LMFDB - Embedded newform 210.3.o.b.61.1

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			61.1
Root			$-3.67087 + 6.35814i$ of defining polynomial
Character	$\chi$	$=$	210.61
Dual form			210.3.o.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-2.59373 + 6.50174i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(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} +(-2.59373 + 6.50174i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(-5.13478 - 8.89370i) q^{11} +(3.00000 + 1.73205i) q^{12} -7.02340i q^{13} +(-6.12892 - 7.77408i) q^{14} +3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(27.4947 - 15.8741i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-26.9408 - 15.5543i) q^{19} +4.47214i q^{20} +(-1.74007 - 11.9988i) q^{21} +14.5234 q^{22} +(11.8441 - 20.5146i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(8.60187 + 4.96629i) q^{26} +5.19615i q^{27} +(13.8551 - 2.00927i) q^{28} +9.19673 q^{29} +(-2.73861 + 4.74342i) q^{30} +(17.4511 - 10.0754i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(15.4043 + 8.89370i) q^{33} +44.8986i q^{34} +(12.2919 - 9.69068i) q^{35} -6.00000 q^{36} +(-24.0823 + 41.7118i) q^{37} +(38.1001 - 21.9971i) q^{38} +(6.08244 + 10.5351i) q^{39} +(-5.47723 - 3.16228i) q^{40} -65.1226i q^{41} +(15.9259 + 6.35331i) q^{42} -3.03497 q^{43} +(-10.2696 + 17.7874i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(16.7501 + 29.0120i) q^{46} +(-53.6472 - 30.9732i) q^{47} -6.92820i q^{48} +(-35.5451 - 33.7275i) q^{49} -7.07107 q^{50} +(-27.4947 + 47.6222i) q^{51} +(-12.1649 + 7.02340i) q^{52} +(-0.690751 - 1.19642i) q^{53} +(-6.36396 - 3.67423i) q^{54} +22.9634i q^{55} +(-7.33617 + 18.3897i) q^{56} +53.8817 q^{57} +(-6.50307 + 11.2636i) q^{58} +(-95.1064 + 54.9097i) q^{59} +(-3.87298 - 6.70820i) q^{60} +(-34.3741 - 19.8459i) q^{61} +28.4976i q^{62} +(13.0014 + 16.4913i) q^{63} +8.00000 q^{64} +(-7.85240 + 13.6008i) q^{65} +(-21.7850 + 12.5776i) q^{66} +(-7.95952 - 13.7863i) q^{67} +(-54.9893 - 31.7481i) q^{68} +41.0292i q^{69} +(3.17693 + 21.9068i) q^{70} +53.3489 q^{71} +(4.24264 - 7.34847i) q^{72} +(62.6830 - 36.1901i) q^{73} +(-34.0576 - 58.9894i) q^{74} +(-7.50000 - 4.33013i) q^{75} +62.2172i q^{76} +(71.1427 - 10.3171i) q^{77} -17.2037 q^{78} +(-53.2229 + 92.1847i) q^{79} +(7.74597 - 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(79.7586 + 46.0486i) q^{82} +49.4298i q^{83} +(-19.0425 + 15.0127i) q^{84} -70.9909 q^{85} +(2.14605 - 3.71707i) q^{86} +(-13.7951 + 7.96460i) q^{87} +(-14.5234 - 25.1552i) q^{88} +(-142.807 - 82.4499i) q^{89} -9.48683i q^{90} +(45.6643 + 18.2168i) q^{91} -47.3765 q^{92} +(-17.4511 + 30.2262i) q^{93} +(75.8686 - 43.8027i) q^{94} +(34.7805 + 60.2416i) q^{95} +(8.48528 + 4.89898i) q^{96} +49.4799i q^{97} +(66.4418 - 19.6848i) q^{98} -30.8087 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
$7$	−2.59373	+	6.50174i	−0.370533	+	0.928819i
$7$	−2.59373	+	6.50174i	−0.370533	+	0.928819i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	2.73861	−	1.58114i	0.273861	−	0.158114i
$11$	−5.13478	−	8.89370i	−0.466798	−	0.808518i	0.532482	−	0.846441i	$-0.321259\pi$
$11$	−5.13478	−	8.89370i	−0.466798	−	0.808518i	−0.999281	+	0.0379228i	$0.987926\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$		−	7.02340i		−	0.540261i	−0.962824	−	0.270131i	$-0.912933\pi$
$13$		−	7.02340i		−	0.540261i	0.962824	−	0.270131i	$-0.0870669\pi$
$14$	−6.12892	−	7.77408i	−0.437780	−	0.555291i
$15$	3.87298			0.258199
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	27.4947	−	15.8741i	1.61733	−	0.933768i	0.629727	−	0.776816i	$-0.283167\pi$
$17$	27.4947	−	15.8741i	1.61733	−	0.933768i	0.987606	−	0.156951i	$-0.0501666\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	−26.9408	−	15.5543i	−1.41794	−	0.818648i	−0.421822	−	0.906679i	$-0.638609\pi$
$19$	−26.9408	−	15.5543i	−1.41794	−	0.818648i	−0.996118	+	0.0880311i	$0.971943\pi$
$20$			4.47214i			0.223607i
$21$	−1.74007	−	11.9988i	−0.0828607	−	0.571373i
$22$	14.5234			0.660152
$23$	11.8441	−	20.5146i	0.514962	−	0.891940i	−0.484888	−	0.874576i	$-0.661140\pi$
$23$	11.8441	−	20.5146i	0.514962	−	0.891940i	0.999849	−	0.0173632i	$-0.00552716\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	8.60187	+	4.96629i	0.330841	+	0.191011i
$27$			5.19615i			0.192450i
$28$	13.8551	−	2.00927i	0.494824	−	0.0717595i
$29$	9.19673			0.317129			0.158564	−	0.987349i	$-0.449313\pi$
$29$	9.19673			0.317129			0.158564	+	0.987349i	$0.449313\pi$
$30$	−2.73861	+	4.74342i	−0.0912871	+	0.158114i
$31$	17.4511	−	10.0754i	0.562940	−	0.325013i	−0.191385	−	0.981515i	$-0.561298\pi$
$31$	17.4511	−	10.0754i	0.562940	−	0.325013i	0.754325	+	0.656502i	$0.227965\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	15.4043	+	8.89370i	0.466798	+	0.269506i
$34$			44.8986i			1.32055i
$35$	12.2919	−	9.69068i	0.351197	−	0.276877i
$36$	−6.00000			−0.166667
$37$	−24.0823	+	41.7118i	−0.650874	+	1.12735i	0.332037	+	0.943266i	$0.392264\pi$
$37$	−24.0823	+	41.7118i	−0.650874	+	1.12735i	−0.982911	+	0.184081i	$0.941069\pi$
$38$	38.1001	−	21.9971i	1.00263	−	0.578871i
$39$	6.08244	+	10.5351i	0.155960	+	0.270131i
$40$	−5.47723	−	3.16228i	−0.136931	−	0.0790569i
$41$		−	65.1226i		−	1.58836i	−0.607685	−	0.794178i	$-0.707902\pi$
$41$		−	65.1226i		−	1.58836i	0.607685	−	0.794178i	$-0.292098\pi$
$42$	15.9259	+	6.35331i	0.379189	+	0.151269i
$43$	−3.03497			−0.0705807			−0.0352904	−	0.999377i	$-0.511236\pi$
$43$	−3.03497			−0.0705807			−0.0352904	+	0.999377i	$0.511236\pi$
$44$	−10.2696	+	17.7874i	−0.233399	+	0.404259i
$45$	−5.80948	+	3.35410i	−0.129099	+	0.0745356i
$46$	16.7501	+	29.0120i	0.364133	+	0.630697i
$47$	−53.6472	−	30.9732i	−1.14143	−	0.659005i	−0.194645	−	0.980874i	$-0.562356\pi$
$47$	−53.6472	−	30.9732i	−1.14143	−	0.659005i	−0.946784	+	0.321869i	$0.895689\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−35.5451	−	33.7275i	−0.725411	−	0.688316i
$50$	−7.07107			−0.141421
$51$	−27.4947	+	47.6222i	−0.539111	+	0.933768i
$52$	−12.1649	+	7.02340i	−0.233940	+	0.135065i
$53$	−0.690751	−	1.19642i	−0.0130330	−	0.0225739i	0.859435	−	0.511244i	$-0.170815\pi$
$53$	−0.690751	−	1.19642i	−0.0130330	−	0.0225739i	−0.872468	+	0.488671i	$0.837482\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$			22.9634i			0.417517i
$56$	−7.33617	+	18.3897i	−0.131003	+	0.328387i
$57$	53.8817			0.945293
$58$	−6.50307	+	11.2636i	−0.112122	+	0.194201i
$59$	−95.1064	+	54.9097i	−1.61197	+	0.930673i	−0.623061	+	0.782173i	$0.714111\pi$
$59$	−95.1064	+	54.9097i	−1.61197	+	0.930673i	−0.988912	+	0.148500i	$0.952555\pi$
$60$	−3.87298	−	6.70820i	−0.0645497	−	0.111803i
$61$	−34.3741	−	19.8459i	−0.563510	−	0.325343i	0.191043	−	0.981582i	$-0.438813\pi$
$61$	−34.3741	−	19.8459i	−0.563510	−	0.325343i	−0.754553	+	0.656239i	$0.772146\pi$
$62$			28.4976i			0.459638i
$63$	13.0014	+	16.4913i	0.206372	+	0.261767i
$64$	8.00000			0.125000
$65$	−7.85240	+	13.6008i	−0.120806	+	0.209242i
$66$	−21.7850	+	12.5776i	−0.330076	+	0.190570i
$67$	−7.95952	−	13.7863i	−0.118799	−	0.205765i	0.800493	−	0.599342i	$-0.204571\pi$
$67$	−7.95952	−	13.7863i	−0.118799	−	0.205765i	−0.919292	+	0.393576i	$0.871238\pi$
$68$	−54.9893	−	31.7481i	−0.808667	−	0.466884i
$69$			41.0292i			0.594626i
$70$	3.17693	+	21.9068i	0.0453847	+	0.312954i
$71$	53.3489			0.751393			0.375696	−	0.926743i	$-0.377404\pi$
$71$	53.3489			0.751393			0.375696	+	0.926743i	$0.377404\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	62.6830	−	36.1901i	0.858672	−	0.495754i	−0.00489557	−	0.999988i	$-0.501558\pi$
$73$	62.6830	−	36.1901i	0.858672	−	0.495754i	0.863567	+	0.504234i	$0.168225\pi$
$74$	−34.0576	−	58.9894i	−0.460237	−	0.797155i
$75$	−7.50000	−	4.33013i	−0.100000	−	0.0577350i
$76$			62.2172i			0.818648i
$77$	71.1427	−	10.3171i	0.923931	−	0.133989i
$78$	−17.2037			−0.220561
$79$	−53.2229	+	92.1847i	−0.673707	+	1.16690i	0.303138	+	0.952947i	$0.401966\pi$
$79$	−53.2229	+	92.1847i	−0.673707	+	1.16690i	−0.976845	+	0.213948i	$0.931368\pi$
$80$	7.74597	−	4.47214i	0.0968246	−	0.0559017i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	79.7586	+	46.0486i	0.972666	+	0.561569i
$83$			49.4298i			0.595540i	0.954638	+	0.297770i	$0.0962429\pi$
$83$			49.4298i			0.595540i	−0.954638	+	0.297770i	$0.903757\pi$
$84$	−19.0425	+	15.0127i	−0.226697	+	0.178723i
$85$	−70.9909			−0.835187
$86$	2.14605	−	3.71707i	0.0249541	−	0.0432217i
$87$	−13.7951	+	7.96460i	−0.158564	+	0.0915472i
$88$	−14.5234	−	25.1552i	−0.165038	−	0.285854i
$89$	−142.807	−	82.4499i	−1.60458	−	0.926403i	−0.990555	−	0.137114i	$-0.956217\pi$
$89$	−142.807	−	82.4499i	−1.60458	−	0.926403i	−0.614022	−	0.789289i	$-0.710449\pi$
$90$		−	9.48683i		−	0.105409i
$91$	45.6643	+	18.2168i	0.501805	+	0.200185i
$92$	−47.3765			−0.514962
$93$	−17.4511	+	30.2262i	−0.187647	+	0.325013i
$94$	75.8686	−	43.8027i	0.807113	−	0.465987i
$95$	34.7805	+	60.2416i	0.366110	+	0.634122i
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$			49.4799i			0.510102i	0.966928	+	0.255051i	$0.0820922\pi$
$97$			49.4799i			0.510102i	−0.966928	+	0.255051i	$0.917908\pi$
$98$	66.4418	−	19.6848i	0.677977	−	0.200865i
$99$	−30.8087			−0.311199
$100$	5.00000	−	8.66025i	0.0500000	−	0.0866025i
$101$	116.803	−	67.4364i	1.15647	−	0.667687i	0.206012	−	0.978549i	$-0.433951\pi$
$101$	116.803	−	67.4364i	1.15647	−	0.667687i	0.950455	+	0.310863i	$0.100618\pi$
$102$	−38.8833	−	67.3479i	−0.381209	−	0.660274i
$103$	−32.3911	−	18.7010i	−0.314477	−	0.181563i	0.334451	−	0.942413i	$-0.391449\pi$
$103$	−32.3911	−	18.7010i	−0.314477	−	0.181563i	−0.648928	+	0.760850i	$0.724782\pi$
$104$		−	19.8652i		−	0.191011i
$105$	−10.0455	+	25.1811i	−0.0956711	+	0.239820i
$106$	1.95374			0.0184315
$107$	12.3980	−	21.4739i	0.115869	−	0.200691i	−0.802258	−	0.596978i	$-0.796368\pi$
$107$	12.3980	−	21.4739i	0.115869	−	0.200691i	0.918127	+	0.396287i	$0.129701\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	28.1448	+	48.7483i	0.258209	+	0.447232i	0.965762	−	0.259429i	$-0.0835342\pi$
$109$	28.1448	+	48.7483i	0.258209	+	0.447232i	−0.707553	+	0.706660i	$0.750201\pi$
$110$	−28.1243	−	16.2376i	−0.255676	−	0.147615i
$111$		−	83.4237i		−	0.751565i
$112$	−17.3352	−	21.9884i	−0.154779	−	0.196325i
$113$	74.9910			0.663637			0.331818	−	0.943343i	$-0.392338\pi$
$113$	74.9910			0.663637			0.331818	+	0.943343i	$0.392338\pi$
$114$	−38.1001	+	65.9913i	−0.334212	+	0.578871i
$115$	−45.8721	+	26.4843i	−0.398888	+	0.230298i
$116$	−9.19673	−	15.9292i	−0.0792822	−	0.137321i
$117$	−18.2473	−	10.5351i	−0.155960	−	0.0900436i
$118$		−	155.308i		−	1.31617i
$119$	31.8952	+	219.936i	0.268027	+	1.84820i
$120$	10.9545			0.0912871
$121$	7.76807	−	13.4547i	0.0641989	−	0.111196i
$122$	48.6124	−	28.0664i	0.398462	−	0.230052i
$123$	56.3978	+	97.6839i	0.458519	+	0.794178i
$124$	−34.9023	−	20.1508i	−0.281470	−	0.162507i
$125$		−	11.1803i		−	0.0894427i
$126$	−29.3910	+	4.26229i	−0.233262	+	0.0338277i
$127$	128.504			1.01184			0.505921	−	0.862580i	$-0.331153\pi$
$127$	128.504			1.01184			0.505921	+	0.862580i	$0.331153\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	4.55246	−	2.62836i	0.0352904	−	0.0203749i
$130$	−11.1050	−	19.2344i	−0.0854228	−	0.147957i
$131$	65.3818	+	37.7482i	0.499098	+	0.288154i	0.728341	−	0.685215i	$-0.240292\pi$
$131$	65.3818	+	37.7482i	0.499098	+	0.288154i	−0.229243	+	0.973369i	$0.573625\pi$
$132$		−	35.5748i		−	0.269506i
$133$	171.007	−	134.819i	1.28577	−	1.01367i
$134$	22.5129			0.168007
$135$	5.80948	−	10.0623i	0.0430331	−	0.0745356i
$136$	77.7667	−	44.8986i	0.571814	−	0.330137i
$137$	−53.7583	−	93.1121i	−0.392396	−	0.679650i	0.600369	−	0.799723i	$-0.295020\pi$
$137$	−53.7583	−	93.1121i	−0.392396	−	0.679650i	−0.992765	+	0.120073i	$0.961687\pi$
$138$	−50.2503	−	29.0120i	−0.364133	−	0.210232i
$139$		−	272.004i		−	1.95686i	−0.206576	−	0.978431i	$-0.566232\pi$
$139$		−	272.004i		−	1.95686i	0.206576	−	0.978431i	$-0.433768\pi$
$140$	−29.0766	−	11.5995i	−0.207690	−	0.0828536i
$141$	107.294			0.760953
$142$	−37.7234	+	65.3388i	−0.265658	+	0.460132i
$143$	−62.4640	+	36.0636i	−0.436811	+	0.252193i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$	−17.8094	−	10.2823i	−0.122823	−	0.0709121i
$146$			102.361i			0.701102i
$147$	82.5266	+	19.8082i	0.561405	+	0.134750i
$148$	96.3294			0.650874
$149$	41.7135	−	72.2498i	0.279956	−	0.484898i	−0.691417	−	0.722456i	$-0.743013\pi$
$149$	41.7135	−	72.2498i	0.279956	−	0.484898i	0.971374	+	0.237557i	$0.0763467\pi$
$150$	10.6066	−	6.12372i	0.0707107	−	0.0408248i
$151$	−63.3973	−	109.807i	−0.419850	−	0.727201i	0.576074	−	0.817397i	$-0.304584\pi$
$151$	−63.3973	−	109.807i	−0.419850	−	0.727201i	−0.995924	+	0.0901962i	$0.971251\pi$
$152$	−76.2002	−	43.9942i	−0.501317	−	0.289436i
$153$		−	95.2443i		−	0.622512i
$154$	−37.6696	+	94.4270i	−0.244608	+	0.613162i
$155$	−45.0586			−0.290701
$156$	12.1649	−	21.0702i	0.0779800	−	0.135065i
$157$	−85.9416	+	49.6184i	−0.547399	+	0.316041i	−0.748072	−	0.663617i	$-0.769020\pi$
$157$	−85.9416	+	49.6184i	−0.547399	+	0.316041i	0.200673	+	0.979658i	$0.435687\pi$
$158$	−75.2685	−	130.369i	−0.476383	−	0.825120i
$159$	2.07225	+	1.19642i	0.0130330	+	0.00752463i
$160$			12.6491i			0.0790569i
$161$	102.660	+	130.217i	0.637641	+	0.808799i
$162$	12.7279			0.0785674
$163$	−139.490	+	241.603i	−0.855765	+	1.48223i	0.0201678	+	0.999797i	$0.493580\pi$
$163$	−139.490	+	241.603i	−0.855765	+	1.48223i	−0.875933	+	0.482433i	$0.839753\pi$
$164$	−112.796	+	65.1226i	−0.687779	+	0.397089i
$165$	−19.8869	−	34.4452i	−0.120527	−	0.208759i
$166$	−60.5389	−	34.9522i	−0.364692	−	0.210555i
$167$		−	29.9435i		−	0.179302i	−0.995973	−	0.0896511i	$-0.971425\pi$
$167$		−	29.9435i		−	0.179302i	0.995973	−	0.0896511i	$-0.0285752\pi$
$168$	−4.92167	−	33.9378i	−0.0292957	−	0.202011i
$169$	119.672			0.708118
$170$	50.1982	−	86.9458i	0.295283	−	0.511446i
$171$	−80.8225	+	46.6629i	−0.472646	+	0.272883i
$172$	3.03497	+	5.25673i	0.0176452	+	0.0305624i
$173$	92.2369	+	53.2530i	0.533161	+	0.307821i	0.742303	−	0.670065i	$-0.233734\pi$
$173$	92.2369	+	53.2530i	0.533161	+	0.307821i	−0.209142	+	0.977885i	$0.567067\pi$
$174$		−	22.5273i		−	0.129467i
$175$	−34.6377	+	5.02316i	−0.197930	+	0.0287038i
$176$	41.0782			0.233399
$177$	95.1064	−	164.729i	0.537324	−	0.930673i
$178$	201.960	−	116.602i	1.13461	−	0.655066i
$179$	119.986	+	207.822i	0.670315	+	1.16102i	0.977815	+	0.209471i	$0.0671743\pi$
$179$	119.986	+	207.822i	0.670315	+	1.16102i	−0.307500	+	0.951548i	$0.599492\pi$
$180$	11.6190	+	6.70820i	0.0645497	+	0.0372678i
$181$		−	309.322i		−	1.70896i	−0.519482	−	0.854482i	$-0.673875\pi$
$181$		−	309.322i		−	1.70896i	0.519482	−	0.854482i	$-0.326125\pi$
$182$	−54.6004	+	43.0459i	−0.300002	+	0.236516i
$183$	68.7483			0.375674
$184$	33.5002	−	58.0241i	0.182066	−	0.315348i
$185$	93.2705	−	53.8497i	0.504165	−	0.291080i
$186$	−24.6796	−	42.7464i	−0.132686	−	0.229819i
$187$	−282.358	−	163.020i	−1.50994	−	0.871762i
$188$			123.893i			0.659005i
$189$	−33.7840	−	13.4774i	−0.178751	−	0.0713091i
$190$	−98.3741			−0.517758
$191$	−1.54480	+	2.67567i	−0.00808796	+	0.0140088i	−0.870041	−	0.492979i	$-0.835908\pi$
$191$	−1.54480	+	2.67567i	−0.00808796	+	0.0140088i	0.861953	+	0.506988i	$0.169241\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	119.349	+	206.718i	0.618387	+	1.07108i	0.989780	+	0.142602i	$0.0455469\pi$
$193$	119.349	+	206.718i	0.618387	+	1.07108i	−0.371393	+	0.928476i	$0.621120\pi$
$194$	−60.6002	−	34.9875i	−0.312372	−	0.180348i
$195$		−	27.2015i		−	0.139495i
$196$	−22.8726	+	95.2935i	−0.116697	+	0.486191i
$197$	−291.539			−1.47989			−0.739946	−	0.672666i	$-0.765149\pi$
$197$	−291.539			−1.47989			−0.739946	+	0.672666i	$0.765149\pi$
$198$	21.7850	−	37.7328i	0.110025	−	0.190570i
$199$	209.224	−	120.796i	1.05138	−	0.607013i	0.128342	−	0.991730i	$-0.459034\pi$
$199$	209.224	−	120.796i	1.05138	−	0.607013i	0.923034	+	0.384717i	$0.125701\pi$
$200$	7.07107	+	12.2474i	0.0353553	+	0.0612372i
$201$	23.8785	+	13.7863i	0.118799	+	0.0685885i
$202$			190.739i			0.944252i
$203$	−23.8538	+	59.7947i	−0.117507	+	0.294555i
$204$	109.979			0.539111
$205$	−72.8093	+	126.109i	−0.355167	+	0.615168i
$206$	45.8080	−	26.4473i	0.222369	−	0.128385i
$207$	−35.5324	−	61.5438i	−0.171654	−	0.297313i
$208$	24.3298	+	14.0468i	0.116970	+	0.0675327i
$209$			319.472i			1.52857i
$210$	−23.7372	−	30.1089i	−0.113034	−	0.143376i
$211$	−263.018			−1.24653			−0.623266	−	0.782010i	$-0.714195\pi$
$211$	−263.018			−1.24653			−0.623266	+	0.782010i	$0.714195\pi$
$212$	−1.38150	+	2.39283i	−0.00651652	+	0.0112869i
$213$	−80.0234	+	46.2015i	−0.375696	+	0.216908i
$214$	17.5334	+	30.3688i	0.0819318	+	0.141910i
$215$	5.87720	+	3.39320i	0.0273358	+	0.0157823i
$216$			14.6969i			0.0680414i
$217$	20.2442	+	139.596i	0.0932911	+	0.643297i
$218$	−79.6056			−0.365163
$219$	−62.6830	+	108.570i	−0.286224	+	0.495754i
$220$	39.7738	−	22.9634i	0.180790	−	0.104379i
$221$	−111.490	−	193.106i	−0.504479	−	0.873783i
$222$	102.173	+	58.9894i	0.460237	+	0.265718i
$223$		−	112.658i		−	0.505193i	−0.967572	−	0.252597i	$-0.918715\pi$
$223$		−	112.658i		−	0.505193i	0.967572	−	0.252597i	$-0.0812845\pi$
$224$	39.1880	−	5.68306i	0.174947	−	0.0253708i
$225$	15.0000			0.0666667
$226$	−53.0266	+	91.8448i	−0.234631	+	0.406393i
$227$	42.4529	−	24.5102i	0.187017	−	0.107974i	−0.403568	−	0.914950i	$-0.632230\pi$
$227$	42.4529	−	24.5102i	0.187017	−	0.107974i	0.590585	+	0.806975i	$0.298897\pi$
$228$	−53.8817	−	93.3258i	−0.236323	−	0.409324i
$229$	24.3476	+	14.0571i	0.106321	+	0.0613846i	0.552218	−	0.833700i	$-0.313782\pi$
$229$	24.3476	+	14.0571i	0.106321	+	0.0613846i	−0.445896	+	0.895085i	$0.647115\pi$
$230$		−	74.9088i		−	0.325690i
$231$	−97.7792	+	77.0871i	−0.423286	+	0.333710i
$232$	26.0123			0.112122
$233$	−88.1014	+	152.596i	−0.378117	+	0.654919i	−0.990788	−	0.135420i	$-0.956762\pi$
$233$	−88.1014	+	152.596i	−0.378117	+	0.654919i	0.612671	+	0.790338i	$0.290095\pi$
$234$	25.8056	−	14.8989i	0.110280	−	0.0636704i
$235$	69.2582	+	119.959i	0.294716	+	0.510463i
$236$	190.213	+	109.819i	0.805987	+	0.465337i
$237$		−	184.369i		−	0.777930i
$238$	−291.919	−	116.455i	−1.22655	−	0.489306i
$239$	34.7150			0.145251			0.0726255	−	0.997359i	$-0.476862\pi$
$239$	34.7150			0.145251			0.0726255	+	0.997359i	$0.476862\pi$
$240$	−7.74597	+	13.4164i	−0.0322749	+	0.0559017i
$241$	−229.871	+	132.716i	−0.953823	+	0.550690i	−0.894266	−	0.447535i	$-0.852302\pi$
$241$	−229.871	+	132.716i	−0.953823	+	0.550690i	−0.0595563	+	0.998225i	$0.518969\pi$
$242$	10.9857	+	19.0278i	0.0453955	+	0.0786273i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$			79.3837i			0.325343i
$245$	31.1244	+	105.054i	0.127038	+	0.428790i
$246$	−159.517			−0.648444
$247$	−109.244	+	189.216i	−0.442284	+	0.766058i
$248$	49.3592	−	28.4976i	0.199029	−	0.114910i
$249$	−42.8075	−	74.1447i	−0.171918	−	0.297770i
$250$	13.6931	+	7.90569i	0.0547723	+	0.0316228i
$251$		−	24.1723i		−	0.0963040i	−0.998840	−	0.0481520i	$-0.984667\pi$
$251$		−	24.1723i		−	0.0963040i	0.998840	−	0.0481520i	$-0.0153332\pi$
$252$	15.5624	−	39.0104i	0.0617555	−	0.154803i
$253$	−243.268			−0.961533
$254$	−90.8659	+	157.384i	−0.357740	+	0.619624i
$255$	106.486	−	61.4799i	0.417594	−	0.241098i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−8.25969	−	4.76874i	−0.0321389	−	0.0185554i	0.483844	−	0.875154i	$-0.339240\pi$
$257$	−8.25969	−	4.76874i	−0.0321389	−	0.0185554i	−0.515983	+	0.856599i	$0.672573\pi$
$258$			7.43413i			0.0288145i
$259$	−208.736	−	264.766i	−0.805932	−	1.02226i
$260$	31.4096			0.120806
$261$	13.7951	−	23.8938i	0.0528548	−	0.0915472i
$262$	−92.4639	+	53.3840i	−0.352916	+	0.203756i
$263$	65.9316	+	114.197i	0.250691	+	0.434209i	0.963716	−	0.266929i	$-0.0860090\pi$
$263$	65.9316	+	114.197i	0.250691	+	0.434209i	−0.713026	+	0.701138i	$0.752676\pi$
$264$	43.5701	+	25.1552i	0.165038	+	0.0952848i
$265$			3.08913i			0.0116571i
$266$	44.1980	+	304.771i	0.166158	+	1.14576i
$267$	285.615			1.06972
$268$	−15.9190	+	27.5726i	−0.0593994	+	0.102883i
$269$	−32.8041	+	18.9395i	−0.121949	+	0.0704070i	−0.559733	−	0.828673i	$-0.689096\pi$
$269$	−32.8041	+	18.9395i	−0.121949	+	0.0704070i	0.437785	+	0.899080i	$0.355763\pi$
$270$	8.21584	+	14.2302i	0.0304290	+	0.0527046i
$271$	313.801	+	181.173i	1.15794	+	0.668535i	0.950809	−	0.309779i	$-0.100255\pi$
$271$	313.801	+	181.173i	1.15794	+	0.668535i	0.207128	+	0.978314i	$0.433588\pi$
$272$			126.992i			0.466884i
$273$	−84.2726	+	12.2212i	−0.308691	+	0.0447664i
$274$	152.051			0.554932
$275$	25.6739	−	44.4685i	0.0933596	−	0.161704i
$276$	71.0647	−	41.0292i	0.257481	−	0.148657i
$277$	56.6495	+	98.1197i	0.204511	+	0.354223i	0.949977	−	0.312321i	$-0.101106\pi$
$277$	56.6495	+	98.1197i	0.204511	+	0.354223i	−0.745466	+	0.666544i	$0.767773\pi$
$278$	333.135	+	192.336i	1.19833	+	0.691855i
$279$		−	60.4525i		−	0.216676i
$280$	34.7667	−	27.4094i	0.124167	−	0.0978907i
$281$	−178.735			−0.636069			−0.318034	−	0.948079i	$-0.603023\pi$
$281$	−178.735			−0.636069			−0.318034	+	0.948079i	$0.603023\pi$
$282$	−75.8686	+	131.408i	−0.269038	+	0.465987i
$283$	37.3850	−	21.5843i	0.132103	−	0.0762695i	−0.432492	−	0.901638i	$-0.642366\pi$
$283$	37.3850	−	21.5843i	0.132103	−	0.0762695i	0.564595	+	0.825368i	$0.309032\pi$
$284$	−53.3489	−	92.4030i	−0.187848	−	0.325363i
$285$	−104.341	−	60.2416i	−0.366110	−	0.211374i
$286$		−	102.003i		−	0.356655i
$287$	423.410	+	168.910i	1.47530	+	0.588538i
$288$	−16.9706			−0.0589256
$289$	359.471	−	622.622i	1.24384	−	2.15440i
$290$	25.1863	−	14.5413i	0.0868493	−	0.0501424i
$291$	−42.8508	−	74.2198i	−0.147254	−	0.255051i
$292$	−125.366	−	72.3801i	−0.429336	−	0.247877i
$293$		−	15.4426i		−	0.0527050i	−0.999653	−	0.0263525i	$-0.991611\pi$
$293$		−	15.4426i		−	0.0527050i	0.999653	−	0.0263525i	$-0.00838923\pi$
$294$	−82.6151	+	87.0675i	−0.281004	+	0.296148i
$295$	245.564			0.832420
$296$	−68.1151	+	117.979i	−0.230119	+	0.398577i
$297$	46.2130	−	26.6811i	0.155599	−	0.0898354i
$298$	58.9917	+	102.177i	0.197959	+	0.342875i
$299$	−144.082	−	83.1859i	−0.481881	−	0.278214i
$300$			17.3205i			0.0577350i
$301$	7.87189	−	19.7326i	0.0261525	−	0.0655568i
$302$	179.315			0.593757
$303$	−116.803	+	202.309i	−0.385489	+	0.667687i
$304$	107.763	−	62.2172i	0.354485	−	0.204662i
$305$	44.3768	+	76.8629i	0.145498	+	0.252009i
$306$	116.650	+	67.3479i	0.381209	+	0.220091i
$307$			234.648i			0.764327i	0.924095	+	0.382163i	$0.124821\pi$
$307$			234.648i			0.764327i	−0.924095	+	0.382163i	$0.875179\pi$
$308$	−89.0125	−	112.906i	−0.289002	−	0.366577i
$309$	64.7823			0.209651
$310$	31.8613	−	55.1853i	0.102778	−	0.178017i
$311$	−345.352	+	199.389i	−1.11045	+	0.641121i	−0.938947	−	0.344061i	$-0.888197\pi$
$311$	−345.352	+	199.389i	−1.11045	+	0.641121i	−0.171508	+	0.985183i	$0.554864\pi$
$312$	17.2037	+	29.7978i	0.0551402	+	0.0955056i
$313$	111.891	+	64.6002i	0.357479	+	0.206390i	0.667974	−	0.744184i	$-0.267162\pi$
$313$	111.891	+	64.6002i	0.357479	+	0.206390i	−0.310495	+	0.950575i	$0.600495\pi$
$314$		−	140.342i		−	0.446949i
$315$	−6.73928	−	46.4713i	−0.0213945	−	0.147528i
$316$	212.892			0.673707
$317$	201.283	−	348.632i	0.634961	−	1.09979i	−0.351562	−	0.936165i	$-0.614349\pi$
$317$	201.283	−	348.632i	0.634961	−	1.09979i	0.986523	−	0.163621i	$-0.0523173\pi$
$318$	−2.93061	+	1.69199i	−0.00921575	+	0.00532072i
$319$	−47.2232	−	81.7930i	−0.148035	−	0.256404i
$320$	−15.4919	−	8.94427i	−0.0484123	−	0.0279508i
$321$			42.9479i			0.133794i
$322$	−232.074	+	33.6554i	−0.720726	+	0.104520i
$323$	−987.640			−3.05771
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$	30.4122	−	17.5585i	0.0935760	−	0.0540261i
$326$	−197.268	−	341.679i	−0.605118	−	1.04809i
$327$	−84.4345	−	48.7483i	−0.258209	−	0.149077i
$328$		−	184.195i		−	0.561569i
$329$	340.526	−	268.464i	1.03503	−	0.815999i
$330$	56.2487			0.170451
$331$	83.4463	−	144.533i	0.252104	−	0.436656i	−0.712001	−	0.702178i	$-0.752211\pi$
$331$	83.4463	−	144.533i	0.252104	−	0.436656i	0.964105	+	0.265522i	$0.0855443\pi$
$332$	85.6150	−	49.4298i	0.257876	−	0.148885i
$333$	72.2470	+	125.136i	0.216958	+	0.375782i
$334$	36.6731	+	21.1732i	0.109800	+	0.0633929i
$335$			35.5960i			0.106257i
$336$	45.0453	+	17.9699i	0.134064	+	0.0534818i
$337$	−541.392			−1.60651			−0.803253	−	0.595638i	$-0.796899\pi$
$337$	−541.392			−1.60651			−0.803253	+	0.595638i	$0.796899\pi$
$338$	−84.6208	+	146.568i	−0.250357	+	0.433632i
$339$	−112.486	+	64.9441i	−0.331818	+	0.191575i
$340$	70.9909	+	122.960i	0.208797	+	0.361647i
$341$	−179.215	−	103.470i	−0.525558	−	0.303431i
$342$		−	131.983i		−	0.385914i
$343$	311.482	−	143.625i	0.908110	−	0.418732i
$344$	−8.58420			−0.0249541
$345$	45.8721	−	79.4528i	0.132963	−	0.230298i
$346$	−130.443	+	75.3111i	−0.377002	+	0.217662i
$347$	−214.342	−	371.251i	−0.617700	−	1.06989i	−0.989904	−	0.141737i	$-0.954731\pi$
$347$	−214.342	−	371.251i	−0.617700	−	1.06989i	0.372204	−	0.928151i	$-0.378602\pi$
$348$	27.5902	+	15.9292i	0.0792822	+	0.0457736i
$349$		−	74.6851i		−	0.213998i	−0.994259	−	0.106999i	$-0.965876\pi$
$349$		−	74.6851i		−	0.213998i	0.994259	−	0.106999i	$-0.0341241\pi$
$350$	18.3404	−	45.9742i	0.0524012	−	0.131355i
$351$	36.4946			0.103973
$352$	−29.0467	+	50.3104i	−0.0825190	+	0.142927i
$353$	316.890	−	182.956i	0.897705	−	0.518290i	0.0212499	−	0.999774i	$-0.493235\pi$
$353$	316.890	−	182.956i	0.897705	−	0.518290i	0.876455	+	0.481484i	$0.159902\pi$
$354$	134.501	+	232.962i	0.379946	+	0.658085i
$355$	−103.310	−	59.6459i	−0.291013	−	0.168017i
$356$			329.799i			0.926403i
$357$	−238.313	−	302.282i	−0.667543	−	0.846728i
$358$	−339.373			−0.947968
$359$	248.793	−	430.922i	0.693017	−	1.20034i	−0.277828	−	0.960631i	$-0.589614\pi$
$359$	248.793	−	430.922i	0.693017	−	1.20034i	0.970845	−	0.239710i	$-0.0770522\pi$
$360$	−16.4317	+	9.48683i	−0.0456435	+	0.0263523i
$361$	303.373	+	525.457i	0.840368	+	1.45556i
$362$	378.841	+	218.724i	1.04652	+	0.604210i
$363$			26.9094i			0.0741305i
$364$	−14.1119	−	97.3096i	−0.0387689	−	0.267334i
$365$	−161.847			−0.443416
$366$	−48.6124	+	84.1991i	−0.132821	+	0.230052i
$367$	120.700	−	69.6861i	0.328882	−	0.189880i	−0.326462	−	0.945210i	$-0.605857\pi$
$367$	120.700	−	69.6861i	0.328882	−	0.189880i	0.655345	+	0.755330i	$0.272523\pi$
$368$	47.3765	+	82.0584i	0.128740	+	0.222985i
$369$	−169.194	−	97.6839i	−0.458519	−	0.264726i
$370$			152.310i			0.411649i
$371$	9.57040	−	1.38790i	0.0257962	−	0.00374098i
$372$	69.8045			0.187647
$373$	−173.760	+	300.961i	−0.465844	+	0.806865i	−0.999239	−	0.0390009i	$-0.987582\pi$
$373$	−173.760	+	300.961i	−0.465844	+	0.806865i	0.533395	+	0.845866i	$0.320916\pi$
$374$	399.315	−	230.544i	1.06769	−	0.616429i
$375$	9.68246	+	16.7705i	0.0258199	+	0.0447214i
$376$	−151.737	−	87.6055i	−0.403556	−	0.232993i
$377$		−	64.5923i		−	0.171332i
$378$	40.3953	−	31.8468i	0.106866	−	0.0842509i
$379$	307.387			0.811048			0.405524	−	0.914084i	$-0.367089\pi$
$379$	307.387			0.811048			0.405524	+	0.914084i	$0.367089\pi$
$380$	69.5610	−	120.483i	0.183055	−	0.317061i
$381$	−192.756	+	111.288i	−0.505921	+	0.292093i
$382$	−2.18468	−	3.78397i	−0.00571905	−	0.00990569i
$383$	−440.572	−	254.364i	−1.15032	−	0.664136i	−0.201353	−	0.979519i	$-0.564534\pi$
$383$	−440.572	−	254.364i	−1.15032	−	0.664136i	−0.948965	+	0.315382i	$0.897867\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−149.302	−	59.5609i	−0.387798	−	0.154704i
$386$	−337.569			−0.874531
$387$	−4.55246	+	7.88509i	−0.0117635	+	0.0203749i
$388$	85.7016	−	49.4799i	0.220880	−	0.127525i
$389$	85.4840	+	148.063i	0.219753	+	0.380624i	0.954732	−	0.297466i	$-0.0961414\pi$
$389$	85.4840	+	148.063i	0.219753	+	0.380624i	−0.734979	+	0.678090i	$0.762808\pi$
$390$	33.3149	+	19.2344i	0.0854228	+	0.0493189i
$391$		−	752.057i		−	1.92342i
$392$	−100.537	−	95.3957i	−0.256472	−	0.243356i
$393$	−130.764			−0.332732
$394$	206.149	−	357.061i	0.523221	−	0.906245i
$395$	206.131	−	119.010i	0.521851	−	0.301291i
$396$	30.8087	+	53.3622i	0.0777997	+	0.134753i
$397$	551.223	+	318.249i	1.38847	+	0.801634i	0.993143	−	0.116906i	$-0.0372975\pi$
$397$	551.223	+	318.249i	1.38847	+	0.801634i	0.395328	+	0.918540i	$0.370631\pi$
$398$			341.661i			0.858446i
$399$	−139.755	+	350.325i	−0.350262	+	0.878006i
$400$	−20.0000			−0.0500000
$401$	296.110	−	512.878i	0.738429	−	1.27900i	−0.214773	−	0.976664i	$-0.568901\pi$
$401$	296.110	−	512.878i	0.738429	−	1.27900i	0.953202	−	0.302333i	$-0.0977654\pi$
$402$	−33.7694	+	19.4968i	−0.0840034	+	0.0484994i
$403$	−70.7636	−	122.566i	−0.175592	−	0.304135i
$404$	−233.606	−	134.873i	−0.578234	−	0.333843i
$405$			20.1246i			0.0496904i
$406$	−56.3661	−	71.4961i	−0.138833	−	0.176099i
$407$	494.630			1.21531
$408$	−77.7667	+	134.696i	−0.190605	+	0.330137i
$409$	−245.717	+	141.865i	−0.600776	+	0.346858i	−0.769347	−	0.638831i	$-0.779418\pi$
$409$	−245.717	+	141.865i	−0.600776	+	0.346858i	0.168571	+	0.985690i	$0.446085\pi$
$410$	−102.968	−	178.346i	−0.251141	−	0.434989i
$411$	161.275	+	93.1121i	0.392396	+	0.226550i
$412$			74.8041i			0.181563i
$413$	−110.328	−	760.778i	−0.267138	−	1.84208i
$414$	100.501			0.242755
$415$	55.2642	−	95.7204i	0.133167	−	0.230652i
$416$	−34.4075	+	19.8652i	−0.0827103	+	0.0477528i
$417$	235.562	+	408.006i	0.564897	+	0.978431i
$418$	−391.271	−	225.901i	−0.936056	−	0.540432i
$419$			482.511i			1.15158i	0.817599	+	0.575789i	$0.195305\pi$
$419$			482.511i			1.15158i	−0.817599	+	0.575789i	$0.804695\pi$
$420$	53.6604	−	7.78185i	0.127763	−	0.0185282i
$421$	762.080			1.81017			0.905083	−	0.425234i	$-0.139808\pi$
$421$	762.080			1.81017			0.905083	+	0.425234i	$0.139808\pi$
$422$	185.982	−	322.130i	0.440716	−	0.763342i
$423$	−160.942	+	92.9197i	−0.380476	+	0.219668i
$424$	−1.95374	−	3.38397i	−0.00460787	−	0.00798107i
$425$	137.473	+	79.3703i	0.323467	+	0.186754i
$426$		−	130.678i		−	0.306755i
$427$	218.190	−	172.017i	0.510984	−	0.402849i
$428$	−49.5920			−0.115869
$429$	62.4640	−	108.191i	0.145604	−	0.252193i
$430$	−8.31161	+	4.79871i	−0.0193293	+	0.0111598i
$431$	−128.008	−	221.717i	−0.297003	−	0.514424i	0.678446	−	0.734650i	$-0.262654\pi$
$431$	−128.008	−	221.717i	−0.297003	−	0.514424i	−0.975449	+	0.220226i	$0.929320\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$			646.579i			1.49325i	0.665243	+	0.746627i	$0.268328\pi$
$433$			646.579i			1.49325i	−0.665243	+	0.746627i	$0.731672\pi$
$434$	−185.284	−	73.9150i	−0.426921	−	0.170311i
$435$	35.6188			0.0818823
$436$	56.2897	−	97.4966i	0.129105	−	0.223616i
$437$	−638.181	+	368.454i	−1.46037	+	0.843144i
$438$	−88.6472	−	153.541i	−0.202391	−	0.350551i
$439$	290.352	+	167.635i	0.661394	+	0.381856i	0.792808	−	0.609472i	$-0.208618\pi$
$439$	290.352	+	167.635i	0.661394	+	0.381856i	−0.131414	+	0.991328i	$0.541952\pi$
$440$			64.9504i			0.147615i
$441$	−140.944	+	41.7578i	−0.319602	+	0.0946888i
$442$	315.341			0.713441
$443$	140.527	−	243.400i	0.317216	−	0.549435i	−0.662690	−	0.748894i	$-0.730585\pi$
$443$	140.527	−	243.400i	0.317216	−	0.549435i	0.979906	+	0.199459i	$0.0639185\pi$
$444$	−144.494	+	83.4237i	−0.325437	+	0.187891i
$445$	184.363	+	319.327i	0.414300	+	0.717589i
$446$	137.977	+	79.6613i	0.309366	+	0.178613i
$447$			144.500i			0.323265i
$448$	−20.7498	+	52.0139i	−0.0463166	+	0.116102i
$449$	47.2320			0.105194			0.0525969	−	0.998616i	$-0.483250\pi$
$449$	47.2320			0.105194			0.0525969	+	0.998616i	$0.483250\pi$
$450$	−10.6066	+	18.3712i	−0.0235702	+	0.0408248i
$451$	−579.181	+	334.390i	−1.28422	+	0.741442i
$452$	−74.9910	−	129.888i	−0.165909	−	0.287363i
$453$	190.192	+	109.807i	0.419850	+	0.242400i
$454$			69.3253i			0.152699i
$455$	−68.0615	−	86.3309i	−0.149586	−	0.189738i
$456$	152.400			0.334212
$457$	−294.396	+	509.909i	−0.644193	+	1.11578i	0.340294	+	0.940319i	$0.389473\pi$
$457$	−294.396	+	509.909i	−0.644193	+	1.11578i	−0.984487	+	0.175456i	$0.943860\pi$
$458$	−34.4327	+	19.8797i	−0.0751805	+	0.0434055i
$459$	82.4840	+	142.866i	0.179704	+	0.311256i
$460$	91.7441	+	52.9685i	0.199444	+	0.115149i
$461$			60.5606i			0.131368i	0.997840	+	0.0656839i	$0.0209229\pi$
$461$			60.5606i			0.131368i	−0.997840	+	0.0656839i	$0.979077\pi$
$462$	−25.2717	−	174.263i	−0.0547007	−	0.377193i
$463$	88.7592			0.191704			0.0958522	−	0.995396i	$-0.469442\pi$
$463$	88.7592			0.191704			0.0958522	+	0.995396i	$0.469442\pi$
$464$	−18.3935	+	31.8584i	−0.0396411	+	0.0686604i
$465$	67.5879	−	39.0219i	0.145350	−	0.0839181i
$466$	−124.594	−	215.803i	−0.267369	−	0.463097i
$467$	261.733	+	151.112i	0.560457	+	0.323580i	0.753329	−	0.657644i	$-0.228447\pi$
$467$	261.733	+	151.112i	0.560457	+	0.323580i	−0.192872	+	0.981224i	$0.561780\pi$
$468$			42.1404i			0.0900436i
$469$	110.280	−	15.9928i	0.235138	−	0.0340997i
$470$	−195.892			−0.416791
$471$	85.9416	−	148.855i	0.182466	−	0.316041i
$472$	−269.002	+	155.308i	−0.569919	+	0.329043i
$473$	15.5839	+	26.9921i	0.0329470	+	0.0570658i
$474$	225.806	+	130.369i	0.476383	+	0.275040i
$475$		−	155.543i		−	0.327459i
$476$	349.045	−	275.180i	0.733288	−	0.578110i
$477$	−4.14451			−0.00868869
$478$	−24.5472	+	42.5170i	−0.0513540	+	0.0889478i
$479$	30.4237	−	17.5651i	0.0635151	−	0.0366704i	−0.467906	−	0.883778i	$-0.654991\pi$
$479$	30.4237	−	17.5651i	0.0635151	−	0.0366704i	0.531421	+	0.847108i	$0.321658\pi$
$480$	−10.9545	−	18.9737i	−0.0228218	−	0.0395285i
$481$	292.959	+	169.140i	0.609062	+	0.351642i
$482$		−	375.378i		−	0.778793i
$483$	−266.761	−	106.419i	−0.552301	−	0.220329i
$484$	−31.0723			−0.0641989
$485$	55.3202	−	95.8173i	0.114062	−	0.197561i
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	−32.3167	−	55.9741i	−0.0663586	−	0.114937i	0.830937	−	0.556366i	$-0.187805\pi$
$487$	−32.3167	−	55.9741i	−0.0663586	−	0.114937i	−0.897296	+	0.441430i	$0.854471\pi$
$488$	−97.2247	−	56.1327i	−0.199231	−	0.115026i
$489$		−	483.207i		−	0.988153i
$490$	−150.672	−	36.1647i	−0.307494	−	0.0738056i
$491$	241.365			0.491578			0.245789	−	0.969323i	$-0.420953\pi$
$491$	241.365			0.491578			0.245789	+	0.969323i	$0.420953\pi$
$492$	112.796	−	195.368i	0.229260	−	0.397089i
$493$	252.861	−	145.989i	0.512903	−	0.296125i
$494$	−154.494	−	267.592i	−0.312742	−	0.541685i
$495$	59.6608	+	34.4452i	0.120527	+	0.0695862i
$496$			80.6033i			0.162507i
$497$	−138.373	+	346.860i	−0.278416	+	0.697908i
$498$	121.078			0.243128
$499$	95.8123	−	165.952i	0.192009	−	0.332569i	−0.753907	−	0.656981i	$-0.771833\pi$
$499$	95.8123	−	165.952i	0.192009	−	0.332569i	0.945916	+	0.324412i	$0.105166\pi$
$500$	−19.3649	+	11.1803i	−0.0387298	+	0.0223607i
$501$	25.9318	+	44.9152i	0.0517601	+	0.0896511i
$502$	29.6049	+	17.0924i	0.0589739	+	0.0340486i
$503$			919.711i			1.82845i	0.405205	+	0.914226i	$0.367200\pi$
$503$			919.711i			1.82845i	−0.405205	+	0.914226i	$0.632800\pi$
$504$	36.7735	+	46.6445i	0.0729634	+	0.0925485i
$505$	−301.585			−0.597197
$506$	172.016	−	297.941i	0.339953	−	0.588816i
$507$	−179.508	+	103.639i	−0.354059	+	0.204416i
$508$	−128.504	−	222.575i	−0.252960	−	0.438140i
$509$	250.976	+	144.901i	0.493076	+	0.284678i	0.725850	−	0.687853i	$-0.241447\pi$
$509$	250.976	+	144.901i	0.493076	+	0.284678i	−0.232773	+	0.972531i	$0.574780\pi$
$510$			173.892i			0.340964i
$511$	72.7154	+	501.416i	0.142300	+	0.981244i
$512$	22.6274			0.0441942
$513$	80.8225	−	139.989i	0.157549	−	0.272883i
$514$	11.6810	−	6.74401i	0.0227256	−	0.0131206i
$515$	41.8168	+	72.4288i	0.0811976	+	0.140638i
$516$	−9.10492	−	5.25673i	−0.0176452	−	0.0101875i
$517$			636.163i			1.23049i
$518$	471.870	−	68.4307i	0.910946	−	0.132106i
$519$	−184.474			−0.355441
$520$	−22.2099	+	38.4687i	−0.0427114	+	0.0739783i
$521$	−653.176	+	377.112i	−1.25370	+	0.723823i	−0.971842	−	0.235634i	$-0.924283\pi$
$521$	−653.176	+	377.112i	−1.25370	+	0.723823i	−0.281856	+	0.959457i	$0.590950\pi$
$522$	19.5092	+	33.7909i	0.0373740	+	0.0647336i
$523$	65.5821	+	37.8638i	0.125396	+	0.0723974i	0.561386	−	0.827554i	$-0.310268\pi$
$523$	65.5821	+	37.8638i	0.125396	+	0.0723974i	−0.435990	+	0.899952i	$0.643602\pi$
$524$		−	150.993i		−	0.288154i
$525$	47.6063	−	37.5318i	0.0906787	−	0.0714892i
$526$	−186.483			−0.354530
$527$	319.875	−	554.040i	0.606974	−	1.05131i
$528$	−61.6174	+	35.5748i	−0.116700	+	0.0673765i
$529$	−16.0662	−	27.8275i	−0.0303709	−	0.0526039i
$530$	−3.78340	−	2.18435i	−0.00713849	−	0.00412141i
$531$			329.458i			0.620449i
$532$	−404.520	−	161.375i	−0.760376	−	0.303336i
$533$	−457.382			−0.858128
$534$	−201.960	+	349.805i	−0.378202	+	0.655066i
$535$	−48.0172	+	27.7228i	−0.0897518	+	0.0518182i
$536$	−22.5129	−	38.9935i	−0.0420017	−	0.0727491i
$537$	−359.959	−	207.822i	−0.670315	−	0.387007i
$538$		−	53.5689i		−	0.0995705i
$539$	−117.446	+	489.311i	−0.217895	+	0.907813i
$540$	−23.2379			−0.0430331
$541$	−493.177	+	854.207i	−0.911602	+	1.57894i	−0.0998002	+	0.995007i	$0.531820\pi$
$541$	−493.177	+	854.207i	−0.911602	+	1.57894i	−0.811802	+	0.583933i	$0.801513\pi$
$542$	−443.782	+	256.217i	−0.818785	+	0.472726i
$543$	267.881	+	463.984i	0.493335	+	0.854482i
$544$	−155.533	−	89.7972i	−0.285907	−	0.165068i
$545$		−	125.868i		−	0.230950i
$546$	44.6218	−	111.854i	0.0817250	−	0.204861i
$547$	346.700			0.633820			0.316910	−	0.948456i	$-0.397355\pi$
$547$	346.700			0.633820			0.316910	+	0.948456i	$0.397355\pi$
$548$	−107.517	+	186.224i	−0.196198	+	0.339825i
$549$	−103.122	+	59.5377i	−0.187837	+	0.108448i
$550$	36.3084	+	62.8880i	0.0660152	+	0.114342i
$551$	−247.768	−	143.049i	−0.449669	−	0.259617i
$552$			116.048i			0.210232i
$553$	−461.315	−	585.143i	−0.834204	−	1.05813i
$554$	−160.229			−0.289222
$555$	−93.2705	+	161.549i	−0.168055	+	0.291080i
$556$	−471.124	+	272.004i	−0.847346	+	0.489215i
$557$	76.7246	+	132.891i	0.137746	+	0.238583i	0.926643	−	0.375942i	$-0.122681\pi$
$557$	76.7246	+	132.891i	0.137746	+	0.238583i	−0.788897	+	0.614525i	$0.789348\pi$
$558$	74.0389	+	42.7464i	0.132686	+	0.0766064i
$559$			21.3158i			0.0381320i
$560$	8.98571	+	61.9617i	0.0160459	+	0.110646i
$561$	564.716			1.00662
$562$	126.385	−	218.905i	0.224884	−	0.389511i
$563$	150.809	−	87.0695i	0.267866	−	0.154653i	−0.360051	−	0.932933i	$-0.617241\pi$
$563$	150.809	−	87.0695i	0.267866	−	0.154653i	0.627918	+	0.778280i	$0.283907\pi$
$564$	−107.294	−	185.839i	−0.190238	−	0.329502i
$565$	−145.219	−	83.8424i	−0.257025	−	0.148394i
$566$			61.0495i			0.107861i
$567$	62.3478	−	9.04169i	0.109961	−	0.0159465i
$568$	150.893			0.265658
$569$	109.591	−	189.817i	0.192603	−	0.333597i	−0.753509	−	0.657437i	$-0.771641\pi$
$569$	109.591	−	189.817i	0.192603	−	0.333597i	0.946112	+	0.323840i	$0.104974\pi$
$570$	147.561	−	85.1944i	0.258879	−	0.149464i
$571$	−478.914	−	829.504i	−0.838729	−	1.45272i	−0.890958	−	0.454087i	$-0.849966\pi$
$571$	−478.914	−	829.504i	−0.838729	−	1.45272i	0.0522282	−	0.998635i	$-0.483368\pi$
$572$	124.928	+	72.1272i	0.218406	+	0.126097i
$573$		−	5.35135i		−	0.00933917i
$574$	−506.268	+	399.132i	−0.882001	+	0.695351i
$575$	118.441			0.205985
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−898.838	+	518.944i	−1.55778	+	0.899384i	−0.560309	+	0.828284i	$0.689318\pi$
$577$	−898.838	+	518.944i	−1.55778	+	0.899384i	−0.997469	+	0.0710997i	$0.977349\pi$
$578$	508.369	+	880.521i	0.879531	+	1.52339i
$579$	−358.046	−	206.718i	−0.618387	−	0.357026i
$580$			41.1290i			0.0709121i
$581$	−321.380	−	128.208i	−0.553149	−	0.220667i
$582$	121.200			0.208248
$583$	−7.09371	+	12.2867i	−0.0121676	+	0.0210749i
$584$	177.294	−	102.361i	0.303586	−	0.175276i
$585$	23.5572	+	40.8023i	0.0402687	+	0.0697474i
$586$	18.9132	+	10.9195i	0.0322751	+	0.0186340i
$587$		−	819.162i		−	1.39551i	−0.716339	−	0.697753i	$-0.754183\pi$
$587$		−	819.162i		−	1.39551i	0.716339	−	0.697753i	$-0.245817\pi$
$588$	−48.2177	−	162.748i	−0.0820029	−	0.276783i
$589$	−626.864			−1.06429
$590$	−173.640	+	300.753i	−0.294305	+	0.509751i
$591$	437.308	−	252.480i	0.739946	−	0.427208i
$592$	−96.3294	−	166.847i	−0.162719	−	0.281837i
$593$	461.919	+	266.689i	0.778953	+	0.449729i	0.836059	−	0.548639i	$-0.184854\pi$
$593$	461.919	+	266.689i	0.778953	+	0.449729i	−0.0571059	+	0.998368i	$0.518187\pi$
$594$			75.4655i			0.127046i
$595$	184.131	−	461.564i	0.309464	−	0.775738i
$596$	−166.854			−0.279956
$597$	−209.224	+	362.387i	−0.350459	+	0.607013i
$598$	203.763	−	117.643i	0.340741	−	0.196727i
$599$	171.452	+	296.963i	0.286230	+	0.495765i	0.972907	−	0.231198i	$-0.0742646\pi$
$599$	171.452	+	296.963i	0.286230	+	0.495765i	−0.686677	+	0.726963i	$0.740931\pi$
$600$	−21.2132	−	12.2474i	−0.0353553	−	0.0204124i
$601$			418.941i			0.697073i	0.937295	+	0.348536i	$0.113321\pi$
$601$			418.941i			0.697073i	−0.937295	+	0.348536i	$0.886679\pi$
$602$	18.6011	+	23.5941i	0.0308989	+	0.0391929i
$603$	−47.7571			−0.0791992
$604$	−126.795	+	219.615i	−0.209925	+	0.363601i
$605$	−30.0856	+	17.3699i	−0.0497282	+	0.0287106i
$606$	−165.185	−	286.108i	−0.272582	−	0.472126i
$607$	122.608	+	70.7875i	0.201989	+	0.116619i	0.597583	−	0.801807i	$-0.296128\pi$
$607$	122.608	+	70.7875i	0.201989	+	0.116619i	−0.395594	+	0.918426i	$0.629461\pi$
$608$			175.977i			0.289436i
$609$	−16.0030	−	110.350i	−0.0262775	−	0.181199i
$610$	−125.517			−0.205765
$611$	−217.537	+	376.786i	−0.356035	+	0.616670i
$612$	−164.968	+	95.2443i	−0.269556	+	0.155628i
$613$	148.520	+	257.244i	0.242284	+	0.419647i	0.961364	−	0.275279i	$-0.0887703\pi$
$613$	148.520	+	257.244i	0.242284	+	0.419647i	−0.719081	+	0.694926i	$0.755437\pi$
$614$	−287.384	−	165.921i	−0.468053	−	0.270230i
$615$		−	252.219i		−	0.410112i
$616$	201.222	−	29.1813i	0.326659	−	0.0473722i
$617$	−674.329			−1.09292			−0.546458	−	0.837486i	$-0.684024\pi$
$617$	−674.329			−1.09292			−0.546458	+	0.837486i	$0.684024\pi$
$618$	−45.8080	+	79.3418i	−0.0741230	+	0.128385i
$619$	−833.055	+	480.965i	−1.34581	+	0.777003i	−0.987653	−	0.156659i	$-0.949928\pi$
$619$	−833.055	+	480.965i	−1.34581	+	0.777003i	−0.358156	+	0.933662i	$0.616594\pi$
$620$	45.0586	+	78.0438i	0.0726752	+	0.125877i
$621$	106.597	+	61.5438i	0.171654	+	0.0991044i
$622$		−	563.957i		−	0.906683i
$623$	906.471	−	714.643i	1.45501	−	1.14710i
$624$	−48.6595			−0.0779800
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−158.238	+	91.3585i	−0.252776	+	0.145940i
$627$	−276.671	−	479.208i	−0.441261	−	0.764287i
$628$	171.883	+	99.2368i	0.273699	+	0.158020i
$629$			1529.14i			2.43106i
$630$	61.6809	+	24.6063i	0.0979062	+	0.0390576i
$631$	1185.17			1.87824			0.939122	−	0.343584i	$-0.111641\pi$
$631$	1185.17			1.87824			0.939122	+	0.343584i	$0.111641\pi$
$632$	−150.537	+	260.738i	−0.238191	+	0.412560i
$633$	394.527	−	227.781i	0.623266	−	0.359843i
$634$	284.657	+	493.040i	0.448985	+	0.777666i
$635$	−248.847	−	143.672i	−0.391884	−	0.226255i
$636$		−	4.78566i		−	0.00752463i
$637$	−236.882	+	249.648i	−0.371871	+	0.391912i
$638$	133.567			0.209353
$639$	80.0234	−	138.605i	0.125232	−	0.216908i
$640$	21.9089	−	12.6491i	0.0342327	−	0.0197642i
$641$	−203.549	−	352.557i	−0.317549	−	0.550011i	0.662427	−	0.749126i	$-0.269526\pi$
$641$	−203.549	−	352.557i	−0.317549	−	0.550011i	−0.979976	+	0.199115i	$0.936193\pi$
$642$	−52.6002	−	30.3688i	−0.0819318	−	0.0473034i
$643$		−	1077.83i		−	1.67626i	−0.545474	−	0.838128i	$-0.683650\pi$
$643$		−	1077.83i		−	1.67626i	0.545474	−	0.838128i	$-0.316350\pi$
$644$	122.882	−	308.029i	0.190810	−	0.478306i
$645$	−11.7544			−0.0182239
$646$	698.367	−	1209.61i	1.08106	−	1.87246i
$647$	1019.05	−	588.349i	1.57504	−	0.909350i	0.579504	−	0.814969i	$-0.303246\pi$
$647$	1019.05	−	588.349i	1.57504	−	0.909350i	0.995536	−	0.0943805i	$-0.0300870\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	976.701	+	563.899i	1.50493	+	0.868873i
$650$			49.6629i			0.0764045i
$651$	−151.260	−	191.861i	−0.232349	−	0.294718i
$652$	557.959			0.855765
$653$	439.563	−	761.345i	0.673144	−	1.16592i	−0.303864	−	0.952715i	$-0.598277\pi$
$653$	439.563	−	761.345i	0.673144	−	1.16592i	0.977008	−	0.213204i	$-0.0683898\pi$
$654$	119.408	−	68.9405i	0.182582	−	0.105414i
$655$	−84.4076	−	146.198i	−0.128867	−	0.223203i
$656$	225.591	+	130.245i	0.343889	+	0.198545i
$657$		−	217.140i		−	0.330503i
$658$	88.0113	+	606.890i	0.133756	+	0.922325i
$659$	65.1550			0.0988696			0.0494348	−	0.998777i	$-0.484258\pi$
$659$	65.1550			0.0988696			0.0494348	+	0.998777i	$0.484258\pi$
$660$	−39.7738	+	68.8903i	−0.0602634	+	0.104379i
$661$	22.0376	−	12.7234i	0.0333397	−	0.0192487i	−0.483237	−	0.875489i	$-0.660539\pi$
$661$	22.0376	−	12.7234i	0.0333397	−	0.0192487i	0.516577	+	0.856241i	$0.327206\pi$
$662$	118.011	+	204.401i	0.178264	+	0.308762i
$663$	334.469	+	193.106i	0.504479	+	0.291261i
$664$			139.809i			0.210555i
$665$	−481.886	+	69.8832i	−0.724641	+	0.105088i
$666$	−204.345			−0.306825
$667$	108.927	−	188.667i	0.163309	−	0.282860i
$668$	−51.8636	+	29.9435i	−0.0776401	+	0.0448256i
$669$	97.5647	+	168.987i	0.145837	+	0.252597i
$670$	−43.5961	−	25.1702i	−0.0650688	−	0.0375675i
$671$			407.618i			0.607478i
$672$	−53.8604	+	42.4624i	−0.0801494	+	0.0631881i
$673$	23.1893			0.0344566			0.0172283	−	0.999852i	$-0.494516\pi$
$673$	23.1893			0.0344566			0.0172283	+	0.999852i	$0.494516\pi$
$674$	382.822	−	663.068i	0.567986	−	0.983780i
$675$	−22.5000	+	12.9904i	−0.0333333	+	0.0192450i
$676$	−119.672	−	207.278i	−0.177029	−	0.306624i
$677$	−123.090	−	71.0658i	−0.181816	−	0.104972i	0.406330	−	0.913727i	$-0.366809\pi$
$677$	−123.090	−	71.0658i	−0.181816	−	0.104972i	−0.588146	+	0.808755i	$0.700142\pi$
$678$		−	183.690i		−	0.270929i
$679$	−321.705	−	128.337i	−0.473792	−	0.189009i
$680$	−200.793			−0.295283
$681$	−42.4529	+	73.5306i	−0.0623391	+	0.107974i
$682$	253.449	−	146.329i	0.371626	−	0.214558i
$683$	−328.352	−	568.722i	−0.480749	−	0.832682i	0.519007	−	0.854770i	$-0.326302\pi$
$683$	−328.352	−	568.722i	−0.480749	−	0.832682i	−0.999756	+	0.0220879i	$0.992969\pi$
$684$	161.645	+	93.3258i	0.236323	+	0.136441i
$685$			240.414i			0.350970i
$686$	−44.3466	+	483.044i	−0.0646452	+	0.704146i
$687$	−48.6951			−0.0708808
$688$	6.06994	−	10.5135i	0.00882259	−	0.0152812i
$689$	−8.40290	+	4.85142i	−0.0121958	+	0.00704125i
$690$	64.8729	+	112.363i	0.0940187	+	0.162845i
$691$	212.350	+	122.600i	0.307308	+	0.177425i	0.645721	−	0.763573i	$-0.276557\pi$
$691$	212.350	+	122.600i	0.307308	+	0.177425i	−0.338413	+	0.940998i	$0.609890\pi$
$692$		−	213.012i		−	0.307821i
$693$	79.9094	−	200.310i	0.115309	−	0.289047i
$694$	606.250			0.873560
$695$	−304.109	+	526.733i	−0.437567	+	0.757889i
$696$	−39.0184	+	22.5273i	−0.0560610	+	0.0323668i
$697$	−1033.76	−	1790.52i	−1.48316	−	2.56890i
$698$	91.4702	+	52.8104i	0.131046	+	0.0756595i
$699$		−	305.192i		−	0.436612i
$700$	43.3380	+	54.9710i	0.0619115	+	0.0785300i
$701$	379.419			0.541254			0.270627	−	0.962684i	$-0.412769\pi$
$701$	379.419			0.541254			0.270627	+	0.962684i	$0.412769\pi$
$702$	−25.8056	+	44.6966i	−0.0367601	+	0.0636704i
$703$	1297.60	−	749.168i	1.84580	−	1.06567i
$704$	−41.0782	−	71.1496i	−0.0583498	−	0.101065i
$705$	−207.775	−	119.959i	−0.294716	−	0.170154i
$706$			517.479i			0.732973i
$707$	135.498	+	934.335i	0.191651	+	1.32155i
$708$	−380.426			−0.537324
$709$	442.054	−	765.661i	0.623490	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$709$	442.054	−	765.661i	0.623490	−	1.07992i	0.988831	−	0.149042i	$-0.0476191\pi$
$710$	146.102	−	84.3520i	0.205777	−	0.118806i
$711$	159.669	+	276.554i	0.224569	+	0.388965i
$712$	−403.920	−	233.203i	−0.567304	−	0.327533i
$713$		−	477.337i		−	0.669477i
$714$	538.731	−	78.1269i	0.754525	−	0.109421i
$715$	161.281			0.225568
$716$	239.973	−	415.645i	0.335157	−	0.580510i
$717$	−52.0725	+	30.0641i	−0.0726255	+	0.0419304i
$718$	351.847	+	609.416i	0.490037	+	0.848769i
$719$	−825.831	−	476.794i	−1.14858	−	0.663135i	−0.200042	−	0.979787i	$-0.564108\pi$
$719$	−825.831	−	476.794i	−1.14858	−	0.663135i	−0.948542	+	0.316653i	$0.897441\pi$
$720$		−	26.8328i		−	0.0372678i
$721$	205.603	−	162.093i	0.285164	−	0.224817i
$722$	−858.068			−1.18846
$723$	229.871	−	398.149i	0.317941	−	0.550690i
$724$	−535.762	+	309.322i	−0.740003	+	0.427241i
$725$	22.9918	+	39.8230i	0.0317129	+	0.0549283i
$726$	−32.9571	−	19.0278i	−0.0453955	−	0.0262091i
$727$		−	1110.82i		−	1.52795i	−0.645248	−	0.763974i	$-0.723246\pi$
$727$		−	1110.82i		−	1.52795i	0.645248	−	0.763974i	$-0.276754\pi$
$728$	129.158	+	51.5249i	0.177415	+	0.0707759i
$729$	−27.0000			−0.0370370
$730$	114.443	−	198.221i	0.156771	−	0.271536i
$731$	−83.4455	+	48.1773i	−0.114153	+	0.0659060i
$732$	−68.7483	−	119.075i	−0.0939184	−	0.162671i
$733$	35.2595	+	20.3571i	0.0481029	+	0.0277722i	0.523859	−	0.851805i	$-0.324492\pi$
$733$	35.2595	+	20.3571i	0.0481029	+	0.0277722i	−0.475756	+	0.879577i	$0.657825\pi$
$734$			197.102i			0.268531i
$735$	−137.666	−	130.626i	−0.187300	−	0.177722i
$736$	−134.001			−0.182066
$737$	−81.7407	+	141.579i	−0.110910	+	0.192102i
$738$	239.276	−	138.146i	0.324222	−	0.187190i
$739$	−422.735	−	732.199i	−0.572037	−	0.990797i	−0.996357	−	0.0852847i	$-0.972820\pi$
$739$	−422.735	−	732.199i	−0.572037	−	0.990797i	0.424320	−	0.905512i	$-0.360513\pi$
$740$	−186.541	−	107.699i	−0.252082	−	0.145540i
$741$		−	378.433i		−	0.510705i
$742$	−5.06747	+	12.7027i	−0.00682947	+	0.0171195i
$743$	355.319			0.478222			0.239111	−	0.970992i	$-0.423144\pi$
$743$	355.319			0.478222			0.239111	+	0.970992i	$0.423144\pi$
$744$	−49.3592	+	85.4927i	−0.0663431	+	0.114910i
$745$	−161.556	+	93.2741i	−0.216853	+	0.125200i
$746$	−245.733	−	425.623i	−0.329401	−	0.570540i
$747$	128.422	+	74.1447i	0.171918	+	0.0992567i
$748$			652.078i			0.871762i
$749$	107.461	+	136.306i	0.143473	+	0.181984i
$750$	−27.3861			−0.0365148
$751$	−108.768	+	188.392i	−0.144831	+	0.250855i	−0.929310	−	0.369300i	$-0.879597\pi$
$751$	−108.768	+	188.392i	−0.144831	+	0.250855i	0.784479	+	0.620156i	$0.212931\pi$
$752$	214.589	−	123.893i	0.285357	−	0.164751i
$753$	20.9338	+	36.2584i	0.0278006	+	0.0481520i
$754$	79.1091	+	45.6737i	0.104919	+	0.0605751i
$755$			283.521i			0.375525i
$756$	10.4404	+	71.9930i	0.0138101	+	0.0952289i
$757$	1178.25			1.55647			0.778233	−	0.627975i	$-0.216116\pi$
$757$	1178.25			1.55647			0.778233	+	0.627975i	$0.216116\pi$
$758$	−217.356	+	376.471i	−0.286749	+	0.496663i
$759$	364.902	−	210.676i	0.480766	−	0.277571i
$760$	98.3741	+	170.389i	0.129440	+	0.224196i
$761$	711.636	+	410.863i	0.935133	+	0.539899i	0.888431	−	0.459010i	$-0.151796\pi$
$761$	711.636	+	410.863i	0.935133	+	0.539899i	0.0467017	+	0.998909i	$0.485129\pi$
$762$		−	314.769i		−	0.413082i
$763$	−389.948	+	56.5504i	−0.511073	+	0.0741159i
$764$	6.17920			0.00808796
$765$	−106.486	+	184.440i	−0.139198	+	0.241098i
$766$	623.063	−	359.725i	0.813398	−	0.469615i
$767$	385.653	+	667.970i	0.502807	+	0.870887i
$768$	24.0000	+	13.8564i	0.0312500	+	0.0180422i
$769$			230.888i			0.300244i	0.988667	+	0.150122i	$0.0479667\pi$
$769$			230.888i			0.300244i	−0.988667	+	0.150122i	$0.952033\pi$
$770$	178.520	−	140.741i	0.231844	−	0.182781i
$771$	16.5194			0.0214259
$772$	238.697	−	413.436i	0.309193	−	0.535539i
$773$	584.107	−	337.234i	0.755636	−	0.436267i	−0.0720908	−	0.997398i	$-0.522967\pi$
$773$	584.107	−	337.234i	0.755636	−	0.436267i	0.827727	+	0.561131i	$0.189634\pi$
$774$	−6.43815	−	11.1512i	−0.00831802	−	0.0144072i
$775$	87.2556	+	50.3771i	0.112588	+	0.0650027i
$776$			139.950i			0.180348i
$777$	542.399	+	216.378i	0.698068	+	0.278479i
$778$	−241.785			−0.310778
$779$	−1012.94	+	1754.46i	−1.30030	+	2.25219i
$780$	−47.1144	+	27.2015i	−0.0604031	+	0.0348737i
$781$	−273.935	−	474.469i	−0.350749	−	0.607515i
$782$	921.077	+	531.784i	1.17785	+	0.680031i
$783$			47.7876i			0.0610314i
$784$	187.926	−	55.6770i	0.239701	−	0.0710166i
$785$	221.900			0.282676
$786$	92.4639	−	160.152i	0.117639	−	0.203756i
$787$	539.438	−	311.445i	0.685436	−	0.395737i	−0.116464	−	0.993195i	$-0.537156\pi$
$787$	539.438	−	311.445i	0.685436	−	0.395737i	0.801900	+	0.597458i	$0.203823\pi$
$788$	291.539	+	504.960i	0.369973	+	0.640812i
$789$	−197.795	−	114.197i	−0.250691	−	0.144736i
$790$			336.611i			0.426090i
$791$	−194.506	+	487.571i	−0.245899	+	0.616399i
$792$	−87.1401			−0.110025
$793$	−139.386	+	241.423i	−0.175770	+	0.304443i
$794$	−779.547	+	450.072i	−0.981797	+	0.566841i
$795$	−2.67527	−	4.63370i	−0.00336512	−	0.00582855i
$796$	−418.448	−	241.591i	−0.525688	−	0.303506i
$797$			1322.28i			1.65907i	0.558452	+	0.829537i	$0.311396\pi$
$797$			1322.28i			1.65907i	−0.558452	+	0.829537i	$0.688604\pi$
$798$	−330.237	−	418.881i	−0.413831	−	0.524913i
$799$	−1966.68			−2.46143
$800$	14.1421	−	24.4949i	0.0176777	−	0.0306186i
$801$	−428.422	+	247.350i	−0.534859	+	0.308801i
$802$	418.763	+	725.319i	0.522148	+	0.904387i
$803$	−643.727	−	371.656i	−0.801653	−	0.462834i
$804$		−	55.1451i		−	0.0685885i
$805$	−53.2139	−	366.941i	−0.0661042	−	0.455827i
$806$	200.150			0.248325
$807$	32.8041	−	56.8185i	0.0406495	−	0.0704070i
$808$	330.369	−	190.739i	0.408873	−	0.236063i
$809$	−521.105	−	902.581i	−0.644135	−	1.11567i	−0.984501	−	0.175381i	$-0.943884\pi$
$809$	−521.105	−	902.581i	−0.644135	−	1.11567i	0.340366	−	0.940293i	$-0.389449\pi$
$810$	−24.6475	−	14.2302i	−0.0304290	−	0.0175682i
$811$		−	782.292i		−	0.964602i	−0.876006	−	0.482301i	$-0.839801\pi$
$811$		−	782.292i		−	0.964602i	0.876006	−	0.482301i	$-0.160199\pi$
$812$	127.421	−	18.4787i	0.156923	−	0.0227570i
$813$	−627.602			−0.771958
$814$	−349.756	+	605.796i	−0.429676	+	0.744221i
$815$	540.242	−	311.909i	0.662873	−	0.382710i
$816$	−109.979	−	190.489i	−0.134778	−	0.233442i
$817$	81.7647	+	47.2069i	0.100079	+	0.0577808i
$818$		−	401.255i		−	0.490532i
$819$	115.825	−	91.3141i	0.141423	−	0.111495i
$820$	291.237			0.355167
$821$	505.805	−	876.080i	0.616084	−	1.06709i	−0.374109	−	0.927385i	$-0.622051\pi$
$821$	505.805	−	876.080i	0.616084	−	1.06709i	0.990193	−	0.139704i	$-0.0446153\pi$
$822$	−228.077	+	131.680i	−0.277466	+	0.160195i
$823$	557.204	+	965.106i	0.677040	+	1.17267i	0.975868	+	0.218361i	$0.0700711\pi$
$823$	557.204	+	965.106i	0.677040	+	1.17267i	−0.298828	+	0.954307i	$0.596596\pi$
$824$	−91.6160	−	52.8945i	−0.111184	−	0.0641924i
$825$			88.9370i			0.107802i
$826$	1009.77	+	402.827i	1.22249	+	0.487684i
$827$	−1267.52			−1.53267			−0.766336	−	0.642440i	$-0.777922\pi$
$827$	−1267.52			−1.53267			−0.766336	+	0.642440i	$0.777922\pi$
$828$	−71.0647	+	123.088i	−0.0858269	+	0.148657i
$829$	−180.535	+	104.232i	−0.217775	+	0.125732i	−0.604919	−	0.796287i	$-0.706795\pi$
$829$	−180.535	+	104.232i	−0.217775	+	0.125732i	0.387145	+	0.922019i	$0.373461\pi$
$830$	78.1554	+	135.369i	0.0941632	+	0.163095i
$831$	−169.948	−	98.1197i	−0.204511	−	0.118074i
$832$		−	56.1872i		−	0.0675327i
$833$	−1512.69	−	363.081i	−1.81596	−	0.435871i
$834$	−666.270			−0.798885
$835$	−33.4778	+	57.9853i	−0.0400932	+	0.0694435i
$836$	553.341	−	319.472i	0.661892	−	0.382143i
$837$	52.3534	+	90.6787i	0.0625488	+	0.108338i
$838$	−590.953	−	341.187i	−0.705194	−	0.407144i
$839$		−	389.239i		−	0.463932i	−0.972724	−	0.231966i	$-0.925484\pi$
$839$		−	389.239i		−	0.463932i	0.972724	−	0.231966i	$-0.0745159\pi$
$840$	−28.4129	+	71.2229i	−0.0338249	+	0.0847892i
$841$	−756.420			−0.899429
$842$	−538.872	+	933.354i	−0.639991	+	1.10850i
$843$	268.103	−	154.789i	0.318034	−	0.183617i
$844$	263.018	+	455.561i	0.311633	+	0.539764i
$845$	−231.744	−	133.797i	−0.274253	−	0.158340i
$846$		−	262.816i		−	0.310658i
$847$	67.3305	+	85.4037i	0.0794930	+	0.100831i
$848$	5.52601			0.00651652
$849$	−37.3850	+	64.7528i	−0.0440342	+	0.0762695i
$850$	−194.417	+	112.247i	−0.228725	+	0.132055i
$851$	570.468	+	988.080i	0.670350	+	1.16108i
$852$	160.047	+	92.4030i	0.187848	+	0.108454i
$853$		−	1239.21i		−	1.45277i	−0.687287	−	0.726386i	$-0.741199\pi$
$853$		−	1239.21i		−	1.45277i	0.687287	−	0.726386i	$-0.258801\pi$
$854$	56.3928	+	388.861i	0.0660337	+	0.455341i
$855$	208.683			0.244074
$856$	35.0668	−	60.7375i	0.0409659	−	0.0709550i
$857$	157.848	−	91.1334i	0.184186	−	0.106340i	−0.405072	−	0.914285i	$-0.632753\pi$
$857$	157.848	−	91.1334i	0.184186	−	0.106340i	0.589258	+	0.807945i	$0.299420\pi$
$858$	88.3374	+	153.005i	0.102957	+	0.178327i
$859$	−366.992	−	211.883i	−0.427232	−	0.246662i	0.270935	−	0.962598i	$-0.412667\pi$
$859$	−366.992	−	211.883i	−0.427232	−	0.246662i	−0.698167	+	0.715935i	$0.746001\pi$
$860$		−	13.5728i		−	0.0157823i
$861$	−781.396	+	113.318i	−0.907544	+	0.131612i
$862$	362.062			0.420026
$863$	8.63152	−	14.9502i	0.0100018	−	0.0173236i	−0.860981	−	0.508637i	$-0.830150\pi$
$863$	8.63152	−	14.9502i	0.0100018	−	0.0173236i	0.870983	+	0.491313i	$0.163483\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$	−119.077	−	206.248i	−0.137662	−	0.238437i
$866$	−791.895	−	457.201i	−0.914428	−	0.527945i
$867$			1245.24i			1.43627i
$868$	221.542	−	174.659i	0.255233	−	0.201221i
$869$	1093.15			1.25794
$870$	−25.1863	+	43.6239i	−0.0289498	+	0.0501424i
$871$	−96.8266	+	55.9028i	−0.111167	+	0.0641824i
$872$	79.6056	+	137.881i	0.0912908	+	0.158120i
$873$	128.552	+	74.2198i	0.147254	+	0.0850169i
$874$		−	1042.15i		−	1.19239i
$875$	72.6916	+	28.9988i	0.0830761	+	0.0331415i
$876$	250.732			0.286224
$877$	183.668	−	318.122i	0.209428	−	0.362739i	−0.742107	−	0.670282i	$-0.766173\pi$
$877$	183.668	−	318.122i	0.209428	−	0.362739i	0.951534	+	0.307542i	$0.0995066\pi$
$878$	−410.620	+	237.071i	−0.467676	+	0.270013i
$879$	13.3737	+	23.1638i	0.0152146	+	0.0263525i
$880$	−79.5477	−	45.9269i	−0.0903951	−	0.0521896i
$881$		−	376.890i		−	0.427798i	−0.976856	−	0.213899i	$-0.931384\pi$
$881$		−	376.890i		−	0.427798i	0.976856	−	0.213899i	$-0.0686164\pi$
$882$	48.5201	−	202.148i	0.0550114	−	0.229193i
$883$	−1101.06			−1.24695			−0.623476	−	0.781842i	$-0.714280\pi$
$883$	−1101.06			−1.24695			−0.623476	+	0.781842i	$0.714280\pi$
$884$	−222.980	+	386.212i	−0.252239	+	0.436891i
$885$	−368.346	+	212.664i	−0.416210	+	0.240299i
$886$	198.735	+	344.219i	0.224306	+	0.388509i
$887$	−105.113	−	60.6873i	−0.118504	−	0.0684186i	0.439576	−	0.898205i	$-0.355129\pi$
$887$	−105.113	−	60.6873i	−0.118504	−	0.0684186i	−0.558081	+	0.829787i	$0.688462\pi$
$888$		−	235.958i		−	0.265718i
$889$	−333.304	+	835.498i	−0.374920	+	0.939818i
$890$	−521.459			−0.585909
$891$	−46.2130	+	80.0433i	−0.0518665	+	0.0898354i
$892$	−195.129	+	112.658i	−0.218755	+	0.126298i
$893$	963.534	+	1668.89i	1.07899	+	1.86886i
$894$	−176.975	−	102.177i	−0.197959	−	0.114292i
$895$		−	536.595i		−	0.599548i
$896$	−49.0314	−	62.1926i	−0.0547225	−	0.0694114i
$897$	288.165			0.321254
$898$	−33.3981	+	57.8472i	−0.0371916	+	0.0644178i
$899$	160.493	−	92.6609i	0.178524	−	0.103071i
$900$	−15.0000	−	25.9808i	−0.0166667	−	0.0288675i
$901$	−37.9839	−	21.9300i	−0.0421575	−	0.0243397i
$902$		−	945.799i		−	1.04856i
$903$	5.28108	+	36.4161i	0.00584837	+	0.0403279i
$904$	212.106			0.234631
$905$	−345.833	+	599.000i	−0.382136	+	0.661879i
$906$	−268.972	+	155.291i	−0.296879	+	0.171403i
$907$	−39.0554	−	67.6459i	−0.0430599	−	0.0745820i	0.843692	−	0.536827i	$-0.180377\pi$
$907$	−39.0554	−	67.6459i	−0.0430599	−	0.0745820i	−0.886752	+	0.462245i	$0.847044\pi$
$908$	−84.9058	−	49.0204i	−0.0935086	−	0.0539872i
$909$		−	404.618i		−	0.445124i
$910$	153.860	−	22.3128i	0.169077	−	0.0245196i
$911$	863.281			0.947619			0.473809	−	0.880627i	$-0.342879\pi$
$911$	863.281			0.947619			0.473809	+	0.880627i	$0.342879\pi$
$912$	−107.763	+	186.652i	−0.118162	+	0.204662i
$913$	439.614	−	253.811i	0.481505	−	0.277997i
$914$	−416.339	−	721.121i	−0.455513	−	0.788973i
$915$	−133.130	−	76.8629i	−0.145498	−	0.0840032i
$916$		−	56.2283i		−	0.0613846i
$917$	−415.012	+	327.187i	−0.452575	+	0.356801i
$918$	−233.300			−0.254139
$919$	−678.926	+	1175.93i	−0.738766	+	1.27958i	0.214285	+	0.976771i	$0.431258\pi$
$919$	−678.926	+	1175.93i	−0.738766	+	1.27958i	−0.953051	+	0.302810i	$0.902075\pi$
$920$	−129.746	+	74.9088i	−0.141028	+	0.0814226i
$921$	−203.211	−	351.973i	−0.220642	−	0.382163i
$922$	−74.1712	−	42.8228i	−0.0804460	−	0.0464455i
$923$		−	374.691i		−	0.405949i
$924$	231.298	+	92.2714i	0.250322	+	0.0998608i
$925$	−240.823			−0.260350
$926$	−62.7622	+	108.707i	−0.0677778	+	0.117395i
$927$	−97.1734	+	56.1031i	−0.104826	+	0.0605211i
$928$	−26.0123	−	45.0546i	−0.0280305	−	0.0485502i
$929$	800.920	+	462.411i	0.862131	+	0.497752i	0.864725	−	0.502245i	$-0.167492\pi$
$929$	800.920	+	462.411i	0.862131	+	0.497752i	−0.00259410	+	0.999997i	$0.500826\pi$
$930$			110.371i			0.118678i
$931$	433.009	+	1461.53i	0.465101	+	1.56985i
$932$	352.405			0.378117
$933$	345.352	−	598.166i	0.370152	−	0.641121i
$934$	−370.147	+	213.704i	−0.396303	+	0.228806i
$935$	364.523	+	631.372i	0.389864	+	0.675264i
$936$	−51.6112	−	29.7978i	−0.0551402	−	0.0318352i
$937$		−	270.668i		−	0.288867i	−0.989515	−	0.144433i	$-0.953864\pi$
$937$		−	270.668i		−	0.288867i	0.989515	−	0.144433i	$-0.0461359\pi$
$938$	−58.3924	+	146.373i	−0.0622520	+	0.156048i
$939$	−223.782			−0.238319
$940$	138.516	−	239.918i	0.147358	−	0.255231i
$941$	−395.174	+	228.154i	−0.419952	+	0.242459i	−0.695057	−	0.718955i	$-0.744621\pi$
$941$	−395.174	+	228.154i	−0.419952	+	0.242459i	0.275105	+	0.961414i	$0.411287\pi$
$942$	121.540	+	210.513i	0.129023	+	0.223475i
$943$	−1335.97	−	771.320i	−1.41672	−	0.817943i
$944$		−	439.278i		−	0.465337i
$945$	50.3543	+	63.8706i	0.0532849	+	0.0675879i
$946$	−44.0780			−0.0465940
$947$	496.787	−	860.460i	0.524590	−	0.908617i	−0.475000	−	0.879986i	$-0.657552\pi$
$947$	496.787	−	860.460i	0.524590	−	0.908617i	0.999590	−	0.0286308i	$-0.00911470\pi$
$948$	−319.337	+	184.369i	−0.336854	+	0.194483i
$949$	−254.177	−	440.248i	−0.267837	−	0.463907i
$950$	190.501	+	109.986i	0.200527	+	0.115774i
$951$			697.264i			0.733190i
$952$	90.2132	+	622.073i	0.0947618	+	0.653438i
$953$	−206.385			−0.216563			−0.108281	−	0.994120i	$-0.534535\pi$
$953$	−206.385			−0.216563			−0.108281	+	0.994120i	$0.534535\pi$
$954$	2.93061	−	5.07596i	0.00307192	−	0.00532072i
$955$	5.98299	−	3.45428i	0.00626491	−	0.00361705i
$956$	−34.7150	−	60.1282i	−0.0363128	−	0.0628956i
$957$	141.670	+	81.7930i	0.148035	+	0.0854681i
$958$			49.6817i			0.0518598i
$959$	744.825	−	108.015i	0.776668	−	0.112633i
$960$	30.9839			0.0322749
$961$	−277.472	+	480.596i	−0.288733	+	0.500100i
$962$	−414.306	+	239.200i	−0.430672	+	0.248649i
$963$	−37.1940	−	64.4218i	−0.0386230	−	0.0668970i
$964$	459.743	+	265.432i	0.476911	+	0.275345i
$965$		−	533.744i		−	0.553102i
$966$	318.964	−	251.465i	0.330191	−	0.260316i
$967$	169.282			0.175058			0.0875292	−	0.996162i	$-0.472103\pi$
$967$	169.282			0.175058			0.0875292	+	0.996162i	$0.472103\pi$
$968$	21.9714	−	38.0556i	0.0226977	−	0.0393136i
$969$	1481.46	−	855.321i	1.52885	−	0.882684i
$970$	78.2345	+	135.506i	0.0806541	+	0.139697i
$971$	−122.891	−	70.9512i	−0.126561	−	0.0730702i	0.435383	−	0.900245i	$-0.356613\pi$
$971$	−122.891	−	70.9512i	−0.126561	−	0.0730702i	−0.561944	+	0.827175i	$0.689946\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	1768.50	+	705.504i	1.81757	+	0.725081i
$974$	91.4053			0.0938453
$975$	−30.4122	+	52.6755i	−0.0311920	+	0.0540261i
$976$	137.497	−	79.3837i	0.140878	−	0.0813357i
$977$	703.901	+	1219.19i	0.720472	+	1.24789i	0.960811	+	0.277204i	$0.0894079\pi$
$977$	703.901	+	1219.19i	0.720472	+	1.24789i	−0.240339	+	0.970689i	$0.577259\pi$
$978$	591.805	+	341.679i	0.605118	+	0.349365i
$979$			1693.45i			1.72977i
$980$	150.834	−	158.963i	0.153912	−	0.162207i
$981$	168.869			0.172140
$982$	−170.671	+	295.610i	−0.173799	+	0.301029i
$983$	777.500	−	448.890i	0.790946	−	0.456653i	−0.0493494	−	0.998782i	$-0.515715\pi$
$983$	777.500	−	448.890i	0.790946	−	0.456653i	0.840296	+	0.542129i	$0.182381\pi$
$984$	159.517	+	276.292i	0.162111	+	0.280784i
$985$	564.562	+	325.950i	0.573160	+	0.330914i
$986$			412.920i			0.418783i
$987$	−278.293	+	697.600i	−0.281958	+	0.706788i
$988$	436.976			0.442284
$989$	−35.9466	+	62.2613i	−0.0363464	+	0.0629538i
$990$	−84.3730	+	48.7128i	−0.0852253	+	0.0492049i
$991$	−762.140	−	1320.06i	−0.769061	−	1.33205i	−0.938072	−	0.346439i	$-0.887391\pi$
$991$	−762.140	−	1320.06i	−0.769061	−	1.33205i	0.169011	−	0.985614i	$-0.445943\pi$
$992$	−98.7185	−	56.9951i	−0.0995146	−	0.0574548i
$993$			289.066i			0.291104i
$994$	−326.971	−	414.739i	−0.328945	−	0.417242i
$995$	−540.214			−0.542929
$996$	−85.6150	+	148.289i	−0.0859588	+	0.148885i
$997$	770.649	−	444.935i	0.772968	−	0.446273i	−0.0609641	−	0.998140i	$-0.519418\pi$
$997$	770.649	−	444.935i	0.772968	−	0.446273i	0.833932	+	0.551866i	$0.186084\pi$
$998$	135.499	+	234.691i	0.135771	+	0.235162i
$999$	−216.741	−	125.136i	−0.216958	−	0.125261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.b.61.1	yes	16
3.2	odd	2		630.3.v.c.271.7		16
5.2	odd	4		1050.3.q.e.649.3		32
5.3	odd	4		1050.3.q.e.649.13		32
5.4	even	2		1050.3.p.i.901.7		16
7.2	even	3		1470.3.f.d.391.12		16
7.3	odd	6	inner	210.3.o.b.31.1	✓	16
7.5	odd	6		1470.3.f.d.391.14		16
21.17	even	6		630.3.v.c.451.7		16
35.3	even	12		1050.3.q.e.199.3		32
35.17	even	12		1050.3.q.e.199.14		32
35.24	odd	6		1050.3.p.i.451.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.1	✓	16	7.3	odd	6	inner
210.3.o.b.61.1	yes	16	1.1	even	1	trivial
630.3.v.c.271.7		16	3.2	odd	2
630.3.v.c.451.7		16	21.17	even	6
1050.3.p.i.451.7		16	35.24	odd	6
1050.3.p.i.901.7		16	5.4	even	2
1050.3.q.e.199.3		32	35.3	even	12
1050.3.q.e.199.14		32	35.17	even	12
1050.3.q.e.649.3		32	5.2	odd	4
1050.3.q.e.649.13		32	5.3	odd	4
1470.3.f.d.391.12		16	7.2	even	3
1470.3.f.d.391.14		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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-2.59373 + 6.50174i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(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} +(-2.59373 + 6.50174i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(-5.13478 - 8.89370i) q^{11} +(3.00000 + 1.73205i) q^{12} -7.02340i q^{13} +(-6.12892 - 7.77408i) q^{14} +3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(27.4947 - 15.8741i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-26.9408 - 15.5543i) q^{19} +4.47214i q^{20} +(-1.74007 - 11.9988i) q^{21} +14.5234 q^{22} +(11.8441 - 20.5146i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(8.60187 + 4.96629i) q^{26} +5.19615i q^{27} +(13.8551 - 2.00927i) q^{28} +9.19673 q^{29} +(-2.73861 + 4.74342i) q^{30} +(17.4511 - 10.0754i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(15.4043 + 8.89370i) q^{33} +44.8986i q^{34} +(12.2919 - 9.69068i) q^{35} -6.00000 q^{36} +(-24.0823 + 41.7118i) q^{37} +(38.1001 - 21.9971i) q^{38} +(6.08244 + 10.5351i) q^{39} +(-5.47723 - 3.16228i) q^{40} -65.1226i q^{41} +(15.9259 + 6.35331i) q^{42} -3.03497 q^{43} +(-10.2696 + 17.7874i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(16.7501 + 29.0120i) q^{46} +(-53.6472 - 30.9732i) q^{47} -6.92820i q^{48} +(-35.5451 - 33.7275i) q^{49} -7.07107 q^{50} +(-27.4947 + 47.6222i) q^{51} +(-12.1649 + 7.02340i) q^{52} +(-0.690751 - 1.19642i) q^{53} +(-6.36396 - 3.67423i) q^{54} +22.9634i q^{55} +(-7.33617 + 18.3897i) q^{56} +53.8817 q^{57} +(-6.50307 + 11.2636i) q^{58} +(-95.1064 + 54.9097i) q^{59} +(-3.87298 - 6.70820i) q^{60} +(-34.3741 - 19.8459i) q^{61} +28.4976i q^{62} +(13.0014 + 16.4913i) q^{63} +8.00000 q^{64} +(-7.85240 + 13.6008i) q^{65} +(-21.7850 + 12.5776i) q^{66} +(-7.95952 - 13.7863i) q^{67} +(-54.9893 - 31.7481i) q^{68} +41.0292i q^{69} +(3.17693 + 21.9068i) q^{70} +53.3489 q^{71} +(4.24264 - 7.34847i) q^{72} +(62.6830 - 36.1901i) q^{73} +(-34.0576 - 58.9894i) q^{74} +(-7.50000 - 4.33013i) q^{75} +62.2172i q^{76} +(71.1427 - 10.3171i) q^{77} -17.2037 q^{78} +(-53.2229 + 92.1847i) q^{79} +(7.74597 - 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(79.7586 + 46.0486i) q^{82} +49.4298i q^{83} +(-19.0425 + 15.0127i) q^{84} -70.9909 q^{85} +(2.14605 - 3.71707i) q^{86} +(-13.7951 + 7.96460i) q^{87} +(-14.5234 - 25.1552i) q^{88} +(-142.807 - 82.4499i) q^{89} -9.48683i q^{90} +(45.6643 + 18.2168i) q^{91} -47.3765 q^{92} +(-17.4511 + 30.2262i) q^{93} +(75.8686 - 43.8027i) q^{94} +(34.7805 + 60.2416i) q^{95} +(8.48528 + 4.89898i) q^{96} +49.4799i q^{97} +(66.4418 - 19.6848i) q^{98} -30.8087 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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