LMFDB - Embedded newform 825.2.n.k.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.2
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	825.751
Dual form			825.2.n.k.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24278 - 1.62947i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.75683 - 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(0.703814 - 2.16612i) q^{7} +(-3.15700 - 9.71623i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(2.24278 - 1.62947i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.75683 - 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(0.703814 - 2.16612i) q^{7} +(-3.15700 - 9.71623i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.105203 + 3.31496i) q^{11} -5.68522 q^{12} +(-0.352519 + 0.256120i) q^{13} +(-1.95113 - 6.00496i) q^{14} +(-13.7139 - 9.96371i) q^{16} +(4.04508 + 2.93893i) q^{17} +(-0.856664 + 2.63654i) q^{18} +(1.45113 + 4.46612i) q^{19} -2.27759 q^{21} +(5.16568 + 7.60613i) q^{22} +0.845811 q^{23} +(-8.26512 + 6.00496i) q^{24} +(-0.373280 + 1.14884i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-10.4756 - 7.61100i) q^{28} +(-0.821093 + 2.52706i) q^{29} +(3.77637 - 2.74369i) q^{31} -26.5602 q^{32} +(3.18522 - 0.924324i) q^{33} +13.8611 q^{34} +(1.75683 + 5.40697i) q^{36} +(2.73863 - 8.42864i) q^{37} +(10.5320 + 7.65193i) q^{38} +(0.352519 + 0.256120i) q^{39} +(-1.32697 - 4.08400i) q^{41} +(-5.10813 + 3.71127i) q^{42} -7.00317 q^{43} +(17.7390 + 6.39264i) q^{44} +(1.89696 - 1.37823i) q^{46} +(-0.144675 - 0.445265i) q^{47} +(-5.23823 + 16.1216i) q^{48} +(1.46641 + 1.06541i) q^{49} +(1.54508 - 4.75528i) q^{51} +(0.765515 + 2.35601i) q^{52} +(-8.76863 + 6.37078i) q^{53} +2.77222 q^{54} -23.2684 q^{56} +(3.79911 - 2.76021i) q^{57} +(2.27625 + 7.00558i) q^{58} +(1.21629 - 3.74334i) q^{59} +(-2.39913 - 1.74307i) q^{61} +(3.99878 - 12.3070i) q^{62} +(0.703814 + 2.16612i) q^{63} +(-32.1409 + 23.3517i) q^{64} +(5.63757 - 7.26328i) q^{66} +2.47048 q^{67} +(22.9972 - 16.7084i) q^{68} +(-0.261370 - 0.804414i) q^{69} +(9.15321 + 6.65020i) q^{71} +(8.26512 + 6.00496i) q^{72} +(-2.60474 + 8.01655i) q^{73} +(-7.59209 - 23.3661i) q^{74} +26.6975 q^{76} +(7.10654 + 2.56099i) q^{77} +1.20796 q^{78} +(8.79457 - 6.38963i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-9.63087 - 6.99723i) q^{82} +(-4.78978 - 3.47998i) q^{83} +(-4.00134 + 12.3149i) q^{84} +(-15.7065 + 11.4115i) q^{86} +2.65711 q^{87} +(32.5410 - 9.44313i) q^{88} +5.89958 q^{89} +(0.306678 + 0.943857i) q^{91} +(1.48595 - 4.57327i) q^{92} +(-3.77637 - 2.74369i) q^{93} +(-1.05002 - 0.762885i) q^{94} +(8.20756 + 25.2603i) q^{96} +(-6.99640 + 5.08318i) q^{97} +5.02487 q^{98} +(-1.86337 - 2.74369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9	$ 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9 - 3 * q^11 - 18 * q^12 - 6 * q^13 - 10 * q^14 - 20 * q^16 + 10 * q^17 + 5 * q^18 + 6 * q^19 - 4 * q^21 + 25 * q^22 + 10 * q^23 - 20 * q^24 - 8 * q^26 + 2 * q^27 - 31 * q^28 + 3 * q^31 - 60 * q^32 - 2 * q^33 + 50 * q^34 - 2 * q^36 + 19 * q^37 + 28 * q^38 + 6 * q^39 - 25 * q^41 - 15 * q^42 + 4 * q^43 + 7 * q^44 - 6 * q^46 - 15 * q^47 - 5 * q^48 + 21 * q^49 - 10 * q^51 - 6 * q^52 - 7 * q^53 + 10 * q^54 + 20 * q^56 + 9 * q^57 + 2 * q^58 + 35 * q^59 + 21 * q^61 + 19 * q^62 - q^63 - 77 * q^64 + 25 * q^66 + 26 * q^67 + 35 * q^68 - 5 * q^69 + 25 * q^71 + 20 * q^72 - q^73 - 29 * q^74 - 14 * q^76 + 61 * q^77 - 12 * q^78 + 30 * q^79 - 2 * q^81 - 57 * q^82 - 11 * q^83 - 34 * q^84 - 34 * q^86 - 10 * q^87 + 85 * q^88 + 32 * q^89 + 37 * q^91 + 10 * q^92 - 3 * q^93 - 39 * q^94 + 10 * q^96 - 5 * q^97 - 50 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	2.24278	−	1.62947i	1.58588	−	1.15221i	0.676347	−	0.736584i	$-0.263562\pi$
$2$	2.24278	−	1.62947i	1.58588	−	1.15221i	0.909535	−	0.415627i	$-0.136438\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.75683	−	5.40697i	0.878415	−	2.70348i
$5$		0			0
$5$		0			0
$6$	−2.24278	−	1.62947i	−0.915609	−	0.665229i
$7$	0.703814	−	2.16612i	0.266017	−	0.818716i	−0.725441	−	0.688285i	$-0.758364\pi$
$7$	0.703814	−	2.16612i	0.266017	−	0.818716i	0.991457	−	0.130431i	$-0.0416360\pi$
$8$	−3.15700	−	9.71623i	−1.11617	−	3.43521i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−0.105203	+	3.31496i	−0.0317198	+	0.999497i
$11$	−0.105203	+	3.31496i	−0.0317198	+	0.999497i
$12$	−5.68522			−1.64118
$13$	−0.352519	+	0.256120i	−0.0977711	+	0.0710348i	−0.635597	−	0.772021i	$-0.719246\pi$
$13$	−0.352519	+	0.256120i	−0.0977711	+	0.0710348i	0.537826	+	0.843056i	$0.319246\pi$
$14$	−1.95113	−	6.00496i	−0.521461	−	1.60489i
$15$		0			0
$16$	−13.7139	−	9.96371i	−3.42847	−	2.49093i
$17$	4.04508	+	2.93893i	0.981077	+	0.712794i	0.957949	−	0.286938i	$-0.0926374\pi$
$17$	4.04508	+	2.93893i	0.981077	+	0.712794i	0.0231281	+	0.999733i	$0.492637\pi$
$18$	−0.856664	+	2.63654i	−0.201918	+	0.621439i
$19$	1.45113	+	4.46612i	0.332912	+	1.02460i	0.967741	+	0.251946i	$0.0810704\pi$
$19$	1.45113	+	4.46612i	0.332912	+	1.02460i	−0.634829	+	0.772652i	$0.718930\pi$
$20$		0			0
$21$	−2.27759			−0.497011
$22$	5.16568	+	7.60613i	1.10133	+	1.62163i
$23$	0.845811			0.176364			0.0881819	−	0.996104i	$-0.471894\pi$
$23$	0.845811			0.176364			0.0881819	+	0.996104i	$0.471894\pi$
$24$	−8.26512	+	6.00496i	−1.68711	+	1.22576i
$25$		0			0
$26$	−0.373280	+	1.14884i	−0.0732063	+	0.225306i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−10.4756	−	7.61100i	−1.97971	−	1.43834i
$29$	−0.821093	+	2.52706i	−0.152473	+	0.469264i	−0.997896	−	0.0648334i	$-0.979348\pi$
$29$	−0.821093	+	2.52706i	−0.152473	+	0.469264i	0.845423	+	0.534097i	$0.179348\pi$
$30$		0			0
$31$	3.77637	−	2.74369i	0.678256	−	0.492782i	−0.194523	−	0.980898i	$-0.562316\pi$
$31$	3.77637	−	2.74369i	0.678256	−	0.492782i	0.872779	+	0.488116i	$0.162316\pi$
$32$	−26.5602			−4.69523
$33$	3.18522	−	0.924324i	0.554476	−	0.160904i
$34$	13.8611			2.37716
$35$		0			0
$36$	1.75683	+	5.40697i	0.292805	+	0.901161i
$37$	2.73863	−	8.42864i	0.450228	−	1.38566i	−0.426419	−	0.904526i	$-0.640225\pi$
$37$	2.73863	−	8.42864i	0.450228	−	1.38566i	0.876647	−	0.481134i	$-0.159775\pi$
$38$	10.5320	+	7.65193i	1.70851	+	1.24131i
$39$	0.352519	+	0.256120i	0.0564481	+	0.0410120i
$40$		0			0
$41$	−1.32697	−	4.08400i	−0.207238	−	0.637814i	−0.999614	−	0.0277805i	$-0.991156\pi$
$41$	−1.32697	−	4.08400i	−0.207238	−	0.637814i	0.792376	−	0.610033i	$-0.208844\pi$
$42$	−5.10813	+	3.71127i	−0.788201	+	0.572661i
$43$	−7.00317			−1.06797			−0.533986	−	0.845493i	$-0.679307\pi$
$43$	−7.00317			−1.06797			−0.533986	+	0.845493i	$0.679307\pi$
$44$	17.7390	+	6.39264i	2.67426	+	0.963727i
$45$		0			0
$46$	1.89696	−	1.37823i	0.279692	−	0.203208i
$47$	−0.144675	−	0.445265i	−0.0211031	−	0.0649485i	0.939950	−	0.341311i	$-0.110871\pi$
$47$	−0.144675	−	0.445265i	−0.0211031	−	0.0649485i	−0.961053	+	0.276363i	$0.910871\pi$
$48$	−5.23823	+	16.1216i	−0.756074	+	2.32696i
$49$	1.46641	+	1.06541i	0.209487	+	0.152201i
$50$		0			0
$51$	1.54508	−	4.75528i	0.216355	−	0.665873i
$52$	0.765515	+	2.35601i	0.106158	+	0.326720i
$53$	−8.76863	+	6.37078i	−1.20446	+	0.875094i	−0.994716	−	0.102662i	$-0.967264\pi$
$53$	−8.76863	+	6.37078i	−1.20446	+	0.875094i	−0.209747	+	0.977756i	$0.567264\pi$
$54$	2.77222			0.377252
$55$		0			0
$56$	−23.2684			−3.10938
$57$	3.79911	−	2.76021i	0.503204	−	0.365599i
$58$	2.27625	+	7.00558i	0.298887	+	0.919878i
$59$	1.21629	−	3.74334i	0.158347	−	0.487341i	−0.840138	−	0.542373i	$-0.817526\pi$
$59$	1.21629	−	3.74334i	0.158347	−	0.487341i	0.998485	+	0.0550316i	$0.0175260\pi$
$60$		0			0
$61$	−2.39913	−	1.74307i	−0.307177	−	0.223177i	0.423507	−	0.905893i	$-0.360799\pi$
$61$	−2.39913	−	1.74307i	−0.307177	−	0.223177i	−0.730684	+	0.682715i	$0.760799\pi$
$62$	3.99878	−	12.3070i	0.507845	−	1.56299i
$63$	0.703814	+	2.16612i	0.0886723	+	0.272905i
$64$	−32.1409	+	23.3517i	−4.01761	+	2.91897i
$65$		0			0
$66$	5.63757	−	7.26328i	0.693937	−	0.894048i
$67$	2.47048			0.301817			0.150909	−	0.988548i	$-0.451780\pi$
$67$	2.47048			0.301817			0.150909	+	0.988548i	$0.451780\pi$
$68$	22.9972	−	16.7084i	2.78882	−	2.02620i
$69$	−0.261370	−	0.804414i	−0.0314653	−	0.0968401i
$70$		0			0
$71$	9.15321	+	6.65020i	1.08629	+	0.789233i	0.978768	−	0.204970i	$-0.0657097\pi$
$71$	9.15321	+	6.65020i	1.08629	+	0.789233i	0.107518	+	0.994203i	$0.465710\pi$
$72$	8.26512	+	6.00496i	0.974054	+	0.707691i
$73$	−2.60474	+	8.01655i	−0.304861	+	0.938266i	0.674868	+	0.737939i	$0.264201\pi$
$73$	−2.60474	+	8.01655i	−0.304861	+	0.938266i	−0.979729	+	0.200328i	$0.935799\pi$
$74$	−7.59209	−	23.3661i	−0.882563	−	2.71625i
$75$		0			0
$76$	26.6975			3.06242
$77$	7.10654	+	2.56099i	0.809866	+	0.291852i
$78$	1.20796			0.136775
$79$	8.79457	−	6.38963i	0.989466	−	0.718889i	0.0296621	−	0.999560i	$-0.490557\pi$
$79$	8.79457	−	6.38963i	0.989466	−	0.718889i	0.959804	+	0.280671i	$0.0905569\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−9.63087	−	6.99723i	−1.06355	−	0.772715i
$83$	−4.78978	−	3.47998i	−0.525747	−	0.381978i	0.293017	−	0.956107i	$-0.405341\pi$
$83$	−4.78978	−	3.47998i	−0.525747	−	0.381978i	−0.818764	+	0.574130i	$0.805341\pi$
$84$	−4.00134	+	12.3149i	−0.436582	+	1.34366i
$85$		0			0
$86$	−15.7065	+	11.4115i	−1.69368	+	1.23053i
$87$	2.65711			0.284872
$88$	32.5410	−	9.44313i	3.46888	−	1.00664i
$89$	5.89958			0.625354			0.312677	−	0.949859i	$-0.398774\pi$
$89$	5.89958			0.625354			0.312677	+	0.949859i	$0.398774\pi$
$90$		0			0
$91$	0.306678	+	0.943857i	0.0321486	+	0.0989431i
$92$	1.48595	−	4.57327i	0.154921	−	0.476796i
$93$	−3.77637	−	2.74369i	−0.391591	−	0.284508i
$94$	−1.05002	−	0.762885i	−0.108301	−	0.0786855i
$95$		0			0
$96$	8.20756	+	25.2603i	0.837681	+	2.57812i
$97$	−6.99640	+	5.08318i	−0.710377	+	0.516119i	−0.883295	−	0.468817i	$-0.844680\pi$
$97$	−6.99640	+	5.08318i	−0.710377	+	0.516119i	0.172918	+	0.984936i	$0.444680\pi$
$98$	5.02487			0.507589
$99$	−1.86337	−	2.74369i	−0.187276	−	0.275751i
$100$		0			0
$101$	4.59624	−	3.33936i	0.457343	−	0.332279i	−0.335145	−	0.942166i	$-0.608785\pi$
$101$	4.59624	−	3.33936i	0.457343	−	0.332279i	0.792488	+	0.609887i	$0.208785\pi$
$102$	−4.28332	−	13.1827i	−0.424112	−	1.30528i
$103$	0.400526	−	1.23269i	0.0394650	−	0.121461i	−0.929383	−	0.369117i	$-0.879660\pi$
$103$	0.400526	−	1.23269i	0.0394650	−	0.121461i	0.968848	+	0.247656i	$0.0796602\pi$
$104$	3.60142	+	2.61658i	0.353148	+	0.256577i
$105$		0			0
$106$	−9.28505	+	28.5765i	−0.901844	+	2.77559i
$107$	3.77024	+	11.6036i	0.364483	+	1.12176i	0.950304	+	0.311324i	$0.100772\pi$
$107$	3.77024	+	11.6036i	0.364483	+	1.12176i	−0.585821	+	0.810441i	$0.699228\pi$
$108$	4.59944	−	3.34169i	0.442581	−	0.321554i
$109$	−12.1644			−1.16514			−0.582568	−	0.812782i	$-0.697952\pi$
$109$	−12.1644			−1.16514			−0.582568	+	0.812782i	$0.697952\pi$
$110$		0			0
$111$	−8.86239			−0.841181
$112$	−31.2346	+	22.6933i	−2.95139	+	2.14431i
$113$	−0.0438966	−	0.135100i	−0.00412944	−	0.0127091i	0.948971	−	0.315365i	$-0.102127\pi$
$113$	−0.0438966	−	0.135100i	−0.00412944	−	0.0127091i	−0.953100	+	0.302656i	$0.902127\pi$
$114$	4.02286	−	12.3811i	0.376775	−	1.15959i
$115$		0			0
$116$	12.2212	+	8.87924i	1.13471	+	0.824417i
$117$	0.134650	−	0.414410i	0.0124484	−	0.0383123i
$118$	−3.37181	−	10.3774i	−0.310401	−	0.955315i
$119$	9.21305	−	6.69367i	0.844559	−	0.613608i
$120$		0			0
$121$	−10.9779	−	0.697484i	−0.997988	−	0.0634077i
$122$	−8.22100			−0.744294
$123$	−3.47406	+	2.52405i	−0.313245	+	0.227586i
$124$	−8.20061	−	25.2389i	−0.736437	−	2.26652i
$125$		0			0
$126$	5.10813	+	3.71127i	0.455068	+	0.330626i
$127$	−0.407512	−	0.296075i	−0.0361609	−	0.0262724i	0.569558	−	0.821951i	$-0.307114\pi$
$127$	−0.407512	−	0.296075i	−0.0361609	−	0.0262724i	−0.605719	+	0.795679i	$0.707114\pi$
$128$	−17.6187	+	54.2248i	−1.55729	+	4.79284i
$129$	2.16410	+	6.66041i	0.190538	+	0.586416i
$130$		0			0
$131$	19.1098			1.66963			0.834816	−	0.550529i	$-0.185574\pi$
$131$	19.1098			1.66963			0.834816	+	0.550529i	$0.185574\pi$
$132$	0.598100	−	18.8463i	0.0520579	−	1.64036i
$133$	10.6955			0.927415
$134$	5.54073	−	4.02558i	0.478646	−	0.347757i
$135$		0			0
$136$	15.7850	−	48.5812i	1.35355	−	4.16580i
$137$	9.98713	+	7.25608i	0.853258	+	0.619929i	0.926043	−	0.377419i	$-0.123188\pi$
$137$	9.98713	+	7.25608i	0.853258	+	0.619929i	−0.0727841	+	0.997348i	$0.523188\pi$
$138$	−1.89696	−	1.37823i	−0.161480	−	0.117322i
$139$	−2.38943	+	7.35391i	−0.202669	+	0.623750i	0.797132	+	0.603805i	$0.206349\pi$
$139$	−2.38943	+	7.35391i	−0.202669	+	0.623750i	−0.999801	+	0.0199456i	$0.993651\pi$
$140$		0			0
$141$	−0.378765	+	0.275189i	−0.0318978	+	0.0231751i
$142$	31.3649			2.63208
$143$	−0.811940	−	1.19553i	−0.0678978	−	0.0999751i
$144$	16.9513			1.41261
$145$		0			0
$146$	7.22091	+	22.2237i	0.597607	+	1.83924i
$147$	0.560118	−	1.72386i	0.0461977	−	0.142182i
$148$	−40.7620	−	29.6154i	−3.35062	−	2.43437i
$149$	−6.15577	−	4.47243i	−0.504301	−	0.366396i	0.306357	−	0.951917i	$-0.400890\pi$
$149$	−6.15577	−	4.47243i	−0.504301	−	0.366396i	−0.810657	+	0.585521i	$0.800890\pi$
$150$		0			0
$151$	−0.826389	−	2.54336i	−0.0672506	−	0.206976i	0.911784	−	0.410670i	$-0.134705\pi$
$151$	−0.826389	−	2.54336i	−0.0672506	−	0.206976i	−0.979035	+	0.203694i	$0.934705\pi$
$152$	38.8126	−	28.1990i	3.14812	−	2.28724i
$153$	−5.00000			−0.404226
$154$	20.1114	−	5.83617i	1.62063	−	0.470292i
$155$		0			0
$156$	2.00415	−	1.45610i	0.160460	−	0.116581i
$157$	−6.24214	−	19.2113i	−0.498177	−	1.53323i	−0.811947	−	0.583731i	$-0.801592\pi$
$157$	−6.24214	−	19.2113i	−0.498177	−	1.53323i	0.313770	−	0.949499i	$-0.398408\pi$
$158$	9.31252	−	28.6610i	0.740865	−	2.28015i
$159$	8.76863	+	6.37078i	0.695397	+	0.505236i
$160$		0			0
$161$	0.595294	−	1.83213i	0.0469157	−	0.144392i
$162$	−0.856664	−	2.63654i	−0.0673059	−	0.207146i
$163$	−7.92498	+	5.75784i	−0.620733	+	0.450989i	−0.853177	−	0.521621i	$-0.825328\pi$
$163$	−7.92498	+	5.75784i	−0.620733	+	0.450989i	0.232445	+	0.972610i	$0.425328\pi$
$164$	−24.4133			−1.90636
$165$		0			0
$166$	−16.4129			−1.27389
$167$	20.6927	−	15.0341i	1.60125	−	1.16338i	0.716185	−	0.697910i	$-0.245886\pi$
$167$	20.6927	−	15.0341i	1.60125	−	1.16338i	0.885065	−	0.465467i	$-0.154114\pi$
$168$	7.19034	+	22.1296i	0.554747	+	1.70734i
$169$	−3.95855	+	12.1832i	−0.304504	+	0.937166i
$170$		0			0
$171$	−3.79911	−	2.76021i	−0.290525	−	0.211079i
$172$	−12.3034	+	37.8659i	−0.938123	+	2.88725i
$173$	2.08712	+	6.42349i	0.158681	+	0.488369i	0.998515	−	0.0544734i	$-0.0173480\pi$
$173$	2.08712	+	6.42349i	0.158681	+	0.488369i	−0.839834	+	0.542843i	$0.817348\pi$
$174$	5.95930	−	4.32969i	0.451774	−	0.328233i
$175$		0			0
$176$	34.4720	−	44.4127i	2.59843	−	3.34773i
$177$	−3.93598			−0.295846
$178$	13.2314	−	9.61320i	0.991738	−	0.720540i
$179$	2.01539	+	6.20274i	0.150638	+	0.463615i	0.997693	−	0.0678901i	$-0.0216267\pi$
$179$	2.01539	+	6.20274i	0.150638	+	0.463615i	−0.847055	+	0.531505i	$0.821627\pi$
$180$		0			0
$181$	−11.1257	−	8.08332i	−0.826970	−	0.600829i	0.0917306	−	0.995784i	$-0.470760\pi$
$181$	−11.1257	−	8.08332i	−0.826970	−	0.600829i	−0.918700	+	0.394955i	$0.870760\pi$
$182$	2.22580	+	1.61714i	0.164987	+	0.119870i
$183$	−0.916387	+	2.82035i	−0.0677412	+	0.208486i
$184$	−2.67022	−	8.21810i	−0.196851	−	0.605846i
$185$		0			0
$186$	−12.9403			−0.948830
$187$	−10.1680	+	13.1001i	−0.743555	+	0.957974i
$188$	−2.66170			−0.194124
$189$	1.84261	−	1.33873i	0.134030	−	0.0973786i
$190$		0			0
$191$	−6.00607	+	18.4848i	−0.434584	+	1.33751i	0.458929	+	0.888473i	$0.348233\pi$
$191$	−6.00607	+	18.4848i	−0.434584	+	1.33751i	−0.893512	+	0.449038i	$0.851767\pi$
$192$	32.1409	+	23.3517i	2.31957	+	1.68527i
$193$	18.2938	+	13.2912i	1.31681	+	0.956722i	0.999966	+	0.00824604i	$0.00262483\pi$
$193$	18.2938	+	13.2912i	1.31681	+	0.956722i	0.316849	+	0.948476i	$0.397375\pi$
$194$	−7.40846	+	22.8009i	−0.531896	+	1.63701i
$195$		0			0
$196$	8.33685	−	6.05707i	0.595489	−	0.432648i
$197$	−23.0300			−1.64082			−0.820410	−	0.571776i	$-0.806255\pi$
$197$	−23.0300			−1.64082			−0.820410	+	0.571776i	$0.806255\pi$
$198$	−8.64989	−	3.11717i	−0.614721	−	0.221528i
$199$	−19.6216			−1.39094			−0.695468	−	0.718557i	$-0.744803\pi$
$199$	−19.6216			−1.39094			−0.695468	+	0.718557i	$0.744803\pi$
$200$		0			0
$201$	−0.763420	−	2.34957i	−0.0538475	−	0.165726i
$202$	4.86693	−	14.9789i	0.342436	−	1.05391i
$203$	4.89602	+	3.55717i	0.343633	+	0.249664i
$204$	−22.9972	−	16.7084i	−1.61013	−	1.16982i
$205$		0			0
$206$	−1.11035	−	3.41730i	−0.0773616	−	0.238095i
$207$	−0.684276	+	0.497155i	−0.0475604	+	0.0345547i
$208$	7.38630			0.512148
$209$	−14.9577	+	4.34059i	−1.03464	+	0.300245i
$210$		0			0
$211$	−0.0403903	+	0.0293453i	−0.00278059	+	0.00202021i	−0.589175	−	0.808006i	$-0.700547\pi$
$211$	−0.0403903	+	0.0293453i	−0.00278059	+	0.00202021i	0.586394	+	0.810026i	$0.300547\pi$
$212$	19.0416	+	58.6040i	1.30778	+	4.02494i
$213$	3.49622	−	10.7602i	0.239557	−	0.737280i
$214$	27.3636	+	19.8808i	1.87054	+	1.35902i
$215$		0			0
$216$	3.15700	−	9.71623i	0.214806	−	0.661106i
$217$	−3.28530	−	10.1111i	−0.223021	−	0.686387i
$218$	−27.2819	+	19.8215i	−1.84777	+	1.34248i
$219$	8.42910			0.569586
$220$		0			0
$221$	−2.17868			−0.146554
$222$	−19.8764	+	14.4410i	−1.33401	+	0.969218i
$223$	−0.233296	−	0.718012i	−0.0156227	−	0.0480816i	0.942941	−	0.332959i	$-0.108047\pi$
$223$	−0.233296	−	0.718012i	−0.0156227	−	0.0480816i	−0.958564	+	0.284877i	$0.908047\pi$
$224$	−18.6935	+	57.5326i	−1.24901	+	3.84406i
$225$		0			0
$226$	−0.318592	−	0.231470i	−0.0211924	−	0.0153972i
$227$	−2.55989	+	7.87855i	−0.169906	+	0.522917i	−0.999364	−	0.0356515i	$-0.988649\pi$
$227$	−2.55989	+	7.87855i	−0.169906	+	0.522917i	0.829458	+	0.558569i	$0.188649\pi$
$228$	−8.24999	−	25.3909i	−0.546369	−	1.68155i
$229$	2.32691	−	1.69060i	0.153767	−	0.111718i	−0.508242	−	0.861214i	$-0.669704\pi$
$229$	2.32691	−	1.69060i	0.153767	−	0.111718i	0.662008	+	0.749496i	$0.269704\pi$
$230$		0			0
$231$	0.239609	−	7.55011i	0.0157651	−	0.496761i
$232$	27.1457			1.78220
$233$	−4.18964	+	3.04395i	−0.274473	+	0.199416i	−0.716503	−	0.697584i	$-0.754258\pi$
$233$	−4.18964	+	3.04395i	−0.274473	+	0.199416i	0.442030	+	0.897000i	$0.354258\pi$
$234$	−0.373280	−	1.14884i	−0.0244021	−	0.0751019i
$235$		0			0
$236$	−18.1033	−	13.1528i	−1.17842	−	0.856176i
$237$	−8.79457	−	6.38963i	−0.571269	−	0.415051i
$238$	9.75565	−	30.0248i	0.632365	−	1.94622i
$239$	3.34751	+	10.3026i	0.216532	+	0.666418i	0.999041	+	0.0437789i	$0.0139397\pi$
$239$	3.34751	+	10.3026i	0.216532	+	0.666418i	−0.782509	+	0.622640i	$0.786060\pi$
$240$		0			0
$241$	−2.96526			−0.191009			−0.0955045	−	0.995429i	$-0.530446\pi$
$241$	−2.96526			−0.191009			−0.0955045	+	0.995429i	$0.530446\pi$
$242$	−25.7574	+	16.3238i	−1.65575	+	1.04933i
$243$	−1.00000			−0.0641500
$244$	−13.6396	+	9.90974i	−0.873185	+	0.634406i
$245$		0			0
$246$	−3.67866	+	11.3218i	−0.234543	+	0.721849i
$247$	−1.65541	−	1.20273i	−0.105331	−	0.0765277i
$248$	−38.5803	−	28.0302i	−2.44985	−	1.77992i
$249$	−1.82953	+	5.63073i	−0.115942	+	0.356833i
$250$		0			0
$251$	14.2504	−	10.3535i	0.899475	−	0.653507i	−0.0388560	−	0.999245i	$-0.512371\pi$
$251$	14.2504	−	10.3535i	0.899475	−	0.653507i	0.938331	+	0.345738i	$0.112371\pi$
$252$	12.9486			0.815685
$253$	−0.0889816	+	2.80383i	−0.00559422	+	0.176275i
$254$	−1.39640			−0.0876182
$255$		0			0
$256$	24.2895	+	74.7554i	1.51809	+	4.67221i
$257$	−6.47845	+	19.9386i	−0.404115	+	1.24374i	0.517518	+	0.855672i	$0.326856\pi$
$257$	−6.47845	+	19.9386i	−0.404115	+	1.24374i	−0.921632	+	0.388064i	$0.873144\pi$
$258$	15.7065	+	11.4115i	0.977846	+	0.710447i
$259$	−16.3299	−	11.8644i	−1.01469	−	0.737217i
$260$		0			0
$261$	−0.821093	−	2.52706i	−0.0508244	−	0.156421i
$262$	42.8590	−	31.1389i	2.64784	−	1.92377i
$263$	−8.43471			−0.520107			−0.260053	−	0.965594i	$-0.583740\pi$
$263$	−8.43471			−0.520107			−0.260053	+	0.965594i	$0.583740\pi$
$264$	−19.0367	−	28.0302i	−1.17163	−	1.72514i
$265$		0			0
$266$	23.9875	−	17.4280i	1.47077	−	1.06858i
$267$	−1.82307	−	5.61084i	−0.111570	−	0.343378i
$268$	4.34021	−	13.3578i	0.265121	−	0.815958i
$269$	−7.80173	−	5.66829i	−0.475680	−	0.345601i	0.323971	−	0.946067i	$-0.394982\pi$
$269$	−7.80173	−	5.66829i	−0.475680	−	0.345601i	−0.799651	+	0.600466i	$0.794982\pi$
$270$		0			0
$271$	3.16056	−	9.72719i	0.191990	−	0.590885i	−0.808008	−	0.589171i	$-0.799454\pi$
$271$	3.16056	−	9.72719i	0.191990	−	0.590885i	0.999999	−	0.00171395i	$-0.000545568\pi$
$272$	−26.1912	−	80.6081i	−1.58807	−	4.88759i
$273$	0.802893	−	0.583336i	0.0485933	−	0.0353051i
$274$	34.2225			2.06746
$275$		0			0
$276$	−4.80862			−0.289445
$277$	−4.72388	+	3.43210i	−0.283830	+	0.206215i	−0.720586	−	0.693365i	$-0.756127\pi$
$277$	−4.72388	+	3.43210i	−0.283830	+	0.206215i	0.436756	+	0.899580i	$0.356127\pi$
$278$	6.62403	+	20.3867i	0.397283	+	1.22271i
$279$	−1.44244	+	4.43939i	−0.0863569	+	0.265779i
$280$		0			0
$281$	−11.6611	−	8.47225i	−0.695640	−	0.505412i	0.182869	−	0.983137i	$-0.441461\pi$
$281$	−11.6611	−	8.47225i	−0.695640	−	0.505412i	−0.878509	+	0.477725i	$0.841461\pi$
$282$	−0.401072	+	1.23437i	−0.0238835	+	0.0735058i
$283$	3.28592	+	10.1130i	0.195327	+	0.601156i	0.999973	+	0.00740011i	$0.00235555\pi$
$283$	3.28592	+	10.1130i	0.195327	+	0.601156i	−0.804645	+	0.593756i	$0.797644\pi$
$284$	52.0380	−	37.8078i	3.08789	−	2.24348i
$285$		0			0
$286$	−3.76908	−	1.35827i	−0.222870	−	0.0803161i
$287$	−9.78037			−0.577317
$288$	21.4877	−	15.6117i	1.26617	−	0.919929i
$289$	2.47214	+	7.60845i	0.145420	+	0.447556i
$290$		0			0
$291$	6.99640	+	5.08318i	0.410136	+	0.297982i
$292$	38.7691	+	28.1674i	2.26879	+	1.64837i
$293$	2.59443	−	7.98484i	0.151568	−	0.466479i	−0.846229	−	0.532820i	$-0.821132\pi$
$293$	2.59443	−	7.98484i	0.151568	−	0.466479i	0.997797	+	0.0663405i	$0.0211323\pi$
$294$	−1.55277	−	4.77894i	−0.0905594	−	0.278713i
$295$		0			0
$296$	−90.5404			−5.26256
$297$	−2.03359	+	2.62002i	−0.118001	+	0.152029i
$298$	−21.0937			−1.22193
$299$	−0.298164	+	0.216629i	−0.0172433	+	0.0125280i
$300$		0			0
$301$	−4.92893	+	15.1697i	−0.284099	+	0.874366i
$302$	−5.99774	−	4.35762i	−0.345131	−	0.250753i
$303$	−4.59624	−	3.33936i	−0.264047	−	0.191841i
$304$	24.5985	−	75.7065i	1.41082	−	4.34206i
$305$		0			0
$306$	−11.2139	+	8.14736i	−0.641055	+	0.465753i
$307$	−4.51902			−0.257914			−0.128957	−	0.991650i	$-0.541163\pi$
$307$	−4.51902			−0.257914			−0.128957	+	0.991650i	$0.541163\pi$
$308$	26.3322	−	33.9256i	1.50042	−	1.93309i
$309$	−1.29613			−0.0737343
$310$		0			0
$311$	7.41548	+	22.8225i	0.420493	+	1.29415i	0.907244	+	0.420604i	$0.138182\pi$
$311$	7.41548	+	22.8225i	0.420493	+	1.29415i	−0.486751	+	0.873541i	$0.661818\pi$
$312$	1.37562	−	4.23372i	0.0778791	−	0.239687i
$313$	−20.9281	−	15.2052i	−1.18293	−	0.859448i	−0.190430	−	0.981701i	$-0.560988\pi$
$313$	−20.9281	−	15.2052i	−1.18293	−	0.859448i	−0.992499	+	0.122253i	$0.960988\pi$
$314$	−45.3040	−	32.9153i	−2.55665	−	1.85752i
$315$		0			0
$316$	−19.0979	−	58.7774i	−1.07434	−	3.30649i
$317$	2.34873	−	1.70645i	0.131918	−	0.0958441i	−0.519869	−	0.854246i	$-0.674019\pi$
$317$	2.34873	−	1.70645i	0.131918	−	0.0958441i	0.651787	+	0.758402i	$0.274019\pi$
$318$	30.0471			1.68496
$319$	−8.29072	−	2.98774i	−0.464191	−	0.167281i
$320$		0			0
$321$	9.87063	−	7.17143i	0.550925	−	0.400270i
$322$	−1.65029	−	5.07906i	−0.0919669	−	0.283045i
$323$	−7.25565	+	22.3306i	−0.403715	+	1.24251i
$324$	−4.59944	−	3.34169i	−0.255524	−	0.185649i
$325$		0			0
$326$	−8.39172	+	25.8271i	−0.464775	+	1.43043i
$327$	3.75900	+	11.5690i	0.207873	+	0.639767i
$328$	−35.4919	+	25.7863i	−1.95971	+	1.42381i
$329$	−1.06632			−0.0587881
$330$		0			0
$331$	10.9837			0.603720			0.301860	−	0.953352i	$-0.402392\pi$
$331$	10.9837			0.603720			0.301860	+	0.953352i	$0.402392\pi$
$332$	−27.2310	+	19.7845i	−1.49449	+	1.08581i
$333$	2.73863	+	8.42864i	0.150076	+	0.461886i
$334$	21.9114	−	67.4364i	1.19894	−	3.68996i
$335$		0			0
$336$	31.2346	+	22.6933i	1.70399	+	1.23802i
$337$	−3.96968	+	12.2174i	−0.216242	+	0.665525i	0.782821	+	0.622247i	$0.213780\pi$
$337$	−3.96968	+	12.2174i	−0.216242	+	0.665525i	−0.999063	+	0.0432780i	$0.986220\pi$
$338$	10.9740	+	33.7744i	0.596906	+	1.83709i
$339$	−0.114923	+	0.0834963i	−0.00624175	+	0.00453490i
$340$		0			0
$341$	8.69793	+	12.8071i	0.471020	+	0.693545i
$342$	−13.0182			−0.703946
$343$	16.2381	−	11.7977i	0.876777	−	0.637016i
$344$	22.1090	+	68.0444i	1.19204	+	3.66871i
$345$		0			0
$346$	15.1478	+	11.0056i	0.814353	+	0.591662i
$347$	−1.52881	−	1.11074i	−0.0820707	−	0.0596279i	0.545993	−	0.837790i	$-0.316152\pi$
$347$	−1.52881	−	1.11074i	−0.0820707	−	0.0596279i	−0.628064	+	0.778162i	$0.716152\pi$
$348$	4.66809	−	14.3669i	0.250236	−	0.770147i
$349$	7.34802	+	22.6149i	0.393330	+	1.21055i	0.930254	+	0.366915i	$0.119586\pi$
$349$	7.34802	+	22.6149i	0.393330	+	1.21055i	−0.536924	+	0.843631i	$0.680414\pi$
$350$		0			0
$351$	−0.435737			−0.0232579
$352$	2.79421	−	88.0460i	0.148932	−	4.69287i
$353$	20.2294			1.07670			0.538352	−	0.842720i	$-0.319047\pi$
$353$	20.2294			1.07670			0.538352	+	0.842720i	$0.319047\pi$
$354$	−8.82752	+	6.41357i	−0.469177	+	0.340877i
$355$		0			0
$356$	10.3646	−	31.8988i	0.549321	−	1.69063i
$357$	−9.21305	−	6.69367i	−0.487606	−	0.354267i
$358$	14.6273	+	10.6273i	0.773075	+	0.561672i
$359$	−5.74455	+	17.6799i	−0.303186	+	0.933109i	0.677162	+	0.735834i	$0.263209\pi$
$359$	−5.74455	+	17.6799i	−0.303186	+	0.933109i	−0.980348	+	0.197276i	$0.936791\pi$
$360$		0			0
$361$	−2.46912	+	1.79392i	−0.129954	+	0.0944170i
$362$	−38.1241			−2.00376
$363$	2.72900	+	10.6561i	0.143235	+	0.559300i
$364$	5.64219			0.295731
$365$		0			0
$366$	2.54043	+	7.81863i	0.132790	+	0.408687i
$367$	−1.82571	+	5.61894i	−0.0953010	+	0.293306i	−0.987332	−	0.158668i	$-0.949280\pi$
$367$	−1.82571	+	5.61894i	−0.0953010	+	0.293306i	0.892031	+	0.451974i	$0.149280\pi$
$368$	−11.5993	−	8.42742i	−0.604658	−	0.439310i
$369$	3.47406	+	2.52405i	0.180852	+	0.131397i
$370$		0			0
$371$	7.62838	+	23.4777i	0.396046	+	1.21890i
$372$	−21.4695	+	15.5985i	−1.11314	+	0.808744i
$373$	1.66992			0.0864650			0.0432325	−	0.999065i	$-0.486234\pi$
$373$	1.66992			0.0864650			0.0432325	+	0.999065i	$0.486234\pi$
$374$	−1.45823	+	45.9490i	−0.0754031	+	2.37597i
$375$		0			0
$376$	−3.86956	+	2.81140i	−0.199557	+	0.144987i
$377$	−0.357780	−	1.10113i	−0.0184266	−	0.0567113i
$378$	1.95113	−	6.00496i	0.100355	−	0.308862i
$379$	−6.82420	−	4.95807i	−0.350536	−	0.254679i	0.398558	−	0.917143i	$-0.369511\pi$
$379$	−6.82420	−	4.95807i	−0.350536	−	0.254679i	−0.749094	+	0.662464i	$0.769511\pi$
$380$		0			0
$381$	−0.155656	+	0.479059i	−0.00797449	+	0.0245430i
$382$	16.6502	+	51.2439i	0.851896	+	2.62187i
$383$	17.7025	−	12.8616i	0.904558	−	0.657199i	−0.0350750	−	0.999385i	$-0.511167\pi$
$383$	17.7025	−	12.8616i	0.904558	−	0.657199i	0.939633	+	0.342185i	$0.111167\pi$
$384$	57.0153			2.90955
$385$		0			0
$386$	62.6865			3.19066
$387$	5.66568	−	4.11636i	0.288003	−	0.209246i
$388$	15.1931	+	46.7596i	0.771314	+	2.37386i
$389$	−0.121163	+	0.372902i	−0.00614322	+	0.0189069i	−0.954081	−	0.299548i	$-0.903164\pi$
$389$	−0.121163	+	0.372902i	−0.00614322	+	0.0189069i	0.947938	+	0.318455i	$0.103164\pi$
$390$		0			0
$391$	3.42138	+	2.48578i	0.173027	+	0.125711i
$392$	5.72230	−	17.6114i	0.289020	−	0.889512i
$393$	−5.90526	−	18.1745i	−0.297881	−	0.916783i
$394$	−51.6511	+	37.5267i	−2.60215	+	1.89057i
$395$		0			0
$396$	−18.1087	+	5.25499i	−0.909995	+	0.264073i
$397$	−35.7823			−1.79586			−0.897932	−	0.440134i	$-0.854931\pi$
$397$	−35.7823			−1.79586			−0.897932	+	0.440134i	$0.854931\pi$
$398$	−44.0068	+	31.9728i	−2.20586	+	1.60265i
$399$	−3.30508	−	10.1720i	−0.165461	−	0.509237i
$400$		0			0
$401$	−24.6074	−	17.8783i	−1.22884	−	0.892802i	−0.232034	−	0.972708i	$-0.574538\pi$
$401$	−24.6074	−	17.8783i	−1.22884	−	0.892802i	−0.996802	+	0.0799056i	$0.974538\pi$
$402$	−5.54073	−	4.02558i	−0.276347	−	0.200778i
$403$	−0.628526	+	1.93440i	−0.0313091	+	0.0963596i
$404$	−9.98101	−	30.7184i	−0.496574	−	1.52830i
$405$		0			0
$406$	16.7770			0.832627
$407$	27.6524	+	9.96515i	1.37068	+	0.493954i
$408$	−51.0813			−2.52890
$409$	13.1625	−	9.56310i	0.650843	−	0.472865i	−0.212715	−	0.977114i	$-0.568231\pi$
$409$	13.1625	−	9.56310i	0.650843	−	0.472865i	0.863558	+	0.504249i	$0.168231\pi$
$410$		0			0
$411$	3.81475	−	11.7406i	0.188168	−	0.579120i
$412$	−5.96147	−	4.33126i	−0.293701	−	0.213386i
$413$	−7.25248	−	5.26923i	−0.356871	−	0.259282i
$414$	−0.724576	+	2.23002i	−0.0356110	+	0.109599i
$415$		0			0
$416$	9.36298	−	6.80260i	0.459058	−	0.333525i
$417$	7.73236			0.378655
$418$	−26.4738	+	34.1080i	−1.29488	+	1.66828i
$419$	−40.0703			−1.95756			−0.978781	−	0.204910i	$-0.934310\pi$
$419$	−40.0703			−1.95756			−0.978781	+	0.204910i	$0.934310\pi$
$420$		0			0
$421$	−5.99316	−	18.4450i	−0.292089	−	0.898956i	−0.984184	−	0.177150i	$-0.943312\pi$
$421$	−5.99316	−	18.4450i	−0.292089	−	0.898956i	0.692095	−	0.721806i	$-0.256688\pi$
$422$	−0.0427691	+	0.131630i	−0.00208197	+	0.00640764i
$423$	0.378765	+	0.275189i	0.0184162	+	0.0133801i
$424$	89.5825	+	65.0855i	4.35051	+	3.16083i
$425$		0			0
$426$	−9.69229	−	29.8298i	−0.469593	−	1.44526i
$427$	−5.46424	+	3.97000i	−0.264433	+	0.192122i
$428$	69.3640			3.35284
$429$	−0.886111	+	1.14164i	−0.0427819	+	0.0551188i
$430$		0			0
$431$	−27.4616	+	19.9520i	−1.32278	+	0.961056i	−0.322887	+	0.946438i	$0.604653\pi$
$431$	−27.4616	+	19.9520i	−1.32278	+	0.961056i	−0.999893	+	0.0146183i	$0.995347\pi$
$432$	−5.23823	−	16.1216i	−0.252025	−	0.775652i
$433$	4.05291	−	12.4736i	0.194770	−	0.599442i	−0.805209	−	0.592991i	$-0.797947\pi$
$433$	4.05291	−	12.4736i	0.194770	−	0.599442i	0.999979	−	0.00645020i	$-0.00205318\pi$
$434$	−23.8440	−	17.3236i	−1.14455	−	0.831562i
$435$		0			0
$436$	−21.3707	+	65.7723i	−1.02347	+	3.14992i
$437$	1.22738	+	3.77749i	0.0587136	+	0.180702i
$438$	18.9046	−	13.7350i	0.903296	−	0.656283i
$439$	−9.64731			−0.460441			−0.230220	−	0.973138i	$-0.573945\pi$
$439$	−9.64731			−0.460441			−0.230220	+	0.973138i	$0.573945\pi$
$440$		0			0
$441$	−1.81258			−0.0863133
$442$	−4.88630	+	3.55010i	−0.232418	+	0.168861i
$443$	2.75461	+	8.47781i	0.130875	+	0.402793i	0.994926	−	0.100613i	$-0.0320802\pi$
$443$	2.75461	+	8.47781i	0.130875	+	0.402793i	−0.864050	+	0.503405i	$0.832080\pi$
$444$	−15.5697	+	47.9187i	−0.738906	+	2.27412i
$445$		0			0
$446$	−1.69321	−	1.23019i	−0.0801759	−	0.0582512i
$447$	−2.35130	+	7.23654i	−0.111212	+	0.342277i
$448$	27.9614	+	86.0562i	1.32105	+	4.06578i
$449$	10.0616	−	7.31019i	0.474837	−	0.344989i	−0.324487	−	0.945890i	$-0.605191\pi$
$449$	10.0616	−	7.31019i	0.474837	−	0.344989i	0.799323	+	0.600901i	$0.205191\pi$
$450$		0			0
$451$	13.6779	−	3.96921i	0.644066	−	0.186903i
$452$	−0.807599			−0.0379863
$453$	−2.16351	+	1.57188i	−0.101651	+	0.0738536i
$454$	7.09660	+	21.8411i	0.333060	+	1.02505i
$455$		0			0
$456$	−38.8126	−	28.1990i	−1.81757	−	1.32054i
$457$	−30.8707	−	22.4289i	−1.44407	−	1.04918i	−0.987172	−	0.159659i	$-0.948960\pi$
$457$	−30.8707	−	22.4289i	−1.44407	−	1.04918i	−0.456898	−	0.889519i	$-0.651040\pi$
$458$	2.46395	−	7.58327i	0.115133	−	0.354343i
$459$	1.54508	+	4.75528i	0.0721184	+	0.221958i
$460$		0			0
$461$	34.3847			1.60145			0.800726	−	0.599030i	$-0.204447\pi$
$461$	34.3847			1.60145			0.800726	+	0.599030i	$0.204447\pi$
$462$	−11.7653	−	17.3236i	−0.547372	−	0.805969i
$463$	40.2561			1.87086			0.935430	−	0.353511i	$-0.115012\pi$
$463$	40.2561			1.87086			0.935430	+	0.353511i	$0.115012\pi$
$464$	36.4393	−	26.4747i	1.69165	−	1.22906i
$465$		0			0
$466$	−4.43639	+	13.6538i	−0.205512	+	0.632501i
$467$	12.2292	+	8.88502i	0.565899	+	0.411150i	0.833613	−	0.552349i	$-0.186268\pi$
$467$	12.2292	+	8.88502i	0.565899	+	0.411150i	−0.267714	+	0.963498i	$0.586268\pi$
$468$	−2.00415	−	1.45610i	−0.0926417	−	0.0673081i
$469$	1.73876	−	5.35135i	0.0802885	−	0.247102i
$470$		0			0
$471$	−16.3421	+	11.8732i	−0.753005	+	0.547090i
$472$	−40.2110			−1.85086
$473$	0.736752	−	23.2152i	0.0338759	−	1.06744i
$474$	−30.1360			−1.38419
$475$		0			0
$476$	−20.0067	−	61.5743i	−0.917005	−	2.82225i
$477$	3.34932	−	10.3081i	0.153355	−	0.471977i
$478$	24.2955	+	17.6517i	1.11125	+	0.807370i
$479$	23.3033	+	16.9308i	1.06476	+	0.773590i	0.974962	−	0.222370i	$-0.0713794\pi$
$479$	23.3033	+	16.9308i	1.06476	+	0.773590i	0.0897931	+	0.995960i	$0.471379\pi$
$480$		0			0
$481$	1.19332	+	3.67267i	0.0544108	+	0.167459i
$482$	−6.65040	+	4.83180i	−0.302918	+	0.220083i
$483$	−1.92641			−0.0876548
$484$	−23.0575	+	58.1316i	−1.04807	+	2.64234i
$485$		0			0
$486$	−2.24278	+	1.62947i	−0.101734	+	0.0739143i
$487$	−8.91592	−	27.4404i	−0.404019	−	1.24344i	−0.921712	−	0.387876i	$-0.873209\pi$
$487$	−8.91592	−	27.4404i	−0.404019	−	1.24344i	0.517693	−	0.855567i	$-0.326791\pi$
$488$	−9.36204	+	28.8134i	−0.423799	+	1.30432i
$489$	7.92498	+	5.75784i	0.358380	+	0.260378i
$490$		0			0
$491$	−4.61569	+	14.2056i	−0.208303	+	0.641092i	0.791258	+	0.611482i	$0.209426\pi$
$491$	−4.61569	+	14.2056i	−0.208303	+	0.641092i	−0.999562	+	0.0296097i	$0.990574\pi$
$492$	7.54413	+	23.2184i	0.340116	+	1.04677i
$493$	−10.7482	+	7.80906i	−0.484076	+	0.351702i
$494$	−5.67253			−0.255219
$495$		0			0
$496$	−79.1260			−3.55286
$497$	20.8473	−	15.1464i	0.935128	−	0.679410i
$498$	5.07188	+	15.6096i	0.227276	+	0.699484i
$499$	6.85987	−	21.1125i	0.307090	−	0.945125i	−0.671799	−	0.740733i	$-0.734478\pi$
$499$	6.85987	−	21.1125i	0.307090	−	0.945125i	0.978889	−	0.204392i	$-0.0655218\pi$
$500$		0			0
$501$	−20.6927	−	15.0341i	−0.924483	−	0.671676i
$502$	15.0896	−	46.4411i	0.673484	−	2.07277i
$503$	−0.0480077	−	0.147752i	−0.00214056	−	0.00658795i	0.949981	−	0.312309i	$-0.101102\pi$
$503$	−0.0480077	−	0.147752i	−0.00214056	−	0.00658795i	−0.952121	+	0.305721i	$0.901102\pi$
$504$	18.8246	−	13.6768i	0.838513	−	0.609215i
$505$		0			0
$506$	4.36919	+	6.43335i	0.194234	+	0.285997i
$507$	12.8101			0.568918
$508$	−2.31680	+	1.68325i	−0.102791	+	0.0746822i
$509$	−5.75932	−	17.7254i	−0.255277	−	0.785663i	−0.993775	−	0.111407i	$-0.964464\pi$
$509$	−5.75932	−	17.7254i	−0.255277	−	0.785663i	0.738498	−	0.674256i	$-0.235536\pi$
$510$		0			0
$511$	15.5315	+	11.2843i	0.687075	+	0.499189i
$512$	84.0350	+	61.0550i	3.71386	+	2.69828i
$513$	−1.45113	+	4.46612i	−0.0640690	+	0.197184i
$514$	17.9597	+	55.2743i	0.792169	+	2.43804i
$515$		0			0
$516$	39.8145			1.75274
$517$	1.49125	−	0.432749i	0.0655852	−	0.0190323i
$518$	−55.9571			−2.45861
$519$	5.46415	−	3.96994i	0.239850	−	0.174261i
$520$		0			0
$521$	9.69969	−	29.8526i	0.424951	−	1.30786i	−0.478090	−	0.878311i	$-0.658671\pi$
$521$	9.69969	−	29.8526i	0.424951	−	1.30786i	0.903041	−	0.429554i	$-0.141329\pi$
$522$	−5.95930	−	4.32969i	−0.260832	−	0.189505i
$523$	−19.4036	−	14.0975i	−0.848459	−	0.616442i	0.0762616	−	0.997088i	$-0.475702\pi$
$523$	−19.4036	−	14.0975i	−0.848459	−	0.616442i	−0.924721	+	0.380646i	$0.875702\pi$
$524$	33.5727	−	103.326i	1.46663	−	4.51382i
$525$		0			0
$526$	−18.9172	+	13.7441i	−0.824828	+	0.599272i
$527$	23.3392			1.01667
$528$	−52.8914	−	19.0606i	−2.30180	−	0.829504i
$529$	−22.2846			−0.968896
$530$		0			0
$531$	1.21629	+	3.74334i	0.0527823	+	0.162447i
$532$	18.7901	−	57.8300i	0.814655	−	2.50725i
$533$	1.51378	+	1.09982i	0.0655689	+	0.0476386i
$534$	−13.2314	−	9.61320i	−0.572580	−	0.416004i
$535$		0			0
$536$	−7.79929	−	24.0038i	−0.336878	−	1.03680i
$537$	5.27637	−	3.83351i	0.227692	−	0.165428i
$538$	−26.7338			−1.15258
$539$	−3.68605	+	4.74899i	−0.158769	+	0.204554i
$540$		0			0
$541$	−8.06851	+	5.86211i	−0.346892	+	0.252032i	−0.747564	−	0.664190i	$-0.768777\pi$
$541$	−8.06851	+	5.86211i	−0.346892	+	0.252032i	0.400672	+	0.916222i	$0.368777\pi$
$542$	−8.76177	−	26.9660i	−0.376350	−	1.15829i
$543$	−4.24966	+	13.0791i	−0.182370	+	0.561278i
$544$	−107.438	−	78.0586i	−4.60638	−	3.34673i
$545$		0			0
$546$	0.850179	−	2.61658i	0.0363843	−	0.111979i
$547$	12.3659	+	38.0582i	0.528726	+	1.62725i	0.756829	+	0.653614i	$0.226748\pi$
$547$	12.3659	+	38.0582i	0.528726	+	1.62725i	−0.228103	+	0.973637i	$0.573252\pi$
$548$	56.7791	−	41.2524i	2.42548	−	1.76222i
$549$	2.96549			0.126564
$550$		0			0
$551$	−12.4777			−0.531567
$552$	−6.99073	+	5.07906i	−0.297545	+	0.216179i
$553$	−7.65094	−	23.5472i	−0.325351	−	1.00133i
$554$	−5.00209	+	15.3948i	−0.212518	+	0.654064i
$555$		0			0
$556$	35.5645	+	25.8391i	1.50827	+	1.09582i
$557$	2.39812	−	7.38064i	0.101611	−	0.312728i	−0.887309	−	0.461176i	$-0.847428\pi$
$557$	2.39812	−	7.38064i	0.101611	−	0.312728i	0.988920	+	0.148448i	$0.0474278\pi$
$558$	3.99878	+	12.3070i	0.169282	+	0.520996i
$559$	2.46875	−	1.79365i	0.104417	−	0.0758633i
$560$		0			0
$561$	15.6010	+	5.62216i	0.658675	+	0.237368i
$562$	−39.9584			−1.68554
$563$	14.9146	−	10.8361i	0.628577	−	0.456688i	−0.227330	−	0.973818i	$-0.573000\pi$
$563$	14.9146	−	10.8361i	0.628577	−	0.456688i	0.855907	+	0.517130i	$0.173000\pi$
$564$	0.822511	+	2.53143i	0.0346340	+	0.106592i
$565$		0			0
$566$	23.8484	+	17.3269i	1.00242	+	0.728304i
$567$	−1.84261	−	1.33873i	−0.0773823	−	0.0562216i
$568$	35.7182	−	109.929i	1.49870	−	4.61253i
$569$	3.40658	+	10.4844i	0.142811	+	0.439528i	0.996723	−	0.0808896i	$-0.0257761\pi$
$569$	3.40658	+	10.4844i	0.142811	+	0.439528i	−0.853912	+	0.520418i	$0.825776\pi$
$570$		0			0
$571$	−38.1338			−1.59585			−0.797926	−	0.602756i	$-0.794069\pi$
$571$	−38.1338			−1.59585			−0.797926	+	0.602756i	$0.794069\pi$
$572$	−7.89062	+	2.28979i	−0.329923	+	0.0957410i
$573$	19.4360			0.811952
$574$	−21.9352	+	15.9368i	−0.915556	+	0.665191i
$575$		0			0
$576$	12.2767	−	37.7839i	0.511530	−	1.57433i
$577$	8.90910	+	6.47284i	0.370891	+	0.269468i	0.757580	−	0.652742i	$-0.226382\pi$
$577$	8.90910	+	6.47284i	0.370891	+	0.269468i	−0.386690	+	0.922210i	$0.626382\pi$
$578$	17.9422	+	13.0358i	0.746297	+	0.542217i
$579$	6.98760	−	21.5056i	0.290395	−	0.893743i
$580$		0			0
$581$	−10.9092	+	7.92597i	−0.452589	+	0.328825i
$582$	23.9743			0.993765
$583$	−20.1964	−	29.7378i	−0.836448	−	1.23162i
$584$	86.1138			3.56341
$585$		0			0
$586$	−7.19234	−	22.1358i	−0.297113	−	0.914420i
$587$	−3.65999	+	11.2643i	−0.151064	+	0.464927i	−0.997741	−	0.0671803i	$-0.978600\pi$
$587$	−3.65999	+	11.2643i	−0.151064	+	0.464927i	0.846677	+	0.532107i	$0.178600\pi$
$588$	−8.33685	−	6.05707i	−0.343806	−	0.249790i
$589$	17.7337	+	12.8843i	0.730703	+	0.530887i
$590$		0			0
$591$	7.11666	+	21.9028i	0.292740	+	0.900962i
$592$	−121.538	+	88.3024i	−4.99517	+	3.62920i
$593$	−9.25062			−0.379877			−0.189939	−	0.981796i	$-0.560829\pi$
$593$	−9.25062			−0.379877			−0.189939	+	0.981796i	$0.560829\pi$
$594$	−0.291645	+	9.18980i	−0.0119663	+	0.377062i
$595$		0			0
$596$	−34.9969	+	25.4267i	−1.43353	+	1.04152i
$597$	6.06340	+	18.6612i	0.248158	+	0.763753i
$598$	−0.315724	+	0.971700i	−0.0129109	+	0.0397358i
$599$	−19.1603	−	13.9208i	−0.782868	−	0.568787i	0.122971	−	0.992410i	$-0.460758\pi$
$599$	−19.1603	−	13.9208i	−0.782868	−	0.568787i	−0.905838	+	0.423624i	$0.860758\pi$
$600$		0			0
$601$	11.2090	−	34.4978i	0.457225	−	1.40719i	−0.411278	−	0.911510i	$-0.634917\pi$
$601$	11.2090	−	34.4978i	0.457225	−	1.40719i	0.868503	−	0.495684i	$-0.165083\pi$
$602$	13.6641	+	42.0537i	0.556907	+	1.71398i
$603$	−1.99866	+	1.45211i	−0.0813918	+	0.0591346i
$604$	−15.2037			−0.618630
$605$		0			0
$606$	−15.7497			−0.639789
$607$	−19.8264	+	14.4047i	−0.804728	+	0.584669i	−0.912297	−	0.409528i	$-0.865693\pi$
$607$	−19.8264	+	14.4047i	−0.804728	+	0.584669i	0.107569	+	0.994198i	$0.465693\pi$
$608$	−38.5424	−	118.621i	−1.56310	−	4.81072i
$609$	1.87011	−	5.75562i	0.0757808	−	0.233229i
$610$		0			0
$611$	0.165042	+	0.119910i	0.00667688	+	0.00485103i
$612$	−8.78415	+	27.0348i	−0.355078	+	1.09282i
$613$	−1.43538	−	4.41763i	−0.0579743	−	0.178427i	0.917876	−	0.396868i	$-0.129903\pi$
$613$	−1.43538	−	4.41763i	−0.0579743	−	0.178427i	−0.975850	+	0.218441i	$0.929903\pi$
$614$	−10.1351	+	7.36361i	−0.409021	+	0.297171i
$615$		0			0
$616$	2.44790	−	77.1339i	0.0986288	−	3.10781i
$617$	−41.7419			−1.68047			−0.840233	−	0.542226i	$-0.817582\pi$
$617$	−41.7419			−1.68047			−0.840233	+	0.542226i	$0.817582\pi$
$618$	−2.90693	+	2.11201i	−0.116934	+	0.0849574i
$619$	−13.6592	−	42.0385i	−0.549008	−	1.68967i	−0.711266	−	0.702923i	$-0.751878\pi$
$619$	−13.6592	−	42.0385i	−0.549008	−	1.68967i	0.162258	−	0.986748i	$-0.448122\pi$
$620$		0			0
$621$	0.684276	+	0.497155i	0.0274590	+	0.0199502i
$622$	53.8199	+	39.1024i	2.15798	+	1.56786i
$623$	4.15221	−	12.7792i	0.166355	−	0.511987i
$624$	−2.28249	−	7.02479i	−0.0913728	−	0.281217i
$625$		0			0
$626$	−71.7136			−2.86625
$627$	8.75031	+	12.8843i	0.349454	+	0.514548i
$628$	−114.841			−4.58267
$629$	35.8491	−	26.0459i	1.42940	−	1.03852i
$630$		0			0
$631$	−4.98015	+	15.3273i	−0.198257	+	0.610171i	0.801667	+	0.597771i	$0.203947\pi$
$631$	−4.98015	+	15.3273i	−0.198257	+	0.610171i	−0.999923	+	0.0123995i	$0.996053\pi$
$632$	−89.8475	−	65.2780i	−3.57394	−	2.59662i
$633$	0.0403903	+	0.0293453i	0.00160537	+	0.00116637i
$634$	2.48706	−	7.65439i	0.0987739	−	0.303995i
$635$		0			0
$636$	49.8516	−	36.2193i	1.97674	−	1.43619i
$637$	−0.789807			−0.0312933
$638$	−23.4627	+	6.80867i	−0.928896	+	0.269558i
$639$	−11.3140			−0.447575
$640$		0			0
$641$	−2.84600	−	8.75909i	−0.112410	−	0.345963i	0.878988	−	0.476844i	$-0.158219\pi$
$641$	−2.84600	−	8.75909i	−0.112410	−	0.345963i	−0.991398	+	0.130881i	$0.958219\pi$
$642$	10.4520	−	32.1678i	0.412506	−	1.26956i
$643$	3.24845	+	2.36014i	0.128106	+	0.0930747i	0.649993	−	0.759940i	$-0.274772\pi$
$643$	3.24845	+	2.36014i	0.128106	+	0.0930747i	−0.521887	+	0.853015i	$0.674772\pi$
$644$	−8.86041	−	6.43747i	−0.349149	−	0.253672i
$645$		0			0
$646$	20.1143	+	61.9054i	0.791386	+	2.43564i
$647$	11.5441	−	8.38728i	0.453846	−	0.329738i	−0.337267	−	0.941409i	$-0.609502\pi$
$647$	11.5441	−	8.38728i	0.453846	−	0.329738i	0.791112	+	0.611671i	$0.209502\pi$
$648$	−10.2163			−0.401332
$649$	12.2811	+	4.42574i	0.482073	+	0.173726i
$650$		0			0
$651$	−8.60102	+	6.24901i	−0.337101	+	0.244918i
$652$	17.2096	+	52.9656i	0.673979	+	2.07429i
$653$	2.01532	−	6.20252i	0.0788656	−	0.242723i	−0.903849	−	0.427852i	$-0.859270\pi$
$653$	2.01532	−	6.20252i	0.0788656	−	0.242723i	0.982714	+	0.185129i	$0.0592703\pi$
$654$	27.2819	+	19.8215i	1.06681	+	0.775082i
$655$		0			0
$656$	−22.4939	+	69.2291i	−0.878239	+	2.70294i
$657$	−2.60474	−	8.01655i	−0.101620	−	0.312755i
$658$	−2.39152	+	1.73754i	−0.0932311	+	0.0677363i
$659$	6.74928			0.262915			0.131457	−	0.991322i	$-0.458034\pi$
$659$	6.74928			0.262915			0.131457	+	0.991322i	$0.458034\pi$
$660$		0			0
$661$	9.65248			0.375438			0.187719	−	0.982223i	$-0.439891\pi$
$661$	9.65248			0.375438			0.187719	+	0.982223i	$0.439891\pi$
$662$	24.6340	−	17.8977i	0.957429	−	0.695613i
$663$	0.673251	+	2.07205i	0.0261469	+	0.0804718i
$664$	−18.6910	+	57.5249i	−0.725351	+	2.23240i
$665$		0			0
$666$	19.8764	+	14.4410i	0.770193	+	0.559578i
$667$	−0.694489	+	2.13742i	−0.0268907	+	0.0827612i
$668$	−44.9355	−	138.297i	−1.73861	−	5.35088i
$669$	−0.610777	+	0.443756i	−0.0236140	+	0.0171566i
$670$		0			0
$671$	6.03060	−	7.76964i	0.232809	−	0.299944i
$672$	60.4934			2.33358
$673$	−22.9433	+	16.6693i	−0.884398	+	0.642553i	−0.934411	−	0.356196i	$-0.884074\pi$
$673$	−22.9433	+	16.6693i	−0.884398	+	0.642553i	0.0500135	+	0.998749i	$0.484074\pi$
$674$	11.0048	+	33.8694i	0.423891	+	1.30460i
$675$		0			0
$676$	58.9194	+	42.8075i	2.26613	+	1.64644i
$677$	−4.11544	−	2.99004i	−0.158169	−	0.114917i	0.505885	−	0.862601i	$-0.331166\pi$
$677$	−4.11544	−	2.99004i	−0.158169	−	0.114917i	−0.664055	+	0.747684i	$0.731166\pi$
$678$	−0.121691	+	0.374527i	−0.00467352	+	0.0143836i
$679$	6.08661	+	18.7327i	0.233583	+	0.718893i
$680$		0			0
$681$	8.28399			0.317443
$682$	40.3764	+	14.5505i	1.54609	+	0.557167i
$683$	−17.3612			−0.664310			−0.332155	−	0.943225i	$-0.607776\pi$
$683$	−17.3612			−0.664310			−0.332155	+	0.943225i	$0.607776\pi$
$684$	−21.5988	+	15.6924i	−0.825849	+	0.600015i
$685$		0			0
$686$	17.1945	−	52.9192i	0.656489	−	2.02046i
$687$	−2.32691	−	1.69060i	−0.0887772	−	0.0645004i
$688$	96.0406	+	69.7776i	3.66151	+	2.66024i
$689$	1.45942	−	4.49164i	0.0555995	−	0.171118i
$690$		0			0
$691$	34.7708	−	25.2625i	1.32274	−	0.961029i	0.322850	−	0.946450i	$-0.395359\pi$
$691$	34.7708	−	25.2625i	1.32274	−	0.961029i	0.999894	−	0.0145791i	$-0.00464085\pi$
$692$	38.3983			1.45969
$693$	−7.25463	+	2.10523i	−0.275581	+	0.0799712i
$694$	−5.23870			−0.198858
$695$		0			0
$696$	−8.38849	−	25.8171i	−0.317965	−	0.978595i
$697$	6.63486	−	20.4200i	0.251313	−	0.773463i
$698$	53.3302	+	38.7467i	2.01858	+	1.46658i
$699$	4.18964	+	3.04395i	0.158467	+	0.115133i
$700$		0			0
$701$	−4.44621	−	13.6840i	−0.167931	−	0.516838i	0.831309	−	0.555810i	$-0.187592\pi$
$701$	−4.44621	−	13.6840i	−0.167931	−	0.516838i	−0.999240	+	0.0389718i	$0.987592\pi$
$702$	−0.977260	+	0.710021i	−0.0368843	+	0.0267980i
$703$	41.6174			1.56963
$704$	−74.0286	−	109.002i	−2.79006	−	4.10818i
$705$		0			0
$706$	45.3701	−	32.9633i	1.70753	−	1.24059i
$707$	−3.99855	−	12.3063i	−0.150381	−	0.462825i
$708$	−6.91485	+	21.2817i	−0.259876	+	0.799816i
$709$	−41.4016	−	30.0800i	−1.55487	−	1.12968i	−0.940064	−	0.340998i	$-0.889235\pi$
$709$	−41.4016	−	30.0800i	−1.55487	−	1.12968i	−0.614805	−	0.788680i	$-0.710765\pi$
$710$		0			0
$711$	−3.35923	+	10.3386i	−0.125981	+	0.387729i
$712$	−18.6250	−	57.3217i	−0.698000	−	2.14822i
$713$	3.19409	−	2.32065i	0.119620	−	0.0869088i
$714$	−31.5700			−1.18148
$715$		0			0
$716$	37.0787			1.38570
$717$	8.76390	−	6.36734i	0.327294	−	0.237793i
$718$	15.9252	+	49.0126i	0.594322	+	1.82913i
$719$	16.0803	−	49.4902i	0.599696	−	1.84567i	0.0698891	−	0.997555i	$-0.477735\pi$
$719$	16.0803	−	49.4902i	0.599696	−	1.84567i	0.529806	−	0.848119i	$-0.322265\pi$
$720$		0			0
$721$	−2.38826	−	1.73517i	−0.0889435	−	0.0646213i
$722$	−2.61454	+	8.04673i	−0.0973032	+	0.299468i
$723$	0.916315	+	2.82013i	0.0340781	+	0.104882i
$724$	−63.2523	+	45.9555i	−2.35075	+	1.70792i
$725$		0			0
$726$	23.4844	+	19.4524i	0.871586	+	0.721947i
$727$	18.2951			0.678528			0.339264	−	0.940691i	$-0.389822\pi$
$727$	18.2951			0.678528			0.339264	+	0.940691i	$0.389822\pi$
$728$	8.20256	−	5.95951i	0.304007	−	0.220874i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−28.3284	−	20.5818i	−1.04776	−	0.761245i
$732$	13.6396	+	9.90974i	0.504134	+	0.366275i
$733$	−11.5929	+	35.6792i	−0.428192	+	1.31784i	0.471712	+	0.881753i	$0.343636\pi$
$733$	−11.5929	+	35.6792i	−0.428192	+	1.31784i	−0.899904	+	0.436088i	$0.856364\pi$
$734$	5.06126	+	15.5770i	0.186815	+	0.574956i
$735$		0			0
$736$	−22.4649			−0.828069
$737$	−0.259901	+	8.18953i	−0.00957358	+	0.301665i
$738$	11.9044			0.438207
$739$	22.0973	−	16.0546i	0.812863	−	0.590579i	−0.101796	−	0.994805i	$-0.532459\pi$
$739$	22.0973	−	16.0546i	0.812863	−	0.590579i	0.914659	+	0.404226i	$0.132459\pi$
$740$		0			0
$741$	−0.632311	+	1.94605i	−0.0232285	+	0.0714900i
$742$	55.3650	+	40.2250i	2.03251	+	1.47671i
$743$	15.2284	+	11.0641i	0.558677	+	0.405902i	0.830974	−	0.556311i	$-0.187784\pi$
$743$	15.2284	+	11.0641i	0.558677	+	0.405902i	−0.272298	+	0.962213i	$0.587784\pi$
$744$	−14.7364	+	45.3539i	−0.540262	+	1.66275i
$745$		0			0
$746$	3.74525	−	2.72108i	0.137123	−	0.0996259i
$747$	5.92050			0.216620
$748$	52.9684	+	77.9925i	1.93672	+	2.85169i
$749$	27.7884			1.01536
$750$		0			0
$751$	−7.78395	−	23.9565i	−0.284040	−	0.874186i	−0.986685	−	0.162645i	$-0.947997\pi$
$751$	−7.78395	−	23.9565i	−0.284040	−	0.874186i	0.702644	−	0.711541i	$-0.252003\pi$
$752$	−2.45243	+	7.54781i	−0.0894310	+	0.275240i
$753$	−14.2504	−	10.3535i	−0.519312	−	0.377302i
$754$	−2.59669	−	1.88660i	−0.0945658	−	0.0687061i
$755$		0			0
$756$	−4.00134	−	12.3149i	−0.145527	−	0.447887i
$757$	37.0481	−	26.9170i	1.34653	−	0.978315i	0.347358	−	0.937733i	$-0.387079\pi$
$757$	37.0481	−	26.9170i	1.34653	−	0.978315i	0.999176	−	0.0405820i	$-0.0129212\pi$
$758$	−23.3842			−0.849352
$759$	2.69409	−	0.781804i	0.0977894	−	0.0283777i
$760$		0			0
$761$	−6.48664	+	4.71282i	−0.235141	+	0.170840i	−0.699116	−	0.715009i	$-0.746423\pi$
$761$	−6.48664	+	4.71282i	−0.235141	+	0.170840i	0.463975	+	0.885848i	$0.346423\pi$
$762$	0.431513	+	1.32806i	0.0156321	+	0.0481105i
$763$	−8.56146	+	26.3495i	−0.309946	+	0.953914i
$764$	89.3949	+	64.9492i	3.23419	+	2.34978i
$765$		0			0
$766$	18.7451	−	57.6916i	0.677289	−	2.08448i
$767$	0.529980	+	1.63111i	0.0191365	+	0.0588960i
$768$	63.5907	−	46.2014i	2.29463	−	1.66715i
$769$	40.0439			1.44402			0.722010	−	0.691883i	$-0.243218\pi$
$769$	40.0439			1.44402			0.722010	+	0.691883i	$0.243218\pi$
$770$		0			0
$771$	20.9647			0.755025
$772$	104.004	−	75.5634i	3.74319	−	2.71959i
$773$	7.36232	+	22.6589i	0.264804	+	0.814984i	0.991738	+	0.128277i	$0.0409445\pi$
$773$	7.36232	+	22.6589i	0.264804	+	0.814984i	−0.726934	+	0.686707i	$0.759055\pi$
$774$	5.99936	−	18.4641i	0.215643	−	0.663680i
$775$		0			0
$776$	71.4770	+	51.9311i	2.56588	+	1.86422i
$777$	−6.23748	+	19.1970i	−0.223768	+	0.688688i
$778$	0.335891	+	1.03377i	0.0120423	+	0.0370624i
$779$	16.3140	−	11.8528i	0.584511	−	0.424672i
$780$		0			0
$781$	−23.0081	+	29.6429i	−0.823293	+	1.06071i
$782$	11.7239			0.419245
$783$	−2.14965	+	1.56181i	−0.0768222	+	0.0558146i
$784$	−9.49471	−	29.2217i	−0.339097	−	1.04363i
$785$		0			0
$786$	−42.8590	−	31.1389i	−1.52873	−	1.11069i
$787$	−7.67659	−	5.57737i	−0.273641	−	0.198812i	0.442498	−	0.896769i	$-0.354092\pi$
$787$	−7.67659	−	5.57737i	−0.273641	−	0.198812i	−0.716139	+	0.697958i	$0.754092\pi$
$788$	−40.4598	+	124.522i	−1.44132	+	4.43593i
$789$	2.60647	+	8.02189i	0.0927928	+	0.285587i
$790$		0			0
$791$	−0.323537			−0.0115037
$792$	−20.7757	+	26.7668i	−0.738232	+	0.951116i
$793$	1.29217			0.0458864
$794$	−80.2517	+	58.3063i	−2.84803	+	2.06921i
$795$		0			0
$796$	−34.4718	+	106.093i	−1.22182	+	3.76037i
$797$	−19.2254	−	13.9680i	−0.680998	−	0.494774i	0.192691	−	0.981259i	$-0.438279\pi$
$797$	−19.2254	−	13.9680i	−0.680998	−	0.494774i	−0.873688	+	0.486486i	$0.838279\pi$
$798$	−23.9875	−	17.4280i	−0.849149	−	0.616943i
$799$	0.723376	−	2.22632i	0.0255912	−	0.0787617i
$800$		0			0
$801$	−4.77286	+	3.46769i	−0.168641	+	0.122525i
$802$	−84.3212			−2.97749
$803$	−26.3005	−	9.47795i	−0.928124	−	0.334469i
$804$	−14.0452			−0.495337
$805$		0			0
$806$	1.74241	+	5.36260i	0.0613739	+	0.188890i
$807$	−2.97999	+	9.17148i	−0.104901	+	0.322851i
$808$	−46.9563	−	34.1158i	−1.65192	−	1.20019i
$809$	14.8963	+	10.8228i	0.523726	+	0.380509i	0.818006	−	0.575210i	$-0.195080\pi$
$809$	14.8963	+	10.8228i	0.523726	+	0.380509i	−0.294280	+	0.955719i	$0.595080\pi$
$810$		0			0
$811$	7.30675	+	22.4879i	0.256575	+	0.789656i	0.993515	+	0.113698i	$0.0362697\pi$
$811$	7.30675	+	22.4879i	0.256575	+	0.789656i	−0.736941	+	0.675957i	$0.763730\pi$
$812$	27.8350	−	20.2233i	0.976815	−	0.709698i
$813$	−10.2278			−0.358704
$814$	78.2562	−	22.7093i	2.74288	−	0.795960i
$815$		0			0
$816$	−68.5694	+	49.8186i	−2.40041	+	1.74400i
$817$	−10.1625	−	31.2770i	−0.355541	−	1.09424i
$818$	13.9377	−	42.8958i	0.487320	−	1.49982i
$819$	−0.802893	−	0.583336i	−0.0280554	−	0.0203834i
$820$		0			0
$821$	8.13186	−	25.0273i	0.283804	−	0.873459i	−0.702951	−	0.711239i	$-0.748135\pi$
$821$	8.13186	−	25.0273i	0.283804	−	0.873459i	0.986755	−	0.162220i	$-0.0518654\pi$
$822$	−10.5753	−	32.5475i	−0.368857	−	1.13522i
$823$	32.7100	−	23.7652i	1.14020	−	0.828403i	0.153051	−	0.988218i	$-0.451090\pi$
$823$	32.7100	−	23.7652i	1.14020	−	0.828403i	0.987147	+	0.159816i	$0.0510900\pi$
$824$	−13.2416			−0.461293
$825$		0			0
$826$	−24.8517			−0.864703
$827$	13.4238	−	9.75293i	0.466790	−	0.339143i	−0.329399	−	0.944191i	$-0.606846\pi$
$827$	13.4238	−	9.75293i	0.466790	−	0.339143i	0.796189	+	0.605048i	$0.206846\pi$
$828$	1.48595	+	4.57327i	0.0516402	+	0.158932i
$829$	−10.6015	+	32.6281i	−0.368206	+	1.13322i	0.579743	+	0.814800i	$0.303153\pi$
$829$	−10.6015	+	32.6281i	−0.368206	+	1.13322i	−0.947949	+	0.318422i	$0.896847\pi$
$830$		0			0
$831$	4.72388	+	3.43210i	0.163869	+	0.119058i
$832$	5.34942	−	16.4638i	0.185458	−	0.570781i
$833$	2.80059	+	8.61932i	0.0970346	+	0.298642i
$834$	17.3419	−	12.5997i	0.600502	−	0.436290i
$835$		0			0
$836$	−2.80865	+	88.5012i	−0.0971393	+	3.06088i
$837$	4.66785			0.161344
$838$	−89.8686	+	65.2934i	−3.10446	+	2.25552i
$839$	−1.04698	−	3.22229i	−0.0361459	−	0.111246i	0.931356	−	0.364111i	$-0.118627\pi$
$839$	−1.04698	−	3.22229i	−0.0361459	−	0.111246i	−0.967502	+	0.252865i	$0.918627\pi$
$840$		0			0
$841$	17.7496	+	12.8959i	0.612056	+	0.444685i
$842$	−43.4970	−	31.6024i	−1.49901	−	1.08909i
$843$	−4.45412	+	13.7084i	−0.153408	+	0.472142i
$844$	0.0877101	+	0.269944i	0.00301910	+	0.00929185i
$845$		0			0
$846$	1.29790			0.0446226
$847$	−9.23721	+	23.2884i	−0.317394	+	0.800201i
$848$	183.729			6.30926
$849$	8.60264	−	6.25018i	0.295242	−	0.214506i
$850$		0			0
$851$	2.31636	−	7.12903i	0.0794039	−	0.244380i
$852$	−52.0380	−	37.8078i	−1.78279	−	1.29527i
$853$	13.2728	+	9.64323i	0.454451	+	0.330178i	0.791351	−	0.611363i	$-0.209378\pi$
$853$	13.2728	+	9.64323i	0.454451	+	0.330178i	−0.336900	+	0.941541i	$0.609378\pi$
$854$	−5.78606	+	17.8076i	−0.197995	+	0.609365i
$855$		0			0
$856$	100.841	−	73.2651i	3.44667	−	2.50415i
$857$	3.37817			0.115396			0.0576981	−	0.998334i	$-0.481624\pi$
$857$	3.37817			0.115396			0.0576981	+	0.998334i	$0.481624\pi$
$858$	−0.127081	+	4.00433i	−0.00433846	+	0.136706i
$859$	−2.32376			−0.0792855			−0.0396428	−	0.999214i	$-0.512622\pi$
$859$	−2.32376			−0.0792855			−0.0396428	+	0.999214i	$0.512622\pi$
$860$		0			0
$861$	3.02230	+	9.30168i	0.103000	+	0.317001i
$862$	−29.0790	+	89.4959i	−0.990434	+	3.04824i
$863$	−16.3949	−	11.9116i	−0.558090	−	0.405476i	0.272670	−	0.962108i	$-0.412093\pi$
$863$	−16.3949	−	11.9116i	−0.558090	−	0.405476i	−0.830759	+	0.556632i	$0.812093\pi$
$864$	−21.4877	−	15.6117i	−0.731026	−	0.531121i
$865$		0			0
$866$	−11.2356	−	34.5795i	−0.381800	−	1.17506i
$867$	6.47214	−	4.70228i	0.219805	−	0.159698i
$868$	−60.4421			−2.05154
$869$	20.2561	+	29.8258i	0.687142	+	1.01177i
$870$		0			0
$871$	−0.870890	+	0.632739i	−0.0295090	+	0.0214395i
$872$	38.4029	+	118.192i	1.30048	+	4.00248i
$873$	2.67239	−	8.22477i	0.0904466	−	0.278366i
$874$	8.90806	+	6.47209i	0.301320	+	0.218922i
$875$		0			0
$876$	14.8085	−	45.5759i	0.500333	−	1.53987i
$877$	5.13611	+	15.8073i	0.173434	+	0.533775i	0.999558	−	0.0297127i	$-0.00945925\pi$
$877$	5.13611	+	15.8073i	0.173434	+	0.533775i	−0.826125	+	0.563488i	$0.809459\pi$
$878$	−21.6367	+	15.7200i	−0.730205	+	0.530525i
$879$	−8.39576			−0.283182
$880$		0			0
$881$	−29.8895			−1.00700			−0.503502	−	0.863994i	$-0.667955\pi$
$881$	−29.8895			−1.00700			−0.503502	+	0.863994i	$0.667955\pi$
$882$	−4.06521	+	2.95355i	−0.136883	+	0.0994511i
$883$	−4.33042	−	13.3277i	−0.145730	−	0.448511i	0.851374	−	0.524559i	$-0.175770\pi$
$883$	−4.33042	−	13.3277i	−0.145730	−	0.448511i	−0.997104	+	0.0760479i	$0.975770\pi$
$884$	−3.82758	+	11.7801i	−0.128735	+	0.396207i
$885$		0			0
$886$	19.9923	+	14.5253i	0.671655	+	0.487986i
$887$	−8.84040	+	27.2079i	−0.296831	+	0.913553i	0.685769	+	0.727820i	$0.259466\pi$
$887$	−8.84040	+	27.2079i	−0.296831	+	0.913553i	−0.982600	+	0.185734i	$0.940534\pi$
$888$	27.9785	+	86.1091i	0.938898	+	2.88963i
$889$	−0.928146	+	0.674338i	−0.0311290	+	0.0226166i
$890$		0			0
$891$	3.12020	+	1.12443i	0.104531	+	0.0376699i
$892$	−4.29213			−0.143711
$893$	1.77866	−	1.29227i	0.0595207	−	0.0432443i
$894$	6.51832	+	20.0613i	0.218005	+	0.670951i
$895$		0			0
$896$	105.057	+	76.3284i	3.50971	+	2.54995i
$897$	0.298164	+	0.216629i	0.00995541	+	0.00723303i
$898$	10.6542	−	32.7902i	0.355535	−	1.09422i
$899$	3.83274	+	11.7959i	0.127829	+	0.393417i
$900$		0			0
$901$	−54.1931			−1.80543
$902$	24.2087	−	31.1898i	0.806062	−	1.03851i
$903$	15.9504			0.530794
$904$	−1.17408	+	0.853019i	−0.0390493	+	0.0283710i
$905$		0			0
$906$	−2.29093	+	7.05077i	−0.0761112	+	0.234246i
$907$	21.8186	+	15.8521i	0.724474	+	0.526361i	0.887811	−	0.460209i	$-0.152226\pi$
$907$	21.8186	+	15.8521i	0.724474	+	0.526361i	−0.163336	+	0.986570i	$0.552226\pi$
$908$	38.1017	+	27.6825i	1.26445	+	0.918677i
$909$	−1.75561	+	5.40320i	−0.0582298	+	0.179213i
$910$		0			0
$911$	−5.77363	+	4.19479i	−0.191289	+	0.138980i	−0.679308	−	0.733854i	$-0.737720\pi$
$911$	−5.77363	+	4.19479i	−0.191289	+	0.138980i	0.488019	+	0.872833i	$0.337720\pi$
$912$	−79.6025			−2.63590
$913$	12.0399	−	15.5118i	0.398462	−	0.513366i
$914$	−105.783			−3.49900
$915$		0			0
$916$	−5.05303	−	15.5516i	−0.166957	−	0.513840i
$917$	13.4498	−	41.3941i	0.444150	−	1.36695i
$918$	11.2139	+	8.14736i	0.370113	+	0.268903i
$919$	5.57755	+	4.05233i	0.183987	+	0.133674i	0.675966	−	0.736933i	$-0.263727\pi$
$919$	5.57755	+	4.05233i	0.183987	+	0.133674i	−0.491980	+	0.870607i	$0.663727\pi$
$920$		0			0
$921$	1.39645	+	4.29784i	0.0460147	+	0.141619i
$922$	77.1171	−	56.0288i	2.53971	−	1.84521i
$923$	−4.92992			−0.162270
$924$	−40.4023	−	14.5598i	−1.32914	−	0.478983i
$925$		0			0
$926$	90.2854	−	65.5962i	2.96696	−	2.15563i
$927$	0.400526	+	1.23269i	0.0131550	+	0.0404869i
$928$	21.8084	−	67.1194i	0.715896	−	2.20330i
$929$	29.4333	+	21.3846i	0.965676	+	0.701605i	0.954462	−	0.298332i	$-0.0964304\pi$
$929$	29.4333	+	21.3846i	0.965676	+	0.701605i	0.0112141	+	0.999937i	$0.496430\pi$
$930$		0			0
$931$	−2.63029	+	8.09519i	−0.0862042	+	0.265309i
$932$	9.09807	+	28.0010i	0.298017	+	0.917202i
$933$	19.4140	−	14.1051i	0.635585	−	0.461780i
$934$	41.9052			1.37118
$935$		0			0
$936$	−4.45160			−0.145505
$937$	42.6299	−	30.9724i	1.39266	−	1.01183i	0.397090	−	0.917780i	$-0.370020\pi$
$937$	42.6299	−	30.9724i	1.39266	−	1.01183i	0.995568	−	0.0940454i	$-0.0299799\pi$
$938$	−4.82023	−	14.8351i	−0.157386	−	0.484385i
$939$	−7.99384	+	24.6025i	−0.260869	+	0.802873i
$940$		0			0
$941$	16.4217	+	11.9311i	0.535334	+	0.388943i	0.822349	−	0.568983i	$-0.192663\pi$
$941$	16.4217	+	11.9311i	0.535334	+	0.388943i	−0.287015	+	0.957926i	$0.592663\pi$
$942$	−17.3046	+	53.2581i	−0.563814	+	1.73524i
$943$	−1.12237	−	3.45429i	−0.0365493	−	0.112487i
$944$	−53.9776	+	39.2170i	−1.75682	+	1.27640i
$945$		0			0
$946$	−36.1761	−	53.2670i	−1.17619	−	1.73186i
$947$	−14.5680			−0.473395			−0.236698	−	0.971583i	$-0.576065\pi$
$947$	−14.5680			−0.473395			−0.236698	+	0.971583i	$0.576065\pi$
$948$	−49.9991	+	36.3264i	−1.62389	+	1.17983i
$949$	−1.13498	−	3.49311i	−0.0368430	−	0.113391i
$950$		0			0
$951$	−2.34873	−	1.70645i	−0.0761629	−	0.0553356i
$952$	−94.1228	−	68.3842i	−3.05054	−	2.21635i
$953$	12.2078	−	37.5718i	0.395450	−	1.21707i	−0.533160	−	0.846014i	$-0.678996\pi$
$953$	12.2078	−	37.5718i	0.395450	−	1.21707i	0.928610	−	0.371056i	$-0.121004\pi$
$954$	−9.28505	−	28.5765i	−0.300615	−	0.925197i
$955$		0			0
$956$	61.5867			1.99186
$957$	−0.279535	+	8.80821i	−0.00903609	+	0.284729i
$958$	79.8524			2.57991
$959$	22.7466	−	16.5264i	0.734526	−	0.533665i
$960$		0			0
$961$	−2.84642	+	8.76037i	−0.0918199	+	0.282592i
$962$	8.66086	+	6.29248i	0.279237	+	0.202878i
$963$	−9.87063	−	7.17143i	−0.318077	−	0.231096i
$964$	−5.20945	+	16.0330i	−0.167785	+	0.516389i
$965$		0			0
$966$	−4.32051	+	3.13903i	−0.139010	+	0.100997i
$967$	44.8051			1.44083			0.720417	−	0.693541i	$-0.243950\pi$
$967$	44.8051			1.44083			0.720417	+	0.693541i	$0.243950\pi$
$968$	27.8801	+	108.865i	0.896102	+	3.49907i
$969$	23.4798			0.754279
$970$		0			0
$971$	5.60723	+	17.2573i	0.179945	+	0.553812i	0.999825	−	0.0187228i	$-0.00596000\pi$
$971$	5.60723	+	17.2573i	0.179945	+	0.553812i	−0.819880	+	0.572535i	$0.805960\pi$
$972$	−1.75683	+	5.40697i	−0.0563503	+	0.173428i
$973$	14.2477	+	10.3516i	0.456761	+	0.331856i
$974$	−64.7097	−	47.0144i	−2.07343	−	1.50644i
$975$		0			0
$976$	15.5339	+	47.8085i	0.497229	+	1.53031i
$977$	42.0662	−	30.5629i	1.34582	−	0.977794i	0.346609	−	0.938010i	$-0.387333\pi$
$977$	42.0662	−	30.5629i	1.34582	−	0.977794i	0.999208	−	0.0397838i	$-0.0126669\pi$
$978$	27.1562			0.868359
$979$	−0.620652	+	19.5569i	−0.0198361	+	0.625040i
$980$		0			0
$981$	9.84118	−	7.15004i	0.314205	−	0.228283i
$982$	12.7957	+	39.3812i	0.408328	+	1.25671i
$983$	−13.6994	+	42.1625i	−0.436943	+	1.34477i	0.454139	+	0.890931i	$0.349947\pi$
$983$	−13.6994	+	42.1625i	−0.436943	+	1.34477i	−0.891082	+	0.453842i	$0.850053\pi$
$984$	35.4919	+	25.7863i	1.13144	+	0.822039i
$985$		0			0
$986$	−11.3813	+	35.0279i	−0.362453	+	1.11552i
$987$	0.329511	+	1.01413i	0.0104885	+	0.0322801i
$988$	−9.41138	+	6.83777i	−0.299416	+	0.217538i
$989$	−5.92336			−0.188352
$990$		0			0
$991$	10.4084			0.330635			0.165317	−	0.986240i	$-0.447135\pi$
$991$	10.4084			0.330635			0.165317	+	0.986240i	$0.447135\pi$
$992$	−100.301	+	72.8731i	−3.18457	+	2.31372i
$993$	−3.39416	−	10.4461i	−0.107710	−	0.331498i
$994$	22.0751	−	67.9401i	0.700179	−	2.15493i
$995$		0			0
$996$	27.2310	+	19.7845i	0.862846	+	0.626895i
$997$	−2.01541	+	6.20281i	−0.0638288	+	0.196445i	−0.977885	−	0.209142i	$-0.932933\pi$
$997$	−2.01541	+	6.20281i	−0.0638288	+	0.196445i	0.914056	+	0.405587i	$0.132933\pi$
$998$	−19.0171	−	58.5286i	−0.601975	−	1.85269i
$999$	7.16983	−	5.20918i	0.226843	−	0.164811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.k.751.2		8
5.2	odd	4		825.2.bx.h.124.4		16
5.3	odd	4		825.2.bx.h.124.1		16
5.4	even	2		165.2.m.a.91.1	✓	8
11.2	odd	10		9075.2.a.dj.1.4		4
11.4	even	5	inner	825.2.n.k.301.2		8
11.9	even	5		9075.2.a.cl.1.1		4
15.14	odd	2		495.2.n.d.91.2		8
55.4	even	10		165.2.m.a.136.1	yes	8
55.9	even	10		1815.2.a.x.1.4		4
55.24	odd	10		1815.2.a.o.1.1		4
55.37	odd	20		825.2.bx.h.499.1		16
55.48	odd	20		825.2.bx.h.499.4		16
165.59	odd	10		495.2.n.d.136.2		8
165.119	odd	10		5445.2.a.be.1.1		4
165.134	even	10		5445.2.a.bv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.91.1	✓	8	5.4	even	2
165.2.m.a.136.1	yes	8	55.4	even	10
495.2.n.d.91.2		8	15.14	odd	2
495.2.n.d.136.2		8	165.59	odd	10
825.2.n.k.301.2		8	11.4	even	5	inner
825.2.n.k.751.2		8	1.1	even	1	trivial
825.2.bx.h.124.1		16	5.3	odd	4
825.2.bx.h.124.4		16	5.2	odd	4
825.2.bx.h.499.1		16	55.37	odd	20
825.2.bx.h.499.4		16	55.48	odd	20
1815.2.a.o.1.1		4	55.24	odd	10
1815.2.a.x.1.4		4	55.9	even	10
5445.2.a.be.1.1		4	165.119	odd	10
5445.2.a.bv.1.4		4	165.134	even	10
9075.2.a.cl.1.1		4	11.9	even	5
9075.2.a.dj.1.4		4	11.2	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24278 - 1.62947i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.75683 - 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(0.703814 - 2.16612i) q^{7} +(-3.15700 - 9.71623i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.24278 - 1.62947i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.75683 - 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(0.703814 - 2.16612i) q^{7} +(-3.15700 - 9.71623i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.105203 + 3.31496i) q^{11} -5.68522 q^{12} +(-0.352519 + 0.256120i) q^{13} +(-1.95113 - 6.00496i) q^{14} +(-13.7139 - 9.96371i) q^{16} +(4.04508 + 2.93893i) q^{17} +(-0.856664 + 2.63654i) q^{18} +(1.45113 + 4.46612i) q^{19} -2.27759 q^{21} +(5.16568 + 7.60613i) q^{22} +0.845811 q^{23} +(-8.26512 + 6.00496i) q^{24} +(-0.373280 + 1.14884i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-10.4756 - 7.61100i) q^{28} +(-0.821093 + 2.52706i) q^{29} +(3.77637 - 2.74369i) q^{31} -26.5602 q^{32} +(3.18522 - 0.924324i) q^{33} +13.8611 q^{34} +(1.75683 + 5.40697i) q^{36} +(2.73863 - 8.42864i) q^{37} +(10.5320 + 7.65193i) q^{38} +(0.352519 + 0.256120i) q^{39} +(-1.32697 - 4.08400i) q^{41} +(-5.10813 + 3.71127i) q^{42} -7.00317 q^{43} +(17.7390 + 6.39264i) q^{44} +(1.89696 - 1.37823i) q^{46} +(-0.144675 - 0.445265i) q^{47} +(-5.23823 + 16.1216i) q^{48} +(1.46641 + 1.06541i) q^{49} +(1.54508 - 4.75528i) q^{51} +(0.765515 + 2.35601i) q^{52} +(-8.76863 + 6.37078i) q^{53} +2.77222 q^{54} -23.2684 q^{56} +(3.79911 - 2.76021i) q^{57} +(2.27625 + 7.00558i) q^{58} +(1.21629 - 3.74334i) q^{59} +(-2.39913 - 1.74307i) q^{61} +(3.99878 - 12.3070i) q^{62} +(0.703814 + 2.16612i) q^{63} +(-32.1409 + 23.3517i) q^{64} +(5.63757 - 7.26328i) q^{66} +2.47048 q^{67} +(22.9972 - 16.7084i) q^{68} +(-0.261370 - 0.804414i) q^{69} +(9.15321 + 6.65020i) q^{71} +(8.26512 + 6.00496i) q^{72} +(-2.60474 + 8.01655i) q^{73} +(-7.59209 - 23.3661i) q^{74} +26.6975 q^{76} +(7.10654 + 2.56099i) q^{77} +1.20796 q^{78} +(8.79457 - 6.38963i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-9.63087 - 6.99723i) q^{82} +(-4.78978 - 3.47998i) q^{83} +(-4.00134 + 12.3149i) q^{84} +(-15.7065 + 11.4115i) q^{86} +2.65711 q^{87} +(32.5410 - 9.44313i) q^{88} +5.89958 q^{89} +(0.306678 + 0.943857i) q^{91} +(1.48595 - 4.57327i) q^{92} +(-3.77637 - 2.74369i) q^{93} +(-1.05002 - 0.762885i) q^{94} +(8.20756 + 25.2603i) q^{96} +(-6.99640 + 5.08318i) q^{97} +5.02487 q^{98} +(-1.86337 - 2.74369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9	\( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9 - 3 * q^11 - 18 * q^12 - 6 * q^13 - 10 * q^14 - 20 * q^16 + 10 * q^17 + 5 * q^18 + 6 * q^19 - 4 * q^21 + 25 * q^22 + 10 * q^23 - 20 * q^24 - 8 * q^26 + 2 * q^27 - 31 * q^28 + 3 * q^31 - 60 * q^32 - 2 * q^33 + 50 * q^34 - 2 * q^36 + 19 * q^37 + 28 * q^38 + 6 * q^39 - 25 * q^41 - 15 * q^42 + 4 * q^43 + 7 * q^44 - 6 * q^46 - 15 * q^47 - 5 * q^48 + 21 * q^49 - 10 * q^51 - 6 * q^52 - 7 * q^53 + 10 * q^54 + 20 * q^56 + 9 * q^57 + 2 * q^58 + 35 * q^59 + 21 * q^61 + 19 * q^62 - q^63 - 77 * q^64 + 25 * q^66 + 26 * q^67 + 35 * q^68 - 5 * q^69 + 25 * q^71 + 20 * q^72 - q^73 - 29 * q^74 - 14 * q^76 + 61 * q^77 - 12 * q^78 + 30 * q^79 - 2 * q^81 - 57 * q^82 - 11 * q^83 - 34 * q^84 - 34 * q^86 - 10 * q^87 + 85 * q^88 + 32 * q^89 + 37 * q^91 + 10 * q^92 - 3 * q^93 - 39 * q^94 + 10 * q^96 - 5 * q^97 - 50 * q^98 - 3 * q^99

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