LMFDB - Embedded newform 425.3.u.a.326.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,0,16,-16,8,0,40,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			326.1
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	425.326
Dual form			425.3.u.a.176.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.63099 - 0.675577i) q^{2} +(-3.96908 - 0.789499i) q^{3} +(-0.624715 + 0.624715i) q^{4} +(-7.00688 + 1.39376i) q^{6} +(2.27356 - 3.40262i) q^{7} +(-3.29916 + 7.96489i) q^{8} +(6.81537 + 2.82302i) q^{9} +(1.35387 + 6.80638i) q^{11} +(2.97275 - 1.98633i) q^{12} +(-2.37416 - 2.37416i) q^{13} +(1.40941 - 7.08560i) q^{14} +11.6855i q^{16} +(8.76791 - 14.5645i) q^{17} +13.0229 q^{18} +(22.7712 - 9.43215i) q^{19} +(-11.7103 + 11.7103i) q^{21} +(6.80638 + 10.1865i) q^{22} +(11.2984 - 2.24740i) q^{23} +(19.3829 - 29.0086i) q^{24} +(-5.47615 - 2.26829i) q^{26} +(5.46144 + 3.64922i) q^{27} +(0.705343 + 3.54600i) q^{28} +(9.98767 - 6.67355i) q^{29} +(7.38055 - 37.1045i) q^{31} +(-5.30218 - 12.8006i) q^{32} -28.0839i q^{33} +(4.46094 - 29.6778i) q^{34} +(-6.02124 + 2.49408i) q^{36} +(31.6486 + 6.29529i) q^{37} +(30.7674 - 30.7674i) q^{38} +(7.54883 + 11.2976i) q^{39} +(18.7852 - 28.1140i) q^{41} +(-11.1881 + 27.0106i) q^{42} +(-3.21547 - 1.33189i) q^{43} +(-5.09783 - 3.40626i) q^{44} +(16.9093 - 11.2984i) q^{46} +(-3.16735 - 3.16735i) q^{47} +(9.22573 - 46.3809i) q^{48} +(12.3427 + 29.7979i) q^{49} +(-46.2992 + 50.8853i) q^{51} +2.96634 q^{52} +(28.3919 - 11.7603i) q^{53} +(11.3729 + 2.26220i) q^{54} +(19.6007 + 29.3345i) q^{56} +(-97.8275 + 19.4591i) q^{57} +(11.7813 - 17.6319i) q^{58} +(-4.49481 + 10.8514i) q^{59} +(58.9263 + 39.3733i) q^{61} +(-13.0294 - 65.5031i) q^{62} +(25.1008 - 16.7718i) q^{63} +(-50.3473 - 50.3473i) q^{64} +(-18.9728 - 45.8045i) q^{66} +28.5842i q^{67} +(3.62119 + 14.5761i) q^{68} -46.6187 q^{69} +(-33.7056 - 6.70446i) q^{71} +(-44.9700 + 44.9700i) q^{72} +(52.0431 + 77.8880i) q^{73} +(55.8713 - 11.1135i) q^{74} +(-8.33312 + 20.1179i) q^{76} +(26.2377 + 10.8680i) q^{77} +(19.9444 + 13.3265i) q^{78} +(4.18708 + 21.0499i) q^{79} +(-65.7422 - 65.7422i) q^{81} +(11.6452 - 58.5443i) q^{82} +(-43.4522 - 104.903i) q^{83} -14.6312i q^{84} -6.14419 q^{86} +(-44.9106 + 18.6026i) q^{87} +(-58.6787 - 11.6719i) q^{88} +(-28.3238 + 28.3238i) q^{89} +(-13.4762 + 2.68058i) q^{91} +(-5.65432 + 8.46229i) q^{92} +(-58.5880 + 141.444i) q^{93} +(-7.30570 - 3.02612i) q^{94} +(10.9387 + 54.9926i) q^{96} +(138.307 - 92.4136i) q^{97} +(40.2616 + 40.2616i) q^{98} +(-9.98738 + 50.2100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 16 q^{7} - 16 q^{8} + 8 q^{9} + 40 q^{11} - 40 q^{12} + 16 q^{14} + 16 q^{17} + 136 q^{18} - 32 q^{19} - 64 q^{21} + 8 q^{23} + 24 q^{24} - 96 q^{27} - 80 q^{28} + 24 q^{29} + 32 q^{31}+ \cdots + 136 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 16 * q^7 - 16 * q^8 + 8 * q^9 + 40 * q^11 - 40 * q^12 + 16 * q^14 + 16 * q^17 + 136 * q^18 - 32 * q^19 - 64 * q^21 + 8 * q^23 + 24 * q^24 - 96 * q^27 - 80 * q^28 + 24 * q^29 + 32 * q^31 + 24 * q^32 + 64 * q^34 - 104 * q^36 + 168 * q^37 - 8 * q^38 - 72 * q^39 + 72 * q^42 - 96 * q^43 - 96 * q^44 + 80 * q^47 - 88 * q^48 + 8 * q^49 - 176 * q^51 - 240 * q^52 - 96 * q^53 + 208 * q^54 + 72 * q^56 - 248 * q^57 + 8 * q^59 + 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 8 * q^66 + 176 * q^68 - 208 * q^69 + 32 * q^71 - 24 * q^72 - 24 * q^73 + 176 * q^74 - 80 * q^76 + 216 * q^77 + 368 * q^78 - 96 * q^79 - 224 * q^81 + 408 * q^82 + 88 * q^83 + 288 * q^86 - 312 * q^87 - 176 * q^88 + 288 * q^89 - 24 * q^91 - 336 * q^92 - 280 * q^93 - 8 * q^94 + 328 * q^96 + 344 * q^97 - 16 * q^98 + 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	1.63099	−	0.675577i	0.815493	−	0.337788i	0.0643498	−	0.997927i	$-0.479503\pi$
$2$	1.63099	−	0.675577i	0.815493	−	0.337788i	0.751143	+	0.660139i	$0.229503\pi$
$3$	−3.96908	−	0.789499i	−1.32303	−	0.263166i	−0.517478	−	0.855696i	$-0.673129\pi$
$3$	−3.96908	−	0.789499i	−1.32303	−	0.263166i	−0.805548	+	0.592530i	$0.798129\pi$
$4$	−0.624715	+	0.624715i	−0.156179	+	0.156179i
$5$		0			0
$5$		0			0
$6$	−7.00688	+	1.39376i	−1.16781	+	0.232293i
$7$	2.27356	−	3.40262i	0.324794	−	0.486089i	−0.632757	−	0.774350i	$-0.718077\pi$
$7$	2.27356	−	3.40262i	0.324794	−	0.486089i	0.957552	+	0.288261i	$0.0930770\pi$
$8$	−3.29916	+	7.96489i	−0.412396	+	0.995611i
$9$	6.81537	+	2.82302i	0.757263	+	0.313669i
$10$		0			0
$11$	1.35387	+	6.80638i	0.123079	+	0.618761i	0.992251	+	0.124251i	$0.0396527\pi$
$11$	1.35387	+	6.80638i	0.123079	+	0.618761i	−0.869172	+	0.494511i	$0.835347\pi$
$12$	2.97275	−	1.98633i	0.247729	−	0.165528i
$13$	−2.37416	−	2.37416i	−0.182628	−	0.182628i	0.609872	−	0.792500i	$-0.291221\pi$
$13$	−2.37416	−	2.37416i	−0.182628	−	0.182628i	−0.792500	+	0.609872i	$0.791221\pi$
$14$	1.40941	−	7.08560i	0.100672	−	0.506114i
$15$		0			0
$16$			11.6855i			0.730347i
$17$	8.76791	−	14.5645i	0.515760	−	0.856733i
$17$	8.76791	−	14.5645i	0.515760	−	0.856733i
$18$	13.0229			0.723496
$19$	22.7712	−	9.43215i	1.19849	−	0.496429i	0.307977	−	0.951394i	$-0.400348\pi$
$19$	22.7712	−	9.43215i	1.19849	−	0.496429i	0.890509	+	0.454965i	$0.150348\pi$
$20$		0			0
$21$	−11.7103	+	11.7103i	−0.557634	+	0.557634i
$22$	6.80638	+	10.1865i	0.309381	+	0.463021i
$23$	11.2984	−	2.24740i	0.491237	−	0.0977131i	0.0567447	−	0.998389i	$-0.481928\pi$
$23$	11.2984	−	2.24740i	0.491237	−	0.0977131i	0.434492	+	0.900676i	$0.356928\pi$
$24$	19.3829	−	29.0086i	0.807622	−	1.20869i
$25$		0			0
$26$	−5.47615	−	2.26829i	−0.210621	−	0.0872421i
$27$	5.46144	+	3.64922i	0.202276	+	0.135156i
$28$	0.705343	+	3.54600i	0.0251908	+	0.126643i
$29$	9.98767	−	6.67355i	0.344402	−	0.230122i	−0.371324	−	0.928504i	$-0.621096\pi$
$29$	9.98767	−	6.67355i	0.344402	−	0.230122i	0.715726	+	0.698381i	$0.246096\pi$
$30$		0			0
$31$	7.38055	−	37.1045i	0.238082	−	1.19692i	−0.657995	−	0.753022i	$-0.728595\pi$
$31$	7.38055	−	37.1045i	0.238082	−	1.19692i	0.896077	−	0.443898i	$-0.146405\pi$
$32$	−5.30218	−	12.8006i	−0.165693	−	0.400019i
$33$		−	28.0839i		−	0.851028i
$34$	4.46094	−	29.6778i	0.131204	−	0.872878i
$35$		0			0
$36$	−6.02124	+	2.49408i	−0.167257	+	0.0692800i
$37$	31.6486	+	6.29529i	0.855366	+	0.170143i	0.603248	−	0.797554i	$-0.293873\pi$
$37$	31.6486	+	6.29529i	0.855366	+	0.170143i	0.252118	+	0.967696i	$0.418873\pi$
$38$	30.7674	−	30.7674i	0.809669	−	0.809669i
$39$	7.54883	+	11.2976i	0.193560	+	0.289683i
$40$		0			0
$41$	18.7852	−	28.1140i	0.458175	−	0.685707i	−0.528404	−	0.848993i	$-0.677209\pi$
$41$	18.7852	−	28.1140i	0.458175	−	0.685707i	0.986579	+	0.163286i	$0.0522094\pi$
$42$	−11.1881	+	27.0106i	−0.266384	+	0.643109i
$43$	−3.21547	−	1.33189i	−0.0747784	−	0.0309742i	0.344981	−	0.938610i	$-0.387885\pi$
$43$	−3.21547	−	1.33189i	−0.0747784	−	0.0309742i	−0.419759	+	0.907636i	$0.637885\pi$
$44$	−5.09783	−	3.40626i	−0.115860	−	0.0774150i
$45$		0			0
$46$	16.9093	−	11.2984i	0.367594	−	0.245618i
$47$	−3.16735	−	3.16735i	−0.0673905	−	0.0673905i	0.672608	−	0.739999i	$-0.265174\pi$
$47$	−3.16735	−	3.16735i	−0.0673905	−	0.0673905i	−0.739999	+	0.672608i	$0.765174\pi$
$48$	9.22573	−	46.3809i	0.192203	−	0.966268i
$49$	12.3427	+	29.7979i	0.251892	+	0.608121i
$50$		0			0
$51$	−46.2992	+	50.8853i	−0.907827	+	0.997750i
$52$	2.96634			0.0570451
$53$	28.3919	−	11.7603i	0.535697	−	0.221893i	−0.0983994	−	0.995147i	$-0.531372\pi$
$53$	28.3919	−	11.7603i	0.535697	−	0.221893i	0.634096	+	0.773254i	$0.281372\pi$
$54$	11.3729	+	2.26220i	0.210609	+	0.0418927i
$55$		0			0
$56$	19.6007	+	29.3345i	0.350012	+	0.523830i
$57$	−97.8275	+	19.4591i	−1.71627	+	0.341388i
$58$	11.7813	−	17.6319i	0.203125	−	0.303998i
$59$	−4.49481	+	10.8514i	−0.0761832	+	0.183923i	−0.957383	−	0.288822i	$-0.906737\pi$
$59$	−4.49481	+	10.8514i	−0.0761832	+	0.183923i	0.881200	+	0.472744i	$0.156737\pi$
$60$		0			0
$61$	58.9263	+	39.3733i	0.966006	+	0.645464i	0.935222	−	0.354062i	$-0.115200\pi$
$61$	58.9263	+	39.3733i	0.966006	+	0.645464i	0.0307835	+	0.999526i	$0.490200\pi$
$62$	−13.0294	−	65.5031i	−0.210151	−	1.05650i
$63$	25.1008	−	16.7718i	0.398426	−	0.266220i
$64$	−50.3473	−	50.3473i	−0.786676	−	0.786676i
$65$		0			0
$66$	−18.9728	−	45.8045i	−0.287467	−	0.694008i
$67$			28.5842i			0.426629i	0.976984	+	0.213315i	$0.0684260\pi$
$67$			28.5842i			0.426629i	−0.976984	+	0.213315i	$0.931574\pi$
$68$	3.62119	+	14.5761i	0.0532528	+	0.214354i
$69$	−46.6187			−0.675634
$70$		0			0
$71$	−33.7056	−	6.70446i	−0.474726	−	0.0944290i	−0.0480724	−	0.998844i	$-0.515308\pi$
$71$	−33.7056	−	6.70446i	−0.474726	−	0.0944290i	−0.426654	+	0.904415i	$0.640308\pi$
$72$	−44.9700	+	44.9700i	−0.624584	+	0.624584i
$73$	52.0431	+	77.8880i	0.712919	+	1.06696i	0.994222	+	0.107340i	$0.0342334\pi$
$73$	52.0431	+	77.8880i	0.712919	+	1.06696i	−0.281303	+	0.959619i	$0.590767\pi$
$74$	55.8713	−	11.1135i	0.755018	−	0.150182i
$75$		0			0
$76$	−8.33312	+	20.1179i	−0.109646	+	0.264710i
$77$	26.2377	+	10.8680i	0.340749	+	0.141143i
$78$	19.9444	+	13.3265i	0.255698	+	0.170852i
$79$	4.18708	+	21.0499i	0.0530011	+	0.266454i	0.998195	−	0.0600549i	$-0.0191276\pi$
$79$	4.18708	+	21.0499i	0.0530011	+	0.266454i	−0.945194	+	0.326509i	$0.894128\pi$
$80$		0			0
$81$	−65.7422	−	65.7422i	−0.811632	−	0.811632i
$82$	11.6452	−	58.5443i	0.142015	−	0.713955i
$83$	−43.4522	−	104.903i	−0.523521	−	1.26389i	−0.935703	−	0.352789i	$-0.885233\pi$
$83$	−43.4522	−	104.903i	−0.523521	−	1.26389i	0.412182	−	0.911102i	$-0.364767\pi$
$84$		−	14.6312i		−	0.174181i
$85$		0			0
$86$	−6.14419			−0.0714440
$87$	−44.9106	+	18.6026i	−0.516214	+	0.213823i
$88$	−58.6787	−	11.6719i	−0.666803	−	0.132635i
$89$	−28.3238	+	28.3238i	−0.318245	+	0.318245i	−0.848093	−	0.529848i	$-0.822249\pi$
$89$	−28.3238	+	28.3238i	−0.318245	+	0.318245i	0.529848	+	0.848093i	$0.322249\pi$
$90$		0			0
$91$	−13.4762	+	2.68058i	−0.148090	+	0.0294569i
$92$	−5.65432	+	8.46229i	−0.0614600	+	0.0919814i
$93$	−58.5880	+	141.444i	−0.629978	+	1.52090i
$94$	−7.30570	−	3.02612i	−0.0777202	−	0.0321928i
$95$		0			0
$96$	10.9387	+	54.9926i	0.113945	+	0.572840i
$97$	138.307	−	92.4136i	1.42584	−	0.952718i	0.427018	−	0.904243i	$-0.359564\pi$
$97$	138.307	−	92.4136i	1.42584	−	0.952718i	0.998824	−	0.0484747i	$-0.0154360\pi$
$98$	40.2616	+	40.2616i	0.410833	+	0.410833i
$99$	−9.98738	+	50.2100i	−0.100883	+	0.507171i
$100$		0			0
$101$			124.444i			1.23211i	0.787701	+	0.616057i	$0.211271\pi$
$101$			124.444i			1.23211i	−0.787701	+	0.616057i	$0.788729\pi$
$102$	−41.1364	+	114.272i	−0.403298	+	1.12031i
$103$	−175.084			−1.69984			−0.849922	−	0.526908i	$-0.823351\pi$
$103$	−175.084			−1.69984			−0.849922	+	0.526908i	$0.823351\pi$
$104$	26.7427	−	11.0772i	0.257141	−	0.106511i
$105$		0			0
$106$	38.3619	−	38.3619i	0.361904	−	0.361904i
$107$	−22.1486	−	33.1477i	−0.206996	−	0.309791i	0.713416	−	0.700740i	$-0.247147\pi$
$107$	−22.1486	−	33.1477i	−0.206996	−	0.309791i	−0.920412	+	0.390949i	$0.872147\pi$
$108$	−5.69157	+	1.13212i	−0.0526997	+	0.0104826i
$109$	−25.4604	+	38.1042i	−0.233582	+	0.349580i	−0.929681	−	0.368366i	$-0.879917\pi$
$109$	−25.4604	+	38.1042i	−0.233582	+	0.349580i	0.696099	+	0.717946i	$0.254917\pi$
$110$		0			0
$111$	−120.645	−	49.9730i	−1.08690	−	0.450207i
$112$	39.7615	+	26.5678i	0.355014	+	0.237213i
$113$	36.5291	+	183.644i	0.323267	+	1.62517i	0.710855	+	0.703338i	$0.248308\pi$
$113$	36.5291	+	183.644i	0.323267	+	1.62517i	−0.387589	+	0.921832i	$0.626692\pi$
$114$	−146.409	+	97.8275i	−1.28429	+	0.858136i
$115$		0			0
$116$	−2.07038	+	10.4085i	−0.0178481	+	0.0897285i
$117$	−9.47847	−	22.8831i	−0.0810126	−	0.195582i
$118$			20.7351i			0.175721i
$119$	−29.6230	−	62.9471i	−0.248933	−	0.528967i
$120$		0			0
$121$	67.2956	−	27.8748i	0.556162	−	0.230370i
$122$	122.708	+	24.4081i	1.00580	+	0.200066i
$123$	−96.7557	+	96.7557i	−0.786632	+	0.786632i
$124$	18.5690	+	27.7905i	0.149750	+	0.224117i
$125$		0			0
$126$	29.6084	−	44.3122i	0.234988	−	0.351684i
$127$	15.7175	−	37.9454i	0.123760	−	0.298783i	−0.849841	−	0.527039i	$-0.823302\pi$
$127$	15.7175	−	37.9454i	0.123760	−	0.298783i	0.973601	+	0.228256i	$0.0733023\pi$
$128$	−64.9268	−	26.8936i	−0.507241	−	0.210106i
$129$	11.7109	+	7.82500i	0.0907825	+	0.0606589i
$130$		0			0
$131$	160.044	−	106.938i	1.22171	−	0.816323i	0.233944	−	0.972250i	$-0.424837\pi$
$131$	160.044	−	106.938i	1.22171	−	0.816323i	0.987769	+	0.155927i	$0.0498366\pi$
$132$	17.5444	+	17.5444i	0.132912	+	0.132912i
$133$	19.6777	−	98.9266i	0.147953	−	0.743809i
$134$	19.3108	+	46.6204i	0.144110	+	0.347913i
$135$		0			0
$136$	87.0776	+	117.886i	0.640276	+	0.866809i
$137$	−52.8361			−0.385665			−0.192832	−	0.981232i	$-0.561767\pi$
$137$	−52.8361			−0.385665			−0.192832	+	0.981232i	$0.561767\pi$
$138$	−76.0345	+	31.4945i	−0.550975	+	0.228221i
$139$	−51.4676	−	10.2376i	−0.370271	−	0.0736514i	0.00644773	−	0.999979i	$-0.497948\pi$
$139$	−51.4676	−	10.2376i	−0.370271	−	0.0736514i	−0.376719	+	0.926328i	$0.622948\pi$
$140$		0			0
$141$	10.0709	+	15.0721i	0.0714245	+	0.106894i
$142$	−59.5027	+	11.8358i	−0.419033	+	0.0833509i
$143$	12.9451	−	19.3737i	0.0905253	−	0.135481i
$144$	−32.9885	+	79.6413i	−0.229087	+	0.553064i
$145$		0			0
$146$	137.501	+	91.8752i	0.941787	+	0.629282i
$147$	−25.4638	−	128.015i	−0.173223	−	0.870850i
$148$	−23.7041	+	15.8386i	−0.160163	+	0.107017i
$149$	36.5973	+	36.5973i	0.245620	+	0.245620i	0.819170	−	0.573551i	$-0.194434\pi$
$149$	36.5973	+	36.5973i	0.245620	+	0.245620i	−0.573551	+	0.819170i	$0.694434\pi$
$150$		0			0
$151$	−91.9670	−	222.028i	−0.609053	−	1.47038i	−0.864032	−	0.503437i	$-0.832069\pi$
$151$	−91.9670	−	222.028i	−0.609053	−	1.47038i	0.254979	−	0.966947i	$-0.417931\pi$
$152$			212.489i			1.39795i
$153$	100.872	−	74.5102i	0.659296	−	0.486995i
$154$	50.1354			0.325555
$155$		0			0
$156$	−11.7737	−	2.34193i	−0.0754721	−	0.0150123i
$157$	190.153	−	190.153i	1.21117	−	1.21117i	0.240522	−	0.970644i	$-0.422681\pi$
$157$	190.153	−	190.153i	1.21117	−	1.21117i	0.970644	−	0.240522i	$-0.0773185\pi$
$158$	21.0499	+	31.5034i	0.133227	+	0.199389i
$159$	−121.975	+	24.2623i	−0.767136	+	0.152593i
$160$		0			0
$161$	18.0406	−	43.5540i	0.112054	−	0.270522i
$162$	−151.638	−	62.8107i	−0.936040	−	0.387720i
$163$	−32.2626	−	21.5571i	−0.197930	−	0.132252i	0.452656	−	0.891685i	$-0.350477\pi$
$163$	−32.2626	−	21.5571i	−0.197930	−	0.132252i	−0.650586	+	0.759433i	$0.725477\pi$
$164$	5.82785	+	29.2986i	0.0355357	+	0.178650i
$165$		0			0
$166$	−141.740	−	141.740i	−0.853855	−	0.853855i
$167$	−7.02867	+	35.3355i	−0.0420878	+	0.211590i	−0.996107	−	0.0881571i	$-0.971902\pi$
$167$	−7.02867	+	35.3355i	−0.0420878	+	0.211590i	0.954019	+	0.299747i	$0.0969022\pi$
$168$	−54.6371	−	131.906i	−0.325221	−	0.785152i
$169$		−	157.727i		−	0.933294i
$170$		0			0
$171$	181.821			1.06328
$172$	2.84081	−	1.17670i	0.0165163	−	0.00684128i
$173$	189.307	+	37.6555i	1.09426	+	0.217662i	0.709043	−	0.705165i	$-0.249127\pi$
$173$	189.307	+	37.6555i	1.09426	+	0.217662i	0.385215	+	0.922827i	$0.374127\pi$
$174$	−60.6811	+	60.6811i	−0.348742	+	0.348742i
$175$		0			0
$176$	−79.5362	+	15.8207i	−0.451910	+	0.0898905i
$177$	26.4075	−	39.5216i	0.149195	−	0.223286i
$178$	−27.0608	+	65.3307i	−0.152027	+	0.367026i
$179$	223.947	+	92.7619i	1.25110	+	0.518223i	0.907167	−	0.420771i	$-0.138241\pi$
$179$	223.947	+	92.7619i	1.25110	+	0.518223i	0.343933	+	0.938994i	$0.388241\pi$
$180$		0			0
$181$	−26.6333	−	133.895i	−0.147146	−	0.739750i	−0.981941	−	0.189190i	$-0.939414\pi$
$181$	−26.6333	−	133.895i	−0.147146	−	0.739750i	0.834795	−	0.550561i	$-0.185586\pi$
$182$	−20.1685	+	13.4762i	−0.110816	+	0.0740449i
$183$	−202.798	−	202.798i	−1.10819	−	1.10819i
$184$	−19.3751	+	97.4054i	−0.105300	+	0.529377i
$185$		0			0
$186$			270.274i			1.45308i
$187$	111.002	+	39.9593i	0.593593	+	0.213686i
$188$	3.95738			0.0210499
$189$	24.8339	−	10.2865i	0.131396	−	0.0544260i
$190$		0			0
$191$	123.244	−	123.244i	0.645254	−	0.645254i	−0.306588	−	0.951842i	$-0.599187\pi$
$191$	123.244	−	123.244i	0.645254	−	0.645254i	0.951842	+	0.306588i	$0.0991874\pi$
$192$	160.083	+	239.581i	0.833767	+	1.24782i
$193$	184.064	−	36.6126i	0.953700	−	0.189703i	0.306370	−	0.951913i	$-0.400886\pi$
$193$	184.064	−	36.6126i	0.953700	−	0.189703i	0.647330	+	0.762210i	$0.275886\pi$
$194$	163.144	−	244.162i	0.840948	−	1.25857i
$195$		0			0
$196$	−26.3259	−	10.9045i	−0.134316	−	0.0556354i
$197$	−238.742	−	159.522i	−1.21189	−	0.809759i	−0.225509	−	0.974241i	$-0.572405\pi$
$197$	−238.742	−	159.522i	−1.21189	−	0.809759i	−0.986380	+	0.164482i	$0.947405\pi$
$198$	17.6314	+	88.6390i	0.0890474	+	0.447672i
$199$	−76.1598	+	50.8883i	−0.382712	+	0.255720i	−0.732013	−	0.681290i	$-0.761419\pi$
$199$	−76.1598	+	50.8883i	−0.382712	+	0.255720i	0.349301	+	0.937011i	$0.386419\pi$
$200$		0			0
$201$	22.5672	−	113.453i	0.112274	−	0.564442i
$202$	84.0712	+	202.966i	0.416194	+	1.00478i
$203$		−	49.1570i		−	0.242153i
$204$	−2.86499	−	60.7125i	−0.0140441	−	0.297610i
$205$		0			0
$206$	−285.560	+	118.283i	−1.38621	+	0.574188i
$207$	83.3475	+	16.5788i	0.402645	+	0.0800911i
$208$	27.7433	−	27.7433i	0.133381	−	0.133381i
$209$	95.0281	+	142.220i	0.454680	+	0.680477i
$210$		0			0
$211$	20.0890	−	30.0653i	0.0952086	−	0.142490i	−0.780807	−	0.624772i	$-0.785192\pi$
$211$	20.0890	−	30.0653i	0.0952086	−	0.142490i	0.876016	+	0.482282i	$0.160192\pi$
$212$	−10.3900	+	25.0837i	−0.0490095	+	0.118319i
$213$	128.487	+	53.2210i	0.603225	+	0.249864i
$214$	−58.5178	−	39.1003i	−0.273448	−	0.182712i
$215$		0			0
$216$	−47.0838	+	31.4604i	−0.217981	+	0.145650i
$217$	−109.473	−	109.473i	−0.504482	−	0.504482i
$218$	−15.7833	+	79.3479i	−0.0724004	+	0.363981i
$219$	−145.071	−	350.232i	−0.662423	−	1.59923i
$220$		0			0
$221$	−55.3948	+	13.7619i	−0.250655	+	0.0622712i
$222$	−230.532			−1.03843
$223$	−372.417	+	154.260i	−1.67003	+	0.691750i	−0.998775	−	0.0494759i	$-0.984245\pi$
$223$	−372.417	+	154.260i	−1.67003	+	0.691750i	−0.671256	+	0.741226i	$0.734245\pi$
$224$	−55.6104	−	11.0616i	−0.248261	−	0.0493822i
$225$		0			0
$226$	183.644	+	274.843i	0.812585	+	1.21612i
$227$	−123.817	+	24.6288i	−0.545450	+	0.108497i	−0.460121	−	0.887856i	$-0.652194\pi$
$227$	−123.817	+	24.6288i	−0.545450	+	0.108497i	−0.0853288	+	0.996353i	$0.527194\pi$
$228$	48.9579	−	73.2707i	0.214728	−	0.321363i
$229$	−47.0477	+	113.583i	−0.205449	+	0.495997i	−0.992696	−	0.120640i	$-0.961505\pi$
$229$	−47.0477	+	113.583i	−0.205449	+	0.495997i	0.787248	+	0.616637i	$0.211505\pi$
$230$		0			0
$231$	−95.5591	−	63.8505i	−0.413676	−	0.276409i
$232$	20.2031	+	101.568i	0.0870823	+	0.437792i
$233$	−50.0074	+	33.4139i	−0.214624	+	0.143407i	−0.658236	−	0.752812i	$-0.728697\pi$
$233$	−50.0074	+	33.4139i	−0.214624	+	0.143407i	0.443612	+	0.896219i	$0.353697\pi$
$234$	−30.9185	−	30.9185i	−0.132130	−	0.132130i
$235$		0			0
$236$	−3.97107	−	9.58702i	−0.0168266	−	0.0406230i
$237$		−	86.8544i		−	0.366474i
$238$	−90.8404	−	82.6533i	−0.381682	−	0.347283i
$239$	−285.920			−1.19632			−0.598160	−	0.801377i	$-0.704101\pi$
$239$	−285.920			−1.19632			−0.598160	+	0.801377i	$0.704101\pi$
$240$		0			0
$241$	121.946	+	24.2566i	0.506002	+	0.100650i	0.441489	−	0.897267i	$-0.354451\pi$
$241$	121.946	+	24.2566i	0.506002	+	0.100650i	0.0645131	+	0.997917i	$0.479451\pi$
$242$	90.9267	−	90.9267i	0.375730	−	0.375730i
$243$	176.189	+	263.686i	0.725060	+	1.08513i
$244$	−61.4092	+	12.2151i	−0.251677	+	0.0500617i
$245$		0			0
$246$	−92.4414	+	223.173i	−0.375778	+	0.907208i
$247$	−76.4560	−	31.6691i	−0.309538	−	0.128215i
$248$	271.184	+	181.199i	1.09348	+	0.730642i
$249$	89.6446	+	450.674i	0.360018	+	1.80993i
$250$		0			0
$251$	−99.6747	−	99.6747i	−0.397110	−	0.397110i	0.480102	−	0.877213i	$-0.340600\pi$
$251$	−99.6747	−	99.6747i	−0.397110	−	0.397110i	−0.877213	+	0.480102i	$0.840600\pi$
$252$	−5.20324	+	26.1585i	−0.0206478	+	0.103803i
$253$	30.5933	+	73.8588i	0.120922	+	0.291932i
$254$		−	72.5069i		−	0.285460i
$255$		0			0
$256$	160.744			0.627906
$257$	−363.098	+	150.400i	−1.41283	+	0.585214i	−0.953048	−	0.302818i	$-0.902073\pi$
$257$	−363.098	+	150.400i	−1.41283	+	0.585214i	−0.459783	+	0.888032i	$0.652073\pi$
$258$	24.3868	+	4.85083i	0.0945224	+	0.0188017i
$259$	93.3754	−	93.3754i	0.360523	−	0.360523i
$260$		0			0
$261$	86.9092	−	17.2873i	0.332985	−	0.0662349i
$262$	188.785	−	282.537i	0.720554	−	1.07839i
$263$	111.542	−	269.286i	0.424113	−	1.02390i	−0.557008	−	0.830507i	$-0.688051\pi$
$263$	111.542	−	269.286i	0.424113	−	1.02390i	0.981121	−	0.193393i	$-0.0619493\pi$
$264$	223.685	+	92.6535i	0.847293	+	0.350960i
$265$		0			0
$266$	−34.7384	−	174.642i	−0.130595	−	0.656548i
$267$	134.781	−	90.0578i	0.504798	−	0.337295i
$268$	−17.8569	−	17.8569i	−0.0666304	−	0.0666304i
$269$	19.8781	−	99.9342i	0.0738965	−	0.371503i	−0.926087	−	0.377311i	$-0.876849\pi$
$269$	19.8781	−	99.9342i	0.0738965	−	0.371503i	0.999983	+	0.00580827i	$0.00184884\pi$
$270$		0			0
$271$			381.059i			1.40612i	0.711129	+	0.703061i	$0.248184\pi$
$271$			381.059i			1.40612i	−0.711129	+	0.703061i	$0.751816\pi$
$272$	170.194	+	102.458i	0.625712	+	0.376683i
$273$	55.6043			0.203679
$274$	−86.1749	+	35.6948i	−0.314507	+	0.130273i
$275$		0			0
$276$	29.1234	−	29.1234i	0.105520	−	0.105520i
$277$	37.3432	+	55.8881i	0.134813	+	0.201762i	0.892734	−	0.450585i	$-0.148785\pi$
$277$	37.3432	+	55.8881i	0.134813	+	0.201762i	−0.757920	+	0.652347i	$0.773785\pi$
$278$	−90.8593	+	18.0730i	−0.326832	+	0.0650109i
$279$	155.048	−	232.046i	0.555727	−	0.831705i
$280$		0			0
$281$	−348.356	−	144.294i	−1.23970	−	0.513501i	−0.336079	−	0.941834i	$-0.609101\pi$
$281$	−348.356	−	144.294i	−1.23970	−	0.513501i	−0.903621	+	0.428333i	$0.859101\pi$
$282$	26.6078	+	17.7788i	0.0943539	+	0.0630452i
$283$	−57.9083	−	291.125i	−0.204623	−	1.02871i	−0.937404	−	0.348245i	$-0.886778\pi$
$283$	−57.9083	−	291.125i	−0.204623	−	1.02871i	0.732781	−	0.680465i	$-0.238222\pi$
$284$	25.2447	−	16.8680i	0.0888899	−	0.0593944i
$285$		0			0
$286$	8.02486	−	40.3437i	0.0280590	−	0.141062i
$287$	−52.9521	−	127.838i	−0.184502	−	0.445428i
$288$		−	102.209i		−	0.354892i
$289$	−135.247	−	255.400i	−0.467984	−	0.883737i
$290$		0			0
$291$	−621.911	+	257.604i	−2.13715	+	0.885237i
$292$	−81.1699	−	16.1457i	−0.277979	−	0.0552935i
$293$	−99.8472	+	99.8472i	−0.340776	+	0.340776i	−0.856659	−	0.515883i	$-0.827464\pi$
$293$	−99.8472	+	99.8472i	−0.340776	+	0.340776i	0.515883	+	0.856659i	$0.327464\pi$
$294$	−128.015	−	191.588i	−0.435425	−	0.651660i
$295$		0			0
$296$	−154.555	+	231.308i	−0.522146	+	0.781446i
$297$	−17.4439	+	42.1132i	−0.0587336	+	0.141795i
$298$	84.4140	+	34.9654i	0.283269	+	0.117334i
$299$	−32.1600	−	21.4886i	−0.107559	−	0.0718683i
$300$		0			0
$301$	−11.8425	+	7.91291i	−0.0393439	+	0.0262887i
$302$	−299.994	−	299.994i	−0.993357	−	0.993357i
$303$	98.2481	−	493.926i	0.324251	−	1.63012i
$304$	110.220	+	266.094i	0.362565	+	0.875310i
$305$		0			0
$306$	114.184	−	189.672i	0.373150	−	0.619843i
$307$	259.641			0.845735			0.422868	−	0.906192i	$-0.361024\pi$
$307$	259.641			0.845735			0.422868	+	0.906192i	$0.361024\pi$
$308$	−23.1804	+	9.60165i	−0.0752612	+	0.0311742i
$309$	694.922	+	138.229i	2.24894	+	0.447342i
$310$		0			0
$311$	313.413	+	469.055i	1.00776	+	1.50822i	0.854112	+	0.520090i	$0.174102\pi$
$311$	313.413	+	469.055i	1.00776	+	1.50822i	0.153646	+	0.988126i	$0.450898\pi$
$312$	−114.889	+	22.8529i	−0.368234	+	0.0732464i
$313$	253.206	−	378.950i	0.808966	−	1.21070i	−0.165509	−	0.986208i	$-0.552927\pi$
$313$	253.206	−	378.950i	0.808966	−	1.21070i	0.974475	−	0.224495i	$-0.0720733\pi$
$314$	181.674	−	438.600i	0.578580	−	1.39681i
$315$		0			0
$316$	−15.7659	−	10.5344i	−0.0498921	−	0.0333368i
$317$	64.7580	+	325.560i	0.204284	+	1.02700i	0.937759	+	0.347288i	$0.112897\pi$
$317$	64.7580	+	325.560i	0.204284	+	1.02700i	−0.733475	+	0.679717i	$0.762103\pi$
$318$	−182.548	+	121.975i	−0.574050	+	0.383568i
$319$	58.9447	+	58.9447i	0.184780	+	0.184780i
$320$		0			0
$321$	61.7394	+	149.052i	0.192334	+	0.464336i
$322$		−	83.2238i		−	0.258459i
$323$	62.2820	−	414.351i	0.192823	−	1.28282i
$324$	82.1402			0.253519
$325$		0			0
$326$	−67.1833	−	13.3636i	−0.206084	−	0.0409926i
$327$	131.138	−	131.138i	0.401033	−	0.401033i
$328$	161.949	+	242.374i	0.493748	+	0.738946i
$329$	−17.9785	+	3.57614i	−0.0546459	+	0.0108697i
$330$		0			0
$331$	225.594	−	544.633i	0.681554	−	1.64542i	−0.0795855	−	0.996828i	$-0.525360\pi$
$331$	225.594	−	544.633i	0.681554	−	1.64542i	0.761139	−	0.648588i	$-0.224640\pi$
$332$	92.6796	+	38.3892i	0.279156	+	0.115630i
$333$	197.925	+	132.249i	0.594369	+	0.397145i
$334$	12.4082	+	62.3801i	0.0371502	+	0.186767i
$335$		0			0
$336$	−136.841	−	136.841i	−0.407266	−	0.407266i
$337$	−63.9095	+	321.295i	−0.189642	+	0.953397i	0.762324	+	0.647195i	$0.224058\pi$
$337$	−63.9095	+	321.295i	−0.189642	+	0.953397i	−0.951967	+	0.306202i	$0.900942\pi$
$338$	−106.557	−	257.250i	−0.315256	−	0.761095i
$339$		−	757.738i		−	2.23522i
$340$		0			0
$341$	262.540			0.769911
$342$	296.548	−	122.834i	0.867100	−	0.359165i
$343$	326.123	+	64.8699i	0.950796	+	0.189125i
$344$	21.2167	−	21.2167i	0.0616766	−	0.0616766i
$345$		0			0
$346$	334.196	−	66.4757i	0.965884	−	0.192126i
$347$	−134.483	+	201.268i	−0.387560	+	0.580024i	−0.973033	−	0.230668i	$-0.925909\pi$
$347$	−134.483	+	201.268i	−0.387560	+	0.580024i	0.585473	+	0.810692i	$0.300909\pi$
$348$	16.4350	−	39.6776i	0.0472270	−	0.114016i
$349$	464.685	+	192.479i	1.33148	+	0.551515i	0.931076	−	0.364826i	$-0.118871\pi$
$349$	464.685	+	192.479i	1.33148	+	0.551515i	0.400399	+	0.916341i	$0.368871\pi$
$350$		0			0
$351$	−4.30251	−	21.6302i	−0.0122579	−	0.0616244i
$352$	79.9472	−	53.4190i	0.227123	−	0.151759i
$353$	231.294	+	231.294i	0.655223	+	0.655223i	0.954246	−	0.299023i	$-0.0966606\pi$
$353$	231.294	+	231.294i	0.655223	+	0.655223i	−0.299023	+	0.954246i	$0.596661\pi$
$354$	16.3704	−	82.2994i	0.0462440	−	0.232484i
$355$		0			0
$356$		−	35.3886i		−	0.0994062i
$357$	67.8794	+	273.230i	0.190138	+	0.765349i
$358$	427.922			1.19531
$359$	−490.942	+	203.355i	−1.36753	+	0.566448i	−0.941117	−	0.338082i	$-0.890222\pi$
$359$	−490.942	+	203.355i	−1.36753	+	0.566448i	−0.426410	+	0.904530i	$0.640222\pi$
$360$		0			0
$361$	174.298	−	174.298i	0.482820	−	0.482820i
$362$	−133.895	−	200.388i	−0.369875	−	0.553557i
$363$	−289.109	+	57.5073i	−0.796443	+	0.158422i
$364$	6.74416	−	10.0934i	0.0185279	−	0.0277290i
$365$		0			0
$366$	−467.767	−	193.755i	−1.27805	−	0.529386i
$367$	275.260	+	183.923i	0.750026	+	0.501152i	0.870866	−	0.491520i	$-0.163559\pi$
$367$	275.260	+	183.923i	0.750026	+	0.501152i	−0.120840	+	0.992672i	$0.538559\pi$
$368$	26.2621	+	132.028i	0.0713644	+	0.358773i
$369$	207.394	−	138.576i	0.562043	−	0.375545i
$370$		0			0
$371$	24.5348	−	123.345i	0.0661316	−	0.332466i
$372$	−51.7613	−	124.963i	−0.139143	−	0.335922i
$373$		−	147.856i		−	0.396396i	−0.980162	−	0.198198i	$-0.936491\pi$
$373$		−	147.856i		−	0.396396i	0.980162	−	0.198198i	$-0.0635089\pi$
$374$	208.038	−	9.81721i	0.556252	−	0.0262492i
$375$		0			0
$376$	35.6772	−	14.7780i	0.0948863	−	0.0393032i
$377$	−39.5564	−	7.86825i	−0.104924	−	0.0208707i
$378$	33.5543	−	33.5543i	0.0887681	−	0.0887681i
$379$	24.2695	+	36.3219i	0.0640357	+	0.0958362i	0.862106	−	0.506729i	$-0.169145\pi$
$379$	24.2695	+	36.3219i	0.0640357	+	0.0958362i	−0.798070	+	0.602565i	$0.794145\pi$
$380$		0			0
$381$	−92.3419	+	138.199i	−0.242367	+	0.362728i
$382$	117.748	−	284.269i	0.308241	−	0.744160i
$383$	−182.570	−	75.6230i	−0.476684	−	0.197449i	0.131387	−	0.991331i	$-0.458057\pi$
$383$	−182.570	−	75.6230i	−0.476684	−	0.197449i	−0.608072	+	0.793882i	$0.708057\pi$
$384$	236.467	+	158.002i	0.615800	+	0.411464i
$385$		0			0
$386$	275.471	−	184.064i	0.713656	−	0.476850i
$387$	−18.1547	−	18.1547i	−0.0469113	−	0.0469113i
$388$	−28.6701	+	144.134i	−0.0738920	+	0.371480i
$389$	8.22534	+	19.8577i	0.0211448	+	0.0510481i	0.934099	−	0.357013i	$-0.116205\pi$
$389$	8.22534	+	19.8577i	0.0211448	+	0.0510481i	−0.912954	+	0.408061i	$0.866205\pi$
$390$		0			0
$391$	66.3316	−	184.261i	0.169646	−	0.471255i
$392$	−278.058			−0.709332
$393$	−719.657	+	298.092i	−1.83119	+	0.758503i
$394$	−497.155	−	98.8903i	−1.26181	−	0.250991i
$395$		0			0
$396$	−25.1276	−	37.6062i	−0.0634536	−	0.0949650i
$397$	34.7954	−	6.92123i	0.0876457	−	0.0174338i	−0.151073	−	0.988523i	$-0.548273\pi$
$397$	34.7954	−	6.92123i	0.0876457	−	0.0174338i	0.238718	+	0.971089i	$0.423273\pi$
$398$	−89.8366	+	134.450i	−0.225720	+	0.337814i
$399$	−156.205	+	377.112i	−0.391491	+	0.945142i
$400$		0			0
$401$	−124.358	−	83.0937i	−0.310121	−	0.207216i	0.390763	−	0.920491i	$-0.372211\pi$
$401$	−124.358	−	83.0937i	−0.310121	−	0.207216i	−0.700884	+	0.713275i	$0.747211\pi$
$402$	−39.8393	−	200.286i	−0.0991028	−	0.498224i
$403$	−105.615	+	70.5695i	−0.262071	+	0.175110i
$404$	−77.7417	−	77.7417i	−0.192430	−	0.192430i
$405$		0			0
$406$	−33.2093	−	80.1744i	−0.0817964	−	0.197474i
$407$			223.935i			0.550209i
$408$	−252.547	−	536.647i	−0.618987	−	1.31531i
$409$	−398.892			−0.975287			−0.487643	−	0.873043i	$-0.662143\pi$
$409$	−398.892			−0.975287			−0.487643	+	0.873043i	$0.662143\pi$
$410$		0			0
$411$	209.711	+	41.7140i	0.510245	+	0.101494i
$412$	109.378	−	109.378i	0.265479	−	0.265479i
$413$	26.7041	+	39.9656i	0.0646589	+	0.0967689i
$414$	147.139	−	29.2678i	0.355408	−	0.0706951i
$415$		0			0
$416$	−17.8024	+	42.9789i	−0.0427943	+	0.103315i
$417$	196.197	+	81.2673i	0.470496	+	0.194886i
$418$	251.070	+	167.760i	0.600646	+	0.401339i
$419$	7.29632	+	36.6811i	0.0174137	+	0.0875444i	0.988515	−	0.151124i	$-0.0482892\pi$
$419$	7.29632	+	36.6811i	0.0174137	+	0.0875444i	−0.971101	+	0.238668i	$0.923289\pi$
$420$		0			0
$421$	312.706	+	312.706i	0.742769	+	0.742769i	0.973110	−	0.230341i	$-0.0739841\pi$
$421$	312.706	+	312.706i	0.742769	+	0.742769i	−0.230341	+	0.973110i	$0.573984\pi$
$422$	12.4535	−	62.6078i	0.0295106	−	0.148360i
$423$	−12.6452	−	30.5282i	−0.0298941	−	0.0721706i
$424$			264.938i			0.624853i
$425$		0			0
$426$	245.515			0.576327
$427$	267.945	−	110.987i	0.627507	−	0.259922i
$428$	34.5444	+	6.87130i	0.0807111	+	0.0160544i
$429$	−66.6757	+	66.6757i	−0.155421	+	0.155421i
$430$		0			0
$431$	−340.230	+	67.6760i	−0.789397	+	0.157021i	−0.573294	−	0.819350i	$-0.694335\pi$
$431$	−340.230	+	67.6760i	−0.789397	+	0.157021i	−0.216103	+	0.976371i	$0.569335\pi$
$432$	−42.6431	+	63.8199i	−0.0987109	+	0.147731i
$433$	20.5680	−	49.6556i	0.0475012	−	0.114678i	−0.898348	−	0.439285i	$-0.855232\pi$
$433$	20.5680	−	49.6556i	0.0475012	−	0.114678i	0.945849	+	0.324607i	$0.105232\pi$
$434$	−252.506	−	104.591i	−0.581810	−	0.240994i
$435$		0			0
$436$	−7.89876	−	39.7098i	−0.0181164	−	0.0910774i
$437$	236.082	−	157.745i	0.540233	−	0.360972i
$438$	−473.217	−	473.217i	−1.08040	−	1.08040i
$439$	47.4571	−	238.583i	0.108103	−	0.543469i	−0.888339	−	0.459188i	$-0.848140\pi$
$439$	47.4571	−	238.583i	0.108103	−	0.543469i	0.996442	−	0.0842815i	$-0.0268595\pi$
$440$		0			0
$441$			237.928i			0.539518i
$442$	−81.0509	+	59.8690i	−0.183373	+	0.135450i
$443$	114.592			0.258673			0.129336	−	0.991601i	$-0.458715\pi$
$443$	114.592			0.258673			0.129336	+	0.991601i	$0.458715\pi$
$444$	106.588	−	44.1501i	0.240063	−	0.0994373i
$445$		0			0
$446$	−503.192	+	503.192i	−1.12823	+	1.12823i
$447$	−116.364	−	174.151i	−0.260322	−	0.389600i
$448$	−285.780	+	56.8453i	−0.637903	+	0.126887i
$449$	−301.785	+	451.653i	−0.672127	+	1.00591i	0.326038	+	0.945357i	$0.394286\pi$
$449$	−301.785	+	451.653i	−0.672127	+	1.00591i	−0.998165	+	0.0605527i	$0.980714\pi$
$450$		0			0
$451$	216.787	+	89.7961i	0.480681	+	0.199104i
$452$	−137.546	−	91.9050i	−0.304304	−	0.203330i
$453$	189.733	+	953.854i	0.418838	+	2.10564i
$454$	−185.305	+	123.817i	−0.408162	+	0.272725i
$455$		0			0
$456$	167.760	−	843.384i	0.367894	−	1.84953i
$457$	85.9222	+	207.434i	0.188014	+	0.453905i	0.989577	−	0.144005i	$-0.0459981\pi$
$457$	85.9222	+	207.434i	0.188014	+	0.453905i	−0.801563	+	0.597910i	$0.795998\pi$
$458$			217.037i			0.473880i
$459$	101.034	−	47.5470i	0.220119	−	0.103588i
$460$		0			0
$461$	−233.070	+	96.5408i	−0.505575	+	0.209416i	−0.620867	−	0.783916i	$-0.713219\pi$
$461$	−233.070	+	96.5408i	−0.505575	+	0.209416i	0.115292	+	0.993332i	$0.463219\pi$
$462$	−198.991	−	39.5819i	−0.430717	−	0.0856750i
$463$	−88.6506	+	88.6506i	−0.191470	+	0.191470i	−0.796331	−	0.604861i	$-0.793229\pi$
$463$	−88.6506	+	88.6506i	−0.191470	+	0.191470i	0.604861	+	0.796331i	$0.293229\pi$
$464$	77.9840	+	116.711i	0.168069	+	0.251533i
$465$		0			0
$466$	−58.9878	+	88.2815i	−0.126583	+	0.189445i
$467$	−265.152	+	640.133i	−0.567777	+	1.37074i	0.335647	+	0.941988i	$0.391045\pi$
$467$	−265.152	+	640.133i	−0.567777	+	1.37074i	−0.903424	+	0.428748i	$0.858955\pi$
$468$	20.2167	+	8.37404i	0.0431981	+	0.0178932i
$469$	97.2612	+	64.9879i	0.207380	+	0.138567i
$470$		0			0
$471$	−904.858	+	604.607i	−1.92114	+	1.28367i
$472$	−71.6013	−	71.6013i	−0.151698	−	0.151698i
$473$	4.71202	−	23.6889i	0.00996199	−	0.0500823i
$474$	−58.6768	−	141.658i	−0.123791	−	0.298857i
$475$		0			0
$476$	57.8299	+	20.8181i	0.121491	+	0.0437354i
$477$	226.701			0.475264
$478$	−466.332	+	193.161i	−0.975591	+	0.404103i
$479$	469.496	+	93.3885i	0.980158	+	0.194965i	0.659068	−	0.752083i	$-0.270951\pi$
$479$	469.496	+	93.3885i	0.980158	+	0.194965i	0.321090	+	0.947049i	$0.395951\pi$
$480$		0			0
$481$	−60.1927	−	90.0847i	−0.125141	−	0.187286i
$482$	215.280	−	42.8219i	0.446639	−	0.0888421i
$483$	−105.991	+	158.626i	−0.219442	+	0.328418i
$484$	−24.6268	+	59.4543i	−0.0508818	+	0.122840i
$485$		0			0
$486$	465.503	+	311.039i	0.957825	+	0.639998i
$487$	−79.1411	−	397.869i	−0.162507	−	0.816980i	−0.972924	−	0.231126i	$-0.925759\pi$
$487$	−79.1411	−	397.869i	−0.162507	−	0.816980i	0.810417	−	0.585854i	$-0.199241\pi$
$488$	−508.012	+	339.443i	−1.04101	+	0.695579i
$489$	111.033	+	111.033i	0.227062	+	0.227062i
$490$		0			0
$491$	−23.7416	−	57.3172i	−0.0483535	−	0.116736i	0.897857	−	0.440287i	$-0.145123\pi$
$491$	−23.7416	−	57.3172i	−0.0483535	−	0.116736i	−0.946211	+	0.323551i	$0.895123\pi$
$492$		−	120.889i		−	0.245710i
$493$	−9.62562	−	203.978i	−0.0195246	−	0.413749i
$494$	−146.094			−0.295736
$495$		0			0
$496$	433.587	+	86.2458i	0.874167	+	0.173883i
$497$	−99.4445	+	99.4445i	−0.200089	+	0.200089i
$498$	450.674	+	674.481i	0.904967	+	1.35438i
$499$	−503.379	+	100.128i	−1.00878	+	0.200658i	−0.671703	−	0.740821i	$-0.734437\pi$
$499$	−503.379	+	100.128i	−1.00878	+	0.200658i	−0.337073	+	0.941479i	$0.609437\pi$
$500$		0			0
$501$	55.7947	−	134.700i	0.111367	−	0.268863i
$502$	−229.906	−	95.2302i	−0.457980	−	0.189702i
$503$	−275.118	−	183.828i	−0.546954	−	0.365463i	0.251182	−	0.967940i	$-0.419181\pi$
$503$	−275.118	−	183.828i	−0.546954	−	0.365463i	−0.798136	+	0.602477i	$0.794181\pi$
$504$	50.7740	+	255.258i	0.100742	+	0.506465i
$505$		0			0
$506$	99.7945	+	99.7945i	0.197222	+	0.197222i
$507$	−124.525	+	626.030i	−0.245612	+	1.23477i
$508$	13.8861	+	33.5240i	0.0273349	+	0.0659922i
$509$			343.247i			0.674355i	0.941441	+	0.337178i	$0.109472\pi$
$509$			343.247i			0.674355i	−0.941441	+	0.337178i	$0.890528\pi$
$510$		0			0
$511$	383.347			0.750190
$512$	521.878	−	216.169i	1.01929	−	0.422205i
$513$	158.784	+	31.5841i	0.309520	+	0.0615674i
$514$	−490.601	+	490.601i	−0.954476	+	0.954476i
$515$		0			0
$516$	−12.2044	+	2.42760i	−0.0236519	+	0.00470466i
$517$	17.2700	−	25.8464i	0.0334043	−	0.0499930i
$518$	89.2118	−	215.376i	0.172224	−	0.415784i
$519$	−721.645	−	298.915i	−1.39045	−	0.575944i
$520$		0			0
$521$	62.1355	+	312.376i	0.119262	+	0.599570i	0.993477	+	0.114032i	$0.0363765\pi$
$521$	62.1355	+	312.376i	0.119262	+	0.599570i	−0.874215	+	0.485539i	$0.838623\pi$
$522$	130.069	−	86.9092i	0.249174	−	0.166493i
$523$	167.575	+	167.575i	0.320410	+	0.320410i	0.848924	−	0.528514i	$-0.177251\pi$
$523$	167.575	+	167.575i	0.320410	+	0.320410i	−0.528514	+	0.848924i	$0.677251\pi$
$524$	−33.1762	+	166.788i	−0.0633133	+	0.318298i
$525$		0			0
$526$		−	514.556i		−	0.978244i
$527$	−475.696	−	432.823i	−0.902649	−	0.821296i
$528$	328.176			0.621545
$529$	−366.128	+	151.655i	−0.692114	+	0.286683i
$530$		0			0
$531$	−61.2676	+	61.2676i	−0.115381	+	0.115381i
$532$	49.5079	+	74.0938i	0.0930600	+	0.139274i
$533$	−111.346	+	22.1481i	−0.208904	+	0.0415537i
$534$	158.985	−	237.938i	0.297725	−	0.445577i
$535$		0			0
$536$	−227.670	−	94.3039i	−0.424757	−	0.175940i
$537$	−815.628	−	544.985i	−1.51886	−	1.01487i
$538$	−35.0922	−	176.421i	−0.0652272	−	0.327919i
$539$	−186.106	+	124.352i	−0.345279	+	0.230708i
$540$		0			0
$541$	51.6826	−	259.826i	0.0955316	−	0.480270i	−0.903168	−	0.429287i	$-0.858765\pi$
$541$	51.6826	−	259.826i	0.0955316	−	0.480270i	0.998700	−	0.0509824i	$-0.0162352\pi$
$542$	257.435	+	621.502i	0.474972	+	1.14668i
$543$			552.466i			1.01743i
$544$	−232.923	−	35.0111i	−0.428167	−	0.0643586i
$545$		0			0
$546$	90.6899	−	37.5650i	0.166099	−	0.0688003i
$547$	−353.859	−	70.3869i	−0.646909	−	0.128678i	−0.139278	−	0.990253i	$-0.544478\pi$
$547$	−353.859	−	70.3869i	−0.646909	−	0.128678i	−0.507630	+	0.861575i	$0.669478\pi$
$548$	33.0075	−	33.0075i	0.0602326	−	0.0602326i
$549$	290.453	+	434.694i	0.529058	+	0.791792i
$550$		0			0
$551$	164.486	−	246.170i	0.298522	−	0.446770i
$552$	153.803	−	371.313i	0.278629	−	0.672669i
$553$	81.1445	+	33.6111i	0.146735	+	0.0607797i
$554$	98.6630	+	65.9245i	0.178092	+	0.118997i
$555$		0			0
$556$	38.5481	−	25.7570i	0.0693312	−	0.0463256i
$557$	367.145	+	367.145i	0.659147	+	0.659147i	0.955178	−	0.296031i	$-0.0956632\pi$
$557$	367.145	+	367.145i	0.659147	+	0.659147i	−0.296031	+	0.955178i	$0.595663\pi$
$558$	96.1164	−	483.210i	0.172252	−	0.865968i
$559$	4.47192	+	10.7962i	0.00799986	+	0.0193134i
$560$		0			0
$561$	−409.027	−	246.237i	−0.729104	−	0.438926i
$562$	−665.645			−1.18442
$563$	−406.232	+	168.267i	−0.721549	+	0.298875i	−0.713074	−	0.701089i	$-0.752698\pi$
$563$	−406.232	+	168.267i	−0.721549	+	0.298875i	−0.00847487	+	0.999964i	$0.502698\pi$
$564$	−15.7072	−	3.12435i	−0.0278496	−	0.00553963i
$565$		0			0
$566$	−291.125	−	435.699i	−0.514355	−	0.769786i
$567$	−373.165	+	74.2271i	−0.658139	+	0.130912i
$568$	164.601	−	246.342i	0.289790	−	0.433701i
$569$	−183.595	+	443.238i	−0.322663	+	0.778977i	0.676435	+	0.736503i	$0.263524\pi$
$569$	−183.595	+	443.238i	−0.322663	+	0.778977i	−0.999098	+	0.0424747i	$0.986476\pi$
$570$		0			0
$571$	452.464	+	302.327i	0.792406	+	0.529469i	0.884643	−	0.466268i	$-0.154402\pi$
$571$	452.464	+	302.327i	0.792406	+	0.529469i	−0.0922371	+	0.995737i	$0.529402\pi$
$572$	4.01605	+	20.1901i	0.00702107	+	0.0352973i
$573$	−586.464	+	391.863i	−1.02350	+	0.683879i
$574$	−172.728	−	172.728i	−0.300920	−	0.300920i
$575$		0			0
$576$	−201.004	−	485.266i	−0.348965	−	0.842476i
$577$			304.419i			0.527589i	0.964579	+	0.263795i	$0.0849741\pi$
$577$			304.419i			0.527589i	−0.964579	+	0.263795i	$0.915026\pi$
$578$	−393.129	−	325.184i	−0.680154	−	0.562602i
$579$	−759.470			−1.31169
$580$		0			0
$581$	−455.737	−	90.6517i	−0.784400	−	0.156027i
$582$	−840.297	+	840.297i	−1.44381	+	1.44381i
$583$	118.484	+	177.324i	0.203232	+	0.304158i
$584$	−792.068	+	157.552i	−1.35628	+	0.269781i
$585$		0			0
$586$	−95.3950	+	230.304i	−0.162790	+	0.393010i
$587$	589.834	+	244.317i	1.00483	+	0.416213i	0.823565	−	0.567221i	$-0.191982\pi$
$587$	589.834	+	244.317i	1.00483	+	0.416213i	0.181263	+	0.983435i	$0.441982\pi$
$588$	95.8804	+	64.0652i	0.163062	+	0.108954i
$589$	−181.911	−	914.531i	−0.308848	−	1.55268i
$590$		0			0
$591$	821.644	+	821.644i	1.39026	+	1.39026i
$592$	−73.5639	+	369.831i	−0.124263	+	0.624714i
$593$	−246.104	−	594.149i	−0.415016	−	1.00194i	−0.983771	−	0.179430i	$-0.942575\pi$
$593$	−246.104	−	594.149i	−0.415016	−	1.00194i	0.568755	−	0.822507i	$-0.307425\pi$
$594$			80.4708i			0.135473i
$595$		0			0
$596$	−45.7258			−0.0767211
$597$	342.460	−	141.852i	0.573636	−	0.237608i
$598$	−66.9697	−	13.3211i	−0.111990	−	0.0222761i
$599$	354.327	−	354.327i	0.591530	−	0.591530i	−0.346514	−	0.938045i	$-0.612635\pi$
$599$	354.327	−	354.327i	0.591530	−	0.591530i	0.938045	+	0.346514i	$0.112635\pi$
$600$		0			0
$601$	558.804	−	111.153i	0.929791	−	0.184947i	0.293114	−	0.956078i	$-0.405309\pi$
$601$	558.804	−	111.153i	0.929791	−	0.184947i	0.636677	+	0.771131i	$0.280309\pi$
$602$	−13.9692	+	20.9064i	−0.0232046	+	0.0347282i
$603$	−80.6936	+	194.812i	−0.133820	+	0.323071i
$604$	196.157	+	81.2510i	0.324764	+	0.134521i
$605$		0			0
$606$	−173.444	−	871.961i	−0.286211	−	1.43888i
$607$	−150.811	+	100.769i	−0.248454	+	0.166011i	−0.673561	−	0.739131i	$-0.735236\pi$
$607$	−150.811	+	100.769i	−0.248454	+	0.166011i	0.425108	+	0.905143i	$0.360236\pi$
$608$	−241.474	−	241.474i	−0.397162	−	0.397162i
$609$	−38.8094	+	195.108i	−0.0637265	+	0.320375i
$610$		0			0
$611$			15.0396i			0.0246147i
$612$	−16.4688	+	109.564i	−0.0269098	+	0.179026i
$613$	155.196			0.253174			0.126587	−	0.991956i	$-0.459598\pi$
$613$	155.196			0.253174			0.126587	+	0.991956i	$0.459598\pi$
$614$	423.470	−	175.407i	0.689691	−	0.285679i
$615$		0			0
$616$	−173.125	+	173.125i	−0.281047	+	0.281047i
$617$	−259.673	−	388.627i	−0.420863	−	0.629866i	0.559087	−	0.829109i	$-0.311152\pi$
$617$	−259.673	−	388.627i	−0.420863	−	0.629866i	−0.979950	+	0.199243i	$0.936152\pi$
$618$	1226.79	−	244.024i	1.98510	−	0.394861i
$619$	213.158	−	319.014i	0.344359	−	0.515370i	−0.618352	−	0.785901i	$-0.712199\pi$
$619$	213.158	−	319.014i	0.344359	−	0.515370i	0.962711	+	0.270531i	$0.0871993\pi$
$620$		0			0
$621$	69.9071	+	28.9565i	0.112572	+	0.0466288i
$622$	828.054	+	553.288i	1.33128	+	0.889531i
$623$	31.9794	+	160.771i	0.0513313	+	0.258060i
$624$	−132.019	+	88.2122i	−0.211569	+	0.141366i
$625$		0			0
$626$	156.966	−	789.123i	0.250745	−	1.26058i
$627$	−264.892	−	639.506i	−0.422475	−	1.01995i
$628$			237.583i			0.378316i
$629$	369.179	−	405.748i	0.586931	−	0.645068i
$630$		0			0
$631$	−308.547	+	127.804i	−0.488980	+	0.202542i	−0.613531	−	0.789671i	$-0.710251\pi$
$631$	−308.547	+	127.804i	−0.488980	+	0.202542i	0.124550	+	0.992213i	$0.460251\pi$
$632$	−181.474	−	36.0974i	−0.287142	−	0.0571162i
$633$	−103.471	+	103.471i	−0.163462	+	0.163462i
$634$	325.560	+	487.236i	0.513502	+	0.768511i
$635$		0			0
$636$	61.0423	−	91.3563i	0.0959785	−	0.143642i
$637$	41.4415	−	100.049i	0.0650573	−	0.157062i
$638$	135.960	+	56.3163i	0.213103	+	0.0882701i
$639$	−210.789	−	140.845i	−0.329873	−	0.220414i
$640$		0			0
$641$	−798.746	+	533.705i	−1.24609	+	0.832613i	−0.990942	−	0.134289i	$-0.957125\pi$
$641$	−798.746	+	533.705i	−1.24609	+	0.832613i	−0.255151	+	0.966901i	$0.582125\pi$
$642$	201.392	+	201.392i	0.313695	+	0.313695i
$643$	204.305	−	1027.11i	0.317737	−	1.59737i	−0.410376	−	0.911917i	$-0.634602\pi$
$643$	204.305	−	1027.11i	0.317737	−	1.59737i	0.728113	−	0.685457i	$-0.240398\pi$
$644$	15.9385	+	38.4791i	0.0247493	+	0.0597501i
$645$		0			0
$646$	−178.345	−	717.877i	−0.276076	−	1.11127i
$647$	−328.253			−0.507346			−0.253673	−	0.967290i	$-0.581639\pi$
$647$	−328.253			−0.507346			−0.253673	+	0.967290i	$0.581639\pi$
$648$	740.523	−	306.735i	1.14278	−	0.473356i
$649$	−79.9443	−	15.9019i	−0.123181	−	0.0245022i
$650$		0			0
$651$	348.077	+	520.934i	0.534681	+	0.800206i
$652$	33.6220	−	6.68782i	0.0515674	−	0.0102574i
$653$	27.7006	−	41.4569i	0.0424206	−	0.0634869i	−0.809653	−	0.586909i	$-0.800345\pi$
$653$	27.7006	−	41.4569i	0.0424206	−	0.0634869i	0.852074	+	0.523422i	$0.175345\pi$
$654$	125.290	−	302.477i	0.191575	−	0.462504i
$655$		0			0
$656$	328.527	+	219.515i	0.500804	+	0.334626i
$657$	134.814	+	677.754i	0.205196	+	1.03159i
$658$	−26.9067	+	17.9785i	−0.0408917	+	0.0273229i
$659$	61.2456	+	61.2456i	0.0929371	+	0.0929371i	0.752047	−	0.659110i	$-0.229067\pi$
$659$	61.2456	+	61.2456i	0.0929371	+	0.0929371i	−0.659110	+	0.752047i	$0.729067\pi$
$660$		0			0
$661$	−314.044	−	758.170i	−0.475105	−	1.14700i	−0.961879	−	0.273476i	$-0.911827\pi$
$661$	−314.044	−	758.170i	−0.475105	−	1.14700i	0.486774	−	0.873528i	$-0.338173\pi$
$662$		−	1040.69i		−	1.57205i
$663$	230.731	−	10.8881i	0.348011	−	0.0164225i
$664$	978.896			1.47424
$665$		0			0
$666$	412.157	+	81.9831i	0.618854	+	0.123098i
$667$	97.8470	−	97.8470i	0.146697	−	0.146697i
$668$	−17.6837	−	26.4655i	−0.0264726	−	0.0396190i
$669$	1599.94	−	318.248i	2.39154	−	0.475707i
$670$		0			0
$671$	−188.211	+	454.381i	−0.280493	+	0.677170i
$672$	211.989	+	87.8088i	0.315460	+	0.130668i
$673$	457.164	+	305.467i	0.679293	+	0.453889i	0.846751	−	0.531990i	$-0.178556\pi$
$673$	457.164	+	305.467i	0.679293	+	0.453889i	−0.167457	+	0.985879i	$0.553556\pi$
$674$	112.824	+	567.203i	0.167394	+	0.841548i
$675$		0			0
$676$	98.5342	+	98.5342i	0.145761	+	0.145761i
$677$	105.702	−	531.400i	0.156133	−	0.784933i	−0.820772	−	0.571257i	$-0.806456\pi$
$677$	105.702	−	531.400i	0.156133	−	0.784933i	0.976904	−	0.213677i	$-0.0685439\pi$
$678$	−511.910	−	1235.86i	−0.755030	−	1.82280i
$679$		−	680.714i		−	1.00252i
$680$		0			0
$681$	510.884			0.750197
$682$	428.199	−	177.366i	0.627857	−	0.260067i
$683$	−388.402	−	77.2580i	−0.568671	−	0.113116i	−0.0976233	−	0.995223i	$-0.531124\pi$
$683$	−388.402	−	77.2580i	−0.568671	−	0.113116i	−0.471048	+	0.882108i	$0.656124\pi$
$684$	−113.587	+	113.587i	−0.166062	+	0.166062i
$685$		0			0
$686$	575.727	−	114.519i	0.839252	−	0.166938i
$687$	276.410	−	413.677i	0.402344	−	0.602150i
$688$	15.5639	−	37.5745i	0.0226219	−	0.0546142i
$689$	−95.3279	−	39.4861i	−0.138357	−	0.0573093i
$690$		0			0
$691$	182.146	+	915.708i	0.263597	+	1.32519i	0.854921	+	0.518758i	$0.173605\pi$
$691$	182.146	+	915.708i	0.263597	+	1.32519i	−0.591324	+	0.806434i	$0.701395\pi$
$692$	−141.787	+	94.7388i	−0.204894	+	0.136906i
$693$	148.139	+	148.139i	0.213764	+	0.213764i
$694$	−83.3681	+	419.120i	−0.120127	+	0.603919i
$695$		0			0
$696$		−	419.081i		−	0.602128i
$697$	−244.758	−	520.097i	−0.351160	−	0.746193i
$698$	887.929			1.27210
$699$	224.864	−	93.1416i	0.321693	−	0.133250i
$700$		0			0
$701$	−411.177	+	411.177i	−0.586558	+	0.586558i	−0.936697	−	0.350140i	$-0.886134\pi$
$701$	−411.177	+	411.177i	−0.586558	+	0.586558i	0.350140	+	0.936697i	$0.386134\pi$
$702$	−21.6302	−	32.3718i	−0.0308122	−	0.0461137i
$703$	780.055	−	155.163i	1.10961	−	0.220715i
$704$	274.519	−	410.846i	0.389941	−	0.583588i
$705$		0			0
$706$	533.494	+	220.980i	0.755657	+	0.313003i
$707$	423.435	+	282.930i	0.598918	+	0.400184i
$708$	8.19257	+	41.1868i	0.0115714	+	0.0581735i
$709$	967.198	−	646.261i	1.36417	−	0.911511i	0.364367	−	0.931255i	$-0.381285\pi$
$709$	967.198	−	646.261i	1.36417	−	0.911511i	0.999805	+	0.0197449i	$0.00628541\pi$
$710$		0			0
$711$	−30.8877	+	155.283i	−0.0434426	+	0.218401i
$712$	−132.151	−	319.041i	−0.185605	−	0.448091i
$713$		−	435.811i		−	0.611235i
$714$	295.298	+	399.776i	0.413583	+	0.559910i
$715$		0			0
$716$	−197.853	+	81.9532i	−0.276330	+	0.114460i
$717$	1134.84	+	225.734i	1.58276	+	0.314831i
$718$	−663.338	+	663.338i	−0.923869	+	0.923869i
$719$	−8.24905	−	12.3456i	−0.0114729	−	0.0171705i	0.825689	−	0.564126i	$-0.190787\pi$
$719$	−8.24905	−	12.3456i	−0.0114729	−	0.0171705i	−0.837162	+	0.546955i	$0.815787\pi$
$720$		0			0
$721$	−398.064	+	595.745i	−0.552100	+	0.826276i
$722$	166.526	−	402.030i	0.230646	−	0.556828i
$723$	−464.864	−	192.553i	−0.642966	−	0.266325i
$724$	100.284	+	67.0078i	0.138514	+	0.0925522i
$725$		0			0
$726$	−432.682	+	289.109i	−0.595981	+	0.398222i
$727$	880.136	+	880.136i	1.21064	+	1.21064i	0.970816	+	0.239825i	$0.0770901\pi$
$727$	880.136	+	880.136i	1.21064	+	1.21064i	0.239825	+	0.970816i	$0.422910\pi$
$728$	23.1096	−	116.180i	0.0317440	−	0.159588i
$729$	−170.915	−	412.626i	−0.234452	−	0.566017i
$730$		0			0
$731$	−47.5913	+	35.1537i	−0.0651044	+	0.0480899i
$732$	253.382			0.346150
$733$	−503.915	+	208.728i	−0.687469	+	0.284759i	−0.698945	−	0.715175i	$-0.746347\pi$
$733$	−503.915	+	208.728i	−0.687469	+	0.284759i	0.0114762	+	0.999934i	$0.496347\pi$
$734$	573.199	+	114.016i	0.780925	+	0.155336i
$735$		0			0
$736$	−88.6744	−	132.711i	−0.120482	−	0.180313i
$737$	−194.555	+	38.6993i	−0.263982	+	0.0525092i
$738$	244.638	−	366.126i	0.331488	−	0.496106i
$739$	−63.1371	+	152.427i	−0.0854359	+	0.206261i	−0.960823	−	0.277161i	$-0.910606\pi$
$739$	−63.1371	+	152.427i	−0.0854359	+	0.206261i	0.875387	+	0.483422i	$0.160606\pi$
$740$		0			0
$741$	278.457	+	186.059i	0.375786	+	0.251092i
$742$	−43.3130	−	217.749i	−0.0583733	−	0.293462i
$743$	−1.91687	+	1.28081i	−0.00257991	+	0.00172384i	−0.556860	−	0.830607i	$-0.687994\pi$
$743$	−1.91687	+	1.28081i	−0.00257991	+	0.00172384i	0.554280	+	0.832331i	$0.312994\pi$
$744$	−933.294	−	933.294i	−1.25443	−	1.25443i
$745$		0			0
$746$	−99.8879	−	241.151i	−0.133898	−	0.323258i
$747$		−	837.618i		−	1.12131i
$748$	−94.3076	+	44.3813i	−0.126080	+	0.0593333i
$749$	−163.145			−0.217817
$750$		0			0
$751$	−1414.78	−	281.416i	−1.88386	−	0.374722i	−0.887559	−	0.460695i	$-0.847600\pi$
$751$	−1414.78	−	281.416i	−1.88386	−	0.374722i	−0.996298	+	0.0859723i	$0.972600\pi$
$752$	37.0123	−	37.0123i	0.0492184	−	0.0492184i
$753$	316.924	+	474.310i	0.420881	+	0.629894i
$754$	−69.8315	+	13.8904i	−0.0926148	+	0.0184222i
$755$		0			0
$756$	−9.08793	+	21.9402i	−0.0120211	+	0.0290214i
$757$	278.634	+	115.414i	0.368077	+	0.152463i	0.559052	−	0.829132i	$-0.311165\pi$
$757$	278.634	+	115.414i	0.368077	+	0.152463i	−0.190975	+	0.981595i	$0.561165\pi$
$758$	64.1215	+	42.8446i	0.0845931	+	0.0565233i
$759$	−63.1158	−	317.305i	−0.0831566	−	0.418056i
$760$		0			0
$761$	−811.549	−	811.549i	−1.06642	−	1.06642i	−0.997631	−	0.0687929i	$-0.978085\pi$
$761$	−811.549	−	811.549i	−1.06642	−	1.06642i	−0.0687929	−	0.997631i	$-0.521915\pi$
$762$	−57.2441	+	287.786i	−0.0751235	+	0.377671i
$763$	71.7685	+	173.265i	0.0940610	+	0.227083i
$764$			153.984i			0.201550i
$765$		0			0
$766$	−348.859			−0.455429
$767$	36.4344	−	15.0916i	0.0475025	−	0.0196762i
$768$	−638.005	−	126.907i	−0.830736	−	0.165244i
$769$	870.130	−	870.130i	1.13151	−	1.13151i	0.141582	−	0.989927i	$-0.454781\pi$
$769$	870.130	−	870.130i	1.13151	−	1.13151i	0.989927	−	0.141582i	$-0.0452189\pi$
$770$		0			0
$771$	1559.90	−	310.284i	2.02322	−	0.402444i
$772$	−92.1150	+	137.860i	−0.119320	+	0.178575i
$773$	−541.282	+	1306.77i	−0.700235	+	1.69052i	0.0228308	+	0.999739i	$0.492732\pi$
$773$	−541.282	+	1306.77i	−0.700235	+	1.69052i	−0.723066	+	0.690779i	$0.757268\pi$
$774$	−41.8749	−	17.3451i	−0.0541019	−	0.0224098i
$775$		0			0
$776$	279.767	+	1406.49i	0.360525	+	1.81248i
$777$	−444.334	+	296.895i	−0.571859	+	0.382104i
$778$	26.8308	+	26.8308i	0.0344869	+	0.0344869i
$779$	162.586	−	817.375i	0.208711	−	1.04926i
$780$		0			0
$781$		−	238.490i		−	0.305365i
$782$	−16.2964	−	345.339i	−0.0208393	−	0.441610i
$783$	78.9004			0.100767
$784$	−348.205	+	144.231i	−0.444139	+	0.183969i
$785$		0			0
$786$	−972.366	+	972.366i	−1.23711	+	1.23711i
$787$	−857.112	−	1282.76i	−1.08909	−	1.62994i	−0.709375	−	0.704831i	$-0.751023\pi$
$787$	−857.112	−	1282.76i	−1.08909	−	1.62994i	−0.379713	−	0.925104i	$-0.623977\pi$
$788$	248.802	−	49.4897i	0.315738	−	0.0628042i
$789$	−655.319	+	980.754i	−0.830569	+	1.24303i
$790$		0			0
$791$	707.924	+	293.232i	0.894973	+	0.370710i
$792$	−366.967	−	245.199i	−0.463342	−	0.309595i
$793$	−46.4220	−	233.379i	−0.0585397	−	0.294299i
$794$	52.0749	−	34.7954i	0.0655856	−	0.0438229i
$795$		0			0
$796$	15.7874	−	79.3688i	0.0198335	−	0.0997095i
$797$	430.853	+	1040.17i	0.540593	+	1.30511i	0.924305	+	0.381654i	$0.124645\pi$
$797$	430.853	+	1040.17i	0.540593	+	1.30511i	−0.383712	+	0.923453i	$0.625355\pi$
$798$			720.593i			0.902998i
$799$	−73.9019	+	18.3597i	−0.0924930	+	0.0229784i
$800$		0			0
$801$	−272.996	+	113.079i	−0.340819	+	0.141172i
$802$	−258.963	−	51.5110i	−0.322897	−	0.0642281i
$803$	−459.675	+	459.675i	−0.572448	+	0.572448i
$804$	56.7776	+	84.9737i	0.0706189	+	0.105689i
$805$		0			0
$806$	−124.581	+	186.449i	−0.154567	+	0.231326i
$807$	−157.796	+	380.953i	−0.195534	+	0.472061i
$808$	−991.179	−	410.560i	−1.22671	−	0.508119i
$809$	−273.249	−	182.579i	−0.337761	−	0.225685i	0.375109	−	0.926981i	$-0.377605\pi$
$809$	−273.249	−	182.579i	−0.337761	−	0.225685i	−0.712870	+	0.701296i	$0.752605\pi$
$810$		0			0
$811$	−242.645	+	162.131i	−0.299193	+	0.199914i	−0.696101	−	0.717944i	$-0.745083\pi$
$811$	−242.645	+	162.131i	−0.299193	+	0.199914i	0.396908	+	0.917859i	$0.370083\pi$
$812$	30.7091	+	30.7091i	0.0378191	+	0.0378191i
$813$	300.846	−	1512.45i	0.370044	−	1.86034i
$814$	151.285	+	365.235i	0.185854	+	0.448692i
$815$		0			0
$816$	−594.622	−	541.031i	−0.728703	−	0.663028i
$817$	−85.7829			−0.104997
$818$	−650.588	+	269.482i	−0.795340	+	0.329441i
$819$	−99.4124	−	19.7743i	−0.121383	−	0.0241445i
$820$		0			0
$821$	−600.209	−	898.276i	−0.731070	−	1.09412i	−0.991686	−	0.128681i	$-0.958926\pi$
$821$	−600.209	−	898.276i	−0.731070	−	1.09412i	0.260616	−	0.965443i	$-0.416074\pi$
$822$	370.216	−	73.6406i	0.450385	−	0.0895871i
$823$	−50.4221	+	75.4620i	−0.0612662	+	0.0916914i	−0.860838	−	0.508879i	$-0.830060\pi$
$823$	−50.4221	+	75.4620i	−0.0612662	+	0.0916914i	0.799572	+	0.600571i	$0.205060\pi$
$824$	577.631	−	1394.52i	0.701008	−	1.69238i
$825$		0			0
$826$	70.5539	+	47.1426i	0.0854163	+	0.0570733i
$827$	94.8310	+	476.748i	0.114669	+	0.576479i	0.994809	+	0.101764i	$0.0324487\pi$
$827$	94.8310	+	476.748i	0.114669	+	0.576479i	−0.880140	+	0.474715i	$0.842551\pi$
$828$	−62.4255	+	41.7114i	−0.0753931	+	0.0503760i
$829$	743.445	+	743.445i	0.896797	+	0.896797i	0.995151	−	0.0983544i	$-0.0313579\pi$
$829$	743.445	+	743.445i	0.896797	+	0.896797i	−0.0983544	+	0.995151i	$0.531358\pi$
$830$		0			0
$831$	−104.095	−	251.307i	−0.125264	−	0.302415i
$832$			239.065i			0.287338i
$833$	542.211	+	81.5008i	0.650914	+	0.0978401i
$834$	374.896			0.449516
$835$		0			0
$836$	−148.212	−	29.4812i	−0.177287	−	0.0352646i
$837$	175.711	−	175.711i	0.209930	−	0.209930i
$838$	36.6811	+	54.8971i	0.0437722	+	0.0655097i
$839$	−449.855	+	89.4817i	−0.536180	+	0.106653i	−0.455751	−	0.890108i	$-0.650629\pi$
$839$	−449.855	+	89.4817i	−0.536180	+	0.106653i	−0.0804292	+	0.996760i	$0.525629\pi$
$840$		0			0
$841$	−266.619	+	643.676i	−0.317027	+	0.765370i
$842$	721.276	+	298.762i	0.856622	+	0.354824i
$843$	1268.73	+	847.739i	1.50502	+	1.00562i
$844$	6.23235	+	31.3321i	0.00738430	+	0.0371234i
$845$		0			0
$846$	−41.2482	−	41.2482i	−0.0487568	−	0.0487568i
$847$	58.1534	−	292.357i	0.0686581	−	0.345167i
$848$	137.426	+	331.775i	0.162059	+	0.391244i
$849$			1201.22i			1.41486i
$850$		0			0
$851$	371.728			0.436813
$852$	−113.516	+	47.0197i	−0.133234	+	0.0551875i
$853$	−7.38457	−	1.46888i	−0.00865717	−	0.00172202i	0.190760	−	0.981637i	$-0.438905\pi$
$853$	−7.38457	−	1.46888i	−0.00865717	−	0.00172202i	−0.199417	+	0.979915i	$0.563905\pi$
$854$	362.035	−	362.035i	0.423929	−	0.423929i
$855$		0			0
$856$	337.089	−	67.0512i	0.393796	−	0.0783309i
$857$	28.1682	−	42.1566i	0.0328683	−	0.0491910i	−0.814672	−	0.579923i	$-0.803083\pi$
$857$	28.1682	−	42.1566i	0.0328683	−	0.0491910i	0.847540	+	0.530732i	$0.178083\pi$
$858$	−63.7026	+	153.792i	−0.0742455	+	0.179244i
$859$	−464.849	−	192.547i	−0.541151	−	0.224152i	0.0953281	−	0.995446i	$-0.469610\pi$
$859$	−464.849	−	192.547i	−0.541151	−	0.224152i	−0.636479	+	0.771294i	$0.719610\pi$
$860$		0			0
$861$	109.243	+	549.204i	0.126880	+	0.637867i
$862$	−509.190	+	340.230i	−0.590708	+	0.394698i
$863$	98.9573	+	98.9573i	0.114667	+	0.114667i	0.762112	−	0.647445i	$-0.224163\pi$
$863$	98.9573	+	98.9573i	0.114667	+	0.114667i	−0.647445	+	0.762112i	$0.724163\pi$
$864$	17.7546	−	89.2585i	0.0205493	−	0.103309i
$865$		0			0
$866$		−	94.8830i		−	0.109565i
$867$	335.169	+	1120.48i	0.386585	+	1.29237i
$868$	136.778			0.157579
$869$	−137.605	+	56.9977i	−0.158348	+	0.0655900i
$870$		0			0
$871$	67.8634	−	67.8634i	0.0779143	−	0.0779143i
$872$	−219.498	−	328.502i	−0.251718	−	0.376722i
$873$	1203.50	−	239.390i	1.37858	−	0.274216i
$874$	278.477	−	416.771i	0.318624	−	0.476855i
$875$		0			0
$876$	309.423	+	128.167i	0.353222	+	0.146309i
$877$	−789.554	−	527.563i	−0.900289	−	0.601554i	0.0169652	−	0.999856i	$-0.494600\pi$
$877$	−789.554	−	527.563i	−0.900289	−	0.601554i	−0.917254	+	0.398302i	$0.869600\pi$
$878$	−83.7792	−	421.187i	−0.0954205	−	0.479711i
$879$	475.131	−	317.472i	0.540536	−	0.361174i
$880$		0			0
$881$	204.085	−	1026.00i	0.231651	−	1.16459i	−0.673398	−	0.739280i	$-0.735166\pi$
$881$	204.085	−	1026.00i	0.231651	−	1.16459i	0.905049	−	0.425308i	$-0.139834\pi$
$882$	160.738	+	388.057i	0.182243	+	0.439974i
$883$		−	1264.99i		−	1.43261i	−0.697789	−	0.716303i	$-0.745833\pi$
$883$		−	1264.99i		−	1.43261i	0.697789	−	0.716303i	$-0.254167\pi$
$884$	26.0086	−	43.2032i	0.0294215	−	0.0488724i
$885$		0			0
$886$	186.898	−	77.4157i	0.210946	−	0.0873766i
$887$	−766.671	−	152.500i	−0.864341	−	0.171928i	−0.257041	−	0.966401i	$-0.582747\pi$
$887$	−766.671	−	152.500i	−0.864341	−	0.171928i	−0.607300	+	0.794472i	$0.707747\pi$
$888$	796.059	−	796.059i	0.896463	−	0.896463i
$889$	−93.3794	−	139.752i	−0.105039	−	0.157201i
$890$		0			0
$891$	358.459	−	536.472i	0.402311	−	0.602101i
$892$	136.286	−	329.023i	0.152787	−	0.368860i
$893$	−102.000	−	42.2496i	−0.114221	−	0.0473120i
$894$	−307.441	−	205.425i	−0.343894	−	0.229782i
$895$		0			0
$896$	−239.124	+	159.777i	−0.266879	+	0.178323i
$897$	110.680	+	110.680i	0.123389	+	0.123389i
$898$	−187.081	+	940.519i	−0.208331	+	1.04735i
$899$	−173.904	−	419.842i	−0.193442	−	0.467010i
$900$		0			0
$901$	77.6552	−	516.627i	0.0861878	−	0.573393i
$902$	414.241			0.459247
$903$	53.2511	−	22.0573i	0.0589713	−	0.0244267i
$904$	−1583.22	−	314.922i	−1.75135	−	0.348365i
$905$		0			0
$906$	953.854	+	1427.54i	1.05282	+	1.57566i
$907$	366.570	−	72.9154i	0.404157	−	0.0803918i	0.0111739	−	0.999938i	$-0.496443\pi$
$907$	366.570	−	72.9154i	0.404157	−	0.0803918i	0.392983	+	0.919546i	$0.371443\pi$
$908$	61.9644	−	92.7363i	0.0682428	−	0.102133i
$909$	−351.306	+	848.129i	−0.386476	+	0.933035i
$910$		0			0
$911$	−101.362	−	67.7280i	−0.111265	−	0.0743447i	0.498693	−	0.866779i	$-0.333814\pi$
$911$	−101.362	−	67.7280i	−0.111265	−	0.0743447i	−0.609958	+	0.792434i	$0.708814\pi$
$912$	−227.390	−	1143.17i	−0.249331	−	1.25347i
$913$	655.180	−	437.777i	0.717612	−	0.479493i
$914$	280.276	+	280.276i	0.306647	+	0.306647i
$915$		0			0
$916$	−41.5657	−	100.349i	−0.0453774	−	0.109551i
$917$		−	787.702i		−	0.858999i
$918$	132.664	−	145.805i	0.144514	−	0.158829i
$919$	1592.00			1.73232			0.866158	−	0.499770i	$-0.166582\pi$
$919$	1592.00			1.73232			0.866158	+	0.499770i	$0.166582\pi$
$920$		0			0
$921$	−1030.53	−	204.986i	−1.11893	−	0.222569i
$922$	−314.913	+	314.913i	−0.341555	+	0.341555i
$923$	64.1050	+	95.9399i	0.0694528	+	0.103944i
$924$	99.5855	−	19.8088i	0.107777	−	0.0214381i
$925$		0			0
$926$	−84.6976	+	204.478i	−0.0914661	+	0.220819i
$927$	−1193.26	−	494.265i	−1.28723	−	0.533188i
$928$	−138.382	−	92.4638i	−0.149118	−	0.0996377i
$929$	−132.478	−	666.010i	−0.142602	−	0.716910i	−0.984236	−	0.176861i	$-0.943406\pi$
$929$	−132.478	−	666.010i	−0.142602	−	0.716910i	0.841633	−	0.540049i	$-0.181594\pi$
$930$		0			0
$931$	562.118	+	562.118i	0.603778	+	0.603778i
$932$	10.3662	−	52.1145i	0.0111226	−	0.0559169i
$933$	−873.641	−	2109.16i	−0.936378	−	2.26062i
$934$			1223.18i			1.30961i
$935$		0			0
$936$	213.532			0.228133
$937$	−271.967	+	112.652i	−0.290253	+	0.120227i	−0.523059	−	0.852296i	$-0.675209\pi$
$937$	−271.967	+	112.652i	−0.290253	+	0.120227i	0.232806	+	0.972523i	$0.425209\pi$
$938$	202.536	+	40.2869i	0.215923	+	0.0429498i
$939$	−1304.18	+	1304.18i	−1.38890	+	1.38890i
$940$		0			0
$941$	819.035	−	162.916i	0.870388	−	0.173131i	0.260361	−	0.965511i	$-0.416159\pi$
$941$	819.035	−	162.916i	0.870388	−	0.173131i	0.610027	+	0.792381i	$0.291159\pi$
$942$	−1067.35	+	1597.41i	−1.13307	+	1.69576i
$943$	149.060	−	359.862i	0.158070	−	0.381614i
$944$	−126.805	−	52.5243i	−0.134327	−	0.0556402i
$945$		0			0
$946$	−8.31845	−	41.8196i	−0.00879328	−	0.0442068i
$947$	−517.880	+	346.036i	−0.546864	+	0.365403i	−0.798102	−	0.602523i	$-0.794162\pi$
$947$	−517.880	+	346.036i	−0.546864	+	0.365403i	0.251238	+	0.967925i	$0.419162\pi$
$948$	54.2592	+	54.2592i	0.0572355	+	0.0572355i
$949$	61.3599	−	308.477i	0.0646575	−	0.325055i
$950$		0			0
$951$		−	1343.30i		−	1.41252i
$952$	599.098	−	28.2711i	0.629305	−	0.0296966i
$953$	373.214			0.391620			0.195810	−	0.980642i	$-0.437266\pi$
$953$	373.214			0.391620			0.195810	+	0.980642i	$0.437266\pi$
$954$	369.746	−	153.154i	0.387575	−	0.160539i
$955$		0			0
$956$	178.619	−	178.619i	0.186840	−	0.186840i
$957$	−187.419	−	280.493i	−0.195841	−	0.293096i
$958$	828.832	−	164.865i	0.865169	−	0.172093i
$959$	−120.126	+	179.781i	−0.125262	+	0.187468i
$960$		0			0
$961$	−434.426	−	179.945i	−0.452056	−	0.187248i
$962$	−159.033	−	106.262i	−0.165315	−	0.110460i
$963$	−57.3741	−	288.439i	−0.0595786	−	0.299522i
$964$	−91.3352	+	61.0282i	−0.0947460	+	0.0633073i
$965$		0			0
$966$	−65.7051	+	330.322i	−0.0680177	+	0.341948i
$967$	392.472	+	947.512i	0.405866	+	0.979847i	0.986213	+	0.165478i	$0.0529167\pi$
$967$	392.472	+	947.512i	0.405866	+	0.979847i	−0.580348	+	0.814369i	$0.697083\pi$
$968$			627.966i			0.648725i
$969$	−574.332	+	1595.42i	−0.592706	+	1.64646i
$970$		0			0
$971$	909.171	−	376.591i	0.936325	−	0.387838i	0.138250	−	0.990397i	$-0.455852\pi$
$971$	909.171	−	376.591i	0.936325	−	0.387838i	0.798074	+	0.602559i	$0.205852\pi$
$972$	−274.797	−	54.6605i	−0.282713	−	0.0562351i
$973$	−151.849	+	151.849i	−0.156063	+	0.156063i
$974$	−397.869	−	595.453i	−0.408490	−	0.611348i
$975$		0			0
$976$	−460.099	+	688.586i	−0.471413	+	0.705519i
$977$	−217.809	+	525.837i	−0.222936	+	0.538216i	−0.995286	−	0.0969814i	$-0.969081\pi$
$977$	−217.809	+	525.837i	−0.222936	+	0.538216i	0.772350	+	0.635197i	$0.219081\pi$
$978$	256.105	+	106.082i	0.261866	+	0.108469i
$979$	−231.129	−	154.436i	−0.236087	−	0.157748i
$980$		0			0
$981$	−281.091	+	187.819i	−0.286535	+	0.191457i
$982$	−77.4444	−	77.4444i	−0.0788639	−	0.0788639i
$983$	280.516	−	1410.25i	0.285368	−	1.43464i	−0.526190	−	0.850367i	$-0.676380\pi$
$983$	280.516	−	1410.25i	0.285368	−	1.43464i	0.811558	−	0.584272i	$-0.198620\pi$
$984$	−451.436	−	1089.86i	−0.458776	−	1.10758i
$985$		0			0
$986$	−153.502	−	326.183i	−0.155682	−	0.330814i
$987$	74.1814			0.0751585
$988$	67.5473	−	27.9790i	0.0683677	−	0.0283188i
$989$	−39.3231	−	7.82186i	−0.0397605	−	0.00790886i
$990$		0			0
$991$	46.6472	+	69.8125i	0.0470709	+	0.0704465i	0.854259	−	0.519848i	$-0.174012\pi$
$991$	46.6472	+	69.8125i	0.0470709	+	0.0704465i	−0.807188	+	0.590295i	$0.799012\pi$
$992$	−514.093	+	102.259i	−0.518239	+	0.103084i
$993$	−1325.39	+	1983.58i	−1.33473	+	1.99757i
$994$	−95.0102	+	229.375i	−0.0955837	+	0.230759i
$995$		0			0
$996$	−337.545	−	225.540i	−0.338900	−	0.226446i
$997$	146.965	+	738.843i	0.147407	+	0.741066i	0.981803	+	0.189901i	$0.0608167\pi$
$997$	146.965	+	738.843i	0.147407	+	0.741066i	−0.834396	+	0.551165i	$0.814183\pi$
$998$	−753.360	+	503.379i	−0.754870	+	0.504388i
$999$	149.874	+	149.874i	0.150024	+	0.150024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.a.326.1		8
5.2	odd	4		425.3.t.d.224.1		8
5.3	odd	4		425.3.t.b.224.1		8
5.4	even	2		17.3.e.b.3.1	✓	8
15.14	odd	2		153.3.p.a.37.1		8
17.6	odd	16	inner	425.3.u.a.176.1		8
20.19	odd	2		272.3.bh.b.241.1		8
85.4	even	4		289.3.e.f.65.1		8
85.9	even	8		289.3.e.n.158.1		8
85.14	odd	16		289.3.e.a.214.1		8
85.19	even	8		289.3.e.e.131.1		8
85.23	even	16		425.3.t.d.74.1		8
85.24	odd	16		289.3.e.h.249.1		8
85.29	odd	16		289.3.e.n.75.1		8
85.39	odd	16		289.3.e.j.75.1		8
85.44	odd	16		289.3.e.f.249.1		8
85.49	even	8		289.3.e.a.131.1		8
85.54	odd	16		289.3.e.e.214.1		8
85.57	even	16		425.3.t.b.74.1		8
85.59	even	8		289.3.e.j.158.1		8
85.64	even	4		289.3.e.h.65.1		8
85.74	odd	16		17.3.e.b.6.1	yes	8
85.79	odd	16		289.3.e.g.40.1		8
85.84	even	2		289.3.e.g.224.1		8
255.74	even	16		153.3.p.a.91.1		8
340.159	even	16		272.3.bh.b.193.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.3.1	✓	8	5.4	even	2
17.3.e.b.6.1	yes	8	85.74	odd	16
153.3.p.a.37.1		8	15.14	odd	2
153.3.p.a.91.1		8	255.74	even	16
272.3.bh.b.193.1		8	340.159	even	16
272.3.bh.b.241.1		8	20.19	odd	2
289.3.e.a.131.1		8	85.49	even	8
289.3.e.a.214.1		8	85.14	odd	16
289.3.e.e.131.1		8	85.19	even	8
289.3.e.e.214.1		8	85.54	odd	16
289.3.e.f.65.1		8	85.4	even	4
289.3.e.f.249.1		8	85.44	odd	16
289.3.e.g.40.1		8	85.79	odd	16
289.3.e.g.224.1		8	85.84	even	2
289.3.e.h.65.1		8	85.64	even	4
289.3.e.h.249.1		8	85.24	odd	16
289.3.e.j.75.1		8	85.39	odd	16
289.3.e.j.158.1		8	85.59	even	8
289.3.e.n.75.1		8	85.29	odd	16
289.3.e.n.158.1		8	85.9	even	8
425.3.t.b.74.1		8	85.57	even	16
425.3.t.b.224.1		8	5.3	odd	4
425.3.t.d.74.1		8	85.23	even	16
425.3.t.d.224.1		8	5.2	odd	4
425.3.u.a.176.1		8	17.6	odd	16	inner
425.3.u.a.326.1		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63099 - 0.675577i) q^{2} +(-3.96908 - 0.789499i) q^{3} +(-0.624715 + 0.624715i) q^{4} +(-7.00688 + 1.39376i) q^{6} +(2.27356 - 3.40262i) q^{7} +(-3.29916 + 7.96489i) q^{8} +(6.81537 + 2.82302i) q^{9} +(1.35387 + 6.80638i) q^{11} +(2.97275 - 1.98633i) q^{12} +(-2.37416 - 2.37416i) q^{13} +(1.40941 - 7.08560i) q^{14} +11.6855i q^{16} +(8.76791 - 14.5645i) q^{17} +13.0229 q^{18} +(22.7712 - 9.43215i) q^{19} +(-11.7103 + 11.7103i) q^{21} +(6.80638 + 10.1865i) q^{22} +(11.2984 - 2.24740i) q^{23} +(19.3829 - 29.0086i) q^{24} +(-5.47615 - 2.26829i) q^{26} +(5.46144 + 3.64922i) q^{27} +(0.705343 + 3.54600i) q^{28} +(9.98767 - 6.67355i) q^{29} +(7.38055 - 37.1045i) q^{31} +(-5.30218 - 12.8006i) q^{32} -28.0839i q^{33} +(4.46094 - 29.6778i) q^{34} +(-6.02124 + 2.49408i) q^{36} +(31.6486 + 6.29529i) q^{37} +(30.7674 - 30.7674i) q^{38} +(7.54883 + 11.2976i) q^{39} +(18.7852 - 28.1140i) q^{41} +(-11.1881 + 27.0106i) q^{42} +(-3.21547 - 1.33189i) q^{43} +(-5.09783 - 3.40626i) q^{44} +(16.9093 - 11.2984i) q^{46} +(-3.16735 - 3.16735i) q^{47} +(9.22573 - 46.3809i) q^{48} +(12.3427 + 29.7979i) q^{49} +(-46.2992 + 50.8853i) q^{51} +2.96634 q^{52} +(28.3919 - 11.7603i) q^{53} +(11.3729 + 2.26220i) q^{54} +(19.6007 + 29.3345i) q^{56} +(-97.8275 + 19.4591i) q^{57} +(11.7813 - 17.6319i) q^{58} +(-4.49481 + 10.8514i) q^{59} +(58.9263 + 39.3733i) q^{61} +(-13.0294 - 65.5031i) q^{62} +(25.1008 - 16.7718i) q^{63} +(-50.3473 - 50.3473i) q^{64} +(-18.9728 - 45.8045i) q^{66} +28.5842i q^{67} +(3.62119 + 14.5761i) q^{68} -46.6187 q^{69} +(-33.7056 - 6.70446i) q^{71} +(-44.9700 + 44.9700i) q^{72} +(52.0431 + 77.8880i) q^{73} +(55.8713 - 11.1135i) q^{74} +(-8.33312 + 20.1179i) q^{76} +(26.2377 + 10.8680i) q^{77} +(19.9444 + 13.3265i) q^{78} +(4.18708 + 21.0499i) q^{79} +(-65.7422 - 65.7422i) q^{81} +(11.6452 - 58.5443i) q^{82} +(-43.4522 - 104.903i) q^{83} -14.6312i q^{84} -6.14419 q^{86} +(-44.9106 + 18.6026i) q^{87} +(-58.6787 - 11.6719i) q^{88} +(-28.3238 + 28.3238i) q^{89} +(-13.4762 + 2.68058i) q^{91} +(-5.65432 + 8.46229i) q^{92} +(-58.5880 + 141.444i) q^{93} +(-7.30570 - 3.02612i) q^{94} +(10.9387 + 54.9926i) q^{96} +(138.307 - 92.4136i) q^{97} +(40.2616 + 40.2616i) q^{98} +(-9.98738 + 50.2100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 16 q^{7} - 16 q^{8} + 8 q^{9} + 40 q^{11} - 40 q^{12} + 16 q^{14} + 16 q^{17} + 136 q^{18} - 32 q^{19} - 64 q^{21} + 8 q^{23} + 24 q^{24} - 96 q^{27} - 80 q^{28} + 24 q^{29} + 32 q^{31}+ \cdots + 136 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 16 * q^7 - 16 * q^8 + 8 * q^9 + 40 * q^11 - 40 * q^12 + 16 * q^14 + 16 * q^17 + 136 * q^18 - 32 * q^19 - 64 * q^21 + 8 * q^23 + 24 * q^24 - 96 * q^27 - 80 * q^28 + 24 * q^29 + 32 * q^31 + 24 * q^32 + 64 * q^34 - 104 * q^36 + 168 * q^37 - 8 * q^38 - 72 * q^39 + 72 * q^42 - 96 * q^43 - 96 * q^44 + 80 * q^47 - 88 * q^48 + 8 * q^49 - 176 * q^51 - 240 * q^52 - 96 * q^53 + 208 * q^54 + 72 * q^56 - 248 * q^57 + 8 * q^59 + 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 8 * q^66 + 176 * q^68 - 208 * q^69 + 32 * q^71 - 24 * q^72 - 24 * q^73 + 176 * q^74 - 80 * q^76 + 216 * q^77 + 368 * q^78 - 96 * q^79 - 224 * q^81 + 408 * q^82 + 88 * q^83 + 288 * q^86 - 312 * q^87 - 176 * q^88 + 288 * q^89 - 24 * q^91 - 336 * q^92 - 280 * q^93 - 8 * q^94 + 328 * q^96 + 344 * q^97 - 16 * q^98 + 136 * q^99

Introduction

L-functions

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