LMFDB - Embedded newform 210.3.k.a.167.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(83,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.k (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			167.5
Character	$\chi$	$=$	210.167
Dual form			210.3.k.a.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-2.14733 + 2.09499i) q^{3} -2.00000i q^{4} +(-1.13661 - 4.86910i) q^{5} +(0.0523328 - 4.24232i) q^{6} +(6.60685 + 2.31291i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.222012 - 8.99726i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.14733 + 2.09499i) q^{3} -2.00000i q^{4} +(-1.13661 - 4.86910i) q^{5} +(0.0523328 - 4.24232i) q^{6} +(6.60685 + 2.31291i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.222012 - 8.99726i) q^{9} +(6.00571 + 3.73249i) q^{10} +16.9733i q^{11} +(4.18999 + 4.29465i) q^{12} +(10.2231 + 10.2231i) q^{13} +(-8.91976 + 4.29394i) q^{14} +(12.6414 + 8.07434i) q^{15} -4.00000 q^{16} +(-8.79877 - 8.79877i) q^{17} +(8.77525 + 9.21927i) q^{18} -24.7369 q^{19} +(-9.73820 + 2.27322i) q^{20} +(-19.0326 + 8.87473i) q^{21} +(-16.9733 - 16.9733i) q^{22} +(19.2569 + 19.2569i) q^{23} +(-8.48464 - 0.104666i) q^{24} +(-22.4162 + 11.0685i) q^{25} -20.4462 q^{26} +(18.3725 + 19.7852i) q^{27} +(4.62582 - 13.2137i) q^{28} +1.67978 q^{29} +(-20.7157 + 4.56706i) q^{30} +36.8991i q^{31} +(4.00000 - 4.00000i) q^{32} +(-35.5589 - 36.4472i) q^{33} +17.5975 q^{34} +(3.75235 - 34.7983i) q^{35} +(-17.9945 - 0.444025i) q^{36} +(40.5381 + 40.5381i) q^{37} +(24.7369 - 24.7369i) q^{38} +(-43.3696 - 0.535003i) q^{39} +(7.46497 - 12.0114i) q^{40} -0.885911 q^{41} +(10.1578 - 27.9073i) q^{42} +(-9.87427 + 9.87427i) q^{43} +33.9466 q^{44} +(-44.0609 + 9.14540i) q^{45} -38.5139 q^{46} +(33.7538 + 33.7538i) q^{47} +(8.58930 - 8.37997i) q^{48} +(38.3009 + 30.5621i) q^{49} +(11.3477 - 33.4848i) q^{50} +(37.3272 + 0.460464i) q^{51} +(20.4462 - 20.4462i) q^{52} +(-11.9694 - 11.9694i) q^{53} +(-38.1576 - 1.41270i) q^{54} +(82.6446 - 19.2920i) q^{55} +(8.58788 + 17.8395i) q^{56} +(53.1183 - 51.8237i) q^{57} +(-1.67978 + 1.67978i) q^{58} +50.5136i q^{59} +(16.1487 - 25.2828i) q^{60} +80.6872i q^{61} +(-36.8991 - 36.8991i) q^{62} +(22.2766 - 58.9301i) q^{63} +8.00000i q^{64} +(38.1575 - 61.3969i) q^{65} +(72.0061 + 0.888260i) q^{66} +(-4.46192 - 4.46192i) q^{67} +(-17.5975 + 17.5975i) q^{68} +(-81.6941 - 1.00777i) q^{69} +(31.0459 + 38.5506i) q^{70} -137.180i q^{71} +(18.4385 - 17.5505i) q^{72} +(-53.3244 - 53.3244i) q^{73} -81.0762 q^{74} +(24.9464 - 70.7296i) q^{75} +49.4739i q^{76} +(-39.2577 + 112.140i) q^{77} +(43.9046 - 42.8346i) q^{78} -127.936i q^{79} +(4.54645 + 19.4764i) q^{80} +(-80.9014 - 3.99500i) q^{81} +(0.885911 - 0.885911i) q^{82} +(60.0077 - 60.0077i) q^{83} +(17.7495 + 38.0652i) q^{84} +(-32.8413 + 52.8429i) q^{85} -19.7485i q^{86} +(-3.60704 + 3.51913i) q^{87} +(-33.9466 + 33.9466i) q^{88} -51.3826i q^{89} +(34.9155 - 53.2063i) q^{90} +(43.8974 + 91.1875i) q^{91} +(38.5139 - 38.5139i) q^{92} +(-77.3034 - 79.2345i) q^{93} -67.5075 q^{94} +(28.1163 + 120.447i) q^{95} +(-0.209331 + 16.9693i) q^{96} +(0.274025 - 0.274025i) q^{97} +(-68.8630 + 7.73884i) q^{98} +(152.713 + 3.76828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9	$ 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9} + 8 q^{14} - 20 q^{15} - 128 q^{16} + 36 q^{18} + 12 q^{21} - 40 q^{22} + 24 q^{23} + 16 q^{25} - 8 q^{28} - 112 q^{29} + 68 q^{30} + 128 q^{32} - 48 q^{35} - 40 q^{36} + 32 q^{37} + 64 q^{39} - 44 q^{42} - 32 q^{43} + 80 q^{44} - 48 q^{46} - 8 q^{50} + 84 q^{51} - 136 q^{53} + 244 q^{57} + 112 q^{58} - 96 q^{60} + 72 q^{63} - 200 q^{65} + 32 q^{67} + 8 q^{72} - 64 q^{74} + 88 q^{77} - 124 q^{78} + 76 q^{81} + 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} + 48 q^{92} - 452 q^{93} + 544 q^{95} + 128 q^{98} + 160 q^{99}+O(q^{100}) $ 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9 + 8 * q^14 - 20 * q^15 - 128 * q^16 + 36 * q^18 + 12 * q^21 - 40 * q^22 + 24 * q^23 + 16 * q^25 - 8 * q^28 - 112 * q^29 + 68 * q^30 + 128 * q^32 - 48 * q^35 - 40 * q^36 + 32 * q^37 + 64 * q^39 - 44 * q^42 - 32 * q^43 + 80 * q^44 - 48 * q^46 - 8 * q^50 + 84 * q^51 - 136 * q^53 + 244 * q^57 + 112 * q^58 - 96 * q^60 + 72 * q^63 - 200 * q^65 + 32 * q^67 + 8 * q^72 - 64 * q^74 + 88 * q^77 - 124 * q^78 + 76 * q^81 + 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 + 48 * q^92 - 452 * q^93 + 544 * q^95 + 128 * q^98 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−2.14733	+	2.09499i	−0.715775	+	0.698331i
$3$	−2.14733	+	2.09499i	−0.715775	+	0.698331i
$4$		−	2.00000i		−	0.500000i
$5$	−1.13661	−	4.86910i	−0.227322	−	0.973820i
$5$	−1.13661	−	4.86910i	−0.227322	−	0.973820i
$6$	0.0523328	−	4.24232i	0.00872213	−	0.707053i
$7$	6.60685	+	2.31291i	0.943836	+	0.330415i
$7$	6.60685	+	2.31291i	0.943836	+	0.330415i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	0.222012	−	8.99726i	0.0246680	−	0.999696i
$10$	6.00571	+	3.73249i	0.600571	+	0.373249i
$11$			16.9733i			1.54303i	0.636213	+	0.771513i	$0.280500\pi$
$11$			16.9733i			1.54303i	−0.636213	+	0.771513i	$0.719500\pi$
$12$	4.18999	+	4.29465i	0.349165	+	0.357888i
$13$	10.2231	+	10.2231i	0.786392	+	0.786392i	0.980901	−	0.194509i	$-0.0623114\pi$
$13$	10.2231	+	10.2231i	0.786392	+	0.786392i	−0.194509	+	0.980901i	$0.562311\pi$
$14$	−8.91976	+	4.29394i	−0.637126	+	0.306710i
$15$	12.6414	+	8.07434i	0.842760	+	0.538290i
$16$	−4.00000			−0.250000
$17$	−8.79877	−	8.79877i	−0.517575	−	0.517575i	0.399262	−	0.916837i	$-0.369266\pi$
$17$	−8.79877	−	8.79877i	−0.517575	−	0.517575i	−0.916837	+	0.399262i	$0.869266\pi$
$18$	8.77525	+	9.21927i	0.487514	+	0.512182i
$19$	−24.7369			−1.30194			−0.650972	−	0.759102i	$-0.725639\pi$
$19$	−24.7369			−1.30194			−0.650972	+	0.759102i	$0.725639\pi$
$20$	−9.73820	+	2.27322i	−0.486910	+	0.113661i
$21$	−19.0326	+	8.87473i	−0.906313	+	0.422606i
$22$	−16.9733	−	16.9733i	−0.771513	−	0.771513i
$23$	19.2569	+	19.2569i	0.837258	+	0.837258i	0.988497	−	0.151239i	$-0.0483263\pi$
$23$	19.2569	+	19.2569i	0.837258	+	0.837258i	−0.151239	+	0.988497i	$0.548326\pi$
$24$	−8.48464	−	0.104666i	−0.353526	−	0.00436106i
$25$	−22.4162	+	11.0685i	−0.896649	+	0.442742i
$26$	−20.4462			−0.786392
$27$	18.3725	+	19.7852i	0.680462	+	0.732784i
$28$	4.62582	−	13.2137i	0.165208	−	0.471918i
$29$	1.67978			0.0579235			0.0289618	−	0.999581i	$-0.490780\pi$
$29$	1.67978			0.0579235			0.0289618	+	0.999581i	$0.490780\pi$
$30$	−20.7157	+	4.56706i	−0.690525	+	0.152235i
$31$			36.8991i			1.19029i	0.803616	+	0.595147i	$0.202906\pi$
$31$			36.8991i			1.19029i	−0.803616	+	0.595147i	$0.797094\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−35.5589	−	36.4472i	−1.07754	−	1.10446i
$34$	17.5975			0.517575
$35$	3.75235	−	34.7983i	0.107210	−	0.994236i
$36$	−17.9945	−	0.444025i	−0.499848	−	0.0123340i
$37$	40.5381	+	40.5381i	1.09562	+	1.09562i	0.994916	+	0.100708i	$0.0321107\pi$
$37$	40.5381	+	40.5381i	1.09562	+	1.09562i	0.100708	+	0.994916i	$0.467889\pi$
$38$	24.7369	−	24.7369i	0.650972	−	0.650972i
$39$	−43.3696	−	0.535003i	−1.11204	−	0.0137180i
$40$	7.46497	−	12.0114i	0.186624	−	0.300285i
$41$	−0.885911			−0.0216076			−0.0108038	−	0.999942i	$-0.503439\pi$
$41$	−0.885911			−0.0216076			−0.0108038	+	0.999942i	$0.503439\pi$
$42$	10.1578	−	27.9073i	0.241853	−	0.664460i
$43$	−9.87427	+	9.87427i	−0.229634	+	0.229634i	−0.812540	−	0.582906i	$-0.801916\pi$
$43$	−9.87427	+	9.87427i	−0.229634	+	0.229634i	0.582906	+	0.812540i	$0.301916\pi$
$44$	33.9466			0.771513
$45$	−44.0609	+	9.14540i	−0.979131	+	0.203231i
$46$	−38.5139			−0.837258
$47$	33.7538	+	33.7538i	0.718165	+	0.718165i	0.968229	−	0.250064i	$-0.0804517\pi$
$47$	33.7538	+	33.7538i	0.718165	+	0.718165i	−0.250064	+	0.968229i	$0.580452\pi$
$48$	8.58930	−	8.37997i	0.178944	−	0.174583i
$49$	38.3009	+	30.5621i	0.781651	+	0.623716i
$50$	11.3477	−	33.4848i	0.226954	−	0.669696i
$51$	37.3272	+	0.460464i	0.731906	+	0.00902871i
$52$	20.4462	−	20.4462i	0.393196	−	0.393196i
$53$	−11.9694	−	11.9694i	−0.225838	−	0.225838i	0.585113	−	0.810952i	$-0.301050\pi$
$53$	−11.9694	−	11.9694i	−0.225838	−	0.225838i	−0.810952	+	0.585113i	$0.801050\pi$
$54$	−38.1576	−	1.41270i	−0.706623	−	0.0261611i
$55$	82.6446	−	19.2920i	1.50263	−	0.350765i
$56$	8.58788	+	17.8395i	0.153355	+	0.318563i
$57$	53.1183	−	51.8237i	0.931899	−	0.909188i
$58$	−1.67978	+	1.67978i	−0.0289618	+	0.0289618i
$59$			50.5136i			0.856162i	0.903740	+	0.428081i	$0.140810\pi$
$59$			50.5136i			0.856162i	−0.903740	+	0.428081i	$0.859190\pi$
$60$	16.1487	−	25.2828i	0.269145	−	0.421380i
$61$			80.6872i			1.32274i	0.750059	+	0.661370i	$0.230025\pi$
$61$			80.6872i			1.32274i	−0.750059	+	0.661370i	$0.769975\pi$
$62$	−36.8991	−	36.8991i	−0.595147	−	0.595147i
$63$	22.2766	−	58.9301i	0.353597	−	0.935398i
$64$			8.00000i			0.125000i
$65$	38.1575	−	61.3969i	0.587039	−	0.944568i
$66$	72.0061	+	0.888260i	1.09100	+	0.0134585i
$67$	−4.46192	−	4.46192i	−0.0665959	−	0.0665959i	0.673024	−	0.739620i	$-0.264995\pi$
$67$	−4.46192	−	4.46192i	−0.0665959	−	0.0665959i	−0.739620	+	0.673024i	$0.764995\pi$
$68$	−17.5975	+	17.5975i	−0.258787	+	0.258787i
$69$	−81.6941	−	1.00777i	−1.18397	−	0.0146053i
$70$	31.0459	+	38.5506i	0.443513	+	0.550723i
$71$		−	137.180i		−	1.93212i	−0.258322	−	0.966059i	$-0.583169\pi$
$71$		−	137.180i		−	1.93212i	0.258322	−	0.966059i	$-0.416831\pi$
$72$	18.4385	−	17.5505i	0.256091	−	0.243757i
$73$	−53.3244	−	53.3244i	−0.730471	−	0.730471i	0.240242	−	0.970713i	$-0.422773\pi$
$73$	−53.3244	−	53.3244i	−0.730471	−	0.730471i	−0.970713	+	0.240242i	$0.922773\pi$
$74$	−81.0762			−1.09562
$75$	24.9464	−	70.7296i	0.332619	−	0.943061i
$76$			49.4739i			0.650972i
$77$	−39.2577	+	112.140i	−0.509840	+	1.45636i
$78$	43.9046	−	42.8346i	0.562880	−	0.549162i
$79$		−	127.936i		−	1.61944i	−0.586816	−	0.809721i	$-0.699619\pi$
$79$		−	127.936i		−	1.61944i	0.586816	−	0.809721i	$-0.300381\pi$
$80$	4.54645	+	19.4764i	0.0568306	+	0.243455i
$81$	−80.9014	−	3.99500i	−0.998783	−	0.0493210i
$82$	0.885911	−	0.885911i	0.0108038	−	0.0108038i
$83$	60.0077	−	60.0077i	0.722985	−	0.722985i	−0.246227	−	0.969212i	$-0.579191\pi$
$83$	60.0077	−	60.0077i	0.722985	−	0.722985i	0.969212	+	0.246227i	$0.0791910\pi$
$84$	17.7495	+	38.0652i	0.211303	+	0.453157i
$85$	−32.8413	+	52.8429i	−0.386368	+	0.621681i
$86$		−	19.7485i		−	0.229634i
$87$	−3.60704	+	3.51913i	−0.0414602	+	0.0404498i
$88$	−33.9466	+	33.9466i	−0.385757	+	0.385757i
$89$		−	51.3826i		−	0.577332i	−0.957430	−	0.288666i	$-0.906788\pi$
$89$		−	51.3826i		−	0.577332i	0.957430	−	0.288666i	$-0.0932117\pi$
$90$	34.9155	−	53.2063i	0.387950	−	0.591181i
$91$	43.8974	+	91.1875i	0.482388	+	1.00206i
$92$	38.5139	−	38.5139i	0.418629	−	0.418629i
$93$	−77.3034	−	79.2345i	−0.831220	−	0.851984i
$94$	−67.5075			−0.718165
$95$	28.1163	+	120.447i	0.295961	+	1.26786i
$96$	−0.209331	+	16.9693i	−0.00218053	+	0.176763i
$97$	0.274025	−	0.274025i	0.00282500	−	0.00282500i	−0.705693	−	0.708518i	$-0.749364\pi$
$97$	0.274025	−	0.274025i	0.00282500	−	0.00282500i	0.708518	+	0.705693i	$0.249364\pi$
$98$	−68.8630	+	7.73884i	−0.702683	+	0.0789678i
$99$	152.713	+	3.76828i	1.54256	+	0.0380634i
$100$	22.1371	+	44.8325i	0.221371	+	0.448325i
$101$	21.6785			0.214638			0.107319	−	0.994225i	$-0.465773\pi$
$101$	21.6785			0.214638			0.107319	+	0.994225i	$0.465773\pi$
$102$	−37.7877	+	36.8667i	−0.370467	+	0.361438i
$103$	49.4148	+	49.4148i	0.479755	+	0.479755i	0.905053	−	0.425298i	$-0.139831\pi$
$103$	49.4148	+	49.4148i	0.479755	+	0.479755i	−0.425298	+	0.905053i	$0.639831\pi$
$104$			40.8924i			0.393196i
$105$	64.8446	+	82.5844i	0.617568	+	0.786518i
$106$	23.9389			0.225838
$107$	−42.7088	+	42.7088i	−0.399147	+	0.399147i	−0.877932	−	0.478785i	$-0.841077\pi$
$107$	−42.7088	+	42.7088i	−0.399147	+	0.399147i	0.478785	+	0.877932i	$0.341077\pi$
$108$	39.5703	−	36.7449i	0.366392	−	0.340231i
$109$		−	69.1171i		−	0.634102i	−0.948408	−	0.317051i	$-0.897307\pi$
$109$		−	69.1171i		−	0.634102i	0.948408	−	0.317051i	$-0.102693\pi$
$110$	−63.3526	+	101.937i	−0.575933	+	0.926697i
$111$	−171.975	−	2.12147i	−1.54933	−	0.0191123i
$112$	−26.4274	−	9.25163i	−0.235959	−	0.0826039i
$113$	58.1205	+	58.1205i	0.514341	+	0.514341i	0.915853	−	0.401513i	$-0.131515\pi$
$113$	58.1205	+	58.1205i	0.514341	+	0.514341i	−0.401513	+	0.915853i	$0.631515\pi$
$114$	−1.29455	+	104.942i	−0.0113557	+	0.920544i
$115$	71.8763	−	115.652i	0.625011	−	1.00567i
$116$		−	3.35956i		−	0.0289618i
$117$	94.2495	−	89.7102i	0.805551	−	0.766754i
$118$	−50.5136	−	50.5136i	−0.428081	−	0.428081i
$119$	−37.7814	−	78.4829i	−0.317491	−	0.659520i
$120$	9.13411	+	41.4315i	0.0761176	+	0.345262i
$121$	−167.093			−1.38093
$122$	−80.6872	−	80.6872i	−0.661370	−	0.661370i
$123$	1.90234	−	1.85598i	0.0154662	−	0.0150892i
$124$	73.7983			0.595147
$125$	79.3724	+	96.5662i	0.634979	+	0.772529i
$126$	36.6534	+	81.2067i	0.290900	+	0.644498i
$127$	−7.40218	−	7.40218i	−0.0582849	−	0.0582849i	0.677364	−	0.735648i	$-0.263122\pi$
$127$	−7.40218	−	7.40218i	−0.0582849	−	0.0582849i	−0.735648	+	0.677364i	$0.763122\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$	0.516748	−	41.8898i	0.00400580	−	0.324727i
$130$	23.2394	+	99.5545i	0.178764	+	0.765804i
$131$	16.3631			0.124909			0.0624544	−	0.998048i	$-0.480107\pi$
$131$	16.3631			0.124909			0.0624544	+	0.998048i	$0.480107\pi$
$132$	−72.8944	+	71.1179i	−0.552230	+	0.538772i
$133$	−163.433	−	57.2143i	−1.22882	−	0.430183i
$134$	8.92385			0.0665959
$135$	75.4535	−	111.945i	0.558915	−	0.829225i
$136$		−	35.1951i		−	0.258787i
$137$	−102.022	+	102.022i	−0.744688	+	0.744688i	−0.973476	−	0.228788i	$-0.926524\pi$
$137$	−102.022	+	102.022i	−0.744688	+	0.744688i	0.228788	+	0.973476i	$0.426524\pi$
$138$	82.7018	−	80.6863i	0.599289	−	0.584683i
$139$	−80.5228			−0.579300			−0.289650	−	0.957133i	$-0.593539\pi$
$139$	−80.5228			−0.579300			−0.289650	+	0.957133i	$0.593539\pi$
$140$	−69.5965	−	7.50470i	−0.497118	−	0.0536050i
$141$	−143.194	−	1.76643i	−1.01556	−	0.0125279i
$142$	137.180	+	137.180i	0.966059	+	0.966059i
$143$	−173.520	+	173.520i	−1.21342	+	1.21342i
$144$	−0.888049	+	35.9890i	−0.00616701	+	0.249924i
$145$	−1.90926	−	8.17902i	−0.0131673	−	0.0564071i
$146$	106.649			0.730471
$147$	−146.272	+	14.6134i	−0.995046	+	0.0994110i
$148$	81.0762	−	81.0762i	0.547812	−	0.547812i
$149$	140.338			0.941864			0.470932	−	0.882170i	$-0.343918\pi$
$149$	140.338			0.941864			0.470932	+	0.882170i	$0.343918\pi$
$150$	45.7832	+	95.6760i	0.305221	+	0.637840i
$151$	32.6929			0.216509			0.108255	−	0.994123i	$-0.465474\pi$
$151$	32.6929			0.216509			0.108255	+	0.994123i	$0.465474\pi$
$152$	−49.4739	−	49.4739i	−0.325486	−	0.325486i
$153$	−81.1183	+	77.2114i	−0.530185	+	0.504650i
$154$	−72.8823	−	151.398i	−0.473262	−	0.983102i
$155$	179.666	−	41.9400i	1.15913	−	0.270581i
$156$	−1.07001	+	86.7392i	−0.00685901	+	0.556021i
$157$	17.9885	−	17.9885i	0.114576	−	0.114576i	−0.647494	−	0.762070i	$-0.724183\pi$
$157$	17.9885	−	17.9885i	0.114576	−	0.114576i	0.762070	+	0.647494i	$0.224183\pi$
$158$	127.936	+	127.936i	0.809721	+	0.809721i
$159$	50.7781	+	0.626394i	0.319359	+	0.00393958i
$160$	−24.0228	−	14.9299i	−0.150143	−	0.0933121i
$161$	82.6882	+	171.767i	0.513591	+	1.06688i
$162$	84.8964	−	76.9064i	0.524052	−	0.474731i
$163$	90.3636	−	90.3636i	0.554378	−	0.554378i	−0.373324	−	0.927701i	$-0.621782\pi$
$163$	90.3636	−	90.3636i	0.554378	−	0.554378i	0.927701	+	0.373324i	$0.121782\pi$
$164$			1.77182i			0.0108038i
$165$	−137.048	+	214.566i	−0.830595	+	1.30040i
$166$			120.015i			0.722985i
$167$	11.1296	+	11.1296i	0.0666444	+	0.0666444i	0.739643	−	0.672999i	$-0.234994\pi$
$167$	11.1296	+	11.1296i	0.0666444	+	0.0666444i	−0.672999	+	0.739643i	$0.734994\pi$
$168$	−55.8146	−	20.3157i	−0.332230	−	0.120927i
$169$			40.0232i			0.236824i
$170$	−20.0016	−	85.6842i	−0.117656	−	0.504024i
$171$	−5.49190	+	222.565i	−0.0321164	+	1.30155i
$172$	19.7485	+	19.7485i	0.114817	+	0.114817i
$173$	−143.704	+	143.704i	−0.830661	+	0.830661i	−0.987607	−	0.156946i	$-0.949835\pi$
$173$	−143.704	+	143.704i	−0.830661	+	0.830661i	0.156946	+	0.987607i	$0.449835\pi$
$174$	0.0879077	−	7.12617i	0.000505216	−	0.0409550i
$175$	−173.701	+	21.2816i	−0.992578	+	0.121609i
$176$		−	67.8932i		−	0.385757i
$177$	−105.826	−	108.469i	−0.597884	−	0.612819i
$178$	51.3826	+	51.3826i	0.288666	+	0.288666i
$179$	−334.691			−1.86978			−0.934891	−	0.354936i	$-0.884503\pi$
$179$	−334.691			−1.86978			−0.934891	+	0.354936i	$0.884503\pi$
$180$	18.2908	+	88.1218i	0.101616	+	0.489565i
$181$		−	99.3599i		−	0.548949i	−0.961594	−	0.274475i	$-0.911496\pi$
$181$		−	99.3599i		−	0.548949i	0.961594	−	0.274475i	$-0.0885040\pi$
$182$	−135.085	−	47.2901i	−0.742224	−	0.259836i
$183$	−169.039	−	173.262i	−0.923711	−	0.946785i
$184$			77.0278i			0.418629i
$185$	151.308	−	243.460i	0.817880	−	1.31600i
$186$	156.538	+	1.93103i	0.841602	+	0.0103819i
$187$	149.344	−	149.344i	0.798632	−	0.798632i
$188$	67.5075	−	67.5075i	0.359083	−	0.359083i
$189$	75.6228	+	173.211i	0.400121	+	0.916462i
$190$	−148.563	−	92.3303i	−0.781910	−	0.485949i
$191$			41.5022i			0.217289i	0.994081	+	0.108645i	$0.0346510\pi$
$191$			41.5022i			0.217289i	−0.994081	+	0.108645i	$0.965349\pi$
$192$	−16.7599	−	17.1786i	−0.0872914	−	0.0894719i
$193$	112.254	−	112.254i	0.581626	−	0.581626i	−0.353724	−	0.935350i	$-0.615085\pi$
$193$	112.254	−	112.254i	0.581626	−	0.581626i	0.935350	+	0.353724i	$0.115085\pi$
$194$			0.548049i			0.00282500i
$195$	46.6894	+	211.779i	0.239433	+	1.08605i
$196$	61.1241	−	76.6018i	0.311858	−	0.390826i
$197$	177.771	−	177.771i	0.902388	−	0.902388i	−0.0932539	−	0.995642i	$-0.529727\pi$
$197$	177.771	−	177.771i	0.902388	−	0.902388i	0.995642	+	0.0932539i	$0.0297268\pi$
$198$	−156.481	+	148.945i	−0.790310	+	0.752247i
$199$	−79.5223			−0.399609			−0.199805	−	0.979836i	$-0.564031\pi$
$199$	−79.5223			−0.399609			−0.199805	+	0.979836i	$0.564031\pi$
$200$	−66.9696	−	22.6954i	−0.334848	−	0.113477i
$201$	18.9289	+	0.233505i	0.0941736	+	0.00116172i
$202$	−21.6785	+	21.6785i	−0.107319	+	0.107319i
$203$	11.0981	+	3.88518i	0.0546703	+	0.0191388i
$204$	0.920928	−	74.6544i	0.00451435	−	0.365953i
$205$	1.00694	+	4.31359i	0.00491189	+	0.0210419i
$206$	−98.8296			−0.479755
$207$	177.535	−	168.984i	0.857657	−	0.816350i
$208$	−40.8924	−	40.8924i	−0.196598	−	0.196598i
$209$		−	419.867i		−	2.00894i
$210$	−147.429	−	17.7398i	−0.702043	−	0.0844750i
$211$	398.914			1.89059			0.945294	−	0.326220i	$-0.105775\pi$
$211$	398.914			1.89059			0.945294	+	0.326220i	$0.105775\pi$
$212$	−23.9389	+	23.9389i	−0.112919	+	0.112919i
$213$	287.392	+	294.571i	1.34926	+	1.38296i
$214$		−	85.4175i		−	0.399147i
$215$	59.3020	+	36.8556i	0.275823	+	0.171421i
$216$	−2.82540	+	76.3152i	−0.0130805	+	0.353311i
$217$	−85.3443	+	243.787i	−0.393292	+	1.12344i
$218$	69.1171	+	69.1171i	0.317051	+	0.317051i
$219$	226.219	+	2.79061i	1.03296	+	0.0127425i
$220$	−38.5841	−	165.289i	−0.175382	−	0.751315i
$221$		−	179.901i		−	0.814033i
$222$	174.097	−	169.854i	0.784220	−	0.765108i
$223$	−162.636	−	162.636i	−0.729308	−	0.729308i	0.241174	−	0.970482i	$-0.422468\pi$
$223$	−162.636	−	162.636i	−0.729308	−	0.729308i	−0.970482	+	0.241174i	$0.922468\pi$
$224$	35.6790	−	17.1758i	0.159281	−	0.0766775i
$225$	94.6100	+	204.142i	0.420489	+	0.907298i
$226$	−116.241			−0.514341
$227$	255.602	+	255.602i	1.12600	+	1.12600i	0.990821	+	0.135179i	$0.0431610\pi$
$227$	255.602	+	255.602i	1.12600	+	1.12600i	0.135179	+	0.990821i	$0.456839\pi$
$228$	−103.647	−	106.237i	−0.454594	−	0.465950i
$229$	−188.516			−0.823212			−0.411606	−	0.911362i	$-0.635032\pi$
$229$	−188.516			−0.823212			−0.411606	+	0.911362i	$0.635032\pi$
$230$	43.7753	+	187.528i	0.190328	+	0.815338i
$231$	−150.633	−	323.046i	−0.652093	−	1.39847i
$232$	3.35956	+	3.35956i	0.0144809	+	0.0144809i
$233$	16.7394	+	16.7394i	0.0718429	+	0.0718429i	0.742115	−	0.670272i	$-0.233823\pi$
$233$	16.7394	+	16.7394i	0.0718429	+	0.0718429i	−0.670272	+	0.742115i	$0.733823\pi$
$234$	−4.53930	+	183.960i	−0.0193987	+	0.786152i
$235$	125.985	−	202.715i	0.536108	−	0.862618i
$236$	101.027			0.428081
$237$	268.025	+	274.720i	1.13091	+	1.15916i
$238$	116.264	+	40.7015i	0.488506	+	0.171015i
$239$	−93.1494			−0.389746			−0.194873	−	0.980828i	$-0.562430\pi$
$239$	−93.1494			−0.389746			−0.194873	+	0.980828i	$0.562430\pi$
$240$	−50.5656	−	32.2974i	−0.210690	−	0.134572i
$241$		−	443.888i		−	1.84186i	−0.389729	−	0.920929i	$-0.627431\pi$
$241$		−	443.888i		−	1.84186i	0.389729	−	0.920929i	$-0.372569\pi$
$242$	167.093	−	167.093i	0.690466	−	0.690466i
$243$	182.091	−	160.909i	0.749346	−	0.662178i
$244$	161.374			0.661370
$245$	105.276	−	221.228i	0.429700	−	0.902972i
$246$	−0.0463622	+	3.75831i	−0.000188464	+	0.0152777i
$247$	−252.888	−	252.888i	−1.02384	−	1.02384i
$248$	−73.7983	+	73.7983i	−0.297574	+	0.297574i
$249$	−3.14037	+	254.572i	−0.0126119	+	1.02238i
$250$	−175.939	−	17.1938i	−0.703754	−	0.0687750i
$251$	−387.377			−1.54334			−0.771668	−	0.636026i	$-0.780577\pi$
$251$	−387.377			−1.54334			−0.771668	+	0.636026i	$0.780577\pi$
$252$	−117.860	−	44.5533i	−0.467699	−	0.176799i
$253$	−326.854	+	326.854i	−1.29191	+	1.29191i
$254$	14.8044			0.0582849
$255$	−40.1845	−	182.273i	−0.157586	−	0.714796i
$256$	16.0000			0.0625000
$257$	−181.485	−	181.485i	−0.706167	−	0.706167i	0.259560	−	0.965727i	$-0.416422\pi$
$257$	−181.485	−	181.485i	−0.706167	−	0.706167i	−0.965727	+	0.259560i	$0.916422\pi$
$258$	41.3730	+	42.4065i	0.160361	+	0.164366i
$259$	174.068	+	361.590i	0.672078	+	1.39610i
$260$	−122.794	−	76.3151i	−0.472284	−	0.293520i
$261$	0.372932	−	15.1134i	0.00142886	−	0.0579059i
$262$	−16.3631	+	16.3631i	−0.0624544	+	0.0624544i
$263$	181.005	+	181.005i	0.688233	+	0.688233i	0.961841	−	0.273608i	$-0.0882171\pi$
$263$	181.005	+	181.005i	0.688233	+	0.688233i	−0.273608	+	0.961841i	$0.588217\pi$
$264$	1.77652	−	144.012i	0.00672924	−	0.545501i
$265$	−44.6757	+	71.8849i	−0.168588	+	0.271264i
$266$	220.648	−	106.219i	0.829502	−	0.399319i
$267$	107.646	+	110.335i	0.403169	+	0.413240i
$268$	−8.92385	+	8.92385i	−0.0332979	+	0.0332979i
$269$		−	197.175i		−	0.732994i	−0.930419	−	0.366497i	$-0.880557\pi$
$269$		−	197.175i		−	0.732994i	0.930419	−	0.366497i	$-0.119443\pi$
$270$	36.4918	+	187.399i	0.135155	+	0.694070i
$271$			311.811i			1.15059i	0.817945	+	0.575296i	$0.195113\pi$
$271$			311.811i			1.15059i	−0.817945	+	0.575296i	$0.804887\pi$
$272$	35.1951	+	35.1951i	0.129394	+	0.129394i
$273$	−285.299	−	103.845i	−1.04505	−	0.380383i
$274$		−	204.044i		−	0.744688i
$275$	−187.870	−	380.477i	−0.683163	−	1.38355i
$276$	−2.01554	+	163.388i	−0.00730267	+	0.591986i
$277$	161.718	+	161.718i	0.583820	+	0.583820i	0.935951	−	0.352131i	$-0.114543\pi$
$277$	161.718	+	161.718i	0.583820	+	0.583820i	−0.352131	+	0.935951i	$0.614543\pi$
$278$	80.5228	−	80.5228i	0.289650	−	0.289650i
$279$	331.991	+	8.19206i	1.18993	+	0.0293622i
$280$	77.1013	−	62.0918i	0.275362	−	0.221757i
$281$		−	182.531i		−	0.649576i	−0.945787	−	0.324788i	$-0.894707\pi$
$281$		−	182.531i		−	0.649576i	0.945787	−	0.324788i	$-0.105293\pi$
$282$	144.961	−	141.428i	0.514045	−	0.501517i
$283$	−13.2471	−	13.2471i	−0.0468095	−	0.0468095i	0.683315	−	0.730124i	$-0.260538\pi$
$283$	−13.2471	−	13.2471i	−0.0468095	−	0.0468095i	−0.730124	+	0.683315i	$0.760538\pi$
$284$	−274.361			−0.966059
$285$	−312.710	−	199.735i	−1.09723	−	0.700823i
$286$		−	347.039i		−	1.21342i
$287$	−5.85308	−	2.04903i	−0.0203940	−	0.00713948i
$288$	−35.1010	−	36.8771i	−0.121878	−	0.128045i
$289$		−	134.163i		−	0.464233i
$290$	10.0883	+	6.26976i	0.0347872	+	0.0216199i
$291$	−0.0143405	+	1.16250i	−4.92800e−5	+	0.00399485i
$292$	−106.649	+	106.649i	−0.365236	+	0.365236i
$293$	45.8307	−	45.8307i	0.156419	−	0.156419i	−0.624559	−	0.780978i	$-0.714721\pi$
$293$	45.8307	−	45.8307i	0.156419	−	0.156419i	0.780978	+	0.624559i	$0.214721\pi$
$294$	131.658	−	160.885i	0.447818	−	0.547229i
$295$	245.955	−	57.4143i	0.833747	−	0.194625i
$296$			162.152i			0.547812i
$297$	−335.819	+	311.841i	−1.13070	+	1.04997i
$298$	−140.338	+	140.338i	−0.470932	+	0.470932i
$299$			393.731i			1.31683i
$300$	−141.459	−	49.8928i	−0.471531	−	0.166309i
$301$	−88.0761	+	42.3995i	−0.292612	+	0.140862i
$302$	−32.6929	+	32.6929i	−0.108255	+	0.108255i
$303$	−46.5508	+	45.4163i	−0.153633	+	0.149889i
$304$	98.9478			0.325486
$305$	392.874	−	91.7100i	1.28811	−	0.300689i
$306$	3.90687	−	158.330i	0.0127675	−	0.517417i
$307$	−273.273	+	273.273i	−0.890140	+	0.890140i	−0.994536	−	0.104396i	$-0.966709\pi$
$307$	−273.273	+	273.273i	−0.890140	+	0.890140i	0.104396	+	0.994536i	$0.466709\pi$
$308$	224.280	+	78.5153i	0.728182	+	0.254920i
$309$	−209.633	−	2.58601i	−0.678425	−	0.00836898i
$310$	−137.726	+	221.606i	−0.444276	+	0.714857i
$311$	408.594			1.31381			0.656903	−	0.753975i	$-0.271866\pi$
$311$	408.594			1.31381			0.656903	+	0.753975i	$0.271866\pi$
$312$	−85.6692	−	87.8092i	−0.274581	−	0.281440i
$313$	269.726	+	269.726i	0.861746	+	0.861746i	0.991541	−	0.129795i	$-0.0414320\pi$
$313$	269.726	+	269.726i	0.861746	+	0.861746i	−0.129795	+	0.991541i	$0.541432\pi$
$314$			35.9770i			0.114576i
$315$	−312.256	−	41.4865i	−0.991289	−	0.131703i
$316$	−255.872			−0.809721
$317$	−265.401	+	265.401i	−0.837227	+	0.837227i	−0.988493	−	0.151266i	$-0.951665\pi$
$317$	−265.401	+	265.401i	−0.837227	+	0.837227i	0.151266	+	0.988493i	$0.451665\pi$
$318$	−51.4045	+	50.1517i	−0.161649	+	0.157710i
$319$			28.5114i			0.0893776i
$320$	38.9528	−	9.09290i	0.121727	−	0.0284153i
$321$	2.23507	−	181.184i	0.00696283	−	0.564437i
$322$	−254.455	−	89.0791i	−0.790234	−	0.276643i
$323$	217.655	+	217.655i	0.673854	+	0.673854i
$324$	−7.99001	+	161.803i	−0.0246605	+	0.499391i
$325$	−342.318	−	116.008i	−1.05329	−	0.356949i
$326$			180.727i			0.554378i
$327$	144.800	+	148.417i	0.442813	+	0.453875i
$328$	−1.77182	−	1.77182i	−0.00540189	−	0.00540189i
$329$	144.937	+	301.075i	0.440537	+	0.915123i
$330$	−77.5180	−	351.614i	−0.234903	−	1.06550i
$331$	383.355			1.15817			0.579086	−	0.815266i	$-0.303409\pi$
$331$	383.355			1.15817			0.579086	+	0.815266i	$0.303409\pi$
$332$	−120.015	−	120.015i	−0.361492	−	0.361492i
$333$	373.732	−	355.732i	1.12232	−	1.06826i
$334$	−22.2592			−0.0666444
$335$	−16.6541	+	26.7970i	−0.0497136	+	0.0799911i
$336$	76.1303	−	35.4989i	0.226578	−	0.105652i
$337$	−207.675	−	207.675i	−0.616246	−	0.616246i	0.328321	−	0.944566i	$-0.393517\pi$
$337$	−207.675	−	207.675i	−0.616246	−	0.616246i	−0.944566	+	0.328321i	$0.893517\pi$
$338$	−40.0232	−	40.0232i	−0.118412	−	0.118412i
$339$	−246.566	−	3.04161i	−0.727333	−	0.00897229i
$340$	105.686	+	65.6826i	0.310840	+	0.193184i
$341$	−626.300			−1.83666
$342$	−217.073	−	228.057i	−0.634716	−	0.666832i
$343$	182.361	+	290.505i	0.531665	+	0.846955i
$344$	−39.4971			−0.114817
$345$	87.9475	+	398.922i	0.254920	+	1.15630i
$346$		−	287.409i		−	0.830661i
$347$	−41.3813	+	41.3813i	−0.119254	+	0.119254i	−0.764215	−	0.644961i	$-0.776874\pi$
$347$	−41.3813	+	41.3813i	−0.119254	+	0.119254i	0.644961	+	0.764215i	$0.276874\pi$
$348$	7.03826	+	7.21408i	0.0202249	+	0.0207301i
$349$	565.082			1.61915			0.809573	−	0.587019i	$-0.199698\pi$
$349$	565.082			1.61915			0.809573	+	0.587019i	$0.199698\pi$
$350$	152.420	−	194.983i	0.435485	−	0.557094i
$351$	−14.4421	+	390.089i	−0.0411457	+	1.11136i
$352$	67.8932	+	67.8932i	0.192878	+	0.192878i
$353$	−121.484	+	121.484i	−0.344146	+	0.344146i	−0.857923	−	0.513778i	$-0.828246\pi$
$353$	−121.484	+	121.484i	−0.344146	+	0.344146i	0.513778	+	0.857923i	$0.328246\pi$
$354$	214.295	+	2.64351i	0.605352	+	0.00746756i
$355$	−667.945	+	155.921i	−1.88153	+	0.439214i
$356$	−102.765			−0.288666
$357$	245.550	+	89.3766i	0.687815	+	0.250355i
$358$	334.691	−	334.691i	0.934891	−	0.934891i
$359$	−129.751			−0.361424			−0.180712	−	0.983536i	$-0.557840\pi$
$359$	−129.751			−0.361424			−0.180712	+	0.983536i	$0.557840\pi$
$360$	−106.413	−	69.8310i	−0.295590	−	0.193975i
$361$	250.916			0.695059
$362$	99.3599	+	99.3599i	0.274475	+	0.274475i
$363$	358.802	−	350.058i	0.988437	−	0.964347i
$364$	182.375	−	87.7947i	0.501030	−	0.241194i
$365$	−199.033	+	320.251i	−0.545295	+	0.877399i
$366$	342.301	+	4.22258i	0.935248	+	0.0115371i
$367$	476.739	−	476.739i	1.29902	−	1.29902i	0.369976	−	0.929041i	$-0.379366\pi$
$367$	476.739	−	476.739i	1.29902	−	1.29902i	0.929041	−	0.369976i	$-0.120634\pi$
$368$	−77.0278	−	77.0278i	−0.209315	−	0.209315i
$369$	−0.196683	+	7.97077i	−0.000533016	+	0.0216010i
$370$	92.1521	+	394.768i	0.249060	+	1.06694i
$371$	−51.3960	−	106.764i	−0.138534	−	0.287775i
$372$	−158.469	+	154.607i	−0.425992	+	0.415610i
$373$	76.1479	−	76.1479i	0.204150	−	0.204150i	−0.597626	−	0.801775i	$-0.703889\pi$
$373$	76.1479	−	76.1479i	0.204150	−	0.204150i	0.801775	+	0.597626i	$0.203889\pi$
$374$			298.688i			0.798632i
$375$	−372.744	−	41.0744i	−0.993983	−	0.109532i
$376$			135.015i			0.359083i
$377$	17.1726	+	17.1726i	0.0455506	+	0.0455506i
$378$	−248.834	−	97.5886i	−0.658292	−	0.258171i
$379$			390.814i			1.03117i	0.856838	+	0.515585i	$0.172426\pi$
$379$			390.814i			1.03117i	−0.856838	+	0.515585i	$0.827574\pi$
$380$	240.893	−	56.2326i	0.633929	−	0.147981i
$381$	31.4024	+	0.387377i	0.0824210	+	0.00101674i
$382$	−41.5022	−	41.5022i	−0.108645	−	0.108645i
$383$	62.8508	−	62.8508i	0.164101	−	0.164101i	−0.620280	−	0.784381i	$-0.712981\pi$
$383$	62.8508	−	62.8508i	0.164101	−	0.164101i	0.784381	+	0.620280i	$0.212981\pi$
$384$	33.9385	+	0.418662i	0.0883816	+	0.00109027i
$385$	590.641	+	63.6898i	1.53413	+	0.165428i
$386$			224.508i			0.581626i
$387$	86.6492	+	91.0336i	0.223900	+	0.235229i
$388$	−0.548049	−	0.548049i	−0.00141250	−	0.00141250i
$389$	24.2532			0.0623476			0.0311738	−	0.999514i	$-0.490075\pi$
$389$	24.2532			0.0623476			0.0311738	+	0.999514i	$0.490075\pi$
$390$	−258.468	−	165.090i	−0.662739	−	0.423306i
$391$		−	338.875i		−	0.866688i
$392$	15.4777	+	137.726i	0.0394839	+	0.351342i
$393$	−35.1368	+	34.2805i	−0.0894066	+	0.0872277i
$394$			355.541i			0.902388i
$395$	−622.932	+	145.413i	−1.57704	+	0.368135i
$396$	7.53656	−	305.426i	0.0190317	−	0.771279i
$397$	176.911	−	176.911i	0.445618	−	0.445618i	−0.448277	−	0.893895i	$-0.647962\pi$
$397$	176.911	−	176.911i	0.445618	−	0.445618i	0.893895	+	0.448277i	$0.147962\pi$
$398$	79.5223	−	79.5223i	0.199805	−	0.199805i
$399$	470.808	−	219.534i	1.17997	−	0.550210i
$400$	89.6649	−	44.2742i	0.224162	−	0.110685i
$401$			48.5936i			0.121181i	0.998163	+	0.0605905i	$0.0192984\pi$
$401$			48.5936i			0.121181i	−0.998163	+	0.0605905i	$0.980702\pi$
$402$	−19.1624	+	18.6954i	−0.0476677	+	0.0465060i
$403$	−377.223	+	377.223i	−0.936038	+	0.936038i
$404$		−	43.3570i		−	0.107319i
$405$	72.5015	+	398.458i	0.179016	+	0.983846i
$406$	−14.9833	+	7.21289i	−0.0369046	+	0.0177657i
$407$	−688.065	+	688.065i	−1.69058	+	1.69058i
$408$	73.7334	+	75.5753i	0.180719	+	0.185234i
$409$	143.848			0.351706			0.175853	−	0.984416i	$-0.443732\pi$
$409$	143.848			0.351706			0.175853	+	0.984416i	$0.443732\pi$
$410$	−5.32052	−	3.30665i	−0.0129769	−	0.00806500i
$411$	5.33910	−	432.811i	0.0129905	−	1.05307i
$412$	98.8296	−	98.8296i	0.239878	−	0.239878i
$413$	−116.833	+	333.735i	−0.282889	+	0.808076i
$414$	−8.55055	+	346.519i	−0.0206535	+	0.837003i
$415$	−360.389	−	223.978i	−0.868407	−	0.539706i
$416$	81.7847			0.196598
$417$	172.909	−	168.695i	0.414649	−	0.404543i
$418$	419.867	+	419.867i	1.00447	+	1.00447i
$419$		−	80.8927i		−	0.193061i	−0.995330	−	0.0965306i	$-0.969225\pi$
$419$		−	80.8927i		−	0.193061i	0.995330	−	0.0965306i	$-0.0307746\pi$
$420$	165.169	−	129.689i	0.393259	−	0.308784i
$421$	−194.231			−0.461355			−0.230678	−	0.973030i	$-0.574094\pi$
$421$	−194.231			−0.461355			−0.230678	+	0.973030i	$0.574094\pi$
$422$	−398.914	+	398.914i	−0.945294	+	0.945294i
$423$	311.185	−	296.198i	0.735662	−	0.700231i
$424$		−	47.8777i		−	0.112919i
$425$	294.625	+	99.8456i	0.693235	+	0.234931i
$426$	−581.963	−	7.17903i	−1.36611	−	0.0168522i
$427$	−186.622	+	533.088i	−0.437054	+	1.24845i
$428$	85.4175	+	85.4175i	0.199574	+	0.199574i
$429$	9.08076	−	736.125i	0.0211673	−	1.71591i
$430$	−96.1576	+	22.4464i	−0.223622	+	0.0522010i
$431$		−	577.019i		−	1.33879i	−0.742906	−	0.669396i	$-0.766553\pi$
$431$		−	577.019i		−	1.33879i	0.742906	−	0.669396i	$-0.233447\pi$
$432$	−73.4899	−	79.1406i	−0.170115	−	0.183196i
$433$	−42.9015	−	42.9015i	−0.0990797	−	0.0990797i	0.655829	−	0.754909i	$-0.272319\pi$
$433$	−42.9015	−	42.9015i	−0.0990797	−	0.0990797i	−0.754909	+	0.655829i	$0.772319\pi$
$434$	−158.443	−	329.131i	−0.365075	−	0.758367i
$435$	21.2348	+	13.5631i	0.0488156	+	0.0311796i
$436$	−138.234			−0.317051
$437$	−476.358	−	476.358i	−1.09006	−	1.09006i
$438$	−229.010	+	223.428i	−0.522853	+	0.510110i
$439$	−73.7420			−0.167977			−0.0839886	−	0.996467i	$-0.526766\pi$
$439$	−73.7420			−0.167977			−0.0839886	+	0.996467i	$0.526766\pi$
$440$	203.873	+	126.705i	0.463349	+	0.287966i
$441$	283.478	−	337.818i	0.642808	−	0.766028i
$442$	179.901	+	179.901i	0.407017	+	0.407017i
$443$	10.4996	+	10.4996i	0.0237011	+	0.0237011i	0.718858	−	0.695157i	$-0.244665\pi$
$443$	10.4996	+	10.4996i	0.0237011	+	0.0237011i	−0.695157	+	0.718858i	$0.744665\pi$
$444$	−4.24294	+	343.951i	−0.00955617	+	0.774664i
$445$	−250.187	+	58.4020i	−0.562217	+	0.131241i
$446$	325.271			0.729308
$447$	−301.351	+	294.006i	−0.674163	+	0.657732i
$448$	−18.5033	+	52.8548i	−0.0413019	+	0.117979i
$449$	−284.237			−0.633044			−0.316522	−	0.948585i	$-0.602515\pi$
$449$	−284.237			−0.633044			−0.316522	+	0.948585i	$0.602515\pi$
$450$	−298.752	−	109.532i	−0.663893	−	0.243405i
$451$		−	15.0368i		−	0.0333411i
$452$	116.241	−	116.241i	0.257170	−	0.257170i
$453$	−70.2023	+	68.4914i	−0.154972	+	0.151195i
$454$	−511.204			−1.12600
$455$	394.107	−	317.385i	0.866168	−	0.697550i
$456$	209.884	+	2.58911i	0.460272	+	0.00567786i
$457$	−117.076	−	117.076i	−0.256184	−	0.256184i	0.567316	−	0.823500i	$-0.307982\pi$
$457$	−117.076	−	117.076i	−0.256184	−	0.256184i	−0.823500	+	0.567316i	$0.807982\pi$
$458$	188.516	−	188.516i	0.411606	−	0.411606i
$459$	12.4300	−	335.740i	0.0270806	−	0.731460i
$460$	−231.303	−	143.753i	−0.502833	−	0.312505i
$461$	221.554			0.480594			0.240297	−	0.970699i	$-0.422755\pi$
$461$	221.554			0.480594			0.240297	+	0.970699i	$0.422755\pi$
$462$	473.679	+	172.412i	1.02528	+	0.373186i
$463$	−315.054	+	315.054i	−0.680462	+	0.680462i	−0.960104	−	0.279642i	$-0.909784\pi$
$463$	−315.054	+	315.054i	−0.680462	+	0.680462i	0.279642	+	0.960104i	$0.409784\pi$
$464$	−6.71913			−0.0144809
$465$	−297.936	+	466.457i	−0.640723	+	1.00313i
$466$	−33.4788			−0.0718429
$467$	229.349	+	229.349i	0.491111	+	0.491111i	0.908656	−	0.417545i	$-0.137109\pi$
$467$	229.349	+	229.349i	0.491111	+	0.491111i	−0.417545	+	0.908656i	$0.637109\pi$
$468$	−179.420	−	188.499i	−0.383377	−	0.402776i
$469$	−19.1592	−	39.7993i	−0.0408513	−	0.0848599i
$470$	76.7299	+	328.701i	0.163255	+	0.699363i
$471$	−0.941388	+	76.3129i	−0.00199870	+	0.162023i
$472$	−101.027	+	101.027i	−0.214041	+	0.214041i
$473$	−167.599	−	167.599i	−0.354332	−	0.354332i
$474$	−542.745	−	6.69524i	−1.14503	−	0.0141250i
$475$	554.509	−	273.802i	1.16739	−	0.576425i
$476$	−156.966	+	75.5628i	−0.329760	+	0.158745i
$477$	−110.349	+	105.035i	−0.231341	+	0.220199i
$478$	93.1494	−	93.1494i	0.194873	−	0.194873i
$479$			166.037i			0.346633i	0.984866	+	0.173316i	$0.0554483\pi$
$479$			166.037i			0.346633i	−0.984866	+	0.173316i	$0.944552\pi$
$480$	82.8630	−	18.2682i	0.172631	−	0.0380588i
$481$			828.849i			1.72318i
$482$	443.888	+	443.888i	0.920929	+	0.920929i
$483$	−537.409	−	195.609i	−1.11265	−	0.404988i
$484$			334.185i			0.690466i
$485$	−1.64571	−	1.02279i	−0.00339322	−	0.00210885i
$486$	−21.1819	+	343.000i	−0.0435841	+	0.705762i
$487$	−639.073	−	639.073i	−1.31226	−	1.31226i	−0.919743	−	0.392521i	$-0.871603\pi$
$487$	−639.073	−	639.073i	−1.31226	−	1.31226i	−0.392521	−	0.919743i	$-0.628397\pi$
$488$	−161.374	+	161.374i	−0.330685	+	0.330685i
$489$	−4.72898	+	383.351i	−0.00967071	+	0.783949i
$490$	115.952	+	326.505i	0.236636	+	0.666336i
$491$		−	148.567i		−	0.302581i	−0.988489	−	0.151291i	$-0.951657\pi$
$491$		−	148.567i		−	0.302581i	0.988489	−	0.151291i	$-0.0483429\pi$
$492$	−3.71195	−	3.80468i	−0.00754462	−	0.00773308i
$493$	−14.7800	−	14.7800i	−0.0299798	−	0.0299798i
$494$	505.776			1.02384
$495$	−155.227	−	747.858i	−0.313591	−	1.51083i
$496$		−	147.597i		−	0.297574i
$497$	317.286	−	906.330i	0.638402	−	1.82360i
$498$	−251.431	−	257.712i	−0.504882	−	0.517494i
$499$			471.498i			0.944885i	0.881361	+	0.472443i	$0.156628\pi$
$499$			471.498i			0.944885i	−0.881361	+	0.472443i	$0.843372\pi$
$500$	193.132	−	158.745i	0.386265	−	0.317490i
$501$	−47.2153	−	0.582443i	−0.0942422	−	0.00116256i
$502$	387.377	−	387.377i	0.771668	−	0.771668i
$503$	−40.7334	+	40.7334i	−0.0809810	+	0.0809810i	−0.746437	−	0.665456i	$-0.768237\pi$
$503$	−40.7334	+	40.7334i	−0.0809810	+	0.0809810i	0.665456	+	0.746437i	$0.268237\pi$
$504$	162.413	−	73.3068i	0.322249	−	0.145450i
$505$	−24.6400	−	105.555i	−0.0487921	−	0.209019i
$506$		−	653.707i		−	1.29191i
$507$	−83.8483	−	85.9428i	−0.165381	−	0.169512i
$508$	−14.8044	+	14.8044i	−0.0291424	+	0.0291424i
$509$		−	834.832i		−	1.64014i	−0.572263	−	0.820070i	$-0.693934\pi$
$509$		−	834.832i		−	1.64014i	0.572263	−	0.820070i	$-0.306066\pi$
$510$	222.458	+	142.089i	0.436191	+	0.278605i
$511$	−228.972	−	475.641i	−0.448086	−	0.930803i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−454.479	−	489.424i	−0.885923	−	0.954044i
$514$	362.970			0.706167
$515$	184.440	−	296.771i	0.358136	−	0.576254i
$516$	−83.7796	−	1.03350i	−0.162364	−	0.00200290i
$517$	−572.913	+	572.913i	−1.10815	+	1.10815i
$518$	−535.658	−	187.522i	−1.03409	−	0.362011i
$519$	7.52045	−	609.640i	0.0144903	−	1.17464i
$520$	199.109	−	46.4788i	0.382902	−	0.0893822i
$521$	690.826			1.32596			0.662980	−	0.748637i	$-0.269291\pi$
$521$	690.826			1.32596			0.662980	+	0.748637i	$0.269291\pi$
$522$	14.7405	+	15.4864i	0.0282385	+	0.0296674i
$523$	560.737	+	560.737i	1.07216	+	1.07216i	0.997186	+	0.0749699i	$0.0238861\pi$
$523$	560.737	+	560.737i	1.07216	+	1.07216i	0.0749699	+	0.997186i	$0.476114\pi$
$524$		−	32.7261i		−	0.0624544i
$525$	328.408	−	409.601i	0.625539	−	0.780193i
$526$	−362.011			−0.688233
$527$	324.667	−	324.667i	0.616067	−	0.616067i
$528$	142.236	+	145.789i	0.269386	+	0.276115i
$529$			212.659i			0.402003i
$530$	−27.2092	−	116.561i	−0.0513381	−	0.219926i
$531$	454.484	+	11.2146i	0.855902	+	0.0211198i
$532$	−114.429	+	326.866i	−0.215091	+	0.614411i
$533$	−9.05675	−	9.05675i	−0.0169920	−	0.0169920i
$534$	−217.981	−	2.68899i	−0.408204	−	0.00503557i
$535$	256.496	+	159.410i	0.479433	+	0.297962i
$536$		−	17.8477i		−	0.0332979i
$537$	718.690	−	701.175i	1.33834	−	1.30573i
$538$	197.175	+	197.175i	0.366497	+	0.366497i
$539$	−518.739	+	650.093i	−0.962410	+	1.20611i
$540$	−223.891	−	150.907i	−0.414612	−	0.279457i
$541$	655.178			1.21105			0.605525	−	0.795827i	$-0.292963\pi$
$541$	655.178			1.21105			0.605525	+	0.795827i	$0.292963\pi$
$542$	−311.811	−	311.811i	−0.575296	−	0.575296i
$543$	208.158	+	213.358i	0.383348	+	0.392924i
$544$	−70.3902			−0.129394
$545$	−336.538	+	78.5594i	−0.617501	+	0.144146i
$546$	389.144	−	181.454i	0.712717	−	0.332334i
$547$	253.750	+	253.750i	0.463894	+	0.463894i	0.899929	−	0.436036i	$-0.143618\pi$
$547$	253.750	+	253.750i	0.463894	+	0.463894i	−0.436036	+	0.899929i	$0.643618\pi$
$548$	204.044	+	204.044i	0.372344	+	0.372344i
$549$	725.964	+	17.9135i	1.32234	+	0.0326294i
$550$	568.347	+	192.607i	1.03336	+	0.350195i
$551$	−41.5527			−0.0754132
$552$	−161.373	−	165.404i	−0.292342	−	0.299644i
$553$	295.904	−	845.253i	0.535088	−	1.52849i
$554$	−323.436			−0.583820
$555$	185.140	+	839.776i	0.333585	+	1.51311i
$556$			161.046i			0.289650i
$557$	468.602	−	468.602i	0.841296	−	0.841296i	−0.147731	−	0.989028i	$-0.547197\pi$
$557$	468.602	−	468.602i	0.841296	−	0.841296i	0.989028	+	0.147731i	$0.0471971\pi$
$558$	−340.183	+	323.799i	−0.609647	+	0.580285i
$559$	−201.891			−0.361165
$560$	−15.0094	+	139.193i	−0.0268025	+	0.248559i
$561$	−7.81559	+	633.565i	−0.0139315	+	1.12935i
$562$	182.531	+	182.531i	0.324788	+	0.324788i
$563$	−10.9862	+	10.9862i	−0.0195137	+	0.0195137i	−0.716796	−	0.697283i	$-0.754392\pi$
$563$	−10.9862	+	10.9862i	−0.0195137	+	0.0195137i	0.697283	+	0.716796i	$0.254392\pi$
$564$	−3.53286	+	286.388i	−0.00626393	+	0.507781i
$565$	216.934	−	349.055i	0.383954	−	0.617796i
$566$	26.4942			0.0468095
$567$	−525.263	−	213.512i	−0.926390	−	0.376564i
$568$	274.361	−	274.361i	0.483029	−	0.483029i
$569$	122.993			0.216157			0.108079	−	0.994142i	$-0.465530\pi$
$569$	122.993			0.216157			0.108079	+	0.994142i	$0.465530\pi$
$570$	512.444	−	112.975i	0.899025	−	0.198202i
$571$	−863.540			−1.51233			−0.756164	−	0.654382i	$-0.772929\pi$
$571$	−863.540			−1.51233			−0.756164	+	0.654382i	$0.772929\pi$
$572$	347.039	+	347.039i	0.606712	+	0.606712i
$573$	−86.9469	−	89.1188i	−0.151740	−	0.155530i
$574$	7.90211	−	3.80405i	0.0137667	−	0.00662726i
$575$	−644.814	−	218.522i	−1.12142	−	0.380037i
$576$	71.9781	+	1.77610i	0.124962	+	0.00308350i
$577$	604.940	−	604.940i	1.04842	−	1.04842i	0.0496572	−	0.998766i	$-0.484187\pi$
$577$	604.940	−	604.940i	1.04842	−	1.04842i	0.998766	−	0.0496572i	$-0.0158129\pi$
$578$	134.163	+	134.163i	0.232116	+	0.232116i
$579$	−5.87455	+	476.216i	−0.0101460	+	0.822481i
$580$	−16.3580	+	3.81852i	−0.0282035	+	0.00658366i
$581$	535.254	−	257.670i	0.921264	−	0.443493i
$582$	−1.14816	−	1.17684i	−0.00197278	−	0.00202206i
$583$	203.161	−	203.161i	0.348475	−	0.348475i
$584$		−	213.298i		−	0.365236i
$585$	−543.933	−	356.944i	−0.929799	−	0.610161i
$586$			91.6614i			0.156419i
$587$	−354.852	−	354.852i	−0.604518	−	0.604518i	0.336990	−	0.941508i	$-0.390591\pi$
$587$	−354.852	−	354.852i	−0.604518	−	0.604518i	−0.941508	+	0.336990i	$0.890591\pi$
$588$	29.2268	+	292.544i	0.0497055	+	0.497523i
$589$		−	912.772i		−	1.54970i
$590$	−188.541	+	303.370i	−0.319561	+	0.514186i
$591$	−9.30322	+	754.159i	−0.0157415	+	1.27607i
$592$	−162.152	−	162.152i	−0.273906	−	0.273906i
$593$	420.895	−	420.895i	0.709772	−	0.709772i	−0.256715	−	0.966487i	$-0.582640\pi$
$593$	420.895	−	420.895i	0.709772	−	0.709772i	0.966487	+	0.256715i	$0.0826403\pi$
$594$	23.9781	−	647.661i	0.0403672	−	1.09034i
$595$	−339.198	+	273.166i	−0.570081	+	0.459102i
$596$		−	280.675i		−	0.470932i
$597$	170.760	−	166.599i	0.286030	−	0.279060i
$598$	−393.731	−	393.731i	−0.658413	−	0.658413i
$599$	761.718			1.27165			0.635824	−	0.771834i	$-0.280660\pi$
$599$	761.718			1.27165			0.635824	+	0.771834i	$0.280660\pi$
$600$	191.352	−	91.5664i	0.318920	−	0.152611i
$601$		−	348.645i		−	0.580109i	−0.957010	−	0.290054i	$-0.906327\pi$
$601$		−	348.645i		−	0.580109i	0.957010	−	0.290054i	$-0.0936734\pi$
$602$	45.6766	−	130.476i	0.0758747	−	0.216737i
$603$	−41.1357	+	39.1545i	−0.0682184	+	0.0649328i
$604$		−	65.3858i		−	0.108255i
$605$	189.920	+	813.591i	0.313917	+	1.34478i
$606$	1.13449	−	91.9670i	0.00187210	−	0.151761i
$607$	520.469	−	520.469i	0.857444	−	0.857444i	−0.133592	−	0.991036i	$-0.542651\pi$
$607$	520.469	−	520.469i	0.857444	−	0.857444i	0.991036	+	0.133592i	$0.0426512\pi$
$608$	−98.9478	+	98.9478i	−0.162743	+	0.162743i
$609$	−31.9706	+	14.9076i	−0.0524969	+	0.0244789i
$610$	−301.164	+	484.584i	−0.493711	+	0.794400i
$611$			690.136i			1.12952i
$612$	154.423	+	162.237i	0.252325	+	0.265092i
$613$	82.1048	−	82.1048i	0.133939	−	0.133939i	−0.636959	−	0.770898i	$-0.719808\pi$
$613$	82.1048	−	82.1048i	0.133939	−	0.133939i	0.770898	+	0.636959i	$0.219808\pi$
$614$		−	546.546i		−	0.890140i
$615$	−11.1992	−	7.15315i	−0.0182100	−	0.0116311i
$616$	−302.795	+	145.765i	−0.491551	+	0.236631i
$617$	−186.511	+	186.511i	−0.302286	+	0.302286i	−0.841908	−	0.539621i	$-0.818567\pi$
$617$	−186.511	+	186.511i	−0.302286	+	0.302286i	0.539621	+	0.841908i	$0.318567\pi$
$618$	212.219	−	207.047i	0.343397	−	0.335028i
$619$	−608.262			−0.982652			−0.491326	−	0.870976i	$-0.663488\pi$
$619$	−608.262			−0.982652			−0.491326	+	0.870976i	$0.663488\pi$
$620$	−83.8800	−	359.331i	−0.135290	−	0.579566i
$621$	−27.2042	+	734.799i	−0.0438072	+	1.18325i
$622$	−408.594	+	408.594i	−0.656903	+	0.656903i
$623$	118.843	−	339.477i	0.190759	−	0.544907i
$624$	173.478	+	2.14001i	0.278010	+	0.00342950i
$625$	379.974	−	496.230i	0.607959	−	0.793968i
$626$	−539.453			−0.861746
$627$	879.619	+	901.592i	1.40290	+	1.43795i
$628$	−35.9770	−	35.9770i	−0.0572882	−	0.0572882i
$629$		−	713.371i		−	1.13413i
$630$	353.743	−	270.770i	0.561496	−	0.429793i
$631$	180.633			0.286265			0.143132	−	0.989704i	$-0.454283\pi$
$631$	180.633			0.286265			0.143132	+	0.989704i	$0.454283\pi$
$632$	255.872	−	255.872i	0.404860	−	0.404860i
$633$	−856.598	+	835.722i	−1.35324	+	1.32026i
$634$		−	530.802i		−	0.837227i
$635$	−27.6285	+	44.4553i	−0.0435095	+	0.0700084i
$636$	1.25279	−	101.556i	0.00196979	−	0.159680i
$637$	79.1149	+	703.993i	0.124199	+	1.10517i
$638$	−28.5114	−	28.5114i	−0.0446888	−	0.0446888i
$639$	−1234.25	−	30.4557i	−1.93153	−	0.0476615i
$640$	−29.8599	+	48.0457i	−0.0466561	+	0.0750714i
$641$			1036.40i			1.61685i	0.588597	+	0.808427i	$0.299681\pi$
$641$			1036.40i			1.61685i	−0.588597	+	0.808427i	$0.700319\pi$
$642$	178.949	+	183.419i	0.278737	+	0.285700i
$643$	−639.514	−	639.514i	−0.994579	−	0.994579i	0.00540613	−	0.999985i	$-0.498279\pi$
$643$	−639.514	−	639.514i	−0.994579	−	0.994579i	−0.999985	+	0.00540613i	$0.998279\pi$
$644$	343.534	−	165.376i	0.533439	−	0.256796i
$645$	−204.553	+	45.0963i	−0.317136	+	0.0699168i
$646$	−435.309			−0.673854
$647$	659.438	+	659.438i	1.01922	+	1.01922i	0.999812	+	0.0194122i	$0.00617949\pi$
$647$	659.438	+	659.438i	1.01922	+	1.01922i	0.0194122	+	0.999812i	$0.493821\pi$
$648$	−153.813	−	169.793i	−0.237365	−	0.262026i
$649$	−857.382			−1.32108
$650$	458.326	−	226.310i	0.705117	−	0.348169i
$651$	−327.470	−	702.286i	−0.503026	−	1.07878i
$652$	−180.727	−	180.727i	−0.277189	−	0.277189i
$653$	334.285	+	334.285i	0.511921	+	0.511921i	0.915115	−	0.403194i	$-0.132100\pi$
$653$	334.285	+	334.285i	0.511921	+	0.511921i	−0.403194	+	0.915115i	$0.632100\pi$
$654$	−293.217	−	3.61709i	−0.448344	−	0.00553072i
$655$	−18.5984	−	79.6733i	−0.0283946	−	0.121639i
$656$	3.54364			0.00540189
$657$	−491.612	+	467.935i	−0.748268	+	0.712229i
$658$	−446.012	−	156.139i	−0.677830	−	0.237293i
$659$	−231.047			−0.350602			−0.175301	−	0.984515i	$-0.556090\pi$
$659$	−231.047			−0.350602			−0.175301	+	0.984515i	$0.556090\pi$
$660$	429.132	+	274.096i	0.650201	+	0.415298i
$661$			513.220i			0.776429i	0.921569	+	0.388215i	$0.126908\pi$
$661$			513.220i			0.776429i	−0.921569	+	0.388215i	$0.873092\pi$
$662$	−383.355	+	383.355i	−0.579086	+	0.579086i
$663$	376.892	+	386.307i	0.568464	+	0.582665i
$664$	240.031			0.361492
$665$	−92.8217	+	860.803i	−0.139582	+	1.29444i
$666$	−17.9999	+	729.463i	−0.0270269	+	1.09529i
$667$	32.3475	+	32.3475i	0.0484970	+	0.0484970i
$668$	22.2592	−	22.2592i	0.0333222	−	0.0333222i
$669$	689.952	+	8.51117i	1.03132	+	0.0127222i
$670$	−10.1430	−	43.4511i	−0.0151387	−	0.0648524i
$671$	−1369.53			−2.04102
$672$	−40.6314	+	111.629i	−0.0604634	+	0.166115i
$673$	−98.5465	+	98.5465i	−0.146429	+	0.146429i	−0.776521	−	0.630092i	$-0.783017\pi$
$673$	−98.5465	+	98.5465i	−0.146429	+	0.146429i	0.630092	+	0.776521i	$0.283017\pi$
$674$	415.350			0.616246
$675$	−630.834	−	240.152i	−0.934569	−	0.355781i
$676$	80.0464			0.118412
$677$	−856.497	−	856.497i	−1.26514	−	1.26514i	−0.948571	−	0.316565i	$-0.897471\pi$
$677$	−856.497	−	856.497i	−1.26514	−	1.26514i	−0.316565	−	0.948571i	$-0.602529\pi$
$678$	249.607	−	243.524i	0.368152	−	0.359180i
$679$	2.44423	−	1.17665i	0.00359976	−	0.00173291i
$680$	−171.368	+	40.0032i	−0.252012	+	0.0588282i
$681$	−1084.35	−	13.3764i	−1.59228	−	0.0196422i
$682$	626.300	−	626.300i	0.918329	−	0.918329i
$683$	−423.420	−	423.420i	−0.619941	−	0.619941i	0.325575	−	0.945516i	$-0.394442\pi$
$683$	−423.420	−	423.420i	−0.619941	−	0.619941i	−0.945516	+	0.325575i	$0.894442\pi$
$684$	445.129	+	10.9838i	0.650774	+	0.0160582i
$685$	612.716	+	380.796i	0.894476	+	0.555907i
$686$	−472.867	−	108.144i	−0.689310	−	0.157645i
$687$	404.804	−	394.939i	0.589235	−	0.574874i
$688$	39.4971	−	39.4971i	0.0574085	−	0.0574085i
$689$		−	244.729i		−	0.355195i
$690$	−486.869	−	310.974i	−0.705608	−	0.450687i
$691$			785.969i			1.13744i	0.822532	+	0.568718i	$0.192561\pi$
$691$			785.969i			1.13744i	−0.822532	+	0.568718i	$0.807439\pi$
$692$	287.409	+	287.409i	0.415331	+	0.415331i
$693$	1000.24	+	378.108i	1.44334	+	0.545610i
$694$		−	82.7625i		−	0.119254i
$695$	91.5231	+	392.073i	0.131688	+	0.564134i
$696$	−14.2523	−	0.175815i	−0.0204775	−	0.000252608i
$697$	7.79493	+	7.79493i	0.0111835	+	0.0111835i
$698$	−565.082	+	565.082i	−0.809573	+	0.809573i
$699$	−71.0138	−	0.876019i	−0.101593	−	0.00125325i
$700$	42.5631	+	347.402i	0.0608045	+	0.496289i
$701$			462.898i			0.660340i	0.943922	+	0.330170i	$0.107106\pi$
$701$			462.898i			0.660340i	−0.943922	+	0.330170i	$0.892894\pi$
$702$	−375.647	−	404.531i	−0.535109	−	0.576255i
$703$	−1002.79	−	1002.79i	−1.42644	−	1.42644i
$704$	−135.786			−0.192878
$705$	154.155	+	699.234i	0.218660	+	0.991822i
$706$		−	242.967i		−	0.344146i
$707$	143.226	+	50.1403i	0.202583	+	0.0709199i
$708$	−216.938	+	211.651i	−0.306410	+	0.298942i
$709$			946.923i			1.33558i	0.744352	+	0.667788i	$0.232759\pi$
$709$			946.923i			1.33558i	−0.744352	+	0.667788i	$0.767241\pi$
$710$	512.024	−	823.865i	0.721160	−	1.16037i
$711$	−1151.07	−	28.4033i	−1.61895	−	0.0399484i
$712$	102.765	−	102.765i	0.144333	−	0.144333i
$713$	−710.565	+	710.565i	−0.996584	+	0.996584i
$714$	−334.927	+	156.174i	−0.469085	+	0.218730i
$715$	1042.11	+	647.659i	1.45749	+	0.905817i
$716$			669.382i			0.934891i
$717$	200.022	−	195.147i	0.278971	−	0.272172i
$718$	129.751	−	129.751i	0.180712	−	0.180712i
$719$			713.422i			0.992242i	0.868254	+	0.496121i	$0.165243\pi$
$719$			713.422i			0.992242i	−0.868254	+	0.496121i	$0.834757\pi$
$720$	176.244	−	36.5816i	0.244783	−	0.0508078i
$721$	212.184	+	440.768i	0.294292	+	0.611329i
$722$	−250.916	+	250.916i	−0.347530	+	0.347530i
$723$	929.942	+	953.172i	1.28623	+	1.31836i
$724$	−198.720			−0.274475
$725$	−37.6544	+	18.5928i	−0.0519371	+	0.0256452i
$726$	−8.74443	+	708.861i	−0.0120447	+	0.976392i
$727$	521.776	−	521.776i	0.717711	−	0.717711i	−0.250425	−	0.968136i	$-0.580570\pi$
$727$	521.776	−	521.776i	0.717711	−	0.717711i	0.968136	+	0.250425i	$0.0805702\pi$
$728$	−94.5803	+	270.170i	−0.129918	+	0.371112i
$729$	−53.9052	+	727.004i	−0.0739440	+	0.997262i
$730$	−121.218	−	519.283i	−0.166052	−	0.711347i
$731$	173.763			0.237706
$732$	−346.523	+	338.078i	−0.473393	+	0.461855i
$733$	121.904	+	121.904i	0.166309	+	0.166309i	0.785355	−	0.619046i	$-0.212481\pi$
$733$	121.904	+	121.904i	0.166309	+	0.166309i	−0.619046	+	0.785355i	$0.712481\pi$
$734$			953.479i			1.29902i
$735$	237.408	+	695.602i	0.323005	+	0.946397i
$736$	154.056			0.209315
$737$	75.7335	−	75.7335i	0.102759	−	0.102759i
$738$	−7.77409	−	8.16745i	−0.0105340	−	0.0110670i
$739$			708.172i			0.958284i	0.877737	+	0.479142i	$0.159052\pi$
$739$			708.172i			0.958284i	−0.877737	+	0.479142i	$0.840948\pi$
$740$	−486.920	−	302.616i	−0.658000	−	0.408940i
$741$	1072.83	+	13.2343i	1.44782	+	0.0178601i
$742$	158.160	+	55.3684i	0.213154	+	0.0746205i
$743$	212.648	+	212.648i	0.286202	+	0.286202i	0.835576	−	0.549374i	$-0.185134\pi$
$743$	212.648	+	212.648i	0.286202	+	0.286202i	−0.549374	+	0.835576i	$0.685134\pi$
$744$	3.86207	−	313.076i	0.00519095	−	0.420801i
$745$	−159.509	−	683.318i	−0.214107	−	0.917205i
$746$			152.296i			0.204150i
$747$	−526.583	−	553.228i	−0.704930	−	0.740599i
$748$	−298.688	−	298.688i	−0.399316	−	0.399316i
$749$	−380.952	+	183.389i	−0.508614	+	0.244845i
$750$	413.818	−	331.669i	0.551757	−	0.442226i
$751$	−588.834			−0.784067			−0.392034	−	0.919951i	$-0.628228\pi$
$751$	−588.834			−0.784067			−0.392034	+	0.919951i	$0.628228\pi$
$752$	−135.015	−	135.015i	−0.179541	−	0.179541i
$753$	831.825	−	811.552i	1.10468	−	1.07776i
$754$	−34.3451			−0.0455506
$755$	−37.1591	−	159.185i	−0.0492174	−	0.210841i
$756$	346.423	−	151.246i	0.458231	−	0.200060i
$757$	−627.004	−	627.004i	−0.828275	−	0.828275i	0.159003	−	0.987278i	$-0.449172\pi$
$757$	−627.004	−	627.004i	−0.828275	−	0.828275i	−0.987278	+	0.159003i	$0.949172\pi$
$758$	−390.814	−	390.814i	−0.515585	−	0.515585i
$759$	17.1052	−	1386.62i	0.0225364	−	1.82690i
$760$	−184.661	+	297.126i	−0.242974	+	0.390955i
$761$	1055.93			1.38756			0.693780	−	0.720187i	$-0.255944\pi$
$761$	1055.93			1.38756			0.693780	+	0.720187i	$0.255944\pi$
$762$	−31.7898	+	31.0150i	−0.0417189	+	0.0407021i
$763$	159.862	−	456.647i	0.209517	−	0.598488i
$764$	83.0045			0.108645
$765$	468.150	+	307.213i	0.611961	+	0.401586i
$766$			125.702i			0.164101i
$767$	−516.405	+	516.405i	−0.673279	+	0.673279i
$768$	−34.3572	+	33.5199i	−0.0447359	+	0.0436457i
$769$	−102.288			−0.133014			−0.0665072	−	0.997786i	$-0.521186\pi$
$769$	−102.288			−0.133014			−0.0665072	+	0.997786i	$0.521186\pi$
$770$	−654.331	+	526.952i	−0.849781	+	0.684353i
$771$	769.916	+	9.49760i	0.998594	+	0.0123186i
$772$	−224.508	−	224.508i	−0.290813	−	0.290813i
$773$	64.6043	−	64.6043i	0.0835761	−	0.0835761i	−0.664083	−	0.747659i	$-0.731178\pi$
$773$	64.6043	−	64.6043i	0.0835761	−	0.0835761i	0.747659	+	0.664083i	$0.231178\pi$
$774$	−177.683	−	4.38442i	−0.229564	−	0.00566462i
$775$	−408.420	−	827.140i	−0.526994	−	1.06728i
$776$	1.09610			0.00141250
$777$	−1131.31	−	411.780i	−1.45600	−	0.529961i
$778$	−24.2532	+	24.2532i	−0.0311738	+	0.0311738i
$779$	21.9147			0.0281319
$780$	423.558	−	93.3789i	0.543023	−	0.119716i
$781$	2328.40			2.98131
$782$	338.875	+	338.875i	0.433344	+	0.433344i
$783$	30.8617	+	33.2348i	0.0394147	+	0.0424454i
$784$	−153.204	−	122.248i	−0.195413	−	0.155929i
$785$	−108.034	−	67.1418i	−0.137623	−	0.0855310i
$786$	0.856324	−	69.4173i	0.00108947	−	0.0883171i
$787$	−370.534	+	370.534i	−0.470819	+	0.470819i	−0.902180	−	0.431361i	$-0.858034\pi$
$787$	−370.534	+	370.534i	−0.470819	+	0.470819i	0.431361	+	0.902180i	$0.358034\pi$
$788$	−355.541	−	355.541i	−0.451194	−	0.451194i
$789$	−767.882	−	9.47251i	−0.973235	−	0.0120057i
$790$	477.519	−	768.346i	0.604454	−	0.972589i
$791$	249.566	+	518.421i	0.315507	+	0.655399i
$792$	297.890	+	312.963i	0.376123	+	0.395155i
$793$	−824.873	+	824.873i	−1.04019	+	1.04019i
$794$			353.821i			0.445618i
$795$	−54.6651	−	247.956i	−0.0687611	−	0.311894i
$796$			159.045i			0.199805i
$797$	−331.906	−	331.906i	−0.416444	−	0.416444i	0.467532	−	0.883976i	$-0.345143\pi$
$797$	−331.906	−	331.906i	−0.416444	−	0.416444i	−0.883976	+	0.467532i	$0.845143\pi$
$798$	−251.274	+	690.342i	−0.314880	+	0.865090i
$799$		−	593.983i		−	0.743408i
$800$	−45.3907	+	133.939i	−0.0567384	+	0.167424i
$801$	−462.302	−	11.4076i	−0.577157	−	0.0142416i
$802$	−48.5936	−	48.5936i	−0.0605905	−	0.0605905i
$803$	905.091	−	905.091i	1.12714	−	1.12714i
$804$	0.467010	−	37.8578i	0.000580858	−	0.0470868i
$805$	742.367	−	597.849i	0.922195	−	0.742670i
$806$		−	754.447i		−	0.936038i
$807$	413.081	+	423.400i	0.511873	+	0.524659i
$808$	43.3570	+	43.3570i	0.0536596	+	0.0536596i
$809$	79.9556			0.0988327			0.0494163	−	0.998778i	$-0.484264\pi$
$809$	79.9556			0.0988327			0.0494163	+	0.998778i	$0.484264\pi$
$810$	−470.959	−	325.956i	−0.581431	−	0.402415i
$811$			601.430i			0.741591i	0.928715	+	0.370795i	$0.120915\pi$
$811$			601.430i			0.741591i	−0.928715	+	0.370795i	$0.879085\pi$
$812$	7.77036	−	22.1961i	0.00956941	−	0.0273351i
$813$	−653.241	−	669.559i	−0.803494	−	0.823565i
$814$		−	1376.13i		−	1.69058i
$815$	−542.697	−	337.281i	−0.665886	−	0.413841i
$816$	−149.309	−	1.84186i	−0.182976	−	0.00225718i
$817$	244.259	−	244.259i	0.298971	−	0.298971i
$818$	−143.848	+	143.848i	−0.175853	+	0.175853i
$819$	830.183	−	374.711i	1.01366	−	0.457523i
$820$	8.62717	−	2.01387i	0.0105209	−	0.00245594i
$821$		−	1419.78i		−	1.72933i	−0.502353	−	0.864663i	$-0.667532\pi$
$821$		−	1419.78i		−	1.72933i	0.502353	−	0.864663i	$-0.332468\pi$
$822$	427.472	+	438.150i	0.520038	+	0.533029i
$823$	−197.094	+	197.094i	−0.239482	+	0.239482i	−0.816636	−	0.577153i	$-0.804163\pi$
$823$	−197.094	+	197.094i	−0.239482	+	0.239482i	0.577153	+	0.816636i	$0.304163\pi$
$824$			197.659i			0.239878i
$825$	1200.51	+	423.423i	1.45517	+	0.513240i
$826$	−216.902	−	450.569i	−0.262594	−	0.545483i
$827$	718.394	−	718.394i	0.868675	−	0.868675i	−0.123651	−	0.992326i	$-0.539460\pi$
$827$	718.394	−	718.394i	0.868675	−	0.868675i	0.992326	+	0.123651i	$0.0394604\pi$
$828$	−337.969	−	355.070i	−0.408175	−	0.428828i
$829$	−671.129			−0.809565			−0.404782	−	0.914413i	$-0.632653\pi$
$829$	−671.129			−0.809565			−0.404782	+	0.914413i	$0.632653\pi$
$830$	584.367	−	136.411i	0.704057	−	0.164351i
$831$	−686.060	−	8.46316i	−0.825584	−	0.0101843i
$832$	−81.7847	+	81.7847i	−0.0982990	+	0.0982990i
$833$	−68.0923	−	605.910i	−0.0817435	−	0.727383i
$834$	−4.21398	+	341.603i	−0.00505273	+	0.409596i
$835$	41.5411	−	66.8412i	0.0497498	−	0.0800494i
$836$	−839.735			−1.00447
$837$	−730.056	+	677.928i	−0.872229	+	0.809950i
$838$	80.8927	+	80.8927i	0.0965306	+	0.0965306i
$839$			1507.60i			1.79690i	0.439077	+	0.898449i	$0.355305\pi$
$839$			1507.60i			1.79690i	−0.439077	+	0.898449i	$0.644695\pi$
$840$	−35.4795	+	294.858i	−0.0422375	+	0.351021i
$841$	−838.178			−0.996645
$842$	194.231	−	194.231i	0.230678	−	0.230678i
$843$	382.401	+	391.953i	0.453619	+	0.464951i
$844$		−	797.828i		−	0.945294i
$845$	194.877	−	45.4908i	0.230624	−	0.0538353i
$846$	−14.9875	+	607.383i	−0.0177157	+	0.717947i
$847$	−1103.96	−	386.470i	−1.30337	−	0.456281i
$848$	47.8777	+	47.8777i	0.0564596	+	0.0564596i
$849$	56.1984	+	0.693257i	0.0661936	+	0.000816557i
$850$	−394.471	+	194.779i	−0.464083	+	0.229152i
$851$			1561.28i			1.83464i
$852$	589.142	−	574.784i	0.691481	−	0.674629i
$853$	−702.377	−	702.377i	−0.823420	−	0.823420i	0.163177	−	0.986597i	$-0.447826\pi$
$853$	−702.377	−	702.377i	−0.823420	−	0.823420i	−0.986597	+	0.163177i	$0.947826\pi$
$854$	−346.466	−	719.710i	−0.405698	−	0.842752i
$855$	1089.93	−	226.229i	1.27477	−	0.264595i
$856$	−170.835			−0.199574
$857$	933.376	+	933.376i	1.08912	+	1.08912i	0.995619	+	0.0935014i	$0.0298060\pi$
$857$	933.376	+	933.376i	1.08912	+	1.08912i	0.0935014	+	0.995619i	$0.470194\pi$
$858$	727.044	+	745.206i	0.847371	+	0.868538i
$859$	−1132.05			−1.31787			−0.658934	−	0.752201i	$-0.728992\pi$
$859$	−1132.05			−1.31787			−0.658934	+	0.752201i	$0.728992\pi$
$860$	73.7111	−	118.604i	0.0857106	−	0.137912i
$861$	16.8612	−	7.86222i	0.0195832	−	0.00913150i
$862$	577.019	+	577.019i	0.669396	+	0.669396i
$863$	−158.115	−	158.115i	−0.183216	−	0.183216i	0.609540	−	0.792755i	$-0.291354\pi$
$863$	−158.115	−	158.115i	−0.183216	−	0.183216i	−0.792755	+	0.609540i	$0.791354\pi$
$864$	152.630	+	5.65079i	0.176656	+	0.00654027i
$865$	863.047	+	536.375i	0.997742	+	0.620086i
$866$	85.8030			0.0990797
$867$	281.071	+	288.092i	0.324188	+	0.332286i
$868$	487.574	+	170.689i	0.561721	+	0.196646i
$869$	2171.49			2.49884
$870$	−34.7979	+	7.67166i	−0.0399976	+	0.00881800i
$871$		−	91.2293i		−	0.104741i
$872$	138.234	−	138.234i	0.158526	−	0.158526i
$873$	−2.40464	−	2.52631i	−0.00275445	−	0.00289382i
$874$	952.716			1.09006
$875$	301.053	+	821.579i	0.344060	+	0.938948i
$876$	5.58123	−	452.438i	0.00637126	−	0.516482i
$877$	809.948	+	809.948i	0.923544	+	0.923544i	0.997278	−	0.0737339i	$-0.0234915\pi$
$877$	809.948	+	809.948i	0.923544	+	0.923544i	−0.0737339	+	0.997278i	$0.523492\pi$
$878$	73.7420	−	73.7420i	0.0839886	−	0.0839886i
$879$	−2.39845	+	194.428i	−0.00272861	+	0.221193i
$880$	−330.579	+	77.1682i	−0.375657	+	0.0876911i
$881$	779.133			0.884373			0.442187	−	0.896923i	$-0.354203\pi$
$881$	779.133			0.884373			0.442187	+	0.896923i	$0.354203\pi$
$882$	54.3400	+	621.296i	0.0616099	+	0.704418i
$883$	1131.33	−	1131.33i	1.28124	−	1.28124i	0.341272	−	0.939965i	$-0.389142\pi$
$883$	1131.33	−	1131.33i	1.28124	−	1.28124i	0.939965	−	0.341272i	$-0.110858\pi$
$884$	−359.803			−0.407017
$885$	−407.864	+	638.562i	−0.460863	+	0.721539i
$886$	−20.9992			−0.0237011
$887$	−146.694	−	146.694i	−0.165382	−	0.165382i	0.619564	−	0.784946i	$-0.287309\pi$
$887$	−146.694	−	146.694i	−0.165382	−	0.165382i	−0.784946	+	0.619564i	$0.787309\pi$
$888$	−339.708	−	348.194i	−0.382554	−	0.392110i
$889$	−31.7845	−	66.0257i	−0.0357531	−	0.0742696i
$890$	191.785	−	308.589i	0.215488	−	0.346729i
$891$	67.8084	−	1373.16i	0.0761037	−	1.54115i
$892$	−325.271	+	325.271i	−0.364654	+	0.364654i
$893$	−834.965	−	834.965i	−0.935011	−	0.935011i
$894$	7.34426	−	595.357i	0.00821506	−	0.665947i
$895$	380.414	+	1629.64i	0.425043	+	1.82083i
$896$	−34.3515	−	71.3581i	−0.0383388	−	0.0796407i
$897$	−824.863	−	845.468i	−0.919580	−	0.942551i
$898$	284.237	−	284.237i	0.316522	−	0.316522i
$899$			61.9825i			0.0689461i
$900$	408.284	−	189.220i	0.453649	−	0.210244i
$901$			210.633i			0.233776i
$902$	15.0368	+	15.0368i	0.0166705	+	0.0166705i
$903$	100.301	−	275.564i	0.111076	−	0.305165i
$904$			232.482i			0.257170i
$905$	−483.793	+	112.934i	−0.534578	+	0.124789i
$906$	1.71091	−	138.694i	0.00188842	−	0.153084i
$907$	517.383	+	517.383i	0.570434	+	0.570434i	0.932250	−	0.361816i	$-0.117843\pi$
$907$	517.383	+	517.383i	0.570434	+	0.570434i	−0.361816	+	0.932250i	$0.617843\pi$
$908$	511.204	−	511.204i	0.563000	−	0.563000i
$909$	4.81289	−	195.047i	0.00529471	−	0.214573i
$910$	−76.7213	+	711.492i	−0.0843091	+	0.781859i
$911$		−	1374.39i		−	1.50866i	−0.656495	−	0.754330i	$-0.727962\pi$
$911$		−	1374.39i		−	1.50866i	0.656495	−	0.754330i	$-0.272038\pi$
$912$	−212.473	+	207.295i	−0.232975	+	0.227297i
$913$	1018.53	+	1018.53i	1.11558	+	1.11558i
$914$	234.152			0.256184
$915$	−651.496	+	1020.00i	−0.712018	+	1.11475i
$916$			377.031i			0.411606i
$917$	108.108	+	37.8462i	0.117893	+	0.0412718i
$918$	323.310	+	348.170i	0.352190	+	0.379270i
$919$			252.031i			0.274245i	0.990554	+	0.137122i	$0.0437854\pi$
$919$			252.031i			0.274245i	−0.990554	+	0.137122i	$0.956215\pi$
$920$	375.056	−	87.5507i	0.407669	−	0.0951638i
$921$	14.3011	−	1159.31i	0.0155278	−	1.25875i
$922$	−221.554	+	221.554i	−0.240297	+	0.240297i
$923$	1402.41	−	1402.41i	1.51940	−	1.51940i
$924$	−646.091	+	301.267i	−0.699233	+	0.326046i
$925$	−1357.41	−	460.013i	−1.46747	−	0.497311i
$926$		−	630.108i		−	0.680462i
$927$	455.569	−	433.627i	0.491444	−	0.467775i
$928$	6.71913	−	6.71913i	0.00724044	−	0.00724044i
$929$			837.498i			0.901504i	0.892649	+	0.450752i	$0.148844\pi$
$929$			837.498i			0.901504i	−0.892649	+	0.450752i	$0.851156\pi$
$930$	−168.520	−	764.393i	−0.181205	−	0.821928i
$931$	−947.447	−	756.012i	−1.01767	−	0.812043i
$932$	33.4788	−	33.4788i	0.0359214	−	0.0359214i
$933$	−877.384	+	856.001i	−0.940390	+	0.917472i
$934$	−458.698			−0.491111
$935$	−896.918	−	557.425i	−0.959270	−	0.596176i
$936$	367.919	+	9.07861i	0.393076	+	0.00969937i
$937$	324.135	−	324.135i	0.345929	−	0.345929i	−0.512662	−	0.858591i	$-0.671340\pi$
$937$	324.135	−	324.135i	0.345929	−	0.345929i	0.858591	+	0.512662i	$0.171340\pi$
$938$	58.9585	+	20.6400i	0.0628556	+	0.0220043i
$939$	−1144.26	−	14.1155i	−1.21860	−	0.0150325i
$940$	−405.431	−	251.971i	−0.431309	−	0.268054i
$941$	−194.663			−0.206868			−0.103434	−	0.994636i	$-0.532983\pi$
$941$	−194.663			−0.206868			−0.103434	+	0.994636i	$0.532983\pi$
$942$	−75.3715	−	77.2543i	−0.0800122	−	0.0820109i
$943$	−17.0599	−	17.0599i	−0.0180911	−	0.0180911i
$944$		−	202.054i		−	0.214041i
$945$	757.429	−	565.089i	0.801513	−	0.597978i
$946$	335.198			0.354332
$947$	−53.7161	+	53.7161i	−0.0567223	+	0.0567223i	−0.734899	−	0.678177i	$-0.762770\pi$
$947$	−53.7161	+	53.7161i	−0.0567223	+	0.0567223i	0.678177	+	0.734899i	$0.262770\pi$
$948$	549.440	−	536.049i	0.579578	−	0.565453i
$949$		−	1090.28i		−	1.14887i
$950$	−280.707	+	828.311i	−0.295481	+	0.871906i
$951$	13.8892	−	1125.91i	0.0146048	−	1.18393i
$952$	81.4030	−	232.529i	0.0855074	−	0.244253i
$953$	0.875943	+	0.875943i	0.000919142	+	0.000919142i	0.707566	−	0.706647i	$-0.249793\pi$
$953$	0.875943	+	0.875943i	0.000919142	+	0.000919142i	−0.706647	+	0.707566i	$0.749793\pi$
$954$	5.31472	−	215.384i	0.00557099	−	0.225770i
$955$	202.078	−	47.1719i	0.211600	−	0.0493947i
$956$			186.299i			0.194873i
$957$	−59.7313	−	61.2233i	−0.0624151	−	0.0639742i
$958$	−166.037	−	166.037i	−0.173316	−	0.173316i
$959$	−910.013	+	438.077i	−0.948919	+	0.456806i
$960$	−64.5947	+	101.131i	−0.0672862	+	0.105345i
$961$	−400.547			−0.416802
$962$	−828.849	−	828.849i	−0.861589	−	0.861589i
$963$	374.780	+	393.744i	0.389180	+	0.408872i
$964$	−887.776			−0.920929
$965$	−674.164	−	418.986i	−0.698615	−	0.434182i
$966$	733.018	−	341.800i	0.758818	−	0.353831i
$967$	552.816	+	552.816i	0.571682	+	0.571682i	0.932598	−	0.360916i	$-0.117536\pi$
$967$	552.816	+	552.816i	0.571682	+	0.571682i	−0.360916	+	0.932598i	$0.617536\pi$
$968$	−334.185	−	334.185i	−0.345233	−	0.345233i
$969$	−923.360	−	11.3905i	−0.952900	−	0.0117549i
$970$	2.66851	−	0.622920i	0.00275104	−	0.000642185i
$971$	333.064			0.343012			0.171506	−	0.985183i	$-0.445137\pi$
$971$	333.064			0.343012			0.171506	+	0.985183i	$0.445137\pi$
$972$	−321.819	−	364.182i	−0.331089	−	0.374673i
$973$	−532.002	−	186.242i	−0.546764	−	0.191410i
$974$	1278.15			1.31226
$975$	978.105	−	468.046i	1.00318	−	0.480047i
$976$		−	322.749i		−	0.330685i
$977$	−206.855	+	206.855i	−0.211724	+	0.211724i	−0.805000	−	0.593275i	$-0.797835\pi$
$977$	−206.855	+	206.855i	−0.211724	+	0.211724i	0.593275	+	0.805000i	$0.297835\pi$
$978$	−378.622	−	388.080i	−0.387139	−	0.396810i
$979$	872.131			0.890839
$980$	−442.456	−	210.553i	−0.451486	−	0.214850i
$981$	−621.865	−	15.3449i	−0.633909	−	0.0156421i
$982$	148.567	+	148.567i	0.151291	+	0.151291i
$983$	583.925	−	583.925i	0.594023	−	0.594023i	−0.344692	−	0.938716i	$-0.612017\pi$
$983$	583.925	−	583.925i	0.594023	−	0.594023i	0.938716	+	0.344692i	$0.112017\pi$
$984$	7.51663	+	0.0927243i	0.00763885	+	9.42320e-5i
$985$	−1067.64	−	663.526i	−1.08390	−	0.673630i
$986$	29.5600			0.0299798
$987$	−941.977	−	342.866i	−0.954384	−	0.347382i
$988$	−505.776	+	505.776i	−0.511919	+	0.511919i
$989$	−380.296			−0.384526
$990$	903.086	+	592.631i	0.912208	+	0.598617i
$991$	−905.597			−0.913821			−0.456911	−	0.889513i	$-0.651044\pi$
$991$	−905.597			−0.913821			−0.456911	+	0.889513i	$0.651044\pi$
$992$	147.597	+	147.597i	0.148787	+	0.148787i
$993$	−823.188	+	803.126i	−0.828991	+	0.808788i
$994$	589.044	+	1223.62i	0.592600	+	1.23100i
$995$	90.3860	+	387.202i	0.0908402	+	0.389147i
$996$	509.144	+	6.28074i	0.511188	+	0.00630596i
$997$	−528.385	+	528.385i	−0.529975	+	0.529975i	−0.920565	−	0.390590i	$-0.872271\pi$
$997$	−528.385	+	528.385i	−0.529975	+	0.529975i	0.390590	+	0.920565i	$0.372271\pi$
$998$	−471.498	−	471.498i	−0.472443	−	0.472443i
$999$	−57.2681	+	1546.84i	−0.0573254	+	1.54839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.k.a.167.5	yes	32
3.2	odd	2		210.3.k.b.167.13	yes	32
5.3	odd	4		210.3.k.b.83.4	yes	32
7.6	odd	2	inner	210.3.k.a.167.12	yes	32
15.8	even	4	inner	210.3.k.a.83.12	yes	32
21.20	even	2		210.3.k.b.167.4	yes	32
35.13	even	4		210.3.k.b.83.13	yes	32
105.83	odd	4	inner	210.3.k.a.83.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.k.a.83.5	✓	32	105.83	odd	4	inner
210.3.k.a.83.12	yes	32	15.8	even	4	inner
210.3.k.a.167.5	yes	32	1.1	even	1	trivial
210.3.k.a.167.12	yes	32	7.6	odd	2	inner
210.3.k.b.83.4	yes	32	5.3	odd	4
210.3.k.b.83.13	yes	32	35.13	even	4
210.3.k.b.167.4	yes	32	21.20	even	2
210.3.k.b.167.13	yes	32	3.2	odd	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.14733 + 2.09499i) q^{3} -2.00000i q^{4} +(-1.13661 - 4.86910i) q^{5} +(0.0523328 - 4.24232i) q^{6} +(6.60685 + 2.31291i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.222012 - 8.99726i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.14733 + 2.09499i) q^{3} -2.00000i q^{4} +(-1.13661 - 4.86910i) q^{5} +(0.0523328 - 4.24232i) q^{6} +(6.60685 + 2.31291i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.222012 - 8.99726i) q^{9} +(6.00571 + 3.73249i) q^{10} +16.9733i q^{11} +(4.18999 + 4.29465i) q^{12} +(10.2231 + 10.2231i) q^{13} +(-8.91976 + 4.29394i) q^{14} +(12.6414 + 8.07434i) q^{15} -4.00000 q^{16} +(-8.79877 - 8.79877i) q^{17} +(8.77525 + 9.21927i) q^{18} -24.7369 q^{19} +(-9.73820 + 2.27322i) q^{20} +(-19.0326 + 8.87473i) q^{21} +(-16.9733 - 16.9733i) q^{22} +(19.2569 + 19.2569i) q^{23} +(-8.48464 - 0.104666i) q^{24} +(-22.4162 + 11.0685i) q^{25} -20.4462 q^{26} +(18.3725 + 19.7852i) q^{27} +(4.62582 - 13.2137i) q^{28} +1.67978 q^{29} +(-20.7157 + 4.56706i) q^{30} +36.8991i q^{31} +(4.00000 - 4.00000i) q^{32} +(-35.5589 - 36.4472i) q^{33} +17.5975 q^{34} +(3.75235 - 34.7983i) q^{35} +(-17.9945 - 0.444025i) q^{36} +(40.5381 + 40.5381i) q^{37} +(24.7369 - 24.7369i) q^{38} +(-43.3696 - 0.535003i) q^{39} +(7.46497 - 12.0114i) q^{40} -0.885911 q^{41} +(10.1578 - 27.9073i) q^{42} +(-9.87427 + 9.87427i) q^{43} +33.9466 q^{44} +(-44.0609 + 9.14540i) q^{45} -38.5139 q^{46} +(33.7538 + 33.7538i) q^{47} +(8.58930 - 8.37997i) q^{48} +(38.3009 + 30.5621i) q^{49} +(11.3477 - 33.4848i) q^{50} +(37.3272 + 0.460464i) q^{51} +(20.4462 - 20.4462i) q^{52} +(-11.9694 - 11.9694i) q^{53} +(-38.1576 - 1.41270i) q^{54} +(82.6446 - 19.2920i) q^{55} +(8.58788 + 17.8395i) q^{56} +(53.1183 - 51.8237i) q^{57} +(-1.67978 + 1.67978i) q^{58} +50.5136i q^{59} +(16.1487 - 25.2828i) q^{60} +80.6872i q^{61} +(-36.8991 - 36.8991i) q^{62} +(22.2766 - 58.9301i) q^{63} +8.00000i q^{64} +(38.1575 - 61.3969i) q^{65} +(72.0061 + 0.888260i) q^{66} +(-4.46192 - 4.46192i) q^{67} +(-17.5975 + 17.5975i) q^{68} +(-81.6941 - 1.00777i) q^{69} +(31.0459 + 38.5506i) q^{70} -137.180i q^{71} +(18.4385 - 17.5505i) q^{72} +(-53.3244 - 53.3244i) q^{73} -81.0762 q^{74} +(24.9464 - 70.7296i) q^{75} +49.4739i q^{76} +(-39.2577 + 112.140i) q^{77} +(43.9046 - 42.8346i) q^{78} -127.936i q^{79} +(4.54645 + 19.4764i) q^{80} +(-80.9014 - 3.99500i) q^{81} +(0.885911 - 0.885911i) q^{82} +(60.0077 - 60.0077i) q^{83} +(17.7495 + 38.0652i) q^{84} +(-32.8413 + 52.8429i) q^{85} -19.7485i q^{86} +(-3.60704 + 3.51913i) q^{87} +(-33.9466 + 33.9466i) q^{88} -51.3826i q^{89} +(34.9155 - 53.2063i) q^{90} +(43.8974 + 91.1875i) q^{91} +(38.5139 - 38.5139i) q^{92} +(-77.3034 - 79.2345i) q^{93} -67.5075 q^{94} +(28.1163 + 120.447i) q^{95} +(-0.209331 + 16.9693i) q^{96} +(0.274025 - 0.274025i) q^{97} +(-68.8630 + 7.73884i) q^{98} +(152.713 + 3.76828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9	\( 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9} + 8 q^{14} - 20 q^{15} - 128 q^{16} + 36 q^{18} + 12 q^{21} - 40 q^{22} + 24 q^{23} + 16 q^{25} - 8 q^{28} - 112 q^{29} + 68 q^{30} + 128 q^{32} - 48 q^{35} - 40 q^{36} + 32 q^{37} + 64 q^{39} - 44 q^{42} - 32 q^{43} + 80 q^{44} - 48 q^{46} - 8 q^{50} + 84 q^{51} - 136 q^{53} + 244 q^{57} + 112 q^{58} - 96 q^{60} + 72 q^{63} - 200 q^{65} + 32 q^{67} + 8 q^{72} - 64 q^{74} + 88 q^{77} - 124 q^{78} + 76 q^{81} + 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} + 48 q^{92} - 452 q^{93} + 544 q^{95} + 128 q^{98} + 160 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 4 * q^7 + 64 * q^8 - 16 * q^9 + 8 * q^14 - 20 * q^15 - 128 * q^16 + 36 * q^18 + 12 * q^21 - 40 * q^22 + 24 * q^23 + 16 * q^25 - 8 * q^28 - 112 * q^29 + 68 * q^30 + 128 * q^32 - 48 * q^35 - 40 * q^36 + 32 * q^37 + 64 * q^39 - 44 * q^42 - 32 * q^43 + 80 * q^44 - 48 * q^46 - 8 * q^50 + 84 * q^51 - 136 * q^53 + 244 * q^57 + 112 * q^58 - 96 * q^60 + 72 * q^63 - 200 * q^65 + 32 * q^67 + 8 * q^72 - 64 * q^74 + 88 * q^77 - 124 * q^78 + 76 * q^81 + 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 + 48 * q^92 - 452 * q^93 + 544 * q^95 + 128 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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