997	+	1.32573i	−0.0698333	+	0.0605109i
$481$	25.7165	−	7.55104i	1.17257	−	0.344298i
$482$	8.77160			0.399536
$483$	−11.0340	−	6.26507i	−0.502064	−	0.285071i
$484$	−14.2455			−0.647524
$485$	−25.5580	+	7.50450i	−1.16053	+	0.340762i
$486$	−0.755750	+	0.654861i	−0.0342815	+	0.0297051i
$487$	−9.40429	+	6.04377i	−0.426149	+	0.273869i	−0.736086	−	0.676888i	$-0.763328\pi$
$487$	−9.40429	+	6.04377i	−0.426149	+	0.273869i	0.309937	+	0.950757i	$0.399692\pi$
$488$	−1.22763	−	8.53839i	−0.0555724	−	0.386515i
$489$	7.65721	−	11.9149i	0.346271	−	0.538808i
$490$	7.98491	+	11.7073i	0.360721	+	0.528883i
$491$	−17.3196	+	19.9878i	−0.781621	+	0.902039i	−0.997225	−	0.0744418i	$-0.976282\pi$
$491$	−17.3196	+	19.9878i	−0.781621	+	0.902039i	0.215604	+	0.976481i	$0.430828\pi$
$492$	−0.557329	+	3.87631i	−0.0251263	+	0.174757i
$493$	12.2590	+	26.8435i	0.552118	+	1.20897i
$494$	5.51378	−	18.7782i	0.248077	−	0.844872i
$495$	−2.86572	+	9.75976i	−0.128805	+	0.438669i
$496$	−8.11105	+	3.70419i	−0.364197	+	0.166323i
$497$	19.6837	−	7.65013i	0.882935	−	0.343155i
$498$	−0.894431	−	0.775029i	−0.0400804	−	0.0347299i
$499$	−11.0214	+	24.1335i	−0.493386	+	1.08036i	0.485177	+	0.874416i	$0.338755\pi$
$499$	−11.0214	+	24.1335i	−0.493386	+	1.08036i	−0.978563	+	0.205949i	$0.933972\pi$
$500$	−10.0509	−	6.45932i	−0.449490	−	0.288869i
$501$	−2.10725	−	14.6563i	−0.0941452	−	0.654794i
$502$	−16.1202	+	10.3598i	−0.719479	+	0.462381i
$503$	25.8264	+	29.8052i	1.15154	+	1.32895i	0.935813	+	0.352497i	$0.114667\pi$
$503$	25.8264	+	29.8052i	1.15154	+	1.32895i	0.215729	+	0.976453i	$0.430787\pi$
$504$	1.89626	+	1.84505i	0.0844661	+	0.0821850i
$505$		−	2.17268i		−	0.0966828i
$506$	−23.3155	+	6.08540i	−1.03650	+	0.270529i
$507$		−	4.06852i		−	0.180689i
$508$	7.65856	−	2.24876i	0.339794	−	0.0997725i
$509$	8.29370	−	7.18653i	0.367612	−	0.318537i	−0.451392	−	0.892326i	$-0.649072\pi$
$509$	8.29370	−	7.18653i	0.367612	−	0.318537i	0.819004	+	0.573788i	$0.194527\pi$
$510$	3.46778	+	5.39597i	0.153556	+	0.238937i
$511$	−19.0534	−	24.7392i	−0.842872	−	1.09440i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−5.95685	−	2.72040i	−0.263001	−	0.120109i
$514$	−13.6906	−	11.8630i	−0.603868	−	0.523255i
$515$	4.43621	−	30.8545i	0.195483	−	1.35961i
$516$	−3.84180	−	8.41236i	−0.169126	−	0.370334i
$517$	−40.4694	−	11.8829i	−1.77984	−	0.522609i
$518$	−23.1143	+	5.36057i	−1.01559	+	0.235530i
$519$	−4.63694	−	10.1535i	−0.203539	−	0.445688i
$520$	5.98858	+	0.861028i	0.262617	+	0.0377586i
$521$	−4.49360	+	5.18589i	−0.196868	+	0.227198i	−0.845597	−	0.533822i	$-0.820755\pi$
$521$	−4.49360	+	5.18589i	−0.196868	+	0.227198i	0.648729	+	0.761019i	$0.275301\pi$
$522$	3.86917	−	8.47231i	0.169349	−	0.370823i
$523$	24.8058	+	15.9417i	1.08468	+	0.697082i	0.955634	−	0.294557i	$-0.0951721\pi$
$523$	24.8058	+	15.9417i	1.08468	+	0.697082i	0.129046	+	0.991639i	$0.458808\pi$
$524$	1.85781	−	0.267113i	0.0811588	−	0.0116689i
$525$	−1.11449	+	2.10916i	−0.0486402	+	0.0920511i
$526$	−5.73133	+	4.96623i	−0.249898	+	0.216538i
$527$	7.95950	+	27.1076i	0.346721	+	1.18082i
$528$	5.02449			0.218663
$529$	−20.0662	+	11.2404i	−0.872445	+	0.488712i
$530$		−	7.35286i		−	0.319388i
$531$	0.00732910	+	0.0249606i	0.000318056	+	0.00108320i
$532$	−5.83208	+	16.3150i	−0.252853	+	0.707345i
$533$	9.84577	−	6.32749i	0.426468	−	0.274074i
$534$	1.10827	−	0.159345i	0.0479594	−	0.00689553i
$535$	−9.72072	+	15.1257i	−0.420264	+	0.653943i
$536$	2.75404	+	1.25773i	0.118956	+	0.0543255i
$537$	−7.06683	−	6.12345i	−0.304956	−	0.264246i
$538$	−4.40011	−	0.632641i	−0.189702	−	0.0272751i
$539$	4.05066	−	34.9374i	0.174474	−	1.50486i
$540$	0.570351	−	1.94244i	0.0245440	−	0.0835892i
$541$	3.81753	+	1.12093i	0.164128	+	0.0481925i	0.362764	−	0.931881i	$-0.381833\pi$
$541$	3.81753	+	1.12093i	0.164128	+	0.0481925i	−0.198636	+	0.980073i	$0.563651\pi$
$542$	−14.5329	+	6.63694i	−0.624240	+	0.285081i
$543$	−12.5898	−	1.81014i	−0.540280	−	0.0776805i
$544$	2.07485	−	2.39450i	0.0889583	−	0.102663i
$545$	−25.1398	−	11.4810i	−1.07687	−	0.491791i
$546$	0.456079	−	7.89382i	0.0195184	−	0.337824i
$547$	−1.09182	−	7.59378i	−0.0466829	−	0.324686i	−0.999759	−	0.0219556i	$-0.993011\pi$
$547$	−1.09182	−	7.59378i	−0.0466829	−	0.324686i	0.953076	−	0.302731i	$-0.0978983\pi$
$548$	−4.32800	−	6.73449i	−0.184883	−	0.287683i
$549$	5.64895	+	6.51924i	0.241091	+	0.278234i
$550$	1.27632	+	4.34675i	0.0544225	+	0.185346i
$551$	60.9939			2.59843
$552$	4.64038	−	1.21115i	0.197508	−	0.0515499i
$553$	21.1559	−	11.9308i	0.899641	−	0.507347i
$554$	−4.75350	+	1.39575i	−0.201957	+	0.0592999i
$555$	11.8895	+	13.7212i	0.504680	+	0.582432i
$556$	9.52429	+	14.8201i	0.403920	+	0.628511i
$557$	37.1456	−	5.34073i	1.57391	−	0.226294i	0.700634	−	0.713521i	$-0.252901\pi$
$557$	37.1456	−	5.34073i	1.57391	−	0.226294i	0.873276	+	0.487227i	$0.161991\pi$
$558$	4.82081	−	7.50133i	0.204081	−	0.317557i
$559$	−11.4814	+	25.1408i	−0.485613	+	1.06334i
$560$	−5.24886	−	1.06680i	−0.221805	−	0.0450803i
$561$	2.26558	−	15.7575i	0.0956528	−	0.665280i
$562$	−9.66975	+	4.41603i	−0.407894	+	0.186279i
$563$	−23.4901	−	6.89731i	−0.989989	−	0.290687i	−0.253647	−	0.967297i	$-0.581630\pi$
$563$	−23.4901	−	6.89731i	−0.989989	−	0.290687i	−0.736342	+	0.676610i	$0.763448\pi$
$564$	8.05443	+	2.36499i	0.339153	+	0.0995843i
$565$	−5.04327	+	2.30318i	−0.212172	+	0.0968956i
$566$	−3.76002	+	26.1515i	−0.158045	+	1.09923i
$567$	−2.59274	−	0.526958i	−0.108885	−	0.0221301i
$568$	−3.31579	+	7.26057i	−0.139128	+	0.304647i
$569$	18.5201	−	28.8179i	0.776405	−	1.20811i	−0.197311	−	0.980341i	$-0.563221\pi$
$569$	18.5201	−	28.8179i	0.776405	−	1.20811i	0.973715	−	0.227768i	$-0.0731429\pi$
$570$	13.1224	−	1.88671i	0.549636	−	0.0790258i
$571$	−3.98556	−	6.20166i	−0.166791	−	0.259531i	0.747790	−	0.663936i	$-0.231115\pi$
$571$	−3.98556	−	6.20166i	−0.166791	−	0.259531i	−0.914580	+	0.404404i	$0.867479\pi$
$572$	−9.83338	−	11.3483i	−0.411154	−	0.474497i
$573$	−3.92707	+	1.15309i	−0.164056	+	0.0481711i
$574$	−9.02500	+	5.08960i	−0.376696	+	0.212436i
$575$	2.22653	+	3.70679i	0.0928526	+	0.154584i
$576$	−1.00000			−0.0416667
$577$	8.03244	+	27.3560i	0.334395	+	1.13884i	0.939457	+	0.342666i	$0.111330\pi$
$577$	8.03244	+	27.3560i	0.334395	+	1.13884i	−0.605062	+	0.796178i	$0.706852\pi$
$578$	4.55873	+	5.26106i	0.189618	+	0.218831i
$579$	9.73504	+	15.1480i	0.404574	+	0.629530i
$580$	2.68344	+	18.6637i	0.111424	+	0.774969i
$581$	0.180612	−	3.12604i	0.00749306	−	0.129690i
$582$	−11.9686	−	5.46590i	−0.496116	−	0.226569i
$583$	−11.9507	+	13.7918i	−0.494946	+	0.571198i
$584$	11.6822	+	1.67964i	0.483411	+	0.0695040i
$585$	−5.50342	+	2.51333i	−0.227538	+	0.103913i
$586$	20.4767	+	6.01249i	0.845883	+	0.248374i
$587$	1.17151	−	3.98980i	0.0483534	−	0.164677i	−0.931777	−	0.363032i	$-0.881742\pi$
$587$	1.17151	−	3.98980i	0.0483534	−	0.164677i	0.980130	+	0.198355i	$0.0635599\pi$
$588$	−0.806183	+	6.95342i	−0.0332464	+	0.286754i
$589$	57.7988	+	8.31022i	2.38156	+	0.342417i
$590$	−0.0398013	−	0.0344880i	−0.00163859	−	0.00141985i
$591$	25.1365	+	11.4795i	1.03398	+	0.472202i
$592$	4.84861	−	7.54458i	0.199277	−	0.310080i
$593$	18.3473	−	2.63794i	0.753432	−	0.108327i	0.245111	−	0.969495i	$-0.421175\pi$
$593$	18.3473	−	2.63794i	0.753432	−	0.108327i	0.508321	+	0.861168i	$0.330266\pi$
$594$	−4.22687	+	2.71645i	−0.173431	+	0.111457i
$595$	−5.71236	+	15.9801i	−0.234184	+	0.655119i
$596$	3.00377	+	10.2299i	0.123039	+	0.419034i
$597$			1.89171i			0.0774225i
$598$	−11.8171	−	8.11044i	−0.483239	−	0.331661i
$599$	4.68156			0.191283			0.0956416	−	0.995416i	$-0.469510\pi$
$599$	4.68156			0.191283			0.0956416	+	0.995416i	$0.469510\pi$
$600$	−0.254020	−	0.865112i	−0.0103703	−	0.0353181i
$601$	−10.1202	+	8.76921i	−0.412812	+	0.357703i	−0.836370	−	0.548165i	$-0.815326\pi$
$601$	−10.1202	+	8.76921i	−0.412812	+	0.357703i	0.423558	+	0.905869i	$0.360781\pi$
$602$	11.4313	−	21.6337i	0.465906	−	0.881723i
$603$	−2.99682	+	0.430878i	−0.122040	+	0.0175467i
$604$	−2.55976	−	1.64506i	−0.104155	−	0.0669364i
$605$	−11.9802	+	26.2331i	−0.487066	+	1.06653i
$606$	0.702811	−	0.811087i	0.0285497	−	0.0329482i
$607$	−43.9171	−	6.31432i	−1.78254	−	0.256290i	−0.829364	−	0.558709i	$-0.811297\pi$
$607$	−43.9171	−	6.31432i	−1.78254	−	0.256290i	−0.953175	+	0.302419i	$0.902206\pi$
$608$	−2.72040	−	5.95685i	−0.110327	−	0.241582i
$609$	24.0054	−	5.56722i	0.972748	−	0.225595i
$610$	−16.7558	−	4.91996i	−0.678424	−	0.199203i
$611$	−10.4217	−	22.8203i	−0.421615	−	0.923209i
$612$	−0.450907	+	3.13613i	−0.0182268	+	0.126770i
$613$	−9.51893	−	8.24820i	−0.384466	−	0.333142i	0.441089	−	0.897463i	$-0.354592\pi$
$613$	−9.51893	−	8.24820i	−0.384466	−	0.333142i	−0.825555	+	0.564322i	$0.809138\pi$
$614$	−16.4728	−	7.52289i	−0.664790	−	0.303599i
$615$	6.66950	+	4.28623i	0.268940	+	0.172837i
$616$	8.11144	+	10.5320i	0.326819	+	0.424347i
$617$	−6.88781	−	10.7176i	−0.277293	−	0.431476i	0.674474	−	0.738299i	$-0.264371\pi$
$617$	−6.88781	−	10.7176i	−0.277293	−	0.431476i	−0.951767	+	0.306823i	$0.900734\pi$
$618$	11.6368	−	10.0834i	0.468101	−	0.405612i
$619$	23.8327	−	6.99790i	0.957916	−	0.281270i	0.234837	−	0.972035i	$-0.424544\pi$
$619$	23.8327	−	6.99790i	0.957916	−	0.281270i	0.723079	+	0.690765i	$0.242726\pi$
$620$			18.0517i			0.724972i
$621$	−3.24894	+	3.52766i	−0.130375	+	0.141560i
$622$		−	16.4916i		−	0.661251i
$623$	2.12317	+	2.06583i	0.0850631	+	0.0827659i
$624$	1.95709	+	2.25860i	0.0783463	+	0.0904164i
$625$	−16.5549	+	10.6392i	−0.662197	+	0.425568i
$626$	−3.66602	−	25.4977i	−0.146524	−	1.01909i
$627$	−27.6802	−	17.7890i	−1.10544	−	0.710424i
$628$	4.54825	−	9.95927i	0.181495	−	0.397418i
$629$	−21.4745	−	18.6078i	−0.856244	−	0.741940i
$630$	4.99237	−	1.94030i	0.198901	−	0.0773034i
$631$	4.48677	−	2.04904i	0.178616	−	0.0815710i	−0.324100	−	0.946023i	$-0.605061\pi$
$631$	4.48677	−	2.04904i	0.178616	−	0.0815710i	0.502716	+	0.864452i	$0.332334\pi$
$632$	−2.58632	+	8.80821i	−0.102878	+	0.350372i
$633$	3.41857	−	11.6426i	0.135876	−	0.462750i
$634$	−5.39692	−	11.8176i	−0.214339	−	0.469337i
$635$	2.29965	−	15.9944i	0.0912587	−	0.634718i
$636$	2.37848	−	2.74492i	0.0943130	−	0.108843i
$637$	17.2828	−	11.7876i	0.684769	−	0.467042i
$638$	25.3010	−	39.3691i	1.00167	−	1.55864i
$639$	−1.13594	−	7.90064i	−0.0449371	−	0.312544i
$640$	1.70307	−	1.09450i	0.0673197	−	0.0432638i
$641$	−3.54803	+	3.07439i	−0.140139	+	0.121431i	−0.722109	−	0.691779i	$-0.756827\pi$
$641$	−3.54803	+	3.07439i	−0.140139	+	0.121431i	0.581971	+	0.813210i	$0.302282\pi$
$642$	−8.52170	+	2.50220i	−0.336325	+	0.0987538i
$643$	−15.7800			−0.622303			−0.311152	−	0.950360i	$-0.600715\pi$
$643$	−15.7800			−0.622303			−0.311152	+	0.950360i	$0.600715\pi$
$644$	10.0301	+	7.77160i	0.395240	+	0.306244i
$645$	−18.7222			−0.737187
$646$	−19.9081	+	5.84554i	−0.783273	+	0.229990i
$647$	−6.51246	+	5.64308i	−0.256031	+	0.221852i	−0.773413	−	0.633902i	$-0.781452\pi$
$647$	−6.51246	+	5.64308i	−0.256031	+	0.221852i	0.517382	+	0.855755i	$0.326907\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	0.0186019	+	0.129379i	0.000730186	+	0.00507856i
$650$	−1.45680	+	2.26683i	−0.0571406	+	0.0889125i
$651$	23.5064	−	2.00493i	0.921289	−	0.0785796i
$652$	−9.27493	+	10.7038i	−0.363234	+	0.419195i
$653$	1.63415	−	11.3658i	0.0639494	−	0.444778i	−0.932541	−	0.361065i	$-0.882413\pi$
$653$	1.63415	−	11.3658i	0.0639494	−	0.444778i	0.996490	−	0.0837125i	$-0.0266777\pi$
$654$	−5.67118	−	12.4182i	−0.221761	−	0.485588i
$655$	1.07050	−	3.64579i	0.0418279	−	0.142453i
$656$	1.10331	−	3.75754i	0.0430771	−	0.146707i
$657$	−10.7357	+	4.90285i	−0.418841	+	0.191278i
$658$	8.04557	+	20.7012i	0.313649	+	0.807016i
$659$	21.3643	+	18.5123i	0.832235	+	0.721136i	0.962774	−	0.270307i	$-0.0871253\pi$
$659$	21.3643	+	18.5123i	0.832235	+	0.721136i	−0.130539	+	0.991443i	$0.541671\pi$
$660$	4.22552	−	9.25259i	0.164478	−	0.360156i
$661$	5.83795	+	3.75182i	0.227070	+	0.145929i	0.649230	−	0.760593i	$-0.275091\pi$
$661$	5.83795	+	3.75182i	0.227070	+	0.145929i	−0.422160	+	0.906522i	$0.638728\pi$
$662$	2.79698	+	19.4534i	0.108708	+	0.756078i
$663$	7.96573	−	5.11926i	0.309363	−	0.198816i
$664$	0.775029	+	0.894431i	0.0300770	+	0.0347107i
$665$	25.1393	+	24.4604i	0.974861	+	0.948534i
$666$			8.96826i			0.347513i
$667$	13.8769	−	42.4581i	0.537315	−	1.64399i
$668$			14.8070i			0.572900i
$669$	−27.5617	+	8.09284i	−1.06560	+	0.312887i
$670$	4.63220	−	4.01382i	0.178957	−	0.155067i
$671$	23.4326	+	36.4618i	0.904604	+	1.40759i
$672$	−1.61438	−	2.09613i	−0.0622761	−	0.0808601i
$673$	42.3036	+	27.1869i	1.63068	+	1.04798i	0.948491	+	0.316806i	$0.102610\pi$
$673$	42.3036	+	27.1869i	1.63068	+	1.04798i	0.682194	+	0.731172i	$0.261026\pi$
$674$	4.65468	+	2.12572i	0.179291	+	0.0818797i
$675$	0.681410	+	0.590445i	0.0262275	+	0.0227262i
$676$	−0.579011	+	4.02711i	−0.0222697	+	0.154889i
$677$	−18.1032	−	39.6406i	−0.695764	−	1.52351i	−0.845033	−	0.534715i	$-0.820419\pi$
$677$	−18.1032	−	39.6406i	−0.695764	−	1.52351i	0.149268	−	0.988797i	$-0.452308\pi$
$678$	−2.62774	−	0.771575i	−0.100918	−	0.0296322i
$679$	−7.86469	−	33.9119i	−0.301819	−	1.30142i
$680$	−2.66455	−	5.83456i	−0.102181	−	0.223745i
$681$	−12.0194	−	1.72812i	−0.460583	−	0.0662218i
$682$	29.3395	−	33.8596i	1.12347	−	1.29655i
$683$	−14.7317	+	32.2580i	−0.563695	+	1.23432i	0.386393	+	0.922334i	$0.373721\pi$
$683$	−14.7317	+	32.2580i	−0.563695	+	1.23432i	−0.950087	+	0.311985i	$0.899006\pi$
$684$	5.50906	+	3.54046i	0.210644	+	0.135373i
$685$	−16.0413	+	2.30639i	−0.612907	+	0.0881228i
$686$	−15.8768	+	9.53560i	−0.606179	+	0.364071i
$687$	6.56564	−	5.68916i	0.250495	−	0.217055i
$688$	2.60549	+	8.87348i	0.0993333	+	0.338298i
$689$	−10.8546			−0.413526
$690$	1.67216	−	9.56380i	0.0636580	−	0.364088i
$691$			29.5310i			1.12341i	0.827337	+	0.561706i	$0.189855\pi$
$691$			29.5310i			1.12341i	−0.827337	+	0.561706i	$0.810145\pi$
$692$	3.14475	+	10.7100i	0.119545	+	0.407134i
$693$	−12.5178	−	4.47471i	−0.475512	−	0.169980i
$694$	−14.3033	+	9.19219i	−0.542947	+	0.348931i
$695$	35.3009	−	5.07550i	1.33904	−	0.192525i
$696$	−5.03553	+	7.83543i	−0.190871	+	0.297001i
$697$	−11.2866	−	5.15443i	−0.427511	−	0.195238i
$698$	22.0214	+	19.0816i	0.833522	+	0.722251i
$699$	8.82943	+	1.26948i	0.333960	+	0.0480162i
$700$	1.40331	−	1.92908i	0.0530400	−	0.0729124i
$701$	−9.84353	+	33.5240i	−0.371785	+	1.26618i	0.535094	+	0.844792i	$0.320276\pi$
$701$	−9.84353	+	33.5240i	−0.371785	+	1.26618i	−0.906879	+	0.421391i	$0.861542\pi$
$702$	−2.86750	−	0.841974i	−0.108227	−	0.0317783i
$703$	−53.4225	+	24.3973i	−2.01487	+	0.920160i
$704$	−4.97335	−	0.715060i	−0.187440	−	0.0269498i
$705$	11.1288	−	12.8433i	0.419134	−	0.483706i
$706$	−22.3659	−	10.2142i	−0.841751	−	0.384415i
$707$	2.83475	+	0.163783i	0.106612	+	0.00615968i
$708$	−0.00370224	−	0.0257496i	−0.000139139	−	0.000967730i
$709$	−18.8460	−	29.3250i	−0.707778	−	1.10132i	−0.989876	−	0.141938i	$-0.954667\pi$
$709$	−18.8460	−	29.3250i	−0.707778	−	1.10132i	0.282098	−	0.959386i	$-0.408970\pi$
$710$	10.5818	+	12.2120i	0.397128	+	0.458310i
$711$	−2.58632	−	8.80821i	−0.0969947	−	0.330334i
$712$	−1.11966			−0.0419612
$713$	18.9347	−	38.3433i	0.709112	−	1.43597i
$714$	−7.30168	+	4.11774i	−0.273259	+	0.154103i
$715$	−29.1676	+	8.56439i	−1.09081	+	0.320290i
$716$	6.12345	+	7.06683i	0.228844	+	0.264100i
$717$	−14.3239	−	22.2884i	−0.534936	−	0.832377i
$718$	15.4652	−	2.22357i	0.577158	−	0.0829828i
$719$	−21.7866	+	33.9006i	−0.812502	+	1.26428i	0.148823	+	0.988864i	$0.452451\pi$
$719$	−21.7866	+	33.9006i	−0.812502	+	1.26428i	−0.961326	+	0.275415i	$0.911185\pi$
$720$	−0.840984	+	1.84150i	−0.0313416	+	0.0686285i
$721$	39.9223	+	8.11394i	1.48678	+	0.302179i
$722$	−3.39913	+	23.6415i	−0.126503	+	0.879845i
$723$	7.97893	−	3.64386i	0.296740	−	0.135516i
$724$	12.2040	+	3.58343i	0.453560	+	0.133177i
$725$	−8.05765	−	2.36594i	−0.299254	−	0.0878688i
$726$	−12.9582	+	5.91780i	−0.480923	+	0.219630i
$727$	5.52990	−	38.4613i	0.205093	−	1.42645i	−0.583789	−	0.811906i	$-0.698430\pi$
$727$	5.52990	−	38.4613i	0.205093	−	1.42645i	0.788881	−	0.614546i	$-0.210661\pi$
$728$	−1.57484	+	7.74856i	−0.0583676	+	0.287181i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	12.9176	−	20.1001i	0.478100	−	0.743939i
$731$	29.0032	−	4.17003i	1.07272	−	0.154234i
$732$	−4.66367	−	7.25681i	−0.172374	−	0.268220i
$733$	22.9187	+	26.4496i	0.846520	+	0.976937i	0.999937	−	0.0112249i	$-0.00357307\pi$
$733$	22.9187	+	26.4496i	0.846520	+	0.976937i	−0.153417	+	0.988162i	$0.549028\pi$
$734$	8.77950	−	2.57790i	0.324057	−	0.0951518i
$735$	12.1267	+	7.33230i	0.447301	+	0.270456i
$736$	−4.76551	+	0.538425i	−0.175659	+	0.0198466i
$737$	−15.2123			−0.560354
$738$	1.10331	+	3.75754i	0.0406135	+	0.138317i
$739$	−17.3151	−	19.9827i	−0.636945	−	0.735074i	0.341886	−	0.939741i	$-0.388934\pi$
$739$	−17.3151	−	19.9827i	−0.636945	−	0.735074i	−0.978832	+	0.204667i	$0.934389\pi$
$740$	−9.81572	−	15.2736i	−0.360833	−	0.561467i
$741$	−2.78524	−	19.3718i	−0.102318	−	0.711640i
$742$	9.59349	+	0.554280i	0.352188	+	0.0203483i
$743$	−39.9497	−	18.2444i	−1.46561	−	0.669323i	−0.486693	−	0.873573i	$-0.661797\pi$
$743$	−39.9497	−	18.2444i	−1.46561	−	0.669323i	−0.978919	+	0.204250i	$0.934524\pi$
$744$	−5.83930	+	6.73891i	−0.214079	+	0.247060i
$745$	21.3645	+	3.07175i	0.782734	+	0.112540i
$746$	0.164258	−	0.0750141i	0.00601391	−	0.00274646i
$747$	−1.13556	−	0.333431i	−0.0415480	−	0.0121996i
$748$	−4.48504	+	15.2746i	−0.163989	+	0.558496i
$749$	−19.0022	−	13.8231i	−0.694325	−	0.505086i
$750$	−11.8259	−	1.70031i	−0.431821	−	0.0620865i
$751$	16.9639	+	14.6993i	0.619023	+	0.536386i	0.906935	−	0.421271i	$-0.138416\pi$
$751$	16.9639	+	14.6993i	0.619023	+	0.536386i	−0.287912	+	0.957657i	$0.592961\pi$
$752$	−7.63588	−	3.48719i	−0.278452	−	0.127165i
$753$	−10.3598	+	16.1202i	−0.377532	+	0.587452i
$754$	27.5521	−	3.96139i	1.00339	−	0.144265i
$755$	−5.18208	+	3.33032i	−0.188595	+	0.121203i
$756$	2.49136	+	0.890580i	0.0906098	+	0.0323901i
$757$	−1.04331	−	3.55319i	−0.0379197	−	0.129143i	0.938358	−	0.345665i	$-0.112347\pi$
$757$	−1.04331	−	3.55319i	−0.0379197	−	0.129143i	−0.976278	+	0.216522i	$0.930529\pi$
$758$			25.9290i			0.941782i
$759$	−18.6806	+	15.2211i	−0.678063	+	0.552491i
$760$	−13.2573			−0.480894
$761$	9.39827	+	32.0076i	0.340687	+	1.16027i	0.934587	+	0.355735i	$0.115769\pi$
$761$	9.39827	+	32.0076i	0.340687	+	1.16027i	−0.593900	+	0.804539i	$0.702412\pi$
$762$	6.03231	−	5.22702i	0.218527	−	0.189355i
$763$	16.8747	−	31.9352i	0.610904	−	1.15613i
$764$	4.05120	−	0.582475i	0.146567	−	0.0210732i
$765$	5.39597	+	3.46778i	0.195092	+	0.125378i
$766$	−7.53220	+	16.4932i	−0.272149	+	0.595924i
$767$	−0.0509125	+	0.0587562i	−0.00183834	+	0.00212156i
$768$	0.989821	+	0.142315i	0.0357171	+	0.00513534i
$769$	18.7968	+	41.1592i	0.677829	+	1.48424i	0.864928	+	0.501897i	$0.167364\pi$
$769$	18.7968	+	41.1592i	0.677829	+	1.48424i	−0.187099	+	0.982341i	$0.559908\pi$
$770$	26.2162	−	6.07995i	0.944768	−	0.219106i
$771$	−17.3815	−	5.10367i	−0.625980	−	0.183804i
$772$	−7.48016	−	16.3793i	−0.269217	−	0.589503i
$773$	−4.00503	+	27.8556i	−0.144051	+	1.00190i	0.781671	+	0.623691i	$0.214368\pi$
$773$	−4.00503	+	27.8556i	−0.144051	+	1.00190i	−0.925722	+	0.378206i	$0.876541\pi$
$774$	−6.98924	−	6.05621i	−0.251223	−	0.217686i
$775$	−7.31321	−	3.33983i	−0.262698	−	0.119970i
$776$	11.0689	+	7.11358i	0.397352	+	0.255363i
$777$	−18.7987	+	14.4782i	−0.674399	+	0.519402i
$778$	−18.2154	−	28.3438i	−0.653055	−	1.01617i
$779$	−19.3816	+	16.7943i	−0.694418	+	0.601717i
$780$	5.80509	−	1.70453i	0.207855	−	0.0610319i
$781$		−	40.1049i		−	1.43507i
$782$	−0.460234	+	15.1880i	−0.0164579	+	0.543123i
$783$		−	9.31400i		−	0.332855i
$784$	1.78755	−	6.76791i	0.0638412	−	0.241711i
$785$	−14.5150	−	16.7512i	−0.518061	−	0.597875i
$786$	1.57896	−	1.01474i	0.0563196	−	0.0361944i
$787$	−3.05308	−	21.2346i	−0.108831	−	0.756933i	−0.969024	−	0.246966i	$-0.920567\pi$
$787$	−3.05308	−	21.2346i	−0.108831	−	0.756933i	0.860194	−	0.509967i	$-0.170343\pi$
$788$	−23.2470	−	14.9399i	−0.828140	−	0.532213i
$789$	−3.15036	+	6.89832i	−0.112156	+	0.245587i
$790$	14.0452	+	12.1703i	0.499707	+	0.432999i
$791$	−2.62485	−	6.75371i	−0.0933290	−	0.240134i
$792$	4.57044	−	2.08725i	0.162403	−	0.0741672i
$793$	−7.26303	+	24.7356i	−0.257918	+	0.878387i
$794$	−7.59121	+	25.8533i	−0.269402	+	0.917499i
$795$	−3.05449	−	6.68840i	−0.108332	−	0.237213i
$796$	0.269218	−	1.87245i	0.00954219	−	0.0663674i
$797$	8.45518	−	9.75780i	0.299498	−	0.345639i	−0.585976	−	0.810329i	$-0.699289\pi$
$797$	8.45518	−	9.75780i	0.299498	−	0.345639i	0.885474	+	0.464690i	$0.153834\pi$
$798$	1.47245	+	17.2634i	0.0521240	+	0.611117i
$799$	−14.3793	+	22.3747i	−0.508705	+	0.791560i
$800$	0.128316	+	0.892458i	0.00453666	+	0.0315531i
$801$	0.941921	−	0.605336i	0.0332812	−	0.0213885i
$802$	2.96386	−	2.56820i	0.104658	−	0.0906864i
$803$	−56.8984	+	16.7069i	−2.00790	+	0.589573i
$804$	3.02764			0.106777
$805$	22.7465	−	11.9345i	0.801709	−	0.420637i
$806$	26.6485			0.938654
$807$	−4.26529	+	1.25240i	−0.150145	+	0.0440867i
$808$	−0.811087	+	0.702811i	−0.0285339	+	0.0247248i
$809$	12.3041	−	7.90740i	0.432591	−	0.278009i	−0.306170	−	0.951977i	$-0.599048\pi$
$809$	12.3041	−	7.90740i	0.432591	−	0.278009i	0.738761	+	0.673968i	$0.235411\pi$
$810$	−0.288108	−	2.00384i	−0.0101231	−	0.0704076i
$811$	16.8982	−	26.2941i	0.593376	−	0.923312i	−0.406577	−	0.913617i	$-0.633278\pi$
$811$	16.8982	−	26.2941i	0.593376	−	0.923312i	0.999953	−	0.00969502i	$-0.00308607\pi$
$812$	−24.5534	+	2.09423i	−0.861654	+	0.0734931i
$813$	−10.4625	+	12.0743i	−0.366935	+	0.423466i
$814$	−6.41284	+	44.6023i	−0.224770	+	1.56331i
$815$	11.9110	+	26.0815i	0.417225	+	0.913596i
$816$	0.892635	−	3.04004i	0.0312485	−	0.106423i
$817$	17.0624	−	58.1092i	0.596938	−	2.03298i
$818$	−1.46120	+	0.667310i	−0.0510898	+	0.0233319i
$819$	−2.86435	−	7.36993i	−0.100088	−	0.257526i
$820$	−5.99162	−	5.19177i	−0.209237	−	0.181305i
$821$	10.9038	−	23.8759i	0.380544	−	0.833275i	−0.618334	−	0.785916i	$-0.712192\pi$
$821$	10.9038	−	23.8759i	0.380544	−	0.833275i	0.998878	−	0.0473598i	$-0.0150807\pi$
$822$	−6.73449	−	4.32800i	−0.234892	−	0.150956i
$823$	4.45999	+	31.0199i	0.155466	+	1.08129i	0.906859	+	0.421433i	$0.138473\pi$
$823$	4.45999	+	31.0199i	0.155466	+	1.08129i	−0.751394	+	0.659854i	$0.770618\pi$
$824$	−12.9534	+	8.32463i	−0.451252	+	0.290002i
$825$	2.96669	+	3.42374i	0.103287	+	0.119199i
$826$	0.0479978	−	0.0493300i	0.00167006	−	0.00171641i
$827$			9.82321i			0.341587i	0.985307	+	0.170793i	$0.0546330\pi$
$827$			9.82321i			0.341587i	−0.985307	+	0.170793i	$0.945367\pi$
$828$	3.71791	−	3.02938i	0.129206	−	0.105278i
$829$			32.9840i			1.14558i	0.819702	+	0.572790i	$0.194139\pi$
$829$			32.9840i			1.14558i	−0.819702	+	0.572790i	$0.805861\pi$
$830$	2.29888	−	0.675012i	0.0797953	−	0.0234300i
$831$	−3.74412	+	3.24430i	−0.129882	+	0.112543i
$832$	−1.61574	−	2.51413i	−0.0560156	−	0.0871619i
$833$	−20.4190	−	8.65770i	−0.707477	−	0.299971i
$834$	14.8201	+	9.52429i	0.513177	+	0.329799i
$835$	27.2670	+	12.4524i	0.943614	+	0.430934i
$836$	24.8668	+	21.5472i	0.860038	+	0.745227i
$837$	1.26900	−	8.82609i	0.0438631	−	0.305074i
$838$	−2.96556	−	6.49366i	−0.102443	−	0.224320i
$839$	−9.62336	−	2.82567i	−0.332235	−	0.0975531i	0.111360	−	0.993780i	$-0.464479\pi$
$839$	−9.62336	−	2.82567i	−0.332235	−	0.0975531i	−0.443596	+	0.896227i	$0.646297\pi$
$840$	−5.21769	+	1.21006i	−0.180027	+	0.0417511i
$841$	23.9904	+	52.5317i	0.827256	+	1.81144i
$842$	31.3199	+	4.50313i	1.07936	+	0.155188i
$843$	−6.96143	+	8.03392i	−0.239764	+	0.276703i
$844$	−5.04068	+	11.0375i	−0.173507	+	0.379928i
$845$	6.92897	+	4.45298i	0.238364	+	0.153187i
$846$	8.30902	−	1.19466i	0.285670	−	0.0410732i
$847$	−33.3239	−	17.6085i	−1.14502	−	0.605035i
$848$	−2.74492	+	2.37848i	−0.0942608	+	0.0816774i
$849$	7.44350	+	25.3502i	0.255460	+	0.870017i
$850$	2.85672			0.0979847
$851$	4.82874	+	42.7383i	0.165527	+	1.46505i
$852$			7.98188i			0.273455i
$853$	2.40420	+	8.18795i	0.0823182	+	0.280350i	0.990358	−	0.138535i	$-0.0442393\pi$
$853$	2.40420	+	8.18795i	0.0823182	+	0.280350i	−0.908039	+	0.418885i	$0.862421\pi$
$854$	7.68231	−	21.4909i	0.262883	−	0.735405i
$855$	11.1528	−	7.16745i	0.381417	−	0.245122i
$856$	8.79106	−	1.26396i	0.300472	−	0.0432014i
$857$	−4.65064	+	7.23654i	−0.158863	+	0.247196i	−0.911556	−	0.411176i	$-0.865118\pi$
$857$	−4.65064	+	7.23654i	−0.158863	+	0.247196i	0.752693	+	0.658372i	$0.228754\pi$
$858$	−13.6590	−	6.23787i	−0.466311	−	0.212957i
$859$	5.90126	+	5.11347i	0.201348	+	0.174469i	0.749699	−	0.661779i	$-0.230198\pi$
$859$	5.90126	+	5.11347i	0.201348	+	0.174469i	−0.548350	+	0.836249i	$0.684744\pi$
$860$	18.5317	+	2.66445i	0.631925	+	0.0908570i
$861$	−6.09513	+	8.37878i	−0.207721	+	0.285548i
$862$	−0.0915929	+	0.311937i	−0.00311967	+	0.0106246i
$863$	−12.9171	−	3.79279i	−0.439702	−	0.129108i	0.0543864	−	0.998520i	$-0.482680\pi$
$863$	−12.9171	−	3.79279i	−0.439702	−	0.129108i	−0.494088	+	0.869412i	$0.664498\pi$
$864$	−0.909632	+	0.415415i	−0.0309463	+	0.0141327i
$865$	22.3672	+	3.21591i	0.760507	+	0.109344i
$866$	−14.7410	+	17.0120i	−0.500920	+	0.578093i
$867$	6.33229	+	2.89186i	0.215056	+	0.0982128i
$868$	−23.5525	−	1.36079i	−0.799424	−	0.0461881i
$869$	−6.56430	−	45.6557i	−0.222678	−	1.54876i
$870$	10.1941	+	15.8624i	0.345613	+	0.537785i
$871$	−5.92536	−	6.83823i	−0.200773	−	0.231704i
$872$	3.84617	+	13.0989i	0.130248	+	0.443583i
$873$	−13.1577			−0.445320
$874$	28.1598	+	13.9059i	0.952518	+	0.470373i
$875$	−15.5274	−	27.5336i	−0.524923	−	0.930807i
$876$	11.3242	−	3.32509i	0.382610	−	0.112344i
$877$	−1.24755	−	1.43975i	−0.0421267	−	0.0486168i	0.734295	−	0.678830i	$-0.237513\pi$
$877$	−1.24755	−	1.43975i	−0.0421267	−	0.0486168i	−0.776422	+	0.630213i	$0.782967\pi$
$878$	4.16578	+	6.48208i	0.140588	+	0.218760i
$879$	21.1239	−	3.03716i	0.712492	−	0.102441i
$880$	−5.49929	+	8.55706i	−0.185381	+	0.288458i
$881$	−4.93745	+	10.8115i	−0.166347	+	0.364249i	−0.974387	−	0.224879i	$-0.927801\pi$
$881$	−4.93745	+	10.8115i	−0.166347	+	0.364249i	0.808040	+	0.589128i	$0.200529\pi$
$882$	2.15523	+	6.65996i	0.0725702	+	0.224252i
$883$	−1.09978	+	7.64911i	−0.0370104	+	0.257413i	−0.999923	−	0.0124001i	$-0.996053\pi$
$883$	−1.09978	+	7.64911i	−0.0370104	+	0.257413i	0.962913	+	0.269813i	$0.0869619\pi$
$884$	−8.61320	+	3.93352i	−0.289693	+	0.132298i
$885$	−0.0505314	−	0.0148373i	−0.00169859	−	0.000498752i
$886$	−19.6354	−	5.76549i	−0.659666	−	0.193695i
$887$	−26.6815	+	12.1850i	−0.895878	+	0.409134i	−0.809494	−	0.587128i	$-0.800258\pi$
$887$	−26.6815	+	12.1850i	−0.895878	+	0.409134i	−0.0863837	+	0.996262i	$0.527531\pi$
$888$	1.27632	−	8.87698i	0.0428304	−	0.297892i
$889$	20.6950	+	4.20612i	0.694087	+	0.141069i
$890$	−0.941619	+	2.06186i	−0.0315631	+	0.0691137i
$891$	−2.71645	+	4.22687i	−0.0910043	+	0.141606i
$892$	28.4329	−	4.08803i	0.952003	−	0.136877i
$893$	29.7203	+	46.2456i	0.994551	+	1.54755i
$894$	6.98199	+	8.05765i	0.233513	+	0.269488i
$895$	18.1633	−	5.33322i	0.607131	−	0.178270i
$896$	1.29964	+	2.30455i	0.0434178	+	0.0769896i
$897$	−14.1184	−	2.46850i	−0.471401	−	0.0824209i
$898$	−41.1277			−1.37245
$899$	23.3983	+	79.6874i	0.780378	+	2.65772i
$900$	−0.590445	−	0.681410i	−0.0196815	−	0.0227137i
$901$	6.22153	+	9.68088i	0.207269	+	0.322517i
$902$	2.80029	+	19.4765i	0.0932396	+	0.648496i
$903$	1.41134	−	24.4274i	0.0469663	−	0.812894i
$904$	2.49119	+	1.13769i	0.0828557	+	0.0378389i
$905$	16.8623	−	19.4601i	0.560521	−	0.646876i
$906$	−3.01182	−	0.433034i	−0.100061	−	0.0143866i
$907$	−13.3763	+	6.10873i	−0.444151	+	0.202837i	−0.624920	−	0.780688i	$-0.714869\pi$
$907$	−13.3763	+	6.10873i	−0.444151	+	0.202837i	0.180769	+	0.983526i	$0.442141\pi$
$908$	11.6511	+	3.42107i	0.386655	+	0.113532i
$909$	0.302362	−	1.02975i	0.0100287	−	0.0341546i
$910$	12.9445	+	9.41648i	0.429107	+	0.312153i
$911$	9.86065	+	1.41775i	0.326698	+	0.0469721i	0.303712	−	0.952764i	$-0.401774\pi$
$911$	9.86065	+	1.41775i	0.326698	+	0.0469721i	0.0229854	+	0.999736i	$0.492683\pi$
$912$	−4.94913	−	4.28844i	−0.163882	−	0.142005i
$913$	−5.40912	−	2.47026i	−0.179016	−	0.0817538i
$914$	−14.7720	+	22.9856i	−0.488613	+	0.760297i
$915$	−17.2855	+	2.48528i	−0.571440	+	0.0821607i
$916$	−7.30847	+	4.69687i	−0.241479	+	0.155189i
$917$	4.67606	+	1.67154i	0.154417	+	0.0551992i
$918$	0.892635	+	3.04004i	0.0294614	+	0.100336i
$919$			12.4282i			0.409970i	0.978765	+	0.204985i	$0.0657145\pi$
$919$			12.4282i			0.409970i	−0.978765	+	0.204985i	$0.934285\pi$
$920$	−3.01621	+	9.22848i	−0.0994415	+	0.304254i
$921$	−18.1093			−0.596723
$922$	−9.09742	−	30.9830i	−0.299608	−	1.02037i
$923$	18.0279	−	15.6213i	0.593395	−	0.514180i
$924$	11.7536	+	6.21064i	0.386664	+	0.204315i
$925$	8.00379	−	1.15077i	0.263163	−	0.0378371i
$926$	−7.95085	−	5.10970i	−0.261281	−	0.167915i
$927$	6.39644	−	14.0062i	0.210087	−	0.460026i
$928$	6.09937	−	7.03905i	0.200222	−	0.231068i
$929$	−1.39345	−	0.200348i	−0.0457176	−	0.00657319i	0.119418	−	0.992844i	$-0.461897\pi$
$929$	−1.39345	−	0.200348i	−0.0457176	−	0.00657319i	−0.165136	+	0.986271i	$0.552806\pi$
$930$	7.49893	+	16.4204i	0.245899	+	0.538445i
$931$	−33.8093	+	30.9561i	−1.10805	+	1.01455i
$932$	−8.55890	−	2.51312i	−0.280356	−	0.0823199i
$933$	−6.85084	−	15.0012i	−0.224286	−	0.491119i
$934$	−1.11022	+	7.72175i	−0.0363275	+	0.252664i
$935$	24.3564	+	21.1049i	0.796538	+	0.690204i
$936$	2.71849	+	1.24149i	0.0888566	+	0.0405794i
$937$	2.76247	+	1.77533i	0.0902460	+	0.0579976i	0.584986	−	0.811044i	$-0.301100\pi$
$937$	2.76247	+	1.77533i	0.0902460	+	0.0579976i	−0.494740	+	0.869041i	$0.664737\pi$
$938$	4.88776	+	6.34633i	0.159591	+	0.207215i
$939$	−13.9269	−	21.6706i	−0.454486	−	0.707194i
$940$	−12.8433	+	11.1288i	−0.418902	+	0.362981i
$941$	13.4760	−	3.95691i	0.439305	−	0.128992i	−0.0545984	−	0.998508i	$-0.517388\pi$
$941$	13.4760	−	3.95691i	0.439305	−	0.128992i	0.493903	+	0.869517i	$0.335570\pi$
$942$		−	10.9487i		−	0.356727i
$943$	7.28100	+	17.3125i	0.237102	+	0.563773i
$944$			0.0260144i			0.000846697i
$945$	3.73519	−	3.83887i	0.121506	−	0.124878i
$946$	−30.4294	−	35.1174i	−0.989345	−	1.14177i
$947$	25.7159	−	16.5266i	0.835653	−	0.537042i	−0.0514166	−	0.998677i	$-0.516374\pi$
$947$	25.7159	−	16.5266i	0.835653	−	0.537042i	0.887070	+	0.461636i	$0.152737\pi$
$948$	1.30646	+	9.08663i	0.0424318	+	0.295120i
$949$	−29.6725	−	19.0694i	−0.963212	−	0.619019i
$950$	2.45281	−	5.37090i	0.0795796	−	0.174255i
$951$	−9.81843	−	8.50772i	−0.318384	−	0.275882i
$952$	7.81338	−	3.03669i	0.253233	−	0.0984198i
$953$	−30.0947	+	13.7438i	−0.974864	+	0.445205i	−0.838171	−	0.545408i	$-0.816375\pi$
$953$	−30.0947	+	13.7438i	−0.974864	+	0.445205i	−0.136693	+	0.990613i	$0.543647\pi$
$954$	1.02327	−	3.48492i	0.0331294	−	0.112828i
$955$	2.33437	−	7.95013i	0.0755384	−	0.257260i
$956$	11.0061	+	24.1001i	0.355964	+	0.779452i
$957$	6.66006	−	46.3218i	0.215289	−	1.49737i
$958$	−9.81545	+	11.3276i	−0.317123	+	0.365979i
$959$	−1.79998	−	21.1034i	−0.0581242	−	0.681465i
$960$	1.09450	−	1.70307i	0.0353247	−	0.0549663i
$961$	6.90373	+	48.0165i	0.222701	+	1.54892i
$962$	−22.5474	+	14.4903i	−0.726958	+	0.467187i
$963$	−6.71216	+	5.81612i	−0.216296	+	0.187422i
$964$	−8.41629	+	2.47125i	−0.271071	+	0.0795935i
$965$	−36.4531			−1.17347
$966$	12.3521	+	2.90266i	0.397423	+	0.0933915i
$967$	−21.1463			−0.680020			−0.340010	−	0.940422i	$-0.610430\pi$
$967$	−21.1463			−0.680020			−0.340010	+	0.940422i	$0.610430\pi$
$968$	13.6685	−	4.01343i	0.439321	−	0.128996i
$969$	−15.6807	+	13.5874i	−0.503737	+	0.436490i
$970$	22.4084	−	14.4010i	0.719491	−	0.462389i
$971$	−5.46674	−	38.0220i	−0.175436	−	1.22018i	−0.867163	−	0.498025i	$-0.834059\pi$
$971$	−5.46674	−	38.0220i	−0.175436	−	1.22018i	0.691727	−	0.722159i	$-0.256850\pi$
$972$	0.540641	−	0.841254i	0.0173411	−	0.0269832i
$973$	3.96107	+	46.4407i	0.126986	+	1.48882i
$974$	7.32062	−	8.44845i	0.234568	−	0.270706i
$975$	−0.383480	+	2.66716i	−0.0122812	+	0.0854175i
$976$	3.58345	+	7.84666i	0.114703	+	0.251165i
$977$	−0.0601803	+	0.204955i	−0.00192534	+	0.00655710i	−0.960450	−	0.278452i	$-0.910179\pi$
$977$	−0.0601803	+	0.204955i	−0.00192534	+	0.00655710i	0.958525	+	0.285009i	$0.0919967\pi$
$978$	−3.99024	+	13.5895i	−0.127594	+	0.434544i
$979$	5.11736	−	2.33702i	0.163551	−	0.0746914i
$980$	−10.9598	−	8.98348i	−0.350098	−	0.286967i
$981$	−10.3174	−	8.94006i	−0.329409	−	0.285434i
$982$	10.9868	−	24.0577i	0.350602	−	0.767712i
$983$	−2.45396	−	1.57706i	−0.0782691	−	0.0503005i	0.500921	−	0.865493i	$-0.332995\pi$
$983$	−2.45396	−	1.57706i	−0.0782691	−	0.0503005i	−0.579190	+	0.815193i	$0.696631\pi$
$984$	−0.557329	−	3.87631i	−0.0177670	−	0.123572i
$985$	−47.0622	+	30.2450i	−1.49953	+	0.963687i
$986$	−19.3251	−	22.3024i	−0.615437	−	0.710252i
$987$	15.9181	+	15.4882i	0.506678	+	0.492995i
$988$			19.5710i			0.622636i
$989$	−36.5681	−	25.0978i	−1.16280	−	0.798063i
$990$		−	10.1718i		−	0.323281i
$991$	1.81390	−	0.532609i	0.0576204	−	0.0169189i	−0.252795	−	0.967520i	$-0.581350\pi$
$991$	1.81390	−	0.532609i	0.0576204	−	0.0169189i	0.310416	+	0.950601i	$0.399532\pi$
$992$	6.73891	−	5.83930i	0.213961	−	0.185398i
$993$	10.6255	+	16.5335i	0.337189	+	0.524676i
$994$	−16.7311	+	12.8858i	−0.530678	+	0.408712i
$995$	−3.22171	−	2.07047i	−0.102135	−	0.0656383i
$996$	1.07655	+	0.491645i	0.0341118	+	0.0155784i
$997$	−3.57024	−	3.09363i	−0.113071	−	0.0979762i	0.596491	−	0.802620i	$-0.296561\pi$
$997$	−3.57024	−	3.09363i	−0.113071	−	0.0979762i	−0.709561	+	0.704644i	$0.751107\pi$
$998$	3.77577	−	26.2610i	0.119520	−	0.831278i
$999$	3.72555	+	8.15782i	0.117871	+	0.258102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.727.3	yes	160
7.6	odd	2	inner	966.2.s.a.727.14	yes	160
23.5	odd	22	inner	966.2.s.a.97.14	yes	160
161.97	even	22	inner	966.2.s.a.97.3	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.3	✓	160	161.97	even	22	inner
966.2.s.a.97.14	yes	160	23.5	odd	22	inner
966.2.s.a.727.3	yes	160	1.1	even	1	trivial
966.2.s.a.727.14	yes	160	7.6	odd	2	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.288108 - 2.00384i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.63618 - 0.224848i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.288108 - 2.00384i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.63618 - 0.224848i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +(0.840984 + 1.84150i) q^{10} +(1.41556 - 4.82096i) q^{11} +(-0.281733 + 0.959493i) q^{12} +(2.71849 - 1.24149i) q^{13} +(-2.46605 + 0.958437i) q^{14} +(1.52997 + 1.32573i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-2.66541 - 1.71295i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-5.50906 + 3.54046i) q^{19} +(-1.32573 - 1.52997i) q^{20} +(-1.84505 + 1.89626i) q^{21} +5.02449i q^{22} +(1.21115 + 4.64038i) q^{23} -1.00000i q^{24} +(0.865112 - 0.254020i) q^{25} +(-2.25860 + 1.95709i) q^{26} +(0.540641 + 0.841254i) q^{27} +(2.09613 - 1.61438i) q^{28} +(-7.83543 - 5.03553i) q^{29} +(-1.84150 - 0.840984i) q^{30} +(-6.73891 - 5.83930i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(2.08725 + 4.57044i) q^{33} +(3.04004 + 0.892635i) q^{34} +(-1.21006 - 5.21769i) q^{35} +(-0.415415 - 0.909632i) q^{36} +(8.87698 + 1.27632i) q^{37} +(4.28844 - 4.94913i) q^{38} +(-1.24149 + 2.71849i) q^{39} +(1.70307 + 1.09450i) q^{40} +(3.87631 - 0.557329i) q^{41} +(1.23607 - 2.33926i) q^{42} +(-6.98924 + 6.05621i) q^{43} +(-1.41556 - 4.82096i) q^{44} -2.02444 q^{45} +(-2.46943 - 4.11119i) q^{46} -8.39447i q^{47} +(0.281733 + 0.959493i) q^{48} +(6.89889 - 1.18548i) q^{49} +(-0.758504 + 0.487461i) q^{50} +(3.13613 - 0.450907i) q^{51} +(1.61574 - 2.51413i) q^{52} +(-3.30382 - 1.50881i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-10.0683 - 1.44760i) q^{55} +(-1.55640 + 2.13954i) q^{56} +(1.84496 - 6.28337i) q^{57} +(8.93671 + 2.62406i) q^{58} +(-0.0236635 + 0.0108068i) q^{59} +(2.00384 + 0.288108i) q^{60} +(-5.64895 + 6.51924i) q^{61} +(8.11105 + 3.70419i) q^{62} +(0.152608 - 2.64135i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.27096 - 5.08972i) q^{65} +(-3.29034 - 3.79726i) q^{66} +(-0.852984 - 2.90500i) q^{67} -3.16838 q^{68} +(-3.95413 - 2.71383i) q^{69} +(2.63104 + 4.66542i) q^{70} +(7.65856 - 2.24876i) q^{71} +(0.654861 + 0.755750i) q^{72} +(-6.38080 - 9.92872i) q^{73} +(-8.87698 + 1.27632i) q^{74} +(-0.487461 + 0.758504i) q^{75} +(-2.72040 + 5.95685i) q^{76} +(2.64770 - 13.0272i) q^{77} +(0.425316 - 2.95814i) q^{78} +(8.35048 - 3.81354i) q^{79} +(-1.94244 - 0.570351i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-3.56227 + 1.62683i) q^{82} +(0.168430 - 1.17146i) q^{83} +(-0.526958 + 2.59274i) q^{84} +(-2.66455 + 5.83456i) q^{85} +(4.99990 - 7.77999i) q^{86} +(9.21919 - 1.32552i) q^{87} +(2.71645 + 4.22687i) q^{88} +(0.733224 + 0.846186i) q^{89} +(1.94244 - 0.570351i) q^{90} +(6.88728 - 3.88404i) q^{91} +(3.52766 + 3.24894i) q^{92} +8.91685 q^{93} +(2.36499 + 8.05443i) q^{94} +(8.68170 + 10.0192i) q^{95} +(-0.540641 - 0.841254i) q^{96} +(-1.87253 - 13.0238i) q^{97} +(-6.28545 + 3.08110i) q^{98} +(-4.57044 - 2.08725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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