LMFDB - Embedded newform 625.2.d.m.126.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			126.2
Root			$-1.63097i$ of defining polynomial
Character	$\chi$	$=$	625.126
Dual form			625.2.d.m.501.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.100972 - 0.310759i) q^{2} +(1.38777 - 1.00827i) q^{3} +(1.53166 - 1.11281i) q^{4} +(-0.453455 - 0.329455i) q^{6} +3.42409 q^{7} +(-1.02917 - 0.747732i) q^{8} +(-0.0177620 + 0.0546659i) q^{9} +O(q^{10})$	\(q+(-0.100972 - 0.310759i) q^{2} +(1.38777 - 1.00827i) q^{3} +(1.53166 - 1.11281i) q^{4} +(-0.453455 - 0.329455i) q^{6} +3.42409 q^{7} +(-1.02917 - 0.747732i) q^{8} +(-0.0177620 + 0.0546659i) q^{9} +(-1.65050 - 5.07970i) q^{11} +(1.00357 - 3.08866i) q^{12} +(-1.08809 + 3.34880i) q^{13} +(-0.345736 - 1.06407i) q^{14} +(1.04163 - 3.20582i) q^{16} +(-2.06936 - 1.50348i) q^{17} +0.0187814 q^{18} +(1.63890 + 1.19073i) q^{19} +(4.75186 - 3.45243i) q^{21} +(-1.41191 + 1.02581i) q^{22} +(2.33951 + 7.20028i) q^{23} -2.18216 q^{24} +1.15054 q^{26} +(1.62071 + 4.98804i) q^{27} +(5.24454 - 3.81038i) q^{28} +(-3.83692 + 2.78769i) q^{29} +(-1.31401 - 0.954685i) q^{31} -3.64565 q^{32} +(-7.41224 - 5.38531i) q^{33} +(-0.258273 + 0.794881i) q^{34} +(0.0336277 + 0.103495i) q^{36} +(-0.00414978 + 0.0127717i) q^{37} +(0.204547 - 0.629532i) q^{38} +(1.86649 + 5.74446i) q^{39} +(2.99048 - 9.20376i) q^{41} +(-1.55267 - 1.12808i) q^{42} +2.32645 q^{43} +(-8.18076 - 5.94367i) q^{44} +(2.00133 - 1.45405i) q^{46} +(-5.61982 + 4.08304i) q^{47} +(-1.78680 - 5.49920i) q^{48} +4.72443 q^{49} -4.38772 q^{51} +(2.06001 + 6.34006i) q^{52} +(-1.39350 + 1.01244i) q^{53} +(1.38643 - 1.00730i) q^{54} +(-3.52396 - 2.56031i) q^{56} +3.47500 q^{57} +(1.25372 + 0.910880i) q^{58} +(-0.00685492 + 0.0210973i) q^{59} +(1.21063 + 3.72593i) q^{61} +(-0.163999 + 0.504737i) q^{62} +(-0.0608188 + 0.187181i) q^{63} +(-1.71516 - 5.27873i) q^{64} +(-0.925105 + 2.84718i) q^{66} +(-3.33179 - 2.42069i) q^{67} -4.84265 q^{68} +(10.5066 + 7.63346i) q^{69} +(-1.89224 + 1.37479i) q^{71} +(0.0591555 - 0.0429790i) q^{72} +(0.467768 + 1.43964i) q^{73} +0.00438793 q^{74} +3.83530 q^{76} +(-5.65145 - 17.3934i) q^{77} +(1.59668 - 1.16005i) q^{78} +(-0.345313 + 0.250885i) q^{79} +(7.13898 + 5.18677i) q^{81} -3.16210 q^{82} +(4.88797 + 3.55132i) q^{83} +(3.43631 - 10.5759i) q^{84} +(-0.234905 - 0.722965i) q^{86} +(-2.51401 + 7.73734i) q^{87} +(-2.09963 + 6.46198i) q^{88} +(-1.88303 - 5.79537i) q^{89} +(-3.72573 + 11.4666i) q^{91} +(11.5959 + 8.42492i) q^{92} -2.78613 q^{93} +(1.83628 + 1.33414i) q^{94} +(-5.05932 + 3.67581i) q^{96} +(12.9458 - 9.40564i) q^{97} +(-0.477033 - 1.46816i) q^{98} +0.307002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9	$ 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9} - 3 q^{11} + 15 q^{12} - 5 q^{13} - q^{14} + q^{16} - 25 q^{17} - 10 q^{18} + 10 q^{19} + 7 q^{21} - 35 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} + 35 q^{28} - 8 q^{31} + 60 q^{32} - 6 q^{34} + q^{36} - 5 q^{37} - 35 q^{38} + q^{39} - 8 q^{41} - 10 q^{42} - 31 q^{44} + 42 q^{46} - 5 q^{47} - 25 q^{48} - 8 q^{49} - 28 q^{51} + 15 q^{52} - 10 q^{53} + 50 q^{54} + 35 q^{56} - 20 q^{57} + 35 q^{58} - 15 q^{59} + 17 q^{61} + 5 q^{62} + 10 q^{63} + 37 q^{64} + 44 q^{66} - 10 q^{67} + 80 q^{68} - 9 q^{69} - 13 q^{71} + 20 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 45 q^{77} + 5 q^{78} - 55 q^{79} - 19 q^{81} - 90 q^{82} - 15 q^{83} + 59 q^{84} + 7 q^{86} - 60 q^{87} + 40 q^{88} - 28 q^{91} + 45 q^{92} - 80 q^{93} + 4 q^{94} - 43 q^{96} + 40 q^{97} + 45 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9 - 3 * q^11 + 15 * q^12 - 5 * q^13 - q^14 + q^16 - 25 * q^17 - 10 * q^18 + 10 * q^19 + 7 * q^21 - 35 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 + 35 * q^28 - 8 * q^31 + 60 * q^32 - 6 * q^34 + q^36 - 5 * q^37 - 35 * q^38 + q^39 - 8 * q^41 - 10 * q^42 - 31 * q^44 + 42 * q^46 - 5 * q^47 - 25 * q^48 - 8 * q^49 - 28 * q^51 + 15 * q^52 - 10 * q^53 + 50 * q^54 + 35 * q^56 - 20 * q^57 + 35 * q^58 - 15 * q^59 + 17 * q^61 + 5 * q^62 + 10 * q^63 + 37 * q^64 + 44 * q^66 - 10 * q^67 + 80 * q^68 - 9 * q^69 - 13 * q^71 + 20 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 45 * q^77 + 5 * q^78 - 55 * q^79 - 19 * q^81 - 90 * q^82 - 15 * q^83 + 59 * q^84 + 7 * q^86 - 60 * q^87 + 40 * q^88 - 28 * q^91 + 45 * q^92 - 80 * q^93 + 4 * q^94 - 43 * q^96 + 40 * q^97 + 45 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.100972	−	0.310759i	−0.0713977	−	0.219740i	0.908990	−	0.416818i	$-0.136855\pi$
$2$	−0.100972	−	0.310759i	−0.0713977	−	0.219740i	−0.980388	+	0.197078i	$0.936855\pi$
$3$	1.38777	−	1.00827i	0.801229	−	0.582127i	−0.110045	−	0.993927i	$-0.535100\pi$
$3$	1.38777	−	1.00827i	0.801229	−	0.582127i	0.911274	+	0.411799i	$0.135100\pi$
$4$	1.53166	−	1.11281i	0.765829	−	0.556407i
$5$		0			0
$5$		0			0
$6$	−0.453455	−	0.329455i	−0.185122	−	0.134499i
$7$	3.42409			1.29419			0.647093	−	0.762411i	$-0.275984\pi$
$7$	3.42409			1.29419			0.647093	+	0.762411i	$0.275984\pi$
$8$	−1.02917	−	0.747732i	−0.363865	−	0.264363i
$9$	−0.0177620	+	0.0546659i	−0.00592067	+	0.0182220i
$10$		0			0
$11$	−1.65050	−	5.07970i	−0.497643	−	1.53159i	−0.812797	−	0.582547i	$-0.802056\pi$
$11$	−1.65050	−	5.07970i	−0.497643	−	1.53159i	0.315154	−	0.949041i	$-0.397944\pi$
$12$	1.00357	−	3.08866i	0.289705	−	0.891620i
$13$	−1.08809	+	3.34880i	−0.301782	+	0.928790i	0.679076	+	0.734068i	$0.262381\pi$
$13$	−1.08809	+	3.34880i	−0.301782	+	0.928790i	−0.980858	+	0.194722i	$0.937619\pi$
$14$	−0.345736	−	1.06407i	−0.0924020	−	0.284384i
$15$		0			0
$16$	1.04163	−	3.20582i	0.260409	−	0.801456i
$17$	−2.06936	−	1.50348i	−0.501894	−	0.364647i	0.307846	−	0.951436i	$-0.400392\pi$
$17$	−2.06936	−	1.50348i	−0.501894	−	0.364647i	−0.809740	+	0.586789i	$0.800392\pi$
$18$	0.0187814			0.00442681
$19$	1.63890	+	1.19073i	0.375989	+	0.273172i	0.759690	−	0.650285i	$-0.225351\pi$
$19$	1.63890	+	1.19073i	0.375989	+	0.273172i	−0.383701	+	0.923457i	$0.625351\pi$
$20$		0			0
$21$	4.75186	−	3.45243i	1.03694	−	0.753381i
$22$	−1.41191	+	1.02581i	−0.301020	+	0.218704i
$23$	2.33951	+	7.20028i	0.487822	+	1.50136i	0.827851	+	0.560947i	$0.189563\pi$
$23$	2.33951	+	7.20028i	0.487822	+	1.50136i	−0.340029	+	0.940415i	$0.610437\pi$
$24$	−2.18216			−0.445432
$25$		0			0
$26$	1.15054			0.225639
$27$	1.62071	+	4.98804i	0.311906	+	0.959948i
$28$	5.24454	−	3.81038i	0.991126	−	0.720095i
$29$	−3.83692	+	2.78769i	−0.712499	+	0.517661i	−0.883979	−	0.467527i	$-0.845145\pi$
$29$	−3.83692	+	2.78769i	−0.712499	+	0.517661i	0.171480	+	0.985188i	$0.445145\pi$
$30$		0			0
$31$	−1.31401	−	0.954685i	−0.236003	−	0.171466i	0.463497	−	0.886098i	$-0.346594\pi$
$31$	−1.31401	−	0.954685i	−0.236003	−	0.171466i	−0.699501	+	0.714632i	$0.746594\pi$
$32$	−3.64565			−0.644466
$33$	−7.41224	−	5.38531i	−1.29030	−	0.937461i
$34$	−0.258273	+	0.794881i	−0.0442934	+	0.136321i
$35$		0			0
$36$	0.0336277	+	0.103495i	0.00560461	+	0.0172492i
$37$	−0.00414978	+	0.0127717i	−0.000682219	+	0.00209966i	−0.951397	−	0.307967i	$-0.900351\pi$
$37$	−0.00414978	+	0.0127717i	−0.000682219	+	0.00209966i	0.950715	+	0.310067i	$0.100351\pi$
$38$	0.204547	−	0.629532i	0.0331820	−	0.102124i
$39$	1.86649	+	5.74446i	0.298877	+	0.919850i
$40$		0			0
$41$	2.99048	−	9.20376i	0.467035	−	1.43739i	−0.389371	−	0.921081i	$-0.627307\pi$
$41$	2.99048	−	9.20376i	0.467035	−	1.43739i	0.856405	−	0.516304i	$-0.172693\pi$
$42$	−1.55267	−	1.12808i	−0.239583	−	0.174067i
$43$	2.32645			0.354780			0.177390	−	0.984141i	$-0.443235\pi$
$43$	2.32645			0.354780			0.177390	+	0.984141i	$0.443235\pi$
$44$	−8.18076	−	5.94367i	−1.23330	−	0.896042i
$45$		0			0
$46$	2.00133	−	1.45405i	0.295079	−	0.214388i
$47$	−5.61982	+	4.08304i	−0.819734	+	0.595572i	−0.916636	−	0.399722i	$-0.869107\pi$
$47$	−5.61982	+	4.08304i	−0.819734	+	0.595572i	0.0969020	+	0.995294i	$0.469107\pi$
$48$	−1.78680	−	5.49920i	−0.257902	−	0.793741i
$49$	4.72443			0.674918
$50$		0			0
$51$	−4.38772			−0.614403
$52$	2.06001	+	6.34006i	0.285672	+	0.879208i
$53$	−1.39350	+	1.01244i	−0.191412	+	0.139069i	−0.679364	−	0.733802i	$-0.737744\pi$
$53$	−1.39350	+	1.01244i	−0.191412	+	0.139069i	0.487952	+	0.872871i	$0.337744\pi$
$54$	1.38643	−	1.00730i	0.188669	−	0.137076i
$55$		0			0
$56$	−3.52396	−	2.56031i	−0.470909	−	0.342135i
$57$	3.47500			0.460275
$58$	1.25372	+	0.910880i	0.164621	+	0.119604i
$59$	−0.00685492	+	0.0210973i	−0.000892435	+	0.00274663i	−0.951502	−	0.307643i	$-0.900460\pi$
$59$	−0.00685492	+	0.0210973i	−0.000892435	+	0.00274663i	0.950609	+	0.310390i	$0.100460\pi$
$60$		0			0
$61$	1.21063	+	3.72593i	0.155005	+	0.477057i	0.998161	−	0.0606117i	$-0.0193051\pi$
$61$	1.21063	+	3.72593i	0.155005	+	0.477057i	−0.843156	+	0.537669i	$0.819305\pi$
$62$	−0.163999	+	0.504737i	−0.0208279	+	0.0641016i
$63$	−0.0608188	+	0.187181i	−0.00766245	+	0.0235826i
$64$	−1.71516	−	5.27873i	−0.214395	−	0.659841i
$65$		0			0
$66$	−0.925105	+	2.84718i	−0.113873	+	0.350464i
$67$	−3.33179	−	2.42069i	−0.407043	−	0.295734i	0.365361	−	0.930866i	$-0.380946\pi$
$67$	−3.33179	−	2.42069i	−0.407043	−	0.295734i	−0.772404	+	0.635132i	$0.780946\pi$
$68$	−4.84265			−0.587258
$69$	10.5066	+	7.63346i	1.26484	+	0.918961i
$70$		0			0
$71$	−1.89224	+	1.37479i	−0.224568	+	0.163158i	−0.694380	−	0.719608i	$-0.744321\pi$
$71$	−1.89224	+	1.37479i	−0.224568	+	0.163158i	0.469813	+	0.882766i	$0.344321\pi$
$72$	0.0591555	−	0.0429790i	0.00697154	−	0.00506512i
$73$	0.467768	+	1.43964i	0.0547481	+	0.168497i	0.974692	−	0.223553i	$-0.0717657\pi$
$73$	0.467768	+	1.43964i	0.0547481	+	0.168497i	−0.919944	+	0.392051i	$0.871766\pi$
$74$	0.00438793			0.000510086
$75$		0			0
$76$	3.83530			0.439939
$77$	−5.65145	−	17.3934i	−0.644043	−	1.98216i
$78$	1.59668	−	1.16005i	0.180788	−	0.131350i
$79$	−0.345313	+	0.250885i	−0.0388508	+	0.0282268i	−0.607041	−	0.794670i	$-0.707644\pi$
$79$	−0.345313	+	0.250885i	−0.0388508	+	0.0282268i	0.568190	+	0.822897i	$0.307644\pi$
$80$		0			0
$81$	7.13898	+	5.18677i	0.793219	+	0.576308i
$82$	−3.16210			−0.349196
$83$	4.88797	+	3.55132i	0.536525	+	0.389808i	0.822793	−	0.568342i	$-0.192415\pi$
$83$	4.88797	+	3.55132i	0.536525	+	0.389808i	−0.286268	+	0.958150i	$0.592415\pi$
$84$	3.43631	−	10.5759i	0.374932	−	1.15392i
$85$		0			0
$86$	−0.234905	−	0.722965i	−0.0253305	−	0.0779593i
$87$	−2.51401	+	7.73734i	−0.269531	+	0.829530i
$88$	−2.09963	+	6.46198i	−0.223821	+	0.688850i
$89$	−1.88303	−	5.79537i	−0.199601	−	0.614308i	−0.999892	−	0.0146967i	$-0.995322\pi$
$89$	−1.88303	−	5.79537i	−0.199601	−	0.614308i	0.800291	−	0.599612i	$-0.204678\pi$
$90$		0			0
$91$	−3.72573	+	11.4666i	−0.390562	+	1.20203i
$92$	11.5959	+	8.42492i	1.20896	+	0.878359i
$93$	−2.78613			−0.288908
$94$	1.83628	+	1.33414i	0.189398	+	0.137606i
$95$		0			0
$96$	−5.05932	+	3.67581i	−0.516365	+	0.375161i
$97$	12.9458	−	9.40564i	1.31444	−	0.954998i	0.314458	−	0.949271i	$-0.398177\pi$
$97$	12.9458	−	9.40564i	1.31444	−	0.954998i	0.999984	−	0.00572672i	$-0.00182288\pi$
$98$	−0.477033	−	1.46816i	−0.0481876	−	0.148306i
$99$	0.307002			0.0308549
$100$		0			0
$101$	1.44418			0.143701			0.0718505	−	0.997415i	$-0.477110\pi$
$101$	1.44418			0.143701			0.0718505	+	0.997415i	$0.477110\pi$
$102$	0.443035	+	1.36352i	0.0438670	+	0.135009i
$103$	−11.8648	+	8.62030i	−1.16908	+	0.849383i	−0.990898	−	0.134615i	$-0.957020\pi$
$103$	−11.8648	+	8.62030i	−1.16908	+	0.849383i	−0.178178	+	0.983998i	$0.557020\pi$
$104$	3.62383	−	2.63287i	0.355346	−	0.258174i
$105$		0			0
$106$	0.455328	+	0.330815i	0.0442253	+	0.0321316i
$107$	12.2169			1.18106			0.590528	−	0.807017i	$-0.298919\pi$
$107$	12.2169			1.18106			0.590528	+	0.807017i	$0.298919\pi$
$108$	8.03314	+	5.83642i	0.772989	+	0.561609i
$109$	−4.74390	+	14.6002i	−0.454383	+	1.39845i	0.417475	+	0.908688i	$0.362915\pi$
$109$	−4.74390	+	14.6002i	−0.454383	+	1.39845i	−0.871858	+	0.489758i	$0.837085\pi$
$110$		0			0
$111$	0.00711844	+	0.0219083i	0.000675652	+	0.00207944i
$112$	3.56666	−	10.9770i	0.337017	−	1.03723i
$113$	5.73363	−	17.6463i	0.539375	−	1.66003i	−0.194627	−	0.980877i	$-0.562350\pi$
$113$	5.73363	−	17.6463i	0.539375	−	1.66003i	0.734002	−	0.679148i	$-0.237650\pi$
$114$	−0.350876	−	1.07989i	−0.0328626	−	0.101141i
$115$		0			0
$116$	−2.77467	+	8.53957i	−0.257622	+	0.792879i
$117$	−0.163738	−	0.118963i	−0.0151376	−	0.0109981i
$118$	0.00724831			0.000667261
$119$	−7.08569	−	5.14806i	−0.649544	−	0.471922i
$120$		0			0
$121$	−14.1801	+	10.3024i	−1.28910	+	0.936583i
$122$	1.03563	−	0.752427i	0.0937613	−	0.0681216i
$123$	−5.12981	−	15.7879i	−0.462539	−	1.42355i
$124$	−3.07500			−0.276144
$125$		0			0
$126$	0.0643092			0.00572911
$127$	0.209483	+	0.644724i	0.0185886	+	0.0572100i	0.959921	−	0.280272i	$-0.0904247\pi$
$127$	0.209483	+	0.644724i	0.0185886	+	0.0572100i	−0.941332	+	0.337482i	$0.890425\pi$
$128$	−7.36601	+	5.35172i	−0.651070	+	0.473030i
$129$	3.22858	−	2.34570i	0.284260	−	0.206527i
$130$		0			0
$131$	−5.70404	−	4.14423i	−0.498364	−	0.362083i	0.310027	−	0.950728i	$-0.399662\pi$
$131$	−5.70404	−	4.14423i	−0.498364	−	0.362083i	−0.808392	+	0.588645i	$0.799662\pi$
$132$	−17.3459			−1.50976
$133$	5.61175	+	4.07717i	0.486600	+	0.353536i
$134$	−0.415834	+	1.27980i	−0.0359226	+	0.110558i
$135$		0			0
$136$	1.00552	+	3.09466i	0.0862222	+	0.265365i
$137$	−3.37403	+	10.3842i	−0.288262	+	0.887181i	0.697139	+	0.716936i	$0.254456\pi$
$137$	−3.37403	+	10.3842i	−0.288262	+	0.887181i	−0.985402	+	0.170245i	$0.945544\pi$
$138$	1.31130	−	4.03577i	0.111625	−	0.343547i
$139$	6.02898	+	18.5553i	0.511371	+	1.57384i	0.789789	+	0.613379i	$0.210190\pi$
$139$	6.02898	+	18.5553i	0.511371	+	1.57384i	−0.278418	+	0.960460i	$0.589810\pi$
$140$		0			0
$141$	−3.68219	+	11.3326i	−0.310097	+	0.954379i
$142$	0.618292	+	0.449215i	0.0518859	+	0.0376973i
$143$	18.8068			1.57270
$144$	0.156748	+	0.113884i	0.0130623	+	0.00949031i
$145$		0			0
$146$	0.400150	−	0.290726i	0.0331167	−	0.0240607i
$147$	6.55642	−	4.76351i	0.540764	−	0.392888i
$148$	0.00785650	+	0.0241798i	0.000645800	+	0.00198757i
$149$	−12.7945			−1.04817			−0.524085	−	0.851666i	$-0.675593\pi$
$149$	−12.7945			−1.04817			−0.524085	+	0.851666i	$0.675593\pi$
$150$		0			0
$151$	2.15617			0.175466			0.0877331	−	0.996144i	$-0.472038\pi$
$151$	2.15617			0.175466			0.0877331	+	0.996144i	$0.472038\pi$
$152$	−0.796351	−	2.45092i	−0.0645926	−	0.198796i
$153$	0.118945	−	0.0864186i	0.00961614	−	0.00698653i
$154$	−4.83451	+	3.51248i	−0.389576	+	0.283043i
$155$		0			0
$156$	9.25134	+	6.72149i	0.740700	+	0.538150i
$157$	−15.7474			−1.25678			−0.628389	−	0.777899i	$-0.716285\pi$
$157$	−15.7474			−1.25678			−0.628389	+	0.777899i	$0.716285\pi$
$158$	0.112832	+	0.0819769i	0.00897640	+	0.00652173i
$159$	−0.913044	+	2.81006i	−0.0724091	+	0.222852i
$160$		0			0
$161$	8.01071	+	24.6544i	0.631333	+	1.94304i
$162$	0.891000	−	2.74222i	0.0700036	−	0.215449i
$163$	2.28431	−	7.03039i	0.178921	−	0.550662i	−0.820870	−	0.571115i	$-0.806511\pi$
$163$	2.28431	−	7.03039i	0.178921	−	0.550662i	0.999791	+	0.0204531i	$0.00651087\pi$
$164$	−5.66168	−	17.4249i	−0.442103	−	1.36065i
$165$		0			0
$166$	0.610057	−	1.87756i	0.0473496	−	0.145727i
$167$	8.75075	+	6.35779i	0.677153	+	0.491981i	0.872412	−	0.488771i	$-0.162555\pi$
$167$	8.75075	+	6.35779i	0.677153	+	0.491981i	−0.195259	+	0.980752i	$0.562555\pi$
$168$	−7.47194			−0.576472
$169$	0.486697	+	0.353606i	0.0374383	+	0.0272005i
$170$		0			0
$171$	−0.0942024	+	0.0684421i	−0.00720384	+	0.00523390i
$172$	3.56333	−	2.58891i	0.271701	−	0.197402i
$173$	4.63473	+	14.2642i	0.352372	+	1.08449i	0.957518	+	0.288374i	$0.0931146\pi$
$173$	4.63473	+	14.2642i	0.352372	+	1.08449i	−0.605146	+	0.796114i	$0.706885\pi$
$174$	2.65829			0.201524
$175$		0			0
$176$	−18.0038			−1.35709
$177$	0.0117588	+	0.0361898i	0.000883844	+	0.00272019i
$178$	−1.61083	+	1.17034i	−0.120737	+	0.0877205i
$179$	−5.98544	+	4.34868i	−0.447373	+	0.325036i	−0.788558	−	0.614961i	$-0.789172\pi$
$179$	−5.98544	+	4.34868i	−0.447373	+	0.325036i	0.341185	+	0.939996i	$0.389172\pi$
$180$		0			0
$181$	8.83257	+	6.41724i	0.656520	+	0.476990i	0.865486	−	0.500933i	$-0.167010\pi$
$181$	8.83257	+	6.41724i	0.656520	+	0.476990i	−0.208966	+	0.977923i	$0.567010\pi$
$182$	3.93954			0.292018
$183$	5.43684	+	3.95009i	0.401903	+	0.291999i
$184$	2.97614	−	9.15961i	0.219404	−	0.675255i
$185$		0			0
$186$	0.281320	+	0.865814i	0.0206274	+	0.0634846i
$187$	−4.22176	+	12.9932i	−0.308725	+	0.950159i
$188$	−4.06397	+	12.5076i	−0.296396	+	0.912213i
$189$	5.54947	+	17.0795i	0.403664	+	1.24235i
$190$		0			0
$191$	−0.541219	+	1.66570i	−0.0391612	+	0.120526i	−0.968726	−	0.248133i	$-0.920183\pi$
$191$	−0.541219	+	1.66570i	−0.0391612	+	0.120526i	0.929565	+	0.368659i	$0.120183\pi$
$192$	−7.70265	−	5.59631i	−0.555891	−	0.403879i
$193$	−9.53146			−0.686089			−0.343045	−	0.939319i	$-0.611458\pi$
$193$	−9.53146			−0.686089			−0.343045	+	0.939319i	$0.611458\pi$
$194$	−4.23004	−	3.07330i	−0.303699	−	0.220650i
$195$		0			0
$196$	7.23621	−	5.25741i	0.516872	−	0.375529i
$197$	−19.3492	+	14.0580i	−1.37857	+	1.00159i	−0.381559	+	0.924344i	$0.624613\pi$
$197$	−19.3492	+	14.0580i	−1.37857	+	1.00159i	−0.997012	+	0.0772463i	$0.975387\pi$
$198$	−0.0309985	−	0.0954037i	−0.00220297	−	0.00678005i
$199$	23.8281			1.68913			0.844566	−	0.535451i	$-0.179858\pi$
$199$	23.8281			1.68913			0.844566	+	0.535451i	$0.179858\pi$
$200$		0			0
$201$	−7.06448			−0.498290
$202$	−0.145821	−	0.448791i	−0.0102599	−	0.0315768i
$203$	−13.1380	+	9.54531i	−0.922106	+	0.669949i
$204$	−6.72048	+	4.88272i	−0.470528	+	0.341859i
$205$		0			0
$206$	3.87685	+	2.81669i	0.270113	+	0.196248i
$207$	−0.435164			−0.0302460
$208$	9.60227	+	6.97646i	0.665797	+	0.483730i
$209$	3.34356	−	10.2904i	0.231279	−	0.711803i
$210$		0			0
$211$	−4.75649	−	14.6390i	−0.327450	−	1.00779i	−0.970322	−	0.241815i	$-0.922257\pi$
$211$	−4.75649	−	14.6390i	−0.327450	−	1.00779i	0.642872	−	0.765973i	$-0.277743\pi$
$212$	−1.00771	+	3.10142i	−0.0692099	+	0.213006i
$213$	−1.23983	+	3.81579i	−0.0849515	+	0.261454i
$214$	−1.23356	−	3.79652i	−0.0843248	−	0.259525i
$215$		0			0
$216$	2.06174	−	6.34537i	0.140283	−	0.431748i
$217$	−4.49930	−	3.26893i	−0.305432	−	0.221910i
$218$	5.01614			0.339736
$219$	2.10071	+	1.52625i	0.141953	+	0.103135i
$220$		0			0
$221$	7.28651	−	5.29396i	0.490144	−	0.356110i
$222$	0.00608944	−	0.00442423i	0.000408696	−	0.000296935i
$223$	−6.04909	−	18.6172i	−0.405077	−	1.24670i	−0.920831	−	0.389963i	$-0.872488\pi$
$223$	−6.04909	−	18.6172i	−0.405077	−	1.24670i	0.515753	−	0.856737i	$-0.327512\pi$
$224$	−12.4831			−0.834059
$225$		0			0
$226$	−6.06268			−0.403283
$227$	0.414721	+	1.27638i	0.0275260	+	0.0847164i	0.963876	−	0.266352i	$-0.0858184\pi$
$227$	0.414721	+	1.27638i	0.0275260	+	0.0847164i	−0.936350	+	0.351069i	$0.885818\pi$
$228$	5.32251	−	3.86703i	0.352492	−	0.256100i
$229$	18.0979	−	13.1489i	1.19594	−	0.868903i	0.202062	−	0.979373i	$-0.435236\pi$
$229$	18.0979	−	13.1489i	1.19594	−	0.868903i	0.993879	+	0.110470i	$0.0352357\pi$
$230$		0			0
$231$	−25.3802	−	18.4398i	−1.66989	−	1.21325i
$232$	6.03327			0.396104
$233$	−14.8577	−	10.7947i	−0.973357	−	0.707185i	−0.0171430	−	0.999853i	$-0.505457\pi$
$233$	−14.8577	−	10.7947i	−0.973357	−	0.707185i	−0.956214	+	0.292668i	$0.905457\pi$
$234$	−0.0204358	+	0.0628950i	−0.00133593	+	0.00411158i
$235$		0			0
$236$	0.0129780	+	0.0399421i	0.000844794	+	0.00260001i
$237$	−0.226255	+	0.696341i	−0.0146968	+	0.0452322i
$238$	−0.884350	+	2.72175i	−0.0573239	+	0.176425i
$239$	−3.70936	−	11.4162i	−0.239939	−	0.738455i	−0.996428	−	0.0844490i	$-0.973087\pi$
$239$	−3.70936	−	11.4162i	−0.239939	−	0.738455i	0.756489	−	0.654006i	$-0.226913\pi$
$240$		0			0
$241$	3.12632	−	9.62182i	0.201384	−	0.619796i	−0.798459	−	0.602050i	$-0.794351\pi$
$241$	3.12632	−	9.62182i	0.201384	−	0.619796i	0.999843	−	0.0177463i	$-0.00564910\pi$
$242$	4.63335	+	3.36632i	0.297843	+	0.216395i
$243$	−0.597258			−0.0383141
$244$	6.00055	+	4.35965i	0.384146	+	0.279098i
$245$		0			0
$246$	−4.38827	+	3.18826i	−0.279786	+	0.203276i
$247$	−5.77079	+	4.19272i	−0.367187	+	0.266777i
$248$	0.638486	+	1.96506i	0.0405439	+	0.124781i
$249$	10.3641			0.656797
$250$		0			0
$251$	16.7258			1.05573			0.527863	−	0.849330i	$-0.322994\pi$
$251$	16.7258			1.05573			0.527863	+	0.849330i	$0.322994\pi$
$252$	0.115144	+	0.354378i	0.00725341	+	0.0223237i
$253$	32.7139	−	23.7681i	2.05671	−	1.49429i
$254$	0.179202	−	0.130198i	0.0112441	−	0.00816932i
$255$		0			0
$256$	−6.57385	−	4.77618i	−0.410866	−	0.298512i
$257$	15.0170			0.936732			0.468366	−	0.883535i	$-0.344843\pi$
$257$	15.0170			0.936732			0.468366	+	0.883535i	$0.344843\pi$
$258$	−1.05494	−	0.766460i	−0.0656778	−	0.0477177i
$259$	−0.0142092	+	0.0437315i	−0.000882919	+	0.00271735i
$260$		0			0
$261$	−0.0842399	−	0.259264i	−0.00521432	−	0.0160480i
$262$	−0.711909	+	2.19103i	−0.0439819	+	0.135362i
$263$	1.90720	−	5.86975i	0.117603	−	0.361945i	−0.874878	−	0.484343i	$-0.839059\pi$
$263$	1.90720	−	5.86975i	0.117603	−	0.361945i	0.992481	+	0.122399i	$0.0390586\pi$
$264$	3.60165	+	11.0847i	0.221666	+	0.682219i
$265$		0			0
$266$	0.700390	−	2.15558i	0.0429437	−	0.132167i
$267$	−8.45654	−	6.14403i	−0.517532	−	0.376009i
$268$	−7.79694			−0.476274
$269$	−8.98433	−	6.52750i	−0.547784	−	0.397988i	0.279184	−	0.960238i	$-0.409936\pi$
$269$	−8.98433	−	6.52750i	−0.547784	−	0.397988i	−0.826968	+	0.562249i	$0.809936\pi$
$270$		0			0
$271$	0.939664	−	0.682706i	0.0570806	−	0.0414714i	−0.558879	−	0.829249i	$-0.688768\pi$
$271$	0.939664	−	0.682706i	0.0570806	−	0.0414714i	0.615960	+	0.787778i	$0.288768\pi$
$272$	−6.97541	+	5.06793i	−0.422946	+	0.307288i
$273$	6.39103	+	19.6696i	0.386803	+	1.19046i
$274$	3.56766			0.215530
$275$		0			0
$276$	24.5871			1.47997
$277$	−0.672069	−	2.06842i	−0.0403807	−	0.124279i	0.928834	−	0.370496i	$-0.120812\pi$
$277$	−0.672069	−	2.06842i	−0.0403807	−	0.124279i	−0.969215	+	0.246217i	$0.920812\pi$
$278$	5.15746	−	3.74712i	0.309324	−	0.224737i
$279$	0.0755282	−	0.0548744i	0.00452175	−	0.00328525i
$280$		0			0
$281$	19.5116	+	14.1760i	1.16396	+	0.845670i	0.990274	−	0.139130i	$-0.0444306\pi$
$281$	19.5116	+	14.1760i	1.16396	+	0.845670i	0.173691	+	0.984800i	$0.444431\pi$
$282$	3.89351			0.231855
$283$	−13.1177	−	9.53058i	−0.779767	−	0.566534i	0.125142	−	0.992139i	$-0.460061\pi$
$283$	−13.1177	−	9.53058i	−0.779767	−	0.566534i	−0.904909	+	0.425605i	$0.860061\pi$
$284$	−1.36838	+	4.21143i	−0.0811982	+	0.249902i
$285$		0			0
$286$	−1.89895	−	5.84438i	−0.112287	−	0.345585i
$287$	10.2397	−	31.5145i	0.604430	−	1.86024i
$288$	0.0647541	−	0.199293i	0.00381567	−	0.0117434i
$289$	−3.23148	−	9.94547i	−0.190087	−	0.585028i
$290$		0			0
$291$	8.48226	−	26.1057i	0.497239	−	1.53034i
$292$	2.31852	+	1.68450i	0.135681	+	0.0985780i
$293$	3.48929			0.203846			0.101923	−	0.994792i	$-0.467500\pi$
$293$	3.48929			0.203846			0.101923	+	0.994792i	$0.467500\pi$
$294$	−2.14232	−	1.55648i	−0.124942	−	0.0907760i
$295$		0			0
$296$	0.0138206	−	0.0100413i	0.000803308	−	0.000583637i
$297$	22.6628	−	16.4655i	1.31503	−	0.955423i
$298$	1.29189	+	3.97602i	0.0748370	+	0.230324i
$299$	−26.6579			−1.54167
$300$		0			0
$301$	7.96599			0.459152
$302$	−0.217712	−	0.670047i	−0.0125279	−	0.0385569i
$303$	2.00418	−	1.45613i	0.115137	−	0.0836522i
$304$	5.52440	−	4.01371i	0.316846	−	0.230202i
$305$		0			0
$306$	−0.0388654	−	0.0282374i	−0.00222179	−	0.00161422i
$307$	8.92690			0.509485			0.254742	−	0.967009i	$-0.418009\pi$
$307$	8.92690			0.509485			0.254742	+	0.967009i	$0.418009\pi$
$308$	−28.0117	−	20.3517i	−1.59612	−	1.15965i
$309$	−7.77402	+	23.9260i	−0.442249	+	1.36110i
$310$		0			0
$311$	−8.37747	−	25.7832i	−0.475043	−	1.46203i	−0.845900	−	0.533341i	$-0.820936\pi$
$311$	−8.37747	−	25.7832i	−0.475043	−	1.46203i	0.370857	−	0.928690i	$-0.379064\pi$
$312$	2.37439	−	7.30763i	0.134424	−	0.413713i
$313$	−6.21351	+	19.1232i	−0.351208	+	1.08091i	0.606967	+	0.794727i	$0.292386\pi$
$313$	−6.21351	+	19.1232i	−0.351208	+	1.08091i	−0.958175	+	0.286181i	$0.907614\pi$
$314$	1.59004	+	4.89364i	0.0897311	+	0.276164i
$315$		0			0
$316$	−0.249714	+	0.768540i	−0.0140475	+	0.0432338i
$317$	−7.83123	−	5.68972i	−0.439846	−	0.319567i	0.345728	−	0.938335i	$-0.387632\pi$
$317$	−7.83123	−	5.68972i	−0.439846	−	0.319567i	−0.785574	+	0.618768i	$0.787632\pi$
$318$	0.965442			0.0541393
$319$	20.4934	+	14.8894i	1.14741	+	0.833644i
$320$		0			0
$321$	16.9543	−	12.3180i	0.946297	−	0.687525i
$322$	6.85273	−	4.97880i	0.381888	−	0.277458i
$323$	−1.60124	−	4.92810i	−0.0890952	−	0.274207i
$324$	16.7064			0.928132
$325$		0			0
$326$	−2.41540			−0.133777
$327$	8.13757	+	25.0449i	0.450009	+	1.38498i
$328$	−9.95965	+	7.23611i	−0.549929	+	0.399547i
$329$	−19.2428	+	13.9807i	−1.06089	+	0.770781i
$330$		0			0
$331$	−15.9181	−	11.5652i	−0.874939	−	0.635680i	0.0569689	−	0.998376i	$-0.481856\pi$
$331$	−15.9181	−	11.5652i	−0.874939	−	0.635680i	−0.931908	+	0.362696i	$0.881856\pi$
$332$	11.4387			0.627778
$333$	−0.000624468	0	0.000453702i	−3.42206e−5	0	2.48627e-5i
$334$	1.09216	−	3.36133i	0.0597604	−	0.183924i
$335$		0			0
$336$	−6.11816	−	18.8298i	−0.333773	−	1.02725i
$337$	5.82658	−	17.9324i	0.317394	−	0.976838i	−0.657364	−	0.753573i	$-0.728329\pi$
$337$	5.82658	−	17.9324i	0.317394	−	0.976838i	0.974758	−	0.223265i	$-0.0716714\pi$
$338$	0.0607436	−	0.186950i	0.00330402	−	0.0101687i
$339$	−9.83535	−	30.2701i	−0.534183	−	1.64405i
$340$		0			0
$341$	−2.68075	+	8.25049i	−0.145171	+	0.446789i
$342$	0.0307808	+	0.0223635i	0.00166443	+	0.00120928i
$343$	−7.79178			−0.420717
$344$	−2.39430	−	1.73956i	−0.129092	−	0.0937909i
$345$		0			0
$346$	3.96475	−	2.88056i	0.213147	−	0.154860i
$347$	−21.0144	+	15.2679i	−1.12811	+	0.819622i	−0.985419	−	0.170145i	$-0.945577\pi$
$347$	−21.0144	+	15.2679i	−1.12811	+	0.819622i	−0.142694	+	0.989767i	$0.545577\pi$
$348$	4.75962	+	14.6486i	0.255142	+	0.785247i
$349$	−26.1490			−1.39972			−0.699861	−	0.714279i	$-0.746755\pi$
$349$	−26.1490			−1.39972			−0.699861	+	0.714279i	$0.746755\pi$
$350$		0			0
$351$	−18.4674			−0.985718
$352$	6.01713	+	18.5188i	0.320714	+	0.987056i
$353$	4.31119	−	3.13226i	0.229461	−	0.166713i	−0.467114	−	0.884197i	$-0.654706\pi$
$353$	4.31119	−	3.13226i	0.229461	−	0.166713i	0.696575	+	0.717484i	$0.254706\pi$
$354$	0.0100590	−	0.00730829i	0.000534629	−	0.000388431i
$355$		0			0
$356$	−9.33334	−	6.78107i	−0.494666	−	0.359396i
$357$	−15.0240			−0.795152
$358$	1.95575	+	1.42094i	0.103365	+	0.0750988i
$359$	3.05905	−	9.41478i	0.161450	−	0.496893i	−0.837307	−	0.546733i	$-0.815871\pi$
$359$	3.05905	−	9.41478i	0.161450	−	0.496893i	0.998757	+	0.0498400i	$0.0158711\pi$
$360$		0			0
$361$	−4.60317	−	14.1671i	−0.242272	−	0.745637i
$362$	1.10237	−	3.39276i	0.0579395	−	0.178319i
$363$	−9.29100	+	28.5947i	−0.487651	+	1.50083i
$364$	7.05367	+	21.7090i	0.369713	+	1.13786i
$365$		0			0
$366$	0.678560	−	2.08839i	0.0354689	−	0.109162i
$367$	−13.2996	−	9.66271i	−0.694232	−	0.504389i	0.183817	−	0.982961i	$-0.441155\pi$
$367$	−13.2996	−	9.66271i	−0.694232	−	0.504389i	−0.878049	+	0.478571i	$0.841155\pi$
$368$	25.5197			1.33031
$369$	0.450014	+	0.326955i	0.0234268	+	0.0170206i
$370$		0			0
$371$	−4.77148	+	3.46668i	−0.247723	+	0.179981i
$372$	−4.26740	+	3.10045i	−0.221254	+	0.160751i
$373$	7.10531	+	21.8679i	0.367899	+	1.13228i	0.948146	+	0.317836i	$0.102956\pi$
$373$	7.10531	+	21.8679i	0.367899	+	1.13228i	−0.580247	+	0.814441i	$0.697044\pi$
$374$	4.46404			0.230830
$375$		0			0
$376$	8.83674			0.455720
$377$	−5.16049	−	15.8824i	−0.265779	−	0.817983i
$378$	4.74727	−	3.44909i	0.244173	−	0.177402i
$379$	−13.2878	+	9.65413i	−0.682547	+	0.495899i	−0.874202	−	0.485563i	$-0.838615\pi$
$379$	−13.2878	+	9.65413i	−0.682547	+	0.495899i	0.191655	+	0.981462i	$0.438615\pi$
$380$		0			0
$381$	0.940773	+	0.683511i	0.0481972	+	0.0350173i
$382$	0.572279			0.0292803
$383$	−3.80645	−	2.76555i	−0.194500	−	0.141313i	0.486273	−	0.873807i	$-0.338356\pi$
$383$	−3.80645	−	2.76555i	−0.194500	−	0.141313i	−0.680773	+	0.732494i	$0.738356\pi$
$384$	−4.82633	+	14.8539i	−0.246293	+	0.758011i
$385$		0			0
$386$	0.962407	+	2.96198i	0.0489852	+	0.150761i
$387$	−0.0413224	+	0.127177i	−0.00210054	+	0.00646479i
$388$	9.36173	−	28.8125i	0.475270	−	1.46273i
$389$	1.09350	+	3.36546i	0.0554428	+	0.170635i	0.974943	−	0.222453i	$-0.0714065\pi$
$389$	1.09350	+	3.36546i	0.0554428	+	0.170635i	−0.919501	+	0.393089i	$0.871407\pi$
$390$		0			0
$391$	5.98418	−	18.4174i	0.302633	−	0.931408i
$392$	−4.86222	−	3.53261i	−0.245579	−	0.178424i
$393$	−12.0944			−0.610082
$394$	6.32236	+	4.59347i	0.318516	+	0.231415i
$395$		0			0
$396$	0.470223	−	0.341637i	0.0236296	−	0.0171679i
$397$	7.09001	−	5.15119i	0.355837	−	0.258531i	−0.395476	−	0.918476i	$-0.629420\pi$
$397$	7.09001	−	5.15119i	0.355837	−	0.258531i	0.751314	+	0.659945i	$0.229420\pi$
$398$	−2.40597	−	7.40480i	−0.120600	−	0.371169i
$399$	11.8987			0.595681
$400$		0			0
$401$	22.7677			1.13697			0.568483	−	0.822695i	$-0.307531\pi$
$401$	22.7677			1.13697			0.568483	+	0.822695i	$0.307531\pi$
$402$	0.713312	+	2.19535i	0.0355768	+	0.109494i
$403$	4.62681	−	3.36158i	0.230478	−	0.167452i
$404$	2.21198	−	1.60710i	0.110050	−	0.0799563i
$405$		0			0
$406$	4.29285	+	3.11894i	0.213051	+	0.154790i
$407$	0.0717256			0.00355531
$408$	4.51569	+	3.28084i	0.223560	+	0.162426i
$409$	8.66565	−	26.6701i	0.428489	−	1.31875i	−0.471125	−	0.882067i	$-0.656152\pi$
$409$	8.66565	−	26.6701i	0.428489	−	1.31875i	0.899614	−	0.436687i	$-0.143848\pi$
$410$		0			0
$411$	5.78773	+	17.8128i	0.285488	+	0.878640i
$412$	−8.58006	+	26.4067i	−0.422709	+	1.30097i
$413$	−0.0234719	+	0.0722391i	−0.00115498	+	0.00355465i
$414$	0.0439392	+	0.135231i	0.00215950	+	0.00664624i
$415$		0			0
$416$	3.96680	−	12.2086i	0.194488	−	0.598574i
$417$	27.0756	+	19.6716i	1.32590	+	0.963323i
$418$	−3.53544			−0.172924
$419$	−27.5795	−	20.0377i	−1.34734	−	0.978903i	−0.999139	−	0.0414853i	$-0.986791\pi$
$419$	−27.5795	−	20.0377i	−1.34734	−	0.978903i	−0.348206	−	0.937418i	$-0.613209\pi$
$420$		0			0
$421$	26.0010	−	18.8908i	1.26721	−	0.920683i	0.268123	−	0.963385i	$-0.413597\pi$
$421$	26.0010	−	18.8908i	1.26721	−	0.920683i	0.999088	+	0.0427019i	$0.0135966\pi$
$422$	−4.06892	+	2.95624i	−0.198072	+	0.143908i
$423$	−0.123383	−	0.379735i	−0.00599911	−	0.0184633i
$424$	2.19117			0.106413
$425$		0			0
$426$	1.31098			0.0635171
$427$	4.14531	+	12.7580i	0.200606	+	0.617401i
$428$	18.7122	−	13.5952i	0.904487	−	0.657149i
$429$	26.0995	−	18.9624i	1.26010	−	0.915513i
$430$		0			0
$431$	14.3640	+	10.4360i	0.691889	+	0.502687i	0.877281	−	0.479978i	$-0.159355\pi$
$431$	14.3640	+	10.4360i	0.691889	+	0.502687i	−0.185392	+	0.982665i	$0.559355\pi$
$432$	17.6789			0.850579
$433$	−2.48177	−	1.80311i	−0.119266	−	0.0866521i	0.526553	−	0.850142i	$-0.323484\pi$
$433$	−2.48177	−	1.80311i	−0.119266	−	0.0866521i	−0.645819	+	0.763490i	$0.723484\pi$
$434$	−0.561548	+	1.72827i	−0.0269552	+	0.0829594i
$435$		0			0
$436$	8.98130	+	27.6416i	0.430126	+	1.32379i
$437$	−4.73936	+	14.5863i	−0.226715	+	0.697756i
$438$	0.262185	−	0.806922i	0.0125277	−	0.0385562i
$439$	4.55724	+	14.0257i	0.217505	+	0.669412i	0.998966	+	0.0454581i	$0.0144747\pi$
$439$	4.55724	+	14.0257i	0.217505	+	0.669412i	−0.781461	+	0.623954i	$0.785525\pi$
$440$		0			0
$441$	−0.0839153	+	0.258265i	−0.00399597	+	0.0122983i
$442$	−2.38087	−	1.72981i	−0.113247	−	0.0822785i
$443$	−10.1857			−0.483935			−0.241968	−	0.970284i	$-0.577793\pi$
$443$	−10.1857			−0.483935			−0.241968	+	0.970284i	$0.577793\pi$
$444$	0.0352829	+	0.0256345i	0.00167445	+	0.00121656i
$445$		0			0
$446$	−5.17467	+	3.75962i	−0.245028	+	0.178023i
$447$	−17.7559	+	12.9004i	−0.839824	+	0.610168i
$448$	−5.87288	−	18.0749i	−0.277467	−	0.853957i
$449$	18.9484			0.894230			0.447115	−	0.894477i	$-0.352451\pi$
$449$	18.9484			0.894230			0.447115	+	0.894477i	$0.352451\pi$
$450$		0			0
$451$	−51.6881			−2.43390
$452$	−10.8551	−	33.4086i	−0.510581	−	1.57141i
$453$	2.99226	−	2.17400i	0.140589	−	0.102144i
$454$	0.354771	−	0.257756i	0.0166502	−	0.0120971i
$455$		0			0
$456$	−3.57635	−	2.59837i	−0.167478	−	0.121680i
$457$	−30.4392			−1.42389			−0.711943	−	0.702237i	$-0.752185\pi$
$457$	−30.4392			−1.42389			−0.711943	+	0.702237i	$0.752185\pi$
$458$	−5.91350	−	4.29641i	−0.276320	−	0.200758i
$459$	4.14557	−	12.7588i	0.193499	−	0.595528i
$460$		0			0
$461$	0.732284	+	2.25374i	0.0341058	+	0.104967i	0.966660	−	0.256063i	$-0.0824253\pi$
$461$	0.732284	+	2.25374i	0.0341058	+	0.104967i	−0.932554	+	0.361030i	$0.882425\pi$
$462$	−3.16765	+	9.74902i	−0.147372	+	0.453565i
$463$	0.0991889	−	0.305272i	0.00460970	−	0.0141872i	−0.948725	−	0.316102i	$-0.897626\pi$
$463$	0.0991889	−	0.305272i	0.00460970	−	0.0141872i	0.953335	+	0.301915i	$0.0976258\pi$
$464$	4.94016	+	15.2042i	0.229341	+	0.705840i
$465$		0			0
$466$	−1.85435	+	5.70711i	−0.0859012	+	0.264377i
$467$	−10.3612	−	7.52785i	−0.479459	−	0.348347i	0.321657	−	0.946856i	$-0.395760\pi$
$467$	−10.3612	−	7.52785i	−0.479459	−	0.348347i	−0.801116	+	0.598509i	$0.795760\pi$
$468$	−0.383175			−0.0177123
$469$	−11.4084	−	8.28867i	−0.526790	−	0.382735i
$470$		0			0
$471$	−21.8537	+	15.8777i	−1.00697	+	0.731605i
$472$	0.0228300	−	0.0165869i	0.00105083	−	0.000763476i
$473$	−3.83979	−	11.8177i	−0.176554	−	0.543377i
$474$	0.239239			0.0109886
$475$		0			0
$476$	−16.5817			−0.760021
$477$	−0.0305944	−	0.0941598i	−0.00140082	−	0.00431128i
$478$	−3.17316	+	2.30543i	−0.145137	+	0.105448i
$479$	16.4591	−	11.9583i	0.752037	−	0.546387i	−0.144421	−	0.989516i	$-0.546132\pi$
$479$	16.4591	−	11.9583i	0.752037	−	0.546387i	0.896458	+	0.443130i	$0.146132\pi$
$480$		0			0
$481$	−0.0382546	−	0.0277936i	−0.00174426	−	0.00126728i
$482$	−3.30573			−0.150572
$483$	35.9755	+	26.1377i	1.63694	+	1.18931i
$484$	−10.2543	+	31.5595i	−0.466105	+	1.43452i
$485$		0			0
$486$	0.0603061	+	0.185603i	0.00273554	+	0.00841912i
$487$	4.78725	−	14.7336i	0.216931	−	0.667645i	−0.782080	−	0.623178i	$-0.785841\pi$
$487$	4.78725	−	14.7336i	0.216931	−	0.667645i	0.999011	−	0.0444667i	$-0.0141588\pi$
$488$	1.54006	−	4.73983i	0.0697154	−	0.214562i
$489$	−3.91846	−	12.0598i	−0.177199	−	0.545362i
$490$		0			0
$491$	−8.50061	+	26.1622i	−0.383627	+	1.18068i	0.553844	+	0.832620i	$0.313160\pi$
$491$	−8.50061	+	26.1622i	−0.383627	+	1.18068i	−0.937471	+	0.348063i	$0.886840\pi$
$492$	−25.4261	−	18.4732i	−1.14630	−	0.832835i
$493$	12.1312			0.546362
$494$	1.88561	+	1.36998i	0.0848377	+	0.0616382i
$495$		0			0
$496$	−4.42927	+	3.21805i	−0.198880	+	0.144495i
$497$	−6.47921	+	4.70742i	−0.290632	+	0.211157i
$498$	−1.04648	−	3.22073i	−0.0468938	−	0.144324i
$499$	4.91044			0.219821			0.109911	−	0.993941i	$-0.464943\pi$
$499$	4.91044			0.219821			0.109911	+	0.993941i	$0.464943\pi$
$500$		0			0
$501$	18.5544			0.828950
$502$	−1.68883	−	5.19770i	−0.0753764	−	0.231985i
$503$	−33.2064	+	24.1259i	−1.48060	+	1.07572i	−0.503238	+	0.864148i	$0.667858\pi$
$503$	−33.2064	+	24.1259i	−1.48060	+	1.07572i	−0.977362	+	0.211572i	$0.932142\pi$
$504$	0.202554	−	0.147164i	0.00902247	−	0.00655521i
$505$		0			0
$506$	−10.6893	−	7.76624i	−0.475198	−	0.345251i
$507$	1.03196			0.0458308
$508$	1.03831	+	0.754380i	0.0460678	+	0.0334702i
$509$	12.8058	−	39.4122i	0.567607	−	1.74691i	−0.0924692	−	0.995716i	$-0.529476\pi$
$509$	12.8058	−	39.4122i	0.567607	−	1.74691i	0.660076	−	0.751199i	$-0.270524\pi$
$510$		0			0
$511$	1.60168	+	4.92947i	0.0708543	+	0.218067i
$512$	−6.44760	+	19.8437i	−0.284946	+	0.876975i
$513$	−3.28322	+	10.1047i	−0.144958	+	0.446134i
$514$	−1.51629	−	4.66665i	−0.0668805	−	0.205837i
$515$		0			0
$516$	2.33475	−	7.18562i	0.102782	−	0.316329i
$517$	30.0161	+	21.8080i	1.32011	+	0.959113i
$518$	0.0150247			0.000660147
$519$	20.8142	+	15.1224i	0.913641	+	0.663799i
$520$		0			0
$521$	1.31422	−	0.954837i	0.0575770	−	0.0418322i	−0.558624	−	0.829421i	$-0.688671\pi$
$521$	1.31422	−	0.954837i	0.0575770	−	0.0418322i	0.616202	+	0.787589i	$0.288671\pi$
$522$	−0.0720626	+	0.0523566i	−0.00315410	+	0.00229158i
$523$	−5.87162	−	18.0710i	−0.256748	−	0.790188i	−0.993480	−	0.114004i	$-0.963632\pi$
$523$	−5.87162	−	18.0710i	−0.256748	−	0.790188i	0.736732	−	0.676184i	$-0.236368\pi$
$524$	−13.3484			−0.583128
$525$		0			0
$526$	−2.01665			−0.0879301
$527$	1.28382	+	3.95118i	0.0559239	+	0.172116i
$528$	−24.9852	+	18.1528i	−1.08734	+	0.789999i
$529$	−27.7633	+	20.1712i	−1.20710	+	0.877010i
$530$		0			0
$531$	−0.00103154		0.000749460i	−4.47652e−5		3.25238e-5i
$532$	13.1324			0.569362
$533$	27.5676	+	20.0291i	1.19409	+	0.867555i
$534$	−1.05544	+	3.24832i	−0.0456734	+	0.140568i
$535$		0			0
$536$	1.61894	+	4.98258i	0.0699274	+	0.215215i
$537$	−3.92176	+	12.0699i	−0.169236	+	0.520856i
$538$	−1.12131	+	3.45105i	−0.0483433	+	0.148785i
$539$	−7.79764	−	23.9987i	−0.335868	−	1.03370i
$540$		0			0
$541$	−10.3581	+	31.8790i	−0.445330	+	1.37058i	0.436792	+	0.899562i	$0.356114\pi$
$541$	−10.3581	+	31.8790i	−0.445330	+	1.37058i	−0.882122	+	0.471021i	$0.843886\pi$
$542$	−0.307036	−	0.223075i	−0.0131883	−	0.00958189i
$543$	18.7279			0.803691
$544$	7.54417	+	5.48116i	0.323454	+	0.235003i
$545$		0			0
$546$	5.46718	−	3.97214i	0.233974	−	0.169992i
$547$	14.0977	−	10.2426i	0.602776	−	0.437943i	−0.244087	−	0.969753i	$-0.578488\pi$
$547$	14.0977	−	10.2426i	0.602776	−	0.437943i	0.846863	+	0.531811i	$0.178488\pi$
$548$	6.38782	+	19.6597i	0.272874	+	0.839820i
$549$	−0.225185			−0.00961065
$550$		0			0
$551$	−9.60771			−0.409302
$552$	−5.10520	−	15.7122i	−0.217292	−	0.668755i
$553$	−1.18239	+	0.859054i	−0.0502802	+	0.0365307i
$554$	−0.574919	+	0.417703i	−0.0244259	+	0.0177465i
$555$		0			0
$556$	29.8829	+	21.7112i	1.26732	+	0.920761i
$557$	−16.2929			−0.690351			−0.345175	−	0.938538i	$-0.612181\pi$
$557$	−16.2929			−0.690351			−0.345175	+	0.938538i	$0.612181\pi$
$558$	−0.0246789	−	0.0179303i	−0.00104474	−	0.000759049i
$559$	−2.53139	+	7.79082i	−0.107066	+	0.329516i
$560$		0			0
$561$	7.24191	+	22.2883i	0.305754	+	0.941013i
$562$	2.43520	−	7.49478i	0.102723	−	0.316148i
$563$	7.13827	−	21.9693i	0.300842	−	0.925897i	−0.680354	−	0.732884i	$-0.738174\pi$
$563$	7.13827	−	21.9693i	0.300842	−	0.925897i	0.981196	−	0.193013i	$-0.0618260\pi$
$564$	6.97125	+	21.4553i	0.293543	+	0.903431i
$565$		0			0
$566$	−1.63719	+	5.03876i	−0.0688164	+	0.211795i
$567$	24.4445	+	17.7600i	1.02657	+	0.745849i
$568$	2.97541			0.124845
$569$	7.51038	+	5.45661i	0.314851	+	0.228753i	0.733975	−	0.679176i	$-0.237663\pi$
$569$	7.51038	+	5.45661i	0.314851	+	0.228753i	−0.419124	+	0.907929i	$0.637663\pi$
$570$		0			0
$571$	−17.9718	+	13.0572i	−0.752094	+	0.546429i	−0.896475	−	0.443094i	$-0.853881\pi$
$571$	−17.9718	+	13.0572i	−0.752094	+	0.546429i	0.144381	+	0.989522i	$0.453881\pi$
$572$	28.8056	−	20.9285i	1.20442	−	0.875064i
$573$	0.928395	+	2.85731i	0.0387843	+	0.119366i
$574$	−10.8273			−0.451924
$575$		0			0
$576$	0.319031			0.0132930
$577$	4.51451	+	13.8942i	0.187942	+	0.578425i	0.999987	−	0.00517008i	$-0.00164570\pi$
$577$	4.51451	+	13.8942i	0.187942	+	0.578425i	−0.812045	+	0.583595i	$0.801646\pi$
$578$	−2.76436	+	2.00842i	−0.114982	+	0.0835393i
$579$	−13.2275	+	9.61032i	−0.549715	+	0.399391i
$580$		0			0
$581$	16.7369	+	12.1601i	0.694363	+	0.504484i
$582$	−8.96905			−0.371779
$583$	7.44285	+	5.40754i	0.308251	+	0.223958i
$584$	0.595057	−	1.83140i	0.0246236	−	0.0757837i
$585$		0			0
$586$	−0.352319	−	1.08433i	−0.0145542	−	0.0447932i
$587$	7.21354	−	22.2010i	0.297734	−	0.916332i	−0.684555	−	0.728961i	$-0.740003\pi$
$587$	7.21354	−	22.2010i	0.297734	−	0.916332i	0.982289	−	0.187371i	$-0.0599967\pi$
$588$	4.74128	−	14.5922i	0.195527	−	0.601770i
$589$	−1.01676	−	3.12926i	−0.0418949	−	0.128939i
$590$		0			0
$591$	−12.6779	+	39.0185i	−0.521499	+	1.60501i
$592$	0.0366213	+	0.0266069i	0.00150512	+	0.00109354i
$593$	−41.9815			−1.72397			−0.861986	−	0.506932i	$-0.830780\pi$
$593$	−41.9815			−1.72397			−0.861986	+	0.506932i	$0.830780\pi$
$594$	−7.40508	−	5.38011i	−0.303834	−	0.220748i
$595$		0			0
$596$	−19.5969	+	14.2380i	−0.802719	+	0.583210i
$597$	33.0680	−	24.0253i	1.35338	−	0.983290i
$598$	2.69169	+	8.28418i	0.110072	+	0.338765i
$599$	−25.4160			−1.03847			−0.519236	−	0.854631i	$-0.673783\pi$
$599$	−25.4160			−1.03847			−0.519236	+	0.854631i	$0.673783\pi$
$600$		0			0
$601$	37.1379			1.51489			0.757444	−	0.652900i	$-0.226448\pi$
$601$	37.1379			1.51489			0.757444	+	0.652900i	$0.226448\pi$
$602$	−0.804339	−	2.47550i	−0.0327824	−	0.100894i
$603$	0.191508	−	0.139139i	0.00779882	−	0.00566618i
$604$	3.30251	−	2.39941i	0.134377	−	0.0976307i
$605$		0			0
$606$	−0.654870	−	0.475791i	−0.0266023	−	0.0193277i
$607$	−18.9242			−0.768109			−0.384054	−	0.923310i	$-0.625473\pi$
$607$	−18.9242			−0.768109			−0.384054	+	0.923310i	$0.625473\pi$
$608$	−5.97485	−	4.34098i	−0.242312	−	0.176050i
$609$	−8.60822	+	26.4934i	−0.348823	+	1.07357i
$610$		0			0
$611$	−7.55840	−	23.2624i	−0.305780	−	0.941094i
$612$	0.0860152	−	0.264728i	0.00347696	−	0.0107010i
$613$	2.84394	−	8.75274i	0.114866	−	0.353520i	−0.877053	−	0.480393i	$-0.840494\pi$
$613$	2.84394	−	8.75274i	0.114866	−	0.353520i	0.991919	+	0.126873i	$0.0404941\pi$
$614$	−0.901364	−	2.77411i	−0.0363761	−	0.111954i
$615$		0			0
$616$	−7.18932	+	22.1264i	−0.289666	+	0.891500i
$617$	26.4852	+	19.2426i	1.06625	+	0.774679i	0.975235	−	0.221170i	$-0.0709876\pi$
$617$	26.4852	+	19.2426i	1.06625	+	0.774679i	0.0910190	+	0.995849i	$0.470988\pi$
$618$	8.22017			0.330664
$619$	−29.4444	−	21.3926i	−1.18347	−	0.859841i	−0.190911	−	0.981607i	$-0.561144\pi$
$619$	−29.4444	−	21.3926i	−1.18347	−	0.859841i	−0.992559	+	0.121767i	$0.961144\pi$
$620$		0			0
$621$	−32.1236	+	23.3392i	−1.28908	+	0.936568i
$622$	−7.16647	+	5.20674i	−0.287349	+	0.208771i
$623$	−6.44768	−	19.8439i	−0.258321	−	0.795029i
$624$	20.3599			0.815049
$625$		0			0
$626$	6.57010			0.262594
$627$	−5.73546	−	17.6519i	−0.229052	−	0.704951i
$628$	−24.1196	+	17.5239i	−0.962477	+	0.699281i
$629$	0.0277894	−	0.0201902i	0.00110804	−	0.000805035i
$630$		0			0
$631$	−9.79582	−	7.11708i	−0.389965	−	0.283326i	0.375476	−	0.926832i	$-0.377479\pi$
$631$	−9.79582	−	7.11708i	−0.389965	−	0.283326i	−0.765441	+	0.643506i	$0.777479\pi$
$632$	0.542980			0.0215986
$633$	−21.3610	−	15.5197i	−0.849024	−	0.616852i
$634$	−0.977399	+	3.00812i	−0.0388175	+	0.119468i
$635$		0			0
$636$	1.72861	+	5.32010i	0.0685437	+	0.210956i
$637$	−5.14061	+	15.8212i	−0.203678	+	0.626857i
$638$	2.55774	−	7.87192i	0.101262	−	0.311652i
$639$	−0.0415443	−	0.127860i	−0.00164347	−	0.00505807i
$640$		0			0
$641$	3.01346	−	9.27448i	0.119025	−	0.366320i	−0.873741	−	0.486392i	$-0.838313\pi$
$641$	3.01346	−	9.27448i	0.119025	−	0.366320i	0.992765	+	0.120072i	$0.0383126\pi$
$642$	−5.53984	−	4.02493i	−0.218640	−	0.158851i
$643$	6.77862			0.267323			0.133661	−	0.991027i	$-0.457327\pi$
$643$	6.77862			0.267323			0.133661	+	0.991027i	$0.457327\pi$
$644$	39.7055	+	28.8477i	1.56462	+	1.13676i
$645$		0			0
$646$	−1.36977	+	0.995197i	−0.0538929	+	0.0391555i
$647$	32.4568	−	23.5812i	1.27601	−	0.927074i	0.276583	−	0.960990i	$-0.410798\pi$
$647$	32.4568	−	23.5812i	1.27601	−	0.927074i	0.999425	+	0.0339163i	$0.0107980\pi$
$648$	−3.46887	−	10.6761i	−0.136270	−	0.419396i
$649$	0.118482			0.00465082
$650$		0			0
$651$	−9.53997			−0.373901
$652$	−4.32473	−	13.3102i	−0.169370	−	0.521266i
$653$	−4.96906	+	3.61024i	−0.194454	+	0.141279i	−0.680752	−	0.732514i	$-0.738347\pi$
$653$	−4.96906	+	3.61024i	−0.194454	+	0.141279i	0.486298	+	0.873793i	$0.338347\pi$
$654$	6.96125	−	5.05764i	0.272206	−	0.197770i
$655$		0			0
$656$	−26.3906	−	19.1739i	−1.03038	−	0.748615i
$657$	−0.0870078			−0.00339450
$658$	6.28760	+	4.56821i	0.245116	+	0.178087i
$659$	−13.6476	+	42.0029i	−0.531634	+	1.63620i	0.219178	+	0.975685i	$0.429662\pi$
$659$	−13.6476	+	42.0029i	−0.531634	+	1.63620i	−0.750812	+	0.660516i	$0.770338\pi$
$660$		0			0
$661$	8.57359	+	26.3868i	0.333474	+	1.02633i	0.967469	+	0.252990i	$0.0814141\pi$
$661$	8.57359	+	26.3868i	0.333474	+	1.02633i	−0.633995	+	0.773337i	$0.718586\pi$
$662$	−1.98671	+	6.11445i	−0.0772155	+	0.237645i
$663$	4.77424	−	14.6936i	0.185416	−	0.570652i
$664$	−2.37510	−	7.30979i	−0.0921716	−	0.283675i
$665$		0			0
$666$	−7.79385e−5	0	0.000239870i	−3.02005e−6	0	9.29477e-6i
$667$	−29.0487	−	21.1051i	−1.12477	−	0.817192i
$668$	20.4782			0.792325
$669$	−27.1660	−	19.7372i	−1.05030	−	0.763086i
$670$		0			0
$671$	16.9285	−	12.2993i	0.653517	−	0.474808i
$672$	−17.3236	+	12.5863i	−0.668272	+	0.485528i
$673$	−12.9269	−	39.7849i	−0.498296	−	1.53360i	−0.811757	−	0.583996i	$-0.801489\pi$
$673$	−12.9269	−	39.7849i	−0.498296	−	1.53360i	0.313461	−	0.949601i	$-0.398511\pi$
$674$	−6.16096			−0.237311
$675$		0			0
$676$	1.13895			0.0438059
$677$	6.99226	+	21.5200i	0.268734	+	0.827079i	0.990810	+	0.135265i	$0.0431885\pi$
$677$	6.99226	+	21.5200i	0.268734	+	0.827079i	−0.722075	+	0.691815i	$0.756812\pi$
$678$	−8.41360	+	6.11284i	−0.323123	+	0.234762i
$679$	44.3275	−	32.2058i	1.70113	−	1.23595i
$680$		0			0
$681$	1.86248	+	1.35317i	0.0713703	+	0.0518536i
$682$	2.83459			0.108542
$683$	39.6438	+	28.8029i	1.51693	+	1.10211i	0.962985	+	0.269556i	$0.0868770\pi$
$683$	39.6438	+	28.8029i	1.51693	+	1.10211i	0.553942	+	0.832555i	$0.313123\pi$
$684$	−0.0681226	+	0.209660i	−0.00260473	+	0.00801654i
$685$		0			0
$686$	0.786749	+	2.42136i	0.0300382	+	0.0924481i
$687$	11.8580	−	36.4952i	0.452412	−	1.39238i
$688$	2.42331	−	7.45819i	0.0923879	−	0.284341i
$689$	−1.87420	−	5.76818i	−0.0714012	−	0.219750i
$690$		0			0
$691$	11.2044	−	34.4837i	0.426236	−	1.31182i	−0.475569	−	0.879678i	$-0.657758\pi$
$691$	11.2044	−	34.4837i	0.426236	−	1.31182i	0.901805	−	0.432142i	$-0.142242\pi$
$692$	22.9722	+	16.6903i	0.873274	+	0.634471i
$693$	1.05121			0.0399320
$694$	6.86649	+	4.98879i	0.260648	+	0.189372i
$695$		0			0
$696$	8.37279	−	6.08319i	0.317370	−	0.230583i
$697$	−20.0260	+	14.5498i	−0.758541	+	0.551112i
$698$	2.64030	+	8.12602i	0.0999370	+	0.307575i
$699$	−31.5030			−1.19155
$700$		0			0
$701$	−8.32362			−0.314379			−0.157189	−	0.987568i	$-0.550243\pi$
$701$	−8.32362			−0.314379			−0.157189	+	0.987568i	$0.550243\pi$
$702$	1.86469	+	5.73891i	0.0703780	+	0.216601i
$703$	−0.0220087	+	0.0159903i	−0.000830075	+	0.000603084i
$704$	−23.9835	+	17.4250i	−0.903912	+	0.656730i
$705$		0			0
$706$	−1.40869	−	1.02347i	−0.0530166	−	0.0385188i
$707$	4.94500			0.185976
$708$	0.0582830	+	0.0423451i	0.00219041	+	0.00159142i
$709$	11.5293	−	35.4836i	0.432993	−	1.33261i	−0.462137	−	0.886809i	$-0.652917\pi$
$709$	11.5293	−	35.4836i	0.432993	−	1.33261i	0.895130	−	0.445806i	$-0.147083\pi$
$710$		0			0
$711$	−0.00758138	−	0.0233331i	−0.000284324	−	0.000875059i
$712$	−2.39544	+	7.37240i	−0.0897729	+	0.276292i
$713$	3.79985	−	11.6947i	0.142306	−	0.437972i
$714$	1.51699	+	4.66883i	0.0567721	+	0.174726i
$715$		0			0
$716$	−4.32838	+	13.3214i	−0.161759	+	0.497843i
$717$	−16.6584	−	12.1031i	−0.622121	−	0.451997i
$718$	−3.23460			−0.120714
$719$	6.20131	+	4.50552i	0.231270	+	0.168027i	0.697385	−	0.716697i	$-0.254347\pi$
$719$	6.20131	+	4.50552i	0.231270	+	0.168027i	−0.466115	+	0.884724i	$0.654347\pi$
$720$		0			0
$721$	−40.6263	+	29.5167i	−1.51300	+	1.09926i
$722$	−3.93776	+	2.86095i	−0.146548	+	0.106474i
$723$	−5.36282	−	16.5051i	−0.199445	−	0.613830i
$724$	20.6697			0.768183
$725$		0			0
$726$	9.82419			0.364610
$727$	−14.1866	−	43.6620i	−0.526153	−	1.61933i	−0.762024	−	0.647549i	$-0.775794\pi$
$727$	−14.1866	−	43.6620i	−0.526153	−	1.61933i	0.235871	−	0.971784i	$-0.424206\pi$
$728$	12.4083	−	9.01519i	0.459884	−	0.334125i
$729$	−22.2458	+	16.1625i	−0.823918	+	0.598611i
$730$		0			0
$731$	−4.81427	−	3.49777i	−0.178062	−	0.129370i
$732$	12.7231			0.470259
$733$	−19.1843	−	13.9382i	−0.708589	−	0.514820i	0.174129	−	0.984723i	$-0.444289\pi$
$733$	−19.1843	−	13.9382i	−0.708589	−	0.514820i	−0.882718	+	0.469903i	$0.844289\pi$
$734$	−1.65989	+	5.10862i	−0.0612677	+	0.188563i
$735$		0			0
$736$	−8.52905	−	26.2497i	−0.314385	−	0.967577i
$737$	−6.79727	+	20.9198i	−0.250381	+	0.770592i
$738$	0.0561653	−	0.172859i	0.00206747	−	0.00636303i
$739$	−1.09294	−	3.36372i	−0.0402045	−	0.123737i	0.928940	−	0.370231i	$-0.120721\pi$
$739$	−1.09294	−	3.36372i	−0.0402045	−	0.123737i	−0.969144	+	0.246494i	$0.920721\pi$
$740$		0			0
$741$	−3.78111	+	11.6371i	−0.138903	+	0.427498i
$742$	1.55909	+	1.13274i	0.0572358	+	0.0415843i
$743$	−15.7201			−0.576715			−0.288358	−	0.957523i	$-0.593109\pi$
$743$	−15.7201			−0.576715			−0.288358	+	0.957523i	$0.593109\pi$
$744$	2.86739	+	2.08328i	0.105124	+	0.0763767i
$745$		0			0
$746$	6.07820	−	4.41607i	0.222539	−	0.161684i
$747$	−0.280956	+	0.204127i	−0.0102797	+	0.00746861i
$748$	7.99277	+	24.5992i	0.292245	+	0.899437i
$749$	41.8320			1.52851
$750$		0			0
$751$	−14.1856			−0.517642			−0.258821	−	0.965925i	$-0.583334\pi$
$751$	−14.1856			−0.517642			−0.258821	+	0.965925i	$0.583334\pi$
$752$	7.23569	+	22.2692i	0.263858	+	0.812073i
$753$	23.2116	−	16.8642i	0.845878	−	0.614566i
$754$	−4.41452	+	3.20733i	−0.160767	+	0.116804i
$755$		0			0
$756$	27.5062	+	19.9844i	1.00039	+	0.726827i
$757$	12.7388			0.463000			0.231500	−	0.972835i	$-0.425637\pi$
$757$	12.7388			0.463000			0.231500	+	0.972835i	$0.425637\pi$
$758$	4.34179	+	3.15450i	0.157701	+	0.114576i
$759$	21.4347	−	65.9692i	0.778030	−	2.39453i
$760$		0			0
$761$	9.95960	+	30.6525i	0.361035	+	1.11115i	0.952427	+	0.304768i	$0.0985788\pi$
$761$	9.95960	+	30.6525i	0.361035	+	1.11115i	−0.591391	+	0.806385i	$0.701421\pi$
$762$	0.117416	−	0.361369i	0.00425352	−	0.0130910i
$763$	−16.2435	+	49.9925i	−0.588056	+	1.80985i
$764$	1.02465	+	3.15356i	0.0370707	+	0.114092i
$765$		0			0
$766$	−0.475075	+	1.46213i	−0.0171651	+	0.0528289i
$767$	−0.0631918	−	0.0459115i	−0.00228172	−	0.00165777i
$768$	−13.9387			−0.502969
$769$	9.19746	+	6.68235i	0.331669	+	0.240972i	0.741139	−	0.671352i	$-0.234286\pi$
$769$	9.19746	+	6.68235i	0.331669	+	0.240972i	−0.409469	+	0.912324i	$0.634286\pi$
$770$		0			0
$771$	20.8401	−	15.1412i	0.750537	−	0.545297i
$772$	−14.5989	+	10.6067i	−0.525427	+	0.381745i
$773$	8.40508	+	25.8682i	0.302310	+	0.930414i	0.980667	+	0.195682i	$0.0626920\pi$
$773$	8.40508	+	25.8682i	0.302310	+	0.930414i	−0.678358	+	0.734732i	$0.737308\pi$
$774$	0.0436939			0.00157054
$775$		0			0
$776$	−20.3562			−0.730746
$777$	0.0243742	+	0.0750161i	0.000874420	+	0.00269119i
$778$	0.935432	−	0.679631i	0.0335369	−	0.0243660i
$779$	15.8603	−	11.5232i	0.568254	−	0.412860i
$780$		0			0
$781$	10.1067	+	7.34293i	0.361645	+	0.262751i
$782$	−6.32760			−0.226275
$783$	−20.1236	−	14.6207i	−0.719160	−	0.522500i
$784$	4.92113	−	15.1457i	0.175755	−	0.540917i
$785$		0			0
$786$	1.22119	+	3.75845i	0.0435585	+	0.134059i
$787$	−7.94995	+	24.4674i	−0.283385	+	0.872170i	0.703493	+	0.710702i	$0.251623\pi$
$787$	−7.94995	+	24.4674i	−0.283385	+	0.872170i	−0.986878	+	0.161468i	$0.948377\pi$
$788$	−13.9924	+	43.0641i	−0.498458	+	1.53409i
$789$	−3.27157	−	10.0688i	−0.116471	−	0.358460i
$790$		0			0
$791$	19.6325	−	60.4226i	0.698052	−	2.14838i
$792$	−0.315956	−	0.229556i	−0.0112270	−	0.00815691i
$793$	−13.7947			−0.489864
$794$	−2.31667	−	1.68316i	−0.0822155	−	0.0597331i
$795$		0			0
$796$	36.4966	−	26.5163i	1.29359	−	0.939846i
$797$	−14.2964	+	10.3869i	−0.506405	+	0.367924i	−0.811458	−	0.584411i	$-0.801326\pi$
$797$	−14.2964	+	10.3869i	−0.506405	+	0.367924i	0.305053	+	0.952335i	$0.401326\pi$
$798$	−1.20143	−	3.69763i	−0.0425303	−	0.130895i
$799$	17.7682			0.628593
$800$		0			0
$801$	0.350256			0.0123757
$802$	−2.29889	−	7.07527i	−0.0811768	−	0.249836i
$803$	6.54091	−	4.75225i	0.230824	−	0.167703i
$804$	−10.8204	+	7.86145i	−0.381605	+	0.277252i
$805$		0			0
$806$	−1.51182	−	1.09840i	−0.0532515	−	0.0386895i
$807$	−19.0497			−0.670580
$808$	−1.48630	−	1.07986i	−0.0522877	−	0.0379893i
$809$	−12.6257	+	38.8578i	−0.443895	+	1.36617i	0.439796	+	0.898098i	$0.355051\pi$
$809$	−12.6257	+	38.8578i	−0.443895	+	1.36617i	−0.883691	+	0.468071i	$0.844949\pi$
$810$		0			0
$811$	5.13629	+	15.8079i	0.180360	+	0.555090i	0.999838	−	0.0180209i	$-0.00573653\pi$
$811$	5.13629	+	15.8079i	0.180360	+	0.555090i	−0.819478	+	0.573111i	$0.805737\pi$
$812$	−9.50075	+	29.2403i	−0.333411	+	1.02613i
$813$	0.615683	−	1.89488i	0.0215930	−	0.0664563i
$814$	−0.00724226	−	0.0222894i	−0.000253841	−	0.000781242i
$815$		0			0
$816$	−4.57040	+	14.0662i	−0.159996	+	0.492417i
$817$	3.81282	+	2.77017i	0.133394	+	0.0969161i
$818$	−9.16296			−0.320375
$819$	−0.560656	−	0.407340i	−0.0195909	−	0.0142336i
$820$		0			0
$821$	35.5145	−	25.8028i	1.23946	−	0.900524i	0.241902	−	0.970301i	$-0.422229\pi$
$821$	35.5145	−	25.8028i	1.23946	−	0.900524i	0.997563	+	0.0697770i	$0.0222288\pi$
$822$	4.95109	−	3.59717i	0.172689	−	0.125466i
$823$	8.09508	+	24.9141i	0.282177	+	0.868450i	0.987231	+	0.159297i	$0.0509227\pi$
$823$	8.09508	+	24.9141i	0.282177	+	0.868450i	−0.705054	+	0.709153i	$0.749077\pi$
$824$	18.6565			0.649932
$825$		0			0
$826$	0.0248189			0.000863561
$827$	6.91662	+	21.2872i	0.240514	+	0.740227i	0.996342	+	0.0854566i	$0.0272349\pi$
$827$	6.91662	+	21.2872i	0.240514	+	0.740227i	−0.755827	+	0.654771i	$0.772765\pi$
$828$	−0.666523	+	0.484257i	−0.0231633	+	0.0168291i
$829$	−0.680611	+	0.494493i	−0.0236386	+	0.0171744i	−0.599542	−	0.800343i	$-0.704651\pi$
$829$	−0.680611	+	0.494493i	−0.0236386	+	0.0171744i	0.575903	+	0.817518i	$0.304651\pi$
$830$		0			0
$831$	−3.01821	−	2.19286i	−0.104700	−	0.0760693i
$832$	19.5437			0.677554
$833$	−9.77655	−	7.10308i	−0.338737	−	0.246107i
$834$	3.37925	−	10.4003i	0.117014	−	0.360132i
$835$		0			0
$836$	−6.33014	−	19.4822i	−0.218932	−	0.673804i
$837$	2.63237	−	8.10160i	0.0909880	−	0.280032i
$838$	−3.44213	+	10.5938i	−0.118906	+	0.365957i
$839$	10.9864	+	33.8127i	0.379293	+	1.16735i	0.940536	+	0.339694i	$0.110323\pi$
$839$	10.9864	+	33.8127i	0.379293	+	1.16735i	−0.561243	+	0.827651i	$0.689677\pi$
$840$		0			0
$841$	−2.01072	+	6.18835i	−0.0693350	+	0.213391i
$842$	−8.49585	−	6.17260i	−0.292786	−	0.212722i
$843$	41.3709			1.42489
$844$	−23.5758	−	17.1288i	−0.811512	−	0.589598i
$845$		0			0
$846$	−0.105548	+	0.0766849i	−0.00362881	+	0.00263648i
$847$	−48.5538	+	35.2764i	−1.66833	+	1.21211i
$848$	1.79418	+	5.52191i	0.0616123	+	0.189623i
$849$	−27.8138			−0.954567
$850$		0			0
$851$	−0.101668			−0.00348515
$852$	2.34728	+	7.22419i	0.0804165	+	0.247497i
$853$	15.8087	−	11.4857i	0.541279	−	0.393262i	−0.283281	−	0.959037i	$-0.591423\pi$
$853$	15.8087	−	11.4857i	0.541279	−	0.393262i	0.824560	+	0.565775i	$0.191423\pi$
$854$	3.54609	−	2.57638i	0.121345	−	0.0881620i
$855$		0			0
$856$	−12.5733	−	9.13500i	−0.429745	−	0.312228i
$857$	−0.570622			−0.0194921			−0.00974604	−	0.999953i	$-0.503102\pi$
$857$	−0.570622			−0.0194921			−0.00974604	+	0.999953i	$0.503102\pi$
$858$	−8.52804	−	6.19599i	−0.291143	−	0.211527i
$859$	−6.21070	+	19.1146i	−0.211906	+	0.652181i	0.787452	+	0.616376i	$0.211400\pi$
$859$	−6.21070	+	19.1146i	−0.211906	+	0.652181i	−0.999359	+	0.0358055i	$0.988600\pi$
$860$		0			0
$861$	−17.5649	−	54.0593i	−0.598612	−	1.84234i
$862$	1.79274	−	5.51748i	0.0610609	−	0.187926i
$863$	4.31528	−	13.2811i	0.146894	−	0.452093i	−0.850356	−	0.526208i	$-0.823613\pi$
$863$	4.31528	−	13.2811i	0.146894	−	0.452093i	0.997250	+	0.0741154i	$0.0236133\pi$
$864$	−5.90855	−	18.1846i	−0.201013	−	0.618654i
$865$		0			0
$866$	−0.309745	+	0.953296i	−0.0105256	+	0.0323943i
$867$	−14.5123	−	10.5438i	−0.492864	−	0.358087i
$868$	−10.5291			−0.357381
$869$	1.84436	+	1.34001i	0.0625656	+	0.0454566i
$870$		0			0
$871$	11.7317	−	8.52358i	0.397513	−	0.288810i
$872$	15.7993	−	11.4789i	0.535032	−	0.388723i
$873$	0.284225	+	0.874754i	0.00961955	+	0.0296059i
$874$	5.01135			0.169511
$875$		0			0
$876$	4.91601			0.166096
$877$	7.24682	+	22.3034i	0.244708	+	0.753133i	0.995684	+	0.0928043i	$0.0295831\pi$
$877$	7.24682	+	22.3034i	0.244708	+	0.753133i	−0.750977	+	0.660329i	$0.770417\pi$
$878$	3.89847	−	2.83240i	0.131567	−	0.0955890i
$879$	4.84233	−	3.51816i	0.163328	−	0.118665i
$880$		0			0
$881$	−35.9781	−	26.1396i	−1.21213	−	0.880666i	−0.216710	−	0.976236i	$-0.569533\pi$
$881$	−35.9781	−	26.1396i	−1.21213	−	0.880666i	−0.995423	+	0.0955699i	$0.969533\pi$
$882$	0.0887311			0.00298773
$883$	0.613371	+	0.445640i	0.0206416	+	0.0149970i	0.598058	−	0.801453i	$-0.295939\pi$
$883$	0.613371	+	0.445640i	0.0206416	+	0.0149970i	−0.577417	+	0.816450i	$0.695939\pi$
$884$	5.26925	−	16.2171i	0.177224	−	0.545439i
$885$		0			0
$886$	1.02846	+	3.16528i	0.0345519	+	0.106340i
$887$	17.1410	−	52.7546i	0.575539	−	1.77133i	−0.0587978	−	0.998270i	$-0.518727\pi$
$887$	17.1410	−	52.7546i	0.575539	−	1.77133i	0.634337	−	0.773057i	$-0.281273\pi$
$888$	0.00905550	−	0.0278700i	0.000303883	−	0.000935254i
$889$	0.717291	+	2.20759i	0.0240572	+	0.0740403i
$890$		0			0
$891$	14.5644	−	44.8246i	0.487926	−	1.50168i
$892$	−29.9826	−	21.7837i	−1.00389	−	0.729371i
$893$	−14.0721			−0.470905
$894$	5.80175	+	4.21522i	0.194040	+	0.140978i
$895$		0			0
$896$	−25.2219	+	18.3248i	−0.842606	+	0.612189i
$897$	−36.9950	+	26.8785i	−1.23523	+	0.897446i
$898$	−1.91325	−	5.88838i	−0.0638460	−	0.196498i
$899$	7.70312			0.256914
$900$		0			0
$901$	4.40584			0.146780
$902$	5.21903	+	16.0625i	0.173775	+	0.534824i
$903$	11.0550	−	8.03189i	0.367886	−	0.267285i
$904$	−19.0956	+	13.8737i	−0.635109	+	0.461434i
$905$		0			0
$906$	−0.977725	−	0.710359i	−0.0324827	−	0.0236001i
$907$	15.8193			0.525271			0.262636	−	0.964895i	$-0.415408\pi$
$907$	15.8193			0.525271			0.262636	+	0.964895i	$0.415408\pi$
$908$	2.05559	+	1.49347i	0.0682170	+	0.0495626i
$909$	−0.0256515	+	0.0789472i	−0.000850806	+	0.00261851i
$910$		0			0
$911$	−2.47959	−	7.63139i	−0.0821524	−	0.252839i	0.901541	−	0.432694i	$-0.142437\pi$
$911$	−2.47959	−	7.63139i	−0.0821524	−	0.252839i	−0.983693	+	0.179855i	$0.942437\pi$
$912$	3.61968	−	11.1402i	0.119859	−	0.368890i
$913$	9.97207	−	30.6909i	0.330027	−	1.01572i
$914$	3.07350	+	9.45925i	0.101662	+	0.312884i
$915$		0			0
$916$	13.0875	−	40.2792i	0.432423	−	1.33086i
$917$	−19.5312	−	14.1902i	−0.644976	−	0.468603i
$918$	−4.38348			−0.144676
$919$	−18.4781	−	13.4251i	−0.609536	−	0.442854i	0.239715	−	0.970843i	$-0.422946\pi$
$919$	−18.4781	−	13.4251i	−0.609536	−	0.442854i	−0.849251	+	0.527990i	$0.822946\pi$
$920$		0			0
$921$	12.3885	−	9.00076i	0.408214	−	0.296585i
$922$	0.626429	−	0.455127i	0.0206303	−	0.0149888i
$923$	−2.54498	−	7.83264i	−0.0837690	−	0.257814i
$924$	−59.3939			−1.95392
$925$		0			0
$926$	−0.104881			−0.00344661
$927$	−0.260493	−	0.801715i	−0.00855571	−	0.0263318i
$928$	13.9881	−	10.1629i	0.459181	−	0.333615i
$929$	32.1405	−	23.3514i	1.05449	−	0.766135i	0.0814326	−	0.996679i	$-0.474050\pi$
$929$	32.1405	−	23.3514i	1.05449	−	0.766135i	0.973062	+	0.230544i	$0.0740505\pi$
$930$		0			0
$931$	7.74286	+	5.62552i	0.253762	+	0.184369i
$932$	−34.7694			−1.13891
$933$	−37.6225	−	27.3344i	−1.23171	−	0.894887i
$934$	−1.29316	+	3.97993i	−0.0423134	+	0.130227i
$935$		0			0
$936$	0.0795615	+	0.244865i	0.00260055	+	0.00800366i
$937$	9.40547	−	28.9471i	0.307263	−	0.945659i	−0.671560	−	0.740950i	$-0.734375\pi$
$937$	9.40547	−	28.9471i	0.307263	−	0.945659i	0.978823	−	0.204709i	$-0.0656247\pi$
$938$	−1.42385	+	4.38217i	−0.0464905	+	0.143083i
$939$	10.6585	+	32.8035i	0.347828	+	1.07050i
$940$		0			0
$941$	7.91444	−	24.3581i	0.258003	−	0.794053i	−0.735220	−	0.677829i	$-0.762921\pi$
$941$	7.91444	−	24.3581i	0.258003	−	0.794053i	0.993223	−	0.116224i	$-0.0370790\pi$
$942$	7.14074	+	5.18805i	0.232658	+	0.169036i
$943$	73.2659			2.38587
$944$	0.0604938	+	0.0439513i	0.00196891	+	0.00143049i
$945$		0			0
$946$	−3.28473	+	2.38650i	−0.106796	+	0.0775918i
$947$	46.9830	−	34.1351i	1.52674	−	1.10924i	0.568725	−	0.822528i	$-0.307437\pi$
$947$	46.9830	−	34.1351i	1.52674	−	1.10924i	0.958016	−	0.286714i	$-0.0925631\pi$
$948$	0.428353	+	1.31834i	0.0139123	+	0.0428176i
$949$	−5.33005			−0.173021
$950$		0			0
$951$	−16.6047			−0.538446
$952$	3.44298	+	10.5964i	0.111588	+	0.343431i
$953$	36.9087	−	26.8157i	1.19559	−	0.868647i	0.201746	−	0.979438i	$-0.435339\pi$
$953$	36.9087	−	26.8157i	1.19559	−	0.868647i	0.993844	+	0.110791i	$0.0353385\pi$
$954$	−0.0261718	+	0.0190149i	−0.000847344	+	0.000615632i
$955$		0			0
$956$	−18.3856	−	13.3579i	−0.594634	−	0.432027i
$957$	43.4527			1.40463
$958$	−5.37804	−	3.90737i	−0.173757	−	0.126242i
$959$	−11.5530	+	35.5564i	−0.373065	+	1.14818i
$960$		0			0
$961$	−8.76432	−	26.9738i	−0.282720	−	0.870123i
$962$	−0.00477447	+	0.0146943i	−0.000153935	+	0.000473763i
$963$	−0.216998	+	0.667850i	−0.00699265	+	0.0215212i
$964$	−5.91885	−	18.2164i	−0.190633	−	0.586709i
$965$		0			0
$966$	4.49002	−	13.8189i	0.144464	−	0.444614i
$967$	34.3386	+	24.9485i	1.10426	+	0.802289i	0.981750	−	0.190179i	$-0.0609067\pi$
$967$	34.3386	+	24.9485i	1.10426	+	0.802289i	0.122507	+	0.992468i	$0.460907\pi$
$968$	22.2971			0.716655
$969$	−7.19103	−	5.22459i	−0.231009	−	0.167838i
$970$		0			0
$971$	11.6767	−	8.48360i	0.374722	−	0.272252i	−0.384444	−	0.923148i	$-0.625607\pi$
$971$	11.6767	−	8.48360i	0.374722	−	0.272252i	0.759166	+	0.650897i	$0.225607\pi$
$972$	−0.914794	+	0.664637i	−0.0293420	+	0.0213182i
$973$	20.6438	+	63.5351i	0.661810	+	2.03684i
$974$	−5.06198			−0.162196
$975$		0			0
$976$	13.2057			0.422705
$977$	5.12190	+	15.7636i	0.163864	+	0.504322i	0.998951	−	0.0457964i	$-0.0145826\pi$
$977$	5.12190	+	15.7636i	0.163864	+	0.504322i	−0.835087	+	0.550118i	$0.814583\pi$
$978$	−3.35203	+	2.43539i	−0.107186	+	0.0778752i
$979$	−26.3308	+	19.1305i	−0.841537	+	0.611413i
$980$		0			0
$981$	−0.713872	−	0.518658i	−0.0227922	−	0.0165595i
$982$	8.98845			0.286833
$983$	−26.9543	−	19.5835i	−0.859710	−	0.624616i	0.0680960	−	0.997679i	$-0.478308\pi$
$983$	−26.9543	−	19.5835i	−0.859710	−	0.624616i	−0.927806	+	0.373063i	$0.878308\pi$
$984$	−6.52572	+	20.0841i	−0.208032	+	0.640258i
$985$		0			0
$986$	−1.22491	−	3.76988i	−0.0390090	−	0.120057i
$987$	−12.6082	+	38.8040i	−0.401323	+	1.23514i
$988$	−4.17315	+	12.8436i	−0.132766	+	0.408611i
$989$	5.44276	+	16.7511i	0.173070	+	0.532654i
$990$		0			0
$991$	−7.56973	+	23.2972i	−0.240460	+	0.740061i	0.755890	+	0.654699i	$0.227205\pi$
$991$	−7.56973	+	23.2972i	−0.240460	+	0.740061i	−0.996350	+	0.0853621i	$0.972795\pi$
$992$	4.79042	+	3.48045i	0.152096	+	0.110504i
$993$	−33.7516			−1.07107
$994$	2.11709	+	1.53816i	0.0671500	+	0.0487873i
$995$		0			0
$996$	15.8742	−	11.5333i	0.502994	−	0.365447i
$997$	48.4258	−	35.1834i	1.53366	−	1.11427i	0.579499	−	0.814973i	$-0.303248\pi$
$997$	48.4258	−	35.1834i	1.53366	−	1.11427i	0.954160	−	0.299296i	$-0.0967519\pi$
$998$	−0.495815	−	1.52596i	−0.0156948	−	0.0483035i
$999$	−0.0704313			−0.00222835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.m.126.2		16
5.2	odd	4		625.2.e.j.499.5		32
5.3	odd	4		625.2.e.j.499.4		32
5.4	even	2		625.2.d.q.126.3		16
25.2	odd	20		625.2.b.d.624.8		16
25.3	odd	20		625.2.e.j.124.5		32
25.4	even	10		625.2.d.q.501.3		16
25.6	even	5		625.2.d.n.376.3		16
25.8	odd	20		625.2.e.k.249.5		32
25.9	even	10		625.2.d.p.251.2		16
25.11	even	5		625.2.a.g.1.3	yes	8
25.12	odd	20		625.2.e.k.374.5		32
25.13	odd	20		625.2.e.k.374.4		32
25.14	even	10		625.2.a.e.1.6	✓	8
25.16	even	5		625.2.d.n.251.3		16
25.17	odd	20		625.2.e.k.249.4		32
25.19	even	10		625.2.d.p.376.2		16
25.21	even	5	inner	625.2.d.m.501.2		16
25.22	odd	20		625.2.e.j.124.4		32
25.23	odd	20		625.2.b.d.624.9		16
75.11	odd	10		5625.2.a.s.1.6		8
75.14	odd	10		5625.2.a.be.1.3		8
100.11	odd	10		10000.2.a.be.1.7		8
100.39	odd	10		10000.2.a.bn.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.6	✓	8	25.14	even	10
625.2.a.g.1.3	yes	8	25.11	even	5
625.2.b.d.624.8		16	25.2	odd	20
625.2.b.d.624.9		16	25.23	odd	20
625.2.d.m.126.2		16	1.1	even	1	trivial
625.2.d.m.501.2		16	25.21	even	5	inner
625.2.d.n.251.3		16	25.16	even	5
625.2.d.n.376.3		16	25.6	even	5
625.2.d.p.251.2		16	25.9	even	10
625.2.d.p.376.2		16	25.19	even	10
625.2.d.q.126.3		16	5.4	even	2
625.2.d.q.501.3		16	25.4	even	10
625.2.e.j.124.4		32	25.22	odd	20
625.2.e.j.124.5		32	25.3	odd	20
625.2.e.j.499.4		32	5.3	odd	4
625.2.e.j.499.5		32	5.2	odd	4
625.2.e.k.249.4		32	25.17	odd	20
625.2.e.k.249.5		32	25.8	odd	20
625.2.e.k.374.4		32	25.13	odd	20
625.2.e.k.374.5		32	25.12	odd	20
5625.2.a.s.1.6		8	75.11	odd	10
5625.2.a.be.1.3		8	75.14	odd	10
10000.2.a.be.1.7		8	100.11	odd	10
10000.2.a.bn.1.2		8	100.39	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.100972 - 0.310759i) q^{2} +(1.38777 - 1.00827i) q^{3} +(1.53166 - 1.11281i) q^{4} +(-0.453455 - 0.329455i) q^{6} +3.42409 q^{7} +(-1.02917 - 0.747732i) q^{8} +(-0.0177620 + 0.0546659i) q^{9} +O(q^{10})\)	\(q+(-0.100972 - 0.310759i) q^{2} +(1.38777 - 1.00827i) q^{3} +(1.53166 - 1.11281i) q^{4} +(-0.453455 - 0.329455i) q^{6} +3.42409 q^{7} +(-1.02917 - 0.747732i) q^{8} +(-0.0177620 + 0.0546659i) q^{9} +(-1.65050 - 5.07970i) q^{11} +(1.00357 - 3.08866i) q^{12} +(-1.08809 + 3.34880i) q^{13} +(-0.345736 - 1.06407i) q^{14} +(1.04163 - 3.20582i) q^{16} +(-2.06936 - 1.50348i) q^{17} +0.0187814 q^{18} +(1.63890 + 1.19073i) q^{19} +(4.75186 - 3.45243i) q^{21} +(-1.41191 + 1.02581i) q^{22} +(2.33951 + 7.20028i) q^{23} -2.18216 q^{24} +1.15054 q^{26} +(1.62071 + 4.98804i) q^{27} +(5.24454 - 3.81038i) q^{28} +(-3.83692 + 2.78769i) q^{29} +(-1.31401 - 0.954685i) q^{31} -3.64565 q^{32} +(-7.41224 - 5.38531i) q^{33} +(-0.258273 + 0.794881i) q^{34} +(0.0336277 + 0.103495i) q^{36} +(-0.00414978 + 0.0127717i) q^{37} +(0.204547 - 0.629532i) q^{38} +(1.86649 + 5.74446i) q^{39} +(2.99048 - 9.20376i) q^{41} +(-1.55267 - 1.12808i) q^{42} +2.32645 q^{43} +(-8.18076 - 5.94367i) q^{44} +(2.00133 - 1.45405i) q^{46} +(-5.61982 + 4.08304i) q^{47} +(-1.78680 - 5.49920i) q^{48} +4.72443 q^{49} -4.38772 q^{51} +(2.06001 + 6.34006i) q^{52} +(-1.39350 + 1.01244i) q^{53} +(1.38643 - 1.00730i) q^{54} +(-3.52396 - 2.56031i) q^{56} +3.47500 q^{57} +(1.25372 + 0.910880i) q^{58} +(-0.00685492 + 0.0210973i) q^{59} +(1.21063 + 3.72593i) q^{61} +(-0.163999 + 0.504737i) q^{62} +(-0.0608188 + 0.187181i) q^{63} +(-1.71516 - 5.27873i) q^{64} +(-0.925105 + 2.84718i) q^{66} +(-3.33179 - 2.42069i) q^{67} -4.84265 q^{68} +(10.5066 + 7.63346i) q^{69} +(-1.89224 + 1.37479i) q^{71} +(0.0591555 - 0.0429790i) q^{72} +(0.467768 + 1.43964i) q^{73} +0.00438793 q^{74} +3.83530 q^{76} +(-5.65145 - 17.3934i) q^{77} +(1.59668 - 1.16005i) q^{78} +(-0.345313 + 0.250885i) q^{79} +(7.13898 + 5.18677i) q^{81} -3.16210 q^{82} +(4.88797 + 3.55132i) q^{83} +(3.43631 - 10.5759i) q^{84} +(-0.234905 - 0.722965i) q^{86} +(-2.51401 + 7.73734i) q^{87} +(-2.09963 + 6.46198i) q^{88} +(-1.88303 - 5.79537i) q^{89} +(-3.72573 + 11.4666i) q^{91} +(11.5959 + 8.42492i) q^{92} -2.78613 q^{93} +(1.83628 + 1.33414i) q^{94} +(-5.05932 + 3.67581i) q^{96} +(12.9458 - 9.40564i) q^{97} +(-0.477033 - 1.46816i) q^{98} +0.307002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9	\( 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9} - 3 q^{11} + 15 q^{12} - 5 q^{13} - q^{14} + q^{16} - 25 q^{17} - 10 q^{18} + 10 q^{19} + 7 q^{21} - 35 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} + 35 q^{28} - 8 q^{31} + 60 q^{32} - 6 q^{34} + q^{36} - 5 q^{37} - 35 q^{38} + q^{39} - 8 q^{41} - 10 q^{42} - 31 q^{44} + 42 q^{46} - 5 q^{47} - 25 q^{48} - 8 q^{49} - 28 q^{51} + 15 q^{52} - 10 q^{53} + 50 q^{54} + 35 q^{56} - 20 q^{57} + 35 q^{58} - 15 q^{59} + 17 q^{61} + 5 q^{62} + 10 q^{63} + 37 q^{64} + 44 q^{66} - 10 q^{67} + 80 q^{68} - 9 q^{69} - 13 q^{71} + 20 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 45 q^{77} + 5 q^{78} - 55 q^{79} - 19 q^{81} - 90 q^{82} - 15 q^{83} + 59 q^{84} + 7 q^{86} - 60 q^{87} + 40 q^{88} - 28 q^{91} + 45 q^{92} - 80 q^{93} + 4 q^{94} - 43 q^{96} + 40 q^{97} + 45 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9 - 3 * q^11 + 15 * q^12 - 5 * q^13 - q^14 + q^16 - 25 * q^17 - 10 * q^18 + 10 * q^19 + 7 * q^21 - 35 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 + 35 * q^28 - 8 * q^31 + 60 * q^32 - 6 * q^34 + q^36 - 5 * q^37 - 35 * q^38 + q^39 - 8 * q^41 - 10 * q^42 - 31 * q^44 + 42 * q^46 - 5 * q^47 - 25 * q^48 - 8 * q^49 - 28 * q^51 + 15 * q^52 - 10 * q^53 + 50 * q^54 + 35 * q^56 - 20 * q^57 + 35 * q^58 - 15 * q^59 + 17 * q^61 + 5 * q^62 + 10 * q^63 + 37 * q^64 + 44 * q^66 - 10 * q^67 + 80 * q^68 - 9 * q^69 - 13 * q^71 + 20 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 45 * q^77 + 5 * q^78 - 55 * q^79 - 19 * q^81 - 90 * q^82 - 15 * q^83 + 59 * q^84 + 7 * q^86 - 60 * q^87 + 40 * q^88 - 28 * q^91 + 45 * q^92 - 80 * q^93 + 4 * q^94 - 43 * q^96 + 40 * q^97 + 45 * q^98 - 44 * q^99

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