LMFDB - Embedded newform 75.2.i.a.34.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(4,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.i (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			34.4
Root			$-2.53767i$ of defining polynomial
Character	$\chi$	$=$	75.34
Dual form			75.2.i.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49161 - 2.05302i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(0.227564 + 2.22446i) q^{5} +(-0.784184 + 2.41347i) q^{6} +1.04054i q^{7} +(-5.88835 - 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(1.49161 - 2.05302i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(0.227564 + 2.22446i) q^{5} +(-0.784184 + 2.41347i) q^{6} +1.04054i q^{7} +(-5.88835 - 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +(4.90630 + 2.85082i) q^{10} +(-2.40360 - 1.74631i) q^{11} +(2.60964 + 3.59186i) q^{12} +(3.33228 + 4.58650i) q^{13} +(2.13624 + 1.55207i) q^{14} +(-0.903822 - 2.04526i) q^{15} +(-5.52731 + 4.01583i) q^{16} +(-4.83480 - 1.57092i) q^{17} -2.53767i q^{18} +(1.65990 - 5.10866i) q^{19} +(9.08054 - 4.01278i) q^{20} +(-0.321543 - 0.989608i) q^{21} +(-7.17044 + 2.32982i) q^{22} +(-2.26908 + 3.12312i) q^{23} +6.19138 q^{24} +(-4.89643 + 1.01241i) q^{25} +14.3866 q^{26} +(-0.587785 + 0.809017i) q^{27} +(4.39365 - 1.42758i) q^{28} +(-0.210038 - 0.646430i) q^{29} +(-5.54712 - 1.19517i) q^{30} +(0.262699 - 0.808503i) q^{31} +4.95495i q^{32} +(2.82560 + 0.918092i) q^{33} +(-10.4368 + 7.58275i) q^{34} +(-2.31463 + 0.236789i) q^{35} +(-3.59186 - 2.60964i) q^{36} +(0.950818 + 1.30869i) q^{37} +(-8.01226 - 11.0279i) q^{38} +(-4.58650 - 3.33228i) q^{39} +(2.91595 - 13.5338i) q^{40} +(-0.942740 + 0.684941i) q^{41} +(-2.51130 - 0.815972i) q^{42} -5.68601i q^{43} +(-4.07613 + 12.5450i) q^{44} +(1.49161 + 1.66587i) q^{45} +(3.02725 + 9.31693i) q^{46} +(-3.12556 + 1.01555i) q^{47} +(4.01583 - 5.52731i) q^{48} +5.91729 q^{49} +(-5.22504 + 11.5626i) q^{50} +5.08361 q^{51} +(14.7946 - 20.3631i) q^{52} +(12.0652 - 3.92023i) q^{53} +(0.784184 + 2.41347i) q^{54} +(3.33763 - 5.74410i) q^{55} +(1.99080 - 6.12704i) q^{56} +5.37156i q^{57} +(-1.64043 - 0.533007i) q^{58} +(2.59846 - 1.88789i) q^{59} +(-7.39609 + 6.62242i) q^{60} +(4.38562 + 3.18634i) q^{61} +(-1.26803 - 1.74530i) q^{62} +(0.611611 + 0.841811i) q^{63} +(-0.881995 - 0.640807i) q^{64} +(-9.44416 + 8.45625i) q^{65} +(6.09954 - 4.43157i) q^{66} +(-0.883665 - 0.287120i) q^{67} +22.5702i q^{68} +(1.19292 - 3.67145i) q^{69} +(-2.96638 + 5.10517i) q^{70} +(-0.436821 - 1.34440i) q^{71} +(-5.88835 + 1.91324i) q^{72} +(-6.65571 + 9.16080i) q^{73} +4.10501 q^{74} +(4.34393 - 2.47594i) q^{75} -23.8486 q^{76} +(1.81710 - 2.50103i) q^{77} +(-13.6825 + 4.44571i) q^{78} +(0.447171 + 1.37625i) q^{79} +(-10.1909 - 11.3814i) q^{80} +(0.309017 - 0.951057i) q^{81} +2.95713i q^{82} +(10.9140 + 3.54616i) q^{83} +(-3.73746 + 2.71542i) q^{84} +(2.39422 - 11.1123i) q^{85} +(-11.6735 - 8.48129i) q^{86} +(0.399516 + 0.549886i) q^{87} +(10.8121 + 14.8816i) q^{88} +(7.33961 + 5.33254i) q^{89} +(5.64495 - 0.577483i) q^{90} +(-4.77241 + 3.46736i) q^{91} +(16.3004 + 5.29633i) q^{92} +0.850111i q^{93} +(-2.57715 + 7.93164i) q^{94} +(11.7417 + 2.52984i) q^{95} +(-1.53117 - 4.71244i) q^{96} +(5.73419 - 1.86315i) q^{97} +(8.82627 - 12.1483i) q^{98} -2.97101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.49161	−	2.05302i	1.05473	−	1.45171i	0.170086	−	0.985429i	$-0.445595\pi$
$2$	1.49161	−	2.05302i	1.05473	−	1.45171i	0.884639	−	0.466276i	$-0.154405\pi$
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	−1.37197	−	4.22249i	−0.685985	−	2.11124i
$5$	0.227564	+	2.22446i	0.101770	+	0.994808i
$5$	0.227564	+	2.22446i	0.101770	+	0.994808i
$6$	−0.784184	+	2.41347i	−0.320142	+	0.985295i
$7$			1.04054i			0.393285i	0.980475	+	0.196643i	$0.0630039\pi$
$7$			1.04054i			0.393285i	−0.980475	+	0.196643i	$0.936996\pi$
$8$	−5.88835	−	1.91324i	−2.08185	−	0.676433i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	4.90630	+	2.85082i	1.55151	+	0.901510i
$11$	−2.40360	−	1.74631i	−0.724711	−	0.526533i	0.163175	−	0.986597i	$-0.447827\pi$
$11$	−2.40360	−	1.74631i	−0.724711	−	0.526533i	−0.887886	+	0.460064i	$0.847827\pi$
$12$	2.60964	+	3.59186i	0.753338	+	1.03688i
$13$	3.33228	+	4.58650i	0.924209	+	1.27207i	0.962076	+	0.272782i	$0.0879439\pi$
$13$	3.33228	+	4.58650i	0.924209	+	1.27207i	−0.0378663	+	0.999283i	$0.512056\pi$
$14$	2.13624	+	1.55207i	0.570934	+	0.414808i
$15$	−0.903822	−	2.04526i	−0.233366	−	0.528085i
$16$	−5.52731	+	4.01583i	−1.38183	+	1.00396i
$17$	−4.83480	−	1.57092i	−1.17261	−	0.381005i	−0.342995	−	0.939337i	$-0.611441\pi$
$17$	−4.83480	−	1.57092i	−1.17261	−	0.381005i	−0.829617	+	0.558333i	$0.811441\pi$
$18$		−	2.53767i		−	0.598135i
$19$	1.65990	−	5.10866i	0.380808	−	1.17201i	−0.558668	−	0.829391i	$-0.688687\pi$
$19$	1.65990	−	5.10866i	0.380808	−	1.17201i	0.939476	−	0.342615i	$-0.111313\pi$
$20$	9.08054	−	4.01278i	2.03047	−	0.897284i
$21$	−0.321543	−	0.989608i	−0.0701665	−	0.215950i
$22$	−7.17044	+	2.32982i	−1.52874	+	0.496719i
$23$	−2.26908	+	3.12312i	−0.473135	+	0.651215i	−0.977168	−	0.212470i	$-0.931849\pi$
$23$	−2.26908	+	3.12312i	−0.473135	+	0.651215i	0.504032	+	0.863685i	$0.331849\pi$
$24$	6.19138			1.26381
$25$	−4.89643	+	1.01241i	−0.979286	+	0.202483i
$26$	14.3866			2.82145
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	4.39365	−	1.42758i	0.830322	−	0.269788i
$29$	−0.210038	−	0.646430i	−0.0390030	−	0.120039i	0.929659	−	0.368421i	$-0.120101\pi$
$29$	−0.210038	−	0.646430i	−0.0390030	−	0.120039i	−0.968662	+	0.248382i	$0.920101\pi$
$30$	−5.54712	−	1.19517i	−1.01276	−	0.218206i
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	−0.924690	−	0.380721i	$-0.875676\pi$
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	0.971872	+	0.235509i	$0.0756759\pi$
$32$			4.95495i			0.875921i
$33$	2.82560	+	0.918092i	0.491873	+	0.159819i
$34$	−10.4368	+	7.58275i	−1.78989	+	1.30043i
$35$	−2.31463	+	0.236789i	−0.391244	+	0.0400246i
$36$	−3.59186	−	2.60964i	−0.598644	−	0.434940i
$37$	0.950818	+	1.30869i	0.156313	+	0.215147i	0.879990	−	0.474992i	$-0.157549\pi$
$37$	0.950818	+	1.30869i	0.156313	+	0.215147i	−0.723676	+	0.690139i	$0.757549\pi$
$38$	−8.01226	−	11.0279i	−1.29976	−	1.78897i
$39$	−4.58650	−	3.33228i	−0.734427	−	0.533593i
$40$	2.91595	−	13.5338i	0.461052	−	2.13988i
$41$	−0.942740	+	0.684941i	−0.147231	+	0.106970i	−0.658962	−	0.752176i	$-0.729004\pi$
$41$	−0.942740	+	0.684941i	−0.147231	+	0.106970i	0.511731	+	0.859146i	$0.329004\pi$
$42$	−2.51130	−	0.815972i	−0.387502	−	0.125907i
$43$		−	5.68601i		−	0.867109i	−0.901127	−	0.433554i	$-0.857259\pi$
$43$		−	5.68601i		−	0.867109i	0.901127	−	0.433554i	$-0.142741\pi$
$44$	−4.07613	+	12.5450i	−0.614500	+	1.89124i
$45$	1.49161	+	1.66587i	0.222356	+	0.248333i
$46$	3.02725	+	9.31693i	0.446344	+	1.37371i
$47$	−3.12556	+	1.01555i	−0.455909	+	0.148134i	−0.527964	−	0.849267i	$-0.677044\pi$
$47$	−3.12556	+	1.01555i	−0.455909	+	0.148134i	0.0720547	+	0.997401i	$0.477044\pi$
$48$	4.01583	−	5.52731i	0.579635	−	0.797798i
$49$	5.91729			0.845327
$50$	−5.22504	+	11.5626i	−0.738932	+	1.63520i
$51$	5.08361			0.711848
$52$	14.7946	−	20.3631i	2.05165	−	2.82385i
$53$	12.0652	−	3.92023i	1.65729	−	0.538485i	0.676986	−	0.735996i	$-0.263286\pi$
$53$	12.0652	−	3.92023i	1.65729	−	0.538485i	0.980301	+	0.197511i	$0.0632857\pi$
$54$	0.784184	+	2.41347i	0.106714	+	0.328432i
$55$	3.33763	−	5.74410i	0.450046	−	0.774534i
$56$	1.99080	−	6.12704i	0.266031	−	0.818760i
$57$			5.37156i			0.711481i
$58$	−1.64043	−	0.533007i	−0.215399	−	0.0699873i
$59$	2.59846	−	1.88789i	0.338290	−	0.245782i	−0.405650	−	0.914029i	$-0.632955\pi$
$59$	2.59846	−	1.88789i	0.338290	−	0.245782i	0.743940	+	0.668246i	$0.232955\pi$
$60$	−7.39609	+	6.62242i	−0.954831	+	0.854950i
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	0.832015	−	0.554753i	$-0.187187\pi$
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	−0.270494	+	0.962722i	$0.587187\pi$
$62$	−1.26803	−	1.74530i	−0.161040	−	0.221653i
$63$	0.611611	+	0.841811i	0.0770558	+	0.106058i
$64$	−0.881995	−	0.640807i	−0.110249	−	0.0801008i
$65$	−9.44416	+	8.45625i	−1.17140	+	1.04887i
$66$	6.09954	−	4.43157i	0.750801	−	0.545489i
$67$	−0.883665	−	0.287120i	−0.107957	−	0.0350773i	0.254540	−	0.967062i	$-0.418076\pi$
$67$	−0.883665	−	0.287120i	−0.107957	−	0.0350773i	−0.362497	+	0.931985i	$0.618076\pi$
$68$			22.5702i			2.73703i
$69$	1.19292	−	3.67145i	0.143611	−	0.441990i
$70$	−2.96638	+	5.10517i	−0.354551	+	0.610185i
$71$	−0.436821	−	1.34440i	−0.0518412	−	0.159551i	0.921784	−	0.387703i	$-0.126731\pi$
$71$	−0.436821	−	1.34440i	−0.0518412	−	0.159551i	−0.973625	+	0.228153i	$0.926731\pi$
$72$	−5.88835	+	1.91324i	−0.693949	+	0.225478i
$73$	−6.65571	+	9.16080i	−0.778992	+	1.07219i	0.216400	+	0.976305i	$0.430568\pi$
$73$	−6.65571	+	9.16080i	−0.778992	+	1.07219i	−0.995392	+	0.0958862i	$0.969432\pi$
$74$	4.10501			0.477198
$75$	4.34393	−	2.47594i	0.501594	−	0.285897i
$76$	−23.8486			−2.73562
$77$	1.81710	−	2.50103i	0.207078	−	0.285018i
$78$	−13.6825	+	4.44571i	−1.54924	+	0.503378i
$79$	0.447171	+	1.37625i	0.0503106	+	0.154840i	0.973055	−	0.230571i	$-0.0740595\pi$
$79$	0.447171	+	1.37625i	0.0503106	+	0.154840i	−0.922745	+	0.385412i	$0.874059\pi$
$80$	−10.1909	−	11.3814i	−1.13937	−	1.27248i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$			2.95713i			0.326560i
$83$	10.9140	+	3.54616i	1.19796	+	0.389242i	0.839011	−	0.544114i	$-0.183134\pi$
$83$	10.9140	+	3.54616i	1.19796	+	0.389242i	0.358952	+	0.933356i	$0.383134\pi$
$84$	−3.73746	+	2.71542i	−0.407790	+	0.296277i
$85$	2.39422	−	11.1123i	0.259690	−	1.20530i
$86$	−11.6735	−	8.48129i	−1.25879	−	0.914561i
$87$	0.399516	+	0.549886i	0.0428326	+	0.0589540i
$88$	10.8121	+	14.8816i	1.15257	+	1.58638i
$89$	7.33961	+	5.33254i	0.777997	+	0.565248i	0.904377	−	0.426734i	$-0.140336\pi$
$89$	7.33961	+	5.33254i	0.777997	+	0.565248i	−0.126380	+	0.991982i	$0.540336\pi$
$90$	5.64495	−	0.577483i	0.595030	−	0.0608721i
$91$	−4.77241	+	3.46736i	−0.500285	+	0.363478i
$92$	16.3004	+	5.29633i	1.69944	+	0.552181i
$93$			0.850111i			0.0881524i
$94$	−2.57715	+	7.93164i	−0.265812	+	0.818086i
$95$	11.7417	+	2.52984i	1.20468	+	0.259556i
$96$	−1.53117	−	4.71244i	−0.156274	−	0.480962i
$97$	5.73419	−	1.86315i	0.582219	−	0.189174i	−0.00307549	−	0.999995i	$-0.500979\pi$
$97$	5.73419	−	1.86315i	0.582219	−	0.189174i	0.585294	+	0.810821i	$0.300979\pi$
$98$	8.82627	−	12.1483i	0.891587	−	1.22716i
$99$	−2.97101			−0.298597
$100$	10.9927	+	19.2861i	1.09927	+	1.92861i
$101$	−15.3408			−1.52647			−0.763236	−	0.646120i	$-0.776390\pi$
$101$	−15.3408			−1.52647			−0.763236	+	0.646120i	$0.776390\pi$
$102$	7.58275	−	10.4368i	0.750804	−	1.03339i
$103$	−11.4688	+	3.72642i	−1.13005	+	0.367175i	−0.813595	−	0.581432i	$-0.802493\pi$
$103$	−11.4688	+	3.72642i	−1.13005	+	0.367175i	−0.316455	+	0.948608i	$0.602493\pi$
$104$	−10.8466	−	33.3824i	−1.06360	−	3.27341i
$105$	2.12817	−	0.940459i	0.207688	−	0.0917794i
$106$	9.94827	−	30.6176i	0.966261	−	2.97385i
$107$			6.49787i			0.628173i	0.949394	+	0.314086i	$0.101698\pi$
$107$			6.49787i			0.628173i	−0.949394	+	0.314086i	$0.898302\pi$
$108$	4.22249	+	1.37197i	0.406309	+	0.132018i
$109$	−1.86929	+	1.35812i	−0.179046	+	0.130084i	−0.673698	−	0.739006i	$-0.735295\pi$
$109$	−1.86929	+	1.35812i	−0.179046	+	0.130084i	0.494653	+	0.869091i	$0.335295\pi$
$110$	−6.81431	−	15.4202i	−0.649719	−	1.47025i
$111$	−1.30869	−	0.950818i	−0.124215	−	0.0902476i
$112$	−4.17861	−	5.75136i	−0.394841	−	0.543453i
$113$	−2.27638	−	3.13317i	−0.214144	−	0.294744i	0.688409	−	0.725323i	$-0.258309\pi$
$113$	−2.27638	−	3.13317i	−0.214144	−	0.294744i	−0.902553	+	0.430579i	$0.858309\pi$
$114$	11.0279	+	8.01226i	1.03286	+	0.750417i
$115$	−7.46361	−	4.33676i	−0.695985	−	0.404405i
$116$	−2.44138	+	1.77376i	−0.226676	+	0.164690i
$117$	5.39175	+	1.75189i	0.498467	+	0.161962i
$118$		−	8.15067i		−	0.750330i
$119$	1.63460	−	5.03078i	0.149844	−	0.461171i
$120$	1.40894	+	13.7725i	0.128618	+	1.25725i
$121$	−0.671530	−	2.06676i	−0.0610482	−	0.187887i
$122$	13.0832	−	4.25101i	1.18450	−	0.384868i
$123$	0.684941	−	0.942740i	0.0617590	−	0.0850040i
$124$	−3.77431			−0.338943
$125$	−3.36632	−	10.6615i	−0.301093	−	0.953595i
$126$	2.64054			0.235238
$127$	−6.87342	+	9.46046i	−0.609918	+	0.839480i	−0.996571	−	0.0827456i	$-0.973631\pi$
$127$	−6.87342	+	9.46046i	−0.609918	+	0.839480i	0.386653	+	0.922225i	$0.373631\pi$
$128$	−12.0561	+	3.91725i	−1.06562	+	0.346239i
$129$	1.75707	+	5.40772i	0.154702	+	0.476123i
$130$	3.27388	+	32.0025i	0.287138	+	2.80680i
$131$	−2.46042	+	7.57241i	−0.214968	+	0.661604i	0.784188	+	0.620524i	$0.213080\pi$
$131$	−2.46042	+	7.57241i	−0.214968	+	0.661604i	−0.999156	+	0.0410805i	$0.986920\pi$
$132$		−	13.1906i		−	1.14810i
$133$	5.31574	+	1.72719i	0.460933	+	0.149766i
$134$	−1.90754	+	1.38591i	−0.164787	+	0.119725i
$135$	−1.93338	−	1.12340i	−0.166399	−	0.0966869i
$136$	25.4635	+	18.5003i	2.18348	+	1.58639i
$137$	−6.49579	−	8.94069i	−0.554973	−	0.763854i	0.435704	−	0.900090i	$-0.356500\pi$
$137$	−6.49579	−	8.94069i	−0.554973	−	0.763854i	−0.990676	+	0.136236i	$0.956500\pi$
$138$	−5.75818	−	7.92545i	−0.490169	−	0.674659i
$139$	−9.92651	−	7.21204i	−0.841956	−	0.611717i	0.0809604	−	0.996717i	$-0.474201\pi$
$139$	−9.92651	−	7.21204i	−0.841956	−	0.611717i	−0.922916	+	0.385000i	$0.874201\pi$
$140$	4.17544	+	9.44862i	0.352889	+	0.798554i
$141$	2.65876	−	1.93170i	0.223908	−	0.162678i
$142$	−3.41164	−	1.10851i	−0.286299	−	0.0930241i
$143$		−	16.8433i		−	1.40851i
$144$	−2.11124	+	6.49774i	−0.175937	+	0.541479i
$145$	1.39016	−	0.614324i	0.115446	−	0.0510169i
$146$	8.87961	+	27.3286i	0.734882	+	2.26173i
$147$	−5.62767	+	1.82854i	−0.464163	+	0.150816i
$148$	4.22143	−	5.81030i	0.346999	−	0.477604i
$149$	4.62832			0.379167			0.189584	−	0.981865i	$-0.439286\pi$
$149$	4.62832			0.379167			0.189584	+	0.981865i	$0.439286\pi$
$150$	1.39627	−	12.6113i	0.114005	−	1.02971i
$151$	−4.67249			−0.380242			−0.190121	−	0.981761i	$-0.560888\pi$
$151$	−4.67249			−0.380242			−0.190121	+	0.981761i	$0.560888\pi$
$152$	−19.5482	+	26.9058i	−1.58557	+	2.18235i
$153$	−4.83480	+	1.57092i	−0.390871	+	0.127002i
$154$	−2.42426	−	7.46110i	−0.195352	−	0.601232i
$155$	1.85826	+	0.400376i	0.149259	+	0.0321590i
$156$	−7.77800	+	23.9382i	−0.622738	+	1.91659i
$157$		−	14.9726i		−	1.19494i	−0.801890	−	0.597472i	$-0.796172\pi$
$157$		−	14.9726i		−	1.19494i	0.801890	−	0.597472i	$-0.203828\pi$
$158$	3.49247	+	1.13477i	0.277846	+	0.0902777i
$159$	−10.2633	+	7.45672i	−0.813932	+	0.591357i
$160$	−11.0221	+	1.12757i	−0.871373	+	0.0891422i
$161$	−3.24972	−	2.36106i	−0.256113	−	0.186077i
$162$	−1.49161	−	2.05302i	−0.117192	−	0.161301i
$163$	−7.00123	−	9.63637i	−0.548379	−	0.754779i	0.441412	−	0.897304i	$-0.354478\pi$
$163$	−7.00123	−	9.63637i	−0.548379	−	0.754779i	−0.989791	+	0.142526i	$0.954478\pi$
$164$	4.18557	+	3.04099i	0.326838	+	0.237462i
$165$	−1.39925	+	6.49434i	−0.108932	+	0.505584i
$166$	23.5597	−	17.1171i	1.82859	−	1.32855i
$167$	10.0889	+	3.27809i	0.780704	+	0.253666i	0.672141	−	0.740424i	$-0.265375\pi$
$167$	10.0889	+	3.27809i	0.780704	+	0.253666i	0.108563	+	0.994090i	$0.465375\pi$
$168$			6.44235i			0.497038i
$169$	−5.91461	+	18.2033i	−0.454970	+	1.40025i
$170$	−19.2426	−	21.4906i	−1.47584	−	1.64825i
$171$	−1.65990	−	5.10866i	−0.126936	−	0.390669i
$172$	−24.0091	+	7.80103i	−1.83068	+	0.594823i
$173$	−0.736719	+	1.01401i	−0.0560117	+	0.0770935i	−0.836104	−	0.548571i	$-0.815172\pi$
$173$	−0.736719	+	1.01401i	−0.0560117	+	0.0770935i	0.780092	+	0.625664i	$0.215172\pi$
$174$	1.72485			0.130760
$175$	−1.05345	−	5.09491i	−0.0796335	−	0.385139i
$176$	20.2983			1.53004
$177$	−1.88789	+	2.59846i	−0.141902	+	0.195312i
$178$	21.8956	−	7.11432i	1.64115	−	0.533241i
$179$	6.43105	+	19.7927i	0.480679	+	1.47938i	0.838143	+	0.545451i	$0.183642\pi$
$179$	6.43105	+	19.7927i	0.480679	+	1.47938i	−0.357464	+	0.933927i	$0.616358\pi$
$180$	4.98766	−	8.58381i	0.371758	−	0.639799i
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	−0.998554	−	0.0537591i	$-0.982880\pi$
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	0.839446	+	0.543443i	$0.182880\pi$
$182$			14.9698i			1.10964i
$183$	−5.15561	−	1.67516i	−0.381113	−	0.123831i
$184$	19.3364	−	14.0487i	1.42550	−	1.03569i
$185$	−2.69475	+	2.41287i	−0.198122	+	0.177397i
$186$	1.74530	+	1.26803i	0.127971	+	0.0929766i
$187$	8.87759	+	12.2189i	0.649193	+	0.893538i
$188$	8.57633	+	11.8043i	0.625494	+	0.860918i
$189$	−0.841811	−	0.611611i	−0.0612327	−	0.0444882i
$190$	22.7079	−	20.3325i	1.64740	−	1.47507i
$191$	−6.60494	+	4.79877i	−0.477916	+	0.347227i	−0.800518	−	0.599308i	$-0.795442\pi$
$191$	−6.60494	+	4.79877i	−0.477916	+	0.347227i	0.322602	+	0.946535i	$0.395442\pi$
$192$	1.03685	+	0.336892i	0.0748280	+	0.0243131i
$193$		−	13.9629i		−	1.00507i	−0.864556	−	0.502537i	$-0.832400\pi$
$193$		−	13.9629i		−	1.00507i	0.864556	−	0.502537i	$-0.167600\pi$
$194$	4.72807	−	14.5515i	0.339456	−	1.04474i
$195$	6.36881	−	10.9608i	0.456080	−	0.784918i
$196$	−8.11834	−	24.9857i	−0.579881	−	1.78469i
$197$	5.48046	−	1.78071i	0.390467	−	0.126870i	−0.107203	−	0.994237i	$-0.534189\pi$
$197$	5.48046	−	1.78071i	0.390467	−	0.126870i	0.497669	+	0.867367i	$0.334189\pi$
$198$	−4.43157	+	6.09954i	−0.314938	+	0.433475i
$199$	26.5748			1.88384			0.941919	−	0.335841i	$-0.109020\pi$
$199$	26.5748			1.88384			0.941919	+	0.335841i	$0.109020\pi$
$200$	30.7689	+	3.40660i	2.17569	+	0.240883i
$201$	0.929140			0.0655365
$202$	−22.8825	+	31.4951i	−1.61001	+	2.21599i
$203$	0.672633	−	0.218552i	0.0472096	−	0.0153393i
$204$	−6.97456	−	21.4655i	−0.488317	−	1.50289i
$205$	−1.73816	−	1.94122i	−0.121398	−	0.135581i
$206$	−9.45644	+	29.1039i	−0.658862	+	2.02777i
$207$			3.86039i			0.268315i
$208$	−36.8371	−	11.9691i	−2.55420	−	0.829909i
$209$	−12.9111	+	9.38043i	−0.893076	+	0.648858i
$210$	1.24361	−	5.77197i	0.0858174	−	0.398304i
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.979533	+	0.201285i	$0.0645116\pi$
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.494125	+	0.869391i	$0.335488\pi$
$212$	−33.1063	−	45.5669i	−2.27375	−	3.12954i
$213$	0.830884	+	1.14361i	0.0569312	+	0.0783591i
$214$	13.3403	+	9.69227i	0.911922	+	0.662550i
$215$	12.6483	−	1.29393i	0.862607	−	0.0882454i
$216$	5.00893	−	3.63920i	0.340815	−	0.247616i
$217$	0.841277	+	0.273347i	0.0571096	+	0.0185560i
$218$			5.86348i			0.397125i
$219$	3.49912	−	10.7692i	0.236448	−	0.727713i
$220$	−28.8335	−	6.21238i	−1.94395	−	0.418839i
$221$	−8.90591	−	27.4096i	−0.599076	−	1.84377i
$222$	−3.90410	+	1.26852i	−0.262026	+	0.0851374i
$223$	−16.1321	+	22.2039i	−1.08029	+	1.48689i	−0.221081	+	0.975255i	$0.570958\pi$
$223$	−16.1321	+	22.2039i	−1.08029	+	1.48689i	−0.859205	+	0.511631i	$0.829042\pi$
$224$	−5.15581			−0.344487
$225$	−3.36621	+	3.69711i	−0.224414	+	0.246474i
$226$	−9.82792			−0.653744
$227$	−0.0765066	+	0.105302i	−0.00507792	+	0.00698916i	−0.811548	−	0.584285i	$-0.801375\pi$
$227$	−0.0765066	+	0.105302i	−0.00507792	+	0.00698916i	0.806470	+	0.591274i	$0.201375\pi$
$228$	22.6813	−	7.36962i	1.50211	−	0.488065i
$229$	−0.873064	−	2.68702i	−0.0576937	−	0.177563i	0.918057	−	0.396449i	$-0.129758\pi$
$229$	−0.873064	−	2.68702i	−0.0576937	−	0.177563i	−0.975750	+	0.218886i	$0.929758\pi$
$230$	−20.0362	+	8.85420i	−1.32115	+	0.583829i
$231$	−0.955307	+	2.94013i	−0.0628546	+	0.193447i
$232$			4.20826i			0.276286i
$233$	7.59617	+	2.46815i	0.497642	+	0.161694i	0.547075	−	0.837084i	$-0.315741\pi$
$233$	7.59617	+	2.46815i	0.497642	+	0.161694i	−0.0494328	+	0.998777i	$0.515741\pi$
$234$	11.6390	−	8.45625i	0.760867	−	0.552802i
$235$	−2.97032	−	6.72157i	−0.193763	−	0.438467i
$236$	−11.5366	−	8.38182i	−0.750968	−	0.545610i
$237$	−0.850569	−	1.17071i	−0.0552504	−	0.0760457i
$238$	−7.89012	−	10.8598i	−0.511441	−	0.703938i
$239$	−15.4214	−	11.2043i	−0.997528	−	0.724747i	−0.0359713	−	0.999353i	$-0.511452\pi$
$239$	−15.4214	−	11.2043i	−0.997528	−	0.724747i	−0.961557	+	0.274606i	$0.911452\pi$
$240$	13.2091	+	7.67522i	0.852646	+	0.495433i
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.981162	−	0.193184i	$-0.938118\pi$
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.119467	+	0.992838i	$0.538118\pi$
$242$	−5.24476	−	1.70413i	−0.337146	−	0.109545i
$243$			1.00000i			0.0641500i
$244$	7.43735	−	22.8898i	0.476127	−	1.46537i
$245$	1.34656	+	13.1628i	0.0860287	+	0.840938i
$246$	−0.913803	−	2.81240i	−0.0582619	−	0.179312i
$247$	28.9621	−	9.41036i	1.84281	−	0.598767i
$248$	−3.09373	+	4.25815i	−0.196452	+	0.270393i
$249$	−11.4756			−0.727238
$250$	−26.9095	−	8.99165i	−1.70191	−	0.568682i
$251$	30.2224			1.90762			0.953811	−	0.300408i	$-0.0971228\pi$
$251$	30.2224			1.90762			0.953811	+	0.300408i	$0.0971228\pi$
$252$	2.71542	−	3.73746i	0.171056	−	0.235438i
$253$	10.9079	−	3.54419i	0.685773	−	0.222821i
$254$	9.17007	+	28.2226i	0.575381	+	1.77084i
$255$	1.15685	+	11.3083i	0.0724446	+	0.708152i
$256$	−9.26692	+	28.5207i	−0.579183	+	1.78254i
$257$		−	5.10215i		−	0.318263i	−0.987257	−	0.159132i	$-0.949131\pi$
$257$		−	5.10215i		−	0.318263i	0.987257	−	0.159132i	$-0.0508695\pi$
$258$	13.7230	+	4.45888i	0.854358	+	0.277598i
$259$	−1.36174	+	0.989360i	−0.0846142	+	0.0614758i
$260$	48.6635	+	28.2761i	3.01798	+	1.75361i
$261$	−0.549886	−	0.399516i	−0.0340371	−	0.0247294i
$262$	11.8763	+	16.3464i	0.733722	+	1.00988i
$263$	−3.77088	−	5.19017i	−0.232522	−	0.320040i	0.676772	−	0.736192i	$-0.263378\pi$
$263$	−3.77088	−	5.19017i	−0.232522	−	0.320040i	−0.909295	+	0.416153i	$0.863378\pi$
$264$	−14.8816	−	10.8121i	−0.915898	−	0.665439i
$265$	11.4660	+	25.9465i	0.704351	+	1.59388i
$266$	11.4749	−	8.33704i	0.703574	−	0.511177i
$267$	−8.62823	−	2.80348i	−0.528039	−	0.171570i
$268$			4.12518i			0.251986i
$269$	5.39518	−	16.6047i	0.328950	−	1.01240i	−0.640676	−	0.767811i	$-0.721346\pi$
$269$	5.39518	−	16.6047i	0.328950	−	1.01240i	0.969626	−	0.244592i	$-0.0786542\pi$
$270$	−5.19021	+	2.29360i	−0.315866	+	0.139584i
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	0.950159	−	0.311765i	$-0.100920\pi$
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	−0.951946	+	0.306266i	$0.900920\pi$
$272$	33.0320	−	10.7328i	2.00286	−	0.650769i
$273$	3.46736	−	4.77241i	0.209854	−	0.288840i
$274$	−28.0446			−1.69424
$275$	13.5370	+	6.11727i	0.816313	+	0.368885i
$276$	−17.1393			−1.03166
$277$	10.8157	−	14.8865i	0.649851	−	0.894443i	−0.349242	−	0.937033i	$-0.613561\pi$
$277$	10.8157	−	14.8865i	0.649851	−	0.894443i	0.999093	+	0.0425895i	$0.0135608\pi$
$278$	−29.6129	+	9.62182i	−1.77606	+	0.577078i
$279$	−0.262699	−	0.808503i	−0.0157274	−	0.0484038i
$280$	14.0824	+	3.03415i	0.841583	+	0.181325i
$281$	5.54254	−	17.0582i	0.330640	−	1.01761i	−0.638189	−	0.769879i	$-0.720316\pi$
$281$	5.54254	−	17.0582i	0.330640	−	1.01761i	0.968830	−	0.247727i	$-0.0796837\pi$
$282$		−	8.33982i		−	0.496629i
$283$	−21.1514	−	6.87252i	−1.25732	−	0.408529i	−0.396783	−	0.917912i	$-0.629874\pi$
$283$	−21.1514	−	6.87252i	−1.25732	−	0.408529i	−0.860540	+	0.509383i	$0.829874\pi$
$284$	−5.07740	+	3.68895i	−0.301288	+	0.218899i
$285$	−11.9488	+	1.22237i	−0.707787	+	0.0724072i
$286$	−34.5796	−	25.1236i	−2.04474	−	1.48559i
$287$	−0.712705	−	0.980955i	−0.0420697	−	0.0579039i
$288$	2.91245	+	4.00864i	0.171618	+	0.236212i
$289$	7.15424	+	5.19786i	0.420837	+	0.305756i
$290$	0.812350	−	3.77036i	0.0477028	−	0.221403i
$291$	−4.87779	+	3.54392i	−0.285941	+	0.207749i
$292$	47.8128	+	15.5353i	2.79803	+	0.909136i
$293$		−	18.7316i		−	1.09431i	−0.837031	−	0.547155i	$-0.815711\pi$
$293$		−	18.7316i		−	1.09431i	0.837031	−	0.547155i	$-0.184289\pi$
$294$	−4.64024	+	14.2812i	−0.270624	+	0.832896i
$295$	4.79084	+	5.35054i	0.278934	+	0.311520i
$296$	−3.09491	−	9.52517i	−0.179888	−	0.553639i
$297$	2.82560	−	0.918092i	0.163958	−	0.0532731i
$298$	6.90364	−	9.50204i	0.399917	−	0.550439i
$299$	−21.8854			−1.26566
$300$	−16.4144	−	14.9453i	−0.947684	−	0.862865i
$301$	5.91650			0.341021
$302$	−6.96952	+	9.59272i	−0.401051	+	0.551999i
$303$	14.5900	−	4.74058i	0.838174	−	0.272339i
$304$	11.3407	+	34.9030i	0.650433	+	2.00183i
$305$	−6.08987	+	10.4807i	−0.348705	+	0.600125i
$306$	−3.98649	+	12.2692i	−0.227892	+	0.701381i
$307$			7.03850i			0.401708i	0.979621	+	0.200854i	$0.0643717\pi$
$307$			7.03850i			0.401708i	−0.979621	+	0.200854i	$0.935628\pi$
$308$	−13.0536	−	4.24136i	−0.743796	−	0.241674i
$309$	9.75590	−	7.08808i	0.554994	−	0.403227i
$310$	3.59378	−	3.21785i	0.204113	−	0.182762i
$311$	23.6872	+	17.2098i	1.34318	+	0.975876i	0.999321	+	0.0368546i	$0.0117338\pi$
$311$	23.6872	+	17.2098i	1.34318	+	0.975876i	0.343858	+	0.939022i	$0.388266\pi$
$312$	20.6314	+	28.3967i	1.16803	+	1.60765i
$313$	9.19024	+	12.6493i	0.519463	+	0.714980i	0.985479	−	0.169796i	$-0.0543110\pi$
$313$	9.19024	+	12.6493i	0.519463	+	0.714980i	−0.466016	+	0.884776i	$0.654311\pi$
$314$	−30.7391	−	22.3333i	−1.73471	−	1.26034i
$315$	−1.73339	+	1.55207i	−0.0976656	+	0.0874492i
$316$	5.19769	−	3.77635i	0.292393	−	0.212436i
$317$	5.93596	+	1.92871i	0.333397	+	0.108327i	0.470932	−	0.882170i	$-0.343918\pi$
$317$	5.93596	+	1.92871i	0.333397	+	0.108327i	−0.137535	+	0.990497i	$0.543918\pi$
$318$			32.1933i			1.80531i
$319$	−0.624024	+	1.92055i	−0.0349386	+	0.107530i
$320$	1.22474	−	2.10778i	0.0684649	−	0.117829i
$321$	−2.00795	−	6.17984i	−0.112073	−	0.344925i
$322$	−9.69460	+	3.14997i	−0.540259	+	0.175541i
$323$	−16.0506	+	22.0918i	−0.893080	+	1.22922i
$324$	−4.43979			−0.246655
$325$	−20.9597	−	19.0838i	−1.16264	−	1.05858i
$326$	−30.2268			−1.67411
$327$	1.35812	−	1.86929i	0.0751042	−	0.103372i
$328$	6.86164	−	2.22948i	0.378871	−	0.123103i
$329$	−1.05672	−	3.25225i	−0.0582589	−	0.179302i
$330$	11.2459	+	12.5597i	0.619066	+	0.691389i
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	−0.585862	−	0.810411i	$-0.699244\pi$
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	0.950320	−	0.311275i	$-0.100756\pi$
$332$		−	50.9493i		−	2.79621i
$333$	1.53846	+	0.499875i	0.0843068	+	0.0273930i
$334$	21.7787	−	15.8231i	1.19168	−	0.865804i
$335$	0.437596	−	2.03101i	0.0239084	−	0.110966i
$336$	5.75136	+	4.17861i	0.313763	+	0.227962i
$337$	−20.4262	−	28.1142i	−1.11269	−	1.53148i	−0.817399	−	0.576072i	$-0.804585\pi$
$337$	−20.4262	−	28.1142i	−1.11269	−	1.53148i	−0.295287	−	0.955409i	$-0.595415\pi$
$338$	28.5495	+	39.2950i	1.55289	+	2.13736i
$339$	3.13317	+	2.27638i	0.170170	+	0.123636i
$340$	−50.2064	+	5.13616i	−2.72282	+	0.278547i
$341$	−2.04332	+	1.48456i	−0.110652	+	0.0803935i
$342$	−12.9641	−	4.21229i	−0.701019	−	0.227775i
$343$			13.4409i			0.725740i
$344$	−10.8787	+	33.4812i	−0.586541	+	1.80519i
$345$	8.43844	+	1.81812i	0.454311	+	0.0978844i
$346$	0.982882	+	3.02500i	0.0528401	+	0.162625i
$347$	−27.3182	+	8.87623i	−1.46652	+	0.476501i	−0.930055	−	0.367421i	$-0.880241\pi$
$347$	−27.3182	+	8.87623i	−1.46652	+	0.476501i	−0.536465	+	0.843922i	$0.680241\pi$
$348$	1.77376	−	2.44138i	0.0950837	−	0.130871i
$349$	12.2834			0.657515			0.328758	−	0.944414i	$-0.393370\pi$
$349$	12.2834			0.657515			0.328758	+	0.944414i	$0.393370\pi$
$350$	−12.0313	−	5.43684i	−0.643100	−	0.290611i
$351$	−5.66922			−0.302601
$352$	8.65291	−	11.9097i	0.461201	−	0.634789i
$353$	−25.6575	+	8.33663i	−1.36561	+	0.443714i	−0.897913	−	0.440174i	$-0.854917\pi$
$353$	−25.6575	+	8.33663i	−1.36561	+	0.443714i	−0.467699	+	0.883888i	$0.654917\pi$
$354$	2.51870	+	7.75175i	0.133867	+	0.412001i
$355$	2.89115	−	1.27763i	0.153446	−	0.0678094i
$356$	12.4469	−	38.3075i	0.659682	−	2.03029i
$357$			5.28968i			0.279960i
$358$	50.2275	+	16.3199i	2.65461	+	0.862533i
$359$	13.2875	−	9.65393i	0.701287	−	0.509515i	−0.179064	−	0.983837i	$-0.557307\pi$
$359$	13.2875	−	9.65393i	0.701287	−	0.509515i	0.880351	+	0.474322i	$0.157307\pi$
$360$	−5.59591	−	12.6630i	−0.294930	−	0.667399i
$361$	−7.97178	−	5.79184i	−0.419567	−	0.304834i
$362$	10.3325	+	14.2214i	0.543062	+	0.747460i
$363$	1.27733	+	1.75809i	0.0670423	+	0.0922758i
$364$	21.1885	+	15.3943i	1.11058	+	0.806883i
$365$	−21.8924	−	12.7207i	−1.14590	−	0.665831i
$366$	−11.1293	+	8.08589i	−0.581737	+	0.422656i
$367$	−28.4321	−	9.23816i	−1.48415	−	0.482228i	−0.548797	−	0.835956i	$-0.684914\pi$
$367$	−28.4321	−	9.23816i	−1.48415	−	0.482228i	−0.935349	+	0.353727i	$0.884914\pi$
$368$		−	26.3747i		−	1.37487i
$369$	−0.360095	+	1.10826i	−0.0187458	+	0.0576936i
$370$	0.934153	+	9.13143i	0.0485643	+	0.474720i
$371$	4.07914	+	12.5543i	0.211778	+	0.651787i
$372$	3.58958	−	1.16633i	0.186111	−	0.0604712i
$373$	14.5951	−	20.0885i	0.755706	−	1.04014i	−0.241853	−	0.970313i	$-0.577755\pi$
$373$	14.5951	−	20.0885i	0.755706	−	1.04014i	0.997559	−	0.0698276i	$-0.0222449\pi$
$374$	38.3276			1.98187
$375$	6.49615	+	9.09945i	0.335460	+	0.469894i
$376$	20.3474			1.04934
$377$	2.26494	−	3.11742i	0.116650	−	0.160556i
$378$	−2.51130	+	0.815972i	−0.129167	+	0.0419690i
$379$	−5.99389	−	18.4473i	−0.307885	−	0.947574i	−0.978585	−	0.205845i	$-0.934006\pi$
$379$	−5.99389	−	18.4473i	−0.307885	−	0.947574i	0.670699	−	0.741729i	$-0.265994\pi$
$380$	−5.42708	−	53.0502i	−0.278403	−	2.72142i
$381$	3.61357	−	11.1214i	0.185129	−	0.569768i
$382$			20.7179i			1.06002i
$383$	10.7002	+	3.47670i	0.546754	+	0.177651i	0.569353	−	0.822094i	$-0.307194\pi$
$383$	10.7002	+	3.47670i	0.546754	+	0.177651i	−0.0225986	+	0.999745i	$0.507194\pi$
$384$	10.2555	−	7.45106i	0.523349	−	0.380235i
$385$	5.97694	+	3.47292i	0.304613	+	0.176997i
$386$	−28.6662	−	20.8272i	−1.45907	−	1.06008i
$387$	−3.34215	−	4.60008i	−0.169891	−	0.233835i
$388$	−15.7343	−	21.6564i	−0.798786	−	1.09944i
$389$	12.0558	+	8.75903i	0.611252	+	0.444100i	0.849855	−	0.527017i	$-0.176690\pi$
$389$	12.0558	+	8.75903i	0.611252	+	0.444100i	−0.238603	+	0.971117i	$0.576690\pi$
$390$	−13.0030	−	29.4245i	−0.658430	−	1.48997i
$391$	15.8767	−	11.5351i	0.802920	−	0.583356i
$392$	−34.8431	−	11.3212i	−1.75984	−	0.571807i
$393$		−	7.96210i		−	0.401635i
$394$	4.51886	−	13.9076i	0.227657	−	0.700656i
$395$	−2.95965	+	1.30790i	−0.148916	+	0.0658075i
$396$	4.07613	+	12.5450i	0.204833	+	0.630412i
$397$	−22.9172	+	7.44626i	−1.15018	+	0.373717i	−0.821212	−	0.570623i	$-0.806702\pi$
$397$	−22.9172	+	7.44626i	−1.15018	+	0.373717i	−0.328971	+	0.944340i	$0.606702\pi$
$398$	39.6392	−	54.5586i	1.98693	−	2.73478i
$399$	−5.58930			−0.279815
$400$	22.9984	−	25.2591i	1.14992	−	1.26296i
$401$	13.4580			0.672059			0.336030	−	0.941851i	$-0.390916\pi$
$401$	13.4580			0.672059			0.336030	+	0.941851i	$0.390916\pi$
$402$	1.38591	−	1.90754i	0.0691230	−	0.0951397i
$403$	4.58358	−	1.48930i	0.228325	−	0.0741872i
$404$	21.0472	+	64.7765i	1.04714	+	3.22275i
$405$	2.18591	+	0.470969i	0.108619	+	0.0234026i
$406$	0.554613	−	1.70692i	0.0275250	−	0.0847132i
$407$		−	4.80598i		−	0.238224i
$408$	−29.9341	−	9.72618i	−1.48196	−	0.481518i
$409$	−28.6988	+	20.8509i	−1.41906	+	1.03101i	−0.427140	+	0.904186i	$0.640479\pi$
$409$	−28.6988	+	20.8509i	−1.41906	+	1.03101i	−0.991925	+	0.126825i	$0.959521\pi$
$410$	−6.57801	+	0.672936i	−0.324865	+	0.0332340i
$411$	8.94069	+	6.49579i	0.441012	+	0.320414i
$412$	31.4696	+	43.3141i	1.55039	+	2.13393i
$413$	1.96441	+	2.70379i	0.0966625	+	0.133045i
$414$	7.92545	+	5.75818i	0.389515	+	0.282999i
$415$	−5.40466	+	25.0846i	−0.265304	+	1.23136i
$416$	−22.7259	+	16.5113i	−1.11423	+	0.809534i
$417$	11.6693	+	3.79159i	0.571449	+	0.185675i
$418$			40.4986i			1.98085i
$419$	−4.88617	+	15.0381i	−0.238705	+	0.734659i	0.757903	+	0.652367i	$0.226224\pi$
$419$	−4.88617	+	15.0381i	−0.238705	+	0.734659i	−0.996608	+	0.0822916i	$0.973776\pi$
$420$	−6.89086	−	7.69589i	−0.336240	−	0.375521i
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	0.999840	−	0.0178752i	$-0.00569015\pi$
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	−0.819394	+	0.573230i	$0.805690\pi$
$422$	63.8590	−	20.7491i	3.10861	−	1.01005i
$423$	−1.93170	+	2.65876i	−0.0939225	+	0.129273i
$424$	−78.5447			−3.81447
$425$	25.2637	+	2.79709i	1.22547	+	0.135679i
$426$	3.58721			0.173801
$427$	−3.31550	+	4.56340i	−0.160448	+	0.220838i
$428$	27.4372	−	8.91488i	1.32623	−	0.430917i
$429$	5.20486	+	16.0189i	0.251293	+	0.773401i
$430$	16.2098	−	27.8973i	0.781707	−	1.34532i
$431$	4.52486	−	13.9261i	0.217955	−	0.670797i	−0.780976	−	0.624562i	$-0.785278\pi$
$431$	4.52486	−	13.9261i	0.217955	−	0.670797i	0.998931	−	0.0462350i	$-0.0147223\pi$
$432$		−	6.83213i		−	0.328711i
$433$	4.06380	+	1.32041i	0.195294	+	0.0634547i	0.405031	−	0.914303i	$-0.367261\pi$
$433$	4.06380	+	1.32041i	0.195294	+	0.0634547i	−0.209737	+	0.977758i	$0.567261\pi$
$434$	1.81604	−	1.31943i	0.0871728	−	0.0633347i
$435$	−1.13228	+	1.01384i	−0.0542888	+	0.0486099i
$436$	8.29926	+	6.02976i	0.397462	+	0.288773i
$437$	12.1885	+	16.7760i	0.583055	+	0.802506i
$438$	−16.8900	−	23.2471i	−0.807037	−	1.11079i
$439$	−16.4289	−	11.9363i	−0.784111	−	0.569690i	0.122099	−	0.992518i	$-0.461037\pi$
$439$	−16.4289	−	11.9363i	−0.784111	−	0.569690i	−0.906210	+	0.422828i	$0.861037\pi$
$440$	−30.6430	+	27.4376i	−1.46085	+	1.30803i
$441$	4.78718	−	3.47809i	0.227961	−	0.165623i
$442$	−69.5565	−	22.6003i	−3.30847	−	1.07499i
$443$			19.0543i			0.905299i	0.891689	+	0.452649i	$0.149521\pi$
$443$			19.0543i			0.905299i	−0.891689	+	0.452649i	$0.850479\pi$
$444$	−2.21934	+	6.83041i	−0.105325	+	0.324157i
$445$	−10.1918	+	17.5401i	−0.483136	+	0.831483i
$446$	21.5224	+	66.2391i	1.01912	+	3.13651i
$447$	−4.40180	+	1.43023i	−0.208198	+	0.0676476i
$448$	0.666782	−	0.917747i	0.0315025	−	0.0433595i
$449$	−29.4793			−1.39122			−0.695608	−	0.718421i	$-0.744865\pi$
$449$	−29.4793			−1.39122			−0.695608	+	0.718421i	$0.744865\pi$
$450$	2.56918	+	12.4255i	0.121112	+	0.585745i
$451$	3.46209			0.163023
$452$	−10.1066	+	13.9106i	−0.475376	+	0.654299i
$453$	4.44380	−	1.44388i	0.208788	−	0.0678394i
$454$	0.102070	+	0.314139i	0.00479038	+	0.0147433i
$455$	−8.79903	−	9.82698i	−0.412505	−	0.460696i
$456$	10.2771	−	31.6296i	0.481269	−	1.48119i
$457$		−	28.3015i		−	1.32389i	−0.749553	−	0.661945i	$-0.769731\pi$
$457$		−	28.3015i		−	1.32389i	0.749553	−	0.661945i	$-0.230269\pi$
$458$	−6.81877	−	2.21555i	−0.318620	−	0.103526i
$459$	4.11273	−	2.98807i	0.191966	−	0.139471i
$460$	−8.07208	+	37.4649i	−0.376362	+	1.74681i
$461$	13.3953	+	9.73223i	0.623879	+	0.453275i	0.854274	−	0.519822i	$-0.174002\pi$
$461$	13.3953	+	9.73223i	0.623879	+	0.453275i	−0.230395	+	0.973097i	$0.574002\pi$
$462$	4.61121	+	6.34679i	0.214533	+	0.295279i
$463$	−5.41311	−	7.45051i	−0.251569	−	0.346254i	0.664491	−	0.747296i	$-0.268648\pi$
$463$	−5.41311	−	7.45051i	−0.251569	−	0.346254i	−0.916060	+	0.401042i	$0.868648\pi$
$464$	3.75689	+	2.72954i	0.174409	+	0.126716i
$465$	−1.89104	+	0.193455i	−0.0876947	+	0.00897125i
$466$	16.3977	−	11.9136i	0.759607	−	0.551887i
$467$	−10.0929	−	3.27938i	−0.467043	−	0.151752i	0.0660353	−	0.997817i	$-0.478965\pi$
$467$	−10.0929	−	3.27938i	−0.467043	−	0.151752i	−0.533079	+	0.846066i	$0.678965\pi$
$468$		−	25.1701i		−	1.16349i
$469$	0.298759	−	0.919485i	0.0137954	−	0.0424579i
$470$	−18.2301	−	3.92780i	−0.840890	−	0.181176i
$471$	4.62679	+	14.2398i	0.213191	+	0.656135i
$472$	−18.9126	+	6.14508i	−0.870524	+	0.282850i
$473$	−9.92956	+	13.6669i	−0.456562	+	0.628403i
$474$	−3.67220			−0.168670
$475$	−2.95552	+	26.6947i	−0.135609	+	1.22484i
$476$	−23.4850			−1.07644
$477$	7.45672	−	10.2633i	0.341420	−	0.469924i
$478$	−46.0054	+	14.9480i	−2.10424	+	0.683708i
$479$	−10.3849	−	31.9613i	−0.474496	−	1.46035i	−0.846636	−	0.532172i	$-0.821376\pi$
$479$	−10.3849	−	31.9613i	−0.474496	−	1.46035i	0.372140	−	0.928177i	$-0.378624\pi$
$480$	10.1342	−	4.47840i	0.462560	−	0.204410i
$481$	−2.83390	+	8.72184i	−0.129215	+	0.397682i
$482$			53.5954i			2.44120i
$483$	3.82027	+	1.24128i	0.173828	+	0.0564802i
$484$	−7.80554	+	5.67106i	−0.354797	+	0.257775i
$485$	5.44940	+	12.3315i	0.247444	+	0.559944i
$486$	2.05302	+	1.49161i	0.0931269	+	0.0676607i
$487$	17.1919	+	23.6626i	0.779039	+	1.07226i	0.995387	+	0.0959389i	$0.0305853\pi$
$487$	17.1919	+	23.6626i	0.779039	+	1.07226i	−0.216348	+	0.976316i	$0.569415\pi$
$488$	−19.7279	−	27.1531i	−0.893038	−	1.22916i
$489$	9.63637	+	7.00123i	0.435772	+	0.316607i
$490$	29.0320	+	16.8691i	1.31153	+	0.762070i
$491$	−11.2898	+	8.20251i	−0.509501	+	0.370174i	−0.812634	−	0.582774i	$-0.801967\pi$
$491$	−11.2898	+	8.20251i	−0.509501	+	0.370174i	0.303133	+	0.952948i	$0.401967\pi$
$492$	−4.92043	−	1.59874i	−0.221830	−	0.0720769i
$493$			3.45531i			0.155619i
$494$	23.8804	−	73.4964i	1.07443	−	3.30676i
$495$	−0.676095	−	6.60888i	−0.0303882	−	0.297047i
$496$	1.79479	+	5.52380i	0.0805885	+	0.248026i
$497$	1.39889	−	0.454528i	0.0627490	−	0.0203884i
$498$	−17.1171	+	23.5597i	−0.767036	+	1.05573i
$499$	35.7533			1.60054			0.800268	−	0.599642i	$-0.204690\pi$
$499$	35.7533			1.60054			0.800268	+	0.599642i	$0.204690\pi$
$500$	−40.3996	+	28.8415i	−1.80673	+	1.28983i
$501$	−10.6081			−0.473936
$502$	45.0800	−	62.0472i	2.01202	−	2.76930i
$503$	11.0744	−	3.59828i	0.493782	−	0.160439i	−0.0515323	−	0.998671i	$-0.516410\pi$
$503$	11.0744	−	3.59828i	0.493782	−	0.160439i	0.545314	+	0.838232i	$0.316410\pi$
$504$	−1.99080	−	6.12704i	−0.0886771	−	0.272920i
$505$	−3.49103	−	34.1251i	−0.155349	−	1.51855i
$506$	8.99399	−	27.6807i	0.399832	−	1.23056i
$507$		−	19.1401i		−	0.850040i
$508$	49.3768	+	16.0435i	2.19074	+	0.711815i
$509$	−6.90384	+	5.01594i	−0.306007	+	0.222327i	−0.730181	−	0.683253i	$-0.760564\pi$
$509$	−6.90384	+	5.01594i	−0.306007	+	0.222327i	0.424174	+	0.905581i	$0.360564\pi$
$510$	24.9417	+	14.4925i	1.10444	+	0.641738i
$511$	−9.53214	−	6.92551i	−0.421677	−	0.306366i
$512$	29.8288	+	41.0558i	1.31826	+	1.81443i
$513$	3.15732	+	4.34568i	0.139399	+	0.191867i
$514$	−10.4748	−	7.61040i	−0.462025	−	0.335681i
$515$	−10.8991	−	24.6638i	−0.480274	−	1.08682i
$516$	20.4234	−	14.8384i	0.899089	−	0.653226i
$517$	9.28605	+	3.01722i	0.408400	+	0.132697i
$518$			4.27141i			0.187675i
$519$	0.387316	−	1.19204i	0.0170013	−	0.0523246i
$520$	71.7894	−	31.7244i	3.14817	−	1.39121i
$521$	0.390998	+	1.20337i	0.0171299	+	0.0527205i	0.959256	−	0.282538i	$-0.0911763\pi$
$521$	0.390998	+	1.20337i	0.0171299	+	0.0527205i	−0.942126	+	0.335259i	$0.891176\pi$
$522$	−1.64043	+	0.533007i	−0.0717996	+	0.0233291i
$523$	15.9998	−	22.0218i	0.699621	−	0.962946i	−0.300337	−	0.953833i	$-0.597099\pi$
$523$	15.9998	−	22.0218i	0.699621	−	0.962946i	0.999958	−	0.00911285i	$-0.00290075\pi$
$524$	35.3500			1.54427
$525$	2.57631	+	4.52001i	0.112439	+	0.197269i
$526$	−16.2802			−0.709850
$527$	−2.54019	+	3.49628i	−0.110653	+	0.152300i
$528$	−19.3048	+	6.27252i	−0.840135	+	0.272976i
$529$	2.50224	+	7.70110i	0.108793	+	0.334831i
$530$	70.3715	+	15.1620i	3.05674	+	0.658597i
$531$	0.992522	−	3.05467i	0.0430718	−	0.132561i
$532$		−	24.8153i		−	1.07588i
$533$	−6.28296	−	2.04146i	−0.272145	−	0.0884253i
$534$	−18.6255	+	13.5322i	−0.806005	+	0.585597i
$535$	−14.4542	+	1.47868i	−0.624911	+	0.0639290i
$536$	4.65400	+	3.38133i	0.201022	+	0.146051i
$537$	−12.2326	−	16.8367i	−0.527875	−	0.726557i
$538$	−26.0422	−	35.8440i	−1.12276	−	1.54535i
$539$	−14.2228	−	10.3334i	−0.612618	−	0.445093i
$540$	−2.09100	+	9.70496i	−0.0899824	+	0.417635i
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.973492	−	0.228719i	$-0.926546\pi$
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.0833007	+	0.996524i	$0.526546\pi$
$542$	−0.229728	−	0.0746431i	−0.00986766	−	0.00320620i
$543$		−	6.92706i		−	0.297269i
$544$	7.78385	−	23.9562i	0.333730	−	1.02711i
$545$	−3.44647	−	3.84910i	−0.147630	−	0.164877i
$546$	−4.62592	−	14.2371i	−0.197971	−	0.609293i
$547$	10.8200	−	3.51564i	0.462631	−	0.150318i	−0.0684223	−	0.997656i	$-0.521797\pi$
$547$	10.8200	−	3.51564i	0.462631	−	0.150318i	0.531053	+	0.847339i	$0.321797\pi$
$548$	−28.8399	+	39.6947i	−1.23198	+	1.69568i
$549$	5.42093			0.231360
$550$	32.7508	−	18.6672i	1.39650	−	0.795974i
$551$	−3.65103			−0.155539
$552$	−14.0487	+	19.3364i	−0.597954	+	0.823012i
$553$	−1.43204	+	0.465297i	−0.0608964	+	0.0197864i
$554$	−14.4296	−	44.4096i	−0.613053	−	1.88678i
$555$	1.81724	−	3.12749i	0.0771377	−	0.132755i
$556$	−16.8339	+	51.8093i	−0.713914	+	2.19720i
$557$			45.7532i			1.93862i	0.245833	+	0.969312i	$0.420938\pi$
$557$			45.7532i			1.93862i	−0.245833	+	0.969312i	$0.579062\pi$
$558$	−2.05172	−	0.666643i	−0.0868561	−	0.0282213i
$559$	26.0789	−	18.9474i	1.10302	−	0.801390i
$560$	11.8428	−	10.6039i	0.500448	−	0.448098i
$561$	−12.2189	−	8.87759i	−0.515884	−	0.374812i
$562$	−26.7535	−	36.8231i	−1.12853	−	1.55329i
$563$	−5.25650	−	7.23495i	−0.221535	−	0.304917i	0.683754	−	0.729712i	$-0.260346\pi$
$563$	−5.25650	−	7.23495i	−0.221535	−	0.304917i	−0.905289	+	0.424796i	$0.860346\pi$
$564$	−11.8043	−	8.57633i	−0.497051	−	0.361129i
$565$	6.45158	−	5.77671i	0.271420	−	0.243028i
$566$	−45.6591	+	33.1733i	−1.91919	+	1.39438i
$567$	0.989608	+	0.321543i	0.0415596	+	0.0135035i
$568$			8.75203i			0.367227i
$569$	0.707365	−	2.17704i	0.0296543	−	0.0912665i	−0.935134	−	0.354294i	$-0.884721\pi$
$569$	0.707365	−	2.17704i	0.0296543	−	0.0912665i	0.964788	+	0.263028i	$0.0847211\pi$
$570$	−15.3134	+	26.3545i	−0.641407	+	1.10387i
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	−0.926774	−	0.375618i	$-0.877430\pi$
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	0.528993	−	0.848626i	$-0.322570\pi$
$572$	−71.1206	+	23.1085i	−2.97370	+	0.966214i
$573$	4.79877	−	6.60494i	0.200471	−	0.275925i
$574$	−3.07700			−0.128431
$575$	7.94849	−	17.5894i	0.331475	−	0.733528i
$576$	−1.09021			−0.0454252
$577$	−3.87484	+	5.33326i	−0.161312	+	0.222027i	−0.882020	−	0.471212i	$-0.843817\pi$
$577$	−3.87484	+	5.33326i	−0.161312	+	0.222027i	0.720708	+	0.693238i	$0.243817\pi$
$578$	21.3426	−	6.93464i	0.887736	−	0.288443i
$579$	4.31479	+	13.2795i	0.179316	+	0.551879i
$580$	−4.50123	−	5.02709i	−0.186904	−	0.208739i
$581$	−3.68991	+	11.3564i	−0.153083	+	0.471141i
$582$			15.3004i			0.634220i
$583$	−35.8459	−	11.6470i	−1.48458	−	0.482371i
$584$	56.7180	−	41.2081i	2.34701	−	1.70520i
$585$	−2.67003	+	12.3924i	−0.110392	+	0.512362i
$586$	−38.4563	−	27.9401i	−1.58861	−	1.15420i
$587$	3.25499	+	4.48010i	0.134348	+	0.184914i	0.870890	−	0.491477i	$-0.163543\pi$
$587$	3.25499	+	4.48010i	0.134348	+	0.184914i	−0.736543	+	0.676391i	$0.763543\pi$
$588$	15.4420	+	21.2541i	0.636817	+	0.876503i
$589$	−3.69431	−	2.68408i	−0.152222	−	0.110595i
$590$	18.1308	−	1.85480i	0.746434	−	0.0763609i
$591$	−4.66196	+	3.38711i	−0.191767	+	0.139327i
$592$	−10.5109	−	3.41521i	−0.431997	−	0.140364i
$593$			1.88122i			0.0772524i	0.999254	+	0.0386262i	$0.0122982\pi$
$593$			1.88122i			0.0772524i	−0.999254	+	0.0386262i	$0.987702\pi$
$594$	2.32982	−	7.17044i	0.0955935	−	0.294207i
$595$	11.5627	+	2.49128i	0.474026	+	0.102132i
$596$	−6.34992	−	19.5430i	−0.260103	−	0.800514i
$597$	−25.2741	+	8.21206i	−1.03440	+	0.336097i
$598$	−32.6444	+	44.9311i	−1.33493	+	1.83737i
$599$	−17.8272			−0.728400			−0.364200	−	0.931321i	$-0.618658\pi$
$599$	−17.8272			−0.728400			−0.364200	+	0.931321i	$0.618658\pi$
$600$	−30.3157	+	6.26824i	−1.23763	+	0.255900i
$601$	33.0994			1.35015			0.675077	−	0.737747i	$-0.264110\pi$
$601$	33.0994			1.35015			0.675077	+	0.737747i	$0.264110\pi$
$602$	8.82509	−	12.1467i	0.359684	−	0.495062i
$603$	−0.883665	+	0.287120i	−0.0359856	+	0.0116924i
$604$	6.41052	+	19.7295i	0.260840	+	0.802784i
$605$	4.44460	−	1.96411i	0.180699	−	0.0798525i
$606$	12.0300	−	37.0247i	0.488687	−	1.50402i
$607$		−	23.4603i		−	0.952226i	−0.879384	−	0.476113i	$-0.842045\pi$
$607$		−	23.4603i		−	0.952226i	0.879384	−	0.476113i	$-0.157955\pi$
$608$	25.3132	+	8.22475i	1.02658	+	0.333558i
$609$	−0.572176	+	0.415710i	−0.0231857	+	0.0168454i
$610$	12.4335	+	28.1358i	0.503416	+	1.13918i
$611$	−15.0731	−	10.9512i	−0.609792	−	0.443039i
$612$	13.2664	+	18.2596i	0.536263	+	0.738102i
$613$	27.7600	+	38.2083i	1.12121	+	1.54322i	0.803769	+	0.594942i	$0.202825\pi$
$613$	27.7600	+	38.2083i	1.12121	+	1.54322i	0.317445	+	0.948277i	$0.397175\pi$
$614$	14.4502	+	10.4987i	0.583162	+	0.423692i
$615$	2.25295	+	1.30909i	0.0908479	+	0.0527875i
$616$	−15.4848	+	11.2504i	−0.623901	+	0.453290i
$617$	15.4735	+	5.02765i	0.622941	+	0.202406i	0.603446	−	0.797404i	$-0.293794\pi$
$617$	15.4735	+	5.02765i	0.622941	+	0.202406i	0.0194952	+	0.999810i	$0.493794\pi$
$618$		−	30.6017i		−	1.23098i
$619$	−10.9577	+	33.7244i	−0.440428	+	1.35550i	0.446993	+	0.894537i	$0.352495\pi$
$619$	−10.9577	+	33.7244i	−0.440428	+	1.35550i	−0.887421	+	0.460960i	$0.847505\pi$
$620$	−0.858898	−	8.39580i	−0.0344942	−	0.337183i
$621$	−1.19292	−	3.67145i	−0.0478704	−	0.147330i
$622$	70.6640	−	22.9601i	2.83337	−	0.920617i
$623$	−5.54869	+	7.63712i	−0.222304	+	0.305975i
$624$	38.7329			1.55056
$625$	22.9500	−	9.91443i	0.918001	−	0.396577i
$626$	39.6775			1.58583
$627$	9.38043	−	12.9111i	0.374618	−	0.515618i
$628$	−63.2217	+	20.5420i	−2.52282	+	0.819714i
$629$	−2.54117	−	7.82091i	−0.101323	−	0.311840i
$630$	0.600892	+	5.87377i	0.0239401	+	0.234017i
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	0.593599	+	0.804761i	$0.297706\pi$
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	−0.953258	+	0.302156i	$0.902294\pi$
$632$		−	8.95939i		−	0.356385i
$633$	−25.1644	−	8.17641i	−1.00020	−	0.324983i
$634$	12.8138	−	9.30978i	0.508901	−	0.369738i
$635$	−22.6085	−	13.1368i	−0.897192	−	0.521317i
$636$	45.5669	+	33.1063i	1.80684	+	1.31275i
$637$	19.7181	+	27.1396i	0.781259	+	1.07531i
$638$	3.01213	+	4.14583i	0.119251	+	0.164135i
$639$	−1.14361	−	0.830884i	−0.0452406	−	0.0328692i
$640$	−11.4573	−	25.9268i	−0.452889	−	1.02485i
$641$	12.7145	−	9.23764i	0.502194	−	0.364865i	−0.307661	−	0.951496i	$-0.599546\pi$
$641$	12.7145	−	9.23764i	0.502194	−	0.364865i	0.809854	+	0.586631i	$0.199546\pi$
$642$	−15.6824	−	5.09553i	−0.618936	−	0.201104i
$643$		−	8.08055i		−	0.318666i	−0.987225	−	0.159333i	$-0.949066\pi$
$643$		−	8.08055i		−	0.318666i	0.987225	−	0.159333i	$-0.0509343\pi$
$644$	−5.51102	+	16.9612i	−0.217165	+	0.668364i
$645$	−11.6294	+	5.13914i	−0.457907	+	0.202353i
$646$	21.4137	+	65.9045i	0.842510	+	2.59298i
$647$	10.4800	−	3.40516i	0.412011	−	0.133870i	−0.0956751	−	0.995413i	$-0.530501\pi$
$647$	10.4800	−	3.40516i	0.412011	−	0.133870i	0.507686	+	0.861542i	$0.330501\pi$
$648$	−3.63920	+	5.00893i	−0.142961	+	0.196769i
$649$	−9.54248			−0.374575
$650$	−70.4431	+	14.5652i	−2.76301	+	0.571295i
$651$	−0.884570			−0.0346691
$652$	−31.0840	+	42.7834i	−1.21734	+	1.67553i
$653$	29.5646	−	9.60613i	1.15695	−	0.375917i	0.333195	−	0.942858i	$-0.391873\pi$
$653$	29.5646	−	9.60613i	1.15695	−	0.375917i	0.823758	+	0.566941i	$0.191873\pi$
$654$	−1.81191	−	5.57650i	−0.0708515	−	0.218058i
$655$	−17.4044	−	3.74990i	−0.680047	−	0.146521i
$656$	2.46021	−	7.57176i	0.0960552	−	0.295628i
$657$			11.3234i			0.441767i
$658$	−8.25315	−	2.68161i	−0.321741	−	0.104540i
$659$	26.2325	−	19.0590i	1.02187	−	0.742435i	0.0552080	−	0.998475i	$-0.482418\pi$
$659$	26.2325	−	19.0590i	1.02187	−	0.742435i	0.966666	+	0.256040i	$0.0824178\pi$
$660$	29.3420	−	3.00172i	1.14214	−	0.116842i
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	0.314490	−	0.949261i	$-0.398166\pi$
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	−0.805618	+	0.592436i	$0.798166\pi$
$662$	−32.0061	−	44.0527i	−1.24395	−	1.71216i
$663$	16.9400	+	23.3160i	0.657897	+	0.905517i
$664$	−57.4806	−	41.7621i	−2.23068	−	1.62068i
$665$	−2.63239	+	12.2177i	−0.102080	+	0.473782i
$666$	3.32102	−	2.41287i	0.128687	−	0.0934966i
$667$	2.49547	+	0.810827i	0.0966249	+	0.0313953i
$668$		−	47.0978i		−	1.82227i
$669$	8.48115	−	26.1023i	0.327900	−	1.00917i
$670$	−3.51699	−	3.92787i	−0.135873	−	0.151747i
$671$	−4.97691	−	15.3173i	−0.192131	−	0.591320i
$672$	4.90346	−	1.59323i	0.189155	−	0.0614602i
$673$	18.2373	−	25.1014i	0.702995	−	0.967589i	−0.296925	−	0.954901i	$-0.595961\pi$
$673$	18.2373	−	25.1014i	0.702995	−	0.967589i	0.999919	−	0.0126883i	$-0.00403893\pi$
$674$	−88.1870			−3.39684
$675$	2.05899	−	4.55638i	0.0792505	−	0.175375i
$676$	84.9778			3.26838
$677$	13.5716	−	18.6796i	0.521597	−	0.717917i	−0.464224	−	0.885718i	$-0.653667\pi$
$677$	13.5716	−	18.6796i	0.521597	−	0.717917i	0.985821	+	0.167801i	$0.0536666\pi$
$678$	9.34691	−	3.03700i	0.358966	−	0.116635i
$679$	1.93868	+	5.96663i	0.0743995	+	0.228978i
$680$	−35.3586	+	60.8524i	−1.35594	+	2.33358i
$681$	0.0402219	−	0.123790i	0.00154131	−	0.00474365i
$682$			6.40936i			0.245427i
$683$	−39.3301	−	12.7791i	−1.50492	−	0.488979i	−0.563474	−	0.826134i	$-0.690536\pi$
$683$	−39.3301	−	12.7791i	−1.50492	−	0.488979i	−0.941449	+	0.337154i	$0.890536\pi$
$684$	−19.2939	+	14.0178i	−0.737721	+	0.535986i
$685$	18.4100	−	16.4842i	0.703409	−	0.629829i
$686$	27.5944	+	20.0485i	1.05356	+	0.765457i
$687$	1.66067	+	2.28571i	0.0633584	+	0.0872053i
$688$	22.8340	+	31.4283i	0.870539	+	1.19819i
$689$	58.1849	+	42.2738i	2.21667	+	1.61050i
$690$	16.3195	−	14.6124i	0.621272	−	0.556284i
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	−0.654429	−	0.756123i	$-0.727091\pi$
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	0.516886	+	0.856054i	$0.327091\pi$
$692$	5.29239	+	1.71960i	0.201186	+	0.0653694i
$693$		−	3.09144i		−	0.117434i
$694$	−22.5250	+	69.3248i	−0.855037	+	2.63153i
$695$	13.7840	−	23.7223i	0.522855	−	0.899839i
$696$	−1.30042	−	4.00229i	−0.0492924	−	0.151707i
$697$	5.63395	−	1.83058i	0.213401	−	0.0693382i
$698$	18.3220	−	25.2181i	0.693498	−	0.954518i
$699$	−7.98709			−0.302099
$700$	−20.0679	+	11.4382i	−0.758495	+	0.432325i
$701$	−25.2265			−0.952791			−0.476396	−	0.879231i	$-0.658057\pi$
$701$	−25.2265			−0.952791			−0.476396	+	0.879231i	$0.658057\pi$
$702$	−8.45625	+	11.6390i	−0.319161	+	0.439287i
$703$	8.26391	−	2.68511i	0.311679	−	0.101271i
$704$	1.00091	+	3.08048i	0.0377231	+	0.116100i
$705$	4.90202	+	5.47471i	0.184621	+	0.206189i
$706$	−21.1556	+	65.1104i	−0.796203	+	2.45046i
$707$		−	15.9627i		−	0.600339i
$708$	13.5621	+	4.40658i	0.509694	+	0.165610i
$709$	1.26199	−	0.916889i	0.0473950	−	0.0344345i	−0.563836	−	0.825887i	$-0.690675\pi$
$709$	1.26199	−	0.916889i	0.0473950	−	0.0344345i	0.611231	+	0.791453i	$0.290675\pi$
$710$	1.68947	−	7.84131i	0.0634045	−	0.294279i
$711$	1.17071	+	0.850569i	0.0439050	+	0.0318988i
$712$	−33.0158	−	45.4423i	−1.23732	−	1.70302i
$713$	1.92897	+	2.65500i	0.0722404	+	0.0994304i
$714$	10.8598	+	7.89012i	0.406419	+	0.295280i
$715$	37.4672	−	3.83293i	1.40119	−	0.143343i
$716$	74.7514	−	54.3100i	2.79359	−	2.02966i
$717$	18.1290	+	5.89045i	0.677038	+	0.219983i
$718$		−	41.6794i		−	1.55546i
$719$	−8.94304	+	27.5238i	−0.333519	+	1.02647i	0.633928	+	0.773392i	$0.281442\pi$
$719$	−8.94304	+	27.5238i	−0.333519	+	1.02647i	−0.967447	+	0.253074i	$0.918558\pi$
$720$	−14.9344	−	3.21772i	−0.556572	−	0.119917i
$721$	−3.87748	−	11.9336i	−0.144405	−	0.444432i
$722$	−23.7815	+	7.72709i	−0.885057	+	0.287572i
$723$	12.4140	−	17.0864i	0.461680	−	0.635448i
$724$	30.7547			1.14299
$725$	1.68289	+	2.95255i	0.0625009	+	0.109655i
$726$	5.51466			0.204668
$727$	−21.7242	+	29.9008i	−0.805707	+	1.10896i	0.186265	+	0.982500i	$0.440362\pi$
$727$	−21.7242	+	29.9008i	−0.805707	+	1.10896i	−0.991972	+	0.126461i	$0.959638\pi$
$728$	34.7355	−	11.2863i	1.28739	−	0.418297i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−58.7707	+	25.9713i	−2.17520	+	0.961243i
$731$	−8.93229	+	27.4907i	−0.330372	+	1.01678i
$732$			24.0678i			0.889570i
$733$	3.95793	+	1.28601i	0.146189	+	0.0474998i	0.381198	−	0.924494i	$-0.375512\pi$
$733$	3.95793	+	1.28601i	0.146189	+	0.0474998i	−0.235008	+	0.971993i	$0.575512\pi$
$734$	−61.3757	+	44.5921i	−2.26542	+	1.64592i
$735$	−5.34817	−	12.1024i	−0.197270	−	0.446404i
$736$	−15.4749	−	11.2432i	−0.570413	−	0.414429i
$737$	1.62257	+	2.23328i	0.0597682	+	0.0822638i
$738$	1.73816	+	2.39237i	0.0639824	+	0.0880642i
$739$	15.3371	+	11.1431i	0.564184	+	0.409904i	0.832988	−	0.553291i	$-0.186628\pi$
$739$	15.3371	+	11.1431i	0.564184	+	0.409904i	−0.268804	+	0.963195i	$0.586628\pi$
$740$	13.8854	+	8.06818i	0.510438	+	0.296592i
$741$	−24.6366	+	17.8996i	−0.905050	+	0.657557i
$742$	31.8587	+	10.3515i	1.16957	+	0.380016i
$743$			11.7060i			0.429452i	0.976674	+	0.214726i	$0.0688859\pi$
$743$			11.7060i			0.429452i	−0.976674	+	0.214726i	$0.931114\pi$
$744$	1.62647	−	5.00575i	0.0596292	−	0.183520i
$745$	1.05324	+	10.2955i	0.0385877	+	0.377198i
$746$	−19.4718	−	59.9281i	−0.712915	−	2.19413i
$747$	10.9140	−	3.54616i	0.399321	−	0.129747i
$748$	39.4146	−	54.2495i	1.44114	−	1.98356i
$749$	−6.76126			−0.247051
$750$	28.3711	+	0.236065i	1.03596	+	0.00861988i
$751$	−4.95672			−0.180873			−0.0904367	−	0.995902i	$-0.528826\pi$
$751$	−4.95672			−0.180873			−0.0904367	+	0.995902i	$0.528826\pi$
$752$	13.1976	−	18.1650i	0.481268	−	0.662408i
$753$	−28.7432	+	9.33924i	−1.04746	+	0.340341i
$754$	−3.02174	−	9.29995i	−0.110045	−	0.338684i
$755$	−1.06329	−	10.3938i	−0.0386971	−	0.378268i
$756$	−1.42758	+	4.39365i	−0.0519207	+	0.159795i
$757$			18.6020i			0.676101i	0.941128	+	0.338051i	$0.109768\pi$
$757$			18.6020i			0.676101i	−0.941128	+	0.338051i	$0.890232\pi$
$758$	−46.8132	−	15.2105i	−1.70033	−	0.552472i
$759$	−9.27881	+	6.74145i	−0.336799	+	0.244699i
$760$	−64.2993	−	37.3614i	−2.33238	−	1.35524i
$761$	9.18925	+	6.67638i	0.333110	+	0.242019i	0.741749	−	0.670677i	$-0.233997\pi$
$761$	9.18925	+	6.67638i	0.333110	+	0.242019i	−0.408639	+	0.912696i	$0.633997\pi$
$762$	−17.4425	−	24.0075i	−0.631875	−	0.869702i
$763$	−1.41317	−	1.94507i	−0.0511603	−	0.0704161i
$764$	29.3245	+	21.3055i	1.06092	+	0.770806i
$765$	−4.59468	−	10.3973i	−0.166121	−	0.375916i
$766$	23.0982	−	16.7818i	0.834572	−	0.606352i
$767$	17.3176	+	5.62682i	0.625302	+	0.203173i
$768$		−	29.9884i		−	1.08211i
$769$	−2.24803	+	6.91872i	−0.0810660	+	0.249495i	−0.983373	−	0.181599i	$-0.941873\pi$
$769$	−2.24803	+	6.91872i	−0.0810660	+	0.249495i	0.902307	+	0.431095i	$0.141873\pi$
$770$	16.0452	−	7.09054i	0.578230	−	0.255525i
$771$	1.57665	+	4.85243i	0.0567817	+	0.174756i
$772$	−58.9584	+	19.1567i	−2.12196	+	0.689466i
$773$	−5.47985	+	7.54237i	−0.197097	+	0.271280i	−0.896114	−	0.443825i	$-0.853621\pi$
$773$	−5.47985	+	7.54237i	−0.197097	+	0.271280i	0.699017	+	0.715105i	$0.253621\pi$
$774$	−14.4292			−0.518648
$775$	−0.467745	+	4.22474i	−0.0168019	+	0.151757i
$776$	−37.3296			−1.34005
$777$	0.989360	−	1.36174i	0.0354931	−	0.0488520i
$778$	35.9649	−	11.6857i	1.28941	−	0.418953i
$779$	1.93427	+	5.95307i	0.0693024	+	0.213291i
$780$	−55.0196	−	11.8544i	−1.97002	−	0.424454i
$781$	−1.29780	+	3.99421i	−0.0464389	+	0.142924i
$782$		−	49.8011i		−	1.78088i
$783$	0.646430	+	0.210038i	0.0231015	+	0.00750614i
$784$	−32.7067	+	23.7628i	−1.16810	+	0.848671i
$785$	33.3060	−	3.40723i	1.18874	−	0.121609i
$786$	−16.3464	−	11.8763i	−0.583055	−	0.423615i
$787$	8.73787	+	12.0266i	0.311471	+	0.428704i	0.935839	−	0.352427i	$-0.114643\pi$
$787$	8.73787	+	12.0266i	0.311471	+	0.428704i	−0.624368	+	0.781130i	$0.714643\pi$
$788$	−15.0381	−	20.6981i	−0.535708	−	0.737339i
$789$	5.19017	+	3.77088i	0.184775	+	0.134247i
$790$	−1.72949	+	8.02709i	−0.0615326	+	0.285591i
$791$	3.26017	−	2.36865i	0.115918	−	0.0842196i
$792$	17.4943	+	5.68426i	0.621634	+	0.201981i
$793$			30.7324i			1.09134i
$794$	−18.8962	+	58.1565i	−0.670600	+	2.06390i
$795$	−18.9227	−	21.1334i	−0.671120	−	0.749524i
$796$	−36.4598	−	112.212i	−1.29228	−	3.97724i
$797$	−9.10680	+	2.95898i	−0.322580	+	0.104812i	−0.465831	−	0.884874i	$-0.654244\pi$
$797$	−9.10680	+	2.95898i	−0.322580	+	0.104812i	0.143251	+	0.989686i	$0.454244\pi$
$798$	−8.33704	+	11.4749i	−0.295128	+	0.406209i
$799$	16.7068			0.591044
$800$	−5.01646	−	24.2616i	−0.177359	−	0.857777i
$801$	9.07225			0.320552
$802$	20.0740	−	27.6295i	0.708838	−	0.975632i
$803$	31.9953	−	10.3959i	1.12909	−	0.366863i
$804$	−1.27475	−	3.92328i	−0.0449570	−	0.138364i
$805$	4.51255	−	7.76615i	0.159047	−	0.273721i
$806$	3.77935	−	11.6316i	0.133122	−	0.409707i
$807$			17.4592i			0.614592i
$808$	90.3323	+	29.3508i	3.17788	+	1.03256i
$809$	33.2859	−	24.1836i	1.17027	−	0.850250i	0.179228	−	0.983808i	$-0.442640\pi$
$809$	33.2859	−	24.1836i	1.17027	−	0.850250i	0.991041	+	0.133557i	$0.0426400\pi$
$810$	4.22742	−	3.78521i	0.148537	−	0.132999i
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.236868	−	0.971542i	$-0.576121\pi$
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.997187	+	0.0749479i	$0.976121\pi$
$812$	−1.84566	−	2.54034i	−0.0647701	−	0.0891484i
$813$	0.0559488	+	0.0770069i	0.00196221	+	0.00270075i
$814$	−9.86679	−	7.16864i	−0.345831	−	0.251261i
$815$	19.8425	−	17.7668i	0.695052	−	0.622345i
$816$	−28.0987	+	20.4149i	−0.983651	+	0.714665i
$817$	−29.0479	−	9.43823i	−1.01626	−	0.330202i
$818$			90.0206i			3.14750i
$819$	−1.82290	+	5.61031i	−0.0636973	+	0.196040i
$820$	−5.81207	+	10.0026i	−0.202966	+	0.349307i
$821$	5.39595	+	16.6070i	0.188320	+	0.579589i	0.999990	−	0.00452746i	$-0.00144114\pi$
$821$	5.39595	+	16.6070i	0.188320	+	0.579589i	−0.811670	+	0.584116i	$0.801441\pi$
$822$	26.6720	−	8.66625i	0.930292	−	0.302270i
$823$	−1.30756	+	1.79970i	−0.0455787	+	0.0627337i	−0.831198	−	0.555976i	$-0.812344\pi$
$823$	−1.30756	+	1.79970i	−0.0455787	+	0.0627337i	0.785619	+	0.618710i	$0.212344\pi$
$824$	74.6616			2.60096
$825$	−14.7648	−	1.63470i	−0.514045	−	0.0569129i
$826$	8.48106			0.295094
$827$	−18.4888	+	25.4476i	−0.642918	+	0.884900i	−0.998767	−	0.0496432i	$-0.984192\pi$
$827$	−18.4888	+	25.4476i	−0.642918	+	0.884900i	0.355849	+	0.934543i	$0.384192\pi$
$828$	16.3004	−	5.29633i	0.566479	−	0.184060i
$829$	−16.4690	−	50.6862i	−0.571990	−	1.76041i	−0.646206	−	0.763163i	$-0.723645\pi$
$829$	−16.4690	−	50.6862i	−0.571990	−	1.76041i	0.0742155	−	0.997242i	$-0.476355\pi$
$830$	43.4376	+	48.5123i	1.50774	+	1.68389i
$831$	−5.68614	+	17.5001i	−0.197250	+	0.607073i
$832$		−	6.18061i		−	0.214274i
$833$	−28.6089	−	9.29560i	−0.991240	−	0.322073i
$834$	25.1903	−	18.3018i	0.872267	−	0.633739i
$835$	−4.99609	+	23.1883i	−0.172897	+	0.802466i
$836$	57.3223	+	41.6471i	1.98253	+	1.44040i
$837$	0.499683	+	0.687754i	0.0172716	+	0.0237723i
$838$	23.5853	+	32.4623i	0.814739	+	1.12139i
$839$	−6.77415	−	4.92171i	−0.233870	−	0.169916i	0.464678	−	0.885480i	$-0.346170\pi$
$839$	−6.77415	−	4.92171i	−0.233870	−	0.169916i	−0.698548	+	0.715563i	$0.746170\pi$
$840$	−14.3307	+	1.46605i	−0.494458	+	0.0505835i
$841$	23.0877	−	16.7742i	0.796129	−	0.578421i
$842$	28.9166	+	9.39558i	0.996532	+	0.323793i
$843$			17.9361i			0.617750i
$844$	36.3015	−	111.725i	1.24955	−	3.84572i
$845$	−41.8384	−	9.01438i	−1.43928	−	0.310104i
$846$	2.57715	+	7.93164i	0.0886041	+	0.272695i
$847$	2.15054	−	0.698751i	0.0738933	−	0.0240094i
$848$	−50.9453	+	70.1202i	−1.74947	+	2.40794i
$849$	22.2399			0.763273
$850$	43.4260	−	47.6947i	1.48950	−	1.63592i
$851$	−6.24467			−0.214064
$852$	3.68895	−	5.07740i	0.126381	−	0.173949i
$853$	1.16381	−	0.378146i	0.0398482	−	0.0129475i	−0.289025	−	0.957322i	$-0.593331\pi$
$853$	1.16381	−	0.378146i	0.0398482	−	0.0129475i	0.328873	+	0.944374i	$0.393331\pi$
$854$	4.42332	+	13.6136i	0.151363	+	0.465847i
$855$	10.9863	−	4.85493i	0.375722	−	0.166035i
$856$	12.4320	−	38.2618i	0.424917	−	1.30776i
$857$			14.3684i			0.490816i	0.969420	+	0.245408i	$0.0789219\pi$
$857$			14.3684i			0.490816i	−0.969420	+	0.245408i	$0.921078\pi$
$858$	40.6508	+	13.2082i	1.38780	+	0.450922i
$859$	−8.34015	+	6.05947i	−0.284562	+	0.206747i	−0.720905	−	0.693034i	$-0.756274\pi$
$859$	−8.34015	+	6.05947i	−0.284562	+	0.206747i	0.436343	+	0.899781i	$0.356274\pi$
$860$	−22.8167	−	51.6320i	−0.778043	−	1.76064i
$861$	0.980955	+	0.712705i	0.0334308	+	0.0242889i
$862$	−21.8413	−	30.0619i	−0.743916	−	1.02391i
$863$	−17.7937	−	24.4909i	−0.605703	−	0.833679i	0.390512	−	0.920598i	$-0.372298\pi$
$863$	−17.7937	−	24.4909i	−0.605703	−	0.833679i	−0.996215	+	0.0869190i	$0.972298\pi$
$864$	−4.00864	−	2.91245i	−0.136377	−	0.0990835i
$865$	−2.42327	−	1.40805i	−0.0823935	−	0.0478751i
$866$	8.77241	−	6.37353i	0.298099	−	0.216581i
$867$	−8.41031	−	2.73268i	−0.285629	−	0.0928065i
$868$		−	3.92730i		−	0.133301i
$869$	1.32855	−	4.08885i	0.0450679	−	0.138705i
$870$	0.392513	+	3.83685i	0.0133075	+	0.130081i
$871$	−1.62775	−	5.00969i	−0.0551541	−	0.169747i
$872$	13.6055	−	4.42068i	0.460739	−	0.149703i
$873$	3.54392	−	4.87779i	0.119944	−	0.165088i
$874$	52.6220			1.77996
$875$	11.0937	−	3.50278i	0.375035	−	0.118416i
$876$	−50.2734			−1.69858
$877$	−18.0065	+	24.7839i	−0.608037	+	0.836892i	−0.996414	−	0.0846091i	$-0.973036\pi$
$877$	−18.0065	+	24.7839i	−0.608037	+	0.836892i	0.388377	+	0.921501i	$0.373036\pi$
$878$	−49.0111	+	15.9247i	−1.65404	+	0.537431i
$879$	5.78837	+	17.8148i	0.195237	+	0.600877i
$880$	4.61917	+	45.1527i	0.155712	+	1.52210i
$881$	4.70359	−	14.4762i	0.158468	−	0.487714i	−0.840028	−	0.542543i	$-0.817461\pi$
$881$	4.70359	−	14.4762i	0.158468	−	0.487714i	0.998496	+	0.0548293i	$0.0174615\pi$
$882$		−	15.0161i		−	0.505620i
$883$	38.2310	+	12.4220i	1.28658	+	0.418034i	0.870892	−	0.491475i	$-0.163542\pi$
$883$	38.2310	+	12.4220i	1.28658	+	0.418034i	0.415684	+	0.909509i	$0.363542\pi$
$884$	−103.518	+	75.2102i	−3.48169	+	2.52959i
$885$	−6.20977	−	3.60821i	−0.208739	−	0.121289i
$886$	39.1189	+	28.4216i	1.31423	+	0.954842i
$887$	−18.7169	−	25.7617i	−0.628453	−	0.864992i	0.369481	−	0.929238i	$-0.379536\pi$
$887$	−18.7169	−	25.7617i	−0.628453	−	0.864992i	−0.997934	+	0.0642465i	$0.979536\pi$
$888$	5.88688	+	8.10259i	0.197551	+	0.271905i
$889$	−9.84394	−	7.15204i	−0.330155	−	0.239872i
$890$	20.8082	+	47.0869i	0.697491	+	1.57836i
$891$	−2.40360	+	1.74631i	−0.0805235	+	0.0585037i
$892$	115.889	+	37.6545i	3.88024	+	1.26077i
$893$			17.6531i			0.590739i
$894$	−3.62946	+	11.1703i	−0.121387	+	0.373591i
$895$	−42.5646	+	18.8097i	−1.42278	+	0.628739i
$896$	−4.07604	−	12.5448i	−0.136171	−	0.419091i
$897$	20.8142	−	6.76296i	0.694967	−	0.225809i
$898$	−43.9716	+	60.5217i	−1.46735	+	2.01964i
$899$	−0.577817			−0.0192713
$900$	20.2293	+	9.14147i	0.674311	+	0.304716i
$901$	−64.4914			−2.14852
$902$	5.16407	−	7.10774i	0.171945	−	0.236662i
$903$	−5.62692	+	1.82830i	−0.187252	+	0.0608419i
$904$	7.40962	+	22.8045i	0.246440	+	0.758465i
$905$	−15.1419	−	3.26243i	−0.503334	−	0.108447i
$906$	3.66409	−	11.2769i	0.121731	−	0.374651i
$907$			28.8507i			0.957970i	0.877823	+	0.478985i	$0.158995\pi$
$907$			28.8507i			0.957970i	−0.877823	+	0.478985i	$0.841005\pi$
$908$	0.549602	+	0.178577i	0.0182392	+	0.00592627i
$909$	−12.4110	+	9.01712i	−0.411647	+	0.299079i
$910$	−33.2997	+	3.40659i	−1.10387	+	0.112927i
$911$	−39.1370	−	28.4347i	−1.29667	−	0.942084i	−0.296750	−	0.954955i	$-0.595903\pi$
$911$	−39.1370	−	28.4347i	−1.29667	−	0.942084i	−0.999917	+	0.0128711i	$0.995903\pi$
$912$	−21.5713	−	29.6903i	−0.714296	−	0.983143i
$913$	−20.0400	−	27.5827i	−0.663228	−	0.912855i
$914$	−58.1036	−	42.2148i	−1.92190	−	1.39634i
$915$	2.55309	−	11.8496i	0.0844025	−	0.391737i
$916$	−10.1481	+	7.37301i	−0.335302	+	0.243611i
$917$	−7.87936	−	2.56016i	−0.260199	−	0.0845439i
$918$		−	12.9006i		−	0.425782i
$919$	2.58963	−	7.97006i	0.0854240	−	0.262908i	−0.899216	−	0.437505i	$-0.855862\pi$
$919$	2.58963	−	7.97006i	0.0854240	−	0.262908i	0.984640	+	0.174597i	$0.0558622\pi$
$920$	35.6511	+	39.8161i	1.17538	+	1.31270i
$921$	−2.17501	−	6.69401i	−0.0716692	−	0.220575i
$922$	39.9609	−	12.9841i	1.31604	−	0.427608i
$923$	4.71046	−	6.48340i	0.155047	−	0.213404i
$924$	13.7253			0.451530
$925$	−5.98055	−	5.44528i	−0.196639	−	0.179040i
$926$	−23.3703			−0.767995
$927$	−7.08808	+	9.75590i	−0.232803	+	0.320426i
$928$	3.20303	−	1.04073i	0.105145	−	0.0341636i
$929$	−4.42283	−	13.6121i	−0.145108	−	0.446597i	0.851917	−	0.523677i	$-0.175440\pi$
$929$	−4.42283	−	13.6121i	−0.145108	−	0.446597i	−0.997025	+	0.0770801i	$0.975440\pi$
$930$	−2.42352	+	4.17090i	−0.0794702	+	0.136769i
$931$	9.82212	−	30.2294i	0.321907	−	0.990728i
$932$		−	35.4610i		−	1.16156i
$933$	−27.8460	−	9.04771i	−0.911637	−	0.296209i
$934$	−21.7873	+	15.8294i	−0.712901	+	0.517953i
$935$	−25.1603	+	22.5284i	−0.822830	+	0.736758i
$936$	−28.3967	−	20.6314i	−0.928177	−	0.674360i
$937$	−12.8869	−	17.7372i	−0.420996	−	0.579451i	0.544862	−	0.838526i	$-0.316582\pi$
$937$	−12.8869	−	17.7372i	−0.420996	−	0.579451i	−0.965857	+	0.259075i	$0.916582\pi$
$938$	−1.44209	−	1.98487i	−0.0470859	−	0.0648082i
$939$	−12.6493	−	9.19024i	−0.412794	−	0.299912i
$940$	−24.3065	+	21.7639i	−0.792792	+	0.709861i
$941$	−18.1167	+	13.1625i	−0.590586	+	0.429086i	−0.842525	−	0.538657i	$-0.818932\pi$
$941$	−18.1167	+	13.1625i	−0.590586	+	0.429086i	0.251939	+	0.967743i	$0.418932\pi$
$942$	36.1360	+	11.7413i	1.17737	+	0.382552i
$943$		−	4.49847i		−	0.146490i
$944$	−6.78104	+	20.8699i	−0.220704	+	0.679257i
$945$	1.16894	−	2.01175i	0.0380256	−	0.0654424i
$946$	13.2474	+	40.7712i	0.430709	+	1.32559i
$947$	41.4316	−	13.4619i	1.34635	−	0.437454i	0.454884	−	0.890550i	$-0.349681\pi$
$947$	41.4316	−	13.4619i	1.34635	−	0.437454i	0.891462	+	0.453096i	$0.149681\pi$
$948$	−3.77635	+	5.19769i	−0.122650	+	0.168813i
$949$	−64.1947			−2.08385
$950$	50.3963	+	45.8857i	1.63507	+	1.48873i
$951$	−6.24144			−0.202393
$952$	−19.2502	+	26.4957i	−0.623903	+	0.858729i
$953$	−2.25561	+	0.732893i	−0.0730664	+	0.0237407i	−0.345322	−	0.938484i	$-0.612230\pi$
$953$	−2.25561	+	0.732893i	−0.0730664	+	0.0237407i	0.272256	+	0.962225i	$0.412230\pi$
$954$	−9.94827	−	30.6176i	−0.322087	−	0.991282i
$955$	−12.1777	−	13.6004i	−0.394061	−	0.440098i
$956$	−26.1524	+	80.4887i	−0.845828	+	2.60319i
$957$		−	2.01938i		−	0.0652774i
$958$	−81.1073	−	26.3534i	−2.62046	−	0.851439i
$959$	9.30310	−	6.75910i	0.300413	−	0.218263i
$960$	−0.513453	+	2.38309i	−0.0165716	+	0.0769138i
$961$	24.4949	+	17.7966i	0.790157	+	0.574082i
$962$	13.6791	+	18.8276i	0.441031	+	0.607027i
$963$	3.81935	+	5.25689i	0.123077	+	0.169401i
$964$	75.8598	+	55.1154i	2.44328	+	1.77515i
$965$	31.0600	−	3.17746i	0.999856	−	0.102286i
$966$	8.24672	−	5.99159i	0.265334	−	0.192776i
$967$	18.8174	+	6.11413i	0.605125	+	0.196617i	0.595525	−	0.803337i	$-0.296944\pi$
$967$	18.8174	+	6.11413i	0.605125	+	0.196617i	0.00960036	+	0.999954i	$0.496944\pi$
$968$			13.4546i			0.432447i
$969$	8.43831	−	25.9704i	0.271077	−	0.834291i
$970$	33.4452	+	7.20599i	1.07386	+	0.231371i
$971$	15.2604	+	46.9668i	0.489731	+	1.50724i	0.825010	+	0.565118i	$0.191169\pi$
$971$	15.2604	+	46.9668i	0.489731	+	1.50724i	−0.335279	+	0.942119i	$0.608831\pi$
$972$	4.22249	−	1.37197i	0.135436	−	0.0440059i
$973$	7.50438	−	10.3289i	0.240579	−	0.331129i
$974$	74.2234			2.37827
$975$	25.8311	+	11.6729i	0.827257	+	0.373831i
$976$	−37.0365			−1.18551
$977$	28.0757	−	38.6429i	0.898221	−	1.23630i	−0.0728110	−	0.997346i	$-0.523197\pi$
$977$	28.0757	−	38.6429i	0.898221	−	1.23630i	0.971032	−	0.238949i	$-0.0768030\pi$
$978$	28.7474	−	9.34058i	0.919239	−	0.298679i
$979$	−8.32916	−	25.6345i	−0.266201	−	0.819283i
$980$	53.7321	−	23.7447i	1.71641	−	0.758498i
$981$	−0.714006	+	2.19749i	−0.0227965	+	0.0701603i
$982$			35.4131i			1.13008i
$983$	49.3867	+	16.0467i	1.57519	+	0.511810i	0.960812	−	0.277201i	$-0.0894067\pi$
$983$	49.3867	+	16.0467i	1.57519	+	0.511810i	0.614379	+	0.789011i	$0.289407\pi$
$984$	−5.83686	+	4.24073i	−0.186072	+	0.135190i
$985$	5.20827	+	11.7858i	0.165949	+	0.375528i
$986$	7.09383	+	5.15397i	0.225914	+	0.164136i
$987$	2.01000	+	2.76653i	0.0639791	+	0.0880596i
$988$	−79.4703	−	109.381i	−2.52829	−	3.47989i
$989$	17.7581	+	12.9020i	0.564674	+	0.410260i
$990$	−14.5766	−	8.46982i	−0.463276	−	0.269188i
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	−0.357083	−	0.934073i	$-0.616229\pi$
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	0.778011	+	0.628250i	$0.216229\pi$
$992$	4.00610	+	1.30166i	0.127194	+	0.0413277i
$993$			21.4575i			0.680933i
$994$	1.15344	−	3.54994i	0.0365850	−	0.112597i
$995$	6.04747	+	59.1145i	0.191718	+	1.87406i
$996$	15.7442	+	48.4557i	0.498874	+	1.53538i
$997$	−21.1625	+	6.87610i	−0.670222	+	0.217768i	−0.624309	−	0.781177i	$-0.714620\pi$
$997$	−21.1625	+	6.87610i	−0.670222	+	0.217768i	−0.0459126	+	0.998945i	$0.514620\pi$
$998$	53.3299	−	73.4022i	1.68813	−	2.32351i
$999$	−1.61763			−0.0511795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.i.a.34.4	✓	16
3.2	odd	2		225.2.m.b.109.1		16
5.2	odd	4		375.2.g.e.76.4		16
5.3	odd	4		375.2.g.d.76.1		16
5.4	even	2		375.2.i.c.49.1		16
25.2	odd	20		375.2.g.e.301.4		16
25.6	even	5		1875.2.b.h.1249.16		16
25.8	odd	20		1875.2.a.p.1.8		8
25.11	even	5		375.2.i.c.199.1		16
25.14	even	10	inner	75.2.i.a.64.4	yes	16
25.17	odd	20		1875.2.a.m.1.1		8
25.19	even	10		1875.2.b.h.1249.1		16
25.23	odd	20		375.2.g.d.301.1		16
75.8	even	20		5625.2.a.t.1.1		8
75.14	odd	10		225.2.m.b.64.1		16
75.17	even	20		5625.2.a.bd.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.4	✓	16	1.1	even	1	trivial
75.2.i.a.64.4	yes	16	25.14	even	10	inner
225.2.m.b.64.1		16	75.14	odd	10
225.2.m.b.109.1		16	3.2	odd	2
375.2.g.d.76.1		16	5.3	odd	4
375.2.g.d.301.1		16	25.23	odd	20
375.2.g.e.76.4		16	5.2	odd	4
375.2.g.e.301.4		16	25.2	odd	20
375.2.i.c.49.1		16	5.4	even	2
375.2.i.c.199.1		16	25.11	even	5
1875.2.a.m.1.1		8	25.17	odd	20
1875.2.a.p.1.8		8	25.8	odd	20
1875.2.b.h.1249.1		16	25.19	even	10
1875.2.b.h.1249.16		16	25.6	even	5
5625.2.a.t.1.1		8	75.8	even	20
5625.2.a.bd.1.8		8	75.17	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.49161 - 2.05302i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(0.227564 + 2.22446i) q^{5} +(-0.784184 + 2.41347i) q^{6} +1.04054i q^{7} +(-5.88835 - 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.49161 - 2.05302i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(0.227564 + 2.22446i) q^{5} +(-0.784184 + 2.41347i) q^{6} +1.04054i q^{7} +(-5.88835 - 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +(4.90630 + 2.85082i) q^{10} +(-2.40360 - 1.74631i) q^{11} +(2.60964 + 3.59186i) q^{12} +(3.33228 + 4.58650i) q^{13} +(2.13624 + 1.55207i) q^{14} +(-0.903822 - 2.04526i) q^{15} +(-5.52731 + 4.01583i) q^{16} +(-4.83480 - 1.57092i) q^{17} -2.53767i q^{18} +(1.65990 - 5.10866i) q^{19} +(9.08054 - 4.01278i) q^{20} +(-0.321543 - 0.989608i) q^{21} +(-7.17044 + 2.32982i) q^{22} +(-2.26908 + 3.12312i) q^{23} +6.19138 q^{24} +(-4.89643 + 1.01241i) q^{25} +14.3866 q^{26} +(-0.587785 + 0.809017i) q^{27} +(4.39365 - 1.42758i) q^{28} +(-0.210038 - 0.646430i) q^{29} +(-5.54712 - 1.19517i) q^{30} +(0.262699 - 0.808503i) q^{31} +4.95495i q^{32} +(2.82560 + 0.918092i) q^{33} +(-10.4368 + 7.58275i) q^{34} +(-2.31463 + 0.236789i) q^{35} +(-3.59186 - 2.60964i) q^{36} +(0.950818 + 1.30869i) q^{37} +(-8.01226 - 11.0279i) q^{38} +(-4.58650 - 3.33228i) q^{39} +(2.91595 - 13.5338i) q^{40} +(-0.942740 + 0.684941i) q^{41} +(-2.51130 - 0.815972i) q^{42} -5.68601i q^{43} +(-4.07613 + 12.5450i) q^{44} +(1.49161 + 1.66587i) q^{45} +(3.02725 + 9.31693i) q^{46} +(-3.12556 + 1.01555i) q^{47} +(4.01583 - 5.52731i) q^{48} +5.91729 q^{49} +(-5.22504 + 11.5626i) q^{50} +5.08361 q^{51} +(14.7946 - 20.3631i) q^{52} +(12.0652 - 3.92023i) q^{53} +(0.784184 + 2.41347i) q^{54} +(3.33763 - 5.74410i) q^{55} +(1.99080 - 6.12704i) q^{56} +5.37156i q^{57} +(-1.64043 - 0.533007i) q^{58} +(2.59846 - 1.88789i) q^{59} +(-7.39609 + 6.62242i) q^{60} +(4.38562 + 3.18634i) q^{61} +(-1.26803 - 1.74530i) q^{62} +(0.611611 + 0.841811i) q^{63} +(-0.881995 - 0.640807i) q^{64} +(-9.44416 + 8.45625i) q^{65} +(6.09954 - 4.43157i) q^{66} +(-0.883665 - 0.287120i) q^{67} +22.5702i q^{68} +(1.19292 - 3.67145i) q^{69} +(-2.96638 + 5.10517i) q^{70} +(-0.436821 - 1.34440i) q^{71} +(-5.88835 + 1.91324i) q^{72} +(-6.65571 + 9.16080i) q^{73} +4.10501 q^{74} +(4.34393 - 2.47594i) q^{75} -23.8486 q^{76} +(1.81710 - 2.50103i) q^{77} +(-13.6825 + 4.44571i) q^{78} +(0.447171 + 1.37625i) q^{79} +(-10.1909 - 11.3814i) q^{80} +(0.309017 - 0.951057i) q^{81} +2.95713i q^{82} +(10.9140 + 3.54616i) q^{83} +(-3.73746 + 2.71542i) q^{84} +(2.39422 - 11.1123i) q^{85} +(-11.6735 - 8.48129i) q^{86} +(0.399516 + 0.549886i) q^{87} +(10.8121 + 14.8816i) q^{88} +(7.33961 + 5.33254i) q^{89} +(5.64495 - 0.577483i) q^{90} +(-4.77241 + 3.46736i) q^{91} +(16.3004 + 5.29633i) q^{92} +0.850111i q^{93} +(-2.57715 + 7.93164i) q^{94} +(11.7417 + 2.52984i) q^{95} +(-1.53117 - 4.71244i) q^{96} +(5.73419 - 1.86315i) q^{97} +(8.82627 - 12.1483i) q^{98} -2.97101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

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