LMFDB - Embedded newform 170.3.p.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(11,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("170.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.p (of order $16$, degree $8$, 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:	$4.63216449413$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	170.11
Dual form			170.3.p.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30656 - 0.541196i) q^{2} +(-0.112730 - 0.566734i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.85922 + 1.24229i) q^{5} +(-0.159425 + 0.801483i) q^{6} +(-10.5747 + 7.06582i) q^{7} +(-1.08239 - 2.61313i) q^{8} +(8.00644 - 3.31637i) q^{9} +O(q^{10})$	\(q+(-1.30656 - 0.541196i) q^{2} +(-0.112730 - 0.566734i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.85922 + 1.24229i) q^{5} +(-0.159425 + 0.801483i) q^{6} +(-10.5747 + 7.06582i) q^{7} +(-1.08239 - 2.61313i) q^{8} +(8.00644 - 3.31637i) q^{9} +(-1.75687 - 2.62934i) q^{10} +(-13.9790 - 2.78060i) q^{11} +(0.642058 - 0.960908i) q^{12} +(-10.9929 + 10.9929i) q^{13} +(17.6406 - 3.50892i) q^{14} +(0.494459 - 1.19373i) q^{15} +4.00000i q^{16} +(13.1489 + 10.7752i) q^{17} -12.2557 q^{18} +(-12.2243 - 5.06349i) q^{19} +(0.872470 + 4.38621i) q^{20} +(5.19653 + 5.19653i) q^{21} +(16.7596 + 11.1984i) q^{22} +(-8.03728 + 40.4061i) q^{23} +(-1.35893 + 0.908007i) q^{24} +(1.91342 + 4.61940i) q^{25} +(20.3122 - 8.41359i) q^{26} +(-5.67133 - 8.48775i) q^{27} +(-24.9475 - 4.96237i) q^{28} +(-15.0353 + 22.5019i) q^{29} +(-1.29208 + 1.29208i) q^{30} +(-2.91513 + 0.579856i) q^{31} +(2.16478 - 5.22625i) q^{32} +8.23586i q^{33} +(-11.3484 - 21.1947i) q^{34} -28.4386 q^{35} +(16.0129 + 6.63275i) q^{36} +(0.587797 + 2.95506i) q^{37} +(13.2315 + 13.2315i) q^{38} +(7.46928 + 4.99081i) q^{39} +(1.23386 - 6.20303i) q^{40} +(7.55297 - 5.04673i) q^{41} +(-3.97725 - 9.60194i) q^{42} +(28.3124 - 11.7274i) q^{43} +(-15.8370 - 23.7017i) q^{44} +(19.0057 + 3.78046i) q^{45} +(32.3689 - 48.4434i) q^{46} +(33.3447 - 33.3447i) q^{47} +(2.26694 - 0.450922i) q^{48} +(43.1479 - 104.168i) q^{49} -7.07107i q^{50} +(4.62440 - 8.66665i) q^{51} -31.0926 q^{52} +(-64.1880 - 26.5875i) q^{53} +(2.81642 + 14.1591i) q^{54} +(-22.5358 - 22.5358i) q^{55} +(29.9099 + 19.9851i) q^{56} +(-1.49160 + 7.49876i) q^{57} +(31.8226 - 21.2631i) q^{58} +(8.41485 + 20.3152i) q^{59} +(2.38746 - 0.988918i) q^{60} +(-2.31848 - 3.46985i) q^{61} +(4.12262 + 0.820040i) q^{62} +(-61.2331 + 91.6418i) q^{63} +(-5.65685 + 5.65685i) q^{64} +(-34.0946 + 6.78184i) q^{65} +(4.45721 - 10.7607i) q^{66} -56.9053i q^{67} +(3.35693 + 33.8339i) q^{68} +23.8056 q^{69} +(37.1568 + 15.3909i) q^{70} +(3.31520 + 16.6666i) q^{71} +(-17.3322 - 17.3322i) q^{72} +(-102.312 - 68.3627i) q^{73} +(0.831271 - 4.17908i) q^{74} +(2.40227 - 1.60515i) q^{75} +(-10.1270 - 24.4487i) q^{76} +(167.472 - 69.3692i) q^{77} +(-7.05807 - 10.5632i) q^{78} +(110.322 + 21.9444i) q^{79} +(-4.96917 + 7.43689i) q^{80} +(50.9798 - 50.9798i) q^{81} +(-12.5997 + 2.50624i) q^{82} +(-26.6822 + 64.4165i) q^{83} +14.6980i q^{84} +(11.0608 + 36.3684i) q^{85} -43.3387 q^{86} +(14.4476 + 5.98437i) q^{87} +(7.86474 + 39.5387i) q^{88} +(67.9298 + 67.9298i) q^{89} +(-22.7861 - 15.2252i) q^{90} +(38.5732 - 193.921i) q^{91} +(-68.5094 + 45.7765i) q^{92} +(0.657248 + 1.58674i) q^{93} +(-61.6130 + 25.5209i) q^{94} +(-16.4374 - 24.6003i) q^{95} +(-3.20593 - 0.637700i) q^{96} +(-22.3249 + 33.4115i) q^{97} +(-112.751 + 112.751i) q^{98} +(-121.144 + 24.0970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{3} + 16 q^{6} - 16 q^{7} + 32 q^{9}+O(q^{10}) $ 48 * q - 16 * q^3 + 16 * q^6 - 16 * q^7 + 32 * q^9	$ 48 q - 16 q^{3} + 16 q^{6} - 16 q^{7} + 32 q^{9} + 48 q^{11} + 32 q^{12} - 48 q^{13} + 32 q^{14} - 16 q^{17} - 32 q^{18} - 128 q^{19} + 160 q^{21} - 144 q^{22} - 48 q^{23} - 64 q^{24} - 64 q^{27} + 144 q^{31} - 48 q^{34} + 64 q^{36} + 128 q^{37} + 96 q^{38} - 352 q^{39} + 240 q^{41} - 160 q^{42} + 96 q^{43} + 160 q^{45} + 160 q^{46} - 48 q^{47} + 64 q^{48} + 32 q^{49} + 192 q^{51} + 64 q^{53} + 112 q^{54} - 80 q^{55} + 176 q^{57} - 256 q^{58} - 160 q^{60} - 352 q^{61} + 192 q^{62} - 832 q^{63} - 400 q^{65} - 208 q^{66} + 64 q^{69} - 80 q^{70} + 16 q^{71} + 288 q^{72} - 192 q^{73} + 160 q^{74} + 160 q^{76} + 32 q^{77} - 160 q^{78} + 384 q^{79} - 256 q^{81} - 320 q^{82} + 144 q^{83} - 160 q^{85} - 32 q^{86} + 960 q^{87} + 64 q^{88} + 1056 q^{89} - 160 q^{90} - 544 q^{91} - 128 q^{92} + 176 q^{94} - 64 q^{96} + 96 q^{97} - 432 q^{98} - 992 q^{99}+O(q^{100}) $ 48 * q - 16 * q^3 + 16 * q^6 - 16 * q^7 + 32 * q^9 + 48 * q^11 + 32 * q^12 - 48 * q^13 + 32 * q^14 - 16 * q^17 - 32 * q^18 - 128 * q^19 + 160 * q^21 - 144 * q^22 - 48 * q^23 - 64 * q^24 - 64 * q^27 + 144 * q^31 - 48 * q^34 + 64 * q^36 + 128 * q^37 + 96 * q^38 - 352 * q^39 + 240 * q^41 - 160 * q^42 + 96 * q^43 + 160 * q^45 + 160 * q^46 - 48 * q^47 + 64 * q^48 + 32 * q^49 + 192 * q^51 + 64 * q^53 + 112 * q^54 - 80 * q^55 + 176 * q^57 - 256 * q^58 - 160 * q^60 - 352 * q^61 + 192 * q^62 - 832 * q^63 - 400 * q^65 - 208 * q^66 + 64 * q^69 - 80 * q^70 + 16 * q^71 + 288 * q^72 - 192 * q^73 + 160 * q^74 + 160 * q^76 + 32 * q^77 - 160 * q^78 + 384 * q^79 - 256 * q^81 - 320 * q^82 + 144 * q^83 - 160 * q^85 - 32 * q^86 + 960 * q^87 + 64 * q^88 + 1056 * q^89 - 160 * q^90 - 544 * q^91 - 128 * q^92 + 176 * q^94 - 64 * q^96 + 96 * q^97 - 432 * q^98 - 992 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.30656	−	0.541196i	−0.653281	−	0.270598i
$2$	−1.30656	−	0.541196i	−0.653281	−	0.270598i
$3$	−0.112730	−	0.566734i	−0.0375768	−	0.188911i	0.957438	−	0.288639i	$-0.0932028\pi$
$3$	−0.112730	−	0.566734i	−0.0375768	−	0.188911i	−0.995015	+	0.0997278i	$0.968203\pi$
$4$	1.41421	+	1.41421i	0.353553	+	0.353553i
$5$	1.85922	+	1.24229i	0.371845	+	0.248459i
$5$	1.85922	+	1.24229i	0.371845	+	0.248459i
$6$	−0.159425	+	0.801483i	−0.0265708	+	0.133581i
$7$	−10.5747	+	7.06582i	−1.51068	+	1.00940i	−0.523099	+	0.852272i	$0.675224\pi$
$7$	−10.5747	+	7.06582i	−1.51068	+	1.00940i	−0.987578	+	0.157130i	$0.949776\pi$
$8$	−1.08239	−	2.61313i	−0.135299	−	0.326641i
$9$	8.00644	−	3.31637i	0.889604	−	0.368486i
$10$	−1.75687	−	2.62934i	−0.175687	−	0.262934i
$11$	−13.9790	−	2.78060i	−1.27082	−	0.252782i	−0.486799	−	0.873514i	$-0.661836\pi$
$11$	−13.9790	−	2.78060i	−1.27082	−	0.252782i	−0.784023	+	0.620732i	$0.786836\pi$
$12$	0.642058	−	0.960908i	0.0535048	−	0.0800757i
$13$	−10.9929	+	10.9929i	−0.845607	+	0.845607i	−0.989581	−	0.143975i	$-0.954012\pi$
$13$	−10.9929	+	10.9929i	−0.845607	+	0.845607i	0.143975	+	0.989581i	$0.454012\pi$
$14$	17.6406	−	3.50892i	1.26004	−	0.250637i
$15$	0.494459	−	1.19373i	0.0329639	−	0.0795819i
$16$			4.00000i			0.250000i
$17$	13.1489	+	10.7752i	0.773467	+	0.633837i
$17$	13.1489	+	10.7752i	0.773467	+	0.633837i
$18$	−12.2557			−0.680873
$19$	−12.2243	−	5.06349i	−0.643386	−	0.266499i	0.0370425	−	0.999314i	$-0.488206\pi$
$19$	−12.2243	−	5.06349i	−0.643386	−	0.266499i	−0.680429	+	0.732814i	$0.738206\pi$
$20$	0.872470	+	4.38621i	0.0436235	+	0.219310i
$21$	5.19653	+	5.19653i	0.247454	+	0.247454i
$22$	16.7596	+	11.1984i	0.761802	+	0.509020i
$23$	−8.03728	+	40.4061i	−0.349447	+	1.75679i	0.261582	+	0.965181i	$0.415756\pi$
$23$	−8.03728	+	40.4061i	−0.349447	+	1.75679i	−0.611029	+	0.791608i	$0.709244\pi$
$24$	−1.35893	+	0.908007i	−0.0566220	+	0.0378336i
$25$	1.91342	+	4.61940i	0.0765367	+	0.184776i
$26$	20.3122	−	8.41359i	0.781239	−	0.323600i
$27$	−5.67133	−	8.48775i	−0.210049	−	0.314361i
$28$	−24.9475	−	4.96237i	−0.890983	−	0.177227i
$29$	−15.0353	+	22.5019i	−0.518459	+	0.775929i	−0.994638	−	0.103420i	$-0.967022\pi$
$29$	−15.0353	+	22.5019i	−0.518459	+	0.775929i	0.476179	+	0.879349i	$0.342022\pi$
$30$	−1.29208	+	1.29208i	−0.0430694	+	0.0430694i
$31$	−2.91513	+	0.579856i	−0.0940365	+	0.0187050i	−0.241884	−	0.970305i	$-0.577765\pi$
$31$	−2.91513	+	0.579856i	−0.0940365	+	0.0187050i	0.147848	+	0.989010i	$0.452765\pi$
$32$	2.16478	−	5.22625i	0.0676495	−	0.163320i
$33$			8.23586i			0.249571i
$34$	−11.3484	−	21.1947i	−0.333777	−	0.623372i
$35$	−28.4386			−0.812532
$36$	16.0129	+	6.63275i	0.444802	+	0.184243i
$37$	0.587797	+	2.95506i	0.0158864	+	0.0798664i	0.987915	−	0.154995i	$-0.0495363\pi$
$37$	0.587797	+	2.95506i	0.0158864	+	0.0798664i	−0.972029	+	0.234862i	$0.924536\pi$
$38$	13.2315	+	13.2315i	0.348198	+	0.348198i
$39$	7.46928	+	4.99081i	0.191520	+	0.127970i
$40$	1.23386	−	6.20303i	0.0308465	−	0.155076i
$41$	7.55297	−	5.04673i	0.184219	−	0.123091i	−0.460041	−	0.887898i	$-0.652165\pi$
$41$	7.55297	−	5.04673i	0.184219	−	0.123091i	0.644260	+	0.764806i	$0.277165\pi$
$42$	−3.97725	−	9.60194i	−0.0946965	−	0.228618i
$43$	28.3124	−	11.7274i	0.658427	−	0.272730i	−0.0283492	−	0.999598i	$-0.509025\pi$
$43$	28.3124	−	11.7274i	0.658427	−	0.272730i	0.686777	+	0.726869i	$0.259025\pi$
$44$	−15.8370	−	23.7017i	−0.359931	−	0.538675i
$45$	19.0057	+	3.78046i	0.422348	+	0.0840102i
$46$	32.3689	−	48.4434i	0.703671	−	1.05312i
$47$	33.3447	−	33.3447i	0.709462	−	0.709462i	−0.256960	−	0.966422i	$-0.582721\pi$
$47$	33.3447	−	33.3447i	0.709462	−	0.709462i	0.966422	+	0.256960i	$0.0827209\pi$
$48$	2.26694	−	0.450922i	0.0472278	−	0.00939420i
$49$	43.1479	−	104.168i	0.880569	−	2.12588i
$50$		−	7.07107i		−	0.141421i
$51$	4.62440	−	8.66665i	0.0906746	−	0.169934i
$52$	−31.0926			−0.597934
$53$	−64.1880	−	26.5875i	−1.21109	−	0.501651i	−0.316526	−	0.948584i	$-0.602516\pi$
$53$	−64.1880	−	26.5875i	−1.21109	−	0.501651i	−0.894568	+	0.446932i	$0.852516\pi$
$54$	2.81642	+	14.1591i	0.0521559	+	0.262205i
$55$	−22.5358	−	22.5358i	−0.409742	−	0.409742i
$56$	29.9099	+	19.9851i	0.534105	+	0.356878i
$57$	−1.49160	+	7.49876i	−0.0261683	+	0.131557i
$58$	31.8226	−	21.2631i	0.548665	−	0.366606i
$59$	8.41485	+	20.3152i	0.142625	+	0.344326i	0.979009	−	0.203817i	$-0.0653348\pi$
$59$	8.41485	+	20.3152i	0.142625	+	0.344326i	−0.836384	+	0.548143i	$0.815335\pi$
$60$	2.38746	−	0.988918i	0.0397910	−	0.0164820i
$61$	−2.31848	−	3.46985i	−0.0380079	−	0.0568829i	0.811979	−	0.583687i	$-0.198390\pi$
$61$	−2.31848	−	3.46985i	−0.0380079	−	0.0568829i	−0.849987	+	0.526804i	$0.823390\pi$
$62$	4.12262	+	0.820040i	0.0664938	+	0.0132264i
$63$	−61.2331	+	91.6418i	−0.971954	+	1.45463i
$64$	−5.65685	+	5.65685i	−0.0883883	+	0.0883883i
$65$	−34.0946	+	6.78184i	−0.524532	+	0.104336i
$66$	4.45721	−	10.7607i	0.0675336	−	0.163040i
$67$		−	56.9053i		−	0.849333i	−0.905350	−	0.424666i	$-0.860391\pi$
$67$		−	56.9053i		−	0.849333i	0.905350	−	0.424666i	$-0.139609\pi$
$68$	3.35693	+	33.8339i	0.0493666	+	0.497557i
$69$	23.8056			0.345009
$70$	37.1568	+	15.3909i	0.530812	+	0.219869i
$71$	3.31520	+	16.6666i	0.0466930	+	0.234742i	0.997084	−	0.0763176i	$-0.0243163\pi$
$71$	3.31520	+	16.6666i	0.0466930	+	0.234742i	−0.950391	+	0.311059i	$0.899316\pi$
$72$	−17.3322	−	17.3322i	−0.240725	−	0.240725i
$73$	−102.312	−	68.3627i	−1.40153	−	0.936476i	−0.999785	−	0.0207262i	$-0.993402\pi$
$73$	−102.312	−	68.3627i	−1.40153	−	0.936476i	−0.401750	−	0.915749i	$-0.631598\pi$
$74$	0.831271	−	4.17908i	0.0112334	−	0.0564740i
$75$	2.40227	−	1.60515i	0.0320303	−	0.0214019i
$76$	−10.1270	−	24.4487i	−0.133250	−	0.321693i
$77$	167.472	−	69.3692i	2.17496	−	0.900898i
$78$	−7.05807	−	10.5632i	−0.0904881	−	0.135425i
$79$	110.322	+	21.9444i	1.39648	+	0.277778i	0.835246	−	0.549877i	$-0.185325\pi$
$79$	110.322	+	21.9444i	1.39648	+	0.277778i	0.561238	+	0.827655i	$0.310325\pi$
$80$	−4.96917	+	7.43689i	−0.0621146	+	0.0929611i
$81$	50.9798	−	50.9798i	0.629380	−	0.629380i
$82$	−12.5997	+	2.50624i	−0.153655	+	0.0305639i
$83$	−26.6822	+	64.4165i	−0.321472	+	0.776102i	0.677697	+	0.735341i	$0.262978\pi$
$83$	−26.6822	+	64.4165i	−0.321472	+	0.776102i	−0.999169	+	0.0407608i	$0.987022\pi$
$84$			14.6980i			0.174976i
$85$	11.0608	+	36.3684i	0.130127	+	0.427863i
$86$	−43.3387			−0.503939
$87$	14.4476	+	5.98437i	0.166064	+	0.0687859i
$88$	7.86474	+	39.5387i	0.0893720	+	0.449303i
$89$	67.9298	+	67.9298i	0.763256	+	0.763256i	0.976909	−	0.213654i	$-0.0685364\pi$
$89$	67.9298	+	67.9298i	0.763256	+	0.763256i	−0.213654	+	0.976909i	$0.568536\pi$
$90$	−22.7861	−	15.2252i	−0.253179	−	0.169169i
$91$	38.5732	−	193.921i	0.423881	−	2.13100i
$92$	−68.5094	+	45.7765i	−0.744667	+	0.497571i
$93$	0.657248	+	1.58674i	0.00706718	+	0.0170617i
$94$	−61.6130	+	25.5209i	−0.655457	+	0.271499i
$95$	−16.4374	−	24.6003i	−0.173026	−	0.258951i
$96$	−3.20593	−	0.637700i	−0.0333951	−	0.00664270i
$97$	−22.3249	+	33.4115i	−0.230153	+	0.344449i	−0.928514	−	0.371297i	$-0.878913\pi$
$97$	−22.3249	+	33.4115i	−0.230153	+	0.344449i	0.698361	+	0.715746i	$0.253913\pi$
$98$	−112.751	+	112.751i	−1.15052	+	1.15052i
$99$	−121.144	+	24.0970i	−1.22368	+	0.243404i
$100$	−3.82683	+	9.23880i	−0.0382683	+	0.0923880i
$101$			189.955i			1.88074i	0.340156	+	0.940369i	$0.389520\pi$
$101$			189.955i			1.88074i	−0.340156	+	0.940369i	$0.610480\pi$
$102$	−10.7324	+	8.82081i	−0.105220	+	0.0864785i
$103$	−154.244			−1.49751			−0.748757	−	0.662845i	$-0.769349\pi$
$103$	−154.244			−1.49751			−0.748757	+	0.662845i	$0.769349\pi$
$104$	40.6244	+	16.8272i	0.390619	+	0.161800i
$105$	3.20590	+	16.1171i	0.0305323	+	0.153496i
$106$	69.4765	+	69.4765i	0.655439	+	0.655439i
$107$	64.2026	+	42.8988i	0.600024	+	0.400923i	0.818156	−	0.574996i	$-0.194996\pi$
$107$	64.2026	+	42.8988i	0.600024	+	0.400923i	−0.218132	+	0.975919i	$0.569996\pi$
$108$	3.98301	−	20.0240i	0.0368798	−	0.185407i
$109$	46.1966	−	30.8676i	0.423822	−	0.283189i	−0.325313	−	0.945607i	$-0.605470\pi$
$109$	46.1966	−	30.8676i	0.423822	−	0.283189i	0.749135	+	0.662418i	$0.230470\pi$
$110$	17.2482	+	41.6408i	0.156802	+	0.378553i
$111$	1.60847	−	0.666249i	0.0144907	−	0.00600225i
$112$	−28.2633	−	42.2990i	−0.252351	−	0.377669i
$113$	109.745	+	21.8297i	0.971197	+	0.193183i	0.655099	−	0.755543i	$-0.272627\pi$
$113$	109.745	+	21.8297i	0.971197	+	0.193183i	0.316099	+	0.948726i	$0.397627\pi$
$114$	6.00716	−	8.99035i	0.0526944	−	0.0788627i
$115$	−65.1394	+	65.1394i	−0.566429	+	0.566429i
$116$	−53.0857	+	10.5594i	−0.457635	+	0.0910293i
$117$	−51.5573	+	124.470i	−0.440661	+	1.06385i
$118$		−	31.0972i		−	0.263536i
$119$	−215.182	−	21.0373i	−1.80825	−	0.176784i
$120$	−3.65456			−0.0304547
$121$	75.8924	+	31.4357i	0.627210	+	0.259799i
$122$	1.15137	+	5.78834i	0.00943748	+	0.0474454i
$123$	−3.71161	−	3.71161i	−0.0301757	−	0.0301757i
$124$	−4.94266	−	3.30258i	−0.0398601	−	0.0266337i
$125$	−2.18118	+	10.9655i	−0.0174494	+	0.0877241i
$126$	129.601	−	86.5967i	1.02858	−	0.687275i
$127$	−67.7776	−	163.630i	−0.533682	−	1.28842i	−0.929069	−	0.369907i	$-0.879389\pi$
$127$	−67.7776	−	163.630i	−0.533682	−	1.28842i	0.395387	−	0.918515i	$-0.370611\pi$
$128$	10.4525	−	4.32957i	0.0816602	−	0.0338248i
$129$	−9.83797	−	14.7236i	−0.0762633	−	0.114136i
$130$	48.2171	+	9.59097i	0.370900	+	0.0737767i
$131$	−55.1036	+	82.4683i	−0.420638	+	0.629529i	−0.979906	−	0.199458i	$-0.936082\pi$
$131$	−55.1036	+	82.4683i	−0.420638	+	0.629529i	0.559269	+	0.828986i	$0.311082\pi$
$132$	−11.6473	+	11.6473i	−0.0882368	+	0.0882368i
$133$	165.047	−	32.8299i	1.24095	−	0.246841i
$134$	−30.7969	+	74.3503i	−0.229828	+	0.554853i
$135$		−	22.8261i		−	0.169082i
$136$	13.9247	−	46.0228i	0.102388	−	0.338403i
$137$	133.631			0.975410			0.487705	−	0.873008i	$-0.337834\pi$
$137$	133.631			0.975410			0.487705	+	0.873008i	$0.337834\pi$
$138$	−31.1035	−	12.8835i	−0.225388	−	0.0933586i
$139$	1.49011	+	7.49127i	0.0107202	+	0.0538940i	0.985775	−	0.168070i	$-0.0537534\pi$
$139$	1.49011	+	7.49127i	0.0107202	+	0.0538940i	−0.975055	+	0.221964i	$0.928753\pi$
$140$	−40.2183	−	40.2183i	−0.287273	−	0.287273i
$141$	−22.6565	−	15.1386i	−0.160685	−	0.107366i
$142$	4.68840	−	23.5702i	0.0330169	−	0.165987i
$143$	184.237	−	123.103i	1.28837	−	0.860861i
$144$	13.2655	+	32.0257i	0.0921215	+	0.222401i
$145$	−55.9080	+	23.1579i	−0.385572	+	0.159709i
$146$	96.6795	+	144.691i	0.662188	+	0.991035i
$147$	−63.8998	−	12.7105i	−0.434692	−	0.0864657i
$148$	−3.34781	+	5.01035i	−0.0226203	+	0.0338537i
$149$	−62.3496	+	62.3496i	−0.418454	+	0.418454i	−0.884671	−	0.466217i	$-0.845617\pi$
$149$	−62.3496	+	62.3496i	−0.418454	+	0.418454i	0.466217	+	0.884671i	$0.345617\pi$
$150$	−4.00742	+	0.797124i	−0.0267161	+	0.00531416i
$151$	−51.8706	+	125.227i	−0.343514	+	0.829316i	0.653841	+	0.756632i	$0.273157\pi$
$151$	−51.8706	+	125.227i	−0.343514	+	0.829316i	−0.997355	+	0.0726842i	$0.976843\pi$
$152$			37.4244i			0.246213i
$153$	141.011	+	42.6644i	0.921639	+	0.278852i
$154$	−256.355			−1.66464
$155$	−6.14023	−	2.54337i	−0.0396144	−	0.0164088i
$156$	3.50508	+	17.6212i	0.0224685	+	0.112957i
$157$	143.156	+	143.156i	0.911821	+	0.911821i	0.996415	−	0.0845943i	$-0.0269594\pi$
$157$	143.156	+	143.156i	0.911821	+	0.911821i	−0.0845943	+	0.996415i	$0.526959\pi$
$158$	−132.267	−	88.3777i	−0.837131	−	0.559353i
$159$	−7.83212	+	39.3747i	−0.0492586	+	0.247640i
$160$	10.5174	−	7.02747i	0.0657334	−	0.0439217i
$161$	−200.510	−	484.074i	−1.24540	−	3.00667i
$162$	−94.1984	+	39.0182i	−0.581471	+	0.240853i
$163$	43.2158	+	64.6771i	0.265128	+	0.396792i	0.940017	−	0.341127i	$-0.110809\pi$
$163$	43.2158	+	64.6771i	0.265128	+	0.396792i	−0.674889	+	0.737919i	$0.735809\pi$
$164$	17.8187	+	3.54436i	0.108650	+	0.0216119i
$165$	−10.2313	+	15.3123i	−0.0620082	+	0.0928018i
$166$	69.7239	−	69.7239i	0.420023	−	0.420023i
$167$	162.456	−	32.3144i	0.972787	−	0.193499i	0.316984	−	0.948431i	$-0.397330\pi$
$167$	162.456	−	32.3144i	0.972787	−	0.193499i	0.655804	+	0.754931i	$0.272330\pi$
$168$	7.95451	−	19.2039i	0.0473483	−	0.114309i
$169$		−	72.6872i		−	0.430102i
$170$	5.23078	−	53.5036i	0.0307693	−	0.314727i
$171$	−114.666			−0.670560
$172$	56.6248	+	23.4547i	0.329214	+	0.136365i
$173$	−34.7060	−	174.479i	−0.200613	−	1.00855i	−0.941524	−	0.336945i	$-0.890606\pi$
$173$	−34.7060	−	174.479i	−0.200613	−	1.00855i	0.740912	−	0.671603i	$-0.234394\pi$
$174$	−15.6379	−	15.6379i	−0.0898731	−	0.0898731i
$175$	−52.8737	−	35.3291i	−0.302135	−	0.201880i
$176$	11.1224	−	55.9162i	0.0631956	−	0.317705i
$177$	10.5647	−	7.05913i	0.0596877	−	0.0398821i
$178$	−51.9912	−	125.518i	−0.292085	−	0.705156i
$179$	242.133	−	100.295i	1.35270	−	0.560306i	0.415656	−	0.909522i	$-0.363552\pi$
$179$	242.133	−	100.295i	1.35270	−	0.560306i	0.937042	+	0.349216i	$0.113552\pi$
$180$	21.5317	+	32.2244i	0.119620	+	0.179025i
$181$	15.3630	+	3.05590i	0.0848786	+	0.0168834i	0.237347	−	0.971425i	$-0.423722\pi$
$181$	15.3630	+	3.05590i	0.0848786	+	0.0168834i	−0.152468	+	0.988308i	$0.548722\pi$
$182$	−155.347	+	232.494i	−0.853557	+	1.27744i
$183$	−1.70512	+	1.70512i	−0.00931760	+	0.00931760i
$184$	114.286	−	22.7329i	0.621119	−	0.123548i
$185$	−2.57820	+	6.22432i	−0.0139362	+	0.0336450i
$186$		−	2.42887i		−	0.0130584i
$187$	−153.848	−	187.189i	−0.822716	−	1.00101i
$188$	94.3131			0.501665
$189$	119.946	+	49.6832i	0.634634	+	0.262874i
$190$	8.16292	+	41.0378i	0.0429627	+	0.215988i
$191$	60.1841	+	60.1841i	0.315100	+	0.315100i	0.846882	−	0.531782i	$-0.178477\pi$
$191$	60.1841	+	60.1841i	0.315100	+	0.315100i	−0.531782	+	0.846882i	$0.678477\pi$
$192$	3.84363	+	2.56823i	0.0200189	+	0.0133762i
$193$	−59.1255	+	297.244i	−0.306350	+	1.54012i	0.454233	+	0.890883i	$0.349913\pi$
$193$	−59.1255	+	297.244i	−0.306350	+	1.54012i	−0.760583	+	0.649241i	$0.775087\pi$
$194$	47.2511	−	31.5721i	0.243562	−	0.162743i
$195$	7.68700	+	18.5581i	0.0394205	+	0.0951695i
$196$	208.336	−	86.2958i	1.06294	−	0.440285i
$197$	−200.081	−	299.443i	−1.01564	−	1.52002i	−0.845060	−	0.534672i	$-0.820435\pi$
$197$	−200.081	−	299.443i	−1.01564	−	1.52002i	−0.170582	−	0.985343i	$-0.554565\pi$
$198$	171.323	+	34.0783i	0.865269	+	0.172113i
$199$	33.0242	−	49.4241i	0.165951	−	0.248363i	−0.739169	−	0.673520i	$-0.764781\pi$
$199$	33.0242	−	49.4241i	0.165951	−	0.248363i	0.905119	+	0.425158i	$0.139781\pi$
$200$	10.0000	−	10.0000i	0.0500000	−	0.0500000i
$201$	−32.2502	+	6.41496i	−0.160449	+	0.0319152i
$202$	102.803	−	248.188i	0.508924	−	1.22865i
$203$		−	344.189i		−	1.69551i
$204$	18.7964	−	5.71659i	0.0921391	−	0.0280225i
$205$	20.3122			0.0990838
$206$	201.529	+	83.4762i	0.978298	+	0.405224i
$207$	69.6519	+	350.164i	0.336483	+	1.69161i
$208$	−43.9716	−	43.9716i	−0.211402	−	0.211402i
$209$	156.805	+	104.774i	0.750263	+	0.501310i
$210$	4.53382	−	22.7931i	0.0215896	−	0.108538i
$211$	−304.696	+	203.591i	−1.44406	+	0.964888i	−0.446518	+	0.894774i	$0.647336\pi$
$211$	−304.696	+	203.591i	−1.44406	+	0.964888i	−0.997539	+	0.0701140i	$0.977664\pi$
$212$	−53.1750	−	128.376i	−0.250826	−	0.605547i
$213$	9.07183	−	3.75768i	0.0425908	−	0.0176417i
$214$	−60.6680	−	90.7961i	−0.283495	−	0.424281i
$215$	67.2078	+	13.3685i	0.312595	+	0.0621789i
$216$	−16.0410	+	24.0070i	−0.0742637	+	0.111143i
$217$	26.7296	−	26.7296i	0.123178	−	0.123178i
$218$	−77.0642	+	15.3290i	−0.353506	+	0.0703166i
$219$	−27.2098	+	65.6903i	−0.124246	+	0.299956i
$220$		−	63.7409i		−	0.289732i
$221$	−262.996	+	26.0939i	−1.19003	+	0.118072i
$222$	−2.46214			−0.0110907
$223$	−55.7834	−	23.1062i	−0.250150	−	0.103615i	0.254086	−	0.967182i	$-0.418226\pi$
$223$	−55.7834	−	23.1062i	−0.250150	−	0.103615i	−0.504235	+	0.863566i	$0.668226\pi$
$224$	14.0357	+	70.5622i	0.0626594	+	0.315010i
$225$	30.6393	+	30.6393i	0.136175	+	0.136175i
$226$	−131.575	−	87.9156i	−0.582190	−	0.389007i
$227$	−74.7101	+	375.593i	−0.329119	+	1.65460i	0.362241	+	0.932085i	$0.382012\pi$
$227$	−74.7101	+	375.593i	−0.329119	+	1.65460i	−0.691360	+	0.722510i	$0.742988\pi$
$228$	−12.7143	+	8.49541i	−0.0557644	+	0.0372606i
$229$	−25.0861	−	60.5632i	−0.109546	−	0.264468i	0.859594	−	0.510977i	$-0.170716\pi$
$229$	−25.0861	−	60.5632i	−0.109546	−	0.264468i	−0.969140	+	0.246509i	$0.920716\pi$
$230$	120.362	−	49.8555i	0.523312	−	0.216763i
$231$	−58.1931	−	87.0921i	−0.251918	−	0.377022i
$232$	75.0745	+	14.9332i	0.323597	+	0.0643675i
$233$	−166.917	+	249.809i	−0.716381	+	1.07214i	0.277396	+	0.960756i	$0.410529\pi$
$233$	−166.917	+	249.809i	−0.716381	+	1.07214i	−0.993777	+	0.111384i	$0.964471\pi$
$234$	134.726	−	134.726i	0.575751	−	0.575751i
$235$	103.419	−	20.5713i	0.440081	−	0.0875376i
$236$	−16.8297	+	40.6305i	−0.0713123	+	0.172163i
$237$		−	64.9972i		−	0.274250i
$238$	269.764	+	143.942i	1.13346	+	0.604800i
$239$	−206.599			−0.864433			−0.432216	−	0.901770i	$-0.642268\pi$
$239$	−206.599			−0.864433			−0.432216	+	0.901770i	$0.642268\pi$
$240$	4.77492	+	1.97784i	0.0198955	+	0.00824098i
$241$	31.4430	+	158.074i	0.130469	+	0.655910i	0.989564	+	0.144095i	$0.0460270\pi$
$241$	31.4430	+	158.074i	0.130469	+	0.655910i	−0.859095	+	0.511816i	$0.828973\pi$
$242$	−82.1454	−	82.1454i	−0.339444	−	0.339444i
$243$	−111.029	−	74.1870i	−0.456908	−	0.305296i
$244$	1.62829	−	8.18595i	0.00667330	−	0.0335490i
$245$	209.629	−	140.070i	0.855628	−	0.571713i
$246$	2.84074	+	6.85815i	0.0115477	+	0.0278787i
$247$	190.043	−	78.7184i	0.769405	−	0.318698i
$248$	4.67055	+	6.98997i	0.0188329	+	0.0281854i
$249$	39.5149	+	7.86000i	0.158694	+	0.0315663i
$250$	8.78434	−	13.1467i	0.0351373	−	0.0525868i
$251$	−23.2568	+	23.2568i	−0.0926565	+	0.0926565i	−0.751916	−	0.659259i	$-0.770870\pi$
$251$	−23.2568	+	23.2568i	−0.0926565	+	0.0926565i	0.659259	+	0.751916i	$0.270870\pi$
$252$	−216.198	+	43.0044i	−0.857928	+	0.170652i
$253$	224.707	−	542.491i	0.888170	−	2.14423i
$254$			250.473i			0.986116i
$255$	19.3643	−	10.3684i	0.0759385	−	0.0406602i
$256$	−16.0000			−0.0625000
$257$	164.898	+	68.3031i	0.641627	+	0.265771i	0.679684	−	0.733505i	$-0.262117\pi$
$257$	164.898	+	68.3031i	0.641627	+	0.265771i	−0.0380569	+	0.999276i	$0.512117\pi$
$258$	4.88559	+	24.5615i	0.0189364	+	0.0951997i
$259$	−27.0957	−	27.0957i	−0.104617	−	0.104617i
$260$	−57.8080	−	38.6261i	−0.222339	−	0.148562i
$261$	−45.7544	+	230.023i	−0.175304	+	0.881315i
$262$	116.628	−	77.9282i	0.445144	−	0.297436i
$263$	137.771	+	332.607i	0.523842	+	1.26467i	0.935499	+	0.353328i	$0.114950\pi$
$263$	137.771	+	332.607i	0.523842	+	1.26467i	−0.411657	+	0.911339i	$0.635050\pi$
$264$	21.5213	−	8.91443i	0.0815202	−	0.0337668i
$265$	−86.3102	−	129.172i	−0.325699	−	0.487443i
$266$	−233.411	−	46.4284i	−0.877487	−	0.174543i
$267$	30.8404	−	46.1559i	0.115507	−	0.172868i
$268$	80.4762	−	80.4762i	0.300284	−	0.300284i
$269$	−99.6921	+	19.8300i	−0.370603	+	0.0737174i	−0.376878	−	0.926263i	$-0.623002\pi$
$269$	−99.6921	+	19.8300i	−0.370603	+	0.0737174i	0.00627550	+	0.999980i	$0.498002\pi$
$270$	−12.3534	+	29.8237i	−0.0457533	+	0.110458i
$271$			143.126i			0.528140i	0.964504	+	0.264070i	$0.0850650\pi$
$271$			143.126i			0.528140i	−0.964504	+	0.264070i	$0.914935\pi$
$272$	−43.1009	+	52.5957i	−0.158459	+	0.193367i
$273$	−114.250			−0.418498
$274$	−174.598	−	72.3207i	−0.637217	−	0.263944i
$275$	−13.9030	−	69.8952i	−0.0505564	−	0.254164i
$276$	33.6662	+	33.6662i	0.121979	+	0.121979i
$277$	−72.6877	−	48.5684i	−0.262411	−	0.175337i	0.417404	−	0.908721i	$-0.362940\pi$
$277$	−72.6877	−	48.5684i	−0.262411	−	0.175337i	−0.679815	+	0.733384i	$0.737940\pi$
$278$	2.10733	−	10.5943i	0.00758032	−	0.0381088i
$279$	−21.4168	+	14.3102i	−0.0767627	+	0.0512912i
$280$	30.7817	+	74.3137i	0.109935	+	0.265406i
$281$	−87.5916	+	36.2816i	−0.311714	+	0.129116i	−0.533056	−	0.846080i	$-0.678956\pi$
$281$	−87.5916	+	36.2816i	−0.311714	+	0.129116i	0.221342	+	0.975196i	$0.428956\pi$
$282$	21.4092	+	32.0412i	0.0759193	+	0.113621i
$283$	372.892	+	74.1728i	1.31764	+	0.262095i	0.803342	−	0.595518i	$-0.203053\pi$
$283$	372.892	+	74.1728i	1.31764	+	0.262095i	0.514297	+	0.857612i	$0.328053\pi$
$284$	−18.8818	+	28.2586i	−0.0664852	+	0.0995021i
$285$	−12.0889	+	12.0889i	−0.0424170	+	0.0424170i
$286$	−307.340	+	61.1337i	−1.07462	+	0.213754i
$287$	−44.2114	+	106.736i	−0.154047	+	0.371902i
$288$		−	49.0229i		−	0.170218i
$289$	56.7890	+	283.366i	0.196502	+	0.980503i
$290$	85.5803			0.295104
$291$	21.4522	+	8.88577i	0.0737187	+	0.0305353i
$292$	−48.0116	−	241.371i	−0.164423	−	0.826612i
$293$	−83.5445	−	83.5445i	−0.285135	−	0.285135i	0.550018	−	0.835153i	$-0.314621\pi$
$293$	−83.5445	−	83.5445i	−0.285135	−	0.285135i	−0.835153	+	0.550018i	$0.814621\pi$
$294$	76.6102	+	51.1893i	0.260579	+	0.174113i
$295$	−9.59240	+	48.2243i	−0.0325166	+	0.163472i
$296$	7.08571	−	4.73452i	0.0239382	−	0.0159950i
$297$	55.6787	+	134.420i	0.187470	+	0.452594i
$298$	115.207	−	47.7203i	0.386601	−	0.160135i
$299$	−355.827	−	532.533i	−1.19006	−	1.78105i
$300$	5.66734	+	1.12730i	0.0188911	+	0.00375768i
$301$	−216.533	+	324.064i	−0.719377	+	1.07662i
$302$	135.544	−	135.544i	0.448823	−	0.448823i
$303$	107.654	−	21.4137i	0.355293	−	0.0706721i
$304$	20.2539	−	48.8973i	0.0666248	−	0.160847i
$305$		−	9.33147i		−	0.0305950i
$306$	−161.150	−	132.058i	−0.526633	−	0.431563i
$307$	−493.225			−1.60660			−0.803299	−	0.595576i	$-0.796924\pi$
$307$	−493.225			−1.60660			−0.803299	+	0.595576i	$0.796924\pi$
$308$	334.944	+	138.738i	1.08748	+	0.450449i
$309$	17.3880	+	87.4153i	0.0562718	+	0.282897i
$310$	6.64613	+	6.64613i	0.0214391	+	0.0214391i
$311$	281.471	+	188.073i	0.905052	+	0.604736i	0.918607	−	0.395172i	$-0.129315\pi$
$311$	281.471	+	188.073i	0.905052	+	0.604736i	−0.0135552	+	0.999908i	$0.504315\pi$
$312$	4.95693	−	24.9202i	0.0158876	−	0.0798724i
$313$	12.5216	−	8.36666i	0.0400051	−	0.0267305i	−0.535407	−	0.844594i	$-0.679842\pi$
$313$	12.5216	−	8.36666i	0.0400051	−	0.0267305i	0.575412	+	0.817864i	$0.304842\pi$
$314$	−109.567	−	264.518i	−0.348939	−	0.842413i
$315$	−227.692	+	94.3131i	−0.722831	+	0.299407i
$316$	124.985	+	187.053i	0.395522	+	0.591941i
$317$	−415.288	−	82.6060i	−1.31006	−	0.260587i	−0.509826	−	0.860277i	$-0.670290\pi$
$317$	−415.288	−	82.6060i	−1.31006	−	0.260587i	−0.800232	+	0.599691i	$0.795290\pi$
$318$	31.5426	−	47.2069i	0.0991906	−	0.148449i
$319$	272.748	−	272.748i	0.855010	−	0.855010i
$320$	−17.5448	+	3.48988i	−0.0548276	+	0.0109059i
$321$	17.0746	−	41.2218i	0.0531920	−	0.128417i
$322$			740.989i			2.30121i
$323$	−106.177	−	198.299i	−0.328721	−	0.613930i
$324$	144.193			0.445039
$325$	−71.8145	−	29.7465i	−0.220968	−	0.0915278i
$326$	−21.4612	−	107.893i	−0.0658320	−	0.330960i
$327$	−22.7015	−	22.7015i	−0.0694235	−	0.0694235i
$328$	−21.3630	−	14.2743i	−0.0651312	−	0.0435193i
$329$	−117.004	+	588.219i	−0.355636	+	1.78790i
$330$	21.6549	−	14.4693i	0.0656208	−	0.0438464i
$331$	−101.728	−	245.593i	−0.307335	−	0.741973i	−0.999790	−	0.0205115i	$-0.993471\pi$
$331$	−101.728	−	245.593i	−0.307335	−	0.741973i	0.692454	−	0.721462i	$-0.256529\pi$
$332$	−128.833	+	53.3644i	−0.388051	+	0.160736i
$333$	14.5062	+	21.7101i	0.0435623	+	0.0651955i
$334$	−229.747	−	45.6995i	−0.687865	−	0.136825i
$335$	70.6930	−	105.800i	0.211024	−	0.315820i
$336$	−20.7861	+	20.7861i	−0.0618635	+	0.0618635i
$337$	−324.561	+	64.5593i	−0.963090	+	0.191571i	−0.651502	−	0.758647i	$-0.725861\pi$
$337$	−324.561	+	64.5593i	−0.963090	+	0.191571i	−0.311588	+	0.950217i	$0.600861\pi$
$338$	−39.3380	+	94.9704i	−0.116385	+	0.280977i
$339$		−	64.6573i		−	0.190729i
$340$	−35.7903	+	67.0750i	−0.105266	+	0.197279i
$341$	42.3631			0.124232
$342$	149.818	+	62.0567i	0.438064	+	0.181452i
$343$	158.178	+	795.213i	0.461159	+	2.31840i
$344$	−61.2902	−	61.2902i	−0.178169	−	0.178169i
$345$	44.2599	+	29.5735i	0.128290	+	0.0857203i
$346$	−49.0817	+	246.750i	−0.141855	+	0.713151i
$347$	333.933	−	223.127i	0.962343	−	0.643017i	0.0280817	−	0.999606i	$-0.491060\pi$
$347$	333.933	−	223.127i	0.962343	−	0.643017i	0.934262	+	0.356588i	$0.116060\pi$
$348$	11.9687	+	28.8951i	0.0343929	+	0.0830319i
$349$	336.872	−	139.537i	0.965249	−	0.399819i	0.156308	−	0.987708i	$-0.450041\pi$
$349$	336.872	−	139.537i	0.965249	−	0.399819i	0.808941	+	0.587889i	$0.200041\pi$
$350$	49.9629	+	74.7747i	0.142751	+	0.213642i
$351$	155.649	+	30.9606i	0.443445	+	0.0882067i
$352$	−44.7938	+	67.0386i	−0.127255	+	0.190451i
$353$	−40.1309	+	40.1309i	−0.113685	+	0.113685i	−0.761661	−	0.647976i	$-0.775616\pi$
$353$	−40.1309	+	40.1309i	−0.113685	+	0.113685i	0.647976	+	0.761661i	$0.275616\pi$
$354$	−17.6239	+	3.50560i	−0.0497849	+	0.00990284i
$355$	−14.5412	+	35.1055i	−0.0409610	+	0.0988886i
$356$			192.134i			0.539703i
$357$	12.3351	+	124.323i	0.0345520	+	0.348243i
$358$	−370.641			−1.03531
$359$	159.996	+	66.2726i	0.445672	+	0.184603i	0.594221	−	0.804302i	$-0.297460\pi$
$359$	159.996	+	66.2726i	0.445672	+	0.184603i	−0.148549	+	0.988905i	$0.547460\pi$
$360$	−10.6928	−	53.7561i	−0.0297021	−	0.149323i
$361$	−131.470	−	131.470i	−0.364183	−	0.364183i
$362$	−18.4189	−	12.3071i	−0.0508810	−	0.0339976i
$363$	9.26028	−	46.5546i	0.0255104	−	0.128250i
$364$	328.796	−	219.694i	0.903286	−	0.603556i
$365$	−105.294	−	254.203i	−0.288478	−	0.696447i
$366$	3.15065	−	1.30504i	0.00860834	−	0.00356569i
$367$	351.366	+	525.857i	0.957401	+	1.43285i	0.900690	+	0.434461i	$0.143061\pi$
$367$	351.366	+	525.857i	0.957401	+	1.43285i	0.0567108	+	0.998391i	$0.481939\pi$
$368$	−161.625	−	32.1491i	−0.439197	−	0.0873618i
$369$	43.7355	−	65.4548i	0.118524	−	0.177384i
$370$	6.73716	−	6.73716i	0.0182085	−	0.0182085i
$371$	866.634	−	172.384i	2.33594	−	0.464647i
$372$	−1.31450	+	3.17347i	−0.00353359	+	0.00853084i
$373$		−	353.921i		−	0.948851i	−0.880296	−	0.474425i	$-0.842656\pi$
$373$		−	353.921i		−	0.948851i	0.880296	−	0.474425i	$-0.157344\pi$
$374$	99.7058	+	327.837i	0.266593	+	0.876568i
$375$	6.46041			0.0172278
$376$	−123.226	−	51.0419i	−0.327729	−	0.135750i
$377$	−82.0798	−	412.643i	−0.217718	−	1.09454i
$378$	−129.828	−	129.828i	−0.343461	−	0.343461i
$379$	−429.528	−	287.001i	−1.13332	−	0.757259i	−0.160091	−	0.987102i	$-0.551179\pi$
$379$	−429.528	−	287.001i	−1.13332	−	0.757259i	−0.973228	+	0.229843i	$0.926179\pi$
$380$	11.5441	−	58.0362i	0.0303792	−	0.152727i
$381$	−85.0939	+	56.8579i	−0.223344	+	0.149233i
$382$	−46.0629	−	111.206i	−0.120584	−	0.291114i
$383$	339.666	−	140.694i	0.886856	−	0.367348i	0.107704	−	0.994183i	$-0.465650\pi$
$383$	339.666	−	140.694i	0.886856	−	0.367348i	0.779152	+	0.626835i	$0.215650\pi$
$384$	−3.63203	−	5.43572i	−0.00945841	−	0.0141555i
$385$	397.544	+	79.0765i	1.03258	+	0.205394i
$386$	238.118	−	356.369i	0.616887	−	0.923237i
$387$	187.789	−	187.789i	0.485243	−	0.485243i
$388$	−78.8232	+	15.6789i	−0.203153	+	0.0404096i
$389$	−13.0607	+	31.5314i	−0.0335752	+	0.0810576i	−0.939778	−	0.341786i	$-0.888968\pi$
$389$	−13.0607	+	31.5314i	−0.0335752	+	0.0810576i	0.906203	+	0.422844i	$0.138968\pi$
$390$		−	28.4074i		−	0.0728396i
$391$	−541.067	+	444.694i	−1.38380	+	1.13733i
$392$	−318.908			−0.813540
$393$	52.9494	+	21.9324i	0.134731	+	0.0558076i
$394$	99.3616	+	499.525i	0.252187	+	1.26783i
$395$	177.852	+	177.852i	0.450258	+	0.450258i
$396$	−205.402	−	137.245i	−0.518691	−	0.346578i
$397$	−56.0052	+	281.557i	−0.141071	+	0.709212i	0.843901	+	0.536499i	$0.180253\pi$
$397$	−56.0052	+	281.557i	−0.141071	+	0.709212i	−0.984972	+	0.172713i	$0.944747\pi$
$398$	−69.8963	+	46.7032i	−0.175619	+	0.117345i
$399$	−37.2116	−	89.8367i	−0.0932621	−	0.225155i
$400$	−18.4776	+	7.65367i	−0.0461940	+	0.0191342i
$401$	−87.2138	−	130.525i	−0.217491	−	0.325498i	0.706641	−	0.707572i	$-0.250210\pi$
$401$	−87.2138	−	130.525i	−0.217491	−	0.325498i	−0.924131	+	0.382075i	$0.875210\pi$
$402$	45.6086	+	9.07212i	0.113454	+	0.0225675i
$403$	25.6714	−	38.4200i	0.0637008	−	0.0953350i
$404$	−268.636	+	268.636i	−0.664941	+	0.664941i
$405$	158.115	−	31.4509i	0.390406	−	0.0776567i
$406$	−186.274	+	449.705i	−0.458802	+	1.10765i
$407$		−	42.9433i		−	0.105512i
$408$	−27.6525	−	2.70344i	−0.0677756	−	0.00662607i
$409$	585.488			1.43151			0.715756	−	0.698350i	$-0.246082\pi$
$409$	585.488			1.43151			0.715756	+	0.698350i	$0.246082\pi$
$410$	−26.5391	−	10.9929i	−0.0647296	−	0.0268119i
$411$	−15.0643	−	75.7334i	−0.0366528	−	0.184266i
$412$	−218.134	−	218.134i	−0.529451	−	0.529451i
$413$	−232.529	−	155.371i	−0.563023	−	0.376200i
$414$	98.5027	−	495.207i	0.237929	−	1.19615i
$415$	−129.632	+	86.6175i	−0.312367	+	0.208717i
$416$	33.6544	+	81.2488i	0.0808999	+	0.195310i
$417$	4.07758	−	1.68899i	0.00977836	−	0.00405033i
$418$	−148.172	−	221.756i	−0.354479	−	0.530516i
$419$	−462.543	−	92.0055i	−1.10392	−	0.219584i	−0.390697	−	0.920519i	$-0.627766\pi$
$419$	−462.543	−	92.0055i	−1.10392	−	0.219584i	−0.713225	+	0.700936i	$0.752766\pi$
$420$	−18.2592	+	27.3269i	−0.0434744	+	0.0650640i
$421$	−305.696	+	305.696i	−0.726119	+	0.726119i	−0.969844	−	0.243725i	$-0.921630\pi$
$421$	−305.696	+	305.696i	−0.726119	+	0.726119i	0.243725	+	0.969844i	$0.421630\pi$
$422$	508.288	−	101.105i	1.20447	−	0.239585i
$423$	156.389	−	377.556i	0.369713	−	0.892567i
$424$			196.509i			0.463465i
$425$	−24.6157	+	81.3577i	−0.0579192	+	0.191430i
$426$	−13.8866			−0.0325976
$427$	49.0347	+	20.3108i	0.114835	+	0.0475664i
$428$	30.1281	+	151.464i	0.0703927	+	0.353888i
$429$	−90.5359	−	90.5359i	−0.211039	−	0.211039i
$430$	−80.5763	−	53.8394i	−0.187387	−	0.125208i
$431$	136.983	−	688.661i	0.317827	−	1.59782i	−0.410016	−	0.912078i	$-0.634477\pi$
$431$	136.983	−	688.661i	0.317827	−	1.59782i	0.727843	−	0.685744i	$-0.240523\pi$
$432$	33.9510	−	22.6853i	0.0785903	−	0.0525123i
$433$	−300.337	−	725.077i	−0.693618	−	1.67454i	−0.737360	−	0.675500i	$-0.763928\pi$
$433$	−300.337	−	725.077i	−0.693618	−	1.67454i	0.0437414	−	0.999043i	$-0.486072\pi$
$434$	−49.3899	+	20.4580i	−0.113802	+	0.0471381i
$435$	19.4269	+	29.0744i	0.0446595	+	0.0668376i
$436$	108.985	+	21.6785i	0.249966	+	0.0497214i
$437$	302.846	−	453.242i	0.693012	−	1.03717i
$438$	71.1027	−	71.1027i	0.162335	−	0.162335i
$439$	62.4870	−	12.4294i	0.142339	−	0.0283131i	−0.123406	−	0.992356i	$-0.539382\pi$
$439$	62.4870	−	12.4294i	0.142339	−	0.0283131i	0.265746	+	0.964043i	$0.414382\pi$
$440$	−34.4963	+	83.2816i	−0.0784008	+	0.189276i
$441$		−	977.111i		−	2.21567i
$442$	357.742	+	108.239i	0.809372	+	0.244884i
$443$	323.517			0.730286			0.365143	−	0.930951i	$-0.381020\pi$
$443$	323.517			0.730286			0.365143	+	0.930951i	$0.381020\pi$
$444$	3.21694	+	1.33250i	0.00724535	+	0.00300112i
$445$	41.9079	+	210.685i	0.0941750	+	0.473450i
$446$	60.3795	+	60.3795i	0.135380	+	0.135380i
$447$	42.3643	+	28.3069i	0.0947748	+	0.0633265i
$448$	19.8495	−	99.7901i	0.0443069	−	0.222746i
$449$	81.5562	−	54.4941i	0.181640	−	0.121368i	−0.461426	−	0.887179i	$-0.652662\pi$
$449$	81.5562	−	54.4941i	0.181640	−	0.121368i	0.643066	+	0.765811i	$0.277662\pi$
$450$	−23.4503	−	56.6141i	−0.0521118	−	0.125809i
$451$	−119.616	+	49.5467i	−0.265225	+	0.109860i
$452$	124.331	+	186.075i	0.275070	+	0.411671i
$453$	76.8177	+	15.2800i	0.169575	+	0.0337306i
$454$	300.883	−	450.303i	0.662738	−	0.991857i
$455$	312.622	−	312.622i	0.687082	−	0.687082i
$456$	21.2097	−	4.21887i	0.0465125	−	0.00925191i
$457$	140.647	−	339.551i	0.307761	−	0.743000i	−0.692016	−	0.721882i	$-0.743277\pi$
$457$	140.647	−	339.551i	0.307761	−	0.743000i	0.999777	−	0.0211181i	$-0.00672259\pi$
$458$			92.7061i			0.202415i
$459$	16.8854	−	172.715i	0.0367874	−	0.376285i
$460$	−184.242			−0.400526
$461$	250.237	+	103.652i	0.542814	+	0.224841i	0.637205	−	0.770694i	$-0.280090\pi$
$461$	250.237	+	103.652i	0.542814	+	0.224841i	−0.0943912	+	0.995535i	$0.530090\pi$
$462$	28.8990	+	145.285i	0.0625520	+	0.314470i
$463$	359.040	+	359.040i	0.775465	+	0.775465i	0.979056	−	0.203591i	$-0.0652612\pi$
$463$	359.040	+	359.040i	0.775465	+	0.775465i	−0.203591	+	0.979056i	$0.565261\pi$
$464$	−90.0078	−	60.1413i	−0.193982	−	0.129615i
$465$	−0.749222	+	3.76659i	−0.00161123	+	0.00810020i
$466$	353.283	−	236.056i	0.758117	−	0.506558i
$467$	−43.4322	−	104.855i	−0.0930026	−	0.224528i	0.870532	−	0.492112i	$-0.163775\pi$
$467$	−43.4322	−	104.855i	−0.0930026	−	0.224528i	−0.963535	+	0.267584i	$0.913775\pi$
$468$	−248.941	+	103.115i	−0.531925	+	0.220330i
$469$	402.082	+	601.759i	0.857318	+	1.28307i
$470$	−146.257	−	29.0923i	−0.311185	−	0.0618985i
$471$	64.9933	−	97.2694i	0.137990	−	0.206517i
$472$	43.9781	−	43.9781i	0.0931740	−	0.0931740i
$473$	−428.389	+	85.2119i	−0.905685	+	0.180152i
$474$	−35.1762	+	84.9229i	−0.0742114	+	0.179162i
$475$		−	66.1576i		−	0.139279i
$476$	−274.563	−	334.065i	−0.576812	−	0.701817i
$477$	−602.091			−1.26225
$478$	269.935	+	111.811i	0.564718	+	0.233914i
$479$	1.77264	+	8.91167i	0.00370071	+	0.0186047i	0.982592	−	0.185779i	$-0.0594809\pi$
$479$	1.77264	+	8.91167i	0.00370071	+	0.0186047i	−0.978891	+	0.204384i	$0.934481\pi$
$480$	−5.16833	−	5.16833i	−0.0107674	−	0.0107674i
$481$	−38.9462	−	26.0230i	−0.0809692	−	0.0541019i
$482$	44.4671	−	223.551i	0.0922553	−	0.463799i
$483$	−251.738	+	168.206i	−0.521196	+	0.348252i
$484$	62.8713	+	151.785i	0.129899	+	0.313605i
$485$	−83.0138	+	34.3855i	−0.171163	+	0.0708979i
$486$	104.916	+	157.018i	0.215877	+	0.323083i
$487$	3.76872	+	0.749645i	0.00773864	+	0.00153931i	0.198958	−	0.980008i	$-0.436244\pi$
$487$	3.76872	+	0.749645i	0.00773864	+	0.00153931i	−0.191219	+	0.981547i	$0.561244\pi$
$488$	−6.55766	+	9.81423i	−0.0134378	+	0.0201111i
$489$	31.7830	−	31.7830i	0.0649959	−	0.0649959i
$490$	−349.699	+	69.5594i	−0.713671	+	0.141958i
$491$	55.9696	−	135.123i	0.113991	−	0.275199i	−0.856580	−	0.516015i	$-0.827415\pi$
$491$	55.9696	−	135.123i	0.113991	−	0.275199i	0.970571	+	0.240816i	$0.0774150\pi$
$492$		−	10.4980i		−	0.0213374i
$493$	−440.162	+	133.868i	−0.892823	+	0.271537i
$494$	−290.905			−0.588877
$495$	−255.169	−	105.694i	−0.515493	−	0.213524i
$496$	−2.31942	−	11.6605i	−0.00467625	−	0.0235091i
$497$	−152.821	−	152.821i	−0.307487	−	0.307487i
$498$	−47.3749	−	31.6549i	−0.0951303	−	0.0635641i
$499$	55.6583	−	279.813i	0.111540	−	0.560748i	−0.884087	−	0.467323i	$-0.845218\pi$
$499$	55.6583	−	279.813i	0.111540	−	0.560748i	0.995626	−	0.0934251i	$-0.0297816\pi$
$500$	−18.5922	+	12.4229i	−0.0371845	+	0.0248459i
$501$	−36.6274	−	88.4263i	−0.0731085	−	0.176500i
$502$	42.9729	−	17.8000i	0.0856034	−	0.0354581i
$503$	372.466	+	557.435i	0.740490	+	1.10822i	0.990167	+	0.139892i	$0.0446756\pi$
$503$	372.466	+	557.435i	0.740490	+	1.10822i	−0.249677	+	0.968329i	$0.580324\pi$
$504$	305.750	+	60.8174i	0.606646	+	0.120669i
$505$	−235.979	+	353.168i	−0.467285	+	0.699342i
$506$	−587.188	+	587.188i	−1.16045	+	1.16045i
$507$	−41.1943	+	8.19406i	−0.0812511	+	0.0161618i
$508$	135.555	−	327.259i	0.266841	−	0.644211i
$509$			410.007i			0.805515i	0.915307	+	0.402757i	$0.131948\pi$
$509$			410.007i			0.805515i	−0.915307	+	0.402757i	$0.868052\pi$
$510$	−30.9120	+	3.06703i	−0.0606118	+	0.00601378i
$511$	1564.96			3.06255
$512$	20.9050	+	8.65914i	0.0408301	+	0.0169124i
$513$	26.3507	+	132.474i	0.0513658	+	0.258234i
$514$	−178.485	−	178.485i	−0.347246	−	0.347246i
$515$	−286.774	−	191.616i	−0.556842	−	0.372070i
$516$	6.90927	−	34.7352i	0.0133901	−	0.0673164i
$517$	−558.846	+	373.409i	−1.08094	+	0.722261i
$518$	20.7381	+	50.0663i	0.0400350	+	0.0966531i
$519$	−94.9706	+	39.3381i	−0.182988	+	0.0757960i
$520$	54.6255	+	81.7529i	0.105049	+	0.157217i
$521$	573.087	+	113.994i	1.09997	+	0.218799i	0.711518	−	0.702668i	$-0.248008\pi$
$521$	573.087	+	113.994i	1.09997	+	0.218799i	0.388457	+	0.921467i	$0.373008\pi$
$522$	184.269	−	275.778i	0.353005	−	0.528309i
$523$	130.310	−	130.310i	0.249158	−	0.249158i	−0.571467	−	0.820625i	$-0.693625\pi$
$523$	130.310	−	130.310i	0.249158	−	0.249158i	0.820625	+	0.571467i	$0.193625\pi$
$524$	−194.556	+	38.6996i	−0.371290	+	0.0738542i
$525$	−14.0617	+	33.9480i	−0.0267842	+	0.0646628i
$526$		−	509.133i		−	0.967934i
$527$	−44.5789	−	23.7867i	−0.0845900	−	0.0451361i
$528$	−32.9434			−0.0623929
$529$	−1079.33	−	447.072i	−2.04031	−	0.845126i
$530$	42.8622	+	215.483i	0.0808720	+	0.406571i
$531$	134.746	+	134.746i	0.253759	+	0.253759i
$532$	279.840	+	186.983i	0.526015	+	0.351472i
$533$	−27.5508	+	138.507i	−0.0516900	+	0.259863i
$534$	−65.2743	+	43.6149i	−0.122236	+	0.0816758i
$535$	66.0740	+	159.517i	0.123503	+	0.298162i
$536$	−148.701	+	61.5938i	−0.277427	+	0.114914i
$537$	−84.1362	−	125.919i	−0.156678	−	0.234486i
$538$	140.986	+	28.0438i	0.262056	+	0.0521261i
$539$	−892.817	+	1336.19i	−1.65643	+	2.47903i
$540$	32.2809	−	32.2809i	0.0597795	−	0.0597795i
$541$	950.347	−	189.036i	1.75665	−	0.349419i	0.791509	−	0.611157i	$-0.209296\pi$
$541$	950.347	−	189.036i	1.75665	−	0.349419i	0.965139	+	0.261738i	$0.0842958\pi$
$542$	77.4592	−	187.003i	0.142914	−	0.345024i
$543$		−	9.05125i		−	0.0166690i
$544$	84.7787	−	45.3936i	0.155843	−	0.0834441i
$545$	124.236			0.227957
$546$	149.275	+	61.8316i	0.273397	+	0.113245i
$547$	−17.9642	−	90.3121i	−0.0328413	−	0.165104i	0.960884	−	0.276950i	$-0.0893237\pi$
$547$	−17.9642	−	90.3121i	−0.0328413	−	0.165104i	−0.993726	+	0.111846i	$0.964324\pi$
$548$	188.983	+	188.983i	0.344860	+	0.344860i
$549$	−30.0701	−	20.0922i	−0.0547725	−	0.0365978i
$550$	−19.6618	+	98.8468i	−0.0357488	+	0.179721i
$551$	297.735	−	198.940i	0.540354	−	0.361053i
$552$	−25.7670	−	62.2070i	−0.0466793	−	0.112694i
$553$	−1321.68	+	547.459i	−2.39002	+	0.989981i
$554$	68.6861	+	102.796i	0.123982	+	0.185552i
$555$	3.81818	+	0.759483i	0.00687960	+	0.00136844i
$556$	−8.48693	+	12.7016i	−0.0152643	+	0.0228446i
$557$	−155.701	+	155.701i	−0.279535	+	0.279535i	−0.832923	−	0.553389i	$-0.813334\pi$
$557$	−155.701	+	155.701i	−0.279535	+	0.279535i	0.553389	+	0.832923i	$0.313334\pi$
$558$	35.7270	−	7.10655i	0.0640269	−	0.0127358i
$559$	−182.317	+	440.152i	−0.326149	+	0.787393i
$560$		−	113.754i		−	0.203133i
$561$	−88.7432	+	108.293i	−0.158188	+	0.193035i
$562$	134.079			0.238576
$563$	−356.181	−	147.535i	−0.632648	−	0.262052i	0.0432295	−	0.999065i	$-0.486235\pi$
$563$	−356.181	−	147.535i	−0.632648	−	0.262052i	−0.675878	+	0.737014i	$0.736235\pi$
$564$	−10.6320	−	53.4504i	−0.0188510	−	0.0947703i
$565$	176.922	+	176.922i	0.313136	+	0.313136i
$566$	−447.065	−	298.719i	−0.789867	−	0.527772i
$567$	−178.884	+	899.312i	−0.315492	+	1.58609i
$568$	39.9637	−	26.7029i	0.0703586	−	0.0470121i
$569$	184.463	+	445.332i	0.324188	+	0.782658i	0.999002	+	0.0446703i	$0.0142237\pi$
$569$	184.463	+	445.332i	0.324188	+	0.782658i	−0.674814	+	0.737988i	$0.735776\pi$
$570$	22.3373	−	9.25241i	0.0391882	−	0.0162323i
$571$	277.778	+	415.724i	0.486476	+	0.728063i	0.990783	−	0.135462i	$-0.0432519\pi$
$571$	277.778	+	415.724i	0.486476	+	0.728063i	−0.504307	+	0.863525i	$0.668252\pi$
$572$	434.645	+	86.4562i	0.759868	+	0.151147i
$573$	27.3238	−	40.8929i	0.0476855	−	0.0713664i
$574$	115.530	−	115.530i	0.201272	−	0.201272i
$575$	−202.031	+	40.1864i	−0.351358	+	0.0698894i
$576$	−26.5310	+	64.0515i	−0.0460608	+	0.111201i
$577$		−	465.628i		−	0.806980i	−0.914984	−	0.403490i	$-0.867797\pi$
$577$		−	465.628i		−	0.806980i	0.914984	−	0.403490i	$-0.132203\pi$
$578$	79.1579	−	400.969i	0.136951	−	0.693718i
$579$	175.124			0.302459
$580$	−111.816	−	46.3157i	−0.192786	−	0.0798547i
$581$	−172.998	−	869.719i	−0.297759	−	1.49693i
$582$	−23.2196	−	23.2196i	−0.0398963	−	0.0398963i
$583$	823.357	+	550.149i	1.41228	+	0.943653i
$584$	−67.8986	+	341.350i	−0.116265	+	0.584503i
$585$	−250.485	+	167.369i	−0.428180	+	0.286101i
$586$	63.9422	+	154.370i	0.109116	+	0.263430i
$587$	624.031	−	258.482i	1.06308	−	0.440344i	0.218539	−	0.975828i	$-0.429871\pi$
$587$	624.031	−	258.482i	1.06308	−	0.440344i	0.844545	+	0.535484i	$0.179871\pi$
$588$	−72.3926	−	108.343i	−0.123117	−	0.184257i
$589$	38.5716	+	7.67237i	0.0654866	+	0.0130261i
$590$	38.6319	−	57.8167i	0.0654777	−	0.0979944i
$591$	−147.149	+	147.149i	−0.248984	+	0.248984i
$592$	−11.8202	+	2.35119i	−0.0199666	+	0.00397160i
$593$	−160.977	+	388.634i	−0.271463	+	0.655369i	−0.999546	−	0.0301194i	$-0.990411\pi$
$593$	−160.977	+	388.634i	−0.271463	+	0.655369i	0.728084	+	0.685488i	$0.240411\pi$
$594$		−	205.762i		−	0.346400i
$595$	−373.937	−	306.432i	−0.628466	−	0.515012i
$596$	−176.351			−0.295891
$597$	−31.7332	−	13.1443i	−0.0531544	−	0.0220173i
$598$	176.706	+	888.360i	0.295495	+	1.48555i
$599$	−258.150	−	258.150i	−0.430969	−	0.430969i	0.457989	−	0.888958i	$-0.348570\pi$
$599$	−258.150	−	258.150i	−0.430969	−	0.430969i	−0.888958	+	0.457989i	$0.848570\pi$
$600$	−6.79465	−	4.54004i	−0.0113244	−	0.00756673i
$601$	−31.0394	+	156.046i	−0.0516462	+	0.259643i	−0.997979	−	0.0635521i	$-0.979757\pi$
$601$	−31.0394	+	156.046i	−0.0516462	+	0.259643i	0.946332	+	0.323195i	$0.104757\pi$
$602$	458.296	−	306.223i	0.761288	−	0.508677i
$603$	−188.719	−	455.609i	−0.312967	−	0.755570i
$604$	−250.453	+	103.741i	−0.414658	+	0.171757i
$605$	102.049	+	152.727i	0.168675	+	0.252441i
$606$	−152.245	−	30.2835i	−0.251230	−	0.0499727i
$607$	−164.860	+	246.730i	−0.271597	+	0.406474i	−0.942047	−	0.335481i	$-0.891101\pi$
$607$	−164.860	+	246.730i	−0.271597	+	0.406474i	0.670450	+	0.741955i	$0.266101\pi$
$608$	−52.9261	+	52.9261i	−0.0870495	+	0.0870495i
$609$	−195.064	+	38.8006i	−0.320302	+	0.0637119i
$610$	−5.05015	+	12.1921i	−0.00827894	+	0.0199871i
$611$			733.109i			1.19985i
$612$	139.083	+	259.756i	0.227260	+	0.424438i
$613$	−171.887			−0.280403			−0.140202	−	0.990123i	$-0.544775\pi$
$613$	−171.887			−0.280403			−0.140202	+	0.990123i	$0.544775\pi$
$614$	644.430	+	266.932i	1.04956	+	0.434742i
$615$	−2.28980	−	11.5116i	−0.00372325	−	0.0187181i
$616$	−362.541	−	362.541i	−0.588540	−	0.588540i
$617$	297.638	+	198.876i	0.482396	+	0.322327i	0.772879	−	0.634553i	$-0.218816\pi$
$617$	297.638	+	198.876i	0.482396	+	0.322327i	−0.290483	+	0.956880i	$0.593816\pi$
$618$	24.5903	−	123.624i	0.0397902	−	0.200039i
$619$	0.688725	−	0.460191i	0.00111264	−	0.000743443i	−0.555014	−	0.831841i	$-0.687287\pi$
$619$	0.688725	−	0.460191i	0.00111264	−	0.000743443i	0.556126	+	0.831098i	$0.312287\pi$
$620$	−5.08673	−	12.2805i	−0.00820441	−	0.0198072i
$621$	388.539	−	160.938i	0.625667	−	0.259160i
$622$	−265.975	−	398.060i	−0.427613	−	0.639968i
$623$	−1198.32	−	238.360i	−1.92347	−	0.382601i
$624$	−19.9632	+	29.8771i	−0.0319924	+	0.0478800i
$625$	−17.6777	+	17.6777i	−0.0282843	+	0.0282843i
$626$	−20.8883	+	4.15493i	−0.0333678	+	0.00663727i
$627$	41.7021	−	100.678i	0.0665106	−	0.160571i
$628$			404.906i			0.644755i
$629$	−24.1125	+	45.1895i	−0.0383346	+	0.0718434i
$630$	348.536			0.553231
$631$	−828.105	−	343.012i	−1.31237	−	0.543601i	−0.386795	−	0.922166i	$-0.626418\pi$
$631$	−828.105	−	343.012i	−1.31237	−	0.543601i	−0.925575	+	0.378565i	$0.876418\pi$
$632$	−62.0683	−	312.038i	−0.0982093	−	0.493731i
$633$	149.731	+	149.731i	0.236541	+	0.236541i
$634$	497.894	+	332.682i	0.785322	+	0.524736i
$635$	77.2622	−	388.424i	0.121673	−	0.611691i
$636$	−66.7606	+	44.6080i	−0.104969	+	0.0701383i
$637$	670.790	+	1619.43i	1.05305	+	2.54228i
$638$	−503.973	+	208.753i	−0.789927	+	0.327198i
$639$	81.8158	+	122.446i	0.128037	+	0.191621i
$640$	24.8121	+	4.93544i	0.0387689	+	0.00771162i
$641$	−24.4498	+	36.5916i	−0.0381431	+	0.0570852i	−0.850051	−	0.526700i	$-0.823429\pi$
$641$	−24.4498	+	36.5916i	−0.0381431	+	0.0570852i	0.811908	+	0.583785i	$0.198429\pi$
$642$	−44.6181	+	44.6181i	−0.0694986	+	0.0694986i
$643$	−803.156	+	159.758i	−1.24908	+	0.248457i	−0.774963	−	0.632007i	$-0.782232\pi$
$643$	−803.156	+	159.758i	−1.24908	+	0.248457i	−0.474114	+	0.880463i	$0.657232\pi$
$644$	401.020	−	968.149i	0.622702	−	1.50334i
$645$		−	39.5960i		−	0.0613892i
$646$	31.4078	+	316.553i	0.0486189	+	0.490020i
$647$	625.084			0.966126			0.483063	−	0.875585i	$-0.339524\pi$
$647$	625.084			0.966126			0.483063	+	0.875585i	$0.339524\pi$
$648$	−188.397	−	78.0365i	−0.290736	−	0.120427i
$649$	−61.1429	−	307.386i	−0.0942109	−	0.473630i
$650$	77.7315	+	77.7315i	0.119587	+	0.119587i
$651$	−18.1618	−	12.1353i	−0.0278983	−	0.0186411i
$652$	−30.3508	+	152.584i	−0.0465503	+	0.234024i
$653$	−916.724	+	612.535i	−1.40387	+	0.938033i	−0.404138	+	0.914698i	$0.632428\pi$
$653$	−916.724	+	612.535i	−1.40387	+	0.938033i	−0.999728	+	0.0233345i	$0.992572\pi$
$654$	17.3750	+	41.9469i	0.0265672	+	0.0641390i
$655$	−204.900	+	84.8722i	−0.312824	+	0.129576i
$656$	20.1869	+	30.2119i	0.0307728	+	0.0460547i
$657$	−1045.87	−	208.037i	−1.59189	−	0.316646i
$658$	471.215	−	705.223i	0.716132	−	1.07177i
$659$	558.589	−	558.589i	0.847632	−	0.847632i	−0.142206	−	0.989837i	$-0.545419\pi$
$659$	558.589	−	558.589i	0.847632	−	0.847632i	0.989837	+	0.142206i	$0.0454194\pi$
$660$	−36.1242	+	7.18554i	−0.0547336	+	0.0108872i
$661$	−440.811	+	1064.21i	−0.666885	+	1.61000i	0.119908	+	0.992785i	$0.461740\pi$
$661$	−440.811	+	1064.21i	−0.666885	+	1.61000i	−0.786792	+	0.617218i	$0.788260\pi$
$662$			375.938i			0.567882i
$663$	44.4359	+	146.107i	0.0670225	+	0.220373i
$664$	197.209			0.297001
$665$	347.643	+	143.998i	0.522772	+	0.216539i
$666$	−7.20388	−	36.2163i	−0.0108166	−	0.0543789i
$667$	−788.374	−	788.374i	−1.18197	−	1.18197i
$668$	275.446	+	184.047i	0.412345	+	0.275520i
$669$	−6.80660	+	34.2191i	−0.0101743	+	0.0511496i
$670$	−149.623	+	99.9750i	−0.223318	+	0.149216i
$671$	22.7619	+	54.9520i	0.0339223	+	0.0818957i
$672$	38.4078	−	15.9090i	0.0571544	−	0.0236741i
$673$	−484.998	−	725.851i	−0.720651	−	1.07853i	−0.993204	−	0.116390i	$-0.962868\pi$
$673$	−484.998	−	725.851i	−0.720651	−	1.07853i	0.272552	−	0.962141i	$-0.412132\pi$
$674$	458.999	+	91.3006i	0.681007	+	0.135461i
$675$	28.3567	−	42.4388i	0.0420099	−	0.0628722i
$676$	102.795	−	102.795i	0.152064	−	0.152064i
$677$	1067.62	−	212.363i	1.57699	−	0.313683i	0.672473	−	0.740121i	$-0.265232\pi$
$677$	1067.62	−	212.363i	1.57699	−	0.313683i	0.904517	+	0.426438i	$0.140232\pi$
$678$	−34.9923	+	84.4788i	−0.0516110	+	0.124600i
$679$		−	511.062i		−	0.752668i
$680$	83.0630	−	68.2681i	0.122151	−	0.100394i
$681$	221.284			0.324939
$682$	−55.3500	−	22.9267i	−0.0811584	−	0.0336169i
$683$	114.309	+	574.672i	0.167364	+	0.841393i	0.969658	+	0.244465i	$0.0786123\pi$
$683$	114.309	+	574.672i	0.167364	+	0.841393i	−0.802295	+	0.596928i	$0.796388\pi$
$684$	−162.162	−	162.162i	−0.237079	−	0.237079i
$685$	248.450	+	166.009i	0.362701	+	0.242349i
$686$	223.697	−	1124.60i	0.326089	−	1.63936i
$687$	−31.4953	+	21.0445i	−0.0458446	+	0.0306324i
$688$	46.9095	+	113.250i	0.0681824	+	0.164607i
$689$	997.885	−	413.337i	1.44831	−	0.599909i
$690$	−41.8233	−	62.5929i	−0.0606134	−	0.0907144i
$691$	97.4924	+	19.3924i	0.141089	+	0.0280643i	0.265129	−	0.964213i	$-0.414585\pi$
$691$	97.4924	+	19.3924i	0.141089	+	0.0280643i	−0.124041	+	0.992277i	$0.539585\pi$
$692$	197.669	−	295.832i	0.285648	−	0.427503i
$693$	1110.80	−	1110.80i	1.60289	−	1.60289i
$694$	−557.060	+	110.806i	−0.802680	+	0.159663i
$695$	−6.53591	+	15.7791i	−0.00940419	+	0.0227037i
$696$		−	44.2307i		−	0.0635499i
$697$	153.693	+	15.0258i	0.220507	+	0.0215578i
$698$	−515.661			−0.738770
$699$	160.392	+	66.4364i	0.229459	+	0.0950449i
$700$	−24.8118	−	124.738i	−0.0354455	−	0.178197i
$701$	−290.684	−	290.684i	−0.414670	−	0.414670i	0.468692	−	0.883362i	$-0.344726\pi$
$701$	−290.684	−	290.684i	−0.414670	−	0.414670i	−0.883362	+	0.468692i	$0.844726\pi$
$702$	−186.610	−	124.689i	−0.265826	−	0.177619i
$703$	7.77745	−	39.0999i	0.0110632	−	0.0556186i
$704$	94.8069	−	63.3479i	0.134669	−	0.0899829i
$705$	−23.3170	−	56.2921i	−0.0330737	−	0.0798470i
$706$	74.1522	−	30.7149i	0.105031	−	0.0435055i
$707$	−1342.18	−	2008.72i	−1.89842	−	2.84119i
$708$	24.9239	+	4.95767i	0.0352033	+	0.00700236i
$709$	526.440	−	787.873i	0.742511	−	1.11125i	−0.247312	−	0.968936i	$-0.579547\pi$
$709$	526.440	−	787.873i	0.742511	−	1.11125i	0.989822	−	0.142310i	$-0.0454529\pi$
$710$	37.9979	−	37.9979i	0.0535181	−	0.0535181i
$711$	956.064	−	190.173i	1.34467	−	0.267472i
$712$	103.982	−	251.036i	0.146043	−	0.352578i
$713$		−	122.450i		−	0.171739i
$714$	51.1664	−	169.111i	0.0716617	−	0.236850i
$715$	495.468			0.692962
$716$	484.266	+	200.590i	0.676349	+	0.280153i
$717$	23.2900	+	117.087i	0.0324826	+	0.163301i
$718$	−173.179	−	173.179i	−0.241196	−	0.241196i
$719$	347.798	+	232.391i	0.483725	+	0.323215i	0.773409	−	0.633908i	$-0.218550\pi$
$719$	347.798	+	232.391i	0.483725	+	0.323215i	−0.289684	+	0.957122i	$0.593550\pi$
$720$	−15.1218	+	76.0226i	−0.0210026	+	0.105587i
$721$	1631.09	−	1089.86i	2.26226	−	1.51159i
$722$	100.623	+	242.925i	0.139367	+	0.336461i
$723$	86.0416	−	35.6396i	0.119006	−	0.0492940i
$724$	17.4049	+	26.0483i	0.0240399	+	0.0359783i
$725$	−132.714	−	26.3985i	−0.183054	−	0.0364117i
$726$	−37.2943	+	55.8149i	−0.0513696	+	0.0768800i
$727$	−221.023	+	221.023i	−0.304020	+	0.304020i	−0.842584	−	0.538564i	$-0.818967\pi$
$727$	−221.023	+	221.023i	−0.304020	+	0.304020i	0.538564	+	0.842584i	$0.318967\pi$
$728$	−548.490	+	109.102i	−0.753421	+	0.149865i
$729$	218.783	−	528.188i	0.300113	−	0.724537i
$730$			389.117i			0.533037i
$731$	498.643	+	150.870i	0.682138	+	0.206388i
$732$	−4.82281			−0.00658854
$733$	−671.959	−	278.334i	−0.916724	−	0.379719i	−0.126097	−	0.992018i	$-0.540245\pi$
$733$	−671.959	−	278.334i	−0.916724	−	0.379719i	−0.790627	+	0.612298i	$0.790245\pi$
$734$	−174.490	−	877.223i	−0.237725	−	1.19513i
$735$	−103.014	−	103.014i	−0.140155	−	0.140155i
$736$	193.774	+	129.475i	0.263280	+	0.175918i
$737$	−158.231	+	795.481i	−0.214696	+	1.07935i
$738$	−92.5671	+	61.8514i	−0.125430	+	0.0838095i
$739$	−95.3660	−	230.234i	−0.129047	−	0.311548i	0.846129	−	0.532978i	$-0.178927\pi$
$739$	−95.3660	−	230.234i	−0.129047	−	0.311548i	−0.975176	+	0.221431i	$0.928927\pi$
$740$	−12.4486	+	5.15640i	−0.0168225	+	0.00696810i
$741$	−66.0360	−	98.8299i	−0.0891175	−	0.133374i
$742$	−1225.60	−	243.788i	−1.65176	−	0.328555i
$743$	136.170	−	203.793i	0.183270	−	0.274283i	−0.728446	−	0.685103i	$-0.759757\pi$
$743$	136.170	−	203.793i	0.183270	−	0.274283i	0.911717	+	0.410819i	$0.134757\pi$
$744$	3.43494	−	3.43494i	0.00461686	−	0.00461686i
$745$	−193.378	+	38.4653i	−0.259568	+	0.0516313i
$746$	−191.541	+	462.420i	−0.256757	+	0.619867i
$747$			604.235i			0.808882i
$748$	47.1519	−	482.299i	0.0630373	−	0.644785i
$749$	−982.040			−1.31114
$750$	−8.44094	−	3.49635i	−0.0112546	−	0.00466180i
$751$	−201.664	−	1013.83i	−0.268527	−	1.34998i	−0.845832	−	0.533450i	$-0.820895\pi$
$751$	−201.664	−	1013.83i	−0.268527	−	1.34998i	0.577304	−	0.816529i	$-0.304105\pi$
$752$	133.379	+	133.379i	0.177365	+	0.177365i
$753$	15.8022	+	10.5587i	0.0209856	+	0.0140221i
$754$	−116.078	+	583.565i	−0.153950	+	0.773959i
$755$	−252.007	+	168.386i	−0.333785	+	0.223028i
$756$	99.3663	+	239.892i	0.131437	+	0.317317i
$757$	742.160	−	307.413i	0.980397	−	0.406094i	0.165824	−	0.986155i	$-0.446972\pi$
$757$	742.160	−	307.413i	0.980397	−	0.406094i	0.814572	+	0.580062i	$0.196972\pi$
$758$	405.881	+	607.444i	0.535463	+	0.801377i
$759$	−332.779	−	66.1939i	−0.438444	−	0.0872120i
$760$	−46.4921	+	69.5803i	−0.0611738	+	0.0915530i
$761$	−1060.34	+	1060.34i	−1.39335	+	1.39335i	−0.575657	+	0.817691i	$0.695254\pi$
$761$	−1060.34	+	1060.34i	−1.39335	+	1.39335i	−0.817691	+	0.575657i	$0.804746\pi$
$762$	141.952	−	28.2360i	0.186288	−	0.0370551i
$763$	−270.413	+	652.834i	−0.354407	+	0.855614i
$764$			170.226i			0.222809i
$765$	209.169	+	254.499i	0.273423	+	0.332679i
$766$	−519.938			−0.678771
$767$	−315.827	−	130.820i	−0.411769	−	0.170560i
$768$	1.80369	+	9.06775i	0.00234855	+	0.0118070i
$769$	69.9681	+	69.9681i	0.0909859	+	0.0909859i	0.751135	−	0.660149i	$-0.229507\pi$
$769$	69.9681	+	69.9681i	0.0909859	+	0.0909859i	−0.660149	+	0.751135i	$0.729507\pi$
$770$	−476.621	−	318.468i	−0.618988	−	0.413595i
$771$	20.1206	−	101.153i	0.0260968	−	0.131198i
$772$	−503.982	+	336.750i	−0.652827	+	0.436205i
$773$	400.933	+	967.937i	0.518671	+	1.25218i	0.938720	+	0.344681i	$0.112013\pi$
$773$	400.933	+	967.937i	0.518671	+	1.25218i	−0.420049	+	0.907502i	$0.637987\pi$
$774$	−346.989	+	143.727i	−0.448306	+	0.185694i
$775$	−8.25645	−	12.3566i	−0.0106535	−	0.0159441i
$776$	111.473	+	22.1733i	0.143651	+	0.0285739i
$777$	−12.3015	+	18.4106i	−0.0158321	+	0.0236944i
$778$	34.1294	−	34.1294i	0.0438681	−	0.0438681i
$779$	−117.884	+	23.4486i	−0.151328	+	0.0301009i
$780$	−15.3740	+	37.1161i	−0.0197103	+	0.0475848i
$781$		−	242.202i		−	0.310118i
$782$	947.605	−	288.198i	1.21177	−	0.368539i
$783$	276.261			0.352824
$784$	416.673	+	172.592i	0.531471	+	0.220142i
$785$	88.3172	+	444.000i	0.112506	+	0.565605i
$786$	−57.3121	−	57.3121i	−0.0729161	−	0.0729161i
$787$	883.556	+	590.373i	1.12269	+	0.750156i	0.971191	−	0.238301i	$-0.0765906\pi$
$787$	883.556	+	590.373i	1.12269	+	0.750156i	0.151497	+	0.988458i	$0.451591\pi$
$788$	140.519	−	706.434i	0.178323	−	0.896490i
$789$	172.969	−	115.574i	0.219226	−	0.146482i
$790$	−136.122	−	328.628i	−0.172306	−	0.415985i
$791$	−1314.77	+	544.597i	−1.66217	+	0.688491i
$792$	194.094	+	290.482i	0.245068	+	0.366770i
$793$	63.6306	+	12.6569i	0.0802403	+	0.0159608i
$794$	225.552	−	337.562i	0.284070	−	0.425141i
$795$	−63.4766	+	63.4766i	−0.0798448	+	0.0798448i
$796$	116.599	−	23.1931i	0.146482	−	0.0291370i
$797$	248.979	−	601.087i	0.312395	−	0.754187i	−0.687221	−	0.726449i	$-0.741169\pi$
$797$	248.979	−	601.087i	0.312395	−	0.754187i	0.999615	−	0.0277385i	$-0.00883058\pi$
$798$			137.516i			0.172326i
$799$	797.744	−	79.1506i	0.998428	−	0.0990621i
$800$	28.2843			0.0353553
$801$	769.156	+	318.595i	0.960245	+	0.397746i
$802$	43.3109	+	217.738i	0.0540036	+	0.271494i
$803$	1240.13	+	1240.13i	1.54438	+	1.54438i
$804$	−54.6807	−	36.5365i	−0.0680109	−	0.0454434i
$805$	228.569	−	1149.09i	0.283937	−	1.42745i
$806$	−54.3341	+	36.3049i	−0.0674120	+	0.0450433i
$807$	22.4767	+	54.2635i	0.0278521	+	0.0672410i
$808$	496.375	−	205.605i	0.614326	−	0.254462i
$809$	179.812	+	269.108i	0.222265	+	0.332643i	0.925797	−	0.378020i	$-0.123395\pi$
$809$	179.812	+	269.108i	0.222265	+	0.332643i	−0.703533	+	0.710663i	$0.748395\pi$
$810$	−223.608	−	44.4784i	−0.276059	−	0.0549115i
$811$	188.827	−	282.600i	0.232833	−	0.348459i	−0.696594	−	0.717465i	$-0.745302\pi$
$811$	188.827	−	282.600i	0.232833	−	0.348459i	0.929427	+	0.369007i	$0.120302\pi$
$812$	486.757	−	486.757i	0.599454	−	0.599454i
$813$	81.1143	−	16.1346i	0.0997716	−	0.0198458i
$814$	−23.2407	+	56.1081i	−0.0285513	+	0.0689289i
$815$			173.936i			0.213418i
$816$	34.6666	+	18.4976i	0.0424836	+	0.0226686i
$817$	−405.481			−0.496305
$818$	−764.978	−	316.864i	−0.935180	−	0.387364i
$819$	−334.280	−	1680.54i	−0.408156	−	2.05194i
$820$	28.7258	+	28.7258i	0.0350314	+	0.0350314i
$821$	−1059.35	−	707.836i	−1.29032	−	0.862163i	−0.294693	−	0.955592i	$-0.595217\pi$
$821$	−1059.35	−	707.836i	−1.29032	−	0.862163i	−0.995626	+	0.0934287i	$0.970217\pi$
$822$	−21.3041	+	107.103i	−0.0259174	+	0.130296i
$823$	−192.154	+	128.393i	−0.233480	+	0.156006i	−0.666807	−	0.745231i	$-0.732339\pi$
$823$	−192.154	+	128.393i	−0.233480	+	0.156006i	0.433327	+	0.901237i	$0.357339\pi$
$824$	166.952	+	403.059i	0.202612	+	0.489149i
$825$	−38.0447	+	15.7586i	−0.0461148	+	0.0191014i
$826$	219.727	+	328.845i	0.266014	+	0.398118i
$827$	306.149	+	60.8969i	0.370193	+	0.0736359i	0.376681	−	0.926343i	$-0.377065\pi$
$827$	306.149	+	60.8969i	0.370193	+	0.0736359i	−0.00648823	+	0.999979i	$0.502065\pi$
$828$	−396.704	+	593.709i	−0.479111	+	0.717040i
$829$	−320.614	+	320.614i	−0.386748	+	0.386748i	−0.873526	−	0.486778i	$-0.838172\pi$
$829$	−320.614	+	320.614i	−0.386748	+	0.386748i	0.486778	+	0.873526i	$0.338172\pi$
$830$	216.250	−	43.0147i	0.260542	−	0.0518250i
$831$	−19.3312	+	46.6698i	−0.0232626	+	0.0561610i
$832$		−	124.370i		−	0.149484i
$833$	1689.79	−	904.773i	2.02855	−	1.08616i
$834$	−6.24169			−0.00748404
$835$	342.185	+	141.738i	0.409802	+	0.169746i
$836$	73.5833	+	369.928i	0.0880183	+	0.442498i
$837$	21.4543	+	21.4543i	0.0256324	+	0.0256324i
$838$	554.549	+	370.538i	0.661753	+	0.442169i
$839$	−159.908	+	803.912i	−0.190594	+	0.958179i	0.760514	+	0.649321i	$0.224947\pi$
$839$	−159.908	+	803.912i	−0.190594	+	0.958179i	−0.951108	+	0.308858i	$0.900053\pi$
$840$	38.6460	−	25.8225i	0.0460072	−	0.0307410i
$841$	41.5602	+	100.335i	0.0494175	+	0.119304i
$842$	564.853	−	233.970i	0.670846	−	0.277874i
$843$	30.4363	+	45.5511i	0.0361047	+	0.0540345i
$844$	−718.827	−	142.984i	−0.851691	−	0.169412i
$845$	90.2987	−	135.142i	0.106862	−	0.159931i
$846$	−408.664	+	408.664i	−0.483054	+	0.483054i
$847$	−1024.66	+	203.818i	−1.20975	+	0.240635i
$848$	106.350	−	256.752i	0.125413	−	0.302773i
$849$		−	219.692i		−	0.258766i
$850$	76.1924	−	92.9770i	0.0896381	−	0.109385i
$851$	−124.127			−0.145860
$852$	18.1437	+	7.51535i	0.0212954	+	0.00882084i
$853$	−81.1245	−	407.841i	−0.0951049	−	0.478125i	−0.998756	−	0.0498562i	$-0.984124\pi$
$853$	−81.1245	−	407.841i	−0.0951049	−	0.478125i	0.903651	−	0.428269i	$-0.140876\pi$
$854$	−53.0748	−	53.0748i	−0.0621485	−	0.0621485i
$855$	−213.189	−	142.448i	−0.249344	−	0.166606i
$856$	42.6076	−	214.203i	0.0497752	−	0.250237i
$857$	−449.826	+	300.564i	−0.524885	+	0.350717i	−0.789612	−	0.613606i	$-0.789718\pi$
$857$	−449.826	+	300.564i	−0.524885	+	0.350717i	0.264727	+	0.964323i	$0.414718\pi$
$858$	69.2932	+	167.288i	0.0807613	+	0.194975i
$859$	−756.618	+	313.402i	−0.880813	+	0.364845i	−0.776812	−	0.629733i	$-0.783164\pi$
$859$	−756.618	+	313.402i	−0.880813	+	0.364845i	−0.104001	+	0.994577i	$0.533164\pi$
$860$	76.1404	+	113.952i	0.0885353	+	0.132502i
$861$	65.4748	+	13.0237i	0.0760451	+	0.0151263i
$862$	−551.678	+	825.645i	−0.639998	+	0.957824i
$863$	744.981	−	744.981i	0.863246	−	0.863246i	−0.128468	−	0.991714i	$-0.541006\pi$
$863$	744.981	−	744.981i	0.863246	−	0.863246i	0.991714	+	0.128468i	$0.0410060\pi$
$864$	−56.6363	+	11.2657i	−0.0655513	+	0.0130390i
$865$	152.228	−	367.510i	0.175986	−	0.424867i
$866$			1109.90i			1.28164i
$867$	154.191	−	64.1282i	0.177844	−	0.0739656i
$868$	75.6027			0.0870999
$869$	−1481.18	−	613.525i	−1.70446	−	0.706012i
$870$	−9.64750	−	48.5013i	−0.0110891	−	0.0557486i
$871$	625.553	+	625.553i	0.718201	+	0.718201i
$872$	−130.664	−	87.3068i	−0.149844	−	0.100122i
$873$	−67.9375	+	341.545i	−0.0778208	+	0.391231i
$874$	−640.980	+	428.289i	−0.733387	+	0.490034i
$875$	−54.4149	−	131.369i	−0.0621885	−	0.150136i
$876$	−131.381	+	54.4196i	−0.149978	+	0.0621228i
$877$	288.717	+	432.095i	0.329210	+	0.492697i	0.958742	−	0.284277i	$-0.0917536\pi$
$877$	288.717	+	432.095i	0.329210	+	0.492697i	−0.629533	+	0.776974i	$0.716754\pi$
$878$	−88.3700	−	17.5779i	−0.100649	−	0.0200204i
$879$	−37.9295	+	56.7655i	−0.0431508	+	0.0645797i
$880$	90.1433	−	90.1433i	0.102436	−	0.102436i
$881$	−807.153	+	160.553i	−0.916179	+	0.182239i	−0.630593	−	0.776114i	$-0.717188\pi$
$881$	−807.153	+	160.553i	−0.916179	+	0.182239i	−0.285586	+	0.958353i	$0.592188\pi$
$882$	−528.809	+	1276.66i	−0.599556	+	1.44746i
$883$		−	897.351i		−	1.01625i	−0.861283	−	0.508126i	$-0.830338\pi$
$883$		−	897.351i		−	1.01625i	0.861283	−	0.508126i	$-0.169662\pi$
$884$	−408.834	−	335.030i	−0.462482	−	0.378993i
$885$	28.4117			0.0321036
$886$	−422.695	−	175.086i	−0.477083	−	0.197614i
$887$	−108.989	−	547.927i	−0.122874	−	0.617731i	−0.992319	−	0.123701i	$-0.960524\pi$
$887$	−108.989	−	547.927i	−0.122874	−	0.617731i	0.869445	−	0.494029i	$-0.164476\pi$
$888$	−3.48199	−	3.48199i	−0.00392116	−	0.00392116i
$889$	1872.91	+	1251.44i	2.10676	+	1.40769i
$890$	59.2667	−	297.954i	0.0665918	−	0.334780i
$891$	−854.403	+	570.894i	−0.958926	+	0.640734i
$892$	−46.2125	−	111.567i	−0.0518077	−	0.125075i
$893$	−576.457	+	238.776i	−0.645529	+	0.267387i
$894$	−40.0321	−	59.9122i	−0.0447786	−	0.0670159i
$895$	574.775	+	114.330i	0.642206	+	0.127743i
$896$	−79.9406	+	119.640i	−0.0892194	+	0.133526i
$897$	−261.692	+	261.692i	−0.291742	+	0.291742i
$898$	−136.050	+	27.0621i	−0.151504	+	0.0301360i
$899$	30.7820	−	74.3144i	0.0342403	−	0.0826634i
$900$			86.6610i			0.0962900i
$901$	−557.517	−	1041.24i	−0.618776	−	1.15565i
$902$	183.101			0.202994
$903$	208.068	+	86.1845i	0.230419	+	0.0954425i
$904$	−61.7437	−	310.407i	−0.0683006	−	0.343370i
$905$	24.7670	+	24.7670i	0.0273668	+	0.0273668i
$906$	−92.0976	−	61.5377i	−0.101653	−	0.0679224i
$907$	51.1508	−	257.153i	0.0563956	−	0.283520i	−0.942289	−	0.334802i	$-0.891331\pi$
$907$	51.1508	−	257.153i	0.0563956	−	0.283520i	0.998684	+	0.0512818i	$0.0163307\pi$
$908$	−636.825	+	425.513i	−0.701349	+	0.468626i
$909$	629.960	+	1520.86i	0.693026	+	1.67311i
$910$	−577.651	+	239.271i	−0.634781	+	0.262935i
$911$	399.647	+	598.115i	0.438691	+	0.656547i	0.983268	−	0.182163i	$-0.0583100\pi$
$911$	399.647	+	598.115i	0.438691	+	0.656547i	−0.544577	+	0.838711i	$0.683310\pi$
$912$	−29.9950	−	5.96638i	−0.0328893	−	0.00654208i
$913$	552.108	−	826.288i	0.604719	−	0.905025i
$914$	−367.527	+	367.527i	−0.402109	+	0.402109i
$915$	−5.28846	+	1.05194i	−0.00577974	+	0.00114966i
$916$	50.1722	−	121.126i	0.0547731	−	0.132234i
$917$		−	1261.43i		−	1.37561i
$918$	−115.534	+	216.524i	−0.125855	+	0.235865i
$919$	−151.437			−0.164785			−0.0823924	−	0.996600i	$-0.526256\pi$
$919$	−151.437			−0.164785			−0.0823924	+	0.996600i	$0.526256\pi$
$920$	240.724	+	99.7110i	0.261656	+	0.108382i
$921$	55.6015	+	279.528i	0.0603708	+	0.303505i
$922$	−270.855	−	270.855i	−0.293769	−	0.293769i
$923$	−219.658	−	146.771i	−0.237983	−	0.159015i
$924$	40.8694	−	205.464i	0.0442309	−	0.222364i
$925$	−12.5259	+	8.36952i	−0.0135415	+	0.00904813i
$926$	−274.798	−	663.420i	−0.296758	−	0.716437i
$927$	−1234.94	+	511.531i	−1.33219	+	0.551813i
$928$	85.0526	+	127.290i	0.0916515	+	0.137166i
$929$	413.291	+	82.2086i	0.444877	+	0.0884915i	0.412445	−	0.910982i	$-0.364675\pi$
$929$	413.291	+	82.2086i	0.444877	+	0.0884915i	0.0324317	+	0.999474i	$0.489675\pi$
$930$	3.01737	−	4.51581i	0.00324448	−	0.00485571i
$931$	−1054.91	+	1054.91i	−1.13309	+	1.13309i
$932$	−589.339	+	117.227i	−0.632338	+	0.125780i
$933$	74.8570	−	180.721i	0.0802326	−	0.193699i
$934$			160.505i			0.171846i
$935$	−53.4935	−	539.151i	−0.0572123	−	0.576632i
$936$	381.062			0.407118
$937$	744.800	+	308.506i	0.794877	+	0.329249i	0.742903	−	0.669399i	$-0.233449\pi$
$937$	744.800	+	308.506i	0.794877	+	0.329249i	0.0519746	+	0.998648i	$0.483449\pi$
$938$	−199.676	−	1003.84i	−0.212875	−	1.07019i
$939$	−6.15324	−	6.15324i	−0.00655297	−	0.00655297i
$940$	175.349	+	117.164i	0.186542	+	0.124643i
$941$	307.864	−	1547.74i	0.327167	−	1.64478i	−0.370847	−	0.928694i	$-0.620932\pi$
$941$	307.864	−	1547.74i	0.327167	−	1.64478i	0.698014	−	0.716085i	$-0.254068\pi$
$942$	−137.560	+	91.9144i	−0.146029	+	0.0975737i
$943$	143.214	+	345.749i	0.151870	+	0.366647i
$944$	−81.2610	+	33.6594i	−0.0860815	+	0.0356561i
$945$	161.285	+	241.380i	0.170672	+	0.255428i
$946$	605.834	+	120.508i	0.640416	+	0.127387i
$947$	220.607	−	330.162i	0.232954	−	0.348640i	−0.696514	−	0.717543i	$-0.745267\pi$
$947$	220.607	−	330.162i	0.232954	−	0.348640i	0.929468	+	0.368903i	$0.120267\pi$
$948$	91.9199	−	91.9199i	0.0969619	−	0.0969619i
$949$	1876.21	−	373.201i	1.97704	−	0.393257i
$950$	−35.8042	+	86.4391i	−0.0376887	+	0.0909885i
$951$			244.670i			0.257277i
$952$	177.939	+	585.069i	0.186910	+	0.614568i
$953$	1064.06			1.11654			0.558268	−	0.829661i	$-0.311466\pi$
$953$	1064.06			1.11654			0.558268	+	0.829661i	$0.311466\pi$
$954$	786.670	+	325.849i	0.824601	+	0.341561i
$955$	37.1294	+	186.662i	0.0388789	+	0.195457i
$956$	−292.176	−	292.176i	−0.305623	−	0.305623i
$957$	−185.323	−	123.829i	−0.193650	−	0.129393i
$958$	2.50689	−	12.6030i	0.00261680	−	0.0131555i
$959$	−1413.12	+	944.213i	−1.47353	+	0.984581i
$960$	3.95567	+	9.54983i	0.00412049	+	0.00994774i
$961$	−879.686	+	364.378i	−0.915387	+	0.379166i
$962$	36.8021	+	55.0782i	0.0382558	+	0.0572539i
$963$	656.302	+	130.547i	0.681518	+	0.135562i
$964$	−179.084	+	268.018i	−0.185772	+	0.278027i
$965$	−479.191	+	479.191i	−0.496571	+	0.496571i
$966$	419.944	−	83.5320i	0.434724	−	0.0864721i
$967$	383.845	−	926.684i	0.396944	−	0.958308i	−0.591442	−	0.806347i	$-0.701441\pi$
$967$	383.845	−	926.684i	0.396944	−	0.958308i	0.988387	−	0.151961i	$-0.0485587\pi$
$968$		−	232.342i		−	0.240023i
$969$	−100.414	+	82.5284i	−0.103626	+	0.0851686i
$970$	127.072			0.131002
$971$	186.282	+	77.1604i	0.191845	+	0.0794649i	0.476538	−	0.879154i	$-0.341892\pi$
$971$	186.282	+	77.1604i	0.191845	+	0.0794649i	−0.284693	+	0.958619i	$0.591892\pi$
$972$	−52.1020	−	261.935i	−0.0536029	−	0.269480i
$973$	−68.6894	−	68.6894i	−0.0705955	−	0.0705955i
$974$	−4.51836	−	3.01907i	−0.00463898	−	0.00309966i
$975$	−8.76270	+	44.0531i	−0.00898738	+	0.0451826i
$976$	13.8794	−	9.27393i	0.0142207	−	0.00950198i
$977$	442.276	+	1067.75i	0.452688	+	1.09288i	0.971296	+	0.237873i	$0.0764502\pi$
$977$	442.276	+	1067.75i	0.452688	+	1.09288i	−0.518609	+	0.855012i	$0.673550\pi$
$978$	−58.7273	+	24.3256i	−0.0600483	+	0.0248728i
$979$	−760.707	−	1138.48i	−0.777025	−	1.16290i
$980$	494.548	+	98.3718i	0.504641	+	0.100379i
$981$	267.502	−	400.345i	0.272683	−	0.408099i
$982$	−146.256	+	146.256i	−0.148936	+	0.148936i
$983$	−1366.27	+	271.768i	−1.38990	+	0.276468i	−0.832614	−	0.553854i	$-0.813156\pi$
$983$	−1366.27	+	271.768i	−1.38990	+	0.276468i	−0.557284	+	0.830322i	$0.688156\pi$
$984$	−5.68148	+	13.7163i	−0.00577386	+	0.0139393i
$985$		−	805.291i		−	0.817554i
$986$	647.548	+	63.3074i	0.656742	+	0.0642063i
$987$	346.554			0.351118
$988$	380.086	+	157.437i	0.384703	+	0.159349i
$989$	246.303	+	1238.25i	0.249043	+	1.25202i
$990$	276.193	+	276.193i	0.278983	+	0.278983i
$991$	−1245.17	−	831.997i	−1.25648	−	0.839553i	−0.264309	−	0.964438i	$-0.585144\pi$
$991$	−1245.17	−	831.997i	−1.25648	−	0.839553i	−0.992171	+	0.124885i	$0.960144\pi$
$992$	−3.28016	+	16.4905i	−0.00330661	+	0.0166235i
$993$	−127.718	+	85.3386i	−0.128619	+	0.0859401i
$994$	116.964	+	282.376i	0.117670	+	0.284081i
$995$	122.799	−	50.8648i	0.123416	−	0.0511204i
$996$	44.7668	+	66.9982i	0.0449466	+	0.0672673i
$997$	461.721	+	91.8420i	0.463110	+	0.0921183i	0.421130	−	0.907000i	$-0.361633\pi$
$997$	461.721	+	91.8420i	0.463110	+	0.0921183i	0.0419798	+	0.999118i	$0.486633\pi$
$998$	−224.155	+	335.472i	−0.224604	+	0.336144i
$999$	21.7482	−	21.7482i	0.0217699	−	0.0217699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.3.p.a.11.4	✓	48
17.14	odd	16	inner	170.3.p.a.31.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.p.a.11.4	✓	48	1.1	even	1	trivial
170.3.p.a.31.4	yes	48	17.14	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30656 - 0.541196i) q^{2} +(-0.112730 - 0.566734i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.85922 + 1.24229i) q^{5} +(-0.159425 + 0.801483i) q^{6} +(-10.5747 + 7.06582i) q^{7} +(-1.08239 - 2.61313i) q^{8} +(8.00644 - 3.31637i) q^{9} +O(q^{10})\)	\(q+(-1.30656 - 0.541196i) q^{2} +(-0.112730 - 0.566734i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.85922 + 1.24229i) q^{5} +(-0.159425 + 0.801483i) q^{6} +(-10.5747 + 7.06582i) q^{7} +(-1.08239 - 2.61313i) q^{8} +(8.00644 - 3.31637i) q^{9} +(-1.75687 - 2.62934i) q^{10} +(-13.9790 - 2.78060i) q^{11} +(0.642058 - 0.960908i) q^{12} +(-10.9929 + 10.9929i) q^{13} +(17.6406 - 3.50892i) q^{14} +(0.494459 - 1.19373i) q^{15} +4.00000i q^{16} +(13.1489 + 10.7752i) q^{17} -12.2557 q^{18} +(-12.2243 - 5.06349i) q^{19} +(0.872470 + 4.38621i) q^{20} +(5.19653 + 5.19653i) q^{21} +(16.7596 + 11.1984i) q^{22} +(-8.03728 + 40.4061i) q^{23} +(-1.35893 + 0.908007i) q^{24} +(1.91342 + 4.61940i) q^{25} +(20.3122 - 8.41359i) q^{26} +(-5.67133 - 8.48775i) q^{27} +(-24.9475 - 4.96237i) q^{28} +(-15.0353 + 22.5019i) q^{29} +(-1.29208 + 1.29208i) q^{30} +(-2.91513 + 0.579856i) q^{31} +(2.16478 - 5.22625i) q^{32} +8.23586i q^{33} +(-11.3484 - 21.1947i) q^{34} -28.4386 q^{35} +(16.0129 + 6.63275i) q^{36} +(0.587797 + 2.95506i) q^{37} +(13.2315 + 13.2315i) q^{38} +(7.46928 + 4.99081i) q^{39} +(1.23386 - 6.20303i) q^{40} +(7.55297 - 5.04673i) q^{41} +(-3.97725 - 9.60194i) q^{42} +(28.3124 - 11.7274i) q^{43} +(-15.8370 - 23.7017i) q^{44} +(19.0057 + 3.78046i) q^{45} +(32.3689 - 48.4434i) q^{46} +(33.3447 - 33.3447i) q^{47} +(2.26694 - 0.450922i) q^{48} +(43.1479 - 104.168i) q^{49} -7.07107i q^{50} +(4.62440 - 8.66665i) q^{51} -31.0926 q^{52} +(-64.1880 - 26.5875i) q^{53} +(2.81642 + 14.1591i) q^{54} +(-22.5358 - 22.5358i) q^{55} +(29.9099 + 19.9851i) q^{56} +(-1.49160 + 7.49876i) q^{57} +(31.8226 - 21.2631i) q^{58} +(8.41485 + 20.3152i) q^{59} +(2.38746 - 0.988918i) q^{60} +(-2.31848 - 3.46985i) q^{61} +(4.12262 + 0.820040i) q^{62} +(-61.2331 + 91.6418i) q^{63} +(-5.65685 + 5.65685i) q^{64} +(-34.0946 + 6.78184i) q^{65} +(4.45721 - 10.7607i) q^{66} -56.9053i q^{67} +(3.35693 + 33.8339i) q^{68} +23.8056 q^{69} +(37.1568 + 15.3909i) q^{70} +(3.31520 + 16.6666i) q^{71} +(-17.3322 - 17.3322i) q^{72} +(-102.312 - 68.3627i) q^{73} +(0.831271 - 4.17908i) q^{74} +(2.40227 - 1.60515i) q^{75} +(-10.1270 - 24.4487i) q^{76} +(167.472 - 69.3692i) q^{77} +(-7.05807 - 10.5632i) q^{78} +(110.322 + 21.9444i) q^{79} +(-4.96917 + 7.43689i) q^{80} +(50.9798 - 50.9798i) q^{81} +(-12.5997 + 2.50624i) q^{82} +(-26.6822 + 64.4165i) q^{83} +14.6980i q^{84} +(11.0608 + 36.3684i) q^{85} -43.3387 q^{86} +(14.4476 + 5.98437i) q^{87} +(7.86474 + 39.5387i) q^{88} +(67.9298 + 67.9298i) q^{89} +(-22.7861 - 15.2252i) q^{90} +(38.5732 - 193.921i) q^{91} +(-68.5094 + 45.7765i) q^{92} +(0.657248 + 1.58674i) q^{93} +(-61.6130 + 25.5209i) q^{94} +(-16.4374 - 24.6003i) q^{95} +(-3.20593 - 0.637700i) q^{96} +(-22.3249 + 33.4115i) q^{97} +(-112.751 + 112.751i) q^{98} +(-121.144 + 24.0970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{3} + 16 q^{6} - 16 q^{7} + 32 q^{9}+O(q^{10}) \) 48 * q - 16 * q^3 + 16 * q^6 - 16 * q^7 + 32 * q^9	\( 48 q - 16 q^{3} + 16 q^{6} - 16 q^{7} + 32 q^{9} + 48 q^{11} + 32 q^{12} - 48 q^{13} + 32 q^{14} - 16 q^{17} - 32 q^{18} - 128 q^{19} + 160 q^{21} - 144 q^{22} - 48 q^{23} - 64 q^{24} - 64 q^{27} + 144 q^{31} - 48 q^{34} + 64 q^{36} + 128 q^{37} + 96 q^{38} - 352 q^{39} + 240 q^{41} - 160 q^{42} + 96 q^{43} + 160 q^{45} + 160 q^{46} - 48 q^{47} + 64 q^{48} + 32 q^{49} + 192 q^{51} + 64 q^{53} + 112 q^{54} - 80 q^{55} + 176 q^{57} - 256 q^{58} - 160 q^{60} - 352 q^{61} + 192 q^{62} - 832 q^{63} - 400 q^{65} - 208 q^{66} + 64 q^{69} - 80 q^{70} + 16 q^{71} + 288 q^{72} - 192 q^{73} + 160 q^{74} + 160 q^{76} + 32 q^{77} - 160 q^{78} + 384 q^{79} - 256 q^{81} - 320 q^{82} + 144 q^{83} - 160 q^{85} - 32 q^{86} + 960 q^{87} + 64 q^{88} + 1056 q^{89} - 160 q^{90} - 544 q^{91} - 128 q^{92} + 176 q^{94} - 64 q^{96} + 96 q^{97} - 432 q^{98} - 992 q^{99}+O(q^{100}) \) 48 * q - 16 * q^3 + 16 * q^6 - 16 * q^7 + 32 * q^9 + 48 * q^11 + 32 * q^12 - 48 * q^13 + 32 * q^14 - 16 * q^17 - 32 * q^18 - 128 * q^19 + 160 * q^21 - 144 * q^22 - 48 * q^23 - 64 * q^24 - 64 * q^27 + 144 * q^31 - 48 * q^34 + 64 * q^36 + 128 * q^37 + 96 * q^38 - 352 * q^39 + 240 * q^41 - 160 * q^42 + 96 * q^43 + 160 * q^45 + 160 * q^46 - 48 * q^47 + 64 * q^48 + 32 * q^49 + 192 * q^51 + 64 * q^53 + 112 * q^54 - 80 * q^55 + 176 * q^57 - 256 * q^58 - 160 * q^60 - 352 * q^61 + 192 * q^62 - 832 * q^63 - 400 * q^65 - 208 * q^66 + 64 * q^69 - 80 * q^70 + 16 * q^71 + 288 * q^72 - 192 * q^73 + 160 * q^74 + 160 * q^76 + 32 * q^77 - 160 * q^78 + 384 * q^79 - 256 * q^81 - 320 * q^82 + 144 * q^83 - 160 * q^85 - 32 * q^86 + 960 * q^87 + 64 * q^88 + 1056 * q^89 - 160 * q^90 - 544 * q^91 - 128 * q^92 + 176 * q^94 - 64 * q^96 + 96 * q^97 - 432 * q^98 - 992 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more