LMFDB - Embedded newform 210.3.o.b.61.7

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			61.7
Root			$0.848921 - 1.47037i$ of defining polynomial
Character	$\chi$	$=$	210.61
Dual form			210.3.o.b.31.7

$q$-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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	−0.816903	−	0.576775i	$-0.804311\pi$
$11$	−9.98749	−	17.2988i	−0.907953	−	1.57262i	−0.0910503	−	0.995846i	$-0.529022\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$		−	3.49788i		−	0.269068i	−0.990909	−	0.134534i	$-0.957046\pi$
$13$		−	3.49788i		−	0.269068i	0.990909	−	0.134534i	$-0.0429537\pi$
$14$	−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	0.0427155	−	0.999087i	$-0.486399\pi$
$17$	15.7982	−	9.12112i	0.929308	−	0.536536i	0.886593	+	0.462551i	$0.153066\pi$
$18$	−2.12132	−	3.67423i	−0.117851	−	0.204124i
$19$	−21.3143	−	12.3058i	−1.12180	−	0.647673i	−0.179942	−	0.983677i	$-0.557591\pi$
$19$	−21.3143	−	12.3058i	−1.12180	−	0.647673i	−0.941861	+	0.336004i	$0.890924\pi$
$20$		−	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	0.450820	+	0.892615i	$0.351131\pi$
$23$	−12.5952	+	21.8155i	−0.547617	+	0.948500i	−0.998437	+	0.0558853i	$0.982202\pi$
$24$	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	−0.0161061	−	0.999870i	$-0.505127\pi$
$31$	26.0944	−	15.0656i	0.841754	−	0.485987i	0.857860	+	0.513883i	$0.171794\pi$
$32$	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	−0.355122	−	0.934820i	$-0.615561\pi$
$37$	23.3846	−	40.5034i	0.632017	−	1.09469i	0.987139	−	0.159866i	$-0.0511061\pi$
$38$	−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	$0.125609\pi$
$41$			31.5250i			0.768903i	−0.923145	+	0.384452i	$0.874391\pi$
$42$	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	0.218657	−	0.975802i	$-0.429832\pi$
$47$	−24.3029	−	14.0313i	−0.517083	−	0.298538i	−0.735740	+	0.677264i	$0.763166\pi$
$48$		−	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	0.990898	+	0.134612i	$0.0429789\pi$
$53$	32.4374	+	56.1833i	0.612027	+	1.06006i	−0.378872	+	0.925449i	$0.623688\pi$
$54$	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	0.471194	−	0.882029i	$-0.343823\pi$
$59$	86.7684	−	50.0958i	1.47065	−	0.849081i	0.999457	+	0.0329486i	$0.0104897\pi$
$60$	3.87298	+	6.70820i	0.0645497	+	0.111803i
$61$	6.94896	+	4.01198i	0.113917	+	0.0657702i	0.555876	−	0.831265i	$-0.312383\pi$
$61$	6.94896	+	4.01198i	0.113917	+	0.0657702i	−0.441959	+	0.897035i	$0.645716\pi$
$62$		−	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	0.798939	−	0.601411i	$-0.205395\pi$
$67$	−8.13165	−	14.0844i	−0.121368	−	0.210215i	−0.920307	+	0.391196i	$0.872061\pi$
$68$	−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	−0.161218	−	0.986919i	$-0.551542\pi$
$73$	44.7395	−	25.8303i	0.612870	−	0.353840i	0.774088	+	0.633078i	$0.218209\pi$
$74$	−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	−0.788065	−	0.615592i	$-0.788917\pi$
$79$	10.9877	−	19.0313i	0.139085	−	0.240903i	0.927151	+	0.374689i	$0.122250\pi$
$80$	−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	$-0.999199\pi$
$83$		−	0.417479i		−	0.00502987i	0.999997	−	0.00251494i	$-0.000800530\pi$
$84$	−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	−0.150672	−	0.988584i	$-0.548144\pi$
$89$	−96.3110	−	55.6052i	−1.08215	−	0.624778i	−0.931475	+	0.363806i	$0.881477\pi$
$90$		−	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	$-0.875029\pi$
$97$		−	74.2244i		−	0.765200i	0.923914	−	0.382600i	$-0.124971\pi$
$98$	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	−0.0750065	−	0.997183i	$-0.523898\pi$
$101$	75.8587	−	43.7970i	0.751076	−	0.433634i	0.826083	+	0.563549i	$0.190564\pi$
$102$	22.3421	+	38.6976i	0.219040	+	0.379388i
$103$	120.413	+	69.5206i	1.16906	+	0.674957i	0.953458	−	0.301525i	$-0.0974956\pi$
$103$	120.413	+	69.5206i	1.16906	+	0.674957i	0.215601	+	0.976482i	$0.430829\pi$
$104$			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	0.253252	+	0.967400i	$0.418500\pi$
$107$	−76.0949	+	131.800i	−0.711168	+	1.23178i	−0.964419	+	0.264378i	$0.914833\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	−32.3777	−	56.0798i	−0.297043	−	0.514494i	0.678415	−	0.734679i	$-0.262667\pi$
$109$	−32.3777	−	56.0798i	−0.297043	−	0.514494i	−0.975458	+	0.220185i	$0.929334\pi$
$110$	−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	0.0257055	−	0.999670i	$-0.491817\pi$
$131$	−108.361	−	62.5621i	−0.827181	−	0.477573i	−0.852887	+	0.522096i	$0.825150\pi$
$132$		−	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	0.928312	−	0.371801i	$-0.121260\pi$
$137$	19.4769	+	33.7349i	0.142167	+	0.246240i	−0.786145	+	0.618042i	$0.787926\pi$
$138$	−53.4368	−	30.8518i	−0.387223	−	0.223564i
$139$		−	98.9454i		−	0.711837i	−0.934517	−	0.355919i	$-0.884168\pi$
$139$		−	98.9454i		−	0.711837i	0.934517	−	0.355919i	$-0.115832\pi$
$140$	−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	−0.362680	−	0.931914i	$-0.618138\pi$
$149$	93.2324	−	161.483i	0.625721	−	1.08378i	0.988401	−	0.151867i	$-0.0485284\pi$
$150$	−10.6066	+	6.12372i	−0.0707107	+	0.0408248i
$151$	−77.4202	−	134.096i	−0.512716	−	0.888051i	−0.999891	−	0.0147462i	$-0.995306\pi$
$151$	−77.4202	−	134.096i	−0.512716	−	0.888051i	0.487175	−	0.873304i	$-0.338027\pi$
$152$	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	−0.632032	−	0.774942i	$-0.717779\pi$
$157$	−43.4777	+	25.1019i	−0.276928	+	0.159885i	0.355104	+	0.934827i	$0.384446\pi$
$158$	−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	−0.631912	−	0.775040i	$-0.717730\pi$
$163$	57.9054	−	100.295i	0.355248	−	0.615308i	0.987160	+	0.159732i	$0.0510631\pi$
$164$	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	$0.0587737\pi$
$167$			61.3210i			0.367191i	−0.983002	+	0.183596i	$0.941226\pi$
$168$	−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	0.577245	−	0.816571i	$-0.304128\pi$
$173$	27.4544	+	15.8508i	0.158696	+	0.0916232i	−0.418549	+	0.908194i	$0.637461\pi$
$174$		−	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	0.620899	−	0.783891i	$-0.286768\pi$
$179$	−65.9472	−	114.224i	−0.368420	−	0.638122i	−0.989319	+	0.145768i	$0.953435\pi$
$180$	−11.6190	−	6.70820i	−0.0645497	−	0.0372678i
$181$		−	55.1431i		−	0.304658i	−0.988330	−	0.152329i	$-0.951323\pi$
$181$		−	55.1431i		−	0.304658i	0.988330	−	0.152329i	$-0.0486773\pi$
$182$	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	0.489019	+	0.872273i	$0.337355\pi$
$191$	−97.5822	+	169.017i	−0.510901	+	0.884907i	−0.999920	+	0.0126340i	$0.995978\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	−174.380	−	302.035i	−0.903523	−	1.56495i	−0.822888	−	0.568204i	$-0.807639\pi$
$193$	−174.380	−	302.035i	−0.903523	−	1.56495i	−0.0806348	−	0.996744i	$-0.525695\pi$
$194$	−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	−0.0785571	−	0.996910i	$-0.525031\pi$
$199$	148.357	−	85.6540i	0.745513	−	0.430422i	0.824070	+	0.566487i	$0.191698\pi$
$200$	−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	$0.305539\pi$
$223$			365.329i			1.63825i	−0.573618	+	0.819123i	$0.694461\pi$
$224$	−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	0.0803928	−	0.996763i	$-0.474383\pi$
$227$	223.325	−	128.937i	0.983811	−	0.568004i	0.903419	+	0.428759i	$0.141049\pi$
$228$	−42.6285	−	73.8347i	−0.186967	−	0.323837i
$229$	−13.3634	−	7.71538i	−0.0583556	−	0.0336916i	0.470538	−	0.882380i	$-0.344060\pi$
$229$	−13.3634	−	7.71538i	−0.0583556	−	0.0336916i	−0.528894	+	0.848688i	$0.677393\pi$
$230$			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	−0.699615	−	0.714520i	$-0.746645\pi$
$233$	62.6734	−	108.553i	0.268984	−	0.465895i	0.968600	+	0.248625i	$0.0799786\pi$
$234$	−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	−0.316213	−	0.948688i	$-0.602412\pi$
$241$	83.6915	−	48.3193i	0.347268	−	0.200495i	0.663481	+	0.748193i	$0.269078\pi$
$242$	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	$0.0188630\pi$
$251$			29.7311i			0.118450i	−0.998245	+	0.0592252i	$0.981137\pi$
$252$	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	0.999909	−	0.0135154i	$-0.00430222\pi$
$257$	382.457	+	220.811i	1.48816	+	0.859189i	0.488250	+	0.872704i	$0.337636\pi$
$258$			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	−0.982593	−	0.185772i	$-0.940521\pi$
$263$	−171.523	−	297.087i	−0.652180	−	1.12961i	0.330413	−	0.943836i	$-0.392812\pi$
$264$	−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	0.491769	−	0.870726i	$-0.336350\pi$
$269$	401.274	−	231.676i	1.49172	−	0.861247i	0.999955	+	0.00947852i	$0.00301715\pi$
$270$	8.21584	+	14.2302i	0.0304290	+	0.0527046i
$271$	211.814	+	122.291i	0.781600	+	0.451257i	0.836997	−	0.547207i	$-0.184309\pi$
$271$	211.814	+	122.291i	0.781600	+	0.451257i	−0.0553967	+	0.998464i	$0.517642\pi$
$272$			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	0.710226	−	0.703974i	$-0.248593\pi$
$277$	−70.5092	−	122.126i	−0.254546	−	0.440887i	−0.964772	+	0.263087i	$0.915259\pi$
$278$	−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	−0.667788	−	0.744351i	$-0.732759\pi$
$283$	−101.047	+	58.3392i	−0.357055	+	0.206146i	0.310733	+	0.950497i	$0.399425\pi$
$284$	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	$-0.927744\pi$
$293$		−	131.882i		−	0.450110i	0.974346	−	0.225055i	$-0.0722562\pi$
$294$	−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	$-0.753132\pi$
$307$		−	429.871i		−	1.40023i	0.714030	−	0.700115i	$-0.246868\pi$
$308$	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	−0.807451	−	0.589935i	$-0.799153\pi$
$311$	−217.786	+	125.739i	−0.700277	+	0.404305i	0.107174	+	0.994240i	$0.465820\pi$
$312$	−8.56803	−	14.8403i	−0.0274616	−	0.0475649i
$313$	11.8674	+	6.85166i	0.0379151	+	0.0218903i	0.518838	−	0.854873i	$-0.326365\pi$
$313$	11.8674	+	6.85166i	0.0379151	+	0.0218903i	−0.480923	+	0.876763i	$0.659698\pi$
$314$			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	−0.838886	−	0.544307i	$-0.816793\pi$
$317$	16.4651	−	28.5183i	0.0519403	−	0.0899632i	0.890827	+	0.454343i	$0.150126\pi$
$318$	−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	−0.356059	−	0.934464i	$-0.615880\pi$
$331$	208.940	−	361.895i	0.631240	−	1.09334i	0.987299	−	0.158876i	$-0.0507869\pi$
$332$	−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	0.555774	−	0.831333i	$-0.312422\pi$
$347$	−153.398	−	265.693i	−0.442069	−	0.765685i	−0.997843	+	0.0656479i	$0.979089\pi$
$348$	−159.367	−	92.0105i	−0.457951	−	0.264398i
$349$			340.162i			0.974676i	0.873214	+	0.487338i	$0.162032\pi$
$349$			340.162i			0.974676i	−0.873214	+	0.487338i	$0.837968\pi$
$350$	−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	−0.883636	−	0.468174i	$-0.844912\pi$
$353$	−324.761	+	187.501i	−0.920004	+	0.531165i	−0.0363676	+	0.999338i	$0.511579\pi$
$354$	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	−0.539989	−	0.841672i	$-0.681572\pi$
$359$	164.750	−	285.356i	0.458915	−	0.794863i	0.998904	+	0.0468084i	$0.0149050\pi$
$360$	−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	−0.467619	−	0.883930i	$-0.654888\pi$
$367$	23.5163	−	13.5772i	0.0640772	−	0.0369950i	0.531696	+	0.846935i	$0.321555\pi$
$368$	−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	−0.938738	−	0.344633i	$-0.888004\pi$
$373$	−63.7488	+	110.416i	−0.170908	+	0.296022i	0.767829	+	0.640654i	$0.221337\pi$
$374$	−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	0.885127	−	0.465350i	$-0.154071\pi$
$383$	354.155	+	204.471i	0.924686	+	0.533867i	0.0395587	+	0.999217i	$0.487405\pi$
$384$			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	0.502370	−	0.864652i	$-0.332461\pi$
$389$	−193.576	−	335.284i	−0.497626	−	0.861913i	−0.999996	+	0.00273932i	$0.999128\pi$
$390$	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	0.532483	−	0.846441i	$-0.321259\pi$
$397$	26.0771	+	15.0556i	0.0656853	+	0.0379234i	−0.466798	+	0.884364i	$0.654592\pi$
$398$		−	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	−0.938608	−	0.344987i	$-0.887883\pi$
$401$	−68.3852	+	118.447i	−0.170537	+	0.295378i	0.768071	+	0.640365i	$0.221217\pi$
$402$	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	−0.920855	−	0.389906i	$-0.872507\pi$
$409$	−426.838	+	246.435i	−1.04361	+	0.602531i	−0.122759	+	0.992437i	$0.539174\pi$
$410$	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	$0.121289\pi$
$419$			311.640i			0.743771i	−0.928279	+	0.371885i	$0.878711\pi$
$420$	−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	0.957481	+	0.288497i	$0.0931555\pi$
$431$	314.021	+	543.900i	0.728586	+	1.26195i	−0.228895	+	0.973451i	$0.573511\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$		−	706.789i		−	1.63231i	−0.577836	−	0.816153i	$-0.696103\pi$
$433$		−	706.789i		−	1.63231i	0.577836	−	0.816153i	$-0.303897\pi$
$434$	−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	0.977896	−	0.209090i	$-0.0670501\pi$
$439$	564.452	+	325.886i	1.28577	+	0.742338i	0.307871	+	0.951428i	$0.400383\pi$
$440$			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	−0.852385	−	0.522915i	$-0.824844\pi$
$443$	11.8129	−	20.4605i	0.0266657	−	0.0461863i	0.879050	+	0.476729i	$0.158178\pi$
$444$	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	−0.991599	−	0.129351i	$-0.958710\pi$
$457$	−175.386	+	303.778i	−0.383778	+	0.664723i	0.607821	+	0.794074i	$0.292044\pi$
$458$	−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	$0.170908\pi$
$461$			471.598i			1.02299i	−0.859287	+	0.511494i	$0.829092\pi$
$462$	−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	0.202702	−	0.979240i	$-0.435028\pi$
$467$	−254.045	−	146.673i	−0.543994	−	0.314075i	−0.746696	+	0.665166i	$0.768361\pi$
$468$			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	−0.992105	−	0.125409i	$-0.959976\pi$
$479$	−660.805	+	381.516i	−1.37955	+	0.796484i	−0.387445	+	0.921893i	$0.626642\pi$
$480$	−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	0.957768	−	0.287542i	$-0.0928382\pi$
$487$	111.944	+	193.893i	0.229865	+	0.398138i	−0.727903	+	0.685680i	$0.759505\pi$
$488$	−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	−0.940160	−	0.340733i	$-0.889325\pi$
$499$	−87.3234	+	151.249i	−0.174997	+	0.303103i	0.765163	+	0.643836i	$0.222658\pi$
$500$	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	$0.266836\pi$
$503$			747.962i			1.48700i	−0.668734	+	0.743501i	$0.733164\pi$
$504$	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	0.287130	−	0.957892i	$-0.407299\pi$
$509$	−203.021	−	117.214i	−0.398863	−	0.230284i	−0.685993	+	0.727608i	$0.740632\pi$
$510$			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	−0.310687	−	0.950512i	$-0.600559\pi$
$521$	186.068	−	107.427i	0.357137	−	0.206193i	0.667824	+	0.744319i	$0.267226\pi$
$522$	112.689	+	195.184i	0.215880	+	0.373915i
$523$	801.108	+	462.520i	1.53176	+	0.884360i	0.999281	+	0.0379137i	$0.0120712\pi$
$523$	801.108	+	462.520i	1.53176	+	0.884360i	0.532475	+	0.846446i	$0.321262\pi$
$524$			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	−0.808354	−	0.588696i	$-0.799641\pi$
$541$	57.1560	−	98.9971i	0.105649	−	0.182989i	0.914003	+	0.405707i	$0.132975\pi$
$542$	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	0.988710	−	0.149841i	$-0.0478762\pi$
$557$	203.076	+	351.738i	0.364589	+	0.631487i	−0.624121	+	0.781328i	$0.714543\pi$
$558$	−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	−0.791824	−	0.610749i	$-0.790869\pi$
$563$	−370.911	+	214.146i	−0.658813	+	0.380366i	0.133012	+	0.991114i	$0.457535\pi$
$564$	−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	−0.111728	−	0.993739i	$-0.535638\pi$
$569$	457.897	−	793.100i	0.804739	−	1.39385i	0.916467	−	0.400110i	$-0.131028\pi$
$570$	116.743	−	67.4016i	0.204812	−	0.118248i
$571$	356.947	+	618.250i	0.625125	+	1.08275i	0.988517	+	0.151112i	$0.0482855\pi$
$571$	356.947	+	618.250i	0.625125	+	1.08275i	−0.363391	+	0.931637i	$0.618381\pi$
$572$	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	−0.564293	−	0.825574i	$-0.690851\pi$
$577$	−75.8591	+	43.7973i	−0.131472	+	0.0759052i	0.432822	+	0.901480i	$0.357518\pi$
$578$	−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	$0.0462300\pi$
$587$			169.908i			0.289452i	−0.989472	+	0.144726i	$0.953770\pi$
$588$	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	0.639047	−	0.769168i	$-0.279329\pi$
$593$	173.424	+	100.126i	0.292452	+	0.168847i	−0.346595	+	0.938015i	$0.612662\pi$
$594$		−	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	0.994920	+	0.100671i	$0.0320988\pi$
$599$	350.201	+	606.566i	0.584643	+	1.01263i	−0.410277	+	0.911961i	$0.634568\pi$
$600$	21.2132	+	12.2474i	0.0353553	+	0.0204124i
$601$		−	1039.21i		−	1.72914i	−0.502515	−	0.864569i	$-0.667592\pi$
$601$		−	1039.21i		−	1.72914i	0.502515	−	0.864569i	$-0.332408\pi$
$602$	−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	0.542994	−	0.839737i	$-0.317291\pi$
$607$	52.9655	+	30.5796i	0.0872578	+	0.0503783i	−0.455736	+	0.890115i	$0.650624\pi$
$608$		−	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	0.996546	−	0.0830371i	$-0.0264620\pi$
$613$	261.359	+	452.688i	0.426361	+	0.738479i	−0.570185	+	0.821516i	$0.693129\pi$
$614$	−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	0.459346	−	0.888257i	$-0.348084\pi$
$619$	902.671	−	521.157i	1.45827	−	0.841934i	0.998927	+	0.0463229i	$0.0147503\pi$
$620$	−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	0.908037	−	0.418891i	$-0.137581\pi$
$641$	58.4900	+	101.308i	0.0912481	+	0.158046i	−0.816788	+	0.576937i	$0.804248\pi$
$642$	−322.843	−	186.394i	−0.502871	−	0.290333i
$643$			874.209i			1.35958i	0.733408	+	0.679789i	$0.237929\pi$
$643$			874.209i			1.35958i	−0.733408	+	0.679789i	$0.762071\pi$
$644$	−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	−0.507799	−	0.861476i	$-0.669541\pi$
$647$	−10.1185	+	5.84189i	−0.0156390	+	0.00902920i	0.492160	+	0.870505i	$0.336207\pi$
$648$	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	−0.999914	−	0.0130935i	$-0.995832\pi$
$653$	−319.067	+	552.641i	−0.488618	+	0.846311i	0.511296	+	0.859404i	$0.329165\pi$
$654$	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	−0.149694	−	0.988732i	$-0.547829\pi$
$661$	417.571	−	241.085i	0.631727	−	0.364728i	0.781420	+	0.624005i	$0.214495\pi$
$662$	−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	0.587671	−	0.809100i	$-0.300045\pi$
$677$	122.405	+	70.6707i	0.180805	+	0.104388i	−0.406866	+	0.913488i	$0.633378\pi$
$678$			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	−0.959626	−	0.281279i	$-0.909241\pi$
$683$	−494.088	−	855.785i	−0.723408	−	1.25298i	0.236218	−	0.971700i	$-0.424092\pi$
$684$	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	0.703468	−	0.710727i	$-0.251634\pi$
$691$	303.829	+	175.415i	0.439694	+	0.253857i	−0.263774	+	0.964585i	$0.584967\pi$
$692$		−	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	−0.829343	−	0.558740i	$-0.811285\pi$
$709$	49.0712	−	84.9938i	0.0692118	−	0.119878i	0.898555	+	0.438862i	$0.144618\pi$
$710$	−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	0.861209	−	0.508251i	$-0.169708\pi$
$719$	612.340	+	353.535i	0.851655	+	0.491703i	−0.00955403	+	0.999954i	$0.503041\pi$
$720$			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	$0.381170\pi$
$727$			1353.85i			1.86225i	−0.364705	+	0.931123i	$0.618830\pi$
$728$	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	0.136359	−	0.990660i	$-0.456460\pi$
$733$	−478.941	−	276.517i	−0.653398	−	0.377240i	−0.789757	+	0.613420i	$0.789793\pi$
$734$		−	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	−0.987228	−	0.159312i	$-0.949072\pi$
$739$	−466.739	−	808.416i	−0.631582	−	1.09393i	0.355646	−	0.934621i	$-0.384261\pi$
$740$	−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	−0.999845	−	0.0176322i	$-0.994387\pi$
$751$	−363.974	+	630.421i	−0.484652	+	0.839442i	0.515192	+	0.857075i	$0.327721\pi$
$752$	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	0.0252080	−	0.999682i	$-0.491975\pi$
$761$	−630.061	−	363.766i	−0.827938	−	0.478010i	−0.853146	+	0.521672i	$0.825309\pi$
$762$		−	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	$-0.648209\pi$
$769$		−	1374.28i		−	1.78709i	0.448969	−	0.893547i	$-0.351791\pi$
$770$	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	−0.447189	−	0.894439i	$-0.647575\pi$
$773$	80.2556	−	46.3356i	0.103824	−	0.0599425i	0.551013	+	0.834497i	$0.314242\pi$
$774$	−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	0.0364974	−	0.999334i	$-0.488380\pi$
$787$	724.193	−	418.113i	0.920195	−	0.531275i	0.883697	+	0.468059i	$0.155047\pi$
$788$	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	$0.0260448\pi$
$797$			130.279i			0.163462i	−0.996654	+	0.0817310i	$0.973955\pi$
$798$	−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	0.607496	−	0.794323i	$-0.292174\pi$
$809$	−310.782	−	538.290i	−0.384156	−	0.665377i	−0.991652	+	0.128946i	$0.958841\pi$
$810$	−24.6475	−	14.2302i	−0.0304290	−	0.0175682i
$811$		−	445.846i		−	0.549748i	−0.961480	−	0.274874i	$-0.911364\pi$
$811$		−	445.846i		−	0.549748i	0.961480	−	0.274874i	$-0.0886361\pi$
$812$	−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	0.174209	+	0.984709i	$0.444263\pi$
$821$	−628.622	+	1088.81i	−0.765678	+	1.32619i	−0.939887	+	0.341485i	$0.889070\pi$
$822$	−82.6334	+	47.7084i	−0.100527	+	0.0580394i
$823$	−60.1709	−	104.219i	−0.0731117	−	0.126633i	0.827152	−	0.561978i	$-0.189960\pi$
$823$	−60.1709	−	104.219i	−0.0731117	−	0.126633i	−0.900264	+	0.435345i	$0.856626\pi$
$824$	−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	−0.362957	−	0.931806i	$-0.618233\pi$
$829$	217.640	−	125.654i	0.262533	−	0.151573i	0.625489	+	0.780233i	$0.284899\pi$
$830$	−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	$0.0962297\pi$
$839$			499.592i			0.595461i	−0.954650	+	0.297730i	$0.903770\pi$
$840$	−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	$-0.733839\pi$
$853$		−	1265.99i		−	1.48416i	0.670310	−	0.742082i	$-0.266161\pi$
$854$	−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	−0.301479	−	0.953473i	$-0.597480\pi$
$857$	320.100	−	184.810i	0.373513	−	0.215648i	0.674992	+	0.737825i	$0.264147\pi$
$858$	−85.5731	−	148.217i	−0.0997355	−	0.172747i
$859$	−1089.49	−	629.015i	−1.26832	−	0.732264i	−0.293649	−	0.955913i	$-0.594870\pi$
$859$	−1089.49	−	629.015i	−1.26832	−	0.732264i	−0.974670	+	0.223649i	$0.928203\pi$
$860$		−	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	−0.789286	−	0.614025i	$-0.789549\pi$
$863$	118.333	−	204.959i	0.137118	−	0.237496i	0.926405	+	0.376530i	$0.122883\pi$
$864$	−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	−0.998922	−	0.0464269i	$-0.985217\pi$
$877$	−402.766	+	697.611i	−0.459254	+	0.795451i	0.539668	+	0.841878i	$0.318550\pi$
$878$	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	$-0.857392\pi$
$881$		−	763.260i		−	0.866356i	0.901308	−	0.433178i	$-0.142608\pi$
$882$	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	0.300960	−	0.953637i	$-0.402693\pi$
$887$	−332.122	−	191.751i	−0.374433	−	0.216179i	−0.675393	+	0.737458i	$0.736026\pi$
$888$		−	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	0.985251	+	0.171115i	$0.0547371\pi$
$907$	581.220	+	1006.70i	0.640816	+	1.10993i	−0.344435	+	0.938810i	$0.611930\pi$
$908$	−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	0.351785	+	0.936081i	$0.385575\pi$
$919$	−583.360	+	1010.41i	−0.634777	+	1.09947i	−0.986562	+	0.163386i	$0.947759\pi$
$920$	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	0.600929	−	0.799303i	$-0.294798\pi$
$929$	194.325	+	112.194i	0.209177	+	0.120768i	−0.391752	+	0.920071i	$0.628131\pi$
$930$			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	$0.111697\pi$
$937$			644.185i			0.687497i	−0.939062	+	0.343749i	$0.888303\pi$
$938$	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	−0.634682	−	0.772774i	$-0.718869\pi$
$941$	−266.097	+	153.631i	−0.282781	+	0.163264i	0.351901	+	0.936037i	$0.385535\pi$
$942$	−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	−0.481555	−	0.876416i	$-0.659928\pi$
$947$	490.755	−	850.013i	0.518221	−	0.897585i	0.999776	−	0.0211694i	$-0.00673894\pi$
$948$	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	0.331993	−	0.943282i	$-0.392279\pi$
$971$	−309.667	−	178.787i	−0.318916	−	0.184126i	−0.650909	+	0.759155i	$0.725612\pi$
$972$		−	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	0.998321	−	0.0579204i	$-0.0184470\pi$
$977$	438.673	+	759.804i	0.449000	+	0.777691i	−0.549321	+	0.835611i	$0.685114\pi$
$978$	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	−0.974766	−	0.223229i	$-0.928340\pi$
$983$	−1247.26	+	720.104i	−1.26883	+	0.732557i	−0.294061	+	0.955787i	$0.595007\pi$
$984$	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	−0.995191	−	0.0979496i	$-0.968772\pi$
$991$	−577.181	−	999.706i	−0.582423	−	1.00879i	0.412769	−	0.910836i	$-0.364562\pi$
$992$	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	0.415916	−	0.909403i	$-0.363461\pi$
$997$	1407.21	−	812.451i	1.41144	−	0.814896i	0.995524	+	0.0945072i	$0.0301275\pi$
$998$	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.61.7	yes	16
3.2	odd	2		630.3.v.c.271.1		16
5.2	odd	4		1050.3.q.e.649.10		32
5.3	odd	4		1050.3.q.e.649.1		32
5.4	even	2		1050.3.p.i.901.4		16
7.2	even	3		1470.3.f.d.391.2		16
7.3	odd	6	inner	210.3.o.b.31.7	✓	16
7.5	odd	6		1470.3.f.d.391.8		16
21.17	even	6		630.3.v.c.451.1		16
35.3	even	12		1050.3.q.e.199.10		32
35.17	even	12		1050.3.q.e.199.1		32
35.24	odd	6		1050.3.p.i.451.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.7	✓	16	7.3	odd	6	inner
210.3.o.b.61.7	yes	16	1.1	even	1	trivial
630.3.v.c.271.1		16	3.2	odd	2
630.3.v.c.451.1		16	21.17	even	6
1050.3.p.i.451.4		16	35.24	odd	6
1050.3.p.i.901.4		16	5.4	even	2
1050.3.q.e.199.1		32	35.17	even	12
1050.3.q.e.199.10		32	35.3	even	12
1050.3.q.e.649.1		32	5.3	odd	4
1050.3.q.e.649.10		32	5.2	odd	4
1470.3.f.d.391.2		16	7.2	even	3
1470.3.f.d.391.8		16	7.5	odd	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.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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