LMFDB - Embedded newform 190.2.f.b.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(37,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("190.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.f (of order $4$, degree $2$, 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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 24x^{14} + 212x^{12} + 880x^{10} + 1858x^{8} + 1960x^{6} + 892x^{4} + 96x^{2} + 1 $ x^16 + 24x^14 + 212x^12 + 880x^10 + 1858x^8 + 1960x^6 + 892x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.7
Root			$1.52212i$ of defining polynomial
Character	$\chi$	$=$	190.37
Dual form			190.2.f.b.113.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +(-1.72906 + 1.41787i) q^{5} +1.83575 q^{6} +(2.12620 + 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +(-1.72906 + 1.41787i) q^{5} +1.83575 q^{6} +(2.12620 + 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +(-0.220040 + 2.22522i) q^{10} +5.08815 q^{11} +(1.29807 - 1.29807i) q^{12} +(-3.71401 - 3.71401i) q^{13} +3.00690 q^{14} +(-4.08493 - 0.403937i) q^{15} -1.00000 q^{16} +(-1.18498 - 1.18498i) q^{17} +(0.261605 + 0.261605i) q^{18} +(-4.18883 - 1.20571i) q^{19} +(1.41787 + 1.72906i) q^{20} +5.51991i q^{21} +(3.59786 - 3.59786i) q^{22} +(-5.59198 + 5.59198i) q^{23} -1.83575i q^{24} +(0.979271 - 4.90317i) q^{25} -5.25240 q^{26} +(3.41397 - 3.41397i) q^{27} +(2.12620 - 2.12620i) q^{28} +0.861689 q^{29} +(-3.17411 + 2.60286i) q^{30} -7.04657i q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.60477 + 6.60477i) q^{33} -1.67582 q^{34} +(-6.69100 - 0.661638i) q^{35} +0.369965 q^{36} +(-3.98104 + 3.98104i) q^{37} +(-3.81451 + 2.10938i) q^{38} -9.64208i q^{39} +(2.22522 + 0.220040i) q^{40} +2.38835i q^{41} +(3.90317 + 3.90317i) q^{42} +(4.14693 - 4.14693i) q^{43} -5.08815i q^{44} +(-0.524563 - 0.639690i) q^{45} +7.90826i q^{46} +(4.04146 + 4.04146i) q^{47} +(-1.29807 - 1.29807i) q^{48} +2.04146i q^{49} +(-2.77461 - 4.15951i) q^{50} -3.07638i q^{51} +(-3.71401 + 3.71401i) q^{52} +(6.57175 + 6.57175i) q^{53} -4.82808i q^{54} +(-8.79769 + 7.21435i) q^{55} -3.00690i q^{56} +(-3.87229 - 7.00248i) q^{57} +(0.609306 - 0.609306i) q^{58} -9.90431 q^{59} +(-0.403937 + 4.08493i) q^{60} -4.21338 q^{61} +(-4.98268 - 4.98268i) q^{62} +(-0.786620 + 0.786620i) q^{63} +1.00000i q^{64} +(11.6877 + 1.15574i) q^{65} +9.34055 q^{66} +(-4.48345 + 4.48345i) q^{67} +(-1.18498 + 1.18498i) q^{68} -14.5176 q^{69} +(-5.19910 + 4.26341i) q^{70} -6.16296i q^{71} +(0.261605 - 0.261605i) q^{72} +(-3.06742 + 3.06742i) q^{73} +5.63004i q^{74} +(7.63581 - 5.09348i) q^{75} +(-1.20571 + 4.18883i) q^{76} +(10.8184 + 10.8184i) q^{77} +(-6.81798 - 6.81798i) q^{78} +14.1483 q^{79} +(1.72906 - 1.41787i) q^{80} +9.97302 q^{81} +(1.68882 + 1.68882i) q^{82} +(0.835746 - 0.835746i) q^{83} +5.51991 q^{84} +(3.72906 + 0.368746i) q^{85} -5.86464i q^{86} +(1.11853 + 1.11853i) q^{87} +(-3.59786 - 3.59786i) q^{88} +4.55806 q^{89} +(-0.823252 - 0.0814070i) q^{90} -15.7935i q^{91} +(5.59198 + 5.59198i) q^{92} +(9.14693 - 9.14693i) q^{93} +5.71548 q^{94} +(8.95226 - 3.85448i) q^{95} -1.83575 q^{96} +(3.92722 - 3.92722i) q^{97} +(1.44353 + 1.44353i) q^{98} +1.88244i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 16 q^{16} - 32 q^{17} + 8 q^{20} - 8 q^{23} + 32 q^{25} - 32 q^{26} + 8 q^{28} + 16 q^{30} - 24 q^{35} + 32 q^{36} + 8 q^{38} - 32 q^{42} + 24 q^{43} + 8 q^{45} + 32 q^{47} - 56 q^{55} - 48 q^{57} - 64 q^{61} - 8 q^{62} - 16 q^{63} + 16 q^{66} - 32 q^{68} + 16 q^{73} - 16 q^{76} + 72 q^{77} + 16 q^{81} + 40 q^{82} - 16 q^{83} + 32 q^{85} - 8 q^{87} + 8 q^{92} + 104 q^{93} + 24 q^{95}+O(q^{100}) $ 16 * q + 8 * q^7 - 16 * q^16 - 32 * q^17 + 8 * q^20 - 8 * q^23 + 32 * q^25 - 32 * q^26 + 8 * q^28 + 16 * q^30 - 24 * q^35 + 32 * q^36 + 8 * q^38 - 32 * q^42 + 24 * q^43 + 8 * q^45 + 32 * q^47 - 56 * q^55 - 48 * q^57 - 64 * q^61 - 8 * q^62 - 16 * q^63 + 16 * q^66 - 32 * q^68 + 16 * q^73 - 16 * q^76 + 72 * q^77 + 16 * q^81 + 40 * q^82 - 16 * q^83 + 32 * q^85 - 8 * q^87 + 8 * q^92 + 104 * q^93 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.29807	+	1.29807i	0.749440	+	0.749440i	0.974374	−	0.224934i	$-0.0722166\pi$
$3$	1.29807	+	1.29807i	0.749440	+	0.749440i	−0.224934	+	0.974374i	$0.572217\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.72906	+	1.41787i	−0.773257	+	0.634092i
$5$	−1.72906	+	1.41787i	−0.773257	+	0.634092i
$6$	1.83575			0.749440
$7$	2.12620	+	2.12620i	0.803628	+	0.803628i	0.983661	−	0.180032i	$-0.0576203\pi$
$7$	2.12620	+	2.12620i	0.803628	+	0.803628i	−0.180032	+	0.983661i	$0.557620\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			0.369965i			0.123322i
$10$	−0.220040	+	2.22522i	−0.0695826	+	0.703675i
$11$	5.08815			1.53413			0.767067	−	0.641567i	$-0.221715\pi$
$11$	5.08815			1.53413			0.767067	+	0.641567i	$0.221715\pi$
$12$	1.29807	−	1.29807i	0.374720	−	0.374720i
$13$	−3.71401	−	3.71401i	−1.03008	−	1.03008i	−0.999533	−	0.0305473i	$-0.990275\pi$
$13$	−3.71401	−	3.71401i	−1.03008	−	1.03008i	−0.0305473	−	0.999533i	$-0.509725\pi$
$14$	3.00690			0.803628
$15$	−4.08493	−	0.403937i	−1.05472	−	0.104296i
$16$	−1.00000			−0.250000
$17$	−1.18498	−	1.18498i	−0.287400	−	0.287400i	0.548651	−	0.836051i	$-0.315142\pi$
$17$	−1.18498	−	1.18498i	−0.287400	−	0.287400i	−0.836051	+	0.548651i	$0.815142\pi$
$18$	0.261605	+	0.261605i	0.0616608	+	0.0616608i
$19$	−4.18883	−	1.20571i	−0.960983	−	0.276609i
$19$	−4.18883	−	1.20571i	−0.960983	−	0.276609i
$20$	1.41787	+	1.72906i	0.317046	+	0.386629i
$21$			5.51991i			1.20454i
$22$	3.59786	−	3.59786i	0.767067	−	0.767067i
$23$	−5.59198	+	5.59198i	−1.16601	+	1.16601i	−0.182872	+	0.983137i	$0.558539\pi$
$23$	−5.59198	+	5.59198i	−1.16601	+	1.16601i	−0.983137	+	0.182872i	$0.941461\pi$
$24$		−	1.83575i		−	0.374720i
$25$	0.979271	−	4.90317i	0.195854	−	0.980633i
$26$	−5.25240			−1.03008
$27$	3.41397	−	3.41397i	0.657018	−	0.657018i
$28$	2.12620	−	2.12620i	0.401814	−	0.401814i
$29$	0.861689			0.160012			0.0800058	−	0.996794i	$-0.474506\pi$
$29$	0.861689			0.160012			0.0800058	+	0.996794i	$0.474506\pi$
$30$	−3.17411	+	2.60286i	−0.579510	+	0.475214i
$31$		−	7.04657i		−	1.26560i	−0.774315	−	0.632800i	$-0.781905\pi$
$31$		−	7.04657i		−	1.26560i	0.774315	−	0.632800i	$-0.218095\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	6.60477	+	6.60477i	1.14974	+	1.14974i
$34$	−1.67582			−0.287400
$35$	−6.69100	−	0.661638i	−1.13099	−	0.111837i
$36$	0.369965			0.0616608
$37$	−3.98104	+	3.98104i	−0.654478	+	0.654478i	−0.954068	−	0.299590i	$-0.903150\pi$
$37$	−3.98104	+	3.98104i	−0.654478	+	0.654478i	0.299590	+	0.954068i	$0.403150\pi$
$38$	−3.81451	+	2.10938i	−0.618796	+	0.342187i
$39$		−	9.64208i		−	1.54397i
$40$	2.22522	+	0.220040i	0.351837	+	0.0347913i
$41$			2.38835i			0.372997i	0.982455	+	0.186499i	$0.0597140\pi$
$41$			2.38835i			0.372997i	−0.982455	+	0.186499i	$0.940286\pi$
$42$	3.90317	+	3.90317i	0.602271	+	0.602271i
$43$	4.14693	−	4.14693i	0.632401	−	0.632401i	−0.316269	−	0.948670i	$-0.602430\pi$
$43$	4.14693	−	4.14693i	0.632401	−	0.632401i	0.948670	+	0.316269i	$0.102430\pi$
$44$		−	5.08815i		−	0.767067i
$45$	−0.524563	−	0.639690i	−0.0781973	−	0.0953594i
$46$			7.90826i			1.16601i
$47$	4.04146	+	4.04146i	0.589507	+	0.589507i	0.937498	−	0.347991i	$-0.113136\pi$
$47$	4.04146	+	4.04146i	0.589507	+	0.589507i	−0.347991	+	0.937498i	$0.613136\pi$
$48$	−1.29807	−	1.29807i	−0.187360	−	0.187360i
$49$			2.04146i			0.291637i
$50$	−2.77461	−	4.15951i	−0.392389	−	0.588244i
$51$		−	3.07638i		−	0.430779i
$52$	−3.71401	+	3.71401i	−0.515040	+	0.515040i
$53$	6.57175	+	6.57175i	0.902699	+	0.902699i	0.995669	−	0.0929696i	$-0.0296359\pi$
$53$	6.57175	+	6.57175i	0.902699	+	0.902699i	−0.0929696	+	0.995669i	$0.529636\pi$
$54$		−	4.82808i		−	0.657018i
$55$	−8.79769	+	7.21435i	−1.18628	+	0.972783i
$56$		−	3.00690i		−	0.401814i
$57$	−3.87229	−	7.00248i	−0.512897	−	0.927501i
$58$	0.609306	−	0.609306i	0.0800058	−	0.0800058i
$59$	−9.90431			−1.28943			−0.644716	−	0.764422i	$-0.723024\pi$
$59$	−9.90431			−1.28943			−0.644716	+	0.764422i	$0.723024\pi$
$60$	−0.403937	+	4.08493i	−0.0521480	+	0.527362i
$61$	−4.21338			−0.539468			−0.269734	−	0.962935i	$-0.586936\pi$
$61$	−4.21338			−0.539468			−0.269734	+	0.962935i	$0.586936\pi$
$62$	−4.98268	−	4.98268i	−0.632800	−	0.632800i
$63$	−0.786620	+	0.786620i	−0.0991048	+	0.0991048i
$64$			1.00000i			0.125000i
$65$	11.6877	+	1.15574i	1.44968	+	0.143351i
$66$	9.34055			1.14974
$67$	−4.48345	+	4.48345i	−0.547740	+	0.547740i	−0.925787	−	0.378047i	$-0.876596\pi$
$67$	−4.48345	+	4.48345i	−0.547740	+	0.547740i	0.378047	+	0.925787i	$0.376596\pi$
$68$	−1.18498	+	1.18498i	−0.143700	+	0.143700i
$69$	−14.5176			−1.74771
$70$	−5.19910	+	4.26341i	−0.621412	+	0.509574i
$71$		−	6.16296i		−	0.731409i	−0.930731	−	0.365705i	$-0.880828\pi$
$71$		−	6.16296i		−	0.731409i	0.930731	−	0.365705i	$-0.119172\pi$
$72$	0.261605	−	0.261605i	0.0308304	−	0.0308304i
$73$	−3.06742	+	3.06742i	−0.359014	+	0.359014i	−0.863449	−	0.504435i	$-0.831701\pi$
$73$	−3.06742	+	3.06742i	−0.359014	+	0.359014i	0.504435	+	0.863449i	$0.331701\pi$
$74$			5.63004i			0.654478i
$75$	7.63581	−	5.09348i	0.881707	−	0.588145i
$76$	−1.20571	+	4.18883i	−0.138305	+	0.480491i
$77$	10.8184	+	10.8184i	1.23287	+	1.23287i
$78$	−6.81798	−	6.81798i	−0.771984	−	0.771984i
$79$	14.1483			1.59181			0.795905	−	0.605421i	$-0.206995\pi$
$79$	14.1483			1.59181			0.795905	+	0.605421i	$0.206995\pi$
$80$	1.72906	−	1.41787i	0.193314	−	0.158523i
$81$	9.97302			1.10811
$82$	1.68882	+	1.68882i	0.186499	+	0.186499i
$83$	0.835746	−	0.835746i	0.0917351	−	0.0917351i	−0.659750	−	0.751485i	$-0.729338\pi$
$83$	0.835746	−	0.835746i	0.0917351	−	0.0917351i	0.751485	+	0.659750i	$0.229338\pi$
$84$	5.51991			0.602271
$85$	3.72906	+	0.368746i	0.404473	+	0.0399962i
$86$		−	5.86464i		−	0.632401i
$87$	1.11853	+	1.11853i	0.119919	+	0.119919i
$88$	−3.59786	−	3.59786i	−0.383534	−	0.383534i
$89$	4.55806			0.483153			0.241577	−	0.970382i	$-0.422335\pi$
$89$	4.55806			0.483153			0.241577	+	0.970382i	$0.422335\pi$
$90$	−0.823252	−	0.0814070i	−0.0867783	−	0.00858105i
$91$		−	15.7935i		−	1.65560i
$92$	5.59198	+	5.59198i	0.583004	+	0.583004i
$93$	9.14693	−	9.14693i	0.948492	−	0.948492i
$94$	5.71548			0.589507
$95$	8.95226	−	3.85448i	0.918483	−	0.395461i
$96$	−1.83575			−0.187360
$97$	3.92722	−	3.92722i	0.398749	−	0.398749i	−0.479043	−	0.877792i	$-0.659016\pi$
$97$	3.92722	−	3.92722i	0.398749	−	0.398749i	0.877792	+	0.479043i	$0.159016\pi$
$98$	1.44353	+	1.44353i	0.145818	+	0.145818i
$99$			1.88244i			0.189192i
$100$	−4.90317	−	0.979271i	−0.490317	−	0.0979271i
$101$	−5.75197			−0.572343			−0.286171	−	0.958178i	$-0.592383\pi$
$101$	−5.75197			−0.572343			−0.286171	+	0.958178i	$0.592383\pi$
$102$	−2.17533	−	2.17533i	−0.215390	−	0.215390i
$103$	2.55770	+	2.55770i	0.252018	+	0.252018i	0.821797	−	0.569780i	$-0.192971\pi$
$103$	2.55770	+	2.55770i	0.252018	+	0.252018i	−0.569780	+	0.821797i	$0.692971\pi$
$104$			5.25240i			0.515040i
$105$	−7.82653	−	9.54423i	−0.763791	−	0.931422i
$106$	9.29386			0.902699
$107$	−9.14167	+	9.14167i	−0.883758	+	0.883758i	−0.993914	−	0.110156i	$-0.964865\pi$
$107$	−9.14167	+	9.14167i	−0.883758	+	0.883758i	0.110156	+	0.993914i	$0.464865\pi$
$108$	−3.41397	−	3.41397i	−0.328509	−	0.328509i
$109$	−3.52386			−0.337524			−0.168762	−	0.985657i	$-0.553977\pi$
$109$	−3.52386			−0.337524			−0.168762	+	0.985657i	$0.553977\pi$
$110$	−1.11959	+	11.3222i	−0.106749	+	1.07953i
$111$	−10.3353			−0.980985
$112$	−2.12620	−	2.12620i	−0.200907	−	0.200907i
$113$	13.1281	+	13.1281i	1.23499	+	1.23499i	0.962024	+	0.272966i	$0.0880048\pi$
$113$	13.1281	+	13.1281i	1.23499	+	1.23499i	0.272966	+	0.962024i	$0.411995\pi$
$114$	−7.68962	−	2.21338i	−0.720199	−	0.207302i
$115$	1.74013	−	17.5976i	0.162268	−	1.64098i
$116$		−	0.861689i		−	0.0800058i
$117$	1.37405	−	1.37405i	0.127031	−	0.127031i
$118$	−7.00340	+	7.00340i	−0.644716	+	0.644716i
$119$		−	5.03902i		−	0.461926i
$120$	2.60286	+	3.17411i	0.237607	+	0.289755i
$121$	14.8892			1.35357
$122$	−2.97931	+	2.97931i	−0.269734	+	0.269734i
$123$	−3.10024	+	3.10024i	−0.279539	+	0.279539i
$124$	−7.04657			−0.632800
$125$	5.25885	+	9.86633i	0.470366	+	0.882471i
$126$			1.11245i			0.0991048i
$127$	0.600084	−	0.600084i	0.0532489	−	0.0532489i	−0.679981	−	0.733230i	$-0.738012\pi$
$127$	0.600084	−	0.600084i	0.0532489	−	0.0532489i	0.733230	+	0.679981i	$0.238012\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	10.7660			0.947893
$130$	9.08170	−	7.44724i	0.796518	−	0.653166i
$131$	−2.73993			−0.239389			−0.119694	−	0.992811i	$-0.538191\pi$
$131$	−2.73993			−0.239389			−0.119694	+	0.992811i	$0.538191\pi$
$132$	6.60477	−	6.60477i	0.574871	−	0.574871i
$133$	−6.34270	−	11.4699i	−0.549982	−	0.994564i
$134$			6.34055i			0.547740i
$135$	−1.06237	+	10.7435i	−0.0914341	+	0.924654i
$136$			1.67582i			0.143700i
$137$	6.89793	+	6.89793i	0.589330	+	0.589330i	0.937450	−	0.348120i	$-0.113180\pi$
$137$	6.89793	+	6.89793i	0.589330	+	0.589330i	−0.348120	+	0.937450i	$0.613180\pi$
$138$	−10.2655	+	10.2655i	−0.873854	+	0.873854i
$139$		−	3.37763i		−	0.286487i	−0.989687	−	0.143244i	$-0.954247\pi$
$139$		−	3.37763i		−	0.286487i	0.989687	−	0.143244i	$-0.0457532\pi$
$140$	−0.661638	+	6.69100i	−0.0559186	+	0.565493i
$141$			10.4922i			0.883601i
$142$	−4.35787	−	4.35787i	−0.365705	−	0.365705i
$143$	−18.8974	−	18.8974i	−1.58028	−	1.58028i
$144$		−	0.369965i		−	0.0308304i
$145$	−1.48991	+	1.22177i	−0.123730	+	0.101462i
$146$			4.33799i			0.359014i
$147$	−2.64995	+	2.64995i	−0.218564	+	0.218564i
$148$	3.98104	+	3.98104i	0.327239	+	0.327239i
$149$			1.36230i			0.111604i	0.998442	+	0.0558018i	$0.0177715\pi$
$149$			1.36230i			0.111604i	−0.998442	+	0.0558018i	$0.982228\pi$
$150$	1.79769	−	9.00097i	0.146781	−	0.734926i
$151$			17.9862i			1.46370i	0.681467	+	0.731849i	$0.261342\pi$
$151$			17.9862i			1.46370i	−0.681467	+	0.731849i	$0.738658\pi$
$152$	2.10938	+	3.81451i	0.171093	+	0.309398i
$153$	0.438402	−	0.438402i	0.0354427	−	0.0354427i
$154$	15.2996			1.23287
$155$	9.99114	+	12.1839i	0.802508	+	0.978635i
$156$	−9.64208			−0.771984
$157$	−11.6368	−	11.6368i	−0.928721	−	0.928721i	0.0689021	−	0.997623i	$-0.478050\pi$
$157$	−11.6368	−	11.6368i	−0.928721	−	0.928721i	−0.997623	+	0.0689021i	$0.978050\pi$
$158$	10.0044	−	10.0044i	0.795905	−	0.795905i
$159$			17.0612i			1.35304i
$160$	0.220040	−	2.22522i	0.0173957	−	0.175919i
$161$	−23.7794			−1.87408
$162$	7.05199	−	7.05199i	0.554057	−	0.554057i
$163$	−2.64736	+	2.64736i	−0.207357	+	0.207357i	−0.803143	−	0.595786i	$-0.796841\pi$
$163$	−2.64736	+	2.64736i	−0.207357	+	0.207357i	0.595786	+	0.803143i	$0.296841\pi$
$164$	2.38835			0.186499
$165$	−20.7847	−	2.05529i	−1.61809	−	0.160004i
$166$		−	1.18192i		−	0.0917351i
$167$	−7.08501	+	7.08501i	−0.548254	+	0.548254i	−0.925936	−	0.377681i	$-0.876721\pi$
$167$	−7.08501	+	7.08501i	−0.548254	+	0.548254i	0.377681	+	0.925936i	$0.376721\pi$
$168$	3.90317	−	3.90317i	0.301136	−	0.301136i
$169$			14.5877i			1.12213i
$170$	2.89758	−	2.37610i	0.222235	−	0.182238i
$171$	0.446071	−	1.54972i	0.0341119	−	0.118510i
$172$	−4.14693	−	4.14693i	−0.316200	−	0.316200i
$173$	−2.32369	−	2.32369i	−0.176667	−	0.176667i	0.613234	−	0.789901i	$-0.289868\pi$
$173$	−2.32369	−	2.32369i	−0.176667	−	0.176667i	−0.789901	+	0.613234i	$0.789868\pi$
$174$	1.58184			0.119919
$175$	12.5072	−	8.34299i	0.945458	−	0.630670i
$176$	−5.08815			−0.383534
$177$	−12.8565	−	12.8565i	−0.966352	−	0.966352i
$178$	3.22304	−	3.22304i	0.241577	−	0.241577i
$179$	2.05124			0.153317			0.0766583	−	0.997057i	$-0.475575\pi$
$179$	2.05124			0.153317			0.0766583	+	0.997057i	$0.475575\pi$
$180$	−0.639690	+	0.524563i	−0.0476797	+	0.0390986i
$181$			9.43492i			0.701292i	0.936508	+	0.350646i	$0.114038\pi$
$181$			9.43492i			0.701292i	−0.936508	+	0.350646i	$0.885962\pi$
$182$	−11.1677	−	11.1677i	−0.827802	−	0.827802i
$183$	−5.46926	−	5.46926i	−0.404299	−	0.404299i
$184$	7.90826			0.583004
$185$	1.23883	−	12.5280i	0.0910807	−	0.921080i
$186$		−	12.9357i		−	0.948492i
$187$	−6.02937	−	6.02937i	−0.440911	−	0.440911i
$188$	4.04146	−	4.04146i	0.294754	−	0.294754i
$189$	14.5176			1.05600
$190$	3.60467	−	9.05573i	0.261511	−	0.656972i
$191$	−13.5487			−0.980349			−0.490175	−	0.871624i	$-0.663067\pi$
$191$	−13.5487			−0.980349			−0.490175	+	0.871624i	$0.663067\pi$
$192$	−1.29807	+	1.29807i	−0.0936800	+	0.0936800i
$193$	3.01172	+	3.01172i	0.216788	+	0.216788i	0.807143	−	0.590355i	$-0.201012\pi$
$193$	3.01172	+	3.01172i	0.216788	+	0.216788i	−0.590355	+	0.807143i	$0.701012\pi$
$194$		−	5.55393i		−	0.398749i
$195$	13.6712	+	16.6717i	0.979018	+	1.19388i
$196$	2.04146			0.145818
$197$	−14.2004	−	14.2004i	−1.01174	−	1.01174i	−0.999930	−	0.0118084i	$-0.996241\pi$
$197$	−14.2004	−	14.2004i	−1.01174	−	1.01174i	−0.0118084	−	0.999930i	$-0.503759\pi$
$198$	1.33108	+	1.33108i	0.0945960	+	0.0945960i
$199$		−	8.94564i		−	0.634140i	−0.948402	−	0.317070i	$-0.897301\pi$
$199$		−	8.94564i		−	0.634140i	0.948402	−	0.317070i	$-0.102699\pi$
$200$	−4.15951	+	2.77461i	−0.294122	+	0.196195i
$201$	−11.6396			−0.820997
$202$	−4.06726	+	4.06726i	−0.286171	+	0.286171i
$203$	1.83212	+	1.83212i	0.128590	+	0.128590i
$204$	−3.07638			−0.215390
$205$	−3.38637	−	4.12959i	−0.236515	−	0.288423i
$206$	3.61713			0.252018
$207$	−2.06884	−	2.06884i	−0.143794	−	0.143794i
$208$	3.71401	+	3.71401i	0.257520	+	0.257520i
$209$	−21.3134	−	6.13484i	−1.47428	−	0.424356i
$210$	−12.2830	−	1.21460i	−0.847607	−	0.0838153i
$211$		−	24.3448i		−	1.67596i	−0.545699	−	0.837981i	$-0.683736\pi$
$211$		−	24.3448i		−	1.67596i	0.545699	−	0.837981i	$-0.316264\pi$
$212$	6.57175	−	6.57175i	0.451350	−	0.451350i
$213$	7.99995	−	7.99995i	0.548148	−	0.548148i
$214$			12.9283i			0.883758i
$215$	−1.29045	+	13.0501i	−0.0880082	+	0.890009i
$216$	−4.82808			−0.328509
$217$	14.9824	−	14.9824i	1.01707	−	1.01707i
$218$	−2.49174	+	2.49174i	−0.168762	+	0.168762i
$219$	−7.96344			−0.538119
$220$	7.21435	+	8.79769i	0.486391	+	0.593140i
$221$			8.80207i			0.592091i
$222$	−7.30817	+	7.30817i	−0.490492	+	0.490492i
$223$	7.74344	+	7.74344i	0.518539	+	0.518539i	0.917129	−	0.398590i	$-0.130500\pi$
$223$	7.74344	+	7.74344i	0.518539	+	0.518539i	−0.398590	+	0.917129i	$0.630500\pi$
$224$	−3.00690			−0.200907
$225$	1.81400	+	0.362296i	0.120933	+	0.0241531i
$226$	18.5660			1.23499
$227$	−1.35188	+	1.35188i	−0.0897277	+	0.0897277i	−0.750546	−	0.660818i	$-0.770209\pi$
$227$	−1.35188	+	1.35188i	−0.0897277	+	0.0897277i	0.660818	+	0.750546i	$0.270209\pi$
$228$	−7.00248	+	3.87229i	−0.463751	+	0.256448i
$229$			29.2012i			1.92967i	0.262852	+	0.964836i	$0.415337\pi$
$229$			29.2012i			1.92967i	−0.262852	+	0.964836i	$0.584663\pi$
$230$	−11.2129	−	13.6738i	−0.739357	−	0.901625i
$231$			28.0861i			1.84793i
$232$	−0.609306	−	0.609306i	−0.0400029	−	0.0400029i
$233$	17.3007	−	17.3007i	1.13340	−	1.13340i	0.143797	−	0.989607i	$-0.454069\pi$
$233$	17.3007	−	17.3007i	1.13340	−	1.13340i	0.989607	−	0.143797i	$-0.0459313\pi$
$234$		−	1.94320i		−	0.127031i
$235$	−12.7182	−	1.25763i	−0.829643	−	0.0820389i
$236$			9.90431i			0.644716i
$237$	18.3655	+	18.3655i	1.19297	+	1.19297i
$238$	−3.56313	−	3.56313i	−0.230963	−	0.230963i
$239$			0.129605i			0.00838347i	0.999991	+	0.00419174i	$0.00133428\pi$
$239$			0.129605i			0.00838347i	−0.999991	+	0.00419174i	$0.998666\pi$
$240$	4.08493	+	0.403937i	0.263681	+	0.0260740i
$241$		−	15.3241i		−	0.987109i	−0.869715	−	0.493555i	$-0.835697\pi$
$241$		−	15.3241i		−	0.987109i	0.869715	−	0.493555i	$-0.164303\pi$
$242$	10.5283	−	10.5283i	0.676784	−	0.676784i
$243$	2.70377	+	2.70377i	0.173447	+	0.173447i
$244$			4.21338i			0.269734i
$245$	−2.89453	−	3.52980i	−0.184925	−	0.225510i
$246$			4.38440i			0.279539i
$247$	11.0793	+	20.0354i	0.704960	+	1.27482i
$248$	−4.98268	+	4.98268i	−0.316400	+	0.316400i
$249$	2.16971			0.137500
$250$	10.6951	+	3.25798i	0.676419	+	0.206053i
$251$	16.8877			1.06594			0.532970	−	0.846134i	$-0.321076\pi$
$251$	16.8877			1.06594			0.532970	+	0.846134i	$0.321076\pi$
$252$	0.786620	+	0.786620i	0.0495524	+	0.0495524i
$253$	−28.4528	+	28.4528i	−1.78881	+	1.78881i
$254$		−	0.848647i		−	0.0532489i
$255$	4.36191	+	5.31923i	0.273154	+	0.333103i
$256$	1.00000			0.0625000
$257$	−3.34251	+	3.34251i	−0.208500	+	0.208500i	−0.803630	−	0.595130i	$-0.797101\pi$
$257$	−3.34251	+	3.34251i	−0.208500	+	0.208500i	0.595130	+	0.803630i	$0.297101\pi$
$258$	7.61271	−	7.61271i	0.473947	−	0.473947i
$259$	−16.9290			−1.05191
$260$	1.15574	−	11.6877i	0.0716757	−	0.724842i
$261$			0.318795i			0.0197329i
$262$	−1.93742	+	1.93742i	−0.119694	+	0.119694i
$263$	12.0052	−	12.0052i	0.740274	−	0.740274i	−0.232356	−	0.972631i	$-0.574644\pi$
$263$	12.0052	−	12.0052i	0.740274	−	0.740274i	0.972631	+	0.232356i	$0.0746436\pi$
$264$		−	9.34055i		−	0.574871i
$265$	−20.6808	−	2.04502i	−1.27041	−	0.125624i
$266$	−12.5954	−	3.62546i	−0.772273	−	0.222291i
$267$	5.91668	+	5.91668i	0.362095	+	0.362095i
$268$	4.48345	+	4.48345i	0.273870	+	0.273870i
$269$	−14.4405			−0.880450			−0.440225	−	0.897887i	$-0.645101\pi$
$269$	−14.4405			−0.880450			−0.440225	+	0.897887i	$0.645101\pi$
$270$	6.84560	+	8.34802i	0.416610	+	0.508044i
$271$	7.96012			0.483543			0.241771	−	0.970333i	$-0.422272\pi$
$271$	7.96012			0.483543			0.241771	+	0.970333i	$0.422272\pi$
$272$	1.18498	+	1.18498i	0.0718501	+	0.0718501i
$273$	20.5010	−	20.5010i	1.24078	−	1.24078i
$274$	9.75515			0.589330
$275$	4.98268	−	24.9480i	0.300467	−	1.50442i
$276$			14.5176i			0.873854i
$277$	−18.9230	−	18.9230i	−1.13697	−	1.13697i	−0.988990	−	0.147985i	$-0.952721\pi$
$277$	−18.9230	−	18.9230i	−1.13697	−	1.13697i	−0.147985	−	0.988990i	$-0.547279\pi$
$278$	−2.38835	−	2.38835i	−0.143244	−	0.143244i
$279$	2.60698			0.156076
$280$	4.26341	+	5.19910i	0.254787	+	0.310706i
$281$			4.26593i			0.254484i	0.991872	+	0.127242i	$0.0406124\pi$
$281$			4.26593i			0.254484i	−0.991872	+	0.127242i	$0.959388\pi$
$282$	7.41909	+	7.41909i	0.441800	+	0.441800i
$283$	−7.11427	+	7.11427i	−0.422899	+	0.422899i	−0.886201	−	0.463301i	$-0.846665\pi$
$283$	−7.11427	+	7.11427i	−0.422899	+	0.422899i	0.463301	+	0.886201i	$0.346665\pi$
$284$	−6.16296			−0.365705
$285$	16.6240	+	6.61727i	0.984723	+	0.391973i
$286$	−26.7250			−1.58028
$287$	−5.07811	+	5.07811i	−0.299751	+	0.299751i
$288$	−0.261605	−	0.261605i	−0.0154152	−	0.0154152i
$289$		−	14.1916i		−	0.834802i
$290$	−0.189606	+	1.91744i	−0.0111340	+	0.112596i
$291$	10.1956			0.597677
$292$	3.06742	+	3.06742i	0.179507	+	0.179507i
$293$	13.8921	+	13.8921i	0.811587	+	0.811587i	0.984872	−	0.173284i	$-0.0554380\pi$
$293$	13.8921	+	13.8921i	0.811587	+	0.811587i	−0.173284	+	0.984872i	$0.555438\pi$
$294$			3.74760i			0.218564i
$295$	17.1251	−	14.0431i	0.997062	−	0.817618i
$296$	5.63004			0.327239
$297$	17.3708	−	17.3708i	1.00795	−	1.00795i
$298$	0.963289	+	0.963289i	0.0558018	+	0.0558018i
$299$	41.5373			2.40217
$300$	−5.09348	−	7.63581i	−0.294072	−	0.440853i
$301$	17.6344			1.01643
$302$	12.7182	+	12.7182i	0.731849	+	0.731849i
$303$	−7.46645	−	7.46645i	−0.428937	−	0.428937i
$304$	4.18883	+	1.20571i	0.240246	+	0.0691523i
$305$	7.28517	−	5.97404i	0.417148	−	0.342072i
$306$		−	0.619994i		−	0.0354427i
$307$	14.3328	−	14.3328i	0.818017	−	0.818017i	−0.167803	−	0.985821i	$-0.553667\pi$
$307$	14.3328	−	14.3328i	0.818017	−	0.818017i	0.985821	+	0.167803i	$0.0536673\pi$
$308$	10.8184	−	10.8184i	0.616437	−	0.616437i
$309$			6.64014i			0.377744i
$310$	15.6801	+	1.55052i	0.890572	+	0.0880639i
$311$	17.3743			0.985208			0.492604	−	0.870253i	$-0.336045\pi$
$311$	17.3743			0.985208			0.492604	+	0.870253i	$0.336045\pi$
$312$	−6.81798	+	6.81798i	−0.385992	+	0.385992i
$313$	−17.5452	+	17.5452i	−0.991716	+	0.991716i	−0.999966	−	0.00825027i	$-0.997374\pi$
$313$	−17.5452	+	17.5452i	−0.991716	+	0.991716i	0.00825027	+	0.999966i	$0.497374\pi$
$314$	−16.4570			−0.928721
$315$	0.244783	−	2.47544i	0.0137919	−	0.139475i
$316$		−	14.1483i		−	0.795905i
$317$	−3.10285	+	3.10285i	−0.174274	+	0.174274i	−0.788854	−	0.614580i	$-0.789325\pi$
$317$	−3.10285	+	3.10285i	−0.174274	+	0.174274i	0.614580	+	0.788854i	$0.289325\pi$
$318$	12.0641	+	12.0641i	0.676519	+	0.676519i
$319$	4.38440			0.245479
$320$	−1.41787	−	1.72906i	−0.0792615	−	0.0966572i
$321$	−23.7330			−1.32465
$322$	−16.8145	+	16.8145i	−0.937038	+	0.937038i
$323$	3.53494	+	6.39243i	0.196689	+	0.355684i
$324$		−	9.97302i		−	0.554057i
$325$	−21.8474	+	14.5734i	−1.21188	+	0.808385i
$326$			3.74393i			0.207357i
$327$	−4.57421	−	4.57421i	−0.252954	−	0.252954i
$328$	1.68882	−	1.68882i	0.0932493	−	0.0932493i
$329$			17.1859i			0.947489i
$330$	−16.1503	+	13.2437i	−0.889047	+	0.729042i
$331$		−	9.73065i		−	0.534845i	−0.963579	−	0.267422i	$-0.913828\pi$
$331$		−	9.73065i		−	0.534845i	0.963579	−	0.267422i	$-0.0861719\pi$
$332$	−0.835746	−	0.835746i	−0.0458675	−	0.0458675i
$333$	−1.47284	−	1.47284i	−0.0807113	−	0.0807113i
$334$			10.0197i			0.548254i
$335$	1.39517	−	14.1091i	0.0762264	−	0.770862i
$336$		−	5.51991i		−	0.301136i
$337$	−8.08845	+	8.08845i	−0.440606	+	0.440606i	−0.892216	−	0.451610i	$-0.850850\pi$
$337$	−8.08845	+	8.08845i	−0.440606	+	0.440606i	0.451610	+	0.892216i	$0.350850\pi$
$338$	10.3151	+	10.3151i	0.561066	+	0.561066i
$339$			34.0824i			1.85110i
$340$	0.368746	−	3.72906i	0.0199981	−	0.202236i
$341$		−	35.8540i		−	1.94160i
$342$	−0.780397	−	1.41124i	−0.0421990	−	0.0763109i
$343$	10.5429	−	10.5429i	0.569261	−	0.569261i
$344$	−5.86464			−0.316200
$345$	25.1017	−	20.5841i	1.35143	−	1.10821i
$346$	−3.28619			−0.176667
$347$	−0.343845	−	0.343845i	−0.0184586	−	0.0184586i	0.697817	−	0.716276i	$-0.254155\pi$
$347$	−0.343845	−	0.343845i	−0.0184586	−	0.0184586i	−0.716276	+	0.697817i	$0.754155\pi$
$348$	1.11853	−	1.11853i	0.0599596	−	0.0599596i
$349$		−	5.83245i		−	0.312204i	−0.987741	−	0.156102i	$-0.950107\pi$
$349$		−	5.83245i		−	0.312204i	0.987741	−	0.156102i	$-0.0498928\pi$
$350$	2.94457	−	14.7433i	0.157394	−	0.788064i
$351$	−25.3590			−1.35356
$352$	−3.59786	+	3.59786i	−0.191767	+	0.191767i
$353$	−13.0183	+	13.0183i	−0.692894	+	0.692894i	−0.962868	−	0.269974i	$-0.912985\pi$
$353$	−13.0183	+	13.0183i	−0.692894	+	0.692894i	0.269974	+	0.962868i	$0.412985\pi$
$354$	−18.1818			−0.966352
$355$	8.73830	+	10.6561i	0.463781	+	0.565568i
$356$		−	4.55806i		−	0.241577i
$357$	6.54100	−	6.54100i	0.346186	−	0.346186i
$358$	1.45044	−	1.45044i	0.0766583	−	0.0766583i
$359$		−	0.962915i		−	0.0508207i	−0.999677	−	0.0254104i	$-0.991911\pi$
$359$		−	0.962915i		−	0.0508207i	0.999677	−	0.0254104i	$-0.00808924\pi$
$360$	−0.0814070	+	0.823252i	−0.00429052	+	0.0433892i
$361$	16.0925	+	10.1010i	0.846975	+	0.531633i
$362$	6.67149	+	6.67149i	0.350646	+	0.350646i
$363$	19.3273	+	19.3273i	1.01442	+	1.01442i
$364$	−15.7935			−0.827802
$365$	0.954529	−	9.65295i	0.0499623	−	0.505259i
$366$	−7.73470			−0.404299
$367$	−13.3776	−	13.3776i	−0.698307	−	0.698307i	0.265738	−	0.964045i	$-0.414384\pi$
$367$	−13.3776	−	13.3776i	−0.698307	−	0.698307i	−0.964045	+	0.265738i	$0.914384\pi$
$368$	5.59198	−	5.59198i	0.291502	−	0.291502i
$369$	−0.883605			−0.0459986
$370$	−7.98268	−	9.73465i	−0.415000	−	0.506080i
$371$			27.9457i			1.45087i
$372$	−9.14693	−	9.14693i	−0.474246	−	0.474246i
$373$	−18.0468	−	18.0468i	−0.934430	−	0.934430i	0.0635491	−	0.997979i	$-0.479758\pi$
$373$	−18.0468	−	18.0468i	−0.934430	−	0.934430i	−0.997979	+	0.0635491i	$0.979758\pi$
$374$	−8.52681			−0.440911
$375$	−5.98082	+	19.6335i	−0.308848	+	1.01387i
$376$		−	5.71548i		−	0.294754i
$377$	−3.20032	−	3.20032i	−0.164825	−	0.164825i
$378$	10.2655	−	10.2655i	0.527998	−	0.527998i
$379$	12.7401			0.654417			0.327208	−	0.944952i	$-0.393892\pi$
$379$	12.7401			0.654417			0.327208	+	0.944952i	$0.393892\pi$
$380$	−3.85448	−	8.95226i	−0.197731	−	0.459241i
$381$	1.55790			0.0798137
$382$	−9.58038	+	9.58038i	−0.490175	+	0.490175i
$383$	−18.5820	−	18.5820i	−0.949496	−	0.949496i	0.0492886	−	0.998785i	$-0.484305\pi$
$383$	−18.5820	−	18.5820i	−0.949496	−	0.949496i	−0.998785	+	0.0492886i	$0.984305\pi$
$384$			1.83575i			0.0936800i
$385$	−34.0448	−	3.36651i	−1.73508	−	0.171573i
$386$	4.25921			0.216788
$387$	1.53422	+	1.53422i	0.0779887	+	0.0779887i
$388$	−3.92722	−	3.92722i	−0.199374	−	0.199374i
$389$		−	20.2721i		−	1.02784i	−0.857839	−	0.513918i	$-0.828193\pi$
$389$		−	20.2721i		−	1.02784i	0.857839	−	0.513918i	$-0.171807\pi$
$390$	21.4557	+	2.12164i	1.08645	+	0.107433i
$391$	13.2528			0.670223
$392$	1.44353	−	1.44353i	0.0729092	−	0.0729092i
$393$	−3.55662	−	3.55662i	−0.179408	−	0.179408i
$394$	−20.0824			−1.01174
$395$	−24.4632	+	20.0605i	−1.23088	+	1.00935i
$396$	1.88244			0.0945960
$397$	2.26530	+	2.26530i	0.113692	+	0.113692i	0.761664	−	0.647972i	$-0.224383\pi$
$397$	2.26530	+	2.26530i	0.113692	+	0.113692i	−0.647972	+	0.761664i	$0.724383\pi$
$398$	−6.32552	−	6.32552i	−0.317070	−	0.317070i
$399$	6.65542	−	23.1219i	0.333188	−	1.15754i
$400$	−0.979271	+	4.90317i	−0.0489636	+	0.245158i
$401$		−	32.2428i		−	1.61013i	−0.593187	−	0.805065i	$-0.702131\pi$
$401$		−	32.2428i		−	1.61013i	0.593187	−	0.805065i	$-0.297869\pi$
$402$	−8.23047	+	8.23047i	−0.410498	+	0.410498i
$403$	−26.1710	+	26.1710i	−1.30367	+	1.30367i
$404$			5.75197i			0.286171i
$405$	−17.2439	+	14.1405i	−0.856857	+	0.702646i
$406$	2.59101			0.128590
$407$	−20.2561	+	20.2561i	−1.00406	+	1.00406i
$408$	−2.17533	+	2.17533i	−0.107695	+	0.107695i
$409$	24.8591			1.22921			0.614603	−	0.788837i	$-0.289316\pi$
$409$	24.8591			1.22921			0.614603	+	0.788837i	$0.289316\pi$
$410$	−5.31459	−	0.525531i	−0.262469	−	0.0259541i
$411$			17.9080i			0.883336i
$412$	2.55770	−	2.55770i	0.126009	−	0.126009i
$413$	−21.0585	−	21.0585i	−1.03622	−	1.03622i
$414$	−2.92578			−0.143794
$415$	−0.260070	+	2.63004i	−0.0127663	+	0.129103i
$416$	5.25240			0.257520
$417$	4.38440	−	4.38440i	0.214705	−	0.214705i
$418$	−19.4088	+	10.7328i	−0.949316	+	0.524960i
$419$		−	22.4745i		−	1.09795i	−0.835838	−	0.548976i	$-0.815018\pi$
$419$		−	22.4745i		−	1.09795i	0.835838	−	0.548976i	$-0.184982\pi$
$420$	−9.54423	+	7.82653i	−0.465711	+	0.381896i
$421$			35.7769i			1.74366i	0.489810	+	0.871829i	$0.337066\pi$
$421$			35.7769i			1.74366i	−0.489810	+	0.871829i	$0.662934\pi$
$422$	−17.2143	−	17.2143i	−0.837981	−	0.837981i
$423$	−1.49520	+	1.49520i	−0.0726990	+	0.0726990i
$424$		−	9.29386i		−	0.451350i
$425$	−6.97058	+	4.64975i	−0.338123	+	0.225546i
$426$		−	11.3136i		−	0.548148i
$427$	−8.95849	−	8.95849i	−0.433532	−	0.433532i
$428$	9.14167	+	9.14167i	0.441879	+	0.441879i
$429$		−	49.0603i		−	2.36865i
$430$	8.31532	+	10.1403i	0.401000	+	0.489009i
$431$		−	12.8172i		−	0.617385i	−0.951162	−	0.308692i	$-0.900109\pi$
$431$		−	12.8172i		−	0.617385i	0.951162	−	0.308692i	$-0.0998913\pi$
$432$	−3.41397	+	3.41397i	−0.164255	+	0.164255i
$433$	2.48060	+	2.48060i	0.119210	+	0.119210i	0.764195	−	0.644985i	$-0.223136\pi$
$433$	2.48060	+	2.48060i	0.119210	+	0.119210i	−0.644985	+	0.764195i	$0.723136\pi$
$434$		−	21.1883i		−	1.01707i
$435$	−3.51994	−	0.348068i	−0.168768	−	0.0166886i
$436$			3.52386i			0.168762i
$437$	30.1662	−	16.6815i	1.44304	−	0.797985i
$438$	−5.63100	+	5.63100i	−0.269060	+	0.269060i
$439$	17.9413			0.856289			0.428145	−	0.903710i	$-0.359167\pi$
$439$	17.9413			0.856289			0.428145	+	0.903710i	$0.359167\pi$
$440$	11.3222	+	1.11959i	0.539766	+	0.0533746i
$441$	−0.755268			−0.0359651
$442$	6.22400	+	6.22400i	0.296046	+	0.296046i
$443$	−5.60748	+	5.60748i	−0.266419	+	0.266419i	−0.827656	−	0.561236i	$-0.810326\pi$
$443$	−5.60748	+	5.60748i	−0.266419	+	0.266419i	0.561236	+	0.827656i	$0.310326\pi$
$444$			10.3353i			0.490492i
$445$	−7.88114	+	6.46275i	−0.373602	+	0.306364i
$446$	10.9509			0.518539
$447$	−1.76835	+	1.76835i	−0.0836403	+	0.0836403i
$448$	−2.12620	+	2.12620i	−0.100454	+	0.100454i
$449$	16.8105			0.793336			0.396668	−	0.917962i	$-0.370166\pi$
$449$	16.8105			0.793336			0.396668	+	0.917962i	$0.370166\pi$
$450$	1.53887	−	1.02651i	0.0725432	−	0.0483901i
$451$			12.1523i			0.572228i
$452$	13.1281	−	13.1281i	0.617495	−	0.617495i
$453$	−23.3474	+	23.3474i	−1.09695	+	1.09695i
$454$			1.91185i			0.0897277i
$455$	22.3931	+	27.3078i	1.04981	+	1.28021i
$456$	−2.21338	+	7.68962i	−0.103651	+	0.360100i
$457$	20.4027	+	20.4027i	0.954400	+	0.954400i	0.999005	−	0.0446050i	$-0.0142029\pi$
$457$	20.4027	+	20.4027i	0.954400	+	0.954400i	−0.0446050	+	0.999005i	$0.514203\pi$
$458$	20.6484	+	20.6484i	0.964836	+	0.964836i
$459$	−8.09098			−0.377655
$460$	−17.5976	−	1.74013i	−0.820491	−	0.0811340i
$461$	27.3301			1.27289			0.636444	−	0.771323i	$-0.280404\pi$
$461$	27.3301			1.27289			0.636444	+	0.771323i	$0.280404\pi$
$462$	19.8599	+	19.8599i	0.923965	+	0.923965i
$463$	11.7495	−	11.7495i	0.546047	−	0.546047i	−0.379248	−	0.925295i	$-0.623817\pi$
$463$	11.7495	−	11.7495i	0.546047	−	0.546047i	0.925295	+	0.379248i	$0.123817\pi$
$464$	−0.861689			−0.0400029
$465$	−2.84637	+	28.7847i	−0.131997	+	1.33486i
$466$		−	24.4668i		−	1.13340i
$467$	9.93355	+	9.93355i	0.459670	+	0.459670i	0.898547	−	0.438877i	$-0.144624\pi$
$467$	9.93355	+	9.93355i	0.459670	+	0.459670i	−0.438877	+	0.898547i	$0.644624\pi$
$468$	−1.37405	−	1.37405i	−0.0635156	−	0.0635156i
$469$	−19.0654			−0.880359
$470$	−9.88239	+	8.10383i	−0.455841	+	0.373802i
$471$		−	30.2108i		−	1.39204i
$472$	7.00340	+	7.00340i	0.322358	+	0.322358i
$473$	21.1002	−	21.1002i	0.970188	−	0.970188i
$474$	25.9727			1.19297
$475$	−10.0138	+	19.3578i	−0.459465	+	0.888196i
$476$	−5.03902			−0.230963
$477$	−2.43132	+	2.43132i	−0.111322	+	0.111322i
$478$	0.0916448	+	0.0916448i	0.00419174	+	0.00419174i
$479$		−	32.9298i		−	1.50460i	−0.658819	−	0.752301i	$-0.728944\pi$
$479$		−	32.9298i		−	1.50460i	0.658819	−	0.752301i	$-0.271056\pi$
$480$	3.17411	−	2.60286i	0.144878	−	0.118804i
$481$	29.5712			1.34833
$482$	−10.8357	−	10.8357i	−0.493555	−	0.493555i
$483$	−30.8672	−	30.8672i	−1.40451	−	1.40451i
$484$		−	14.8892i		−	0.676784i
$485$	−1.22208	+	12.3587i	−0.0554920	+	0.561179i
$486$	3.82370			0.173447
$487$	11.4970	−	11.4970i	0.520979	−	0.520979i	−0.396888	−	0.917867i	$-0.629910\pi$
$487$	11.4970	−	11.4970i	0.520979	−	0.520979i	0.917867	+	0.396888i	$0.129910\pi$
$488$	2.97931	+	2.97931i	0.134867	+	0.134867i
$489$	−6.87291			−0.310804
$490$	−4.54268	−	0.449202i	−0.205217	−	0.0202929i
$491$	−44.0285			−1.98698			−0.993488	−	0.113935i	$-0.963654\pi$
$491$	−44.0285			−1.98698			−0.993488	+	0.113935i	$0.963654\pi$
$492$	3.10024	+	3.10024i	0.139770	+	0.139770i
$493$	−1.02109	−	1.02109i	−0.0459874	−	0.0459874i
$494$	22.0014	+	6.33288i	0.989889	+	0.284930i
$495$	−2.66906	−	3.25484i	−0.119965	−	0.146294i
$496$			7.04657i			0.316400i
$497$	13.1037	−	13.1037i	0.587781	−	0.587781i
$498$	1.53422	−	1.53422i	0.0687500	−	0.0687500i
$499$			28.2982i			1.26680i	0.773823	+	0.633401i	$0.218342\pi$
$499$			28.2982i			1.26680i	−0.773823	+	0.633401i	$0.781658\pi$
$500$	9.86633	−	5.25885i	0.441236	−	0.235183i
$501$	−18.3936			−0.821768
$502$	11.9414	−	11.9414i	0.532970	−	0.532970i
$503$	16.2003	−	16.2003i	0.722334	−	0.722334i	−0.246746	−	0.969080i	$-0.579361\pi$
$503$	16.2003	−	16.2003i	0.722334	−	0.722334i	0.969080	+	0.246746i	$0.0793613\pi$
$504$	1.11245			0.0495524
$505$	9.94548	−	8.15557i	0.442568	−	0.362918i
$506$			40.2384i			1.78881i
$507$	−18.9359	+	18.9359i	−0.840971	+	0.840971i
$508$	−0.600084	−	0.600084i	−0.0266244	−	0.0266244i
$509$	2.34337			0.103868			0.0519341	−	0.998651i	$-0.483461\pi$
$509$	2.34337			0.103868			0.0519341	+	0.998651i	$0.483461\pi$
$510$	6.84560	+	0.676925i	0.303128	+	0.0299747i
$511$	−13.0439			−0.577028
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−18.4168	+	10.1843i	−0.813120	+	0.449646i
$514$			4.72703i			0.208500i
$515$	−8.04890	−	0.795913i	−0.354677	−	0.0350721i
$516$		−	10.7660i		−	0.473947i
$517$	20.5635	+	20.5635i	0.904383	+	0.904383i
$518$	−11.9706	+	11.9706i	−0.525957	+	0.525957i
$519$		−	6.03261i		−	0.264802i
$520$	−7.44724	−	9.08170i	−0.326583	−	0.398259i
$521$			28.9799i			1.26963i	0.772663	+	0.634817i	$0.218924\pi$
$521$			28.9799i			1.26963i	−0.772663	+	0.634817i	$0.781076\pi$
$522$	0.225422	+	0.225422i	0.00986645	+	0.00986645i
$523$	−3.06442	−	3.06442i	−0.133998	−	0.133998i	0.636927	−	0.770924i	$-0.280205\pi$
$523$	−3.06442	−	3.06442i	−0.133998	−	0.133998i	−0.770924	+	0.636927i	$0.780205\pi$
$524$			2.73993i			0.119694i
$525$	27.0650	+	5.40549i	1.18121	+	0.235915i
$526$		−	16.9780i		−	0.740274i
$527$	−8.35006	+	8.35006i	−0.363734	+	0.363734i
$528$	−6.60477	−	6.60477i	−0.287436	−	0.287436i
$529$		−	39.5405i		−	1.71915i
$530$	−16.0696	+	13.1775i	−0.698019	+	0.572395i
$531$		−	3.66425i		−	0.159015i
$532$	−11.4699	+	6.34270i	−0.497282	+	0.274991i
$533$	8.87034	−	8.87034i	0.384217	−	0.384217i
$534$	8.36744			0.362095
$535$	2.84473	−	28.7682i	0.122988	−	1.24376i
$536$	6.34055			0.273870
$537$	2.66265	+	2.66265i	0.114902	+	0.114902i
$538$	−10.2109	+	10.2109i	−0.440225	+	0.440225i
$539$			10.3872i			0.447410i
$540$	10.7435	+	1.06237i	0.462327	+	0.0457171i
$541$	33.9129			1.45803			0.729015	−	0.684497i	$-0.239978\pi$
$541$	33.9129			1.45803			0.729015	+	0.684497i	$0.239978\pi$
$542$	5.62865	−	5.62865i	0.241771	−	0.241771i
$543$	−12.2472	+	12.2472i	−0.525576	+	0.525576i
$544$	1.67582			0.0718501
$545$	6.09295	−	4.99638i	0.260993	−	0.214021i
$546$		−	28.9928i		−	1.24078i
$547$	−17.4092	+	17.4092i	−0.744364	+	0.744364i	−0.973414	−	0.229051i	$-0.926438\pi$
$547$	−17.4092	+	17.4092i	−0.744364	+	0.744364i	0.229051	+	0.973414i	$0.426438\pi$
$548$	6.89793	−	6.89793i	0.294665	−	0.294665i
$549$		−	1.55880i		−	0.0665281i
$550$	−14.1176	−	21.1642i	−0.601978	−	0.902445i
$551$	−3.60947	−	1.03895i	−0.153768	−	0.0442607i
$552$	10.2655	+	10.2655i	0.436927	+	0.436927i
$553$	30.0822	+	30.0822i	1.27922	+	1.27922i
$554$	−26.7612			−1.13697
$555$	17.8703	−	14.6542i	0.758554	−	0.622035i
$556$	−3.37763			−0.143244
$557$	−1.84342	−	1.84342i	−0.0781080	−	0.0781080i	0.666973	−	0.745081i	$-0.267589\pi$
$557$	−1.84342	−	1.84342i	−0.0781080	−	0.0781080i	−0.745081	+	0.666973i	$0.767589\pi$
$558$	1.84342	−	1.84342i	0.0780380	−	0.0780380i
$559$	−30.8035			−1.30285
$560$	6.69100	+	0.661638i	0.282746	+	0.0279593i
$561$		−	15.6531i		−	0.660873i
$562$	3.01646	+	3.01646i	0.127242	+	0.127242i
$563$	−16.3506	−	16.3506i	−0.689094	−	0.689094i	0.272937	−	0.962032i	$-0.412005\pi$
$563$	−16.3506	−	16.3506i	−0.689094	−	0.689094i	−0.962032	+	0.272937i	$0.912005\pi$
$564$	10.4922			0.441800
$565$	−41.3133	−	4.08525i	−1.73806	−	0.171868i
$566$			10.0611i			0.422899i
$567$	21.2046	+	21.2046i	0.890511	+	0.890511i
$568$	−4.35787	+	4.35787i	−0.182852	+	0.182852i
$569$	−30.4112			−1.27490			−0.637451	−	0.770491i	$-0.720011\pi$
$569$	−30.4112			−1.27490			−0.637451	+	0.770491i	$0.720011\pi$
$570$	16.4341	−	7.07585i	0.688348	−	0.296375i
$571$	30.4118			1.27270			0.636348	−	0.771402i	$-0.280444\pi$
$571$	30.4118			1.27270			0.636348	+	0.771402i	$0.280444\pi$
$572$	−18.8974	+	18.8974i	−0.790141	+	0.790141i
$573$	−17.5871	−	17.5871i	−0.734713	−	0.734713i
$574$			7.18153i			0.299751i
$575$	21.9423	+	32.8945i	0.915059	+	1.37179i
$576$	−0.369965			−0.0154152
$577$	7.89112	+	7.89112i	0.328512	+	0.328512i	0.852020	−	0.523509i	$-0.175377\pi$
$577$	7.89112	+	7.89112i	0.328512	+	0.328512i	−0.523509	+	0.852020i	$0.675377\pi$
$578$	−10.0350	−	10.0350i	−0.417401	−	0.417401i
$579$			7.81883i			0.324940i
$580$	1.22177	+	1.48991i	0.0507311	+	0.0618651i
$581$	3.55393			0.147442
$582$	7.20938	−	7.20938i	0.298838	−	0.298838i
$583$	33.4380	+	33.4380i	1.38486	+	1.38486i
$584$	4.33799			0.179507
$585$	−0.427582	+	4.32405i	−0.0176783	+	0.178777i
$586$	19.6464			0.811587
$587$	16.8305	+	16.8305i	0.694668	+	0.694668i	0.963255	−	0.268588i	$-0.0865569\pi$
$587$	16.8305	+	16.8305i	0.694668	+	0.694668i	−0.268588	+	0.963255i	$0.586557\pi$
$588$	2.64995	+	2.64995i	0.109282	+	0.109282i
$589$	−8.49613	+	29.5168i	−0.350077	+	1.21622i
$590$	2.17934	−	22.0392i	0.0897220	−	0.907340i
$591$		−	36.8663i		−	1.51648i
$592$	3.98104	−	3.98104i	0.163620	−	0.163620i
$593$	−18.8140	+	18.8140i	−0.772598	+	0.772598i	−0.978560	−	0.205962i	$-0.933968\pi$
$593$	−18.8140	+	18.8140i	−0.772598	+	0.772598i	0.205962	+	0.978560i	$0.433968\pi$
$594$		−	24.5660i		−	1.00795i
$595$	7.14469	+	8.71275i	0.292904	+	0.357188i
$596$	1.36230			0.0558018
$597$	11.6121	−	11.6121i	0.475250	−	0.475250i
$598$	29.3713	−	29.3713i	1.20108	−	1.20108i
$599$	−9.11726			−0.372521			−0.186261	−	0.982500i	$-0.559637\pi$
$599$	−9.11726			−0.372521			−0.186261	+	0.982500i	$0.559637\pi$
$600$	−9.00097	−	1.79769i	−0.367463	−	0.0733905i
$601$			38.3056i			1.56252i	0.624207	+	0.781259i	$0.285422\pi$
$601$			38.3056i			1.56252i	−0.624207	+	0.781259i	$0.714578\pi$
$602$	12.4694	−	12.4694i	0.508215	−	0.508215i
$603$	−1.65872	−	1.65872i	−0.0675482	−	0.0675482i
$604$	17.9862			0.731849
$605$	−25.7443	+	21.1111i	−1.04666	+	0.858287i
$606$	−10.5592			−0.428937
$607$	28.8183	−	28.8183i	1.16970	−	1.16970i	0.187416	−	0.982281i	$-0.439989\pi$
$607$	28.8183	−	28.8183i	1.16970	−	1.16970i	0.982281	−	0.187416i	$-0.0600113\pi$
$608$	3.81451	−	2.10938i	0.154699	−	0.0855467i
$609$			4.75645i			0.192741i
$610$	0.927111	−	9.37568i	0.0375376	−	0.379610i
$611$		−	30.0200i		−	1.21448i
$612$	−0.438402	−	0.438402i	−0.0177213	−	0.0177213i
$613$	14.2307	−	14.2307i	0.574773	−	0.574773i	−0.358686	−	0.933458i	$-0.616775\pi$
$613$	14.2307	−	14.2307i	0.574773	−	0.574773i	0.933458	+	0.358686i	$0.116775\pi$
$614$		−	20.2697i		−	0.818017i
$615$	0.964742	−	9.75624i	0.0389022	−	0.393409i
$616$		−	15.2996i		−	0.616437i
$617$	−1.34578	−	1.34578i	−0.0541791	−	0.0541791i	0.679498	−	0.733677i	$-0.262198\pi$
$617$	−1.34578	−	1.34578i	−0.0541791	−	0.0541791i	−0.733677	+	0.679498i	$0.762198\pi$
$618$	4.69529	+	4.69529i	0.188872	+	0.188872i
$619$			4.97546i			0.199981i	0.994988	+	0.0999903i	$0.0318812\pi$
$619$			4.97546i			0.199981i	−0.994988	+	0.0999903i	$0.968119\pi$
$620$	12.1839	−	9.99114i	0.489318	−	0.401254i
$621$			38.1817i			1.53218i
$622$	12.2855	−	12.2855i	0.492604	−	0.492604i
$623$	9.69135	+	9.69135i	0.388276	+	0.388276i
$624$			9.64208i			0.385992i
$625$	−23.0821	−	9.60306i	−0.923282	−	0.384122i
$626$			24.8127i			0.991716i
$627$	−19.7028	−	35.6297i	−0.786853	−	1.42291i
$628$	−11.6368	+	11.6368i	−0.464361	+	0.464361i
$629$	9.43492			0.376195
$630$	−1.57731	−	1.92349i	−0.0628416	−	0.0766335i
$631$	−45.2032			−1.79951			−0.899755	−	0.436395i	$-0.856255\pi$
$631$	−45.2032			−1.79951			−0.899755	+	0.436395i	$0.856255\pi$
$632$	−10.0044	−	10.0044i	−0.397953	−	0.397953i
$633$	31.6012	−	31.6012i	1.25603	−	1.25603i
$634$			4.38810i			0.174274i
$635$	−0.186736	+	1.88842i	−0.00741039	+	0.0749398i
$636$	17.0612			0.676519
$637$	7.58199	−	7.58199i	0.300409	−	0.300409i
$638$	3.10024	−	3.10024i	0.122740	−	0.122740i
$639$	2.28008			0.0901986
$640$	−2.22522	−	0.220040i	−0.0879594	−	0.00869783i
$641$		−	15.9890i		−	0.631529i	−0.948838	−	0.315764i	$-0.897739\pi$
$641$		−	15.9890i		−	0.631529i	0.948838	−	0.315764i	$-0.102261\pi$
$642$	−16.7818	+	16.7818i	−0.662324	+	0.662324i
$643$	2.95575	−	2.95575i	0.116563	−	0.116563i	−0.646419	−	0.762982i	$-0.723734\pi$
$643$	2.95575	−	2.95575i	0.116563	−	0.116563i	0.762982	+	0.646419i	$0.223734\pi$
$644$			23.7794i			0.937038i
$645$	−18.6150	+	15.2648i	−0.732966	+	0.601052i
$646$	7.01971	+	2.02055i	0.276187	+	0.0794976i
$647$	−6.22116	−	6.22116i	−0.244579	−	0.244579i	0.574162	−	0.818741i	$-0.305328\pi$
$647$	−6.22116	−	6.22116i	−0.244579	−	0.244579i	−0.818741	+	0.574162i	$0.805328\pi$
$648$	−7.05199	−	7.05199i	−0.277028	−	0.277028i
$649$	−50.3946			−1.97816
$650$	−5.14352	+	25.7534i	−0.201746	+	1.01013i
$651$	38.8964			1.52447
$652$	2.64736	+	2.64736i	0.103679	+	0.103679i
$653$	−24.5703	+	24.5703i	−0.961512	+	0.961512i	−0.999286	−	0.0377745i	$-0.987973\pi$
$653$	−24.5703	+	24.5703i	−0.961512	+	0.961512i	0.0377745	+	0.999286i	$0.487973\pi$
$654$	−6.46891			−0.252954
$655$	4.73749	−	3.88487i	0.185109	−	0.151795i
$656$		−	2.38835i		−	0.0932493i
$657$	−1.13484	−	1.13484i	−0.0442742	−	0.0442742i
$658$	12.1523	+	12.1523i	0.473745	+	0.473745i
$659$	34.2721			1.33505			0.667526	−	0.744586i	$-0.267353\pi$
$659$	34.2721			1.33505			0.667526	+	0.744586i	$0.267353\pi$
$660$	−2.05529	+	20.7847i	−0.0800021	+	0.809045i
$661$			3.17654i			0.123553i	0.998090	+	0.0617765i	$0.0196766\pi$
$661$			3.17654i			0.123553i	−0.998090	+	0.0617765i	$0.980323\pi$
$662$	−6.88061	−	6.88061i	−0.267422	−	0.267422i
$663$	−11.4257	+	11.4257i	−0.443737	+	0.443737i
$664$	−1.18192			−0.0458675
$665$	27.2297	+	10.8389i	1.05592	+	0.420315i
$666$	−2.08292			−0.0807113
$667$	−4.81855	+	4.81855i	−0.186575	+	0.186575i
$668$	7.08501	+	7.08501i	0.274127	+	0.274127i
$669$			20.1030i			0.777228i
$670$	−8.99009	−	10.9632i	−0.347318	−	0.423544i
$671$	−21.4383			−0.827616
$672$	−3.90317	−	3.90317i	−0.150568	−	0.150568i
$673$	1.20017	+	1.20017i	0.0462631	+	0.0462631i	0.729860	−	0.683597i	$-0.239585\pi$
$673$	1.20017	+	1.20017i	0.0462631	+	0.0462631i	−0.683597	+	0.729860i	$0.739585\pi$
$674$			11.4388i			0.440606i
$675$	−13.3960	−	20.0824i	−0.515614	−	0.772973i
$676$	14.5877			0.561066
$677$	3.35361	−	3.35361i	0.128890	−	0.128890i	−0.639719	−	0.768609i	$-0.720949\pi$
$677$	3.35361	−	3.35361i	0.128890	−	0.128890i	0.768609	+	0.639719i	$0.220949\pi$
$678$	24.0999	+	24.0999i	0.925551	+	0.925551i
$679$	16.7001			0.640892
$680$	−2.37610	−	2.89758i	−0.0911192	−	0.111117i
$681$	−3.50968			−0.134491
$682$	−25.3526	−	25.3526i	−0.970801	−	0.970801i
$683$	−23.9988	−	23.9988i	−0.918289	−	0.918289i	0.0786159	−	0.996905i	$-0.474950\pi$
$683$	−23.9988	−	23.9988i	−0.918289	−	0.918289i	−0.996905	+	0.0786159i	$0.974950\pi$
$684$	−1.54972	−	0.446071i	−0.0592550	−	0.0170559i
$685$	−21.7073	−	2.14652i	−0.829394	−	0.0820143i
$686$		−	14.9098i		−	0.569261i
$687$	−37.9052	+	37.9052i	−1.44617	+	1.44617i
$688$	−4.14693	+	4.14693i	−0.158100	+	0.158100i
$689$		−	48.8151i		−	1.85971i
$690$	3.19444	−	32.3047i	0.121610	−	1.22982i
$691$	−14.1434			−0.538039			−0.269019	−	0.963135i	$-0.586700\pi$
$691$	−14.1434			−0.538039			−0.269019	+	0.963135i	$0.586700\pi$
$692$	−2.32369	+	2.32369i	−0.0883333	+	0.0883333i
$693$	−4.00244	+	4.00244i	−0.152040	+	0.152040i
$694$	−0.486270			−0.0184586
$695$	4.78906	+	5.84012i	0.181659	+	0.221528i
$696$		−	1.58184i		−	0.0599596i
$697$	2.83015	−	2.83015i	0.107200	−	0.107200i
$698$	−4.12417	−	4.12417i	−0.156102	−	0.156102i
$699$	44.9149			1.69884
$700$	−8.34299	−	12.5072i	−0.315335	−	0.472729i
$701$	5.47101			0.206637			0.103319	−	0.994648i	$-0.467054\pi$
$701$	5.47101			0.206637			0.103319	+	0.994648i	$0.467054\pi$
$702$	−17.9315	+	17.9315i	−0.676782	+	0.676782i
$703$	21.4758	−	11.8759i	0.809977	−	0.447907i
$704$			5.08815i			0.191767i
$705$	−14.8766	−	18.1416i	−0.560284	−	0.683251i
$706$			18.4106i			0.692894i
$707$	−12.2298	−	12.2298i	−0.459951	−	0.459951i
$708$	−12.8565	+	12.8565i	−0.483176	+	0.483176i
$709$			0.200479i			0.00752916i	0.999993	+	0.00376458i	$0.00119831\pi$
$709$			0.200479i			0.00752916i	−0.999993	+	0.00376458i	$0.998802\pi$
$710$	13.7139	+	1.35610i	0.514674	+	0.0508934i
$711$			5.23438i			0.196305i
$712$	−3.22304	−	3.22304i	−0.120788	−	0.120788i
$713$	39.4043	+	39.4043i	1.47570	+	1.47570i
$714$		−	9.25036i		−	0.346186i
$715$	59.4689	+	5.88056i	2.22401	+	0.219920i
$716$		−	2.05124i		−	0.0766583i
$717$	−0.168237	+	0.168237i	−0.00628291	+	0.00628291i
$718$	−0.680884	−	0.680884i	−0.0254104	−	0.0254104i
$719$			30.9955i			1.15594i	0.816059	+	0.577969i	$0.196155\pi$
$719$			30.9955i			1.15594i	−0.816059	+	0.577969i	$0.803845\pi$
$720$	0.524563	+	0.639690i	0.0195493	+	0.0238398i
$721$			10.8764i			0.405057i
$722$	18.5216	−	4.23662i	0.689304	−	0.157671i
$723$	19.8917	−	19.8917i	0.739780	−	0.739780i
$724$	9.43492			0.350646
$725$	0.843827	−	4.22500i	0.0313390	−	0.156913i
$726$	27.3329			1.01442
$727$	−31.2393	−	31.2393i	−1.15860	−	1.15860i	−0.984777	−	0.173825i	$-0.944387\pi$
$727$	−31.2393	−	31.2393i	−1.15860	−	1.15860i	−0.173825	−	0.984777i	$-0.555613\pi$
$728$	−11.1677	+	11.1677i	−0.413901	+	0.413901i
$729$		−	22.8997i		−	0.848137i
$730$	−6.15071	−	7.50062i	−0.227648	−	0.277610i
$731$	−9.82808			−0.363505
$732$	−5.46926	+	5.46926i	−0.202150	+	0.202150i
$733$	18.8184	−	18.8184i	0.695072	−	0.695072i	−0.268271	−	0.963343i	$-0.586452\pi$
$733$	18.8184	−	18.8184i	0.695072	−	0.695072i	0.963343	+	0.268271i	$0.0864523\pi$
$734$	−18.9188			−0.698307
$735$	0.824620	−	8.33921i	0.0304166	−	0.307597i
$736$		−	7.90826i		−	0.291502i
$737$	−22.8124	+	22.8124i	−0.840307	+	0.840307i
$738$	−0.624803	+	0.624803i	−0.0229993	+	0.0229993i
$739$			14.0680i			0.517499i	0.965944	+	0.258749i	$0.0833104\pi$
$739$			14.0680i			0.517499i	−0.965944	+	0.258749i	$0.916690\pi$
$740$	−12.5280	−	1.23883i	−0.460540	−	0.0455403i
$741$	−11.6256	+	40.3890i	−0.427076	+	1.48373i
$742$	19.7606	+	19.7606i	0.725435	+	0.725435i
$743$	−4.38124	−	4.38124i	−0.160732	−	0.160732i	0.622159	−	0.782891i	$-0.286256\pi$
$743$	−4.38124	−	4.38124i	−0.160732	−	0.160732i	−0.782891	+	0.622159i	$0.786256\pi$
$744$	−12.9357			−0.474246
$745$	−1.93156	−	2.35549i	−0.0707670	−	0.0862983i
$746$	−25.5221			−0.934430
$747$	0.309197	+	0.309197i	0.0113129	+	0.0113129i
$748$	−6.02937	+	6.02937i	−0.220455	+	0.220455i
$749$	−38.8740			−1.42043
$750$	9.65392	+	18.1121i	0.352511	+	0.661360i
$751$		−	13.3649i		−	0.487691i	−0.969814	−	0.243846i	$-0.921591\pi$
$751$		−	13.3649i		−	0.487691i	0.969814	−	0.243846i	$-0.0784090\pi$
$752$	−4.04146	−	4.04146i	−0.147377	−	0.147377i
$753$	21.9214	+	21.9214i	0.798859	+	0.798859i
$754$	−4.52594			−0.164825
$755$	−25.5022	−	31.0992i	−0.928120	−	1.13182i
$756$		−	14.5176i		−	0.527998i
$757$	−20.6682	−	20.6682i	−0.751198	−	0.751198i	0.223505	−	0.974703i	$-0.428250\pi$
$757$	−20.6682	−	20.6682i	−0.751198	−	0.751198i	−0.974703	+	0.223505i	$0.928250\pi$
$758$	9.00864	−	9.00864i	0.327208	−	0.327208i
$759$	−73.8675			−2.68122
$760$	−9.05573	−	3.60467i	−0.328486	−	0.130755i
$761$	−1.48072			−0.0536760			−0.0268380	−	0.999640i	$-0.508544\pi$
$761$	−1.48072			−0.0536760			−0.0268380	+	0.999640i	$0.508544\pi$
$762$	1.10160	−	1.10160i	0.0399069	−	0.0399069i
$763$	−7.49242	−	7.49242i	−0.271244	−	0.271244i
$764$			13.5487i			0.490175i
$765$	−0.136423	+	1.37962i	−0.00493239	+	0.0498803i
$766$	−26.2789			−0.949496
$767$	36.7847	+	36.7847i	1.32822	+	1.32822i
$768$	1.29807	+	1.29807i	0.0468400	+	0.0468400i
$769$			37.5080i			1.35257i	0.736639	+	0.676286i	$0.236412\pi$
$769$			37.5080i			1.35257i	−0.736639	+	0.676286i	$0.763588\pi$
$770$	−26.4538	+	21.6928i	−0.953329	+	0.781756i
$771$	−8.67763			−0.312517
$772$	3.01172	−	3.01172i	0.108394	−	0.108394i
$773$	10.2801	+	10.2801i	0.369750	+	0.369750i	0.867386	−	0.497636i	$-0.165798\pi$
$773$	10.2801	+	10.2801i	0.369750	+	0.369750i	−0.497636	+	0.867386i	$0.665798\pi$
$774$	2.16971			0.0779887
$775$	−34.5505	−	6.90050i	−1.24109	−	0.247873i
$776$	−5.55393			−0.199374
$777$	−21.9750	−	21.9750i	−0.788347	−	0.788347i
$778$	−14.3345	−	14.3345i	−0.513918	−	0.513918i
$779$	2.87966	−	10.0044i	0.103174	−	0.358444i
$780$	16.6717	−	13.6712i	0.596942	−	0.489509i
$781$		−	31.3581i		−	1.12208i
$782$	9.37115	−	9.37115i	0.335111	−	0.335111i
$783$	2.94178	−	2.94178i	0.105131	−	0.105131i
$784$		−	2.04146i		−	0.0729092i
$785$	36.6203	+	3.62119i	1.30704	+	0.129246i
$786$	−5.02982			−0.179408
$787$	23.0345	−	23.0345i	0.821091	−	0.821091i	−0.165174	−	0.986264i	$-0.552819\pi$
$787$	23.0345	−	23.0345i	0.821091	−	0.821091i	0.986264	+	0.165174i	$0.0528185\pi$
$788$	−14.2004	+	14.2004i	−0.505869	+	0.505869i
$789$	31.1672			1.10958
$790$	−3.11319	+	31.4831i	−0.110762	+	1.12012i
$791$			55.8260i			1.98495i
$792$	1.33108	−	1.33108i	0.0472980	−	0.0472980i
$793$	15.6485	+	15.6485i	0.555696	+	0.555696i
$794$	3.20362			0.113692
$795$	−24.1906	−	29.4997i	−0.857951	−	1.04625i
$796$	−8.94564			−0.317070
$797$	11.4253	−	11.4253i	0.404706	−	0.404706i	−0.475182	−	0.879888i	$-0.657618\pi$
$797$	11.4253	−	11.4253i	0.404706	−	0.404706i	0.879888	+	0.475182i	$0.157618\pi$
$798$	−11.6436	−	21.0558i	−0.412179	−	0.745366i
$799$		−	9.57811i		−	0.338849i
$800$	2.77461	+	4.15951i	0.0980974	+	0.147061i
$801$			1.68632i			0.0595833i
$802$	−22.7991	−	22.7991i	−0.805065	−	0.805065i
$803$	−15.6075	+	15.6075i	−0.550776	+	0.550776i
$804$			11.6396i			0.410498i
$805$	41.1158	−	33.7161i	1.44914	−	1.18834i
$806$			37.0114i			1.30367i
$807$	−18.7447	−	18.7447i	−0.659845	−	0.659845i
$808$	4.06726	+	4.06726i	0.143086	+	0.143086i
$809$			20.2274i			0.711156i	0.934647	+	0.355578i	$0.115716\pi$
$809$			20.2274i			0.711156i	−0.934647	+	0.355578i	$0.884284\pi$
$810$	−2.19446	+	22.1921i	−0.0771055	+	0.779752i
$811$			4.69034i			0.164700i	0.996603	+	0.0823501i	$0.0262426\pi$
$811$			4.69034i			0.164700i	−0.996603	+	0.0823501i	$0.973757\pi$
$812$	1.83212	−	1.83212i	0.0642949	−	0.0642949i
$813$	10.3328	+	10.3328i	0.362387	+	0.362387i
$814$			28.6464i			1.00406i
$815$	0.823813	−	8.33105i	0.0288569	−	0.291824i
$816$			3.07638i			0.107695i
$817$	−22.3708	+	12.3708i	−0.782654	+	0.432798i
$818$	17.5781	−	17.5781i	0.614603	−	0.614603i
$819$	5.84302			0.204172
$820$	−4.12959	+	3.38637i	−0.144211	+	0.118257i
$821$	−20.4026			−0.712055			−0.356027	−	0.934476i	$-0.615869\pi$
$821$	−20.4026			−0.712055			−0.356027	+	0.934476i	$0.615869\pi$
$822$	12.6629	+	12.6629i	0.441668	+	0.441668i
$823$	−4.18493	+	4.18493i	−0.145878	+	0.145878i	−0.776274	−	0.630396i	$-0.782892\pi$
$823$	−4.18493	+	4.18493i	−0.145878	+	0.145878i	0.630396	+	0.776274i	$0.282892\pi$
$824$		−	3.61713i		−	0.126009i
$825$	38.8521	−	25.9164i	1.35266	−	0.902293i
$826$	−29.7813			−1.03622
$827$	0.0540683	−	0.0540683i	0.00188014	−	0.00188014i	−0.706166	−	0.708046i	$-0.749577\pi$
$827$	0.0540683	−	0.0540683i	0.00188014	−	0.00188014i	0.708046	+	0.706166i	$0.249577\pi$
$828$	−2.06884	+	2.06884i	−0.0718971	+	0.0718971i
$829$	41.6466			1.44644			0.723222	−	0.690615i	$-0.242660\pi$
$829$	41.6466			1.44644			0.723222	+	0.690615i	$0.242660\pi$
$830$	1.67582	+	2.04361i	0.0581685	+	0.0709348i
$831$		−	49.1268i		−	1.70419i
$832$	3.71401	−	3.71401i	0.128760	−	0.128760i
$833$	2.41909	−	2.41909i	0.0838166	−	0.0838166i
$834$		−	6.20048i		−	0.214705i
$835$	2.20473	−	22.2960i	0.0762980	−	0.771585i
$836$	−6.13484	+	21.3134i	−0.212178	+	0.737138i
$837$	−24.0567	−	24.0567i	−0.831523	−	0.831523i
$838$	−15.8919	−	15.8919i	−0.548976	−	0.548976i
$839$	3.89309			0.134404			0.0672022	−	0.997739i	$-0.478593\pi$
$839$	3.89309			0.134404			0.0672022	+	0.997739i	$0.478593\pi$
$840$	−1.21460	+	12.2830i	−0.0419076	+	0.423803i
$841$	−28.2575			−0.974396
$842$	25.2981	+	25.2981i	0.871829	+	0.871829i
$843$	−5.53746	+	5.53746i	−0.190720	+	0.190720i
$844$	−24.3448			−0.837981
$845$	−20.6835	−	25.2230i	−0.711535	−	0.867697i
$846$			2.11453i			0.0726990i
$847$	31.6575	+	31.6575i	1.08777	+	1.08777i
$848$	−6.57175	−	6.57175i	−0.225675	−	0.225675i
$849$	−18.4696			−0.633876
$850$	−1.64108	+	8.21681i	−0.0562886	+	0.281834i
$851$		−	44.5238i		−	1.52625i
$852$	−7.99995	−	7.99995i	−0.274074	−	0.274074i
$853$	−10.0390	+	10.0390i	−0.343730	+	0.343730i	−0.857767	−	0.514038i	$-0.828149\pi$
$853$	−10.0390	+	10.0390i	−0.343730	+	0.343730i	0.514038	+	0.857767i	$0.328149\pi$
$854$	−12.6692			−0.433532
$855$	1.42602	+	3.31202i	0.0487690	+	0.113269i
$856$	12.9283			0.441879
$857$	3.48995	−	3.48995i	0.119214	−	0.119214i	−0.644983	−	0.764197i	$-0.723135\pi$
$857$	3.48995	−	3.48995i	0.119214	−	0.119214i	0.764197	+	0.644983i	$0.223135\pi$
$858$	−34.6909	−	34.6909i	−1.18433	−	1.18433i
$859$		−	21.6236i		−	0.737789i	−0.929471	−	0.368894i	$-0.879736\pi$
$859$		−	21.6236i		−	0.737789i	0.929471	−	0.368894i	$-0.120264\pi$
$860$	13.0501	+	1.29045i	0.445005	+	0.0440041i
$861$	−13.1835			−0.449291
$862$	−9.06315	−	9.06315i	−0.308692	−	0.308692i
$863$	−25.9867	−	25.9867i	−0.884599	−	0.884599i	0.109399	−	0.993998i	$-0.465107\pi$
$863$	−25.9867	−	25.9867i	−0.884599	−	0.884599i	−0.993998	+	0.109399i	$0.965107\pi$
$864$			4.82808i			0.164255i
$865$	7.31248	+	0.723092i	0.248632	+	0.0245859i
$866$	3.50810			0.119210
$867$	18.4217	−	18.4217i	0.625634	−	0.625634i
$868$	−14.9824	−	14.9824i	−0.508536	−	0.508536i
$869$	71.9887			2.44205
$870$	−2.73509	+	2.24285i	−0.0927284	+	0.0760398i
$871$	33.3031			1.12843
$872$	2.49174	+	2.49174i	0.0843810	+	0.0843810i
$873$	1.45293	+	1.45293i	0.0491744	+	0.0491744i
$874$	9.53508	−	33.1263i	0.322529	−	1.12051i
$875$	−9.79642	+	32.1592i	−0.331180	+	1.08718i
$876$			7.96344i			0.269060i
$877$	−20.4804	+	20.4804i	−0.691573	+	0.691573i	−0.962578	−	0.271005i	$-0.912644\pi$
$877$	−20.4804	+	20.4804i	−0.691573	+	0.691573i	0.271005	+	0.962578i	$0.412644\pi$
$878$	12.6864	−	12.6864i	0.428145	−	0.428145i
$879$			36.0659i			1.21647i
$880$	8.79769	−	7.21435i	0.296570	−	0.243196i
$881$	−26.3529			−0.887852			−0.443926	−	0.896063i	$-0.646415\pi$
$881$	−26.3529			−0.887852			−0.443926	+	0.896063i	$0.646415\pi$
$882$	−0.534055	+	0.534055i	−0.0179826	+	0.0179826i
$883$	15.8220	−	15.8220i	0.532452	−	0.532452i	−0.388849	−	0.921301i	$-0.627127\pi$
$883$	15.8220	−	15.8220i	0.532452	−	0.532452i	0.921301	+	0.388849i	$0.127127\pi$
$884$	8.80207			0.296046
$885$	40.4584	+	4.00072i	1.35999	+	0.134483i
$886$			7.93017i			0.266419i
$887$	32.2731	−	32.2731i	1.08363	−	1.08363i	0.0874579	−	0.996168i	$-0.472126\pi$
$887$	32.2731	−	32.2731i	1.08363	−	1.08363i	0.996168	−	0.0874579i	$-0.0278743\pi$
$888$	7.30817	+	7.30817i	0.245246	+	0.245246i
$889$	2.55180			0.0855846
$890$	−1.00295	+	10.1427i	−0.0336191	+	0.339983i
$891$	50.7442			1.69999
$892$	7.74344	−	7.74344i	0.259269	−	0.259269i
$893$	−12.0561	−	21.8018i	−0.403443	−	0.729569i
$894$			2.50083i			0.0836403i
$895$	−3.54670	+	2.90839i	−0.118553	+	0.0972169i
$896$			3.00690i			0.100454i
$897$	53.9183	+	53.9183i	1.80028	+	1.80028i
$898$	11.8868	−	11.8868i	0.396668	−	0.396668i
$899$		−	6.07195i		−	0.202511i
$900$	0.362296	−	1.81400i	0.0120765	−	0.0604666i
$901$		−	15.5748i		−	0.518872i
$902$	8.59295	+	8.59295i	0.286114	+	0.286114i
$903$	22.8907	+	22.8907i	0.761754	+	0.761754i
$904$		−	18.5660i		−	0.617495i
$905$	−13.3775	−	16.3135i	−0.444684	−	0.542279i
$906$			33.0182i			1.09695i
$907$	−17.8874	+	17.8874i	−0.593942	+	0.593942i	−0.938694	−	0.344752i	$-0.887963\pi$
$907$	−17.8874	+	17.8874i	−0.593942	+	0.593942i	0.344752	+	0.938694i	$0.387963\pi$
$908$	1.35188	+	1.35188i	0.0448638	+	0.0448638i
$909$		−	2.12803i		−	0.0705822i
$910$	35.1438	+	3.47519i	1.16501	+	0.115201i
$911$		−	8.78015i		−	0.290899i	−0.989366	−	0.145450i	$-0.953537\pi$
$911$		−	8.78015i		−	0.290899i	0.989366	−	0.145450i	$-0.0464629\pi$
$912$	3.87229	+	7.00248i	0.128224	+	0.231875i
$913$	4.25240	−	4.25240i	0.140734	−	0.140734i
$914$	28.8538			0.954400
$915$	17.2114	+	1.70194i	0.568990	+	0.0562644i
$916$	29.2012			0.964836
$917$	−5.82564	−	5.82564i	−0.192380	−	0.192380i
$918$	−5.72119	+	5.72119i	−0.188827	+	0.188827i
$919$			21.7772i			0.718365i	0.933267	+	0.359182i	$0.116944\pi$
$919$			21.7772i			0.718365i	−0.933267	+	0.359182i	$0.883056\pi$
$920$	−13.6738	+	11.2129i	−0.450813	+	0.369679i
$921$	37.2100			1.22611
$922$	19.3253	−	19.3253i	0.636444	−	0.636444i
$923$	−22.8893	+	22.8893i	−0.753410	+	0.753410i
$924$	28.0861			0.923965
$925$	15.6212	+	23.4182i	0.513621	+	0.769985i
$926$		−	16.6164i		−	0.546047i
$927$	−0.946259	+	0.946259i	−0.0310792	+	0.0310792i
$928$	−0.609306	+	0.609306i	−0.0200015	+	0.0200015i
$929$			29.3526i			0.963027i	0.876439	+	0.481514i	$0.159913\pi$
$929$			29.3526i			0.963027i	−0.876439	+	0.481514i	$0.840087\pi$
$930$	18.3412	+	22.3666i	0.601432	+	0.733429i
$931$	2.46141	−	8.55131i	0.0806694	−	0.280258i
$932$	−17.3007	−	17.3007i	−0.566702	−	0.566702i
$933$	22.5531	+	22.5531i	0.738355	+	0.738355i
$934$	14.0482			0.459670
$935$	18.9740	+	1.87624i	0.620516	+	0.0613595i
$936$	−1.94320			−0.0635156
$937$	−39.6877	−	39.6877i	−1.29654	−	1.29654i	−0.930662	−	0.365880i	$-0.880768\pi$
$937$	−39.6877	−	39.6877i	−1.29654	−	1.29654i	−0.365880	−	0.930662i	$-0.619232\pi$
$938$	−13.4813	+	13.4813i	−0.440179	+	0.440179i
$939$	−45.5499			−1.48646
$940$	−1.25763	+	12.7182i	−0.0410195	+	0.414821i
$941$			24.8913i			0.811432i	0.913999	+	0.405716i	$0.132978\pi$
$941$			24.8913i			0.811432i	−0.913999	+	0.405716i	$0.867022\pi$
$942$	−21.3623	−	21.3623i	−0.696021	−	0.696021i
$943$	−13.3556	−	13.3556i	−0.434918	−	0.434918i
$944$	9.90431			0.322358
$945$	−25.1017	+	20.5841i	−0.816557	+	0.669599i
$946$		−	29.8402i		−	0.970188i
$947$	−17.8063	−	17.8063i	−0.578628	−	0.578628i	0.355897	−	0.934525i	$-0.384175\pi$
$947$	−17.8063	−	17.8063i	−0.578628	−	0.578628i	−0.934525	+	0.355897i	$0.884175\pi$
$948$	18.3655	−	18.3655i	0.596483	−	0.596483i
$949$	22.7848			0.739627
$950$	6.60720	+	20.7688i	0.214366	+	0.673830i
$951$	−8.05544			−0.261215
$952$	−3.56313	+	3.56313i	−0.115482	+	0.115482i
$953$	−40.1672	−	40.1672i	−1.30114	−	1.30114i	−0.927622	−	0.373521i	$-0.878150\pi$
$953$	−40.1672	−	40.1672i	−1.30114	−	1.30114i	−0.373521	−	0.927622i	$-0.621850\pi$
$954$			3.43840i			0.111322i
$955$	23.4265	−	19.2103i	0.758062	−	0.621632i
$956$	0.129605			0.00419174
$957$	5.69125	+	5.69125i	0.183972	+	0.183972i
$958$	−23.2849	−	23.2849i	−0.752301	−	0.752301i
$959$			29.3328i			0.947205i
$960$	0.403937	−	4.08493i	0.0130370	−	0.131841i
$961$	−18.6541			−0.601746
$962$	20.9100	−	20.9100i	0.674165	−	0.674165i
$963$	−3.38210	−	3.38210i	−0.108987	−	0.108987i
$964$	−15.3241			−0.493555
$965$	−9.47766	−	0.937195i	−0.305097	−	0.0301694i
$966$	−43.6529			−1.40451
$967$	37.7044	+	37.7044i	1.21249	+	1.21249i	0.970204	+	0.242288i	$0.0778979\pi$
$967$	37.7044	+	37.7044i	1.21249	+	1.21249i	0.242288	+	0.970204i	$0.422102\pi$
$968$	−10.5283	−	10.5283i	−0.338392	−	0.338392i
$969$	−3.70922	+	12.8864i	−0.119157	+	0.413971i
$970$	7.87477	+	9.60306i	0.252844	+	0.308336i
$971$			59.9297i			1.92323i	0.274394	+	0.961617i	$0.411523\pi$
$971$			59.9297i			1.92323i	−0.274394	+	0.961617i	$0.588477\pi$
$972$	2.70377	−	2.70377i	0.0867234	−	0.0867234i
$973$	7.18153	−	7.18153i	0.230229	−	0.230229i
$974$		−	16.2592i		−	0.520979i
$975$	−47.2767	−	9.44221i	−1.51407	−	0.302393i
$976$	4.21338			0.134867
$977$	−42.1006	+	42.1006i	−1.34692	+	1.34692i	−0.457927	+	0.888990i	$0.651408\pi$
$977$	−42.1006	+	42.1006i	−1.34692	+	1.34692i	−0.888990	+	0.457927i	$0.848592\pi$
$978$	−4.85988	+	4.85988i	−0.155402	+	0.155402i
$979$	23.1921			0.741222
$980$	−3.52980	+	2.89453i	−0.112755	+	0.0924623i
$981$		−	1.30370i		−	0.0416240i
$982$	−31.1328	+	31.1328i	−0.993488	+	0.993488i
$983$	17.8001	+	17.8001i	0.567736	+	0.567736i	0.931494	−	0.363758i	$-0.118506\pi$
$983$	17.8001	+	17.8001i	0.567736	+	0.567736i	−0.363758	+	0.931494i	$0.618506\pi$
$984$	4.38440			0.139770
$985$	44.6877	+	4.41893i	1.42387	+	0.140799i
$986$	−1.44403			−0.0459874
$987$	−22.3085	+	22.3085i	−0.710087	+	0.710087i
$988$	20.0354	−	11.0793i	0.637410	−	0.352480i
$989$			46.3791i			1.47477i
$990$	−4.18883	−	0.414211i	−0.133130	−	0.0131645i
$991$			52.1903i			1.65788i	0.559337	+	0.828940i	$0.311056\pi$
$991$			52.1903i			1.65788i	−0.559337	+	0.828940i	$0.688944\pi$
$992$	4.98268	+	4.98268i	0.158200	+	0.158200i
$993$	12.6311	−	12.6311i	0.400834	−	0.400834i
$994$		−	18.5314i		−	0.587781i
$995$	12.6838	+	15.4675i	0.402103	+	0.490353i
$996$		−	2.16971i		−	0.0687500i
$997$	15.2861	+	15.2861i	0.484117	+	0.484117i	0.906444	−	0.422327i	$-0.138787\pi$
$997$	15.2861	+	15.2861i	0.484117	+	0.484117i	−0.422327	+	0.906444i	$0.638787\pi$
$998$	20.0099	+	20.0099i	0.633401	+	0.633401i
$999$			27.1822i			0.860008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.f.b.37.7	yes	16
3.2	odd	2		1710.2.p.b.37.3		16
5.2	odd	4		950.2.f.c.493.7		16
5.3	odd	4	inner	190.2.f.b.113.2	yes	16
5.4	even	2		950.2.f.c.607.2		16
15.8	even	4		1710.2.p.b.1063.7		16
19.18	odd	2	inner	190.2.f.b.37.2	✓	16
57.56	even	2		1710.2.p.b.37.7		16
95.18	even	4	inner	190.2.f.b.113.7	yes	16
95.37	even	4		950.2.f.c.493.2		16
95.94	odd	2		950.2.f.c.607.7		16
285.113	odd	4		1710.2.p.b.1063.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.f.b.37.2	✓	16	19.18	odd	2	inner
190.2.f.b.37.7	yes	16	1.1	even	1	trivial
190.2.f.b.113.2	yes	16	5.3	odd	4	inner
190.2.f.b.113.7	yes	16	95.18	even	4	inner
950.2.f.c.493.2		16	95.37	even	4
950.2.f.c.493.7		16	5.2	odd	4
950.2.f.c.607.2		16	5.4	even	2
950.2.f.c.607.7		16	95.94	odd	2
1710.2.p.b.37.3		16	3.2	odd	2
1710.2.p.b.37.7		16	57.56	even	2
1710.2.p.b.1063.3		16	285.113	odd	4
1710.2.p.b.1063.7		16	15.8	even	4

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +(-1.72906 + 1.41787i) q^{5} +1.83575 q^{6} +(2.12620 + 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.29807 + 1.29807i) q^{3} -1.00000i q^{4} +(-1.72906 + 1.41787i) q^{5} +1.83575 q^{6} +(2.12620 + 2.12620i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.369965i q^{9} +(-0.220040 + 2.22522i) q^{10} +5.08815 q^{11} +(1.29807 - 1.29807i) q^{12} +(-3.71401 - 3.71401i) q^{13} +3.00690 q^{14} +(-4.08493 - 0.403937i) q^{15} -1.00000 q^{16} +(-1.18498 - 1.18498i) q^{17} +(0.261605 + 0.261605i) q^{18} +(-4.18883 - 1.20571i) q^{19} +(1.41787 + 1.72906i) q^{20} +5.51991i q^{21} +(3.59786 - 3.59786i) q^{22} +(-5.59198 + 5.59198i) q^{23} -1.83575i q^{24} +(0.979271 - 4.90317i) q^{25} -5.25240 q^{26} +(3.41397 - 3.41397i) q^{27} +(2.12620 - 2.12620i) q^{28} +0.861689 q^{29} +(-3.17411 + 2.60286i) q^{30} -7.04657i q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.60477 + 6.60477i) q^{33} -1.67582 q^{34} +(-6.69100 - 0.661638i) q^{35} +0.369965 q^{36} +(-3.98104 + 3.98104i) q^{37} +(-3.81451 + 2.10938i) q^{38} -9.64208i q^{39} +(2.22522 + 0.220040i) q^{40} +2.38835i q^{41} +(3.90317 + 3.90317i) q^{42} +(4.14693 - 4.14693i) q^{43} -5.08815i q^{44} +(-0.524563 - 0.639690i) q^{45} +7.90826i q^{46} +(4.04146 + 4.04146i) q^{47} +(-1.29807 - 1.29807i) q^{48} +2.04146i q^{49} +(-2.77461 - 4.15951i) q^{50} -3.07638i q^{51} +(-3.71401 + 3.71401i) q^{52} +(6.57175 + 6.57175i) q^{53} -4.82808i q^{54} +(-8.79769 + 7.21435i) q^{55} -3.00690i q^{56} +(-3.87229 - 7.00248i) q^{57} +(0.609306 - 0.609306i) q^{58} -9.90431 q^{59} +(-0.403937 + 4.08493i) q^{60} -4.21338 q^{61} +(-4.98268 - 4.98268i) q^{62} +(-0.786620 + 0.786620i) q^{63} +1.00000i q^{64} +(11.6877 + 1.15574i) q^{65} +9.34055 q^{66} +(-4.48345 + 4.48345i) q^{67} +(-1.18498 + 1.18498i) q^{68} -14.5176 q^{69} +(-5.19910 + 4.26341i) q^{70} -6.16296i q^{71} +(0.261605 - 0.261605i) q^{72} +(-3.06742 + 3.06742i) q^{73} +5.63004i q^{74} +(7.63581 - 5.09348i) q^{75} +(-1.20571 + 4.18883i) q^{76} +(10.8184 + 10.8184i) q^{77} +(-6.81798 - 6.81798i) q^{78} +14.1483 q^{79} +(1.72906 - 1.41787i) q^{80} +9.97302 q^{81} +(1.68882 + 1.68882i) q^{82} +(0.835746 - 0.835746i) q^{83} +5.51991 q^{84} +(3.72906 + 0.368746i) q^{85} -5.86464i q^{86} +(1.11853 + 1.11853i) q^{87} +(-3.59786 - 3.59786i) q^{88} +4.55806 q^{89} +(-0.823252 - 0.0814070i) q^{90} -15.7935i q^{91} +(5.59198 + 5.59198i) q^{92} +(9.14693 - 9.14693i) q^{93} +5.71548 q^{94} +(8.95226 - 3.85448i) q^{95} -1.83575 q^{96} +(3.92722 - 3.92722i) q^{97} +(1.44353 + 1.44353i) q^{98} +1.88244i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 16 q^{16} - 32 q^{17} + 8 q^{20} - 8 q^{23} + 32 q^{25} - 32 q^{26} + 8 q^{28} + 16 q^{30} - 24 q^{35} + 32 q^{36} + 8 q^{38} - 32 q^{42} + 24 q^{43} + 8 q^{45} + 32 q^{47} - 56 q^{55} - 48 q^{57} - 64 q^{61} - 8 q^{62} - 16 q^{63} + 16 q^{66} - 32 q^{68} + 16 q^{73} - 16 q^{76} + 72 q^{77} + 16 q^{81} + 40 q^{82} - 16 q^{83} + 32 q^{85} - 8 q^{87} + 8 q^{92} + 104 q^{93} + 24 q^{95}+O(q^{100}) \) 16 * q + 8 * q^7 - 16 * q^16 - 32 * q^17 + 8 * q^20 - 8 * q^23 + 32 * q^25 - 32 * q^26 + 8 * q^28 + 16 * q^30 - 24 * q^35 + 32 * q^36 + 8 * q^38 - 32 * q^42 + 24 * q^43 + 8 * q^45 + 32 * q^47 - 56 * q^55 - 48 * q^57 - 64 * q^61 - 8 * q^62 - 16 * q^63 + 16 * q^66 - 32 * q^68 + 16 * q^73 - 16 * q^76 + 72 * q^77 + 16 * q^81 + 40 * q^82 - 16 * q^83 + 32 * q^85 - 8 * q^87 + 8 * q^92 + 104 * q^93 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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