LMFDB - Embedded newform 96.2.n.a.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(13,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			61.7
Character	$\chi$	$=$	96.61
Dual form			96.2.n.a.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.890433 - 1.09869i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-0.414259 - 1.95663i) q^{4} +(-0.00259461 - 0.00626394i) q^{5} +(1.24310 - 0.674307i) q^{6} +(-2.41880 + 2.41880i) q^{7} +(-2.51860 - 1.28710i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.890433 - 1.09869i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-0.414259 - 1.95663i) q^{4} +(-0.00259461 - 0.00626394i) q^{5} +(1.24310 - 0.674307i) q^{6} +(-2.41880 + 2.41880i) q^{7} +(-2.51860 - 1.28710i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-0.00919248 - 0.00272694i) q^{10} +(1.29952 - 0.538278i) q^{11} +(0.366044 - 1.96622i) q^{12} +(-0.559497 + 1.35074i) q^{13} +(0.503742 + 4.81130i) q^{14} -0.00678004i q^{15} +(-3.65678 + 1.62110i) q^{16} -5.82199i q^{17} +(1.40653 - 0.147263i) q^{18} +(-2.67819 + 6.46573i) q^{19} +(-0.0111814 + 0.00767157i) q^{20} +(-3.16031 + 1.30904i) q^{21} +(0.565730 - 1.90707i) q^{22} +(0.178878 + 0.178878i) q^{23} +(-1.83433 - 2.15296i) q^{24} +(3.53550 - 3.53550i) q^{25} +(0.985861 + 1.81746i) q^{26} +(0.382683 + 0.923880i) q^{27} +(5.73469 + 3.73068i) q^{28} +(5.72901 + 2.37303i) q^{29} +(-0.00744919 - 0.00603717i) q^{30} -6.19719 q^{31} +(-1.47502 + 5.46116i) q^{32} +1.40659 q^{33} +(-6.39659 - 5.18409i) q^{34} +(0.0214270 + 0.00887537i) q^{35} +(1.09062 - 1.67647i) q^{36} +(-2.02932 - 4.89922i) q^{37} +(4.71911 + 8.69981i) q^{38} +(-1.03381 + 1.03381i) q^{39} +(-0.00152753 + 0.0191159i) q^{40} +(-3.36712 - 3.36712i) q^{41} +(-1.37581 + 4.63783i) q^{42} +(9.37558 - 3.88349i) q^{43} +(-1.59154 - 2.31968i) q^{44} +(0.00259461 - 0.00626394i) q^{45} +(0.355812 - 0.0372534i) q^{46} -12.5050i q^{47} +(-3.99879 + 0.0983114i) q^{48} -4.70117i q^{49} +(-0.736309 - 7.03256i) q^{50} +(2.22798 - 5.37882i) q^{51} +(2.87468 + 0.535169i) q^{52} +(-8.36811 + 3.46618i) q^{53} +(1.35582 + 0.402201i) q^{54} +(-0.00674348 - 0.00674348i) q^{55} +(9.20523 - 2.97876i) q^{56} +(-4.94866 + 4.94866i) q^{57} +(7.70854 - 4.18140i) q^{58} +(1.59507 + 3.85084i) q^{59} +(-0.0132660 + 0.00280869i) q^{60} +(7.27395 + 3.01297i) q^{61} +(-5.51818 + 6.80881i) q^{62} -3.42070 q^{63} +(4.68674 + 6.48340i) q^{64} +0.00991266 q^{65} +(1.25247 - 1.54541i) q^{66} +(-4.38775 - 1.81747i) q^{67} +(-11.3915 + 2.41181i) q^{68} +(0.0968082 + 0.233716i) q^{69} +(0.0288307 - 0.0156388i) q^{70} +(5.95188 - 5.95188i) q^{71} +(-0.870804 - 2.69104i) q^{72} +(7.85539 + 7.85539i) q^{73} +(-7.18972 - 2.13282i) q^{74} +(4.61936 - 1.91340i) q^{75} +(13.7605 + 2.56174i) q^{76} +(-1.84128 + 4.44525i) q^{77} +(0.215304 + 2.05639i) q^{78} +1.42456i q^{79} +(0.0196424 + 0.0186997i) q^{80} +1.00000i q^{81} +(-6.69763 + 0.701242i) q^{82} +(-3.03596 + 7.32946i) q^{83} +(3.87050 + 5.64127i) q^{84} +(-0.0364686 + 0.0151058i) q^{85} +(4.08155 - 13.7589i) q^{86} +(4.38479 + 4.38479i) q^{87} +(-3.96579 - 0.316902i) q^{88} +(-9.96127 + 9.96127i) q^{89} +(-0.00457183 - 0.00842830i) q^{90} +(-1.91387 - 4.62049i) q^{91} +(0.275896 - 0.424100i) q^{92} +(-5.72545 - 2.37156i) q^{93} +(-13.7392 - 11.1349i) q^{94} +0.0474498 q^{95} +(-3.45264 + 4.48099i) q^{96} -1.24058 q^{97} +(-5.16515 - 4.18607i) q^{98} +(1.29952 + 0.538278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	0.890433	−	1.09869i	0.629631	−	0.776894i
$2$	0.890433	−	1.09869i	0.629631	−	0.776894i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$	−0.414259	−	1.95663i	−0.207129	−	0.978314i
$5$	−0.00259461	−	0.00626394i	−0.00116034	−	0.00280132i	0.923298	−	0.384084i	$-0.125483\pi$
$5$	−0.00259461	−	0.00626394i	−0.00116034	−	0.00280132i	−0.924459	+	0.381282i	$0.875483\pi$
$6$	1.24310	−	0.674307i	0.507495	−	0.275285i
$7$	−2.41880	+	2.41880i	−0.914220	+	0.914220i	−0.996601	−	0.0823812i	$-0.973747\pi$
$7$	−2.41880	+	2.41880i	−0.914220	+	0.914220i	0.0823812	+	0.996601i	$0.473747\pi$
$8$	−2.51860	−	1.28710i	−0.890461	−	0.455059i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	−0.00919248	−	0.00272694i	−0.00290692	−	0.000862333i
$11$	1.29952	−	0.538278i	0.391819	−	0.162297i	−0.178071	−	0.984018i	$-0.556986\pi$
$11$	1.29952	−	0.538278i	0.391819	−	0.162297i	0.569890	+	0.821721i	$0.306986\pi$
$12$	0.366044	−	1.96622i	0.105668	−	0.567598i
$13$	−0.559497	+	1.35074i	−0.155176	+	0.374629i	−0.982280	−	0.187421i	$-0.939987\pi$
$13$	−0.559497	+	1.35074i	−0.155176	+	0.374629i	0.827103	+	0.562050i	$0.189987\pi$
$14$	0.503742	+	4.81130i	0.134631	+	1.28587i
$15$		−	0.00678004i		−	0.00175060i
$16$	−3.65678	+	1.62110i	−0.914195	+	0.405275i
$17$		−	5.82199i		−	1.41204i	−0.708192	−	0.706020i	$-0.750489\pi$
$17$		−	5.82199i		−	1.41204i	0.708192	−	0.706020i	$-0.249511\pi$
$18$	1.40653	−	0.147263i	0.331521	−	0.0347102i
$19$	−2.67819	+	6.46573i	−0.614420	+	1.48334i	0.243679	+	0.969856i	$0.421646\pi$
$19$	−2.67819	+	6.46573i	−0.614420	+	1.48334i	−0.858099	+	0.513484i	$0.828354\pi$
$20$	−0.0111814	+	0.00767157i	−0.00250023	+	0.00171542i
$21$	−3.16031	+	1.30904i	−0.689637	+	0.285657i
$22$	0.565730	−	1.90707i	0.120614	−	0.406589i
$23$	0.178878	+	0.178878i	0.0372987	+	0.0372987i	0.725510	−	0.688211i	$-0.241604\pi$
$23$	0.178878	+	0.178878i	0.0372987	+	0.0372987i	−0.688211	+	0.725510i	$0.741604\pi$
$24$	−1.83433	−	2.15296i	−0.374432	−	0.439470i
$25$	3.53550	−	3.53550i	0.707100	−	0.707100i
$26$	0.985861	+	1.81746i	0.193343	+	0.356434i
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$	5.73469	+	3.73068i	1.08376	+	0.705032i
$29$	5.72901	+	2.37303i	1.06385	+	0.440661i	0.844817	−	0.535056i	$-0.179710\pi$
$29$	5.72901	+	2.37303i	1.06385	+	0.440661i	0.219034	+	0.975717i	$0.429710\pi$
$30$	−0.00744919	−	0.00603717i	−0.00136003	−	0.00110223i
$31$	−6.19719			−1.11305			−0.556524	−	0.830832i	$-0.687865\pi$
$31$	−6.19719			−1.11305			−0.556524	+	0.830832i	$0.687865\pi$
$32$	−1.47502	+	5.46116i	−0.260750	+	0.965406i
$33$	1.40659			0.244855
$34$	−6.39659	−	5.18409i	−1.09701	−	0.889064i
$35$	0.0214270	+	0.00887537i	0.00362183	+	0.00150021i
$36$	1.09062	−	1.67647i	0.181770	−	0.279412i
$37$	−2.02932	−	4.89922i	−0.333619	−	0.805427i	−0.998299	−	0.0582992i	$-0.981432\pi$
$37$	−2.02932	−	4.89922i	−0.333619	−	0.805427i	0.664680	−	0.747128i	$-0.268568\pi$
$38$	4.71911	+	8.69981i	0.765541	+	1.41130i
$39$	−1.03381	+	1.03381i	−0.165543	+	0.165543i
$40$	−0.00152753	+	0.0191159i	−0.000241524	+	0.00302249i
$41$	−3.36712	−	3.36712i	−0.525856	−	0.525856i	0.393478	−	0.919334i	$-0.371272\pi$
$41$	−3.36712	−	3.36712i	−0.525856	−	0.525856i	−0.919334	+	0.393478i	$0.871272\pi$
$42$	−1.37581	+	4.63783i	−0.212292	+	0.715633i
$43$	9.37558	−	3.88349i	1.42976	−	0.592227i	0.472470	−	0.881347i	$-0.343363\pi$
$43$	9.37558	−	3.88349i	1.42976	−	0.592227i	0.957293	+	0.289120i	$0.0933625\pi$
$44$	−1.59154	−	2.31968i	−0.239934	−	0.349706i
$45$	0.00259461	−	0.00626394i	0.000386782	−	0.000933773i
$46$	0.355812	−	0.0372534i	0.0524616	−	0.00549272i
$47$		−	12.5050i		−	1.82405i	−0.410137	−	0.912024i	$-0.634519\pi$
$47$		−	12.5050i		−	1.82405i	0.410137	−	0.912024i	$-0.365481\pi$
$48$	−3.99879	+	0.0983114i	−0.577176	+	0.0141900i
$49$		−	4.70117i		−	0.671595i
$50$	−0.736309	−	7.03256i	−0.104130	−	0.994554i
$51$	2.22798	−	5.37882i	0.311979	−	0.753185i
$52$	2.87468	+	0.535169i	0.398646	+	0.0742146i
$53$	−8.36811	+	3.46618i	−1.14945	+	0.476117i	−0.874348	−	0.485299i	$-0.838711\pi$
$53$	−8.36811	+	3.46618i	−1.14945	+	0.476117i	−0.275100	+	0.961416i	$0.588711\pi$
$54$	1.35582	+	0.402201i	0.184503	+	0.0547326i
$55$	−0.00674348	−	0.00674348i	−0.000909291	−	0.000909291i
$56$	9.20523	−	2.97876i	1.23010	−	0.398053i
$57$	−4.94866	+	4.94866i	−0.655465	+	0.655465i
$58$	7.70854	−	4.18140i	1.01218	−	0.549045i
$59$	1.59507	+	3.85084i	0.207661	+	0.501337i	0.993054	−	0.117660i	$-0.0375392\pi$
$59$	1.59507	+	3.85084i	0.207661	+	0.501337i	−0.785393	+	0.618997i	$0.787539\pi$
$60$	−0.0132660	+	0.00280869i	−0.00171263	+	0.000362600i
$61$	7.27395	+	3.01297i	0.931333	+	0.385771i	0.796184	−	0.605054i	$-0.206849\pi$
$61$	7.27395	+	3.01297i	0.931333	+	0.385771i	0.135149	+	0.990825i	$0.456849\pi$
$62$	−5.51818	+	6.80881i	−0.700809	+	0.864720i
$63$	−3.42070			−0.430967
$64$	4.68674	+	6.48340i	0.585842	+	0.810425i
$65$	0.00991266			0.00122951
$66$	1.25247	−	1.54541i	0.154169	−	0.190227i
$67$	−4.38775	−	1.81747i	−0.536049	−	0.222039i	0.0982011	−	0.995167i	$-0.468691\pi$
$67$	−4.38775	−	1.81747i	−0.536049	−	0.222039i	−0.634250	+	0.773128i	$0.718691\pi$
$68$	−11.3915	+	2.41181i	−1.38142	+	0.292475i
$69$	0.0968082	+	0.233716i	0.0116543	+	0.0281361i
$70$	0.0288307	−	0.0156388i	0.00344592	−	0.00186920i
$71$	5.95188	−	5.95188i	0.706358	−	0.706358i	−0.259409	−	0.965768i	$-0.583528\pi$
$71$	5.95188	−	5.95188i	0.706358	−	0.706358i	0.965768	+	0.259409i	$0.0835278\pi$
$72$	−0.870804	−	2.69104i	−0.102625	−	0.317142i
$73$	7.85539	+	7.85539i	0.919404	+	0.919404i	0.996986	−	0.0775823i	$-0.0247201\pi$
$73$	7.85539	+	7.85539i	0.919404	+	0.919404i	−0.0775823	+	0.996986i	$0.524720\pi$
$74$	−7.18972	−	2.13282i	−0.835788	−	0.247935i
$75$	4.61936	−	1.91340i	0.533397	−	0.220940i
$76$	13.7605	+	2.56174i	1.57844	+	0.293852i
$77$	−1.84128	+	4.44525i	−0.209834	+	0.506584i
$78$	0.215304	+	2.05639i	0.0243784	+	0.232840i
$79$			1.42456i			0.160276i	0.996784	+	0.0801378i	$0.0255360\pi$
$79$			1.42456i			0.160276i	−0.996784	+	0.0801378i	$0.974464\pi$
$80$	0.0196424	+	0.0186997i	0.00219609	+	0.00209069i
$81$			1.00000i			0.111111i
$82$	−6.69763	+	0.701242i	−0.739630	+	0.0774392i
$83$	−3.03596	+	7.32946i	−0.333240	+	0.804513i	0.665091	+	0.746763i	$0.268393\pi$
$83$	−3.03596	+	7.32946i	−0.333240	+	0.804513i	−0.998331	+	0.0577507i	$0.981607\pi$
$84$	3.87050	+	5.64127i	0.422306	+	0.615513i
$85$	−0.0364686	+	0.0151058i	−0.00395557	+	0.00163845i
$86$	4.08155	−	13.7589i	0.440125	−	1.48366i
$87$	4.38479	+	4.38479i	0.470099	+	0.470099i
$88$	−3.96579	−	0.316902i	−0.422754	−	0.0337819i
$89$	−9.96127	+	9.96127i	−1.05589	+	1.05589i	−0.0575498	+	0.998343i	$0.518329\pi$
$89$	−9.96127	+	9.96127i	−1.05589	+	1.05589i	−0.998343	+	0.0575498i	$0.981671\pi$
$90$	−0.00457183	−	0.00842830i	−0.000481913	−	0.000888421i
$91$	−1.91387	−	4.62049i	−0.200628	−	0.484359i
$92$	0.275896	−	0.424100i	0.0287642	−	0.0442155i
$93$	−5.72545	−	2.37156i	−0.593702	−	0.245919i
$94$	−13.7392	−	11.1349i	−1.41709	−	1.14848i
$95$	0.0474498			0.00486825
$96$	−3.45264	+	4.48099i	−0.352384	+	0.457339i
$97$	−1.24058			−0.125961			−0.0629807	−	0.998015i	$-0.520061\pi$
$97$	−1.24058			−0.125961			−0.0629807	+	0.998015i	$0.520061\pi$
$98$	−5.16515	−	4.18607i	−0.521758	−	0.422857i
$99$	1.29952	+	0.538278i	0.130606	+	0.0540989i
$100$	−8.38227	−	5.45305i	−0.838227	−	0.545305i
$101$	6.15953	+	14.8704i	0.612896	+	1.47966i	0.859804	+	0.510624i	$0.170585\pi$
$101$	6.15953	+	14.8704i	0.612896	+	1.47966i	−0.246908	+	0.969039i	$0.579415\pi$
$102$	−3.92581	−	7.23734i	−0.388713	−	0.716604i
$103$	−5.60558	+	5.60558i	−0.552334	+	0.552334i	−0.927114	−	0.374779i	$-0.877718\pi$
$103$	−5.60558	+	5.60558i	−0.552334	+	0.552334i	0.374779	+	0.927114i	$0.377718\pi$
$104$	3.14770	−	2.68186i	0.308657	−	0.262978i
$105$	0.0163995	+	0.0163995i	0.00160043	+	0.00160043i
$106$	−3.64296	+	12.2804i	−0.353836	+	1.19278i
$107$	−5.46375	+	2.26316i	−0.528201	+	0.218788i	−0.630815	−	0.775933i	$-0.717279\pi$
$107$	−5.46375	+	2.26316i	−0.528201	+	0.218788i	0.102614	+	0.994721i	$0.467279\pi$
$108$	1.64916	−	1.13149i	0.158690	−	0.108878i
$109$	−0.982918	+	2.37297i	−0.0941464	+	0.227290i	−0.963936	−	0.266132i	$-0.914254\pi$
$109$	−0.982918	+	2.37297i	−0.0941464	+	0.227290i	0.869790	+	0.493422i	$0.164254\pi$
$110$	−0.0134136	+	0.00140441i	−0.00127894	+	0.000133905i
$111$		−	5.30288i		−	0.503327i
$112$	4.92390	−	12.7661i	0.465265	−	1.20629i
$113$		−	4.42809i		−	0.416560i	−0.978069	−	0.208280i	$-0.933213\pi$
$113$		−	4.42809i		−	0.416560i	0.978069	−	0.208280i	$-0.0667865\pi$
$114$	1.03061	+	9.84350i	0.0965259	+	0.921929i
$115$	0.000656364	−	0.00158460i	6.12062e−5	−	0.000147765i
$116$	2.26985	−	12.1926i	0.210750	−	1.13205i
$117$	−1.35074	+	0.559497i	−0.124876	+	0.0517255i
$118$	5.65121	+	1.67642i	0.520236	+	0.154327i
$119$	14.0822	+	14.0822i	1.29091	+	1.29091i
$120$	−0.00872660	+	0.0170762i	−0.000796626	+	0.00155884i
$121$	−6.37917	+	6.37917i	−0.579925	+	0.579925i
$122$	9.78729	−	5.30900i	0.886100	−	0.480654i
$123$	−1.82227	−	4.39936i	−0.164309	−	0.396677i
$124$	2.56724	+	12.1256i	0.230545	+	1.08891i
$125$	−0.0626391	−	0.0259460i	−0.00560261	−	0.00232068i
$126$	−3.04590	+	3.75830i	−0.271350	+	0.334816i
$127$	14.5930			1.29492			0.647458	−	0.762101i	$-0.275832\pi$
$127$	14.5930			1.29492			0.647458	+	0.762101i	$0.275832\pi$
$128$	11.2965	+	0.623739i	0.998479	+	0.0551313i
$129$	10.1481			0.893487
$130$	0.00882656	−	0.0108910i	0.000774140	−	0.000955202i
$131$	−8.62727	−	3.57353i	−0.753768	−	0.312221i	−0.0274902	−	0.999622i	$-0.508752\pi$
$131$	−8.62727	−	3.57353i	−0.753768	−	0.312221i	−0.726278	+	0.687401i	$0.758752\pi$
$132$	−0.582691	−	2.75217i	−0.0507167	−	0.239545i
$133$	−9.16129	−	22.1173i	−0.794384	−	1.91781i
$134$	−5.90384	+	3.20247i	−0.510014	+	0.276651i
$135$	0.00479421	−	0.00479421i	0.000412620	−	0.000412620i
$136$	−7.49349	+	14.6633i	−0.642561	+	1.25737i
$137$	−0.109126	−	0.109126i	−0.00932323	−	0.00932323i	0.702430	−	0.711753i	$-0.252098\pi$
$137$	−0.109126	−	0.109126i	−0.00932323	−	0.00932323i	−0.711753	+	0.702430i	$0.752098\pi$
$138$	0.342983	+	0.101745i	0.0291967	+	0.00866115i
$139$	5.80724	−	2.40544i	0.492564	−	0.204027i	−0.122554	−	0.992462i	$-0.539108\pi$
$139$	5.80724	−	2.40544i	0.492564	−	0.204027i	0.615118	+	0.788435i	$0.289108\pi$
$140$	0.00848946	−	0.0456014i	0.000717490	−	0.00385402i
$141$	4.78547	−	11.5532i	0.403009	−	0.972951i
$142$	−1.23955	−	11.8391i	−0.104021	−	0.993511i
$143$			2.05648i			0.171971i
$144$	−3.73202	−	1.43944i	−0.311002	−	0.119954i
$145$		−	0.0420433i		−	0.00349150i
$146$	15.6254	−	1.63597i	1.29316	−	0.135394i
$147$	1.79906	−	4.34331i	0.148384	−	0.358230i
$148$	−8.74529	+	6.00018i	−0.718858	+	0.493211i
$149$	15.4722	−	6.40879i	1.26753	−	0.525028i	0.355318	−	0.934745i	$-0.384373\pi$
$149$	15.4722	−	6.40879i	1.26753	−	0.525028i	0.912213	+	0.409717i	$0.134373\pi$
$150$	2.01098	−	6.77901i	0.164196	−	0.553504i
$151$	−9.38822	−	9.38822i	−0.764003	−	0.764003i	0.213041	−	0.977043i	$-0.431663\pi$
$151$	−9.38822	−	9.38822i	−0.764003	−	0.764003i	−0.977043	+	0.213041i	$0.931663\pi$
$152$	15.0674	−	12.8375i	1.22212	−	1.04126i
$153$	4.11677	−	4.11677i	0.332821	−	0.332821i
$154$	3.24444	+	5.98121i	0.261444	+	0.481980i
$155$	0.0160793	+	0.0388188i	0.00129152	+	0.00311800i
$156$	2.45106	+	1.59452i	0.196242	+	0.127664i
$157$	−0.959615	−	0.397486i	−0.0765856	−	0.0317228i	0.344062	−	0.938947i	$-0.388197\pi$
$157$	−0.959615	−	0.397486i	−0.0765856	−	0.0317228i	−0.420647	+	0.907224i	$0.638197\pi$
$158$	1.56516	+	1.26848i	0.124517	+	0.100915i
$159$	−9.05757			−0.718312
$160$	0.0380355	−	0.00493012i	0.00300697	−	0.000389760i
$161$	−0.865341			−0.0681984
$162$	1.09869	+	0.890433i	0.0863216	+	0.0699590i
$163$	−7.39543	−	3.06329i	−0.579255	−	0.239935i	0.0737655	−	0.997276i	$-0.476498\pi$
$163$	−7.39543	−	3.06329i	−0.579255	−	0.239935i	−0.653020	+	0.757340i	$0.726498\pi$
$164$	−5.19334	+	7.98306i	−0.405532	+	0.623372i
$165$	−0.00364954	−	0.00881078i	−0.000284117	−	0.000685918i
$166$	5.34952	+	9.86199i	0.415203	+	0.765439i
$167$	0.697073	−	0.697073i	0.0539412	−	0.0539412i	−0.679622	−	0.733563i	$-0.737856\pi$
$167$	0.697073	−	0.697073i	0.0539412	−	0.0539412i	0.733563	+	0.679622i	$0.237856\pi$
$168$	9.64445	+	0.770678i	0.744085	+	0.0594591i
$169$	7.68091	+	7.68091i	0.590840	+	0.590840i
$170$	−0.0158762	+	0.0535185i	−0.00121765	+	0.00410468i
$171$	−6.46573	+	2.67819i	−0.494447	+	0.204807i
$172$	−11.4825	−	16.7357i	−0.875530	−	1.27609i
$173$	6.61178	−	15.9623i	0.502685	−	1.21359i	−0.445331	−	0.895366i	$-0.646914\pi$
$173$	6.61178	−	15.9623i	0.502685	−	1.21359i	0.948016	−	0.318222i	$-0.103086\pi$
$174$	8.72191	−	0.913184i	0.661207	−	0.0692283i
$175$			17.1033i			1.29289i
$176$	−3.87945	+	4.07501i	−0.292424	+	0.307165i
$177$			4.16812i			0.313295i
$178$	2.07455	+	19.8142i	0.155494	+	1.48514i
$179$	1.14101	−	2.75465i	0.0852832	−	0.205892i	−0.875484	−	0.483246i	$-0.839458\pi$
$179$	1.14101	−	2.75465i	0.0852832	−	0.205892i	0.960768	+	0.277354i	$0.0894576\pi$
$180$	−0.0133310	−	0.00248179i	−0.000993637	−	0.000184982i
$181$	−6.23325	+	2.58190i	−0.463314	+	0.191911i	−0.602115	−	0.798409i	$-0.705675\pi$
$181$	−6.23325	+	2.58190i	−0.463314	+	0.191911i	0.138801	+	0.990320i	$0.455675\pi$
$182$	−6.78067	−	2.01148i	−0.502617	−	0.149101i
$183$	5.56724	+	5.56724i	0.411542	+	0.411542i
$184$	−0.220289	−	0.680758i	−0.0162399	−	0.0501861i
$185$	−0.0254231	+	0.0254231i	−0.00186915	+	0.00186915i
$186$	−7.70375	+	4.17881i	−0.564867	+	0.306405i
$187$	−3.13385	−	7.56577i	−0.229170	−	0.553264i
$188$	−24.4677	+	5.18032i	−1.78449	+	0.377814i
$189$	−3.16031	−	1.30904i	−0.229879	−	0.0952189i
$190$	0.0422509	−	0.0521328i	0.00306520	−	0.00378211i
$191$	−5.12197			−0.370613			−0.185306	−	0.982681i	$-0.559328\pi$
$191$	−5.12197			−0.370613			−0.185306	+	0.982681i	$0.559328\pi$
$192$	1.84889	+	7.78342i	0.133432	+	0.561720i
$193$	−20.7951			−1.49686			−0.748431	−	0.663213i	$-0.769192\pi$
$193$	−20.7951			−1.49686			−0.748431	+	0.663213i	$0.769192\pi$
$194$	−1.10465	+	1.36301i	−0.0793093	+	0.0978588i
$195$	0.00915810	+	0.00379341i	0.000655825	+	0.000271652i
$196$	−9.19843	+	1.94750i	−0.657031	+	0.139107i
$197$	−3.47339	−	8.38550i	−0.247469	−	0.597442i	0.750519	−	0.660849i	$-0.229804\pi$
$197$	−3.47339	−	8.38550i	−0.247469	−	0.597442i	−0.997988	+	0.0634065i	$0.979804\pi$
$198$	1.74854	−	0.948472i	0.124263	−	0.0674050i
$199$	9.79652	−	9.79652i	0.694457	−	0.694457i	−0.268753	−	0.963209i	$-0.586611\pi$
$199$	9.79652	−	9.79652i	0.694457	−	0.694457i	0.963209	+	0.268753i	$0.0866114\pi$
$200$	−13.4551	+	4.35398i	−0.951418	+	0.307873i
$201$	−3.35824	−	3.35824i	−0.236872	−	0.236872i
$202$	21.8227	+	6.47367i	1.53544	+	0.455486i
$203$	−19.5972	+	8.11743i	−1.37545	+	0.569732i
$204$	−11.4473	−	2.13110i	−0.801471	−	0.149207i
$205$	−0.0123551	+	0.0298278i	−0.000862917	+	0.00208326i
$206$	1.16743	+	11.1502i	0.0813385	+	0.776872i
$207$			0.252972i			0.0175828i
$208$	−0.143735	−	5.84637i	−0.00996620	−	0.405373i
$209$			9.84394i			0.680919i
$210$	0.0326208	−	0.00341539i	0.00225105	−	0.000235685i
$211$	−2.59646	+	6.26841i	−0.178748	+	0.431535i	−0.987704	−	0.156333i	$-0.950033\pi$
$211$	−2.59646	+	6.26841i	−0.178748	+	0.431535i	0.808957	+	0.587868i	$0.200033\pi$
$212$	10.2486	+	14.9374i	0.703876	+	1.02590i
$213$	7.77651	−	3.22114i	0.532838	−	0.220709i
$214$	−2.37858	+	8.01818i	−0.162597	+	0.548112i
$215$	−0.0486519	−	0.0486519i	−0.00331804	−	0.00331804i
$216$	0.225299	−	2.81944i	0.0153296	−	0.191839i
$217$	14.9897	−	14.9897i	1.01757	−	1.01757i
$218$	1.73195	+	3.19290i	0.117302	+	0.216250i
$219$	4.25131	+	10.2636i	0.287277	+	0.693547i
$220$	−0.0104009	+	0.0159880i	−0.000701231	+	0.00107791i
$221$	7.86402	+	3.25738i	0.528991	+	0.219115i
$222$	−5.82624	−	4.72186i	−0.391032	−	0.316910i
$223$	14.6051			0.978032			0.489016	−	0.872275i	$-0.337356\pi$
$223$	14.6051			0.978032			0.489016	+	0.872275i	$0.337356\pi$
$224$	−9.64166	−	16.7772i	−0.644211	−	1.12098i
$225$	4.99995			0.333330
$226$	−4.86512	−	3.94292i	−0.323623	−	0.262279i
$227$	−3.75119	−	1.55379i	−0.248975	−	0.103129i	0.254706	−	0.967019i	$-0.418021\pi$
$227$	−3.75119	−	1.55379i	−0.248975	−	0.103129i	−0.503681	+	0.863890i	$0.668021\pi$
$228$	11.7327	+	7.63265i	0.777017	+	0.505485i
$229$	2.06540	+	4.98631i	0.136485	+	0.329505i	0.977314	−	0.211797i	$-0.0679316\pi$
$229$	2.06540	+	4.98631i	0.136485	+	0.329505i	−0.840828	+	0.541302i	$0.817932\pi$
$230$	−0.00115655	−	0.00213212i	−7.62603e−5	−	0.000140588i
$231$	−3.40225	+	3.40225i	−0.223852	+	0.223852i
$232$	−11.3748	−	13.3506i	−0.746791	−	0.876507i
$233$	−20.5003	−	20.5003i	−1.34302	−	1.34302i	−0.893035	−	0.449987i	$-0.851428\pi$
$233$	−20.5003	−	20.5003i	−1.34302	−	1.34302i	−0.449987	−	0.893035i	$-0.648572\pi$
$234$	−0.588031	+	1.98225i	−0.0384408	+	0.129584i
$235$	−0.0783308	+	0.0324457i	−0.00510974	+	0.00211652i
$236$	6.87389	−	4.71621i	0.447452	−	0.306999i
$237$	−0.545156	+	1.31612i	−0.0354117	+	0.0854913i
$238$	28.0113	−	2.93278i	1.81570	−	0.190104i
$239$			2.23671i			0.144680i	0.997380	+	0.0723402i	$0.0230467\pi$
$239$			2.23671i			0.144680i	−0.997380	+	0.0723402i	$0.976953\pi$
$240$	0.0109911	+	0.0247931i	0.000709474	+	0.00160039i
$241$			19.6755i			1.26741i	0.773575	+	0.633704i	$0.218466\pi$
$241$			19.6755i			1.26741i	−0.773575	+	0.633704i	$0.781534\pi$
$242$	1.32854	+	12.6890i	0.0854015	+	0.815679i
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$	2.88196	−	15.4805i	0.184498	−	0.991040i
$245$	−0.0294478	+	0.0121977i	−0.00188135	+	0.000779282i
$246$	−6.45616	−	1.91521i	−0.411630	−	0.122109i
$247$	−7.23511	−	7.23511i	−0.460359	−	0.460359i
$248$	15.6083	+	7.97641i	0.991126	+	0.506502i
$249$	−5.60973	+	5.60973i	−0.355502	+	0.355502i
$250$	−0.0842826	+	0.0457181i	−0.00533050	+	0.00289147i
$251$	2.41942	+	5.84100i	0.152712	+	0.368680i	0.981658	−	0.190648i	$-0.0610590\pi$
$251$	2.41942	+	5.84100i	0.152712	+	0.368680i	−0.828946	+	0.559329i	$0.811059\pi$
$252$	1.41705	+	6.69303i	0.0892659	+	0.421621i
$253$	0.328742	+	0.136169i	0.0206678	+	0.00856088i
$254$	12.9940	−	16.0332i	0.815319	−	1.00601i
$255$	−0.0394733			−0.00247191
$256$	10.7441	−	11.8560i	0.671505	−	0.741000i
$257$	9.46013			0.590106			0.295053	−	0.955481i	$-0.404663\pi$
$257$	9.46013			0.590106			0.295053	+	0.955481i	$0.404663\pi$
$258$	9.03616	−	11.1496i	0.562567	−	0.694145i
$259$	16.7588	+	6.94170i	1.04134	+	0.431336i
$260$	−0.00410640	−	0.0193954i	−0.000254668	−	0.00120285i
$261$	2.37303	+	5.72901i	0.146887	+	0.354617i
$262$	−11.6082	+	6.29674i	−0.717159	+	0.389014i
$263$	−7.01762	+	7.01762i	−0.432725	+	0.432725i	−0.889554	−	0.456829i	$-0.848985\pi$
$263$	−7.01762	+	7.01762i	−0.432725	+	0.432725i	0.456829	+	0.889554i	$0.348985\pi$
$264$	−3.54264	−	1.81042i	−0.218034	−	0.111424i
$265$	0.0434239	+	0.0434239i	0.00266751	+	0.00266751i
$266$	−32.4577	−	9.62852i	−1.99011	−	0.590362i
$267$	−13.0150	+	5.39100i	−0.796507	+	0.329924i
$268$	−1.73844	+	9.33810i	−0.106192	+	0.570415i
$269$	0.579856	−	1.39990i	0.0353545	−	0.0853532i	−0.905216	−	0.424952i	$-0.860291\pi$
$269$	0.579856	−	1.39990i	0.0353545	−	0.0853532i	0.940571	+	0.339598i	$0.110291\pi$
$270$	−0.000998450	−	0.00953630i	−6.07637e−5	−	0.000580361i
$271$			2.19594i			0.133394i	0.997773	+	0.0666969i	$0.0212460\pi$
$271$			2.19594i			0.133394i	−0.997773	+	0.0666969i	$0.978754\pi$
$272$	9.43802	+	21.2897i	0.572264	+	1.29088i
$273$		−	5.00118i		−	0.302685i
$274$	−0.217065	+	0.0227267i	−0.0131134	+	0.00137297i
$275$	2.69136	−	6.49753i	0.162295	−	0.391816i
$276$	0.417191	−	0.286236i	0.0251119	−	0.0172294i
$277$	24.0612	−	9.96649i	1.44570	−	0.598829i	0.484527	−	0.874776i	$-0.338992\pi$
$277$	24.0612	−	9.96649i	1.44570	−	0.598829i	0.961173	+	0.275948i	$0.0889916\pi$
$278$	2.52812	−	8.52226i	0.151626	−	0.511131i
$279$	−4.38207	−	4.38207i	−0.262348	−	0.262348i
$280$	−0.0425427	−	0.0499323i	−0.00254242	−	0.00298403i
$281$	18.0180	−	18.0180i	1.07487	−	1.07487i	0.0779048	−	0.996961i	$-0.475177\pi$
$281$	18.0180	−	18.0180i	1.07487	−	1.07487i	0.996961	−	0.0779048i	$-0.0248230\pi$
$282$	−8.43224	−	15.5451i	−0.502133	−	0.925696i
$283$	−1.15856	−	2.79702i	−0.0688695	−	0.166266i	0.885697	−	0.464264i	$-0.153681\pi$
$283$	−1.15856	−	2.79702i	−0.0688695	−	0.166266i	−0.954566	+	0.297998i	$0.903681\pi$
$284$	−14.1112	−	9.18000i	−0.837348	−	0.544733i
$285$	0.0438379	+	0.0181583i	0.00259673	+	0.00107560i
$286$	2.25944	+	1.83116i	0.133604	+	0.108279i
$287$	16.2888			0.961496
$288$	−4.90463	+	2.81863i	−0.289008	+	0.166089i
$289$	−16.8955			−0.993855
$290$	−0.0461927	−	0.0374367i	−0.00271253	−	0.00219836i
$291$	−1.14614	−	0.474748i	−0.0671881	−	0.0278302i
$292$	12.1159	−	18.6242i	0.709030	−	1.08990i
$293$	3.52001	+	8.49805i	0.205641	+	0.496461i	0.992728	−	0.120381i	$-0.0384116\pi$
$293$	3.52001	+	8.49805i	0.205641	+	0.496461i	−0.787087	+	0.616842i	$0.788412\pi$
$294$	−3.17003	−	5.84404i	−0.184880	−	0.340831i
$295$	0.0199829	−	0.0199829i	0.00116345	−	0.00116345i
$296$	−1.19473	+	14.9511i	−0.0694423	+	0.869018i
$297$	0.994607	+	0.994607i	0.0577130	+	0.0577130i
$298$	6.73564	−	22.7058i	0.390185	−	1.31531i
$299$	−0.341700	+	0.141537i	−0.0197610	+	0.00818529i
$300$	−5.65742	−	8.24571i	−0.326631	−	0.476066i
$301$	−13.2843	+	32.0710i	−0.765692	+	1.84854i
$302$	−18.6744	+	1.95520i	−1.07459	+	0.112509i
$303$			16.0956i			0.924670i
$304$	−0.688028	−	27.9854i	−0.0394611	−	1.60507i
$305$		−	0.0533810i		−	0.00305659i
$306$	−0.857364	−	8.18877i	−0.0490122	−	0.468121i
$307$	−1.41754	+	3.42224i	−0.0809032	+	0.195318i	−0.959155	−	0.282881i	$-0.908710\pi$
$307$	−1.41754	+	3.42224i	−0.0809032	+	0.195318i	0.878252	+	0.478198i	$0.158710\pi$
$308$	9.46047	+	1.76122i	0.539061	+	0.100355i
$309$	−7.32405	+	3.03372i	−0.416650	+	0.172582i
$310$	0.0569675	+	0.0168993i	0.00323554	+	0.000959818i
$311$	−22.4396	−	22.4396i	−1.27243	−	1.27243i	−0.944809	−	0.327622i	$-0.893753\pi$
$311$	−22.4396	−	22.4396i	−1.27243	−	1.27243i	−0.327622	−	0.944809i	$-0.606247\pi$
$312$	3.93440	−	1.27315i	0.222741	−	0.0720777i
$313$	−2.24961	+	2.24961i	−0.127155	+	0.127155i	−0.767821	−	0.640665i	$-0.778659\pi$
$313$	−2.24961	+	2.24961i	−0.127155	+	0.127155i	0.640665	+	0.767821i	$0.278659\pi$
$314$	−1.29119	+	0.700390i	−0.0728660	+	0.0395253i
$315$	0.00887537	+	0.0214270i	0.000500071	+	0.00120728i
$316$	2.78733	−	0.590137i	0.156800	−	0.0331978i
$317$	−31.4340	−	13.0204i	−1.76551	−	0.731298i	−0.995659	−	0.0930756i	$-0.970330\pi$
$317$	−31.4340	−	13.0204i	−1.76551	−	0.731298i	−0.769852	−	0.638223i	$-0.779670\pi$
$318$	−8.06516	+	9.95151i	−0.452272	+	0.558053i
$319$	8.72230			0.488355
$320$	0.0284514	−	0.0461793i	0.00159048	−	0.00258150i
$321$	−5.91392			−0.330083
$322$	−0.770528	+	0.950745i	−0.0429398	+	0.0529829i
$323$	37.6434	+	15.5924i	2.09453	+	0.867585i
$324$	1.95663	−	0.414259i	0.108702	−	0.0230144i
$325$	2.79746	+	6.75366i	0.155175	+	0.374626i
$326$	−9.95075	+	5.39767i	−0.551121	+	0.298949i
$327$	−1.81620	+	1.81620i	−0.100436	+	0.100436i
$328$	4.14662	+	12.8143i	0.228959	+	0.707550i
$329$	30.2472	+	30.2472i	1.66758	+	1.66758i
$330$	−0.0129300	−	0.00383567i	−0.000711775	−	0.000211147i
$331$	24.6043	−	10.1914i	1.35237	−	0.560172i	0.415422	−	0.909629i	$-0.363634\pi$
$331$	24.6043	−	10.1914i	1.35237	−	0.560172i	0.936952	+	0.349457i	$0.113634\pi$
$332$	15.5987	+	2.90396i	0.856090	+	0.159375i
$333$	2.02932	−	4.89922i	0.111206	−	0.268476i
$334$	−0.145174	−	1.38657i	−0.00794354	−	0.0758696i
$335$			0.0322002i			0.00175929i
$336$	9.43447	−	9.91006i	0.514693	−	0.540638i
$337$			20.1009i			1.09497i	0.836817	+	0.547483i	$0.184414\pi$
$337$			20.1009i			1.09497i	−0.836817	+	0.547483i	$0.815586\pi$
$338$	15.2783	−	1.59964i	0.831031	−	0.0870089i
$339$	1.69456	−	4.09103i	0.0920358	−	0.222194i
$340$	0.0446638	+	0.0650977i	0.00242224	+	0.00353042i
$341$	−8.05335	+	3.33581i	−0.436113	+	0.180644i
$342$	−2.81478	+	9.48861i	−0.152206	+	0.513085i
$343$	−5.56041	−	5.56041i	−0.300234	−	0.300234i
$344$	−28.6118	−	2.28634i	−1.54265	−	0.123271i
$345$	0.00121280	−	0.00121280i	6.52950e−5	−	6.52950e-5i
$346$	−11.6503	−	21.4777i	−0.626324	−	1.15465i
$347$	−5.23707	−	12.6434i	−0.281141	−	0.678734i	0.718722	−	0.695297i	$-0.244727\pi$
$347$	−5.23707	−	12.6434i	−0.281141	−	0.678734i	−0.999863	+	0.0165638i	$0.994727\pi$
$348$	6.76297	−	10.3958i	0.362533	−	0.557276i
$349$	−16.5877	−	6.87085i	−0.887920	−	0.367788i	−0.108357	−	0.994112i	$-0.534559\pi$
$349$	−16.5877	−	6.87085i	−0.887920	−	0.367788i	−0.779563	+	0.626324i	$0.784559\pi$
$350$	18.7913	+	15.2294i	1.00444	+	0.814044i
$351$	−1.46203			−0.0780377
$352$	1.02280	+	7.89085i	0.0545156	+	0.420584i
$353$	10.8817			0.579174			0.289587	−	0.957152i	$-0.406482\pi$
$353$	10.8817			0.579174			0.289587	+	0.957152i	$0.406482\pi$
$354$	4.57949	+	3.71143i	0.243397	+	0.197261i
$355$	−0.0527250	−	0.0218394i	−0.00279835	−	0.00115912i
$356$	23.6170	+	15.3639i	1.25170	+	0.814288i
$357$	7.62124	+	18.3993i	0.403359	+	0.973794i
$358$	−2.01052	−	3.70645i	−0.106259	−	0.195892i
$359$	5.54201	−	5.54201i	0.292496	−	0.292496i	−0.545570	−	0.838066i	$-0.683687\pi$
$359$	5.54201	−	5.54201i	0.292496	−	0.292496i	0.838066	+	0.545570i	$0.183687\pi$
$360$	−0.0145971	+	0.0124369i	−0.000769336	+	0.000655480i
$361$	−21.1979	−	21.1979i	−1.11568	−	1.11568i
$362$	−2.71357	+	9.14744i	−0.142622	+	0.480779i
$363$	−8.33479	+	3.45238i	−0.437463	+	0.181203i
$364$	−8.24773	+	5.65880i	−0.432299	+	0.296602i
$365$	0.0288240	−	0.0695874i	0.00150872	−	0.00364237i
$366$	11.0739	−	1.15944i	0.578844	−	0.0606049i
$367$		−	2.99994i		−	0.156596i	−0.996930	−	0.0782979i	$-0.975051\pi$
$367$		−	2.99994i		−	0.156596i	0.996930	−	0.0782979i	$-0.0249485\pi$
$368$	−0.944098	−	0.364139i	−0.0492145	−	0.0189821i
$369$		−	4.76183i		−	0.247891i
$370$	0.00529466	+	0.0505698i	0.000275256	+	0.00262900i
$371$	11.8568	−	28.6248i	0.615572	−	1.48612i
$372$	−2.26844	+	12.1850i	−0.117613	+	0.631764i
$373$	−15.3503	+	6.35832i	−0.794811	+	0.329221i	−0.742876	−	0.669429i	$-0.766539\pi$
$373$	−15.3503	+	6.35832i	−0.794811	+	0.329221i	−0.0519347	+	0.998650i	$0.516539\pi$
$374$	−11.1030	−	3.29367i	−0.574120	−	0.170312i
$375$	−0.0479419	−	0.0479419i	−0.00247571	−	0.00247571i
$376$	−16.0953	+	31.4953i	−0.830050	+	1.62424i
$377$	−6.41072	+	6.41072i	−0.330169	+	0.330169i
$378$	−4.25228	+	2.30660i	−0.218714	+	0.118639i
$379$	−2.50517	−	6.04801i	−0.128682	−	0.310665i	0.846387	−	0.532568i	$-0.178773\pi$
$379$	−2.50517	−	6.04801i	−0.128682	−	0.310665i	−0.975069	+	0.221903i	$0.928773\pi$
$380$	−0.0196565	−	0.0928416i	−0.00100836	−	0.00476267i
$381$	13.4821	+	5.58448i	0.690711	+	0.286102i
$382$	−4.56077	+	5.62748i	−0.233349	+	0.287927i
$383$	−32.1450			−1.64253			−0.821266	−	0.570545i	$-0.806732\pi$
$383$	−32.1450			−1.64253			−0.821266	+	0.570545i	$0.806732\pi$
$384$	10.1979	+	4.89924i	0.520410	+	0.250013i
$385$	0.0326222			0.00166258
$386$	−18.5166	+	22.8474i	−0.942471	+	1.16290i
$387$	9.37558	+	3.88349i	0.476588	+	0.197409i
$388$	0.513920	+	2.42735i	0.0260903	+	0.123230i
$389$	2.48310	+	5.99473i	0.125898	+	0.303945i	0.974244	−	0.225498i	$-0.0724010\pi$
$389$	2.48310	+	5.99473i	0.125898	+	0.303945i	−0.848346	+	0.529443i	$0.822401\pi$
$390$	0.0123225	−	0.00668418i	0.000623973	−	0.000338466i
$391$	1.04143	−	1.04143i	0.0526672	−	0.0526672i
$392$	−6.05088	+	11.8404i	−0.305616	+	0.598029i
$393$	−6.60303	−	6.60303i	−0.333079	−	0.333079i
$394$	−12.3059	−	3.65053i	−0.619963	−	0.183911i
$395$	0.00892336	−	0.00369618i	0.000448983	−	0.000185975i
$396$	0.514873	−	2.76566i	0.0258733	−	0.138979i
$397$	−9.62118	+	23.2276i	−0.482873	+	1.16576i	0.475365	+	0.879788i	$0.342316\pi$
$397$	−9.62118	+	23.2276i	−0.482873	+	1.16576i	−0.958238	+	0.285970i	$0.907684\pi$
$398$	−2.04024	−	19.4865i	−0.102268	−	0.976771i
$399$		−	23.9396i		−	1.19848i
$400$	−7.19715	+	18.6599i	−0.359858	+	0.932997i
$401$		−	4.48158i		−	0.223800i	−0.993719	−	0.111900i	$-0.964306\pi$
$401$		−	4.48158i		−	0.223800i	0.993719	−	0.111900i	$-0.0356936\pi$
$402$	−6.67997	+	0.699392i	−0.333167	+	0.0348825i
$403$	3.46730	−	8.37081i	0.172719	−	0.416980i
$404$	26.5442	−	18.2121i	1.32063	−	0.906086i
$405$	0.00626394	−	0.00259461i	0.000311258	−	0.000128927i
$406$	−8.53142	+	28.7594i	−0.423407	+	1.42730i
$407$	−5.27428	−	5.27428i	−0.261437	−	0.261437i
$408$	−12.5345	+	10.6795i	−0.620549	+	0.528713i
$409$	22.1171	−	22.1171i	1.09362	−	1.09362i	0.0984792	−	0.995139i	$-0.468602\pi$
$409$	22.1171	−	22.1171i	1.09362	−	1.09362i	0.995139	−	0.0984792i	$-0.0313978\pi$
$410$	0.0217703	+	0.0401341i	0.00107516	+	0.00198208i
$411$	−0.0590584	−	0.142579i	−0.00291313	−	0.00703293i
$412$	13.2902	+	8.64587i	0.654761	+	0.425952i
$413$	−13.1726	−	5.45626i	−0.648180	−	0.268485i
$414$	0.277939	+	0.225255i	0.0136600	+	0.0110707i
$415$	0.0537885			0.00264037
$416$	−6.55136	−	5.04788i	−0.321207	−	0.247493i
$417$	6.28571			0.307813
$418$	10.8155	+	8.76537i	0.529002	+	0.428728i
$419$	−8.59414	−	3.55981i	−0.419851	−	0.173908i	0.162748	−	0.986668i	$-0.447964\pi$
$419$	−8.59414	−	3.55981i	−0.419851	−	0.173908i	−0.582599	+	0.812760i	$0.697964\pi$
$420$	0.0252941	−	0.0388815i	0.00123423	−	0.00189722i
$421$	7.82429	+	18.8895i	0.381333	+	0.920619i	0.991709	+	0.128507i	$0.0410184\pi$
$421$	7.82429	+	18.8895i	0.381333	+	0.920619i	−0.610376	+	0.792112i	$0.708982\pi$
$422$	4.57509	+	8.43432i	0.222712	+	0.410576i
$423$	8.84240	−	8.84240i	0.429932	−	0.429932i
$424$	25.5373	+	2.04066i	1.24020	+	0.0991031i
$425$	−20.5836	−	20.5836i	−0.998453	−	0.998453i
$426$	3.38542	−	11.4122i	0.164024	−	0.552923i
$427$	−24.8820	+	10.3064i	−1.20412	+	0.498764i
$428$	6.69156	+	9.75299i	0.323449	+	0.471428i
$429$	−0.786981	+	1.89994i	−0.0379958	+	0.0917300i
$430$	−0.0967749	+	0.0101323i	−0.00466690	+	0.000488624i
$431$			17.2386i			0.830353i	0.909741	+	0.415177i	$0.136280\pi$
$431$			17.2386i			0.830353i	−0.909741	+	0.415177i	$0.863720\pi$
$432$	−2.89709	−	2.75806i	−0.139386	−	0.132697i
$433$		−	20.8456i		−	1.00177i	−0.865513	−	0.500887i	$-0.833007\pi$
$433$		−	20.8456i		−	1.00177i	0.865513	−	0.500887i	$-0.166993\pi$
$434$	−3.12179	−	29.8165i	−0.149851	−	1.43124i
$435$	0.0160893	−	0.0388429i	0.000771421	−	0.00186238i
$436$	5.05021	+	0.940179i	0.241861	+	0.0450264i
$437$	−1.63565	+	0.677508i	−0.0782437	+	0.0324096i
$438$	15.0620	+	4.46813i	0.719691	+	0.213495i
$439$	−11.5583	−	11.5583i	−0.551648	−	0.551648i	0.375269	−	0.926916i	$-0.377550\pi$
$439$	−11.5583	−	11.5583i	−0.551648	−	0.551648i	−0.926916	+	0.375269i	$0.877550\pi$
$440$	0.00830462	+	0.0256637i	0.000395907	+	0.00122347i
$441$	3.32423	−	3.32423i	0.158297	−	0.158297i
$442$	10.5812	−	5.73967i	0.503299	−	0.273008i
$443$	7.86432	+	18.9861i	0.373645	+	0.902059i	0.993126	+	0.117047i	$0.0373429\pi$
$443$	7.86432	+	18.9861i	0.373645	+	0.902059i	−0.619481	+	0.785011i	$0.712657\pi$
$444$	−10.3758	+	2.19676i	−0.492412	+	0.104254i
$445$	0.0882424	+	0.0365512i	0.00418309	+	0.00173269i
$446$	13.0049	−	16.0466i	0.615799	−	0.759827i
$447$	16.7470			0.792105
$448$	−27.0183	−	4.34576i	−1.27650	−	0.205318i
$449$	−2.11825			−0.0999665			−0.0499832	−	0.998750i	$-0.515917\pi$
$449$	−2.11825			−0.0999665			−0.0499832	+	0.998750i	$0.515917\pi$
$450$	4.45212	−	5.49342i	0.209875	−	0.258962i
$451$	−6.18808	−	2.56319i	−0.291385	−	0.120696i
$452$	−8.66413	+	1.83438i	−0.407526	+	0.0862818i
$453$	−5.08087	−	12.2663i	−0.238720	−	0.576321i
$454$	−5.04733	+	2.73786i	−0.236883	+	0.128494i
$455$	−0.0239767	+	0.0239767i	−0.00112405	+	0.00112405i
$456$	18.8331	−	6.09428i	0.881942	−	0.285391i
$457$	7.54089	+	7.54089i	0.352748	+	0.352748i	0.861131	−	0.508383i	$-0.169757\pi$
$457$	7.54089	+	7.54089i	0.352748	+	0.352748i	−0.508383	+	0.861131i	$0.669757\pi$
$458$	7.31753	+	2.17073i	0.341926	+	0.101432i
$459$	5.37882	−	2.22798i	0.251062	−	0.103993i
$460$	−0.00337238		0.000627824i	−0.000157238		2.92724e-5i
$461$	−1.56851	+	3.78672i	−0.0730529	+	0.176365i	−0.956188	−	0.292754i	$-0.905428\pi$
$461$	−1.56851	+	3.78672i	−0.0730529	+	0.176365i	0.883135	+	0.469119i	$0.155428\pi$
$462$	0.708558	+	6.76751i	0.0329651	+	0.314853i
$463$		−	8.35374i		−	0.388231i	−0.980979	−	0.194116i	$-0.937816\pi$
$463$		−	8.35374i		−	0.388231i	0.980979	−	0.194116i	$-0.0621837\pi$
$464$	−24.7966	+	0.609632i	−1.15116	+	0.0283015i
$465$			0.0420172i			0.00194850i
$466$	−40.7778	+	4.26943i	−1.88899	+	0.197778i
$467$	11.8505	−	28.6097i	0.548377	−	1.32390i	−0.370308	−	0.928909i	$-0.620748\pi$
$467$	11.8505	−	28.6097i	0.548377	−	1.32390i	0.918685	−	0.394990i	$-0.129252\pi$
$468$	1.65428	+	2.41113i	0.0764693	+	0.111454i
$469$	15.0092	−	6.21700i	0.693059	−	0.287075i
$470$	−0.0341005	+	0.114952i	−0.00157294	+	0.00530236i
$471$	−0.734458	−	0.734458i	−0.0338420	−	0.0338420i
$472$	0.939072	−	11.7518i	0.0432243	−	0.540919i
$473$	10.0933	−	10.0933i	0.464092	−	0.464092i
$474$	0.960592	+	1.77088i	0.0441214	+	0.0813391i
$475$	13.3908	+	32.3283i	0.614414	+	1.48333i
$476$	21.7200	−	33.3873i	0.995533	−	1.53031i
$477$	−8.36811	−	3.46618i	−0.383149	−	0.158706i
$478$	2.45746	+	1.99164i	0.112401	+	0.0910953i
$479$	−4.36086			−0.199253			−0.0996264	−	0.995025i	$-0.531765\pi$
$479$	−4.36086			−0.199253			−0.0996264	+	0.995025i	$0.531765\pi$
$480$	0.0370269	+	0.0100007i	0.00169004	+	0.000456469i
$481$	7.75299			0.353506
$482$	21.6173	+	17.5197i	0.984643	+	0.798000i
$483$	−0.799470	−	0.331151i	−0.0363772	−	0.0150679i
$484$	15.1243	+	9.83903i	0.687468	+	0.447229i
$485$	0.00321881	+	0.00777090i	0.000146159	+	0.000352858i
$486$	0.674307	+	1.24310i	0.0305872	+	0.0563884i
$487$	7.91861	−	7.91861i	0.358827	−	0.358827i	−0.504554	−	0.863380i	$-0.668343\pi$
$487$	7.91861	−	7.91861i	0.358827	−	0.358827i	0.863380	+	0.504554i	$0.168343\pi$
$488$	−14.4422	−	16.9508i	−0.653768	−	0.767326i
$489$	−5.66022	−	5.66022i	−0.255964	−	0.255964i
$490$	−0.0128198	+	0.0432154i	−0.000579139	+	0.00195227i
$491$	37.8921	−	15.6954i	1.71005	−	0.708324i	0.710054	−	0.704147i	$-0.248671\pi$
$491$	37.8921	−	15.6954i	1.71005	−	0.708324i	0.999991	−	0.00417652i	$-0.00132943\pi$
$492$	−7.85301	+	5.38798i	−0.354041	+	0.242909i
$493$	13.8158	−	33.3542i	0.622231	−	1.50220i
$494$	−14.3915	+	1.50679i	−0.647506	+	0.0677939i
$495$		−	0.00953672i		−	0.000428644i
$496$	22.6617	−	10.0463i	1.01754	−	0.451090i
$497$			28.7928i			1.29153i
$498$	1.16829	+	11.1585i	0.0523524	+	0.500023i
$499$	−9.18191	+	22.1671i	−0.411039	+	0.992336i	0.573821	+	0.818981i	$0.305461\pi$
$499$	−9.18191	+	22.1671i	−0.411039	+	0.992336i	−0.984859	+	0.173355i	$0.944539\pi$
$500$	−0.0248178	+	0.133310i	−0.00110989	+	0.00596179i
$501$	0.910770	−	0.377253i	0.0406902	−	0.0168544i
$502$	8.57180	+	2.54281i	0.382578	+	0.113491i
$503$	16.5963	+	16.5963i	0.739995	+	0.739995i	0.972577	−	0.232582i	$-0.0747175\pi$
$503$	16.5963	+	16.5963i	0.739995	+	0.739995i	−0.232582	+	0.972577i	$0.574717\pi$
$504$	8.61538	+	4.40278i	0.383760	+	0.196116i
$505$	0.0771659	−	0.0771659i	0.00343384	−	0.00343384i
$506$	0.442331	−	0.239937i	0.0196640	−	0.0106665i
$507$	4.15688	+	10.0356i	0.184614	+	0.445697i
$508$	−6.04526	−	28.5530i	−0.268215	−	1.26683i
$509$	5.26058	+	2.17900i	0.233171	+	0.0965826i	0.496210	−	0.868203i	$-0.334725\pi$
$509$	5.26058	+	2.17900i	0.233171	+	0.0965826i	−0.263039	+	0.964785i	$0.584725\pi$
$510$	−0.0351483	+	0.0433691i	−0.00155639	+	0.00192042i
$511$	−38.0012			−1.68107
$512$	−3.45925	−	22.3614i	−0.152879	−	0.988245i
$513$	−6.99846			−0.308989
$514$	8.42361	−	10.3938i	0.371549	−	0.458450i
$515$	0.0496573	+	0.0205687i	0.00218816	+	0.000906367i
$516$	−4.20392	−	19.8560i	−0.185067	−	0.874110i
$517$	−6.73118	−	16.2505i	−0.296037	−	0.714697i
$518$	22.5494	−	12.2316i	0.990762	−	0.537427i
$519$	12.2170	−	12.2170i	0.536266	−	0.536266i
$520$	−0.0249661	−	0.0127586i	−0.00109483	−	0.000559501i
$521$	13.8290	+	13.8290i	0.605861	+	0.605861i	0.941862	−	0.336001i	$-0.109074\pi$
$521$	13.8290	+	13.8290i	0.605861	+	0.605861i	−0.336001	+	0.941862i	$0.609074\pi$
$522$	8.40746	+	2.49406i	0.367984	+	0.109162i
$523$	−20.8657	+	8.64286i	−0.912393	+	0.377926i	−0.788972	−	0.614429i	$-0.789387\pi$
$523$	−20.8657	+	8.64286i	−0.912393	+	0.377926i	−0.123421	+	0.992354i	$0.539387\pi$
$524$	−3.41815	+	18.3607i	−0.149323	+	0.802092i
$525$	−6.54516	+	15.8014i	−0.285654	+	0.689630i
$526$	1.46150	+	13.9589i	0.0637244	+	0.608639i
$527$			36.0799i			1.57167i
$528$	−5.14358	+	2.28022i	−0.223846	+	0.0992337i
$529$		−	22.9360i		−	0.997218i
$530$	0.0863757	−	0.00904353i	0.00375192	−	0.000392826i
$531$	−1.59507	+	3.85084i	−0.0692202	+	0.167112i
$532$	−39.4802	+	27.0875i	−1.71168	+	1.17439i
$533$	6.43201	−	2.66423i	0.278601	−	0.115400i
$534$	−5.66595	+	19.0999i	−0.245189	+	0.826532i
$535$	0.0283526	+	0.0283526i	0.00122579	+	0.00122579i
$536$	8.71175	+	10.2250i	0.376290	+	0.441651i
$537$	2.10832	−	2.10832i	0.0909805	−	0.0909805i
$538$	−1.02174	−	1.88360i	−0.0440502	−	0.0812077i
$539$	−2.53053	−	6.10925i	−0.108998	−	0.263144i
$540$	−0.0113665	−	0.00739444i	−0.000489138	−	0.000318206i
$541$	24.5863	+	10.1840i	1.05705	+	0.437843i	0.842402	−	0.538849i	$-0.181141\pi$
$541$	24.5863	+	10.1840i	1.05705	+	0.437843i	0.214645	+	0.976692i	$0.431141\pi$
$542$	2.41267	+	1.95534i	0.103633	+	0.0839889i
$543$	−6.74682			−0.289534
$544$	31.7948	+	8.58757i	1.36319	+	0.368189i
$545$	0.0174145			0.000745953
$546$	−5.49477	−	4.45321i	−0.235154	−	0.190580i
$547$	9.15022	+	3.79015i	0.391235	+	0.162055i	0.569625	−	0.821905i	$-0.307089\pi$
$547$	9.15022	+	3.79015i	0.391235	+	0.162055i	−0.178389	+	0.983960i	$0.557089\pi$
$548$	−0.168312	+	0.258724i	−0.00718993	+	0.0110522i
$549$	3.01297	+	7.27395i	0.128590	+	0.310444i
$550$	−4.74232	−	8.74260i	−0.202213	−	0.372786i
$551$	−30.6868	+	30.6868i	−1.30730	+	1.30730i
$552$	0.0569942	−	0.713239i	0.00242584	−	0.0303575i
$553$	−3.44572	−	3.44572i	−0.146527	−	0.146527i
$554$	10.4748	−	35.3104i	0.445031	−	1.50020i
$555$	−0.0332169	+	0.0137589i	−0.00140998	+	0.000584033i
$556$	−7.11224	−	10.3661i	−0.301626	−	0.439622i
$557$	−2.57099	+	6.20693i	−0.108936	+	0.262996i	−0.968942	−	0.247289i	$-0.920460\pi$
$557$	−2.57099	+	6.20693i	−0.108936	+	0.262996i	0.860005	+	0.510285i	$0.170460\pi$
$558$	−8.71650	+	0.912617i	−0.368999	+	0.0386342i
$559$			14.8368i			0.627530i
$560$	−0.0927418	+	0.00228008i	−0.00391906	+	9.63511e-5i
$561$		−	8.18913i		−	0.345746i
$562$	−3.75246	−	35.8402i	−0.158288	−	1.51183i
$563$	−16.2626	+	39.2615i	−0.685388	+	1.65467i	0.0684842	+	0.997652i	$0.478184\pi$
$563$	−16.2626	+	39.2615i	−0.685388	+	1.65467i	−0.753872	+	0.657021i	$0.771816\pi$
$564$	−24.5876	−	4.57739i	−1.03533	−	0.192743i
$565$	−0.0277373	+	0.0114892i	−0.00116692	+	0.000483353i
$566$	−4.10469	−	1.21765i	−0.172533	−	0.0511817i
$567$	−2.41880	−	2.41880i	−0.101580	−	0.101580i
$568$	−22.6511	+	7.32976i	−0.950420	+	0.307550i
$569$	−23.1230	+	23.1230i	−0.969368	+	0.969368i	−0.999545	−	0.0301764i	$-0.990393\pi$
$569$	−23.1230	+	23.1230i	−0.969368	+	0.969368i	0.0301764	+	0.999545i	$0.490393\pi$
$570$	0.0589851	−	0.0319958i	0.00247061	−	0.00134015i
$571$	−3.47053	−	8.37861i	−0.145237	−	0.350634i	0.834474	−	0.551047i	$-0.185772\pi$
$571$	−3.47053	−	8.37861i	−0.145237	−	0.350634i	−0.979711	+	0.200413i	$0.935772\pi$
$572$	4.02376	−	0.851914i	0.168242	−	0.0356203i
$573$	−4.73208	−	1.96009i	−0.197686	−	0.0818841i
$574$	14.5041	−	17.8964i	0.605388	−	0.746981i
$575$	1.26485			0.0527478
$576$	−1.27043	+	7.89848i	−0.0529346	+	0.329103i
$577$	18.7910			0.782278			0.391139	−	0.920332i	$-0.372081\pi$
$577$	18.7910			0.782278			0.391139	+	0.920332i	$0.372081\pi$
$578$	−15.0443	+	18.5630i	−0.625762	+	0.772120i
$579$	−19.2121	−	7.95793i	−0.798429	−	0.330720i
$580$	−0.0822630	+	0.0174168i	−0.00341579	+	0.000723193i
$581$	−10.3851	−	25.0719i	−0.430847	−	1.04016i
$582$	−1.54217	+	0.836530i	−0.0639249	+	0.0346753i
$583$	−9.00873	+	9.00873i	−0.373104	+	0.373104i
$584$	−9.67393	−	29.8953i	−0.400310	−	1.23708i
$585$	0.00700931	+	0.00700931i	0.000289799	+	0.000289799i
$586$	12.4711	+	3.69953i	0.515176	+	0.152826i
$587$	−28.1601	+	11.6643i	−1.16229	+	0.481436i	−0.878637	−	0.477490i	$-0.841547\pi$
$587$	−28.1601	+	11.6643i	−1.16229	+	0.481436i	−0.283653	+	0.958927i	$0.591547\pi$
$588$	−9.24352	−	1.72083i	−0.381196	−	0.0709659i
$589$	16.5973	−	40.0693i	0.683878	−	1.65103i
$590$	−0.00416166	−	0.0397485i	−0.000171333	−	0.00163642i
$591$		−	9.07640i		−	0.373353i
$592$	15.3629	+	14.6256i	0.631412	+	0.601110i
$593$			12.2535i			0.503189i	0.967833	+	0.251594i	$0.0809549\pi$
$593$			12.2535i			0.503189i	−0.967833	+	0.251594i	$0.919045\pi$
$594$	1.97840	−	0.207138i	0.0811748	−	0.00849899i
$595$	0.0516723	−	0.124748i	0.00211836	−	0.00511417i
$596$	−18.9491	−	27.6184i	−0.776185	−	1.13129i
$597$	12.7998	−	5.30184i	0.523859	−	0.216990i
$598$	−0.148755	+	0.501454i	−0.00608306	+	0.0205060i
$599$	8.63937	+	8.63937i	0.352995	+	0.352995i	0.861223	−	0.508228i	$-0.169699\pi$
$599$	8.63937	+	8.63937i	0.352995	+	0.352995i	−0.508228	+	0.861223i	$0.669699\pi$
$600$	−14.0971	−	1.12648i	−0.575510	−	0.0459884i
$601$	−14.3695	+	14.3695i	−0.586143	+	0.586143i	−0.936585	−	0.350441i	$-0.886032\pi$
$601$	−14.3695	+	14.3695i	−0.586143	+	0.586143i	0.350441	+	0.936585i	$0.386032\pi$
$602$	23.4075	+	43.1524i	0.954019	+	1.75876i
$603$	−1.81747	−	4.38775i	−0.0740130	−	0.178683i
$604$	−14.4801	+	22.2584i	−0.589187	+	0.905681i
$605$	0.0565102	+	0.0234073i	0.00229747	+	0.000951642i
$606$	17.6842	+	14.3321i	0.718371	+	0.582201i
$607$	21.4916			0.872319			0.436159	−	0.899869i	$-0.356338\pi$
$607$	21.4916			0.872319			0.436159	+	0.899869i	$0.356338\pi$
$608$	−31.3600	−	24.1632i	−1.27182	−	0.979945i
$609$	−21.2119			−0.859548
$610$	−0.0586494	−	0.0475322i	−0.00237465	−	0.00192452i
$611$	16.8911	+	6.99653i	0.683341	+	0.283049i
$612$	−9.76038	−	6.34957i	−0.394540	−	0.256666i
$613$	12.3921	+	29.9172i	0.500513	+	1.20834i	0.949205	+	0.314658i	$0.101890\pi$
$613$	12.3921	+	29.9172i	0.500513	+	1.20834i	−0.448693	+	0.893686i	$0.648110\pi$
$614$	2.49777	+	4.60472i	0.100802	+	0.185831i
$615$	−0.0228292	+	0.0228292i	−0.000920563	+	0.000920563i
$616$	10.3590	−	8.82592i	0.417374	−	0.355606i
$617$	17.5651	+	17.5651i	0.707143	+	0.707143i	0.965933	−	0.258790i	$-0.0833239\pi$
$617$	17.5651	+	17.5651i	0.707143	+	0.707143i	−0.258790	+	0.965933i	$0.583324\pi$
$618$	−3.18844	+	10.7482i	−0.128258	+	0.432357i
$619$	−16.3569	+	6.77526i	−0.657440	+	0.272321i	−0.686361	−	0.727261i	$-0.740793\pi$
$619$	−16.3569	+	6.77526i	−0.657440	+	0.272321i	0.0289208	+	0.999582i	$0.490793\pi$
$620$	0.0692930	−	0.0475422i	0.00278287	−	0.00190934i
$621$	−0.0968082	+	0.233716i	−0.00388478	+	0.00937869i
$622$	−44.6351	+	4.67330i	−1.78971	+	0.187382i
$623$		−	48.1886i		−	1.93064i
$624$	2.10452	−	5.45635i	0.0842481	−	0.218429i
$625$		−	24.9993i		−	0.999972i
$626$	0.468507	+	4.47476i	0.0187253	+	0.178847i
$627$	−3.76711	+	9.09461i	−0.150444	+	0.363204i
$628$	−0.380202	+	2.04227i	−0.0151717	+	0.0814955i
$629$	−28.5232	+	11.8147i	−1.13729	+	0.471083i
$630$	0.0314447	+	0.00932802i	0.00125279	+	0.000371637i
$631$	23.6874	+	23.6874i	0.942982	+	0.942982i	0.998460	−	0.0554784i	$-0.0176684\pi$
$631$	23.6874	+	23.6874i	0.942982	+	0.942982i	−0.0554784	+	0.998460i	$0.517668\pi$
$632$	1.83355	−	3.58791i	0.0729349	−	0.142719i
$633$	−4.79763	+	4.79763i	−0.190689	+	0.190689i
$634$	−42.2953	+	22.9426i	−1.67976	+	0.911167i
$635$	−0.0378630	−	0.0914094i	−0.00150255	−	0.00362747i
$636$	3.75218	+	17.7223i	0.148784	+	0.702735i
$637$	6.35007	+	2.63029i	0.251599	+	0.104216i
$638$	7.76662	−	9.58314i	0.307483	−	0.379400i
$639$	8.41723			0.332981
$640$	−0.0254029	−	0.0723790i	−0.00100414	−	0.00286103i
$641$	6.79529			0.268398			0.134199	−	0.990954i	$-0.457154\pi$
$641$	6.79529			0.268398			0.134199	+	0.990954i	$0.457154\pi$
$642$	−5.26595	+	6.49759i	−0.207830	+	0.256439i
$643$	−18.4729	−	7.65173i	−0.728500	−	0.301755i	−0.0125646	−	0.999921i	$-0.504000\pi$
$643$	−18.4729	−	7.65173i	−0.728500	−	0.301755i	−0.715935	+	0.698166i	$0.754000\pi$
$644$	0.358475	+	1.69315i	0.0141259	+	0.0667194i
$645$	−0.0263302	−	0.0635668i	−0.00103675	−	0.00250294i
$646$	50.6502	−	27.4746i	1.99281	−	1.08097i
$647$	−5.34732	+	5.34732i	−0.210225	+	0.210225i	−0.804363	−	0.594138i	$-0.797493\pi$
$647$	−5.34732	+	5.34732i	−0.210225	+	0.210225i	0.594138	+	0.804363i	$0.297493\pi$
$648$	1.28710	−	2.51860i	0.0505621	−	0.0989401i
$649$	4.14565	+	4.14565i	0.162731	+	0.162731i
$650$	9.91115	+	2.94013i	0.388747	+	0.115321i
$651$	19.5850	−	8.11239i	0.767598	−	0.317950i
$652$	−2.93009	+	15.7391i	−0.114751	+	0.616390i
$653$	−1.51225	+	3.65091i	−0.0591791	+	0.142871i	−0.950703	−	0.310102i	$-0.899637\pi$
$653$	−1.51225	+	3.65091i	−0.0591791	+	0.142871i	0.891524	+	0.452973i	$0.149637\pi$
$654$	0.378243	+	3.61264i	0.0147905	+	0.141266i
$655$			0.0633126i			0.00247383i
$656$	17.7713	+	6.85438i	0.693851	+	0.267619i
$657$			11.1092i			0.433411i
$658$	60.1655	−	6.29932i	2.34549	−	0.245573i
$659$	−7.07771	+	17.0871i	−0.275708	+	0.665619i	−0.999708	−	0.0241818i	$-0.992302\pi$
$659$	−7.07771	+	17.0871i	−0.275708	+	0.665619i	0.723999	+	0.689801i	$0.242302\pi$
$660$	−0.0157276	+	0.0107907i	−0.000612194	+	0.000420029i
$661$	15.2261	−	6.30685i	0.592226	−	0.245308i	−0.0663821	−	0.997794i	$-0.521146\pi$
$661$	15.2261	−	6.30685i	0.592226	−	0.245308i	0.658608	+	0.752486i	$0.271146\pi$
$662$	10.7112	−	36.1074i	0.416303	−	1.40335i
$663$	6.01886	+	6.01886i	0.233753	+	0.233753i
$664$	17.0802	−	14.5524i	0.662839	−	0.564744i
$665$	−0.114772	+	0.114772i	−0.00445065	+	0.00445065i
$666$	−3.57577	−	6.59203i	−0.138558	−	0.255436i
$667$	0.600311	+	1.44928i	0.0232441	+	0.0561163i
$668$	−1.65268	−	1.07514i	−0.0639442	−	0.0415986i
$669$	13.4934	+	5.58914i	0.521684	+	0.216089i
$670$	0.0353782	+	0.0286722i	0.00136678	+	0.00110770i
$671$	11.0744			0.427524
$672$	−2.48737	−	19.1898i	−0.0959522	−	0.740265i
$673$	5.46222			0.210553			0.105276	−	0.994443i	$-0.466427\pi$
$673$	5.46222			0.210553			0.105276	+	0.994443i	$0.466427\pi$
$674$	22.0848	+	17.8985i	0.850673	+	0.689425i
$675$	4.61936	+	1.91340i	0.177799	+	0.0736468i
$676$	11.8468	−	18.2106i	0.455646	−	0.700407i
$677$	−4.02477	−	9.71665i	−0.154684	−	0.373441i	0.827472	−	0.561507i	$-0.189778\pi$
$677$	−4.02477	−	9.71665i	−0.154684	−	0.373441i	−0.982156	+	0.188066i	$0.939778\pi$
$678$	−2.98590	−	5.50458i	−0.114673	−	0.211402i
$679$	3.00070	−	3.00070i	0.115156	−	0.115156i
$680$	0.111293	+	0.00889328i	0.00426788	+	0.000341042i
$681$	−2.87104	−	2.87104i	−0.110018	−	0.110018i
$682$	−3.50594	+	11.8185i	−0.134249	+	0.452553i
$683$	39.7212	−	16.4530i	1.51989	−	0.629558i	0.542319	−	0.840173i	$-0.317547\pi$
$683$	39.7212	−	16.4530i	1.51989	−	0.629558i	0.977569	+	0.210615i	$0.0675466\pi$
$684$	7.91871	+	11.5416i	0.302779	+	0.441302i
$685$	−0.000400418	0	0.000966695i	−1.52992e−5	0	3.69355e-5i
$686$	−11.0604	+	1.15802i	−0.422287	+	0.0442134i
$687$			5.39714i			0.205914i
$688$	−27.9889	+	29.3998i	−1.06707	+	1.12086i
$689$		−	13.2425i		−	0.504499i
$690$	−0.000252580	−	0.00241242i	−9.61555e−6	−	9.18391e-5i
$691$	7.36888	−	17.7900i	0.280325	−	0.676765i	−0.719518	−	0.694474i	$-0.755637\pi$
$691$	7.36888	−	17.7900i	0.280325	−	0.676765i	0.999843	+	0.0177088i	$0.00563718\pi$
$692$	−33.9712	−	6.32429i	−1.29139	−	0.240414i
$693$	−4.44525	+	1.84128i	−0.168861	+	0.0699446i
$694$	−18.5545	−	5.50416i	−0.704319	−	0.208935i
$695$	−0.0301350	−	0.0301350i	−0.00114309	−	0.00114309i
$696$	−5.39989	−	16.6872i	−0.204682	−	0.632528i
$697$	−19.6033	+	19.6033i	−0.742529	+	0.742529i
$698$	−22.3192	+	12.1068i	−0.844795	+	0.458249i
$699$	−11.0947	−	26.7850i	−0.419640	−	1.01310i
$700$	33.4648	−	7.08520i	1.26485	−	0.267795i
$701$	0.759834	+	0.314734i	0.0286985	+	0.0118873i	0.396987	−	0.917824i	$-0.370056\pi$
$701$	0.759834	+	0.314734i	0.0286985	+	0.0118873i	−0.368288	+	0.929712i	$0.620056\pi$
$702$	−1.30184	+	1.60633i	−0.0491349	+	0.0606270i
$703$	37.1120			1.39970
$704$	9.58037	+	5.90252i	0.361074	+	0.222460i
$705$	−0.0847847			−0.00319318
$706$	9.68941	−	11.9556i	0.364666	−	0.449957i
$707$	−50.8672	−	21.0699i	−1.91306	−	0.792415i
$708$	8.15546	−	1.72668i	0.306501	−	0.0648927i
$709$	−18.3991	−	44.4194i	−0.690994	−	1.66821i	−0.742768	−	0.669548i	$-0.766488\pi$
$709$	−18.3991	−	44.4194i	−0.690994	−	1.66821i	0.0517745	−	0.998659i	$-0.483512\pi$
$710$	−0.0709430	+	0.0384822i	−0.00266244	+	0.00144421i
$711$	−1.00732	+	1.00732i	−0.0377773	+	0.0377773i
$712$	37.9097	−	12.2673i	1.42072	−	0.459738i
$713$	−1.10854	−	1.10854i	−0.0415152	−	0.0415152i
$714$	27.0014	+	8.00993i	1.01050	+	0.299764i
$715$	0.0128817	−	0.00533576i	0.000481747	−	0.000199546i
$716$	−5.86249	−	1.09140i	−0.219092	−	0.0407875i
$717$	−0.855950	+	2.06645i	−0.0319660	+	0.0771729i
$718$	−1.15419	−	11.0238i	−0.0430739	−	0.411403i
$719$		−	0.494401i		−	0.0184380i	−0.999958	−	0.00921901i	$-0.997065\pi$
$719$		−	0.494401i		−	0.0184380i	0.999958	−	0.00921901i	$-0.00293455\pi$
$720$	0.000666555		0.0271120i	2.48410e−5		0.00101040i
$721$		−	27.1175i		−	1.00991i
$722$	−42.1653	+	4.41471i	−1.56923	+	0.164298i
$723$	−7.52948	+	18.1778i	−0.280024	+	0.676039i
$724$	7.63398	+	11.1266i	0.283715	+	0.413516i
$725$	28.6448	−	11.8651i	1.06384	−	0.440657i
$726$	−3.62846	+	12.2315i	−0.134665	+	0.453954i
$727$	13.9621	+	13.9621i	0.517826	+	0.517826i	0.916913	−	0.399087i	$-0.130673\pi$
$727$	13.9621	+	13.9621i	0.517826	+	0.517826i	−0.399087	+	0.916913i	$0.630673\pi$
$728$	−1.12676	+	14.1005i	−0.0417604	+	0.522600i
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$	−0.0507894	−	0.0936317i	−0.00187980	−	0.00346546i
$731$	−22.6097	−	54.5845i	−0.836248	−	2.01888i
$732$	8.58673	−	13.1993i	0.317375	−	0.487859i
$733$	21.0117	+	8.70335i	0.776087	+	0.321466i	0.735335	−	0.677704i	$-0.237025\pi$
$733$	21.0117	+	8.70335i	0.776087	+	0.321466i	0.0407515	+	0.999169i	$0.487025\pi$
$734$	−3.29602	−	2.67125i	−0.121658	−	0.0985976i
$735$	−0.0318741			−0.00117569
$736$	−1.24073	+	0.713033i	−0.0457340	+	0.0262828i
$737$	−6.68026			−0.246071
$738$	−5.23179	−	4.24009i	−0.192585	−	0.156080i
$739$	−23.9176	−	9.90698i	−0.879822	−	0.364434i	−0.103394	−	0.994640i	$-0.532970\pi$
$739$	−23.9176	−	9.90698i	−0.879822	−	0.364434i	−0.776428	+	0.630206i	$0.782970\pi$
$740$	0.0602753	+	0.0392118i	0.00221577	+	0.00144146i
$741$	−3.91561	−	9.45312i	−0.143844	−	0.347269i
$742$	−20.8922	−	38.5154i	−0.766977	−	1.41394i
$743$	22.7644	−	22.7644i	0.835144	−	0.835144i	−0.153071	−	0.988215i	$-0.548916\pi$
$743$	22.7644	−	22.7644i	0.835144	−	0.835144i	0.988215	+	0.153071i	$0.0489164\pi$
$744$	11.3677	+	13.3423i	0.416761	+	0.489151i
$745$	−0.0802886	−	0.0802886i	−0.00294155	−	0.00294155i
$746$	−6.68260	+	22.5270i	−0.244667	+	0.824772i
$747$	−7.32946	+	3.03596i	−0.268171	+	0.111080i
$748$	−13.5052	+	9.26595i	−0.493798	+	0.338797i
$749$	7.74158	−	18.6898i	0.282871	−	0.682912i
$750$	−0.0953626	+	0.00998445i	−0.00348215	+	0.000364581i
$751$		−	31.4436i		−	1.14739i	−0.819068	−	0.573697i	$-0.805509\pi$
$751$		−	31.4436i		−	1.14739i	0.819068	−	0.573697i	$-0.194491\pi$
$752$	20.2719	+	45.7282i	0.739241	+	1.66754i
$753$			6.32225i			0.230396i
$754$	1.33511	+	12.7517i	0.0486217	+	0.464391i
$755$	−0.0344485	+	0.0831660i	−0.00125371	+	0.00302672i
$756$	−1.25212	+	6.72583i	−0.0455393	+	0.244616i
$757$	−23.6692	+	9.80412i	−0.860273	+	0.356337i	−0.768814	−	0.639472i	$-0.779153\pi$
$757$	−23.6692	+	9.80412i	−0.860273	+	0.356337i	−0.0914586	+	0.995809i	$0.529153\pi$
$758$	−8.87560	−	2.63293i	−0.322376	−	0.0956324i
$759$	0.251608	+	0.251608i	0.00913279	+	0.00913279i
$760$	−0.119507	−	0.0610727i	−0.00433499	−	0.00221534i
$761$	−5.35154	+	5.35154i	−0.193993	+	0.193993i	−0.797419	−	0.603426i	$-0.793802\pi$
$761$	−5.35154	+	5.35154i	−0.193993	+	0.193993i	0.603426	+	0.797419i	$0.293802\pi$
$762$	18.1406	−	9.84014i	0.657164	−	0.356471i
$763$	−3.36226	−	8.11722i	−0.121722	−	0.293863i
$764$	2.12182	+	10.0218i	0.0767647	+	0.362575i
$765$	−0.0364686	−	0.0151058i	−0.00131852	−	0.000546151i
$766$	−28.6230	+	35.3175i	−1.03419	+	1.27607i
$767$	−6.09394			−0.220040
$768$	14.4633	−	6.84194i	0.521900	−	0.246887i
$769$	16.9993			0.613011			0.306505	−	0.951869i	$-0.400840\pi$
$769$	16.9993			0.613011			0.306505	+	0.951869i	$0.400840\pi$
$770$	0.0290479	−	0.0358419i	0.00104681	−	0.00129165i
$771$	8.74002	+	3.62023i	0.314764	+	0.130380i
$772$	8.61453	+	40.6882i	0.310044	+	1.46440i
$773$	−16.2444	−	39.2174i	−0.584269	−	1.41055i	−0.888910	−	0.458083i	$-0.848536\pi$
$773$	−16.2444	−	39.2174i	−0.584269	−	1.41055i	0.304640	−	0.952467i	$-0.401464\pi$
$774$	12.6151	−	6.84291i	0.453440	−	0.245963i
$775$	−21.9102	+	21.9102i	−0.787036	+	0.787036i
$776$	3.12452	+	1.59675i	0.112164	+	0.0573199i
$777$	12.8266	+	12.8266i	0.460151	+	0.460151i
$778$	8.79740	+	2.60974i	0.315402	+	0.0935636i
$779$	30.7887	−	12.7531i	1.10312	−	0.456927i
$780$	0.00362847	−	0.0194904i	0.000129920	−	0.000697870i
$781$	4.53081	−	10.9383i	0.162125	−	0.391405i
$782$	−0.216889	−	2.07153i	−0.00775594	−	0.0740778i
$783$			6.20104i			0.221607i
$784$	7.62106	+	17.1911i	0.272181	+	0.613969i
$785$			0.00704229i			0.000251350i
$786$	−13.1343	+	1.37516i	−0.468484	+	0.0490502i
$787$	1.91880	−	4.63239i	0.0683978	−	0.165127i	−0.885984	−	0.463716i	$-0.846516\pi$
$787$	1.91880	−	4.63239i	0.0683978	−	0.165127i	0.954382	+	0.298589i	$0.0965159\pi$
$788$	−14.9684	+	10.2699i	−0.533228	+	0.365850i
$789$	−9.16896	+	3.79791i	−0.326424	+	0.135209i
$790$	0.00388469	−	0.0130952i	0.000138211	−	0.000465908i
$791$	10.7107	+	10.7107i	0.380827	+	0.380827i
$792$	−2.58015	−	3.02832i	−0.0916817	−	0.107607i
$793$	−8.13949	+	8.13949i	−0.289042	+	0.289042i
$794$	16.9530	+	31.2533i	0.601639	+	1.10914i
$795$	0.0235009	+	0.0567361i	0.000833490	+	0.00201222i
$796$	−23.2264	−	15.1098i	−0.823239	−	0.535554i
$797$	−8.85578	−	3.66818i	−0.313688	−	0.129934i	0.220285	−	0.975436i	$-0.429301\pi$
$797$	−8.85578	−	3.66818i	−0.313688	−	0.129934i	−0.533972	+	0.845502i	$0.679301\pi$
$798$	−26.3023	−	21.3166i	−0.931091	−	0.754599i
$799$	−72.8042			−2.57563
$800$	14.0930	+	24.5229i	0.498263	+	0.867015i
$801$	−14.0874			−0.497752
$802$	−4.92389	−	3.99055i	−0.173869	−	0.140911i
$803$	14.4366	+	5.97983i	0.509456	+	0.211024i
$804$	−5.17964	+	7.96200i	−0.182672	+	0.280798i
$805$	0.00224522	+	0.00542044i	7.91336e−5	+	0.000191045i
$806$	−6.10956	−	11.2632i	−0.215200	−	0.396728i
$807$	1.07143	−	1.07143i	0.0377163	−	0.0377163i
$808$	3.62632	−	45.3807i	0.127574	−	1.59649i
$809$	13.2208	+	13.2208i	0.464819	+	0.464819i	0.900231	−	0.435412i	$-0.143397\pi$
$809$	13.2208	+	13.2208i	0.464819	+	0.464819i	−0.435412	+	0.900231i	$0.643397\pi$
$810$	0.00272694	−	0.00919248i	9.58148e−5	−	0.000322991i
$811$	−9.46797	+	3.92176i	−0.332465	+	0.137712i	−0.542671	−	0.839946i	$-0.682587\pi$
$811$	−9.46797	+	3.92176i	−0.332465	+	0.137712i	0.210205	+	0.977657i	$0.432587\pi$
$812$	24.0011	+	34.9817i	0.842273	+	1.22762i
$813$	−0.840349	+	2.02878i	−0.0294723	+	0.0711525i
$814$	−10.4912	+	1.09843i	−0.367717	+	0.0385000i
$815$			0.0542726i			0.00190109i
$816$	0.572368	+	23.2809i	0.0200369	+	0.814995i
$817$			71.0207i			2.48470i
$818$	−4.60613	−	43.9937i	−0.161050	−	1.53820i
$819$	1.91387	−	4.62049i	0.0668760	−	0.161453i
$820$	0.0634801	+	0.0118179i	0.00221682	+	0.000412698i
$821$	−47.1649	+	19.5363i	−1.64607	+	0.681823i	−0.996889	−	0.0788144i	$-0.974887\pi$
$821$	−47.1649	+	19.5363i	−1.64607	+	0.681823i	−0.649177	+	0.760637i	$0.724887\pi$
$822$	−0.209239	−	0.0620704i	−0.00729804	−	0.00216495i
$823$	17.1355	+	17.1355i	0.597306	+	0.597306i	0.939595	−	0.342289i	$-0.111202\pi$
$823$	17.1355	+	17.1355i	0.597306	+	0.597306i	−0.342289	+	0.939595i	$0.611202\pi$
$824$	21.3332	−	6.90329i	0.743177	−	0.240488i
$825$	4.97299	−	4.97299i	0.173137	−	0.173137i
$826$	−17.7241	+	9.61420i	−0.616699	+	0.334521i
$827$	7.74891	+	18.7075i	0.269456	+	0.650524i	0.999458	−	0.0329210i	$-0.0104810\pi$
$827$	7.74891	+	18.7075i	0.269456	+	0.650524i	−0.730002	+	0.683445i	$0.760481\pi$
$828$	0.494972	−	0.104796i	0.0172015	−	0.00364191i
$829$	2.18250	+	0.904020i	0.0758013	+	0.0313979i	0.420262	−	0.907403i	$-0.361938\pi$
$829$	2.18250	+	0.904020i	0.0758013	+	0.0313979i	−0.344461	+	0.938801i	$0.611938\pi$
$830$	0.0478950	−	0.0590971i	0.00166246	−	0.00205129i
$831$	26.0437			0.903446
$832$	−11.3796	+	2.70315i	−0.394518	+	0.0937147i
$833$	−27.3701			−0.948319
$834$	5.59700	−	6.90607i	0.193808	−	0.239138i
$835$	−0.00617506	−	0.00255779i	−0.000213697	−	8.85161e-5i
$836$	19.2609	−	4.07794i	0.666153	−	0.141038i
$837$	−2.37156	−	5.72545i	−0.0819731	−	0.197901i
$838$	−11.5636	+	6.27256i	−0.399460	+	0.216682i
$839$	19.2057	−	19.2057i	0.663056	−	0.663056i	−0.293043	−	0.956099i	$-0.594668\pi$
$839$	19.2057	−	19.2057i	0.663056	−	0.663056i	0.956099	+	0.293043i	$0.0946680\pi$
$840$	−0.0201961	−	0.0624119i	−0.000696831	−	0.00215341i
$841$	6.68416	+	6.68416i	0.230488	+	0.230488i
$842$	27.7208	+	8.22334i	0.955322	+	0.283395i
$843$	23.5417	−	9.75129i	0.810819	−	0.335852i
$844$	13.3405	+	2.48356i	0.459201	+	0.0854877i
$845$	0.0281838	−	0.0680418i	0.000969553	−	0.00234071i
$846$	−1.84153	−	17.5887i	−0.0633131	−	0.604711i
$847$		−	30.8599i		−	1.06036i
$848$	24.9813	−	26.2406i	0.857861	−	0.901106i
$849$		−	3.02747i		−	0.103903i
$850$	−40.9435	+	4.28678i	−1.40435	+	0.147035i
$851$	0.513362	−	1.23937i	0.0175978	−	0.0424849i
$852$	−9.52405	−	13.8813i	−0.326288	−	0.475567i
$853$	−35.6393	+	14.7623i	−1.22026	+	0.505450i	−0.897494	−	0.441027i	$-0.854614\pi$
$853$	−35.6393	+	14.7623i	−1.22026	+	0.505450i	−0.322771	+	0.946477i	$0.604614\pi$
$854$	−10.8321	+	36.5149i	−0.370666	+	1.24951i
$855$	0.0335521	+	0.0335521i	0.00114746	+	0.00114746i
$856$	16.6739	+	1.33240i	0.569904	+	0.0455404i
$857$	8.16918	−	8.16918i	0.279054	−	0.279054i	−0.553677	−	0.832731i	$-0.686776\pi$
$857$	8.16918	−	8.16918i	0.279054	−	0.279054i	0.832731	+	0.553677i	$0.186776\pi$
$858$	1.38670	+	2.55642i	0.0473411	+	0.0872747i
$859$	2.26963	+	5.47938i	0.0774389	+	0.186954i	0.957858	−	0.287243i	$-0.0927386\pi$
$859$	2.26963	+	5.47938i	0.0774389	+	0.186954i	−0.880419	+	0.474197i	$0.842739\pi$
$860$	−0.0750392	+	0.115348i	−0.00255882	+	0.00393334i
$861$	15.0489	+	6.23344i	0.512864	+	0.212435i
$862$	18.9399	+	15.3498i	0.645097	+	0.522816i
$863$	40.5672			1.38092			0.690462	−	0.723369i	$-0.257407\pi$
$863$	40.5672			1.38092			0.690462	+	0.723369i	$0.257407\pi$
$864$	−5.60992	+	0.727152i	−0.190853	+	0.0247382i
$865$	−0.117142			−0.00398294
$866$	−22.9029	−	18.5616i	−0.778273	−	0.630748i
$867$	−15.6094	−	6.46564i	−0.530125	−	0.219585i
$868$	−35.5390	−	23.1197i	−1.20627	−	0.784734i
$869$	0.766809	+	1.85124i	0.0260122	+	0.0627991i
$870$	−0.0283501	−	0.0522642i	−0.000961158	−	0.00177192i
$871$	4.90987	−	4.90987i	0.166364	−	0.166364i
$872$	5.52984	−	4.71147i	0.187264	−	0.159550i
$873$	−0.877220	−	0.877220i	−0.0296894	−	0.0296894i
$874$	−0.712061	+	2.40035i	−0.0240858	+	0.0811932i
$875$	0.214269	−	0.0887533i	0.00724363	−	0.00300041i
$876$	18.3208	−	12.5700i	0.619003	−	0.424701i
$877$	0.389401	−	0.940098i	0.0131491	−	0.0317449i	−0.917169	−	0.398499i	$-0.869531\pi$
$877$	0.389401	−	0.940098i	0.0131491	−	0.0317449i	0.930318	+	0.366755i	$0.119531\pi$
$878$	−22.9909	+	2.40715i	−0.775906	+	0.0812373i
$879$			9.19822i			0.310248i
$880$	0.0355913	+	0.0137276i	0.00119978	+	0.000462756i
$881$		−	19.7730i		−	0.666169i	−0.942897	−	0.333085i	$-0.891910\pi$
$881$		−	19.7730i		−	0.666169i	0.942897	−	0.333085i	$-0.108090\pi$
$882$	−0.692308	−	6.61231i	−0.0233112	−	0.222648i
$883$	1.09620	−	2.64647i	0.0368902	−	0.0890608i	−0.904361	−	0.426769i	$-0.859652\pi$
$883$	1.09620	−	2.64647i	0.0368902	−	0.0890608i	0.941251	+	0.337708i	$0.109652\pi$
$884$	3.11575	−	16.7363i	0.104794	−	0.562904i
$885$	0.0261089	−	0.0108147i	0.000877641	−	0.000363531i
$886$	27.8626	+	8.26540i	0.936063	+	0.277682i
$887$	−24.5575	−	24.5575i	−0.824561	−	0.824561i	0.162198	−	0.986758i	$-0.448142\pi$
$887$	−24.5575	−	24.5575i	−0.824561	−	0.824561i	−0.986758	+	0.162198i	$0.948142\pi$
$888$	−6.82534	+	13.3559i	−0.229044	+	0.448193i
$889$	−35.2974	+	35.2974i	−1.18384	+	1.18384i
$890$	0.118733	−	0.0644050i	0.00397992	−	0.00215886i
$891$	0.538278	+	1.29952i	0.0180330	+	0.0435355i
$892$	−6.05030	−	28.5768i	−0.202579	−	0.956822i
$893$	80.8542	+	33.4909i	2.70568	+	1.12073i
$894$	14.9121	−	18.3998i	0.498734	−	0.615382i
$895$	−0.0202154			−0.000675727
$896$	−28.8327	+	25.8153i	−0.963231	+	0.862427i
$897$	−0.369854			−0.0123491
$898$	−1.88616	+	2.32731i	−0.0629420	+	0.0776634i
$899$	−35.5037	−	14.7061i	−1.18412	−	0.490477i
$900$	−2.07127	−	9.78305i	−0.0690425	−	0.326102i
$901$	20.1801	+	48.7190i	0.672296	+	1.62307i
$902$	−8.32623	+	4.51646i	−0.277233	+	0.150382i
$903$	−24.5461	+	24.5461i	−0.816843	+	0.816843i
$904$	−5.69941	+	11.1526i	−0.189559	+	0.370931i
$905$	0.0323457	+	0.0323457i	0.00107521	+	0.00107521i
$906$	−18.0011	−	5.34000i	−0.598046	−	0.177410i
$907$	20.3745	−	8.43938i	0.676523	−	0.280225i	−0.0178494	−	0.999841i	$-0.505682\pi$
$907$	20.3745	−	8.43938i	0.676523	−	0.280225i	0.694373	+	0.719616i	$0.255682\pi$
$908$	−1.48623	+	7.98336i	−0.0493224	+	0.264937i
$909$	−6.15953	+	14.8704i	−0.204299	+	0.493221i
$910$	0.00499343	+	0.0476927i	0.000165530	+	0.00158100i
$911$			15.6069i			0.517081i	0.966000	+	0.258540i	$0.0832415\pi$
$911$			15.6069i			0.517081i	−0.966000	+	0.258540i	$0.916758\pi$
$912$	10.0739	−	26.1184i	0.333580	−	0.864867i
$913$			11.1590i			0.369308i
$914$	14.9998	−	1.57048i	0.496149	−	0.0519467i
$915$	0.0204280	−	0.0493176i	0.000675330	−	0.00163039i
$916$	8.90074	−	6.10684i	0.294089	−	0.201776i
$917$	29.5113	−	12.2240i	0.974548	−	0.403671i
$918$	2.34161	−	7.89354i	0.0772845	−	0.260526i
$919$	37.7928	+	37.7928i	1.24667	+	1.24667i	0.957181	+	0.289489i	$0.0934854\pi$
$919$	37.7928	+	37.7928i	1.24667	+	1.24667i	0.289489	+	0.957181i	$0.406515\pi$
$920$	−0.00369266	+	0.00314618i	−0.000121744	+	0.000103726i
$921$	−2.61927	+	2.61927i	−0.0863078	+	0.0863078i
$922$	2.76380	+	5.09514i	0.0910207	+	0.167799i
$923$	4.70941	+	11.3695i	0.155012	+	0.374233i
$924$	8.06635	+	5.24752i	0.265363	+	0.172631i
$925$	−24.4959	−	10.1465i	−0.805420	−	0.333616i
$926$	−9.17821	−	7.43845i	−0.301615	−	0.244443i
$927$	−7.92749			−0.260373
$928$	−21.4100	+	27.7868i	−0.702816	+	0.912146i
$929$	8.36281			0.274375			0.137187	−	0.990545i	$-0.456194\pi$
$929$	8.36281			0.274375			0.137187	+	0.990545i	$0.456194\pi$
$930$	0.0461640	+	0.0374135i	0.00151378	+	0.00122684i
$931$	30.3965	+	12.5906i	0.996204	+	0.412641i
$932$	−31.6191	+	48.6040i	−1.03572	+	1.59208i
$933$	−12.1442	−	29.3187i	−0.397583	−	0.959851i
$934$	−20.8812	−	38.4951i	−0.683255	−	1.25960i
$935$	−0.0392605	+	0.0392605i	−0.00128395	+	0.00128395i
$936$	4.12212	+	0.329394i	0.134736	+	0.0107666i
$937$	−37.8809	−	37.8809i	−1.23752	−	1.23752i	−0.961013	−	0.276502i	$-0.910825\pi$
$937$	−37.8809	−	37.8809i	−1.23752	−	1.23752i	−0.276502	−	0.961013i	$-0.589175\pi$
$938$	6.53407	−	22.0263i	0.213345	−	0.719185i
$939$	−2.93926	+	1.21748i	−0.0959190	+	0.0397310i
$940$	0.0959334	+	0.139823i	0.00312900	+	0.00456053i
$941$	−19.7558	+	47.6947i	−0.644020	+	1.55480i	0.177191	+	0.984176i	$0.443299\pi$
$941$	−19.7558	+	47.6947i	−0.644020	+	1.55480i	−0.821211	+	0.570625i	$0.806701\pi$
$942$	−1.46093	+	0.152959i	−0.0475997	+	0.00498368i
$943$		−	1.20461i		−	0.0392275i
$944$	−12.0754	−	11.4959i	−0.393022	−	0.374160i
$945$			0.0231925i			0.000754451i
$946$	−2.10205	−	20.0769i	−0.0683436	−	0.652757i
$947$	2.05678	−	4.96550i	0.0668363	−	0.161357i	−0.886932	−	0.461900i	$-0.847168\pi$
$947$	2.05678	−	4.96550i	0.0668363	−	0.161357i	0.953768	+	0.300543i	$0.0971679\pi$
$948$	2.80100	+	0.521452i	0.0909721	+	0.0169360i
$949$	−15.0057	+	6.21556i	−0.487105	+	0.201766i
$950$	47.4426	+	14.0738i	1.53924	+	0.456614i
$951$	−24.0586	−	24.0586i	−0.780152	−	0.780152i
$952$	−17.3423	−	53.5928i	−0.562067	−	1.73695i
$953$	−4.72605	+	4.72605i	−0.153092	+	0.153092i	−0.779497	−	0.626406i	$-0.784525\pi$
$953$	−4.72605	+	4.72605i	−0.153092	+	0.153092i	0.626406	+	0.779497i	$0.284525\pi$
$954$	−11.2595	+	6.10759i	−0.364540	+	0.197740i
$955$	0.0132895	+	0.0320837i	0.000430038	+	0.00103820i
$956$	4.37640	−	0.926574i	0.141543	−	0.0299676i
$957$	8.05835	+	3.33788i	0.260490	+	0.107898i
$958$	−3.88305	+	4.79125i	−0.125456	+	0.154798i
$959$	0.527906			0.0170470
$960$	0.0439577	−	0.0317763i	0.00141873	−	0.00102558i
$961$	7.40512			0.238875
$962$	6.90352	−	8.51817i	0.222578	−	0.274637i
$963$	−5.46375	−	2.26316i	−0.176067	−	0.0729293i
$964$	38.4976	−	8.15073i	1.23992	−	0.262517i
$965$	0.0539551	+	0.130259i	0.00173688	+	0.00419319i
$966$	−1.07571	+	0.583505i	−0.0346104	+	0.0187740i
$967$	29.3805	−	29.3805i	0.944812	−	0.944812i	−0.0537426	−	0.998555i	$-0.517115\pi$
$967$	29.3805	−	29.3805i	0.944812	−	0.944812i	0.998555	+	0.0537426i	$0.0171150\pi$
$968$	24.2773	−	7.85597i	0.780301	−	0.252500i
$969$	28.8110	+	28.8110i	0.925543	+	0.925543i
$970$	0.0114040	+	0.00338297i	0.000366160	+	0.000108621i
$971$	−22.4822	+	9.31244i	−0.721489	+	0.298850i	−0.713049	−	0.701114i	$-0.752686\pi$
$971$	−22.4822	+	9.31244i	−0.721489	+	0.298850i	−0.00843940	+	0.999964i	$0.502686\pi$
$972$	1.96622	+	0.366044i	0.0630665	+	0.0117409i
$973$	−8.22827	+	19.8648i	−0.263786	+	0.636836i
$974$	−1.64914	−	15.7511i	−0.0528419	−	0.504699i
$975$			7.31011i			0.234111i
$976$	−31.4835	+	0.774031i	−1.00776	+	0.0247761i
$977$		−	30.9704i		−	0.990831i	−0.868656	−	0.495415i	$-0.835016\pi$
$977$		−	30.9704i		−	0.990831i	0.868656	−	0.495415i	$-0.164984\pi$
$978$	−11.2589	+	1.17881i	−0.360020	+	0.0376940i
$979$	−7.58291	+	18.3068i	−0.242351	+	0.585087i
$980$	0.0360653	+	0.0525654i	0.00115207	+	0.00167914i
$981$	−2.37297	+	0.982918i	−0.0757632	+	0.0313821i
$982$	16.4959	−	55.6075i	0.526405	−	1.77451i
$983$	8.78738	+	8.78738i	0.280274	+	0.280274i	0.833218	−	0.552944i	$-0.186496\pi$
$983$	8.78738	+	8.78738i	0.280274	+	0.280274i	−0.552944	+	0.833218i	$0.686496\pi$
$984$	−1.07283	+	13.4257i	−0.0342007	+	0.427995i
$985$	−0.0435142	+	0.0435142i	−0.00138648	+	0.00138648i
$986$	−24.3441	−	44.8790i	−0.775273	−	1.42924i
$987$	16.3696	+	39.5198i	0.521052	+	1.25793i
$988$	−11.1592	+	17.1536i	−0.355021	+	0.545729i
$989$	2.37176	+	0.982415i	0.0754176	+	0.0312390i
$990$	−0.0104779	−	0.00849181i	−0.000333011	−	0.000269887i
$991$	−43.3371			−1.37665			−0.688324	−	0.725403i	$-0.741653\pi$
$991$	−43.3371			−1.37665			−0.688324	+	0.725403i	$0.741653\pi$
$992$	9.14100	−	33.8438i	0.290227	−	1.07454i
$993$	26.6315			0.845125
$994$	31.6345	+	25.6381i	1.00338	+	0.813190i
$995$	−0.0867829	−	0.0359467i	−0.00275120	−	0.00113959i
$996$	13.3000	+	8.65227i	0.421428	+	0.274158i
$997$	4.40977	+	10.6461i	0.139659	+	0.337166i	0.978198	−	0.207675i	$-0.0665897\pi$
$997$	4.40977	+	10.6461i	0.139659	+	0.337166i	−0.838539	+	0.544842i	$0.816590\pi$
$998$	16.1790	+	29.8264i	0.512137	+	0.944139i
$999$	3.74970	−	3.74970i	0.118635	−	0.118635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.61.7	✓	32
3.2	odd	2		288.2.v.d.253.2		32
4.3	odd	2		384.2.n.a.337.3		32
8.3	odd	2		768.2.n.b.673.6		32
8.5	even	2		768.2.n.a.673.2		32
12.11	even	2		1152.2.v.c.721.5		32
32.5	even	8		768.2.n.a.97.2		32
32.11	odd	8		384.2.n.a.49.3		32
32.21	even	8	inner	96.2.n.a.85.7	yes	32
32.27	odd	8		768.2.n.b.97.6		32
96.11	even	8		1152.2.v.c.433.5		32
96.53	odd	8		288.2.v.d.181.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.7	✓	32	1.1	even	1	trivial
96.2.n.a.85.7	yes	32	32.21	even	8	inner
288.2.v.d.181.2		32	96.53	odd	8
288.2.v.d.253.2		32	3.2	odd	2
384.2.n.a.49.3		32	32.11	odd	8
384.2.n.a.337.3		32	4.3	odd	2
768.2.n.a.97.2		32	32.5	even	8
768.2.n.a.673.2		32	8.5	even	2
768.2.n.b.97.6		32	32.27	odd	8
768.2.n.b.673.6		32	8.3	odd	2
1152.2.v.c.433.5		32	96.11	even	8
1152.2.v.c.721.5		32	12.11	even	2

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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.890433 - 1.09869i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-0.414259 - 1.95663i) q^{4} +(-0.00259461 - 0.00626394i) q^{5} +(1.24310 - 0.674307i) q^{6} +(-2.41880 + 2.41880i) q^{7} +(-2.51860 - 1.28710i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.890433 - 1.09869i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-0.414259 - 1.95663i) q^{4} +(-0.00259461 - 0.00626394i) q^{5} +(1.24310 - 0.674307i) q^{6} +(-2.41880 + 2.41880i) q^{7} +(-2.51860 - 1.28710i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-0.00919248 - 0.00272694i) q^{10} +(1.29952 - 0.538278i) q^{11} +(0.366044 - 1.96622i) q^{12} +(-0.559497 + 1.35074i) q^{13} +(0.503742 + 4.81130i) q^{14} -0.00678004i q^{15} +(-3.65678 + 1.62110i) q^{16} -5.82199i q^{17} +(1.40653 - 0.147263i) q^{18} +(-2.67819 + 6.46573i) q^{19} +(-0.0111814 + 0.00767157i) q^{20} +(-3.16031 + 1.30904i) q^{21} +(0.565730 - 1.90707i) q^{22} +(0.178878 + 0.178878i) q^{23} +(-1.83433 - 2.15296i) q^{24} +(3.53550 - 3.53550i) q^{25} +(0.985861 + 1.81746i) q^{26} +(0.382683 + 0.923880i) q^{27} +(5.73469 + 3.73068i) q^{28} +(5.72901 + 2.37303i) q^{29} +(-0.00744919 - 0.00603717i) q^{30} -6.19719 q^{31} +(-1.47502 + 5.46116i) q^{32} +1.40659 q^{33} +(-6.39659 - 5.18409i) q^{34} +(0.0214270 + 0.00887537i) q^{35} +(1.09062 - 1.67647i) q^{36} +(-2.02932 - 4.89922i) q^{37} +(4.71911 + 8.69981i) q^{38} +(-1.03381 + 1.03381i) q^{39} +(-0.00152753 + 0.0191159i) q^{40} +(-3.36712 - 3.36712i) q^{41} +(-1.37581 + 4.63783i) q^{42} +(9.37558 - 3.88349i) q^{43} +(-1.59154 - 2.31968i) q^{44} +(0.00259461 - 0.00626394i) q^{45} +(0.355812 - 0.0372534i) q^{46} -12.5050i q^{47} +(-3.99879 + 0.0983114i) q^{48} -4.70117i q^{49} +(-0.736309 - 7.03256i) q^{50} +(2.22798 - 5.37882i) q^{51} +(2.87468 + 0.535169i) q^{52} +(-8.36811 + 3.46618i) q^{53} +(1.35582 + 0.402201i) q^{54} +(-0.00674348 - 0.00674348i) q^{55} +(9.20523 - 2.97876i) q^{56} +(-4.94866 + 4.94866i) q^{57} +(7.70854 - 4.18140i) q^{58} +(1.59507 + 3.85084i) q^{59} +(-0.0132660 + 0.00280869i) q^{60} +(7.27395 + 3.01297i) q^{61} +(-5.51818 + 6.80881i) q^{62} -3.42070 q^{63} +(4.68674 + 6.48340i) q^{64} +0.00991266 q^{65} +(1.25247 - 1.54541i) q^{66} +(-4.38775 - 1.81747i) q^{67} +(-11.3915 + 2.41181i) q^{68} +(0.0968082 + 0.233716i) q^{69} +(0.0288307 - 0.0156388i) q^{70} +(5.95188 - 5.95188i) q^{71} +(-0.870804 - 2.69104i) q^{72} +(7.85539 + 7.85539i) q^{73} +(-7.18972 - 2.13282i) q^{74} +(4.61936 - 1.91340i) q^{75} +(13.7605 + 2.56174i) q^{76} +(-1.84128 + 4.44525i) q^{77} +(0.215304 + 2.05639i) q^{78} +1.42456i q^{79} +(0.0196424 + 0.0186997i) q^{80} +1.00000i q^{81} +(-6.69763 + 0.701242i) q^{82} +(-3.03596 + 7.32946i) q^{83} +(3.87050 + 5.64127i) q^{84} +(-0.0364686 + 0.0151058i) q^{85} +(4.08155 - 13.7589i) q^{86} +(4.38479 + 4.38479i) q^{87} +(-3.96579 - 0.316902i) q^{88} +(-9.96127 + 9.96127i) q^{89} +(-0.00457183 - 0.00842830i) q^{90} +(-1.91387 - 4.62049i) q^{91} +(0.275896 - 0.424100i) q^{92} +(-5.72545 - 2.37156i) q^{93} +(-13.7392 - 11.1349i) q^{94} +0.0474498 q^{95} +(-3.45264 + 4.48099i) q^{96} -1.24058 q^{97} +(-5.16515 - 4.18607i) q^{98} +(1.29952 + 0.538278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Introduction

L-functions

Modular forms

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