LMFDB - Embedded newform 210.3.o.b.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(31,210)]

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, 0, 1]))

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

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

chi := DirichletCharacter("210.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.o (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.7
Root			$0.848921 + 1.47037i$ of defining polynomial
Character	$\chi$	$=$	210.31
Dual form			210.3.o.b.61.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.38854 + 2.86123i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.38854 + 2.86123i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.73861 + 1.58114i) q^{10} +(-9.98749 + 17.2988i) q^{11} +(3.00000 - 1.73205i) q^{12} +3.49788i q^{13} +(-8.02165 - 5.80113i) q^{14} -3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(15.7982 + 9.12112i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-21.3143 + 12.3058i) q^{19} +4.47214i q^{20} +(12.0607 + 1.24079i) q^{21} -28.2489 q^{22} +(-12.5952 - 21.8155i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-4.28401 + 2.47338i) q^{26} -5.19615i q^{27} +(1.43274 - 13.9265i) q^{28} -53.1223 q^{29} +(-2.73861 - 4.74342i) q^{30} +(26.0944 + 15.0656i) q^{31} +(2.82843 - 4.89898i) q^{32} +(29.9625 - 17.2988i) q^{33} +25.7984i q^{34} +(-9.17240 + 12.6833i) q^{35} -6.00000 q^{36} +(23.3846 + 40.5034i) q^{37} +(-30.1429 - 17.4030i) q^{38} +(3.02925 - 5.24682i) q^{39} +(-5.47723 + 3.16228i) q^{40} -31.5250i q^{41} +(7.00855 + 15.6487i) q^{42} +64.4116 q^{43} +(-19.9750 - 34.5977i) q^{44} +(5.80948 + 3.35410i) q^{45} +(17.8123 - 30.8518i) q^{46} +(-24.3029 + 14.0313i) q^{47} +6.92820i q^{48} +(32.6268 - 36.5581i) q^{49} +7.07107 q^{50} +(-15.7982 - 27.3634i) q^{51} +(-6.05851 - 3.49788i) q^{52} +(32.4374 - 56.1833i) q^{53} +(6.36396 - 3.67423i) q^{54} +44.6654i q^{55} +(18.0695 - 8.09277i) q^{56} +42.6285 q^{57} +(-37.5631 - 65.0613i) q^{58} +(86.7684 + 50.0958i) q^{59} +(3.87298 - 6.70820i) q^{60} +(6.94896 - 4.01198i) q^{61} +42.6119i q^{62} +(-17.0165 - 12.3061i) q^{63} +8.00000 q^{64} +(3.91075 + 6.77362i) q^{65} +(42.3733 + 24.4642i) q^{66} +(-8.13165 + 14.0844i) q^{67} +(-31.5965 + 18.2422i) q^{68} +43.6310i q^{69} +(-22.0197 - 2.26537i) q^{70} -107.725 q^{71} +(-4.24264 - 7.34847i) q^{72} +(44.7395 + 25.8303i) q^{73} +(-33.0709 + 57.2804i) q^{74} +(-7.50000 + 4.33013i) q^{75} -49.2232i q^{76} +(14.3095 - 139.091i) q^{77} +8.56803 q^{78} +(10.9877 + 19.0313i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(38.6101 - 22.2916i) q^{82} +0.417479i q^{83} +(-14.2098 + 19.6489i) q^{84} +40.7909 q^{85} +(45.5459 + 78.8878i) q^{86} +(79.6835 + 46.0053i) q^{87} +(28.2489 - 48.9285i) q^{88} +(-96.3110 + 55.6052i) q^{89} +9.48683i q^{90} +(-10.0082 - 22.3463i) q^{91} +50.3807 q^{92} +(-26.0944 - 45.1968i) q^{93} +(-34.3695 - 19.8432i) q^{94} +(-27.5166 + 47.6601i) q^{95} +(-8.48528 + 4.89898i) q^{96} +74.2244i q^{97} +(67.8449 + 14.1090i) q^{98} -59.9249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		−	2.44949i		−	0.408248i
$7$	−6.38854	+	2.86123i	−0.912648	+	0.408747i
$7$	−6.38854	+	2.86123i	−0.912648	+	0.408747i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	−9.98749	+	17.2988i	−0.907953	+	1.57262i	−0.0910503	+	0.995846i	$0.529022\pi$
$11$	−9.98749	+	17.2988i	−0.907953	+	1.57262i	−0.816903	+	0.576775i	$0.804311\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$			3.49788i			0.269068i	0.990909	+	0.134534i	$0.0429537\pi$
$13$			3.49788i			0.269068i	−0.990909	+	0.134534i	$0.957046\pi$
$14$	−8.02165	−	5.80113i	−0.572975	−	0.414367i
$15$	−3.87298			−0.258199
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	15.7982	+	9.12112i	0.929308	+	0.536536i	0.886593	−	0.462551i	$-0.153066\pi$
$17$	15.7982	+	9.12112i	0.929308	+	0.536536i	0.0427155	+	0.999087i	$0.486399\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	−21.3143	+	12.3058i	−1.12180	+	0.647673i	−0.941861	−	0.336004i	$-0.890924\pi$
$19$	−21.3143	+	12.3058i	−1.12180	+	0.647673i	−0.179942	+	0.983677i	$0.557591\pi$
$20$			4.47214i			0.223607i
$21$	12.0607	+	1.24079i	0.574319	+	0.0590854i
$22$	−28.2489			−1.28404
$23$	−12.5952	−	21.8155i	−0.547617	−	0.948500i	−0.998437	−	0.0558853i	$-0.982202\pi$
$23$	−12.5952	−	21.8155i	−0.547617	−	0.948500i	0.450820	−	0.892615i	$-0.351131\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−4.28401	+	2.47338i	−0.164770	+	0.0951299i
$27$		−	5.19615i		−	0.192450i
$28$	1.43274	−	13.9265i	0.0511694	−	0.497375i
$29$	−53.1223			−1.83180			−0.915902	−	0.401402i	$-0.868523\pi$
$29$	−53.1223			−1.83180			−0.915902	+	0.401402i	$0.868523\pi$
$30$	−2.73861	−	4.74342i	−0.0912871	−	0.158114i
$31$	26.0944	+	15.0656i	0.841754	+	0.485987i	0.857860	−	0.513883i	$-0.171794\pi$
$31$	26.0944	+	15.0656i	0.841754	+	0.485987i	−0.0161061	+	0.999870i	$0.505127\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	29.9625	−	17.2988i	0.907953	−	0.524207i
$34$			25.7984i			0.758777i
$35$	−9.17240	+	12.6833i	−0.262068	+	0.362381i
$36$	−6.00000			−0.166667
$37$	23.3846	+	40.5034i	0.632017	+	1.09469i	0.987139	+	0.159866i	$0.0511061\pi$
$37$	23.3846	+	40.5034i	0.632017	+	1.09469i	−0.355122	+	0.934820i	$0.615561\pi$
$38$	−30.1429	−	17.4030i	−0.793234	−	0.457974i
$39$	3.02925	−	5.24682i	0.0776732	−	0.134534i
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$		−	31.5250i		−	0.768903i	−0.923145	−	0.384452i	$-0.874391\pi$
$41$		−	31.5250i		−	0.768903i	0.923145	−	0.384452i	$-0.125609\pi$
$42$	7.00855	+	15.6487i	0.166870	+	0.372587i
$43$	64.4116			1.49794			0.748972	−	0.662602i	$-0.230548\pi$
$43$	64.4116			1.49794			0.748972	+	0.662602i	$0.230548\pi$
$44$	−19.9750	−	34.5977i	−0.453977	−	0.786311i
$45$	5.80948	+	3.35410i	0.129099	+	0.0745356i
$46$	17.8123	−	30.8518i	0.387223	−	0.670691i
$47$	−24.3029	+	14.0313i	−0.517083	+	0.298538i	−0.735740	−	0.677264i	$-0.763166\pi$
$47$	−24.3029	+	14.0313i	−0.517083	+	0.298538i	0.218657	+	0.975802i	$0.429832\pi$
$48$			6.92820i			0.144338i
$49$	32.6268	−	36.5581i	0.665852	−	0.746084i
$50$	7.07107			0.141421
$51$	−15.7982	−	27.3634i	−0.309769	−	0.536536i
$52$	−6.05851	−	3.49788i	−0.116510	−	0.0672670i
$53$	32.4374	−	56.1833i	0.612027	−	1.06006i	−0.378872	−	0.925449i	$-0.623688\pi$
$53$	32.4374	−	56.1833i	0.612027	−	1.06006i	0.990898	−	0.134612i	$-0.0429789\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$			44.6654i			0.812098i
$56$	18.0695	−	8.09277i	0.322670	−	0.144514i
$57$	42.6285			0.747869
$58$	−37.5631	−	65.0613i	−0.647640	−	1.12175i
$59$	86.7684	+	50.0958i	1.47065	+	0.849081i	0.999457	−	0.0329486i	$-0.0104897\pi$
$59$	86.7684	+	50.0958i	1.47065	+	0.849081i	0.471194	+	0.882029i	$0.343823\pi$
$60$	3.87298	−	6.70820i	0.0645497	−	0.111803i
$61$	6.94896	−	4.01198i	0.113917	−	0.0657702i	−0.441959	−	0.897035i	$-0.645716\pi$
$61$	6.94896	−	4.01198i	0.113917	−	0.0657702i	0.555876	+	0.831265i	$0.312383\pi$
$62$			42.6119i			0.687289i
$63$	−17.0165	−	12.3061i	−0.270103	−	0.195334i
$64$	8.00000			0.125000
$65$	3.91075	+	6.77362i	0.0601654	+	0.104210i
$66$	42.3733	+	24.4642i	0.642020	+	0.370670i
$67$	−8.13165	+	14.0844i	−0.121368	+	0.210215i	−0.920307	−	0.391196i	$-0.872061\pi$
$67$	−8.13165	+	14.0844i	−0.121368	+	0.210215i	0.798939	+	0.601411i	$0.205395\pi$
$68$	−31.5965	+	18.2422i	−0.464654	+	0.268268i
$69$			43.6310i			0.632333i
$70$	−22.0197	−	2.26537i	−0.314567	−	0.0323624i
$71$	−107.725			−1.51725			−0.758625	−	0.651528i	$-0.774128\pi$
$71$	−107.725			−1.51725			−0.758625	+	0.651528i	$0.774128\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	44.7395	+	25.8303i	0.612870	+	0.353840i	0.774088	−	0.633078i	$-0.218209\pi$
$73$	44.7395	+	25.8303i	0.612870	+	0.353840i	−0.161218	+	0.986919i	$0.551542\pi$
$74$	−33.0709	+	57.2804i	−0.446904	+	0.774060i
$75$	−7.50000	+	4.33013i	−0.100000	+	0.0577350i
$76$		−	49.2232i		−	0.647673i
$77$	14.3095	−	139.091i	0.185838	−	1.80637i
$78$	8.56803			0.109846
$79$	10.9877	+	19.0313i	0.139085	+	0.240903i	0.927151	−	0.374689i	$-0.122250\pi$
$79$	10.9877	+	19.0313i	0.139085	+	0.240903i	−0.788065	+	0.615592i	$0.788917\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	38.6101	−	22.2916i	0.470855	−	0.271848i
$83$			0.417479i			0.00502987i	0.999997	+	0.00251494i	$0.000800530\pi$
$83$			0.417479i			0.00502987i	−0.999997	+	0.00251494i	$0.999199\pi$
$84$	−14.2098	+	19.6489i	−0.169164	+	0.233916i
$85$	40.7909			0.479893
$86$	45.5459	+	78.8878i	0.529603	+	0.917300i
$87$	79.6835	+	46.0053i	0.915902	+	0.528796i
$88$	28.2489	−	48.9285i	0.321010	−	0.556006i
$89$	−96.3110	+	55.6052i	−1.08215	+	0.624778i	−0.931475	−	0.363806i	$-0.881477\pi$
$89$	−96.3110	+	55.6052i	−1.08215	+	0.624778i	−0.150672	+	0.988584i	$0.548144\pi$
$90$			9.48683i			0.105409i
$91$	−10.0082	−	22.3463i	−0.109981	−	0.245564i
$92$	50.3807			0.547617
$93$	−26.0944	−	45.1968i	−0.280585	−	0.485987i
$94$	−34.3695	−	19.8432i	−0.365633	−	0.211098i
$95$	−27.5166	+	47.6601i	−0.289648	+	0.501686i
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$			74.2244i			0.765200i	0.923914	+	0.382600i	$0.124971\pi$
$97$			74.2244i			0.765200i	−0.923914	+	0.382600i	$0.875029\pi$
$98$	67.8449	+	14.1090i	0.692295	+	0.143969i
$99$	−59.9249			−0.605302
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	75.8587	+	43.7970i	0.751076	+	0.433634i	0.826083	−	0.563549i	$-0.190564\pi$
$101$	75.8587	+	43.7970i	0.751076	+	0.433634i	−0.0750065	+	0.997183i	$0.523898\pi$
$102$	22.3421	−	38.6976i	0.219040	−	0.379388i
$103$	120.413	−	69.5206i	1.16906	−	0.674957i	0.215601	−	0.976482i	$-0.430829\pi$
$103$	120.413	−	69.5206i	1.16906	−	0.674957i	0.953458	+	0.301525i	$0.0974956\pi$
$104$		−	9.89350i		−	0.0951299i
$105$	24.7427	−	11.0815i	0.235645	−	0.105538i
$106$	91.7469			0.865537
$107$	−76.0949	−	131.800i	−0.711168	−	1.23178i	−0.964419	−	0.264378i	$-0.914833\pi$
$107$	−76.0949	−	131.800i	−0.711168	−	1.23178i	0.253252	−	0.967400i	$-0.418500\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	−32.3777	+	56.0798i	−0.297043	+	0.514494i	−0.975458	−	0.220185i	$-0.929334\pi$
$109$	−32.3777	+	56.0798i	−0.297043	+	0.514494i	0.678415	+	0.734679i	$0.262667\pi$
$110$	−54.7037	+	31.5832i	−0.497307	+	0.287120i
$111$		−	81.0068i		−	0.729791i
$112$	22.6887	+	16.4081i	0.202577	+	0.146501i
$113$	3.25860			0.0288372			0.0144186	−	0.999896i	$-0.495410\pi$
$113$	3.25860			0.0288372			0.0144186	+	0.999896i	$0.495410\pi$
$114$	30.1429	+	52.2090i	0.264411	+	0.457974i
$115$	−48.7809	−	28.1637i	−0.424182	−	0.244902i
$116$	53.1223	−	92.0105i	0.457951	−	0.793194i
$117$	−9.08776	+	5.24682i	−0.0776732	+	0.0448446i
$118$			141.692i			1.20078i
$119$	−127.025	−	13.0682i	−1.06744	−	0.109817i
$120$	10.9545			0.0912871
$121$	−139.000	−	240.755i	−1.14876	−	1.98971i
$122$	9.82731	+	5.67380i	0.0805517	+	0.0465066i
$123$	−27.3015	+	47.2875i	−0.221963	+	0.384452i
$124$	−52.1887	+	30.1312i	−0.420877	+	0.242993i
$125$		−	11.1803i		−	0.0894427i
$126$	3.03931	−	29.5426i	0.0241215	−	0.234465i
$127$	−88.5772			−0.697458			−0.348729	−	0.937224i	$-0.613387\pi$
$127$	−88.5772			−0.697458			−0.348729	+	0.937224i	$0.613387\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−96.6174	−	55.7821i	−0.748972	−	0.432419i
$130$	−5.53064	+	9.57934i	−0.0425434	+	0.0736873i
$131$	−108.361	+	62.5621i	−0.827181	+	0.477573i	−0.852887	−	0.522096i	$-0.825150\pi$
$131$	−108.361	+	62.5621i	−0.827181	+	0.477573i	0.0257055	+	0.999670i	$0.491817\pi$
$132$			69.1953i			0.524207i
$133$	100.957	−	139.601i	0.759077	−	1.04963i
$134$	−22.9998			−0.171640
$135$	−5.80948	−	10.0623i	−0.0430331	−	0.0745356i
$136$	−44.6842	−	25.7984i	−0.328560	−	0.189694i
$137$	19.4769	−	33.7349i	0.142167	−	0.246240i	−0.786145	−	0.618042i	$-0.787926\pi$
$137$	19.4769	−	33.7349i	0.142167	−	0.246240i	0.928312	+	0.371801i	$0.121260\pi$
$138$	−53.4368	+	30.8518i	−0.387223	+	0.223564i
$139$			98.9454i			0.711837i	0.934517	+	0.355919i	$0.115832\pi$
$139$			98.9454i			0.711837i	−0.934517	+	0.355919i	$0.884168\pi$
$140$	−12.7958	−	28.5704i	−0.0913985	−	0.204074i
$141$	48.6058			0.344722
$142$	−76.1729	−	131.935i	−0.536429	−	0.929122i
$143$	−60.5093	−	34.9351i	−0.423142	−	0.244301i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	−102.871	+	59.3925i	−0.709455	+	0.409604i
$146$			73.0593i			0.500406i
$147$	−80.6004	+	26.5815i	−0.548302	+	0.180827i
$148$	−93.5385			−0.632017
$149$	93.2324	+	161.483i	0.625721	+	1.08378i	0.988401	+	0.151867i	$0.0485284\pi$
$149$	93.2324	+	161.483i	0.625721	+	1.08378i	−0.362680	+	0.931914i	$0.618138\pi$
$150$	−10.6066	−	6.12372i	−0.0707107	−	0.0408248i
$151$	−77.4202	+	134.096i	−0.512716	+	0.888051i	0.487175	+	0.873304i	$0.338027\pi$
$151$	−77.4202	+	134.096i	−0.512716	+	0.888051i	−0.999891	+	0.0147462i	$0.995306\pi$
$152$	60.2858	−	34.8060i	0.396617	−	0.228987i
$153$			54.7267i			0.357691i
$154$	180.469	−	80.8265i	1.17188	−	0.524847i
$155$	67.3754			0.434680
$156$	6.05851	+	10.4936i	0.0388366	+	0.0672670i
$157$	−43.4777	−	25.1019i	−0.276928	−	0.159885i	0.355104	−	0.934827i	$-0.384446\pi$
$157$	−43.4777	−	25.1019i	−0.276928	−	0.159885i	−0.632032	+	0.774942i	$0.717779\pi$
$158$	−15.5390	+	26.9143i	−0.0983481	+	0.170344i
$159$	−97.3123	+	56.1833i	−0.612027	+	0.353354i
$160$		−	12.6491i		−	0.0790569i
$161$	142.884	+	103.331i	0.887477	+	0.641810i
$162$	−12.7279			−0.0785674
$163$	57.9054	+	100.295i	0.355248	+	0.615308i	0.987160	−	0.159732i	$-0.0510631\pi$
$163$	57.9054	+	100.295i	0.355248	+	0.615308i	−0.631912	+	0.775040i	$0.717730\pi$
$164$	54.6029	+	31.5250i	0.332945	+	0.192226i
$165$	38.6814	−	66.9981i	0.234433	−	0.406049i
$166$	−0.511306	+	0.295202i	−0.00308015	+	0.00177833i
$167$		−	61.3210i		−	0.367191i	−0.983002	−	0.183596i	$-0.941226\pi$
$167$		−	61.3210i		−	0.367191i	0.983002	−	0.183596i	$-0.0587737\pi$
$168$	−34.1128	−	3.50949i	−0.203052	−	0.0208898i
$169$	156.765			0.927602
$170$	28.8435	+	49.9584i	0.169668	+	0.293873i
$171$	−63.9428	−	36.9174i	−0.373934	−	0.215891i
$172$	−64.4116	+	111.564i	−0.374486	+	0.648629i
$173$	27.4544	−	15.8508i	0.158696	−	0.0916232i	−0.418549	−	0.908194i	$-0.637461\pi$
$173$	27.4544	−	15.8508i	0.158696	−	0.0916232i	0.577245	+	0.816571i	$0.304128\pi$
$174$			130.123i			0.747831i
$175$	−3.58186	+	34.8162i	−0.0204678	+	0.198950i
$176$	79.8999			0.453977
$177$	−86.7684	−	150.287i	−0.490217	−	0.849081i
$178$	−136.204	−	78.6376i	−0.765193	−	0.441784i
$179$	−65.9472	+	114.224i	−0.368420	+	0.638122i	−0.989319	−	0.145768i	$-0.953435\pi$
$179$	−65.9472	+	114.224i	−0.368420	+	0.638122i	0.620899	+	0.783891i	$0.286768\pi$
$180$	−11.6190	+	6.70820i	−0.0645497	+	0.0372678i
$181$			55.1431i			0.304658i	0.988330	+	0.152329i	$0.0486773\pi$
$181$			55.1431i			0.304658i	−0.988330	+	0.152329i	$0.951323\pi$
$182$	20.2917	−	28.0588i	0.111493	−	0.154169i
$183$	−13.8979			−0.0759449
$184$	35.6246	+	61.7035i	0.193612	+	0.335345i
$185$	90.5683	+	52.2896i	0.489558	+	0.282647i
$186$	36.9030	−	63.9179i	0.198403	−	0.343645i
$187$	−315.569	+	182.194i	−1.68754	+	0.974300i
$188$		−	56.1252i		−	0.298538i
$189$	14.8674	+	33.1958i	0.0786633	+	0.175639i
$190$	−77.8287			−0.409625
$191$	−97.5822	−	169.017i	−0.510901	−	0.884907i	−0.999920	−	0.0126340i	$-0.995978\pi$
$191$	−97.5822	−	169.017i	−0.510901	−	0.884907i	0.489019	−	0.872273i	$-0.337355\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	−174.380	+	302.035i	−0.903523	+	1.56495i	−0.0806348	+	0.996744i	$0.525695\pi$
$193$	−174.380	+	302.035i	−0.903523	+	1.56495i	−0.822888	+	0.568204i	$0.807639\pi$
$194$	−90.9060	+	52.4846i	−0.468588	+	0.270539i
$195$		−	13.5472i		−	0.0694730i
$196$	30.6937	+	93.0693i	0.156601	+	0.474843i
$197$	−56.3808			−0.286197			−0.143098	−	0.989708i	$-0.545707\pi$
$197$	−56.3808			−0.286197			−0.143098	+	0.989708i	$0.545707\pi$
$198$	−42.3733	−	73.3927i	−0.214007	−	0.370670i
$199$	148.357	+	85.6540i	0.745513	+	0.430422i	0.824070	−	0.566487i	$-0.191698\pi$
$199$	148.357	+	85.6540i	0.745513	+	0.430422i	−0.0785571	+	0.996910i	$0.525031\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$	24.3950	−	14.0844i	0.121368	−	0.0700718i
$202$			123.877i			0.613251i
$203$	339.374	−	151.995i	1.67179	−	0.748744i
$204$	63.1930			0.309769
$205$	−35.2460	−	61.0479i	−0.171932	−	0.297795i
$206$	170.290	+	98.3169i	0.826650	+	0.477267i
$207$	37.7856	−	65.4465i	0.182539	−	0.316167i
$208$	12.1170	−	6.99576i	0.0582549	−	0.0336335i
$209$		−	491.616i		−	2.35223i
$210$	31.0677	+	22.4677i	0.147942	+	0.106989i
$211$	162.038			0.767954			0.383977	−	0.923343i	$-0.374554\pi$
$211$	162.038			0.767954			0.383977	+	0.923343i	$0.374554\pi$
$212$	64.8748	+	112.367i	0.306013	+	0.530031i
$213$	161.587	+	93.2923i	0.758625	+	0.437992i
$214$	107.614	−	186.394i	0.502871	−	0.870999i
$215$	124.733	−	72.0144i	0.580151	−	0.334951i
$216$			14.6969i			0.0680414i
$217$	−209.811	−	21.5851i	−0.966870	−	0.0994707i
$218$	−91.5779			−0.420082
$219$	−44.7395	−	77.4910i	−0.204290	−	0.353840i
$220$	−77.3627	−	44.6654i	−0.351649	−	0.203025i
$221$	−31.9046	+	55.2604i	−0.144365	+	0.250047i
$222$	99.2126	−	57.2804i	0.446904	−	0.258020i
$223$		−	365.329i		−	1.63825i	−0.573618	−	0.819123i	$-0.694461\pi$
$223$		−	365.329i		−	1.63825i	0.573618	−	0.819123i	$-0.305539\pi$
$224$	−4.05241	+	39.3901i	−0.0180911	+	0.175849i
$225$	15.0000			0.0666667
$226$	2.30418	+	3.99096i	0.0101955	+	0.0176591i
$227$	223.325	+	128.937i	0.983811	+	0.568004i	0.903419	−	0.428759i	$-0.141049\pi$
$227$	223.325	+	128.937i	0.983811	+	0.568004i	0.0803928	+	0.996763i	$0.474383\pi$
$228$	−42.6285	+	73.8347i	−0.186967	+	0.323837i
$229$	−13.3634	+	7.71538i	−0.0583556	+	0.0336916i	−0.528894	−	0.848688i	$-0.677393\pi$
$229$	−13.3634	+	7.71538i	−0.0583556	+	0.0336916i	0.470538	+	0.882380i	$0.344060\pi$
$230$		−	79.6589i		−	0.346343i
$231$	−141.920	+	196.244i	−0.614374	+	0.849539i
$232$	150.253			0.647640
$233$	62.6734	+	108.553i	0.268984	+	0.465895i	0.968600	−	0.248625i	$-0.0799786\pi$
$233$	62.6734	+	108.553i	0.268984	+	0.465895i	−0.699615	+	0.714520i	$0.746645\pi$
$234$	−12.8520	−	7.42013i	−0.0549232	−	0.0317100i
$235$	−31.3749	+	54.3430i	−0.133510	+	0.231247i
$236$	−173.537	+	100.192i	−0.735326	+	0.424540i
$237$		−	38.0626i		−	0.160602i
$238$	−73.8151	−	164.814i	−0.310148	−	0.692496i
$239$	−3.62565			−0.0151701			−0.00758503	−	0.999971i	$-0.502414\pi$
$239$	−3.62565			−0.0151701			−0.00758503	+	0.999971i	$0.502414\pi$
$240$	7.74597	+	13.4164i	0.0322749	+	0.0559017i
$241$	83.6915	+	48.3193i	0.347268	+	0.200495i	0.663481	−	0.748193i	$-0.269078\pi$
$241$	83.6915	+	48.3193i	0.347268	+	0.200495i	−0.316213	+	0.948688i	$0.602412\pi$
$242$	196.575	−	340.479i	0.812295	−	1.40694i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$			16.0479i			0.0657702i
$245$	22.3083	−	107.272i	0.0910541	−	0.437846i
$246$	−77.2202			−0.313903
$247$	−43.0442	−	74.5548i	−0.174268	−	0.301841i
$248$	−73.8060	−	42.6119i	−0.297605	−	0.171822i
$249$	0.361548	−	0.626219i	0.00145200	−	0.00251494i
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$		−	29.7311i		−	0.118450i	−0.998245	−	0.0592252i	$-0.981137\pi$
$251$		−	29.7311i		−	0.118450i	0.998245	−	0.0592252i	$-0.0188630\pi$
$252$	38.3312	−	17.1674i	0.152108	−	0.0681245i
$253$	503.177			1.98884
$254$	−62.6336	−	108.484i	−0.246589	−	0.427104i
$255$	−61.1863	−	35.3259i	−0.239946	−	0.138533i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	382.457	−	220.811i	1.48816	−	0.859189i	0.488250	−	0.872704i	$-0.337636\pi$
$257$	382.457	−	220.811i	1.48816	−	0.859189i	0.999909	+	0.0135154i	$0.00430222\pi$
$258$		−	157.776i		−	0.611533i
$259$	−265.283	−	191.848i	−1.02426	−	0.740728i
$260$	−15.6430			−0.0601654
$261$	−79.6835	−	138.016i	−0.305301	−	0.528796i
$262$	−153.245	−	88.4762i	−0.584905	−	0.337695i
$263$	−171.523	+	297.087i	−0.652180	+	1.12961i	0.330413	+	0.943836i	$0.392812\pi$
$263$	−171.523	+	297.087i	−0.652180	+	1.12961i	−0.982593	+	0.185772i	$0.940521\pi$
$264$	−84.7466	+	48.9285i	−0.321010	+	0.185335i
$265$		−	145.065i		−	0.547413i
$266$	242.363	+	24.9341i	0.911139	+	0.0937371i
$267$	192.622			0.721431
$268$	−16.2633	−	28.1689i	−0.0606840	−	0.105108i
$269$	401.274	+	231.676i	1.49172	+	0.861247i	0.999955	−	0.00947852i	$-0.00301715\pi$
$269$	401.274	+	231.676i	1.49172	+	0.861247i	0.491769	+	0.870726i	$0.336350\pi$
$270$	8.21584	−	14.2302i	0.0304290	−	0.0527046i
$271$	211.814	−	122.291i	0.781600	−	0.451257i	−0.0553967	−	0.998464i	$-0.517642\pi$
$271$	211.814	−	122.291i	0.781600	−	0.451257i	0.836997	+	0.547207i	$0.184309\pi$
$272$		−	72.9689i		−	0.268268i
$273$	−4.34015	+	42.1869i	−0.0158980	+	0.154531i
$274$	55.0889			0.201054
$275$	49.9374	+	86.4942i	0.181591	+	0.314524i
$276$	−75.5711	−	43.6310i	−0.273808	−	0.158083i
$277$	−70.5092	+	122.126i	−0.254546	+	0.440887i	−0.964772	−	0.263087i	$-0.915259\pi$
$277$	−70.5092	+	122.126i	−0.254546	+	0.440887i	0.710226	+	0.703974i	$0.248593\pi$
$278$	−121.183	+	69.9650i	−0.435910	+	0.251673i
$279$			90.3935i			0.323991i
$280$	25.9435	−	35.8739i	0.0926552	−	0.128121i
$281$	84.9953			0.302475			0.151237	−	0.988497i	$-0.451674\pi$
$281$	84.9953			0.302475			0.151237	+	0.988497i	$0.451674\pi$
$282$	34.3695	+	59.5297i	0.121878	+	0.211098i
$283$	−101.047	−	58.3392i	−0.357055	−	0.206146i	0.310733	−	0.950497i	$-0.399425\pi$
$283$	−101.047	−	58.3392i	−0.357055	−	0.206146i	−0.667788	+	0.744351i	$0.732759\pi$
$284$	107.725	−	186.585i	0.379312	−	0.656988i
$285$	82.5498	−	47.6601i	0.289648	−	0.167229i
$286$		−	98.8112i		−	0.345494i
$287$	90.2003	+	201.399i	0.314287	+	0.701738i
$288$	16.9706			0.0589256
$289$	21.8896	+	37.9138i	0.0757424	+	0.131190i
$290$	−145.481	−	83.9937i	−0.501660	−	0.289634i
$291$	64.2802	−	111.337i	0.220894	−	0.382600i
$292$	−89.4789	+	51.6607i	−0.306435	+	0.176920i
$293$			131.882i			0.450110i	0.974346	+	0.225055i	$0.0722562\pi$
$293$			131.882i			0.450110i	−0.974346	+	0.225055i	$0.927744\pi$
$294$	−89.5487	−	79.9189i	−0.304587	−	0.271833i
$295$	224.035			0.759441
$296$	−66.1417	−	114.561i	−0.223452	−	0.387030i
$297$	89.8874	+	51.8965i	0.302651	+	0.174736i
$298$	−131.851	+	228.372i	−0.442451	+	0.766348i
$299$	76.3080	−	44.0565i	0.255211	−	0.147346i
$300$		−	17.3205i		−	0.0577350i
$301$	−411.496	+	184.296i	−1.36710	+	0.612280i
$302$	−218.977			−0.725090
$303$	−75.8587	−	131.391i	−0.250359	−	0.433634i
$304$	85.2570	+	49.2232i	0.280451	+	0.161918i
$305$	8.97107	−	15.5383i	0.0294133	−	0.0509454i
$306$	−67.0263	+	38.6976i	−0.219040	+	0.126463i
$307$			429.871i			1.40023i	0.714030	+	0.700115i	$0.246868\pi$
$307$			429.871i			1.40023i	−0.714030	+	0.700115i	$0.753132\pi$
$308$	226.603	+	163.875i	0.735723	+	0.532063i
$309$	−240.826			−0.779373
$310$	47.6416	+	82.5176i	0.153683	+	0.266186i
$311$	−217.786	−	125.739i	−0.700277	−	0.404305i	0.107174	−	0.994240i	$-0.465820\pi$
$311$	−217.786	−	125.739i	−0.700277	−	0.404305i	−0.807451	+	0.589935i	$0.799153\pi$
$312$	−8.56803	+	14.8403i	−0.0274616	+	0.0475649i
$313$	11.8674	−	6.85166i	0.0379151	−	0.0218903i	−0.480923	−	0.876763i	$-0.659698\pi$
$313$	11.8674	−	6.85166i	0.0379151	−	0.0218903i	0.518838	+	0.854873i	$0.326365\pi$
$314$		−	70.9988i		−	0.226111i
$315$	−46.7109	−	4.80557i	−0.148289	−	0.0152558i
$316$	−43.9509			−0.139085
$317$	16.4651	+	28.5183i	0.0519403	+	0.0899632i	0.890827	−	0.454343i	$-0.150126\pi$
$317$	16.4651	+	28.5183i	0.0519403	+	0.0899632i	−0.838886	+	0.544307i	$0.816793\pi$
$318$	−137.620	−	79.4551i	−0.432768	−	0.249859i
$319$	530.558	−	918.954i	1.66319	−	2.88073i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$			263.601i			0.821186i
$322$	−25.5204	+	248.063i	−0.0792560	+	0.770381i
$323$	−448.970			−1.39000
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	15.1463	+	8.74471i	0.0466039	+	0.0269068i
$326$	−81.8906	+	141.839i	−0.251198	+	0.435088i
$327$	97.1331	−	56.0798i	0.297043	−	0.171498i
$328$			89.1662i			0.271848i
$329$	115.113	−	159.176i	0.349888	−	0.483816i
$330$	109.407			0.331538
$331$	208.940	+	361.895i	0.631240	+	1.09334i	0.987299	+	0.158876i	$0.0507869\pi$
$331$	208.940	+	361.895i	0.631240	+	1.09334i	−0.356059	+	0.934464i	$0.615880\pi$
$332$	−0.723095	−	0.417479i	−0.00217800	−	0.00125747i
$333$	−70.1539	+	121.510i	−0.210672	+	0.364895i
$334$	75.1025	−	43.3605i	0.224858	−	0.129822i
$335$			36.3658i			0.108555i
$336$	−19.8232	−	44.2611i	−0.0589975	−	0.131729i
$337$	−286.688			−0.850705			−0.425353	−	0.905028i	$-0.639850\pi$
$337$	−286.688			−0.850705			−0.425353	+	0.905028i	$0.639850\pi$
$338$	110.849	+	191.997i	0.327957	+	0.568038i
$339$	−4.88790	−	2.82203i	−0.0144186	−	0.00832458i
$340$	−40.7909	+	70.6519i	−0.119973	+	0.207800i
$341$	−521.234	+	300.935i	−1.52855	+	0.882507i
$342$		−	104.418i		−	0.305316i
$343$	−103.836	+	326.905i	−0.302729	+	0.953077i
$344$	−182.184			−0.529603
$345$	48.7809	+	84.4911i	0.141394	+	0.244902i
$346$	38.8264	+	22.4164i	0.112215	+	0.0647874i
$347$	−153.398	+	265.693i	−0.442069	+	0.765685i	−0.997843	−	0.0656479i	$-0.979089\pi$
$347$	−153.398	+	265.693i	−0.442069	+	0.765685i	0.555774	+	0.831333i	$0.312422\pi$
$348$	−159.367	+	92.0105i	−0.457951	+	0.264398i
$349$		−	340.162i		−	0.974676i	−0.873214	−	0.487338i	$-0.837968\pi$
$349$		−	340.162i		−	0.974676i	0.873214	−	0.487338i	$-0.162032\pi$
$350$	−45.1738	+	20.2319i	−0.129068	+	0.0578055i
$351$	18.1755			0.0517821
$352$	56.4978	+	97.8570i	0.160505	+	0.278003i
$353$	−324.761	−	187.501i	−0.920004	−	0.531165i	−0.0363676	−	0.999338i	$-0.511579\pi$
$353$	−324.761	−	187.501i	−0.920004	−	0.531165i	−0.883636	+	0.468174i	$0.844912\pi$
$354$	122.709	−	212.538i	0.346636	−	0.600391i
$355$	−208.608	+	120.440i	−0.587628	+	0.339267i
$356$		−	222.421i		−	0.624778i
$357$	179.220	+	129.609i	0.502018	+	0.363051i
$358$	−186.527			−0.521025
$359$	164.750	+	285.356i	0.458915	+	0.794863i	0.998904	−	0.0468084i	$-0.0149050\pi$
$359$	164.750	+	285.356i	0.458915	+	0.794863i	−0.539989	+	0.841672i	$0.681572\pi$
$360$	−16.4317	−	9.48683i	−0.0456435	−	0.0263523i
$361$	122.365	−	211.942i	0.338961	−	0.587098i
$362$	−67.5362	+	38.9920i	−0.186564	+	0.107713i
$363$			481.509i			1.32647i
$364$	48.7132	+	5.01157i	0.133828	+	0.0137681i
$365$	115.517			0.316484
$366$	−9.82731	−	17.0214i	−0.0268506	−	0.0465066i
$367$	23.5163	+	13.5772i	0.0640772	+	0.0369950i	0.531696	−	0.846935i	$-0.321555\pi$
$367$	23.5163	+	13.5772i	0.0640772	+	0.0369950i	−0.467619	+	0.883930i	$0.654888\pi$
$368$	−50.3807	+	87.2620i	−0.136904	+	0.237125i
$369$	81.9044	−	47.2875i	0.221963	−	0.128151i
$370$			147.897i			0.399723i
$371$	−46.4745	+	451.740i	−0.125268	+	1.21763i
$372$	104.377			0.280585
$373$	−63.7488	−	110.416i	−0.170908	−	0.296022i	0.767829	−	0.640654i	$-0.221337\pi$
$373$	−63.7488	−	110.416i	−0.170908	−	0.296022i	−0.938738	+	0.344633i	$0.888004\pi$
$374$	−446.283	−	257.661i	−1.19327	−	0.688934i
$375$	−9.68246	+	16.7705i	−0.0258199	+	0.0447214i
$376$	68.7390	−	39.6865i	0.182817	−	0.105549i
$377$		−	185.816i		−	0.492880i
$378$	−30.1436	+	41.6817i	−0.0797449	+	0.110269i
$379$	319.795			0.843785			0.421893	−	0.906646i	$-0.361366\pi$
$379$	319.795			0.843785			0.421893	+	0.906646i	$0.361366\pi$
$380$	−55.0332	−	95.3202i	−0.144824	−	0.250843i
$381$	132.866	+	76.7101i	0.348729	+	0.201339i
$382$	138.002	−	239.027i	0.361262	−	0.625724i
$383$	354.155	−	204.471i	0.924686	−	0.533867i	0.0395587	−	0.999217i	$-0.487405\pi$
$383$	354.155	−	204.471i	0.924686	−	0.533867i	0.885127	+	0.465350i	$0.154071\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−127.798	−	285.346i	−0.331942	−	0.741160i
$386$	−493.221			−1.27777
$387$	96.6174	+	167.346i	0.249657	+	0.432419i
$388$	−128.560	−	74.2244i	−0.331341	−	0.191300i
$389$	−193.576	+	335.284i	−0.497626	+	0.861913i	−0.999996	−	0.00273932i	$-0.999128\pi$
$389$	−193.576	+	335.284i	−0.497626	+	0.861913i	0.502370	+	0.864652i	$0.332461\pi$
$390$	16.5919	−	9.57934i	0.0425434	−	0.0245624i
$391$		−	459.529i		−	1.17526i
$392$	−92.2824	+	103.402i	−0.235414	+	0.263780i
$393$	216.721			0.551454
$394$	−39.8672	−	69.0521i	−0.101186	−	0.175259i
$395$	42.5553	+	24.5693i	0.107735	+	0.0622008i
$396$	59.9249	−	103.793i	0.151326	−	0.262104i
$397$	26.0771	−	15.0556i	0.0656853	−	0.0379234i	−0.466798	−	0.884364i	$-0.654592\pi$
$397$	26.0771	−	15.0556i	0.0656853	−	0.0379234i	0.532483	+	0.846441i	$0.321259\pi$
$398$			242.266i			0.608709i
$399$	−272.334	+	121.970i	−0.682541	+	0.305689i
$400$	−20.0000			−0.0500000
$401$	−68.3852	−	118.447i	−0.170537	−	0.295378i	0.768071	−	0.640365i	$-0.221217\pi$
$401$	−68.3852	−	118.447i	−0.170537	−	0.295378i	−0.938608	+	0.344987i	$0.887883\pi$
$402$	34.4997	+	19.9184i	0.0858201	+	0.0495482i
$403$	−52.6977	+	91.2750i	−0.130763	+	0.226489i
$404$	−151.717	+	87.5941i	−0.375538	+	0.216817i
$405$			20.1246i			0.0496904i
$406$	426.129	+	308.170i	1.04958	+	0.759038i
$407$	−934.215			−2.29537
$408$	44.6842	+	77.3952i	0.109520	+	0.189694i
$409$	−426.838	−	246.435i	−1.04361	−	0.602531i	−0.122759	−	0.992437i	$-0.539174\pi$
$409$	−426.838	−	246.435i	−1.04361	−	0.602531i	−0.920855	+	0.389906i	$0.872507\pi$
$410$	49.8454	−	86.3348i	0.121574	−	0.210573i
$411$	−58.4306	+	33.7349i	−0.142167	+	0.0820801i
$412$			278.082i			0.674957i
$413$	−697.659	−	71.7744i	−1.68925	−	0.173788i
$414$	106.874			0.258149
$415$	0.466756	+	0.808445i	0.00112471	+	0.00194806i
$416$	17.1361	+	9.89350i	0.0411924	+	0.0237825i
$417$	85.6892	−	148.418i	0.205490	−	0.355919i
$418$	602.104	−	347.625i	1.44044	−	0.831638i
$419$		−	311.640i		−	0.743771i	−0.928279	−	0.371885i	$-0.878711\pi$
$419$		−	311.640i		−	0.743771i	0.928279	−	0.371885i	$-0.121289\pi$
$420$	−5.54900	+	53.9371i	−0.0132119	+	0.128422i
$421$	−539.935			−1.28250			−0.641252	−	0.767330i	$-0.721585\pi$
$421$	−539.935			−1.28250			−0.641252	+	0.767330i	$0.721585\pi$
$422$	114.578	+	198.456i	0.271513	+	0.470274i
$423$	−72.9087	−	42.0939i	−0.172361	−	0.0995127i
$424$	−91.7469	+	158.910i	−0.216384	+	0.374788i
$425$	78.9912	−	45.6056i	0.185862	−	0.107307i
$426$			263.871i			0.619414i
$427$	−32.9145	+	45.5132i	−0.0770831	+	0.106588i
$428$	304.380			0.711168
$429$	60.5093	+	104.805i	0.141047	+	0.244301i
$430$	176.398	+	101.844i	0.410229	+	0.236846i
$431$	314.021	−	543.900i	0.728586	−	1.26195i	−0.228895	−	0.973451i	$-0.573511\pi$
$431$	314.021	−	543.900i	0.728586	−	1.26195i	0.957481	−	0.288497i	$-0.0931555\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$			706.789i			1.63231i	0.577836	+	0.816153i	$0.303897\pi$
$433$			706.789i			1.63231i	−0.577836	+	0.816153i	$0.696103\pi$
$434$	−121.922	−	272.228i	−0.280927	−	0.627253i
$435$	205.742			0.472970
$436$	−64.7554	−	112.160i	−0.148522	−	0.257247i
$437$	536.914	+	309.987i	1.22864	+	0.709353i
$438$	63.2712	−	109.589i	0.144455	−	0.250203i
$439$	564.452	−	325.886i	1.28577	−	0.742338i	0.307871	−	0.951428i	$-0.400383\pi$
$439$	564.452	−	325.886i	1.28577	−	0.742338i	0.977896	+	0.209090i	$0.0670501\pi$
$440$		−	126.333i		−	0.287120i
$441$	143.921	+	29.9297i	0.326351	+	0.0678677i
$442$	−90.2398			−0.204162
$443$	11.8129	+	20.4605i	0.0266657	+	0.0461863i	0.879050	−	0.476729i	$-0.158178\pi$
$443$	11.8129	+	20.4605i	0.0266657	+	0.0461863i	−0.852385	+	0.522915i	$0.824844\pi$
$444$	140.308	+	81.0068i	0.316009	+	0.182448i
$445$	−124.337	+	215.358i	−0.279409	+	0.483951i
$446$	447.435	−	258.326i	1.00322	−	0.579207i
$447$		−	322.967i		−	0.722520i
$448$	−51.1083	+	22.8898i	−0.114081	+	0.0510933i
$449$	−55.1499			−0.122828			−0.0614141	−	0.998112i	$-0.519561\pi$
$449$	−55.1499			−0.122828			−0.0614141	+	0.998112i	$0.519561\pi$
$450$	10.6066	+	18.3712i	0.0235702	+	0.0408248i
$451$	545.346	+	314.856i	1.20919	+	0.698128i
$452$	−3.25860	+	5.64407i	−0.00720930	+	0.0124869i
$453$	232.260	−	134.096i	0.512716	−	0.296017i
$454$			364.689i			0.803279i
$455$	−44.3648	−	32.0840i	−0.0975051	−	0.0705142i
$456$	−120.572			−0.264411
$457$	−175.386	−	303.778i	−0.383778	−	0.664723i	0.607821	−	0.794074i	$-0.292044\pi$
$457$	−175.386	−	303.778i	−0.383778	−	0.664723i	−0.991599	+	0.129351i	$0.958710\pi$
$458$	−18.8987	−	10.9112i	−0.0412636	−	0.0238236i
$459$	47.3947	−	82.0901i	0.103256	−	0.178845i
$460$	97.5619	−	56.3274i	0.212091	−	0.122451i
$461$		−	471.598i		−	1.02299i	−0.859287	−	0.511494i	$-0.829092\pi$
$461$		−	471.598i		−	1.02299i	0.859287	−	0.511494i	$-0.170908\pi$
$462$	−340.701	−	35.0510i	−0.737448	−	0.0758680i
$463$	387.112			0.836094			0.418047	−	0.908425i	$-0.362715\pi$
$463$	387.112			0.836094			0.418047	+	0.908425i	$0.362715\pi$
$464$	106.245	+	184.021i	0.228975	+	0.396597i
$465$	−101.063	−	58.3488i	−0.217340	−	0.125481i
$466$	−88.6336	+	153.518i	−0.190201	+	0.329437i
$467$	−254.045	+	146.673i	−0.543994	+	0.314075i	−0.746696	−	0.665166i	$-0.768361\pi$
$467$	−254.045	+	146.673i	−0.543994	+	0.314075i	0.202702	+	0.979240i	$0.435028\pi$
$468$		−	20.9873i		−	0.0448446i
$469$	11.6506	−	113.245i	0.0248413	−	0.241461i
$470$	−88.7417			−0.188812
$471$	43.4777	+	75.3056i	0.0923094	+	0.159885i
$472$	−245.418	−	141.692i	−0.519954	−	0.300195i
$473$	−643.310	+	1114.25i	−1.36006	+	2.35570i
$474$	46.6170	−	26.9143i	0.0983481	−	0.0567813i
$475$			123.058i			0.259069i
$476$	149.660	−	206.946i	0.314412	−	0.434760i
$477$	194.625			0.408018
$478$	−2.56372	−	4.44049i	−0.00536343	−	0.00928973i
$479$	−660.805	−	381.516i	−1.37955	−	0.796484i	−0.387445	−	0.921893i	$-0.626642\pi$
$479$	−660.805	−	381.516i	−1.37955	−	0.796484i	−0.992105	+	0.125409i	$0.959976\pi$
$480$	−10.9545	+	18.9737i	−0.0228218	+	0.0395285i
$481$	−141.676	+	81.7967i	−0.294545	+	0.170056i
$482$			136.668i			0.283543i
$483$	−124.838	−	278.738i	−0.258464	−	0.577098i
$484$	555.999			1.14876
$485$	82.9854	+	143.735i	0.171104	+	0.296361i
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	111.944	−	193.893i	0.229865	−	0.398138i	−0.727903	−	0.685680i	$-0.759505\pi$
$487$	111.944	−	193.893i	0.229865	−	0.398138i	0.957768	+	0.287542i	$0.0928382\pi$
$488$	−19.6546	+	11.3476i	−0.0402759	+	0.0232533i
$489$		−	200.590i		−	0.410205i
$490$	147.155	−	48.5310i	0.300317	−	0.0990429i
$491$	−837.694			−1.70610			−0.853049	−	0.521830i	$-0.825249\pi$
$491$	−837.694			−1.70610			−0.853049	+	0.521830i	$0.825249\pi$
$492$	−54.6029	−	94.5751i	−0.110982	−	0.192226i
$493$	−839.239	−	484.535i	−1.70231	−	0.982829i
$494$	60.8737	−	105.436i	0.123226	−	0.213434i
$495$	−116.044	+	66.9981i	−0.234433	+	0.135350i
$496$		−	120.525i		−	0.242993i
$497$	688.203	−	308.225i	1.38471	−	0.620171i
$498$	1.02261			0.00205344
$499$	−87.3234	−	151.249i	−0.174997	−	0.303103i	0.765163	−	0.643836i	$-0.222658\pi$
$499$	−87.3234	−	151.249i	−0.174997	−	0.303103i	−0.940160	+	0.340733i	$0.889325\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$	−53.1055	+	91.9814i	−0.105999	+	0.183596i
$502$	36.4130	−	21.0230i	0.0725358	−	0.0418786i
$503$		−	747.962i		−	1.48700i	−0.668734	−	0.743501i	$-0.733164\pi$
$503$		−	747.962i		−	1.48700i	0.668734	−	0.743501i	$-0.266836\pi$
$504$	48.1299	+	34.8068i	0.0954958	+	0.0690611i
$505$	195.866			0.387854
$506$	355.800	+	616.263i	0.703162	+	1.21791i
$507$	−235.147	−	135.762i	−0.463801	−	0.267776i
$508$	88.5772	−	153.420i	0.174365	−	0.302008i
$509$	−203.021	+	117.214i	−0.398863	+	0.230284i	−0.685993	−	0.727608i	$-0.740632\pi$
$509$	−203.021	+	117.214i	−0.398863	+	0.230284i	0.287130	+	0.957892i	$0.407299\pi$
$510$		−	99.9168i		−	0.195915i
$511$	−359.726	−	37.0083i	−0.703965	−	0.0724233i
$512$	−22.6274			−0.0441942
$513$	63.9428	+	110.752i	0.124645	+	0.215891i
$514$	540.875	+	312.275i	1.05229	+	0.607538i
$515$	155.453	−	269.252i	0.301850	−	0.522819i
$516$	193.235	−	111.564i	0.374486	−	0.216210i
$517$		−	560.549i		−	1.08423i
$518$	47.3821	−	460.561i	0.0914712	−	0.889114i
$519$	−54.9088			−0.105797
$520$	−11.0613	−	19.1587i	−0.0212717	−	0.0368436i
$521$	186.068	+	107.427i	0.357137	+	0.206193i	0.667824	−	0.744319i	$-0.267226\pi$
$521$	186.068	+	107.427i	0.357137	+	0.206193i	−0.310687	+	0.950512i	$0.600559\pi$
$522$	112.689	−	195.184i	0.215880	−	0.373915i
$523$	801.108	−	462.520i	1.53176	−	0.884360i	0.532475	−	0.846446i	$-0.321262\pi$
$523$	801.108	−	462.520i	1.53176	−	0.884360i	0.999281	−	0.0379137i	$-0.0120712\pi$
$524$		−	250.248i		−	0.477573i
$525$	35.5245	−	49.1224i	0.0676658	−	0.0935664i
$526$	−485.141			−0.922321
$527$	274.830	+	476.020i	0.521499	+	0.903263i
$528$	−119.850	−	69.1953i	−0.226988	−	0.131052i
$529$	−52.7773	+	91.4130i	−0.0997681	+	0.172803i
$530$	177.667	−	102.576i	0.335221	−	0.193540i
$531$			300.575i			0.566054i
$532$	140.839	+	314.464i	0.264734	+	0.591098i
$533$	110.271			0.206887
$534$	136.204	+	235.913i	0.255064	+	0.441784i
$535$	−294.714	−	170.153i	−0.550868	−	0.318044i
$536$	22.9998	−	39.8368i	0.0429100	−	0.0743224i
$537$	197.842	−	114.224i	0.368420	−	0.212707i
$538$			655.277i			1.21799i
$539$	306.553	+	929.528i	0.568744	+	1.72454i
$540$	23.2379			0.0430331
$541$	57.1560	+	98.9971i	0.105649	+	0.182989i	0.914003	−	0.405707i	$-0.132975\pi$
$541$	57.1560	+	98.9971i	0.105649	+	0.182989i	−0.808354	+	0.588696i	$0.799641\pi$
$542$	299.550	+	172.945i	0.552675	+	0.319087i
$543$	47.7553	−	82.7146i	0.0879472	−	0.152329i
$544$	89.3683	−	51.5968i	0.164280	−	0.0948471i
$545$			144.797i			0.265683i
$546$	−54.7371	+	24.5151i	−0.100251	+	0.0448994i
$547$	−57.7698			−0.105612			−0.0528060	−	0.998605i	$-0.516817\pi$
$547$	−57.7698			−0.105612			−0.0528060	+	0.998605i	$0.516817\pi$
$548$	38.9538	+	67.4699i	0.0710835	+	0.123120i
$549$	20.8469	+	12.0359i	0.0379725	+	0.0219234i
$550$	−70.6222	+	122.321i	−0.128404	+	0.222402i
$551$	1132.26	−	653.712i	2.05492	−	1.18641i
$552$		−	123.407i		−	0.223564i
$553$	−124.648	−	90.1438i	−0.225404	−	0.163009i
$554$	−199.430			−0.359982
$555$	−90.5683	−	156.869i	−0.163186	−	0.282647i
$556$	−171.378	−	98.9454i	−0.308235	−	0.177959i
$557$	203.076	−	351.738i	0.364589	−	0.631487i	−0.624121	−	0.781328i	$-0.714543\pi$
$557$	203.076	−	351.738i	0.364589	−	0.631487i	0.988710	+	0.149841i	$0.0478762\pi$
$558$	−110.709	+	63.9179i	−0.198403	+	0.114548i
$559$			225.304i			0.403049i
$560$	62.2812	+	6.40743i	0.111216	+	0.0114418i
$561$	631.139			1.12502
$562$	60.1008	+	104.098i	0.106941	+	0.185227i
$563$	−370.911	−	214.146i	−0.658813	−	0.380366i	0.133012	−	0.991114i	$-0.457535\pi$
$563$	−370.911	−	214.146i	−0.658813	−	0.380366i	−0.791824	+	0.610749i	$0.790869\pi$
$564$	−48.6058	+	84.1878i	−0.0861805	+	0.149269i
$565$	6.31026	−	3.64323i	0.0111686	−	0.00644819i
$566$		−	165.008i		−	0.291534i
$567$	6.44735	−	62.6692i	0.0113710	−	0.110528i
$568$	304.691			0.536429
$569$	457.897	+	793.100i	0.804739	+	1.39385i	0.916467	+	0.400110i	$0.131028\pi$
$569$	457.897	+	793.100i	0.804739	+	1.39385i	−0.111728	+	0.993739i	$0.535638\pi$
$570$	116.743	+	67.4016i	0.204812	+	0.118248i
$571$	356.947	−	618.250i	0.625125	−	1.08275i	−0.363391	−	0.931637i	$-0.618381\pi$
$571$	356.947	−	618.250i	0.625125	−	1.08275i	0.988517	−	0.151112i	$-0.0482855\pi$
$572$	121.019	−	69.8701i	0.211571	−	0.122151i
$573$			338.035i			0.589938i
$574$	−182.881	+	252.883i	−0.318608	+	0.440562i
$575$	−125.952			−0.219047
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−75.8591	−	43.7973i	−0.131472	−	0.0759052i	0.432822	−	0.901480i	$-0.357518\pi$
$577$	−75.8591	−	43.7973i	−0.131472	−	0.0759052i	−0.564293	+	0.825574i	$0.690851\pi$
$578$	−30.9565	+	53.6183i	−0.0535580	+	0.0927652i
$579$	523.140	−	302.035i	0.903523	−	0.521649i
$580$		−	237.570i		−	0.409604i
$581$	−1.19450	−	2.66708i	−0.00205594	−	0.00459050i
$582$	181.812			0.312392
$583$	647.937	+	1122.26i	1.11138	+	1.92497i
$584$	−126.542	−	73.0593i	−0.216682	−	0.125101i
$585$	−11.7323	+	20.3209i	−0.0200551	+	0.0347365i
$586$	−161.522	+	93.2548i	−0.275635	+	0.159138i
$587$		−	169.908i		−	0.289452i	−0.989472	−	0.144726i	$-0.953770\pi$
$587$		−	169.908i		−	0.289452i	0.989472	−	0.144726i	$-0.0462300\pi$
$588$	34.5598	−	166.186i	0.0587752	−	0.282628i
$589$	−741.576			−1.25904
$590$	158.417	+	274.386i	0.268503	+	0.465061i
$591$	84.5712	+	48.8272i	0.143098	+	0.0826179i
$592$	93.5385	−	162.014i	0.158004	−	0.273671i
$593$	173.424	−	100.126i	0.292452	−	0.168847i	−0.346595	−	0.938015i	$-0.612662\pi$
$593$	173.424	−	100.126i	0.292452	−	0.168847i	0.639047	+	0.769168i	$0.279329\pi$
$594$			146.785i			0.247114i
$595$	−260.594	+	116.712i	−0.437973	+	0.196155i
$596$	−372.930			−0.625721
$597$	−148.357	−	256.962i	−0.248504	−	0.430422i
$598$	107.916	+	62.3053i	0.180461	+	0.104189i
$599$	350.201	−	606.566i	0.584643	−	1.01263i	−0.410277	−	0.911961i	$-0.634568\pi$
$599$	350.201	−	606.566i	0.584643	−	1.01263i	0.994920	−	0.100671i	$-0.0320988\pi$
$600$	21.2132	−	12.2474i	0.0353553	−	0.0204124i
$601$			1039.21i			1.72914i	0.502515	+	0.864569i	$0.332408\pi$
$601$			1039.21i			1.72914i	−0.502515	+	0.864569i	$0.667592\pi$
$602$	−516.687	−	373.660i	−0.858285	−	0.620698i
$603$	−48.7899			−0.0809119
$604$	−154.840	−	268.191i	−0.256358	−	0.444025i
$605$	−538.344	−	310.813i	−0.889825	−	0.513740i
$606$	107.280	−	185.815i	0.177030	−	0.306626i
$607$	52.9655	−	30.5796i	0.0872578	−	0.0503783i	−0.455736	−	0.890115i	$-0.650624\pi$
$607$	52.9655	−	30.5796i	0.0872578	−	0.0503783i	0.542994	+	0.839737i	$0.317291\pi$
$608$			139.224i			0.228987i
$609$	−640.692	−	65.9138i	−1.05204	−	0.108233i
$610$	25.3740			0.0415967
$611$	−49.0798	−	85.0087i	−0.0803270	−	0.139130i
$612$	−94.7894	−	54.7267i	−0.154885	−	0.0894227i
$613$	261.359	−	452.688i	0.426361	−	0.738479i	−0.570185	−	0.821516i	$-0.693129\pi$
$613$	261.359	−	452.688i	0.426361	−	0.738479i	0.996546	+	0.0830371i	$0.0264620\pi$
$614$	−526.482	+	303.965i	−0.857462	+	0.495056i
$615$			122.096i			0.198530i
$616$	−40.4734	+	393.408i	−0.0657036	+	0.638649i
$617$	−608.200			−0.985738			−0.492869	−	0.870104i	$-0.664052\pi$
$617$	−608.200			−0.985738			−0.492869	+	0.870104i	$0.664052\pi$
$618$	−170.290	−	294.951i	−0.275550	−	0.477267i
$619$	902.671	+	521.157i	1.45827	+	0.841934i	0.998927	−	0.0463229i	$-0.0147503\pi$
$619$	902.671	+	521.157i	1.45827	+	0.841934i	0.459346	+	0.888257i	$0.348084\pi$
$620$	−67.3754	+	116.698i	−0.108670	+	0.188222i
$621$	−113.357	+	65.4465i	−0.182539	+	0.105389i
$622$		−	355.643i		−	0.571774i
$623$	456.187	−	630.804i	0.732243	−	1.01253i
$624$	−24.2340			−0.0388366
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	16.7831	+	9.68972i	0.0268100	+	0.0154788i
$627$	−425.752	+	737.424i	−0.679030	+	1.17611i
$628$	86.9554	−	50.2037i	0.138464	−	0.0799423i
$629$			853.176i			1.35640i
$630$	−27.1440	−	60.6070i	−0.0430857	−	0.0962015i
$631$	−235.274			−0.372859			−0.186430	−	0.982468i	$-0.559692\pi$
$631$	−235.274			−0.372859			−0.186430	+	0.982468i	$0.559692\pi$
$632$	−31.0780	−	53.8287i	−0.0491741	−	0.0851720i
$633$	−243.057	−	140.329i	−0.383977	−	0.221689i
$634$	−23.2851	+	40.3310i	−0.0367273	+	0.0636136i
$635$	−171.529	+	99.0323i	−0.270124	+	0.155956i
$636$		−	224.733i		−	0.353354i
$637$	127.876	+	114.125i	0.200747	+	0.179159i
$638$	1500.65			2.35211
$639$	−161.587	−	279.877i	−0.252875	−	0.437992i
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	58.4900	−	101.308i	0.0912481	−	0.158046i	−0.816788	−	0.576937i	$-0.804248\pi$
$641$	58.4900	−	101.308i	0.0912481	−	0.158046i	0.908037	+	0.418891i	$0.137581\pi$
$642$	−322.843	+	186.394i	−0.502871	+	0.290333i
$643$		−	874.209i		−	1.35958i	−0.733408	−	0.679789i	$-0.762071\pi$
$643$		−	874.209i		−	1.35958i	0.733408	−	0.679789i	$-0.237929\pi$
$644$	−321.859	+	144.151i	−0.499781	+	0.223837i
$645$	−249.465			−0.386768
$646$	−317.470	−	549.874i	−0.491439	−	0.851198i
$647$	−10.1185	−	5.84189i	−0.0156390	−	0.00902920i	0.492160	−	0.870505i	$-0.336207\pi$
$647$	−10.1185	−	5.84189i	−0.0156390	−	0.00902920i	−0.507799	+	0.861476i	$0.669541\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−1733.20	+	1000.66i	−2.67057	+	1.54185i
$650$			24.7338i			0.0380519i
$651$	296.023	+	214.079i	0.454720	+	0.328847i
$652$	−231.622			−0.355248
$653$	−319.067	−	552.641i	−0.488618	−	0.846311i	0.511296	−	0.859404i	$-0.329165\pi$
$653$	−319.067	−	552.641i	−0.488618	−	0.846311i	−0.999914	+	0.0130935i	$0.995832\pi$
$654$	137.367	+	79.3088i	0.210041	+	0.121267i
$655$	−139.893	+	242.302i	−0.213577	+	0.369927i
$656$	−109.206	+	63.0500i	−0.166472	+	0.0961129i
$657$			154.982i			0.235894i
$658$	276.347	+	28.4303i	0.419980	+	0.0432071i
$659$	870.363			1.32073			0.660367	−	0.750943i	$-0.270401\pi$
$659$	870.363			1.32073			0.660367	+	0.750943i	$0.270401\pi$
$660$	77.3627	+	133.996i	0.117216	+	0.203025i
$661$	417.571	+	241.085i	0.631727	+	0.364728i	0.781420	−	0.624005i	$-0.214495\pi$
$661$	417.571	+	241.085i	0.631727	+	0.364728i	−0.149694	+	0.988732i	$0.547829\pi$
$662$	−295.486	+	511.797i	−0.446354	+	0.773108i
$663$	95.7138	−	55.2604i	0.144365	−	0.0833490i
$664$		−	1.18081i		−	0.00177833i
$665$	39.4242	−	383.210i	0.0592846	−	0.576255i
$666$	−198.425			−0.297936
$667$	669.085	+	1158.89i	1.00313	+	1.73747i
$668$	106.211	+	61.3210i	0.158999	+	0.0917978i
$669$	−316.384	+	547.993i	−0.472921	+	0.819123i
$670$	−44.5389	+	25.7145i	−0.0664759	+	0.0383799i
$671$			160.279i			0.238865i
$672$	40.1914	−	55.5756i	0.0598087	−	0.0827018i
$673$	−399.323			−0.593347			−0.296674	−	0.954979i	$-0.595877\pi$
$673$	−399.323			−0.593347			−0.296674	+	0.954979i	$0.595877\pi$
$674$	−202.719	−	351.119i	−0.300770	−	0.520948i
$675$	−22.5000	−	12.9904i	−0.0333333	−	0.0192450i
$676$	−156.765	+	271.525i	−0.231901	+	0.401664i
$677$	122.405	−	70.6707i	0.180805	−	0.104388i	−0.406866	−	0.913488i	$-0.633378\pi$
$677$	122.405	−	70.6707i	0.180805	−	0.104388i	0.587671	+	0.809100i	$0.300045\pi$
$678$		−	7.98191i		−	0.0117727i
$679$	−212.373	−	474.185i	−0.312773	−	0.698358i
$680$	−115.374			−0.169668
$681$	−223.325	−	386.811i	−0.327937	−	0.568004i
$682$	−737.137	−	425.586i	−1.08085	−	0.624026i
$683$	−494.088	+	855.785i	−0.723408	+	1.25298i	0.236218	+	0.971700i	$0.424092\pi$
$683$	−494.088	+	855.785i	−0.723408	+	1.25298i	−0.959626	+	0.281279i	$0.909241\pi$
$684$	127.886	−	73.8347i	0.186967	−	0.107946i
$685$		−	87.1032i		−	0.127158i
$686$	−473.799	+	103.984i	−0.690669	+	0.151580i
$687$	26.7268			0.0389037
$688$	−128.823	−	223.128i	−0.187243	−	0.324314i
$689$	196.522	+	113.462i	0.285228	+	0.164677i
$690$	−68.9867	+	119.488i	−0.0999807	+	0.173172i
$691$	303.829	−	175.415i	0.439694	−	0.253857i	−0.263774	−	0.964585i	$-0.584967\pi$
$691$	303.829	−	175.415i	0.439694	−	0.253857i	0.703468	+	0.710727i	$0.251634\pi$
$692$			63.4033i			0.0916232i
$693$	382.832	−	171.459i	0.552428	−	0.247415i
$694$	−433.875			−0.625180
$695$	110.624	+	191.607i	0.159172	+	0.275693i
$696$	−225.379	−	130.123i	−0.323820	−	0.186958i
$697$	287.543	−	498.040i	0.412544	−	0.714548i
$698$	416.611	−	240.531i	0.596864	−	0.344600i
$699$		−	217.107i		−	0.310597i
$700$	−56.7216	−	41.0202i	−0.0810309	−	0.0586003i
$701$	307.500			0.438659			0.219330	−	0.975651i	$-0.429613\pi$
$701$	307.500			0.438659			0.219330	+	0.975651i	$0.429613\pi$
$702$	12.8520	+	22.2604i	0.0183077	+	0.0317100i
$703$	−996.852	−	575.533i	−1.41800	−	0.818681i
$704$	−79.8999	+	138.391i	−0.113494	+	0.196578i
$705$	94.1248	−	54.3430i	0.133510	−	0.0770822i
$706$		−	530.333i		−	0.751180i
$707$	−609.939	−	62.7500i	−0.862715	−	0.0887552i
$708$	347.074			0.490217
$709$	49.0712	+	84.9938i	0.0692118	+	0.119878i	0.898555	−	0.438862i	$-0.144618\pi$
$709$	49.0712	+	84.9938i	0.0692118	+	0.119878i	−0.829343	+	0.558740i	$0.811285\pi$
$710$	−295.016	−	170.328i	−0.415516	−	0.239898i
$711$	−32.9632	+	57.0939i	−0.0463617	+	0.0803009i
$712$	272.409	−	157.275i	0.382597	−	0.220892i
$713$		−	759.016i		−	1.06454i
$714$	−32.0105	+	311.147i	−0.0448326	+	0.435780i
$715$	−156.234			−0.218510
$716$	−131.894	−	228.448i	−0.184210	−	0.319061i
$717$	5.43847	+	3.13990i	0.00758503	+	0.00437922i
$718$	−232.992	+	403.554i	−0.324502	+	0.562053i
$719$	612.340	−	353.535i	0.851655	−	0.491703i	−0.00955403	−	0.999954i	$-0.503041\pi$
$719$	612.340	−	353.535i	0.851655	−	0.491703i	0.861209	+	0.508251i	$0.169708\pi$
$720$		−	26.8328i		−	0.0372678i
$721$	−570.349	+	788.664i	−0.791053	+	1.09385i
$722$	346.100			0.479363
$723$	−83.6915	−	144.958i	−0.115756	−	0.200495i
$724$	−95.5106	−	55.1431i	−0.131921	−	0.0761645i
$725$	−132.806	+	230.026i	−0.183180	+	0.317278i
$726$	−589.726	+	340.479i	−0.812295	+	0.468979i
$727$		−	1353.85i		−	1.86225i	−0.364705	−	0.931123i	$-0.618830\pi$
$727$		−	1353.85i		−	1.86225i	0.364705	−	0.931123i	$-0.381170\pi$
$728$	28.3076	+	63.2050i	0.0388840	+	0.0868201i
$729$	−27.0000			−0.0370370
$730$	81.6827	+	141.479i	0.111894	+	0.193806i
$731$	1017.59	+	587.506i	1.39205	+	0.803701i
$732$	13.8979	−	24.0719i	0.0189862	−	0.0328851i
$733$	−478.941	+	276.517i	−0.653398	+	0.377240i	−0.789757	−	0.613420i	$-0.789793\pi$
$733$	−478.941	+	276.517i	−0.653398	+	0.377240i	0.136359	+	0.990660i	$0.456460\pi$
$734$			38.4020i			0.0523188i
$735$	−126.363	+	141.589i	−0.171922	+	0.192638i
$736$	−142.498			−0.193612
$737$	−162.429	−	281.336i	−0.220393	−	0.381732i
$738$	115.830	+	66.8747i	0.156952	+	0.0906161i
$739$	−466.739	+	808.416i	−0.631582	+	1.09393i	0.355646	+	0.934621i	$0.384261\pi$
$739$	−466.739	+	808.416i	−0.631582	+	1.09393i	−0.987228	+	0.159312i	$0.949072\pi$
$740$	−181.137	+	104.579i	−0.244779	+	0.141323i
$741$			149.110i			0.201227i
$742$	−586.128	+	262.509i	−0.789930	+	0.353785i
$743$	554.921			0.746865			0.373432	−	0.927657i	$-0.378181\pi$
$743$	554.921			0.746865			0.373432	+	0.927657i	$0.378181\pi$
$744$	73.8060	+	127.836i	0.0992016	+	0.171822i
$745$	361.088	+	208.474i	0.484681	+	0.279831i
$746$	90.1544	−	156.152i	0.120850	−	0.209319i
$747$	−1.08464	+	0.626219i	−0.00145200	+	0.000838312i
$748$		−	728.776i		−	0.974300i
$749$	863.246	+	624.286i	1.15253	+	0.833492i
$750$	−27.3861			−0.0365148
$751$	−363.974	−	630.421i	−0.484652	−	0.839442i	0.515192	−	0.857075i	$-0.327721\pi$
$751$	−363.974	−	630.421i	−0.484652	−	0.839442i	−0.999845	+	0.0176322i	$0.994387\pi$
$752$	97.2117	+	56.1252i	0.129271	+	0.0746345i
$753$	−25.7479	+	44.5966i	−0.0341937	+	0.0592252i
$754$	227.577	−	131.391i	0.301826	−	0.174259i
$755$			346.233i			0.458587i
$756$	−72.3642	−	7.44476i	−0.0957198	−	0.00984756i
$757$	667.167			0.881330			0.440665	−	0.897672i	$-0.354743\pi$
$757$	667.167			0.881330			0.440665	+	0.897672i	$0.354743\pi$
$758$	226.129	+	391.667i	0.298323	+	0.516711i
$759$	−754.765	−	435.764i	−0.994421	−	0.574129i
$760$	77.8287	−	134.803i	0.102406	−	0.177373i
$761$	−630.061	+	363.766i	−0.827938	+	0.478010i	−0.853146	−	0.521672i	$-0.825309\pi$
$761$	−630.061	+	363.766i	−0.827938	+	0.478010i	0.0252080	+	0.999682i	$0.491975\pi$
$762$			216.969i			0.284736i
$763$	46.3890	−	450.908i	0.0607981	−	0.590967i
$764$	390.329			0.510901
$765$	61.1863	+	105.978i	0.0799821	+	0.138533i
$766$	500.850	+	289.166i	0.653851	+	0.377501i
$767$	−175.229	+	303.506i	−0.228460	+	0.395705i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$			1374.28i			1.78709i	0.448969	+	0.893547i	$0.351791\pi$
$769$			1374.28i			1.78709i	−0.448969	+	0.893547i	$0.648209\pi$
$770$	259.110	−	358.290i	0.336506	−	0.465312i
$771$	−764.913			−0.992106
$772$	−348.760	−	604.070i	−0.451761	−	0.782474i
$773$	80.2556	+	46.3356i	0.103824	+	0.0599425i	0.551013	−	0.834497i	$-0.314242\pi$
$773$	80.2556	+	46.3356i	0.103824	+	0.0599425i	−0.447189	+	0.894439i	$0.647575\pi$
$774$	−136.638	+	236.663i	−0.176534	+	0.305767i
$775$	130.472	−	75.3280i	0.168351	−	0.0971974i
$776$		−	209.938i		−	0.270539i
$777$	231.779	+	517.514i	0.298300	+	0.666042i
$778$	−547.517			−0.703749
$779$	387.940	+	671.932i	0.497998	+	0.862558i
$780$	23.4645	+	13.5472i	0.0300827	+	0.0173683i
$781$	1075.90	−	1863.51i	1.37759	−	2.38606i
$782$	562.805	−	324.936i	0.719700	−	0.415519i
$783$			276.032i			0.352531i
$784$	−191.894	−	39.9062i	−0.244763	−	0.0509008i
$785$	−112.259			−0.143005
$786$	153.245	+	265.428i	0.194968	+	0.337695i
$787$	724.193	+	418.113i	0.920195	+	0.531275i	0.883697	−	0.468059i	$-0.155047\pi$
$787$	724.193	+	418.113i	0.920195	+	0.531275i	0.0364974	+	0.999334i	$0.488380\pi$
$788$	56.3808	−	97.6544i	0.0715492	−	0.123927i
$789$	514.570	−	297.087i	0.652180	−	0.376536i
$790$			69.4925i			0.0879652i
$791$	−20.8177	+	9.32360i	−0.0263182	+	0.0117871i
$792$	169.493			0.214007
$793$	14.0334	+	24.3066i	0.0176967	+	0.0306515i
$794$	36.8785	+	21.2918i	0.0464465	+	0.0268159i
$795$	−125.630	+	217.597i	−0.158025	+	0.273707i
$796$	−296.714	+	171.308i	−0.372757	+	0.215211i
$797$		−	130.279i		−	0.163462i	−0.996654	−	0.0817310i	$-0.973955\pi$
$797$		−	130.279i		−	0.163462i	0.996654	−	0.0817310i	$-0.0260448\pi$
$798$	−341.951	−	247.294i	−0.428510	−	0.309892i
$799$	−511.924			−0.640706
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$	−288.933	−	166.816i	−0.360716	−	0.208259i
$802$	96.7113	−	167.509i	0.120588	−	0.208864i
$803$	−893.670	+	515.960i	−1.11291	+	0.642541i
$804$			56.3377i			0.0700718i
$805$	392.221	+	40.3514i	0.487232	+	0.0501259i
$806$	−149.052			−0.184927
$807$	−401.274	−	695.027i	−0.497241	−	0.861247i
$808$	−214.561	−	123.877i	−0.265546	−	0.153313i
$809$	−310.782	+	538.290i	−0.384156	+	0.665377i	−0.991652	−	0.128946i	$-0.958841\pi$
$809$	−310.782	+	538.290i	−0.384156	+	0.665377i	0.607496	+	0.794323i	$0.292174\pi$
$810$	−24.6475	+	14.2302i	−0.0304290	+	0.0175682i
$811$			445.846i			0.549748i	0.961480	+	0.274874i	$0.0886361\pi$
$811$			445.846i			0.549748i	−0.961480	+	0.274874i	$0.911364\pi$
$812$	−76.1107	+	739.808i	−0.0937324	+	0.911093i
$813$	−423.627			−0.521067
$814$	−660.590	−	1144.17i	−0.811535	−	1.40562i
$815$	224.267	+	129.480i	0.275174	+	0.158872i
$816$	−63.1930	+	109.453i	−0.0774423	+	0.134134i
$817$	−1372.89	+	792.636i	−1.68040	+	0.970178i
$818$		−	697.023i		−	0.852107i
$819$	43.0451	−	59.5217i	0.0525582	−	0.0726760i
$820$	140.984			0.171932
$821$	−628.622	−	1088.81i	−0.765678	−	1.32619i	−0.939887	−	0.341485i	$-0.889070\pi$
$821$	−628.622	−	1088.81i	−0.765678	−	1.32619i	0.174209	−	0.984709i	$-0.444263\pi$
$822$	−82.6334	−	47.7084i	−0.100527	−	0.0580394i
$823$	−60.1709	+	104.219i	−0.0731117	+	0.126633i	−0.900264	−	0.435345i	$-0.856626\pi$
$823$	−60.1709	+	104.219i	−0.0731117	+	0.126633i	0.827152	+	0.561978i	$0.189960\pi$
$824$	−340.580	+	196.634i	−0.413325	+	0.238633i
$825$		−	172.988i		−	0.209683i
$826$	−405.414	−	905.206i	−0.490816	−	1.09589i
$827$	151.053			0.182652			0.0913258	−	0.995821i	$-0.470890\pi$
$827$	151.053			0.182652			0.0913258	+	0.995821i	$0.470890\pi$
$828$	75.5711	+	130.893i	0.0912695	+	0.158083i
$829$	217.640	+	125.654i	0.262533	+	0.151573i	0.625489	−	0.780233i	$-0.284899\pi$
$829$	217.640	+	125.654i	0.262533	+	0.151573i	−0.362957	+	0.931806i	$0.618233\pi$
$830$	−0.660093	+	1.14331i	−0.000795292	+	0.00137749i
$831$	211.528	−	122.126i	0.254546	−	0.146962i
$832$			27.9831i			0.0336335i
$833$	848.896	−	279.961i	1.01908	−	0.336088i
$834$	242.366			0.290606
$835$	−68.5589	−	118.748i	−0.0821065	−	0.142213i
$836$	851.503	+	491.616i	1.01854	+	0.588057i
$837$	78.2831	−	135.590i	0.0935282	−	0.161996i
$838$	381.679	−	220.363i	0.455465	−	0.262963i
$839$		−	499.592i		−	0.595461i	−0.954650	−	0.297730i	$-0.903770\pi$
$839$		−	499.592i		−	0.595461i	0.954650	−	0.297730i	$-0.0962297\pi$
$840$	−69.9829	+	31.3432i	−0.0833130	+	0.0373133i
$841$	1980.98			2.35550
$842$	−381.791	−	661.282i	−0.453434	−	0.785371i
$843$	−127.493	−	73.6081i	−0.151237	−	0.0873169i
$844$	−162.038	+	280.658i	−0.191988	+	0.332534i
$845$	303.574	−	175.268i	0.359259	−	0.207418i
$846$		−	119.059i		−	0.140732i
$847$	1576.86	+	1140.36i	1.86170	+	1.34635i
$848$	−259.499			−0.306013
$849$	101.047	+	175.018i	0.119018	+	0.206146i
$850$	111.710	+	64.4960i	0.131424	+	0.0758777i
$851$	589.068	−	1020.30i	0.692206	−	1.19894i
$852$	−323.174	+	186.585i	−0.379312	+	0.218996i
$853$			1265.99i			1.48416i	0.670310	+	0.742082i	$0.266161\pi$
$853$			1265.99i			1.48416i	−0.670310	+	0.742082i	$0.733839\pi$
$854$	−79.0162	−	8.12911i	−0.0925248	−	0.00951886i
$855$	−165.100			−0.193099
$856$	215.229	+	372.788i	0.251436	+	0.435499i
$857$	320.100	+	184.810i	0.373513	+	0.215648i	0.674992	−	0.737825i	$-0.264147\pi$
$857$	320.100	+	184.810i	0.373513	+	0.215648i	−0.301479	+	0.953473i	$0.597480\pi$
$858$	−85.5731	+	148.217i	−0.0997355	+	0.172747i
$859$	−1089.49	+	629.015i	−1.26832	+	0.732264i	−0.974670	−	0.223649i	$-0.928203\pi$
$859$	−1089.49	+	629.015i	−1.26832	+	0.732264i	−0.293649	+	0.955913i	$0.594870\pi$
$860$			288.057i			0.334951i
$861$	39.1160	−	380.214i	0.0454309	−	0.441596i
$862$	888.184			1.03038
$863$	118.333	+	204.959i	0.137118	+	0.237496i	0.926405	−	0.376530i	$-0.122883\pi$
$863$	118.333	+	204.959i	0.137118	+	0.237496i	−0.789286	+	0.614025i	$0.789549\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	35.4435	−	61.3900i	0.0409752	−	0.0709711i
$866$	−865.636	+	499.775i	−0.999579	+	0.577107i
$867$		−	75.8277i		−	0.0874598i
$868$	247.197	−	341.818i	0.284790	−	0.393799i
$869$	−438.959			−0.505132
$870$	145.481	+	251.981i	0.167220	+	0.289634i
$871$	−49.2657	−	28.4436i	−0.0565622	−	0.0326562i
$872$	91.5779	−	158.618i	0.105021	−	0.181901i
$873$	−192.841	+	111.337i	−0.220894	+	0.127533i
$874$			876.777i			1.00318i
$875$	31.9895	+	71.4260i	0.0365594	+	0.0816297i
$876$	178.958			0.204290
$877$	−402.766	−	697.611i	−0.459254	−	0.795451i	0.539668	−	0.841878i	$-0.318550\pi$
$877$	−402.766	−	697.611i	−0.459254	−	0.795451i	−0.998922	+	0.0464269i	$0.985217\pi$
$878$	798.256	+	460.873i	0.909175	+	0.524912i
$879$	114.213	−	197.823i	0.129936	−	0.225055i
$880$	154.725	−	89.3308i	0.175824	−	0.101512i
$881$			763.260i			0.866356i	0.901308	+	0.433178i	$0.142608\pi$
$881$			763.260i			0.866356i	−0.901308	+	0.433178i	$0.857392\pi$
$882$	65.1112	+	197.430i	0.0738222	+	0.223843i
$883$	574.986			0.651173			0.325587	−	0.945512i	$-0.394438\pi$
$883$	574.986			0.651173			0.325587	+	0.945512i	$0.394438\pi$
$884$	−63.8092	−	110.521i	−0.0721823	−	0.125023i
$885$	−336.053	−	194.020i	−0.379721	−	0.219232i
$886$	−16.7060	+	28.9356i	−0.0188555	+	0.0326587i
$887$	−332.122	+	191.751i	−0.374433	+	0.216179i	−0.675393	−	0.737458i	$-0.736026\pi$
$887$	−332.122	+	191.751i	−0.374433	+	0.216179i	0.300960	+	0.953637i	$0.402693\pi$
$888$			229.122i			0.258020i
$889$	565.879	−	253.440i	0.636534	−	0.285084i
$890$	−351.678			−0.395144
$891$	−89.8874	−	155.690i	−0.100884	−	0.174736i
$892$	632.768	+	365.329i	0.709381	+	0.409561i
$893$	345.332	−	598.133i	0.386710	−	0.669802i
$894$	395.552	−	228.372i	0.442451	−	0.255449i
$895$			294.925i			0.329525i
$896$	−64.1732	−	46.4091i	−0.0716219	−	0.0517958i
$897$	−152.616			−0.170141
$898$	−38.9968	−	67.5445i	−0.0434263	−	0.0752166i
$899$	−1386.19	−	800.319i	−1.54193	−	0.890232i
$900$	−15.0000	+	25.9808i	−0.0166667	+	0.0288675i
$901$	1024.91	−	591.731i	1.13752	−	0.656749i
$902$			890.547i			0.987302i
$903$	776.849	+	79.9215i	0.860298	+	0.0885066i
$904$	−9.21672			−0.0101955
$905$	61.6518	+	106.784i	0.0681236	+	0.117993i
$906$	328.466	+	189.640i	0.362545	+	0.209316i
$907$	581.220	−	1006.70i	0.640816	−	1.10993i	−0.344435	−	0.938810i	$-0.611930\pi$
$907$	581.220	−	1006.70i	0.640816	−	1.10993i	0.985251	−	0.171115i	$-0.0547371\pi$
$908$	−446.650	+	257.874i	−0.491906	+	0.284002i
$909$			262.782i			0.289089i
$910$	7.92399	−	77.0224i	0.00870768	−	0.0846400i
$911$	1070.03			1.17457			0.587284	−	0.809381i	$-0.300197\pi$
$911$	1070.03			1.17457			0.587284	+	0.809381i	$0.300197\pi$
$912$	−85.2570	−	147.669i	−0.0934836	−	0.161918i
$913$	−7.22190	−	4.16957i	−0.00791008	−	0.00456689i
$914$	248.034	−	429.607i	0.271372	−	0.470030i
$915$	−26.9132	+	15.5383i	−0.0294133	+	0.0169818i
$916$		−	30.8615i		−	0.0336916i
$917$	513.262	−	709.725i	0.559719	−	0.773964i
$918$	134.053			0.146027
$919$	−583.360	−	1010.41i	−0.634777	−	1.09947i	−0.986562	−	0.163386i	$-0.947759\pi$
$919$	−583.360	−	1010.41i	−0.634777	−	1.09947i	0.351785	−	0.936081i	$-0.385575\pi$
$920$	137.973	+	79.6589i	0.149971	+	0.0865858i
$921$	372.279	−	644.806i	0.404212	−	0.700115i
$922$	577.587	−	333.470i	0.626450	−	0.361681i
$923$		−	376.808i		−	0.408243i
$924$	−197.984	−	442.057i	−0.214268	−	0.478416i
$925$	233.846			0.252807
$926$	273.729	+	474.113i	0.295604	+	0.512001i
$927$	361.239	+	208.562i	0.389686	+	0.224986i
$928$	−150.253	+	260.245i	−0.161910	+	0.280437i
$929$	194.325	−	112.194i	0.209177	−	0.120768i	−0.391752	−	0.920071i	$-0.628131\pi$
$929$	194.325	−	112.194i	0.209177	−	0.120768i	0.600929	+	0.799303i	$0.294798\pi$
$930$		−	165.035i		−	0.177457i
$931$	−245.539	+	1180.71i	−0.263737	+	1.26821i
$932$	−250.694			−0.268984
$933$	217.786	+	377.217i	0.233426	+	0.404305i
$934$	−359.274	−	207.427i	−0.384662	−	0.222084i
$935$	−407.398	+	705.635i	−0.435720	+	0.754689i
$936$	25.7041	−	14.8403i	0.0274616	−	0.0158550i
$937$		−	644.185i		−	0.687497i	−0.939062	−	0.343749i	$-0.888303\pi$
$937$		−	644.185i		−	0.687497i	0.939062	−	0.343749i	$-0.111697\pi$
$938$	146.935	−	65.8076i	0.156647	−	0.0701573i
$939$	−23.7349			−0.0252767
$940$	−62.7499	−	108.686i	−0.0667552	−	0.115623i
$941$	−266.097	−	153.631i	−0.282781	−	0.163264i	0.351901	−	0.936037i	$-0.385535\pi$
$941$	−266.097	−	153.631i	−0.282781	−	0.163264i	−0.634682	+	0.772774i	$0.718869\pi$
$942$	−61.4868	+	106.498i	−0.0652726	+	0.113055i
$943$	−687.734	+	397.063i	−0.729305	+	0.421064i
$944$		−	400.766i		−	0.424540i
$945$	65.9046	+	47.6612i	0.0697403	+	0.0504351i
$946$	−1819.56			−1.92342
$947$	490.755	+	850.013i	0.518221	+	0.897585i	0.999776	+	0.0211694i	$0.00673894\pi$
$947$	490.755	+	850.013i	0.518221	+	0.897585i	−0.481555	+	0.876416i	$0.659928\pi$
$948$	65.9264	+	38.0626i	0.0695426	+	0.0401504i
$949$	−90.3515	+	156.493i	−0.0952071	+	0.164903i
$950$	−150.715	+	87.0151i	−0.158647	+	0.0915948i
$951$		−	57.0367i		−	0.0599755i
$952$	359.281	+	36.9625i	0.377397	+	0.0388262i
$953$	1258.67			1.32075			0.660375	−	0.750936i	$-0.270397\pi$
$953$	1258.67			1.32075			0.660375	+	0.750936i	$0.270397\pi$
$954$	137.620	+	238.365i	0.144256	+	0.249859i
$955$	−377.934	−	218.200i	−0.395743	−	0.228482i
$956$	3.62565	−	6.27980i	0.00379252	−	0.00656883i
$957$	−1591.68	+	918.954i	−1.66319	+	0.960245i
$958$		−	1079.09i		−	1.12640i
$959$	−27.9054	+	271.245i	−0.0290984	+	0.282841i
$960$	−30.9839			−0.0322749
$961$	−26.5559	−	45.9962i	−0.0276336	−	0.0478628i
$962$	−200.360	−	115.678i	−0.208275	−	0.120247i
$963$	228.285	−	395.401i	0.237056	−	0.410593i
$964$	−167.383	+	96.6387i	−0.173634	+	0.100248i
$965$			779.851i			0.808135i
$966$	253.109	−	349.993i	0.262018	−	0.362311i
$967$	−992.744			−1.02662			−0.513311	−	0.858202i	$-0.671581\pi$
$967$	−992.744			−1.02662			−0.513311	+	0.858202i	$0.671581\pi$
$968$	393.151	+	680.957i	0.406147	+	0.703468i
$969$	673.455	+	388.820i	0.695000	+	0.401259i
$970$	−117.359	+	203.272i	−0.120989	+	0.209559i
$971$	−309.667	+	178.787i	−0.318916	+	0.184126i	−0.650909	−	0.759155i	$-0.725612\pi$
$971$	−309.667	+	178.787i	−0.318916	+	0.184126i	0.331993	+	0.943282i	$0.392279\pi$
$972$			31.1769i			0.0320750i
$973$	−283.105	−	632.116i	−0.290961	−	0.649657i
$974$	316.626			0.325078
$975$	−15.1463	−	26.2341i	−0.0155346	−	0.0269068i
$976$	−27.7958	−	16.0479i	−0.0284793	−	0.0164426i
$977$	438.673	−	759.804i	0.449000	−	0.777691i	−0.549321	−	0.835611i	$-0.685114\pi$
$977$	438.673	−	759.804i	0.449000	−	0.777691i	0.998321	+	0.0579204i	$0.0184470\pi$
$978$	245.672	−	141.839i	0.251198	−	0.145029i
$979$		−	2221.43i		−	2.26908i
$980$	163.493	+	145.911i	0.166829	+	0.148889i
$981$	−194.266			−0.198029
$982$	−592.339	−	1025.96i	−0.603197	−	1.04477i
$983$	−1247.26	−	720.104i	−1.26883	−	0.732557i	−0.294061	−	0.955787i	$-0.595007\pi$
$983$	−1247.26	−	720.104i	−1.26883	−	0.732557i	−0.974766	+	0.223229i	$0.928340\pi$
$984$	77.2202	−	133.749i	0.0784758	−	0.135924i
$985$	−109.181	+	63.0356i	−0.110844	+	0.0639956i
$986$		−	1370.47i		−	1.38993i
$987$	−310.520	+	139.072i	−0.314610	+	0.140904i
$988$	172.177			0.174268
$989$	−811.276	−	1405.17i	−0.820299	−	1.42080i
$990$	−164.111	−	94.7496i	−0.165769	−	0.0957067i
$991$	−577.181	+	999.706i	−0.582423	+	1.00879i	0.412769	+	0.910836i	$0.364562\pi$
$991$	−577.181	+	999.706i	−0.582423	+	1.00879i	−0.995191	+	0.0979496i	$0.968772\pi$
$992$	147.612	−	85.2239i	0.148802	−	0.0859111i
$993$		−	723.791i		−	0.728893i
$994$	864.130	+	624.925i	0.869346	+	0.628697i
$995$	383.057			0.384981
$996$	0.723095	+	1.25244i	0.000725999	+	0.00125747i
$997$	1407.21	+	812.451i	1.41144	+	0.814896i	0.995524	−	0.0945072i	$-0.0301275\pi$
$997$	1407.21	+	812.451i	1.41144	+	0.814896i	0.415916	+	0.909403i	$0.363461\pi$
$998$	123.494	−	213.898i	0.123741	−	0.214326i
$999$	210.462	−	121.510i	0.210672	−	0.121632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.b.31.7	✓	16
3.2	odd	2		630.3.v.c.451.1		16
5.2	odd	4		1050.3.q.e.199.1		32
5.3	odd	4		1050.3.q.e.199.10		32
5.4	even	2		1050.3.p.i.451.4		16
7.3	odd	6		1470.3.f.d.391.2		16
7.4	even	3		1470.3.f.d.391.8		16
7.5	odd	6	inner	210.3.o.b.61.7	yes	16
21.5	even	6		630.3.v.c.271.1		16
35.12	even	12		1050.3.q.e.649.10		32
35.19	odd	6		1050.3.p.i.901.4		16
35.33	even	12		1050.3.q.e.649.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.7	✓	16	1.1	even	1	trivial
210.3.o.b.61.7	yes	16	7.5	odd	6	inner
630.3.v.c.271.1		16	21.5	even	6
630.3.v.c.451.1		16	3.2	odd	2
1050.3.p.i.451.4		16	5.4	even	2
1050.3.p.i.901.4		16	35.19	odd	6
1050.3.q.e.199.1		32	5.2	odd	4
1050.3.q.e.199.10		32	5.3	odd	4
1050.3.q.e.649.1		32	35.33	even	12
1050.3.q.e.649.10		32	35.12	even	12
1470.3.f.d.391.2		16	7.3	odd	6
1470.3.f.d.391.8		16	7.4	even	3

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.38854 + 2.86123i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.38854 + 2.86123i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.73861 + 1.58114i) q^{10} +(-9.98749 + 17.2988i) q^{11} +(3.00000 - 1.73205i) q^{12} +3.49788i q^{13} +(-8.02165 - 5.80113i) q^{14} -3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(15.7982 + 9.12112i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-21.3143 + 12.3058i) q^{19} +4.47214i q^{20} +(12.0607 + 1.24079i) q^{21} -28.2489 q^{22} +(-12.5952 - 21.8155i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-4.28401 + 2.47338i) q^{26} -5.19615i q^{27} +(1.43274 - 13.9265i) q^{28} -53.1223 q^{29} +(-2.73861 - 4.74342i) q^{30} +(26.0944 + 15.0656i) q^{31} +(2.82843 - 4.89898i) q^{32} +(29.9625 - 17.2988i) q^{33} +25.7984i q^{34} +(-9.17240 + 12.6833i) q^{35} -6.00000 q^{36} +(23.3846 + 40.5034i) q^{37} +(-30.1429 - 17.4030i) q^{38} +(3.02925 - 5.24682i) q^{39} +(-5.47723 + 3.16228i) q^{40} -31.5250i q^{41} +(7.00855 + 15.6487i) q^{42} +64.4116 q^{43} +(-19.9750 - 34.5977i) q^{44} +(5.80948 + 3.35410i) q^{45} +(17.8123 - 30.8518i) q^{46} +(-24.3029 + 14.0313i) q^{47} +6.92820i q^{48} +(32.6268 - 36.5581i) q^{49} +7.07107 q^{50} +(-15.7982 - 27.3634i) q^{51} +(-6.05851 - 3.49788i) q^{52} +(32.4374 - 56.1833i) q^{53} +(6.36396 - 3.67423i) q^{54} +44.6654i q^{55} +(18.0695 - 8.09277i) q^{56} +42.6285 q^{57} +(-37.5631 - 65.0613i) q^{58} +(86.7684 + 50.0958i) q^{59} +(3.87298 - 6.70820i) q^{60} +(6.94896 - 4.01198i) q^{61} +42.6119i q^{62} +(-17.0165 - 12.3061i) q^{63} +8.00000 q^{64} +(3.91075 + 6.77362i) q^{65} +(42.3733 + 24.4642i) q^{66} +(-8.13165 + 14.0844i) q^{67} +(-31.5965 + 18.2422i) q^{68} +43.6310i q^{69} +(-22.0197 - 2.26537i) q^{70} -107.725 q^{71} +(-4.24264 - 7.34847i) q^{72} +(44.7395 + 25.8303i) q^{73} +(-33.0709 + 57.2804i) q^{74} +(-7.50000 + 4.33013i) q^{75} -49.2232i q^{76} +(14.3095 - 139.091i) q^{77} +8.56803 q^{78} +(10.9877 + 19.0313i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(38.6101 - 22.2916i) q^{82} +0.417479i q^{83} +(-14.2098 + 19.6489i) q^{84} +40.7909 q^{85} +(45.5459 + 78.8878i) q^{86} +(79.6835 + 46.0053i) q^{87} +(28.2489 - 48.9285i) q^{88} +(-96.3110 + 55.6052i) q^{89} +9.48683i q^{90} +(-10.0082 - 22.3463i) q^{91} +50.3807 q^{92} +(-26.0944 - 45.1968i) q^{93} +(-34.3695 - 19.8432i) q^{94} +(-27.5166 + 47.6601i) q^{95} +(-8.48528 + 4.89898i) q^{96} +74.2244i q^{97} +(67.8449 + 14.1090i) q^{98} -59.9249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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