LMFDB - Embedded newform 861.2.i.e.247.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.i (of order $3$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.2
Character	$\chi$	$=$	861.247
Dual form			861.2.i.e.739.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22451 + 2.12091i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.99885 - 3.46211i) q^{4} +(-2.00914 + 3.47993i) q^{5} +2.44902 q^{6} +(-2.60950 - 0.436464i) q^{7} +4.89242 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.22451 + 2.12091i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.99885 - 3.46211i) q^{4} +(-2.00914 + 3.47993i) q^{5} +2.44902 q^{6} +(-2.60950 - 0.436464i) q^{7} +4.89242 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.92043 - 8.52243i) q^{10} +(-0.695352 - 1.20438i) q^{11} +(-1.99885 + 3.46211i) q^{12} -3.69638 q^{13} +(4.12107 - 5.00007i) q^{14} +4.01828 q^{15} +(-1.99312 + 3.45218i) q^{16} +(0.277423 + 0.480510i) q^{17} +(-1.22451 - 2.12091i) q^{18} +(-3.03167 + 5.25101i) q^{19} +16.0639 q^{20} +(0.926762 + 2.47813i) q^{21} +3.40586 q^{22} +(1.20164 - 2.08130i) q^{23} +(-2.44621 - 4.23696i) q^{24} +(-5.57329 - 9.65322i) q^{25} +(4.52626 - 7.83971i) q^{26} +1.00000 q^{27} +(3.70492 + 9.90682i) q^{28} +0.267006 q^{29} +(-4.92043 + 8.52243i) q^{30} +(0.704906 + 1.22093i) q^{31} +(0.0112344 + 0.0194586i) q^{32} +(-0.695352 + 1.20438i) q^{33} -1.35883 q^{34} +(6.76172 - 8.20397i) q^{35} +3.99771 q^{36} +(2.73348 - 4.73452i) q^{37} +(-7.42463 - 12.8598i) q^{38} +(1.84819 + 3.20116i) q^{39} +(-9.82956 + 17.0253i) q^{40} -1.00000 q^{41} +(-6.39072 - 1.06891i) q^{42} -3.21046 q^{43} +(-2.77981 + 4.81477i) q^{44} +(-2.00914 - 3.47993i) q^{45} +(2.94284 + 5.09714i) q^{46} +(0.100975 - 0.174894i) q^{47} +3.98624 q^{48} +(6.61900 + 2.27791i) q^{49} +27.2982 q^{50} +(0.277423 - 0.480510i) q^{51} +(7.38852 + 12.7973i) q^{52} +(3.21071 + 5.56112i) q^{53} +(-1.22451 + 2.12091i) q^{54} +5.58824 q^{55} +(-12.7668 - 2.13537i) q^{56} +6.06334 q^{57} +(-0.326952 + 0.566297i) q^{58} +(3.29207 + 5.70203i) q^{59} +(-8.03195 - 13.9117i) q^{60} +(4.65294 - 8.05914i) q^{61} -3.45266 q^{62} +(1.68274 - 2.04166i) q^{63} -8.02750 q^{64} +(7.42655 - 12.8632i) q^{65} +(-1.70293 - 2.94956i) q^{66} +(6.79562 + 11.7704i) q^{67} +(1.10905 - 1.92094i) q^{68} -2.40328 q^{69} +(9.12012 + 24.3869i) q^{70} +12.4476 q^{71} +(-2.44621 + 4.23696i) q^{72} +(-6.77656 - 11.7373i) q^{73} +(6.69435 + 11.5949i) q^{74} +(-5.57329 + 9.65322i) q^{75} +24.2395 q^{76} +(1.28885 + 3.44634i) q^{77} -9.05251 q^{78} +(7.74551 - 13.4156i) q^{79} +(-8.00891 - 13.8718i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.22451 - 2.12091i) q^{82} +4.93822 q^{83} +(6.72710 - 8.16196i) q^{84} -2.22952 q^{85} +(3.93125 - 6.80912i) q^{86} +(-0.133503 - 0.231234i) q^{87} +(-3.40195 - 5.89236i) q^{88} +(-4.84072 + 8.38438i) q^{89} +9.84085 q^{90} +(9.64571 + 1.61334i) q^{91} -9.60759 q^{92} +(0.704906 - 1.22093i) q^{93} +(0.247290 + 0.428319i) q^{94} +(-12.1821 - 21.1000i) q^{95} +(0.0112344 - 0.0194586i) q^{96} +5.14594 q^{97} +(-12.9363 + 11.2490i) q^{98} +1.39070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 12 q^{3} - 10 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 12 * q^3 - 10 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^9	\( 24 q + 2 q^{2} - 12 q^{3} - 10 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{9} - 11 q^{10} - 10 q^{11} - 10 q^{12} + 30 q^{13} + 4 q^{14} + 24 q^{15} - 14 q^{16} - 8 q^{17} + 2 q^{18} - 2 q^{19} + 32 q^{20} - 14 q^{22} - 5 q^{23} - 20 q^{25} + 24 q^{27} + 37 q^{28} + 40 q^{29} - 11 q^{30} - 10 q^{31} - 3 q^{32} - 10 q^{33} - 46 q^{34} - 4 q^{35} + 20 q^{36} + 17 q^{37} - 6 q^{38} - 15 q^{39} - 39 q^{40} - 24 q^{41} - 8 q^{42} + 24 q^{43} - 20 q^{44} - 12 q^{45} + 36 q^{46} - 34 q^{47} + 28 q^{48} - 10 q^{49} + 118 q^{50} - 8 q^{51} - 26 q^{52} - 6 q^{53} + 2 q^{54} - 2 q^{55} - q^{56} + 4 q^{57} + 11 q^{58} - 27 q^{59} - 16 q^{60} - 22 q^{61} - 90 q^{62} + 52 q^{64} + 7 q^{66} + 26 q^{67} - 33 q^{68} + 10 q^{69} + 50 q^{70} + 100 q^{71} - 21 q^{73} + 35 q^{74} - 20 q^{75} - 48 q^{76} + 52 q^{77} + 10 q^{79} - 22 q^{80} - 12 q^{81} - 2 q^{82} + 16 q^{83} - 29 q^{84} + 16 q^{85} + 17 q^{86} - 20 q^{87} + 46 q^{88} - 11 q^{89} + 22 q^{90} + 5 q^{91} + 126 q^{92} - 10 q^{93} - 10 q^{94} - 35 q^{95} - 3 q^{96} + 64 q^{97} - 75 q^{98} + 20 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 12 * q^3 - 10 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^9 - 11 * q^10 - 10 * q^11 - 10 * q^12 + 30 * q^13 + 4 * q^14 + 24 * q^15 - 14 * q^16 - 8 * q^17 + 2 * q^18 - 2 * q^19 + 32 * q^20 - 14 * q^22 - 5 * q^23 - 20 * q^25 + 24 * q^27 + 37 * q^28 + 40 * q^29 - 11 * q^30 - 10 * q^31 - 3 * q^32 - 10 * q^33 - 46 * q^34 - 4 * q^35 + 20 * q^36 + 17 * q^37 - 6 * q^38 - 15 * q^39 - 39 * q^40 - 24 * q^41 - 8 * q^42 + 24 * q^43 - 20 * q^44 - 12 * q^45 + 36 * q^46 - 34 * q^47 + 28 * q^48 - 10 * q^49 + 118 * q^50 - 8 * q^51 - 26 * q^52 - 6 * q^53 + 2 * q^54 - 2 * q^55 - q^56 + 4 * q^57 + 11 * q^58 - 27 * q^59 - 16 * q^60 - 22 * q^61 - 90 * q^62 + 52 * q^64 + 7 * q^66 + 26 * q^67 - 33 * q^68 + 10 * q^69 + 50 * q^70 + 100 * q^71 - 21 * q^73 + 35 * q^74 - 20 * q^75 - 48 * q^76 + 52 * q^77 + 10 * q^79 - 22 * q^80 - 12 * q^81 - 2 * q^82 + 16 * q^83 - 29 * q^84 + 16 * q^85 + 17 * q^86 - 20 * q^87 + 46 * q^88 - 11 * q^89 + 22 * q^90 + 5 * q^91 + 126 * q^92 - 10 * q^93 - 10 * q^94 - 35 * q^95 - 3 * q^96 + 64 * q^97 - 75 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.22451	+	2.12091i	−0.865860	+	1.49971i	0.000331188		1.00000i	$0.499895\pi$
$2$	−1.22451	+	2.12091i	−0.865860	+	1.49971i	−0.866191	+	0.499713i	$0.833439\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.99885	−	3.46211i	−0.999426	−	1.73106i
$5$	−2.00914	+	3.47993i	−0.898515	+	1.55627i	−0.0691213	+	0.997608i	$0.522020\pi$
$5$	−2.00914	+	3.47993i	−0.898515	+	1.55627i	−0.829393	+	0.558665i	$0.811314\pi$
$6$	2.44902			0.999809
$7$	−2.60950	−	0.436464i	−0.986299	−	0.164968i
$7$	−2.60950	−	0.436464i	−0.986299	−	0.164968i
$8$	4.89242			1.72973
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.92043	−	8.52243i	−1.55598	−	2.69503i
$11$	−0.695352	−	1.20438i	−0.209656	−	0.363136i	0.741950	−	0.670455i	$-0.233901\pi$
$11$	−0.695352	−	1.20438i	−0.209656	−	0.363136i	−0.951606	+	0.307320i	$0.900568\pi$
$12$	−1.99885	+	3.46211i	−0.577019	+	0.999426i
$13$	−3.69638			−1.02519			−0.512596	−	0.858630i	$-0.671316\pi$
$13$	−3.69638			−1.02519			−0.512596	+	0.858630i	$0.671316\pi$
$14$	4.12107	−	5.00007i	1.10140	−	1.33633i
$15$	4.01828			1.03752
$16$	−1.99312	+	3.45218i	−0.498279	+	0.863045i
$17$	0.277423	+	0.480510i	0.0672849	+	0.116541i	0.897705	−	0.440596i	$-0.145233\pi$
$17$	0.277423	+	0.480510i	0.0672849	+	0.116541i	−0.830420	+	0.557137i	$0.811900\pi$
$18$	−1.22451	−	2.12091i	−0.288620	−	0.499904i
$19$	−3.03167	+	5.25101i	−0.695513	+	1.20466i	0.274494	+	0.961589i	$0.411490\pi$
$19$	−3.03167	+	5.25101i	−0.695513	+	1.20466i	−0.970007	+	0.243075i	$0.921844\pi$
$20$	16.0639			3.59200
$21$	0.926762	+	2.47813i	0.202236	+	0.540772i
$22$	3.40586			0.726132
$23$	1.20164	−	2.08130i	0.250559	−	0.433981i	−0.713121	−	0.701041i	$-0.752719\pi$
$23$	1.20164	−	2.08130i	0.250559	−	0.433981i	0.963680	+	0.267060i	$0.0860523\pi$
$24$	−2.44621	−	4.23696i	−0.499331	−	0.864866i
$25$	−5.57329	−	9.65322i	−1.11466	−	1.93064i
$26$	4.52626	−	7.83971i	0.887672	−	1.53749i
$27$	1.00000			0.192450
$28$	3.70492	+	9.90682i	0.700164	+	1.87221i
$29$	0.267006			0.0495818			0.0247909	−	0.999693i	$-0.492108\pi$
$29$	0.267006			0.0495818			0.0247909	+	0.999693i	$0.492108\pi$
$30$	−4.92043	+	8.52243i	−0.898343	+	1.55598i
$31$	0.704906	+	1.22093i	0.126605	+	0.219286i	0.922359	−	0.386334i	$-0.126259\pi$
$31$	0.704906	+	1.22093i	0.126605	+	0.219286i	−0.795754	+	0.605620i	$0.792925\pi$
$32$	0.0112344	+	0.0194586i	0.00198599	+	0.00343983i
$33$	−0.695352	+	1.20438i	−0.121045	+	0.209656i
$34$	−1.35883			−0.233037
$35$	6.76172	−	8.20397i	1.14294	−	1.38672i
$36$	3.99771			0.666284
$37$	2.73348	−	4.73452i	0.449381	−	0.778351i	−0.548965	−	0.835846i	$-0.684978\pi$
$37$	2.73348	−	4.73452i	0.449381	−	0.778351i	0.998346	+	0.0574946i	$0.0183112\pi$
$38$	−7.42463	−	12.8598i	−1.20443	−	2.08614i
$39$	1.84819	+	3.20116i	0.295947	+	0.512596i
$40$	−9.82956	+	17.0253i	−1.55419	+	2.69194i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	−6.39072	−	1.06891i	−0.986110	−	0.164937i
$43$	−3.21046			−0.489591			−0.244796	−	0.969575i	$-0.578721\pi$
$43$	−3.21046			−0.489591			−0.244796	+	0.969575i	$0.578721\pi$
$44$	−2.77981	+	4.81477i	−0.419072	+	0.725854i
$45$	−2.00914	−	3.47993i	−0.299505	−	0.518758i
$46$	2.94284	+	5.09714i	0.433898	+	0.751533i
$47$	0.100975	−	0.174894i	0.0147287	−	0.0255109i	−0.858567	−	0.512701i	$-0.828645\pi$
$47$	0.100975	−	0.174894i	0.0147287	−	0.0255109i	0.873296	+	0.487190i	$0.161978\pi$
$48$	3.98624			0.575364
$49$	6.61900	+	2.27791i	0.945571	+	0.325416i
$50$	27.2982			3.86055
$51$	0.277423	−	0.480510i	0.0388469	−	0.0672849i
$52$	7.38852	+	12.7973i	1.02460	+	1.77466i
$53$	3.21071	+	5.56112i	0.441025	+	0.763878i	0.997766	−	0.0668083i	$-0.0212816\pi$
$53$	3.21071	+	5.56112i	0.441025	+	0.763878i	−0.556741	+	0.830686i	$0.687948\pi$
$54$	−1.22451	+	2.12091i	−0.166635	+	0.288620i
$55$	5.58824			0.753518
$56$	−12.7668	−	2.13537i	−1.70603	−	0.285351i
$57$	6.06334			0.803109
$58$	−0.326952	+	0.566297i	−0.0429309	+	0.0743584i
$59$	3.29207	+	5.70203i	0.428591	+	0.742341i	0.996748	−	0.0805791i	$-0.0256769\pi$
$59$	3.29207	+	5.70203i	0.428591	+	0.742341i	−0.568158	+	0.822920i	$0.692344\pi$
$60$	−8.03195	−	13.9117i	−1.03692	−	1.79600i
$61$	4.65294	−	8.05914i	0.595749	−	1.03187i	−0.397692	−	0.917519i	$-0.630189\pi$
$61$	4.65294	−	8.05914i	0.595749	−	1.03187i	0.993441	−	0.114348i	$-0.0364778\pi$
$62$	−3.45266			−0.438488
$63$	1.68274	−	2.04166i	0.212005	−	0.257225i
$64$	−8.02750			−1.00344
$65$	7.42655	−	12.8632i	0.921150	−	1.59548i
$66$	−1.70293	−	2.94956i	−0.209616	−	0.363066i
$67$	6.79562	+	11.7704i	0.830217	+	1.43798i	0.897866	+	0.440269i	$0.145117\pi$
$67$	6.79562	+	11.7704i	0.830217	+	1.43798i	−0.0676487	+	0.997709i	$0.521550\pi$
$68$	1.10905	−	1.92094i	0.134493	−	0.232948i
$69$	−2.40328			−0.289320
$70$	9.12012	+	24.3869i	1.09006	+	2.91479i
$71$	12.4476			1.47725			0.738627	−	0.674114i	$-0.235475\pi$
$71$	12.4476			1.47725			0.738627	+	0.674114i	$0.235475\pi$
$72$	−2.44621	+	4.23696i	−0.288289	+	0.499331i
$73$	−6.77656	−	11.7373i	−0.793136	−	1.37375i	−0.924016	−	0.382354i	$-0.875114\pi$
$73$	−6.77656	−	11.7373i	−0.793136	−	1.37375i	0.130880	−	0.991398i	$-0.458220\pi$
$74$	6.69435	+	11.5949i	0.778202	+	1.34789i
$75$	−5.57329	+	9.65322i	−0.643548	+	1.11466i
$76$	24.2395			2.78046
$77$	1.28885	+	3.44634i	0.146878	+	0.392747i
$78$	−9.05251			−1.02500
$79$	7.74551	−	13.4156i	0.871438	−	1.50937i	0.0109280	−	0.999940i	$-0.496521\pi$
$79$	7.74551	−	13.4156i	0.871438	−	1.50937i	0.860510	−	0.509434i	$-0.170145\pi$
$80$	−8.00891	−	13.8718i	−0.895423	−	1.55092i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.22451	−	2.12091i	0.135225	−	0.234216i
$83$	4.93822			0.542040			0.271020	−	0.962574i	$-0.412639\pi$
$83$	4.93822			0.542040			0.271020	+	0.962574i	$0.412639\pi$
$84$	6.72710	−	8.16196i	0.733987	−	0.890543i
$85$	−2.22952			−0.241826
$86$	3.93125	−	6.80912i	0.423917	−	0.734246i
$87$	−0.133503	−	0.231234i	−0.0143130	−	0.0247909i
$88$	−3.40195	−	5.89236i	−0.362650	−	0.628127i
$89$	−4.84072	+	8.38438i	−0.513116	+	0.888743i	0.486769	+	0.873531i	$0.338176\pi$
$89$	−4.84072	+	8.38438i	−0.513116	+	0.888743i	−0.999884	+	0.0152115i	$0.995158\pi$
$90$	9.84085			1.03732
$91$	9.64571	+	1.61334i	1.01115	+	0.169124i
$92$	−9.60759			−1.00166
$93$	0.704906	−	1.22093i	0.0730954	−	0.126605i
$94$	0.247290	+	0.428319i	0.0255060	+	0.0441777i
$95$	−12.1821	−	21.1000i	−1.24986	−	2.16482i
$96$	0.0112344	−	0.0194586i	0.00114661	−	0.00198599i
$97$	5.14594			0.522491			0.261245	−	0.965272i	$-0.415867\pi$
$97$	5.14594			0.522491			0.261245	+	0.965272i	$0.415867\pi$
$98$	−12.9363	+	11.2490i	−1.30676	+	1.13632i
$99$	1.39070			0.139771
$100$	−22.2804	+	38.5907i	−2.22804	+	3.85907i
$101$	−1.64611	−	2.85115i	−0.163795	−	0.283700i	0.772432	−	0.635097i	$-0.219040\pi$
$101$	−1.64611	−	2.85115i	−0.163795	−	0.283700i	−0.936227	+	0.351397i	$0.885707\pi$
$102$	0.679414	+	1.17678i	0.0672720	+	0.116519i
$103$	−7.52023	+	13.0254i	−0.740990	+	1.28343i	0.211055	+	0.977474i	$0.432310\pi$
$103$	−7.52023	+	13.0254i	−0.740990	+	1.28343i	−0.952045	+	0.305958i	$0.901023\pi$
$104$	−18.0843			−1.77331
$105$	−10.4857	−	1.75384i	−1.02330	−	0.171157i
$106$	−15.7262			−1.52746
$107$	−8.41222	+	14.5704i	−0.813240	+	1.40857i	0.0973455	+	0.995251i	$0.468965\pi$
$107$	−8.41222	+	14.5704i	−0.813240	+	1.40857i	−0.910585	+	0.413322i	$0.864369\pi$
$108$	−1.99885	−	3.46211i	−0.192340	−	0.333142i
$109$	−3.02637	−	5.24182i	−0.289874	−	0.502076i	0.683906	−	0.729570i	$-0.260280\pi$
$109$	−3.02637	−	5.24182i	−0.289874	−	0.502076i	−0.973779	+	0.227495i	$0.926947\pi$
$110$	−6.84285	+	11.8522i	−0.652441	+	1.13006i
$111$	−5.46696			−0.518901
$112$	6.70780	−	8.13855i	0.633827	−	0.769020i
$113$	−19.6802			−1.85136			−0.925681	−	0.378306i	$-0.876507\pi$
$113$	−19.6802			−1.85136			−0.925681	+	0.378306i	$0.876507\pi$
$114$	−7.42463	+	12.8598i	−0.695380	+	1.20443i
$115$	4.82852	+	8.36324i	0.450262	+	0.779876i
$116$	−0.533706	−	0.924405i	−0.0495533	−	0.0858289i
$117$	1.84819	−	3.20116i	0.170865	−	0.295947i
$118$	−16.1247			−1.48440
$119$	−0.514209	−	1.37498i	−0.0471375	−	0.126044i
$120$	19.6591			1.79462
$121$	4.53297	−	7.85134i	0.412088	−	0.713758i
$122$	11.3952	+	19.7370i	1.03167	+	1.78690i
$123$	0.500000	+	0.866025i	0.0450835	+	0.0780869i
$124$	2.81801	−	4.88093i	0.253065	−	0.438321i
$125$	24.6987			2.20912
$126$	2.26966	+	6.06899i	0.202197	+	0.540668i
$127$	−14.7424			−1.30818			−0.654088	−	0.756419i	$-0.726947\pi$
$127$	−14.7424			−1.30818			−0.654088	+	0.756419i	$0.726947\pi$
$128$	9.80729	−	16.9867i	0.866850	−	1.50143i
$129$	1.60523	+	2.78034i	0.141333	+	0.244796i
$130$	18.1878	+	31.5021i	1.59517	+	2.76292i
$131$	3.38990	−	5.87148i	0.296177	−	0.512994i	−0.679081	−	0.734063i	$-0.737621\pi$
$131$	3.38990	−	5.87148i	0.296177	−	0.512994i	0.975258	+	0.221070i	$0.0709548\pi$
$132$	5.55962			0.483903
$133$	10.2030	−	12.3793i	0.884715	−	1.07342i
$134$	−33.2852			−2.87541
$135$	−2.00914	+	3.47993i	−0.172919	+	0.299505i
$136$	1.35727	+	2.35086i	0.116385	+	0.201584i
$137$	−8.09545	−	14.0217i	−0.691641	−	1.19796i	−0.971300	−	0.237858i	$-0.923555\pi$
$137$	−8.09545	−	14.0217i	−0.691641	−	1.19796i	0.279659	−	0.960099i	$-0.409779\pi$
$138$	2.94284	−	5.09714i	0.250511	−	0.433898i
$139$	5.75297			0.487961			0.243980	−	0.969780i	$-0.421547\pi$
$139$	5.75297			0.487961			0.243980	+	0.969780i	$0.421547\pi$
$140$	−41.9188	−	7.01132i	−3.54278	−	0.592565i
$141$	−0.201950			−0.0170073
$142$	−15.2422	+	26.4002i	−1.27909	+	2.21546i
$143$	2.57028	+	4.45186i	0.214938	+	0.372283i
$144$	−1.99312	−	3.45218i	−0.166093	−	0.287682i
$145$	−0.536453	+	0.929163i	−0.0445500	+	0.0771628i
$146$	33.1919			2.74698
$147$	−1.33677	−	6.87117i	−0.110255	−	0.566725i
$148$	−21.8553			−1.79649
$149$	8.12189	−	14.0675i	0.665371	−	1.15246i	−0.313813	−	0.949485i	$-0.601607\pi$
$149$	8.12189	−	14.0675i	0.665371	−	1.15246i	0.979185	−	0.202972i	$-0.0650601\pi$
$150$	−13.6491	−	23.6409i	−1.11444	−	1.93027i
$151$	−6.80601	−	11.7884i	−0.553865	−	0.959322i	−0.997991	−	0.0633580i	$-0.979819\pi$
$151$	−6.80601	−	11.7884i	−0.553865	−	0.959322i	0.444126	−	0.895964i	$-0.353514\pi$
$152$	−14.8322	+	25.6902i	−1.20305	+	2.08375i
$153$	−0.554845			−0.0448566
$154$	−8.88760	−	1.48654i	−0.716183	−	0.119789i
$155$	−5.66502			−0.455026
$156$	7.38852	−	12.7973i	0.591555	−	1.02460i
$157$	−11.7173	−	20.2949i	−0.935139	−	1.61971i	−0.774386	−	0.632713i	$-0.781941\pi$
$157$	−11.7173	−	20.2949i	−0.935139	−	1.61971i	−0.160752	−	0.986995i	$-0.551392\pi$
$158$	18.9689	+	32.8551i	1.50909	+	2.61381i
$159$	3.21071	−	5.56112i	0.254626	−	0.441025i
$160$	−0.0902863			−0.00713776
$161$	−4.04409	+	4.90668i	−0.318719	+	0.386701i
$162$	2.44902			0.192413
$163$	4.94950	−	8.57278i	0.387674	−	0.671472i	−0.604462	−	0.796634i	$-0.706612\pi$
$163$	4.94950	−	8.57278i	0.387674	−	0.671472i	0.992136	+	0.125162i	$0.0399452\pi$
$164$	1.99885	+	3.46211i	0.156084	+	0.270346i
$165$	−2.79412	−	4.83955i	−0.217522	−	0.376759i
$166$	−6.04690	+	10.4735i	−0.469331	+	0.812904i
$167$	6.20468			0.480133			0.240066	−	0.970756i	$-0.422831\pi$
$167$	6.20468			0.480133			0.240066	+	0.970756i	$0.422831\pi$
$168$	4.53411	+	12.1240i	0.349814	+	0.935390i
$169$	0.663226			0.0510174
$170$	2.73008	−	4.72863i	0.209387	−	0.362669i
$171$	−3.03167	−	5.25101i	−0.231838	−	0.401555i
$172$	6.41725	+	11.1150i	0.489310	+	0.847510i
$173$	10.6754	−	18.4903i	0.811636	−	1.40580i	−0.100082	−	0.994979i	$-0.531911\pi$
$173$	10.6754	−	18.4903i	0.811636	−	1.40580i	0.911718	−	0.410816i	$-0.134756\pi$
$174$	0.653903			0.0495723
$175$	10.3302	+	27.6226i	0.780891	+	2.08807i
$176$	5.54367			0.417870
$177$	3.29207	−	5.70203i	0.247447	−	0.428591i
$178$	−11.8550	−	20.5335i	−0.888573	−	1.53905i
$179$	5.25417	+	9.10049i	0.392715	+	0.680203i	0.992807	−	0.119729i	$-0.0382025\pi$
$179$	5.25417	+	9.10049i	0.392715	+	0.680203i	−0.600091	+	0.799931i	$0.704869\pi$
$180$	−8.03195	+	13.9117i	−0.598666	+	1.03692i
$181$	16.5010			1.22651			0.613253	−	0.789886i	$-0.289861\pi$
$181$	16.5010			1.22651			0.613253	+	0.789886i	$0.289861\pi$
$182$	−15.2330	+	18.4822i	−1.12915	+	1.36999i
$183$	−9.30589			−0.687911
$184$	5.87892	−	10.1826i	0.433400	−	0.750671i
$185$	10.9839	+	19.0246i	0.807551	+	1.39872i
$186$	1.72633	+	2.99009i	0.126581	+	0.219244i
$187$	0.385813	−	0.668247i	0.0282134	−	0.0488671i
$188$	−0.807337			−0.0588811
$189$	−2.60950	−	0.436464i	−0.189813	−	0.0317481i
$190$	59.6685			4.32881
$191$	1.53992	−	2.66721i	0.111424	−	0.192993i	−0.804920	−	0.593383i	$-0.797792\pi$
$191$	1.53992	−	2.66721i	0.111424	−	0.192993i	0.916345	+	0.400390i	$0.131125\pi$
$192$	4.01375	+	6.95202i	0.289667	+	0.501719i
$193$	−7.67841	−	13.2994i	−0.552704	−	0.957311i	−0.998078	−	0.0619665i	$-0.980263\pi$
$193$	−7.67841	−	13.2994i	−0.552704	−	0.957311i	0.445375	−	0.895344i	$-0.353071\pi$
$194$	−6.30125	+	10.9141i	−0.452404	+	0.783586i
$195$	−14.8531			−1.06365
$196$	−5.34402	−	27.4689i	−0.381716	−	1.96207i
$197$	−17.4582			−1.24384			−0.621921	−	0.783080i	$-0.713647\pi$
$197$	−17.4582			−1.24384			−0.621921	+	0.783080i	$0.713647\pi$
$198$	−1.70293	+	2.94956i	−0.121022	+	0.209616i
$199$	7.56287	+	13.0993i	0.536118	+	0.928583i	0.999108	+	0.0422197i	$0.0134430\pi$
$199$	7.56287	+	13.0993i	0.536118	+	0.928583i	−0.462991	+	0.886363i	$0.653224\pi$
$200$	−27.2669	−	47.2276i	−1.92806	−	3.33950i
$201$	6.79562	−	11.7704i	0.479326	−	0.830217i
$202$	8.06274			0.567292
$203$	−0.696753	−	0.116539i	−0.0489024	−	0.00817941i
$204$	−2.21811			−0.155299
$205$	2.00914	−	3.47993i	0.140324	−	0.243049i
$206$	−18.4172	−	31.8995i	−1.28319	−	2.22255i
$207$	1.20164	+	2.08130i	0.0835196	+	0.144660i
$208$	7.36732	−	12.7606i	0.510832	−	0.884787i
$209$	8.43231			0.583275
$210$	16.5596	−	20.0917i	1.14272	−	1.38646i
$211$	16.7167			1.15083			0.575414	−	0.817862i	$-0.304841\pi$
$211$	16.7167			1.15083			0.575414	+	0.817862i	$0.304841\pi$
$212$	12.8355	−	22.2317i	0.881544	−	1.52688i
$213$	−6.22378	−	10.7799i	−0.426446	−	0.738627i
$214$	−20.6017	−	35.6832i	−1.40830	−	2.43925i
$215$	6.45027	−	11.1722i	0.439905	−	0.761938i
$216$	4.89242			0.332887
$217$	−1.30656	−	3.49370i	−0.0886951	−	0.237167i
$218$	14.8233			1.00396
$219$	−6.77656	+	11.7373i	−0.457917	+	0.793136i
$220$	−11.1701	−	19.3471i	−0.753085	−	1.30438i
$221$	−1.02546	−	1.77615i	−0.0689799	−	0.119477i
$222$	6.69435	−	11.5949i	0.449295	−	0.778202i
$223$	−15.4929			−1.03748			−0.518739	−	0.854933i	$-0.673598\pi$
$223$	−15.4929			−1.03748			−0.518739	+	0.854933i	$0.673598\pi$
$224$	−0.0208233	−	0.0556807i	−0.00139131	−	0.00372033i
$225$	11.1466			0.743105
$226$	24.0987	−	41.7401i	1.60302	−	2.77651i
$227$	0.191213	+	0.331190i	0.0126912	+	0.0219818i	0.872301	−	0.488969i	$-0.162627\pi$
$227$	0.191213	+	0.331190i	0.0126912	+	0.0219818i	−0.859610	+	0.510951i	$0.829293\pi$
$228$	−12.1197	−	20.9920i	−0.802649	−	1.39023i
$229$	−10.0965	+	17.4876i	−0.667192	+	1.15561i	0.311494	+	0.950248i	$0.399171\pi$
$229$	−10.0965	+	17.4876i	−0.667192	+	1.15561i	−0.978686	+	0.205363i	$0.934163\pi$
$230$	−23.6503			−1.55945
$231$	2.34019	−	2.83935i	0.153973	−	0.186815i
$232$	1.30631			0.0857632
$233$	4.36317	−	7.55724i	0.285841	−	0.495091i	−0.686972	−	0.726684i	$-0.741060\pi$
$233$	4.36317	−	7.55724i	0.285841	−	0.495091i	0.972813	+	0.231593i	$0.0743937\pi$
$234$	4.52626	+	7.83971i	0.295891	+	0.512498i
$235$	0.405746	+	0.702773i	0.0264680	+	0.0458438i
$236$	13.1607	−	22.7950i	0.856689	−	1.48383i
$237$	−15.4910			−1.00625
$238$	3.54586	+	0.593080i	0.229844	+	0.0384437i
$239$	12.4387			0.804590			0.402295	−	0.915510i	$-0.368213\pi$
$239$	12.4387			0.804590			0.402295	+	0.915510i	$0.368213\pi$
$240$	−8.00891	+	13.8718i	−0.516973	+	0.895423i
$241$	12.7872	+	22.1482i	0.823699	+	1.42669i	0.902909	+	0.429831i	$0.141427\pi$
$241$	12.7872	+	22.1482i	0.823699	+	1.42669i	−0.0792104	+	0.996858i	$0.525240\pi$
$242$	11.1013	+	19.2281i	0.713621	+	1.23603i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−37.2022			−2.38163
$245$	−21.2255	+	18.4570i	−1.35605	+	1.17918i
$246$	−2.44902			−0.156144
$247$	11.2062	−	19.4097i	0.713034	−	1.23501i
$248$	3.44870	+	5.97332i	0.218993	+	0.379306i
$249$	−2.46911	−	4.27662i	−0.156473	−	0.271020i
$250$	−30.2438	+	52.3838i	−1.91278	+	3.31304i
$251$	−29.3668			−1.85362			−0.926808	−	0.375534i	$-0.877459\pi$
$251$	−29.3668			−1.85362			−0.926808	+	0.375534i	$0.877459\pi$
$252$	−10.4320	−	1.74486i	−0.657155	−	0.109916i
$253$	−3.34224			−0.210125
$254$	18.0522	−	31.2673i	1.13270	−	1.96189i
$255$	1.11476	+	1.93082i	0.0698091	+	0.120913i
$256$	15.9908	+	27.6968i	0.999422	+	1.73105i
$257$	3.28432	−	5.68861i	0.204870	−	0.354846i	−0.745221	−	0.666817i	$-0.767656\pi$
$257$	3.28432	−	5.68861i	0.204870	−	0.354846i	0.950091	+	0.311972i	$0.100989\pi$
$258$	−7.86250			−0.489498
$259$	−9.19947	+	11.1617i	−0.571627	+	0.693553i
$260$	−59.3783			−3.68248
$261$	−0.133503	+	0.231234i	−0.00826363	+	0.0143130i
$262$	8.30194	+	14.3794i	0.512896	+	0.888361i
$263$	−6.57234	−	11.3836i	−0.405268	−	0.701944i	0.589085	−	0.808071i	$-0.299488\pi$
$263$	−6.57234	−	11.3836i	−0.405268	−	0.701944i	−0.994353	+	0.106127i	$0.966155\pi$
$264$	−3.40195	+	5.89236i	−0.209376	+	0.362650i
$265$	−25.8031			−1.58507
$266$	13.7617	+	36.7983i	0.843785	+	2.25625i
$267$	9.68145			0.592495
$268$	27.1669	−	47.0544i	1.65948	−	2.87431i
$269$	−5.83239	−	10.1020i	−0.355607	−	0.615930i	0.631615	−	0.775283i	$-0.282393\pi$
$269$	−5.83239	−	10.1020i	−0.355607	−	0.615930i	−0.987222	+	0.159353i	$0.949059\pi$
$270$	−4.92043	−	8.52243i	−0.299448	−	0.518659i
$271$	1.68435	−	2.91738i	0.102317	−	0.177218i	−0.810322	−	0.585985i	$-0.800708\pi$
$271$	1.68435	−	2.91738i	0.102317	−	0.177218i	0.912639	+	0.408767i	$0.134041\pi$
$272$	−2.21174			−0.134107
$273$	−3.42566	−	9.16010i	−0.207331	−	0.554394i
$274$	39.6519			2.39546
$275$	−7.75079	+	13.4248i	−0.467390	+	0.809544i
$276$	4.80380	+	8.32042i	0.289154	+	0.500830i
$277$	−7.06440	−	12.2359i	−0.424459	−	0.735184i	0.571911	−	0.820316i	$-0.306202\pi$
$277$	−7.06440	−	12.2359i	−0.424459	−	0.735184i	−0.996370	+	0.0851316i	$0.972869\pi$
$278$	−7.04457	+	12.2016i	−0.422505	+	0.731801i
$279$	−1.40981			−0.0844033
$280$	33.0812	−	40.1373i	1.97698	−	2.39866i
$281$	−14.5035			−0.865207			−0.432603	−	0.901584i	$-0.642405\pi$
$281$	−14.5035			−0.865207			−0.432603	+	0.901584i	$0.642405\pi$
$282$	0.247290	−	0.428319i	0.0147259	−	0.0255060i
$283$	−10.4044	−	18.0210i	−0.618480	−	1.07124i	−0.989763	−	0.142719i	$-0.954415\pi$
$283$	−10.4044	−	18.0210i	−0.618480	−	1.07124i	0.371283	−	0.928520i	$-0.378918\pi$
$284$	−24.8808	−	43.0949i	−1.47641	−	2.55721i
$285$	−12.1821	+	21.1000i	−0.721606	+	1.24986i
$286$	−12.5894			−0.744425
$287$	2.60950	+	0.436464i	0.154034	+	0.0257637i
$288$	−0.0224689			−0.00132399
$289$	8.34607	−	14.4558i	0.490945	−	0.850343i
$290$	−1.31378	−	2.27554i	−0.0771480	−	0.133624i
$291$	−2.57297	−	4.45651i	−0.150830	−	0.261245i
$292$	−27.0907	+	46.9224i	−1.58536	+	2.74593i
$293$	15.7241			0.918611			0.459306	−	0.888278i	$-0.348098\pi$
$293$	15.7241			0.918611			0.459306	+	0.888278i	$0.348098\pi$
$294$	16.2101	+	5.57865i	0.945390	+	0.325353i
$295$	−26.4569			−1.54038
$296$	13.3733	−	23.1633i	0.777309	−	1.34634i
$297$	−0.695352	−	1.20438i	−0.0403484	−	0.0698855i
$298$	19.8907	+	34.4517i	1.15224	+	1.99573i
$299$	−4.44171	+	7.69327i	−0.256871	+	0.444913i
$300$	44.5607			2.57271
$301$	8.37771	+	1.40125i	0.482883	+	0.0807669i
$302$	33.3361			1.91828
$303$	−1.64611	+	2.85115i	−0.0945668	+	0.163795i
$304$	−12.0850	−	20.9318i	−0.693120	−	1.20052i
$305$	18.6968	+	32.3839i	1.07058	+	1.85429i
$306$	0.679414	−	1.17678i	0.0388395	−	0.0672720i
$307$	11.4617			0.654153			0.327076	−	0.944998i	$-0.393937\pi$
$307$	11.4617			0.654153			0.327076	+	0.944998i	$0.393937\pi$
$308$	9.35540	−	11.3509i	0.533073	−	0.646776i
$309$	15.0405			0.855622
$310$	6.93688	−	12.0150i	0.393988	−	0.682408i
$311$	−0.269725	−	0.467177i	−0.0152947	−	0.0264912i	0.858277	−	0.513187i	$-0.171535\pi$
$311$	−0.269725	−	0.467177i	−0.0152947	−	0.0264912i	−0.873571	+	0.486696i	$0.838202\pi$
$312$	9.04213	+	15.6614i	0.511910	+	0.886653i
$313$	1.65272	−	2.86260i	0.0934174	−	0.161804i	−0.815530	−	0.578715i	$-0.803554\pi$
$313$	1.65272	−	2.86260i	0.0934174	−	0.161804i	0.908947	+	0.416912i	$0.136888\pi$
$314$	57.3916			3.23880
$315$	3.72399	+	9.95781i	0.209823	+	0.561059i
$316$	−61.9285			−3.48375
$317$	−15.6759	+	27.1515i	−0.880448	+	1.52498i	−0.0296041	+	0.999562i	$0.509425\pi$
$317$	−15.6759	+	27.1515i	−0.880448	+	1.52498i	−0.850844	+	0.525419i	$0.823909\pi$
$318$	7.86310	+	13.6193i	0.440941	+	0.763732i
$319$	−0.185663	−	0.321578i	−0.0103951	−	0.0180049i
$320$	16.1284	−	27.9352i	0.901603	−	1.56162i
$321$	16.8244			0.939048
$322$	−5.45462	−	14.5855i	−0.303974	−	0.812815i
$323$	−3.36422			−0.187190
$324$	−1.99885	+	3.46211i	−0.111047	+	0.192340i
$325$	20.6010	+	35.6820i	1.14274	+	1.97928i
$326$	12.1214	+	20.9949i	0.671343	+	1.16280i
$327$	−3.02637	+	5.24182i	−0.167359	+	0.289874i
$328$	−4.89242			−0.270139
$329$	−0.339830	+	0.412314i	−0.0187354	+	0.0227316i
$330$	13.6857			0.753373
$331$	8.19991	−	14.2027i	0.450708	−	0.780649i	−0.547722	−	0.836660i	$-0.684505\pi$
$331$	8.19991	−	14.2027i	0.450708	−	0.780649i	0.998430	+	0.0560115i	$0.0178383\pi$
$332$	−9.87077	−	17.0967i	−0.541729	−	0.938302i
$333$	2.73348	+	4.73452i	0.149794	+	0.259450i
$334$	−7.59770	+	13.1596i	−0.415728	+	0.720061i
$335$	−54.6134			−2.98385
$336$	−10.4021	−	1.73985i	−0.567480	−	0.0949166i
$337$	7.79793			0.424780			0.212390	−	0.977185i	$-0.431875\pi$
$337$	7.79793			0.424780			0.212390	+	0.977185i	$0.431875\pi$
$338$	−0.812128	+	1.40665i	−0.0441739	+	0.0765115i
$339$	9.84012	+	17.0436i	0.534442	+	0.925681i
$340$	4.45649	+	7.71887i	0.241687	+	0.418614i
$341$	0.980316	−	1.69796i	0.0530871	−	0.0919495i
$342$	14.8493			0.802956
$343$	−16.2781	−	8.83317i	−0.878933	−	0.476946i
$344$	−15.7069			−0.846862
$345$	4.82852	−	8.36324i	0.259959	−	0.450262i
$346$	26.1443	+	45.2833i	1.40553	+	2.43444i
$347$	13.1424	+	22.7633i	0.705520	+	1.22200i	0.966504	+	0.256653i	$0.0826197\pi$
$347$	13.1424	+	22.7633i	0.705520	+	1.22200i	−0.260984	+	0.965343i	$0.584047\pi$
$348$	−0.533706	+	0.924405i	−0.0286096	+	0.0495533i
$349$	−10.5647			−0.565516			−0.282758	−	0.959191i	$-0.591249\pi$
$349$	−10.5647			−0.565516			−0.282758	+	0.959191i	$0.591249\pi$
$350$	−71.2347	−	11.9147i	−3.80765	−	0.636867i
$351$	−3.69638			−0.197298
$352$	0.0156238	−	0.0270612i	0.000832750	−	0.00144237i
$353$	16.1630	+	27.9951i	0.860269	+	1.49003i	0.871669	+	0.490094i	$0.163038\pi$
$353$	16.1630	+	27.9951i	0.860269	+	1.49003i	−0.0114007	+	0.999935i	$0.503629\pi$
$354$	8.06234	+	13.9644i	0.428509	+	0.742199i
$355$	−25.0089	+	43.3167i	−1.32733	+	2.29901i
$356$	38.7036			2.05129
$357$	−0.933660	+	1.13281i	−0.0494145	+	0.0599545i
$358$	−25.7352			−1.36015
$359$	−4.61266	+	7.98936i	−0.243447	+	0.421662i	−0.961694	−	0.274126i	$-0.911611\pi$
$359$	−4.61266	+	7.98936i	−0.243447	+	0.421662i	0.718247	+	0.695788i	$0.244945\pi$
$360$	−9.82956	−	17.0253i	−0.518063	−	0.897312i
$361$	−8.88207	−	15.3842i	−0.467477	−	0.809694i
$362$	−20.2056	+	34.9971i	−1.06198	+	1.83941i
$363$	−9.06594			−0.475839
$364$	−13.6948	−	36.6194i	−0.717802	−	1.91938i
$365$	54.4602			2.85058
$366$	11.3952	−	19.7370i	0.595635	−	1.03167i
$367$	−13.4863	−	23.3590i	−0.703982	−	1.21933i	−0.967058	−	0.254557i	$-0.918070\pi$
$367$	−13.4863	−	23.3590i	−0.703982	−	1.21933i	0.263076	−	0.964775i	$-0.415263\pi$
$368$	4.79001	+	8.29655i	0.249697	+	0.432487i
$369$	0.500000	−	0.866025i	0.0260290	−	0.0450835i
$370$	−53.7995			−2.79690
$371$	−5.95113	−	15.9131i	−0.308967	−	0.826167i
$372$	−5.63602			−0.292214
$373$	−12.5784	+	21.7864i	−0.651284	+	1.12806i	0.331527	+	0.943446i	$0.392436\pi$
$373$	−12.5784	+	21.7864i	−0.651284	+	1.12806i	−0.982811	+	0.184612i	$0.940897\pi$
$374$	0.944863	+	1.63655i	0.0488577	+	0.0846240i
$375$	−12.3493	−	21.3897i	−0.637717	−	1.10456i
$376$	0.494013	−	0.855655i	0.0254768	−	0.0441270i
$377$	−0.986956			−0.0508308
$378$	4.12107	−	5.00007i	0.211965	−	0.257176i
$379$	26.9410			1.38387			0.691934	−	0.721961i	$-0.256759\pi$
$379$	26.9410			1.38387			0.691934	+	0.721961i	$0.256759\pi$
$380$	−48.7005	+	84.3517i	−2.49828	+	4.32715i
$381$	7.37119	+	12.7673i	0.377638	+	0.654088i
$382$	3.77129	+	6.53207i	0.192956	+	0.334210i
$383$	8.04640	−	13.9368i	0.411152	−	0.712136i	−0.583864	−	0.811851i	$-0.698460\pi$
$383$	8.04640	−	13.9368i	0.411152	−	0.712136i	0.995016	+	0.0997155i	$0.0317933\pi$
$384$	−19.6146			−1.00095
$385$	−14.5825	−	2.43907i	−0.743194	−	0.124306i
$386$	37.6092			1.91426
$387$	1.60523	−	2.78034i	0.0815985	−	0.141333i
$388$	−10.2860	−	17.8158i	−0.522191	−	0.904461i
$389$	−2.88547	−	4.99778i	−0.146299	−	0.253397i	0.783558	−	0.621319i	$-0.213403\pi$
$389$	−2.88547	−	4.99778i	−0.146299	−	0.253397i	−0.929857	+	0.367922i	$0.880069\pi$
$390$	18.1878	−	31.5021i	0.920973	−	1.59517i
$391$	1.33345			0.0674353
$392$	32.3829	+	11.1445i	1.63558	+	0.562882i
$393$	−6.77980			−0.341996
$394$	21.3777	−	37.0273i	1.07699	−	1.86541i
$395$	31.1236	+	53.9077i	1.56600	+	2.71239i
$396$	−2.77981	−	4.81477i	−0.139691	−	0.241951i
$397$	−12.8223	+	22.2090i	−0.643535	+	1.11464i	0.341103	+	0.940026i	$0.389200\pi$
$397$	−12.8223	+	22.2090i	−0.643535	+	1.11464i	−0.984638	+	0.174610i	$0.944134\pi$
$398$	−37.0433			−1.85681
$399$	−15.8223	−	2.64643i	−0.792106	−	0.132487i
$400$	44.4329			2.22164
$401$	−1.98084	+	3.43092i	−0.0989186	+	0.171332i	−0.911237	−	0.411882i	$-0.864872\pi$
$401$	−1.98084	+	3.43092i	−0.0989186	+	0.171332i	0.812319	+	0.583214i	$0.198205\pi$
$402$	16.6426	+	28.8259i	0.830058	+	1.43770i
$403$	−2.60560	−	4.51304i	−0.129794	−	0.224810i
$404$	−6.58068	+	11.3981i	−0.327401	+	0.567075i
$405$	4.01828			0.199670
$406$	1.10035	−	1.33505i	0.0546094	−	0.0662574i
$407$	−7.60292			−0.376863
$408$	1.35727	−	2.35086i	0.0671948	−	0.116385i
$409$	−11.4339	−	19.8041i	−0.565370	−	0.979250i	−0.997015	−	0.0772065i	$-0.975400\pi$
$409$	−11.4339	−	19.8041i	−0.565370	−	0.979250i	0.431645	−	0.902044i	$-0.357933\pi$
$410$	4.92043	+	8.52243i	0.243003	+	0.420893i
$411$	−8.09545	+	14.0217i	−0.399319	+	0.691641i
$412$	60.1273			2.96226
$413$	−6.10192	−	16.3163i	−0.300256	−	0.802874i
$414$	−5.88568			−0.289265
$415$	−9.92157	+	17.1847i	−0.487031	+	0.843562i
$416$	−0.0415268	−	0.0719265i	−0.00203602	−	0.00352648i
$417$	−2.87648	−	4.98222i	−0.140862	−	0.243980i
$418$	−10.3255	+	17.8842i	−0.505035	+	0.874745i
$419$	−16.0852			−0.785811			−0.392906	−	0.919579i	$-0.628530\pi$
$419$	−16.0852			−0.785811			−0.392906	+	0.919579i	$0.628530\pi$
$420$	14.8874	+	39.8084i	0.726431	+	1.94245i
$421$	−2.27709			−0.110979			−0.0554894	−	0.998459i	$-0.517672\pi$
$421$	−2.27709			−0.110979			−0.0554894	+	0.998459i	$0.517672\pi$
$422$	−20.4698	+	35.4548i	−0.996455	+	1.72591i
$423$	0.100975	+	0.174894i	0.00490958	+	0.00850363i
$424$	15.7082	+	27.2073i	0.762856	+	1.32130i
$425$	3.09231	−	5.35604i	0.149999	−	0.259806i
$426$	30.4843			1.47697
$427$	−15.6594	+	18.9995i	−0.757811	+	0.919450i
$428$	67.2591			3.25109
$429$	2.57028	−	4.45186i	0.124094	−	0.214938i
$430$	15.7969	+	27.3610i	0.761792	+	1.31946i
$431$	−3.40514	−	5.89788i	−0.164020	−	0.284091i	0.772287	−	0.635274i	$-0.219113\pi$
$431$	−3.40514	−	5.89788i	−0.164020	−	0.284091i	−0.936307	+	0.351183i	$0.885780\pi$
$432$	−1.99312	+	3.45218i	−0.0958939	+	0.166093i
$433$	−2.89923			−0.139328			−0.0696641	−	0.997571i	$-0.522193\pi$
$433$	−2.89923			−0.139328			−0.0696641	+	0.997571i	$0.522193\pi$
$434$	9.00973	+	1.50696i	0.432481	+	0.0723366i
$435$	1.07291			0.0514419
$436$	−12.0985	+	20.9553i	−0.579414	+	1.00358i
$437$	7.28595	+	12.6196i	0.348534	+	0.603679i
$438$	−16.5959	−	28.7450i	−0.792984	−	1.37349i
$439$	11.3238	−	19.6135i	0.540458	−	0.936100i	−0.458420	−	0.888736i	$-0.651584\pi$
$439$	11.3238	−	19.6135i	0.540458	−	0.936100i	0.998878	−	0.0473644i	$-0.0150822\pi$
$440$	27.3400			1.30338
$441$	−5.28223	+	4.59327i	−0.251535	+	0.218727i
$442$	5.02274			0.238908
$443$	3.46320	−	5.99844i	0.164542	−	0.284995i	−0.771951	−	0.635682i	$-0.780719\pi$
$443$	3.46320	−	5.99844i	0.164542	−	0.284995i	0.936492	+	0.350688i	$0.114052\pi$
$444$	10.9276	+	18.9272i	0.518603	+	0.898247i
$445$	−19.4514	−	33.6908i	−0.922084	−	1.59710i
$446$	18.9712	−	32.8590i	0.898311	−	1.55592i
$447$	−16.2438			−0.768305
$448$	20.9478	+	3.50372i	0.989689	+	0.165535i
$449$	22.3941			1.05684			0.528421	−	0.848982i	$-0.322784\pi$
$449$	22.3941			1.05684			0.528421	+	0.848982i	$0.322784\pi$
$450$	−13.6491	+	23.6409i	−0.643425	+	1.11444i
$451$	0.695352	+	1.20438i	0.0327428	+	0.0567122i
$452$	39.3379	+	68.1352i	1.85030	+	3.20481i
$453$	−6.80601	+	11.7884i	−0.319774	+	0.553865i
$454$	−0.936567			−0.0439553
$455$	−24.9939	+	30.3250i	−1.17173	+	1.42166i
$456$	29.6644			1.38916
$457$	12.6973	−	21.9923i	0.593952	−	1.02876i	−0.399741	−	0.916628i	$-0.630900\pi$
$457$	12.6973	−	21.9923i	0.593952	−	1.02876i	0.993694	−	0.112128i	$-0.0357666\pi$
$458$	−24.7264	−	42.8274i	−1.15539	−	2.00119i
$459$	0.277423	+	0.480510i	0.0129490	+	0.0224283i
$460$	19.3030	−	33.4338i	0.900007	−	1.55886i
$461$	21.2080			0.987756			0.493878	−	0.869531i	$-0.335579\pi$
$461$	21.2080			0.987756			0.493878	+	0.869531i	$0.335579\pi$
$462$	3.15642	+	8.44016i	0.146850	+	0.392672i
$463$	25.7346			1.19599			0.597994	−	0.801501i	$-0.295965\pi$
$463$	25.7346			1.19599			0.597994	+	0.801501i	$0.295965\pi$
$464$	−0.532174	+	0.921753i	−0.0247056	+	0.0427913i
$465$	2.83251	+	4.90605i	0.131355	+	0.227513i
$466$	10.6855	+	18.5078i	0.494997	+	0.857359i
$467$	−9.47057	+	16.4035i	−0.438246	+	0.759064i	−0.997554	−	0.0698957i	$-0.977733\pi$
$467$	−9.47057	+	16.4035i	−0.438246	+	0.759064i	0.559309	+	0.828960i	$0.311067\pi$
$468$	−14.7770			−0.683069
$469$	−12.5958	−	33.6808i	−0.581622	−	1.55524i
$470$	−1.98736			−0.0916702
$471$	−11.7173	+	20.2949i	−0.539903	+	0.935139i
$472$	16.1062	+	27.8967i	0.741347	+	1.28405i
$473$	2.23240	+	3.86663i	0.102646	+	0.177788i
$474$	18.9689	−	32.8551i	0.871271	−	1.50909i
$475$	67.5855			3.10104
$476$	−3.73250	+	4.52863i	−0.171079	+	0.207569i
$477$	−6.42142			−0.294017
$478$	−15.2313	+	26.3813i	−0.696662	+	1.20665i
$479$	5.17960	+	8.97133i	0.236662	+	0.409910i	0.959754	−	0.280841i	$-0.0906133\pi$
$479$	5.17960	+	8.97133i	0.236662	+	0.409910i	−0.723092	+	0.690751i	$0.757280\pi$
$480$	0.0451431	+	0.0781902i	0.00206049	+	0.00356888i
$481$	−10.1040	+	17.5006i	−0.460702	+	0.797959i
$482$	−62.6325			−2.85283
$483$	6.27135	+	1.04894i	0.285356	+	0.0477286i
$484$	−36.2430			−1.64741
$485$	−10.3389	+	17.9075i	−0.469466	+	0.813138i
$486$	−1.22451	−	2.12091i	−0.0555449	−	0.0962066i
$487$	−10.1295	−	17.5448i	−0.459011	−	0.795030i	0.539898	−	0.841730i	$-0.318463\pi$
$487$	−10.1295	−	17.5448i	−0.459011	−	0.795030i	−0.998909	+	0.0467006i	$0.985129\pi$
$488$	22.7642	−	39.4287i	1.03049	−	1.78485i
$489$	−9.89899			−0.447648
$490$	−13.1550	−	67.6182i	−0.594281	−	3.05468i
$491$	5.99278			0.270450			0.135225	−	0.990815i	$-0.456824\pi$
$491$	5.99278			0.270450			0.135225	+	0.990815i	$0.456824\pi$
$492$	1.99885	−	3.46211i	0.0901152	−	0.156084i
$493$	0.0740735	+	0.128299i	0.00333610	+	0.00577830i
$494$	27.4442	+	47.5348i	1.23478	+	2.13869i
$495$	−2.79412	+	4.83955i	−0.125586	+	0.217522i
$496$	−5.61985			−0.252339
$497$	−32.4819	−	5.43292i	−1.45701	−	0.243700i
$498$	12.0938			0.541936
$499$	6.18755	−	10.7171i	0.276993	−	0.479765i	−0.693643	−	0.720319i	$-0.743996\pi$
$499$	6.18755	−	10.7171i	0.276993	−	0.479765i	0.970636	+	0.240553i	$0.0773289\pi$
$500$	−49.3690	−	85.5096i	−2.20785	−	3.82411i
$501$	−3.10234	−	5.37341i	−0.138602	−	0.240066i
$502$	35.9600	−	62.2845i	1.60497	−	2.77989i
$503$	21.5226			0.959647			0.479824	−	0.877365i	$-0.340701\pi$
$503$	21.5226			0.959647			0.479824	+	0.877365i	$0.340701\pi$
$504$	8.23267	−	9.98867i	0.366712	−	0.444931i
$505$	13.2291			0.588687
$506$	4.09261	−	7.08862i	0.181939	−	0.315127i
$507$	−0.331613	−	0.574371i	−0.0147275	−	0.0255087i
$508$	29.4679	+	51.0398i	1.30742	+	2.26453i
$509$	6.05601	−	10.4893i	0.268428	−	0.464931i	−0.700028	−	0.714115i	$-0.746829\pi$
$509$	6.05601	−	10.4893i	0.268428	−	0.464931i	0.968456	+	0.249184i	$0.0801625\pi$
$510$	−5.46015			−0.241780
$511$	12.5605	+	33.5863i	0.555644	+	1.48577i
$512$	−39.0943			−1.72774
$513$	−3.03167	+	5.25101i	−0.133852	+	0.231838i
$514$	8.04337	+	13.9315i	0.354778	+	0.614493i
$515$	−30.2184	−	52.3398i	−1.33158	−	2.30637i
$516$	6.41725	−	11.1150i	0.282503	−	0.489310i
$517$	−0.280853			−0.0123519
$518$	−12.4081	−	33.1789i	−0.545182	−	1.45780i
$519$	−21.3508			−0.937197
$520$	36.3338	−	62.9320i	1.59334	−	2.75975i
$521$	15.2850	+	26.4744i	0.669649	+	1.15987i	0.978002	+	0.208594i	$0.0668888\pi$
$521$	15.2850	+	26.4744i	0.669649	+	1.15987i	−0.308353	+	0.951272i	$0.599778\pi$
$522$	−0.326952	−	0.566297i	−0.0143103	−	0.0247861i
$523$	3.31964	−	5.74978i	0.145158	−	0.251420i	−0.784274	−	0.620414i	$-0.786964\pi$
$523$	3.31964	−	5.74978i	0.145158	−	0.251420i	0.929432	+	0.368994i	$0.120298\pi$
$524$	−27.1037			−1.18403
$525$	18.7568	−	22.7575i	0.818613	−	0.993221i
$526$	32.1916			1.40362
$527$	−0.391114	+	0.677429i	−0.0170372	+	0.0295093i
$528$	−2.77184	−	4.80096i	−0.120629	−	0.208935i
$529$	8.61213	+	14.9166i	0.374440	+	0.648550i
$530$	31.5961	−	54.7261i	1.37245	−	2.37715i
$531$	−6.58413			−0.285727
$532$	−63.2529	−	10.5797i	−2.74236	−	0.458687i
$533$	3.69638			0.160108
$534$	−11.8550	+	20.5335i	−0.513018	+	0.888573i
$535$	−33.8026	−	58.5479i	−1.46142	−	2.53125i
$536$	33.2470	+	57.5856i	1.43605	+	2.48732i
$537$	5.25417	−	9.10049i	0.226734	−	0.392715i
$538$	28.5673			1.23162
$539$	−1.85905	−	9.55577i	−0.0800751	−	0.411596i
$540$	16.0639			0.691280
$541$	12.6677	−	21.9411i	0.544627	−	0.943322i	−0.454003	−	0.891000i	$-0.650005\pi$
$541$	12.6677	−	21.9411i	0.544627	−	0.943322i	0.998630	−	0.0523217i	$-0.0166621\pi$
$542$	4.12501	+	7.14473i	0.177184	+	0.306892i
$543$	−8.25048	−	14.2902i	−0.354062	−	0.613253i
$544$	−0.00623338	+	0.0107965i	−0.000267254	+	0.000462897i
$545$	24.3216			1.04182
$546$	23.6225	+	3.95110i	1.01095	+	0.169091i
$547$	5.33483			0.228101			0.114050	−	0.993475i	$-0.463617\pi$
$547$	5.33483			0.228101			0.114050	+	0.993475i	$0.463617\pi$
$548$	−32.3632	+	56.0547i	−1.38249	+	2.39454i
$549$	4.65294	+	8.05914i	0.198583	+	0.343956i
$550$	−18.9818	−	32.8775i	−0.809389	−	1.40190i
$551$	−0.809475	+	1.40205i	−0.0344848	+	0.0597294i
$552$	−11.7578			−0.500447
$553$	−26.0674	+	31.6274i	−1.10850	+	1.34493i
$554$	34.6017			1.47009
$555$	10.9839	−	19.0246i	0.466240	−	0.807551i
$556$	−11.4993	−	19.9174i	−0.487681	−	0.844688i
$557$	−0.637168	−	1.10361i	−0.0269977	−	0.0467614i	0.852211	−	0.523198i	$-0.175261\pi$
$557$	−0.637168	−	1.10361i	−0.0269977	−	0.0467614i	−0.879209	+	0.476437i	$0.841928\pi$
$558$	1.72633	−	2.99009i	0.0730814	−	0.126581i
$559$	11.8671			0.501925
$560$	14.8447	+	39.6942i	0.627303	+	1.67738i
$561$	−0.771625			−0.0325780
$562$	17.7597	−	30.7607i	0.749148	−	1.29756i
$563$	−7.15245	−	12.3884i	−0.301440	−	0.522109i	0.675023	−	0.737797i	$-0.264134\pi$
$563$	−7.15245	−	12.3884i	−0.301440	−	0.522109i	−0.976462	+	0.215688i	$0.930801\pi$
$564$	0.403669	+	0.699174i	0.0169975	+	0.0294406i
$565$	39.5404	−	68.4859i	1.66348	−	2.88122i
$566$	50.9614			2.14207
$567$	0.926762	+	2.47813i	0.0389203	+	0.104072i
$568$	60.8987			2.55525
$569$	−10.7218	+	18.5707i	−0.449482	+	0.778526i	−0.998352	−	0.0573816i	$-0.981725\pi$
$569$	−10.7218	+	18.5707i	−0.449482	+	0.778526i	0.548870	+	0.835908i	$0.315058\pi$
$570$	−29.8342	−	51.6744i	−1.24962	−	2.16440i
$571$	12.4041	+	21.4846i	0.519097	+	0.899103i	0.999754	+	0.0221939i	$0.00706512\pi$
$571$	12.4041	+	21.4846i	0.519097	+	0.899103i	−0.480656	+	0.876909i	$0.659602\pi$
$572$	10.2752	−	17.7972i	0.429629	−	0.744140i
$573$	−3.07983			−0.128662
$574$	−4.12107	+	5.00007i	−0.172010	+	0.208699i
$575$	−26.7883			−1.11715
$576$	4.01375	−	6.95202i	0.167240	−	0.289667i
$577$	8.56547	+	14.8358i	0.356585	+	0.617624i	0.987388	−	0.158319i	$-0.0506076\pi$
$577$	8.56547	+	14.8358i	0.356585	+	0.617624i	−0.630803	+	0.775943i	$0.717274\pi$
$578$	20.4397	+	35.4026i	0.850180	+	1.47255i
$579$	−7.67841	+	13.2994i	−0.319104	+	0.552704i
$580$	4.28916			0.178098
$581$	−12.8863	−	2.15536i	−0.534613	−	0.0894193i
$582$	12.6025			0.522391
$583$	4.46515	−	7.73386i	0.184928	−	0.320304i
$584$	−33.1538	−	57.4240i	−1.37191	−	2.37622i
$585$	7.42655	+	12.8632i	0.307050	+	0.531826i
$586$	−19.2543	+	33.3495i	−0.795389	+	1.37765i
$587$	−5.46590			−0.225602			−0.112801	−	0.993618i	$-0.535982\pi$
$587$	−5.46590			−0.225602			−0.112801	+	0.993618i	$0.535982\pi$
$588$	−21.1168	+	18.3625i	−0.870841	+	0.757258i
$589$	−8.54818			−0.352222
$590$	32.3967	−	56.1128i	1.33375	−	2.31013i
$591$	8.72908	+	15.1192i	0.359066	+	0.621921i
$592$	10.8963	+	18.8729i	0.447835	+	0.775673i
$593$	4.23784	−	7.34015i	0.174027	−	0.301424i	−0.765797	−	0.643082i	$-0.777655\pi$
$593$	4.23784	−	7.34015i	0.174027	−	0.301424i	0.939824	+	0.341659i	$0.110989\pi$
$594$	3.40586			0.139744
$595$	5.81795	+	0.973108i	0.238513	+	0.0398935i
$596$	−64.9379			−2.65996
$597$	7.56287	−	13.0993i	0.309528	−	0.536118i
$598$	−10.8778	−	18.8410i	−0.444828	−	0.770465i
$599$	−13.0564	−	22.6143i	−0.533470	−	0.923997i	−0.999236	−	0.0390888i	$-0.987554\pi$
$599$	−13.0564	−	22.6143i	−0.533470	−	0.923997i	0.465766	−	0.884908i	$-0.345779\pi$
$600$	−27.2669	+	47.2276i	−1.11317	+	1.92806i
$601$	−21.7494			−0.887176			−0.443588	−	0.896231i	$-0.646295\pi$
$601$	−21.7494			−0.887176			−0.443588	+	0.896231i	$0.646295\pi$
$602$	−13.2305	+	16.0526i	−0.539236	+	0.654254i
$603$	−13.5912			−0.553478
$604$	−27.2084	+	47.1264i	−1.10709	+	1.91754i
$605$	18.2148	+	31.5489i	0.740535	+	1.28264i
$606$	−4.03137	−	6.98254i	−0.163763	−	0.283646i
$607$	0.221034	−	0.382842i	0.00897150	−	0.0155391i	−0.861505	−	0.507749i	$-0.830478\pi$
$607$	0.221034	−	0.382842i	0.00897150	−	0.0155391i	0.870476	+	0.492210i	$0.163811\pi$
$608$	−0.136237			−0.00552512
$609$	0.247451	+	0.661675i	0.0100272	+	0.0268124i
$610$	−91.5779			−3.70788
$611$	−0.373242	+	0.646475i	−0.0150998	+	0.0261536i
$612$	1.10905	+	1.92094i	0.0448308	+	0.0776493i
$613$	4.75495	+	8.23581i	0.192051	+	0.332641i	0.945930	−	0.324372i	$-0.105153\pi$
$613$	4.75495	+	8.23581i	0.192051	+	0.332641i	−0.753879	+	0.657013i	$0.771820\pi$
$614$	−14.0350	+	24.3093i	−0.566405	+	0.981042i
$615$	−4.01828			−0.162033
$616$	6.30560	+	16.8609i	0.254060	+	0.679347i
$617$	−3.83993			−0.154590			−0.0772949	−	0.997008i	$-0.524628\pi$
$617$	−3.83993			−0.154590			−0.0772949	+	0.997008i	$0.524628\pi$
$618$	−18.4172	+	31.8995i	−0.740848	+	1.28319i
$619$	14.8388	+	25.7016i	0.596422	+	1.03303i	0.993344	+	0.115181i	$0.0367449\pi$
$619$	14.8388	+	25.7016i	0.596422	+	1.03303i	−0.396922	+	0.917852i	$0.629922\pi$
$620$	11.3235	+	19.6130i	0.454765	+	0.787675i
$621$	1.20164	−	2.08130i	0.0482201	−	0.0835196i
$622$	1.32112			0.0529722
$623$	16.2914	−	19.7662i	0.652700	−	0.791918i
$624$	−14.7346			−0.589858
$625$	−21.7566	+	37.6836i	−0.870265	+	1.50734i
$626$	4.04755	+	7.01057i	0.161773	+	0.280199i
$627$	−4.21616	−	7.30260i	−0.168377	−	0.291638i
$628$	−46.8421	+	81.1329i	−1.86920	+	3.23756i
$629$	3.03332			0.120946
$630$	−25.6797	−	4.29518i	−1.02310	−	0.171124i
$631$	3.78576			0.150709			0.0753545	−	0.997157i	$-0.475991\pi$
$631$	3.78576			0.150709			0.0753545	+	0.997157i	$0.475991\pi$
$632$	37.8943	−	65.6348i	1.50735	−	2.61081i
$633$	−8.35837	−	14.4771i	−0.332215	−	0.575414i
$634$	−38.3907	−	66.4946i	−1.52469	−	2.64084i
$635$	29.6195	−	51.3025i	1.17541	−	2.03588i
$636$	−25.6710			−1.01792
$637$	−24.4663	−	8.42002i	−0.969391	−	0.333613i
$638$	0.909386			0.0360029
$639$	−6.22378	+	10.7799i	−0.246209	+	0.426446i
$640$	39.4084	+	68.2574i	1.55775	+	2.69811i
$641$	−0.674980	−	1.16910i	−0.0266601	−	0.0461767i	0.852388	−	0.522911i	$-0.175154\pi$
$641$	−0.674980	−	1.16910i	−0.0266601	−	0.0461767i	−0.879048	+	0.476734i	$0.841821\pi$
$642$	−20.6017	+	35.6832i	−0.813084	+	1.40830i
$643$	−32.4546			−1.27988			−0.639942	−	0.768423i	$-0.721042\pi$
$643$	−32.4546			−1.27988			−0.639942	+	0.768423i	$0.721042\pi$
$644$	25.0710	+	4.19337i	0.987937	+	0.165242i
$645$	−12.9005			−0.507959
$646$	4.11952	−	7.13522i	0.162080	−	0.280731i
$647$	−23.7689	−	41.1690i	−0.934453	−	1.61852i	−0.775606	−	0.631217i	$-0.782556\pi$
$647$	−23.7689	−	41.1690i	−0.934453	−	1.61852i	−0.158847	−	0.987303i	$-0.550778\pi$
$648$	−2.44621	−	4.23696i	−0.0960962	−	0.166444i
$649$	4.57829	−	7.92983i	0.179714	−	0.311273i
$650$	−100.905			−3.95780
$651$	−2.37235	+	2.87836i	−0.0929797	+	0.112812i
$652$	−39.5732			−1.54981
$653$	−22.2290	+	38.5018i	−0.869890	+	1.50669i	−0.00778094	+	0.999970i	$0.502477\pi$
$653$	−22.2290	+	38.5018i	−0.869890	+	1.50669i	−0.862109	+	0.506723i	$0.830857\pi$
$654$	−7.41164	−	12.8373i	−0.289818	−	0.501980i
$655$	13.6216	+	23.5933i	0.532239	+	0.921865i
$656$	1.99312	−	3.45218i	0.0778182	−	0.134785i
$657$	13.5531			0.528757
$658$	−0.458358	−	1.22563i	−0.0178687	−	0.0477801i
$659$	−13.7462			−0.535474			−0.267737	−	0.963492i	$-0.586276\pi$
$659$	−13.7462			−0.535474			−0.267737	+	0.963492i	$0.586276\pi$
$660$	−11.1701	+	19.3471i	−0.434794	+	0.753085i
$661$	−8.29378	−	14.3652i	−0.322591	−	0.558743i	0.658431	−	0.752641i	$-0.271220\pi$
$661$	−8.29378	−	14.3652i	−0.322591	−	0.558743i	−0.981022	+	0.193898i	$0.937887\pi$
$662$	20.0817	+	34.7826i	0.780499	+	1.35186i
$663$	−1.02546	+	1.77615i	−0.0398255	+	0.0689799i
$664$	24.1598			0.937584
$665$	22.5798	+	60.3776i	0.875608	+	2.34134i
$666$	−13.3887			−0.518801
$667$	0.320845	−	0.555719i	0.0124232	−	0.0215175i
$668$	−12.4022	−	21.4813i	−0.479857	−	0.831137i
$669$	7.74643	+	13.4172i	0.299494	+	0.518739i
$670$	66.8747	−	115.830i	2.58360	−	4.47492i
$671$	−12.9417			−0.499610
$672$	−0.0378093	+	0.0458739i	−0.00145852	+	0.00176962i
$673$	48.9067			1.88522			0.942608	−	0.333902i	$-0.108365\pi$
$673$	48.9067			1.88522			0.942608	+	0.333902i	$0.108365\pi$
$674$	−9.54864	+	16.5387i	−0.367800	+	0.637048i
$675$	−5.57329	−	9.65322i	−0.214516	−	0.371553i
$676$	−1.32569	−	2.29617i	−0.0509881	−	0.0883141i
$677$	7.63705	−	13.2278i	0.293516	−	0.508384i	−0.681123	−	0.732169i	$-0.738508\pi$
$677$	7.63705	−	13.2278i	0.293516	−	0.508384i	0.974639	+	0.223785i	$0.0718414\pi$
$678$	−48.1973			−1.85101
$679$	−13.4283	−	2.24602i	−0.515332	−	0.0861943i
$680$	−10.9078			−0.418294
$681$	0.191213	−	0.331190i	0.00732728	−	0.0126912i
$682$	2.40081	+	4.15833i	0.0919319	+	0.159231i
$683$	20.6411	+	35.7515i	0.789811	+	1.36799i	0.926082	+	0.377321i	$0.123155\pi$
$683$	20.6411	+	35.7515i	0.789811	+	1.36799i	−0.136272	+	0.990672i	$0.543512\pi$
$684$	−12.1197	+	20.9920i	−0.463409	+	0.802649i
$685$	65.0596			2.48580
$686$	38.6670	−	23.7081i	1.47631	−	0.905178i
$687$	20.1929			0.770407
$688$	6.39883	−	11.0831i	0.243953	−	0.422539i
$689$	−11.8680	−	20.5560i	−0.452135	−	0.783121i
$690$	11.8251	+	20.4818i	0.450176	+	0.779727i
$691$	−4.12387	+	7.14275i	−0.156879	+	0.271723i	−0.933742	−	0.357947i	$-0.883477\pi$
$691$	−4.12387	+	7.14275i	−0.156879	+	0.271723i	0.776862	+	0.629670i	$0.216810\pi$
$692$	−85.3543			−3.24468
$693$	−3.62904	−	0.606993i	−0.137856	−	0.0230577i
$694$	−64.3719			−2.44352
$695$	−11.5585	+	20.0199i	−0.438440	+	0.759400i
$696$	−0.653153	−	1.13129i	−0.0247577	−	0.0428816i
$697$	−0.277423	−	0.480510i	−0.0105081	−	0.0182006i
$698$	12.9366	−	22.4068i	0.489657	−	0.848111i
$699$	−8.72635			−0.330061
$700$	74.9841	−	90.9780i	2.83413	−	3.43864i
$701$	−7.14293			−0.269785			−0.134892	−	0.990860i	$-0.543069\pi$
$701$	−7.14293			−0.269785			−0.134892	+	0.990860i	$0.543069\pi$
$702$	4.52626	−	7.83971i	0.170833	−	0.295891i
$703$	16.5740	+	28.7070i	0.625101	+	1.08271i
$704$	5.58193	+	9.66819i	0.210377	+	0.364384i
$705$	0.405746	−	0.702773i	0.0152813	−	0.0264680i
$706$	−79.1670			−2.97949
$707$	3.05111	+	8.15856i	0.114749	+	0.306834i
$708$	−26.3214			−0.989220
$709$	7.04509	−	12.2024i	0.264584	−	0.458273i	−0.702871	−	0.711318i	$-0.748099\pi$
$709$	7.04509	−	12.2024i	0.264584	−	0.458273i	0.967454	+	0.253045i	$0.0814321\pi$
$710$	−61.2473	−	106.083i	−2.29857	−	3.98124i
$711$	7.74551	+	13.4156i	0.290479	+	0.503125i
$712$	−23.6829	+	41.0199i	−0.887553	+	1.53729i
$713$	3.38817			0.126888
$714$	−1.25931	−	3.36735i	−0.0471285	−	0.126020i
$715$	−20.6562			−0.772500
$716$	21.0046	−	36.3811i	0.784980	−	1.35962i
$717$	−6.21933	−	10.7722i	−0.232265	−	0.402295i
$718$	−11.2965	−	19.5661i	−0.421581	−	0.730200i
$719$	3.88978	−	6.73730i	0.145064	−	0.251259i	−0.784333	−	0.620341i	$-0.786994\pi$
$719$	3.88978	−	6.73730i	0.145064	−	0.251259i	0.929397	+	0.369082i	$0.120328\pi$
$720$	16.0178			0.596949
$721$	25.3092	−	30.7075i	0.942563	−	1.14361i
$722$	43.5047			1.61908
$723$	12.7872	−	22.1482i	0.475563	−	0.823699i
$724$	−32.9830	−	57.1282i	−1.22580	−	2.12315i
$725$	−1.48810	−	2.57747i	−0.0552667	−	0.0957247i
$726$	11.1013	−	19.2281i	0.412010	−	0.713621i
$727$	−9.28850			−0.344492			−0.172246	−	0.985054i	$-0.555102\pi$
$727$	−9.28850			−0.344492			−0.172246	+	0.985054i	$0.555102\pi$
$728$	47.1909	+	7.89313i	1.74901	+	0.292539i
$729$	1.00000			0.0370370
$730$	−66.6871	+	115.505i	−2.46820	+	4.27505i
$731$	−0.890655	−	1.54266i	−0.0329421	−	0.0570574i
$732$	18.6011	+	32.2181i	0.687516	+	1.19081i
$733$	−5.31194	+	9.20056i	−0.196201	+	0.339830i	−0.947294	−	0.320367i	$-0.896194\pi$
$733$	−5.31194	+	9.20056i	−0.196201	+	0.339830i	0.751093	+	0.660197i	$0.229527\pi$
$734$	66.0567			2.43820
$735$	26.5970	+	9.15328i	0.981045	+	0.337624i
$736$	0.0539989			0.00199043
$737$	9.45069	−	16.3691i	0.348121	−	0.602963i
$738$	1.22451	+	2.12091i	0.0450749	+	0.0780719i
$739$	6.74268	+	11.6787i	0.248034	+	0.429607i	0.962980	−	0.269572i	$-0.0868824\pi$
$739$	6.74268	+	11.6787i	0.248034	+	0.429607i	−0.714947	+	0.699179i	$0.753549\pi$
$740$	43.9103	−	76.0549i	1.61418	−	2.79583i
$741$	−22.4124			−0.823341
$742$	41.0376	+	6.86393i	1.50654	+	0.251983i
$743$	−6.89411			−0.252920			−0.126460	−	0.991972i	$-0.540362\pi$
$743$	−6.89411			−0.252920			−0.126460	+	0.991972i	$0.540362\pi$
$744$	3.44870	−	5.97332i	0.126435	−	0.218993i
$745$	32.6360	+	56.5273i	1.19569	+	2.07100i
$746$	−30.8047	−	53.3554i	−1.12784	−	1.95348i
$747$	−2.46911	+	4.27662i	−0.0903400	+	0.156473i
$748$	−3.08473			−0.112789
$749$	28.3111	−	34.3498i	1.03447	−	1.25511i
$750$	60.4876			2.20869
$751$	−7.71924	+	13.3701i	−0.281679	+	0.487883i	−0.971798	−	0.235813i	$-0.924225\pi$
$751$	−7.71924	+	13.3701i	−0.281679	+	0.487883i	0.690119	+	0.723696i	$0.257558\pi$
$752$	0.402510	+	0.697168i	0.0146780	+	0.0254231i
$753$	14.6834	+	25.4324i	0.535093	+	0.926808i
$754$	1.20854	−	2.09325i	0.0440124	−	0.0762316i
$755$	54.6969			1.99062
$756$	3.70492	+	9.90682i	0.134747	+	0.360308i
$757$	−0.0468098			−0.00170133			−0.000850666	−	1.00000i	$-0.500271\pi$
$757$	−0.0468098			−0.00170133			−0.000850666		1.00000i	$0.500271\pi$
$758$	−32.9896	+	57.1396i	−1.19824	+	2.07540i
$759$	1.67112	+	2.89447i	0.0606579	+	0.105063i
$760$	−59.6000	−	103.230i	−2.16192	−	3.74455i
$761$	15.7120	−	27.2140i	0.569561	−	0.986509i	−0.427048	−	0.904229i	$-0.640447\pi$
$761$	15.7120	−	27.2140i	0.569561	−	0.986509i	0.996609	−	0.0822797i	$-0.0262201\pi$
$762$	−36.1044			−1.30792
$763$	5.60944	+	14.9995i	0.203075	+	0.543017i
$764$	−12.3123			−0.445442
$765$	1.11476	−	1.93082i	0.0403043	−	0.0698091i
$766$	19.7058	+	34.1315i	0.712000	+	1.23322i
$767$	−12.1687	−	21.0769i	−0.439387	−	0.761041i
$768$	15.9908	−	27.6968i	0.577017	−	0.999422i
$769$	−12.9324			−0.466353			−0.233176	−	0.972434i	$-0.574912\pi$
$769$	−12.9324			−0.466353			−0.233176	+	0.972434i	$0.574912\pi$
$770$	23.0295	−	27.9416i	0.829925	−	1.00695i
$771$	−6.56864			−0.236564
$772$	−30.6960	+	53.1670i	−1.10477	+	1.91352i
$773$	−6.24019	−	10.8083i	−0.224444	−	0.388749i	0.731708	−	0.681618i	$-0.238723\pi$
$773$	−6.24019	−	10.8083i	−0.224444	−	0.388749i	−0.956153	+	0.292869i	$0.905390\pi$
$774$	3.93125	+	6.80912i	0.141306	+	0.244749i
$775$	7.85729	−	13.6092i	0.282242	−	0.488858i
$776$	25.1761			0.903769
$777$	14.2660	+	2.38613i	0.511791	+	0.0856020i
$778$	14.1331			0.506698
$779$	3.03167	−	5.25101i	0.108621	−	0.188137i
$780$	29.6891	+	51.4231i	1.06304	+	1.84124i
$781$	−8.65543	−	14.9917i	−0.309716	−	0.536443i
$782$	−1.63282	+	2.82813i	−0.0583895	+	0.101134i
$783$	0.267006			0.00954202
$784$	−21.0562	+	18.3098i	−0.752007	+	0.653923i
$785$	94.1664			3.36094
$786$	8.30194	−	14.3794i	0.296120	−	0.512896i
$787$	23.0067	+	39.8487i	0.820099	+	1.42045i	0.905608	+	0.424116i	$0.139415\pi$
$787$	23.0067	+	39.8487i	0.820099	+	1.42045i	−0.0855084	+	0.996337i	$0.527251\pi$
$788$	34.8963	+	60.4421i	1.24313	+	2.15316i
$789$	−6.57234	+	11.3836i	−0.233981	+	0.405268i
$790$	−152.445			−5.42374
$791$	51.3556	+	8.58972i	1.82600	+	0.305415i
$792$	6.80391			0.241766
$793$	−17.1991	+	29.7896i	−0.610756	+	1.05786i
$794$	−31.4022	−	54.3902i	−1.11442	−	1.93024i
$795$	12.9015	+	22.3461i	0.457570	+	0.792535i
$796$	30.2341	−	52.3670i	1.07162	−	1.85610i
$797$	54.4612			1.92911			0.964557	−	0.263876i	$-0.0850008\pi$
$797$	54.4612			1.92911			0.964557	+	0.263876i	$0.0850008\pi$
$798$	24.9874	−	30.3172i	0.884546	−	1.07322i
$799$	0.112051			0.00396408
$800$	0.125226	−	0.216897i	0.00442739	−	0.00766847i
$801$	−4.84072	−	8.38438i	−0.171039	−	0.296248i
$802$	−4.85113	−	8.40240i	−0.171299	−	0.296699i
$803$	−9.42418	+	16.3232i	−0.332572	+	0.576032i
$804$	−54.3338			−1.91620
$805$	−8.94977	−	23.9314i	−0.315438	−	0.843470i
$806$	12.7624			0.449535
$807$	−5.83239	+	10.1020i	−0.205310	+	0.355607i
$808$	−8.05349	−	13.9491i	−0.283321	−	0.490726i
$809$	−11.5622	−	20.0264i	−0.406507	−	0.704091i	0.587989	−	0.808869i	$-0.299920\pi$
$809$	−11.5622	−	20.0264i	−0.406507	−	0.704091i	−0.994496	+	0.104778i	$0.966587\pi$
$810$	−4.92043	+	8.52243i	−0.172886	+	0.299448i
$811$	6.43373			0.225919			0.112959	−	0.993600i	$-0.463967\pi$
$811$	6.43373			0.225919			0.112959	+	0.993600i	$0.463967\pi$
$812$	0.989236	+	2.64518i	0.0347154	+	0.0928276i
$813$	−3.36870			−0.118146
$814$	9.30985	−	16.1251i	0.326310	−	0.565186i
$815$	19.8885	+	34.4478i	0.696662	+	1.20665i
$816$	1.10587	+	1.91543i	0.0387133	+	0.0670533i
$817$	9.73307	−	16.8582i	0.340517	−	0.589793i
$818$	56.0038			1.95813
$819$	−6.22005	+	7.54676i	−0.217346	+	0.263705i
$820$	−16.0639			−0.560976
$821$	22.0647	−	38.2172i	0.770064	−	1.33379i	−0.167463	−	0.985878i	$-0.553558\pi$
$821$	22.0647	−	38.2172i	0.770064	−	1.33379i	0.937527	−	0.347911i	$-0.113109\pi$
$822$	−19.8259	−	34.3395i	−0.691509	−	1.19773i
$823$	−3.06520	−	5.30908i	−0.106846	−	0.185063i	0.807645	−	0.589669i	$-0.200742\pi$
$823$	−3.06520	−	5.30908i	−0.106846	−	0.185063i	−0.914491	+	0.404606i	$0.867409\pi$
$824$	−36.7921	+	63.7258i	−1.28171	+	2.22000i
$825$	15.5016			0.539696
$826$	42.0774	+	7.03785i	1.46406	+	0.244878i
$827$	9.52187			0.331108			0.165554	−	0.986201i	$-0.447059\pi$
$827$	9.52187			0.331108			0.165554	+	0.986201i	$0.447059\pi$
$828$	4.80380	−	8.32042i	0.166943	−	0.289154i
$829$	−24.1256	−	41.7868i	−0.837918	−	1.45132i	−0.891632	−	0.452760i	$-0.850439\pi$
$829$	−24.1256	−	41.7868i	−0.837918	−	1.45132i	0.0537146	−	0.998556i	$-0.482894\pi$
$830$	−24.2981	−	42.0856i	−0.843401	−	1.46081i
$831$	−7.06440	+	12.2359i	−0.245061	+	0.424459i
$832$	29.6727			1.02872
$833$	0.741701	+	3.81244i	0.0256984	+	0.132093i
$834$	14.0891			0.487867
$835$	−12.4661	+	21.5919i	−0.431406	+	0.747218i
$836$	−16.8549	−	29.1936i	−0.582941	−	1.00968i
$837$	0.704906	+	1.22093i	0.0243651	+	0.0422016i
$838$	19.6964	−	34.1152i	0.680402	−	1.17849i
$839$	−10.5415			−0.363935			−0.181967	−	0.983305i	$-0.558246\pi$
$839$	−10.5415			−0.363935			−0.181967	+	0.983305i	$0.558246\pi$
$840$	−51.3005	−	8.58051i	−1.77004	−	0.296056i
$841$	−28.9287			−0.997542
$842$	2.78833	−	4.82952i	0.0960920	−	0.166436i
$843$	7.25175	+	12.5604i	0.249764	+	0.432603i
$844$	−33.4143	−	57.8752i	−1.15017	−	1.99215i
$845$	−1.33251	+	2.30798i	−0.0458399	+	0.0793970i
$846$	−0.494580			−0.0170040
$847$	−15.2556	+	18.5096i	−0.524190	+	0.635997i
$848$	−25.5973			−0.879015
$849$	−10.4044	+	18.0210i	−0.357080	+	0.618480i
$850$	7.57314	+	13.1171i	0.259756	+	0.449911i
$851$	−6.56930	−	11.3784i	−0.225193	−	0.390045i
$852$	−24.8808	+	43.0949i	−0.852404	+	1.47641i
$853$	44.3427			1.51827			0.759133	−	0.650935i	$-0.225623\pi$
$853$	44.3427			1.51827			0.759133	+	0.650935i	$0.225623\pi$
$854$	−21.1212	−	56.4773i	−0.722752	−	1.93261i
$855$	24.3642			0.833238
$856$	−41.1561	+	71.2845i	−1.40669	+	2.43645i
$857$	7.35048	+	12.7314i	0.251088	+	0.434896i	0.963826	−	0.266534i	$-0.0858785\pi$
$857$	7.35048	+	12.7314i	0.251088	+	0.434896i	−0.712738	+	0.701430i	$0.752545\pi$
$858$	6.29468	+	10.9027i	0.214897	+	0.372212i
$859$	−3.44141	+	5.96070i	−0.117420	+	0.203377i	−0.918744	−	0.394853i	$-0.870796\pi$
$859$	−3.44141	+	5.96070i	−0.117420	+	0.203377i	0.801325	+	0.598230i	$0.204129\pi$
$860$	−51.5726			−1.75861
$861$	−0.926762	−	2.47813i	−0.0315839	−	0.0844543i
$862$	16.6785			0.568073
$863$	−0.612051	+	1.06010i	−0.0208345	+	0.0360863i	−0.876255	−	0.481848i	$-0.839966\pi$
$863$	−0.612051	+	1.06010i	−0.0208345	+	0.0360863i	0.855420	+	0.517935i	$0.173299\pi$
$864$	0.0112344	+	0.0194586i	0.000382203	+	0.000661996i
$865$	42.8968	+	74.2994i	1.45853	+	2.52626i
$866$	3.55014	−	6.14902i	0.120639	−	0.208952i
$867$	−16.6921			−0.566895
$868$	−9.48395	+	11.5068i	−0.321906	+	0.390568i
$869$	−21.5434			−0.730810
$870$	−1.31378	+	2.27554i	−0.0445414	+	0.0771480i
$871$	−25.1192	−	43.5077i	−0.851132	−	1.47420i
$872$	−14.8063	−	25.6452i	−0.501404	−	0.868457i
$873$	−2.57297	+	4.45651i	−0.0870818	+	0.150830i
$874$	−35.6869			−1.20713
$875$	−64.4512	−	10.7801i	−2.17885	−	0.364434i
$876$	54.1814			1.83062
$877$	4.91774	−	8.51778i	0.166060	−	0.287625i	−0.770971	−	0.636870i	$-0.780229\pi$
$877$	4.91774	−	8.51778i	0.166060	−	0.287625i	0.937031	+	0.349245i	$0.113562\pi$
$878$	27.7323	+	48.0338i	0.935921	+	1.62106i
$879$	−7.86205	−	13.6175i	−0.265180	−	0.459306i
$880$	−11.1380	+	19.2916i	−0.375462	+	0.650320i
$881$	−45.2512			−1.52455			−0.762276	−	0.647252i	$-0.775918\pi$
$881$	−45.2512			−1.52455			−0.762276	+	0.647252i	$0.775918\pi$
$882$	−3.27378	−	16.8277i	−0.110234	−	0.566617i
$883$	42.9341			1.44485			0.722423	−	0.691451i	$-0.243028\pi$
$883$	42.9341			1.44485			0.722423	+	0.691451i	$0.243028\pi$
$884$	−4.09948	+	7.10052i	−0.137881	+	0.238816i
$885$	13.2284	+	22.9123i	0.444669	+	0.770190i
$886$	8.48146	+	14.6903i	0.284940	+	0.493531i
$887$	−25.4981	+	44.1641i	−0.856143	+	1.48288i	0.0194367	+	0.999811i	$0.493813\pi$
$887$	−25.4981	+	44.1641i	−0.856143	+	1.48288i	−0.875580	+	0.483073i	$0.839521\pi$
$888$	−26.7467			−0.897559
$889$	38.4703	+	6.43453i	1.29025	+	0.215807i
$890$	95.2737			3.19358
$891$	−0.695352	+	1.20438i	−0.0232952	+	0.0403484i
$892$	30.9679	+	53.6380i	1.03688	+	1.79593i
$893$	0.612247	+	1.06044i	0.0204880	+	0.0354863i
$894$	19.8907	−	34.4517i	0.665244	−	1.15224i
$895$	−42.2255			−1.41144
$896$	−33.0062	+	40.0463i	−1.10266	+	1.33785i
$897$	8.88342			0.296609
$898$	−27.4218	+	47.4960i	−0.915077	+	1.58496i
$899$	0.188214	+	0.325997i	0.00627730	+	0.0108726i
$900$	−22.2804	−	38.5907i	−0.742679	−	1.28636i
$901$	−1.78145	+	3.08556i	−0.0593486	+	0.102795i
$902$	−3.40586			−0.113403
$903$	−2.97533	−	7.95594i	−0.0990129	−	0.264757i
$904$	−96.2840			−3.20236
$905$	−33.1527	+	57.4222i	−1.10203	+	1.90878i
$906$	−16.6681	−	28.8699i	−0.553759	−	0.959139i
$907$	−11.5465	−	19.9991i	−0.383394	−	0.664058i	0.608151	−	0.793821i	$-0.291912\pi$
$907$	−11.5465	−	19.9991i	−0.383394	−	0.664058i	−0.991545	+	0.129763i	$0.958578\pi$
$908$	0.764411	−	1.32400i	0.0253679	−	0.0439385i
$909$	3.29223			0.109196
$910$	−33.7114	−	90.1432i	−1.11752	−	2.98822i
$911$	−38.5509			−1.27725			−0.638625	−	0.769518i	$-0.720496\pi$
$911$	−38.5509			−1.27725			−0.638625	+	0.769518i	$0.720496\pi$
$912$	−12.0850	+	20.9318i	−0.400173	+	0.693120i
$913$	−3.43380	−	5.94751i	−0.113642	−	0.196834i
$914$	31.0958	+	53.8596i	1.02856	+	1.78152i
$915$	18.6968	−	32.3839i	0.618098	−	1.07058i
$916$	80.7253			2.66724
$917$	−11.4086	+	13.8421i	−0.376747	+	0.457105i
$918$	−1.35883			−0.0448480
$919$	19.8257	−	34.3391i	0.653990	−	1.13274i	−0.328156	−	0.944623i	$-0.606427\pi$
$919$	19.8257	−	34.3391i	0.653990	−	1.13274i	0.982146	−	0.188120i	$-0.0602393\pi$
$920$	23.6232	+	40.9165i	0.778832	+	1.34898i
$921$	−5.73084	−	9.92611i	−0.188838	−	0.327076i
$922$	−25.9694	+	44.9804i	−0.855258	+	1.48135i
$923$	−46.0109			−1.51447
$924$	−14.5078	−	2.42658i	−0.477273	−	0.0798285i
$925$	−60.9379			−2.00362
$926$	−31.5123	+	54.5809i	−1.03556	+	1.79364i
$927$	−7.52023	−	13.0254i	−0.246997	−	0.427811i
$928$	0.00299966	+	0.00519557i	9.84688e−5	+	0.000170553i
$929$	−24.6497	+	42.6946i	−0.808731	+	1.40076i	0.105013	+	0.994471i	$0.466512\pi$
$929$	−24.6497	+	42.6946i	−0.808731	+	1.40076i	−0.913743	+	0.406292i	$0.866822\pi$
$930$	−13.8738			−0.454939
$931$	−32.0280	+	27.8505i	−1.04967	+	0.912765i
$932$	−34.8854			−1.14271
$933$	−0.269725	+	0.467177i	−0.00883039	+	0.0152947i
$934$	−23.1936	−	40.1725i	−0.758919	−	1.31449i
$935$	1.55030	+	2.68520i	0.0507003	+	0.0878155i
$936$	9.04213	−	15.6614i	0.295551	−	0.511910i
$937$	29.7098			0.970577			0.485288	−	0.874354i	$-0.338715\pi$
$937$	29.7098			0.970577			0.485288	+	0.874354i	$0.338715\pi$
$938$	86.8579	+	14.5278i	2.83601	+	0.474350i
$939$	−3.30545			−0.107869
$940$	1.62205	−	2.80948i	0.0529055	−	0.0916351i
$941$	−15.0147	−	26.0063i	−0.489466	−	0.847781i	0.510460	−	0.859901i	$-0.329475\pi$
$941$	−15.0147	−	26.0063i	−0.489466	−	0.847781i	−0.999927	+	0.0121208i	$0.996142\pi$
$942$	−28.6958	−	49.7026i	−0.934960	−	1.61940i
$943$	−1.20164	+	2.08130i	−0.0391307	+	0.0677764i
$944$	−26.2459			−0.854232
$945$	6.76172	−	8.20397i	0.219959	−	0.266875i
$946$	−10.9344			−0.355508
$947$	28.0471	−	48.5789i	0.911407	−	1.57860i	0.0993294	−	0.995055i	$-0.468330\pi$
$947$	28.0471	−	48.5789i	0.911407	−	1.57860i	0.812078	−	0.583549i	$-0.198336\pi$
$948$	30.9643	+	53.6317i	1.00567	+	1.74188i
$949$	25.0487	+	43.3857i	0.813116	+	1.40836i
$950$	−82.7592	+	143.343i	−2.68506	+	4.65066i
$951$	31.3519			1.01665
$952$	−2.51573	−	6.72697i	−0.0815352	−	0.218022i
$953$	−35.0470			−1.13528			−0.567642	−	0.823275i	$-0.692144\pi$
$953$	−35.0470			−1.13528			−0.567642	+	0.823275i	$0.692144\pi$
$954$	7.86310	−	13.6193i	0.254577	−	0.440941i
$955$	6.18782	+	10.7176i	0.200233	+	0.346814i
$956$	−24.8631	−	43.0641i	−0.804129	−	1.39279i
$957$	−0.185663	+	0.321578i	−0.00600164	+	0.0103951i
$958$	−25.3699			−0.819664
$959$	15.0051	+	40.1231i	0.484540	+	1.29564i
$960$	−32.2567			−1.04108
$961$	14.5062	−	25.1255i	0.467942	−	0.810500i
$962$	−24.7449	−	42.8593i	−0.797806	−	1.38184i
$963$	−8.41222	−	14.5704i	−0.271080	−	0.469524i
$964$	51.1196	−	88.5418i	1.64645	−	2.85174i
$965$	61.7080			1.98645
$966$	−9.90406	+	12.0166i	−0.318658	+	0.386627i
$967$	3.10220			0.0997601			0.0498800	−	0.998755i	$-0.484116\pi$
$967$	3.10220			0.0997601			0.0498800	+	0.998755i	$0.484116\pi$
$968$	22.1772	−	38.4121i	0.712803	−	1.23461i
$969$	1.68211	+	2.91350i	0.0540371	+	0.0935950i
$970$	−25.3202	−	43.8559i	−0.812983	−	1.40813i
$971$	6.04442	−	10.4692i	0.193975	−	0.335974i	−0.752589	−	0.658490i	$-0.771195\pi$
$971$	6.04442	−	10.4692i	0.193975	−	0.335974i	0.946564	+	0.322516i	$0.104529\pi$
$972$	3.99771			0.128226
$973$	−15.0124	−	2.51097i	−0.481275	−	0.0804979i
$974$	49.6146			1.58976
$975$	20.6010	−	35.6820i	0.659760	−	1.14274i
$976$	18.5477	+	32.1256i	0.593698	+	1.02832i
$977$	−29.4043	−	50.9297i	−0.940726	−	1.62939i	−0.764091	−	0.645109i	$-0.776812\pi$
$977$	−29.4043	−	50.9297i	−0.940726	−	1.62939i	−0.176635	−	0.984276i	$-0.556521\pi$
$978$	12.1214	−	20.9949i	0.387600	−	0.671343i
$979$	13.4640			0.430312
$980$	106.327	+	36.5921i	3.39649	+	1.16889i
$981$	6.05274			0.193249
$982$	−7.33822	+	12.7102i	−0.234172	+	0.405598i
$983$	−19.8964	−	34.4615i	−0.634595	−	1.09915i	−0.986601	−	0.163153i	$-0.947833\pi$
$983$	−19.8964	−	34.4615i	−0.634595	−	1.09915i	0.352005	−	0.935998i	$-0.385500\pi$
$984$	2.44621	+	4.23696i	0.0779824	+	0.135069i
$985$	35.0759	−	60.7532i	1.11761	−	1.93576i
$986$	−0.362815			−0.0115544
$987$	0.526989	+	0.0881441i	0.0167743	+	0.00280566i
$988$	−89.5983			−2.85050
$989$	−3.85782	+	6.68194i	−0.122671	+	0.212473i
$990$	−6.84285	−	11.8522i	−0.217480	−	0.376687i
$991$	−10.5296	−	18.2377i	−0.334483	−	0.579341i	0.648903	−	0.760871i	$-0.275228\pi$
$991$	−10.5296	−	18.2377i	−0.334483	−	0.579341i	−0.983385	+	0.181531i	$0.941895\pi$
$992$	−0.0158385	+	0.0274330i	−0.000502872	+	0.000870999i
$993$	−16.3998			−0.520432
$994$	51.2972	−	62.2387i	1.62705	−	1.97409i
$995$	−60.7795			−1.92684
$996$	−9.87077	+	17.0967i	−0.312767	+	0.541729i
$997$	−7.31968	−	12.6780i	−0.231816	−	0.401518i	0.726526	−	0.687139i	$-0.241134\pi$
$997$	−7.31968	−	12.6780i	−0.231816	−	0.401518i	−0.958343	+	0.285621i	$0.907800\pi$
$998$	15.1534	+	26.2465i	0.479674	+	0.830819i
$999$	2.73348	−	4.73452i	0.0864834	−	0.149794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.e.247.2	✓	24
7.2	even	3		6027.2.a.bg.1.11		12
7.4	even	3	inner	861.2.i.e.739.2	yes	24
7.5	odd	6		6027.2.a.bf.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.e.247.2	✓	24	1.1	even	1	trivial
861.2.i.e.739.2	yes	24	7.4	even	3	inner
6027.2.a.bf.1.11		12	7.5	odd	6
6027.2.a.bg.1.11		12	7.2	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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22451 + 2.12091i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.99885 - 3.46211i) q^{4} +(-2.00914 + 3.47993i) q^{5} +2.44902 q^{6} +(-2.60950 - 0.436464i) q^{7} +4.89242 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.22451 + 2.12091i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.99885 - 3.46211i) q^{4} +(-2.00914 + 3.47993i) q^{5} +2.44902 q^{6} +(-2.60950 - 0.436464i) q^{7} +4.89242 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.92043 - 8.52243i) q^{10} +(-0.695352 - 1.20438i) q^{11} +(-1.99885 + 3.46211i) q^{12} -3.69638 q^{13} +(4.12107 - 5.00007i) q^{14} +4.01828 q^{15} +(-1.99312 + 3.45218i) q^{16} +(0.277423 + 0.480510i) q^{17} +(-1.22451 - 2.12091i) q^{18} +(-3.03167 + 5.25101i) q^{19} +16.0639 q^{20} +(0.926762 + 2.47813i) q^{21} +3.40586 q^{22} +(1.20164 - 2.08130i) q^{23} +(-2.44621 - 4.23696i) q^{24} +(-5.57329 - 9.65322i) q^{25} +(4.52626 - 7.83971i) q^{26} +1.00000 q^{27} +(3.70492 + 9.90682i) q^{28} +0.267006 q^{29} +(-4.92043 + 8.52243i) q^{30} +(0.704906 + 1.22093i) q^{31} +(0.0112344 + 0.0194586i) q^{32} +(-0.695352 + 1.20438i) q^{33} -1.35883 q^{34} +(6.76172 - 8.20397i) q^{35} +3.99771 q^{36} +(2.73348 - 4.73452i) q^{37} +(-7.42463 - 12.8598i) q^{38} +(1.84819 + 3.20116i) q^{39} +(-9.82956 + 17.0253i) q^{40} -1.00000 q^{41} +(-6.39072 - 1.06891i) q^{42} -3.21046 q^{43} +(-2.77981 + 4.81477i) q^{44} +(-2.00914 - 3.47993i) q^{45} +(2.94284 + 5.09714i) q^{46} +(0.100975 - 0.174894i) q^{47} +3.98624 q^{48} +(6.61900 + 2.27791i) q^{49} +27.2982 q^{50} +(0.277423 - 0.480510i) q^{51} +(7.38852 + 12.7973i) q^{52} +(3.21071 + 5.56112i) q^{53} +(-1.22451 + 2.12091i) q^{54} +5.58824 q^{55} +(-12.7668 - 2.13537i) q^{56} +6.06334 q^{57} +(-0.326952 + 0.566297i) q^{58} +(3.29207 + 5.70203i) q^{59} +(-8.03195 - 13.9117i) q^{60} +(4.65294 - 8.05914i) q^{61} -3.45266 q^{62} +(1.68274 - 2.04166i) q^{63} -8.02750 q^{64} +(7.42655 - 12.8632i) q^{65} +(-1.70293 - 2.94956i) q^{66} +(6.79562 + 11.7704i) q^{67} +(1.10905 - 1.92094i) q^{68} -2.40328 q^{69} +(9.12012 + 24.3869i) q^{70} +12.4476 q^{71} +(-2.44621 + 4.23696i) q^{72} +(-6.77656 - 11.7373i) q^{73} +(6.69435 + 11.5949i) q^{74} +(-5.57329 + 9.65322i) q^{75} +24.2395 q^{76} +(1.28885 + 3.44634i) q^{77} -9.05251 q^{78} +(7.74551 - 13.4156i) q^{79} +(-8.00891 - 13.8718i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.22451 - 2.12091i) q^{82} +4.93822 q^{83} +(6.72710 - 8.16196i) q^{84} -2.22952 q^{85} +(3.93125 - 6.80912i) q^{86} +(-0.133503 - 0.231234i) q^{87} +(-3.40195 - 5.89236i) q^{88} +(-4.84072 + 8.38438i) q^{89} +9.84085 q^{90} +(9.64571 + 1.61334i) q^{91} -9.60759 q^{92} +(0.704906 - 1.22093i) q^{93} +(0.247290 + 0.428319i) q^{94} +(-12.1821 - 21.1000i) q^{95} +(0.0112344 - 0.0194586i) q^{96} +5.14594 q^{97} +(-12.9363 + 11.2490i) q^{98} +1.39070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 12 q^{3} - 10 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 12 * q^3 - 10 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^9	\( 24 q + 2 q^{2} - 12 q^{3} - 10 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{9} - 11 q^{10} - 10 q^{11} - 10 q^{12} + 30 q^{13} + 4 q^{14} + 24 q^{15} - 14 q^{16} - 8 q^{17} + 2 q^{18} - 2 q^{19} + 32 q^{20} - 14 q^{22} - 5 q^{23} - 20 q^{25} + 24 q^{27} + 37 q^{28} + 40 q^{29} - 11 q^{30} - 10 q^{31} - 3 q^{32} - 10 q^{33} - 46 q^{34} - 4 q^{35} + 20 q^{36} + 17 q^{37} - 6 q^{38} - 15 q^{39} - 39 q^{40} - 24 q^{41} - 8 q^{42} + 24 q^{43} - 20 q^{44} - 12 q^{45} + 36 q^{46} - 34 q^{47} + 28 q^{48} - 10 q^{49} + 118 q^{50} - 8 q^{51} - 26 q^{52} - 6 q^{53} + 2 q^{54} - 2 q^{55} - q^{56} + 4 q^{57} + 11 q^{58} - 27 q^{59} - 16 q^{60} - 22 q^{61} - 90 q^{62} + 52 q^{64} + 7 q^{66} + 26 q^{67} - 33 q^{68} + 10 q^{69} + 50 q^{70} + 100 q^{71} - 21 q^{73} + 35 q^{74} - 20 q^{75} - 48 q^{76} + 52 q^{77} + 10 q^{79} - 22 q^{80} - 12 q^{81} - 2 q^{82} + 16 q^{83} - 29 q^{84} + 16 q^{85} + 17 q^{86} - 20 q^{87} + 46 q^{88} - 11 q^{89} + 22 q^{90} + 5 q^{91} + 126 q^{92} - 10 q^{93} - 10 q^{94} - 35 q^{95} - 3 q^{96} + 64 q^{97} - 75 q^{98} + 20 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 12 * q^3 - 10 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^9 - 11 * q^10 - 10 * q^11 - 10 * q^12 + 30 * q^13 + 4 * q^14 + 24 * q^15 - 14 * q^16 - 8 * q^17 + 2 * q^18 - 2 * q^19 + 32 * q^20 - 14 * q^22 - 5 * q^23 - 20 * q^25 + 24 * q^27 + 37 * q^28 + 40 * q^29 - 11 * q^30 - 10 * q^31 - 3 * q^32 - 10 * q^33 - 46 * q^34 - 4 * q^35 + 20 * q^36 + 17 * q^37 - 6 * q^38 - 15 * q^39 - 39 * q^40 - 24 * q^41 - 8 * q^42 + 24 * q^43 - 20 * q^44 - 12 * q^45 + 36 * q^46 - 34 * q^47 + 28 * q^48 - 10 * q^49 + 118 * q^50 - 8 * q^51 - 26 * q^52 - 6 * q^53 + 2 * q^54 - 2 * q^55 - q^56 + 4 * q^57 + 11 * q^58 - 27 * q^59 - 16 * q^60 - 22 * q^61 - 90 * q^62 + 52 * q^64 + 7 * q^66 + 26 * q^67 - 33 * q^68 + 10 * q^69 + 50 * q^70 + 100 * q^71 - 21 * q^73 + 35 * q^74 - 20 * q^75 - 48 * q^76 + 52 * q^77 + 10 * q^79 - 22 * q^80 - 12 * q^81 - 2 * q^82 + 16 * q^83 - 29 * q^84 + 16 * q^85 + 17 * q^86 - 20 * q^87 + 46 * q^88 - 11 * q^89 + 22 * q^90 + 5 * q^91 + 126 * q^92 - 10 * q^93 - 10 * q^94 - 35 * q^95 - 3 * q^96 + 64 * q^97 - 75 * q^98 + 20 * q^99

Introduction

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