LMFDB - Embedded newform 38.3.d.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,3,Mod(27,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	38.d (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:	$1.03542500457$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.3.d.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(2.72474 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +6.89898 q^{7} -2.82843i q^{8} +(0.449490 + 0.778539i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(2.72474 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +6.89898 q^{7} -2.82843i q^{8} +(0.449490 + 0.778539i) q^{9} +(-1.22474 + 0.707107i) q^{10} -14.8990 q^{11} +6.29253i q^{12} +(-14.8485 + 8.57277i) q^{13} +(-8.44949 - 4.87832i) q^{14} +(2.72474 - 1.57313i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.05051 - 1.81954i) q^{17} -1.27135i q^{18} +(11.3485 - 15.2385i) q^{19} +2.00000 q^{20} +(18.7980 + 10.8530i) q^{21} +(18.2474 + 10.5352i) q^{22} +(-13.5227 - 23.4220i) q^{23} +(4.44949 - 7.70674i) q^{24} +(12.0000 + 20.7846i) q^{25} +24.2474 q^{26} -25.4880i q^{27} +(6.89898 + 11.9494i) q^{28} +(-5.54541 + 3.20164i) q^{29} -4.44949 q^{30} +31.1769i q^{31} +(4.89898 - 2.82843i) q^{32} +(-40.5959 - 23.4381i) q^{33} +(-2.57321 + 1.48565i) q^{34} +(3.44949 - 5.97469i) q^{35} +(-0.898979 + 1.55708i) q^{36} +28.9199i q^{37} +(-24.6742 + 10.6387i) q^{38} -53.9444 q^{39} +(-2.44949 - 1.41421i) q^{40} +(55.9393 + 32.2966i) q^{41} +(-15.3485 - 26.5843i) q^{42} +(37.6691 - 65.2449i) q^{43} +(-14.8990 - 25.8058i) q^{44} +0.898979 q^{45} +38.2480i q^{46} +(5.77015 + 9.99420i) q^{47} +(-10.8990 + 6.29253i) q^{48} -1.40408 q^{49} -33.9411i q^{50} +(5.72474 - 3.30518i) q^{51} +(-29.6969 - 17.1455i) q^{52} +(-69.2878 + 40.0033i) q^{53} +(-18.0227 + 31.2162i) q^{54} +(-7.44949 + 12.9029i) q^{55} -19.5133i q^{56} +(54.8939 - 23.6684i) q^{57} +9.05561 q^{58} +(50.9166 + 29.3967i) q^{59} +(5.44949 + 3.14626i) q^{60} +(-1.09592 - 1.89819i) q^{61} +(22.0454 - 38.1838i) q^{62} +(3.10102 + 5.37113i) q^{63} -8.00000 q^{64} +17.1455i q^{65} +(33.1464 + 57.4113i) q^{66} +(-51.6589 + 29.8253i) q^{67} +4.20204 q^{68} -85.0920i q^{69} +(-8.44949 + 4.87832i) q^{70} +(87.5227 + 50.5313i) q^{71} +(2.20204 - 1.27135i) q^{72} +(63.6918 - 110.317i) q^{73} +(20.4495 - 35.4196i) q^{74} +75.5103i q^{75} +(37.7423 + 4.41761i) q^{76} -102.788 q^{77} +(66.0681 + 38.1444i) q^{78} +(-5.78036 - 3.33729i) q^{79} +(2.00000 + 3.46410i) q^{80} +(44.1413 - 76.4550i) q^{81} +(-45.6742 - 79.1101i) q^{82} -1.30306 q^{83} +43.4120i q^{84} +(-1.05051 - 1.81954i) q^{85} +(-92.2702 + 53.2722i) q^{86} -20.1464 q^{87} +42.1407i q^{88} +(5.84847 - 3.37662i) q^{89} +(-1.10102 - 0.635674i) q^{90} +(-102.439 + 59.1433i) q^{91} +(27.0454 - 46.8440i) q^{92} +(-49.0454 + 84.9491i) q^{93} -16.3205i q^{94} +(-7.52270 - 17.4473i) q^{95} +17.7980 q^{96} +(-114.152 - 65.9054i) q^{97} +(1.71964 + 0.992836i) q^{98} +(-6.69694 - 11.5994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9	$ 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 40 q^{11} - 30 q^{13} - 24 q^{14} + 6 q^{15} - 8 q^{16} + 14 q^{17} + 16 q^{19} + 8 q^{20} + 36 q^{21} + 24 q^{22} - 10 q^{23} + 8 q^{24} + 48 q^{25} + 48 q^{26} + 8 q^{28} + 66 q^{29} - 8 q^{30} - 84 q^{33} + 24 q^{34} + 4 q^{35} + 16 q^{36} - 84 q^{38} - 108 q^{39} + 18 q^{41} - 32 q^{42} + 38 q^{43} - 40 q^{44} - 16 q^{45} - 70 q^{47} - 24 q^{48} - 84 q^{49} + 18 q^{51} - 60 q^{52} - 42 q^{53} - 28 q^{54} - 20 q^{55} + 102 q^{57} + 144 q^{58} + 42 q^{59} + 12 q^{60} + 74 q^{61} + 32 q^{63} - 32 q^{64} + 64 q^{66} + 102 q^{67} + 56 q^{68} - 24 q^{70} + 306 q^{71} + 48 q^{72} + 98 q^{73} + 72 q^{74} + 4 q^{76} - 176 q^{77} + 132 q^{78} - 126 q^{79} + 8 q^{80} + 10 q^{81} - 168 q^{82} - 64 q^{83} - 14 q^{85} - 276 q^{86} - 12 q^{87} - 6 q^{89} - 24 q^{90} - 204 q^{91} + 20 q^{92} - 108 q^{93} + 14 q^{95} + 32 q^{96} - 486 q^{97} - 96 q^{98} + 32 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 40 * q^11 - 30 * q^13 - 24 * q^14 + 6 * q^15 - 8 * q^16 + 14 * q^17 + 16 * q^19 + 8 * q^20 + 36 * q^21 + 24 * q^22 - 10 * q^23 + 8 * q^24 + 48 * q^25 + 48 * q^26 + 8 * q^28 + 66 * q^29 - 8 * q^30 - 84 * q^33 + 24 * q^34 + 4 * q^35 + 16 * q^36 - 84 * q^38 - 108 * q^39 + 18 * q^41 - 32 * q^42 + 38 * q^43 - 40 * q^44 - 16 * q^45 - 70 * q^47 - 24 * q^48 - 84 * q^49 + 18 * q^51 - 60 * q^52 - 42 * q^53 - 28 * q^54 - 20 * q^55 + 102 * q^57 + 144 * q^58 + 42 * q^59 + 12 * q^60 + 74 * q^61 + 32 * q^63 - 32 * q^64 + 64 * q^66 + 102 * q^67 + 56 * q^68 - 24 * q^70 + 306 * q^71 + 48 * q^72 + 98 * q^73 + 72 * q^74 + 4 * q^76 - 176 * q^77 + 132 * q^78 - 126 * q^79 + 8 * q^80 + 10 * q^81 - 168 * q^82 - 64 * q^83 - 14 * q^85 - 276 * q^86 - 12 * q^87 - 6 * q^89 - 24 * q^90 - 204 * q^91 + 20 * q^92 - 108 * q^93 + 14 * q^95 + 32 * q^96 - 486 * q^97 - 96 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	2.72474	+	1.57313i	0.908248	+	0.524377i	0.879867	−	0.475220i	$-0.157631\pi$
$3$	2.72474	+	1.57313i	0.908248	+	0.524377i	0.0283812	+	0.999597i	$0.490965\pi$
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.100000	−	0.173205i	−0.811684	−	0.584096i	$-0.801449\pi$
$5$	0.500000	−	0.866025i	0.100000	−	0.173205i	0.911684	+	0.410891i	$0.134782\pi$
$6$	−2.22474	−	3.85337i	−0.370791	−	0.642229i
$7$	6.89898			0.985568			0.492784	−	0.870152i	$-0.335979\pi$
$7$	6.89898			0.985568			0.492784	+	0.870152i	$0.335979\pi$
$8$		−	2.82843i		−	0.353553i
$9$	0.449490	+	0.778539i	0.0499433	+	0.0865043i
$10$	−1.22474	+	0.707107i	−0.122474	+	0.0707107i
$11$	−14.8990			−1.35445			−0.677226	−	0.735775i	$-0.736818\pi$
$11$	−14.8990			−1.35445			−0.677226	+	0.735775i	$0.736818\pi$
$12$			6.29253i			0.524377i
$13$	−14.8485	+	8.57277i	−1.14219	+	0.659444i	−0.946972	−	0.321316i	$-0.895875\pi$
$13$	−14.8485	+	8.57277i	−1.14219	+	0.659444i	−0.195218	+	0.980760i	$0.562541\pi$
$14$	−8.44949	−	4.87832i	−0.603535	−	0.348451i
$15$	2.72474	−	1.57313i	0.181650	−	0.104875i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	1.05051	−	1.81954i	0.0617947	−	0.107032i	−0.833473	−	0.552560i	$-0.813651\pi$
$17$	1.05051	−	1.81954i	0.0617947	−	0.107032i	0.895268	+	0.445529i	$0.146984\pi$
$18$		−	1.27135i		−	0.0706305i
$19$	11.3485	−	15.2385i	0.597288	−	0.802027i
$19$	11.3485	−	15.2385i	0.597288	−	0.802027i
$20$	2.00000			0.100000
$21$	18.7980	+	10.8530i	0.895141	+	0.516810i
$22$	18.2474	+	10.5352i	0.829429	+	0.478871i
$23$	−13.5227	−	23.4220i	−0.587944	−	1.01835i	−0.994501	−	0.104723i	$-0.966604\pi$
$23$	−13.5227	−	23.4220i	−0.587944	−	1.01835i	0.406558	−	0.913625i	$-0.366729\pi$
$24$	4.44949	−	7.70674i	0.185395	−	0.321114i
$25$	12.0000	+	20.7846i	0.480000	+	0.831384i
$26$	24.2474			0.932594
$27$		−	25.4880i		−	0.943998i
$28$	6.89898	+	11.9494i	0.246392	+	0.426764i
$29$	−5.54541	+	3.20164i	−0.191221	+	0.110401i	−0.592554	−	0.805531i	$-0.701880\pi$
$29$	−5.54541	+	3.20164i	−0.191221	+	0.110401i	0.401333	+	0.915932i	$0.368547\pi$
$30$	−4.44949			−0.148316
$31$			31.1769i			1.00571i	0.864372	+	0.502853i	$0.167716\pi$
$31$			31.1769i			1.00571i	−0.864372	+	0.502853i	$0.832284\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	−40.5959	−	23.4381i	−1.23018	−	0.710244i
$34$	−2.57321	+	1.48565i	−0.0756828	+	0.0436955i
$35$	3.44949	−	5.97469i	0.0985568	−	0.170705i
$36$	−0.898979	+	1.55708i	−0.0249717	+	0.0432522i
$37$			28.9199i			0.781620i	0.920471	+	0.390810i	$0.127805\pi$
$37$			28.9199i			0.781620i	−0.920471	+	0.390810i	$0.872195\pi$
$38$	−24.6742	+	10.6387i	−0.649322	+	0.279966i
$39$	−53.9444			−1.38319
$40$	−2.44949	−	1.41421i	−0.0612372	−	0.0353553i
$41$	55.9393	+	32.2966i	1.36437	+	0.787721i	0.990202	−	0.139639i	$-0.0445942\pi$
$41$	55.9393	+	32.2966i	1.36437	+	0.787721i	0.374170	+	0.927360i	$0.377928\pi$
$42$	−15.3485	−	26.5843i	−0.365440	−	0.632960i
$43$	37.6691	−	65.2449i	0.876026	−	1.51732i	0.0203609	−	0.999793i	$-0.493518\pi$
$43$	37.6691	−	65.2449i	0.876026	−	1.51732i	0.855665	−	0.517529i	$-0.173148\pi$
$44$	−14.8990	−	25.8058i	−0.338613	−	0.586495i
$45$	0.898979			0.0199773
$46$			38.2480i			0.831478i
$47$	5.77015	+	9.99420i	0.122769	+	0.212642i	0.920859	−	0.389896i	$-0.127489\pi$
$47$	5.77015	+	9.99420i	0.122769	+	0.212642i	−0.798090	+	0.602539i	$0.794156\pi$
$48$	−10.8990	+	6.29253i	−0.227062	+	0.131094i
$49$	−1.40408			−0.0286547
$50$		−	33.9411i		−	0.678823i
$51$	5.72474	−	3.30518i	0.112250	−	0.0648075i
$52$	−29.6969	−	17.1455i	−0.571095	−	0.329722i
$53$	−69.2878	+	40.0033i	−1.30732	+	0.754779i	−0.981647	−	0.190705i	$-0.938923\pi$
$53$	−69.2878	+	40.0033i	−1.30732	+	0.754779i	−0.325669	+	0.945484i	$0.605589\pi$
$54$	−18.0227	+	31.2162i	−0.333754	+	0.578078i
$55$	−7.44949	+	12.9029i	−0.135445	+	0.234598i
$56$		−	19.5133i		−	0.348451i
$57$	54.8939	−	23.6684i	0.963050	−	0.415235i
$58$	9.05561			0.156131
$59$	50.9166	+	29.3967i	0.862993	+	0.498249i	0.865013	−	0.501749i	$-0.167310\pi$
$59$	50.9166	+	29.3967i	0.862993	+	0.498249i	−0.00202049	+	0.999998i	$0.500643\pi$
$60$	5.44949	+	3.14626i	0.0908248	+	0.0524377i
$61$	−1.09592	−	1.89819i	−0.0179659	−	0.0311178i	0.856903	−	0.515478i	$-0.172386\pi$
$61$	−1.09592	−	1.89819i	−0.0179659	−	0.0311178i	−0.874869	+	0.484360i	$0.839052\pi$
$62$	22.0454	−	38.1838i	0.355571	−	0.615867i
$63$	3.10102	+	5.37113i	0.0492225	+	0.0852560i
$64$	−8.00000			−0.125000
$65$			17.1455i			0.263777i
$66$	33.1464	+	57.4113i	0.502219	+	0.869868i
$67$	−51.6589	+	29.8253i	−0.771029	+	0.445154i	−0.833241	−	0.552909i	$-0.813518\pi$
$67$	−51.6589	+	29.8253i	−0.771029	+	0.445154i	0.0622127	+	0.998063i	$0.480184\pi$
$68$	4.20204			0.0617947
$69$		−	85.0920i		−	1.23322i
$70$	−8.44949	+	4.87832i	−0.120707	+	0.0696902i
$71$	87.5227	+	50.5313i	1.23271	+	0.711708i	0.967595	−	0.252508i	$-0.0812553\pi$
$71$	87.5227	+	50.5313i	1.23271	+	0.711708i	0.265119	+	0.964216i	$0.414589\pi$
$72$	2.20204	−	1.27135i	0.0305839	−	0.0176576i
$73$	63.6918	−	110.317i	0.872491	−	1.51120i	0.0130791	−	0.999914i	$-0.495837\pi$
$73$	63.6918	−	110.317i	0.872491	−	1.51120i	0.859412	−	0.511284i	$-0.170830\pi$
$74$	20.4495	−	35.4196i	0.276344	−	0.478643i
$75$			75.5103i			1.00680i
$76$	37.7423	+	4.41761i	0.496610	+	0.0581265i
$77$	−102.788			−1.33491
$78$	66.0681	+	38.1444i	0.847027	+	0.489031i
$79$	−5.78036	−	3.33729i	−0.0731691	−	0.0422442i	0.462969	−	0.886374i	$-0.346784\pi$
$79$	−5.78036	−	3.33729i	−0.0731691	−	0.0422442i	−0.536138	+	0.844130i	$0.680117\pi$
$80$	2.00000	+	3.46410i	0.0250000	+	0.0433013i
$81$	44.1413	−	76.4550i	0.544955	−	0.943889i
$82$	−45.6742	−	79.1101i	−0.557003	−	0.964757i
$83$	−1.30306			−0.0156995			−0.00784977	−	0.999969i	$-0.502499\pi$
$83$	−1.30306			−0.0156995			−0.00784977	+	0.999969i	$0.502499\pi$
$84$			43.4120i			0.516810i
$85$	−1.05051	−	1.81954i	−0.0123589	−	0.0214063i
$86$	−92.2702	+	53.2722i	−1.07291	+	0.619444i
$87$	−20.1464			−0.231568
$88$			42.1407i			0.478871i
$89$	5.84847	−	3.37662i	0.0657131	−	0.0379395i	−0.466783	−	0.884372i	$-0.654587\pi$
$89$	5.84847	−	3.37662i	0.0657131	−	0.0379395i	0.532497	+	0.846432i	$0.321254\pi$
$90$	−1.10102	−	0.635674i	−0.0122336	−	0.00706305i
$91$	−102.439	+	59.1433i	−1.12571	+	0.649927i
$92$	27.0454	−	46.8440i	0.293972	−	0.509174i
$93$	−49.0454	+	84.9491i	−0.527370	+	0.913432i
$94$		−	16.3205i		−	0.173622i
$95$	−7.52270	−	17.4473i	−0.0791864	−	0.183656i
$96$	17.7980			0.185395
$97$	−114.152	−	65.9054i	−1.17682	−	0.679437i	−0.221543	−	0.975151i	$-0.571109\pi$
$97$	−114.152	−	65.9054i	−1.17682	−	0.679437i	−0.955277	+	0.295713i	$0.904443\pi$
$98$	1.71964	+	0.992836i	0.0175474	+	0.0101310i
$99$	−6.69694	−	11.5994i	−0.0676458	−	0.117166i
$100$	−24.0000	+	41.5692i	−0.240000	+	0.415692i
$101$	−3.24235	−	5.61591i	−0.0321024	−	0.0556031i	0.849528	−	0.527544i	$-0.176887\pi$
$101$	−3.24235	−	5.61591i	−0.0321024	−	0.0556031i	−0.881630	+	0.471941i	$0.843554\pi$
$102$	−9.34847			−0.0916517
$103$		−	80.0243i		−	0.776935i	−0.921462	−	0.388467i	$-0.873005\pi$
$103$		−	80.0243i		−	0.776935i	0.921462	−	0.388467i	$-0.126995\pi$
$104$	24.2474	+	41.9978i	0.233149	+	0.403825i
$105$	18.7980	−	10.8530i	0.179028	−	0.103362i
$106$	113.146			1.06742
$107$		−	80.0243i		−	0.747890i	−0.927451	−	0.373945i	$-0.878005\pi$
$107$		−	80.0243i		−	0.747890i	0.927451	−	0.373945i	$-0.121995\pi$
$108$	44.1464	−	25.4880i	0.408763	−	0.236000i
$109$	−14.2423	−	8.22282i	−0.130664	−	0.0754387i	0.433243	−	0.901277i	$-0.357369\pi$
$109$	−14.2423	−	8.22282i	−0.130664	−	0.0754387i	−0.563907	+	0.825838i	$0.690702\pi$
$110$	18.2474	−	10.5352i	0.165886	−	0.0957743i
$111$	−45.4949	+	78.7995i	−0.409864	+	0.709905i
$112$	−13.7980	+	23.8988i	−0.123196	+	0.213382i
$113$			132.843i			1.17560i	0.809006	+	0.587801i	$0.200006\pi$
$113$			132.843i			1.17560i	−0.809006	+	0.587801i	$0.799994\pi$
$114$	−83.9671	−	9.82806i	−0.736553	−	0.0862111i
$115$	−27.0454			−0.235177
$116$	−11.0908	−	6.40329i	−0.0956105	−	0.0552007i
$117$	−13.3485	−	7.70674i	−0.114089	−	0.0658696i
$118$	−41.5732	−	72.0069i	−0.352315	−	0.610228i
$119$	7.24745	−	12.5529i	0.0609029	−	0.105487i
$120$	−4.44949	−	7.70674i	−0.0370791	−	0.0642229i
$121$	100.980			0.834542
$122$			3.09972i			0.0254076i
$123$	101.614	+	176.000i	0.826126	+	1.43089i
$124$	−54.0000	+	31.1769i	−0.435484	+	0.251427i
$125$	49.0000			0.392000
$126$		−	8.77101i		−	0.0696112i
$127$	108.826	−	62.8306i	0.856896	−	0.494729i	−0.00607575	−	0.999982i	$-0.501934\pi$
$127$	108.826	−	62.8306i	0.856896	−	0.494729i	0.862972	+	0.505253i	$0.168601\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	205.278	−	118.517i	1.59130	−	0.918737i
$130$	12.1237	−	20.9989i	0.0932594	−	0.161530i
$131$	−53.6237	+	92.8790i	−0.409341	+	0.709000i	−0.994816	−	0.101691i	$-0.967575\pi$
$131$	−53.6237	+	92.8790i	−0.409341	+	0.709000i	0.585475	+	0.810691i	$0.300908\pi$
$132$		−	93.7523i		−	0.710244i
$133$	78.2929	−	105.130i	0.588668	−	0.790452i
$134$	84.3587			0.629542
$135$	−22.0732	−	12.7440i	−0.163505	−	0.0943998i
$136$	−5.14643	−	2.97129i	−0.0378414	−	0.0218477i
$137$	1.05051	+	1.81954i	0.00766796	+	0.0132813i	0.869834	−	0.493345i	$-0.164226\pi$
$137$	1.05051	+	1.81954i	0.00766796	+	0.0132813i	−0.862166	+	0.506626i	$0.830893\pi$
$138$	−60.1691	+	104.216i	−0.436008	+	0.755188i
$139$	15.8712	+	27.4897i	0.114181	+	0.197767i	0.917452	−	0.397846i	$-0.130242\pi$
$139$	15.8712	+	27.4897i	0.114181	+	0.197767i	−0.803271	+	0.595614i	$0.796909\pi$
$140$	13.7980			0.0985568
$141$			36.3089i			0.257510i
$142$	−71.4620	−	123.776i	−0.503253	−	0.871661i
$143$	221.227	−	127.725i	1.54704	−	0.893185i
$144$	−3.59592			−0.0249717
$145$			6.40329i			0.0441606i
$146$	−156.012	+	90.0739i	−1.06858	+	0.616944i
$147$	−3.82577	−	2.20881i	−0.0260256	−	0.0150259i
$148$	−50.0908	+	28.9199i	−0.338451	+	0.195405i
$149$	−94.8383	+	164.265i	−0.636498	+	1.10245i	0.349697	+	0.936863i	$0.386284\pi$
$149$	−94.8383	+	164.265i	−0.636498	+	1.10245i	−0.986196	+	0.165585i	$0.947049\pi$
$150$	53.3939	−	92.4809i	0.355959	−	0.616539i
$151$		−	16.2707i		−	0.107753i	−0.998548	−	0.0538764i	$-0.982842\pi$
$151$		−	16.2707i		−	0.107753i	0.998548	−	0.0538764i	$-0.0171577\pi$
$152$	−43.1010	−	32.0983i	−0.283559	−	0.211173i
$153$	1.88877			0.0123449
$154$	125.889	+	72.6819i	0.817460	+	0.471961i
$155$	27.0000	+	15.5885i	0.174194	+	0.100571i
$156$	−53.9444	−	93.4344i	−0.345797	−	0.598939i
$157$	−135.076	+	233.958i	−0.860354	+	1.49018i	0.0112344	+	0.999937i	$0.496424\pi$
$157$	−135.076	+	233.958i	−0.860354	+	1.49018i	−0.871588	+	0.490239i	$0.836909\pi$
$158$	4.71964	+	8.17466i	0.0298712	+	0.0517384i
$159$	−251.722			−1.58316
$160$		−	5.65685i		−	0.0353553i
$161$	−93.2929	−	161.588i	−0.579459	−	1.00365i
$162$	−108.124	+	62.4253i	−0.667430	+	0.385341i
$163$	−156.697			−0.961331			−0.480665	−	0.876904i	$-0.659605\pi$
$163$	−156.697			−0.961331			−0.480665	+	0.876904i	$0.659605\pi$
$164$			129.186i			0.787721i
$165$	−40.5959	+	23.4381i	−0.246036	+	0.142049i
$166$	1.59592	+	0.921404i	0.00961396	+	0.00555062i
$167$	−78.0834	+	45.0815i	−0.467565	+	0.269949i	−0.715220	−	0.698899i	$-0.753674\pi$
$167$	−78.0834	+	45.0815i	−0.467565	+	0.269949i	0.247655	+	0.968848i	$0.420340\pi$
$168$	30.6969	−	53.1687i	0.182720	−	0.316480i
$169$	62.4847	−	108.227i	0.369732	−	0.640394i
$170$			2.97129i			0.0174782i
$171$	16.9648	+	1.98567i	0.0992093	+	0.0116121i
$172$	150.677			0.876026
$173$	−263.379	−	152.062i	−1.52242	−	0.878969i	−0.999649	−	0.0264959i	$-0.991565\pi$
$173$	−263.379	−	152.062i	−1.52242	−	0.878969i	−0.522771	−	0.852473i	$-0.675102\pi$
$174$	24.6742	+	14.2457i	0.141806	+	0.0818717i
$175$	82.7878	+	143.393i	0.473073	+	0.819386i
$176$	29.7980	−	51.6116i	0.169307	−	0.293248i
$177$	92.4898	+	160.197i	0.522541	+	0.905068i
$178$	−9.55051			−0.0536546
$179$		−	315.198i		−	1.76088i	−0.474156	−	0.880441i	$-0.657247\pi$
$179$		−	315.198i		−	1.76088i	0.474156	−	0.880441i	$-0.342753\pi$
$180$	0.898979	+	1.55708i	0.00499433	+	0.00865043i
$181$	−27.8939	+	16.1045i	−0.154110	+	0.0889753i	−0.575072	−	0.818103i	$-0.695026\pi$
$181$	−27.8939	+	16.1045i	−0.154110	+	0.0889753i	0.420962	+	0.907078i	$0.361693\pi$
$182$	167.283			0.919135
$183$		−	6.89610i		−	0.0376836i
$184$	−66.2474	+	38.2480i	−0.360040	+	0.207869i
$185$	25.0454	+	14.4600i	0.135381	+	0.0781620i
$186$	120.136	−	69.3607i	0.645894	−	0.372907i
$187$	−15.6515	+	27.1092i	−0.0836980	+	0.144969i
$188$	−11.5403	+	19.9884i	−0.0613846	+	0.106321i
$189$		−	175.841i		−	0.930375i
$190$	−3.12372	+	26.6879i	−0.0164407	+	0.140462i
$191$	280.252			1.46729			0.733644	−	0.679534i	$-0.237818\pi$
$191$	280.252			1.46729			0.733644	+	0.679534i	$0.237818\pi$
$192$	−21.7980	−	12.5851i	−0.113531	−	0.0655472i
$193$	42.0153	+	24.2575i	0.217696	+	0.125687i	0.604883	−	0.796314i	$-0.293220\pi$
$193$	42.0153	+	24.2575i	0.217696	+	0.125687i	−0.387187	+	0.922001i	$0.626553\pi$
$194$	93.2043	+	161.435i	0.480435	+	0.832137i
$195$	−26.9722	+	46.7172i	−0.138319	+	0.239575i
$196$	−1.40408	−	2.43194i	−0.00716368	−	0.0124079i
$197$	251.909			1.27873			0.639363	−	0.768905i	$-0.279198\pi$
$197$	251.909			1.27873			0.639363	+	0.768905i	$0.279198\pi$
$198$			18.9418i			0.0956657i
$199$	−129.694	−	224.637i	−0.651729	−	1.12883i	−0.982703	−	0.185188i	$-0.940710\pi$
$199$	−129.694	−	224.637i	−0.651729	−	1.12883i	0.330974	−	0.943640i	$-0.392623\pi$
$200$	58.7878	−	33.9411i	0.293939	−	0.169706i
$201$	−187.677			−0.933714
$202$			9.17074i			0.0453997i
$203$	−38.2577	+	22.0881i	−0.188461	+	0.108808i
$204$	11.4495	+	6.61037i	0.0561249	+	0.0324038i
$205$	55.9393	−	32.2966i	0.272875	−	0.157544i
$206$	−56.5857	+	98.0093i	−0.274688	+	0.475773i
$207$	12.1566	−	21.0559i	0.0587277	−	0.101719i
$208$		−	68.5821i		−	0.329722i
$209$	−169.081	+	227.038i	−0.808998	+	1.08631i
$210$	−30.6969			−0.146176
$211$	60.2503	+	34.7855i	0.285546	+	0.164860i	0.635932	−	0.771745i	$-0.280616\pi$
$211$	60.2503	+	34.7855i	0.285546	+	0.164860i	−0.350385	+	0.936606i	$0.613949\pi$
$212$	−138.576	−	80.0066i	−0.653658	−	0.377390i
$213$	158.985	+	275.370i	0.746407	+	1.29281i
$214$	−56.5857	+	98.0093i	−0.264419	+	0.457988i
$215$	−37.6691	−	65.2449i	−0.175205	−	0.303464i
$216$	−72.0908			−0.333754
$217$			215.089i			0.991193i
$218$	11.6288	+	20.1417i	0.0533432	+	0.0923932i
$219$	347.088	−	200.391i	1.58488	−	0.915029i
$220$	−29.7980			−0.135445
$221$			36.0231i			0.163001i
$222$	111.439	−	64.3395i	0.501979	−	0.289818i
$223$	−5.47730	−	3.16232i	−0.0245619	−	0.0141808i	0.487669	−	0.873029i	$-0.337847\pi$
$223$	−5.47730	−	3.16232i	−0.0245619	−	0.0141808i	−0.512231	+	0.858848i	$0.671181\pi$
$224$	33.7980	−	19.5133i	0.150884	−	0.0871128i
$225$	−10.7878	+	18.6849i	−0.0479456	+	0.0830442i
$226$	93.9342	−	162.699i	0.415638	−	0.719906i
$227$		−	55.7402i		−	0.245552i	−0.992434	−	0.122776i	$-0.960820\pi$
$227$		−	55.7402i		−	0.245552i	0.992434	−	0.122776i	$-0.0391796\pi$
$228$	95.8888	+	71.4106i	0.420565	+	0.313204i
$229$	−132.313			−0.577787			−0.288894	−	0.957361i	$-0.593287\pi$
$229$	−132.313			−0.577787			−0.288894	+	0.957361i	$0.593287\pi$
$230$	33.1237	+	19.1240i	0.144016	+	0.0831478i
$231$	−280.070	−	161.699i	−1.21243	−	0.699994i
$232$	9.05561	+	15.6848i	0.0390328	+	0.0676068i
$233$	111.859	−	193.745i	0.480080	−	0.831523i	−0.519659	−	0.854374i	$-0.673941\pi$
$233$	111.859	−	193.745i	0.480080	−	0.831523i	0.999739	+	0.0228507i	$0.00727424\pi$
$234$	10.8990	+	18.8776i	0.0465768	+	0.0806734i
$235$	11.5403			0.0491077
$236$			117.587i			0.498249i
$237$	−10.5000	−	18.1865i	−0.0443038	−	0.0767364i
$238$	−17.7526	+	10.2494i	−0.0745906	+	0.0430649i
$239$	−71.3235			−0.298425			−0.149212	−	0.988805i	$-0.547674\pi$
$239$	−71.3235			−0.298425			−0.149212	+	0.988805i	$0.547674\pi$
$240$			12.5851i			0.0524377i
$241$	120.727	−	69.7018i	0.500942	−	0.289219i	−0.228160	−	0.973624i	$-0.573271\pi$
$241$	120.727	−	69.7018i	0.500942	−	0.289219i	0.729103	+	0.684405i	$0.239938\pi$
$242$	−123.674	−	71.4034i	−0.511051	−	0.295055i
$243$	41.8888	−	24.1845i	0.172382	−	0.0995247i
$244$	2.19184	−	3.79637i	0.00898293	−	0.0155589i
$245$	−0.702041	+	1.21597i	−0.00286547	+	0.00496315i
$246$		−	287.406i		−	1.16832i
$247$	−37.8712	+	323.556i	−0.153325	+	1.30994i
$248$	88.1816			0.355571
$249$	−3.55051	−	2.04989i	−0.0142591	−	0.00823248i
$250$	−60.0125	−	34.6482i	−0.240050	−	0.138593i
$251$	−120.038	−	207.912i	−0.478239	−	0.828334i	0.521450	−	0.853282i	$-0.325391\pi$
$251$	−120.038	−	207.912i	−0.478239	−	0.828334i	−0.999689	+	0.0249476i	$0.992058\pi$
$252$	−6.20204	+	10.7423i	−0.0246113	+	0.0426280i
$253$	201.474	+	348.964i	0.796342	+	1.37930i
$254$	−177.712			−0.699652
$255$		−	6.61037i		−	0.0259230i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	8.37857	−	4.83737i	0.0326014	−	0.0188224i	−0.483611	−	0.875283i	$-0.660675\pi$
$257$	8.37857	−	4.83737i	0.0326014	−	0.0188224i	0.516212	+	0.856461i	$0.327342\pi$
$258$	−335.217			−1.29929
$259$			199.518i			0.770340i
$260$	−29.6969	+	17.1455i	−0.114219	+	0.0659444i
$261$	−4.98521	−	2.87821i	−0.0191004	−	0.0110276i
$262$	131.351	−	75.8354i	0.501339	−	0.289448i
$263$	56.9620	−	98.6611i	0.216586	−	0.375137i	−0.737176	−	0.675700i	$-0.763841\pi$
$263$	56.9620	−	98.6611i	0.216586	−	0.375137i	0.953762	+	0.300563i	$0.0971747\pi$
$264$	−66.2929	+	114.823i	−0.251109	+	0.434934i
$265$			80.0066i			0.301912i
$266$	−170.227	+	73.3962i	−0.639951	+	0.275926i
$267$	21.2474			0.0795785
$268$	−103.318	−	59.6506i	−0.385514	−	0.222577i
$269$	−348.090	−	200.970i	−1.29402	−	0.747100i	−0.314652	−	0.949207i	$-0.601888\pi$
$269$	−348.090	−	200.970i	−1.29402	−	0.747100i	−0.979364	+	0.202106i	$0.935221\pi$
$270$	18.0227	+	31.2162i	0.0667508	+	0.115616i
$271$	−199.492	+	345.530i	−0.736133	+	1.27502i	0.218091	+	0.975928i	$0.430017\pi$
$271$	−199.492	+	345.530i	−0.736133	+	1.27502i	−0.954224	+	0.299092i	$0.903316\pi$
$272$	4.20204	+	7.27815i	0.0154487	+	0.0267579i
$273$	−372.161			−1.36323
$274$		−	2.97129i		−	0.0108441i
$275$	−178.788	−	309.669i	−0.650137	−	1.12607i
$276$	147.384	−	85.0920i	0.533999	−	0.308304i
$277$	529.444			1.91135			0.955675	−	0.294424i	$-0.0951278\pi$
$277$	529.444			1.91135			0.955675	+	0.294424i	$0.0951278\pi$
$278$		−	44.8905i		−	0.161476i
$279$	−24.2724	+	14.0137i	−0.0869980	+	0.0502283i
$280$	−16.8990	−	9.75663i	−0.0603535	−	0.0348451i
$281$	47.4092	−	27.3717i	0.168716	−	0.0974082i	−0.413264	−	0.910611i	$-0.635611\pi$
$281$	47.4092	−	27.3717i	0.168716	−	0.0974082i	0.581980	+	0.813203i	$0.302278\pi$
$282$	25.6742	−	44.4691i	0.0910434	−	0.157692i
$283$	74.4671	−	128.981i	0.263135	−	0.455762i	−0.703939	−	0.710261i	$-0.748577\pi$
$283$	74.4671	−	128.981i	0.263135	−	0.455762i	0.967073	+	0.254498i	$0.0819103\pi$
$284$			202.125i			0.711708i
$285$	6.94949	−	59.3737i	0.0243842	−	0.208329i
$286$	−361.262			−1.26315
$287$	385.924	+	222.813i	1.34468	+	0.776353i
$288$	4.40408	+	2.54270i	0.0152920	+	0.00882881i
$289$	142.293	+	246.458i	0.492363	+	0.852797i
$290$	4.52781	−	7.84239i	0.0156131	−	0.0270427i
$291$	−207.356	−	359.151i	−0.712563	−	1.23420i
$292$	254.767			0.872491
$293$			145.685i			0.497218i	0.968604	+	0.248609i	$0.0799734\pi$
$293$			145.685i			0.497218i	−0.968604	+	0.248609i	$0.920027\pi$
$294$	3.12372	+	5.41045i	0.0106249	+	0.0184029i
$295$	50.9166	−	29.3967i	0.172599	−	0.0996498i
$296$	81.7980			0.276344
$297$			379.744i			1.27860i
$298$	232.305	−	134.122i	0.779548	−	0.450072i
$299$	401.583	+	231.854i	1.34309	+	0.775431i
$300$	−130.788	+	75.5103i	−0.435959	+	0.251701i
$301$	259.879	−	450.123i	0.863384	−	1.49542i
$302$	−11.5051	+	19.9274i	−0.0380964	+	0.0659848i
$303$		−	20.4026i		−	0.0673352i
$304$	30.0908	+	69.7893i	0.0989829	+	0.229570i
$305$	−2.19184			−0.00718635
$306$	−2.31327	−	1.33557i	−0.00755970	−	0.00436459i
$307$	98.0380	+	56.6023i	0.319342	+	0.184372i	0.651099	−	0.758993i	$-0.274308\pi$
$307$	98.0380	+	56.6023i	0.319342	+	0.184372i	−0.331757	+	0.943365i	$0.607641\pi$
$308$	−102.788	−	178.034i	−0.333726	−	0.578031i
$309$	125.889	−	218.046i	0.407407	−	0.705650i
$310$	−22.0454	−	38.1838i	−0.0711142	−	0.123173i
$311$	−105.666			−0.339763			−0.169882	−	0.985464i	$-0.554339\pi$
$311$	−105.666			−0.339763			−0.169882	+	0.985464i	$0.554339\pi$
$312$			152.578i			0.489031i
$313$	−124.121	−	214.984i	−0.396552	−	0.686849i	0.596746	−	0.802431i	$-0.296460\pi$
$313$	−124.121	−	214.984i	−0.396552	−	0.686849i	−0.993298	+	0.115582i	$0.963127\pi$
$314$	330.866	−	191.026i	1.05371	−	0.608362i
$315$	6.20204			0.0196890
$316$		−	13.3492i		−	0.0422442i
$317$	−196.061	+	113.196i	−0.618488	+	0.357084i	−0.776280	−	0.630388i	$-0.782896\pi$
$317$	−196.061	+	113.196i	−0.618488	+	0.357084i	0.157792	+	0.987472i	$0.449562\pi$
$318$	308.295	+	177.994i	0.969482	+	0.559730i
$319$	82.6209	−	47.7012i	0.259000	−	0.149534i
$320$	−4.00000	+	6.92820i	−0.0125000	+	0.0216506i
$321$	125.889	−	218.046i	0.392177	−	0.679270i
$322$			263.872i			0.819478i
$323$	−15.8054	−	36.6572i	−0.0489330	−	0.113490i
$324$	176.565			0.544955
$325$	−356.363	−	205.746i	−1.09650	−	0.633066i
$326$	191.914	+	110.801i	0.588693	+	0.339882i
$327$	−25.8712	−	44.8102i	−0.0791167	−	0.137034i
$328$	91.3485	−	158.220i	0.278501	−	0.482379i
$329$	39.8082	+	68.9498i	0.120997	+	0.209574i
$330$	66.2929			0.200887
$331$			293.328i			0.886188i	0.896475	+	0.443094i	$0.146119\pi$
$331$			293.328i			0.886188i	−0.896475	+	0.443094i	$0.853881\pi$
$332$	−1.30306	−	2.25697i	−0.00392488	−	0.00679810i
$333$	−22.5153	+	12.9992i	−0.0676135	+	0.0390367i
$334$	127.510			0.381766
$335$			59.6506i			0.178061i
$336$	−75.1918	+	43.4120i	−0.223785	+	0.129202i
$337$	−399.393	−	230.590i	−1.18514	−	0.684243i	−0.227945	−	0.973674i	$-0.573201\pi$
$337$	−399.393	−	230.590i	−1.18514	−	0.684243i	−0.957199	+	0.289431i	$0.906534\pi$
$338$	−153.056	+	88.3667i	−0.452827	+	0.261440i
$339$	−208.980	+	361.963i	−0.616459	+	1.06774i
$340$	2.10102	−	3.63907i	0.00617947	−	0.0107032i
$341$		−	464.504i		−	1.36218i
$342$	−19.3735	−	14.4279i	−0.0566476	−	0.0421867i
$343$	−347.737			−1.01381
$344$	−184.540	−	106.544i	−0.536454	−	0.309722i
$345$	−73.6918	−	42.5460i	−0.213600	−	0.123322i
$346$	215.048	+	372.474i	0.621525	+	1.07651i
$347$	−152.129	+	263.495i	−0.438412	+	0.759351i	−0.997567	−	0.0697116i	$-0.977792\pi$
$347$	−152.129	+	263.495i	−0.438412	+	0.759351i	0.559156	+	0.829063i	$0.311125\pi$
$348$	−20.1464	−	34.8946i	−0.0578920	−	0.100272i
$349$	50.4337			0.144509			0.0722545	−	0.997386i	$-0.476981\pi$
$349$	50.4337			0.144509			0.0722545	+	0.997386i	$0.476981\pi$
$350$		−	234.159i		−	0.669026i
$351$	218.502	+	378.457i	0.622514	+	1.07823i
$352$	−72.9898	+	42.1407i	−0.207357	+	0.119718i
$353$	−316.817			−0.897500			−0.448750	−	0.893657i	$-0.648131\pi$
$353$	−316.817			−0.897500			−0.448750	+	0.893657i	$0.648131\pi$
$354$		−	261.601i		−	0.738985i
$355$	87.5227	−	50.5313i	0.246543	−	0.142342i
$356$	11.6969	+	6.75323i	0.0328566	+	0.0189697i
$357$	39.4949	−	22.8024i	0.110630	−	0.0638722i
$358$	−222.879	+	386.037i	−0.622566	+	1.07832i
$359$	−74.7043	+	129.392i	−0.208090	+	0.360423i	−0.951113	−	0.308844i	$-0.900058\pi$
$359$	−74.7043	+	129.392i	−0.208090	+	0.360423i	0.743023	+	0.669266i	$0.233391\pi$
$360$		−	2.54270i		−	0.00706305i
$361$	−103.424	−	345.868i	−0.286494	−	0.958082i
$362$	45.5505			0.125830
$363$	275.144	+	158.854i	0.757971	+	0.437615i
$364$	−204.879	−	118.287i	−0.562853	−	0.324963i
$365$	−63.6918	−	110.317i	−0.174498	−	0.302240i
$366$	−4.87628	+	8.44596i	−0.0133232	+	0.0230764i
$367$	−117.038	−	202.716i	−0.318905	−	0.552359i	0.661355	−	0.750073i	$-0.269982\pi$
$367$	−117.038	−	202.716i	−0.318905	−	0.552359i	−0.980260	+	0.197714i	$0.936648\pi$
$368$	108.182			0.293972
$369$			58.0679i			0.157366i
$370$	−20.4495	−	35.4196i	−0.0552689	−	0.0957285i
$371$	−478.015	+	275.982i	−1.28845	+	0.743887i
$372$	−196.182			−0.527370
$373$		−	639.738i		−	1.71512i	−0.514387	−	0.857558i	$-0.671981\pi$
$373$		−	639.738i		−	1.71512i	0.514387	−	0.857558i	$-0.328019\pi$
$374$	38.3383	−	22.1346i	0.102509	−	0.0591834i
$375$	133.512	+	77.0835i	0.356033	+	0.205556i
$376$	28.2679	−	16.3205i	0.0751805	−	0.0434055i
$377$	54.8939	−	95.0790i	0.145607	−	0.252199i
$378$	−124.338	+	215.360i	−0.328937	+	0.569736i
$379$			108.366i			0.285927i	0.989728	+	0.142963i	$0.0456631\pi$
$379$			108.366i			0.285927i	−0.989728	+	0.142963i	$0.954337\pi$
$380$	22.6969	−	30.4770i	0.0597288	−	0.0802027i
$381$	395.363			1.03770
$382$	−343.237	−	198.168i	−0.898527	−	0.518765i
$383$	215.552	+	124.449i	0.562800	+	0.324933i	0.754268	−	0.656566i	$-0.227992\pi$
$383$	215.552	+	124.449i	0.562800	+	0.324933i	−0.191469	+	0.981499i	$0.561325\pi$
$384$	17.7980	+	30.8270i	0.0463489	+	0.0802786i
$385$	−51.3939	+	89.0168i	−0.133491	+	0.231212i
$386$	−34.3054	−	59.4186i	−0.0888740	−	0.153934i
$387$	67.7276			0.175007
$388$		−	263.622i		−	0.679437i
$389$	335.560	+	581.207i	0.862623	+	1.49411i	0.869389	+	0.494129i	$0.164513\pi$
$389$	335.560	+	581.207i	0.862623	+	1.49411i	−0.00676592	+	0.999977i	$0.502154\pi$
$390$	66.0681	−	38.1444i	0.169405	−	0.0978063i
$391$	−56.8230			−0.145327
$392$			3.97134i			0.0101310i
$393$	−292.222	+	168.714i	−0.743567	+	0.429299i
$394$	−308.524	−	178.127i	−0.783057	−	0.452098i
$395$	−5.78036	+	3.33729i	−0.0146338	+	0.00844884i
$396$	13.3939	−	23.1989i	0.0338229	−	0.0585830i
$397$	46.6816	−	80.8550i	0.117586	−	0.203665i	−0.801225	−	0.598364i	$-0.795818\pi$
$397$	46.6816	−	80.8550i	0.117586	−	0.203665i	0.918811	+	0.394699i	$0.129151\pi$
$398$			366.830i			0.921684i
$399$	378.712	−	163.288i	0.949152	−	0.409243i
$400$	−96.0000			−0.240000
$401$	242.484	+	139.998i	0.604699	+	0.349123i	0.770888	−	0.636971i	$-0.219813\pi$
$401$	242.484	+	139.998i	0.604699	+	0.349123i	−0.166189	+	0.986094i	$0.553146\pi$
$402$	229.856	+	132.707i	0.571781	+	0.330118i
$403$	−267.272	−	462.929i	−0.663207	−	1.14871i
$404$	6.48469	−	11.2318i	0.0160512	−	0.0278015i
$405$	−44.1413	−	76.4550i	−0.108991	−	0.188778i
$406$	62.4745			0.153878
$407$		−	430.878i		−	1.05867i
$408$	−9.34847	−	16.1920i	−0.0229129	−	0.0396863i
$409$	−555.833	+	320.910i	−1.35900	+	0.784621i	−0.989490	−	0.144604i	$-0.953809\pi$
$409$	−555.833	+	320.910i	−1.35900	+	0.784621i	−0.369514	+	0.929225i	$0.620476\pi$
$410$	−91.3485			−0.222801
$411$			6.61037i			0.0160836i
$412$	138.606	−	80.0243i	0.336423	−	0.194234i
$413$	351.272	+	202.807i	0.850539	+	0.491059i
$414$	−29.7775	+	17.1921i	−0.0719264	+	0.0415268i
$415$	−0.651531	+	1.12848i	−0.00156995	+	0.00271924i
$416$	−48.4949	+	83.9956i	−0.116574	+	0.201913i
$417$			99.8698i			0.239496i
$418$	367.621	−	158.506i	0.879476	−	0.379201i
$419$	668.879			1.59637			0.798184	−	0.602413i	$-0.205794\pi$
$419$	668.879			1.59637			0.798184	+	0.602413i	$0.205794\pi$
$420$	37.5959	+	21.7060i	0.0895141	+	0.0516810i
$421$	433.711	+	250.403i	1.03019	+	0.594782i	0.917040	−	0.398795i	$-0.130572\pi$
$421$	433.711	+	250.403i	1.03019	+	0.594782i	0.113153	+	0.993578i	$0.463905\pi$
$422$	−49.1941	−	85.2067i	−0.116574	−	0.201912i
$423$	−5.18725	+	8.98458i	−0.0122630	+	0.0212401i
$424$	113.146	+	195.975i	0.266855	+	0.462206i
$425$	50.4245			0.118646
$426$		−	449.677i		−	1.05558i
$427$	−7.56072	−	13.0955i	−0.0177066	−	0.0306687i
$428$	138.606	−	80.0243i	0.323846	−	0.186973i
$429$	803.716			1.87346
$430$			106.544i			0.247778i
$431$	120.553	−	69.6015i	0.279706	−	0.161488i	−0.353584	−	0.935403i	$-0.615037\pi$
$431$	120.553	−	69.6015i	0.279706	−	0.161488i	0.633290	+	0.773914i	$0.281704\pi$
$432$	88.2929	+	50.9759i	0.204382	+	0.118000i
$433$	180.349	−	104.125i	0.416510	−	0.240472i	−0.277073	−	0.960849i	$-0.589364\pi$
$433$	180.349	−	104.125i	0.416510	−	0.240472i	0.693583	+	0.720377i	$0.256031\pi$
$434$	152.091	−	263.429i	0.350440	−	0.606979i
$435$	−10.0732	+	17.4473i	−0.0231568	+	0.0401088i
$436$		−	32.8913i		−	0.0754387i
$437$	−510.379	−	59.7381i	−1.16791	−	0.136700i
$438$	−566.792			−1.29405
$439$	65.6748	+	37.9173i	0.149601	+	0.0863721i	0.572932	−	0.819603i	$-0.305806\pi$
$439$	65.6748	+	37.9173i	0.149601	+	0.0863721i	−0.423331	+	0.905975i	$0.639139\pi$
$440$	36.4949	+	21.0703i	0.0829429	+	0.0478871i
$441$	−0.631120	−	1.09313i	−0.00143111	−	0.00247876i
$442$	25.4722	−	44.1191i	0.0576294	−	0.0998170i
$443$	227.628	+	394.264i	0.513834	+	0.889986i	0.999871	+	0.0160481i	$0.00510848\pi$
$443$	227.628	+	394.264i	0.513834	+	0.889986i	−0.486038	+	0.873938i	$0.661558\pi$
$444$	−181.980			−0.409864
$445$		−	6.75323i		−	0.0151758i
$446$	4.47219	+	7.74607i	0.0100273	+	0.0173679i
$447$	−516.820	+	298.386i	−1.15620	+	0.667531i
$448$	−55.1918			−0.123196
$449$			8.44993i			0.0188194i	0.999956	+	0.00940972i	$0.00299525\pi$
$449$			8.44993i			0.0188194i	−0.999956	+	0.00940972i	$0.997005\pi$
$450$	26.4245	−	15.2562i	0.0587211	−	0.0339026i
$451$	−833.438	−	481.186i	−1.84798	−	1.06693i
$452$	−230.091	+	132.843i	−0.509050	+	0.293900i
$453$	25.5959	−	44.3334i	0.0565031	−	0.0978663i
$454$	−39.4143	+	68.2675i	−0.0868156	+	0.150369i
$455$			118.287i			0.259971i
$456$	−66.9444	−	155.263i	−0.146808	−	0.340490i
$457$	208.424			0.456071			0.228036	−	0.973653i	$-0.426770\pi$
$457$	208.424			0.456071			0.228036	+	0.973653i	$0.426770\pi$
$458$	162.050	+	93.5596i	0.353821	+	0.204279i
$459$	−46.3763	−	26.7754i	−0.101038	−	0.0583341i
$460$	−27.0454	−	46.8440i	−0.0587944	−	0.101835i
$461$	308.808	−	534.871i	0.669865	−	1.16024i	−0.308077	−	0.951361i	$-0.599685\pi$
$461$	308.808	−	534.871i	0.669865	−	1.16024i	0.977942	−	0.208878i	$-0.0669813\pi$
$462$	228.677	+	396.079i	0.494971	+	0.857315i
$463$	640.958			1.38436			0.692179	−	0.721725i	$-0.256651\pi$
$463$	640.958			1.38436			0.692179	+	0.721725i	$0.256651\pi$
$464$		−	25.6131i		−	0.0552007i
$465$	49.0454	+	84.9491i	0.105474	+	0.182686i
$466$	−273.997	+	158.192i	−0.587976	+	0.339468i
$467$	164.111			0.351416			0.175708	−	0.984442i	$-0.443779\pi$
$467$	164.111			0.351416			0.175708	+	0.984442i	$0.443779\pi$
$468$		−	30.8270i		−	0.0658696i
$469$	−356.394	+	205.764i	−0.759902	+	0.438729i
$470$	−14.1339	−	8.16023i	−0.0300722	−	0.0173622i
$471$	−736.093	+	424.983i	−1.56283	+	0.902300i
$472$	83.1464	−	144.014i	0.176158	−	0.305114i
$473$	−561.232	+	972.082i	−1.18654	+	2.05514i
$474$			29.6985i			0.0626550i
$475$	452.908	+	53.0114i	0.953491	+	0.111603i
$476$	28.9898			0.0609029
$477$	−62.2883	−	35.9621i	−0.130583	−	0.0753923i
$478$	87.3531	+	50.4333i	0.182747	+	0.105509i
$479$	−401.401	−	695.247i	−0.837998	−	1.45146i	−0.891566	−	0.452892i	$-0.850392\pi$
$479$	−401.401	−	695.247i	−0.837998	−	1.45146i	0.0535671	−	0.998564i	$-0.482941\pi$
$480$	8.89898	−	15.4135i	0.0185395	−	0.0321114i
$481$	−247.924	−	429.417i	−0.515434	−	0.892759i
$482$	−197.146			−0.409017
$483$		−	587.048i		−	1.21542i
$484$	100.980	+	174.902i	0.208636	+	0.361367i
$485$	−114.152	+	65.9054i	−0.235364	+	0.135887i
$486$	−68.4041			−0.140749
$487$		−	454.391i		−	0.933041i	−0.884510	−	0.466521i	$-0.845507\pi$
$487$		−	454.391i		−	0.933041i	0.884510	−	0.466521i	$-0.154493\pi$
$488$	−5.36888	+	3.09972i	−0.0110018	+	0.00635189i
$489$	−426.959	−	246.505i	−0.873127	−	0.504100i
$490$	1.71964	−	0.992836i	0.00350947	−	0.00202620i
$491$	−259.826	+	450.031i	−0.529177	+	0.916561i	0.470244	+	0.882536i	$0.344166\pi$
$491$	−259.826	+	450.031i	−0.529177	+	0.916561i	−0.999421	+	0.0340247i	$0.989168\pi$
$492$	−203.227	+	352.000i	−0.413063	+	0.715446i
$493$			13.4534i			0.0272889i
$494$	275.171	−	369.495i	0.557027	−	0.747966i
$495$	−13.3939			−0.0270583
$496$	−108.000	−	62.3538i	−0.217742	−	0.125713i
$497$	603.817	+	348.614i	1.21492	+	0.701437i
$498$	2.89898	+	5.02118i	0.00582124	+	0.0100827i
$499$	−221.543	+	383.724i	−0.443974	+	0.768986i	−0.997980	−	0.0635269i	$-0.979765\pi$
$499$	−221.543	+	383.724i	−0.443974	+	0.768986i	0.554006	+	0.832513i	$0.313098\pi$
$500$	49.0000	+	84.8705i	0.0980000	+	0.169741i
$501$	−283.677			−0.566221
$502$			339.519i			0.676332i
$503$	120.841	+	209.302i	0.240240	+	0.416107i	0.960782	−	0.277303i	$-0.0894406\pi$
$503$	120.841	+	209.302i	0.240240	+	0.416107i	−0.720543	+	0.693410i	$0.756107\pi$
$504$	15.1918	−	8.77101i	0.0301425	−	0.0174028i
$505$	−6.48469			−0.0128410
$506$		−	569.856i		−	1.12620i
$507$	340.510	−	196.593i	0.671617	−	0.387758i
$508$	217.652	+	125.661i	0.428448	+	0.247365i
$509$	357.485	−	206.394i	0.702329	−	0.405490i	−0.105886	−	0.994378i	$-0.533768\pi$
$509$	357.485	−	206.394i	0.702329	−	0.405490i	0.808214	+	0.588889i	$0.200434\pi$
$510$	−4.67423	+	8.09601i	−0.00916517	+	0.0158745i
$511$	439.409	−	761.078i	0.859900	−	1.48939i
$512$			22.6274i			0.0441942i
$513$	−388.398	−	289.249i	−0.757112	−	0.563839i
$514$	−13.6821			−0.0266190
$515$	−69.3031	−	40.0121i	−0.134569	−	0.0776935i
$516$	410.555	+	237.034i	0.795649	+	0.459368i
$517$	−85.9694	−	148.903i	−0.166285	−	0.288014i
$518$	141.081	−	244.359i	0.272356	−	0.471735i
$519$	−478.426	−	828.659i	−0.921823	−	1.59664i
$520$	48.4949			0.0932594
$521$			888.839i			1.70602i	0.521891	+	0.853012i	$0.325227\pi$
$521$			888.839i			1.70602i	−0.521891	+	0.853012i	$0.674773\pi$
$522$	4.07041	+	7.05015i	0.00779771	+	0.0135060i
$523$	132.856	−	76.7047i	0.254027	−	0.146663i	−0.367580	−	0.929992i	$-0.619813\pi$
$523$	132.856	−	76.7047i	0.254027	−	0.146663i	0.621607	+	0.783329i	$0.286480\pi$
$524$	−214.495			−0.409341
$525$			520.944i			0.992275i
$526$	−139.528	+	80.5564i	−0.265262	+	0.153149i
$527$	56.7276	+	32.7517i	0.107642	+	0.0621474i
$528$	162.384	−	93.7523i	0.307545	−	0.177561i
$529$	−101.227	+	175.330i	−0.191355	+	0.331437i
$530$	56.5732	−	97.9877i	0.106742	−	0.184882i
$531$			52.8541i			0.0995368i
$532$	260.384	+	30.4770i	0.489443	+	0.0572876i
$533$	−1107.48			−2.07783
$534$	−26.0227	−	15.0242i	−0.0487317	−	0.0281352i
$535$	−69.3031	−	40.0121i	−0.129538	−	0.0747890i
$536$	84.3587	+	146.114i	0.157386	+	0.272600i
$537$	495.848	−	858.834i	0.923367	−	1.59932i
$538$	284.215	+	492.274i	0.528280	+	0.915007i
$539$	20.9194			0.0388115
$540$		−	50.9759i		−	0.0943998i
$541$	446.424	+	773.229i	0.825183	+	1.42926i	0.901779	+	0.432197i	$0.142261\pi$
$541$	446.424	+	773.229i	0.825183	+	1.42926i	−0.0765964	+	0.997062i	$0.524405\pi$
$542$	488.654	−	282.124i	0.901575	−	0.520525i
$543$	−101.338			−0.186627
$544$		−	11.8852i		−	0.0218477i
$545$	−14.2423	+	8.22282i	−0.0261327	+	0.0150877i
$546$	455.803	+	263.158i	0.834803	+	0.481974i
$547$	−748.841	+	432.343i	−1.36900	+	0.790390i	−0.990800	−	0.135336i	$-0.956789\pi$
$547$	−748.841	+	432.343i	−1.36900	+	0.790390i	−0.378196	+	0.925726i	$0.623455\pi$
$548$	−2.10102	+	3.63907i	−0.00383398	+	0.00664065i
$549$	0.985208	−	1.70643i	0.00179455	−	0.00310825i
$550$			505.688i			0.919433i
$551$	−14.1436	+	120.838i	−0.0256690	+	0.219306i
$552$	−240.677			−0.436008
$553$	−39.8786	−	23.0239i	−0.0721131	−	0.0416345i
$554$	−648.434	−	374.373i	−1.17046	−	0.675764i
$555$	45.4949	+	78.7995i	0.0819728	+	0.141981i
$556$	−31.7423	+	54.9794i	−0.0570906	+	0.0988837i
$557$	−374.853	−	649.265i	−0.672986	−	1.16565i	−0.977053	−	0.212995i	$-0.931678\pi$
$557$	−374.853	−	649.265i	−0.672986	−	1.16565i	0.304068	−	0.952650i	$-0.401655\pi$
$558$	39.6367			0.0710336
$559$			1291.71i			2.31076i
$560$	13.7980	+	23.8988i	0.0246392	+	0.0426764i
$561$	−85.2929	+	49.2439i	−0.152037	+	0.0877787i
$562$	−77.4189			−0.137756
$563$		−	162.777i		−	0.289125i	−0.989496	−	0.144563i	$-0.953823\pi$
$563$		−	162.777i		−	0.289125i	0.989496	−	0.144563i	$-0.0461775\pi$
$564$	−62.8888	+	36.3089i	−0.111505	+	0.0643774i
$565$	115.045	+	66.4215i	0.203620	+	0.117560i
$566$	−182.406	+	105.312i	−0.322273	+	0.186064i
$567$	304.530	−	527.462i	0.537090	−	0.930267i
$568$	142.924	−	247.552i	0.251627	−	0.435830i
$569$		−	296.076i		−	0.520345i	−0.965562	−	0.260173i	$-0.916221\pi$
$569$		−	296.076i		−	0.520345i	0.965562	−	0.260173i	$-0.0837795\pi$
$570$	−50.4949	+	67.8036i	−0.0885875	+	0.118954i
$571$	274.758			0.481188			0.240594	−	0.970626i	$-0.422658\pi$
$571$	274.758			0.481188			0.240594	+	0.970626i	$0.422658\pi$
$572$	442.454	+	255.451i	0.773521	+	0.446593i
$573$	763.615	+	440.873i	1.33266	+	0.769413i
$574$	−315.106	−	545.779i	−0.548964	−	0.950834i
$575$	324.545	−	562.128i	0.564426	−	0.977614i
$576$	−3.59592	−	6.22831i	−0.00624291	−	0.0108130i
$577$	524.595			0.909177			0.454588	−	0.890702i	$-0.349786\pi$
$577$	524.595			0.909177			0.454588	+	0.890702i	$0.349786\pi$
$578$		−	402.465i		−	0.696306i
$579$	76.3207	+	132.191i	0.131815	+	0.228310i
$580$	−11.0908	+	6.40329i	−0.0191221	+	0.0110401i
$581$	−8.98979			−0.0154730
$582$			586.491i			1.00772i
$583$	1032.32	−	596.008i	1.77070	−	1.02231i
$584$	−312.025	−	180.148i	−0.534289	−	0.308472i
$585$	−13.3485	+	7.70674i	−0.0228179	+	0.0131739i
$586$	103.015	−	178.427i	0.175793	−	0.304483i
$587$	375.568	−	650.503i	0.639809	−	1.10818i	−0.345665	−	0.938358i	$-0.612347\pi$
$587$	375.568	−	650.503i	0.639809	−	1.10818i	0.985474	−	0.169824i	$-0.0543200\pi$
$588$		−	8.83523i		−	0.0150259i
$589$	475.090	+	353.810i	0.806604	+	0.600697i
$590$	−83.1464			−0.140926
$591$	686.388	+	396.286i	1.16140	+	0.670535i
$592$	−100.182	−	57.8399i	−0.169226	−	0.0977025i
$593$	285.030	+	493.687i	0.480658	+	0.832524i	0.999754	−	0.0221922i	$-0.00706458\pi$
$593$	285.030	+	493.687i	0.480658	+	0.832524i	−0.519096	+	0.854716i	$0.673731\pi$
$594$	268.520	−	465.090i	0.452054	−	0.782980i
$595$	−7.24745	−	12.5529i	−0.0121806	−	0.0210974i
$596$	−379.353			−0.636498
$597$		−	816.104i		−	1.36701i
$598$	−327.891	−	567.924i	−0.548313	−	0.949706i
$599$	−341.447	+	197.134i	−0.570028	+	0.329106i	−0.757160	−	0.653229i	$-0.773414\pi$
$599$	−341.447	+	197.134i	−0.570028	+	0.329106i	0.187133	+	0.982335i	$0.440081\pi$
$600$	213.576			0.355959
$601$			241.665i			0.402105i	0.979580	+	0.201053i	$0.0644362\pi$
$601$			241.665i			0.402105i	−0.979580	+	0.201053i	$0.935564\pi$
$602$	−636.570	+	367.524i	−1.05743	+	0.610505i
$603$	−46.4403	−	26.8123i	−0.0770154	−	0.0444649i
$604$	28.1816	−	16.2707i	0.0466583	−	0.0269382i
$605$	50.4898	−	87.4509i	0.0834542	−	0.144547i
$606$	−14.4268	+	24.9879i	−0.0238066	+	0.0412342i
$607$			369.224i			0.608276i	0.952628	+	0.304138i	$0.0983685\pi$
$607$			369.224i			0.608276i	−0.952628	+	0.304138i	$0.901632\pi$
$608$	12.4949	−	106.751i	0.0205508	−	0.175578i
$609$	−138.990			−0.228226
$610$	2.68444	+	1.54986i	0.00440072	+	0.00254076i
$611$	−171.356	−	98.9324i	−0.280451	−	0.161919i
$612$	1.88877	+	3.27145i	0.00308623	+	0.00534551i
$613$	−190.171	+	329.386i	−0.310230	+	0.537334i	−0.978412	−	0.206664i	$-0.933739\pi$
$613$	−190.171	+	329.386i	−0.310230	+	0.537334i	0.668182	+	0.743998i	$0.267073\pi$
$614$	−80.0477	−	138.647i	−0.130371	−	0.225809i
$615$	203.227			0.330450
$616$			290.728i			0.471961i
$617$	−277.869	−	481.283i	−0.450355	−	0.780037i	0.548053	−	0.836444i	$-0.315369\pi$
$617$	−277.869	−	481.283i	−0.450355	−	0.780037i	−0.998408	+	0.0564062i	$0.982036\pi$
$618$	−308.363	+	178.034i	−0.498970	+	0.288080i
$619$	−624.152			−1.00832			−0.504162	−	0.863609i	$-0.668198\pi$
$619$	−624.152			−1.00832			−0.504162	+	0.863609i	$0.668198\pi$
$620$			62.3538i			0.100571i
$621$	−596.979	+	344.666i	−0.961319	+	0.555018i
$622$	129.414	+	74.7174i	0.208062	+	0.120124i
$623$	40.3485	−	23.2952i	0.0647648	−	0.0373920i
$624$	107.889	−	186.869i	0.172899	−	0.299469i
$625$	−275.500	+	477.180i	−0.440800	+	0.763488i
$626$			351.067i			0.560810i
$627$	−817.863	+	352.635i	−1.30441	+	0.562417i
$628$	−540.302			−0.860354
$629$	52.6209	+	30.3807i	0.0836581	+	0.0483000i
$630$	−7.59592	−	4.38551i	−0.0120570	−	0.00696112i
$631$	−42.7247	−	74.0014i	−0.0677096	−	0.117276i	0.830183	−	0.557491i	$-0.188236\pi$
$631$	−42.7247	−	74.0014i	−0.0677096	−	0.117276i	−0.897893	+	0.440214i	$0.854902\pi$
$632$	−9.43928	+	16.3493i	−0.0149356	+	0.0258692i
$633$	109.444	+	189.563i	0.172898	+	0.299468i
$634$	320.166			0.504993
$635$		−	125.661i		−	0.197892i
$636$	−251.722	−	435.995i	−0.395789	−	0.685527i
$637$	20.8485	−	12.0369i	0.0327292	−	0.0188962i
$638$	−134.919			−0.211472
$639$			90.8531i			0.142180i
$640$	9.79796	−	5.65685i	0.0153093	−	0.00883883i
$641$	599.893	+	346.348i	0.935870	+	0.540325i	0.888663	−	0.458560i	$-0.151635\pi$
$641$	599.893	+	346.348i	0.935870	+	0.540325i	0.0472069	+	0.998885i	$0.484968\pi$
$642$	−308.363	+	178.034i	−0.480317	+	0.277311i
$643$	252.123	−	436.690i	0.392105	−	0.679145i	−0.600622	−	0.799533i	$-0.705080\pi$
$643$	252.123	−	436.690i	0.392105	−	0.679145i	0.992727	+	0.120388i	$0.0384138\pi$
$644$	186.586	−	323.176i	0.289729	−	0.501826i
$645$		−	237.034i		−	0.367495i
$646$	−6.56301	+	56.0718i	−0.0101595	+	0.0867984i
$647$	−797.868			−1.23318			−0.616591	−	0.787284i	$-0.711487\pi$
$647$	−797.868			−1.23318			−0.616591	+	0.787284i	$0.711487\pi$
$648$	−216.247	−	124.851i	−0.333715	−	0.192671i
$649$	−758.605	−	437.981i	−1.16888	−	0.674855i
$650$	290.969	+	503.974i	0.447645	+	0.775344i
$651$	−338.363	+	586.062i	−0.519759	+	0.900249i
$652$	−156.697	−	271.407i	−0.240333	−	0.416268i
$653$	−651.383			−0.997523			−0.498762	−	0.866739i	$-0.666212\pi$
$653$	−651.383			−0.997523			−0.498762	+	0.866739i	$0.666212\pi$
$654$			73.1747i			0.111888i
$655$	53.6237	+	92.8790i	0.0818683	+	0.141800i
$656$	−223.757	+	129.186i	−0.341093	+	0.196930i
$657$	114.515			0.174300
$658$		−	112.594i		−	0.171116i
$659$	−395.082	+	228.101i	−0.599518	+	0.346132i	−0.768852	−	0.639427i	$-0.779172\pi$
$659$	−395.082	+	228.101i	−0.599518	+	0.346132i	0.169334	+	0.985559i	$0.445838\pi$
$660$	−81.1918	−	46.8761i	−0.123018	−	0.0710244i
$661$	495.696	−	286.190i	0.749919	−	0.432966i	−0.0757457	−	0.997127i	$-0.524134\pi$
$661$	495.696	−	286.190i	0.749919	−	0.432966i	0.825665	+	0.564161i	$0.190800\pi$
$662$	207.414	−	359.252i	0.313315	−	0.542677i
$663$	−56.6691	+	98.1538i	−0.0854738	+	0.148045i
$664$			3.68561i			0.00555062i
$665$	−51.8990	−	120.369i	−0.0780436	−	0.181006i
$666$	36.7673			0.0552062
$667$	149.978	+	86.5897i	0.224854	+	0.129820i
$668$	−156.167	−	90.1630i	−0.233783	−	0.134975i
$669$	−9.94949	−	17.2330i	−0.0148722	−	0.0257594i
$670$	42.1793	−	73.0568i	0.0629542	−	0.109040i
$671$	16.3281	+	28.2810i	0.0243339	+	0.0421476i
$672$	122.788			0.182720
$673$			914.574i			1.35895i	0.733698	+	0.679476i	$0.237793\pi$
$673$			914.574i			1.35895i	−0.733698	+	0.679476i	$0.762207\pi$
$674$	326.103	+	564.828i	0.483833	+	0.838023i
$675$	529.757	−	305.855i	0.784825	−	0.453119i
$676$	249.939			0.369732
$677$			272.492i			0.402500i	0.979540	+	0.201250i	$0.0645003\pi$
$677$			272.492i			0.402500i	−0.979540	+	0.201250i	$0.935500\pi$
$678$	511.893	−	295.542i	0.755005	−	0.435902i
$679$	−787.529	−	454.680i	−1.15984	−	0.669632i
$680$	−5.14643	+	2.97129i	−0.00756828	+	0.00436955i
$681$	87.6867	−	151.878i	0.128762	−	0.223022i
$682$	−328.454	+	568.899i	−0.481604	+	0.834163i
$683$		−	164.842i		−	0.241350i	−0.992692	−	0.120675i	$-0.961494\pi$
$683$		−	164.842i		−	0.241350i	0.992692	−	0.120675i	$-0.0385058\pi$
$684$	13.5255	+	31.3696i	0.0197741	+	0.0458619i
$685$	2.10102			0.00306718
$686$	425.889	+	245.887i	0.620829	+	0.358436i
$687$	−360.520	−	208.146i	−0.524774	−	0.302979i
$688$	150.677	+	260.979i	0.219007	+	0.379331i
$689$	685.878	−	1187.98i	0.995469	−	1.72420i
$690$	60.1691	+	104.216i	0.0872016	+	0.151038i
$691$	1040.21			1.50537			0.752685	−	0.658380i	$-0.228758\pi$
$691$	1040.21			1.50537			0.752685	+	0.658380i	$0.228758\pi$
$692$		−	608.247i		−	0.878969i
$693$	−46.2020	−	80.0243i	−0.0666696	−	0.115475i
$694$	372.638	−	215.143i	0.536942	−	0.310004i
$695$	31.7423			0.0456724
$696$			56.9827i			0.0818717i
$697$	117.530	−	67.8557i	0.168622	−	0.0973540i
$698$	−61.7684	−	35.6620i	−0.0884934	−	0.0510917i
$699$	609.573	−	351.937i	0.872064	−	0.503486i
$700$	−165.576	+	286.785i	−0.236536	+	0.409693i
$701$	37.8179	−	65.5024i	0.0539484	−	0.0934414i	−0.837790	−	0.545993i	$-0.816153\pi$
$701$	37.8179	−	65.5024i	0.0539484	−	0.0934414i	0.891738	+	0.452551i	$0.149486\pi$
$702$		−	618.018i		−	0.880367i
$703$	440.697	+	328.197i	0.626880	+	0.466852i
$704$	119.192			0.169307
$705$	31.4444	+	18.1544i	0.0446020	+	0.0257510i
$706$	388.020	+	224.024i	0.549604	+	0.317314i
$707$	−22.3689	−	38.7440i	−0.0316392	−	0.0548006i
$708$	−184.980	+	320.394i	−0.261271	+	0.452534i
$709$	451.379	+	781.811i	0.636641	+	1.10269i	0.986165	+	0.165767i	$0.0530101\pi$
$709$	451.379	+	781.811i	0.636641	+	1.10269i	−0.349524	+	0.936928i	$0.613657\pi$
$710$	−142.924			−0.201301
$711$		−	6.00031i		−	0.00843926i
$712$	−9.55051	−	16.5420i	−0.0134136	−	0.0232331i
$713$	730.226	−	421.596i	1.02416	−	0.591299i
$714$	−64.4949			−0.0903290
$715$		−	255.451i		−	0.357274i
$716$	545.939	−	315.198i	0.762484	−	0.440221i
$717$	−194.338	−	112.201i	−0.271044	−	0.156487i
$718$	182.988	−	105.648i	0.254857	−	0.147142i
$719$	−586.734	+	1016.25i	−0.816042	+	1.41343i	0.0925359	+	0.995709i	$0.470503\pi$
$719$	−586.734	+	1016.25i	−0.816042	+	1.41343i	−0.908578	+	0.417716i	$0.862831\pi$
$720$	−1.79796	+	3.11416i	−0.00249717	+	0.00432522i
$721$		−	552.086i		−	0.765722i
$722$	−117.897	+	496.732i	−0.163292	+	0.687994i
$723$	438.601			0.606640
$724$	−55.7878	−	32.2091i	−0.0770549	−	0.0444877i
$725$	−133.090	−	76.8394i	−0.183572	−	0.105985i
$726$	−224.654	−	389.112i	−0.309441	−	0.535967i
$727$	−288.552	+	499.787i	−0.396908	+	0.687465i	−0.993343	−	0.115197i	$-0.963250\pi$
$727$	−288.552	+	499.787i	−0.396908	+	0.687465i	0.596434	+	0.802662i	$0.296584\pi$
$728$	167.283	+	289.742i	0.229784	+	0.397997i
$729$	−642.362			−0.881155
$730$			180.148i			0.246778i
$731$	−79.1436	−	137.081i	−0.108268	−	0.187525i
$732$	11.9444	−	6.89610i	0.0163175	−	0.00942090i
$733$	−812.332			−1.10823			−0.554114	−	0.832441i	$-0.686943\pi$
$733$	−812.332			−1.10823			−0.554114	+	0.832441i	$0.686943\pi$
$734$			331.033i			0.450999i
$735$	−3.82577	+	2.20881i	−0.00520512	+	0.00300518i
$736$	−132.495	−	76.4960i	−0.180020	−	0.103935i
$737$	769.665	−	444.366i	1.04432	−	0.602940i
$738$	41.0602	−	71.1184i	0.0556371	−	0.0963663i
$739$	380.931	−	659.792i	0.515469	−	0.892818i	−0.484370	−	0.874863i	$-0.660951\pi$
$739$	380.931	−	659.792i	0.515469	−	0.892818i	0.999839	−	0.0179548i	$-0.00571549\pi$
$740$			57.8399i			0.0781620i
$741$	−612.186	+	822.032i	−0.826162	+	1.10936i
$742$	780.595			1.05201
$743$	−118.810	−	68.5950i	−0.159906	−	0.0923216i	0.417912	−	0.908488i	$-0.362762\pi$
$743$	−118.810	−	68.5950i	−0.159906	−	0.0923216i	−0.577817	+	0.816166i	$0.696095\pi$
$744$	240.272	+	138.721i	0.322947	+	0.186453i
$745$	94.8383	+	164.265i	0.127300	+	0.220490i
$746$	−452.363	+	783.516i	−0.606385	+	1.05029i
$747$	−0.585713	−	1.01448i	−0.000784087	−	0.00135808i
$748$	−62.6061			−0.0836980
$749$		−	552.086i		−	0.737097i
$750$	−109.012	−	188.815i	−0.145350	−	0.251754i
$751$	95.0686	−	54.8879i	0.126589	−	0.0730864i	−0.435368	−	0.900253i	$-0.643382\pi$
$751$	95.0686	−	54.8879i	0.126589	−	0.0730864i	0.561957	+	0.827166i	$0.310048\pi$
$752$	−46.1612			−0.0613846
$753$		−	755.343i		−	1.00311i
$754$	−134.462	+	77.6317i	−0.178332	+	0.102960i
$755$	−14.0908	−	8.13534i	−0.0186633	−	0.0107753i
$756$	304.565	−	175.841i	0.402864	−	0.232594i
$757$	−133.257	+	230.808i	−0.176033	+	0.304898i	−0.940518	−	0.339743i	$-0.889660\pi$
$757$	−133.257	+	230.808i	−0.176033	+	0.304898i	0.764485	+	0.644641i	$0.222993\pi$
$758$	76.6265	−	132.721i	0.101090	−	0.175094i
$759$			1267.78i			1.67033i
$760$	−49.3485	+	21.2774i	−0.0649322	+	0.0279966i
$761$	1227.85			1.61346			0.806732	−	0.590918i	$-0.201234\pi$
$761$	1227.85			1.61346			0.806732	+	0.590918i	$0.201234\pi$
$762$	−484.219	−	279.564i	−0.635458	−	0.366882i
$763$	−98.2577	−	56.7291i	−0.128778	−	0.0743500i
$764$	280.252	+	485.411i	0.366822	+	0.635354i
$765$	0.944387	−	1.63573i	0.00123449	−	0.00213820i
$766$	−175.998	−	304.837i	−0.229762	−	0.397959i
$767$	−1008.04			−1.31427
$768$		−	50.3402i		−	0.0655472i
$769$	−334.115	−	578.705i	−0.434480	−	0.752542i	0.562773	−	0.826612i	$-0.309735\pi$
$769$	−334.115	−	578.705i	−0.434480	−	0.752542i	−0.997253	+	0.0740698i	$0.976401\pi$
$770$	125.889	−	72.6819i	0.163492	−	0.0943921i
$771$	30.4393			0.0394803
$772$			97.0302i			0.125687i
$773$	−492.591	+	284.397i	−0.637246	+	0.367914i	−0.783553	−	0.621325i	$-0.786595\pi$
$773$	−492.591	+	284.397i	−0.637246	+	0.367914i	0.146307	+	0.989239i	$0.453261\pi$
$774$	−82.9490	−	47.8906i	−0.107169	−	0.0618742i
$775$	−648.000	+	374.123i	−0.836129	+	0.482739i
$776$	−186.409	+	322.869i	−0.240217	+	0.416069i
$777$	−313.868	+	543.636i	−0.403949	+	0.699660i
$778$		−	949.108i		−	1.21993i
$779$	1126.98	−	485.915i	1.44670	−	0.623768i
$780$	−107.889			−0.138319
$781$	−1304.00	−	752.864i	−1.66965	−	0.963975i
$782$	69.5936	+	40.1799i	0.0889944	+	0.0513809i
$783$	81.6033	+	141.341i	0.104219	+	0.180512i
$784$	2.80816	−	4.86388i	0.00358184	−	0.00620393i
$785$	135.076	+	233.958i	0.172071	+	0.298035i
$786$	477.196			0.607120
$787$		−	460.132i		−	0.584665i	−0.956317	−	0.292333i	$-0.905569\pi$
$787$		−	460.132i		−	0.584665i	0.956317	−	0.292333i	$-0.0944315\pi$
$788$	251.909	+	436.320i	0.319682	+	0.553705i
$789$	310.414	−	179.217i	0.393427	−	0.227145i
$790$	9.43928			0.0119485
$791$			916.481i			1.15864i
$792$	−32.8082	+	18.9418i	−0.0414244	+	0.0239164i
$793$	32.5454	+	18.7901i	0.0410409	+	0.0236950i
$794$	−114.346	+	66.0178i	−0.144013	+	0.0831458i
$795$	−125.861	+	217.998i	−0.158316	+	0.274211i
$796$	259.388	−	449.274i	0.325865	−	0.564414i
$797$		−	1211.02i		−	1.51947i	−0.650234	−	0.759734i	$-0.725329\pi$
$797$		−	1211.02i		−	1.51947i	0.650234	−	0.759734i	$-0.274671\pi$
$798$	−579.287	−	67.8036i	−0.725924	−	0.0849669i
$799$	24.2464			0.0303460
$800$	117.576	+	67.8823i	0.146969	+	0.0848528i
$801$	5.25765	+	3.03551i	0.00656386	+	0.00378965i
$802$	−197.988	−	342.924i	−0.246867	−	0.427587i
$803$	−948.943	+	1643.62i	−1.18175	+	2.04685i
$804$	−187.677	−	325.065i	−0.233429	−	0.404310i
$805$	−186.586			−0.231783
$806$			755.961i			0.937916i
$807$	−632.305	−	1095.18i	−0.783525	−	1.35711i
$808$	−15.8842	+	9.17074i	−0.0196586	+	0.0113499i
$809$	914.089			1.12990			0.564950	−	0.825125i	$-0.308896\pi$
$809$	914.089			1.12990			0.564950	+	0.825125i	$0.308896\pi$
$810$			124.851i			0.154136i
$811$	−403.234	+	232.808i	−0.497206	+	0.287062i	−0.727559	−	0.686045i	$-0.759345\pi$
$811$	−403.234	+	232.808i	−0.497206	+	0.287062i	0.230353	+	0.973107i	$0.426012\pi$
$812$	−76.5153	−	44.1761i	−0.0942307	−	0.0544041i
$813$	−1087.13	+	627.655i	−1.33718	+	0.772023i
$814$	−304.677	+	527.715i	−0.374295	+	0.648299i
$815$	−78.3485	+	135.704i	−0.0961331	+	0.166507i
$816$			26.4415i			0.0324038i
$817$	−566.747	−	1314.45i	−0.693693	−	1.60887i
$818$	907.671			1.10962
$819$	−92.0908	−	53.1687i	−0.112443	−	0.0649190i
$820$	111.879	+	64.5931i	0.136437	+	0.0787721i
$821$	48.5556	+	84.1008i	0.0591420	+	0.102437i	0.894081	−	0.447906i	$-0.147830\pi$
$821$	48.5556	+	84.1008i	0.0591420	+	0.102437i	−0.834938	+	0.550343i	$0.814497\pi$
$822$	4.67423	−	8.09601i	0.00568642	−	0.00984916i
$823$	562.052	+	973.502i	0.682930	+	1.18287i	0.974082	+	0.226193i	$0.0726281\pi$
$823$	562.052	+	973.502i	0.682930	+	1.18287i	−0.291152	+	0.956677i	$0.594039\pi$
$824$	−226.343			−0.274688
$825$		−	1125.03i		−	1.36367i
$826$	−286.813	−	496.774i	−0.347231	−	0.601422i
$827$	−56.8722	+	32.8352i	−0.0687693	+	0.0397040i	−0.533990	−	0.845491i	$-0.679308\pi$
$827$	−56.8722	+	32.8352i	−0.0687693	+	0.0397040i	0.465221	+	0.885195i	$0.345975\pi$
$828$	48.6265			0.0587277
$829$			276.987i			0.334121i	0.985947	+	0.167061i	$0.0534276\pi$
$829$			276.987i			0.334121i	−0.985947	+	0.167061i	$0.946572\pi$
$830$	1.59592	−	0.921404i	0.00192279	−	0.00111012i
$831$	1442.60	+	832.885i	1.73598	+	1.00227i
$832$	118.788	−	68.5821i	0.142774	−	0.0824305i
$833$	−1.47500	+	2.55478i	−0.00177071	+	0.00306696i
$834$	70.6186	−	122.315i	0.0846746	−	0.146661i
$835$			90.1630i			0.107980i
$836$	−562.322	−	65.8179i	−0.672634	−	0.0787296i
$837$	794.636			0.949386
$838$	−819.206	−	472.969i	−0.977572	−	0.564402i
$839$	−159.598	−	92.1438i	−0.190224	−	0.109826i	0.401864	−	0.915700i	$-0.368363\pi$
$839$	−159.598	−	92.1438i	−0.190224	−	0.109826i	−0.592087	+	0.805874i	$0.701696\pi$
$840$	−30.6969	−	53.1687i	−0.0365440	−	0.0632960i
$841$	−399.999	+	692.819i	−0.475623	+	0.823803i
$842$	−354.124	−	613.360i	−0.420574	−	0.728456i
$843$	172.237			0.204315
$844$			139.142i			0.164860i
$845$	−62.4847	−	108.227i	−0.0739464	−	0.128079i
$846$	12.7061	−	7.33588i	0.0150190	−	0.00867125i
$847$	696.656			0.822498
$848$		−	320.026i		−	0.377390i
$849$	405.808	−	234.293i	0.477983	−	0.275964i
$850$	−61.7571	−	35.6555i	−0.0726555	−	0.0419476i
$851$	677.363	−	391.076i	0.795962	−	0.459549i
$852$	−317.969	+	550.739i	−0.373204	+	0.646407i
$853$	640.620	−	1109.59i	0.751020	−	1.30081i	−0.196308	−	0.980542i	$-0.562895\pi$
$853$	640.620	−	1109.59i	0.751020	−	1.30081i	0.947329	−	0.320263i	$-0.103771\pi$
$854$			21.3849i			0.0250409i
$855$	10.2020	−	13.6991i	0.0119322	−	0.0160224i
$856$	−226.343			−0.264419
$857$	90.2265	+	52.0923i	0.105282	+	0.0607845i	0.551716	−	0.834032i	$-0.313973\pi$
$857$	90.2265	+	52.0923i	0.105282	+	0.0607845i	−0.446435	+	0.894816i	$0.647306\pi$
$858$	−984.347	−	568.313i	−1.14726	−	0.662370i
$859$	374.183	+	648.105i	0.435604	+	0.754487i	0.997345	−	0.0728256i	$-0.0232017\pi$
$859$	374.183	+	648.105i	0.435604	+	0.754487i	−0.561741	+	0.827313i	$0.689868\pi$
$860$	75.3383	−	130.490i	0.0876026	−	0.151732i
$861$	701.030	+	1214.22i	0.814204	+	1.41024i
$862$	−196.863			−0.228379
$863$		−	19.3495i		−	0.0224212i	−0.999937	−	0.0112106i	$-0.996431\pi$
$863$		−	19.3495i		−	0.0224212i	0.999937	−	0.0112106i	$-0.00356852\pi$
$864$	−72.0908	−	124.865i	−0.0834384	−	0.144520i
$865$	−263.379	+	152.062i	−0.304484	+	0.175794i
$866$	−294.509			−0.340079
$867$			895.382i			1.03274i
$868$	−372.545	+	215.089i	−0.429199	+	0.247798i
$869$	86.1214	+	49.7222i	0.0991041	+	0.0572178i
$870$	24.6742	−	14.2457i	0.0283612	−	0.0163743i
$871$	511.371	−	885.720i	0.587108	−	1.01690i
$872$	−23.2577	+	40.2834i	−0.0266716	+	0.0461966i
$873$		−	118.495i		−	0.135733i
$874$	582.842	+	434.056i	0.666868	+	0.496632i
$875$	338.050			0.386343
$876$	694.176	+	400.783i	0.792438	+	0.457515i
$877$	−303.060	−	174.972i	−0.345564	−	0.199512i	0.317166	−	0.948370i	$-0.397269\pi$
$877$	−303.060	−	174.972i	−0.345564	−	0.199512i	−0.662730	+	0.748859i	$0.730602\pi$
$878$	−53.6232	−	92.8781i	−0.0610743	−	0.105784i
$879$	−229.182	+	396.954i	−0.260730	+	0.451598i
$880$	−29.7980	−	51.6116i	−0.0338613	−	0.0586495i
$881$	−449.707			−0.510451			−0.255225	−	0.966882i	$-0.582150\pi$
$881$	−449.707			−0.510451			−0.255225	+	0.966882i	$0.582150\pi$
$882$			1.78508i			0.00202390i
$883$	−557.532	−	965.674i	−0.631406	−	1.09363i	−0.987264	−	0.159088i	$-0.949145\pi$
$883$	−557.532	−	965.674i	−0.631406	−	1.09363i	0.355858	−	0.934540i	$-0.384189\pi$
$884$	−62.3939	+	36.0231i	−0.0705813	+	0.0407501i
$885$	184.980			0.209016
$886$		−	643.830i		−	0.726671i
$887$	818.675	−	472.662i	0.922970	−	0.532877i	0.0383889	−	0.999263i	$-0.487777\pi$
$887$	818.675	−	472.662i	0.922970	−	0.532877i	0.884581	+	0.466386i	$0.154444\pi$
$888$	222.879	+	128.679i	0.250989	+	0.144909i
$889$	750.787	−	433.467i	0.844529	−	0.487589i
$890$	−4.77526	+	8.27098i	−0.00536546	+	0.00929324i
$891$	−657.661	+	1139.10i	−0.738115	+	1.27845i
$892$		−	12.6493i		−	0.0141808i
$893$	217.779	+	25.4903i	0.243874	+	0.0285446i
$894$	843.964			0.944031
$895$	−272.969	−	157.599i	−0.304994	−	0.176088i
$896$	67.5959	+	39.0265i	0.0754419	+	0.0435564i
$897$	729.474	+	1263.49i	0.813237	+	1.40857i
$898$	5.97500	−	10.3490i	0.00665368	−	0.0115245i
$899$	−99.8173	−	172.889i	−0.111032	−	0.192312i
$900$	−43.1510			−0.0479456
$901$			168.096i			0.186566i
$902$	680.499	+	1178.66i	0.754434	+	1.30672i
$903$	1416.21	−	817.647i	1.56833	−	0.905478i
$904$	375.737			0.415638
$905$			32.2091i			0.0355901i
$906$	−62.6969	+	36.1981i	−0.0692019	+	0.0399537i
$907$	617.886	+	356.737i	0.681241	+	0.393315i	0.800323	−	0.599570i	$-0.204662\pi$
$907$	617.886	+	356.737i	0.681241	+	0.393315i	−0.119081	+	0.992885i	$0.537995\pi$
$908$	96.5449	−	55.7402i	0.106327	−	0.0613879i
$909$	2.91480	−	5.04859i	0.00320660	−	0.00555400i
$910$	83.6413	−	144.871i	0.0919135	−	0.159199i
$911$		−	1490.37i		−	1.63597i	−0.575242	−	0.817984i	$-0.695092\pi$
$911$		−	1490.37i		−	1.63597i	0.575242	−	0.817984i	$-0.304908\pi$
$912$	−27.7980	+	237.495i	−0.0304802	+	0.260411i
$913$	19.4143			0.0212643
$914$	−255.267	−	147.378i	−0.279285	−	0.161245i
$915$	−5.97219	−	3.44805i	−0.00652699	−	0.00376836i
$916$	−132.313	−	229.173i	−0.144447	−	0.250189i
$917$	−369.949	+	640.770i	−0.403434	+	0.698768i
$918$	37.8661	+	65.5860i	0.0412484	+	0.0714444i
$919$	−543.666			−0.591585			−0.295792	−	0.955252i	$-0.595584\pi$
$919$	−543.666			−0.591585			−0.295792	+	0.955252i	$0.595584\pi$
$920$			76.4960i			0.0831478i
$921$	178.086	+	308.454i	0.193361	+	0.334912i
$922$	−756.421	+	436.720i	−0.820413	+	0.473666i
$923$	−1732.77			−1.87732
$924$		−	646.795i		−	0.699994i
$925$	−601.090	+	347.039i	−0.649827	+	0.375178i
$926$	−785.010	−	453.226i	−0.847743	−	0.489445i
$927$	62.3020	−	35.9701i	0.0672082	−	0.0388027i
$928$	−18.1112	+	31.3696i	−0.0195164	+	0.0338034i
$929$	−56.2582	+	97.4420i	−0.0605578	+	0.104889i	−0.894715	−	0.446638i	$-0.852621\pi$
$929$	−56.2582	+	97.4420i	−0.0605578	+	0.104889i	0.834157	+	0.551527i	$0.185955\pi$
$930$		−	138.721i		−	0.149163i
$931$	−15.9342	+	21.3961i	−0.0171151	+	0.0229819i
$932$	447.435			0.480080
$933$	−287.914	−	166.227i	−0.308589	−	0.178164i
$934$	−200.994	−	116.044i	−0.215197	−	0.124244i
$935$	15.6515	+	27.1092i	0.0167396	+	0.0289938i
$936$	−21.7980	+	37.7552i	−0.0232884	+	0.0403367i
$937$	125.894	+	218.055i	0.134358	+	0.232716i	0.925352	−	0.379109i	$-0.123769\pi$
$937$	125.894	+	218.055i	0.134358	+	0.232716i	−0.790994	+	0.611824i	$0.790436\pi$
$938$	581.989			0.620457
$939$		−	781.034i		−	0.831773i
$940$	11.5403	+	19.9884i	0.0122769	+	0.0212642i
$941$	−18.6520	+	10.7688i	−0.0198215	+	0.0114440i	−0.509878	−	0.860247i	$-0.670309\pi$
$941$	−18.6520	+	10.7688i	−0.0198215	+	0.0114440i	0.490057	+	0.871691i	$0.336976\pi$
$942$	1202.03			1.27604
$943$		−	1746.95i		−	1.85254i
$944$	−203.666	+	117.587i	−0.215748	+	0.124562i
$945$	−152.283	−	87.9204i	−0.161146	−	0.0930375i
$946$	1374.73	−	793.701i	1.45320	−	0.839008i
$947$	−314.735	+	545.137i	−0.332349	+	0.575646i	−0.982972	−	0.183755i	$-0.941175\pi$
$947$	−314.735	+	545.137i	−0.332349	+	0.575646i	0.650623	+	0.759401i	$0.274508\pi$
$948$	21.0000	−	36.3731i	0.0221519	−	0.0383682i
$949$			2184.06i			2.30143i
$950$	−517.212	−	385.180i	−0.544434	−	0.405452i
$951$	−712.287			−0.748988
$952$	−35.5051	−	20.4989i	−0.0372953	−	0.0215324i
$953$	−420.863	−	242.986i	−0.441619	−	0.254969i	0.262665	−	0.964887i	$-0.415399\pi$
$953$	−420.863	−	242.986i	−0.441619	−	0.254969i	−0.704284	+	0.709918i	$0.748732\pi$
$954$	50.8582	+	88.0889i	0.0533104	+	0.0923364i
$955$	140.126	−	242.705i	0.146729	−	0.254142i
$956$	−71.3235	−	123.536i	−0.0746061	−	0.129222i
$957$	300.161			0.313648
$958$			1135.33i			1.18511i
$959$	7.24745	+	12.5529i	0.00755730	+	0.0130896i
$960$	−21.7980	+	12.5851i	−0.0227062	+	0.0131094i
$961$	−11.0000			−0.0114464
$962$			701.235i			0.728934i
$963$	62.3020	−	35.9701i	0.0646958	−	0.0373521i
$964$	241.454	+	139.404i	0.250471	+	0.144610i
$965$	42.0153	−	24.2575i	0.0435392	−	0.0251374i
$966$	−415.106	+	718.984i	−0.429716	+	0.744290i
$967$	−216.372	+	374.767i	−0.223756	+	0.387556i	−0.955945	−	0.293545i	$-0.905165\pi$
$967$	−216.372	+	374.767i	−0.223756	+	0.387556i	0.732190	+	0.681101i	$0.238498\pi$
$968$		−	285.613i		−	0.295055i
$969$	14.6010	−	124.745i	0.0150681	−	0.128736i
$970$	186.409			0.192174
$971$	−1058.42	−	611.077i	−1.09003	−	0.629327i	−0.156443	−	0.987687i	$-0.550003\pi$
$971$	−1058.42	−	611.077i	−1.09003	−	0.629327i	−0.933584	+	0.358360i	$0.883336\pi$
$972$	83.7775	+	48.3690i	0.0861909	+	0.0497623i
$973$	109.495	+	189.651i	0.112533	+	0.194913i
$974$	−321.303	+	556.513i	−0.329880	+	0.571369i
$975$	−647.333	−	1121.21i	−0.663931	−	1.14996i
$976$	8.76734			0.00898293
$977$		−	867.932i		−	0.888365i	−0.895936	−	0.444182i	$-0.853494\pi$
$977$		−	867.932i		−	0.888365i	0.895936	−	0.444182i	$-0.146506\pi$
$978$	348.611	+	603.811i	0.356453	+	0.617394i
$979$	−87.1362	+	50.3081i	−0.0890053	+	0.0513873i
$980$	−2.80816			−0.00286547
$981$		−	14.7843i		−	0.0150706i
$982$	636.441	−	367.449i	0.648106	−	0.374184i
$983$	930.158	+	537.027i	0.946245	+	0.546315i	0.891912	−	0.452208i	$-0.149364\pi$
$983$	930.158	+	537.027i	0.946245	+	0.546315i	0.0543322	+	0.998523i	$0.482697\pi$
$984$	497.803	−	287.406i	0.505897	−	0.292080i
$985$	125.955	−	218.160i	0.127873	−	0.221482i
$986$	9.51301	−	16.4770i	0.00964809	−	0.0167110i
$987$			250.494i			0.253793i
$988$	−598.287	+	257.962i	−0.605554	+	0.261095i
$989$	−2037.55			−2.06022
$990$	16.4041	+	9.47090i	0.0165698	+	0.00956657i
$991$	−1527.57	−	881.941i	−1.54144	−	0.889951i	−0.998748	−	0.0500189i	$-0.984072\pi$
$991$	−1527.57	−	881.941i	−1.54144	−	0.889951i	−0.542692	−	0.839932i	$-0.682595\pi$
$992$	88.1816	+	152.735i	0.0888928	+	0.153967i
$993$	−461.444	+	799.244i	−0.464697	+	0.804878i
$994$	−493.015	−	853.927i	−0.495991	−	0.859081i
$995$	−259.388			−0.260692
$996$		−	8.19955i		−	0.00823248i
$997$	11.6214	+	20.1289i	0.0116564	+	0.0201895i	0.871795	−	0.489871i	$-0.162956\pi$
$997$	11.6214	+	20.1289i	0.0116564	+	0.0201895i	−0.860138	+	0.510061i	$0.829623\pi$
$998$	542.668	−	313.309i	0.543755	−	0.313937i
$999$	737.110			0.737848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.3.d.a.27.1	✓	4
3.2	odd	2		342.3.m.a.217.2		4
4.3	odd	2		304.3.r.a.65.1		4
19.8	odd	6		722.3.b.b.721.2		4
19.11	even	3		722.3.b.b.721.3		4
19.12	odd	6	inner	38.3.d.a.31.1	yes	4
57.50	even	6		342.3.m.a.145.2		4
76.31	even	6		304.3.r.a.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.d.a.27.1	✓	4	1.1	even	1	trivial
38.3.d.a.31.1	yes	4	19.12	odd	6	inner
304.3.r.a.65.1		4	4.3	odd	2
304.3.r.a.145.1		4	76.31	even	6
342.3.m.a.145.2		4	57.50	even	6
342.3.m.a.217.2		4	3.2	odd	2
722.3.b.b.721.2		4	19.8	odd	6
722.3.b.b.721.3		4	19.11	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(2.72474 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +6.89898 q^{7} -2.82843i q^{8} +(0.449490 + 0.778539i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(2.72474 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +6.89898 q^{7} -2.82843i q^{8} +(0.449490 + 0.778539i) q^{9} +(-1.22474 + 0.707107i) q^{10} -14.8990 q^{11} +6.29253i q^{12} +(-14.8485 + 8.57277i) q^{13} +(-8.44949 - 4.87832i) q^{14} +(2.72474 - 1.57313i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.05051 - 1.81954i) q^{17} -1.27135i q^{18} +(11.3485 - 15.2385i) q^{19} +2.00000 q^{20} +(18.7980 + 10.8530i) q^{21} +(18.2474 + 10.5352i) q^{22} +(-13.5227 - 23.4220i) q^{23} +(4.44949 - 7.70674i) q^{24} +(12.0000 + 20.7846i) q^{25} +24.2474 q^{26} -25.4880i q^{27} +(6.89898 + 11.9494i) q^{28} +(-5.54541 + 3.20164i) q^{29} -4.44949 q^{30} +31.1769i q^{31} +(4.89898 - 2.82843i) q^{32} +(-40.5959 - 23.4381i) q^{33} +(-2.57321 + 1.48565i) q^{34} +(3.44949 - 5.97469i) q^{35} +(-0.898979 + 1.55708i) q^{36} +28.9199i q^{37} +(-24.6742 + 10.6387i) q^{38} -53.9444 q^{39} +(-2.44949 - 1.41421i) q^{40} +(55.9393 + 32.2966i) q^{41} +(-15.3485 - 26.5843i) q^{42} +(37.6691 - 65.2449i) q^{43} +(-14.8990 - 25.8058i) q^{44} +0.898979 q^{45} +38.2480i q^{46} +(5.77015 + 9.99420i) q^{47} +(-10.8990 + 6.29253i) q^{48} -1.40408 q^{49} -33.9411i q^{50} +(5.72474 - 3.30518i) q^{51} +(-29.6969 - 17.1455i) q^{52} +(-69.2878 + 40.0033i) q^{53} +(-18.0227 + 31.2162i) q^{54} +(-7.44949 + 12.9029i) q^{55} -19.5133i q^{56} +(54.8939 - 23.6684i) q^{57} +9.05561 q^{58} +(50.9166 + 29.3967i) q^{59} +(5.44949 + 3.14626i) q^{60} +(-1.09592 - 1.89819i) q^{61} +(22.0454 - 38.1838i) q^{62} +(3.10102 + 5.37113i) q^{63} -8.00000 q^{64} +17.1455i q^{65} +(33.1464 + 57.4113i) q^{66} +(-51.6589 + 29.8253i) q^{67} +4.20204 q^{68} -85.0920i q^{69} +(-8.44949 + 4.87832i) q^{70} +(87.5227 + 50.5313i) q^{71} +(2.20204 - 1.27135i) q^{72} +(63.6918 - 110.317i) q^{73} +(20.4495 - 35.4196i) q^{74} +75.5103i q^{75} +(37.7423 + 4.41761i) q^{76} -102.788 q^{77} +(66.0681 + 38.1444i) q^{78} +(-5.78036 - 3.33729i) q^{79} +(2.00000 + 3.46410i) q^{80} +(44.1413 - 76.4550i) q^{81} +(-45.6742 - 79.1101i) q^{82} -1.30306 q^{83} +43.4120i q^{84} +(-1.05051 - 1.81954i) q^{85} +(-92.2702 + 53.2722i) q^{86} -20.1464 q^{87} +42.1407i q^{88} +(5.84847 - 3.37662i) q^{89} +(-1.10102 - 0.635674i) q^{90} +(-102.439 + 59.1433i) q^{91} +(27.0454 - 46.8440i) q^{92} +(-49.0454 + 84.9491i) q^{93} -16.3205i q^{94} +(-7.52270 - 17.4473i) q^{95} +17.7980 q^{96} +(-114.152 - 65.9054i) q^{97} +(1.71964 + 0.992836i) q^{98} +(-6.69694 - 11.5994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9	\( 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 40 q^{11} - 30 q^{13} - 24 q^{14} + 6 q^{15} - 8 q^{16} + 14 q^{17} + 16 q^{19} + 8 q^{20} + 36 q^{21} + 24 q^{22} - 10 q^{23} + 8 q^{24} + 48 q^{25} + 48 q^{26} + 8 q^{28} + 66 q^{29} - 8 q^{30} - 84 q^{33} + 24 q^{34} + 4 q^{35} + 16 q^{36} - 84 q^{38} - 108 q^{39} + 18 q^{41} - 32 q^{42} + 38 q^{43} - 40 q^{44} - 16 q^{45} - 70 q^{47} - 24 q^{48} - 84 q^{49} + 18 q^{51} - 60 q^{52} - 42 q^{53} - 28 q^{54} - 20 q^{55} + 102 q^{57} + 144 q^{58} + 42 q^{59} + 12 q^{60} + 74 q^{61} + 32 q^{63} - 32 q^{64} + 64 q^{66} + 102 q^{67} + 56 q^{68} - 24 q^{70} + 306 q^{71} + 48 q^{72} + 98 q^{73} + 72 q^{74} + 4 q^{76} - 176 q^{77} + 132 q^{78} - 126 q^{79} + 8 q^{80} + 10 q^{81} - 168 q^{82} - 64 q^{83} - 14 q^{85} - 276 q^{86} - 12 q^{87} - 6 q^{89} - 24 q^{90} - 204 q^{91} + 20 q^{92} - 108 q^{93} + 14 q^{95} + 32 q^{96} - 486 q^{97} - 96 q^{98} + 32 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 40 * q^11 - 30 * q^13 - 24 * q^14 + 6 * q^15 - 8 * q^16 + 14 * q^17 + 16 * q^19 + 8 * q^20 + 36 * q^21 + 24 * q^22 - 10 * q^23 + 8 * q^24 + 48 * q^25 + 48 * q^26 + 8 * q^28 + 66 * q^29 - 8 * q^30 - 84 * q^33 + 24 * q^34 + 4 * q^35 + 16 * q^36 - 84 * q^38 - 108 * q^39 + 18 * q^41 - 32 * q^42 + 38 * q^43 - 40 * q^44 - 16 * q^45 - 70 * q^47 - 24 * q^48 - 84 * q^49 + 18 * q^51 - 60 * q^52 - 42 * q^53 - 28 * q^54 - 20 * q^55 + 102 * q^57 + 144 * q^58 + 42 * q^59 + 12 * q^60 + 74 * q^61 + 32 * q^63 - 32 * q^64 + 64 * q^66 + 102 * q^67 + 56 * q^68 - 24 * q^70 + 306 * q^71 + 48 * q^72 + 98 * q^73 + 72 * q^74 + 4 * q^76 - 176 * q^77 + 132 * q^78 - 126 * q^79 + 8 * q^80 + 10 * q^81 - 168 * q^82 - 64 * q^83 - 14 * q^85 - 276 * q^86 - 12 * q^87 - 6 * q^89 - 24 * q^90 - 204 * q^91 + 20 * q^92 - 108 * q^93 + 14 * q^95 + 32 * q^96 - 486 * q^97 - 96 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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