LMFDB - Embedded newform 70.2.g.a.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,2,Mod(13,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("70.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	70.g (of order $4$, degree $2$, 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:	$0.558952814149$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.2
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	70.27
Dual form			70.2.g.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.30656 + 1.30656i) q^{3} +1.00000i q^{4} +(0.158513 + 2.23044i) q^{5} -1.84776i q^{6} +(-0.941740 - 2.47247i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.414214i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.30656 + 1.30656i) q^{3} +1.00000i q^{4} +(0.158513 + 2.23044i) q^{5} -1.84776i q^{6} +(-0.941740 - 2.47247i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.414214i q^{9} +(1.46508 - 1.68925i) q^{10} +2.82843 q^{11} +(-1.30656 + 1.30656i) q^{12} +(-4.23671 - 4.23671i) q^{13} +(-1.08239 + 2.41421i) q^{14} +(-2.70711 + 3.12132i) q^{15} -1.00000 q^{16} +(-3.69552 + 3.69552i) q^{17} +(0.292893 - 0.292893i) q^{18} +1.39942 q^{19} +(-2.23044 + 0.158513i) q^{20} +(2.00000 - 4.46088i) q^{21} +(-2.00000 - 2.00000i) q^{22} +(0.414214 - 0.414214i) q^{23} +1.84776 q^{24} +(-4.94975 + 0.707107i) q^{25} +5.99162i q^{26} +(3.37849 - 3.37849i) q^{27} +(2.47247 - 0.941740i) q^{28} -0.828427i q^{29} +(4.12132 - 0.292893i) q^{30} +1.53073i q^{31} +(0.707107 + 0.707107i) q^{32} +(3.69552 + 3.69552i) q^{33} +5.22625 q^{34} +(5.36543 - 2.49242i) q^{35} -0.414214 q^{36} +(2.58579 + 2.58579i) q^{37} +(-0.989538 - 0.989538i) q^{38} -11.0711i q^{39} +(1.68925 + 1.46508i) q^{40} +3.69552i q^{41} +(-4.56854 + 1.74011i) q^{42} +(4.00000 - 4.00000i) q^{43} +2.82843i q^{44} +(-0.923880 + 0.0656581i) q^{45} -0.585786 q^{46} +(1.08239 - 1.08239i) q^{47} +(-1.30656 - 1.30656i) q^{48} +(-5.22625 + 4.65685i) q^{49} +(4.00000 + 3.00000i) q^{50} -9.65685 q^{51} +(4.23671 - 4.23671i) q^{52} +(-8.24264 + 8.24264i) q^{53} -4.77791 q^{54} +(0.448342 + 6.30864i) q^{55} +(-2.41421 - 1.08239i) q^{56} +(1.82843 + 1.82843i) q^{57} +(-0.585786 + 0.585786i) q^{58} -9.23880 q^{59} +(-3.12132 - 2.70711i) q^{60} -6.43996i q^{61} +(1.08239 - 1.08239i) q^{62} +(1.02413 - 0.390081i) q^{63} -1.00000i q^{64} +(8.77817 - 10.1213i) q^{65} -5.22625i q^{66} +(10.4853 + 10.4853i) q^{67} +(-3.69552 - 3.69552i) q^{68} +1.08239 q^{69} +(-5.55634 - 2.03153i) q^{70} -0.585786 q^{71} +(0.292893 + 0.292893i) q^{72} +(4.14386 + 4.14386i) q^{73} -3.65685i q^{74} +(-7.39104 - 5.54328i) q^{75} +1.39942i q^{76} +(-2.66364 - 6.99321i) q^{77} +(-7.82843 + 7.82843i) q^{78} +5.07107i q^{79} +(-0.158513 - 2.23044i) q^{80} +10.0711 q^{81} +(2.61313 - 2.61313i) q^{82} +(5.31911 + 5.31911i) q^{83} +(4.46088 + 2.00000i) q^{84} +(-8.82843 - 7.65685i) q^{85} -5.65685 q^{86} +(1.08239 - 1.08239i) q^{87} +(2.00000 - 2.00000i) q^{88} +11.3492 q^{89} +(0.699709 + 0.606854i) q^{90} +(-6.48528 + 14.4650i) q^{91} +(0.414214 + 0.414214i) q^{92} +(-2.00000 + 2.00000i) q^{93} -1.53073 q^{94} +(0.221825 + 3.12132i) q^{95} +1.84776i q^{96} +(-4.59220 + 4.59220i) q^{97} +(6.98841 + 0.402625i) q^{98} +1.17157i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} - 16 q^{15} - 8 q^{16} + 8 q^{18} + 16 q^{21} - 16 q^{22} - 8 q^{23} + 8 q^{28} + 16 q^{30} - 8 q^{35} + 8 q^{36} + 32 q^{37} + 32 q^{43} - 16 q^{46} + 32 q^{50} - 32 q^{51} - 32 q^{53} - 8 q^{56} - 8 q^{57} - 16 q^{58} - 8 q^{60} + 8 q^{65} + 16 q^{67} - 24 q^{70} - 16 q^{71} + 8 q^{72} - 16 q^{77} - 40 q^{78} + 24 q^{81} - 48 q^{85} + 16 q^{88} + 16 q^{91} - 8 q^{92} - 16 q^{93} + 64 q^{95} + 32 q^{98}+O(q^{100}) $ 8 * q - 8 * q^7 - 16 * q^15 - 8 * q^16 + 8 * q^18 + 16 * q^21 - 16 * q^22 - 8 * q^23 + 8 * q^28 + 16 * q^30 - 8 * q^35 + 8 * q^36 + 32 * q^37 + 32 * q^43 - 16 * q^46 + 32 * q^50 - 32 * q^51 - 32 * q^53 - 8 * q^56 - 8 * q^57 - 16 * q^58 - 8 * q^60 + 8 * q^65 + 16 * q^67 - 24 * q^70 - 16 * q^71 + 8 * q^72 - 16 * q^77 - 40 * q^78 + 24 * q^81 - 48 * q^85 + 16 * q^88 + 16 * q^91 - 8 * q^92 - 16 * q^93 + 64 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.30656	+	1.30656i	0.754344	+	0.754344i	0.975287	−	0.220942i	$-0.0709133\pi$
$3$	1.30656	+	1.30656i	0.754344	+	0.754344i	−0.220942	+	0.975287i	$0.570913\pi$
$4$			1.00000i			0.500000i
$5$	0.158513	+	2.23044i	0.0708890	+	0.997484i
$5$	0.158513	+	2.23044i	0.0708890	+	0.997484i
$6$		−	1.84776i		−	0.754344i
$7$	−0.941740	−	2.47247i	−0.355944	−	0.934507i
$7$	−0.941740	−	2.47247i	−0.355944	−	0.934507i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			0.414214i			0.138071i
$10$	1.46508	−	1.68925i	0.463298	−	0.534187i
$11$	2.82843			0.852803			0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843			0.852803			0.426401	+	0.904534i	$0.359781\pi$
$12$	−1.30656	+	1.30656i	−0.377172	+	0.377172i
$13$	−4.23671	−	4.23671i	−1.17505	−	1.17505i	−0.980989	−	0.194064i	$-0.937833\pi$
$13$	−4.23671	−	4.23671i	−1.17505	−	1.17505i	−0.194064	−	0.980989i	$-0.562167\pi$
$14$	−1.08239	+	2.41421i	−0.289281	+	0.645226i
$15$	−2.70711	+	3.12132i	−0.698972	+	0.805921i
$16$	−1.00000			−0.250000
$17$	−3.69552	+	3.69552i	−0.896295	+	0.896295i	−0.995106	−	0.0988114i	$-0.968496\pi$
$17$	−3.69552	+	3.69552i	−0.896295	+	0.896295i	0.0988114	+	0.995106i	$0.468496\pi$
$18$	0.292893	−	0.292893i	0.0690356	−	0.0690356i
$19$	1.39942			0.321048			0.160524	−	0.987032i	$-0.448682\pi$
$19$	1.39942			0.321048			0.160524	+	0.987032i	$0.448682\pi$
$20$	−2.23044	+	0.158513i	−0.498742	+	0.0354445i
$21$	2.00000	−	4.46088i	0.436436	−	0.973445i
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	0.414214	−	0.414214i	0.0863695	−	0.0863695i	−0.662602	−	0.748972i	$-0.730548\pi$
$23$	0.414214	−	0.414214i	0.0863695	−	0.0863695i	0.748972	+	0.662602i	$0.230548\pi$
$24$	1.84776			0.377172
$25$	−4.94975	+	0.707107i	−0.989949	+	0.141421i
$26$			5.99162i			1.17505i
$27$	3.37849	−	3.37849i	0.650191	−	0.650191i
$28$	2.47247	−	0.941740i	0.467254	−	0.177972i
$29$		−	0.828427i		−	0.153835i	−0.997037	−	0.0769175i	$-0.975492\pi$
$29$		−	0.828427i		−	0.153835i	0.997037	−	0.0769175i	$-0.0245078\pi$
$30$	4.12132	−	0.292893i	0.752447	−	0.0534747i
$31$			1.53073i			0.274928i	0.990507	+	0.137464i	$0.0438951\pi$
$31$			1.53073i			0.274928i	−0.990507	+	0.137464i	$0.956105\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.69552	+	3.69552i	0.643307	+	0.643307i
$34$	5.22625			0.896295
$35$	5.36543	−	2.49242i	0.906924	−	0.421295i
$36$	−0.414214			−0.0690356
$37$	2.58579	+	2.58579i	0.425101	+	0.425101i	0.886956	−	0.461855i	$-0.152816\pi$
$37$	2.58579	+	2.58579i	0.425101	+	0.425101i	−0.461855	+	0.886956i	$0.652816\pi$
$38$	−0.989538	−	0.989538i	−0.160524	−	0.160524i
$39$		−	11.0711i		−	1.77279i
$40$	1.68925	+	1.46508i	0.267093	+	0.231649i
$41$			3.69552i			0.577143i	0.957458	+	0.288571i	$0.0931803\pi$
$41$			3.69552i			0.577143i	−0.957458	+	0.288571i	$0.906820\pi$
$42$	−4.56854	+	1.74011i	−0.704940	+	0.268505i
$43$	4.00000	−	4.00000i	0.609994	−	0.609994i	−0.332950	−	0.942944i	$-0.608044\pi$
$43$	4.00000	−	4.00000i	0.609994	−	0.609994i	0.942944	+	0.332950i	$0.108044\pi$
$44$			2.82843i			0.426401i
$45$	−0.923880	+	0.0656581i	−0.137724	+	0.00978773i
$46$	−0.585786			−0.0863695
$47$	1.08239	−	1.08239i	0.157883	−	0.157883i	−0.623745	−	0.781628i	$-0.714390\pi$
$47$	1.08239	−	1.08239i	0.157883	−	0.157883i	0.781628	+	0.623745i	$0.214390\pi$
$48$	−1.30656	−	1.30656i	−0.188586	−	0.188586i
$49$	−5.22625	+	4.65685i	−0.746607	+	0.665265i
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$	−9.65685			−1.35223
$52$	4.23671	−	4.23671i	0.587527	−	0.587527i
$53$	−8.24264	+	8.24264i	−1.13221	+	1.13221i	−0.142405	+	0.989808i	$0.545484\pi$
$53$	−8.24264	+	8.24264i	−1.13221	+	1.13221i	−0.989808	+	0.142405i	$0.954516\pi$
$54$	−4.77791			−0.650191
$55$	0.448342	+	6.30864i	0.0604544	+	0.850657i
$56$	−2.41421	−	1.08239i	−0.322613	−	0.144641i
$57$	1.82843	+	1.82843i	0.242181	+	0.242181i
$58$	−0.585786	+	0.585786i	−0.0769175	+	0.0769175i
$59$	−9.23880			−1.20279			−0.601394	−	0.798952i	$-0.705388\pi$
$59$	−9.23880			−1.20279			−0.601394	+	0.798952i	$0.705388\pi$
$60$	−3.12132	−	2.70711i	−0.402961	−	0.349486i
$61$		−	6.43996i		−	0.824552i	−0.911059	−	0.412276i	$-0.864734\pi$
$61$		−	6.43996i		−	0.824552i	0.911059	−	0.412276i	$-0.135266\pi$
$62$	1.08239	−	1.08239i	0.137464	−	0.137464i
$63$	1.02413	−	0.390081i	0.129029	−	0.0491456i
$64$		−	1.00000i		−	0.125000i
$65$	8.77817	−	10.1213i	1.08880	−	1.25540i
$66$		−	5.22625i		−	0.643307i
$67$	10.4853	+	10.4853i	1.28098	+	1.28098i	0.940110	+	0.340871i	$0.110722\pi$
$67$	10.4853	+	10.4853i	1.28098	+	1.28098i	0.340871	+	0.940110i	$0.389278\pi$
$68$	−3.69552	−	3.69552i	−0.448147	−	0.448147i
$69$	1.08239			0.130305
$70$	−5.55634	−	2.03153i	−0.664109	−	0.242814i
$71$	−0.585786			−0.0695201			−0.0347600	−	0.999396i	$-0.511067\pi$
$71$	−0.585786			−0.0695201			−0.0347600	+	0.999396i	$0.511067\pi$
$72$	0.292893	+	0.292893i	0.0345178	+	0.0345178i
$73$	4.14386	+	4.14386i	0.485002	+	0.485002i	0.906725	−	0.421723i	$-0.138574\pi$
$73$	4.14386	+	4.14386i	0.485002	+	0.485002i	−0.421723	+	0.906725i	$0.638574\pi$
$74$		−	3.65685i		−	0.425101i
$75$	−7.39104	−	5.54328i	−0.853443	−	0.640083i
$76$			1.39942i			0.160524i
$77$	−2.66364	−	6.99321i	−0.303550	−	0.796950i
$78$	−7.82843	+	7.82843i	−0.886395	+	0.886395i
$79$			5.07107i			0.570540i	0.958447	+	0.285270i	$0.0920832\pi$
$79$			5.07107i			0.570540i	−0.958447	+	0.285270i	$0.907917\pi$
$80$	−0.158513	−	2.23044i	−0.0177223	−	0.249371i
$81$	10.0711			1.11901
$82$	2.61313	−	2.61313i	0.288571	−	0.288571i
$83$	5.31911	+	5.31911i	0.583848	+	0.583848i	0.935958	−	0.352111i	$-0.114536\pi$
$83$	5.31911	+	5.31911i	0.583848	+	0.583848i	−0.352111	+	0.935958i	$0.614536\pi$
$84$	4.46088	+	2.00000i	0.486722	+	0.218218i
$85$	−8.82843	−	7.65685i	−0.957577	−	0.830502i
$86$	−5.65685			−0.609994
$87$	1.08239	−	1.08239i	0.116045	−	0.116045i
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	11.3492			1.20301			0.601506	−	0.798869i	$-0.294568\pi$
$89$	11.3492			1.20301			0.601506	+	0.798869i	$0.294568\pi$
$90$	0.699709	+	0.606854i	0.0737558	+	0.0639680i
$91$	−6.48528	+	14.4650i	−0.679842	+	1.51635i
$92$	0.414214	+	0.414214i	0.0431847	+	0.0431847i
$93$	−2.00000	+	2.00000i	−0.207390	+	0.207390i
$94$	−1.53073			−0.157883
$95$	0.221825	+	3.12132i	0.0227588	+	0.320241i
$96$			1.84776i			0.188586i
$97$	−4.59220	+	4.59220i	−0.466267	+	0.466267i	−0.900703	−	0.434436i	$-0.856948\pi$
$97$	−4.59220	+	4.59220i	−0.466267	+	0.466267i	0.434436	+	0.900703i	$0.356948\pi$
$98$	6.98841	+	0.402625i	0.705936	+	0.0406713i
$99$			1.17157i			0.117748i
$100$	−0.707107	−	4.94975i	−0.0707107	−	0.494975i
$101$		−	2.74444i		−	0.273082i	−0.990634	−	0.136541i	$-0.956401\pi$
$101$		−	2.74444i		−	0.273082i	0.990634	−	0.136541i	$-0.0435986\pi$
$102$	6.82843	+	6.82843i	0.676115	+	0.676115i
$103$	−10.0042	−	10.0042i	−0.985739	−	0.985739i	0.0141603	−	0.999900i	$-0.495492\pi$
$103$	−10.0042	−	10.0042i	−0.985739	−	0.985739i	−0.999900	+	0.0141603i	$0.995492\pi$
$104$	−5.99162			−0.587527
$105$	10.2668	+	3.75378i	1.00193	+	0.366331i
$106$	11.6569			1.13221
$107$	−3.65685	−	3.65685i	−0.353521	−	0.353521i	0.507897	−	0.861418i	$-0.330423\pi$
$107$	−3.65685	−	3.65685i	−0.353521	−	0.353521i	−0.861418	+	0.507897i	$0.830423\pi$
$108$	3.37849	+	3.37849i	0.325096	+	0.325096i
$109$		−	12.1421i		−	1.16301i	−0.813544	−	0.581503i	$-0.802465\pi$
$109$		−	12.1421i		−	1.16301i	0.813544	−	0.581503i	$-0.197535\pi$
$110$	4.14386	−	4.77791i	0.395102	−	0.455556i
$111$			6.75699i			0.641345i
$112$	0.941740	+	2.47247i	0.0889861	+	0.233627i
$113$	1.17157	−	1.17157i	0.110212	−	0.110212i	−0.649850	−	0.760062i	$-0.725168\pi$
$113$	1.17157	−	1.17157i	0.110212	−	0.110212i	0.760062	+	0.649850i	$0.225168\pi$
$114$		−	2.58579i		−	0.242181i
$115$	0.989538	+	0.858221i	0.0922749	+	0.0800296i
$116$	0.828427			0.0769175
$117$	1.75490	−	1.75490i	0.162241	−	0.162241i
$118$	6.53281	+	6.53281i	0.601394	+	0.601394i
$119$	12.6173	+	5.65685i	1.15662	+	0.518563i
$120$	0.292893	+	4.12132i	0.0267374	+	0.376223i
$121$	−3.00000			−0.272727
$122$	−4.55374	+	4.55374i	−0.412276	+	0.412276i
$123$	−4.82843	+	4.82843i	−0.435365	+	0.435365i
$124$	−1.53073			−0.137464
$125$	−2.36176	−	10.9280i	−0.211242	−	0.977434i
$126$	−1.00000	−	0.448342i	−0.0890871	−	0.0399414i
$127$	3.58579	+	3.58579i	0.318187	+	0.318187i	0.848071	−	0.529883i	$-0.177764\pi$
$127$	3.58579	+	3.58579i	0.318187	+	0.318187i	−0.529883	+	0.848071i	$0.677764\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	10.4525			0.920292
$130$	−13.3640	+	0.949747i	−1.17210	+	0.0832984i
$131$		−	14.6508i		−	1.28004i	−0.768357	−	0.640021i	$-0.778926\pi$
$131$		−	14.6508i		−	1.28004i	0.768357	−	0.640021i	$-0.221074\pi$
$132$	−3.69552	+	3.69552i	−0.321654	+	0.321654i
$133$	−1.31789	−	3.46002i	−0.114275	−	0.300022i
$134$		−	14.8284i		−	1.28098i
$135$	8.07107	+	7.00000i	0.694647	+	0.602464i
$136$			5.22625i			0.448147i
$137$	−8.17157	−	8.17157i	−0.698145	−	0.698145i	0.265866	−	0.964010i	$-0.414342\pi$
$137$	−8.17157	−	8.17157i	−0.698145	−	0.698145i	−0.964010	+	0.265866i	$0.914342\pi$
$138$	−0.765367	−	0.765367i	−0.0651524	−	0.0651524i
$139$	−8.60474			−0.729845			−0.364922	−	0.931038i	$-0.618905\pi$
$139$	−8.60474			−0.729845			−0.364922	+	0.931038i	$0.618905\pi$
$140$	2.49242	+	5.36543i	0.210648	+	0.453462i
$141$	2.82843			0.238197
$142$	0.414214	+	0.414214i	0.0347600	+	0.0347600i
$143$	−11.9832	−	11.9832i	−1.00209	−	1.00209i
$144$		−	0.414214i		−	0.0345178i
$145$	1.84776	−	0.131316i	0.153448	−	0.0109052i
$146$		−	5.86030i		−	0.485002i
$147$	−12.9129	−	0.743954i	−1.06504	−	0.0613603i
$148$	−2.58579	+	2.58579i	−0.212550	+	0.212550i
$149$			17.3137i			1.41839i	0.705010	+	0.709197i	$0.250942\pi$
$149$			17.3137i			1.41839i	−0.705010	+	0.709197i	$0.749058\pi$
$150$	1.30656	+	9.14594i	0.106680	+	0.746763i
$151$	−8.82843			−0.718447			−0.359224	−	0.933252i	$-0.616958\pi$
$151$	−8.82843			−0.718447			−0.359224	+	0.933252i	$0.616958\pi$
$152$	0.989538	−	0.989538i	0.0802621	−	0.0802621i
$153$	−1.53073	−	1.53073i	−0.123752	−	0.123752i
$154$	−3.06147	+	6.82843i	−0.246700	+	0.550250i
$155$	−3.41421	+	0.242641i	−0.274236	+	0.0194894i
$156$	11.0711			0.886395
$157$	10.2283	−	10.2283i	0.816310	−	0.816310i	−0.169261	−	0.985571i	$-0.554138\pi$
$157$	10.2283	−	10.2283i	0.816310	−	0.816310i	0.985571	+	0.169261i	$0.0541382\pi$
$158$	3.58579	−	3.58579i	0.285270	−	0.285270i
$159$	−21.5391			−1.70816
$160$	−1.46508	+	1.68925i	−0.115824	+	0.133547i
$161$	−1.41421	−	0.634051i	−0.111456	−	0.0499702i
$162$	−7.12132	−	7.12132i	−0.559504	−	0.559504i
$163$	13.6569	−	13.6569i	1.06969	−	1.06969i	0.0723048	−	0.997383i	$-0.476965\pi$
$163$	13.6569	−	13.6569i	1.06969	−	1.06969i	0.997383	−	0.0723048i	$-0.0230354\pi$
$164$	−3.69552			−0.288571
$165$	−7.65685	+	8.82843i	−0.596085	+	0.687292i
$166$		−	7.52235i		−	0.583848i
$167$	−1.71644	+	1.71644i	−0.132822	+	0.132822i	−0.770392	−	0.637570i	$-0.779940\pi$
$167$	−1.71644	+	1.71644i	−0.132822	+	0.132822i	0.637570	+	0.770392i	$0.279940\pi$
$168$	−1.74011	−	4.56854i	−0.134252	−	0.352470i
$169$			22.8995i			1.76150i
$170$	0.828427	+	11.6569i	0.0635375	+	0.894040i
$171$			0.579658i			0.0443275i
$172$	4.00000	+	4.00000i	0.304997	+	0.304997i
$173$	13.2898	+	13.2898i	1.01040	+	1.01040i	0.999945	+	0.0104595i	$0.00332943\pi$
$173$	13.2898	+	13.2898i	1.01040	+	1.01040i	0.0104595	+	0.999945i	$0.496671\pi$
$174$	−1.53073			−0.116045
$175$	6.40968	+	11.5722i	0.484526	+	0.874777i
$176$	−2.82843			−0.213201
$177$	−12.0711	−	12.0711i	−0.907317	−	0.907317i
$178$	−8.02509	−	8.02509i	−0.601506	−	0.601506i
$179$		−	13.6569i		−	1.02076i	−0.859949	−	0.510381i	$-0.829505\pi$
$179$		−	13.6569i		−	1.02076i	0.859949	−	0.510381i	$-0.170495\pi$
$180$	−0.0656581	−	0.923880i	−0.00489387	−	0.0688619i
$181$		−	8.79045i		−	0.653389i	−0.945130	−	0.326695i	$-0.894065\pi$
$181$		−	8.79045i		−	0.653389i	0.945130	−	0.326695i	$-0.105935\pi$
$182$	14.8141	−	5.64255i	1.09810	−	0.418253i
$183$	8.41421	−	8.41421i	0.621997	−	0.621997i
$184$		−	0.585786i		−	0.0431847i
$185$	−5.35757	+	6.17733i	−0.393896	+	0.454166i
$186$	2.82843			0.207390
$187$	−10.4525	+	10.4525i	−0.764363	+	0.764363i
$188$	1.08239	+	1.08239i	0.0789416	+	0.0789416i
$189$	−11.5349	−	5.17157i	−0.839040	−	0.376177i
$190$	2.05025	−	2.36396i	0.148741	−	0.171500i
$191$	1.75736			0.127158			0.0635790	−	0.997977i	$-0.479749\pi$
$191$	1.75736			0.127158			0.0635790	+	0.997977i	$0.479749\pi$
$192$	1.30656	−	1.30656i	0.0942931	−	0.0942931i
$193$	8.24264	−	8.24264i	0.593318	−	0.593318i	−0.345208	−	0.938526i	$-0.612192\pi$
$193$	8.24264	−	8.24264i	0.593318	−	0.593318i	0.938526	+	0.345208i	$0.112192\pi$
$194$	6.49435			0.466267
$195$	24.6934	−	1.75490i	1.76833	−	0.125671i
$196$	−4.65685	−	5.22625i	−0.332632	−	0.373304i
$197$	0.585786	+	0.585786i	0.0417356	+	0.0417356i	0.727667	−	0.685931i	$-0.240605\pi$
$197$	0.585786	+	0.585786i	0.0417356	+	0.0417356i	−0.685931	+	0.727667i	$0.740605\pi$
$198$	0.828427	−	0.828427i	0.0588738	−	0.0588738i
$199$	28.0334			1.98724			0.993618	−	0.112798i	$-0.0359814\pi$
$199$	28.0334			1.98724			0.993618	+	0.112798i	$0.0359814\pi$
$200$	−3.00000	+	4.00000i	−0.212132	+	0.282843i
$201$			27.3994i			1.93260i
$202$	−1.94061	+	1.94061i	−0.136541	+	0.136541i
$203$	−2.04826	+	0.780163i	−0.143760	+	0.0547567i
$204$		−	9.65685i		−	0.676115i
$205$	−8.24264	+	0.585786i	−0.575691	+	0.0409131i
$206$			14.1480i			0.985739i
$207$	0.171573	+	0.171573i	0.0119251	+	0.0119251i
$208$	4.23671	+	4.23671i	0.293763	+	0.293763i
$209$	3.95815			0.273791
$210$	−4.60538	−	9.91403i	−0.317802	−	0.684133i
$211$	−10.3431			−0.712052			−0.356026	−	0.934476i	$-0.615868\pi$
$211$	−10.3431			−0.712052			−0.356026	+	0.934476i	$0.615868\pi$
$212$	−8.24264	−	8.24264i	−0.566107	−	0.566107i
$213$	−0.765367	−	0.765367i	−0.0524421	−	0.0524421i
$214$			5.17157i			0.353521i
$215$	9.55582	+	8.28772i	0.651702	+	0.565218i
$216$		−	4.77791i		−	0.325096i
$217$	3.78470	−	1.44155i	0.256922	−	0.0978590i
$218$	−8.58579	+	8.58579i	−0.581503	+	0.581503i
$219$			10.8284i			0.731717i
$220$	−6.30864	+	0.448342i	−0.425329	+	0.0302272i
$221$	31.3137			2.10639
$222$	4.77791	−	4.77791i	0.320672	−	0.320672i
$223$	6.75699	+	6.75699i	0.452481	+	0.452481i	0.896177	−	0.443696i	$-0.146333\pi$
$223$	6.75699	+	6.75699i	0.452481	+	0.452481i	−0.443696	+	0.896177i	$0.646333\pi$
$224$	1.08239	−	2.41421i	0.0723204	−	0.161306i
$225$	−0.292893	−	2.05025i	−0.0195262	−	0.136684i
$226$	−1.65685			−0.110212
$227$	−8.38057	+	8.38057i	−0.556238	+	0.556238i	−0.928234	−	0.371996i	$-0.878673\pi$
$227$	−8.38057	+	8.38057i	−0.556238	+	0.556238i	0.371996	+	0.928234i	$0.378673\pi$
$228$	−1.82843	+	1.82843i	−0.121091	+	0.121091i
$229$	7.70806			0.509363			0.254682	−	0.967025i	$-0.418029\pi$
$229$	7.70806			0.509363			0.254682	+	0.967025i	$0.418029\pi$
$230$	−0.0928546	−	1.30656i	−0.00612265	−	0.0861522i
$231$	5.65685	−	12.6173i	0.372194	−	0.830157i
$232$	−0.585786	−	0.585786i	−0.0384588	−	0.0384588i
$233$	3.00000	−	3.00000i	0.196537	−	0.196537i	−0.601977	−	0.798513i	$-0.705620\pi$
$233$	3.00000	−	3.00000i	0.196537	−	0.196537i	0.798513	+	0.601977i	$0.205620\pi$
$234$	−2.48181			−0.162241
$235$	2.58579	+	2.24264i	0.168678	+	0.146294i
$236$		−	9.23880i		−	0.601394i
$237$	−6.62567	+	6.62567i	−0.430383	+	0.430383i
$238$	−4.92177	−	12.9218i	−0.319031	−	0.837594i
$239$		−	6.48528i		−	0.419498i	−0.977755	−	0.209749i	$-0.932735\pi$
$239$		−	6.48528i		−	0.419498i	0.977755	−	0.209749i	$-0.0672647\pi$
$240$	2.70711	−	3.12132i	0.174743	−	0.201480i
$241$		−	6.75699i		−	0.435256i	−0.976032	−	0.217628i	$-0.930168\pi$
$241$		−	6.75699i		−	0.435256i	0.976032	−	0.217628i	$-0.0698319\pi$
$242$	2.12132	+	2.12132i	0.136364	+	0.136364i
$243$	3.02301	+	3.02301i	0.193926	+	0.193926i
$244$	6.43996			0.412276
$245$	−11.2153	−	10.9187i	−0.716517	−	0.697569i
$246$	6.82843			0.435365
$247$	−5.92893	−	5.92893i	−0.377249	−	0.377249i
$248$	1.08239	+	1.08239i	0.0687320	+	0.0687320i
$249$			13.8995i			0.880845i
$250$	−6.05728	+	9.39731i	−0.383096	+	0.594338i
$251$		−	14.0936i		−	0.889582i	−0.895634	−	0.444791i	$-0.853278\pi$
$251$		−	14.0936i		−	0.889582i	0.895634	−	0.444791i	$-0.146722\pi$
$252$	0.390081	+	1.02413i	0.0245728	+	0.0645143i
$253$	1.17157	−	1.17157i	0.0736562	−	0.0736562i
$254$		−	5.07107i		−	0.318187i
$255$	−1.53073	−	21.5391i	−0.0958583	−	1.34883i
$256$	1.00000			0.0625000
$257$	−7.83938	+	7.83938i	−0.489007	+	0.489007i	−0.907993	−	0.418986i	$-0.862386\pi$
$257$	−7.83938	+	7.83938i	−0.489007	+	0.489007i	0.418986	+	0.907993i	$0.362386\pi$
$258$	−7.39104	−	7.39104i	−0.460146	−	0.460146i
$259$	3.95815	−	8.82843i	0.245948	−	0.548572i
$260$	10.1213	+	8.77817i	0.627698	+	0.544399i
$261$	0.343146			0.0212402
$262$	−10.3596	+	10.3596i	−0.640021	+	0.640021i
$263$	−19.4142	+	19.4142i	−1.19713	+	1.19713i	−0.222110	+	0.975022i	$0.571294\pi$
$263$	−19.4142	+	19.4142i	−1.19713	+	1.19713i	−0.975022	+	0.222110i	$0.928706\pi$
$264$	5.22625			0.321654
$265$	−19.6913	−	17.0782i	−1.20963	−	1.04910i
$266$	−1.51472	+	3.37849i	−0.0928734	+	0.207149i
$267$	14.8284	+	14.8284i	0.907485	+	0.907485i
$268$	−10.4853	+	10.4853i	−0.640490	+	0.640490i
$269$	−26.8966			−1.63992			−0.819958	−	0.572424i	$-0.806003\pi$
$269$	−26.8966			−1.63992			−0.819958	+	0.572424i	$0.806003\pi$
$270$	−0.757359	−	10.6569i	−0.0460914	−	0.648555i
$271$			18.7402i			1.13839i	0.822203	+	0.569194i	$0.192745\pi$
$271$			18.7402i			1.13839i	−0.822203	+	0.569194i	$0.807255\pi$
$272$	3.69552	−	3.69552i	0.224074	−	0.224074i
$273$	−27.3729	+	10.4261i	−1.65668	+	0.631014i
$274$			11.5563i			0.698145i
$275$	−14.0000	+	2.00000i	−0.844232	+	0.120605i
$276$			1.08239i			0.0651524i
$277$	−1.75736	−	1.75736i	−0.105589	−	0.105589i	0.652338	−	0.757928i	$-0.273788\pi$
$277$	−1.75736	−	1.75736i	−0.105589	−	0.105589i	−0.757928	+	0.652338i	$0.773788\pi$
$278$	6.08447	+	6.08447i	0.364922	+	0.364922i
$279$	−0.634051			−0.0379596
$280$	2.03153	−	5.55634i	0.121407	−	0.332055i
$281$	−5.65685			−0.337460			−0.168730	−	0.985662i	$-0.553967\pi$
$281$	−5.65685			−0.337460			−0.168730	+	0.985662i	$0.553967\pi$
$282$	−2.00000	−	2.00000i	−0.119098	−	0.119098i
$283$	3.15432	+	3.15432i	0.187505	+	0.187505i	0.794617	−	0.607112i	$-0.207672\pi$
$283$	3.15432	+	3.15432i	0.187505	+	0.187505i	−0.607112	+	0.794617i	$0.707672\pi$
$284$		−	0.585786i		−	0.0347600i
$285$	−3.78837	+	4.36803i	−0.224404	+	0.258740i
$286$			16.9469i			1.00209i
$287$	9.13707	−	3.48022i	0.539344	−	0.205431i
$288$	−0.292893	+	0.292893i	−0.0172589	+	0.0172589i
$289$		−	10.3137i		−	0.606689i
$290$	−1.39942	−	1.21371i	−0.0821766	−	0.0712714i
$291$	−12.0000			−0.703452
$292$	−4.14386	+	4.14386i	−0.242501	+	0.242501i
$293$	−2.38896	−	2.38896i	−0.139564	−	0.139564i	0.633873	−	0.773437i	$-0.281464\pi$
$293$	−2.38896	−	2.38896i	−0.139564	−	0.139564i	−0.773437	+	0.633873i	$0.781464\pi$
$294$	8.60474	+	9.65685i	0.501839	+	0.563199i
$295$	−1.46447	−	20.6066i	−0.0852645	−	1.19976i
$296$	3.65685			0.212550
$297$	9.55582	−	9.55582i	0.554485	−	0.554485i
$298$	12.2426	−	12.2426i	0.709197	−	0.709197i
$299$	−3.50981			−0.202977
$300$	5.54328	−	7.39104i	0.320041	−	0.426722i
$301$	−13.6569	−	6.12293i	−0.787168	−	0.352920i
$302$	6.24264	+	6.24264i	0.359224	+	0.359224i
$303$	3.58579	−	3.58579i	0.205998	−	0.205998i
$304$	−1.39942			−0.0802621
$305$	14.3640	−	1.02082i	0.822478	−	0.0584517i
$306$			2.16478i			0.123752i
$307$	23.1626	−	23.1626i	1.32196	−	1.32196i	0.409776	−	0.912186i	$-0.365607\pi$
$307$	23.1626	−	23.1626i	1.32196	−	1.32196i	0.912186	−	0.409776i	$-0.134393\pi$
$308$	6.99321	−	2.66364i	0.398475	−	0.151775i
$309$		−	26.1421i		−	1.48717i
$310$	2.58579	+	2.24264i	0.146863	+	0.127373i
$311$			3.43289i			0.194661i	0.995252	+	0.0973305i	$0.0310304\pi$
$311$			3.43289i			0.194661i	−0.995252	+	0.0973305i	$0.968970\pi$
$312$	−7.82843	−	7.82843i	−0.443197	−	0.443197i
$313$	−6.75699	−	6.75699i	−0.381927	−	0.381927i	0.489869	−	0.871796i	$-0.337045\pi$
$313$	−6.75699	−	6.75699i	−0.381927	−	0.381927i	−0.871796	+	0.489869i	$0.837045\pi$
$314$	−14.4650			−0.816310
$315$	1.03239	+	2.22243i	0.0581687	+	0.125220i
$316$	−5.07107			−0.285270
$317$	21.8995	+	21.8995i	1.23000	+	1.23000i	0.963963	+	0.266035i	$0.0857136\pi$
$317$	21.8995	+	21.8995i	1.23000	+	1.23000i	0.266035	+	0.963963i	$0.414286\pi$
$318$	15.2304	+	15.2304i	0.854079	+	0.854079i
$319$		−	2.34315i		−	0.131191i
$320$	2.23044	−	0.158513i	0.124686	−	0.00886113i
$321$		−	9.55582i		−	0.533354i
$322$	0.551658	+	1.44834i	0.0307427	+	0.0807129i
$323$	−5.17157	+	5.17157i	−0.287754	+	0.287754i
$324$			10.0711i			0.559504i
$325$	23.9665	+	17.9749i	1.32942	+	0.997066i
$326$	−19.3137			−1.06969
$327$	15.8645	−	15.8645i	0.877307	−	0.877307i
$328$	2.61313	+	2.61313i	0.144286	+	0.144286i
$329$	−3.69552	−	1.65685i	−0.203741	−	0.0913453i
$330$	11.6569	−	0.828427i	0.641689	−	0.0456034i
$331$	23.3137			1.28144			0.640719	−	0.767776i	$-0.278637\pi$
$331$	23.3137			1.28144			0.640719	+	0.767776i	$0.278637\pi$
$332$	−5.31911	+	5.31911i	−0.291924	+	0.291924i
$333$	−1.07107	+	1.07107i	−0.0586942	+	0.0586942i
$334$	2.42742			0.132822
$335$	−21.7248	+	25.0489i	−1.18695	+	1.36857i
$336$	−2.00000	+	4.46088i	−0.109109	+	0.243361i
$337$	3.75736	+	3.75736i	0.204676	+	0.204676i	0.802000	−	0.597324i	$-0.203769\pi$
$337$	3.75736	+	3.75736i	0.204676	+	0.204676i	−0.597324	+	0.802000i	$0.703769\pi$
$338$	16.1924	−	16.1924i	0.880750	−	0.880750i
$339$	3.06147			0.166276
$340$	7.65685	−	8.82843i	0.415251	−	0.478789i
$341$			4.32957i			0.234459i
$342$	0.409880	−	0.409880i	0.0221638	−	0.0221638i
$343$	16.4357	+	8.53622i	0.887445	+	0.460913i
$344$		−	5.65685i		−	0.304997i
$345$	0.171573	+	2.41421i	0.00923717	+	0.129977i
$346$		−	18.7946i		−	1.01040i
$347$	−5.31371	−	5.31371i	−0.285255	−	0.285255i	0.549946	−	0.835200i	$-0.314648\pi$
$347$	−5.31371	−	5.31371i	−0.285255	−	0.285255i	−0.835200	+	0.549946i	$0.814648\pi$
$348$	1.08239	+	1.08239i	0.0580223	+	0.0580223i
$349$	2.66752			0.142789			0.0713945	−	0.997448i	$-0.477255\pi$
$349$	2.66752			0.142789			0.0713945	+	0.997448i	$0.477255\pi$
$350$	3.65046	−	12.7151i	0.195125	−	0.679651i
$351$	−28.6274			−1.52802
$352$	2.00000	+	2.00000i	0.106600	+	0.106600i
$353$	8.47343	+	8.47343i	0.450995	+	0.450995i	0.895685	−	0.444690i	$-0.146686\pi$
$353$	8.47343	+	8.47343i	0.450995	+	0.450995i	−0.444690	+	0.895685i	$0.646686\pi$
$354$			17.0711i			0.907317i
$355$	−0.0928546	−	1.30656i	−0.00492821	−	0.0693452i
$356$			11.3492i			0.601506i
$357$	9.09425	+	23.8763i	0.481318	+	1.26367i
$358$	−9.65685	+	9.65685i	−0.510381	+	0.510381i
$359$		−	16.9706i		−	0.895672i	−0.894116	−	0.447836i	$-0.852195\pi$
$359$		−	16.9706i		−	0.895672i	0.894116	−	0.447836i	$-0.147805\pi$
$360$	−0.606854	+	0.699709i	−0.0319840	+	0.0368779i
$361$	−17.0416			−0.896928
$362$	−6.21579	+	6.21579i	−0.326695	+	0.326695i
$363$	−3.91969	−	3.91969i	−0.205730	−	0.205730i
$364$	−14.4650	−	6.48528i	−0.758174	−	0.339921i
$365$	−8.58579	+	9.89949i	−0.449401	+	0.518163i
$366$	−11.8995			−0.621997
$367$	3.06147	−	3.06147i	0.159807	−	0.159807i	−0.622674	−	0.782481i	$-0.713954\pi$
$367$	3.06147	−	3.06147i	0.159807	−	0.159807i	0.782481	+	0.622674i	$0.213954\pi$
$368$	−0.414214	+	0.414214i	−0.0215924	+	0.0215924i
$369$	−1.53073			−0.0796868
$370$	8.15640	−	0.579658i	0.424031	−	0.0301350i
$371$	28.1421	+	12.6173i	1.46107	+	0.655057i
$372$	−2.00000	−	2.00000i	−0.103695	−	0.103695i
$373$	−15.0711	+	15.0711i	−0.780350	+	0.780350i	−0.979890	−	0.199539i	$-0.936055\pi$
$373$	−15.0711	+	15.0711i	−0.780350	+	0.780350i	0.199539	+	0.979890i	$0.436055\pi$
$374$	14.7821			0.764363
$375$	11.1924	−	17.3640i	0.577972	−	0.896671i
$376$		−	1.53073i		−	0.0789416i
$377$	−3.50981	+	3.50981i	−0.180764	+	0.180764i
$378$	4.49955	+	11.8133i	0.231432	+	0.607608i
$379$			6.14214i			0.315500i	0.987479	+	0.157750i	$0.0504241\pi$
$379$			6.14214i			0.315500i	−0.987479	+	0.157750i	$0.949576\pi$
$380$	−3.12132	+	0.221825i	−0.160120	+	0.0113794i
$381$			9.37011i			0.480045i
$382$	−1.24264	−	1.24264i	−0.0635790	−	0.0635790i
$383$	−10.6382	−	10.6382i	−0.543587	−	0.543587i	0.380991	−	0.924579i	$-0.375583\pi$
$383$	−10.6382	−	10.6382i	−0.543587	−	0.543587i	−0.924579	+	0.380991i	$0.875583\pi$
$384$	−1.84776			−0.0942931
$385$	15.1757	−	7.04961i	0.773427	−	0.359282i
$386$	−11.6569			−0.593318
$387$	1.65685	+	1.65685i	0.0842226	+	0.0842226i
$388$	−4.59220	−	4.59220i	−0.233134	−	0.233134i
$389$			0.142136i			0.00720656i	0.999994	+	0.00360328i	$0.00114696\pi$
$389$			0.142136i			0.00720656i	−0.999994	+	0.00360328i	$0.998853\pi$
$390$	−18.7018	−	16.2200i	−0.947001	−	0.821329i
$391$			3.06147i			0.154825i
$392$	−0.402625	+	6.98841i	−0.0203356	+	0.352968i
$393$	19.1421	−	19.1421i	0.965593	−	0.965593i
$394$		−	0.828427i		−	0.0417356i
$395$	−11.3107	+	0.803828i	−0.569104	+	0.0404450i
$396$	−1.17157			−0.0588738
$397$	1.12085	−	1.12085i	0.0562540	−	0.0562540i	−0.678420	−	0.734674i	$-0.737335\pi$
$397$	1.12085	−	1.12085i	0.0562540	−	0.0562540i	0.734674	+	0.678420i	$0.237335\pi$
$398$	−19.8226	−	19.8226i	−0.993618	−	0.993618i
$399$	2.79884	−	6.24264i	0.140117	−	0.312523i
$400$	4.94975	−	0.707107i	0.247487	−	0.0353553i
$401$	−19.7574			−0.986635			−0.493318	−	0.869849i	$-0.664216\pi$
$401$	−19.7574			−0.986635			−0.493318	+	0.869849i	$0.664216\pi$
$402$	19.3743	−	19.3743i	0.966301	−	0.966301i
$403$	6.48528	−	6.48528i	0.323055	−	0.323055i
$404$	2.74444			0.136541
$405$	1.59639	+	22.4629i	0.0793253	+	1.11619i
$406$	2.00000	+	0.896683i	0.0992583	+	0.0445016i
$407$	7.31371	+	7.31371i	0.362527	+	0.362527i
$408$	−6.82843	+	6.82843i	−0.338058	+	0.338058i
$409$	−24.9719			−1.23478			−0.617392	−	0.786656i	$-0.711811\pi$
$409$	−24.9719			−1.23478			−0.617392	+	0.786656i	$0.711811\pi$
$410$	6.24264	+	5.41421i	0.308302	+	0.267389i
$411$		−	21.3533i		−	1.05328i
$412$	10.0042	−	10.0042i	0.492870	−	0.492870i
$413$	8.70054	+	22.8427i	0.428126	+	1.12401i
$414$		−	0.242641i		−	0.0119251i
$415$	−11.0208	+	12.7071i	−0.540991	+	0.623767i
$416$		−	5.99162i		−	0.293763i
$417$	−11.2426	−	11.2426i	−0.550554	−	0.550554i
$418$	−2.79884	−	2.79884i	−0.136895	−	0.136895i
$419$	11.5893			0.566174			0.283087	−	0.959094i	$-0.408642\pi$
$419$	11.5893			0.566174			0.283087	+	0.959094i	$0.408642\pi$
$420$	−3.75378	+	10.2668i	−0.183166	+	0.500967i
$421$	17.7990			0.867470			0.433735	−	0.901041i	$-0.357195\pi$
$421$	17.7990			0.867470			0.433735	+	0.901041i	$0.357195\pi$
$422$	7.31371	+	7.31371i	0.356026	+	0.356026i
$423$	0.448342	+	0.448342i	0.0217991	+	0.0217991i
$424$			11.6569i			0.566107i
$425$	15.6788	−	20.9050i	0.760531	−	1.01404i
$426$			1.08239i			0.0524421i
$427$	−15.9226	+	6.06477i	−0.770550	+	0.293495i
$428$	3.65685	−	3.65685i	0.176761	−	0.176761i
$429$		−	31.3137i		−	1.51184i
$430$	−0.896683	−	12.6173i	−0.0432419	−	0.608460i
$431$	5.65685			0.272481			0.136241	−	0.990676i	$-0.456498\pi$
$431$	5.65685			0.272481			0.136241	+	0.990676i	$0.456498\pi$
$432$	−3.37849	+	3.37849i	−0.162548	+	0.162548i
$433$	−10.4525	−	10.4525i	−0.502315	−	0.502315i	0.409841	−	0.912157i	$-0.365584\pi$
$433$	−10.4525	−	10.4525i	−0.502315	−	0.502315i	−0.912157	+	0.409841i	$0.865584\pi$
$434$	−3.69552	−	1.65685i	−0.177391	−	0.0795315i
$435$	2.58579	+	2.24264i	0.123979	+	0.107526i
$436$	12.1421			0.581503
$437$	0.579658	−	0.579658i	0.0277288	−	0.0277288i
$438$	7.65685	−	7.65685i	0.365859	−	0.365859i
$439$	−13.8854			−0.662713			−0.331357	−	0.943506i	$-0.607506\pi$
$439$	−13.8854			−0.662713			−0.331357	+	0.943506i	$0.607506\pi$
$440$	4.77791	+	4.14386i	0.227778	+	0.197551i
$441$	−1.92893	−	2.16478i	−0.0918539	−	0.103085i
$442$	−22.1421	−	22.1421i	−1.05319	−	1.05319i
$443$	−4.14214	+	4.14214i	−0.196799	+	0.196799i	−0.798626	−	0.601827i	$-0.794440\pi$
$443$	−4.14214	+	4.14214i	−0.196799	+	0.196799i	0.601827	+	0.798626i	$0.294440\pi$
$444$	−6.75699			−0.320672
$445$	1.79899	+	25.3137i	0.0852803	+	1.19998i
$446$		−	9.55582i		−	0.452481i
$447$	−22.6215	+	22.6215i	−1.06996	+	1.06996i
$448$	−2.47247	+	0.941740i	−0.116813	+	0.0444930i
$449$			25.6569i			1.21082i	0.795913	+	0.605411i	$0.206991\pi$
$449$			25.6569i			1.21082i	−0.795913	+	0.605411i	$0.793009\pi$
$450$	−1.24264	+	1.65685i	−0.0585786	+	0.0781049i
$451$			10.4525i			0.492189i
$452$	1.17157	+	1.17157i	0.0551062	+	0.0551062i
$453$	−11.5349	−	11.5349i	−0.541957	−	0.541957i
$454$	11.8519			0.556238
$455$	−33.2915	−	12.1722i	−1.56073	−	0.570639i
$456$	2.58579			0.121091
$457$	−1.65685	−	1.65685i	−0.0775044	−	0.0775044i	0.667292	−	0.744796i	$-0.267453\pi$
$457$	−1.65685	−	1.65685i	−0.0775044	−	0.0775044i	−0.744796	+	0.667292i	$0.767453\pi$
$458$	−5.45042	−	5.45042i	−0.254682	−	0.254682i
$459$			24.9706i			1.16553i
$460$	−0.858221	+	0.989538i	−0.0400148	+	0.0461374i
$461$			34.0250i			1.58470i	0.610064	+	0.792352i	$0.291144\pi$
$461$			34.0250i			1.58470i	−0.610064	+	0.792352i	$0.708856\pi$
$462$	−12.9218	+	4.92177i	−0.601175	+	0.228981i
$463$	−12.9706	+	12.9706i	−0.602793	+	0.602793i	−0.941053	−	0.338260i	$-0.890162\pi$
$463$	−12.9706	+	12.9706i	−0.602793	+	0.602793i	0.338260	+	0.941053i	$0.390162\pi$
$464$			0.828427i			0.0384588i
$465$	−4.77791	−	4.14386i	−0.221570	−	0.192167i
$466$	−4.24264			−0.196537
$467$	17.4337	−	17.4337i	0.806734	−	0.806734i	−0.177404	−	0.984138i	$-0.556770\pi$
$467$	17.4337	−	17.4337i	0.806734	−	0.806734i	0.984138	+	0.177404i	$0.0567701\pi$
$468$	1.75490	+	1.75490i	0.0811205	+	0.0811205i
$469$	16.0502	−	35.7990i	0.741128	−	1.65304i
$470$	−0.242641	−	3.41421i	−0.0111922	−	0.157486i
$471$	26.7279			1.23156
$472$	−6.53281	+	6.53281i	−0.300697	+	0.300697i
$473$	11.3137	−	11.3137i	0.520205	−	0.520205i
$474$	9.37011			0.430383
$475$	−6.92676	+	0.989538i	−0.317822	+	0.0454031i
$476$	−5.65685	+	12.6173i	−0.259281	+	0.578312i
$477$	−3.41421	−	3.41421i	−0.156326	−	0.156326i
$478$	−4.58579	+	4.58579i	−0.209749	+	0.209749i
$479$	−11.0866			−0.506558			−0.253279	−	0.967393i	$-0.581509\pi$
$479$	−11.0866			−0.506558			−0.253279	+	0.967393i	$0.581509\pi$
$480$	−4.12132	+	0.292893i	−0.188112	+	0.0133687i
$481$		−	21.9105i		−	0.999032i
$482$	−4.77791	+	4.77791i	−0.217628	+	0.217628i
$483$	−1.01933	−	2.67619i	−0.0463812	−	0.121771i
$484$		−	3.00000i		−	0.136364i
$485$	−10.9706	−	9.51472i	−0.498148	−	0.432041i
$486$		−	4.27518i		−	0.193926i
$487$	1.10051	+	1.10051i	0.0498686	+	0.0498686i	0.731601	−	0.681733i	$-0.238773\pi$
$487$	1.10051	+	1.10051i	0.0498686	+	0.0498686i	−0.681733	+	0.731601i	$0.738773\pi$
$488$	−4.55374	−	4.55374i	−0.206138	−	0.206138i
$489$	35.6871			1.61383
$490$	0.209720	+	15.6511i	0.00947418	+	0.707043i
$491$	25.1716			1.13598			0.567989	−	0.823036i	$-0.307722\pi$
$491$	25.1716			1.13598			0.567989	+	0.823036i	$0.307722\pi$
$492$	−4.82843	−	4.82843i	−0.217682	−	0.217682i
$493$	3.06147	+	3.06147i	0.137882	+	0.137882i
$494$			8.38478i			0.377249i
$495$	−2.61313	+	0.185709i	−0.117451	+	0.00834701i
$496$		−	1.53073i		−	0.0687320i
$497$	0.551658	+	1.44834i	0.0247453	+	0.0649670i
$498$	9.82843	−	9.82843i	0.440422	−	0.440422i
$499$			7.51472i			0.336405i	0.985752	+	0.168203i	$0.0537963\pi$
$499$			7.51472i			0.336405i	−0.985752	+	0.168203i	$0.946204\pi$
$500$	10.9280	−	2.36176i	0.488717	−	0.105621i
$501$	−4.48528			−0.200388
$502$	−9.96570	+	9.96570i	−0.444791	+	0.444791i
$503$	18.1062	+	18.1062i	0.807314	+	0.807314i	0.984227	−	0.176912i	$-0.0566109\pi$
$503$	18.1062	+	18.1062i	0.807314	+	0.807314i	−0.176912	+	0.984227i	$0.556611\pi$
$504$	0.448342	−	1.00000i	0.0199707	−	0.0445435i
$505$	6.12132	−	0.435029i	0.272395	−	0.0193585i
$506$	−1.65685			−0.0736562
$507$	−29.9196	+	29.9196i	−1.32878	+	1.32878i
$508$	−3.58579	+	3.58579i	−0.159094	+	0.159094i
$509$	14.4650			0.641152			0.320576	−	0.947223i	$-0.396124\pi$
$509$	14.4650			0.641152			0.320576	+	0.947223i	$0.396124\pi$
$510$	−14.1480	+	16.3128i	−0.626485	+	0.722343i
$511$	6.34315	−	14.1480i	0.280604	−	0.625872i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.72792	−	4.72792i	0.208743	−	0.208743i
$514$	11.0866			0.489007
$515$	20.7279	−	23.8995i	0.913381	−	1.05314i
$516$			10.4525i			0.460146i
$517$	3.06147	−	3.06147i	0.134643	−	0.134643i
$518$	−9.04148	+	3.44381i	−0.397260	+	0.151312i
$519$			34.7279i			1.52439i
$520$	−0.949747	−	13.3640i	−0.0416492	−	0.586048i
$521$		−	36.6925i		−	1.60753i	−0.594947	−	0.803765i	$-0.702827\pi$
$521$		−	36.6925i		−	1.60753i	0.594947	−	0.803765i	$-0.297173\pi$
$522$	−0.242641	−	0.242641i	−0.0106201	−	0.0106201i
$523$	1.75490	+	1.75490i	0.0767366	+	0.0767366i	0.744433	−	0.667697i	$-0.232720\pi$
$523$	1.75490	+	1.75490i	0.0767366	+	0.0767366i	−0.667697	+	0.744433i	$0.732720\pi$
$524$	14.6508			0.640021
$525$	−6.74517	+	23.4945i	−0.294383	+	1.02538i
$526$	27.4558			1.19713
$527$	−5.65685	−	5.65685i	−0.246416	−	0.246416i
$528$	−3.69552	−	3.69552i	−0.160827	−	0.160827i
$529$			22.6569i			0.985081i
$530$	1.84776	+	25.9999i	0.0802615	+	1.12937i
$531$		−	3.82683i		−	0.166070i
$532$	3.46002	−	1.31789i	0.150011	−	0.0571377i
$533$	15.6569	−	15.6569i	0.678174	−	0.678174i
$534$		−	20.9706i		−	0.907485i
$535$	7.57675	−	8.73606i	0.327571	−	0.377693i
$536$	14.8284			0.640490
$537$	17.8435	−	17.8435i	0.770006	−	0.770006i
$538$	19.0188	+	19.0188i	0.819958	+	0.819958i
$539$	−14.7821	+	13.1716i	−0.636709	+	0.567340i
$540$	−7.00000	+	8.07107i	−0.301232	+	0.347323i
$541$	10.9706			0.471661			0.235831	−	0.971794i	$-0.424219\pi$
$541$	10.9706			0.471661			0.235831	+	0.971794i	$0.424219\pi$
$542$	13.2513	−	13.2513i	0.569194	−	0.569194i
$543$	11.4853	−	11.4853i	0.492881	−	0.492881i
$544$	−5.22625			−0.224074
$545$	27.0823	−	1.92468i	1.16008	−	0.0824443i
$546$	26.7279	+	11.9832i	1.14385	+	0.512835i
$547$	−30.6274	−	30.6274i	−1.30953	−	1.30953i	−0.921751	−	0.387783i	$-0.873241\pi$
$547$	−30.6274	−	30.6274i	−1.30953	−	1.30953i	−0.387783	−	0.921751i	$-0.626759\pi$
$548$	8.17157	−	8.17157i	0.349072	−	0.349072i
$549$	2.66752			0.113847
$550$	11.3137	+	8.48528i	0.482418	+	0.361814i
$551$		−	1.15932i		−	0.0493885i
$552$	0.765367	−	0.765367i	0.0325762	−	0.0325762i
$553$	12.5381	−	4.77563i	0.533173	−	0.203080i
$554$			2.48528i			0.105589i
$555$	−15.0711	+	1.07107i	−0.639731	+	0.0454643i
$556$		−	8.60474i		−	0.364922i
$557$	−26.7279	−	26.7279i	−1.13250	−	1.13250i	−0.989761	−	0.142738i	$-0.954409\pi$
$557$	−26.7279	−	26.7279i	−1.13250	−	1.13250i	−0.142738	−	0.989761i	$-0.545591\pi$
$558$	0.448342	+	0.448342i	0.0189798	+	0.0189798i
$559$	−33.8937			−1.43355
$560$	−5.36543	+	2.49242i	−0.226731	+	0.105324i
$561$	−27.3137			−1.15319
$562$	4.00000	+	4.00000i	0.168730	+	0.168730i
$563$	3.54827	+	3.54827i	0.149542	+	0.149542i	0.777913	−	0.628372i	$-0.216278\pi$
$563$	3.54827	+	3.54827i	0.149542	+	0.149542i	−0.628372	+	0.777913i	$0.716278\pi$
$564$			2.82843i			0.119098i
$565$	2.79884	+	2.42742i	0.117748	+	0.102122i
$566$		−	4.46088i		−	0.187505i
$567$	−9.48433	−	24.9004i	−0.398304	−	1.04572i
$568$	−0.414214	+	0.414214i	−0.0173800	+	0.0173800i
$569$			1.41421i			0.0592869i	0.999561	+	0.0296435i	$0.00943719\pi$
$569$			1.41421i			0.0592869i	−0.999561	+	0.0296435i	$0.990563\pi$
$570$	5.76745	−	0.409880i	0.241572	−	0.0171680i
$571$	−25.4558			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$571$	−25.4558			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$572$	11.9832	−	11.9832i	0.501044	−	0.501044i
$573$	2.29610	+	2.29610i	0.0959210	+	0.0959210i
$574$	−8.92177	−	4.00000i	−0.372387	−	0.166957i
$575$	−1.75736	+	2.34315i	−0.0732869	+	0.0977159i
$576$	0.414214			0.0172589
$577$	−26.3170	+	26.3170i	−1.09559	+	1.09559i	−0.100670	+	0.994920i	$0.532099\pi$
$577$	−26.3170	+	26.3170i	−1.09559	+	1.09559i	−0.994920	+	0.100670i	$0.967901\pi$
$578$	−7.29289	+	7.29289i	−0.303344	+	0.303344i
$579$	21.5391			0.895133
$580$	0.131316	+	1.84776i	0.00545261	+	0.0767240i
$581$	8.14214	−	18.1606i	0.337793	−	0.753427i
$582$	8.48528	+	8.48528i	0.351726	+	0.351726i
$583$	−23.3137	+	23.3137i	−0.965555	+	0.965555i
$584$	5.86030			0.242501
$585$	4.19239	+	3.63604i	0.173334	+	0.150332i
$586$			3.37849i			0.139564i
$587$	16.0886	−	16.0886i	0.664049	−	0.664049i	−0.292283	−	0.956332i	$-0.594415\pi$
$587$	16.0886	−	16.0886i	0.664049	−	0.664049i	0.956332	+	0.292283i	$0.0944149\pi$
$588$	0.743954	−	12.9129i	0.0306801	−	0.532519i
$589$			2.14214i			0.0882652i
$590$	−13.5355	+	15.6066i	−0.557249	+	0.642514i
$591$			1.53073i			0.0629660i
$592$	−2.58579	−	2.58579i	−0.106275	−	0.106275i
$593$	−22.8841	−	22.8841i	−0.939737	−	0.939737i	0.0585480	−	0.998285i	$-0.481353\pi$
$593$	−22.8841	−	22.8841i	−0.939737	−	0.939737i	−0.998285	+	0.0585480i	$0.981353\pi$
$594$	−13.5140			−0.554485
$595$	−10.6173	+	29.0388i	−0.435266	+	1.19048i
$596$	−17.3137			−0.709197
$597$	36.6274	+	36.6274i	1.49906	+	1.49906i
$598$	2.48181	+	2.48181i	0.101489	+	0.101489i
$599$			18.5269i			0.756989i	0.925604	+	0.378495i	$0.123558\pi$
$599$			18.5269i			0.756989i	−0.925604	+	0.378495i	$0.876442\pi$
$600$	−9.14594	+	1.30656i	−0.373381	+	0.0533402i
$601$			16.5754i			0.676126i	0.941123	+	0.338063i	$0.109772\pi$
$601$			16.5754i			0.676126i	−0.941123	+	0.338063i	$0.890228\pi$
$602$	5.32729	+	13.9864i	0.217124	+	0.570044i
$603$	−4.34315	+	4.34315i	−0.176867	+	0.176867i
$604$		−	8.82843i		−	0.359224i
$605$	−0.475538	−	6.69133i	−0.0193334	−	0.272041i
$606$	−5.07107			−0.205998
$607$	−21.5391	+	21.5391i	−0.874243	+	0.874243i	−0.992932	−	0.118688i	$-0.962131\pi$
$607$	−21.5391	+	21.5391i	−0.874243	+	0.874243i	0.118688	+	0.992932i	$0.462131\pi$
$608$	0.989538	+	0.989538i	0.0401311	+	0.0401311i
$609$	−3.69552	−	1.65685i	−0.149750	−	0.0671391i
$610$	−10.8787	−	9.43503i	−0.440465	−	0.382013i
$611$	−9.17157			−0.371042
$612$	1.53073	−	1.53073i	0.0618762	−	0.0618762i
$613$	19.8995	−	19.8995i	0.803733	−	0.803733i	−0.179944	−	0.983677i	$-0.557592\pi$
$613$	19.8995	−	19.8995i	0.803733	−	0.803733i	0.983677	+	0.179944i	$0.0575916\pi$
$614$	−32.7569			−1.32196
$615$	−11.5349	−	10.0042i	−0.465132	−	0.403407i
$616$	−6.82843	−	3.06147i	−0.275125	−	0.123350i
$617$	−28.4853	−	28.4853i	−1.14677	−	1.14677i	−0.987183	−	0.159591i	$-0.948982\pi$
$617$	−28.4853	−	28.4853i	−1.14677	−	1.14677i	−0.159591	−	0.987183i	$-0.551018\pi$
$618$	−18.4853	+	18.4853i	−0.743587	+	0.743587i
$619$	−0.688444			−0.0276709			−0.0138354	−	0.999904i	$-0.504404\pi$
$619$	−0.688444			−0.0276709			−0.0138354	+	0.999904i	$0.504404\pi$
$620$	−0.242641	−	3.41421i	−0.00974468	−	0.137118i
$621$		−	2.79884i		−	0.112313i
$622$	2.42742	−	2.42742i	0.0973305	−	0.0973305i
$623$	−10.6880	−	28.0606i	−0.428205	−	1.12422i
$624$			11.0711i			0.443197i
$625$	24.0000	−	7.00000i	0.960000	−	0.280000i
$626$			9.55582i			0.381927i
$627$	5.17157	+	5.17157i	0.206533	+	0.206533i
$628$	10.2283	+	10.2283i	0.408155	+	0.408155i
$629$	−19.1116			−0.762031
$630$	0.841487	−	2.30151i	0.0335257	−	0.0916944i
$631$	41.3553			1.64633			0.823165	−	0.567802i	$-0.192206\pi$
$631$	41.3553			1.64633			0.823165	+	0.567802i	$0.192206\pi$
$632$	3.58579	+	3.58579i	0.142635	+	0.142635i
$633$	−13.5140	−	13.5140i	−0.537132	−	0.537132i
$634$		−	30.9706i		−	1.23000i
$635$	−7.42950	+	8.56628i	−0.294831	+	0.339943i
$636$		−	21.5391i		−	0.854079i
$637$	41.8719	+	2.41237i	1.65902	+	0.0955818i
$638$	−1.65685	+	1.65685i	−0.0655955	+	0.0655955i
$639$		−	0.242641i		−	0.00959872i
$640$	−1.68925	−	1.46508i	−0.0667733	−	0.0579122i
$641$	−37.2132			−1.46983			−0.734917	−	0.678158i	$-0.762779\pi$
$641$	−37.2132			−1.46983			−0.734917	+	0.678158i	$0.762779\pi$
$642$	−6.75699	+	6.75699i	−0.266677	+	0.266677i
$643$	−20.9435	−	20.9435i	−0.825930	−	0.825930i	0.161021	−	0.986951i	$-0.448521\pi$
$643$	−20.9435	−	20.9435i	−0.825930	−	0.825930i	−0.986951	+	0.161021i	$0.948521\pi$
$644$	0.634051	−	1.41421i	0.0249851	−	0.0557278i
$645$	1.65685	+	23.3137i	0.0652386	+	0.917976i
$646$	7.31371			0.287754
$647$	23.8896	−	23.8896i	0.939195	−	0.939195i	−0.0590593	−	0.998254i	$-0.518810\pi$
$647$	23.8896	−	23.8896i	0.939195	−	0.939195i	0.998254	+	0.0590593i	$0.0188101\pi$
$648$	7.12132	−	7.12132i	0.279752	−	0.279752i
$649$	−26.1313			−1.02574
$650$	−4.23671	−	29.6570i	−0.166178	−	1.16324i
$651$	6.82843	+	3.06147i	0.267627	+	0.119988i
$652$	13.6569	+	13.6569i	0.534844	+	0.534844i
$653$	8.72792	−	8.72792i	0.341550	−	0.341550i	−0.515400	−	0.856950i	$-0.672357\pi$
$653$	8.72792	−	8.72792i	0.341550	−	0.341550i	0.856950	+	0.515400i	$0.172357\pi$
$654$	−22.4357			−0.877307
$655$	32.6777	−	2.32233i	1.27682	−	0.0907410i
$656$		−	3.69552i		−	0.144286i
$657$	−1.71644	+	1.71644i	−0.0669648	+	0.0669648i
$658$	1.44155	+	3.78470i	0.0561976	+	0.147543i
$659$		−	29.6569i		−	1.15527i	−0.816296	−	0.577634i	$-0.803976\pi$
$659$		−	29.6569i		−	1.15527i	0.816296	−	0.577634i	$-0.196024\pi$
$660$	−8.82843	−	7.65685i	−0.343646	−	0.298043i
$661$			47.5390i			1.84905i	0.381118	+	0.924526i	$0.375539\pi$
$661$			47.5390i			1.84905i	−0.381118	+	0.924526i	$0.624461\pi$
$662$	−16.4853	−	16.4853i	−0.640719	−	0.640719i
$663$	40.9133	+	40.9133i	1.58894	+	1.58894i
$664$	7.52235			0.291924
$665$	7.50848	−	3.48793i	0.291166	−	0.135256i
$666$	1.51472			0.0586942
$667$	−0.343146	−	0.343146i	−0.0132867	−	0.0132867i
$668$	−1.71644	−	1.71644i	−0.0664112	−	0.0664112i
$669$			17.6569i			0.682653i
$670$	33.0740	−	2.35049i	1.27776	−	0.0908075i
$671$		−	18.2150i		−	0.703181i
$672$	4.56854	−	1.74011i	0.176235	−	0.0671261i
$673$	−22.7990	+	22.7990i	−0.878836	+	0.878836i	−0.993414	−	0.114578i	$-0.963448\pi$
$673$	−22.7990	+	22.7990i	−0.878836	+	0.878836i	0.114578	+	0.993414i	$0.463448\pi$
$674$		−	5.31371i		−	0.204676i
$675$	−14.3337	+	19.1116i	−0.551706	+	0.735607i
$676$	−22.8995			−0.880750
$677$	−22.4742	+	22.4742i	−0.863754	+	0.863754i	−0.991772	−	0.128018i	$-0.959138\pi$
$677$	−22.4742	+	22.4742i	−0.863754	+	0.863754i	0.128018	+	0.991772i	$0.459138\pi$
$678$	−2.16478	−	2.16478i	−0.0831380	−	0.0831380i
$679$	15.6788	+	7.02944i	0.601695	+	0.269765i
$680$	−11.6569	+	0.828427i	−0.447020	+	0.0317687i
$681$	−21.8995			−0.839190
$682$	3.06147	−	3.06147i	0.117230	−	0.117230i
$683$	−25.3137	+	25.3137i	−0.968602	+	0.968602i	−0.999522	−	0.0309197i	$-0.990156\pi$
$683$	−25.3137	+	25.3137i	−0.968602	+	0.968602i	0.0309197	+	0.999522i	$0.490156\pi$
$684$	−0.579658			−0.0221638
$685$	16.9309	−	19.5215i	0.646897	−	0.745879i
$686$	−5.58579	−	17.6578i	−0.213266	−	0.674179i
$687$	10.0711	+	10.0711i	0.384235	+	0.384235i
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	69.8434			2.66082
$690$	1.58579	−	1.82843i	0.0603699	−	0.0696070i
$691$			25.1033i			0.954973i	0.878639	+	0.477487i	$0.158452\pi$
$691$			25.1033i			0.954973i	−0.878639	+	0.477487i	$0.841548\pi$
$692$	−13.2898	+	13.2898i	−0.505202	+	0.505202i
$693$	2.89668	−	1.10332i	0.110036	−	0.0419115i
$694$			7.51472i			0.285255i
$695$	−1.36396	−	19.1924i	−0.0517380	−	0.728009i
$696$		−	1.53073i		−	0.0580223i
$697$	−13.6569	−	13.6569i	−0.517290	−	0.517290i
$698$	−1.88622	−	1.88622i	−0.0713945	−	0.0713945i
$699$	7.83938			0.296512
$700$	−11.5722	+	6.40968i	−0.437388	+	0.242263i
$701$	−13.1127			−0.495260			−0.247630	−	0.968855i	$-0.579652\pi$
$701$	−13.1127			−0.495260			−0.247630	+	0.968855i	$0.579652\pi$
$702$	20.2426	+	20.2426i	0.764009	+	0.764009i
$703$	3.61859	+	3.61859i	0.136478	+	0.136478i
$704$		−	2.82843i		−	0.106600i
$705$	0.448342	+	6.30864i	0.0168855	+	0.237597i
$706$		−	11.9832i		−	0.450995i
$707$	−6.78556	+	2.58455i	−0.255197	+	0.0972020i
$708$	12.0711	−	12.0711i	0.453659	−	0.453659i
$709$		−	41.3137i		−	1.55157i	−0.630998	−	0.775784i	$-0.717354\pi$
$709$		−	41.3137i		−	1.55157i	0.630998	−	0.775784i	$-0.282646\pi$
$710$	−0.858221	+	0.989538i	−0.0322085	+	0.0371367i
$711$	−2.10051			−0.0787751
$712$	8.02509	−	8.02509i	0.300753	−	0.300753i
$713$	0.634051	+	0.634051i	0.0237454	+	0.0237454i
$714$	10.4525	−	23.3137i	0.391175	−	0.872494i
$715$	24.8284	−	28.6274i	0.928531	−	1.07060i
$716$	13.6569			0.510381
$717$	8.47343	−	8.47343i	0.316446	−	0.316446i
$718$	−12.0000	+	12.0000i	−0.447836	+	0.447836i
$719$	43.7122			1.63019			0.815094	−	0.579328i	$-0.196685\pi$
$719$	43.7122			1.63019			0.815094	+	0.579328i	$0.196685\pi$
$720$	0.923880	−	0.0656581i	0.0344310	−	0.00244693i
$721$	−15.3137	+	34.1563i	−0.570312	+	1.27205i
$722$	12.0503	+	12.0503i	0.448464	+	0.448464i
$723$	8.82843	−	8.82843i	0.328333	−	0.328333i
$724$	8.79045			0.326695
$725$	0.585786	+	4.10051i	0.0217556	+	0.152289i
$726$			5.54328i			0.205730i
$727$	−22.8841	+	22.8841i	−0.848724	+	0.848724i	−0.989974	−	0.141250i	$-0.954888\pi$
$727$	−22.8841	+	22.8841i	−0.848724	+	0.848724i	0.141250	+	0.989974i	$0.454888\pi$
$728$	5.64255	+	14.8141i	0.209127	+	0.549048i
$729$		−	22.3137i		−	0.826434i
$730$	13.0711	−	0.928932i	0.483782	−	0.0343813i
$731$			29.5641i			1.09347i
$732$	8.41421	+	8.41421i	0.310998	+	0.310998i
$733$	21.9489	+	21.9489i	0.810703	+	0.810703i	0.984739	−	0.174037i	$-0.0556811\pi$
$733$	21.9489	+	21.9489i	0.810703	+	0.810703i	−0.174037	+	0.984739i	$0.555681\pi$
$734$	−4.32957			−0.159807
$735$	−0.387512	−	28.9194i	−0.0142936	−	1.06671i
$736$	0.585786			0.0215924
$737$	29.6569	+	29.6569i	1.09242	+	1.09242i
$738$	1.08239	+	1.08239i	0.0398434	+	0.0398434i
$739$		−	9.65685i		−	0.355233i	−0.984100	−	0.177617i	$-0.943161\pi$
$739$		−	9.65685i		−	0.355233i	0.984100	−	0.177617i	$-0.0568387\pi$
$740$	−6.17733	−	5.35757i	−0.227083	−	0.196948i
$741$		−	15.4930i		−	0.569151i
$742$	−10.9777	−	28.8213i	−0.403005	−	1.05806i
$743$	27.0416	−	27.0416i	0.992061	−	0.992061i	−0.00790753	−	0.999969i	$-0.502517\pi$
$743$	27.0416	−	27.0416i	0.992061	−	0.992061i	0.999969	+	0.00790753i	$0.00251707\pi$
$744$			2.82843i			0.103695i
$745$	−38.6172	+	2.74444i	−1.41483	+	0.100549i
$746$	21.3137			0.780350
$747$	−2.20325	+	2.20325i	−0.0806126	+	0.0806126i
$748$	−10.4525	−	10.4525i	−0.382181	−	0.382181i
$749$	−5.59767	+	12.4853i	−0.204534	+	0.456202i
$750$	−20.1924	+	4.36396i	−0.737322	+	0.159349i
$751$	−2.48528			−0.0906892			−0.0453446	−	0.998971i	$-0.514439\pi$
$751$	−2.48528			−0.0906892			−0.0453446	+	0.998971i	$0.514439\pi$
$752$	−1.08239	+	1.08239i	−0.0394708	+	0.0394708i
$753$	18.4142	−	18.4142i	0.671051	−	0.671051i
$754$	4.96362			0.180764
$755$	−1.39942	−	19.6913i	−0.0509300	−	0.716640i
$756$	5.17157	−	11.5349i	0.188088	−	0.419520i
$757$	7.89949	+	7.89949i	0.287112	+	0.287112i	0.835937	−	0.548825i	$-0.184925\pi$
$757$	7.89949	+	7.89949i	0.287112	+	0.287112i	−0.548825	+	0.835937i	$0.684925\pi$
$758$	4.34315	−	4.34315i	0.157750	−	0.157750i
$759$	3.06147			0.111124
$760$	2.36396	+	2.05025i	0.0857499	+	0.0743705i
$761$			26.3939i			0.956778i	0.878148	+	0.478389i	$0.158779\pi$
$761$			26.3939i			0.956778i	−0.878148	+	0.478389i	$0.841221\pi$
$762$	6.62567	−	6.62567i	0.240023	−	0.240023i
$763$	−30.0211	+	11.4347i	−1.08684	+	0.413965i
$764$			1.75736i			0.0635790i
$765$	3.17157	−	3.65685i	0.114668	−	0.132214i
$766$			15.0447i			0.543587i
$767$	39.1421	+	39.1421i	1.41334	+	1.41334i
$768$	1.30656	+	1.30656i	0.0471465	+	0.0471465i
$769$	−17.5809			−0.633984			−0.316992	−	0.948428i	$-0.602673\pi$
$769$	−17.5809			−0.633984			−0.316992	+	0.948428i	$0.602673\pi$
$770$	−15.7157	−	5.74603i	−0.566354	−	0.207073i
$771$	−20.4853			−0.737759
$772$	8.24264	+	8.24264i	0.296659	+	0.296659i
$773$	−14.6892	−	14.6892i	−0.528334	−	0.528334i	0.391741	−	0.920076i	$-0.371873\pi$
$773$	−14.6892	−	14.6892i	−0.528334	−	0.528334i	−0.920076	+	0.391741i	$0.871873\pi$
$774$		−	2.34315i		−	0.0842226i
$775$	−1.08239	−	7.57675i	−0.0388807	−	0.272165i
$776$			6.49435i			0.233134i
$777$	16.7065	−	6.36332i	0.599341	−	0.228283i
$778$	0.100505	−	0.100505i	0.00360328	−	0.00360328i
$779$			5.17157i			0.185291i
$780$	1.75490	+	24.6934i	0.0628357	+	0.884165i
$781$	−1.65685			−0.0592869
$782$	2.16478	−	2.16478i	0.0774125	−	0.0774125i
$783$	−2.79884	−	2.79884i	−0.100022	−	0.100022i
$784$	5.22625	−	4.65685i	0.186652	−	0.166316i
$785$	24.4350	+	21.1924i	0.872124	+	0.756389i
$786$	−27.0711			−0.965593
$787$	24.3764	−	24.3764i	0.868923	−	0.868923i	−0.123430	−	0.992353i	$-0.539389\pi$
$787$	24.3764	−	24.3764i	0.868923	−	0.868923i	0.992353	+	0.123430i	$0.0393895\pi$
$788$	−0.585786	+	0.585786i	−0.0208678	+	0.0208678i
$789$	−50.7318			−1.80610
$790$	8.56628	+	7.42950i	0.304775	+	0.264330i
$791$	−4.00000	−	1.79337i	−0.142224	−	0.0637648i
$792$	0.828427	+	0.828427i	0.0294369	+	0.0294369i
$793$	−27.2843	+	27.2843i	−0.968893	+	0.968893i
$794$	−1.58513			−0.0562540
$795$	−3.41421	−	48.0416i	−0.121090	−	1.70386i
$796$			28.0334i			0.993618i
$797$	16.6683	−	16.6683i	0.590421	−	0.590421i	−0.347324	−	0.937745i	$-0.612910\pi$
$797$	16.6683	−	16.6683i	0.590421	−	0.590421i	0.937745	+	0.347324i	$0.112910\pi$
$798$	−6.39329	+	2.43514i	−0.226320	+	0.0862030i
$799$			8.00000i			0.283020i
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$			4.70099i			0.166101i
$802$	13.9706	+	13.9706i	0.493318	+	0.493318i
$803$	11.7206	+	11.7206i	0.413611	+	0.413611i
$804$	−27.3994			−0.966301
$805$	1.19004	−	3.25483i	0.0419435	−	0.114718i
$806$	−9.17157			−0.323055
$807$	−35.1421	−	35.1421i	−1.23706	−	1.23706i
$808$	−1.94061	−	1.94061i	−0.0682705	−	0.0682705i
$809$			33.8995i			1.19184i	0.803043	+	0.595921i	$0.203213\pi$
$809$			33.8995i			1.19184i	−0.803043	+	0.595921i	$0.796787\pi$
$810$	14.7549	−	17.0125i	0.518433	−	0.597759i
$811$		−	50.6005i		−	1.77682i	−0.459048	−	0.888411i	$-0.651809\pi$
$811$		−	50.6005i		−	1.77682i	0.459048	−	0.888411i	$-0.348191\pi$
$812$	−0.780163	−	2.04826i	−0.0273784	−	0.0718800i
$813$	−24.4853	+	24.4853i	−0.858736	+	0.858736i
$814$		−	10.3431i		−	0.362527i
$815$	32.6256	+	28.2960i	1.14283	+	0.991167i
$816$	9.65685			0.338058
$817$	5.59767	−	5.59767i	0.195838	−	0.195838i
$818$	17.6578	+	17.6578i	0.617392	+	0.617392i
$819$	−5.99162	−	2.68629i	−0.209364	−	0.0938666i
$820$	−0.585786	−	8.24264i	−0.0204565	−	0.287845i
$821$	−34.4853			−1.20354			−0.601772	−	0.798668i	$-0.705539\pi$
$821$	−34.4853			−1.20354			−0.601772	+	0.798668i	$0.705539\pi$
$822$	−15.0991	+	15.0991i	−0.526642	+	0.526642i
$823$	−2.34315	+	2.34315i	−0.0816769	+	0.0816769i	−0.746765	−	0.665088i	$-0.768394\pi$
$823$	−2.34315	+	2.34315i	−0.0816769	+	0.0816769i	0.665088	+	0.746765i	$0.268394\pi$
$824$	−14.1480			−0.492870
$825$	−20.9050	−	15.6788i	−0.727819	−	0.545864i
$826$	10.0000	−	22.3044i	0.347945	−	0.776070i
$827$	−7.51472	−	7.51472i	−0.261312	−	0.261312i	0.564275	−	0.825587i	$-0.309156\pi$
$827$	−7.51472	−	7.51472i	−0.261312	−	0.261312i	−0.825587	+	0.564275i	$0.809156\pi$
$828$	−0.171573	+	0.171573i	−0.00596257	+	0.00596257i
$829$	−40.8589			−1.41909			−0.709545	−	0.704660i	$-0.751099\pi$
$829$	−40.8589			−1.41909			−0.709545	+	0.704660i	$0.751099\pi$
$830$	16.7782	−	1.19239i	0.582379	−	0.0413884i
$831$		−	4.59220i		−	0.159302i
$832$	−4.23671	+	4.23671i	−0.146882	+	0.146882i
$833$	2.10422	−	36.5232i	0.0729069	−	1.26545i
$834$			15.8995i			0.550554i
$835$	−4.10051	−	3.55635i	−0.141904	−	0.123073i
$836$			3.95815i			0.136895i
$837$	5.17157	+	5.17157i	0.178756	+	0.178756i
$838$	−8.19486	−	8.19486i	−0.283087	−	0.283087i
$839$	−20.6424			−0.712654			−0.356327	−	0.934361i	$-0.615971\pi$
$839$	−20.6424			−0.712654			−0.356327	+	0.934361i	$0.615971\pi$
$840$	9.91403	−	4.60538i	0.342066	−	0.158901i
$841$	28.3137			0.976335
$842$	−12.5858	−	12.5858i	−0.433735	−	0.433735i
$843$	−7.39104	−	7.39104i	−0.254561	−	0.254561i
$844$		−	10.3431i		−	0.356026i
$845$	−51.0760	+	3.62986i	−1.75707	+	0.124871i
$846$		−	0.634051i		−	0.0217991i
$847$	2.82522	+	7.41742i	0.0970757	+	0.254866i
$848$	8.24264	−	8.24264i	0.283053	−	0.283053i
$849$			8.24264i			0.282887i
$850$	−25.8686	+	3.69552i	−0.887287	+	0.126755i
$851$	2.14214			0.0734315
$852$	0.765367	−	0.765367i	0.0262210	−	0.0262210i
$853$	26.7268	+	26.7268i	0.915110	+	0.915110i	0.996669	−	0.0815587i	$-0.0259898\pi$
$853$	26.7268	+	26.7268i	0.915110	+	0.915110i	−0.0815587	+	0.996669i	$0.525990\pi$
$854$	15.5474	+	6.97056i	0.532022	+	0.238528i
$855$	−1.29289	+	0.0918831i	−0.0442160	+	0.00314234i
$856$	−5.17157			−0.176761
$857$	11.4580	−	11.4580i	0.391397	−	0.391397i	−0.483788	−	0.875185i	$-0.660739\pi$
$857$	11.4580	−	11.4580i	0.391397	−	0.391397i	0.875185	+	0.483788i	$0.160739\pi$
$858$	−22.1421	+	22.1421i	−0.755920	+	0.755920i
$859$	40.6732			1.38775			0.693876	−	0.720094i	$-0.255901\pi$
$859$	40.6732			1.38775			0.693876	+	0.720094i	$0.255901\pi$
$860$	−8.28772	+	9.55582i	−0.282609	+	0.325851i
$861$	16.4853	+	7.39104i	0.561817	+	0.251886i
$862$	−4.00000	−	4.00000i	−0.136241	−	0.136241i
$863$	−2.44365	+	2.44365i	−0.0831828	+	0.0831828i	−0.747474	−	0.664291i	$-0.768734\pi$
$863$	−2.44365	+	2.44365i	−0.0831828	+	0.0831828i	0.664291	+	0.747474i	$0.268734\pi$
$864$	4.77791			0.162548
$865$	−27.5355	+	31.7487i	−0.936236	+	1.07949i
$866$			14.7821i			0.502315i
$867$	13.4755	−	13.4755i	0.457652	−	0.457652i
$868$	1.44155	+	3.78470i	0.0489295	+	0.128461i
$869$			14.3431i			0.486558i
$870$	−0.242641	−	3.41421i	−0.00822629	−	0.115753i
$871$		−	88.8463i		−	3.01044i
$872$	−8.58579	−	8.58579i	−0.290751	−	0.290751i
$873$	−1.90215	−	1.90215i	−0.0643781	−	0.0643781i
$874$	−0.819760			−0.0277288
$875$	−24.7951	+	16.1308i	−0.838228	+	0.545319i
$876$	−10.8284			−0.365859
$877$	−21.5563	−	21.5563i	−0.727906	−	0.727906i	0.242296	−	0.970202i	$-0.422099\pi$
$877$	−21.5563	−	21.5563i	−0.727906	−	0.727906i	−0.970202	+	0.242296i	$0.922099\pi$
$878$	9.81845	+	9.81845i	0.331357	+	0.331357i
$879$		−	6.24264i		−	0.210559i
$880$	−0.448342	−	6.30864i	−0.0151136	−	0.212664i
$881$			13.5140i			0.455297i	0.973743	+	0.227649i	$0.0731038\pi$
$881$			13.5140i			0.455297i	−0.973743	+	0.227649i	$0.926896\pi$
$882$	−0.166773	+	2.89469i	−0.00561553	+	0.0974694i
$883$	−28.8284	+	28.8284i	−0.970154	+	0.970154i	−0.999567	−	0.0294135i	$-0.990636\pi$
$883$	−28.8284	+	28.8284i	−0.970154	+	0.970154i	0.0294135	+	0.999567i	$0.490636\pi$
$884$			31.3137i			1.05319i
$885$	25.0104	−	28.8372i	0.840716	−	0.969353i
$886$	5.85786			0.196799
$887$	−32.5487	+	32.5487i	−1.09288	+	1.09288i	−0.0976580	+	0.995220i	$0.531135\pi$
$887$	−32.5487	+	32.5487i	−1.09288	+	1.09288i	−0.995220	+	0.0976580i	$0.968865\pi$
$888$	4.77791	+	4.77791i	0.160336	+	0.160336i
$889$	5.48888	−	12.2426i	0.184091	−	0.410605i
$890$	16.6274	−	19.1716i	0.557352	−	0.642633i
$891$	28.4853			0.954293
$892$	−6.75699	+	6.75699i	−0.226241	+	0.226241i
$893$	1.51472	−	1.51472i	0.0506881	−	0.0506881i
$894$	31.9916			1.06996
$895$	30.4608	−	2.16478i	1.01819	−	0.0723608i
$896$	2.41421	+	1.08239i	0.0806532	+	0.0361602i
$897$	−4.58579	−	4.58579i	−0.153115	−	0.153115i
$898$	18.1421	−	18.1421i	0.605411	−	0.605411i
$899$	1.26810			0.0422935
$900$	2.05025	−	0.292893i	0.0683418	−	0.00976311i
$901$		−	60.9217i		−	2.02959i
$902$	7.39104	−	7.39104i	0.246095	−	0.246095i
$903$	−9.84354	−	25.8435i	−0.327572	−	0.860019i
$904$		−	1.65685i		−	0.0551062i
$905$	19.6066	−	1.39340i	0.651745	−	0.0463181i
$906$			16.3128i			0.541957i
$907$	11.1716	+	11.1716i	0.370946	+	0.370946i	0.867822	−	0.496876i	$-0.165520\pi$
$907$	11.1716	+	11.1716i	0.370946	+	0.370946i	−0.496876	+	0.867822i	$0.665520\pi$
$908$	−8.38057	−	8.38057i	−0.278119	−	0.278119i
$909$	1.13679			0.0377048
$910$	14.9336	+	32.1476i	0.495044	+	1.06568i
$911$	−28.1421			−0.932391			−0.466195	−	0.884682i	$-0.654376\pi$
$911$	−28.1421			−0.932391			−0.466195	+	0.884682i	$0.654376\pi$
$912$	−1.82843	−	1.82843i	−0.0605453	−	0.0605453i
$913$	15.0447	+	15.0447i	0.497907	+	0.497907i
$914$			2.34315i			0.0775044i
$915$	20.1012	+	17.4337i	0.664524	+	0.576339i
$916$			7.70806i			0.254682i
$917$	−36.2236	+	13.7972i	−1.19621	+	0.455624i
$918$	17.6569	−	17.6569i	0.582763	−	0.582763i
$919$			8.38478i			0.276588i	0.990391	+	0.138294i	$0.0441619\pi$
$919$			8.38478i			0.276588i	−0.990391	+	0.138294i	$0.955838\pi$
$920$	1.30656	−	0.0928546i	0.0430761	−	0.00306132i
$921$	60.5269			1.99443
$922$	24.0593	−	24.0593i	0.792352	−	0.792352i
$923$	2.48181	+	2.48181i	0.0816898	+	0.0816898i
$924$	12.6173	+	5.65685i	0.415078	+	0.186097i
$925$	−14.6274	−	10.9706i	−0.480947	−	0.360710i
$926$	18.3431			0.602793
$927$	4.14386	−	4.14386i	0.136102	−	0.136102i
$928$	0.585786	−	0.585786i	0.0192294	−	0.0192294i
$929$	−33.2597			−1.09121			−0.545607	−	0.838041i	$-0.683701\pi$
$929$	−33.2597			−1.09121			−0.545607	+	0.838041i	$0.683701\pi$
$930$	0.448342	+	6.30864i	0.0147017	+	0.206869i
$931$	−7.31371	+	6.51688i	−0.239697	+	0.213582i
$932$	3.00000	+	3.00000i	0.0982683	+	0.0982683i
$933$	−4.48528	+	4.48528i	−0.146842	+	0.146842i
$934$	−24.6549			−0.806734
$935$	−24.9706	−	21.6569i	−0.816625	−	0.708255i
$936$		−	2.48181i		−	0.0811205i
$937$	−17.7666	+	17.7666i	−0.580410	+	0.580410i	−0.935016	−	0.354606i	$-0.884615\pi$
$937$	−17.7666	+	17.7666i	−0.580410	+	0.580410i	0.354606	+	0.935016i	$0.384615\pi$
$938$	−36.6629	+	13.9645i	−1.19709	+	0.455958i
$939$		−	17.6569i		−	0.576210i
$940$	−2.24264	+	2.58579i	−0.0731469	+	0.0843391i
$941$		−	23.3099i		−	0.759881i	−0.925011	−	0.379940i	$-0.875944\pi$
$941$		−	23.3099i		−	0.759881i	0.925011	−	0.379940i	$-0.124056\pi$
$942$	−18.8995	−	18.8995i	−0.615779	−	0.615779i
$943$	1.53073	+	1.53073i	0.0498475	+	0.0498475i
$944$	9.23880			0.300697
$945$	9.70647	−	26.5477i	0.315751	−	0.863596i
$946$	−16.0000			−0.520205
$947$	22.9706	+	22.9706i	0.746443	+	0.746443i	0.973809	−	0.227366i	$-0.0730115\pi$
$947$	22.9706	+	22.9706i	0.746443	+	0.746443i	−0.227366	+	0.973809i	$0.573011\pi$
$948$	−6.62567	−	6.62567i	−0.215192	−	0.215192i
$949$		−	35.1127i		−	1.13981i
$950$	5.59767	+	4.19825i	0.181612	+	0.136209i
$951$			57.2261i			1.85568i
$952$	12.9218	−	4.92177i	0.418797	−	0.159515i
$953$	23.1421	−	23.1421i	0.749647	−	0.749647i	−0.224766	−	0.974413i	$-0.572162\pi$
$953$	23.1421	−	23.1421i	0.749647	−	0.749647i	0.974413	+	0.224766i	$0.0721616\pi$
$954$			4.82843i			0.156326i
$955$	0.278564	+	3.91969i	0.00901411	+	0.126838i
$956$	6.48528			0.209749
$957$	3.06147	−	3.06147i	0.0989632	−	0.0989632i
$958$	7.83938	+	7.83938i	0.253279	+	0.253279i
$959$	−12.5085	+	27.8995i	−0.403921	+	0.900922i
$960$	3.12132	+	2.70711i	0.100740	+	0.0873715i
$961$	28.6569			0.924415
$962$	−15.4930	+	15.4930i	−0.499516	+	0.499516i
$963$	1.51472	−	1.51472i	0.0488111	−	0.0488111i
$964$	6.75699			0.217628
$965$	19.6913	+	17.0782i	0.633885	+	0.549766i
$966$	−1.17157	+	2.61313i	−0.0376947	+	0.0840759i
$967$	−2.21320	−	2.21320i	−0.0711718	−	0.0711718i	0.670625	−	0.741797i	$-0.266026\pi$
$967$	−2.21320	−	2.21320i	−0.0711718	−	0.0711718i	−0.741797	+	0.670625i	$0.766026\pi$
$968$	−2.12132	+	2.12132i	−0.0681818	+	0.0681818i
$969$	−13.5140			−0.434131
$970$	1.02944	+	14.4853i	0.0330532	+	0.465094i
$971$			18.5320i			0.594720i	0.954765	+	0.297360i	$0.0961061\pi$
$971$			18.5320i			0.594720i	−0.954765	+	0.297360i	$0.903894\pi$
$972$	−3.02301	+	3.02301i	−0.0969630	+	0.0969630i
$973$	8.10343	+	21.2750i	0.259784	+	0.682045i
$974$		−	1.55635i		−	0.0498686i
$975$	7.82843	+	54.7990i	0.250710	+	1.75497i
$976$			6.43996i			0.206138i
$977$	−25.8284	−	25.8284i	−0.826325	−	0.826325i	0.160682	−	0.987006i	$-0.448631\pi$
$977$	−25.8284	−	25.8284i	−0.826325	−	0.826325i	−0.987006	+	0.160682i	$0.948631\pi$
$978$	−25.2346	−	25.2346i	−0.806913	−	0.806913i
$979$	32.1003			1.02593
$980$	10.9187	−	11.2153i	0.348785	−	0.358259i
$981$	5.02944			0.160578
$982$	−17.7990	−	17.7990i	−0.567989	−	0.567989i
$983$	28.7444	+	28.7444i	0.916804	+	0.916804i	0.996796	−	0.0799920i	$-0.0254895\pi$
$983$	28.7444	+	28.7444i	0.916804	+	0.916804i	−0.0799920	+	0.996796i	$0.525489\pi$
$984$			6.82843i			0.217682i
$985$	−1.21371	+	1.39942i	−0.0386720	+	0.0445892i
$986$		−	4.32957i		−	0.137882i
$987$	−2.66364	−	6.99321i	−0.0847847	−	0.222596i
$988$	5.92893	−	5.92893i	0.188624	−	0.188624i
$989$		−	3.31371i		−	0.105370i
$990$	1.97908	+	1.71644i	0.0628991	+	0.0545521i
$991$	−32.5858			−1.03512			−0.517561	−	0.855646i	$-0.673160\pi$
$991$	−32.5858			−1.03512			−0.517561	+	0.855646i	$0.673160\pi$
$992$	−1.08239	+	1.08239i	−0.0343660	+	0.0343660i
$993$	30.4608	+	30.4608i	0.966645	+	0.966645i
$994$	0.634051	−	1.41421i	0.0201109	−	0.0448561i
$995$	4.44365	+	62.5269i	0.140873	+	1.98224i
$996$	−13.8995			−0.440422
$997$	−0.464273	+	0.464273i	−0.0147037	+	0.0147037i	−0.714420	−	0.699717i	$-0.753310\pi$
$997$	−0.464273	+	0.464273i	−0.0147037	+	0.0147037i	0.699717	+	0.714420i	$0.253310\pi$
$998$	5.31371	−	5.31371i	0.168203	−	0.168203i
$999$	17.4721			0.552793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.g.a.27.2	yes	8
3.2	odd	2		630.2.p.a.307.3		8
4.3	odd	2		560.2.bj.c.97.1		8
5.2	odd	4		350.2.g.a.293.4		8
5.3	odd	4	inner	70.2.g.a.13.1	✓	8
5.4	even	2		350.2.g.a.307.3		8
7.2	even	3		490.2.l.a.227.1		16
7.3	odd	6		490.2.l.a.117.3		16
7.4	even	3		490.2.l.a.117.4		16
7.5	odd	6		490.2.l.a.227.2		16
7.6	odd	2	inner	70.2.g.a.27.1	yes	8
15.8	even	4		630.2.p.a.433.4		8
20.3	even	4		560.2.bj.c.433.4		8
21.20	even	2		630.2.p.a.307.4		8
28.27	even	2		560.2.bj.c.97.4		8
35.3	even	12		490.2.l.a.313.1		16
35.13	even	4	inner	70.2.g.a.13.2	yes	8
35.18	odd	12		490.2.l.a.313.2		16
35.23	odd	12		490.2.l.a.423.3		16
35.27	even	4		350.2.g.a.293.3		8
35.33	even	12		490.2.l.a.423.4		16
35.34	odd	2		350.2.g.a.307.4		8
105.83	odd	4		630.2.p.a.433.3		8
140.83	odd	4		560.2.bj.c.433.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.g.a.13.1	✓	8	5.3	odd	4	inner
70.2.g.a.13.2	yes	8	35.13	even	4	inner
70.2.g.a.27.1	yes	8	7.6	odd	2	inner
70.2.g.a.27.2	yes	8	1.1	even	1	trivial
350.2.g.a.293.3		8	35.27	even	4
350.2.g.a.293.4		8	5.2	odd	4
350.2.g.a.307.3		8	5.4	even	2
350.2.g.a.307.4		8	35.34	odd	2
490.2.l.a.117.3		16	7.3	odd	6
490.2.l.a.117.4		16	7.4	even	3
490.2.l.a.227.1		16	7.2	even	3
490.2.l.a.227.2		16	7.5	odd	6
490.2.l.a.313.1		16	35.3	even	12
490.2.l.a.313.2		16	35.18	odd	12
490.2.l.a.423.3		16	35.23	odd	12
490.2.l.a.423.4		16	35.33	even	12
560.2.bj.c.97.1		8	4.3	odd	2
560.2.bj.c.97.4		8	28.27	even	2
560.2.bj.c.433.1		8	140.83	odd	4
560.2.bj.c.433.4		8	20.3	even	4
630.2.p.a.307.3		8	3.2	odd	2
630.2.p.a.307.4		8	21.20	even	2
630.2.p.a.433.3		8	105.83	odd	4
630.2.p.a.433.4		8	15.8	even	4

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.30656 + 1.30656i) q^{3} +1.00000i q^{4} +(0.158513 + 2.23044i) q^{5} -1.84776i q^{6} +(-0.941740 - 2.47247i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.414214i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.30656 + 1.30656i) q^{3} +1.00000i q^{4} +(0.158513 + 2.23044i) q^{5} -1.84776i q^{6} +(-0.941740 - 2.47247i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.414214i q^{9} +(1.46508 - 1.68925i) q^{10} +2.82843 q^{11} +(-1.30656 + 1.30656i) q^{12} +(-4.23671 - 4.23671i) q^{13} +(-1.08239 + 2.41421i) q^{14} +(-2.70711 + 3.12132i) q^{15} -1.00000 q^{16} +(-3.69552 + 3.69552i) q^{17} +(0.292893 - 0.292893i) q^{18} +1.39942 q^{19} +(-2.23044 + 0.158513i) q^{20} +(2.00000 - 4.46088i) q^{21} +(-2.00000 - 2.00000i) q^{22} +(0.414214 - 0.414214i) q^{23} +1.84776 q^{24} +(-4.94975 + 0.707107i) q^{25} +5.99162i q^{26} +(3.37849 - 3.37849i) q^{27} +(2.47247 - 0.941740i) q^{28} -0.828427i q^{29} +(4.12132 - 0.292893i) q^{30} +1.53073i q^{31} +(0.707107 + 0.707107i) q^{32} +(3.69552 + 3.69552i) q^{33} +5.22625 q^{34} +(5.36543 - 2.49242i) q^{35} -0.414214 q^{36} +(2.58579 + 2.58579i) q^{37} +(-0.989538 - 0.989538i) q^{38} -11.0711i q^{39} +(1.68925 + 1.46508i) q^{40} +3.69552i q^{41} +(-4.56854 + 1.74011i) q^{42} +(4.00000 - 4.00000i) q^{43} +2.82843i q^{44} +(-0.923880 + 0.0656581i) q^{45} -0.585786 q^{46} +(1.08239 - 1.08239i) q^{47} +(-1.30656 - 1.30656i) q^{48} +(-5.22625 + 4.65685i) q^{49} +(4.00000 + 3.00000i) q^{50} -9.65685 q^{51} +(4.23671 - 4.23671i) q^{52} +(-8.24264 + 8.24264i) q^{53} -4.77791 q^{54} +(0.448342 + 6.30864i) q^{55} +(-2.41421 - 1.08239i) q^{56} +(1.82843 + 1.82843i) q^{57} +(-0.585786 + 0.585786i) q^{58} -9.23880 q^{59} +(-3.12132 - 2.70711i) q^{60} -6.43996i q^{61} +(1.08239 - 1.08239i) q^{62} +(1.02413 - 0.390081i) q^{63} -1.00000i q^{64} +(8.77817 - 10.1213i) q^{65} -5.22625i q^{66} +(10.4853 + 10.4853i) q^{67} +(-3.69552 - 3.69552i) q^{68} +1.08239 q^{69} +(-5.55634 - 2.03153i) q^{70} -0.585786 q^{71} +(0.292893 + 0.292893i) q^{72} +(4.14386 + 4.14386i) q^{73} -3.65685i q^{74} +(-7.39104 - 5.54328i) q^{75} +1.39942i q^{76} +(-2.66364 - 6.99321i) q^{77} +(-7.82843 + 7.82843i) q^{78} +5.07107i q^{79} +(-0.158513 - 2.23044i) q^{80} +10.0711 q^{81} +(2.61313 - 2.61313i) q^{82} +(5.31911 + 5.31911i) q^{83} +(4.46088 + 2.00000i) q^{84} +(-8.82843 - 7.65685i) q^{85} -5.65685 q^{86} +(1.08239 - 1.08239i) q^{87} +(2.00000 - 2.00000i) q^{88} +11.3492 q^{89} +(0.699709 + 0.606854i) q^{90} +(-6.48528 + 14.4650i) q^{91} +(0.414214 + 0.414214i) q^{92} +(-2.00000 + 2.00000i) q^{93} -1.53073 q^{94} +(0.221825 + 3.12132i) q^{95} +1.84776i q^{96} +(-4.59220 + 4.59220i) q^{97} +(6.98841 + 0.402625i) q^{98} +1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} - 16 q^{15} - 8 q^{16} + 8 q^{18} + 16 q^{21} - 16 q^{22} - 8 q^{23} + 8 q^{28} + 16 q^{30} - 8 q^{35} + 8 q^{36} + 32 q^{37} + 32 q^{43} - 16 q^{46} + 32 q^{50} - 32 q^{51} - 32 q^{53} - 8 q^{56} - 8 q^{57} - 16 q^{58} - 8 q^{60} + 8 q^{65} + 16 q^{67} - 24 q^{70} - 16 q^{71} + 8 q^{72} - 16 q^{77} - 40 q^{78} + 24 q^{81} - 48 q^{85} + 16 q^{88} + 16 q^{91} - 8 q^{92} - 16 q^{93} + 64 q^{95} + 32 q^{98}+O(q^{100}) \) 8 * q - 8 * q^7 - 16 * q^15 - 8 * q^16 + 8 * q^18 + 16 * q^21 - 16 * q^22 - 8 * q^23 + 8 * q^28 + 16 * q^30 - 8 * q^35 + 8 * q^36 + 32 * q^37 + 32 * q^43 - 16 * q^46 + 32 * q^50 - 32 * q^51 - 32 * q^53 - 8 * q^56 - 8 * q^57 - 16 * q^58 - 8 * q^60 + 8 * q^65 + 16 * q^67 - 24 * q^70 - 16 * q^71 + 8 * q^72 - 16 * q^77 - 40 * q^78 + 24 * q^81 - 48 * q^85 + 16 * q^88 + 16 * q^91 - 8 * q^92 - 16 * q^93 + 64 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

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