LMFDB - Embedded newform 70.2.g.a.27.3

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			27.3
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	70.27
Dual form			70.2.g.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.541196 - 0.541196i) q^{3} +1.00000i q^{4} +(2.23044 - 0.158513i) q^{5} -0.765367i q^{6} +(-2.14065 + 1.55487i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +O(q^{10})$	\(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} +(-2.14065 + 1.55487i) 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} +(-1.55487 - 2.14065i) 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} +(-4.52814 + 3.80736i) 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} +(1.19004 + 1.63838i) 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} +(3.75378 + 5.16799i) 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} +(-5.89409 - 0.509666i) 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} +(6.05468 - 4.39782i) 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} +(6.23784 - 3.17637i) 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	0.533402	−	0.845862i	$-0.320913\pi$
$3$	−0.541196	−	0.541196i	−0.312460	−	0.312460i	−0.845862	+	0.533402i	$0.820913\pi$
$4$			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
$7$	−2.14065	+	1.55487i	−0.809091	+	0.587684i
$7$	−2.14065	+	1.55487i	−0.809091	+	0.587684i
$8$	−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	0.194064	−	0.980989i	$-0.437833\pi$
$13$	−2.83730	−	2.83730i	−0.786925	−	0.786925i	−0.980989	+	0.194064i	$0.937833\pi$
$14$	−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	−0.867935	−	0.496678i	$-0.834553\pi$
$17$	−1.53073	+	1.53073i	−0.371257	+	0.371257i	0.496678	+	0.867935i	$0.334553\pi$
$18$	1.70711	−	1.70711i	0.402369	−	0.402369i
$19$	7.07401			1.62289			0.811445	−	0.584429i	$-0.198682\pi$
$19$	7.07401			1.62289			0.811445	+	0.584429i	$0.198682\pi$
$20$	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
$28$	−1.55487	−	2.14065i	−0.293842	−	0.404545i
$29$			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	$-0.892321\pi$
$31$		−	3.69552i		−	0.663735i	0.943326	−	0.331867i	$-0.107679\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.53073	+	1.53073i	0.266467	+	0.266467i
$34$	−2.16478			−0.371257
$35$	−4.52814	+	3.80736i	−0.765395	+	0.643561i
$36$	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	$0.0381388\pi$
$41$			1.53073i			0.239060i	−0.992831	+	0.119530i	$0.961861\pi$
$42$	1.19004	+	1.63838i	0.183628	+	0.252808i
$43$	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	−0.490358	−	0.871521i	$-0.663134\pi$
$47$	2.61313	−	2.61313i	0.381164	−	0.381164i	0.871521	+	0.490358i	$0.163134\pi$
$48$	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	$-0.580137\pi$
$59$	−3.82683			−0.498211			−0.249106	+	0.968476i	$0.580137\pi$
$60$	1.12132	−	1.29289i	0.144762	−	0.166912i
$61$			10.3212i			1.32149i	0.750609	+	0.660746i	$0.229760\pi$
$61$			10.3212i			1.32149i	−0.750609	+	0.660746i	$0.770240\pi$
$62$	2.61313	−	2.61313i	0.331867	−	0.331867i
$63$	3.75378	+	5.16799i	0.472932	+	0.651106i
$64$		−	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
$70$	−5.89409	−	0.509666i	−0.704478	−	0.0609167i
$71$	−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	0.369871	−	0.929083i	$-0.379402\pi$
$73$	−4.77791	−	4.77791i	−0.559212	−	0.559212i	−0.929083	+	0.369871i	$0.879402\pi$
$74$			7.65685i			0.890091i
$75$	−3.06147	−	2.29610i	−0.353508	−	0.265131i
$76$			7.07401i			0.811445i
$77$	6.05468	−	4.39782i	0.689995	−	0.501179i
$78$	−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	0.939850	−	0.341588i	$-0.110965\pi$
$83$	5.45042	+	5.45042i	0.598262	+	0.598262i	−0.341588	+	0.939850i	$0.610965\pi$
$84$	−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	$-0.855111\pi$
$89$	−16.9469			−1.79636			−0.898182	+	0.439625i	$0.855111\pi$
$90$	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	$-0.456962\pi$
$97$	11.0866	−	11.0866i	1.12567	−	1.12567i	0.990873	−	0.134796i	$-0.0430378\pi$
$98$	6.23784	−	3.17637i	0.630117	−	0.320862i
$99$			6.82843i			0.686283i
$100$	0.707107	+	4.94975i	0.0707107	+	0.494975i
$101$			11.8519i			1.17931i	0.807655	+	0.589655i	$0.200736\pi$
$101$			11.8519i			1.17931i	−0.807655	+	0.589655i	$0.799264\pi$
$102$	1.17157	+	1.17157i	0.116003	+	0.116003i
$103$	−1.97908	−	1.97908i	−0.195004	−	0.195004i	0.602850	−	0.797854i	$-0.294032\pi$
$103$	−1.97908	−	1.97908i	−0.195004	−	0.195004i	−0.797854	+	0.602850i	$0.794032\pi$
$104$	4.01254			0.393462
$105$	4.51114	+	0.390081i	0.440242	+	0.0380681i
$106$	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
$112$	2.14065	−	1.55487i	0.202273	−	0.146921i
$113$	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	$-0.735794\pi$
$131$		−	16.8925i		−	1.47590i	0.674855	−	0.737951i	$-0.264206\pi$
$132$	−1.53073	+	1.53073i	−0.133233	+	0.133233i
$133$	−15.1430	+	10.9991i	−1.31306	+	0.953746i
$134$		−	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	$-0.430675\pi$
$139$	5.09494			0.432147			0.216073	+	0.976377i	$0.430675\pi$
$140$	−3.80736	−	4.52814i	−0.321781	−	0.382697i
$141$	−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
$147$	−4.77424	+	2.43109i	−0.393772	+	0.200513i
$148$	−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	−0.752447	−	0.658652i	$-0.771127\pi$
$157$	−1.17525	+	1.17525i	−0.0937949	+	0.0937949i	0.658652	+	0.752447i	$0.271127\pi$
$158$	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	−0.994767	−	0.102170i	$-0.967421\pi$
$167$	−11.5349	+	11.5349i	−0.892597	+	0.892597i	0.102170	+	0.994767i	$0.467421\pi$
$168$	−1.63838	+	1.19004i	−0.126404	+	0.0918138i
$169$			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	0.302019	−	0.953302i	$-0.402339\pi$
$173$	−8.56628	−	8.56628i	−0.651282	−	0.651282i	−0.953302	+	0.302019i	$0.902339\pi$
$174$	3.69552			0.280157
$175$	−9.49623	+	9.20986i	−0.717848	+	0.696200i
$176$	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	$-0.877065\pi$
$181$		−	10.1355i		−	0.753364i	0.926343	−	0.376682i	$-0.122935\pi$
$182$	6.23897	+	8.58946i	0.462463	+	0.636693i
$183$	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	$-0.308866\pi$
$199$	15.9414			1.13006			0.565028	+	0.825072i	$0.308866\pi$
$200$	−3.00000	+	4.00000i	−0.212132	+	0.282843i
$201$			7.01962i			0.495126i
$202$	−8.38057	+	8.38057i	−0.589655	+	0.589655i
$203$	−7.50756	−	10.3360i	−0.526927	−	0.725444i
$204$			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
$210$	2.91403	+	3.46569i	0.201087	+	0.239155i
$211$	−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
$217$	5.74603	+	7.91082i	0.390066	+	0.537021i
$218$	−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	0.483120	−	0.875554i	$-0.339504\pi$
$223$	−5.86030	−	5.86030i	−0.392435	−	0.392435i	−0.875554	+	0.483120i	$0.839504\pi$
$224$	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	−0.639766	−	0.768569i	$-0.720969\pi$
$227$	1.94061	−	1.94061i	0.128803	−	0.128803i	0.768569	+	0.639766i	$0.220969\pi$
$228$	3.82843	−	3.82843i	0.253544	−	0.253544i
$229$	7.52235			0.497091			0.248546	−	0.968620i	$-0.420047\pi$
$229$	7.52235			0.497091			0.248546	+	0.968620i	$0.420047\pi$
$230$	−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
$238$	4.63405	−	3.36595i	0.300381	−	0.218182i
$239$			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	$0.0604428\pi$
$241$			5.86030i			0.377495i	−0.982026	+	0.188748i	$0.939557\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$	10.9937	+	10.9937i	0.705246	+	0.705246i
$244$	−10.3212			−0.660746
$245$	3.77323	−	15.1909i	0.241063	−	0.970509i
$246$	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	$0.363062\pi$
$251$			28.7988i			1.81776i	−0.417055	+	0.908881i	$0.636938\pi$
$252$	−5.16799	+	3.75378i	−0.325553	+	0.236466i
$253$	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	−0.598540	−	0.801093i	$-0.704252\pi$
$257$	3.24718	−	3.24718i	0.202553	−	0.202553i	0.801093	+	0.598540i	$0.204252\pi$
$258$	−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	$-0.373752\pi$
$269$	12.6717			0.772606			0.386303	+	0.922372i	$0.373752\pi$
$270$	−9.24264	+	0.656854i	−0.562489	+	0.0399749i
$271$		−	13.8854i		−	0.843477i	−0.906717	−	0.421739i	$-0.861420\pi$
$271$		−	13.8854i		−	0.843477i	0.906717	−	0.421739i	$-0.138580\pi$
$272$	1.53073	−	1.53073i	0.0928144	−	0.0928144i
$273$	−4.77510	−	6.57409i	−0.289002	−	0.397882i
$274$		−	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
$280$	0.509666	−	5.89409i	0.0304584	−	0.352239i
$281$	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	0.713738	−	0.700413i	$-0.247001\pi$
$283$	0.224171	+	0.224171i	0.0133256	+	0.0133256i	−0.700413	+	0.713738i	$0.747001\pi$
$284$		−	3.41421i		−	0.202596i
$285$	−9.14594	−	7.93223i	−0.541759	−	0.469865i
$286$			11.3492i			0.671091i
$287$	−2.38009	−	3.27677i	−0.140492	−	0.193422i
$288$	−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	0.643990	−	0.765034i	$-0.277278\pi$
$293$	−2.07193	−	2.07193i	−0.121043	−	0.121043i	−0.765034	+	0.643990i	$0.777278\pi$
$294$	−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	−0.577613	−	0.816311i	$-0.696016\pi$
$307$	4.18232	−	4.18232i	0.238698	−	0.238698i	0.816311	+	0.577613i	$0.196016\pi$
$308$	4.39782	+	6.05468i	0.250589	+	0.344997i
$309$			2.14214i			0.121862i
$310$	5.41421	−	6.24264i	0.307507	−	0.354558i
$311$			23.0698i			1.30817i	0.756422	+	0.654084i	$0.226946\pi$
$311$			23.0698i			1.30817i	−0.756422	+	0.654084i	$0.773054\pi$
$312$	−2.17157	−	2.17157i	−0.122941	−	0.122941i
$313$	5.86030	+	5.86030i	0.331244	+	0.331244i	0.853059	−	0.521815i	$-0.174745\pi$
$313$	5.86030	+	5.86030i	0.331244	+	0.331244i	−0.521815	+	0.853059i	$0.674745\pi$
$314$	−1.66205			−0.0937949
$315$	9.19178	+	10.9319i	0.517898	+	0.615942i
$316$	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
$322$	7.30864	−	5.30864i	0.407295	−	0.295839i
$323$	−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
$343$	5.71646	+	17.6160i	0.308660	+	0.951172i
$344$			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	$-0.267620\pi$
$349$	24.9176			1.33381			0.666903	+	0.745145i	$0.267620\pi$
$350$	−13.2272	−	0.202493i	−0.707024	−	0.0108237i
$351$	16.6274			0.887506
$352$	2.00000	+	2.00000i	0.106600	+	0.106600i
$353$	5.67459	+	5.67459i	0.302028	+	0.302028i	0.841807	−	0.539779i	$-0.181492\pi$
$353$	5.67459	+	5.67459i	0.302028	+	0.302028i	−0.539779	+	0.841807i	$0.681492\pi$
$354$			2.92893i			0.155671i
$355$	−7.61521	+	0.541196i	−0.404173	+	0.0287237i
$356$		−	16.9469i		−	0.898182i
$357$	−3.54675	+	2.57619i	−0.187714	+	0.136346i
$358$	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	−0.873190	−	0.487381i	$-0.837952\pi$
$367$	−7.39104	+	7.39104i	−0.385809	+	0.385809i	0.487381	+	0.873190i	$0.337952\pi$
$368$	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
$378$	8.87056	−	6.44315i	0.456253	−	0.331400i
$379$		−	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	0.371447	−	0.928454i	$-0.378862\pi$
$383$	−10.9008	−	10.9008i	−0.557007	−	0.557007i	−0.928454	+	0.371447i	$0.878862\pi$
$384$	−0.765367			−0.0390575
$385$	12.8075	−	10.7688i	0.652731	−	0.548831i
$386$	−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
$392$	3.17637	+	6.23784i	0.160431	+	0.315059i
$393$	−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	−0.981747	−	0.190192i	$-0.939089\pi$
$397$	−15.7716	+	15.7716i	−0.791554	+	0.791554i	0.190192	+	0.981747i	$0.439089\pi$
$398$	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	$-0.695721\pi$
$409$	−23.3324			−1.15371			−0.576857	+	0.816845i	$0.695721\pi$
$410$	−2.24264	+	2.58579i	−0.110756	+	0.127703i
$411$			14.9678i			0.738306i
$412$	1.97908	−	1.97908i	0.0975020	−	0.0975020i
$413$	8.19192	−	5.95021i	0.403098	−	0.292791i
$414$			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	$-0.297879\pi$
$419$	24.2835			1.18633			0.593163	+	0.805082i	$0.297879\pi$
$420$	−0.390081	+	4.51114i	−0.0190340	+	0.220121i
$421$	−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
$427$	−16.0481	−	22.0941i	−0.776620	−	1.06921i
$428$	−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	0.803445	−	0.595379i	$-0.202998\pi$
$433$	4.32957	+	4.32957i	0.208066	+	0.208066i	−0.595379	+	0.803445i	$0.702998\pi$
$434$	−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	$-0.647583\pi$
$439$	−18.7402			−0.894422			−0.447211	+	0.894428i	$0.647583\pi$
$440$	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
$448$	1.55487	+	2.14065i	0.0734605	+	0.101136i
$449$			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
$455$	23.6503	+	2.04506i	1.10874	+	0.0958737i
$456$	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	$0.0896022\pi$
$461$			11.9288i			0.555582i	−0.960642	+	0.277791i	$0.910398\pi$
$462$	−3.36595	−	4.63405i	−0.156598	−	0.215596i
$463$	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	−0.944888	−	0.327393i	$-0.893830\pi$
$467$	−13.3442	+	13.3442i	−0.617496	+	0.617496i	0.327393	+	0.944888i	$0.393830\pi$
$468$	−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	$-0.533456\pi$
$479$	−4.59220			−0.209823			−0.104912	+	0.994482i	$0.533456\pi$
$480$	0.121320	+	1.70711i	0.00553749	+	0.0779184i
$481$		−	30.7235i		−	1.40087i
$482$	−4.14386	+	4.14386i	−0.188748	+	0.188748i
$483$	−5.59379	+	4.06306i	−0.254526	+	0.184876i
$484$		−	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
$490$	13.4096	−	8.07349i	0.605786	−	0.364723i
$491$	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
$497$	7.30864	−	5.30864i	0.327837	−	0.238125i
$498$	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	$-0.994567\pi$
$503$	−22.8072	−	22.8072i	−1.01692	−	1.01692i	−0.0170666	−	0.999854i	$-0.505433\pi$
$504$	−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	$-0.488273\pi$
$509$	1.66205			0.0736691			0.0368345	+	0.999321i	$0.488273\pi$
$510$	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
$518$	−11.9054	−	16.3907i	−0.523092	−	0.720164i
$519$			9.27208i			0.406999i
$520$	8.94975	−	0.636039i	0.392472	−	0.0278922i
$521$		−	36.8464i		−	1.61427i	−0.590367	−	0.807135i	$-0.701017\pi$
$521$		−	36.8464i		−	1.61427i	0.590367	−	0.807135i	$-0.298983\pi$
$522$	8.24264	+	8.24264i	0.360771	+	0.360771i
$523$	−6.84984	−	6.84984i	−0.299523	−	0.299523i	0.541304	−	0.840827i	$-0.317931\pi$
$523$	−6.84984	−	6.84984i	−0.299523	−	0.299523i	−0.840827	+	0.541304i	$0.817931\pi$
$524$	16.8925			0.737951
$525$	10.1237	+	0.154982i	0.441833	+	0.00676396i
$526$	−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
$532$	−10.9991	−	15.1430i	−0.476873	−	0.656532i
$533$	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
$553$	14.1043	+	19.4180i	0.599776	+	0.825737i
$554$		−	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
$560$	4.52814	−	3.80736i	0.191349	−	0.160890i
$561$	−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	$-0.844615\pi$
$563$	−32.0844	−	32.0844i	−1.35220	−	1.35220i	−0.468997	−	0.883200i	$-0.655385\pi$
$564$		−	2.82843i		−	0.119098i
$565$	14.1480	−	16.3128i	0.595212	−	0.686285i
$566$			0.317025i			0.0133256i
$567$	8.71474	−	6.32996i	0.365985	−	0.265834i
$568$	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	−0.792855	−	0.609410i	$-0.791406\pi$
$577$	−4.40649	+	4.40649i	−0.183445	+	0.183445i	0.609410	+	0.792855i	$0.291406\pi$
$578$	−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	−0.582470	−	0.812853i	$-0.697913\pi$
$587$	5.58174	−	5.58174i	0.230383	−	0.230383i	0.812853	+	0.582470i	$0.197913\pi$
$588$	−2.43109	−	4.77424i	−0.100256	−	0.196886i
$589$		−	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	0.977473	−	0.211063i	$-0.0676924\pi$
$593$	18.6633	+	18.6633i	0.766410	+	0.766410i	−0.211063	+	0.977473i	$0.567692\pi$
$594$	11.7206			0.480902
$595$	1.10332	−	12.7594i	0.0452316	−	0.523085i
$596$	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	$-0.872548\pi$
$601$		−	19.1116i		−	0.779580i	0.920904	−	0.389790i	$-0.127452\pi$
$602$	−12.1094	+	8.79565i	−0.493541	+	0.358484i
$603$	−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	−0.712417	−	0.701757i	$-0.752399\pi$
$607$	−0.262632	+	0.262632i	−0.0106599	+	0.0106599i	0.701757	+	0.712417i	$0.252399\pi$
$608$	−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	$-0.747625\pi$
$619$	−34.9217			−1.40362			−0.701811	+	0.712363i	$0.747625\pi$
$620$	8.24264	−	0.585786i	0.331032	−	0.0235257i
$621$		−	14.1480i		−	0.567741i
$622$	−16.3128	+	16.3128i	−0.654084	+	0.654084i
$623$	36.2773	−	26.3501i	1.45342	−	1.05569i
$624$		−	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
$630$	−1.23044	+	14.2296i	−0.0490220	+	0.566920i
$631$	−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
$637$	−25.0296	+	12.7453i	−0.991709	+	0.504989i
$638$	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	$0.0219430\pi$
$643$	27.0439	+	27.0439i	1.06651	+	1.06651i	0.0688814	+	0.997625i	$0.478057\pi$
$644$	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	−0.170754	−	0.985314i	$-0.554620\pi$
$647$	20.7193	−	20.7193i	0.814560	−	0.814560i	0.985314	+	0.170754i	$0.0546203\pi$
$648$	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
$658$	−7.91082	+	5.74603i	−0.308396	+	0.224004i
$659$		−	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	$0.00128909\pi$
$661$			0.208239i			0.00809958i	−0.999992	+	0.00404979i	$0.998711\pi$
$662$	0.485281	+	0.485281i	0.0188610	+	0.0188610i
$663$	−4.70099	−	4.70099i	−0.182571	−	0.182571i
$664$	−7.70806			−0.299131
$665$	−32.0321	+	26.9333i	−1.24215	+	1.04443i
$666$	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
$672$	−1.19004	−	1.63838i	−0.0459069	−	0.0632020i
$673$	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	$-0.435246\pi$
$677$	30.7394	−	30.7394i	1.18141	−	1.18141i	0.979379	−	0.202032i	$-0.0647545\pi$
$678$	−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	$0.0768057\pi$
$691$			12.5629i			0.477915i	−0.971030	+	0.238958i	$0.923194\pi$
$692$	8.56628	−	8.56628i	0.325641	−	0.325641i
$693$	−10.6173	−	14.6173i	−0.403317	−	0.555265i
$694$			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
$700$	−9.20986	−	9.49623i	−0.348100	−	0.358924i
$701$	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
$707$	−18.4281	−	25.3708i	−0.693062	−	0.954169i
$708$	−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	$-0.443633\pi$
$719$	9.44703			0.352315			0.176157	+	0.984362i	$0.443633\pi$
$720$	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	−0.270528	−	0.962712i	$-0.587198\pi$
$727$	18.6633	−	18.6633i	0.692183	−	0.692183i	0.962712	+	0.270528i	$0.0871984\pi$
$728$	−8.58946	+	6.23897i	−0.318347	+	0.231231i
$729$			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	0.897255	−	0.441513i	$-0.145558\pi$
$733$	12.3387	+	12.3387i	0.455741	+	0.455741i	−0.441513	+	0.897255i	$0.645558\pi$
$734$	−10.4525			−0.385809
$735$	−10.2633	+	6.17918i	−0.378568	+	0.227923i
$736$	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
$742$	−0.734556	+	0.533546i	−0.0269664	+	0.0195871i
$743$	−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	$-0.800475\pi$
$761$		−	32.3630i		−	1.17316i	0.809892	−	0.586579i	$-0.199525\pi$
$762$	4.90923	−	4.90923i	0.177843	−	0.177843i
$763$	−25.0989	−	34.5547i	−0.908640	−	1.25096i
$764$			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	$-0.619100\pi$
$769$	−20.2710			−0.730989			−0.365495	+	0.930813i	$0.619100\pi$
$770$	16.6710	+	1.44155i	0.600781	+	0.0519500i
$771$	−3.51472			−0.126579
$772$	−0.242641	−	0.242641i	−0.00873283	−	0.00873283i
$773$	1.49227	+	1.49227i	0.0536733	+	0.0536733i	0.733434	−	0.679761i	$-0.237916\pi$
$773$	1.49227	+	1.49227i	0.0536733	+	0.0536733i	−0.679761	+	0.733434i	$0.737916\pi$
$774$		−	13.6569i		−	0.490885i
$775$	−2.61313	−	18.2919i	−0.0938663	−	0.657064i
$776$			15.6788i			0.562835i
$777$	9.11198	+	12.5449i	0.326891	+	0.450045i
$778$	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	−0.774381	−	0.632720i	$-0.781938\pi$
$787$	−3.97408	+	3.97408i	−0.141661	+	0.141661i	0.632720	+	0.774381i	$0.281938\pi$
$788$	−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	−0.880770	−	0.473545i	$-0.842974\pi$
$797$	−11.4964	+	11.4964i	−0.407225	+	0.407225i	0.473545	+	0.880770i	$0.342974\pi$
$798$	8.41838	+	11.5899i	0.298007	+	0.410280i
$799$			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
$805$	1.74011	−	20.1237i	0.0613308	−	0.709266i
$806$	−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	$0.0402496\pi$
$811$			7.18280i			0.252222i	−0.992016	+	0.126111i	$0.959750\pi$
$812$	10.3360	−	7.50756i	0.362722	−	0.263464i
$813$	−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	$-0.321011\pi$
$829$	30.7009			1.06629			0.533144	+	0.846025i	$0.321011\pi$
$830$	1.22183	+	17.1924i	0.0424102	+	0.596757i
$831$			11.0866i			0.384588i
$832$	−2.83730	+	2.83730i	−0.0983656	+	0.0983656i
$833$	6.87616	+	13.5036i	0.238245	+	0.467871i
$834$		−	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	$-0.571367\pi$
$839$	−12.8799			−0.444664			−0.222332	+	0.974971i	$0.571367\pi$
$840$	−3.46569	+	2.91403i	−0.119577	+	0.100543i
$841$	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
$847$	6.42196	−	4.66460i	0.220661	−	0.160277i
$848$	−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	0.930541	−	0.366188i	$-0.119337\pi$
$853$	16.4826	+	16.4826i	0.564353	+	0.564353i	−0.366188	+	0.930541i	$0.619337\pi$
$854$	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	$-0.428597\pi$
$857$	35.0530	−	35.0530i	1.19739	−	1.19739i	0.974946	−	0.222443i	$-0.0714031\pi$
$858$	6.14214	−	6.14214i	0.209689	−	0.209689i
$859$	−45.9313			−1.56716			−0.783579	−	0.621293i	$-0.786608\pi$
$859$	−45.9313			−1.56716			−0.783579	+	0.621293i	$0.786608\pi$
$860$	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
$868$	−7.91082	+	5.74603i	−0.268511	+	0.195033i
$869$			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
$875$	−19.7209	+	22.0473i	−0.666689	+	0.745336i
$876$	−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	$-0.936738\pi$
$881$		−	11.7206i		−	0.394877i	0.980315	−	0.197439i	$-0.0632623\pi$
$882$	−7.66844	−	15.0595i	−0.258210	−	0.507079i
$883$	−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	$0.701172\pi$
$887$	−41.6243	+	41.6243i	−1.39761	+	1.39761i	−0.806847	+	0.590760i	$0.798828\pi$
$888$	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
$903$	9.26810	−	6.73190i	0.308423	−	0.224024i
$904$			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
$910$	15.2772	+	18.1693i	0.506434	+	0.602308i
$911$	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
$917$	26.2655	+	36.1609i	0.867364	+	1.19414i
$918$	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	$-0.572564\pi$
$929$	−13.7766			−0.451996			−0.225998	+	0.974128i	$0.572564\pi$
$930$	−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	$0.556075\pi$
$937$	−35.5014	+	35.5014i	−1.15978	+	1.15978i	−0.984523	+	0.175256i	$0.943925\pi$
$938$	14.2606	+	19.6331i	0.465624	+	0.641045i
$939$		−	6.34315i		−	0.207001i
$940$	6.24264	+	5.41421i	0.203612	+	0.176592i
$941$		−	37.7975i		−	1.23216i	−0.787683	−	0.616081i	$-0.788719\pi$
$941$		−	37.7975i		−	1.23216i	0.787683	−	0.616081i	$-0.211281\pi$
$942$	0.899495	+	0.899495i	0.0293071	+	0.0293071i
$943$	−3.69552	−	3.69552i	−0.120343	−	0.120343i
$944$	3.82683			0.124553
$945$	2.11198	−	24.4243i	0.0687029	−	0.794521i
$946$	−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
$952$	3.36595	+	4.63405i	0.109091	+	0.150190i
$953$	−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	$0.181575\pi$
$971$			33.6536i			1.08000i	−0.841666	+	0.539998i	$0.818425\pi$
$972$	−10.9937	+	10.9937i	−0.352623	+	0.352623i
$973$	−10.9065	+	7.92194i	−0.349646	+	0.253966i
$974$			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
$980$	15.1909	+	3.77323i	0.485255	+	0.120531i
$981$	38.9706			1.24423
$982$	21.7990	+	21.7990i	0.695634	+	0.695634i
$983$	−11.9063	−	11.9063i	−0.379752	−	0.379752i	0.491260	−	0.871013i	$-0.336536\pi$
$983$	−11.9063	−	11.9063i	−0.379752	−	0.379752i	−0.871013	+	0.491260i	$0.836536\pi$
$984$			1.17157i			0.0373484i
$985$	8.15640	+	7.07401i	0.259885	+	0.225397i
$986$		−	10.4525i		−	0.332876i
$987$	6.05468	−	4.39782i	0.192723	−	0.139984i
$988$	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	$0.575028\pi$
$997$	−38.0760	+	38.0760i	−1.20588	+	1.20588i	−0.972349	+	0.233531i	$0.924972\pi$
$998$	−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.27.3	yes	8
3.2	odd	2		630.2.p.a.307.1		8
4.3	odd	2		560.2.bj.c.97.3		8
5.2	odd	4		350.2.g.a.293.1		8
5.3	odd	4	inner	70.2.g.a.13.4	yes	8
5.4	even	2		350.2.g.a.307.2		8
7.2	even	3		490.2.l.a.227.4		16
7.3	odd	6		490.2.l.a.117.2		16
7.4	even	3		490.2.l.a.117.1		16
7.5	odd	6		490.2.l.a.227.3		16
7.6	odd	2	inner	70.2.g.a.27.4	yes	8
15.8	even	4		630.2.p.a.433.2		8
20.3	even	4		560.2.bj.c.433.2		8
21.20	even	2		630.2.p.a.307.2		8
28.27	even	2		560.2.bj.c.97.2		8
35.3	even	12		490.2.l.a.313.4		16
35.13	even	4	inner	70.2.g.a.13.3	✓	8
35.18	odd	12		490.2.l.a.313.3		16
35.23	odd	12		490.2.l.a.423.2		16
35.27	even	4		350.2.g.a.293.2		8
35.33	even	12		490.2.l.a.423.1		16
35.34	odd	2		350.2.g.a.307.1		8
105.83	odd	4		630.2.p.a.433.1		8
140.83	odd	4		560.2.bj.c.433.3		8

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.541196 - 0.541196i) q^{3} +1.00000i q^{4} +(2.23044 - 0.158513i) q^{5} -0.765367i q^{6} +(-2.14065 + 1.55487i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +O(q^{10})\)	\(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} +(-2.14065 + 1.55487i) 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} +(-1.55487 - 2.14065i) 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} +(-4.52814 + 3.80736i) 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} +(1.19004 + 1.63838i) 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} +(3.75378 + 5.16799i) 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} +(-5.89409 - 0.509666i) 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} +(6.05468 - 4.39782i) 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} +(6.23784 - 3.17637i) 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

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