LMFDB - Embedded newform 784.2.m.h.589.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			589.6
Root			$0.402577 - 1.35570i$ of defining polynomial
Character	$\chi$	$=$	784.589
Dual form			784.2.m.h.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35570 - 0.402577i) q^{2} +(-0.631188 - 0.631188i) q^{3} +(1.67586 - 1.09155i) q^{4} +(2.34259 - 2.34259i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} -2.20320i q^{9} +O(q^{10})$	\(q+(1.35570 - 0.402577i) q^{2} +(-0.631188 - 0.631188i) q^{3} +(1.67586 - 1.09155i) q^{4} +(2.34259 - 2.34259i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} -2.20320i q^{9} +(2.23279 - 4.11894i) q^{10} +(-2.18310 + 2.18310i) q^{11} +(-1.74676 - 0.368812i) q^{12} +(4.03390 + 4.03390i) q^{13} -2.95723 q^{15} +(1.61704 - 3.65858i) q^{16} -0.347931 q^{17} +(-0.886959 - 2.98689i) q^{18} +(-4.26332 - 4.26332i) q^{19} +(1.36881 - 6.48293i) q^{20} +(-2.08077 + 3.83850i) q^{22} +6.23788i q^{23} +(-2.51656 + 0.203204i) q^{24} -5.97550i q^{25} +(7.09272 + 3.84481i) q^{26} +(-3.28420 + 3.28420i) q^{27} +(1.21961 + 1.21961i) q^{29} +(-4.00913 + 1.19051i) q^{30} +1.26238 q^{31} +(0.719369 - 5.61093i) q^{32} +2.75589 q^{33} +(-0.471692 + 0.140069i) q^{34} +(-2.40491 - 3.69227i) q^{36} +(-6.42281 + 6.42281i) q^{37} +(-7.49611 - 4.06348i) q^{38} -5.09229i q^{39} +(-0.754173 - 9.33998i) q^{40} +2.68519i q^{41} +(4.05478 - 4.05478i) q^{43} +(-1.27562 + 6.04154i) q^{44} +(-5.16121 - 5.16121i) q^{45} +(2.51122 + 8.45671i) q^{46} -4.64498 q^{47} +(-3.32990 + 1.28859i) q^{48} +(-2.40560 - 8.10101i) q^{50} +(0.219610 + 0.219610i) q^{51} +(11.1635 + 2.35706i) q^{52} +(8.44108 - 8.44108i) q^{53} +(-3.13026 + 5.77454i) q^{54} +10.2282i q^{55} +5.38191i q^{57} +(2.14442 + 1.16244i) q^{58} +(5.17776 - 5.17776i) q^{59} +(-4.95592 + 3.22797i) q^{60} +(0.00533660 + 0.00533660i) q^{61} +(1.71141 - 0.508203i) q^{62} +(-1.28358 - 7.89636i) q^{64} +18.8996 q^{65} +(3.73617 - 1.10946i) q^{66} +(3.02011 + 3.02011i) q^{67} +(-0.583086 + 0.379784i) q^{68} +(3.93727 - 3.93727i) q^{69} +0.828913i q^{71} +(-4.74676 - 4.03746i) q^{72} +6.25173i q^{73} +(-6.12176 + 11.2931i) q^{74} +(-3.77166 + 3.77166i) q^{75} +(-11.7984 - 2.49112i) q^{76} +(-2.05004 - 6.90364i) q^{78} -0.755891 q^{79} +(-4.78249 - 12.3586i) q^{80} -2.46372 q^{81} +(1.08099 + 3.64032i) q^{82} +(3.66586 + 3.66586i) q^{83} +(-0.815062 + 0.815062i) q^{85} +(3.86472 - 7.12944i) q^{86} -1.53961i q^{87} +(0.702825 + 8.70407i) q^{88} -6.24461i q^{89} +(-9.07486 - 4.91929i) q^{90} +(6.80895 + 10.4538i) q^{92} +(-0.796796 - 0.796796i) q^{93} +(-6.29721 + 1.86996i) q^{94} -19.9745 q^{95} +(-3.99561 + 3.08749i) q^{96} -2.18393 q^{97} +(4.80981 + 4.80981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8	$ 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{10} - 8 q^{12} - 24 q^{15} + 10 q^{16} + 8 q^{17} + 20 q^{20} + 14 q^{22} + 8 q^{24} + 20 q^{26} - 4 q^{27} - 4 q^{29} - 28 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{34} - 16 q^{36} - 20 q^{37} - 16 q^{38} + 8 q^{40} + 16 q^{43} + 14 q^{44} - 40 q^{45} - 28 q^{46} - 16 q^{47} - 16 q^{48} + 44 q^{50} - 16 q^{51} + 16 q^{52} + 4 q^{53} - 64 q^{54} + 14 q^{58} + 16 q^{59} + 60 q^{60} + 20 q^{61} - 8 q^{62} - 18 q^{64} + 32 q^{65} - 12 q^{66} + 24 q^{67} + 28 q^{68} + 4 q^{69} + 6 q^{72} - 38 q^{74} + 40 q^{75} - 48 q^{76} - 76 q^{78} + 24 q^{79} - 24 q^{80} - 44 q^{81} + 16 q^{82} + 20 q^{83} - 8 q^{85} + 38 q^{86} - 14 q^{88} + 40 q^{90} + 32 q^{92} - 48 q^{93} + 24 q^{94} + 16 q^{96} - 48 q^{97} + 32 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^10 - 8 * q^12 - 24 * q^15 + 10 * q^16 + 8 * q^17 + 20 * q^20 + 14 * q^22 + 8 * q^24 + 20 * q^26 - 4 * q^27 - 4 * q^29 - 28 * q^30 + 8 * q^31 + 12 * q^32 - 8 * q^34 - 16 * q^36 - 20 * q^37 - 16 * q^38 + 8 * q^40 + 16 * q^43 + 14 * q^44 - 40 * q^45 - 28 * q^46 - 16 * q^47 - 16 * q^48 + 44 * q^50 - 16 * q^51 + 16 * q^52 + 4 * q^53 - 64 * q^54 + 14 * q^58 + 16 * q^59 + 60 * q^60 + 20 * q^61 - 8 * q^62 - 18 * q^64 + 32 * q^65 - 12 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 6 * q^72 - 38 * q^74 + 40 * q^75 - 48 * q^76 - 76 * q^78 + 24 * q^79 - 24 * q^80 - 44 * q^81 + 16 * q^82 + 20 * q^83 - 8 * q^85 + 38 * q^86 - 14 * q^88 + 40 * q^90 + 32 * q^92 - 48 * q^93 + 24 * q^94 + 16 * q^96 - 48 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.35570	−	0.402577i	0.958627	−	0.284665i
$2$	1.35570	−	0.402577i	0.958627	−	0.284665i
$3$	−0.631188	−	0.631188i	−0.364416	−	0.364416i	0.501020	−	0.865436i	$-0.332958\pi$
$3$	−0.631188	−	0.631188i	−0.364416	−	0.364416i	−0.865436	+	0.501020i	$0.832958\pi$
$4$	1.67586	−	1.09155i	0.837932	−	0.545775i
$5$	2.34259	−	2.34259i	1.04764	−	1.04764i	0.0488333	−	0.998807i	$-0.484450\pi$
$5$	2.34259	−	2.34259i	1.04764	−	1.04764i	0.998807	−	0.0488333i	$-0.0155503\pi$
$6$	−1.10981	−	0.601602i	−0.453076	−	0.245603i
$7$		0			0
$7$		0			0
$8$	1.83254	−	2.15448i	0.647902	−	0.761724i
$9$		−	2.20320i		−	0.734401i
$10$	2.23279	−	4.11894i	0.706070	−	1.30252i
$11$	−2.18310	+	2.18310i	−0.658229	+	0.658229i	−0.954961	−	0.296732i	$-0.904103\pi$
$11$	−2.18310	+	2.18310i	−0.658229	+	0.658229i	0.296732	+	0.954961i	$0.404103\pi$
$12$	−1.74676	−	0.368812i	−0.504245	−	0.106467i
$13$	4.03390	+	4.03390i	1.11880	+	1.11880i	0.991918	+	0.126884i	$0.0404976\pi$
$13$	4.03390	+	4.03390i	1.11880	+	1.11880i	0.126884	+	0.991918i	$0.459502\pi$
$14$		0			0
$15$	−2.95723			−0.763555
$16$	1.61704	−	3.65858i	0.404260	−	0.914644i
$17$	−0.347931			−0.0843858			−0.0421929	−	0.999109i	$-0.513434\pi$
$17$	−0.347931			−0.0843858			−0.0421929	+	0.999109i	$0.513434\pi$
$18$	−0.886959	−	2.98689i	−0.209058	−	0.704017i
$19$	−4.26332	−	4.26332i	−0.978072	−	0.978072i	0.0216925	−	0.999765i	$-0.493095\pi$
$19$	−4.26332	−	4.26332i	−0.978072	−	0.978072i	−0.999765	+	0.0216925i	$0.993095\pi$
$20$	1.36881	−	6.48293i	0.306076	−	1.44963i
$21$		0			0
$22$	−2.08077	+	3.83850i	−0.443622	+	0.818371i
$23$			6.23788i			1.30069i	0.759640	+	0.650344i	$0.225375\pi$
$23$			6.23788i			1.30069i	−0.759640	+	0.650344i	$0.774625\pi$
$24$	−2.51656	+	0.203204i	−0.513691	+	0.0414788i
$25$		−	5.97550i		−	1.19510i
$26$	7.09272	+	3.84481i	1.39100	+	0.754030i
$27$	−3.28420	+	3.28420i	−0.632044	+	0.632044i
$28$		0			0
$29$	1.21961	+	1.21961i	0.226476	+	0.226476i	0.811219	−	0.584743i	$-0.198805\pi$
$29$	1.21961	+	1.21961i	0.226476	+	0.226476i	−0.584743	+	0.811219i	$0.698805\pi$
$30$	−4.00913	+	1.19051i	−0.731964	+	0.217357i
$31$	1.26238			0.226729			0.113365	−	0.993553i	$-0.463837\pi$
$31$	1.26238			0.226729			0.113365	+	0.993553i	$0.463837\pi$
$32$	0.719369	−	5.61093i	0.127168	−	0.991881i
$33$	2.75589			0.479739
$34$	−0.471692	+	0.140069i	−0.0808945	+	0.0240216i
$35$		0			0
$36$	−2.40491	−	3.69227i	−0.400818	−	0.615378i
$37$	−6.42281	+	6.42281i	−1.05590	+	1.05590i	−0.0575622	+	0.998342i	$0.518333\pi$
$37$	−6.42281	+	6.42281i	−1.05590	+	1.05590i	−0.998342	+	0.0575622i	$0.981667\pi$
$38$	−7.49611	−	4.06348i	−1.21603	−	0.659184i
$39$		−	5.09229i		−	0.815419i
$40$	−0.754173	−	9.33998i	−0.119245	−	1.47678i
$41$			2.68519i			0.419356i	0.977770	+	0.209678i	$0.0672416\pi$
$41$			2.68519i			0.419356i	−0.977770	+	0.209678i	$0.932758\pi$
$42$		0			0
$43$	4.05478	−	4.05478i	0.618348	−	0.618348i	−0.326760	−	0.945107i	$-0.605957\pi$
$43$	4.05478	−	4.05478i	0.618348	−	0.618348i	0.945107	+	0.326760i	$0.105957\pi$
$44$	−1.27562	+	6.04154i	−0.192306	+	0.910796i
$45$	−5.16121	−	5.16121i	−0.769388	−	0.769388i
$46$	2.51122	+	8.45671i	0.370260	+	1.24687i
$47$	−4.64498			−0.677540			−0.338770	−	0.940869i	$-0.610011\pi$
$47$	−4.64498			−0.677540			−0.338770	+	0.940869i	$0.610011\pi$
$48$	−3.32990	+	1.28859i	−0.480630	+	0.185992i
$49$		0			0
$50$	−2.40560	−	8.10101i	−0.340203	−	1.14566i
$51$	0.219610	+	0.219610i	0.0307516	+	0.0307516i
$52$	11.1635	+	2.35706i	1.54809	+	0.326866i
$53$	8.44108	−	8.44108i	1.15947	−	1.15947i	0.174882	−	0.984589i	$-0.444046\pi$
$53$	8.44108	−	8.44108i	1.15947	−	1.15947i	0.984589	−	0.174882i	$-0.0559544\pi$
$54$	−3.13026	+	5.77454i	−0.425974	+	0.785816i
$55$			10.2282i			1.37917i
$56$		0			0
$57$			5.38191i			0.712851i
$58$	2.14442	+	1.16244i	0.281576	+	0.152636i
$59$	5.17776	−	5.17776i	0.674087	−	0.674087i	−0.284568	−	0.958656i	$-0.591850\pi$
$59$	5.17776	−	5.17776i	0.674087	−	0.674087i	0.958656	+	0.284568i	$0.0918503\pi$
$60$	−4.95592	+	3.22797i	−0.639807	+	0.416729i
$61$	0.00533660	+	0.00533660i	0.000683281	+	0.000683281i	0.707448	−	0.706765i	$-0.249846\pi$
$61$	0.00533660	+	0.00533660i	0.000683281	+	0.000683281i	−0.706765	+	0.707448i	$0.749846\pi$
$62$	1.71141	−	0.508203i	0.217349	−	0.0645419i
$63$		0			0
$64$	−1.28358	−	7.89636i	−0.160447	−	0.987044i
$65$	18.8996			2.34420
$66$	3.73617	−	1.10946i	0.459891	−	0.136565i
$67$	3.02011	+	3.02011i	0.368965	+	0.368965i	0.867100	−	0.498135i	$-0.165982\pi$
$67$	3.02011	+	3.02011i	0.368965	+	0.368965i	−0.498135	+	0.867100i	$0.665982\pi$
$68$	−0.583086	+	0.379784i	−0.0707095	+	0.0460556i
$69$	3.93727	−	3.93727i	0.473992	−	0.473992i
$70$		0			0
$71$			0.828913i			0.0983739i	0.998790	+	0.0491869i	$0.0156630\pi$
$71$			0.828913i			0.0983739i	−0.998790	+	0.0491869i	$0.984337\pi$
$72$	−4.74676	−	4.03746i	−0.559411	−	0.475820i
$73$			6.25173i			0.731709i	0.930672	+	0.365855i	$0.119223\pi$
$73$			6.25173i			0.731709i	−0.930672	+	0.365855i	$0.880777\pi$
$74$	−6.12176	+	11.2931i	−0.711640	+	1.31280i
$75$	−3.77166	+	3.77166i	−0.435514	+	0.435514i
$76$	−11.7984	−	2.49112i	−1.35337	−	0.285751i
$77$		0			0
$78$	−2.05004	−	6.90364i	−0.232121	−	0.781683i
$79$	−0.755891			−0.0850443			−0.0425222	−	0.999096i	$-0.513539\pi$
$79$	−0.755891			−0.0850443			−0.0425222	+	0.999096i	$0.513539\pi$
$80$	−4.78249	−	12.3586i	−0.534699	−	1.38174i
$81$	−2.46372			−0.273747
$82$	1.08099	+	3.64032i	0.119376	+	0.402006i
$83$	3.66586	+	3.66586i	0.402380	+	0.402380i	0.879071	−	0.476691i	$-0.158164\pi$
$83$	3.66586	+	3.66586i	0.402380	+	0.402380i	−0.476691	+	0.879071i	$0.658164\pi$
$84$		0			0
$85$	−0.815062	+	0.815062i	−0.0884059	+	0.0884059i
$86$	3.86472	−	7.12944i	0.416743	−	0.768787i
$87$		−	1.53961i		−	0.165063i
$88$	0.702825	+	8.70407i	0.0749213	+	0.927857i
$89$		−	6.24461i		−	0.661928i	−0.943643	−	0.330964i	$-0.892626\pi$
$89$		−	6.24461i		−	0.661928i	0.943643	−	0.330964i	$-0.107374\pi$
$90$	−9.07486	−	4.91929i	−0.956574	−	0.518539i
$91$		0			0
$92$	6.80895	+	10.4538i	0.709882	+	1.08989i
$93$	−0.796796	−	0.796796i	−0.0826239	−	0.0826239i
$94$	−6.29721	+	1.86996i	−0.649508	+	0.192872i
$95$	−19.9745			−2.04934
$96$	−3.99561	+	3.08749i	−0.407800	+	0.315116i
$97$	−2.18393			−0.221745			−0.110872	−	0.993835i	$-0.535365\pi$
$97$	−2.18393			−0.221745			−0.110872	+	0.993835i	$0.535365\pi$
$98$		0			0
$99$	4.80981	+	4.80981i	0.483404	+	0.483404i
$100$	−6.52255	−	10.0141i	−0.652255	−	1.00141i
$101$	4.75325	−	4.75325i	0.472967	−	0.472967i	−0.429907	−	0.902873i	$-0.641454\pi$
$101$	4.75325	−	4.75325i	0.472967	−	0.472967i	0.902873	+	0.429907i	$0.141454\pi$
$102$	0.386136	+	0.209316i	0.0382332	+	0.0207254i
$103$			15.7259i			1.54952i	0.632256	+	0.774760i	$0.282129\pi$
$103$			15.7259i			1.54952i	−0.632256	+	0.774760i	$0.717871\pi$
$104$	16.0832	−	1.29867i	1.57709	−	0.127345i
$105$		0			0
$106$	8.04542	−	14.8418i	0.781440	−	1.44156i
$107$	−6.68080	+	6.68080i	−0.645857	+	0.645857i	−0.951989	−	0.306132i	$-0.900965\pi$
$107$	−6.68080	+	6.68080i	−0.645857	+	0.645857i	0.306132	+	0.951989i	$0.400965\pi$
$108$	−1.91901	+	9.08874i	−0.184656	+	0.874564i
$109$	−0.812507	−	0.812507i	−0.0778241	−	0.0778241i	0.667123	−	0.744947i	$-0.267525\pi$
$109$	−0.812507	−	0.812507i	−0.0778241	−	0.0778241i	−0.744947	+	0.667123i	$0.767525\pi$
$110$	4.11765	+	13.8664i	0.392602	+	1.32211i
$111$	8.10800			0.769578
$112$		0			0
$113$	−18.5170			−1.74193			−0.870966	−	0.491343i	$-0.836506\pi$
$113$	−18.5170			−1.74193			−0.870966	+	0.491343i	$0.836506\pi$
$114$	2.16663	+	7.29627i	0.202924	+	0.683359i
$115$	14.6128	+	14.6128i	1.36265	+	1.36265i
$116$	3.37517	+	0.712636i	0.313376	+	0.0661666i
$117$	8.88750	−	8.88750i	0.821649	−	0.821649i
$118$	4.93506	−	9.10396i	0.454309	−	0.838087i
$119$		0			0
$120$	−5.41926	+	6.37131i	−0.494708	+	0.581618i
$121$			1.46816i			0.133469i
$122$	0.00938323	+	0.00508645i	0.000849518	+	0.000460506i
$123$	1.69486	−	1.69486i	0.152820	−	0.152820i
$124$	2.11557	−	1.37795i	0.189984	−	0.123743i
$125$	−2.28520	−	2.28520i	−0.204395	−	0.204395i
$126$		0			0
$127$	13.7063			1.21624			0.608121	−	0.793845i	$-0.291924\pi$
$127$	13.7063			1.21624			0.608121	+	0.793845i	$0.291924\pi$
$128$	−4.91904	−	10.1884i	−0.434786	−	0.900534i
$129$	−5.11865			−0.450672
$130$	25.6222	−	7.60853i	2.24722	−	0.667312i
$131$	3.52925	+	3.52925i	0.308352	+	0.308352i	0.844270	−	0.535918i	$-0.180034\pi$
$131$	3.52925	+	3.52925i	0.308352	+	0.308352i	−0.535918	+	0.844270i	$0.680034\pi$
$132$	4.61850	−	3.00819i	0.401989	−	0.261829i
$133$		0			0
$134$	5.31019	+	2.87854i	0.458731	+	0.248668i
$135$			15.3871i			1.32431i
$136$	−0.637599	+	0.749612i	−0.0546737	+	0.0642787i
$137$			15.6540i			1.33741i	0.743529	+	0.668704i	$0.233151\pi$
$137$			15.6540i			1.33741i	−0.743529	+	0.668704i	$0.766849\pi$
$138$	3.75272	−	6.92283i	0.319453	−	0.589310i
$139$	−1.52569	+	1.52569i	−0.129408	+	0.129408i	−0.768844	−	0.639436i	$-0.779168\pi$
$139$	−1.52569	+	1.52569i	−0.129408	+	0.129408i	0.639436	+	0.768844i	$0.279168\pi$
$140$		0			0
$141$	2.93185	+	2.93185i	0.246907	+	0.246907i
$142$	0.333701	+	1.12376i	0.0280036	+	0.0943039i
$143$	−17.6128			−1.47286
$144$	−8.06059	−	3.56267i	−0.671716	−	0.296889i
$145$	5.71410			0.474531
$146$	2.51680	+	8.47549i	0.208292	+	0.701436i
$147$		0			0
$148$	−3.75294	+	17.7746i	−0.308490	+	1.46106i
$149$	9.23788	−	9.23788i	0.756796	−	0.756796i	−0.218942	−	0.975738i	$-0.570260\pi$
$149$	9.23788	−	9.23788i	0.756796	−	0.756796i	0.975738	+	0.218942i	$0.0702604\pi$
$150$	−3.59487	+	6.63164i	−0.293520	+	0.541471i
$151$			11.7266i			0.954297i	0.878823	+	0.477149i	$0.158330\pi$
$151$			11.7266i			0.954297i	−0.878823	+	0.477149i	$0.841670\pi$
$152$	−16.9979	+	1.37253i	−1.37872	+	0.111327i
$153$			0.766564i			0.0619730i
$154$		0			0
$155$	2.95723	−	2.95723i	0.237531	−	0.237531i
$156$	−5.55849	−	8.53399i	−0.445035	−	0.683266i
$157$	10.3818	+	10.3818i	0.828560	+	0.828560i	0.987318	−	0.158758i	$-0.0507488\pi$
$157$	10.3818	+	10.3818i	0.828560	+	0.828560i	−0.158758	+	0.987318i	$0.550749\pi$
$158$	−1.02476	+	0.304304i	−0.0815258	+	0.0242091i
$159$	−10.6558			−0.845061
$160$	−11.4589	−	14.8293i	−0.905909	−	1.17236i
$161$		0			0
$162$	−3.34007	+	0.991836i	−0.262421	+	0.0779260i
$163$	−15.6554	−	15.6554i	−1.22623	−	1.22623i	−0.965380	−	0.260849i	$-0.915997\pi$
$163$	−15.6554	−	15.6554i	−1.22623	−	1.22623i	−0.260849	−	0.965380i	$-0.584003\pi$
$164$	2.93102	+	4.50001i	0.228874	+	0.351392i
$165$	6.45593	−	6.45593i	0.502594	−	0.502594i
$166$	6.44561	+	3.49403i	0.500276	+	0.271189i
$167$		−	2.12023i		−	0.164068i	−0.996630	−	0.0820341i	$-0.973858\pi$
$167$		−	2.12023i		−	0.164068i	0.996630	−	0.0820341i	$-0.0261416\pi$
$168$		0			0
$169$			19.5446i			1.50343i
$170$	−0.776858	+	1.43311i	−0.0595823	+	0.109914i
$171$	−9.39296	+	9.39296i	−0.718298	+	0.718298i
$172$	2.36927	−	11.2212i	0.180655	−	0.855612i
$173$	−2.12654	−	2.12654i	−0.161678	−	0.161678i	0.621632	−	0.783310i	$-0.286470\pi$
$173$	−2.12654	−	2.12654i	−0.161678	−	0.161678i	−0.783310	+	0.621632i	$0.786470\pi$
$174$	−0.619810	−	2.08725i	−0.0469876	−	0.158234i
$175$		0			0
$176$	4.45688	+	11.5172i	0.335950	+	0.868141i
$177$	−6.53628			−0.491297
$178$	−2.51394	−	8.46584i	−0.188427	−	0.634542i
$179$	1.41911	+	1.41911i	0.106070	+	0.106070i	0.758150	−	0.652080i	$-0.226104\pi$
$179$	1.41911	+	1.41911i	0.106070	+	0.106070i	−0.652080	+	0.758150i	$0.726104\pi$
$180$	−14.2832	−	3.01577i	−1.06461	−	0.224782i
$181$	−14.3191	+	14.3191i	−1.06433	+	1.06433i	−0.0665470	+	0.997783i	$0.521198\pi$
$181$	−14.3191	+	14.3191i	−1.06433	+	1.06433i	−0.997783	+	0.0665470i	$0.978802\pi$
$182$		0			0
$183$		−	0.00673679i		−	0.000497998i
$184$	13.4394	+	11.4312i	0.990765	+	0.842717i
$185$			30.0921i			2.21242i
$186$	−1.40099	−	0.759448i	−0.102726	−	0.0556854i
$187$	0.759569	−	0.759569i	0.0555452	−	0.0555452i
$188$	−7.78435	+	5.07022i	−0.567732	+	0.369784i
$189$		0			0
$190$	−27.0794	+	8.04125i	−1.96455	+	0.583374i
$191$	6.22279			0.450265			0.225133	−	0.974328i	$-0.427718\pi$
$191$	6.22279			0.450265			0.225133	+	0.974328i	$0.427718\pi$
$192$	−4.17390	+	5.79426i	−0.301226	+	0.418165i
$193$	1.57618			0.113456			0.0567280	−	0.998390i	$-0.481933\pi$
$193$	1.57618			0.113456			0.0567280	+	0.998390i	$0.481933\pi$
$194$	−2.96077	+	0.879201i	−0.212571	+	0.0631230i
$195$	−11.9292	−	11.9292i	−0.854266	−	0.854266i
$196$		0			0
$197$	10.7183	−	10.7183i	0.763648	−	0.763648i	−0.213332	−	0.976980i	$-0.568432\pi$
$197$	10.7183	−	10.7183i	0.763648	−	0.763648i	0.976980	+	0.213332i	$0.0684315\pi$
$198$	8.45700	+	4.58436i	0.601013	+	0.325796i
$199$		−	25.5363i		−	1.81022i	−0.425180	−	0.905109i	$-0.639789\pi$
$199$		−	25.5363i		−	1.81022i	0.425180	−	0.905109i	$-0.360211\pi$
$200$	−12.8741	−	10.9504i	−0.910337	−	0.774307i
$201$		−	3.81251i		−	0.268914i
$202$	4.53045	−	8.35755i	0.318762	−	0.588035i
$203$		0			0
$204$	0.607752	+	0.128321i	0.0425511	+	0.00898429i
$205$	6.29031	+	6.29031i	0.439334	+	0.439334i
$206$	6.33088	+	21.3197i	0.441094	+	1.48541i
$207$	13.7433			0.955226
$208$	21.2813	−	8.23535i	1.47559	−	0.571019i
$209$	18.6145			1.28759
$210$		0			0
$211$	9.19881	+	9.19881i	0.633272	+	0.633272i	0.948887	−	0.315615i	$-0.102211\pi$
$211$	9.19881	+	9.19881i	0.633272	+	0.633272i	−0.315615	+	0.948887i	$0.602211\pi$
$212$	4.93225	−	23.3600i	0.338748	−	1.60437i
$213$	0.523200	−	0.523200i	0.0358491	−	0.0358491i
$214$	−6.36764	+	11.7467i	−0.435283	+	0.802989i
$215$		−	18.9974i		−	1.29561i
$216$	1.05731	+	13.0942i	0.0719409	+	0.890946i
$217$		0			0
$218$	−1.42862	−	0.774422i	−0.0967580	−	0.0524505i
$219$	3.94601	−	3.94601i	0.266647	−	0.266647i
$220$	11.1646	+	17.1411i	0.752719	+	1.15565i
$221$	−1.40352	−	1.40352i	−0.0944109	−	0.0944109i
$222$	10.9920	−	3.26409i	0.737738	−	0.219072i
$223$	−12.7530			−0.854003			−0.427001	−	0.904251i	$-0.640430\pi$
$223$	−12.7530			−0.854003			−0.427001	+	0.904251i	$0.640430\pi$
$224$		0			0
$225$	−13.1652			−0.877683
$226$	−25.1035	+	7.45451i	−1.66986	+	0.495867i
$227$	12.2451	+	12.2451i	0.812733	+	0.812733i	0.985043	−	0.172310i	$-0.0551231\pi$
$227$	12.2451	+	12.2451i	0.812733	+	0.812733i	−0.172310	+	0.985043i	$0.555123\pi$
$228$	5.87462	+	9.01935i	0.389056	+	0.597321i
$229$	9.93193	−	9.93193i	0.656321	−	0.656321i	−0.298187	−	0.954508i	$-0.596382\pi$
$229$	9.93193	−	9.93193i	0.656321	−	0.656321i	0.954508	+	0.298187i	$0.0963818\pi$
$230$	25.6934	+	13.9279i	1.69417	+	0.918376i
$231$		0			0
$232$	4.86261	−	0.392640i	0.319246	−	0.0257781i
$233$		−	18.3143i		−	1.19981i	−0.800072	−	0.599905i	$-0.795205\pi$
$233$		−	18.3143i		−	1.19981i	0.800072	−	0.599905i	$-0.204795\pi$
$234$	8.47091	−	15.6267i	0.553761	−	1.02155i
$235$	−10.8813	+	10.8813i	−0.709818	+	0.709818i
$236$	3.02544	−	14.3290i	0.196939	−	0.932739i
$237$	0.477109	+	0.477109i	0.0309916	+	0.0309916i
$238$		0			0
$239$	−18.3443			−1.18660			−0.593298	−	0.804983i	$-0.702174\pi$
$239$	−18.3443			−1.18660			−0.593298	+	0.804983i	$0.702174\pi$
$240$	−4.78197	+	10.8193i	−0.308675	+	0.698381i
$241$	−25.4147			−1.63710			−0.818552	−	0.574433i	$-0.805223\pi$
$241$	−25.4147			−1.63710			−0.818552	+	0.574433i	$0.805223\pi$
$242$	0.591047	+	1.99039i	0.0379939	+	0.127947i
$243$	11.4077	+	11.4077i	0.731802	+	0.731802i
$244$	0.0147686	+	0.00311825i	0.000945461	+	0.000199626i
$245$		0			0
$246$	1.61542	−	2.98004i	0.102995	−	0.190000i
$247$		−	34.3956i		−	2.18854i
$248$	2.31336	−	2.71976i	0.146898	−	0.172705i
$249$		−	4.62769i		−	0.293268i
$250$	−4.01803	−	2.17809i	−0.254122	−	0.137754i
$251$	10.9301	−	10.9301i	0.689903	−	0.689903i	−0.272307	−	0.962210i	$-0.587787\pi$
$251$	10.9301	−	10.9301i	0.689903	−	0.689903i	0.962210	+	0.272307i	$0.0877867\pi$
$252$		0			0
$253$	−13.6179	−	13.6179i	−0.856150	−	0.856150i
$254$	18.5817	−	5.51786i	1.16592	−	0.346221i
$255$	1.02891			0.0644331
$256$	−10.7704	−	11.8321i	−0.673148	−	0.739508i
$257$	−2.29652			−0.143253			−0.0716265	−	0.997432i	$-0.522819\pi$
$257$	−2.29652			−0.143253			−0.0716265	+	0.997432i	$0.522819\pi$
$258$	−6.93937	+	2.06065i	−0.432027	+	0.128290i
$259$		0			0
$260$	31.6731	−	20.6298i	1.96428	−	1.27941i
$261$	2.68705	−	2.68705i	0.166324	−	0.166324i
$262$	6.20541	+	3.36382i	0.383372	+	0.207818i
$263$		−	11.8508i		−	0.730749i	−0.930861	−	0.365375i	$-0.880941\pi$
$263$		−	11.8508i		−	0.730749i	0.930861	−	0.365375i	$-0.119059\pi$
$264$	5.05029	−	5.93751i	0.310824	−	0.365429i
$265$		−	39.5481i		−	2.42942i
$266$		0			0
$267$	−3.94152	+	3.94152i	−0.241217	+	0.241217i
$268$	8.35788	+	1.76469i	0.510539	+	0.107796i
$269$	−5.70791	−	5.70791i	−0.348017	−	0.348017i	0.511353	−	0.859371i	$-0.329144\pi$
$269$	−5.70791	−	5.70791i	−0.348017	−	0.348017i	−0.859371	+	0.511353i	$0.829144\pi$
$270$	6.19449	+	20.8603i	0.376984	+	1.26952i
$271$	−26.1234			−1.58688			−0.793441	−	0.608648i	$-0.791712\pi$
$271$	−26.1234			−1.58688			−0.793441	+	0.608648i	$0.791712\pi$
$272$	−0.562619	+	1.27293i	−0.0341138	+	0.0771829i
$273$		0			0
$274$	6.30192	+	21.2221i	0.380713	+	1.28208i
$275$	13.0451	+	13.0451i	0.786650	+	0.786650i
$276$	2.30060	−	10.8961i	0.138480	−	0.655866i
$277$	1.98274	−	1.98274i	0.119131	−	0.119131i	−0.645028	−	0.764159i	$-0.723154\pi$
$277$	1.98274	−	1.98274i	0.119131	−	0.119131i	0.764159	+	0.645028i	$0.223154\pi$
$278$	−1.45418	+	2.68260i	−0.0872159	+	0.160891i
$279$		−	2.78127i		−	0.166510i
$280$		0			0
$281$		−	6.52475i		−	0.389234i	−0.980879	−	0.194617i	$-0.937654\pi$
$281$		−	6.52475i		−	0.389234i	0.980879	−	0.194617i	$-0.0623464\pi$
$282$	5.15502	+	2.79443i	0.306977	+	0.166406i
$283$	13.9578	−	13.9578i	0.829705	−	0.829705i	−0.157771	−	0.987476i	$-0.550431\pi$
$283$	13.9578	−	13.9578i	0.829705	−	0.829705i	0.987476	+	0.157771i	$0.0504307\pi$
$284$	0.904800	+	1.38915i	0.0536900	+	0.0824306i
$285$	12.6076	+	12.6076i	0.746812	+	0.746812i
$286$	−23.8777	+	7.09050i	−1.41192	+	0.419270i
$287$		0			0
$288$	−12.3620	−	1.58492i	−0.728439	−	0.0933921i
$289$	−16.8789			−0.992879
$290$	7.74663	−	2.30037i	0.454898	−	0.135082i
$291$	1.37847	+	1.37847i	0.0808075	+	0.0808075i
$292$	6.82407	+	10.4770i	0.399348	+	0.613123i
$293$	2.57087	−	2.57087i	0.150192	−	0.150192i	−0.628012	−	0.778204i	$-0.716131\pi$
$293$	2.57087	−	2.57087i	0.150192	−	0.150192i	0.778204	+	0.628012i	$0.216131\pi$
$294$		0			0
$295$		−	24.2588i		−	1.41240i
$296$	2.06775	+	25.6079i	0.120186	+	1.48843i
$297$		−	14.3395i		−	0.832060i
$298$	8.80487	−	16.2428i	0.510052	−	0.940919i
$299$	−25.1629	+	25.1629i	−1.45521	+	1.45521i
$300$	−2.20384	+	10.4378i	−0.127239	+	0.602624i
$301$		0			0
$302$	4.72086	+	15.8978i	0.271655	+	0.914815i
$303$	−6.00039			−0.344714
$304$	−22.4916	+	8.70372i	−1.28998	+	0.499193i
$305$	0.0250030			0.00143167
$306$	0.308601	+	1.03923i	0.0176415	+	0.0594090i
$307$	−18.8253	−	18.8253i	−1.07441	−	1.07441i	−0.996999	−	0.0774148i	$-0.975333\pi$
$307$	−18.8253	−	18.8253i	−1.07441	−	1.07441i	−0.0774148	−	0.996999i	$-0.524667\pi$
$308$		0			0
$309$	9.92600	−	9.92600i	0.564670	−	0.564670i
$310$	2.81862	−	5.19965i	0.160087	−	0.295320i
$311$		−	23.8918i		−	1.35478i	−0.735625	−	0.677389i	$-0.763111\pi$
$311$		−	23.8918i		−	1.35478i	0.735625	−	0.677389i	$-0.236889\pi$
$312$	−10.9712	−	9.33184i	−0.621125	−	0.528311i
$313$			18.0884i			1.02242i	0.859457	+	0.511208i	$0.170802\pi$
$313$			18.0884i			1.02242i	−0.859457	+	0.511208i	$0.829198\pi$
$314$	18.2542	+	9.89520i	1.03014	+	0.558418i
$315$		0			0
$316$	−1.26677	+	0.825092i	−0.0712614	+	0.0464150i
$317$	−5.36465	−	5.36465i	−0.301309	−	0.301309i	0.540217	−	0.841526i	$-0.318342\pi$
$317$	−5.36465	−	5.36465i	−0.301309	−	0.301309i	−0.841526	+	0.540217i	$0.818342\pi$
$318$	−14.4461	+	4.28978i	−0.810098	+	0.240559i
$319$	−5.32506			−0.298146
$320$	−21.5049	−	15.4911i	−1.20216	−	0.865976i
$321$	8.43367			0.470722
$322$		0			0
$323$	1.48334	+	1.48334i	0.0825354	+	0.0825354i
$324$	−4.12886	+	2.68927i	−0.229381	+	0.149404i
$325$	24.1046	−	24.1046i	1.33708	−	1.33708i
$326$	−27.5267	−	14.9216i	−1.52456	−	0.826432i
$327$			1.02569i			0.0567207i
$328$	5.78519	+	4.92072i	0.319434	+	0.271701i
$329$		0			0
$330$	6.15332	−	11.3513i	0.338729	−	0.624871i
$331$	−22.3563	+	22.3563i	−1.22881	+	1.22881i	−0.264402	+	0.964413i	$0.585174\pi$
$331$	−22.3563	+	22.3563i	−1.22881	+	1.22881i	−0.964413	+	0.264402i	$0.914826\pi$
$332$	10.1449	+	2.14202i	0.556776	+	0.117558i
$333$	14.1508	+	14.1508i	0.775457	+	0.775457i
$334$	−0.853555	−	2.87440i	−0.0467044	−	0.157280i
$335$	14.1498			0.773084
$336$		0			0
$337$	11.5086			0.626914			0.313457	−	0.949602i	$-0.398513\pi$
$337$	11.5086			0.626914			0.313457	+	0.949602i	$0.398513\pi$
$338$	7.86822	+	26.4967i	0.427975	+	1.44123i
$339$	11.6877	+	11.6877i	0.634789	+	0.634789i
$340$	−0.476253	+	2.25561i	−0.0258284	+	0.122328i
$341$	−2.75589	+	2.75589i	−0.149240	+	0.149240i
$342$	−8.95268	+	16.5155i	−0.484106	+	0.893053i
$343$		0			0
$344$	−1.30539	−	16.1665i	−0.0703820	−	0.871639i
$345$		−	18.4469i		−	0.993146i
$346$	−3.73906	−	2.02686i	−0.201013	−	0.108965i
$347$	12.3190	−	12.3190i	0.661319	−	0.661319i	−0.294372	−	0.955691i	$-0.595110\pi$
$347$	12.3190	−	12.3190i	0.661319	−	0.661319i	0.955691	+	0.294372i	$0.0951104\pi$
$348$	−1.68056	−	2.58017i	−0.0900873	−	0.138312i
$349$	−0.251501	−	0.251501i	−0.0134625	−	0.0134625i	0.700343	−	0.713806i	$-0.253030\pi$
$349$	−0.251501	−	0.251501i	−0.0134625	−	0.0134625i	−0.713806	+	0.700343i	$0.753030\pi$
$350$		0			0
$351$	−26.4962			−1.41426
$352$	10.6788	+	13.8197i	0.569180	+	0.736590i
$353$	−16.6888			−0.888255			−0.444128	−	0.895964i	$-0.646486\pi$
$353$	−16.6888			−0.888255			−0.444128	+	0.895964i	$0.646486\pi$
$354$	−8.86126	+	2.63135i	−0.470971	+	0.139855i
$355$	1.94181	+	1.94181i	0.103060	+	0.103060i
$356$	−6.81630	−	10.4651i	−0.361263	−	0.554650i
$357$		0			0
$358$	2.49520	+	1.35260i	0.131876	+	0.0714869i
$359$			17.9781i			0.948849i	0.880296	+	0.474425i	$0.157344\pi$
$359$			17.9781i			0.948849i	−0.880296	+	0.474425i	$0.842656\pi$
$360$	−20.5779	+	1.66160i	−1.08455	+	0.0875738i
$361$			17.3518i			0.913251i
$362$	−13.6479	+	25.1770i	−0.717319	+	1.32327i
$363$	0.926684	−	0.926684i	0.0486383	−	0.0486383i
$364$		0			0
$365$	14.6453	+	14.6453i	0.766568	+	0.766568i
$366$	−0.00271207	−	0.00913309i	−0.000141762	−	0.000477394i
$367$	−21.6270			−1.12892			−0.564461	−	0.825460i	$-0.690916\pi$
$367$	−21.6270			−1.12892			−0.564461	+	0.825460i	$0.690916\pi$
$368$	22.8217	+	10.0869i	1.18967	+	0.525816i
$369$	5.91602			0.307976
$370$	12.1144	+	40.7960i	0.629797	+	2.12088i
$371$		0			0
$372$	−2.20506	−	0.465580i	−0.114327	−	0.0241392i
$373$	−12.1124	+	12.1124i	−0.627159	+	0.627159i	−0.947352	−	0.320194i	$-0.896252\pi$
$373$	−12.1124	+	12.1124i	−0.627159	+	0.627159i	0.320194	+	0.947352i	$0.396252\pi$
$374$	0.723965	−	1.33553i	0.0374353	−	0.0690588i
$375$			2.88478i			0.148970i
$376$	−8.51212	+	10.0075i	−0.438979	+	0.516098i
$377$			9.83956i			0.506763i
$378$		0			0
$379$	4.34251	−	4.34251i	0.223060	−	0.223060i	−0.586726	−	0.809786i	$-0.699583\pi$
$379$	4.34251	−	4.34251i	0.223060	−	0.223060i	0.809786	+	0.586726i	$0.199583\pi$
$380$	−33.4745	+	21.8031i	−1.71720	+	1.11848i
$381$	−8.65128	−	8.65128i	−0.443218	−	0.443218i
$382$	8.43626	−	2.50515i	0.431636	−	0.128175i
$383$	32.8242			1.67724			0.838619	−	0.544718i	$-0.183363\pi$
$383$	32.8242			1.67724			0.838619	+	0.544718i	$0.183363\pi$
$384$	−3.32594	+	9.53562i	−0.169726	+	0.486612i
$385$		0			0
$386$	2.13684	−	0.634534i	0.108762	−	0.0322969i
$387$	−8.93350	−	8.93350i	−0.454115	−	0.454115i
$388$	−3.65998	+	2.38387i	−0.185807	+	0.121023i
$389$	0.234988	−	0.234988i	0.0119143	−	0.0119143i	−0.701125	−	0.713039i	$-0.747318\pi$
$389$	0.234988	−	0.234988i	0.0119143	−	0.0119143i	0.713039	+	0.701125i	$0.247318\pi$
$390$	−20.9748	−	11.3700i	−1.06210	−	0.575743i
$391$		−	2.17035i		−	0.109759i
$392$		0			0
$393$		−	4.45524i		−	0.224737i
$394$	10.2159	−	18.8458i	0.514670	−	0.949437i
$395$	−1.77075	+	1.77075i	−0.0890959	+	0.0890959i
$396$	13.3107	+	2.81044i	0.668890	+	0.141230i
$397$	−1.97983	−	1.97983i	−0.0993650	−	0.0993650i	0.655677	−	0.755042i	$-0.272383\pi$
$397$	−1.97983	−	1.97983i	−0.0993650	−	0.0993650i	−0.755042	+	0.655677i	$0.772383\pi$
$398$	−10.2803	−	34.6196i	−0.515305	−	1.73532i
$399$		0			0
$400$	−21.8618	−	9.66262i	−1.09309	−	0.483131i
$401$	−5.15044			−0.257200			−0.128600	−	0.991697i	$-0.541048\pi$
$401$	−5.15044			−0.257200			−0.128600	+	0.991697i	$0.541048\pi$
$402$	−1.53483	−	5.16863i	−0.0765502	−	0.257788i
$403$	5.09229	+	5.09229i	0.253665	+	0.253665i
$404$	2.77740	−	13.1542i	0.138181	−	0.654447i
$405$	−5.77150	+	5.77150i	−0.286788	+	0.286788i
$406$		0			0
$407$		−	28.0433i		−	1.39005i
$408$	0.875590	−	0.0707010i	0.0433482	−	0.00350022i
$409$		−	0.0729036i		−	0.00360485i	−0.999998	−	0.00180243i	$-0.999426\pi$
$409$		−	0.0729036i		−	0.00360485i	0.999998	−	0.00180243i	$-0.000573731\pi$
$410$	11.0601	+	5.99546i	0.546221	+	0.296095i
$411$	9.88058	−	9.88058i	0.487373	−	0.487373i
$412$	17.1656	+	26.3545i	0.845688	+	1.29839i
$413$		0			0
$414$	18.6319	−	5.53274i	0.915706	−	0.271919i
$415$	17.1752			0.843100
$416$	25.5358	−	19.7320i	1.25199	−	0.967443i
$417$	1.92600			0.0943165
$418$	25.2357	−	7.49376i	1.23432	−	0.366532i
$419$	13.7426	+	13.7426i	0.671370	+	0.671370i	0.958032	−	0.286662i	$-0.0925456\pi$
$419$	13.7426	+	13.7426i	0.671370	+	0.671370i	−0.286662	+	0.958032i	$0.592546\pi$
$420$		0			0
$421$	3.88097	−	3.88097i	0.189147	−	0.189147i	−0.606180	−	0.795327i	$-0.707299\pi$
$421$	3.88097	−	3.88097i	0.189147	−	0.189147i	0.795327	+	0.606180i	$0.207299\pi$
$422$	16.1741	+	8.76763i	0.787342	+	0.426802i
$423$			10.2338i			0.497586i
$424$	−2.71751	−	33.6548i	−0.131974	−	1.63442i
$425$			2.07906i			0.100849i
$426$	0.498676	−	0.919932i	0.0241609	−	0.0445708i
$427$		0			0
$428$	−3.90369	+	18.4885i	−0.188692	+	0.893676i
$429$	11.1170	+	11.1170i	0.536733	+	0.536733i
$430$	−7.64791	−	25.7548i	−0.368815	−	1.24201i
$431$	−33.8033			−1.62825			−0.814125	−	0.580690i	$-0.802783\pi$
$431$	−33.8033			−1.62825			−0.814125	+	0.580690i	$0.802783\pi$
$432$	6.70481	+	17.3262i	0.322585	+	0.833606i
$433$	−18.6931			−0.898334			−0.449167	−	0.893448i	$-0.648279\pi$
$433$	−18.6931			−0.898334			−0.449167	+	0.893448i	$0.648279\pi$
$434$		0			0
$435$	−3.60667	−	3.60667i	−0.172927	−	0.172927i
$436$	−2.24854	−	0.474760i	−0.107686	−	0.0227369i
$437$	26.5940	−	26.5940i	1.27217	−	1.27217i
$438$	3.76105	−	6.93820i	0.179710	−	0.331520i
$439$		−	6.03142i		−	0.287864i	−0.989588	−	0.143932i	$-0.954025\pi$
$439$		−	6.03142i		−	0.287864i	0.989588	−	0.143932i	$-0.0459747\pi$
$440$	22.0365	+	18.7437i	1.05055	+	0.893569i
$441$		0			0
$442$	−2.46778	−	1.33773i	−0.117380	−	0.0636294i
$443$	24.9158	−	24.9158i	1.18378	−	1.18378i	0.205027	−	0.978756i	$-0.434272\pi$
$443$	24.9158	−	24.9158i	1.18378	−	1.18378i	0.978756	−	0.205027i	$-0.0657284\pi$
$444$	13.5879	−	8.85029i	0.644854	−	0.420016i
$445$	−14.6286	−	14.6286i	−0.693462	−	0.693462i
$446$	−17.2893	+	5.13405i	−0.818670	+	0.243105i
$447$	−11.6617			−0.551578
$448$		0			0
$449$	21.9883			1.03769			0.518846	−	0.854868i	$-0.326362\pi$
$449$	21.9883			1.03769			0.518846	+	0.854868i	$0.326362\pi$
$450$	−17.8482	+	5.30002i	−0.841371	+	0.249845i
$451$	−5.86203	−	5.86203i	−0.276032	−	0.276032i
$452$	−31.0320	+	20.2122i	−1.45962	+	0.950702i
$453$	7.40169	−	7.40169i	0.347762	−	0.347762i
$454$	21.5302	+	11.6711i	1.01046	+	0.547751i
$455$		0			0
$456$	11.5952	+	9.86257i	0.542996	+	0.461857i
$457$			26.7381i			1.25076i	0.780322	+	0.625378i	$0.215055\pi$
$457$			26.7381i			1.25076i	−0.780322	+	0.625378i	$0.784945\pi$
$458$	9.46639	−	17.4631i	0.442335	−	0.815998i
$459$	1.14268	−	1.14268i	0.0533355	−	0.0533355i
$460$	40.4397	+	8.53848i	1.88551	+	0.398109i
$461$	−23.5563	−	23.5563i	−1.09713	−	1.09713i	−0.994745	−	0.102381i	$-0.967354\pi$
$461$	−23.5563	−	23.5563i	−1.09713	−	1.09713i	−0.102381	−	0.994745i	$-0.532646\pi$
$462$		0			0
$463$	−9.83629			−0.457131			−0.228566	−	0.973529i	$-0.573404\pi$
$463$	−9.83629			−0.457131			−0.228566	+	0.973529i	$0.573404\pi$
$464$	6.43419	−	2.48988i	0.298700	−	0.115590i
$465$	−3.73314			−0.173120
$466$	−7.37291	−	24.8287i	−0.341543	−	1.15017i
$467$	−1.96594	−	1.96594i	−0.0909727	−	0.0909727i	0.660156	−	0.751129i	$-0.270490\pi$
$467$	−1.96594	−	1.96594i	−0.0909727	−	0.0909727i	−0.751129	+	0.660156i	$0.770490\pi$
$468$	5.19309	−	24.5954i	0.240051	−	1.13692i
$469$		0			0
$470$	−10.3713	+	19.1324i	−0.478391	+	0.882511i
$471$		−	13.1058i		−	0.603882i
$472$	−1.66692	−	20.6439i	−0.0767264	−	0.950211i
$473$			17.7040i			0.814029i
$474$	0.838891	+	0.454745i	0.0385315	+	0.0208871i
$475$	−25.4755	+	25.4755i	−1.16889	+	1.16889i
$476$		0			0
$477$	−18.5974	−	18.5974i	−0.851517	−	0.851517i
$478$	−24.8695	+	7.38500i	−1.13750	+	0.337782i
$479$	−3.78688			−0.173027			−0.0865136	−	0.996251i	$-0.527573\pi$
$479$	−3.78688			−0.173027			−0.0865136	+	0.996251i	$0.527573\pi$
$480$	−2.12734	+	16.5928i	−0.0970994	+	0.757356i
$481$	−51.8179			−2.36269
$482$	−34.4548	+	10.2314i	−1.56937	+	0.466026i
$483$		0			0
$484$	1.60257	+	2.46044i	0.0728440	+	0.111838i
$485$	−5.11607	+	5.11607i	−0.232309	+	0.232309i
$486$	20.0579	+	10.8730i	0.909844	+	0.493207i
$487$		−	16.8200i		−	0.762186i	−0.924537	−	0.381093i	$-0.875548\pi$
$487$		−	16.8200i		−	0.762186i	0.924537	−	0.381093i	$-0.124452\pi$
$488$	0.0212771	−	0.00171806i	0.000963171	−	7.77728e-5i
$489$			19.7630i			0.893716i
$490$		0			0
$491$	−6.41618	+	6.41618i	−0.289558	+	0.289558i	−0.836906	−	0.547347i	$-0.815638\pi$
$491$	−6.41618	+	6.41618i	−0.289558	+	0.289558i	0.547347	+	0.836906i	$0.315638\pi$
$492$	0.990331	−	4.69038i	0.0446476	−	0.211458i
$493$	−0.424341	−	0.424341i	−0.0191113	−	0.0191113i
$494$	−13.8469	−	46.6302i	−0.622999	−	2.09799i
$495$	22.5349			1.01287
$496$	2.04131	−	4.61850i	0.0916576	−	0.207377i
$497$		0			0
$498$	−1.86300	−	6.27378i	−0.0834831	−	0.281135i
$499$	−4.69302	−	4.69302i	−0.210088	−	0.210088i	0.594217	−	0.804305i	$-0.297462\pi$
$499$	−4.69302	−	4.69302i	−0.210088	−	0.210088i	−0.804305	+	0.594217i	$0.797462\pi$
$500$	−6.32410	−	1.33528i	−0.282822	−	0.0597154i
$501$	−1.33826	+	1.33826i	−0.0597891	+	0.0597891i
$502$	10.4178	−	19.2182i	0.464969	−	0.857751i
$503$			4.37360i			0.195009i	0.995235	+	0.0975045i	$0.0310860\pi$
$503$			4.37360i			0.195009i	−0.995235	+	0.0975045i	$0.968914\pi$
$504$		0			0
$505$		−	22.2699i		−	0.990998i
$506$	−23.9441	−	12.9796i	−1.06444	−	0.577013i
$507$	12.3363	−	12.3363i	0.547876	−	0.547876i
$508$	22.9700	−	14.9612i	1.01913	−	0.663794i
$509$	−1.93619	−	1.93619i	−0.0858200	−	0.0858200i	0.662894	−	0.748714i	$-0.269328\pi$
$509$	−1.93619	−	1.93619i	−0.0858200	−	0.0858200i	−0.748714	+	0.662894i	$0.769328\pi$
$510$	1.39490	−	0.414217i	0.0617674	−	0.0183418i
$511$		0			0
$512$	−19.3648	−	11.7050i	−0.855810	−	0.517291i
$513$	28.0032			1.23637
$514$	−3.11340	+	0.924525i	−0.137326	+	0.0407791i
$515$	36.8394	+	36.8394i	1.62334	+	1.62334i
$516$	−8.57816	+	5.58726i	−0.377633	+	0.245965i
$517$	10.1404	−	10.1404i	0.445976	−	0.445976i
$518$		0			0
$519$			2.68449i			0.117836i
$520$	34.6343	−	40.7188i	1.51881	−	1.78564i
$521$			35.3300i			1.54783i	0.633287	+	0.773917i	$0.281705\pi$
$521$			35.3300i			1.54783i	−0.633287	+	0.773917i	$0.718295\pi$
$522$	2.56110	−	4.72459i	0.112096	−	0.206790i
$523$	23.3854	−	23.3854i	1.02257	−	1.02257i	0.0228331	−	0.999739i	$-0.492731\pi$
$523$	23.3854	−	23.3854i	1.02257	−	1.02257i	0.999739	−	0.0228331i	$-0.00726864\pi$
$524$	9.76690	+	2.06219i	0.426669	+	0.0900873i
$525$		0			0
$526$	−4.77084	−	16.0661i	−0.208019	−	0.700516i
$527$	−0.439220			−0.0191327
$528$	4.45638	−	10.0826i	0.193939	−	0.438790i
$529$	−15.9111			−0.691787
$530$	−15.9211	−	53.6154i	−0.691570	−	2.32891i
$531$	−11.4077	−	11.4077i	−0.495051	−	0.495051i
$532$		0			0
$533$	−10.8318	+	10.8318i	−0.469176	+	0.469176i
$534$	−3.75677	+	6.93030i	−0.162571	+	0.299904i
$535$			31.3008i			1.35325i
$536$	12.0412	−	0.972290i	0.520102	−	0.0419965i
$537$		−	1.79146i		−	0.0773070i
$538$	−10.0361	−	5.44036i	−0.432687	−	0.234551i
$539$		0			0
$540$	16.7958	+	25.7867i	0.722775	+	1.10968i
$541$	−5.13176	−	5.13176i	−0.220631	−	0.220631i	0.588133	−	0.808764i	$-0.299863\pi$
$541$	−5.13176	−	5.13176i	−0.220631	−	0.220631i	−0.808764	+	0.588133i	$0.799863\pi$
$542$	−35.4155	+	10.5167i	−1.52123	+	0.451729i
$543$	18.0761			0.775719
$544$	−0.250291	+	1.95222i	−0.0107311	+	0.0837006i
$545$	−3.80675			−0.163063
$546$		0			0
$547$	16.8157	+	16.8157i	0.718989	+	0.718989i	0.968398	−	0.249409i	$-0.0802365\pi$
$547$	16.8157	+	16.8157i	0.718989	+	0.718989i	−0.249409	+	0.968398i	$0.580236\pi$
$548$	17.0871	+	26.2339i	0.729923	+	1.12066i
$549$	0.0117576	−	0.0117576i	0.000501803	−	0.000501803i
$550$	22.9370	+	12.4336i	0.978035	+	0.530172i
$551$		−	10.3992i		−	0.443020i
$552$	−1.26756	−	15.6980i	−0.0539510	−	0.668151i
$553$		0			0
$554$	1.88980	−	3.48621i	0.0802899	−	0.148115i
$555$	18.9938	−	18.9938i	0.806240	−	0.806240i
$556$	−0.891485	+	4.22222i	−0.0378074	+	0.179062i
$557$	−11.0874	−	11.0874i	−0.469789	−	0.469789i	0.432057	−	0.901846i	$-0.357788\pi$
$557$	−11.0874	−	11.0874i	−0.469789	−	0.469789i	−0.901846	+	0.432057i	$0.857788\pi$
$558$	−1.11967	−	3.77058i	−0.0473996	−	0.159621i
$559$	32.7131			1.38362
$560$		0			0
$561$	−0.958861			−0.0404831
$562$	−2.62671	−	8.84563i	−0.110801	−	0.373130i
$563$	−22.2057	−	22.2057i	−0.935857	−	0.935857i	0.0622066	−	0.998063i	$-0.480186\pi$
$563$	−22.2057	−	22.2057i	−0.935857	−	0.935857i	−0.998063	+	0.0622066i	$0.980186\pi$
$564$	8.11365	+	1.71313i	0.341646	+	0.0721356i
$565$	−43.3778	+	43.3778i	−1.82492	+	1.82492i
$566$	13.3036	−	24.5417i	0.559190	−	1.03157i
$567$		0			0
$568$	1.78588	+	1.51902i	0.0749338	+	0.0637366i
$569$		−	0.317171i		−	0.0132965i	−0.999978	−	0.00664825i	$-0.997884\pi$
$569$		−	0.317171i		−	0.0132965i	0.999978	−	0.00664825i	$-0.00211622\pi$
$570$	22.1677	+	12.0167i	0.928505	+	0.503323i
$571$	−7.80358	+	7.80358i	−0.326570	+	0.326570i	−0.851280	−	0.524711i	$-0.824173\pi$
$571$	−7.80358	+	7.80358i	−0.326570	+	0.326570i	0.524711	+	0.851280i	$0.324173\pi$
$572$	−29.5166	+	19.2252i	−1.23415	+	0.803847i
$573$	−3.92775	−	3.92775i	−0.164084	−	0.164084i
$574$		0			0
$575$	37.2744			1.55445
$576$	−17.3973	+	2.82798i	−0.724887	+	0.117833i
$577$	10.2699			0.427540			0.213770	−	0.976884i	$-0.431426\pi$
$577$	10.2699			0.427540			0.213770	+	0.976884i	$0.431426\pi$
$578$	−22.8828	+	6.79507i	−0.951801	+	0.282638i
$579$	−0.994867	−	0.994867i	−0.0413453	−	0.0413453i
$580$	9.57606	−	6.23723i	0.397624	−	0.258987i
$581$		0			0
$582$	2.42374	+	1.31386i	0.100467	+	0.0544612i
$583$			36.8554i			1.52640i
$584$	13.4692	+	11.4566i	0.557361	+	0.474076i
$585$		−	41.6396i		−	1.72159i
$586$	2.45037	−	4.52031i	0.101224	−	0.186732i
$587$	27.9965	−	27.9965i	1.15554	−	1.15554i	0.170113	−	0.985425i	$-0.445587\pi$
$587$	27.9965	−	27.9965i	1.15554	−	1.15554i	0.985425	−	0.170113i	$-0.0544133\pi$
$588$		0			0
$589$	−5.38191	−	5.38191i	−0.221758	−	0.221758i
$590$	−9.76603	−	32.8877i	−0.402061	−	1.35397i
$591$	−13.5305			−0.556572
$592$	13.1124	+	33.8843i	0.538917	+	1.39264i
$593$	34.5902			1.42045			0.710225	−	0.703974i	$-0.248593\pi$
$593$	34.5902			1.42045			0.710225	+	0.703974i	$0.248593\pi$
$594$	−5.77273	−	19.4401i	−0.236858	−	0.797635i
$595$		0			0
$596$	5.39783	−	25.5650i	0.221104	−	1.04718i
$597$	−16.1182	+	16.1182i	−0.659673	+	0.659673i
$598$	−23.9835	+	44.2435i	−0.980757	+	1.80925i
$599$		−	14.0866i		−	0.575562i	−0.957696	−	0.287781i	$-0.907082\pi$
$599$		−	14.0866i		−	0.575562i	0.957696	−	0.287781i	$-0.0929176\pi$
$600$	1.21425	+	15.0377i	0.0495714	+	0.613912i
$601$		−	7.07501i		−	0.288595i	−0.989534	−	0.144298i	$-0.953908\pi$
$601$		−	7.07501i		−	0.288595i	0.989534	−	0.144298i	$-0.0460923\pi$
$602$		0			0
$603$	6.65391	−	6.65391i	0.270968	−	0.270968i
$604$	12.8002	+	19.6522i	0.520831	+	0.799636i
$605$	3.43930	+	3.43930i	0.139828	+	0.139828i
$606$	−8.13475	+	2.41562i	−0.330452	+	0.0981278i
$607$	−5.99294			−0.243246			−0.121623	−	0.992576i	$-0.538810\pi$
$607$	−5.99294			−0.243246			−0.121623	+	0.992576i	$0.538810\pi$
$608$	−26.9881	+	20.8543i	−1.09451	+	0.845752i
$609$		0			0
$610$	0.0338966	−	0.0100656i	0.00137243	−	0.000407545i
$611$	−18.7374	−	18.7374i	−0.758033	−	0.758033i
$612$	0.836742	+	1.28466i	0.0338233	+	0.0519292i
$613$	−12.3166	+	12.3166i	−0.497464	+	0.497464i	−0.910648	−	0.413184i	$-0.864417\pi$
$613$	−12.3166	+	12.3166i	−0.497464	+	0.497464i	0.413184	+	0.910648i	$0.364417\pi$
$614$	−33.1001	−	17.9429i	−1.33581	−	0.724115i
$615$		−	7.94074i		−	0.320201i
$616$		0			0
$617$			40.3690i			1.62519i	0.582827	+	0.812596i	$0.301947\pi$
$617$			40.3690i			1.62519i	−0.582827	+	0.812596i	$0.698053\pi$
$618$	9.46073	−	17.4527i	0.380567	−	0.702050i
$619$	−30.9375	+	30.9375i	−1.24348	+	1.24348i	−0.284938	+	0.958546i	$0.591973\pi$
$619$	−30.9375	+	30.9375i	−1.24348	+	1.24348i	−0.958546	+	0.284938i	$0.908027\pi$
$620$	1.72796	−	8.18389i	0.0693963	−	0.328673i
$621$	−20.4864	−	20.4864i	−0.822092	−	0.822092i
$622$	−9.61828	−	32.3902i	−0.385658	−	1.29873i
$623$		0			0
$624$	−18.6305	−	8.23444i	−0.745819	−	0.329641i
$625$	19.1709			0.766836
$626$	7.28196	+	24.5225i	0.291046	+	0.980115i
$627$	−11.7492	−	11.7492i	−0.469219	−	0.469219i
$628$	28.7308	+	6.06625i	1.14648	+	0.242070i
$629$	2.23470	−	2.23470i	0.0891033	−	0.0891033i
$630$		0			0
$631$			23.7329i			0.944792i	0.881386	+	0.472396i	$0.156611\pi$
$631$			23.7329i			0.944792i	−0.881386	+	0.472396i	$0.843389\pi$
$632$	−1.38520	+	1.62855i	−0.0551004	+	0.0647803i
$633$		−	11.6124i		−	0.461550i
$634$	−9.43255	−	5.11319i	−0.374614	−	0.203071i
$635$	32.1084	−	32.1084i	1.27418	−	1.27418i
$636$	−17.8577	+	11.6313i	−0.708104	+	0.461213i
$637$		0			0
$638$	−7.21920	+	2.14374i	−0.285811	+	0.0848717i
$639$	1.82626			0.0722459
$640$	−35.3906	−	12.3439i	−1.39893	−	0.487936i
$641$	−14.9883			−0.592000			−0.296000	−	0.955188i	$-0.595653\pi$
$641$	−14.9883			−0.592000			−0.296000	+	0.955188i	$0.595653\pi$
$642$	11.4336	−	3.39520i	0.451247	−	0.133998i
$643$	11.8452	+	11.8452i	0.467130	+	0.467130i	0.900983	−	0.433854i	$-0.142847\pi$
$643$	11.8452	+	11.8452i	0.467130	+	0.467130i	−0.433854	+	0.900983i	$0.642847\pi$
$644$		0			0
$645$	−11.9909	+	11.9909i	−0.472142	+	0.472142i
$646$	2.60813	+	1.41381i	0.102616	+	0.0556257i
$647$		−	4.12471i		−	0.162159i	−0.996708	−	0.0810795i	$-0.974163\pi$
$647$		−	4.12471i		−	0.162159i	0.996708	−	0.0810795i	$-0.0258368\pi$
$648$	−4.51487	+	5.30804i	−0.177361	+	0.208519i
$649$			22.6071i			0.887408i
$650$	22.9747	−	42.3826i	0.901142	−	1.66238i
$651$		0			0
$652$	−43.3251	−	9.14770i	−1.69674	−	0.358252i
$653$	−25.4516	−	25.4516i	−0.995997	−	0.995997i	0.00399544	−	0.999992i	$-0.498728\pi$
$653$	−25.4516	−	25.4516i	−0.995997	−	0.995997i	−0.999992	+	0.00399544i	$0.998728\pi$
$654$	0.412919	+	1.39053i	0.0161464	+	0.0543740i
$655$	16.5352			0.646084
$656$	9.82397	+	4.34206i	0.383562	+	0.169529i
$657$	13.7738			0.537368
$658$		0			0
$659$	7.38409	+	7.38409i	0.287643	+	0.287643i	0.836148	−	0.548504i	$-0.184803\pi$
$659$	7.38409	+	7.38409i	0.287643	+	0.287643i	−0.548504	+	0.836148i	$0.684803\pi$
$660$	3.77230	−	17.8662i	0.146836	−	0.695442i
$661$	−14.0924	+	14.0924i	−0.548130	+	0.548130i	−0.925900	−	0.377770i	$-0.876691\pi$
$661$	−14.0924	+	14.0924i	−0.548130	+	0.548130i	0.377770	+	0.925900i	$0.376691\pi$
$662$	−21.3084	+	39.3087i	−0.828175	+	1.52777i
$663$			1.77177i			0.0688098i
$664$	14.6159	−	1.18018i	0.567206	−	0.0458000i
$665$		0			0
$666$	24.8810	+	13.4875i	0.964120	+	0.522629i
$667$	−7.60778	+	7.60778i	−0.294574	+	0.294574i
$668$	−2.31433	−	3.55321i	−0.0895443	−	0.137478i
$669$	8.04953	+	8.04953i	0.311213	+	0.311213i
$670$	19.1829	−	5.69637i	0.741100	−	0.220070i
$671$	−0.0233006			−0.000899511
$672$		0			0
$673$	−35.0089			−1.34949			−0.674746	−	0.738050i	$-0.735747\pi$
$673$	−35.0089			−1.34949			−0.674746	+	0.738050i	$0.735747\pi$
$674$	15.6023	−	4.63310i	0.600977	−	0.178460i
$675$	19.6247	+	19.6247i	0.755356	+	0.755356i
$676$	21.3339	+	32.7542i	0.820536	+	1.25978i
$677$	−11.2860	+	11.2860i	−0.433755	+	0.433755i	−0.889904	−	0.456148i	$-0.849229\pi$
$677$	−11.2860	+	11.2860i	−0.433755	+	0.433755i	0.456148	+	0.889904i	$0.349229\pi$
$678$	20.5502	+	11.1399i	0.789228	+	0.427824i
$679$		0			0
$680$	0.262400	+	3.24967i	0.0100626	+	0.124619i
$681$		−	15.4579i		−	0.592346i
$682$	−2.62671	+	4.84563i	−0.100582	+	0.185549i
$683$	33.4270	−	33.4270i	1.27905	−	1.27905i	0.337848	−	0.941201i	$-0.390301\pi$
$683$	33.4270	−	33.4270i	1.27905	−	1.27905i	0.941201	−	0.337848i	$-0.109699\pi$
$684$	−5.48844	+	25.9942i	−0.209856	+	0.993913i
$685$	36.6709	+	36.6709i	1.40112	+	1.40112i
$686$		0			0
$687$	−12.5378			−0.478348
$688$	−8.27798	−	21.3915i	−0.315595	−	0.815541i
$689$	68.1009			2.59444
$690$	−7.42628	−	25.0085i	−0.282714	−	0.952056i
$691$	5.03700	+	5.03700i	0.191616	+	0.191616i	0.796394	−	0.604778i	$-0.206738\pi$
$691$	5.03700	+	5.03700i	0.191616	+	0.191616i	−0.604778	+	0.796394i	$0.706738\pi$
$692$	−5.88502	−	1.24257i	−0.223715	−	0.0472354i
$693$		0			0
$694$	11.7416	−	21.6603i	0.445704	−	0.822213i
$695$			7.14816i			0.271145i
$696$	−3.31705	−	2.82139i	−0.125733	−	0.106945i
$697$		−	0.934262i		−	0.0353877i
$698$	−0.442209	−	0.239712i	−0.0167379	−	0.00907324i
$699$	−11.5598	+	11.5598i	−0.437230	+	0.437230i
$700$		0			0
$701$	1.77330	+	1.77330i	0.0669766	+	0.0669766i	0.739802	−	0.672825i	$-0.234919\pi$
$701$	1.77330	+	1.77330i	0.0669766	+	0.0669766i	−0.672825	+	0.739802i	$0.734919\pi$
$702$	−35.9210	+	10.6668i	−1.35575	+	0.402591i
$703$	54.7650			2.06550
$704$	20.0407	+	14.4363i	0.755312	+	0.544090i
$705$	13.7363			0.517339
$706$	−22.6251	+	6.71852i	−0.851505	+	0.252855i
$707$		0			0
$708$	−10.9539	+	7.13467i	−0.411673	+	0.268137i
$709$	−8.84781	+	8.84781i	−0.332286	+	0.332286i	−0.853454	−	0.521168i	$-0.825497\pi$
$709$	−8.84781	+	8.84781i	−0.332286	+	0.332286i	0.521168	+	0.853454i	$0.325497\pi$
$710$	3.41424	+	1.85079i	0.128134	+	0.0694589i
$711$			1.66538i			0.0624567i
$712$	−13.4539	−	11.4435i	−0.504206	−	0.428864i
$713$			7.87454i			0.294904i
$714$		0			0
$715$	−41.2596	+	41.2596i	−1.54302	+	1.54302i
$716$	3.92728	+	0.829209i	0.146769	+	0.0309890i
$717$	11.5787	+	11.5787i	0.432415	+	0.432415i
$718$	7.23758	+	24.3730i	0.270104	+	0.909593i
$719$	11.8257			0.441025			0.220512	−	0.975384i	$-0.429227\pi$
$719$	11.8257			0.441025			0.220512	+	0.975384i	$0.429227\pi$
$720$	−27.2286	+	10.5368i	−1.01475	+	0.392684i
$721$		0			0
$722$	6.98542	+	23.5238i	0.259970	+	0.875467i
$723$	16.0414	+	16.0414i	0.596587	+	0.596587i
$724$	−8.36686	+	39.6269i	−0.310952	+	1.47272i
$725$	7.28778	−	7.28778i	0.270661	−	0.270661i
$726$	0.883248	−	1.62937i	0.0327804	−	0.0604716i
$727$		−	27.7703i		−	1.02994i	−0.857207	−	0.514972i	$-0.827802\pi$
$727$		−	27.7703i		−	1.02994i	0.857207	−	0.514972i	$-0.172198\pi$
$728$		0			0
$729$		−	7.00960i		−	0.259615i
$730$	25.7505	+	13.9588i	0.953068	+	0.516638i
$731$	−1.41078	+	1.41078i	−0.0521797	+	0.0521797i
$732$	−0.00735354	−	0.0112899i	−0.000271795	−	0.000417288i
$733$	−35.8466	−	35.8466i	−1.32402	−	1.32402i	−0.910488	−	0.413535i	$-0.864294\pi$
$733$	−35.8466	−	35.8466i	−1.32402	−	1.32402i	−0.413535	−	0.910488i	$-0.635706\pi$
$734$	−29.3198	+	8.70654i	−1.08221	+	0.321364i
$735$		0			0
$736$	35.0003	+	4.48733i	1.29013	+	0.165405i
$737$	−13.1864			−0.485726
$738$	8.02037	−	2.38165i	0.295234	−	0.0876698i
$739$	−10.1088	−	10.1088i	−0.371860	−	0.371860i	0.496295	−	0.868154i	$-0.334694\pi$
$739$	−10.1088	−	10.1088i	−0.371860	−	0.371860i	−0.868154	+	0.496295i	$0.834694\pi$
$740$	32.8470	+	50.4303i	1.20748	+	1.85385i
$741$	−21.7101	+	21.7101i	−0.797539	+	0.797539i
$742$		0			0
$743$			31.4037i			1.15209i	0.817418	+	0.576045i	$0.195405\pi$
$743$			31.4037i			1.15209i	−0.817418	+	0.576045i	$0.804595\pi$
$744$	−3.17684	+	0.256520i	−0.116469	+	0.00940447i
$745$		−	43.2812i		−	1.58570i
$746$	−11.5447	+	21.2971i	−0.422681	+	0.779741i
$747$	8.07664	−	8.07664i	0.295509	−	0.295509i
$748$	0.443827	−	2.10204i	0.0162279	−	0.0768582i
$749$		0			0
$750$	1.16135	+	3.91091i	0.0424064	+	0.142806i
$751$	12.6531			0.461717			0.230859	−	0.972987i	$-0.425847\pi$
$751$	12.6531			0.461717			0.230859	+	0.972987i	$0.425847\pi$
$752$	−7.51112	+	16.9940i	−0.273902	+	0.619708i
$753$	−13.7979			−0.502824
$754$	3.96118	+	13.3395i	0.144258	+	0.485797i
$755$	27.4707	+	27.4707i	0.999760	+	0.999760i
$756$		0			0
$757$	19.6555	−	19.6555i	0.714391	−	0.714391i	−0.253060	−	0.967451i	$-0.581437\pi$
$757$	19.6555	−	19.6555i	0.714391	−	0.714391i	0.967451	+	0.253060i	$0.0814370\pi$
$758$	4.13896	−	7.63535i	0.150334	−	0.277328i
$759$			17.1909i			0.623990i
$760$	−36.6040	+	43.0346i	−1.32777	+	1.56103i
$761$			12.2754i			0.444984i	0.974934	+	0.222492i	$0.0714192\pi$
$761$			12.2754i			0.444984i	−0.974934	+	0.222492i	$0.928581\pi$
$762$	−15.2114	−	8.24576i	−0.551050	−	0.298713i
$763$		0			0
$764$	10.4285	−	6.79248i	0.377292	−	0.245743i
$765$	1.79575	+	1.79575i	0.0649254	+	0.0649254i
$766$	44.4999	−	13.2143i	1.60785	−	0.477451i
$767$	41.7731			1.50834
$768$	−0.670172	+	14.2664i	−0.0241828	+	0.514795i
$769$	−44.0633			−1.58896			−0.794481	−	0.607289i	$-0.792257\pi$
$769$	−44.0633			−1.58896			−0.794481	+	0.607289i	$0.792257\pi$
$770$		0			0
$771$	1.44954	+	1.44954i	0.0522037	+	0.0522037i
$772$	2.64147	−	1.72048i	0.0950685	−	0.0619215i
$773$	−30.9188	+	30.9188i	−1.11207	+	1.11207i	−0.119200	+	0.992870i	$0.538033\pi$
$773$	−30.9188	+	30.9188i	−1.11207	+	1.11207i	−0.992870	+	0.119200i	$0.961967\pi$
$774$	−15.7076	−	8.51476i	−0.564598	−	0.306057i
$775$		−	7.54333i		−	0.270964i
$776$	−4.00215	+	4.70524i	−0.143669	+	0.168908i
$777$		0			0
$778$	0.223973	−	0.413174i	0.00802982	−	0.0148130i
$779$	11.4478	−	11.4478i	0.410161	−	0.410161i
$780$	−33.0130	−	6.97039i	−1.18205	−	0.249580i
$781$	−1.80960	−	1.80960i	−0.0647526	−	0.0647526i
$782$	−0.873734	−	2.94235i	−0.0312446	−	0.105218i
$783$	−8.01088			−0.286286
$784$		0			0
$785$	48.6408			1.73607
$786$	−1.79358	−	6.03998i	−0.0639747	−	0.215439i
$787$	−13.3994	−	13.3994i	−0.477638	−	0.477638i	0.426738	−	0.904375i	$-0.359663\pi$
$787$	−13.3994	−	13.3994i	−0.477638	−	0.477638i	−0.904375	+	0.426738i	$0.859663\pi$
$788$	6.26286	−	29.6620i	0.223105	−	1.05666i
$789$	−7.48006	+	7.48006i	−0.266297	+	0.266297i
$790$	−1.68774	+	3.11347i	−0.0600473	+	0.110772i
$791$		0			0
$792$	19.1768	−	1.54847i	0.681419	−	0.0550223i
$793$			0.0430546i			0.00152891i
$794$	−3.48110	−	1.88703i	−0.123540	−	0.0669683i
$795$	−24.9623	+	24.9623i	−0.885320	+	0.885320i
$796$	−27.8741	−	42.7953i	−0.987971	−	1.51684i
$797$	16.1055	+	16.1055i	0.570485	+	0.570485i	0.932264	−	0.361779i	$-0.117831\pi$
$797$	16.1055	+	16.1055i	0.570485	+	0.570485i	−0.361779	+	0.932264i	$0.617831\pi$
$798$		0			0
$799$	1.61613			0.0571747
$800$	−33.5281	−	4.29859i	−1.18540	−	0.151978i
$801$	−13.7582			−0.486121
$802$	−6.98246	+	2.07345i	−0.246559	+	0.0732159i
$803$	−13.6481	−	13.6481i	−0.481632	−	0.481632i
$804$	−4.16154	−	6.38924i	−0.146766	−	0.225331i
$805$		0			0
$806$	8.95368	+	4.85360i	0.315380	+	0.170961i
$807$			7.20553i			0.253647i
$808$	−1.53026	−	18.9513i	−0.0538343	−	0.666706i
$809$			37.6047i			1.32211i	0.750336	+	0.661056i	$0.229891\pi$
$809$			37.6047i			1.32211i	−0.750336	+	0.661056i	$0.770109\pi$
$810$	−5.50097	+	10.1479i	−0.193284	+	0.356561i
$811$	−7.00106	+	7.00106i	−0.245841	+	0.245841i	−0.819261	−	0.573421i	$-0.805616\pi$
$811$	−7.00106	+	7.00106i	−0.245841	+	0.245841i	0.573421	+	0.819261i	$0.305616\pi$
$812$		0			0
$813$	16.4887	+	16.4887i	0.578286	+	0.578286i
$814$	−11.2896	−	38.0184i	−0.395699	−	1.33254i
$815$	−73.3487			−2.56929
$816$	1.15858	−	0.448342i	0.0405584	−	0.0156951i
$817$	−34.5736			−1.20958
$818$	−0.0293493	−	0.0988357i	−0.00102617	−	0.00345571i
$819$		0			0
$820$	17.4079	+	3.67552i	0.607910	+	0.128355i
$821$	0.711892	−	0.711892i	0.0248452	−	0.0248452i	−0.694575	−	0.719420i	$-0.744408\pi$
$821$	0.711892	−	0.711892i	0.0248452	−	0.0248452i	0.719420	+	0.694575i	$0.244408\pi$
$822$	9.41745	−	17.3728i	0.328471	−	0.605947i
$823$			12.0278i			0.419262i	0.977781	+	0.209631i	$0.0672263\pi$
$823$			12.0278i			0.419262i	−0.977781	+	0.209631i	$0.932774\pi$
$824$	33.8812	+	28.8184i	1.18031	+	1.00394i
$825$		−	16.4678i		−	0.573336i
$826$		0			0
$827$	16.1838	−	16.1838i	0.562764	−	0.562764i	−0.367328	−	0.930092i	$-0.619727\pi$
$827$	16.1838	−	16.1838i	0.562764	−	0.562764i	0.930092	+	0.367328i	$0.119727\pi$
$828$	23.0319	−	15.0015i	0.800415	−	0.521338i
$829$	−3.31569	−	3.31569i	−0.115159	−	0.115159i	0.647179	−	0.762338i	$-0.275949\pi$
$829$	−3.31569	−	3.31569i	−0.115159	−	0.115159i	−0.762338	+	0.647179i	$0.775949\pi$
$830$	23.2845	−	6.91436i	0.808218	−	0.240001i
$831$	−2.50296			−0.0868267
$832$	26.6753	−	37.0309i	0.924798	−	1.28382i
$833$		0			0
$834$	2.61108	−	0.775362i	0.0904144	−	0.0268486i
$835$	−4.96684	−	4.96684i	−0.171884	−	0.171884i
$836$	31.1954	−	20.3186i	1.07891	−	0.702735i
$837$	−4.14589	+	4.14589i	−0.143303	+	0.143303i
$838$	24.1633	+	13.0984i	0.834709	+	0.452478i
$839$			47.4324i			1.63755i	0.574116	+	0.818774i	$0.305346\pi$
$839$			47.4324i			1.63755i	−0.574116	+	0.818774i	$0.694654\pi$
$840$		0			0
$841$		−	26.0251i		−	0.897417i
$842$	3.69906	−	6.82383i	0.127478	−	0.235165i
$843$	−4.11834	+	4.11834i	−0.141843	+	0.141843i
$844$	25.4569	+	5.37500i	0.876263	+	0.185015i
$845$	45.7852	+	45.7852i	1.57506	+	1.57506i
$846$	4.11990	+	13.8740i	0.141645	+	0.477000i
$847$		0			0
$848$	−17.2328	−	44.5319i	−0.591776	−	1.52923i
$849$	−17.6200			−0.604716
$850$	0.836983	+	2.81859i	0.0287083	+	0.0966770i
$851$	−40.0647	−	40.0647i	−1.37340	−	1.37340i
$852$	0.305713	−	1.44791i	0.0104736	−	0.0496046i
$853$	−3.99601	+	3.99601i	−0.136821	+	0.136821i	−0.772200	−	0.635379i	$-0.780844\pi$
$853$	−3.99601	+	3.99601i	−0.136821	+	0.136821i	0.635379	+	0.772200i	$0.280844\pi$
$854$		0			0
$855$			44.0078i			1.50503i
$856$	2.15081	+	26.6365i	0.0735131	+	0.910416i
$857$			11.1854i			0.382086i	0.981582	+	0.191043i	$0.0611869\pi$
$857$			11.1854i			0.382086i	−0.981582	+	0.191043i	$0.938813\pi$
$858$	19.5468	+	10.5959i	0.667315	+	0.361738i
$859$	−15.0707	+	15.0707i	−0.514207	+	0.514207i	−0.915813	−	0.401606i	$-0.868452\pi$
$859$	−15.0707	+	15.0707i	−0.514207	+	0.514207i	0.401606	+	0.915813i	$0.368452\pi$
$860$	−20.7366	−	31.8371i	−0.707112	−	1.08563i
$861$		0			0
$862$	−45.8273	+	13.6084i	−1.56088	+	0.463505i
$863$	29.6751			1.01015			0.505076	−	0.863075i	$-0.331464\pi$
$863$	29.6751			1.01015			0.505076	+	0.863075i	$0.331464\pi$
$864$	16.0649	+	20.7900i	0.546537	+	0.707289i
$865$	−9.96325			−0.338761
$866$	−25.3423	+	7.52541i	−0.861167	+	0.255724i
$867$	10.6538	+	10.6538i	0.361821	+	0.361821i
$868$		0			0
$869$	1.65018	−	1.65018i	0.0559787	−	0.0559787i
$870$	−6.34154	−	3.43762i	−0.214998	−	0.116546i
$871$			24.3656i			0.825596i
$872$	−3.23948	+	0.261578i	−0.109703	+	0.00885814i
$873$			4.81165i			0.162850i
$874$	25.3475	−	46.7598i	0.857392	−	1.58167i
$875$		0			0
$876$	2.30571	−	10.9203i	0.0779028	−	0.368961i
$877$	2.85105	+	2.85105i	0.0962730	+	0.0962730i	0.753603	−	0.657330i	$-0.228314\pi$
$877$	2.85105	+	2.85105i	0.0962730	+	0.0962730i	−0.657330	+	0.753603i	$0.728314\pi$
$878$	−2.42811	−	8.17682i	−0.0819447	−	0.275954i
$879$	−3.24541			−0.109465
$880$	37.4208	+	16.5395i	1.26145	+	0.557545i
$881$	23.4719			0.790789			0.395394	−	0.918511i	$-0.370608\pi$
$881$	23.4719			0.790789			0.395394	+	0.918511i	$0.370608\pi$
$882$		0			0
$883$	−22.0401	−	22.0401i	−0.741710	−	0.741710i	0.231197	−	0.972907i	$-0.425736\pi$
$883$	−22.0401	−	22.0401i	−0.741710	−	0.741710i	−0.972907	+	0.231197i	$0.925736\pi$
$884$	−3.88412	−	0.820097i	−0.130637	−	0.0275828i
$885$	−15.3119	+	15.3119i	−0.514702	+	0.514702i
$886$	23.7479	−	43.8089i	0.797826	−	1.47179i
$887$			18.6629i			0.626640i	0.949648	+	0.313320i	$0.101441\pi$
$887$			18.6629i			0.626640i	−0.949648	+	0.313320i	$0.898559\pi$
$888$	14.8583	−	17.4685i	0.498611	−	0.586206i
$889$		0			0
$890$	−25.7212	−	13.9429i	−0.862176	−	0.467367i
$891$	5.37854	−	5.37854i	0.180188	−	0.180188i
$892$	−21.3723	+	13.9205i	−0.715596	+	0.466093i
$893$	19.8030	+	19.8030i	0.662683	+	0.662683i
$894$	−15.8098	+	4.69472i	−0.528758	+	0.157015i
$895$	6.64882			0.222246
$896$		0			0
$897$	31.7651			1.06061
$898$	29.8096	−	8.85198i	0.994760	−	0.295394i
$899$	1.53961	+	1.53961i	0.0513487	+	0.0513487i
$900$	−22.0632	+	14.3705i	−0.735439	+	0.479017i
$901$	−2.93692	+	2.93692i	−0.0978429	+	0.0978429i
$902$	−10.3071	−	5.58726i	−0.343189	−	0.186035i
$903$		0			0
$904$	−33.9332	+	39.8945i	−1.12860	+	1.32687i
$905$			67.0877i			2.23007i
$906$	7.05474	−	13.0142i	0.234378	−	0.432369i
$907$	−2.95043	+	2.95043i	−0.0979673	+	0.0979673i	−0.754392	−	0.656424i	$-0.772068\pi$
$907$	−2.95043	+	2.95043i	−0.0979673	+	0.0979673i	0.656424	+	0.754392i	$0.272068\pi$
$908$	33.8871	+	7.15496i	1.12458	+	0.237446i
$909$	−10.4724	−	10.4724i	−0.347347	−	0.347347i
$910$		0			0
$911$	−26.5648			−0.880132			−0.440066	−	0.897965i	$-0.645045\pi$
$911$	−26.5648			−0.880132			−0.440066	+	0.897965i	$0.645045\pi$
$912$	19.6901	+	8.70276i	0.652005	+	0.288177i
$913$	−16.0059			−0.529717
$914$	10.7641	+	36.2489i	0.356046	+	1.19901i
$915$	−0.0157816	−	0.0157816i	−0.000521723	−	0.000521723i
$916$	5.80337	−	27.4858i	0.191749	−	0.908155i
$917$		0			0
$918$	1.08911	−	2.00914i	0.0359461	−	0.0663116i
$919$		−	21.9819i		−	0.725116i	−0.931961	−	0.362558i	$-0.881904\pi$
$919$		−	21.9819i		−	0.725116i	0.931961	−	0.362558i	$-0.118096\pi$
$920$	58.2616	−	4.70443i	1.92083	−	0.155101i
$921$			23.7645i			0.783068i
$922$	−41.4186	−	22.4521i	−1.36405	−	0.739422i
$923$	−3.34375	+	3.34375i	−0.110061	+	0.110061i
$924$		0			0
$925$	38.3795	+	38.3795i	1.26191	+	1.26191i
$926$	−13.3351	+	3.95986i	−0.438218	+	0.130129i
$927$	34.6474			1.13797
$928$	7.72049	−	5.96579i	0.253438	−	0.195837i
$929$	−14.0560			−0.461163			−0.230581	−	0.973053i	$-0.574063\pi$
$929$	−14.0560			−0.461163			−0.230581	+	0.973053i	$0.574063\pi$
$930$	−5.06103	+	1.50288i	−0.165958	+	0.0492812i
$931$		0			0
$932$	−19.9910	−	30.6923i	−0.654825	−	1.00536i
$933$	−15.0802	+	15.0802i	−0.493704	+	0.493704i
$934$	−3.45667	−	1.87379i	−0.113106	−	0.0613122i
$935$		−	3.55872i		−	0.116383i
$936$	−2.86123	−	35.4347i	−0.0935223	−	1.15822i
$937$			57.9965i			1.89466i	0.320256	+	0.947331i	$0.396231\pi$
$937$			57.9965i			1.89466i	−0.320256	+	0.947331i	$0.603769\pi$
$938$		0			0
$939$	11.4172	−	11.4172i	0.372585	−	0.372585i
$940$	−6.35810	+	30.1131i	−0.207378	+	0.982180i
$941$	15.4672	+	15.4672i	0.504217	+	0.504217i	0.912745	−	0.408529i	$-0.133958\pi$
$941$	15.4672	+	15.4672i	0.504217	+	0.504217i	−0.408529	+	0.912745i	$0.633958\pi$
$942$	−5.27608	−	17.7675i	−0.171904	−	0.578898i
$943$	−16.7499			−0.545451
$944$	−10.5706	−	27.3159i	−0.344043	−	0.889056i
$945$		0			0
$946$	7.12720	+	24.0013i	0.231725	+	0.780350i
$947$	18.9435	+	18.9435i	0.615580	+	0.615580i	0.944395	−	0.328814i	$-0.106649\pi$
$947$	18.9435	+	18.9435i	0.615580	+	0.615580i	−0.328814	+	0.944395i	$0.606649\pi$
$948$	1.32036	+	0.278782i	0.0428832	+	0.00905441i
$949$	−25.2188	+	25.2188i	−0.818638	+	0.818638i
$950$	−24.2813	+	44.7930i	−0.787791	+	1.45328i
$951$			6.77220i			0.219604i
$952$		0			0
$953$			20.2198i			0.654983i	0.944854	+	0.327491i	$0.106203\pi$
$953$			20.2198i			0.654983i	−0.944854	+	0.327491i	$0.893797\pi$
$954$	−32.6995	−	17.7257i	−1.05868	−	0.573891i
$955$	14.5775	−	14.5775i	0.471716	−	0.471716i
$956$	−30.7426	+	20.0237i	−0.994287	+	0.647614i
$957$	3.36111	+	3.36111i	0.108649	+	0.108649i
$958$	−5.13389	+	1.52451i	−0.165869	+	0.0492547i
$959$		0			0
$960$	3.79584	+	23.3514i	0.122510	+	0.753662i
$961$	−29.4064			−0.948594
$962$	−70.2498	+	20.8607i	−2.26494	+	0.672576i
$963$	14.7192	+	14.7192i	0.474318	+	0.474318i
$964$	−42.5915	+	27.7414i	−1.37178	+	0.893490i
$965$	3.69236	−	3.69236i	0.118861	−	0.118861i
$966$		0			0
$967$		−	33.3933i		−	1.07385i	−0.843628	−	0.536927i	$-0.819585\pi$
$967$		−	33.3933i		−	1.07385i	0.843628	−	0.536927i	$-0.180415\pi$
$968$	3.16312	+	2.69046i	0.101667	+	0.0864748i
$969$		−	1.87253i		−	0.0601545i
$970$	−4.87627	+	8.99549i	−0.156567	+	0.288828i
$971$	−7.52202	+	7.52202i	−0.241393	+	0.241393i	−0.817426	−	0.576033i	$-0.804600\pi$
$971$	−7.52202	+	7.52202i	−0.241393	+	0.241393i	0.576033	+	0.817426i	$0.304600\pi$
$972$	31.5697	+	6.66567i	1.01260	+	0.213801i
$973$		0			0
$974$	−6.77134	−	22.8029i	−0.216968	−	0.730653i
$975$	−30.4290			−0.974508
$976$	0.0281538	−	0.0108949i	0.000901182	−	0.000348736i
$977$	28.2764			0.904641			0.452321	−	0.891855i	$-0.350596\pi$
$977$	28.2764			0.904641			0.452321	+	0.891855i	$0.350596\pi$
$978$	7.95614	+	26.7928i	0.254409	+	0.856740i
$979$	13.6326	+	13.6326i	0.435700	+	0.435700i
$980$		0			0
$981$	−1.79012	+	1.79012i	−0.0571541	+	0.0571541i
$982$	−6.11544	+	11.2814i	−0.195151	+	0.360005i
$983$		−	1.94376i		−	0.0619964i	−0.999519	−	0.0309982i	$-0.990131\pi$
$983$		−	1.94376i		−	0.0619964i	0.999519	−	0.0309982i	$-0.00986862\pi$
$984$	−0.545641	−	6.75744i	−0.0173944	−	0.215419i
$985$		−	50.2173i		−	1.60006i
$986$	−0.746110	−	0.404450i	−0.0237610	−	0.0128803i
$987$		0			0
$988$	−37.5445	−	57.6423i	−1.19445	−	1.83385i
$989$	25.2932	+	25.2932i	0.804277	+	0.804277i
$990$	30.5506	−	9.07202i	0.970962	−	0.288328i
$991$	−8.60542			−0.273360			−0.136680	−	0.990615i	$-0.543643\pi$
$991$	−8.60542			−0.273360			−0.136680	+	0.990615i	$0.543643\pi$
$992$	0.908114	−	7.08310i	0.0288326	−	0.224889i
$993$	28.2221			0.895600
$994$		0			0
$995$	−59.8211	−	59.8211i	−1.89646	−	1.89646i
$996$	−5.05135	−	7.75538i	−0.160058	−	0.245739i
$997$	−7.78348	+	7.78348i	−0.246505	+	0.246505i	−0.819535	−	0.573029i	$-0.805768\pi$
$997$	−7.78348	+	7.78348i	−0.246505	+	0.246505i	0.573029	+	0.819535i	$0.305768\pi$
$998$	−8.25164	−	4.47304i	−0.261201	−	0.141592i
$999$		−	42.1876i		−	1.33476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.h.589.6		12
7.2	even	3		784.2.x.m.557.2		24
7.3	odd	6		784.2.x.l.765.3		24
7.4	even	3		784.2.x.m.765.3		24
7.5	odd	6		784.2.x.l.557.2		24
7.6	odd	2		112.2.m.d.29.6	✓	12
16.5	even	4	inner	784.2.m.h.197.6		12
28.27	even	2		448.2.m.d.337.3		12
56.13	odd	2		896.2.m.g.673.3		12
56.27	even	2		896.2.m.h.673.4		12
112.5	odd	12		784.2.x.l.165.3		24
112.13	odd	4		896.2.m.g.225.3		12
112.27	even	4		448.2.m.d.113.3		12
112.37	even	12		784.2.x.m.165.3		24
112.53	even	12		784.2.x.m.373.2		24
112.69	odd	4		112.2.m.d.85.6	yes	12
112.83	even	4		896.2.m.h.225.4		12
112.101	odd	12		784.2.x.l.373.2		24
224.27	even	8		7168.2.a.bi.1.9		12
224.69	odd	8		7168.2.a.bj.1.4		12
224.139	even	8		7168.2.a.bi.1.4		12
224.181	odd	8		7168.2.a.bj.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.6	✓	12	7.6	odd	2
112.2.m.d.85.6	yes	12	112.69	odd	4
448.2.m.d.113.3		12	112.27	even	4
448.2.m.d.337.3		12	28.27	even	2
784.2.m.h.197.6		12	16.5	even	4	inner
784.2.m.h.589.6		12	1.1	even	1	trivial
784.2.x.l.165.3		24	112.5	odd	12
784.2.x.l.373.2		24	112.101	odd	12
784.2.x.l.557.2		24	7.5	odd	6
784.2.x.l.765.3		24	7.3	odd	6
784.2.x.m.165.3		24	112.37	even	12
784.2.x.m.373.2		24	112.53	even	12
784.2.x.m.557.2		24	7.2	even	3
784.2.x.m.765.3		24	7.4	even	3
896.2.m.g.225.3		12	112.13	odd	4
896.2.m.g.673.3		12	56.13	odd	2
896.2.m.h.225.4		12	112.83	even	4
896.2.m.h.673.4		12	56.27	even	2
7168.2.a.bi.1.4		12	224.139	even	8
7168.2.a.bi.1.9		12	224.27	even	8
7168.2.a.bj.1.4		12	224.69	odd	8
7168.2.a.bj.1.9		12	224.181	odd	8

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35570 - 0.402577i) q^{2} +(-0.631188 - 0.631188i) q^{3} +(1.67586 - 1.09155i) q^{4} +(2.34259 - 2.34259i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} -2.20320i q^{9} +O(q^{10})\)	\(q+(1.35570 - 0.402577i) q^{2} +(-0.631188 - 0.631188i) q^{3} +(1.67586 - 1.09155i) q^{4} +(2.34259 - 2.34259i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} -2.20320i q^{9} +(2.23279 - 4.11894i) q^{10} +(-2.18310 + 2.18310i) q^{11} +(-1.74676 - 0.368812i) q^{12} +(4.03390 + 4.03390i) q^{13} -2.95723 q^{15} +(1.61704 - 3.65858i) q^{16} -0.347931 q^{17} +(-0.886959 - 2.98689i) q^{18} +(-4.26332 - 4.26332i) q^{19} +(1.36881 - 6.48293i) q^{20} +(-2.08077 + 3.83850i) q^{22} +6.23788i q^{23} +(-2.51656 + 0.203204i) q^{24} -5.97550i q^{25} +(7.09272 + 3.84481i) q^{26} +(-3.28420 + 3.28420i) q^{27} +(1.21961 + 1.21961i) q^{29} +(-4.00913 + 1.19051i) q^{30} +1.26238 q^{31} +(0.719369 - 5.61093i) q^{32} +2.75589 q^{33} +(-0.471692 + 0.140069i) q^{34} +(-2.40491 - 3.69227i) q^{36} +(-6.42281 + 6.42281i) q^{37} +(-7.49611 - 4.06348i) q^{38} -5.09229i q^{39} +(-0.754173 - 9.33998i) q^{40} +2.68519i q^{41} +(4.05478 - 4.05478i) q^{43} +(-1.27562 + 6.04154i) q^{44} +(-5.16121 - 5.16121i) q^{45} +(2.51122 + 8.45671i) q^{46} -4.64498 q^{47} +(-3.32990 + 1.28859i) q^{48} +(-2.40560 - 8.10101i) q^{50} +(0.219610 + 0.219610i) q^{51} +(11.1635 + 2.35706i) q^{52} +(8.44108 - 8.44108i) q^{53} +(-3.13026 + 5.77454i) q^{54} +10.2282i q^{55} +5.38191i q^{57} +(2.14442 + 1.16244i) q^{58} +(5.17776 - 5.17776i) q^{59} +(-4.95592 + 3.22797i) q^{60} +(0.00533660 + 0.00533660i) q^{61} +(1.71141 - 0.508203i) q^{62} +(-1.28358 - 7.89636i) q^{64} +18.8996 q^{65} +(3.73617 - 1.10946i) q^{66} +(3.02011 + 3.02011i) q^{67} +(-0.583086 + 0.379784i) q^{68} +(3.93727 - 3.93727i) q^{69} +0.828913i q^{71} +(-4.74676 - 4.03746i) q^{72} +6.25173i q^{73} +(-6.12176 + 11.2931i) q^{74} +(-3.77166 + 3.77166i) q^{75} +(-11.7984 - 2.49112i) q^{76} +(-2.05004 - 6.90364i) q^{78} -0.755891 q^{79} +(-4.78249 - 12.3586i) q^{80} -2.46372 q^{81} +(1.08099 + 3.64032i) q^{82} +(3.66586 + 3.66586i) q^{83} +(-0.815062 + 0.815062i) q^{85} +(3.86472 - 7.12944i) q^{86} -1.53961i q^{87} +(0.702825 + 8.70407i) q^{88} -6.24461i q^{89} +(-9.07486 - 4.91929i) q^{90} +(6.80895 + 10.4538i) q^{92} +(-0.796796 - 0.796796i) q^{93} +(-6.29721 + 1.86996i) q^{94} -19.9745 q^{95} +(-3.99561 + 3.08749i) q^{96} -2.18393 q^{97} +(4.80981 + 4.80981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8	\( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{10} - 8 q^{12} - 24 q^{15} + 10 q^{16} + 8 q^{17} + 20 q^{20} + 14 q^{22} + 8 q^{24} + 20 q^{26} - 4 q^{27} - 4 q^{29} - 28 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{34} - 16 q^{36} - 20 q^{37} - 16 q^{38} + 8 q^{40} + 16 q^{43} + 14 q^{44} - 40 q^{45} - 28 q^{46} - 16 q^{47} - 16 q^{48} + 44 q^{50} - 16 q^{51} + 16 q^{52} + 4 q^{53} - 64 q^{54} + 14 q^{58} + 16 q^{59} + 60 q^{60} + 20 q^{61} - 8 q^{62} - 18 q^{64} + 32 q^{65} - 12 q^{66} + 24 q^{67} + 28 q^{68} + 4 q^{69} + 6 q^{72} - 38 q^{74} + 40 q^{75} - 48 q^{76} - 76 q^{78} + 24 q^{79} - 24 q^{80} - 44 q^{81} + 16 q^{82} + 20 q^{83} - 8 q^{85} + 38 q^{86} - 14 q^{88} + 40 q^{90} + 32 q^{92} - 48 q^{93} + 24 q^{94} + 16 q^{96} - 48 q^{97} + 32 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^10 - 8 * q^12 - 24 * q^15 + 10 * q^16 + 8 * q^17 + 20 * q^20 + 14 * q^22 + 8 * q^24 + 20 * q^26 - 4 * q^27 - 4 * q^29 - 28 * q^30 + 8 * q^31 + 12 * q^32 - 8 * q^34 - 16 * q^36 - 20 * q^37 - 16 * q^38 + 8 * q^40 + 16 * q^43 + 14 * q^44 - 40 * q^45 - 28 * q^46 - 16 * q^47 - 16 * q^48 + 44 * q^50 - 16 * q^51 + 16 * q^52 + 4 * q^53 - 64 * q^54 + 14 * q^58 + 16 * q^59 + 60 * q^60 + 20 * q^61 - 8 * q^62 - 18 * q^64 + 32 * q^65 - 12 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 6 * q^72 - 38 * q^74 + 40 * q^75 - 48 * q^76 - 76 * q^78 + 24 * q^79 - 24 * q^80 - 44 * q^81 + 16 * q^82 + 20 * q^83 - 8 * q^85 + 38 * q^86 - 14 * q^88 + 40 * q^90 + 32 * q^92 - 48 * q^93 + 24 * q^94 + 16 * q^96 - 48 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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