LMFDB - Embedded newform 755.2.h.d.321.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,2,Mod(321,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.321"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [16,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 14 x^{14} - 22 x^{13} + 54 x^{12} - 181 x^{11} + 697 x^{10} - 1743 x^{9} + 3507 x^{8} + \cdots + 16 $ x^16 - 5x^15 + 14x^14 - 22x^13 + 54x^12 - 181x^11 + 697x^10 - 1743x^9 + 3507x^8 - 5479x^7 + 7616x^6 - 7799x^5 + 6803x^4 - 3330x^3 + 948x^2 - 136*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			321.3
Root			$0.662424 + 2.03873i$ of defining polynomial
Character	$\chi$	$=$	755.321
Dual form			755.2.h.d.461.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.488177 q^{2} +(-0.778897 + 2.39720i) q^{3} -1.76168 q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.380239 + 1.17026i) q^{6} +(-2.04327 - 1.48452i) q^{7} -1.83637 q^{8} +(-2.71283 - 1.97099i) q^{9} +(0.394943 + 0.286943i) q^{10} +(-0.818155 - 2.51802i) q^{11} +(1.37217 - 4.22311i) q^{12} +(0.391104 - 1.20370i) q^{13} +(-0.997475 - 0.724708i) q^{14} +(-2.03918 + 1.48155i) q^{15} +2.62690 q^{16} +(1.99426 - 1.44891i) q^{17} +(-1.32434 - 0.962191i) q^{18} -2.81911 q^{19} +(-1.42523 - 1.03549i) q^{20} +(5.15018 - 3.74183i) q^{21} +(-0.399404 - 1.22924i) q^{22} -1.14711 q^{23} +(1.43034 - 4.40214i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.190928 - 0.587616i) q^{26} +(0.720334 - 0.523353i) q^{27} +(3.59959 + 2.61525i) q^{28} +(-1.55483 - 4.78528i) q^{29} +(-0.995480 + 0.723258i) q^{30} +(1.37129 - 0.996297i) q^{31} +4.95512 q^{32} +6.67346 q^{33} +(0.973550 - 0.707325i) q^{34} +(-0.780458 - 2.40200i) q^{35} +(4.77915 + 3.47226i) q^{36} +(1.27506 - 3.92423i) q^{37} -1.37622 q^{38} +(2.58087 + 1.87511i) q^{39} +(-1.48565 - 1.07939i) q^{40} +(-0.471546 + 1.45127i) q^{41} +(2.51420 - 1.82667i) q^{42} +(4.74909 - 3.45041i) q^{43} +(1.44133 + 4.43596i) q^{44} +(-1.03621 - 3.18913i) q^{45} -0.559992 q^{46} +(-0.632339 + 1.94614i) q^{47} +(-2.04608 + 6.29720i) q^{48} +(-0.191982 - 0.590859i) q^{49} +(0.150855 + 0.464284i) q^{50} +(1.92001 + 5.90919i) q^{51} +(-0.689002 + 2.12053i) q^{52} +(0.922429 + 2.83894i) q^{53} +(0.351650 - 0.255489i) q^{54} +(0.818155 - 2.51802i) q^{55} +(3.75218 + 2.72612i) q^{56} +(2.19580 - 6.75796i) q^{57} +(-0.759032 - 2.33606i) q^{58} -3.94628 q^{59} +(3.59239 - 2.61002i) q^{60} +(-2.62955 - 8.09292i) q^{61} +(0.669430 - 0.486369i) q^{62} +(2.61707 + 8.05451i) q^{63} -2.83482 q^{64} +(1.02392 - 0.743925i) q^{65} +3.25783 q^{66} +(-1.58385 + 1.15074i) q^{67} +(-3.51325 + 2.55253i) q^{68} +(0.893481 - 2.74985i) q^{69} +(-0.381001 - 1.17260i) q^{70} +(-9.62246 - 6.99112i) q^{71} +(4.98176 + 3.61946i) q^{72} +(-0.984339 - 0.715164i) q^{73} +(0.622454 - 1.91572i) q^{74} -2.52056 q^{75} +4.96638 q^{76} +(-2.06635 + 6.35956i) q^{77} +(1.25992 + 0.915385i) q^{78} +(-13.6221 - 9.89704i) q^{79} +(2.12520 + 1.54405i) q^{80} +(-2.41511 - 7.43296i) q^{81} +(-0.230198 + 0.708475i) q^{82} +(-1.32704 + 0.964149i) q^{83} +(-9.07300 + 6.59192i) q^{84} +2.46504 q^{85} +(2.31839 - 1.68441i) q^{86} +12.6823 q^{87} +(1.50243 + 4.62401i) q^{88} +(2.76691 - 2.01028i) q^{89} +(-0.505854 - 1.55686i) q^{90} +(-2.58604 + 1.87887i) q^{91} +2.02084 q^{92} +(1.32023 + 4.06326i) q^{93} +(-0.308693 + 0.950059i) q^{94} +(-2.28071 - 1.65703i) q^{95} +(-3.85953 + 11.8784i) q^{96} +(9.51327 - 6.91180i) q^{97} +(-0.0937209 - 0.288443i) q^{98} +(-2.74348 + 8.44355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} - 18 q^{6} - q^{7} - 18 q^{8} - q^{10} + 13 q^{11} - 19 q^{12} + 7 q^{13} - q^{14} - q^{15} + 16 q^{16} + 9 q^{17} - 3 q^{18} - 34 q^{19} - 9 q^{20} + 2 q^{21}+ \cdots + 75 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 + 24 * q^4 + 4 * q^5 - 18 * q^6 - q^7 - 18 * q^8 - q^10 + 13 * q^11 - 19 * q^12 + 7 * q^13 - q^14 - q^15 + 16 * q^16 + 9 * q^17 - 3 * q^18 - 34 * q^19 - 9 * q^20 + 2 * q^21 + 14 * q^22 + 58 * q^23 + 8 * q^24 - 4 * q^25 - 19 * q^26 - 34 * q^27 + 19 * q^28 - 16 * q^29 - 12 * q^30 - 3 * q^31 + 14 * q^34 + 11 * q^35 + 57 * q^36 + 20 * q^37 - 16 * q^38 + 5 * q^39 + 3 * q^40 + 24 * q^41 + 34 * q^42 - 28 * q^43 + 73 * q^44 + 15 * q^45 - 22 * q^46 + 18 * q^47 - 74 * q^48 - 19 * q^49 + q^50 - 8 * q^51 + 2 * q^52 + 23 * q^53 + 48 * q^54 - 13 * q^55 - 7 * q^56 - 22 * q^57 + 8 * q^58 - 44 * q^59 - 6 * q^60 - 25 * q^61 + 56 * q^62 - 7 * q^63 + 42 * q^64 + 3 * q^65 - 102 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^70 - 22 * q^71 - 39 * q^72 - 26 * q^73 - 2 * q^74 + 6 * q^75 + 16 * q^76 + 11 * q^77 + 12 * q^78 - 32 * q^79 - 21 * q^80 + 11 * q^81 + 46 * q^82 + 4 * q^83 - 19 * q^84 + 36 * q^85 + 39 * q^86 + 88 * q^87 + 24 * q^88 + 38 * q^89 - 22 * q^90 - 6 * q^91 + 114 * q^92 - 31 * q^93 - 31 * q^94 - 21 * q^95 + 59 * q^96 + 75 * q^97 - 56 * q^98 + 75 * q^99

Character values

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

$n$	$6$	$152$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.488177			0.345193			0.172596	−	0.984993i	$-0.444784\pi$
$2$	0.488177			0.345193			0.172596	+	0.984993i	$0.444784\pi$
$3$	−0.778897	+	2.39720i	−0.449697	+	1.38402i	0.427553	+	0.903990i	$0.359376\pi$
$3$	−0.778897	+	2.39720i	−0.449697	+	1.38402i	−0.877250	+	0.480034i	$0.840624\pi$
$4$	−1.76168			−0.880842
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−0.380239	+	1.17026i	−0.155232	+	0.477755i
$7$	−2.04327	−	1.48452i	−0.772282	−	0.561096i	0.130371	−	0.991465i	$-0.458383\pi$
$7$	−2.04327	−	1.48452i	−0.772282	−	0.561096i	−0.902653	+	0.430370i	$0.858383\pi$
$8$	−1.83637			−0.649253
$9$	−2.71283	−	1.97099i	−0.904278	−	0.656996i
$10$	0.394943	+	0.286943i	0.124892	+	0.0907393i
$11$	−0.818155	−	2.51802i	−0.246683	−	0.759213i	−0.995355	−	0.0962720i	$-0.969308\pi$
$11$	−0.818155	−	2.51802i	−0.246683	−	0.759213i	0.748672	−	0.662941i	$-0.230692\pi$
$12$	1.37217	−	4.22311i	0.396112	−	1.21911i
$13$	0.391104	−	1.20370i	0.108473	−	0.333845i	−0.882057	−	0.471143i	$-0.843842\pi$
$13$	0.391104	−	1.20370i	0.108473	−	0.333845i	0.990530	+	0.137298i	$0.0438417\pi$
$14$	−0.997475	−	0.724708i	−0.266586	−	0.193686i
$15$	−2.03918	+	1.48155i	−0.526514	+	0.382535i
$16$	2.62690			0.656724
$17$	1.99426	−	1.44891i	0.483679	−	0.351413i	−0.319070	−	0.947731i	$-0.603370\pi$
$17$	1.99426	−	1.44891i	0.483679	−	0.351413i	0.802748	+	0.596318i	$0.203370\pi$
$18$	−1.32434	−	0.962191i	−0.312150	−	0.226791i
$19$	−2.81911			−0.646748			−0.323374	−	0.946271i	$-0.604817\pi$
$19$	−2.81911			−0.646748			−0.323374	+	0.946271i	$0.604817\pi$
$20$	−1.42523	−	1.03549i	−0.318692	−	0.231543i
$21$	5.15018	−	3.74183i	1.12386	−	0.816534i
$22$	−0.399404	−	1.22924i	−0.0851533	−	0.262075i
$23$	−1.14711			−0.239189			−0.119594	−	0.992823i	$-0.538159\pi$
$23$	−1.14711			−0.239189			−0.119594	+	0.992823i	$0.538159\pi$
$24$	1.43034	−	4.40214i	0.291967	−	0.898582i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.190928	−	0.587616i	0.0374441	−	0.115241i
$27$	0.720334	−	0.523353i	0.138628	−	0.100719i
$28$	3.59959	+	2.61525i	0.680258	+	0.494237i
$29$	−1.55483	−	4.78528i	−0.288725	−	0.888604i	−0.985257	−	0.171079i	$-0.945275\pi$
$29$	−1.55483	−	4.78528i	−0.288725	−	0.888604i	0.696532	−	0.717525i	$-0.254725\pi$
$30$	−0.995480	+	0.723258i	−0.181749	+	0.132048i
$31$	1.37129	−	0.996297i	0.246290	−	0.178940i	−0.457791	−	0.889060i	$-0.651359\pi$
$31$	1.37129	−	0.996297i	0.246290	−	0.178940i	0.704081	+	0.710120i	$0.251359\pi$
$32$	4.95512			0.875950
$33$	6.67346			1.16170
$34$	0.973550	−	0.707325i	0.166962	−	0.121305i
$35$	−0.780458	−	2.40200i	−0.131922	−	0.406013i
$36$	4.77915	+	3.47226i	0.796526	+	0.578710i
$37$	1.27506	−	3.92423i	0.209618	−	0.645139i	−0.789874	−	0.613270i	$-0.789854\pi$
$37$	1.27506	−	3.92423i	0.209618	−	0.645139i	0.999492	−	0.0318694i	$-0.0101461\pi$
$38$	−1.37622			−0.223253
$39$	2.58087	+	1.87511i	0.413270	+	0.300258i
$40$	−1.48565	−	1.07939i	−0.234902	−	0.170666i
$41$	−0.471546	+	1.45127i	−0.0736431	+	0.226650i	−0.981102	−	0.193490i	$-0.938019\pi$
$41$	−0.471546	+	1.45127i	−0.0736431	+	0.226650i	0.907459	+	0.420140i	$0.138019\pi$
$42$	2.51420	−	1.82667i	0.387949	−	0.281862i
$43$	4.74909	−	3.45041i	0.724229	−	0.526183i	−0.163503	−	0.986543i	$-0.552279\pi$
$43$	4.74909	−	3.45041i	0.724229	−	0.526183i	0.887733	+	0.460360i	$0.152279\pi$
$44$	1.44133	+	4.43596i	0.217289	+	0.668746i
$45$	−1.03621	−	3.18913i	−0.154469	−	0.475407i
$46$	−0.559992			−0.0825663
$47$	−0.632339	+	1.94614i	−0.0922361	+	0.283873i	−0.986524	−	0.163620i	$-0.947683\pi$
$47$	−0.632339	+	1.94614i	−0.0922361	+	0.283873i	0.894287	+	0.447493i	$0.147683\pi$
$48$	−2.04608	+	6.29720i	−0.295327	+	0.908922i
$49$	−0.191982	−	0.590859i	−0.0274259	−	0.0844084i
$50$	0.150855	+	0.464284i	0.0213341	+	0.0656596i
$51$	1.92001	+	5.90919i	0.268855	+	0.827452i
$52$	−0.689002	+	2.12053i	−0.0955474	+	0.294065i
$53$	0.922429	+	2.83894i	0.126705	+	0.389959i	0.994208	−	0.107474i	$-0.0342762\pi$
$53$	0.922429	+	2.83894i	0.126705	+	0.389959i	−0.867503	+	0.497433i	$0.834276\pi$
$54$	0.351650	−	0.255489i	0.0478535	−	0.0347676i
$55$	0.818155	−	2.51802i	0.110320	−	0.339530i
$56$	3.75218	+	2.72612i	0.501407	+	0.364293i
$57$	2.19580	−	6.75796i	0.290840	−	0.895114i
$58$	−0.759032	−	2.33606i	−0.0996658	−	0.306740i
$59$	−3.94628			−0.513762			−0.256881	−	0.966443i	$-0.582695\pi$
$59$	−3.94628			−0.513762			−0.256881	+	0.966443i	$0.582695\pi$
$60$	3.59239	−	2.61002i	0.463776	−	0.336953i
$61$	−2.62955	−	8.09292i	−0.336679	−	1.03619i	−0.965889	−	0.258957i	$-0.916621\pi$
$61$	−2.62955	−	8.09292i	−0.336679	−	1.03619i	0.629210	−	0.777236i	$-0.283379\pi$
$62$	0.669430	−	0.486369i	0.0850176	−	0.0617689i
$63$	2.61707	+	8.05451i	0.329720	+	1.01477i
$64$	−2.83482			−0.354352
$65$	1.02392	−	0.743925i	0.127002	−	0.0922725i
$66$	3.25783			0.401011
$67$	−1.58385	+	1.15074i	−0.193498	+	0.140585i	−0.680316	−	0.732919i	$-0.738158\pi$
$67$	−1.58385	+	1.15074i	−0.193498	+	0.140585i	0.486818	+	0.873504i	$0.338158\pi$
$68$	−3.51325	+	2.55253i	−0.426044	+	0.309539i
$69$	0.893481	−	2.74985i	0.107562	−	0.331043i
$70$	−0.381001	−	1.17260i	−0.0455384	−	0.140153i
$71$	−9.62246	−	6.99112i	−1.14198	−	0.829694i	−0.154582	−	0.987980i	$-0.549403\pi$
$71$	−9.62246	−	6.99112i	−1.14198	−	0.829694i	−0.987393	+	0.158286i	$0.949403\pi$
$72$	4.98176	+	3.61946i	0.587105	+	0.426557i
$73$	−0.984339	−	0.715164i	−0.115208	−	0.0837036i	0.528689	−	0.848815i	$-0.322684\pi$
$73$	−0.984339	−	0.715164i	−0.115208	−	0.0837036i	−0.643897	+	0.765112i	$0.722684\pi$
$74$	0.622454	−	1.91572i	0.0723588	−	0.222697i
$75$	−2.52056			−0.291050
$76$	4.96638			0.569682
$77$	−2.06635	+	6.35956i	−0.235482	+	0.724739i
$78$	1.25992	+	0.915385i	0.142658	+	0.103647i
$79$	−13.6221	−	9.89704i	−1.53261	−	1.11350i	−0.954768	−	0.297352i	$-0.903896\pi$
$79$	−13.6221	−	9.89704i	−1.53261	−	1.11350i	−0.577838	−	0.816151i	$-0.696104\pi$
$80$	2.12520	+	1.54405i	0.237605	+	0.172630i
$81$	−2.41511	−	7.43296i	−0.268346	−	0.825884i
$82$	−0.230198	+	0.708475i	−0.0254211	+	0.0782380i
$83$	−1.32704	+	0.964149i	−0.145661	+	0.105829i	−0.658229	−	0.752818i	$-0.728694\pi$
$83$	−1.32704	+	0.964149i	−0.145661	+	0.105829i	0.512568	+	0.858647i	$0.328694\pi$
$84$	−9.07300	+	6.59192i	−0.989945	+	0.719237i
$85$	2.46504			0.267371
$86$	2.31839	−	1.68441i	0.249999	−	0.181635i
$87$	12.6823			1.35969
$88$	1.50243	+	4.62401i	0.160160	+	0.492921i
$89$	2.76691	−	2.01028i	0.293292	−	0.213089i	−0.431402	−	0.902160i	$-0.641981\pi$
$89$	2.76691	−	2.01028i	0.293292	−	0.213089i	0.724694	+	0.689071i	$0.241981\pi$
$90$	−0.505854	−	1.55686i	−0.0533217	−	0.164107i
$91$	−2.58604	+	1.87887i	−0.271091	+	0.196959i
$92$	2.02084			0.210688
$93$	1.32023	+	4.06326i	0.136902	+	0.421340i
$94$	−0.308693	+	0.950059i	−0.0318392	+	0.0979911i
$95$	−2.28071	−	1.65703i	−0.233995	−	0.170008i
$96$	−3.85953	+	11.8784i	−0.393912	+	1.21234i
$97$	9.51327	−	6.91180i	0.965927	−	0.701787i	0.0114070	−	0.999935i	$-0.496369\pi$
$97$	9.51327	−	6.91180i	0.965927	−	0.701787i	0.954520	+	0.298148i	$0.0963690\pi$
$98$	−0.0937209	−	0.288443i	−0.00946724	−	0.0291372i
$99$	−2.74348	+	8.44355i	−0.275730	+	0.848609i
$100$	−0.544390	−	1.67546i	−0.0544390	−	0.167546i
$101$	−1.01923	−	3.13686i	−0.101417	−	0.312130i	0.887456	−	0.460893i	$-0.152471\pi$
$101$	−1.01923	−	3.13686i	−0.101417	−	0.312130i	−0.988873	+	0.148763i	$0.952471\pi$
$102$	0.937305	+	2.88473i	0.0928070	+	0.285631i
$103$	2.45597	−	7.55870i	0.241994	−	0.744781i	−0.754122	−	0.656734i	$-0.771937\pi$
$103$	2.45597	−	7.55870i	0.241994	−	0.744781i	0.996116	−	0.0880468i	$-0.0280625\pi$
$104$	−0.718211	+	2.21043i	−0.0704264	+	0.216750i
$105$	6.36598			0.621256
$106$	0.450308	+	1.38591i	0.0437378	+	0.134611i
$107$	0.0592246	+	0.182275i	0.00572546	+	0.0176211i	0.953878	−	0.300193i	$-0.0970511\pi$
$107$	0.0592246	+	0.182275i	0.00572546	+	0.0176211i	−0.948153	+	0.317814i	$0.897051\pi$
$108$	−1.26900	+	0.921983i	−0.122110	+	0.0887179i
$109$	−16.6033	+	12.0630i	−1.59031	+	1.15543i	−0.686804	+	0.726842i	$0.740987\pi$
$109$	−16.6033	+	12.0630i	−1.59031	+	1.15543i	−0.903502	+	0.428583i	$0.859013\pi$
$110$	0.399404	−	1.22924i	0.0380817	−	0.117203i
$111$	8.41402	+	6.11314i	0.798623	+	0.580234i
$112$	−5.36745	−	3.89968i	−0.507176	−	0.368485i
$113$	−13.1780			−1.23969			−0.619843	−	0.784726i	$-0.712804\pi$
$113$	−13.1780			−1.23969			−0.619843	+	0.784726i	$0.712804\pi$
$114$	1.07194	−	3.29908i	0.100396	−	0.308987i
$115$	−0.928031	−	0.674254i	−0.0865394	−	0.0628745i
$116$	2.73912	+	8.43015i	0.254321	+	0.782720i
$117$	−3.43347	+	2.49456i	−0.317425	+	0.230623i
$118$	−1.92648			−0.177347
$119$	−6.22574			−0.570713
$120$	3.74468	−	2.72067i	0.341841	−	0.248362i
$121$	3.22812	−	2.34537i	0.293466	−	0.213215i
$122$	−1.28368	−	3.95077i	−0.116219	−	0.357686i
$123$	−3.11169	−	2.26078i	−0.280572	−	0.203848i
$124$	−2.41577	+	1.75516i	−0.216943	+	0.157618i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	1.27759	+	3.93202i	0.113817	+	0.350292i
$127$	−5.69277	+	17.5205i	−0.505152	+	1.55470i	0.295364	+	0.955385i	$0.404559\pi$
$127$	−5.69277	+	17.5205i	−0.505152	+	1.55470i	−0.800515	+	0.599312i	$0.795441\pi$
$128$	−11.2941			−0.998270
$129$	4.57228	+	14.0720i	0.402567	+	1.23897i
$130$	0.499856	−	0.363167i	0.0438403	−	0.0318518i
$131$	−8.00312	−	5.81461i	−0.699236	−	0.508025i	0.180447	−	0.983585i	$-0.442246\pi$
$131$	−8.00312	−	5.81461i	−0.699236	−	0.508025i	−0.879683	+	0.475560i	$0.842246\pi$
$132$	−11.7565			−1.02327
$133$	5.76019	+	4.18502i	0.499471	+	0.362887i
$134$	−0.773200	+	0.561762i	−0.0667943	+	0.0485289i
$135$	0.890382			0.0766319
$136$	−3.66219	+	2.66073i	−0.314030	+	0.228156i
$137$	10.5726	+	7.68143i	0.903276	+	0.656269i	0.939305	−	0.343082i	$-0.111471\pi$
$137$	10.5726	+	7.68143i	0.903276	+	0.656269i	−0.0360290	+	0.999351i	$0.511471\pi$
$138$	0.436176	−	1.34241i	0.0371298	−	0.114274i
$139$	−1.56264	+	4.80932i	−0.132542	+	0.407921i	−0.995200	−	0.0978666i	$-0.968798\pi$
$139$	−1.56264	+	4.80932i	−0.132542	+	0.407921i	0.862658	+	0.505788i	$0.168798\pi$
$140$	1.37492	+	4.23157i	0.116202	+	0.357633i
$141$	−4.17275	−	3.03168i	−0.351409	−	0.255314i
$142$	−4.69746	−	3.41290i	−0.394202	−	0.286404i
$143$	−3.35092			−0.280218
$144$	−7.12633	−	5.17758i	−0.593861	−	0.431465i
$145$	1.55483	−	4.78528i	0.129122	−	0.397396i
$146$	−0.480531	−	0.349126i	−0.0397690	−	0.0288939i
$147$	1.56594			0.129157
$148$	−2.24625	+	6.91325i	−0.184641	+	0.568265i
$149$	−7.20538			−0.590288			−0.295144	−	0.955453i	$-0.595368\pi$
$149$	−7.20538			−0.590288			−0.295144	+	0.955453i	$0.595368\pi$
$150$	−1.23048			−0.100468
$151$	−7.27232	+	9.90522i	−0.591813	+	0.806075i
$151$	−7.27232	+	9.90522i	−0.591813	+	0.806075i
$152$	5.17691			0.419903
$153$	−8.26588			−0.668257
$154$	−1.00874	+	3.10459i	−0.0812867	+	0.250175i
$155$	1.69500			0.136146
$156$	−4.54667	−	3.30335i	−0.364025	−	0.264480i
$157$	−0.114905	+	0.353642i	−0.00917044	+	0.0282237i	−0.955537	−	0.294871i	$-0.904723\pi$
$157$	−0.114905	+	0.353642i	−0.00917044	+	0.0282237i	0.946367	+	0.323095i	$0.104723\pi$
$158$	−6.64999	−	4.83150i	−0.529045	−	0.384374i
$159$	−7.52399			−0.596691
$160$	4.00878	+	2.91255i	0.316922	+	0.230257i
$161$	2.34385	+	1.70291i	0.184721	+	0.134208i
$162$	−1.17900	−	3.62860i	−0.0926312	−	0.285089i
$163$	5.09571	−	15.6830i	0.399127	−	1.22839i	−0.526573	−	0.850130i	$-0.676523\pi$
$163$	5.09571	−	15.6830i	0.399127	−	1.22839i	0.925700	−	0.378257i	$-0.123477\pi$
$164$	0.830714	−	2.55668i	0.0648679	−	0.199643i
$165$	5.39895	+	3.92256i	0.420307	+	0.305371i
$166$	−0.647829	+	0.470675i	−0.0502813	+	0.0365315i
$167$	6.79703			0.525970			0.262985	−	0.964800i	$-0.415293\pi$
$167$	6.79703			0.525970			0.262985	+	0.964800i	$0.415293\pi$
$168$	−9.45762	+	6.87136i	−0.729671	+	0.530137i
$169$	9.22130	+	6.69967i	0.709331	+	0.515359i
$170$	1.20337			0.0922946
$171$	7.64777	+	5.55643i	0.584840	+	0.424911i
$172$	−8.36639	+	6.07854i	−0.637931	+	0.463484i
$173$	1.44824	+	4.45724i	0.110108	+	0.338878i	0.990895	−	0.134634i	$-0.0429860\pi$
$173$	1.44824	+	4.45724i	0.110108	+	0.338878i	−0.880787	+	0.473512i	$0.842986\pi$
$174$	6.19121			0.469355
$175$	0.780458	−	2.40200i	0.0589971	−	0.181574i
$176$	−2.14921	−	6.61459i	−0.162003	−	0.498593i
$177$	3.07374	−	9.46001i	0.231037	−	0.711058i
$178$	1.35074	−	0.981371i	0.101242	−	0.0735569i
$179$	3.41684	+	2.48248i	0.255387	+	0.185549i	0.708111	−	0.706101i	$-0.249548\pi$
$179$	3.41684	+	2.48248i	0.255387	+	0.185549i	−0.452724	+	0.891651i	$0.649548\pi$
$180$	1.82547	+	5.61823i	0.136063	+	0.418758i
$181$	8.01886	−	5.82604i	0.596037	−	0.433046i	−0.248433	−	0.968649i	$-0.579916\pi$
$181$	8.01886	−	5.82604i	0.596037	−	0.433046i	0.844470	+	0.535603i	$0.179916\pi$
$182$	−1.26244	+	0.917219i	−0.0935786	+	0.0679888i
$183$	21.4485			1.58552
$184$	2.10651			0.155294
$185$	3.33815	−	2.42531i	0.245425	−	0.178312i
$186$	0.644507	+	1.98359i	0.0472575	+	0.145444i
$187$	−5.28001	−	3.83615i	−0.386113	−	0.280527i
$188$	1.11398	−	3.42848i	0.0812454	−	0.250048i
$189$	−2.24876			−0.163573
$190$	−1.11339	−	0.808923i	−0.0807736	−	0.0586854i
$191$	0.368440	+	0.267688i	0.0266594	+	0.0193692i	0.601035	−	0.799223i	$-0.294755\pi$
$191$	0.368440	+	0.267688i	0.0266594	+	0.0193692i	−0.574376	+	0.818592i	$0.694755\pi$
$192$	2.20803	−	6.79563i	0.159351	−	0.490432i
$193$	−11.3171	+	8.22239i	−0.814626	+	0.591861i	−0.915168	−	0.403072i	$-0.867942\pi$
$193$	−11.3171	+	8.22239i	−0.814626	+	0.591861i	0.100542	+	0.994933i	$0.467942\pi$
$194$	4.64416	−	3.37418i	0.333431	−	0.242252i
$195$	0.985804	+	3.03399i	0.0705949	+	0.217269i
$196$	0.338211	+	1.04091i	0.0241579	+	0.0743504i
$197$	5.55681			0.395907			0.197953	−	0.980211i	$-0.436571\pi$
$197$	5.55681			0.395907			0.197953	+	0.980211i	$0.436571\pi$
$198$	−1.33930	+	4.12195i	−0.0951800	+	0.292934i
$199$	2.04543	−	6.29518i	0.144997	−	0.446254i	−0.852014	−	0.523519i	$-0.824619\pi$
$199$	2.04543	−	6.29518i	0.144997	−	0.446254i	0.997011	+	0.0772654i	$0.0246189\pi$
$200$	−0.567468	−	1.74649i	−0.0401261	−	0.123495i
$201$	−1.52489	−	4.69312i	−0.107557	−	0.331027i
$202$	−0.497564	−	1.53134i	−0.0350085	−	0.107745i
$203$	−3.92691	+	12.0858i	−0.275615	+	0.848255i
$204$	−3.38245	−	10.4101i	−0.236819	−	0.728854i
$205$	−1.23452	+	0.896933i	−0.0862228	+	0.0626445i
$206$	1.19895	−	3.68998i	0.0835346	−	0.257093i
$207$	3.11192	+	2.26094i	0.216293	+	0.157146i
$208$	1.02739	−	3.16198i	0.0712367	−	0.219244i
$209$	2.30647	+	7.09858i	0.159542	+	0.491019i
$210$	3.10772			0.214453
$211$	−13.7370	+	9.98055i	−0.945697	+	0.687089i	−0.949785	−	0.312902i	$-0.898699\pi$
$211$	−13.7370	+	9.98055i	−0.945697	+	0.687089i	0.00408810	+	0.999992i	$0.498699\pi$
$212$	−1.62503	−	5.00132i	−0.111607	−	0.343492i
$213$	24.2540	−	17.6216i	1.66186	−	1.20741i
$214$	0.0289121	+	0.0889822i	0.00197639	+	0.00608269i
$215$	5.87020			0.400344
$216$	−1.32280	+	0.961068i	−0.0900049	+	0.0653924i
$217$	−4.28092			−0.290608
$218$	−8.10534	+	5.88887i	−0.548963	+	0.398845i
$219$	2.48109	−	1.80262i	0.167657	−	0.121810i
$220$	−1.44133	+	4.43596i	−0.0971745	+	0.299072i
$221$	−0.964087	−	2.96716i	−0.0648515	−	0.199592i
$222$	4.10753	+	2.98429i	0.275679	+	0.200293i
$223$	−7.79199	−	5.66121i	−0.521790	−	0.379103i	0.295488	−	0.955347i	$-0.404518\pi$
$223$	−7.79199	−	5.66121i	−0.521790	−	0.379103i	−0.817278	+	0.576244i	$0.804518\pi$
$224$	−10.1246	−	7.35597i	−0.676480	−	0.491492i
$225$	1.03621	−	3.18913i	0.0690807	−	0.212608i
$226$	−6.43321			−0.427931
$227$	11.1068			0.737186			0.368593	−	0.929591i	$-0.379840\pi$
$227$	11.1068			0.737186			0.368593	+	0.929591i	$0.379840\pi$
$228$	−3.86830	+	11.9054i	−0.256184	+	0.788454i
$229$	11.0516	+	8.02946i	0.730310	+	0.530602i	0.889662	−	0.456620i	$-0.150940\pi$
$229$	11.0516	+	8.02946i	0.730310	+	0.530602i	−0.159351	+	0.987222i	$0.550940\pi$
$230$	−0.453043	−	0.329155i	−0.0298728	−	0.0217038i
$231$	−13.6357	−	9.90689i	−0.897161	−	0.651825i
$232$	2.85524	+	8.78753i	0.187456	+	0.576929i
$233$	6.57640	−	20.2401i	0.430834	−	1.32597i	−0.466461	−	0.884542i	$-0.654471\pi$
$233$	6.57640	−	20.2401i	0.430834	−	1.32597i	0.897296	−	0.441430i	$-0.145529\pi$
$234$	−1.67614	+	1.21779i	−0.109573	+	0.0796093i
$235$	−1.65548	+	1.20278i	−0.107992	+	0.0784607i
$236$	6.95209			0.452543
$237$	34.3354	−	24.9461i	2.23032	−	1.62042i
$238$	−3.03926			−0.197006
$239$	5.15714	+	15.8720i	0.333587	+	1.02668i	0.967414	+	0.253201i	$0.0814834\pi$
$239$	5.15714	+	15.8720i	0.333587	+	1.02668i	−0.633826	+	0.773475i	$0.718517\pi$
$240$	−5.35671	+	3.89188i	−0.345774	+	0.251220i
$241$	−6.06687	−	18.6719i	−0.390802	−	1.20276i	−0.932183	−	0.361987i	$-0.882099\pi$
$241$	−6.06687	−	18.6719i	−0.390802	−	1.20276i	0.541381	−	0.840777i	$-0.317901\pi$
$242$	1.57589	−	1.14495i	0.101302	−	0.0736004i
$243$	22.3706			1.43507
$244$	4.63243	+	14.2572i	0.296561	+	0.912721i
$245$	0.191982	−	0.590859i	0.0122653	−	0.0377486i
$246$	−1.51906	−	1.10366i	−0.0968515	−	0.0703667i
$247$	−1.10257	+	3.39335i	−0.0701546	+	0.215914i
$248$	−2.51818	+	1.82957i	−0.159905	+	0.116178i
$249$	−1.27763	−	3.93215i	−0.0809667	−	0.249190i
$250$	−0.150855	+	0.464284i	−0.00954090	+	0.0293639i
$251$	0.339278	+	1.04419i	0.0214151	+	0.0659088i	0.961193	−	0.275877i	$-0.0889683\pi$
$251$	0.339278	+	1.04419i	0.0214151	+	0.0659088i	−0.939778	+	0.341786i	$0.888968\pi$
$252$	−4.61045	−	14.1895i	−0.290431	−	0.893854i
$253$	0.938514	+	2.88845i	0.0590039	+	0.181595i
$254$	−2.77908	+	8.55312i	−0.174375	+	0.536670i
$255$	−1.92001	+	5.90919i	−0.120236	+	0.370048i
$256$	0.156107			0.00975666
$257$	0.489912	+	1.50779i	0.0305598	+	0.0940535i	0.965173	−	0.261612i	$-0.0842542\pi$
$257$	0.489912	+	1.50779i	0.0305598	+	0.0940535i	−0.934613	+	0.355666i	$0.884254\pi$
$258$	2.23208	+	6.86964i	0.138963	+	0.427685i
$259$	−8.43088	+	6.12539i	−0.523869	+	0.380613i
$260$	−1.80383	+	1.31056i	−0.111869	+	0.0812775i
$261$	−5.21374	+	16.0462i	−0.322722	+	0.993237i
$262$	−3.90694	−	2.83856i	−0.241371	−	0.175367i
$263$	−19.2378	−	13.9771i	−1.18626	−	0.861865i	−0.193392	−	0.981122i	$-0.561949\pi$
$263$	−19.2378	−	13.9771i	−1.18626	−	0.861865i	−0.992863	+	0.119257i	$0.961949\pi$
$264$	−12.2549			−0.754238
$265$	−0.922429	+	2.83894i	−0.0566643	+	0.174395i
$266$	2.81199	+	2.04303i	0.172414	+	0.125266i
$267$	2.66390	+	8.19864i	0.163028	+	0.501749i
$268$	2.79025	−	2.02723i	0.170441	−	0.123833i
$269$	17.4397			1.06332			0.531660	−	0.846958i	$-0.321568\pi$
$269$	17.4397			1.06332			0.531660	+	0.846958i	$0.321568\pi$
$270$	0.434664			0.0264528
$271$	−22.9831	+	16.6982i	−1.39612	+	1.01434i	−0.400962	+	0.916094i	$0.631324\pi$
$271$	−22.9831	+	16.6982i	−1.39612	+	1.01434i	−0.995162	+	0.0982492i	$0.968676\pi$
$272$	5.23871	−	3.80614i	0.317643	−	0.230781i
$273$	−2.48976	−	7.66270i	−0.150687	−	0.463768i
$274$	5.16129	+	3.74989i	0.311805	+	0.226539i
$275$	2.14196	−	1.55622i	0.129165	−	0.0938438i
$276$	−1.57403	+	4.84437i	−0.0947455	+	0.291597i
$277$	4.47620	+	13.7763i	0.268949	+	0.827739i	0.990757	+	0.135646i	$0.0433110\pi$
$277$	4.47620	+	13.7763i	0.268949	+	0.827739i	−0.721809	+	0.692093i	$0.756689\pi$
$278$	−0.762846	+	2.34780i	−0.0457524	+	0.140812i
$279$	−5.68376			−0.340278
$280$	1.43321	+	4.41096i	0.0856505	+	0.263605i
$281$	22.1167	−	16.0687i	1.31937	−	0.958579i	0.319431	−	0.947610i	$-0.396508\pi$
$281$	22.1167	−	16.0687i	1.31937	−	0.958579i	0.999940	−	0.0109693i	$-0.00349170\pi$
$282$	−2.03704	−	1.48000i	−0.121304	−	0.0881325i
$283$	5.14080			0.305589			0.152794	−	0.988258i	$-0.451173\pi$
$283$	5.14080			0.305589			0.152794	+	0.988258i	$0.451173\pi$
$284$	16.9517	+	12.3161i	1.00590	+	0.730829i
$285$	5.74867	−	4.17665i	0.340522	−	0.247403i
$286$	−1.63584			−0.0967292
$287$	3.11793	−	2.26531i	0.184046	−	0.133717i
$288$	−13.4424	−	9.76649i	−0.792102	−	0.575496i
$289$	−3.37557	+	10.3889i	−0.198563	+	0.611115i
$290$	0.759032	−	2.33606i	0.0445719	−	0.137178i
$291$	9.15910	+	28.1888i	0.536916	+	1.65246i
$292$	1.73409	+	1.25989i	0.101480	+	0.0737296i
$293$	6.07834	+	4.41617i	0.355100	+	0.257995i	0.751006	−	0.660296i	$-0.229569\pi$
$293$	6.07834	+	4.41617i	0.355100	+	0.257995i	−0.395905	+	0.918291i	$0.629569\pi$
$294$	0.764455			0.0445839
$295$	−3.19261	−	2.31956i	−0.185881	−	0.135050i
$296$	−2.34147	+	7.20632i	−0.136095	+	0.418859i
$297$	−1.90716	−	1.38563i	−0.110665	−	0.0804026i
$298$	−3.51750			−0.203763
$299$	−0.448640	+	1.38077i	−0.0259455	+	0.0798521i
$300$	4.44044			0.256369
$301$	−14.8259			−0.854548
$302$	−3.55018	+	4.83549i	−0.204290	+	0.278251i
$303$	8.31357			0.477602
$304$	−7.40550			−0.424735
$305$	2.62955	−	8.09292i	0.150568	−	0.463399i
$306$	−4.03521			−0.230678
$307$	6.33880	+	4.60541i	0.361774	+	0.262844i	0.753792	−	0.657113i	$-0.228223\pi$
$307$	6.33880	+	4.60541i	0.361774	+	0.262844i	−0.392017	+	0.919958i	$0.628223\pi$
$308$	3.64025	−	11.2035i	0.207422	−	0.638380i
$309$	16.2068	+	11.7749i	0.921970	+	0.669851i
$310$	0.827460			0.0469966
$311$	−17.5154	−	12.7257i	−0.993207	−	0.721607i	−0.0325862	−	0.999469i	$-0.510374\pi$
$311$	−17.5154	−	12.7257i	−0.993207	−	0.721607i	−0.960621	+	0.277862i	$0.910374\pi$
$312$	−4.73942	−	3.44339i	−0.268317	−	0.194944i
$313$	−4.06570	−	12.5129i	−0.229807	−	0.707272i	−0.997768	−	0.0667761i	$-0.978729\pi$
$313$	−4.06570	−	12.5129i	−0.229807	−	0.707272i	0.767961	−	0.640496i	$-0.221271\pi$
$314$	−0.0560941	+	0.172640i	−0.00316557	+	0.00974263i
$315$	−2.61707	+	8.05451i	−0.147455	+	0.453820i
$316$	23.9978	+	17.4354i	1.34998	+	0.980821i
$317$	23.6261	−	17.1653i	1.32697	−	0.964102i	0.327155	−	0.944971i	$-0.393910\pi$
$317$	23.6261	−	17.1653i	1.32697	−	0.964102i	0.999817	−	0.0191309i	$-0.00608992\pi$
$318$	−3.67304			−0.205974
$319$	−10.7774	+	7.83021i	−0.603416	+	0.438407i
$320$	−2.29342	−	1.66626i	−0.128206	−	0.0931470i
$321$	−0.483078			−0.0269628
$322$	1.14421	+	0.831319i	0.0637645	+	0.0463276i
$323$	−5.62203	+	4.08464i	−0.312818	+	0.227276i
$324$	4.25467	+	13.0945i	0.236370	+	0.727473i
$325$	1.26564			0.0702051
$326$	2.48761	−	7.65607i	0.137776	−	0.424031i
$327$	−15.9852	−	49.1972i	−0.883981	−	2.72061i
$328$	0.865931	−	2.66506i	0.0478130	−	0.147153i
$329$	4.18112	−	3.03776i	0.230512	−	0.167477i
$330$	2.63564	+	1.91490i	0.145087	+	0.105412i
$331$	−4.07934	−	12.5549i	−0.224221	−	0.690081i	−0.998370	−	0.0570775i	$-0.981822\pi$
$331$	−4.07934	−	12.5549i	−0.224221	−	0.690081i	0.774149	−	0.633004i	$-0.218178\pi$
$332$	2.33782	−	1.69853i	0.128305	−	0.0932187i
$333$	−11.1936	+	8.13265i	−0.613407	+	0.445666i
$334$	3.31815			0.181561
$335$	−1.95775			−0.106963
$336$	13.5290	−	9.82939i	0.738068	−	0.536237i
$337$	−0.0793030	−	0.244069i	−0.00431991	−	0.0132953i	0.948873	−	0.315657i	$-0.102225\pi$
$337$	−0.0793030	−	0.244069i	−0.00431991	−	0.0132953i	−0.953193	+	0.302362i	$0.902225\pi$
$338$	4.50162	+	3.27062i	0.244856	+	0.177898i
$339$	10.2643	−	31.5904i	0.557483	−	1.71576i
$340$	−4.34262			−0.235511
$341$	−3.63062	−	2.63780i	−0.196609	−	0.142845i
$342$	3.73346	+	2.71252i	0.201882	+	0.146676i
$343$	−5.94808	+	18.3063i	−0.321166	+	0.988448i
$344$	−8.72106	+	6.33622i	−0.470208	+	0.341626i
$345$	2.33916	−	1.69950i	0.125936	−	0.0914981i
$346$	0.706999	+	2.17592i	0.0380085	+	0.116978i
$347$	5.65041	+	17.3902i	0.303330	+	0.933553i	0.980295	+	0.197538i	$0.0632947\pi$
$347$	5.65041	+	17.3902i	0.303330	+	0.933553i	−0.676965	+	0.736015i	$0.736705\pi$
$348$	−22.3422			−1.19767
$349$	−10.4484	+	32.1569i	−0.559291	+	1.72132i	0.125042	+	0.992151i	$0.460093\pi$
$349$	−10.4484	+	32.1569i	−0.559291	+	1.72132i	−0.684333	+	0.729169i	$0.739907\pi$
$350$	0.381001	−	1.17260i	0.0203654	−	0.0626782i
$351$	−0.348232	−	1.07175i	−0.0185873	−	0.0572057i
$352$	−4.05406	−	12.4771i	−0.216082	−	0.665032i
$353$	−4.98371	−	15.3383i	−0.265256	−	0.816375i	−0.991634	−	0.129079i	$-0.958798\pi$
$353$	−4.98371	−	15.3383i	−0.265256	−	0.816375i	0.726378	−	0.687295i	$-0.241202\pi$
$354$	1.50053	−	4.61816i	0.0797523	−	0.245452i
$355$	−3.67545	−	11.3119i	−0.195073	−	0.600372i
$356$	−4.87442	+	3.54148i	−0.258344	+	0.187698i
$357$	4.84921	−	14.9243i	0.256647	−	0.789880i
$358$	1.66802	+	1.21189i	0.0881576	+	0.0640503i
$359$	−0.0849648	+	0.261495i	−0.00448427	+	0.0138012i	−0.953274	−	0.302108i	$-0.902310\pi$
$359$	−0.0849648	+	0.261495i	−0.00448427	+	0.0138012i	0.948789	+	0.315909i	$0.102310\pi$
$360$	1.90286	+	5.85640i	0.100290	+	0.308660i
$361$	−11.0526			−0.581718
$362$	3.91462	−	2.84414i	0.205748	−	0.149485i
$363$	3.10794	+	9.56526i	0.163125	+	0.502046i
$364$	4.55579	−	3.30997i	0.238788	−	0.173490i
$365$	−0.375984	−	1.15716i	−0.0196799	−	0.0605685i
$366$	10.4707			0.547310
$367$	−14.3527	+	10.4278i	−0.749203	+	0.544327i	−0.895580	−	0.444901i	$-0.853239\pi$
$367$	−14.3527	+	10.4278i	−0.749203	+	0.544327i	0.146377	+	0.989229i	$0.453239\pi$
$368$	−3.01334			−0.157081
$369$	4.13966	−	3.00764i	0.215502	−	0.156571i
$370$	1.62961	−	1.18398i	0.0847191	−	0.0615521i
$371$	2.32970	−	7.17008i	0.120952	−	0.372252i
$372$	−2.32583	−	7.15818i	−0.120589	−	0.371134i
$373$	−1.24157	−	0.902056i	−0.0642863	−	0.0467067i	0.555178	−	0.831732i	$-0.312650\pi$
$373$	−1.24157	−	0.902056i	−0.0642863	−	0.0467067i	−0.619464	+	0.785025i	$0.712650\pi$
$374$	−2.57758	−	1.87272i	−0.133283	−	0.0968360i
$375$	−2.03918	−	1.48155i	−0.105303	−	0.0765070i
$376$	1.16120	−	3.57382i	0.0598846	−	0.184306i
$377$	−6.36812			−0.327975
$378$	−1.09779			−0.0564644
$379$	4.16460	−	12.8173i	0.213921	−	0.658382i	−0.785307	−	0.619106i	$-0.787495\pi$
$379$	4.16460	−	12.8173i	0.213921	−	0.658382i	0.999228	−	0.0392758i	$-0.0125051\pi$
$380$	4.01788	+	2.91916i	0.206113	+	0.149750i
$381$	−37.5662	−	27.2934i	−1.92457	−	1.39828i
$382$	0.179864	+	0.130679i	0.00920264	+	0.00668611i
$383$	−8.56814	−	26.3700i	−0.437812	−	1.34745i	−0.890178	−	0.455613i	$-0.849420\pi$
$383$	−8.56814	−	26.3700i	−0.437812	−	1.34745i	0.452366	−	0.891832i	$-0.350580\pi$
$384$	8.79697	−	27.0743i	0.448919	−	1.38163i
$385$	−5.40976	+	3.93042i	−0.275707	+	0.200313i
$386$	−5.52477	+	4.01398i	−0.281203	+	0.204306i
$387$	−19.6842			−1.00060
$388$	−16.7594	+	12.1764i	−0.850829	+	0.618163i
$389$	28.5544			1.44776			0.723882	−	0.689924i	$-0.242356\pi$
$389$	28.5544			1.44776			0.723882	+	0.689924i	$0.242356\pi$
$390$	0.481246	+	1.48112i	0.0243689	+	0.0749996i
$391$	−2.28763	+	1.66206i	−0.115691	+	0.0840541i
$392$	0.352548	+	1.08503i	0.0178064	+	0.0548024i
$393$	20.1724	−	14.6561i	1.01756	−	0.739303i
$394$	2.71271			0.136664
$395$	−5.20318	−	16.0137i	−0.261800	−	0.805739i
$396$	4.83314	−	14.8749i	0.242874	−	0.747490i
$397$	−1.20654	−	0.876606i	−0.0605547	−	0.0439956i	0.557096	−	0.830448i	$-0.311915\pi$
$397$	−1.20654	−	0.876606i	−0.0605547	−	0.0439956i	−0.617651	+	0.786452i	$0.711915\pi$
$398$	0.998530	−	3.07316i	0.0500518	−	0.154044i
$399$	−14.5189	+	10.5486i	−0.726855	+	0.528091i
$400$	0.811756	+	2.49833i	0.0405878	+	0.124916i
$401$	−1.49992	+	4.61628i	−0.0749024	+	0.230526i	−0.981497	−	0.191476i	$-0.938673\pi$
$401$	−1.49992	+	4.61628i	−0.0749024	+	0.230526i	0.906595	+	0.422002i	$0.138673\pi$
$402$	−0.744413	−	2.29107i	−0.0371280	−	0.114268i
$403$	−0.662923	−	2.04027i	−0.0330225	−	0.101633i
$404$	1.79556	+	5.52616i	0.0893324	+	0.274937i
$405$	2.41511	−	7.43296i	0.120008	−	0.369347i
$406$	−1.91702	+	5.89999i	−0.0951403	+	0.292812i
$407$	−10.9245			−0.541507
$408$	−3.52584	−	10.8514i	−0.174555	−	0.537226i
$409$	−4.91741	−	15.1342i	−0.243150	−	0.748340i	−0.995935	−	0.0900733i	$-0.971290\pi$
$409$	−4.91741	−	15.1342i	−0.243150	−	0.748340i	0.752785	−	0.658267i	$-0.228710\pi$
$410$	−0.602665	+	0.437862i	−0.0297635	+	0.0216245i
$411$	−26.6489	+	19.3615i	−1.31449	+	0.955034i
$412$	−4.32664	+	13.3160i	−0.213158	+	0.656034i
$413$	8.06329	+	5.85833i	0.396769	+	0.288269i
$414$	1.51917	+	1.10374i	0.0746629	+	0.0542458i
$415$	−1.64031			−0.0805196
$416$	1.93797	−	5.96446i	0.0950168	−	0.292432i
$417$	−10.3118	−	7.49193i	−0.504969	−	0.366882i
$418$	1.12596	+	3.46536i	0.0550727	+	0.169496i
$419$	16.6017	−	12.0618i	0.811046	−	0.589260i	−0.103088	−	0.994672i	$-0.532872\pi$
$419$	16.6017	−	12.0618i	0.811046	−	0.589260i	0.914134	+	0.405413i	$0.132872\pi$
$420$	−11.2148			−0.547228
$421$	2.49095			0.121401			0.0607007	−	0.998156i	$-0.480666\pi$
$421$	2.49095			0.121401			0.0607007	+	0.998156i	$0.480666\pi$
$422$	−6.70610	+	4.87227i	−0.326448	+	0.237178i
$423$	5.55125	−	4.03322i	0.269911	−	0.196102i
$424$	−1.69392	−	5.21334i	−0.0822639	−	0.253182i
$425$	1.99426	+	1.44891i	0.0967357	+	0.0702826i
$426$	11.8402	−	8.60244i	0.573662	−	0.416790i
$427$	−6.64123	+	20.4396i	−0.321392	+	0.989142i
$428$	−0.104335	−	0.321110i	−0.00504322	−	0.0155214i
$429$	2.61002	−	8.03282i	0.126013	−	0.387828i
$430$	2.86569			0.138196
$431$	7.92838	+	24.4011i	0.381897	+	1.17536i	0.938706	+	0.344717i	$0.112025\pi$
$431$	7.92838	+	24.4011i	0.381897	+	1.17536i	−0.556810	+	0.830640i	$0.687975\pi$
$432$	1.89224	−	1.37480i	0.0910406	−	0.0661449i
$433$	−3.13691	−	2.27910i	−0.150750	−	0.109526i	0.509854	−	0.860261i	$-0.329700\pi$
$433$	−3.13691	−	2.27910i	−0.150750	−	0.109526i	−0.660604	+	0.750735i	$0.729700\pi$
$434$	−2.08985			−0.100316
$435$	10.2602	+	7.45448i	0.491940	+	0.357415i
$436$	29.2497	−	21.2512i	1.40081	−	1.01775i
$437$	3.23383			0.154695
$438$	1.21121	−	0.879996i	0.0578739	−	0.0420478i
$439$	−5.23174	−	3.80108i	−0.249697	−	0.181416i	0.455895	−	0.890033i	$-0.349319\pi$
$439$	−5.23174	−	3.80108i	−0.249697	−	0.181416i	−0.705593	+	0.708618i	$0.749319\pi$
$440$	−1.50243	+	4.62401i	−0.0716257	+	0.220441i
$441$	−0.643762	+	1.98129i	−0.0306553	+	0.0943474i
$442$	−0.470645	−	1.44850i	−0.0223863	−	0.0688979i
$443$	15.8614	+	11.5240i	0.753600	+	0.547522i	0.896941	−	0.442151i	$-0.145784\pi$
$443$	15.8614	+	11.5240i	0.753600	+	0.547522i	−0.143341	+	0.989673i	$0.545784\pi$
$444$	−14.8228	−	10.7694i	−0.703461	−	0.511094i
$445$	3.42009			0.162128
$446$	−3.80387	−	2.76367i	−0.180118	−	0.130864i
$447$	5.61225	−	17.2727i	0.265450	−	0.816973i
$448$	5.79229	+	4.20834i	0.273660	+	0.198826i
$449$	−2.00893			−0.0948073			−0.0474037	−	0.998876i	$-0.515095\pi$
$449$	−2.00893			−0.0948073			−0.0474037	+	0.998876i	$0.515095\pi$
$450$	0.505854	−	1.55686i	0.0238462	−	0.0733910i
$451$	4.04013			0.190242
$452$	23.2155			1.09197
$453$	−18.0804	−	25.1484i	−0.849491	−	1.18157i
$454$	5.42210			0.254472
$455$	−3.19652			−0.149855
$456$	−4.03228	+	12.4101i	−0.188829	+	0.581156i
$457$	−22.3737			−1.04660			−0.523298	−	0.852150i	$-0.675299\pi$
$457$	−22.3737			−1.04660			−0.523298	+	0.852150i	$0.675299\pi$
$458$	5.39513	+	3.91979i	0.252098	+	0.183160i
$459$	0.678238	−	2.08740i	0.0316575	−	0.0974316i
$460$	1.63490	+	1.18782i	0.0762275	+	0.0553825i
$461$	20.2341			0.942396			0.471198	−	0.882027i	$-0.343822\pi$
$461$	20.2341			0.942396			0.471198	+	0.882027i	$0.343822\pi$
$462$	−6.65661	−	4.83631i	−0.309694	−	0.225006i
$463$	6.95214	+	5.05103i	0.323093	+	0.234741i	0.737494	−	0.675353i	$-0.236009\pi$
$463$	6.95214	+	5.05103i	0.323093	+	0.234741i	−0.414401	+	0.910094i	$0.636009\pi$
$464$	−4.08438	−	12.5704i	−0.189613	−	0.583568i
$465$	−1.32023	+	4.06326i	−0.0612243	+	0.188429i
$466$	3.21044	−	9.88073i	0.148721	−	0.457716i
$467$	15.7235	+	11.4238i	0.727598	+	0.528631i	0.888803	−	0.458290i	$-0.151538\pi$
$467$	15.7235	+	11.4238i	0.727598	+	0.528631i	−0.161205	+	0.986921i	$0.551538\pi$
$468$	6.04869	−	4.39463i	0.279601	−	0.203142i
$469$	4.94452			0.228317
$470$	−0.808168	+	0.587169i	−0.0372780	+	0.0270841i
$471$	−0.758252	−	0.550902i	−0.0349384	−	0.0253842i
$472$	7.24681			0.333561
$473$	−12.5737	−	9.13534i	−0.578140	−	0.420043i
$474$	16.7617	−	12.1781i	0.769892	−	0.559359i
$475$	−0.871152	−	2.68113i	−0.0399712	−	0.123019i
$476$	10.9678			0.502707
$477$	3.09313	−	9.51968i	0.141625	−	0.435876i
$478$	2.51759	+	7.74835i	0.115152	+	0.354401i
$479$	7.23335	−	22.2620i	0.330500	−	1.01717i	−0.638396	−	0.769708i	$-0.720402\pi$
$479$	7.23335	−	22.2620i	0.330500	−	1.01717i	0.968896	−	0.247467i	$-0.0795981\pi$
$480$	−10.1044	+	7.34126i	−0.461200	+	0.335081i
$481$	−4.22489	−	3.06957i	−0.192639	−	0.139960i
$482$	−2.96171	−	9.11519i	−0.134902	−	0.415186i
$483$	−5.90783	+	4.29229i	−0.268815	+	0.195306i
$484$	−5.68693	+	4.13180i	−0.258497	+	0.187809i
$485$	11.7591			0.533951
$486$	10.9208			0.495377
$487$	27.6215	−	20.0682i	1.25165	−	0.909376i	0.253333	−	0.967379i	$-0.418473\pi$
$487$	27.6215	−	20.0682i	1.25165	−	0.909376i	0.998316	+	0.0580031i	$0.0184733\pi$
$488$	4.82881	+	14.8616i	0.218590	+	0.672751i
$489$	33.6262	+	24.4309i	1.52063	+	1.10480i
$490$	0.0937209	−	0.288443i	0.00423388	−	0.0130305i
$491$	20.1337			0.908621			0.454311	−	0.890843i	$-0.349886\pi$
$491$	20.1337			0.908621			0.454311	+	0.890843i	$0.349886\pi$
$492$	5.48182	+	3.98278i	0.247140	+	0.179557i
$493$	−10.0342	−	7.29027i	−0.451917	−	0.328337i
$494$	−0.538247	+	1.65655i	−0.0242169	+	0.0745318i
$495$	−7.18252	+	5.21840i	−0.322830	+	0.234550i
$496$	3.60223	−	2.61717i	0.161745	−	0.117514i
$497$	9.28278	+	28.5695i	0.416389	+	1.28152i
$498$	−0.623710	−	1.91958i	−0.0279491	−	0.0860185i
$499$	2.82655			0.126534			0.0632670	−	0.997997i	$-0.479848\pi$
$499$	2.82655			0.126534			0.0632670	+	0.997997i	$0.479848\pi$
$500$	0.544390	−	1.67546i	0.0243459	−	0.0749289i
$501$	−5.29419	+	16.2938i	−0.236527	+	0.727955i
$502$	0.165628	+	0.509750i	0.00739233	+	0.0227512i
$503$	2.91108	+	8.95938i	0.129799	+	0.399479i	0.994745	−	0.102386i	$-0.0326475\pi$
$503$	2.91108	+	8.95938i	0.129799	+	0.399479i	−0.864946	+	0.501865i	$0.832648\pi$
$504$	−4.80590	−	14.7910i	−0.214072	−	0.658845i
$505$	1.01923	−	3.13686i	0.0453551	−	0.139589i
$506$	0.458161	+	1.41007i	0.0203677	+	0.0626854i
$507$	−23.2429	+	16.8869i	−1.03225	+	0.749976i
$508$	10.0289	−	30.8657i	0.444959	−	1.36944i
$509$	−31.6916	−	23.0253i	−1.40471	−	1.02058i	−0.994066	−	0.108781i	$-0.965305\pi$
$509$	−31.6916	−	23.0253i	−1.40471	−	1.02058i	−0.410640	−	0.911798i	$-0.634695\pi$
$510$	−0.937305	+	2.88473i	−0.0415045	+	0.127738i
$511$	0.949591	+	2.92254i	0.0420074	+	0.129286i
$512$	22.6645			1.00164
$513$	−2.03070	+	1.47539i	−0.0896576	+	0.0651400i
$514$	0.239163	+	0.736069i	0.0105490	+	0.0324666i
$515$	6.42981	−	4.67153i	0.283331	−	0.205852i
$516$	−8.05491	−	24.7905i	−0.354598	−	1.09134i
$517$	5.41777			0.238273
$518$	−4.11576	+	2.99027i	−0.180836	+	0.131385i
$519$	−11.8129			−0.518530
$520$	−1.88030	+	1.36612i	−0.0824566	+	0.0599082i
$521$	6.06183	−	4.40418i	0.265574	−	0.192951i	−0.447027	−	0.894520i	$-0.647517\pi$
$521$	6.06183	−	4.40418i	0.265574	−	0.192951i	0.712601	+	0.701570i	$0.247517\pi$
$522$	−2.54522	+	7.83339i	−0.111401	+	0.342858i
$523$	0.351405	+	1.08151i	0.0153659	+	0.0472913i	0.958445	−	0.285276i	$-0.0920852\pi$
$523$	0.351405	+	1.08151i	0.0153659	+	0.0472913i	−0.943080	+	0.332567i	$0.892085\pi$
$524$	14.0990	+	10.2435i	0.615917	+	0.447490i
$525$	5.15018	+	3.74183i	0.224772	+	0.163307i
$526$	−9.39146	−	6.82329i	−0.409487	−	0.297510i
$527$	1.29115	−	3.97375i	0.0562433	−	0.173099i
$528$	17.5305			0.762917
$529$	−21.6841			−0.942789
$530$	−0.450308	+	1.38591i	−0.0195601	+	0.0601999i
$531$	10.7056	+	7.77807i	0.464583	+	0.337539i
$532$	−10.1476	−	7.37268i	−0.439955	−	0.319646i
$533$	1.56246	+	1.13520i	0.0676778	+	0.0491708i
$534$	1.30045	+	4.00238i	0.0562761	+	0.173200i
$535$	−0.0592246	+	0.182275i	−0.00256050	+	0.00788041i
$536$	2.90853	−	2.11317i	0.125629	−	0.0912751i
$537$	−8.61236	+	6.25725i	−0.371651	+	0.270020i
$538$	8.51367			0.367051
$539$	−1.33073	+	0.966828i	−0.0573184	+	0.0416442i
$540$	−1.56857			−0.0675006
$541$	4.64525	+	14.2966i	0.199715	+	0.614659i	0.999889	+	0.0148917i	$0.00474036\pi$
$541$	4.64525	+	14.2966i	0.199715	+	0.614659i	−0.800174	+	0.599768i	$0.795260\pi$
$542$	−11.2198	+	8.15167i	−0.481932	+	0.350144i
$543$	7.72032	+	23.7607i	0.331311	+	1.01967i
$544$	9.88179	−	7.17954i	0.423678	−	0.307820i
$545$	−20.5228			−0.879100
$546$	−1.21544	−	3.74075i	−0.0520162	−	0.160089i
$547$	−6.82292	+	20.9988i	−0.291727	+	0.897843i	0.692574	+	0.721346i	$0.256476\pi$
$547$	−6.82292	+	20.9988i	−0.291727	+	0.897843i	−0.984301	+	0.176496i	$0.943524\pi$
$548$	−18.6255	−	13.5322i	−0.795644	−	0.578069i
$549$	−8.81753	+	27.1376i	−0.376323	+	1.15820i
$550$	1.04565	−	0.759712i	0.0445868	−	0.0323942i
$551$	4.38324	+	13.4902i	0.186732	+	0.574703i
$552$	−1.64076	+	5.04973i	−0.0698353	+	0.214931i
$553$	13.1412	+	40.4446i	0.558822	+	1.71988i
$554$	2.18517	+	6.72528i	0.0928392	+	0.285730i
$555$	3.21387	+	9.89127i	0.136421	+	0.419861i
$556$	2.75288	−	8.47250i	0.116748	−	0.359314i
$557$	−2.78049	+	8.55747i	−0.117813	+	0.362592i	−0.992523	−	0.122055i	$-0.961052\pi$
$557$	−2.78049	+	8.55747i	−0.117813	+	0.362592i	0.874710	+	0.484646i	$0.161052\pi$
$558$	−2.77468			−0.117462
$559$	−2.29586	−	7.06593i	−0.0971045	−	0.298857i
$560$	−2.05018	−	6.30981i	−0.0866360	−	0.266638i
$561$	13.3086	−	9.66927i	0.561890	−	0.408237i
$562$	10.7968	−	7.84437i	0.455437	−	0.330895i
$563$	−7.20312	+	22.1689i	−0.303575	+	0.934309i	0.676630	+	0.736323i	$0.263440\pi$
$563$	−7.20312	+	22.1689i	−0.303575	+	0.934309i	−0.980205	+	0.197985i	$0.936560\pi$
$564$	7.35107	+	5.34087i	0.309536	+	0.224891i
$565$	−10.6613	−	7.74586i	−0.448523	−	0.325871i
$566$	2.50962			0.105487
$567$	−6.09965	+	18.7728i	−0.256161	+	0.788383i
$568$	17.6704	+	12.8383i	0.741431	+	0.538681i
$569$	0.618922	+	1.90484i	0.0259465	+	0.0798552i	0.963191	−	0.268817i	$-0.0866327\pi$
$569$	0.618922	+	1.90484i	0.0259465	+	0.0798552i	−0.937245	+	0.348672i	$0.886633\pi$
$570$	2.80636	−	2.03894i	0.117546	−	0.0854019i
$571$	−15.1867			−0.635544			−0.317772	−	0.948167i	$-0.602935\pi$
$571$	−15.1867			−0.635544			−0.317772	+	0.948167i	$0.602935\pi$
$572$	5.90326			0.246828
$573$	−0.928678	+	0.674724i	−0.0387961	+	0.0281870i
$574$	1.52210	−	1.10587i	0.0635312	−	0.0461582i
$575$	−0.354476	−	1.09097i	−0.0147827	−	0.0454964i
$576$	7.69039	+	5.58740i	0.320433	+	0.232808i
$577$	−10.9523	+	7.95732i	−0.455951	+	0.331267i	−0.791941	−	0.610598i	$-0.790929\pi$
$577$	−10.9523	+	7.95732i	−0.455951	+	0.331267i	0.335990	+	0.941865i	$0.390929\pi$
$578$	−1.64788	+	5.07164i	−0.0685426	+	0.210952i
$579$	−10.8958	−	33.5339i	−0.452814	−	1.39362i
$580$	−2.73912	+	8.43015i	−0.113736	+	0.350043i
$581$	4.14279			0.171872
$582$	4.47126	+	13.7611i	0.185340	+	0.570416i
$583$	6.39384	−	4.64539i	0.264806	−	0.192393i
$584$	1.80761	+	1.31330i	0.0747993	+	0.0543449i
$585$	−4.24401			−0.175468
$586$	2.96730	+	2.15587i	0.122578	+	0.0890582i
$587$	16.3667	−	11.8911i	0.675526	−	0.490798i	−0.196345	−	0.980535i	$-0.562907\pi$
$587$	16.3667	−	11.8911i	0.675526	−	0.490798i	0.871870	+	0.489737i	$0.162907\pi$
$588$	−2.75869			−0.113766
$589$	−3.86580	+	2.80867i	−0.159288	+	0.115729i
$590$	−1.55856	−	1.13236i	−0.0641647	−	0.0466184i
$591$	−4.32819	+	13.3208i	−0.178038	+	0.547944i
$592$	3.34945	−	10.3085i	0.137661	−	0.423678i
$593$	13.8837	+	42.7297i	0.570137	+	1.75470i	0.652172	+	0.758071i	$0.273858\pi$
$593$	13.8837	+	42.7297i	0.570137	+	1.75470i	−0.0820354	+	0.996629i	$0.526142\pi$
$594$	−0.931032	−	0.676434i	−0.0382007	−	0.0277544i
$595$	−5.03673	−	3.65940i	−0.206486	−	0.150021i
$596$	12.6936			0.519950
$597$	13.4976	+	9.80660i	0.552421	+	0.401357i
$598$	−0.219015	+	0.674060i	−0.00895621	+	0.0275644i
$599$	−33.7013	−	24.4854i	−1.37700	−	1.00045i	−0.997154	−	0.0753980i	$-0.975977\pi$
$599$	−33.7013	−	24.4854i	−1.37700	−	1.00045i	−0.379845	−	0.925050i	$-0.624023\pi$
$600$	4.62868			0.188965
$601$	1.83995	−	5.66278i	0.0750531	−	0.230990i	−0.906491	−	0.422225i	$-0.861249\pi$
$601$	1.83995	−	5.66278i	0.0750531	−	0.230990i	0.981544	+	0.191235i	$0.0612493\pi$
$602$	−7.23764			−0.294984
$603$	6.56482			0.267340
$604$	12.8115	−	17.4499i	0.521294	−	0.710025i
$605$	3.99018			0.162224
$606$	4.05849			0.164865
$607$	−7.26893	+	22.3715i	−0.295037	+	0.908029i	0.688173	+	0.725547i	$0.258413\pi$
$607$	−7.26893	+	22.3715i	−0.295037	+	0.908029i	−0.983209	+	0.182482i	$0.941587\pi$
$608$	−13.9690			−0.566518
$609$	−25.9134	−	18.8272i	−1.05006	−	0.762915i
$610$	1.28368	−	3.95077i	0.0519749	−	0.159962i
$611$	2.09525	+	1.52229i	0.0847646	+	0.0615851i
$612$	14.5619			0.588629
$613$	−12.8293	−	9.32103i	−0.518170	−	0.376473i	0.297744	−	0.954646i	$-0.403766\pi$
$613$	−12.8293	−	9.32103i	−0.518170	−	0.376473i	−0.815914	+	0.578173i	$0.803766\pi$
$614$	3.09445	+	2.24825i	0.124882	+	0.0907321i
$615$	−1.18856	−	3.65802i	−0.0479274	−	0.147505i
$616$	3.79457	−	11.6785i	0.152887	−	0.470539i
$617$	−7.75053	+	23.8537i	−0.312025	+	0.960313i	0.664937	+	0.746899i	$0.268458\pi$
$617$	−7.75053	+	23.8537i	−0.312025	+	0.960313i	−0.976962	+	0.213414i	$0.931542\pi$
$618$	7.91176	+	5.74823i	0.318258	+	0.231228i
$619$	10.6147	−	7.71200i	0.426639	−	0.309972i	−0.353664	−	0.935372i	$-0.615065\pi$
$619$	10.6147	−	7.71200i	0.426639	−	0.309972i	0.780304	+	0.625401i	$0.215065\pi$
$620$	−2.98606			−0.119923
$621$	−0.826302	+	0.600344i	−0.0331584	+	0.0240910i
$622$	−8.55061	−	6.21238i	−0.342848	−	0.249094i
$623$	−8.63783			−0.346068
$624$	6.77968	+	4.92572i	0.271404	+	0.197187i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−1.98478	−	6.10852i	−0.0793277	−	0.244145i
$627$	−18.8132			−0.751327
$628$	0.202427	−	0.623006i	0.00807771	−	0.0248606i
$629$	−3.14307	−	9.67337i	−0.125322	−	0.385702i
$630$	−1.27759	+	3.93202i	−0.0509005	+	0.156656i
$631$	28.6732	−	20.8323i	1.14146	−	0.829321i	0.154141	−	0.988049i	$-0.450739\pi$
$631$	28.6732	−	20.8323i	1.14146	−	0.829321i	0.987322	+	0.158727i	$0.0507391\pi$
$632$	25.0152	+	18.1746i	0.995050	+	0.722946i
$633$	−13.2256	−	40.7043i	−0.525671	−	1.61785i
$634$	11.5337	−	8.37972i	0.458061	−	0.332801i
$635$	−14.9039	+	10.8283i	−0.591442	+	0.429708i
$636$	13.2549			0.525591
$637$	−0.786299			−0.0311543
$638$	−5.26125	+	3.82252i	−0.208295	+	0.151335i
$639$	12.3247	+	37.9315i	0.487557	+	1.50055i
$640$	−9.13715	−	6.63853i	−0.361177	−	0.262411i
$641$	2.33953	−	7.20034i	0.0924060	−	0.284397i	−0.894163	−	0.447742i	$-0.852228\pi$
$641$	2.33953	−	7.20034i	0.0924060	−	0.284397i	0.986569	+	0.163345i	$0.0522284\pi$
$642$	−0.235827			−0.00930737
$643$	15.8052	+	11.4831i	0.623295	+	0.452850i	0.854071	−	0.520157i	$-0.174126\pi$
$643$	15.8052	+	11.4831i	0.623295	+	0.452850i	−0.230776	+	0.973007i	$0.574126\pi$
$644$	−4.12912	−	2.99998i	−0.162710	−	0.118216i
$645$	−4.57228	+	14.0720i	−0.180033	+	0.554086i
$646$	−2.74454	+	1.99403i	−0.107983	+	0.0784539i
$647$	4.03973	−	2.93503i	0.158818	−	0.115388i	−0.505538	−	0.862804i	$-0.668706\pi$
$647$	4.03973	−	2.93503i	0.158818	−	0.115388i	0.664356	+	0.747416i	$0.268706\pi$
$648$	4.43503	+	13.6496i	0.174225	+	0.536208i
$649$	3.22867	+	9.93682i	0.126736	+	0.390054i
$650$	0.617856			0.0242343
$651$	3.33440	−	10.2622i	0.130685	−	0.402208i
$652$	−8.97704	+	27.6285i	−0.351568	+	1.08201i
$653$	1.72155	+	5.29838i	0.0673693	+	0.207341i	0.979074	−	0.203505i	$-0.0652333\pi$
$653$	1.72155	+	5.29838i	0.0673693	+	0.207341i	−0.911705	+	0.410846i	$0.865233\pi$
$654$	−7.80358	−	24.0169i	−0.305144	−	0.939137i
$655$	−3.05692	−	9.40824i	−0.119444	−	0.367610i
$656$	−1.23870	+	3.81233i	−0.0483632	+	0.148847i
$657$	1.26077	+	3.88024i	0.0491872	+	0.151383i
$658$	2.04112	−	1.48296i	0.0795712	−	0.0578119i
$659$	2.11079	−	6.49633i	0.0822246	−	0.253061i	−0.901490	−	0.432801i	$-0.857525\pi$
$659$	2.11079	−	6.49633i	0.0822246	−	0.253061i	0.983714	+	0.179739i	$0.0575254\pi$
$660$	−9.51123	−	6.91032i	−0.370224	−	0.268984i
$661$	6.37703	−	19.6265i	0.248038	−	0.763381i	−0.747084	−	0.664729i	$-0.768547\pi$
$661$	6.37703	−	19.6265i	0.248038	−	0.763381i	0.995122	−	0.0986520i	$-0.0314531\pi$
$662$	−1.99144	−	6.12902i	−0.0773995	−	0.238211i
$663$	7.86379			0.305404
$664$	2.43693	−	1.77053i	0.0945711	−	0.0687099i
$665$	2.20020	+	6.77150i	0.0853199	+	0.262588i
$666$	−5.46447	+	3.97017i	−0.211744	+	0.153841i
$667$	1.78356	+	5.48924i	0.0690598	+	0.212544i
$668$	−11.9742			−0.463296
$669$	19.6402	−	14.2694i	0.759334	−	0.551689i
$670$	−0.955727			−0.0369230
$671$	−18.2268	+	13.2425i	−0.703637	+	0.511222i
$672$	25.5198	−	18.5412i	0.984447	−	0.715243i
$673$	−11.8629	+	36.5103i	−0.457282	+	1.40737i	0.411154	+	0.911566i	$0.365126\pi$
$673$	−11.8629	+	36.5103i	−0.457282	+	1.40737i	−0.868435	+	0.495802i	$0.834874\pi$
$674$	−0.0387139	−	0.119149i	−0.00149120	−	0.00458945i
$675$	0.720334	+	0.523353i	0.0277257	+	0.0201439i
$676$	−16.2450	−	11.8027i	−0.624808	−	0.453950i
$677$	−39.8427	−	28.9474i	−1.53128	−	1.11254i	−0.955523	−	0.294916i	$-0.904708\pi$
$677$	−39.8427	−	28.9474i	−1.53128	−	1.11254i	−0.575755	−	0.817622i	$-0.695292\pi$
$678$	5.01081	−	15.4217i	0.192439	−	0.592267i
$679$	−29.6988			−1.13974
$680$	−4.52671			−0.173591
$681$	−8.65108	+	26.6253i	−0.331510	+	1.02028i
$682$	−1.77239	−	1.28771i	−0.0678682	−	0.0493091i
$683$	−5.08286	−	3.69292i	−0.194490	−	0.141305i	0.486278	−	0.873804i	$-0.338354\pi$
$683$	−5.08286	−	3.69292i	−0.194490	−	0.141305i	−0.680769	+	0.732498i	$0.738354\pi$
$684$	−13.4730	−	9.78867i	−0.515151	−	0.374279i
$685$	4.03837	+	12.4288i	0.154298	+	0.474881i
$686$	−2.90371	+	8.93671i	−0.110864	+	0.341205i
$687$	−27.8563	+	20.2388i	−1.06278	+	0.772157i
$688$	12.4754	−	9.06388i	0.475619	−	0.345557i
$689$	3.77799			0.143930
$690$	1.14192	−	0.829657i	0.0434723	−	0.0315845i
$691$	1.26434			0.0480977			0.0240488	−	0.999711i	$-0.492344\pi$
$691$	1.26434			0.0480977			0.0240488	+	0.999711i	$0.492344\pi$
$692$	−2.55135	−	7.85225i	−0.0969878	−	0.298498i
$693$	18.1403	−	13.1797i	0.689092	−	0.500655i
$694$	2.75840	+	8.48948i	0.104707	+	0.322256i
$695$	−4.09105	+	2.97232i	−0.155182	+	0.112747i
$696$	−23.2894			−0.882782
$697$	1.16238	+	3.57743i	0.0440282	+	0.135505i
$698$	−5.10067	+	15.6983i	−0.193063	+	0.594188i
$699$	43.3972	+	31.5299i	1.64143	+	1.19257i
$700$	−1.37492	+	4.23157i	−0.0519671	+	0.159938i
$701$	11.5633	−	8.40121i	0.436739	−	0.317309i	−0.347599	−	0.937643i	$-0.613003\pi$
$701$	11.5633	−	8.40121i	0.436739	−	0.317309i	0.784338	+	0.620334i	$0.213003\pi$
$702$	−0.169999	−	0.523203i	−0.00641619	−	0.0197470i
$703$	−3.59453	+	11.0628i	−0.135570	+	0.417242i
$704$	2.31932	+	7.13814i	0.0874128	+	0.269029i
$705$	−1.59385	−	4.90537i	−0.0600279	−	0.184747i
$706$	−2.43293	−	7.48779i	−0.0915646	−	0.281807i
$707$	−2.57418	+	7.92251i	−0.0968120	+	0.297957i
$708$	−5.41497	+	16.6656i	−0.203507	+	0.626330i
$709$	−40.0703			−1.50487			−0.752435	−	0.658666i	$-0.771121\pi$
$709$	−40.0703			−1.50487			−0.752435	+	0.658666i	$0.771121\pi$
$710$	−1.79427	−	5.52219i	−0.0673377	−	0.207244i
$711$	17.4475	+	53.6980i	0.654334	+	2.01383i
$712$	−5.08106	+	3.69161i	−0.190421	+	0.138349i
$713$	−1.57302	+	1.14286i	−0.0589099	+	0.0428005i
$714$	2.36727	−	7.28571i	0.0885929	−	0.272661i
$715$	−2.71095	−	1.96962i	−0.101384	−	0.0736596i
$716$	−6.01939	−	4.37334i	−0.224955	−	0.163439i
$717$	−42.0653			−1.57096
$718$	−0.0414778	+	0.127656i	−0.00154794	+	0.00476406i
$719$	−14.1503	−	10.2808i	−0.527718	−	0.383410i	0.291785	−	0.956484i	$-0.405751\pi$
$719$	−14.1503	−	10.2808i	−0.527718	−	0.383410i	−0.819504	+	0.573074i	$0.805751\pi$
$720$	−2.72202	−	8.37751i	−0.101444	−	0.312211i
$721$	−16.2392	+	11.7985i	−0.604781	+	0.439399i
$722$	−5.39564			−0.200805
$723$	49.4858			1.84040
$724$	−14.1267	+	10.2636i	−0.525015	+	0.381445i
$725$	4.07060	−	2.95747i	0.151178	−	0.109838i
$726$	1.51722	+	4.66953i	0.0563094	+	0.173303i
$727$	−25.1435	−	18.2678i	−0.932520	−	0.677515i	0.0140886	−	0.999901i	$-0.495515\pi$
$727$	−25.1435	−	18.2678i	−0.932520	−	0.677515i	−0.946609	+	0.322385i	$0.895515\pi$
$728$	4.74892	−	3.45029i	0.176007	−	0.127876i
$729$	−10.1790	+	31.3278i	−0.377001	+	1.16029i
$730$	−0.183547	−	0.564898i	−0.00679336	−	0.0209078i
$731$	4.47155	−	13.7620i	0.165386	−	0.509007i
$732$	−37.7855			−1.39659
$733$	10.7952	+	33.2244i	0.398732	+	1.22717i	0.926017	+	0.377481i	$0.123210\pi$
$733$	10.7952	+	33.2244i	0.398732	+	1.22717i	−0.527286	+	0.849688i	$0.676790\pi$
$734$	−7.00663	+	5.09061i	−0.258619	+	0.187898i
$735$	1.26687	+	0.920436i	0.0467293	+	0.0339508i
$736$	−5.68407			−0.209518
$737$	4.19342	+	3.04670i	0.154467	+	0.112226i
$738$	2.02088	−	1.46826i	0.0743898	−	0.0540474i
$739$	−9.95202			−0.366091			−0.183045	−	0.983104i	$-0.558596\pi$
$739$	−9.95202			−0.366091			−0.183045	+	0.983104i	$0.558596\pi$
$740$	−5.88076	+	4.27262i	−0.216181	+	0.157065i
$741$	−7.27575	−	5.28614i	−0.267281	−	0.194191i
$742$	1.13731	−	3.50027i	0.0417518	−	0.128499i
$743$	11.7505	−	36.1643i	0.431084	−	1.32674i	−0.465964	−	0.884804i	$-0.654292\pi$
$743$	11.7505	−	36.1643i	0.431084	−	1.32674i	0.897047	−	0.441935i	$-0.145708\pi$
$744$	−2.42443	−	7.46163i	−0.0888839	−	0.273557i
$745$	−5.82928	−	4.23522i	−0.213568	−	0.155166i
$746$	−0.606107	−	0.440363i	−0.0221912	−	0.0161228i
$747$	5.50036			0.201248
$748$	9.30171	+	6.75809i	0.340104	+	0.247100i
$749$	0.149579	−	0.460355i	0.00546548	−	0.0168210i
$750$	−0.995480	−	0.723258i	−0.0363498	−	0.0264097i
$751$	−46.1925			−1.68559			−0.842794	−	0.538236i	$-0.819091\pi$
$751$	−46.1925			−1.68559			−0.842794	+	0.538236i	$0.819091\pi$
$752$	−1.66109	+	5.11230i	−0.0605736	+	0.186426i
$753$	−2.76740			−0.100850
$754$	−3.10877			−0.113215
$755$	−11.7056	+	3.73892i	−0.426009	+	0.136073i
$756$	3.96161			0.144082
$757$	−15.9198			−0.578617			−0.289308	−	0.957236i	$-0.593425\pi$
$757$	−15.9198			−0.578617			−0.289308	+	0.957236i	$0.593425\pi$
$758$	2.03306	−	6.25712i	0.0738441	−	0.227269i
$759$	−7.65520			−0.277866
$760$	4.18821	+	3.04291i	0.151922	+	0.110378i
$761$	1.41699	−	4.36105i	0.0513659	−	0.158088i	−0.922083	−	0.386992i	$-0.873514\pi$
$761$	1.41699	−	4.36105i	0.0513659	−	0.158088i	0.973449	+	0.228904i	$0.0735142\pi$
$762$	−18.3389	−	13.3240i	−0.664349	−	0.482678i
$763$	51.8327			1.87647
$764$	−0.649075	−	0.471581i	−0.0234827	−	0.0170612i
$765$	−6.68724	−	4.85856i	−0.241778	−	0.175662i
$766$	−4.18277	−	12.8732i	−0.151130	−	0.465129i
$767$	−1.54341	+	4.75012i	−0.0557292	+	0.171517i
$768$	−0.121591	+	0.374219i	−0.00438754	+	0.0135035i
$769$	−7.59515	−	5.51820i	−0.273888	−	0.198991i	0.442359	−	0.896838i	$-0.354142\pi$
$769$	−7.59515	−	5.51820i	−0.273888	−	0.198991i	−0.716247	+	0.697847i	$0.754142\pi$
$770$	−2.64092	+	1.91874i	−0.0951722	+	0.0691466i
$771$	−3.99607			−0.143915
$772$	19.9372	−	14.4852i	0.717557	−	0.521336i
$773$	−0.779236	−	0.566148i	−0.0280272	−	0.0203629i	0.573683	−	0.819077i	$-0.305514\pi$
$773$	−0.779236	−	0.566148i	−0.0280272	−	0.0203629i	−0.601711	+	0.798714i	$0.705514\pi$
$774$	−9.60937			−0.345402
$775$	1.37129	+	0.996297i	0.0492580	+	0.0357881i
$776$	−17.4699	+	12.6926i	−0.627131	+	0.455637i
$777$	−8.11700	−	24.9815i	−0.291196	−	0.896208i
$778$	13.9396			0.499758
$779$	1.32934	−	4.09128i	0.0476285	−	0.146585i
$780$	−1.73668	−	5.34494i	−0.0621829	−	0.191379i
$781$	−9.73115	+	29.9494i	−0.348208	+	1.07167i
$782$	−1.11677	+	0.811380i	−0.0399356	+	0.0290149i
$783$	−3.62439	−	2.63327i	−0.129525	−	0.0941055i
$784$	−0.504316	−	1.55212i	−0.0180113	−	0.0554330i
$785$	−0.300826	+	0.218563i	−0.0107369	+	0.00780085i
$786$	9.84769	−	7.15477i	0.351255	−	0.255202i
$787$	48.6922			1.73569			0.867845	−	0.496835i	$-0.165505\pi$
$787$	48.6922			1.73569			0.867845	+	0.496835i	$0.165505\pi$
$788$	−9.78935			−0.348731
$789$	48.4902	−	35.2302i	1.72630	−	1.25423i
$790$	−2.54007	−	7.81753i	−0.0903717	−	0.278135i
$791$	26.9262	+	19.5631i	0.957387	+	0.695583i
$792$	5.03803	−	15.5055i	0.179019	−	0.550962i
$793$	−10.7698			−0.382448
$794$	−0.589007	−	0.427938i	−0.0209031	−	0.0151870i
$795$	−6.08704	−	4.42249i	−0.215885	−	0.156850i
$796$	−3.60340	+	11.0901i	−0.127719	+	0.393079i
$797$	−18.1771	+	13.2064i	−0.643865	+	0.467795i	−0.861176	−	0.508307i	$-0.830272\pi$
$797$	−18.1771	+	13.2064i	−0.643865	+	0.467795i	0.217311	+	0.976102i	$0.430272\pi$
$798$	−7.08780	+	5.14959i	−0.250905	+	0.182293i
$799$	1.55874	+	4.79730i	0.0551442	+	0.169716i
$800$	1.53122	+	4.71260i	0.0541367	+	0.166616i
$801$	−11.4684			−0.405216
$802$	−0.732226	+	2.25356i	−0.0258558	+	0.0795760i
$803$	−0.995458	+	3.06370i	−0.0351289	+	0.108116i
$804$	2.68637	+	8.26778i	0.0947408	+	0.291582i
$805$	0.895271	+	2.75536i	0.0315542	+	0.0971137i
$806$	−0.323623	−	0.996011i	−0.0113991	−	0.0350830i
$807$	−13.5838	+	41.8065i	−0.478171	+	1.47166i
$808$	1.87168	+	5.76043i	0.0658454	+	0.202651i
$809$	−3.53493	+	2.56828i	−0.124282	+	0.0902958i	−0.648190	−	0.761479i	$-0.724474\pi$
$809$	−3.53493	+	2.56828i	−0.124282	+	0.0902958i	0.523908	+	0.851775i	$0.324474\pi$
$810$	1.17900	−	3.62860i	0.0414259	−	0.127496i
$811$	9.77898	+	7.10484i	0.343386	+	0.249485i	0.746089	−	0.665846i	$-0.231929\pi$
$811$	9.77898	+	7.10484i	0.343386	+	0.249485i	−0.402703	+	0.915331i	$0.631929\pi$
$812$	6.91797	−	21.2913i	0.242773	−	0.747179i
$813$	−22.1274	−	68.1013i	−0.776043	−	2.38842i
$814$	−5.33308			−0.186924
$815$	13.3408	−	9.69262i	0.467306	−	0.339518i
$816$	5.04367	+	15.5228i	0.176564	+	0.543408i
$817$	−13.3882	+	9.72709i	−0.468393	+	0.340308i
$818$	−2.40057	−	7.38818i	−0.0839338	−	0.258322i
$819$	10.7187			0.374543
$820$	2.17484	−	1.58011i	0.0759487	−	0.0551799i
$821$	3.94256			0.137596			0.0687982	−	0.997631i	$-0.478084\pi$
$821$	3.94256			0.137596			0.0687982	+	0.997631i	$0.478084\pi$
$822$	−13.0094	+	9.45185i	−0.453753	+	0.329671i
$823$	21.9776	−	15.9677i	0.766092	−	0.556599i	−0.134681	−	0.990889i	$-0.543001\pi$
$823$	21.9776	−	15.9677i	0.766092	−	0.556599i	0.900773	+	0.434290i	$0.143001\pi$
$824$	−4.51006	+	13.8805i	−0.157115	+	0.483551i
$825$	2.06221	+	6.34684i	0.0717971	+	0.220969i
$826$	3.93631	+	2.85990i	0.136962	+	0.0995086i
$827$	30.1083	+	21.8749i	1.04697	+	0.760666i	0.971633	−	0.236492i	$-0.0759977\pi$
$827$	30.1083	+	21.8749i	1.04697	+	0.760666i	0.0753339	+	0.997158i	$0.475998\pi$
$828$	−5.48222	−	3.98306i	−0.190520	−	0.138421i
$829$	11.1377	−	34.2782i	0.386827	−	1.19053i	−0.548319	−	0.836269i	$-0.684732\pi$
$829$	11.1377	−	34.2782i	0.386827	−	1.19053i	0.935146	−	0.354263i	$-0.115268\pi$
$830$	−0.800760			−0.0277948
$831$	−36.5111			−1.26656
$832$	−1.10871	+	3.41226i	−0.0384376	+	0.118299i
$833$	−1.23896	−	0.900160i	−0.0429275	−	0.0311887i
$834$	−5.03396	−	3.65739i	−0.174312	−	0.126645i
$835$	5.49891	+	3.99519i	0.190298	+	0.138259i
$836$	−4.06327	−	12.5054i	−0.140531	−	0.432510i
$837$	0.466368	−	1.43533i	0.0161200	−	0.0496124i
$838$	8.10456	−	5.88831i	0.279967	−	0.203408i
$839$	2.06790	−	1.50242i	0.0713920	−	0.0518693i	−0.551517	−	0.834164i	$-0.685951\pi$
$839$	2.06790	−	1.50242i	0.0713920	−	0.0518693i	0.622909	+	0.782294i	$0.285951\pi$
$840$	−11.6903			−0.403352
$841$	2.98009	−	2.16516i	0.102762	−	0.0746607i
$842$	1.21602			0.0419069
$843$	21.2933	+	65.5340i	0.733380	+	2.25711i
$844$	24.2003	−	17.5826i	0.833010	−	0.605217i
$845$	3.52222	+	10.8403i	0.121168	+	0.372917i
$846$	2.70999	−	1.96892i	0.0931713	−	0.0676929i
$847$	−10.0777			−0.346272
$848$	2.42312	+	7.45761i	0.0832104	+	0.256095i
$849$	−4.00416	+	12.3235i	−0.137422	+	0.422942i
$850$	0.973550	+	0.707325i	0.0333925	+	0.0242611i
$851$	−1.46263	+	4.50152i	−0.0501384	+	0.154310i
$852$	−42.7279	+	31.0437i	−1.46383	+	1.06354i
$853$	11.4827	+	35.3402i	0.393162	+	1.21003i	0.930384	+	0.366586i	$0.119474\pi$
$853$	11.4827	+	35.3402i	0.393162	+	1.21003i	−0.537222	+	0.843441i	$0.680526\pi$
$854$	−3.24209	+	9.97814i	−0.110942	+	0.341445i
$855$	2.92119	+	8.99049i	0.0999025	+	0.307468i
$856$	−0.108758	−	0.334723i	−0.00371727	−	0.0114406i
$857$	8.86477	+	27.2830i	0.302815	+	0.931968i	0.980484	+	0.196601i	$0.0629904\pi$
$857$	8.86477	+	27.2830i	0.302815	+	0.931968i	−0.677669	+	0.735367i	$0.737010\pi$
$858$	1.27415	−	3.92143i	0.0434988	−	0.133876i
$859$	3.73958	−	11.5093i	0.127593	−	0.392691i	−0.866772	−	0.498705i	$-0.833809\pi$
$859$	3.73958	−	11.5093i	0.127593	−	0.392691i	0.994365	+	0.106014i	$0.0338090\pi$
$860$	−10.3414			−0.352640
$861$	3.00185	+	9.23874i	0.102303	+	0.314856i
$862$	3.87045	+	11.9120i	0.131828	+	0.405725i
$863$	25.8067	−	18.7497i	0.878472	−	0.638247i	−0.0543748	−	0.998521i	$-0.517317\pi$
$863$	25.8067	−	18.7497i	0.878472	−	0.638247i	0.932847	+	0.360273i	$0.117317\pi$
$864$	3.56934	−	2.59328i	0.121432	−	0.0882252i
$865$	−1.44824	+	4.45724i	−0.0492418	+	0.151551i
$866$	−1.53136	−	1.11260i	−0.0520379	−	0.0378077i
$867$	−22.2752	−	16.1839i	−0.756504	−	0.549632i
$868$	7.54163			0.255980
$869$	−13.7760	+	42.3981i	−0.467318	+	1.43826i
$870$	5.00880	+	3.63910i	0.169814	+	0.123377i
$871$	0.765684	+	2.35653i	0.0259442	+	0.0798481i
$872$	30.4897	−	22.1521i	1.03251	−	0.750164i
$873$	−39.4310			−1.33454
$874$	1.57868			0.0533996
$875$	2.04327	−	1.48452i	0.0690750	−	0.0501859i
$876$	−4.37090	+	3.17564i	−0.147679	+	0.107295i
$877$	−7.27551	−	22.3917i	−0.245676	−	0.756114i	−0.995524	−	0.0945041i	$-0.969873\pi$
$877$	−7.27551	−	22.3917i	−0.245676	−	0.756114i	0.749848	−	0.661610i	$-0.230127\pi$
$878$	−2.55401	−	1.85560i	−0.0861937	−	0.0626234i
$879$	−15.3208	+	11.1312i	−0.516759	+	0.375448i
$880$	2.14921	−	6.61459i	0.0724498	−	0.222978i
$881$	11.3949	+	35.0698i	0.383903	+	1.18153i	0.937273	+	0.348597i	$0.113342\pi$
$881$	11.3949	+	35.0698i	0.383903	+	1.18153i	−0.553369	+	0.832936i	$0.686658\pi$
$882$	−0.314269	+	0.967222i	−0.0105820	+	0.0325681i
$883$	−3.20404			−0.107825			−0.0539123	−	0.998546i	$-0.517169\pi$
$883$	−3.20404			−0.107825			−0.0539123	+	0.998546i	$0.517169\pi$
$884$	1.69842	+	5.22719i	0.0571239	+	0.175809i
$885$	8.04717	−	5.84661i	0.270503	−	0.196532i
$886$	7.74319	+	5.62575i	0.260137	+	0.189001i
$887$	−44.9416			−1.50899			−0.754496	−	0.656304i	$-0.772119\pi$
$887$	−44.9416			−1.50899			−0.754496	+	0.656304i	$0.772119\pi$
$888$	−15.4512	−	11.2260i	−0.518509	−	0.376719i
$889$	37.6414	−	27.3481i	1.26245	−	0.917226i
$890$	1.66961			0.0559654
$891$	−16.7404	+	12.1626i	−0.560825	+	0.407463i
$892$	13.7270	+	9.97326i	0.459615	+	0.333930i
$893$	1.78263	−	5.48637i	0.0596534	−	0.183594i
$894$	2.73977	−	8.43215i	0.0916316	−	0.282013i
$895$	1.30512	+	4.01673i	0.0436252	+	0.134265i
$896$	23.0769	+	16.7664i	0.770946	+	0.560125i
$897$	−2.96054	−	2.15096i	−0.0988495	−	0.0718184i
$898$	−0.980713			−0.0327268
$899$	−6.89968	−	5.01291i	−0.230117	−	0.167190i
$900$	−1.82547	+	5.61823i	−0.0608492	+	0.187274i
$901$	5.95294	+	4.32507i	0.198321	+	0.144089i
$902$	1.97229			0.0656702
$903$	11.5478	−	35.5405i	0.384287	−	1.18272i
$904$	24.1997			0.804870
$905$	9.91186			0.329481
$906$	−8.82642	−	12.2768i	−0.293238	−	0.407871i
$907$	−31.9392			−1.06052			−0.530261	−	0.847834i	$-0.677906\pi$
$907$	−31.9392			−1.06052			−0.530261	+	0.847834i	$0.677906\pi$
$908$	−19.5667			−0.649345
$909$	−3.41773	+	10.5187i	−0.113359	+	0.348883i
$910$	−1.56047			−0.0517290
$911$	29.0881	+	21.1338i	0.963732	+	0.700192i	0.954015	−	0.299760i	$-0.0969067\pi$
$911$	29.0881	+	21.1338i	0.963732	+	0.700192i	0.00971762	+	0.999953i	$0.496907\pi$
$912$	5.76813	−	17.7525i	0.191002	−	0.587843i
$913$	3.51347	+	2.55269i	0.116279	+	0.0844817i
$914$	−10.9223			−0.361278
$915$	17.3522	+	12.6071i	0.573646	+	0.416778i
$916$	−19.4694	−	14.1454i	−0.643288	−	0.467376i
$917$	7.72061	+	23.7616i	0.254957	+	0.784677i
$918$	0.331100	−	1.01902i	0.0109279	−	0.0336327i
$919$	0.824745	−	2.53830i	0.0272058	−	0.0837309i	−0.936532	−	0.350583i	$-0.885983\pi$
$919$	0.824745	−	2.53830i	0.0272058	−	0.0837309i	0.963738	+	0.266852i	$0.0859835\pi$
$920$	1.70420	+	1.23818i	0.0561860	+	0.0408215i
$921$	−15.9774	+	11.6082i	−0.526472	+	0.382504i
$922$	9.87781			0.325308
$923$	−12.1786	+	8.84825i	−0.400863	+	0.291244i
$924$	24.0217	+	17.4528i	0.790257	+	0.574155i
$925$	4.12618			0.135668
$926$	3.39387	+	2.46579i	0.111530	+	0.0810310i
$927$	−21.5608	+	15.6648i	−0.708148	+	0.514500i
$928$	−7.70438	−	23.7116i	−0.252909	−	0.778373i
$929$	47.1549			1.54710			0.773551	−	0.633734i	$-0.218478\pi$
$929$	47.1549			1.54710			0.773551	+	0.633734i	$0.218478\pi$
$930$	−0.644507	+	1.98359i	−0.0211342	+	0.0650444i
$931$	0.541217	+	1.66569i	0.0177377	+	0.0545909i
$932$	−11.5855	+	35.6566i	−0.379497	+	1.16797i
$933$	44.1487	−	32.0759i	1.44536	−	1.05012i
$934$	7.67586	+	5.57684i	0.251162	+	0.182480i
$935$	−2.01678	−	6.20702i	−0.0659559	−	0.202991i
$936$	6.30511	−	4.58093i	0.206089	−	0.149732i
$937$	−29.6394	+	21.5343i	−0.968278	+	0.703495i	−0.955058	−	0.296418i	$-0.904208\pi$
$937$	−29.6394	+	21.5343i	−0.968278	+	0.703495i	−0.0132194	+	0.999913i	$0.504208\pi$
$938$	2.41380			0.0788133
$939$	33.1627			1.08223
$940$	2.91644	−	2.11892i	0.0951237	−	0.0691114i
$941$	−17.0079	−	52.3448i	−0.554441	−	1.70639i	−0.697416	−	0.716667i	$-0.745667\pi$
$941$	−17.0079	−	52.3448i	−0.554441	−	1.70639i	0.142975	−	0.989726i	$-0.454333\pi$
$942$	−0.370161	−	0.268937i	−0.0120605	−	0.00876246i
$943$	0.540915	−	1.66476i	0.0176146	−	0.0542122i
$944$	−10.3665			−0.337400
$945$	−1.81929	−	1.32179i	−0.0591814	−	0.0429978i
$946$	−6.13819	−	4.45966i	−0.199570	−	0.144996i
$947$	−10.7319	+	33.0295i	−0.348741	+	1.07331i	0.610810	+	0.791777i	$0.290844\pi$
$947$	−10.7319	+	33.0295i	−0.348741	+	1.07331i	−0.959551	+	0.281536i	$0.909156\pi$
$948$	−60.4881	+	43.9472i	−1.96456	+	1.42734i
$949$	−1.24582	+	0.905141i	−0.0404410	+	0.0293821i
$950$	−0.425276	−	1.30887i	−0.0137978	−	0.0424652i
$951$	22.7465	+	70.0064i	0.737605	+	2.27011i
$952$	11.4327			0.370537
$953$	18.4256	−	56.7082i	0.596864	−	1.83696i	0.0516467	−	0.998665i	$-0.483553\pi$
$953$	18.4256	−	56.7082i	0.596864	−	1.83696i	0.545218	−	0.838294i	$-0.316447\pi$
$954$	1.50999	−	4.64728i	0.0488879	−	0.150461i
$955$	0.140732	+	0.433128i	0.00455397	+	0.0140157i
$956$	−9.08524	−	27.9615i	−0.293838	−	0.904339i
$957$	−10.3761	−	31.9344i	−0.335412	−	1.03229i
$958$	3.53115	−	10.8678i	0.114086	−	0.351122i
$959$	−10.1994	−	31.3904i	−0.329355	−	1.01365i
$960$	5.78071	−	4.19993i	0.186571	−	0.135552i
$961$	−8.69171	+	26.7503i	−0.280378	+	0.862914i
$962$	−2.06249	−	1.49849i	−0.0664975	−	0.0483133i
$963$	0.198595	−	0.611212i	0.00639962	−	0.0196960i
$964$	10.6879	+	32.8940i	0.344234	+	1.05944i
$965$	−13.9888			−0.450314
$966$	−2.88406	+	2.09539i	−0.0927932	+	0.0674182i
$967$	6.87290	+	21.1526i	0.221018	+	0.680222i	0.998671	+	0.0515296i	$0.0164096\pi$
$967$	6.87290	+	21.1526i	0.221018	+	0.680222i	−0.777654	+	0.628693i	$0.783590\pi$
$968$	−5.92801	+	4.30695i	−0.190534	+	0.138431i
$969$	−5.41272	−	16.6586i	−0.173882	−	0.535152i
$970$	5.74049			0.184316
$971$	−12.5376	+	9.10908i	−0.402350	+	0.292324i	−0.770498	−	0.637443i	$-0.779992\pi$
$971$	−12.5376	+	9.10908i	−0.402350	+	0.292324i	0.368147	+	0.929767i	$0.379992\pi$
$972$	−39.4098			−1.26407
$973$	10.3324	−	7.50695i	0.331242	−	0.240662i
$974$	13.4842	−	9.79682i	0.432060	−	0.313910i
$975$	−0.985804	+	3.03399i	−0.0315710	+	0.0971655i
$976$	−6.90755	−	21.2593i	−0.221105	−	0.680492i
$977$	−23.7772	−	17.2751i	−0.760699	−	0.552680i	0.138426	−	0.990373i	$-0.455796\pi$
$977$	−23.7772	−	17.2751i	−0.760699	−	0.552680i	−0.899125	+	0.437693i	$0.855796\pi$
$978$	16.4155	+	11.9266i	0.524911	+	0.381370i
$979$	−7.32569	−	5.32243i	−0.234130	−	0.170106i
$980$	−0.338211	+	1.04091i	−0.0108037	+	0.0332505i
$981$	68.8180			2.19719
$982$	9.82880			0.313650
$983$	7.76452	−	23.8967i	0.247650	−	0.762187i	−0.747540	−	0.664217i	$-0.768765\pi$
$983$	7.76452	−	23.8967i	0.247650	−	0.762187i	0.995189	−	0.0979701i	$-0.0312349\pi$
$984$	5.71421	+	4.15162i	0.182162	+	0.132349i
$985$	4.49556	+	3.26621i	0.143240	+	0.104070i
$986$	−4.89846	−	3.55894i	−0.155999	−	0.113340i
$987$	4.02545	+	12.3891i	0.128132	+	0.394348i
$988$	1.94237	−	5.97800i	0.0617951	−	0.190186i
$989$	−5.44772	+	3.95800i	−0.173228	+	0.125857i
$990$	−3.50634	+	2.54750i	−0.111439	+	0.0809649i
$991$	57.0751			1.81305			0.906526	−	0.422150i	$-0.138725\pi$
$991$	57.0751			1.81305			0.906526	+	0.422150i	$0.138725\pi$
$992$	6.79489	−	4.93677i	0.215738	−	0.156743i
$993$	33.2741			1.05592
$994$	4.53163	+	13.9469i	0.143735	+	0.442370i
$995$	5.35500	−	3.89064i	0.169765	−	0.123341i
$996$	2.25078	+	6.92720i	0.0713188	+	0.219497i
$997$	47.9875	−	34.8649i	1.51978	−	1.10418i	0.558182	−	0.829719i	$-0.311499\pi$
$997$	47.9875	−	34.8649i	1.51978	−	1.10418i	0.961597	−	0.274465i	$-0.0885008\pi$
$998$	1.37986			0.0436786
$999$	−1.13529	−	3.49406i	−0.0359190	−	0.110547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.h.d.321.3	✓	16
151.8	even	5	inner	755.2.h.d.461.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.h.d.321.3	✓	16	1.1	even	1	trivial
755.2.h.d.461.3	yes	16	151.8	even	5	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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.488177 q^{2} +(-0.778897 + 2.39720i) q^{3} -1.76168 q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.380239 + 1.17026i) q^{6} +(-2.04327 - 1.48452i) q^{7} -1.83637 q^{8} +(-2.71283 - 1.97099i) q^{9} +(0.394943 + 0.286943i) q^{10} +(-0.818155 - 2.51802i) q^{11} +(1.37217 - 4.22311i) q^{12} +(0.391104 - 1.20370i) q^{13} +(-0.997475 - 0.724708i) q^{14} +(-2.03918 + 1.48155i) q^{15} +2.62690 q^{16} +(1.99426 - 1.44891i) q^{17} +(-1.32434 - 0.962191i) q^{18} -2.81911 q^{19} +(-1.42523 - 1.03549i) q^{20} +(5.15018 - 3.74183i) q^{21} +(-0.399404 - 1.22924i) q^{22} -1.14711 q^{23} +(1.43034 - 4.40214i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.190928 - 0.587616i) q^{26} +(0.720334 - 0.523353i) q^{27} +(3.59959 + 2.61525i) q^{28} +(-1.55483 - 4.78528i) q^{29} +(-0.995480 + 0.723258i) q^{30} +(1.37129 - 0.996297i) q^{31} +4.95512 q^{32} +6.67346 q^{33} +(0.973550 - 0.707325i) q^{34} +(-0.780458 - 2.40200i) q^{35} +(4.77915 + 3.47226i) q^{36} +(1.27506 - 3.92423i) q^{37} -1.37622 q^{38} +(2.58087 + 1.87511i) q^{39} +(-1.48565 - 1.07939i) q^{40} +(-0.471546 + 1.45127i) q^{41} +(2.51420 - 1.82667i) q^{42} +(4.74909 - 3.45041i) q^{43} +(1.44133 + 4.43596i) q^{44} +(-1.03621 - 3.18913i) q^{45} -0.559992 q^{46} +(-0.632339 + 1.94614i) q^{47} +(-2.04608 + 6.29720i) q^{48} +(-0.191982 - 0.590859i) q^{49} +(0.150855 + 0.464284i) q^{50} +(1.92001 + 5.90919i) q^{51} +(-0.689002 + 2.12053i) q^{52} +(0.922429 + 2.83894i) q^{53} +(0.351650 - 0.255489i) q^{54} +(0.818155 - 2.51802i) q^{55} +(3.75218 + 2.72612i) q^{56} +(2.19580 - 6.75796i) q^{57} +(-0.759032 - 2.33606i) q^{58} -3.94628 q^{59} +(3.59239 - 2.61002i) q^{60} +(-2.62955 - 8.09292i) q^{61} +(0.669430 - 0.486369i) q^{62} +(2.61707 + 8.05451i) q^{63} -2.83482 q^{64} +(1.02392 - 0.743925i) q^{65} +3.25783 q^{66} +(-1.58385 + 1.15074i) q^{67} +(-3.51325 + 2.55253i) q^{68} +(0.893481 - 2.74985i) q^{69} +(-0.381001 - 1.17260i) q^{70} +(-9.62246 - 6.99112i) q^{71} +(4.98176 + 3.61946i) q^{72} +(-0.984339 - 0.715164i) q^{73} +(0.622454 - 1.91572i) q^{74} -2.52056 q^{75} +4.96638 q^{76} +(-2.06635 + 6.35956i) q^{77} +(1.25992 + 0.915385i) q^{78} +(-13.6221 - 9.89704i) q^{79} +(2.12520 + 1.54405i) q^{80} +(-2.41511 - 7.43296i) q^{81} +(-0.230198 + 0.708475i) q^{82} +(-1.32704 + 0.964149i) q^{83} +(-9.07300 + 6.59192i) q^{84} +2.46504 q^{85} +(2.31839 - 1.68441i) q^{86} +12.6823 q^{87} +(1.50243 + 4.62401i) q^{88} +(2.76691 - 2.01028i) q^{89} +(-0.505854 - 1.55686i) q^{90} +(-2.58604 + 1.87887i) q^{91} +2.02084 q^{92} +(1.32023 + 4.06326i) q^{93} +(-0.308693 + 0.950059i) q^{94} +(-2.28071 - 1.65703i) q^{95} +(-3.85953 + 11.8784i) q^{96} +(9.51327 - 6.91180i) q^{97} +(-0.0937209 - 0.288443i) q^{98} +(-2.74348 + 8.44355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} - 18 q^{6} - q^{7} - 18 q^{8} - q^{10} + 13 q^{11} - 19 q^{12} + 7 q^{13} - q^{14} - q^{15} + 16 q^{16} + 9 q^{17} - 3 q^{18} - 34 q^{19} - 9 q^{20} + 2 q^{21}+ \cdots + 75 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 + 24 * q^4 + 4 * q^5 - 18 * q^6 - q^7 - 18 * q^8 - q^10 + 13 * q^11 - 19 * q^12 + 7 * q^13 - q^14 - q^15 + 16 * q^16 + 9 * q^17 - 3 * q^18 - 34 * q^19 - 9 * q^20 + 2 * q^21 + 14 * q^22 + 58 * q^23 + 8 * q^24 - 4 * q^25 - 19 * q^26 - 34 * q^27 + 19 * q^28 - 16 * q^29 - 12 * q^30 - 3 * q^31 + 14 * q^34 + 11 * q^35 + 57 * q^36 + 20 * q^37 - 16 * q^38 + 5 * q^39 + 3 * q^40 + 24 * q^41 + 34 * q^42 - 28 * q^43 + 73 * q^44 + 15 * q^45 - 22 * q^46 + 18 * q^47 - 74 * q^48 - 19 * q^49 + q^50 - 8 * q^51 + 2 * q^52 + 23 * q^53 + 48 * q^54 - 13 * q^55 - 7 * q^56 - 22 * q^57 + 8 * q^58 - 44 * q^59 - 6 * q^60 - 25 * q^61 + 56 * q^62 - 7 * q^63 + 42 * q^64 + 3 * q^65 - 102 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^70 - 22 * q^71 - 39 * q^72 - 26 * q^73 - 2 * q^74 + 6 * q^75 + 16 * q^76 + 11 * q^77 + 12 * q^78 - 32 * q^79 - 21 * q^80 + 11 * q^81 + 46 * q^82 + 4 * q^83 - 19 * q^84 + 36 * q^85 + 39 * q^86 + 88 * q^87 + 24 * q^88 + 38 * q^89 - 22 * q^90 - 6 * q^91 + 114 * q^92 - 31 * q^93 - 31 * q^94 - 21 * q^95 + 59 * q^96 + 75 * q^97 - 56 * q^98 + 75 * q^99

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