LMFDB - Embedded newform 357.2.k.b.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(64,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("357.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 32 x^{18} + 426 x^{16} + 3072 x^{14} + 13121 x^{12} + 34148 x^{10} + 53608 x^{8} + 48276 x^{6} + \cdots + 4 $ x^20 + 32x^18 + 426x^16 + 3072x^14 + 13121x^12 + 34148x^10 + 53608x^8 + 48276x^6 + 22224x^4 + 3920*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.5
Root			$-1.23743i$ of defining polynomial
Character	$\chi$	$=$	357.64
Dual form			357.2.k.b.106.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23743i q^{2} +(0.707107 + 0.707107i) q^{3} +0.468767 q^{4} +(-1.28416 - 1.28416i) q^{5} +(0.874995 - 0.874995i) q^{6} +(0.707107 - 0.707107i) q^{7} -3.05493i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.23743i q^{2} +(0.707107 + 0.707107i) q^{3} +0.468767 q^{4} +(-1.28416 - 1.28416i) q^{5} +(0.874995 - 0.874995i) q^{6} +(0.707107 - 0.707107i) q^{7} -3.05493i q^{8} +1.00000i q^{9} +(-1.58906 + 1.58906i) q^{10} +(1.66762 - 1.66762i) q^{11} +(0.331468 + 0.331468i) q^{12} -1.26858 q^{13} +(-0.874995 - 0.874995i) q^{14} -1.81608i q^{15} -2.84272 q^{16} +(3.15626 - 2.65293i) q^{17} +1.23743 q^{18} +3.42380i q^{19} +(-0.601973 - 0.601973i) q^{20} +1.00000 q^{21} +(-2.06357 - 2.06357i) q^{22} +(0.635667 - 0.635667i) q^{23} +(2.16016 - 2.16016i) q^{24} -1.70185i q^{25} +1.56978i q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.331468 - 0.331468i) q^{28} +(-0.0171546 - 0.0171546i) q^{29} -2.24727 q^{30} +(4.77634 + 4.77634i) q^{31} -2.59218i q^{32} +2.35837 q^{33} +(-3.28282 - 3.90565i) q^{34} -1.81608 q^{35} +0.468767i q^{36} +(0.843721 + 0.843721i) q^{37} +4.23672 q^{38} +(-0.897020 - 0.897020i) q^{39} +(-3.92302 + 3.92302i) q^{40} +(-5.01497 + 5.01497i) q^{41} -1.23743i q^{42} +5.21815i q^{43} +(0.781726 - 0.781726i) q^{44} +(1.28416 - 1.28416i) q^{45} +(-0.786594 - 0.786594i) q^{46} -8.50780 q^{47} +(-2.01011 - 2.01011i) q^{48} -1.00000i q^{49} -2.10592 q^{50} +(4.10772 + 0.355903i) q^{51} -0.594667 q^{52} +1.07752i q^{53} +(0.874995 + 0.874995i) q^{54} -4.28300 q^{55} +(-2.16016 - 2.16016i) q^{56} +(-2.42099 + 2.42099i) q^{57} +(-0.0212276 + 0.0212276i) q^{58} +5.43516i q^{59} -0.851318i q^{60} +(-4.45420 + 4.45420i) q^{61} +(5.91039 - 5.91039i) q^{62} +(0.707107 + 0.707107i) q^{63} -8.89309 q^{64} +(1.62906 + 1.62906i) q^{65} -2.91832i q^{66} -0.516299 q^{67} +(1.47955 - 1.24361i) q^{68} +0.898969 q^{69} +2.24727i q^{70} +(5.12841 + 5.12841i) q^{71} +3.05493 q^{72} +(9.43285 + 9.43285i) q^{73} +(1.04405 - 1.04405i) q^{74} +(1.20339 - 1.20339i) q^{75} +1.60496i q^{76} -2.35837i q^{77} +(-1.11000 + 1.11000i) q^{78} +(7.61388 - 7.61388i) q^{79} +(3.65052 + 3.65052i) q^{80} -1.00000 q^{81} +(6.20568 + 6.20568i) q^{82} +7.22647i q^{83} +0.468767 q^{84} +(-7.45995 - 0.646350i) q^{85} +6.45709 q^{86} -0.0242602i q^{87} +(-5.09446 - 5.09446i) q^{88} -10.2051 q^{89} +(-1.58906 - 1.58906i) q^{90} +(-0.897020 + 0.897020i) q^{91} +(0.297980 - 0.297980i) q^{92} +6.75476i q^{93} +10.5278i q^{94} +(4.39672 - 4.39672i) q^{95} +(1.83295 - 1.83295i) q^{96} +(0.145058 + 0.145058i) q^{97} -1.23743 q^{98} +(1.66762 + 1.66762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) $ 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6	$ 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6} + 16 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 40 q^{16} + 4 q^{17} + 8 q^{18} - 52 q^{20} + 20 q^{21} - 24 q^{22} - 4 q^{23} + 4 q^{24} - 8 q^{29} + 8 q^{31} - 4 q^{33} - 44 q^{34} + 12 q^{35} + 24 q^{37} - 64 q^{38} - 12 q^{39} - 52 q^{40} - 20 q^{41} + 72 q^{44} - 8 q^{45} + 28 q^{46} - 32 q^{47} + 32 q^{48} + 104 q^{50} + 8 q^{51} + 48 q^{52} - 4 q^{54} - 36 q^{55} - 4 q^{56} - 16 q^{57} - 60 q^{58} + 28 q^{61} + 36 q^{62} - 112 q^{64} - 4 q^{65} + 40 q^{67} - 52 q^{68} + 36 q^{69} + 16 q^{71} - 24 q^{72} - 72 q^{73} - 24 q^{74} - 8 q^{75} + 40 q^{78} - 8 q^{79} + 120 q^{80} - 20 q^{81} + 108 q^{82} - 24 q^{84} + 40 q^{85} - 28 q^{88} - 64 q^{89} + 16 q^{90} - 12 q^{91} - 56 q^{92} + 60 q^{95} + 16 q^{96} + 60 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6 + 16 * q^10 + 4 * q^11 - 12 * q^13 + 4 * q^14 + 40 * q^16 + 4 * q^17 + 8 * q^18 - 52 * q^20 + 20 * q^21 - 24 * q^22 - 4 * q^23 + 4 * q^24 - 8 * q^29 + 8 * q^31 - 4 * q^33 - 44 * q^34 + 12 * q^35 + 24 * q^37 - 64 * q^38 - 12 * q^39 - 52 * q^40 - 20 * q^41 + 72 * q^44 - 8 * q^45 + 28 * q^46 - 32 * q^47 + 32 * q^48 + 104 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^54 - 36 * q^55 - 4 * q^56 - 16 * q^57 - 60 * q^58 + 28 * q^61 + 36 * q^62 - 112 * q^64 - 4 * q^65 + 40 * q^67 - 52 * q^68 + 36 * q^69 + 16 * q^71 - 24 * q^72 - 72 * q^73 - 24 * q^74 - 8 * q^75 + 40 * q^78 - 8 * q^79 + 120 * q^80 - 20 * q^81 + 108 * q^82 - 24 * q^84 + 40 * q^85 - 28 * q^88 - 64 * q^89 + 16 * q^90 - 12 * q^91 - 56 * q^92 + 60 * q^95 + 16 * q^96 + 60 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		−	1.23743i		−	0.874995i	−0.899220	−	0.437498i	$-0.855865\pi$
$2$		−	1.23743i		−	0.874995i	0.899220	−	0.437498i	$-0.144135\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	0.468767			0.234383
$5$	−1.28416	−	1.28416i	−0.574295	−	0.574295i	0.359031	−	0.933326i	$-0.383107\pi$
$5$	−1.28416	−	1.28416i	−0.574295	−	0.574295i	−0.933326	+	0.359031i	$0.883107\pi$
$6$	0.874995	−	0.874995i	0.357215	−	0.357215i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		−	3.05493i		−	1.08008i
$9$			1.00000i			0.333333i
$10$	−1.58906	+	1.58906i	−0.502506	+	0.502506i
$11$	1.66762	−	1.66762i	0.502807	−	0.502807i	−0.409502	−	0.912309i	$-0.634298\pi$
$11$	1.66762	−	1.66762i	0.502807	−	0.502807i	0.912309	+	0.409502i	$0.134298\pi$
$12$	0.331468	+	0.331468i	0.0956866	+	0.0956866i
$13$	−1.26858			−0.351840			−0.175920	−	0.984404i	$-0.556290\pi$
$13$	−1.26858			−0.351840			−0.175920	+	0.984404i	$0.556290\pi$
$14$	−0.874995	−	0.874995i	−0.233852	−	0.233852i
$15$		−	1.81608i		−	0.468910i
$16$	−2.84272			−0.710681
$17$	3.15626	−	2.65293i	0.765504	−	0.643431i
$17$	3.15626	−	2.65293i	0.765504	−	0.643431i
$18$	1.23743			0.291665
$19$			3.42380i			0.785474i	0.919651	+	0.392737i	$0.128472\pi$
$19$			3.42380i			0.785474i	−0.919651	+	0.392737i	$0.871528\pi$
$20$	−0.601973	−	0.601973i	−0.134605	−	0.134605i
$21$	1.00000			0.218218
$22$	−2.06357	−	2.06357i	−0.439954	−	0.439954i
$23$	0.635667	−	0.635667i	0.132546	−	0.132546i	−0.637721	−	0.770267i	$-0.720123\pi$
$23$	0.635667	−	0.635667i	0.132546	−	0.132546i	0.770267	+	0.637721i	$0.220123\pi$
$24$	2.16016	−	2.16016i	0.440941	−	0.440941i
$25$		−	1.70185i		−	0.340370i
$26$			1.56978i			0.307858i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.331468	−	0.331468i	0.0626416	−	0.0626416i
$29$	−0.0171546	−	0.0171546i	−0.00318553	−	0.00318553i	0.705512	−	0.708698i	$-0.250717\pi$
$29$	−0.0171546	−	0.0171546i	−0.00318553	−	0.00318553i	−0.708698	+	0.705512i	$0.750717\pi$
$30$	−2.24727			−0.410294
$31$	4.77634	+	4.77634i	0.857856	+	0.857856i	0.991085	−	0.133229i	$-0.0425347\pi$
$31$	4.77634	+	4.77634i	0.857856	+	0.857856i	−0.133229	+	0.991085i	$0.542535\pi$
$32$		−	2.59218i		−	0.458237i
$33$	2.35837			0.410540
$34$	−3.28282	−	3.90565i	−0.562999	−	0.669813i
$35$	−1.81608			−0.306974
$36$			0.468767i			0.0781278i
$37$	0.843721	+	0.843721i	0.138707	+	0.138707i	0.773051	−	0.634344i	$-0.218730\pi$
$37$	0.843721	+	0.843721i	0.138707	+	0.138707i	−0.634344	+	0.773051i	$0.718730\pi$
$38$	4.23672			0.687286
$39$	−0.897020	−	0.897020i	−0.143638	−	0.143638i
$40$	−3.92302	+	3.92302i	−0.620285	+	0.620285i
$41$	−5.01497	+	5.01497i	−0.783208	+	0.783208i	−0.980371	−	0.197163i	$-0.936827\pi$
$41$	−5.01497	+	5.01497i	−0.783208	+	0.783208i	0.197163	+	0.980371i	$0.436827\pi$
$42$		−	1.23743i		−	0.190940i
$43$			5.21815i			0.795760i	0.917437	+	0.397880i	$0.130254\pi$
$43$			5.21815i			0.795760i	−0.917437	+	0.397880i	$0.869746\pi$
$44$	0.781726	−	0.781726i	0.117850	−	0.117850i
$45$	1.28416	−	1.28416i	0.191432	−	0.191432i
$46$	−0.786594	−	0.786594i	−0.115977	−	0.115977i
$47$	−8.50780			−1.24099			−0.620495	−	0.784210i	$-0.713068\pi$
$47$	−8.50780			−1.24099			−0.620495	+	0.784210i	$0.713068\pi$
$48$	−2.01011	−	2.01011i	−0.290134	−	0.290134i
$49$		−	1.00000i		−	0.142857i
$50$	−2.10592			−0.297822
$51$	4.10772	+	0.355903i	0.575195	+	0.0498365i
$52$	−0.594667			−0.0824654
$53$			1.07752i			0.148008i	0.997258	+	0.0740042i	$0.0235778\pi$
$53$			1.07752i			0.148008i	−0.997258	+	0.0740042i	$0.976422\pi$
$54$	0.874995	+	0.874995i	0.119072	+	0.119072i
$55$	−4.28300			−0.577519
$56$	−2.16016	−	2.16016i	−0.288663	−	0.288663i
$57$	−2.42099	+	2.42099i	−0.320668	+	0.320668i
$58$	−0.0212276	+	0.0212276i	−0.00278732	+	0.00278732i
$59$			5.43516i			0.707597i	0.935322	+	0.353799i	$0.115110\pi$
$59$			5.43516i			0.707597i	−0.935322	+	0.353799i	$0.884890\pi$
$60$		−	0.851318i		−	0.109905i
$61$	−4.45420	+	4.45420i	−0.570302	+	0.570302i	−0.932213	−	0.361911i	$-0.882124\pi$
$61$	−4.45420	+	4.45420i	−0.570302	+	0.570302i	0.361911	+	0.932213i	$0.382124\pi$
$62$	5.91039	−	5.91039i	0.750620	−	0.750620i
$63$	0.707107	+	0.707107i	0.0890871	+	0.0890871i
$64$	−8.89309			−1.11164
$65$	1.62906	+	1.62906i	0.202060	+	0.202060i
$66$		−	2.91832i		−	0.359221i
$67$	−0.516299			−0.0630759			−0.0315380	−	0.999503i	$-0.510041\pi$
$67$	−0.516299			−0.0630759			−0.0315380	+	0.999503i	$0.510041\pi$
$68$	1.47955	−	1.24361i	0.179421	−	0.150809i
$69$	0.898969			0.108223
$70$			2.24727i			0.268601i
$71$	5.12841	+	5.12841i	0.608630	+	0.608630i	0.942588	−	0.333958i	$-0.108384\pi$
$71$	5.12841	+	5.12841i	0.608630	+	0.608630i	−0.333958	+	0.942588i	$0.608384\pi$
$72$	3.05493			0.360027
$73$	9.43285	+	9.43285i	1.10403	+	1.10403i	0.993919	+	0.110112i	$0.0351210\pi$
$73$	9.43285	+	9.43285i	1.10403	+	1.10403i	0.110112	+	0.993919i	$0.464879\pi$
$74$	1.04405	−	1.04405i	0.121368	−	0.121368i
$75$	1.20339	−	1.20339i	0.138955	−	0.138955i
$76$			1.60496i			0.184102i
$77$		−	2.35837i		−	0.268762i
$78$	−1.11000	+	1.11000i	−0.125683	+	0.125683i
$79$	7.61388	−	7.61388i	0.856628	−	0.856628i	−0.134311	−	0.990939i	$-0.542882\pi$
$79$	7.61388	−	7.61388i	0.856628	−	0.856628i	0.990939	+	0.134311i	$0.0428821\pi$
$80$	3.65052	+	3.65052i	0.408141	+	0.408141i
$81$	−1.00000			−0.111111
$82$	6.20568	+	6.20568i	0.685303	+	0.685303i
$83$			7.22647i			0.793208i	0.917990	+	0.396604i	$0.129811\pi$
$83$			7.22647i			0.793208i	−0.917990	+	0.396604i	$0.870189\pi$
$84$	0.468767			0.0511466
$85$	−7.45995	−	0.646350i	−0.809145	−	0.0701065i
$86$	6.45709			0.696286
$87$		−	0.0242602i		−	0.00260097i
$88$	−5.09446	−	5.09446i	−0.543071	−	0.543071i
$89$	−10.2051			−1.08174			−0.540872	−	0.841105i	$-0.681906\pi$
$89$	−10.2051			−1.08174			−0.540872	+	0.841105i	$0.681906\pi$
$90$	−1.58906	−	1.58906i	−0.167502	−	0.167502i
$91$	−0.897020	+	0.897020i	−0.0940332	+	0.0940332i
$92$	0.297980	−	0.297980i	0.0310665	−	0.0310665i
$93$			6.75476i			0.700436i
$94$			10.5278i			1.08586i
$95$	4.39672	−	4.39672i	0.451094	−	0.451094i
$96$	1.83295	−	1.83295i	0.187074	−	0.187074i
$97$	0.145058	+	0.145058i	0.0147284	+	0.0147284i	0.714433	−	0.699704i	$-0.246685\pi$
$97$	0.145058	+	0.145058i	0.0147284	+	0.0147284i	−0.699704	+	0.714433i	$0.746685\pi$
$98$	−1.23743			−0.124999
$99$	1.66762	+	1.66762i	0.167602	+	0.167602i
$100$		−	0.797770i		−	0.0797770i
$101$	10.0435			0.999361			0.499680	−	0.866210i	$-0.333451\pi$
$101$	10.0435			0.999361			0.499680	+	0.866210i	$0.333451\pi$
$102$	0.440406	−	5.08301i	0.0436067	−	0.503293i
$103$	0.982712			0.0968295			0.0484147	−	0.998827i	$-0.484583\pi$
$103$	0.982712			0.0968295			0.0484147	+	0.998827i	$0.484583\pi$
$104$			3.87541i			0.380015i
$105$	−1.28416	−	1.28416i	−0.125322	−	0.125322i
$106$	1.33335			0.129507
$107$	9.56506	+	9.56506i	0.924689	+	0.924689i	0.997356	−	0.0726670i	$-0.0231510\pi$
$107$	9.56506	+	9.56506i	0.924689	+	0.924689i	−0.0726670	+	0.997356i	$0.523151\pi$
$108$	−0.331468	+	0.331468i	−0.0318955	+	0.0318955i
$109$	−6.76586	+	6.76586i	−0.648052	+	0.648052i	−0.952522	−	0.304470i	$-0.901521\pi$
$109$	−6.76586	+	6.76586i	−0.648052	+	0.648052i	0.304470	+	0.952522i	$0.401521\pi$
$110$			5.29991i			0.505327i
$111$			1.19320i			0.113254i
$112$	−2.01011	+	2.01011i	−0.189938	+	0.189938i
$113$	8.08789	−	8.08789i	0.760845	−	0.760845i	−0.215630	−	0.976475i	$-0.569181\pi$
$113$	8.08789	−	8.08789i	0.760845	−	0.760845i	0.976475	+	0.215630i	$0.0691806\pi$
$114$	2.99581	+	2.99581i	0.280583	+	0.280583i
$115$	−1.63260			−0.152241
$116$	−0.00804150	−	0.00804150i	−0.000746634	−	0.000746634i
$117$		−	1.26858i		−	0.117280i
$118$	6.72563			0.619144
$119$	0.355903	−	4.10772i	0.0326256	−	0.376554i
$120$	−5.54799			−0.506460
$121$			5.43807i			0.494370i
$122$	5.51176	+	5.51176i	0.499011	+	0.499011i
$123$	−7.09225			−0.639486
$124$	2.23899	+	2.23899i	0.201067	+	0.201067i
$125$	−8.60627	+	8.60627i	−0.769768	+	0.769768i
$126$	0.874995	−	0.874995i	0.0779508	−	0.0779508i
$127$		−	17.4380i		−	1.54737i	−0.633570	−	0.773685i	$-0.718411\pi$
$127$		−	17.4380i		−	1.54737i	0.633570	−	0.773685i	$-0.281589\pi$
$128$			5.82022i			0.514439i
$129$	−3.68979	+	3.68979i	−0.324868	+	0.324868i
$130$	2.01585	−	2.01585i	0.176802	−	0.176802i
$131$	1.62969	+	1.62969i	0.142387	+	0.142387i	0.774707	−	0.632320i	$-0.217897\pi$
$131$	1.62969	+	1.62969i	0.142387	+	0.142387i	−0.632320	+	0.774707i	$0.717897\pi$
$132$	1.10553			0.0962238
$133$	2.42099	+	2.42099i	0.209927	+	0.209927i
$134$			0.638883i			0.0551911i
$135$	1.81608			0.156303
$136$	−8.10451	−	9.64213i	−0.694956	−	0.826806i
$137$	−0.591167			−0.0505068			−0.0252534	−	0.999681i	$-0.508039\pi$
$137$	−0.591167			−0.0505068			−0.0252534	+	0.999681i	$0.508039\pi$
$138$		−	1.11241i		−	0.0946948i
$139$	−4.09327	−	4.09327i	−0.347187	−	0.347187i	0.511874	−	0.859061i	$-0.328952\pi$
$139$	−4.09327	−	4.09327i	−0.347187	−	0.347187i	−0.859061	+	0.511874i	$0.828952\pi$
$140$	−0.851318			−0.0719495
$141$	−6.01592	−	6.01592i	−0.506632	−	0.506632i
$142$	6.34605	−	6.34605i	0.532548	−	0.532548i
$143$	−2.11551	+	2.11551i	−0.176908	+	0.176908i
$144$		−	2.84272i		−	0.236894i
$145$			0.0440586i			0.00365886i
$146$	11.6725	−	11.6725i	0.966022	−	0.966022i
$147$	0.707107	−	0.707107i	0.0583212	−	0.0583212i
$148$	0.395508	+	0.395508i	0.0325106	+	0.0325106i
$149$	−20.6031			−1.68787			−0.843936	−	0.536444i	$-0.819767\pi$
$149$	−20.6031			−1.68787			−0.843936	+	0.536444i	$0.819767\pi$
$150$	−1.48911	−	1.48911i	−0.121585	−	0.121585i
$151$		−	14.8292i		−	1.20679i	−0.797444	−	0.603393i	$-0.793815\pi$
$151$		−	14.8292i		−	1.20679i	0.797444	−	0.603393i	$-0.206185\pi$
$152$	10.4595			0.848374
$153$	2.65293	+	3.15626i	0.214477	+	0.255168i
$154$	−2.91832			−0.235165
$155$		−	12.2672i		−	0.985325i
$156$	−0.420493	−	0.420493i	−0.0336664	−	0.0336664i
$157$	−3.79172			−0.302612			−0.151306	−	0.988487i	$-0.548348\pi$
$157$	−3.79172			−0.302612			−0.151306	+	0.988487i	$0.548348\pi$
$158$	−9.42164	−	9.42164i	−0.749546	−	0.749546i
$159$	−0.761920	+	0.761920i	−0.0604242	+	0.0604242i
$160$	−3.32878	+	3.32878i	−0.263163	+	0.263163i
$161$		−	0.898969i		−	0.0708487i
$162$			1.23743i			0.0972217i
$163$	15.3052	−	15.3052i	1.19880	−	1.19880i	0.224273	−	0.974526i	$-0.427999\pi$
$163$	15.3052	−	15.3052i	1.19880	−	1.19880i	0.974526	−	0.224273i	$-0.0720007\pi$
$164$	−2.35085	+	2.35085i	−0.183571	+	0.183571i
$165$	−3.02854	−	3.02854i	−0.235771	−	0.235771i
$166$	8.94225			0.694053
$167$	−18.0062	−	18.0062i	−1.39336	−	1.39336i	−0.817659	−	0.575703i	$-0.804728\pi$
$167$	−18.0062	−	18.0062i	−1.39336	−	1.39336i	−0.575703	−	0.817659i	$-0.695272\pi$
$168$		−	3.05493i		−	0.235693i
$169$	−11.3907			−0.876209
$170$	−0.799812	+	9.23116i	−0.0613428	+	0.707998i
$171$	−3.42380			−0.261825
$172$			2.44609i			0.186513i
$173$	−2.10892	−	2.10892i	−0.160338	−	0.160338i	0.622378	−	0.782717i	$-0.286167\pi$
$173$	−2.10892	−	2.10892i	−0.160338	−	0.160338i	−0.782717	+	0.622378i	$0.786167\pi$
$174$	−0.0300204			−0.00227584
$175$	−1.20339	−	1.20339i	−0.0909677	−	0.0909677i
$176$	−4.74059	+	4.74059i	−0.357335	+	0.357335i
$177$	−3.84324	+	3.84324i	−0.288875	+	0.288875i
$178$			12.6282i			0.946520i
$179$			7.72272i			0.577223i	0.957446	+	0.288612i	$0.0931936\pi$
$179$			7.72272i			0.577223i	−0.957446	+	0.288612i	$0.906806\pi$
$180$	0.601973	−	0.601973i	0.0448684	−	0.0448684i
$181$	15.4505	−	15.4505i	1.14842	−	1.14842i	0.161561	−	0.986863i	$-0.448347\pi$
$181$	15.4505	−	15.4505i	1.14842	−	1.14842i	0.986863	−	0.161561i	$-0.0516528\pi$
$182$	1.11000	+	1.11000i	0.0822786	+	0.0822786i
$183$	−6.29919			−0.465649
$184$	−1.94192	−	1.94192i	−0.143160	−	0.143160i
$185$		−	2.16695i		−	0.159317i
$186$	8.35855			0.612878
$187$	0.839353	−	9.68753i	0.0613796	−	0.708422i
$188$	−3.98817			−0.290867
$189$			1.00000i			0.0727393i
$190$	−5.44063	−	5.44063i	−0.394705	−	0.394705i
$191$	−22.7283			−1.64456			−0.822282	−	0.569081i	$-0.807299\pi$
$191$	−22.7283			−1.64456			−0.822282	+	0.569081i	$0.807299\pi$
$192$	−6.28836	−	6.28836i	−0.453824	−	0.453824i
$193$	−16.6127	+	16.6127i	−1.19581	+	1.19581i	−0.220400	+	0.975410i	$0.570736\pi$
$193$	−16.6127	+	16.6127i	−1.19581	+	1.19581i	−0.975410	+	0.220400i	$0.929264\pi$
$194$	0.179499	−	0.179499i	0.0128873	−	0.0128873i
$195$			2.30384i			0.164981i
$196$		−	0.468767i		−	0.0334833i
$197$	4.80175	−	4.80175i	0.342111	−	0.342111i	−0.515050	−	0.857160i	$-0.672227\pi$
$197$	4.80175	−	4.80175i	0.342111	−	0.342111i	0.857160	+	0.515050i	$0.172227\pi$
$198$	2.06357	−	2.06357i	0.146651	−	0.146651i
$199$	3.56463	+	3.56463i	0.252690	+	0.252690i	0.822073	−	0.569383i	$-0.192818\pi$
$199$	3.56463	+	3.56463i	0.252690	+	0.252690i	−0.569383	+	0.822073i	$0.692818\pi$
$200$	−5.19902			−0.367627
$201$	−0.365078	−	0.365078i	−0.0257506	−	0.0257506i
$202$		−	12.4281i		−	0.874436i
$203$	−0.0242602			−0.00170273
$204$	1.92556	+	0.166836i	0.134816	+	0.0116808i
$205$	12.8801			0.899585
$206$		−	1.21604i		−	0.0847253i
$207$	0.635667	+	0.635667i	0.0441819	+	0.0441819i
$208$	3.60622			0.250046
$209$	5.70961	+	5.70961i	0.394942	+	0.394942i
$210$	−1.58906	+	1.58906i	−0.109656	+	0.109656i
$211$	5.56798	−	5.56798i	0.383315	−	0.383315i	−0.488980	−	0.872295i	$-0.662631\pi$
$211$	5.56798	−	5.56798i	0.383315	−	0.383315i	0.872295	+	0.488980i	$0.162631\pi$
$212$			0.505104i			0.0346907i
$213$			7.25266i			0.496944i
$214$	11.8361	−	11.8361i	0.809099	−	0.809099i
$215$	6.70095	−	6.70095i	0.457001	−	0.457001i
$216$	2.16016	+	2.16016i	0.146980	+	0.146980i
$217$	6.75476			0.458543
$218$	8.37227	+	8.37227i	0.567042	+	0.567042i
$219$			13.3401i			0.901438i
$220$	−2.00773			−0.135361
$221$	−4.00395	+	3.36545i	−0.269335	+	0.226385i
$222$	1.47650			0.0990964
$223$		−	20.5049i		−	1.37311i	−0.727077	−	0.686556i	$-0.759122\pi$
$223$		−	20.5049i		−	1.37311i	0.727077	−	0.686556i	$-0.240878\pi$
$224$	−1.83295	−	1.83295i	−0.122469	−	0.122469i
$225$	1.70185			0.113457
$226$	−10.0082	−	10.0082i	−0.665736	−	0.665736i
$227$	6.24987	−	6.24987i	0.414819	−	0.414819i	−0.468595	−	0.883413i	$-0.655240\pi$
$227$	6.24987	−	6.24987i	0.414819	−	0.414819i	0.883413	+	0.468595i	$0.155240\pi$
$228$	−1.13488	+	1.13488i	−0.0751593	+	0.0751593i
$229$		−	6.26192i		−	0.413799i	−0.978362	−	0.206900i	$-0.933663\pi$
$229$		−	6.26192i		−	0.413799i	0.978362	−	0.206900i	$-0.0663374\pi$
$230$			2.02023i			0.133210i
$231$	1.66762	−	1.66762i	0.109721	−	0.109721i
$232$	−0.0524060	+	0.0524060i	−0.00344062	+	0.00344062i
$233$	16.0632	+	16.0632i	1.05234	+	1.05234i	0.998552	+	0.0537860i	$0.0171289\pi$
$233$	16.0632	+	16.0632i	1.05234	+	1.05234i	0.0537860	+	0.998552i	$0.482871\pi$
$234$	−1.56978			−0.102619
$235$	10.9254	+	10.9254i	0.712695	+	0.712695i
$236$			2.54782i			0.165849i
$237$	10.7677			0.699434
$238$	−5.08301	−	0.440406i	−0.329483	−	0.0285473i
$239$	−5.42712			−0.351052			−0.175526	−	0.984475i	$-0.556163\pi$
$239$	−5.42712			−0.351052			−0.175526	+	0.984475i	$0.556163\pi$
$240$			5.16262i			0.333246i
$241$	19.0689	+	19.0689i	1.22834	+	1.22834i	0.964593	+	0.263743i	$0.0849572\pi$
$241$	19.0689	+	19.0689i	1.22834	+	1.22834i	0.263743	+	0.964593i	$0.415043\pi$
$242$	6.72924			0.432572
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−2.08798	+	2.08798i	−0.133669	+	0.133669i
$245$	−1.28416	+	1.28416i	−0.0820422	+	0.0820422i
$246$			8.77616i			0.559547i
$247$		−	4.34336i		−	0.276361i
$248$	14.5914	−	14.5914i	0.926552	−	0.926552i
$249$	−5.10989	+	5.10989i	−0.323826	+	0.323826i
$250$	10.6497	+	10.6497i	0.673543	+	0.673543i
$251$	−11.3447			−0.716074			−0.358037	−	0.933707i	$-0.616554\pi$
$251$	−11.3447			−0.716074			−0.358037	+	0.933707i	$0.616554\pi$
$252$	0.331468	+	0.331468i	0.0208805	+	0.0208805i
$253$		−	2.12011i		−	0.133290i
$254$	−21.5783			−1.35394
$255$	−4.81794	−	5.73202i	−0.301711	−	0.358953i
$256$	−10.5841			−0.661504
$257$		−	26.4860i		−	1.65215i	−0.563557	−	0.826077i	$-0.690568\pi$
$257$		−	26.4860i		−	1.65215i	0.563557	−	0.826077i	$-0.309432\pi$
$258$	4.56585	+	4.56585i	0.284258	+	0.284258i
$259$	1.19320			0.0741419
$260$	0.763649	+	0.763649i	0.0473595	+	0.0473595i
$261$	0.0171546	−	0.0171546i	0.00106184	−	0.00106184i
$262$	2.01663	−	2.01663i	0.124588	−	0.124588i
$263$			0.781732i			0.0482036i	0.999710	+	0.0241018i	$0.00767259\pi$
$263$			0.781732i			0.0482036i	−0.999710	+	0.0241018i	$0.992327\pi$
$264$		−	7.20466i		−	0.443416i
$265$	1.38371	−	1.38371i	0.0850006	−	0.0850006i
$266$	2.99581	−	2.99581i	0.183685	−	0.183685i
$267$	−7.21613	−	7.21613i	−0.441620	−	0.441620i
$268$	−0.242024			−0.0147839
$269$	7.14131	+	7.14131i	0.435413	+	0.435413i	0.890465	−	0.455052i	$-0.150379\pi$
$269$	7.14131	+	7.14131i	0.435413	+	0.435413i	−0.455052	+	0.890465i	$0.650379\pi$
$270$		−	2.24727i		−	0.136765i
$271$	16.8897			1.02597			0.512987	−	0.858397i	$-0.328539\pi$
$271$	16.8897			1.02597			0.512987	+	0.858397i	$0.328539\pi$
$272$	−8.97237	+	7.54156i	−0.544030	+	0.457274i
$273$	−1.26858			−0.0767778
$274$			0.731527i			0.0441932i
$275$	−2.83804	−	2.83804i	−0.171140	−	0.171140i
$276$	0.421407			0.0253657
$277$	3.05228	+	3.05228i	0.183394	+	0.183394i	0.792833	−	0.609439i	$-0.208605\pi$
$277$	3.05228	+	3.05228i	0.183394	+	0.183394i	−0.609439	+	0.792833i	$0.708605\pi$
$278$	−5.06514	+	5.06514i	−0.303787	+	0.303787i
$279$	−4.77634	+	4.77634i	−0.285952	+	0.285952i
$280$			5.54799i			0.331556i
$281$			14.7023i			0.877067i	0.898715	+	0.438534i	$0.144502\pi$
$281$			14.7023i			0.877067i	−0.898715	+	0.438534i	$0.855498\pi$
$282$	−7.44428	+	7.44428i	−0.443301	+	0.443301i
$283$	−7.32159	+	7.32159i	−0.435224	+	0.435224i	−0.890401	−	0.455177i	$-0.849576\pi$
$283$	−7.32159	+	7.32159i	−0.435224	+	0.435224i	0.455177	+	0.890401i	$0.349576\pi$
$284$	2.40403	+	2.40403i	0.142653	+	0.142653i
$285$	6.21790			0.368317
$286$	2.61779	+	2.61779i	0.154793	+	0.154793i
$287$			7.09225i			0.418642i
$288$	2.59218			0.152746
$289$	2.92390	−	16.7467i	0.171994	−	0.985098i
$290$	0.0545194			0.00320149
$291$			0.205143i			0.0120257i
$292$	4.42180	+	4.42180i	0.258767	+	0.258767i
$293$	−10.9848			−0.641741			−0.320871	−	0.947123i	$-0.603975\pi$
$293$	−10.9848			−0.641741			−0.320871	+	0.947123i	$0.603975\pi$
$294$	−0.874995	−	0.874995i	−0.0510308	−	0.0510308i
$295$	6.97963	−	6.97963i	0.406370	−	0.406370i
$296$	2.57750	−	2.57750i	0.149814	−	0.149814i
$297$			2.35837i			0.136847i
$298$			25.4949i			1.47688i
$299$	−0.806393	+	0.806393i	−0.0466349	+	0.0466349i
$300$	0.564109	−	0.564109i	0.0325688	−	0.0325688i
$301$	3.68979	+	3.68979i	0.212676	+	0.212676i
$302$	−18.3501			−1.05593
$303$	7.10179	+	7.10179i	0.407987	+	0.407987i
$304$		−	9.73293i		−	0.558222i
$305$	11.4398			0.655043
$306$	3.90565	−	3.28282i	0.223271	−	0.187666i
$307$	13.8104			0.788203			0.394102	−	0.919067i	$-0.371056\pi$
$307$	13.8104			0.788203			0.394102	+	0.919067i	$0.371056\pi$
$308$		−	1.10553i		−	0.0629932i
$309$	0.694882	+	0.694882i	0.0395305	+	0.0395305i
$310$	−15.1798			−0.862155
$311$	−17.1579	−	17.1579i	−0.972936	−	0.972936i	0.0267073	−	0.999643i	$-0.491498\pi$
$311$	−17.1579	−	17.1579i	−0.972936	−	0.972936i	−0.999643	+	0.0267073i	$0.991498\pi$
$312$	−2.74033	+	2.74033i	−0.155141	+	0.155141i
$313$	11.3705	−	11.3705i	0.642699	−	0.642699i	−0.308519	−	0.951218i	$-0.599833\pi$
$313$	11.3705	−	11.3705i	0.642699	−	0.642699i	0.951218	+	0.308519i	$0.0998334\pi$
$314$			4.69199i			0.264784i
$315$		−	1.81608i		−	0.102325i
$316$	3.56913	−	3.56913i	0.200779	−	0.200779i
$317$	3.03419	−	3.03419i	0.170417	−	0.170417i	−0.616746	−	0.787162i	$-0.711549\pi$
$317$	3.03419	−	3.03419i	0.170417	−	0.170417i	0.787162	+	0.616746i	$0.211549\pi$
$318$	0.942823	+	0.942823i	0.0528709	+	0.0528709i
$319$	−0.0572147			−0.00320341
$320$	11.4202	+	11.4202i	0.638407	+	0.638407i
$321$			13.5270i			0.755006i
$322$	−1.11241			−0.0619923
$323$	9.08311	+	10.8064i	0.505398	+	0.601284i
$324$	−0.468767			−0.0260426
$325$			2.15893i			0.119756i
$326$	−18.9392	−	18.9392i	−1.04894	−	1.04894i
$327$	−9.56837			−0.529132
$328$	15.3204	+	15.3204i	0.845926	+	0.845926i
$329$	−6.01592	+	6.01592i	−0.331669	+	0.331669i
$330$	−3.74760	+	3.74760i	−0.206299	+	0.206299i
$331$		−	19.3135i		−	1.06156i	−0.847508	−	0.530782i	$-0.821898\pi$
$331$		−	19.3135i		−	1.06156i	0.847508	−	0.530782i	$-0.178102\pi$
$332$			3.38753i			0.185915i
$333$	−0.843721	+	0.843721i	−0.0462356	+	0.0462356i
$334$	−22.2814	+	22.2814i	−1.21919	+	1.21919i
$335$	0.663012	+	0.663012i	0.0362242	+	0.0362242i
$336$	−2.84272			−0.155083
$337$	13.8651	+	13.8651i	0.755280	+	0.755280i	0.975459	−	0.220180i	$-0.0706644\pi$
$337$	13.8651	+	13.8651i	0.755280	+	0.755280i	−0.220180	+	0.975459i	$0.570664\pi$
$338$			14.0952i			0.766678i
$339$	11.4380			0.621227
$340$	−3.49697	−	0.302987i	−0.189650	−	0.0164318i
$341$	15.9303			0.862672
$342$			4.23672i			0.229095i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	15.9411			0.859484
$345$	−1.15442	−	1.15442i	−0.0621521	−	0.0621521i
$346$	−2.60964	+	2.60964i	−0.140295	+	0.140295i
$347$	−1.58456	+	1.58456i	−0.0850636	+	0.0850636i	−0.748358	−	0.663295i	$-0.769158\pi$
$347$	−1.58456	+	1.58456i	−0.0850636	+	0.0850636i	0.663295	+	0.748358i	$0.269158\pi$
$348$		−	0.0113724i		−	0.000609624i
$349$			22.3354i			1.19559i	0.801650	+	0.597794i	$0.203956\pi$
$349$			22.3354i			1.19559i	−0.801650	+	0.597794i	$0.796044\pi$
$350$	−1.48911	+	1.48911i	−0.0795963	+	0.0795963i
$351$	0.897020	−	0.897020i	0.0478794	−	0.0478794i
$352$	−4.32278	−	4.32278i	−0.230405	−	0.230405i
$353$	−7.98083			−0.424777			−0.212388	−	0.977185i	$-0.568124\pi$
$353$	−7.98083			−0.424777			−0.212388	+	0.977185i	$0.568124\pi$
$354$	4.75574	+	4.75574i	0.252765	+	0.252765i
$355$		−	13.1714i		−	0.699067i
$356$	−4.78383			−0.253543
$357$	3.15626	−	2.65293i	0.167047	−	0.140408i
$358$	9.55633			0.505068
$359$			21.3945i			1.12916i	0.825379	+	0.564579i	$0.190962\pi$
$359$			21.3945i			1.12916i	−0.825379	+	0.564579i	$0.809038\pi$
$360$	−3.92302	−	3.92302i	−0.206762	−	0.206762i
$361$	7.27758			0.383031
$362$	−19.1189	−	19.1189i	−1.00487	−	1.00487i
$363$	−3.84530	+	3.84530i	−0.201826	+	0.201826i
$364$	−0.420493	+	0.420493i	−0.0220398	+	0.0220398i
$365$		−	24.2266i		−	1.26808i
$366$			7.79480i			0.407441i
$367$	−0.781447	+	0.781447i	−0.0407912	+	0.0407912i	−0.727208	−	0.686417i	$-0.759183\pi$
$367$	−0.781447	+	0.781447i	−0.0407912	+	0.0407912i	0.686417	+	0.727208i	$0.259183\pi$
$368$	−1.80703	+	1.80703i	−0.0941978	+	0.0941978i
$369$	−5.01497	−	5.01497i	−0.261069	−	0.261069i
$370$	−2.68145			−0.139402
$371$	0.761920	+	0.761920i	0.0395569	+	0.0395569i
$372$			3.16641i			0.164171i
$373$	−26.1722			−1.35514			−0.677572	−	0.735457i	$-0.736968\pi$
$373$	−26.1722			−1.35514			−0.677572	+	0.735457i	$0.736968\pi$
$374$	−11.9876	−	1.03864i	−0.619866	−	0.0537069i
$375$	−12.1711			−0.628513
$376$			25.9907i			1.34037i
$377$	0.0217619	+	0.0217619i	0.00112080	+	0.00112080i
$378$	1.23743			0.0636465
$379$	−19.6286	−	19.6286i	−1.00826	−	1.00826i	−0.999966	−	0.00828990i	$-0.997361\pi$
$379$	−19.6286	−	19.6286i	−1.00826	−	1.00826i	−0.00828990	−	0.999966i	$-0.502639\pi$
$380$	2.06104	−	2.06104i	0.105729	−	0.105729i
$381$	12.3305	−	12.3305i	0.631711	−	0.631711i
$382$			28.1247i			1.43899i
$383$		−	17.8180i		−	0.910459i	−0.890374	−	0.455230i	$-0.849557\pi$
$383$		−	17.8180i		−	0.910459i	0.890374	−	0.455230i	$-0.150443\pi$
$384$	−4.11552	+	4.11552i	−0.210019	+	0.210019i
$385$	−3.02854	+	3.02854i	−0.154349	+	0.154349i
$386$	20.5571	+	20.5571i	1.04633	+	1.04633i
$387$	−5.21815			−0.265253
$388$	0.0679982	+	0.0679982i	0.00345209	+	0.00345209i
$389$			22.5784i			1.14477i	0.819984	+	0.572386i	$0.193982\pi$
$389$			22.5784i			1.14477i	−0.819984	+	0.572386i	$0.806018\pi$
$390$	2.85084			0.144358
$391$	0.319946	−	3.69271i	0.0161804	−	0.186748i
$392$	−3.05493			−0.154297
$393$			2.30473i			0.116258i
$394$	−5.94183	−	5.94183i	−0.299345	−	0.299345i
$395$	−19.5549			−0.983915
$396$	0.781726	+	0.781726i	0.0392832	+	0.0392832i
$397$	−25.5061	+	25.5061i	−1.28011	+	1.28011i	−0.339511	+	0.940602i	$0.610262\pi$
$397$	−25.5061	+	25.5061i	−1.28011	+	1.28011i	−0.940602	+	0.339511i	$0.889738\pi$
$398$	4.41098	−	4.41098i	0.221102	−	0.221102i
$399$			3.42380i			0.171404i
$400$			4.83789i			0.241894i
$401$	−1.91643	+	1.91643i	−0.0957021	+	0.0957021i	−0.753337	−	0.657635i	$-0.771557\pi$
$401$	−1.91643	+	1.91643i	−0.0957021	+	0.0957021i	0.657635	+	0.753337i	$0.271557\pi$
$402$	−0.451759	+	0.451759i	−0.0225317	+	0.0225317i
$403$	−6.05915	−	6.05915i	−0.301828	−	0.301828i
$404$	4.70804			0.234234
$405$	1.28416	+	1.28416i	0.0638106	+	0.0638106i
$406$			0.0300204i			0.00148988i
$407$	2.81401			0.139486
$408$	1.08726	−	12.5488i	0.0538273	−	0.621257i
$409$	−32.7262			−1.61821			−0.809103	−	0.587667i	$-0.800047\pi$
$409$	−32.7262			−1.61821			−0.809103	+	0.587667i	$0.800047\pi$
$410$		−	15.9382i		−	0.787132i
$411$	−0.418018	−	0.418018i	−0.0206193	−	0.0206193i
$412$	0.460662			0.0226952
$413$	3.84324	+	3.84324i	0.189113	+	0.189113i
$414$	0.786594	−	0.786594i	0.0386590	−	0.0386590i
$415$	9.27997	−	9.27997i	0.455536	−	0.455536i
$416$			3.28838i			0.161226i
$417$		−	5.78876i		−	0.283477i
$418$	7.06524	−	7.06524i	0.345572	−	0.345572i
$419$	−0.602340	+	0.602340i	−0.0294262	+	0.0294262i	−0.721667	−	0.692241i	$-0.756624\pi$
$419$	−0.602340	+	0.602340i	−0.0294262	+	0.0294262i	0.692241	+	0.721667i	$0.256624\pi$
$420$	−0.601973	−	0.601973i	−0.0293733	−	0.0293733i
$421$	1.46190			0.0712489			0.0356244	−	0.999365i	$-0.488658\pi$
$421$	1.46190			0.0712489			0.0356244	+	0.999365i	$0.488658\pi$
$422$	−6.88998	−	6.88998i	−0.335399	−	0.335399i
$423$		−	8.50780i		−	0.413663i
$424$	3.29174			0.159861
$425$	−4.51489	−	5.37147i	−0.219004	−	0.260555i
$426$	8.97467			0.434824
$427$			6.29919i			0.304839i
$428$	4.48378	+	4.48378i	0.216732	+	0.216732i
$429$	−2.99178			−0.144444
$430$	−8.29196	−	8.29196i	−0.399874	−	0.399874i
$431$	15.5055	−	15.5055i	0.746872	−	0.746872i	−0.227019	−	0.973890i	$-0.572898\pi$
$431$	15.5055	−	15.5055i	0.746872	−	0.746872i	0.973890	+	0.227019i	$0.0728979\pi$
$432$	2.01011	−	2.01011i	0.0967114	−	0.0967114i
$433$		−	25.4725i		−	1.22413i	−0.790807	−	0.612065i	$-0.790339\pi$
$433$		−	25.4725i		−	1.22413i	0.790807	−	0.612065i	$-0.209661\pi$
$434$		−	8.35855i		−	0.401223i
$435$	−0.0311541	+	0.0311541i	−0.00149373	+	0.00149373i
$436$	−3.17161	+	3.17161i	−0.151892	+	0.151892i
$437$	2.17640	+	2.17640i	0.104111	+	0.104111i
$438$	16.5074			0.788754
$439$	−26.3658	−	26.3658i	−1.25837	−	1.25837i	−0.951871	−	0.306498i	$-0.900843\pi$
$439$	−26.3658	−	26.3658i	−1.25837	−	1.25837i	−0.306498	−	0.951871i	$-0.599157\pi$
$440$			13.0842i			0.623767i
$441$	1.00000			0.0476190
$442$	4.16451	+	4.95461i	0.198085	+	0.235667i
$443$	40.4670			1.92264			0.961321	−	0.275429i	$-0.0888199\pi$
$443$	40.4670			1.92264			0.961321	+	0.275429i	$0.0888199\pi$
$444$			0.559333i			0.0265448i
$445$	13.1051	+	13.1051i	0.621240	+	0.621240i
$446$	−25.3734			−1.20147
$447$	−14.5686	−	14.5686i	−0.689071	−	0.689071i
$448$	−6.28836	+	6.28836i	−0.297097	+	0.297097i
$449$	6.73113	−	6.73113i	0.317662	−	0.317662i	−0.530207	−	0.847868i	$-0.677886\pi$
$449$	6.73113	−	6.73113i	0.317662	−	0.317662i	0.847868	+	0.530207i	$0.177886\pi$
$450$		−	2.10592i		−	0.0992740i
$451$			16.7262i			0.787604i
$452$	3.79133	−	3.79133i	0.178329	−	0.178329i
$453$	10.4859	−	10.4859i	0.492669	−	0.492669i
$454$	−7.73378	−	7.73378i	−0.362964	−	0.362964i
$455$	2.30384			0.108006
$456$	7.39596	+	7.39596i	0.346347	+	0.346347i
$457$		−	8.05510i		−	0.376802i	−0.982092	−	0.188401i	$-0.939670\pi$
$457$		−	8.05510i		−	0.376802i	0.982092	−	0.188401i	$-0.0603304\pi$
$458$	−7.74869			−0.362073
$459$	−0.355903	+	4.10772i	−0.0166122	+	0.191732i
$460$	−0.765309			−0.0356827
$461$			33.2395i			1.54812i	0.633113	+	0.774059i	$0.281777\pi$
$461$			33.2395i			1.54812i	−0.633113	+	0.774059i	$0.718223\pi$
$462$	−2.06357	−	2.06357i	−0.0960058	−	0.0960058i
$463$	18.4862			0.859125			0.429563	−	0.903037i	$-0.358668\pi$
$463$	18.4862			0.859125			0.429563	+	0.903037i	$0.358668\pi$
$464$	0.0487657	+	0.0487657i	0.00226389	+	0.00226389i
$465$	8.67422	−	8.67422i	0.402257	−	0.402257i
$466$	19.8771	−	19.8771i	0.920791	−	0.920791i
$467$			7.79833i			0.360864i	0.983587	+	0.180432i	$0.0577495\pi$
$467$			7.79833i			0.360864i	−0.983587	+	0.180432i	$0.942250\pi$
$468$		−	0.594667i		−	0.0274885i
$469$	−0.365078	+	0.365078i	−0.0168577	+	0.0168577i
$470$	13.5194	−	13.5194i	0.623604	−	0.623604i
$471$	−2.68115	−	2.68115i	−0.123541	−	0.123541i
$472$	16.6040			0.764262
$473$	8.70190	+	8.70190i	0.400114	+	0.400114i
$474$		−	13.3242i		−	0.612001i
$475$	5.82680			0.267352
$476$	0.166836	−	1.92556i	0.00764690	−	0.0882579i
$477$	−1.07752			−0.0493362
$478$			6.71569i			0.307168i
$479$	−12.8498	−	12.8498i	−0.587121	−	0.587121i	0.349729	−	0.936851i	$-0.386274\pi$
$479$	−12.8498	−	12.8498i	−0.587121	−	0.587121i	−0.936851	+	0.349729i	$0.886274\pi$
$480$	−4.70761			−0.214872
$481$	−1.07033	−	1.07033i	−0.0488026	−	0.0488026i
$482$	23.5964	−	23.5964i	1.07479	−	1.07479i
$483$	0.635667	−	0.635667i	0.0289239	−	0.0289239i
$484$			2.54919i			0.115872i
$485$		−	0.372555i		−	0.0169169i
$486$	−0.874995	+	0.874995i	−0.0396906	+	0.0396906i
$487$	−3.29305	+	3.29305i	−0.149223	+	0.149223i	−0.777771	−	0.628548i	$-0.783650\pi$
$487$	−3.29305	+	3.29305i	−0.149223	+	0.149223i	0.628548	+	0.777771i	$0.283650\pi$
$488$	13.6072	+	13.6072i	0.615971	+	0.615971i
$489$	21.6449			0.978816
$490$	1.58906	+	1.58906i	0.0717865	+	0.0717865i
$491$			41.8043i			1.88660i	0.331942	+	0.943300i	$0.392296\pi$
$491$			41.8043i			1.88660i	−0.331942	+	0.943300i	$0.607704\pi$
$492$	−3.32461			−0.149885
$493$	−0.0996542	−	0.00863430i	−0.00448820	−	0.000388869i
$494$	−5.37460			−0.241815
$495$		−	4.28300i		−	0.192506i
$496$	−13.5778	−	13.5778i	−0.609662	−	0.609662i
$497$	7.25266			0.325326
$498$	6.32313	+	6.32313i	0.283346	+	0.283346i
$499$	−7.48438	+	7.48438i	−0.335047	+	0.335047i	−0.854499	−	0.519453i	$-0.826136\pi$
$499$	−7.48438	+	7.48438i	−0.335047	+	0.335047i	0.519453	+	0.854499i	$0.326136\pi$
$500$	−4.03433	+	4.03433i	−0.180421	+	0.180421i
$501$		−	25.4646i		−	1.13768i
$502$			14.0383i			0.626561i
$503$	19.3628	−	19.3628i	0.863343	−	0.863343i	−0.128382	−	0.991725i	$-0.540978\pi$
$503$	19.3628	−	19.3628i	0.863343	−	0.863343i	0.991725	+	0.128382i	$0.0409784\pi$
$504$	2.16016	−	2.16016i	0.0962211	−	0.0962211i
$505$	−12.8974	−	12.8974i	−0.573928	−	0.573928i
$506$	−2.62348			−0.116628
$507$	−8.05445	−	8.05445i	−0.357711	−	0.357711i
$508$		−	8.17435i		−	0.362678i
$509$	−9.14311			−0.405261			−0.202631	−	0.979255i	$-0.564949\pi$
$509$	−9.14311			−0.405261			−0.202631	+	0.979255i	$0.564949\pi$
$510$	−7.09297	+	5.96186i	−0.314082	+	0.263996i
$511$	13.3401			0.590130
$512$			24.7375i			1.09325i
$513$	−2.42099	−	2.42099i	−0.106889	−	0.106889i
$514$	−32.7746			−1.44563
$515$	−1.26196	−	1.26196i	−0.0556087	−	0.0556087i
$516$	−1.72965	+	1.72965i	−0.0761436	+	0.0761436i
$517$	−14.1878	+	14.1878i	−0.623978	+	0.623978i
$518$		−	1.47650i		−	0.0648738i
$519$		−	2.98246i		−	0.130916i
$520$	4.97666	−	4.97666i	0.218241	−	0.218241i
$521$	−12.4615	+	12.4615i	−0.545949	+	0.545949i	−0.925267	−	0.379317i	$-0.876159\pi$
$521$	−12.4615	+	12.4615i	−0.545949	+	0.545949i	0.379317	+	0.925267i	$0.376159\pi$
$522$	−0.0212276	−	0.0212276i	−0.000929107	−	0.000929107i
$523$	3.52171			0.153994			0.0769969	−	0.997031i	$-0.475467\pi$
$523$	3.52171			0.153994			0.0769969	+	0.997031i	$0.475467\pi$
$524$	0.763944	+	0.763944i	0.0333730	+	0.0333730i
$525$		−	1.70185i		−	0.0742748i
$526$	0.967338			0.0421779
$527$	27.7466	+	2.40404i	1.20866	+	0.104722i
$528$	−6.70421			−0.291763
$529$			22.1919i			0.964863i
$530$	−1.71224	−	1.71224i	−0.0743751	−	0.0743751i
$531$	−5.43516			−0.235866
$532$	1.13488	+	1.13488i	0.0492033	+	0.0492033i
$533$	6.36188	−	6.36188i	0.275564	−	0.275564i
$534$	−8.92945	+	8.92945i	−0.386415	+	0.386415i
$535$		−	24.5662i		−	1.06209i
$536$			1.57725i			0.0681270i
$537$	−5.46079	+	5.46079i	−0.235650	+	0.235650i
$538$	8.83687	−	8.83687i	0.380984	−	0.380984i
$539$	−1.66762	−	1.66762i	−0.0718296	−	0.0718296i
$540$	0.851318			0.0366349
$541$	−24.5762	−	24.5762i	−1.05662	−	1.05662i	−0.998298	−	0.0583174i	$-0.981426\pi$
$541$	−24.5762	−	24.5762i	−1.05662	−	1.05662i	−0.0583174	−	0.998298i	$-0.518574\pi$
$542$		−	20.8998i		−	0.897722i
$543$	21.8503			0.937684
$544$	−6.87688	−	8.18158i	−0.294844	−	0.350782i
$545$	17.3769			0.744346
$546$			1.56978i			0.0671802i
$547$	23.2069	+	23.2069i	0.992254	+	0.992254i	0.999970	−	0.00771605i	$-0.00245612\pi$
$547$	23.2069	+	23.2069i	0.992254	+	0.992254i	−0.00771605	+	0.999970i	$0.502456\pi$
$548$	−0.277119			−0.0118379
$549$	−4.45420	−	4.45420i	−0.190101	−	0.190101i
$550$	−3.51188	+	3.51188i	−0.149747	+	0.149747i
$551$	0.0587339	−	0.0587339i	0.00250215	−	0.00250215i
$552$		−	2.74629i		−	0.116890i
$553$		−	10.7677i		−	0.457887i
$554$	3.77698	−	3.77698i	0.160469	−	0.160469i
$555$	1.53227	−	1.53227i	0.0650410	−	0.0650410i
$556$	−1.91879	−	1.91879i	−0.0813748	−	0.0813748i
$557$	33.5274			1.42060			0.710300	−	0.703899i	$-0.248559\pi$
$557$	33.5274			1.42060			0.710300	+	0.703899i	$0.248559\pi$
$558$	5.91039	+	5.91039i	0.250207	+	0.250207i
$559$		−	6.61962i		−	0.279980i
$560$	5.16262			0.218160
$561$	7.44363	−	6.25661i	0.314270	−	0.264154i
$562$	18.1931			0.767430
$563$		−	39.1139i		−	1.64845i	−0.566260	−	0.824226i	$-0.691610\pi$
$563$		−	39.1139i		−	1.64845i	0.566260	−	0.824226i	$-0.308390\pi$
$564$	−2.82006	−	2.82006i	−0.118746	−	0.118746i
$565$	−20.7723			−0.873899
$566$	9.05996	+	9.05996i	0.380819	+	0.380819i
$567$	−0.707107	+	0.707107i	−0.0296957	+	0.0296957i
$568$	15.6669	−	15.6669i	0.657369	−	0.657369i
$569$		−	18.6068i		−	0.780037i	−0.920807	−	0.390018i	$-0.872469\pi$
$569$		−	18.6068i		−	0.780037i	0.920807	−	0.390018i	$-0.127531\pi$
$570$		−	7.69422i		−	0.322275i
$571$	1.41482	−	1.41482i	0.0592085	−	0.0592085i	−0.676883	−	0.736091i	$-0.736670\pi$
$571$	1.41482	−	1.41482i	0.0592085	−	0.0592085i	0.736091	+	0.676883i	$0.236670\pi$
$572$	−0.991679	+	0.991679i	−0.0414642	+	0.0414642i
$573$	−16.0713	−	16.0713i	−0.671390	−	0.671390i
$574$	8.77616			0.366310
$575$	−1.08181	−	1.08181i	−0.0451146	−	0.0451146i
$576$		−	8.89309i		−	0.370545i
$577$	10.9555			0.456083			0.228042	−	0.973651i	$-0.426768\pi$
$577$	10.9555			0.456083			0.228042	+	0.973651i	$0.426768\pi$
$578$	−20.7228	−	3.61812i	−0.861956	−	0.150494i
$579$	−23.4939			−0.976375
$580$			0.0206532i			0.000857577i
$581$	5.10989	+	5.10989i	0.211994	+	0.211994i
$582$	0.253850			0.0105224
$583$	1.79689	+	1.79689i	0.0744197	+	0.0744197i
$584$	28.8167	−	28.8167i	1.19244	−	1.19244i
$585$	−1.62906	+	1.62906i	−0.0673534	+	0.0673534i
$586$			13.5930i			0.561520i
$587$			4.27209i			0.176328i	0.996106	+	0.0881640i	$0.0281000\pi$
$587$			4.27209i			0.176328i	−0.996106	+	0.0881640i	$0.971900\pi$
$588$	0.331468	−	0.331468i	0.0136695	−	0.0136695i
$589$	−16.3532	+	16.3532i	−0.673823	+	0.673823i
$590$	−8.63681	−	8.63681i	−0.355572	−	0.355572i
$591$	6.79070			0.279332
$592$	−2.39847	−	2.39847i	−0.0985763	−	0.0985763i
$593$			19.2572i			0.790799i	0.918509	+	0.395399i	$0.129394\pi$
$593$			19.2572i			0.790799i	−0.918509	+	0.395399i	$0.870606\pi$
$594$	2.91832			0.119740
$595$	−5.73202	+	4.81794i	−0.234990	+	0.197516i
$596$	−9.65805			−0.395609
$597$			5.04115i			0.206320i
$598$	0.997855	+	0.997855i	0.0408053	+	0.0408053i
$599$	4.47849			0.182986			0.0914931	−	0.995806i	$-0.470836\pi$
$599$	4.47849			0.182986			0.0914931	+	0.995806i	$0.470836\pi$
$600$	−3.67627	−	3.67627i	−0.150083	−	0.150083i
$601$	−24.4616	+	24.4616i	−0.997811	+	0.997811i	−0.999998	−	0.00218683i	$-0.999304\pi$
$601$	−24.4616	+	24.4616i	−0.997811	+	0.997811i	0.00218683	+	0.999998i	$0.499304\pi$
$602$	4.56585	−	4.56585i	0.186090	−	0.186090i
$603$		−	0.516299i		−	0.0210253i
$604$		−	6.95145i		−	0.282851i
$605$	6.98338	−	6.98338i	0.283915	−	0.283915i
$606$	8.78797	−	8.78797i	0.356987	−	0.356987i
$607$	1.88069	+	1.88069i	0.0763350	+	0.0763350i	0.744243	−	0.667908i	$-0.232810\pi$
$607$	1.88069	+	1.88069i	0.0763350	+	0.0763350i	−0.667908	+	0.744243i	$0.732810\pi$
$608$	8.87511			0.359933
$609$	−0.0171546	−	0.0171546i	−0.000695139	−	0.000695139i
$610$		−	14.1560i		−	0.573160i
$611$	10.7928			0.436630
$612$	1.24361	+	1.47955i	0.0502698	+	0.0598072i
$613$	−8.81178			−0.355905			−0.177952	−	0.984039i	$-0.556947\pi$
$613$	−8.81178			−0.355905			−0.177952	+	0.984039i	$0.556947\pi$
$614$		−	17.0895i		−	0.689674i
$615$	9.10760	+	9.10760i	0.367254	+	0.367254i
$616$	−7.20466			−0.290284
$617$	−17.5550	−	17.5550i	−0.706738	−	0.706738i	0.259110	−	0.965848i	$-0.416571\pi$
$617$	−17.5550	−	17.5550i	−0.706738	−	0.706738i	−0.965848	+	0.259110i	$0.916571\pi$
$618$	0.859868	−	0.859868i	0.0345890	−	0.0345890i
$619$	−13.3538	+	13.3538i	−0.536733	+	0.536733i	−0.922568	−	0.385835i	$-0.873913\pi$
$619$	−13.3538	+	13.3538i	−0.536733	+	0.536733i	0.385835	+	0.922568i	$0.373913\pi$
$620$		−	5.75045i		−	0.230944i
$621$			0.898969i			0.0360744i
$622$	−21.2317	+	21.2317i	−0.851314	+	0.851314i
$623$	−7.21613	+	7.21613i	−0.289108	+	0.289108i
$624$	2.54998	+	2.54998i	0.102081	+	0.102081i
$625$	13.5945			0.543778
$626$	−14.0702	−	14.0702i	−0.562359	−	0.562359i
$627$			8.07460i			0.322469i
$628$	−1.77743			−0.0709273
$629$	4.90133	+	0.424665i	0.195429	+	0.0169325i
$630$	−2.24727			−0.0895335
$631$			33.5614i			1.33606i	0.744135	+	0.668030i	$0.232862\pi$
$631$			33.5614i			1.33606i	−0.744135	+	0.668030i	$0.767138\pi$
$632$	−23.2598	−	23.2598i	−0.925227	−	0.925227i
$633$	7.87431			0.312976
$634$	−3.75459	−	3.75459i	−0.149114	−	0.149114i
$635$	−22.3932	+	22.3932i	−0.888648	+	0.888648i
$636$	−0.357163	+	0.357163i	−0.0141624	+	0.0141624i
$637$			1.26858i			0.0502629i
$638$			0.0707992i			0.00280297i
$639$	−5.12841	+	5.12841i	−0.202877	+	0.202877i
$640$	7.47411	−	7.47411i	0.295440	−	0.295440i
$641$	12.7679	+	12.7679i	0.504302	+	0.504302i	0.912772	−	0.408470i	$-0.133937\pi$
$641$	12.7679	+	12.7679i	0.504302	+	0.504302i	−0.408470	+	0.912772i	$0.633937\pi$
$642$	16.7388			0.660626
$643$	−18.7783	−	18.7783i	−0.740543	−	0.740543i	0.232139	−	0.972683i	$-0.425428\pi$
$643$	−18.7783	−	18.7783i	−0.740543	−	0.740543i	−0.972683	+	0.232139i	$0.925428\pi$
$644$		−	0.421407i		−	0.0166058i
$645$	9.47658			0.373140
$646$	13.3722	−	11.2397i	0.526121	−	0.442221i
$647$	−12.7877			−0.502735			−0.251367	−	0.967892i	$-0.580880\pi$
$647$	−12.7877			−0.502735			−0.251367	+	0.967892i	$0.580880\pi$
$648$			3.05493i			0.120009i
$649$	9.06379	+	9.06379i	0.355785	+	0.355785i
$650$	2.67152			0.104786
$651$	4.77634	+	4.77634i	0.187199	+	0.187199i
$652$	7.17459	−	7.17459i	0.280979	−	0.280979i
$653$	−0.199511	+	0.199511i	−0.00780745	+	0.00780745i	−0.711000	−	0.703192i	$-0.751757\pi$
$653$	−0.199511	+	0.199511i	−0.00780745	+	0.00780745i	0.703192	+	0.711000i	$0.251757\pi$
$654$			11.8402i			0.462988i
$655$		−	4.18557i		−	0.163544i
$656$	14.2562	−	14.2562i	0.556611	−	0.556611i
$657$	−9.43285	+	9.43285i	−0.368010	+	0.368010i
$658$	7.44428	+	7.44428i	0.290208	+	0.290208i
$659$	−38.5587			−1.50203			−0.751017	−	0.660283i	$-0.770436\pi$
$659$	−38.5587			−1.50203			−0.751017	+	0.660283i	$0.770436\pi$
$660$	−1.41968	−	1.41968i	−0.0552609	−	0.0552609i
$661$		−	19.9752i		−	0.776944i	−0.921461	−	0.388472i	$-0.873003\pi$
$661$		−	19.9752i		−	0.776944i	0.921461	−	0.388472i	$-0.126997\pi$
$662$	−23.8991			−0.928863
$663$	−5.21096	−	0.451491i	−0.202377	−	0.0175345i
$664$	22.0763			0.856728
$665$		−	6.21790i		−	0.241120i
$666$	1.04405	+	1.04405i	0.0404559	+	0.0404559i
$667$	−0.0218092			−0.000844456
$668$	−8.44071	−	8.44071i	−0.326581	−	0.326581i
$669$	14.4992	−	14.4992i	0.560570	−	0.560570i
$670$	0.820431	−	0.820431i	0.0316960	−	0.0316960i
$671$			14.8558i			0.573503i
$672$		−	2.59218i		−	0.0999955i
$673$	−29.9293	+	29.9293i	−1.15369	+	1.15369i	−0.167882	+	0.985807i	$0.553693\pi$
$673$	−29.9293	+	29.9293i	−1.15369	+	1.15369i	−0.985807	+	0.167882i	$0.946307\pi$
$674$	17.1571	−	17.1571i	0.660866	−	0.660866i
$675$	1.20339	+	1.20339i	0.0463185	+	0.0463185i
$676$	−5.33959			−0.205369
$677$	−29.6635	−	29.6635i	−1.14006	−	1.14006i	−0.988438	−	0.151624i	$-0.951550\pi$
$677$	−29.6635	−	29.6635i	−1.14006	−	1.14006i	−0.151624	−	0.988438i	$-0.548450\pi$
$678$		−	14.1537i		−	0.543571i
$679$	0.205143			0.00787265
$680$	−1.97455	+	22.7896i	−0.0757205	+	0.873941i
$681$	8.83865			0.338698
$682$		−	19.7126i		−	0.754834i
$683$	13.1896	+	13.1896i	0.504686	+	0.504686i	0.912891	−	0.408205i	$-0.133845\pi$
$683$	13.1896	+	13.1896i	0.504686	+	0.504686i	−0.408205	+	0.912891i	$0.633845\pi$
$684$	−1.60496			−0.0613673
$685$	0.759154	+	0.759154i	0.0290058	+	0.0290058i
$686$	−0.874995	+	0.874995i	−0.0334075	+	0.0334075i
$687$	4.42785	−	4.42785i	0.168933	−	0.168933i
$688$		−	14.8338i		−	0.565532i
$689$		−	1.36691i		−	0.0520753i
$690$	−1.42852	+	1.42852i	−0.0543828	+	0.0543828i
$691$	−21.1245	+	21.1245i	−0.803615	+	0.803615i	−0.983659	−	0.180043i	$-0.942376\pi$
$691$	−21.1245	+	21.1245i	−0.803615	+	0.803615i	0.180043	+	0.983659i	$0.442376\pi$
$692$	−0.988591	−	0.988591i	−0.0375806	−	0.0375806i
$693$	2.35837			0.0895872
$694$	1.96078	+	1.96078i	0.0744303	+	0.0744303i
$695$			10.5129i			0.398776i
$696$	−0.0741132			−0.00280926
$697$	−2.52415	+	29.1329i	−0.0956092	+	1.10349i
$698$	27.6385			1.04613
$699$			22.7169i			0.859231i
$700$	−0.564109	−	0.564109i	−0.0213213	−	0.0213213i
$701$	−29.6430			−1.11960			−0.559800	−	0.828628i	$-0.689122\pi$
$701$	−29.6430			−1.11960			−0.559800	+	0.828628i	$0.689122\pi$
$702$	−1.11000	−	1.11000i	−0.0418942	−	0.0418942i
$703$	−2.88873	+	2.88873i	−0.108951	+	0.108951i
$704$	−14.8303	+	14.8303i	−0.558938	+	0.558938i
$705$			15.4509i			0.581913i
$706$			9.87572i			0.371677i
$707$	7.10179	−	7.10179i	0.267090	−	0.267090i
$708$	−1.80158	+	1.80158i	−0.0677076	+	0.0677076i
$709$	−34.5354	−	34.5354i	−1.29700	−	1.29700i	−0.930363	−	0.366640i	$-0.880508\pi$
$709$	−34.5354	−	34.5354i	−1.29700	−	1.29700i	−0.366640	−	0.930363i	$-0.619492\pi$
$710$	−16.2987			−0.611680
$711$	7.61388	+	7.61388i	0.285543	+	0.285543i
$712$			31.1760i			1.16837i
$713$	6.07233			0.227410
$714$	−3.28282	−	3.90565i	−0.122856	−	0.146165i
$715$	5.43331			0.203194
$716$			3.62015i			0.135292i
$717$	−3.83756	−	3.83756i	−0.143316	−	0.143316i
$718$	26.4742			0.988008
$719$	23.9009	+	23.9009i	0.891354	+	0.891354i	0.994651	−	0.103297i	$-0.0329391\pi$
$719$	23.9009	+	23.9009i	0.891354	+	0.891354i	−0.103297	+	0.994651i	$0.532939\pi$
$720$	−3.65052	+	3.65052i	−0.136047	+	0.136047i
$721$	0.694882	−	0.694882i	0.0258788	−	0.0258788i
$722$		−	9.00550i		−	0.335150i
$723$			26.9675i			1.00293i
$724$	7.24266	−	7.24266i	0.269171	−	0.269171i
$725$	−0.0291945	+	0.0291945i	−0.00108426	+	0.00108426i
$726$	4.75829	+	4.75829i	0.176597	+	0.176597i
$727$	−12.4398			−0.461367			−0.230684	−	0.973029i	$-0.574096\pi$
$727$	−12.4398			−0.461367			−0.230684	+	0.973029i	$0.574096\pi$
$728$	2.74033	+	2.74033i	0.101563	+	0.101563i
$729$		−	1.00000i		−	0.0370370i
$730$	−29.9788			−1.10956
$731$	13.8434	+	16.4698i	0.512016	+	0.609158i
$732$	−2.95285			−0.109140
$733$		−	13.2154i		−	0.488123i	−0.969760	−	0.244061i	$-0.921520\pi$
$733$		−	13.2154i		−	0.488123i	0.969760	−	0.244061i	$-0.0784798\pi$
$734$	0.966986	+	0.966986i	0.0356921	+	0.0356921i
$735$	−1.81608			−0.0669872
$736$	−1.64776	−	1.64776i	−0.0607374	−	0.0607374i
$737$	−0.860991	+	0.860991i	−0.0317150	+	0.0317150i
$738$	−6.20568	+	6.20568i	−0.228434	+	0.228434i
$739$			32.3074i			1.18845i	0.804300	+	0.594223i	$0.202540\pi$
$739$			32.3074i			1.18845i	−0.804300	+	0.594223i	$0.797460\pi$
$740$		−	1.01579i		−	0.0373413i
$741$	3.07122	−	3.07122i	0.112824	−	0.112824i
$742$	0.942823	−	0.942823i	0.0346121	−	0.0346121i
$743$	−32.4829	−	32.4829i	−1.19168	−	1.19168i	−0.976595	−	0.215088i	$-0.930996\pi$
$743$	−32.4829	−	32.4829i	−1.19168	−	1.19168i	−0.215088	−	0.976595i	$-0.569004\pi$
$744$	20.6353			0.756527
$745$	26.4577	+	26.4577i	0.969337	+	0.969337i
$746$			32.3862i			1.18574i
$747$	−7.22647			−0.264403
$748$	0.393461	−	4.54119i	0.0143864	−	0.166042i
$749$	13.5270			0.494267
$750$			15.0609i			0.549946i
$751$	34.9317	+	34.9317i	1.27468	+	1.27468i	0.943606	+	0.331071i	$0.107410\pi$
$751$	34.9317	+	34.9317i	1.27468	+	1.27468i	0.331071	+	0.943606i	$0.392590\pi$
$752$	24.1853			0.881948
$753$	−8.02195	−	8.02195i	−0.292336	−	0.292336i
$754$	0.0269288	−	0.0269288i	0.000980691	−	0.000980691i
$755$	−19.0432	+	19.0432i	−0.693052	+	0.693052i
$756$			0.468767i			0.0170489i
$757$			44.2730i			1.60913i	0.593866	+	0.804564i	$0.297601\pi$
$757$			44.2730i			1.60913i	−0.593866	+	0.804564i	$0.702399\pi$
$758$	−24.2891	+	24.2891i	−0.882219	+	0.882219i
$759$	1.49914	−	1.49914i	0.0544154	−	0.0544154i
$760$	−13.4317	−	13.4317i	−0.487217	−	0.487217i
$761$	5.71316			0.207102			0.103551	−	0.994624i	$-0.466979\pi$
$761$	5.71316			0.207102			0.103551	+	0.994624i	$0.466979\pi$
$762$	−15.2582	−	15.2582i	−0.552745	−	0.552745i
$763$			9.56837i			0.346398i
$764$	−10.6543			−0.385458
$765$	0.646350	−	7.45995i	0.0233688	−	0.269715i
$766$	−22.0486			−0.796648
$767$		−	6.89492i		−	0.248961i
$768$	−7.48407	−	7.48407i	−0.270058	−	0.270058i
$769$	27.7810			1.00181			0.500904	−	0.865503i	$-0.333001\pi$
$769$	27.7810			1.00181			0.500904	+	0.865503i	$0.333001\pi$
$770$	3.74760	+	3.74760i	0.135054	+	0.135054i
$771$	18.7285	−	18.7285i	0.674489	−	0.674489i
$772$	−7.78749	+	7.78749i	−0.280278	+	0.280278i
$773$		−	14.0849i		−	0.506600i	−0.967388	−	0.253300i	$-0.918484\pi$
$773$		−	14.0849i		−	0.506600i	0.967388	−	0.253300i	$-0.0815160\pi$
$774$			6.45709i			0.232095i
$775$	8.12861	−	8.12861i	0.291988	−	0.291988i
$776$	0.443141	−	0.443141i	0.0159078	−	0.0159078i
$777$	0.843721	+	0.843721i	0.0302683	+	0.0302683i
$778$	27.9392			1.00167
$779$	−17.1703	−	17.1703i	−0.615189	−	0.615189i
$780$			1.07996i			0.0386689i
$781$	17.1045			0.612047
$782$	−4.56947	−	0.395911i	−0.163404	−	0.0141578i
$783$	0.0242602			0.000866990
$784$			2.84272i			0.101526i
$785$	4.86919	+	4.86919i	0.173789	+	0.173789i
$786$	2.85194			0.101725
$787$	12.3554	+	12.3554i	0.440422	+	0.440422i	0.892154	−	0.451732i	$-0.149194\pi$
$787$	12.3554	+	12.3554i	0.440422	+	0.440422i	−0.451732	+	0.892154i	$0.649194\pi$
$788$	2.25090	−	2.25090i	0.0801850	−	0.0801850i
$789$	−0.552768	+	0.552768i	−0.0196790	+	0.0196790i
$790$			24.1979i			0.860921i
$791$		−	11.4380i		−	0.406689i
$792$	5.09446	−	5.09446i	0.181024	−	0.181024i
$793$	5.65049	−	5.65049i	0.200655	−	0.200655i
$794$	31.5620	+	31.5620i	1.12009	+	1.12009i
$795$	1.95686			0.0694027
$796$	1.67098	+	1.67098i	0.0592263	+	0.0592263i
$797$			16.4792i			0.583724i	0.956460	+	0.291862i	$0.0942748\pi$
$797$			16.4792i			0.583724i	−0.956460	+	0.291862i	$0.905725\pi$
$798$	4.23672			0.149978
$799$	−26.8528	+	22.5706i	−0.949983	+	0.798491i
$800$	−4.41150			−0.155970
$801$		−	10.2051i		−	0.360581i
$802$	2.37145	+	2.37145i	0.0837389	+	0.0837389i
$803$	31.4608			1.11023
$804$	−0.171137	−	0.171137i	−0.00603552	−	0.00603552i
$805$	−1.15442	+	1.15442i	−0.0406881	+	0.0406881i
$806$	−7.49778	+	7.49778i	−0.264098	+	0.264098i
$807$			10.0993i			0.355513i
$808$		−	30.6820i		−	1.07939i
$809$	22.2206	−	22.2206i	0.781235	−	0.781235i	−0.198804	−	0.980039i	$-0.563706\pi$
$809$	22.2206	−	22.2206i	0.781235	−	0.781235i	0.980039	+	0.198804i	$0.0637057\pi$
$810$	1.58906	−	1.58906i	0.0558340	−	0.0558340i
$811$	−15.5129	−	15.5129i	−0.544732	−	0.544732i	0.380181	−	0.924912i	$-0.375862\pi$
$811$	−15.5129	−	15.5129i	−0.544732	−	0.544732i	−0.924912	+	0.380181i	$0.875862\pi$
$812$	−0.0113724			−0.000399093
$813$	11.9428	+	11.9428i	0.418852	+	0.418852i
$814$		−	3.48215i		−	0.122049i
$815$	−39.3089			−1.37693
$816$	−11.6771	−	1.01174i	−0.408780	−	0.0354178i
$817$	−17.8659			−0.625049
$818$			40.4964i			1.41592i
$819$	−0.897020	−	0.897020i	−0.0313444	−	0.0313444i
$820$	6.03776			0.210848
$821$	15.2116	+	15.2116i	0.530888	+	0.530888i	0.920837	−	0.389948i	$-0.127507\pi$
$821$	15.2116	+	15.2116i	0.530888	+	0.530888i	−0.389948	+	0.920837i	$0.627507\pi$
$822$	−0.517268	+	0.517268i	−0.0180418	+	0.0180418i
$823$	30.4939	−	30.4939i	1.06295	−	1.06295i	0.0650702	−	0.997881i	$-0.479273\pi$
$823$	30.4939	−	30.4939i	1.06295	−	1.06295i	0.997881	−	0.0650702i	$-0.0207271\pi$
$824$		−	3.00211i		−	0.104584i
$825$		−	4.01360i		−	0.139735i
$826$	4.75574	−	4.75574i	0.165473	−	0.165473i
$827$	−18.6909	+	18.6909i	−0.649947	+	0.649947i	−0.952980	−	0.303033i	$-0.902001\pi$
$827$	−18.6909	+	18.6909i	−0.649947	+	0.649947i	0.303033	+	0.952980i	$0.402001\pi$
$828$	0.297980	+	0.297980i	0.0103555	+	0.0103555i
$829$	−4.62524			−0.160641			−0.0803205	−	0.996769i	$-0.525594\pi$
$829$	−4.62524			−0.160641			−0.0803205	+	0.996769i	$0.525594\pi$
$830$	−11.4833	−	11.4833i	−0.398592	−	0.398592i
$831$			4.31657i			0.149740i
$832$	11.2816			0.391118
$833$	−2.65293	−	3.15626i	−0.0919187	−	0.109358i
$834$	−7.16319			−0.248041
$835$			46.2458i			1.60040i
$836$	2.67647	+	2.67647i	0.0925678	+	0.0925678i
$837$	−6.75476			−0.233479
$838$	0.745353	+	0.745353i	0.0257478	+	0.0257478i
$839$	22.3535	−	22.3535i	0.771729	−	0.771729i	−0.206679	−	0.978409i	$-0.566266\pi$
$839$	22.3535	−	22.3535i	0.771729	−	0.771729i	0.978409	+	0.206679i	$0.0662657\pi$
$840$	−3.92302	+	3.92302i	−0.135357	+	0.135357i
$841$		−	28.9994i		−	0.999980i
$842$		−	1.80900i		−	0.0623424i
$843$	−10.3961	+	10.3961i	−0.358061	+	0.358061i
$844$	2.61008	−	2.61008i	0.0898427	−	0.0898427i
$845$	14.6275	+	14.6275i	0.503202	+	0.503202i
$846$	−10.5278			−0.361953
$847$	3.84530	+	3.84530i	0.132126	+	0.132126i
$848$		−	3.06309i		−	0.105187i
$849$	−10.3543			−0.355359
$850$	−6.64682	+	5.58686i	−0.227984	+	0.191628i
$851$	1.07265			0.0367700
$852$			3.39981i			0.116475i
$853$	3.57097	+	3.57097i	0.122268	+	0.122268i	0.765593	−	0.643325i	$-0.222446\pi$
$853$	3.57097	+	3.57097i	0.122268	+	0.122268i	−0.643325	+	0.765593i	$0.722446\pi$
$854$	7.79480			0.266733
$855$	4.39672	+	4.39672i	0.150365	+	0.150365i
$856$	29.2206	−	29.2206i	0.998738	−	0.998738i
$857$	−8.28814	+	8.28814i	−0.283117	+	0.283117i	−0.834351	−	0.551234i	$-0.814157\pi$
$857$	−8.28814	+	8.28814i	−0.283117	+	0.283117i	0.551234	+	0.834351i	$0.314157\pi$
$858$			3.70212i			0.126388i
$859$		−	48.5065i		−	1.65502i	−0.561450	−	0.827510i	$-0.689756\pi$
$859$		−	48.5065i		−	1.65502i	0.561450	−	0.827510i	$-0.310244\pi$
$860$	3.14118	−	3.14118i	0.107113	−	0.107113i
$861$	−5.01497	+	5.01497i	−0.170910	+	0.170910i
$862$	−19.1869	−	19.1869i	−0.653509	−	0.653509i
$863$	−13.5157			−0.460081			−0.230041	−	0.973181i	$-0.573886\pi$
$863$	−13.5157			−0.460081			−0.230041	+	0.973181i	$0.573886\pi$
$864$	1.83295	+	1.83295i	0.0623582	+	0.0623582i
$865$			5.41639i			0.184163i
$866$	−31.5204			−1.07111
$867$	13.9092	−	9.77417i	0.472381	−	0.331948i
$868$	3.16641			0.107475
$869$		−	25.3941i		−	0.861437i
$870$	0.0385510	+	0.0385510i	0.00130700	+	0.00130700i
$871$	0.654965			0.0221926
$872$	20.6692	+	20.6692i	0.699947	+	0.699947i
$873$	−0.145058	+	0.145058i	−0.00490946	+	0.00490946i
$874$	2.69314	−	2.69314i	0.0910969	−	0.0910969i
$875$			12.1711i			0.411458i
$876$			6.25338i			0.211282i
$877$	−28.3876	+	28.3876i	−0.958582	+	0.958582i	−0.999176	−	0.0405941i	$-0.987075\pi$
$877$	−28.3876	+	28.3876i	−0.958582	+	0.958582i	0.0405941	+	0.999176i	$0.487075\pi$
$878$	−32.6258	+	32.6258i	−1.10107	+	1.10107i
$879$	−7.76745	−	7.76745i	−0.261990	−	0.261990i
$880$	12.1754			0.410432
$881$	−18.6392	−	18.6392i	−0.627969	−	0.627969i	0.319588	−	0.947557i	$-0.396456\pi$
$881$	−18.6392	−	18.6392i	−0.627969	−	0.627969i	−0.947557	+	0.319588i	$0.896456\pi$
$882$		−	1.23743i		−	0.0416664i
$883$	50.3856			1.69561			0.847805	−	0.530308i	$-0.177924\pi$
$883$	50.3856			1.69561			0.847805	+	0.530308i	$0.177924\pi$
$884$	−1.87692	+	1.57761i	−0.0631277	+	0.0530608i
$885$	9.87069			0.331800
$886$		−	50.0750i		−	1.68230i
$887$	14.6144	+	14.6144i	0.490703	+	0.490703i	0.908528	−	0.417824i	$-0.137207\pi$
$887$	14.6144	+	14.6144i	0.490703	+	0.490703i	−0.417824	+	0.908528i	$0.637207\pi$
$888$	3.64514			0.122323
$889$	−12.3305	−	12.3305i	−0.413552	−	0.413552i
$890$	16.2166	−	16.2166i	0.543582	−	0.543582i
$891$	−1.66762	+	1.66762i	−0.0558674	+	0.0558674i
$892$		−	9.61203i		−	0.321834i
$893$		−	29.1290i		−	0.974765i
$894$	−18.0276	+	18.0276i	−0.602934	+	0.602934i
$895$	9.91724	−	9.91724i	0.331497	−	0.331497i
$896$	4.11552	+	4.11552i	0.137490	+	0.137490i
$897$	−1.14041			−0.0380773
$898$	−8.32930	−	8.32930i	−0.277952	−	0.277952i
$899$		−	0.163872i		−	0.00546544i
$900$	0.797770			0.0265923
$901$	2.85858	+	3.40092i	0.0952332	+	0.113301i
$902$	20.6975			0.689150
$903$			5.21815i			0.173649i
$904$	−24.7079	−	24.7079i	−0.821773	−	0.821773i
$905$	−39.6818			−1.31907
$906$	−12.9755	−	12.9755i	−0.431083	−	0.431083i
$907$	−2.60816	+	2.60816i	−0.0866027	+	0.0866027i	−0.749081	−	0.662478i	$-0.769505\pi$
$907$	−2.60816	+	2.60816i	−0.0866027	+	0.0866027i	0.662478	+	0.749081i	$0.269505\pi$
$908$	2.92973	−	2.92973i	0.0972265	−	0.0972265i
$909$			10.0435i			0.333120i
$910$		−	2.85084i		−	0.0945044i
$911$	4.02408	−	4.02408i	0.133324	−	0.133324i	−0.637296	−	0.770619i	$-0.719947\pi$
$911$	4.02408	−	4.02408i	0.133324	−	0.133324i	0.770619	+	0.637296i	$0.219947\pi$
$912$	6.88222	−	6.88222i	0.227893	−	0.227893i
$913$	12.0510	+	12.0510i	0.398831	+	0.398831i
$914$	−9.96762			−0.329700
$915$	8.08918	+	8.08918i	0.267420	+	0.267420i
$916$		−	2.93538i		−	0.0969877i
$917$	2.30473			0.0761088
$918$	5.08301	+	0.440406i	0.167764	+	0.0145356i
$919$	14.4789			0.477614			0.238807	−	0.971067i	$-0.423244\pi$
$919$	14.4789			0.477614			0.238807	+	0.971067i	$0.423244\pi$
$920$			4.98748i			0.164432i
$921$	9.76546	+	9.76546i	0.321783	+	0.321783i
$922$	41.1316			1.35460
$923$	−6.50578	−	6.50578i	−0.214140	−	0.214140i
$924$	0.781726	−	0.781726i	0.0257169	−	0.0257169i
$925$	1.43589	−	1.43589i	0.0472116	−	0.0472116i
$926$		−	22.8754i		−	0.751731i
$927$			0.982712i			0.0322765i
$928$	−0.0444678	+	0.0444678i	−0.00145973	+	0.00145973i
$929$	−7.28149	+	7.28149i	−0.238898	+	0.238898i	−0.816394	−	0.577496i	$-0.804030\pi$
$929$	−7.28149	+	7.28149i	−0.238898	+	0.238898i	0.577496	+	0.816394i	$0.304030\pi$
$930$	−10.7337	−	10.7337i	−0.351973	−	0.351973i
$931$	3.42380			0.112211
$932$	7.52992	+	7.52992i	0.246651	+	0.246651i
$933$		−	24.2650i		−	0.794399i
$934$	9.64989			0.315754
$935$	−13.5182	+	11.3625i	−0.442094	+	0.371594i
$936$	−3.87541			−0.126672
$937$		−	32.4551i		−	1.06026i	−0.847915	−	0.530132i	$-0.822142\pi$
$937$		−	32.4551i		−	1.06026i	0.847915	−	0.530132i	$-0.177858\pi$
$938$	0.451759	+	0.451759i	0.0147504	+	0.0147504i
$939$	16.0803			0.524762
$940$	5.12146	+	5.12146i	0.167044	+	0.167044i
$941$	−10.3355	+	10.3355i	−0.336929	+	0.336929i	−0.855210	−	0.518282i	$-0.826572\pi$
$941$	−10.3355	+	10.3355i	−0.336929	+	0.336929i	0.518282	+	0.855210i	$0.326572\pi$
$942$	−3.31774	+	3.31774i	−0.108098	+	0.108098i
$943$			6.37571i			0.207622i
$944$		−	15.4507i		−	0.502876i
$945$	1.28416	−	1.28416i	0.0417738	−	0.0417738i
$946$	10.7680	−	10.7680i	0.350098	−	0.350098i
$947$	0.492002	+	0.492002i	0.0159879	+	0.0159879i	0.715056	−	0.699068i	$-0.246401\pi$
$947$	0.492002	+	0.492002i	0.0159879	+	0.0159879i	−0.699068	+	0.715056i	$0.746401\pi$
$948$	5.04752			0.163936
$949$	−11.9663	−	11.9663i	−0.388442	−	0.388442i
$950$		−	7.21025i		−	0.233931i
$951$	4.29099			0.139145
$952$	−12.5488	−	1.08726i	−0.406708	−	0.0352383i
$953$	−36.8109			−1.19242			−0.596210	−	0.802828i	$-0.703328\pi$
$953$	−36.8109			−1.19242			−0.596210	+	0.802828i	$0.703328\pi$
$954$			1.33335i			0.0431689i
$955$	29.1869	+	29.1869i	0.944465	+	0.944465i
$956$	−2.54406			−0.0822806
$957$	−0.0404569	−	0.0404569i	−0.00130779	−	0.00130779i
$958$	−15.9007	+	15.9007i	−0.513728	+	0.513728i
$959$	−0.418018	+	0.418018i	−0.0134985	+	0.0134985i
$960$			16.1506i			0.521258i
$961$			14.6268i			0.471833i
$962$	−1.32445	+	1.32445i	−0.0427021	+	0.0427021i
$963$	−9.56506	+	9.56506i	−0.308230	+	0.308230i
$964$	8.93887	+	8.93887i	0.287902	+	0.287902i
$965$	42.6669			1.37350
$966$	−0.786594	−	0.786594i	−0.0253082	−	0.0253082i
$967$			3.34730i			0.107642i	0.998551	+	0.0538210i	$0.0171400\pi$
$967$			3.34730i			0.107642i	−0.998551	+	0.0538210i	$0.982860\pi$
$968$	16.6129			0.533959
$969$	−1.21854	+	14.0640i	−0.0391452	+	0.451801i
$970$	−0.461011			−0.0148022
$971$		−	5.99767i		−	0.192474i	−0.995358	−	0.0962372i	$-0.969319\pi$
$971$		−	5.99767i		−	0.192474i	0.995358	−	0.0962372i	$-0.0306807\pi$
$972$	−0.331468	−	0.331468i	−0.0106318	−	0.0106318i
$973$	−5.78876			−0.185579
$974$	4.07492	+	4.07492i	0.130569	+	0.130569i
$975$	−1.52659	+	1.52659i	−0.0488901	+	0.0488901i
$976$	12.6621	−	12.6621i	0.405303	−	0.405303i
$977$		−	30.5729i		−	0.978115i	−0.872252	−	0.489058i	$-0.837341\pi$
$977$		−	30.5729i		−	0.978115i	0.872252	−	0.489058i	$-0.162659\pi$
$978$		−	26.7840i		−	0.856459i
$979$	−17.0183	+	17.0183i	−0.543908	+	0.543908i
$980$	−0.601973	+	0.601973i	−0.0192293	+	0.0192293i
$981$	−6.76586	−	6.76586i	−0.216017	−	0.216017i
$982$	51.7298			1.65077
$983$	0.787273	+	0.787273i	0.0251101	+	0.0251101i	0.719550	−	0.694440i	$-0.244348\pi$
$983$	0.787273	+	0.787273i	0.0251101	+	0.0251101i	−0.694440	+	0.719550i	$0.744348\pi$
$984$			21.6663i			0.690696i
$985$	−12.3325			−0.392945
$986$	−0.0106843	+	0.123315i	−0.000340259	+	0.00392715i
$987$	−8.50780			−0.270806
$988$		−	2.03602i		−	0.0647745i
$989$	3.31701	+	3.31701i	0.105475	+	0.105475i
$990$	−5.29991			−0.168442
$991$	−28.8371	−	28.8371i	−0.916039	−	0.916039i	0.0806990	−	0.996739i	$-0.474285\pi$
$991$	−28.8371	−	28.8371i	−0.916039	−	0.916039i	−0.996739	+	0.0806990i	$0.974285\pi$
$992$	12.3811	−	12.3811i	0.393101	−	0.393101i
$993$	13.6567	−	13.6567i	0.433382	−	0.433382i
$994$		−	8.97467i		−	0.284659i
$995$		−	9.15513i		−	0.290237i
$996$	−2.39534	+	2.39534i	−0.0758994	+	0.0758994i
$997$	−17.7613	+	17.7613i	−0.562505	+	0.562505i	−0.930018	−	0.367513i	$-0.880209\pi$
$997$	−17.7613	+	17.7613i	−0.562505	+	0.562505i	0.367513	+	0.930018i	$0.380209\pi$
$998$	9.26139	+	9.26139i	0.293164	+	0.293164i
$999$	−1.19320			−0.0377512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.k.b.64.5	✓	20
3.2	odd	2		1071.2.n.b.64.6		20
17.2	even	8		6069.2.a.be.1.6		10
17.4	even	4	inner	357.2.k.b.106.6	yes	20
17.15	even	8		6069.2.a.bd.1.6		10
51.38	odd	4		1071.2.n.b.820.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.5	✓	20	1.1	even	1	trivial
357.2.k.b.106.6	yes	20	17.4	even	4	inner
1071.2.n.b.64.6		20	3.2	odd	2
1071.2.n.b.820.5		20	51.38	odd	4
6069.2.a.bd.1.6		10	17.15	even	8
6069.2.a.be.1.6		10	17.2	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.23743i q^{2} +(0.707107 + 0.707107i) q^{3} +0.468767 q^{4} +(-1.28416 - 1.28416i) q^{5} +(0.874995 - 0.874995i) q^{6} +(0.707107 - 0.707107i) q^{7} -3.05493i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.23743i q^{2} +(0.707107 + 0.707107i) q^{3} +0.468767 q^{4} +(-1.28416 - 1.28416i) q^{5} +(0.874995 - 0.874995i) q^{6} +(0.707107 - 0.707107i) q^{7} -3.05493i q^{8} +1.00000i q^{9} +(-1.58906 + 1.58906i) q^{10} +(1.66762 - 1.66762i) q^{11} +(0.331468 + 0.331468i) q^{12} -1.26858 q^{13} +(-0.874995 - 0.874995i) q^{14} -1.81608i q^{15} -2.84272 q^{16} +(3.15626 - 2.65293i) q^{17} +1.23743 q^{18} +3.42380i q^{19} +(-0.601973 - 0.601973i) q^{20} +1.00000 q^{21} +(-2.06357 - 2.06357i) q^{22} +(0.635667 - 0.635667i) q^{23} +(2.16016 - 2.16016i) q^{24} -1.70185i q^{25} +1.56978i q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.331468 - 0.331468i) q^{28} +(-0.0171546 - 0.0171546i) q^{29} -2.24727 q^{30} +(4.77634 + 4.77634i) q^{31} -2.59218i q^{32} +2.35837 q^{33} +(-3.28282 - 3.90565i) q^{34} -1.81608 q^{35} +0.468767i q^{36} +(0.843721 + 0.843721i) q^{37} +4.23672 q^{38} +(-0.897020 - 0.897020i) q^{39} +(-3.92302 + 3.92302i) q^{40} +(-5.01497 + 5.01497i) q^{41} -1.23743i q^{42} +5.21815i q^{43} +(0.781726 - 0.781726i) q^{44} +(1.28416 - 1.28416i) q^{45} +(-0.786594 - 0.786594i) q^{46} -8.50780 q^{47} +(-2.01011 - 2.01011i) q^{48} -1.00000i q^{49} -2.10592 q^{50} +(4.10772 + 0.355903i) q^{51} -0.594667 q^{52} +1.07752i q^{53} +(0.874995 + 0.874995i) q^{54} -4.28300 q^{55} +(-2.16016 - 2.16016i) q^{56} +(-2.42099 + 2.42099i) q^{57} +(-0.0212276 + 0.0212276i) q^{58} +5.43516i q^{59} -0.851318i q^{60} +(-4.45420 + 4.45420i) q^{61} +(5.91039 - 5.91039i) q^{62} +(0.707107 + 0.707107i) q^{63} -8.89309 q^{64} +(1.62906 + 1.62906i) q^{65} -2.91832i q^{66} -0.516299 q^{67} +(1.47955 - 1.24361i) q^{68} +0.898969 q^{69} +2.24727i q^{70} +(5.12841 + 5.12841i) q^{71} +3.05493 q^{72} +(9.43285 + 9.43285i) q^{73} +(1.04405 - 1.04405i) q^{74} +(1.20339 - 1.20339i) q^{75} +1.60496i q^{76} -2.35837i q^{77} +(-1.11000 + 1.11000i) q^{78} +(7.61388 - 7.61388i) q^{79} +(3.65052 + 3.65052i) q^{80} -1.00000 q^{81} +(6.20568 + 6.20568i) q^{82} +7.22647i q^{83} +0.468767 q^{84} +(-7.45995 - 0.646350i) q^{85} +6.45709 q^{86} -0.0242602i q^{87} +(-5.09446 - 5.09446i) q^{88} -10.2051 q^{89} +(-1.58906 - 1.58906i) q^{90} +(-0.897020 + 0.897020i) q^{91} +(0.297980 - 0.297980i) q^{92} +6.75476i q^{93} +10.5278i q^{94} +(4.39672 - 4.39672i) q^{95} +(1.83295 - 1.83295i) q^{96} +(0.145058 + 0.145058i) q^{97} -1.23743 q^{98} +(1.66762 + 1.66762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) \) 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6	\( 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6} + 16 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 40 q^{16} + 4 q^{17} + 8 q^{18} - 52 q^{20} + 20 q^{21} - 24 q^{22} - 4 q^{23} + 4 q^{24} - 8 q^{29} + 8 q^{31} - 4 q^{33} - 44 q^{34} + 12 q^{35} + 24 q^{37} - 64 q^{38} - 12 q^{39} - 52 q^{40} - 20 q^{41} + 72 q^{44} - 8 q^{45} + 28 q^{46} - 32 q^{47} + 32 q^{48} + 104 q^{50} + 8 q^{51} + 48 q^{52} - 4 q^{54} - 36 q^{55} - 4 q^{56} - 16 q^{57} - 60 q^{58} + 28 q^{61} + 36 q^{62} - 112 q^{64} - 4 q^{65} + 40 q^{67} - 52 q^{68} + 36 q^{69} + 16 q^{71} - 24 q^{72} - 72 q^{73} - 24 q^{74} - 8 q^{75} + 40 q^{78} - 8 q^{79} + 120 q^{80} - 20 q^{81} + 108 q^{82} - 24 q^{84} + 40 q^{85} - 28 q^{88} - 64 q^{89} + 16 q^{90} - 12 q^{91} - 56 q^{92} + 60 q^{95} + 16 q^{96} + 60 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6 + 16 * q^10 + 4 * q^11 - 12 * q^13 + 4 * q^14 + 40 * q^16 + 4 * q^17 + 8 * q^18 - 52 * q^20 + 20 * q^21 - 24 * q^22 - 4 * q^23 + 4 * q^24 - 8 * q^29 + 8 * q^31 - 4 * q^33 - 44 * q^34 + 12 * q^35 + 24 * q^37 - 64 * q^38 - 12 * q^39 - 52 * q^40 - 20 * q^41 + 72 * q^44 - 8 * q^45 + 28 * q^46 - 32 * q^47 + 32 * q^48 + 104 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^54 - 36 * q^55 - 4 * q^56 - 16 * q^57 - 60 * q^58 + 28 * q^61 + 36 * q^62 - 112 * q^64 - 4 * q^65 + 40 * q^67 - 52 * q^68 + 36 * q^69 + 16 * q^71 - 24 * q^72 - 72 * q^73 - 24 * q^74 - 8 * q^75 + 40 * q^78 - 8 * q^79 + 120 * q^80 - 20 * q^81 + 108 * q^82 - 24 * q^84 + 40 * q^85 - 28 * q^88 - 64 * q^89 + 16 * q^90 - 12 * q^91 - 56 * q^92 + 60 * q^95 + 16 * q^96 + 60 * q^97 - 8 * q^98 + 4 * q^99

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