LMFDB - Embedded newform 210.3.o.b.31.1

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			31.1
Root			$-3.67087 - 6.35814i$ of defining polynomial
Character	$\chi$	$=$	210.31
Dual form			210.3.o.b.61.1

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

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

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
$7$	−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	−0.999281	−	0.0379228i	$-0.987926\pi$
$11$	−5.13478	+	8.89370i	−0.466798	+	0.808518i	0.532482	+	0.846441i	$0.321259\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$			7.02340i			0.540261i	0.962824	+	0.270131i	$0.0870669\pi$
$13$			7.02340i			0.540261i	−0.962824	+	0.270131i	$0.912933\pi$
$14$	−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	0.987606	+	0.156951i	$0.0501666\pi$
$17$	27.4947	+	15.8741i	1.61733	+	0.933768i	0.629727	+	0.776816i	$0.283167\pi$
$18$	2.12132	−	3.67423i	0.117851	−	0.204124i
$19$	−26.9408	+	15.5543i	−1.41794	+	0.818648i	−0.996118	−	0.0880311i	$-0.971943\pi$
$19$	−26.9408	+	15.5543i	−1.41794	+	0.818648i	−0.421822	+	0.906679i	$0.638609\pi$
$20$		−	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	0.999849	+	0.0173632i	$0.00552716\pi$
$23$	11.8441	+	20.5146i	0.514962	+	0.891940i	−0.484888	+	0.874576i	$0.661140\pi$
$24$	−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	0.754325	−	0.656502i	$-0.227965\pi$
$31$	17.4511	+	10.0754i	0.562940	+	0.325013i	−0.191385	+	0.981515i	$0.561298\pi$
$32$	−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	−0.982911	−	0.184081i	$-0.941069\pi$
$37$	−24.0823	−	41.7118i	−0.650874	−	1.12735i	0.332037	−	0.943266i	$-0.392264\pi$
$38$	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	$0.292098\pi$
$41$			65.1226i			1.58836i	−0.607685	+	0.794178i	$0.707902\pi$
$42$	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	−0.946784	−	0.321869i	$-0.895689\pi$
$47$	−53.6472	+	30.9732i	−1.14143	+	0.659005i	−0.194645	+	0.980874i	$0.562356\pi$
$48$			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	−0.872468	−	0.488671i	$-0.837482\pi$
$53$	−0.690751	+	1.19642i	−0.0130330	+	0.0225739i	0.859435	+	0.511244i	$0.170815\pi$
$54$	−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	−0.988912	−	0.148500i	$-0.952555\pi$
$59$	−95.1064	−	54.9097i	−1.61197	−	0.930673i	−0.623061	−	0.782173i	$-0.714111\pi$
$60$	−3.87298	+	6.70820i	−0.0645497	+	0.111803i
$61$	−34.3741	+	19.8459i	−0.563510	+	0.325343i	−0.754553	−	0.656239i	$-0.772146\pi$
$61$	−34.3741	+	19.8459i	−0.563510	+	0.325343i	0.191043	+	0.981582i	$0.438813\pi$
$62$		−	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	−0.919292	−	0.393576i	$-0.871238\pi$
$67$	−7.95952	+	13.7863i	−0.118799	+	0.205765i	0.800493	+	0.599342i	$0.204571\pi$
$68$	−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	0.863567	−	0.504234i	$-0.168225\pi$
$73$	62.6830	+	36.1901i	0.858672	+	0.495754i	−0.00489557	+	0.999988i	$0.501558\pi$
$74$	−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	−0.976845	−	0.213948i	$-0.931368\pi$
$79$	−53.2229	−	92.1847i	−0.673707	−	1.16690i	0.303138	−	0.952947i	$-0.401966\pi$
$80$	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	$-0.903757\pi$
$83$		−	49.4298i		−	0.595540i	0.954638	−	0.297770i	$-0.0962429\pi$
$84$	−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	−0.614022	+	0.789289i	$0.710449\pi$
$89$	−142.807	+	82.4499i	−1.60458	+	0.926403i	−0.990555	+	0.137114i	$0.956217\pi$
$90$			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	$-0.917908\pi$
$97$		−	49.4799i		−	0.510102i	0.966928	−	0.255051i	$-0.0820922\pi$
$98$	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	0.950455	−	0.310863i	$-0.100618\pi$
$101$	116.803	+	67.4364i	1.15647	+	0.667687i	0.206012	+	0.978549i	$0.433951\pi$
$102$	−38.8833	+	67.3479i	−0.381209	+	0.660274i
$103$	−32.3911	+	18.7010i	−0.314477	+	0.181563i	−0.648928	−	0.760850i	$-0.724782\pi$
$103$	−32.3911	+	18.7010i	−0.314477	+	0.181563i	0.334451	+	0.942413i	$0.391449\pi$
$104$			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	0.918127	−	0.396287i	$-0.129701\pi$
$107$	12.3980	+	21.4739i	0.115869	+	0.200691i	−0.802258	+	0.596978i	$0.796368\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	28.1448	−	48.7483i	0.258209	−	0.447232i	−0.707553	−	0.706660i	$-0.750201\pi$
$109$	28.1448	−	48.7483i	0.258209	−	0.447232i	0.965762	+	0.259429i	$0.0835342\pi$
$110$	−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	−0.229243	−	0.973369i	$-0.573625\pi$
$131$	65.3818	−	37.7482i	0.499098	−	0.288154i	0.728341	+	0.685215i	$0.240292\pi$
$132$			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	−0.992765	−	0.120073i	$-0.961687\pi$
$137$	−53.7583	+	93.1121i	−0.392396	+	0.679650i	0.600369	+	0.799723i	$0.295020\pi$
$138$	−50.2503	+	29.0120i	−0.364133	+	0.210232i
$139$			272.004i			1.95686i	0.206576	+	0.978431i	$0.433768\pi$
$139$			272.004i			1.95686i	−0.206576	+	0.978431i	$0.566232\pi$
$140$	−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	0.971374	−	0.237557i	$-0.0763467\pi$
$149$	41.7135	+	72.2498i	0.279956	+	0.484898i	−0.691417	+	0.722456i	$0.743013\pi$
$150$	10.6066	+	6.12372i	0.0707107	+	0.0408248i
$151$	−63.3973	+	109.807i	−0.419850	+	0.727201i	−0.995924	−	0.0901962i	$-0.971251\pi$
$151$	−63.3973	+	109.807i	−0.419850	+	0.727201i	0.576074	+	0.817397i	$0.304584\pi$
$152$	−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	0.200673	−	0.979658i	$-0.435687\pi$
$157$	−85.9416	−	49.6184i	−0.547399	−	0.316041i	−0.748072	+	0.663617i	$0.769020\pi$
$158$	−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	−0.875933	−	0.482433i	$-0.839753\pi$
$163$	−139.490	−	241.603i	−0.855765	−	1.48223i	0.0201678	−	0.999797i	$-0.493580\pi$
$164$	−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	$0.0285752\pi$
$167$			29.9435i			0.179302i	−0.995973	+	0.0896511i	$0.971425\pi$
$168$	−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	−0.209142	−	0.977885i	$-0.567067\pi$
$173$	92.2369	−	53.2530i	0.533161	−	0.307821i	0.742303	+	0.670065i	$0.233734\pi$
$174$			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	−0.307500	−	0.951548i	$-0.599492\pi$
$179$	119.986	−	207.822i	0.670315	−	1.16102i	0.977815	−	0.209471i	$-0.0671743\pi$
$180$	11.6190	−	6.70820i	0.0645497	−	0.0372678i
$181$			309.322i			1.70896i	0.519482	+	0.854482i	$0.326125\pi$
$181$			309.322i			1.70896i	−0.519482	+	0.854482i	$0.673875\pi$
$182$	−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	0.861953	−	0.506988i	$-0.169241\pi$
$191$	−1.54480	−	2.67567i	−0.00808796	−	0.0140088i	−0.870041	+	0.492979i	$0.835908\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	119.349	−	206.718i	0.618387	−	1.07108i	−0.371393	−	0.928476i	$-0.621120\pi$
$193$	119.349	−	206.718i	0.618387	−	1.07108i	0.989780	−	0.142602i	$-0.0455469\pi$
$194$	−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	0.923034	−	0.384717i	$-0.125701\pi$
$199$	209.224	+	120.796i	1.05138	+	0.607013i	0.128342	+	0.991730i	$0.459034\pi$
$200$	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	$0.0812845\pi$
$223$			112.658i			0.505193i	−0.967572	+	0.252597i	$0.918715\pi$
$224$	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	0.590585	−	0.806975i	$-0.298897\pi$
$227$	42.4529	+	24.5102i	0.187017	+	0.107974i	−0.403568	+	0.914950i	$0.632230\pi$
$228$	−53.8817	+	93.3258i	−0.236323	+	0.409324i
$229$	24.3476	−	14.0571i	0.106321	−	0.0613846i	−0.445896	−	0.895085i	$-0.647115\pi$
$229$	24.3476	−	14.0571i	0.106321	−	0.0613846i	0.552218	+	0.833700i	$0.313782\pi$
$230$			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	0.612671	−	0.790338i	$-0.290095\pi$
$233$	−88.1014	−	152.596i	−0.378117	−	0.654919i	−0.990788	+	0.135420i	$0.956762\pi$
$234$	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	−0.0595563	−	0.998225i	$-0.518969\pi$
$241$	−229.871	−	132.716i	−0.953823	−	0.550690i	−0.894266	+	0.447535i	$0.852302\pi$
$242$	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	$0.0153332\pi$
$251$			24.1723i			0.0963040i	−0.998840	+	0.0481520i	$0.984667\pi$
$252$	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	−0.515983	−	0.856599i	$-0.672573\pi$
$257$	−8.25969	+	4.76874i	−0.0321389	+	0.0185554i	0.483844	+	0.875154i	$0.339240\pi$
$258$		−	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	−0.713026	−	0.701138i	$-0.752676\pi$
$263$	65.9316	−	114.197i	0.250691	−	0.434209i	0.963716	+	0.266929i	$0.0860090\pi$
$264$	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	0.437785	−	0.899080i	$-0.355763\pi$
$269$	−32.8041	−	18.9395i	−0.121949	−	0.0704070i	−0.559733	+	0.828673i	$0.689096\pi$
$270$	8.21584	−	14.2302i	0.0304290	−	0.0527046i
$271$	313.801	−	181.173i	1.15794	−	0.668535i	0.207128	−	0.978314i	$-0.433588\pi$
$271$	313.801	−	181.173i	1.15794	−	0.668535i	0.950809	+	0.309779i	$0.100255\pi$
$272$		−	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	−0.745466	−	0.666544i	$-0.767773\pi$
$277$	56.6495	−	98.1197i	0.204511	−	0.354223i	0.949977	+	0.312321i	$0.101106\pi$
$278$	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	0.564595	−	0.825368i	$-0.309032\pi$
$283$	37.3850	+	21.5843i	0.132103	+	0.0762695i	−0.432492	+	0.901638i	$0.642366\pi$
$284$	−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	$0.00838923\pi$
$293$			15.4426i			0.0527050i	−0.999653	+	0.0263525i	$0.991611\pi$
$294$	−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	$-0.875179\pi$
$307$		−	234.648i		−	0.764327i	0.924095	−	0.382163i	$-0.124821\pi$
$308$	−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	−0.171508	−	0.985183i	$-0.554864\pi$
$311$	−345.352	−	199.389i	−1.11045	−	0.641121i	−0.938947	+	0.344061i	$0.888197\pi$
$312$	17.2037	−	29.7978i	0.0551402	−	0.0955056i
$313$	111.891	−	64.6002i	0.357479	−	0.206390i	−0.310495	−	0.950575i	$-0.600495\pi$
$313$	111.891	−	64.6002i	0.357479	−	0.206390i	0.667974	+	0.744184i	$0.267162\pi$
$314$			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	0.986523	+	0.163621i	$0.0523173\pi$
$317$	201.283	+	348.632i	0.634961	+	1.09979i	−0.351562	+	0.936165i	$0.614349\pi$
$318$	−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	0.964105	−	0.265522i	$-0.0855443\pi$
$331$	83.4463	+	144.533i	0.252104	+	0.436656i	−0.712001	+	0.702178i	$0.752211\pi$
$332$	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	0.372204	+	0.928151i	$0.378602\pi$
$347$	−214.342	+	371.251i	−0.617700	+	1.06989i	−0.989904	+	0.141737i	$0.954731\pi$
$348$	27.5902	−	15.9292i	0.0792822	−	0.0457736i
$349$			74.6851i			0.213998i	0.994259	+	0.106999i	$0.0341241\pi$
$349$			74.6851i			0.213998i	−0.994259	+	0.106999i	$0.965876\pi$
$350$	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	0.876455	−	0.481484i	$-0.159902\pi$
$353$	316.890	+	182.956i	0.897705	+	0.518290i	0.0212499	+	0.999774i	$0.493235\pi$
$354$	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	0.970845	+	0.239710i	$0.0770522\pi$
$359$	248.793	+	430.922i	0.693017	+	1.20034i	−0.277828	+	0.960631i	$0.589614\pi$
$360$	−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	0.655345	−	0.755330i	$-0.272523\pi$
$367$	120.700	+	69.6861i	0.328882	+	0.189880i	−0.326462	+	0.945210i	$0.605857\pi$
$368$	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	0.533395	−	0.845866i	$-0.320916\pi$
$373$	−173.760	−	300.961i	−0.465844	−	0.806865i	−0.999239	+	0.0390009i	$0.987582\pi$
$374$	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	−0.948965	−	0.315382i	$-0.897867\pi$
$383$	−440.572	+	254.364i	−1.15032	+	0.664136i	−0.201353	+	0.979519i	$0.564534\pi$
$384$			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	−0.734979	−	0.678090i	$-0.762808\pi$
$389$	85.4840	−	148.063i	0.219753	−	0.380624i	0.954732	+	0.297466i	$0.0961414\pi$
$390$	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	0.395328	−	0.918540i	$-0.370631\pi$
$397$	551.223	−	318.249i	1.38847	−	0.801634i	0.993143	+	0.116906i	$0.0372975\pi$
$398$		−	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	0.953202	+	0.302333i	$0.0977654\pi$
$401$	296.110	+	512.878i	0.738429	+	1.27900i	−0.214773	+	0.976664i	$0.568901\pi$
$402$	−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	0.168571	−	0.985690i	$-0.446085\pi$
$409$	−245.717	−	141.865i	−0.600776	−	0.346858i	−0.769347	+	0.638831i	$0.779418\pi$
$410$	−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	$-0.804695\pi$
$419$		−	482.511i		−	1.15158i	0.817599	−	0.575789i	$-0.195305\pi$
$420$	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	−0.975449	−	0.220226i	$-0.929320\pi$
$431$	−128.008	+	221.717i	−0.297003	+	0.514424i	0.678446	+	0.734650i	$0.262654\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$		−	646.579i		−	1.49325i	−0.665243	−	0.746627i	$-0.731672\pi$
$433$		−	646.579i		−	1.49325i	0.665243	−	0.746627i	$-0.268328\pi$
$434$	−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	−0.131414	−	0.991328i	$-0.541952\pi$
$439$	290.352	−	167.635i	0.661394	−	0.381856i	0.792808	+	0.609472i	$0.208618\pi$
$440$		−	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	0.979906	−	0.199459i	$-0.0639185\pi$
$443$	140.527	+	243.400i	0.317216	+	0.549435i	−0.662690	+	0.748894i	$0.730585\pi$
$444$	−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	−0.984487	−	0.175456i	$-0.943860\pi$
$457$	−294.396	−	509.909i	−0.644193	−	1.11578i	0.340294	−	0.940319i	$-0.389473\pi$
$458$	−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	$-0.979077\pi$
$461$		−	60.5606i		−	0.131368i	0.997840	−	0.0656839i	$-0.0209229\pi$
$462$	−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	−0.192872	−	0.981224i	$-0.561780\pi$
$467$	261.733	−	151.112i	0.560457	−	0.323580i	0.753329	+	0.657644i	$0.228447\pi$
$468$		−	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	0.531421	−	0.847108i	$-0.321658\pi$
$479$	30.4237	+	17.5651i	0.0635151	+	0.0366704i	−0.467906	+	0.883778i	$0.654991\pi$
$480$	−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	−0.897296	−	0.441430i	$-0.854471\pi$
$487$	−32.3167	+	55.9741i	−0.0663586	+	0.114937i	0.830937	+	0.556366i	$0.187805\pi$
$488$	−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	0.945916	−	0.324412i	$-0.105166\pi$
$499$	95.8123	+	165.952i	0.192009	+	0.332569i	−0.753907	+	0.656981i	$0.771833\pi$
$500$	−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	$-0.632800\pi$
$503$		−	919.711i		−	1.82845i	0.405205	−	0.914226i	$-0.367200\pi$
$504$	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	−0.232773	−	0.972531i	$-0.574780\pi$
$509$	250.976	−	144.901i	0.493076	−	0.284678i	0.725850	+	0.687853i	$0.241447\pi$
$510$		−	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	−0.281856	−	0.959457i	$-0.590950\pi$
$521$	−653.176	−	377.112i	−1.25370	−	0.723823i	−0.971842	+	0.235634i	$0.924283\pi$
$522$	19.5092	−	33.7909i	0.0373740	−	0.0647336i
$523$	65.5821	−	37.8638i	0.125396	−	0.0723974i	−0.435990	−	0.899952i	$-0.643602\pi$
$523$	65.5821	−	37.8638i	0.125396	−	0.0723974i	0.561386	+	0.827554i	$0.310268\pi$
$524$			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	−0.811802	−	0.583933i	$-0.801513\pi$
$541$	−493.177	−	854.207i	−0.911602	−	1.57894i	−0.0998002	−	0.995007i	$-0.531820\pi$
$542$	−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	−0.788897	−	0.614525i	$-0.789348\pi$
$557$	76.7246	−	132.891i	0.137746	−	0.238583i	0.926643	+	0.375942i	$0.122681\pi$
$558$	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	0.627918	−	0.778280i	$-0.283907\pi$
$563$	150.809	+	87.0695i	0.267866	+	0.154653i	−0.360051	+	0.932933i	$0.617241\pi$
$564$	−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	0.946112	−	0.323840i	$-0.104974\pi$
$569$	109.591	+	189.817i	0.192603	+	0.333597i	−0.753509	+	0.657437i	$0.771641\pi$
$570$	147.561	+	85.1944i	0.258879	+	0.149464i
$571$	−478.914	+	829.504i	−0.838729	+	1.45272i	0.0522282	+	0.998635i	$0.483368\pi$
$571$	−478.914	+	829.504i	−0.838729	+	1.45272i	−0.890958	+	0.454087i	$0.849966\pi$
$572$	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	−0.997469	−	0.0710997i	$-0.977349\pi$
$577$	−898.838	−	518.944i	−1.55778	−	0.899384i	−0.560309	−	0.828284i	$-0.689318\pi$
$578$	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	$0.245817\pi$
$587$			819.162i			1.39551i	−0.716339	+	0.697753i	$0.754183\pi$
$588$	−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	−0.0571059	−	0.998368i	$-0.518187\pi$
$593$	461.919	−	266.689i	0.778953	−	0.449729i	0.836059	+	0.548639i	$0.184854\pi$
$594$		−	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	−0.686677	−	0.726963i	$-0.740931\pi$
$599$	171.452	−	296.963i	0.286230	−	0.495765i	0.972907	+	0.231198i	$0.0742646\pi$
$600$	−21.2132	+	12.2474i	−0.0353553	+	0.0204124i
$601$		−	418.941i		−	0.697073i	−0.937295	−	0.348536i	$-0.886679\pi$
$601$		−	418.941i		−	0.697073i	0.937295	−	0.348536i	$-0.113321\pi$
$602$	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	−0.395594	−	0.918426i	$-0.629461\pi$
$607$	122.608	−	70.7875i	0.201989	−	0.116619i	0.597583	+	0.801807i	$0.296128\pi$
$608$		−	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	−0.719081	−	0.694926i	$-0.755437\pi$
$613$	148.520	−	257.244i	0.242284	−	0.419647i	0.961364	+	0.275279i	$0.0887703\pi$
$614$	−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	−0.358156	−	0.933662i	$-0.616594\pi$
$619$	−833.055	−	480.965i	−1.34581	−	0.777003i	−0.987653	+	0.156659i	$0.949928\pi$
$620$	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	−0.979976	−	0.199115i	$-0.936193\pi$
$641$	−203.549	+	352.557i	−0.317549	+	0.550011i	0.662427	+	0.749126i	$0.269526\pi$
$642$	−52.6002	+	30.3688i	−0.0819318	+	0.0473034i
$643$			1077.83i			1.67626i	0.545474	+	0.838128i	$0.316350\pi$
$643$			1077.83i			1.67626i	−0.545474	+	0.838128i	$0.683650\pi$
$644$	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	0.995536	+	0.0943805i	$0.0300870\pi$
$647$	1019.05	+	588.349i	1.57504	+	0.909350i	0.579504	+	0.814969i	$0.303246\pi$
$648$	−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	0.977008	+	0.213204i	$0.0683898\pi$
$653$	439.563	+	761.345i	0.673144	+	1.16592i	−0.303864	+	0.952715i	$0.598277\pi$
$654$	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	0.516577	−	0.856241i	$-0.327206\pi$
$661$	22.0376	+	12.7234i	0.0333397	+	0.0192487i	−0.483237	+	0.875489i	$0.660539\pi$
$662$	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	−0.588146	−	0.808755i	$-0.700142\pi$
$677$	−123.090	+	71.0658i	−0.181816	+	0.104972i	0.406330	+	0.913727i	$0.366809\pi$
$678$			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	−0.999756	−	0.0220879i	$-0.992969\pi$
$683$	−328.352	+	568.722i	−0.480749	+	0.832682i	0.519007	+	0.854770i	$0.326302\pi$
$684$	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	−0.338413	−	0.940998i	$-0.609890\pi$
$691$	212.350	−	122.600i	0.307308	−	0.177425i	0.645721	+	0.763573i	$0.276557\pi$
$692$			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	0.988831	+	0.149042i	$0.0476191\pi$
$709$	442.054	+	765.661i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$710$	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	−0.948542	−	0.316653i	$-0.897441\pi$
$719$	−825.831	+	476.794i	−1.14858	+	0.663135i	−0.200042	+	0.979787i	$0.564108\pi$
$720$			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	$0.276754\pi$
$727$			1110.82i			1.52795i	−0.645248	+	0.763974i	$0.723246\pi$
$728$	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	−0.475756	−	0.879577i	$-0.657825\pi$
$733$	35.2595	−	20.3571i	0.0481029	−	0.0277722i	0.523859	+	0.851805i	$0.324492\pi$
$734$		−	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	0.424320	+	0.905512i	$0.360513\pi$
$739$	−422.735	+	732.199i	−0.572037	+	0.990797i	−0.996357	+	0.0852847i	$0.972820\pi$
$740$	−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	0.784479	−	0.620156i	$-0.212931\pi$
$751$	−108.768	−	188.392i	−0.144831	−	0.250855i	−0.929310	+	0.369300i	$0.879597\pi$
$752$	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	0.0467017	−	0.998909i	$-0.485129\pi$
$761$	711.636	−	410.863i	0.935133	−	0.539899i	0.888431	+	0.459010i	$0.151796\pi$
$762$			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	$-0.952033\pi$
$769$		−	230.888i		−	0.300244i	0.988667	−	0.150122i	$-0.0479667\pi$
$770$	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	0.827727	−	0.561131i	$-0.189634\pi$
$773$	584.107	+	337.234i	0.755636	+	0.436267i	−0.0720908	+	0.997398i	$0.522967\pi$
$774$	−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	0.801900	−	0.597458i	$-0.203823\pi$
$787$	539.438	+	311.445i	0.685436	+	0.395737i	−0.116464	+	0.993195i	$0.537156\pi$
$788$	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	$-0.688604\pi$
$797$		−	1322.28i		−	1.65907i	0.558452	−	0.829537i	$-0.311396\pi$
$798$	−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	0.340366	+	0.940293i	$0.389449\pi$
$809$	−521.105	+	902.581i	−0.644135	+	1.11567i	−0.984501	+	0.175381i	$0.943884\pi$
$810$	−24.6475	+	14.2302i	−0.0304290	+	0.0175682i
$811$			782.292i			0.964602i	0.876006	+	0.482301i	$0.160199\pi$
$811$			782.292i			0.964602i	−0.876006	+	0.482301i	$0.839801\pi$
$812$	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	0.990193	+	0.139704i	$0.0446153\pi$
$821$	505.805	+	876.080i	0.616084	+	1.06709i	−0.374109	+	0.927385i	$0.622051\pi$
$822$	−228.077	−	131.680i	−0.277466	−	0.160195i
$823$	557.204	−	965.106i	0.677040	−	1.17267i	−0.298828	−	0.954307i	$-0.596596\pi$
$823$	557.204	−	965.106i	0.677040	−	1.17267i	0.975868	−	0.218361i	$-0.0700711\pi$
$824$	−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	0.387145	−	0.922019i	$-0.373461\pi$
$829$	−180.535	−	104.232i	−0.217775	−	0.125732i	−0.604919	+	0.796287i	$0.706795\pi$
$830$	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	$0.0745159\pi$
$839$			389.239i			0.463932i	−0.972724	+	0.231966i	$0.925484\pi$
$840$	−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	$0.258801\pi$
$853$			1239.21i			1.45277i	−0.687287	+	0.726386i	$0.741199\pi$
$854$	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	0.589258	−	0.807945i	$-0.299420\pi$
$857$	157.848	+	91.1334i	0.184186	+	0.106340i	−0.405072	+	0.914285i	$0.632753\pi$
$858$	88.3374	−	153.005i	0.102957	−	0.178327i
$859$	−366.992	+	211.883i	−0.427232	+	0.246662i	−0.698167	−	0.715935i	$-0.746001\pi$
$859$	−366.992	+	211.883i	−0.427232	+	0.246662i	0.270935	+	0.962598i	$0.412667\pi$
$860$			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	0.870983	−	0.491313i	$-0.163483\pi$
$863$	8.63152	+	14.9502i	0.0100018	+	0.0173236i	−0.860981	+	0.508637i	$0.830150\pi$
$864$	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	0.951534	−	0.307542i	$-0.0995066\pi$
$877$	183.668	+	318.122i	0.209428	+	0.362739i	−0.742107	+	0.670282i	$0.766173\pi$
$878$	−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	$0.0686164\pi$
$881$			376.890i			0.427798i	−0.976856	+	0.213899i	$0.931384\pi$
$882$	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	−0.558081	−	0.829787i	$-0.688462\pi$
$887$	−105.113	+	60.6873i	−0.118504	+	0.0684186i	0.439576	+	0.898205i	$0.355129\pi$
$888$			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	−0.886752	−	0.462245i	$-0.847044\pi$
$907$	−39.0554	+	67.6459i	−0.0430599	+	0.0745820i	0.843692	+	0.536827i	$0.180377\pi$
$908$	−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	−0.953051	−	0.302810i	$-0.902075\pi$
$919$	−678.926	−	1175.93i	−0.738766	−	1.27958i	0.214285	−	0.976771i	$-0.431258\pi$
$920$	−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	−0.00259410	−	0.999997i	$-0.500826\pi$
$929$	800.920	−	462.411i	0.862131	−	0.497752i	0.864725	+	0.502245i	$0.167492\pi$
$930$		−	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	$0.0461359\pi$
$937$			270.668i			0.288867i	−0.989515	+	0.144433i	$0.953864\pi$
$938$	−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	0.275105	−	0.961414i	$-0.411287\pi$
$941$	−395.174	−	228.154i	−0.419952	−	0.242459i	−0.695057	+	0.718955i	$0.744621\pi$
$942$	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	0.999590	+	0.0286308i	$0.00911470\pi$
$947$	496.787	+	860.460i	0.524590	+	0.908617i	−0.475000	+	0.879986i	$0.657552\pi$
$948$	−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	−0.561944	−	0.827175i	$-0.689946\pi$
$971$	−122.891	+	70.9512i	−0.126561	+	0.0730702i	0.435383	+	0.900245i	$0.356613\pi$
$972$			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	−0.240339	−	0.970689i	$-0.577259\pi$
$977$	703.901	−	1219.19i	0.720472	−	1.24789i	0.960811	−	0.277204i	$-0.0894079\pi$
$978$	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	0.840296	−	0.542129i	$-0.182381\pi$
$983$	777.500	+	448.890i	0.790946	+	0.456653i	−0.0493494	+	0.998782i	$0.515715\pi$
$984$	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	0.169011	+	0.985614i	$0.445943\pi$
$991$	−762.140	+	1320.06i	−0.769061	+	1.33205i	−0.938072	+	0.346439i	$0.887391\pi$
$992$	−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	0.833932	−	0.551866i	$-0.186084\pi$
$997$	770.649	+	444.935i	0.772968	+	0.446273i	−0.0609641	+	0.998140i	$0.519418\pi$
$998$	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.31.1	✓	16
3.2	odd	2		630.3.v.c.451.7		16
5.2	odd	4		1050.3.q.e.199.14		32
5.3	odd	4		1050.3.q.e.199.3		32
5.4	even	2		1050.3.p.i.451.7		16
7.3	odd	6		1470.3.f.d.391.12		16
7.4	even	3		1470.3.f.d.391.14		16
7.5	odd	6	inner	210.3.o.b.61.1	yes	16
21.5	even	6		630.3.v.c.271.7		16
35.12	even	12		1050.3.q.e.649.3		32
35.19	odd	6		1050.3.p.i.901.7		16
35.33	even	12		1050.3.q.e.649.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.1	✓	16	1.1	even	1	trivial
210.3.o.b.61.1	yes	16	7.5	odd	6	inner
630.3.v.c.271.7		16	21.5	even	6
630.3.v.c.451.7		16	3.2	odd	2
1050.3.p.i.451.7		16	5.4	even	2
1050.3.p.i.901.7		16	35.19	odd	6
1050.3.q.e.199.3		32	5.3	odd	4
1050.3.q.e.199.14		32	5.2	odd	4
1050.3.q.e.649.3		32	35.12	even	12
1050.3.q.e.649.13		32	35.33	even	12
1470.3.f.d.391.12		16	7.3	odd	6
1470.3.f.d.391.14		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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(-2.59373 - 6.50174i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(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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