LMFDB - Embedded newform 70.2.g.a.27.4

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			27.4
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	70.27
Dual form			70.2.g.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.541196 + 0.541196i) q^{3} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +0.765367i q^{6} +(1.55487 - 2.14065i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.541196 + 0.541196i) q^{3} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +0.765367i q^{6} +(1.55487 - 2.14065i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +(-1.68925 - 1.46508i) q^{10} -2.82843 q^{11} +(-0.541196 + 0.541196i) q^{12} +(2.83730 + 2.83730i) q^{13} +(2.61313 - 0.414214i) q^{14} +(-1.29289 - 1.12132i) q^{15} -1.00000 q^{16} +(1.53073 - 1.53073i) q^{17} +(1.70711 - 1.70711i) q^{18} -7.07401 q^{19} +(-0.158513 - 2.23044i) q^{20} +(2.00000 - 0.317025i) q^{21} +(-2.00000 - 2.00000i) q^{22} +(-2.41421 + 2.41421i) q^{23} -0.765367 q^{24} +(4.94975 - 0.707107i) q^{25} +4.01254i q^{26} +(2.93015 - 2.93015i) q^{27} +(2.14065 + 1.55487i) q^{28} +4.82843i q^{29} +(-0.121320 - 1.70711i) q^{30} +3.69552i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.53073 - 1.53073i) q^{33} +2.16478 q^{34} +(-3.12872 + 5.02107i) q^{35} +2.41421 q^{36} +(5.41421 + 5.41421i) q^{37} +(-5.00208 - 5.00208i) q^{38} +3.07107i q^{39} +(1.46508 - 1.68925i) q^{40} -1.53073i q^{41} +(1.63838 + 1.19004i) q^{42} +(4.00000 - 4.00000i) q^{43} -2.82843i q^{44} +(0.382683 + 5.38476i) q^{45} -3.41421 q^{46} +(-2.61313 + 2.61313i) q^{47} +(-0.541196 - 0.541196i) q^{48} +(-2.16478 - 6.65685i) q^{49} +(4.00000 + 3.00000i) q^{50} +1.65685 q^{51} +(-2.83730 + 2.83730i) q^{52} +(0.242641 - 0.242641i) q^{53} +4.14386 q^{54} +(6.30864 - 0.448342i) q^{55} +(0.414214 + 2.61313i) q^{56} +(-3.82843 - 3.82843i) q^{57} +(-3.41421 + 3.41421i) q^{58} +3.82683 q^{59} +(1.12132 - 1.29289i) q^{60} -10.3212i q^{61} +(-2.61313 + 2.61313i) q^{62} +(-5.16799 - 3.75378i) q^{63} -1.00000i q^{64} +(-6.77817 - 5.87868i) q^{65} -2.16478i q^{66} +(-6.48528 - 6.48528i) q^{67} +(1.53073 + 1.53073i) q^{68} -2.61313 q^{69} +(-5.76277 + 1.33809i) q^{70} -3.41421 q^{71} +(1.70711 + 1.70711i) q^{72} +(4.77791 + 4.77791i) q^{73} +7.65685i q^{74} +(3.06147 + 2.29610i) q^{75} -7.07401i q^{76} +(-4.39782 + 6.05468i) q^{77} +(-2.17157 + 2.17157i) q^{78} -9.07107i q^{79} +(2.23044 - 0.158513i) q^{80} -4.07107 q^{81} +(1.08239 - 1.08239i) q^{82} +(-5.45042 - 5.45042i) q^{83} +(0.317025 + 2.00000i) q^{84} +(-3.17157 + 3.65685i) q^{85} +5.65685 q^{86} +(-2.61313 + 2.61313i) q^{87} +(2.00000 - 2.00000i) q^{88} +16.9469 q^{89} +(-3.53701 + 4.07820i) q^{90} +(10.4853 - 1.66205i) q^{91} +(-2.41421 - 2.41421i) q^{92} +(-2.00000 + 2.00000i) q^{93} -3.69552 q^{94} +(15.7782 - 1.12132i) q^{95} -0.765367i q^{96} +(-11.0866 + 11.0866i) q^{97} +(3.17637 - 6.23784i) q^{98} +6.82843i 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
$3$	0.541196	+	0.541196i	0.312460	+	0.312460i	0.845862	−	0.533402i	$-0.179087\pi$
$3$	0.541196	+	0.541196i	0.312460	+	0.312460i	−0.533402	+	0.845862i	$0.679087\pi$
$4$			1.00000i			0.500000i
$5$	−2.23044	+	0.158513i	−0.997484	+	0.0708890i
$5$	−2.23044	+	0.158513i	−0.997484	+	0.0708890i
$6$			0.765367i			0.312460i
$7$	1.55487	−	2.14065i	0.587684	−	0.809091i
$7$	1.55487	−	2.14065i	0.587684	−	0.809091i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	2.41421i		−	0.804738i
$10$	−1.68925	−	1.46508i	−0.534187	−	0.463298i
$11$	−2.82843			−0.852803			−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843			−0.852803			−0.426401	+	0.904534i	$0.640219\pi$
$12$	−0.541196	+	0.541196i	−0.156230	+	0.156230i
$13$	2.83730	+	2.83730i	0.786925	+	0.786925i	0.980989	−	0.194064i	$-0.0621670\pi$
$13$	2.83730	+	2.83730i	0.786925	+	0.786925i	−0.194064	+	0.980989i	$0.562167\pi$
$14$	2.61313	−	0.414214i	0.698387	−	0.110703i
$15$	−1.29289	−	1.12132i	−0.333824	−	0.289524i
$16$	−1.00000			−0.250000
$17$	1.53073	−	1.53073i	0.371257	−	0.371257i	−0.496678	−	0.867935i	$-0.665447\pi$
$17$	1.53073	−	1.53073i	0.371257	−	0.371257i	0.867935	+	0.496678i	$0.165447\pi$
$18$	1.70711	−	1.70711i	0.402369	−	0.402369i
$19$	−7.07401			−1.62289			−0.811445	−	0.584429i	$-0.801318\pi$
$19$	−7.07401			−1.62289			−0.811445	+	0.584429i	$0.801318\pi$
$20$	−0.158513	−	2.23044i	−0.0354445	−	0.498742i
$21$	2.00000	−	0.317025i	0.436436	−	0.0691806i
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	−2.41421	+	2.41421i	−0.503398	+	0.503398i	−0.912492	−	0.409094i	$-0.865845\pi$
$23$	−2.41421	+	2.41421i	−0.503398	+	0.503398i	0.409094	+	0.912492i	$0.365845\pi$
$24$	−0.765367			−0.156230
$25$	4.94975	−	0.707107i	0.989949	−	0.141421i
$26$			4.01254i			0.786925i
$27$	2.93015	−	2.93015i	0.563908	−	0.563908i
$28$	2.14065	+	1.55487i	0.404545	+	0.293842i
$29$			4.82843i			0.896616i	0.893879	+	0.448308i	$0.147973\pi$
$29$			4.82843i			0.896616i	−0.893879	+	0.448308i	$0.852027\pi$
$30$	−0.121320	−	1.70711i	−0.0221500	−	0.311674i
$31$			3.69552i			0.663735i	0.943326	+	0.331867i	$0.107679\pi$
$31$			3.69552i			0.663735i	−0.943326	+	0.331867i	$0.892321\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.53073	−	1.53073i	−0.266467	−	0.266467i
$34$	2.16478			0.371257
$35$	−3.12872	+	5.02107i	−0.528850	+	0.848715i
$36$	2.41421			0.402369
$37$	5.41421	+	5.41421i	0.890091	+	0.890091i	0.994531	−	0.104440i	$-0.0333050\pi$
$37$	5.41421	+	5.41421i	0.890091	+	0.890091i	−0.104440	+	0.994531i	$0.533305\pi$
$38$	−5.00208	−	5.00208i	−0.811445	−	0.811445i
$39$			3.07107i			0.491764i
$40$	1.46508	−	1.68925i	0.231649	−	0.267093i
$41$		−	1.53073i		−	0.239060i	−0.992831	−	0.119530i	$-0.961861\pi$
$41$		−	1.53073i		−	0.239060i	0.992831	−	0.119530i	$-0.0381388\pi$
$42$	1.63838	+	1.19004i	0.252808	+	0.183628i
$43$	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
$45$	0.382683	+	5.38476i	0.0570471	+	0.802713i
$46$	−3.41421			−0.503398
$47$	−2.61313	+	2.61313i	−0.381164	+	0.381164i	−0.871521	−	0.490358i	$-0.836866\pi$
$47$	−2.61313	+	2.61313i	−0.381164	+	0.381164i	0.490358	+	0.871521i	$0.336866\pi$
$48$	−0.541196	−	0.541196i	−0.0781149	−	0.0781149i
$49$	−2.16478	−	6.65685i	−0.309255	−	0.950979i
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$	1.65685			0.232006
$52$	−2.83730	+	2.83730i	−0.393462	+	0.393462i
$53$	0.242641	−	0.242641i	0.0333293	−	0.0333293i	−0.690246	−	0.723575i	$-0.742498\pi$
$53$	0.242641	−	0.242641i	0.0333293	−	0.0333293i	0.723575	+	0.690246i	$0.242498\pi$
$54$	4.14386			0.563908
$55$	6.30864	−	0.448342i	0.850657	−	0.0604544i
$56$	0.414214	+	2.61313i	0.0553516	+	0.349194i
$57$	−3.82843	−	3.82843i	−0.507088	−	0.507088i
$58$	−3.41421	+	3.41421i	−0.448308	+	0.448308i
$59$	3.82683			0.498211			0.249106	−	0.968476i	$-0.419863\pi$
$59$	3.82683			0.498211			0.249106	+	0.968476i	$0.419863\pi$
$60$	1.12132	−	1.29289i	0.144762	−	0.166912i
$61$		−	10.3212i		−	1.32149i	−0.750609	−	0.660746i	$-0.770240\pi$
$61$		−	10.3212i		−	1.32149i	0.750609	−	0.660746i	$-0.229760\pi$
$62$	−2.61313	+	2.61313i	−0.331867	+	0.331867i
$63$	−5.16799	−	3.75378i	−0.651106	−	0.472932i
$64$		−	1.00000i		−	0.125000i
$65$	−6.77817	−	5.87868i	−0.840729	−	0.729160i
$66$		−	2.16478i		−	0.266467i
$67$	−6.48528	−	6.48528i	−0.792303	−	0.792303i	0.189565	−	0.981868i	$-0.439292\pi$
$67$	−6.48528	−	6.48528i	−0.792303	−	0.792303i	−0.981868	+	0.189565i	$0.939292\pi$
$68$	1.53073	+	1.53073i	0.185629	+	0.185629i
$69$	−2.61313			−0.314583
$70$	−5.76277	+	1.33809i	−0.688783	+	0.159933i
$71$	−3.41421			−0.405193			−0.202596	−	0.979262i	$-0.564938\pi$
$71$	−3.41421			−0.405193			−0.202596	+	0.979262i	$0.564938\pi$
$72$	1.70711	+	1.70711i	0.201184	+	0.201184i
$73$	4.77791	+	4.77791i	0.559212	+	0.559212i	0.929083	−	0.369871i	$-0.120598\pi$
$73$	4.77791	+	4.77791i	0.559212	+	0.559212i	−0.369871	+	0.929083i	$0.620598\pi$
$74$			7.65685i			0.890091i
$75$	3.06147	+	2.29610i	0.353508	+	0.265131i
$76$		−	7.07401i		−	0.811445i
$77$	−4.39782	+	6.05468i	−0.501179	+	0.689995i
$78$	−2.17157	+	2.17157i	−0.245882	+	0.245882i
$79$		−	9.07107i		−	1.02057i	−0.860004	−	0.510287i	$-0.829539\pi$
$79$		−	9.07107i		−	1.02057i	0.860004	−	0.510287i	$-0.170461\pi$
$80$	2.23044	−	0.158513i	0.249371	−	0.0177223i
$81$	−4.07107			−0.452341
$82$	1.08239	−	1.08239i	0.119530	−	0.119530i
$83$	−5.45042	−	5.45042i	−0.598262	−	0.598262i	0.341588	−	0.939850i	$-0.389035\pi$
$83$	−5.45042	−	5.45042i	−0.598262	−	0.598262i	−0.939850	+	0.341588i	$0.889035\pi$
$84$	0.317025	+	2.00000i	0.0345903	+	0.218218i
$85$	−3.17157	+	3.65685i	−0.344005	+	0.396642i
$86$	5.65685			0.609994
$87$	−2.61313	+	2.61313i	−0.280157	+	0.280157i
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	16.9469			1.79636			0.898182	−	0.439625i	$-0.144889\pi$
$89$	16.9469			1.79636			0.898182	+	0.439625i	$0.144889\pi$
$90$	−3.53701	+	4.07820i	−0.372833	+	0.429880i
$91$	10.4853	−	1.66205i	1.09916	−	0.174230i
$92$	−2.41421	−	2.41421i	−0.251699	−	0.251699i
$93$	−2.00000	+	2.00000i	−0.207390	+	0.207390i
$94$	−3.69552			−0.381164
$95$	15.7782	−	1.12132i	1.61881	−	0.115045i
$96$		−	0.765367i		−	0.0781149i
$97$	−11.0866	+	11.0866i	−1.12567	+	1.12567i	−0.134796	+	0.990873i	$0.543038\pi$
$97$	−11.0866	+	11.0866i	−1.12567	+	1.12567i	−0.990873	+	0.134796i	$0.956962\pi$
$98$	3.17637	−	6.23784i	0.320862	−	0.630117i
$99$			6.82843i			0.686283i
$100$	0.707107	+	4.94975i	0.0707107	+	0.494975i
$101$		−	11.8519i		−	1.17931i	−0.807655	−	0.589655i	$-0.799264\pi$
$101$		−	11.8519i		−	1.17931i	0.807655	−	0.589655i	$-0.200736\pi$
$102$	1.17157	+	1.17157i	0.116003	+	0.116003i
$103$	1.97908	+	1.97908i	0.195004	+	0.195004i	0.797854	−	0.602850i	$-0.205968\pi$
$103$	1.97908	+	1.97908i	0.195004	+	0.195004i	−0.602850	+	0.797854i	$0.705968\pi$
$104$	−4.01254			−0.393462
$105$	−4.41063	+	1.02413i	−0.430434	+	0.0999451i
$106$	0.343146			0.0333293
$107$	7.65685	+	7.65685i	0.740216	+	0.740216i	0.972619	−	0.232403i	$-0.0746590\pi$
$107$	7.65685	+	7.65685i	0.740216	+	0.740216i	−0.232403	+	0.972619i	$0.574659\pi$
$108$	2.93015	+	2.93015i	0.281954	+	0.281954i
$109$			16.1421i			1.54614i	0.634323	+	0.773068i	$0.281279\pi$
$109$			16.1421i			1.54614i	−0.634323	+	0.773068i	$0.718721\pi$
$110$	4.77791	+	4.14386i	0.455556	+	0.395102i
$111$			5.86030i			0.556235i
$112$	−1.55487	+	2.14065i	−0.146921	+	0.202273i
$113$	6.82843	−	6.82843i	0.642364	−	0.642364i	−0.308772	−	0.951136i	$-0.599918\pi$
$113$	6.82843	−	6.82843i	0.642364	−	0.642364i	0.951136	+	0.308772i	$0.0999179\pi$
$114$		−	5.41421i		−	0.507088i
$115$	5.00208	−	5.76745i	0.466446	−	0.537817i
$116$	−4.82843			−0.448308
$117$	6.84984	−	6.84984i	0.633268	−	0.633268i
$118$	2.70598	+	2.70598i	0.249106	+	0.249106i
$119$	−0.896683	−	5.65685i	−0.0821988	−	0.518563i
$120$	1.70711	−	0.121320i	0.155837	−	0.0110750i
$121$	−3.00000			−0.272727
$122$	7.29818	−	7.29818i	0.660746	−	0.660746i
$123$	0.828427	−	0.828427i	0.0746968	−	0.0746968i
$124$	−3.69552			−0.331867
$125$	−10.9280	+	2.36176i	−0.977434	+	0.211242i
$126$	−1.00000	−	6.30864i	−0.0890871	−	0.562019i
$127$	6.41421	+	6.41421i	0.569169	+	0.569169i	0.931896	−	0.362726i	$-0.118154\pi$
$127$	6.41421	+	6.41421i	0.569169	+	0.569169i	−0.362726	+	0.931896i	$0.618154\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.32957			0.381197
$130$	−0.636039	−	8.94975i	−0.0557843	−	0.784945i
$131$			16.8925i			1.47590i	0.674855	+	0.737951i	$0.264206\pi$
$131$			16.8925i			1.47590i	−0.674855	+	0.737951i	$0.735794\pi$
$132$	1.53073	−	1.53073i	0.133233	−	0.133233i
$133$	−10.9991	+	15.1430i	−0.953746	+	1.31306i
$134$		−	9.17157i		−	0.792303i
$135$	−6.07107	+	7.00000i	−0.522514	+	0.602464i
$136$			2.16478i			0.185629i
$137$	−13.8284	−	13.8284i	−1.18144	−	1.18144i	−0.979371	−	0.202071i	$-0.935233\pi$
$137$	−13.8284	−	13.8284i	−1.18144	−	1.18144i	−0.202071	−	0.979371i	$-0.564767\pi$
$138$	−1.84776	−	1.84776i	−0.157292	−	0.157292i
$139$	−5.09494			−0.432147			−0.216073	−	0.976377i	$-0.569325\pi$
$139$	−5.09494			−0.432147			−0.216073	+	0.976377i	$0.569325\pi$
$140$	−5.02107	−	3.12872i	−0.424358	−	0.264425i
$141$	−2.82843			−0.238197
$142$	−2.41421	−	2.41421i	−0.202596	−	0.202596i
$143$	−8.02509	−	8.02509i	−0.671091	−	0.671091i
$144$			2.41421i			0.201184i
$145$	−0.765367	−	10.7695i	−0.0635603	−	0.894361i
$146$			6.75699i			0.559212i
$147$	2.43109	−	4.77424i	0.200513	−	0.393772i
$148$	−5.41421	+	5.41421i	−0.445046	+	0.445046i
$149$		−	5.31371i		−	0.435316i	−0.976025	−	0.217658i	$-0.930158\pi$
$149$		−	5.31371i		−	0.435316i	0.976025	−	0.217658i	$-0.0698417\pi$
$150$	0.541196	+	3.78837i	0.0441885	+	0.309319i
$151$	−3.17157			−0.258099			−0.129049	−	0.991638i	$-0.541193\pi$
$151$	−3.17157			−0.258099			−0.129049	+	0.991638i	$0.541193\pi$
$152$	5.00208	−	5.00208i	0.405722	−	0.405722i
$153$	−3.69552	−	3.69552i	−0.298765	−	0.298765i
$154$	−7.39104	+	1.17157i	−0.595587	+	0.0944080i
$155$	−0.585786	−	8.24264i	−0.0470515	−	0.662065i
$156$	−3.07107			−0.245882
$157$	1.17525	−	1.17525i	0.0937949	−	0.0937949i	−0.658652	−	0.752447i	$-0.728873\pi$
$157$	1.17525	−	1.17525i	0.0937949	−	0.0937949i	0.752447	+	0.658652i	$0.228873\pi$
$158$	6.41421	−	6.41421i	0.510287	−	0.510287i
$159$	0.262632			0.0208281
$160$	1.68925	+	1.46508i	0.133547	+	0.115824i
$161$	1.41421	+	8.92177i	0.111456	+	0.703134i
$162$	−2.87868	−	2.87868i	−0.226170	−	0.226170i
$163$	2.34315	−	2.34315i	0.183529	−	0.183529i	−0.609362	−	0.792892i	$-0.708575\pi$
$163$	2.34315	−	2.34315i	0.183529	−	0.183529i	0.792892	+	0.609362i	$0.208575\pi$
$164$	1.53073			0.119530
$165$	3.65685	+	3.17157i	0.284686	+	0.246907i
$166$		−	7.70806i		−	0.598262i
$167$	11.5349	−	11.5349i	0.892597	−	0.892597i	−0.102170	−	0.994767i	$-0.532579\pi$
$167$	11.5349	−	11.5349i	0.892597	−	0.892597i	0.994767	+	0.102170i	$0.0325785\pi$
$168$	−1.19004	+	1.63838i	−0.0918138	+	0.126404i
$169$			3.10051i			0.238500i
$170$	−4.82843	+	0.343146i	−0.370323	+	0.0263181i
$171$			17.0782i			1.30600i
$172$	4.00000	+	4.00000i	0.304997	+	0.304997i
$173$	8.56628	+	8.56628i	0.651282	+	0.651282i	0.953302	−	0.302019i	$-0.0976607\pi$
$173$	8.56628	+	8.56628i	0.651282	+	0.651282i	−0.302019	+	0.953302i	$0.597661\pi$
$174$	−3.69552			−0.280157
$175$	6.18252	−	11.6951i	0.467355	−	0.884070i
$176$	2.82843			0.213201
$177$	2.07107	+	2.07107i	0.155671	+	0.155671i
$178$	11.9832	+	11.9832i	0.898182	+	0.898182i
$179$		−	2.34315i		−	0.175135i	−0.996159	−	0.0875675i	$-0.972091\pi$
$179$		−	2.34315i		−	0.175135i	0.996159	−	0.0875675i	$-0.0279093\pi$
$180$	−5.38476	+	0.382683i	−0.401357	+	0.0285235i
$181$			10.1355i			0.753364i	0.926343	+	0.376682i	$0.122935\pi$
$181$			10.1355i			0.753364i	−0.926343	+	0.376682i	$0.877065\pi$
$182$	8.58946	+	6.23897i	0.636693	+	0.462463i
$183$	5.58579	−	5.58579i	0.412913	−	0.412913i
$184$		−	3.41421i		−	0.251699i
$185$	−12.9343	−	11.2179i	−0.950950	−	0.824754i
$186$	−2.82843			−0.207390
$187$	−4.32957	+	4.32957i	−0.316609	+	0.316609i
$188$	−2.61313	−	2.61313i	−0.190582	−	0.190582i
$189$	−1.71644	−	10.8284i	−0.124853	−	0.787652i
$190$	11.9497	+	10.3640i	0.866926	+	0.751881i
$191$	10.2426			0.741131			0.370566	−	0.928806i	$-0.379164\pi$
$191$	10.2426			0.741131			0.370566	+	0.928806i	$0.379164\pi$
$192$	0.541196	−	0.541196i	0.0390575	−	0.0390575i
$193$	−0.242641	+	0.242641i	−0.0174657	+	0.0174657i	−0.715786	−	0.698320i	$-0.753931\pi$
$193$	−0.242641	+	0.242641i	−0.0174657	+	0.0174657i	0.698320	+	0.715786i	$0.253931\pi$
$194$	−15.6788			−1.12567
$195$	−0.486803	−	6.84984i	−0.0348607	−	0.490527i
$196$	6.65685	−	2.16478i	0.475490	−	0.154627i
$197$	3.41421	+	3.41421i	0.243253	+	0.243253i	0.818194	−	0.574942i	$-0.194975\pi$
$197$	3.41421	+	3.41421i	0.243253	+	0.243253i	−0.574942	+	0.818194i	$0.694975\pi$
$198$	−4.82843	+	4.82843i	−0.343141	+	0.343141i
$199$	−15.9414			−1.13006			−0.565028	−	0.825072i	$-0.691134\pi$
$199$	−15.9414			−1.13006			−0.565028	+	0.825072i	$0.691134\pi$
$200$	−3.00000	+	4.00000i	−0.212132	+	0.282843i
$201$		−	7.01962i		−	0.495126i
$202$	8.38057	−	8.38057i	0.589655	−	0.589655i
$203$	10.3360	+	7.50756i	0.725444	+	0.526927i
$204$			1.65685i			0.116003i
$205$	0.242641	+	3.41421i	0.0169468	+	0.238459i
$206$			2.79884i			0.195004i
$207$	5.82843	+	5.82843i	0.405104	+	0.405104i
$208$	−2.83730	−	2.83730i	−0.196731	−	0.196731i
$209$	20.0083			1.38400
$210$	−3.84296	−	2.39462i	−0.265189	−	0.165244i
$211$	−21.6569			−1.49092			−0.745460	−	0.666551i	$-0.767770\pi$
$211$	−21.6569			−1.49092			−0.745460	+	0.666551i	$0.767770\pi$
$212$	0.242641	+	0.242641i	0.0166646	+	0.0166646i
$213$	−1.84776	−	1.84776i	−0.126606	−	0.126606i
$214$			10.8284i			0.740216i
$215$	−8.28772	+	9.55582i	−0.565218	+	0.651702i
$216$			4.14386i			0.281954i
$217$	7.91082	+	5.74603i	0.537021	+	0.390066i
$218$	−11.4142	+	11.4142i	−0.773068	+	0.773068i
$219$			5.17157i			0.349463i
$220$	0.448342	+	6.30864i	0.0302272	+	0.425329i
$221$	8.68629			0.584303
$222$	−4.14386	+	4.14386i	−0.278118	+	0.278118i
$223$	5.86030	+	5.86030i	0.392435	+	0.392435i	0.875554	−	0.483120i	$-0.160496\pi$
$223$	5.86030	+	5.86030i	0.392435	+	0.392435i	−0.483120	+	0.875554i	$0.660496\pi$
$224$	−2.61313	+	0.414214i	−0.174597	+	0.0276758i
$225$	−1.70711	−	11.9497i	−0.113807	−	0.796650i
$226$	9.65685			0.642364
$227$	−1.94061	+	1.94061i	−0.128803	+	0.128803i	−0.768569	−	0.639766i	$-0.779031\pi$
$227$	−1.94061	+	1.94061i	−0.128803	+	0.128803i	0.639766	+	0.768569i	$0.279031\pi$
$228$	3.82843	−	3.82843i	0.253544	−	0.253544i
$229$	−7.52235			−0.497091			−0.248546	−	0.968620i	$-0.579953\pi$
$229$	−7.52235			−0.497091			−0.248546	+	0.968620i	$0.579953\pi$
$230$	7.61521	−	0.541196i	0.502132	−	0.0356854i
$231$	−5.65685	+	0.896683i	−0.372194	+	0.0589974i
$232$	−3.41421	−	3.41421i	−0.224154	−	0.224154i
$233$	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	$0.205620\pi$
$234$	9.68714			0.633268
$235$	5.41421	−	6.24264i	0.353184	−	0.407225i
$236$			3.82683i			0.249106i
$237$	4.90923	−	4.90923i	0.318889	−	0.318889i
$238$	3.36595	−	4.63405i	0.218182	−	0.300381i
$239$			10.4853i			0.678236i	0.940744	+	0.339118i	$0.110129\pi$
$239$			10.4853i			0.678236i	−0.940744	+	0.339118i	$0.889871\pi$
$240$	1.29289	+	1.12132i	0.0834559	+	0.0723809i
$241$		−	5.86030i		−	0.377495i	−0.982026	−	0.188748i	$-0.939557\pi$
$241$		−	5.86030i		−	0.377495i	0.982026	−	0.188748i	$-0.0604428\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$	−10.9937	−	10.9937i	−0.705246	−	0.705246i
$244$	10.3212			0.660746
$245$	5.88362	+	14.5046i	0.375891	+	0.926664i
$246$	1.17157			0.0746968
$247$	−20.0711	−	20.0711i	−1.27709	−	1.27709i
$248$	−2.61313	−	2.61313i	−0.165934	−	0.165934i
$249$		−	5.89949i		−	0.373865i
$250$	−9.39731	−	6.05728i	−0.594338	−	0.383096i
$251$		−	28.7988i		−	1.81776i	−0.417055	−	0.908881i	$-0.636938\pi$
$251$		−	28.7988i		−	1.81776i	0.417055	−	0.908881i	$-0.363062\pi$
$252$	3.75378	−	5.16799i	0.236466	−	0.325553i
$253$	6.82843	−	6.82843i	0.429300	−	0.429300i
$254$			9.07107i			0.569169i
$255$	−3.69552	+	0.262632i	−0.231422	+	0.0164467i
$256$	1.00000			0.0625000
$257$	−3.24718	+	3.24718i	−0.202553	+	0.202553i	−0.801093	−	0.598540i	$-0.795748\pi$
$257$	−3.24718	+	3.24718i	−0.202553	+	0.202553i	0.598540	+	0.801093i	$0.295748\pi$
$258$	3.06147	+	3.06147i	0.190599	+	0.190599i
$259$	20.0083	−	3.17157i	1.24326	−	0.197072i
$260$	5.87868	−	6.77817i	0.364580	−	0.420365i
$261$	11.6569			0.721541
$262$	−11.9448	+	11.9448i	−0.737951	+	0.737951i
$263$	−16.5858	+	16.5858i	−1.02272	+	1.02272i	−0.0229877	+	0.999736i	$0.507318\pi$
$263$	−16.5858	+	16.5858i	−1.02272	+	1.02272i	−0.999736	+	0.0229877i	$0.992682\pi$
$264$	2.16478			0.133233
$265$	−0.502734	+	0.579658i	−0.0308827	+	0.0356081i
$266$	−18.4853	+	2.93015i	−1.13341	+	0.179659i
$267$	9.17157	+	9.17157i	0.561291	+	0.561291i
$268$	6.48528	−	6.48528i	0.396152	−	0.396152i
$269$	−12.6717			−0.772606			−0.386303	−	0.922372i	$-0.626248\pi$
$269$	−12.6717			−0.772606			−0.386303	+	0.922372i	$0.626248\pi$
$270$	−9.24264	+	0.656854i	−0.562489	+	0.0399749i
$271$			13.8854i			0.843477i	0.906717	+	0.421739i	$0.138580\pi$
$271$			13.8854i			0.843477i	−0.906717	+	0.421739i	$0.861420\pi$
$272$	−1.53073	+	1.53073i	−0.0928144	+	0.0928144i
$273$	6.57409	+	4.77510i	0.397882	+	0.289002i
$274$		−	19.5563i		−	1.18144i
$275$	−14.0000	+	2.00000i	−0.844232	+	0.120605i
$276$		−	2.61313i		−	0.157292i
$277$	−10.2426	−	10.2426i	−0.615421	−	0.615421i	0.328933	−	0.944353i	$-0.393311\pi$
$277$	−10.2426	−	10.2426i	−0.615421	−	0.615421i	−0.944353	+	0.328933i	$0.893311\pi$
$278$	−3.60266	−	3.60266i	−0.216073	−	0.216073i
$279$	8.92177			0.534132
$280$	−1.33809	−	5.76277i	−0.0799664	−	0.344391i
$281$	5.65685			0.337460			0.168730	−	0.985662i	$-0.446033\pi$
$281$	5.65685			0.337460			0.168730	+	0.985662i	$0.446033\pi$
$282$	−2.00000	−	2.00000i	−0.119098	−	0.119098i
$283$	−0.224171	−	0.224171i	−0.0133256	−	0.0133256i	0.700413	−	0.713738i	$-0.252999\pi$
$283$	−0.224171	−	0.224171i	−0.0133256	−	0.0133256i	−0.713738	+	0.700413i	$0.752999\pi$
$284$		−	3.41421i		−	0.202596i
$285$	9.14594	+	7.93223i	0.541759	+	0.469865i
$286$		−	11.3492i		−	0.671091i
$287$	−3.27677	−	2.38009i	−0.193422	−	0.140492i
$288$	−1.70711	+	1.70711i	−0.100592	+	0.100592i
$289$			12.3137i			0.724336i
$290$	7.07401	−	8.15640i	0.415400	−	0.478960i
$291$	−12.0000			−0.703452
$292$	−4.77791	+	4.77791i	−0.279606	+	0.279606i
$293$	2.07193	+	2.07193i	0.121043	+	0.121043i	0.765034	−	0.643990i	$-0.222722\pi$
$293$	2.07193	+	2.07193i	0.121043	+	0.121043i	−0.643990	+	0.765034i	$0.722722\pi$
$294$	5.09494	−	1.65685i	0.297143	−	0.0966297i
$295$	−8.53553	+	0.606602i	−0.496958	+	0.0353177i
$296$	−7.65685			−0.445046
$297$	−8.28772	+	8.28772i	−0.480902	+	0.480902i
$298$	3.75736	−	3.75736i	0.217658	−	0.217658i
$299$	−13.6997			−0.792273
$300$	−2.29610	+	3.06147i	−0.132565	+	0.176754i
$301$	−2.34315	−	14.7821i	−0.135057	−	0.852024i
$302$	−2.24264	−	2.24264i	−0.129049	−	0.129049i
$303$	6.41421	−	6.41421i	0.368487	−	0.368487i
$304$	7.07401			0.405722
$305$	1.63604	+	23.0208i	0.0936793	+	1.31817i
$306$		−	5.22625i		−	0.298765i
$307$	−4.18232	+	4.18232i	−0.238698	+	0.238698i	−0.816311	−	0.577613i	$-0.803984\pi$
$307$	−4.18232	+	4.18232i	−0.238698	+	0.238698i	0.577613	+	0.816311i	$0.303984\pi$
$308$	−6.05468	−	4.39782i	−0.344997	−	0.250589i
$309$			2.14214i			0.121862i
$310$	5.41421	−	6.24264i	0.307507	−	0.354558i
$311$		−	23.0698i		−	1.30817i	−0.756422	−	0.654084i	$-0.773054\pi$
$311$		−	23.0698i		−	1.30817i	0.756422	−	0.654084i	$-0.226946\pi$
$312$	−2.17157	−	2.17157i	−0.122941	−	0.122941i
$313$	−5.86030	−	5.86030i	−0.331244	−	0.331244i	0.521815	−	0.853059i	$-0.325255\pi$
$313$	−5.86030	−	5.86030i	−0.331244	−	0.331244i	−0.853059	+	0.521815i	$0.825255\pi$
$314$	1.66205			0.0937949
$315$	12.1219	+	7.55339i	0.682993	+	0.425586i
$316$	9.07107			0.510287
$317$	2.10051	+	2.10051i	0.117976	+	0.117976i	0.763630	−	0.645654i	$-0.223415\pi$
$317$	2.10051	+	2.10051i	0.117976	+	0.117976i	−0.645654	+	0.763630i	$0.723415\pi$
$318$	0.185709	+	0.185709i	0.0104141	+	0.0104141i
$319$		−	13.6569i		−	0.764637i
$320$	0.158513	+	2.23044i	0.00886113	+	0.124686i
$321$			8.28772i			0.462575i
$322$	−5.30864	+	7.30864i	−0.295839	+	0.407295i
$323$	−10.8284	+	10.8284i	−0.602510	+	0.602510i
$324$		−	4.07107i		−	0.226170i
$325$	16.0502	+	12.0376i	0.890303	+	0.667728i
$326$	3.31371			0.183529
$327$	−8.73606	+	8.73606i	−0.483105	+	0.483105i
$328$	1.08239	+	1.08239i	0.0597651	+	0.0597651i
$329$	1.53073	+	9.65685i	0.0843921	+	0.532400i
$330$	0.343146	+	4.82843i	0.0188896	+	0.265796i
$331$	0.686292			0.0377220			0.0188610	−	0.999822i	$-0.493996\pi$
$331$	0.686292			0.0377220			0.0188610	+	0.999822i	$0.493996\pi$
$332$	5.45042	−	5.45042i	0.299131	−	0.299131i
$333$	13.0711	−	13.0711i	0.716290	−	0.716290i
$334$	16.3128			0.892597
$335$	15.4930	+	13.4370i	0.846476	+	0.734144i
$336$	−2.00000	+	0.317025i	−0.109109	+	0.0172951i
$337$	12.2426	+	12.2426i	0.666899	+	0.666899i	0.956997	−	0.290098i	$-0.0936879\pi$
$337$	12.2426	+	12.2426i	0.666899	+	0.666899i	−0.290098	+	0.956997i	$0.593688\pi$
$338$	−2.19239	+	2.19239i	−0.119250	+	0.119250i
$339$	7.39104			0.401426
$340$	−3.65685	−	3.17157i	−0.198321	−	0.172003i
$341$		−	10.4525i		−	0.566035i
$342$	−12.0761	+	12.0761i	−0.653000	+	0.653000i
$343$	−17.6160	−	5.71646i	−0.951172	−	0.308660i
$344$			5.65685i			0.304997i
$345$	5.82843	−	0.414214i	0.313792	−	0.0223005i
$346$			12.1146i			0.651282i
$347$	17.3137	+	17.3137i	0.929449	+	0.929449i	0.997670	−	0.0682216i	$-0.0217325\pi$
$347$	17.3137	+	17.3137i	0.929449	+	0.929449i	−0.0682216	+	0.997670i	$0.521732\pi$
$348$	−2.61313	−	2.61313i	−0.140078	−	0.140078i
$349$	−24.9176			−1.33381			−0.666903	−	0.745145i	$-0.732380\pi$
$349$	−24.9176			−1.33381			−0.666903	+	0.745145i	$0.732380\pi$
$350$	12.6414	−	3.89801i	0.675712	−	0.208357i
$351$	16.6274			0.887506
$352$	2.00000	+	2.00000i	0.106600	+	0.106600i
$353$	−5.67459	−	5.67459i	−0.302028	−	0.302028i	0.539779	−	0.841807i	$-0.318508\pi$
$353$	−5.67459	−	5.67459i	−0.302028	−	0.302028i	−0.841807	+	0.539779i	$0.818508\pi$
$354$			2.92893i			0.155671i
$355$	7.61521	−	0.541196i	0.404173	−	0.0287237i
$356$			16.9469i			0.898182i
$357$	2.57619	−	3.54675i	0.136346	−	0.187714i
$358$	1.65685	−	1.65685i	0.0875675	−	0.0875675i
$359$			16.9706i			0.895672i	0.894116	+	0.447836i	$0.147805\pi$
$359$			16.9706i			0.895672i	−0.894116	+	0.447836i	$0.852195\pi$
$360$	−4.07820	−	3.53701i	−0.214940	−	0.186417i
$361$	31.0416			1.63377
$362$	−7.16687	+	7.16687i	−0.376682	+	0.376682i
$363$	−1.62359	−	1.62359i	−0.0852163	−	0.0852163i
$364$	1.66205	+	10.4853i	0.0871151	+	0.549578i
$365$	−11.4142	−	9.89949i	−0.597447	−	0.518163i
$366$	7.89949			0.412913
$367$	7.39104	−	7.39104i	0.385809	−	0.385809i	−0.487381	−	0.873190i	$-0.662048\pi$
$367$	7.39104	−	7.39104i	0.385809	−	0.385809i	0.873190	+	0.487381i	$0.162048\pi$
$368$	2.41421	−	2.41421i	0.125850	−	0.125850i
$369$	−3.69552			−0.192381
$370$	−1.21371	−	17.0782i	−0.0630977	−	0.887852i
$371$	−0.142136	−	0.896683i	−0.00737931	−	0.0465535i
$372$	−2.00000	−	2.00000i	−0.103695	−	0.103695i
$373$	−0.928932	+	0.928932i	−0.0480983	+	0.0480983i	−0.730747	−	0.682649i	$-0.760828\pi$
$373$	−0.928932	+	0.928932i	−0.0480983	+	0.0480983i	0.682649	+	0.730747i	$0.260828\pi$
$374$	−6.12293			−0.316609
$375$	−7.19239	−	4.63604i	−0.371413	−	0.239404i
$376$		−	3.69552i		−	0.190582i
$377$	−13.6997	+	13.6997i	−0.705569	+	0.705569i
$378$	6.44315	−	8.87056i	0.331400	−	0.456253i
$379$		−	22.1421i		−	1.13737i	−0.822557	−	0.568683i	$-0.807453\pi$
$379$		−	22.1421i		−	1.13737i	0.822557	−	0.568683i	$-0.192547\pi$
$380$	1.12132	+	15.7782i	0.0575225	+	0.809403i
$381$			6.94269i			0.355685i
$382$	7.24264	+	7.24264i	0.370566	+	0.370566i
$383$	10.9008	+	10.9008i	0.557007	+	0.557007i	0.928454	−	0.371447i	$-0.121138\pi$
$383$	10.9008	+	10.9008i	0.557007	+	0.557007i	−0.371447	+	0.928454i	$0.621138\pi$
$384$	0.765367			0.0390575
$385$	8.84935	−	14.2017i	0.451005	−	0.723787i
$386$	−0.343146			−0.0174657
$387$	−9.65685	−	9.65685i	−0.490885	−	0.490885i
$388$	−11.0866	−	11.0866i	−0.562835	−	0.562835i
$389$		−	28.1421i		−	1.42686i	−0.700725	−	0.713431i	$-0.747140\pi$
$389$		−	28.1421i		−	1.42686i	0.700725	−	0.713431i	$-0.252860\pi$
$390$	4.49935	−	5.18779i	0.227833	−	0.262694i
$391$			7.39104i			0.373781i
$392$	6.23784	+	3.17637i	0.315059	+	0.160431i
$393$	−9.14214	+	9.14214i	−0.461160	+	0.461160i
$394$			4.82843i			0.243253i
$395$	1.43788	+	20.2325i	0.0723476	+	1.01801i
$396$	−6.82843			−0.343141
$397$	15.7716	−	15.7716i	0.791554	−	0.791554i	−0.190192	−	0.981747i	$-0.560911\pi$
$397$	15.7716	−	15.7716i	0.791554	−	0.791554i	0.981747	+	0.190192i	$0.0609112\pi$
$398$	−11.2723	−	11.2723i	−0.565028	−	0.565028i
$399$	−14.1480	+	2.24264i	−0.708287	+	0.112272i
$400$	−4.94975	+	0.707107i	−0.247487	+	0.0353553i
$401$	−28.2426			−1.41037			−0.705185	−	0.709023i	$-0.749136\pi$
$401$	−28.2426			−1.41037			−0.705185	+	0.709023i	$0.749136\pi$
$402$	4.96362	−	4.96362i	0.247563	−	0.247563i
$403$	−10.4853	+	10.4853i	−0.522309	+	0.522309i
$404$	11.8519			0.589655
$405$	9.08028	−	0.645316i	0.451203	−	0.0320660i
$406$	2.00000	+	12.6173i	0.0992583	+	0.626185i
$407$	−15.3137	−	15.3137i	−0.759072	−	0.759072i
$408$	−1.17157	+	1.17157i	−0.0580015	+	0.0580015i
$409$	23.3324			1.15371			0.576857	−	0.816845i	$-0.304279\pi$
$409$	23.3324			1.15371			0.576857	+	0.816845i	$0.304279\pi$
$410$	−2.24264	+	2.58579i	−0.110756	+	0.127703i
$411$		−	14.9678i		−	0.738306i
$412$	−1.97908	+	1.97908i	−0.0975020	+	0.0975020i
$413$	5.95021	−	8.19192i	0.292791	−	0.403098i
$414$			8.24264i			0.405104i
$415$	13.0208	+	11.2929i	0.639167	+	0.554346i
$416$		−	4.01254i		−	0.196731i
$417$	−2.75736	−	2.75736i	−0.135028	−	0.135028i
$418$	14.1480	+	14.1480i	0.692002	+	0.692002i
$419$	−24.2835			−1.18633			−0.593163	−	0.805082i	$-0.702121\pi$
$419$	−24.2835			−1.18633			−0.593163	+	0.805082i	$0.702121\pi$
$420$	−1.02413	−	4.41063i	−0.0499725	−	0.215217i
$421$	−21.7990			−1.06242			−0.531209	−	0.847241i	$-0.678262\pi$
$421$	−21.7990			−1.06242			−0.531209	+	0.847241i	$0.678262\pi$
$422$	−15.3137	−	15.3137i	−0.745460	−	0.745460i
$423$	6.30864	+	6.30864i	0.306737	+	0.306737i
$424$			0.343146i			0.0166646i
$425$	6.49435	−	8.65914i	0.315022	−	0.420030i
$426$		−	2.61313i		−	0.126606i
$427$	−22.0941	−	16.0481i	−1.06921	−	0.776620i
$428$	−7.65685	+	7.65685i	−0.370108	+	0.370108i
$429$		−	8.68629i		−	0.419378i
$430$	−12.6173	+	0.896683i	−0.608460	+	0.0432419i
$431$	−5.65685			−0.272481			−0.136241	−	0.990676i	$-0.543502\pi$
$431$	−5.65685			−0.272481			−0.136241	+	0.990676i	$0.543502\pi$
$432$	−2.93015	+	2.93015i	−0.140977	+	0.140977i
$433$	−4.32957	−	4.32957i	−0.208066	−	0.208066i	0.595379	−	0.803445i	$-0.297002\pi$
$433$	−4.32957	−	4.32957i	−0.208066	−	0.208066i	−0.803445	+	0.595379i	$0.797002\pi$
$434$	1.53073	+	9.65685i	0.0734776	+	0.463544i
$435$	5.41421	−	6.24264i	0.259592	−	0.299312i
$436$	−16.1421			−0.773068
$437$	17.0782	−	17.0782i	0.816960	−	0.816960i
$438$	−3.65685	+	3.65685i	−0.174731	+	0.174731i
$439$	18.7402			0.894422			0.447211	−	0.894428i	$-0.352417\pi$
$439$	18.7402			0.894422			0.447211	+	0.894428i	$0.352417\pi$
$440$	−4.14386	+	4.77791i	−0.197551	+	0.227778i
$441$	−16.0711	+	5.22625i	−0.765289	+	0.248869i
$442$	6.14214	+	6.14214i	0.292152	+	0.292152i
$443$	24.1421	−	24.1421i	1.14703	−	1.14703i	0.159893	−	0.987134i	$-0.448885\pi$
$443$	24.1421	−	24.1421i	1.14703	−	1.14703i	0.987134	−	0.159893i	$-0.0511150\pi$
$444$	−5.86030			−0.278118
$445$	−37.7990	+	2.68629i	−1.79184	+	0.127342i
$446$			8.28772i			0.392435i
$447$	2.87576	−	2.87576i	0.136019	−	0.136019i
$448$	−2.14065	−	1.55487i	−0.101136	−	0.0734605i
$449$			14.3431i			0.676895i	0.940985	+	0.338447i	$0.109902\pi$
$449$			14.3431i			0.676895i	−0.940985	+	0.338447i	$0.890098\pi$
$450$	7.24264	−	9.65685i	0.341421	−	0.455228i
$451$			4.32957i			0.203871i
$452$	6.82843	+	6.82843i	0.321182	+	0.321182i
$453$	−1.71644	−	1.71644i	−0.0806455	−	0.0806455i
$454$	−2.74444			−0.128803
$455$	−23.1234	+	5.36916i	−1.08404	+	0.251710i
$456$	5.41421			0.253544
$457$	9.65685	+	9.65685i	0.451729	+	0.451729i	0.895928	−	0.444199i	$-0.146512\pi$
$457$	9.65685	+	9.65685i	0.451729	+	0.451729i	−0.444199	+	0.895928i	$0.646512\pi$
$458$	−5.31911	−	5.31911i	−0.248546	−	0.248546i
$459$		−	8.97056i		−	0.418710i
$460$	5.76745	+	5.00208i	0.268909	+	0.233223i
$461$		−	11.9288i		−	0.555582i	−0.960642	−	0.277791i	$-0.910398\pi$
$461$		−	11.9288i		−	0.555582i	0.960642	−	0.277791i	$-0.0896022\pi$
$462$	−4.63405	−	3.36595i	−0.215596	−	0.156598i
$463$	20.9706	−	20.9706i	0.974585	−	0.974585i	−0.0251002	−	0.999685i	$-0.507990\pi$
$463$	20.9706	−	20.9706i	0.974585	−	0.974585i	0.999685	+	0.0251002i	$0.00799049\pi$
$464$		−	4.82843i		−	0.224154i
$465$	4.14386	−	4.77791i	0.192167	−	0.221570i
$466$	4.24264			0.196537
$467$	13.3442	−	13.3442i	0.617496	−	0.617496i	−0.327393	−	0.944888i	$-0.606170\pi$
$467$	13.3442	−	13.3442i	0.617496	−	0.617496i	0.944888	+	0.327393i	$0.106170\pi$
$468$	6.84984	+	6.84984i	0.316634	+	0.316634i
$469$	−23.9665	+	3.79899i	−1.10667	+	0.175421i
$470$	8.24264	−	0.585786i	0.380205	−	0.0270203i
$471$	1.27208			0.0586143
$472$	−2.70598	+	2.70598i	−0.124553	+	0.124553i
$473$	−11.3137	+	11.3137i	−0.520205	+	0.520205i
$474$	6.94269			0.318889
$475$	−35.0146	+	5.00208i	−1.60658	+	0.229511i
$476$	5.65685	−	0.896683i	0.259281	−	0.0410994i
$477$	−0.585786	−	0.585786i	−0.0268213	−	0.0268213i
$478$	−7.41421	+	7.41421i	−0.339118	+	0.339118i
$479$	4.59220			0.209823			0.104912	−	0.994482i	$-0.466544\pi$
$479$	4.59220			0.209823			0.104912	+	0.994482i	$0.466544\pi$
$480$	0.121320	+	1.70711i	0.00553749	+	0.0779184i
$481$			30.7235i			1.40087i
$482$	4.14386	−	4.14386i	0.188748	−	0.188748i
$483$	−4.06306	+	5.59379i	−0.184876	+	0.254526i
$484$		−	3.00000i		−	0.136364i
$485$	22.9706	−	26.4853i	1.04304	−	1.20263i
$486$		−	15.5474i		−	0.705246i
$487$	20.8995	+	20.8995i	0.947047	+	0.947047i	0.998667	−	0.0516203i	$-0.0164385\pi$
$487$	20.8995	+	20.8995i	0.947047	+	0.947047i	−0.0516203	+	0.998667i	$0.516439\pi$
$488$	7.29818	+	7.29818i	0.330373	+	0.330373i
$489$	2.53620			0.114691
$490$	−6.09594	+	14.4166i	−0.275387	+	0.651277i
$491$	30.8284			1.39127			0.695634	−	0.718397i	$-0.255124\pi$
$491$	30.8284			1.39127			0.695634	+	0.718397i	$0.255124\pi$
$492$	0.828427	+	0.828427i	0.0373484	+	0.0373484i
$493$	7.39104	+	7.39104i	0.332876	+	0.332876i
$494$		−	28.3848i		−	1.27709i
$495$	−1.08239	−	15.2304i	−0.0486499	−	0.684556i
$496$		−	3.69552i		−	0.165934i
$497$	−5.30864	+	7.30864i	−0.238125	+	0.327837i
$498$	4.17157	−	4.17157i	0.186933	−	0.186933i
$499$			24.4853i			1.09611i	0.836442	+	0.548056i	$0.184632\pi$
$499$			24.4853i			1.09611i	−0.836442	+	0.548056i	$0.815368\pi$
$500$	−2.36176	−	10.9280i	−0.105621	−	0.488717i
$501$	12.4853			0.557801
$502$	20.3638	−	20.3638i	0.908881	−	0.908881i
$503$	22.8072	+	22.8072i	1.01692	+	1.01692i	0.999854	+	0.0170666i	$0.00543274\pi$
$503$	22.8072	+	22.8072i	1.01692	+	1.01692i	0.0170666	+	0.999854i	$0.494567\pi$
$504$	6.30864	−	1.00000i	0.281009	−	0.0445435i
$505$	1.87868	+	26.4350i	0.0836001	+	1.17634i
$506$	9.65685			0.429300
$507$	−1.67798	+	1.67798i	−0.0745218	+	0.0745218i
$508$	−6.41421	+	6.41421i	−0.284585	+	0.284585i
$509$	−1.66205			−0.0736691			−0.0368345	−	0.999321i	$-0.511727\pi$
$509$	−1.66205			−0.0736691			−0.0368345	+	0.999321i	$0.511727\pi$
$510$	−2.79884	−	2.42742i	−0.123935	−	0.107488i
$511$	17.6569	−	2.79884i	0.781093	−	0.123813i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−20.7279	+	20.7279i	−0.915160	+	0.915160i
$514$	−4.59220			−0.202553
$515$	−4.72792	−	4.10051i	−0.208337	−	0.180690i
$516$			4.32957i			0.190599i
$517$	7.39104	−	7.39104i	0.325057	−	0.325057i
$518$	16.3907	+	11.9054i	0.720164	+	0.523092i
$519$			9.27208i			0.406999i
$520$	8.94975	−	0.636039i	0.392472	−	0.0278922i
$521$			36.8464i			1.61427i	0.590367	+	0.807135i	$0.298983\pi$
$521$			36.8464i			1.61427i	−0.590367	+	0.807135i	$0.701017\pi$
$522$	8.24264	+	8.24264i	0.360771	+	0.360771i
$523$	6.84984	+	6.84984i	0.299523	+	0.299523i	0.840827	−	0.541304i	$-0.182069\pi$
$523$	6.84984	+	6.84984i	0.299523	+	0.299523i	−0.541304	+	0.840827i	$0.682069\pi$
$524$	−16.8925			−0.737951
$525$	9.67532	−	2.98341i	0.422266	−	0.130207i
$526$	−23.4558			−1.02272
$527$	5.65685	+	5.65685i	0.246416	+	0.246416i
$528$	1.53073	+	1.53073i	0.0666166	+	0.0666166i
$529$			11.3431i			0.493180i
$530$	−0.765367	+	0.0543929i	−0.0332454	+	0.00236268i
$531$		−	9.23880i		−	0.400930i
$532$	−15.1430	−	10.9991i	−0.656532	−	0.476873i
$533$	4.34315	−	4.34315i	0.188123	−	0.188123i
$534$			12.9706i			0.561291i
$535$	−18.2919	−	15.8645i	−0.790827	−	0.685881i
$536$	9.17157			0.396152
$537$	1.26810	−	1.26810i	0.0547226	−	0.0547226i
$538$	−8.96023	−	8.96023i	−0.386303	−	0.386303i
$539$	6.12293	+	18.8284i	0.263733	+	0.810998i
$540$	−7.00000	−	6.07107i	−0.301232	−	0.261257i
$541$	−22.9706			−0.987582			−0.493791	−	0.869581i	$-0.664389\pi$
$541$	−22.9706			−0.987582			−0.493791	+	0.869581i	$0.664389\pi$
$542$	−9.81845	+	9.81845i	−0.421739	+	0.421739i
$543$	−5.48528	+	5.48528i	−0.235396	+	0.235396i
$544$	−2.16478			−0.0928144
$545$	−2.55873	−	36.0041i	−0.109604	−	1.54225i
$546$	1.27208	+	8.02509i	0.0544399	+	0.343442i
$547$	14.6274	+	14.6274i	0.625423	+	0.625423i	0.946913	−	0.321490i	$-0.104184\pi$
$547$	14.6274	+	14.6274i	0.625423	+	0.625423i	−0.321490	+	0.946913i	$0.604184\pi$
$548$	13.8284	−	13.8284i	0.590721	−	0.590721i
$549$	−24.9176			−1.06346
$550$	−11.3137	−	8.48528i	−0.482418	−	0.361814i
$551$		−	34.1563i		−	1.45511i
$552$	1.84776	−	1.84776i	0.0786458	−	0.0786458i
$553$	−19.4180	−	14.1043i	−0.825737	−	0.599776i
$554$		−	14.4853i		−	0.615421i
$555$	−0.928932	−	13.0711i	−0.0394310	−	0.554836i
$556$		−	5.09494i		−	0.216073i
$557$	−1.27208	−	1.27208i	−0.0538997	−	0.0538997i	0.679643	−	0.733543i	$-0.262135\pi$
$557$	−1.27208	−	1.27208i	−0.0538997	−	0.0538997i	−0.733543	+	0.679643i	$0.762135\pi$
$558$	6.30864	+	6.30864i	0.267066	+	0.267066i
$559$	22.6984			0.960039
$560$	3.12872	−	5.02107i	0.132212	−	0.212179i
$561$	−4.68629			−0.197855
$562$	4.00000	+	4.00000i	0.168730	+	0.168730i
$563$	32.0844	+	32.0844i	1.35220	+	1.35220i	0.883200	+	0.468997i	$0.155385\pi$
$563$	32.0844	+	32.0844i	1.35220	+	1.35220i	0.468997	+	0.883200i	$0.344615\pi$
$564$		−	2.82843i		−	0.119098i
$565$	−14.1480	+	16.3128i	−0.595212	+	0.686285i
$566$		−	0.317025i		−	0.0133256i
$567$	−6.32996	+	8.71474i	−0.265834	+	0.365985i
$568$	2.41421	−	2.41421i	0.101298	−	0.101298i
$569$		−	1.41421i		−	0.0592869i	−0.999561	−	0.0296435i	$-0.990563\pi$
$569$		−	1.41421i		−	0.0592869i	0.999561	−	0.0296435i	$-0.00943719\pi$
$570$	0.858221	+	12.0761i	0.0359469	+	0.505812i
$571$	25.4558			1.06529			0.532647	−	0.846338i	$-0.321197\pi$
$571$	25.4558			1.06529			0.532647	+	0.846338i	$0.321197\pi$
$572$	8.02509	−	8.02509i	0.335546	−	0.335546i
$573$	5.54328	+	5.54328i	0.231574	+	0.231574i
$574$	−0.634051	−	4.00000i	−0.0264648	−	0.166957i
$575$	−10.2426	+	13.6569i	−0.427148	+	0.569530i
$576$	−2.41421			−0.100592
$577$	4.40649	−	4.40649i	0.183445	−	0.183445i	−0.609410	−	0.792855i	$-0.708594\pi$
$577$	4.40649	−	4.40649i	0.183445	−	0.183445i	0.792855	+	0.609410i	$0.208594\pi$
$578$	−8.70711	+	8.70711i	−0.362168	+	0.362168i
$579$	−0.262632			−0.0109146
$580$	10.7695	−	0.765367i	0.447180	−	0.0317801i
$581$	−20.1421	+	3.19278i	−0.835637	+	0.132459i
$582$	−8.48528	−	8.48528i	−0.351726	−	0.351726i
$583$	−0.686292	+	0.686292i	−0.0284233	+	0.0284233i
$584$	−6.75699			−0.279606
$585$	−14.1924	+	16.3640i	−0.586783	+	0.676567i
$586$			2.93015i			0.121043i
$587$	−5.58174	+	5.58174i	−0.230383	+	0.230383i	−0.812853	−	0.582470i	$-0.802087\pi$
$587$	−5.58174	+	5.58174i	−0.230383	+	0.230383i	0.582470	+	0.812853i	$0.302087\pi$
$588$	4.77424	+	2.43109i	0.196886	+	0.100256i
$589$		−	26.1421i		−	1.07717i
$590$	−6.46447	−	5.60660i	−0.266138	−	0.230820i
$591$			3.69552i			0.152013i
$592$	−5.41421	−	5.41421i	−0.222523	−	0.222523i
$593$	−18.6633	−	18.6633i	−0.766410	−	0.766410i	0.211063	−	0.977473i	$-0.432308\pi$
$593$	−18.6633	−	18.6633i	−0.766410	−	0.766410i	−0.977473	+	0.211063i	$0.932308\pi$
$594$	−11.7206			−0.480902
$595$	2.89668	+	12.4752i	0.118752	+	0.511431i
$596$	5.31371			0.217658
$597$	−8.62742	−	8.62742i	−0.353097	−	0.353097i
$598$	−9.68714	−	9.68714i	−0.396136	−	0.396136i
$599$		−	46.5269i		−	1.90104i	−0.310666	−	0.950519i	$-0.600552\pi$
$599$		−	46.5269i		−	1.90104i	0.310666	−	0.950519i	$-0.399448\pi$
$600$	−3.78837	+	0.541196i	−0.154660	+	0.0220942i
$601$			19.1116i			0.779580i	0.920904	+	0.389790i	$0.127452\pi$
$601$			19.1116i			0.779580i	−0.920904	+	0.389790i	$0.872548\pi$
$602$	8.79565	−	12.1094i	0.358484	−	0.493541i
$603$	−15.6569	+	15.6569i	−0.637596	+	0.637596i
$604$		−	3.17157i		−	0.129049i
$605$	6.69133	−	0.475538i	0.272041	−	0.0193334i
$606$	9.07107			0.368487
$607$	0.262632	−	0.262632i	0.0106599	−	0.0106599i	−0.701757	−	0.712417i	$-0.747601\pi$
$607$	0.262632	−	0.262632i	0.0106599	−	0.0106599i	0.712417	+	0.701757i	$0.247601\pi$
$608$	5.00208	+	5.00208i	0.202861	+	0.202861i
$609$	1.53073	+	9.65685i	0.0620285	+	0.391315i
$610$	−15.1213	+	17.4350i	−0.612244	+	0.705924i
$611$	−14.8284			−0.599894
$612$	3.69552	−	3.69552i	0.149382	−	0.149382i
$613$	0.100505	−	0.100505i	0.00405936	−	0.00405936i	−0.705074	−	0.709134i	$-0.749086\pi$
$613$	0.100505	−	0.100505i	0.00405936	−	0.00405936i	0.709134	+	0.705074i	$0.249086\pi$
$614$	−5.91470			−0.238698
$615$	−1.71644	+	1.97908i	−0.0692137	+	0.0798040i
$616$	−1.17157	−	7.39104i	−0.0472040	−	0.297793i
$617$	−11.5147	−	11.5147i	−0.463565	−	0.463565i	0.436257	−	0.899822i	$-0.356304\pi$
$617$	−11.5147	−	11.5147i	−0.463565	−	0.463565i	−0.899822	+	0.436257i	$0.856304\pi$
$618$	−1.51472	+	1.51472i	−0.0609309	+	0.0609309i
$619$	34.9217			1.40362			0.701811	−	0.712363i	$-0.252375\pi$
$619$	34.9217			1.40362			0.701811	+	0.712363i	$0.252375\pi$
$620$	8.24264	−	0.585786i	0.331032	−	0.0235257i
$621$			14.1480i			0.567741i
$622$	16.3128	−	16.3128i	0.654084	−	0.654084i
$623$	26.3501	−	36.2773i	1.05569	−	1.45342i
$624$		−	3.07107i		−	0.122941i
$625$	24.0000	−	7.00000i	0.960000	−	0.280000i
$626$		−	8.28772i		−	0.331244i
$627$	10.8284	+	10.8284i	0.432446	+	0.432446i
$628$	1.17525	+	1.17525i	0.0468975	+	0.0468975i
$629$	16.5754			0.660906
$630$	3.23044	+	13.9126i	0.128704	+	0.554289i
$631$	−29.3553			−1.16862			−0.584309	−	0.811531i	$-0.698634\pi$
$631$	−29.3553			−1.16862			−0.584309	+	0.811531i	$0.698634\pi$
$632$	6.41421	+	6.41421i	0.255144	+	0.255144i
$633$	−11.7206	−	11.7206i	−0.465852	−	0.465852i
$634$			2.97056i			0.117976i
$635$	−15.3233	−	13.2898i	−0.608085	−	0.527390i
$636$			0.262632i			0.0104141i
$637$	12.7453	−	25.0296i	0.504989	−	0.991709i
$638$	9.65685	−	9.65685i	0.382319	−	0.382319i
$639$			8.24264i			0.326074i
$640$	−1.46508	+	1.68925i	−0.0579122	+	0.0667733i
$641$	5.21320			0.205909			0.102955	−	0.994686i	$-0.467170\pi$
$641$	5.21320			0.205909			0.102955	+	0.994686i	$0.467170\pi$
$642$	−5.86030	+	5.86030i	−0.231288	+	0.231288i
$643$	−27.0439	−	27.0439i	−1.06651	−	1.06651i	−0.997625	−	0.0688814i	$-0.978057\pi$
$643$	−27.0439	−	27.0439i	−1.06651	−	1.06651i	−0.0688814	−	0.997625i	$-0.521943\pi$
$644$	−8.92177	+	1.41421i	−0.351567	+	0.0557278i
$645$	−9.65685	+	0.686292i	−0.380238	+	0.0270227i
$646$	−15.3137			−0.602510
$647$	−20.7193	+	20.7193i	−0.814560	+	0.814560i	−0.985314	−	0.170754i	$-0.945380\pi$
$647$	−20.7193	+	20.7193i	−0.814560	+	0.814560i	0.170754	+	0.985314i	$0.445380\pi$
$648$	2.87868	−	2.87868i	0.113085	−	0.113085i
$649$	−10.8239			−0.424876
$650$	2.83730	+	19.8611i	0.111288	+	0.779016i
$651$	1.17157	+	7.39104i	0.0459176	+	0.289678i
$652$	2.34315	+	2.34315i	0.0917647	+	0.0917647i
$653$	−16.7279	+	16.7279i	−0.654614	+	0.654614i	−0.954101	−	0.299486i	$-0.903185\pi$
$653$	−16.7279	+	16.7279i	−0.654614	+	0.654614i	0.299486	+	0.954101i	$0.403185\pi$
$654$	−12.3547			−0.483105
$655$	−2.67767	−	37.6777i	−0.104625	−	1.47219i
$656$			1.53073i			0.0597651i
$657$	11.5349	−	11.5349i	0.450019	−	0.450019i
$658$	−5.74603	+	7.91082i	−0.224004	+	0.308396i
$659$		−	18.3431i		−	0.714548i	−0.934000	−	0.357274i	$-0.883706\pi$
$659$		−	18.3431i		−	0.714548i	0.934000	−	0.357274i	$-0.116294\pi$
$660$	−3.17157	+	3.65685i	−0.123453	+	0.142343i
$661$		−	0.208239i		−	0.00809958i	−0.999992	−	0.00404979i	$-0.998711\pi$
$661$		−	0.208239i		−	0.00809958i	0.999992	−	0.00404979i	$-0.00128909\pi$
$662$	0.485281	+	0.485281i	0.0188610	+	0.0188610i
$663$	4.70099	+	4.70099i	0.182571	+	0.182571i
$664$	7.70806			0.299131
$665$	22.1326	−	35.5191i	0.858265	−	1.37737i
$666$	18.4853			0.716290
$667$	−11.6569	−	11.6569i	−0.451355	−	0.451355i
$668$	11.5349	+	11.5349i	0.446299	+	0.446299i
$669$			6.34315i			0.245240i
$670$	1.45381	+	20.4567i	0.0561656	+	0.790310i
$671$			29.1927i			1.12697i
$672$	−1.63838	−	1.19004i	−0.0632020	−	0.0459069i
$673$	16.7990	−	16.7990i	0.647553	−	0.647553i	−0.304848	−	0.952401i	$-0.598606\pi$
$673$	16.7990	−	16.7990i	0.647553	−	0.647553i	0.952401	+	0.304848i	$0.0986055\pi$
$674$			17.3137i			0.666899i
$675$	12.4316	−	16.5754i	0.478492	−	0.637989i
$676$	−3.10051			−0.119250
$677$	−30.7394	+	30.7394i	−1.18141	+	1.18141i	−0.202032	+	0.979379i	$0.564754\pi$
$677$	−30.7394	+	30.7394i	−1.18141	+	1.18141i	−0.979379	+	0.202032i	$0.935246\pi$
$678$	5.22625	+	5.22625i	0.200713	+	0.200713i
$679$	6.49435	+	40.9706i	0.249230	+	1.57231i
$680$	−0.343146	−	4.82843i	−0.0131590	−	0.185162i
$681$	−2.10051			−0.0804915
$682$	7.39104	−	7.39104i	0.283017	−	0.283017i
$683$	−2.68629	+	2.68629i	−0.102788	+	0.102788i	−0.756631	−	0.653843i	$-0.773156\pi$
$683$	−2.68629	+	2.68629i	−0.102788	+	0.102788i	0.653843	+	0.756631i	$0.273156\pi$
$684$	−17.0782			−0.653000
$685$	33.0355	+	28.6515i	1.26222	+	1.09472i
$686$	−8.41421	−	16.4985i	−0.321256	−	0.629916i
$687$	−4.07107	−	4.07107i	−0.155321	−	0.155321i
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	1.37689			0.0524552
$690$	4.41421	+	3.82843i	0.168046	+	0.145746i
$691$		−	12.5629i		−	0.477915i	−0.971030	−	0.238958i	$-0.923194\pi$
$691$		−	12.5629i		−	0.477915i	0.971030	−	0.238958i	$-0.0768057\pi$
$692$	−8.56628	+	8.56628i	−0.325641	+	0.325641i
$693$	14.6173	+	10.6173i	0.555265	+	0.403317i
$694$			24.4853i			0.929449i
$695$	11.3640	−	0.807612i	0.431060	−	0.0306345i
$696$		−	3.69552i		−	0.140078i
$697$	−2.34315	−	2.34315i	−0.0887530	−	0.0887530i
$698$	−17.6194	−	17.6194i	−0.666903	−	0.666903i
$699$	3.24718			0.122819
$700$	11.6951	+	6.18252i	0.442035	+	0.233677i
$701$	49.1127			1.85496			0.927481	−	0.373872i	$-0.121970\pi$
$701$	49.1127			1.85496			0.927481	+	0.373872i	$0.121970\pi$
$702$	11.7574	+	11.7574i	0.443753	+	0.443753i
$703$	−38.3002	−	38.3002i	−1.44452	−	1.44452i
$704$			2.82843i			0.106600i
$705$	6.30864	−	0.448342i	0.237597	−	0.0168855i
$706$		−	8.02509i		−	0.302028i
$707$	−25.3708	−	18.4281i	−0.954169	−	0.693062i
$708$	−2.07107	+	2.07107i	−0.0778355	+	0.0778355i
$709$		−	18.6863i		−	0.701778i	−0.936417	−	0.350889i	$-0.885879\pi$
$709$		−	18.6863i		−	0.701778i	0.936417	−	0.350889i	$-0.114121\pi$
$710$	5.76745	+	5.00208i	0.216448	+	0.187725i
$711$	−21.8995			−0.821295
$712$	−11.9832	+	11.9832i	−0.449091	+	0.449091i
$713$	−8.92177	−	8.92177i	−0.334123	−	0.334123i
$714$	4.32957	−	0.686292i	0.162030	−	0.0256838i
$715$	19.1716	+	16.6274i	0.716976	+	0.621830i
$716$	2.34315			0.0875675
$717$	−5.67459	+	5.67459i	−0.211922	+	0.211922i
$718$	−12.0000	+	12.0000i	−0.447836	+	0.447836i
$719$	−9.44703			−0.352315			−0.176157	−	0.984362i	$-0.556367\pi$
$719$	−9.44703			−0.352315			−0.176157	+	0.984362i	$0.556367\pi$
$720$	−0.382683	−	5.38476i	−0.0142618	−	0.200678i
$721$	7.31371	−	1.15932i	0.272377	−	0.0431752i
$722$	21.9497	+	21.9497i	0.816885	+	0.816885i
$723$	3.17157	−	3.17157i	0.117952	−	0.117952i
$724$	−10.1355			−0.376682
$725$	3.41421	+	23.8995i	0.126801	+	0.887605i
$726$		−	2.29610i		−	0.0852163i
$727$	−18.6633	+	18.6633i	−0.692183	+	0.692183i	−0.962712	−	0.270528i	$-0.912802\pi$
$727$	−18.6633	+	18.6633i	−0.692183	+	0.692183i	0.270528	+	0.962712i	$0.412802\pi$
$728$	−6.23897	+	8.58946i	−0.231231	+	0.318347i
$729$			0.313708i			0.0116188i
$730$	−1.07107	−	15.0711i	−0.0396420	−	0.557805i
$731$		−	12.2459i		−	0.452930i
$732$	5.58579	+	5.58579i	0.206457	+	0.206457i
$733$	−12.3387	−	12.3387i	−0.455741	−	0.455741i	0.441513	−	0.897255i	$-0.354442\pi$
$733$	−12.3387	−	12.3387i	−0.455741	−	0.455741i	−0.897255	+	0.441513i	$0.854442\pi$
$734$	10.4525			0.385809
$735$	−4.66563	+	11.0340i	−0.172094	+	0.406996i
$736$	3.41421			0.125850
$737$	18.3431	+	18.3431i	0.675678	+	0.675678i
$738$	−2.61313	−	2.61313i	−0.0961905	−	0.0961905i
$739$			1.65685i			0.0609484i	0.999536	+	0.0304742i	$0.00970174\pi$
$739$			1.65685i			0.0609484i	−0.999536	+	0.0304742i	$0.990298\pi$
$740$	11.2179	−	12.9343i	0.412377	−	0.475475i
$741$		−	21.7248i		−	0.798079i
$742$	0.533546	−	0.734556i	0.0195871	−	0.0269664i
$743$	−21.0416	+	21.0416i	−0.771943	+	0.771943i	−0.978446	−	0.206503i	$-0.933792\pi$
$743$	−21.0416	+	21.0416i	−0.771943	+	0.771943i	0.206503	+	0.978446i	$0.433792\pi$
$744$		−	2.82843i		−	0.103695i
$745$	0.842290	+	11.8519i	0.0308591	+	0.434221i
$746$	−1.31371			−0.0480983
$747$	−13.1585	+	13.1585i	−0.481444	+	0.481444i
$748$	−4.32957	−	4.32957i	−0.158305	−	0.158305i
$749$	28.2960	−	4.48528i	1.03391	−	0.163889i
$750$	−1.80761	−	8.36396i	−0.0660047	−	0.305409i
$751$	14.4853			0.528575			0.264288	−	0.964444i	$-0.414863\pi$
$751$	14.4853			0.528575			0.264288	+	0.964444i	$0.414863\pi$
$752$	2.61313	−	2.61313i	0.0952909	−	0.0952909i
$753$	15.5858	−	15.5858i	0.567978	−	0.567978i
$754$	−19.3743			−0.705569
$755$	7.07401	−	0.502734i	0.257450	−	0.0182964i
$756$	10.8284	−	1.71644i	0.393826	−	0.0624264i
$757$	−11.8995	−	11.8995i	−0.432494	−	0.432494i	0.456982	−	0.889476i	$-0.348931\pi$
$757$	−11.8995	−	11.8995i	−0.432494	−	0.432494i	−0.889476	+	0.456982i	$0.848931\pi$
$758$	15.6569	−	15.6569i	0.568683	−	0.568683i
$759$	7.39104			0.268278
$760$	−10.3640	+	11.9497i	−0.375940	+	0.433463i
$761$			32.3630i			1.17316i	0.809892	+	0.586579i	$0.199525\pi$
$761$			32.3630i			1.17316i	−0.809892	+	0.586579i	$0.800475\pi$
$762$	−4.90923	+	4.90923i	−0.177843	+	0.177843i
$763$	34.5547	+	25.0989i	1.25096	+	0.908640i
$764$			10.2426i			0.370566i
$765$	8.82843	+	7.65685i	0.319192	+	0.276834i
$766$			15.4161i			0.557007i
$767$	10.8579	+	10.8579i	0.392055	+	0.392055i
$768$	0.541196	+	0.541196i	0.0195287	+	0.0195287i
$769$	20.2710			0.730989			0.365495	−	0.930813i	$-0.380900\pi$
$769$	20.2710			0.730989			0.365495	+	0.930813i	$0.380900\pi$
$770$	16.2996	−	3.78470i	0.587396	−	0.136391i
$771$	−3.51472			−0.126579
$772$	−0.242641	−	0.242641i	−0.00873283	−	0.00873283i
$773$	−1.49227	−	1.49227i	−0.0536733	−	0.0536733i	0.679761	−	0.733434i	$-0.262084\pi$
$773$	−1.49227	−	1.49227i	−0.0536733	−	0.0536733i	−0.733434	+	0.679761i	$0.762084\pi$
$774$		−	13.6569i		−	0.490885i
$775$	2.61313	+	18.2919i	0.0938663	+	0.657064i
$776$		−	15.6788i		−	0.562835i
$777$	12.5449	+	9.11198i	0.450045	+	0.326891i
$778$	19.8995	−	19.8995i	0.713431	−	0.713431i
$779$			10.8284i			0.387969i
$780$	6.84984	−	0.486803i	0.245264	−	0.0174303i
$781$	9.65685			0.345549
$782$	−5.22625	+	5.22625i	−0.186890	+	0.186890i
$783$	14.1480	+	14.1480i	0.505609	+	0.505609i
$784$	2.16478	+	6.65685i	0.0773137	+	0.237745i
$785$	−2.43503	+	2.80761i	−0.0869099	+	0.100208i
$786$	−12.9289			−0.461160
$787$	3.97408	−	3.97408i	0.141661	−	0.141661i	−0.632720	−	0.774381i	$-0.718062\pi$
$787$	3.97408	−	3.97408i	0.141661	−	0.141661i	0.774381	+	0.632720i	$0.218062\pi$
$788$	−3.41421	+	3.41421i	−0.121626	+	0.121626i
$789$	−17.9523			−0.639120
$790$	−13.2898	+	15.3233i	−0.472830	+	0.545177i
$791$	−4.00000	−	25.2346i	−0.142224	−	0.897238i
$792$	−4.82843	−	4.82843i	−0.171571	−	0.171571i
$793$	29.2843	−	29.2843i	1.03991	−	1.03991i
$794$	22.3044			0.791554
$795$	−0.585786	+	0.0416306i	−0.0207757	+	0.00147648i
$796$		−	15.9414i		−	0.565028i
$797$	11.4964	−	11.4964i	0.407225	−	0.407225i	−0.473545	−	0.880770i	$-0.657026\pi$
$797$	11.4964	−	11.4964i	0.407225	−	0.407225i	0.880770	+	0.473545i	$0.157026\pi$
$798$	−11.5899	−	8.41838i	−0.410280	−	0.298007i
$799$			8.00000i			0.283020i
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$		−	40.9133i		−	1.44560i
$802$	−19.9706	−	19.9706i	−0.705185	−	0.705185i
$803$	−13.5140	−	13.5140i	−0.476898	−	0.476898i
$804$	7.01962			0.247563
$805$	−4.56854	−	19.6753i	−0.161020	−	0.693464i
$806$	−14.8284			−0.522309
$807$	−6.85786	−	6.85786i	−0.241408	−	0.241408i
$808$	8.38057	+	8.38057i	0.294828	+	0.294828i
$809$			14.1005i			0.495747i	0.968792	+	0.247874i	$0.0797318\pi$
$809$			14.1005i			0.495747i	−0.968792	+	0.247874i	$0.920268\pi$
$810$	6.87704	+	5.96442i	0.241634	+	0.209568i
$811$		−	7.18280i		−	0.252222i	−0.992016	−	0.126111i	$-0.959750\pi$
$811$		−	7.18280i		−	0.252222i	0.992016	−	0.126111i	$-0.0402496\pi$
$812$	−7.50756	+	10.3360i	−0.263464	+	0.362722i
$813$	−7.51472	+	7.51472i	−0.263553	+	0.263553i
$814$		−	21.6569i		−	0.759072i
$815$	−4.85483	+	5.59767i	−0.170057	+	0.196078i
$816$	−1.65685			−0.0580015
$817$	−28.2960	+	28.2960i	−0.989953	+	0.989953i
$818$	16.4985	+	16.4985i	0.576857	+	0.576857i
$819$	−4.01254	−	25.3137i	−0.140210	−	0.884533i
$820$	−3.41421	+	0.242641i	−0.119230	+	0.00847338i
$821$	−17.5147			−0.611268			−0.305634	−	0.952149i	$-0.598868\pi$
$821$	−17.5147			−0.611268			−0.305634	+	0.952149i	$0.598868\pi$
$822$	10.5838	−	10.5838i	0.369153	−	0.369153i
$823$	−13.6569	+	13.6569i	−0.476048	+	0.476048i	−0.903865	−	0.427817i	$-0.859283\pi$
$823$	−13.6569	+	13.6569i	−0.476048	+	0.476048i	0.427817	+	0.903865i	$0.359283\pi$
$824$	−2.79884			−0.0975020
$825$	−8.65914	−	6.49435i	−0.301472	−	0.226104i
$826$	10.0000	−	1.58513i	0.347945	−	0.0551536i
$827$	−24.4853	−	24.4853i	−0.851437	−	0.851437i	0.138873	−	0.990310i	$-0.455652\pi$
$827$	−24.4853	−	24.4853i	−0.851437	−	0.851437i	−0.990310	+	0.138873i	$0.955652\pi$
$828$	−5.82843	+	5.82843i	−0.202552	+	0.202552i
$829$	−30.7009			−1.06629			−0.533144	−	0.846025i	$-0.678989\pi$
$829$	−30.7009			−1.06629			−0.533144	+	0.846025i	$0.678989\pi$
$830$	1.22183	+	17.1924i	0.0424102	+	0.596757i
$831$		−	11.0866i		−	0.384588i
$832$	2.83730	−	2.83730i	0.0983656	−	0.0983656i
$833$	−13.5036	−	6.87616i	−0.467871	−	0.238245i
$834$		−	3.89949i		−	0.135028i
$835$	−23.8995	+	27.5563i	−0.827076	+	0.953627i
$836$			20.0083i			0.692002i
$837$	10.8284	+	10.8284i	0.374285	+	0.374285i
$838$	−17.1710	−	17.1710i	−0.593163	−	0.593163i
$839$	12.8799			0.444664			0.222332	−	0.974971i	$-0.428633\pi$
$839$	12.8799			0.444664			0.222332	+	0.974971i	$0.428633\pi$
$840$	2.39462	−	3.84296i	0.0826221	−	0.132595i
$841$	5.68629			0.196079
$842$	−15.4142	−	15.4142i	−0.531209	−	0.531209i
$843$	3.06147	+	3.06147i	0.105443	+	0.105443i
$844$		−	21.6569i		−	0.745460i
$845$	−0.491469	−	6.91550i	−0.0169071	−	0.237900i
$846$			8.92177i			0.306737i
$847$	−4.66460	+	6.42196i	−0.160277	+	0.220661i
$848$	−0.242641	+	0.242641i	−0.00833232	+	0.00833232i
$849$		−	0.242641i		−	0.00832741i
$850$	10.7151	−	1.53073i	0.367526	−	0.0525037i
$851$	−26.1421			−0.896141
$852$	1.84776	−	1.84776i	0.0633032	−	0.0633032i
$853$	−16.4826	−	16.4826i	−0.564353	−	0.564353i	0.366188	−	0.930541i	$-0.380663\pi$
$853$	−16.4826	−	16.4826i	−0.564353	−	0.564353i	−0.930541	+	0.366188i	$0.880663\pi$
$854$	−4.27518	−	26.9706i	−0.146294	−	0.922914i
$855$	−2.70711	−	38.0919i	−0.0925811	−	1.30271i
$856$	−10.8284			−0.370108
$857$	−35.0530	+	35.0530i	−1.19739	+	1.19739i	−0.222443	+	0.974946i	$0.571403\pi$
$857$	−35.0530	+	35.0530i	−1.19739	+	1.19739i	−0.974946	+	0.222443i	$0.928597\pi$
$858$	6.14214	−	6.14214i	0.209689	−	0.209689i
$859$	45.9313			1.56716			0.783579	−	0.621293i	$-0.213392\pi$
$859$	45.9313			1.56716			0.783579	+	0.621293i	$0.213392\pi$
$860$	−9.55582	−	8.28772i	−0.325851	−	0.282609i
$861$	−0.485281	−	3.06147i	−0.0165383	−	0.104335i
$862$	−4.00000	−	4.00000i	−0.136241	−	0.136241i
$863$	−33.5563	+	33.5563i	−1.14227	+	1.14227i	−0.154238	+	0.988034i	$0.549292\pi$
$863$	−33.5563	+	33.5563i	−1.14227	+	1.14227i	−0.988034	+	0.154238i	$0.950708\pi$
$864$	−4.14386			−0.140977
$865$	−20.4645	−	17.7487i	−0.695813	−	0.603475i
$866$		−	6.12293i		−	0.208066i
$867$	−6.66413	+	6.66413i	−0.226326	+	0.226326i
$868$	−5.74603	+	7.91082i	−0.195033	+	0.268511i
$869$			25.6569i			0.870349i
$870$	8.24264	−	0.585786i	0.279452	−	0.0198600i
$871$		−	36.8013i		−	1.24697i
$872$	−11.4142	−	11.4142i	−0.386534	−	0.386534i
$873$	26.7653	+	26.7653i	0.905868	+	0.905868i
$874$	24.1522			0.816960
$875$	−11.9359	+	27.0654i	−0.403508	+	0.914976i
$876$	−5.17157			−0.174731
$877$	9.55635	+	9.55635i	0.322695	+	0.322695i	0.849800	−	0.527105i	$-0.176723\pi$
$877$	9.55635	+	9.55635i	0.322695	+	0.322695i	−0.527105	+	0.849800i	$0.676723\pi$
$878$	13.2513	+	13.2513i	0.447211	+	0.447211i
$879$			2.24264i			0.0756424i
$880$	−6.30864	+	0.448342i	−0.212664	+	0.0151136i
$881$			11.7206i			0.394877i	0.980315	+	0.197439i	$0.0632623\pi$
$881$			11.7206i			0.394877i	−0.980315	+	0.197439i	$0.936738\pi$
$882$	−15.0595	−	7.66844i	−0.507079	−	0.258210i
$883$	−23.1716	+	23.1716i	−0.779786	+	0.779786i	−0.979794	−	0.200009i	$-0.935903\pi$
$883$	−23.1716	+	23.1716i	−0.779786	+	0.779786i	0.200009	+	0.979794i	$0.435903\pi$
$884$			8.68629i			0.292152i
$885$	−4.94769	−	4.29111i	−0.166315	−	0.144244i
$886$	34.1421			1.14703
$887$	41.6243	−	41.6243i	1.39761	−	1.39761i	0.590760	−	0.806847i	$-0.298828\pi$
$887$	41.6243	−	41.6243i	1.39761	−	1.39761i	0.806847	−	0.590760i	$-0.201172\pi$
$888$	−4.14386	−	4.14386i	−0.139059	−	0.139059i
$889$	23.7038	−	3.75736i	0.795001	−	0.126018i
$890$	−28.6274	−	24.8284i	−0.959593	−	0.832251i
$891$	11.5147			0.385758
$892$	−5.86030	+	5.86030i	−0.196217	+	0.196217i
$893$	18.4853	−	18.4853i	0.618586	−	0.618586i
$894$	4.06694			0.136019
$895$	0.371418	+	5.22625i	0.0124151	+	0.174694i
$896$	−0.414214	−	2.61313i	−0.0138379	−	0.0872984i
$897$	−7.41421	−	7.41421i	−0.247553	−	0.247553i
$898$	−10.1421	+	10.1421i	−0.338447	+	0.338447i
$899$	−17.8435			−0.595115
$900$	11.9497	−	1.70711i	0.398325	−	0.0569036i
$901$		−	0.742837i		−	0.0247475i
$902$	−3.06147	+	3.06147i	−0.101936	+	0.101936i
$903$	6.73190	−	9.26810i	0.224024	−	0.308423i
$904$			9.65685i			0.321182i
$905$	−1.60660	−	22.6066i	−0.0534052	−	0.751469i
$906$		−	2.42742i		−	0.0806455i
$907$	16.8284	+	16.8284i	0.558779	+	0.558779i	0.928960	−	0.370181i	$-0.120704\pi$
$907$	16.8284	+	16.8284i	0.558779	+	0.558779i	−0.370181	+	0.928960i	$0.620704\pi$
$908$	−1.94061	−	1.94061i	−0.0644015	−	0.0644015i
$909$	−28.6131			−0.949036
$910$	−20.1473	−	12.5541i	−0.667875	−	0.416165i
$911$	0.142136			0.00470916			0.00235458	−	0.999997i	$-0.499251\pi$
$911$	0.142136			0.00470916			0.00235458	+	0.999997i	$0.499251\pi$
$912$	3.82843	+	3.82843i	0.126772	+	0.126772i
$913$	15.4161	+	15.4161i	0.510199	+	0.510199i
$914$			13.6569i			0.451729i
$915$	−11.5734	+	13.3442i	−0.382603	+	0.441145i
$916$		−	7.52235i		−	0.248546i
$917$	36.1609	+	26.2655i	1.19414	+	0.867364i
$918$	6.34315	−	6.34315i	0.209355	−	0.209355i
$919$		−	28.3848i		−	0.936327i	−0.883642	−	0.468164i	$-0.844916\pi$
$919$		−	28.3848i		−	0.936327i	0.883642	−	0.468164i	$-0.155084\pi$
$920$	0.541196	+	7.61521i	0.0178427	+	0.251066i
$921$	−4.52691			−0.149167
$922$	8.43497	−	8.43497i	0.277791	−	0.277791i
$923$	−9.68714	−	9.68714i	−0.318856	−	0.318856i
$924$	−0.896683	−	5.65685i	−0.0294987	−	0.186097i
$925$	30.6274	+	22.9706i	1.00702	+	0.755267i
$926$	29.6569			0.974585
$927$	4.77791	−	4.77791i	0.156927	−	0.156927i
$928$	3.41421	−	3.41421i	0.112077	−	0.112077i
$929$	13.7766			0.451996			0.225998	−	0.974128i	$-0.427436\pi$
$929$	13.7766			0.451996			0.225998	+	0.974128i	$0.427436\pi$
$930$	6.30864	−	0.448342i	0.206869	−	0.0147017i
$931$	15.3137	+	47.0907i	0.501887	+	1.54333i
$932$	3.00000	+	3.00000i	0.0982683	+	0.0982683i
$933$	12.4853	−	12.4853i	0.408750	−	0.408750i
$934$	18.8715			0.617496
$935$	8.97056	−	10.3431i	0.293369	−	0.338257i
$936$			9.68714i			0.316634i
$937$	35.5014	−	35.5014i	1.15978	−	1.15978i	0.175256	−	0.984523i	$-0.443925\pi$
$937$	35.5014	−	35.5014i	1.15978	−	1.15978i	0.984523	−	0.175256i	$-0.0560754\pi$
$938$	−19.6331	−	14.2606i	−0.641045	−	0.465624i
$939$		−	6.34315i		−	0.207001i
$940$	6.24264	+	5.41421i	0.203612	+	0.176592i
$941$			37.7975i			1.23216i	0.787683	+	0.616081i	$0.211281\pi$
$941$			37.7975i			1.23216i	−0.787683	+	0.616081i	$0.788719\pi$
$942$	0.899495	+	0.899495i	0.0293071	+	0.0293071i
$943$	3.69552	+	3.69552i	0.120343	+	0.120343i
$944$	−3.82683			−0.124553
$945$	5.54487	+	23.8801i	0.180375	+	0.776820i
$946$	−16.0000			−0.520205
$947$	−10.9706	−	10.9706i	−0.356495	−	0.356495i	0.506024	−	0.862519i	$-0.331115\pi$
$947$	−10.9706	−	10.9706i	−0.356495	−	0.356495i	−0.862519	+	0.506024i	$0.831115\pi$
$948$	4.90923	+	4.90923i	0.159444	+	0.159444i
$949$			27.1127i			0.880115i
$950$	−28.2960	−	21.2220i	−0.918045	−	0.688534i
$951$			2.27357i			0.0737256i
$952$	4.63405	+	3.36595i	0.150190	+	0.109091i
$953$	−5.14214	+	5.14214i	−0.166570	+	0.166570i	−0.785470	−	0.618900i	$-0.787579\pi$
$953$	−5.14214	+	5.14214i	−0.166570	+	0.166570i	0.618900	+	0.785470i	$0.287579\pi$
$954$		−	0.828427i		−	0.0268213i
$955$	−22.8456	+	1.62359i	−0.739267	+	0.0525381i
$956$	−10.4853			−0.339118
$957$	7.39104	−	7.39104i	0.238918	−	0.238918i
$958$	3.24718	+	3.24718i	0.104912	+	0.104912i
$959$	−51.1032	+	8.10051i	−1.65021	+	0.261579i
$960$	−1.12132	+	1.29289i	−0.0361905	+	0.0417279i
$961$	17.3431			0.559456
$962$	−21.7248	+	21.7248i	−0.700435	+	0.700435i
$963$	18.4853	−	18.4853i	0.595680	−	0.595680i
$964$	5.86030			0.188748
$965$	0.502734	−	0.579658i	0.0161836	−	0.0186598i
$966$	−6.82843	+	1.08239i	−0.219701	+	0.0348254i
$967$	40.2132	+	40.2132i	1.29317	+	1.29317i	0.932816	+	0.360354i	$0.117344\pi$
$967$	40.2132	+	40.2132i	1.29317	+	1.29317i	0.360354	+	0.932816i	$0.382656\pi$
$968$	2.12132	−	2.12132i	0.0681818	−	0.0681818i
$969$	−11.7206			−0.376520
$970$	34.9706	−	2.48528i	1.12284	−	0.0797976i
$971$		−	33.6536i		−	1.08000i	−0.841666	−	0.539998i	$-0.818425\pi$
$971$		−	33.6536i		−	1.08000i	0.841666	−	0.539998i	$-0.181575\pi$
$972$	10.9937	−	10.9937i	0.352623	−	0.352623i
$973$	−7.92194	+	10.9065i	−0.253966	+	0.349646i
$974$			29.5563i			0.947047i
$975$	2.17157	+	15.2010i	0.0695460	+	0.486822i
$976$			10.3212i			0.330373i
$977$	−20.1716	−	20.1716i	−0.645346	−	0.645346i	0.306519	−	0.951865i	$-0.400836\pi$
$977$	−20.1716	−	20.1716i	−0.645346	−	0.645346i	−0.951865	+	0.306519i	$0.900836\pi$
$978$	1.79337	+	1.79337i	0.0573455	+	0.0573455i
$979$	−47.9329			−1.53194
$980$	−14.5046	+	5.88362i	−0.463332	+	0.187945i
$981$	38.9706			1.24423
$982$	21.7990	+	21.7990i	0.695634	+	0.695634i
$983$	11.9063	+	11.9063i	0.379752	+	0.379752i	0.871013	−	0.491260i	$-0.163464\pi$
$983$	11.9063	+	11.9063i	0.379752	+	0.379752i	−0.491260	+	0.871013i	$0.663464\pi$
$984$			1.17157i			0.0373484i
$985$	−8.15640	−	7.07401i	−0.259885	−	0.225397i
$986$			10.4525i			0.332876i
$987$	−4.39782	+	6.05468i	−0.139984	+	0.192723i
$988$	20.0711	−	20.0711i	0.638546	−	0.638546i
$989$			19.3137i			0.614140i
$990$	10.0042	−	11.5349i	0.317953	−	0.366603i
$991$	−35.4142			−1.12497			−0.562485	−	0.826808i	$-0.690155\pi$
$991$	−35.4142			−1.12497			−0.562485	+	0.826808i	$0.690155\pi$
$992$	2.61313	−	2.61313i	0.0829668	−	0.0829668i
$993$	0.371418	+	0.371418i	0.0117866	+	0.0117866i
$994$	−8.92177	+	1.41421i	−0.282981	+	0.0448561i
$995$	35.5563	−	2.52691i	1.12721	−	0.0801085i
$996$	5.89949			0.186933
$997$	38.0760	−	38.0760i	1.20588	−	1.20588i	0.233531	−	0.972349i	$-0.424972\pi$
$997$	38.0760	−	38.0760i	1.20588	−	1.20588i	0.972349	−	0.233531i	$-0.0750279\pi$
$998$	−17.3137	+	17.3137i	−0.548056	+	0.548056i
$999$	31.7289			1.00386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.g.a.27.4	yes	8
3.2	odd	2		630.2.p.a.307.2		8
4.3	odd	2		560.2.bj.c.97.2		8
5.2	odd	4		350.2.g.a.293.2		8
5.3	odd	4	inner	70.2.g.a.13.3	✓	8
5.4	even	2		350.2.g.a.307.1		8
7.2	even	3		490.2.l.a.227.3		16
7.3	odd	6		490.2.l.a.117.1		16
7.4	even	3		490.2.l.a.117.2		16
7.5	odd	6		490.2.l.a.227.4		16
7.6	odd	2	inner	70.2.g.a.27.3	yes	8
15.8	even	4		630.2.p.a.433.1		8
20.3	even	4		560.2.bj.c.433.3		8
21.20	even	2		630.2.p.a.307.1		8
28.27	even	2		560.2.bj.c.97.3		8
35.3	even	12		490.2.l.a.313.3		16
35.13	even	4	inner	70.2.g.a.13.4	yes	8
35.18	odd	12		490.2.l.a.313.4		16
35.23	odd	12		490.2.l.a.423.1		16
35.27	even	4		350.2.g.a.293.1		8
35.33	even	12		490.2.l.a.423.2		16
35.34	odd	2		350.2.g.a.307.2		8
105.83	odd	4		630.2.p.a.433.2		8
140.83	odd	4		560.2.bj.c.433.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.g.a.13.3	✓	8	5.3	odd	4	inner
70.2.g.a.13.4	yes	8	35.13	even	4	inner
70.2.g.a.27.3	yes	8	7.6	odd	2	inner
70.2.g.a.27.4	yes	8	1.1	even	1	trivial
350.2.g.a.293.1		8	35.27	even	4
350.2.g.a.293.2		8	5.2	odd	4
350.2.g.a.307.1		8	5.4	even	2
350.2.g.a.307.2		8	35.34	odd	2
490.2.l.a.117.1		16	7.3	odd	6
490.2.l.a.117.2		16	7.4	even	3
490.2.l.a.227.3		16	7.2	even	3
490.2.l.a.227.4		16	7.5	odd	6
490.2.l.a.313.3		16	35.3	even	12
490.2.l.a.313.4		16	35.18	odd	12
490.2.l.a.423.1		16	35.23	odd	12
490.2.l.a.423.2		16	35.33	even	12
560.2.bj.c.97.2		8	4.3	odd	2
560.2.bj.c.97.3		8	28.27	even	2
560.2.bj.c.433.2		8	140.83	odd	4
560.2.bj.c.433.3		8	20.3	even	4
630.2.p.a.307.1		8	21.20	even	2
630.2.p.a.307.2		8	3.2	odd	2
630.2.p.a.433.1		8	15.8	even	4
630.2.p.a.433.2		8	105.83	odd	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.541196 + 0.541196i) q^{3} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +0.765367i q^{6} +(1.55487 - 2.14065i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.541196 + 0.541196i) q^{3} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +0.765367i q^{6} +(1.55487 - 2.14065i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +(-1.68925 - 1.46508i) q^{10} -2.82843 q^{11} +(-0.541196 + 0.541196i) q^{12} +(2.83730 + 2.83730i) q^{13} +(2.61313 - 0.414214i) q^{14} +(-1.29289 - 1.12132i) q^{15} -1.00000 q^{16} +(1.53073 - 1.53073i) q^{17} +(1.70711 - 1.70711i) q^{18} -7.07401 q^{19} +(-0.158513 - 2.23044i) q^{20} +(2.00000 - 0.317025i) q^{21} +(-2.00000 - 2.00000i) q^{22} +(-2.41421 + 2.41421i) q^{23} -0.765367 q^{24} +(4.94975 - 0.707107i) q^{25} +4.01254i q^{26} +(2.93015 - 2.93015i) q^{27} +(2.14065 + 1.55487i) q^{28} +4.82843i q^{29} +(-0.121320 - 1.70711i) q^{30} +3.69552i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.53073 - 1.53073i) q^{33} +2.16478 q^{34} +(-3.12872 + 5.02107i) q^{35} +2.41421 q^{36} +(5.41421 + 5.41421i) q^{37} +(-5.00208 - 5.00208i) q^{38} +3.07107i q^{39} +(1.46508 - 1.68925i) q^{40} -1.53073i q^{41} +(1.63838 + 1.19004i) q^{42} +(4.00000 - 4.00000i) q^{43} -2.82843i q^{44} +(0.382683 + 5.38476i) q^{45} -3.41421 q^{46} +(-2.61313 + 2.61313i) q^{47} +(-0.541196 - 0.541196i) q^{48} +(-2.16478 - 6.65685i) q^{49} +(4.00000 + 3.00000i) q^{50} +1.65685 q^{51} +(-2.83730 + 2.83730i) q^{52} +(0.242641 - 0.242641i) q^{53} +4.14386 q^{54} +(6.30864 - 0.448342i) q^{55} +(0.414214 + 2.61313i) q^{56} +(-3.82843 - 3.82843i) q^{57} +(-3.41421 + 3.41421i) q^{58} +3.82683 q^{59} +(1.12132 - 1.29289i) q^{60} -10.3212i q^{61} +(-2.61313 + 2.61313i) q^{62} +(-5.16799 - 3.75378i) q^{63} -1.00000i q^{64} +(-6.77817 - 5.87868i) q^{65} -2.16478i q^{66} +(-6.48528 - 6.48528i) q^{67} +(1.53073 + 1.53073i) q^{68} -2.61313 q^{69} +(-5.76277 + 1.33809i) q^{70} -3.41421 q^{71} +(1.70711 + 1.70711i) q^{72} +(4.77791 + 4.77791i) q^{73} +7.65685i q^{74} +(3.06147 + 2.29610i) q^{75} -7.07401i q^{76} +(-4.39782 + 6.05468i) q^{77} +(-2.17157 + 2.17157i) q^{78} -9.07107i q^{79} +(2.23044 - 0.158513i) q^{80} -4.07107 q^{81} +(1.08239 - 1.08239i) q^{82} +(-5.45042 - 5.45042i) q^{83} +(0.317025 + 2.00000i) q^{84} +(-3.17157 + 3.65685i) q^{85} +5.65685 q^{86} +(-2.61313 + 2.61313i) q^{87} +(2.00000 - 2.00000i) q^{88} +16.9469 q^{89} +(-3.53701 + 4.07820i) q^{90} +(10.4853 - 1.66205i) q^{91} +(-2.41421 - 2.41421i) q^{92} +(-2.00000 + 2.00000i) q^{93} -3.69552 q^{94} +(15.7782 - 1.12132i) q^{95} -0.765367i q^{96} +(-11.0866 + 11.0866i) q^{97} +(3.17637 - 6.23784i) q^{98} +6.82843i 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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