LMFDB - Embedded newform 896.2.bn.a.533.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			533.37
Character	$\chi$	$=$	896.533
Dual form			896.2.bn.a.701.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09447 - 0.895616i) q^{2} +(1.12869 + 0.926290i) q^{3} +(0.395745 - 1.96046i) q^{4} +(-1.23096 - 4.05794i) q^{5} +(2.06492 + 0.00292944i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-1.32268 - 2.50010i) q^{8} +(-0.169349 - 0.851373i) q^{9} +O(q^{10})$	\(q+(1.09447 - 0.895616i) q^{2} +(1.12869 + 0.926290i) q^{3} +(0.395745 - 1.96046i) q^{4} +(-1.23096 - 4.05794i) q^{5} +(2.06492 + 0.00292944i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-1.32268 - 2.50010i) q^{8} +(-0.169349 - 0.851373i) q^{9} +(-4.98161 - 3.33884i) q^{10} +(-0.421950 + 4.28413i) q^{11} +(2.26262 - 1.84617i) q^{12} +(0.651086 + 0.197505i) q^{13} +(-1.24817 + 0.664886i) q^{14} +(2.36946 - 5.72037i) q^{15} +(-3.68677 - 1.55168i) q^{16} +(1.40233 + 3.38551i) q^{17} +(-0.947851 - 0.780134i) q^{18} +(-2.02331 - 3.78534i) q^{19} +(-8.44255 + 0.807339i) q^{20} +(-0.926290 - 1.12869i) q^{21} +(3.37512 + 5.06678i) q^{22} +(4.91450 - 7.35506i) q^{23} +(0.822923 - 4.04702i) q^{24} +(-10.7942 + 7.21249i) q^{25} +(0.889484 - 0.366959i) q^{26} +(2.66236 - 4.98093i) q^{27} +(-0.770607 + 1.84558i) q^{28} +(-3.85926 + 0.380104i) q^{29} +(-2.52995 - 8.38292i) q^{30} +(-1.16419 - 1.16419i) q^{31} +(-5.42478 + 1.60366i) q^{32} +(-4.44460 + 4.44460i) q^{33} +(4.56693 + 2.44941i) q^{34} +(0.415645 + 4.22012i) q^{35} +(-1.73610 - 0.00492592i) q^{36} +(7.61959 + 4.07276i) q^{37} +(-5.60467 - 2.33085i) q^{38} +(0.551925 + 0.826015i) q^{39} +(-8.51709 + 8.44490i) q^{40} +(-3.24421 - 2.16771i) q^{41} +(-2.02467 - 0.405719i) q^{42} +(0.615507 - 0.505133i) q^{43} +(8.23187 + 2.52264i) q^{44} +(-3.24636 + 1.73521i) q^{45} +(-1.20852 - 12.4514i) q^{46} +(7.24834 - 3.00236i) q^{47} +(-2.72391 - 5.16638i) q^{48} +(0.923880 + 0.382683i) q^{49} +(-5.35440 + 17.5614i) q^{50} +(-1.55318 + 5.12015i) q^{51} +(0.644863 - 1.19826i) q^{52} +(5.87243 + 0.578384i) q^{53} +(-1.54711 - 7.83595i) q^{54} +(17.9042 - 3.56136i) q^{55} +(0.809522 + 2.71011i) q^{56} +(1.22264 - 6.14664i) q^{57} +(-3.88343 + 3.87243i) q^{58} +(2.04696 - 0.620938i) q^{59} +(-10.2768 - 6.90902i) q^{60} +(-4.40086 + 5.36246i) q^{61} +(-2.31684 - 0.231508i) q^{62} +0.868052i q^{63} +(-4.50102 + 6.61368i) q^{64} -2.88519i q^{65} +(-0.883843 + 8.84515i) q^{66} +(0.487954 - 0.594574i) q^{67} +(7.19211 - 1.40940i) q^{68} +(12.3598 - 3.74932i) q^{69} +(4.23451 + 4.24655i) q^{70} +(-0.169867 + 0.853981i) q^{71} +(-1.90452 + 1.54949i) q^{72} +(10.5631 - 2.10112i) q^{73} +(11.9871 - 2.36670i) q^{74} +(-18.8642 - 1.85796i) q^{75} +(-8.22171 + 2.46858i) q^{76} +(1.24964 - 4.11950i) q^{77} +(1.34386 + 0.409738i) q^{78} +(-1.37885 - 0.571139i) q^{79} +(-1.75834 + 16.8708i) q^{80} +(5.21283 - 2.15923i) q^{81} +(-5.49213 + 0.533062i) q^{82} +(10.5599 - 5.64437i) q^{83} +(-2.57932 + 1.36928i) q^{84} +(12.0120 - 9.85799i) q^{85} +(0.221250 - 1.10411i) q^{86} +(-4.70799 - 3.14578i) q^{87} +(11.2689 - 4.61163i) q^{88} +(-4.38910 - 6.56876i) q^{89} +(-1.99897 + 4.80663i) q^{90} +(-0.600044 - 0.320730i) q^{91} +(-12.4744 - 12.5454i) q^{92} +(-0.235629 - 2.39238i) q^{93} +(5.24415 - 9.77773i) q^{94} +(-12.8701 + 12.8701i) q^{95} +(-7.60834 - 3.21489i) q^{96} +(-4.64545 - 4.64545i) q^{97} +(1.35390 - 0.408604i) q^{98} +(3.71885 - 0.366275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q+O(q^{10}) $ 752 * q	$ 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) $ 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{32}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.09447	−	0.895616i	0.773910	−	0.633296i
$2$	1.09447	−	0.895616i	0.773910	−	0.633296i
$3$	1.12869	+	0.926290i	0.651648	+	0.534794i	0.901110	−	0.433591i	$-0.142754\pi$
$3$	1.12869	+	0.926290i	0.651648	+	0.534794i	−0.249462	+	0.968385i	$0.580254\pi$
$4$	0.395745	−	1.96046i	0.197872	−	0.980228i
$5$	−1.23096	−	4.05794i	−0.550503	−	1.81477i	−0.579211	−	0.815177i	$-0.696639\pi$
$5$	−1.23096	−	4.05794i	−0.550503	−	1.81477i	0.0287083	−	0.999588i	$-0.490861\pi$
$6$	2.06492	+	0.00292944i	0.842999	+	0.00119594i
$7$	−0.980785	−	0.195090i	−0.370702	−	0.0737372i
$7$	−0.980785	−	0.195090i	−0.370702	−	0.0737372i
$8$	−1.32268	−	2.50010i	−0.467639	−	0.883920i
$9$	−0.169349	−	0.851373i	−0.0564495	−	0.283791i
$10$	−4.98161	−	3.33884i	−1.57532	−	1.05583i
$11$	−0.421950	+	4.28413i	−0.127223	+	1.29171i	0.693529	+	0.720429i	$0.256055\pi$
$11$	−0.421950	+	4.28413i	−0.127223	+	1.29171i	−0.820751	+	0.571286i	$0.806445\pi$
$12$	2.26262	−	1.84617i	0.653163	−	0.532943i
$13$	0.651086	+	0.197505i	0.180579	+	0.0547779i	0.379279	−	0.925282i	$-0.376172\pi$
$13$	0.651086	+	0.197505i	0.180579	+	0.0547779i	−0.198700	+	0.980060i	$0.563672\pi$
$14$	−1.24817	+	0.664886i	−0.333587	+	0.177698i
$15$	2.36946	−	5.72037i	0.611791	−	1.47699i
$16$	−3.68677	−	1.55168i	−0.921693	−	0.387920i
$17$	1.40233	+	3.38551i	0.340114	+	0.821108i	0.997704	+	0.0677314i	$0.0215761\pi$
$17$	1.40233	+	3.38551i	0.340114	+	0.821108i	−0.657590	+	0.753376i	$0.728424\pi$
$18$	−0.947851	−	0.780134i	−0.223411	−	0.183879i
$19$	−2.02331	−	3.78534i	−0.464179	−	0.868417i	−0.999714	−	0.0239044i	$-0.992390\pi$
$19$	−2.02331	−	3.78534i	−0.464179	−	0.868417i	0.535536	−	0.844513i	$-0.320110\pi$
$20$	−8.44255	+	0.807339i	−1.88781	+	0.180526i
$21$	−0.926290	−	1.12869i	−0.202133	−	0.246300i
$22$	3.37512	+	5.06678i	0.719579	+	1.08024i
$23$	4.91450	−	7.35506i	1.02474	−	1.53364i	0.190919	−	0.981606i	$-0.438853\pi$
$23$	4.91450	−	7.35506i	1.02474	−	1.53364i	0.833824	−	0.552031i	$-0.186147\pi$
$24$	0.822923	−	4.04702i	0.167979	−	0.826095i
$25$	−10.7942	+	7.21249i	−2.15885	+	1.44250i
$26$	0.889484	−	0.366959i	0.174442	−	0.0719666i
$27$	2.66236	−	4.98093i	0.512372	−	0.958580i
$28$	−0.770607	+	1.84558i	−0.145631	+	0.348782i
$29$	−3.85926	+	0.380104i	−0.716647	+	0.0705836i	−0.449767	−	0.893146i	$-0.648493\pi$
$29$	−3.85926	+	0.380104i	−0.716647	+	0.0705836i	−0.266880	+	0.963730i	$0.585993\pi$
$30$	−2.52995	−	8.38292i	−0.461903	−	1.53050i
$31$	−1.16419	−	1.16419i	−0.209094	−	0.209094i	0.594788	−	0.803883i	$-0.297236\pi$
$31$	−1.16419	−	1.16419i	−0.209094	−	0.209094i	−0.803883	+	0.594788i	$0.797236\pi$
$32$	−5.42478	+	1.60366i	−0.958975	+	0.283490i
$33$	−4.44460	+	4.44460i	−0.773705	+	0.773705i
$34$	4.56693	+	2.44941i	0.783222	+	0.420070i
$35$	0.415645	+	4.22012i	0.0702568	+	0.713330i
$36$	−1.73610	−	0.00492592i	−0.289350	−	0.000820986i
$37$	7.61959	+	4.07276i	1.25265	+	0.669557i	0.958197	−	0.286108i	$-0.0923616\pi$
$37$	7.61959	+	4.07276i	1.25265	+	0.669557i	0.294456	+	0.955665i	$0.404862\pi$
$38$	−5.60467	−	2.33085i	−0.909197	−	0.378114i
$39$	0.551925	+	0.826015i	0.0883788	+	0.132268i
$40$	−8.51709	+	8.44490i	−1.34667	+	1.33526i
$41$	−3.24421	−	2.16771i	−0.506660	−	0.338539i	0.275826	−	0.961208i	$-0.411049\pi$
$41$	−3.24421	−	2.16771i	−0.506660	−	0.338539i	−0.782486	+	0.622668i	$0.786049\pi$
$42$	−2.02467	−	0.405719i	−0.312413	−	0.0626038i
$43$	0.615507	−	0.505133i	0.0938639	−	0.0770321i	−0.586291	−	0.810100i	$-0.699412\pi$
$43$	0.615507	−	0.505133i	0.0938639	−	0.0770321i	0.680155	+	0.733068i	$0.261912\pi$
$44$	8.23187	+	2.52264i	1.24100	+	0.380302i
$45$	−3.24636	+	1.73521i	−0.483938	+	0.258670i
$46$	−1.20852	−	12.4514i	−0.178187	−	1.83586i
$47$	7.24834	−	3.00236i	1.05728	−	0.437939i	0.214794	−	0.976659i	$-0.431092\pi$
$47$	7.24834	−	3.00236i	1.05728	−	0.437939i	0.842485	+	0.538720i	$0.181092\pi$
$48$	−2.72391	−	5.16638i	−0.393162	−	0.745703i
$49$	0.923880	+	0.382683i	0.131983	+	0.0546691i
$50$	−5.35440	+	17.5614i	−0.757227	+	2.48355i
$51$	−1.55318	+	5.12015i	−0.217489	+	0.716964i
$52$	0.644863	−	1.19826i	0.0894264	−	0.166169i
$53$	5.87243	+	0.578384i	0.806641	+	0.0794472i	0.492927	−	0.870071i	$-0.335927\pi$
$53$	5.87243	+	0.578384i	0.806641	+	0.0794472i	0.313713	+	0.949518i	$0.398427\pi$
$54$	−1.54711	−	7.83595i	−0.210536	−	1.06634i
$55$	17.9042	−	3.56136i	2.41420	−	0.480213i
$56$	0.809522	+	2.71011i	0.108177	+	0.362153i
$57$	1.22264	−	6.14664i	0.161943	−	0.814142i
$58$	−3.88343	+	3.87243i	−0.509920	+	0.508475i
$59$	2.04696	−	0.620938i	0.266491	−	0.0808393i	−0.154211	−	0.988038i	$-0.549284\pi$
$59$	2.04696	−	0.620938i	0.266491	−	0.0808393i	0.420703	+	0.907199i	$0.361784\pi$
$60$	−10.2768	−	6.90902i	−1.32673	−	0.891950i
$61$	−4.40086	+	5.36246i	−0.563472	+	0.686593i	−0.974335	−	0.225104i	$-0.927728\pi$
$61$	−4.40086	+	5.36246i	−0.563472	+	0.686593i	0.410862	+	0.911697i	$0.365228\pi$
$62$	−2.31684	−	0.231508i	−0.294239	−	0.0294015i
$63$			0.868052i			0.109364i
$64$	−4.50102	+	6.61368i	−0.562628	+	0.826711i
$65$		−	2.88519i		−	0.357863i
$66$	−0.883843	+	8.84515i	−0.108794	+	1.08876i
$67$	0.487954	−	0.594574i	0.0596131	−	0.0726388i	−0.742350	−	0.670012i	$-0.766289\pi$
$67$	0.487954	−	0.594574i	0.0596131	−	0.0726388i	0.801963	+	0.597373i	$0.203789\pi$
$68$	7.19211	−	1.40940i	0.872172	−	0.170915i
$69$	12.3598	−	3.74932i	1.48795	−	0.451365i
$70$	4.23451	+	4.24655i	0.506121	+	0.507559i
$71$	−0.169867	+	0.853981i	−0.0201596	+	0.101349i	−0.989555	−	0.144155i	$-0.953954\pi$
$71$	−0.169867	+	0.853981i	−0.0201596	+	0.101349i	0.969396	+	0.245504i	$0.0789535\pi$
$72$	−1.90452	+	1.54949i	−0.224450	+	0.182609i
$73$	10.5631	−	2.10112i	1.23631	−	0.245918i	0.466692	−	0.884420i	$-0.345446\pi$
$73$	10.5631	−	2.10112i	1.23631	−	0.245918i	0.769620	+	0.638502i	$0.220446\pi$
$74$	11.9871	−	2.36670i	1.39347	−	0.275124i
$75$	−18.8642	−	1.85796i	−2.17825	−	0.214539i
$76$	−8.22171	+	2.46858i	−0.943095	+	0.283165i
$77$	1.24964	−	4.11950i	0.142409	−	0.469460i
$78$	1.34386	+	0.409738i	0.152162	+	0.0463937i
$79$	−1.37885	−	0.571139i	−0.155133	−	0.0642582i	0.303766	−	0.952747i	$-0.401756\pi$
$79$	−1.37885	−	0.571139i	−0.155133	−	0.0642582i	−0.458899	+	0.888489i	$0.651756\pi$
$80$	−1.75834	+	16.8708i	−0.196589	+	1.88621i
$81$	5.21283	−	2.15923i	0.579204	−	0.239914i
$82$	−5.49213	+	0.533062i	−0.606505	+	0.0588668i
$83$	10.5599	−	5.64437i	1.15910	−	0.619550i	0.224226	−	0.974537i	$-0.428015\pi$
$83$	10.5599	−	5.64437i	1.15910	−	0.619550i	0.934871	+	0.354987i	$0.115515\pi$
$84$	−2.57932	+	1.36928i	−0.281426	+	0.149400i
$85$	12.0120	−	9.85799i	1.30288	−	1.06925i
$86$	0.221250	−	1.10411i	0.0238580	−	0.119059i
$87$	−4.70799	−	3.14578i	−0.504749	−	0.337263i
$88$	11.2689	−	4.61163i	1.20127	−	0.491602i
$89$	−4.38910	−	6.56876i	−0.465244	−	0.696287i	0.522453	−	0.852668i	$-0.325017\pi$
$89$	−4.38910	−	6.56876i	−0.465244	−	0.696287i	−0.987697	+	0.156381i	$0.950017\pi$
$90$	−1.99897	+	4.80663i	−0.210710	+	0.506664i
$91$	−0.600044	−	0.320730i	−0.0629017	−	0.0336217i
$92$	−12.4744	−	12.5454i	−1.30054	−	1.30795i
$93$	−0.235629	−	2.39238i	−0.0244336	−	0.248078i
$94$	5.24415	−	9.77773i	0.540893	−	1.00850i
$95$	−12.8701	+	12.8701i	−1.32044	+	1.32044i
$96$	−7.60834	−	3.21489i	−0.776523	−	0.328119i
$97$	−4.64545	−	4.64545i	−0.471674	−	0.471674i	0.430782	−	0.902456i	$-0.358238\pi$
$97$	−4.64545	−	4.64545i	−0.471674	−	0.471674i	−0.902456	+	0.430782i	$0.858238\pi$
$98$	1.35390	−	0.408604i	0.136764	−	0.0412753i
$99$	3.71885	−	0.366275i	0.373759	−	0.0368120i
$100$	9.86799	+	24.0159i	0.986799	+	2.40159i
$101$	3.10100	−	5.80157i	0.308561	−	0.577278i	−0.679070	−	0.734074i	$-0.737617\pi$
$101$	3.10100	−	5.80157i	0.308561	−	0.577278i	0.987631	+	0.156796i	$0.0501166\pi$
$102$	2.88577	+	6.99492i	0.285734	+	0.692600i
$103$	13.9323	−	9.30929i	1.37279	−	0.917271i	0.372850	−	0.927892i	$-0.378381\pi$
$103$	13.9323	−	9.30929i	1.37279	−	0.917271i	0.999944	+	0.0106204i	$0.00338063\pi$
$104$	−0.367398	−	1.88902i	−0.0360263	−	0.185233i
$105$	−3.43992	+	5.14820i	−0.335701	+	0.502413i
$106$	6.94523	−	4.62642i	0.674581	−	0.449357i
$107$	10.6877	+	13.0230i	1.03322	+	1.25898i	0.965259	+	0.261294i	$0.0841492\pi$
$107$	10.6877	+	13.0230i	1.03322	+	1.25898i	0.0679606	+	0.997688i	$0.478351\pi$
$108$	−8.71128	−	7.19062i	−0.838243	−	0.691918i
$109$	2.07754	+	3.88681i	0.198993	+	0.372289i	0.961549	−	0.274633i	$-0.0885562\pi$
$109$	2.07754	+	3.88681i	0.198993	+	0.372289i	−0.762557	+	0.646921i	$0.776056\pi$
$110$	16.4060	−	19.9331i	1.56425	−	1.90054i
$111$	4.82758	+	11.6548i	0.458214	+	1.10623i
$112$	3.31321	+	2.24112i	0.313069	+	0.211766i
$113$	−3.37437	+	8.14645i	−0.317434	+	0.766353i	0.681955	+	0.731394i	$0.261130\pi$
$113$	−3.37437	+	8.14645i	−0.317434	+	0.766353i	−0.999389	+	0.0349589i	$0.988870\pi$
$114$	−4.16688	−	7.82235i	−0.390264	−	0.732630i
$115$	−35.8959	−	10.8889i	−3.34731	−	1.01540i
$116$	−0.782105	+	7.71634i	−0.0726167	+	0.716444i
$117$	0.0578897	−	0.587764i	0.00535190	−	0.0543388i
$118$	1.68422	−	2.51289i	0.155045	−	0.231330i
$119$	−0.714899	−	3.59404i	−0.0655347	−	0.329465i
$120$	−17.4355	+	1.64236i	−1.59164	+	0.149926i
$121$	−7.38712	−	1.46939i	−0.671556	−	0.133581i
$122$	−0.0139180	+	9.81056i	−0.00126007	+	0.888206i
$123$	−1.65377	−	5.45174i	−0.149115	−	0.491567i
$124$	−2.74306	+	1.82162i	−0.246334	+	0.163586i
$125$	26.1653	+	21.4733i	2.34029	+	1.92063i
$126$	0.777441	+	0.950060i	0.0692600	+	0.0846381i
$127$	−11.7825			−1.04553			−0.522764	−	0.852478i	$-0.675099\pi$
$127$	−11.7825			−1.04553			−0.522764	+	0.852478i	$0.675099\pi$
$128$	0.997073	+	11.2697i	0.0881296	+	0.996109i
$129$	1.16261			0.102362
$130$	−2.58402	−	3.15776i	−0.226633	−	0.276954i
$131$	14.1058	+	11.5763i	1.23243	+	1.01143i	0.999239	+	0.0389994i	$0.0124171\pi$
$131$	14.1058	+	11.5763i	1.23243	+	1.01143i	0.233192	+	0.972431i	$0.425083\pi$
$132$	6.95451	+	10.4724i	0.605313	+	0.911502i
$133$	1.24595	+	4.10734i	0.108037	+	0.356151i
$134$	0.00154318	−	1.08776i	0.000133311	−	0.0939686i
$135$	−23.4896	−	4.67237i	−2.02166	−	0.402133i
$136$	6.60930	−	7.98392i	0.566743	−	0.684615i
$137$	4.11231	+	20.6740i	0.351338	+	1.76630i	0.602270	+	0.798292i	$0.294263\pi$
$137$	4.11231	+	20.6740i	0.351338	+	1.76630i	−0.250932	+	0.968005i	$0.580737\pi$
$138$	10.1696	−	15.1732i	0.865692	−	1.29163i
$139$	1.55362	−	15.7741i	0.131776	−	1.33794i	−0.670908	−	0.741540i	$-0.734096\pi$
$139$	1.55362	−	15.7741i	0.131776	−	1.33794i	0.802684	−	0.596404i	$-0.203404\pi$
$140$	8.43784	+	0.855235i	0.713127	+	0.0722805i
$141$	10.9622	+	3.32534i	0.923180	+	0.280044i
$142$	0.578924	+	1.08680i	0.0485822	+	0.0912019i
$143$	−1.12086	+	2.70600i	−0.0937312	+	0.226287i
$144$	−0.696708	+	3.40159i	−0.0580590	+	0.283466i
$145$	6.29305	+	15.1928i	0.522609	+	1.26169i
$146$	9.67919	−	11.7601i	0.801056	−	0.973270i
$147$	0.688295	+	1.28771i	0.0567696	+	0.106209i
$148$	10.9999	−	13.3261i	0.904184	−	1.09540i
$149$	6.55271	+	7.98450i	0.536819	+	0.654116i	0.968822	−	0.247756i	$-0.0796931\pi$
$149$	6.55271	+	7.98450i	0.536819	+	0.654116i	−0.432003	+	0.901872i	$0.642193\pi$
$150$	−22.3104	+	14.8616i	−1.82163	+	1.21344i
$151$	6.80492	−	10.1843i	0.553776	−	0.828785i	−0.443959	−	0.896047i	$-0.646426\pi$
$151$	6.80492	−	10.1843i	0.553776	−	0.828785i	0.997735	+	0.0672623i	$0.0214264\pi$
$152$	−6.78755	+	10.0653i	−0.550543	+	0.816402i
$153$	2.64485	−	1.76723i	0.213824	−	0.142872i
$154$	−2.32179	−	5.62787i	−0.187095	−	0.453507i
$155$	−3.29113	+	6.15728i	−0.264350	+	0.494564i
$156$	1.83779	−	0.755134i	0.147141	−	0.0604591i
$157$	−6.39061	+	0.629420i	−0.510026	+	0.0502332i	−0.349758	−	0.936840i	$-0.613736\pi$
$157$	−6.39061	+	0.629420i	−0.510026	+	0.0502332i	−0.160269	+	0.987073i	$0.551236\pi$
$158$	−2.02064	+	0.609825i	−0.160753	+	0.0485151i
$159$	6.09239	+	6.09239i	0.483158	+	0.483158i
$160$	13.1853	+	20.0394i	1.04239	+	1.58425i
$161$	−6.25497	+	6.25497i	−0.492960	+	0.492960i
$162$	3.77147	−	7.03191i	0.296315	−	0.552479i
$163$	0.227186	+	2.30666i	0.0177946	+	0.180671i	0.999974	−	0.00727685i	$-0.00231631\pi$
$163$	0.227186	+	2.30666i	0.0177946	+	0.180671i	−0.982179	+	0.187948i	$0.939816\pi$
$164$	−5.53358	+	5.50226i	−0.432100	+	0.429655i
$165$	23.5070	+	12.5648i	1.83002	+	0.978166i
$166$	6.50232	−	15.6352i	0.504678	−	1.21353i
$167$	−0.297665	−	0.445487i	−0.0230340	−	0.0344728i	0.819774	−	0.572687i	$-0.194099\pi$
$167$	−0.297665	−	0.445487i	−0.0230340	−	0.0344728i	−0.842808	+	0.538214i	$0.819099\pi$
$168$	−1.59665	+	3.80871i	−0.123184	+	0.293849i
$169$	−10.4242	−	6.96523i	−0.801862	−	0.535787i
$170$	4.31784	−	21.5474i	0.331163	−	1.65261i
$171$	−2.88009	+	2.36363i	−0.220246	+	0.180751i
$172$	−0.746708	−	1.40658i	−0.0569359	−	0.107250i
$173$	−8.90682	+	4.76079i	−0.677173	+	0.361956i	−0.773859	−	0.633359i	$-0.781676\pi$
$173$	−8.90682	+	4.76079i	−0.677173	+	0.361956i	0.0966856	+	0.995315i	$0.469176\pi$
$174$	−7.97017	+	0.773579i	−0.604217	+	0.0586448i
$175$	11.9939	−	4.96805i	0.906656	−	0.375549i
$176$	8.20324	−	15.1399i	0.618342	−	1.14121i
$177$	2.88555	+	1.19523i	0.216891	+	0.0898392i
$178$	−10.6868	−	3.25838i	−0.801012	−	0.244226i
$179$	−6.82506	+	22.4992i	−0.510129	+	1.68167i	0.201806	+	0.979425i	$0.435319\pi$
$179$	−6.82506	+	22.4992i	−0.510129	+	1.68167i	−0.711936	+	0.702245i	$0.752181\pi$
$180$	2.11708	+	7.05104i	0.157798	+	0.525554i
$181$	−21.4223	−	2.10991i	−1.59230	−	0.156828i	−0.737343	−	0.675519i	$-0.763920\pi$
$181$	−21.4223	−	2.10991i	−1.59230	−	0.156828i	−0.854962	+	0.518691i	$0.826420\pi$
$182$	−0.943983	+	0.186378i	−0.0699727	+	0.0138153i
$183$	−9.93439	+	1.97607i	−0.734371	+	0.146076i
$184$	−24.8887	−	2.55833i	−1.83482	−	0.188602i
$185$	7.14757	−	35.9332i	0.525500	−	2.64186i
$186$	−2.40054	−	2.40736i	−0.176016	−	0.176516i
$187$	−15.0957	+	4.57923i	−1.10391	+	0.334867i
$188$	−3.01750	−	15.3982i	−0.220074	−	1.12303i
$189$	−3.58294	+	4.36582i	−0.260620	+	0.317567i
$190$	−2.55931	+	25.6126i	−0.185672	+	1.85813i
$191$		−	8.29514i		−	0.600215i	−0.953905	−	0.300108i	$-0.902977\pi$
$191$		−	8.29514i		−	0.600215i	0.953905	−	0.300108i	$-0.0970226\pi$
$192$	−11.2064	+	3.29553i	−0.808755	+	0.237835i
$193$			11.6111i			0.835783i	0.908497	+	0.417892i	$0.137231\pi$
$193$			11.6111i			0.835783i	−0.908497	+	0.417892i	$0.862769\pi$
$194$	−9.24487	−	0.923784i	−0.663743	−	0.0663238i
$195$	2.67252	−	3.25647i	0.191383	−	0.233201i
$196$	1.11585	−	1.65978i	0.0797039	−	0.118556i
$197$	−20.6352	+	6.25963i	−1.47020	+	0.445980i	−0.920951	−	0.389679i	$-0.872586\pi$
$197$	−20.6352	+	6.25963i	−1.47020	+	0.445980i	−0.549249	+	0.835659i	$0.685086\pi$
$198$	3.74214	−	3.73154i	0.265943	−	0.265189i
$199$	−1.32378	+	6.65508i	−0.0938400	+	0.471766i	0.905077	+	0.425247i	$0.139813\pi$
$199$	−1.32378	+	6.65508i	−0.0938400	+	0.471766i	−0.998917	+	0.0465188i	$0.985187\pi$
$200$	32.3093	+	17.4469i	2.28461	+	1.23368i
$201$	1.10150	−	0.219101i	0.0776935	−	0.0154542i
$202$	−1.80201	−	9.12697i	−0.126789	−	0.642171i
$203$	3.85926	+	0.380104i	0.270867	+	0.0266781i
$204$	9.42316	+	5.07121i	0.659753	+	0.355056i
$205$	−4.80294	+	15.8332i	−0.335452	+	1.10584i
$206$	6.91103	−	22.6668i	0.481514	−	1.57927i
$207$	−7.09416	−	2.93850i	−0.493078	−	0.204240i
$208$	−2.09394	−	1.73843i	−0.145189	−	0.120538i
$209$	17.0706	−	7.07089i	1.18080	−	0.489104i
$210$	0.845910	+	8.71541i	0.0583734	+	0.601420i
$211$	−17.2188	+	9.20362i	−1.18539	+	0.633603i	−0.941767	−	0.336267i	$-0.890836\pi$
$211$	−17.2188	+	9.20362i	−1.18539	+	0.633603i	−0.243622	+	0.969870i	$0.578336\pi$
$212$	3.45788	−	11.2837i	0.237488	−	0.774971i
$213$	−0.982761	+	0.806531i	−0.0673377	+	0.0552626i
$214$	23.3610	+	4.68126i	1.59693	+	0.320004i
$215$	−2.80746	−	1.87589i	−0.191467	−	0.127934i
$216$	−15.9743	−	0.0679872i	−1.08691	−	0.00462594i
$217$	0.914697	+	1.36894i	0.0620937	+	0.0929297i
$218$	5.75490	+	2.39333i	0.389771	+	0.162097i
$219$	13.8686	+	7.41294i	0.937156	+	0.500920i
$220$	0.103591	−	36.5097i	0.00698409	−	2.46148i
$221$	0.244379	+	2.48122i	0.0164387	+	0.166905i
$222$	15.7219	+	8.43223i	1.05519	+	0.565934i
$223$	9.00693	−	9.00693i	0.603149	−	0.603149i	−0.337998	−	0.941147i	$-0.609750\pi$
$223$	9.00693	−	9.00693i	0.603149	−	0.603149i	0.941147	+	0.337998i	$0.109750\pi$
$224$	5.63341	−	0.514522i	0.376398	−	0.0343780i
$225$	7.96851	+	7.96851i	0.531234	+	0.531234i
$226$	3.60293	+	11.9382i	0.239663	+	0.794118i
$227$	−3.97788	+	0.391787i	−0.264021	+	0.0260038i	−0.229162	−	0.973388i	$-0.573598\pi$
$227$	−3.97788	+	0.391787i	−0.264021	+	0.0260038i	−0.0348598	+	0.999392i	$0.511098\pi$
$228$	−11.5664	−	4.82943i	−0.766001	−	0.319837i
$229$	12.8534	−	24.0471i	0.849379	−	1.58908i	0.0419442	−	0.999120i	$-0.486645\pi$
$229$	12.8534	−	24.0471i	0.849379	−	1.58908i	0.807435	−	0.589957i	$-0.200855\pi$
$230$	−49.0395	+	20.2313i	−3.23357	+	1.33402i
$231$	5.22630	−	3.49210i	0.343865	−	0.229763i
$232$	6.05488	+	9.14579i	0.397522	+	0.600451i
$233$	−0.836921	+	1.25254i	−0.0548285	+	0.0820567i	−0.857871	−	0.513865i	$-0.828213\pi$
$233$	−0.836921	+	1.25254i	−0.0548285	+	0.0820567i	0.803042	+	0.595922i	$0.203213\pi$
$234$	−0.463052	−	0.695139i	−0.0302706	−	0.0454426i
$235$	−21.1058	−	25.7175i	−1.37679	−	1.67763i
$236$	−0.407249	−	4.25871i	−0.0265096	−	0.277218i
$237$	−1.02725	−	1.92185i	−0.0667272	−	0.124838i
$238$	−4.00132	−	3.29331i	−0.259367	−	0.213473i
$239$	0.795937	+	1.92156i	0.0514849	+	0.124296i	0.947529	−	0.319669i	$-0.103572\pi$
$239$	0.795937	+	1.92156i	0.0514849	+	0.124296i	−0.896044	+	0.443964i	$0.853572\pi$
$240$	−17.6118	+	17.4131i	−1.13684	+	1.12401i
$241$	−0.612668	+	1.47911i	−0.0394654	+	0.0952779i	−0.942383	−	0.334535i	$-0.891421\pi$
$241$	−0.612668	+	1.47911i	−0.0394654	+	0.0952779i	0.902918	+	0.429813i	$0.141421\pi$
$242$	−9.40101	+	5.00781i	−0.604320	+	0.321914i
$243$	−8.33015	−	2.52692i	−0.534379	−	0.162102i
$244$	8.77126	+	10.7499i	0.561522	+	0.688189i
$245$	0.415645	−	4.22012i	0.0265546	−	0.269613i
$246$	−6.69267	−	4.48565i	−0.426709	−	0.285994i
$247$	−0.569724	−	2.86419i	−0.0362506	−	0.182244i
$248$	−1.37074	+	4.45044i	−0.0870419	+	0.282603i
$249$	17.1471	+	3.41078i	1.08666	+	0.216149i
$250$	47.8690	+	0.0679104i	3.02750	+	0.00429503i
$251$	8.12244	+	26.7761i	0.512684	+	1.69009i	0.705377	+	0.708832i	$0.250778\pi$
$251$	8.12244	+	26.7761i	0.512684	+	1.69009i	−0.192693	+	0.981259i	$0.561722\pi$
$252$	1.70178	+	0.343527i	0.107202	+	0.0216402i
$253$	29.4364	+	24.1578i	1.85065	+	1.51879i
$254$	−12.8956	+	10.5526i	−0.809144	+	0.662128i
$255$	22.6891			1.42085
$256$	11.1846	+	11.4414i	0.699036	+	0.715086i
$257$	−19.0836			−1.19040			−0.595201	−	0.803577i	$-0.702927\pi$
$257$	−19.0836			−1.19040			−0.595201	+	0.803577i	$0.702927\pi$
$258$	1.27245	−	1.04126i	0.0792193	−	0.0648257i
$259$	−6.67863	−	5.48101i	−0.414990	−	0.340573i
$260$	−5.65628	−	1.14180i	−0.350788	−	0.0708112i
$261$	0.977171	+	3.22130i	0.0604854	+	0.199394i
$262$	25.8064	+	0.0366108i	1.59433	+	0.00226182i
$263$	3.42868	+	0.682008i	0.211422	+	0.0420544i	0.299665	−	0.954045i	$-0.403125\pi$
$263$	3.42868	+	0.682008i	0.211422	+	0.0420544i	−0.0882430	+	0.996099i	$0.528125\pi$
$264$	16.9907	+	5.23316i	1.04571	+	0.322078i
$265$	−4.88169	−	24.5419i	−0.299880	−	1.50760i
$266$	5.04225	+	3.37948i	0.309160	+	0.207209i
$267$	1.13065	−	11.4797i	0.0691945	−	0.702543i
$268$	−0.972530	−	1.19191i	−0.0594067	−	0.0728076i
$269$	10.6884	+	3.24230i	0.651685	+	0.197686i	0.598781	−	0.800913i	$-0.295652\pi$
$269$	10.6884	+	3.24230i	0.651685	+	0.197686i	0.0529043	+	0.998600i	$0.483152\pi$
$270$	−29.8934	+	15.9239i	−1.81925	+	0.969095i
$271$	2.53671	−	6.12416i	0.154094	−	0.372016i	−0.827914	−	0.560855i	$-0.810472\pi$
$271$	2.53671	−	6.12416i	0.154094	−	0.372016i	0.982008	+	0.188839i	$0.0604725\pi$
$272$	0.0831780	−	14.6576i	0.00504341	−	0.888746i
$273$	−0.380173	−	0.917819i	−0.0230091	−	0.0555489i
$274$	23.0168	+	18.9441i	1.39049	+	1.14445i
$275$	−26.3446	−	49.2873i	−1.58864	−	2.97214i
$276$	−2.45903	−	25.7147i	−0.148016	−	1.54784i
$277$	0.927120	+	1.12970i	0.0557053	+	0.0678771i	0.800118	−	0.599843i	$-0.204770\pi$
$277$	0.927120	+	1.12970i	0.0557053	+	0.0678771i	−0.744412	+	0.667720i	$0.767270\pi$
$278$	−12.4272	−	18.6558i	−0.745332	−	1.11890i
$279$	−0.794005	+	1.18831i	−0.0475358	+	0.0711424i
$280$	10.0010	−	6.62103i	0.597671	−	0.395682i
$281$	22.8452	−	15.2647i	1.36283	−	0.910614i	0.363054	−	0.931768i	$-0.381734\pi$
$281$	22.8452	−	15.2647i	1.36283	−	0.910614i	0.999776	+	0.0211537i	$0.00673393\pi$
$282$	14.9760	−	6.17839i	0.891809	−	0.367918i
$283$	7.29561	−	13.6491i	0.433679	−	0.811357i	−0.566238	−	0.824242i	$-0.691602\pi$
$283$	7.29561	−	13.6491i	0.433679	−	0.811357i	0.999917	+	0.0128854i	$0.00410165\pi$
$284$	1.60697	+	0.670976i	0.0953560	+	0.0398151i
$285$	−26.4477	+	2.60487i	−1.56663	+	0.154299i
$286$	1.19678	+	3.96551i	0.0707672	+	0.234485i
$287$	2.75897	+	2.75897i	0.162857	+	0.162857i
$288$	2.28399	+	4.34694i	0.134585	+	0.256146i
$289$	2.52563	−	2.52563i	0.148566	−	0.148566i
$290$	20.4944	+	10.9919i	1.20348	+	0.645468i
$291$	−0.940228	−	9.54630i	−0.0551172	−	0.559614i
$292$	0.0611163	−	21.5399i	0.00357656	−	1.26053i
$293$	−26.8227	−	14.3370i	−1.56700	−	0.837577i	−0.999903	−	0.0139239i	$-0.995568\pi$
$293$	−26.8227	−	14.3370i	−1.56700	−	0.837577i	−0.567094	−	0.823653i	$-0.691932\pi$
$294$	1.90661	+	0.792916i	0.111196	+	0.0462438i
$295$	−5.03946	−	7.54208i	−0.293409	−	0.439117i
$296$	0.104004	−	24.4367i	0.00604509	−	1.42036i
$297$	20.2156	+	13.5076i	1.17303	+	0.783792i
$298$	14.3228	+	2.87012i	0.829699	+	0.166261i
$299$	4.65242	−	3.81814i	0.269056	−	0.220809i
$300$	−11.1078	+	36.2471i	−0.641312	+	2.09273i
$301$	−0.702226	+	0.375348i	−0.0404757	+	0.0216347i
$302$	−1.67340	−	17.2410i	−0.0962933	−	0.992109i
$303$	8.87399	−	3.67573i	0.509798	−	0.211165i
$304$	1.58583	+	17.0952i	0.0909539	+	0.980478i
$305$	27.1778	+	11.2574i	1.55620	+	0.644599i
$306$	1.31196	−	4.30296i	0.0749997	−	0.245984i
$307$	−9.30788	+	30.6840i	−0.531229	+	1.75123i	0.120437	+	0.992721i	$0.461571\pi$
$307$	−9.30788	+	30.6840i	−0.531229	+	1.75123i	−0.651666	+	0.758506i	$0.725929\pi$
$308$	−7.58155	−	4.08012i	−0.431999	−	0.232487i
$309$	24.3483	+	2.39810i	1.38513	+	0.136423i
$310$	1.91250	+	9.68657i	0.108622	+	0.550160i
$311$	2.72297	−	0.541632i	0.154405	−	0.0307131i	−0.117282	−	0.993099i	$-0.537418\pi$
$311$	2.72297	−	0.541632i	0.154405	−	0.0307131i	0.271688	+	0.962386i	$0.412418\pi$
$312$	1.33510	−	2.47243i	0.0755851	−	0.139974i
$313$	5.33848	−	26.8383i	0.301749	−	1.51699i	−0.470916	−	0.882178i	$-0.656076\pi$
$313$	5.33848	−	26.8383i	0.301749	−	1.51699i	0.772664	−	0.634815i	$-0.218924\pi$
$314$	−6.43064	+	6.41242i	−0.362902	+	0.361874i
$315$	3.52250	−	1.06854i	0.198471	−	0.0602054i
$316$	−1.66537	+	2.47715i	−0.0936842	+	0.139351i
$317$	−5.82457	+	7.09726i	−0.327140	+	0.398622i	−0.910444	−	0.413633i	$-0.864260\pi$
$317$	−5.82457	+	7.09726i	−0.327140	+	0.398622i	0.583304	+	0.812254i	$0.301760\pi$
$318$	12.1244	+	1.21152i	0.679902	+	0.0679386i
$319$		−	16.6940i		−	0.934684i
$320$	32.3785	+	10.1237i	1.81001	+	0.565930i
$321$			24.5988i			1.37297i
$322$	−1.24385	+	12.4479i	−0.0693170	+	0.693697i
$323$	9.97799	−	12.1582i	0.555190	−	0.676501i
$324$	−2.17012	−	11.0740i	−0.120562	−	0.615224i
$325$	−8.45248	+	2.56403i	−0.468859	+	0.142227i
$326$	2.31453	+	2.32110i	0.128190	+	0.128554i
$327$	−1.25542	+	6.31140i	−0.0694246	+	0.349021i
$328$	−1.12844	+	10.9780i	−0.0623076	+	0.606161i
$329$	−7.69479	+	1.53059i	−0.424228	+	0.0843841i
$330$	36.9810	−	7.30146i	2.03574	−	0.401932i
$331$	−1.90337	−	0.187465i	−0.104619	−	0.0103040i	0.0455724	−	0.998961i	$-0.485489\pi$
$331$	−1.90337	−	0.187465i	−0.104619	−	0.0103040i	−0.150191	+	0.988657i	$0.547989\pi$
$332$	−6.88653	−	22.9359i	−0.377947	−	1.25877i
$333$	2.17707	−	7.17683i	0.119303	−	0.393288i
$334$	−0.724771	−	0.220980i	−0.0396577	−	0.0120915i
$335$	−3.01340	−	1.24819i	−0.164639	−	0.0681959i
$336$	1.66366	+	5.59852i	0.0907600	+	0.305424i
$337$	2.86351	−	1.18611i	0.155986	−	0.0646113i	−0.303325	−	0.952887i	$-0.598097\pi$
$337$	2.86351	−	1.18611i	0.155986	−	0.0646113i	0.459310	+	0.888276i	$0.348097\pi$
$338$	−17.6472	+	1.71282i	−0.959880	+	0.0931652i
$339$	−11.3546	+	6.06915i	−0.616696	+	0.329631i
$340$	−14.5725	−	27.4502i	−0.790303	−	1.48870i
$341$	5.47877	−	4.49631i	0.296692	−	0.243489i
$342$	−1.03528	+	5.16639i	−0.0559815	+	0.279366i
$343$	−0.831470	−	0.555570i	−0.0448951	−	0.0299980i
$344$	−2.07700	−	0.870698i	−0.111985	−	0.0469449i
$345$	−30.4290	−	45.5402i	−1.63824	−	2.45180i
$346$	−5.48444	+	13.1877i	−0.294845	+	0.708973i
$347$	−10.6922	−	5.71511i	−0.573989	−	0.306803i	0.158744	−	0.987320i	$-0.449255\pi$
$347$	−10.6922	−	5.71511i	−0.573989	−	0.306803i	−0.732733	+	0.680516i	$0.761755\pi$
$348$	−8.03032	+	7.98488i	−0.430470	+	0.428034i
$349$	3.33367	+	33.8473i	0.178447	+	1.81180i	0.501213	+	0.865324i	$0.332887\pi$
$349$	3.33367	+	33.8473i	0.178447	+	1.81180i	−0.322766	+	0.946479i	$0.604613\pi$
$350$	8.67757	−	16.1793i	0.463836	−	0.864822i
$351$	2.71718	−	2.71718i	0.145032	−	0.145032i
$352$	−4.58130	−	23.9172i	−0.244184	−	1.27479i
$353$	9.53936	+	9.53936i	0.507729	+	0.507729i	0.913829	−	0.406100i	$-0.133111\pi$
$353$	9.53936	+	9.53936i	0.507729	+	0.507729i	−0.406100	+	0.913829i	$0.633111\pi$
$354$	4.22862	−	1.27619i	0.224749	−	0.0678288i
$355$	3.67450	−	0.361907i	0.195022	−	0.0192080i
$356$	−14.6147	+	6.00509i	−0.774579	+	0.318269i
$357$	2.52223	−	4.71875i	0.133490	−	0.249743i
$358$	12.6808	+	30.7374i	0.670201	+	1.62452i
$359$	0.0122833	−	0.00820747i	0.000648290	−	0.000433174i	−0.555246	−	0.831686i	$-0.687376\pi$
$359$	0.0122833	−	0.00820747i	0.000648290	−	0.000433174i	0.555894	+	0.831253i	$0.312376\pi$
$360$	8.63211	+	5.82109i	0.454952	+	0.306798i
$361$	0.320792	−	0.480099i	0.0168838	−	0.0252684i
$362$	−25.3358	+	16.8769i	−1.33162	+	0.887029i
$363$	−6.97667	−	8.50109i	−0.366180	−	0.446192i
$364$	−0.866241	+	1.04943i	−0.0454034	+	0.0550052i
$365$	−21.5290	−	40.2778i	−1.12688	−	2.10824i
$366$	−9.10313	+	11.0602i	−0.475828	+	0.578124i
$367$	−1.65836	−	4.00363i	−0.0865655	−	0.208988i	0.874668	−	0.484722i	$-0.161079\pi$
$367$	−1.65836	−	4.00363i	−0.0865655	−	0.208988i	−0.961234	+	0.275734i	$0.911079\pi$
$368$	−29.5313	+	19.4907i	−1.53943	+	1.01602i
$369$	−1.29613	+	3.12913i	−0.0674737	+	0.162896i
$370$	−24.3596	−	45.7295i	−1.26639	−	2.37736i
$371$	−5.64676	−	1.71293i	−0.293165	−	0.0889306i
$372$	−4.78340	−	0.484832i	−0.248008	−	0.0251374i
$373$	−2.55405	+	25.9317i	−0.132244	+	1.34269i	0.668512	+	0.743701i	$0.266932\pi$
$373$	−2.55405	+	25.9317i	−0.132244	+	1.34269i	−0.800756	+	0.598991i	$0.795568\pi$
$374$	−12.4206	+	18.5318i	−0.642255	+	0.958256i
$375$	9.64192	+	48.4732i	0.497907	+	2.50315i
$376$	−17.0935	−	14.1504i	−0.881528	−	0.729752i
$377$	−2.58778	−	0.514742i	−0.133278	−	0.0265106i
$378$	−0.0113312	+	7.98721i	−0.000582816	+	0.410818i
$379$	−5.22459	−	17.2232i	−0.268369	−	0.884694i	−0.982750	−	0.184938i	$-0.940792\pi$
$379$	−5.22459	−	17.2232i	−0.268369	−	0.884694i	0.714381	−	0.699757i	$-0.246708\pi$
$380$	20.1379	+	30.3245i	1.03305	+	1.55561i
$381$	−13.2988	−	10.9140i	−0.681316	−	0.559141i
$382$	−7.42926	−	9.07881i	−0.380114	−	0.464512i
$383$	1.34117			0.0685305			0.0342653	−	0.999413i	$-0.489091\pi$
$383$	1.34117			0.0685305			0.0342653	+	0.999413i	$0.489091\pi$
$384$	−9.31361	+	13.6435i	−0.475283	+	0.696244i
$385$	−18.2549			−0.930357
$386$	10.3991	+	12.7080i	0.529298	+	0.646821i
$387$	−0.534292	−	0.438482i	−0.0271596	−	0.0222893i
$388$	−10.9456	+	7.26879i	−0.555679	+	0.369017i
$389$	5.42894	+	17.8968i	0.275258	+	0.907404i	0.980178	+	0.198118i	$0.0634828\pi$
$389$	5.42894	+	17.8968i	0.275258	+	0.907404i	−0.704920	+	0.709287i	$0.749017\pi$
$390$	0.00845198	−	5.95767i	0.000427983	−	0.301678i
$391$	31.7924	+	6.32390i	1.60781	+	0.319813i
$392$	−0.265252	−	2.81596i	−0.0133972	−	0.142228i
$393$	5.19801	+	26.1322i	0.262205	+	1.31819i
$394$	−16.9785	+	25.3322i	−0.855364	+	1.27622i
$395$	−0.620333	+	6.29835i	−0.0312124	+	0.316904i
$396$	0.753650	−	7.43560i	0.0378723	−	0.373653i
$397$	1.49976	+	0.454946i	0.0752706	+	0.0228331i	0.327695	−	0.944783i	$-0.393728\pi$
$397$	1.49976	+	0.454946i	0.0752706	+	0.0228331i	−0.252425	+	0.967617i	$0.581228\pi$
$398$	4.51155	+	8.46940i	0.226144	+	0.424533i
$399$	−2.39830	+	5.79001i	−0.120065	+	0.289863i
$400$	50.9874	−	9.84158i	2.54937	−	0.492079i
$401$	−6.27061	−	15.1386i	−0.313139	−	0.755986i	−0.999585	−	0.0288044i	$-0.990830\pi$
$401$	−6.27061	−	15.1386i	−0.313139	−	0.755986i	0.686446	−	0.727181i	$-0.259170\pi$
$402$	1.00933	−	1.22632i	0.0503407	−	0.0611631i
$403$	−0.528054	−	0.987919i	−0.0263042	−	0.0492117i
$404$	−10.1465	−	8.37532i	−0.504808	−	0.416688i
$405$	−15.1788	−	18.4954i	−0.754241	−	0.919045i
$406$	4.56429	−	3.04040i	0.226522	−	0.150893i
$407$	−20.6633	+	30.9248i	−1.02424	+	1.53289i
$408$	14.8553	−	2.88922i	0.735445	−	0.143038i
$409$	−32.0532	+	21.4173i	−1.58493	+	1.05902i	−0.624300	+	0.781184i	$0.714616\pi$
$409$	−32.0532	+	21.4173i	−1.58493	+	1.05902i	−0.960630	+	0.277832i	$0.910384\pi$
$410$	8.92374	+	21.6306i	0.440712	+	1.06826i
$411$	−14.5086	+	27.1436i	−0.715656	+	1.33890i
$412$	−12.7368	−	30.9978i	−0.627497	−	1.52715i
$413$	−2.12877	+	0.209665i	−0.104750	+	0.0103170i
$414$	−10.3961	+	3.13754i	−0.510942	+	0.154201i
$415$	−35.9033	−	35.9033i	−1.76243	−	1.76243i
$416$	−3.84873	−	0.0273009i	−0.188699	−	0.00133853i
$417$	16.3650	−	16.3650i	0.801396	−	0.801396i
$418$	12.3506	−	23.0276i	0.604086	−	1.12632i
$419$	0.425305	+	4.31820i	0.0207775	+	0.210958i	0.999968	+	0.00801388i	$0.00255092\pi$
$419$	0.425305	+	4.31820i	0.0207775	+	0.210958i	−0.979190	+	0.202944i	$0.934949\pi$
$420$	8.73149	+	8.78117i	0.426053	+	0.428477i
$421$	−15.4119	−	8.23785i	−0.751131	−	0.401488i	0.0509513	−	0.998701i	$-0.483775\pi$
$421$	−15.4119	−	8.23785i	−0.751131	−	0.401488i	−0.802083	+	0.597213i	$0.796275\pi$
$422$	−10.6026	+	25.4945i	−0.516125	+	1.24105i
$423$	−3.78362	−	5.66259i	−0.183966	−	0.275325i
$424$	−6.32135	−	15.4467i	−0.306992	−	0.750158i
$425$	−39.5550	−	26.4298i	−1.91870	−	1.28203i
$426$	−0.353264	+	1.76290i	−0.0171157	+	0.0854129i
$427$	5.36246	−	4.40086i	0.259508	−	0.212973i
$428$	29.7606	−	15.7990i	1.43853	−	0.763673i
$429$	−3.77164	+	2.01599i	−0.182097	+	0.0973327i
$430$	−4.75277	+	0.461300i	−0.229199	+	0.0222459i
$431$	19.2592	−	7.97744i	0.927685	−	0.384260i	0.132885	−	0.991131i	$-0.457576\pi$
$431$	19.2592	−	7.97744i	0.927685	−	0.384260i	0.794800	+	0.606872i	$0.207576\pi$
$432$	−17.5443	+	14.2324i	−0.844102	+	0.684758i
$433$	−14.9030	−	6.17301i	−0.716191	−	0.296656i	−0.00532710	−	0.999986i	$-0.501696\pi$
$433$	−14.9030	−	6.17301i	−0.716191	−	0.296656i	−0.710864	+	0.703330i	$0.751696\pi$
$434$	2.22716	+	0.679052i	0.106907	+	0.0325956i
$435$	−6.97001	+	22.9771i	−0.334187	+	1.10167i
$436$	8.44209	−	2.53475i	0.404303	−	0.121392i
$437$	−37.7850	−	3.72149i	−1.80750	−	0.178023i
$438$	21.8180	−	4.30770i	1.04250	−	0.205830i
$439$	−1.34897	+	0.268326i	−0.0643826	+	0.0128065i	−0.227177	−	0.973854i	$-0.572949\pi$
$439$	−1.34897	+	0.268326i	−0.0643826	+	0.0128065i	0.162794	+	0.986660i	$0.447949\pi$
$440$	−32.5853	−	40.0517i	−1.55344	−	1.90939i
$441$	0.169349	−	0.851373i	0.00806422	−	0.0405416i
$442$	2.48969	+	2.49676i	0.118423	+	0.118759i
$443$	7.17759	−	2.17730i	0.341018	−	0.103447i	−0.115131	−	0.993350i	$-0.536729\pi$
$443$	7.17759	−	2.17730i	0.341018	−	0.103447i	0.456148	+	0.889904i	$0.349229\pi$
$444$	24.7592	−	4.85193i	1.17502	−	0.230262i
$445$	−21.2528	+	25.8966i	−1.00748	+	1.22762i
$446$	1.79110	−	17.9246i	0.0848109	−	0.848754i
$447$			15.0817i			0.713341i
$448$	5.70480	−	5.60850i	0.269526	−	0.264977i
$449$		−	25.2135i		−	1.18990i	−0.803763	−	0.594949i	$-0.797172\pi$
$449$		−	25.2135i		−	1.18990i	0.803763	−	0.594949i	$-0.202828\pi$
$450$	15.8580	+	1.58460i	0.747555	+	0.0746987i
$451$	10.6557	−	12.9839i	0.501755	−	0.611390i
$452$	14.6354	+	9.83921i	0.688389	+	0.462798i
$453$	17.1142	−	5.19154i	0.804096	−	0.243920i
$454$	−4.00280	+	3.99146i	−0.187861	+	0.187328i
$455$	−0.562872	+	2.82975i	−0.0263878	+	0.132661i
$456$	−16.9844	+	5.07332i	−0.795367	+	0.237580i
$457$	19.5600	−	3.89072i	0.914976	−	0.182000i	0.284921	−	0.958551i	$-0.408033\pi$
$457$	19.5600	−	3.89072i	0.914976	−	0.182000i	0.630055	+	0.776551i	$0.283033\pi$
$458$	−7.46921	−	37.8306i	−0.349013	−	1.76771i
$459$	20.5965	+	2.02858i	0.961363	+	0.0946859i
$460$	−35.5529	+	66.0632i	−1.65766	+	3.08021i
$461$	−7.94972	+	26.2067i	−0.370255	+	1.22057i	0.551953	+	0.833875i	$0.313883\pi$
$461$	−7.94972	+	26.2067i	−0.370255	+	1.22057i	−0.922208	+	0.386693i	$0.873617\pi$
$462$	2.59246	−	8.50276i	0.120612	−	0.395584i
$463$	−9.60738	−	3.97951i	−0.446493	−	0.184943i	0.148097	−	0.988973i	$-0.452685\pi$
$463$	−9.60738	−	3.97951i	−0.446493	−	0.184943i	−0.594589	+	0.804030i	$0.702685\pi$
$464$	14.8180	+	4.58698i	0.687909	+	0.212945i
$465$	−9.41808	+	3.90110i	−0.436753	+	0.180909i
$466$	0.205807	+	2.12043i	0.00953385	+	0.0982272i
$467$	−12.5289	+	6.69682i	−0.579767	+	0.309892i	−0.735088	−	0.677972i	$-0.762859\pi$
$467$	−12.5289	+	6.69682i	−0.579767	+	0.309892i	0.155320	+	0.987864i	$0.450359\pi$
$468$	−1.12938	−	0.346095i	−0.0522054	−	0.0159982i
$469$	−0.594574	+	0.487954i	−0.0274549	+	0.0225316i
$470$	−46.1328	−	9.24443i	−2.12795	−	0.426414i
$471$	−7.79603	−	5.20914i	−0.359222	−	0.240024i
$472$	−4.25989	−	4.29630i	−0.196077	−	0.197753i
$473$	1.90434	+	2.85005i	0.0875619	+	0.131046i
$474$	−2.84554	−	1.18340i	−0.130700	−	0.0543552i
$475$	49.1418	+	26.2668i	2.25478	+	1.20521i
$476$	−7.32888	−	0.0207946i	−0.335919	−	0.000953118i
$477$	−0.502068	−	5.09758i	−0.0229881	−	0.233402i
$478$	2.59211	+	1.39025i	0.118561	+	0.0635884i
$479$	2.83637	−	2.83637i	0.129597	−	0.129597i	−0.639333	−	0.768930i	$-0.720789\pi$
$479$	2.83637	−	2.83637i	0.129597	−	0.129597i	0.768930	+	0.639333i	$0.220789\pi$
$480$	−3.68026	+	34.8316i	−0.167980	+	1.58984i
$481$	4.15662	+	4.15662i	0.189525	+	0.189525i
$482$	0.654167	+	2.16756i	0.0297965	+	0.0987298i
$483$	−12.8538	+	1.26599i	−0.584869	+	0.0576045i
$484$	−5.80409	+	13.9006i	−0.263822	+	0.631846i
$485$	−13.1326	+	24.5693i	−0.596320	+	1.11564i
$486$	−11.3803	+	4.69496i	−0.516220	+	0.212968i
$487$	9.29361	−	6.20979i	0.421134	−	0.281393i	−0.326893	−	0.945061i	$-0.606002\pi$
$487$	9.29361	−	6.20979i	0.421134	−	0.281393i	0.748027	+	0.663669i	$0.231002\pi$
$488$	19.2277	+	3.90976i	0.870395	+	0.176987i
$489$	−1.88021	+	2.81393i	−0.0850261	+	0.127250i
$490$	−3.32469	−	4.99106i	−0.150194	−	0.225473i
$491$	25.3766	+	30.9214i	1.14523	+	1.39547i	0.905352	+	0.424662i	$0.139607\pi$
$491$	25.3766	+	30.9214i	1.14523	+	1.39547i	0.239877	+	0.970803i	$0.422893\pi$
$492$	−11.3424	+	1.08464i	−0.511353	+	0.0488994i
$493$	−6.69879	−	12.5326i	−0.301698	−	0.564438i
$494$	−3.18877	−	2.62453i	−0.143469	−	0.118083i
$495$	−6.06409	−	14.6400i	−0.272560	−	0.658019i
$496$	2.48565	+	6.09854i	0.111609	+	0.273833i
$497$	0.333207	−	0.804433i	0.0149464	−	0.0360837i
$498$	21.8218	−	11.6242i	0.977859	−	0.520894i
$499$	3.46751	+	1.05186i	0.155227	+	0.0470877i	0.366942	−	0.930244i	$-0.380405\pi$
$499$	3.46751	+	1.05186i	0.155227	+	0.0470877i	−0.211715	+	0.977332i	$0.567905\pi$
$500$	52.4521	−	42.7979i	2.34573	−	1.91398i
$501$	0.0766794	−	0.778539i	0.00342578	−	0.0347826i
$502$	32.8709	+	22.0311i	1.46710	+	0.983298i
$503$	0.0726651	+	0.365312i	0.00323998	+	0.0162885i	0.982371	−	0.186939i	$-0.0598568\pi$
$503$	0.0726651	+	0.365312i	0.00323998	+	0.0162885i	−0.979131	+	0.203228i	$0.934857\pi$
$504$	2.17022	−	1.14816i	0.0966692	−	0.0511430i
$505$	−27.3596	−	5.44217i	−1.21749	−	0.242173i
$506$	53.8535	+	0.0764004i	2.39408	+	0.00339641i
$507$	−5.31384	−	17.5174i	−0.235996	−	0.777975i
$508$	−4.66286	+	23.0991i	−0.206881	+	1.02486i
$509$	−2.42944	−	1.99379i	−0.107683	−	0.0883731i	0.579011	−	0.815320i	$-0.303439\pi$
$509$	−2.42944	−	1.99379i	−0.107683	−	0.0883731i	−0.686694	+	0.726947i	$0.740939\pi$
$510$	24.8327	−	20.3208i	1.09961	−	0.899818i
$511$	−10.7700			−0.476437
$512$	22.4883	+	2.50520i	0.993852	+	0.110715i
$513$	−24.2413			−1.07028
$514$	−20.8865	+	17.0916i	−0.921263	+	0.753877i
$515$	−54.9267	−	45.0772i	−2.42036	−	1.98634i
$516$	0.460098	−	2.27925i	0.0202547	−	0.100339i
$517$	9.80407	+	32.3197i	0.431183	+	1.42142i
$518$	−12.2185	−	0.0173340i	−0.536848	−	0.000761612i
$519$	−14.4629	−	2.87685i	−0.634850	−	0.126280i
$520$	−7.21326	+	3.81619i	−0.316322	+	0.167351i
$521$	3.85724	+	19.3917i	0.168989	+	0.849564i	0.968519	+	0.248939i	$0.0800817\pi$
$521$	3.85724	+	19.3917i	0.168989	+	0.849564i	−0.799530	+	0.600625i	$0.794918\pi$
$522$	3.95454	+	2.65046i	0.173085	+	0.116007i
$523$	1.66600	−	16.9152i	0.0728491	−	0.739649i	−0.887492	−	0.460822i	$-0.847554\pi$
$523$	1.66600	−	16.9152i	0.0728491	−	0.739649i	0.960341	−	0.278827i	$-0.0899455\pi$
$524$	28.2772	−	23.0726i	1.23530	−	1.00793i
$525$	18.1392	+	5.50248i	0.791661	+	0.240148i
$526$	4.36342	−	2.32434i	0.190254	−	0.101346i
$527$	2.30880	−	5.57395i	0.100573	−	0.242805i
$528$	23.2828	−	9.48963i	1.01325	−	0.412983i
$529$	−21.1430	−	51.0436i	−0.919259	−	2.21929i
$530$	−27.3230	−	22.4884i	−1.18684	−	0.976833i
$531$	−0.875300	−	1.63757i	−0.0379848	−	0.0710645i
$532$	8.54533	−	0.817167i	0.370487	−	0.0354287i
$533$	−1.68412	−	2.05211i	−0.0729475	−	0.0888868i
$534$	−9.04389	−	13.5768i	−0.391368	−	0.587526i
$535$	39.6904	−	59.4009i	1.71597	−	2.56812i
$536$	−2.13190	−	0.433503i	−0.0920842	−	0.0187245i
$537$	−28.5442	+	19.0726i	−1.23177	+	0.823043i
$538$	14.6021	−	6.02411i	0.629539	−	0.259718i
$539$	−2.02930	+	3.79655i	−0.0874081	+	0.163529i
$540$	−18.4558	+	44.2012i	−0.794213	+	1.90212i
$541$	−24.5464	+	2.41761i	−1.05533	+	0.103941i	−0.610771	−	0.791807i	$-0.709140\pi$
$541$	−24.5464	+	2.41761i	−1.05533	+	0.103941i	−0.444561	+	0.895749i	$0.646640\pi$
$542$	−2.70853	−	8.97464i	−0.116341	−	0.385494i
$543$	−22.2247	−	22.2247i	−0.953751	−	0.953751i
$544$	−13.0365	−	16.1168i	−0.558936	−	0.691003i
$545$	13.2151	−	13.2151i	0.566071	−	0.566071i
$546$	−1.23810	−	0.664039i	−0.0529859	−	0.0284183i
$547$	1.22115	+	12.3986i	0.0522127	+	0.530124i	0.985343	+	0.170586i	$0.0545659\pi$
$547$	1.22115	+	12.3986i	0.0522127	+	0.530124i	−0.933130	+	0.359539i	$0.882934\pi$
$548$	42.1578	+	0.119617i	1.80089	+	0.00510976i
$549$	5.31074	+	2.83865i	0.226657	+	0.121151i
$550$	−72.9760	−	30.3490i	−3.11171	−	1.29409i
$551$	9.24730	+	13.8396i	0.393948	+	0.589585i
$552$	−25.7218	−	25.9417i	−1.09479	−	1.10415i
$553$	1.24093	+	0.829166i	0.0527699	+	0.0352597i
$554$	2.02649	+	0.406082i	0.0860971	+	0.0172528i
$555$	41.3520	−	33.9367i	1.75529	−	1.44053i
$556$	−30.3097	−	9.28833i	−1.28542	−	0.393913i
$557$	19.0021	−	10.1568i	0.805144	−	0.430358i	−0.0168476	−	0.999858i	$-0.505363\pi$
$557$	19.0021	−	10.1568i	0.805144	−	0.430358i	0.821992	+	0.569500i	$0.192863\pi$
$558$	0.195254	+	2.01170i	0.00826575	+	0.0851620i
$559$	0.500514	−	0.207319i	0.0211695	−	0.00876868i
$560$	5.01588	−	16.2036i	0.211960	−	0.684725i
$561$	−21.2800	−	8.81447i	−0.898443	−	0.372147i
$562$	11.3322	−	37.1673i	0.478019	−	1.56781i
$563$	−3.65330	+	12.0433i	−0.153968	+	0.507566i	−0.999659	−	0.0261076i	$-0.991689\pi$
$563$	−3.65330	+	12.0433i	−0.153968	+	0.507566i	0.845691	+	0.533673i	$0.179189\pi$
$564$	10.8574	−	20.1748i	0.457179	−	0.849514i
$565$	37.2115	+	3.66501i	1.56550	+	0.154188i
$566$	−4.23952	−	21.4727i	−0.178200	−	0.902564i
$567$	−5.53391	+	1.10076i	−0.232402	+	0.0462277i
$568$	2.35972	−	0.704860i	0.0990117	−	0.0295753i
$569$	−4.36314	+	21.9350i	−0.182912	+	0.919563i	0.774881	+	0.632107i	$0.217810\pi$
$569$	−4.36314	+	21.9350i	−0.182912	+	0.919563i	−0.957794	+	0.287456i	$0.907190\pi$
$570$	−26.6133	+	26.5379i	−1.11471	+	1.11155i
$571$	−24.9559	+	7.57029i	−1.04437	+	0.316807i	−0.765442	−	0.643505i	$-0.777480\pi$
$571$	−24.9559	+	7.57029i	−1.04437	+	0.316807i	−0.278930	+	0.960312i	$0.589980\pi$
$572$	4.86142	+	3.26829i	0.203266	+	0.136654i
$573$	7.68370	−	9.36262i	0.320991	−	0.391129i
$574$	5.49060	+	0.548643i	0.229173	+	0.0228999i
$575$			114.838i			4.78908i
$576$	6.39295	+	2.71203i	0.266373	+	0.113001i
$577$			20.4058i			0.849506i	0.905309	+	0.424753i	$0.139639\pi$
$577$			20.4058i			0.849506i	−0.905309	+	0.424753i	$0.860361\pi$
$578$	0.502241	−	5.02623i	0.0208905	−	0.209064i
$579$	−10.7552	+	13.1053i	−0.446971	+	0.544636i
$580$	32.2752	−	6.32478i	1.34015	−	0.262622i
$581$	−11.4581	+	3.47579i	−0.475364	+	0.144200i
$582$	−9.57887	−	9.60609i	−0.397057	−	0.398185i
$583$	−4.95575	+	24.9142i	−0.205246	+	1.03184i
$584$	−19.2246	−	23.6296i	−0.795520	−	0.977800i
$585$	−2.45637	+	0.488602i	−0.101558	+	0.0202012i
$586$	−42.1972	+	8.33132i	−1.74315	+	0.344164i
$587$	20.7884	+	2.04748i	0.858028	+	0.0845084i	0.517456	−	0.855710i	$-0.326879\pi$
$587$	20.7884	+	2.04748i	0.858028	+	0.0845084i	0.340572	+	0.940218i	$0.389379\pi$
$588$	2.79689	−	0.839768i	0.115342	−	0.0346315i
$589$	−2.05134	+	6.76236i	−0.0845240	+	0.278638i
$590$	−12.2704	−	3.74119i	−0.505163	−	0.154022i
$591$	−29.0890	−	12.0490i	−1.19656	−	0.495631i
$592$	−21.7721	−	26.8385i	−0.894827	−	1.10306i
$593$	12.4457	−	5.15518i	0.511084	−	0.211698i	−0.112212	−	0.993684i	$-0.535793\pi$
$593$	12.4457	−	5.15518i	0.511084	−	0.211698i	0.623295	+	0.781987i	$0.285793\pi$
$594$	34.2231	−	3.32166i	1.40419	−	0.136289i
$595$	−13.7044	+	7.32515i	−0.561825	+	0.300302i
$596$	18.2465	−	9.68648i	0.747405	−	0.396774i
$597$	−7.65866	+	6.28530i	−0.313448	+	0.257240i
$598$	1.67236	−	8.34563i	0.0683879	−	0.341278i
$599$	36.9682	+	24.7013i	1.51048	+	1.00927i	0.987623	+	0.156849i	$0.0501336\pi$
$599$	36.9682	+	24.7013i	1.51048	+	1.00927i	0.522856	+	0.852421i	$0.324866\pi$
$600$	20.3062	+	49.6199i	0.828999	+	2.02572i
$601$	8.52329	+	12.7560i	0.347672	+	0.520329i	0.963555	−	0.267509i	$-0.0862006\pi$
$601$	8.52329	+	12.7560i	0.347672	+	0.520329i	−0.615883	+	0.787838i	$0.711201\pi$
$602$	−0.432401	+	1.03973i	−0.0176233	+	0.0423764i
$603$	−0.588838	−	0.314741i	−0.0239794	−	0.0128172i
$604$	−17.2728	−	17.3711i	−0.702821	−	0.706821i
$605$	3.13057	+	31.7852i	0.127276	+	1.29225i
$606$	6.42031	−	11.9707i	0.260807	−	0.486276i
$607$	13.8404	−	13.8404i	0.561765	−	0.561765i	−0.368044	−	0.929809i	$-0.619972\pi$
$607$	13.8404	−	13.8404i	0.561765	−	0.561765i	0.929809	+	0.368044i	$0.119972\pi$
$608$	17.0464	+	17.2900i	0.691323	+	0.701201i
$609$	4.00381	+	4.00381i	0.162243	+	0.162243i
$610$	39.8278	−	12.0199i	1.61258	−	0.486673i
$611$	5.31227	−	0.523213i	0.214911	−	0.0211669i
$612$	−2.41790	−	5.88449i	−0.0977377	−	0.237866i
$613$	12.3686	−	23.1400i	0.499562	−	0.934615i	−0.498155	−	0.867088i	$-0.665989\pi$
$613$	12.3686	−	23.1400i	0.499562	−	0.934615i	0.997717	−	0.0675271i	$-0.0215109\pi$
$614$	17.2938	+	41.9191i	0.697922	+	1.69172i
$615$	−20.0871	+	13.4218i	−0.809990	+	0.541218i
$616$	−11.9520	+	2.32457i	−0.481561	+	0.0936596i
$617$	2.53488	−	3.79372i	0.102051	−	0.152729i	−0.776930	−	0.629587i	$-0.783224\pi$
$617$	2.53488	−	3.79372i	0.102051	−	0.152729i	0.878981	+	0.476857i	$0.158224\pi$
$618$	28.7964	−	19.1821i	1.15836	−	0.771617i
$619$	23.1677	+	28.2300i	0.931190	+	1.13466i	0.990650	+	0.136428i	$0.0435622\pi$
$619$	23.1677	+	28.2300i	0.931190	+	1.13466i	−0.0594599	+	0.998231i	$0.518938\pi$
$620$	10.7686	+	8.88883i	0.432478	+	0.356984i
$621$	−23.5509	−	44.0606i	−0.945064	−	1.76809i
$622$	2.49512	−	3.03153i	0.100045	−	0.121553i
$623$	3.02327	+	7.29881i	0.121125	+	0.292421i
$624$	−0.753113	−	3.90174i	−0.0301486	−	0.156195i
$625$	30.0885	−	72.6401i	1.20354	−	2.90560i
$626$	−18.1940	−	34.1551i	−0.727179	−	1.36511i
$627$	25.8171	+	7.83154i	1.03104	+	0.312761i
$628$	−1.29510	+	12.7776i	−0.0516801	+	0.509882i
$629$	−3.10322	+	31.5076i	−0.123734	+	1.25629i
$630$	2.89829	−	4.32430i	0.115470	−	0.172284i
$631$	2.06922	+	10.4027i	0.0823743	+	0.414124i	0.999866	+	0.0163688i	$0.00521057\pi$
$631$	2.06922	+	10.4027i	0.0823743	+	0.414124i	−0.917492	+	0.397755i	$0.869789\pi$
$632$	0.395878	+	4.20271i	0.0157472	+	0.167175i
$633$	−27.9598	−	5.56155i	−1.11130	−	0.221052i
$634$	−0.0184205	+	12.9843i	−0.000731572	+	0.515674i
$635$	14.5038	+	47.8126i	0.575566	+	1.89739i
$636$	14.3549	−	9.53283i	0.569208	−	0.378001i
$637$	0.525943	+	0.431630i	0.0208386	+	0.0171018i
$638$	−14.9514	−	18.2711i	−0.591931	−	0.723361i
$639$	0.755823			0.0298999
$640$	44.5043	−	17.9186i	1.75919	−	0.708296i
$641$	7.58085			0.299426			0.149713	−	0.988730i	$-0.452165\pi$
$641$	7.58085			0.299426			0.149713	+	0.988730i	$0.452165\pi$
$642$	22.0311	+	26.9228i	0.869498	+	1.06256i
$643$	19.5412	+	16.0371i	0.770632	+	0.632441i	0.935279	−	0.353911i	$-0.115149\pi$
$643$	19.5412	+	16.0371i	0.770632	+	0.632441i	−0.164647	+	0.986353i	$0.552649\pi$
$644$	9.78721	+	14.7380i	0.385670	+	0.580757i
$645$	−1.43113	−	4.71782i	−0.0563508	−	0.185764i
$646$	0.0315559	−	22.2433i	0.00124155	−	0.875151i
$647$	−16.6437	−	3.31064i	−0.654331	−	0.130155i	−0.143249	−	0.989687i	$-0.545755\pi$
$647$	−16.6437	−	3.31064i	−0.654331	−	0.130155i	−0.511082	+	0.859532i	$0.670755\pi$
$648$	−12.2932	−	10.1766i	−0.482923	−	0.399776i
$649$	1.79647	+	9.03145i	0.0705175	+	0.354516i
$650$	−6.95463	+	10.3764i	−0.272783	+	0.406997i
$651$	−0.235629	+	2.39238i	−0.00923502	+	0.0937648i
$652$	4.61201	+	0.467459i	0.180620	+	0.0183071i
$653$	43.5018	+	13.1961i	1.70236	+	0.516404i	0.983832	−	0.179096i	$-0.0573174\pi$
$653$	43.5018	+	13.1961i	1.70236	+	0.516404i	0.718525	+	0.695501i	$0.244817\pi$
$654$	4.27857	+	8.03203i	0.167305	+	0.314077i
$655$	29.6124	−	71.4906i	1.15705	−	2.79337i
$656$	8.59706	+	13.0258i	0.335659	+	0.508573i
$657$	−3.57768	−	8.63728i	−0.139579	−	0.336972i
$658$	−7.05093	+	8.56677i	−0.274874	+	0.333967i
$659$	−23.9473	−	44.8022i	−0.932853	−	1.74525i	−0.594154	−	0.804351i	$-0.702513\pi$
$659$	−23.9473	−	44.8022i	−0.932853	−	1.74525i	−0.338699	−	0.940895i	$-0.609987\pi$
$660$	33.9355	−	41.1121i	1.32094	−	1.60029i
$661$	5.85356	+	7.13259i	0.227677	+	0.277425i	0.874302	−	0.485383i	$-0.161320\pi$
$661$	5.85356	+	7.13259i	0.227677	+	0.277425i	−0.646624	+	0.762809i	$0.723820\pi$
$662$	−2.25108	+	1.49951i	−0.0874908	+	0.0582801i
$663$	−2.02251	+	3.02689i	−0.0785476	+	0.117555i
$664$	−28.0789	−	18.9351i	−1.08967	−	0.734823i
$665$	15.1336	−	10.1119i	0.586856	−	0.392125i
$666$	−4.04494	−	9.80467i	−0.156738	−	0.379923i
$667$	−16.1706	+	30.2531i	−0.626130	+	1.17141i
$668$	−0.991156	+	0.407260i	−0.0383490	+	0.0157573i
$669$	18.5090	−	1.82298i	0.715600	−	0.0704805i
$670$	−4.41598	+	1.33274i	−0.170604	+	0.0514881i
$671$	−21.1166	−	21.1166i	−0.815196	−	0.815196i
$672$	6.83495	+	4.63743i	0.263664	+	0.178893i
$673$	−8.79758	+	8.79758i	−0.339122	+	0.339122i	−0.856037	−	0.516915i	$-0.827080\pi$
$673$	−8.79758	+	8.79758i	−0.339122	+	0.339122i	0.516915	+	0.856037i	$0.327080\pi$
$674$	2.07175	−	3.86277i	0.0798006	−	0.148788i
$675$	7.18669	+	72.9676i	0.276616	+	2.80853i
$676$	−17.7803	+	17.6797i	−0.683859	+	0.679990i
$677$	−10.4231	−	5.57126i	−0.400592	−	0.214121i	0.258782	−	0.965936i	$-0.416679\pi$
$677$	−10.4231	−	5.57126i	−0.400592	−	0.214121i	−0.659374	+	0.751815i	$0.729179\pi$
$678$	−6.99166	+	16.8119i	−0.268513	+	0.645655i
$679$	3.64991	+	5.46247i	0.140071	+	0.209631i
$680$	−40.5340	−	16.9922i	−1.55441	−	0.651622i
$681$	−4.85270	−	3.24247i	−0.185956	−	0.124252i
$682$	1.96940	−	9.82796i	0.0754123	−	0.376332i
$683$	−38.6469	+	31.7167i	−1.47878	+	1.21361i	−0.554338	+	0.832292i	$0.687028\pi$
$683$	−38.6469	+	31.7167i	−1.47878	+	1.21361i	−0.924446	+	0.381314i	$0.875472\pi$
$684$	3.49401	+	6.58169i	0.133597	+	0.251657i
$685$	78.8316	−	42.1364i	3.01200	−	1.60995i
$686$	−1.40760	+	0.136620i	−0.0537424	+	0.00521619i
$687$	36.7821	−	15.2356i	1.40332	−	0.581276i
$688$	−3.05304	+	0.907242i	−0.116396	+	0.0345883i
$689$	3.70922	+	1.53641i	0.141310	+	0.0585326i
$690$	−74.0903	−	22.5899i	−2.82057	−	0.859982i
$691$	2.09463	−	6.90508i	0.0796836	−	0.262682i	−0.908042	−	0.418878i	$-0.862423\pi$
$691$	2.09463	−	6.90508i	0.0796836	−	0.262682i	0.987726	+	0.156197i	$0.0499234\pi$
$692$	5.80850	+	19.3455i	0.220806	+	0.735405i
$693$	−3.71885	−	0.366275i	−0.141267	−	0.0139136i
$694$	−16.8209	+	3.32108i	−0.638513	+	0.126067i
$695$	−65.9229	+	13.1129i	−2.50060	+	0.497400i
$696$	−1.63759	+	15.9313i	−0.0620726	+	0.603875i
$697$	2.78938	−	14.0231i	0.105655	−	0.531164i
$698$	33.9628	+	34.0593i	1.28551	+	1.28916i
$699$	−2.10484	+	0.638496i	−0.0796123	+	0.0241501i
$700$	−4.99310	−	25.4796i	−0.188722	−	0.963040i
$701$	−26.3886	+	32.1546i	−0.996683	+	1.21446i	−0.0199942	+	0.999800i	$0.506365\pi$
$701$	−26.3886	+	32.1546i	−0.996683	+	1.21446i	−0.976689	+	0.214661i	$0.931135\pi$
$702$	0.540333	−	5.40744i	0.0203935	−	0.204091i
$703$		−	37.0832i		−	1.39862i
$704$	−26.4347	−	22.0736i	−0.996295	−	0.831931i
$705$		−	48.5771i		−	1.82952i
$706$	18.9842	+	1.89698i	0.714479	+	0.0713937i
$707$	−4.17325	+	5.08512i	−0.156951	+	0.191245i
$708$	3.48514	−	5.18398i	0.130980	−	0.194826i
$709$	−5.87773	+	1.78299i	−0.220743	+	0.0669616i	−0.398719	−	0.917073i	$-0.630545\pi$
$709$	−5.87773	+	1.78299i	−0.220743	+	0.0669616i	0.177976	+	0.984035i	$0.443045\pi$
$710$	3.69752	−	3.68704i	0.138765	−	0.138372i
$711$	−0.252746	+	1.27064i	−0.00947871	+	0.0476527i
$712$	−10.6172	+	19.6616i	−0.397895	+	0.736849i
$713$	−14.2841	+	2.84128i	−0.534943	+	0.106407i
$714$	−1.46568	−	7.42350i	−0.0548517	−	0.277817i
$715$	12.3605	+	1.21741i	0.462257	+	0.0455284i
$716$	41.4077	+	22.2842i	1.54748	+	0.832799i
$717$	−0.881560	+	2.90611i	−0.0329224	+	0.108531i
$718$	0.00609306	−	0.0199840i	0.000227391	−	0.000745797i
$719$	−18.8880	−	7.82365i	−0.704402	−	0.291773i	0.00158409	−	0.999999i	$-0.499496\pi$
$719$	−18.8880	−	7.82365i	−0.704402	−	0.291773i	−0.705986	+	0.708226i	$0.749496\pi$
$720$	14.6611	−	1.36003i	0.546386	−	0.0506854i
$721$	−15.4808	+	6.41235i	−0.576534	+	0.238808i
$722$	−0.0788861	−	0.812763i	−0.00293584	−	0.0302479i
$723$	−2.06160	+	1.10195i	−0.0766716	+	0.0409818i
$724$	−12.6141	+	41.1624i	−0.468801	+	1.52979i
$725$	38.9163	−	31.9378i	1.44532	−	1.18614i
$726$	−15.2495	−	3.05581i	−0.565962	−	0.113412i
$727$	5.23986	+	3.50117i	0.194336	+	0.129851i	0.648931	−	0.760847i	$-0.275216\pi$
$727$	5.23986	+	3.50117i	0.194336	+	0.129851i	−0.454596	+	0.890698i	$0.650216\pi$
$728$	−0.00819030	+	1.92440i	−0.000303553	+	0.0713228i
$729$	−16.4656	−	24.6425i	−0.609837	−	0.912685i
$730$	−59.6363	−	24.8014i	−2.20724	−	0.917940i
$731$	2.57328	+	1.37544i	0.0951760	+	0.0508727i
$732$	−0.0574789	+	20.2580i	−0.00212448	+	0.748756i
$733$	−4.55160	−	46.2132i	−0.168117	−	1.70692i	−0.595913	−	0.803049i	$-0.703210\pi$
$733$	−4.55160	−	46.2132i	−0.168117	−	1.70692i	0.427796	−	0.903875i	$-0.359290\pi$
$734$	−5.40074	−	2.89661i	−0.199345	−	0.106916i
$735$	4.37818	−	4.37818i	0.161492	−	0.161492i
$736$	−14.8651	+	47.7808i	−0.547934	+	1.76122i
$737$	2.34134	+	2.34134i	0.0862444	+	0.0862444i
$738$	1.38392	+	4.58558i	0.0509428	+	0.168798i
$739$	50.5984	−	4.98351i	1.86129	−	0.183321i	0.895923	−	0.444209i	$-0.146515\pi$
$739$	50.5984	−	4.98351i	1.86129	−	0.183321i	0.965369	+	0.260888i	$0.0840153\pi$
$740$	−67.6169	−	28.2329i	−2.48565	−	1.03786i
$741$	2.01003	−	3.76051i	0.0738404	−	0.138146i
$742$	−7.71435	+	3.18257i	−0.283203	+	0.116836i
$743$	23.3986	−	15.6345i	0.858413	−	0.573573i	−0.0466210	−	0.998913i	$-0.514845\pi$
$743$	23.3986	−	15.6345i	0.858413	−	0.573573i	0.905034	+	0.425340i	$0.139845\pi$
$744$	−5.66953	+	3.75346i	−0.207855	+	0.137608i
$745$	24.3345	−	36.4191i	0.891547	−	1.33429i
$746$	20.4295	+	30.6690i	0.747977	+	1.12287i
$747$	−6.59377	−	8.03453i	−0.241253	−	0.293968i
$748$	3.00334	+	31.4067i	0.109813	+	1.14834i
$749$	−7.94168	−	14.8578i	−0.290183	−	0.542894i
$750$	53.9662	+	44.4172i	1.97057	+	1.62189i
$751$	−15.7273	−	37.9690i	−0.573896	−	1.38551i	−0.898213	−	0.439560i	$-0.855134\pi$
$751$	−15.7273	−	37.9690i	−0.573896	−	1.38551i	0.324317	−	0.945949i	$-0.394866\pi$
$752$	−31.3817	−	0.178083i	−1.14437	−	0.00649402i
$753$	−15.6347	+	37.7456i	−0.569761	+	1.37552i
$754$	−3.29327	+	1.75429i	−0.119934	+	0.0638874i
$755$	−49.7038	−	15.0775i	−1.80891	−	0.548725i
$756$	7.14107	+	8.75194i	0.259718	+	0.318305i
$757$	4.64993	−	47.2115i	0.169005	−	1.71593i	−0.419766	−	0.907632i	$-0.637888\pi$
$757$	4.64993	−	47.2115i	0.169005	−	1.71593i	0.588771	−	0.808300i	$-0.299612\pi$
$758$	−21.1435	−	14.1711i	−0.767967	−	0.514717i
$759$	10.8473	+	54.5333i	0.393734	+	1.97943i
$760$	49.1995	+	15.1535i	1.78465	+	0.549674i
$761$	−20.7822	−	4.13385i	−0.753356	−	0.149852i	−0.196549	−	0.980494i	$-0.562974\pi$
$761$	−20.7822	−	4.13385i	−0.753356	−	0.149852i	−0.556807	+	0.830642i	$0.687974\pi$
$762$	−24.3299	−	0.0345161i	−0.881379	−	0.00125039i
$763$	−1.27934	−	4.21743i	−0.0463154	−	0.152681i
$764$	−16.2623	−	3.28276i	−0.588348	−	0.118766i
$765$	−10.4270	−	8.55725i	−0.376990	−	0.309388i
$766$	1.46787	−	1.20117i	0.0530364	−	0.0434001i
$767$	1.45538			0.0525509
$768$	2.02586	+	23.2739i	0.0731019	+	0.839825i
$769$	−17.0508			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$769$	−17.0508			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$770$	−19.9795	+	16.3494i	−0.720012	+	0.589191i
$771$	−21.5394	−	17.6769i	−0.775723	−	0.636619i
$772$	22.7630	+	4.59502i	0.819258	+	0.165378i
$773$	−14.5215	−	47.8708i	−0.522301	−	1.72179i	−0.678991	−	0.734146i	$-0.737583\pi$
$773$	−14.5215	−	47.8708i	−0.522301	−	1.72179i	0.156691	−	0.987648i	$-0.449917\pi$
$774$	−0.977480	−	0.00138672i	−0.0351348	−	4.98447e-5i
$775$	20.9632	+	4.16985i	0.753021	+	0.149785i
$776$	−5.46964	+	17.7586i	−0.196349	+	0.637495i
$777$	−2.46108	−	12.3727i	−0.0882908	−	0.443868i
$778$	21.9705	+	14.7253i	0.787680	+	0.527929i
$779$	−1.64149	+	16.6664i	−0.0588127	+	0.597135i
$780$	−5.32654	−	6.52808i	−0.190721	−	0.233743i
$781$	−3.58689	−	1.08807i	−0.128349	−	0.0389343i
$782$	40.4597	−	21.5524i	1.44684	−	0.770713i
$783$	−8.38148	+	20.2347i	−0.299530	+	0.723129i
$784$	−2.81233	−	2.84443i	−0.100440	−	0.101587i
$785$	10.4208	+	25.1579i	0.371933	+	0.897925i
$786$	29.0935	+	23.9455i	1.03773	+	0.854109i
$787$	3.53421	+	6.61204i	0.125981	+	0.235694i	0.937003	−	0.349322i	$-0.113588\pi$
$787$	3.53421	+	6.61204i	0.125981	+	0.235694i	−0.811022	+	0.585016i	$0.801088\pi$
$788$	4.10544	+	42.9317i	0.146250	+	1.52938i
$789$	3.23818	+	3.94573i	0.115282	+	0.140472i
$790$	4.96196	+	7.44896i	0.176539	+	0.265022i
$791$	4.89882	−	7.33161i	0.174182	−	0.260682i
$792$	−5.83459	−	8.81304i	−0.207323	−	0.313158i
$793$	−3.92445	+	2.62223i	−0.139361	+	0.0931182i
$794$	2.04890	−	0.845279i	0.0727127	−	0.0299978i
$795$	17.2230	−	32.2220i	0.610838	−	1.14280i
$796$	12.5231	+	5.22892i	0.443870	+	0.185334i
$797$	7.16450	−	0.705642i	0.253780	−	0.0249951i	0.0296727	−	0.999560i	$-0.490554\pi$
$797$	7.16450	−	0.705642i	0.253780	−	0.0249951i	0.224107	+	0.974565i	$0.428054\pi$
$798$	2.56075	+	8.48496i	0.0906494	+	0.300364i
$799$	20.3291	+	20.3291i	0.719190	+	0.719190i
$800$	46.9901	−	56.4365i	1.66135	−	1.99533i
$801$	−4.84917	+	4.84917i	−0.171337	+	0.171337i
$802$	−20.4214	−	10.9527i	−0.721104	−	0.386755i
$803$	4.54441	+	46.1401i	0.160369	+	1.62825i
$804$	0.00637309	−	2.24614i	0.000224761	−	0.0792153i
$805$	33.0819	+	17.6826i	1.16598	+	0.623231i
$806$	−1.46274	−	0.608318i	−0.0515227	−	0.0214271i
$807$	9.06058	+	13.5601i	0.318948	+	0.477339i
$808$	−18.6062	−	0.0791885i	−0.654562	−	0.00278584i
$809$	45.7590	+	30.5752i	1.60880	+	1.07497i	0.945008	+	0.327048i	$0.106054\pi$
$809$	45.7590	+	30.5752i	1.60880	+	1.07497i	0.663792	+	0.747917i	$0.268946\pi$
$810$	−33.1776	−	6.64838i	−1.16574	−	0.233600i
$811$	9.59896	−	7.87766i	0.337065	−	0.276622i	−0.450600	−	0.892726i	$-0.648790\pi$
$811$	9.59896	−	7.87766i	0.337065	−	0.276622i	0.787665	+	0.616104i	$0.211290\pi$
$812$	2.27246	−	7.41549i	0.0797477	−	0.260233i
$813$	8.53589	−	4.56253i	0.299367	−	0.160015i
$814$	5.08132	+	52.3528i	0.178100	+	1.83497i
$815$	9.08061	−	3.76131i	0.318080	−	0.131753i
$816$	13.6710	−	16.4668i	0.478582	−	0.576452i
$817$	−3.15746	−	1.30786i	−0.110466	−	0.0457563i
$818$	−15.8998	+	52.1480i	−0.555922	+	1.82331i
$819$	−0.171444	+	0.565176i	−0.00599075	+	0.0197489i
$820$	29.1395	+	15.6818i	1.01759	+	0.547633i
$821$	16.2980	+	1.60522i	0.568805	+	0.0560224i	0.378332	−	0.925670i	$-0.376498\pi$
$821$	16.2980	+	1.60522i	0.568805	+	0.0560224i	0.190473	+	0.981692i	$0.438998\pi$
$822$	8.43102	+	42.7021i	0.294066	+	1.48941i
$823$	−40.8805	+	8.13163i	−1.42500	+	0.283451i	−0.846570	−	0.532278i	$-0.821336\pi$
$823$	−40.8805	+	8.13163i	−1.42500	+	0.283451i	−0.578435	+	0.815729i	$0.696336\pi$
$824$	−41.7022	−	22.5190i	−1.45277	−	0.784487i
$825$	15.9195	−	80.0327i	0.554246	−	2.78638i
$826$	−2.14210	+	2.13603i	−0.0745332	+	0.0743220i
$827$	38.2662	−	11.6079i	1.33064	−	0.403647i	0.456678	−	0.889632i	$-0.349039\pi$
$827$	38.2662	−	11.6079i	1.33064	−	0.403647i	0.873967	+	0.485986i	$0.161539\pi$
$828$	−8.56827	+	12.7449i	−0.297768	+	0.442916i
$829$	20.1609	−	24.5661i	0.700217	−	0.853217i	−0.294523	−	0.955644i	$-0.595161\pi$
$829$	20.1609	−	24.5661i	0.700217	−	0.853217i	0.994741	+	0.102427i	$0.0326609\pi$
$830$	−71.4508	−	7.13966i	−2.48009	−	0.247821i
$831$			2.13386i			0.0740228i
$832$	−4.23678	+	3.41710i	−0.146884	+	0.118467i
$833$			3.66445i			0.126966i
$834$	3.25430	−	32.5677i	0.112687	−	1.12773i
$835$	−1.44134	+	1.75628i	−0.0498798	+	0.0607787i
$836$	−7.10655	−	36.2645i	−0.245785	−	1.25423i
$837$	−8.89823	+	2.69925i	−0.307568	+	0.0932997i
$838$	4.33293	+	4.34524i	0.149679	+	0.150104i
$839$	2.10789	−	10.5971i	0.0727725	−	0.365852i	−0.927189	−	0.374593i	$-0.877782\pi$
$839$	2.10789	−	10.5971i	0.0727725	−	0.365852i	0.999962	+	0.00874105i	$0.00278240\pi$
$840$	17.4209	+	1.79071i	0.601079	+	0.0617853i
$841$	−13.6933	+	2.72378i	−0.472184	+	0.0939233i
$842$	−24.2459	+	4.78706i	−0.835568	+	0.164973i
$843$	39.9246	+	3.93223i	1.37508	+	0.135433i
$844$	11.2291	+	37.3989i	0.386520	+	1.28732i
$845$	−15.4327	+	50.8747i	−0.530900	+	1.75014i
$846$	−9.21258	−	2.80888i	−0.316735	−	0.0965714i
$847$	6.95851	+	2.88231i	0.239097	+	0.0990374i
$848$	−20.7529	−	11.2445i	−0.712656	−	0.386138i
$849$	20.8775	−	8.64775i	0.716514	−	0.296790i
$850$	−66.9629	+	6.49936i	−2.29681	+	0.222926i
$851$	67.4018	−	36.0270i	2.31051	−	1.23499i
$852$	1.19225	+	2.24584i	0.0408457	+	0.0769412i
$853$	19.7677	−	16.2229i	0.676834	−	0.555463i	−0.231951	−	0.972727i	$-0.574511\pi$
$853$	19.7677	−	16.2229i	0.676834	−	0.555463i	0.908785	+	0.417264i	$0.137011\pi$
$854$	1.92760	−	9.61933i	0.0659609	−	0.329167i
$855$	13.1368	+	8.77770i	0.449268	+	0.300191i
$856$	18.4224	−	43.9457i	0.629665	−	1.50203i
$857$	9.54702	+	14.2881i	0.326120	+	0.488073i	0.957911	−	0.287066i	$-0.0926799\pi$
$857$	9.54702	+	14.2881i	0.326120	+	0.488073i	−0.631791	+	0.775139i	$0.717680\pi$
$858$	−2.32242	+	5.58439i	−0.0792859	+	0.190648i
$859$	29.0274	+	15.5155i	0.990403	+	0.529382i	0.885270	−	0.465077i	$-0.153973\pi$
$859$	29.0274	+	15.5155i	0.990403	+	0.529382i	0.105133	+	0.994458i	$0.466473\pi$
$860$	−4.78863	+	4.76154i	−0.163291	+	0.162367i
$861$	0.558409	+	5.66962i	0.0190305	+	0.193220i
$862$	13.9340	−	25.9800i	0.474594	−	0.884882i
$863$	25.2120	−	25.2120i	0.858228	−	0.858228i	−0.132901	−	0.991129i	$-0.542429\pi$
$863$	25.2120	−	25.2120i	0.858228	−	0.858228i	0.991129	+	0.132901i	$0.0424293\pi$
$864$	−6.45503	+	31.2900i	−0.219605	+	1.06451i
$865$	30.2830	+	30.2830i	1.02965	+	1.02965i
$866$	−21.8395	+	6.59113i	−0.742138	+	0.223976i
$867$	5.19011	−	0.511181i	0.176265	−	0.0173606i
$868$	3.04573	−	1.25147i	0.103379	−	0.0424777i
$869$	3.02864	−	5.66620i	0.102740	−	0.192213i
$870$	12.9501	+	31.3902i	0.439050	+	1.06423i
$871$	0.435131	−	0.290745i	0.0147439	−	0.00985153i
$872$	6.96949	−	10.3351i	0.236017	−	0.349990i
$873$	−3.16831	+	4.74171i	−0.107231	+	0.160483i
$874$	−44.6877	+	29.7677i	−1.51158	+	1.00691i
$875$	−21.4733	−	26.1653i	−0.725929	−	0.884547i
$876$	20.0212	−	24.2552i	0.676453	−	0.819508i
$877$	22.5696	+	42.2248i	0.762122	+	1.42583i	0.900231	+	0.435412i	$0.143397\pi$
$877$	22.5696	+	42.2248i	0.762122	+	1.42583i	−0.138110	+	0.990417i	$0.544103\pi$
$878$	−1.23609	+	1.50183i	−0.0417160	+	0.0506843i
$879$	−16.9942	−	41.0276i	−0.573199	−	1.38383i
$880$	−71.5346	−	14.6516i	−2.41143	−	0.493905i
$881$	−16.9101	+	40.8246i	−0.569716	+	1.37542i	0.332079	+	0.943252i	$0.392250\pi$
$881$	−16.9101	+	40.8246i	−0.569716	+	1.37542i	−0.901795	+	0.432164i	$0.857750\pi$
$882$	−0.577155	−	1.08348i	−0.0194338	−	0.0364825i
$883$	−28.6668	−	8.69599i	−0.964716	−	0.292643i	−0.231649	−	0.972799i	$-0.574412\pi$
$883$	−28.6668	−	8.69599i	−0.964716	−	0.292643i	−0.733067	+	0.680156i	$0.761912\pi$
$884$	4.96104	+	0.502837i	0.166858	+	0.0169122i
$885$	1.29818	−	13.1807i	0.0436379	−	0.443063i
$886$	5.90566	−	8.81136i	0.198405	−	0.296023i
$887$	0.0388871	+	0.195499i	0.00130570	+	0.00656421i	0.981433	−	0.191807i	$-0.0614348\pi$
$887$	0.0388871	+	0.195499i	0.00130570	+	0.00656421i	−0.980127	+	0.198371i	$0.936435\pi$
$888$	22.7529	−	27.4851i	0.763536	−	0.922339i
$889$	11.5561	+	2.29865i	0.387579	+	0.0770943i
$890$	−0.0672131	+	47.3775i	−0.00225299	+	1.58810i
$891$	7.05085	+	23.2436i	0.236213	+	0.778688i
$892$	−14.0932	−	21.2221i	−0.471877	−	0.710569i
$893$	−26.0306	−	21.3627i	−0.871080	−	0.714877i
$894$	13.5074	+	16.5065i	0.451756	+	0.552061i
$895$	99.7018			3.33266
$896$	1.22069	−	11.2477i	0.0407805	−	0.375758i
$897$	8.78783			0.293417
$898$	−22.5816	−	27.5955i	−0.753558	−	0.920874i
$899$	4.93542	+	4.05040i	0.164606	+	0.135088i
$900$	18.7754	−	12.4684i	0.625847	−	0.415614i
$901$	6.27693	+	20.6923i	0.209115	+	0.689360i
$902$	0.0336991	−	23.7540i	0.00112206	−	0.790920i
$903$	−1.14027	−	0.226815i	−0.0379460	−	0.00754792i
$904$	24.8302	−	2.33890i	0.825839	−	0.0777906i
$905$	17.8081	+	89.5275i	0.591962	+	2.97599i
$906$	14.0814	−	21.0098i	0.467824	−	0.698003i
$907$	−2.45827	+	24.9593i	−0.0816257	+	0.828759i	0.863998	+	0.503496i	$0.167953\pi$
$907$	−2.45827	+	24.9593i	−0.0816257	+	0.828759i	−0.945623	+	0.325264i	$0.894547\pi$
$908$	−0.806145	+	7.95351i	−0.0267529	+	0.263947i
$909$	−5.46445	−	1.65762i	−0.181244	−	0.0549799i
$910$	1.91832	+	3.60120i	0.0635916	+	0.119379i
$911$	12.9106	−	31.1689i	0.427747	−	1.03267i	−0.552254	−	0.833676i	$-0.686232\pi$
$911$	12.9106	−	31.1689i	0.427747	−	1.03267i	0.980000	−	0.198996i	$-0.0637680\pi$
$912$	−14.0452	+	20.7641i	−0.465084	+	0.687568i
$913$	19.7255	+	47.6216i	0.652819	+	1.57604i
$914$	17.9233	−	21.7765i	0.592849	−	0.720302i
$915$	20.2476	+	37.8807i	0.669366	+	1.25230i
$916$	−42.0566	−	34.7151i	−1.38959	−	1.14702i
$917$	−11.5763	−	14.1058i	−0.382285	−	0.465815i
$918$	24.3592	−	16.2263i	0.803972	−	0.535549i
$919$	−16.5779	+	24.8106i	−0.546855	+	0.818426i	−0.997227	−	0.0744146i	$-0.976291\pi$
$919$	−16.5779	+	24.8106i	−0.546855	+	0.818426i	0.450372	+	0.892841i	$0.351291\pi$
$920$	20.2556	+	104.146i	0.667806	+	3.43360i
$921$	−38.9279	+	26.0108i	−1.28272	+	0.857086i
$922$	14.7704	+	35.8025i	0.486437	+	1.17909i
$923$	−0.279263	+	0.522465i	−0.00919207	+	0.0171971i
$924$	−4.77783	−	11.6279i	−0.157179	−	0.382530i
$925$	−111.622	+	10.9939i	−3.67012	+	0.361476i
$926$	−14.0791	+	4.24906i	−0.462669	+	0.139633i
$927$	−10.2851	−	10.2851i	−0.337807	−	0.337807i
$928$	20.3261	−	8.25092i	0.667237	−	0.270850i
$929$	2.98488	−	2.98488i	0.0979307	−	0.0979307i	−0.656444	−	0.754375i	$-0.727940\pi$
$929$	2.98488	−	2.98488i	0.0979307	−	0.0979307i	0.754375	+	0.656444i	$0.227940\pi$
$930$	−6.81396	+	12.7046i	−0.223438	+	0.416601i
$931$	−0.420705	−	4.27149i	−0.0137880	−	0.139992i
$932$	2.12434	+	2.13643i	0.0695852	+	0.0699812i
$933$	3.57508	+	1.91092i	0.117043	+	0.0625608i
$934$	−7.71474	+	18.5506i	−0.252434	+	0.606993i
$935$	37.1645	+	55.6206i	1.21541	+	1.81899i
$936$	−1.54604	+	0.632695i	−0.0505339	+	0.0206803i
$937$	−37.7793	−	25.2433i	−1.23420	−	0.824664i	−0.244753	−	0.969585i	$-0.578707\pi$
$937$	−37.7793	−	25.2433i	−1.23420	−	0.824664i	−0.989443	+	0.144922i	$0.953707\pi$
$938$	−0.213726	+	1.06656i	−0.00697840	+	0.0348245i
$939$	30.8856	−	25.3471i	1.00791	−	0.827172i
$940$	−58.7706	+	31.1994i	−1.91688	+	1.01761i
$941$	−8.05385	+	4.30487i	−0.262548	+	0.140335i	−0.597419	−	0.801929i	$-0.703807\pi$
$941$	−8.05385	+	4.30487i	−0.262548	+	0.140335i	0.334871	+	0.942264i	$0.391307\pi$
$942$	−13.1979	+	1.28098i	−0.430012	+	0.0417366i
$943$	−31.8873	+	13.2081i	−1.03839	+	0.430116i
$944$	−8.51017	−	0.886967i	−0.276982	−	0.0288683i
$945$	22.1267	+	9.16518i	0.719781	+	0.298143i
$946$	4.63681	+	1.41375i	0.150756	+	0.0459649i
$947$	−7.37183	+	24.3017i	−0.239552	+	0.789698i	0.751906	+	0.659271i	$0.229135\pi$
$947$	−7.37183	+	24.3017i	−0.239552	+	0.789698i	−0.991458	+	0.130427i	$0.958365\pi$
$948$	−4.17424	+	1.25332i	−0.135573	+	0.0407059i
$949$	7.29244	+	0.718242i	0.236723	+	0.0233151i
$950$	77.3094	−	15.2638i	2.50825	−	0.495224i
$951$	−13.1482	+	2.61535i	−0.426361	+	0.0848084i
$952$	−8.03989	+	6.54110i	−0.260574	+	0.211998i
$953$	1.25229	−	6.29569i	0.0405657	−	0.203938i	−0.955187	−	0.296002i	$-0.904347\pi$
$953$	1.25229	−	6.29569i	0.0405657	−	0.203938i	0.995753	+	0.0920643i	$0.0293465\pi$
$954$	−5.11497	−	5.12950i	−0.165603	−	0.166074i
$955$	−33.6612	+	10.2110i	−1.08925	+	0.330420i
$956$	4.08213	−	0.799952i	0.132025	−	0.0258723i
$957$	15.4635	−	18.8423i	0.499863	−	0.609085i
$958$	0.564035	−	5.64464i	0.0182231	−	0.182370i
$959$		−	21.0790i		−	0.680677i
$960$	27.1678	+	41.4183i	0.876836	+	1.33677i
$961$		−	28.2893i		−	0.912559i
$962$	8.27204	+	0.826576i	0.266701	+	0.0266499i
$963$	9.27749	−	11.3047i	0.298963	−	0.364287i
$964$	2.65727	+	1.78646i	0.0855850	+	0.0575380i
$965$	47.1170	−	14.2928i	1.51675	−	0.460101i
$966$	−12.9343	+	12.8977i	−0.416155	+	0.414976i
$967$	−8.09296	+	40.6860i	−0.260252	+	1.30837i	0.600612	+	0.799540i	$0.294923\pi$
$967$	−8.09296	+	40.6860i	−0.260252	+	1.30837i	−0.860864	+	0.508835i	$0.830077\pi$
$968$	6.09719	+	20.4121i	0.195971	+	0.656069i
$969$	22.5241	−	4.48031i	0.723577	−	0.143928i
$970$	7.63142	+	38.6522i	0.245030	+	1.24105i
$971$	−20.6824	−	2.03704i	−0.663730	−	0.0653717i	−0.239458	−	0.970907i	$-0.576970\pi$
$971$	−20.6824	−	2.03704i	−0.663730	−	0.0653717i	−0.424271	+	0.905535i	$0.639470\pi$
$972$	−8.25053	+	15.3309i	−0.264636	+	0.491738i
$973$	−4.60114	+	15.1679i	−0.147506	+	0.486262i
$974$	4.61002	−	15.1200i	0.147715	−	0.484475i
$975$	−11.9152	−	4.93545i	−0.381593	−	0.158061i
$976$	24.5458	−	12.9415i	0.785692	−	0.414246i
$977$	−13.8435	+	5.73417i	−0.442893	+	0.183452i	−0.592974	−	0.805221i	$-0.702046\pi$
$977$	−13.8435	+	5.73417i	−0.442893	+	0.183452i	0.150081	+	0.988674i	$0.452046\pi$
$978$	0.462363	+	4.76372i	0.0147847	+	0.152327i
$979$	29.9934	−	16.0318i	0.958594	−	0.512379i
$980$	−8.10886	−	2.48494i	−0.259028	−	0.0793786i
$981$	2.95730	−	2.42699i	0.0944192	−	0.0774878i
$982$	55.4677	+	11.1150i	1.77005	+	0.354695i
$983$	14.6198	+	9.76862i	0.466298	+	0.311570i	0.766431	−	0.642327i	$-0.222031\pi$
$983$	14.6198	+	9.76862i	0.466298	+	0.311570i	−0.300132	+	0.953898i	$0.597031\pi$
$984$	−11.4425	+	11.3455i	−0.364774	+	0.361682i
$985$	50.8024	+	76.0312i	1.61870	+	2.42255i
$986$	−18.5560	−	7.71701i	−0.590944	−	0.245760i
$987$	−10.1028	−	5.40005i	−0.321575	−	0.171886i
$988$	−5.84059	−	0.0165718i	−0.185814	−	0.000527219i
$989$	−0.690382	−	7.00956i	−0.0219529	−	0.222891i
$990$	−19.7488	−	10.5920i	−0.627658	−	0.336636i
$991$	10.9745	−	10.9745i	0.348617	−	0.348617i	−0.510977	−	0.859594i	$-0.670716\pi$
$991$	10.9745	−	10.9745i	0.348617	−	0.348617i	0.859594	+	0.510977i	$0.170716\pi$
$992$	8.18243	+	4.44851i	0.259792	+	0.141240i
$993$	−1.97466	−	1.97466i	−0.0626639	−	0.0626639i
$994$	−0.355776	−	1.17886i	−0.0112845	−	0.0373910i
$995$	28.6354	−	2.82034i	0.907803	−	0.0894108i
$996$	13.4726	−	32.2664i	0.426894	−	1.02240i
$997$	−25.3543	+	47.4346i	−0.802979	+	1.50227i	0.0606599	+	0.998158i	$0.480679\pi$
$997$	−25.3543	+	47.4346i	−0.802979	+	1.50227i	−0.863639	+	0.504110i	$0.831821\pi$
$998$	4.73716	−	1.95433i	0.149952	−	0.0618632i
$999$	40.5722	−	27.1095i	1.28365	−	0.857707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.a.533.37	✓	752
128.61	even	32	inner	896.2.bn.a.701.37	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.a.533.37	✓	752	1.1	even	1	trivial
896.2.bn.a.701.37	yes	752	128.61	even	32	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09447 - 0.895616i) q^{2} +(1.12869 + 0.926290i) q^{3} +(0.395745 - 1.96046i) q^{4} +(-1.23096 - 4.05794i) q^{5} +(2.06492 + 0.00292944i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-1.32268 - 2.50010i) q^{8} +(-0.169349 - 0.851373i) q^{9} +O(q^{10})\)	\(q+(1.09447 - 0.895616i) q^{2} +(1.12869 + 0.926290i) q^{3} +(0.395745 - 1.96046i) q^{4} +(-1.23096 - 4.05794i) q^{5} +(2.06492 + 0.00292944i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-1.32268 - 2.50010i) q^{8} +(-0.169349 - 0.851373i) q^{9} +(-4.98161 - 3.33884i) q^{10} +(-0.421950 + 4.28413i) q^{11} +(2.26262 - 1.84617i) q^{12} +(0.651086 + 0.197505i) q^{13} +(-1.24817 + 0.664886i) q^{14} +(2.36946 - 5.72037i) q^{15} +(-3.68677 - 1.55168i) q^{16} +(1.40233 + 3.38551i) q^{17} +(-0.947851 - 0.780134i) q^{18} +(-2.02331 - 3.78534i) q^{19} +(-8.44255 + 0.807339i) q^{20} +(-0.926290 - 1.12869i) q^{21} +(3.37512 + 5.06678i) q^{22} +(4.91450 - 7.35506i) q^{23} +(0.822923 - 4.04702i) q^{24} +(-10.7942 + 7.21249i) q^{25} +(0.889484 - 0.366959i) q^{26} +(2.66236 - 4.98093i) q^{27} +(-0.770607 + 1.84558i) q^{28} +(-3.85926 + 0.380104i) q^{29} +(-2.52995 - 8.38292i) q^{30} +(-1.16419 - 1.16419i) q^{31} +(-5.42478 + 1.60366i) q^{32} +(-4.44460 + 4.44460i) q^{33} +(4.56693 + 2.44941i) q^{34} +(0.415645 + 4.22012i) q^{35} +(-1.73610 - 0.00492592i) q^{36} +(7.61959 + 4.07276i) q^{37} +(-5.60467 - 2.33085i) q^{38} +(0.551925 + 0.826015i) q^{39} +(-8.51709 + 8.44490i) q^{40} +(-3.24421 - 2.16771i) q^{41} +(-2.02467 - 0.405719i) q^{42} +(0.615507 - 0.505133i) q^{43} +(8.23187 + 2.52264i) q^{44} +(-3.24636 + 1.73521i) q^{45} +(-1.20852 - 12.4514i) q^{46} +(7.24834 - 3.00236i) q^{47} +(-2.72391 - 5.16638i) q^{48} +(0.923880 + 0.382683i) q^{49} +(-5.35440 + 17.5614i) q^{50} +(-1.55318 + 5.12015i) q^{51} +(0.644863 - 1.19826i) q^{52} +(5.87243 + 0.578384i) q^{53} +(-1.54711 - 7.83595i) q^{54} +(17.9042 - 3.56136i) q^{55} +(0.809522 + 2.71011i) q^{56} +(1.22264 - 6.14664i) q^{57} +(-3.88343 + 3.87243i) q^{58} +(2.04696 - 0.620938i) q^{59} +(-10.2768 - 6.90902i) q^{60} +(-4.40086 + 5.36246i) q^{61} +(-2.31684 - 0.231508i) q^{62} +0.868052i q^{63} +(-4.50102 + 6.61368i) q^{64} -2.88519i q^{65} +(-0.883843 + 8.84515i) q^{66} +(0.487954 - 0.594574i) q^{67} +(7.19211 - 1.40940i) q^{68} +(12.3598 - 3.74932i) q^{69} +(4.23451 + 4.24655i) q^{70} +(-0.169867 + 0.853981i) q^{71} +(-1.90452 + 1.54949i) q^{72} +(10.5631 - 2.10112i) q^{73} +(11.9871 - 2.36670i) q^{74} +(-18.8642 - 1.85796i) q^{75} +(-8.22171 + 2.46858i) q^{76} +(1.24964 - 4.11950i) q^{77} +(1.34386 + 0.409738i) q^{78} +(-1.37885 - 0.571139i) q^{79} +(-1.75834 + 16.8708i) q^{80} +(5.21283 - 2.15923i) q^{81} +(-5.49213 + 0.533062i) q^{82} +(10.5599 - 5.64437i) q^{83} +(-2.57932 + 1.36928i) q^{84} +(12.0120 - 9.85799i) q^{85} +(0.221250 - 1.10411i) q^{86} +(-4.70799 - 3.14578i) q^{87} +(11.2689 - 4.61163i) q^{88} +(-4.38910 - 6.56876i) q^{89} +(-1.99897 + 4.80663i) q^{90} +(-0.600044 - 0.320730i) q^{91} +(-12.4744 - 12.5454i) q^{92} +(-0.235629 - 2.39238i) q^{93} +(5.24415 - 9.77773i) q^{94} +(-12.8701 + 12.8701i) q^{95} +(-7.60834 - 3.21489i) q^{96} +(-4.64545 - 4.64545i) q^{97} +(1.35390 - 0.408604i) q^{98} +(3.71885 - 0.366275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q+O(q^{10}) \) 752 * q	\( 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) \) 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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