LMFDB - Embedded newform 825.2.n.k.301.2

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			301.2
Root			$1.69513 + 1.23158i$ of defining polynomial
Character	$\chi$	$=$	825.301
Dual form			825.2.n.k.751.2

$q$-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 $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

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

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	0.909535	+	0.415627i	$0.136438\pi$
$2$	2.24278	+	1.62947i	1.58588	+	1.15221i	0.676347	+	0.736584i	$0.263562\pi$
$3$	−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	0.991457	+	0.130431i	$0.0416360\pi$
$7$	0.703814	+	2.16612i	0.266017	+	0.818716i	−0.725441	+	0.688285i	$0.758364\pi$
$8$	−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	0.537826	−	0.843056i	$-0.319246\pi$
$13$	−0.352519	−	0.256120i	−0.0977711	−	0.0710348i	−0.635597	+	0.772021i	$0.719246\pi$
$14$	−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	0.0231281	−	0.999733i	$-0.492637\pi$
$17$	4.04508	−	2.93893i	0.981077	−	0.712794i	0.957949	+	0.286938i	$0.0926374\pi$
$18$	−0.856664	−	2.63654i	−0.201918	−	0.621439i
$19$	1.45113	−	4.46612i	0.332912	−	1.02460i	−0.634829	−	0.772652i	$-0.718930\pi$
$19$	1.45113	−	4.46612i	0.332912	−	1.02460i	0.967741	−	0.251946i	$-0.0810704\pi$
$20$		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	0.845423	−	0.534097i	$-0.179348\pi$
$29$	−0.821093	−	2.52706i	−0.152473	−	0.469264i	−0.997896	+	0.0648334i	$0.979348\pi$
$30$		0			0
$31$	3.77637	+	2.74369i	0.678256	+	0.492782i	0.872779	−	0.488116i	$-0.162316\pi$
$31$	3.77637	+	2.74369i	0.678256	+	0.492782i	−0.194523	+	0.980898i	$0.562316\pi$
$32$	−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	0.876647	+	0.481134i	$0.159775\pi$
$37$	2.73863	+	8.42864i	0.450228	+	1.38566i	−0.426419	+	0.904526i	$0.640225\pi$
$38$	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	0.792376	+	0.610033i	$0.208844\pi$
$41$	−1.32697	+	4.08400i	−0.207238	+	0.637814i	−0.999614	+	0.0277805i	$0.991156\pi$
$42$	−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	−0.961053	−	0.276363i	$-0.910871\pi$
$47$	−0.144675	+	0.445265i	−0.0211031	+	0.0649485i	0.939950	+	0.341311i	$0.110871\pi$
$48$	−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	−0.209747	−	0.977756i	$-0.567264\pi$
$53$	−8.76863	−	6.37078i	−1.20446	−	0.875094i	−0.994716	+	0.102662i	$0.967264\pi$
$54$	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	0.998485	−	0.0550316i	$-0.0175260\pi$
$59$	1.21629	+	3.74334i	0.158347	+	0.487341i	−0.840138	+	0.542373i	$0.817526\pi$
$60$		0			0
$61$	−2.39913	+	1.74307i	−0.307177	+	0.223177i	−0.730684	−	0.682715i	$-0.760799\pi$
$61$	−2.39913	+	1.74307i	−0.307177	+	0.223177i	0.423507	+	0.905893i	$0.360799\pi$
$62$	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	0.107518	−	0.994203i	$-0.465710\pi$
$71$	9.15321	−	6.65020i	1.08629	−	0.789233i	0.978768	+	0.204970i	$0.0657097\pi$
$72$	8.26512	−	6.00496i	0.974054	−	0.707691i
$73$	−2.60474	−	8.01655i	−0.304861	−	0.938266i	−0.979729	−	0.200328i	$-0.935799\pi$
$73$	−2.60474	−	8.01655i	−0.304861	−	0.938266i	0.674868	−	0.737939i	$-0.264201\pi$
$74$	−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	0.959804	−	0.280671i	$-0.0905569\pi$
$79$	8.79457	+	6.38963i	0.989466	+	0.718889i	0.0296621	+	0.999560i	$0.490557\pi$
$80$		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	−0.818764	−	0.574130i	$-0.805341\pi$
$83$	−4.78978	+	3.47998i	−0.525747	+	0.381978i	0.293017	+	0.956107i	$0.405341\pi$
$84$	−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	0.172918	−	0.984936i	$-0.444680\pi$
$97$	−6.99640	−	5.08318i	−0.710377	−	0.516119i	−0.883295	+	0.468817i	$0.844680\pi$
$98$	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	0.792488	−	0.609887i	$-0.208785\pi$
$101$	4.59624	+	3.33936i	0.457343	+	0.332279i	−0.335145	+	0.942166i	$0.608785\pi$
$102$	−4.28332	+	13.1827i	−0.424112	+	1.30528i
$103$	0.400526	+	1.23269i	0.0394650	+	0.121461i	0.968848	−	0.247656i	$-0.0796602\pi$
$103$	0.400526	+	1.23269i	0.0394650	+	0.121461i	−0.929383	+	0.369117i	$0.879660\pi$
$104$	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	−0.585821	−	0.810441i	$-0.699228\pi$
$107$	3.77024	−	11.6036i	0.364483	−	1.12176i	0.950304	−	0.311324i	$-0.100772\pi$
$108$	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	−0.953100	−	0.302656i	$-0.902127\pi$
$113$	−0.0438966	+	0.135100i	−0.00412944	+	0.0127091i	0.948971	+	0.315365i	$0.102127\pi$
$114$	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	−0.605719	−	0.795679i	$-0.707114\pi$
$127$	−0.407512	+	0.296075i	−0.0361609	+	0.0262724i	0.569558	+	0.821951i	$0.307114\pi$
$128$	−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	−0.0727841	−	0.997348i	$-0.523188\pi$
$137$	9.98713	−	7.25608i	0.853258	−	0.619929i	0.926043	+	0.377419i	$0.123188\pi$
$138$	−1.89696	+	1.37823i	−0.161480	+	0.117322i
$139$	−2.38943	−	7.35391i	−0.202669	−	0.623750i	−0.999801	−	0.0199456i	$-0.993651\pi$
$139$	−2.38943	−	7.35391i	−0.202669	−	0.623750i	0.797132	−	0.603805i	$-0.206349\pi$
$140$		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	−0.810657	−	0.585521i	$-0.800890\pi$
$149$	−6.15577	+	4.47243i	−0.504301	+	0.366396i	0.306357	+	0.951917i	$0.400890\pi$
$150$		0			0
$151$	−0.826389	+	2.54336i	−0.0672506	+	0.206976i	−0.979035	−	0.203694i	$-0.934705\pi$
$151$	−0.826389	+	2.54336i	−0.0672506	+	0.206976i	0.911784	+	0.410670i	$0.134705\pi$
$152$	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	0.313770	+	0.949499i	$0.398408\pi$
$157$	−6.24214	+	19.2113i	−0.498177	+	1.53323i	−0.811947	+	0.583731i	$0.801592\pi$
$158$	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	0.232445	−	0.972610i	$-0.425328\pi$
$163$	−7.92498	−	5.75784i	−0.620733	−	0.450989i	−0.853177	+	0.521621i	$0.825328\pi$
$164$	−24.4133			−1.90636
$165$		0			0
$166$	−16.4129			−1.27389
$167$	20.6927	+	15.0341i	1.60125	+	1.16338i	0.885065	+	0.465467i	$0.154114\pi$
$167$	20.6927	+	15.0341i	1.60125	+	1.16338i	0.716185	+	0.697910i	$0.245886\pi$
$168$	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	−0.839834	−	0.542843i	$-0.817348\pi$
$173$	2.08712	−	6.42349i	0.158681	−	0.488369i	0.998515	+	0.0544734i	$0.0173480\pi$
$174$	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	−0.847055	−	0.531505i	$-0.821627\pi$
$179$	2.01539	−	6.20274i	0.150638	−	0.463615i	0.997693	+	0.0678901i	$0.0216267\pi$
$180$		0			0
$181$	−11.1257	+	8.08332i	−0.826970	+	0.600829i	−0.918700	−	0.394955i	$-0.870760\pi$
$181$	−11.1257	+	8.08332i	−0.826970	+	0.600829i	0.0917306	+	0.995784i	$0.470760\pi$
$182$	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	−0.893512	−	0.449038i	$-0.851767\pi$
$191$	−6.00607	−	18.4848i	−0.434584	−	1.33751i	0.458929	−	0.888473i	$-0.348233\pi$
$192$	32.1409	−	23.3517i	2.31957	−	1.68527i
$193$	18.2938	−	13.2912i	1.31681	−	0.956722i	0.316849	−	0.948476i	$-0.397375\pi$
$193$	18.2938	−	13.2912i	1.31681	−	0.956722i	0.999966	−	0.00824604i	$-0.00262483\pi$
$194$	−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	0.586394	−	0.810026i	$-0.300547\pi$
$211$	−0.0403903	−	0.0293453i	−0.00278059	−	0.00202021i	−0.589175	+	0.808006i	$0.700547\pi$
$212$	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	−0.958564	−	0.284877i	$-0.908047\pi$
$223$	−0.233296	+	0.718012i	−0.0156227	+	0.0480816i	0.942941	+	0.332959i	$0.108047\pi$
$224$	−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	0.829458	−	0.558569i	$-0.188649\pi$
$227$	−2.55989	−	7.87855i	−0.169906	−	0.522917i	−0.999364	+	0.0356515i	$0.988649\pi$
$228$	−8.24999	+	25.3909i	−0.546369	+	1.68155i
$229$	2.32691	+	1.69060i	0.153767	+	0.111718i	0.662008	−	0.749496i	$-0.269704\pi$
$229$	2.32691	+	1.69060i	0.153767	+	0.111718i	−0.508242	+	0.861214i	$0.669704\pi$
$230$		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	0.442030	−	0.897000i	$-0.354258\pi$
$233$	−4.18964	−	3.04395i	−0.274473	−	0.199416i	−0.716503	+	0.697584i	$0.754258\pi$
$234$	−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	−0.782509	−	0.622640i	$-0.786060\pi$
$239$	3.34751	−	10.3026i	0.216532	−	0.666418i	0.999041	−	0.0437789i	$-0.0139397\pi$
$240$		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	0.938331	−	0.345738i	$-0.112371\pi$
$251$	14.2504	+	10.3535i	0.899475	+	0.653507i	−0.0388560	+	0.999245i	$0.512371\pi$
$252$	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	−0.921632	−	0.388064i	$-0.873144\pi$
$257$	−6.47845	−	19.9386i	−0.404115	−	1.24374i	0.517518	−	0.855672i	$-0.326856\pi$
$258$	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	−0.799651	−	0.600466i	$-0.794982\pi$
$269$	−7.80173	+	5.66829i	−0.475680	+	0.345601i	0.323971	+	0.946067i	$0.394982\pi$
$270$		0			0
$271$	3.16056	+	9.72719i	0.191990	+	0.590885i	0.999999	+	0.00171395i	$0.000545568\pi$
$271$	3.16056	+	9.72719i	0.191990	+	0.590885i	−0.808008	+	0.589171i	$0.799454\pi$
$272$	−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	0.436756	−	0.899580i	$-0.356127\pi$
$277$	−4.72388	−	3.43210i	−0.283830	−	0.206215i	−0.720586	+	0.693365i	$0.756127\pi$
$278$	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	−0.878509	−	0.477725i	$-0.841461\pi$
$281$	−11.6611	+	8.47225i	−0.695640	+	0.505412i	0.182869	+	0.983137i	$0.441461\pi$
$282$	−0.401072	−	1.23437i	−0.0238835	−	0.0735058i
$283$	3.28592	−	10.1130i	0.195327	−	0.601156i	−0.804645	−	0.593756i	$-0.797644\pi$
$283$	3.28592	−	10.1130i	0.195327	−	0.601156i	0.999973	−	0.00740011i	$-0.00235555\pi$
$284$	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	0.997797	−	0.0663405i	$-0.0211323\pi$
$293$	2.59443	+	7.98484i	0.151568	+	0.466479i	−0.846229	+	0.532820i	$0.821132\pi$
$294$	−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	−0.486751	−	0.873541i	$-0.661818\pi$
$311$	7.41548	−	22.8225i	0.420493	−	1.29415i	0.907244	−	0.420604i	$-0.138182\pi$
$312$	1.37562	+	4.23372i	0.0778791	+	0.239687i
$313$	−20.9281	+	15.2052i	−1.18293	+	0.859448i	−0.992499	−	0.122253i	$-0.960988\pi$
$313$	−20.9281	+	15.2052i	−1.18293	+	0.859448i	−0.190430	+	0.981701i	$0.560988\pi$
$314$	−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	0.651787	−	0.758402i	$-0.274019\pi$
$317$	2.34873	+	1.70645i	0.131918	+	0.0958441i	−0.519869	+	0.854246i	$0.674019\pi$
$318$	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	−0.999063	−	0.0432780i	$-0.986220\pi$
$337$	−3.96968	−	12.2174i	−0.216242	−	0.665525i	0.782821	−	0.622247i	$-0.213780\pi$
$338$	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	−0.628064	−	0.778162i	$-0.716152\pi$
$347$	−1.52881	+	1.11074i	−0.0820707	+	0.0596279i	0.545993	+	0.837790i	$0.316152\pi$
$348$	4.66809	+	14.3669i	0.250236	+	0.770147i
$349$	7.34802	−	22.6149i	0.393330	−	1.21055i	−0.536924	−	0.843631i	$-0.680414\pi$
$349$	7.34802	−	22.6149i	0.393330	−	1.21055i	0.930254	−	0.366915i	$-0.119586\pi$
$350$		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	−0.980348	−	0.197276i	$-0.936791\pi$
$359$	−5.74455	−	17.6799i	−0.303186	−	0.933109i	0.677162	−	0.735834i	$-0.263209\pi$
$360$		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	0.892031	−	0.451974i	$-0.149280\pi$
$367$	−1.82571	−	5.61894i	−0.0953010	−	0.293306i	−0.987332	+	0.158668i	$0.949280\pi$
$368$	−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	−0.749094	−	0.662464i	$-0.769511\pi$
$379$	−6.82420	+	4.95807i	−0.350536	+	0.254679i	0.398558	+	0.917143i	$0.369511\pi$
$380$		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	0.939633	−	0.342185i	$-0.111167\pi$
$383$	17.7025	+	12.8616i	0.904558	+	0.657199i	−0.0350750	+	0.999385i	$0.511167\pi$
$384$	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	0.947938	−	0.318455i	$-0.103164\pi$
$389$	−0.121163	−	0.372902i	−0.00614322	−	0.0189069i	−0.954081	+	0.299548i	$0.903164\pi$
$390$		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	−0.996802	−	0.0799056i	$-0.974538\pi$
$401$	−24.6074	+	17.8783i	−1.22884	+	0.892802i	−0.232034	+	0.972708i	$0.574538\pi$
$402$	−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	0.863558	−	0.504249i	$-0.168231\pi$
$409$	13.1625	+	9.56310i	0.650843	+	0.472865i	−0.212715	+	0.977114i	$0.568231\pi$
$410$		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	0.692095	+	0.721806i	$0.256688\pi$
$421$	−5.99316	+	18.4450i	−0.292089	+	0.898956i	−0.984184	+	0.177150i	$0.943312\pi$
$422$	−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	−0.999893	−	0.0146183i	$-0.995347\pi$
$431$	−27.4616	−	19.9520i	−1.32278	−	0.961056i	−0.322887	−	0.946438i	$-0.604653\pi$
$432$	−5.23823	+	16.1216i	−0.252025	+	0.775652i
$433$	4.05291	+	12.4736i	0.194770	+	0.599442i	0.999979	+	0.00645020i	$0.00205318\pi$
$433$	4.05291	+	12.4736i	0.194770	+	0.599442i	−0.805209	+	0.592991i	$0.797947\pi$
$434$	−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	−0.864050	−	0.503405i	$-0.832080\pi$
$443$	2.75461	−	8.47781i	0.130875	−	0.402793i	0.994926	+	0.100613i	$0.0320802\pi$
$444$	−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	0.799323	−	0.600901i	$-0.205191\pi$
$449$	10.0616	+	7.31019i	0.474837	+	0.344989i	−0.324487	+	0.945890i	$0.605191\pi$
$450$		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	−0.456898	+	0.889519i	$0.651040\pi$
$457$	−30.8707	+	22.4289i	−1.44407	+	1.04918i	−0.987172	+	0.159659i	$0.948960\pi$
$458$	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	−0.267714	−	0.963498i	$-0.586268\pi$
$467$	12.2292	−	8.88502i	0.565899	−	0.411150i	0.833613	+	0.552349i	$0.186268\pi$
$468$	−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	0.0897931	−	0.995960i	$-0.471379\pi$
$479$	23.3033	−	16.9308i	1.06476	−	0.773590i	0.974962	+	0.222370i	$0.0713794\pi$
$480$		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	0.517693	+	0.855567i	$0.326791\pi$
$487$	−8.91592	+	27.4404i	−0.404019	+	1.24344i	−0.921712	+	0.387876i	$0.873209\pi$
$488$	−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	−0.999562	−	0.0296097i	$-0.990574\pi$
$491$	−4.61569	−	14.2056i	−0.208303	−	0.641092i	0.791258	−	0.611482i	$-0.209426\pi$
$492$	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	0.978889	+	0.204392i	$0.0655218\pi$
$499$	6.85987	+	21.1125i	0.307090	+	0.945125i	−0.671799	+	0.740733i	$0.734478\pi$
$500$		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	−0.952121	−	0.305721i	$-0.901102\pi$
$503$	−0.0480077	+	0.147752i	−0.00214056	+	0.00658795i	0.949981	+	0.312309i	$0.101102\pi$
$504$	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	0.738498	+	0.674256i	$0.235536\pi$
$509$	−5.75932	+	17.7254i	−0.255277	+	0.785663i	−0.993775	+	0.111407i	$0.964464\pi$
$510$		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	0.903041	+	0.429554i	$0.141329\pi$
$521$	9.69969	+	29.8526i	0.424951	+	1.30786i	−0.478090	+	0.878311i	$0.658671\pi$
$522$	−5.95930	+	4.32969i	−0.260832	+	0.189505i
$523$	−19.4036	+	14.0975i	−0.848459	+	0.616442i	−0.924721	−	0.380646i	$-0.875702\pi$
$523$	−19.4036	+	14.0975i	−0.848459	+	0.616442i	0.0762616	+	0.997088i	$0.475702\pi$
$524$	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	0.400672	−	0.916222i	$-0.368777\pi$
$541$	−8.06851	−	5.86211i	−0.346892	−	0.252032i	−0.747564	+	0.664190i	$0.768777\pi$
$542$	−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	−0.228103	−	0.973637i	$-0.573252\pi$
$547$	12.3659	−	38.0582i	0.528726	−	1.62725i	0.756829	−	0.653614i	$-0.226748\pi$
$548$	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	0.988920	−	0.148448i	$-0.0474278\pi$
$557$	2.39812	+	7.38064i	0.101611	+	0.312728i	−0.887309	+	0.461176i	$0.847428\pi$
$558$	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	0.855907	−	0.517130i	$-0.173000\pi$
$563$	14.9146	+	10.8361i	0.628577	+	0.456688i	−0.227330	+	0.973818i	$0.573000\pi$
$564$	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	−0.853912	−	0.520418i	$-0.825776\pi$
$569$	3.40658	−	10.4844i	0.142811	−	0.439528i	0.996723	+	0.0808896i	$0.0257761\pi$
$570$		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	−0.386690	−	0.922210i	$-0.626382\pi$
$577$	8.90910	−	6.47284i	0.370891	−	0.269468i	0.757580	+	0.652742i	$0.226382\pi$
$578$	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	0.846677	−	0.532107i	$-0.178600\pi$
$587$	−3.65999	−	11.2643i	−0.151064	−	0.464927i	−0.997741	+	0.0671803i	$0.978600\pi$
$588$	−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	−0.905838	−	0.423624i	$-0.860758\pi$
$599$	−19.1603	+	13.9208i	−0.782868	+	0.568787i	0.122971	+	0.992410i	$0.460758\pi$
$600$		0			0
$601$	11.2090	+	34.4978i	0.457225	+	1.40719i	0.868503	+	0.495684i	$0.165083\pi$
$601$	11.2090	+	34.4978i	0.457225	+	1.40719i	−0.411278	+	0.911510i	$0.634917\pi$
$602$	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	0.107569	−	0.994198i	$-0.465693\pi$
$607$	−19.8264	−	14.4047i	−0.804728	−	0.584669i	−0.912297	+	0.409528i	$0.865693\pi$
$608$	−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	−0.975850	−	0.218441i	$-0.929903\pi$
$613$	−1.43538	+	4.41763i	−0.0579743	+	0.178427i	0.917876	+	0.396868i	$0.129903\pi$
$614$	−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	0.162258	+	0.986748i	$0.448122\pi$
$619$	−13.6592	+	42.0385i	−0.549008	+	1.68967i	−0.711266	+	0.702923i	$0.751878\pi$
$620$		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	−0.999923	−	0.0123995i	$-0.996053\pi$
$631$	−4.98015	−	15.3273i	−0.198257	−	0.610171i	0.801667	−	0.597771i	$-0.203947\pi$
$632$	−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	−0.991398	−	0.130881i	$-0.958219\pi$
$641$	−2.84600	+	8.75909i	−0.112410	+	0.345963i	0.878988	+	0.476844i	$0.158219\pi$
$642$	10.4520	+	32.1678i	0.412506	+	1.26956i
$643$	3.24845	−	2.36014i	0.128106	−	0.0930747i	−0.521887	−	0.853015i	$-0.674772\pi$
$643$	3.24845	−	2.36014i	0.128106	−	0.0930747i	0.649993	+	0.759940i	$0.274772\pi$
$644$	−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	0.791112	−	0.611671i	$-0.209502\pi$
$647$	11.5441	+	8.38728i	0.453846	+	0.329738i	−0.337267	+	0.941409i	$0.609502\pi$
$648$	−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	0.982714	−	0.185129i	$-0.0592703\pi$
$653$	2.01532	+	6.20252i	0.0788656	+	0.242723i	−0.903849	+	0.427852i	$0.859270\pi$
$654$	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	0.0500135	−	0.998749i	$-0.484074\pi$
$673$	−22.9433	−	16.6693i	−0.884398	−	0.642553i	−0.934411	+	0.356196i	$0.884074\pi$
$674$	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	−0.664055	−	0.747684i	$-0.731166\pi$
$677$	−4.11544	+	2.99004i	−0.158169	+	0.114917i	0.505885	+	0.862601i	$0.331166\pi$
$678$	−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	0.999894	+	0.0145791i	$0.00464085\pi$
$691$	34.7708	+	25.2625i	1.32274	+	0.961029i	0.322850	+	0.946450i	$0.395359\pi$
$692$	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	−0.999240	−	0.0389718i	$-0.987592\pi$
$701$	−4.44621	+	13.6840i	−0.167931	+	0.516838i	0.831309	+	0.555810i	$0.187592\pi$
$702$	−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	−0.614805	+	0.788680i	$0.710765\pi$
$709$	−41.4016	+	30.0800i	−1.55487	+	1.12968i	−0.940064	+	0.340998i	$0.889235\pi$
$710$		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	0.529806	+	0.848119i	$0.322265\pi$
$719$	16.0803	+	49.4902i	0.599696	+	1.84567i	0.0698891	+	0.997555i	$0.477735\pi$
$720$		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	−0.899904	−	0.436088i	$-0.856364\pi$
$733$	−11.5929	−	35.6792i	−0.428192	−	1.31784i	0.471712	−	0.881753i	$-0.343636\pi$
$734$	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	0.914659	−	0.404226i	$-0.132459\pi$
$739$	22.0973	+	16.0546i	0.812863	+	0.590579i	−0.101796	+	0.994805i	$0.532459\pi$
$740$		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	−0.272298	−	0.962213i	$-0.587784\pi$
$743$	15.2284	−	11.0641i	0.558677	−	0.405902i	0.830974	+	0.556311i	$0.187784\pi$
$744$	−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	0.702644	+	0.711541i	$0.252003\pi$
$751$	−7.78395	+	23.9565i	−0.284040	+	0.874186i	−0.986685	+	0.162645i	$0.947997\pi$
$752$	−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	0.999176	+	0.0405820i	$0.0129212\pi$
$757$	37.0481	+	26.9170i	1.34653	+	0.978315i	0.347358	+	0.937733i	$0.387079\pi$
$758$	−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	0.463975	−	0.885848i	$-0.346423\pi$
$761$	−6.48664	−	4.71282i	−0.235141	−	0.170840i	−0.699116	+	0.715009i	$0.746423\pi$
$762$	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	−0.726934	−	0.686707i	$-0.759055\pi$
$773$	7.36232	−	22.6589i	0.264804	−	0.814984i	0.991738	−	0.128277i	$-0.0409445\pi$
$774$	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	−0.716139	−	0.697958i	$-0.754092\pi$
$787$	−7.67659	+	5.57737i	−0.273641	+	0.198812i	0.442498	+	0.896769i	$0.354092\pi$
$788$	−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	−0.873688	−	0.486486i	$-0.838279\pi$
$797$	−19.2254	+	13.9680i	−0.680998	+	0.494774i	0.192691	+	0.981259i	$0.438279\pi$
$798$	−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	−0.294280	−	0.955719i	$-0.595080\pi$
$809$	14.8963	−	10.8228i	0.523726	−	0.380509i	0.818006	+	0.575210i	$0.195080\pi$
$810$		0			0
$811$	7.30675	−	22.4879i	0.256575	−	0.789656i	−0.736941	−	0.675957i	$-0.763730\pi$
$811$	7.30675	−	22.4879i	0.256575	−	0.789656i	0.993515	−	0.113698i	$-0.0362697\pi$
$812$	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	0.986755	+	0.162220i	$0.0518654\pi$
$821$	8.13186	+	25.0273i	0.283804	+	0.873459i	−0.702951	+	0.711239i	$0.748135\pi$
$822$	−10.5753	+	32.5475i	−0.368857	+	1.13522i
$823$	32.7100	+	23.7652i	1.14020	+	0.828403i	0.987147	−	0.159816i	$-0.0510900\pi$
$823$	32.7100	+	23.7652i	1.14020	+	0.828403i	0.153051	+	0.988218i	$0.451090\pi$
$824$	−13.2416			−0.461293
$825$		0			0
$826$	−24.8517			−0.864703
$827$	13.4238	+	9.75293i	0.466790	+	0.339143i	0.796189	−	0.605048i	$-0.206846\pi$
$827$	13.4238	+	9.75293i	0.466790	+	0.339143i	−0.329399	+	0.944191i	$0.606846\pi$
$828$	1.48595	−	4.57327i	0.0516402	−	0.158932i
$829$	−10.6015	−	32.6281i	−0.368206	−	1.13322i	−0.947949	−	0.318422i	$-0.896847\pi$
$829$	−10.6015	−	32.6281i	−0.368206	−	1.13322i	0.579743	−	0.814800i	$-0.303153\pi$
$830$		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	−0.967502	−	0.252865i	$-0.918627\pi$
$839$	−1.04698	+	3.22229i	−0.0361459	+	0.111246i	0.931356	+	0.364111i	$0.118627\pi$
$840$		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	−0.336900	−	0.941541i	$-0.609378\pi$
$853$	13.2728	−	9.64323i	0.454451	−	0.330178i	0.791351	+	0.611363i	$0.209378\pi$
$854$	−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	−0.830759	−	0.556632i	$-0.812093\pi$
$863$	−16.3949	+	11.9116i	−0.558090	+	0.405476i	0.272670	+	0.962108i	$0.412093\pi$
$864$	−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	−0.826125	−	0.563488i	$-0.809459\pi$
$877$	5.13611	−	15.8073i	0.173434	−	0.533775i	0.999558	+	0.0297127i	$0.00945925\pi$
$878$	−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	−0.997104	−	0.0760479i	$-0.975770\pi$
$883$	−4.33042	+	13.3277i	−0.145730	+	0.448511i	0.851374	+	0.524559i	$0.175770\pi$
$884$	−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	−0.982600	−	0.185734i	$-0.940534\pi$
$887$	−8.84040	−	27.2079i	−0.296831	−	0.913553i	0.685769	−	0.727820i	$-0.259466\pi$
$888$	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	−0.163336	−	0.986570i	$-0.552226\pi$
$907$	21.8186	−	15.8521i	0.724474	−	0.526361i	0.887811	+	0.460209i	$0.152226\pi$
$908$	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	0.488019	−	0.872833i	$-0.337720\pi$
$911$	−5.77363	−	4.19479i	−0.191289	−	0.138980i	−0.679308	+	0.733854i	$0.737720\pi$
$912$	−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	−0.491980	−	0.870607i	$-0.663727\pi$
$919$	5.57755	−	4.05233i	0.183987	−	0.133674i	0.675966	+	0.736933i	$0.263727\pi$
$920$		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	0.0112141	−	0.999937i	$-0.496430\pi$
$929$	29.4333	−	21.3846i	0.965676	−	0.701605i	0.954462	+	0.298332i	$0.0964304\pi$
$930$		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	0.995568	+	0.0940454i	$0.0299799\pi$
$937$	42.6299	+	30.9724i	1.39266	+	1.01183i	0.397090	+	0.917780i	$0.370020\pi$
$938$	−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	−0.287015	−	0.957926i	$-0.592663\pi$
$941$	16.4217	−	11.9311i	0.535334	−	0.388943i	0.822349	+	0.568983i	$0.192663\pi$
$942$	−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	0.928610	+	0.371056i	$0.121004\pi$
$953$	12.2078	+	37.5718i	0.395450	+	1.21707i	−0.533160	+	0.846014i	$0.678996\pi$
$954$	−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	−0.819880	−	0.572535i	$-0.805960\pi$
$971$	5.60723	−	17.2573i	0.179945	−	0.553812i	0.999825	+	0.0187228i	$0.00596000\pi$
$972$	−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	0.999208	+	0.0397838i	$0.0126669\pi$
$977$	42.0662	+	30.5629i	1.34582	+	0.977794i	0.346609	+	0.938010i	$0.387333\pi$
$978$	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	−0.891082	−	0.453842i	$-0.850053\pi$
$983$	−13.6994	−	42.1625i	−0.436943	−	1.34477i	0.454139	−	0.890931i	$-0.349947\pi$
$984$	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	0.914056	−	0.405587i	$-0.132933\pi$
$997$	−2.01541	−	6.20281i	−0.0638288	−	0.196445i	−0.977885	+	0.209142i	$0.932933\pi$
$998$	−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.301.2		8
5.2	odd	4		825.2.bx.h.499.1		16
5.3	odd	4		825.2.bx.h.499.4		16
5.4	even	2		165.2.m.a.136.1	yes	8
11.3	even	5	inner	825.2.n.k.751.2		8
11.5	even	5		9075.2.a.cl.1.1		4
11.6	odd	10		9075.2.a.dj.1.4		4
15.14	odd	2		495.2.n.d.136.2		8
55.3	odd	20		825.2.bx.h.124.1		16
55.14	even	10		165.2.m.a.91.1	✓	8
55.39	odd	10		1815.2.a.o.1.1		4
55.47	odd	20		825.2.bx.h.124.4		16
55.49	even	10		1815.2.a.x.1.4		4
165.14	odd	10		495.2.n.d.91.2		8
165.104	odd	10		5445.2.a.be.1.1		4
165.149	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	55.14	even	10
165.2.m.a.136.1	yes	8	5.4	even	2
495.2.n.d.91.2		8	165.14	odd	10
495.2.n.d.136.2		8	15.14	odd	2
825.2.n.k.301.2		8	1.1	even	1	trivial
825.2.n.k.751.2		8	11.3	even	5	inner
825.2.bx.h.124.1		16	55.3	odd	20
825.2.bx.h.124.4		16	55.47	odd	20
825.2.bx.h.499.1		16	5.2	odd	4
825.2.bx.h.499.4		16	5.3	odd	4
1815.2.a.o.1.1		4	55.39	odd	10
1815.2.a.x.1.4		4	55.49	even	10
5445.2.a.be.1.1		4	165.104	odd	10
5445.2.a.bv.1.4		4	165.149	even	10
9075.2.a.cl.1.1		4	11.5	even	5
9075.2.a.dj.1.4		4	11.6	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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