LMFDB - Embedded newform 406.2.e.a.291.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [406,2,Mod(233,406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(406, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("406.233");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 406 = 2 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	406.e (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:	$3.24192632206$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			291.4
Root			$2.31940 + 0.319028i$ of defining polynomial
Character	$\chi$	$=$	406.291
Dual form			406.2.e.a.233.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.357289 - 0.618843i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.116584 - 0.201930i) q^{5} -0.714579 q^{6} +(2.36799 - 1.18009i) q^{7} +1.00000 q^{8} +(1.24469 + 2.15586i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.357289 - 0.618843i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.116584 - 0.201930i) q^{5} -0.714579 q^{6} +(2.36799 - 1.18009i) q^{7} +1.00000 q^{8} +(1.24469 + 2.15586i) q^{9} +(-0.116584 + 0.201930i) q^{10} +(-0.146694 + 0.254082i) q^{11} +(0.357289 + 0.618843i) q^{12} +4.15740 q^{13} +(-2.20598 - 1.46070i) q^{14} -0.166617 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.304717 + 0.527786i) q^{17} +(1.24469 - 2.15586i) q^{18} +(-3.33870 - 5.78280i) q^{19} +0.233169 q^{20} +(0.115767 - 1.88705i) q^{21} +0.293388 q^{22} +(0.743871 + 1.28842i) q^{23} +(0.357289 - 0.618843i) q^{24} +(2.47282 - 4.28304i) q^{25} +(-2.07870 - 3.60041i) q^{26} +3.92259 q^{27} +(-0.162007 + 2.64079i) q^{28} -1.00000 q^{29} +(0.0833087 + 0.144295i) q^{30} +(0.675875 - 1.17065i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.104824 + 0.181561i) q^{33} +0.609435 q^{34} +(-0.514366 - 0.340588i) q^{35} -2.48938 q^{36} +(-0.318586 - 0.551807i) q^{37} +(-3.33870 + 5.78280i) q^{38} +(1.48539 - 2.57278i) q^{39} +(-0.116584 - 0.201930i) q^{40} +3.31605 q^{41} +(-1.69212 + 0.843268i) q^{42} -3.29502 q^{43} +(-0.146694 - 0.254082i) q^{44} +(0.290222 - 0.502680i) q^{45} +(0.743871 - 1.28842i) q^{46} +(-1.09046 - 1.88873i) q^{47} -0.714579 q^{48} +(4.21477 - 5.58889i) q^{49} -4.94563 q^{50} +(0.217745 + 0.377145i) q^{51} +(-2.07870 + 3.60041i) q^{52} +(-5.99610 + 10.3855i) q^{53} +(-1.96130 - 3.39706i) q^{54} +0.0684089 q^{55} +(2.36799 - 1.18009i) q^{56} -4.77153 q^{57} +(0.500000 + 0.866025i) q^{58} +(-2.15057 + 3.72489i) q^{59} +(0.0833087 - 0.144295i) q^{60} +(-1.82401 - 3.15928i) q^{61} -1.35175 q^{62} +(5.49153 + 3.63622i) q^{63} +1.00000 q^{64} +(-0.484687 - 0.839503i) q^{65} +(0.104824 - 0.181561i) q^{66} +(-2.47824 + 4.29245i) q^{67} +(-0.304717 - 0.527786i) q^{68} +1.06311 q^{69} +(-0.0377749 + 0.615749i) q^{70} +4.21106 q^{71} +(1.24469 + 2.15586i) q^{72} +(-2.92149 + 5.06017i) q^{73} +(-0.318586 + 0.551807i) q^{74} +(-1.76702 - 3.06057i) q^{75} +6.67740 q^{76} +(-0.0475309 + 0.774776i) q^{77} -2.97079 q^{78} +(-1.05339 - 1.82452i) q^{79} +(-0.116584 + 0.201930i) q^{80} +(-2.33257 + 4.04012i) q^{81} +(-1.65802 - 2.87178i) q^{82} +6.73621 q^{83} +(1.57635 + 1.04378i) q^{84} +0.142101 q^{85} +(1.64751 + 2.85357i) q^{86} +(-0.357289 + 0.618843i) q^{87} +(-0.146694 + 0.254082i) q^{88} +(6.31233 + 10.9333i) q^{89} -0.580445 q^{90} +(9.84468 - 4.90611i) q^{91} -1.48774 q^{92} +(-0.482966 - 0.836522i) q^{93} +(-1.09046 + 1.88873i) q^{94} +(-0.778480 + 1.34837i) q^{95} +(0.357289 + 0.618843i) q^{96} +5.70498 q^{97} +(-6.94751 - 0.855651i) q^{98} -0.730354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/406\mathbb{Z}\right)^\times$.

$n$	$59$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.357289	−	0.618843i	0.206281	−	0.357289i	−0.744259	−	0.667891i	$-0.767197\pi$
$3$	0.357289	−	0.618843i	0.206281	−	0.357289i	0.950540	+	0.310602i	$0.100531\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.116584	−	0.201930i	−0.0521381	−	0.0903058i	0.838778	−	0.544473i	$-0.183270\pi$
$5$	−0.116584	−	0.201930i	−0.0521381	−	0.0903058i	−0.890917	+	0.454167i	$0.849937\pi$
$6$	−0.714579			−0.291726
$7$	2.36799	−	1.18009i	0.895017	−	0.446033i
$7$	2.36799	−	1.18009i	0.895017	−	0.446033i
$8$	1.00000			0.353553
$9$	1.24469	+	2.15586i	0.414896	+	0.718621i
$10$	−0.116584	+	0.201930i	−0.0368672	+	0.0638559i
$11$	−0.146694	+	0.254082i	−0.0442299	+	0.0766085i	−0.887293	−	0.461206i	$-0.847417\pi$
$11$	−0.146694	+	0.254082i	−0.0442299	+	0.0766085i	0.843063	+	0.537815i	$0.180750\pi$
$12$	0.357289	+	0.618843i	0.103141	+	0.178645i
$13$	4.15740			1.15305			0.576527	−	0.817078i	$-0.304408\pi$
$13$	4.15740			1.15305			0.576527	+	0.817078i	$0.304408\pi$
$14$	−2.20598	−	1.46070i	−0.589574	−	0.390387i
$15$	−0.166617			−0.0430204
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.304717	+	0.527786i	−0.0739048	+	0.128007i	−0.900610	−	0.434629i	$-0.856879\pi$
$17$	−0.304717	+	0.527786i	−0.0739048	+	0.128007i	0.826705	+	0.562636i	$0.190213\pi$
$18$	1.24469	−	2.15586i	0.293376	−	0.508142i
$19$	−3.33870	−	5.78280i	−0.765950	−	1.32666i	−0.939743	−	0.341882i	$-0.888936\pi$
$19$	−3.33870	−	5.78280i	−0.765950	−	1.32666i	0.173793	−	0.984782i	$-0.444398\pi$
$20$	0.233169			0.0521381
$21$	0.115767	−	1.88705i	0.0252624	−	0.411788i
$22$	0.293388			0.0625506
$23$	0.743871	+	1.28842i	0.155108	+	0.268655i	0.933098	−	0.359621i	$-0.117094\pi$
$23$	0.743871	+	1.28842i	0.155108	+	0.268655i	−0.777990	+	0.628276i	$0.783761\pi$
$24$	0.357289	−	0.618843i	0.0729314	−	0.126321i
$25$	2.47282	−	4.28304i	0.494563	−	0.856609i
$26$	−2.07870	−	3.60041i	−0.407666	−	0.706099i
$27$	3.92259			0.754903
$28$	−0.162007	+	2.64079i	−0.0306164	+	0.499062i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	0.0833087	+	0.144295i	0.0152100	+	0.0263445i
$31$	0.675875	−	1.17065i	0.121391	−	0.210255i	−0.798926	−	0.601430i	$-0.794598\pi$
$31$	0.675875	−	1.17065i	0.121391	−	0.210255i	0.920316	+	0.391175i	$0.127931\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.104824	+	0.181561i	0.0182476	+	0.0316058i
$34$	0.609435			0.104517
$35$	−0.514366	−	0.340588i	−0.0869438	−	0.0575699i
$36$	−2.48938			−0.414896
$37$	−0.318586	−	0.551807i	−0.0523752	−	0.0907164i	0.838649	−	0.544672i	$-0.183346\pi$
$37$	−0.318586	−	0.551807i	−0.0523752	−	0.0907164i	−0.891024	+	0.453956i	$0.850012\pi$
$38$	−3.33870	+	5.78280i	−0.541609	+	0.938094i
$39$	1.48539	−	2.57278i	0.237853	−	0.411974i
$40$	−0.116584	−	0.201930i	−0.0184336	−	0.0319279i
$41$	3.31605			0.517880			0.258940	−	0.965893i	$-0.416627\pi$
$41$	3.31605			0.517880			0.258940	+	0.965893i	$0.416627\pi$
$42$	−1.69212	+	0.843268i	−0.261099	+	0.130119i
$43$	−3.29502			−0.502486			−0.251243	−	0.967924i	$-0.580839\pi$
$43$	−3.29502			−0.502486			−0.251243	+	0.967924i	$0.580839\pi$
$44$	−0.146694	−	0.254082i	−0.0221150	−	0.0383042i
$45$	0.290222	−	0.502680i	0.0432638	−	0.0749351i
$46$	0.743871	−	1.28842i	0.109678	−	0.189967i
$47$	−1.09046	−	1.88873i	−0.159060	−	0.275499i	0.775470	−	0.631384i	$-0.217513\pi$
$47$	−1.09046	−	1.88873i	−0.159060	−	0.275499i	−0.934530	+	0.355885i	$0.884180\pi$
$48$	−0.714579			−0.103141
$49$	4.21477	−	5.58889i	0.602110	−	0.798413i
$50$	−4.94563			−0.699418
$51$	0.217745	+	0.377145i	0.0304903	+	0.0528108i
$52$	−2.07870	+	3.60041i	−0.288264	+	0.499287i
$53$	−5.99610	+	10.3855i	−0.823627	+	1.42656i	0.0793369	+	0.996848i	$0.474720\pi$
$53$	−5.99610	+	10.3855i	−0.823627	+	1.42656i	−0.902964	+	0.429716i	$0.858614\pi$
$54$	−1.96130	−	3.39706i	−0.266899	−	0.462282i
$55$	0.0684089			0.00922426
$56$	2.36799	−	1.18009i	0.316436	−	0.157696i
$57$	−4.77153			−0.632004
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	−2.15057	+	3.72489i	−0.279980	+	0.484939i	−0.971379	−	0.237533i	$-0.923661\pi$
$59$	−2.15057	+	3.72489i	−0.279980	+	0.484939i	0.691400	+	0.722473i	$0.256994\pi$
$60$	0.0833087	−	0.144295i	0.0107551	−	0.0186284i
$61$	−1.82401	−	3.15928i	−0.233541	−	0.404505i	0.725307	−	0.688426i	$-0.241698\pi$
$61$	−1.82401	−	3.15928i	−0.233541	−	0.404505i	−0.958848	+	0.283921i	$0.908365\pi$
$62$	−1.35175			−0.171672
$63$	5.49153	+	3.63622i	0.691868	+	0.458121i
$64$	1.00000			0.125000
$65$	−0.484687	−	0.839503i	−0.0601180	−	0.104128i
$66$	0.104824	−	0.181561i	0.0129030	−	0.0223487i
$67$	−2.47824	+	4.29245i	−0.302766	+	0.524406i	−0.976761	−	0.214330i	$-0.931243\pi$
$67$	−2.47824	+	4.29245i	−0.302766	+	0.524406i	0.673996	+	0.738735i	$0.264577\pi$
$68$	−0.304717	−	0.527786i	−0.0369524	−	0.0640035i
$69$	1.06311			0.127983
$70$	−0.0377749	+	0.615749i	−0.00451497	+	0.0735960i
$71$	4.21106			0.499761			0.249881	−	0.968277i	$-0.419609\pi$
$71$	4.21106			0.499761			0.249881	+	0.968277i	$0.419609\pi$
$72$	1.24469	+	2.15586i	0.146688	+	0.254071i
$73$	−2.92149	+	5.06017i	−0.341935	+	0.592248i	−0.984792	−	0.173738i	$-0.944416\pi$
$73$	−2.92149	+	5.06017i	−0.341935	+	0.592248i	0.642857	+	0.765986i	$0.277749\pi$
$74$	−0.318586	+	0.551807i	−0.0370348	+	0.0641462i
$75$	−1.76702	−	3.06057i	−0.204038	−	0.353404i
$76$	6.67740			0.765950
$77$	−0.0475309	+	0.774776i	−0.00541665	+	0.0882939i
$78$	−2.97079			−0.336375
$79$	−1.05339	−	1.82452i	−0.118516	−	0.205275i	0.800664	−	0.599114i	$-0.204480\pi$
$79$	−1.05339	−	1.82452i	−0.118516	−	0.205275i	−0.919180	+	0.393839i	$0.871147\pi$
$80$	−0.116584	+	0.201930i	−0.0130345	+	0.0225765i
$81$	−2.33257	+	4.04012i	−0.259174	+	0.448902i
$82$	−1.65802	−	2.87178i	−0.183098	−	0.317135i
$83$	6.73621			0.739395			0.369697	−	0.929152i	$-0.379461\pi$
$83$	6.73621			0.739395			0.369697	+	0.929152i	$0.379461\pi$
$84$	1.57635	+	1.04378i	0.171994	+	0.113886i
$85$	0.142101			0.0154130
$86$	1.64751	+	2.85357i	0.177656	+	0.307709i
$87$	−0.357289	+	0.618843i	−0.0383054	+	0.0663470i
$88$	−0.146694	+	0.254082i	−0.0156376	+	0.0270852i
$89$	6.31233	+	10.9333i	0.669106	+	1.15893i	0.978154	+	0.207879i	$0.0666561\pi$
$89$	6.31233	+	10.9333i	0.669106	+	1.15893i	−0.309048	+	0.951046i	$0.600011\pi$
$90$	−0.580445			−0.0611842
$91$	9.84468	−	4.90611i	1.03200	−	0.514300i
$92$	−1.48774			−0.155108
$93$	−0.482966	−	0.836522i	−0.0500812	−	0.0867433i
$94$	−1.09046	+	1.88873i	−0.112472	+	0.194807i
$95$	−0.778480	+	1.34837i	−0.0798704	+	0.138340i
$96$	0.357289	+	0.618843i	0.0364657	+	0.0631604i
$97$	5.70498			0.579253			0.289626	−	0.957140i	$-0.406469\pi$
$97$	5.70498			0.579253			0.289626	+	0.957140i	$0.406469\pi$
$98$	−6.94751	−	0.855651i	−0.701804	−	0.0864338i
$99$	−0.730354			−0.0734033
$100$	2.47282	+	4.28304i	0.247282	+	0.428304i
$101$	−7.86693	+	13.6259i	−0.782789	+	1.35583i	0.147522	+	0.989059i	$0.452870\pi$
$101$	−7.86693	+	13.6259i	−0.782789	+	1.35583i	−0.930311	+	0.366772i	$0.880463\pi$
$102$	0.217745	−	0.377145i	0.0215599	−	0.0373429i
$103$	2.44775	+	4.23962i	0.241184	+	0.417742i	0.961052	−	0.276369i	$-0.0891310\pi$
$103$	2.44775	+	4.23962i	0.241184	+	0.417742i	−0.719868	+	0.694111i	$0.755798\pi$
$104$	4.15740			0.407666
$105$	−0.394549	+	0.196624i	−0.0385040	+	0.0191885i
$106$	11.9922			1.16478
$107$	−5.61573	−	9.72674i	−0.542894	−	0.940319i	−0.998736	−	0.0502589i	$-0.983995\pi$
$107$	−5.61573	−	9.72674i	−0.542894	−	0.940319i	0.455843	−	0.890060i	$-0.349338\pi$
$108$	−1.96130	+	3.39706i	−0.188726	+	0.326883i
$109$	−7.59327	+	13.1519i	−0.727304	+	1.25973i	0.230715	+	0.973021i	$0.425893\pi$
$109$	−7.59327	+	13.1519i	−0.727304	+	1.25973i	−0.958019	+	0.286705i	$0.907440\pi$
$110$	−0.0342045	−	0.0592439i	−0.00326127	−	0.00564868i
$111$	−0.455309			−0.0432160
$112$	−2.20598	−	1.46070i	−0.208446	−	0.138023i
$113$	−10.2976			−0.968717			−0.484359	−	0.874870i	$-0.660947\pi$
$113$	−10.2976			−0.968717			−0.484359	+	0.874870i	$0.660947\pi$
$114$	2.38576	+	4.13226i	0.223447	+	0.387022i
$115$	0.173447	−	0.300420i	0.0161741	−	0.0280143i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	5.17466	+	8.96278i	0.478398	+	0.828609i
$118$	4.30113			0.395951
$119$	−0.0987327	+	1.60939i	−0.00905081	+	0.147532i
$120$	−0.166617			−0.0152100
$121$	5.45696	+	9.45173i	0.496087	+	0.859249i
$122$	−1.82401	+	3.15928i	−0.165138	+	0.286028i
$123$	1.18479	−	2.05211i	0.106829	−	0.185033i
$124$	0.675875	+	1.17065i	0.0606954	+	0.105127i
$125$	−2.31901			−0.207419
$126$	0.403296	−	6.57391i	0.0359285	−	0.585651i
$127$	−15.3053			−1.35813			−0.679065	−	0.734078i	$-0.737615\pi$
$127$	−15.3053			−1.35813			−0.679065	+	0.734078i	$0.737615\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.17728	+	2.03910i	−0.103653	+	0.179533i
$130$	−0.484687	+	0.839503i	−0.0425099	+	0.0736293i
$131$	−6.10878	−	10.5807i	−0.533726	−	0.924441i	−0.999224	−	0.0393918i	$-0.987458\pi$
$131$	−6.10878	−	10.5807i	−0.533726	−	0.924441i	0.465498	−	0.885049i	$-0.345875\pi$
$132$	−0.209649			−0.0182476
$133$	−14.7302	−	9.75365i	−1.27727	−	0.845748i
$134$	4.95649			0.428175
$135$	−0.457313	−	0.792089i	−0.0393592	−	0.0681722i
$136$	−0.304717	+	0.527786i	−0.0261293	+	0.0452573i
$137$	−8.91455	+	15.4405i	−0.761622	+	1.31917i	0.180393	+	0.983595i	$0.442263\pi$
$137$	−8.91455	+	15.4405i	−0.761622	+	1.31917i	−0.942014	+	0.335573i	$0.891070\pi$
$138$	−0.531554	−	0.920679i	−0.0452489	−	0.0783734i
$139$	7.99852			0.678426			0.339213	−	0.940710i	$-0.389839\pi$
$139$	7.99852			0.678426			0.339213	+	0.940710i	$0.389839\pi$
$140$	0.552141	−	0.275160i	0.0466645	−	0.0232553i
$141$	−1.55844			−0.131244
$142$	−2.10553	−	3.64689i	−0.176692	−	0.306040i
$143$	−0.609865	+	1.05632i	−0.0509995	+	0.0883338i
$144$	1.24469	−	2.15586i	0.103724	−	0.179655i
$145$	0.116584	+	0.201930i	0.00968180	+	0.0167694i
$146$	5.84298			0.483569
$147$	−1.95276	−	4.60513i	−0.161061	−	0.379825i
$148$	0.637171			0.0523752
$149$	−3.90799	−	6.76883i	−0.320155	−	0.554524i	0.660365	−	0.750945i	$-0.270402\pi$
$149$	−3.90799	−	6.76883i	−0.320155	−	0.554524i	−0.980520	+	0.196421i	$0.937068\pi$
$150$	−1.76702	+	3.06057i	−0.144277	+	0.249895i
$151$	8.10878	−	14.0448i	0.659883	−	1.14295i	−0.320763	−	0.947160i	$-0.603939\pi$
$151$	8.10878	−	14.0448i	0.659883	−	1.14295i	0.980646	−	0.195791i	$-0.0627274\pi$
$152$	−3.33870	−	5.78280i	−0.270804	−	0.469047i
$153$	−1.51711			−0.122651
$154$	0.694741	−	0.346225i	0.0559838	−	0.0278996i
$155$	−0.315186			−0.0253163
$156$	1.48539	+	2.57278i	0.118927	+	0.205987i
$157$	11.8227	−	20.4776i	0.943556	−	1.63429i	0.184940	−	0.982750i	$-0.440791\pi$
$157$	11.8227	−	20.4776i	0.943556	−	1.63429i	0.758616	−	0.651538i	$-0.225876\pi$
$158$	−1.05339	+	1.82452i	−0.0838032	+	0.145151i
$159$	4.28468	+	7.42129i	0.339797	+	0.588546i
$160$	0.233169			0.0184336
$161$	3.28194	+	2.17314i	0.258653	+	0.171267i
$162$	4.66513			0.366527
$163$	6.80624	+	11.7888i	0.533106	+	0.923367i	0.999252	+	0.0386591i	$0.0123086\pi$
$163$	6.80624	+	11.7888i	0.533106	+	0.923367i	−0.466146	+	0.884708i	$0.654358\pi$
$164$	−1.65802	+	2.87178i	−0.129470	+	0.224248i
$165$	0.0244418	−	0.0423344i	0.00190279	−	0.00329573i
$166$	−3.36810	−	5.83373i	−0.261415	−	0.452785i
$167$	−3.59710			−0.278352			−0.139176	−	0.990268i	$-0.544445\pi$
$167$	−3.59710			−0.278352			−0.139176	+	0.990268i	$0.544445\pi$
$168$	0.115767	−	1.88705i	0.00893159	−	0.145589i
$169$	4.28394			0.329534
$170$	−0.0710506	−	0.123063i	−0.00544933	−	0.00943851i
$171$	8.31128	−	14.3956i	0.635580	−	1.10086i
$172$	1.64751	−	2.85357i	0.125622	−	0.217583i
$173$	−6.19782	−	10.7349i	−0.471212	−	0.816162i	0.528246	−	0.849091i	$-0.322850\pi$
$173$	−6.19782	−	10.7349i	−0.471212	−	0.816162i	−0.999458	+	0.0329288i	$0.989517\pi$
$174$	0.714579			0.0541721
$175$	0.801226	−	13.0604i	0.0605670	−	0.987270i
$176$	0.293388			0.0221150
$177$	1.53675	+	2.66173i	0.115509	+	0.200068i
$178$	6.31233	−	10.9333i	0.473129	−	0.819484i
$179$	−4.79172	+	8.29950i	−0.358150	+	0.620334i	−0.987652	−	0.156665i	$-0.949926\pi$
$179$	−4.79172	+	8.29950i	−0.358150	+	0.620334i	0.629502	+	0.776999i	$0.283259\pi$
$180$	0.290222	+	0.502680i	0.0216319	+	0.0374675i
$181$	0.148655			0.0110495			0.00552473	−	0.999985i	$-0.498241\pi$
$181$	0.148655			0.0110495			0.00552473	+	0.999985i	$0.498241\pi$
$182$	−9.17115	−	6.07269i	−0.679811	−	0.450138i
$183$	−2.60680			−0.192700
$184$	0.743871	+	1.28842i	0.0548389	+	0.0949837i
$185$	−0.0742842	+	0.128664i	−0.00546148	+	0.00945956i
$186$	−0.482966	+	0.836522i	−0.0354128	+	0.0613367i
$187$	−0.0894005	−	0.154846i	−0.00653761	−	0.0113235i
$188$	2.18092			0.159060
$189$	9.28867	−	4.62902i	0.675651	−	0.336711i
$190$	1.55696			0.112954
$191$	−5.14154	−	8.90541i	−0.372029	−	0.644373i	0.617849	−	0.786297i	$-0.288004\pi$
$191$	−5.14154	−	8.90541i	−0.372029	−	0.644373i	−0.989878	+	0.141924i	$0.954671\pi$
$192$	0.357289	−	0.618843i	0.0257851	−	0.0446612i
$193$	−6.23407	+	10.7977i	−0.448738	+	0.777237i	−0.998304	−	0.0582133i	$-0.981460\pi$
$193$	−6.23407	+	10.7977i	−0.448738	+	0.777237i	0.549566	+	0.835450i	$0.314793\pi$
$194$	−2.85249	−	4.94065i	−0.204797	−	0.354718i
$195$	−0.692694			−0.0496049
$196$	2.73274	+	6.44454i	0.195196	+	0.460325i
$197$	−19.0312			−1.35591			−0.677957	−	0.735101i	$-0.737135\pi$
$197$	−19.0312			−1.35591			−0.677957	+	0.735101i	$0.737135\pi$
$198$	0.365177	+	0.632505i	0.0259520	+	0.0449502i
$199$	5.30417	−	9.18709i	0.376003	−	0.651256i	−0.614474	−	0.788937i	$-0.710632\pi$
$199$	5.30417	−	9.18709i	0.376003	−	0.651256i	0.990477	+	0.137681i	$0.0439650\pi$
$200$	2.47282	−	4.28304i	0.174855	−	0.302857i
$201$	1.77090	+	3.06729i	0.124910	+	0.216350i
$202$	15.7339			1.10703
$203$	−2.36799	+	1.18009i	−0.166200	+	0.0828262i
$204$	−0.435489			−0.0304903
$205$	−0.386599	−	0.669609i	−0.0270012	−	0.0467675i
$206$	2.44775	−	4.23962i	0.170543	−	0.295389i
$207$	−1.85178	+	3.20737i	−0.128707	+	0.222928i
$208$	−2.07870	−	3.60041i	−0.144132	−	0.249644i
$209$	1.95907			0.135512
$210$	0.367555	+	0.243377i	0.0253637	+	0.0167946i
$211$	−8.69020			−0.598258			−0.299129	−	0.954213i	$-0.596696\pi$
$211$	−8.69020			−0.598258			−0.299129	+	0.954213i	$0.596696\pi$
$212$	−5.99610	−	10.3855i	−0.411814	−	0.713282i
$213$	1.50457	−	2.60599i	0.103091	−	0.178559i
$214$	−5.61573	+	9.72674i	−0.383884	+	0.664906i
$215$	0.384148	+	0.665364i	0.0261987	+	0.0453774i
$216$	3.92259			0.266899
$217$	0.218993	−	3.56968i	0.0148662	−	0.242326i
$218$	15.1865			1.02856
$219$	2.08764	+	3.61589i	0.141069	+	0.244339i
$220$	−0.0342045	+	0.0592439i	−0.00230606	+	0.00399422i
$221$	−1.26683	+	2.19422i	−0.0852163	+	0.147599i
$222$	0.227655	+	0.394309i	0.0152792	+	0.0264643i
$223$	9.99383			0.669236			0.334618	−	0.942354i	$-0.391393\pi$
$223$	9.99383			0.669236			0.334618	+	0.942354i	$0.391393\pi$
$224$	−0.162007	+	2.64079i	−0.0108245	+	0.176445i
$225$	12.3115			0.820770
$226$	5.14880	+	8.91799i	0.342493	+	0.593216i
$227$	12.6545	−	21.9183i	0.839910	−	1.45477i	−0.0500595	−	0.998746i	$-0.515941\pi$
$227$	12.6545	−	21.9183i	0.839910	−	1.45477i	0.889969	−	0.456020i	$-0.150726\pi$
$228$	2.38576	−	4.13226i	0.158001	−	0.273666i
$229$	−9.23923	−	16.0028i	−0.610545	−	1.05750i	−0.991149	−	0.132757i	$-0.957617\pi$
$229$	−9.23923	−	16.0028i	−0.610545	−	1.05750i	0.380603	−	0.924738i	$-0.375716\pi$
$230$	−0.346895			−0.0228736
$231$	0.462482	+	0.306233i	0.0304291	+	0.0201487i
$232$	−1.00000			−0.0656532
$233$	4.67954	+	8.10520i	0.306567	+	0.530989i	0.977609	−	0.210430i	$-0.0674864\pi$
$233$	4.67954	+	8.10520i	0.306567	+	0.530989i	−0.671042	+	0.741419i	$0.734153\pi$
$234$	5.17466	−	8.96278i	0.338278	−	0.585915i
$235$	−0.254261	+	0.440392i	−0.0165861	+	0.0287280i
$236$	−2.15057	−	3.72489i	−0.139990	−	0.242470i
$237$	−1.50546			−0.0977901
$238$	1.44314	−	0.719189i	0.0935447	−	0.0466181i
$239$	−17.5424			−1.13473			−0.567363	−	0.823468i	$-0.692036\pi$
$239$	−17.5424			−1.13473			−0.567363	+	0.823468i	$0.692036\pi$
$240$	0.0833087	+	0.144295i	0.00537755	+	0.00931419i
$241$	−1.52113	+	2.63467i	−0.0979845	+	0.169714i	−0.910850	−	0.412737i	$-0.864573\pi$
$241$	−1.52113	+	2.63467i	−0.0979845	+	0.169714i	0.812866	+	0.582451i	$0.197906\pi$
$242$	5.45696	−	9.45173i	0.350787	−	0.607581i
$243$	7.55069	+	13.0782i	0.484377	+	0.838966i
$244$	3.64803			0.233541
$245$	−1.61994	−	0.199511i	−0.103494	−	0.0127463i
$246$	−2.36958			−0.151079
$247$	−13.8803	−	24.0414i	−0.883182	−	1.52972i
$248$	0.675875	−	1.17065i	0.0429181	−	0.0743363i
$249$	2.40677	−	4.16866i	0.152523	−	0.264178i
$250$	1.15950	+	2.00832i	0.0733335	+	0.127017i
$251$	−17.2275			−1.08739			−0.543694	−	0.839283i	$-0.682975\pi$
$251$	−17.2275			−1.08739			−0.543694	+	0.839283i	$0.682975\pi$
$252$	−5.89482	+	2.93769i	−0.371339	+	0.185057i
$253$	−0.436486			−0.0274416
$254$	7.65267	+	13.2548i	0.480172	+	0.831681i
$255$	0.0507712	−	0.0879383i	0.00317942	−	0.00550691i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.3227	−	17.8795i	−0.643913	−	1.11529i	−0.984551	−	0.175096i	$-0.943976\pi$
$257$	−10.3227	−	17.8795i	−0.643913	−	1.11529i	0.340638	−	0.940195i	$-0.389357\pi$
$258$	2.35455			0.146588
$259$	−1.40559	−	0.930713i	−0.0873391	−	0.0578317i
$260$	0.969374			0.0601180
$261$	−1.24469	−	2.15586i	−0.0770443	−	0.133445i
$262$	−6.10878	+	10.5807i	−0.377401	+	0.653678i
$263$	8.28531	−	14.3506i	0.510894	−	0.884895i	−0.489026	−	0.872269i	$-0.662648\pi$
$263$	8.28531	−	14.3506i	0.510894	−	0.884895i	0.999920	−	0.0126254i	$-0.00401891\pi$
$264$	0.104824	+	0.181561i	0.00645150	+	0.0111743i
$265$	2.79620			0.171769
$266$	−1.08178	+	17.6336i	−0.0663285	+	1.08118i
$267$	9.02132			0.552096
$268$	−2.47824	−	4.29245i	−0.151383	−	0.262203i
$269$	1.31413	−	2.27614i	0.0801239	−	0.138779i	−0.823179	−	0.567782i	$-0.807802\pi$
$269$	1.31413	−	2.27614i	0.0801239	−	0.138779i	0.903303	+	0.429003i	$0.141135\pi$
$270$	−0.457313	+	0.792089i	−0.0278312	+	0.0482050i
$271$	6.31120	+	10.9313i	0.383378	+	0.664030i	0.991543	−	0.129781i	$-0.0414274\pi$
$271$	6.31120	+	10.9313i	0.383378	+	0.664030i	−0.608165	+	0.793811i	$0.708094\pi$
$272$	0.609435			0.0369524
$273$	0.481288	−	7.84522i	0.0291289	−	0.474814i
$274$	17.8291			1.07710
$275$	0.725495	+	1.25659i	0.0437490	+	0.0757755i
$276$	−0.531554	+	0.920679i	−0.0319958	+	0.0554184i
$277$	−9.72977	+	16.8525i	−0.584605	+	1.01257i	0.410319	+	0.911942i	$0.365417\pi$
$277$	−9.72977	+	16.8525i	−0.584605	+	1.01257i	−0.994924	+	0.100624i	$0.967916\pi$
$278$	−3.99926	−	6.92692i	−0.239860	−	0.415449i
$279$	3.36502			0.201458
$280$	−0.514366	−	0.340588i	−0.0307393	−	0.0203540i
$281$	15.9906			0.953917			0.476958	−	0.878926i	$-0.341739\pi$
$281$	15.9906			0.953917			0.476958	+	0.878926i	$0.341739\pi$
$282$	0.779218	+	1.34965i	0.0464018	+	0.0803702i
$283$	−13.9913	+	24.2337i	−0.831699	+	1.44054i	0.0649910	+	0.997886i	$0.479298\pi$
$283$	−13.9913	+	24.2337i	−0.831699	+	1.44054i	−0.896690	+	0.442659i	$0.854035\pi$
$284$	−2.10553	+	3.64689i	−0.124940	+	0.216403i
$285$	0.556285	+	0.963514i	0.0329515	+	0.0570737i
$286$	1.21973			0.0721242
$287$	7.85237	−	3.91324i	0.463511	−	0.230991i
$288$	−2.48938			−0.146688
$289$	8.31429	+	14.4008i	0.489076	+	0.847105i
$290$	0.116584	−	0.201930i	0.00684607	−	0.0118577i
$291$	2.03833	−	3.53049i	0.119489	−	0.206961i
$292$	−2.92149	−	5.06017i	−0.170967	−	0.296124i
$293$	20.6845			1.20840			0.604202	−	0.796832i	$-0.293492\pi$
$293$	20.6845			1.20840			0.604202	+	0.796832i	$0.293492\pi$
$294$	−3.01178	+	3.99370i	−0.175651	+	0.232918i
$295$	1.00289			0.0583905
$296$	−0.318586	−	0.551807i	−0.0185174	−	0.0320731i
$297$	−0.575421	+	0.996659i	−0.0333893	+	0.0578320i
$298$	−3.90799	+	6.76883i	−0.226384	+	0.392108i
$299$	3.09257	+	5.35648i	0.178848	+	0.309773i
$300$	3.53404			0.204038
$301$	−7.80259	+	3.88843i	−0.449734	+	0.224125i
$302$	−16.2176			−0.933215
$303$	5.62154	+	9.73680i	0.322949	+	0.559365i
$304$	−3.33870	+	5.78280i	−0.191488	+	0.331666i
$305$	−0.425303	+	0.736646i	−0.0243528	+	0.0421802i
$306$	0.758557	+	1.31386i	0.0433638	+	0.0751083i
$307$	−28.6540			−1.63537			−0.817686	−	0.575664i	$-0.804744\pi$
$307$	−28.6540			−1.63537			−0.817686	+	0.575664i	$0.804744\pi$
$308$	−0.647210	−	0.428551i	−0.0368782	−	0.0244189i
$309$	3.49822			0.199007
$310$	0.157593	+	0.272959i	0.00895067	+	0.0155030i
$311$	−5.23235	+	9.06270i	−0.296699	+	0.513898i	−0.975379	−	0.220536i	$-0.929219\pi$
$311$	−5.23235	+	9.06270i	−0.296699	+	0.513898i	0.678679	+	0.734435i	$0.262553\pi$
$312$	1.48539	−	2.57278i	0.0840939	−	0.145655i
$313$	15.7086	+	27.2081i	0.887901	+	1.53789i	0.842352	+	0.538928i	$0.181171\pi$
$313$	15.7086	+	27.2081i	0.887901	+	1.53789i	0.0455495	+	0.998962i	$0.485496\pi$
$314$	−23.6455			−1.33439
$315$	0.0940360	−	1.53283i	0.00529833	−	0.0863652i
$316$	2.10678			0.118516
$317$	−6.37389	−	11.0399i	−0.357993	−	0.620062i	0.629632	−	0.776893i	$-0.283206\pi$
$317$	−6.37389	−	11.0399i	−0.357993	−	0.620062i	−0.987625	+	0.156831i	$0.949872\pi$
$318$	4.28468	−	7.42129i	0.240273	−	0.416165i
$319$	0.146694	−	0.254082i	0.00821329	−	0.0142258i
$320$	−0.116584	−	0.201930i	−0.00651726	−	0.0112882i
$321$	−8.02577			−0.447955
$322$	0.241024	−	3.92881i	0.0134318	−	0.218944i
$323$	4.06944			0.226430
$324$	−2.33257	−	4.04012i	−0.129587	−	0.224451i
$325$	10.2805	−	17.8063i	0.570258	−	0.987716i
$326$	6.80624	−	11.7888i	0.376963	−	0.652919i
$327$	5.42599	+	9.39809i	0.300058	+	0.519716i
$328$	3.31605			0.183098
$329$	−4.81107	−	3.18565i	−0.265243	−	0.175631i
$330$	−0.0488836			−0.00269095
$331$	5.13096	+	8.88709i	0.282023	+	0.488479i	0.971883	−	0.235465i	$-0.0756612\pi$
$331$	5.13096	+	8.88709i	0.282023	+	0.488479i	−0.689860	+	0.723943i	$0.742328\pi$
$332$	−3.36810	+	5.83373i	−0.184849	+	0.320167i
$333$	0.793080	−	1.37365i	0.0434605	−	0.0752758i
$334$	1.79855	+	3.11518i	0.0984123	+	0.170455i
$335$	1.15570			0.0631425
$336$	−1.69212	+	0.843268i	−0.0923125	+	0.0460040i
$337$	−26.9868			−1.47007			−0.735033	−	0.678031i	$-0.762833\pi$
$337$	−26.9868			−1.47007			−0.735033	+	0.678031i	$0.762833\pi$
$338$	−2.14197	−	3.71001i	−0.116508	−	0.201798i
$339$	−3.67923	+	6.37260i	−0.199828	+	0.346112i
$340$	−0.0710506	+	0.123063i	−0.00385326	+	0.00667404i
$341$	0.198294	+	0.343455i	0.0107382	+	0.0185991i
$342$	−16.6226			−0.898845
$343$	3.38514	−	18.2083i	0.182780	−	0.983154i
$344$	−3.29502			−0.177656
$345$	−0.123942	−	0.214674i	−0.00667280	−	0.0115576i
$346$	−6.19782	+	10.7349i	−0.333197	+	0.577114i
$347$	−0.0149934	+	0.0259694i	−0.000804890	+	0.00139411i	−0.866428	−	0.499303i	$-0.833590\pi$
$347$	−0.0149934	+	0.0259694i	−0.000804890	+	0.00139411i	0.865623	+	0.500697i	$0.166923\pi$
$348$	−0.357289	−	0.618843i	−0.0191527	−	0.0331735i
$349$	6.30027			0.337246			0.168623	−	0.985681i	$-0.446068\pi$
$349$	6.30027			0.337246			0.168623	+	0.985681i	$0.446068\pi$
$350$	−11.7112	+	5.83630i	−0.625991	+	0.311963i
$351$	16.3078			0.870444
$352$	−0.146694	−	0.254082i	−0.00781882	−	0.0135426i
$353$	−13.8172	+	23.9321i	−0.735415	+	1.27378i	0.219126	+	0.975696i	$0.429679\pi$
$353$	−13.8172	+	23.9321i	−0.735415	+	1.27378i	−0.954541	+	0.298079i	$0.903654\pi$
$354$	1.53675	−	2.66173i	0.0816773	−	0.141469i
$355$	−0.490944	−	0.850340i	−0.0260566	−	0.0451313i
$356$	−12.6247			−0.669106
$357$	0.960683	+	0.636117i	0.0508447	+	0.0336669i
$358$	9.58344			0.506501
$359$	9.23986	+	16.0039i	0.487661	+	0.844654i	0.999899	−	0.0141898i	$-0.00451691\pi$
$359$	9.23986	+	16.0039i	0.487661	+	0.844654i	−0.512238	+	0.858843i	$0.671184\pi$
$360$	0.290222	−	0.502680i	0.0152961	−	0.0264936i
$361$	−12.7938	+	22.1596i	−0.673359	+	1.16629i
$362$	−0.0743276	−	0.128739i	−0.00390657	−	0.00676638i
$363$	7.79886			0.409334
$364$	−0.673527	+	10.9788i	−0.0353024	+	0.575445i
$365$	1.36240			0.0713113
$366$	1.30340	+	2.25756i	0.0681299	+	0.118004i
$367$	8.86676	−	15.3577i	0.462841	−	0.801665i	−0.536260	−	0.844053i	$-0.680163\pi$
$367$	8.86676	−	15.3577i	0.462841	−	0.801665i	0.999101	+	0.0423883i	$0.0134967\pi$
$368$	0.743871	−	1.28842i	0.0387770	−	0.0671637i
$369$	4.12745	+	7.14895i	0.214866	+	0.372159i
$370$	0.148568			0.00772370
$371$	−1.94282	+	31.6688i	−0.100866	+	1.64416i
$372$	0.965932			0.0500812
$373$	−7.11961	−	12.3315i	−0.368639	−	0.638502i	0.620714	−	0.784037i	$-0.286843\pi$
$373$	−7.11961	−	12.3315i	−0.368639	−	0.638502i	−0.989353	+	0.145535i	$0.953510\pi$
$374$	−0.0894005	+	0.154846i	−0.00462279	+	0.00800691i
$375$	−0.828558	+	1.43510i	−0.0427865	+	0.0741084i
$376$	−1.09046	−	1.88873i	−0.0562361	−	0.0974037i
$377$	−4.15740			−0.214117
$378$	−8.65318	−	5.72971i	−0.445072	−	0.294705i
$379$	33.9879			1.74584			0.872920	−	0.487863i	$-0.162224\pi$
$379$	33.9879			1.74584			0.872920	+	0.487863i	$0.162224\pi$
$380$	−0.778480	−	1.34837i	−0.0399352	−	0.0691698i
$381$	−5.46844	+	9.47161i	−0.280157	+	0.485246i
$382$	−5.14154	+	8.90541i	−0.263064	+	0.455641i
$383$	8.54059	+	14.7927i	0.436404	+	0.755873i	0.997409	−	0.0719387i	$-0.0229186\pi$
$383$	8.54059	+	14.7927i	0.436404	+	0.755873i	−0.561005	+	0.827812i	$0.689585\pi$
$384$	−0.714579			−0.0364657
$385$	0.161992	−	0.0807288i	0.00825586	−	0.00411432i
$386$	12.4681			0.634611
$387$	−4.10128	−	7.10362i	−0.208480	−	0.361097i
$388$	−2.85249	+	4.94065i	−0.144813	+	0.250824i
$389$	5.65882	−	9.80136i	0.286913	−	0.496949i	−0.686158	−	0.727453i	$-0.740704\pi$
$389$	5.65882	−	9.80136i	0.286913	−	0.496949i	0.973071	+	0.230504i	$0.0740375\pi$
$390$	0.346347	+	0.599891i	0.0175380	+	0.0303767i
$391$	−0.906682			−0.0458529
$392$	4.21477	−	5.58889i	0.212878	−	0.282282i
$393$	−8.73040			−0.440391
$394$	9.51558	+	16.4815i	0.479388	+	0.830325i
$395$	−0.245617	+	0.425422i	−0.0123584	+	0.0214053i
$396$	0.365177	−	0.632505i	0.0183508	−	0.0317846i
$397$	−5.12573	−	8.87803i	−0.257253	−	0.445575i	0.708252	−	0.705960i	$-0.249484\pi$
$397$	−5.12573	−	8.87803i	−0.257253	−	0.445575i	−0.965505	+	0.260384i	$0.916151\pi$
$398$	−10.6083			−0.531748
$399$	−11.2989	+	5.63084i	−0.565654	+	0.281894i
$400$	−4.94563			−0.247282
$401$	8.80508	+	15.2509i	0.439705	+	0.761591i	0.997667	−	0.0682755i	$-0.0217497\pi$
$401$	8.80508	+	15.2509i	0.439705	+	0.761591i	−0.557962	+	0.829867i	$0.688416\pi$
$402$	1.77090	−	3.06729i	0.0883245	−	0.152983i
$403$	2.80988	−	4.86686i	0.139970	−	0.242435i
$404$	−7.86693	−	13.6259i	−0.391395	−	0.677915i
$405$	1.08776			0.0540513
$406$	2.20598	+	1.46070i	0.109481	+	0.0724931i
$407$	0.186939			0.00926620
$408$	0.217745	+	0.377145i	0.0107800	+	0.0186714i
$409$	19.4479	−	33.6848i	0.961639	−	1.66561i	0.243254	−	0.969963i	$-0.421785\pi$
$409$	19.4479	−	33.6848i	0.961639	−	1.66561i	0.718386	−	0.695645i	$-0.244881\pi$
$410$	−0.386599	+	0.669609i	−0.0190928	+	0.0330696i
$411$	6.37015	+	11.0334i	0.314216	+	0.544239i
$412$	−4.89549			−0.241184
$413$	−0.696813	+	11.3584i	−0.0342879	+	0.558909i
$414$	3.70355			0.182020
$415$	−0.785336	−	1.36024i	−0.0385506	−	0.0667716i
$416$	−2.07870	+	3.60041i	−0.101917	+	0.176525i
$417$	2.85779	−	4.94983i	0.139946	−	0.242394i
$418$	−0.979535	−	1.69660i	−0.0479106	−	0.0829836i
$419$	−12.6437			−0.617683			−0.308842	−	0.951113i	$-0.599941\pi$
$419$	−12.6437			−0.617683			−0.308842	+	0.951113i	$0.599941\pi$
$420$	0.0269932	−	0.440001i	0.00131713	−	0.0214698i
$421$	−10.7981			−0.526267			−0.263133	−	0.964759i	$-0.584756\pi$
$421$	−10.7981			−0.526267			−0.263133	+	0.964759i	$0.584756\pi$
$422$	4.34510	+	7.52593i	0.211516	+	0.366357i
$423$	2.71456	−	4.70176i	0.131986	−	0.228607i
$424$	−5.99610	+	10.3855i	−0.291196	+	0.504367i
$425$	1.50702	+	2.61024i	0.0731012	+	0.126615i
$426$	−3.00914			−0.145793
$427$	−8.04749	−	5.32866i	−0.389445	−	0.257872i
$428$	11.2315			0.542894
$429$	0.435797	+	0.754822i	0.0210405	+	0.0364432i
$430$	0.384148	−	0.665364i	0.0185253	−	0.0320867i
$431$	18.0906	−	31.3339i	0.871394	−	1.50930i	0.0108397	−	0.999941i	$-0.496550\pi$
$431$	18.0906	−	31.3339i	0.871394	−	1.50930i	0.860555	−	0.509358i	$-0.170117\pi$
$432$	−1.96130	−	3.39706i	−0.0943629	−	0.163441i
$433$	10.6350			0.511084			0.255542	−	0.966798i	$-0.417746\pi$
$433$	10.6350			0.511084			0.255542	+	0.966798i	$0.417746\pi$
$434$	−3.20093	+	1.59519i	−0.153650	+	0.0765715i
$435$	0.166617			0.00798869
$436$	−7.59327	−	13.1519i	−0.363652	−	0.629863i
$437$	4.96712	−	8.60331i	0.237610	−	0.411552i
$438$	2.08764	−	3.61589i	0.0997511	−	0.172774i
$439$	1.48753	+	2.57648i	0.0709961	+	0.122969i	0.899338	−	0.437254i	$-0.144049\pi$
$439$	1.48753	+	2.57648i	0.0709961	+	0.122969i	−0.828342	+	0.560223i	$0.810716\pi$
$440$	0.0684089			0.00326127
$441$	17.2950	+	2.13004i	0.823570	+	0.101430i
$442$	2.53366			0.120514
$443$	13.9715	+	24.1993i	0.663804	+	1.14974i	0.979608	+	0.200917i	$0.0643923\pi$
$443$	13.9715	+	24.1993i	0.663804	+	1.14974i	−0.315805	+	0.948824i	$0.602274\pi$
$444$	0.227655	−	0.394309i	0.0108040	−	0.0187131i
$445$	1.47184	−	2.54930i	0.0697718	−	0.120848i
$446$	−4.99691	−	8.65491i	−0.236611	−	0.409822i
$447$	−5.58513			−0.264167
$448$	2.36799	−	1.18009i	0.111877	−	0.0557541i
$449$	−0.604431			−0.0285248			−0.0142624	−	0.999898i	$-0.504540\pi$
$449$	−0.604431			−0.0285248			−0.0142624	+	0.999898i	$0.504540\pi$
$450$	−6.15577	−	10.6621i	−0.290186	−	0.502617i
$451$	−0.486444	+	0.842547i	−0.0229058	+	0.0396740i
$452$	5.14880	−	8.91799i	0.242179	−	0.419467i
$453$	−5.79436	−	10.0361i	−0.272243	−	0.471538i
$454$	−25.3090			−1.18781
$455$	−2.13843	−	1.41596i	−0.100251	−	0.0663813i
$456$	−4.77153			−0.223447
$457$	3.55156	+	6.15148i	0.166135	+	0.287754i	0.937058	−	0.349175i	$-0.113538\pi$
$457$	3.55156	+	6.15148i	0.166135	+	0.287754i	−0.770923	+	0.636929i	$0.780205\pi$
$458$	−9.23923	+	16.0028i	−0.431721	+	0.747762i
$459$	−1.19528	+	2.07029i	−0.0557910	+	0.0966329i
$460$	0.173447	+	0.300420i	0.00808703	+	0.0140071i
$461$	3.81028			0.177462			0.0887312	−	0.996056i	$-0.471719\pi$
$461$	3.81028			0.177462			0.0887312	+	0.996056i	$0.471719\pi$
$462$	0.0339646	−	0.553638i	0.00158018	−	0.0257576i
$463$	−3.42327			−0.159093			−0.0795464	−	0.996831i	$-0.525347\pi$
$463$	−3.42327			−0.159093			−0.0795464	+	0.996831i	$0.525347\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	−0.112613	+	0.195051i	−0.00522228	+	0.00904525i
$466$	4.67954	−	8.10520i	0.216775	−	0.375466i
$467$	−11.4351	−	19.8061i	−0.529151	−	0.916517i	−0.999422	−	0.0339945i	$-0.989177\pi$
$467$	−11.4351	−	19.8061i	−0.529151	−	0.916517i	0.470271	−	0.882522i	$-0.344156\pi$
$468$	−10.3493			−0.478398
$469$	−0.802985	+	13.0890i	−0.0370784	+	0.604395i
$470$	0.508521			0.0234563
$471$	−8.44827	−	14.6328i	−0.389276	−	0.674245i
$472$	−2.15057	+	3.72489i	−0.0989878	+	0.171452i
$473$	0.483360	−	0.837205i	0.0222249	−	0.0384947i
$474$	0.752730	+	1.30377i	0.0345740	+	0.0598840i
$475$	−33.0240			−1.51524
$476$	−1.34440	−	0.890199i	−0.0616207	−	0.0408022i
$477$	−29.8531			−1.36688
$478$	8.77121	+	15.1922i	0.401186	+	0.694874i
$479$	2.28610	−	3.95963i	0.104454	−	0.180920i	−0.809061	−	0.587725i	$-0.800024\pi$
$479$	2.28610	−	3.95963i	0.104454	−	0.180920i	0.913515	+	0.406805i	$0.133357\pi$
$480$	0.0833087	−	0.144295i	0.00380250	−	0.00658613i
$481$	−1.32449	−	2.29408i	−0.0603914	−	0.104601i
$482$	3.04226			0.138571
$483$	2.51743	−	1.25457i	0.114547	−	0.0570847i
$484$	−10.9139			−0.496087
$485$	−0.665111	−	1.15201i	−0.0302011	−	0.0523099i
$486$	7.55069	−	13.0782i	0.342506	−	0.593238i
$487$	−10.8284	+	18.7554i	−0.490683	+	0.849889i	−0.999942	−	0.0107247i	$-0.996586\pi$
$487$	−10.8284	+	18.7554i	−0.490683	+	0.849889i	0.509259	+	0.860613i	$0.329919\pi$
$488$	−1.82401	−	3.15928i	−0.0825692	−	0.143014i
$489$	9.72719			0.439879
$490$	0.637189	+	1.50267i	0.0287853	+	0.0678835i
$491$	32.0537			1.44656			0.723281	−	0.690554i	$-0.242633\pi$
$491$	32.0537			1.44656			0.723281	+	0.690554i	$0.242633\pi$
$492$	1.18479	+	2.05211i	0.0534144	+	0.0925164i
$493$	0.304717	−	0.527786i	0.0137238	−	0.0237703i
$494$	−13.8803	+	24.0414i	−0.624504	+	1.08167i
$495$	0.0851478	+	0.147480i	0.00382711	+	0.00662875i
$496$	−1.35175			−0.0606954
$497$	9.97176	−	4.96944i	0.447295	−	0.222910i
$498$	−4.81355			−0.215700
$499$	−12.3057	−	21.3140i	−0.550877	−	0.954147i	−0.998212	−	0.0597801i	$-0.980960\pi$
$499$	−12.3057	−	21.3140i	−0.550877	−	0.954147i	0.447335	−	0.894367i	$-0.352373\pi$
$500$	1.15950	−	2.00832i	0.0518546	−	0.0898149i
$501$	−1.28521	+	2.22604i	−0.0574188	+	0.0994523i
$502$	8.61374	+	14.9194i	0.384450	+	0.665887i
$503$	−35.0600			−1.56325			−0.781623	−	0.623751i	$-0.785608\pi$
$503$	−35.0600			−1.56325			−0.781623	+	0.623751i	$0.785608\pi$
$504$	5.49153	+	3.63622i	0.244612	+	0.161970i
$505$	3.66864			0.163253
$506$	0.218243	+	0.378008i	0.00970208	+	0.0168045i
$507$	1.53061	−	2.65109i	0.0679767	−	0.117739i
$508$	7.65267	−	13.2548i	0.339533	−	0.588088i
$509$	15.8796	+	27.5043i	0.703851	+	1.21910i	0.967105	+	0.254378i	$0.0818708\pi$
$509$	15.8796	+	27.5043i	0.703851	+	1.21910i	−0.263254	+	0.964726i	$0.584796\pi$
$510$	−0.101542			−0.00449638
$511$	−0.946604	+	15.4301i	−0.0418753	+	0.682586i
$512$	1.00000			0.0441942
$513$	−13.0964	−	22.6836i	−0.578218	−	1.00150i
$514$	−10.3227	+	17.8795i	−0.455315	+	0.788630i
$515$	0.570738	−	0.988547i	0.0251497	−	0.0435606i
$516$	−1.17728	−	2.03910i	−0.0518267	−	0.0897665i
$517$	0.639855			0.0281408
$518$	−0.103226	+	1.68263i	−0.00453550	+	0.0739307i
$519$	−8.85766			−0.388808
$520$	−0.484687	−	0.839503i	−0.0212549	−	0.0368146i
$521$	7.08405	−	12.2699i	0.310358	−	0.537556i	−0.668082	−	0.744088i	$-0.732884\pi$
$521$	7.08405	−	12.2699i	0.310358	−	0.537556i	0.978440	+	0.206532i	$0.0662178\pi$
$522$	−1.24469	+	2.15586i	−0.0544785	+	0.0943596i
$523$	9.85144	+	17.0632i	0.430774	+	0.746122i	0.996940	−	0.0781692i	$-0.0249075\pi$
$523$	9.85144	+	17.0632i	0.430774	+	0.746122i	−0.566167	+	0.824291i	$0.691574\pi$
$524$	12.2176			0.533726
$525$	−7.79605	−	5.16216i	−0.340247	−	0.225295i
$526$	−16.5706			−0.722513
$527$	0.411902	+	0.713435i	0.0179427	+	0.0310777i
$528$	0.104824	−	0.181561i	0.00456190	−	0.00790144i
$529$	10.3933	−	18.0017i	0.451883	−	0.782685i
$530$	−1.39810	−	2.42158i	−0.0607296	−	0.105187i
$531$	−10.7071			−0.464650
$532$	15.8120	−	7.87994i	0.685538	−	0.341639i
$533$	13.7861			0.597143
$534$	−4.51066	−	7.81269i	−0.195195	−	0.338088i
$535$	−1.30941	+	2.26797i	−0.0566109	+	0.0980529i
$536$	−2.47824	+	4.29245i	−0.107044	+	0.185405i
$537$	3.42406	+	5.93065i	0.147759	+	0.255926i
$538$	−2.62826			−0.113312
$539$	0.801753	+	1.89075i	0.0345339	+	0.0814405i
$540$	0.914626			0.0393592
$541$	6.64270	+	11.5055i	0.285592	+	0.494660i	0.972753	−	0.231846i	$-0.0744765\pi$
$541$	6.64270	+	11.5055i	0.285592	+	0.494660i	−0.687161	+	0.726505i	$0.741143\pi$
$542$	6.31120	−	10.9313i	0.271089	−	0.469540i
$543$	0.0531129	−	0.0919943i	0.00227929	−	0.00394785i
$544$	−0.304717	−	0.527786i	−0.0130647	−	0.0226286i
$545$	3.54103			0.151681
$546$	−7.03480	+	3.50580i	−0.301062	+	0.150034i
$547$	−3.77149			−0.161257			−0.0806287	−	0.996744i	$-0.525693\pi$
$547$	−3.77149			−0.161257			−0.0806287	+	0.996744i	$0.525693\pi$
$548$	−8.91455	−	15.4405i	−0.380811	−	0.659584i
$549$	4.54066	−	7.86465i	0.193791	−	0.335655i
$550$	0.725495	−	1.25659i	0.0309352	−	0.0535814i
$551$	3.33870	+	5.78280i	0.142233	+	0.246355i
$552$	1.06311			0.0452489
$553$	−4.64752	−	3.07736i	−0.197633	−	0.130863i
$554$	19.4595			0.826757
$555$	0.0530819	+	0.0919405i	0.00225320	+	0.00390266i
$556$	−3.99926	+	6.92692i	−0.169606	+	0.293767i
$557$	20.6721	−	35.8052i	0.875907	−	1.51712i	0.0201136	−	0.999798i	$-0.493597\pi$
$557$	20.6721	−	35.8052i	0.875907	−	1.51712i	0.855793	−	0.517318i	$-0.173069\pi$
$558$	−1.68251	−	2.91419i	−0.0712262	−	0.123367i
$559$	−13.6987			−0.579394
$560$	−0.0377749	+	0.615749i	−0.00159628	+	0.0260201i
$561$	−0.127767			−0.00539434
$562$	−7.99528	−	13.8482i	−0.337260	−	0.584152i
$563$	3.31295	−	5.73821i	0.139624	−	0.241837i	−0.787730	−	0.616021i	$-0.788744\pi$
$563$	3.31295	−	5.73821i	0.139624	−	0.241837i	0.927354	+	0.374184i	$0.122077\pi$
$564$	0.779218	−	1.34965i	0.0328110	−	0.0568303i
$565$	1.20054	+	2.07939i	0.0505071	+	0.0874808i
$566$	27.9827			1.17620
$567$	−0.755783	+	12.3196i	−0.0317399	+	0.517375i
$568$	4.21106			0.176692
$569$	6.97747	+	12.0853i	0.292511	+	0.506644i	0.974403	−	0.224809i	$-0.0721759\pi$
$569$	6.97747	+	12.0853i	0.292511	+	0.506644i	−0.681892	+	0.731453i	$0.738843\pi$
$570$	0.556285	−	0.963514i	0.0233002	−	0.0403572i
$571$	1.05581	−	1.82871i	0.0441841	−	0.0765291i	−0.843088	−	0.537776i	$-0.819265\pi$
$571$	1.05581	−	1.82871i	0.0441841	−	0.0765291i	0.887272	+	0.461247i	$0.152598\pi$
$572$	−0.609865	−	1.05632i	−0.0254998	−	0.0441669i
$573$	−7.34807			−0.306970
$574$	−7.31515	−	4.84373i	−0.305328	−	0.202174i
$575$	7.35782			0.306842
$576$	1.24469	+	2.15586i	0.0518620	+	0.0898277i
$577$	−1.39881	+	2.42281i	−0.0582331	+	0.100863i	−0.893672	−	0.448720i	$-0.851880\pi$
$577$	−1.39881	+	2.42281i	−0.0582331	+	0.100863i	0.835439	+	0.549583i	$0.185213\pi$
$578$	8.31429	−	14.4008i	0.345829	−	0.598994i
$579$	4.45473	+	7.71582i	0.185132	+	0.320659i
$580$	−0.233169			−0.00968180
$581$	15.9513	−	7.94934i	0.661771	−	0.329794i
$582$	−4.07666			−0.168983
$583$	−1.75918	−	3.04700i	−0.0728579	−	0.126194i
$584$	−2.92149	+	5.06017i	−0.120892	+	0.209391i
$585$	1.20657	−	2.08984i	0.0498855	−	0.0864042i
$586$	−10.3423	−	17.9133i	−0.427235	−	0.739993i
$587$	6.93586			0.286274			0.143137	−	0.989703i	$-0.454281\pi$
$587$	6.93586			0.286274			0.143137	+	0.989703i	$0.454281\pi$
$588$	4.96454	+	0.611430i	0.204734	+	0.0252150i
$589$	−9.02617			−0.371917
$590$	−0.501445	−	0.868528i	−0.0206441	−	0.0357567i
$591$	−6.79963	+	11.7773i	−0.279700	+	0.484454i
$592$	−0.318586	+	0.551807i	−0.0130938	+	0.0226791i
$593$	−1.69542	−	2.93655i	−0.0696225	−	0.120590i	0.829113	−	0.559082i	$-0.188846\pi$
$593$	−1.69542	−	2.93655i	−0.0696225	−	0.120590i	−0.898735	+	0.438492i	$0.855513\pi$
$594$	1.15084			0.0472196
$595$	0.336494	−	0.167692i	0.0137949	−	0.00687471i
$596$	7.81597			0.320155
$597$	−3.79025	−	6.56490i	−0.155124	−	0.268684i
$598$	3.09257	−	5.35648i	0.126464	−	0.219043i
$599$	15.3624	−	26.6084i	0.627689	−	1.08719i	−0.360325	−	0.932827i	$-0.617334\pi$
$599$	15.3624	−	26.6084i	0.627689	−	1.08719i	0.988014	−	0.154363i	$-0.0493325\pi$
$600$	−1.76702	−	3.06057i	−0.0721384	−	0.124947i
$601$	32.5720			1.32864			0.664320	−	0.747448i	$-0.268721\pi$
$601$	32.5720			1.32864			0.664320	+	0.747448i	$0.268721\pi$
$602$	7.26877	+	4.81303i	0.296253	+	0.196164i
$603$	−12.3386			−0.502465
$604$	8.10878	+	14.0448i	0.329941	+	0.571475i
$605$	1.27239	−	2.20385i	0.0517301	−	0.0895992i
$606$	5.62154	−	9.73680i	0.228360	−	0.395530i
$607$	0.960031	+	1.66282i	0.0389664	+	0.0674919i	0.884851	−	0.465874i	$-0.154260\pi$
$607$	0.960031	+	1.66282i	0.0389664	+	0.0674919i	−0.845884	+	0.533366i	$0.820927\pi$
$608$	6.67740			0.270804
$609$	−0.115767	+	1.88705i	−0.00469110	+	0.0764671i
$610$	0.850606			0.0344400
$611$	−4.53347	−	7.85219i	−0.183404	−	0.317666i
$612$	0.758557	−	1.31386i	0.0306628	−	0.0531096i
$613$	14.4028	−	24.9463i	0.581722	−	1.00757i	−0.413553	−	0.910480i	$-0.635713\pi$
$613$	14.4028	−	24.9463i	0.581722	−	1.00757i	0.995275	−	0.0970922i	$-0.0309542\pi$
$614$	14.3270	+	24.8151i	0.578191	+	1.00146i
$615$	−0.552511			−0.0222794
$616$	−0.0475309	+	0.774776i	−0.00191507	+	0.0312166i
$617$	41.9416			1.68850			0.844252	−	0.535946i	$-0.180045\pi$
$617$	41.9416			1.68850			0.844252	+	0.535946i	$0.180045\pi$
$618$	−1.74911	−	3.02954i	−0.0703595	−	0.121866i
$619$	0.376352	−	0.651862i	0.0151269	−	0.0262005i	−0.858363	−	0.513043i	$-0.828518\pi$
$619$	0.376352	−	0.651862i	0.0151269	−	0.0262005i	0.873490	+	0.486843i	$0.161851\pi$
$620$	0.157593	−	0.272959i	0.00632908	−	0.0109623i
$621$	2.91790	+	5.05396i	0.117091	+	0.202808i
$622$	10.4647			0.419596
$623$	27.8498	+	18.4408i	1.11578	+	0.738815i
$624$	−2.97079			−0.118927
$625$	−12.0937	−	20.9469i	−0.483749	−	0.837878i
$626$	15.7086	−	27.2081i	0.627841	−	1.08745i
$627$	0.699955	−	1.21236i	0.0279535	−	0.0484169i
$628$	11.8227	+	20.4776i	0.471778	+	0.817144i
$629$	0.388314			0.0154831
$630$	−1.37449	+	0.684978i	−0.0547609	+	0.0272902i
$631$	−36.3961			−1.44891			−0.724453	−	0.689325i	$-0.757907\pi$
$631$	−36.3961			−1.44891			−0.724453	+	0.689325i	$0.757907\pi$
$632$	−1.05339	−	1.82452i	−0.0419016	−	0.0725757i
$633$	−3.10492	+	5.37787i	−0.123409	+	0.213751i
$634$	−6.37389	+	11.0399i	−0.253139	+	0.438450i
$635$	1.78436	+	3.09061i	0.0708103	+	0.122647i
$636$	−8.56937			−0.339797
$637$	17.5225	−	23.2352i	0.694265	−	0.920614i
$638$	−0.293388			−0.0116153
$639$	5.24146	+	9.07848i	0.207349	+	0.359139i
$640$	−0.116584	+	0.201930i	−0.00460840	+	0.00798198i
$641$	10.2287	−	17.7167i	0.404010	−	0.699766i	−0.590195	−	0.807260i	$-0.700949\pi$
$641$	10.2287	−	17.7167i	0.404010	−	0.699766i	0.994206	+	0.107494i	$0.0342827\pi$
$642$	4.01289	+	6.95052i	0.158376	+	0.274315i
$643$	−36.0350			−1.42108			−0.710541	−	0.703656i	$-0.751550\pi$
$643$	−36.0350			−1.42108			−0.710541	+	0.703656i	$0.751550\pi$
$644$	−3.52296	+	1.75567i	−0.138824	+	0.0691831i
$645$	0.549008			0.0216172
$646$	−2.03472	−	3.52424i	−0.0800550	−	0.138659i
$647$	−21.3888	+	37.0464i	−0.840879	+	1.45645i	0.0482734	+	0.998834i	$0.484628\pi$
$647$	−21.3888	+	37.0464i	−0.840879	+	1.45645i	−0.889152	+	0.457611i	$0.848705\pi$
$648$	−2.33257	+	4.04012i	−0.0916318	+	0.158711i
$649$	−0.630951	−	1.09284i	−0.0247670	−	0.0428977i
$650$	−20.5610			−0.806467
$651$	−2.13083	−	1.41093i	−0.0835139	−	0.0552988i
$652$	−13.6125			−0.533106
$653$	−14.0161	−	24.2766i	−0.548493	−	0.950017i	−0.998378	−	0.0569310i	$-0.981868\pi$
$653$	−14.0161	−	24.2766i	−0.548493	−	0.950017i	0.449885	−	0.893086i	$-0.351465\pi$
$654$	5.42599	−	9.39809i	0.212173	−	0.367495i
$655$	−1.42437	+	2.46709i	−0.0556549	+	0.0963972i
$656$	−1.65802	−	2.87178i	−0.0647349	−	0.112124i
$657$	−14.5454			−0.567470
$658$	−0.353323	+	5.75933i	−0.0137740	+	0.224522i
$659$	36.2772			1.41316			0.706579	−	0.707634i	$-0.250238\pi$
$659$	36.2772			1.41316			0.706579	+	0.707634i	$0.250238\pi$
$660$	0.0244418	+	0.0423344i	0.000951395	+	0.00164786i
$661$	3.01525	−	5.22256i	0.117279	−	0.203134i	−0.801409	−	0.598116i	$-0.795916\pi$
$661$	3.01525	−	5.22256i	0.117279	−	0.203134i	0.918689	+	0.394983i	$0.129249\pi$
$662$	5.13096	−	8.88709i	0.199421	−	0.345406i
$663$	0.905251	+	1.56794i	0.0351570	+	0.0608938i
$664$	6.73621			0.261415
$665$	−0.252238	+	4.11160i	−0.00978138	+	0.159441i
$666$	−1.58616			−0.0614624
$667$	−0.743871	−	1.28842i	−0.0288028	−	0.0498879i
$668$	1.79855	−	3.11518i	0.0695880	−	0.120530i
$669$	3.57069	−	6.18461i	0.138051	−	0.239111i
$670$	−0.577849	−	1.00086i	−0.0223242	−	0.0386667i
$671$	1.07029			0.0413180
$672$	1.57635	+	1.04378i	0.0608090	+	0.0402648i
$673$	16.7412			0.645327			0.322663	−	0.946514i	$-0.395422\pi$
$673$	16.7412			0.645327			0.322663	+	0.946514i	$0.395422\pi$
$674$	13.4934	+	23.3713i	0.519747	+	0.900228i
$675$	9.69985	−	16.8006i	0.373347	−	0.646657i
$676$	−2.14197	+	3.71001i	−0.0823836	+	0.142693i
$677$	−20.4963	−	35.5007i	−0.787737	−	1.36440i	−0.927350	−	0.374195i	$-0.877919\pi$
$677$	−20.4963	−	35.5007i	−0.787737	−	1.36440i	0.139613	−	0.990206i	$-0.455414\pi$
$678$	7.35845			0.282600
$679$	13.5093	−	6.73239i	0.518441	−	0.258366i
$680$	0.142101			0.00544933
$681$	−9.04265	−	15.6623i	−0.346515	−	0.600182i
$682$	0.198294	−	0.343455i	0.00759306	−	0.0131516i
$683$	17.0734	−	29.5720i	0.653296	−	1.13154i	−0.329022	−	0.944322i	$-0.606719\pi$
$683$	17.0734	−	29.5720i	0.653296	−	1.13154i	0.982318	−	0.187220i	$-0.0599477\pi$
$684$	8.31128	+	14.3956i	0.317790	+	0.550428i
$685$	4.15719			0.158838
$686$	−17.4614	+	6.17252i	−0.666679	+	0.235668i
$687$	−13.2043			−0.503776
$688$	1.64751	+	2.85357i	0.0628108	+	0.108791i
$689$	−24.9281	+	43.1768i	−0.949687	+	1.64491i
$690$	−0.123942	+	0.214674i	−0.00471838	+	0.00817248i
$691$	11.3172	+	19.6019i	0.430525	+	0.745692i	0.996919	−	0.0784434i	$-0.0249950\pi$
$691$	11.3172	+	19.6019i	0.430525	+	0.745692i	−0.566393	+	0.824135i	$0.691662\pi$
$692$	12.3956			0.471212
$693$	−1.72947	+	0.861884i	−0.0656972	+	0.0327403i
$694$	0.0299869			0.00113829
$695$	−0.932502	−	1.61514i	−0.0353718	−	0.0612658i
$696$	−0.357289	+	0.618843i	−0.0135430	+	0.0234572i
$697$	−1.01046	+	1.75016i	−0.0382738	+	0.0662922i
$698$	−3.15014	−	5.45620i	−0.119234	−	0.206520i
$699$	6.68780			0.252956
$700$	10.9100	+	7.22406i	0.412359	+	0.273044i
$701$	−15.1951			−0.573911			−0.286955	−	0.957944i	$-0.592643\pi$
$701$	−15.1951			−0.573911			−0.286955	+	0.957944i	$0.592643\pi$
$702$	−8.15389	−	14.1229i	−0.307749	−	0.533036i
$703$	−2.12732	+	3.68463i	−0.0802335	+	0.138969i
$704$	−0.146694	+	0.254082i	−0.00552874	+	0.00957606i
$705$	0.181689	+	0.314695i	0.00684281	+	0.0118521i
$706$	27.6344			1.04003
$707$	−2.54899	+	41.5498i	−0.0958648	+	1.56264i
$708$	−3.07350			−0.115509
$709$	−4.00781	−	6.94172i	−0.150516	−	0.260702i	0.780901	−	0.624655i	$-0.214760\pi$
$709$	−4.00781	−	6.94172i	−0.150516	−	0.260702i	−0.931417	+	0.363953i	$0.881427\pi$
$710$	−0.490944	+	0.850340i	−0.0184248	+	0.0319127i
$711$	2.62228	−	4.54193i	0.0983433	−	0.170336i
$712$	6.31233	+	10.9333i	0.236565	+	0.409742i
$713$	2.01106			0.0753146
$714$	0.0705523	−	1.15003i	0.00264035	−	0.0430390i
$715$	0.284403			0.0106361
$716$	−4.79172	−	8.29950i	−0.179075	−	0.310167i
$717$	−6.26772	+	10.8560i	−0.234072	+	0.405425i
$718$	9.23986	−	16.0039i	0.344828	−	0.597260i
$719$	−1.08801	−	1.88448i	−0.0405757	−	0.0702793i	0.845024	−	0.534728i	$-0.179586\pi$
$719$	−1.08801	−	1.88448i	−0.0405757	−	0.0702793i	−0.885600	+	0.464449i	$0.846253\pi$
$720$	−0.580445			−0.0216319
$721$	10.7994	+	7.15083i	0.402190	+	0.266311i
$722$	25.5877			0.952274
$723$	1.08697	+	1.88268i	0.0404247	+	0.0700177i
$724$	−0.0743276	+	0.128739i	−0.00276236	+	0.00478455i
$725$	−2.47282	+	4.28304i	−0.0918381	+	0.159068i
$726$	−3.89943	−	6.75401i	−0.144721	−	0.250665i
$727$	−53.7791			−1.99456			−0.997278	−	0.0737366i	$-0.976508\pi$
$727$	−53.7791			−1.99456			−0.997278	+	0.0737366i	$0.976508\pi$
$728$	9.84468	−	4.90611i	0.364868	−	0.181832i
$729$	−3.20426			−0.118676
$730$	−0.681200	−	1.17987i	−0.0252124	−	0.0436691i
$731$	1.00405	−	1.73907i	0.0371362	−	0.0643217i
$732$	1.30340	−	2.25756i	0.0481751	−	0.0834417i
$733$	−13.3872	−	23.1874i	−0.494469	−	0.856445i	0.505511	−	0.862820i	$-0.331304\pi$
$733$	−13.3872	−	23.1874i	−0.494469	−	0.856445i	−0.999980	+	0.00637498i	$0.997971\pi$
$734$	−17.7335			−0.654556
$735$	−0.702254	+	0.931206i	−0.0259030	+	0.0343481i
$736$	−1.48774			−0.0548389
$737$	−0.727088	−	1.25935i	−0.0267826	−	0.0463889i
$738$	4.12745	−	7.14895i	0.151933	−	0.263156i
$739$	−14.6468	+	25.3690i	−0.538791	+	0.933213i	0.460179	+	0.887826i	$0.347785\pi$
$739$	−14.6468	+	25.3690i	−0.538791	+	0.933213i	−0.998969	+	0.0453869i	$0.985548\pi$
$740$	−0.0742842	−	0.128664i	−0.00273074	−	0.00472978i
$741$	−19.8371			−0.728735
$742$	28.3974	−	14.1519i	1.04250	−	0.519532i
$743$	6.53498			0.239745			0.119873	−	0.992789i	$-0.461751\pi$
$743$	6.53498			0.239745			0.119873	+	0.992789i	$0.461751\pi$
$744$	−0.482966	−	0.836522i	−0.0177064	−	0.0306684i
$745$	−0.911220	+	1.57828i	−0.0333845	+	0.0578237i
$746$	−7.11961	+	12.3315i	−0.260667	+	0.451489i
$747$	8.38448	+	14.5223i	0.306772	+	0.531345i
$748$	0.178801			0.00653761
$749$	−24.7765	−	16.4058i	−0.905312	−	0.599453i
$750$	1.65712			0.0605093
$751$	−15.0999	−	26.1537i	−0.551002	−	0.954363i	−0.998203	−	0.0599296i	$-0.980912\pi$
$751$	−15.0999	−	26.1537i	−0.551002	−	0.954363i	0.447201	−	0.894434i	$-0.352421\pi$
$752$	−1.09046	+	1.88873i	−0.0397649	+	0.0688748i
$753$	−6.15519	+	10.6611i	−0.224308	+	0.388512i
$754$	2.07870	+	3.60041i	0.0757017	+	0.131119i
$755$	−3.78142			−0.137620
$756$	−0.635487	+	10.3587i	−0.0231124	+	0.376743i
$757$	−26.5008			−0.963189			−0.481595	−	0.876394i	$-0.659942\pi$
$757$	−26.5008			−0.963189			−0.481595	+	0.876394i	$0.659942\pi$
$758$	−16.9939	−	29.4344i	−0.617248	−	1.06910i
$759$	−0.155952	+	0.270116i	−0.00566069	+	0.00980460i
$760$	−0.778480	+	1.34837i	−0.0282384	+	0.0489104i
$761$	−2.18705	−	3.78808i	−0.0792805	−	0.137318i	0.823659	−	0.567085i	$-0.191929\pi$
$761$	−2.18705	−	3.78808i	−0.0792805	−	0.137318i	−0.902940	+	0.429767i	$0.858596\pi$
$762$	10.9369			0.396201
$763$	−2.46032	+	40.1044i	−0.0890697	+	1.45188i
$764$	10.2831			0.372029
$765$	0.176872	+	0.306351i	0.00639481	+	0.0110761i
$766$	8.54059	−	14.7927i	0.308584	−	0.534483i
$767$	−8.94076	+	15.4858i	−0.322832	+	0.559161i
$768$	0.357289	+	0.618843i	0.0128926	+	0.0223306i
$769$	43.7523			1.57775			0.788874	−	0.614555i	$-0.210665\pi$
$769$	43.7523			1.57775			0.788874	+	0.614555i	$0.210665\pi$
$770$	−0.150909	−	0.0999246i	−0.00543838	−	0.00360103i
$771$	−14.7528			−0.531309
$772$	−6.23407	−	10.7977i	−0.224369	−	0.388618i
$773$	−7.17176	+	12.4219i	−0.257950	+	0.446783i	−0.965693	−	0.259687i	$-0.916380\pi$
$773$	−7.17176	+	12.4219i	−0.257950	+	0.446783i	0.707742	+	0.706471i	$0.249714\pi$
$774$	−4.10128	+	7.10362i	−0.147417	+	0.255334i
$775$	−3.34263	−	5.78960i	−0.120071	−	0.207969i
$776$	5.70498			0.204797
$777$	−1.07817	+	0.537306i	−0.0386791	+	0.0192758i
$778$	−11.3176			−0.405757
$779$	−11.0713	−	19.1760i	−0.396670	−	0.687052i
$780$	0.346347	−	0.599891i	0.0124012	−	0.0214795i
$781$	−0.617738	+	1.06995i	−0.0221044	+	0.0382859i
$782$	0.453341	+	0.785210i	0.0162114	+	0.0280790i
$783$	−3.92259			−0.140182
$784$	−6.94751	−	0.855651i	−0.248125	−	0.0305590i
$785$	−5.51338			−0.196781
$786$	4.36520	+	7.56075i	0.155702	+	0.269683i
$787$	15.8209	−	27.4025i	0.563953	−	0.976794i	−0.433194	−	0.901301i	$-0.642613\pi$
$787$	15.8209	−	27.4025i	0.563953	−	0.976794i	0.997146	−	0.0754936i	$-0.0240532\pi$
$788$	9.51558	−	16.4815i	0.338979	−	0.587128i
$789$	−5.92051	−	10.2546i	−0.210776	−	0.365074i
$790$	0.491235			0.0174773
$791$	−24.3846	+	12.1521i	−0.867018	+	0.432079i
$792$	−0.730354			−0.0259520
$793$	−7.58315	−	13.1344i	−0.269285	−	0.466416i
$794$	−5.12573	+	8.87803i	−0.181905	+	0.315069i
$795$	0.999054	−	1.73041i	0.0354328	−	0.0613714i
$796$	5.30417	+	9.18709i	0.188001	+	0.325628i
$797$	−12.6909			−0.449536			−0.224768	−	0.974412i	$-0.572162\pi$
$797$	−12.6909			−0.449536			−0.224768	+	0.974412i	$0.572162\pi$
$798$	10.5259	+	6.96975i	0.372613	+	0.246726i
$799$	1.32913			0.0470211
$800$	2.47282	+	4.28304i	0.0874273	+	0.151428i
$801$	−15.7138	+	27.2171i	−0.555219	+	0.961668i
$802$	8.80508	−	15.2509i	0.310918	−	0.538526i
$803$	−0.857131	−	1.48460i	−0.0302475	−	0.0523902i
$804$	−3.54180			−0.124910
$805$	0.0561993	−	0.916075i	0.00198077	−	0.0322874i
$806$	−5.61976			−0.197948
$807$	−0.939049	−	1.62648i	−0.0330561	−	0.0572548i
$808$	−7.86693	+	13.6259i	−0.276758	+	0.479359i
$809$	−5.29226	+	9.16647i	−0.186066	+	0.322276i	−0.943935	−	0.330131i	$-0.892907\pi$
$809$	−5.29226	+	9.16647i	−0.186066	+	0.322276i	0.757869	+	0.652407i	$0.226241\pi$
$810$	−0.543881	−	0.942030i	−0.0191100	−	0.0330995i
$811$	−47.2614			−1.65957			−0.829786	−	0.558082i	$-0.811537\pi$
$811$	−47.2614			−1.65957			−0.829786	+	0.558082i	$0.811537\pi$
$812$	0.162007	−	2.64079i	0.00568533	−	0.0926734i
$813$	9.01969			0.316334
$814$	−0.0934693	−	0.161894i	−0.00327610	−	0.00567436i
$815$	1.58700	−	2.74877i	0.0555903	−	0.0962851i
$816$	0.217745	−	0.377145i	0.00762259	−	0.0132027i
$817$	11.0011	+	19.0545i	0.384880	+	0.666631i
$818$	−38.8959			−1.35996
$819$	22.8305	+	15.1172i	0.797761	+	0.528238i
$820$	0.773198			0.0270012
$821$	0.410163	+	0.710423i	0.0143148	+	0.0247939i	0.873094	−	0.487552i	$-0.162110\pi$
$821$	0.410163	+	0.710423i	0.0143148	+	0.0247939i	−0.858779	+	0.512346i	$0.828777\pi$
$822$	6.37015	−	11.0334i	0.222184	−	0.384835i
$823$	−20.5851	+	35.6544i	−0.717551	+	1.24283i	0.244416	+	0.969670i	$0.421404\pi$
$823$	−20.5851	+	35.6544i	−0.717551	+	1.24283i	−0.961967	+	0.273165i	$0.911930\pi$
$824$	2.44775	+	4.23962i	0.0852713	+	0.147694i
$825$	1.03685			0.0360984
$826$	10.1850	−	5.07573i	0.354383	−	0.176607i
$827$	−24.2372			−0.842810			−0.421405	−	0.906872i	$-0.638463\pi$
$827$	−24.2372			−0.842810			−0.421405	+	0.906872i	$0.638463\pi$
$828$	−1.85178	−	3.20737i	−0.0643536	−	0.111464i
$829$	14.8873	−	25.7855i	0.517057	−	0.895568i	−0.482747	−	0.875760i	$-0.660361\pi$
$829$	14.8873	−	25.7855i	0.517057	−	0.895568i	0.999804	−	0.0198086i	$-0.00630570\pi$
$830$	−0.785336	+	1.36024i	−0.0272594	+	0.0472147i
$831$	6.95269	+	12.0424i	0.241186	+	0.417747i
$832$	4.15740			0.144132
$833$	1.66543	+	3.92753i	0.0577036	+	0.136081i
$834$	−5.71558			−0.197914
$835$	0.419366	+	0.726363i	0.0145127	+	0.0251368i
$836$	−0.979535	+	1.69660i	−0.0338779	+	0.0586783i
$837$	2.65118	−	4.59198i	0.0916383	−	0.158722i
$838$	6.32183	+	10.9497i	0.218384	+	0.378252i
$839$	14.8726			0.513459			0.256730	−	0.966483i	$-0.417355\pi$
$839$	14.8726			0.513459			0.256730	+	0.966483i	$0.417355\pi$
$840$	−0.394549	+	0.196624i	−0.0136132	+	0.00678416i
$841$	1.00000			0.0344828
$842$	5.39905	+	9.35143i	0.186063	+	0.322271i
$843$	5.71326	−	9.89565i	0.196775	−	0.340824i
$844$	4.34510	−	7.52593i	0.149564	−	0.259053i
$845$	−0.499441	−	0.865057i	−0.0171813	−	0.0297589i
$846$	−5.42912			−0.186657
$847$	24.0759	+	15.9419i	0.827259	+	0.547771i
$848$	11.9922			0.411814
$849$	9.99792	+	17.3169i	0.343128	+	0.594314i
$850$	1.50702	−	2.61024i	0.0516904	−	0.0895304i
$851$	0.473973	−	0.820946i	0.0162476	−	0.0281417i
$852$	1.50457	+	2.60599i	0.0515456	+	0.0892797i
$853$	48.2468			1.65194			0.825970	−	0.563715i	$-0.190628\pi$
$853$	48.2468			1.65194			0.825970	+	0.563715i	$0.190628\pi$
$854$	−0.591006	+	9.63366i	−0.0202238	+	0.329657i
$855$	−3.87586			−0.132552
$856$	−5.61573	−	9.72674i	−0.191942	−	0.332453i
$857$	11.1442	−	19.3023i	0.380677	−	0.659352i	−0.610482	−	0.792030i	$-0.709024\pi$
$857$	11.1442	−	19.3023i	0.380677	−	0.659352i	0.991159	+	0.132678i	$0.0423576\pi$
$858$	0.435797	−	0.754822i	0.0148779	−	0.0257692i
$859$	−16.5053	−	28.5881i	−0.563155	−	0.975413i	−0.997219	−	0.0745311i	$-0.976254\pi$
$859$	−16.5053	−	28.5881i	−0.563155	−	0.975413i	0.434063	−	0.900882i	$-0.357079\pi$
$860$	−0.768296			−0.0261987
$861$	0.383888	−	6.25755i	0.0130829	−	0.213257i
$862$	−36.1812			−1.23234
$863$	−1.49100	−	2.58249i	−0.0507543	−	0.0879090i	0.839532	−	0.543310i	$-0.182829\pi$
$863$	−1.49100	−	2.58249i	−0.0507543	−	0.0879090i	−0.890286	+	0.455401i	$0.849496\pi$
$864$	−1.96130	+	3.39706i	−0.0667247	+	0.115570i
$865$	−1.44514	+	2.50305i	−0.0491361	+	0.0851063i
$866$	−5.31749	−	9.21016i	−0.180696	−	0.312974i
$867$	11.8824			0.403549
$868$	2.98194	+	1.97450i	0.101214	+	0.0670187i
$869$	0.618104			0.0209677
$870$	−0.0833087	−	0.144295i	−0.00282443	−	0.00489205i
$871$	−10.3030	+	17.8454i	−0.349105	+	0.604668i
$872$	−7.59327	+	13.1519i	−0.257141	+	0.445381i
$873$	7.10092	+	12.2992i	0.240330	+	0.416263i
$874$	−9.93425			−0.336031
$875$	−5.49140	+	2.73664i	−0.185643	+	0.0925154i
$876$	−4.17527			−0.141069
$877$	4.80059	+	8.31486i	0.162104	+	0.280773i	0.935623	−	0.353000i	$-0.114839\pi$
$877$	4.80059	+	8.31486i	0.162104	+	0.280773i	−0.773519	+	0.633773i	$0.781505\pi$
$878$	1.48753	−	2.57648i	0.0502018	−	0.0869521i
$879$	7.39036	−	12.8005i	0.249271	−	0.431750i
$880$	−0.0342045	−	0.0592439i	−0.00115303	−	0.00199711i
$881$	11.0461			0.372153			0.186076	−	0.982535i	$-0.440423\pi$
$881$	11.0461			0.372153			0.186076	+	0.982535i	$0.440423\pi$
$882$	−6.80282	−	16.0429i	−0.229063	−	0.540193i
$883$	−30.8011			−1.03654			−0.518269	−	0.855218i	$-0.673423\pi$
$883$	−30.8011			−1.03654			−0.518269	+	0.855218i	$0.673423\pi$
$884$	−1.26683	−	2.19422i	−0.0426081	−	0.0737995i
$885$	0.358322	−	0.620631i	0.0120449	−	0.0208623i
$886$	13.9715	−	24.1993i	0.469380	−	0.812990i
$887$	19.5367	+	33.8386i	0.655980	+	1.13619i	0.981647	+	0.190706i	$0.0610777\pi$
$887$	19.5367	+	33.8386i	0.655980	+	1.13619i	−0.325667	+	0.945484i	$0.605589\pi$
$888$	−0.455309			−0.0152792
$889$	−36.2429	+	18.0617i	−1.21555	+	0.605770i
$890$	−2.94368			−0.0986723
$891$	−0.684347	−	1.18532i	−0.0229265	−	0.0397098i
$892$	−4.99691	+	8.65491i	−0.167309	+	0.289788i
$893$	−7.28142	+	12.6118i	−0.243664	+	0.422038i
$894$	2.79256	+	4.83686i	0.0933973	+	0.161769i
$895$	2.23456			0.0746930
$896$	−2.20598	−	1.46070i	−0.0736968	−	0.0487984i
$897$	4.41976			0.147572
$898$	0.302215	+	0.523452i	0.0100851	+	0.0174678i
$899$	−0.675875	+	1.17065i	−0.0225417	+	0.0390434i
$900$	−6.15577	+	10.6621i	−0.205192	+	0.355404i
$901$	−3.65423	−	6.32931i	−0.121740	−	0.210860i
$902$	0.972889			0.0323937
$903$	−0.381454	+	6.21787i	−0.0126940	+	0.206918i
$904$	−10.2976			−0.342493
$905$	−0.0173309	−	0.0300179i	−0.000576097	−	0.000997830i
$906$	−5.79436	+	10.0361i	−0.192505	+	0.333428i
$907$	0.206207	−	0.357160i	0.00684697	−	0.0118593i	−0.862582	−	0.505918i	$-0.831154\pi$
$907$	0.206207	−	0.357160i	0.00684697	−	0.0118593i	0.869429	+	0.494059i	$0.164487\pi$
$908$	12.6545	+	21.9183i	0.419955	+	0.727383i
$909$	−39.1675			−1.29911
$910$	−0.157045	+	2.55991i	−0.00520600	+	0.0848602i
$911$	31.6863			1.04981			0.524907	−	0.851160i	$-0.324100\pi$
$911$	31.6863			1.04981			0.524907	+	0.851160i	$0.324100\pi$
$912$	2.38576	+	4.13226i	0.0790005	+	0.136833i
$913$	−0.988162	+	1.71155i	−0.0327034	+	0.0566439i
$914$	3.55156	−	6.15148i	0.117475	−	0.203473i
$915$	0.303912	+	0.526392i	0.0100470	+	0.0174020i
$916$	18.4785			0.610545
$917$	−26.9517	−	17.8461i	−0.890025	−	0.589331i
$918$	2.39057			0.0789004
$919$	27.5749	+	47.7611i	0.909611	+	1.57549i	0.814606	+	0.580015i	$0.196953\pi$
$919$	27.5749	+	47.7611i	0.909611	+	1.57549i	0.0950047	+	0.995477i	$0.469713\pi$
$920$	0.173447	−	0.300420i	0.00571839	−	0.00990454i
$921$	−10.2378	+	17.7324i	−0.337346	+	0.584301i
$922$	−1.90514	−	3.29980i	−0.0627424	−	0.108673i
$923$	17.5071			0.576252
$924$	−0.496447	+	0.247405i	−0.0163319	+	0.00813902i
$925$	−3.15122			−0.103611
$926$	1.71164	+	2.96464i	0.0562478	+	0.0974241i
$927$	−6.09337	+	10.5540i	−0.200132	+	0.346640i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	−19.8498	−	34.3809i	−0.651251	−	1.12800i	−0.982820	−	0.184568i	$-0.940911\pi$
$929$	−19.8498	−	34.3809i	−0.651251	−	1.12800i	0.331569	−	0.943431i	$-0.392422\pi$
$930$	0.225225			0.00738542
$931$	−46.3913	−	5.71352i	−1.52041	−	0.187253i
$932$	−9.35908			−0.306567
$933$	3.73893	+	6.47601i	0.122407	+	0.212015i
$934$	−11.4351	+	19.8061i	−0.374166	+	0.648075i
$935$	−0.0208454	+	0.0361053i	−0.000681717	+	0.00118077i
$936$	5.17466	+	8.96278i	0.169139	+	0.292958i
$937$	2.47672			0.0809108			0.0404554	−	0.999181i	$-0.487119\pi$
$937$	2.47672			0.0809108			0.0404554	+	0.999181i	$0.487119\pi$
$938$	11.7369	−	5.84911i	0.383224	−	0.190980i
$939$	22.4500			0.732629
$940$	−0.254261	−	0.440392i	−0.00829307	−	0.0143640i
$941$	−12.5890	+	21.8048i	−0.410390	+	0.710817i	−0.994932	−	0.100547i	$-0.967941\pi$
$941$	−12.5890	+	21.8048i	−0.410390	+	0.710817i	0.584542	+	0.811363i	$0.301274\pi$
$942$	−8.44827	+	14.6328i	−0.275260	+	0.476764i
$943$	2.46671	+	4.27247i	0.0803272	+	0.139131i
$944$	4.30113			0.139990
$945$	−2.01765	−	1.33599i	−0.0656342	−	0.0434597i
$946$	−0.966721			−0.0314308
$947$	19.0860	+	33.0579i	0.620212	+	1.07424i	0.989446	+	0.144902i	$0.0462867\pi$
$947$	19.0860	+	33.0579i	0.620212	+	1.07424i	−0.369234	+	0.929336i	$0.620380\pi$
$948$	0.752730	−	1.30377i	0.0244475	−	0.0423444i
$949$	−12.1458	+	21.0371i	−0.394269	+	0.682895i
$950$	16.5120	+	28.5996i	0.535719	+	0.927893i
$951$	−9.10929			−0.295389
$952$	−0.0987327	+	1.60939i	−0.00319994	+	0.0521606i
$953$	41.3605			1.33980			0.669900	−	0.742452i	$-0.266337\pi$
$953$	41.3605			1.33980			0.669900	+	0.742452i	$0.266337\pi$
$954$	14.9265	+	25.8535i	0.483265	+	0.837039i
$955$	−1.19885	+	2.07646i	−0.0387938	+	0.0671928i
$956$	8.77121	−	15.1922i	0.283681	−	0.491350i
$957$	−0.104824	−	0.181561i	−0.00338849	−	0.00586904i
$958$	−4.57219			−0.147721
$959$	−2.88844	+	47.0829i	−0.0932725	+	1.52038i
$960$	−0.166617			−0.00537755
$961$	14.5864	+	25.2644i	0.470529	+	0.814979i
$962$	−1.32449	+	2.29408i	−0.0427032	+	0.0739641i
$963$	13.9797	−	24.2135i	0.450489	−	0.780270i
$964$	−1.52113	−	2.63467i	−0.0489923	−	0.0848571i
$965$	2.90718			0.0935853
$966$	−2.34520	−	1.55288i	−0.0754556	−	0.0499630i
$967$	7.05786			0.226965			0.113483	−	0.993540i	$-0.463799\pi$
$967$	7.05786			0.226965			0.113483	+	0.993540i	$0.463799\pi$
$968$	5.45696	+	9.45173i	0.175393	+	0.303790i
$969$	1.45397	−	2.51835i	0.0467082	−	0.0809009i
$970$	−0.665111	+	1.15201i	−0.0213554	+	0.0369887i
$971$	−17.7494	−	30.7428i	−0.569605	−	0.986585i	−0.996605	−	0.0823332i	$-0.973763\pi$
$971$	−17.7494	−	30.7428i	−0.569605	−	0.986585i	0.427000	−	0.904252i	$-0.359570\pi$
$972$	−15.1014			−0.484377
$973$	18.9404	−	9.43899i	0.607203	−	0.302600i
$974$	21.6569			0.693931
$975$	−7.34621	−	12.7240i	−0.235267	−	0.407494i
$976$	−1.82401	+	3.15928i	−0.0583853	+	0.101126i
$977$	−7.43503	+	12.8778i	−0.237868	+	0.411999i	−0.960102	−	0.279649i	$-0.909782\pi$
$977$	−7.43503	+	12.8778i	−0.237868	+	0.411999i	0.722235	+	0.691648i	$0.243115\pi$
$978$	−4.86360	−	8.42400i	−0.155521	−	0.269370i
$979$	−3.70393			−0.118378
$980$	0.982752	−	1.30315i	0.0313929	−	0.0416277i
$981$	−37.8050			−1.20702
$982$	−16.0268	−	27.7593i	−0.511437	−	0.885834i
$983$	−18.3841	+	31.8422i	−0.586362	+	1.01561i	0.408343	+	0.912829i	$0.366107\pi$
$983$	−18.3841	+	31.8422i	−0.586362	+	1.01561i	−0.994704	+	0.102779i	$0.967226\pi$
$984$	1.18479	−	2.05211i	0.0377697	−	0.0654190i
$985$	2.21874	+	3.84296i	0.0706948	+	0.122447i
$986$	−0.609435			−0.0194084
$987$	−3.69036	+	1.83910i	−0.117466	+	0.0585391i
$988$	27.7606			0.883182
$989$	−2.45107	−	4.24538i	−0.0779396	−	0.134995i
$990$	0.0851478	−	0.147480i	0.00270617	−	0.00468723i
$991$	13.4811	−	23.3500i	0.428242	−	0.741736i	−0.568475	−	0.822700i	$-0.692467\pi$
$991$	13.4811	−	23.3500i	0.428242	−	0.741736i	0.996717	+	0.0809641i	$0.0257999\pi$
$992$	0.675875	+	1.17065i	0.0214591	+	0.0371682i
$993$	7.33295			0.232704
$994$	−9.28954	−	6.15108i	−0.294646	−	0.195100i
$995$	−2.47353			−0.0784162
$996$	2.40677	+	4.16866i	0.0762616	+	0.132089i
$997$	−3.73465	+	6.46860i	−0.118278	+	0.204863i	−0.919085	−	0.394059i	$-0.871071\pi$
$997$	−3.73465	+	6.46860i	−0.118278	+	0.204863i	0.800808	+	0.598922i	$0.204404\pi$
$998$	−12.3057	+	21.3140i	−0.389529	+	0.674684i
$999$	−1.24968	−	2.16451i	−0.0395382	−	0.0684821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	406.2.e.a.291.4	yes	10
7.2	even	3	inner	406.2.e.a.233.4	✓	10
7.3	odd	6		2842.2.a.x.1.4		5
7.4	even	3		2842.2.a.z.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.4	✓	10	7.2	even	3	inner
406.2.e.a.291.4	yes	10	1.1	even	1	trivial
2842.2.a.x.1.4		5	7.3	odd	6
2842.2.a.z.1.2		5	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 406 = 2 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	406.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.357289 - 0.618843i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.116584 - 0.201930i) q^{5} -0.714579 q^{6} +(2.36799 - 1.18009i) q^{7} +1.00000 q^{8} +(1.24469 + 2.15586i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.357289 - 0.618843i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.116584 - 0.201930i) q^{5} -0.714579 q^{6} +(2.36799 - 1.18009i) q^{7} +1.00000 q^{8} +(1.24469 + 2.15586i) q^{9} +(-0.116584 + 0.201930i) q^{10} +(-0.146694 + 0.254082i) q^{11} +(0.357289 + 0.618843i) q^{12} +4.15740 q^{13} +(-2.20598 - 1.46070i) q^{14} -0.166617 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.304717 + 0.527786i) q^{17} +(1.24469 - 2.15586i) q^{18} +(-3.33870 - 5.78280i) q^{19} +0.233169 q^{20} +(0.115767 - 1.88705i) q^{21} +0.293388 q^{22} +(0.743871 + 1.28842i) q^{23} +(0.357289 - 0.618843i) q^{24} +(2.47282 - 4.28304i) q^{25} +(-2.07870 - 3.60041i) q^{26} +3.92259 q^{27} +(-0.162007 + 2.64079i) q^{28} -1.00000 q^{29} +(0.0833087 + 0.144295i) q^{30} +(0.675875 - 1.17065i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.104824 + 0.181561i) q^{33} +0.609435 q^{34} +(-0.514366 - 0.340588i) q^{35} -2.48938 q^{36} +(-0.318586 - 0.551807i) q^{37} +(-3.33870 + 5.78280i) q^{38} +(1.48539 - 2.57278i) q^{39} +(-0.116584 - 0.201930i) q^{40} +3.31605 q^{41} +(-1.69212 + 0.843268i) q^{42} -3.29502 q^{43} +(-0.146694 - 0.254082i) q^{44} +(0.290222 - 0.502680i) q^{45} +(0.743871 - 1.28842i) q^{46} +(-1.09046 - 1.88873i) q^{47} -0.714579 q^{48} +(4.21477 - 5.58889i) q^{49} -4.94563 q^{50} +(0.217745 + 0.377145i) q^{51} +(-2.07870 + 3.60041i) q^{52} +(-5.99610 + 10.3855i) q^{53} +(-1.96130 - 3.39706i) q^{54} +0.0684089 q^{55} +(2.36799 - 1.18009i) q^{56} -4.77153 q^{57} +(0.500000 + 0.866025i) q^{58} +(-2.15057 + 3.72489i) q^{59} +(0.0833087 - 0.144295i) q^{60} +(-1.82401 - 3.15928i) q^{61} -1.35175 q^{62} +(5.49153 + 3.63622i) q^{63} +1.00000 q^{64} +(-0.484687 - 0.839503i) q^{65} +(0.104824 - 0.181561i) q^{66} +(-2.47824 + 4.29245i) q^{67} +(-0.304717 - 0.527786i) q^{68} +1.06311 q^{69} +(-0.0377749 + 0.615749i) q^{70} +4.21106 q^{71} +(1.24469 + 2.15586i) q^{72} +(-2.92149 + 5.06017i) q^{73} +(-0.318586 + 0.551807i) q^{74} +(-1.76702 - 3.06057i) q^{75} +6.67740 q^{76} +(-0.0475309 + 0.774776i) q^{77} -2.97079 q^{78} +(-1.05339 - 1.82452i) q^{79} +(-0.116584 + 0.201930i) q^{80} +(-2.33257 + 4.04012i) q^{81} +(-1.65802 - 2.87178i) q^{82} +6.73621 q^{83} +(1.57635 + 1.04378i) q^{84} +0.142101 q^{85} +(1.64751 + 2.85357i) q^{86} +(-0.357289 + 0.618843i) q^{87} +(-0.146694 + 0.254082i) q^{88} +(6.31233 + 10.9333i) q^{89} -0.580445 q^{90} +(9.84468 - 4.90611i) q^{91} -1.48774 q^{92} +(-0.482966 - 0.836522i) q^{93} +(-1.09046 + 1.88873i) q^{94} +(-0.778480 + 1.34837i) q^{95} +(0.357289 + 0.618843i) q^{96} +5.70498 q^{97} +(-6.94751 - 0.855651i) q^{98} -0.730354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

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