LMFDB - Embedded newform 210.3.o.b.31.6

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			31.6
Root			$2.81422 + 4.87437i$ of defining polynomial
Character	$\chi$	$=$	210.31
Dual form			210.3.o.b.61.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(6.99242 - 0.325616i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(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} +(6.99242 - 0.325616i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-6.09582 + 10.5583i) q^{11} +(3.00000 - 1.73205i) q^{12} +25.3938i q^{13} +(5.34319 + 8.33369i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-24.9196 - 14.3873i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-13.9147 + 8.03365i) q^{19} -4.47214i q^{20} +(-10.7706 - 5.56719i) q^{21} -17.2416 q^{22} +(11.8709 + 20.5610i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-31.1010 + 17.9562i) q^{26} -5.19615i q^{27} +(-6.42844 + 12.4368i) q^{28} +27.9121 q^{29} +(2.73861 + 4.74342i) q^{30} +(20.0480 + 11.5747i) q^{31} +(2.82843 - 4.89898i) q^{32} +(18.2875 - 10.5583i) q^{33} -40.6936i q^{34} +(-13.1767 + 8.44832i) q^{35} -6.00000 q^{36} +(14.5321 + 25.1703i) q^{37} +(-19.6783 - 11.3613i) q^{38} +(21.9917 - 38.0908i) q^{39} +(5.47723 - 3.16228i) q^{40} -56.9065i q^{41} +(-0.797593 - 17.1279i) q^{42} +7.83839 q^{43} +(-12.1916 - 21.1165i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-16.7880 + 29.0777i) q^{46} +(-19.7390 + 11.3963i) q^{47} +6.92820i q^{48} +(48.7879 - 4.55369i) q^{49} +7.07107 q^{50} +(24.9196 + 43.1620i) q^{51} +(-43.9834 - 25.3938i) q^{52} +(-24.2781 + 42.0510i) q^{53} +(6.36396 - 3.67423i) q^{54} -27.2613i q^{55} +(-19.7776 + 0.920981i) q^{56} +27.8294 q^{57} +(19.7368 + 34.1852i) q^{58} +(-62.3779 - 36.0139i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(99.2512 - 57.3027i) q^{61} +32.7382i q^{62} +(11.3346 + 17.6784i) q^{63} +8.00000 q^{64} +(-28.3912 - 49.1750i) q^{65} +(25.8624 + 14.9316i) q^{66} +(35.2674 - 61.0850i) q^{67} +(49.8392 - 28.7747i) q^{68} -41.1221i q^{69} +(-19.6644 - 10.1643i) q^{70} +6.41501 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-34.2569 - 19.7782i) q^{73} +(-20.5514 + 35.5961i) q^{74} +(-7.50000 + 4.33013i) q^{75} -32.1346i q^{76} +(-39.1866 + 75.8127i) q^{77} +62.2019 q^{78} +(27.3985 + 47.4555i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(69.6960 - 40.2390i) q^{82} +135.934i q^{83} +(20.4133 - 13.0881i) q^{84} +64.3422 q^{85} +(5.54258 + 9.60002i) q^{86} +(-41.8682 - 24.1726i) q^{87} +(17.2416 - 29.8633i) q^{88} +(124.905 - 72.1140i) q^{89} -9.48683i q^{90} +(8.26863 + 177.564i) q^{91} -47.4837 q^{92} +(-20.0480 - 34.7241i) q^{93} +(-27.9152 - 16.1168i) q^{94} +(17.9638 - 31.1142i) q^{95} +(-8.48528 + 4.89898i) q^{96} -78.9980i q^{97} +(40.0754 + 56.5328i) q^{98} -36.5749 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
$7$	6.99242	−	0.325616i	0.998918	−	0.0465165i
$7$	6.99242	−	0.325616i	0.998918	−	0.0465165i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	−6.09582	+	10.5583i	−0.554165	+	0.959842i	0.443803	+	0.896125i	$0.353629\pi$
$11$	−6.09582	+	10.5583i	−0.554165	+	0.959842i	−0.997968	+	0.0637178i	$0.979704\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$			25.3938i			1.95337i	0.214672	+	0.976686i	$0.431132\pi$
$13$			25.3938i			1.95337i	−0.214672	+	0.976686i	$0.568868\pi$
$14$	5.34319	+	8.33369i	0.381656	+	0.595263i
$15$	3.87298			0.258199
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−24.9196	−	14.3873i	−1.46586	−	0.846315i	−0.466588	−	0.884475i	$-0.654517\pi$
$17$	−24.9196	−	14.3873i	−1.46586	−	0.846315i	−0.999272	+	0.0381599i	$0.987850\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	−13.9147	+	8.03365i	−0.732352	+	0.422824i	−0.819282	−	0.573391i	$-0.805628\pi$
$19$	−13.9147	+	8.03365i	−0.732352	+	0.422824i	0.0869298	+	0.996214i	$0.472294\pi$
$20$		−	4.47214i		−	0.223607i
$21$	−10.7706	−	5.56719i	−0.512887	−	0.265104i
$22$	−17.2416			−0.783708
$23$	11.8709	+	20.5610i	0.516127	+	0.893958i	0.999825	+	0.0187231i	$0.00596009\pi$
$23$	11.8709	+	20.5610i	0.516127	+	0.893958i	−0.483698	+	0.875235i	$0.660707\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−31.1010	+	17.9562i	−1.19619	+	0.690621i
$27$		−	5.19615i		−	0.192450i
$28$	−6.42844	+	12.4368i	−0.229587	+	0.444173i
$29$	27.9121			0.962486			0.481243	−	0.876587i	$-0.340185\pi$
$29$	27.9121			0.962486			0.481243	+	0.876587i	$0.340185\pi$
$30$	2.73861	+	4.74342i	0.0912871	+	0.158114i
$31$	20.0480	+	11.5747i	0.646709	+	0.373378i	0.787194	−	0.616705i	$-0.211533\pi$
$31$	20.0480	+	11.5747i	0.646709	+	0.373378i	−0.140485	+	0.990083i	$0.544866\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	18.2875	−	10.5583i	0.554165	−	0.319947i
$34$		−	40.6936i		−	1.19687i
$35$	−13.1767	+	8.44832i	−0.376478	+	0.241381i
$36$	−6.00000			−0.166667
$37$	14.5321	+	25.1703i	0.392758	+	0.680277i	0.992812	−	0.119682i	$-0.0381876\pi$
$37$	14.5321	+	25.1703i	0.392758	+	0.680277i	−0.600054	+	0.799960i	$0.704854\pi$
$38$	−19.6783	−	11.3613i	−0.517851	−	0.298982i
$39$	21.9917	−	38.0908i	0.563890	−	0.976686i
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$		−	56.9065i		−	1.38796i	−0.719992	−	0.693982i	$-0.755855\pi$
$41$		−	56.9065i		−	1.38796i	0.719992	−	0.693982i	$-0.244145\pi$
$42$	−0.797593	−	17.1279i	−0.0189903	−	0.407806i
$43$	7.83839			0.182288			0.0911440	−	0.995838i	$-0.470948\pi$
$43$	7.83839			0.182288			0.0911440	+	0.995838i	$0.470948\pi$
$44$	−12.1916	−	21.1165i	−0.277083	−	0.479921i
$45$	−5.80948	−	3.35410i	−0.129099	−	0.0745356i
$46$	−16.7880	+	29.0777i	−0.364957	+	0.632124i
$47$	−19.7390	+	11.3963i	−0.419979	+	0.242475i	−0.695068	−	0.718944i	$-0.744626\pi$
$47$	−19.7390	+	11.3963i	−0.419979	+	0.242475i	0.275089	+	0.961419i	$0.411293\pi$
$48$			6.92820i			0.144338i
$49$	48.7879	−	4.55369i	0.995672	−	0.0929324i
$50$	7.07107			0.141421
$51$	24.9196	+	43.1620i	0.488620	+	0.846315i
$52$	−43.9834	−	25.3938i	−0.845835	−	0.488343i
$53$	−24.2781	+	42.0510i	−0.458078	+	0.793414i	−0.998859	−	0.0477489i	$-0.984795\pi$
$53$	−24.2781	+	42.0510i	−0.458078	+	0.793414i	0.540781	+	0.841163i	$0.318129\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		−	27.2613i		−	0.495660i
$56$	−19.7776	+	0.920981i	−0.353171	+	0.0164461i
$57$	27.8294			0.488235
$58$	19.7368	+	34.1852i	0.340290	+	0.589400i
$59$	−62.3779	−	36.0139i	−1.05725	−	0.610405i	−0.132581	−	0.991172i	$-0.542327\pi$
$59$	−62.3779	−	36.0139i	−1.05725	−	0.610405i	−0.924671	+	0.380767i	$0.875660\pi$
$60$	−3.87298	+	6.70820i	−0.0645497	+	0.111803i
$61$	99.2512	−	57.3027i	1.62707	−	0.939388i	0.642107	−	0.766615i	$-0.278060\pi$
$61$	99.2512	−	57.3027i	1.62707	−	0.939388i	0.984962	−	0.172773i	$-0.0552729\pi$
$62$			32.7382i			0.528036i
$63$	11.3346	+	17.6784i	0.179914	+	0.280610i
$64$	8.00000			0.125000
$65$	−28.3912	−	49.1750i	−0.436787	−	0.756538i
$66$	25.8624	+	14.9316i	0.391854	+	0.226237i
$67$	35.2674	−	61.0850i	0.526380	−	0.911716i	−0.473148	−	0.880983i	$-0.656882\pi$
$67$	35.2674	−	61.0850i	0.526380	−	0.911716i	0.999528	−	0.0307332i	$-0.00978424\pi$
$68$	49.8392	−	28.7747i	0.732930	−	0.423157i
$69$		−	41.1221i		−	0.595972i
$70$	−19.6644	−	10.1643i	−0.280920	−	0.145204i
$71$	6.41501			0.0903522			0.0451761	−	0.998979i	$-0.485615\pi$
$71$	6.41501			0.0903522			0.0451761	+	0.998979i	$0.485615\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	−34.2569	−	19.7782i	−0.469272	−	0.270934i	0.246663	−	0.969101i	$-0.420666\pi$
$73$	−34.2569	−	19.7782i	−0.469272	−	0.270934i	−0.715935	+	0.698167i	$0.753999\pi$
$74$	−20.5514	+	35.5961i	−0.277722	+	0.481029i
$75$	−7.50000	+	4.33013i	−0.100000	+	0.0577350i
$76$		−	32.1346i		−	0.422824i
$77$	−39.1866	+	75.8127i	−0.508917	+	0.984581i
$78$	62.2019			0.797461
$79$	27.3985	+	47.4555i	0.346816	+	0.600703i	0.985682	−	0.168615i	$-0.0539295\pi$
$79$	27.3985	+	47.4555i	0.346816	+	0.600703i	−0.638866	+	0.769318i	$0.720596\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	69.6960	−	40.2390i	0.849951	−	0.490719i
$83$			135.934i			1.63775i	0.573969	+	0.818877i	$0.305403\pi$
$83$			135.934i			1.63775i	−0.573969	+	0.818877i	$0.694597\pi$
$84$	20.4133	−	13.0881i	0.243015	−	0.155810i
$85$	64.3422			0.756967
$86$	5.54258	+	9.60002i	0.0644486	+	0.111628i
$87$	−41.8682	−	24.1726i	−0.481243	−	0.277846i
$88$	17.2416	−	29.8633i	0.195927	−	0.339356i
$89$	124.905	−	72.1140i	1.40343	−	0.810270i	0.408686	−	0.912675i	$-0.365987\pi$
$89$	124.905	−	72.1140i	1.40343	−	0.810270i	0.994743	+	0.102405i	$0.0326537\pi$
$90$		−	9.48683i		−	0.105409i
$91$	8.26863	+	177.564i	0.0908641	+	1.95126i
$92$	−47.4837			−0.516127
$93$	−20.0480	−	34.7241i	−0.215570	−	0.373378i
$94$	−27.9152	−	16.1168i	−0.296970	−	0.171456i
$95$	17.9638	−	31.1142i	0.189093	−	0.327518i
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$		−	78.9980i		−	0.814412i	−0.913336	−	0.407206i	$-0.866503\pi$
$97$		−	78.9980i		−	0.814412i	0.913336	−	0.407206i	$-0.133497\pi$
$98$	40.0754	+	56.5328i	0.408933	+	0.576866i
$99$	−36.5749			−0.369443
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−40.4728	−	23.3670i	−0.400721	−	0.231356i	0.286074	−	0.958208i	$-0.407650\pi$
$101$	−40.4728	−	23.3670i	−0.400721	−	0.231356i	−0.686795	+	0.726851i	$0.740983\pi$
$102$	−35.2417	+	61.0404i	−0.345507	+	0.598435i
$103$	−144.022	+	83.1514i	−1.39828	+	0.807295i	−0.994212	−	0.107435i	$-0.965736\pi$
$103$	−144.022	+	83.1514i	−1.39828	+	0.807295i	−0.404064	+	0.914731i	$0.632403\pi$
$104$		−	71.8246i		−	0.690621i
$105$	27.0815	−	1.26110i	0.257919	−	0.0120105i
$106$	−68.6689			−0.647820
$107$	16.4908	+	28.5629i	0.154120	+	0.266943i	0.932738	−	0.360554i	$-0.117413\pi$
$107$	16.4908	+	28.5629i	0.154120	+	0.266943i	−0.778618	+	0.627498i	$0.784079\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	75.8575	−	131.389i	0.695940	−	1.20540i	−0.273923	−	0.961752i	$-0.588321\pi$
$109$	75.8575	−	131.389i	0.695940	−	1.20540i	0.969863	−	0.243652i	$-0.0783454\pi$
$110$	33.3882	−	19.2767i	0.303529	−	0.175242i
$111$		−	50.3405i		−	0.453518i
$112$	−15.1128	−	23.5712i	−0.134936	−	0.210457i
$113$	−42.1910			−0.373372			−0.186686	−	0.982420i	$-0.559775\pi$
$113$	−42.1910			−0.373372			−0.186686	+	0.982420i	$0.559775\pi$
$114$	19.6783	+	34.0839i	0.172617	+	0.298982i
$115$	−45.9759	−	26.5442i	−0.399790	−	0.230819i
$116$	−27.9121	+	48.3452i	−0.240622	+	0.416769i
$117$	−65.9751	+	38.0908i	−0.563890	+	0.325562i
$118$		−	101.863i		−	0.863243i
$119$	−178.933	−	92.4882i	−1.50364	−	0.777212i
$120$	−10.9545			−0.0912871
$121$	−13.8180	−	23.9334i	−0.114198	−	0.197797i
$122$	140.362	+	81.0383i	1.15051	+	0.664248i
$123$	−49.2825	+	85.3598i	−0.400671	+	0.693982i
$124$	−40.0960	+	23.1494i	−0.323354	+	0.186689i
$125$			11.1803i			0.0894427i
$126$	−13.6368	+	26.3825i	−0.108228	+	0.209385i
$127$	49.3159			0.388314			0.194157	−	0.980970i	$-0.437803\pi$
$127$	49.3159			0.388314			0.194157	+	0.980970i	$0.437803\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−11.7576	−	6.78824i	−0.0911440	−	0.0526220i
$130$	40.1512	−	69.5439i	0.308855	−	0.534953i
$131$	−12.6892	+	7.32612i	−0.0968642	+	0.0559246i	−0.547650	−	0.836708i	$-0.684477\pi$
$131$	−12.6892	+	7.32612i	−0.0968642	+	0.0559246i	0.450785	+	0.892632i	$0.351144\pi$
$132$			42.2331i			0.319947i
$133$	−94.6815	+	60.7055i	−0.711891	+	0.456433i
$134$	99.7514			0.744413
$135$	5.80948	+	10.0623i	0.0430331	+	0.0745356i
$136$	70.4833	+	40.6936i	0.518260	+	0.299217i
$137$	8.61062	−	14.9140i	0.0628512	−	0.108862i	−0.832888	−	0.553442i	$-0.813314\pi$
$137$	8.61062	−	14.9140i	0.0628512	−	0.108862i	0.895739	+	0.444581i	$0.146647\pi$
$138$	50.3641	−	29.0777i	0.364957	−	0.210708i
$139$		−	31.2612i		−	0.224901i	−0.993657	−	0.112450i	$-0.964130\pi$
$139$		−	31.2612i		−	0.224901i	0.993657	−	0.112450i	$-0.0358699\pi$
$140$	−1.45620	−	31.2711i	−0.0104014	−	0.223365i
$141$	39.4780			0.279986
$142$	4.53610	+	7.85675i	0.0319443	+	0.0553292i
$143$	−268.115	−	154.796i	−1.87493	−	1.08249i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	−54.0516	+	31.2067i	−0.372769	+	0.215218i
$146$		−	55.9412i		−	0.383159i
$147$	−77.1255	−	35.4211i	−0.524663	−	0.240960i
$148$	−58.1282			−0.392758
$149$	71.5886	+	123.995i	0.480460	+	0.832182i	0.999749	−	0.0224175i	$-0.00713631\pi$
$149$	71.5886	+	123.995i	0.480460	+	0.832182i	−0.519288	+	0.854599i	$0.673803\pi$
$150$	−10.6066	−	6.12372i	−0.0707107	−	0.0408248i
$151$	−23.1788	+	40.1468i	−0.153502	+	0.265873i	−0.932512	−	0.361138i	$-0.882388\pi$
$151$	−23.1788	+	40.1468i	−0.153502	+	0.265873i	0.779011	+	0.627011i	$0.215722\pi$
$152$	39.3567	−	22.7226i	0.258926	−	0.149491i
$153$		−	86.3241i		−	0.564210i
$154$	−120.560	+	5.61413i	−0.782860	+	0.0364554i
$155$	−51.7637			−0.333959
$156$	43.9834	+	76.1815i	0.281945	+	0.488343i
$157$	71.4553	+	41.2548i	0.455130	+	0.262769i	0.709994	−	0.704208i	$-0.248698\pi$
$157$	71.4553	+	41.2548i	0.455130	+	0.262769i	−0.254865	+	0.966977i	$0.582031\pi$
$158$	−38.7473	+	67.1122i	−0.245236	+	0.424761i
$159$	72.8344	−	42.0510i	0.458078	−	0.264471i
$160$			12.6491i			0.0790569i
$161$	89.7015	+	139.906i	0.557152	+	0.868982i
$162$	−12.7279			−0.0785674
$163$	123.208	+	213.403i	0.755879	+	1.30922i	0.944936	+	0.327254i	$0.106123\pi$
$163$	123.208	+	213.403i	0.755879	+	1.30922i	−0.189058	+	0.981966i	$0.560543\pi$
$164$	98.5650	+	56.9065i	0.601006	+	0.346991i
$165$	−23.6090	+	40.8920i	−0.143085	+	0.247830i
$166$	−166.484	+	96.1195i	−1.00292	+	0.579033i
$167$			287.387i			1.72088i	0.509549	+	0.860441i	$0.329812\pi$
$167$			287.387i			1.72088i	−0.509549	+	0.860441i	$0.670188\pi$
$168$	30.4639	+	15.7464i	0.181333	+	0.0937286i
$169$	−475.847			−2.81566
$170$	45.4968	+	78.8028i	0.267628	+	0.463546i
$171$	−41.7441	−	24.1010i	−0.244117	−	0.140941i
$172$	−7.83839	+	13.5765i	−0.0455720	+	0.0789330i
$173$	236.901	−	136.775i	1.36937	−	0.790605i	0.378521	−	0.925593i	$-0.376433\pi$
$173$	236.901	−	136.775i	1.36937	−	0.790605i	0.990847	+	0.134988i	$0.0430995\pi$
$174$		−	68.3704i		−	0.392933i
$175$	16.0711	−	31.0921i	0.0918349	−	0.177669i
$176$	48.7665			0.277083
$177$	62.3779	+	108.042i	0.352417	+	0.610405i
$178$	176.643	+	101.985i	0.992374	+	0.572948i
$179$	50.3990	−	87.2936i	0.281558	−	0.487674i	−0.690210	−	0.723609i	$-0.742482\pi$
$179$	50.3990	−	87.2936i	0.281558	−	0.487674i	0.971769	+	0.235935i	$0.0758153\pi$
$180$	11.6190	−	6.70820i	0.0645497	−	0.0372678i
$181$			135.147i			0.746667i	0.927697	+	0.373333i	$0.121785\pi$
$181$			135.147i			0.746667i	−0.927697	+	0.373333i	$0.878215\pi$
$182$	−211.624	+	135.684i	−1.16277	+	0.745516i
$183$	−198.502			−1.08471
$184$	−33.5760	−	58.1554i	−0.182478	−	0.316062i
$185$	−56.2824	−	32.4947i	−0.304229	−	0.175647i
$186$	28.3521	−	49.1073i	0.152431	−	0.264018i
$187$	303.811	−	175.405i	1.62466	−	0.937996i
$188$		−	45.5853i		−	0.242475i
$189$	−1.69195	−	36.3337i	−0.00895211	−	0.192242i
$190$	50.8093			0.267417
$191$	−89.0902	−	154.309i	−0.466441	−	0.807900i	0.532824	−	0.846226i	$-0.321131\pi$
$191$	−89.0902	−	154.309i	−0.466441	−	0.807900i	−0.999265	+	0.0383263i	$0.987797\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	−67.5577	+	117.013i	−0.350040	+	0.606287i	−0.986256	−	0.165224i	$-0.947165\pi$
$193$	−67.5577	+	117.013i	−0.350040	+	0.606287i	0.636216	+	0.771511i	$0.280499\pi$
$194$	96.7523	−	55.8600i	0.498723	−	0.287938i
$195$			98.3499i			0.504359i
$196$	−40.9007	+	89.0569i	−0.208677	+	0.454372i
$197$	64.7529			0.328695			0.164347	−	0.986403i	$-0.447448\pi$
$197$	64.7529			0.328695			0.164347	+	0.986403i	$0.447448\pi$
$198$	−25.8624	−	44.7949i	−0.130618	−	0.226237i
$199$	116.757	+	67.4097i	0.586719	+	0.338742i	0.763799	−	0.645454i	$-0.223332\pi$
$199$	116.757	+	67.4097i	0.586719	+	0.338742i	−0.177080	+	0.984196i	$0.556665\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$	−105.802	+	61.0850i	−0.526380	+	0.303905i
$202$		−	66.0918i		−	0.327187i
$203$	195.173	−	9.08862i	0.961444	−	0.0447715i
$204$	−99.6785			−0.488620
$205$	63.6234	+	110.199i	0.310358	+	0.537556i
$206$	−203.679	−	117.594i	−0.988731	−	0.570844i
$207$	−35.6128	+	61.6831i	−0.172042	+	0.297986i
$208$	87.9668	−	50.7877i	0.422917	−	0.244172i
$209$		−	195.887i		−	0.937257i
$210$	20.6941	+	32.2762i	0.0985432	+	0.153696i
$211$	−116.352			−0.551432			−0.275716	−	0.961239i	$-0.588915\pi$
$211$	−116.352			−0.551432			−0.275716	+	0.961239i	$0.588915\pi$
$212$	−48.5563	−	84.1019i	−0.229039	−	0.396707i
$213$	−9.62251	−	5.55556i	−0.0451761	−	0.0260824i
$214$	−23.3215	+	40.3941i	−0.108979	+	0.188757i
$215$	−15.1790	+	8.76358i	−0.0705999	+	0.0407608i
$216$			14.6969i			0.0680414i
$217$	143.953	+	74.4073i	0.663377	+	0.342891i
$218$	214.557			0.984208
$219$	34.2569	+	59.3346i	0.156424	+	0.270934i
$220$	47.2180	+	27.2613i	0.214627	+	0.123915i
$221$	365.350	−	632.805i	1.65317	−	2.86337i
$222$	61.6543	−	35.5961i	0.277722	−	0.160343i
$223$			30.0511i			0.134758i	0.997727	+	0.0673791i	$0.0214637\pi$
$223$			30.0511i			0.134758i	−0.997727	+	0.0673791i	$0.978536\pi$
$224$	18.1824	−	35.1767i	0.0811713	−	0.157039i
$225$	15.0000			0.0666667
$226$	−29.8335	−	51.6732i	−0.132007	−	0.228642i
$227$	122.698	+	70.8400i	0.540522	+	0.312070i	0.745290	−	0.666740i	$-0.232311\pi$
$227$	122.698	+	70.8400i	0.540522	+	0.312070i	−0.204769	+	0.978810i	$0.565644\pi$
$228$	−27.8294	+	48.2019i	−0.122059	+	0.211412i
$229$	−188.648	+	108.916i	−0.823792	+	0.475617i	−0.851722	−	0.523993i	$-0.824442\pi$
$229$	−188.648	+	108.916i	−0.823792	+	0.475617i	0.0279303	+	0.999610i	$0.491108\pi$
$230$		−	75.0783i		−	0.326427i
$231$	124.436	−	79.7825i	0.538683	−	0.345379i
$232$	−78.9473			−0.340290
$233$	2.12597	+	3.68229i	0.00912435	+	0.0158038i	0.870552	−	0.492077i	$-0.163762\pi$
$233$	2.12597	+	3.68229i	0.00912435	+	0.0158038i	−0.861427	+	0.507881i	$0.830429\pi$
$234$	−93.3029	−	53.8685i	−0.398730	−	0.230207i
$235$	25.4830	−	44.1378i	0.108438	−	0.187820i
$236$	124.756	−	72.0278i	0.528626	−	0.305202i
$237$		−	94.9110i		−	0.400468i
$238$	−13.2505	−	284.547i	−0.0556742	−	1.19557i
$239$	261.513			1.09419			0.547097	−	0.837069i	$-0.315733\pi$
$239$	261.513			1.09419			0.547097	+	0.837069i	$0.315733\pi$
$240$	−7.74597	−	13.4164i	−0.0322749	−	0.0559017i
$241$	−86.5156	−	49.9498i	−0.358986	−	0.207261i	0.309650	−	0.950851i	$-0.399788\pi$
$241$	−86.5156	−	49.9498i	−0.358986	−	0.207261i	−0.668636	+	0.743590i	$0.733121\pi$
$242$	19.5416	−	33.8470i	0.0807503	−	0.139864i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$			229.211i			0.939388i
$245$	−89.3863	+	63.3648i	−0.364842	+	0.258632i
$246$	−139.392			−0.566634
$247$	−204.005	−	353.347i	−0.825932	−	1.43056i
$248$	−56.7042	−	32.7382i	−0.228646	−	0.132009i
$249$	117.722	−	203.900i	0.472779	−	0.818877i
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$			250.563i			0.998258i	0.866528	+	0.499129i	$0.166347\pi$
$251$			250.563i			0.998258i	−0.866528	+	0.499129i	$0.833653\pi$
$252$	−41.9545	+	1.95369i	−0.166486	+	0.00775276i
$253$	−289.452			−1.14408
$254$	34.8716	+	60.3993i	0.137290	+	0.237793i
$255$	−96.5133	−	55.7220i	−0.378483	−	0.218518i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	151.261	−	87.3305i	0.588563	−	0.339807i	−0.175966	−	0.984396i	$-0.556305\pi$
$257$	151.261	−	87.3305i	0.588563	−	0.339807i	0.764529	+	0.644589i	$0.222971\pi$
$258$		−	19.2000i		−	0.0744188i
$259$	109.810	+	171.269i	0.423977	+	0.661271i
$260$	113.565			0.436787
$261$	41.8682	+	72.5178i	0.160414	+	0.277846i
$262$	−17.9452	−	10.3607i	−0.0684933	−	0.0395446i
$263$	−10.4417	+	18.0856i	−0.0397023	+	0.0687664i	−0.885194	−	0.465223i	$-0.845974\pi$
$263$	−10.4417	+	18.0856i	−0.0397023	+	0.0687664i	0.845491	+	0.533989i	$0.179308\pi$
$264$	−51.7247	+	29.8633i	−0.195927	+	0.113119i
$265$		−	108.575i		−	0.409717i
$266$	−141.299	−	73.0354i	−0.531198	−	0.274569i
$267$	−249.810			−0.935619
$268$	70.5349	+	122.170i	0.263190	+	0.455858i
$269$	0.255741	+	0.147652i	0.000950712	+	0.000548894i	0.500475	−	0.865751i	$-0.333159\pi$
$269$	0.255741	+	0.147652i	0.000950712	+	0.000548894i	−0.499525	+	0.866300i	$0.666492\pi$
$270$	−8.21584	+	14.2302i	−0.0304290	+	0.0527046i
$271$	284.141	−	164.049i	1.04849	−	0.605346i	0.126264	−	0.991997i	$-0.459702\pi$
$271$	284.141	−	164.049i	1.04849	−	0.605346i	0.922226	+	0.386651i	$0.126368\pi$
$272$			115.099i			0.423157i
$273$	141.372	−	273.508i	0.517848	−	1.00186i
$274$	24.3545			0.0888851
$275$	30.4791	+	52.7913i	0.110833	+	0.191968i
$276$	71.2255	+	41.1221i	0.258064	+	0.148993i
$277$	251.485	−	435.585i	0.907888	−	1.57251i	0.0908951	−	0.995860i	$-0.471027\pi$
$277$	251.485	−	435.585i	0.907888	−	1.57251i	0.816993	−	0.576648i	$-0.195639\pi$
$278$	38.2870	−	22.1050i	0.137723	−	0.0795144i
$279$			69.4482i			0.248918i
$280$	37.2694	−	23.8955i	0.133105	−	0.0853409i
$281$	264.481			0.941213			0.470607	−	0.882343i	$-0.344035\pi$
$281$	264.481			0.941213			0.470607	+	0.882343i	$0.344035\pi$
$282$	27.9152	+	48.3505i	0.0989900	+	0.171456i
$283$	−399.801	−	230.825i	−1.41272	−	0.815636i	−0.417079	−	0.908870i	$-0.636946\pi$
$283$	−399.801	−	230.825i	−1.41272	−	0.815636i	−0.995644	+	0.0932336i	$0.970280\pi$
$284$	−6.41501	+	11.1111i	−0.0225881	+	0.0391237i
$285$	−53.8914	+	31.1142i	−0.189093	+	0.109173i
$286$		−	437.830i		−	1.53087i
$287$	−18.5297	−	397.914i	−0.0645633	−	1.38646i
$288$	16.9706			0.0589256
$289$	269.492	+	466.773i	0.932497	+	1.61513i
$290$	−76.4404	−	44.1329i	−0.263588	−	0.152182i
$291$	−68.4142	+	118.497i	−0.235100	+	0.407206i
$292$	68.5137	−	39.5564i	0.234636	−	0.135467i
$293$			134.788i			0.460027i	0.973187	+	0.230014i	$0.0738771\pi$
$293$			134.788i			0.460027i	−0.973187	+	0.230014i	$0.926123\pi$
$294$	−11.1542	−	119.506i	−0.0379395	−	0.406482i
$295$	161.059			0.545963
$296$	−41.1029	−	71.1922i	−0.138861	−	0.240514i
$297$	54.8624	+	31.6748i	0.184722	+	0.106649i
$298$	−101.242	+	175.355i	−0.339737	+	0.588441i
$299$	−522.124	+	301.448i	−1.74623	+	1.00819i
$300$		−	17.3205i		−	0.0577350i
$301$	54.8093	−	2.55230i	0.182091	−	0.00847941i
$302$	−65.5595			−0.217084
$303$	40.4728	+	70.1010i	0.133574	+	0.231356i
$304$	55.6588	+	32.1346i	0.183088	+	0.105706i
$305$	−128.133	+	221.932i	−0.420107	+	0.727647i
$306$	105.725	−	61.0404i	0.345507	−	0.199478i
$307$			23.7237i			0.0772760i	0.999253	+	0.0386380i	$0.0123019\pi$
$307$			23.7237i			0.0772760i	−0.999253	+	0.0386380i	$0.987698\pi$
$308$	−92.1249	−	143.686i	−0.299107	−	0.466513i
$309$	288.045			0.932184
$310$	−36.6024	−	63.3973i	−0.118072	−	0.204507i
$311$	245.097	+	141.507i	0.788092	+	0.455005i	0.839290	−	0.543683i	$-0.182971\pi$
$311$	245.097	+	141.507i	0.788092	+	0.455005i	−0.0511984	+	0.998689i	$0.516304\pi$
$312$	−62.2019	+	107.737i	−0.199365	+	0.345311i
$313$	367.522	−	212.189i	1.17419	−	0.677920i	0.219528	−	0.975606i	$-0.429548\pi$
$313$	367.522	−	212.189i	1.17419	−	0.677920i	0.954664	+	0.297687i	$0.0962150\pi$
$314$			116.686i			0.371612i
$315$	−41.7145	−	21.5616i	−0.132427	−	0.0684497i
$316$	−109.594			−0.346816
$317$	14.0641	+	24.3597i	0.0443661	+	0.0768444i	0.887356	−	0.461085i	$-0.152540\pi$
$317$	14.0641	+	24.3597i	0.0443661	+	0.0768444i	−0.842990	+	0.537930i	$0.819207\pi$
$318$	103.003	+	59.4690i	0.323910	+	0.187010i
$319$	−170.147	+	294.703i	−0.533376	+	0.923835i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$		−	57.1258i		−	0.177962i
$322$	−107.921	+	208.790i	−0.335158	+	0.648416i
$323$	462.332			1.43137
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	109.959	+	63.4846i	0.338334	+	0.195337i
$326$	−174.243	+	301.797i	−0.534487	+	0.925758i
$327$	−227.572	+	131.389i	−0.695940	+	0.401801i
$328$			160.956i			0.490719i
$329$	−134.313	+	86.1153i	−0.408245	+	0.261749i
$330$	−66.7763			−0.202353
$331$	−130.940	−	226.795i	−0.395590	−	0.685182i	0.597586	−	0.801805i	$-0.296127\pi$
$331$	−130.940	−	226.795i	−0.395590	−	0.685182i	−0.993176	+	0.116623i	$0.962793\pi$
$332$	−235.444	−	135.934i	−0.709168	−	0.409438i
$333$	−43.5962	+	75.5108i	−0.130919	+	0.226759i
$334$	−351.976	+	203.214i	−1.05382	+	0.608424i
$335$			157.721i			0.470808i
$336$	2.25593	+	48.4449i	0.00671408	+	0.144181i
$337$	−539.998			−1.60237			−0.801185	−	0.598417i	$-0.795796\pi$
$337$	−539.998			−1.60237			−0.801185	+	0.598417i	$0.795796\pi$
$338$	−336.475	−	582.791i	−0.995487	−	1.72423i
$339$	63.2865	+	36.5385i	0.186686	+	0.107783i
$340$	−64.3422	+	111.444i	−0.189242	+	0.327776i
$341$	−244.418	+	141.115i	−0.716767	+	0.413826i
$342$		−	68.1678i		−	0.199321i
$343$	339.663	−	47.7274i	0.990272	−	0.139147i
$344$	−22.1703			−0.0644486
$345$	45.9759	+	79.6326i	0.133263	+	0.230819i
$346$	335.028	+	193.429i	0.968289	+	0.559042i
$347$	19.9273	−	34.5150i	0.0574273	−	0.0994670i	−0.835883	−	0.548908i	$-0.815044\pi$
$347$	19.9273	−	34.5150i	0.0574273	−	0.0994670i	0.893310	+	0.449441i	$0.148377\pi$
$348$	83.7363	−	48.3452i	0.240622	−	0.138923i
$349$			326.000i			0.934099i	0.884231	+	0.467049i	$0.154683\pi$
$349$			326.000i			0.934099i	−0.884231	+	0.467049i	$0.845317\pi$
$350$	49.4439	−	2.30245i	0.141268	−	0.00657843i
$351$	131.950			0.375927
$352$	34.4832	+	59.7266i	0.0979635	+	0.169678i
$353$	−126.505	−	73.0374i	−0.358370	−	0.206905i	0.309996	−	0.950738i	$-0.399672\pi$
$353$	−126.505	−	73.0374i	−0.358370	−	0.206905i	−0.668365	+	0.743833i	$0.733006\pi$
$354$	−88.2156	+	152.794i	−0.249197	+	0.431621i
$355$	−12.4226	+	7.17220i	−0.0349933	+	0.0202034i
$356$			288.456i			0.810270i
$357$	188.303	+	293.693i	0.527459	+	0.822670i
$358$	142.550			0.398184
$359$	−10.7785	−	18.6689i	−0.0300237	−	0.0520026i	0.850623	−	0.525776i	$-0.176225\pi$
$359$	−10.7785	−	18.6689i	−0.0300237	−	0.0520026i	−0.880647	+	0.473773i	$0.842892\pi$
$360$	16.4317	+	9.48683i	0.0456435	+	0.0263523i
$361$	−51.4209	+	89.0636i	−0.142440	+	0.246714i
$362$	−165.520	+	95.5632i	−0.457238	+	0.263987i
$363$			47.8669i			0.131865i
$364$	−315.819	−	163.243i	−0.867635	−	0.448469i
$365$	88.4508			0.242331
$366$	−140.362	−	243.115i	−0.383504	−	0.664248i
$367$	176.974	+	102.176i	0.482217	+	0.278408i	0.721340	−	0.692581i	$-0.243527\pi$
$367$	176.974	+	102.176i	0.482217	+	0.278408i	−0.239123	+	0.970989i	$0.576860\pi$
$368$	47.4837	−	82.2442i	0.129032	−	0.223490i
$369$	147.847	−	85.3598i	0.400671	−	0.231327i
$370$		−	91.9088i		−	0.248402i
$371$	−156.070	+	301.943i	−0.420675	+	0.813864i
$372$	80.1919			0.215570
$373$	−281.632	−	487.800i	−0.755045	−	1.30778i	−0.945352	−	0.326051i	$-0.894282\pi$
$373$	−281.632	−	487.800i	−0.755045	−	1.30778i	0.190308	−	0.981724i	$-0.439051\pi$
$374$	429.654	+	248.061i	1.14881	+	0.663264i
$375$	9.68246	−	16.7705i	0.0258199	−	0.0447214i
$376$	55.8304	−	32.2337i	0.148485	−	0.0857279i
$377$			708.795i			1.88009i
$378$	43.3031	−	27.7640i	0.114559	−	0.0734498i
$379$	300.642			0.793250			0.396625	−	0.917981i	$-0.370181\pi$
$379$	300.642			0.793250			0.396625	+	0.917981i	$0.370181\pi$
$380$	35.9276	+	62.2284i	0.0945463	+	0.163759i
$381$	−73.9738	−	42.7088i	−0.194157	−	0.112097i
$382$	125.993	−	218.226i	0.329824	−	0.571271i
$383$	−9.34543	+	5.39559i	−0.0244006	+	0.0140877i	−0.512151	−	0.858896i	$-0.671151\pi$
$383$	−9.34543	+	5.39559i	−0.0244006	+	0.0140877i	0.487750	+	0.872983i	$0.337818\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−8.87672	−	190.623i	−0.0230564	−	0.495124i
$386$	−191.082			−0.495031
$387$	11.7576	+	20.3647i	0.0303813	+	0.0526220i
$388$	136.828	+	78.9980i	0.352651	+	0.203603i
$389$	65.7124	−	113.817i	0.168927	−	0.292589i	−0.769116	−	0.639109i	$-0.779303\pi$
$389$	65.7124	−	113.817i	0.168927	−	0.292589i	0.938043	+	0.346520i	$0.112637\pi$
$390$	−120.454	+	69.5439i	−0.308855	+	0.178318i
$391$		−	683.164i		−	1.74722i
$392$	−137.993	+	12.8798i	−0.352023	+	0.0328566i
$393$	25.3784			0.0645761
$394$	45.7872	+	79.3058i	0.116211	+	0.201284i
$395$	−106.114	−	61.2648i	−0.268642	−	0.155101i
$396$	36.5749	−	63.3496i	0.0923609	−	0.159974i
$397$	−485.778	+	280.464i	−1.22362	+	0.706459i	−0.965689	−	0.259703i	$-0.916375\pi$
$397$	−485.778	+	280.464i	−1.22362	+	0.706459i	−0.257935	+	0.966162i	$0.583042\pi$
$398$			190.664i			0.479054i
$399$	194.595	−	9.06169i	0.487706	−	0.0227110i
$400$	−20.0000			−0.0500000
$401$	−170.877	−	295.967i	−0.426126	−	0.738072i	0.570399	−	0.821368i	$-0.306789\pi$
$401$	−170.877	−	295.967i	−0.426126	−	0.738072i	−0.996525	+	0.0832958i	$0.973455\pi$
$402$	−149.627	−	86.3872i	−0.372207	−	0.214894i
$403$	−293.926	+	509.095i	−0.729345	+	1.26326i
$404$	80.9456	−	46.7340i	0.200360	−	0.115678i
$405$		−	20.1246i		−	0.0496904i
$406$	149.140	+	232.611i	0.367339	+	0.572933i
$407$	−354.339			−0.870612
$408$	−70.4833	−	122.081i	−0.172753	−	0.299217i
$409$	19.6793	+	11.3619i	0.0481157	+	0.0277796i	0.523865	−	0.851801i	$-0.324490\pi$
$409$	19.6793	+	11.3619i	0.0481157	+	0.0277796i	−0.475749	+	0.879581i	$0.657823\pi$
$410$	−89.9771	+	155.845i	−0.219456	+	0.380110i
$411$	−25.8319	+	14.9140i	−0.0628512	+	0.0362872i
$412$		−	332.606i		−	0.807295i
$413$	−447.899	−	231.513i	−1.08450	−	0.560564i
$414$	−100.728			−0.243305
$415$	−151.978	−	263.234i	−0.366213	−	0.634299i
$416$	124.404	+	71.8246i	0.299048	+	0.172655i
$417$	−27.0730	+	46.8918i	−0.0649232	+	0.112450i
$418$	239.911	−	138.513i	0.573950	−	0.331370i
$419$			347.375i			0.829057i	0.910036	+	0.414529i	$0.136054\pi$
$419$			347.375i			0.829057i	−0.910036	+	0.414529i	$0.863946\pi$
$420$	−24.8972	+	48.1677i	−0.0592791	+	0.114685i
$421$	−340.381			−0.808507			−0.404253	−	0.914647i	$-0.632469\pi$
$421$	−340.381			−0.808507			−0.404253	+	0.914647i	$0.632469\pi$
$422$	−82.2734	−	142.502i	−0.194961	−	0.337682i
$423$	−59.2170	−	34.1890i	−0.139993	−	0.0808250i
$424$	68.6689	−	118.938i	0.161955	−	0.280514i
$425$	−124.598	+	71.9367i	−0.293172	+	0.169263i
$426$		−	15.7135i		−	0.0368861i
$427$	675.348	−	433.002i	1.58161	−	1.01406i
$428$	−65.9632			−0.154120
$429$	268.115	+	464.389i	0.624976	+	1.08249i
$430$	−21.4663	−	12.3936i	−0.0499216	−	0.0288223i
$431$	21.7871	−	37.7363i	0.0505500	−	0.0875552i	−0.839643	−	0.543138i	$-0.817236\pi$
$431$	21.7871	−	37.7363i	0.0505500	−	0.0875552i	0.890193	+	0.455583i	$0.150569\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$		−	304.620i		−	0.703509i	−0.936092	−	0.351755i	$-0.885585\pi$
$433$		−	304.620i		−	0.703509i	0.936092	−	0.351755i	$-0.114415\pi$
$434$	10.6601	+	228.919i	0.0245624	+	0.527464i
$435$	108.103			0.248513
$436$	151.715	+	262.778i	0.347970	+	0.602702i
$437$	−330.360	−	190.734i	−0.755974	−	0.436462i
$438$	−48.4465	+	83.9118i	−0.110608	+	0.191579i
$439$	−539.136	+	311.270i	−1.22810	+	0.709044i	−0.966632	−	0.256168i	$-0.917540\pi$
$439$	−539.136	+	311.270i	−1.22810	+	0.709044i	−0.261468	+	0.965212i	$0.584207\pi$
$440$			77.1067i			0.175242i
$441$	85.0127	+	119.924i	0.192773	+	0.271937i
$442$	1033.37			2.33793
$443$	42.8024	+	74.1360i	0.0966195	+	0.167350i	0.910283	−	0.413986i	$-0.135864\pi$
$443$	42.8024	+	74.1360i	0.0966195	+	0.167350i	−0.813664	+	0.581336i	$0.802530\pi$
$444$	87.1923	+	50.3405i	0.196379	+	0.113380i
$445$	−161.252	+	279.297i	−0.362364	+	0.627633i
$446$	−36.8049	+	21.2493i	−0.0825222	+	0.0476442i
$447$		−	247.990i		−	0.554788i
$448$	55.9394	−	2.60493i	0.124865	−	0.00581457i
$449$	−143.625			−0.319876			−0.159938	−	0.987127i	$-0.551129\pi$
$449$	−143.625			−0.319876			−0.159938	+	0.987127i	$0.551129\pi$
$450$	10.6066	+	18.3712i	0.0235702	+	0.0408248i
$451$	600.834	+	346.892i	1.33223	+	0.769161i
$452$	42.1910	−	73.0769i	0.0933429	−	0.161675i
$453$	69.5363	−	40.1468i	0.153502	−	0.0886243i
$454$			200.366i			0.441334i
$455$	−214.535	−	334.607i	−0.471506	−	0.735401i
$456$	−78.7134			−0.172617
$457$	11.7226	+	20.3041i	0.0256512	+	0.0444292i	0.878566	−	0.477621i	$-0.158501\pi$
$457$	11.7226	+	20.3041i	0.0256512	+	0.0444292i	−0.852915	+	0.522050i	$0.825167\pi$
$458$	−266.789	−	154.031i	−0.582509	−	0.336312i
$459$	−74.7589	+	129.486i	−0.162873	+	0.282105i
$460$	91.9518	−	53.0884i	0.199895	−	0.115410i
$461$			170.444i			0.369728i	0.982764	+	0.184864i	$0.0591844\pi$
$461$			170.444i			0.369728i	−0.982764	+	0.184864i	$0.940816\pi$
$462$	185.703	+	95.9872i	0.401954	+	0.207764i
$463$	475.871			1.02780			0.513899	−	0.857850i	$-0.328200\pi$
$463$	475.871			1.02780			0.513899	+	0.857850i	$0.328200\pi$
$464$	−55.8242	−	96.6904i	−0.120311	−	0.208384i
$465$	77.6455	+	44.8286i	0.166980	+	0.0964057i
$466$	−3.00658	+	5.20755i	−0.00645189	+	0.0111750i
$467$	−188.847	+	109.031i	−0.404384	+	0.233471i	−0.688374	−	0.725356i	$-0.741675\pi$
$467$	−188.847	+	109.031i	−0.404384	+	0.233471i	0.283990	+	0.958827i	$0.408342\pi$
$468$		−	152.363i		−	0.325562i
$469$	226.715	−	438.616i	0.483400	−	0.935215i
$470$	72.0767			0.153355
$471$	−71.4553	−	123.764i	−0.151710	−	0.262769i
$472$	176.431	+	101.863i	0.373795	+	0.215811i
$473$	−47.7814	+	82.7598i	−0.101018	+	0.174968i
$474$	116.242	−	67.1122i	0.245236	−	0.141587i
$475$			80.3365i			0.169130i
$476$	339.128	−	217.433i	0.712453	−	0.456793i
$477$	−145.669			−0.305385
$478$	184.917	+	320.286i	0.386856	+	0.670055i
$479$	−482.916	−	278.812i	−1.00817	−	0.582070i	−0.0975181	−	0.995234i	$-0.531090\pi$
$479$	−482.916	−	278.812i	−1.00817	−	0.582070i	−0.910657	+	0.413164i	$0.864424\pi$
$480$	10.9545	−	18.9737i	0.0228218	−	0.0395285i
$481$	−639.170	+	369.025i	−1.32883	+	0.767203i
$482$		−	141.279i		−	0.293111i
$483$	−13.3900	−	287.543i	−0.0277226	−	0.595327i
$484$	55.2719			0.114198
$485$	88.3224	+	152.979i	0.182108	+	0.315420i
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	258.122	−	447.080i	0.530024	−	0.918029i	−0.469362	−	0.883006i	$-0.655516\pi$
$487$	258.122	−	447.080i	0.530024	−	0.918029i	0.999386	−	0.0350234i	$-0.0111506\pi$
$488$	−280.725	+	162.077i	−0.575256	+	0.332124i
$489$		−	426.806i		−	0.872813i
$490$	−140.811	−	64.6697i	−0.287370	−	0.131979i
$491$	122.586			0.249666			0.124833	−	0.992178i	$-0.460161\pi$
$491$	122.586			0.249666			0.124833	+	0.992178i	$0.460161\pi$
$492$	−98.5650	−	170.720i	−0.200335	−	0.346991i
$493$	−695.559	−	401.581i	−1.41087	−	0.814566i
$494$	288.507	−	499.709i	0.584022	−	1.01156i
$495$	70.8270	−	40.8920i	0.143085	−	0.0826101i
$496$		−	92.5976i		−	0.186689i
$497$	44.8565	−	2.08883i	0.0902544	−	0.00420287i
$498$	332.968			0.668610
$499$	−187.525	−	324.802i	−0.375801	−	0.650906i	0.614646	−	0.788803i	$-0.289299\pi$
$499$	−187.525	−	324.802i	−0.375801	−	0.650906i	−0.990447	+	0.137897i	$0.955966\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$	248.885	−	431.081i	0.496776	−	0.860441i
$502$	−306.875	+	177.175i	−0.611306	+	0.352938i
$503$		−	303.836i		−	0.604048i	−0.953300	−	0.302024i	$-0.902338\pi$
$503$		−	303.836i		−	0.604048i	0.953300	−	0.302024i	$-0.0976622\pi$
$504$	−32.0591	−	50.0021i	−0.0636094	−	0.0992106i
$505$	104.500			0.206931
$506$	−204.673	−	354.505i	−0.404493	−	0.700602i
$507$	713.771	+	412.096i	1.40783	+	0.812812i
$508$	−49.3159	+	85.4176i	−0.0970784	+	0.168145i
$509$	−161.864	+	93.4522i	−0.318004	+	0.183600i	−0.650503	−	0.759504i	$-0.725442\pi$
$509$	−161.864	+	93.4522i	−0.318004	+	0.183600i	0.332499	+	0.943104i	$0.392108\pi$
$510$		−	157.606i		−	0.309030i
$511$	−245.978	−	127.143i	−0.481367	−	0.248812i
$512$	−22.6274			−0.0441942
$513$	41.7441	+	72.3029i	0.0813725	+	0.140941i
$514$	213.915	+	123.504i	0.416177	+	0.240280i
$515$	185.932	−	322.044i	0.361033	−	0.625328i
$516$	23.5152	−	13.5765i	0.0455720	−	0.0263110i
$517$		−	277.880i		−	0.537485i
$518$	−132.114	+	255.595i	−0.255046	+	0.493427i
$519$	−473.801			−0.912912
$520$	80.3024	+	139.088i	0.154428	+	0.267477i
$521$	518.758	+	299.505i	0.995697	+	0.574866i	0.906972	−	0.421190i	$-0.138388\pi$
$521$	518.758	+	299.505i	0.995697	+	0.574866i	0.0887246	+	0.996056i	$0.471721\pi$
$522$	−59.2105	+	102.556i	−0.113430	+	0.196467i
$523$	132.497	−	76.4975i	0.253341	−	0.146267i	−0.367952	−	0.929845i	$-0.619941\pi$
$523$	132.497	−	76.4975i	0.253341	−	0.146267i	0.621293	+	0.783578i	$0.286608\pi$
$524$		−	29.3045i		−	0.0559246i
$525$	−51.0332	+	32.7202i	−0.0972061	+	0.0623242i
$526$	−29.5336			−0.0561475
$527$	−333.059	−	576.875i	−0.631990	−	1.09464i
$528$	−73.1498	−	42.2331i	−0.138541	−	0.0799869i
$529$	−17.3376	+	30.0295i	−0.0327742	+	0.0567666i
$530$	132.977	−	76.7742i	0.250900	−	0.144857i
$531$		−	216.083i		−	0.406937i
$532$	−10.4635	−	224.699i	−0.0196683	−	0.422366i
$533$	1445.07			2.71121
$534$	−176.643	−	305.954i	−0.330791	−	0.572948i
$535$	−63.8686	−	36.8746i	−0.119381	−	0.0689244i
$536$	−99.7514	+	172.774i	−0.186103	+	0.322340i
$537$	−151.197	+	87.2936i	−0.281558	+	0.162558i
$538$			0.417624i			0.000776253i
$539$	−249.323	+	542.875i	−0.462567	+	1.00719i
$540$	−23.2379			−0.0430331
$541$	−71.7086	−	124.203i	−0.132548	−	0.229580i	0.792110	−	0.610378i	$-0.208983\pi$
$541$	−71.7086	−	124.203i	−0.132548	−	0.229580i	−0.924658	+	0.380798i	$0.875649\pi$
$542$	401.836	+	232.000i	0.741394	+	0.428044i
$543$	117.040	−	202.720i	0.215544	−	0.373333i
$544$	−140.967	+	81.3871i	−0.259130	+	0.149609i
$545$			339.245i			0.622468i
$546$	434.942	−	20.2539i	0.796598	−	0.0370951i
$547$	−103.778			−0.189721			−0.0948607	−	0.995491i	$-0.530241\pi$
$547$	−103.778			−0.189721			−0.0948607	+	0.995491i	$0.530241\pi$
$548$	17.2212	+	29.8281i	0.0314256	+	0.0544308i
$549$	297.754	+	171.908i	0.542356	+	0.313129i
$550$	−43.1039	+	74.6582i	−0.0783708	+	0.135742i
$551$	−388.388	+	224.236i	−0.704879	+	0.406962i
$552$			116.311i			0.210708i
$553$	207.034	+	322.908i	0.374383	+	0.583920i
$554$	711.307			1.28395
$555$	56.2824	+	97.4840i	0.101410	+	0.175647i
$556$	54.1460	+	31.2612i	0.0973848	+	0.0562251i
$557$	−412.613	+	714.666i	−0.740777	+	1.28306i	0.211366	+	0.977407i	$0.432209\pi$
$557$	−412.613	+	714.666i	−0.740777	+	1.28306i	−0.952142	+	0.305656i	$0.901124\pi$
$558$	−85.0564	+	49.1073i	−0.152431	+	0.0880059i
$559$			199.047i			0.356076i
$560$	55.6193	+	28.7489i	0.0993201	+	0.0513372i
$561$	−607.622			−1.08310
$562$	187.016	+	323.922i	0.332769	+	0.576373i
$563$	331.959	+	191.657i	0.589626	+	0.340421i	0.764949	−	0.644090i	$-0.222764\pi$
$563$	331.959	+	191.657i	0.589626	+	0.340421i	−0.175324	+	0.984511i	$0.556097\pi$
$564$	−39.4780	+	68.3780i	−0.0699965	+	0.121238i
$565$	81.7025	−	47.1710i	0.144606	−	0.0834884i
$566$		−	652.872i		−	1.15348i
$567$	−28.9280	+	55.9658i	−0.0510194	+	0.0987051i
$568$	−18.1444			−0.0319443
$569$	−377.462	−	653.783i	−0.663377	−	1.14900i	−0.979723	−	0.200359i	$-0.935789\pi$
$569$	−377.462	−	653.783i	−0.663377	−	1.14900i	0.316345	−	0.948644i	$-0.397544\pi$
$570$	−76.2139	−	44.0021i	−0.133709	−	0.0771967i
$571$	345.652	−	598.687i	0.605346	−	1.04849i	−0.386651	−	0.922226i	$-0.626368\pi$
$571$	345.652	−	598.687i	0.605346	−	1.04849i	0.991997	−	0.126263i	$-0.0402984\pi$
$572$	536.230	−	309.592i	0.937465	−	0.541245i
$573$			308.618i			0.538600i
$574$	474.241	−	304.062i	0.826204	−	0.529725i
$575$	118.709			0.206451
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	338.973	+	195.706i	0.587476	+	0.339179i	0.764099	−	0.645099i	$-0.223184\pi$
$577$	338.973	+	195.706i	0.587476	+	0.339179i	−0.176623	+	0.984279i	$0.556517\pi$
$578$	−381.119	+	660.117i	−0.659375	+	1.14207i
$579$	202.673	−	117.013i	0.350040	−	0.202096i
$580$		−	124.827i		−	0.215218i
$581$	44.2621	+	950.505i	0.0761826	+	1.63598i
$582$	−193.505			−0.332482
$583$	−295.990	−	512.670i	−0.507702	−	0.879365i
$584$	96.8930	+	55.9412i	0.165913	+	0.0957897i
$585$	85.1735	−	147.525i	0.145596	−	0.252179i
$586$	−165.081	+	95.3095i	−0.281708	+	0.162644i
$587$		−	1027.13i		−	1.74979i	−0.484312	−	0.874896i	$-0.660930\pi$
$587$		−	1027.13i		−	1.74979i	0.484312	−	0.874896i	$-0.339070\pi$
$588$	138.477	−	98.1643i	0.235504	−	0.166946i
$589$	−371.949			−0.631492
$590$	113.886	+	197.256i	0.193027	+	0.334332i
$591$	−97.1294	−	56.0777i	−0.164347	−	0.0948861i
$592$	58.1282	−	100.681i	0.0981896	−	0.170069i
$593$	116.894	−	67.4886i	0.197123	−	0.113809i	−0.398190	−	0.917303i	$-0.630362\pi$
$593$	116.894	−	67.4886i	0.197123	−	0.113809i	0.595313	+	0.803494i	$0.297028\pi$
$594$			89.5899i			0.150825i
$595$	449.908	−	20.9508i	0.756147	−	0.0352115i
$596$	−286.354			−0.480460
$597$	−116.757	−	202.229i	−0.195573	−	0.338742i
$598$	−738.394	−	426.312i	−1.23477	−	0.712897i
$599$	380.159	−	658.455i	0.634656	−	1.09926i	−0.351932	−	0.936026i	$-0.614475\pi$
$599$	380.159	−	658.455i	0.634656	−	1.09926i	0.986588	−	0.163231i	$-0.0521917\pi$
$600$	21.2132	−	12.2474i	0.0353553	−	0.0204124i
$601$			604.796i			1.00632i	0.864194	+	0.503158i	$0.167829\pi$
$601$			604.796i			1.00632i	−0.864194	+	0.503158i	$0.832171\pi$
$602$	41.8820	+	65.3227i	0.0695714	+	0.108509i
$603$	211.605			0.350920
$604$	−46.3575	−	80.2936i	−0.0767509	−	0.132936i
$605$	53.5168	+	30.8979i	0.0884575	+	0.0510710i
$606$	−57.2372	+	99.1377i	−0.0944508	+	0.163594i
$607$	11.2280	−	6.48250i	0.0184976	−	0.0106796i	−0.490723	−	0.871316i	$-0.663267\pi$
$607$	11.2280	−	6.48250i	0.0184976	−	0.0106796i	0.509220	+	0.860636i	$0.329934\pi$
$608$			90.8904i			0.149491i
$609$	−300.631	−	155.392i	−0.493647	−	0.255159i
$610$	−362.414			−0.594121
$611$	−289.396	−	501.249i	−0.473644	−	0.820375i
$612$	149.518	+	86.3241i	0.244310	+	0.141052i
$613$	−566.514	+	981.231i	−0.924167	+	1.60070i	−0.131271	+	0.991347i	$0.541906\pi$
$613$	−566.514	+	981.231i	−0.924167	+	1.60070i	−0.792896	+	0.609357i	$0.791428\pi$
$614$	−29.0555	+	16.7752i	−0.0473217	+	0.0273212i
$615$		−	220.398i		−	0.358371i
$616$	110.836	−	214.431i	0.179929	−	0.348102i
$617$	19.5534			0.0316910			0.0158455	−	0.999874i	$-0.494956\pi$
$617$	19.5534			0.0316910			0.0158455	+	0.999874i	$0.494956\pi$
$618$	203.679	+	352.782i	0.329577	+	0.570844i
$619$	574.387	+	331.623i	0.927928	+	0.535739i	0.886156	−	0.463388i	$-0.153366\pi$
$619$	574.387	+	331.623i	0.927928	+	0.535739i	0.0417724	+	0.999127i	$0.486700\pi$
$620$	51.7637	−	89.6573i	0.0834898	−	0.144609i
$621$	106.838	−	61.6831i	0.172042	−	0.0993287i
$622$			400.241i			0.643474i
$623$	849.908	−	544.923i	1.36422	−	0.874676i
$624$	−175.934			−0.281945
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	519.754	+	300.080i	0.830279	+	0.479362i
$627$	−169.643	+	293.830i	−0.270563	+	0.468628i
$628$	−142.911	+	82.5095i	−0.227565	+	0.131385i
$629$		−	836.311i		−	1.32959i
$630$	−3.08906	−	66.3359i	−0.00490327	−	0.105295i
$631$	−303.828			−0.481503			−0.240752	−	0.970587i	$-0.577394\pi$
$631$	−303.828			−0.481503			−0.240752	+	0.970587i	$0.577394\pi$
$632$	−77.4945	−	134.224i	−0.122618	−	0.212380i
$633$	174.528	+	100.764i	0.275716	+	0.159185i
$634$	−19.8896	+	34.4498i	−0.0313716	+	0.0543372i
$635$	−95.4997	+	55.1368i	−0.150393	+	0.0868296i
$636$			168.204i			0.264471i
$637$	115.636	+	1238.91i	0.181532	+	1.94492i
$638$	−481.249			−0.754308
$639$	9.62251	+	16.6667i	0.0150587	+	0.0260824i
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	470.134	−	814.296i	0.733439	−	1.27035i	−0.221967	−	0.975054i	$-0.571248\pi$
$641$	470.134	−	814.296i	0.733439	−	1.27035i	0.955405	−	0.295298i	$-0.0954191\pi$
$642$	69.9646	−	40.3941i	0.108979	−	0.0629191i
$643$			1143.40i			1.77823i	0.457681	+	0.889116i	$0.348680\pi$
$643$			1143.40i			1.77823i	−0.457681	+	0.889116i	$0.651320\pi$
$644$	−332.026	+	15.4614i	−0.515568	+	0.0240084i
$645$	30.3579			0.0470666
$646$	326.918	+	566.239i	0.506065	+	0.876530i
$647$	790.146	+	456.191i	1.22125	+	0.705087i	0.965184	−	0.261573i	$-0.0842413\pi$
$647$	790.146	+	456.191i	1.22125	+	0.705087i	0.256063	+	0.966660i	$0.417575\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	760.488	−	439.068i	1.17178	−	0.676530i
$650$			179.562i			0.276249i
$651$	−151.491	−	236.278i	−0.232705	−	0.362946i
$652$	−492.833			−0.755879
$653$	−109.628	−	189.881i	−0.167884	−	0.290783i	0.769792	−	0.638295i	$-0.220360\pi$
$653$	−109.628	−	189.881i	−0.167884	−	0.290783i	−0.937676	+	0.347512i	$0.887027\pi$
$654$	−321.836	−	185.812i	−0.492104	−	0.284116i
$655$	16.3817	−	28.3739i	0.0250102	−	0.0433190i
$656$	−197.130	+	113.813i	−0.300503	+	0.173495i
$657$		−	118.669i		−	0.180623i
$658$	−200.443	−	103.606i	−0.304624	−	0.157456i
$659$	661.525			1.00383			0.501916	−	0.864916i	$-0.332629\pi$
$659$	661.525			1.00383			0.501916	+	0.864916i	$0.332629\pi$
$660$	−47.2180	−	81.7840i	−0.0715424	−	0.123915i
$661$	−481.878	−	278.212i	−0.729013	−	0.420896i	0.0890478	−	0.996027i	$-0.471618\pi$
$661$	−481.878	−	278.212i	−0.729013	−	0.420896i	−0.818061	+	0.575131i	$0.804951\pi$
$662$	185.178	−	320.737i	0.279724	−	0.484497i
$663$	−1096.05	+	632.805i	−1.65317	+	0.954457i
$664$		−	384.478i		−	0.579033i
$665$	115.479	−	223.413i	0.173653	−	0.335959i
$666$	−123.309			−0.185148
$667$	331.342	+	573.902i	0.496765	+	0.860423i
$668$	−497.770	−	287.387i	−0.745164	−	0.430221i
$669$	26.0250	−	45.0766i	0.0389014	−	0.0673791i
$670$	−193.168	+	111.525i	−0.288310	+	0.166456i
$671$			1397.23i			2.08231i
$672$	−57.7375	+	37.0187i	−0.0859189	+	0.0550873i
$673$	−153.903			−0.228682			−0.114341	−	0.993442i	$-0.536476\pi$
$673$	−153.903			−0.228682			−0.114341	+	0.993442i	$0.536476\pi$
$674$	−381.837	−	661.360i	−0.566523	−	0.981247i
$675$	−22.5000	−	12.9904i	−0.0333333	−	0.0192450i
$676$	475.847	−	824.191i	0.703916	−	1.21922i
$677$	−362.794	+	209.459i	−0.535886	+	0.309394i	−0.743410	−	0.668836i	$-0.766793\pi$
$677$	−362.794	+	209.459i	−0.535886	+	0.309394i	0.207524	+	0.978230i	$0.433459\pi$
$678$			103.346i			0.152428i
$679$	−25.7230	−	552.387i	−0.0378836	−	0.813530i
$680$	−181.987			−0.267628
$681$	−122.698	−	212.520i	−0.180174	−	0.312070i
$682$	−345.659	−	199.566i	−0.506831	−	0.292619i
$683$	−614.628	+	1064.57i	−0.899895	+	1.55866i	−0.0722678	+	0.997385i	$0.523024\pi$
$683$	−614.628	+	1064.57i	−0.899895	+	1.55866i	−0.827627	+	0.561278i	$0.810310\pi$
$684$	83.4882	−	48.2019i	0.122059	−	0.0704706i
$685$			38.5079i			0.0562158i
$686$	298.632	+	382.252i	0.435324	+	0.557219i
$687$	377.297			0.549195
$688$	−15.6768	−	27.1530i	−0.0227860	−	0.0394665i
$689$	−1067.84	−	616.515i	−1.54983	−	0.894797i
$690$	−65.0197	+	112.617i	−0.0942315	+	0.163214i
$691$	314.293	−	181.457i	0.454838	−	0.262601i	−0.255033	−	0.966932i	$-0.582086\pi$
$691$	314.293	−	181.457i	0.454838	−	0.262601i	0.709871	+	0.704331i	$0.248753\pi$
$692$			547.099i			0.790605i
$693$	−255.747	+	11.9094i	−0.369044	+	0.0171852i
$694$	56.3628			0.0812144
$695$	34.9511	+	60.5370i	0.0502893	+	0.0871036i
$696$	118.421	+	68.3704i	0.170145	+	0.0982333i
$697$	−818.734	+	1418.09i	−1.17465	+	2.03456i
$698$	−399.267	+	230.517i	−0.572016	+	0.330254i
$699$		−	7.36459i		−	0.0105359i
$700$	37.7820	+	58.9281i	0.0539743	+	0.0841830i
$701$	−319.012			−0.455081			−0.227541	−	0.973769i	$-0.573068\pi$
$701$	−319.012			−0.455081			−0.227541	+	0.973769i	$0.573068\pi$
$702$	93.3029	+	161.605i	0.132910	+	0.230207i
$703$	−404.418	−	233.491i	−0.575275	−	0.332135i
$704$	−48.7665	+	84.4661i	−0.0692707	+	0.119980i
$705$	−76.4489	+	44.1378i	−0.108438	+	0.0626068i
$706$		−	206.581i		−	0.292608i
$707$	−290.612	−	150.213i	−0.411049	−	0.212466i
$708$	−249.512			−0.352417
$709$	−565.639	−	979.716i	−0.797799	−	1.38183i	−0.921047	−	0.389452i	$-0.872664\pi$
$709$	−565.639	−	979.716i	−0.797799	−	1.38183i	0.123248	−	0.992376i	$-0.460669\pi$
$710$	−17.5682	−	10.1430i	−0.0247440	−	0.0142859i
$711$	−82.1954	+	142.367i	−0.115605	+	0.200234i
$712$	−353.285	+	203.969i	−0.496187	+	0.286474i
$713$			549.610i			0.770841i
$714$	−226.549	+	438.295i	−0.317295	+	0.613859i
$715$	692.270			0.968209
$716$	100.798	+	174.587i	0.140779	+	0.243837i
$717$	−392.269	−	226.477i	−0.547097	−	0.315867i
$718$	15.2431	−	26.4018i	0.0212300	−	0.0367714i
$719$	−243.094	+	140.350i	−0.338100	+	0.195202i	−0.659431	−	0.751765i	$-0.729203\pi$
$719$	−243.094	+	140.350i	−0.338100	+	0.195202i	0.321332	+	0.946967i	$0.395870\pi$
$720$			26.8328i			0.0372678i
$721$	−979.991	+	628.326i	−1.35921	+	0.871464i
$722$	−145.440			−0.201441
$723$	86.5156	+	149.849i	0.119662	+	0.207261i
$724$	−234.081	−	135.147i	−0.323316	−	0.186667i
$725$	69.7803	−	120.863i	0.0962486	−	0.166708i
$726$	−58.6247	+	33.8470i	−0.0807503	+	0.0466212i
$727$		−	737.233i		−	1.01408i	−0.861924	−	0.507038i	$-0.830740\pi$
$727$		−	737.233i		−	1.01408i	0.861924	−	0.507038i	$-0.169260\pi$
$728$	−23.3872	−	502.228i	−0.0321253	−	0.689874i
$729$	−27.0000			−0.0370370
$730$	62.5442	+	108.330i	0.0856769	+	0.148397i
$731$	−195.330	−	112.774i	−0.267209	−	0.154273i
$732$	198.502	−	343.816i	0.271178	−	0.469694i
$733$	1172.96	−	677.208i	1.60022	−	0.923886i	0.608775	−	0.793343i	$-0.291661\pi$
$733$	1172.96	−	677.208i	1.60022	−	0.923886i	0.991443	−	0.130543i	$-0.0416719\pi$
$734$			288.997i			0.393728i
$735$	188.955	−	17.6364i	0.257082	−	0.0239950i
$736$	134.304			0.182478
$737$	429.968	+	744.726i	0.583403	+	1.01048i
$738$	209.088	+	120.717i	0.283317	+	0.163573i
$739$	−2.66286	+	4.61222i	−0.00360333	+	0.00624116i	−0.867821	−	0.496876i	$-0.834480\pi$
$739$	−2.66286	+	4.61222i	−0.00360333	+	0.00624116i	0.864218	+	0.503117i	$0.167814\pi$
$740$	112.565	−	64.9893i	0.152115	−	0.0878234i
$741$			706.695i			0.953704i
$742$	−480.162	+	22.3597i	−0.647119	+	0.0301343i
$743$	58.3655			0.0785539			0.0392769	−	0.999228i	$-0.487495\pi$
$743$	58.3655			0.0785539			0.0392769	+	0.999228i	$0.487495\pi$
$744$	56.7042	+	98.2146i	0.0762154	+	0.132009i
$745$	−277.261	−	160.077i	−0.372163	−	0.214868i
$746$	398.287	−	689.854i	0.533897	−	0.924737i
$747$	−353.166	+	203.900i	−0.472779	+	0.272959i
$748$			701.621i			0.937996i
$749$	124.611	+	194.354i	0.166370	+	0.259485i
$750$	27.3861			0.0365148
$751$	−139.145	−	241.006i	−0.185279	−	0.320913i	0.758391	−	0.651800i	$-0.225986\pi$
$751$	−139.145	−	241.006i	−0.185279	−	0.320913i	−0.943671	+	0.330886i	$0.892652\pi$
$752$	78.9561	+	45.5853i	0.104995	+	0.0606188i
$753$	216.994	−	375.844i	0.288172	−	0.499129i
$754$	−868.094	+	501.194i	−1.15132	+	0.664714i
$755$		−	103.659i		−	0.137296i
$756$	64.6238	+	33.4032i	0.0854812	+	0.0441841i
$757$	−59.2916			−0.0783244			−0.0391622	−	0.999233i	$-0.512469\pi$
$757$	−59.2916			−0.0783244			−0.0391622	+	0.999233i	$0.512469\pi$
$758$	212.586	+	368.209i	0.280456	+	0.485764i
$759$	434.178	+	250.673i	0.572039	+	0.330267i
$760$	−50.8093	+	88.0042i	−0.0668543	+	0.115795i
$761$	788.790	−	455.408i	1.03652	−	0.598434i	0.117673	−	0.993052i	$-0.462457\pi$
$761$	788.790	−	455.408i	1.03652	−	0.598434i	0.918845	+	0.394619i	$0.129123\pi$
$762$		−	120.799i		−	0.158528i
$763$	487.645	−	943.428i	0.639115	−	1.23647i
$764$	356.361			0.466441
$765$	96.5133	+	167.166i	0.126161	+	0.218518i
$766$	−13.2164	−	7.63051i	−0.0172538	−	0.00996150i
$767$	914.531	−	1584.01i	1.19235	−	2.06521i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$		−	660.381i		−	0.858753i	−0.903126	−	0.429376i	$-0.858733\pi$
$769$		−	660.381i		−	0.858753i	0.903126	−	0.429376i	$-0.141267\pi$
$770$	227.187	−	145.662i	0.295049	−	0.189172i
$771$	−302.522			−0.392376
$772$	−135.115	−	234.027i	−0.175020	−	0.303143i
$773$	1201.60	+	693.744i	1.55446	+	0.897469i	0.997770	+	0.0667508i	$0.0212632\pi$
$773$	1201.60	+	693.744i	1.55446	+	0.897469i	0.556693	+	0.830718i	$0.312070\pi$
$774$	−16.6277	+	28.8001i	−0.0214829	+	0.0372094i
$775$	100.240	−	57.8735i	0.129342	−	0.0746755i
$776$			223.440i			0.287938i
$777$	−16.3917	−	352.002i	−0.0210961	−	0.453027i
$778$	185.863			0.238898
$779$	457.167	+	791.837i	0.586864	+	1.01648i
$780$	−170.347	−	98.3499i	−0.218394	−	0.126090i
$781$	−39.1047	+	67.7314i	−0.0500701	+	0.0867239i
$782$	836.702	−	483.070i	1.06995	−	0.617737i
$783$		−	145.036i		−	0.185231i
$784$	−113.350	−	159.899i	−0.144580	−	0.203953i
$785$	−184.497			−0.235028
$786$	17.9452	+	31.0821i	0.0228311	+	0.0395446i
$787$	−1188.71	−	686.304i	−1.51044	−	0.872050i	−0.999926	−	0.0121785i	$-0.996123\pi$
$787$	−1188.71	−	686.304i	−1.51044	−	0.872050i	−0.510510	−	0.859872i	$-0.670543\pi$
$788$	−64.7529	+	112.155i	−0.0821737	+	0.142329i
$789$	31.3251	−	18.0856i	0.0397023	−	0.0229221i
$790$		−	173.283i		−	0.219346i
$791$	−295.017	+	13.7381i	−0.372967	+	0.0173680i
$792$	103.449			0.130618
$793$	1455.14	+	2520.37i	1.83498	+	3.17827i
$794$	−686.995	−	396.636i	−0.865232	−	0.499542i
$795$	−94.0288	+	162.863i	−0.118275	+	0.204859i
$796$	−233.514	+	134.819i	−0.293359	+	0.169371i
$797$			64.7049i			0.0811855i	0.999176	+	0.0405928i	$0.0129246\pi$
$797$			64.7049i			0.0811855i	−0.999176	+	0.0405928i	$0.987075\pi$
$798$	148.698	+	231.921i	0.186338	+	0.290628i
$799$	655.852			0.820841
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$	374.716	+	216.342i	0.467810	+	0.270090i
$802$	241.656	−	418.560i	0.301317	−	0.521896i
$803$	417.647	−	241.129i	0.520108	−	0.300285i
$804$		−	244.340i		−	0.303905i
$805$	−330.126	−	170.638i	−0.410094	−	0.211972i
$806$	−831.349			−1.03145
$807$	−0.255741	−	0.442957i	−0.000316904	−	0.000548894i
$808$	114.474	+	66.0918i	0.141676	+	0.0817968i
$809$	−268.427	+	464.929i	−0.331801	+	0.574696i	−0.982865	−	0.184327i	$-0.940990\pi$
$809$	−268.427	+	464.929i	−0.331801	+	0.574696i	0.651064	+	0.759023i	$0.274323\pi$
$810$	24.6475	−	14.2302i	0.0304290	−	0.0175682i
$811$			1472.44i			1.81559i	0.419418	+	0.907793i	$0.362234\pi$
$811$			1472.44i			1.81559i	−0.419418	+	0.907793i	$0.637766\pi$
$812$	−179.431	+	347.139i	−0.220974	+	0.427511i
$813$	−568.281			−0.698993
$814$	−250.556	−	433.975i	−0.307808	−	0.533139i
$815$	−477.183	−	275.502i	−0.585501	−	0.338039i
$816$	99.6785	−	172.648i	0.122155	−	0.211579i
$817$	−109.069	+	62.9709i	−0.133499	+	0.0770757i
$818$			32.1362i			0.0392863i
$819$	−448.923	+	287.829i	−0.548136	+	0.351440i
$820$	−254.494			−0.310358
$821$	114.603	+	198.498i	0.139590	+	0.241776i	0.927341	−	0.374217i	$-0.122088\pi$
$821$	114.603	+	198.498i	0.139590	+	0.241776i	−0.787752	+	0.615993i	$0.788755\pi$
$822$	−36.5318	−	21.0916i	−0.0444425	−	0.0256589i
$823$	7.10905	−	12.3132i	0.00863797	−	0.0149614i	−0.861674	−	0.507462i	$-0.830584\pi$
$823$	7.10905	−	12.3132i	0.00863797	−	0.0149614i	0.870312	+	0.492501i	$0.163917\pi$
$824$	407.357	−	235.188i	0.494365	−	0.285422i
$825$		−	105.583i		−	0.127979i
$826$	−33.1681	−	712.267i	−0.0401551	−	0.862308i
$827$	−136.480			−0.165030			−0.0825151	−	0.996590i	$-0.526295\pi$
$827$	−136.480			−0.165030			−0.0825151	+	0.996590i	$0.526295\pi$
$828$	−71.2255	−	123.366i	−0.0860212	−	0.148993i
$829$	254.554	+	146.967i	0.307061	+	0.177282i	0.645611	−	0.763667i	$-0.276603\pi$
$829$	254.554	+	146.967i	0.307061	+	0.177282i	−0.338549	+	0.940949i	$0.609936\pi$
$830$	214.930	−	372.269i	0.258952	−	0.448517i
$831$	−754.455	+	435.585i	−0.907888	+	0.524169i
$832$			203.151i			0.244172i
$833$	−1281.29	−	588.453i	−1.53817	−	0.706426i
$834$	−76.5739			−0.0918153
$835$	−321.309	−	556.523i	−0.384801	−	0.666495i
$836$	339.286	+	195.887i	0.405844	+	0.234314i
$837$	60.1439	−	104.172i	0.0718565	−	0.124459i
$838$	−425.446	+	245.631i	−0.507692	+	0.293116i
$839$		−	658.476i		−	0.784834i	−0.919787	−	0.392417i	$-0.871639\pi$
$839$		−	658.476i		−	0.784834i	0.919787	−	0.392417i	$-0.128361\pi$
$840$	−76.5982	+	3.56694i	−0.0911883	+	0.00424636i
$841$	−61.9146			−0.0736202
$842$	−240.686	−	416.880i	−0.285850	−	0.495107i
$843$	−396.721	−	229.047i	−0.470607	−	0.271705i
$844$	116.352	−	201.528i	0.137858	−	0.238777i
$845$	921.474	−	532.013i	1.09050	−	0.629601i
$846$		−	96.7010i		−	0.114304i
$847$	−104.414	−	162.853i	−0.123275	−	0.192271i
$848$	194.225			0.229039
$849$	399.801	+	692.475i	0.470908	+	0.815636i
$850$	−176.208	−	101.734i	−0.207304	−	0.119687i
$851$	−345.018	+	597.588i	−0.405426	+	0.702219i
$852$	19.2450	−	11.1111i	0.0225881	−	0.0130412i
$853$		−	1026.25i		−	1.20310i	−0.798834	−	0.601552i	$-0.794549\pi$
$853$		−	1026.25i		−	1.20310i	0.798834	−	0.601552i	$-0.205451\pi$
$854$	1007.86	+	520.950i	1.18016	+	0.610011i
$855$	107.783			0.126062
$856$	−46.6431	−	80.7881i	−0.0544896	−	0.0943787i
$857$	1405.85	+	811.667i	1.64043	+	0.947103i	0.980680	+	0.195619i	$0.0626716\pi$
$857$	1405.85	+	811.667i	1.64043	+	0.947103i	0.659751	+	0.751484i	$0.270662\pi$
$858$	−379.172	+	656.745i	−0.441925	+	0.765437i
$859$	894.833	−	516.632i	1.04171	−	0.601434i	0.121396	−	0.992604i	$-0.461263\pi$
$859$	894.833	−	516.632i	1.04171	−	0.601434i	0.920318	+	0.391170i	$0.127930\pi$
$860$		−	35.0543i		−	0.0407608i
$861$	−316.809	+	612.919i	−0.367955	+	0.711868i
$862$	61.6231			0.0714885
$863$	141.684	+	245.403i	0.164176	+	0.284361i	0.936362	−	0.351035i	$-0.114170\pi$
$863$	141.684	+	245.403i	0.164176	+	0.284361i	−0.772187	+	0.635396i	$0.780837\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	−305.837	+	529.726i	−0.353569	+	0.612400i
$866$	373.081	−	215.399i	0.430810	−	0.248728i
$867$		−	933.547i		−	1.07675i
$868$	−272.830	+	174.926i	−0.314320	+	0.201528i
$869$	−668.064			−0.768773
$870$	76.4404	+	132.399i	0.0878626	+	0.152182i
$871$	1551.18	+	895.575i	1.78092	+	1.02822i
$872$	−214.557	+	371.624i	−0.246052	+	0.426174i
$873$	205.243	−	118.497i	0.235100	−	0.135735i
$874$		−	539.476i		−	0.617250i
$875$	3.64050	+	78.1777i	0.00416057	+	0.0893459i
$876$	−137.027			−0.156424
$877$	254.904	+	441.507i	0.290655	+	0.503429i	0.973965	−	0.226700i	$-0.0727935\pi$
$877$	254.904	+	441.507i	0.290655	+	0.503429i	−0.683310	+	0.730128i	$0.739460\pi$
$878$	−762.454	−	440.203i	−0.868398	−	0.501370i
$879$	116.730	−	202.182i	0.132798	−	0.230014i
$880$	−94.4360	+	54.5226i	−0.107314	+	0.0619576i
$881$		−	846.387i		−	0.960711i	−0.877074	−	0.480356i	$-0.840508\pi$
$881$		−	846.387i		−	0.960711i	0.877074	−	0.480356i	$-0.159492\pi$
$882$	−86.7636	+	188.918i	−0.0983714	+	0.214193i
$883$	−350.886			−0.397379			−0.198690	−	0.980062i	$-0.563669\pi$
$883$	−350.886			−0.397379			−0.198690	+	0.980062i	$0.563669\pi$
$884$	730.700	+	1265.61i	0.826584	+	1.43169i
$885$	−241.588	−	139.481i	−0.272981	−	0.157606i
$886$	−60.5318	+	104.844i	−0.0683203	+	0.118334i
$887$	434.565	−	250.896i	0.489927	−	0.282859i	−0.234617	−	0.972088i	$-0.575384\pi$
$887$	434.565	−	250.896i	0.489927	−	0.282859i	0.724544	+	0.689228i	$0.242050\pi$
$888$			142.384i			0.160343i
$889$	344.837	−	16.0580i	0.387893	−	0.0180630i
$890$	−456.089			−0.512460
$891$	−54.8624	−	95.0244i	−0.0615739	−	0.106649i
$892$	−52.0500	−	30.0511i	−0.0583520	−	0.0336896i
$893$	183.108	−	317.153i	0.205048	−	0.355154i
$894$	303.725	−	175.355i	0.339737	−	0.196147i
$895$			225.391i			0.251834i
$896$	42.7455	+	66.6695i	0.0477070	+	0.0744079i
$897$	1044.25			1.16416
$898$	−101.558	−	175.903i	−0.113093	−	0.195883i
$899$	559.581	+	323.074i	0.622448	+	0.359371i
$900$	−15.0000	+	25.9808i	−0.0166667	+	0.0288675i
$901$	1210.00	−	698.596i	1.34296	−	0.775356i
$902$			981.158i			1.08776i
$903$	−84.4243	−	43.6378i	−0.0934932	−	0.0483254i
$904$	119.334			0.132007
$905$	−151.099	−	261.711i	−0.166960	−	0.289183i
$906$	98.3392	+	56.7762i	0.108542	+	0.0626668i
$907$	−831.238	+	1439.75i	−0.916470	+	1.58737i	−0.111735	+	0.993738i	$0.535641\pi$
$907$	−831.238	+	1439.75i	−0.916470	+	1.58737i	−0.804735	+	0.593634i	$0.797693\pi$
$908$	−245.397	+	141.680i	−0.270261	+	0.156035i
$909$		−	140.202i		−	0.154238i
$910$	258.109	−	499.354i	0.283637	−	0.548741i
$911$	−143.213			−0.157204			−0.0786019	−	0.996906i	$-0.525046\pi$
$911$	−143.213			−0.157204			−0.0786019	+	0.996906i	$0.525046\pi$
$912$	−55.6588	−	96.4038i	−0.0610294	−	0.105706i
$913$	−1435.22	−	828.626i	−1.57199	−	0.907586i
$914$	−16.5783	+	28.7144i	−0.0181381	+	0.0314162i
$915$	384.398	−	221.932i	0.420107	−	0.242549i
$916$		−	435.665i		−	0.475617i
$917$	−86.3428	+	55.3591i	−0.0941579	+	0.0603698i
$918$	−211.450			−0.230338
$919$	−435.504	−	754.315i	−0.473889	−	0.820800i	0.525664	−	0.850692i	$-0.323817\pi$
$919$	−435.504	−	754.315i	−0.473889	−	0.820800i	−0.999553	+	0.0298922i	$0.990484\pi$
$920$	130.039	+	75.0783i	0.141347	+	0.0816068i
$921$	20.5453	−	35.5856i	0.0223077	−	0.0386380i
$922$	−208.751	+	120.522i	−0.226411	+	0.130718i
$923$			162.902i			0.176492i
$924$	13.7518	+	295.311i	0.0148828	+	0.319601i
$925$	145.321			0.157103
$926$	336.492	+	582.820i	0.363382	+	0.629396i
$927$	−432.067	−	249.454i	−0.466092	−	0.269098i
$928$	78.9473	−	136.741i	0.0850726	−	0.147350i
$929$	1308.36	−	755.381i	1.40835	−	0.813112i	0.413123	−	0.910675i	$-0.364438\pi$
$929$	1308.36	−	755.381i	1.40835	−	0.813112i	0.995229	+	0.0975629i	$0.0311047\pi$
$930$			126.795i			0.136338i
$931$	−642.287	+	455.309i	−0.689889	+	0.489053i
$932$	−8.50390			−0.00912435
$933$	−245.097	−	424.520i	−0.262697	−	0.455005i
$934$	−267.071	−	154.193i	−0.285943	−	0.165089i
$935$	−392.218	+	679.342i	−0.419485	+	0.726569i
$936$	186.606	−	107.737i	0.199365	−	0.115104i
$937$		−	485.168i		−	0.517788i	−0.965906	−	0.258894i	$-0.916642\pi$
$937$		−	485.168i		−	0.517788i	0.965906	−	0.258894i	$-0.0833581\pi$
$938$	697.504	−	32.4806i	0.743607	−	0.0346275i
$939$	−735.044			−0.782794
$940$	50.9659	+	88.2756i	0.0542191	+	0.0939102i
$941$	215.272	+	124.288i	0.228770	+	0.132080i	0.610004	−	0.792398i	$-0.291168\pi$
$941$	215.272	+	124.288i	0.228770	+	0.132080i	−0.381235	+	0.924478i	$0.624501\pi$
$942$	101.053	−	175.029i	0.107275	−	0.185806i
$943$	1170.06	−	675.533i	1.24078	−	0.716366i
$944$			288.111i			0.305202i
$945$	43.8988	+	68.4682i	0.0464537	+	0.0724532i
$946$	−135.146			−0.142861
$947$	−681.531	−	1180.45i	−0.719674	−	1.24651i	−0.961129	−	0.276100i	$-0.910958\pi$
$947$	−681.531	−	1180.45i	−0.719674	−	1.24651i	0.241455	−	0.970412i	$-0.422375\pi$
$948$	164.391	+	94.9110i	0.173408	+	0.100117i
$949$	502.244	−	869.913i	0.529235	−	0.916663i
$950$	−98.3917	+	56.8065i	−0.103570	+	0.0597963i
$951$		−	48.7193i		−	0.0512296i
$952$	506.100	+	261.596i	0.531617	+	0.274786i
$953$	879.838			0.923230			0.461615	−	0.887080i	$-0.347270\pi$
$953$	879.838			0.923230			0.461615	+	0.887080i	$0.347270\pi$
$954$	−103.003	−	178.407i	−0.107970	−	0.187010i
$955$	345.045	+	199.212i	0.361304	+	0.208599i
$956$	−261.513	+	452.953i	−0.273549	+	0.473800i
$957$	510.441	−	294.703i	0.533376	−	0.307945i
$958$		−	788.598i		−	0.823171i
$959$	55.3528	−	107.089i	0.0577193	−	0.111667i
$960$	30.9839			0.0322749
$961$	−212.552	−	368.152i	−0.221178	−	0.383092i
$962$	−903.922	−	521.880i	−0.939628	−	0.542495i
$963$	−49.4724	+	85.6888i	−0.0513732	+	0.0889811i
$964$	173.031	−	99.8996i	0.179493	−	0.103630i
$965$		−	302.127i		−	0.313085i
$966$	342.699	−	219.723i	0.354760	−	0.227456i
$967$	−186.884			−0.193262			−0.0966310	−	0.995320i	$-0.530807\pi$
$967$	−186.884			−0.193262			−0.0966310	+	0.995320i	$0.530807\pi$
$968$	39.0832	+	67.6940i	0.0403752	+	0.0699318i
$969$	−693.498	−	400.391i	−0.715684	−	0.413200i
$970$	−124.907	+	216.345i	−0.128770	+	0.223036i
$971$	−159.547	+	92.1145i	−0.164312	+	0.0948656i	−0.579901	−	0.814687i	$-0.696909\pi$
$971$	−159.547	+	92.1145i	−0.164312	+	0.0948656i	0.415589	+	0.909553i	$0.363575\pi$
$972$			31.1769i			0.0320750i
$973$	−10.1791	−	218.591i	−0.0104616	−	0.224657i
$974$	730.079			0.749568
$975$	−109.959	−	190.454i	−0.112778	−	0.195337i
$976$	−397.005	−	229.211i	−0.406767	−	0.234847i
$977$	554.021	−	959.592i	0.567063	−	0.982183i	−0.429791	−	0.902928i	$-0.641413\pi$
$977$	554.021	−	959.592i	0.567063	−	0.982183i	0.996854	−	0.0792543i	$-0.0252539\pi$
$978$	522.728	−	301.797i	0.534487	−	0.308586i
$979$			1758.38i			1.79609i
$980$	−20.3647	−	218.186i	−0.0207803	−	0.222639i
$981$	455.145			0.463960
$982$	86.6813	+	150.136i	0.0882702	+	0.152888i
$983$	−1216.86	−	702.557i	−1.23791	−	0.714707i	−0.269242	−	0.963072i	$-0.586773\pi$
$983$	−1216.86	−	702.557i	−1.23791	−	0.714707i	−0.968666	+	0.248365i	$0.920107\pi$
$984$	139.392	−	241.434i	0.141658	−	0.245360i
$985$	−125.393	+	72.3959i	−0.127303	+	0.0734984i
$986$		−	1135.84i		−	1.15197i
$987$	276.047	−	12.8547i	0.279683	−	0.0130240i
$988$	816.021			0.825932
$989$	93.0489	+	161.165i	0.0940838	+	0.162958i
$990$	100.165	+	57.8300i	0.101176	+	0.0584141i
$991$	−218.084	+	377.732i	−0.220064	+	0.381162i	−0.954827	−	0.297161i	$-0.903960\pi$
$991$	−218.084	+	377.732i	−0.220064	+	0.381162i	0.734763	+	0.678324i	$0.237293\pi$
$992$	113.408	−	65.4764i	0.114323	−	0.0660045i
$993$			453.591i			0.456788i
$994$	34.2766	+	53.4607i	0.0344835	+	0.0537834i
$995$	−301.465			−0.302980
$996$	235.444	+	407.801i	0.236389	+	0.409438i
$997$	−77.2090	−	44.5767i	−0.0774414	−	0.0447108i	0.460779	−	0.887515i	$-0.347570\pi$
$997$	−77.2090	−	44.5767i	−0.0774414	−	0.0447108i	−0.538221	+	0.842804i	$0.680903\pi$
$998$	265.200	−	459.340i	0.265731	−	0.460260i
$999$	130.789	−	75.5108i	0.130919	−	0.0755864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.b.31.6	✓	16
3.2	odd	2		630.3.v.c.451.4		16
5.2	odd	4		1050.3.q.e.199.8		32
5.3	odd	4		1050.3.q.e.199.9		32
5.4	even	2		1050.3.p.i.451.1		16
7.3	odd	6		1470.3.f.d.391.4		16
7.4	even	3		1470.3.f.d.391.6		16
7.5	odd	6	inner	210.3.o.b.61.6	yes	16
21.5	even	6		630.3.v.c.271.4		16
35.12	even	12		1050.3.q.e.649.9		32
35.19	odd	6		1050.3.p.i.901.1		16
35.33	even	12		1050.3.q.e.649.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.6	✓	16	1.1	even	1	trivial
210.3.o.b.61.6	yes	16	7.5	odd	6	inner
630.3.v.c.271.4		16	21.5	even	6
630.3.v.c.451.4		16	3.2	odd	2
1050.3.p.i.451.1		16	5.4	even	2
1050.3.p.i.901.1		16	35.19	odd	6
1050.3.q.e.199.8		32	5.2	odd	4
1050.3.q.e.199.9		32	5.3	odd	4
1050.3.q.e.649.8		32	35.33	even	12
1050.3.q.e.649.9		32	35.12	even	12
1470.3.f.d.391.4		16	7.3	odd	6
1470.3.f.d.391.6		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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(6.99242 - 0.325616i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(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} +(6.99242 - 0.325616i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-6.09582 + 10.5583i) q^{11} +(3.00000 - 1.73205i) q^{12} +25.3938i q^{13} +(5.34319 + 8.33369i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-24.9196 - 14.3873i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-13.9147 + 8.03365i) q^{19} -4.47214i q^{20} +(-10.7706 - 5.56719i) q^{21} -17.2416 q^{22} +(11.8709 + 20.5610i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-31.1010 + 17.9562i) q^{26} -5.19615i q^{27} +(-6.42844 + 12.4368i) q^{28} +27.9121 q^{29} +(2.73861 + 4.74342i) q^{30} +(20.0480 + 11.5747i) q^{31} +(2.82843 - 4.89898i) q^{32} +(18.2875 - 10.5583i) q^{33} -40.6936i q^{34} +(-13.1767 + 8.44832i) q^{35} -6.00000 q^{36} +(14.5321 + 25.1703i) q^{37} +(-19.6783 - 11.3613i) q^{38} +(21.9917 - 38.0908i) q^{39} +(5.47723 - 3.16228i) q^{40} -56.9065i q^{41} +(-0.797593 - 17.1279i) q^{42} +7.83839 q^{43} +(-12.1916 - 21.1165i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-16.7880 + 29.0777i) q^{46} +(-19.7390 + 11.3963i) q^{47} +6.92820i q^{48} +(48.7879 - 4.55369i) q^{49} +7.07107 q^{50} +(24.9196 + 43.1620i) q^{51} +(-43.9834 - 25.3938i) q^{52} +(-24.2781 + 42.0510i) q^{53} +(6.36396 - 3.67423i) q^{54} -27.2613i q^{55} +(-19.7776 + 0.920981i) q^{56} +27.8294 q^{57} +(19.7368 + 34.1852i) q^{58} +(-62.3779 - 36.0139i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(99.2512 - 57.3027i) q^{61} +32.7382i q^{62} +(11.3346 + 17.6784i) q^{63} +8.00000 q^{64} +(-28.3912 - 49.1750i) q^{65} +(25.8624 + 14.9316i) q^{66} +(35.2674 - 61.0850i) q^{67} +(49.8392 - 28.7747i) q^{68} -41.1221i q^{69} +(-19.6644 - 10.1643i) q^{70} +6.41501 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-34.2569 - 19.7782i) q^{73} +(-20.5514 + 35.5961i) q^{74} +(-7.50000 + 4.33013i) q^{75} -32.1346i q^{76} +(-39.1866 + 75.8127i) q^{77} +62.2019 q^{78} +(27.3985 + 47.4555i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(69.6960 - 40.2390i) q^{82} +135.934i q^{83} +(20.4133 - 13.0881i) q^{84} +64.3422 q^{85} +(5.54258 + 9.60002i) q^{86} +(-41.8682 - 24.1726i) q^{87} +(17.2416 - 29.8633i) q^{88} +(124.905 - 72.1140i) q^{89} -9.48683i q^{90} +(8.26863 + 177.564i) q^{91} -47.4837 q^{92} +(-20.0480 - 34.7241i) q^{93} +(-27.9152 - 16.1168i) q^{94} +(17.9638 - 31.1142i) q^{95} +(-8.48528 + 4.89898i) q^{96} -78.9980i q^{97} +(40.0754 + 56.5328i) q^{98} -36.5749 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

Properties

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