LMFDB - Embedded newform 755.2.f.e.452.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,2,Mod(452,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.452"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			452.17
Character	$\chi$	$=$	755.452
Dual form			755.2.f.e.603.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02416 - 1.02416i) q^{2} +(-1.50524 - 1.50524i) q^{3} +0.0978212i q^{4} +(-1.59568 + 1.56646i) q^{5} +3.08322i q^{6} +(-1.61807 + 1.61807i) q^{7} +(-1.94814 + 1.94814i) q^{8} +1.53150i q^{9} +(3.23855 + 0.0299191i) q^{10} -3.89135 q^{11} +(0.147244 - 0.147244i) q^{12} +(3.39143 + 3.39143i) q^{13} +3.31433 q^{14} +(4.75979 + 0.0439729i) q^{15} +4.18607 q^{16} +(-1.95449 - 1.95449i) q^{17} +(1.56851 - 1.56851i) q^{18} -5.23589i q^{19} +(-0.153233 - 0.156091i) q^{20} +4.87116 q^{21} +(3.98538 + 3.98538i) q^{22} +(1.01371 + 1.01371i) q^{23} +5.86484 q^{24} +(0.0923762 - 4.99915i) q^{25} -6.94676i q^{26} +(-2.21045 + 2.21045i) q^{27} +(-0.158281 - 0.158281i) q^{28} -2.26555i q^{29} +(-4.82976 - 4.91983i) q^{30} +6.03258 q^{31} +(-0.390939 - 0.390939i) q^{32} +(5.85743 + 5.85743i) q^{33} +4.00343i q^{34} +(0.0472689 - 5.11656i) q^{35} -0.149813 q^{36} +(0.341972 + 0.341972i) q^{37} +(-5.36241 + 5.36241i) q^{38} -10.2098i q^{39} +(0.0569114 - 6.16030i) q^{40} +0.909743i q^{41} +(-4.98886 - 4.98886i) q^{42} +(-3.13702 + 3.13702i) q^{43} -0.380657i q^{44} +(-2.39904 - 2.44378i) q^{45} -2.07641i q^{46} +(-0.568201 - 0.568201i) q^{47} +(-6.30105 - 6.30105i) q^{48} +1.76372i q^{49} +(-5.21455 + 5.02533i) q^{50} +5.88395i q^{51} +(-0.331754 + 0.331754i) q^{52} +(3.49745 + 3.49745i) q^{53} +4.52772 q^{54} +(6.20935 - 6.09567i) q^{55} -6.30444i q^{56} +(-7.88128 + 7.88128i) q^{57} +(-2.32030 + 2.32030i) q^{58} -8.62899i q^{59} +(-0.00430148 + 0.465608i) q^{60} +9.34466i q^{61} +(-6.17835 - 6.17835i) q^{62} +(-2.47807 - 2.47807i) q^{63} -7.57138i q^{64} +(-10.7242 - 0.0990744i) q^{65} -11.9979i q^{66} +(7.42355 - 7.42355i) q^{67} +(0.191190 - 0.191190i) q^{68} -3.05176i q^{69} +(-5.28860 + 5.19178i) q^{70} -5.66988i q^{71} +(-2.98358 - 2.98358i) q^{72} +(-5.20174 - 5.20174i) q^{73} -0.700470i q^{74} +(-7.66397 + 7.38587i) q^{75} +0.512181 q^{76} +(6.29647 - 6.29647i) q^{77} +(-10.4565 + 10.4565i) q^{78} +7.68350 q^{79} +(-6.67962 + 6.55734i) q^{80} +11.2490 q^{81} +(0.931726 - 0.931726i) q^{82} +(-3.07254 - 3.07254i) q^{83} +0.476502i q^{84} +(6.18037 + 0.0570968i) q^{85} +6.42564 q^{86} +(-3.41020 + 3.41020i) q^{87} +(7.58091 - 7.58091i) q^{88} +9.17958 q^{89} +(-0.0458210 + 4.95984i) q^{90} -10.9751 q^{91} +(-0.0991625 + 0.0991625i) q^{92} +(-9.08048 - 9.08048i) q^{93} +1.16386i q^{94} +(8.20184 + 8.35480i) q^{95} +1.17692i q^{96} +(-2.31637 - 2.31637i) q^{97} +(1.80634 - 1.80634i) q^{98} -5.95961i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 12 q^{5} + 12 q^{8} + 16 q^{10} - 24 q^{16} + 8 q^{17} + 4 q^{18} + 48 q^{20} - 44 q^{21} - 32 q^{22} - 40 q^{25} + 20 q^{31} - 56 q^{32} - 304 q^{36} - 8 q^{37} + 16 q^{38} + 44 q^{42} + 20 q^{43}+ \cdots - 188 q^{98}+O(q^{100}) $ 108 * q - 12 * q^5 + 12 * q^8 + 16 * q^10 - 24 * q^16 + 8 * q^17 + 4 * q^18 + 48 * q^20 - 44 * q^21 - 32 * q^22 - 40 * q^25 + 20 * q^31 - 56 * q^32 - 304 * q^36 - 8 * q^37 + 16 * q^38 + 44 * q^42 + 20 * q^43 + 12 * q^45 + 20 * q^47 + 56 * q^50 - 80 * q^55 - 52 * q^58 - 48 * q^62 + 176 * q^68 + 80 * q^72 + 128 * q^76 - 60 * q^80 + 36 * q^81 + 48 * q^85 - 160 * q^86 + 24 * q^88 + 36 * q^90 - 96 * q^91 - 24 * q^95 + 104 * q^97 - 188 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.02416	−	1.02416i	−0.724193	−	0.724193i	0.245264	−	0.969456i	$-0.421125\pi$
$2$	−1.02416	−	1.02416i	−0.724193	−	0.724193i	−0.969456	+	0.245264i	$0.921125\pi$
$3$	−1.50524	−	1.50524i	−0.869051	−	0.869051i	0.123316	−	0.992367i	$-0.460647\pi$
$3$	−1.50524	−	1.50524i	−0.869051	−	0.869051i	−0.992367	+	0.123316i	$0.960647\pi$
$4$			0.0978212i			0.0489106i
$5$	−1.59568	+	1.56646i	−0.713609	+	0.700544i
$5$	−1.59568	+	1.56646i	−0.713609	+	0.700544i
$6$			3.08322i			1.25872i
$7$	−1.61807	+	1.61807i	−0.611572	+	0.611572i	−0.943355	−	0.331784i	$-0.892350\pi$
$7$	−1.61807	+	1.61807i	−0.611572	+	0.611572i	0.331784	+	0.943355i	$0.392350\pi$
$8$	−1.94814	+	1.94814i	−0.688772	+	0.688772i
$9$			1.53150i			0.510500i
$10$	3.23855	+	0.0299191i	1.02412	+	0.00946124i
$11$	−3.89135			−1.17329			−0.586644	−	0.809845i	$-0.699551\pi$
$11$	−3.89135			−1.17329			−0.586644	+	0.809845i	$0.699551\pi$
$12$	0.147244	−	0.147244i	0.0425058	−	0.0425058i
$13$	3.39143	+	3.39143i	0.940613	+	0.940613i	0.998333	−	0.0577196i	$-0.0183829\pi$
$13$	3.39143	+	3.39143i	0.940613	+	0.940613i	−0.0577196	+	0.998333i	$0.518383\pi$
$14$	3.31433			0.885791
$15$	4.75979	+	0.0439729i	1.22897	+	0.0113537i
$16$	4.18607			1.04652
$17$	−1.95449	−	1.95449i	−0.474033	−	0.474033i	0.429184	−	0.903217i	$-0.358801\pi$
$17$	−1.95449	−	1.95449i	−0.474033	−	0.474033i	−0.903217	+	0.429184i	$0.858801\pi$
$18$	1.56851	−	1.56851i	0.369700	−	0.369700i
$19$		−	5.23589i		−	1.20120i	−0.799551	−	0.600598i	$-0.794929\pi$
$19$		−	5.23589i		−	1.20120i	0.799551	−	0.600598i	$-0.205071\pi$
$20$	−0.153233	−	0.156091i	−0.0342640	−	0.0349030i
$21$	4.87116			1.06297
$22$	3.98538	+	3.98538i	0.849687	+	0.849687i
$23$	1.01371	+	1.01371i	0.211374	+	0.211374i	0.804851	−	0.593477i	$-0.202245\pi$
$23$	1.01371	+	1.01371i	0.211374	+	0.211374i	−0.593477	+	0.804851i	$0.702245\pi$
$24$	5.86484			1.19716
$25$	0.0923762	−	4.99915i	0.0184752	−	0.999829i
$26$		−	6.94676i		−	1.36237i
$27$	−2.21045	+	2.21045i	−0.425401	+	0.425401i
$28$	−0.158281	−	0.158281i	−0.0299123	−	0.0299123i
$29$		−	2.26555i		−	0.420703i	−0.977626	−	0.210351i	$-0.932539\pi$
$29$		−	2.26555i		−	0.420703i	0.977626	−	0.210351i	$-0.0674608\pi$
$30$	−4.82976	−	4.91983i	−0.881790	−	0.898235i
$31$	6.03258			1.08348			0.541742	−	0.840545i	$-0.317765\pi$
$31$	6.03258			1.08348			0.541742	+	0.840545i	$0.317765\pi$
$32$	−0.390939	−	0.390939i	−0.0691090	−	0.0691090i
$33$	5.85743	+	5.85743i	1.01965	+	1.01965i
$34$			4.00343i			0.686583i
$35$	0.0472689	−	5.11656i	0.00798989	−	0.864856i
$36$	−0.149813			−0.0249688
$37$	0.341972	+	0.341972i	0.0562198	+	0.0562198i	0.734658	−	0.678438i	$-0.237343\pi$
$37$	0.341972	+	0.341972i	0.0562198	+	0.0562198i	−0.678438	+	0.734658i	$0.737343\pi$
$38$	−5.36241	+	5.36241i	−0.869898	+	0.869898i
$39$		−	10.2098i		−	1.63488i
$40$	0.0569114	−	6.16030i	0.00899848	−	0.974029i
$41$			0.909743i			0.142078i	0.997474	+	0.0710390i	$0.0226315\pi$
$41$			0.909743i			0.142078i	−0.997474	+	0.0710390i	$0.977369\pi$
$42$	−4.98886	−	4.98886i	−0.769798	−	0.769798i
$43$	−3.13702	+	3.13702i	−0.478391	+	0.478391i	−0.904617	−	0.426226i	$-0.859843\pi$
$43$	−3.13702	+	3.13702i	−0.478391	+	0.478391i	0.426226	+	0.904617i	$0.359843\pi$
$44$		−	0.380657i		−	0.0573862i
$45$	−2.39904	−	2.44378i	−0.357628	−	0.364297i
$46$		−	2.07641i		−	0.306150i
$47$	−0.568201	−	0.568201i	−0.0828806	−	0.0828806i	0.664451	−	0.747332i	$-0.268665\pi$
$47$	−0.568201	−	0.568201i	−0.0828806	−	0.0828806i	−0.747332	+	0.664451i	$0.768665\pi$
$48$	−6.30105	−	6.30105i	−0.909478	−	0.909478i
$49$			1.76372i			0.251961i
$50$	−5.21455	+	5.02533i	−0.737449	+	0.710690i
$51$			5.88395i			0.823918i
$52$	−0.331754	+	0.331754i	−0.0460059	+	0.0460059i
$53$	3.49745	+	3.49745i	0.480412	+	0.480412i	0.905263	−	0.424851i	$-0.139674\pi$
$53$	3.49745	+	3.49745i	0.480412	+	0.480412i	−0.424851	+	0.905263i	$0.639674\pi$
$54$	4.52772			0.616144
$55$	6.20935	−	6.09567i	0.837268	−	0.821940i
$56$		−	6.30444i		−	0.842467i
$57$	−7.88128	+	7.88128i	−1.04390	+	1.04390i
$58$	−2.32030	+	2.32030i	−0.304670	+	0.304670i
$59$		−	8.62899i		−	1.12340i	−0.827341	−	0.561699i	$-0.810148\pi$
$59$		−	8.62899i		−	1.12340i	0.827341	−	0.561699i	$-0.189852\pi$
$60$	−0.00430148	+	0.465608i	−0.000555318	+	0.0601097i
$61$			9.34466i			1.19646i	0.801324	+	0.598231i	$0.204129\pi$
$61$			9.34466i			1.19646i	−0.801324	+	0.598231i	$0.795871\pi$
$62$	−6.17835	−	6.17835i	−0.784651	−	0.784651i
$63$	−2.47807	−	2.47807i	−0.312207	−	0.312207i
$64$		−	7.57138i		−	0.946422i
$65$	−10.7242	−	0.0990744i	−1.33017	−	0.0122887i
$66$		−	11.9979i		−	1.47684i
$67$	7.42355	−	7.42355i	0.906931	−	0.906931i	−0.0890925	−	0.996023i	$-0.528397\pi$
$67$	7.42355	−	7.42355i	0.906931	−	0.906931i	0.996023	+	0.0890925i	$0.0283967\pi$
$68$	0.191190	−	0.191190i	0.0231852	−	0.0231852i
$69$		−	3.05176i		−	0.367389i
$70$	−5.28860	+	5.19178i	−0.632109	+	0.620536i
$71$		−	5.66988i		−	0.672892i	−0.941703	−	0.336446i	$-0.890775\pi$
$71$		−	5.66988i		−	0.672892i	0.941703	−	0.336446i	$-0.109225\pi$
$72$	−2.98358	−	2.98358i	−0.351618	−	0.351618i
$73$	−5.20174	−	5.20174i	−0.608818	−	0.608818i	0.333819	−	0.942637i	$-0.391662\pi$
$73$	−5.20174	−	5.20174i	−0.608818	−	0.608818i	−0.942637	+	0.333819i	$0.891662\pi$
$74$		−	0.700470i		−	0.0814280i
$75$	−7.66397	+	7.38587i	−0.884959	+	0.852847i
$76$	0.512181			0.0587512
$77$	6.29647	−	6.29647i	0.717549	−	0.717549i
$78$	−10.4565	+	10.4565i	−1.18397	+	1.18397i
$79$	7.68350			0.864461			0.432231	−	0.901763i	$-0.357727\pi$
$79$	7.68350			0.864461			0.432231	+	0.901763i	$0.357727\pi$
$80$	−6.67962	+	6.55734i	−0.746805	+	0.733133i
$81$	11.2490			1.24989
$82$	0.931726	−	0.931726i	0.102892	−	0.102892i
$83$	−3.07254	−	3.07254i	−0.337255	−	0.337255i	0.518078	−	0.855333i	$-0.326648\pi$
$83$	−3.07254	−	3.07254i	−0.337255	−	0.337255i	−0.855333	+	0.518078i	$0.826648\pi$
$84$			0.476502i			0.0519907i
$85$	6.18037	+	0.0570968i	0.670355	+	0.00619302i
$86$	6.42564			0.692895
$87$	−3.41020	+	3.41020i	−0.365612	+	0.365612i
$88$	7.58091	−	7.58091i	0.808128	−	0.808128i
$89$	9.17958			0.973033			0.486517	−	0.873671i	$-0.338267\pi$
$89$	9.17958			0.973033			0.486517	+	0.873671i	$0.338267\pi$
$90$	−0.0458210	+	4.95984i	−0.00482996	+	0.522813i
$91$	−10.9751			−1.15050
$92$	−0.0991625	+	0.0991625i	−0.0103384	+	0.0103384i
$93$	−9.08048	−	9.08048i	−0.941602	−	0.941602i
$94$			1.16386i			0.120043i
$95$	8.20184	+	8.35480i	0.841491	+	0.857185i
$96$			1.17692i			0.120118i
$97$	−2.31637	−	2.31637i	−0.235192	−	0.235192i	0.579664	−	0.814856i	$-0.303184\pi$
$97$	−2.31637	−	2.31637i	−0.235192	−	0.235192i	−0.814856	+	0.579664i	$0.803184\pi$
$98$	1.80634	−	1.80634i	0.182468	−	0.182468i
$99$		−	5.95961i		−	0.598963i
$100$	0.489022	+	0.00903635i	0.0489022	+	0.000903635i
$101$			1.48124i			0.147389i	0.997281	+	0.0736944i	$0.0234789\pi$
$101$			1.48124i			0.147389i	−0.997281	+	0.0736944i	$0.976521\pi$
$102$	6.02613	−	6.02613i	0.596676	−	0.596676i
$103$	−8.37437	+	8.37437i	−0.825151	+	0.825151i	−0.986842	−	0.161690i	$-0.948305\pi$
$103$	−8.37437	+	8.37437i	−0.825151	+	0.825151i	0.161690	+	0.986842i	$0.448305\pi$
$104$	−13.2140			−1.29574
$105$	−7.77280	+	7.63050i	−0.758548	+	0.744660i
$106$		−	7.16393i		−	0.695822i
$107$	5.72708	−	5.72708i	0.553658	−	0.553658i	−0.373837	−	0.927495i	$-0.621958\pi$
$107$	5.72708	−	5.72708i	0.553658	−	0.553658i	0.927495	+	0.373837i	$0.121958\pi$
$108$	−0.216229	−	0.216229i	−0.0208066	−	0.0208066i
$109$	19.3084			1.84941			0.924705	−	0.380684i	$-0.124311\pi$
$109$	19.3084			1.84941			0.924705	+	0.380684i	$0.124311\pi$
$110$	−12.6023	−	0.116426i	−1.20159	−	0.0111008i
$111$		−	1.02950i		−	0.0977158i
$112$	−6.77334	+	6.77334i	−0.640021	+	0.640021i
$113$	14.7988	+	14.7988i	1.39215	+	1.39215i	0.820493	+	0.571657i	$0.193699\pi$
$113$	14.7988	+	14.7988i	1.39215	+	1.39215i	0.571657	+	0.820493i	$0.306301\pi$
$114$	16.1434			1.51197
$115$	−3.20550	−	0.0296137i	−0.298915	−	0.00276150i
$116$	0.221619			0.0205768
$117$	−5.19397	+	5.19397i	−0.480183	+	0.480183i
$118$	−8.83750	+	8.83750i	−0.813557	+	0.813557i
$119$	6.32498			0.579810
$120$	−9.35840	+	9.18707i	−0.854301	+	0.838661i
$121$	4.14264			0.376604
$122$	9.57046	−	9.57046i	0.866469	−	0.866469i
$123$	1.36938	−	1.36938i	0.123473	−	0.123473i
$124$			0.590114i			0.0529938i
$125$	7.68358	+	8.12173i	0.687241	+	0.726430i
$126$			5.07589i			0.452196i
$127$	8.24946	+	8.24946i	0.732021	+	0.732021i	0.971020	−	0.238999i	$-0.0768191\pi$
$127$	8.24946	+	8.24946i	0.732021	+	0.732021i	−0.238999	+	0.971020i	$0.576819\pi$
$128$	−8.53620	+	8.53620i	−0.754501	+	0.754501i
$129$	9.44394			0.831493
$130$	10.8818	+	11.0848i	0.954401	+	0.972200i
$131$			15.7771i			1.37846i	0.724545	+	0.689228i	$0.242050\pi$
$131$			15.7771i			1.37846i	−0.724545	+	0.689228i	$0.757950\pi$
$132$	−0.572980	+	0.572980i	−0.0498715	+	0.0498715i
$133$	8.47202	+	8.47202i	0.734618	+	0.734618i
$134$	−15.2059			−1.31359
$135$	0.0645742	−	6.98975i	0.00555766	−	0.601582i
$136$	7.61524			0.653002
$137$	7.11810	+	7.11810i	0.608141	+	0.608141i	0.942460	−	0.334319i	$-0.108506\pi$
$137$	7.11810	+	7.11810i	0.608141	+	0.608141i	−0.334319	+	0.942460i	$0.608506\pi$
$138$	−3.12550	+	3.12550i	−0.266060	+	0.266060i
$139$		−	9.63234i		−	0.817005i	−0.912757	−	0.408502i	$-0.866051\pi$
$139$		−	9.63234i		−	0.817005i	0.912757	−	0.408502i	$-0.133949\pi$
$140$	0.500508	+	0.00462390i	0.0423006	+	0.000390790i
$141$			1.71056i			0.144055i
$142$	−5.80689	+	5.80689i	−0.487303	+	0.487303i
$143$	−13.1973	−	13.1973i	−1.10361	−	1.10361i
$144$			6.41097i			0.534247i
$145$	3.54891	+	3.61509i	0.294721	+	0.300217i
$146$			10.6549i			0.881803i
$147$	2.65483	−	2.65483i	0.218967	−	0.218967i
$148$	−0.0334521	+	0.0334521i	−0.00274975	+	0.00274975i
$149$	−8.50873			−0.697062			−0.348531	−	0.937297i	$-0.613319\pi$
$149$	−8.50873			−0.697062			−0.348531	+	0.937297i	$0.613319\pi$
$150$	15.4135	+	0.284817i	1.25851	+	0.0232552i
$151$	10.3324	−	6.65144i	0.840838	−	0.541286i
$151$	10.3324	−	6.65144i	0.840838	−	0.541286i
$152$	10.2003	+	10.2003i	0.827351	+	0.827351i
$153$	2.99330	−	2.99330i	0.241994	−	0.241994i
$154$	−12.8972			−1.03929
$155$	−9.62605	+	9.44982i	−0.773183	+	0.759028i
$156$	0.998738			0.0799630
$157$	10.3804	−	10.3804i	0.828445	−	0.828445i	−0.158857	−	0.987302i	$-0.550781\pi$
$157$	10.3804	−	10.3804i	0.828445	−	0.828445i	0.987302	+	0.158857i	$0.0507807\pi$
$158$	−7.86916	−	7.86916i	−0.626037	−	0.626037i
$159$		−	10.5290i		−	0.835005i
$160$	1.23621	+	0.0114206i	0.0977306	+	0.000902876i
$161$	−3.28051			−0.258540
$162$	−11.5208	−	11.5208i	−0.905161	−	0.905161i
$163$	−15.8721	−	15.8721i	−1.24320	−	1.24320i	−0.958667	−	0.284531i	$-0.908162\pi$
$163$	−15.8721	−	15.8721i	−1.24320	−	1.24320i	−0.284531	−	0.958667i	$-0.591838\pi$
$164$	−0.0889922			−0.00694912
$165$	−18.5220	−	0.171114i	−1.44194	−	0.0133212i
$166$			6.29357i			0.488476i
$167$	11.3166	+	11.3166i	0.875703	+	0.875703i	0.993087	−	0.117384i	$-0.0374507\pi$
$167$	11.3166	+	11.3166i	0.875703	+	0.875703i	−0.117384	+	0.993087i	$0.537451\pi$
$168$	−9.48971	+	9.48971i	−0.732147	+	0.732147i
$169$			10.0036i			0.769507i
$170$	−6.27123	−	6.38819i	−0.480982	−	0.489952i
$171$	8.01877			0.613210
$172$	−0.306867	−	0.306867i	−0.0233984	−	0.0233984i
$173$	7.91225	−	7.91225i	0.601557	−	0.601557i	−0.339168	−	0.940726i	$-0.610146\pi$
$173$	7.91225	−	7.91225i	0.601557	−	0.601557i	0.940726	+	0.339168i	$0.110146\pi$
$174$	6.98521			0.529547
$175$	7.93948	+	8.23842i	0.600168	+	0.622766i
$176$	−16.2895			−1.22787
$177$	−12.9887	+	12.9887i	−0.976291	+	0.976291i
$178$	−9.40139	−	9.40139i	−0.704664	−	0.704664i
$179$	−25.7277			−1.92298			−0.961491	−	0.274838i	$-0.911376\pi$
$179$	−25.7277			−1.92298			−0.961491	+	0.274838i	$0.911376\pi$
$180$	0.239053	−	0.234677i	0.0178180	−	0.0174918i
$181$			18.6620i			1.38713i	0.720393	+	0.693566i	$0.243961\pi$
$181$			18.6620i			1.38713i	−0.720393	+	0.693566i	$0.756039\pi$
$182$	11.2403	+	11.2403i	0.833187	+	0.833187i
$183$	14.0660	−	14.0660i	1.03979	−	1.03979i
$184$	−3.94971			−0.291176
$185$	−1.08136	−	0.00999009i	−0.0795035	−	0.000734486i
$186$			18.5998i			1.36380i
$187$	7.60561	+	7.60561i	0.556177	+	0.556177i
$188$	0.0555821	−	0.0555821i	0.00405374	−	0.00405374i
$189$		−	7.15330i		−	0.520326i
$190$	0.156653	−	16.9567i	0.0113648	−	1.23017i
$191$	4.80675			0.347804			0.173902	−	0.984763i	$-0.444362\pi$
$191$	4.80675			0.347804			0.173902	+	0.984763i	$0.444362\pi$
$192$	−11.3967	+	11.3967i	−0.822489	+	0.822489i
$193$	3.94027	−	3.94027i	0.283627	−	0.283627i	−0.550927	−	0.834554i	$-0.685726\pi$
$193$	3.94027	−	3.94027i	0.283627	−	0.283627i	0.834554	+	0.550927i	$0.185726\pi$
$194$			4.74469i			0.340649i
$195$	15.9933	+	16.2916i	1.14531	+	1.16667i
$196$	−0.172530			−0.0123235
$197$	−1.56471	+	1.56471i	−0.111481	+	0.111481i	−0.760647	−	0.649166i	$-0.775118\pi$
$197$	−1.56471	+	1.56471i	−0.111481	+	0.111481i	0.649166	+	0.760647i	$0.275118\pi$
$198$	−6.10361	+	6.10361i	−0.433765	+	0.433765i
$199$	8.43614			0.598022			0.299011	−	0.954250i	$-0.403343\pi$
$199$	8.43614			0.598022			0.299011	+	0.954250i	$0.403343\pi$
$200$	9.55908	+	9.91901i	0.675929	+	0.701380i
$201$	−22.3485			−1.57634
$202$	1.51703	−	1.51703i	0.106738	−	0.106738i
$203$	3.66581	+	3.66581i	0.257290	+	0.257290i
$204$	−0.575575			−0.0402983
$205$	−1.42508	−	1.45166i	−0.0995320	−	0.101388i
$206$	17.1535			1.19514
$207$	−1.55250	+	1.55250i	−0.107906	+	0.107906i
$208$	14.1968	+	14.1968i	0.984369	+	0.984369i
$209$			20.3747i			1.40935i
$210$	15.7755	+	0.145740i	1.08861	+	0.0100570i
$211$			26.9327i			1.85413i	0.374905	+	0.927063i	$0.377675\pi$
$211$			26.9327i			1.85413i	−0.374905	+	0.927063i	$0.622325\pi$
$212$	−0.342125	+	0.342125i	−0.0234972	+	0.0234972i
$213$	−8.53454	+	8.53454i	−0.584777	+	0.584777i
$214$	−11.7309			−0.801910
$215$	0.0916424	−	9.91971i	0.00624996	−	0.676519i
$216$		−	8.61253i		−	0.586009i
$217$	−9.76111	+	9.76111i	−0.662628	+	0.662628i
$218$	−19.7750	−	19.7750i	−1.33933	−	1.33933i
$219$			15.6597i			1.05819i
$220$	0.596286	+	0.607406i	0.0402016	+	0.0409513i
$221$		−	13.2570i		−	0.891764i
$222$	−1.05438	+	1.05438i	−0.0707651	+	0.0707651i
$223$	6.45689	−	6.45689i	0.432385	−	0.432385i	−0.457054	−	0.889439i	$-0.651095\pi$
$223$	6.45689	−	6.45689i	0.432385	−	0.432385i	0.889439	+	0.457054i	$0.151095\pi$
$224$	1.26513			0.0845301
$225$	7.65619	+	0.141474i	0.510412	+	0.00943161i
$226$		−	30.3127i		−	2.01637i
$227$	−1.72903	−	1.72903i	−0.114759	−	0.114759i	0.647395	−	0.762155i	$-0.275858\pi$
$227$	−1.72903	−	1.72903i	−0.114759	−	0.114759i	−0.762155	+	0.647395i	$0.775858\pi$
$228$	−0.770956	−	0.770956i	−0.0510578	−	0.0510578i
$229$			16.6245i			1.09858i	0.835632	+	0.549290i	$0.185102\pi$
$229$			16.6245i			1.09858i	−0.835632	+	0.549290i	$0.814898\pi$
$230$	3.25263	+	3.31329i	0.214472	+	0.218472i
$231$	−18.9554			−1.24717
$232$	4.41362	+	4.41362i	0.289768	+	0.289768i
$233$	−6.30147	−	6.30147i	−0.412823	−	0.412823i	0.469898	−	0.882721i	$-0.344291\pi$
$233$	−6.30147	−	6.30147i	−0.412823	−	0.412823i	−0.882721	+	0.469898i	$0.844291\pi$
$234$	10.6389			0.695490
$235$	1.79673	+	0.0165990i	0.117206	+	0.00108280i
$236$	0.844098			0.0549461
$237$	−11.5655	−	11.5655i	−0.751261	−	0.751261i
$238$	−6.47782	−	6.47782i	−0.419894	−	0.419894i
$239$		−	27.0204i		−	1.74780i	−0.486104	−	0.873901i	$-0.661582\pi$
$239$		−	27.0204i		−	1.74780i	0.486104	−	0.873901i	$-0.338418\pi$
$240$	19.9248	+	0.184074i	1.28614	+	0.0118819i
$241$	25.8554			1.66549			0.832745	−	0.553657i	$-0.186768\pi$
$241$	25.8554			1.66549			0.832745	+	0.553657i	$0.186768\pi$
$242$	−4.24274	−	4.24274i	−0.272734	−	0.272734i
$243$	−10.3011	−	10.3011i	−0.660817	−	0.660817i
$244$	−0.914106			−0.0585196
$245$	−2.76281	−	2.81434i	−0.176510	−	0.179801i
$246$	−2.80494			−0.178837
$247$	17.7572	−	17.7572i	1.12986	−	1.12986i
$248$	−11.7523	+	11.7523i	−0.746273	+	0.746273i
$249$			9.24983i			0.586184i
$250$	0.448735	−	16.1872i	0.0283805	−	1.02377i
$251$	1.57563			0.0994530			0.0497265	−	0.998763i	$-0.484165\pi$
$251$	1.57563			0.0994530			0.0497265	+	0.998763i	$0.484165\pi$
$252$	0.242407	−	0.242407i	0.0152702	−	0.0152702i
$253$	−3.94471	−	3.94471i	−0.248002	−	0.248002i
$254$		−	16.8976i		−	1.06025i
$255$	−9.21700	−	9.38889i	−0.577191	−	0.587955i
$256$	2.34218			0.146386
$257$	8.81254	−	8.81254i	0.549711	−	0.549711i	−0.376646	−	0.926357i	$-0.622923\pi$
$257$	8.81254	−	8.81254i	0.549711	−	0.549711i	0.926357	+	0.376646i	$0.122923\pi$
$258$	−9.67214	−	9.67214i	−0.602161	−	0.602161i
$259$	−1.10667			−0.0687649
$260$	0.00969158	−	1.04905i	0.000601046	−	0.0650595i
$261$	3.46969			0.214769
$262$	16.1584	−	16.1584i	0.998267	−	0.998267i
$263$	4.15625	+	4.15625i	0.256285	+	0.256285i	0.823541	−	0.567256i	$-0.191995\pi$
$263$	4.15625	+	4.15625i	0.256285	+	0.256285i	−0.567256	+	0.823541i	$0.691995\pi$
$264$	−22.8222			−1.40461
$265$	−11.0594	−	0.102172i	−0.679376	−	0.00627636i
$266$		−	17.3535i		−	1.06401i
$267$	−13.8175	−	13.8175i	−0.845616	−	0.845616i
$268$	0.726180	+	0.726180i	0.0443585	+	0.0443585i
$269$			24.6302i			1.50173i	0.660454	+	0.750866i	$0.270364\pi$
$269$			24.6302i			1.50173i	−0.660454	+	0.750866i	$0.729636\pi$
$270$	−7.22478	+	7.09251i	−0.439686	+	0.431637i
$271$			1.28890i			0.0782949i	0.999233	+	0.0391475i	$0.0124642\pi$
$271$			1.28890i			0.0782949i	−0.999233	+	0.0391475i	$0.987536\pi$
$272$	−8.18163	−	8.18163i	−0.496084	−	0.496084i
$273$	16.5202	+	16.5202i	0.999847	+	0.999847i
$274$		−	14.5802i		−	0.880822i
$275$	−0.359469	+	19.4535i	−0.0216768	+	1.17309i
$276$	0.298527			0.0179692
$277$	−3.15554	+	3.15554i	−0.189598	+	0.189598i	−0.795522	−	0.605924i	$-0.792803\pi$
$277$	−3.15554	+	3.15554i	−0.189598	+	0.189598i	0.605924	+	0.795522i	$0.292803\pi$
$278$	−9.86509	+	9.86509i	−0.591669	+	0.591669i
$279$			9.23889i			0.553118i
$280$	9.87569	+	10.0599i	0.590185	+	0.601192i
$281$			7.91571i			0.472212i	0.971727	+	0.236106i	$0.0758712\pi$
$281$			7.91571i			0.472212i	−0.971727	+	0.236106i	$0.924129\pi$
$282$	1.75189	−	1.75189i	0.104324	−	0.104324i
$283$	13.5039	+	13.5039i	0.802723	+	0.802723i	0.983520	−	0.180798i	$-0.0578679\pi$
$283$	13.5039	+	13.5039i	0.802723	+	0.802723i	−0.180798	+	0.983520i	$0.557868\pi$
$284$	0.554635			0.0329115
$285$	0.230237	−	24.9217i	0.0136381	−	1.47624i
$286$			27.0323i			1.59845i
$287$	−1.47202	−	1.47202i	−0.0868909	−	0.0868909i
$288$	0.598723	−	0.598723i	0.0352801	−	0.0352801i
$289$		−	9.35995i		−	0.550585i
$290$	0.0677832	−	7.33711i	0.00398037	−	0.430850i
$291$			6.97340i			0.408788i
$292$	0.508840	−	0.508840i	0.0297776	−	0.0297776i
$293$	−0.131887	−	0.131887i	−0.00770494	−	0.00770494i	0.703244	−	0.710949i	$-0.251734\pi$
$293$	−0.131887	−	0.131887i	−0.00770494	−	0.00770494i	−0.710949	+	0.703244i	$0.751734\pi$
$294$	−5.43796			−0.317148
$295$	13.5170	+	13.7691i	0.786991	+	0.801667i
$296$	−1.33242			−0.0774453
$297$	8.60164	−	8.60164i	0.499118	−	0.499118i
$298$	8.71433	+	8.71433i	0.504807	+	0.504807i
$299$			6.87587i			0.397642i
$300$	−0.722495	−	0.749698i	−0.0417132	−	0.0432839i
$301$		−	10.1518i		−	0.585141i
$302$	−17.3942	−	3.76990i	−1.00092	−	0.216933i
$303$	2.22962	−	2.22962i	0.128088	−	0.128088i
$304$		−	21.9178i		−	1.25707i
$305$	−14.6381	−	14.9111i	−0.838174	−	0.853805i
$306$	−6.13125			−0.350500
$307$	−17.7482	−	17.7482i	−1.01294	−	1.01294i	−0.999915	−	0.0130256i	$-0.995854\pi$
$307$	−17.7482	−	17.7482i	−1.01294	−	1.01294i	−0.0130256	−	0.999915i	$-0.504146\pi$
$308$	0.615928	+	0.615928i	0.0350958	+	0.0350958i
$309$	25.2109			1.43420
$310$	19.5368	+	0.180489i	1.10962	+	0.0102511i
$311$	8.95991			0.508070			0.254035	−	0.967195i	$-0.418242\pi$
$311$	8.95991			0.508070			0.254035	+	0.967195i	$0.418242\pi$
$312$	19.8902	+	19.8902i	1.12606	+	1.12606i
$313$	9.33716	−	9.33716i	0.527768	−	0.527768i	−0.392139	−	0.919906i	$-0.628265\pi$
$313$	9.33716	−	9.33716i	0.527768	−	0.527768i	0.919906	+	0.392139i	$0.128265\pi$
$314$	−21.2624			−1.19991
$315$	7.83600	+	0.0723922i	0.441509	+	0.00407884i
$316$			0.751609i			0.0422813i
$317$	0.718402	−	0.718402i	0.0403495	−	0.0403495i	−0.686644	−	0.726994i	$-0.740917\pi$
$317$	0.718402	−	0.718402i	0.0403495	−	0.0403495i	0.726994	+	0.686644i	$0.240917\pi$
$318$	−10.7834	+	10.7834i	−0.604705	+	0.604705i
$319$			8.81607i			0.493605i
$320$	11.8603	+	12.0815i	0.663011	+	0.675375i
$321$	−17.2413			−0.962314
$322$	3.35977	+	3.35977i	0.187233	+	0.187233i
$323$	−10.2335	+	10.2335i	−0.569407	+	0.569407i
$324$			1.10039i			0.0611328i
$325$	17.2675	−	16.6410i	0.957831	−	0.923075i
$326$			32.5112i			1.80063i
$327$	−29.0638	−	29.0638i	−1.60723	−	1.60723i
$328$	−1.77231	−	1.77231i	−0.0978594	−	0.0978594i
$329$	1.83877			0.101375
$330$	18.7943	+	19.1448i	1.03459	+	1.05389i
$331$	19.7692			1.08661			0.543307	−	0.839534i	$-0.317172\pi$
$331$	19.7692			1.08661			0.543307	+	0.839534i	$0.317172\pi$
$332$	0.300560	−	0.300560i	0.0164954	−	0.0164954i
$333$	−0.523730	+	0.523730i	−0.0287002	+	0.0287002i
$334$		−	23.1801i		−	1.26836i
$335$	−0.216865	+	23.4743i	−0.0118486	+	1.28254i
$336$	20.3910			1.11242
$337$	−11.8333	+	11.8333i	−0.644600	+	0.644600i	−0.951683	−	0.307083i	$-0.900647\pi$
$337$	−11.8333	+	11.8333i	−0.644600	+	0.644600i	0.307083	+	0.951683i	$0.400647\pi$
$338$	10.2453	−	10.2453i	0.557271	−	0.557271i
$339$		−	44.5514i		−	2.41970i
$340$	−0.00558528	+	0.604571i	−0.000302904	+	0.0327875i
$341$	−23.4749			−1.27124
$342$	−8.21253	−	8.21253i	−0.444083	−	0.444083i
$343$	−14.1803	−	14.1803i	−0.765663	−	0.765663i
$344$		−	12.2227i		−	0.659005i
$345$	4.78048	+	4.86963i	0.257372	+	0.262172i
$346$	−16.2069			−0.871287
$347$	−22.1860	−	22.1860i	−1.19100	−	1.19100i	−0.976786	−	0.214219i	$-0.931280\pi$
$347$	−22.1860	−	22.1860i	−1.19100	−	1.19100i	−0.214219	−	0.976786i	$-0.568720\pi$
$348$	−0.333590	−	0.333590i	−0.0178823	−	0.0178823i
$349$			11.6900i			0.625754i	0.949794	+	0.312877i	$0.101293\pi$
$349$			11.6900i			0.625754i	−0.949794	+	0.312877i	$0.898707\pi$
$350$	0.306165	−	16.5688i	0.0163652	−	0.885640i
$351$	−14.9932			−0.800275
$352$	1.52128	+	1.52128i	0.0810847	+	0.0810847i
$353$	10.1118	+	10.1118i	0.538197	+	0.538197i	0.922999	−	0.384802i	$-0.125730\pi$
$353$	10.1118	+	10.1118i	0.538197	+	0.538197i	−0.384802	+	0.922999i	$0.625730\pi$
$354$	26.6051			1.41405
$355$	8.88167	+	9.04731i	0.471390	+	0.480181i
$356$			0.897957i			0.0475916i
$357$	−9.52062	−	9.52062i	−0.503885	−	0.503885i
$358$	26.3494	+	26.3494i	1.39261	+	1.39261i
$359$	15.9331			0.840916			0.420458	−	0.907312i	$-0.361869\pi$
$359$	15.9331			0.840916			0.420458	+	0.907312i	$0.361869\pi$
$360$	9.43450	+	0.0871598i	0.497242	+	0.00459372i
$361$	−8.41459			−0.442873
$362$	19.1129	−	19.1129i	1.00455	−	1.00455i
$363$	−6.23567	−	6.23567i	−0.327288	−	0.327288i
$364$		−	1.07360i		−	0.0562719i
$365$	16.4486	+	0.151959i	0.860962	+	0.00795392i
$366$	−28.8117			−1.50601
$367$	10.4159	−	10.4159i	0.543706	−	0.543706i	−0.380907	−	0.924613i	$-0.624388\pi$
$367$	10.4159	−	10.4159i	0.543706	−	0.543706i	0.924613	+	0.380907i	$0.124388\pi$
$368$	4.24347	+	4.24347i	0.221206	+	0.221206i
$369$	−1.39327			−0.0725308
$370$	1.09726	+	1.11772i	0.0570439	+	0.0581078i
$371$	−11.3182			−0.587613
$372$	0.888264	−	0.888264i	0.0460543	−	0.0460543i
$373$	−11.1987	−	11.1987i	−0.579846	−	0.579846i	0.355015	−	0.934861i	$-0.384476\pi$
$373$	−11.1987	−	11.1987i	−0.579846	−	0.579846i	−0.934861	+	0.355015i	$0.884476\pi$
$374$		−	15.5788i		−	0.805559i
$375$	0.659518	−	23.7908i	0.0340574	−	1.22855i
$376$	2.21387			0.114172
$377$	7.68346	−	7.68346i	0.395718	−	0.395718i
$378$	−7.32615	+	7.32615i	−0.376816	+	0.376816i
$379$	6.44019			0.330810			0.165405	−	0.986226i	$-0.447107\pi$
$379$	6.44019			0.330810			0.165405	+	0.986226i	$0.447107\pi$
$380$	−0.817276	+	0.802314i	−0.0419254	+	0.0411578i
$381$		−	24.8348i		−	1.27233i
$382$	−4.92289	−	4.92289i	−0.251877	−	0.251877i
$383$	−10.9241	+	10.9241i	−0.558195	+	0.558195i	−0.928793	−	0.370598i	$-0.879153\pi$
$383$	−10.9241	+	10.9241i	−0.558195	+	0.558195i	0.370598	+	0.928793i	$0.379153\pi$
$384$	25.6981			1.31140
$385$	−0.183940	+	19.9103i	−0.00937444	+	1.01472i
$386$	−8.07096			−0.410801
$387$	−4.80434	−	4.80434i	−0.244219	−	0.244219i
$388$	0.226590	−	0.226590i	0.0115034	−	0.0115034i
$389$	−32.8285			−1.66447			−0.832237	−	0.554420i	$-0.812940\pi$
$389$	−32.8285			−1.66447			−0.832237	+	0.554420i	$0.812940\pi$
$390$	0.305469	−	33.0651i	0.0154680	−	1.67431i
$391$		−	3.96258i		−	0.200396i
$392$	−3.43598	−	3.43598i	−0.173543	−	0.173543i
$393$	23.7484	−	23.7484i	1.19795	−	1.19795i
$394$	3.20503			0.161467
$395$	−12.2604	+	12.0359i	−0.616887	+	0.605594i
$396$	0.582976			0.0292956
$397$	12.4365	+	12.4365i	0.624168	+	0.624168i	0.946595	−	0.322426i	$-0.104498\pi$
$397$	12.4365	+	12.4365i	0.624168	+	0.624168i	−0.322426	+	0.946595i	$0.604498\pi$
$398$	−8.63999	−	8.63999i	−0.433084	−	0.433084i
$399$		−	25.5049i		−	1.27684i
$400$	0.386694	−	20.9268i	0.0193347	−	1.04634i
$401$	5.27485			0.263414			0.131707	−	0.991289i	$-0.457954\pi$
$401$	5.27485			0.263414			0.131707	+	0.991289i	$0.457954\pi$
$402$	22.8885	+	22.8885i	1.14157	+	1.14157i
$403$	20.4591	+	20.4591i	1.01914	+	1.01914i
$404$	−0.144897			−0.00720888
$405$	−17.9498	+	17.6212i	−0.891932	+	0.875603i
$406$		−	7.50879i		−	0.372655i
$407$	−1.33073	−	1.33073i	−0.0659620	−	0.0659620i
$408$	−11.4628	−	11.4628i	−0.567492	−	0.567492i
$409$	−38.4432			−1.90090			−0.950448	−	0.310884i	$-0.899375\pi$
$409$	−38.4432			−1.90090			−0.950448	+	0.310884i	$0.899375\pi$
$410$	−0.0272187	+	2.94625i	−0.00134423	+	0.145505i
$411$		−	21.4289i		−	1.05701i
$412$	−0.819191	−	0.819191i	−0.0403586	−	0.0403586i
$413$	13.9623	+	13.9623i	0.687039	+	0.687039i
$414$	3.18002			0.156290
$415$	9.71581	+	0.0897587i	0.476931	+	0.00440608i
$416$		−	2.65169i		−	0.130010i
$417$	−14.4990	+	14.4990i	−0.710019	+	0.710019i
$418$	20.8670	−	20.8670i	1.02064	−	1.02064i
$419$	22.9048			1.11897			0.559486	−	0.828840i	$-0.310999\pi$
$419$	22.9048			1.11897			0.559486	+	0.828840i	$0.310999\pi$
$420$	−0.746424	−	0.760344i	−0.0364218	−	0.0371010i
$421$		−	10.0352i		−	0.489085i	−0.969639	−	0.244542i	$-0.921362\pi$
$421$		−	10.0352i		−	0.489085i	0.969639	−	0.244542i	$-0.0786377\pi$
$422$	27.5835	−	27.5835i	1.34275	−	1.34275i
$423$	0.870199	−	0.870199i	0.0423105	−	0.0423105i
$424$	−13.6271			−0.661789
$425$	−9.95132	+	9.59023i	−0.482710	+	0.465194i
$426$	17.4815			0.846983
$427$	−15.1203	−	15.1203i	−0.731722	−	0.731722i
$428$	0.560230	+	0.560230i	0.0270797	+	0.0270797i
$429$			39.7301i			1.91819i
$430$	−10.2533	+	10.0655i	−0.494456	+	0.485404i
$431$			6.26071i			0.301568i	0.988567	+	0.150784i	$0.0481798\pi$
$431$			6.26071i			0.301568i	−0.988567	+	0.150784i	$0.951820\pi$
$432$	−9.25310	+	9.25310i	−0.445190	+	0.445190i
$433$	−5.15242	−	5.15242i	−0.247609	−	0.247609i	0.572379	−	0.819989i	$-0.306020\pi$
$433$	−5.15242	−	5.15242i	−0.247609	−	0.247609i	−0.819989	+	0.572379i	$0.806020\pi$
$434$	19.9939			0.959740
$435$	0.0996228	−	10.7835i	0.00477655	−	0.517031i
$436$			1.88877i			0.0904558i
$437$	5.30769	−	5.30769i	0.253901	−	0.253901i
$438$	16.0381	−	16.0381i	0.766332	−	0.766332i
$439$			26.3739i			1.25876i	0.777098	+	0.629379i	$0.216691\pi$
$439$			26.3739i			1.25876i	−0.777098	+	0.629379i	$0.783309\pi$
$440$	−0.221463	+	23.9719i	−0.0105578	+	1.14282i
$441$	−2.70114			−0.128626
$442$	−13.5774	+	13.5774i	−0.645809	+	0.645809i
$443$	3.24985	+	3.24985i	0.154405	+	0.154405i	0.780082	−	0.625677i	$-0.215177\pi$
$443$	3.24985	+	3.24985i	0.154405	+	0.154405i	−0.625677	+	0.780082i	$0.715177\pi$
$444$	0.100707			0.00477934
$445$	−14.6477	+	14.3795i	−0.694365	+	0.681653i
$446$	−13.2258			−0.626261
$447$	12.8077	+	12.8077i	0.605783	+	0.605783i
$448$	12.2510	+	12.2510i	0.578805	+	0.578805i
$449$	2.06066			0.0972487			0.0486243	−	0.998817i	$-0.484516\pi$
$449$	2.06066			0.0972487			0.0486243	+	0.998817i	$0.484516\pi$
$450$	−7.69629	−	7.98608i	−0.362807	−	0.376467i
$451$		−	3.54013i		−	0.166698i
$452$	−1.44763	+	1.44763i	−0.0680909	+	0.0680909i
$453$	−25.5648	−	5.54072i	−1.20114	−	0.260326i
$454$			3.54161i			0.166216i
$455$	17.5127	−	17.1921i	0.821010	−	0.805979i
$456$		−	30.7077i		−	1.43802i
$457$	−21.4026	−	21.4026i	−1.00117	−	1.00117i	−0.999999	−	0.00117364i	$-0.999626\pi$
$457$	−21.4026	−	21.4026i	−1.00117	−	1.00117i	−0.00117364	−	0.999999i	$-0.500374\pi$
$458$	17.0262	−	17.0262i	0.795584	−	0.795584i
$459$	8.64059			0.403308
$460$	0.00289685	−	0.313566i	0.000135066	−	0.0146201i
$461$	−21.1897			−0.986901			−0.493451	−	0.869774i	$-0.664265\pi$
$461$	−21.1897			−0.986901			−0.493451	+	0.869774i	$0.664265\pi$
$462$	19.4134	+	19.4134i	0.903195	+	0.903195i
$463$	9.02486	−	9.02486i	0.419421	−	0.419421i	−0.465583	−	0.885004i	$-0.654155\pi$
$463$	9.02486	−	9.02486i	0.419421	−	0.419421i	0.885004	+	0.465583i	$0.154155\pi$
$464$		−	9.48377i		−	0.440273i
$465$	28.7138	+	0.265270i	1.33157	+	0.0123016i
$466$			12.9075i			0.597927i
$467$	2.02167	−	2.02167i	0.0935519	−	0.0935519i	−0.658782	−	0.752334i	$-0.728928\pi$
$467$	2.02167	−	2.02167i	0.0935519	−	0.0935519i	0.752334	+	0.658782i	$0.228928\pi$
$468$	−0.508080	−	0.508080i	−0.0234860	−	0.0234860i
$469$			24.0236i			1.10931i
$470$	−1.82315	−	1.85715i	−0.0840955	−	0.0856638i
$471$	−31.2500			−1.43992
$472$	16.8105	+	16.8105i	0.773766	+	0.773766i
$473$	12.2073	−	12.2073i	0.561291	−	0.561291i
$474$			23.6900i			1.08812i
$475$	−26.1750	−	0.483672i	−1.20099	−	0.0221924i
$476$			0.618717i			0.0283589i
$477$	−5.35635	+	5.35635i	−0.245250	+	0.245250i
$478$	−27.6733	+	27.6733i	−1.26575	+	1.26575i
$479$	−31.4472			−1.43686			−0.718430	−	0.695599i	$-0.755139\pi$
$479$	−31.4472			−1.43686			−0.718430	+	0.695599i	$0.755139\pi$
$480$	−1.84360	−	1.87798i	−0.0841483	−	0.0857176i
$481$			2.31955i			0.105762i
$482$	−26.4801	−	26.4801i	−1.20614	−	1.20614i
$483$	4.93795	+	4.93795i	0.224685	+	0.224685i
$484$			0.405238i			0.0184199i
$485$	7.32470	+	0.0676686i	0.332598	+	0.00307267i
$486$			21.1001i			0.957118i
$487$	−12.8981	−	12.8981i	−0.584469	−	0.584469i	0.351659	−	0.936128i	$-0.385618\pi$
$487$	−12.8981	−	12.8981i	−0.584469	−	0.584469i	−0.936128	+	0.351659i	$0.885618\pi$
$488$	−18.2047	−	18.2047i	−0.824089	−	0.824089i
$489$			47.7826i			2.16081i
$490$	−0.0527690	+	5.71191i	−0.00238386	+	0.258038i
$491$	−18.4117			−0.830910			−0.415455	−	0.909614i	$-0.636378\pi$
$491$	−18.4117			−0.830910			−0.415455	+	0.909614i	$0.636378\pi$
$492$	0.133955	+	0.133955i	0.00603914	+	0.00603914i
$493$	−4.42800	+	4.42800i	−0.199427	+	0.199427i
$494$	−36.3725			−1.63648
$495$	9.33551	+	9.50961i	0.419600	+	0.427425i
$496$	25.2528			1.13389
$497$	9.17425	+	9.17425i	0.411521	+	0.411521i
$498$	9.47334	−	9.47334i	0.424510	−	0.424510i
$499$	−28.9664			−1.29671			−0.648357	−	0.761337i	$-0.724543\pi$
$499$	−28.9664			−1.29671			−0.648357	+	0.761337i	$0.724543\pi$
$500$	−0.794477	+	0.751617i	−0.0355301	+	0.0336133i
$501$		−	34.0683i		−	1.52206i
$502$	−1.61370	−	1.61370i	−0.0720232	−	0.0720232i
$503$	5.83543	−	5.83543i	0.260189	−	0.260189i	−0.564942	−	0.825131i	$-0.691101\pi$
$503$	5.83543	−	5.83543i	0.260189	−	0.260189i	0.825131	+	0.564942i	$0.191101\pi$
$504$	9.65525			0.430079
$505$	−2.32031	−	2.36358i	−0.103252	−	0.105178i
$506$			8.08006i			0.359203i
$507$	15.0578	−	15.0578i	0.668741	−	0.668741i
$508$	−0.806972	+	0.806972i	−0.0358036	+	0.0358036i
$509$	39.6593			1.75787			0.878934	−	0.476943i	$-0.158255\pi$
$509$	39.6593			1.75787			0.878934	+	0.476943i	$0.158255\pi$
$510$	−0.176042	+	19.0555i	−0.00779529	+	0.843791i
$511$	16.8335			0.744671
$512$	14.6736	+	14.6736i	0.648489	+	0.648489i
$513$	11.5737	+	11.5737i	0.510990	+	0.510990i
$514$	−18.0510			−0.796194
$515$	0.244642	−	26.4810i	0.0107802	−	1.16689i
$516$			0.923818i			0.0406688i
$517$	2.21107	+	2.21107i	0.0972428	+	0.0972428i
$518$	1.13341	+	1.13341i	0.0497991	+	0.0497991i
$519$	−23.8197			−1.04557
$520$	21.0852	−	20.6992i	0.924649	−	0.907721i
$521$	32.3087			1.41547			0.707736	−	0.706477i	$-0.249717\pi$
$521$	32.3087			1.41547			0.707736	+	0.706477i	$0.249717\pi$
$522$	−3.55353	−	3.55353i	−0.155534	−	0.155534i
$523$	12.6695	+	12.6695i	0.553999	+	0.553999i	0.927593	−	0.373594i	$-0.121875\pi$
$523$	12.6695	+	12.6695i	0.553999	+	0.553999i	−0.373594	+	0.927593i	$0.621875\pi$
$524$	−1.54334			−0.0674210
$525$	0.449979	−	24.3516i	0.0196387	−	1.06279i
$526$		−	8.51335i		−	0.371200i
$527$	−11.7906	−	11.7906i	−0.513607	−	0.513607i
$528$	24.5196	+	24.5196i	1.06708	+	1.06708i
$529$		−	20.9448i		−	0.910642i
$530$	11.2220	+	11.4313i	0.487454	+	0.496545i
$531$	13.2153			0.573495
$532$	−0.828743	+	0.828743i	−0.0359306	+	0.0359306i
$533$	−3.08533	+	3.08533i	−0.133640	+	0.133640i
$534$			28.3027i			1.22478i
$535$	−0.167306	+	18.1098i	−0.00723328	+	0.782957i
$536$			28.9243i			1.24934i
$537$	38.7264	+	38.7264i	1.67117	+	1.67117i
$538$	25.2254	−	25.2254i	1.08754	−	1.08754i
$539$		−	6.86327i		−	0.295622i
$540$	0.683746	+	0.00631672i	0.0294237	+	0.000271829i
$541$	−19.1475			−0.823217			−0.411608	−	0.911361i	$-0.635033\pi$
$541$	−19.1475			−0.823217			−0.411608	+	0.911361i	$0.635033\pi$
$542$	1.32004	−	1.32004i	0.0567006	−	0.0567006i
$543$	28.0907	−	28.0907i	1.20549	−	1.20549i
$544$			1.52817i			0.0655199i
$545$	−30.8100	+	30.2460i	−1.31976	+	1.29559i
$546$		−	33.8387i		−	1.44816i
$547$	21.6525	+	21.6525i	0.925794	+	0.925794i	0.997431	−	0.0716372i	$-0.0228224\pi$
$547$	21.6525	+	21.6525i	0.925794	+	0.925794i	−0.0716372	+	0.997431i	$0.522822\pi$
$548$	−0.696301	+	0.696301i	−0.0297445	+	0.0297445i
$549$	−14.3113			−0.610793
$550$	20.2917	−	19.5554i	0.865240	−	0.833843i
$551$	−11.8622			−0.505347
$552$	5.94526	+	5.94526i	0.253047	+	0.253047i
$553$	−12.4324	+	12.4324i	−0.528680	+	0.528680i
$554$	6.46358			0.274611
$555$	1.61268	+	1.64275i	0.0684543	+	0.0697309i
$556$	0.942247			0.0399602
$557$	−7.68227	+	7.68227i	−0.325508	+	0.325508i	−0.850876	−	0.525367i	$-0.823928\pi$
$557$	−7.68227	+	7.68227i	−0.325508	+	0.325508i	0.525367	+	0.850876i	$0.323928\pi$
$558$	9.46213	−	9.46213i	0.400564	−	0.400564i
$559$	−21.2780			−0.899962
$560$	0.197871	−	21.4183i	0.00836157	−	0.905088i
$561$		−	22.8965i		−	0.966693i
$562$	8.10698	−	8.10698i	0.341972	−	0.341972i
$563$	27.6370	−	27.6370i	1.16476	−	1.16476i	0.181342	−	0.983420i	$-0.441956\pi$
$563$	27.6370	−	27.6370i	1.16476	−	1.16476i	0.983420	−	0.181342i	$-0.0580441\pi$
$564$	−0.167329			−0.00704581
$565$	−46.7958	−	0.432319i	−1.96871	−	0.0181878i
$566$		−	27.6604i		−	1.16265i
$567$	−18.2016	+	18.2016i	−0.764397	+	0.764397i
$568$	11.0457	+	11.0457i	0.463469	+	0.463469i
$569$		−	2.68404i		−	0.112521i	−0.998416	−	0.0562605i	$-0.982082\pi$
$569$		−	2.68404i		−	0.112521i	0.998416	−	0.0562605i	$-0.0179177\pi$
$570$	−25.7597	+	25.2881i	−1.07896	+	1.05920i
$571$	−24.4895			−1.02485			−0.512427	−	0.858731i	$-0.671254\pi$
$571$	−24.4895			−1.02485			−0.512427	+	0.858731i	$0.671254\pi$
$572$	1.29097	−	1.29097i	0.0539782	−	0.0539782i
$573$	−7.23531	−	7.23531i	−0.302259	−	0.302259i
$574$			3.01519i			0.125852i
$575$	5.16134	−	4.97405i	0.215243	−	0.207432i
$576$	11.5956			0.483148
$577$	12.8249	+	12.8249i	0.533906	+	0.533906i	0.921732	−	0.387827i	$-0.126774\pi$
$577$	12.8249	+	12.8249i	0.533906	+	0.533906i	−0.387827	+	0.921732i	$0.626774\pi$
$578$	−9.58612	+	9.58612i	−0.398730	+	0.398730i
$579$	−11.8621			−0.492973
$580$	−0.353633	+	0.347158i	−0.0146838	+	0.0144150i
$581$	9.94315			0.412511
$582$	7.14190	−	7.14190i	0.296041	−	0.296041i
$583$	−13.6098	−	13.6098i	−0.563662	−	0.563662i
$584$	20.2675			0.838674
$585$	0.151732	−	16.4241i	0.00627336	−	0.679052i
$586$			0.270148i			0.0111597i
$587$	−21.5052	+	21.5052i	−0.887613	+	0.887613i	−0.994293	−	0.106680i	$-0.965978\pi$
$587$	−21.5052	+	21.5052i	−0.887613	+	0.887613i	0.106680	+	0.994293i	$0.465978\pi$
$588$	0.259698	+	0.259698i	0.0107098	+	0.0107098i
$589$		−	31.5859i		−	1.30148i
$590$	0.258171	−	27.9454i	0.0106287	−	1.15049i
$591$	4.71053			0.193765
$592$	1.43152	+	1.43152i	0.0588351	+	0.0588351i
$593$	23.6825	+	23.6825i	0.972524	+	0.972524i	0.999632	−	0.0271087i	$-0.00863002\pi$
$593$	23.6825	+	23.6825i	0.972524	+	0.972524i	−0.0271087	+	0.999632i	$0.508630\pi$
$594$	−17.6190			−0.722915
$595$	−10.0926	+	9.90786i	−0.413758	+	0.406183i
$596$		−	0.832334i		−	0.0340937i
$597$	−12.6984	−	12.6984i	−0.519712	−	0.519712i
$598$	7.04201	−	7.04201i	0.287969	−	0.287969i
$599$	35.2676			1.44100			0.720498	−	0.693457i	$-0.243913\pi$
$599$	35.2676			1.44100			0.720498	+	0.693457i	$0.243913\pi$
$600$	0.541772	−	29.3192i	0.0221178	−	1.19695i
$601$	23.5101			0.958997			0.479498	−	0.877543i	$-0.340819\pi$
$601$	23.5101			0.958997			0.479498	+	0.877543i	$0.340819\pi$
$602$	−10.3971	+	10.3971i	−0.423755	+	0.423755i
$603$	11.3692	+	11.3692i	0.462988	+	0.462988i
$604$	0.650652	+	1.01073i	0.0264746	+	0.0411259i
$605$	−6.61032	+	6.48930i	−0.268748	+	0.263828i
$606$	−4.56699			−0.185521
$607$	−23.3439	+	23.3439i	−0.947500	+	0.947500i	−0.998689	−	0.0511890i	$-0.983699\pi$
$607$	−23.3439	+	23.3439i	−0.947500	+	0.947500i	0.0511890	+	0.998689i	$0.483699\pi$
$608$	−2.04692	+	2.04692i	−0.0830134	+	0.0830134i
$609$		−	11.0359i		−	0.447196i
$610$	−0.279584	+	30.2632i	−0.0113200	+	1.22532i
$611$		−	3.85403i		−	0.155917i
$612$	0.292808	+	0.292808i	0.0118361	+	0.0118361i
$613$	−32.5328	+	32.5328i	−1.31399	+	1.31399i	−0.395536	+	0.918450i	$0.629441\pi$
$613$	−32.5328	+	32.5328i	−1.31399	+	1.31399i	−0.918450	+	0.395536i	$0.870559\pi$
$614$			36.3540i			1.46713i
$615$	−0.0400040	+	4.33018i	−0.00161312	+	0.174610i
$616$			24.5328i			0.988456i
$617$	6.36711	−	6.36711i	0.256330	−	0.256330i	−0.567229	−	0.823560i	$-0.691985\pi$
$617$	6.36711	−	6.36711i	0.256330	−	0.256330i	0.823560	+	0.567229i	$0.191985\pi$
$618$	−25.8201	−	25.8201i	−1.03864	−	1.03864i
$619$	1.44338			0.0580144			0.0290072	−	0.999579i	$-0.490765\pi$
$619$	1.44338			0.0580144			0.0290072	+	0.999579i	$0.490765\pi$
$620$	−0.924393	−	0.941632i	−0.0371245	−	0.0378168i
$621$	−4.48151			−0.179837
$622$	−9.17641	−	9.17641i	−0.367941	−	0.367941i
$623$	−14.8532	+	14.8532i	−0.595080	+	0.595080i
$624$		−	42.7391i		−	1.71093i
$625$	−24.9829	−	0.923605i	−0.999317	−	0.0369442i
$626$	−19.1256			−0.764411
$627$	30.6689	−	30.6689i	1.22480	−	1.22480i
$628$	1.01542	+	1.01542i	0.0405197	+	0.0405197i
$629$		−	1.33676i		−	0.0533001i
$630$	−7.95120	−	8.09949i	−0.316784	−	0.322691i
$631$			9.73385i			0.387499i	0.981051	+	0.193749i	$0.0620648\pi$
$631$			9.73385i			0.387499i	−0.981051	+	0.193749i	$0.937935\pi$
$632$	−14.9686	+	14.9686i	−0.595417	+	0.595417i
$633$	40.5403	−	40.5403i	1.61133	−	1.61133i
$634$	−1.47152			−0.0584416
$635$	−26.0860	−	0.240993i	−1.03519	−	0.00956351i
$636$	1.02996			0.0408406
$637$	−5.98154	+	5.98154i	−0.236997	+	0.236997i
$638$	9.02910	−	9.02910i	0.357465	−	0.357465i
$639$	8.68342			0.343511
$640$	0.249370	−	26.9927i	0.00985720	−	1.06698i
$641$	39.0462			1.54223			0.771117	−	0.636694i	$-0.219699\pi$
$641$	39.0462			1.54223			0.771117	+	0.636694i	$0.219699\pi$
$642$	17.6579	+	17.6579i	0.696901	+	0.696901i
$643$	21.0572	−	21.0572i	0.830415	−	0.830415i	−0.157158	−	0.987573i	$-0.550233\pi$
$643$	21.0572	−	21.0572i	0.830415	−	0.830415i	0.987573	+	0.157158i	$0.0502333\pi$
$644$		−	0.320903i		−	0.0126453i
$645$	−15.0695	+	14.7936i	−0.593361	+	0.582498i
$646$	20.9615			0.824721
$647$	21.0075	+	21.0075i	0.825889	+	0.825889i	0.986945	−	0.161056i	$-0.0514900\pi$
$647$	21.0075	+	21.0075i	0.825889	+	0.825889i	−0.161056	+	0.986945i	$0.551490\pi$
$648$	−21.9147	+	21.9147i	−0.860889	+	0.860889i
$649$			33.5785i			1.31807i
$650$	−34.7278	−	0.641715i	−1.36214	−	0.0251701i
$651$	29.3856			1.15171
$652$	1.55263	−	1.55263i	0.0608056	−	0.0608056i
$653$	−19.3008	+	19.3008i	−0.755300	+	0.755300i	−0.975463	−	0.220163i	$-0.929341\pi$
$653$	−19.3008	+	19.3008i	−0.755300	+	0.755300i	0.220163	+	0.975463i	$0.429341\pi$
$654$			59.5322i			2.32789i
$655$	−24.7143	−	25.1752i	−0.965669	−	0.983678i
$656$			3.80825i			0.148687i
$657$	7.96646	−	7.96646i	0.310801	−	0.310801i
$658$	−1.88320	−	1.88320i	−0.0734150	−	0.0734150i
$659$		−	31.7996i		−	1.23874i	−0.785101	−	0.619368i	$-0.787389\pi$
$659$		−	31.7996i		−	1.23874i	0.785101	−	0.619368i	$-0.212611\pi$
$660$	0.0167386	−	1.81185i	0.000651548	−	0.0705260i
$661$			1.31704i			0.0512269i	0.999672	+	0.0256134i	$0.00815390\pi$
$661$			1.31704i			0.0512269i	−0.999672	+	0.0256134i	$0.991846\pi$
$662$	−20.2469	−	20.2469i	−0.786918	−	0.786918i
$663$	−19.9550	+	19.9550i	−0.774988	+	0.774988i
$664$	11.9715			0.464584
$665$	−26.7897	−	0.247495i	−1.03886	−	0.00959743i
$666$	1.07277			0.0415690
$667$	2.29662	−	2.29662i	0.0889254	−	0.0889254i
$668$	−1.10700	+	1.10700i	−0.0428312	+	0.0428312i
$669$	−19.4383			−0.751530
$670$	24.2636	−	23.8194i	0.937386	−	0.920225i
$671$		−	36.3634i		−	1.40379i
$672$	−1.90433	−	1.90433i	−0.0734610	−	0.0734610i
$673$	−17.1772	+	17.1772i	−0.662133	+	0.662133i	−0.955882	−	0.293750i	$-0.905097\pi$
$673$	−17.1772	+	17.1772i	−0.662133	+	0.662133i	0.293750	+	0.955882i	$0.405097\pi$
$674$	24.2384			0.933629
$675$	10.8462	+	11.2545i	0.417469	+	0.433188i
$676$	−0.978562			−0.0376370
$677$	−21.0327	+	21.0327i	−0.808352	+	0.808352i	−0.984384	−	0.176032i	$-0.943674\pi$
$677$	−21.0327	+	21.0327i	−0.808352	+	0.808352i	0.176032	+	0.984384i	$0.443674\pi$
$678$	−45.6279	+	45.6279i	−1.75233	+	1.75233i
$679$	7.49609			0.287674
$680$	−12.1515	+	11.9290i	−0.465988	+	0.457457i
$681$			5.20520i			0.199464i
$682$	24.0421	+	24.0421i	0.920621	+	0.920621i
$683$	32.7677	+	32.7677i	1.25382	+	1.25382i	0.953994	+	0.299826i	$0.0969286\pi$
$683$	32.7677	+	32.7677i	1.25382	+	1.25382i	0.299826	+	0.953994i	$0.403071\pi$
$684$			0.784405i			0.0299925i
$685$	−22.5085	−	0.207942i	−0.860004	−	0.00794507i
$686$			29.0459i			1.10898i
$687$	25.0239	−	25.0239i	0.954722	−	0.954722i
$688$	−13.1318	+	13.1318i	−0.500645	+	0.500645i
$689$			23.7227i			0.903764i
$690$	0.0913058	−	9.88328i	0.00347595	−	0.376250i
$691$			41.7477i			1.58816i	0.607815	+	0.794079i	$0.292046\pi$
$691$			41.7477i			1.58816i	−0.607815	+	0.794079i	$0.707954\pi$
$692$	0.773986	+	0.773986i	0.0294225	+	0.0294225i
$693$	9.64304	+	9.64304i	0.366309	+	0.366309i
$694$			45.4441i			1.72503i
$695$	15.0887	+	15.3701i	0.572348	+	0.583022i
$696$		−	13.2871i		−	0.503647i
$697$	1.77808	−	1.77808i	0.0673497	−	0.0673497i
$698$	11.9725	−	11.9725i	0.453166	−	0.453166i
$699$			18.9704i			0.717528i
$700$	−0.805892	+	0.776649i	−0.0304599	+	0.0293546i
$701$	43.7305			1.65168			0.825839	−	0.563906i	$-0.190702\pi$
$701$	43.7305			1.65168			0.825839	+	0.563906i	$0.190702\pi$
$702$	15.3554	+	15.3554i	0.579554	+	0.579554i
$703$	1.79053	−	1.79053i	0.0675311	−	0.0675311i
$704$			29.4629i			1.11043i
$705$	−2.67953	−	2.72950i	−0.100917	−	0.102799i
$706$		−	20.7123i		−	0.779517i
$707$	−2.39674	−	2.39674i	−0.0901388	−	0.0901388i
$708$	−1.27057	−	1.27057i	−0.0477510	−	0.0477510i
$709$			23.7423i			0.891659i	0.895118	+	0.445830i	$0.147091\pi$
$709$			23.7423i			0.891659i	−0.895118	+	0.445830i	$0.852909\pi$
$710$	0.169638	−	18.3622i	0.00636639	−	0.689121i
$711$			11.7673i			0.441307i
$712$	−17.8831	+	17.8831i	−0.670198	+	0.670198i
$713$	6.11530	+	6.11530i	0.229020	+	0.229020i
$714$			19.5013i			0.729820i
$715$	41.7316	+	0.385534i	1.56067	+	0.0144181i
$716$		−	2.51672i		−	0.0940541i
$717$	−40.6721	+	40.6721i	−1.51893	+	1.51893i
$718$	−16.3181	−	16.3181i	−0.608985	−	0.608985i
$719$	42.3081			1.57782			0.788912	−	0.614506i	$-0.210645\pi$
$719$	42.3081			1.57782			0.788912	+	0.614506i	$0.210645\pi$
$720$	−10.0426	−	10.2298i	−0.374264	−	0.381244i
$721$		−	27.1006i		−	1.00928i
$722$	8.61791	+	8.61791i	0.320726	+	0.320726i
$723$	−38.9185	−	38.9185i	−1.44740	−	1.44740i
$724$	−1.82553			−0.0678455
$725$	−11.3258	−	0.209283i	−0.420631	−	0.00777259i
$726$			12.7727i			0.474039i
$727$	21.1365	+	21.1365i	0.783910	+	0.783910i	0.980488	−	0.196578i	$-0.0629830\pi$
$727$	21.1365	+	21.1365i	0.783910	+	0.783910i	−0.196578	+	0.980488i	$0.562983\pi$
$728$	21.3811	−	21.3811i	0.792436	−	0.792436i
$729$		−	2.73569i		−	0.101322i
$730$	−16.6905	−	17.0017i	−0.617742	−	0.629262i
$731$	12.2625			0.453547
$732$	1.37595	+	1.37595i	0.0508565	+	0.0508565i
$733$	−28.5346	−	28.5346i	−1.05395	−	1.05395i	−0.998459	−	0.0554887i	$-0.982328\pi$
$733$	−28.5346	−	28.5346i	−1.05395	−	1.05395i	−0.0554887	−	0.998459i	$-0.517672\pi$
$734$	−21.3352			−0.787496
$735$	−0.0775560	+	8.39495i	−0.00286070	+	0.309652i
$736$		−	0.792600i		−	0.0292156i
$737$	−28.8877	+	28.8877i	−1.06409	+	1.06409i
$738$	1.42694	+	1.42694i	0.0525263	+	0.0525263i
$739$	37.0093			1.36141			0.680704	−	0.732559i	$-0.261674\pi$
$739$	37.0093			1.36141			0.680704	+	0.732559i	$0.261674\pi$
$740$	0.000977242	−	0.105780i	3.59241e−5	−	0.00388856i
$741$	−53.4576			−1.96381
$742$	11.5917	+	11.5917i	0.425545	+	0.425545i
$743$	23.6279	−	23.6279i	0.866822	−	0.866822i	−0.125297	−	0.992119i	$-0.539988\pi$
$743$	23.6279	−	23.6279i	0.866822	−	0.866822i	0.992119	+	0.125297i	$0.0399884\pi$
$744$	35.3801			1.29710
$745$	13.5772	−	13.3286i	0.497430	−	0.488323i
$746$			22.9386i			0.839841i
$747$	4.70559	−	4.70559i	0.172169	−	0.172169i
$748$	−0.743990	+	0.743990i	−0.0272030	+	0.0272030i
$749$			18.5336i			0.677203i
$750$	−25.0411	+	23.6902i	−0.914373	+	0.865044i
$751$		−	23.5877i		−	0.860728i	−0.902655	−	0.430364i	$-0.858385\pi$
$751$		−	23.5877i		−	0.860728i	0.902655	−	0.430364i	$-0.141615\pi$
$752$	−2.37853	−	2.37853i	−0.0867361	−	0.0867361i
$753$	−2.37171	−	2.37171i	−0.0864298	−	0.0864298i
$754$	−15.7382			−0.573153
$755$	−6.06793	+	26.7989i	−0.220834	+	0.975311i
$756$	0.699744			0.0254495
$757$	−29.4275	−	29.4275i	−1.06956	−	1.06956i	−0.997393	−	0.0721677i	$-0.977008\pi$
$757$	−29.4275	−	29.4275i	−1.06956	−	1.06956i	−0.0721677	−	0.997393i	$-0.522992\pi$
$758$	−6.59581	−	6.59581i	−0.239571	−	0.239571i
$759$			11.8755i			0.431053i
$760$	−32.2547	−	0.297982i	−1.17000	−	0.0108089i
$761$		−	44.2984i		−	1.60582i	−0.596102	−	0.802909i	$-0.703285\pi$
$761$		−	44.2984i		−	1.60582i	0.596102	−	0.802909i	$-0.296715\pi$
$762$	−25.4349	+	25.4349i	−0.921411	+	0.921411i
$763$	−31.2423	+	31.2423i	−1.13105	+	1.13105i
$764$			0.470202i			0.0170113i
$765$	−0.0874437	+	9.46523i	−0.00316153	+	0.342216i
$766$	22.3761			0.808481
$767$	29.2646	−	29.2646i	1.05668	−	1.05668i
$768$	−3.52555	−	3.52555i	−0.127217	−	0.127217i
$769$	−9.83353			−0.354606			−0.177303	−	0.984156i	$-0.556737\pi$
$769$	−9.83353			−0.354606			−0.177303	+	0.984156i	$0.556737\pi$
$770$	20.5798	−	20.2031i	0.741645	−	0.728067i
$771$	−26.5300			−0.955454
$772$	0.385442	+	0.385442i	0.0138724	+	0.0138724i
$773$	23.4758	−	23.4758i	0.844364	−	0.844364i	−0.145059	−	0.989423i	$-0.546337\pi$
$773$	23.4758	−	23.4758i	0.844364	−	0.844364i	0.989423	+	0.145059i	$0.0463372\pi$
$774$			9.84087i			0.353723i
$775$	0.557267	−	30.1577i	0.0200176	−	1.08330i
$776$	9.02525			0.323988
$777$	1.66580	+	1.66580i	0.0597602	+	0.0597602i
$778$	33.6218	+	33.6218i	1.20540	+	1.20540i
$779$	4.76332			0.170664
$780$	−1.59366	+	1.56449i	−0.0570623	+	0.0560177i
$781$			22.0635i			0.789495i
$782$	−4.05833	+	4.05833i	−0.145125	+	0.145125i
$783$	5.00789	+	5.00789i	0.178967	+	0.178967i
$784$			7.38308i			0.263681i
$785$	−0.303244	+	32.8243i	−0.0108232	+	1.17155i
$786$	−48.6445			−1.73509
$787$	−21.5201	−	21.5201i	−0.767107	−	0.767107i	0.210489	−	0.977596i	$-0.432494\pi$
$787$	−21.5201	−	21.5201i	−0.767107	−	0.767107i	−0.977596	+	0.210489i	$0.932494\pi$
$788$	−0.153062	−	0.153062i	−0.00545260	−	0.00545260i
$789$		−	12.5123i		−	0.445450i
$790$	24.8834	+	0.229883i	0.885312	+	0.00817888i
$791$	−47.8907			−1.70280
$792$	11.6102	+	11.6102i	0.412549	+	0.412549i
$793$	−31.6918	+	31.6918i	−1.12541	+	1.12541i
$794$		−	25.4739i		−	0.904036i
$795$	16.4933	+	16.8009i	0.584958	+	0.595867i
$796$			0.825234i			0.0292496i
$797$	−10.0417	−	10.0417i	−0.355697	−	0.355697i	0.506527	−	0.862224i	$-0.330929\pi$
$797$	−10.0417	−	10.0417i	−0.355697	−	0.355697i	−0.862224	+	0.506527i	$0.830929\pi$
$798$	−26.1212	+	26.1212i	−0.924679	+	0.924679i
$799$			2.22108i			0.0785763i
$800$	−1.99048	+	1.91825i	−0.0703740	+	0.0678204i
$801$			14.0585i			0.496733i
$802$	−5.40231	−	5.40231i	−0.190762	−	0.190762i
$803$	20.2418	+	20.2418i	0.714318	+	0.714318i
$804$		−	2.18615i		−	0.0770996i
$805$	5.23463	−	5.13880i	0.184497	−	0.181119i
$806$		−	41.9069i		−	1.47611i
$807$	37.0745	−	37.0745i	1.30508	−	1.30508i
$808$	−2.88566	−	2.88566i	−0.101517	−	0.101517i
$809$	−33.8527			−1.19020			−0.595098	−	0.803653i	$-0.702887\pi$
$809$	−33.8527			−1.19020			−0.595098	+	0.803653i	$0.702887\pi$
$810$	36.4305	+	0.336560i	1.28004	+	0.0118255i
$811$			11.2856i			0.396292i	0.980172	+	0.198146i	$0.0634921\pi$
$811$			11.2856i			0.396292i	−0.980172	+	0.198146i	$0.936508\pi$
$812$	−0.358594	+	0.358594i	−0.0125842	+	0.0125842i
$813$	1.94010	−	1.94010i	0.0680423	−	0.0680423i
$814$			2.72578i			0.0955385i
$815$	50.1898	+	0.463674i	1.75807	+	0.0162418i
$816$			24.6307i			0.862245i
$817$	16.4251	+	16.4251i	0.574642	+	0.574642i
$818$	39.3722	+	39.3722i	1.37662	+	1.37662i
$819$		−	16.8084i		−	0.587332i
$820$	0.142003	−	0.139403i	0.00495895	−	0.00486817i
$821$			7.56295i			0.263949i	0.991253	+	0.131974i	$0.0421316\pi$
$821$			7.56295i			0.263949i	−0.991253	+	0.131974i	$0.957868\pi$
$822$	−21.9467	+	21.9467i	−0.765479	+	0.765479i
$823$	1.53884	−	1.53884i	0.0536407	−	0.0536407i	−0.679778	−	0.733418i	$-0.737924\pi$
$823$	1.53884	−	1.53884i	0.0536407	−	0.0536407i	0.733418	+	0.679778i	$0.237924\pi$
$824$		−	32.6289i		−	1.13668i
$825$	29.8232	−	28.7410i	1.03831	−	1.00063i
$826$		−	28.5993i		−	0.995097i
$827$	−14.0520	−	14.0520i	−0.488637	−	0.488637i	0.419239	−	0.907876i	$-0.362297\pi$
$827$	−14.0520	−	14.0520i	−0.488637	−	0.488637i	−0.907876	+	0.419239i	$0.862297\pi$
$828$	−0.151867	−	0.151867i	−0.00527775	−	0.00527775i
$829$		−	43.9734i		−	1.52726i	−0.645654	−	0.763630i	$-0.723415\pi$
$829$		−	43.9734i		−	1.52726i	0.645654	−	0.763630i	$-0.276585\pi$
$830$	−9.85865	−	10.0425i	−0.342199	−	0.348581i
$831$	9.49970			0.329541
$832$	25.6778	−	25.6778i	0.890217	−	0.890217i
$833$	3.44718	−	3.44718i	0.119438	−	0.119438i
$834$	29.6987			1.02838
$835$	−35.7846	−	0.330593i	−1.23838	−	0.0114407i
$836$	−1.99308			−0.0689321
$837$	−13.3347	+	13.3347i	−0.460915	+	0.460915i
$838$	−23.4582	−	23.4582i	−0.810351	−	0.810351i
$839$			15.4171i			0.532256i	0.963938	+	0.266128i	$0.0857444\pi$
$839$			15.4171i			0.532256i	−0.963938	+	0.266128i	$0.914256\pi$
$840$	0.277224	−	30.0078i	0.00956515	−	1.03537i
$841$	23.8673			0.823009
$842$	−10.2777	+	10.2777i	−0.354192	+	0.354192i
$843$	11.9151	−	11.9151i	0.410376	−	0.410376i
$844$	−2.63459			−0.0906864
$845$	−15.6703	−	15.9625i	−0.539073	−	0.549127i
$846$	−1.78245			−0.0612820
$847$	−6.70307	+	6.70307i	−0.230320	+	0.230320i
$848$	14.6406	+	14.6406i	0.502760	+	0.502760i
$849$		−	40.6532i		−	1.39521i
$850$	20.0137	+	0.369822i	0.686466	+	0.0126848i
$851$			0.693322i			0.0237668i
$852$	−0.834859	−	0.834859i	−0.0286018	−	0.0286018i
$853$	−25.8981	+	25.8981i	−0.886734	+	0.886734i	−0.994208	−	0.107474i	$-0.965724\pi$
$853$	−25.8981	+	25.8981i	−0.886734	+	0.886734i	0.107474	+	0.994208i	$0.465724\pi$
$854$			30.9713i			1.05982i
$855$	−12.7954	+	12.5611i	−0.437592	+	0.429581i
$856$			22.3143i			0.762688i
$857$	18.9810	−	18.9810i	0.648377	−	0.648377i	−0.304223	−	0.952601i	$-0.598397\pi$
$857$	18.9810	−	18.9810i	0.648377	−	0.648377i	0.952601	+	0.304223i	$0.0983970\pi$
$858$	40.6901	−	40.6901i	1.38914	−	1.38914i
$859$	4.47754			0.152772			0.0763859	−	0.997078i	$-0.475662\pi$
$859$	4.47754			0.152772			0.0763859	+	0.997078i	$0.475662\pi$
$860$	0.970358	+	0.00896456i	0.0330889	+	0.000305689i
$861$			4.43150i			0.151025i
$862$	6.41199	−	6.41199i	0.218393	−	0.218393i
$863$	−23.2449	−	23.2449i	−0.791266	−	0.791266i	0.190434	−	0.981700i	$-0.439011\pi$
$863$	−23.2449	−	23.2449i	−0.791266	−	0.791266i	−0.981700	+	0.190434i	$0.939011\pi$
$864$	1.72830			0.0587980
$865$	−0.231142	+	25.0197i	−0.00785906	+	0.850694i
$866$			10.5538i			0.358634i
$867$	−14.0890	+	14.0890i	−0.478487	+	0.478487i
$868$	−0.954844	−	0.954844i	−0.0324095	−	0.0324095i
$869$	−29.8992			−1.01426
$870$	−11.1461	+	10.9421i	−0.377890	+	0.370971i
$871$	50.3529			1.70614
$872$	−37.6155	+	37.6155i	−1.27382	+	1.27382i
$873$	3.54752	−	3.54752i	0.120065	−	0.120065i
$874$	−10.8719			−0.367747
$875$	−25.5740	−	0.708952i	−0.864561	−	0.0239670i
$876$	−1.53185			−0.0517566
$877$	18.7993	−	18.7993i	0.634809	−	0.634809i	−0.314461	−	0.949270i	$-0.601824\pi$
$877$	18.7993	−	18.7993i	0.634809	−	0.634809i	0.949270	+	0.314461i	$0.101824\pi$
$878$	27.0112	−	27.0112i	0.911584	−	0.911584i
$879$			0.397044i			0.0133920i
$880$	25.9928	−	25.5169i	0.876217	−	0.860175i
$881$		−	27.1596i		−	0.915032i	−0.889202	−	0.457516i	$-0.848739\pi$
$881$		−	27.1596i		−	0.915032i	0.889202	−	0.457516i	$-0.151261\pi$
$882$	2.76641	+	2.76641i	0.0931499	+	0.0931499i
$883$	−6.66095	+	6.66095i	−0.224159	+	0.224159i	−0.810247	−	0.586088i	$-0.800667\pi$
$883$	−6.66095	+	6.66095i	−0.224159	+	0.224159i	0.586088	+	0.810247i	$0.300667\pi$
$884$	1.29682			0.0436167
$885$	0.379441	−	41.0721i	0.0127548	−	1.38063i
$886$		−	6.65675i		−	0.223638i
$887$	−33.1187	+	33.1187i	−1.11202	+	1.11202i	−0.119141	+	0.992877i	$0.538014\pi$
$887$	−33.1187	+	33.1187i	−1.11202	+	1.11202i	−0.992877	+	0.119141i	$0.961986\pi$
$888$	2.00561	+	2.00561i	0.0673039	+	0.0673039i
$889$	−26.6963			−0.895367
$890$	29.7285	+	0.274644i	0.996503	+	0.00920610i
$891$	−43.7739			−1.46648
$892$	0.631621	+	0.631621i	0.0211482	+	0.0211482i
$893$	−2.97504	+	2.97504i	−0.0995559	+	0.0995559i
$894$		−	26.2343i		−	0.877407i
$895$	41.0532	−	40.3016i	1.37226	−	1.34713i
$896$		−	27.6243i		−	0.922863i
$897$	10.3498	−	10.3498i	0.345571	−	0.345571i
$898$	−2.11045	−	2.11045i	−0.0704268	−	0.0704268i
$899$		−	13.6671i		−	0.455824i
$900$	−0.0138392	+	0.748937i	−0.000461305	+	0.0249646i
$901$		−	13.6715i		−	0.455462i
$902$	−3.62568	+	3.62568i	−0.120722	+	0.120722i
$903$	−15.2809	+	15.2809i	−0.508517	+	0.508517i
$904$	−57.6601			−1.91775
$905$	−29.2333	−	29.7785i	−0.971748	−	0.989870i
$906$	20.5079	+	31.8571i	0.681329	+	1.05838i
$907$	−25.9678	−	25.9678i	−0.862246	−	0.862246i	0.129352	−	0.991599i	$-0.458710\pi$
$907$	−25.9678	−	25.9678i	−0.862246	−	0.862246i	−0.991599	+	0.129352i	$0.958710\pi$
$908$	0.169135	−	0.169135i	0.00561295	−	0.00561295i
$909$	−2.26852			−0.0752420
$910$	−35.5435	−	0.328365i	−1.17825	−	0.0108852i
$911$	−21.8858			−0.725108			−0.362554	−	0.931963i	$-0.618095\pi$
$911$	−21.8858			−0.725108			−0.362554	+	0.931963i	$0.618095\pi$
$912$	−32.9916	+	32.9916i	−1.09246	+	1.09246i
$913$	11.9563	+	11.9563i	0.395697	+	0.395697i
$914$			43.8396i			1.45008i
$915$	−0.410912	+	44.4786i	−0.0135843	+	1.47042i
$916$	−1.62623			−0.0537322
$917$	−25.5285	−	25.5285i	−0.843024	−	0.843024i
$918$	−8.84937	−	8.84937i	−0.292073	−	0.292073i
$919$	30.4412			1.00416			0.502082	−	0.864820i	$-0.332568\pi$
$919$	30.4412			1.00416			0.502082	+	0.864820i	$0.332568\pi$
$920$	6.30246	−	6.18708i	0.207786	−	0.203982i
$921$			53.4305i			1.76059i
$922$	21.7017	+	21.7017i	0.714707	+	0.714707i
$923$	19.2290	−	19.2290i	0.632931	−	0.632931i
$924$		−	1.85424i		−	0.0610000i
$925$	1.74116	−	1.67798i	0.0572489	−	0.0551716i
$926$	−18.4859			−0.607483
$927$	−12.8253	−	12.8253i	−0.421240	−	0.421240i
$928$	−0.885694	+	0.885694i	−0.0290743	+	0.0290743i
$929$	26.7133			0.876435			0.438218	−	0.898869i	$-0.355610\pi$
$929$	26.7133			0.876435			0.438218	+	0.898869i	$0.355610\pi$
$930$	−29.1359	−	29.6793i	−0.955405	−	0.973222i
$931$	9.23467			0.302654
$932$	0.616417	−	0.616417i	0.0201914	−	0.0201914i
$933$	−13.4868	−	13.4868i	−0.441539	−	0.441539i
$934$	−4.14105			−0.135499
$935$	−24.0500	−	0.222184i	−0.786520	−	0.00726619i
$936$		−	20.2372i		−	0.661473i
$937$	18.5312	+	18.5312i	0.605387	+	0.605387i	0.941737	−	0.336350i	$-0.109193\pi$
$937$	18.5312	+	18.5312i	0.605387	+	0.605387i	−0.336350	+	0.941737i	$0.609193\pi$
$938$	24.6041	−	24.6041i	0.803352	−	0.803352i
$939$	−28.1094			−0.917314
$940$	−0.00162373	+	0.175758i	−5.29602e−5	+	0.00573261i
$941$			3.66320i			0.119417i	0.998216	+	0.0597084i	$0.0190171\pi$
$941$			3.66320i			0.119417i	−0.998216	+	0.0597084i	$0.980983\pi$
$942$	32.0051	+	32.0051i	1.04278	+	1.04278i
$943$	−0.922218	+	0.922218i	−0.0300315	+	0.0300315i
$944$		−	36.1216i		−	1.17566i
$945$	11.2054	+	11.4144i	0.364511	+	0.371309i
$946$	−25.0045			−0.812965
$947$	38.9964	−	38.9964i	1.26721	−	1.26721i	0.319691	−	0.947522i	$-0.396421\pi$
$947$	38.9964	−	38.9964i	1.26721	−	1.26721i	0.947522	−	0.319691i	$-0.103579\pi$
$948$	1.13135	−	1.13135i	0.0367446	−	0.0367446i
$949$		−	35.2827i		−	1.14532i
$950$	26.3121	+	27.3028i	0.853678	+	0.885821i
$951$	−2.16274			−0.0701315
$952$	−12.3220	+	12.3220i	−0.399357	+	0.399357i
$953$	41.4646	−	41.4646i	1.34317	−	1.34317i	0.450284	−	0.892885i	$-0.351323\pi$
$953$	41.4646	−	41.4646i	1.34317	−	1.34317i	0.892885	−	0.450284i	$-0.148677\pi$
$954$	10.9715			0.355217
$955$	−7.67002	+	7.52960i	−0.248196	+	0.243652i
$956$	2.64316			0.0854860
$957$	13.2703	−	13.2703i	0.428968	−	0.428968i
$958$	32.2071	+	32.2071i	1.04056	+	1.04056i
$959$	−23.0351			−0.743843
$960$	0.332935	−	36.0381i	0.0107454	−	1.16313i
$961$	5.39202			0.173936
$962$	2.37560	−	2.37560i	0.0765923	−	0.0765923i
$963$	8.77102	+	8.77102i	0.282642	+	0.282642i
$964$			2.52920i			0.0814601i
$965$	−0.115108	+	12.4597i	−0.00370545	+	0.401092i
$966$		−	10.1145i		−	0.325430i
$967$	5.53167	−	5.53167i	0.177887	−	0.177887i	−0.612547	−	0.790434i	$-0.709855\pi$
$967$	5.53167	−	5.53167i	0.177887	−	0.177887i	0.790434	+	0.612547i	$0.209855\pi$
$968$	−8.07045	+	8.07045i	−0.259394	+	0.259394i
$969$	30.8077			0.989687
$970$	−7.43239	−	7.57100i	−0.238640	−	0.243090i
$971$		−	25.9263i		−	0.832014i	−0.909361	−	0.416007i	$-0.863429\pi$
$971$		−	25.9263i		−	0.832014i	0.909361	−	0.416007i	$-0.136571\pi$
$972$	1.00767	−	1.00767i	0.0323210	−	0.0323210i
$973$	15.5858	+	15.5858i	0.499657	+	0.499657i
$974$			26.4195i			0.846537i
$975$	−51.0405	−	0.943146i	−1.63460	−	0.0302048i
$976$			39.1174i			1.25212i
$977$	21.7619	−	21.7619i	0.696223	−	0.696223i	−0.267370	−	0.963594i	$-0.586155\pi$
$977$	21.7619	−	21.7619i	0.696223	−	0.696223i	0.963594	+	0.267370i	$0.0861547\pi$
$978$	48.9372	−	48.9372i	1.56484	−	1.56484i
$979$	−35.7210			−1.14165
$980$	0.275302	−	0.270261i	0.00879419	−	0.00863318i
$981$			29.5708i			0.944123i
$982$	18.8566	+	18.8566i	0.601739	+	0.601739i
$983$	21.5710	+	21.5710i	0.688007	+	0.688007i	0.961791	−	0.273784i	$-0.0882754\pi$
$983$	21.5710	+	21.5710i	0.688007	+	0.688007i	−0.273784	+	0.961791i	$0.588275\pi$
$984$			5.33550i			0.170090i
$985$	0.0457101	−	4.94783i	0.00145645	−	0.157651i
$986$	9.06998			0.288847
$987$	−2.76780	−	2.76780i	−0.0880999	−	0.0880999i
$988$	1.73703	+	1.73703i	0.0552622	+	0.0552622i
$989$	−6.36007			−0.202239
$990$	0.178306	−	19.3005i	0.00566693	−	0.613410i
$991$	−27.0109			−0.858031			−0.429015	−	0.903297i	$-0.641139\pi$
$991$	−27.0109			−0.858031			−0.429015	+	0.903297i	$0.641139\pi$
$992$	−2.35837	−	2.35837i	−0.0748784	−	0.0748784i
$993$	−29.7574	−	29.7574i	−0.944323	−	0.944323i
$994$		−	18.7919i		−	0.596042i
$995$	−13.4614	+	13.2149i	−0.426754	+	0.418941i
$996$	−0.904829			−0.0286706
$997$	31.3919	+	31.3919i	0.994190	+	0.994190i	0.999983	−	0.00579293i	$-0.00184396\pi$
$997$	31.3919	+	31.3919i	0.994190	+	0.994190i	−0.00579293	+	0.999983i	$0.501844\pi$
$998$	29.6663	+	29.6663i	0.939071	+	0.939071i
$999$	−1.51182			−0.0478319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.f.e.452.17	✓	108
5.3	odd	4	inner	755.2.f.e.603.18	yes	108
151.150	odd	2	inner	755.2.f.e.452.18	yes	108
755.603	even	4	inner	755.2.f.e.603.17	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.f.e.452.17	✓	108	1.1	even	1	trivial
755.2.f.e.452.18	yes	108	151.150	odd	2	inner
755.2.f.e.603.17	yes	108	755.603	even	4	inner
755.2.f.e.603.18	yes	108	5.3	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:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02416 - 1.02416i) q^{2} +(-1.50524 - 1.50524i) q^{3} +0.0978212i q^{4} +(-1.59568 + 1.56646i) q^{5} +3.08322i q^{6} +(-1.61807 + 1.61807i) q^{7} +(-1.94814 + 1.94814i) q^{8} +1.53150i q^{9} +(3.23855 + 0.0299191i) q^{10} -3.89135 q^{11} +(0.147244 - 0.147244i) q^{12} +(3.39143 + 3.39143i) q^{13} +3.31433 q^{14} +(4.75979 + 0.0439729i) q^{15} +4.18607 q^{16} +(-1.95449 - 1.95449i) q^{17} +(1.56851 - 1.56851i) q^{18} -5.23589i q^{19} +(-0.153233 - 0.156091i) q^{20} +4.87116 q^{21} +(3.98538 + 3.98538i) q^{22} +(1.01371 + 1.01371i) q^{23} +5.86484 q^{24} +(0.0923762 - 4.99915i) q^{25} -6.94676i q^{26} +(-2.21045 + 2.21045i) q^{27} +(-0.158281 - 0.158281i) q^{28} -2.26555i q^{29} +(-4.82976 - 4.91983i) q^{30} +6.03258 q^{31} +(-0.390939 - 0.390939i) q^{32} +(5.85743 + 5.85743i) q^{33} +4.00343i q^{34} +(0.0472689 - 5.11656i) q^{35} -0.149813 q^{36} +(0.341972 + 0.341972i) q^{37} +(-5.36241 + 5.36241i) q^{38} -10.2098i q^{39} +(0.0569114 - 6.16030i) q^{40} +0.909743i q^{41} +(-4.98886 - 4.98886i) q^{42} +(-3.13702 + 3.13702i) q^{43} -0.380657i q^{44} +(-2.39904 - 2.44378i) q^{45} -2.07641i q^{46} +(-0.568201 - 0.568201i) q^{47} +(-6.30105 - 6.30105i) q^{48} +1.76372i q^{49} +(-5.21455 + 5.02533i) q^{50} +5.88395i q^{51} +(-0.331754 + 0.331754i) q^{52} +(3.49745 + 3.49745i) q^{53} +4.52772 q^{54} +(6.20935 - 6.09567i) q^{55} -6.30444i q^{56} +(-7.88128 + 7.88128i) q^{57} +(-2.32030 + 2.32030i) q^{58} -8.62899i q^{59} +(-0.00430148 + 0.465608i) q^{60} +9.34466i q^{61} +(-6.17835 - 6.17835i) q^{62} +(-2.47807 - 2.47807i) q^{63} -7.57138i q^{64} +(-10.7242 - 0.0990744i) q^{65} -11.9979i q^{66} +(7.42355 - 7.42355i) q^{67} +(0.191190 - 0.191190i) q^{68} -3.05176i q^{69} +(-5.28860 + 5.19178i) q^{70} -5.66988i q^{71} +(-2.98358 - 2.98358i) q^{72} +(-5.20174 - 5.20174i) q^{73} -0.700470i q^{74} +(-7.66397 + 7.38587i) q^{75} +0.512181 q^{76} +(6.29647 - 6.29647i) q^{77} +(-10.4565 + 10.4565i) q^{78} +7.68350 q^{79} +(-6.67962 + 6.55734i) q^{80} +11.2490 q^{81} +(0.931726 - 0.931726i) q^{82} +(-3.07254 - 3.07254i) q^{83} +0.476502i q^{84} +(6.18037 + 0.0570968i) q^{85} +6.42564 q^{86} +(-3.41020 + 3.41020i) q^{87} +(7.58091 - 7.58091i) q^{88} +9.17958 q^{89} +(-0.0458210 + 4.95984i) q^{90} -10.9751 q^{91} +(-0.0991625 + 0.0991625i) q^{92} +(-9.08048 - 9.08048i) q^{93} +1.16386i q^{94} +(8.20184 + 8.35480i) q^{95} +1.17692i q^{96} +(-2.31637 - 2.31637i) q^{97} +(1.80634 - 1.80634i) q^{98} -5.95961i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 12 q^{5} + 12 q^{8} + 16 q^{10} - 24 q^{16} + 8 q^{17} + 4 q^{18} + 48 q^{20} - 44 q^{21} - 32 q^{22} - 40 q^{25} + 20 q^{31} - 56 q^{32} - 304 q^{36} - 8 q^{37} + 16 q^{38} + 44 q^{42} + 20 q^{43}+ \cdots - 188 q^{98}+O(q^{100}) \) 108 * q - 12 * q^5 + 12 * q^8 + 16 * q^10 - 24 * q^16 + 8 * q^17 + 4 * q^18 + 48 * q^20 - 44 * q^21 - 32 * q^22 - 40 * q^25 + 20 * q^31 - 56 * q^32 - 304 * q^36 - 8 * q^37 + 16 * q^38 + 44 * q^42 + 20 * q^43 + 12 * q^45 + 20 * q^47 + 56 * q^50 - 80 * q^55 - 52 * q^58 - 48 * q^62 + 176 * q^68 + 80 * q^72 + 128 * q^76 - 60 * q^80 + 36 * q^81 + 48 * q^85 - 160 * q^86 + 24 * q^88 + 36 * q^90 - 96 * q^91 - 24 * q^95 + 104 * q^97 - 188 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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