LMFDB - Embedded newform 680.2.bl.a.123.16

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			123.16
Character	$\chi$	$=$	680.123
Dual form			680.2.bl.a.387.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24114 + 0.677911i) q^{2} +1.66129 q^{3} +(1.08087 - 1.68277i) q^{4} +(0.0270834 + 2.23590i) q^{5} +(-2.06190 + 1.12621i) q^{6} +2.02798i q^{7} +(-0.200753 + 2.82129i) q^{8} -0.240104 q^{9} +(-1.54936 - 2.75672i) q^{10} +(3.80452 + 3.80452i) q^{11} +(1.79565 - 2.79557i) q^{12} +(-1.67131 + 1.67131i) q^{13} +(-1.37479 - 2.51702i) q^{14} +(0.0449935 + 3.71449i) q^{15} +(-1.66342 - 3.63772i) q^{16} +(-2.14745 - 3.51972i) q^{17} +(0.298003 - 0.162769i) q^{18} -0.391006 q^{19} +(3.79178 + 2.37116i) q^{20} +3.36908i q^{21} +(-7.30108 - 2.14283i) q^{22} -2.62296 q^{23} +(-0.333509 + 4.68700i) 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} +(-2.57394 - 4.57972i) q^{30} +(-0.605139 - 0.605139i) q^{31} +(4.53060 + 3.38728i) q^{32} +(6.32043 + 6.32043i) q^{33} +(5.05136 + 2.91270i) q^{34} +(-4.53438 + 0.0549247i) q^{35} +(-0.259522 + 0.404039i) q^{36} -3.34301 q^{37} +(0.485294 - 0.265067i) q^{38} +(-2.77654 + 2.77654i) q^{39} +(-6.31358 - 0.372453i) q^{40} +(5.77901 + 5.77901i) q^{41} +(-2.28393 - 4.18151i) q^{42} +(1.25512 - 1.25512i) q^{43} +(10.5143 - 2.28992i) q^{44} +(-0.00650283 - 0.536849i) q^{45} +(3.25547 - 1.77813i) q^{46} +(0.349785 + 0.349785i) q^{47} +(-2.76343 - 6.04333i) q^{48} +2.88728 q^{49} +(6.12179 - 3.53888i) q^{50} +(-3.56755 - 5.84729i) q^{51} +(1.00596 + 4.61891i) q^{52} +(8.03639 + 8.03639i) q^{53} +(6.68078 - 3.64903i) q^{54} +(-8.40350 + 8.60958i) q^{55} +(-5.72154 - 0.407123i) q^{56} -0.649575 q^{57} +(-1.18549 + 4.03920i) q^{58} +14.2763 q^{59} +(6.29927 + 3.93919i) 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} +(-8.24401 - 0.190706i) q^{68} -4.35751 q^{69} +(5.59058 - 3.14207i) q^{70} +(-2.26465 - 2.26465i) q^{71} +(0.0482014 - 0.677403i) q^{72} +5.49453 q^{73} +(4.14916 - 2.26626i) 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} +(8.08855 - 3.81778i) 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} +(0.372007 + 0.661898i) 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} +(7.52665 + 5.62727i) q^{96} +15.7512i q^{97} +(-3.58353 + 1.95732i) 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 $

$2$	−1.24114	+	0.677911i	−0.877621	+	0.479355i
$2$	−1.24114	+	0.677911i	−0.877621	+	0.479355i
$3$	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
$6$	−2.06190	+	1.12621i	−0.841769	+	0.459773i
$7$			2.02798i			0.766506i	0.923643	+	0.383253i	$0.125196\pi$
$7$			2.02798i			0.766506i	−0.923643	+	0.383253i	$0.874804\pi$
$8$	−0.200753	+	2.82129i	−0.0709768	+	0.997478i
$9$	−0.240104			−0.0800346
$10$	−1.54936	−	2.75672i	−0.489950	−	0.871751i
$11$	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	−0.899814	−	0.436275i	$-0.856298\pi$
$13$	−1.67131	+	1.67131i	−0.463539	+	0.463539i	0.436275	+	0.899814i	$0.356298\pi$
$14$	−1.37479	−	2.51702i	−0.367429	−	0.672702i
$15$	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
$18$	0.298003	−	0.162769i	0.0702400	−	0.0383650i
$19$	−0.391006			−0.0897029			−0.0448514	−	0.998994i	$-0.514281\pi$
$19$	−0.391006			−0.0897029			−0.0448514	+	0.998994i	$0.514281\pi$
$20$	3.79178	+	2.37116i	0.847869	+	0.530206i
$21$			3.36908i			0.735193i
$22$	−7.30108	−	2.14283i	−1.55660	−	0.456853i
$23$	−2.62296			−0.546925			−0.273462	−	0.961883i	$-0.588169\pi$
$23$	−2.62296			−0.546925			−0.273462	+	0.961883i	$0.588169\pi$
$24$	−0.333509	+	4.68700i	−0.0680772	+	0.956729i
$25$	−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	−0.484141	−	0.874990i	$-0.660868\pi$
$29$	2.10479	−	2.10479i	0.390849	−	0.390849i	0.874990	+	0.484141i	$0.160868\pi$
$30$	−2.57394	−	4.57972i	−0.469935	−	0.836138i
$31$	−0.605139	−	0.605139i	−0.108686	−	0.108686i	0.650672	−	0.759359i	$-0.274487\pi$
$31$	−0.605139	−	0.605139i	−0.108686	−	0.108686i	−0.759359	+	0.650672i	$0.774487\pi$
$32$	4.53060	+	3.38728i	0.800904	+	0.598793i
$33$	6.32043	+	6.32043i	1.10025	+	1.10025i
$34$	5.05136	+	2.91270i	0.866300	+	0.499523i
$35$	−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	$-0.588610\pi$
$37$	−3.34301			−0.549588			−0.274794	+	0.961503i	$0.588610\pi$
$38$	0.485294	−	0.265067i	0.0787251	−	0.0429995i
$39$	−2.77654	+	2.77654i	−0.444603	+	0.444603i
$40$	−6.31358	−	0.372453i	−0.998264	−	0.0588900i
$41$	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	$0.529685\pi$
$42$	−2.28393	−	4.18151i	−0.352419	−	0.645221i
$43$	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	$0.206786\pi$
$44$	10.5143	−	2.28992i	1.58510	−	0.345219i
$45$	−0.00650283	−	0.536849i	−0.000969384	−	0.0800287i
$46$	3.25547	−	1.77813i	0.479993	−	0.262171i
$47$	0.349785	+	0.349785i	0.0510214	+	0.0510214i	0.732157	−	0.681136i	$-0.238514\pi$
$47$	0.349785	+	0.349785i	0.0510214	+	0.0510214i	−0.681136	+	0.732157i	$0.738514\pi$
$48$	−2.76343	−	6.04333i	−0.398867	−	0.872279i
$49$	2.88728			0.412468
$50$	6.12179	−	3.53888i	0.865752	−	0.500473i
$51$	−3.56755	−	5.84729i	−0.499557	−	0.818784i
$52$	1.00596	+	4.61891i	0.139501	+	0.640528i
$53$	8.03639	+	8.03639i	1.10388	+	1.10388i	0.993938	+	0.109945i	$0.0350675\pi$
$53$	8.03639	+	8.03639i	1.10388	+	1.10388i	0.109945	+	0.993938i	$0.464932\pi$
$54$	6.68078	−	3.64903i	0.909139	−	0.496571i
$55$	−8.40350	+	8.60958i	−1.13313	+	1.16092i
$56$	−5.72154	−	0.407123i	−0.764573	−	0.0544041i
$57$	−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	$0.120404\pi$
$60$	6.29927	+	3.93919i	0.813232	+	0.508547i
$61$	−2.23576	+	2.23576i	−0.286260	+	0.286260i	−0.835599	−	0.549339i	$-0.814879\pi$
$61$	−2.23576	+	2.23576i	−0.286260	+	0.286260i	0.549339	+	0.835599i	$0.314879\pi$
$62$	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	$0.351656\pi$
$68$	−8.24401	−	0.190706i	−0.999733	−	0.0231265i
$69$	−4.35751			−0.524582
$70$	5.59058	−	3.14207i	0.668202	−	0.375550i
$71$	−2.26465	−	2.26465i	−0.268764	−	0.268764i	0.559838	−	0.828602i	$-0.310863\pi$
$71$	−2.26465	−	2.26465i	−0.268764	−	0.268764i	−0.828602	+	0.559838i	$0.810863\pi$
$72$	0.0482014	−	0.677403i	0.00568059	−	0.0798327i
$73$	5.49453			0.643086			0.321543	−	0.946895i	$-0.395799\pi$
$73$	5.49453			0.643086			0.321543	+	0.946895i	$0.395799\pi$
$74$	4.14916	−	2.26626i	0.482330	−	0.263448i
$75$	−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	0.741805	−	0.670615i	$-0.233970\pi$
$79$	0.632749	+	0.632749i	0.0711899	+	0.0711899i	−0.670615	+	0.741805i	$0.733970\pi$
$80$	8.08855	−	3.81778i	0.904327	−	0.426840i
$81$	−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	$0.975582\pi$
$90$	0.372007	+	0.661898i	0.0392129	+	0.0697702i
$91$	−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
$96$	7.52665	+	5.62727i	0.768186	+	0.574331i
$97$			15.7512i			1.59930i	0.600468	+	0.799649i	$0.294981\pi$
$97$			15.7512i			1.59930i	−0.600468	+	0.799649i	$0.705019\pi$
$98$	−3.58353	+	1.95732i	−0.361991	+	0.197719i
$99$	−0.913480	−	0.913480i	−0.0918082	−	0.0918082i
$100$	−5.19898	+	8.54228i	−0.519898	+	0.854228i
$101$		−	9.19554i		−	0.914990i	−0.889212	−	0.457495i	$-0.848747\pi$
$101$		−	9.19554i		−	0.914990i	0.889212	−	0.457495i	$-0.151253\pi$
$102$	8.39178	+	4.83884i	0.830911	+	0.479117i
$103$	−5.23005	+	5.23005i	−0.515332	+	0.515332i	−0.916155	−	0.400823i	$-0.868724\pi$
$103$	−5.23005	+	5.23005i	−0.515332	+	0.515332i	0.400823	+	0.916155i	$0.368724\pi$
$104$	−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	0.199051	−	0.979989i	$-0.436214\pi$
$109$	−8.15324	−	8.15324i	−0.780939	−	0.780939i	−0.979989	+	0.199051i	$0.936214\pi$
$110$	4.59343	−	16.3826i	0.437966	−	1.56202i
$111$	−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	$0.875133\pi$
$114$	0.806216	−	0.440354i	0.0755091	−	0.0412429i
$115$	−0.0710387	−	5.86469i	−0.00662439	−	0.546885i
$116$	−1.26686	−	5.81688i	−0.117625	−	0.540084i
$117$	0.401289	−	0.401289i	0.0370991	−	0.0370991i
$118$	−17.7189	+	9.67806i	−1.63116	+	0.890938i
$119$	7.13794	−	4.35500i	0.654334	−	0.399223i
$120$	−10.4887	−	0.618754i	−0.957484	−	0.0564843i
$121$			17.9488i			1.63171i
$122$	1.25925	−	4.29055i	0.114007	−	0.388448i
$123$	9.60064	+	9.60064i	0.865660	+	0.865660i
$124$	−1.67239	+	0.364230i	−0.150185	+	0.0327088i
$125$	−0.406172	−	11.1730i	−0.0363291	−	0.999340i
$126$	0.330093	+	0.604346i	0.0294070	+	0.0538394i
$127$	11.9192	−	11.9192i	1.05766	−	1.05766i	0.0594222	−	0.998233i	$-0.481074\pi$
$127$	11.9192	−	11.9192i	1.05766	−	1.05766i	0.998233	−	0.0594222i	$-0.0189258\pi$
$128$	10.5970	−	3.96272i	0.936653	−	0.350258i
$129$	2.08513	−	2.08513i	0.183585	−	0.183585i
$130$	7.19680	+	2.01788i	0.631201	+	0.176979i
$131$	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	$0.0641092\pi$
$132$	17.4674	−	3.80423i	1.52034	−	0.331116i
$133$		−	0.792954i		−	0.0687578i
$134$	2.04699	−	6.97452i	0.176833	−	0.602507i
$135$	−0.145784	−	12.0353i	−0.0125471	−	1.03584i
$136$	10.3613	−	5.35201i	0.888472	−	0.458931i
$137$	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	$0.0275153\pi$
$138$	5.40829	−	2.95400i	0.460384	−	0.251461i
$139$	−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	$0.968962\pi$
$140$	−4.80867	+	7.68968i	−0.406407	+	0.649897i
$141$	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
$146$	−6.81950	+	3.72480i	−0.564386	+	0.308267i
$147$	4.79662			0.395618
$148$	−3.61338	+	5.62552i	−0.297018	+	0.462415i
$149$	10.3389			0.846995			0.423498	−	0.905897i	$-0.360802\pi$
$149$	10.3389			0.846995			0.423498	+	0.905897i	$0.360802\pi$
$150$	10.1701	−	5.87911i	0.830385	−	0.480028i
$151$	20.2404			1.64714			0.823570	−	0.567214i	$-0.191979\pi$
$151$	20.2404			1.64714			0.823570	+	0.567214i	$0.191979\pi$
$152$	0.0784954	−	1.10314i	0.00636682	−	0.0894766i
$153$	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
$156$	1.67119	+	7.67337i	0.133802	+	0.614361i
$157$	16.9071	+	16.9071i	1.34933	+	1.34933i	0.886385	+	0.462949i	$0.153209\pi$
$157$	16.9071	+	16.9071i	1.34933	+	1.34933i	0.462949	+	0.886385i	$0.346791\pi$
$158$	−1.21428	−	0.356385i	−0.0966030	−	0.0283525i
$159$	13.3508	+	13.3508i	1.05879	+	1.05879i
$160$	−7.45094	+	10.2217i	−0.589048	+	0.808098i
$161$		−	5.31932i		−	0.419221i
$162$	10.2047	−	5.57381i	0.801759	−	0.437920i
$163$		−	13.1876i		−	1.03293i	−0.856308	−	0.516466i	$-0.827247\pi$
$163$		−	13.1876i		−	1.03293i	0.856308	−	0.516466i	$-0.172753\pi$
$164$	15.9711	−	3.47836i	1.24714	−	0.271614i
$165$	−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	$-0.776559\pi$
$167$	−19.7352			−1.52716			−0.763578	+	0.645715i	$0.776559\pi$
$168$	−9.50516	−	0.676351i	−0.733339	−	0.0521816i
$169$			7.41342i			0.570263i
$170$	−6.37570	+	11.3732i	−0.488994	+	0.872287i
$171$	0.0938819			0.00717933
$172$	−0.755452	−	3.46871i	−0.0576027	−	0.264487i
$173$		−	9.28097i		−	0.705619i	−0.935695	−	0.352810i	$-0.885226\pi$
$173$		−	9.28097i		−	0.705619i	0.935695	−	0.352810i	$-0.114774\pi$
$174$	−1.96944	+	6.71030i	−0.149303	+	0.508707i
$175$	−0.245613	−	10.1369i	−0.0185666	−	0.766281i
$176$	7.51127	−	20.1683i	0.566183	−	1.52024i
$177$	23.7171			1.78269
$178$	−0.980251	−	1.79468i	−0.0734729	−	0.134517i
$179$	13.7415			1.02709			0.513544	−	0.858063i	$-0.328332\pi$
$179$	13.7415			1.02709			0.513544	+	0.858063i	$0.328332\pi$
$180$	−0.910421	−	0.569323i	−0.0678588	−	0.0424348i
$181$	14.5581	−	14.5581i	1.08210	−	1.08210i	0.0857812	−	0.996314i	$-0.472661\pi$
$181$	14.5581	−	14.5581i	1.08210	−	1.08210i	0.996314	−	0.0857812i	$-0.0273386\pi$
$182$	6.50444	+	1.90902i	0.482141	+	0.141506i
$183$	−3.71426	+	3.71426i	−0.274566	+	0.274566i
$184$	0.526566	−	7.40014i	0.0388190	−	0.545546i
$185$	−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
$188$	0.966682	−	0.210534i	0.0705025	−	0.0153548i
$189$		−	10.9162i		−	0.794034i
$190$	0.605808	+	1.07789i	0.0439499	+	0.0781985i
$191$			8.75406i			0.633421i	0.948522	+	0.316711i	$0.102578\pi$
$191$			8.75406i			0.633421i	−0.948522	+	0.316711i	$0.897422\pi$
$192$	−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	$0.806860\pi$
$194$	−10.6779	−	19.5496i	−0.766631	−	1.40358i
$195$	−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	$0.151748\pi$
$197$			12.8813i			0.917752i	−0.888500	+	0.458876i	$0.848252\pi$
$198$	1.75302	+	0.514502i	0.124581	+	0.0365640i
$199$	2.10297	−	2.10297i	0.149075	−	0.149075i	−0.628630	−	0.777705i	$-0.716384\pi$
$199$	2.10297	−	2.10297i	0.149075	−	0.149075i	0.777705	+	0.628630i	$0.216384\pi$
$200$	0.661776	−	14.1266i	0.0467947	−	0.998905i
$201$	−6.03772	+	6.03772i	−0.425868	+	0.425868i
$202$	6.23375	+	11.4130i	0.438605	+	0.803014i
$203$	4.26848	+	4.26848i	0.299589	+	0.299589i
$204$	−13.6957	−	0.316819i	−0.958892	−	0.0221818i
$205$	−12.7648	+	13.0778i	−0.891533	+	0.913396i
$206$	2.94574	−	10.0368i	0.205239	−	0.699294i
$207$	0.629782			0.0437729
$208$	8.85988	+	3.29967i	0.614322	+	0.228791i
$209$	−1.48759	−	1.48759i	−0.102899	−	0.102899i
$210$	9.28760	−	5.21991i	0.640905	−	0.360208i
$211$	−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	$-0.543702\pi$
$212$	22.2097	−	4.83706i	1.52537	−	0.332211i
$213$	−3.76224	−	3.76224i	−0.257785	−	0.257785i
$214$	0.792511	+	1.45096i	0.0541750	+	0.0991855i
$215$	2.84033	+	2.77234i	0.193709	+	0.189072i
$216$	1.08060	−	15.1864i	0.0735258	−	1.03330i
$217$	1.22721	−	1.22721i	0.0833086	−	0.0833086i
$218$	15.6465	+	4.59217i	1.05972	+	0.311021i
$219$	9.12803			0.616815
$220$	5.40481	+	23.4470i	0.364392	+	1.58080i
$221$	9.47163	+	2.29349i	0.637131	+	0.154277i
$222$	6.89297	−	3.76493i	0.462626	−	0.252686i
$223$	−11.1310	−	11.1310i	−0.745386	−	0.745386i	0.228223	−	0.973609i	$-0.426709\pi$
$223$	−11.1310	−	11.1310i	−0.745386	−	0.745386i	−0.973609	+	0.228223i	$0.926709\pi$
$224$	−6.86936	+	9.18798i	−0.458978	+	0.613898i
$225$	1.20017	−	0.0290794i	0.0800111	−	0.00193863i
$226$	−5.50989	−	10.0877i	−0.366512	−	0.671024i
$227$	−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	$-0.780289\pi$
$229$		−	19.2708i		−	1.27345i	0.771092	−	0.636724i	$-0.219711\pi$
$230$	4.06390	+	7.23076i	0.267966	+	0.476782i
$231$	−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
$238$	−5.90691	+	10.2441i	−0.382888	+	0.664025i
$239$	2.05961			0.133225			0.0666126	−	0.997779i	$-0.478781\pi$
$239$	2.05961			0.133225			0.0666126	+	0.997779i	$0.478781\pi$
$240$	13.4375	−	6.34245i	0.867384	−	0.409403i
$241$	−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	$0.334580\pi$
$242$	−12.1677	−	22.2770i	−0.782167	−	1.43202i
$243$	2.48907			0.159674
$244$	1.34569	+	6.17885i	0.0861492	+	0.395560i
$245$	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
$250$	8.07839	+	13.5919i	0.510922	+	0.859627i
$251$	−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
$260$	−10.3002	+	2.37431i	−0.638791	+	0.147249i
$261$	−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	$-0.988444\pi$
$263$	−16.7952	−	16.7952i	−1.03564	−	1.03564i	−0.0362977	−	0.999341i	$-0.511556\pi$
$264$	−19.1006	+	16.5629i	−1.17556	+	1.01938i
$265$	−17.7509	+	18.1862i	−1.09043	+	1.11717i
$266$	0.537552	+	0.984169i	0.0329594	+	0.0603433i
$267$			2.40221i			0.147013i
$268$	2.18750	+	10.0440i	0.133623	+	0.613538i
$269$	3.81403	−	3.81403i	0.232546	−	0.232546i	−0.581209	−	0.813754i	$-0.697420\pi$
$269$	3.81403	−	3.81403i	0.232546	−	0.232546i	0.813754	+	0.581209i	$0.197420\pi$
$270$	8.33983	+	14.8388i	0.507546	+	0.903058i
$271$		−	17.3406i		−	1.05337i	−0.850061	−	0.526684i	$-0.823435\pi$
$271$		−	17.3406i		−	1.05337i	0.850061	−	0.526684i	$-0.176565\pi$
$272$	−9.23165	+	13.6666i	−0.559751	+	0.828661i
$273$	−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	$-0.464274\pi$
$277$	3.72812			0.224001			0.112000	+	0.993708i	$0.464274\pi$
$278$	20.3151	+	5.96239i	1.21842	+	0.357600i
$279$	0.145296	+	0.145296i	0.00869865	+	0.00869865i
$280$	0.755330	−	12.8038i	0.0451396	−	0.765176i
$281$			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	$-0.0159820\pi$
$284$	−6.25867	+	1.36308i	−0.371384	+	0.0808838i
$285$	−0.0175927	−	1.45239i	−0.00104210	−	0.0860320i
$286$	15.7837	−	8.62106i	0.933312	−	0.509774i
$287$	−11.7198	+	11.7198i	−0.691795	+	0.691795i
$288$	−1.08781	−	0.813299i	−0.0641000	−	0.0479241i
$289$	−7.77688	+	15.1169i	−0.457464	+	0.889228i
$290$	−9.06338	−	2.54124i	−0.532220	−	0.149227i
$291$			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	$-0.402557\pi$
$293$	21.4800	−	21.4800i	1.25487	−	1.25487i	0.953508	−	0.301366i	$-0.0974427\pi$
$294$	−5.95329	+	3.25168i	−0.347203	+	0.189642i
$295$	0.386651	+	31.9204i	0.0225117	+	1.85848i
$296$	0.671119	−	9.43162i	0.0390080	−	0.548202i
$297$	−20.4788	−	20.4788i	−1.18830	−	1.18830i
$298$	−12.8321	+	7.00885i	−0.743341	+	0.406012i
$299$	4.38379	−	4.38379i	0.253521	−	0.253521i
$300$	−8.63703	+	14.1912i	−0.498659	+	0.819332i
$301$	2.54537	+	2.54537i	0.146713	+	0.146713i
$302$	−25.1212	+	13.7212i	−1.44557	+	0.789566i
$303$		−	15.2765i		−	0.877611i
$304$	0.650408	+	1.42237i	0.0373034	+	0.0815785i
$305$	−5.05950	−	4.93840i	−0.289706	−	0.282772i
$306$	−1.21285	−	0.699349i	−0.0693340	−	0.0399791i
$307$	−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	$0.359984\pi$
$308$	4.64393	+	21.3229i	0.264612	+	1.21499i
$309$	−8.68865	+	8.68865i	−0.494280	+	0.494280i
$310$	−0.730621	+	2.60577i	−0.0414965	+	0.147998i
$311$	19.8394	+	19.8394i	1.12499	+	1.12499i	0.990980	+	0.134006i	$0.0427843\pi$
$311$	19.8394	+	19.8394i	1.12499	+	1.12499i	0.134006	+	0.990980i	$0.457216\pi$
$312$	−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
$316$	1.74869	−	0.380849i	0.0983717	−	0.0214244i
$317$			19.8739i			1.11623i	0.829763	+	0.558116i	$0.188475\pi$
$317$			19.8739i			1.11623i	−0.829763	+	0.558116i	$0.811525\pi$
$318$	−25.6209	−	7.51961i	−1.43675	−	0.421679i
$319$	16.0154			0.896692
$320$	2.31827	−	17.7377i	0.129595	−	0.991567i
$321$		−	1.94213i		−	0.108399i
$322$	3.60603	+	6.60204i	0.200956	+	0.367917i
$323$	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
$326$	8.94001	+	16.3677i	0.495142	+	0.906523i
$327$	−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
$330$	7.63103	−	27.2162i	0.420074	−	1.49820i
$331$			22.2818i			1.22472i	0.790580	+	0.612359i	$0.209779\pi$
$331$			22.2818i			1.22472i	−0.790580	+	0.612359i	$0.790221\pi$
$332$	−2.59183	−	11.9006i	−0.142245	−	0.653128i
$333$	0.802670			0.0439860
$334$	24.4942	−	13.3787i	1.34026	−	0.732050i
$335$	−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	$-0.157810\pi$
$338$	−5.02564	−	9.20112i	−0.273359	−	0.500475i
$339$			13.5026i			0.733360i
$340$	0.203125	−	18.4380i	0.0110160	−	0.999939i
$341$		−	4.60453i		−	0.249349i
$342$	−0.116521	+	0.0636436i	−0.00630073	+	0.00344145i
$343$			20.0512i			1.08267i
$344$	3.28910	+	3.79304i	0.177337	+	0.204507i
$345$	−0.118016	−	9.74296i	−0.00635377	−	0.524544i
$346$	6.29167	+	11.5190i	0.338242	+	0.619266i
$347$	4.81572			0.258521			0.129261	−	0.991611i	$-0.458740\pi$
$347$	4.81572			0.258521			0.129261	+	0.991611i	$0.458740\pi$
$348$	−2.10463	−	9.66355i	−0.112820	−	0.518021i
$349$			33.3515i			1.78526i	0.450788	+	0.892631i	$0.351143\pi$
$349$			33.3515i			1.78526i	−0.450788	+	0.892631i	$0.648857\pi$
$350$	7.17679	+	12.4149i	0.383615	+	0.663605i
$351$	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	$0.834991\pi$
$354$	−29.4364	+	16.0781i	−1.56452	+	0.854541i
$355$	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
$358$	−17.0552	+	9.31551i	−0.901394	+	0.492340i
$359$			34.9508i			1.84463i	0.386436	+	0.922316i	$0.373706\pi$
$359$			34.9508i			1.84463i	−0.386436	+	0.922316i	$0.626294\pi$
$360$	1.51591	+	0.0894274i	0.0798957	+	0.00471324i
$361$	−18.8471			−0.991953
$362$	−8.19960	+	27.9378i	−0.430961	+	1.46838i
$363$			29.8182i			1.56505i
$364$	−9.36709	+	2.04006i	−0.490969	+	0.106928i
$365$	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	$-0.637034\pi$
$367$		−	34.8185i		−	1.81751i	0.417330	−	0.908755i	$-0.362966\pi$
$368$	4.36309	+	9.54160i	0.227442	+	0.497390i
$369$	−1.38756	−	1.38756i	−0.0722336	−	0.0722336i
$370$	5.17952	+	9.21574i	0.269271	+	0.479104i
$371$	−16.2977	+	16.2977i	−0.846133	+	0.846133i
$372$	−2.77833	+	0.605093i	−0.144050	+	0.0313726i
$373$	18.8892	−	18.8892i	0.978047	−	0.978047i	−0.0217171	−	0.999764i	$-0.506913\pi$
$373$	18.8892	−	18.8892i	0.978047	−	0.978047i	0.999764	+	0.0217171i	$0.00691331\pi$
$374$	8.13657	+	30.2994i	0.420732	+	1.56675i
$375$	−0.674770	−	18.5616i	−0.0348450	−	0.958515i
$376$	−1.05707	+	0.916627i	−0.0545141	+	0.0472714i
$377$			7.03552i			0.362348i
$378$	7.40018	+	13.5485i	0.380624	+	0.696861i
$379$	−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	$0.963250\pi$
$380$	−1.48261	−	0.927135i	−0.0760562	−	0.0475610i
$381$	19.8012	−	19.8012i	1.01445	−	1.01445i
$382$	−5.93447	−	10.8650i	−0.303634	−	0.555904i
$383$	4.65399	+	4.65399i	0.237808	+	0.237808i	0.815942	−	0.578134i	$-0.196219\pi$
$383$	4.65399	+	4.65399i	0.237808	+	0.237808i	−0.578134	+	0.815942i	$0.696219\pi$
$384$	17.6048	−	6.58324i	0.898389	−	0.335950i
$385$	−17.4601	−	17.0422i	−0.889849	−	0.868550i
$386$	−10.7404	−	19.6639i	−0.546672	−	1.00087i
$387$	−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	$-0.790062\pi$
$389$		−	24.1708i		−	1.22551i	0.790275	−	0.612753i	$-0.209938\pi$
$390$	11.9560	+	3.35229i	0.605416	+	0.169750i
$391$	5.63269	+	9.23209i	0.284857	+	0.466887i
$392$	−0.579628	+	8.14586i	−0.0292757	+	0.411428i
$393$	14.8263	−	14.8263i	0.747887	−	0.747887i
$394$	−8.73234	−	15.9875i	−0.439929	−	0.805438i
$395$	−1.39763	+	1.43190i	−0.0703224	+	0.0720469i
$396$	−2.52453	+	0.549819i	−0.126862	+	0.0276294i
$397$			35.1264i			1.76294i	0.472239	+	0.881471i	$0.343446\pi$
$397$			35.1264i			1.76294i	−0.472239	+	0.881471i	$0.656554\pi$
$398$	−1.18446	+	4.03571i	−0.0593716	+	0.202292i
$399$		−	1.31733i		−	0.0659489i
$400$	8.75524	+	17.9818i	0.437762	+	0.899091i
$401$	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
$408$	17.2131	−	8.89125i	0.852176	−	0.440183i
$409$		−	3.44732i		−	0.170459i	−0.996361	−	0.0852294i	$-0.972838\pi$
$409$		−	3.44732i		−	0.170459i	0.996361	−	0.0852294i	$-0.0271623\pi$
$410$	6.97735	−	24.8849i	0.344587	−	1.22898i
$411$	17.6936	−	17.6936i	0.872760	−	0.872760i
$412$	3.14794	+	14.4540i	0.155088	+	0.712097i
$413$			28.9521i			1.42464i
$414$	−0.781650	+	0.426936i	−0.0384160	+	0.0209828i
$415$	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	$0.329079\pi$
$420$	−7.98861	+	12.7748i	−0.389804	+	0.623347i
$421$		−	9.88208i		−	0.481623i	−0.970572	−	0.240812i	$-0.922586\pi$
$421$		−	9.88208i		−	0.481623i	0.970572	−	0.240812i	$-0.0774136\pi$
$422$	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
$430$	−5.40466	−	1.51539i	−0.260636	−	0.0730784i
$431$	−5.70212	+	5.70212i	−0.274662	+	0.274662i	−0.830974	−	0.556312i	$-0.812216\pi$
$431$	−5.70212	+	5.70212i	−0.274662	+	0.274662i	0.556312	+	0.830974i	$0.312216\pi$
$432$	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
$436$	−22.5326	+	4.90739i	−1.07912	+	0.235021i
$437$	1.02559			0.0490607
$438$	−11.3292	+	6.18799i	−0.541330	+	0.295673i
$439$	3.40492	−	3.40492i	0.162508	−	0.162508i	−0.621169	−	0.783677i	$-0.713342\pi$
$439$	3.40492	−	3.40492i	0.162508	−	0.162508i	0.783677	+	0.621169i	$0.213342\pi$
$440$	−22.6031	−	25.4372i	−1.07756	−	1.21267i
$441$	−0.693246			−0.0330117
$442$	−13.3104	+	3.57437i	−0.633113	+	0.170015i
$443$	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	$0.197741\pi$
$450$	−1.46987	+	0.849697i	−0.0692901	+	0.0400551i
$451$			43.9728i			2.07060i
$452$	13.6771	+	8.78508i	0.643318	+	0.413215i
$453$	33.6253			1.57985
$454$	23.3942	−	12.7779i	1.09794	−	0.599695i
$455$	7.48657	−	7.67017i	0.350976	−	0.359583i
$456$	0.130404	−	1.83264i	0.00610672	−	0.0858214i
$457$	−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	$0.964667\pi$
$458$	13.0639	+	23.9178i	0.610434	+	1.11760i
$459$	11.5592	+	18.9458i	0.539539	+	0.884316i
$460$	−9.94570	−	6.21945i	−0.463720	−	0.289983i
$461$	−37.7181			−1.75671			−0.878355	−	0.478009i	$-0.841358\pi$
$461$	−37.7181			−1.75671			−0.878355	+	0.478009i	$0.841358\pi$
$462$	7.21936	−	24.5979i	0.335875	−	1.14440i
$463$	11.9943	−	11.9943i	0.557421	−	0.557421i	−0.371151	−	0.928573i	$-0.621037\pi$
$463$	11.9943	−	11.9943i	0.557421	−	0.557421i	0.928573	+	0.371151i	$0.121037\pi$
$464$	−11.1578	−	4.15548i	−0.517987	−	0.192914i
$465$	2.22056	−	2.27501i	0.102976	−	0.105501i
$466$	6.56662	−	3.58668i	0.304193	−	0.166150i
$467$	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	$0.710367\pi$
$468$	−0.241534	−	1.10902i	−0.0111649	−	0.0512644i
$469$	−7.37041	−	7.37041i	−0.340334	−	0.340334i
$470$	0.422317	−	1.50620i	0.0194800	−	0.0694759i
$471$	28.0877	+	28.0877i	1.29421	+	1.29421i
$472$	−2.86600	+	40.2776i	−0.131919	+	1.85393i
$473$	9.55029			0.439123
$474$	−2.01728	−	0.592060i	−0.0926566	−	0.0271942i
$475$	1.95445	−	0.0473554i	0.0896765	−	0.00217282i
$476$	0.386750	−	16.7187i	0.0177266	−	0.766301i
$477$	−1.92957	−	1.92957i	−0.0883488	−	0.0883488i
$478$	−2.55627	+	1.39623i	−0.116921	+	0.0638622i
$479$	26.2920	−	26.2920i	1.20131	−	1.20131i	0.227543	−	0.973768i	$-0.426931\pi$
$479$	26.2920	−	26.2920i	1.20131	−	1.20131i	0.973768	−	0.227543i	$-0.0730694\pi$
$480$	−12.3782	+	16.9813i	−0.564985	+	0.775086i
$481$	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
$486$	−3.08929	+	1.68737i	−0.140133	+	0.0765405i
$487$		−	18.8448i		−	0.853938i	−0.904266	−	0.426969i	$-0.859581\pi$
$487$		−	18.8448i		−	0.853938i	0.904266	−	0.426969i	$-0.140419\pi$
$488$	−5.85890	−	6.75657i	−0.265220	−	0.305856i
$489$		−	21.9085i		−	0.990735i
$490$	−4.47343	−	7.95941i	−0.202089	−	0.359569i
$491$			13.6969i			0.618133i	0.951040	+	0.309067i	$0.100017\pi$
$491$			13.6969i			0.618133i	−0.951040	+	0.309067i	$0.899983\pi$
$492$	26.5327	−	5.77858i	1.19619	−	0.260518i
$493$	−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
$496$	−1.19473	+	3.20793i	−0.0536448	+	0.144040i
$497$	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	$0.0607940\pi$
$500$	−19.2405	−	11.3931i	−0.860463	−	0.509514i
$501$	−32.7860			−1.46477
$502$	11.3868	−	6.21947i	0.508219	−	0.277588i
$503$	−26.8518			−1.19726			−0.598631	−	0.801025i	$-0.704289\pi$
$503$	−26.8518			−1.19726			−0.598631	+	0.801025i	$0.704289\pi$
$504$	1.37376	+	0.0977518i	0.0611923	+	0.00435421i
$505$	20.5603	−	0.249046i	0.914923	−	0.0110824i
$506$	19.1504	+	5.62056i	0.851341	+	0.249864i
$507$			12.3159i			0.546967i
$508$	−7.17409	−	32.9403i	−0.318299	−	1.46149i
$509$	4.40293			0.195157			0.0975783	−	0.995228i	$-0.468890\pi$
$509$	4.40293			0.195157			0.0975783	+	0.995228i	$0.468890\pi$
$510$	−10.5919	+	18.8943i	−0.469018	+	0.836653i
$511$			11.1428i			0.492929i
$512$	4.78570	−	22.1155i	0.211500	−	0.977378i
$513$	2.10469			0.0929244
$514$	−30.2810	−	8.88733i	−1.33564	−	0.392003i
$515$	−11.8355	−	11.5522i	−0.521536	−	0.509053i
$516$	−1.25503	−	5.76255i	−0.0552495	−	0.253682i
$517$			2.66153i			0.117054i
$518$	4.59595	+	8.41443i	0.201934	+	0.369709i
$519$		−	15.4184i		−	0.676793i
$520$	11.1745	−	9.92948i	0.490032	−	0.435437i
$521$	−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	$-0.504394\pi$
$524$	−5.37163	−	24.6642i	−0.234661	−	1.07746i
$525$	−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
$528$	12.4784	−	33.5055i	0.543053	−	1.45814i
$529$	−16.1201			−0.700873
$530$	9.70281	−	34.6053i	0.421463	−	1.50316i
$531$	−3.42779			−0.148754
$532$	−1.33436	−	0.857083i	−0.0578517	−	0.0371593i
$533$	−19.3171			−0.836716
$534$	−1.62849	−	2.98149i	−0.0704715	−	0.129022i
$535$	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
$540$	−20.4103	−	12.7634i	−0.878318	−	0.549248i
$541$	21.8221	+	21.8221i	0.938205	+	0.938205i	0.998199	−	0.0599937i	$-0.0191080\pi$
$541$	21.8221	+	21.8221i	0.938205	+	0.938205i	−0.0599937	+	0.998199i	$0.519108\pi$
$542$	11.7554	+	21.5222i	0.504938	+	0.924458i
$543$	24.1853	−	24.1853i	1.03789	−	1.03789i
$544$	2.19304	−	23.2205i	0.0940260	−	0.995570i
$545$	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	$-0.318359\pi$
$548$	−6.41047	−	29.4341i	−0.273842	−	1.25736i
$549$	0.536815	−	0.536815i	0.0229107	−	0.0229107i
$550$	36.7542	+	9.82676i	1.56721	+	0.419015i
$551$	−0.822984	+	0.822984i	−0.0350603	+	0.0350603i
$552$	0.874781	−	12.2938i	0.0372331	−	0.523259i
$553$	−1.28321	+	1.28321i	−0.0545675	+	0.0545675i
$554$	−4.62713	+	2.52733i	−0.196588	+	0.107376i
$555$	−0.150414	−	12.4176i	−0.00638471	−	0.527098i
$556$	−29.2560	+	6.37167i	−1.24073	+	0.270219i
$557$	−24.6084	−	24.6084i	−1.04269	−	1.04269i	−0.999047	−	0.0436458i	$-0.986103\pi$
$557$	−24.6084	−	24.6084i	−1.04269	−	1.04269i	−0.0436458	−	0.999047i	$-0.513897\pi$
$558$	−0.278831	−	0.0818355i	−0.0118039	−	0.00346437i
$559$			4.19541i			0.177447i
$560$	7.74239	+	16.4035i	0.327176	+	0.693172i
$561$	8.67331	−	35.8190i	0.366188	−	1.51228i
$562$	−7.31734	−	13.3969i	−0.308664	−	0.565112i
$563$	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	$0.240142\pi$
$564$	1.60594	−	0.349759i	0.0676224	−	0.0147275i
$565$	−18.1729	+	0.220127i	−0.764539	+	0.00926082i
$566$	1.14471	+	2.09577i	0.0481156	+	0.0880918i
$567$		−	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	$0.513966\pi$
$570$	1.00642	+	1.79070i	0.0421545	+	0.0750040i
$571$	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	$0.894861\pi$
$578$	−0.595673	−	24.0343i	−0.0247767	−	0.999693i
$579$			26.3205i			1.09384i
$580$	12.9717	−	2.99012i	0.538620	−	0.124158i
$581$	8.73273	+	8.73273i	0.362295	+	0.362295i
$582$	−17.7392	−	32.4776i	−0.735313	−	1.34624i
$583$			61.1492i			2.53254i
$584$	−1.10304	+	15.5017i	−0.0456442	+	0.641464i
$585$	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
$590$	−22.1191	−	39.3557i	−0.910629	−	1.62025i
$591$			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	$-0.580544\pi$
$599$	−12.2541			−0.500691			−0.250345	+	0.968157i	$0.580544\pi$
$600$	1.09940	−	23.4685i	0.0448830	−	0.958098i
$601$	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
$606$	10.3561	+	18.9603i	0.420687	+	0.770210i
$607$	10.7760			0.437383			0.218691	−	0.975794i	$-0.429821\pi$
$607$	10.7760			0.437383			0.218691	+	0.975794i	$0.429821\pi$
$608$	−1.77149	−	1.32445i	−0.0718434	−	0.0537134i
$609$	7.09120	+	7.09120i	0.287350	+	0.287350i
$610$	9.62736	+	2.69937i	0.389800	+	0.109294i
$611$	−1.16920			−0.0473009
$612$	1.97942	+	0.0457893i	0.0800132	+	0.00185092i
$613$	−18.2214	+	18.2214i	−0.735954	+	0.735954i	−0.971792	−	0.235839i	$-0.924216\pi$
$613$	−18.2214	+	18.2214i	−0.735954	+	0.735954i	0.235839	+	0.971792i	$0.424216\pi$
$614$	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	$0.978913\pi$
$620$	−0.859678	−	3.72944i	−0.0345255	−	0.149778i
$621$	14.1188			0.566567
$622$	−38.0728	−	11.1742i	−1.52658	−	0.448044i
$623$	−2.93244			−0.117486
$624$	14.7189	+	5.48173i	0.589226	+	0.219445i
$625$	24.9707	−	1.21076i	0.998827	−	0.0484305i
$626$	19.3898	+	35.4996i	0.774973	+	1.41885i
$627$	−2.47132	−	2.47132i	−0.0986951	−	0.0986951i
$628$	46.7252	−	10.1763i	1.86454	−	0.406079i
$629$	7.17897	+	11.7665i	0.286244	+	0.469160i
$630$	−1.34232	+	0.754424i	−0.0534793	+	0.0300570i
$631$	−45.3466			−1.80522			−0.902610	−	0.430458i	$-0.858352\pi$
$631$	−45.3466			−1.80522			−0.902610	+	0.430458i	$0.858352\pi$
$632$	−1.91220	+	1.65815i	−0.0760632	+	0.0659575i
$633$	−27.2073	−	27.2073i	−1.08139	−	1.08139i
$634$	−13.4727	−	24.6664i	−0.535071	−	0.979628i
$635$	26.9729	+	26.3273i	1.07039	+	1.04477i
$636$	36.8968	−	8.03578i	1.46306	−	0.318639i
$637$	−4.82555	+	4.82555i	−0.191195	+	0.191195i
$638$	−19.8774	+	10.8570i	−0.786955	+	0.429834i
$639$	0.543750	+	0.543750i	0.0215104	+	0.0215104i
$640$	9.14727	+	23.5866i	0.361578	+	0.932342i
$641$	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	$0.197296\pi$
$642$	1.31659	+	2.41047i	0.0519618	+	0.0951336i
$643$	−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
$646$	−1.97511	−	1.13888i	−0.0777096	−	0.0448087i
$647$	15.5377	+	15.5377i	0.610848	+	0.610848i	0.943167	−	0.332319i	$-0.107831\pi$
$647$	15.5377	+	15.5377i	0.610848	+	0.610848i	−0.332319	+	0.943167i	$0.607831\pi$
$648$	1.65060	−	23.1968i	0.0648415	−	0.911256i
$649$	54.3145	+	54.3145i	2.13203	+	2.13203i
$650$	−4.31686	+	16.1460i	−0.169321	+	0.633299i
$651$	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	$-0.340320\pi$
$653$	24.5762			0.961743			0.480871	+	0.876791i	$0.340320\pi$
$654$	25.9934	+	7.62894i	1.01642	+	0.298315i
$655$	20.1961	+	19.7127i	0.789128	+	0.770239i
$656$	11.4095	−	30.6354i	0.445466	−	1.19611i
$657$	−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	$0.925652\pi$
$660$	8.97897	+	38.9524i	0.349506	+	1.51622i
$661$	31.5825			1.22842			0.614209	−	0.789144i	$-0.289475\pi$
$661$	31.5825			1.22842			0.614209	+	0.789144i	$0.289475\pi$
$662$	−15.1051	−	27.6549i	−0.587075	−	1.07484i
$663$	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
$666$	−0.996229	+	0.544139i	−0.0386031	+	0.0210849i
$667$	−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
$670$	15.6498	+	4.38797i	0.604604	+	0.169522i
$671$	−17.0120			−0.656741
$672$	−11.4120	+	15.2639i	−0.440228	+	0.588819i
$673$			8.10867i			0.312566i	0.987712	+	0.156283i	$0.0499512\pi$
$673$			8.10867i			0.312566i	−0.987712	+	0.156283i	$0.950049\pi$
$674$	11.8403	+	21.6777i	0.456072	+	0.834994i
$675$	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	$-0.609105\pi$
$677$	−17.4897			−0.672185			−0.336093	+	0.941829i	$0.609105\pi$
$678$	−9.15355	−	16.7586i	−0.351540	−	0.643612i
$679$	−31.9433			−1.22587
$680$	12.2472	+	23.0219i	0.469658	+	0.882848i
$681$	−31.3135			−1.19994
$682$	3.12146	+	5.71488i	0.119527	+	0.218834i
$683$	−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
$686$	−13.5930	−	24.8865i	−0.518982	−	0.950170i
$687$		−	32.0144i		−	1.22143i
$688$	−6.65359	−	2.47799i	−0.253666	−	0.0944725i
$689$	−26.8626			−1.02339
$690$	6.75134	+	12.0124i	0.257019	+	0.457305i
$691$	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
$694$	−5.97700	+	3.26463i	−0.226884	+	0.123924i
$695$	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
$698$	−22.6093	−	41.3939i	−0.855775	−	1.56678i
$699$	−8.78954			−0.332451
$700$	−17.3236	−	10.5435i	−0.654771	−	0.398505i
$701$			29.7379i			1.12319i	0.827414	+	0.561593i	$0.189811\pi$
$701$			29.7379i			1.12319i	−0.827414	+	0.561593i	$0.810189\pi$
$702$	−5.06700	+	17.2644i	−0.191242	+	0.651601i
$703$	1.30714			0.0492996
$704$	−25.8199	−	34.4391i	−0.973124	−	1.29797i
$705$	−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	−0.870928	−	0.491411i	$-0.836481\pi$
$709$	−10.1054	+	10.1054i	−0.379517	+	0.379517i	0.491411	+	0.870928i	$0.336481\pi$
$710$	−2.73424	+	9.75173i	−0.102614	+	0.365976i
$711$	−0.151925	−	0.151925i	−0.00569765	−	0.00569765i
$712$	−4.07956	−	0.290286i	−0.152888	−	0.0108789i
$713$	1.58726	+	1.58726i	0.0594432	+	0.0594432i
$714$	−9.81310	+	17.0184i	−0.367246	+	0.636898i
$715$	−0.344422	−	28.4342i	−0.0128807	−	1.06338i
$716$	14.8528	−	23.1238i	0.555076	−	0.864176i
$717$	3.42162			0.127783
$718$	−23.6935	−	43.3790i	−0.884234	−	1.61889i
$719$	−23.6636	+	23.6636i	−0.882502	+	0.882502i	−0.993788	−	0.111287i	$-0.964503\pi$
$719$	−23.6636	+	23.6636i	−0.882502	+	0.882502i	0.111287	+	0.993788i	$0.464503\pi$
$720$	−1.94209	+	0.916662i	−0.0723774	+	0.0341620i
$721$	−10.6065	−	10.6065i	−0.395005	−	0.395005i
$722$	23.3920	−	12.7767i	0.870559	−	0.475498i
$723$	−9.57777	+	9.57777i	−0.356201	+	0.356201i
$724$	−8.76245	−	40.2334i	−0.325654	−	1.49526i
$725$	−10.2659	+	10.7758i	−0.381267	+	0.400202i
$726$	−20.2141	−	37.0086i	−0.750214	−	1.37352i
$727$	−15.9581	−	15.9581i	−0.591853	−	0.591853i	0.346278	−	0.938132i	$-0.387445\pi$
$727$	−15.9581	−	15.9581i	−0.591853	−	0.591853i	−0.938132	+	0.346278i	$0.887445\pi$
$728$	10.2429	−	8.88206i	0.379628	−	0.329191i
$729$	28.8012			1.06671
$730$	−8.51299	−	15.1469i	−0.315080	−	0.560611i
$731$	−7.11300	−	1.72236i	−0.263084	−	0.0637040i
$732$	2.23559	+	10.2649i	0.0826298	+	0.379401i
$733$	−26.9181	−	26.9181i	−0.994242	−	0.994242i	0.00574169	−	0.999984i	$-0.498172\pi$
$733$	−26.9181	−	26.9181i	−0.994242	−	0.994242i	−0.999984	+	0.00574169i	$0.998172\pi$
$734$	23.6038	+	43.2147i	0.871233	+	1.59509i
$735$	0.129909	+	10.7248i	0.00479176	+	0.395589i
$736$	−11.8836	−	8.88471i	−0.438034	−	0.327495i
$737$	−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	$0.385985\pi$
$740$	−12.6760	−	7.92681i	−0.465978	−	0.291395i
$741$	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	$0.0665413\pi$
$743$			11.3135i			0.415053i	−0.978229	+	0.207526i	$0.933459\pi$
$744$	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
$748$	−30.6389	−	32.0900i	−1.12027	−	1.17333i
$749$	2.37082			0.0866277
$750$	13.4206	+	22.5801i	0.490050	+	0.824510i
$751$	−23.2235	−	23.2235i	−0.847438	−	0.847438i	0.142375	−	0.989813i	$-0.454526\pi$
$751$	−23.2235	−	23.2235i	−0.847438	−	0.847438i	−0.989813	+	0.142375i	$0.954526\pi$
$752$	0.690581	−	1.85426i	0.0251829	−	0.0676180i
$753$	−15.2415			−0.555430
$754$	−4.76946	−	8.73209i	−0.173693	−	0.318004i
$755$	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	−0.688772	−	0.724978i	$-0.741850\pi$
$757$	0.996139	−	0.996139i	0.0362053	−	0.0362053i	0.724978	+	0.688772i	$0.241850\pi$
$758$	32.8075	+	9.62884i	1.19162	+	0.349735i
$759$	−16.5782	−	16.5782i	−0.601751	−	0.601751i
$760$	2.46865	+	0.145631i	0.0895472	+	0.00528260i
$761$	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	$-0.135414\pi$
$770$	33.2236	+	9.31540i	1.19729	+	0.335704i
$771$	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	0.939783	−	0.341770i	$-0.111027\pi$
$773$	16.6265	+	16.6265i	0.598013	+	0.598013i	−0.341770	+	0.939783i	$0.611027\pi$
$774$	0.169736	−	0.578326i	0.00610102	−	0.0207875i
$775$	3.09810	+	2.95152i	0.111287	+	0.106022i
$776$	−44.4389	−	3.16210i	−1.59526	−	0.113513i
$777$		−	11.2629i		−	0.404053i
$778$	16.3856	+	29.9994i	0.587453	+	1.07553i
$779$	−2.25963	−	2.25963i	−0.0809596	−	0.0809596i
$780$	−17.1117	+	3.94443i	−0.612696	+	0.141233i
$781$		−	17.2318i		−	0.616602i
$782$	−13.2495	−	7.63989i	−0.473801	−	0.273202i
$783$	−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
$790$	0.763956	−	2.72467i	0.0271803	−	0.0969393i
$791$	−16.4830			−0.586067
$792$	2.76058	−	2.39381i	0.0980929	−	0.0850604i
$793$		−	7.47332i		−	0.265385i
$794$	−23.8125	−	43.5968i	−0.845075	−	1.54719i
$795$	−29.4895	+	30.2127i	−1.04589	+	1.07153i
$796$	−1.26577	−	5.81185i	−0.0448639	−	0.205996i
$797$	−4.40772	+	4.40772i	−0.156130	+	0.156130i	−0.780849	−	0.624720i	$-0.785213\pi$
$797$	−4.40772	+	4.40772i	−0.156130	+	0.156130i	0.624720	+	0.780849i	$0.285213\pi$
$798$	0.893031	+	1.63499i	0.0316130	+	0.0578782i
$799$	0.479999	−	1.98230i	0.0169811	−	0.0701286i
$800$	−23.0566	−	16.3827i	−0.815173	−	0.579217i
$801$		−	0.347187i		−	0.0122673i
$802$	−0.249252	−	0.0731542i	−0.00880139	−	0.00258316i
$803$	20.9041	+	20.9041i	0.737688	+	0.737688i
$804$	3.63408	+	16.6861i	0.128164	+	0.588474i
$805$	11.8935	−	0.144065i	0.419191	−	0.00507764i
$806$	−2.51053	+	1.37125i	−0.0884296	+	0.0483001i
$807$	6.33623	−	6.33623i	0.223046	−	0.223046i
$808$	25.9433	+	1.84603i	0.912682	+	0.0649430i
$809$	−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	$0.375890\pi$
$810$	12.7389	+	22.6658i	0.447599	+	0.796396i
$811$	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	$0.127880\pi$
$812$	11.7966	−	2.56918i	0.413978	−	0.0901604i
$813$		−	28.8079i		−	1.01034i
$814$	24.4076	+	7.16351i	0.855487	+	0.251081i
$815$	29.4862	−	0.357165i	1.03286	−	0.0125109i
$816$	−15.3365	+	22.7043i	−0.536884	+	0.794809i
$817$	−0.490760	+	0.490760i	−0.0171695	+	0.0171695i
$818$	2.33697	+	4.27861i	0.0817104	+	0.149598i
$819$	0.813807	+	0.813807i	0.0284367	+	0.0284367i
$820$	8.20983	+	35.6157i	0.286700	+	1.24375i
$821$	6.89783	+	6.89783i	0.240736	+	0.240736i	0.817155	−	0.576419i	$-0.195550\pi$
$821$	6.89783	+	6.89783i	0.240736	+	0.240736i	−0.576419	+	0.817155i	$0.695550\pi$
$822$	−9.96560	+	33.9549i	−0.347590	+	1.18431i
$823$	−27.4990			−0.958555			−0.479277	−	0.877663i	$-0.659101\pi$
$823$	−27.4990			−0.958555			−0.479277	+	0.877663i	$0.659101\pi$
$824$	−13.7056	−	15.8055i	−0.477456	−	0.550609i
$825$	−32.3583	−	30.8274i	−1.12657	−	1.07327i
$826$	−19.6270	−	35.9337i	−0.682909	−	1.25029i
$827$	−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	$-0.273396\pi$
$829$	37.6185			1.30654			0.653272	+	0.757123i	$0.273396\pi$
$830$	−18.5424	−	5.19903i	−0.643618	−	0.180461i
$831$	6.19350			0.214850
$832$	15.1290	−	11.3426i	0.524504	−	0.393234i
$833$	−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
$836$	−4.11117	+	0.895372i	−0.142188	+	0.0309671i
$837$	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	0.848970	−	0.528441i	$-0.177223\pi$
$839$	9.28426	+	9.28426i	0.320528	+	0.320528i	−0.528441	+	0.848970i	$0.677223\pi$
$840$	1.25482	−	21.2709i	0.0432955	−	0.733917i
$841$			20.1397i			0.694473i
$842$	6.69917	+	12.2651i	0.230869	+	0.422683i
$843$			17.9319i			0.617609i
$844$	−45.2607	+	9.85735i	−1.55794	+	0.339304i
$845$	−16.5757	+	0.200781i	−0.570221	+	0.00690707i
$846$	0.161171	+	0.0473030i	0.00554118	+	0.00162631i
$847$	−36.3998			−1.25071
$848$	15.8662	−	42.6021i	0.544849	−	1.46296i
$849$		−	2.80523i		−	0.0962751i
$850$	−25.6021	−	13.9474i	−0.878146	−	0.478393i
$851$	8.76859			0.300583
$852$	−10.3975	+	2.26447i	−0.356212	+	0.0775796i
$853$		−	0.850374i		−	0.0291162i	−0.999894	−	0.0145581i	$-0.995366\pi$
$853$		−	0.850374i		−	0.0291162i	0.999894	−	0.0145581i	$-0.00463416\pi$
$854$	8.70116	+	2.55375i	0.297748	+	0.0873874i
$855$	0.00254264	+	0.209911i	8.69565e−5	+	0.00717880i
$856$	3.29823	+	0.234690i	0.112731	+	0.00802153i
$857$	40.7991			1.39367			0.696836	−	0.717231i	$-0.254591\pi$
$857$	40.7991			1.39367			0.696836	+	0.717231i	$0.254591\pi$
$858$	26.2214	−	14.3221i	0.895185	−	0.488949i
$859$	−18.1487			−0.619227			−0.309614	−	0.950862i	$-0.600200\pi$
$859$	−18.1487			−0.619227			−0.309614	+	0.950862i	$0.600200\pi$
$860$	7.73525	−	1.78306i	0.263770	−	0.0608020i
$861$	−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	−0.0792669	−	0.996853i	$-0.525258\pi$
$863$	26.9558	−	26.9558i	0.917587	−	0.917587i	0.996853	+	0.0792669i	$0.0252579\pi$
$864$	−24.3871	−	18.2329i	−0.829667	−	0.620297i
$865$	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
$868$	−0.738653	−	3.39158i	−0.0250715	−	0.115118i
$869$			4.81462i			0.163325i
$870$	−15.0569	−	4.22174i	−0.510478	−	0.143130i
$871$		−	12.1483i		−	0.411629i
$872$	24.6395	−	21.3659i	0.834398	−	0.723541i
$873$		−	3.78193i		−	0.127999i
$874$	−1.27291	+	0.695260i	−0.0430567	+	0.0235175i
$875$	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	$-0.975537\pi$
$877$		−	4.54735i		−	0.153553i	0.997048	−	0.0767765i	$-0.0244628\pi$
$878$	−1.91776	+	6.53422i	−0.0647213	+	0.220519i
$879$	35.6846	−	35.6846i	1.20361	−	1.20361i
$880$	45.2979	+	16.2482i	1.52699	+	0.547728i
$881$	−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	$0.287298\pi$
$882$	0.860418	−	0.469959i	0.0289718	−	0.0158243i
$883$	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	$0.744714\pi$
$884$	14.0970	−	13.4596i	0.474135	−	0.452695i
$885$	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	$-0.642083\pi$
$887$	−25.7137			−0.863381			−0.431691	+	0.902022i	$0.642083\pi$
$888$	1.11493	−	15.6687i	0.0374144	−	0.525807i
$889$	24.1719	+	24.1719i	0.810699	+	0.810699i
$890$	3.98618	−	2.24035i	0.133617	−	0.0750968i
$891$	−31.2809	−	31.2809i	−1.04795	−	1.04795i
$892$	−30.7621	+	6.69969i	−1.02999	+	0.224322i
$893$	−0.136768	−	0.136768i	−0.00457677	−	0.00457677i
$894$	−21.3178	+	11.6438i	−0.712974	+	0.389425i
$895$	0.372167	+	30.7247i	0.0124402	+	1.02701i
$896$	8.03634	+	21.4906i	0.268475	+	0.717950i
$897$	7.28276	−	7.28276i	0.243164	−	0.243164i
$898$	−2.75857	+	9.39903i	−0.0920546	+	0.313650i
$899$	−2.54738			−0.0849599
$900$	1.24829	−	2.05103i	0.0416098	−	0.0683678i
$901$	11.0281	−	45.5436i	0.367398	−	1.51728i
$902$	−29.8096	−	54.5765i	−0.992551	−	1.81720i
$903$	4.22861	+	4.22861i	0.140719	+	0.140719i
$904$	−22.9308	−	1.63167i	−0.762666	−	0.0542685i
$905$	32.9448	+	32.1562i	1.09512	+	1.06891i
$906$	−41.7338	+	22.7949i	−1.38651	+	0.757311i
$907$	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
$910$	−4.09222	+	14.5950i	−0.135656	+	0.483820i
$911$	−7.27657	+	7.27657i	−0.241083	+	0.241083i	−0.817298	−	0.576215i	$-0.804529\pi$
$911$	−7.27657	+	7.27657i	−0.241083	+	0.241083i	0.576215	+	0.817298i	$0.304529\pi$
$912$	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
$918$	−27.1903	−	15.6784i	−0.897412	−	0.517463i
$919$	−55.9667			−1.84617			−0.923086	−	0.384593i	$-0.874342\pi$
$919$	−55.9667			−1.84617			−0.923086	+	0.384593i	$0.874342\pi$
$920$	16.5603	+	0.976930i	0.545976	+	0.0322084i
$921$	−13.9423	+	13.9423i	−0.459416	+	0.459416i
$922$	46.8136	−	25.5695i	1.54172	−	0.842088i
$923$	7.56987			0.249165
$924$	7.71493	+	35.4236i	0.253802	+	1.16535i
$925$	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	$0.318838\pi$
$930$	−1.21378	+	4.32896i	−0.0398013	+	0.141952i
$931$	−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
$940$	0.496915	+	2.15571i	0.0162076	+	0.0703114i
$941$	41.1366	−	41.1366i	1.34101	−	1.34101i	0.445963	−	0.895051i	$-0.352861\pi$
$941$	41.1366	−	41.1366i	1.34101	−	1.34101i	0.895051	−	0.445963i	$-0.147139\pi$
$942$	−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
$946$	−11.8533	+	6.47424i	−0.385383	+	0.210496i
$947$			13.7599i			0.447137i	0.974688	+	0.223569i	$0.0717707\pi$
$947$			13.7599i			0.447137i	−0.974688	+	0.223569i	$0.928229\pi$
$948$	2.90509	−	0.632701i	0.0943531	−	0.0205492i
$949$	−9.18308	+	9.18308i	−0.298095	+	0.298095i
$950$	−2.39366	+	1.38372i	−0.0776605	+	0.0448938i
$951$			33.0164i			1.07063i
$952$	10.8538	+	21.0125i	0.351773	+	0.681019i
$953$	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
$960$	3.85132	−	29.4675i	0.124301	−	0.951060i
$961$		−	30.2676i		−	0.976375i
$962$	−3.14691	+	10.7222i	−0.101460	+	0.345697i
$963$			0.280693i			0.00904521i
$964$	3.47007	+	15.9331i	0.111764	+	0.513170i
$965$	−35.4243	+	0.429093i	−1.14035	+	0.0138130i
$966$	5.99067	+	10.9679i	0.192747	+	0.352887i
$967$	4.48443	−	4.48443i	0.144210	−	0.144210i	−0.631316	−	0.775526i	$-0.717485\pi$
$967$	4.48443	−	4.48443i	0.144210	−	0.144210i	0.775526	+	0.631316i	$0.217485\pi$
$968$	−50.6387	−	3.60326i	−1.62759	−	0.115813i
$969$	1.39493	+	2.28632i	0.0448117	+	0.0734473i
$970$	43.4217	−	24.4043i	1.39419	−	0.783575i
$971$		−	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
$974$	12.7751	+	23.3890i	0.409339	+	0.749433i
$975$	13.5424	−	14.2149i	0.433703	−	0.455241i
$976$	11.8521	+	4.41406i	0.379376	+	0.141291i
$977$	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	$0.636354\pi$
$978$	14.8520	+	27.1916i	0.474914	+	0.869490i
$979$	−5.50129	+	5.50129i	−0.175822	+	0.175822i
$980$	10.9479	+	6.84618i	0.349719	+	0.218693i
$981$	1.95762	+	1.95762i	0.0625021	+	0.0625021i
$982$	−9.28529	−	16.9998i	−0.296305	−	0.542487i
$983$			36.4754i			1.16338i	0.813409	+	0.581692i	$0.197609\pi$
$983$			36.4754i			1.16338i	−0.813409	+	0.581692i	$0.802391\pi$
$984$	−29.0136	+	25.1589i	−0.924919	+	0.802035i
$985$	−28.8013	+	0.348868i	−0.917684	+	0.0111159i
$986$	16.7626	−	4.50142i	0.533831	−	0.143355i
$987$	−1.17845	+	1.17845i	−0.0375106	+	0.0375106i
$988$	−0.393334	−	1.80602i	−0.0125136	−	0.0574572i
$989$	−3.29214	+	3.29214i	−0.104684	+	0.104684i
$990$	−1.10290	+	3.93351i	−0.0350524	+	0.125015i
$991$	−16.0396	−	16.0396i	−0.509514	−	0.509514i	0.404863	−	0.914377i	$-0.367319\pi$
$991$	−16.0396	−	16.0396i	−0.509514	−	0.509514i	−0.914377	+	0.404863i	$0.867319\pi$
$992$	−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
$996$	−4.30579	−	19.7703i	−0.136434	−	0.626446i
$997$		−	14.2198i		−	0.450345i	−0.974319	−	0.225172i	$-0.927705\pi$
$997$		−	14.2198i		−	0.450345i	0.974319	−	0.225172i	$-0.0722946\pi$
$998$	−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.123.16	yes	208
5.2	odd	4		680.2.t.a.667.37	yes	208
8.3	odd	2	inner	680.2.bl.a.123.68	yes	208
17.13	even	4		680.2.t.a.523.89	yes	208
40.27	even	4		680.2.t.a.667.89	yes	208
85.47	odd	4	inner	680.2.bl.a.387.68	yes	208
136.115	odd	4		680.2.t.a.523.37	✓	208
680.387	even	4	inner	680.2.bl.a.387.16	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.37	✓	208	136.115	odd	4
680.2.t.a.523.89	yes	208	17.13	even	4
680.2.t.a.667.37	yes	208	5.2	odd	4
680.2.t.a.667.89	yes	208	40.27	even	4
680.2.bl.a.123.16	yes	208	1.1	even	1	trivial
680.2.bl.a.123.68	yes	208	8.3	odd	2	inner
680.2.bl.a.387.16	yes	208	680.387	even	4	inner
680.2.bl.a.387.68	yes	208	85.47	odd	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+(-1.24114 + 0.677911i) q^{2} +1.66129 q^{3} +(1.08087 - 1.68277i) q^{4} +(0.0270834 + 2.23590i) q^{5} +(-2.06190 + 1.12621i) q^{6} +2.02798i q^{7} +(-0.200753 + 2.82129i) q^{8} -0.240104 q^{9} +(-1.54936 - 2.75672i) q^{10} +(3.80452 + 3.80452i) q^{11} +(1.79565 - 2.79557i) q^{12} +(-1.67131 + 1.67131i) q^{13} +(-1.37479 - 2.51702i) q^{14} +(0.0449935 + 3.71449i) q^{15} +(-1.66342 - 3.63772i) q^{16} +(-2.14745 - 3.51972i) q^{17} +(0.298003 - 0.162769i) q^{18} -0.391006 q^{19} +(3.79178 + 2.37116i) q^{20} +3.36908i q^{21} +(-7.30108 - 2.14283i) q^{22} -2.62296 q^{23} +(-0.333509 + 4.68700i) 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} +(-2.57394 - 4.57972i) q^{30} +(-0.605139 - 0.605139i) q^{31} +(4.53060 + 3.38728i) q^{32} +(6.32043 + 6.32043i) q^{33} +(5.05136 + 2.91270i) q^{34} +(-4.53438 + 0.0549247i) q^{35} +(-0.259522 + 0.404039i) q^{36} -3.34301 q^{37} +(0.485294 - 0.265067i) q^{38} +(-2.77654 + 2.77654i) q^{39} +(-6.31358 - 0.372453i) q^{40} +(5.77901 + 5.77901i) q^{41} +(-2.28393 - 4.18151i) q^{42} +(1.25512 - 1.25512i) q^{43} +(10.5143 - 2.28992i) q^{44} +(-0.00650283 - 0.536849i) q^{45} +(3.25547 - 1.77813i) q^{46} +(0.349785 + 0.349785i) q^{47} +(-2.76343 - 6.04333i) q^{48} +2.88728 q^{49} +(6.12179 - 3.53888i) q^{50} +(-3.56755 - 5.84729i) q^{51} +(1.00596 + 4.61891i) q^{52} +(8.03639 + 8.03639i) q^{53} +(6.68078 - 3.64903i) q^{54} +(-8.40350 + 8.60958i) q^{55} +(-5.72154 - 0.407123i) q^{56} -0.649575 q^{57} +(-1.18549 + 4.03920i) q^{58} +14.2763 q^{59} +(6.29927 + 3.93919i) 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} +(-8.24401 - 0.190706i) q^{68} -4.35751 q^{69} +(5.59058 - 3.14207i) q^{70} +(-2.26465 - 2.26465i) q^{71} +(0.0482014 - 0.677403i) q^{72} +5.49453 q^{73} +(4.14916 - 2.26626i) 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} +(8.08855 - 3.81778i) 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} +(0.372007 + 0.661898i) 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} +(7.52665 + 5.62727i) q^{96} +15.7512i q^{97} +(-3.58353 + 1.95732i) 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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