LMFDB - Embedded newform 210.3.p.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(19,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("210.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.p (of order $6$, 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 $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	210.19
Dual form			210.3.p.a.199.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.95025 + 4.60397i) q^{5} -2.44949i q^{6} +(-2.31437 + 6.60634i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.95025 + 4.60397i) q^{5} -2.44949i q^{6} +(-2.31437 + 6.60634i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-0.866933 + 7.01772i) q^{10} +(-0.676822 - 1.17229i) q^{11} +(1.73205 - 3.00000i) q^{12} -5.90570 q^{13} +(-7.50590 + 6.45457i) q^{14} +(5.21698 - 6.91253i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(6.21669 + 10.7676i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(27.5764 + 15.9212i) q^{19} +(-6.02405 + 7.98190i) q^{20} +(11.9138 - 2.24971i) q^{21} -1.91434i q^{22} +(-1.31291 - 0.758007i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-17.3930 + 17.9578i) q^{25} +(-7.23297 - 4.17596i) q^{26} +5.19615 q^{27} +(-13.7569 + 2.59774i) q^{28} -15.0401 q^{29} +(11.2774 - 4.77713i) q^{30} +(40.3078 - 23.2717i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-1.17229 + 2.03047i) q^{33} +17.5835i q^{34} +(-34.9290 + 2.22876i) q^{35} -6.00000 q^{36} +(-0.441269 - 0.254767i) q^{37} +(22.5160 + 38.9989i) q^{38} +(5.11448 + 8.85855i) q^{39} +(-13.0220 + 5.51615i) q^{40} -36.0723i q^{41} +(16.1822 + 5.66902i) q^{42} -67.6102i q^{43} +(1.35364 - 2.34458i) q^{44} +(-14.8868 - 1.83904i) q^{45} +(-1.07198 - 1.85673i) q^{46} +(24.7767 - 42.9145i) q^{47} +6.92820 q^{48} +(-38.2874 - 30.5790i) q^{49} +(-34.0001 + 9.69500i) q^{50} +(10.7676 - 18.6501i) q^{51} +(-5.90570 - 10.2290i) q^{52} +(-45.5850 + 26.3185i) q^{53} +(6.36396 + 3.67423i) q^{54} +(4.07721 - 5.40233i) q^{55} +(-18.6855 - 6.54602i) q^{56} -55.1527i q^{57} +(-18.4203 - 10.6350i) q^{58} +(-62.0731 + 35.8379i) q^{59} +(17.1898 + 2.12354i) q^{60} +(50.6801 + 29.2602i) q^{61} +65.8224 q^{62} +(-13.6922 - 15.9224i) q^{63} -8.00000 q^{64} +(-11.5176 - 27.1896i) q^{65} +(-2.87151 + 1.65787i) q^{66} +(109.299 - 63.1041i) q^{67} +(-12.4334 + 21.5353i) q^{68} +2.62581i q^{69} +(-44.3550 - 21.9688i) q^{70} -55.4750 q^{71} +(-7.34847 - 4.24264i) q^{72} +(26.5796 + 46.0373i) q^{73} +(-0.360295 - 0.624048i) q^{74} +(41.9995 + 10.5376i) q^{75} +63.6849i q^{76} +(9.31097 - 1.75821i) q^{77} +14.4659i q^{78} +(19.9706 - 34.5901i) q^{79} +(-19.8491 - 2.45206i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(25.5069 - 44.1793i) q^{82} +120.455 q^{83} +(15.8104 + 18.3856i) q^{84} +(-37.4497 + 49.6211i) q^{85} +(47.8076 - 82.8052i) q^{86} +(13.0252 + 22.5602i) q^{87} +(3.31574 - 1.91434i) q^{88} +(-5.68455 - 3.28198i) q^{89} +(-16.9322 - 12.7789i) q^{90} +(13.6680 - 39.0150i) q^{91} -3.03203i q^{92} +(-69.8152 - 40.3078i) q^{93} +(60.6903 - 35.0395i) q^{94} +(-19.5199 + 158.011i) q^{95} +(8.48528 + 4.89898i) q^{96} +154.334 q^{97} +(-25.2697 - 64.5247i) q^{98} +4.06093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	1.95025	+	4.60397i	0.390051	+	0.920793i
$5$	1.95025	+	4.60397i	0.390051	+	0.920793i
$6$		−	2.44949i		−	0.408248i
$7$	−2.31437	+	6.60634i	−0.330624	+	0.943763i
$7$	−2.31437	+	6.60634i	−0.330624	+	0.943763i
$8$			2.82843i			0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	−0.866933	+	7.01772i	−0.0866933	+	0.701772i
$11$	−0.676822	−	1.17229i	−0.0615293	−	0.106572i	0.833620	−	0.552339i	$-0.186264\pi$
$11$	−0.676822	−	1.17229i	−0.0615293	−	0.106572i	−0.895149	+	0.445767i	$0.852931\pi$
$12$	1.73205	−	3.00000i	0.144338	−	0.250000i
$13$	−5.90570			−0.454284			−0.227142	−	0.973862i	$-0.572938\pi$
$13$	−5.90570			−0.454284			−0.227142	+	0.973862i	$0.572938\pi$
$14$	−7.50590	+	6.45457i	−0.536135	+	0.461041i
$15$	5.21698	−	6.91253i	0.347799	−	0.460835i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	6.21669	+	10.7676i	0.365688	+	0.633390i	0.988886	−	0.148674i	$-0.0475004\pi$
$17$	6.21669	+	10.7676i	0.365688	+	0.633390i	−0.623198	+	0.782064i	$0.714167\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	27.5764	+	15.9212i	1.45139	+	0.837959i	0.998560	−	0.0536396i	$-0.0170822\pi$
$19$	27.5764	+	15.9212i	1.45139	+	0.837959i	0.452827	+	0.891598i	$0.350416\pi$
$20$	−6.02405	+	7.98190i	−0.301203	+	0.399095i
$21$	11.9138	−	2.24971i	0.567324	−	0.107129i
$22$		−	1.91434i		−	0.0870156i
$23$	−1.31291	−	0.758007i	−0.0570829	−	0.0329568i	0.471187	−	0.882033i	$-0.343826\pi$
$23$	−1.31291	−	0.758007i	−0.0570829	−	0.0329568i	−0.528270	+	0.849077i	$0.677159\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$	−17.3930	+	17.9578i	−0.695721	+	0.718312i
$26$	−7.23297	−	4.17596i	−0.278191	−	0.160614i
$27$	5.19615			0.192450
$28$	−13.7569	+	2.59774i	−0.491317	+	0.0927763i
$29$	−15.0401			−0.518626			−0.259313	−	0.965793i	$-0.583496\pi$
$29$	−15.0401			−0.518626			−0.259313	+	0.965793i	$0.583496\pi$
$30$	11.2774	−	4.77713i	0.375912	−	0.159238i
$31$	40.3078	−	23.2717i	1.30025	−	0.750701i	0.319805	−	0.947484i	$-0.396383\pi$
$31$	40.3078	−	23.2717i	1.30025	−	0.750701i	0.980447	+	0.196783i	$0.0630494\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	−1.17229	+	2.03047i	−0.0355240	+	0.0615293i
$34$			17.5835i			0.517161i
$35$	−34.9290	+	2.22876i	−0.997970	+	0.0636790i
$36$	−6.00000			−0.166667
$37$	−0.441269	−	0.254767i	−0.0119262	−	0.00688559i	0.494025	−	0.869448i	$-0.335525\pi$
$37$	−0.441269	−	0.254767i	−0.0119262	−	0.00688559i	−0.505951	+	0.862562i	$0.668858\pi$
$38$	22.5160	+	38.9989i	0.592526	+	1.02629i
$39$	5.11448	+	8.85855i	0.131141	+	0.227142i
$40$	−13.0220	+	5.51615i	−0.325550	+	0.137904i
$41$		−	36.0723i		−	0.879811i	−0.898044	−	0.439906i	$-0.855012\pi$
$41$		−	36.0723i		−	0.879811i	0.898044	−	0.439906i	$-0.144988\pi$
$42$	16.1822	+	5.66902i	0.385289	+	0.134977i
$43$		−	67.6102i		−	1.57233i	−0.618017	−	0.786165i	$-0.712064\pi$
$43$		−	67.6102i		−	1.57233i	0.618017	−	0.786165i	$-0.287936\pi$
$44$	1.35364	−	2.34458i	0.0307647	−	0.0532860i
$45$	−14.8868	−	1.83904i	−0.330819	−	0.0408676i
$46$	−1.07198	−	1.85673i	−0.0233040	−	0.0403637i
$47$	24.7767	−	42.9145i	0.527164	−	0.913074i	−0.472335	−	0.881419i	$-0.656589\pi$
$47$	24.7767	−	42.9145i	0.527164	−	0.913074i	0.999499	−	0.0316553i	$-0.0100779\pi$
$48$	6.92820			0.144338
$49$	−38.2874	−	30.5790i	−0.781376	−	0.624061i
$50$	−34.0001	+	9.69500i	−0.680002	+	0.193900i
$51$	10.7676	−	18.6501i	0.211130	−	0.365688i
$52$	−5.90570	−	10.2290i	−0.113571	−	0.196711i
$53$	−45.5850	+	26.3185i	−0.860095	+	0.496576i	−0.864044	−	0.503416i	$-0.832076\pi$
$53$	−45.5850	+	26.3185i	−0.860095	+	0.496576i	0.00394923	+	0.999992i	$0.498743\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$	4.07721	−	5.40233i	0.0741312	−	0.0982242i
$56$	−18.6855	−	6.54602i	−0.333670	−	0.116893i
$57$		−	55.1527i		−	0.967592i
$58$	−18.4203	−	10.6350i	−0.317592	−	0.183362i
$59$	−62.0731	+	35.8379i	−1.05209	+	0.607422i	−0.923232	−	0.384242i	$-0.874463\pi$
$59$	−62.0731	+	35.8379i	−1.05209	+	0.607422i	−0.128853	+	0.991664i	$0.541130\pi$
$60$	17.1898	+	2.12354i	0.286497	+	0.0353924i
$61$	50.6801	+	29.2602i	0.830822	+	0.479675i	0.854134	−	0.520053i	$-0.174088\pi$
$61$	50.6801	+	29.2602i	0.830822	+	0.479675i	−0.0233124	+	0.999728i	$0.507421\pi$
$62$	65.8224			1.06165
$63$	−13.6922	−	15.9224i	−0.217337	−	0.252737i
$64$	−8.00000			−0.125000
$65$	−11.5176	−	27.1896i	−0.177194	−	0.418302i
$66$	−2.87151	+	1.65787i	−0.0435078	+	0.0251192i
$67$	109.299	−	63.1041i	1.63134	−	0.941852i	0.647654	−	0.761935i	$-0.275750\pi$
$67$	109.299	−	63.1041i	1.63134	−	0.941852i	0.983682	−	0.179917i	$-0.0575830\pi$
$68$	−12.4334	+	21.5353i	−0.182844	+	0.316695i
$69$			2.62581i			0.0380553i
$70$	−44.3550	−	21.9688i	−0.633643	−	0.313841i
$71$	−55.4750			−0.781337			−0.390669	−	0.920531i	$-0.627756\pi$
$71$	−55.4750			−0.781337			−0.390669	+	0.920531i	$0.627756\pi$
$72$	−7.34847	−	4.24264i	−0.102062	−	0.0589256i
$73$	26.5796	+	46.0373i	0.364105	+	0.630648i	0.988632	−	0.150355i	$-0.0480417\pi$
$73$	26.5796	+	46.0373i	0.364105	+	0.630648i	−0.624527	+	0.781003i	$0.714708\pi$
$74$	−0.360295	−	0.624048i	−0.00486885	−	0.00843309i
$75$	41.9995	+	10.5376i	0.559993	+	0.140502i
$76$			63.6849i			0.837959i
$77$	9.31097	−	1.75821i	0.120922	−	0.0228339i
$78$			14.4659i			0.185461i
$79$	19.9706	−	34.5901i	0.252792	−	0.437849i	−0.711501	−	0.702685i	$-0.751984\pi$
$79$	19.9706	−	34.5901i	0.252792	−	0.437849i	0.964294	+	0.264836i	$0.0853177\pi$
$80$	−19.8491	−	2.45206i	−0.248114	−	0.0306507i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	25.5069	−	44.1793i	0.311060	−	0.538772i
$83$	120.455			1.45127			0.725635	−	0.688079i	$-0.241546\pi$
$83$	120.455			1.45127			0.725635	+	0.688079i	$0.241546\pi$
$84$	15.8104	+	18.3856i	0.188219	+	0.218876i
$85$	−37.4497	+	49.6211i	−0.440585	+	0.583777i
$86$	47.8076	−	82.8052i	0.555902	−	0.962851i
$87$	13.0252	+	22.5602i	0.149714	+	0.259313i
$88$	3.31574	−	1.91434i	0.0376789	−	0.0217539i
$89$	−5.68455	−	3.28198i	−0.0638714	−	0.0368761i	0.467724	−	0.883874i	$-0.345074\pi$
$89$	−5.68455	−	3.28198i	−0.0638714	−	0.0368761i	−0.531596	+	0.846998i	$0.678407\pi$
$90$	−16.9322	−	12.7789i	−0.188135	−	0.141988i
$91$	13.6680	−	39.0150i	0.150197	−	0.428737i
$92$		−	3.03203i		−	0.0329568i
$93$	−69.8152	−	40.3078i	−0.750701	−	0.433417i
$94$	60.6903	−	35.0395i	0.645641	−	0.372761i
$95$	−19.5199	+	158.011i	−0.205472	+	1.66327i
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$	154.334			1.59107			0.795536	−	0.605906i	$-0.207189\pi$
$97$	154.334			1.59107			0.795536	+	0.605906i	$0.207189\pi$
$98$	−25.2697	−	64.5247i	−0.257854	−	0.658416i
$99$	4.06093			0.0410195
$100$	−48.4969	−	12.1678i	−0.484969	−	0.121678i
$101$	−132.684	+	76.6052i	−1.31370	+	0.758467i	−0.982707	−	0.185165i	$-0.940718\pi$
$101$	−132.684	+	76.6052i	−1.31370	+	0.758467i	−0.330996	+	0.943632i	$0.607385\pi$
$102$	26.3752	−	15.2277i	0.258580	−	0.149291i
$103$	−8.66031	+	15.0001i	−0.0840806	+	0.145632i	−0.904999	−	0.425413i	$-0.860129\pi$
$103$	−8.66031	+	15.0001i	−0.0840806	+	0.145632i	0.820918	+	0.571045i	$0.193462\pi$
$104$		−	16.7038i		−	0.160614i
$105$	33.5925	+	50.4633i	0.319929	+	0.480603i
$106$	−74.4400			−0.702264
$107$	−79.1146	−	45.6768i	−0.739388	−	0.426886i	0.0824585	−	0.996594i	$-0.473723\pi$
$107$	−79.1146	−	45.6768i	−0.739388	−	0.426886i	−0.821847	+	0.569708i	$0.807056\pi$
$108$	5.19615	+	9.00000i	0.0481125	+	0.0833333i
$109$	−49.5239	−	85.7779i	−0.454347	−	0.786953i	0.544303	−	0.838889i	$-0.316794\pi$
$109$	−49.5239	−	85.7779i	−0.454347	−	0.786953i	−0.998650	+	0.0519359i	$0.983461\pi$
$110$	8.81357	−	3.73345i	0.0801234	−	0.0339405i
$111$			0.882538i			0.00795079i
$112$	−18.2563	−	21.2299i	−0.163003	−	0.189552i
$113$			96.7492i			0.856187i	0.903734	+	0.428094i	$0.140815\pi$
$113$			96.7492i			0.856187i	−0.903734	+	0.428094i	$0.859185\pi$
$114$	38.9989	−	67.5480i	0.342095	−	0.592526i
$115$	0.929339	−	7.52288i	0.00808120	−	0.0654164i
$116$	−15.0401	−	26.0503i	−0.129656	−	0.224572i
$117$	8.85855	−	15.3435i	0.0757141	−	0.131141i
$118$	−101.365			−0.859024
$119$	−85.5223	+	16.1493i	−0.718675	+	0.135709i
$120$	19.5516	+	14.7559i	0.162930	+	0.122965i
$121$	59.5838	−	103.202i	0.492428	−	0.852911i
$122$	41.3801	+	71.6725i	0.339181	+	0.587480i
$123$	−54.1084	+	31.2395i	−0.439906	+	0.253980i
$124$	80.6156	+	46.5434i	0.650126	+	0.375350i
$125$	−116.598	−	45.0546i	−0.932784	−	0.360437i
$126$	−5.51063	−	29.1828i	−0.0437352	−	0.231609i
$127$			54.9283i			0.432506i	0.976337	+	0.216253i	$0.0693836\pi$
$127$			54.9283i			0.432506i	−0.976337	+	0.216253i	$0.930616\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	−101.415	+	58.5521i	−0.786165	+	0.453892i
$130$	5.11985	−	41.4445i	0.0393834	−	0.318804i
$131$	108.556	+	62.6747i	0.828670	+	0.478433i	0.853397	−	0.521262i	$-0.174538\pi$
$131$	108.556	+	62.6747i	0.828670	+	0.478433i	−0.0247273	+	0.999694i	$0.507872\pi$
$132$	−4.68916			−0.0355240
$133$	−169.003	+	145.331i	−1.27070	+	1.09272i
$134$	178.485			1.33198
$135$	10.1338	+	23.9229i	0.0750653	+	0.177207i
$136$	−30.4555	+	17.5835i	−0.223937	+	0.129290i
$137$	40.2829	−	23.2574i	0.294036	−	0.169762i	−0.345725	−	0.938336i	$-0.612367\pi$
$137$	40.2829	−	23.2574i	0.294036	−	0.169762i	0.639761	+	0.768574i	$0.279033\pi$
$138$	−1.85673	+	3.21595i	−0.0134546	+	0.0233040i
$139$		−	40.5702i		−	0.291872i	−0.989294	−	0.145936i	$-0.953381\pi$
$139$		−	40.5702i		−	0.291872i	0.989294	−	0.145936i	$-0.0466193\pi$
$140$	−38.7893	−	58.2700i	−0.277066	−	0.416214i
$141$	−85.8290			−0.608716
$142$	−67.9427	−	39.2267i	−0.478469	−	0.276244i
$143$	3.99711	+	6.92320i	0.0279518	+	0.0484140i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$	−29.3321	−	69.2443i	−0.202290	−	0.477547i
$146$			75.1786i			0.514922i
$147$	−12.7106	+	83.9133i	−0.0864667	+	0.570839i
$148$		−	1.01907i		−	0.00688559i
$149$	45.7984	−	79.3252i	0.307372	−	0.532384i	−0.670415	−	0.741987i	$-0.733884\pi$
$149$	45.7984	−	79.3252i	0.307372	−	0.532384i	0.977787	+	0.209603i	$0.0672171\pi$
$150$	43.9875	+	42.6040i	0.293250	+	0.284027i
$151$	145.015	+	251.174i	0.960366	+	1.66340i	0.721582	+	0.692329i	$0.243415\pi$
$151$	145.015	+	251.174i	0.960366	+	1.66340i	0.238784	+	0.971073i	$0.423251\pi$
$152$	−45.0320	+	77.9977i	−0.296263	+	0.513143i
$153$	−37.3002			−0.243792
$154$	12.6468	+	4.43049i	0.0821221	+	0.0287694i
$155$	185.753	+	140.190i	1.19840	+	0.904452i
$156$	−10.2290	+	17.7171i	−0.0655703	+	0.113571i
$157$	2.97022	+	5.14457i	0.0189186	+	0.0327679i	0.875330	−	0.483527i	$-0.160644\pi$
$157$	2.97022	+	5.14457i	0.0189186	+	0.0327679i	−0.856411	+	0.516294i	$0.827311\pi$
$158$	48.9178	−	28.2427i	0.309606	−	0.178751i
$159$	78.9556	+	45.5850i	0.496576	+	0.286698i
$160$	−22.5762	−	17.0386i	−0.141101	−	0.106491i
$161$	8.04620	−	6.91920i	0.0499764	−	0.0429764i
$162$		−	12.7279i		−	0.0785674i
$163$	80.5338	+	46.4962i	0.494073	+	0.285253i	0.726262	−	0.687418i	$-0.241256\pi$
$163$	80.5338	+	46.4962i	0.494073	+	0.285253i	−0.232190	+	0.972670i	$0.574589\pi$
$164$	62.4790	−	36.0723i	0.380969	−	0.219953i
$165$	−11.6345	−	1.43726i	−0.0705119	−	0.00871068i
$166$	147.527	+	85.1749i	0.888718	+	0.513102i
$167$	41.4461			0.248180			0.124090	−	0.992271i	$-0.460399\pi$
$167$	41.4461			0.248180			0.124090	+	0.992271i	$0.460399\pi$
$168$	6.36313	+	33.6973i	0.0378758	+	0.200579i
$169$	−134.123			−0.793626
$170$	−80.9537	+	34.2922i	−0.476198	+	0.201719i
$171$	−82.7291	+	47.7637i	−0.483796	+	0.279320i
$172$	117.104	−	67.6102i	0.680839	−	0.393082i
$173$	93.0768	−	161.214i	0.538016	−	0.931872i	−0.460994	−	0.887403i	$-0.652507\pi$
$173$	93.0768	−	161.214i	0.538016	−	0.931872i	0.999011	−	0.0444687i	$-0.0141595\pi$
$174$			36.8407i			0.211728i
$175$	−78.3815	−	156.465i	−0.447894	−	0.894087i
$176$	5.41458			0.0307647
$177$	107.514	+	62.0731i	0.607422	+	0.350695i
$178$	−4.64142	−	8.03917i	−0.0260754	−	0.0451639i
$179$	10.4003	+	18.0139i	0.0581024	+	0.100636i	0.893614	−	0.448837i	$-0.148162\pi$
$179$	10.4003	+	18.0139i	0.0581024	+	0.100636i	−0.835511	+	0.549473i	$0.814828\pi$
$180$	−11.7015	−	27.6238i	−0.0650084	−	0.153466i
$181$			331.793i			1.83311i	0.399910	+	0.916554i	$0.369041\pi$
$181$			331.793i			1.83311i	−0.399910	+	0.916554i	$0.630959\pi$
$182$	44.3276	−	38.1188i	0.243558	−	0.209444i
$183$		−	101.360i		−	0.553881i
$184$	2.14397	−	3.71346i	0.0116520	−	0.0201819i
$185$	0.312351	−	2.52845i	0.00168839	−	0.0136673i
$186$	−57.0038	−	98.7335i	−0.306472	−	0.530826i
$187$	8.41520	−	14.5755i	0.0450011	−	0.0779441i
$188$	99.1068			0.527164
$189$	−12.0258	+	34.3275i	−0.0636286	+	0.181627i
$190$	−135.638	+	179.721i	−0.713882	+	0.945898i
$191$	−1.37480	+	2.38122i	−0.00719789	+	0.0124671i	−0.869602	−	0.493753i	$-0.835625\pi$
$191$	−1.37480	+	2.38122i	−0.00719789	+	0.0124671i	0.862404	+	0.506221i	$0.168958\pi$
$192$	6.92820	+	12.0000i	0.0360844	+	0.0625000i
$193$	−96.4891	+	55.7080i	−0.499943	+	0.288642i	−0.728690	−	0.684844i	$-0.759871\pi$
$193$	−96.4891	+	55.7080i	−0.499943	+	0.288642i	0.228747	+	0.973486i	$0.426537\pi$
$194$	189.020	+	109.131i	0.974329	+	0.562529i
$195$	−30.8099	+	40.8233i	−0.158000	+	0.209350i
$196$	14.6769	−	96.8947i	0.0748824	−	0.494361i
$197$		−	10.4776i		−	0.0531855i	−0.999646	−	0.0265928i	$-0.991534\pi$
$197$		−	10.4776i		−	0.0531855i	0.999646	−	0.0265928i	$-0.00846574\pi$
$198$	4.97361	+	2.87151i	0.0251192	+	0.0145026i
$199$	−318.334	+	183.790i	−1.59967	+	0.923569i	−0.608118	+	0.793846i	$0.708075\pi$
$199$	−318.334	+	183.790i	−1.59967	+	0.923569i	−0.991550	+	0.129723i	$0.958591\pi$
$200$	−50.7923	−	49.1949i	−0.253962	−	0.245975i
$201$	−189.312	−	109.299i	−0.941852	−	0.543779i
$202$	−216.672			−1.07263
$203$	34.8084	−	99.3603i	0.171470	−	0.489460i
$204$	43.0705			0.211130
$205$	166.076	−	70.3500i	0.810124	−	0.343171i
$206$	−21.2133	+	12.2475i	−0.102977	+	0.0594540i
$207$	3.93872	−	2.27402i	0.0190276	−	0.0109856i
$208$	11.8114	−	20.4579i	0.0567856	−	0.0983555i
$209$		−	43.1034i		−	0.206236i
$210$	5.45933	+	85.5581i	0.0259968	+	0.407420i
$211$	42.7117			0.202425			0.101212	−	0.994865i	$-0.467728\pi$
$211$	42.7117			0.202425			0.101212	+	0.994865i	$0.467728\pi$
$212$	−91.1700	−	52.6371i	−0.430047	−	0.248288i
$213$	48.0427	+	83.2124i	0.225553	+	0.390669i
$214$	−64.5968	−	111.885i	−0.301854	−	0.522827i
$215$	311.275	−	131.857i	1.44779	−	0.613288i
$216$			14.6969i			0.0680414i
$217$	60.4538	+	320.146i	0.278589	+	1.47533i
$218$		−	140.075i		−	0.642544i
$219$	46.0373	−	79.7389i	0.210216	−	0.364105i
$220$	13.4343	+	1.65961i	0.0610651	+	0.00754367i
$221$	−36.7139	−	63.5904i	−0.166126	−	0.287739i
$222$	−0.624048	+	1.08088i	−0.00281103	+	0.00486885i
$223$	157.529			0.706407			0.353204	−	0.935546i	$-0.385092\pi$
$223$	157.529			0.706407			0.353204	+	0.935546i	$0.385092\pi$
$224$	−7.34751	−	38.9103i	−0.0328014	−	0.173707i
$225$	−20.5662	−	72.1251i	−0.0914054	−	0.320556i
$226$	−68.4120	+	118.493i	−0.302708	+	0.524305i
$227$	−218.771	−	378.922i	−0.963747	−	1.66926i	−0.712944	−	0.701221i	$-0.752639\pi$
$227$	−218.771	−	378.922i	−0.963747	−	1.66926i	−0.250803	−	0.968038i	$-0.580695\pi$
$228$	95.5273	−	55.1527i	0.418979	−	0.241898i
$229$	−180.452	−	104.184i	−0.787999	−	0.454951i	0.0512586	−	0.998685i	$-0.483677\pi$
$229$	−180.452	−	104.184i	−0.787999	−	0.454951i	−0.839258	+	0.543734i	$0.817010\pi$
$230$	6.45768	−	8.55647i	0.0280769	−	0.0372021i
$231$	−10.7008	−	12.4438i	−0.0463240	−	0.0538693i
$232$		−	42.5400i		−	0.183362i
$233$	−112.593	−	65.0056i	−0.483232	−	0.278994i	0.238530	−	0.971135i	$-0.423334\pi$
$233$	−112.593	−	65.0056i	−0.483232	−	0.278994i	−0.721762	+	0.692141i	$0.756668\pi$
$234$	21.6989	−	12.5279i	0.0927304	−	0.0535379i
$235$	245.898	+	30.3769i	1.04637	+	0.129264i
$236$	−124.146	−	71.6758i	−0.526043	−	0.303711i
$237$	−69.1802			−0.291900
$238$	−116.162	−	40.6946i	−0.488077	−	0.170986i
$239$	339.124			1.41893			0.709464	−	0.704742i	$-0.248937\pi$
$239$	339.124			1.41893			0.709464	+	0.704742i	$0.248937\pi$
$240$	13.5118	+	31.8972i	0.0562990	+	0.132905i
$241$	263.990	−	152.415i	1.09539	−	0.632426i	0.160386	−	0.987054i	$-0.448726\pi$
$241$	263.990	−	152.415i	1.09539	−	0.632426i	0.935007	+	0.354628i	$0.115393\pi$
$242$	145.950	−	84.2643i	0.603099	−	0.348199i
$243$	−7.79423	+	13.5000i	−0.0320750	+	0.0555556i
$244$			117.041i			0.479675i
$245$	66.1145	−	235.911i	0.269855	−	0.962901i
$246$	−88.3586			−0.359181
$247$	−162.858	−	94.0259i	−0.659343	−	0.380672i
$248$	65.8224	+	114.008i	0.265413	+	0.459708i
$249$	−104.318	−	180.683i	−0.418946	−	0.725635i
$250$	−110.944	−	137.628i	−0.443777	−	0.550511i
$251$		−	331.340i		−	1.32008i	−0.751230	−	0.660041i	$-0.770539\pi$
$251$		−	331.340i		−	1.32008i	0.751230	−	0.660041i	$-0.229461\pi$
$252$	13.8862	−	39.6380i	0.0551040	−	0.157294i
$253$			2.05214i			0.00811124i
$254$	−38.8402	+	67.2731i	−0.152914	+	0.264855i
$255$	106.864	+	13.2014i	0.419074	+	0.0517703i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−5.96569	+	10.3329i	−0.0232128	+	0.0402058i	−0.877398	−	0.479762i	$-0.840723\pi$
$257$	−5.96569	+	10.3329i	−0.0232128	+	0.0402058i	0.854186	+	0.519968i	$0.174056\pi$
$258$	−165.610			−0.641901
$259$	2.70433	−	2.32555i	0.0104414	−	0.00897895i
$260$	35.5762	−	47.1387i	0.136832	−	0.181303i
$261$	22.5602	−	39.0755i	0.0864376	−	0.149714i
$262$	88.6354	+	153.521i	0.338303	+	0.585958i
$263$	−83.0662	+	47.9583i	−0.315841	+	0.182351i	−0.649537	−	0.760330i	$-0.725037\pi$
$263$	−83.0662	+	47.9583i	−0.315841	+	0.182351i	0.333696	+	0.942681i	$0.391704\pi$
$264$	−5.74303	−	3.31574i	−0.0217539	−	0.0125596i
$265$	−210.072	−	158.544i	−0.792724	−	0.598280i
$266$	−309.750	+	58.4907i	−1.16447	+	0.219890i
$267$			11.3691i			0.0425809i
$268$	218.599	+	126.208i	0.815668	+	0.470926i
$269$	−317.461	+	183.286i	−1.18015	+	0.681362i	−0.956050	−	0.293204i	$-0.905279\pi$
$269$	−317.461	+	183.286i	−1.18015	+	0.681362i	−0.224103	+	0.974565i	$0.571945\pi$
$270$	−4.50472	+	36.4652i	−0.0166841	+	0.135056i
$271$	−217.872	−	125.788i	−0.803954	−	0.464163i	0.0408977	−	0.999163i	$-0.486978\pi$
$271$	−217.872	−	125.788i	−0.803954	−	0.464163i	−0.844852	+	0.535000i	$0.820312\pi$
$272$	−49.7336			−0.182844
$273$	−70.3594	+	13.2861i	−0.257727	+	0.0486670i
$274$	65.7818			0.240079
$275$	32.8238	+	8.23544i	0.119359	+	0.0299470i
$276$	−4.54804	+	2.62581i	−0.0164784	+	0.00951382i
$277$	−112.564	+	64.9891i	−0.406370	+	0.234618i	−0.689229	−	0.724544i	$-0.742051\pi$
$277$	−112.564	+	64.9891i	−0.406370	+	0.234618i	0.282859	+	0.959162i	$0.408717\pi$
$278$	28.6875	−	49.6881i	0.103192	−	0.178734i
$279$			139.630i			0.500467i
$280$	−6.30390	−	98.7940i	−0.0225139	−	0.352836i
$281$	2.88851			0.0102794			0.00513970	−	0.999987i	$-0.498364\pi$
$281$	2.88851			0.0102794			0.00513970	+	0.999987i	$0.498364\pi$
$282$	−105.119	−	60.6903i	−0.372761	−	0.215214i
$283$	−256.903	−	444.969i	−0.907785	−	1.57233i	−0.817135	−	0.576446i	$-0.804439\pi$
$283$	−256.903	−	444.969i	−0.907785	−	1.57233i	−0.0906498	−	0.995883i	$-0.528894\pi$
$284$	−55.4750	−	96.0854i	−0.195334	−	0.338329i
$285$	253.921	−	107.562i	0.890952	−	0.377410i
$286$			11.3055i			0.0395298i
$287$	238.306	+	83.4845i	0.830333	+	0.290887i
$288$		−	16.9706i		−	0.0589256i
$289$	67.2054	−	116.403i	0.232545	−	0.402779i
$290$	13.0388	−	105.548i	0.0449614	−	0.363957i
$291$	−133.657	−	231.501i	−0.459303	−	0.795536i
$292$	−53.1593	+	92.0746i	−0.182052	+	0.315324i
$293$	407.492			1.39076			0.695378	−	0.718644i	$-0.255237\pi$
$293$	407.492			1.39076			0.695378	+	0.718644i	$0.255237\pi$
$294$	−74.9029	+	93.7846i	−0.254772	+	0.318995i
$295$	−286.055	−	215.889i	−0.969677	−	0.731828i
$296$	0.720589	−	1.24810i	0.00243442	−	0.00421654i
$297$	−3.51687	−	6.09140i	−0.0118413	−	0.0205098i
$298$	112.183	−	64.7687i	0.376452	−	0.217345i
$299$	7.75363	+	4.47656i	0.0259319	+	0.0149718i
$300$	23.7478	+	83.2829i	0.0791594	+	0.277610i
$301$	446.656	+	156.475i	1.48391	+	0.519850i
$302$			410.165i			1.35816i
$303$	229.816	+	132.684i	0.758467	+	0.437901i
$304$	−110.305	+	63.6849i	−0.362847	+	0.209490i
$305$	−35.8738	+	290.394i	−0.117619	+	0.952113i
$306$	−45.6832	−	26.3752i	−0.149291	−	0.0861935i
$307$	−247.277			−0.805462			−0.402731	−	0.915318i	$-0.631939\pi$
$307$	−247.277			−0.805462			−0.402731	+	0.915318i	$0.631939\pi$
$308$	12.3563	+	14.3689i	0.0401178	+	0.0466521i
$309$	30.0002			0.0970880
$310$	128.370	+	303.044i	0.414098	+	0.977561i
$311$	305.411	−	176.329i	0.982029	−	0.566975i	0.0791468	−	0.996863i	$-0.474780\pi$
$311$	305.411	−	176.329i	0.982029	−	0.566975i	0.902882	+	0.429888i	$0.141447\pi$
$312$	−25.0558	+	14.4659i	−0.0803069	+	0.0463652i
$313$	43.2915	−	74.9830i	0.138311	−	0.239562i	−0.788546	−	0.614976i	$-0.789166\pi$
$313$	43.2915	−	74.9830i	0.138311	−	0.239562i	0.926858	+	0.375413i	$0.122499\pi$
$314$			8.40104i			0.0267549i
$315$	46.6029	−	94.0913i	0.147946	−	0.298702i
$316$	79.8824			0.252792
$317$	−517.971	−	299.051i	−1.63398	−	0.943378i	−0.982849	−	0.184410i	$-0.940962\pi$
$317$	−517.971	−	299.051i	−1.63398	−	0.943378i	−0.651129	−	0.758967i	$-0.725704\pi$
$318$	64.4670	+	111.660i	0.202726	+	0.351132i
$319$	10.1795	+	17.6314i	0.0319107	+	0.0552709i
$320$	−15.6020	−	36.8317i	−0.0487563	−	0.115099i
$321$			158.229i			0.492926i
$322$	14.7472	−	2.78473i	0.0457986	−	0.00864823i
$323$			395.909i			1.22573i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$	102.718	−	106.053i	0.316055	−	0.326318i
$326$	65.7556	+	113.892i	0.201704	+	0.349362i
$327$	−85.7779	+	148.572i	−0.262318	+	0.454347i
$328$	102.028			0.311060
$329$	226.165	+	263.003i	0.687433	+	0.799402i
$330$	−13.2330	−	9.98709i	−0.0400999	−	0.0302639i
$331$	37.9179	−	65.6758i	0.114556	−	0.198416i	−0.803046	−	0.595917i	$-0.796789\pi$
$331$	37.9179	−	65.6758i	0.114556	−	0.198416i	0.917602	+	0.397500i	$0.130122\pi$
$332$	120.455	+	208.635i	0.362818	+	0.628419i
$333$	1.32381	−	0.764300i	0.00397540	−	0.00229520i
$334$	50.7609	+	29.3068i	0.151979	+	0.0877450i
$335$	503.691	+	380.142i	1.50355	+	1.13475i
$336$	−16.0344	+	45.7701i	−0.0477214	+	0.136220i
$337$		−	62.0075i		−	0.183999i	−0.995759	−	0.0919993i	$-0.970674\pi$
$337$		−	62.0075i		−	0.183999i	0.995759	−	0.0919993i	$-0.0293257\pi$
$338$	−164.266	−	94.8391i	−0.485994	−	0.280589i
$339$	145.124	−	83.7872i	0.428094	−	0.247160i
$340$	−123.396	−	15.2437i	−0.362929	−	0.0448344i
$341$	−54.5625	−	31.5016i	−0.160007	−	0.0923802i
$342$	−135.096			−0.395018
$343$	290.626	−	182.169i	0.847307	−	0.531104i
$344$	191.230			0.555902
$345$	−12.0892	+	5.12100i	−0.0350410	+	0.0148435i
$346$	227.991	−	131.631i	0.658933	−	0.380435i
$347$	−462.376	+	266.953i	−1.33250	+	0.769317i	−0.985682	−	0.168617i	$-0.946070\pi$
$347$	−462.376	+	266.953i	−1.33250	+	0.769317i	−0.346814	+	0.937934i	$0.612737\pi$
$348$	−26.0503	+	45.1204i	−0.0748572	+	0.129656i
$349$		−	105.400i		−	0.302005i	−0.988533	−	0.151003i	$-0.951750\pi$
$349$		−	105.400i		−	0.302005i	0.988533	−	0.151003i	$-0.0482502\pi$
$350$	14.6402	−	247.054i	0.0418293	−	0.705868i
$351$	−30.6869			−0.0874271
$352$	6.63148	+	3.82869i	0.0188394	+	0.0108769i
$353$	60.1309	+	104.150i	0.170342	+	0.295042i	0.938540	−	0.345172i	$-0.112179\pi$
$353$	60.1309	+	104.150i	0.170342	+	0.295042i	−0.768197	+	0.640213i	$0.778846\pi$
$354$	87.7845	+	152.047i	0.247979	+	0.429512i
$355$	−108.190	−	255.405i	−0.304761	−	0.719450i
$356$		−	13.1279i		−	0.0368761i
$357$	98.2885	+	114.298i	0.275318	+	0.320162i
$358$			29.4166i			0.0821692i
$359$	−191.129	+	331.046i	−0.532394	+	0.922133i	0.466891	+	0.884315i	$0.345374\pi$
$359$	−191.129	+	331.046i	−0.532394	+	0.922133i	−0.999285	+	0.0378181i	$0.987959\pi$
$360$	5.20160	−	42.1063i	0.0144489	−	0.116962i
$361$	326.470	+	565.463i	0.904350	+	1.56638i
$362$	−234.613	+	406.361i	−0.648102	+	1.12255i
$363$	−206.404			−0.568607
$364$	81.2440	−	15.3414i	0.223198	−	0.0421468i
$365$	−160.117	+	212.156i	−0.438677	+	0.581250i
$366$	71.6725	−	124.140i	0.195827	−	0.339181i
$367$	−48.2640	−	83.5957i	−0.131510	−	0.227781i	0.792749	−	0.609548i	$-0.208649\pi$
$367$	−48.2640	−	83.5957i	−0.131510	−	0.227781i	−0.924259	+	0.381767i	$0.875316\pi$
$368$	5.25163	−	3.03203i	0.0142707	−	0.00823921i
$369$	93.7185	+	54.1084i	0.253980	+	0.146635i
$370$	2.17043	−	2.87584i	0.00586603	−	0.00777253i
$371$	−68.3686	−	362.061i	−0.184282	−	0.975905i
$372$		−	161.231i		−	0.433417i
$373$	−7.44155	−	4.29638i	−0.0199505	−	0.0115184i	0.489992	−	0.871727i	$-0.337000\pi$
$373$	−7.44155	−	4.29638i	−0.0199505	−	0.0115184i	−0.509942	+	0.860209i	$0.670333\pi$
$374$	20.6129	−	11.9009i	0.0551148	−	0.0318206i
$375$	33.3948	+	213.915i	0.0890528	+	0.570441i
$376$	121.381	+	70.0791i	0.322821	+	0.186381i
$377$	88.8226			0.235604
$378$	−39.0018	+	33.5390i	−0.103179	+	0.0887274i
$379$	−262.222			−0.691879			−0.345939	−	0.938257i	$-0.612440\pi$
$379$	−262.222			−0.691879			−0.345939	+	0.938257i	$0.612440\pi$
$380$	−293.203	+	124.202i	−0.771587	+	0.326846i
$381$	82.3924	−	47.5693i	0.216253	−	0.124854i
$382$	−3.36755	+	1.94426i	−0.00881557	+	0.00508967i
$383$	−308.804	+	534.864i	−0.806277	+	1.39651i	0.109149	+	0.994025i	$0.465187\pi$
$383$	−308.804	+	534.864i	−0.806277	+	1.39651i	−0.915426	+	0.402487i	$0.868146\pi$
$384$			19.5959i			0.0510310i
$385$	26.2535	+	39.4384i	0.0681908	+	0.102437i
$386$	−157.566			−0.408202
$387$	175.656	+	101.415i	0.453892	+	0.262055i
$388$	154.334	+	267.314i	0.397768	+	0.688955i
$389$	−255.682	−	442.854i	−0.657279	−	1.13844i	−0.981317	−	0.192397i	$-0.938374\pi$
$389$	−255.682	−	442.854i	−0.657279	−	1.13844i	0.324038	−	0.946044i	$-0.394959\pi$
$390$	−66.6007	+	28.2123i	−0.170771	+	0.0723391i
$391$		−	18.8492i		−	0.0482076i
$392$	86.4904	−	108.293i	0.220639	−	0.276258i
$393$		−	217.111i		−	0.552446i
$394$	7.40875	−	12.8323i	0.0188039	−	0.0325694i
$395$	198.199	+	24.4845i	0.501771	+	0.0619862i
$396$	4.06093	+	7.03375i	0.0102549	+	0.0177620i
$397$	−229.904	+	398.205i	−0.579103	+	1.00304i	0.416479	+	0.909145i	$0.363264\pi$
$397$	−229.904	+	398.205i	−0.579103	+	1.00304i	−0.995582	+	0.0938911i	$0.970069\pi$
$398$	−519.837			−1.30612
$399$	364.358	+	127.644i	0.913177	+	0.319909i
$400$	−27.4216	−	96.1668i	−0.0685540	−	0.240417i
$401$	−360.388	+	624.210i	−0.898723	+	1.55663i	−0.0695940	+	0.997575i	$0.522170\pi$
$401$	−360.388	+	624.210i	−0.898723	+	1.55663i	−0.829129	+	0.559058i	$0.811163\pi$
$402$	−154.573	−	267.728i	−0.384509	−	0.665990i
$403$	−238.046	+	137.436i	−0.590684	+	0.341032i
$404$	−265.368	−	153.210i	−0.656852	−	0.379234i
$405$	27.1082	−	35.9186i	0.0669339	−	0.0886878i
$406$	112.890	−	97.0778i	0.278054	−	0.239108i
$407$			0.689727i			0.00169466i
$408$	52.7504	+	30.4555i	0.129290	+	0.0746457i
$409$	−63.6513	+	36.7491i	−0.155627	+	0.0898511i	−0.575791	−	0.817597i	$-0.695306\pi$
$409$	−63.6513	+	36.7491i	−0.155627	+	0.0898511i	0.420164	+	0.907448i	$0.361972\pi$
$410$	253.145	+	31.2723i	0.617427	+	0.0762738i
$411$	−69.7721	−	40.2829i	−0.169762	−	0.0980120i
$412$	−34.6412			−0.0840806
$413$	−93.0974	−	493.018i	−0.225417	−	1.19375i
$414$	6.43190			0.0155360
$415$	234.919	+	554.573i	0.566069	+	1.33632i
$416$	28.9319	−	16.7038i	0.0695478	−	0.0401535i
$417$	−60.8553	+	35.1348i	−0.145936	+	0.0842562i
$418$	30.4787	−	52.7906i	0.0729155	−	0.126293i
$419$		−	777.529i		−	1.85568i	−0.372980	−	0.927839i	$-0.621664\pi$
$419$		−	777.529i		−	1.85568i	0.372980	−	0.927839i	$-0.378336\pi$
$420$	−53.8125	+	108.647i	−0.128125	+	0.258684i
$421$	479.018			1.13781			0.568906	−	0.822403i	$-0.307367\pi$
$421$	479.018			1.13781			0.568906	+	0.822403i	$0.307367\pi$
$422$	52.3109	+	30.2017i	0.123959	+	0.0715680i
$423$	74.3301	+	128.743i	0.175721	+	0.304358i
$424$	−74.4400	−	128.934i	−0.175566	−	0.304089i
$425$	−301.490	−	75.6435i	−0.709389	−	0.177985i
$426$			135.885i			0.318980i
$427$	−310.595	+	267.091i	−0.727389	+	0.625506i
$428$		−	182.707i		−	0.426886i
$429$	6.92320	−	11.9913i	0.0161380	−	0.0279518i
$430$	474.469	+	58.6135i	1.10342	+	0.136310i
$431$	20.2238	+	35.0286i	0.0469229	+	0.0812728i	0.888533	−	0.458813i	$-0.151725\pi$
$431$	20.2238	+	35.0286i	0.0469229	+	0.0812728i	−0.841610	+	0.540086i	$0.818392\pi$
$432$	−10.3923	+	18.0000i	−0.0240563	+	0.0416667i
$433$	408.513			0.943447			0.471724	−	0.881746i	$-0.343632\pi$
$433$	408.513			0.943447			0.471724	+	0.881746i	$0.343632\pi$
$434$	−152.337	+	434.845i	−0.351007	+	1.00195i
$435$	−78.4642	+	103.966i	−0.180377	+	0.239001i
$436$	99.0477	−	171.556i	0.227174	−	0.393476i
$437$	−24.1368	−	41.8061i	−0.0552329	−	0.0956662i
$438$	112.768	−	65.1066i	0.257461	−	0.148645i
$439$	−99.9207	−	57.6892i	−0.227610	−	0.131411i	0.381859	−	0.924221i	$-0.375284\pi$
$439$	−99.9207	−	57.6892i	−0.227610	−	0.131411i	−0.609469	+	0.792810i	$0.708617\pi$
$440$	15.2801	+	11.5321i	0.0347275	+	0.0262093i
$441$	136.878	−	53.6051i	0.310380	−	0.121554i
$442$		−	103.843i		−	0.234938i
$443$	219.511	+	126.735i	0.495511	+	0.286083i	0.726858	−	0.686788i	$-0.240980\pi$
$443$	219.511	+	126.735i	0.495511	+	0.286083i	−0.231347	+	0.972871i	$0.574313\pi$
$444$	−1.52860	+	0.882538i	−0.00344279	+	0.00198770i
$445$	4.02380	−	32.5722i	0.00904225	−	0.0731959i
$446$	192.933	+	111.390i	0.432584	+	0.249753i
$447$	−158.650			−0.354922
$448$	18.5149	−	52.8507i	0.0413280	−	0.117970i
$449$	624.246			1.39030			0.695151	−	0.718863i	$-0.255337\pi$
$449$	624.246			1.39030			0.695151	+	0.718863i	$0.255337\pi$
$450$	25.8118	−	102.877i	0.0573595	−	0.228616i
$451$	−42.2872	+	24.4145i	−0.0937632	+	0.0541342i
$452$	−167.574	+	96.7492i	−0.370740	+	0.214047i
$453$	251.174	−	435.046i	0.554467	−	0.960366i
$454$		−	618.777i		−	1.36294i
$455$	206.280	−	13.1624i	0.453362	−	0.0289284i
$456$	155.995			0.342095
$457$	−185.563	−	107.135i	−0.406046	−	0.234431i	0.283044	−	0.959107i	$-0.408656\pi$
$457$	−185.563	−	107.135i	−0.406046	−	0.234431i	−0.689089	+	0.724676i	$0.741989\pi$
$458$	−147.338	−	255.197i	−0.321699	−	0.557200i
$459$	32.3029	+	55.9503i	0.0703767	+	0.121896i
$460$	13.9594	−	5.91322i	0.0303464	−	0.0128548i
$461$		−	662.143i		−	1.43632i	−0.695879	−	0.718159i	$-0.744985\pi$
$461$		−	662.143i		−	1.43632i	0.695879	−	0.718159i	$-0.255015\pi$
$462$	−4.30671	−	22.8071i	−0.00932188	−	0.0493661i
$463$		−	422.198i		−	0.911875i	−0.890012	−	0.455938i	$-0.849304\pi$
$463$		−	422.198i		−	0.911875i	0.890012	−	0.455938i	$-0.150696\pi$
$464$	30.0803	−	52.1006i	0.0648282	−	0.112286i
$465$	49.4185	−	400.037i	0.106276	−	0.860295i
$466$	−91.9319	−	159.231i	−0.197279	−	0.341697i
$467$	−384.769	+	666.439i	−0.823916	+	1.42706i	0.0788296	+	0.996888i	$0.474882\pi$
$467$	−384.769	+	666.439i	−0.823916	+	1.42706i	−0.902745	+	0.430176i	$0.858452\pi$
$468$	35.4342			0.0757141
$469$	163.928	+	868.115i	0.349526	+	1.85099i
$470$	279.682	+	211.080i	0.595069	+	0.449106i
$471$	5.14457	−	8.91065i	0.0109226	−	0.0189186i
$472$	−101.365	−	175.569i	−0.214756	−	0.371968i
$473$	−79.2588	+	45.7601i	−0.167566	+	0.0967443i
$474$	−84.7281	−	48.9178i	−0.178751	−	0.103202i
$475$	−765.546	+	218.293i	−1.61168	+	0.459564i
$476$	−113.494	−	131.980i	−0.238432	−	0.277268i
$477$		−	157.911i		−	0.331051i
$478$	415.340	+	239.797i	0.868912	+	0.501667i
$479$	−724.543	+	418.315i	−1.51262	+	0.873309i	−0.512725	+	0.858553i	$0.671364\pi$
$479$	−724.543	+	418.315i	−1.51262	+	0.873309i	−0.999891	+	0.0147567i	$0.995303\pi$
$480$	−6.00629	+	48.6202i	−0.0125131	+	0.101292i
$481$	2.60600	+	1.50458i	0.00541788	+	0.00312802i
$482$	431.094			0.894385
$483$	−17.3470	−	6.07710i	−0.0359151	−	0.0125820i
$484$	238.335			0.492428
$485$	300.991	+	710.549i	0.620599	+	1.46505i
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	573.294	−	330.992i	1.17720	−	0.679654i	0.221831	−	0.975085i	$-0.428797\pi$
$487$	573.294	−	330.992i	1.17720	−	0.679654i	0.955364	+	0.295431i	$0.0954632\pi$
$488$	−82.7603	+	143.345i	−0.169591	+	0.293740i
$489$		−	161.068i		−	0.329382i
$490$	247.787	−	242.180i	0.505689	−	0.494246i
$491$	−902.434			−1.83795			−0.918976	−	0.394314i	$-0.870982\pi$
$491$	−902.434			−1.83795			−0.918976	+	0.394314i	$0.870982\pi$
$492$	−108.217	−	62.4790i	−0.219953	−	0.126990i
$493$	−93.5000	−	161.947i	−0.189655	−	0.328492i
$494$	−132.973	−	230.315i	−0.269176	−	0.466226i
$495$	7.91985	+	18.6964i	0.0159997	+	0.0377705i
$496$			186.174i			0.375350i
$497$	128.389	−	366.486i	0.258329	−	0.737397i
$498$		−	295.054i		−	0.592479i
$499$	355.916	−	616.465i	0.713259	−	1.23540i	−0.250368	−	0.968151i	$-0.580552\pi$
$499$	355.916	−	616.465i	0.713259	−	1.23540i	0.963627	−	0.267251i	$-0.0861152\pi$
$500$	−38.5610	−	247.008i	−0.0771220	−	0.494016i
$501$	−35.8934	−	62.1692i	−0.0716435	−	0.124090i
$502$	234.293	−	405.807i	0.466719	−	0.808381i
$503$	151.178			0.300553			0.150277	−	0.988644i	$-0.451984\pi$
$503$	151.178			0.300553			0.150277	+	0.988644i	$0.451984\pi$
$504$	45.0354	−	38.7274i	0.0893559	−	0.0768402i
$505$	−611.455	−	461.474i	−1.21080	−	0.913809i
$506$	−1.45109	+	2.51335i	−0.00286776	+	0.00496710i
$507$	116.154	+	201.184i	0.229100	+	0.396813i
$508$	−95.1386	+	54.9283i	−0.187281	+	0.108127i
$509$	82.4902	+	47.6257i	0.162063	+	0.0935672i	0.578838	−	0.815443i	$-0.303506\pi$
$509$	82.4902	+	47.6257i	0.162063	+	0.0935672i	−0.416775	+	0.909010i	$0.636840\pi$
$510$	121.546	+	91.7326i	0.238326	+	0.179868i
$511$	−365.653	+	69.0469i	−0.715564	+	0.135121i
$512$		−	22.6274i		−	0.0441942i
$513$	143.291	+	82.7291i	0.279320	+	0.161265i
$514$	−14.6129	+	8.43677i	−0.0284298	+	0.0164139i
$515$	−85.9497	−	10.6178i	−0.166893	−	0.0206171i
$516$	−202.830	−	117.104i	−0.393082	−	0.226946i
$517$	−67.0777			−0.129744
$518$	4.95653	−	0.935950i	0.00956859	−	0.00180685i
$519$	−322.428			−0.621248
$520$	76.9039	−	32.5767i	0.147892	−	0.0626475i
$521$	179.815	−	103.816i	0.345135	−	0.199264i	−0.317406	−	0.948290i	$-0.602812\pi$
$521$	179.815	−	103.816i	0.345135	−	0.199264i	0.662540	+	0.749026i	$0.269478\pi$
$522$	55.2610	−	31.9050i	0.105864	−	0.0611206i
$523$	−116.980	+	202.616i	−0.223672	+	0.387411i	−0.955920	−	0.293627i	$-0.905138\pi$
$523$	−116.980	+	202.616i	−0.223672	+	0.387411i	0.732248	+	0.681038i	$0.238471\pi$
$524$			250.699i			0.478433i
$525$	−166.817	+	253.075i	−0.317747	+	0.482048i
$526$	−135.647			−0.257883
$527$	501.163	+	289.346i	0.950973	+	0.549044i
$528$	−4.68916	−	8.12187i	−0.00888099	−	0.0153823i
$529$	−263.351	−	456.137i	−0.497828	−	0.862263i
$530$	−145.177	−	342.719i	−0.273919	−	0.646640i
$531$		−	215.027i		−	0.404948i
$532$	−420.724	−	147.390i	−0.790834	−	0.277049i
$533$			213.032i			0.399685i
$534$	−8.03917	+	13.9242i	−0.0150546	+	0.0260754i
$535$	56.0011	−	453.322i	0.104675	−	0.847331i
$536$	178.485	+	309.146i	0.332995	+	0.576764i
$537$	18.0139	−	31.2010i	0.0335455	−	0.0581024i
$538$	−518.412			−0.963591
$539$	−9.93369	+	65.5805i	−0.0184298	+	0.121671i
$540$	−31.3019	+	41.4752i	−0.0579665	+	0.0768059i
$541$	−450.994	+	781.145i	−0.833631	+	1.44389i	0.0615089	+	0.998107i	$0.480409\pi$
$541$	−450.994	+	781.145i	−0.833631	+	1.44389i	−0.895140	+	0.445785i	$0.852925\pi$
$542$	−177.891	−	308.117i	−0.328213	−	0.568482i
$543$	497.689	−	287.341i	0.916554	−	0.529173i
$544$	−60.9109	−	35.1669i	−0.111969	−	0.0646451i
$545$	298.334	−	395.295i	0.547402	−	0.725312i
$546$	−95.5669	−	33.4795i	−0.175031	−	0.0613178i
$547$		−	642.470i		−	1.17453i	−0.809393	−	0.587267i	$-0.800204\pi$
$547$		−	642.470i		−	1.17453i	0.809393	−	0.587267i	$-0.199796\pi$
$548$	80.5659	+	46.5147i	0.147018	+	0.0848809i
$549$	−152.040	+	87.7805i	−0.276941	+	0.159892i
$550$	34.3774	+	33.2962i	0.0625044	+	0.0605386i
$551$	−414.753	−	239.457i	−0.752727	−	0.434587i
$552$	−7.42692			−0.0134546
$553$	182.295	+	211.987i	0.329647	+	0.383339i
$554$	−183.817			−0.331800
$555$	−4.06317	+	1.72117i	−0.00732104	+	0.00310121i
$556$	70.2696	−	40.5702i	0.126384	−	0.0729680i
$557$	405.155	−	233.916i	0.727388	−	0.419958i	−0.0900778	−	0.995935i	$-0.528712\pi$
$557$	405.155	−	233.916i	0.727388	−	0.419958i	0.817466	+	0.575977i	$0.195378\pi$
$558$	−98.7335	+	171.012i	−0.176942	+	0.306472i
$559$			399.285i			0.714285i
$560$	62.1373	−	125.455i	0.110959	−	0.224027i
$561$	−29.1511			−0.0519627
$562$	3.53769	+	2.04249i	0.00629482	+	0.00363432i
$563$	−276.979	−	479.741i	−0.491969	−	0.852116i	0.507988	−	0.861364i	$-0.330389\pi$
$563$	−276.979	−	479.741i	−0.491969	−	0.852116i	−0.999957	+	0.00924837i	$0.997056\pi$
$564$	−85.8290	−	148.660i	−0.152179	−	0.263582i
$565$	−445.430	+	188.685i	−0.788372	+	0.333956i
$566$		−	726.632i		−	1.28380i
$567$	61.9060	−	11.6898i	0.109182	−	0.0206170i
$568$		−	156.907i		−	0.276244i
$569$	−77.1487	+	133.626i	−0.135587	+	0.234843i	−0.925821	−	0.377961i	$-0.876625\pi$
$569$	−77.1487	+	133.626i	−0.135587	+	0.234843i	0.790235	+	0.612804i	$0.209959\pi$
$570$	387.046	+	47.8137i	0.679029	+	0.0838837i
$571$	−382.752	−	662.947i	−0.670320	−	1.16103i	−0.977813	−	0.209478i	$-0.932824\pi$
$571$	−382.752	−	662.947i	−0.670320	−	1.16103i	0.307494	−	0.951550i	$-0.400510\pi$
$572$	−7.99422	+	13.8464i	−0.0139759	+	0.0242070i
$573$	4.76243			0.00831140
$574$	232.831	+	270.755i	0.405629	+	0.471698i
$575$	36.4476	−	10.3929i	0.0633871	−	0.0180746i
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	423.234	+	733.062i	0.733507	+	1.27047i	0.955375	+	0.295395i	$0.0954513\pi$
$577$	423.234	+	733.062i	0.733507	+	1.27047i	−0.221868	+	0.975077i	$0.571215\pi$
$578$	164.619	−	95.0428i	0.284808	−	0.164434i
$579$	167.124	+	96.4891i	0.288642	+	0.166648i
$580$	90.6026	−	120.049i	0.156211	−	0.206981i
$581$	−278.778	+	795.770i	−0.479825	+	1.36966i
$582$		−	378.040i		−	0.649553i
$583$	61.7059	+	35.6259i	0.105842	+	0.0611080i
$584$	−130.213	+	75.1786i	−0.222968	+	0.128730i
$585$	87.9172	+	10.8608i	0.150286	+	0.0185655i
$586$	499.073	+	288.140i	0.851661	+	0.491706i
$587$	450.957			0.768240			0.384120	−	0.923283i	$-0.374505\pi$
$587$	450.957			0.768240			0.384120	+	0.923283i	$0.374505\pi$
$588$	−158.053	+	61.8979i	−0.268797	+	0.105268i
$589$	1482.06			2.51622
$590$	−197.687	−	466.680i	−0.335063	−	0.790984i
$591$	−15.7163	+	9.07383i	−0.0265928	+	0.0153533i
$592$	1.76508	−	1.01907i	0.00298155	−	0.00172140i
$593$	157.954	−	273.584i	0.266364	−	0.461356i	−0.701556	−	0.712614i	$-0.747511\pi$
$593$	157.954	−	273.584i	0.266364	−	0.461356i	0.967920	+	0.251258i	$0.0808444\pi$
$594$		−	9.94722i		−	0.0167462i
$595$	−241.141	−	362.247i	−0.405279	−	0.608818i
$596$	183.194			0.307372
$597$	551.371	+	318.334i	0.923569	+	0.533223i
$598$	6.33081	+	10.9653i	0.0105866	+	0.0183366i
$599$	46.7212	+	80.9236i	0.0779987	+	0.135098i	0.902386	−	0.430928i	$-0.141814\pi$
$599$	46.7212	+	80.9236i	0.0779987	+	0.135098i	−0.824388	+	0.566026i	$0.808480\pi$
$600$	−29.8049	+	118.793i	−0.0496748	+	0.197988i
$601$			267.479i			0.445057i	0.974926	+	0.222529i	$0.0714311\pi$
$601$			267.479i			0.445057i	−0.974926	+	0.222529i	$0.928569\pi$
$602$	436.395	+	507.475i	0.724908	+	0.842981i
$603$			378.625i			0.627901i
$604$	−290.030	+	502.347i	−0.480183	+	0.831701i
$605$	591.343	+	73.0515i	0.977427	+	0.120746i
$606$	187.644	+	325.008i	0.309643	+	0.536317i
$607$	−109.120	+	189.001i	−0.179769	+	0.311369i	−0.941801	−	0.336170i	$-0.890868\pi$
$607$	−109.120	+	189.001i	−0.179769	+	0.311369i	0.762032	+	0.647539i	$0.224202\pi$
$608$	−180.128			−0.296263
$609$	−179.185	+	33.8359i	−0.294229	+	0.0555598i
$610$	−249.276	+	330.292i	−0.408649	+	0.541463i
$611$	−146.324	+	253.440i	−0.239482	+	0.414795i
$612$	−37.3002	−	64.6058i	−0.0609480	−	0.105565i
$613$	−207.425	+	119.757i	−0.338377	+	0.195362i	−0.659554	−	0.751657i	$-0.729255\pi$
$613$	−207.425	+	119.757i	−0.338377	+	0.195362i	0.321177	+	0.947019i	$0.395922\pi$
$614$	−302.851	−	174.851i	−0.493243	−	0.284774i
$615$	−249.351	−	188.188i	−0.405448	−	0.305997i
$616$	4.97296	+	26.3354i	0.00807299	+	0.0427523i
$617$		−	513.996i		−	0.833057i	−0.909123	−	0.416529i	$-0.863247\pi$
$617$		−	513.996i		−	0.833057i	0.909123	−	0.416529i	$-0.136753\pi$
$618$	36.7426	+	21.2133i	0.0594540	+	0.0343258i
$619$	55.5870	−	32.0932i	0.0898013	−	0.0518468i	−0.454427	−	0.890784i	$-0.650156\pi$
$619$	55.5870	−	32.0932i	0.0898013	−	0.0518468i	0.544228	+	0.838937i	$0.316823\pi$
$620$	−57.0636	+	461.923i	−0.0920381	+	0.745037i
$621$	−6.82206	−	3.93872i	−0.0109856	−	0.00634254i
$622$	498.734			0.801823
$623$	34.8380	−	29.9584i	0.0559197	−	0.0480873i
$624$	−40.9159			−0.0655703
$625$	−19.9655	−	624.681i	−0.0319447	−	0.999490i
$626$	106.042	−	61.2234i	0.169396	−	0.0978009i
$627$	−64.6550	+	37.3286i	−0.103118	+	0.0595352i
$628$	−5.94044	+	10.2891i	−0.00945929	+	0.0163840i
$629$		−	6.33523i		−	0.0100719i
$630$	123.609	−	82.2845i	0.196205	−	0.130610i
$631$	−86.9074			−0.137730			−0.0688648	−	0.997626i	$-0.521938\pi$
$631$	−86.9074			−0.137730			−0.0688648	+	0.997626i	$0.521938\pi$
$632$	97.8356	+	56.4854i	0.154803	+	0.0893756i
$633$	−36.9894	−	64.0675i	−0.0584351	−	0.101212i
$634$	−422.922	−	732.522i	−0.667069	−	1.15540i
$635$	−252.888	+	107.124i	−0.398249	+	0.168699i
$636$			182.340i			0.286698i
$637$	226.114	+	180.590i	0.354967	+	0.283501i
$638$			28.7920i			0.0451285i
$639$	83.2124	−	144.128i	0.130223	−	0.225553i
$640$	6.93547	−	56.1418i	0.0108367	−	0.0877215i
$641$	517.808	+	896.871i	0.807813	+	1.39917i	0.914375	+	0.404868i	$0.132682\pi$
$641$	517.808	+	896.871i	0.807813	+	1.39917i	−0.106562	+	0.994306i	$0.533984\pi$
$642$	−111.885	+	193.790i	−0.174276	+	0.301854i
$643$	−413.852			−0.643626			−0.321813	−	0.946803i	$-0.604292\pi$
$643$	−413.852			−0.643626			−0.321813	+	0.946803i	$0.604292\pi$
$644$	20.0306	+	7.01723i	0.0311034	+	0.0108963i
$645$	−467.357	−	352.721i	−0.724585	−	0.546854i
$646$	−279.950	+	484.888i	−0.433359	+	0.750601i
$647$	−433.148	−	750.235i	−0.669472	−	1.15956i	−0.978052	−	0.208361i	$-0.933187\pi$
$647$	−433.148	−	750.235i	−0.669472	−	1.15956i	0.308580	−	0.951198i	$-0.400146\pi$
$648$	22.0454	−	12.7279i	0.0340207	−	0.0196419i
$649$	84.0249	+	48.5118i	0.129468	+	0.0747485i
$650$	200.794	−	57.2558i	0.308914	−	0.0880858i
$651$	427.865	−	367.936i	0.657243	−	0.565185i
$652$			185.985i			0.285253i
$653$	−628.566	−	362.902i	−0.962581	−	0.555747i	−0.0656147	−	0.997845i	$-0.520901\pi$
$653$	−628.566	−	362.902i	−0.962581	−	0.555747i	−0.896967	+	0.442099i	$0.854234\pi$
$654$	−210.112	+	121.308i	−0.321272	+	0.185487i
$655$	−76.8410	+	622.018i	−0.117314	+	0.949646i
$656$	124.958	+	72.1445i	0.190485	+	0.109976i
$657$	−159.478			−0.242737
$658$	91.0235	+	482.035i	0.138334	+	0.732576i
$659$	825.106			1.25206			0.626029	−	0.779800i	$-0.284679\pi$
$659$	825.106			1.25206			0.626029	+	0.779800i	$0.284679\pi$
$660$	−9.14506	−	21.5888i	−0.0138561	−	0.0327102i
$661$	350.757	−	202.510i	0.530646	−	0.306369i	−0.210633	−	0.977565i	$-0.567553\pi$
$661$	350.757	−	202.510i	0.530646	−	0.306369i	0.741280	+	0.671196i	$0.234219\pi$
$662$	92.8796	−	53.6241i	0.140301	−	0.0810031i
$663$	−63.5904	+	110.142i	−0.0959131	+	0.166126i
$664$			340.700i			0.513102i
$665$	−998.698	−	494.650i	−1.50180	−	0.743835i
$666$	2.16177			0.00324590
$667$	19.7463	+	11.4005i	0.0296047	+	0.0170923i
$668$	41.4461	+	71.7868i	0.0620451	+	0.107465i
$669$	−136.424	−	236.293i	−0.203922	−	0.353204i
$670$	348.092	+	821.740i	0.519540	+	1.22648i
$671$		−	79.2158i		−	0.118056i
$672$	−52.0024	+	44.7186i	−0.0773845	+	0.0665455i
$673$			681.947i			1.01329i	0.862153	+	0.506647i	$0.169115\pi$
$673$			681.947i			1.01329i	−0.862153	+	0.506647i	$0.830885\pi$
$674$	43.8459	−	75.9434i	0.0650533	−	0.112676i
$675$	−90.3768	+	93.3115i	−0.133892	+	0.138239i
$676$	−134.123	−	232.307i	−0.198406	−	0.343650i
$677$	341.393	−	591.310i	0.504273	−	0.873427i	−0.495714	−	0.868486i	$-0.665094\pi$
$677$	341.393	−	591.310i	0.504273	−	0.873427i	0.999988	−	0.00494144i	$-0.00157291\pi$
$678$	236.986			0.349537
$679$	−357.186	+	1019.58i	−0.526047	+	1.50160i
$680$	−140.350	−	105.924i	−0.206396	−	0.155770i
$681$	−378.922	+	656.312i	−0.556420	+	0.963747i
$682$	−44.5501	−	77.1630i	−0.0653227	−	0.113142i
$683$	−1009.82	+	583.020i	−1.47851	+	0.853616i	−0.999705	−	0.0243066i	$-0.992262\pi$
$683$	−1009.82	+	583.020i	−1.47851	+	0.853616i	−0.478802	+	0.877923i	$0.658929\pi$
$684$	−165.458	−	95.5273i	−0.241898	−	0.139660i
$685$	185.638	+	140.104i	0.271005	+	0.204531i
$686$	484.756	−	17.6063i	0.706641	−	0.0256651i
$687$			360.904i			0.525333i
$688$	234.208	+	135.220i	0.340419	+	0.196541i
$689$	269.211	−	155.429i	0.390728	−	0.225587i
$690$	−18.4272	−	2.27641i	−0.0267061	−	0.00329914i
$691$	−927.418	−	535.445i	−1.34214	−	0.774884i	−0.355018	−	0.934859i	$-0.615525\pi$
$691$	−927.418	−	535.445i	−1.34214	−	0.774884i	−0.987121	+	0.159975i	$0.948859\pi$
$692$	372.307			0.538016
$693$	−9.39849	+	26.8279i	−0.0135620	+	0.0387127i
$694$	−755.057			−1.08798
$695$	186.784	−	79.1222i	0.268754	−	0.113845i
$696$	−63.8099	+	36.8407i	−0.0916810	+	0.0529320i
$697$	388.413	−	224.250i	0.557264	−	0.321736i
$698$	74.5289	−	129.088i	0.106775	−	0.184940i
$699$			225.186i			0.322155i
$700$	192.624	−	292.226i	0.275177	−	0.417466i
$701$	915.662			1.30622			0.653111	−	0.757262i	$-0.273463\pi$
$701$	915.662			1.30622			0.653111	+	0.757262i	$0.273463\pi$
$702$	−37.5836	−	21.6989i	−0.0535379	−	0.0309101i
$703$	−8.11239	−	14.0511i	−0.0115397	−	0.0199873i
$704$	5.41458	+	9.37833i	0.00769116	+	0.0133215i
$705$	−167.388	−	395.154i	−0.237430	−	0.560502i
$706$			170.076i			0.240901i
$707$	−199.000	−	1053.85i	−0.281471	−	1.49059i
$708$			248.292i			0.350695i
$709$	346.985	−	600.996i	0.489401	−	0.847667i	−0.510525	−	0.859863i	$-0.670549\pi$
$709$	346.985	−	600.996i	0.489401	−	0.847667i	0.999926	+	0.0121961i	$0.00388222\pi$
$710$	48.0931	−	389.308i	0.0677368	−	0.548321i
$711$	59.9118	+	103.770i	0.0842641	+	0.145950i
$712$	9.28283	−	16.0783i	0.0130377	−	0.0225819i
$713$	−70.5605			−0.0989628
$714$	39.5576	+	209.486i	0.0554028	+	0.293398i
$715$	−24.0788	+	31.9045i	−0.0336766	+	0.0446217i
$716$	−20.8007	+	36.0278i	−0.0290512	+	0.0503182i
$717$	−293.690	−	508.686i	−0.409609	−	0.709464i
$718$	−468.169	+	270.298i	−0.652046	+	0.376459i
$719$	1020.94	+	589.438i	1.41994	+	0.819803i	0.996293	−	0.0860250i	$-0.0274165\pi$
$719$	1020.94	+	589.438i	1.41994	+	0.819803i	0.423647	+	0.905828i	$0.360750\pi$
$720$	36.1443	−	47.8914i	0.0502004	−	0.0665159i
$721$	−79.0525	−	91.9286i	−0.109643	−	0.127502i
$722$			923.398i			1.27894i
$723$	−457.244	−	263.990i	−0.632426	−	0.365131i
$724$	−574.682	+	331.793i	−0.793759	+	0.458277i
$725$	261.594	−	270.088i	0.360819	−	0.372535i
$726$	−252.793	−	145.950i	−0.348199	−	0.201033i
$727$	183.363			0.252218			0.126109	−	0.992016i	$-0.459751\pi$
$727$	183.363			0.252218			0.126109	+	0.992016i	$0.459751\pi$
$728$	110.351	+	38.6588i	0.151581	+	0.0531028i
$729$	27.0000			0.0370370
$730$	−346.120	+	146.617i	−0.474137	+	0.200846i
$731$	728.001	−	420.312i	0.995898	−	0.574982i
$732$	175.561	−	101.360i	0.239838	−	0.138470i
$733$	−132.309	+	229.165i	−0.180503	+	0.312640i	−0.942052	−	0.335467i	$-0.891106\pi$
$733$	−132.309	+	229.165i	−0.180503	+	0.312640i	0.761549	+	0.648107i	$0.224439\pi$
$734$		−	136.511i		−	0.185983i
$735$	−411.123	+	105.133i	−0.559351	+	0.143038i
$736$	8.57587			0.0116520
$737$	−147.953	−	85.4205i	−0.200750	−	0.115903i
$738$	76.5208	+	132.538i	0.103687	+	0.179591i
$739$	−412.229	−	714.002i	−0.557820	−	0.966173i	−0.997678	−	0.0681056i	$-0.978305\pi$
$739$	−412.229	−	714.002i	−0.557820	−	0.966173i	0.439858	−	0.898067i	$-0.355029\pi$
$740$	4.69175	−	1.98744i	0.00634020	−	0.00268573i
$741$			325.715i			0.439562i
$742$	172.282	−	491.776i	0.232185	−	0.662771i
$743$			1155.38i			1.55502i	0.628874	+	0.777508i	$0.283516\pi$
$743$			1155.38i			1.55502i	−0.628874	+	0.777508i	$0.716484\pi$
$744$	114.008	−	197.467i	0.153236	−	0.265413i
$745$	454.529	+	56.1502i	0.610106	+	0.0753694i
$746$	−6.07600	−	10.5239i	−0.00814477	−	0.0141072i
$747$	−180.683	+	312.953i	−0.241878	+	0.418946i
$748$	33.6608			0.0450011
$749$	484.857	−	416.945i	0.647339	−	0.556668i
$750$	−110.361	+	285.605i	−0.147148	+	0.380807i
$751$	298.504	−	517.024i	0.397475	−	0.688447i	−0.595939	−	0.803030i	$-0.703220\pi$
$751$	298.504	−	517.024i	0.397475	−	0.688447i	0.993414	+	0.114583i	$0.0365532\pi$
$752$	99.1068	+	171.658i	0.131791	+	0.228269i
$753$	−497.011	+	286.949i	−0.660041	+	0.381075i
$754$	108.785	+	62.8070i	0.144277	+	0.0832985i
$755$	−873.579	+	1157.50i	−1.15706	+	1.53311i
$756$	−71.4828	+	13.4982i	−0.0945540	+	0.0178548i
$757$			493.526i			0.651949i	0.945378	+	0.325975i	$0.105692\pi$
$757$			493.526i			0.651949i	−0.945378	+	0.325975i	$0.894308\pi$
$758$	−321.155	−	185.419i	−0.423687	−	0.244616i
$759$	3.07822	−	1.77721i	0.00405562	−	0.00234151i
$760$	−446.923	−	55.2105i	−0.588056	−	0.0726455i
$761$	743.656	+	429.350i	0.977209	+	0.564192i	0.901426	−	0.432932i	$-0.142521\pi$
$761$	743.656	+	429.350i	0.977209	+	0.564192i	0.0757829	+	0.997124i	$0.475854\pi$
$762$	134.546			0.176570
$763$	681.294	−	128.650i	0.892915	−	0.168611i
$764$	−5.49918			−0.00719789
$765$	−72.7448	−	171.729i	−0.0950912	−	0.224482i
$766$	−756.412	+	436.715i	−0.987483	+	0.570124i
$767$	366.585	−	211.648i	0.477946	−	0.275942i
$768$	−13.8564	+	24.0000i	−0.0180422	+	0.0312500i
$769$		−	188.778i		−	0.245485i	−0.992439	−	0.122743i	$-0.960831\pi$
$769$		−	188.778i		−	0.245485i	0.992439	−	0.122743i	$-0.0391690\pi$
$770$	4.26662	+	66.8660i	0.00554106	+	0.0868390i
$771$	20.6658			0.0268039
$772$	−192.978	−	111.416i	−0.249972	−	0.144321i
$773$	287.687	+	498.288i	0.372169	+	0.644615i	0.989899	−	0.141775i	$-0.0452809\pi$
$773$	287.687	+	498.288i	0.372169	+	0.644615i	−0.617730	+	0.786390i	$0.711948\pi$
$774$	143.423	+	248.416i	0.185301	+	0.320950i
$775$	−283.166	+	1128.61i	−0.365375	+	1.45626i
$776$			436.523i			0.562529i
$777$	−5.83034	−	2.04252i	−0.00750366	−	0.00262872i
$778$		−	723.177i		−	0.929533i
$779$	574.314	−	994.742i	0.737246	−	1.27695i
$780$	−101.518	−	12.5410i	−0.130151	−	0.0160782i
$781$	37.5467	+	65.0328i	0.0480752	+	0.0832686i
$782$	13.3284	−	23.0854i	0.0170440	−	0.0295210i
$783$	−78.1509			−0.0998096
$784$	182.504	−	71.4735i	0.232785	−	0.0911652i
$785$	−17.8927	+	23.7080i	−0.0227933	+	0.0302013i
$786$	153.521	−	265.906i	0.195319	−	0.338303i
$787$	534.158	+	925.189i	0.678727	+	1.17559i	0.975364	+	0.220600i	$0.0708015\pi$
$787$	534.158	+	925.189i	0.678727	+	1.17559i	−0.296637	+	0.954990i	$0.595865\pi$
$788$	18.1477	−	10.4776i	0.0230300	−	0.0132964i
$789$	143.875	+	83.0662i	0.182351	+	0.105280i
$790$	225.431	+	170.135i	0.285355	+	0.215361i
$791$	−639.158	−	223.913i	−0.808038	−	0.283076i
$792$			11.4861i			0.0145026i
$793$	−299.301	−	172.802i	−0.377429	−	0.217909i
$794$	−563.148	+	325.133i	−0.709254	+	0.409488i
$795$	−55.8886	+	452.411i	−0.0703001	+	0.569071i
$796$	−636.668	−	367.580i	−0.799834	−	0.461785i
$797$	−403.448			−0.506208			−0.253104	−	0.967439i	$-0.581451\pi$
$797$	−403.448			−0.506208			−0.253104	+	0.967439i	$0.581451\pi$
$798$	355.987	+	413.971i	0.446099	+	0.518760i
$799$	616.117			0.771110
$800$	34.4157	−	137.170i	0.0430197	−	0.171462i
$801$	17.0537	−	9.84593i	0.0212905	−	0.0122920i
$802$	−882.766	+	509.665i	−1.10071	+	0.635493i
$803$	35.9794	−	62.3182i	0.0448062	−	0.0776067i
$804$		−	437.198i		−	0.543779i
$805$	47.5479	+	23.5502i	0.0590657	+	0.0292550i
$806$	−388.727			−0.482292
$807$	549.859	+	317.461i	0.681362	+	0.393384i
$808$	−216.672	−	375.287i	−0.268159	−	0.464464i
$809$	−193.079	−	334.422i	−0.238663	−	0.413377i	0.721668	−	0.692240i	$-0.243376\pi$
$809$	−193.079	−	334.422i	−0.238663	−	0.413377i	−0.960331	+	0.278863i	$0.910043\pi$
$810$	58.5989	−	24.8227i	0.0723444	−	0.0306453i
$811$		−	610.150i		−	0.752343i	−0.926550	−	0.376171i	$-0.877240\pi$
$811$		−	610.150i		−	0.752343i	0.926550	−	0.376171i	$-0.122760\pi$
$812$	206.906	−	39.0703i	0.254810	−	0.0481162i
$813$			435.743i			0.535970i
$814$	−0.487711	+	0.844740i	−0.000599153	+	0.00103776i
$815$	−57.0057	+	461.455i	−0.0699457	+	0.566202i
$816$	43.0705	+	74.6003i	0.0527825	+	0.0914220i
$817$	1076.44	−	1864.44i	1.31755	−	2.28206i
$818$	−103.942			−0.127069
$819$	80.8621	+	94.0329i	0.0987327	+	0.114814i
$820$	287.925	+	217.301i	0.351128	+	0.265001i
$821$	−18.6625	+	32.3243i	−0.0227314	+	0.0393719i	−0.877167	−	0.480185i	$-0.840570\pi$
$821$	−18.6625	+	32.3243i	−0.0227314	+	0.0393719i	0.854436	+	0.519557i	$0.173903\pi$
$822$	−56.9687	−	98.6727i	−0.0693050	−	0.120040i
$823$	694.123	−	400.752i	0.843405	−	0.486940i	−0.0150149	−	0.999887i	$-0.504780\pi$
$823$	694.123	−	400.752i	0.843405	−	0.486940i	0.858420	+	0.512947i	$0.171446\pi$
$824$	−42.4267	−	24.4950i	−0.0514887	−	0.0297270i
$825$	−16.0731	−	56.3677i	−0.0194825	−	0.0683245i
$826$	234.596	−	669.651i	0.284014	−	0.810715i
$827$		−	938.887i		−	1.13529i	−0.823273	−	0.567646i	$-0.807854\pi$
$827$		−	938.887i		−	1.13529i	0.823273	−	0.567646i	$-0.192146\pi$
$828$	7.87744	+	4.54804i	0.00951382	+	0.00549280i
$829$	−420.725	+	242.906i	−0.507509	+	0.293010i	−0.731809	−	0.681510i	$-0.761324\pi$
$829$	−420.725	+	242.906i	−0.507509	+	0.293010i	0.224300	+	0.974520i	$0.427990\pi$
$830$	−104.427	+	845.323i	−0.125816	+	1.01846i
$831$	194.967	+	112.564i	0.234618	+	0.135457i
$832$	47.2456			0.0567856
$833$	91.2421	−	602.365i	0.109534	−	0.723127i
$834$	−99.3763			−0.119156
$835$	80.8304	+	190.816i	0.0968029	+	0.228523i
$836$	74.6572	−	43.1034i	0.0893029	−	0.0515590i
$837$	209.445	−	120.923i	0.250234	−	0.144472i
$838$	549.796	−	952.275i	0.656082	−	1.13637i
$839$			1096.58i			1.30701i	0.756923	+	0.653504i	$0.226702\pi$
$839$			1096.58i			1.30701i	−0.756923	+	0.653504i	$0.773298\pi$
$840$	−142.732	+	95.0140i	−0.169919	+	0.113112i
$841$	−614.794			−0.731027
$842$	586.675	+	338.717i	0.696764	+	0.402277i
$843$	−2.50152	−	4.33277i	−0.00296741	−	0.00513970i
$844$	42.7117	+	73.9788i	0.0506062	+	0.0876526i
$845$	−261.573	−	617.497i	−0.309554	−	0.730765i
$846$			210.237i			0.248507i
$847$	543.890	+	632.479i	0.642137	+	0.746728i
$848$		−	210.548i		−	0.248288i
$849$	−444.969	+	770.709i	−0.524110	+	0.907785i
$850$	−315.760	−	305.830i	−0.371483	−	0.359800i
$851$	0.386230	+	0.668970i	0.000453854	+	0.000786098i
$852$	−96.0854	+	166.425i	−0.112776	+	0.195334i
$853$	−507.488			−0.594945			−0.297473	−	0.954730i	$-0.596144\pi$
$853$	−507.488			−0.594945			−0.297473	+	0.954730i	$0.596144\pi$
$854$	−569.262	+	107.495i	−0.666583	+	0.125872i
$855$	−381.245	−	287.731i	−0.445901	−	0.336527i
$856$	129.194	−	223.770i	0.150927	−	0.261413i
$857$	124.033	+	214.831i	0.144729	+	0.250678i	0.929272	−	0.369396i	$-0.120436\pi$
$857$	124.033	+	214.831i	0.144729	+	0.250678i	−0.784543	+	0.620075i	$0.787102\pi$
$858$	16.9583	−	9.79088i	0.0197649	−	0.0114113i
$859$	1186.28	+	684.900i	1.38100	+	0.797322i	0.992278	−	0.124032i	$-0.0395825\pi$
$859$	1186.28	+	684.900i	1.38100	+	0.797322i	0.388724	+	0.921354i	$0.372916\pi$
$860$	539.658	+	407.287i	0.627509	+	0.473590i
$861$	−81.1520	−	429.758i	−0.0942532	−	0.499138i
$862$			57.2015i			0.0663590i
$863$	−640.818	−	369.976i	−0.742546	−	0.428709i	0.0804480	−	0.996759i	$-0.474365\pi$
$863$	−640.818	−	369.976i	−0.742546	−	0.428709i	−0.822994	+	0.568049i	$0.807698\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$	923.746	+	114.115i	1.06791	+	0.131925i
$866$	500.324	+	288.862i	0.577741	+	0.333559i
$867$	−232.806			−0.268519
$868$	−494.056	+	424.855i	−0.569189	+	0.489465i
$869$	−54.0662			−0.0622166
$870$	−169.613	+	71.8487i	−0.194958	+	0.0825847i
$871$	−645.490	+	372.674i	−0.741090	+	0.427869i
$872$	242.616	−	140.075i	0.278230	−	0.160636i
$873$	−231.501	+	400.972i	−0.265179	+	0.459303i
$874$		−	68.2691i		−	0.0781111i
$875$	567.497	−	666.012i	0.648568	−	0.761157i
$876$	184.149			0.210216
$877$	−1221.52	−	705.244i	−1.39284	−	0.804155i	−0.399208	−	0.916860i	$-0.630715\pi$
$877$	−1221.52	−	705.244i	−1.39284	−	0.804155i	−0.993628	+	0.112706i	$0.964048\pi$
$878$	−81.5849	−	141.309i	−0.0929213	−	0.160944i
$879$	−352.898	−	611.237i	−0.401477	−	0.695378i
$880$	10.5598	+	24.9285i	0.0119998	+	0.0283279i
$881$		−	218.508i		−	0.248023i	−0.992281	−	0.124011i	$-0.960424\pi$
$881$		−	218.508i		−	0.248023i	0.992281	−	0.124011i	$-0.0395759\pi$
$882$	205.545	+	31.1345i	0.233044	+	0.0352999i
$883$		−	532.277i		−	0.602806i	−0.953497	−	0.301403i	$-0.902545\pi$
$883$		−	532.277i		−	0.602806i	0.953497	−	0.301403i	$-0.0974549\pi$
$884$	73.4278	−	127.181i	0.0830632	−	0.143870i
$885$	−76.1034	+	616.048i	−0.0859925	+	0.696099i
$886$	179.230	+	310.436i	0.202291	+	0.350379i
$887$	600.251	−	1039.67i	0.676721	−	1.17211i	−0.299242	−	0.954177i	$-0.596734\pi$
$887$	600.251	−	1039.67i	0.676721	−	1.17211i	0.975963	−	0.217937i	$-0.0699329\pi$
$888$	−2.49619			−0.00281103
$889$	−362.875	−	127.124i	−0.408183	−	0.142997i
$890$	27.9601	−	37.0473i	0.0314159	−	0.0416262i
$891$	−6.09140	+	10.5506i	−0.00683659	+	0.0118413i
$892$	157.529	+	272.848i	0.176602	+	0.305883i
$893$	1366.50	−	788.950i	1.53024	−	0.883483i
$894$	−194.306	−	112.183i	−0.217345	−	0.125484i
$895$	−62.6522	+	83.0145i	−0.0700024	+	0.0927536i
$896$	60.0472	−	51.6366i	0.0670169	−	0.0576301i
$897$		−	15.5073i		−	0.0172879i
$898$	764.542	+	441.409i	0.851383	+	0.491546i
$899$	−606.235	+	350.010i	−0.674344	+	0.389333i
$900$	104.358	−	107.747i	0.115953	−	0.119719i
$901$	−566.776	−	327.228i	−0.629053	−	0.363184i
$902$	−69.0547			−0.0765573
$903$	−152.103	−	805.494i	−0.168442	−	0.892020i
$904$	−273.648			−0.302708
$905$	−1527.56	+	647.080i	−1.68791	+	0.715005i
$906$	615.247	−	355.213i	0.679081	−	0.392068i
$907$	306.051	−	176.699i	0.337432	−	0.194817i	−0.321704	−	0.946840i	$-0.604256\pi$
$907$	306.051	−	176.699i	0.337432	−	0.194817i	0.659136	+	0.752024i	$0.270922\pi$
$908$	437.541	−	757.844i	0.481874	−	0.834629i
$909$		−	459.631i		−	0.505645i
$910$	261.947	+	129.741i	0.287854	+	0.142573i
$911$	−604.734			−0.663813			−0.331907	−	0.943312i	$-0.607692\pi$
$911$	−604.734			−0.663813			−0.331907	+	0.943312i	$0.607692\pi$
$912$	191.055	+	110.305i	0.209490	+	0.120949i
$913$	−81.5270	−	141.209i	−0.0892957	−	0.154665i
$914$	−151.511	−	262.426i	−0.165767	−	0.287118i
$915$	466.659	−	197.678i	0.510010	−	0.216042i
$916$		−	416.736i		−	0.454951i
$917$	−665.288	+	572.104i	−0.725505	+	0.623886i
$918$			91.3664i			0.0995276i
$919$	223.857	−	387.731i	0.243587	−	0.421906i	−0.718146	−	0.695892i	$-0.755009\pi$
$919$	223.857	−	387.731i	0.243587	−	0.421906i	0.961733	+	0.273987i	$0.0883424\pi$
$920$	21.2779	+	2.62857i	0.0231282	+	0.00285714i
$921$	214.148	+	370.915i	0.232517	+	0.402731i
$922$	468.206	−	810.956i	0.507815	−	0.879562i
$923$	327.618			0.354949
$924$	10.8524	−	30.9782i	0.0117451	−	0.0335262i
$925$	12.2501	−	3.49306i	0.0132433	−	0.00377628i
$926$	298.539	−	517.085i	0.322397	−	0.558407i
$927$	−25.9809	−	45.0003i	−0.0280269	−	0.0485440i
$928$	73.6814	−	42.5400i	0.0793980	−	0.0458405i
$929$	−999.292	−	576.941i	−1.07566	−	0.621035i	−0.145940	−	0.989293i	$-0.546621\pi$
$929$	−999.292	−	576.941i	−1.07566	−	0.621035i	−0.929723	+	0.368259i	$0.879954\pi$
$930$	343.394	−	454.999i	0.369241	−	0.489246i
$931$	−568.973	−	1452.84i	−0.611141	−	1.56051i
$932$		−	260.023i		−	0.278994i
$933$	−528.987	−	305.411i	−0.566975	−	0.327343i
$934$	−942.487	+	544.145i	−1.00909	+	0.582596i
$935$	83.5171	+	10.3173i	0.0893231	+	0.0110345i
$936$	43.3978	+	25.0558i	0.0463652	+	0.0267690i
$937$	757.572			0.808508			0.404254	−	0.914647i	$-0.367531\pi$
$937$	757.572			0.808508			0.404254	+	0.914647i	$0.367531\pi$
$938$	−413.081	+	1179.13i	−0.440384	+	1.25707i
$939$	−149.966			−0.159708
$940$	193.283	+	456.284i	0.205621	+	0.485409i
$941$	30.0047	−	17.3232i	0.0318860	−	0.0184094i	−0.483972	−	0.875083i	$-0.660806\pi$
$941$	30.0047	−	17.3232i	0.0318860	−	0.0184094i	0.515858	+	0.856674i	$0.327473\pi$
$942$	12.6016	−	7.27552i	0.0133775	−	0.00772348i
$943$	−27.3430	+	47.3595i	−0.0289958	+	0.0502222i
$944$		−	286.703i		−	0.303711i
$945$	−181.496	+	11.5810i	−0.192059	+	0.0122550i
$946$	−129.429			−0.136817
$947$	1352.07	+	780.617i	1.42774	+	0.824305i	0.996942	−	0.0781447i	$-0.0248996\pi$
$947$	1352.07	+	780.617i	1.42774	+	0.824305i	0.430796	+	0.902449i	$0.358233\pi$
$948$	−69.1802	−	119.824i	−0.0729749	−	0.126396i
$949$	−156.971	−	271.882i	−0.165407	−	0.286494i
$950$	−1091.96	−	273.970i	−1.14943	−	0.288390i
$951$			1035.94i			1.08932i
$952$	−45.6772	−	241.894i	−0.0479803	−	0.254090i
$953$			688.879i			0.722853i	0.932401	+	0.361427i	$0.117710\pi$
$953$			688.879i			0.722853i	−0.932401	+	0.361427i	$0.882290\pi$
$954$	111.660	−	193.401i	0.117044	−	0.202726i
$955$	−13.6442	−	1.68554i	−0.0142872	−	0.00176496i
$956$	339.124	+	587.380i	0.354732	+	0.614414i
$957$	17.6314	−	30.5385i	0.0184236	−	0.0319107i
$958$	−1183.17			−1.23505
$959$	60.4165	+	319.949i	0.0629995	+	0.333628i
$960$	−41.7359	+	55.3003i	−0.0434748	+	0.0576044i
$961$	602.646	−	1043.81i	0.627103	−	1.08617i
$962$	2.12779	+	3.68544i	0.00221184	+	0.00383102i
$963$	237.344	−	137.030i	0.246463	−	0.142295i
$964$	527.980	+	304.829i	0.547697	+	0.316213i
$965$	−444.656	−	335.588i	−0.460783	−	0.347759i
$966$	−16.9485	−	19.7091i	−0.0175450	−	0.0204028i
$967$			311.612i			0.322246i	0.986934	+	0.161123i	$0.0515116\pi$
$967$			311.612i			0.322246i	−0.986934	+	0.161123i	$0.948488\pi$
$968$	291.900	+	168.529i	0.301550	+	0.174100i
$969$	593.864	−	342.868i	0.612863	−	0.353837i
$970$	−133.797	+	1083.07i	−0.137935	+	1.11657i
$971$	907.429	+	523.904i	0.934530	+	0.539551i	0.888241	−	0.459377i	$-0.151927\pi$
$971$	907.429	+	523.904i	0.934530	+	0.539551i	0.0462887	+	0.998928i	$0.485261\pi$
$972$	−31.1769			−0.0320750
$973$	268.020	+	93.8943i	0.275458	+	0.0964998i
$974$	936.186			0.961176
$975$	−248.036	−	62.2320i	−0.254396	−	0.0638277i
$976$	−202.720	+	117.041i	−0.207705	+	0.119919i
$977$	−948.192	+	547.439i	−0.970514	+	0.560327i	−0.899393	−	0.437141i	$-0.855991\pi$
$977$	−948.192	+	547.439i	−0.970514	+	0.560327i	−0.0711212	+	0.997468i	$0.522658\pi$
$978$	113.892	−	197.267i	0.116454	−	0.201704i
$979$			8.88526i			0.00907586i
$980$	474.724	−	121.397i	0.484412	−	0.123875i
$981$	297.143			0.302898
$982$	−1105.25	−	638.117i	−1.12551	−	0.649814i
$983$	289.000	+	500.562i	0.293998	+	0.509219i	0.974751	−	0.223294i	$-0.0716809\pi$
$983$	289.000	+	500.562i	0.293998	+	0.509219i	−0.680754	+	0.732512i	$0.738348\pi$
$984$	−88.3586	−	153.042i	−0.0897954	−	0.155530i
$985$	48.2383	−	20.4339i	0.0489729	−	0.0207451i
$986$		−	264.458i		−	0.268213i
$987$	198.640	−	567.015i	0.201256	−	0.574484i
$988$		−	376.104i		−	0.380672i
$989$	−51.2490	+	88.7658i	−0.0518190	+	0.0897531i
$990$	−3.52056	+	28.4985i	−0.00355612	+	0.0287864i
$991$	−152.356	−	263.889i	−0.153740	−	0.266285i	0.778860	−	0.627198i	$-0.215798\pi$
$991$	−152.356	−	263.889i	−0.153740	−	0.266285i	−0.932599	+	0.360913i	$0.882465\pi$
$992$	−131.645	+	228.015i	−0.132706	+	0.229854i
$993$	−131.352			−0.132278
$994$	416.389	−	358.067i	0.418903	−	0.360229i
$995$	−1467.00	−	1107.16i	−1.47437	−	1.11273i
$996$	208.635	−	361.366i	0.209473	−	0.362818i
$997$	862.135	+	1493.26i	0.864729	+	1.49776i	0.867316	+	0.497759i	$0.165843\pi$
$997$	862.135	+	1493.26i	0.864729	+	1.49776i	−0.00258626	+	0.999997i	$0.500823\pi$
$998$	871.814	−	503.342i	0.873561	−	0.504351i
$999$	−2.29290	−	1.32381i	−0.00229520	−	0.00132513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.p.a.19.11	yes	32
3.2	odd	2		630.3.bc.b.19.5		32
5.2	odd	4		1050.3.p.g.901.1		16
5.3	odd	4		1050.3.p.h.901.8		16
5.4	even	2	inner	210.3.p.a.19.8	✓	32
7.2	even	3		1470.3.h.a.979.3		32
7.3	odd	6	inner	210.3.p.a.199.8	yes	32
7.5	odd	6		1470.3.h.a.979.5		32
15.14	odd	2		630.3.bc.b.19.15		32
21.17	even	6		630.3.bc.b.199.15		32
35.3	even	12		1050.3.p.h.451.8		16
35.9	even	6		1470.3.h.a.979.6		32
35.17	even	12		1050.3.p.g.451.1		16
35.19	odd	6		1470.3.h.a.979.4		32
35.24	odd	6	inner	210.3.p.a.199.11	yes	32
105.59	even	6		630.3.bc.b.199.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.p.a.19.8	✓	32	5.4	even	2	inner
210.3.p.a.19.11	yes	32	1.1	even	1	trivial
210.3.p.a.199.8	yes	32	7.3	odd	6	inner
210.3.p.a.199.11	yes	32	35.24	odd	6	inner
630.3.bc.b.19.5		32	3.2	odd	2
630.3.bc.b.19.15		32	15.14	odd	2
630.3.bc.b.199.5		32	105.59	even	6
630.3.bc.b.199.15		32	21.17	even	6
1050.3.p.g.451.1		16	35.17	even	12
1050.3.p.g.901.1		16	5.2	odd	4
1050.3.p.h.451.8		16	35.3	even	12
1050.3.p.h.901.8		16	5.3	odd	4
1470.3.h.a.979.3		32	7.2	even	3
1470.3.h.a.979.4		32	35.19	odd	6
1470.3.h.a.979.5		32	7.5	odd	6
1470.3.h.a.979.6		32	35.9	even	6

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.95025 + 4.60397i) q^{5} -2.44949i q^{6} +(-2.31437 + 6.60634i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.95025 + 4.60397i) q^{5} -2.44949i q^{6} +(-2.31437 + 6.60634i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-0.866933 + 7.01772i) q^{10} +(-0.676822 - 1.17229i) q^{11} +(1.73205 - 3.00000i) q^{12} -5.90570 q^{13} +(-7.50590 + 6.45457i) q^{14} +(5.21698 - 6.91253i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(6.21669 + 10.7676i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(27.5764 + 15.9212i) q^{19} +(-6.02405 + 7.98190i) q^{20} +(11.9138 - 2.24971i) q^{21} -1.91434i q^{22} +(-1.31291 - 0.758007i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-17.3930 + 17.9578i) q^{25} +(-7.23297 - 4.17596i) q^{26} +5.19615 q^{27} +(-13.7569 + 2.59774i) q^{28} -15.0401 q^{29} +(11.2774 - 4.77713i) q^{30} +(40.3078 - 23.2717i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-1.17229 + 2.03047i) q^{33} +17.5835i q^{34} +(-34.9290 + 2.22876i) q^{35} -6.00000 q^{36} +(-0.441269 - 0.254767i) q^{37} +(22.5160 + 38.9989i) q^{38} +(5.11448 + 8.85855i) q^{39} +(-13.0220 + 5.51615i) q^{40} -36.0723i q^{41} +(16.1822 + 5.66902i) q^{42} -67.6102i q^{43} +(1.35364 - 2.34458i) q^{44} +(-14.8868 - 1.83904i) q^{45} +(-1.07198 - 1.85673i) q^{46} +(24.7767 - 42.9145i) q^{47} +6.92820 q^{48} +(-38.2874 - 30.5790i) q^{49} +(-34.0001 + 9.69500i) q^{50} +(10.7676 - 18.6501i) q^{51} +(-5.90570 - 10.2290i) q^{52} +(-45.5850 + 26.3185i) q^{53} +(6.36396 + 3.67423i) q^{54} +(4.07721 - 5.40233i) q^{55} +(-18.6855 - 6.54602i) q^{56} -55.1527i q^{57} +(-18.4203 - 10.6350i) q^{58} +(-62.0731 + 35.8379i) q^{59} +(17.1898 + 2.12354i) q^{60} +(50.6801 + 29.2602i) q^{61} +65.8224 q^{62} +(-13.6922 - 15.9224i) q^{63} -8.00000 q^{64} +(-11.5176 - 27.1896i) q^{65} +(-2.87151 + 1.65787i) q^{66} +(109.299 - 63.1041i) q^{67} +(-12.4334 + 21.5353i) q^{68} +2.62581i q^{69} +(-44.3550 - 21.9688i) q^{70} -55.4750 q^{71} +(-7.34847 - 4.24264i) q^{72} +(26.5796 + 46.0373i) q^{73} +(-0.360295 - 0.624048i) q^{74} +(41.9995 + 10.5376i) q^{75} +63.6849i q^{76} +(9.31097 - 1.75821i) q^{77} +14.4659i q^{78} +(19.9706 - 34.5901i) q^{79} +(-19.8491 - 2.45206i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(25.5069 - 44.1793i) q^{82} +120.455 q^{83} +(15.8104 + 18.3856i) q^{84} +(-37.4497 + 49.6211i) q^{85} +(47.8076 - 82.8052i) q^{86} +(13.0252 + 22.5602i) q^{87} +(3.31574 - 1.91434i) q^{88} +(-5.68455 - 3.28198i) q^{89} +(-16.9322 - 12.7789i) q^{90} +(13.6680 - 39.0150i) q^{91} -3.03203i q^{92} +(-69.8152 - 40.3078i) q^{93} +(60.6903 - 35.0395i) q^{94} +(-19.5199 + 158.011i) q^{95} +(8.48528 + 4.89898i) q^{96} +154.334 q^{97} +(-25.2697 - 64.5247i) q^{98} +4.06093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more