LMFDB - Embedded newform 322.2.e.c.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, 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("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$2.11692 + 0.978886i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.c.93.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.43049 - 2.47769i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.686423 - 1.18892i) q^{5} +2.86099 q^{6} +(-2.30334 - 1.30178i) q^{7} -1.00000 q^{8} +(-2.59262 - 4.49055i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.43049 - 2.47769i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.686423 - 1.18892i) q^{5} +2.86099 q^{6} +(-2.30334 - 1.30178i) q^{7} -1.00000 q^{8} +(-2.59262 - 4.49055i) q^{9} +(0.686423 - 1.18892i) q^{10} +(1.21072 - 2.09702i) q^{11} +(1.43049 + 2.47769i) q^{12} +5.67338 q^{13} +(-0.0242947 - 2.64564i) q^{14} -3.92769 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.18642 + 3.78700i) q^{17} +(2.59262 - 4.49055i) q^{18} +(0.735012 + 1.27308i) q^{19} +1.37285 q^{20} +(-6.52031 + 3.84476i) q^{21} +2.42143 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.43049 + 2.47769i) q^{24} +(1.55765 - 2.69792i) q^{25} +(2.83669 + 4.91329i) q^{26} -6.25195 q^{27} +(2.27904 - 1.34386i) q^{28} +3.06671 q^{29} +(-1.96385 - 3.40148i) q^{30} +(-3.65027 + 6.32245i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.46385 - 5.99956i) q^{33} -4.37285 q^{34} +(0.0333529 + 3.63205i) q^{35} +5.18524 q^{36} +(2.13503 + 3.69798i) q^{37} +(-0.735012 + 1.27308i) q^{38} +(8.11574 - 14.0569i) q^{39} +(0.686423 + 1.18892i) q^{40} +6.92769 q^{41} +(-6.58982 - 3.72437i) q^{42} -2.39772 q^{43} +(1.21072 + 2.09702i) q^{44} +(-3.55927 + 6.16483i) q^{45} +(0.500000 - 0.866025i) q^{46} +(0.915257 + 1.58527i) q^{47} -2.86099 q^{48} +(3.61074 + 5.99688i) q^{49} +3.11530 q^{50} +(6.25533 + 10.8345i) q^{51} +(-2.83669 + 4.91329i) q^{52} +(-2.12759 + 3.68510i) q^{53} +(-3.12597 - 5.41435i) q^{54} -3.32426 q^{55} +(2.30334 + 1.30178i) q^{56} +4.20572 q^{57} +(1.53335 + 2.65585i) q^{58} +(-0.416437 + 0.721290i) q^{59} +(1.96385 - 3.40148i) q^{60} +(7.67220 + 13.2886i) q^{61} -7.30054 q^{62} +(0.125974 + 13.7183i) q^{63} +1.00000 q^{64} +(-3.89434 - 6.74519i) q^{65} +(3.46385 - 5.99956i) q^{66} +(4.79148 - 8.29909i) q^{67} +(-2.18642 - 3.78700i) q^{68} -2.86099 q^{69} +(-3.12878 + 1.84491i) q^{70} -14.1410 q^{71} +(2.59262 + 4.49055i) q^{72} +(2.22883 - 3.86045i) q^{73} +(-2.13503 + 3.69798i) q^{74} +(-4.45641 - 7.71873i) q^{75} -1.47002 q^{76} +(-5.51856 + 3.25407i) q^{77} +16.2315 q^{78} +(-7.50508 - 12.9992i) q^{79} +(-0.686423 + 1.18892i) q^{80} +(-1.16551 + 2.01871i) q^{81} +(3.46385 + 5.99956i) q^{82} +5.16388 q^{83} +(-0.0695069 - 7.56914i) q^{84} +6.00324 q^{85} +(-1.19886 - 2.07648i) q^{86} +(4.38690 - 7.59834i) q^{87} +(-1.21072 + 2.09702i) q^{88} +(-8.98696 - 15.5659i) q^{89} -7.11854 q^{90} +(-13.0677 - 7.38550i) q^{91} +1.00000 q^{92} +(10.4434 + 18.0884i) q^{93} +(-0.915257 + 1.58527i) q^{94} +(1.00906 - 1.74774i) q^{95} +(-1.43049 - 2.47769i) q^{96} -2.26106 q^{97} +(-3.38808 + 6.12543i) q^{98} -12.5557 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.43049	−	2.47769i	0.825896	−	1.43049i	−0.0753373	−	0.997158i	$-0.524003\pi$
$3$	1.43049	−	2.47769i	0.825896	−	1.43049i	0.901233	−	0.433335i	$-0.142663\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.686423	−	1.18892i	−0.306978	−	0.531701i	0.670722	−	0.741709i	$-0.265984\pi$
$5$	−0.686423	−	1.18892i	−0.306978	−	0.531701i	−0.977700	+	0.210008i	$0.932651\pi$
$6$	2.86099			1.16799
$7$	−2.30334	−	1.30178i	−0.870580	−	0.492027i
$7$	−2.30334	−	1.30178i	−0.870580	−	0.492027i
$8$	−1.00000			−0.353553
$9$	−2.59262	−	4.49055i	−0.864207	−	1.49685i
$10$	0.686423	−	1.18892i	0.217066	−	0.375969i
$11$	1.21072	−	2.09702i	0.365045	−	0.632277i	−0.623738	−	0.781633i	$-0.714387\pi$
$11$	1.21072	−	2.09702i	0.365045	−	0.632277i	0.988783	+	0.149357i	$0.0477202\pi$
$12$	1.43049	+	2.47769i	0.412948	+	0.715247i
$13$	5.67338			1.57351			0.786757	−	0.617263i	$-0.211759\pi$
$13$	5.67338			1.57351			0.786757	+	0.617263i	$0.211759\pi$
$14$	−0.0242947	−	2.64564i	−0.00649304	−	0.707077i
$15$	−3.92769			−1.01413
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.18642	+	3.78700i	−0.530285	+	0.918481i	0.469090	+	0.883150i	$0.344582\pi$
$17$	−2.18642	+	3.78700i	−0.530285	+	0.918481i	−0.999376	+	0.0353310i	$0.988751\pi$
$18$	2.59262	−	4.49055i	0.611087	−	1.05843i
$19$	0.735012	+	1.27308i	0.168623	+	0.292064i	0.937936	−	0.346808i	$-0.112735\pi$
$19$	0.735012	+	1.27308i	0.168623	+	0.292064i	−0.769313	+	0.638872i	$0.779401\pi$
$20$	1.37285			0.306978
$21$	−6.52031	+	3.84476i	−1.42285	+	0.838996i
$22$	2.42143			0.516252
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−1.43049	+	2.47769i	−0.291998	+	0.505756i
$25$	1.55765	−	2.69792i	0.311530	−	0.539585i
$26$	2.83669	+	4.91329i	0.556321	+	0.963576i
$27$	−6.25195			−1.20319
$28$	2.27904	−	1.34386i	0.430699	−	0.253966i
$29$	3.06671			0.569473			0.284736	−	0.958606i	$-0.408094\pi$
$29$	3.06671			0.569473			0.284736	+	0.958606i	$0.408094\pi$
$30$	−1.96385	−	3.40148i	−0.358548	−	0.621023i
$31$	−3.65027	+	6.32245i	−0.655608	+	1.13555i	0.326133	+	0.945324i	$0.394254\pi$
$31$	−3.65027	+	6.32245i	−0.655608	+	1.13555i	−0.981741	+	0.190222i	$0.939079\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.46385	−	5.99956i	−0.602978	−	1.04439i
$34$	−4.37285			−0.749937
$35$	0.0333529	+	3.63205i	0.00563767	+	0.613929i
$36$	5.18524			0.864207
$37$	2.13503	+	3.69798i	0.350997	+	0.607945i	0.986424	−	0.164216i	$-0.0525094\pi$
$37$	2.13503	+	3.69798i	0.350997	+	0.607945i	−0.635427	+	0.772161i	$0.719176\pi$
$38$	−0.735012	+	1.27308i	−0.119235	+	0.206521i
$39$	8.11574	−	14.0569i	1.29956	−	2.25090i
$40$	0.686423	+	1.18892i	0.108533	+	0.187985i
$41$	6.92769			1.08192			0.540962	−	0.841047i	$-0.318060\pi$
$41$	6.92769			1.08192			0.540962	+	0.841047i	$0.318060\pi$
$42$	−6.58982	−	3.72437i	−1.01683	−	0.574684i
$43$	−2.39772			−0.365648			−0.182824	−	0.983146i	$-0.558524\pi$
$43$	−2.39772			−0.365648			−0.182824	+	0.983146i	$0.558524\pi$
$44$	1.21072	+	2.09702i	0.182523	+	0.316138i
$45$	−3.55927	+	6.16483i	−0.530584	+	0.918999i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	0.915257	+	1.58527i	0.133504	+	0.231236i	0.925025	−	0.379906i	$-0.124044\pi$
$47$	0.915257	+	1.58527i	0.133504	+	0.231236i	−0.791521	+	0.611142i	$0.790710\pi$
$48$	−2.86099			−0.412948
$49$	3.61074	+	5.99688i	0.515820	+	0.856697i
$50$	3.11530			0.440569
$51$	6.25533	+	10.8345i	0.875921	+	1.51714i
$52$	−2.83669	+	4.91329i	−0.393378	+	0.681351i
$53$	−2.12759	+	3.68510i	−0.292248	+	0.506188i	−0.974341	−	0.225077i	$-0.927736\pi$
$53$	−2.12759	+	3.68510i	−0.292248	+	0.506188i	0.682093	+	0.731265i	$0.261070\pi$
$54$	−3.12597	−	5.41435i	−0.425391	−	0.736799i
$55$	−3.32426			−0.448243
$56$	2.30334	+	1.30178i	0.307797	+	0.173958i
$57$	4.20572			0.557061
$58$	1.53335	+	2.65585i	0.201339	+	0.348730i
$59$	−0.416437	+	0.721290i	−0.0542155	+	0.0939040i	−0.891859	−	0.452313i	$-0.850599\pi$
$59$	−0.416437	+	0.721290i	−0.0542155	+	0.0939040i	0.837644	+	0.546217i	$0.183932\pi$
$60$	1.96385	−	3.40148i	0.253531	−	0.439129i
$61$	7.67220	+	13.2886i	0.982325	+	1.70144i	0.653269	+	0.757126i	$0.273397\pi$
$61$	7.67220	+	13.2886i	0.982325	+	1.70144i	0.329056	+	0.944310i	$0.393269\pi$
$62$	−7.30054			−0.927169
$63$	0.125974	+	13.7183i	0.0158712	+	1.72834i
$64$	1.00000			0.125000
$65$	−3.89434	−	6.74519i	−0.483033	−	0.836638i
$66$	3.46385	−	5.99956i	0.426370	−	0.738494i
$67$	4.79148	−	8.29909i	0.585372	−	1.01389i	−0.409457	−	0.912330i	$-0.634282\pi$
$67$	4.79148	−	8.29909i	0.585372	−	1.01389i	0.994829	−	0.101565i	$-0.0323850\pi$
$68$	−2.18642	−	3.78700i	−0.265143	−	0.459241i
$69$	−2.86099			−0.344422
$70$	−3.12878	+	1.84491i	−0.373960	+	0.220509i
$71$	−14.1410			−1.67823			−0.839117	−	0.543951i	$-0.816928\pi$
$71$	−14.1410			−1.67823			−0.839117	+	0.543951i	$0.816928\pi$
$72$	2.59262	+	4.49055i	0.305543	+	0.529217i
$73$	2.22883	−	3.86045i	0.260865	−	0.451832i	−0.705607	−	0.708604i	$-0.749325\pi$
$73$	2.22883	−	3.86045i	0.260865	−	0.451832i	0.966472	+	0.256772i	$0.0826588\pi$
$74$	−2.13503	+	3.69798i	−0.248192	+	0.429882i
$75$	−4.45641	−	7.71873i	−0.514582	−	0.891282i
$76$	−1.47002			−0.168623
$77$	−5.51856	+	3.25407i	−0.628898	+	0.370836i
$78$	16.2315			1.83785
$79$	−7.50508	−	12.9992i	−0.844387	−	1.46252i	−0.886152	−	0.463394i	$-0.846632\pi$
$79$	−7.50508	−	12.9992i	−0.844387	−	1.46252i	0.0417653	−	0.999127i	$-0.486702\pi$
$80$	−0.686423	+	1.18892i	−0.0767444	+	0.132925i
$81$	−1.16551	+	2.01871i	−0.129501	+	0.224302i
$82$	3.46385	+	5.99956i	0.382518	+	0.662540i
$83$	5.16388			0.566810			0.283405	−	0.959000i	$-0.408536\pi$
$83$	5.16388			0.566810			0.283405	+	0.959000i	$0.408536\pi$
$84$	−0.0695069	−	7.56914i	−0.00758382	−	0.825861i
$85$	6.00324			0.651143
$86$	−1.19886	−	2.07648i	−0.129276	−	0.223913i
$87$	4.38690	−	7.59834i	0.470325	−	0.814627i
$88$	−1.21072	+	2.09702i	−0.129063	+	0.223544i
$89$	−8.98696	−	15.5659i	−0.952616	−	1.64998i	−0.739732	−	0.672902i	$-0.765048\pi$
$89$	−8.98696	−	15.5659i	−0.952616	−	1.64998i	−0.212884	−	0.977078i	$-0.568286\pi$
$90$	−7.11854			−0.750360
$91$	−13.0677	−	7.38550i	−1.36987	−	0.774210i
$92$	1.00000			0.104257
$93$	10.4434	+	18.0884i	1.08293	+	1.87568i
$94$	−0.915257	+	1.58527i	−0.0944015	+	0.163508i
$95$	1.00906	−	1.74774i	0.103527	−	0.179314i
$96$	−1.43049	−	2.47769i	−0.145999	−	0.252878i
$97$	−2.26106			−0.229576			−0.114788	−	0.993390i	$-0.536619\pi$
$97$	−2.26106			−0.229576			−0.114788	+	0.993390i	$0.536619\pi$
$98$	−3.38808	+	6.12543i	−0.342248	+	0.618762i
$99$	−12.5557			−1.26190
$100$	1.55765	+	2.69792i	0.155765	+	0.269792i
$101$	−6.49720	+	11.2535i	−0.646495	+	1.11976i	0.337458	+	0.941340i	$0.390433\pi$
$101$	−6.49720	+	11.2535i	−0.646495	+	1.11976i	−0.983954	+	0.178423i	$0.942901\pi$
$102$	−6.25533	+	10.8345i	−0.619370	+	1.07278i
$103$	7.26881	+	12.5899i	0.716217	+	1.24052i	0.962488	+	0.271323i	$0.0874611\pi$
$103$	7.26881	+	12.5899i	0.716217	+	1.24052i	−0.246272	+	0.969201i	$0.579206\pi$
$104$	−5.67338			−0.556321
$105$	9.04680	+	5.11299i	0.882878	+	0.498977i
$106$	−4.25519			−0.413301
$107$	0.954788	+	1.65374i	0.0923028	+	0.159873i	0.908480	−	0.417929i	$-0.137244\pi$
$107$	0.954788	+	1.65374i	0.0923028	+	0.159873i	−0.816177	+	0.577802i	$0.803911\pi$
$108$	3.12597	−	5.41435i	0.300797	−	0.520996i
$109$	−4.61293	+	7.98984i	−0.441839	+	0.765288i	−0.997826	−	0.0659034i	$-0.979007\pi$
$109$	−4.61293	+	7.98984i	−0.441839	+	0.765288i	0.555987	+	0.831191i	$0.312340\pi$
$110$	−1.66213	−	2.87889i	−0.158478	−	0.274491i
$111$	12.2166			1.15955
$112$	0.0242947	+	2.64564i	0.00229564	+	0.249989i
$113$	−13.3500			−1.25586			−0.627932	−	0.778269i	$-0.716098\pi$
$113$	−13.3500			−1.25586			−0.627932	+	0.778269i	$0.716098\pi$
$114$	2.10286	+	3.64226i	0.196951	+	0.341129i
$115$	−0.686423	+	1.18892i	−0.0640093	+	0.110867i
$116$	−1.53335	+	2.65585i	−0.142368	+	0.246589i
$117$	−14.7089	−	25.4766i	−1.35984	−	2.35531i
$118$	−0.832874			−0.0766723
$119$	9.96591	−	5.87649i	0.913573	−	0.538697i
$120$	3.92769			0.358548
$121$	2.56833	+	4.44847i	0.233484	+	0.404407i
$122$	−7.67220	+	13.2886i	−0.694609	+	1.20310i
$123$	9.91002	−	17.1647i	0.893556	−	1.54768i
$124$	−3.65027	−	6.32245i	−0.327804	−	0.567773i
$125$	−11.1410			−0.996485
$126$	−11.8174	+	6.96824i	−1.05278	+	0.620780i
$127$	19.2326			1.70662			0.853310	−	0.521404i	$-0.174592\pi$
$127$	19.2326			1.70662			0.853310	+	0.521404i	$0.174592\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−3.42992	+	5.94079i	−0.301987	+	0.523057i
$130$	3.89434	−	6.74519i	0.341556	−	0.591593i
$131$	−8.58526	−	14.8701i	−0.750098	−	1.29921i	−0.947775	−	0.318940i	$-0.896673\pi$
$131$	−8.58526	−	14.8701i	−0.750098	−	1.29921i	0.197677	−	0.980267i	$-0.436660\pi$
$132$	6.92769			0.602978
$133$	−0.0357138	−	3.88915i	−0.00309678	−	0.337233i
$134$	9.58296			0.827842
$135$	4.29148	+	7.43306i	0.369352	+	0.639736i
$136$	2.18642	−	3.78700i	0.187484	−	0.324732i
$137$	−6.87504	+	11.9079i	−0.587375	+	1.01736i	0.407200	+	0.913339i	$0.366505\pi$
$137$	−6.87504	+	11.9079i	−0.587375	+	1.01736i	−0.994575	+	0.104024i	$0.966828\pi$
$138$	−1.43049	−	2.47769i	−0.121772	−	0.210915i
$139$	7.43719			0.630814			0.315407	−	0.948956i	$-0.397859\pi$
$139$	7.43719			0.630814			0.315407	+	0.948956i	$0.397859\pi$
$140$	−3.16213	−	1.78714i	−0.267249	−	0.151041i
$141$	5.23707			0.441041
$142$	−7.07052	−	12.2465i	−0.593345	−	1.02770i
$143$	6.86886	−	11.8972i	0.574403	−	0.994896i
$144$	−2.59262	+	4.49055i	−0.216052	+	0.374213i
$145$	−2.10506	−	3.64607i	−0.174815	−	0.302789i
$146$	4.45767			0.368919
$147$	20.0235	−	0.367780i	1.65151	−	0.0303340i
$148$	−4.27006			−0.350997
$149$	−3.53997	−	6.13141i	−0.290006	−	0.502305i	0.683805	−	0.729665i	$-0.260324\pi$
$149$	−3.53997	−	6.13141i	−0.290006	−	0.502305i	−0.973811	+	0.227360i	$0.926991\pi$
$150$	4.45641	−	7.71873i	0.363864	−	0.630231i
$151$	−7.40958	+	12.8338i	−0.602983	+	1.04440i	0.389384	+	0.921075i	$0.372688\pi$
$151$	−7.40958	+	12.8338i	−0.602983	+	1.04440i	−0.992367	+	0.123321i	$0.960645\pi$
$152$	−0.735012	−	1.27308i	−0.0596174	−	0.103260i
$153$	22.6743			1.83311
$154$	−5.57738	−	3.15218i	−0.449438	−	0.254010i
$155$	10.0225			0.805027
$156$	8.11574	+	14.0569i	0.649779	+	1.12545i
$157$	7.06715	−	12.2407i	0.564020	−	0.976911i	−0.433120	−	0.901336i	$-0.642588\pi$
$157$	7.06715	−	12.2407i	0.564020	−	0.976911i	0.997140	−	0.0755747i	$-0.0240791\pi$
$158$	7.50508	−	12.9992i	0.597072	−	1.03416i
$159$	6.08702	+	10.5430i	0.482732	+	0.836116i
$160$	−1.37285			−0.108533
$161$	0.0242947	+	2.64564i	0.00191469	+	0.208506i
$162$	−2.33101			−0.183141
$163$	−0.544032	−	0.942291i	−0.0426119	−	0.0738059i	0.843933	−	0.536449i	$-0.180235\pi$
$163$	−0.544032	−	0.942291i	−0.0426119	−	0.0738059i	−0.886545	+	0.462643i	$0.846901\pi$
$164$	−3.46385	+	5.99956i	−0.270481	+	0.468487i
$165$	−4.75533	+	8.23647i	−0.370202	+	0.641208i
$166$	2.58194	+	4.47206i	0.200398	+	0.347099i
$167$	−1.86187			−0.144076			−0.0720378	−	0.997402i	$-0.522950\pi$
$167$	−1.86187			−0.144076			−0.0720378	+	0.997402i	$0.522950\pi$
$168$	6.52031	−	3.84476i	0.503053	−	0.296630i
$169$	19.1873			1.47594
$170$	3.00162	+	5.19896i	0.230214	+	0.398742i
$171$	3.81122	−	6.60122i	0.291451	−	0.504808i
$172$	1.19886	−	2.07648i	0.0914121	−	0.158330i
$173$	−5.81695	−	10.0753i	−0.442255	−	0.766008i	0.555602	−	0.831449i	$-0.312488\pi$
$173$	−5.81695	−	10.0753i	−0.442255	−	0.766008i	−0.997856	+	0.0654408i	$0.979155\pi$
$174$	8.77380			0.665140
$175$	−7.09989	+	4.18652i	−0.536702	+	0.316471i
$176$	−2.42143			−0.182523
$177$	1.19142	+	2.06360i	0.0895527	+	0.155110i
$178$	8.98696	−	15.5659i	0.673601	−	1.16671i
$179$	7.07214	−	12.2493i	0.528597	−	0.915557i	−0.470847	−	0.882215i	$-0.656052\pi$
$179$	7.07214	−	12.2493i	0.528597	−	0.915557i	0.999444	−	0.0333418i	$-0.0106150\pi$
$180$	−3.55927	−	6.16483i	−0.265292	−	0.459500i
$181$	3.34337			0.248511			0.124255	−	0.992250i	$-0.460346\pi$
$181$	3.34337			0.248511			0.124255	+	0.992250i	$0.460346\pi$
$182$	−0.137833	−	15.0097i	−0.0102169	−	1.11260i
$183$	43.9001			3.24519
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	2.93107	−	5.07676i	0.215497	−	0.373251i
$186$	−10.4434	+	18.0884i	−0.765745	+	1.32631i
$187$	5.29428	+	9.16996i	0.387156	+	0.670574i
$188$	−1.83051			−0.133504
$189$	14.4004	+	8.13866i	1.04747	+	0.592000i
$190$	2.01812			0.146410
$191$	−8.02987	−	13.9081i	−0.581021	−	1.00636i	−0.995359	−	0.0962346i	$-0.969320\pi$
$191$	−8.02987	−	13.9081i	−0.581021	−	1.00636i	0.414338	−	0.910123i	$-0.364013\pi$
$192$	1.43049	−	2.47769i	0.103237	−	0.178812i
$193$	−3.23221	+	5.59835i	−0.232660	+	0.402978i	−0.958590	−	0.284790i	$-0.908076\pi$
$193$	−3.23221	+	5.59835i	−0.232660	+	0.402978i	0.725930	+	0.687768i	$0.241409\pi$
$194$	−1.13053	−	1.95814i	−0.0811675	−	0.140586i
$195$	−22.2833			−1.59574
$196$	−6.99882	+	0.128550i	−0.499916	+	0.00918216i
$197$	12.7264			0.906716			0.453358	−	0.891329i	$-0.350226\pi$
$197$	12.7264			0.906716			0.453358	+	0.891329i	$0.350226\pi$
$198$	−6.27786	−	10.8736i	−0.446148	−	0.772752i
$199$	−7.74465	+	13.4141i	−0.549003	+	0.950902i	0.449340	+	0.893361i	$0.351659\pi$
$199$	−7.74465	+	13.4141i	−0.549003	+	0.950902i	−0.998343	+	0.0575409i	$0.981674\pi$
$200$	−1.55765	+	2.69792i	−0.110142	+	0.190772i
$201$	−13.7084	−	23.7436i	−0.966913	−	1.67474i
$202$	−12.9944			−0.914283
$203$	−7.06366	−	3.99218i	−0.495772	−	0.280196i
$204$	−12.5107			−0.875921
$205$	−4.75533	−	8.23647i	−0.332126	−	0.575260i
$206$	−7.26881	+	12.5899i	−0.506442	+	0.877183i
$207$	−2.59262	+	4.49055i	−0.180200	+	0.312115i
$208$	−2.83669	−	4.91329i	−0.196689	−	0.340676i
$209$	3.55957			0.246220
$210$	0.0954222	+	10.3913i	0.00658476	+	0.717065i
$211$	−9.32662			−0.642071			−0.321035	−	0.947067i	$-0.604031\pi$
$211$	−9.32662			−0.642071			−0.321035	+	0.947067i	$0.604031\pi$
$212$	−2.12759	−	3.68510i	−0.146124	−	0.253094i
$213$	−20.2287	+	35.0371i	−1.38605	+	2.40070i
$214$	−0.954788	+	1.65374i	−0.0652680	+	0.113047i
$215$	1.64585	+	2.85069i	0.112246	+	0.194415i
$216$	6.25195			0.425391
$217$	16.6382	−	9.81090i	1.12948	−	0.666007i
$218$	−9.22587			−0.624855
$219$	−6.37666	−	11.0447i	−0.430895	−	0.746332i
$220$	1.66213	−	2.87889i	0.112061	−	0.194095i
$221$	−12.4044	+	21.4851i	−0.834411	+	1.44524i
$222$	6.10830	+	10.5799i	0.409962	+	0.710075i
$223$	22.6719			1.51822			0.759111	−	0.650961i	$-0.225634\pi$
$223$	22.6719			1.51822			0.759111	+	0.650961i	$0.225634\pi$
$224$	−2.27904	+	1.34386i	−0.152275	+	0.0897904i
$225$	−16.1536			−1.07690
$226$	−6.67500	−	11.5614i	−0.444015	−	0.769056i
$227$	−2.12435	+	3.67949i	−0.140998	+	0.244216i	−0.927873	−	0.372897i	$-0.878365\pi$
$227$	−2.12435	+	3.67949i	−0.140998	+	0.244216i	0.786875	+	0.617113i	$0.211698\pi$
$228$	−2.10286	+	3.64226i	−0.139265	+	0.241215i
$229$	1.34007	+	2.32107i	0.0885542	+	0.153380i	0.906900	−	0.421345i	$-0.138442\pi$
$229$	1.34007	+	2.32107i	0.0885542	+	0.153380i	−0.818346	+	0.574726i	$0.805109\pi$
$230$	−1.37285			−0.0905228
$231$	0.168306	+	18.3282i	0.0110737	+	1.20591i
$232$	−3.06671			−0.201339
$233$	−12.2429	−	21.2053i	−0.802058	−	1.38921i	−0.918259	−	0.395980i	$-0.870405\pi$
$233$	−12.2429	−	21.2053i	−0.802058	−	1.38921i	0.116201	−	0.993226i	$-0.462928\pi$
$234$	14.7089	−	25.4766i	0.961553	−	1.66546i
$235$	1.25651	−	2.17633i	0.0819654	−	0.141968i
$236$	−0.416437	−	0.721290i	−0.0271077	−	0.0469520i
$237$	−42.9438			−2.78950
$238$	10.0721	+	5.69248i	0.652880	+	0.368989i
$239$	−10.1729			−0.658029			−0.329015	−	0.944325i	$-0.606717\pi$
$239$	−10.1729			−0.658029			−0.329015	+	0.944325i	$0.606717\pi$
$240$	1.96385	+	3.40148i	0.126766	+	0.219565i
$241$	−5.28692	+	9.15722i	−0.340561	+	0.589868i	−0.984537	−	0.175177i	$-0.943950\pi$
$241$	−5.28692	+	9.15722i	−0.340561	+	0.589868i	0.643976	+	0.765045i	$0.277283\pi$
$242$	−2.56833	+	4.44847i	−0.165098	+	0.285959i
$243$	−6.04343	−	10.4675i	−0.387686	−	0.671492i
$244$	−15.3444			−0.982325
$245$	4.65131	−	8.40927i	0.297161	−	0.537249i
$246$	19.8200			1.26368
$247$	4.17001	+	7.22266i	0.265331	+	0.459567i
$248$	3.65027	−	6.32245i	0.231792	−	0.401476i
$249$	7.38690	−	12.7945i	0.468126	−	0.810818i
$250$	−5.57052	−	9.64843i	−0.352311	−	0.610220i
$251$	20.6497			1.30340			0.651698	−	0.758479i	$-0.274057\pi$
$251$	20.6497			1.30340			0.651698	+	0.758479i	$0.274057\pi$
$252$	−11.9434	−	6.75004i	−0.752362	−	0.425213i
$253$	−2.42143			−0.152234
$254$	9.61631	+	16.6559i	0.603381	+	1.04509i
$255$	8.58760	−	14.8742i	0.537776	−	0.931455i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.8574	+	27.4659i	0.989160	+	1.71328i	0.621747	+	0.783218i	$0.286423\pi$
$257$	15.8574	+	27.4659i	0.989160	+	1.71328i	0.367413	+	0.930058i	$0.380244\pi$
$258$	−6.85983			−0.427075
$259$	−0.103740	−	11.2971i	−0.00644609	−	0.701965i
$260$	7.78868			0.483033
$261$	−7.95081	−	13.7712i	−0.492143	−	0.852416i
$262$	8.58526	−	14.8701i	0.530399	−	0.918678i
$263$	4.26337	−	7.38437i	0.262890	−	0.455340i	−0.704118	−	0.710083i	$-0.748658\pi$
$263$	4.26337	−	7.38437i	0.262890	−	0.455340i	0.967009	+	0.254743i	$0.0819909\pi$
$264$	3.46385	+	5.99956i	0.213185	+	0.369247i
$265$	5.84172			0.358854
$266$	3.35025	−	1.97551i	0.205417	−	0.121126i
$267$	−51.4231			−3.14705
$268$	4.79148	+	8.29909i	0.292686	+	0.506947i
$269$	−14.2688	+	24.7143i	−0.869984	+	1.50686i	−0.00797307	+	0.999968i	$0.502538\pi$
$269$	−14.2688	+	24.7143i	−0.869984	+	1.50686i	−0.862011	+	0.506889i	$0.830795\pi$
$270$	−4.29148	+	7.43306i	−0.261171	+	0.452362i
$271$	−6.05147	−	10.4815i	−0.367601	−	0.636703i	0.621589	−	0.783343i	$-0.286487\pi$
$271$	−6.05147	−	10.4815i	−0.367601	−	0.636703i	−0.989190	+	0.146640i	$0.953154\pi$
$272$	4.37285			0.265143
$273$	−36.9922	+	21.8128i	−2.23887	+	1.32017i
$274$	−13.7501			−0.830673
$275$	−3.77174	−	6.53285i	−0.227445	−	0.393946i
$276$	1.43049	−	2.47769i	0.0861056	−	0.149139i
$277$	−1.90670	+	3.30249i	−0.114562	+	0.198428i	−0.917605	−	0.397494i	$-0.869880\pi$
$277$	−1.90670	+	3.30249i	−0.114562	+	0.198428i	0.803042	+	0.595922i	$0.203213\pi$
$278$	3.71860	+	6.44080i	0.223027	+	0.386293i
$279$	37.8551			2.26632
$280$	−0.0333529	−	3.63205i	−0.00199322	−	0.217057i
$281$	5.02136			0.299549			0.149775	−	0.988720i	$-0.452145\pi$
$281$	5.02136			0.299549			0.149775	+	0.988720i	$0.452145\pi$
$282$	2.61854	+	4.53544i	0.155932	+	0.270081i
$283$	2.85997	−	4.95361i	0.170008	−	0.294462i	−0.768415	−	0.639952i	$-0.778954\pi$
$283$	2.85997	−	4.95361i	0.170008	−	0.294462i	0.938422	+	0.345491i	$0.112287\pi$
$284$	7.07052	−	12.2465i	0.419558	−	0.726696i
$285$	−2.88690	−	5.00026i	−0.171005	−	0.296190i
$286$	13.7377			0.812329
$287$	−15.9568	−	9.01833i	−0.941901	−	0.532335i
$288$	−5.18524			−0.305543
$289$	−1.06089	−	1.83751i	−0.0624052	−	0.108089i
$290$	2.10506	−	3.64607i	0.123613	−	0.214104i
$291$	−3.23444	+	5.60221i	−0.189606	+	0.328407i
$292$	2.22883	+	3.86045i	0.130433	+	0.225916i
$293$	−14.4045			−0.841518			−0.420759	−	0.907172i	$-0.638236\pi$
$293$	−14.4045			−0.841518			−0.420759	+	0.907172i	$0.638236\pi$
$294$	10.3303	+	17.1570i	0.602474	+	1.00062i
$295$	1.14341			0.0665718
$296$	−2.13503	−	3.69798i	−0.124096	−	0.214941i
$297$	−7.56934	+	13.1105i	−0.439218	+	0.760748i
$298$	3.53997	−	6.13141i	0.205065	−	0.355183i
$299$	−2.83669	−	4.91329i	−0.164050	−	0.284143i
$300$	8.91282			0.514582
$301$	5.52275	+	3.12130i	0.318326	+	0.179909i
$302$	−14.8192			−0.852746
$303$	18.5884	+	32.1960i	1.06788	+	1.84961i
$304$	0.735012	−	1.27308i	0.0421558	−	0.0730161i
$305$	10.5327	−	18.2433i	0.603103	−	1.04461i
$306$	11.3371	+	19.6365i	0.648101	+	1.12254i
$307$	−10.2596			−0.585545			−0.292773	−	0.956182i	$-0.594578\pi$
$307$	−10.2596			−0.585545			−0.292773	+	0.956182i	$0.594578\pi$
$308$	−0.0588281	−	6.40624i	−0.00335204	−	0.365030i
$309$	41.5919			2.36608
$310$	5.01126	+	8.67975i	0.284620	+	0.492977i
$311$	−15.0500	+	26.0674i	−0.853410	+	1.47815i	0.0247026	+	0.999695i	$0.492136\pi$
$311$	−15.0500	+	26.0674i	−0.853410	+	1.47815i	−0.878112	+	0.478454i	$0.841197\pi$
$312$	−8.11574	+	14.0569i	−0.459463	+	0.795813i
$313$	7.85525	+	13.6057i	0.444005	+	0.769039i	0.997982	−	0.0634927i	$-0.0202240\pi$
$313$	7.85525	+	13.6057i	0.444005	+	0.769039i	−0.553977	+	0.832532i	$0.686891\pi$
$314$	14.1343			0.797644
$315$	16.2235	−	9.56631i	0.914088	−	0.539001i
$316$	15.0102			0.844387
$317$	13.6693	+	23.6760i	0.767746	+	1.32977i	0.938783	+	0.344510i	$0.111955\pi$
$317$	13.6693	+	23.6760i	0.767746	+	1.32977i	−0.171037	+	0.985265i	$0.554712\pi$
$318$	−6.08702	+	10.5430i	−0.341343	+	0.591224i
$319$	3.71291	−	6.43096i	0.207883	−	0.360064i
$320$	−0.686423	−	1.18892i	−0.0383722	−	0.0664626i
$321$	5.46327			0.304930
$322$	−2.27904	+	1.34386i	−0.127006	+	0.0748904i
$323$	−6.42819			−0.357674
$324$	−1.16551	−	2.01871i	−0.0647503	−	0.112151i
$325$	8.83713	−	15.3064i	0.490196	−	0.849044i
$326$	0.544032	−	0.942291i	0.0301311	−	0.0521886i
$327$	13.1975	+	22.8588i	0.729826	+	1.26410i
$328$	−6.92769			−0.382518
$329$	−0.0444718	−	4.84288i	−0.00245181	−	0.266997i
$330$	−9.51065			−0.523544
$331$	−11.5219	−	19.9566i	−0.633303	−	1.09691i	−0.986872	−	0.161504i	$-0.948365\pi$
$331$	−11.5219	−	19.9566i	−0.633303	−	1.09691i	0.353569	−	0.935408i	$-0.384968\pi$
$332$	−2.58194	+	4.47206i	−0.141702	+	0.245436i
$333$	11.0707	−	19.1749i	0.606668	−	1.05078i
$334$	−0.930933	−	1.61242i	−0.0509384	−	0.0882279i
$335$	−13.1559			−0.718785
$336$	6.58982	+	3.72437i	0.359504	+	0.203181i
$337$	3.30493			0.180031			0.0900155	−	0.995940i	$-0.471308\pi$
$337$	3.30493			0.180031			0.0900155	+	0.995940i	$0.471308\pi$
$338$	9.59364	+	16.6167i	0.521825	+	0.903828i
$339$	−19.0971	+	33.0771i	−1.03721	+	1.79650i
$340$	−3.00162	+	5.19896i	−0.162786	+	0.281953i
$341$	8.83889	+	15.3094i	0.478653	+	0.829051i
$342$	7.62243			0.412174
$343$	−0.510132	−	18.5132i	−0.0275445	−	0.999621i
$344$	2.39772			0.129276
$345$	1.96385	+	3.40148i	0.105730	+	0.183130i
$346$	5.81695	−	10.0753i	0.312721	−	0.541649i
$347$	−8.33781	+	14.4415i	−0.447597	+	0.775261i	−0.998229	−	0.0594869i	$-0.981054\pi$
$347$	−8.33781	+	14.4415i	−0.447597	+	0.775261i	0.550632	+	0.834748i	$0.314387\pi$
$348$	4.38690	+	7.59834i	0.235163	+	0.407314i
$349$	−23.6991			−1.26859			−0.634293	−	0.773093i	$-0.718709\pi$
$349$	−23.6991			−1.26859			−0.634293	+	0.773093i	$0.718709\pi$
$350$	−7.17558	−	4.05543i	−0.383551	−	0.216772i
$351$	−35.4697			−1.89323
$352$	−1.21072	−	2.09702i	−0.0645315	−	0.111772i
$353$	−9.23663	+	15.9983i	−0.491616	+	0.851505i	−0.999953	−	0.00965369i	$-0.996927\pi$
$353$	−9.23663	+	15.9983i	−0.491616	+	0.851505i	0.508337	+	0.861158i	$0.330260\pi$
$354$	−1.19142	+	2.06360i	−0.0633233	+	0.109679i
$355$	9.70674	+	16.8126i	0.515180	+	0.892318i
$356$	17.9739			0.952616
$357$	−0.303943	−	33.0987i	−0.0160864	−	1.75177i
$358$	14.1443			0.747549
$359$	−9.41644	−	16.3097i	−0.496981	−	0.860796i	0.503013	−	0.864279i	$-0.332225\pi$
$359$	−9.41644	−	16.3097i	−0.496981	−	0.860796i	−0.999994	+	0.00348307i	$0.998891\pi$
$360$	3.55927	−	6.16483i	0.187590	−	0.324915i
$361$	8.41951	−	14.5830i	0.443132	−	0.767528i
$362$	1.67168	+	2.89544i	0.0878617	+	0.152181i
$363$	14.6959			0.771334
$364$	12.9299	−	7.62423i	0.677710	−	0.399618i
$365$	−6.11969			−0.320319
$366$	21.9501	+	38.0186i	1.14735	+	1.98727i
$367$	−9.58398	+	16.5999i	−0.500279	+	0.866509i	0.499721	+	0.866187i	$0.333436\pi$
$367$	−9.58398	+	16.5999i	−0.500279	+	0.866509i	−1.00000		0.000322685i	$0.999897\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	−17.9609	−	31.1092i	−0.935006	−	1.61948i
$370$	5.86214			0.304758
$371$	9.69776	−	5.71838i	0.503483	−	0.296883i
$372$	−20.8867			−1.08293
$373$	10.7957	+	18.6988i	0.558982	+	0.968185i	0.997582	+	0.0695028i	$0.0221413\pi$
$373$	10.7957	+	18.6988i	0.558982	+	0.968185i	−0.438600	+	0.898683i	$0.644525\pi$
$374$	−5.29428	+	9.16996i	−0.273761	+	0.474167i
$375$	−15.9372	+	27.6040i	−0.822993	+	1.42547i
$376$	−0.915257	−	1.58527i	−0.0472008	−	0.0817541i
$377$	17.3986			0.896073
$378$	0.151889	+	16.5404i	0.00781235	+	0.850747i
$379$	−36.0921			−1.85393			−0.926964	−	0.375150i	$-0.877591\pi$
$379$	−36.0921			−1.85393			−0.926964	+	0.375150i	$0.877591\pi$
$380$	1.00906	+	1.74774i	0.0517636	+	0.0896572i
$381$	27.5121	−	47.6524i	1.40949	−	2.44131i
$382$	8.02987	−	13.9081i	0.410844	−	0.711602i
$383$	6.79985	+	11.7777i	0.347456	+	0.601812i	0.985797	−	0.167942i	$-0.0537122\pi$
$383$	6.79985	+	11.7777i	0.347456	+	0.601812i	−0.638341	+	0.769754i	$0.720379\pi$
$384$	2.86099			0.145999
$385$	7.65689	+	4.32745i	0.390231	+	0.220547i
$386$	−6.46442			−0.329030
$387$	6.21637	+	10.7671i	0.315996	+	0.547321i
$388$	1.13053	−	1.95814i	0.0573941	−	0.0994094i
$389$	2.46267	−	4.26546i	0.124862	−	0.216268i	−0.796817	−	0.604221i	$-0.793484\pi$
$389$	2.46267	−	4.26546i	0.124862	−	0.216268i	0.921679	+	0.387953i	$0.126818\pi$
$390$	−11.1417	−	19.2979i	−0.564179	−	0.977187i
$391$	4.37285			0.221144
$392$	−3.61074	−	5.99688i	−0.182370	−	0.302888i
$393$	−49.1246			−2.47801
$394$	6.36318	+	11.0214i	0.320573	+	0.555248i
$395$	−10.3033	+	17.8459i	−0.518416	+	0.897923i
$396$	6.27786	−	10.8736i	0.315475	−	0.546418i
$397$	−15.1636	−	26.2641i	−0.761038	−	1.31816i	−0.942316	−	0.334725i	$-0.891356\pi$
$397$	−15.1636	−	26.2641i	−0.761038	−	1.31816i	0.181277	−	0.983432i	$-0.441977\pi$
$398$	−15.4893			−0.776408
$399$	−9.68720	−	5.47492i	−0.484966	−	0.274089i
$400$	−3.11530			−0.155765
$401$	−1.06882	−	1.85126i	−0.0533745	−	0.0924474i	0.838104	−	0.545511i	$-0.183664\pi$
$401$	−1.06882	−	1.85126i	−0.0533745	−	0.0924474i	−0.891478	+	0.453064i	$0.850331\pi$
$402$	13.7084	−	23.7436i	0.683711	−	1.18422i
$403$	−20.7094	+	35.8697i	−1.03161	+	1.78680i
$404$	−6.49720	−	11.2535i	−0.323248	−	0.559881i
$405$	3.20012			0.159015
$406$	−0.0745048	−	8.11340i	−0.00369761	−	0.402661i
$407$	10.3397			0.512519
$408$	−6.25533	−	10.8345i	−0.309685	−	0.536390i
$409$	10.8072	−	18.7187i	0.534383	−	0.925579i	−0.464810	−	0.885411i	$-0.653877\pi$
$409$	10.8072	−	18.7187i	0.534383	−	0.925579i	0.999193	−	0.0401685i	$-0.0127895\pi$
$410$	4.75533	−	8.23647i	0.234849	−	0.406770i
$411$	19.6694	+	34.0684i	0.970220	+	1.68047i
$412$	−14.5376			−0.716217
$413$	1.89816	−	1.11927i	0.0934022	−	0.0550755i
$414$	−5.18524			−0.254841
$415$	−3.54461	−	6.13944i	−0.173998	−	0.301373i
$416$	2.83669	−	4.91329i	0.139080	−	0.240894i
$417$	10.6388	−	18.4270i	0.520987	−	0.902375i
$418$	1.77978	+	3.08268i	0.0870521	+	0.150779i
$419$	−13.1978			−0.644753			−0.322376	−	0.946612i	$-0.604482\pi$
$419$	−13.1978			−0.644753			−0.322376	+	0.946612i	$0.604482\pi$
$420$	−8.95138	+	5.27827i	−0.436783	+	0.257553i
$421$	11.4270			0.556917			0.278458	−	0.960448i	$-0.410177\pi$
$421$	11.4270			0.556917			0.278458	+	0.960448i	$0.410177\pi$
$422$	−4.66331	−	8.07709i	−0.227006	−	0.393186i
$423$	4.74583	−	8.22001i	0.230750	−	0.399671i
$424$	2.12759	−	3.68510i	0.103325	−	0.178964i
$425$	6.81135	+	11.7976i	0.330399	+	0.572268i
$426$	−40.4573			−1.96016
$427$	−0.372788	−	40.5958i	−0.0180405	−	1.96457i
$428$	−1.90958			−0.0923028
$429$	−19.6517	−	34.0378i	−0.948794	−	1.64336i
$430$	−1.64585	+	2.85069i	−0.0793698	+	0.137473i
$431$	10.4265	−	18.0592i	0.502227	−	0.869883i	−0.497769	−	0.867309i	$-0.665847\pi$
$431$	10.4265	−	18.0592i	0.502227	−	0.869883i	0.999997	−	0.00257388i	$-0.000819293\pi$
$432$	3.12597	+	5.41435i	0.150398	+	0.260498i
$433$	2.16152			0.103876			0.0519381	−	0.998650i	$-0.483460\pi$
$433$	2.16152			0.103876			0.0519381	+	0.998650i	$0.483460\pi$
$434$	16.8156	+	9.50369i	0.807175	+	0.456192i
$435$	−12.0451			−0.577517
$436$	−4.61293	−	7.98984i	−0.220919	−	0.382644i
$437$	0.735012	−	1.27308i	0.0351604	−	0.0608996i
$438$	6.37666	−	11.0447i	0.304689	−	0.527736i
$439$	3.90864	+	6.76996i	0.186549	+	0.323113i	0.944097	−	0.329667i	$-0.106936\pi$
$439$	3.90864	+	6.76996i	0.186549	+	0.323113i	−0.757548	+	0.652779i	$0.773603\pi$
$440$	3.32426			0.158478
$441$	17.5680	−	31.7618i	0.836573	−	1.51247i
$442$	−24.8088			−1.18004
$443$	−5.97290	−	10.3454i	−0.283781	−	0.491524i	0.688532	−	0.725206i	$-0.258256\pi$
$443$	−5.97290	−	10.3454i	−0.283781	−	0.491524i	−0.972313	+	0.233683i	$0.924922\pi$
$444$	−6.10830	+	10.5799i	−0.289887	+	0.502099i
$445$	−12.3377	+	21.3695i	−0.584863	+	1.01301i
$446$	11.3360	+	19.6344i	0.536773	+	0.929718i
$447$	−20.2556			−0.958058
$448$	−2.30334	−	1.30178i	−0.108823	−	0.0615033i
$449$	7.69249			0.363031			0.181516	−	0.983388i	$-0.441900\pi$
$449$	7.69249			0.363031			0.181516	+	0.983388i	$0.441900\pi$
$450$	−8.07678	−	13.9894i	−0.380743	−	0.659466i
$451$	8.38748	−	14.5275i	0.394951	−	0.684075i
$452$	6.67500	−	11.5614i	0.313966	−	0.543805i
$453$	21.1987	+	36.7172i	0.996002	+	1.72513i
$454$	−4.24871			−0.199402
$455$	0.189224	+	20.6060i	0.00887095	+	0.966026i
$456$	−4.20572			−0.196951
$457$	13.2368	+	22.9269i	0.619194	+	1.07247i	0.989633	+	0.143618i	$0.0458737\pi$
$457$	13.2368	+	22.9269i	0.619194	+	1.07247i	−0.370440	+	0.928857i	$0.620793\pi$
$458$	−1.34007	+	2.32107i	−0.0626173	+	0.108456i
$459$	13.6694	−	23.6761i	0.638033	−	1.10511i
$460$	−0.686423	−	1.18892i	−0.0320046	−	0.0554336i
$461$	9.94208			0.463049			0.231524	−	0.972829i	$-0.425629\pi$
$461$	9.94208			0.463049			0.231524	+	0.972829i	$0.425629\pi$
$462$	−15.7885	+	9.30985i	−0.734548	+	0.433133i
$463$	−30.3503			−1.41050			−0.705249	−	0.708960i	$-0.749165\pi$
$463$	−30.3503			−1.41050			−0.705249	+	0.708960i	$0.749165\pi$
$464$	−1.53335	−	2.65585i	−0.0711841	−	0.123295i
$465$	14.3371	−	24.8326i	0.664869	−	1.15159i
$466$	12.2429	−	21.2053i	0.567141	−	0.982317i
$467$	10.1121	+	17.5146i	0.467930	+	0.810479i	0.999328	−	0.0366434i	$-0.0116666\pi$
$467$	10.1121	+	17.5146i	0.467930	+	0.810479i	−0.531398	+	0.847122i	$0.678333\pi$
$468$	29.4179			1.35984
$469$	−21.8400	+	12.8782i	−1.00848	+	0.594658i
$470$	2.51301			0.115917
$471$	−20.2190	−	35.0203i	−0.931643	−	1.61365i
$472$	0.416437	−	0.721290i	0.0191681	−	0.0332001i
$473$	−2.90296	+	5.02807i	−0.133478	+	0.231191i
$474$	−21.4719	−	37.1905i	−0.986238	−	1.70821i
$475$	4.57956			0.210125
$476$	0.106237	+	11.5690i	0.00486937	+	0.530263i
$477$	22.0642			1.01025
$478$	−5.08644	−	8.80998i	−0.232648	−	0.402959i
$479$	−7.49152	+	12.9757i	−0.342296	+	0.592874i	−0.984859	−	0.173359i	$-0.944538\pi$
$479$	−7.49152	+	12.9757i	−0.342296	+	0.592874i	0.642563	+	0.766233i	$0.277871\pi$
$480$	−1.96385	+	3.40148i	−0.0896369	+	0.155256i
$481$	12.1129	+	20.9801i	0.552299	+	0.956609i
$482$	−10.5738			−0.481625
$483$	6.58982	+	3.72437i	0.299847	+	0.169465i
$484$	−5.13665			−0.233484
$485$	1.55205	+	2.68822i	0.0704748	+	0.122066i
$486$	6.04343	−	10.4675i	0.274135	−	0.474817i
$487$	−6.44921	+	11.1704i	−0.292242	+	0.506178i	−0.974339	−	0.225083i	$-0.927735\pi$
$487$	−6.44921	+	11.1704i	−0.292242	+	0.506178i	0.682098	+	0.731261i	$0.261068\pi$
$488$	−7.67220	−	13.2886i	−0.347304	−	0.601549i
$489$	−3.11293			−0.140772
$490$	9.60830	−	0.176480i	0.434059	−	0.00797253i
$491$	8.82355			0.398201			0.199101	−	0.979979i	$-0.436198\pi$
$491$	8.82355			0.398201			0.199101	+	0.979979i	$0.436198\pi$
$492$	9.91002	+	17.1647i	0.446778	+	0.773842i
$493$	−6.70512	+	11.6136i	−0.301983	+	0.523050i
$494$	−4.17001	+	7.22266i	−0.187617	+	0.324963i
$495$	8.61854	+	14.9277i	0.387374	+	0.670952i
$496$	7.30054			0.327804
$497$	32.5716	+	18.4085i	1.46104	+	0.825736i
$498$	14.7738			0.662030
$499$	10.4163	+	18.0415i	0.466296	+	0.807649i	0.999259	−	0.0384897i	$-0.0122547\pi$
$499$	10.4163	+	18.0415i	0.466296	+	0.807649i	−0.532963	+	0.846139i	$0.678921\pi$
$500$	5.57052	−	9.64843i	0.249121	−	0.431491i
$501$	−2.66339	+	4.61312i	−0.118991	+	0.206099i
$502$	10.3248	+	17.8831i	0.460820	+	0.798163i
$503$	20.3341			0.906652			0.453326	−	0.891345i	$-0.350237\pi$
$503$	20.3341			0.906652			0.453326	+	0.891345i	$0.350237\pi$
$504$	−0.125974	−	13.7183i	−0.00561133	−	0.611061i
$505$	17.8393			0.793838
$506$	−1.21072	−	2.09702i	−0.0538230	−	0.0932241i
$507$	27.4473	−	47.5401i	1.21898	−	2.11133i
$508$	−9.61631	+	16.6559i	−0.426655	+	0.738988i
$509$	−1.59482	−	2.76231i	−0.0706891	−	0.122437i	0.828514	−	0.559968i	$-0.189186\pi$
$509$	−1.59482	−	2.76231i	−0.0706891	−	0.122437i	−0.899203	+	0.437531i	$0.855853\pi$
$510$	17.1752			0.760530
$511$	−10.1592	+	5.99048i	−0.449417	+	0.265003i
$512$	−1.00000			−0.0441942
$513$	−4.59526	−	7.95922i	−0.202886	−	0.351408i
$514$	−15.8574	+	27.4659i	−0.699442	+	1.21147i
$515$	9.97895	−	17.2840i	0.439725	−	0.761626i
$516$	−3.42992	−	5.94079i	−0.150994	−	0.261529i
$517$	4.43247			0.194940
$518$	9.73166	−	5.73837i	0.427585	−	0.252129i
$519$	−33.2845			−1.46103
$520$	3.89434	+	6.74519i	0.170778	+	0.295796i
$521$	5.38616	−	9.32910i	0.235972	−	0.408716i	−0.723583	−	0.690238i	$-0.757506\pi$
$521$	5.38616	−	9.32910i	0.235972	−	0.408716i	0.959555	+	0.281522i	$0.0908393\pi$
$522$	7.95081	−	13.7712i	0.347997	−	0.602749i
$523$	15.2458	+	26.4064i	0.666651	+	1.15467i	0.978835	+	0.204652i	$0.0656062\pi$
$523$	15.2458	+	26.4064i	0.666651	+	1.15467i	−0.312184	+	0.950022i	$0.601061\pi$
$524$	17.1705			0.750098
$525$	0.216534	+	23.5801i	0.00945034	+	1.02912i
$526$	8.52673			0.371783
$527$	−15.9621	−	27.6471i	−0.695318	−	1.20433i
$528$	−3.46385	+	5.99956i	−0.150745	+	0.261097i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	2.92086	+	5.05908i	0.126874	+	0.219752i
$531$	4.31865			0.187414
$532$	3.38596	+	1.91365i	0.146800	+	0.0829672i
$533$	39.3035			1.70242
$534$	−25.7116	−	44.5337i	−1.11265	−	1.92716i
$535$	1.31078	−	2.27033i	0.0566698	−	0.0981550i
$536$	−4.79148	+	8.29909i	−0.206960	+	0.358466i
$537$	−20.2333	−	35.0451i	−0.873132	−	1.51231i
$538$	−28.5376			−1.23034
$539$	16.9472	−	0.311276i	0.729967	−	0.0134076i
$540$	−8.58296			−0.369352
$541$	−23.0981	−	40.0071i	−0.993065	−	1.72004i	−0.598346	−	0.801238i	$-0.704175\pi$
$541$	−23.0981	−	40.0071i	−0.993065	−	1.72004i	−0.394719	−	0.918802i	$-0.629158\pi$
$542$	6.05147	−	10.4815i	0.259933	−	0.450217i
$543$	4.78266	−	8.28382i	0.205244	−	0.355493i
$544$	2.18642	+	3.78700i	0.0937421	+	0.162366i
$545$	12.6657			0.542539
$546$	−37.3866	−	21.1298i	−1.60000	−	0.904272i
$547$	30.2044			1.29145			0.645723	−	0.763571i	$-0.276556\pi$
$547$	30.2044			1.29145			0.645723	+	0.763571i	$0.276556\pi$
$548$	−6.87504	−	11.9079i	−0.293687	−	0.508681i
$549$	39.7822	−	68.9048i	1.69786	−	2.94079i
$550$	3.77174	−	6.53285i	0.160828	−	0.278562i
$551$	2.25407	+	3.90416i	0.0960264	+	0.166323i
$552$	2.86099			0.121772
$553$	0.364668	+	39.7115i	0.0155072	+	1.68870i
$554$	−3.81339			−0.162015
$555$	−8.38575	−	14.5245i	−0.355955	−	0.616533i
$556$	−3.71860	+	6.44080i	−0.157704	+	0.273151i
$557$	19.9208	−	34.5038i	0.844070	−	1.46197i	−0.0423559	−	0.999103i	$-0.513486\pi$
$557$	19.9208	−	34.5038i	0.844070	−	1.46197i	0.886426	−	0.462870i	$-0.153180\pi$
$558$	18.9275	+	32.7834i	0.801266	+	1.38783i
$559$	−13.6032			−0.575353
$560$	3.12878	−	1.84491i	0.132215	−	0.0779618i
$561$	30.2937			1.27900
$562$	2.51068	+	4.34862i	0.105907	+	0.183436i
$563$	8.19098	−	14.1872i	0.345209	−	0.597919i	−0.640183	−	0.768222i	$-0.721141\pi$
$563$	8.19098	−	14.1872i	0.345209	−	0.597919i	0.985392	+	0.170304i	$0.0544748\pi$
$564$	−2.61854	+	4.53544i	−0.110260	+	0.190976i
$565$	9.16375	+	15.8721i	0.385522	+	0.667743i
$566$	5.71994			0.240427
$567$	5.31248	−	3.13255i	0.223103	−	0.131555i
$568$	14.1410			0.593345
$569$	−2.99775	−	5.19225i	−0.125672	−	0.217670i	0.796323	−	0.604871i	$-0.206775\pi$
$569$	−2.99775	−	5.19225i	−0.125672	−	0.217670i	−0.921995	+	0.387201i	$0.873442\pi$
$570$	2.88690	−	5.00026i	0.120919	−	0.209438i
$571$	−1.04571	+	1.81122i	−0.0437616	+	0.0757973i	−0.887077	−	0.461622i	$-0.847268\pi$
$571$	−1.04571	+	1.81122i	−0.0437616	+	0.0757973i	0.843315	+	0.537420i	$0.180601\pi$
$572$	6.86886	+	11.8972i	0.287202	+	0.497448i
$573$	−45.9467			−1.91945
$574$	−0.168306	−	18.3282i	−0.00702497	−	0.765003i
$575$	−3.11530			−0.129917
$576$	−2.59262	−	4.49055i	−0.108026	−	0.187106i
$577$	−6.27575	+	10.8699i	−0.261263	+	0.452520i	−0.966578	−	0.256374i	$-0.917472\pi$
$577$	−6.27575	+	10.8699i	−0.261263	+	0.452520i	0.705315	+	0.708894i	$0.250806\pi$
$578$	1.06089	−	1.83751i	0.0441272	−	0.0764305i
$579$	9.24731	+	16.0168i	0.384305	+	0.665636i
$580$	4.21011			0.174815
$581$	−11.8942	−	6.72224i	−0.493454	−	0.278886i
$582$	−6.46887			−0.268143
$583$	5.15183	+	8.92323i	0.213367	+	0.369563i
$584$	−2.22883	+	3.86045i	−0.0922298	+	0.159747i
$585$	−20.1931	+	34.9755i	−0.834882	+	1.44606i
$586$	−7.20224	−	12.4746i	−0.297522	−	0.515323i
$587$	−13.2722			−0.547803			−0.273901	−	0.961758i	$-0.588314\pi$
$587$	−13.2722			−0.547803			−0.273901	+	0.961758i	$0.588314\pi$
$588$	−9.69326	+	17.5248i	−0.399743	+	0.722709i
$589$	−10.7320			−0.442203
$590$	0.571704	+	0.990220i	0.0235367	+	0.0407667i
$591$	18.2050	−	31.5319i	0.748853	−	1.29705i
$592$	2.13503	−	3.69798i	0.0877493	−	0.151986i
$593$	−16.3241	−	28.2743i	−0.670352	−	1.16108i	−0.977804	−	0.209521i	$-0.932810\pi$
$593$	−16.3241	−	28.2743i	−0.670352	−	1.16108i	0.307452	−	0.951564i	$-0.400524\pi$
$594$	−15.1387			−0.621148
$595$	−13.8275	−	7.81490i	−0.566872	−	0.320380i
$596$	7.07994			0.290006
$597$	22.1573	+	38.3776i	0.906839	+	1.57069i
$598$	2.83669	−	4.91329i	0.116001	−	0.200920i
$599$	−3.72079	+	6.44460i	−0.152027	+	0.263319i	−0.931973	−	0.362529i	$-0.881914\pi$
$599$	−3.72079	+	6.44460i	−0.152027	+	0.263319i	0.779945	+	0.625848i	$0.215247\pi$
$600$	4.45641	+	7.71873i	0.181932	+	0.315116i
$601$	13.8561			0.565202			0.282601	−	0.959237i	$-0.408803\pi$
$601$	13.8561			0.565202			0.282601	+	0.959237i	$0.408803\pi$
$602$	0.0582519	+	6.34349i	0.00237417	+	0.258542i
$603$	−49.6900			−2.02353
$604$	−7.40958	−	12.8338i	−0.301491	−	0.522198i
$605$	3.52592	−	6.10706i	0.143349	−	0.248287i
$606$	−18.5884	+	32.1960i	−0.755102	+	1.30788i
$607$	−4.16940	−	7.22162i	−0.169231	−	0.293116i	0.768919	−	0.639346i	$-0.220795\pi$
$607$	−4.16940	−	7.22162i	−0.169231	−	0.293116i	−0.938150	+	0.346230i	$0.887462\pi$
$608$	1.47002			0.0596174
$609$	−19.9959	+	11.7908i	−0.810274	+	0.477786i
$610$	21.0655			0.852917
$611$	5.19260	+	8.99385i	0.210070	+	0.363852i
$612$	−11.3371	+	19.6365i	−0.458276	+	0.793758i
$613$	−4.66713	+	8.08370i	−0.188503	+	0.326498i	−0.944751	−	0.327787i	$-0.893697\pi$
$613$	−4.66713	+	8.08370i	−0.188503	+	0.326498i	0.756248	+	0.654285i	$0.227030\pi$
$614$	−5.12979	−	8.88506i	−0.207022	−	0.358572i
$615$	−27.2098			−1.09721
$616$	5.51856	−	3.25407i	0.222349	−	0.131110i
$617$	14.0901			0.567246			0.283623	−	0.958936i	$-0.408464\pi$
$617$	14.0901			0.567246			0.283623	+	0.958936i	$0.408464\pi$
$618$	20.7960	+	36.0196i	0.836536	+	1.44892i
$619$	4.55839	−	7.89536i	0.183217	−	0.317341i	−0.759757	−	0.650207i	$-0.774682\pi$
$619$	4.55839	−	7.89536i	0.183217	−	0.317341i	0.942974	+	0.332866i	$0.108016\pi$
$620$	−5.01126	+	8.67975i	−0.201257	+	0.348587i
$621$	3.12597	+	5.41435i	0.125441	+	0.217270i
$622$	−30.1001			−1.20690
$623$	0.436671	+	47.5525i	0.0174949	+	1.90515i
$624$	−16.2315			−0.649779
$625$	−0.140770	−	0.243822i	−0.00563082	−	0.00975286i
$626$	−7.85525	+	13.6057i	−0.313959	+	0.543793i
$627$	5.09194	−	8.81950i	0.203352	−	0.352217i
$628$	7.06715	+	12.2407i	0.282010	+	0.488455i
$629$	−18.6723			−0.744515
$630$	16.3964	+	9.26677i	0.653248	+	0.369197i
$631$	−6.19660			−0.246683			−0.123341	−	0.992364i	$-0.539361\pi$
$631$	−6.19660			−0.246683			−0.123341	+	0.992364i	$0.539361\pi$
$632$	7.50508	+	12.9992i	0.298536	+	0.517079i
$633$	−13.3417	+	23.1084i	−0.530283	+	0.918478i
$634$	−13.6693	+	23.6760i	−0.542878	+	0.940293i
$635$	−13.2017	−	22.8660i	−0.523894	−	0.907411i
$636$	−12.1740			−0.482732
$637$	20.4851	+	34.0226i	0.811649	+	1.34802i
$638$	7.42583			0.293991
$639$	36.6624	+	63.5011i	1.45034	+	2.51206i
$640$	0.686423	−	1.18892i	0.0271332	−	0.0469962i
$641$	−19.5246	+	33.8175i	−0.771174	+	1.33571i	0.165746	+	0.986169i	$0.446997\pi$
$641$	−19.5246	+	33.8175i	−0.771174	+	1.33571i	−0.936920	+	0.349544i	$0.886336\pi$
$642$	2.73163	+	4.73133i	0.107809	+	0.186731i
$643$	−35.2213			−1.38899			−0.694495	−	0.719497i	$-0.744372\pi$
$643$	−35.2213			−1.38899			−0.694495	+	0.719497i	$0.744372\pi$
$644$	−2.30334	−	1.30178i	−0.0907643	−	0.0512973i
$645$	9.41749			0.370813
$646$	−3.21409	−	5.56698i	−0.126457	−	0.219030i
$647$	2.95300	−	5.11475i	0.116095	−	0.201082i	−0.802122	−	0.597160i	$-0.796296\pi$
$647$	2.95300	−	5.11475i	0.116095	−	0.201082i	0.918217	+	0.396078i	$0.129629\pi$
$648$	1.16551	−	2.01871i	0.0457854	−	0.0793026i
$649$	1.00838	+	1.74656i	0.0395822	+	0.0685584i
$650$	17.6743			0.693242
$651$	−0.507438	−	55.2588i	−0.0198880	−	2.16576i
$652$	1.08806			0.0426119
$653$	−0.936095	−	1.62136i	−0.0366322	−	0.0634489i	0.847128	−	0.531389i	$-0.178330\pi$
$653$	−0.936095	−	1.62136i	−0.0366322	−	0.0634489i	−0.883760	+	0.467940i	$0.844996\pi$
$654$	−13.1975	+	22.8588i	−0.516065	+	0.893850i
$655$	−11.7862	+	20.4144i	−0.460526	+	0.797655i
$656$	−3.46385	−	5.99956i	−0.135240	−	0.234243i
$657$	−23.1141			−0.901766
$658$	4.17182	−	2.45995i	0.162634	−	0.0958989i
$659$	8.71358			0.339433			0.169716	−	0.985493i	$-0.445715\pi$
$659$	8.71358			0.339433			0.169716	+	0.985493i	$0.445715\pi$
$660$	−4.75533	−	8.23647i	−0.185101	−	0.320604i
$661$	11.4035	−	19.7514i	0.443544	−	0.768240i	−0.554406	−	0.832247i	$-0.687054\pi$
$661$	11.4035	−	19.7514i	0.443544	−	0.768240i	0.997950	+	0.0640061i	$0.0203877\pi$
$662$	11.5219	−	19.9566i	0.447813	−	0.775634i
$663$	35.4889	+	61.4685i	1.37827	+	2.38724i
$664$	−5.16388			−0.200398
$665$	−4.59938	+	2.71207i	−0.178356	+	0.105169i
$666$	22.1413			0.857959
$667$	−1.53335	−	2.65585i	−0.0593717	−	0.102835i
$668$	0.930933	−	1.61242i	0.0360189	−	0.0623865i
$669$	32.4320	−	56.1739i	1.25389	−	2.17181i
$670$	−6.57796	−	11.3934i	−0.254129	−	0.440164i
$671$	37.1555			1.43437
$672$	0.0695069	+	7.56914i	0.00268129	+	0.291986i
$673$	−1.44855			−0.0558376			−0.0279188	−	0.999610i	$-0.508888\pi$
$673$	−1.44855			−0.0558376			−0.0279188	+	0.999610i	$0.508888\pi$
$674$	1.65247	+	2.86215i	0.0636506	+	0.110246i
$675$	−9.73833	+	16.8673i	−0.374829	+	0.649222i
$676$	−9.59364	+	16.6167i	−0.368986	+	0.639103i
$677$	−10.8383	−	18.7725i	−0.416550	−	0.721486i	0.579040	−	0.815299i	$-0.303428\pi$
$677$	−10.8383	−	18.7725i	−0.416550	−	0.721486i	−0.995590	+	0.0938133i	$0.970094\pi$
$678$	−38.1942			−1.46684
$679$	5.20800	+	2.94341i	0.199865	+	0.112958i
$680$	−6.00324			−0.230214
$681$	6.07775	+	10.5270i	0.232900	+	0.403394i
$682$	−8.83889	+	15.3094i	−0.338459	+	0.586227i
$683$	−15.4502	+	26.7605i	−0.591186	+	1.02396i	0.402888	+	0.915249i	$0.368007\pi$
$683$	−15.4502	+	26.7605i	−0.591186	+	1.02396i	−0.994073	+	0.108714i	$0.965327\pi$
$684$	3.81122	+	6.60122i	0.145725	+	0.252404i
$685$	18.8767			0.721243
$686$	15.7779	−	9.69840i	0.602402	−	0.370287i
$687$	7.66784			0.292546
$688$	1.19886	+	2.07648i	0.0457060	+	0.0791652i
$689$	−12.0707	+	20.9070i	−0.459855	+	0.796493i
$690$	−1.96385	+	3.40148i	−0.0747623	+	0.129492i
$691$	−15.2567	−	26.4254i	−0.580392	−	1.00527i	−0.995433	−	0.0954660i	$-0.969566\pi$
$691$	−15.2567	−	26.4254i	−0.580392	−	1.00527i	0.415040	−	0.909803i	$-0.363767\pi$
$692$	11.6339			0.442255
$693$	28.9201	+	16.3448i	1.09858	+	0.620887i
$694$	−16.6756			−0.632998
$695$	−5.10506	−	8.84222i	−0.193646	−	0.335404i
$696$	−4.38690	+	7.59834i	−0.166285	+	0.288014i
$697$	−15.1469	+	26.2351i	−0.573728	+	0.993727i
$698$	−11.8496	−	20.5241i	−0.448513	−	0.776847i
$699$	−70.0535			−2.64967
$700$	−0.0756852	−	8.24195i	−0.00286063	−	0.311516i
$701$	4.10294			0.154966			0.0774829	−	0.996994i	$-0.475312\pi$
$701$	4.10294			0.154966			0.0774829	+	0.996994i	$0.475312\pi$
$702$	−17.7348	−	30.7177i	−0.669359	−	1.15936i
$703$	−3.13855	+	5.43613i	−0.118373	+	0.205027i
$704$	1.21072	−	2.09702i	0.0456306	−	0.0790346i
$705$	−3.59485	−	6.22646i	−0.135390	−	0.234502i
$706$	−18.4733			−0.695251
$707$	29.6148	−	17.4626i	1.11378	−	0.656750i
$708$	−2.38284			−0.0895527
$709$	−18.8288	−	32.6124i	−0.707130	−	1.22478i	−0.965917	−	0.258851i	$-0.916656\pi$
$709$	−18.8288	−	32.6124i	−0.707130	−	1.22478i	0.258787	−	0.965934i	$-0.416677\pi$
$710$	−9.70674	+	16.8126i	−0.364287	+	0.630964i
$711$	−38.9156	+	67.4039i	−1.45945	+	2.52784i
$712$	8.98696	+	15.5659i	0.336801	+	0.583356i
$713$	7.30054			0.273407
$714$	28.5123	−	16.8126i	1.06705	−	0.629194i
$715$	−18.8598			−0.705316
$716$	7.07214	+	12.2493i	0.264298	+	0.457778i
$717$	−14.5522	+	25.2052i	−0.543463	+	0.941306i
$718$	9.41644	−	16.3097i	0.351418	−	0.608674i
$719$	−6.16051	−	10.6703i	−0.229748	−	0.397935i	0.727985	−	0.685593i	$-0.240457\pi$
$719$	−6.16051	−	10.6703i	−0.229748	−	0.397935i	−0.957733	+	0.287657i	$0.907124\pi$
$720$	7.11854			0.265292
$721$	−0.353187	−	38.4613i	−0.0131534	−	1.43237i
$722$	16.8390			0.626684
$723$	15.1258	+	26.1987i	0.562535	+	0.974339i
$724$	−1.67168	+	2.89544i	−0.0621276	+	0.107608i
$725$	4.77685	−	8.27374i	0.177408	−	0.307279i
$726$	7.34795	+	12.7270i	0.272708	+	0.472344i
$727$	24.7221			0.916893			0.458447	−	0.888722i	$-0.348406\pi$
$727$	24.7221			0.916893			0.458447	+	0.888722i	$0.348406\pi$
$728$	13.0677	+	7.38550i	0.484322	+	0.273725i
$729$	−41.5734			−1.53975
$730$	−3.05984	−	5.29981i	−0.113250	−	0.196155i
$731$	5.24242	−	9.08014i	0.193898	−	0.335841i
$732$	−21.9501	+	38.0186i	−0.811298	+	1.40521i
$733$	−23.5240	−	40.7447i	−0.868878	−	1.50494i	−0.863145	−	0.504956i	$-0.831509\pi$
$733$	−23.5240	−	40.7447i	−0.868878	−	1.50494i	−0.00573271	−	0.999984i	$-0.501825\pi$
$734$	−19.1680			−0.707502
$735$	−14.1819	−	23.5539i	−0.523106	−	0.868799i
$736$	−1.00000			−0.0368605
$737$	−11.6023	−	20.0957i	−0.427375	−	0.740234i
$738$	17.9609	−	31.1092i	0.661149	−	1.14514i
$739$	−0.875149	+	1.51580i	−0.0321929	+	0.0557597i	−0.881673	−	0.471861i	$-0.843582\pi$
$739$	−0.875149	+	1.51580i	−0.0321929	+	0.0557597i	0.849480	+	0.527621i	$0.176916\pi$
$740$	2.93107	+	5.07676i	0.107748	+	0.186625i
$741$	23.8607			0.876543
$742$	9.80114	+	5.53932i	0.359811	+	0.203355i
$743$	40.0900			1.47076			0.735380	−	0.677654i	$-0.237003\pi$
$743$	40.0900			1.47076			0.735380	+	0.677654i	$0.237003\pi$
$744$	−10.4434	−	18.0884i	−0.382872	−	0.663155i
$745$	−4.85983	+	8.41748i	−0.178051	+	0.308393i
$746$	−10.7957	+	18.6988i	−0.395260	+	0.684610i
$747$	−13.3880	−	23.1887i	−0.489841	−	0.848430i
$748$	−10.5886			−0.387156
$749$	−0.0463926	−	5.05205i	−0.00169515	−	0.184598i
$750$	−31.8744			−1.16389
$751$	−8.75171	−	15.1584i	−0.319354	−	0.553138i	0.660999	−	0.750387i	$-0.270133\pi$
$751$	−8.75171	−	15.1584i	−0.319354	−	0.553138i	−0.980353	+	0.197249i	$0.936799\pi$
$752$	0.915257	−	1.58527i	0.0333760	−	0.0578089i
$753$	29.5392	−	51.1634i	1.07647	−	1.86450i
$754$	8.69930	+	15.0676i	0.316810	+	0.548731i
$755$	20.3444			0.740409
$756$	−14.2485	+	8.40174i	−0.518212	+	0.305568i
$757$	19.7164			0.716604			0.358302	−	0.933606i	$-0.383356\pi$
$757$	19.7164			0.716604			0.358302	+	0.933606i	$0.383356\pi$
$758$	−18.0461	−	31.2567i	−0.655463	−	1.13529i
$759$	−3.46385	+	5.99956i	−0.125730	+	0.217770i
$760$	−1.00906	+	1.74774i	−0.0366024	+	0.0633972i
$761$	−1.61079	−	2.78998i	−0.0583913	−	0.101137i	0.835352	−	0.549715i	$-0.185264\pi$
$761$	−1.61079	−	2.78998i	−0.0583913	−	0.101137i	−0.893743	+	0.448579i	$0.851930\pi$
$762$	55.0243			1.99332
$763$	21.0262	−	12.3983i	0.761198	−	0.448848i
$764$	16.0597			0.581021
$765$	−15.5641	−	26.9579i	−0.562722	−	0.974664i
$766$	−6.79985	+	11.7777i	−0.245689	+	0.425545i
$767$	−2.36261	+	4.09216i	−0.0853088	+	0.147759i
$768$	1.43049	+	2.47769i	0.0516185	+	0.0894058i
$769$	31.8342			1.14797			0.573985	−	0.818866i	$-0.305397\pi$
$769$	31.8342			1.14797			0.573985	+	0.818866i	$0.305397\pi$
$770$	0.0807619	+	8.79478i	0.00291046	+	0.316942i

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.43049 - 2.47769i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.686423 - 1.18892i) q^{5} +2.86099 q^{6} +(-2.30334 - 1.30178i) q^{7} -1.00000 q^{8} +(-2.59262 - 4.49055i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.43049 - 2.47769i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.686423 - 1.18892i) q^{5} +2.86099 q^{6} +(-2.30334 - 1.30178i) q^{7} -1.00000 q^{8} +(-2.59262 - 4.49055i) q^{9} +(0.686423 - 1.18892i) q^{10} +(1.21072 - 2.09702i) q^{11} +(1.43049 + 2.47769i) q^{12} +5.67338 q^{13} +(-0.0242947 - 2.64564i) q^{14} -3.92769 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.18642 + 3.78700i) q^{17} +(2.59262 - 4.49055i) q^{18} +(0.735012 + 1.27308i) q^{19} +1.37285 q^{20} +(-6.52031 + 3.84476i) q^{21} +2.42143 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.43049 + 2.47769i) q^{24} +(1.55765 - 2.69792i) q^{25} +(2.83669 + 4.91329i) q^{26} -6.25195 q^{27} +(2.27904 - 1.34386i) q^{28} +3.06671 q^{29} +(-1.96385 - 3.40148i) q^{30} +(-3.65027 + 6.32245i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.46385 - 5.99956i) q^{33} -4.37285 q^{34} +(0.0333529 + 3.63205i) q^{35} +5.18524 q^{36} +(2.13503 + 3.69798i) q^{37} +(-0.735012 + 1.27308i) q^{38} +(8.11574 - 14.0569i) q^{39} +(0.686423 + 1.18892i) q^{40} +6.92769 q^{41} +(-6.58982 - 3.72437i) q^{42} -2.39772 q^{43} +(1.21072 + 2.09702i) q^{44} +(-3.55927 + 6.16483i) q^{45} +(0.500000 - 0.866025i) q^{46} +(0.915257 + 1.58527i) q^{47} -2.86099 q^{48} +(3.61074 + 5.99688i) q^{49} +3.11530 q^{50} +(6.25533 + 10.8345i) q^{51} +(-2.83669 + 4.91329i) q^{52} +(-2.12759 + 3.68510i) q^{53} +(-3.12597 - 5.41435i) q^{54} -3.32426 q^{55} +(2.30334 + 1.30178i) q^{56} +4.20572 q^{57} +(1.53335 + 2.65585i) q^{58} +(-0.416437 + 0.721290i) q^{59} +(1.96385 - 3.40148i) q^{60} +(7.67220 + 13.2886i) q^{61} -7.30054 q^{62} +(0.125974 + 13.7183i) q^{63} +1.00000 q^{64} +(-3.89434 - 6.74519i) q^{65} +(3.46385 - 5.99956i) q^{66} +(4.79148 - 8.29909i) q^{67} +(-2.18642 - 3.78700i) q^{68} -2.86099 q^{69} +(-3.12878 + 1.84491i) q^{70} -14.1410 q^{71} +(2.59262 + 4.49055i) q^{72} +(2.22883 - 3.86045i) q^{73} +(-2.13503 + 3.69798i) q^{74} +(-4.45641 - 7.71873i) q^{75} -1.47002 q^{76} +(-5.51856 + 3.25407i) q^{77} +16.2315 q^{78} +(-7.50508 - 12.9992i) q^{79} +(-0.686423 + 1.18892i) q^{80} +(-1.16551 + 2.01871i) q^{81} +(3.46385 + 5.99956i) q^{82} +5.16388 q^{83} +(-0.0695069 - 7.56914i) q^{84} +6.00324 q^{85} +(-1.19886 - 2.07648i) q^{86} +(4.38690 - 7.59834i) q^{87} +(-1.21072 + 2.09702i) q^{88} +(-8.98696 - 15.5659i) q^{89} -7.11854 q^{90} +(-13.0677 - 7.38550i) q^{91} +1.00000 q^{92} +(10.4434 + 18.0884i) q^{93} +(-0.915257 + 1.58527i) q^{94} +(1.00906 - 1.74774i) q^{95} +(-1.43049 - 2.47769i) q^{96} -2.26106 q^{97} +(-3.38808 + 6.12543i) q^{98} -12.5557 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more