LMFDB - Embedded newform 231.2.j.d.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	231.64
Dual form			231.2.j.d.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} -4.23607 q^{10} +(-0.809017 - 3.21644i) q^{11} +0.618034 q^{12} +(-0.309017 + 0.951057i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(2.11803 + 1.53884i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(0.0729490 + 0.224514i) q^{17} +(-1.30902 - 0.951057i) q^{18} +(-0.500000 + 1.53884i) q^{20} +1.00000 q^{21} +(-5.35410 - 0.363271i) q^{22} +1.23607 q^{23} +(-0.690983 + 2.12663i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(1.30902 + 0.951057i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.190983 + 0.587785i) q^{28} +(5.42705 + 3.94298i) q^{29} +(3.42705 - 2.48990i) q^{30} +(-1.78115 + 5.48183i) q^{31} -3.38197 q^{32} +(2.54508 + 2.12663i) q^{33} +0.381966 q^{34} +(-0.809017 + 2.48990i) q^{35} +(-0.500000 + 0.363271i) q^{36} +(8.85410 + 6.43288i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(-4.73607 - 3.44095i) q^{40} +(4.92705 - 3.57971i) q^{41} +(0.500000 - 1.53884i) q^{42} -1.00000 q^{43} +(-0.763932 + 1.90211i) q^{44} -2.61803 q^{45} +(0.618034 - 1.90211i) q^{46} +(-6.73607 + 4.89404i) q^{47} +(3.92705 + 2.85317i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.927051 + 2.85317i) q^{50} +(-0.190983 - 0.138757i) q^{51} +(0.500000 - 0.363271i) q^{52} +(1.66312 - 5.11855i) q^{53} +1.61803 q^{54} +(-7.35410 + 4.61653i) q^{55} -2.23607 q^{56} +(8.78115 - 6.37988i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-0.500000 - 1.53884i) q^{60} +(-3.16312 - 9.73508i) q^{61} +(7.54508 + 5.48183i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(1.30902 - 4.02874i) q^{64} +2.61803 q^{65} +(4.54508 - 2.85317i) q^{66} -4.76393 q^{67} +(0.0450850 - 0.138757i) q^{68} +(-1.00000 + 0.726543i) q^{69} +(3.42705 + 2.48990i) q^{70} +(0.454915 + 1.40008i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(6.92705 + 5.03280i) q^{73} +(14.3262 - 10.4086i) q^{74} +(0.572949 - 1.76336i) q^{75} +(-1.23607 + 3.07768i) q^{77} -1.61803 q^{78} +(1.28115 - 3.94298i) q^{79} +(-10.2812 + 7.46969i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.04508 - 9.37181i) q^{82} +(-1.85410 - 5.70634i) q^{83} +(-0.500000 - 0.363271i) q^{84} +(0.500000 - 0.363271i) q^{85} +(-0.500000 + 1.53884i) q^{86} -6.70820 q^{87} +(-5.69098 - 4.75528i) q^{88} -8.61803 q^{89} +(-1.30902 + 4.02874i) q^{90} +(0.809017 - 0.587785i) q^{91} +(-0.618034 - 0.449028i) q^{92} +(-1.78115 - 5.48183i) q^{93} +(4.16312 + 12.8128i) q^{94} +(2.73607 - 1.98787i) q^{96} +(-5.25329 + 16.1680i) q^{97} +1.61803 q^{98} +(-3.30902 - 0.224514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} + q^{13} - 3 q^{14} + 4 q^{15} - 6 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{20} + 4 q^{21} - 8 q^{22} - 4 q^{23} - 5 q^{24} - 6 q^{25} + 3 q^{26} - q^{27} + 3 q^{28} + 15 q^{29} + 7 q^{30} + 13 q^{31} - 18 q^{32} - q^{33} + 6 q^{34} - q^{35} - 2 q^{36} + 22 q^{37} + q^{39} - 10 q^{40} + 13 q^{41} + 2 q^{42} - 4 q^{43} - 12 q^{44} - 6 q^{45} - 2 q^{46} - 18 q^{47} + 9 q^{48} - q^{49} - 3 q^{50} - 3 q^{51} + 2 q^{52} - 9 q^{53} + 2 q^{54} - 16 q^{55} + 15 q^{58} + 15 q^{59} - 2 q^{60} + 3 q^{61} + 19 q^{62} - q^{63} + 3 q^{64} + 6 q^{65} + 7 q^{66} - 28 q^{67} - 11 q^{68} - 4 q^{69} + 7 q^{70} + 13 q^{71} - 5 q^{72} + 21 q^{73} + 26 q^{74} + 9 q^{75} + 4 q^{77} - 2 q^{78} - 15 q^{79} - 21 q^{80} - q^{81} - q^{82} + 6 q^{83} - 2 q^{84} + 2 q^{85} - 2 q^{86} - 25 q^{88} - 30 q^{89} - 3 q^{90} + q^{91} + 2 q^{92} + 13 q^{93} + q^{94} + 2 q^{96} + 17 q^{97} + 2 q^{98} - 11 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 + q^13 - 3 * q^14 + 4 * q^15 - 6 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^20 + 4 * q^21 - 8 * q^22 - 4 * q^23 - 5 * q^24 - 6 * q^25 + 3 * q^26 - q^27 + 3 * q^28 + 15 * q^29 + 7 * q^30 + 13 * q^31 - 18 * q^32 - q^33 + 6 * q^34 - q^35 - 2 * q^36 + 22 * q^37 + q^39 - 10 * q^40 + 13 * q^41 + 2 * q^42 - 4 * q^43 - 12 * q^44 - 6 * q^45 - 2 * q^46 - 18 * q^47 + 9 * q^48 - q^49 - 3 * q^50 - 3 * q^51 + 2 * q^52 - 9 * q^53 + 2 * q^54 - 16 * q^55 + 15 * q^58 + 15 * q^59 - 2 * q^60 + 3 * q^61 + 19 * q^62 - q^63 + 3 * q^64 + 6 * q^65 + 7 * q^66 - 28 * q^67 - 11 * q^68 - 4 * q^69 + 7 * q^70 + 13 * q^71 - 5 * q^72 + 21 * q^73 + 26 * q^74 + 9 * q^75 + 4 * q^77 - 2 * q^78 - 15 * q^79 - 21 * q^80 - q^81 - q^82 + 6 * q^83 - 2 * q^84 + 2 * q^85 - 2 * q^86 - 25 * q^88 - 30 * q^89 - 3 * q^90 + q^91 + 2 * q^92 + 13 * q^93 + q^94 + 2 * q^96 + 17 * q^97 + 2 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	−0.603290	−	0.797522i	$-0.706144\pi$
$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	0.956844	−	0.290604i	$-0.0938561\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.500000	−	0.363271i	−0.250000	−	0.181636i
$5$	−0.809017	−	2.48990i	−0.361803	−	1.11352i	−0.951959	−	0.306227i	$-0.900933\pi$
$5$	−0.809017	−	2.48990i	−0.361803	−	1.11352i	0.590155	−	0.807290i	$-0.299067\pi$
$6$	0.500000	+	1.53884i	0.204124	+	0.628230i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−4.23607			−1.33956
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$12$	0.618034			0.178411
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	−0.984720	−	0.174143i	$-0.944284\pi$
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	0.899014	+	0.437919i	$0.144284\pi$
$14$	−1.30902	+	0.951057i	−0.349850	+	0.254181i
$15$	2.11803	+	1.53884i	0.546874	+	0.397327i
$16$	−1.50000	−	4.61653i	−0.375000	−	1.15413i
$17$	0.0729490	+	0.224514i	0.0176927	+	0.0544526i	0.959513	−	0.281664i	$-0.0908864\pi$
$17$	0.0729490	+	0.224514i	0.0176927	+	0.0544526i	−0.941820	+	0.336117i	$0.890886\pi$
$18$	−1.30902	−	0.951057i	−0.308538	−	0.224166i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	−0.500000	+	1.53884i	−0.111803	+	0.344095i
$21$	1.00000			0.218218
$22$	−5.35410	−	0.363271i	−1.14150	−	0.0774497i
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$	−1.50000	+	1.08981i	−0.300000	+	0.217963i
$26$	1.30902	+	0.951057i	0.256719	+	0.186518i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.190983	+	0.587785i	0.0360924	+	0.111081i
$29$	5.42705	+	3.94298i	1.00778	+	0.732194i	0.963742	−	0.266836i	$-0.0859783\pi$
$29$	5.42705	+	3.94298i	1.00778	+	0.732194i	0.0440362	+	0.999030i	$0.485978\pi$
$30$	3.42705	−	2.48990i	0.625691	−	0.454591i
$31$	−1.78115	+	5.48183i	−0.319905	+	0.984565i	0.653784	+	0.756681i	$0.273181\pi$
$31$	−1.78115	+	5.48183i	−0.319905	+	0.984565i	−0.973688	+	0.227884i	$0.926819\pi$
$32$	−3.38197			−0.597853
$33$	2.54508	+	2.12663i	0.443042	+	0.370198i
$34$	0.381966			0.0655066
$35$	−0.809017	+	2.48990i	−0.136749	+	0.420870i
$36$	−0.500000	+	0.363271i	−0.0833333	+	0.0605452i
$37$	8.85410	+	6.43288i	1.45561	+	1.05756i	0.984481	+	0.175493i	$0.0561518\pi$
$37$	8.85410	+	6.43288i	1.45561	+	1.05756i	0.471125	+	0.882067i	$0.343848\pi$
$38$		0			0
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$	−4.73607	−	3.44095i	−0.748838	−	0.544063i
$41$	4.92705	−	3.57971i	0.769476	−	0.559057i	−0.132326	−	0.991206i	$-0.542245\pi$
$41$	4.92705	−	3.57971i	0.769476	−	0.559057i	0.901802	+	0.432149i	$0.142245\pi$
$42$	0.500000	−	1.53884i	0.0771517	−	0.237448i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−0.763932	+	1.90211i	−0.115167	+	0.286754i
$45$	−2.61803			−0.390273
$46$	0.618034	−	1.90211i	0.0911241	−	0.280451i
$47$	−6.73607	+	4.89404i	−0.982556	+	0.713869i	−0.958279	−	0.285836i	$-0.907729\pi$
$47$	−6.73607	+	4.89404i	−0.982556	+	0.713869i	−0.0242780	+	0.999705i	$0.507729\pi$
$48$	3.92705	+	2.85317i	0.566821	+	0.411820i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.927051	+	2.85317i	0.131105	+	0.403499i
$51$	−0.190983	−	0.138757i	−0.0267430	−	0.0194299i
$52$	0.500000	−	0.363271i	0.0693375	−	0.0503767i
$53$	1.66312	−	5.11855i	0.228447	−	0.703087i	−0.769476	−	0.638675i	$-0.779483\pi$
$53$	1.66312	−	5.11855i	0.228447	−	0.703087i	0.997923	−	0.0644122i	$-0.0205173\pi$
$54$	1.61803			0.220187
$55$	−7.35410	+	4.61653i	−0.991627	+	0.622492i
$56$	−2.23607			−0.298807
$57$		0			0
$58$	8.78115	−	6.37988i	1.15302	−	0.837719i
$59$	8.78115	+	6.37988i	1.14321	+	0.830590i	0.987563	−	0.157223i	$-0.0502542\pi$
$59$	8.78115	+	6.37988i	1.14321	+	0.830590i	0.155646	+	0.987813i	$0.450254\pi$
$60$	−0.500000	−	1.53884i	−0.0645497	−	0.198664i
$61$	−3.16312	−	9.73508i	−0.404996	−	1.24645i	−0.920899	−	0.389802i	$-0.872543\pi$
$61$	−3.16312	−	9.73508i	−0.404996	−	1.24645i	0.515903	−	0.856647i	$-0.327457\pi$
$62$	7.54508	+	5.48183i	0.958227	+	0.696192i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	1.30902	−	4.02874i	0.163627	−	0.503593i
$65$	2.61803			0.324727
$66$	4.54508	−	2.85317i	0.559461	−	0.351201i
$67$	−4.76393			−0.582007			−0.291003	−	0.956722i	$-0.593989\pi$
$67$	−4.76393			−0.582007			−0.291003	+	0.956722i	$0.593989\pi$
$68$	0.0450850	−	0.138757i	0.00546736	−	0.0168268i
$69$	−1.00000	+	0.726543i	−0.120386	+	0.0874654i
$70$	3.42705	+	2.48990i	0.409611	+	0.297600i
$71$	0.454915	+	1.40008i	0.0539885	+	0.166159i	0.974415	−	0.224756i	$-0.0721585\pi$
$71$	0.454915	+	1.40008i	0.0539885	+	0.166159i	−0.920427	+	0.390915i	$0.872158\pi$
$72$	−0.690983	−	2.12663i	−0.0814331	−	0.250625i
$73$	6.92705	+	5.03280i	0.810750	+	0.589044i	0.914048	−	0.405606i	$-0.132940\pi$
$73$	6.92705	+	5.03280i	0.810750	+	0.589044i	−0.103298	+	0.994650i	$0.532940\pi$
$74$	14.3262	−	10.4086i	1.66539	−	1.20998i
$75$	0.572949	−	1.76336i	0.0661585	−	0.203615i
$76$		0			0
$77$	−1.23607	+	3.07768i	−0.140863	+	0.350735i
$78$	−1.61803			−0.183206
$79$	1.28115	−	3.94298i	0.144141	−	0.443620i	−0.852759	−	0.522305i	$-0.825072\pi$
$79$	1.28115	−	3.94298i	0.144141	−	0.443620i	0.996900	+	0.0786850i	$0.0250721\pi$
$80$	−10.2812	+	7.46969i	−1.14947	+	0.835137i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−3.04508	−	9.37181i	−0.336273	−	1.03494i
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	−0.999771	−	0.0213936i	$-0.993190\pi$
$83$	−1.85410	−	5.70634i	−0.203514	−	0.626352i	0.796257	−	0.604959i	$-0.206810\pi$
$84$	−0.500000	−	0.363271i	−0.0545545	−	0.0396361i
$85$	0.500000	−	0.363271i	0.0542326	−	0.0394023i
$86$	−0.500000	+	1.53884i	−0.0539164	+	0.165938i
$87$	−6.70820			−0.719195
$88$	−5.69098	−	4.75528i	−0.606661	−	0.506915i
$89$	−8.61803			−0.913510			−0.456755	−	0.889593i	$-0.650988\pi$
$89$	−8.61803			−0.913510			−0.456755	+	0.889593i	$0.650988\pi$
$90$	−1.30902	+	4.02874i	−0.137983	+	0.424666i
$91$	0.809017	−	0.587785i	0.0848080	−	0.0616166i
$92$	−0.618034	−	0.449028i	−0.0644345	−	0.0468144i
$93$	−1.78115	−	5.48183i	−0.184697	−	0.568439i
$94$	4.16312	+	12.8128i	0.429393	+	1.32154i
$95$		0			0
$96$	2.73607	−	1.98787i	0.279249	−	0.202886i
$97$	−5.25329	+	16.1680i	−0.533391	+	1.64161i	0.213710	+	0.976897i	$0.431445\pi$
$97$	−5.25329	+	16.1680i	−0.533391	+	1.64161i	−0.747101	+	0.664711i	$0.768555\pi$
$98$	1.61803			0.163446
$99$	−3.30902	−	0.224514i	−0.332569	−	0.0225645i
$100$	1.14590			0.114590
$101$	5.61803	−	17.2905i	0.559015	−	1.72047i	−0.126081	−	0.992020i	$-0.540240\pi$
$101$	5.61803	−	17.2905i	0.559015	−	1.72047i	0.685097	−	0.728452i	$-0.259760\pi$
$102$	−0.309017	+	0.224514i	−0.0305972	+	0.0222302i
$103$	−0.572949	−	0.416272i	−0.0564543	−	0.0410165i	0.559200	−	0.829033i	$-0.311108\pi$
$103$	−0.572949	−	0.416272i	−0.0564543	−	0.0410165i	−0.615655	+	0.788016i	$0.711108\pi$
$104$	0.690983	+	2.12663i	0.0677565	+	0.208533i
$105$	−0.809017	−	2.48990i	−0.0789520	−	0.242989i
$106$	−7.04508	−	5.11855i	−0.684279	−	0.497158i
$107$	−16.3713	+	11.8945i	−1.58268	+	1.14988i	−0.669129	+	0.743146i	$0.733333\pi$
$107$	−16.3713	+	11.8945i	−1.58268	+	1.14988i	−0.913546	+	0.406735i	$0.866667\pi$
$108$	0.190983	−	0.587785i	0.0183773	−	0.0565597i
$109$	12.5623			1.20325			0.601625	−	0.798778i	$-0.294520\pi$
$109$	12.5623			1.20325			0.601625	+	0.798778i	$0.294520\pi$
$110$	3.42705	+	13.6251i	0.326756	+	1.29910i
$111$	−10.9443			−1.03878
$112$	−1.50000	+	4.61653i	−0.141737	+	0.436221i
$113$	−15.8992	+	11.5514i	−1.49567	+	1.08667i	−0.523603	+	0.851962i	$0.675413\pi$
$113$	−15.8992	+	11.5514i	−1.49567	+	1.08667i	−0.972067	+	0.234705i	$0.924587\pi$
$114$		0			0
$115$	−1.00000	−	3.07768i	−0.0932505	−	0.286995i
$116$	−1.28115	−	3.94298i	−0.118952	−	0.366097i
$117$	0.809017	+	0.587785i	0.0747936	+	0.0543408i
$118$	14.2082	−	10.3229i	1.30797	−	0.950297i
$119$	0.0729490	−	0.224514i	0.00668723	−	0.0205812i
$120$	5.85410			0.534404
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$	−16.5623			−1.49948
$123$	−1.88197	+	5.79210i	−0.169691	+	0.522256i
$124$	2.88197	−	2.09387i	0.258808	−	0.188035i
$125$	−6.66312	−	4.84104i	−0.595967	−	0.432996i
$126$	0.500000	+	1.53884i	0.0445435	+	0.137091i
$127$	2.57295	+	7.91872i	0.228312	+	0.702673i	0.997938	+	0.0641782i	$0.0204426\pi$
$127$	2.57295	+	7.91872i	0.228312	+	0.702673i	−0.769626	+	0.638495i	$0.779557\pi$
$128$	−11.0172	−	8.00448i	−0.973794	−	0.707503i
$129$	0.809017	−	0.587785i	0.0712300	−	0.0517516i
$130$	1.30902	−	4.02874i	0.114808	−	0.353344i
$131$	12.3262			1.07695			0.538474	−	0.842642i	$-0.319001\pi$
$131$	12.3262			1.07695			0.538474	+	0.842642i	$0.319001\pi$
$132$	−0.500000	−	1.98787i	−0.0435194	−	0.173022i
$133$		0			0
$134$	−2.38197	+	7.33094i	−0.205771	+	0.633297i
$135$	2.11803	−	1.53884i	0.182291	−	0.132442i
$136$	0.427051	+	0.310271i	0.0366193	+	0.0266055i
$137$	−6.47214	−	19.9192i	−0.552952	−	1.70181i	−0.701292	−	0.712874i	$-0.747393\pi$
$137$	−6.47214	−	19.9192i	−0.552952	−	1.70181i	0.148340	−	0.988936i	$-0.452607\pi$
$138$	0.618034	+	1.90211i	0.0526105	+	0.161919i
$139$	−2.07295	−	1.50609i	−0.175825	−	0.127745i	0.496392	−	0.868099i	$-0.334658\pi$
$139$	−2.07295	−	1.50609i	−0.175825	−	0.127745i	−0.672217	+	0.740354i	$0.734658\pi$
$140$	1.30902	−	0.951057i	0.110632	−	0.0803789i
$141$	2.57295	−	7.91872i	0.216681	−	0.666877i
$142$	2.38197			0.199890
$143$	3.30902	+	0.224514i	0.276714	+	0.0187748i
$144$	−4.85410			−0.404508
$145$	5.42705	−	16.7027i	0.450692	−	1.38709i
$146$	11.2082	−	8.14324i	0.927598	−	0.673939i
$147$	−0.809017	−	0.587785i	−0.0667266	−	0.0484797i
$148$	−2.09017	−	6.43288i	−0.171811	−	0.528780i
$149$	−0.590170	−	1.81636i	−0.0483486	−	0.148802i	0.923968	−	0.382471i	$-0.124927\pi$
$149$	−0.590170	−	1.81636i	−0.0483486	−	0.148802i	−0.972316	+	0.233669i	$0.924927\pi$
$150$	−2.42705	−	1.76336i	−0.198168	−	0.143977i
$151$	8.01722	−	5.82485i	0.652432	−	0.474020i	−0.211667	−	0.977342i	$-0.567889\pi$
$151$	8.01722	−	5.82485i	0.652432	−	0.474020i	0.864099	+	0.503322i	$0.167889\pi$
$152$		0			0
$153$	0.236068			0.0190850
$154$	4.11803	+	3.44095i	0.331841	+	0.277280i
$155$	15.0902			1.21207
$156$	−0.190983	+	0.587785i	−0.0152909	+	0.0470605i
$157$	14.0172	−	10.1841i	1.11870	−	0.812780i	0.134685	−	0.990888i	$-0.456998\pi$
$157$	14.0172	−	10.1841i	1.11870	−	0.812780i	0.984011	+	0.178108i	$0.0569977\pi$
$158$	−5.42705	−	3.94298i	−0.431753	−	0.313687i
$159$	1.66312	+	5.11855i	0.131894	+	0.405928i
$160$	2.73607	+	8.42075i	0.216305	+	0.665719i
$161$	−1.00000	−	0.726543i	−0.0788110	−	0.0572596i
$162$	−1.30902	+	0.951057i	−0.102846	+	0.0747221i
$163$	−7.11803	+	21.9071i	−0.557527	+	1.71589i	0.131646	+	0.991297i	$0.457974\pi$
$163$	−7.11803	+	21.9071i	−0.557527	+	1.71589i	−0.689174	+	0.724596i	$0.742026\pi$
$164$	−3.76393			−0.293914
$165$	3.23607	−	8.05748i	0.251928	−	0.627274i
$166$	−9.70820			−0.753503
$167$	3.59017	−	11.0494i	0.277816	−	0.855029i	−0.710645	−	0.703551i	$-0.751597\pi$
$167$	3.59017	−	11.0494i	0.277816	−	0.855029i	0.988461	−	0.151478i	$-0.0484033\pi$
$168$	1.80902	−	1.31433i	0.139569	−	0.101403i
$169$	9.70820	+	7.05342i	0.746785	+	0.542571i
$170$	−0.309017	−	0.951057i	−0.0237005	−	0.0729427i
$171$		0			0
$172$	0.500000	+	0.363271i	0.0381246	+	0.0276992i
$173$	10.0172	−	7.27794i	0.761595	−	0.553331i	−0.137804	−	0.990460i	$-0.544004\pi$
$173$	10.0172	−	7.27794i	0.761595	−	0.553331i	0.899399	+	0.437128i	$0.144004\pi$
$174$	−3.35410	+	10.3229i	−0.254274	+	0.782574i
$175$	1.85410			0.140157
$176$	−13.6353	+	8.55951i	−1.02780	+	0.645197i
$177$	−10.8541			−0.815844
$178$	−4.30902	+	13.2618i	−0.322974	+	0.994013i
$179$	−1.80902	+	1.31433i	−0.135212	+	0.0982375i	−0.653335	−	0.757069i	$-0.726631\pi$
$179$	−1.80902	+	1.31433i	−0.135212	+	0.0982375i	0.518123	+	0.855306i	$0.326631\pi$
$180$	1.30902	+	0.951057i	0.0975684	+	0.0708876i
$181$	1.30902	+	4.02874i	0.0972985	+	0.299454i	0.987846	−	0.155437i	$-0.0496784\pi$
$181$	1.30902	+	4.02874i	0.0972985	+	0.299454i	−0.890547	+	0.454890i	$0.849678\pi$
$182$	−0.500000	−	1.53884i	−0.0370625	−	0.114067i
$183$	8.28115	+	6.01661i	0.612160	+	0.444761i
$184$	2.23607	−	1.62460i	0.164845	−	0.119767i
$185$	8.85410	−	27.2501i	0.650967	−	2.00347i
$186$	−9.32624			−0.683833
$187$	0.663119	−	0.416272i	0.0484921	−	0.0304408i
$188$	5.14590			0.375303
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$		0			0
$191$	−11.5172	−	8.36775i	−0.833357	−	0.605469i	0.0871502	−	0.996195i	$-0.472224\pi$
$191$	−11.5172	−	8.36775i	−0.833357	−	0.605469i	−0.920507	+	0.390726i	$0.872224\pi$
$192$	1.30902	+	4.02874i	0.0944702	+	0.290749i
$193$	7.09017	+	21.8213i	0.510362	+	1.57073i	0.791566	+	0.611084i	$0.209266\pi$
$193$	7.09017	+	21.8213i	0.510362	+	1.57073i	−0.281204	+	0.959648i	$0.590734\pi$
$194$	22.2533	+	16.1680i	1.59769	+	1.16079i
$195$	−2.11803	+	1.53884i	−0.151676	+	0.110199i
$196$	0.190983	−	0.587785i	0.0136416	−	0.0419847i
$197$	−4.76393			−0.339416			−0.169708	−	0.985494i	$-0.554282\pi$
$197$	−4.76393			−0.339416			−0.169708	+	0.985494i	$0.554282\pi$
$198$	−2.00000	+	4.97980i	−0.142134	+	0.353899i
$199$	12.5623			0.890518			0.445259	−	0.895402i	$-0.353112\pi$
$199$	12.5623			0.890518			0.445259	+	0.895402i	$0.353112\pi$
$200$	−1.28115	+	3.94298i	−0.0905912	+	0.278811i
$201$	3.85410	−	2.80017i	0.271847	−	0.197509i
$202$	−23.7984	−	17.2905i	−1.67445	−	1.21656i
$203$	−2.07295	−	6.37988i	−0.145492	−	0.447780i
$204$	0.0450850	+	0.138757i	0.00315658	+	0.00971495i
$205$	−12.8992	−	9.37181i	−0.900918	−	0.654555i
$206$	−0.927051	+	0.673542i	−0.0645907	+	0.0469279i
$207$	0.381966	−	1.17557i	0.0265485	−	0.0817078i
$208$	4.85410			0.336571
$209$		0			0
$210$	−4.23607			−0.292316
$211$	5.78115	−	17.7926i	0.397991	−	1.22489i	−0.528617	−	0.848861i	$-0.677289\pi$
$211$	5.78115	−	17.7926i	0.397991	−	1.22489i	0.926608	−	0.376030i	$-0.122711\pi$
$212$	−2.69098	+	1.95511i	−0.184817	+	0.134278i
$213$	−1.19098	−	0.865300i	−0.0816048	−	0.0592894i
$214$	10.1180	+	31.1401i	0.691655	+	2.12869i
$215$	0.809017	+	2.48990i	0.0551745	+	0.169810i
$216$	1.80902	+	1.31433i	0.123088	+	0.0894287i
$217$	4.66312	−	3.38795i	0.316553	−	0.229989i
$218$	6.28115	−	19.3314i	0.425413	−	1.30929i
$219$	−8.56231			−0.578587
$220$	5.35410	+	0.363271i	0.360973	+	0.0244917i
$221$	−0.236068			−0.0158797
$222$	−5.47214	+	16.8415i	−0.367266	+	1.13033i
$223$	−0.572949	+	0.416272i	−0.0383675	+	0.0278756i	−0.606804	−	0.794852i	$-0.707549\pi$
$223$	−0.572949	+	0.416272i	−0.0383675	+	0.0278756i	0.568436	+	0.822727i	$0.307549\pi$
$224$	2.73607	+	1.98787i	0.182811	+	0.132820i
$225$	0.572949	+	1.76336i	0.0381966	+	0.117557i
$226$	9.82624	+	30.2421i	0.653632	+	2.01167i
$227$	22.6353	+	16.4455i	1.50235	+	1.09152i	0.969432	+	0.245361i	$0.0789064\pi$
$227$	22.6353	+	16.4455i	1.50235	+	1.09152i	0.532923	+	0.846164i	$0.321094\pi$
$228$		0			0
$229$	0.527864	−	1.62460i	0.0348822	−	0.107356i	−0.932099	−	0.362203i	$-0.882025\pi$
$229$	0.527864	−	1.62460i	0.0348822	−	0.107356i	0.966982	+	0.254846i	$0.0820248\pi$
$230$	−5.23607			−0.345256
$231$	−0.809017	−	3.21644i	−0.0532294	−	0.211626i
$232$	15.0000			0.984798
$233$	0.545085	−	1.67760i	0.0357097	−	0.109903i	−0.931613	−	0.363452i	$-0.881598\pi$
$233$	0.545085	−	1.67760i	0.0357097	−	0.109903i	0.967323	+	0.253549i	$0.0815980\pi$
$234$	1.30902	−	0.951057i	0.0855731	−	0.0621725i
$235$	17.6353	+	12.8128i	1.15040	+	0.835812i
$236$	−2.07295	−	6.37988i	−0.134937	−	0.415295i
$237$	1.28115	+	3.94298i	0.0832198	+	0.256124i
$238$	−0.309017	−	0.224514i	−0.0200306	−	0.0145531i
$239$	−20.9164	+	15.1967i	−1.35297	+	0.982990i	−0.354112	+	0.935203i	$0.615217\pi$
$239$	−20.9164	+	15.1967i	−1.35297	+	0.982990i	−0.998858	+	0.0477873i	$0.984783\pi$
$240$	3.92705	−	12.0862i	0.253490	−	0.780162i
$241$	−11.2918			−0.727369			−0.363684	−	0.931522i	$-0.618481\pi$
$241$	−11.2918			−0.727369			−0.363684	+	0.931522i	$0.618481\pi$
$242$	3.16312	+	17.5150i	0.203333	+	1.12591i
$243$	1.00000			0.0641500
$244$	−1.95492	+	6.01661i	−0.125151	+	0.385174i
$245$	2.11803	−	1.53884i	0.135316	−	0.0983130i
$246$	7.97214	+	5.79210i	0.508285	+	0.369291i
$247$		0			0
$248$	3.98278	+	12.2577i	0.252907	+	0.778367i
$249$	4.85410	+	3.52671i	0.307616	+	0.223496i
$250$	−10.7812	+	7.83297i	−0.681860	+	0.495400i
$251$	−6.98278	+	21.4908i	−0.440749	+	1.35649i	0.446330	+	0.894869i	$0.352731\pi$
$251$	−6.98278	+	21.4908i	−0.440749	+	1.35649i	−0.887079	+	0.461618i	$0.847269\pi$
$252$	0.618034			0.0389325
$253$	−1.00000	−	3.97574i	−0.0628695	−	0.249953i
$254$	13.4721			0.845317
$255$	−0.190983	+	0.587785i	−0.0119598	+	0.0368085i
$256$	−10.9721	+	7.97172i	−0.685758	+	0.498233i
$257$	−7.32624	−	5.32282i	−0.456998	−	0.332029i	0.335354	−	0.942092i	$-0.391144\pi$
$257$	−7.32624	−	5.32282i	−0.456998	−	0.332029i	−0.792353	+	0.610063i	$0.791144\pi$
$258$	−0.500000	−	1.53884i	−0.0311286	−	0.0958041i
$259$	−3.38197	−	10.4086i	−0.210145	−	0.646760i
$260$	−1.30902	−	0.951057i	−0.0811818	−	0.0589820i
$261$	5.42705	−	3.94298i	0.335926	−	0.244065i
$262$	6.16312	−	18.9681i	0.380759	−	1.17185i
$263$	−12.7082			−0.783621			−0.391811	−	0.920046i	$-0.628151\pi$
$263$	−12.7082			−0.783621			−0.391811	+	0.920046i	$0.628151\pi$
$264$	7.39919	+	0.502029i	0.455388	+	0.0308977i
$265$	−14.0902			−0.865552
$266$		0			0
$267$	6.97214	−	5.06555i	0.426688	−	0.310007i
$268$	2.38197	+	1.73060i	0.145502	+	0.105713i
$269$	1.87132	+	5.75934i	0.114097	+	0.351153i	0.991758	−	0.128129i	$-0.0408971\pi$
$269$	1.87132	+	5.75934i	0.114097	+	0.351153i	−0.877661	+	0.479282i	$0.840897\pi$
$270$	−1.30902	−	4.02874i	−0.0796642	−	0.245181i
$271$	−16.5172	−	12.0005i	−1.00335	−	0.728976i	−0.0405459	−	0.999178i	$-0.512910\pi$
$271$	−16.5172	−	12.0005i	−1.00335	−	0.728976i	−0.962804	+	0.270201i	$0.912910\pi$
$272$	0.927051	−	0.673542i	0.0562107	−	0.0408395i
$273$	−0.309017	+	0.951057i	−0.0187026	+	0.0575606i
$274$	−33.8885			−2.04728
$275$	4.71885	+	3.94298i	0.284557	+	0.237771i
$276$	0.763932			0.0459833
$277$	0.437694	−	1.34708i	0.0262985	−	0.0809384i	−0.937046	−	0.349206i	$-0.886451\pi$
$277$	0.437694	−	1.34708i	0.0262985	−	0.0809384i	0.963344	+	0.268268i	$0.0864512\pi$
$278$	−3.35410	+	2.43690i	−0.201166	+	0.146155i
$279$	4.66312	+	3.38795i	0.279174	+	0.202832i
$280$	1.80902	+	5.56758i	0.108109	+	0.332727i
$281$	4.13525	+	12.7270i	0.246689	+	0.759230i	0.995354	+	0.0962816i	$0.0306949\pi$
$281$	4.13525	+	12.7270i	0.246689	+	0.759230i	−0.748666	+	0.662948i	$0.769305\pi$
$282$	−10.8992	−	7.91872i	−0.649037	−	0.471553i
$283$	−16.7533	+	12.1720i	−0.995880	+	0.723549i	−0.961201	−	0.275850i	$-0.911041\pi$
$283$	−16.7533	+	12.1720i	−0.995880	+	0.723549i	−0.0346788	+	0.999399i	$0.511041\pi$
$284$	0.281153	−	0.865300i	0.0166834	−	0.0513461i
$285$		0			0
$286$	2.00000	−	4.97980i	0.118262	−	0.294462i
$287$	−6.09017			−0.359491
$288$	−1.04508	+	3.21644i	−0.0615822	+	0.189531i
$289$	13.7082	−	9.95959i	0.806365	−	0.585858i
$290$	−22.9894	−	16.7027i	−1.34998	−	0.980819i
$291$	−5.25329	−	16.1680i	−0.307953	−	0.947783i
$292$	−1.63525	−	5.03280i	−0.0956961	−	0.294522i
$293$	7.09017	+	5.15131i	0.414212	+	0.300943i	0.775305	−	0.631587i	$-0.217596\pi$
$293$	7.09017	+	5.15131i	0.414212	+	0.300943i	−0.361093	+	0.932530i	$0.617596\pi$
$294$	−1.30902	+	0.951057i	−0.0763434	+	0.0554667i
$295$	8.78115	−	27.0256i	0.511258	−	1.57349i
$296$	24.4721			1.42241
$297$	2.80902	−	1.76336i	0.162996	−	0.102320i
$298$	−3.09017			−0.179009
$299$	−0.381966	+	1.17557i	−0.0220897	+	0.0679850i
$300$	−0.927051	+	0.673542i	−0.0535233	+	0.0388870i
$301$	0.809017	+	0.587785i	0.0466310	+	0.0338794i
$302$	−4.95492	−	15.2497i	−0.285123	−	0.877519i
$303$	5.61803	+	17.2905i	0.322748	+	0.993315i
$304$		0			0
$305$	−21.6803	+	15.7517i	−1.24141	+	0.901939i
$306$	0.118034	−	0.363271i	0.00674755	−	0.0207668i
$307$	−3.18034			−0.181512			−0.0907558	−	0.995873i	$-0.528928\pi$
$307$	−3.18034			−0.181512			−0.0907558	+	0.995873i	$0.528928\pi$
$308$	1.73607	−	1.08981i	0.0989217	−	0.0620979i
$309$	0.708204			0.0402883
$310$	7.54508	−	23.2214i	0.428532	−	1.31889i
$311$	6.30902	−	4.58377i	0.357752	−	0.259922i	−0.394362	−	0.918955i	$-0.629034\pi$
$311$	6.30902	−	4.58377i	0.357752	−	0.259922i	0.752114	+	0.659033i	$0.229034\pi$
$312$	−1.80902	−	1.31433i	−0.102415	−	0.0744092i
$313$	2.71885	+	8.36775i	0.153678	+	0.472973i	0.998025	−	0.0628247i	$-0.0200109\pi$
$313$	2.71885	+	8.36775i	0.153678	+	0.472973i	−0.844346	+	0.535798i	$0.820011\pi$
$314$	−8.66312	−	26.6623i	−0.488888	−	1.50464i
$315$	2.11803	+	1.53884i	0.119338	+	0.0867039i
$316$	−2.07295	+	1.50609i	−0.116612	+	0.0847239i
$317$	−5.98278	+	18.4131i	−0.336026	+	1.03418i	0.630188	+	0.776443i	$0.282978\pi$
$317$	−5.98278	+	18.4131i	−0.336026	+	1.03418i	−0.966214	+	0.257740i	$0.917022\pi$
$318$	8.70820			0.488332
$319$	8.29180	−	20.6457i	0.464251	−	1.15594i
$320$	−11.0902			−0.619959
$321$	6.25329	−	19.2456i	0.349025	−	1.07419i
$322$	−1.61803	+	1.17557i	−0.0901695	+	0.0655120i
$323$		0			0
$324$	0.190983	+	0.587785i	0.0106102	+	0.0326547i
$325$	−0.572949	−	1.76336i	−0.0317815	−	0.0978134i
$326$	30.1525	+	21.9071i	1.66999	+	1.21332i
$327$	−10.1631	+	7.38394i	−0.562022	+	0.408333i
$328$	4.20820	−	12.9515i	0.232359	−	0.715128i
$329$	8.32624			0.459040
$330$	−10.7812	−	9.00854i	−0.593483	−	0.495904i
$331$	−1.29180			−0.0710035			−0.0355018	−	0.999370i	$-0.511303\pi$
$331$	−1.29180			−0.0710035			−0.0355018	+	0.999370i	$0.511303\pi$
$332$	−1.14590	+	3.52671i	−0.0628893	+	0.193553i
$333$	8.85410	−	6.43288i	0.485202	−	0.352520i
$334$	−15.2082	−	11.0494i	−0.832156	−	0.604597i
$335$	3.85410	+	11.8617i	0.210572	+	0.648074i
$336$	−1.50000	−	4.61653i	−0.0818317	−	0.251852i
$337$	−11.8992	−	8.64527i	−0.648190	−	0.470938i	0.214464	−	0.976732i	$-0.431199\pi$
$337$	−11.8992	−	8.64527i	−0.648190	−	0.470938i	−0.862654	+	0.505794i	$0.831199\pi$
$338$	15.7082	−	11.4127i	0.854414	−	0.620768i
$339$	6.07295	−	18.6906i	0.329837	−	1.01513i
$340$	−0.381966			−0.0207150
$341$	19.0729	+	1.29408i	1.03286	+	0.0700785i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−1.80902	+	1.31433i	−0.0975357	+	0.0708638i
$345$	2.61803	+	1.90211i	0.140950	+	0.102406i
$346$	−6.19098	−	19.0539i	−0.332829	−	1.02434i
$347$	0.437694	+	1.34708i	0.0234967	+	0.0723153i	0.962117	−	0.272636i	$-0.0878955\pi$
$347$	0.437694	+	1.34708i	0.0234967	+	0.0723153i	−0.938621	+	0.344951i	$0.887895\pi$
$348$	3.35410	+	2.43690i	0.179799	+	0.130631i
$349$	24.2082	−	17.5883i	1.29584	−	0.941480i	0.295930	−	0.955210i	$-0.404371\pi$
$349$	24.2082	−	17.5883i	1.29584	−	0.941480i	0.999906	+	0.0137302i	$0.00437058\pi$
$350$	0.927051	−	2.85317i	0.0495530	−	0.152508i
$351$	−1.00000			−0.0533761
$352$	2.73607	+	10.8779i	0.145833	+	0.579794i
$353$	−16.5279			−0.879689			−0.439845	−	0.898074i	$-0.644967\pi$
$353$	−16.5279			−0.879689			−0.439845	+	0.898074i	$0.644967\pi$
$354$	−5.42705	+	16.7027i	−0.288445	+	0.887741i
$355$	3.11803	−	2.26538i	0.165488	−	0.120234i
$356$	4.30902	+	3.13068i	0.228377	+	0.165926i
$357$	0.0729490	+	0.224514i	0.00386087	+	0.0118825i
$358$	1.11803	+	3.44095i	0.0590899	+	0.181860i
$359$	−14.7361	−	10.7064i	−0.777740	−	0.565061i	0.126560	−	0.991959i	$-0.459606\pi$
$359$	−14.7361	−	10.7064i	−0.777740	−	0.565061i	−0.904300	+	0.426898i	$0.859606\pi$
$360$	−4.73607	+	3.44095i	−0.249613	+	0.181354i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$	6.85410			0.360244
$363$	4.78115	−	9.90659i	0.250945	−	0.519961i
$364$	−0.618034			−0.0323938
$365$	6.92705	−	21.3193i	0.362578	−	1.11590i
$366$	13.3992	−	9.73508i	0.700387	−	0.508861i
$367$	−19.9894	−	14.5231i	−1.04344	−	0.758101i	−0.0724826	−	0.997370i	$-0.523092\pi$
$367$	−19.9894	−	14.5231i	−1.04344	−	0.758101i	−0.970953	+	0.239269i	$0.923092\pi$
$368$	−1.85410	−	5.70634i	−0.0966517	−	0.297463i
$369$	−1.88197	−	5.79210i	−0.0979712	−	0.301524i
$370$	−37.5066	−	27.2501i	−1.94987	−	1.41667i
$371$	−4.35410	+	3.16344i	−0.226054	+	0.164238i
$372$	−1.10081	+	3.38795i	−0.0570745	+	0.175657i
$373$	7.81966			0.404887			0.202443	−	0.979294i	$-0.435112\pi$
$373$	7.81966			0.404887			0.202443	+	0.979294i	$0.435112\pi$
$374$	−0.309017	−	1.22857i	−0.0159789	−	0.0635279i
$375$	8.23607			0.425309
$376$	−5.75329	+	17.7068i	−0.296703	+	0.913159i
$377$	−5.42705	+	3.94298i	−0.279507	+	0.203074i
$378$	−1.30902	−	0.951057i	−0.0673286	−	0.0489171i
$379$	−1.28115	−	3.94298i	−0.0658084	−	0.202537i	0.912745	−	0.408529i	$-0.133958\pi$
$379$	−1.28115	−	3.94298i	−0.0658084	−	0.202537i	−0.978554	+	0.205991i	$0.933958\pi$
$380$		0			0
$381$	−6.73607	−	4.89404i	−0.345099	−	0.250729i
$382$	−18.6353	+	13.5393i	−0.953463	+	0.692731i
$383$	−5.89919	+	18.1558i	−0.301434	+	0.927720i	0.679549	+	0.733630i	$0.262175\pi$
$383$	−5.89919	+	18.1558i	−0.301434	+	0.927720i	−0.980984	+	0.194090i	$0.937825\pi$
$384$	13.6180			0.694942
$385$	8.66312	+	0.587785i	0.441513	+	0.0299563i
$386$	37.1246			1.88959
$387$	−0.309017	+	0.951057i	−0.0157082	+	0.0483449i
$388$	8.50000	−	6.17561i	0.431522	−	0.313519i
$389$	8.61803	+	6.26137i	0.436952	+	0.317464i	0.784423	−	0.620227i	$-0.212959\pi$
$389$	8.61803	+	6.26137i	0.436952	+	0.317464i	−0.347471	+	0.937691i	$0.612959\pi$
$390$	1.30902	+	4.02874i	0.0662847	+	0.204003i
$391$	0.0901699	+	0.277515i	0.00456009	+	0.0140345i
$392$	1.80902	+	1.31433i	0.0913692	+	0.0663836i
$393$	−9.97214	+	7.24518i	−0.503028	+	0.365471i
$394$	−2.38197	+	7.33094i	−0.120002	+	0.369327i
$395$	−10.8541			−0.546129
$396$	1.57295	+	1.31433i	0.0790437	+	0.0660475i
$397$	−34.6869			−1.74089			−0.870443	−	0.492269i	$-0.836168\pi$
$397$	−34.6869			−1.74089			−0.870443	+	0.492269i	$0.836168\pi$
$398$	6.28115	−	19.3314i	0.314846	−	0.968996i
$399$		0			0
$400$	7.28115	+	5.29007i	0.364058	+	0.264503i
$401$	8.44427	+	25.9888i	0.421687	+	1.29782i	0.906131	+	0.422997i	$0.139022\pi$
$401$	8.44427	+	25.9888i	0.421687	+	1.29782i	−0.484444	+	0.874822i	$0.660978\pi$
$402$	−2.38197	−	7.33094i	−0.118802	−	0.365634i
$403$	−4.66312	−	3.38795i	−0.232287	−	0.168766i
$404$	−9.09017	+	6.60440i	−0.452253	+	0.328581i
$405$	−0.809017	+	2.48990i	−0.0402004	+	0.123724i
$406$	−10.8541			−0.538680
$407$	13.5279	−	33.6830i	0.670551	−	1.66960i
$408$	−0.527864			−0.0261332
$409$	−8.84346	+	27.2174i	−0.437281	+	1.34581i	0.453450	+	0.891282i	$0.350193\pi$
$409$	−8.84346	+	27.2174i	−0.437281	+	1.34581i	−0.890731	+	0.454531i	$0.849807\pi$
$410$	−20.8713	+	15.1639i	−1.03076	+	0.748892i
$411$	16.9443	+	12.3107i	0.835799	+	0.607244i
$412$	0.135255	+	0.416272i	0.00666353	+	0.0205082i
$413$	−3.35410	−	10.3229i	−0.165045	−	0.507955i
$414$	−1.61803	−	1.17557i	−0.0795220	−	0.0577761i
$415$	−12.7082	+	9.23305i	−0.623821	+	0.453233i
$416$	1.04508	−	3.21644i	0.0512395	−	0.157699i
$417$	2.56231			0.125477
$418$		0			0
$419$	0.326238			0.0159378			0.00796888	−	0.999968i	$-0.497463\pi$
$419$	0.326238			0.0159378			0.00796888	+	0.999968i	$0.497463\pi$
$420$	−0.500000	+	1.53884i	−0.0243975	+	0.0750878i
$421$	−29.3435	+	21.3193i	−1.43011	+	1.03904i	−0.440117	+	0.897940i	$0.645063\pi$
$421$	−29.3435	+	21.3193i	−1.43011	+	1.03904i	−0.989996	+	0.141097i	$0.954937\pi$
$422$	−24.4894	−	17.7926i	−1.19212	−	0.866128i
$423$	2.57295	+	7.91872i	0.125101	+	0.385021i
$424$	−3.71885	−	11.4454i	−0.180603	−	0.555839i
$425$	−0.354102	−	0.257270i	−0.0171765	−	0.0124794i
$426$	−1.92705	+	1.40008i	−0.0933659	+	0.0678343i
$427$	−3.16312	+	9.73508i	−0.153074	+	0.471114i
$428$	12.5066			0.604528
$429$	−2.80902	+	1.76336i	−0.135621	+	0.0851356i
$430$	4.23607			0.204281
$431$	−4.07953	+	12.5555i	−0.196504	+	0.604777i	0.803452	+	0.595370i	$0.202994\pi$
$431$	−4.07953	+	12.5555i	−0.196504	+	0.604777i	−0.999956	+	0.00940707i	$0.997006\pi$
$432$	3.92705	−	2.85317i	0.188940	−	0.137273i
$433$	23.7984	+	17.2905i	1.14368	+	0.830930i	0.987627	−	0.156819i	$-0.0501240\pi$
$433$	23.7984	+	17.2905i	1.14368	+	0.830930i	0.156050	+	0.987749i	$0.450124\pi$
$434$	−2.88197	−	8.86978i	−0.138339	−	0.425763i
$435$	5.42705	+	16.7027i	0.260207	+	0.800835i
$436$	−6.28115	−	4.56352i	−0.300813	−	0.218553i
$437$		0			0
$438$	−4.28115	+	13.1760i	−0.204561	+	0.629575i
$439$	9.47214			0.452080			0.226040	−	0.974118i	$-0.427422\pi$
$439$	9.47214			0.452080			0.226040	+	0.974118i	$0.427422\pi$
$440$	−7.23607	+	18.0171i	−0.344966	+	0.858930i
$441$	1.00000			0.0476190
$442$	−0.118034	+	0.363271i	−0.00561430	+	0.0172791i
$443$	4.32624	−	3.14320i	0.205546	−	0.149338i	−0.480250	−	0.877131i	$-0.659454\pi$
$443$	4.32624	−	3.14320i	0.205546	−	0.149338i	0.685796	+	0.727794i	$0.259454\pi$
$444$	5.47214	+	3.97574i	0.259696	+	0.188680i
$445$	6.97214	+	21.4580i	0.330511	+	1.01721i
$446$	0.354102	+	1.08981i	0.0167672	+	0.0516042i
$447$	1.54508	+	1.12257i	0.0730800	+	0.0530957i
$448$	−3.42705	+	2.48990i	−0.161913	+	0.117637i
$449$	−4.83688	+	14.8864i	−0.228267	+	0.702532i	0.769677	+	0.638433i	$0.220417\pi$
$449$	−4.83688	+	14.8864i	−0.228267	+	0.702532i	−0.997944	+	0.0640987i	$0.979583\pi$
$450$	3.00000			0.141421
$451$	−15.5000	−	12.9515i	−0.729866	−	0.609863i
$452$	12.1459			0.571295
$453$	−3.06231	+	9.42481i	−0.143880	+	0.442816i
$454$	36.6246	−	26.6093i	1.71888	−	1.24884i
$455$	−2.11803	−	1.53884i	−0.0992950	−	0.0721420i
$456$		0			0
$457$	−6.57295	−	20.2295i	−0.307470	−	0.946294i	−0.978744	−	0.205085i	$-0.934253\pi$
$457$	−6.57295	−	20.2295i	−0.307470	−	0.946294i	0.671275	−	0.741209i	$-0.265747\pi$
$458$	−2.23607	−	1.62460i	−0.104485	−	0.0759125i
$459$	−0.190983	+	0.138757i	−0.00891432	+	0.00647663i
$460$	−0.618034	+	1.90211i	−0.0288160	+	0.0886865i
$461$	0.819660			0.0381754			0.0190877	−	0.999818i	$-0.493924\pi$
$461$	0.819660			0.0381754			0.0190877	+	0.999818i	$0.493924\pi$
$462$	−5.35410	−	0.363271i	−0.249095	−	0.0169009i
$463$	28.9230			1.34417			0.672083	−	0.740476i	$-0.265400\pi$
$463$	28.9230			1.34417			0.672083	+	0.740476i	$0.265400\pi$
$464$	10.0623	−	30.9686i	0.467131	−	1.43768i
$465$	−12.2082	+	8.86978i	−0.566142	+	0.411326i
$466$	−2.30902	−	1.67760i	−0.106963	−	0.0777133i
$467$	4.34346	+	13.3678i	0.200991	+	0.618588i	0.999854	+	0.0170745i	$0.00543525\pi$
$467$	4.34346	+	13.3678i	0.200991	+	0.618588i	−0.798863	+	0.601513i	$0.794565\pi$
$468$	−0.190983	−	0.587785i	−0.00882819	−	0.0271704i
$469$	3.85410	+	2.80017i	0.177966	+	0.129300i
$470$	28.5344	−	20.7315i	1.31620	−	0.956272i
$471$	−5.35410	+	16.4782i	−0.246704	+	0.759277i
$472$	24.2705			1.11714
$473$	0.809017	+	3.21644i	0.0371986	+	0.147892i
$474$	6.70820			0.308118
$475$		0			0
$476$	−0.118034	+	0.0857567i	−0.00541008	+	0.00393065i
$477$	−4.35410	−	3.16344i	−0.199361	−	0.144844i
$478$	12.9271	+	39.7854i	0.591270	+	1.81974i
$479$	−5.10081	−	15.6987i	−0.233062	−	0.717291i	−0.997373	−	0.0724429i	$-0.976920\pi$
$479$	−5.10081	−	15.6987i	−0.233062	−	0.717291i	0.764310	−	0.644848i	$-0.223080\pi$
$480$	−7.16312	−	5.20431i	−0.326950	−	0.237543i
$481$	−8.85410	+	6.43288i	−0.403712	+	0.293314i
$482$	−5.64590	+	17.3763i	−0.257164	+	0.791468i
$483$	1.23607			0.0562430
$484$	6.73607	+	0.918300i	0.306185	+	0.0417409i
$485$	44.5066			2.02094
$486$	0.500000	−	1.53884i	0.0226805	−	0.0698033i
$487$	−11.6353	+	8.45351i	−0.527244	+	0.383065i	−0.819326	−	0.573328i	$-0.805652\pi$
$487$	−11.6353	+	8.45351i	−0.527244	+	0.383065i	0.292082	+	0.956393i	$0.405652\pi$
$488$	−18.5172	−	13.4535i	−0.838235	−	0.609014i
$489$	−7.11803	−	21.9071i	−0.321889	−	0.990671i
$490$	−1.30902	−	4.02874i	−0.0591354	−	0.182000i
$491$	7.85410	+	5.70634i	0.354451	+	0.257523i	0.750734	−	0.660605i	$-0.229700\pi$
$491$	7.85410	+	5.70634i	0.354451	+	0.257523i	−0.396283	+	0.918128i	$0.629700\pi$
$492$	3.04508	−	2.21238i	0.137283	−	0.0997420i
$493$	−0.489357	+	1.50609i	−0.0220395	+	0.0678307i
$494$		0			0
$495$	2.11803	+	8.42075i	0.0951985	+	0.378485i
$496$	27.9787			1.25628
$497$	0.454915	−	1.40008i	0.0204057	−	0.0628024i
$498$	7.85410	−	5.70634i	0.351951	−	0.255707i
$499$	4.04508	+	2.93893i	0.181083	+	0.131564i	0.674634	−	0.738152i	$-0.264301\pi$
$499$	4.04508	+	2.93893i	0.181083	+	0.131564i	−0.493551	+	0.869717i	$0.664301\pi$
$500$	1.57295	+	4.84104i	0.0703444	+	0.216498i
$501$	3.59017	+	11.0494i	0.160397	+	0.493651i
$502$	29.5795	+	21.4908i	1.32020	+	0.959181i
$503$	−24.5172	+	17.8128i	−1.09317	+	0.794234i	−0.979932	−	0.199334i	$-0.936122\pi$
$503$	−24.5172	+	17.8128i	−1.09317	+	0.794234i	−0.113237	+	0.993568i	$0.536122\pi$
$504$	−0.690983	+	2.12663i	−0.0307788	+	0.0947275i
$505$	−47.5967			−2.11803
$506$	−6.61803	−	0.449028i	−0.294207	−	0.0199617i
$507$	−12.0000			−0.532939
$508$	1.59017	−	4.89404i	0.0705524	−	0.217138i
$509$	9.57295	−	6.95515i	0.424314	−	0.308282i	−0.355058	−	0.934844i	$-0.615539\pi$
$509$	9.57295	−	6.95515i	0.424314	−	0.308282i	0.779371	+	0.626563i	$0.215539\pi$
$510$	0.809017	+	0.587785i	0.0358239	+	0.0260276i
$511$	−2.64590	−	8.14324i	−0.117048	−	0.360236i
$512$	−1.63525	−	5.03280i	−0.0722687	−	0.222420i
$513$		0			0
$514$	−11.8541	+	8.61251i	−0.522862	+	0.379881i
$515$	−0.572949	+	1.76336i	−0.0252472	+	0.0777027i
$516$	−0.618034			−0.0272074
$517$	21.1910	+	17.7068i	0.931978	+	0.778744i
$518$	−17.7082			−0.778054
$519$	−3.82624	+	11.7759i	−0.167953	+	0.516907i
$520$	4.73607	−	3.44095i	0.207690	−	0.150896i
$521$	−2.57295	−	1.86936i	−0.112723	−	0.0818980i	0.529996	−	0.848000i	$-0.322194\pi$
$521$	−2.57295	−	1.86936i	−0.112723	−	0.0818980i	−0.642719	+	0.766102i	$0.722194\pi$
$522$	−3.35410	−	10.3229i	−0.146805	−	0.451820i
$523$	−13.0729	−	40.2344i	−0.571640	−	1.75933i	−0.647345	−	0.762197i	$-0.724121\pi$
$523$	−13.0729	−	40.2344i	−0.571640	−	1.75933i	0.0757048	−	0.997130i	$-0.475879\pi$
$524$	−6.16312	−	4.47777i	−0.269237	−	0.195612i
$525$	−1.50000	+	1.08981i	−0.0654654	+	0.0475634i
$526$	−6.35410	+	19.5559i	−0.277052	+	0.852678i
$527$	−1.36068			−0.0592721
$528$	6.00000	−	14.9394i	0.261116	−	0.650153i
$529$	−21.4721			−0.933571
$530$	−7.04508	+	21.6825i	−0.306019	+	0.941829i
$531$	8.78115	−	6.37988i	0.381070	−	0.276863i
$532$		0			0
$533$	1.88197	+	5.79210i	0.0815170	+	0.250884i
$534$	−4.30902	−	13.2618i	−0.186469	−	0.573894i
$535$	42.8607	+	31.1401i	1.85303	+	1.34630i
$536$	−8.61803	+	6.26137i	−0.372242	+	0.270450i
$537$	0.690983	−	2.12663i	0.0298181	−	0.0917707i
$538$	9.79837			0.422438
$539$	2.80902	−	1.76336i	0.120993	−	0.0759531i
$540$	−1.61803			−0.0696291
$541$	2.75329	−	8.47375i	0.118373	−	0.364315i	−0.874262	−	0.485454i	$-0.838655\pi$
$541$	2.75329	−	8.47375i	0.118373	−	0.364315i	0.992636	+	0.121138i	$0.0386545\pi$
$542$	−26.7254	+	19.4172i	−1.14796	+	0.834038i
$543$	−3.42705	−	2.48990i	−0.147069	−	0.106852i
$544$	−0.246711	−	0.759299i	−0.0105777	−	0.0325547i
$545$	−10.1631	−	31.2789i	−0.435340	−	1.33984i
$546$	1.30902	+	0.951057i	0.0560208	+	0.0407015i
$547$	21.5172	−	15.6332i	0.920010	−	0.668426i	−0.0235166	−	0.999723i	$-0.507486\pi$
$547$	21.5172	−	15.6332i	0.920010	−	0.668426i	0.943526	+	0.331297i	$0.107486\pi$
$548$	−4.00000	+	12.3107i	−0.170872	+	0.525888i
$549$	−10.2361			−0.436865
$550$	8.42705	−	5.29007i	0.359331	−	0.225569i
$551$		0			0
$552$	−0.854102	+	2.62866i	−0.0363530	+	0.111883i
$553$	−3.35410	+	2.43690i	−0.142631	+	0.103627i
$554$	−1.85410	−	1.34708i	−0.0787732	−	0.0572321i
$555$	8.85410	+	27.2501i	0.375836	+	1.15670i
$556$	0.489357	+	1.50609i	0.0207534	+	0.0638723i
$557$	−4.23607	−	3.07768i	−0.179488	−	0.130406i	0.494414	−	0.869227i	$-0.335383\pi$
$557$	−4.23607	−	3.07768i	−0.179488	−	0.130406i	−0.673902	+	0.738821i	$0.735383\pi$
$558$	7.54508	−	5.48183i	0.319409	−	0.232064i
$559$	0.309017	−	0.951057i	0.0130700	−	0.0402254i
$560$	12.7082			0.537020
$561$	−0.291796	+	0.726543i	−0.0123196	+	0.0306746i
$562$	21.6525			0.913355
$563$	4.03851	−	12.4292i	0.170203	−	0.523830i	−0.829179	−	0.558983i	$-0.811192\pi$
$563$	4.03851	−	12.4292i	0.170203	−	0.523830i	0.999382	+	0.0351526i	$0.0111917\pi$
$564$	−4.16312	+	3.02468i	−0.175299	+	0.127362i
$565$	41.6246	+	30.2421i	1.75116	+	1.27229i
$566$	10.3541	+	31.8666i	0.435215	+	1.33946i
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$	2.66312	+	1.93487i	0.111742	+	0.0811853i
$569$	15.4271	−	11.2084i	0.646736	−	0.469881i	−0.215422	−	0.976521i	$-0.569113\pi$
$569$	15.4271	−	11.2084i	0.646736	−	0.469881i	0.862158	+	0.506640i	$0.169113\pi$
$570$		0			0
$571$	7.00000			0.292941			0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000			0.292941			0.146470	+	0.989215i	$0.453209\pi$
$572$	−1.57295	−	1.31433i	−0.0657683	−	0.0549548i
$573$	14.2361			0.594720
$574$	−3.04508	+	9.37181i	−0.127099	+	0.391172i
$575$	−1.85410	+	1.34708i	−0.0773214	+	0.0561773i
$576$	−3.42705	−	2.48990i	−0.142794	−	0.103746i
$577$	−9.13525	−	28.1154i	−0.380306	−	1.17046i	−0.939829	−	0.341646i	$-0.889016\pi$
$577$	−9.13525	−	28.1154i	−0.380306	−	1.17046i	0.559523	−	0.828815i	$-0.310984\pi$
$578$	−8.47214	−	26.0746i	−0.352394	−	1.08456i
$579$	−18.5623	−	13.4863i	−0.771423	−	0.560472i
$580$	−8.78115	+	6.37988i	−0.364618	+	0.264910i
$581$	−1.85410	+	5.70634i	−0.0769211	+	0.236739i
$582$	−27.5066			−1.14018
$583$	−17.8090	−	1.20833i	−0.737574	−	0.0500438i
$584$	19.1459			0.792263
$585$	0.809017	−	2.48990i	0.0334487	−	0.102945i
$586$	11.4721	−	8.33499i	0.473910	−	0.344315i
$587$	−0.0901699	−	0.0655123i	−0.00372171	−	0.00270398i	0.585923	−	0.810367i	$-0.300732\pi$
$587$	−0.0901699	−	0.0655123i	−0.00372171	−	0.00270398i	−0.589645	+	0.807663i	$0.700732\pi$
$588$	0.190983	+	0.587785i	0.00787601	+	0.0242399i
$589$		0			0
$590$	−37.1976	−	27.0256i	−1.53140	−	1.11263i
$591$	3.85410	−	2.80017i	0.158537	−	0.115184i
$592$	16.4164	−	50.5245i	0.674710	−	2.07654i
$593$	11.8885			0.488204			0.244102	−	0.969750i	$-0.421507\pi$
$593$	11.8885			0.488204			0.244102	+	0.969750i	$0.421507\pi$
$594$	−1.30902	−	5.20431i	−0.0537096	−	0.213535i
$595$	−0.618034			−0.0253369
$596$	−0.364745	+	1.12257i	−0.0149405	+	0.0459823i
$597$	−10.1631	+	7.38394i	−0.415949	+	0.302204i
$598$	1.61803	+	1.17557i	0.0661663	+	0.0480727i
$599$	−2.01064	−	6.18812i	−0.0821527	−	0.252840i	0.901541	−	0.432695i	$-0.142437\pi$
$599$	−2.01064	−	6.18812i	−0.0821527	−	0.252840i	−0.983693	+	0.179855i	$0.942437\pi$
$600$	−1.28115	−	3.94298i	−0.0523029	−	0.160972i
$601$	−31.4164	−	22.8254i	−1.28150	−	0.931066i	−0.281905	−	0.959442i	$-0.590966\pi$
$601$	−31.4164	−	22.8254i	−1.28150	−	0.931066i	−0.999597	+	0.0283767i	$0.990966\pi$
$602$	1.30902	−	0.951057i	0.0533515	−	0.0387622i
$603$	−1.47214	+	4.53077i	−0.0599500	+	0.184507i
$604$	−6.12461			−0.249207
$605$	20.7984	+	19.9192i	0.845574	+	0.809830i
$606$	29.4164			1.19496
$607$	−7.06231	+	21.7355i	−0.286650	+	0.882218i	0.699249	+	0.714878i	$0.253518\pi$
$607$	−7.06231	+	21.7355i	−0.286650	+	0.882218i	−0.985899	+	0.167340i	$0.946482\pi$
$608$		0			0
$609$	5.42705	+	3.94298i	0.219915	+	0.159778i
$610$	13.3992	+	41.2385i	0.542517	+	1.66970i
$611$	−2.57295	−	7.91872i	−0.104090	−	0.320357i
$612$	−0.118034	−	0.0857567i	−0.00477124	−	0.00346651i
$613$	17.3541	−	12.6085i	0.700926	−	0.509252i	−0.179308	−	0.983793i	$-0.557386\pi$
$613$	17.3541	−	12.6085i	0.700926	−	0.509252i	0.880234	+	0.474541i	$0.157386\pi$
$614$	−1.59017	+	4.89404i	−0.0641740	+	0.197507i
$615$	15.9443			0.642935
$616$	1.80902	+	7.19218i	0.0728874	+	0.289781i
$617$	1.09017			0.0438886			0.0219443	−	0.999759i	$-0.493014\pi$
$617$	1.09017			0.0438886			0.0219443	+	0.999759i	$0.493014\pi$
$618$	0.354102	−	1.08981i	0.0142441	−	0.0438387i
$619$	4.14590	−	3.01217i	0.166638	−	0.121069i	−0.501341	−	0.865250i	$-0.667160\pi$
$619$	4.14590	−	3.01217i	0.166638	−	0.121069i	0.667979	+	0.744180i	$0.267160\pi$
$620$	−7.54508	−	5.48183i	−0.303018	−	0.220155i
$621$	0.381966	+	1.17557i	0.0153278	+	0.0471740i
$622$	−3.89919	−	12.0005i	−0.156343	−	0.481175i
$623$	6.97214	+	5.06555i	0.279333	+	0.202947i
$624$	−3.92705	+	2.85317i	−0.157208	+	0.114218i
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$	14.2361			0.568988
$627$		0			0
$628$	−10.7082			−0.427304
$629$	−0.798374	+	2.45714i	−0.0318333	+	0.0979727i
$630$	3.42705	−	2.48990i	0.136537	−	0.0991999i
$631$	−10.6631	−	7.74721i	−0.424492	−	0.308412i	0.354951	−	0.934885i	$-0.384498\pi$
$631$	−10.6631	−	7.74721i	−0.424492	−	0.308412i	−0.779443	+	0.626473i	$0.784498\pi$
$632$	−2.86475	−	8.81678i	−0.113953	−	0.350713i
$633$	5.78115	+	17.7926i	0.229780	+	0.707191i
$634$	25.3435	+	18.4131i	1.00652	+	0.731278i
$635$	17.6353	−	12.8128i	0.699834	−	0.508459i
$636$	1.02786	−	3.16344i	0.0407575	−	0.125439i
$637$	−1.00000			−0.0396214
$638$	−27.6246	−	23.0826i	−1.09367	−	0.913850i
$639$	1.47214			0.0582368
$640$	−11.0172	+	33.9075i	−0.435494	+	1.34031i
$641$	15.3541	−	11.1554i	0.606451	−	0.440612i	−0.241712	−	0.970348i	$-0.577709\pi$
$641$	15.3541	−	11.1554i	0.606451	−	0.440612i	0.848163	+	0.529736i	$0.177709\pi$
$642$	−26.4894	−	19.2456i	−1.04545	−	0.759565i
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	−0.999977	−	0.00681282i	$-0.997831\pi$
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	0.804994	−	0.593283i	$-0.202169\pi$
$644$	0.236068	+	0.726543i	0.00930238	+	0.0286298i
$645$	−2.11803	−	1.53884i	−0.0833975	−	0.0605918i
$646$		0			0
$647$	10.3992	−	32.0054i	0.408834	−	1.25826i	−0.508817	−	0.860875i	$-0.669917\pi$
$647$	10.3992	−	32.0054i	0.408834	−	1.25826i	0.917651	−	0.397387i	$-0.130083\pi$
$648$	−2.23607			−0.0878410
$649$	13.4164	−	33.4055i	0.526640	−	1.31128i
$650$	−3.00000			−0.117670
$651$	−1.78115	+	5.48183i	−0.0698089	+	0.214850i
$652$	11.5172	−	8.36775i	0.451049	−	0.327706i
$653$	10.2812	+	7.46969i	0.402333	+	0.292312i	0.770490	−	0.637452i	$-0.220011\pi$
$653$	10.2812	+	7.46969i	0.402333	+	0.292312i	−0.368158	+	0.929763i	$0.620011\pi$
$654$	6.28115	+	19.3314i	0.245613	+	0.755918i
$655$	−9.97214	−	30.6911i	−0.389644	−	1.19920i
$656$	−23.9164	−	17.3763i	−0.933779	−	0.678430i
$657$	6.92705	−	5.03280i	0.270250	−	0.196348i
$658$	4.16312	−	12.8128i	0.162295	−	0.499493i
$659$	−11.8328			−0.460941			−0.230471	−	0.973079i	$-0.574027\pi$
$659$	−11.8328			−0.460941			−0.230471	+	0.973079i	$0.574027\pi$
$660$	−4.54508	+	2.85317i	−0.176917	+	0.111059i
$661$	−3.00000			−0.116686			−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000			−0.116686			−0.0583432	+	0.998297i	$0.518582\pi$
$662$	−0.645898	+	1.98787i	−0.0251035	+	0.0772608i
$663$	0.190983	−	0.138757i	0.00741717	−	0.00538889i
$664$	−10.8541	−	7.88597i	−0.421221	−	0.306035i
$665$		0			0
$666$	−5.47214	−	16.8415i	−0.212041	−	0.652595i
$667$	6.70820	+	4.87380i	0.259743	+	0.188714i
$668$	−5.80902	+	4.22050i	−0.224758	+	0.163296i
$669$	0.218847	−	0.673542i	0.00846112	−	0.0260406i
$670$	20.1803			0.779635
$671$	−28.7533	+	18.0498i	−1.11001	+	0.696806i
$672$	−3.38197			−0.130462
$673$	−10.6353	+	32.7319i	−0.409959	+	1.26172i	0.506724	+	0.862108i	$0.330856\pi$
$673$	−10.6353	+	32.7319i	−0.409959	+	1.26172i	−0.916683	+	0.399616i	$0.869144\pi$
$674$	−19.2533	+	13.9883i	−0.741609	+	0.538810i
$675$	−1.50000	−	1.08981i	−0.0577350	−	0.0419470i
$676$	−2.29180	−	7.05342i	−0.0881460	−	0.271286i
$677$	−10.0279	−	30.8626i	−0.385402	−	1.18615i	−0.936188	−	0.351499i	$-0.885672\pi$
$677$	−10.0279	−	30.8626i	−0.385402	−	1.18615i	0.550786	−	0.834646i	$-0.314328\pi$
$678$	−25.7254	−	18.6906i	−0.987979	−	0.717809i
$679$	13.7533	−	9.99235i	0.527803	−	0.383471i
$680$	0.427051	−	1.31433i	0.0163767	−	0.0504022i
$681$	−27.9787			−1.07215
$682$	11.5279	−	28.7032i	0.441425	−	1.09910i
$683$	30.3050			1.15959			0.579793	−	0.814764i	$-0.303133\pi$
$683$	30.3050			1.15959			0.579793	+	0.814764i	$0.303133\pi$
$684$		0			0
$685$	−44.3607	+	32.2299i	−1.69493	+	1.23144i
$686$	−1.30902	−	0.951057i	−0.0499785	−	0.0363115i
$687$	0.527864	+	1.62460i	0.0201393	+	0.0619823i
$688$	1.50000	+	4.61653i	0.0571870	+	0.176003i
$689$	4.35410	+	3.16344i	0.165878	+	0.120517i
$690$	4.23607	−	3.07768i	0.161264	−	0.117165i
$691$	−1.71885	+	5.29007i	−0.0653880	+	0.201244i	−0.978413	−	0.206661i	$-0.933740\pi$
$691$	−1.71885	+	5.29007i	−0.0653880	+	0.201244i	0.913025	+	0.407904i	$0.133740\pi$
$692$	−7.65248			−0.290903
$693$	2.54508	+	2.12663i	0.0966798	+	0.0807839i
$694$	2.29180			0.0869954
$695$	−2.07295	+	6.37988i	−0.0786314	+	0.242003i
$696$	−12.1353	+	8.81678i	−0.459986	+	0.334199i
$697$	1.16312	+	0.845055i	0.0440563	+	0.0320088i
$698$	−14.9615	−	46.0467i	−0.566301	−	1.74289i
$699$	0.545085	+	1.67760i	0.0206170	+	0.0634526i
$700$	−0.927051	−	0.673542i	−0.0350392	−	0.0254575i
$701$	−21.8435	+	15.8702i	−0.825016	+	0.599409i	−0.918145	−	0.396245i	$-0.870313\pi$
$701$	−21.8435	+	15.8702i	−0.825016	+	0.599409i	0.0931288	+	0.995654i	$0.470313\pi$
$702$	−0.500000	+	1.53884i	−0.0188713	+	0.0580798i
$703$		0			0
$704$	−14.0172	−	0.951057i	−0.528294	−	0.0358443i
$705$	−21.7984			−0.820974
$706$	−8.26393	+	25.4338i	−0.311017	+	0.957212i
$707$	−14.7082	+	10.6861i	−0.553159	+	0.401893i
$708$	5.42705	+	3.94298i	0.203961	+	0.148186i
$709$	−5.97871	−	18.4006i	−0.224535	−	0.691049i	−0.998338	−	0.0576225i	$-0.981648\pi$
$709$	−5.97871	−	18.4006i	−0.224535	−	0.691049i	0.773803	−	0.633426i	$-0.218352\pi$
$710$	−1.92705	−	5.93085i	−0.0723209	−	0.222581i
$711$	−3.35410	−	2.43690i	−0.125789	−	0.0913908i
$712$	−15.5902	+	11.3269i	−0.584266	+	0.424494i
$713$	−2.20163	+	6.77591i	−0.0824515	+	0.253760i
$714$	0.381966			0.0142947
$715$	−2.11803	−	8.42075i	−0.0792100	−	0.314918i
$716$	1.38197			0.0516465
$717$	7.98936	−	24.5887i	0.298368	−	0.918282i
$718$	−23.8435	+	17.3233i	−0.889830	+	0.646499i
$719$	5.16312	+	3.75123i	0.192552	+	0.139897i	0.679884	−	0.733319i	$-0.262030\pi$
$719$	5.16312	+	3.75123i	0.192552	+	0.139897i	−0.487332	+	0.873217i	$0.662030\pi$
$720$	3.92705	+	12.0862i	0.146353	+	0.450427i
$721$	0.218847	+	0.673542i	0.00815029	+	0.0250840i
$722$	24.8713	+	18.0701i	0.925615	+	0.672499i
$723$	9.13525	−	6.63715i	0.339744	−	0.246838i
$724$	0.809017	−	2.48990i	0.0300669	−	0.0925363i
$725$	−12.4377			−0.461924
$726$	−12.8541	−	12.3107i	−0.477060	−	0.456894i
$727$	28.8541			1.07014			0.535070	−	0.844808i	$-0.320285\pi$
$727$	28.8541			1.07014			0.535070	+	0.844808i	$0.320285\pi$
$728$	0.690983	−	2.12663i	0.0256095	−	0.0788180i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−29.3435	−	21.3193i	−1.08605	−	0.789062i
$731$	−0.0729490	−	0.224514i	−0.00269812	−	0.00830395i
$732$	−1.95492	−	6.01661i	−0.0722557	−	0.222380i
$733$	29.2254	+	21.2335i	1.07947	+	0.784278i	0.977590	−	0.210519i	$-0.0675155\pi$
$733$	29.2254	+	21.2335i	1.07947	+	0.784278i	0.101876	+	0.994797i	$0.467516\pi$
$734$	−32.3435	+	23.4989i	−1.19382	+	0.867360i
$735$	−0.809017	+	2.48990i	−0.0298410	+	0.0918413i
$736$	−4.18034			−0.154089
$737$	3.85410	+	15.3229i	0.141968	+	0.564426i
$738$	−9.85410			−0.362735
$739$	−5.46556	+	16.8213i	−0.201054	+	0.618780i	0.798799	+	0.601599i	$0.205469\pi$
$739$	−5.46556	+	16.8213i	−0.201054	+	0.618780i	−0.999852	+	0.0171814i	$0.994531\pi$
$740$	−14.3262	+	10.4086i	−0.526643	+	0.382629i
$741$		0			0
$742$	2.69098	+	8.28199i	0.0987891	+	0.304042i
$743$	11.4615	+	35.2748i	0.420481	+	1.29411i	0.907255	+	0.420581i	$0.138174\pi$
$743$	11.4615	+	35.2748i	0.420481	+	1.29411i	−0.486774	+	0.873528i	$0.661826\pi$
$744$	−10.4271	−	7.57570i	−0.382274	−	0.277738i
$745$	−4.04508	+	2.93893i	−0.148200	+	0.107674i
$746$	3.90983	−	12.0332i	0.143149	−	0.440567i
$747$	−6.00000			−0.219529
$748$	−0.482779	−	0.0327561i	−0.0176522	−	0.00119768i
$749$	20.2361			0.739410
$750$	4.11803	−	12.6740i	0.150369	−	0.462789i
$751$	17.9164	−	13.0170i	0.653779	−	0.474998i	−0.210777	−	0.977534i	$-0.567600\pi$
$751$	17.9164	−	13.0170i	0.653779	−	0.474998i	0.864556	+	0.502536i	$0.167600\pi$
$752$	32.6976	+	23.7562i	1.19236	+	0.866298i
$753$	−6.98278	−	21.4908i	−0.254467	−	0.783168i
$754$	3.35410	+	10.3229i	0.122149	+	0.375937i
$755$	−20.9894	−	15.2497i	−0.763881	−	0.554992i
$756$	−0.500000	+	0.363271i	−0.0181848	+	0.0132120i
$757$	12.5967	−	38.7688i	0.457837	−	1.40908i	−0.409936	−	0.912114i	$-0.634449\pi$
$757$	12.5967	−	38.7688i	0.457837	−	1.40908i	0.867772	−	0.496962i	$-0.165551\pi$
$758$	−6.70820			−0.243653
$759$	3.14590	+	2.62866i	0.114189	+	0.0954142i
$760$		0			0
$761$	−3.42705	+	10.5474i	−0.124231	+	0.382342i	−0.993760	−	0.111539i	$-0.964422\pi$
$761$	−3.42705	+	10.5474i	−0.124231	+	0.382342i	0.869530	+	0.493881i	$0.164422\pi$
$762$	−10.8992	+	7.91872i	−0.394836	+	0.286865i
$763$	−10.1631	−	7.38394i	−0.367930	−	0.267317i
$764$	2.71885	+	8.36775i	0.0983644	+	0.302735i
$765$	−0.190983	−	0.587785i	−0.00690501	−	0.0212514i
$766$	24.9894	+	18.1558i	0.902902	+	0.655997i
$767$	−8.78115	+	6.37988i	−0.317069	+	0.230364i
$768$	4.19098	−	12.8985i	0.151229	−	0.465435i
$769$	35.5279			1.28117			0.640584	−	0.767888i	$-0.278692\pi$
$769$	35.5279			1.28117			0.640584	+	0.767888i	$0.278692\pi$
$770$	5.23607	−	13.0373i	0.188695	−	0.469831i
$771$	9.05573			0.326134
$772$	4.38197	−	13.4863i	0.157710	−	0.485383i
$773$	−30.2705	+	21.9928i	−1.08875	+	0.791026i	−0.979188	−	0.202953i	$-0.934946\pi$
$773$	−30.2705	+	21.9928i	−1.08875	+	0.791026i	−0.109566	+	0.993980i	$0.534946\pi$
$774$	1.30902	+	0.951057i	0.0470516	+	0.0341850i
$775$	−3.30244	−	10.1639i	−0.118627	−	0.365097i
$776$	11.7467	+	36.1527i	0.421682	+	1.29780i
$777$	8.85410	+	6.43288i	0.317639	+	0.230778i
$778$	13.9443	−	10.1311i	0.499926	−	0.363218i
$779$		0			0
$780$	1.61803			0.0579349
$781$	4.13525	−	2.59590i	0.147971	−	0.0928886i
$782$	0.472136			0.0168835
$783$	−2.07295	+	6.37988i	−0.0740812	+	0.227998i
$784$	3.92705	−	2.85317i	0.140252	−	0.101899i
$785$	−36.6976	−	26.6623i	−1.30979	−	0.951620i
$786$	6.16312	+	18.9681i	0.219831	+	0.676571i
$787$	−8.07953	−	24.8662i	−0.288004	−	0.886385i	−0.985482	−	0.169779i	$-0.945695\pi$
$787$	−8.07953	−	24.8662i	−0.288004	−	0.886385i	0.697478	−	0.716606i	$-0.254305\pi$
$788$	2.38197	+	1.73060i	0.0848540	+	0.0616501i
$789$	10.2812	−	7.46969i	0.366019	−	0.265928i
$790$	−5.42705	+	16.7027i	−0.193086	+	0.594257i
$791$	19.6525			0.698762
$792$	−6.28115	+	3.94298i	−0.223191	+	0.140108i
$793$	10.2361			0.363493
$794$	−17.3435	+	53.3777i	−0.615496	+	1.89430i
$795$	11.3992	−	8.28199i	0.404287	−	0.293732i
$796$	−6.28115	−	4.56352i	−0.222630	−	0.161750i
$797$	7.24671	+	22.3031i	0.256692	+	0.790016i	0.993492	+	0.113905i	$0.0363359\pi$
$797$	7.24671	+	22.3031i	0.256692	+	0.790016i	−0.736800	+	0.676111i	$0.763664\pi$
$798$		0			0
$799$	−1.59017	−	1.15533i	−0.0562562	−	0.0408725i
$800$	5.07295	−	3.68571i	0.179356	−	0.130310i
$801$	−2.66312	+	8.19624i	−0.0940967	+	0.289600i
$802$	44.2148			1.56128
$803$	10.5836	−	26.3521i	0.373487	−	0.929944i
$804$	−2.94427			−0.103836
$805$	−1.00000	+	3.07768i	−0.0352454	+	0.108474i
$806$	−7.54508	+	5.48183i	−0.265764	+	0.193089i
$807$	−4.89919	−	3.55947i	−0.172460	−	0.125299i
$808$	−12.5623	−	38.6628i	−0.441940	−	1.36015i
$809$	−4.93769	−	15.1967i	−0.173600	−	0.534286i	0.825967	−	0.563719i	$-0.190630\pi$
$809$	−4.93769	−	15.1967i	−0.173600	−	0.534286i	−0.999567	+	0.0294328i	$0.990630\pi$
$810$	3.42705	+	2.48990i	0.120414	+	0.0874861i
$811$	−13.8541	+	10.0656i	−0.486483	+	0.353451i	−0.803830	−	0.594859i	$-0.797208\pi$
$811$	−13.8541	+	10.0656i	−0.486483	+	0.353451i	0.317347	+	0.948309i	$0.397208\pi$
$812$	−1.28115	+	3.94298i	−0.0449597	+	0.138372i
$813$	20.4164			0.716035
$814$	−45.0689	−	37.6587i	−1.57966	−	1.31994i
$815$	60.3050			2.11239
$816$	−0.354102	+	1.08981i	−0.0123960	+	0.0381511i
$817$		0			0
$818$	37.4615	+	27.2174i	1.30981	+	0.951633i
$819$	−0.309017	−	0.951057i	−0.0107979	−	0.0332326i
$820$	3.04508	+	9.37181i	0.106339	+	0.327278i
$821$	−22.7984	−	16.5640i	−0.795669	−	0.578087i	0.113972	−	0.993484i	$-0.463643\pi$
$821$	−22.7984	−	16.5640i	−0.795669	−	0.578087i	−0.909640	+	0.415397i	$0.863643\pi$
$822$	27.4164	−	19.9192i	0.956257	−	0.694761i
$823$	16.7639	−	51.5941i	0.584354	−	1.79846i	−0.0174955	−	0.999847i	$-0.505569\pi$
$823$	16.7639	−	51.5941i	0.584354	−	1.79846i	0.601849	−	0.798610i	$-0.294431\pi$
$824$	−1.58359			−0.0551670
$825$	−6.13525	−	0.416272i	−0.213602	−	0.0144927i
$826$	−17.5623			−0.611071
$827$	12.6353	−	38.8873i	0.439371	−	1.35224i	−0.449170	−	0.893446i	$-0.648280\pi$
$827$	12.6353	−	38.8873i	0.439371	−	1.35224i	0.888541	−	0.458798i	$-0.151720\pi$
$828$	−0.618034	+	0.449028i	−0.0214782	+	0.0156048i
$829$	18.3541	+	13.3350i	0.637464	+	0.463145i	0.858978	−	0.512012i	$-0.171100\pi$
$829$	18.3541	+	13.3350i	0.637464	+	0.463145i	−0.221514	+	0.975157i	$0.571100\pi$
$830$	7.85410	+	24.1724i	0.272620	+	0.839038i
$831$	0.437694	+	1.34708i	0.0151834	+	0.0467298i
$832$	3.42705	+	2.48990i	0.118812	+	0.0863217i
$833$	−0.190983	+	0.138757i	−0.00661717	+	0.00480765i
$834$	1.28115	−	3.94298i	0.0443627	−	0.136534i
$835$	−30.4164			−1.05260
$836$		0			0
$837$	−5.76393			−0.199231
$838$	0.163119	−	0.502029i	0.00563485	−	0.0173423i
$839$	23.5172	−	17.0863i	0.811905	−	0.589883i	−0.102478	−	0.994735i	$-0.532677\pi$
$839$	23.5172	−	17.0863i	0.811905	−	0.589883i	0.914382	+	0.404852i	$0.132677\pi$
$840$	−4.73607	−	3.44095i	−0.163410	−	0.118724i
$841$	4.94427	+	15.2169i	0.170492	+	0.524721i
$842$	18.1353	+	55.8146i	0.624982	+	1.92350i
$843$	−10.8262	−	7.86572i	−0.372875	−	0.270910i
$844$	−9.35410	+	6.79615i	−0.321981	+	0.233933i
$845$	9.70820	−	29.8788i	0.333972	−	1.02786i
$846$	13.4721			0.463182
$847$	10.8992	+	1.48584i	0.374500	+	0.0510541i
$848$	−26.1246			−0.897123
$849$	6.39919	−	19.6947i	0.219620	−	0.675919i
$850$	−0.572949	+	0.416272i	−0.0196520	+	0.0142780i
$851$	10.9443	+	7.95148i	0.375165	+	0.272573i
$852$	0.281153	+	0.865300i	0.00963214	+	0.0296447i
$853$	10.4443	+	32.1442i	0.357605	+	1.10060i	0.954484	+	0.298264i	$0.0964074\pi$
$853$	10.4443	+	32.1442i	0.357605	+	1.10060i	−0.596878	+	0.802332i	$0.703593\pi$
$854$	13.3992	+	9.73508i	0.458511	+	0.333128i
$855$		0			0
$856$	−13.9828	+	43.0346i	−0.477922	+	1.47089i
$857$	−49.7639			−1.69990			−0.849952	−	0.526861i	$-0.823369\pi$
$857$	−49.7639			−1.69990			−0.849952	+	0.526861i	$0.823369\pi$
$858$	1.30902	+	5.20431i	0.0446891	+	0.177672i
$859$	11.8328			0.403730			0.201865	−	0.979413i	$-0.435300\pi$
$859$	11.8328			0.403730			0.201865	+	0.979413i	$0.435300\pi$
$860$	0.500000	−	1.53884i	0.0170499	−	0.0524741i
$861$	4.92705	−	3.57971i	0.167913	−	0.121996i
$862$	17.2812	+	12.5555i	0.588598	+	0.427642i
$863$	−4.12868	−	12.7068i	−0.140542	−	0.432543i	0.855869	−	0.517193i	$-0.173023\pi$
$863$	−4.12868	−	12.7068i	−0.140542	−	0.432543i	−0.996411	+	0.0846495i	$0.973023\pi$
$864$	−1.04508	−	3.21644i	−0.0355545	−	0.109426i
$865$	−26.2254	−	19.0539i	−0.891691	−	0.647852i
$866$	38.5066	−	27.9767i	1.30851	−	0.950686i
$867$	−5.23607	+	16.1150i	−0.177826	+	0.547293i
$868$	−3.56231			−0.120913
$869$	−13.7188	−	0.930812i	−0.465380	−	0.0315756i
$870$	28.4164			0.963406
$871$	1.47214	−	4.53077i	0.0498814	−	0.153519i
$872$	22.7254	−	16.5110i	0.769580	−	0.559133i
$873$	13.7533	+	9.99235i	0.465478	+	0.338190i
$874$		0			0
$875$	2.54508	+	7.83297i	0.0860396	+	0.264803i
$876$	4.28115	+	3.11044i	0.144647	+	0.105092i
$877$	0.600813	−	0.436516i	0.0202880	−	0.0147401i	−0.577595	−	0.816323i	$-0.696009\pi$
$877$	0.600813	−	0.436516i	0.0202880	−	0.0147401i	0.597883	+	0.801583i	$0.296009\pi$
$878$	4.73607	−	14.5761i	0.159835	−	0.491920i
$879$	−8.76393			−0.295600
$880$	32.3435	+	27.0256i	1.09030	+	0.911033i
$881$	5.94427			0.200268			0.100134	−	0.994974i	$-0.468073\pi$
$881$	5.94427			0.200268			0.100134	+	0.994974i	$0.468073\pi$
$882$	0.500000	−	1.53884i	0.0168359	−	0.0518155i
$883$	3.20820	−	2.33090i	0.107965	−	0.0784409i	−0.532493	−	0.846434i	$-0.678745\pi$
$883$	3.20820	−	2.33090i	0.107965	−	0.0784409i	0.640458	+	0.767994i	$0.278745\pi$
$884$	0.118034	+	0.0857567i	0.00396991	+	0.00288431i
$885$	8.78115	+	27.0256i	0.295175	+	0.908456i
$886$	−2.67376	−	8.22899i	−0.0898268	−	0.276458i
$887$	10.1353	+	7.36369i	0.340309	+	0.247249i	0.744792	−	0.667297i	$-0.232549\pi$
$887$	10.1353	+	7.36369i	0.340309	+	0.247249i	−0.404483	+	0.914545i	$0.632549\pi$
$888$	−19.7984	+	14.3844i	−0.664390	+	0.482708i
$889$	2.57295	−	7.91872i	0.0862939	−	0.265585i
$890$	36.5066			1.22370
$891$	−1.23607	+	3.07768i	−0.0414098	+	0.103106i
$892$	0.437694			0.0146551
$893$		0			0
$894$	2.50000	−	1.81636i	0.0836125	−	0.0607480i
$895$	4.73607	+	3.44095i	0.158309	+	0.115018i
$896$	4.20820	+	12.9515i	0.140586	+	0.432680i
$897$	−0.381966	−	1.17557i	−0.0127535	−	0.0392512i
$898$	20.4894	+	14.8864i	0.683739	+	0.496765i
$899$	−31.2812	+	22.7271i	−1.04328	+	0.757991i
$900$	0.354102	−	1.08981i	0.0118034	−	0.0363271i
$901$	1.27051			0.0423268
$902$	−27.6803	+	17.3763i	−0.921655	+	0.578567i
$903$	−1.00000			−0.0332779
$904$	−13.5795	+	41.7935i	−0.451648	+	1.39003i
$905$	8.97214	−	6.51864i	0.298244	−	0.216687i
$906$	12.9721	+	9.42481i	0.430970	+	0.313118i
$907$	−8.64590	−	26.6093i	−0.287082	−	0.883549i	−0.985767	−	0.168119i	$-0.946231\pi$
$907$	−8.64590	−	26.6093i	−0.287082	−	0.883549i	0.698684	−	0.715430i	$-0.253769\pi$
$908$	−5.34346	−	16.4455i	−0.177329	−	0.545762i
$909$	−14.7082	−	10.6861i	−0.487840	−	0.354437i
$910$	−3.42705	+	2.48990i	−0.113606	+	0.0825393i
$911$	−14.9336	+	45.9610i	−0.494773	+	1.52276i	0.322537	+	0.946557i	$0.395464\pi$
$911$	−14.9336	+	45.9610i	−0.494773	+	1.52276i	−0.817310	+	0.576198i	$0.804536\pi$
$912$		0			0
$913$	−16.8541	+	10.5801i	−0.557789	+	0.350151i
$914$	−34.4164			−1.13839
$915$	8.28115	−	25.4868i	0.273766	−	0.842567i
$916$	−0.854102	+	0.620541i	−0.0282203	+	0.0205033i
$917$	−9.97214	−	7.24518i	−0.329309	−	0.239257i
$918$	0.118034	+	0.363271i	0.00389570	+	0.0119897i
$919$	−13.4164	−	41.2915i	−0.442566	−	1.36208i	−0.885131	−	0.465343i	$-0.845931\pi$
$919$	−13.4164	−	41.2915i	−0.442566	−	1.36208i	0.442564	−	0.896737i	$-0.354069\pi$
$920$	−5.85410	−	4.25325i	−0.193004	−	0.140226i
$921$	2.57295	−	1.86936i	0.0847816	−	0.0615974i
$922$	0.409830	−	1.26133i	0.0134970	−	0.0415396i
$923$	−1.47214			−0.0484559
$924$	−0.763932	+	1.90211i	−0.0251315	+	0.0625749i
$925$	−20.2918			−0.667190
$926$	14.4615	−	44.5079i	0.475234	−	1.46262i
$927$	−0.572949	+	0.416272i	−0.0188181	+	0.0136722i
$928$	−18.3541	−	13.3350i	−0.602503	−	0.437744i
$929$	17.2361	+	53.0472i	0.565497	+	1.74042i	0.666470	+	0.745532i	$0.267804\pi$
$929$	17.2361	+	53.0472i	0.565497	+	1.74042i	−0.100973	+	0.994889i	$0.532196\pi$
$930$	7.54508	+	23.2214i	0.247413	+	0.761459i
$931$		0			0
$932$	−0.881966	+	0.640786i	−0.0288898	+	0.0209896i
$933$	−2.40983	+	7.41669i	−0.0788943	+	0.242812i
$934$	22.7426			0.744162
$935$	−1.57295	−	1.31433i	−0.0514409	−	0.0429831i
$936$	2.23607			0.0730882
$937$	−2.16312	+	6.65740i	−0.0706660	+	0.217488i	−0.980152	−	0.198247i	$-0.936475\pi$
$937$	−2.16312	+	6.65740i	−0.0706660	+	0.217488i	0.909486	+	0.415734i	$0.136475\pi$
$938$	6.23607	−	4.53077i	0.203615	−	0.147935i
$939$	−7.11803	−	5.17155i	−0.232288	−	0.168767i
$940$	−4.16312	−	12.8128i	−0.135786	−	0.417906i
$941$	−9.83282	−	30.2623i	−0.320541	−	0.986523i	−0.973413	−	0.229055i	$-0.926436\pi$
$941$	−9.83282	−	30.2623i	−0.320541	−	0.986523i	0.652873	−	0.757468i	$-0.273564\pi$
$942$	22.6803	+	16.4782i	0.738965	+	0.536890i
$943$	6.09017	−	4.42477i	0.198323	−	0.144090i
$944$	16.2812	−	50.1082i	0.529906	−	1.63088i
$945$	−2.61803			−0.0851647
$946$	5.35410	+	0.363271i	0.174077	+	0.0118110i
$947$	1.61803			0.0525790			0.0262895	−	0.999654i	$-0.491631\pi$
$947$	1.61803			0.0525790			0.0262895	+	0.999654i	$0.491631\pi$
$948$	0.791796	−	2.43690i	0.0257163	−	0.0791468i
$949$	−6.92705	+	5.03280i	−0.224862	+	0.163372i
$950$		0			0
$951$	−5.98278	−	18.4131i	−0.194005	−	0.597086i
$952$	−0.163119	−	0.502029i	−0.00528672	−	0.0162708i
$953$	−35.4336	−	25.7440i	−1.14781	−	0.833931i	−0.159620	−	0.987179i	$-0.551027\pi$
$953$	−35.4336	−	25.7440i	−1.14781	−	0.833931i	−0.988188	+	0.153247i	$0.951027\pi$
$954$	−7.04508	+	5.11855i	−0.228093	+	0.165719i
$955$	−11.5172	+	35.4464i	−0.372689	+	1.14702i
$956$	15.9787			0.516789
$957$	5.42705	+	21.5765i	0.175432	+	0.697471i
$958$	−26.7082			−0.862903
$959$	−6.47214	+	19.9192i	−0.208996	+	0.643224i
$960$	8.97214	−	6.51864i	0.289574	−	0.210388i
$961$	−1.79837	−	1.30660i	−0.0580121	−	0.0421482i
$962$	5.47214	+	16.8415i	0.176429	+	0.542992i
$963$	6.25329	+	19.2456i	0.201509	+	0.620182i
$964$	5.64590	+	4.10199i	0.181842	+	0.132116i
$965$	48.5967	−	35.3076i	1.56438	−	1.13659i
$966$	0.618034	−	1.90211i	0.0198849	−	0.0611995i
$967$	49.7082			1.59851			0.799254	−	0.600993i	$-0.205228\pi$
$967$	49.7082			1.59851			0.799254	+	0.600993i	$0.205228\pi$
$968$	−10.6910	+	22.1518i	−0.343621	+	0.711986i
$969$		0			0
$970$	22.2533	−	68.4886i	0.714510	−	2.19904i
$971$	9.13525	−	6.63715i	0.293164	−	0.212996i	−0.431475	−	0.902125i	$-0.642007\pi$
$971$	9.13525	−	6.63715i	0.293164	−	0.212996i	0.724639	+	0.689129i	$0.242007\pi$
$972$	−0.500000	−	0.363271i	−0.0160375	−	0.0116519i
$973$	0.791796	+	2.43690i	0.0253838	+	0.0781234i
$974$	7.19098	+	22.1316i	0.230414	+	0.709141i
$975$	1.50000	+	1.08981i	0.0480384	+	0.0349020i
$976$	−40.1976	+	29.2052i	−1.28669	+	0.934837i
$977$	10.1976	−	31.3849i	0.326249	−	1.00409i	−0.644625	−	0.764499i	$-0.722986\pi$
$977$	10.1976	−	31.3849i	0.326249	−	1.00409i	0.970874	−	0.239592i	$-0.0770136\pi$
$978$	−37.2705			−1.19178
$979$	6.97214	+	27.7194i	0.222830	+	0.885916i
$980$	−1.61803			−0.0516862
$981$	3.88197	−	11.9475i	0.123942	−	0.381453i
$982$	12.7082	−	9.23305i	0.405535	−	0.294638i
$983$	9.75329	+	7.08618i	0.311082	+	0.226014i	0.732360	−	0.680917i	$-0.238419\pi$
$983$	9.75329	+	7.08618i	0.311082	+	0.226014i	−0.421279	+	0.906931i	$0.638419\pi$
$984$	4.20820	+	12.9515i	0.134153	+	0.412879i
$985$	3.85410	+	11.8617i	0.122802	+	0.377945i
$986$	2.07295	+	1.50609i	0.0660161	+	0.0479635i
$987$	−6.73607	+	4.89404i	−0.214411	+	0.155779i
$988$		0			0
$989$	−1.23607			−0.0393047
$990$	14.0172	+	0.951057i	0.445497	+	0.0302266i
$991$	−44.6312			−1.41776			−0.708878	−	0.705331i	$-0.750798\pi$
$991$	−44.6312			−1.41776			−0.708878	+	0.705331i	$0.750798\pi$
$992$	6.02380	−	18.5393i	0.191256	−	0.588625i
$993$	1.04508	−	0.759299i	0.0331648	−	0.0240956i
$994$	−1.92705	−	1.40008i	−0.0611223	−	0.0444080i
$995$	−10.1631	−	31.2789i	−0.322193	−	0.991607i
$996$	−1.14590	−	3.52671i	−0.0363092	−	0.111748i
$997$	20.5623	+	14.9394i	0.651215	+	0.473135i	0.863685	−	0.504032i	$-0.168151\pi$
$997$	20.5623	+	14.9394i	0.651215	+	0.473135i	−0.212470	+	0.977168i	$0.568151\pi$
$998$	6.54508	−	4.75528i	0.207181	−	0.150526i
$999$	−3.38197	+	10.4086i	−0.107001	+	0.329314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.d.64.1	✓	4
3.2	odd	2		693.2.m.b.64.1		4
11.4	even	5		2541.2.a.bb.1.2		2
11.5	even	5	inner	231.2.j.d.148.1	yes	4
11.7	odd	10		2541.2.a.s.1.1		2
33.5	odd	10		693.2.m.b.379.1		4
33.26	odd	10		7623.2.a.ba.1.1		2
33.29	even	10		7623.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.d.64.1	✓	4	1.1	even	1	trivial
231.2.j.d.148.1	yes	4	11.5	even	5	inner
693.2.m.b.64.1		4	3.2	odd	2
693.2.m.b.379.1		4	33.5	odd	10
2541.2.a.s.1.1		2	11.7	odd	10
2541.2.a.bb.1.2		2	11.4	even	5
7623.2.a.ba.1.1		2	33.26	odd	10
7623.2.a.bp.1.2		2	33.29	even	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} -4.23607 q^{10} +(-0.809017 - 3.21644i) q^{11} +0.618034 q^{12} +(-0.309017 + 0.951057i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(2.11803 + 1.53884i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(0.0729490 + 0.224514i) q^{17} +(-1.30902 - 0.951057i) q^{18} +(-0.500000 + 1.53884i) q^{20} +1.00000 q^{21} +(-5.35410 - 0.363271i) q^{22} +1.23607 q^{23} +(-0.690983 + 2.12663i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(1.30902 + 0.951057i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.190983 + 0.587785i) q^{28} +(5.42705 + 3.94298i) q^{29} +(3.42705 - 2.48990i) q^{30} +(-1.78115 + 5.48183i) q^{31} -3.38197 q^{32} +(2.54508 + 2.12663i) q^{33} +0.381966 q^{34} +(-0.809017 + 2.48990i) q^{35} +(-0.500000 + 0.363271i) q^{36} +(8.85410 + 6.43288i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(-4.73607 - 3.44095i) q^{40} +(4.92705 - 3.57971i) q^{41} +(0.500000 - 1.53884i) q^{42} -1.00000 q^{43} +(-0.763932 + 1.90211i) q^{44} -2.61803 q^{45} +(0.618034 - 1.90211i) q^{46} +(-6.73607 + 4.89404i) q^{47} +(3.92705 + 2.85317i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.927051 + 2.85317i) q^{50} +(-0.190983 - 0.138757i) q^{51} +(0.500000 - 0.363271i) q^{52} +(1.66312 - 5.11855i) q^{53} +1.61803 q^{54} +(-7.35410 + 4.61653i) q^{55} -2.23607 q^{56} +(8.78115 - 6.37988i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-0.500000 - 1.53884i) q^{60} +(-3.16312 - 9.73508i) q^{61} +(7.54508 + 5.48183i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(1.30902 - 4.02874i) q^{64} +2.61803 q^{65} +(4.54508 - 2.85317i) q^{66} -4.76393 q^{67} +(0.0450850 - 0.138757i) q^{68} +(-1.00000 + 0.726543i) q^{69} +(3.42705 + 2.48990i) q^{70} +(0.454915 + 1.40008i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(6.92705 + 5.03280i) q^{73} +(14.3262 - 10.4086i) q^{74} +(0.572949 - 1.76336i) q^{75} +(-1.23607 + 3.07768i) q^{77} -1.61803 q^{78} +(1.28115 - 3.94298i) q^{79} +(-10.2812 + 7.46969i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.04508 - 9.37181i) q^{82} +(-1.85410 - 5.70634i) q^{83} +(-0.500000 - 0.363271i) q^{84} +(0.500000 - 0.363271i) q^{85} +(-0.500000 + 1.53884i) q^{86} -6.70820 q^{87} +(-5.69098 - 4.75528i) q^{88} -8.61803 q^{89} +(-1.30902 + 4.02874i) q^{90} +(0.809017 - 0.587785i) q^{91} +(-0.618034 - 0.449028i) q^{92} +(-1.78115 - 5.48183i) q^{93} +(4.16312 + 12.8128i) q^{94} +(2.73607 - 1.98787i) q^{96} +(-5.25329 + 16.1680i) q^{97} +1.61803 q^{98} +(-3.30902 - 0.224514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} + q^{13} - 3 q^{14} + 4 q^{15} - 6 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{20} + 4 q^{21} - 8 q^{22} - 4 q^{23} - 5 q^{24} - 6 q^{25} + 3 q^{26} - q^{27} + 3 q^{28} + 15 q^{29} + 7 q^{30} + 13 q^{31} - 18 q^{32} - q^{33} + 6 q^{34} - q^{35} - 2 q^{36} + 22 q^{37} + q^{39} - 10 q^{40} + 13 q^{41} + 2 q^{42} - 4 q^{43} - 12 q^{44} - 6 q^{45} - 2 q^{46} - 18 q^{47} + 9 q^{48} - q^{49} - 3 q^{50} - 3 q^{51} + 2 q^{52} - 9 q^{53} + 2 q^{54} - 16 q^{55} + 15 q^{58} + 15 q^{59} - 2 q^{60} + 3 q^{61} + 19 q^{62} - q^{63} + 3 q^{64} + 6 q^{65} + 7 q^{66} - 28 q^{67} - 11 q^{68} - 4 q^{69} + 7 q^{70} + 13 q^{71} - 5 q^{72} + 21 q^{73} + 26 q^{74} + 9 q^{75} + 4 q^{77} - 2 q^{78} - 15 q^{79} - 21 q^{80} - q^{81} - q^{82} + 6 q^{83} - 2 q^{84} + 2 q^{85} - 2 q^{86} - 25 q^{88} - 30 q^{89} - 3 q^{90} + q^{91} + 2 q^{92} + 13 q^{93} + q^{94} + 2 q^{96} + 17 q^{97} + 2 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 + q^13 - 3 * q^14 + 4 * q^15 - 6 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^20 + 4 * q^21 - 8 * q^22 - 4 * q^23 - 5 * q^24 - 6 * q^25 + 3 * q^26 - q^27 + 3 * q^28 + 15 * q^29 + 7 * q^30 + 13 * q^31 - 18 * q^32 - q^33 + 6 * q^34 - q^35 - 2 * q^36 + 22 * q^37 + q^39 - 10 * q^40 + 13 * q^41 + 2 * q^42 - 4 * q^43 - 12 * q^44 - 6 * q^45 - 2 * q^46 - 18 * q^47 + 9 * q^48 - q^49 - 3 * q^50 - 3 * q^51 + 2 * q^52 - 9 * q^53 + 2 * q^54 - 16 * q^55 + 15 * q^58 + 15 * q^59 - 2 * q^60 + 3 * q^61 + 19 * q^62 - q^63 + 3 * q^64 + 6 * q^65 + 7 * q^66 - 28 * q^67 - 11 * q^68 - 4 * q^69 + 7 * q^70 + 13 * q^71 - 5 * q^72 + 21 * q^73 + 26 * q^74 + 9 * q^75 + 4 * q^77 - 2 * q^78 - 15 * q^79 - 21 * q^80 - q^81 - q^82 + 6 * q^83 - 2 * q^84 + 2 * q^85 - 2 * q^86 - 25 * q^88 - 30 * q^89 - 3 * q^90 + q^91 + 2 * q^92 + 13 * q^93 + q^94 + 2 * q^96 + 17 * q^97 + 2 * q^98 - 11 * q^99

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