LMFDB - Embedded newform 680.2.bl.a.123.68

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(123,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.123"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$104$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			123.68
Character	$\chi$	$=$	680.123
Dual form			680.2.bl.a.387.68

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.677911 - 1.24114i) q^{2} +1.66129 q^{3} +(-1.08087 - 1.68277i) q^{4} +(-0.0270834 - 2.23590i) q^{5} +(1.12621 - 2.06190i) q^{6} -2.02798i q^{7} +(-2.82129 + 0.200753i) q^{8} -0.240104 q^{9} +(-2.79344 - 1.48213i) q^{10} +(3.80452 + 3.80452i) q^{11} +(-1.79565 - 2.79557i) q^{12} +(1.67131 - 1.67131i) q^{13} +(-2.51702 - 1.37479i) q^{14} +(-0.0449935 - 3.71449i) q^{15} +(-1.66342 + 3.63772i) q^{16} +(-2.14745 - 3.51972i) q^{17} +(-0.162769 + 0.298003i) q^{18} -0.391006 q^{19} +(-3.73324 + 2.46231i) q^{20} -3.36908i q^{21} +(7.30108 - 2.14283i) q^{22} +2.62296 q^{23} +(-4.68700 + 0.333509i) q^{24} +(-4.99853 + 0.121112i) q^{25} +(-0.941338 - 3.20734i) q^{26} -5.38276 q^{27} +(-3.41263 + 2.19200i) q^{28} +(-2.10479 + 2.10479i) q^{29} +(-4.64072 - 2.46225i) q^{30} +(0.605139 + 0.605139i) q^{31} +(3.38728 + 4.53060i) q^{32} +(6.32043 + 6.32043i) q^{33} +(-5.82426 + 0.279242i) q^{34} +(-4.53438 + 0.0549247i) q^{35} +(0.259522 + 0.404039i) q^{36} +3.34301 q^{37} +(-0.265067 + 0.485294i) q^{38} +(2.77654 - 2.77654i) q^{39} +(0.525274 + 6.30270i) q^{40} +(5.77901 + 5.77901i) q^{41} +(-4.18151 - 2.28393i) q^{42} +(1.25512 - 1.25512i) q^{43} +(2.28992 - 10.5143i) q^{44} +(0.00650283 + 0.536849i) q^{45} +(1.77813 - 3.25547i) q^{46} +(-0.349785 - 0.349785i) q^{47} +(-2.76343 + 6.04333i) q^{48} +2.88728 q^{49} +(-3.23824 + 6.28600i) q^{50} +(-3.56755 - 5.84729i) q^{51} +(-4.61891 - 1.00596i) q^{52} +(-8.03639 - 8.03639i) q^{53} +(-3.64903 + 6.68078i) q^{54} +(8.40350 - 8.60958i) q^{55} +(0.407123 + 5.72154i) q^{56} -0.649575 q^{57} +(1.18549 + 4.03920i) q^{58} +14.2763 q^{59} +(-6.20200 + 4.09061i) q^{60} +(2.23576 - 2.23576i) q^{61} +(1.16129 - 0.340834i) q^{62} +0.486927i q^{63} +(7.91940 - 1.13276i) q^{64} +(-3.78216 - 3.69163i) q^{65} +(12.1292 - 3.55987i) q^{66} +(-3.63435 + 3.63435i) q^{67} +(-3.60175 + 7.41805i) q^{68} +4.35751 q^{69} +(-3.00573 + 5.66505i) q^{70} +(2.26465 + 2.26465i) q^{71} +(0.677403 - 0.0482014i) q^{72} +5.49453 q^{73} +(2.26626 - 4.14916i) q^{74} +(-8.30403 + 0.201202i) q^{75} +(0.422628 + 0.657972i) q^{76} +(7.71551 - 7.71551i) q^{77} +(-1.56384 - 5.32834i) q^{78} +(-0.632749 - 0.632749i) q^{79} +(8.17865 + 3.62073i) q^{80} -8.22204 q^{81} +(11.0902 - 3.25493i) q^{82} +(4.30611 - 4.30611i) q^{83} +(-5.66938 + 3.64155i) q^{84} +(-7.81160 + 4.89683i) q^{85} +(-0.706927 - 2.40865i) q^{86} +(-3.49667 + 3.49667i) q^{87} +(-11.4974 - 9.96990i) q^{88} +1.44599i q^{89} +(0.670715 + 0.355865i) q^{90} +(-3.38940 - 3.38940i) q^{91} +(-2.83509 - 4.41384i) q^{92} +(1.00531 + 1.00531i) q^{93} +(-0.671257 + 0.197011i) q^{94} +(0.0105898 + 0.874251i) q^{95} +(5.62727 + 7.52665i) q^{96} +15.7512i q^{97} +(1.95732 - 3.58353i) q^{98} +(-0.913480 - 0.913480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{3} - 8 q^{6} + 192 q^{9} - 6 q^{10} - 8 q^{11} + 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} - 16 q^{24} - 32 q^{27} - 24 q^{30} - 20 q^{32} - 8 q^{33} + 4 q^{34} - 8 q^{35} - 12 q^{38} + 38 q^{40}+ \cdots - 24 q^{99}+O(q^{100}) $ 208 * q - 8 * q^3 - 8 * q^6 + 192 * q^9 - 6 * q^10 - 8 * q^11 + 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 - 16 * q^24 - 32 * q^27 - 24 * q^30 - 20 * q^32 - 8 * q^33 + 4 * q^34 - 8 * q^35 - 12 * q^38 + 38 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^44 - 16 * q^46 + 68 * q^48 - 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 - 36 * q^54 + 4 * q^56 - 32 * q^57 + 64 * q^59 - 32 * q^60 - 72 * q^62 + 32 * q^65 - 8 * q^67 - 28 * q^68 + 28 * q^70 - 56 * q^72 + 32 * q^73 - 8 * q^74 - 16 * q^75 - 10 * q^80 + 128 * q^81 + 8 * q^86 - 16 * q^88 - 118 * q^90 + 24 * q^91 - 56 * q^92 - 64 * q^94 - 48 * q^96 - 40 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.677911	−	1.24114i	0.479355	−	0.877621i
$2$	0.677911	−	1.24114i	0.479355	−	0.877621i
$3$	1.66129			0.959148			0.479574	−	0.877501i	$-0.340791\pi$
$3$	1.66129			0.959148			0.479574	+	0.877501i	$0.340791\pi$
$4$	−1.08087	−	1.68277i	−0.540437	−	0.841384i
$5$	−0.0270834	−	2.23590i	−0.0121121	−	0.999927i
$5$	−0.0270834	−	2.23590i	−0.0121121	−	0.999927i
$6$	1.12621	−	2.06190i	0.459773	−	0.841769i
$7$		−	2.02798i		−	0.766506i	−0.923643	−	0.383253i	$-0.874804\pi$
$7$		−	2.02798i		−	0.766506i	0.923643	−	0.383253i	$-0.125196\pi$
$8$	−2.82129	+	0.200753i	−0.997478	+	0.0709768i
$9$	−0.240104			−0.0800346
$10$	−2.79344	−	1.48213i	−0.883363	−	0.468690i
$11$	3.80452	+	3.80452i	1.14711	+	1.14711i	0.987119	+	0.159987i	$0.0511453\pi$
$11$	3.80452	+	3.80452i	1.14711	+	1.14711i	0.159987	+	0.987119i	$0.448855\pi$
$12$	−1.79565	−	2.79557i	−0.518359	−	0.807012i
$13$	1.67131	−	1.67131i	0.463539	−	0.463539i	−0.436275	−	0.899814i	$-0.643702\pi$
$13$	1.67131	−	1.67131i	0.463539	−	0.463539i	0.899814	+	0.436275i	$0.143702\pi$
$14$	−2.51702	−	1.37479i	−0.672702	−	0.367429i
$15$	−0.0449935	−	3.71449i	−0.0116173	−	0.959078i
$16$	−1.66342	+	3.63772i	−0.415856	+	0.909431i
$17$	−2.14745	−	3.51972i	−0.520834	−	0.853658i
$17$	−2.14745	−	3.51972i	−0.520834	−	0.853658i
$18$	−0.162769	+	0.298003i	−0.0383650	+	0.0702400i
$19$	−0.391006			−0.0897029			−0.0448514	−	0.998994i	$-0.514281\pi$
$19$	−0.391006			−0.0897029			−0.0448514	+	0.998994i	$0.514281\pi$
$20$	−3.73324	+	2.46231i	−0.834777	+	0.550588i
$21$		−	3.36908i		−	0.735193i
$22$	7.30108	−	2.14283i	1.55660	−	0.456853i
$23$	2.62296			0.546925			0.273462	−	0.961883i	$-0.411831\pi$
$23$	2.62296			0.546925			0.273462	+	0.961883i	$0.411831\pi$
$24$	−4.68700	+	0.333509i	−0.956729	+	0.0680772i
$25$	−4.99853	+	0.121112i	−0.999707	+	0.0242224i
$26$	−0.941338	−	3.20734i	−0.184612	−	0.629011i
$27$	−5.38276			−1.03591
$28$	−3.41263	+	2.19200i	−0.644926	+	0.414248i
$29$	−2.10479	+	2.10479i	−0.390849	+	0.390849i	−0.874990	−	0.484141i	$-0.839132\pi$
$29$	−2.10479	+	2.10479i	−0.390849	+	0.390849i	0.484141	+	0.874990i	$0.339132\pi$
$30$	−4.64072	−	2.46225i	−0.847276	−	0.449544i
$31$	0.605139	+	0.605139i	0.108686	+	0.108686i	0.759359	−	0.650672i	$-0.225513\pi$
$31$	0.605139	+	0.605139i	0.108686	+	0.108686i	−0.650672	+	0.759359i	$0.725513\pi$
$32$	3.38728	+	4.53060i	0.598793	+	0.800904i
$33$	6.32043	+	6.32043i	1.10025	+	1.10025i
$34$	−5.82426	+	0.279242i	−0.998853	+	0.0478896i
$35$	−4.53438	+	0.0549247i	−0.766450	+	0.00928398i
$36$	0.259522	+	0.404039i	0.0432536	+	0.0673398i
$37$	3.34301			0.549588			0.274794	−	0.961503i	$-0.411390\pi$
$37$	3.34301			0.549588			0.274794	+	0.961503i	$0.411390\pi$
$38$	−0.265067	+	0.485294i	−0.0429995	+	0.0787251i
$39$	2.77654	−	2.77654i	0.444603	−	0.444603i
$40$	0.525274	+	6.30270i	0.0830531	+	0.996545i
$41$	5.77901	+	5.77901i	0.902530	+	0.902530i	0.995655	−	0.0931242i	$-0.0296854\pi$
$41$	5.77901	+	5.77901i	0.902530	+	0.902530i	−0.0931242	+	0.995655i	$0.529685\pi$
$42$	−4.18151	−	2.28393i	−0.645221	−	0.352419i
$43$	1.25512	−	1.25512i	0.191405	−	0.191405i	−0.604898	−	0.796303i	$-0.706786\pi$
$43$	1.25512	−	1.25512i	0.191405	−	0.191405i	0.796303	+	0.604898i	$0.206786\pi$
$44$	2.28992	−	10.5143i	0.345219	−	1.58510i
$45$	0.00650283	+	0.536849i	0.000969384	+	0.0800287i
$46$	1.77813	−	3.25547i	0.262171	−	0.479993i
$47$	−0.349785	−	0.349785i	−0.0510214	−	0.0510214i	0.681136	−	0.732157i	$-0.261486\pi$
$47$	−0.349785	−	0.349785i	−0.0510214	−	0.0510214i	−0.732157	+	0.681136i	$0.761486\pi$
$48$	−2.76343	+	6.04333i	−0.398867	+	0.872279i
$49$	2.88728			0.412468
$50$	−3.23824	+	6.28600i	−0.457957	+	0.888975i
$51$	−3.56755	−	5.84729i	−0.499557	−	0.818784i
$52$	−4.61891	−	1.00596i	−0.640528	−	0.139501i
$53$	−8.03639	−	8.03639i	−1.10388	−	1.10388i	−0.993938	−	0.109945i	$-0.964932\pi$
$53$	−8.03639	−	8.03639i	−1.10388	−	1.10388i	−0.109945	−	0.993938i	$-0.535068\pi$
$54$	−3.64903	+	6.68078i	−0.496571	+	0.909139i
$55$	8.40350	−	8.60958i	1.13313	−	1.16092i
$56$	0.407123	+	5.72154i	0.0544041	+	0.764573i
$57$	−0.649575			−0.0860383
$58$	1.18549	+	4.03920i	0.155662	+	0.530373i
$59$	14.2763			1.85862			0.929308	−	0.369305i	$-0.120404\pi$
$59$	14.2763			1.85862			0.929308	+	0.369305i	$0.120404\pi$
$60$	−6.20200	+	4.09061i	−0.800675	+	0.528096i
$61$	2.23576	−	2.23576i	0.286260	−	0.286260i	−0.549339	−	0.835599i	$-0.685121\pi$
$61$	2.23576	−	2.23576i	0.286260	−	0.286260i	0.835599	+	0.549339i	$0.185121\pi$
$62$	1.16129	−	0.340834i	0.147485	−	0.0432860i
$63$			0.486927i			0.0613470i
$64$	7.91940	−	1.13276i	0.989925	−	0.141596i
$65$	−3.78216	−	3.69163i	−0.469119	−	0.457891i
$66$	12.1292	−	3.55987i	1.49301	−	0.438190i
$67$	−3.63435	+	3.63435i	−0.444007	+	0.444007i	−0.893356	−	0.449349i	$-0.851656\pi$
$67$	−3.63435	+	3.63435i	−0.444007	+	0.444007i	0.449349	+	0.893356i	$0.351656\pi$
$68$	−3.60175	+	7.41805i	−0.436776	+	0.899570i
$69$	4.35751			0.524582
$70$	−3.00573	+	5.66505i	−0.359254	+	0.677103i
$71$	2.26465	+	2.26465i	0.268764	+	0.268764i	0.828602	−	0.559838i	$-0.189137\pi$
$71$	2.26465	+	2.26465i	0.268764	+	0.268764i	−0.559838	+	0.828602i	$0.689137\pi$
$72$	0.677403	−	0.0482014i	0.0798327	−	0.00568059i
$73$	5.49453			0.643086			0.321543	−	0.946895i	$-0.395799\pi$
$73$	5.49453			0.643086			0.321543	+	0.946895i	$0.395799\pi$
$74$	2.26626	−	4.14916i	0.263448	−	0.482330i
$75$	−8.30403	+	0.201202i	−0.958867	+	0.0232328i
$76$	0.422628	+	0.657972i	0.0484787	+	0.0754746i
$77$	7.71551	−	7.71551i	0.879264	−	0.879264i
$78$	−1.56384	−	5.32834i	−0.177070	−	0.603315i
$79$	−0.632749	−	0.632749i	−0.0711899	−	0.0711899i	0.670615	−	0.741805i	$-0.266030\pi$
$79$	−0.632749	−	0.632749i	−0.0711899	−	0.0711899i	−0.741805	+	0.670615i	$0.766030\pi$
$80$	8.17865	+	3.62073i	0.914401	+	0.404810i
$81$	−8.22204			−0.913560
$82$	11.0902	−	3.25493i	1.22471	−	0.359447i
$83$	4.30611	−	4.30611i	0.472657	−	0.472657i	−0.430116	−	0.902773i	$-0.641527\pi$
$83$	4.30611	−	4.30611i	0.472657	−	0.472657i	0.902773	+	0.430116i	$0.141527\pi$
$84$	−5.66938	+	3.64155i	−0.618580	+	0.397326i
$85$	−7.81160	+	4.89683i	−0.847287	+	0.531136i
$86$	−0.706927	−	2.40865i	−0.0762298	−	0.259731i
$87$	−3.49667	+	3.49667i	−0.374883	+	0.374883i
$88$	−11.4974	−	9.96990i	−1.22563	−	1.06280i
$89$			1.44599i			0.153275i	0.997059	+	0.0766373i	$0.0244183\pi$
$89$			1.44599i			0.153275i	−0.997059	+	0.0766373i	$0.975582\pi$
$90$	0.670715	+	0.355865i	0.0706995	+	0.0375114i
$91$	−3.38940	−	3.38940i	−0.355305	−	0.355305i
$92$	−2.83509	−	4.41384i	−0.295578	−	0.460174i
$93$	1.00531	+	1.00531i	0.104246	+	0.104246i
$94$	−0.671257	+	0.197011i	−0.0692349	+	0.0203201i
$95$	0.0105898	+	0.874251i	0.00108649	+	0.0896963i
$96$	5.62727	+	7.52665i	0.574331	+	0.768186i
$97$			15.7512i			1.59930i	0.600468	+	0.799649i	$0.294981\pi$
$97$			15.7512i			1.59930i	−0.600468	+	0.799649i	$0.705019\pi$
$98$	1.95732	−	3.58353i	0.197719	−	0.361991i
$99$	−0.913480	−	0.913480i	−0.0918082	−	0.0918082i
$100$	5.60659	+	8.28047i	0.560659	+	0.828047i
$101$			9.19554i			0.914990i	0.889212	+	0.457495i	$0.151253\pi$
$101$			9.19554i			0.914990i	−0.889212	+	0.457495i	$0.848747\pi$
$102$	−9.67581	+	0.463902i	−0.958048	+	0.0459332i
$103$	5.23005	−	5.23005i	0.515332	−	0.515332i	−0.400823	−	0.916155i	$-0.631276\pi$
$103$	5.23005	−	5.23005i	0.515332	−	0.515332i	0.916155	+	0.400823i	$0.131276\pi$
$104$	−4.37975	+	5.05079i	−0.429469	+	0.495270i
$105$	−7.53294	+	0.0912461i	−0.735139	+	0.00890471i
$106$	−15.4223	+	4.52636i	−1.49794	+	0.439639i
$107$		−	1.16905i		−	0.113016i	−0.998402	−	0.0565081i	$-0.982003\pi$
$107$		−	1.16905i		−	0.113016i	0.998402	−	0.0565081i	$-0.0179967\pi$
$108$	5.81809	+	9.05795i	0.559846	+	0.871601i
$109$	8.15324	+	8.15324i	0.780939	+	0.780939i	0.979989	−	0.199051i	$-0.0637858\pi$
$109$	8.15324	+	8.15324i	0.780939	+	0.780939i	−0.199051	+	0.979989i	$0.563786\pi$
$110$	−4.98890	−	16.2665i	−0.475673	−	1.55095i
$111$	5.55373			0.527136
$112$	7.37725	+	3.37340i	0.697084	+	0.318756i
$113$			8.12775i			0.764595i	0.924039	+	0.382297i	$0.124867\pi$
$113$			8.12775i			0.764595i	−0.924039	+	0.382297i	$0.875133\pi$
$114$	−0.440354	+	0.806216i	−0.0412429	+	0.0755091i
$115$	−0.0710387	−	5.86469i	−0.00662439	−	0.546885i
$116$	5.81688	+	1.26686i	0.540084	+	0.117625i
$117$	−0.401289	+	0.401289i	−0.0370991	+	0.0370991i
$118$	9.67806	−	17.7189i	0.890938	−	1.63116i
$119$	−7.13794	+	4.35500i	−0.654334	+	0.399223i
$120$	0.872634	+	10.4706i	0.0796602	+	0.955835i
$121$			17.9488i			1.63171i
$122$	−1.25925	−	4.29055i	−0.114007	−	0.388448i
$123$	9.60064	+	9.60064i	0.865660	+	0.865660i
$124$	0.364230	−	1.67239i	0.0327088	−	0.150185i
$125$	0.406172	+	11.1730i	0.0363291	+	0.999340i
$126$	0.604346	+	0.330093i	0.0538394	+	0.0294070i
$127$	−11.9192	+	11.9192i	−1.05766	+	1.05766i	−0.0594222	+	0.998233i	$0.518926\pi$
$127$	−11.9192	+	11.9192i	−1.05766	+	1.05766i	−0.998233	+	0.0594222i	$0.981074\pi$
$128$	3.96272	−	10.5970i	0.350258	−	0.936653i
$129$	2.08513	−	2.08513i	0.183585	−	0.183585i
$130$	−7.14581	+	2.19161i	−0.626729	+	0.192217i
$131$	8.92454	−	8.92454i	0.779740	−	0.779740i	−0.200046	−	0.979786i	$-0.564109\pi$
$131$	8.92454	−	8.92454i	0.779740	−	0.779740i	0.979786	+	0.200046i	$0.0641092\pi$
$132$	3.80423	−	17.4674i	0.331116	−	1.52034i
$133$			0.792954i			0.0687578i
$134$	2.04699	+	6.97452i	0.176833	+	0.602507i
$135$	0.145784	+	12.0353i	0.0125471	+	1.03584i
$136$	6.76519	+	9.49906i	0.580110	+	0.814538i
$137$	10.6505	−	10.6505i	0.909932	−	0.909932i	−0.0863342	−	0.996266i	$-0.527515\pi$
$137$	10.6505	−	10.6505i	0.909932	−	0.909932i	0.996266	+	0.0863342i	$0.0275153\pi$
$138$	2.95400	−	5.40829i	0.251461	−	0.460384i
$139$	−10.5860	−	10.5860i	−0.897894	−	0.897894i	0.0973558	−	0.995250i	$-0.468962\pi$
$139$	−10.5860	−	10.5860i	−0.897894	−	0.897894i	−0.995250	+	0.0973558i	$0.968962\pi$
$140$	4.99352	+	7.57095i	0.422029	+	0.639862i
$141$	−0.581096	−	0.581096i	−0.0489371	−	0.0489371i
$142$	4.34598	−	1.27552i	0.364706	−	0.107039i
$143$	12.7171			1.06346
$144$	0.399394	−	0.873431i	0.0332828	−	0.0727859i
$145$	4.76311	+	4.64910i	0.395555	+	0.386087i
$146$	3.72480	−	6.81950i	0.308267	−	0.564386i
$147$	4.79662			0.395618
$148$	−3.61338	−	5.62552i	−0.297018	−	0.462415i
$149$	−10.3389			−0.846995			−0.423498	−	0.905897i	$-0.639198\pi$
$149$	−10.3389			−0.846995			−0.423498	+	0.905897i	$0.639198\pi$
$150$	−5.37967	+	10.4429i	−0.439248	+	0.852658i
$151$	−20.2404			−1.64714			−0.823570	−	0.567214i	$-0.808021\pi$
$151$	−20.2404			−1.64714			−0.823570	+	0.567214i	$0.808021\pi$
$152$	1.10314	−	0.0784954i	0.0894766	−	0.00636682i
$153$	0.515612	+	0.845098i	0.0416847	+	0.0683221i
$154$	−4.34563	−	14.8065i	−0.350181	−	1.19314i
$155$	1.33664	−	1.36942i	0.107362	−	0.109995i
$156$	−7.67337	−	1.67119i	−0.614361	−	0.133802i
$157$	−16.9071	−	16.9071i	−1.34933	−	1.34933i	−0.886385	−	0.462949i	$-0.846791\pi$
$157$	−16.9071	−	16.9071i	−1.34933	−	1.34933i	−0.462949	−	0.886385i	$-0.653209\pi$
$158$	−1.21428	+	0.356385i	−0.0966030	+	0.0283525i
$159$	−13.3508	−	13.3508i	−1.05879	−	1.05879i
$160$	10.0382	−	7.69634i	0.793593	−	0.608449i
$161$		−	5.31932i		−	0.419221i
$162$	−5.57381	+	10.2047i	−0.437920	+	0.801759i
$163$		−	13.1876i		−	1.03293i	−0.856308	−	0.516466i	$-0.827247\pi$
$163$		−	13.1876i		−	1.03293i	0.856308	−	0.516466i	$-0.172753\pi$
$164$	3.47836	−	15.9711i	0.271614	−	1.24714i
$165$	13.9607	−	14.3030i	1.08684	−	1.11349i
$166$	−2.42534	−	8.26366i	−0.188243	−	0.641385i
$167$	19.7352			1.52716			0.763578	−	0.645715i	$-0.223441\pi$
$167$	19.7352			1.52716			0.763578	+	0.645715i	$0.223441\pi$
$168$	0.676351	+	9.50516i	0.0521816	+	0.733339i
$169$			7.41342i			0.570263i
$170$	0.782098	+	13.0149i	0.0599842	+	0.998199i
$171$	0.0938819			0.00717933
$172$	−3.46871	−	0.755452i	−0.264487	−	0.0576027i
$173$			9.28097i			0.705619i	0.935695	+	0.352810i	$0.114774\pi$
$173$			9.28097i			0.705619i	−0.935695	+	0.352810i	$0.885226\pi$
$174$	1.96944	+	6.71030i	0.149303	+	0.508707i
$175$	0.245613	+	10.1369i	0.0185666	+	0.766281i
$176$	−20.1683	+	7.51127i	−1.52024	+	0.566183i
$177$	23.7171			1.78269
$178$	1.79468	+	0.980251i	0.134517	+	0.0734729i
$179$	13.7415			1.02709			0.513544	−	0.858063i	$-0.328332\pi$
$179$	13.7415			1.02709			0.513544	+	0.858063i	$0.328332\pi$
$180$	0.896364	−	0.591209i	0.0668110	−	0.0440661i
$181$	−14.5581	+	14.5581i	−1.08210	+	1.08210i	−0.0857812	+	0.996314i	$0.527339\pi$
$181$	−14.5581	+	14.5581i	−1.08210	+	1.08210i	−0.996314	+	0.0857812i	$0.972661\pi$
$182$	−6.50444	+	1.90902i	−0.482141	+	0.141506i
$183$	3.71426	−	3.71426i	0.274566	−	0.274566i
$184$	−7.40014	+	0.526566i	−0.545546	+	0.0388190i
$185$	−0.0905402	−	7.47466i	−0.00665665	−	0.549548i
$186$	1.92925	−	0.566226i	0.141460	−	0.0415177i
$187$	5.22082	−	21.5609i	0.381784	−	1.57669i
$188$	−0.210534	+	0.966682i	−0.0153548	+	0.0705025i
$189$			10.9162i			0.794034i
$190$	1.09225	+	0.579521i	0.0792401	+	0.0420429i
$191$		−	8.75406i		−	0.633421i	−0.948522	−	0.316711i	$-0.897422\pi$
$191$		−	8.75406i		−	0.633421i	0.948522	−	0.316711i	$-0.102578\pi$
$192$	13.1564	−	1.88185i	0.949484	−	0.135811i
$193$			15.8434i			1.14043i	0.821495	+	0.570216i	$0.193140\pi$
$193$			15.8434i			1.14043i	−0.821495	+	0.570216i	$0.806860\pi$
$194$	19.5496	+	10.6779i	1.40358	+	0.766631i
$195$	−6.28328	−	6.13288i	−0.449955	−	0.439185i
$196$	−3.12078	−	4.85862i	−0.222913	−	0.347044i
$197$		−	12.8813i		−	0.917752i	−0.888500	−	0.458876i	$-0.848252\pi$
$197$		−	12.8813i		−	0.917752i	0.888500	−	0.458876i	$-0.151748\pi$
$198$	−1.75302	+	0.514502i	−0.124581	+	0.0365640i
$199$	−2.10297	+	2.10297i	−0.149075	+	0.149075i	−0.777705	−	0.628630i	$-0.783616\pi$
$199$	−2.10297	+	2.10297i	−0.149075	+	0.149075i	0.628630	+	0.777705i	$0.283616\pi$
$200$	14.0780	−	1.34516i	0.995466	−	0.0951172i
$201$	−6.03772	+	6.03772i	−0.425868	+	0.425868i
$202$	11.4130	+	6.23375i	0.803014	+	0.438605i
$203$	4.26848	+	4.26848i	0.299589	+	0.299589i
$204$	−5.98357	+	12.3236i	−0.418933	+	0.862821i
$205$	12.7648	−	13.0778i	0.891533	−	0.913396i
$206$	−2.94574	−	10.0368i	−0.205239	−	0.699294i
$207$	−0.629782			−0.0437729
$208$	3.29967	+	8.85988i	0.228791	+	0.614322i
$209$	−1.48759	−	1.48759i	−0.102899	−	0.102899i
$210$	−4.99341	+	9.41131i	−0.344578	+	0.649442i
$211$	−16.3772	−	16.3772i	−1.12745	−	1.12745i	−0.990590	−	0.136862i	$-0.956298\pi$
$211$	−16.3772	−	16.3772i	−1.12745	−	1.12745i	−0.136862	−	0.990590i	$-0.543702\pi$
$212$	−4.83706	+	22.2097i	−0.332211	+	1.52537i
$213$	3.76224	+	3.76224i	0.257785	+	0.257785i
$214$	−1.45096	−	0.792511i	−0.0991855	−	0.0541750i
$215$	−2.84033	−	2.77234i	−0.193709	−	0.189072i
$216$	15.1864	−	1.08060i	1.03330	−	0.0735258i
$217$	1.22721	−	1.22721i	0.0833086	−	0.0833086i
$218$	15.6465	−	4.59217i	1.05972	−	0.311021i
$219$	9.12803			0.616815
$220$	−23.5711	−	4.83528i	−1.58916	−	0.325995i
$221$	−9.47163	−	2.29349i	−0.637131	−	0.154277i
$222$	3.76493	−	6.89297i	0.252686	−	0.462626i
$223$	11.1310	+	11.1310i	0.745386	+	0.745386i	0.973609	−	0.228223i	$-0.0732914\pi$
$223$	11.1310	+	11.1310i	0.745386	+	0.745386i	−0.228223	+	0.973609i	$0.573291\pi$
$224$	9.18798	−	6.86936i	0.613898	−	0.458978i
$225$	1.20017	−	0.0290794i	0.0800111	−	0.00193863i
$226$	10.0877	+	5.50989i	0.671024	+	0.366512i
$227$	−18.8489			−1.25104			−0.625522	−	0.780206i	$-0.715114\pi$
$227$	−18.8489			−1.25104			−0.625522	+	0.780206i	$0.715114\pi$
$228$	0.702109	+	1.09309i	0.0464983	+	0.0723913i
$229$			19.2708i			1.27345i	0.771092	+	0.636724i	$0.219711\pi$
$229$			19.2708i			1.27345i	−0.771092	+	0.636724i	$0.780289\pi$
$230$	−7.32707	−	3.88756i	−0.483133	−	0.256338i
$231$	12.8177	−	12.8177i	0.843345	−	0.843345i
$232$	5.51569	−	6.36077i	0.362122	−	0.417605i
$233$	−5.29078			−0.346611			−0.173305	−	0.984868i	$-0.555445\pi$
$233$	−5.29078			−0.346611			−0.173305	+	0.984868i	$0.555445\pi$
$234$	0.226019	+	0.770094i	0.0147753	+	0.0503427i
$235$	−0.772613	+	0.791560i	−0.0503997	+	0.0516357i
$236$	−15.4309	−	24.0237i	−1.00447	−	1.56381i
$237$	−1.05118	−	1.05118i	−0.0682817	−	0.0682817i
$238$	0.566298	+	11.8115i	0.0367076	+	0.765627i
$239$	−2.05961			−0.133225			−0.0666126	−	0.997779i	$-0.521219\pi$
$239$	−2.05961			−0.133225			−0.0666126	+	0.997779i	$0.521219\pi$
$240$	13.5871	+	6.01510i	0.877046	+	0.388273i
$241$	−5.76525	+	5.76525i	−0.371372	+	0.371372i	−0.867977	−	0.496605i	$-0.834580\pi$
$241$	−5.76525	+	5.76525i	−0.371372	+	0.371372i	0.496605	+	0.867977i	$0.334580\pi$
$242$	22.2770	+	12.1677i	1.43202	+	0.782167i
$243$	2.48907			0.159674
$244$	−6.17885	−	1.34569i	−0.395560	−	0.0861492i
$245$	−0.0781973	−	6.45568i	−0.00499584	−	0.412438i
$246$	18.4241	−	5.40739i	1.17468	−	0.344763i
$247$	−0.653493	+	0.653493i	−0.0415808	+	0.0415808i
$248$	−1.82876	−	1.58579i	−0.116126	−	0.100698i
$249$	7.15372	−	7.15372i	0.453348	−	0.453348i
$250$	14.1426	+	7.07015i	0.894456	+	0.447156i
$251$	−9.17446			−0.579087			−0.289544	−	0.957165i	$-0.593503\pi$
$251$	−9.17446			−0.579087			−0.289544	+	0.957165i	$0.593503\pi$
$252$	0.819385	−	0.526306i	0.0516164	−	0.0331542i
$253$	9.97911	+	9.97911i	0.627381	+	0.627381i
$254$	6.71327	+	22.8735i	0.421228	+	1.43521i
$255$	−12.9774	+	8.13507i	−0.812674	+	0.509438i
$256$	−10.4661	−	12.1021i	−0.654128	−	0.756384i
$257$	15.7791	+	15.7791i	0.984276	+	0.984276i	0.999878	−	0.0156020i	$-0.00496647\pi$
$257$	15.7791	+	15.7791i	0.984276	+	0.984276i	−0.0156020	+	0.999878i	$0.504966\pi$
$258$	−1.17441	−	4.00147i	−0.0731157	−	0.249121i
$259$		−	6.77958i		−	0.421263i
$260$	−2.12412	+	10.3547i	−0.131733	+	0.642171i
$261$	0.505368	−	0.505368i	0.0312815	−	0.0312815i
$262$	−5.02659	−	17.1267i	−0.310544	−	1.05809i
$263$	16.7952	+	16.7952i	1.03564	+	1.03564i	0.999341	+	0.0362977i	$0.0115565\pi$
$263$	16.7952	+	16.7952i	1.03564	+	1.03564i	0.0362977	+	0.999341i	$0.488444\pi$
$264$	−19.1006	−	16.5629i	−1.17556	−	1.01938i
$265$	−17.7509	+	18.1862i	−1.09043	+	1.11717i
$266$	0.984169	+	0.537552i	0.0603433	+	0.0329594i
$267$			2.40221i			0.147013i
$268$	10.0440	+	2.18750i	0.613538	+	0.133623i
$269$	−3.81403	+	3.81403i	−0.232546	+	0.232546i	−0.813754	−	0.581209i	$-0.802580\pi$
$269$	−3.81403	+	3.81403i	−0.232546	+	0.232546i	0.581209	+	0.813754i	$0.302580\pi$
$270$	15.0364	+	7.97795i	0.915087	+	0.485523i
$271$			17.3406i			1.05337i	0.850061	+	0.526684i	$0.176565\pi$
$271$			17.3406i			1.05337i	−0.850061	+	0.526684i	$0.823435\pi$
$272$	16.3759	−	1.95706i	0.992934	−	0.118664i
$273$	−5.63079	−	5.63079i	−0.340791	−	0.340791i
$274$	−5.99870	−	20.4389i	−0.362395	−	1.23476i
$275$	−19.4778	−	18.5563i	−1.17456	−	1.11898i
$276$	−4.70992	−	7.33268i	−0.283504	−	0.441375i
$277$	−3.72812			−0.224001			−0.112000	−	0.993708i	$-0.535726\pi$
$277$	−3.72812			−0.224001			−0.112000	+	0.993708i	$0.535726\pi$
$278$	−20.3151	+	5.96239i	−1.21842	+	0.357600i
$279$	−0.145296	−	0.145296i	−0.00869865	−	0.00869865i
$280$	12.7818	−	1.06525i	0.763858	−	0.0636607i
$281$			10.7940i			0.643914i	0.946754	+	0.321957i	$0.104341\pi$
$281$			10.7940i			0.643914i	−0.946754	+	0.321957i	$0.895659\pi$
$282$	−1.11516	+	0.327292i	−0.0664065	+	0.0194900i
$283$		−	1.68858i		−	0.100376i	−0.998740	−	0.0501878i	$-0.984018\pi$
$283$		−	1.68858i		−	0.100376i	0.998740	−	0.0501878i	$-0.0159820\pi$
$284$	1.36308	−	6.25867i	0.0808838	−	0.371384i
$285$	0.0175927	+	1.45239i	0.00104210	+	0.0860320i
$286$	8.62106	−	15.7837i	0.509774	−	0.933312i
$287$	11.7198	−	11.7198i	0.691795	−	0.691795i
$288$	−0.813299	−	1.08781i	−0.0479241	−	0.0641000i
$289$	−7.77688	+	15.1169i	−0.457464	+	0.889228i
$290$	8.99916	−	2.76003i	0.528449	−	0.162074i
$291$			26.1674i			1.53396i
$292$	−5.93889	−	9.24602i	−0.347548	−	0.541083i
$293$	−21.4800	+	21.4800i	−1.25487	+	1.25487i	−0.301366	+	0.953508i	$0.597443\pi$
$293$	−21.4800	+	21.4800i	−1.25487	+	1.25487i	−0.953508	+	0.301366i	$0.902557\pi$
$294$	3.25168	−	5.95329i	0.189642	−	0.347203i
$295$	−0.386651	−	31.9204i	−0.0225117	−	1.85848i
$296$	−9.43162	+	0.671119i	−0.548202	+	0.0390080i
$297$	−20.4788	−	20.4788i	−1.18830	−	1.18830i
$298$	−7.00885	+	12.8321i	−0.406012	+	0.743341i
$299$	4.38379	−	4.38379i	0.253521	−	0.253521i
$300$	9.31419	+	13.7563i	0.537755	+	0.794220i
$301$	−2.54537	−	2.54537i	−0.146713	−	0.146713i
$302$	−13.7212	+	25.1212i	−0.789566	+	1.44557i
$303$			15.2765i			0.877611i
$304$	0.650408	−	1.42237i	0.0373034	−	0.0815785i
$305$	−5.05950	−	4.93840i	−0.289706	−	0.282772i
$306$	1.39843	−	0.0670470i	0.0799427	−	0.00383282i
$307$	−8.39246	+	8.39246i	−0.478983	+	0.478983i	−0.904806	−	0.425823i	$-0.859984\pi$
$307$	−8.39246	+	8.39246i	−0.478983	+	0.478983i	0.425823	+	0.904806i	$0.359984\pi$
$308$	−21.3229	−	4.64393i	−1.21499	−	0.264612i
$309$	8.68865	−	8.68865i	0.494280	−	0.494280i
$310$	−0.793524	−	2.58731i	−0.0450691	−	0.146949i
$311$	−19.8394	−	19.8394i	−1.12499	−	1.12499i	−0.990980	−	0.134006i	$-0.957216\pi$
$311$	−19.8394	−	19.8394i	−1.12499	−	1.12499i	−0.134006	−	0.990980i	$-0.542784\pi$
$312$	−7.27604	+	8.39084i	−0.411925	+	0.475038i
$313$		−	28.6023i		−	1.61670i	−0.588704	−	0.808349i	$-0.700362\pi$
$313$		−	28.6023i		−	1.61670i	0.588704	−	0.808349i	$-0.299638\pi$
$314$	−32.4457	+	9.52264i	−1.83101	+	0.537393i
$315$	1.08872	−	0.0131876i	0.0613425	−	0.000743039i
$316$	−0.380849	+	1.74869i	−0.0214244	+	0.0983717i
$317$		−	19.8739i		−	1.11623i	−0.829763	−	0.558116i	$-0.811525\pi$
$317$		−	19.8739i		−	1.11623i	0.829763	−	0.558116i	$-0.188475\pi$
$318$	−25.6209	+	7.51961i	−1.43675	+	0.421679i
$319$	−16.0154			−0.896692
$320$	−2.74724	−	17.6763i	−0.153575	−	0.988137i
$321$		−	1.94213i		−	0.108399i
$322$	−6.60204	−	3.60603i	−0.367917	−	0.200956i
$323$	0.839667	+	1.37623i	0.0467203	+	0.0765756i
$324$	8.88699	+	13.8358i	0.493722	+	0.768655i
$325$	−8.15170	+	8.55653i	−0.452175	+	0.474631i
$326$	−16.3677	−	8.94001i	−0.906523	−	0.495142i
$327$	13.5449	+	13.5449i	0.749036	+	0.749036i
$328$	−17.4644	−	15.1441i	−0.964313	−	0.836195i
$329$	−0.709360	+	0.709360i	−0.0391083	+	0.0391083i
$330$	−8.28803	−	27.0234i	−0.456241	−	1.48759i
$331$			22.2818i			1.22472i	0.790580	+	0.612359i	$0.209779\pi$
$331$			22.2818i			1.22472i	−0.790580	+	0.612359i	$0.790221\pi$
$332$	−11.9006	−	2.59183i	−0.653128	−	0.142245i
$333$	−0.802670			−0.0439860
$334$	13.3787	−	24.4942i	0.732050	−	1.34026i
$335$	8.22449	+	8.02763i	0.449352	+	0.438596i
$336$	12.2558	+	5.60420i	0.668607	+	0.305734i
$337$		−	17.4659i		−	0.951429i	−0.879600	−	0.475714i	$-0.842190\pi$
$337$		−	17.4659i		−	0.951429i	0.879600	−	0.475714i	$-0.157810\pi$
$338$	9.20112	+	5.02564i	0.500475	+	0.273359i
$339$			13.5026i			0.733360i
$340$	16.6836	+	7.85226i	0.904794	+	0.425849i
$341$			4.60453i			0.249349i
$342$	0.0636436	−	0.116521i	0.00344145	−	0.00630073i
$343$		−	20.0512i		−	1.08267i
$344$	−3.28910	+	3.79304i	−0.177337	+	0.204507i
$345$	−0.118016	−	9.74296i	−0.00635377	−	0.524544i
$346$	11.5190	+	6.29167i	0.619266	+	0.338242i
$347$	4.81572			0.258521			0.129261	−	0.991611i	$-0.458740\pi$
$347$	4.81572			0.258521			0.129261	+	0.991611i	$0.458740\pi$
$348$	9.66355	+	2.10463i	0.518021	+	0.112820i
$349$		−	33.3515i		−	1.78526i	−0.450788	−	0.892631i	$-0.648857\pi$
$349$		−	33.3515i		−	1.78526i	0.450788	−	0.892631i	$-0.351143\pi$
$350$	12.7479	+	6.56711i	0.681405	+	0.351027i
$351$	−8.99629	+	8.99629i	−0.480186	+	0.480186i
$352$	−4.34976	+	30.1237i	−0.231843	+	1.60560i
$353$	−7.01055	−	7.01055i	−0.373134	−	0.373134i	0.495484	−	0.868617i	$-0.334991\pi$
$353$	−7.01055	−	7.01055i	−0.373134	−	0.373134i	−0.868617	+	0.495484i	$0.834991\pi$
$354$	16.0781	−	29.4364i	0.854541	−	1.56452i
$355$	5.00220	−	5.12486i	0.265489	−	0.272000i
$356$	2.43327	−	1.56293i	0.128963	−	0.0828352i
$357$	−11.8582	+	7.23494i	−0.627603	+	0.382914i
$358$	9.31551	−	17.0552i	0.492340	−	0.901394i
$359$		−	34.9508i		−	1.84463i	−0.386436	−	0.922316i	$-0.626294\pi$
$359$		−	34.9508i		−	1.84463i	0.386436	−	0.922316i	$-0.373706\pi$
$360$	−0.126120	−	1.51330i	−0.00664712	−	0.0797581i
$361$	−18.8471			−0.991953
$362$	8.19960	+	27.9378i	0.430961	+	1.46838i
$363$			29.8182i			1.56505i
$364$	−2.04006	+	9.36709i	−0.106928	+	0.490969i
$365$	−0.148811	−	12.2852i	−0.00778910	−	0.643039i
$366$	−2.09199	−	7.12786i	−0.109350	−	0.372579i
$367$			34.8185i			1.81751i	0.417330	+	0.908755i	$0.362966\pi$
$367$			34.8185i			1.81751i	−0.417330	+	0.908755i	$0.637034\pi$
$368$	−4.36309	+	9.54160i	−0.227442	+	0.497390i
$369$	−1.38756	−	1.38756i	−0.0722336	−	0.0722336i
$370$	−9.33850	−	4.95478i	−0.485486	−	0.257587i
$371$	−16.2977	+	16.2977i	−0.846133	+	0.846133i
$372$	0.605093	−	2.77833i	0.0313726	−	0.144050i
$373$	−18.8892	+	18.8892i	−0.978047	+	0.978047i	−0.999764	−	0.0217171i	$-0.993087\pi$
$373$	−18.8892	+	18.8892i	−0.978047	+	0.978047i	0.0217171	+	0.999764i	$0.493087\pi$
$374$	−23.2209	−	21.0961i	−1.20072	−	1.09086i
$375$	0.674770	+	18.5616i	0.0348450	+	0.958515i
$376$	1.05707	+	0.916627i	0.0545141	+	0.0472714i
$377$			7.03552i			0.362348i
$378$	13.5485	+	7.40018i	0.696861	+	0.380624i
$379$	−17.0957	−	17.0957i	−0.878145	−	0.878145i	0.115197	−	0.993343i	$-0.463250\pi$
$379$	−17.0957	−	17.0957i	−0.878145	−	0.878145i	−0.993343	+	0.115197i	$0.963250\pi$
$380$	1.45972	−	0.962776i	0.0748819	−	0.0493893i
$381$	−19.8012	+	19.8012i	−1.01445	+	1.01445i
$382$	−10.8650	−	5.93447i	−0.555904	−	0.303634i
$383$	−4.65399	−	4.65399i	−0.237808	−	0.237808i	0.578134	−	0.815942i	$-0.303781\pi$
$383$	−4.65399	−	4.65399i	−0.237808	−	0.237808i	−0.815942	+	0.578134i	$0.803781\pi$
$384$	6.58324	−	17.6048i	0.335950	−	0.898389i
$385$	−17.4601	−	17.0422i	−0.889849	−	0.868550i
$386$	19.6639	+	10.7404i	1.00087	+	0.546672i
$387$	−0.301360	+	0.301360i	−0.0153190	+	0.0153190i
$388$	26.5057	−	17.0251i	1.34562	−	0.864319i
$389$			24.1708i			1.22551i	0.790275	+	0.612753i	$0.209938\pi$
$389$			24.1708i			1.22551i	−0.790275	+	0.612753i	$0.790062\pi$
$390$	−11.8713	+	3.64090i	−0.601126	+	0.184364i
$391$	−5.63269	−	9.23209i	−0.284857	−	0.466887i
$392$	−8.14586	+	0.579628i	−0.411428	+	0.0292757i
$393$	14.8263	−	14.8263i	0.747887	−	0.747887i
$394$	−15.9875	−	8.73234i	−0.805438	−	0.439929i
$395$	−1.39763	+	1.43190i	−0.0703224	+	0.0720469i
$396$	−0.549819	+	2.52453i	−0.0276294	+	0.126862i
$397$		−	35.1264i		−	1.76294i	−0.472239	−	0.881471i	$-0.656554\pi$
$397$		−	35.1264i		−	1.76294i	0.472239	−	0.881471i	$-0.343446\pi$
$398$	1.18446	+	4.03571i	0.0593716	+	0.202292i
$399$			1.31733i			0.0659489i
$400$	7.87410	−	18.3847i	0.393705	−	0.919237i
$401$	0.129883	+	0.129883i	0.00648603	+	0.00648603i	0.710342	−	0.703856i	$-0.248540\pi$
$401$	0.129883	+	0.129883i	0.00648603	+	0.00648603i	−0.703856	+	0.710342i	$0.748540\pi$
$402$	3.40064	+	11.5867i	0.169609	+	0.577893i
$403$	2.02275			0.100761
$404$	15.4740	−	9.93922i	0.769858	−	0.494494i
$405$	0.222681	+	18.3837i	0.0110651	+	0.913493i
$406$	8.19144	−	2.40415i	0.406534	−	0.119316i
$407$	12.7186	+	12.7186i	0.630436	+	0.630436i
$408$	11.2390	+	15.7807i	0.556412	+	0.781263i
$409$		−	3.44732i		−	0.170459i	−0.996361	−	0.0852294i	$-0.972838\pi$
$409$		−	3.44732i		−	0.170459i	0.996361	−	0.0852294i	$-0.0271623\pi$
$410$	−7.57807	−	24.7086i	−0.374254	−	1.22027i
$411$	17.6936	−	17.6936i	0.872760	−	0.872760i
$412$	−14.4540	−	3.14794i	−0.712097	−	0.155088i
$413$		−	28.9521i		−	1.42464i
$414$	−0.426936	+	0.781650i	−0.0209828	+	0.0384160i
$415$	−9.74468	−	9.51143i	−0.478347	−	0.466898i
$416$	13.2333	+	1.91084i	0.648814	+	0.0936864i
$417$	−17.5865	−	17.5865i	−0.861213	−	0.861213i
$418$	−2.85476	+	0.837859i	−0.139631	+	0.0409810i
$419$	−7.11796	+	7.11796i	−0.347735	+	0.347735i	−0.859265	−	0.511530i	$-0.829079\pi$
$419$	−7.11796	+	7.11796i	−0.347735	+	0.347735i	0.511530	+	0.859265i	$0.329079\pi$
$420$	8.29570	+	12.5776i	0.404789	+	0.613722i
$421$			9.88208i			0.481623i	0.970572	+	0.240812i	$0.0774136\pi$
$421$			9.88208i			0.481623i	−0.970572	+	0.240812i	$0.922586\pi$
$422$	−31.4287	+	9.22417i	−1.52993	+	0.449026i
$423$	0.0839848	+	0.0839848i	0.00408348	+	0.00408348i
$424$	24.2863	+	21.0597i	1.17945	+	1.02275i
$425$	11.1604	+	17.3334i	0.541359	+	0.840792i
$426$	7.21994	−	2.11902i	0.349807	−	0.102667i
$427$	−4.53409	−	4.53409i	−0.219420	−	0.219420i
$428$	−1.96724	+	1.26360i	−0.0950902	+	0.0610782i
$429$	21.1268			1.02001
$430$	−5.36636	+	1.64585i	−0.258789	+	0.0793701i
$431$	5.70212	−	5.70212i	0.274662	−	0.274662i	−0.556312	−	0.830974i	$-0.687784\pi$
$431$	5.70212	−	5.70212i	0.274662	−	0.274662i	0.830974	+	0.556312i	$0.187784\pi$
$432$	8.95381	−	19.5810i	0.430790	−	0.942091i
$433$	1.92567	−	1.92567i	0.0925418	−	0.0925418i	−0.659320	−	0.751862i	$-0.729156\pi$
$433$	1.92567	−	1.92567i	0.0925418	−	0.0925418i	0.751862	+	0.659320i	$0.229156\pi$
$434$	−0.691206	−	2.35509i	−0.0331790	−	0.113048i
$435$	7.91292	+	7.72352i	0.379396	+	0.370314i
$436$	4.90739	−	22.5326i	0.235021	−	1.07912i
$437$	−1.02559			−0.0490607
$438$	6.18799	−	11.3292i	0.295673	−	0.541330i
$439$	−3.40492	+	3.40492i	−0.162508	+	0.162508i	−0.783677	−	0.621169i	$-0.786658\pi$
$439$	−3.40492	+	3.40492i	−0.162508	+	0.162508i	0.621169	+	0.783677i	$0.286658\pi$
$440$	−21.9804	+	25.9772i	−1.04787	+	1.23841i
$441$	−0.693246			−0.0330117
$442$	−9.26747	+	10.2009i	−0.440808	+	0.485206i
$443$	11.7307	+	11.7307i	0.557345	+	0.557345i	0.928551	−	0.371206i	$-0.121056\pi$
$443$	11.7307	+	11.7307i	0.557345	+	0.557345i	−0.371206	+	0.928551i	$0.621056\pi$
$444$	−6.00288	−	9.34564i	−0.284884	−	0.443524i
$445$	3.23309	−	0.0391623i	0.153263	−	0.00185647i
$446$	21.3610	−	6.26934i	1.01147	−	0.296862i
$447$	−17.1759			−0.812394
$448$	−2.29723	−	16.0604i	−0.108534	−	0.758783i
$449$	4.89774	−	4.89774i	0.231139	−	0.231139i	−0.582029	−	0.813168i	$-0.697741\pi$
$449$	4.89774	−	4.89774i	0.231139	−	0.231139i	0.813168	+	0.582029i	$0.197741\pi$
$450$	0.777514	−	1.50929i	0.0366524	−	0.0711487i
$451$			43.9728i			2.07060i
$452$	13.6771	−	8.78508i	0.643318	−	0.413215i
$453$	−33.6253			−1.57985
$454$	−12.7779	+	23.3942i	−0.599695	+	1.09794i
$455$	−7.48657	+	7.67017i	−0.350976	+	0.359583i
$456$	1.83264	−	0.130404i	0.0858214	−	0.00610672i
$457$	−18.8779	−	18.8779i	−0.883073	−	0.883073i	0.110773	−	0.993846i	$-0.464667\pi$
$457$	−18.8779	−	18.8779i	−0.883073	−	0.883073i	−0.993846	+	0.110773i	$0.964667\pi$
$458$	23.9178	+	13.0639i	1.11760	+	0.610434i
$459$	11.5592	+	18.9458i	0.539539	+	0.884316i
$460$	−9.79213	+	6.45853i	−0.456560	+	0.301130i
$461$	37.7181			1.75671			0.878355	−	0.478009i	$-0.158642\pi$
$461$	37.7181			1.75671			0.878355	+	0.478009i	$0.158642\pi$
$462$	−7.21936	−	24.5979i	−0.335875	−	1.14440i
$463$	−11.9943	+	11.9943i	−0.557421	+	0.557421i	−0.928573	−	0.371151i	$-0.878963\pi$
$463$	−11.9943	+	11.9943i	−0.557421	+	0.557421i	0.371151	+	0.928573i	$0.378963\pi$
$464$	−4.15548	−	11.1578i	−0.192914	−	0.517987i
$465$	2.22056	−	2.27501i	0.102976	−	0.105501i
$466$	−3.58668	+	6.56662i	−0.166150	+	0.304193i
$467$	3.79544	+	3.79544i	0.175632	+	0.175632i	0.789449	−	0.613817i	$-0.210367\pi$
$467$	3.79544	+	3.79544i	0.175632	+	0.175632i	−0.613817	+	0.789449i	$0.710367\pi$
$468$	1.10902	+	0.241534i	0.0512644	+	0.0111649i
$469$	7.37041	+	7.37041i	0.340334	+	0.340334i
$470$	0.458677	+	1.49553i	0.0211572	+	0.0689837i
$471$	−28.0877	−	28.0877i	−1.29421	−	1.29421i
$472$	−40.2776	+	2.86600i	−1.85393	+	0.131919i
$473$	9.55029			0.439123
$474$	−2.01728	+	0.592060i	−0.0926566	+	0.0271942i
$475$	1.95445	−	0.0473554i	0.0896765	−	0.00217282i
$476$	15.0437	+	7.30430i	0.689526	+	0.334792i
$477$	1.92957	+	1.92957i	0.0883488	+	0.0883488i
$478$	−1.39623	+	2.55627i	−0.0638622	+	0.116921i
$479$	−26.2920	+	26.2920i	−1.20131	+	1.20131i	−0.227543	+	0.973768i	$0.573069\pi$
$479$	−26.2920	+	26.2920i	−1.20131	+	1.20131i	−0.973768	+	0.227543i	$0.926931\pi$
$480$	16.6765	−	12.7859i	0.761173	−	0.583593i
$481$	5.58722	−	5.58722i	0.254755	−	0.254755i
$482$	3.24718	+	11.0638i	0.147905	+	0.503943i
$483$		−	8.83696i		−	0.402095i
$484$	30.2036	−	19.4004i	1.37289	−	0.881834i
$485$	35.2183	−	0.426598i	1.59918	−	0.0193708i
$486$	1.68737	−	3.08929i	0.0765405	−	0.140133i
$487$			18.8448i			0.853938i	0.904266	+	0.426969i	$0.140419\pi$
$487$			18.8448i			0.853938i	−0.904266	+	0.426969i	$0.859581\pi$
$488$	−5.85890	+	6.75657i	−0.265220	+	0.305856i
$489$		−	21.9085i		−	0.990735i
$490$	−8.06543	−	4.27932i	−0.364359	−	0.193320i
$491$			13.6969i			0.618133i	0.951040	+	0.309067i	$0.100017\pi$
$491$			13.6969i			0.618133i	−0.951040	+	0.309067i	$0.899983\pi$
$492$	5.77858	−	26.5327i	0.260518	−	1.19619i
$493$	11.9282	+	2.88833i	0.537219	+	0.130084i
$494$	0.368069	+	1.25409i	0.0165602	+	0.0564241i
$495$	−2.01771	+	2.06719i	−0.0906894	+	0.0929134i
$496$	−3.20793	+	1.19473i	−0.144040	+	0.0536448i
$497$	4.59267	−	4.59267i	0.206009	−	0.206009i
$498$	−4.02921	−	13.7284i	−0.180553	−	0.615183i
$499$	17.6916	−	17.6916i	0.791986	−	0.791986i	−0.189831	−	0.981817i	$-0.560794\pi$
$499$	17.6916	−	17.6916i	0.791986	−	0.791986i	0.981817	+	0.189831i	$0.0607940\pi$
$500$	18.3625	−	12.7601i	0.821195	−	0.570647i
$501$	32.7860			1.46477
$502$	−6.21947	+	11.3868i	−0.277588	+	0.508219i
$503$	26.8518			1.19726			0.598631	−	0.801025i	$-0.295711\pi$
$503$	26.8518			1.19726			0.598631	+	0.801025i	$0.295711\pi$
$504$	−0.0977518	−	1.37376i	−0.00435421	−	0.0611923i
$505$	20.5603	−	0.249046i	0.914923	−	0.0110824i
$506$	19.1504	−	5.62056i	0.851341	−	0.249864i
$507$			12.3159i			0.546967i
$508$	32.9403	+	7.17409i	1.46149	+	0.318299i
$509$	−4.40293			−0.195157			−0.0975783	−	0.995228i	$-0.531110\pi$
$509$	−4.40293			−0.195157			−0.0975783	+	0.995228i	$0.531110\pi$
$510$	1.29930	+	21.6216i	0.0575338	+	0.957421i
$511$		−	11.1428i		−	0.492929i
$512$	−22.1155	+	4.78570i	−0.977378	+	0.211500i
$513$	2.10469			0.0929244
$514$	30.2810	−	8.88733i	1.33564	−	0.392003i
$515$	−11.8355	−	11.5522i	−0.521536	−	0.509053i
$516$	−5.76255	−	1.25503i	−0.253682	−	0.0552495i
$517$		−	2.66153i		−	0.117054i
$518$	−8.41443	−	4.59595i	−0.369709	−	0.201934i
$519$			15.4184i			0.676793i
$520$	11.4117	+	9.65590i	0.500436	+	0.423439i
$521$	−4.39568	−	4.39568i	−0.192578	−	0.192578i	0.604231	−	0.796809i	$-0.293480\pi$
$521$	−4.39568	−	4.39568i	−0.192578	−	0.192578i	−0.796809	+	0.604231i	$0.793480\pi$
$522$	−0.284640	−	0.969828i	−0.0124583	−	0.0424482i
$523$	−23.1827	−	23.1827i	−1.01371	−	1.01371i	−0.999905	−	0.0138053i	$-0.995606\pi$
$523$	−23.1827	−	23.1827i	−1.01371	−	1.01371i	−0.0138053	−	0.999905i	$-0.504394\pi$
$524$	−24.6642	−	5.37163i	−1.07746	−	0.234661i
$525$	0.408035	+	16.8404i	0.0178081	+	0.734977i
$526$	32.2310	−	9.45963i	1.40534	−	0.412459i
$527$	0.830413	−	3.42943i	0.0361733	−	0.149388i
$528$	−33.5055	+	12.4784i	−1.45814	+	0.543053i
$529$	−16.1201			−0.700873
$530$	10.5382	+	34.3601i	0.457750	+	1.49251i
$531$	−3.42779			−0.148754
$532$	1.33436	−	0.857083i	0.0578517	−	0.0371593i
$533$	19.3171			0.836716
$534$	2.98149	+	1.62849i	0.129022	+	0.0704715i
$535$	−2.61388	+	0.0316619i	−0.113008	+	0.00136886i
$536$	9.52397	−	10.9832i	0.411373	−	0.474401i
$537$	22.8287			0.985129
$538$	2.14819	+	7.31933i	0.0926149	+	0.315559i
$539$	10.9847	+	10.9847i	0.473145	+	0.473145i
$540$	20.0951	−	13.2540i	0.864757	−	0.570362i
$541$	−21.8221	−	21.8221i	−0.938205	−	0.938205i	0.0599937	−	0.998199i	$-0.480892\pi$
$541$	−21.8221	−	21.8221i	−0.938205	−	0.938205i	−0.998199	+	0.0599937i	$0.980892\pi$
$542$	21.5222	+	11.7554i	0.924458	+	0.504938i
$543$	−24.1853	+	24.1853i	−1.03789	+	1.03789i
$544$	8.67240	−	21.6515i	0.371826	−	0.928302i
$545$	18.0090	−	18.4507i	0.771423	−	0.790340i
$546$	−10.8058	+	3.17144i	−0.462445	+	0.135725i
$547$		−	39.3646i		−	1.68311i	−0.540173	−	0.841554i	$-0.681641\pi$
$547$		−	39.3646i		−	1.68311i	0.540173	−	0.841554i	$-0.318359\pi$
$548$	−29.4341	−	6.41047i	−1.25736	−	0.273842i
$549$	−0.536815	+	0.536815i	−0.0229107	+	0.0229107i
$550$	−36.2352	+	11.5953i	−1.54507	+	0.494423i
$551$	0.822984	−	0.822984i	0.0350603	−	0.0350603i
$552$	−12.2938	+	0.874781i	−0.523259	+	0.0372331i
$553$	−1.28321	+	1.28321i	−0.0545675	+	0.0545675i
$554$	−2.52733	+	4.62713i	−0.107376	+	0.196588i
$555$	−0.150414	−	12.4176i	−0.00638471	−	0.527098i
$556$	−6.37167	+	29.2560i	−0.270219	+	1.24073i
$557$	24.6084	+	24.6084i	1.04269	+	1.04269i	0.999047	+	0.0436458i	$0.0138973\pi$
$557$	24.6084	+	24.6084i	1.04269	+	1.04269i	0.0436458	+	0.999047i	$0.486103\pi$
$558$	−0.278831	+	0.0818355i	−0.0118039	+	0.00346437i
$559$		−	4.19541i		−	0.177447i
$560$	7.34279	−	16.5862i	0.310289	−	0.700894i
$561$	8.67331	−	35.8190i	0.366188	−	1.51228i
$562$	13.3969	+	7.31734i	0.565112	+	0.308664i
$563$	1.03909	−	1.03909i	0.0437924	−	0.0437924i	−0.684871	−	0.728664i	$-0.740142\pi$
$563$	1.03909	−	1.03909i	0.0437924	−	0.0437924i	0.728664	+	0.684871i	$0.240142\pi$
$564$	−0.349759	+	1.60594i	−0.0147275	+	0.0676224i
$565$	18.1729	−	0.220127i	0.764539	−	0.00926082i
$566$	−2.09577	−	1.14471i	−0.0880918	−	0.0481156i
$567$			16.6742i			0.700249i
$568$	−6.84386	−	5.93460i	−0.287162	−	0.249010i
$569$	−2.09247			−0.0877209			−0.0438605	−	0.999038i	$-0.513966\pi$
$569$	−2.09247			−0.0877209			−0.0438605	+	0.999038i	$0.513966\pi$
$570$	1.81455	+	0.962754i	0.0760031	+	0.0403253i
$571$	2.08508	+	2.08508i	0.0872581	+	0.0872581i	0.749389	−	0.662130i	$-0.230348\pi$
$571$	2.08508	+	2.08508i	0.0872581	+	0.0872581i	−0.662130	+	0.749389i	$0.730348\pi$
$572$	−13.7456	−	21.3999i	−0.574731	−	0.894776i
$573$		−	14.5431i		−	0.607545i
$574$	−6.60095	−	22.4908i	−0.275518	−	0.938750i
$575$	−13.1110	+	0.317671i	−0.546764	+	0.0132478i
$576$	−1.90148	+	0.271981i	−0.0792282	+	0.0113325i
$577$	−30.5131	+	30.5131i	−1.27028	+	1.27028i	−0.324332	+	0.945943i	$0.605139\pi$
$577$	−30.5131	+	30.5131i	−1.27028	+	1.27028i	−0.945943	+	0.324332i	$0.894861\pi$
$578$	13.4902	+	19.9001i	0.561118	+	0.827736i
$579$			26.3205i			1.09384i
$580$	2.67504	−	13.0403i	0.111075	−	0.541469i
$581$	−8.73273	−	8.73273i	−0.362295	−	0.362295i
$582$	32.4776	+	17.7392i	1.34624	+	0.735313i
$583$		−	61.1492i		−	2.53254i
$584$	−15.5017	+	1.10304i	−0.641464	+	0.0456442i
$585$	0.908111	+	0.886374i	0.0375458	+	0.0366471i
$586$	12.0982	+	41.2213i	0.499774	+	1.70284i
$587$	28.5467	+	28.5467i	1.17825	+	1.17825i	0.980190	+	0.198059i	$0.0634638\pi$
$587$	28.5467	+	28.5467i	1.17825	+	1.17825i	0.198059	+	0.980190i	$0.436536\pi$
$588$	−5.18454	−	8.07160i	−0.213807	−	0.332867i
$589$	−0.236613	−	0.236613i	−0.00974946	−	0.00974946i
$590$	−39.8800	−	21.1593i	−1.64183	−	0.871115i
$591$		−	21.3995i		−	0.880260i
$592$	−5.56084	+	12.1610i	−0.228549	+	0.499812i
$593$	31.2705	−	31.2705i	1.28412	−	1.28412i	0.345824	−	0.938299i	$-0.387599\pi$
$593$	31.2705	−	31.2705i	1.28412	−	1.28412i	0.938299	−	0.345824i	$-0.112401\pi$
$594$	−39.3000	+	11.5344i	−1.61250	+	0.473260i
$595$	9.93069	+	15.8418i	0.407119	+	0.649451i
$596$	11.1750	+	17.3980i	0.457748	+	0.712649i
$597$	−3.49365	+	3.49365i	−0.142985	+	0.142985i
$598$	−2.46909	−	8.41273i	−0.100969	−	0.344022i
$599$	12.2541			0.500691			0.250345	−	0.968157i	$-0.419456\pi$
$599$	12.2541			0.500691			0.250345	+	0.968157i	$0.419456\pi$
$600$	23.3877	−	2.23471i	0.954800	−	0.0912315i
$601$	2.35845	+	2.35845i	0.0962031	+	0.0962031i	0.753570	−	0.657367i	$-0.228330\pi$
$601$	2.35845	+	2.35845i	0.0962031	+	0.0962031i	−0.657367	+	0.753570i	$0.728330\pi$
$602$	−4.88471	+	1.43364i	−0.199086	+	0.0584307i
$603$	0.872621	−	0.872621i	0.0355359	−	0.0355359i
$604$	21.8773	+	34.0599i	0.890176	+	1.38588i
$605$	40.1317	−	0.486114i	1.63159	−	0.0197633i
$606$	18.9603	+	10.3561i	0.770210	+	0.420687i
$607$	−10.7760			−0.437383			−0.218691	−	0.975794i	$-0.570179\pi$
$607$	−10.7760			−0.437383			−0.218691	+	0.975794i	$0.570179\pi$
$608$	−1.32445	−	1.77149i	−0.0537134	−	0.0718434i
$609$	7.09120	+	7.09120i	0.287350	+	0.287350i
$610$	−9.55915	+	2.93177i	−0.387038	+	0.118704i
$611$	−1.16920			−0.0473009
$612$	0.864794	−	1.78110i	0.0349572	−	0.0719967i
$613$	18.2214	−	18.2214i	0.735954	−	0.735954i	−0.235839	−	0.971792i	$-0.575784\pi$
$613$	18.2214	−	18.2214i	0.735954	−	0.735954i	0.971792	+	0.235839i	$0.0757837\pi$
$614$	4.72691	+	16.1056i	0.190762	+	0.649968i
$615$	21.2061	−	21.7261i	0.855112	−	0.876082i
$616$	−20.2188	+	23.3166i	−0.814639	+	0.939454i
$617$			27.5364i			1.10858i	0.832325	+	0.554288i	$0.187009\pi$
$617$			27.5364i			1.10858i	−0.832325	+	0.554288i	$0.812991\pi$
$618$	−4.89373	−	16.6740i	−0.196855	−	0.670726i
$619$	−26.4722	+	26.4722i	−1.06401	+	1.06401i	−0.0661992	+	0.997806i	$0.521087\pi$
$619$	−26.4722	+	26.4722i	−1.06401	+	1.06401i	−0.997806	+	0.0661992i	$0.978913\pi$
$620$	−3.74916	−	0.769090i	−0.150570	−	0.0308874i
$621$	−14.1188			−0.566567
$622$	−38.0728	+	11.1742i	−1.52658	+	0.448044i
$623$	2.93244			0.117486
$624$	5.48173	+	14.7189i	0.219445	+	0.589226i
$625$	24.9707	−	1.21076i	0.998827	−	0.0484305i
$626$	−35.4996	−	19.3898i	−1.41885	−	0.774973i
$627$	−2.47132	−	2.47132i	−0.0986951	−	0.0986951i
$628$	−10.1763	+	46.7252i	−0.406079	+	1.86454i
$629$	−7.17897	−	11.7665i	−0.286244	−	0.469160i
$630$	0.721688	−	1.36020i	0.0287527	−	0.0541916i
$631$	45.3466			1.80522			0.902610	−	0.430458i	$-0.141648\pi$
$631$	45.3466			1.80522			0.902610	+	0.430458i	$0.141648\pi$
$632$	1.91220	+	1.65815i	0.0760632	+	0.0659575i
$633$	−27.2073	−	27.2073i	−1.08139	−	1.08139i
$634$	−24.6664	−	13.4727i	−0.979628	−	0.535071i
$635$	26.9729	+	26.3273i	1.07039	+	1.04477i
$636$	−8.03578	+	36.8968i	−0.318639	+	1.46306i
$637$	4.82555	−	4.82555i	0.191195	−	0.191195i
$638$	−10.8570	+	19.8774i	−0.429834	+	0.786955i
$639$	−0.543750	−	0.543750i	−0.0215104	−	0.0215104i
$640$	−23.8012	−	8.57326i	−0.940827	−	0.338888i
$641$	5.90140	−	5.90140i	0.233091	−	0.233091i	−0.580891	−	0.813982i	$-0.697296\pi$
$641$	5.90140	−	5.90140i	0.233091	−	0.233091i	0.813982	+	0.580891i	$0.197296\pi$
$642$	−2.41047	−	1.31659i	−0.0951336	−	0.0519618i
$643$	−3.51517			−0.138625			−0.0693124	−	0.997595i	$-0.522081\pi$
$643$	−3.51517			−0.138625			−0.0693124	+	0.997595i	$0.522081\pi$
$644$	−8.95119	+	5.74952i	−0.352726	+	0.226563i
$645$	−4.71862	−	4.60567i	−0.185795	−	0.181348i
$646$	2.27732	−	0.109185i	0.0895999	−	0.00429583i
$647$	−15.5377	−	15.5377i	−0.610848	−	0.610848i	0.332319	−	0.943167i	$-0.392169\pi$
$647$	−15.5377	−	15.5377i	−0.610848	−	0.610848i	−0.943167	+	0.332319i	$0.892169\pi$
$648$	23.1968	−	1.65060i	0.911256	−	0.0648415i
$649$	54.3145	+	54.3145i	2.13203	+	2.13203i
$650$	5.09376	+	15.9180i	0.199794	+	0.624355i
$651$	2.03876	−	2.03876i	0.0799053	−	0.0799053i
$652$	−22.1917	+	14.2541i	−0.869093	+	0.558235i
$653$	−24.5762			−0.961743			−0.480871	−	0.876791i	$-0.659680\pi$
$653$	−24.5762			−0.961743			−0.480871	+	0.876791i	$0.659680\pi$
$654$	25.9934	−	7.62894i	1.01642	−	0.298315i
$655$	−20.1961	−	19.7127i	−0.789128	−	0.770239i
$656$	−30.6354	+	11.4095i	−1.19611	+	0.445466i
$657$	−1.31926			−0.0514691
$658$	0.399534	+	1.36130i	0.0155755	+	0.0530690i
$659$			11.8832i			0.462904i	0.972846	+	0.231452i	$0.0743477\pi$
$659$			11.8832i			0.462904i	−0.972846	+	0.231452i	$0.925652\pi$
$660$	−39.1585	−	8.03282i	−1.52424	−	0.312677i
$661$	−31.5825			−1.22842			−0.614209	−	0.789144i	$-0.710525\pi$
$661$	−31.5825			−1.22842			−0.614209	+	0.789144i	$0.710525\pi$
$662$	27.6549	+	15.1051i	1.07484	+	0.587075i
$663$	−15.7352	−	3.81016i	−0.611103	−	0.147974i
$664$	−11.2843	+	13.0133i	−0.437917	+	0.505013i
$665$	1.77297	−	0.0214759i	0.0687528	−	0.000832799i
$666$	−0.544139	+	0.996229i	−0.0210849	+	0.0386031i
$667$	−5.52078	+	5.52078i	−0.213765	+	0.213765i
$668$	−21.3313	−	33.2098i	−0.825332	−	1.28493i
$669$	18.4918	+	18.4918i	0.714936	+	0.714936i
$670$	15.5389	−	4.76576i	0.600321	−	0.184117i
$671$	17.0120			0.656741
$672$	15.2639	−	11.4120i	0.588819	−	0.440228i
$673$			8.10867i			0.312566i	0.987712	+	0.156283i	$0.0499512\pi$
$673$			8.10867i			0.312566i	−0.987712	+	0.156283i	$0.950049\pi$
$674$	−21.6777	−	11.8403i	−0.834994	−	0.456072i
$675$	26.9059	−	0.651916i	1.03561	−	0.0250923i
$676$	12.4751	−	8.01298i	0.479811	−	0.308191i
$677$	17.4897			0.672185			0.336093	−	0.941829i	$-0.390895\pi$
$677$	17.4897			0.672185			0.336093	+	0.941829i	$0.390895\pi$
$678$	16.7586	+	9.15355i	0.643612	+	0.351540i
$679$	31.9433			1.22587
$680$	21.0558	−	15.3836i	0.807452	−	0.589934i
$681$	−31.3135			−1.19994
$682$	5.71488	+	3.12146i	0.218834	+	0.119527i
$683$	−19.6076			−0.750262			−0.375131	−	0.926972i	$-0.622402\pi$
$683$	−19.6076			−0.750262			−0.375131	+	0.926972i	$0.622402\pi$
$684$	−0.101475	−	0.157982i	−0.00387998	−	0.00604058i
$685$	−24.1019	−	23.5250i	−0.920886	−	0.898844i
$686$	−24.8865	−	13.5930i	−0.950170	−	0.518982i
$687$			32.0144i			1.22143i
$688$	2.47799	+	6.65359i	0.0944725	+	0.253666i
$689$	−26.8626			−1.02339
$690$	−12.1724	−	6.45839i	−0.463396	−	0.245867i
$691$	32.2386	+	32.2386i	1.22641	+	1.22641i	0.965312	+	0.261101i	$0.0840855\pi$
$691$	32.2386	+	32.2386i	1.22641	+	1.22641i	0.261101	+	0.965312i	$0.415914\pi$
$692$	15.6177	−	10.0316i	0.593697	−	0.381343i
$693$	−1.85252	+	1.85252i	−0.0703715	+	0.0703715i
$694$	3.26463	−	5.97700i	0.123924	−	0.226884i
$695$	−23.3826	+	23.9560i	−0.886953	+	0.908703i
$696$	9.16317	−	10.5671i	0.347329	−	0.400545i
$697$	7.93035	−	32.7507i	0.300383	−	1.24052i
$698$	−41.3939	−	22.6093i	−1.56678	−	0.855775i
$699$	−8.78954			−0.332451
$700$	16.7927	−	11.3701i	0.634703	−	0.429748i
$701$		−	29.7379i		−	1.12319i	−0.827414	−	0.561593i	$-0.810189\pi$
$701$		−	29.7379i		−	1.12319i	0.827414	−	0.561593i	$-0.189811\pi$
$702$	5.06700	+	17.2644i	0.191242	+	0.651601i
$703$	−1.30714			−0.0492996
$704$	34.4391	+	25.8199i	1.29797	+	0.973124i
$705$	−1.28354	+	1.31501i	−0.0483408	+	0.0495263i
$706$	−13.4536	+	3.94857i	−0.506334	+	0.148606i
$707$	18.6484			0.701345
$708$	−25.6352	−	39.9104i	−0.963431	−	1.49993i
$709$	10.1054	−	10.1054i	0.379517	−	0.379517i	−0.491411	−	0.870928i	$-0.663519\pi$
$709$	10.1054	−	10.1054i	0.379517	−	0.379517i	0.870928	+	0.491411i	$0.163519\pi$
$710$	−2.96965	−	9.68264i	−0.111449	−	0.363383i
$711$	0.151925	+	0.151925i	0.00569765	+	0.00569765i
$712$	−0.290286	−	4.07956i	−0.0108789	−	0.152888i
$713$	1.58726	+	1.58726i	0.0594432	+	0.0594432i
$714$	0.940787	+	19.6224i	0.0352081	+	0.734350i
$715$	−0.344422	−	28.4342i	−0.0128807	−	1.06338i
$716$	−14.8528	−	23.1238i	−0.555076	−	0.864176i
$717$	−3.42162			−0.127783
$718$	−43.3790	−	23.6935i	−1.61889	−	0.884234i
$719$	23.6636	−	23.6636i	0.882502	−	0.882502i	−0.111287	−	0.993788i	$-0.535497\pi$
$719$	23.6636	−	23.6636i	0.882502	−	0.882502i	0.993788	+	0.111287i	$0.0354972\pi$
$720$	−1.96372	−	0.869351i	−0.0731837	−	0.0323988i
$721$	−10.6065	−	10.6065i	−0.395005	−	0.395005i
$722$	−12.7767	+	23.3920i	−0.475498	+	0.870559i
$723$	−9.57777	+	9.57777i	−0.356201	+	0.356201i
$724$	40.2334	+	8.76245i	1.49526	+	0.325654i
$725$	10.2659	−	10.7758i	0.381267	−	0.400202i
$726$	37.0086	+	20.2141i	1.37352	+	0.750214i
$727$	15.9581	+	15.9581i	0.591853	+	0.591853i	0.938132	−	0.346278i	$-0.112555\pi$
$727$	15.9581	+	15.9581i	0.591853	+	0.591853i	−0.346278	+	0.938132i	$0.612555\pi$
$728$	10.2429	+	8.88206i	0.379628	+	0.329191i
$729$	28.8012			1.06671
$730$	−15.3486	−	8.14360i	−0.568078	−	0.301408i
$731$	−7.11300	−	1.72236i	−0.263084	−	0.0637040i
$732$	−10.2649	−	2.23559i	−0.379401	−	0.0826298i
$733$	26.9181	+	26.9181i	0.994242	+	0.994242i	0.999984	−	0.00574169i	$-0.00182765\pi$
$733$	26.9181	+	26.9181i	0.994242	+	0.994242i	−0.00574169	+	0.999984i	$0.501828\pi$
$734$	43.2147	+	23.6038i	1.59509	+	0.871233i
$735$	−0.129909	−	10.7248i	−0.00479176	−	0.395589i
$736$	8.88471	+	11.8836i	0.327495	+	0.438034i
$737$	−27.6539			−1.01865
$738$	−2.66281	+	0.781521i	−0.0980193	+	0.0287682i
$739$	19.0607			0.701158			0.350579	−	0.936533i	$-0.385985\pi$
$739$	19.0607			0.701158			0.350579	+	0.936533i	$0.385985\pi$
$740$	−12.4803	+	8.23152i	−0.458783	+	0.302597i
$741$	−1.08564	+	1.08564i	−0.0398821	+	0.0398821i
$742$	9.17938	+	31.2761i	0.336986	+	1.14818i
$743$		−	11.3135i		−	0.415053i	−0.978229	−	0.207526i	$-0.933459\pi$
$743$		−	11.3135i		−	0.415053i	0.978229	−	0.207526i	$-0.0665413\pi$
$744$	−3.03810	−	2.63447i	−0.111382	−	0.0965842i
$745$	0.280013	+	23.1168i	0.0102589	+	0.846933i
$746$	10.6390	+	36.2494i	0.389523	+	1.32719i
$747$	−1.03391	+	1.03391i	−0.0378289	+	0.0378289i
$748$	−41.9250	+	14.5192i	−1.53293	+	0.530874i
$749$	−2.37082			−0.0866277
$750$	23.4950	+	11.7456i	0.857916	+	0.428889i
$751$	23.2235	+	23.2235i	0.847438	+	0.847438i	0.989813	−	0.142375i	$-0.0454738\pi$
$751$	23.2235	+	23.2235i	0.847438	+	0.847438i	−0.142375	+	0.989813i	$0.545474\pi$
$752$	1.85426	−	0.690581i	0.0676180	−	0.0251829i
$753$	−15.2415			−0.555430
$754$	8.73209	+	4.76946i	0.318004	+	0.173693i
$755$	0.548179	+	45.2556i	0.0199503	+	1.64702i
$756$	18.3694	−	11.7990i	0.668088	−	0.429125i
$757$	−0.996139	+	0.996139i	−0.0362053	+	0.0362053i	−0.724978	−	0.688772i	$-0.758150\pi$
$757$	−0.996139	+	0.996139i	−0.0362053	+	0.0362053i	0.688772	+	0.724978i	$0.258150\pi$
$758$	−32.8075	+	9.62884i	−1.19162	+	0.349735i
$759$	16.5782	+	16.5782i	0.601751	+	0.601751i
$760$	−0.205385	−	2.46439i	−0.00745010	−	0.0893929i
$761$	28.5821			1.03610			0.518050	−	0.855351i	$-0.326658\pi$
$761$	28.5821			1.03610			0.518050	+	0.855351i	$0.326658\pi$
$762$	11.1527	+	37.9996i	0.404020	+	1.37658i
$763$	16.5346	−	16.5346i	0.598594	−	0.598594i
$764$	−14.7311	+	9.46203i	−0.532951	+	0.342324i
$765$	1.87559	−	1.17575i	0.0678122	−	0.0425092i
$766$	−8.93126	+	2.62128i	−0.322700	+	0.0947107i
$767$	23.8602	−	23.8602i	0.861541	−	0.861541i
$768$	−17.3872	−	20.1052i	−0.627406	−	0.725484i
$769$		−	22.8890i		−	0.825399i	−0.910867	−	0.412699i	$-0.864586\pi$
$769$		−	22.8890i		−	0.825399i	0.910867	−	0.412699i	$-0.135414\pi$
$770$	−32.9882	+	10.1174i	−1.18881	+	0.364606i
$771$	26.2138	+	26.2138i	0.944067	+	0.944067i
$772$	26.6607	−	17.1247i	0.959541	−	0.616331i
$773$	−16.6265	−	16.6265i	−0.598013	−	0.598013i	0.341770	−	0.939783i	$-0.388973\pi$
$773$	−16.6265	−	16.6265i	−0.598013	−	0.598013i	−0.939783	+	0.341770i	$0.888973\pi$
$774$	0.169736	+	0.578326i	0.00610102	+	0.0207875i
$775$	−3.09810	−	2.95152i	−0.111287	−	0.106022i
$776$	−3.16210	−	44.4389i	−0.113513	−	1.59526i
$777$		−	11.2629i		−	0.404053i
$778$	29.9994	+	16.3856i	1.07553	+	0.587453i
$779$	−2.25963	−	2.25963i	−0.0809596	−	0.0809596i
$780$	−3.52879	+	17.2022i	−0.126351	+	0.615937i
$781$			17.2318i			0.616602i
$782$	−15.2768	+	0.732440i	−0.546297	+	0.0261920i
$783$	11.3296	−	11.3296i	0.404886	−	0.404886i
$784$	−4.80276	+	10.5031i	−0.171527	+	0.375111i
$785$	−37.3448	+	38.2606i	−1.33289	+	1.36558i
$786$	−8.35064	−	28.4524i	−0.297858	−	1.01486i
$787$		−	38.3124i		−	1.36569i	−0.730563	−	0.682845i	$-0.760742\pi$
$787$		−	38.3124i		−	1.36569i	0.730563	−	0.682845i	$-0.239258\pi$
$788$	−21.6762	+	13.9230i	−0.772182	+	0.495987i
$789$	27.9018	+	27.9018i	0.993331	+	0.993331i
$790$	0.829730	+	2.70536i	0.0295205	+	0.0962525i
$791$	16.4830			0.586067
$792$	2.76058	+	2.39381i	0.0980929	+	0.0850604i
$793$		−	7.47332i		−	0.265385i
$794$	−43.5968	−	23.8125i	−1.54719	−	0.845075i
$795$	−29.4895	+	30.2127i	−1.04589	+	1.07153i
$796$	5.81185	+	1.26577i	0.205996	+	0.0448639i
$797$	4.40772	−	4.40772i	0.156130	−	0.156130i	−0.624720	−	0.780849i	$-0.714787\pi$
$797$	4.40772	−	4.40772i	0.156130	−	0.156130i	0.780849	+	0.624720i	$0.214787\pi$
$798$	1.63499	+	0.893031i	0.0578782	+	0.0316130i
$799$	−0.479999	+	1.98230i	−0.0169811	+	0.0701286i
$800$	−17.4802	−	22.2361i	−0.618017	−	0.786165i
$801$		−	0.347187i		−	0.0122673i
$802$	0.249252	−	0.0731542i	0.00880139	−	0.00258316i
$803$	20.9041	+	20.9041i	0.737688	+	0.737688i
$804$	16.6861	+	3.63408i	0.588474	+	0.128164i
$805$	−11.8935	+	0.144065i	−0.419191	+	0.00507764i
$806$	1.37125	−	2.51053i	0.0483001	−	0.0884296i
$807$	−6.33623	+	6.33623i	−0.223046	+	0.223046i
$808$	−1.84603	−	25.9433i	−0.0649430	−	0.912682i
$809$	−15.4970	+	15.4970i	−0.544847	+	0.544847i	−0.924946	−	0.380099i	$-0.875890\pi$
$809$	−15.4970	+	15.4970i	−0.544847	+	0.544847i	0.380099	+	0.924946i	$0.375890\pi$
$810$	22.9678	+	12.1861i	0.807005	+	0.428177i
$811$	15.0750	−	15.0750i	0.529354	−	0.529354i	−0.391026	−	0.920380i	$-0.627880\pi$
$811$	15.0750	−	15.0750i	0.529354	−	0.529354i	0.920380	+	0.391026i	$0.127880\pi$
$812$	2.56918	−	11.7966i	0.0901604	−	0.413978i
$813$			28.8079i			1.01034i
$814$	24.4076	−	7.16351i	0.855487	−	0.251081i
$815$	−29.4862	+	0.357165i	−1.03286	+	0.0125109i
$816$	27.2052	−	3.25125i	0.952371	−	0.113816i
$817$	−0.490760	+	0.490760i	−0.0171695	+	0.0171695i
$818$	−4.27861	−	2.33697i	−0.149598	−	0.0817104i
$819$	0.813807	+	0.813807i	0.0284367	+	0.0284367i
$820$	−35.8041	−	7.34472i	−1.25033	−	0.256489i
$821$	−6.89783	−	6.89783i	−0.240736	−	0.240736i	0.576419	−	0.817155i	$-0.304450\pi$
$821$	−6.89783	−	6.89783i	−0.240736	−	0.240736i	−0.817155	+	0.576419i	$0.804450\pi$
$822$	−9.96560	−	33.9549i	−0.347590	−	1.18431i
$823$	27.4990			0.958555			0.479277	−	0.877663i	$-0.340899\pi$
$823$	27.4990			0.958555			0.479277	+	0.877663i	$0.340899\pi$
$824$	−13.7056	+	15.8055i	−0.477456	+	0.550609i
$825$	−32.3583	−	30.8274i	−1.12657	−	1.07327i
$826$	−35.9337	−	19.6270i	−1.25029	−	0.682909i
$827$	−33.7721			−1.17437			−0.587185	−	0.809453i	$-0.699764\pi$
$827$	−33.7721			−1.17437			−0.587185	+	0.809453i	$0.699764\pi$
$828$	0.680715	+	1.05978i	0.0236565	+	0.0368298i
$829$	−37.6185			−1.30654			−0.653272	−	0.757123i	$-0.726604\pi$
$829$	−37.6185			−1.30654			−0.653272	+	0.757123i	$0.726604\pi$
$830$	−18.4111	+	5.64664i	−0.639058	+	0.195998i
$831$	−6.19350			−0.214850
$832$	11.3426	−	15.1290i	0.393234	−	0.524504i
$833$	−6.20030	−	10.1624i	−0.214828	−	0.352107i
$834$	−33.7494	+	9.90528i	−1.16865	+	0.342992i
$835$	−0.534497	−	44.1260i	−0.0184970	−	1.52704i
$836$	−0.895372	+	4.11117i	−0.0309671	+	0.142188i
$837$	−3.25732	−	3.25732i	−0.112589	−	0.112589i
$838$	4.00907	+	13.6598i	0.138491	+	0.471869i
$839$	−9.28426	−	9.28426i	−0.320528	−	0.320528i	0.528441	−	0.848970i	$-0.322777\pi$
$839$	−9.28426	−	9.28426i	−0.320528	−	0.320528i	−0.848970	+	0.528441i	$0.822777\pi$
$840$	21.2343	−	1.76969i	0.732653	−	0.0610600i
$841$			20.1397i			0.694473i
$842$	12.2651	+	6.69917i	0.422683	+	0.230869i
$843$			17.9319i			0.617609i
$844$	−9.85735	+	45.2607i	−0.339304	+	1.55794i
$845$	16.5757	−	0.200781i	0.570221	−	0.00690707i
$846$	0.161171	−	0.0473030i	0.00554118	−	0.00162631i
$847$	36.3998			1.25071
$848$	42.6021	−	15.8662i	1.46296	−	0.544849i
$849$		−	2.80523i		−	0.0962751i
$850$	29.0789	−	2.10119i	0.997400	−	0.0720701i
$851$	8.76859			0.300583
$852$	2.26447	−	10.3975i	0.0775796	−	0.356212i
$853$			0.850374i			0.0291162i	0.999894	+	0.0145581i	$0.00463416\pi$
$853$			0.850374i			0.0291162i	−0.999894	+	0.0145581i	$0.995366\pi$
$854$	−8.70116	+	2.55375i	−0.297748	+	0.0873874i
$855$	−0.00254264	−	0.209911i	−8.69565e−5	−	0.00717880i
$856$	0.234690	+	3.29823i	0.00802153	+	0.112731i
$857$	40.7991			1.39367			0.696836	−	0.717231i	$-0.254591\pi$
$857$	40.7991			1.39367			0.696836	+	0.717231i	$0.254591\pi$
$858$	14.3221	−	26.2214i	0.488949	−	0.895185i
$859$	−18.1487			−0.619227			−0.309614	−	0.950862i	$-0.600200\pi$
$859$	−18.1487			−0.619227			−0.309614	+	0.950862i	$0.600200\pi$
$860$	−1.59517	+	7.77617i	−0.0543950	+	0.265165i
$861$	19.4699	−	19.4699i	0.663534	−	0.663534i
$862$	−3.21162	−	10.9427i	−0.109388	−	0.372709i
$863$	−26.9558	+	26.9558i	−0.917587	+	0.917587i	−0.996853	−	0.0792669i	$-0.974742\pi$
$863$	−26.9558	+	26.9558i	−0.917587	+	0.917587i	0.0792669	+	0.996853i	$0.474742\pi$
$864$	−18.2329	−	24.3871i	−0.620297	−	0.829667i
$865$	20.7514	−	0.251360i	0.705567	−	0.00854651i
$866$	−1.08460	−	3.69547i	−0.0368562	−	0.125577i
$867$	−12.9197	+	25.1136i	−0.438775	+	0.852902i
$868$	−3.39158	−	0.738653i	−0.115118	−	0.0250715i
$869$		−	4.81462i		−	0.163325i
$870$	14.9503	−	4.58522i	0.506861	−	0.155453i
$871$			12.1483i			0.411629i
$872$	−24.6395	−	21.3659i	−0.834398	−	0.723541i
$873$		−	3.78193i		−	0.127999i
$874$	−0.695260	+	1.27291i	−0.0235175	+	0.0430567i
$875$	22.6586	−	0.823710i	0.766000	−	0.0278465i
$876$	−9.86625	−	15.3604i	−0.333350	−	0.518978i
$877$			4.54735i			0.153553i	0.997048	+	0.0767765i	$0.0244628\pi$
$877$			4.54735i			0.153553i	−0.997048	+	0.0767765i	$0.975537\pi$
$878$	1.91776	+	6.53422i	0.0647213	+	0.220519i
$879$	−35.6846	+	35.6846i	−1.20361	+	1.20361i
$880$	17.3407	+	44.8910i	0.584555	+	1.51328i
$881$	−4.90738	+	4.90738i	−0.165334	+	0.165334i	−0.784925	−	0.619591i	$-0.787298\pi$
$881$	−4.90738	+	4.90738i	−0.165334	+	0.165334i	0.619591	+	0.784925i	$0.287298\pi$
$882$	−0.469959	+	0.860418i	−0.0158243	+	0.0289718i
$883$	0.697857	+	0.697857i	0.0234848	+	0.0234848i	0.718752	−	0.695267i	$-0.244714\pi$
$883$	0.697857	+	0.697857i	0.0234848	+	0.0234848i	−0.695267	+	0.718752i	$0.744714\pi$
$884$	6.37822	+	18.4175i	0.214523	+	0.619449i
$885$	−0.642341	−	53.0292i	−0.0215920	−	1.78256i
$886$	22.5119	−	6.60714i	0.756303	−	0.221971i
$887$	25.7137			0.863381			0.431691	−	0.902022i	$-0.357917\pi$
$887$	25.7137			0.863381			0.431691	+	0.902022i	$0.357917\pi$
$888$	−15.6687	+	1.11493i	−0.525807	+	0.0374144i
$889$	24.1719	+	24.1719i	0.810699	+	0.810699i
$890$	2.14314	−	4.03928i	0.0718383	−	0.135397i
$891$	−31.2809	−	31.2809i	−1.04795	−	1.04795i
$892$	6.69969	−	30.7621i	0.224322	−	1.02999i
$893$	0.136768	+	0.136768i	0.00457677	+	0.00457677i
$894$	−11.6438	+	21.3178i	−0.389425	+	0.712974i
$895$	−0.372167	−	30.7247i	−0.0124402	−	1.02701i
$896$	−21.4906	−	8.03634i	−0.717950	−	0.268475i
$897$	7.28276	−	7.28276i	0.243164	−	0.243164i
$898$	−2.75857	−	9.39903i	−0.0920546	−	0.313650i
$899$	−2.54738			−0.0849599
$900$	−1.34616	−	1.98817i	−0.0448721	−	0.0662724i
$901$	−11.0281	+	45.5436i	−0.367398	+	1.51728i
$902$	54.5765	+	29.8096i	1.81720	+	0.992551i
$903$	−4.22861	−	4.22861i	−0.140719	−	0.140719i
$904$	−1.63167	−	22.9308i	−0.0542685	−	0.762666i
$905$	32.9448	+	32.1562i	1.09512	+	1.06891i
$906$	−22.7949	+	41.7338i	−0.757311	+	1.38651i
$907$	14.8081			0.491695			0.245848	−	0.969309i	$-0.420934\pi$
$907$	14.8081			0.491695			0.245848	+	0.969309i	$0.420934\pi$
$908$	20.3733	+	31.7183i	0.676111	+	1.05261i
$909$		−	2.20788i		−	0.0732308i
$910$	4.44455	+	14.4916i	0.147335	+	0.480392i
$911$	7.27657	−	7.27657i	0.241083	−	0.241083i	−0.576215	−	0.817298i	$-0.695471\pi$
$911$	7.27657	−	7.27657i	0.241083	−	0.241083i	0.817298	+	0.576215i	$0.195471\pi$
$912$	1.08052	−	2.36297i	0.0357795	−	0.0782459i
$913$	32.7654			1.08438
$914$	−36.2278	+	10.6327i	−1.19831	+	0.351698i
$915$	−8.40531	−	8.20412i	−0.277871	−	0.271220i
$916$	32.4282	−	20.8293i	1.07146	−	0.688218i
$917$	−18.0988	−	18.0988i	−0.597676	−	0.597676i
$918$	31.3506	−	1.50309i	1.03472	−	0.0496094i
$919$	55.9667			1.84617			0.923086	−	0.384593i	$-0.125658\pi$
$919$	55.9667			1.84617			0.923086	+	0.384593i	$0.125658\pi$
$920$	1.37777	+	16.5317i	0.0454238	+	0.545035i
$921$	−13.9423	+	13.9423i	−0.459416	+	0.459416i
$922$	25.5695	−	46.8136i	0.842088	−	1.54172i
$923$	7.56987			0.249165
$924$	−35.4236	−	7.71493i	−1.16535	−	0.253802i
$925$	−16.7102	+	0.404878i	−0.549427	+	0.0133123i
$926$	6.75557	+	23.0177i	0.222002	+	0.756408i
$927$	−1.25575	+	1.25575i	−0.0412444	+	0.0412444i
$928$	−16.6655	−	2.40643i	−0.547071	−	0.0789951i
$929$	−9.24929	+	9.24929i	−0.303459	+	0.303459i	−0.842366	−	0.538906i	$-0.818838\pi$
$929$	−9.24929	+	9.24929i	−0.303459	+	0.303459i	0.538906	+	0.842366i	$0.318838\pi$
$930$	−1.31828	−	4.29829i	−0.0432280	−	0.140946i
$931$	−1.12894			−0.0369996
$932$	5.71867	+	8.90316i	0.187321	+	0.291633i
$933$	−32.9590	−	32.9590i	−1.07903	−	1.07903i
$934$	7.28366	−	2.13772i	0.238329	−	0.0699482i
$935$	−48.3495	−	11.0893i	−1.58120	−	0.362659i
$936$	1.05159	−	1.21271i	0.0343724	−	0.0396388i
$937$	8.77168	+	8.77168i	0.286558	+	0.286558i	0.835718	−	0.549159i	$-0.185052\pi$
$937$	8.77168	+	8.77168i	0.286558	+	0.286558i	−0.549159	+	0.835718i	$0.685052\pi$
$938$	14.1442	−	4.15126i	0.461825	−	0.135543i
$939$		−	47.5168i		−	1.55065i
$940$	2.16711	+	0.444553i	0.0706833	+	0.0144997i
$941$	−41.1366	+	41.1366i	−1.34101	+	1.34101i	−0.445963	+	0.895051i	$0.647139\pi$
$941$	−41.1366	+	41.1366i	−1.34101	+	1.34101i	−0.895051	+	0.445963i	$0.852861\pi$
$942$	−53.9018	+	15.8199i	−1.75621	+	0.515440i
$943$	15.1581	+	15.1581i	0.493616	+	0.493616i
$944$	−23.7475	+	51.9332i	−0.772916	+	1.69028i
$945$	24.4075	−	0.295647i	0.793976	−	0.00961739i
$946$	6.47424	−	11.8533i	0.210496	−	0.385383i
$947$			13.7599i			0.447137i	0.974688	+	0.223569i	$0.0717707\pi$
$947$			13.7599i			0.447137i	−0.974688	+	0.223569i	$0.928229\pi$
$948$	−0.632701	+	2.90509i	−0.0205492	+	0.0943531i
$949$	9.18308	−	9.18308i	0.298095	−	0.298095i
$950$	1.26617	−	2.45786i	0.0410800	−	0.0797436i
$951$		−	33.0164i		−	1.07063i
$952$	19.2640	−	13.7197i	0.624348	−	0.444658i
$953$	2.96837	+	2.96837i	0.0961550	+	0.0961550i	0.753548	−	0.657393i	$-0.228341\pi$
$953$	2.96837	+	2.96837i	0.0961550	+	0.0961550i	−0.657393	+	0.753548i	$0.728341\pi$
$954$	3.70294	−	1.08680i	0.119887	−	0.0351863i
$955$	−19.5732	+	0.237090i	−0.633375	+	0.00767204i
$956$	2.22618	+	3.46585i	0.0719998	+	0.112094i
$957$	−26.6063			−0.860060
$958$	14.8085	+	50.4557i	0.478441	+	1.63015i
$959$	−21.5990	−	21.5990i	−0.697469	−	0.697469i
$960$	−4.56397	−	29.3656i	−0.147301	−	0.947770i
$961$		−	30.2676i		−	0.976375i
$962$	−3.14691	−	10.7222i	−0.101460	−	0.345697i
$963$			0.280693i			0.00904521i
$964$	15.9331	+	3.47007i	0.513170	+	0.111764i
$965$	35.4243	−	0.429093i	1.14035	−	0.0138130i
$966$	−10.9679	−	5.99067i	−0.352887	−	0.192747i
$967$	−4.48443	+	4.48443i	−0.144210	+	0.144210i	−0.775526	−	0.631316i	$-0.782515\pi$
$967$	−4.48443	+	4.48443i	−0.144210	+	0.144210i	0.631316	+	0.775526i	$0.282515\pi$
$968$	−3.60326	−	50.6387i	−0.115813	−	1.62759i
$969$	1.39493	+	2.28632i	0.0448117	+	0.0734473i
$970$	23.3454	−	44.0001i	0.749575	−	1.41276i
$971$		−	30.5032i		−	0.978893i	−0.872033	−	0.489446i	$-0.837199\pi$
$971$		−	30.5032i		−	0.978893i	0.872033	−	0.489446i	$-0.162801\pi$
$972$	−2.69037	−	4.18853i	−0.0862937	−	0.134347i
$973$	−21.4683	+	21.4683i	−0.688241	+	0.688241i
$974$	23.3890	+	12.7751i	0.749433	+	0.409339i
$975$	−13.5424	+	14.2149i	−0.433703	+	0.455241i
$976$	4.41406	+	11.8521i	0.141291	+	0.379376i
$977$	15.4491	+	15.4491i	0.494259	+	0.494259i	0.909645	−	0.415386i	$-0.136354\pi$
$977$	15.4491	+	15.4491i	0.494259	+	0.494259i	−0.415386	+	0.909645i	$0.636354\pi$
$978$	−27.1916	−	14.8520i	−0.869490	−	0.474914i
$979$	−5.50129	+	5.50129i	−0.175822	+	0.175822i
$980$	−10.7789	+	7.10936i	−0.344319	+	0.227100i
$981$	−1.95762	−	1.95762i	−0.0625021	−	0.0625021i
$982$	16.9998	+	9.28529i	0.542487	+	0.296305i
$983$		−	36.4754i		−	1.16338i	−0.813409	−	0.581692i	$-0.802391\pi$
$983$		−	36.4754i		−	1.16338i	0.813409	−	0.581692i	$-0.197609\pi$
$984$	−29.0136	−	25.1589i	−0.924919	−	0.802035i
$985$	−28.8013	+	0.348868i	−0.917684	+	0.0111159i
$986$	11.6711	−	12.8466i	0.371683	−	0.409119i
$987$	−1.17845	+	1.17845i	−0.0375106	+	0.0375106i
$988$	1.80602	+	0.393334i	0.0574572	+	0.0125136i
$989$	3.29214	−	3.29214i	0.104684	−	0.104684i
$990$	1.19785	+	3.90564i	0.0380703	+	0.124129i
$991$	16.0396	+	16.0396i	0.509514	+	0.509514i	0.914377	−	0.404863i	$-0.132681\pi$
$991$	16.0396	+	16.0396i	0.509514	+	0.509514i	−0.404863	+	0.914377i	$0.632681\pi$
$992$	−0.691864	+	4.79142i	−0.0219667	+	0.152128i
$993$			37.0166i			1.17469i
$994$	−2.58674	−	8.81358i	−0.0820464	−	0.279550i
$995$	4.75899	+	4.64508i	0.150870	+	0.147259i
$996$	−19.7703	−	4.30579i	−0.626446	−	0.136434i
$997$			14.2198i			0.450345i	0.974319	+	0.225172i	$0.0722946\pi$
$997$			14.2198i			0.450345i	−0.974319	+	0.225172i	$0.927705\pi$
$998$	−9.96450	−	33.9512i	−0.315421	−	1.07471i
$999$	−17.9947			−0.569326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bl.a.123.68	yes	208
5.2	odd	4		680.2.t.a.667.89	yes	208
8.3	odd	2	inner	680.2.bl.a.123.16	yes	208
17.13	even	4		680.2.t.a.523.37	✓	208
40.27	even	4		680.2.t.a.667.37	yes	208
85.47	odd	4	inner	680.2.bl.a.387.16	yes	208
136.115	odd	4		680.2.t.a.523.89	yes	208
680.387	even	4	inner	680.2.bl.a.387.68	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.37	✓	208	17.13	even	4
680.2.t.a.523.89	yes	208	136.115	odd	4
680.2.t.a.667.37	yes	208	40.27	even	4
680.2.t.a.667.89	yes	208	5.2	odd	4
680.2.bl.a.123.16	yes	208	8.3	odd	2	inner
680.2.bl.a.123.68	yes	208	1.1	even	1	trivial
680.2.bl.a.387.16	yes	208	85.47	odd	4	inner
680.2.bl.a.387.68	yes	208	680.387	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.677911 - 1.24114i) q^{2} +1.66129 q^{3} +(-1.08087 - 1.68277i) q^{4} +(-0.0270834 - 2.23590i) q^{5} +(1.12621 - 2.06190i) q^{6} -2.02798i q^{7} +(-2.82129 + 0.200753i) q^{8} -0.240104 q^{9} +(-2.79344 - 1.48213i) q^{10} +(3.80452 + 3.80452i) q^{11} +(-1.79565 - 2.79557i) q^{12} +(1.67131 - 1.67131i) q^{13} +(-2.51702 - 1.37479i) q^{14} +(-0.0449935 - 3.71449i) q^{15} +(-1.66342 + 3.63772i) q^{16} +(-2.14745 - 3.51972i) q^{17} +(-0.162769 + 0.298003i) q^{18} -0.391006 q^{19} +(-3.73324 + 2.46231i) q^{20} -3.36908i q^{21} +(7.30108 - 2.14283i) q^{22} +2.62296 q^{23} +(-4.68700 + 0.333509i) q^{24} +(-4.99853 + 0.121112i) q^{25} +(-0.941338 - 3.20734i) q^{26} -5.38276 q^{27} +(-3.41263 + 2.19200i) q^{28} +(-2.10479 + 2.10479i) q^{29} +(-4.64072 - 2.46225i) q^{30} +(0.605139 + 0.605139i) q^{31} +(3.38728 + 4.53060i) q^{32} +(6.32043 + 6.32043i) q^{33} +(-5.82426 + 0.279242i) q^{34} +(-4.53438 + 0.0549247i) q^{35} +(0.259522 + 0.404039i) q^{36} +3.34301 q^{37} +(-0.265067 + 0.485294i) q^{38} +(2.77654 - 2.77654i) q^{39} +(0.525274 + 6.30270i) q^{40} +(5.77901 + 5.77901i) q^{41} +(-4.18151 - 2.28393i) q^{42} +(1.25512 - 1.25512i) q^{43} +(2.28992 - 10.5143i) q^{44} +(0.00650283 + 0.536849i) q^{45} +(1.77813 - 3.25547i) q^{46} +(-0.349785 - 0.349785i) q^{47} +(-2.76343 + 6.04333i) q^{48} +2.88728 q^{49} +(-3.23824 + 6.28600i) q^{50} +(-3.56755 - 5.84729i) q^{51} +(-4.61891 - 1.00596i) q^{52} +(-8.03639 - 8.03639i) q^{53} +(-3.64903 + 6.68078i) q^{54} +(8.40350 - 8.60958i) q^{55} +(0.407123 + 5.72154i) q^{56} -0.649575 q^{57} +(1.18549 + 4.03920i) q^{58} +14.2763 q^{59} +(-6.20200 + 4.09061i) q^{60} +(2.23576 - 2.23576i) q^{61} +(1.16129 - 0.340834i) q^{62} +0.486927i q^{63} +(7.91940 - 1.13276i) q^{64} +(-3.78216 - 3.69163i) q^{65} +(12.1292 - 3.55987i) q^{66} +(-3.63435 + 3.63435i) q^{67} +(-3.60175 + 7.41805i) q^{68} +4.35751 q^{69} +(-3.00573 + 5.66505i) q^{70} +(2.26465 + 2.26465i) q^{71} +(0.677403 - 0.0482014i) q^{72} +5.49453 q^{73} +(2.26626 - 4.14916i) q^{74} +(-8.30403 + 0.201202i) q^{75} +(0.422628 + 0.657972i) q^{76} +(7.71551 - 7.71551i) q^{77} +(-1.56384 - 5.32834i) q^{78} +(-0.632749 - 0.632749i) q^{79} +(8.17865 + 3.62073i) q^{80} -8.22204 q^{81} +(11.0902 - 3.25493i) q^{82} +(4.30611 - 4.30611i) q^{83} +(-5.66938 + 3.64155i) q^{84} +(-7.81160 + 4.89683i) q^{85} +(-0.706927 - 2.40865i) q^{86} +(-3.49667 + 3.49667i) q^{87} +(-11.4974 - 9.96990i) q^{88} +1.44599i q^{89} +(0.670715 + 0.355865i) q^{90} +(-3.38940 - 3.38940i) q^{91} +(-2.83509 - 4.41384i) q^{92} +(1.00531 + 1.00531i) q^{93} +(-0.671257 + 0.197011i) q^{94} +(0.0105898 + 0.874251i) q^{95} +(5.62727 + 7.52665i) q^{96} +15.7512i q^{97} +(1.95732 - 3.58353i) q^{98} +(-0.913480 - 0.913480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{3} - 8 q^{6} + 192 q^{9} - 6 q^{10} - 8 q^{11} + 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} - 16 q^{24} - 32 q^{27} - 24 q^{30} - 20 q^{32} - 8 q^{33} + 4 q^{34} - 8 q^{35} - 12 q^{38} + 38 q^{40}+ \cdots - 24 q^{99}+O(q^{100}) \) 208 * q - 8 * q^3 - 8 * q^6 + 192 * q^9 - 6 * q^10 - 8 * q^11 + 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 - 16 * q^24 - 32 * q^27 - 24 * q^30 - 20 * q^32 - 8 * q^33 + 4 * q^34 - 8 * q^35 - 12 * q^38 + 38 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^44 - 16 * q^46 + 68 * q^48 - 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 - 36 * q^54 + 4 * q^56 - 32 * q^57 + 64 * q^59 - 32 * q^60 - 72 * q^62 + 32 * q^65 - 8 * q^67 - 28 * q^68 + 28 * q^70 - 56 * q^72 + 32 * q^73 - 8 * q^74 - 16 * q^75 - 10 * q^80 + 128 * q^81 + 8 * q^86 - 16 * q^88 - 118 * q^90 + 24 * q^91 - 56 * q^92 - 64 * q^94 - 48 * q^96 - 40 * q^98 - 24 * q^99

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