LMFDB - Embedded newform 38.3.d.a.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [38,3,Mod(27,38)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			31.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.3.d.a.27.1

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	0.0283812	−	0.999597i	$-0.490965\pi$
$3$	2.72474	−	1.57313i	0.908248	−	0.524377i	0.879867	+	0.475220i	$0.157631\pi$
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.100000	+	0.173205i	0.911684	−	0.410891i	$-0.134782\pi$
$5$	0.500000	+	0.866025i	0.100000	+	0.173205i	−0.811684	+	0.584096i	$0.801449\pi$
$6$	−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	−0.195218	−	0.980760i	$-0.562541\pi$
$13$	−14.8485	−	8.57277i	−1.14219	−	0.659444i	−0.946972	+	0.321316i	$0.895875\pi$
$14$	−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	0.895268	−	0.445529i	$-0.146984\pi$
$17$	1.05051	+	1.81954i	0.0617947	+	0.107032i	−0.833473	+	0.552560i	$0.813651\pi$
$18$			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	0.406558	+	0.913625i	$0.366729\pi$
$23$	−13.5227	+	23.4220i	−0.587944	+	1.01835i	−0.994501	+	0.104723i	$0.966604\pi$
$24$	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	0.401333	−	0.915932i	$-0.368547\pi$
$29$	−5.54541	−	3.20164i	−0.191221	−	0.110401i	−0.592554	+	0.805531i	$0.701880\pi$
$30$	−4.44949			−0.148316
$31$		−	31.1769i		−	1.00571i	−0.864372	−	0.502853i	$-0.832284\pi$
$31$		−	31.1769i		−	1.00571i	0.864372	−	0.502853i	$-0.167716\pi$
$32$	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	$-0.872195\pi$
$37$		−	28.9199i		−	0.781620i	0.920471	−	0.390810i	$-0.127805\pi$
$38$	−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	0.374170	−	0.927360i	$-0.377928\pi$
$41$	55.9393	−	32.2966i	1.36437	−	0.787721i	0.990202	+	0.139639i	$0.0445942\pi$
$42$	−15.3485	+	26.5843i	−0.365440	+	0.632960i
$43$	37.6691	+	65.2449i	0.876026	+	1.51732i	0.855665	+	0.517529i	$0.173148\pi$
$43$	37.6691	+	65.2449i	0.876026	+	1.51732i	0.0203609	+	0.999793i	$0.493518\pi$
$44$	−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	−0.798090	−	0.602539i	$-0.794156\pi$
$47$	5.77015	−	9.99420i	0.122769	−	0.212642i	0.920859	+	0.389896i	$0.127489\pi$
$48$	−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	−0.325669	−	0.945484i	$-0.605589\pi$
$53$	−69.2878	−	40.0033i	−1.30732	−	0.754779i	−0.981647	+	0.190705i	$0.938923\pi$
$54$	−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	−0.00202049	−	0.999998i	$-0.500643\pi$
$59$	50.9166	−	29.3967i	0.862993	−	0.498249i	0.865013	+	0.501749i	$0.167310\pi$
$60$	5.44949	−	3.14626i	0.0908248	−	0.0524377i
$61$	−1.09592	+	1.89819i	−0.0179659	+	0.0311178i	−0.874869	−	0.484360i	$-0.839052\pi$
$61$	−1.09592	+	1.89819i	−0.0179659	+	0.0311178i	0.856903	+	0.515478i	$0.172386\pi$
$62$	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	0.0622127	−	0.998063i	$-0.480184\pi$
$67$	−51.6589	−	29.8253i	−0.771029	−	0.445154i	−0.833241	+	0.552909i	$0.813518\pi$
$68$	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	0.265119	−	0.964216i	$-0.414589\pi$
$71$	87.5227	−	50.5313i	1.23271	−	0.711708i	0.967595	+	0.252508i	$0.0812553\pi$
$72$	2.20204	+	1.27135i	0.0305839	+	0.0176576i
$73$	63.6918	+	110.317i	0.872491	+	1.51120i	0.859412	+	0.511284i	$0.170830\pi$
$73$	63.6918	+	110.317i	0.872491	+	1.51120i	0.0130791	+	0.999914i	$0.495837\pi$
$74$	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	−0.536138	−	0.844130i	$-0.680117\pi$
$79$	−5.78036	+	3.33729i	−0.0731691	+	0.0422442i	0.462969	+	0.886374i	$0.346784\pi$
$80$	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	0.532497	−	0.846432i	$-0.321254\pi$
$89$	5.84847	+	3.37662i	0.0657131	+	0.0379395i	−0.466783	+	0.884372i	$0.654587\pi$
$90$	−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	−0.955277	−	0.295713i	$-0.904443\pi$
$97$	−114.152	+	65.9054i	−1.17682	+	0.679437i	−0.221543	+	0.975151i	$0.571109\pi$
$98$	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	−0.881630	−	0.471941i	$-0.843554\pi$
$101$	−3.24235	+	5.61591i	−0.0321024	+	0.0556031i	0.849528	+	0.527544i	$0.176887\pi$
$102$	−9.34847			−0.0916517
$103$			80.0243i			0.776935i	0.921462	+	0.388467i	$0.126995\pi$
$103$			80.0243i			0.776935i	−0.921462	+	0.388467i	$0.873005\pi$
$104$	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	$0.121995\pi$
$107$			80.0243i			0.747890i	−0.927451	+	0.373945i	$0.878005\pi$
$108$	44.1464	+	25.4880i	0.408763	+	0.236000i
$109$	−14.2423	+	8.22282i	−0.130664	+	0.0754387i	−0.563907	−	0.825838i	$-0.690702\pi$
$109$	−14.2423	+	8.22282i	−0.130664	+	0.0754387i	0.433243	+	0.901277i	$0.357369\pi$
$110$	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	$-0.799994\pi$
$113$		−	132.843i		−	1.17560i	0.809006	−	0.587801i	$-0.200006\pi$
$114$	−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	0.862972	−	0.505253i	$-0.168601\pi$
$127$	108.826	+	62.8306i	0.856896	+	0.494729i	−0.00607575	+	0.999982i	$0.501934\pi$
$128$	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	0.585475	−	0.810691i	$-0.300908\pi$
$131$	−53.6237	−	92.8790i	−0.409341	−	0.709000i	−0.994816	+	0.101691i	$0.967575\pi$
$132$			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	−0.862166	−	0.506626i	$-0.830893\pi$
$137$	1.05051	−	1.81954i	0.00766796	−	0.0132813i	0.869834	+	0.493345i	$0.164226\pi$
$138$	−60.1691	−	104.216i	−0.436008	−	0.755188i
$139$	15.8712	−	27.4897i	0.114181	−	0.197767i	−0.803271	−	0.595614i	$-0.796909\pi$
$139$	15.8712	−	27.4897i	0.114181	−	0.197767i	0.917452	+	0.397846i	$0.130242\pi$
$140$	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	−0.986196	−	0.165585i	$-0.947049\pi$
$149$	−94.8383	−	164.265i	−0.636498	−	1.10245i	0.349697	−	0.936863i	$-0.386284\pi$
$150$	53.3939	+	92.4809i	0.355959	+	0.616539i
$151$			16.2707i			0.107753i	0.998548	+	0.0538764i	$0.0171577\pi$
$151$			16.2707i			0.107753i	−0.998548	+	0.0538764i	$0.982842\pi$
$152$	−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	−0.871588	−	0.490239i	$-0.836909\pi$
$157$	−135.076	−	233.958i	−0.860354	−	1.49018i	0.0112344	−	0.999937i	$-0.496424\pi$
$158$	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	0.247655	−	0.968848i	$-0.420340\pi$
$167$	−78.0834	−	45.0815i	−0.467565	−	0.269949i	−0.715220	+	0.698899i	$0.753674\pi$
$168$	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	−0.522771	+	0.852473i	$0.675102\pi$
$173$	−263.379	+	152.062i	−1.52242	+	0.878969i	−0.999649	+	0.0264959i	$0.991565\pi$
$174$	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	$0.342753\pi$
$179$			315.198i			1.76088i	−0.474156	+	0.880441i	$0.657247\pi$
$180$	0.898979	−	1.55708i	0.00499433	−	0.00865043i
$181$	−27.8939	−	16.1045i	−0.154110	−	0.0889753i	0.420962	−	0.907078i	$-0.361693\pi$
$181$	−27.8939	−	16.1045i	−0.154110	−	0.0889753i	−0.575072	+	0.818103i	$0.695026\pi$
$182$	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	−0.387187	−	0.922001i	$-0.626553\pi$
$193$	42.0153	−	24.2575i	0.217696	−	0.125687i	0.604883	+	0.796314i	$0.293220\pi$
$194$	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	0.330974	+	0.943640i	$0.392623\pi$
$199$	−129.694	+	224.637i	−0.651729	+	1.12883i	−0.982703	+	0.185188i	$0.940710\pi$
$200$	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	−0.350385	−	0.936606i	$-0.613949\pi$
$211$	60.2503	−	34.7855i	0.285546	−	0.164860i	0.635932	+	0.771745i	$0.280616\pi$
$212$	−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	−0.512231	−	0.858848i	$-0.671181\pi$
$223$	−5.47730	+	3.16232i	−0.0245619	+	0.0141808i	0.487669	+	0.873029i	$0.337847\pi$
$224$	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	$0.0391796\pi$
$227$			55.7402i			0.245552i	−0.992434	+	0.122776i	$0.960820\pi$
$228$	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	0.999739	−	0.0228507i	$-0.00727424\pi$
$233$	111.859	+	193.745i	0.480080	+	0.831523i	−0.519659	+	0.854374i	$0.673941\pi$
$234$	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	0.729103	−	0.684405i	$-0.239938\pi$
$241$	120.727	+	69.7018i	0.500942	+	0.289219i	−0.228160	+	0.973624i	$0.573271\pi$
$242$	−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	−0.999689	−	0.0249476i	$-0.992058\pi$
$251$	−120.038	+	207.912i	−0.478239	+	0.828334i	0.521450	+	0.853282i	$0.325391\pi$
$252$	−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	0.516212	−	0.856461i	$-0.327342\pi$
$257$	8.37857	+	4.83737i	0.0326014	+	0.0188224i	−0.483611	+	0.875283i	$0.660675\pi$
$258$	−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	0.953762	−	0.300563i	$-0.0971747\pi$
$263$	56.9620	+	98.6611i	0.216586	+	0.375137i	−0.737176	+	0.675700i	$0.763841\pi$
$264$	−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	−0.979364	−	0.202106i	$-0.935221\pi$
$269$	−348.090	+	200.970i	−1.29402	+	0.747100i	−0.314652	+	0.949207i	$0.601888\pi$
$270$	18.0227	−	31.2162i	0.0667508	−	0.115616i
$271$	−199.492	−	345.530i	−0.736133	−	1.27502i	−0.954224	−	0.299092i	$-0.903316\pi$
$271$	−199.492	−	345.530i	−0.736133	−	1.27502i	0.218091	−	0.975928i	$-0.430017\pi$
$272$	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	0.581980	−	0.813203i	$-0.302278\pi$
$281$	47.4092	+	27.3717i	0.168716	+	0.0974082i	−0.413264	+	0.910611i	$0.635611\pi$
$282$	25.6742	+	44.4691i	0.0910434	+	0.157692i
$283$	74.4671	+	128.981i	0.263135	+	0.455762i	0.967073	−	0.254498i	$-0.0819103\pi$
$283$	74.4671	+	128.981i	0.263135	+	0.455762i	−0.703939	+	0.710261i	$0.748577\pi$
$284$		−	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	$-0.920027\pi$
$293$		−	145.685i		−	0.497218i	0.968604	−	0.248609i	$-0.0799734\pi$
$294$	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	−0.331757	−	0.943365i	$-0.607641\pi$
$307$	98.0380	−	56.6023i	0.319342	−	0.184372i	0.651099	+	0.758993i	$0.274308\pi$
$308$	−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	−0.993298	−	0.115582i	$-0.963127\pi$
$313$	−124.121	+	214.984i	−0.396552	+	0.686849i	0.596746	+	0.802431i	$0.296460\pi$
$314$	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	0.157792	−	0.987472i	$-0.449562\pi$
$317$	−196.061	−	113.196i	−0.618488	−	0.357084i	−0.776280	+	0.630388i	$0.782896\pi$
$318$	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	$-0.853881\pi$
$331$		−	293.328i		−	0.886188i	0.896475	−	0.443094i	$-0.146119\pi$
$332$	−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	−0.957199	−	0.289431i	$-0.906534\pi$
$337$	−399.393	+	230.590i	−1.18514	+	0.684243i	−0.227945	+	0.973674i	$0.573201\pi$
$338$	−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	0.559156	−	0.829063i	$-0.311125\pi$
$347$	−152.129	−	263.495i	−0.438412	−	0.759351i	−0.997567	+	0.0697116i	$0.977792\pi$
$348$	−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	0.743023	−	0.669266i	$-0.233391\pi$
$359$	−74.7043	−	129.392i	−0.208090	−	0.360423i	−0.951113	+	0.308844i	$0.900058\pi$
$360$			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	−0.980260	−	0.197714i	$-0.936648\pi$
$367$	−117.038	+	202.716i	−0.318905	+	0.552359i	0.661355	+	0.750073i	$0.269982\pi$
$368$	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	$0.328019\pi$
$373$			639.738i			1.71512i	−0.514387	+	0.857558i	$0.671981\pi$
$374$	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	$-0.954337\pi$
$379$		−	108.366i		−	0.285927i	0.989728	−	0.142963i	$-0.0456631\pi$
$380$	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	−0.191469	−	0.981499i	$-0.561325\pi$
$383$	215.552	−	124.449i	0.562800	−	0.324933i	0.754268	+	0.656566i	$0.227992\pi$
$384$	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	−0.00676592	−	0.999977i	$-0.502154\pi$
$389$	335.560	−	581.207i	0.862623	−	1.49411i	0.869389	−	0.494129i	$-0.164513\pi$
$390$	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	0.918811	−	0.394699i	$-0.129151\pi$
$397$	46.6816	+	80.8550i	0.117586	+	0.203665i	−0.801225	+	0.598364i	$0.795818\pi$
$398$		−	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	−0.166189	−	0.986094i	$-0.553146\pi$
$401$	242.484	−	139.998i	0.604699	−	0.349123i	0.770888	+	0.636971i	$0.219813\pi$
$402$	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	−0.369514	−	0.929225i	$-0.620476\pi$
$409$	−555.833	−	320.910i	−1.35900	−	0.784621i	−0.989490	+	0.144604i	$0.953809\pi$
$410$	−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	0.113153	−	0.993578i	$-0.463905\pi$
$421$	433.711	−	250.403i	1.03019	−	0.594782i	0.917040	+	0.398795i	$0.130572\pi$
$422$	−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	0.633290	−	0.773914i	$-0.281704\pi$
$431$	120.553	+	69.6015i	0.279706	+	0.161488i	−0.353584	+	0.935403i	$0.615037\pi$
$432$	88.2929	−	50.9759i	0.204382	−	0.118000i
$433$	180.349	+	104.125i	0.416510	+	0.240472i	0.693583	−	0.720377i	$-0.256031\pi$
$433$	180.349	+	104.125i	0.416510	+	0.240472i	−0.277073	+	0.960849i	$0.589364\pi$
$434$	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	−0.423331	−	0.905975i	$-0.639139\pi$
$439$	65.6748	−	37.9173i	0.149601	−	0.0863721i	0.572932	+	0.819603i	$0.305806\pi$
$440$	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	−0.486038	−	0.873938i	$-0.661558\pi$
$443$	227.628	−	394.264i	0.513834	−	0.889986i	0.999871	−	0.0160481i	$-0.00510848\pi$
$444$	−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	$-0.997005\pi$
$449$		−	8.44993i		−	0.0188194i	0.999956	−	0.00940972i	$-0.00299525\pi$
$450$	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	0.977942	+	0.208878i	$0.0669813\pi$
$461$	308.808	+	534.871i	0.669865	+	1.16024i	−0.308077	+	0.951361i	$0.599685\pi$
$462$	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	0.0535671	+	0.998564i	$0.482941\pi$
$479$	−401.401	+	695.247i	−0.837998	+	1.45146i	−0.891566	+	0.452892i	$0.850392\pi$
$480$	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	$0.154493\pi$
$487$			454.391i			0.933041i	−0.884510	+	0.466521i	$0.845507\pi$
$488$	−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	−0.999421	−	0.0340247i	$-0.989168\pi$
$491$	−259.826	−	450.031i	−0.529177	−	0.916561i	0.470244	−	0.882536i	$-0.344166\pi$
$492$	−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	0.554006	−	0.832513i	$-0.313098\pi$
$499$	−221.543	−	383.724i	−0.443974	−	0.768986i	−0.997980	+	0.0635269i	$0.979765\pi$
$500$	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	−0.720543	−	0.693410i	$-0.756107\pi$
$503$	120.841	−	209.302i	0.240240	−	0.416107i	0.960782	+	0.277303i	$0.0894406\pi$
$504$	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	0.808214	−	0.588889i	$-0.200434\pi$
$509$	357.485	+	206.394i	0.702329	+	0.405490i	−0.105886	+	0.994378i	$0.533768\pi$
$510$	−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	$-0.674773\pi$
$521$		−	888.839i		−	1.70602i	0.521891	−	0.853012i	$-0.325227\pi$
$522$	4.07041	−	7.05015i	0.00779771	−	0.0135060i
$523$	132.856	+	76.7047i	0.254027	+	0.146663i	0.621607	−	0.783329i	$-0.286480\pi$
$523$	132.856	+	76.7047i	0.254027	+	0.146663i	−0.367580	+	0.929992i	$0.619813\pi$
$524$	−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	−0.0765964	−	0.997062i	$-0.524405\pi$
$541$	446.424	−	773.229i	0.825183	−	1.42926i	0.901779	−	0.432197i	$-0.142261\pi$
$542$	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	−0.378196	−	0.925726i	$-0.623455\pi$
$547$	−748.841	−	432.343i	−1.36900	−	0.790390i	−0.990800	+	0.135336i	$0.956789\pi$
$548$	−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	0.304068	+	0.952650i	$0.401655\pi$
$557$	−374.853	+	649.265i	−0.672986	+	1.16565i	−0.977053	+	0.212995i	$0.931678\pi$
$558$	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	$0.0461775\pi$
$563$			162.777i			0.289125i	−0.989496	+	0.144563i	$0.953823\pi$
$564$	−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	$0.0837795\pi$
$569$			296.076i			0.520345i	−0.965562	+	0.260173i	$0.916221\pi$
$570$	−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	0.985474	+	0.169824i	$0.0543200\pi$
$587$	375.568	+	650.503i	0.639809	+	1.10818i	−0.345665	+	0.938358i	$0.612347\pi$
$588$			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	−0.519096	−	0.854716i	$-0.673731\pi$
$593$	285.030	−	493.687i	0.480658	−	0.832524i	0.999754	+	0.0221922i	$0.00706458\pi$
$594$	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	0.187133	−	0.982335i	$-0.440081\pi$
$599$	−341.447	−	197.134i	−0.570028	−	0.329106i	−0.757160	+	0.653229i	$0.773414\pi$
$600$	213.576			0.355959
$601$		−	241.665i		−	0.402105i	−0.979580	−	0.201053i	$-0.935564\pi$
$601$		−	241.665i		−	0.402105i	0.979580	−	0.201053i	$-0.0644362\pi$
$602$	−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	$-0.901632\pi$
$607$		−	369.224i		−	0.608276i	0.952628	−	0.304138i	$-0.0983685\pi$
$608$	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	0.668182	−	0.743998i	$-0.267073\pi$
$613$	−190.171	−	329.386i	−0.310230	−	0.537334i	−0.978412	+	0.206664i	$0.933739\pi$
$614$	−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	−0.998408	−	0.0564062i	$-0.982036\pi$
$617$	−277.869	+	481.283i	−0.450355	+	0.780037i	0.548053	+	0.836444i	$0.315369\pi$
$618$	−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	−0.897893	−	0.440214i	$-0.854902\pi$
$631$	−42.7247	+	74.0014i	−0.0677096	+	0.117276i	0.830183	+	0.557491i	$0.188236\pi$
$632$	−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	0.0472069	−	0.998885i	$-0.484968\pi$
$641$	599.893	−	346.348i	0.935870	−	0.540325i	0.888663	+	0.458560i	$0.151635\pi$
$642$	−308.363	−	178.034i	−0.480317	−	0.277311i
$643$	252.123	+	436.690i	0.392105	+	0.679145i	0.992727	−	0.120388i	$-0.0384138\pi$
$643$	252.123	+	436.690i	0.392105	+	0.679145i	−0.600622	+	0.799533i	$0.705080\pi$
$644$	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	0.169334	−	0.985559i	$-0.445838\pi$
$659$	−395.082	−	228.101i	−0.599518	−	0.346132i	−0.768852	+	0.639427i	$0.779172\pi$
$660$	−81.1918	+	46.8761i	−0.123018	+	0.0710244i
$661$	495.696	+	286.190i	0.749919	+	0.432966i	0.825665	−	0.564161i	$-0.190800\pi$
$661$	495.696	+	286.190i	0.749919	+	0.432966i	−0.0757457	+	0.997127i	$0.524134\pi$
$662$	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	$-0.762207\pi$
$673$		−	914.574i		−	1.35895i	0.733698	−	0.679476i	$-0.237793\pi$
$674$	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	$-0.935500\pi$
$677$		−	272.492i		−	0.402500i	0.979540	−	0.201250i	$-0.0645003\pi$
$678$	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	$0.0385058\pi$
$683$			164.842i			0.241350i	−0.992692	+	0.120675i	$0.961494\pi$
$684$	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	0.891738	−	0.452551i	$-0.149486\pi$
$701$	37.8179	+	65.5024i	0.0539484	+	0.0934414i	−0.837790	+	0.545993i	$0.816153\pi$
$702$			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	−0.349524	−	0.936928i	$-0.613657\pi$
$709$	451.379	−	781.811i	0.636641	−	1.10269i	0.986165	−	0.165767i	$-0.0530101\pi$
$710$	−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	−0.908578	−	0.417716i	$-0.862831\pi$
$719$	−586.734	−	1016.25i	−0.816042	−	1.41343i	0.0925359	−	0.995709i	$-0.470503\pi$
$720$	−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	0.596434	−	0.802662i	$-0.296584\pi$
$727$	−288.552	−	499.787i	−0.396908	−	0.687465i	−0.993343	+	0.115197i	$0.963250\pi$
$728$	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	0.999839	+	0.0179548i	$0.00571549\pi$
$739$	380.931	+	659.792i	0.515469	+	0.892818i	−0.484370	+	0.874863i	$0.660951\pi$
$740$		−	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	−0.577817	−	0.816166i	$-0.696095\pi$
$743$	−118.810	+	68.5950i	−0.159906	+	0.0923216i	0.417912	+	0.908488i	$0.362762\pi$
$744$	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	0.561957	−	0.827166i	$-0.310048\pi$
$751$	95.0686	+	54.8879i	0.126589	+	0.0730864i	−0.435368	+	0.900253i	$0.643382\pi$
$752$	−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	0.764485	−	0.644641i	$-0.222993\pi$
$757$	−133.257	−	230.808i	−0.176033	−	0.304898i	−0.940518	+	0.339743i	$0.889660\pi$
$758$	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	−0.997253	−	0.0740698i	$-0.976401\pi$
$769$	−334.115	+	578.705i	−0.434480	+	0.752542i	0.562773	+	0.826612i	$0.309735\pi$
$770$	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	0.146307	−	0.989239i	$-0.453261\pi$
$773$	−492.591	−	284.397i	−0.637246	−	0.367914i	−0.783553	+	0.621325i	$0.786595\pi$
$774$	−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	$0.0944315\pi$
$787$			460.132i			0.584665i	−0.956317	+	0.292333i	$0.905569\pi$
$788$	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	$0.274671\pi$
$797$			1211.02i			1.51947i	−0.650234	+	0.759734i	$0.725329\pi$
$798$	−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	0.230353	−	0.973107i	$-0.426012\pi$
$811$	−403.234	−	232.808i	−0.497206	−	0.287062i	−0.727559	+	0.686045i	$0.759345\pi$
$812$	−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	−0.834938	−	0.550343i	$-0.814497\pi$
$821$	48.5556	−	84.1008i	0.0591420	−	0.102437i	0.894081	+	0.447906i	$0.147830\pi$
$822$	4.67423	+	8.09601i	0.00568642	+	0.00984916i
$823$	562.052	−	973.502i	0.682930	−	1.18287i	−0.291152	−	0.956677i	$-0.594039\pi$
$823$	562.052	−	973.502i	0.682930	−	1.18287i	0.974082	−	0.226193i	$-0.0726281\pi$
$824$	−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	0.465221	−	0.885195i	$-0.345975\pi$
$827$	−56.8722	−	32.8352i	−0.0687693	−	0.0397040i	−0.533990	+	0.845491i	$0.679308\pi$
$828$	48.6265			0.0587277
$829$		−	276.987i		−	0.334121i	−0.985947	−	0.167061i	$-0.946572\pi$
$829$		−	276.987i		−	0.334121i	0.985947	−	0.167061i	$-0.0534276\pi$
$830$	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	−0.592087	−	0.805874i	$-0.701696\pi$
$839$	−159.598	+	92.1438i	−0.190224	+	0.109826i	0.401864	+	0.915700i	$0.368363\pi$
$840$	−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	0.947329	+	0.320263i	$0.103771\pi$
$853$	640.620	+	1109.59i	0.751020	+	1.30081i	−0.196308	+	0.980542i	$0.562895\pi$
$854$		−	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	−0.446435	−	0.894816i	$-0.647306\pi$
$857$	90.2265	−	52.0923i	0.105282	−	0.0607845i	0.551716	+	0.834032i	$0.313973\pi$
$858$	−984.347	+	568.313i	−1.14726	+	0.662370i
$859$	374.183	−	648.105i	0.435604	−	0.754487i	−0.561741	−	0.827313i	$-0.689868\pi$
$859$	374.183	−	648.105i	0.435604	−	0.754487i	0.997345	+	0.0728256i	$0.0232017\pi$
$860$	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	$0.00356852\pi$
$863$			19.3495i			0.0224212i	−0.999937	+	0.0112106i	$0.996431\pi$
$864$	−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	−0.662730	−	0.748859i	$-0.730602\pi$
$877$	−303.060	+	174.972i	−0.345564	+	0.199512i	0.317166	+	0.948370i	$0.397269\pi$
$878$	−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	0.355858	+	0.934540i	$0.384189\pi$
$883$	−557.532	+	965.674i	−0.631406	+	1.09363i	−0.987264	+	0.159088i	$0.949145\pi$
$884$	−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	0.884581	−	0.466386i	$-0.154444\pi$
$887$	818.675	+	472.662i	0.922970	+	0.532877i	0.0383889	+	0.999263i	$0.487777\pi$
$888$	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	−0.119081	−	0.992885i	$-0.537995\pi$
$907$	617.886	−	356.737i	0.681241	−	0.393315i	0.800323	+	0.599570i	$0.204662\pi$
$908$	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	$0.304908\pi$
$911$			1490.37i			1.63597i	−0.575242	+	0.817984i	$0.695092\pi$
$912$	−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	0.834157	−	0.551527i	$-0.185955\pi$
$929$	−56.2582	−	97.4420i	−0.0605578	−	0.104889i	−0.894715	+	0.446638i	$0.852621\pi$
$930$			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	−0.790994	−	0.611824i	$-0.790436\pi$
$937$	125.894	−	218.055i	0.134358	−	0.232716i	0.925352	+	0.379109i	$0.123769\pi$
$938$	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	0.490057	−	0.871691i	$-0.336976\pi$
$941$	−18.6520	−	10.7688i	−0.0198215	−	0.0114440i	−0.509878	+	0.860247i	$0.670309\pi$
$942$	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	0.650623	−	0.759401i	$-0.274508\pi$
$947$	−314.735	−	545.137i	−0.332349	−	0.575646i	−0.982972	+	0.183755i	$0.941175\pi$
$948$	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	−0.704284	−	0.709918i	$-0.748732\pi$
$953$	−420.863	+	242.986i	−0.441619	+	0.254969i	0.262665	+	0.964887i	$0.415399\pi$
$954$	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	0.732190	−	0.681101i	$-0.238498\pi$
$967$	−216.372	−	374.767i	−0.223756	−	0.387556i	−0.955945	+	0.293545i	$0.905165\pi$
$968$			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	−0.933584	−	0.358360i	$-0.883336\pi$
$971$	−1058.42	+	611.077i	−1.09003	+	0.629327i	−0.156443	+	0.987687i	$0.550003\pi$
$972$	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	$0.146506\pi$
$977$			867.932i			0.888365i	−0.895936	+	0.444182i	$0.853494\pi$
$978$	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	0.0543322	−	0.998523i	$-0.482697\pi$
$983$	930.158	−	537.027i	0.946245	−	0.546315i	0.891912	+	0.452208i	$0.149364\pi$
$984$	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	−0.542692	+	0.839932i	$0.682595\pi$
$991$	−1527.57	+	881.941i	−1.54144	+	0.889951i	−0.998748	+	0.0500189i	$0.984072\pi$
$992$	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	−0.860138	−	0.510061i	$-0.829623\pi$
$997$	11.6214	−	20.1289i	0.0116564	−	0.0201895i	0.871795	+	0.489871i	$0.162956\pi$
$998$	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.31.1	yes	4
3.2	odd	2		342.3.m.a.145.2		4
4.3	odd	2		304.3.r.a.145.1		4
19.7	even	3		722.3.b.b.721.2		4
19.8	odd	6	inner	38.3.d.a.27.1	✓	4
19.12	odd	6		722.3.b.b.721.3		4
57.8	even	6		342.3.m.a.217.2		4
76.27	even	6		304.3.r.a.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.d.a.27.1	✓	4	19.8	odd	6	inner
38.3.d.a.31.1	yes	4	1.1	even	1	trivial
304.3.r.a.65.1		4	76.27	even	6
304.3.r.a.145.1		4	4.3	odd	2
342.3.m.a.145.2		4	3.2	odd	2
342.3.m.a.217.2		4	57.8	even	6
722.3.b.b.721.2		4	19.7	even	3
722.3.b.b.721.3		4	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 40 q^{11} - 30 q^{13} - 24 q^{14} + 6 q^{15} - 8 q^{16} + 14 q^{17} + 16 q^{19} + 8 q^{20} + 36 q^{21} + 24 q^{22} - 10 q^{23} + 8 q^{24}+ \cdots + 32 q^{99}+O(q^{100}) \) 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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