LMFDB - Embedded newform 966.2.s.a.97.3

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			97.3
Character	$\chi$	$=$	966.97
Dual form			966.2.s.a.727.3

$q$-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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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	0.818175	+	0.574970i	$0.194986\pi$
$5$	−0.288108	+	2.00384i	−0.128846	+	0.896143i	−0.947021	+	0.321173i	$0.895923\pi$
$6$	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	0.839828	+	0.542853i	$0.182656\pi$
$11$	1.41556	+	4.82096i	0.426808	+	1.45358i	−0.413019	+	0.910722i	$0.635526\pi$
$12$	−0.281733	−	0.959493i	−0.0813292	−	0.276982i
$13$	2.71849	+	1.24149i	0.753973	+	0.344328i	0.755046	−	0.655672i	$-0.227614\pi$
$13$	2.71849	+	1.24149i	0.753973	+	0.344328i	−0.00107335	+	0.999999i	$0.500342\pi$
$14$	−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	−0.822370	−	0.568953i	$-0.807349\pi$
$17$	−2.66541	+	1.71295i	−0.646457	+	0.415452i	0.175913	+	0.984406i	$0.443712\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	−5.50906	−	3.54046i	−1.26387	−	0.812237i	−0.275057	−	0.961428i	$-0.588697\pi$
$19$	−5.50906	−	3.54046i	−1.26387	−	0.812237i	−0.988808	+	0.149191i	$0.952333\pi$
$20$	−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	−0.456021	+	0.889969i	$0.650726\pi$
$29$	−7.83543	+	5.03553i	−1.45500	+	0.935074i	−0.998982	+	0.0451046i	$0.985638\pi$
$30$	−1.84150	+	0.840984i	−0.336210	+	0.153542i
$31$	−6.73891	+	5.83930i	−1.21034	+	1.04877i	−0.212917	+	0.977070i	$0.568296\pi$
$31$	−6.73891	+	5.83930i	−1.21034	+	1.04877i	−0.997426	+	0.0716984i	$0.977158\pi$
$32$	−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	0.633522	−	0.773724i	$-0.281608\pi$
$37$	8.87698	−	1.27632i	1.45937	−	0.209825i	0.825844	+	0.563899i	$0.190699\pi$
$38$	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	0.438186	−	0.898884i	$-0.355621\pi$
$41$	3.87631	+	0.557329i	0.605377	+	0.0870401i	0.167191	+	0.985924i	$0.446530\pi$
$42$	1.23607	+	2.33926i	0.190730	+	0.360955i
$43$	−6.98924	−	6.05621i	−1.06585	−	0.923564i	−0.0685974	−	0.997644i	$-0.521852\pi$
$43$	−6.98924	−	6.05621i	−1.06585	−	0.923564i	−0.997252	+	0.0740805i	$0.976398\pi$
$44$	−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	$0.209727\pi$
$47$			8.39447i			1.22446i	−0.790680	+	0.612230i	$0.790273\pi$
$48$	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	−0.629190	−	0.777251i	$-0.716613\pi$
$53$	−3.30382	+	1.50881i	−0.453815	+	0.207250i	0.175375	+	0.984502i	$0.443886\pi$
$54$	−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	0.413874	−	0.910334i	$-0.364175\pi$
$59$	−0.0236635	−	0.0108068i	−0.00308073	−	0.00140692i	−0.416955	+	0.908927i	$0.636903\pi$
$60$	2.00384	−	0.288108i	0.258694	−	0.0371946i
$61$	−5.64895	−	6.51924i	−0.723274	−	0.834703i	0.268422	−	0.963301i	$-0.413498\pi$
$61$	−5.64895	−	6.51924i	−0.723274	−	0.834703i	−0.991697	+	0.128598i	$0.958952\pi$
$62$	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	−0.995045	−	0.0994216i	$-0.968301\pi$
$67$	−0.852984	+	2.90500i	−0.104209	+	0.354902i	0.890837	+	0.454323i	$0.150119\pi$
$68$	−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	0.702579	−	0.711605i	$-0.252032\pi$
$71$	7.65856	+	2.24876i	0.908904	+	0.266878i	0.206324	+	0.978484i	$0.433850\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−6.38080	+	9.92872i	−0.746816	+	1.16207i	0.234956	+	0.972006i	$0.424505\pi$
$73$	−6.38080	+	9.92872i	−0.746816	+	1.16207i	−0.981772	+	0.190063i	$0.939131\pi$
$74$	−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	0.825486	−	0.564422i	$-0.190901\pi$
$79$	8.35048	+	3.81354i	0.939503	+	0.429056i	0.114016	+	0.993479i	$0.463628\pi$
$80$	−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	0.996975	−	0.0777223i	$-0.0247648\pi$
$83$	0.168430	+	1.17146i	0.0184876	+	0.128584i	−0.978487	+	0.206306i	$0.933856\pi$
$84$	−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	−0.715557	−	0.698554i	$-0.753827\pi$
$89$	0.733224	−	0.846186i	0.0777216	−	0.0896955i	0.793279	+	0.608859i	$0.208372\pi$
$90$	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	0.641541	+	0.767089i	$0.278295\pi$
$97$	−1.87253	+	13.0238i	−0.190127	+	1.32236i	−0.831668	+	0.555273i	$0.812614\pi$
$98$	−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	−0.0892605	−	0.996008i	$-0.528450\pi$
$101$	1.06230	−	0.152735i	0.105703	−	0.0151977i	0.194963	+	0.980811i	$0.437541\pi$
$102$	−2.88206	−	1.31619i	−0.285366	−	0.130322i
$103$	14.7740	−	4.33804i	1.45572	−	0.427439i	0.544295	−	0.838894i	$-0.316797\pi$
$103$	14.7740	−	4.33804i	1.45572	−	0.427439i	0.911430	+	0.411455i	$0.134979\pi$
$104$	−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	−0.915889	−	0.401431i	$-0.868513\pi$
$107$	−6.71216	+	5.81612i	−0.648889	+	0.562266i	0.267000	+	0.963696i	$0.413968\pi$
$108$	0.909632	−	0.415415i	0.0875294	−	0.0399733i
$109$	7.38075	+	11.4847i	0.706947	+	1.10003i	0.990019	+	0.140933i	$0.0450101\pi$
$109$	7.38075	+	11.4847i	0.706947	+	1.10003i	−0.283072	+	0.959099i	$0.591353\pi$
$110$	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	−0.987791	−	0.155787i	$-0.950209\pi$
$113$	−0.771575	+	2.62774i	−0.0725836	+	0.247197i	0.915207	+	0.402984i	$0.132027\pi$
$114$		−	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	0.0763196	−	0.997083i	$-0.475683\pi$
$127$	7.65856	−	2.24876i	0.679588	−	0.199545i	0.603268	+	0.797538i	$0.293865\pi$
$128$	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	−0.339433	−	0.940630i	$-0.610235\pi$
$131$	1.70730	−	0.779698i	0.149168	−	0.0681225i	0.488600	+	0.872508i	$0.337508\pi$
$132$	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	$0.111094\pi$
$137$			8.00531i			0.683940i	−0.939711	+	0.341970i	$0.888906\pi$
$138$	4.55853	−	1.48990i	0.388048	−	0.126828i
$139$		−	17.6167i		−	1.49423i	−0.664697	−	0.747113i	$-0.731439\pi$
$139$		−	17.6167i		−	1.49423i	0.664697	−	0.747113i	$-0.268561\pi$
$140$	−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	−0.986195	−	0.165588i	$-0.947048\pi$
$149$	−3.00377	−	10.2299i	−0.246079	−	0.838067i	0.740116	−	0.672479i	$-0.234770\pi$
$150$	0.254020	+	0.865112i	0.0207406	+	0.0706361i
$151$	−1.26402	+	2.76782i	−0.102864	+	0.225242i	−0.954066	−	0.299598i	$-0.903147\pi$
$151$	−1.26402	+	2.76782i	−0.102864	+	0.225242i	0.851201	+	0.524840i	$0.175875\pi$
$152$	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	0.853856	−	0.520510i	$-0.174258\pi$
$157$	9.21062	+	5.91930i	0.735087	+	0.472412i	−0.118768	+	0.992922i	$0.537895\pi$
$158$	−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	−0.297785	−	0.954633i	$-0.596248\pi$
$163$	−13.5895	−	3.99024i	−1.06441	−	0.312540i	−0.766627	+	0.642093i	$0.778066\pi$
$164$	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	−0.999246	−	0.0388307i	$-0.987637\pi$
$167$	−8.00526	−	12.4564i	−0.619466	−	0.963908i	0.379780	−	0.925077i	$-0.376000\pi$
$168$	−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	−0.988377	−	0.152022i	$-0.951421\pi$
$173$	−3.14475	−	10.7100i	−0.239091	−	0.814269i	0.749286	−	0.662246i	$-0.230397\pi$
$174$	−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	−0.877684	−	0.479240i	$-0.840912\pi$
$179$	1.33075	−	9.25558i	0.0994651	−	0.691795i	0.977149	−	0.212555i	$-0.0681785\pi$
$180$	−1.70307	−	1.09450i	−0.126939	−	0.0815789i
$181$	8.32934	−	9.61258i	0.619115	−	0.714497i	−0.356423	−	0.934325i	$-0.616004\pi$
$181$	8.32934	−	9.61258i	0.619115	−	0.714497i	0.975539	+	0.219827i	$0.0705494\pi$
$182$	−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	−0.276142	−	0.961117i	$-0.589056\pi$
$191$	3.72300	−	1.70024i	0.269387	−	0.123025i	0.545529	+	0.838092i	$0.316329\pi$
$192$	0.755750	−	0.654861i	0.0545415	−	0.0472605i
$193$	2.56259	+	17.8232i	0.184459	+	1.28294i	0.846061	+	0.533087i	$0.178968\pi$
$193$	2.56259	+	17.8232i	0.184459	+	1.28294i	−0.661601	+	0.749856i	$0.730123\pi$
$194$	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	−0.248953	+	0.968516i	$0.580086\pi$
$197$	−11.4795	+	25.1365i	−0.817879	+	1.79090i	−0.568926	+	0.822389i	$0.692641\pi$
$198$	4.97335	−	0.715060i	0.353441	−	0.0508171i
$199$	1.23881	+	1.42966i	0.0878166	+	0.101346i	0.797957	−	0.602714i	$-0.205914\pi$
$199$	1.23881	+	1.42966i	0.0878166	+	0.101346i	−0.710141	+	0.704060i	$0.751369\pi$
$200$	−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	0.139857	−	0.990172i	$-0.455336\pi$
$211$	−10.2078	−	6.56018i	−0.702737	−	0.451621i	−0.842593	+	0.538550i	$0.818972\pi$
$212$	−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	0.761146	−	0.648580i	$-0.224637\pi$
$223$	26.1294	−	11.9329i	1.74976	−	0.799087i	0.988609	−	0.150506i	$-0.0480904\pi$
$224$	−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	−0.427775	−	0.903885i	$-0.640702\pi$
$227$	7.95194	−	9.17703i	0.527789	−	0.609101i	0.955564	+	0.294784i	$0.0952478\pi$
$228$	−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	−0.914113	−	0.405459i	$-0.867112\pi$
$233$	−5.84151	+	6.74146i	−0.382690	+	0.441648i	0.531424	+	0.847106i	$0.321657\pi$
$234$	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	−0.632204	−	0.774802i	$-0.717850\pi$
$239$	−3.77053	−	26.2246i	−0.243896	−	1.69633i	0.388309	−	0.921529i	$-0.373059\pi$
$240$	1.84150	+	0.840984i	0.118868	+	0.0542853i
$241$	−8.41629	+	2.47125i	−0.542141	+	0.159187i	−0.541326	−	0.840813i	$-0.682078\pi$
$241$	−8.41629	+	2.47125i	−0.542141	+	0.159187i	−0.000814869		1.00000i	$0.500259\pi$
$242$	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	0.804630	−	0.593777i	$-0.202364\pi$
$251$	18.3859	+	5.39859i	1.16051	+	0.340756i	0.355878	+	0.934533i	$0.384182\pi$
$252$	−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	−0.388648	−	0.921387i	$-0.627058\pi$
$257$	9.79388	−	15.2396i	0.610925	−	0.950618i	0.999573	−	0.0292316i	$-0.00930603\pi$
$258$	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	0.616585	−	0.787289i	$-0.288516\pi$
$263$	6.89832	+	3.15036i	0.425369	+	0.194259i	−0.191216	+	0.981548i	$0.561243\pi$
$264$	−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	−0.288310	−	0.957537i	$-0.593093\pi$
$269$	4.04364	−	1.84667i	0.246545	−	0.112593i	0.534855	+	0.844944i	$0.320366\pi$
$270$	−1.09450	−	1.70307i	−0.0666089	−	0.103645i
$271$	15.8140	+	2.27371i	0.960634	+	0.138118i	0.604753	−	0.796413i	$-0.293272\pi$
$271$	15.8140	+	2.27371i	0.960634	+	0.138118i	0.355881	+	0.934531i	$0.384181\pi$
$272$	−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	0.448822	−	0.893621i	$-0.351844\pi$
$281$	10.5222	+	1.51286i	0.627702	+	0.0902499i	0.178879	+	0.983871i	$0.442753\pi$
$282$	−7.06188	+	4.53839i	−0.420529	+	0.270257i
$283$	10.9754	+	24.0329i	0.652422	+	1.42861i	0.889418	+	0.457095i	$0.151110\pi$
$283$	10.9754	+	24.0329i	0.652422	+	1.42861i	−0.236995	+	0.971511i	$0.576163\pi$
$284$	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	−0.947158	−	0.320766i	$-0.896060\pi$
$293$	−17.9533	+	11.5379i	−1.04884	+	0.674051i	−0.101685	+	0.994817i	$0.532423\pi$
$294$	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	−0.170085	−	0.985429i	$-0.554404\pi$
$307$	13.6861	−	11.8591i	0.781109	−	0.676834i	0.951194	+	0.308595i	$0.0998587\pi$
$308$	−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	−0.979878	−	0.199597i	$-0.936037\pi$
$311$	−4.64621	−	15.8235i	−0.263462	−	0.897270i	0.716416	−	0.697674i	$-0.245781\pi$
$312$	−1.24149	+	2.71849i	−0.0702856	+	0.153904i
$313$	−3.66602	−	25.4977i	−0.207216	−	1.44122i	−0.782188	−	0.623043i	$-0.785896\pi$
$313$	−3.66602	−	25.4977i	−0.207216	−	1.44122i	0.574972	−	0.818173i	$-0.305013\pi$
$314$	−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	−0.869670	−	0.493633i	$-0.835669\pi$
$317$	1.84890	−	12.8594i	0.103845	−	0.722256i	0.973515	−	0.228623i	$-0.0734223\pi$
$318$	−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	0.909886	+	0.414858i	$0.136169\pi$
$331$	2.79698	+	19.4534i	0.153736	+	1.06926i	−0.756151	+	0.654398i	$0.772922\pi$
$332$	−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	−0.753800	−	0.657103i	$-0.771781\pi$
$337$	−3.86724	+	3.35099i	−0.210662	+	0.182540i	0.543138	+	0.839643i	$0.317236\pi$
$338$	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	0.688565	−	0.725174i	$-0.258241\pi$
$347$	16.3137	+	4.79013i	0.875764	+	0.257148i	0.187199	+	0.982322i	$0.440059\pi$
$348$	7.03905	+	6.09937i	0.377333	+	0.326961i
$349$	−15.7535	+	24.5129i	−0.843263	+	1.31214i	0.104940	+	0.994479i	$0.466535\pi$
$349$	−15.7535	+	24.5129i	−0.843263	+	1.31214i	−0.948203	+	0.317664i	$0.897101\pi$
$350$	−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	−0.000690163	−	1.00000i	$-0.500220\pi$
$353$	18.5822	−	16.1016i	0.989033	−	0.857002i	0.989723	+	0.142998i	$0.0456742\pi$
$354$	−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	−0.537767	−	0.843093i	$-0.680732\pi$
$359$	−15.4652	+	2.22357i	−0.816224	+	0.117355i	−0.278457	+	0.960449i	$0.589823\pi$
$360$	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	0.137686	−	0.990476i	$-0.456034\pi$
$373$	−0.178738	−	0.0256987i	−0.00925472	−	0.00133063i	−0.146941	+	0.989145i	$0.546943\pi$
$374$	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	0.903404	+	0.428791i	$0.141060\pi$
$379$	7.30503	+	24.8787i	0.375234	+	1.27793i	−0.528169	+	0.849139i	$0.677121\pi$
$380$	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	0.973129	−	0.230261i	$-0.0739579\pi$
$383$	11.8738	+	13.7031i	0.606721	+	0.700194i	−0.366408	+	0.930454i	$0.619412\pi$
$384$	−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	−0.258351	−	0.966051i	$-0.583179\pi$
$389$	9.49221	−	32.3275i	0.481274	−	1.63907i	0.739625	−	0.673019i	$-0.235003\pi$
$390$	−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	0.985358	+	0.170501i	$0.0545385\pi$
$397$	14.5674	+	22.6674i	0.731118	+	1.13764i	−0.254239	+	0.967141i	$0.581825\pi$
$398$	−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	0.324346	−	0.945938i	$-0.394856\pi$
$401$	−3.56735	−	1.62915i	−0.178145	−	0.0813561i	−0.502491	+	0.864582i	$0.667583\pi$
$402$	−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	0.181513	−	0.983389i	$-0.441900\pi$
$409$	1.59002	+	0.228610i	0.0786214	+	0.0113040i	−0.102892	+	0.994693i	$0.532810\pi$
$410$	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	−0.949840	−	0.312736i	$-0.898755\pi$
$419$	1.01595	−	7.06612i	0.0496326	−	0.345202i	0.999473	−	0.0324668i	$-0.0103363\pi$
$420$	5.34725	−	0.308947i	0.260919	−	0.0150751i
$421$	−28.7826	+	13.1446i	−1.40278	+	0.640627i	−0.965905	−	0.258897i	$-0.916641\pi$
$421$	−28.7826	+	13.1446i	−1.40278	+	0.640627i	−0.436872	+	0.899524i	$0.643914\pi$
$422$	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	0.845461	−	0.534037i	$-0.179326\pi$
$431$	0.175765	+	0.273496i	0.00846633	+	0.0131739i	−0.836995	+	0.547211i	$0.815689\pi$
$432$	0.989821	+	0.142315i	0.0476228	+	0.00684713i
$433$	18.9368	+	12.1699i	0.910042	+	0.584849i	0.909752	−	0.415151i	$-0.136271\pi$
$433$	18.9368	+	12.1699i	0.910042	+	0.584849i	0.000289984		1.00000i	$0.499908\pi$
$434$	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	−0.994937	−	0.100501i	$-0.967955\pi$
$439$	−2.17082	+	7.39314i	−0.103608	+	0.352856i	0.891329	+	0.453357i	$0.149774\pi$
$440$	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	−0.0634812	−	0.997983i	$-0.520220\pi$
$443$	17.2158	−	11.0639i	0.817945	−	0.525661i	0.881426	+	0.472322i	$0.156584\pi$
$444$	−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	0.863195	−	0.504870i	$-0.168460\pi$
$449$	39.4617	−	11.5870i	1.86231	−	0.546825i	0.999119	−	0.0419551i	$-0.0133586\pi$
$450$	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	0.986660	−	0.162795i	$-0.0520509\pi$
$457$	20.6494	+	17.8928i	0.965938	+	0.836990i	−0.0207215	+	0.999785i	$0.506596\pi$
$458$	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	$-0.729104\pi$
$461$		−	32.2910i		−	1.50394i	0.659197	−	0.751970i	$-0.270896\pi$
$462$	−9.52774	+	9.27043i	−0.443271	+	0.431299i
$463$	6.18922	−	7.14274i	0.287637	−	0.331951i	−0.593480	−	0.804849i	$-0.702246\pi$
$463$	6.18922	−	7.14274i	0.287637	−	0.331951i	0.881117	+	0.472898i	$0.156792\pi$
$464$	−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	0.969673	−	0.244406i	$-0.0785929\pi$
$467$	3.24072	+	7.09618i	0.149963	+	0.328372i	−0.819710	+	0.572778i	$0.805866\pi$
$468$	−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	0.796022	−	0.605268i	$-0.206934\pi$
$479$	12.6092	+	8.10345i	0.576130	+	0.370256i	−0.219892	+	0.975524i	$0.570570\pi$
$480$	−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	0.309937	−	0.950757i	$-0.399692\pi$
$487$	−9.40429	−	6.04377i	−0.426149	−	0.273869i	−0.736086	+	0.676888i	$0.763328\pi$
$488$	−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	0.215604	−	0.976481i	$-0.430828\pi$
$491$	−17.3196	−	19.9878i	−0.781621	−	0.902039i	−0.997225	+	0.0744418i	$0.976282\pi$
$492$	−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	−0.978563	−	0.205949i	$-0.933972\pi$
$499$	−11.0214	−	24.1335i	−0.493386	−	1.08036i	0.485177	−	0.874416i	$-0.338755\pi$
$500$	−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	0.215729	−	0.976453i	$-0.430787\pi$
$503$	25.8264	−	29.8052i	1.15154	−	1.32895i	0.935813	−	0.352497i	$-0.114667\pi$
$504$	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	0.819004	−	0.573788i	$-0.194527\pi$
$509$	8.29370	+	7.18653i	0.367612	+	0.318537i	−0.451392	+	0.892326i	$0.649072\pi$
$510$	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	0.648729	−	0.761019i	$-0.275301\pi$
$521$	−4.49360	−	5.18589i	−0.196868	−	0.227198i	−0.845597	+	0.533822i	$0.820755\pi$
$522$	3.86917	+	8.47231i	0.169349	+	0.370823i
$523$	24.8058	−	15.9417i	1.08468	−	0.697082i	0.129046	−	0.991639i	$-0.458808\pi$
$523$	24.8058	−	15.9417i	1.08468	−	0.697082i	0.955634	+	0.294557i	$0.0951721\pi$
$524$	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	−0.198636	−	0.980073i	$-0.563651\pi$
$541$	3.81753	−	1.12093i	0.164128	−	0.0481925i	0.362764	+	0.931881i	$0.381833\pi$
$542$	−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	0.953076	+	0.302731i	$0.0978983\pi$
$547$	−1.09182	+	7.59378i	−0.0466829	+	0.324686i	−0.999759	+	0.0219556i	$0.993011\pi$
$548$	−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	0.873276	−	0.487227i	$-0.161991\pi$
$557$	37.1456	+	5.34073i	1.57391	+	0.226294i	0.700634	+	0.713521i	$0.252901\pi$
$558$	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	−0.736342	−	0.676610i	$-0.763448\pi$
$563$	−23.4901	+	6.89731i	−0.989989	+	0.290687i	−0.253647	+	0.967297i	$0.581630\pi$
$564$	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	0.973715	+	0.227768i	$0.0731429\pi$
$569$	18.5201	+	28.8179i	0.776405	+	1.20811i	−0.197311	+	0.980341i	$0.563221\pi$
$570$	13.1224	+	1.88671i	0.549636	+	0.0790258i
$571$	−3.98556	+	6.20166i	−0.166791	+	0.259531i	−0.914580	−	0.404404i	$-0.867479\pi$
$571$	−3.98556	+	6.20166i	−0.166791	+	0.259531i	0.747790	+	0.663936i	$0.231115\pi$
$572$	−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	−0.605062	−	0.796178i	$-0.706852\pi$
$577$	8.03244	−	27.3560i	0.334395	−	1.13884i	0.939457	−	0.342666i	$-0.111330\pi$
$578$	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	0.980130	−	0.198355i	$-0.0635599\pi$
$587$	1.17151	+	3.98980i	0.0483534	+	0.164677i	−0.931777	+	0.363032i	$0.881742\pi$
$588$	−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	0.508321	−	0.861168i	$-0.330266\pi$
$593$	18.3473	+	2.63794i	0.753432	+	0.108327i	0.245111	+	0.969495i	$0.421175\pi$
$594$	−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	0.423558	−	0.905869i	$-0.360781\pi$
$601$	−10.1202	−	8.76921i	−0.412812	−	0.357703i	−0.836370	+	0.548165i	$0.815326\pi$
$602$	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	−0.953175	−	0.302419i	$-0.902206\pi$
$607$	−43.9171	+	6.31432i	−1.78254	+	0.256290i	−0.829364	+	0.558709i	$0.811297\pi$
$608$	−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	−0.825555	−	0.564322i	$-0.809138\pi$
$613$	−9.51893	+	8.24820i	−0.384466	+	0.333142i	0.441089	+	0.897463i	$0.354592\pi$
$614$	−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	−0.951767	−	0.306823i	$-0.900734\pi$
$617$	−6.88781	+	10.7176i	−0.277293	+	0.431476i	0.674474	+	0.738299i	$0.264371\pi$
$618$	11.6368	+	10.0834i	0.468101	+	0.405612i
$619$	23.8327	+	6.99790i	0.957916	+	0.281270i	0.723079	−	0.690765i	$-0.242726\pi$
$619$	23.8327	+	6.99790i	0.957916	+	0.281270i	0.234837	+	0.972035i	$0.424544\pi$
$620$		−	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	0.502716	−	0.864452i	$-0.332334\pi$
$631$	4.48677	+	2.04904i	0.178616	+	0.0815710i	−0.324100	+	0.946023i	$0.605061\pi$
$632$	−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	0.581971	−	0.813210i	$-0.302282\pi$
$641$	−3.54803	−	3.07439i	−0.140139	−	0.121431i	−0.722109	+	0.691779i	$0.756827\pi$
$642$	−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	0.517382	−	0.855755i	$-0.326907\pi$
$647$	−6.51246	−	5.64308i	−0.256031	−	0.221852i	−0.773413	+	0.633902i	$0.781452\pi$
$648$	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	0.996490	+	0.0837125i	$0.0266777\pi$
$653$	1.63415	+	11.3658i	0.0639494	+	0.444778i	−0.932541	+	0.361065i	$0.882413\pi$
$654$	−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	−0.130539	−	0.991443i	$-0.541671\pi$
$659$	21.3643	−	18.5123i	0.832235	−	0.721136i	0.962774	+	0.270307i	$0.0871253\pi$
$660$	4.22552	+	9.25259i	0.164478	+	0.360156i
$661$	5.83795	−	3.75182i	0.227070	−	0.145929i	−0.422160	−	0.906522i	$-0.638728\pi$
$661$	5.83795	−	3.75182i	0.227070	−	0.145929i	0.649230	+	0.760593i	$0.275091\pi$
$662$	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	0.682194	−	0.731172i	$-0.261026\pi$
$673$	42.3036	−	27.1869i	1.63068	−	1.04798i	0.948491	−	0.316806i	$-0.102610\pi$
$674$	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	0.149268	+	0.988797i	$0.452308\pi$
$677$	−18.1032	+	39.6406i	−0.695764	+	1.52351i	−0.845033	+	0.534715i	$0.820419\pi$
$678$	−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	−0.950087	−	0.311985i	$-0.899006\pi$
$683$	−14.7317	−	32.2580i	−0.563695	−	1.23432i	0.386393	−	0.922334i	$-0.373721\pi$
$684$	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	$-0.810145\pi$
$691$		−	29.5310i		−	1.12341i	0.827337	−	0.561706i	$-0.189855\pi$
$692$	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	−0.906879	−	0.421391i	$-0.861542\pi$
$701$	−9.84353	−	33.5240i	−0.371785	−	1.26618i	0.535094	−	0.844792i	$-0.320276\pi$
$702$	−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	0.282098	+	0.959386i	$0.408970\pi$
$709$	−18.8460	+	29.3250i	−0.707778	+	1.10132i	−0.989876	+	0.141938i	$0.954667\pi$
$710$	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	−0.961326	−	0.275415i	$-0.911185\pi$
$719$	−21.7866	−	33.9006i	−0.812502	−	1.26428i	0.148823	−	0.988864i	$-0.452451\pi$
$720$	−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	0.788881	+	0.614546i	$0.210661\pi$
$727$	5.52990	+	38.4613i	0.205093	+	1.42645i	−0.583789	+	0.811906i	$0.698430\pi$
$728$	−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	−0.153417	−	0.988162i	$-0.549028\pi$
$733$	22.9187	−	26.4496i	0.846520	−	0.976937i	0.999937	+	0.0112249i	$0.00357307\pi$
$734$	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	−0.978832	−	0.204667i	$-0.934389\pi$
$739$	−17.3151	+	19.9827i	−0.636945	+	0.735074i	0.341886	+	0.939741i	$0.388934\pi$
$740$	−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	−0.978919	−	0.204250i	$-0.934524\pi$
$743$	−39.9497	+	18.2444i	−1.46561	+	0.669323i	−0.486693	+	0.873573i	$0.661797\pi$
$744$	−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	−0.287912	−	0.957657i	$-0.592961\pi$
$751$	16.9639	−	14.6993i	0.619023	−	0.536386i	0.906935	+	0.421271i	$0.138416\pi$
$752$	−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	−0.976278	−	0.216522i	$-0.930529\pi$
$757$	−1.04331	+	3.55319i	−0.0379197	+	0.129143i	0.938358	+	0.345665i	$0.112347\pi$
$758$		−	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	−0.593900	−	0.804539i	$-0.702412\pi$
$761$	9.39827	−	32.0076i	0.340687	−	1.16027i	0.934587	−	0.355735i	$-0.115769\pi$
$762$	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	−0.187099	−	0.982341i	$-0.559908\pi$
$769$	18.7968	−	41.1592i	0.677829	−	1.48424i	0.864928	−	0.501897i	$-0.167364\pi$
$770$	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	−0.925722	−	0.378206i	$-0.876541\pi$
$773$	−4.00503	−	27.8556i	−0.144051	−	1.00190i	0.781671	−	0.623691i	$-0.214368\pi$
$774$	−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	0.860194	+	0.509967i	$0.170343\pi$
$787$	−3.05308	+	21.2346i	−0.108831	+	0.756933i	−0.969024	+	0.246966i	$0.920567\pi$
$788$	−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	0.885474	−	0.464690i	$-0.153834\pi$
$797$	8.45518	+	9.75780i	0.299498	+	0.345639i	−0.585976	+	0.810329i	$0.699289\pi$
$798$	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	0.738761	−	0.673968i	$-0.235411\pi$
$809$	12.3041	+	7.90740i	0.432591	+	0.278009i	−0.306170	+	0.951977i	$0.599048\pi$
$810$	−0.288108	+	2.00384i	−0.0101231	+	0.0704076i
$811$	16.8982	+	26.2941i	0.593376	+	0.923312i	0.999953	+	0.00969502i	$0.00308607\pi$
$811$	16.8982	+	26.2941i	0.593376	+	0.923312i	−0.406577	+	0.913617i	$0.633278\pi$
$812$	−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	0.998878	+	0.0473598i	$0.0150807\pi$
$821$	10.9038	+	23.8759i	0.380544	+	0.833275i	−0.618334	+	0.785916i	$0.712192\pi$
$822$	−6.73449	+	4.32800i	−0.234892	+	0.150956i
$823$	4.45999	−	31.0199i	0.155466	−	1.08129i	−0.751394	−	0.659854i	$-0.770618\pi$
$823$	4.45999	−	31.0199i	0.155466	−	1.08129i	0.906859	−	0.421433i	$-0.138473\pi$
$824$	−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	$-0.945367\pi$
$827$		−	9.82321i		−	0.341587i	0.985307	−	0.170793i	$-0.0546330\pi$
$828$	3.71791	+	3.02938i	0.129206	+	0.105278i
$829$		−	32.9840i		−	1.14558i	−0.819702	−	0.572790i	$-0.805861\pi$
$829$		−	32.9840i		−	1.14558i	0.819702	−	0.572790i	$-0.194139\pi$
$830$	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	−0.443596	−	0.896227i	$-0.646297\pi$
$839$	−9.62336	+	2.82567i	−0.332235	+	0.0975531i	0.111360	+	0.993780i	$0.464479\pi$
$840$	−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	−0.908039	−	0.418885i	$-0.862421\pi$
$853$	2.40420	−	8.18795i	0.0823182	−	0.280350i	0.990358	+	0.138535i	$0.0442393\pi$
$854$	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	0.752693	−	0.658372i	$-0.228754\pi$
$857$	−4.65064	−	7.23654i	−0.158863	−	0.247196i	−0.911556	+	0.411176i	$0.865118\pi$
$858$	−13.6590	+	6.23787i	−0.466311	+	0.212957i
$859$	5.90126	−	5.11347i	0.201348	−	0.174469i	−0.548350	−	0.836249i	$-0.684744\pi$
$859$	5.90126	−	5.11347i	0.201348	−	0.174469i	0.749699	+	0.661779i	$0.230198\pi$
$860$	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	−0.494088	−	0.869412i	$-0.664498\pi$
$863$	−12.9171	+	3.79279i	−0.439702	+	0.129108i	0.0543864	+	0.998520i	$0.482680\pi$
$864$	−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	−0.776422	−	0.630213i	$-0.782967\pi$
$877$	−1.24755	+	1.43975i	−0.0421267	+	0.0486168i	0.734295	+	0.678830i	$0.237513\pi$
$878$	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	0.808040	−	0.589128i	$-0.200529\pi$
$881$	−4.93745	−	10.8115i	−0.166347	−	0.364249i	−0.974387	+	0.224879i	$0.927801\pi$
$882$	2.15523	−	6.65996i	0.0725702	−	0.224252i
$883$	−1.09978	−	7.64911i	−0.0370104	−	0.257413i	0.962913	−	0.269813i	$-0.0869619\pi$
$883$	−1.09978	−	7.64911i	−0.0370104	−	0.257413i	−0.999923	+	0.0124001i	$0.996053\pi$
$884$	−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	−0.0863837	−	0.996262i	$-0.527531\pi$
$887$	−26.6815	−	12.1850i	−0.895878	−	0.409134i	−0.809494	+	0.587128i	$0.800258\pi$
$888$	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	0.180769	−	0.983526i	$-0.442141\pi$
$907$	−13.3763	−	6.10873i	−0.444151	−	0.202837i	−0.624920	+	0.780688i	$0.714869\pi$
$908$	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	0.0229854	−	0.999736i	$-0.492683\pi$
$911$	9.86065	−	1.41775i	0.326698	−	0.0469721i	0.303712	+	0.952764i	$0.401774\pi$
$912$	−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	$-0.934285\pi$
$919$		−	12.4282i		−	0.409970i	0.978765	−	0.204985i	$-0.0657145\pi$
$920$	−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	−0.165136	−	0.986271i	$-0.552806\pi$
$929$	−1.39345	+	0.200348i	−0.0457176	+	0.00657319i	0.119418	+	0.992844i	$0.461897\pi$
$930$	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	−0.494740	−	0.869041i	$-0.664737\pi$
$937$	2.76247	−	1.77533i	0.0902460	−	0.0579976i	0.584986	+	0.811044i	$0.301100\pi$
$938$	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	0.493903	−	0.869517i	$-0.335570\pi$
$941$	13.4760	+	3.95691i	0.439305	+	0.128992i	−0.0545984	+	0.998508i	$0.517388\pi$
$942$			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	0.887070	−	0.461636i	$-0.152737\pi$
$947$	25.7159	+	16.5266i	0.835653	+	0.537042i	−0.0514166	+	0.998677i	$0.516374\pi$
$948$	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	−0.136693	−	0.990613i	$-0.543647\pi$
$953$	−30.0947	−	13.7438i	−0.974864	−	0.445205i	−0.838171	+	0.545408i	$0.816375\pi$
$954$	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	0.691727	+	0.722159i	$0.256850\pi$
$971$	−5.46674	+	38.0220i	−0.175436	+	1.22018i	−0.867163	+	0.498025i	$0.834059\pi$
$972$	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	0.958525	−	0.285009i	$-0.0919967\pi$
$977$	−0.0601803	−	0.204955i	−0.00192534	−	0.00655710i	−0.960450	+	0.278452i	$0.910179\pi$
$978$	−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	−0.579190	−	0.815193i	$-0.696631\pi$
$983$	−2.45396	+	1.57706i	−0.0782691	+	0.0503005i	0.500921	+	0.865493i	$0.332995\pi$
$984$	−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	0.310416	−	0.950601i	$-0.399532\pi$
$991$	1.81390	+	0.532609i	0.0576204	+	0.0169189i	−0.252795	+	0.967520i	$0.581350\pi$
$992$	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	−0.709561	−	0.704644i	$-0.751107\pi$
$997$	−3.57024	+	3.09363i	−0.113071	+	0.0979762i	0.596491	+	0.802620i	$0.296561\pi$
$998$	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.97.3	✓	160
7.6	odd	2	inner	966.2.s.a.97.14	yes	160
23.14	odd	22	inner	966.2.s.a.727.14	yes	160
161.83	even	22	inner	966.2.s.a.727.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.3	✓	160	1.1	even	1	trivial
966.2.s.a.97.14	yes	160	7.6	odd	2	inner
966.2.s.a.727.3	yes	160	161.83	even	22	inner
966.2.s.a.727.14	yes	160	23.14	odd	22	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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